LMFDB - Embedded newform 756.2.ba.a.71.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(71,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("756.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.19
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0344832 + 1.41379i) q^{2} +(-1.99762 - 0.0975041i) q^{4} +(0.948457 + 0.547592i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(0.206735 - 2.82086i) q^{8} +O(q^{10})$	\(q+(-0.0344832 + 1.41379i) q^{2} +(-1.99762 - 0.0975041i) q^{4} +(0.948457 + 0.547592i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(0.206735 - 2.82086i) q^{8} +(-0.806888 + 1.32204i) q^{10} +(1.84953 + 3.20347i) q^{11} +(0.713436 - 1.23571i) q^{13} +(-0.677033 - 1.24162i) q^{14} +(3.98099 + 0.389553i) q^{16} +2.54456i q^{17} +6.13291i q^{19} +(-1.84127 - 1.18636i) q^{20} +(-4.59282 + 2.50438i) q^{22} +(-2.50677 + 4.34185i) q^{23} +(-1.90029 - 3.29139i) q^{25} +(1.72243 + 1.05126i) q^{26} +(1.77874 - 0.914370i) q^{28} +(-5.59043 + 3.22763i) q^{29} +(-5.71386 - 3.29890i) q^{31} +(-0.688024 + 5.61486i) q^{32} +(-3.59748 - 0.0877445i) q^{34} -1.09518 q^{35} +8.53349 q^{37} +(-8.67066 - 0.211482i) q^{38} +(1.74076 - 2.56226i) q^{40} +(5.23022 + 3.01967i) q^{41} +(-4.32074 + 2.49458i) q^{43} +(-3.38230 - 6.57966i) q^{44} +(-6.05204 - 3.69378i) q^{46} +(1.55938 + 2.70093i) q^{47} +(0.500000 - 0.866025i) q^{49} +(4.71887 - 2.57311i) q^{50} +(-1.54566 + 2.39891i) q^{52} +0.388379i q^{53} +4.05114i q^{55} +(1.23139 + 2.54631i) q^{56} +(-4.37043 - 8.01500i) q^{58} +(-5.77576 + 10.0039i) q^{59} +(-3.37148 - 5.83957i) q^{61} +(4.86100 - 7.96447i) q^{62} +(-7.91452 - 1.16634i) q^{64} +(1.35333 - 0.781344i) q^{65} +(11.5692 + 6.67947i) q^{67} +(0.248105 - 5.08307i) q^{68} +(0.0377654 - 1.54836i) q^{70} -7.82636 q^{71} -5.60423 q^{73} +(-0.294262 + 12.0646i) q^{74} +(0.597984 - 12.2512i) q^{76} +(-3.20347 - 1.84953i) q^{77} +(6.35916 - 3.67146i) q^{79} +(3.56248 + 2.54943i) q^{80} +(-4.44954 + 7.29032i) q^{82} +(-5.88918 - 10.2004i) q^{83} +(-1.39338 + 2.41341i) q^{85} +(-3.37783 - 6.19465i) q^{86} +(9.41891 - 4.55499i) q^{88} -10.4010i q^{89} +1.42687i q^{91} +(5.43093 - 8.42896i) q^{92} +(-3.87232 + 2.11151i) q^{94} +(-3.35833 + 5.81680i) q^{95} +(2.46220 + 4.26466i) q^{97} +(1.20714 + 0.736760i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) $ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−0.0344832	+	1.41379i	−0.0243833	+	0.999703i
$2$	−0.0344832	+	1.41379i	−0.0243833	+	0.999703i
$3$		0			0
$3$		0			0
$4$	−1.99762	−	0.0975041i	−0.998811	−	0.0487521i
$5$	0.948457	+	0.547592i	0.424163	+	0.244891i	0.696857	−	0.717210i	$-0.254581\pi$
$5$	0.948457	+	0.547592i	0.424163	+	0.244891i	−0.272694	+	0.962101i	$0.587915\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$	0.206735	−	2.82086i	0.0730918	−	0.997325i
$9$		0			0
$10$	−0.806888	+	1.32204i	−0.255160	+	0.418066i
$11$	1.84953	+	3.20347i	0.557653	+	0.965883i	0.997692	+	0.0679044i	$0.0216313\pi$
$11$	1.84953	+	3.20347i	0.557653	+	0.965883i	−0.440039	+	0.897979i	$0.645035\pi$
$12$		0			0
$13$	0.713436	−	1.23571i	0.197872	−	0.342724i	−0.749966	−	0.661476i	$-0.769930\pi$
$13$	0.713436	−	1.23571i	0.197872	−	0.342724i	0.947838	+	0.318752i	$0.103264\pi$
$14$	−0.677033	−	1.24162i	−0.180945	−	0.331838i
$15$		0			0
$16$	3.98099	+	0.389553i	0.995246	+	0.0973882i
$17$			2.54456i			0.617147i	0.951201	+	0.308573i	$0.0998516\pi$
$17$			2.54456i			0.617147i	−0.951201	+	0.308573i	$0.900148\pi$
$18$		0			0
$19$			6.13291i			1.40699i	0.710702	+	0.703493i	$0.248377\pi$
$19$			6.13291i			1.40699i	−0.710702	+	0.703493i	$0.751623\pi$
$20$	−1.84127	−	1.18636i	−0.411720	−	0.265278i
$21$		0			0
$22$	−4.59282	+	2.50438i	−0.979193	+	0.533936i
$23$	−2.50677	+	4.34185i	−0.522698	+	0.905339i	0.476953	+	0.878929i	$0.341741\pi$
$23$	−2.50677	+	4.34185i	−0.522698	+	0.905339i	−0.999651	+	0.0264105i	$0.991592\pi$
$24$		0			0
$25$	−1.90029	−	3.29139i	−0.380057	−	0.658278i
$26$	1.72243	+	1.05126i	0.337797	+	0.206170i
$27$		0			0
$28$	1.77874	−	0.914370i	0.336151	−	0.172800i
$29$	−5.59043	+	3.22763i	−1.03812	+	0.599357i	−0.919299	−	0.393560i	$-0.871244\pi$
$29$	−5.59043	+	3.22763i	−1.03812	+	0.599357i	−0.118817	+	0.992916i	$0.537910\pi$
$30$		0			0
$31$	−5.71386	−	3.29890i	−1.02624	−	0.592500i	−0.110335	−	0.993894i	$-0.535192\pi$
$31$	−5.71386	−	3.29890i	−1.02624	−	0.592500i	−0.915905	+	0.401394i	$0.868526\pi$
$32$	−0.688024	+	5.61486i	−0.121627	+	0.992576i
$33$		0			0
$34$	−3.59748	−	0.0877445i	−0.616963	−	0.0150481i
$35$	−1.09518			−0.185120
$36$		0			0
$37$	8.53349			1.40290			0.701449	−	0.712720i	$-0.252537\pi$
$37$	8.53349			1.40290			0.701449	+	0.712720i	$0.252537\pi$
$38$	−8.67066	−	0.211482i	−1.40657	−	0.0343069i
$39$		0			0
$40$	1.74076	−	2.56226i	0.275238	−	0.405129i
$41$	5.23022	+	3.01967i	0.816823	+	0.471593i	0.849320	−	0.527879i	$-0.177013\pi$
$41$	5.23022	+	3.01967i	0.816823	+	0.471593i	−0.0324969	+	0.999472i	$0.510346\pi$
$42$		0			0
$43$	−4.32074	+	2.49458i	−0.658906	+	0.380420i	−0.791860	−	0.610703i	$-0.790887\pi$
$43$	−4.32074	+	2.49458i	−0.658906	+	0.380420i	0.132954	+	0.991122i	$0.457554\pi$
$44$	−3.38230	−	6.57966i	−0.509901	−	0.991921i
$45$		0			0
$46$	−6.05204	−	3.69378i	−0.892325	−	0.544618i
$47$	1.55938	+	2.70093i	0.227459	+	0.393971i	0.957054	−	0.289908i	$-0.0936249\pi$
$47$	1.55938	+	2.70093i	0.227459	+	0.393971i	−0.729595	+	0.683879i	$0.760292\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	4.71887	−	2.57311i	0.667350	−	0.363893i
$51$		0			0
$52$	−1.54566	+	2.39891i	−0.214345	+	0.332670i
$53$			0.388379i			0.0533480i	0.999644	+	0.0266740i	$0.00849160\pi$
$53$			0.388379i			0.0533480i	−0.999644	+	0.0266740i	$0.991508\pi$
$54$		0			0
$55$			4.05114i			0.546256i
$56$	1.23139	+	2.54631i	0.164552	+	0.340264i
$57$		0			0
$58$	−4.37043	−	8.01500i	−0.573866	−	1.05242i
$59$	−5.77576	+	10.0039i	−0.751940	+	1.30240i	0.194941	+	0.980815i	$0.437548\pi$
$59$	−5.77576	+	10.0039i	−0.751940	+	1.30240i	−0.946881	+	0.321584i	$0.895785\pi$
$60$		0			0
$61$	−3.37148	−	5.83957i	−0.431673	−	0.747680i	0.565344	−	0.824855i	$-0.308743\pi$
$61$	−3.37148	−	5.83957i	−0.431673	−	0.747680i	−0.997018	+	0.0771751i	$0.975410\pi$
$62$	4.86100	−	7.96447i	0.617347	−	1.01149i
$63$		0			0
$64$	−7.91452	−	1.16634i	−0.989315	−	0.145793i
$65$	1.35333	−	0.781344i	0.167860	−	0.0969138i
$66$		0			0
$67$	11.5692	+	6.67947i	1.41340	+	0.816027i	0.995707	−	0.0925616i	$-0.0295055\pi$
$67$	11.5692	+	6.67947i	1.41340	+	0.816027i	0.417693	+	0.908588i	$0.362839\pi$
$68$	0.248105	−	5.08307i	0.0300872	−	0.616413i
$69$		0			0
$70$	0.0377654	−	1.54836i	0.00451383	−	0.185065i
$71$	−7.82636			−0.928818			−0.464409	−	0.885621i	$-0.653733\pi$
$71$	−7.82636			−0.928818			−0.464409	+	0.885621i	$0.653733\pi$
$72$		0			0
$73$	−5.60423			−0.655925			−0.327963	−	0.944691i	$-0.606362\pi$
$73$	−5.60423			−0.655925			−0.327963	+	0.944691i	$0.606362\pi$
$74$	−0.294262	+	12.0646i	−0.0342072	+	1.40248i
$75$		0			0
$76$	0.597984	−	12.2512i	0.0685934	−	1.40531i
$77$	−3.20347	−	1.84953i	−0.365069	−	0.210773i
$78$		0			0
$79$	6.35916	−	3.67146i	0.715461	−	0.413072i	−0.0976186	−	0.995224i	$-0.531123\pi$
$79$	6.35916	−	3.67146i	0.715461	−	0.413072i	0.813080	+	0.582152i	$0.197789\pi$
$80$	3.56248	+	2.54943i	0.398297	+	0.285035i
$81$		0			0
$82$	−4.44954	+	7.29032i	−0.491369	+	0.805081i
$83$	−5.88918	−	10.2004i	−0.646421	−	1.11963i	−0.983971	−	0.178327i	$-0.942932\pi$
$83$	−5.88918	−	10.2004i	−0.646421	−	1.11963i	0.337550	−	0.941308i	$-0.390402\pi$
$84$		0			0
$85$	−1.39338	+	2.41341i	−0.151133	+	0.261771i
$86$	−3.37783	−	6.19465i	−0.364240	−	0.667986i
$87$		0			0
$88$	9.41891	−	4.55499i	1.00406	−	0.485563i
$89$		−	10.4010i		−	1.10250i	−0.834340	−	0.551250i	$-0.814151\pi$
$89$		−	10.4010i		−	1.10250i	0.834340	−	0.551250i	$-0.185849\pi$
$90$		0			0
$91$			1.42687i			0.149577i
$92$	5.43093	−	8.42896i	0.566213	−	0.878780i
$93$		0			0
$94$	−3.87232	+	2.11151i	−0.399400	+	0.217785i
$95$	−3.35833	+	5.81680i	−0.344558	+	0.596791i
$96$		0			0
$97$	2.46220	+	4.26466i	0.249999	+	0.433010i	0.963525	−	0.267618i	$-0.0862365\pi$
$97$	2.46220	+	4.26466i	0.249999	+	0.433010i	−0.713526	+	0.700628i	$0.752903\pi$
$98$	1.20714	+	0.736760i	0.121939	+	0.0744240i
$99$		0			0
$100$	3.47513	+	6.76024i	0.347513	+	0.676024i
$101$	6.05327	−	3.49486i	0.602323	−	0.347751i	−0.167632	−	0.985850i	$-0.553612\pi$
$101$	6.05327	−	3.49486i	0.602323	−	0.347751i	0.769955	+	0.638098i	$0.220279\pi$
$102$		0			0
$103$	8.94719	+	5.16566i	0.881592	+	0.508988i	0.871183	−	0.490958i	$-0.163353\pi$
$103$	8.94719	+	5.16566i	0.881592	+	0.508988i	0.0104093	+	0.999946i	$0.496687\pi$
$104$	−3.33827	−	2.26797i	−0.327344	−	0.222393i
$105$		0			0
$106$	−0.549088	−	0.0133925i	−0.0533321	−	0.00130080i
$107$	9.88512			0.955631			0.477816	−	0.878460i	$-0.341429\pi$
$107$	9.88512			0.955631			0.477816	+	0.878460i	$0.341429\pi$
$108$		0			0
$109$	12.6573			1.21235			0.606176	−	0.795331i	$-0.292703\pi$
$109$	12.6573			1.21235			0.606176	+	0.795331i	$0.292703\pi$
$110$	−5.72748	−	0.139696i	−0.546093	−	0.0133195i
$111$		0			0
$112$	−3.64241	+	1.65313i	−0.344176	+	0.156206i
$113$	13.1211	+	7.57547i	1.23433	+	0.712640i	0.967929	−	0.251223i	$-0.0808327\pi$
$113$	13.1211	+	7.57547i	1.23433	+	0.712640i	0.266399	+	0.963863i	$0.414166\pi$
$114$		0			0
$115$	−4.75513	+	2.74538i	−0.443418	+	0.256008i
$116$	11.4823	−	5.90250i	1.06610	−	0.548034i
$117$		0			0
$118$	−13.9443	−	8.51070i	−1.28368	−	0.783473i
$119$	−1.27228	−	2.20366i	−0.116630	−	0.202009i
$120$		0			0
$121$	−1.34149	+	2.32352i	−0.121953	+	0.211229i
$122$	8.37220	−	4.56520i	0.757983	−	0.413314i
$123$		0			0
$124$	11.0925	+	7.14708i	0.996134	+	0.641827i
$125$		−	9.63825i		−	0.862071i
$126$		0			0
$127$		−	1.03805i		−	0.0921119i	−0.998939	−	0.0460559i	$-0.985335\pi$
$127$		−	1.03805i		−	0.0921119i	0.998939	−	0.0460559i	$-0.0146652\pi$
$128$	1.92188	−	11.1493i	0.169872	−	0.985466i
$129$		0			0
$130$	1.05799	+	1.94027i	0.0927921	+	0.170173i
$131$	2.23398	−	3.86937i	0.195184	−	0.338068i	−0.751777	−	0.659417i	$-0.770803\pi$
$131$	2.23398	−	3.86937i	0.195184	−	0.338068i	0.946961	+	0.321349i	$0.104136\pi$
$132$		0			0
$133$	−3.06645	−	5.31125i	−0.265895	−	0.460544i
$134$	−9.84233	+	16.1261i	−0.850247	+	1.39308i
$135$		0			0
$136$	7.17786	+	0.526050i	0.615496	+	0.0451084i
$137$	−2.70871	+	1.56388i	−0.231421	+	0.133611i	−0.611227	−	0.791455i	$-0.709324\pi$
$137$	−2.70871	+	1.56388i	−0.231421	+	0.133611i	0.379806	+	0.925066i	$0.375991\pi$
$138$		0			0
$139$	1.47545	+	0.851850i	0.125146	+	0.0722530i	0.561266	−	0.827635i	$-0.310314\pi$
$139$	1.47545	+	0.851850i	0.125146	+	0.0722530i	−0.436120	+	0.899888i	$0.643648\pi$
$140$	2.18776	+	0.106785i	0.184900	+	0.00902498i
$141$		0			0
$142$	0.269878	−	11.0648i	0.0226476	−	0.928542i
$143$	5.27808			0.441375
$144$		0			0
$145$	−7.06971			−0.587107
$146$	0.193251	−	7.92322i	0.0159936	−	0.655730i
$147$		0			0
$148$	−17.0467	−	0.832051i	−1.40123	−	0.0683942i
$149$	−3.07128	−	1.77320i	−0.251609	−	0.145267i	0.368892	−	0.929472i	$-0.379737\pi$
$149$	−3.07128	−	1.77320i	−0.251609	−	0.145267i	−0.620501	+	0.784206i	$0.713071\pi$
$150$		0			0
$151$	0.805760	−	0.465206i	0.0655719	−	0.0378579i	−0.466856	−	0.884334i	$-0.654613\pi$
$151$	0.805760	−	0.465206i	0.0655719	−	0.0378579i	0.532427	+	0.846476i	$0.321280\pi$
$152$	17.3001	+	1.26789i	1.40322	+	0.102839i
$153$		0			0
$154$	2.72531	−	4.46527i	0.219612	−	0.359822i
$155$	−3.61290	−	6.25773i	−0.290195	−	0.502633i
$156$		0			0
$157$	−8.77396	+	15.1969i	−0.700238	+	1.21285i	0.268145	+	0.963379i	$0.413589\pi$
$157$	−8.77396	+	15.1969i	−0.700238	+	1.21285i	−0.968383	+	0.249469i	$0.919744\pi$
$158$	4.97140	+	9.11714i	0.395504	+	0.725321i
$159$		0			0
$160$	−3.72721	+	4.94870i	−0.294662	+	0.391229i
$161$		−	5.01354i		−	0.395122i
$162$		0			0
$163$		−	14.7523i		−	1.15549i	−0.816216	−	0.577747i	$-0.803932\pi$
$163$		−	14.7523i		−	1.15549i	0.816216	−	0.577747i	$-0.196068\pi$
$164$	−10.1536	−	6.54212i	−0.792860	−	0.510854i
$165$		0			0
$166$	14.6243	−	7.97434i	1.13506	−	0.618929i
$167$	4.12813	−	7.15012i	0.319444	−	0.553293i	−0.660928	−	0.750449i	$-0.729837\pi$
$167$	4.12813	−	7.15012i	0.319444	−	0.553293i	0.980372	+	0.197156i	$0.0631706\pi$
$168$		0			0
$169$	5.48202	+	9.49513i	0.421694	+	0.730395i
$170$	−3.36401	−	2.05318i	−0.258008	−	0.157471i
$171$		0			0
$172$	8.87443	−	4.56194i	0.676669	−	0.347844i
$173$	6.38451	−	3.68610i	0.485405	−	0.280249i	−0.237261	−	0.971446i	$-0.576250\pi$
$173$	6.38451	−	3.68610i	0.485405	−	0.280249i	0.722666	+	0.691197i	$0.242916\pi$
$174$		0			0
$175$	3.29139	+	1.90029i	0.248806	+	0.143648i
$176$	6.11501	+	13.4735i	0.460936	+	1.01560i
$177$		0			0
$178$	14.7048	+	0.358658i	1.10217	+	0.0268826i
$179$	−8.52164			−0.636937			−0.318469	−	0.947933i	$-0.603169\pi$
$179$	−8.52164			−0.636937			−0.318469	+	0.947933i	$0.603169\pi$
$180$		0			0
$181$	24.8360			1.84605			0.923024	−	0.384742i	$-0.125710\pi$
$181$	24.8360			1.84605			0.923024	+	0.384742i	$0.125710\pi$
$182$	−2.01730	−	0.0492031i	−0.149532	−	0.00364718i
$183$		0			0
$184$	11.7295	+	7.96887i	0.864713	+	0.587473i
$185$	8.09365	+	4.67287i	0.595057	+	0.343557i
$186$		0			0
$187$	−8.15143	+	4.70623i	−0.596092	+	0.344154i
$188$	−2.85170	−	5.54748i	−0.207982	−	0.404591i
$189$		0			0
$190$	−8.10795	−	4.94857i	−0.588212	−	0.359007i
$191$	10.3880	+	17.9925i	0.751648	+	1.30189i	0.947024	+	0.321164i	$0.104074\pi$
$191$	10.3880	+	17.9925i	0.751648	+	1.30189i	−0.195375	+	0.980729i	$0.562593\pi$
$192$		0			0
$193$	−10.4316	+	18.0680i	−0.750881	+	1.30056i	0.196515	+	0.980501i	$0.437038\pi$
$193$	−10.4316	+	18.0680i	−0.750881	+	1.30056i	−0.947396	+	0.320063i	$0.896296\pi$
$194$	−6.11425	+	3.33398i	−0.438978	+	0.239366i
$195$		0			0
$196$	−1.08325	+	1.68124i	−0.0773751	+	0.120089i
$197$			19.4029i			1.38240i	0.722665	+	0.691198i	$0.242917\pi$
$197$			19.4029i			1.38240i	−0.722665	+	0.691198i	$0.757083\pi$
$198$		0			0
$199$		−	17.0805i		−	1.21081i	−0.795919	−	0.605403i	$-0.793012\pi$
$199$		−	17.0805i		−	1.21081i	0.795919	−	0.605403i	$-0.206988\pi$
$200$	−9.67742	+	4.68000i	−0.684297	+	0.330926i
$201$		0			0
$202$	4.73227	+	8.67858i	0.332961	+	0.610623i
$203$	3.22763	−	5.59043i	0.226535	−	0.392371i
$204$		0			0
$205$	3.30709	+	5.72805i	0.230977	+	0.400064i
$206$	−7.61170	+	12.4713i	−0.530332	+	0.868920i
$207$		0			0
$208$	3.32155	−	4.64142i	0.230308	−	0.321824i
$209$	−19.6466	+	11.3430i	−1.35898	+	0.784609i
$210$		0			0
$211$	4.51195	+	2.60498i	0.310615	+	0.179334i	0.647202	−	0.762319i	$-0.275939\pi$
$211$	4.51195	+	2.60498i	0.310615	+	0.179334i	−0.336586	+	0.941653i	$0.609272\pi$
$212$	0.0378686	−	0.775835i	0.00260082	−	0.0532846i
$213$		0			0
$214$	−0.340870	+	13.9755i	−0.0233014	+	0.955347i
$215$	−5.46405			−0.372645
$216$		0			0
$217$	6.59780			0.447888
$218$	−0.436465	+	17.8948i	−0.0295611	+	1.21199i
$219$		0			0
$220$	0.395003	−	8.09265i	0.0266311	−	0.545606i
$221$	3.14434	+	1.81538i	0.211511	+	0.122116i
$222$		0			0
$223$	9.09410	−	5.25048i	0.608986	−	0.351598i	−0.163582	−	0.986530i	$-0.552305\pi$
$223$	9.09410	−	5.25048i	0.608986	−	0.351598i	0.772569	+	0.634931i	$0.218972\pi$
$224$	−2.21158	−	5.20662i	−0.147768	−	0.347882i
$225$		0			0
$226$	−11.1626	+	18.2893i	−0.742525	+	1.21658i
$227$	−8.22092	−	14.2391i	−0.545642	−	0.945079i	−0.998566	−	0.0535302i	$-0.982953\pi$
$227$	−8.22092	−	14.2391i	−0.545642	−	0.945079i	0.452925	−	0.891549i	$-0.350381\pi$
$228$		0			0
$229$	12.3928	−	21.4650i	0.818942	−	1.41845i	−0.0875208	−	0.996163i	$-0.527894\pi$
$229$	12.3928	−	21.4650i	0.818942	−	1.41845i	0.906463	−	0.422286i	$-0.138772\pi$
$230$	−3.71742	−	6.81744i	−0.245119	−	0.449529i
$231$		0			0
$232$	7.94897	+	16.4371i	0.521876	+	1.07915i
$233$			28.1529i			1.84436i	0.386760	+	0.922180i	$0.373594\pi$
$233$			28.1529i			1.84436i	−0.386760	+	0.922180i	$0.626406\pi$
$234$		0			0
$235$			3.41562i			0.222810i
$236$	12.5132	−	19.4209i	0.814541	−	1.26419i
$237$		0			0
$238$	3.15938	−	1.72275i	0.204792	−	0.111669i
$239$	8.29535	−	14.3680i	0.536582	−	0.929387i	−0.462503	−	0.886618i	$-0.653049\pi$
$239$	8.29535	−	14.3680i	0.536582	−	0.929387i	0.999085	−	0.0427692i	$-0.0136180\pi$
$240$		0			0
$241$	−13.3011	−	23.0382i	−0.856800	−	1.48402i	−0.874965	−	0.484187i	$-0.839116\pi$
$241$	−13.3011	−	23.0382i	−0.856800	−	1.48402i	0.0181642	−	0.999835i	$-0.494218\pi$
$242$	−3.23872	−	1.97671i	−0.208193	−	0.127068i
$243$		0			0
$244$	6.16555	+	11.9940i	0.394709	+	0.767836i
$245$	0.948457	−	0.547592i	0.0605947	−	0.0349844i
$246$		0			0
$247$	7.57848	+	4.37544i	0.482207	+	0.278403i
$248$	−10.4870	+	15.4360i	−0.665925	+	0.980188i
$249$		0			0
$250$	13.6265	+	0.332357i	0.861815	+	0.0210201i
$251$	25.8568			1.63207			0.816035	−	0.578003i	$-0.196168\pi$
$251$	25.8568			1.63207			0.816035	+	0.578003i	$0.196168\pi$
$252$		0			0
$253$	−18.5453			−1.16594
$254$	1.46758	+	0.0357952i	0.0920845	+	0.00224599i
$255$		0			0
$256$	15.6965	+	3.10161i	0.981031	+	0.193850i
$257$	−12.6539	−	7.30571i	−0.789327	−	0.455718i	0.0503989	−	0.998729i	$-0.483951\pi$
$257$	−12.6539	−	7.30571i	−0.789327	−	0.455718i	−0.839725	+	0.543011i	$0.817284\pi$
$258$		0			0
$259$	−7.39022	+	4.26675i	−0.459206	+	0.265123i
$260$	−2.77962	+	1.42888i	−0.172385	+	0.0886151i
$261$		0			0
$262$	5.39345	+	3.29181i	0.333209	+	0.203369i
$263$	−4.49682	−	7.78873i	−0.277286	−	0.480274i	0.693423	−	0.720531i	$-0.256102\pi$
$263$	−4.49682	−	7.78873i	−0.277286	−	0.480274i	−0.970709	+	0.240257i	$0.922768\pi$
$264$		0			0
$265$	−0.212673	+	0.368361i	−0.0130644	+	0.0226282i
$266$	7.61475	−	4.15218i	0.466891	−	0.254587i
$267$		0			0
$268$	−22.4596	−	14.4711i	−1.37194	−	0.883963i
$269$		−	25.5390i		−	1.55714i	−0.627557	−	0.778571i	$-0.715945\pi$
$269$		−	25.5390i		−	1.55714i	0.627557	−	0.778571i	$-0.284055\pi$
$270$		0			0
$271$		−	23.4547i		−	1.42477i	−0.701788	−	0.712386i	$-0.747614\pi$
$271$		−	23.4547i		−	1.42477i	0.701788	−	0.712386i	$-0.252386\pi$
$272$	−0.991241	+	10.1299i	−0.0601028	+	0.614213i
$273$		0			0
$274$	−2.11759	−	3.88349i	−0.127928	−	0.234610i
$275$	7.02925	−	12.1750i	0.423880	−	0.734182i
$276$		0			0
$277$	−11.6314	−	20.1462i	−0.698863	−	1.21047i	−0.968861	−	0.247606i	$-0.920356\pi$
$277$	−11.6314	−	20.1462i	−0.698863	−	1.21047i	0.269998	−	0.962861i	$-0.412977\pi$
$278$	−1.25522	+	2.05660i	−0.0752830	+	0.123347i
$279$		0			0
$280$	−0.226413	+	3.08936i	−0.0135308	+	0.184625i
$281$	−6.82332	+	3.93944i	−0.407045	+	0.235007i	−0.689519	−	0.724267i	$-0.742178\pi$
$281$	−6.82332	+	3.93944i	−0.407045	+	0.235007i	0.282474	+	0.959275i	$0.408845\pi$
$282$		0			0
$283$	−7.04941	−	4.06998i	−0.419044	−	0.241935i	0.275624	−	0.961265i	$-0.411115\pi$
$283$	−7.04941	−	4.06998i	−0.419044	−	0.241935i	−0.694668	+	0.719330i	$0.744449\pi$
$284$	15.6341	+	0.763102i	0.927713	+	0.0452818i
$285$		0			0
$286$	−0.182005	+	7.46211i	−0.0107622	+	0.441244i
$287$	−6.03933			−0.356491
$288$		0			0
$289$	10.5252			0.619130
$290$	0.243786	−	9.99510i	0.0143156	−	0.586933i
$291$		0			0
$292$	11.1951	+	0.546435i	0.655145	+	0.0319777i
$293$	−9.52615	−	5.49993i	−0.556524	−	0.321309i	0.195225	−	0.980758i	$-0.437456\pi$
$293$	−9.52615	−	5.49993i	−0.556524	−	0.321309i	−0.751749	+	0.659449i	$0.770790\pi$
$294$		0			0
$295$	−10.9561	+	6.32552i	−0.637890	+	0.368286i
$296$	1.76417	−	24.0718i	0.102540	−	1.39915i
$297$		0			0
$298$	2.61285	−	4.28101i	0.151358	−	0.247992i
$299$	3.57684	+	6.19527i	0.206854	+	0.358282i
$300$		0			0
$301$	2.49458	−	4.32074i	0.143785	−	0.249043i
$302$	0.629920	+	1.15522i	0.0362478	+	0.0664755i
$303$		0			0
$304$	−2.38909	+	24.4150i	−0.137024	+	1.40030i
$305$		−	7.38477i		−	0.422851i
$306$		0			0
$307$			2.92460i			0.166916i	0.996511	+	0.0834580i	$0.0265964\pi$
$307$			2.92460i			0.166916i	−0.996511	+	0.0834580i	$0.973404\pi$
$308$	6.21899	+	4.00700i	0.354360	+	0.228320i
$309$		0			0
$310$	8.97172	−	4.89211i	0.509560	−	0.277853i
$311$	−6.46219	+	11.1928i	−0.366437	+	0.634688i	−0.989006	−	0.147878i	$-0.952756\pi$
$311$	−6.46219	+	11.1928i	−0.366437	+	0.634688i	0.622569	+	0.782565i	$0.286089\pi$
$312$		0			0
$313$	2.68684	+	4.65374i	0.151869	+	0.263045i	0.931915	−	0.362678i	$-0.118137\pi$
$313$	2.68684	+	4.65374i	0.151869	+	0.263045i	−0.780045	+	0.625723i	$0.784804\pi$
$314$	−21.1828	−	12.9286i	−1.19541	−	0.729603i
$315$		0			0
$316$	−13.0612	+	6.71415i	−0.734749	+	0.377700i
$317$	−13.9585	+	8.05894i	−0.783987	+	0.452635i	−0.837842	−	0.545914i	$-0.816183\pi$
$317$	−13.9585	+	8.05894i	−0.783987	+	0.452635i	0.0538542	+	0.998549i	$0.482849\pi$
$318$		0			0
$319$	−20.6793	−	11.9392i	−1.15782	−	0.668466i
$320$	−6.86791	−	5.44015i	−0.383928	−	0.304114i
$321$		0			0
$322$	7.08811	+	0.172883i	0.395005	+	0.00963438i
$323$	−15.6056			−0.868317
$324$		0			0
$325$	−5.42293			−0.300810
$326$	20.8568	+	0.508708i	1.15515	+	0.0281747i
$327$		0			0
$328$	9.59933	−	14.1294i	0.530034	−	0.780168i
$329$	−2.70093	−	1.55938i	−0.148907	−	0.0859714i
$330$		0			0
$331$	−3.64248	+	2.10299i	−0.200209	+	0.115591i	−0.596753	−	0.802425i	$-0.703543\pi$
$331$	−3.64248	+	2.10299i	−0.200209	+	0.115591i	0.396544	+	0.918016i	$0.370209\pi$
$332$	10.7698	+	20.9507i	0.591068	+	1.14982i
$333$		0			0
$334$	9.96644	+	6.08287i	0.545340	+	0.332840i
$335$	7.31525	+	12.6704i	0.399675	+	0.692257i
$336$		0			0
$337$	−12.2696	+	21.2516i	−0.668368	+	1.15765i	0.309993	+	0.950739i	$0.399673\pi$
$337$	−12.2696	+	21.2516i	−0.668368	+	1.15765i	−0.978360	+	0.206908i	$0.933660\pi$
$338$	−13.6132	+	7.42302i	−0.740460	+	0.403759i
$339$		0			0
$340$	3.01877	−	4.68522i	0.163716	−	0.254092i
$341$		−	24.4056i		−	1.32164i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	6.14361	+	12.7039i	0.331241	+	0.684949i
$345$		0			0
$346$	4.99122	+	9.15348i	0.268330	+	0.492094i
$347$	11.6467	−	20.1727i	0.625228	−	1.08293i	−0.363269	−	0.931684i	$-0.618339\pi$
$347$	11.6467	−	20.1727i	0.625228	−	1.08293i	0.988497	−	0.151242i	$-0.0483272\pi$
$348$		0			0
$349$	−10.2865	−	17.8168i	−0.550626	−	0.953711i	−0.998230	−	0.0594795i	$-0.981056\pi$
$349$	−10.2865	−	17.8168i	−0.550626	−	0.953711i	0.447604	−	0.894232i	$-0.352277\pi$
$350$	−2.80011	+	4.58782i	−0.149672	+	0.245229i
$351$		0			0
$352$	−19.2596	+	8.18076i	−1.02654	+	0.436036i
$353$	19.3063	−	11.1465i	1.02757	−	0.593269i	0.111283	−	0.993789i	$-0.464504\pi$
$353$	19.3063	−	11.1465i	1.02757	−	0.593269i	0.916288	+	0.400520i	$0.131171\pi$
$354$		0			0
$355$	−7.42297	−	4.28565i	−0.393970	−	0.227459i
$356$	−1.01414	+	20.7772i	−0.0537492	+	1.10119i
$357$		0			0
$358$	0.293853	−	12.0478i	0.0155306	−	0.636748i
$359$	23.8166			1.25699			0.628495	−	0.777814i	$-0.283671\pi$
$359$	23.8166			1.25699			0.628495	+	0.777814i	$0.283671\pi$
$360$		0			0
$361$	−18.6126			−0.979608
$362$	−0.856425	+	35.1130i	−0.0450127	+	1.84550i
$363$		0			0
$364$	0.139126	−	2.85035i	0.00729218	−	0.149399i
$365$	−5.31537	−	3.06883i	−0.278219	−	0.160630i
$366$		0			0
$367$	−14.7428	+	8.51177i	−0.769569	+	0.444311i	−0.832721	−	0.553693i	$-0.813218\pi$
$367$	−14.7428	+	8.51177i	−0.769569	+	0.444311i	0.0631520	+	0.998004i	$0.479885\pi$
$368$	−11.6708	+	16.3083i	−0.608382	+	0.850131i
$369$		0			0
$370$	−6.88557	+	11.2816i	−0.357964	+	0.586503i
$371$	−0.194190	−	0.336346i	−0.0100818	−	0.0174622i
$372$		0			0
$373$	−2.96579	+	5.13691i	−0.153563	+	0.265979i	−0.932535	−	0.361080i	$-0.882408\pi$
$373$	−2.96579	+	5.13691i	−0.153563	+	0.265979i	0.778972	+	0.627059i	$0.215741\pi$
$374$	−6.37255	−	11.6867i	−0.329517	−	0.604306i
$375$		0			0
$376$	7.94132	−	3.84042i	0.409542	−	0.198055i
$377$			9.21085i			0.474383i
$378$		0			0
$379$		−	30.4670i		−	1.56498i	−0.622660	−	0.782492i	$-0.713948\pi$
$379$		−	30.4670i		−	1.56498i	0.622660	−	0.782492i	$-0.286052\pi$
$380$	7.27584	−	11.2923i	0.373243	−	0.579284i
$381$		0			0
$382$	−25.7959	+	14.0660i	−1.31983	+	0.719680i
$383$	−5.40944	+	9.36943i	−0.276410	+	0.478755i	−0.970490	−	0.241142i	$-0.922478\pi$
$383$	−5.40944	+	9.36943i	−0.276410	+	0.478755i	0.694080	+	0.719898i	$0.255811\pi$
$384$		0			0
$385$	−2.02557	−	3.50839i	−0.103233	−	0.178804i
$386$	−25.1847	−	15.3711i	−1.28187	−	0.782370i
$387$		0			0
$388$	−4.50273	−	8.75925i	−0.228591	−	0.444684i
$389$	14.5583	−	8.40523i	0.738134	−	0.426162i	−0.0832565	−	0.996528i	$-0.526532\pi$
$389$	14.5583	−	8.40523i	0.738134	−	0.426162i	0.821390	+	0.570366i	$0.193199\pi$
$390$		0			0
$391$	−11.0481	−	6.37863i	−0.558727	−	0.322581i
$392$	−2.33957	−	1.58947i	−0.118166	−	0.0802803i
$393$		0			0
$394$	−27.4316	−	0.669072i	−1.38199	−	0.0337074i
$395$	8.04185			0.404630
$396$		0			0
$397$	−11.1767			−0.560944			−0.280472	−	0.959862i	$-0.590491\pi$
$397$	−11.1767			−0.560944			−0.280472	+	0.959862i	$0.590491\pi$
$398$	24.1483	+	0.588990i	1.21045	+	0.0295234i
$399$		0			0
$400$	−6.28284	−	13.8432i	−0.314142	−	0.692162i
$401$	3.02358	+	1.74567i	0.150990	+	0.0871744i	0.573592	−	0.819141i	$-0.305550\pi$
$401$	3.02358	+	1.74567i	0.150990	+	0.0871744i	−0.422601	+	0.906316i	$0.638883\pi$
$402$		0			0
$403$	−8.15296	+	4.70711i	−0.406128	+	0.234478i
$404$	−12.4329	+	6.39118i	−0.618560	+	0.317973i
$405$		0			0
$406$	7.79241	+	4.75598i	0.386731	+	0.236035i
$407$	15.7829	+	27.3368i	0.782330	+	1.35504i
$408$		0			0
$409$	−11.0382	+	19.1188i	−0.545806	+	0.945364i	0.452750	+	0.891638i	$0.350443\pi$
$409$	−11.0382	+	19.1188i	−0.545806	+	0.945364i	−0.998556	+	0.0537260i	$0.982890\pi$
$410$	−8.21232	+	4.47802i	−0.405577	+	0.221154i
$411$		0			0
$412$	−17.3694	−	11.1914i	−0.855730	−	0.551362i
$413$		−	11.5515i		−	0.568413i
$414$		0			0
$415$		−	12.8995i		−	0.633210i
$416$	6.44746	+	4.85604i	0.316113	+	0.238087i
$417$		0			0
$418$	−15.3591	−	28.1674i	−0.751240	−	1.37771i
$419$	−5.08880	+	8.81406i	−0.248604	+	0.430595i	−0.963139	−	0.269005i	$-0.913305\pi$
$419$	−5.08880	+	8.81406i	−0.248604	+	0.430595i	0.714535	+	0.699600i	$0.246639\pi$
$420$		0			0
$421$	9.67457	+	16.7569i	0.471510	+	0.816679i	0.999469	−	0.0325909i	$-0.0103758\pi$
$421$	9.67457	+	16.7569i	0.471510	+	0.816679i	−0.527959	+	0.849270i	$0.677043\pi$
$422$	−3.83848	+	6.28913i	−0.186854	+	0.306150i
$423$		0			0
$424$	1.09556	+	0.0802916i	0.0532053	+	0.00389930i
$425$	8.37515	−	4.83539i	0.406254	−	0.234551i
$426$		0			0
$427$	5.83957	+	3.37148i	0.282596	+	0.163157i
$428$	−19.7467	−	0.963840i	−0.954495	−	0.0465890i
$429$		0			0
$430$	0.188418	−	7.72503i	0.00908630	−	0.372534i
$431$	−18.0472			−0.869302			−0.434651	−	0.900599i	$-0.643128\pi$
$431$	−18.0472			−0.869302			−0.434651	+	0.900599i	$0.643128\pi$
$432$		0			0
$433$	3.99550			0.192011			0.0960057	−	0.995381i	$-0.469393\pi$
$433$	3.99550			0.192011			0.0960057	+	0.995381i	$0.469393\pi$
$434$	−0.227513	+	9.32793i	−0.0109210	+	0.447755i
$435$		0			0
$436$	−25.2845	−	1.23414i	−1.21091	−	0.0591046i
$437$	−26.6282	−	15.3738i	−1.27380	−	0.735428i
$438$		0			0
$439$	0.156662	−	0.0904486i	0.00747705	−	0.00431687i	−0.496257	−	0.868176i	$-0.665293\pi$
$439$	0.156662	−	0.0904486i	0.00747705	−	0.00431687i	0.503734	+	0.863859i	$0.331959\pi$
$440$	11.4277	+	0.837513i	0.544795	+	0.0399268i
$441$		0			0
$442$	−2.67500	+	4.38284i	−0.127237	+	0.208470i
$443$	−11.0857	−	19.2011i	−0.526699	−	0.912269i	−0.999516	−	0.0311088i	$-0.990096\pi$
$443$	−11.0857	−	19.2011i	−0.526699	−	0.912269i	0.472817	−	0.881161i	$-0.343237\pi$
$444$		0			0
$445$	5.69549	−	9.86488i	0.269992	−	0.467640i
$446$	7.10950	+	13.0382i	0.336645	+	0.617378i
$447$		0			0
$448$	7.43735	−	2.94718i	0.351382	−	0.139241i
$449$			10.7639i			0.507982i	0.967207	+	0.253991i	$0.0817434\pi$
$449$			10.7639i			0.507982i	−0.967207	+	0.253991i	$0.918257\pi$
$450$		0			0
$451$			22.3398i			1.05194i
$452$	−25.4723	−	16.4123i	−1.19812	−	0.771969i
$453$		0			0
$454$	20.4146	−	11.1317i	0.958103	−	0.522435i
$455$	−0.781344	+	1.35333i	−0.0366300	+	0.0634450i
$456$		0			0
$457$	11.0116	+	19.0726i	0.515100	+	0.892179i	0.999846	+	0.0175241i	$0.00557839\pi$
$457$	11.0116	+	19.0726i	0.515100	+	0.892179i	−0.484747	+	0.874654i	$0.661088\pi$
$458$	29.9198	+	18.2611i	1.39806	+	0.853285i
$459$		0			0
$460$	9.76664	−	5.02058i	0.455372	−	0.234086i
$461$	0.943871	−	0.544944i	0.0439605	−	0.0253806i	−0.477859	−	0.878437i	$-0.658587\pi$
$461$	0.943871	−	0.544944i	0.0439605	−	0.0253806i	0.521819	+	0.853056i	$0.325254\pi$
$462$		0			0
$463$	−6.14401	−	3.54725i	−0.285537	−	0.164855i	0.350391	−	0.936604i	$-0.386049\pi$
$463$	−6.14401	−	3.54725i	−0.285537	−	0.164855i	−0.635927	+	0.771749i	$0.719382\pi$
$464$	−23.5127	+	10.6714i	−1.09155	+	0.495407i
$465$		0			0
$466$	−39.8024	−	0.970803i	−1.84381	−	0.0449716i
$467$	6.67705			0.308977			0.154488	−	0.987995i	$-0.450627\pi$
$467$	6.67705			0.308977			0.154488	+	0.987995i	$0.450627\pi$
$468$		0			0
$469$	−13.3589			−0.616858
$470$	−4.82898	−	0.117781i	−0.222744	−	0.00543285i
$471$		0			0
$472$	27.0256	+	18.3608i	1.24395	+	0.845124i
$473$	−15.9826	−	9.22757i	−0.734882	−	0.424284i
$474$		0			0
$475$	20.1858	−	11.6543i	0.926188	−	0.534735i
$476$	2.32667	+	4.52612i	0.106643	+	0.207454i
$477$		0			0
$478$	20.0273	+	12.2234i	0.916027	+	0.559084i
$479$	−9.81883	−	17.0067i	−0.448634	−	0.777057i	0.549663	−	0.835386i	$-0.314756\pi$
$479$	−9.81883	−	17.0067i	−0.448634	−	0.777057i	−0.998297	+	0.0583294i	$0.981423\pi$
$480$		0			0
$481$	6.08811	−	10.5449i	0.277594	−	0.480806i
$482$	33.0299	−	18.0106i	1.50447	−	0.820360i
$483$		0			0
$484$	2.90634	−	4.51072i	0.132106	−	0.205033i
$485$			5.39313i			0.244889i
$486$		0			0
$487$			31.0088i			1.40514i	0.711612	+	0.702572i	$0.247965\pi$
$487$			31.0088i			1.40514i	−0.711612	+	0.702572i	$0.752035\pi$
$488$	−17.1696	+	8.30322i	−0.777232	+	0.375869i
$489$		0			0
$490$	0.741476	+	1.35981i	0.0334965	+	0.0614297i
$491$	−10.4584	+	18.1145i	−0.471982	+	0.817498i	−0.999486	−	0.0320551i	$-0.989795\pi$
$491$	−10.4584	+	18.1145i	−0.471982	+	0.817498i	0.527504	+	0.849553i	$0.323128\pi$
$492$		0			0
$493$	−8.21291	−	14.2252i	−0.369891	−	0.640670i
$494$	−6.44730	+	10.5635i	−0.290078	+	0.475276i
$495$		0			0
$496$	−21.4617	−	15.3587i	−0.963660	−	0.689627i
$497$	6.77782	−	3.91318i	0.304027	−	0.175530i
$498$		0			0
$499$	16.3990	+	9.46794i	0.734118	+	0.423843i	0.819927	−	0.572468i	$-0.194014\pi$
$499$	16.3990	+	9.46794i	0.734118	+	0.423843i	−0.0858088	+	0.996312i	$0.527347\pi$
$500$	−0.939769	+	19.2536i	−0.0420277	+	0.861046i
$501$		0			0
$502$	−0.891626	+	36.5562i	−0.0397952	+	1.63158i
$503$	−26.6026			−1.18615			−0.593077	−	0.805146i	$-0.702087\pi$
$503$	−26.6026			−1.18615			−0.593077	+	0.805146i	$0.702087\pi$
$504$		0			0
$505$	7.65502			0.340644
$506$	0.639502	−	26.2193i	0.0284293	−	1.16559i
$507$		0			0
$508$	−0.101214	+	2.07363i	−0.00449064	+	0.0920023i
$509$	−30.0561	−	17.3529i	−1.33221	−	0.769153i	−0.346573	−	0.938023i	$-0.612655\pi$
$509$	−30.0561	−	17.3529i	−1.33221	−	0.769153i	−0.985638	+	0.168870i	$0.945988\pi$
$510$		0			0
$511$	4.85340	−	2.80211i	0.214702	−	0.123958i
$512$	−4.92630	+	22.0846i	−0.217714	+	0.976013i
$513$		0			0
$514$	10.7651	−	17.6380i	0.474829	−	0.777980i
$515$	5.65735	+	9.79882i	0.249293	+	0.431787i
$516$		0			0
$517$	−5.76823	+	9.99086i	−0.253686	+	0.439398i
$518$	−5.77746	−	10.5954i	−0.253847	−	0.465534i
$519$		0			0
$520$	−1.92428	−	3.97908i	−0.0843854	−	0.174494i
$521$			45.5272i			1.99458i	0.0735459	+	0.997292i	$0.476568\pi$
$521$			45.5272i			1.99458i	−0.0735459	+	0.997292i	$0.523432\pi$
$522$		0			0
$523$			23.2951i			1.01862i	0.860582	+	0.509312i	$0.170100\pi$
$523$			23.2951i			1.01862i	−0.860582	+	0.509312i	$0.829900\pi$
$524$	−4.83993	+	7.51171i	−0.211433	+	0.328151i
$525$		0			0
$526$	11.1667	−	6.08900i	0.486892	−	0.265493i
$527$	8.39426	−	14.5393i	0.365660	−	0.633341i
$528$		0			0
$529$	−1.06780	−	1.84948i	−0.0464259	−	0.0804121i
$530$	−0.513453	−	0.313378i	−0.0223030	−	0.0136123i
$531$		0			0
$532$	5.60775	+	10.9089i	0.243127	+	0.472959i
$533$	7.46285	−	4.30868i	0.323252	−	0.186630i
$534$		0			0
$535$	9.37562	+	5.41302i	0.405343	+	0.234025i
$536$	21.2336	−	31.2542i	0.917152	−	1.34997i
$537$		0			0
$538$	36.1069	+	0.880666i	1.55668	+	0.0379682i
$539$	3.69905			0.159329
$540$		0			0
$541$	41.9442			1.80332			0.901660	−	0.432446i	$-0.142349\pi$
$541$	41.9442			1.80332			0.901660	+	0.432446i	$0.142349\pi$
$542$	33.1601	+	0.808793i	1.42435	+	0.0347406i
$543$		0			0
$544$	−14.2874	−	1.75072i	−0.612565	−	0.0750615i
$545$	12.0049	+	6.93105i	0.514235	+	0.296894i
$546$		0			0
$547$	26.9809	−	15.5775i	1.15362	−	0.666044i	0.203855	−	0.979001i	$-0.434653\pi$
$547$	26.9809	−	15.5775i	1.15362	−	0.666044i	0.949767	+	0.312957i	$0.101320\pi$
$548$	5.56347	−	2.85992i	0.237660	−	0.122170i
$549$		0			0
$550$	16.9706	+	10.3577i	0.723628	+	0.441656i
$551$	−19.7948	−	34.2856i	−0.843286	−	1.46061i
$552$		0			0
$553$	−3.67146	+	6.35916i	−0.156126	+	0.270419i
$554$	28.8836	−	15.7497i	1.22715	−	0.669140i
$555$		0			0
$556$	−2.86433	−	1.84554i	−0.121475	−	0.0782682i
$557$		−	4.86612i		−	0.206184i	−0.994672	−	0.103092i	$-0.967126\pi$
$557$		−	4.86612i		−	0.206184i	0.994672	−	0.103092i	$-0.0328736\pi$
$558$		0			0
$559$			7.11889i			0.301097i
$560$	−4.35991	−	0.426632i	−0.184240	−	0.0180285i
$561$		0			0
$562$	−5.33427	−	9.78260i	−0.225013	−	0.412654i
$563$	−13.3802	+	23.1752i	−0.563908	+	0.976716i	0.433243	+	0.901277i	$0.357369\pi$
$563$	−13.3802	+	23.1752i	−0.563908	+	0.976716i	−0.997150	+	0.0754393i	$0.975964\pi$
$564$		0			0
$565$	8.29653	+	14.3700i	0.349038	+	0.604551i
$566$	5.99719	−	9.82606i	0.252081	−	0.413020i
$567$		0			0
$568$	−1.61798	+	22.0771i	−0.0678890	+	0.926333i
$569$	2.16686	−	1.25104i	0.0908394	−	0.0524461i	−0.453892	−	0.891057i	$-0.649965\pi$
$569$	2.16686	−	1.25104i	0.0908394	−	0.0524461i	0.544732	+	0.838610i	$0.316632\pi$
$570$		0			0
$571$	−20.6537	−	11.9244i	−0.864328	−	0.499020i	0.00113090	−	0.999999i	$-0.499640\pi$
$571$	−20.6537	−	11.9244i	−0.864328	−	0.499020i	−0.865459	+	0.500979i	$0.832973\pi$
$572$	−10.5436	−	0.514634i	−0.440850	−	0.0215179i
$573$		0			0
$574$	0.208255	−	8.53837i	0.00869241	−	0.356385i
$575$	19.0543			0.794620
$576$		0			0
$577$	5.02946			0.209379			0.104690	−	0.994505i	$-0.466615\pi$
$577$	5.02946			0.209379			0.104690	+	0.994505i	$0.466615\pi$
$578$	−0.362942	+	14.8805i	−0.0150964	+	0.618946i
$579$		0			0
$580$	14.1226	+	0.689326i	0.586409	+	0.0286227i
$581$	10.2004	+	5.88918i	0.423182	+	0.244324i
$582$		0			0
$583$	−1.24416	+	0.718317i	−0.0515279	+	0.0297497i
$584$	−1.15859	+	15.8088i	−0.0479428	+	0.654171i
$585$		0			0
$586$	8.10425	−	13.2784i	0.334784	−	0.548524i
$587$	18.3177	+	31.7271i	0.756051	+	1.30952i	0.944850	+	0.327503i	$0.106207\pi$
$587$	18.3177	+	31.7271i	0.756051	+	1.30952i	−0.188799	+	0.982016i	$0.560459\pi$
$588$		0			0
$589$	20.2319	−	35.0426i	0.833639	−	1.44391i
$590$	−8.56518	−	15.7078i	−0.352623	−	0.646681i
$591$		0			0
$592$	33.9717	+	3.32425i	1.39623	+	0.136626i
$593$			22.6612i			0.930583i	0.885157	+	0.465292i	$0.154051\pi$
$593$			22.6612i			0.930583i	−0.885157	+	0.465292i	$0.845949\pi$
$594$		0			0
$595$		−	2.78676i		−	0.114246i
$596$	5.96236	+	3.84166i	0.244228	+	0.157360i
$597$		0			0
$598$	−8.88218	+	4.84328i	−0.363219	+	0.198057i
$599$	16.8470	−	29.1798i	0.688349	−	1.19226i	−0.284023	−	0.958818i	$-0.591669\pi$
$599$	16.8470	−	29.1798i	0.688349	−	1.19226i	0.972372	−	0.233438i	$-0.0749975\pi$
$600$		0			0
$601$	9.07185	+	15.7129i	0.370048	+	0.640943i	0.989573	−	0.144035i	$-0.0460077\pi$
$601$	9.07185	+	15.7129i	0.370048	+	0.640943i	−0.619524	+	0.784978i	$0.712674\pi$
$602$	6.02261	+	3.67581i	0.245463	+	0.149815i
$603$		0			0
$604$	−1.65496	+	0.850741i	−0.0673395	+	0.0346162i
$605$	−2.54469	+	1.46918i	−0.103456	+	0.0597305i
$606$		0			0
$607$	7.53903	+	4.35266i	0.306000	+	0.176669i	0.645135	−	0.764069i	$-0.276801\pi$
$607$	7.53903	+	4.35266i	0.306000	+	0.176669i	−0.339135	+	0.940738i	$0.610134\pi$
$608$	−34.4354	−	4.21959i	−1.39654	−	0.171127i
$609$		0			0
$610$	10.4405	+	0.254650i	0.422725	+	0.0103105i
$611$	4.45008			0.180031
$612$		0			0
$613$	8.54050			0.344948			0.172474	−	0.985014i	$-0.444824\pi$
$613$	8.54050			0.344948			0.172474	+	0.985014i	$0.444824\pi$
$614$	−4.13479	−	0.100850i	−0.166866	−	0.00406996i
$615$		0			0
$616$	−5.87952	+	8.65419i	−0.236893	+	0.348687i
$617$	13.4378	+	7.75834i	0.540987	+	0.312339i	0.745479	−	0.666529i	$-0.232221\pi$
$617$	13.4378	+	7.75834i	0.540987	+	0.312339i	−0.204492	+	0.978868i	$0.565554\pi$
$618$		0			0
$619$	14.4534	−	8.34468i	0.580932	−	0.335401i	−0.180572	−	0.983562i	$-0.557795\pi$
$619$	14.4534	−	8.34468i	0.580932	−	0.335401i	0.761504	+	0.648161i	$0.224461\pi$
$620$	6.60706	+	12.8529i	0.265346	+	0.516183i
$621$		0			0
$622$	−15.6015	−	9.52216i	−0.625564	−	0.381804i
$623$	5.20048	+	9.00750i	0.208353	+	0.360878i
$624$		0			0
$625$	−4.22360	+	7.31549i	−0.168944	+	0.292620i
$626$	−6.67208	+	3.63816i	−0.266670	+	0.145410i
$627$		0			0
$628$	19.0088	−	29.5022i	0.758534	−	1.17727i
$629$			21.7140i			0.865794i
$630$		0			0
$631$			0.308880i			0.0122963i	0.999981	+	0.00614815i	$0.00195703\pi$
$631$			0.308880i			0.0122963i	−0.999981	+	0.00614815i	$0.998043\pi$
$632$	−9.04203	−	18.6973i	−0.359673	−	0.743740i
$633$		0			0
$634$	−10.9123	−	20.0123i	−0.433385	−	0.794791i
$635$	0.568427	−	0.984544i	0.0225573	−	0.0390704i
$636$		0			0
$637$	−0.713436	−	1.23571i	−0.0282674	−	0.0489605i
$638$	17.5926	−	28.8245i	0.696498	−	1.14117i
$639$		0			0
$640$	7.92808	−	9.52220i	0.313385	−	0.376398i
$641$	−8.28442	+	4.78301i	−0.327215	+	0.188918i	−0.654604	−	0.755972i	$-0.727165\pi$
$641$	−8.28442	+	4.78301i	−0.327215	+	0.188918i	0.327389	+	0.944890i	$0.393831\pi$
$642$		0			0
$643$	−11.0542	−	6.38212i	−0.435934	−	0.251686i	0.265938	−	0.963990i	$-0.414318\pi$
$643$	−11.0542	−	6.38212i	−0.435934	−	0.251686i	−0.701871	+	0.712304i	$0.747652\pi$
$644$	−0.488841	+	10.0152i	−0.0192630	+	0.394653i
$645$		0			0
$646$	0.538129	−	22.0630i	0.0211724	−	0.868059i
$647$	−16.6855			−0.655977			−0.327988	−	0.944682i	$-0.606371\pi$
$647$	−16.6855			−0.655977			−0.327988	+	0.944682i	$0.606371\pi$
$648$		0			0
$649$	−42.7297			−1.67729
$650$	0.187000	−	7.66691i	0.00733474	−	0.300721i
$651$		0			0
$652$	−1.43841	+	29.4696i	−0.0563327	+	1.15412i
$653$	5.82947	+	3.36565i	0.228125	+	0.131708i	0.609707	−	0.792627i	$-0.291287\pi$
$653$	5.82947	+	3.36565i	0.228125	+	0.131708i	−0.381582	+	0.924335i	$0.624621\pi$
$654$		0			0
$655$	4.23767	−	2.44662i	0.165579	−	0.0955974i
$656$	19.6451	+	14.0587i	0.767012	+	0.548900i
$657$		0			0
$658$	2.29778	−	3.76478i	0.0895767	−	0.146766i
$659$	2.35452	+	4.07815i	0.0917191	+	0.158862i	0.908235	−	0.418461i	$-0.137430\pi$
$659$	2.35452	+	4.07815i	0.0917191	+	0.158862i	−0.816515	+	0.577324i	$0.804097\pi$
$660$		0			0
$661$	22.5207	−	39.0070i	0.875953	−	1.51720i	0.0202093	−	0.999796i	$-0.493567\pi$
$661$	22.5207	−	39.0070i	0.875953	−	1.51720i	0.855744	−	0.517400i	$-0.173100\pi$
$662$	−2.84759	−	5.22224i	−0.110675	−	0.202968i
$663$		0			0
$664$	−29.9913	+	14.5038i	−1.16389	+	0.562856i
$665$		−	6.71666i		−	0.260461i
$666$		0			0
$667$		−	32.3638i		−	1.25313i
$668$	−8.94360	+	13.8807i	−0.346038	+	0.537062i
$669$		0			0
$670$	−18.1655	+	9.90533i	−0.701796	+	0.382676i
$671$	12.4713	−	21.6009i	0.481448	−	0.833892i
$672$		0			0
$673$	7.64821	+	13.2471i	0.294817	+	0.510637i	0.974942	−	0.222458i	$-0.0714081\pi$
$673$	7.64821	+	13.2471i	0.294817	+	0.510637i	−0.680126	+	0.733096i	$0.738075\pi$
$674$	−29.6222	−	18.0795i	−1.14101	−	0.696396i
$675$		0			0
$676$	−10.0252	−	19.5022i	−0.385584	−	0.750085i
$677$	20.6303	−	11.9109i	0.792887	−	0.457773i	−0.0480910	−	0.998843i	$-0.515314\pi$
$677$	20.6303	−	11.9109i	0.792887	−	0.457773i	0.840978	+	0.541069i	$0.181980\pi$
$678$		0			0
$679$	−4.26466	−	2.46220i	−0.163663	−	0.0944906i
$680$	6.51983	+	4.42947i	0.250024	+	0.169863i
$681$		0			0
$682$	34.5045	+	0.841582i	1.32124	+	0.0322259i
$683$	−26.4666			−1.01272			−0.506359	−	0.862323i	$-0.669009\pi$
$683$	−26.4666			−1.01272			−0.506359	+	0.862323i	$0.669009\pi$
$684$		0			0
$685$	−3.42546			−0.130880
$686$	−1.41379	−	0.0344832i	−0.0539789	−	0.00131657i
$687$		0			0
$688$	−18.1726	+	8.24773i	−0.692822	+	0.314442i
$689$	0.479923	+	0.277084i	0.0182836	+	0.0105561i
$690$		0			0
$691$	−18.2433	+	10.5328i	−0.694009	+	0.400686i	−0.805112	−	0.593123i	$-0.797895\pi$
$691$	−18.2433	+	10.5328i	−0.694009	+	0.400686i	0.111103	+	0.993809i	$0.464562\pi$
$692$	−13.1132	+	6.74091i	−0.498491	+	0.256251i
$693$		0			0
$694$	28.1184	+	17.1616i	1.06736	+	0.651447i
$695$	0.932933	+	1.61589i	0.0353882	+	0.0612941i
$696$		0			0
$697$	−7.68373	+	13.3086i	−0.291042	+	0.504100i
$698$	25.5440	−	13.9287i	0.966854	−	0.527207i
$699$		0			0
$700$	−6.38967	−	4.11698i	−0.241507	−	0.155607i
$701$		−	22.0598i		−	0.833187i	−0.909093	−	0.416594i	$-0.863224\pi$
$701$		−	22.0598i		−	0.833187i	0.909093	−	0.416594i	$-0.136776\pi$
$702$		0			0
$703$			52.3351i			1.97386i
$704$	−10.9018	−	27.5111i	−0.410876	−	1.03686i
$705$		0			0
$706$	15.0931	+	27.6795i	0.568037	+	1.04173i
$707$	−3.49486	+	6.05327i	−0.131438	+	0.227657i
$708$		0			0
$709$	18.5517	+	32.1324i	0.696723	+	1.20676i	0.969597	+	0.244709i	$0.0786925\pi$
$709$	18.5517	+	32.1324i	0.696723	+	1.20676i	−0.272874	+	0.962050i	$0.587974\pi$
$710$	6.31499	−	10.3468i	0.236997	−	0.388307i
$711$		0			0
$712$	−29.3397	−	2.15024i	−1.09955	−	0.0805838i
$713$	28.6467	−	16.5392i	1.07283	−	0.619397i
$714$		0			0
$715$	5.00603	+	2.89023i	0.187215	+	0.108089i
$716$	17.0230	+	0.830895i	0.636180	+	0.0310520i
$717$		0			0
$718$	−0.821270	+	33.6717i	−0.0306495	+	1.25662i
$719$	−12.8753			−0.480168			−0.240084	−	0.970752i	$-0.577175\pi$
$719$	−12.8753			−0.480168			−0.240084	+	0.970752i	$0.577175\pi$
$720$		0			0
$721$	−10.3313			−0.384759
$722$	0.641820	−	26.3143i	0.0238861	−	0.979317i
$723$		0			0
$724$	−49.6130	−	2.42162i	−1.84385	−	0.0899986i
$725$	21.2468	+	12.2669i	0.789087	+	0.455580i
$726$		0			0
$727$	27.3677	−	15.8007i	1.01501	−	0.586016i	0.102356	−	0.994748i	$-0.467362\pi$
$727$	27.3677	−	15.8007i	1.01501	−	0.586016i	0.912655	+	0.408731i	$0.134029\pi$
$728$	4.02501	+	0.294985i	0.149177	+	0.0109329i
$729$		0			0
$730$	4.52198	−	7.40901i	0.167366	−	0.274220i
$731$	−6.34761	−	10.9944i	−0.234775	−	0.406642i
$732$		0			0
$733$	2.93614	−	5.08554i	0.108449	−	0.187839i	−0.806693	−	0.590970i	$-0.798745\pi$
$733$	2.93614	−	5.08554i	0.108449	−	0.187839i	0.915142	+	0.403132i	$0.132078\pi$
$734$	−11.5255	−	21.1368i	−0.425414	−	0.780174i
$735$		0			0
$736$	−22.6542	−	17.0625i	−0.835044	−	0.628931i
$737$			49.4154i			1.82024i
$738$		0			0
$739$		−	18.8805i		−	0.694529i	−0.937767	−	0.347264i	$-0.887111\pi$
$739$		−	18.8805i		−	0.694529i	0.937767	−	0.347264i	$-0.112889\pi$
$740$	−15.7124	−	10.1238i	−0.577601	−	0.372158i
$741$		0			0
$742$	0.482220	−	0.262946i	0.0177029	−	0.00965304i
$743$	4.97478	−	8.61657i	0.182507	−	0.316111i	−0.760227	−	0.649658i	$-0.774912\pi$
$743$	4.97478	−	8.61657i	0.182507	−	0.316111i	0.942734	+	0.333547i	$0.108245\pi$
$744$		0			0
$745$	−1.94199	−	3.36362i	−0.0711489	−	0.123233i
$746$	−7.16025	−	4.37016i	−0.262155	−	0.160003i
$747$		0			0
$748$	16.7424	−	8.60647i	0.612161	−	0.314684i
$749$	−8.56077	+	4.94256i	−0.312804	+	0.180597i
$750$		0			0
$751$	22.0777	+	12.7466i	0.805627	+	0.465129i	0.845435	−	0.534078i	$-0.179341\pi$
$751$	22.0777	+	12.7466i	0.805627	+	0.465129i	−0.0398081	+	0.999207i	$0.512675\pi$
$752$	5.15572	+	11.3598i	0.188010	+	0.414250i
$753$		0			0
$754$	−13.0222	−	0.317619i	−0.474242	−	0.0115670i
$755$	1.01897			0.0370842
$756$		0			0
$757$	10.9279			0.397180			0.198590	−	0.980083i	$-0.436364\pi$
$757$	10.9279			0.397180			0.198590	+	0.980083i	$0.436364\pi$
$758$	43.0740	+	1.05060i	1.56452	+	0.0381594i
$759$		0			0
$760$	15.7141	+	10.6759i	0.570011	+	0.387256i
$761$	34.0621	+	19.6658i	1.23475	+	0.712884i	0.968017	−	0.250886i	$-0.0807221\pi$
$761$	34.0621	+	19.6658i	1.23475	+	0.712884i	0.266734	+	0.963770i	$0.414055\pi$
$762$		0			0
$763$	−10.9616	+	6.32866i	−0.396835	+	0.229113i
$764$	−18.9969	−	36.9551i	−0.687284	−	1.33699i
$765$		0			0
$766$	−13.0599	−	7.97092i	−0.471873	−	0.288001i
$767$	8.24128	+	14.2743i	0.297575	+	0.515416i
$768$		0			0
$769$	−4.90765	+	8.50030i	−0.176974	+	0.306529i	−0.940843	−	0.338843i	$-0.889964\pi$
$769$	−4.90765	+	8.50030i	−0.176974	+	0.306529i	0.763868	+	0.645372i	$0.223298\pi$
$770$	5.02999	−	2.74276i	0.181268	−	0.0988421i
$771$		0			0
$772$	22.6000	−	35.0759i	0.813393	−	1.26241i
$773$		−	33.6953i		−	1.21194i	−0.795489	−	0.605968i	$-0.792786\pi$
$773$		−	33.6953i		−	1.21194i	0.795489	−	0.605968i	$-0.207214\pi$
$774$		0			0
$775$			25.0754i			0.900736i
$776$	12.5390	−	6.06388i	0.450125	−	0.217680i
$777$		0			0
$778$	11.3812	+	20.8722i	0.408037	+	0.748306i
$779$	−18.5193	+	32.0764i	−0.663524	+	1.14926i
$780$		0			0
$781$	−14.4750	−	25.0715i	−0.517958	−	0.897129i
$782$	9.39904	−	15.3998i	0.336109	−	0.550696i
$783$		0			0
$784$	2.32786	−	3.25286i	0.0831377	−	0.116174i
$785$	−16.6434	+	9.60910i	−0.594030	+	0.342963i
$786$		0			0
$787$	25.6645	+	14.8174i	0.914839	+	0.528183i	0.881985	−	0.471277i	$-0.156207\pi$
$787$	25.6645	+	14.8174i	0.914839	+	0.528183i	0.0328543	+	0.999460i	$0.489540\pi$
$788$	1.89186	−	38.7596i	0.0673947	−	1.38075i
$789$		0			0
$790$	−0.277309	+	11.3695i	−0.00986620	+	0.404509i
$791$	−15.1509			−0.538705
$792$		0			0
$793$	−9.62133			−0.341664
$794$	0.385409	−	15.8016i	0.0136777	−	0.560777i
$795$		0			0
$796$	−1.66542	+	34.1204i	−0.0590292	+	1.20937i
$797$	−6.96345	−	4.02035i	−0.246658	−	0.142408i	0.371575	−	0.928403i	$-0.378818\pi$
$797$	−6.96345	−	4.02035i	−0.246658	−	0.142408i	−0.618233	+	0.785995i	$0.712151\pi$
$798$		0			0
$799$	−6.87268	+	3.96794i	−0.243138	+	0.140376i
$800$	19.7881	−	8.40528i	0.699616	−	0.297171i
$801$		0			0
$802$	−2.57227	+	4.21452i	−0.0908301	+	0.148820i
$803$	−10.3652	−	17.9530i	−0.365779	−	0.633547i
$804$		0			0
$805$	2.74538	−	4.75513i	0.0967618	−	0.167596i
$806$	−6.37374	−	11.6889i	−0.224506	−	0.411724i
$807$		0			0
$808$	−8.60709	−	17.7979i	−0.302796	−	0.626130i
$809$		−	33.7331i		−	1.18599i	−0.805205	−	0.592996i	$-0.797945\pi$
$809$		−	33.7331i		−	1.18599i	0.805205	−	0.592996i	$-0.202055\pi$
$810$		0			0
$811$			19.1962i			0.674068i	0.941492	+	0.337034i	$0.109424\pi$
$811$			19.1962i			0.674068i	−0.941492	+	0.337034i	$0.890576\pi$
$812$	−6.99268	+	10.8528i	−0.245395	+	0.380860i
$813$		0			0
$814$	−39.1928	+	21.3711i	−1.37371	+	0.749057i
$815$	8.07827	−	13.9920i	0.282969	−	0.490117i
$816$		0			0
$817$	−15.2990	−	26.4987i	−0.535245	−	0.927072i
$818$	−26.6494	−	16.2651i	−0.931774	−	0.568695i
$819$		0			0
$820$	−6.04781	−	11.7649i	−0.211199	−	0.410849i
$821$	−4.72698	+	2.72912i	−0.164973	+	0.0952470i	−0.580213	−	0.814465i	$-0.697031\pi$
$821$	−4.72698	+	2.72912i	−0.164973	+	0.0952470i	0.415241	+	0.909712i	$0.363697\pi$
$822$		0			0
$823$	−16.1855	−	9.34469i	−0.564190	−	0.325735i	0.190635	−	0.981661i	$-0.438945\pi$
$823$	−16.1855	−	9.34469i	−0.564190	−	0.325735i	−0.754826	+	0.655926i	$0.772279\pi$
$824$	16.4213	−	24.1709i	0.572063	−	0.842032i
$825$		0			0
$826$	16.3315	+	0.398333i	0.568244	+	0.0138598i
$827$	6.51950			0.226705			0.113353	−	0.993555i	$-0.463841\pi$
$827$	6.51950			0.226705			0.113353	+	0.993555i	$0.463841\pi$
$828$		0			0
$829$	2.12913			0.0739478			0.0369739	−	0.999316i	$-0.488228\pi$
$829$	2.12913			0.0739478			0.0369739	+	0.999316i	$0.488228\pi$
$830$	18.2372	+	0.444814i	0.633022	+	0.0154397i
$831$		0			0
$832$	−7.08777	+	8.94793i	−0.245724	+	0.310214i
$833$	2.20366	+	1.27228i	0.0763521	+	0.0440819i
$834$		0			0
$835$	7.83070	−	4.52106i	0.270993	−	0.156458i
$836$	40.3525	−	20.7433i	1.39562	−	0.717423i
$837$		0			0
$838$	−12.2858	−	7.49845i	−0.424405	−	0.259030i
$839$	12.4714	+	21.6011i	0.430560	+	0.745751i	0.996922	−	0.0784055i	$-0.0249829\pi$
$839$	12.4714	+	21.6011i	0.430560	+	0.745751i	−0.566362	+	0.824157i	$0.691650\pi$
$840$		0			0
$841$	6.33524	−	10.9730i	0.218457	−	0.378378i
$842$	−24.0243	+	13.1000i	−0.827933	+	0.451456i
$843$		0			0
$844$	−8.75917	−	5.64369i	−0.301503	−	0.194264i
$845$			12.0076i			0.413075i
$846$		0			0
$847$		−	2.68297i		−	0.0921881i
$848$	−0.151294	+	1.54613i	−0.00519546	+	0.0530944i
$849$		0			0
$850$	6.54745	+	12.0075i	0.224576	+	0.411853i
$851$	−21.3915	+	37.0512i	−0.733292	+	1.27010i
$852$		0			0
$853$	9.27722	+	16.0686i	0.317646	+	0.550179i	0.979996	−	0.199015i	$-0.0637743\pi$
$853$	9.27722	+	16.0686i	0.317646	+	0.550179i	−0.662350	+	0.749194i	$0.730441\pi$
$854$	−4.96794	+	8.13968i	−0.169999	+	0.278534i
$855$		0			0
$856$	2.04360	−	27.8846i	0.0698488	−	0.953075i
$857$	−13.8638	+	8.00424i	−0.473577	+	0.273420i	−0.717736	−	0.696316i	$-0.754821\pi$
$857$	−13.8638	+	8.00424i	−0.473577	+	0.273420i	0.244159	+	0.969735i	$0.421488\pi$
$858$		0			0
$859$	−5.87655	−	3.39283i	−0.200505	−	0.115762i	0.396386	−	0.918084i	$-0.370264\pi$
$859$	−5.87655	−	3.39283i	−0.200505	−	0.115762i	−0.596891	+	0.802322i	$0.703598\pi$
$860$	10.9151	+	0.532767i	0.372202	+	0.0181672i
$861$		0			0
$862$	0.622324	−	25.5150i	0.0211964	−	0.869044i
$863$	−0.874006			−0.0297515			−0.0148758	−	0.999889i	$-0.504735\pi$
$863$	−0.874006			−0.0297515			−0.0148758	+	0.999889i	$0.504735\pi$
$864$		0			0
$865$	8.07391			0.274521
$866$	−0.137777	+	5.64881i	−0.00468187	+	0.191954i
$867$		0			0
$868$	−13.1799	−	0.643313i	−0.447355	−	0.0218355i
$869$	23.5229	+	13.5809i	0.797958	+	0.460701i
$870$		0			0
$871$	16.5077	−	9.53075i	0.559344	−	0.322937i
$872$	2.61671	−	35.7046i	0.0886130	−	1.20911i
$873$		0			0
$874$	22.6536	−	37.1166i	0.766269	−	1.25549i
$875$	4.81912	+	8.34697i	0.162916	+	0.282179i
$876$		0			0
$877$	16.4863	−	28.5551i	0.556703	−	0.964239i	−0.441065	−	0.897475i	$-0.645399\pi$
$877$	16.4863	−	28.5551i	0.556703	−	0.964239i	0.997769	−	0.0667636i	$-0.0212673\pi$
$878$	0.122473	+	0.224606i	0.00413328	+	0.00758008i
$879$		0			0
$880$	−1.57813	+	16.1275i	−0.0531989	+	0.543659i
$881$		−	3.42882i		−	0.115520i	−0.998331	−	0.0577599i	$-0.981604\pi$
$881$		−	3.42882i		−	0.115520i	0.998331	−	0.0577599i	$-0.0183958\pi$
$882$		0			0
$883$			19.2293i			0.647116i	0.946208	+	0.323558i	$0.104879\pi$
$883$			19.2293i			0.647116i	−0.946208	+	0.323558i	$0.895121\pi$
$884$	−6.10419	−	3.93303i	−0.205306	−	0.132282i
$885$		0			0
$886$	27.5286	−	15.0108i	0.924841	−	0.504298i
$887$	−3.84453	+	6.65892i	−0.129087	+	0.223585i	−0.923323	−	0.384024i	$-0.874538\pi$
$887$	−3.84453	+	6.65892i	−0.129087	+	0.223585i	0.794236	+	0.607609i	$0.207871\pi$
$888$		0			0
$889$	0.519024	+	0.898976i	0.0174075	+	0.0301507i
$890$	13.7505	+	8.39241i	0.460918	+	0.281314i
$891$		0			0
$892$	−18.6785	+	9.60177i	−0.625403	+	0.321491i
$893$	−16.5645	+	9.56354i	−0.554311	+	0.320032i
$894$		0			0
$895$	−8.08241	−	4.66638i	−0.270165	−	0.155980i
$896$	3.91024	+	10.6165i	0.130632	+	0.354672i
$897$		0			0
$898$	−15.2180	−	0.371175i	−0.507831	−	0.0123863i
$899$	42.5906			1.42048
$900$		0			0
$901$	−0.988255			−0.0329235
$902$	−31.5839	−	0.770347i	−1.05163	−	0.0256497i
$903$		0			0
$904$	24.0819	−	35.4467i	0.800953	−	1.17894i
$905$	23.5559	+	13.6000i	0.783025	+	0.452080i
$906$		0			0
$907$	−0.124941	+	0.0721349i	−0.00414861	+	0.00239520i	−0.502073	−	0.864825i	$-0.667429\pi$
$907$	−0.124941	+	0.0721349i	−0.00414861	+	0.00239520i	0.497924	+	0.867221i	$0.334096\pi$
$908$	15.0339	+	29.2458i	0.498918	+	0.970556i
$909$		0			0
$910$	−1.88638	−	1.15133i	−0.0625330	−	0.0381661i
$911$	11.4250	+	19.7887i	0.378527	+	0.655628i	0.990848	−	0.134981i	$-0.0430974\pi$
$911$	11.4250	+	19.7887i	0.378527	+	0.655628i	−0.612321	+	0.790609i	$0.709764\pi$
$912$		0			0
$913$	21.7844	−	37.7316i	0.720957	−	1.24873i
$914$	−27.3444	+	14.9104i	−0.904473	+	0.493192i
$915$		0			0
$916$	−26.8491	+	41.6707i	−0.887120	+	1.37684i
$917$			4.46796i			0.147545i
$918$		0			0
$919$			21.3020i			0.702688i	0.936246	+	0.351344i	$0.114275\pi$
$919$			21.3020i			0.702688i	−0.936246	+	0.351344i	$0.885725\pi$
$920$	6.76127	+	13.9811i	0.222913	+	0.460944i
$921$		0			0
$922$	0.737891	+	1.35323i	0.0243011	+	0.0445663i
$923$	−5.58361	+	9.67109i	−0.183787	+	0.318328i
$924$		0			0
$925$	−16.2161	−	28.0871i	−0.533181	−	0.923497i
$926$	5.22694	−	8.56404i	0.171768	−	0.281432i
$927$		0			0
$928$	−14.2764	−	33.6101i	−0.468644	−	1.10331i
$929$	2.95541	−	1.70631i	0.0969640	−	0.0559822i	−0.450734	−	0.892658i	$-0.648838\pi$
$929$	2.95541	−	1.70631i	0.0969640	−	0.0559822i	0.547698	+	0.836676i	$0.315504\pi$
$930$		0			0
$931$	5.31125	+	3.06645i	0.174069	+	0.100499i
$932$	2.74503	−	56.2389i	0.0899164	−	1.84217i
$933$		0			0
$934$	−0.230246	+	9.43997i	−0.00753387	+	0.308885i
$935$	−10.3084			−0.337120
$936$		0			0
$937$	29.6959			0.970123			0.485061	−	0.874480i	$-0.338797\pi$
$937$	29.6959			0.970123			0.485061	+	0.874480i	$0.338797\pi$
$938$	0.460658	−	18.8868i	0.0150410	−	0.616675i
$939$		0			0
$940$	0.333037	−	6.82311i	0.0108625	−	0.222545i
$941$	−45.4609	−	26.2469i	−1.48198	−	0.855623i	−0.482192	−	0.876066i	$-0.660159\pi$
$941$	−45.4609	−	26.2469i	−1.48198	−	0.855623i	−0.999791	+	0.0204426i	$0.993492\pi$
$942$		0			0
$943$	−26.2219	+	15.1392i	−0.853903	+	0.493001i
$944$	−26.8903	+	37.5755i	−0.875204	+	1.22298i
$945$		0			0
$946$	13.5970	−	22.2779i	0.442077	−	0.724318i
$947$	−19.2922	−	33.4151i	−0.626912	−	1.08584i	−0.988168	−	0.153377i	$-0.950985\pi$
$947$	−19.2922	−	33.4151i	−0.626912	−	1.08584i	0.361255	−	0.932467i	$-0.382348\pi$
$948$		0			0
$949$	−3.99826	+	6.92519i	−0.129789	+	0.224801i
$950$	15.7807	+	28.9404i	0.511992	+	0.938951i
$951$		0			0
$952$	−6.47923	+	3.13336i	−0.209993	+	0.101553i
$953$		−	37.4376i		−	1.21272i	−0.795189	−	0.606362i	$-0.792628\pi$
$953$		−	37.4376i		−	1.21272i	0.795189	−	0.606362i	$-0.207372\pi$
$954$		0			0
$955$			22.7535i			0.736286i
$956$	−17.9719	+	27.8929i	−0.581253	+	0.902122i
$957$		0			0
$958$	24.3826	−	13.2954i	0.787765	−	0.429553i
$959$	1.56388	−	2.70871i	0.0505002	−	0.0874689i
$960$		0			0
$961$	6.26550	+	10.8522i	0.202113	+	0.350070i
$962$	14.6984	+	8.97094i	0.473895	+	0.289235i
$963$		0			0
$964$	24.3243	+	47.3186i	0.783432	+	1.52403i
$965$	−19.7878	+	11.4245i	−0.636992	+	0.367767i
$966$		0			0
$967$	38.8190	+	22.4121i	1.24833	+	0.720726i	0.970777	−	0.239984i	$-0.0771420\pi$
$967$	38.8190	+	22.4121i	1.24833	+	0.720726i	0.277557	+	0.960709i	$0.410475\pi$
$968$	6.27701	+	4.26450i	0.201751	+	0.137066i
$969$		0			0
$970$	−7.62477	−	0.185972i	−0.244817	−	0.00597121i
$971$	−2.48908			−0.0798783			−0.0399391	−	0.999202i	$-0.512716\pi$
$971$	−2.48908			−0.0798783			−0.0399391	+	0.999202i	$0.512716\pi$
$972$		0			0
$973$	−1.70370			−0.0546181
$974$	−43.8401	−	1.06928i	−1.40473	−	0.0342620i
$975$		0			0
$976$	−11.1470	−	24.5606i	−0.356806	−	0.786166i
$977$	26.3274	+	15.2002i	0.842289	+	0.486296i	0.858042	−	0.513580i	$-0.171681\pi$
$977$	26.3274	+	15.2002i	0.842289	+	0.486296i	−0.0157525	+	0.999876i	$0.505014\pi$
$978$		0			0
$979$	33.3192	−	19.2369i	1.06489	−	0.614813i
$980$	−1.94805	+	1.00140i	−0.0622282	+	0.0319887i
$981$		0			0
$982$	−25.2496	−	15.4107i	−0.805746	−	0.491775i
$983$	−17.2234	−	29.8319i	−0.549342	−	0.951489i	−0.998320	−	0.0579459i	$-0.981545\pi$
$983$	−17.2234	−	29.8319i	−0.549342	−	0.951489i	0.448977	−	0.893543i	$-0.351788\pi$
$984$		0			0
$985$	−10.6249	+	18.4028i	−0.338536	+	0.586362i
$986$	20.3947	−	11.1208i	0.649499	−	0.354159i
$987$		0			0
$988$	−14.7123	−	9.47941i	−0.468061	−	0.301580i
$989$		−	25.0133i		−	0.795378i
$990$		0			0
$991$		−	18.6311i		−	0.591837i	−0.955213	−	0.295918i	$-0.904374\pi$
$991$		−	18.6311i		−	0.591837i	0.955213	−	0.295918i	$-0.0956256\pi$
$992$	22.4541	−	29.8128i	0.712919	−	0.946558i
$993$		0			0
$994$	5.29870	+	9.71738i	0.168065	+	0.308217i
$995$	9.35315	−	16.2001i	0.296515	−	0.513579i
$996$		0			0
$997$	27.5985	+	47.8020i	0.874052	+	1.51390i	0.857769	+	0.514036i	$0.171850\pi$
$997$	27.5985	+	47.8020i	0.874052	+	1.51390i	0.0162835	+	0.999867i	$0.494817\pi$
$998$	−13.9512	+	22.8582i	−0.441617	+	0.723565i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.71.19		72
3.2	odd	2		252.2.ba.a.239.18	yes	72
4.3	odd	2	inner	756.2.ba.a.71.7		72
9.2	odd	6	inner	756.2.ba.a.575.7		72
9.7	even	3		252.2.ba.a.155.30	yes	72
12.11	even	2		252.2.ba.a.239.30	yes	72
36.7	odd	6		252.2.ba.a.155.18	✓	72
36.11	even	6	inner	756.2.ba.a.575.19		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.18	✓	72	36.7	odd	6
252.2.ba.a.155.30	yes	72	9.7	even	3
252.2.ba.a.239.18	yes	72	3.2	odd	2
252.2.ba.a.239.30	yes	72	12.11	even	2
756.2.ba.a.71.7		72	4.3	odd	2	inner
756.2.ba.a.71.19		72	1.1	even	1	trivial
756.2.ba.a.575.7		72	9.2	odd	6	inner
756.2.ba.a.575.19		72	36.11	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0344832 + 1.41379i) q^{2} +(-1.99762 - 0.0975041i) q^{4} +(0.948457 + 0.547592i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(0.206735 - 2.82086i) q^{8} +O(q^{10})\)	\(q+(-0.0344832 + 1.41379i) q^{2} +(-1.99762 - 0.0975041i) q^{4} +(0.948457 + 0.547592i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(0.206735 - 2.82086i) q^{8} +(-0.806888 + 1.32204i) q^{10} +(1.84953 + 3.20347i) q^{11} +(0.713436 - 1.23571i) q^{13} +(-0.677033 - 1.24162i) q^{14} +(3.98099 + 0.389553i) q^{16} +2.54456i q^{17} +6.13291i q^{19} +(-1.84127 - 1.18636i) q^{20} +(-4.59282 + 2.50438i) q^{22} +(-2.50677 + 4.34185i) q^{23} +(-1.90029 - 3.29139i) q^{25} +(1.72243 + 1.05126i) q^{26} +(1.77874 - 0.914370i) q^{28} +(-5.59043 + 3.22763i) q^{29} +(-5.71386 - 3.29890i) q^{31} +(-0.688024 + 5.61486i) q^{32} +(-3.59748 - 0.0877445i) q^{34} -1.09518 q^{35} +8.53349 q^{37} +(-8.67066 - 0.211482i) q^{38} +(1.74076 - 2.56226i) q^{40} +(5.23022 + 3.01967i) q^{41} +(-4.32074 + 2.49458i) q^{43} +(-3.38230 - 6.57966i) q^{44} +(-6.05204 - 3.69378i) q^{46} +(1.55938 + 2.70093i) q^{47} +(0.500000 - 0.866025i) q^{49} +(4.71887 - 2.57311i) q^{50} +(-1.54566 + 2.39891i) q^{52} +0.388379i q^{53} +4.05114i q^{55} +(1.23139 + 2.54631i) q^{56} +(-4.37043 - 8.01500i) q^{58} +(-5.77576 + 10.0039i) q^{59} +(-3.37148 - 5.83957i) q^{61} +(4.86100 - 7.96447i) q^{62} +(-7.91452 - 1.16634i) q^{64} +(1.35333 - 0.781344i) q^{65} +(11.5692 + 6.67947i) q^{67} +(0.248105 - 5.08307i) q^{68} +(0.0377654 - 1.54836i) q^{70} -7.82636 q^{71} -5.60423 q^{73} +(-0.294262 + 12.0646i) q^{74} +(0.597984 - 12.2512i) q^{76} +(-3.20347 - 1.84953i) q^{77} +(6.35916 - 3.67146i) q^{79} +(3.56248 + 2.54943i) q^{80} +(-4.44954 + 7.29032i) q^{82} +(-5.88918 - 10.2004i) q^{83} +(-1.39338 + 2.41341i) q^{85} +(-3.37783 - 6.19465i) q^{86} +(9.41891 - 4.55499i) q^{88} -10.4010i q^{89} +1.42687i q^{91} +(5.43093 - 8.42896i) q^{92} +(-3.87232 + 2.11151i) q^{94} +(-3.35833 + 5.81680i) q^{95} +(2.46220 + 4.26466i) q^{97} +(1.20714 + 0.736760i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Introduction

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