LMFDB - Embedded newform 990.2.m.d.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(307,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("990.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.m (of order $4$, degree $2$, 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	990.307
Dual form			990.2.m.d.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-2.12132 + 2.12132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 + 2.00000i) q^{10} +(1.41421 - 3.00000i) q^{11} +(-3.00000 - 3.00000i) q^{13} -3.00000i q^{14} -1.00000 q^{16} +(-5.12132 + 5.12132i) q^{17} +3.00000 q^{19} +(-2.12132 - 0.707107i) q^{20} +(1.12132 + 3.12132i) q^{22} +(0.171573 - 0.171573i) q^{23} +(-4.00000 - 3.00000i) q^{25} +4.24264 q^{26} +(2.12132 + 2.12132i) q^{28} -1.24264 q^{29} -7.24264 q^{31} +(0.707107 - 0.707107i) q^{32} -7.24264i q^{34} +(3.00000 + 6.00000i) q^{35} +(0.121320 + 0.121320i) q^{37} +(-2.12132 + 2.12132i) q^{38} +(2.00000 - 1.00000i) q^{40} -1.75736i q^{41} +(-1.24264 - 1.24264i) q^{43} +(-3.00000 - 1.41421i) q^{44} +0.242641i q^{46} +(-4.41421 - 4.41421i) q^{47} -2.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-3.00000 + 3.00000i) q^{52} +(-9.53553 + 9.53553i) q^{53} +(-5.36396 - 5.12132i) q^{55} -3.00000 q^{56} +(0.878680 - 0.878680i) q^{58} -1.41421i q^{59} +7.24264i q^{61} +(5.12132 - 5.12132i) q^{62} +1.00000i q^{64} +(-8.48528 + 4.24264i) q^{65} +(-4.00000 - 4.00000i) q^{67} +(5.12132 + 5.12132i) q^{68} +(-6.36396 - 2.12132i) q^{70} +1.24264 q^{71} +(-6.00000 - 6.00000i) q^{73} -0.171573 q^{74} -3.00000i q^{76} +(3.36396 + 9.36396i) q^{77} -10.2426 q^{79} +(-0.707107 + 2.12132i) q^{80} +(1.24264 + 1.24264i) q^{82} +(-7.24264 - 7.24264i) q^{83} +(7.24264 + 14.4853i) q^{85} +1.75736 q^{86} +(3.12132 - 1.12132i) q^{88} -5.48528i q^{89} +12.7279 q^{91} +(-0.171573 - 0.171573i) q^{92} +6.24264 q^{94} +(2.12132 - 6.36396i) q^{95} +(-2.24264 - 2.24264i) q^{97} +(1.41421 + 1.41421i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{10} - 12 q^{13} - 4 q^{16} - 12 q^{17} + 12 q^{19} - 4 q^{22} + 12 q^{23} - 16 q^{25} + 12 q^{29} - 12 q^{31} + 12 q^{35} - 8 q^{37} + 8 q^{40} + 12 q^{43} - 12 q^{44} - 12 q^{47} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) $ 4 * q + 4 * q^10 - 12 * q^13 - 4 * q^16 - 12 * q^17 + 12 * q^19 - 4 * q^22 + 12 * q^23 - 16 * q^25 + 12 * q^29 - 12 * q^31 + 12 * q^35 - 8 * q^37 + 8 * q^40 + 12 * q^43 - 12 * q^44 - 12 * q^47 - 12 * q^52 - 24 * q^53 + 4 * q^55 - 12 * q^56 + 12 * q^58 + 12 * q^62 - 16 * q^67 + 12 * q^68 - 12 * q^71 - 24 * q^73 - 12 * q^74 - 12 * q^77 - 24 * q^79 - 12 * q^82 - 12 * q^83 + 12 * q^85 + 24 * q^86 + 4 * q^88 - 12 * q^92 + 8 * q^94 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$6$		0			0
$7$	−2.12132	+	2.12132i	−0.801784	+	0.801784i	−0.983374	−	0.181591i	$-0.941875\pi$
$7$	−2.12132	+	2.12132i	−0.801784	+	0.801784i	0.181591	+	0.983374i	$0.441875\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$	1.41421	−	3.00000i	0.426401	−	0.904534i
$11$	1.41421	−	3.00000i	0.426401	−	0.904534i
$12$		0			0
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	0.155747	−	0.987797i	$-0.450222\pi$
$13$	−3.00000	−	3.00000i	−0.832050	−	0.832050i	−0.987797	+	0.155747i	$0.950222\pi$
$14$		−	3.00000i		−	0.801784i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−5.12132	+	5.12132i	−1.24210	+	1.24210i	−0.282975	+	0.959127i	$0.591322\pi$
$17$	−5.12132	+	5.12132i	−1.24210	+	1.24210i	−0.959127	+	0.282975i	$0.908678\pi$
$18$		0			0
$19$	3.00000			0.688247			0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000			0.688247			0.344124	+	0.938924i	$0.388176\pi$
$20$	−2.12132	−	0.707107i	−0.474342	−	0.158114i
$21$		0			0
$22$	1.12132	+	3.12132i	0.239066	+	0.665468i
$23$	0.171573	−	0.171573i	0.0357754	−	0.0357754i	−0.688993	−	0.724768i	$-0.741947\pi$
$23$	0.171573	−	0.171573i	0.0357754	−	0.0357754i	0.724768	+	0.688993i	$0.241947\pi$
$24$		0			0
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$	4.24264			0.832050
$27$		0			0
$28$	2.12132	+	2.12132i	0.400892	+	0.400892i
$29$	−1.24264			−0.230753			−0.115376	−	0.993322i	$-0.536807\pi$
$29$	−1.24264			−0.230753			−0.115376	+	0.993322i	$0.536807\pi$
$30$		0			0
$31$	−7.24264			−1.30082			−0.650408	−	0.759585i	$-0.725402\pi$
$31$	−7.24264			−1.30082			−0.650408	+	0.759585i	$0.725402\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	7.24264i		−	1.24210i
$35$	3.00000	+	6.00000i	0.507093	+	1.01419i
$36$		0			0
$37$	0.121320	+	0.121320i	0.0199449	+	0.0199449i	0.717009	−	0.697064i	$-0.245511\pi$
$37$	0.121320	+	0.121320i	0.0199449	+	0.0199449i	−0.697064	+	0.717009i	$0.745511\pi$
$38$	−2.12132	+	2.12132i	−0.344124	+	0.344124i
$39$		0			0
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$		−	1.75736i		−	0.274453i	−0.990540	−	0.137227i	$-0.956181\pi$
$41$		−	1.75736i		−	0.274453i	0.990540	−	0.137227i	$-0.0438189\pi$
$42$		0			0
$43$	−1.24264	−	1.24264i	−0.189501	−	0.189501i	0.605979	−	0.795480i	$-0.292781\pi$
$43$	−1.24264	−	1.24264i	−0.189501	−	0.189501i	−0.795480	+	0.605979i	$0.792781\pi$
$44$	−3.00000	−	1.41421i	−0.452267	−	0.213201i
$45$		0			0
$46$			0.242641i			0.0357754i
$47$	−4.41421	−	4.41421i	−0.643879	−	0.643879i	0.307628	−	0.951507i	$-0.400465\pi$
$47$	−4.41421	−	4.41421i	−0.643879	−	0.643879i	−0.951507	+	0.307628i	$0.900465\pi$
$48$		0			0
$49$		−	2.00000i		−	0.285714i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$		0			0
$52$	−3.00000	+	3.00000i	−0.416025	+	0.416025i
$53$	−9.53553	+	9.53553i	−1.30981	+	1.30981i	−0.388254	+	0.921552i	$0.626922\pi$
$53$	−9.53553	+	9.53553i	−1.30981	+	1.30981i	−0.921552	+	0.388254i	$0.873078\pi$
$54$		0			0
$55$	−5.36396	−	5.12132i	−0.723276	−	0.690559i
$56$	−3.00000			−0.400892
$57$		0			0
$58$	0.878680	−	0.878680i	0.115376	−	0.115376i
$59$		−	1.41421i		−	0.184115i	−0.995754	−	0.0920575i	$-0.970656\pi$
$59$		−	1.41421i		−	0.184115i	0.995754	−	0.0920575i	$-0.0293443\pi$
$60$		0			0
$61$			7.24264i			0.927325i	0.886012	+	0.463663i	$0.153465\pi$
$61$			7.24264i			0.927325i	−0.886012	+	0.463663i	$0.846535\pi$
$62$	5.12132	−	5.12132i	0.650408	−	0.650408i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−8.48528	+	4.24264i	−1.05247	+	0.526235i
$66$		0			0
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	0.419211	−	0.907889i	$-0.362307\pi$
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	−0.907889	+	0.419211i	$0.862307\pi$
$68$	5.12132	+	5.12132i	0.621051	+	0.621051i
$69$		0			0
$70$	−6.36396	−	2.12132i	−0.760639	−	0.253546i
$71$	1.24264			0.147474			0.0737372	−	0.997278i	$-0.476507\pi$
$71$	1.24264			0.147474			0.0737372	+	0.997278i	$0.476507\pi$
$72$		0			0
$73$	−6.00000	−	6.00000i	−0.702247	−	0.702247i	0.262646	−	0.964892i	$-0.415405\pi$
$73$	−6.00000	−	6.00000i	−0.702247	−	0.702247i	−0.964892	+	0.262646i	$0.915405\pi$
$74$	−0.171573			−0.0199449
$75$		0			0
$76$		−	3.00000i		−	0.344124i
$77$	3.36396	+	9.36396i	0.383359	+	1.06712i
$78$		0			0
$79$	−10.2426			−1.15239			−0.576194	−	0.817313i	$-0.695463\pi$
$79$	−10.2426			−1.15239			−0.576194	+	0.817313i	$0.695463\pi$
$80$	−0.707107	+	2.12132i	−0.0790569	+	0.237171i
$81$		0			0
$82$	1.24264	+	1.24264i	0.137227	+	0.137227i
$83$	−7.24264	−	7.24264i	−0.794983	−	0.794983i	0.187317	−	0.982300i	$-0.440021\pi$
$83$	−7.24264	−	7.24264i	−0.794983	−	0.794983i	−0.982300	+	0.187317i	$0.940021\pi$
$84$		0			0
$85$	7.24264	+	14.4853i	0.785575	+	1.57115i
$86$	1.75736			0.189501
$87$		0			0
$88$	3.12132	−	1.12132i	0.332734	−	0.119533i
$89$		−	5.48528i		−	0.581439i	−0.956808	−	0.290719i	$-0.906105\pi$
$89$		−	5.48528i		−	0.581439i	0.956808	−	0.290719i	$-0.0938946\pi$
$90$		0			0
$91$	12.7279			1.33425
$92$	−0.171573	−	0.171573i	−0.0178877	−	0.0178877i
$93$		0			0
$94$	6.24264			0.643879
$95$	2.12132	−	6.36396i	0.217643	−	0.652929i
$96$		0			0
$97$	−2.24264	−	2.24264i	−0.227706	−	0.227706i	0.584028	−	0.811734i	$-0.301476\pi$
$97$	−2.24264	−	2.24264i	−0.227706	−	0.227706i	−0.811734	+	0.584028i	$0.801476\pi$
$98$	1.41421	+	1.41421i	0.142857	+	0.142857i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$		−	2.48528i		−	0.247295i	−0.992326	−	0.123647i	$-0.960541\pi$
$101$		−	2.48528i		−	0.247295i	0.992326	−	0.123647i	$-0.0394592\pi$
$102$		0			0
$103$	6.24264	−	6.24264i	0.615106	−	0.615106i	−0.329166	−	0.944272i	$-0.606768\pi$
$103$	6.24264	−	6.24264i	0.615106	−	0.615106i	0.944272	+	0.329166i	$0.106768\pi$
$104$		−	4.24264i		−	0.416025i
$105$		0			0
$106$		−	13.4853i		−	1.30981i
$107$	10.2426	−	10.2426i	0.990193	−	0.990193i	−0.00975893	−	0.999952i	$-0.503106\pi$
$107$	10.2426	−	10.2426i	0.990193	−	0.990193i	0.999952	+	0.00975893i	$0.00310641\pi$
$108$		0			0
$109$	−2.48528			−0.238047			−0.119023	−	0.992891i	$-0.537976\pi$
$109$	−2.48528			−0.238047			−0.119023	+	0.992891i	$0.537976\pi$
$110$	7.41421	−	0.171573i	0.706918	−	0.0163588i
$111$		0			0
$112$	2.12132	−	2.12132i	0.200446	−	0.200446i
$113$	4.41421	−	4.41421i	0.415254	−	0.415254i	−0.468310	−	0.883564i	$-0.655137\pi$
$113$	4.41421	−	4.41421i	0.415254	−	0.415254i	0.883564	+	0.468310i	$0.155137\pi$
$114$		0			0
$115$	−0.242641	−	0.485281i	−0.0226264	−	0.0452527i
$116$			1.24264i			0.115376i
$117$		0			0
$118$	1.00000	+	1.00000i	0.0920575	+	0.0920575i
$119$		−	21.7279i		−	1.99180i
$120$		0			0
$121$	−7.00000	−	8.48528i	−0.636364	−	0.771389i
$122$	−5.12132	−	5.12132i	−0.463663	−	0.463663i
$123$		0			0
$124$			7.24264i			0.650408i
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$		0			0
$127$	4.24264	−	4.24264i	0.376473	−	0.376473i	−0.493355	−	0.869828i	$-0.664230\pi$
$127$	4.24264	−	4.24264i	0.376473	−	0.376473i	0.869828	+	0.493355i	$0.164230\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	3.00000	−	9.00000i	0.263117	−	0.789352i
$131$		−	13.9706i		−	1.22061i	−0.792165	−	0.610307i	$-0.791046\pi$
$131$		−	13.9706i		−	1.22061i	0.792165	−	0.610307i	$-0.208954\pi$
$132$		0			0
$133$	−6.36396	+	6.36396i	−0.551825	+	0.551825i
$134$	5.65685			0.488678
$135$		0			0
$136$	−7.24264			−0.621051
$137$	11.6569	+	11.6569i	0.995912	+	0.995912i	0.999992	−	0.00407941i	$-0.00129852\pi$
$137$	11.6569	+	11.6569i	0.995912	+	0.995912i	−0.00407941	+	0.999992i	$0.501299\pi$
$138$		0			0
$139$	14.4853			1.22863			0.614313	−	0.789063i	$-0.289433\pi$
$139$	14.4853			1.22863			0.614313	+	0.789063i	$0.289433\pi$
$140$	6.00000	−	3.00000i	0.507093	−	0.253546i
$141$		0			0
$142$	−0.878680	+	0.878680i	−0.0737372	+	0.0737372i
$143$	−13.2426	+	4.75736i	−1.10741	+	0.397830i
$144$		0			0
$145$	−0.878680	+	2.63604i	−0.0729704	+	0.218911i
$146$	8.48528			0.702247
$147$		0			0
$148$	0.121320	−	0.121320i	0.00997247	−	0.00997247i
$149$	−19.2426			−1.57642			−0.788209	−	0.615407i	$-0.788992\pi$
$149$	−19.2426			−1.57642			−0.788209	+	0.615407i	$0.788992\pi$
$150$		0			0
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$	2.12132	+	2.12132i	0.172062	+	0.172062i
$153$		0			0
$154$	−9.00000	−	4.24264i	−0.725241	−	0.341882i
$155$	−5.12132	+	15.3640i	−0.411354	+	1.23406i
$156$		0			0
$157$	16.3640	+	16.3640i	1.30599	+	1.30599i	0.924286	+	0.381700i	$0.124661\pi$
$157$	16.3640	+	16.3640i	1.30599	+	1.30599i	0.381700	+	0.924286i	$0.375339\pi$
$158$	7.24264	−	7.24264i	0.576194	−	0.576194i
$159$		0			0
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$			0.727922i			0.0573683i
$162$		0			0
$163$	−13.8492	+	13.8492i	−1.08476	+	1.08476i	−0.0886978	+	0.996059i	$0.528271\pi$
$163$	−13.8492	+	13.8492i	−1.08476	+	1.08476i	−0.996059	+	0.0886978i	$0.971729\pi$
$164$	−1.75736			−0.137227
$165$		0			0
$166$	10.2426			0.794983
$167$	−6.36396	+	6.36396i	−0.492458	+	0.492458i	−0.909080	−	0.416622i	$-0.863214\pi$
$167$	−6.36396	+	6.36396i	−0.492458	+	0.492458i	0.416622	+	0.909080i	$0.363214\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	−15.3640	−	5.12132i	−1.17836	−	0.392787i
$171$		0			0
$172$	−1.24264	+	1.24264i	−0.0947505	+	0.0947505i
$173$	16.2426	+	16.2426i	1.23491	+	1.23491i	0.962057	+	0.272848i	$0.0879656\pi$
$173$	16.2426	+	16.2426i	1.23491	+	1.23491i	0.272848	+	0.962057i	$0.412034\pi$
$174$		0			0
$175$	14.8492	−	2.12132i	1.12250	−	0.160357i
$176$	−1.41421	+	3.00000i	−0.106600	+	0.226134i
$177$		0			0
$178$	3.87868	+	3.87868i	0.290719	+	0.290719i
$179$			13.7574i			1.02827i	0.857708	+	0.514137i	$0.171888\pi$
$179$			13.7574i			1.02827i	−0.857708	+	0.514137i	$0.828112\pi$
$180$		0			0
$181$	12.0000			0.891953			0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000			0.891953			0.445976	+	0.895045i	$0.352856\pi$
$182$	−9.00000	+	9.00000i	−0.667124	+	0.667124i
$183$		0			0
$184$	0.242641			0.0178877
$185$	0.343146	−	0.171573i	0.0252286	−	0.0126143i
$186$		0			0
$187$	8.12132	+	22.6066i	0.593890	+	1.65316i
$188$	−4.41421	+	4.41421i	−0.321940	+	0.321940i
$189$		0			0
$190$	3.00000	+	6.00000i	0.217643	+	0.435286i
$191$	−2.82843			−0.204658			−0.102329	−	0.994751i	$-0.532629\pi$
$191$	−2.82843			−0.204658			−0.102329	+	0.994751i	$0.532629\pi$
$192$		0			0
$193$	−0.878680	−	0.878680i	−0.0632487	−	0.0632487i	0.674775	−	0.738024i	$-0.264241\pi$
$193$	−0.878680	−	0.878680i	−0.0632487	−	0.0632487i	−0.738024	+	0.674775i	$0.764241\pi$
$194$	3.17157			0.227706
$195$		0			0
$196$	−2.00000			−0.142857
$197$	−1.24264	+	1.24264i	−0.0885345	+	0.0885345i	−0.749987	−	0.661453i	$-0.769940\pi$
$197$	−1.24264	+	1.24264i	−0.0885345	+	0.0885345i	0.661453	+	0.749987i	$0.269940\pi$
$198$		0			0
$199$			4.75736i			0.337240i	0.985681	+	0.168620i	$0.0539311\pi$
$199$			4.75736i			0.337240i	−0.985681	+	0.168620i	$0.946069\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$		0			0
$202$	1.75736	+	1.75736i	0.123647	+	0.123647i
$203$	2.63604	−	2.63604i	0.185014	−	0.185014i
$204$		0			0
$205$	−3.72792	−	1.24264i	−0.260369	−	0.0867898i
$206$			8.82843i			0.615106i
$207$		0			0
$208$	3.00000	+	3.00000i	0.208013	+	0.208013i
$209$	4.24264	−	9.00000i	0.293470	−	0.622543i
$210$		0			0
$211$			17.4853i			1.20374i	0.798595	+	0.601868i	$0.205577\pi$
$211$			17.4853i			1.20374i	−0.798595	+	0.601868i	$0.794423\pi$
$212$	9.53553	+	9.53553i	0.654903	+	0.654903i
$213$		0			0
$214$			14.4853i			0.990193i
$215$	−3.51472	+	1.75736i	−0.239702	+	0.119851i
$216$		0			0
$217$	15.3640	−	15.3640i	1.04297	−	1.04297i
$218$	1.75736	−	1.75736i	0.119023	−	0.119023i
$219$		0			0
$220$	−5.12132	+	5.36396i	−0.345279	+	0.361638i
$221$	30.7279			2.06698
$222$		0			0
$223$	−3.75736	+	3.75736i	−0.251611	+	0.251611i	−0.821631	−	0.570020i	$-0.806936\pi$
$223$	−3.75736	+	3.75736i	−0.251611	+	0.251611i	0.570020	+	0.821631i	$0.306936\pi$
$224$			3.00000i			0.200446i
$225$		0			0
$226$			6.24264i			0.415254i
$227$	15.0000	−	15.0000i	0.995585	−	0.995585i	−0.00440533	−	0.999990i	$-0.501402\pi$
$227$	15.0000	−	15.0000i	0.995585	−	0.995585i	0.999990	+	0.00440533i	$0.00140226\pi$
$228$		0			0
$229$		−	15.2132i		−	1.00532i	−0.864485	−	0.502658i	$-0.832355\pi$
$229$		−	15.2132i		−	1.00532i	0.864485	−	0.502658i	$-0.167645\pi$
$230$	0.514719	+	0.171573i	0.0339395	+	0.0113132i
$231$		0			0
$232$	−0.878680	−	0.878680i	−0.0576881	−	0.0576881i
$233$	1.60660	+	1.60660i	0.105252	+	0.105252i	0.757772	−	0.652520i	$-0.226288\pi$
$233$	1.60660	+	1.60660i	0.105252	+	0.105252i	−0.652520	+	0.757772i	$0.726288\pi$
$234$		0			0
$235$	−12.4853	+	6.24264i	−0.814450	+	0.407225i
$236$	−1.41421			−0.0920575
$237$		0			0
$238$	15.3640	+	15.3640i	0.995898	+	0.995898i
$239$	−0.727922			−0.0470854			−0.0235427	−	0.999723i	$-0.507495\pi$
$239$	−0.727922			−0.0470854			−0.0235427	+	0.999723i	$0.507495\pi$
$240$		0			0
$241$			6.72792i			0.433384i	0.976240	+	0.216692i	$0.0695267\pi$
$241$			6.72792i			0.433384i	−0.976240	+	0.216692i	$0.930473\pi$
$242$	10.9497	+	1.05025i	0.703876	+	0.0675128i
$243$		0			0
$244$	7.24264			0.463663
$245$	−4.24264	−	1.41421i	−0.271052	−	0.0903508i
$246$		0			0
$247$	−9.00000	−	9.00000i	−0.572656	−	0.572656i
$248$	−5.12132	−	5.12132i	−0.325204	−	0.325204i
$249$		0			0
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$	−3.51472			−0.221847			−0.110924	−	0.993829i	$-0.535381\pi$
$251$	−3.51472			−0.221847			−0.110924	+	0.993829i	$0.535381\pi$
$252$		0			0
$253$	−0.272078	−	0.757359i	−0.0171054	−	0.0476148i
$254$			6.00000i			0.376473i
$255$		0			0
$256$	1.00000			0.0625000
$257$	1.92893	+	1.92893i	0.120323	+	0.120323i	0.764705	−	0.644381i	$-0.222885\pi$
$257$	1.92893	+	1.92893i	0.120323	+	0.120323i	−0.644381	+	0.764705i	$0.722885\pi$
$258$		0			0
$259$	−0.514719			−0.0319831
$260$	4.24264	+	8.48528i	0.263117	+	0.526235i
$261$		0			0
$262$	9.87868	+	9.87868i	0.610307	+	0.610307i
$263$	6.36396	+	6.36396i	0.392419	+	0.392419i	0.875549	−	0.483130i	$-0.160500\pi$
$263$	6.36396	+	6.36396i	0.392419	+	0.392419i	−0.483130	+	0.875549i	$0.660500\pi$
$264$		0			0
$265$	13.4853	+	26.9706i	0.828394	+	1.65679i
$266$		−	9.00000i		−	0.551825i
$267$		0			0
$268$	−4.00000	+	4.00000i	−0.244339	+	0.244339i
$269$		−	19.7990i		−	1.20717i	−0.797300	−	0.603583i	$-0.793739\pi$
$269$		−	19.7990i		−	1.20717i	0.797300	−	0.603583i	$-0.206261\pi$
$270$		0			0
$271$		−	6.72792i		−	0.408692i	−0.978899	−	0.204346i	$-0.934493\pi$
$271$		−	6.72792i		−	0.408692i	0.978899	−	0.204346i	$-0.0655068\pi$
$272$	5.12132	−	5.12132i	0.310526	−	0.310526i
$273$		0			0
$274$	−16.4853			−0.995912
$275$	−14.6569	+	7.75736i	−0.883842	+	0.467786i
$276$		0			0
$277$	−10.2426	+	10.2426i	−0.615421	+	0.615421i	−0.944353	−	0.328933i	$-0.893311\pi$
$277$	−10.2426	+	10.2426i	−0.615421	+	0.615421i	0.328933	+	0.944353i	$0.393311\pi$
$278$	−10.2426	+	10.2426i	−0.614313	+	0.614313i
$279$		0			0
$280$	−2.12132	+	6.36396i	−0.126773	+	0.380319i
$281$			22.9706i			1.37031i	0.728398	+	0.685154i	$0.240265\pi$
$281$			22.9706i			1.37031i	−0.728398	+	0.685154i	$0.759735\pi$
$282$		0			0
$283$	−13.2426	−	13.2426i	−0.787193	−	0.787193i	0.193840	−	0.981033i	$-0.437906\pi$
$283$	−13.2426	−	13.2426i	−0.787193	−	0.787193i	−0.981033	+	0.193840i	$0.937906\pi$
$284$		−	1.24264i		−	0.0737372i
$285$		0			0
$286$	6.00000	−	12.7279i	0.354787	−	0.752618i
$287$	3.72792	+	3.72792i	0.220052	+	0.220052i
$288$		0			0
$289$		−	35.4558i		−	2.08564i
$290$	−1.24264	−	2.48528i	−0.0729704	−	0.145941i
$291$		0			0
$292$	−6.00000	+	6.00000i	−0.351123	+	0.351123i
$293$	−15.7279	−	15.7279i	−0.918835	−	0.918835i	0.0781097	−	0.996945i	$-0.475112\pi$
$293$	−15.7279	−	15.7279i	−0.918835	−	0.918835i	−0.996945	+	0.0781097i	$0.975112\pi$
$294$		0			0
$295$	−3.00000	−	1.00000i	−0.174667	−	0.0582223i
$296$			0.171573i			0.00997247i
$297$		0			0
$298$	13.6066	−	13.6066i	0.788209	−	0.788209i
$299$	−1.02944			−0.0595339
$300$		0			0
$301$	5.27208			0.303878
$302$	8.48528	+	8.48528i	0.488273	+	0.488273i
$303$		0			0
$304$	−3.00000			−0.172062
$305$	15.3640	+	5.12132i	0.879738	+	0.293246i
$306$		0			0
$307$	11.4853	−	11.4853i	0.655500	−	0.655500i	−0.298812	−	0.954312i	$-0.596590\pi$
$307$	11.4853	−	11.4853i	0.655500	−	0.655500i	0.954312	+	0.298812i	$0.0965904\pi$
$308$	9.36396	−	3.36396i	0.533561	−	0.191679i
$309$		0			0
$310$	−7.24264	−	14.4853i	−0.411354	−	0.822709i
$311$	9.72792			0.551620			0.275810	−	0.961212i	$-0.411054\pi$
$311$	9.72792			0.551620			0.275810	+	0.961212i	$0.411054\pi$
$312$		0			0
$313$	3.75736	−	3.75736i	0.212379	−	0.212379i	−0.592899	−	0.805277i	$-0.702017\pi$
$313$	3.75736	−	3.75736i	0.212379	−	0.212379i	0.805277	+	0.592899i	$0.202017\pi$
$314$	−23.1421			−1.30599
$315$		0			0
$316$			10.2426i			0.576194i
$317$	9.53553	+	9.53553i	0.535569	+	0.535569i	0.922224	−	0.386655i	$-0.126370\pi$
$317$	9.53553	+	9.53553i	0.535569	+	0.535569i	−0.386655	+	0.922224i	$0.626370\pi$
$318$		0			0
$319$	−1.75736	+	3.72792i	−0.0983932	+	0.208724i
$320$	2.12132	+	0.707107i	0.118585	+	0.0395285i
$321$		0			0
$322$	−0.514719	−	0.514719i	−0.0286841	−	0.0286841i
$323$	−15.3640	+	15.3640i	−0.854874	+	0.854874i
$324$		0			0
$325$	3.00000	+	21.0000i	0.166410	+	1.16487i
$326$		−	19.5858i		−	1.08476i
$327$		0			0
$328$	1.24264	−	1.24264i	0.0686134	−	0.0686134i
$329$	18.7279			1.03250
$330$		0			0
$331$	24.7279			1.35917			0.679585	−	0.733597i	$-0.262160\pi$
$331$	24.7279			1.35917			0.679585	+	0.733597i	$0.262160\pi$
$332$	−7.24264	+	7.24264i	−0.397492	+	0.397492i
$333$		0			0
$334$		−	9.00000i		−	0.492458i
$335$	−11.3137	+	5.65685i	−0.618134	+	0.309067i
$336$		0			0
$337$	12.8787	−	12.8787i	0.701546	−	0.701546i	−0.263196	−	0.964742i	$-0.584777\pi$
$337$	12.8787	−	12.8787i	0.701546	−	0.701546i	0.964742	+	0.263196i	$0.0847766\pi$
$338$	−3.53553	−	3.53553i	−0.192308	−	0.192308i
$339$		0			0
$340$	14.4853	−	7.24264i	0.785575	−	0.392787i
$341$	−10.2426	+	21.7279i	−0.554670	+	1.17663i
$342$		0			0
$343$	−10.6066	−	10.6066i	−0.572703	−	0.572703i
$344$		−	1.75736i		−	0.0947505i
$345$		0			0
$346$	−22.9706			−1.23491
$347$	6.72792	−	6.72792i	0.361174	−	0.361174i	−0.503071	−	0.864245i	$-0.667797\pi$
$347$	6.72792	−	6.72792i	0.361174	−	0.361174i	0.864245	+	0.503071i	$0.167797\pi$
$348$		0			0
$349$	−10.9706			−0.587241			−0.293620	−	0.955922i	$-0.594860\pi$
$349$	−10.9706			−0.587241			−0.293620	+	0.955922i	$0.594860\pi$
$350$	−9.00000	+	12.0000i	−0.481070	+	0.641427i
$351$		0			0
$352$	−1.12132	−	3.12132i	−0.0597666	−	0.166367i
$353$	14.8284	−	14.8284i	0.789238	−	0.789238i	−0.192132	−	0.981369i	$-0.561540\pi$
$353$	14.8284	−	14.8284i	0.789238	−	0.789238i	0.981369	+	0.192132i	$0.0615401\pi$
$354$		0			0
$355$	0.878680	−	2.63604i	0.0466355	−	0.139906i
$356$	−5.48528			−0.290719
$357$		0			0
$358$	−9.72792	−	9.72792i	−0.514137	−	0.514137i
$359$	34.9706			1.84568			0.922838	−	0.385189i	$-0.125864\pi$
$359$	34.9706			1.84568			0.922838	+	0.385189i	$0.125864\pi$
$360$		0			0
$361$	−10.0000			−0.526316
$362$	−8.48528	+	8.48528i	−0.445976	+	0.445976i
$363$		0			0
$364$		−	12.7279i		−	0.667124i
$365$	−16.9706	+	8.48528i	−0.888280	+	0.444140i
$366$		0			0
$367$	−2.00000	−	2.00000i	−0.104399	−	0.104399i	0.652978	−	0.757377i	$-0.273519\pi$
$367$	−2.00000	−	2.00000i	−0.104399	−	0.104399i	−0.757377	+	0.652978i	$0.773519\pi$
$368$	−0.171573	+	0.171573i	−0.00894385	+	0.00894385i
$369$		0			0
$370$	−0.121320	+	0.363961i	−0.00630714	+	0.0189214i
$371$		−	40.4558i		−	2.10036i
$372$		0			0
$373$	1.24264	+	1.24264i	0.0643415	+	0.0643415i	0.738545	−	0.674204i	$-0.235513\pi$
$373$	1.24264	+	1.24264i	0.0643415	+	0.0643415i	−0.674204	+	0.738545i	$0.735513\pi$
$374$	−21.7279	−	10.2426i	−1.12352	−	0.529634i
$375$		0			0
$376$		−	6.24264i		−	0.321940i
$377$	3.72792	+	3.72792i	0.191998	+	0.191998i
$378$		0			0
$379$		−	4.97056i		−	0.255321i	−0.991818	−	0.127660i	$-0.959253\pi$
$379$		−	4.97056i		−	0.255321i	0.991818	−	0.127660i	$-0.0407467\pi$
$380$	−6.36396	−	2.12132i	−0.326464	−	0.108821i
$381$		0			0
$382$	2.00000	−	2.00000i	0.102329	−	0.102329i
$383$	1.41421	−	1.41421i	0.0722629	−	0.0722629i	−0.670052	−	0.742315i	$-0.733728\pi$
$383$	1.41421	−	1.41421i	0.0722629	−	0.0722629i	0.742315	+	0.670052i	$0.233728\pi$
$384$		0			0
$385$	22.2426	−	0.514719i	1.13359	−	0.0262325i
$386$	1.24264			0.0632487
$387$		0			0
$388$	−2.24264	+	2.24264i	−0.113853	+	0.113853i
$389$		−	2.82843i		−	0.143407i	−0.997426	−	0.0717035i	$-0.977156\pi$
$389$		−	2.82843i		−	0.143407i	0.997426	−	0.0717035i	$-0.0228435\pi$
$390$		0			0
$391$			1.75736i			0.0888735i
$392$	1.41421	−	1.41421i	0.0714286	−	0.0714286i
$393$		0			0
$394$		−	1.75736i		−	0.0885345i
$395$	−7.24264	+	21.7279i	−0.364417	+	1.09325i
$396$		0			0
$397$	−1.51472	−	1.51472i	−0.0760215	−	0.0760215i	0.668074	−	0.744095i	$-0.267119\pi$
$397$	−1.51472	−	1.51472i	−0.0760215	−	0.0760215i	−0.744095	+	0.668074i	$0.767119\pi$
$398$	−3.36396	−	3.36396i	−0.168620	−	0.168620i
$399$		0			0
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$	−2.31371			−0.115541			−0.0577705	−	0.998330i	$-0.518399\pi$
$401$	−2.31371			−0.115541			−0.0577705	+	0.998330i	$0.518399\pi$
$402$		0			0
$403$	21.7279	+	21.7279i	1.08234	+	1.08234i
$404$	−2.48528			−0.123647
$405$		0			0
$406$			3.72792i			0.185014i
$407$	0.535534	−	0.192388i	0.0265454	−	0.00953633i
$408$		0			0
$409$	22.9706			1.13582			0.567911	−	0.823090i	$-0.307752\pi$
$409$	22.9706			1.13582			0.567911	+	0.823090i	$0.307752\pi$
$410$	3.51472	−	1.75736i	0.173580	−	0.0867898i
$411$		0			0
$412$	−6.24264	−	6.24264i	−0.307553	−	0.307553i
$413$	3.00000	+	3.00000i	0.147620	+	0.147620i
$414$		0			0
$415$	−20.4853	+	10.2426i	−1.00558	+	0.502791i
$416$	−4.24264			−0.208013
$417$		0			0
$418$	3.36396	+	9.36396i	0.164537	+	0.458006i
$419$		−	6.00000i		−	0.293119i	−0.989202	−	0.146560i	$-0.953180\pi$
$419$		−	6.00000i		−	0.293119i	0.989202	−	0.146560i	$-0.0468200\pi$
$420$		0			0
$421$	−9.51472			−0.463719			−0.231860	−	0.972749i	$-0.574481\pi$
$421$	−9.51472			−0.463719			−0.231860	+	0.972749i	$0.574481\pi$
$422$	−12.3640	−	12.3640i	−0.601868	−	0.601868i
$423$		0			0
$424$	−13.4853			−0.654903
$425$	35.8492	−	5.12132i	1.73894	−	0.248421i
$426$		0			0
$427$	−15.3640	−	15.3640i	−0.743514	−	0.743514i
$428$	−10.2426	−	10.2426i	−0.495097	−	0.495097i
$429$		0			0
$430$	1.24264	−	3.72792i	0.0599255	−	0.179776i
$431$			3.51472i			0.169298i	0.996411	+	0.0846490i	$0.0269769\pi$
$431$			3.51472i			0.169298i	−0.996411	+	0.0846490i	$0.973023\pi$
$432$		0			0
$433$	−21.9706	+	21.9706i	−1.05584	+	1.05584i	−0.0574919	+	0.998346i	$0.518310\pi$
$433$	−21.9706	+	21.9706i	−1.05584	+	1.05584i	−0.998346	+	0.0574919i	$0.981690\pi$
$434$			21.7279i			1.04297i
$435$		0			0
$436$			2.48528i			0.119023i
$437$	0.514719	−	0.514719i	0.0246223	−	0.0246223i
$438$		0			0
$439$	−0.727922			−0.0347418			−0.0173709	−	0.999849i	$-0.505530\pi$
$439$	−0.727922			−0.0347418			−0.0173709	+	0.999849i	$0.505530\pi$
$440$	−0.171573	−	7.41421i	−0.00817942	−	0.353459i
$441$		0			0
$442$	−21.7279	+	21.7279i	−1.03349	+	1.03349i
$443$	19.0711	−	19.0711i	0.906094	−	0.906094i	−0.0898606	−	0.995954i	$-0.528642\pi$
$443$	19.0711	−	19.0711i	0.906094	−	0.906094i	0.995954	+	0.0898606i	$0.0286421\pi$
$444$		0			0
$445$	−11.6360	−	3.87868i	−0.551601	−	0.183867i
$446$		−	5.31371i		−	0.251611i
$447$		0			0
$448$	−2.12132	−	2.12132i	−0.100223	−	0.100223i
$449$			20.4853i			0.966760i	0.875411	+	0.483380i	$0.160591\pi$
$449$			20.4853i			0.966760i	−0.875411	+	0.483380i	$0.839409\pi$
$450$		0			0
$451$	−5.27208	−	2.48528i	−0.248252	−	0.117027i
$452$	−4.41421	−	4.41421i	−0.207627	−	0.207627i
$453$		0			0
$454$			21.2132i			0.995585i
$455$	9.00000	−	27.0000i	0.421927	−	1.26578i
$456$		0			0
$457$	−7.60660	+	7.60660i	−0.355822	+	0.355822i	−0.862270	−	0.506448i	$-0.830958\pi$
$457$	−7.60660	+	7.60660i	−0.355822	+	0.355822i	0.506448	+	0.862270i	$0.330958\pi$
$458$	10.7574	+	10.7574i	0.502658	+	0.502658i
$459$		0			0
$460$	−0.485281	+	0.242641i	−0.0226264	+	0.0113132i
$461$			1.24264i			0.0578755i	0.999581	+	0.0289378i	$0.00921247\pi$
$461$			1.24264i			0.0578755i	−0.999581	+	0.0289378i	$0.990788\pi$
$462$		0			0
$463$	−15.9706	+	15.9706i	−0.742215	+	0.742215i	−0.973004	−	0.230789i	$-0.925869\pi$
$463$	−15.9706	+	15.9706i	−0.742215	+	0.742215i	0.230789	+	0.973004i	$0.425869\pi$
$464$	1.24264			0.0576881
$465$		0			0
$466$	−2.27208			−0.105252
$467$	−16.7782	−	16.7782i	−0.776401	−	0.776401i	0.202816	−	0.979217i	$-0.434991\pi$
$467$	−16.7782	−	16.7782i	−0.776401	−	0.776401i	−0.979217	+	0.202816i	$0.934991\pi$
$468$		0			0
$469$	16.9706			0.783628
$470$	4.41421	−	13.2426i	0.203612	−	0.610837i
$471$		0			0
$472$	1.00000	−	1.00000i	0.0460287	−	0.0460287i
$473$	−5.48528	+	1.97056i	−0.252214	+	0.0906066i
$474$		0			0
$475$	−12.0000	−	9.00000i	−0.550598	−	0.412948i
$476$	−21.7279			−0.995898
$477$		0			0
$478$	0.514719	−	0.514719i	0.0235427	−	0.0235427i
$479$	−36.7279			−1.67814			−0.839071	−	0.544022i	$-0.816901\pi$
$479$	−36.7279			−1.67814			−0.839071	+	0.544022i	$0.816901\pi$
$480$		0			0
$481$		−	0.727922i		−	0.0331904i
$482$	−4.75736	−	4.75736i	−0.216692	−	0.216692i
$483$		0			0
$484$	−8.48528	+	7.00000i	−0.385695	+	0.318182i
$485$	−6.34315	+	3.17157i	−0.288027	+	0.144014i
$486$		0			0
$487$	−11.9706	−	11.9706i	−0.542438	−	0.542438i	0.381805	−	0.924243i	$-0.375303\pi$
$487$	−11.9706	−	11.9706i	−0.542438	−	0.542438i	−0.924243	+	0.381805i	$0.875303\pi$
$488$	−5.12132	+	5.12132i	−0.231831	+	0.231831i
$489$		0			0
$490$	4.00000	−	2.00000i	0.180702	−	0.0903508i
$491$			5.48528i			0.247547i	0.992310	+	0.123774i	$0.0394997\pi$
$491$			5.48528i			0.247547i	−0.992310	+	0.123774i	$0.960500\pi$
$492$		0			0
$493$	6.36396	−	6.36396i	0.286618	−	0.286618i
$494$	12.7279			0.572656
$495$		0			0
$496$	7.24264			0.325204
$497$	−2.63604	+	2.63604i	−0.118243	+	0.118243i
$498$		0			0
$499$		−	34.9706i		−	1.56550i	−0.622338	−	0.782749i	$-0.713817\pi$
$499$		−	34.9706i		−	1.56550i	0.622338	−	0.782749i	$-0.286183\pi$
$500$	6.36396	+	9.19239i	0.284605	+	0.411096i
$501$		0			0
$502$	2.48528	−	2.48528i	0.110924	−	0.110924i
$503$	0.727922	+	0.727922i	0.0324564	+	0.0324564i	0.723149	−	0.690692i	$-0.242694\pi$
$503$	0.727922	+	0.727922i	0.0324564	+	0.0324564i	−0.690692	+	0.723149i	$0.742694\pi$
$504$		0			0
$505$	−5.27208	−	1.75736i	−0.234604	−	0.0782015i
$506$	0.727922	+	0.343146i	0.0323601	+	0.0152547i
$507$		0			0
$508$	−4.24264	−	4.24264i	−0.188237	−	0.188237i
$509$		−	32.1421i		−	1.42468i	−0.701837	−	0.712338i	$-0.747637\pi$
$509$		−	32.1421i		−	1.42468i	0.701837	−	0.712338i	$-0.252363\pi$
$510$		0			0
$511$	25.4558			1.12610
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−2.72792			−0.120323
$515$	−8.82843	−	17.6569i	−0.389027	−	0.778054i
$516$		0			0
$517$	−19.4853	+	7.00000i	−0.856962	+	0.307860i
$518$	0.363961	−	0.363961i	0.0159915	−	0.0159915i
$519$		0			0
$520$	−9.00000	−	3.00000i	−0.394676	−	0.131559i
$521$	−41.6569			−1.82502			−0.912510	−	0.409054i	$-0.865859\pi$
$521$	−41.6569			−1.82502			−0.912510	+	0.409054i	$0.865859\pi$
$522$		0			0
$523$	−18.7279	−	18.7279i	−0.818915	−	0.818915i	0.167036	−	0.985951i	$-0.446580\pi$
$523$	−18.7279	−	18.7279i	−0.818915	−	0.818915i	−0.985951	+	0.167036i	$0.946580\pi$
$524$	−13.9706			−0.610307
$525$		0			0
$526$	−9.00000			−0.392419
$527$	37.0919	−	37.0919i	1.61575	−	1.61575i
$528$		0			0
$529$			22.9411i			0.997440i
$530$	−28.6066	−	9.53553i	−1.24259	−	0.414197i
$531$		0			0
$532$	6.36396	+	6.36396i	0.275913	+	0.275913i
$533$	−5.27208	+	5.27208i	−0.228359	+	0.228359i
$534$		0			0
$535$	−14.4853	−	28.9706i	−0.626253	−	1.25251i
$536$		−	5.65685i		−	0.244339i
$537$		0			0
$538$	14.0000	+	14.0000i	0.603583	+	0.603583i
$539$	−6.00000	−	2.82843i	−0.258438	−	0.121829i
$540$		0			0
$541$		−	10.7574i		−	0.462495i	−0.972895	−	0.231248i	$-0.925719\pi$
$541$		−	10.7574i		−	0.462495i	0.972895	−	0.231248i	$-0.0742807\pi$
$542$	4.75736	+	4.75736i	0.204346	+	0.204346i
$543$		0			0
$544$			7.24264i			0.310526i
$545$	−1.75736	+	5.27208i	−0.0752770	+	0.225831i
$546$		0			0
$547$	30.7279	−	30.7279i	1.31383	−	1.31383i	0.395263	−	0.918568i	$-0.370653\pi$
$547$	30.7279	−	30.7279i	1.31383	−	1.31383i	0.918568	−	0.395263i	$-0.129347\pi$
$548$	11.6569	−	11.6569i	0.497956	−	0.497956i
$549$		0			0
$550$	4.87868	−	15.8492i	0.208028	−	0.675814i
$551$	−3.72792			−0.158815
$552$		0			0
$553$	21.7279	−	21.7279i	0.923965	−	0.923965i
$554$		−	14.4853i		−	0.615421i
$555$		0			0
$556$		−	14.4853i		−	0.614313i
$557$	6.51472	−	6.51472i	0.276037	−	0.276037i	−0.555487	−	0.831525i	$-0.687468\pi$
$557$	6.51472	−	6.51472i	0.276037	−	0.276037i	0.831525	+	0.555487i	$0.187468\pi$
$558$		0			0
$559$			7.45584i			0.315349i
$560$	−3.00000	−	6.00000i	−0.126773	−	0.253546i
$561$		0			0
$562$	−16.2426	−	16.2426i	−0.685154	−	0.685154i
$563$	−5.48528	−	5.48528i	−0.231177	−	0.231177i	0.582007	−	0.813184i	$-0.302268\pi$
$563$	−5.48528	−	5.48528i	−0.231177	−	0.231177i	−0.813184	+	0.582007i	$0.802268\pi$
$564$		0			0
$565$	−6.24264	−	12.4853i	−0.262630	−	0.525260i
$566$	18.7279			0.787193
$567$		0			0
$568$	0.878680	+	0.878680i	0.0368686	+	0.0368686i
$569$	−2.48528			−0.104188			−0.0520942	−	0.998642i	$-0.516590\pi$
$569$	−2.48528			−0.104188			−0.0520942	+	0.998642i	$0.516590\pi$
$570$		0			0
$571$			29.4853i			1.23392i	0.786994	+	0.616960i	$0.211636\pi$
$571$			29.4853i			1.23392i	−0.786994	+	0.616960i	$0.788364\pi$
$572$	4.75736	+	13.2426i	0.198915	+	0.553703i
$573$		0			0
$574$	−5.27208			−0.220052
$575$	−1.20101	+	0.171573i	−0.0500856	+	0.00715508i
$576$		0			0
$577$	−19.7279	−	19.7279i	−0.821284	−	0.821284i	0.165008	−	0.986292i	$-0.447235\pi$
$577$	−19.7279	−	19.7279i	−0.821284	−	0.821284i	−0.986292	+	0.165008i	$0.947235\pi$
$578$	25.0711	+	25.0711i	1.04282	+	1.04282i
$579$		0			0
$580$	2.63604	+	0.878680i	0.109456	+	0.0364852i
$581$	30.7279			1.27481
$582$		0			0
$583$	15.1213	+	42.0919i	0.626261	+	1.74327i
$584$		−	8.48528i		−	0.351123i
$585$		0			0
$586$	22.2426			0.918835
$587$	20.6777	+	20.6777i	0.853459	+	0.853459i	0.990557	−	0.137099i	$-0.0437777\pi$
$587$	20.6777	+	20.6777i	0.853459	+	0.853459i	−0.137099	+	0.990557i	$0.543778\pi$
$588$		0			0
$589$	−21.7279			−0.895283
$590$	2.82843	−	1.41421i	0.116445	−	0.0582223i
$591$		0			0
$592$	−0.121320	−	0.121320i	−0.00498624	−	0.00498624i
$593$	−13.7574	−	13.7574i	−0.564947	−	0.564947i	0.365762	−	0.930709i	$-0.380809\pi$
$593$	−13.7574	−	13.7574i	−0.564947	−	0.564947i	−0.930709	+	0.365762i	$0.880809\pi$
$594$		0			0
$595$	−46.0919	−	15.3640i	−1.88958	−	0.629861i
$596$			19.2426i			0.788209i
$597$		0			0
$598$	0.727922	−	0.727922i	0.0297669	−	0.0297669i
$599$			3.72792i			0.152319i	0.997096	+	0.0761594i	$0.0242658\pi$
$599$			3.72792i			0.152319i	−0.997096	+	0.0761594i	$0.975734\pi$
$600$		0			0
$601$			27.9411i			1.13974i	0.821734	+	0.569871i	$0.193007\pi$
$601$			27.9411i			1.13974i	−0.821734	+	0.569871i	$0.806993\pi$
$602$	−3.72792	+	3.72792i	−0.151939	+	0.151939i
$603$		0			0
$604$	−12.0000			−0.488273
$605$	−22.9497	+	8.84924i	−0.933040	+	0.359773i
$606$		0			0
$607$	15.8787	−	15.8787i	0.644496	−	0.644496i	−0.307162	−	0.951657i	$-0.599379\pi$
$607$	15.8787	−	15.8787i	0.644496	−	0.644496i	0.951657	+	0.307162i	$0.0993792\pi$
$608$	2.12132	−	2.12132i	0.0860309	−	0.0860309i
$609$		0			0
$610$	−14.4853	+	7.24264i	−0.586492	+	0.293246i
$611$			26.4853i			1.07148i
$612$		0			0
$613$	18.0000	+	18.0000i	0.727013	+	0.727013i	0.970024	−	0.243011i	$-0.0781350\pi$
$613$	18.0000	+	18.0000i	0.727013	+	0.727013i	−0.243011	+	0.970024i	$0.578135\pi$
$614$			16.2426i			0.655500i
$615$		0			0
$616$	−4.24264	+	9.00000i	−0.170941	+	0.362620i
$617$	−31.0711	−	31.0711i	−1.25087	−	1.25087i	−0.955329	−	0.295545i	$-0.904499\pi$
$617$	−31.0711	−	31.0711i	−1.25087	−	1.25087i	−0.295545	−	0.955329i	$-0.595501\pi$
$618$		0			0
$619$		−	10.0000i		−	0.401934i	−0.979598	−	0.200967i	$-0.935592\pi$
$619$		−	10.0000i		−	0.401934i	0.979598	−	0.200967i	$-0.0644084\pi$
$620$	15.3640	+	5.12132i	0.617032	+	0.205677i
$621$		0			0
$622$	−6.87868	+	6.87868i	−0.275810	+	0.275810i
$623$	11.6360	+	11.6360i	0.466188	+	0.466188i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$			5.31371i			0.212379i
$627$		0			0
$628$	16.3640	−	16.3640i	0.652993	−	0.652993i
$629$	−1.24264			−0.0495473
$630$		0			0
$631$	1.72792			0.0687875			0.0343937	−	0.999408i	$-0.489050\pi$
$631$	1.72792			0.0687875			0.0343937	+	0.999408i	$0.489050\pi$
$632$	−7.24264	−	7.24264i	−0.288097	−	0.288097i
$633$		0			0
$634$	−13.4853			−0.535569
$635$	−6.00000	−	12.0000i	−0.238103	−	0.476205i
$636$		0			0
$637$	−6.00000	+	6.00000i	−0.237729	+	0.237729i
$638$	−1.39340	−	3.87868i	−0.0551652	−	0.153558i
$639$		0			0
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$	6.17157			0.243762			0.121881	−	0.992545i	$-0.461107\pi$
$641$	6.17157			0.243762			0.121881	+	0.992545i	$0.461107\pi$
$642$		0			0
$643$	32.5772	−	32.5772i	1.28472	−	1.28472i	0.346766	−	0.937952i	$-0.387280\pi$
$643$	32.5772	−	32.5772i	1.28472	−	1.28472i	0.937952	−	0.346766i	$-0.112720\pi$
$644$	0.727922			0.0286841
$645$		0			0
$646$		−	21.7279i		−	0.854874i
$647$	−28.1127	−	28.1127i	−1.10522	−	1.10522i	−0.993770	−	0.111455i	$-0.964449\pi$
$647$	−28.1127	−	28.1127i	−1.10522	−	1.10522i	−0.111455	−	0.993770i	$-0.535551\pi$
$648$		0			0
$649$	−4.24264	−	2.00000i	−0.166538	−	0.0785069i
$650$	−16.9706	−	12.7279i	−0.665640	−	0.499230i
$651$		0			0
$652$	13.8492	+	13.8492i	0.542378	+	0.542378i
$653$	9.53553	−	9.53553i	0.373154	−	0.373154i	−0.495470	−	0.868625i	$-0.665004\pi$
$653$	9.53553	−	9.53553i	0.373154	−	0.373154i	0.868625	+	0.495470i	$0.165004\pi$
$654$		0			0
$655$	−29.6360	−	9.87868i	−1.15798	−	0.385992i
$656$			1.75736i			0.0686134i
$657$		0			0
$658$	−13.2426	+	13.2426i	−0.516252	+	0.516252i
$659$	−28.4558			−1.10848			−0.554241	−	0.832356i	$-0.686991\pi$
$659$	−28.4558			−1.10848			−0.554241	+	0.832356i	$0.686991\pi$
$660$		0			0
$661$	−16.7279			−0.650641			−0.325320	−	0.945604i	$-0.605472\pi$
$661$	−16.7279			−0.650641			−0.325320	+	0.945604i	$0.605472\pi$
$662$	−17.4853	+	17.4853i	−0.679585	+	0.679585i
$663$		0			0
$664$		−	10.2426i		−	0.397492i
$665$	9.00000	+	18.0000i	0.349005	+	0.698010i
$666$		0			0
$667$	−0.213203	+	0.213203i	−0.00825527	+	0.00825527i
$668$	6.36396	+	6.36396i	0.246229	+	0.246229i
$669$		0			0
$670$	4.00000	−	12.0000i	0.154533	−	0.463600i
$671$	21.7279	+	10.2426i	0.838797	+	0.395413i
$672$		0			0
$673$	−2.63604	−	2.63604i	−0.101612	−	0.101612i	0.654473	−	0.756085i	$-0.272890\pi$
$673$	−2.63604	−	2.63604i	−0.101612	−	0.101612i	−0.756085	+	0.654473i	$0.772890\pi$
$674$			18.2132i			0.701546i
$675$		0			0
$676$	5.00000			0.192308
$677$	−33.2132	+	33.2132i	−1.27649	+	1.27649i	−0.333867	+	0.942620i	$0.608354\pi$
$677$	−33.2132	+	33.2132i	−1.27649	+	1.27649i	−0.942620	+	0.333867i	$0.891646\pi$
$678$		0			0
$679$	9.51472			0.365141
$680$	−5.12132	+	15.3640i	−0.196394	+	0.589181i
$681$		0			0
$682$	−8.12132	−	22.6066i	−0.310981	−	0.865652i
$683$	−12.1924	+	12.1924i	−0.466529	+	0.466529i	−0.900788	−	0.434259i	$-0.857010\pi$
$683$	−12.1924	+	12.1924i	−0.466529	+	0.466529i	0.434259	+	0.900788i	$0.357010\pi$
$684$		0			0
$685$	32.9706	−	16.4853i	1.25974	−	0.629870i
$686$	15.0000			0.572703
$687$		0			0
$688$	1.24264	+	1.24264i	0.0473752	+	0.0473752i
$689$	57.2132			2.17965
$690$		0			0
$691$	13.2721			0.504894			0.252447	−	0.967611i	$-0.418765\pi$
$691$	13.2721			0.504894			0.252447	+	0.967611i	$0.418765\pi$
$692$	16.2426	−	16.2426i	0.617453	−	0.617453i
$693$		0			0
$694$			9.51472i			0.361174i
$695$	10.2426	−	30.7279i	0.388526	−	1.16558i
$696$		0			0
$697$	9.00000	+	9.00000i	0.340899	+	0.340899i
$698$	7.75736	−	7.75736i	0.293620	−	0.293620i
$699$		0			0
$700$	−2.12132	−	14.8492i	−0.0801784	−	0.561249i
$701$		−	27.7279i		−	1.04727i	−0.851943	−	0.523635i	$-0.824576\pi$
$701$		−	27.7279i		−	1.04727i	0.851943	−	0.523635i	$-0.175424\pi$
$702$		0			0
$703$	0.363961	+	0.363961i	0.0137271	+	0.0137271i
$704$	3.00000	+	1.41421i	0.113067	+	0.0533002i
$705$		0			0
$706$			20.9706i			0.789238i
$707$	5.27208	+	5.27208i	0.198277	+	0.198277i
$708$		0			0
$709$			10.0000i			0.375558i	0.982211	+	0.187779i	$0.0601289\pi$
$709$			10.0000i			0.375558i	−0.982211	+	0.187779i	$0.939871\pi$
$710$	1.24264	+	2.48528i	0.0466355	+	0.0932709i
$711$		0			0
$712$	3.87868	−	3.87868i	0.145360	−	0.145360i
$713$	−1.24264	+	1.24264i	−0.0465373	+	0.0465373i
$714$		0			0
$715$	0.727922	+	31.4558i	0.0272227	+	1.17638i
$716$	13.7574			0.514137
$717$		0			0
$718$	−24.7279	+	24.7279i	−0.922838	+	0.922838i
$719$			20.6985i			0.771923i	0.922515	+	0.385962i	$0.126130\pi$
$719$			20.6985i			0.771923i	−0.922515	+	0.385962i	$0.873870\pi$
$720$		0			0
$721$			26.4853i			0.986363i
$722$	7.07107	−	7.07107i	0.263158	−	0.263158i
$723$		0			0
$724$		−	12.0000i		−	0.445976i
$725$	4.97056	+	3.72792i	0.184602	+	0.138452i
$726$		0			0
$727$	−6.97056	−	6.97056i	−0.258524	−	0.258524i	0.565930	−	0.824454i	$-0.308517\pi$
$727$	−6.97056	−	6.97056i	−0.258524	−	0.258524i	−0.824454	+	0.565930i	$0.808517\pi$
$728$	9.00000	+	9.00000i	0.333562	+	0.333562i
$729$		0			0
$730$	6.00000	−	18.0000i	0.222070	−	0.666210i
$731$	12.7279			0.470759
$732$		0			0
$733$	−25.9706	−	25.9706i	−0.959245	−	0.959245i	0.0399568	−	0.999201i	$-0.487278\pi$
$733$	−25.9706	−	25.9706i	−0.959245	−	0.959245i	−0.999201	+	0.0399568i	$0.987278\pi$
$734$	2.82843			0.104399
$735$		0			0
$736$		−	0.242641i		−	0.00894385i
$737$	−17.6569	+	6.34315i	−0.650399	+	0.233653i
$738$		0			0
$739$	33.9411			1.24854			0.624272	−	0.781207i	$-0.285396\pi$
$739$	33.9411			1.24854			0.624272	+	0.781207i	$0.285396\pi$
$740$	−0.171573	−	0.343146i	−0.00630714	−	0.0126143i
$741$		0			0
$742$	28.6066	+	28.6066i	1.05018	+	1.05018i
$743$	8.12132	+	8.12132i	0.297942	+	0.297942i	0.840207	−	0.542265i	$-0.182433\pi$
$743$	8.12132	+	8.12132i	0.297942	+	0.297942i	−0.542265	+	0.840207i	$0.682433\pi$
$744$		0			0
$745$	−13.6066	+	40.8198i	−0.498507	+	1.49552i
$746$	−1.75736			−0.0643415
$747$		0			0
$748$	22.6066	−	8.12132i	0.826579	−	0.296945i
$749$			43.4558i			1.58784i
$750$		0			0
$751$	−43.1838			−1.57580			−0.787899	−	0.615804i	$-0.788831\pi$
$751$	−43.1838			−1.57580			−0.787899	+	0.615804i	$0.788831\pi$
$752$	4.41421	+	4.41421i	0.160970	+	0.160970i
$753$		0			0
$754$	−5.27208			−0.191998
$755$	−25.4558	−	8.48528i	−0.926433	−	0.308811i
$756$		0			0
$757$	13.2132	+	13.2132i	0.480242	+	0.480242i	0.905209	−	0.424967i	$-0.139714\pi$
$757$	13.2132	+	13.2132i	0.480242	+	0.480242i	−0.424967	+	0.905209i	$0.639714\pi$
$758$	3.51472	+	3.51472i	0.127660	+	0.127660i
$759$		0			0
$760$	6.00000	−	3.00000i	0.217643	−	0.108821i
$761$			18.7279i			0.678887i	0.940627	+	0.339443i	$0.110239\pi$
$761$			18.7279i			0.678887i	−0.940627	+	0.339443i	$0.889761\pi$
$762$		0			0
$763$	5.27208	−	5.27208i	0.190862	−	0.190862i
$764$			2.82843i			0.102329i
$765$		0			0
$766$			2.00000i			0.0722629i
$767$	−4.24264	+	4.24264i	−0.153193	+	0.153193i
$768$		0			0
$769$	−43.4558			−1.56706			−0.783529	−	0.621355i	$-0.786582\pi$
$769$	−43.4558			−1.56706			−0.783529	+	0.621355i	$0.786582\pi$
$770$	−15.3640	+	16.0919i	−0.553679	+	0.579911i
$771$		0			0
$772$	−0.878680	+	0.878680i	−0.0316244	+	0.0316244i
$773$	−16.2635	+	16.2635i	−0.584956	+	0.584956i	−0.936261	−	0.351305i	$-0.885738\pi$
$773$	−16.2635	+	16.2635i	−0.584956	+	0.584956i	0.351305	+	0.936261i	$0.385738\pi$
$774$		0			0
$775$	28.9706	+	21.7279i	1.04065	+	0.780490i
$776$		−	3.17157i		−	0.113853i
$777$		0			0
$778$	2.00000	+	2.00000i	0.0717035	+	0.0717035i
$779$		−	5.27208i		−	0.188892i
$780$		0			0
$781$	1.75736	−	3.72792i	0.0628833	−	0.133396i
$782$	−1.24264	−	1.24264i	−0.0444367	−	0.0444367i
$783$		0			0
$784$			2.00000i			0.0714286i
$785$	46.2843	−	23.1421i	1.65196	−	0.825978i
$786$		0			0
$787$	5.48528	−	5.48528i	0.195529	−	0.195529i	−0.602551	−	0.798080i	$-0.705849\pi$
$787$	5.48528	−	5.48528i	0.195529	−	0.195529i	0.798080	+	0.602551i	$0.205849\pi$
$788$	1.24264	+	1.24264i	0.0442672	+	0.0442672i
$789$		0			0
$790$	−10.2426	−	20.4853i	−0.364417	−	0.728834i
$791$			18.7279i			0.665888i
$792$		0			0
$793$	21.7279	−	21.7279i	0.771581	−	0.771581i
$794$	2.14214			0.0760215
$795$		0			0
$796$	4.75736			0.168620
$797$	−8.14214	−	8.14214i	−0.288409	−	0.288409i	0.548042	−	0.836451i	$-0.315373\pi$
$797$	−8.14214	−	8.14214i	−0.288409	−	0.288409i	−0.836451	+	0.548042i	$0.815373\pi$
$798$		0			0
$799$	45.2132			1.59953
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$		0			0
$802$	1.63604	−	1.63604i	0.0577705	−	0.0577705i
$803$	−26.4853	+	9.51472i	−0.934645	+	0.335767i
$804$		0			0
$805$	1.54416	+	0.514719i	0.0544243	+	0.0181414i
$806$	−30.7279			−1.08234
$807$		0			0
$808$	1.75736	−	1.75736i	0.0618237	−	0.0618237i
$809$	37.4558			1.31688			0.658439	−	0.752634i	$-0.271217\pi$
$809$	37.4558			1.31688			0.658439	+	0.752634i	$0.271217\pi$
$810$		0			0
$811$		−	4.45584i		−	0.156466i	−0.996935	−	0.0782329i	$-0.975072\pi$
$811$		−	4.45584i		−	0.156466i	0.996935	−	0.0782329i	$-0.0249278\pi$
$812$	−2.63604	−	2.63604i	−0.0925068	−	0.0925068i
$813$		0			0
$814$	−0.242641	+	0.514719i	−0.00850455	+	0.0180409i
$815$	19.5858	+	39.1716i	0.686060	+	1.37212i
$816$		0			0
$817$	−3.72792	−	3.72792i	−0.130423	−	0.130423i
$818$	−16.2426	+	16.2426i	−0.567911	+	0.567911i
$819$		0			0
$820$	−1.24264	+	3.72792i	−0.0433949	+	0.130185i
$821$			49.4558i			1.72602i	0.505186	+	0.863010i	$0.331424\pi$
$821$			49.4558i			1.72602i	−0.505186	+	0.863010i	$0.668576\pi$
$822$		0			0
$823$	28.6985	−	28.6985i	1.00037	−	1.00037i	0.000366361	−	1.00000i	$-0.499883\pi$
$823$	28.6985	−	28.6985i	1.00037	−	1.00037i	1.00000		0.000366361i	$-0.000116616\pi$
$824$	8.82843			0.307553
$825$		0			0
$826$	−4.24264			−0.147620
$827$	−3.00000	+	3.00000i	−0.104320	+	0.104320i	−0.757340	−	0.653020i	$-0.773502\pi$
$827$	−3.00000	+	3.00000i	−0.104320	+	0.104320i	0.653020	+	0.757340i	$0.273502\pi$
$828$		0			0
$829$			45.4558i			1.57875i	0.613913	+	0.789373i	$0.289594\pi$
$829$			45.4558i			1.57875i	−0.613913	+	0.789373i	$0.710406\pi$
$830$	7.24264	−	21.7279i	0.251396	−	0.754187i
$831$		0			0
$832$	3.00000	−	3.00000i	0.104006	−	0.104006i
$833$	10.2426	+	10.2426i	0.354886	+	0.354886i
$834$		0			0
$835$	9.00000	+	18.0000i	0.311458	+	0.622916i
$836$	−9.00000	−	4.24264i	−0.311272	−	0.146735i
$837$		0			0
$838$	4.24264	+	4.24264i	0.146560	+	0.146560i
$839$			33.1716i			1.14521i	0.819831	+	0.572605i	$0.194067\pi$
$839$			33.1716i			1.14521i	−0.819831	+	0.572605i	$0.805933\pi$
$840$		0			0
$841$	−27.4558			−0.946753
$842$	6.72792	−	6.72792i	0.231860	−	0.231860i
$843$		0			0
$844$	17.4853			0.601868
$845$	10.6066	+	3.53553i	0.364878	+	0.121626i
$846$		0			0
$847$	32.8492	+	3.15076i	1.12871	+	0.108261i
$848$	9.53553	−	9.53553i	0.327452	−	0.327452i
$849$		0			0
$850$	−21.7279	+	28.9706i	−0.745262	+	0.993682i
$851$	0.0416306			0.00142708
$852$		0			0
$853$	−31.9706	−	31.9706i	−1.09465	−	1.09465i	−0.995025	−	0.0996263i	$-0.968235\pi$
$853$	−31.9706	−	31.9706i	−1.09465	−	1.09465i	−0.0996263	−	0.995025i	$-0.531765\pi$
$854$	21.7279			0.743514
$855$		0			0
$856$	14.4853			0.495097
$857$	−4.39340	+	4.39340i	−0.150076	+	0.150076i	−0.778152	−	0.628076i	$-0.783843\pi$
$857$	−4.39340	+	4.39340i	−0.150076	+	0.150076i	0.628076	+	0.778152i	$0.283843\pi$
$858$		0			0
$859$			32.0000i			1.09183i	0.837842	+	0.545913i	$0.183817\pi$
$859$			32.0000i			1.09183i	−0.837842	+	0.545913i	$0.816183\pi$
$860$	1.75736	+	3.51472i	0.0599255	+	0.119851i
$861$		0			0
$862$	−2.48528	−	2.48528i	−0.0846490	−	0.0846490i
$863$	0.899495	−	0.899495i	0.0306192	−	0.0306192i	−0.691631	−	0.722251i	$-0.743108\pi$
$863$	0.899495	−	0.899495i	0.0306192	−	0.0306192i	0.722251	+	0.691631i	$0.243108\pi$
$864$		0			0
$865$	45.9411	−	22.9706i	1.56205	−	0.781023i
$866$		−	31.0711i		−	1.05584i
$867$		0			0
$868$	−15.3640	−	15.3640i	−0.521487	−	0.521487i
$869$	−14.4853	+	30.7279i	−0.491380	+	1.04237i
$870$		0			0
$871$			24.0000i			0.813209i
$872$	−1.75736	−	1.75736i	−0.0595117	−	0.0595117i
$873$		0			0
$874$			0.727922i			0.0246223i
$875$	6.00000	−	33.0000i	0.202837	−	1.11560i
$876$		0			0
$877$	−5.27208	+	5.27208i	−0.178025	+	0.178025i	−0.790495	−	0.612469i	$-0.790176\pi$
$877$	−5.27208	+	5.27208i	−0.178025	+	0.178025i	0.612469	+	0.790495i	$0.290176\pi$
$878$	0.514719	−	0.514719i	0.0173709	−	0.0173709i
$879$		0			0
$880$	5.36396	+	5.12132i	0.180819	+	0.172640i
$881$	−8.48528			−0.285876			−0.142938	−	0.989732i	$-0.545655\pi$
$881$	−8.48528			−0.285876			−0.142938	+	0.989732i	$0.545655\pi$
$882$		0			0
$883$	−8.39340	+	8.39340i	−0.282460	+	0.282460i	−0.834089	−	0.551629i	$-0.814006\pi$
$883$	−8.39340	+	8.39340i	−0.282460	+	0.282460i	0.551629	+	0.834089i	$0.314006\pi$
$884$		−	30.7279i		−	1.03349i
$885$		0			0
$886$			26.9706i			0.906094i
$887$	13.7574	−	13.7574i	0.461927	−	0.461927i	−0.437360	−	0.899287i	$-0.644086\pi$
$887$	13.7574	−	13.7574i	0.461927	−	0.461927i	0.899287	+	0.437360i	$0.144086\pi$
$888$		0			0
$889$			18.0000i			0.603701i
$890$	10.9706	−	5.48528i	0.367734	−	0.183867i
$891$		0			0
$892$	3.75736	+	3.75736i	0.125806	+	0.125806i
$893$	−13.2426	−	13.2426i	−0.443148	−	0.443148i
$894$		0			0
$895$	29.1838	+	9.72792i	0.975506	+	0.325169i
$896$	3.00000			0.100223
$897$		0			0
$898$	−14.4853	−	14.4853i	−0.483380	−	0.483380i
$899$	9.00000			0.300167
$900$		0			0
$901$		−	97.6690i		−	3.25383i
$902$	5.48528	−	1.97056i	0.182640	−	0.0656126i
$903$		0			0
$904$	6.24264			0.207627
$905$	8.48528	−	25.4558i	0.282060	−	0.846181i
$906$		0			0
$907$	−11.3640	−	11.3640i	−0.377334	−	0.377334i	0.492805	−	0.870140i	$-0.335971\pi$
$907$	−11.3640	−	11.3640i	−0.377334	−	0.377334i	−0.870140	+	0.492805i	$0.835971\pi$
$908$	−15.0000	−	15.0000i	−0.497792	−	0.497792i
$909$		0			0
$910$	12.7279	+	25.4558i	0.421927	+	0.843853i
$911$	−26.3553			−0.873191			−0.436596	−	0.899658i	$-0.643816\pi$
$911$	−26.3553			−0.873191			−0.436596	+	0.899658i	$0.643816\pi$
$912$		0			0
$913$	−31.9706	+	11.4853i	−1.05807	+	0.380107i
$914$		−	10.7574i		−	0.355822i
$915$		0			0
$916$	−15.2132			−0.502658
$917$	29.6360	+	29.6360i	0.978668	+	0.978668i
$918$		0			0
$919$	13.7574			0.453813			0.226907	−	0.973916i	$-0.427139\pi$
$919$	13.7574			0.453813			0.226907	+	0.973916i	$0.427139\pi$
$920$	0.171573	−	0.514719i	0.00565659	−	0.0169698i
$921$		0			0
$922$	−0.878680	−	0.878680i	−0.0289378	−	0.0289378i
$923$	−3.72792	−	3.72792i	−0.122706	−	0.122706i
$924$		0			0
$925$	−0.121320	−	0.849242i	−0.00398899	−	0.0279229i
$926$		−	22.5858i		−	0.742215i
$927$		0			0
$928$	−0.878680	+	0.878680i	−0.0288441	+	0.0288441i
$929$		−	42.1716i		−	1.38360i	−0.722087	−	0.691802i	$-0.756817\pi$
$929$		−	42.1716i		−	1.38360i	0.722087	−	0.691802i	$-0.243183\pi$
$930$		0			0
$931$		−	6.00000i		−	0.196642i
$932$	1.60660	−	1.60660i	0.0526260	−	0.0526260i
$933$		0			0
$934$	23.7279			0.776401
$935$	53.6985	−	1.24264i	1.75613	−	0.0406387i
$936$		0			0
$937$	−24.7279	+	24.7279i	−0.807826	+	0.807826i	−0.984304	−	0.176478i	$-0.943529\pi$
$937$	−24.7279	+	24.7279i	−0.807826	+	0.807826i	0.176478	+	0.984304i	$0.443529\pi$
$938$	−12.0000	+	12.0000i	−0.391814	+	0.391814i
$939$		0			0
$940$	6.24264	+	12.4853i	0.203612	+	0.407225i
$941$		−	43.6690i		−	1.42357i	−0.702397	−	0.711785i	$-0.747887\pi$
$941$		−	43.6690i		−	1.42357i	0.702397	−	0.711785i	$-0.252113\pi$
$942$		0			0
$943$	−0.301515	−	0.301515i	−0.00981869	−	0.00981869i
$944$			1.41421i			0.0460287i
$945$		0			0
$946$	2.48528	−	5.27208i	0.0808035	−	0.171410i
$947$	−22.4350	−	22.4350i	−0.729040	−	0.729040i	0.241388	−	0.970429i	$-0.422397\pi$
$947$	−22.4350	−	22.4350i	−0.729040	−	0.729040i	−0.970429	+	0.241388i	$0.922397\pi$
$948$		0			0
$949$			36.0000i			1.16861i
$950$	14.8492	−	2.12132i	0.481773	−	0.0688247i
$951$		0			0
$952$	15.3640	−	15.3640i	0.497949	−	0.497949i
$953$	−29.1213	−	29.1213i	−0.943332	−	0.943332i	0.0551462	−	0.998478i	$-0.482438\pi$
$953$	−29.1213	−	29.1213i	−0.943332	−	0.943332i	−0.998478	+	0.0551462i	$0.982438\pi$
$954$		0			0
$955$	−2.00000	+	6.00000i	−0.0647185	+	0.194155i
$956$			0.727922i			0.0235427i
$957$		0			0
$958$	25.9706	−	25.9706i	0.839071	−	0.839071i
$959$	−49.4558			−1.59701
$960$		0			0
$961$	21.4558			0.692124
$962$	0.514719	+	0.514719i	0.0165952	+	0.0165952i
$963$		0			0
$964$	6.72792			0.216692
$965$	−2.48528	+	1.24264i	−0.0800040	+	0.0400020i
$966$		0			0
$967$	8.12132	−	8.12132i	0.261164	−	0.261164i	−0.564363	−	0.825527i	$-0.690878\pi$
$967$	8.12132	−	8.12132i	0.261164	−	0.261164i	0.825527	+	0.564363i	$0.190878\pi$
$968$	1.05025	−	10.9497i	0.0337564	−	0.351938i
$969$		0			0
$970$	2.24264	−	6.72792i	0.0720069	−	0.216021i
$971$	−13.1127			−0.420807			−0.210403	−	0.977615i	$-0.567478\pi$
$971$	−13.1127			−0.420807			−0.210403	+	0.977615i	$0.567478\pi$
$972$		0			0
$973$	−30.7279	+	30.7279i	−0.985092	+	0.985092i
$974$	16.9289			0.542438
$975$		0			0
$976$		−	7.24264i		−	0.231831i
$977$	3.55635	+	3.55635i	0.113778	+	0.113778i	0.761703	−	0.647926i	$-0.224363\pi$
$977$	3.55635	+	3.55635i	0.113778	+	0.113778i	−0.647926	+	0.761703i	$0.724363\pi$
$978$		0			0
$979$	−16.4558	−	7.75736i	−0.525931	−	0.247926i
$980$	−1.41421	+	4.24264i	−0.0451754	+	0.135526i
$981$		0			0
$982$	−3.87868	−	3.87868i	−0.123774	−	0.123774i
$983$	−9.17157	+	9.17157i	−0.292528	+	0.292528i	−0.838078	−	0.545550i	$-0.816321\pi$
$983$	−9.17157	+	9.17157i	−0.292528	+	0.292528i	0.545550	+	0.838078i	$0.316321\pi$
$984$		0			0
$985$	1.75736	+	3.51472i	0.0559941	+	0.111988i
$986$			9.00000i			0.286618i
$987$		0			0
$988$	−9.00000	+	9.00000i	−0.286328	+	0.286328i
$989$	−0.426407			−0.0135589
$990$		0			0
$991$	−25.4558			−0.808632			−0.404316	−	0.914619i	$-0.632490\pi$
$991$	−25.4558			−0.808632			−0.404316	+	0.914619i	$0.632490\pi$
$992$	−5.12132	+	5.12132i	−0.162602	+	0.162602i
$993$		0			0
$994$		−	3.72792i		−	0.118243i
$995$	10.0919	+	3.36396i	0.319934	+	0.106645i
$996$		0			0
$997$	−41.4853	+	41.4853i	−1.31385	+	1.31385i	−0.395300	+	0.918552i	$0.629359\pi$
$997$	−41.4853	+	41.4853i	−1.31385	+	1.31385i	−0.918552	+	0.395300i	$0.870641\pi$
$998$	24.7279	+	24.7279i	0.782749	+	0.782749i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.m.d.307.1		4
3.2	odd	2		110.2.f.c.87.2	yes	4
5.3	odd	4		990.2.m.c.703.2		4
11.10	odd	2		990.2.m.c.307.2		4
12.11	even	2		880.2.bd.b.417.1		4
15.2	even	4		550.2.f.a.43.2		4
15.8	even	4		110.2.f.b.43.1	✓	4
15.14	odd	2		550.2.f.b.307.1		4
33.32	even	2		110.2.f.b.87.1	yes	4
55.43	even	4	inner	990.2.m.d.703.1		4
60.23	odd	4		880.2.bd.c.593.1		4
132.131	odd	2		880.2.bd.c.417.1		4
165.32	odd	4		550.2.f.b.43.1		4
165.98	odd	4		110.2.f.c.43.2	yes	4
165.164	even	2		550.2.f.a.307.2		4
660.263	even	4		880.2.bd.b.593.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.f.b.43.1	✓	4	15.8	even	4
110.2.f.b.87.1	yes	4	33.32	even	2
110.2.f.c.43.2	yes	4	165.98	odd	4
110.2.f.c.87.2	yes	4	3.2	odd	2
550.2.f.a.43.2		4	15.2	even	4
550.2.f.a.307.2		4	165.164	even	2
550.2.f.b.43.1		4	165.32	odd	4
550.2.f.b.307.1		4	15.14	odd	2
880.2.bd.b.417.1		4	12.11	even	2
880.2.bd.b.593.1		4	660.263	even	4
880.2.bd.c.417.1		4	132.131	odd	2
880.2.bd.c.593.1		4	60.23	odd	4
990.2.m.c.307.2		4	11.10	odd	2
990.2.m.c.703.2		4	5.3	odd	4
990.2.m.d.307.1		4	1.1	even	1	trivial
990.2.m.d.703.1		4	55.43	even	4	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-2.12132 + 2.12132i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 + 2.00000i) q^{10} +(1.41421 - 3.00000i) q^{11} +(-3.00000 - 3.00000i) q^{13} -3.00000i q^{14} -1.00000 q^{16} +(-5.12132 + 5.12132i) q^{17} +3.00000 q^{19} +(-2.12132 - 0.707107i) q^{20} +(1.12132 + 3.12132i) q^{22} +(0.171573 - 0.171573i) q^{23} +(-4.00000 - 3.00000i) q^{25} +4.24264 q^{26} +(2.12132 + 2.12132i) q^{28} -1.24264 q^{29} -7.24264 q^{31} +(0.707107 - 0.707107i) q^{32} -7.24264i q^{34} +(3.00000 + 6.00000i) q^{35} +(0.121320 + 0.121320i) q^{37} +(-2.12132 + 2.12132i) q^{38} +(2.00000 - 1.00000i) q^{40} -1.75736i q^{41} +(-1.24264 - 1.24264i) q^{43} +(-3.00000 - 1.41421i) q^{44} +0.242641i q^{46} +(-4.41421 - 4.41421i) q^{47} -2.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-3.00000 + 3.00000i) q^{52} +(-9.53553 + 9.53553i) q^{53} +(-5.36396 - 5.12132i) q^{55} -3.00000 q^{56} +(0.878680 - 0.878680i) q^{58} -1.41421i q^{59} +7.24264i q^{61} +(5.12132 - 5.12132i) q^{62} +1.00000i q^{64} +(-8.48528 + 4.24264i) q^{65} +(-4.00000 - 4.00000i) q^{67} +(5.12132 + 5.12132i) q^{68} +(-6.36396 - 2.12132i) q^{70} +1.24264 q^{71} +(-6.00000 - 6.00000i) q^{73} -0.171573 q^{74} -3.00000i q^{76} +(3.36396 + 9.36396i) q^{77} -10.2426 q^{79} +(-0.707107 + 2.12132i) q^{80} +(1.24264 + 1.24264i) q^{82} +(-7.24264 - 7.24264i) q^{83} +(7.24264 + 14.4853i) q^{85} +1.75736 q^{86} +(3.12132 - 1.12132i) q^{88} -5.48528i q^{89} +12.7279 q^{91} +(-0.171573 - 0.171573i) q^{92} +6.24264 q^{94} +(2.12132 - 6.36396i) q^{95} +(-2.24264 - 2.24264i) q^{97} +(1.41421 + 1.41421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{10} - 12 q^{13} - 4 q^{16} - 12 q^{17} + 12 q^{19} - 4 q^{22} + 12 q^{23} - 16 q^{25} + 12 q^{29} - 12 q^{31} + 12 q^{35} - 8 q^{37} + 8 q^{40} + 12 q^{43} - 12 q^{44} - 12 q^{47} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) \) 4 * q + 4 * q^10 - 12 * q^13 - 4 * q^16 - 12 * q^17 + 12 * q^19 - 4 * q^22 + 12 * q^23 - 16 * q^25 + 12 * q^29 - 12 * q^31 + 12 * q^35 - 8 * q^37 + 8 * q^40 + 12 * q^43 - 12 * q^44 - 12 * q^47 - 12 * q^52 - 24 * q^53 + 4 * q^55 - 12 * q^56 + 12 * q^58 + 12 * q^62 - 16 * q^67 + 12 * q^68 - 12 * q^71 - 24 * q^73 - 12 * q^74 - 12 * q^77 - 24 * q^79 - 12 * q^82 - 12 * q^83 + 12 * q^85 + 24 * q^86 + 4 * q^88 - 12 * q^92 + 8 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more