LMFDB - Embedded newform 1170.2.bs.f.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(361,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1170.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bs (of order $6$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.17284886784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 $ x^8 - 2x^7 + 2x^6 + 30x^5 + 185x^4 + 36x^3 + 8x^2 + 208*x + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$3.17270 + 3.17270i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.f.901.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-2.01141 - 1.16129i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-2.01141 - 1.16129i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-4.62926 + 2.67270i) q^{11} +(-3.60194 - 0.161290i) q^{13} -2.32258 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-3.48387 - 2.01141i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-2.67270 + 4.62926i) q^{22} +(2.46797 + 4.27464i) q^{23} -1.00000 q^{25} +(-3.20002 + 1.66129i) q^{26} +(-2.01141 + 1.16129i) q^{28} +(2.14539 + 3.71592i) q^{29} -3.47183i q^{31} +(-0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(-1.16129 + 2.01141i) q^{35} +(-2.72733 + 1.57463i) q^{37} -4.02283 q^{38} -1.00000 q^{40} +(-2.29078 + 1.32258i) q^{41} +(6.12539 - 10.6095i) q^{43} +5.34541i q^{44} +(4.27464 + 2.46797i) q^{46} -1.81894i q^{47} +(-0.802812 - 1.39051i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-1.94065 + 3.03873i) q^{52} +5.48693 q^{53} +(2.67270 + 4.62926i) q^{55} +(-1.16129 + 2.01141i) q^{56} +(3.71592 + 2.14539i) q^{58} +(-5.87744 - 3.39334i) q^{59} +(-0.267949 + 0.464102i) q^{61} +(-1.73592 - 3.00670i) q^{62} -1.00000 q^{64} +(-0.161290 + 3.60194i) q^{65} +(3.55872 - 2.05463i) q^{67} +(2.00000 + 3.46410i) q^{68} +2.32258i q^{70} +(-13.7454 - 7.93593i) q^{71} +13.5734i q^{73} +(-1.57463 + 2.72733i) q^{74} +(-3.48387 + 2.01141i) q^{76} +12.4151 q^{77} -7.96774 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-1.32258 + 2.29078i) q^{82} -11.3360i q^{83} +(3.46410 + 2.00000i) q^{85} -12.2508i q^{86} +(2.67270 + 4.62926i) q^{88} +(1.50670 - 0.869891i) q^{89} +(7.05769 + 4.50732i) q^{91} +4.93593 q^{92} +(-0.909471 - 1.57525i) q^{94} +(-2.01141 + 3.48387i) q^{95} +(-13.9510 - 8.05463i) q^{97} +(-1.39051 - 0.802812i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 4 q^{10} - 6 q^{11} - 12 q^{13} - 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} + 2 q^{22} - 4 q^{23} - 8 q^{25} + 12 q^{26} + 8 q^{29} - 2 q^{35} + 30 q^{37} - 8 q^{40} + 14 q^{43} - 6 q^{46} + 14 q^{49} - 6 q^{52} - 16 q^{53} - 2 q^{55} - 2 q^{56} - 6 q^{58} - 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} + 6 q^{65} + 24 q^{67} + 16 q^{68} + 12 q^{71} - 10 q^{74} - 6 q^{76} - 16 q^{77} - 20 q^{79} + 4 q^{82} - 2 q^{88} - 42 q^{89} - 10 q^{91} - 8 q^{92} - 8 q^{94} - 24 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^10 - 6 * q^11 - 12 * q^13 - 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 + 2 * q^22 - 4 * q^23 - 8 * q^25 + 12 * q^26 + 8 * q^29 - 2 * q^35 + 30 * q^37 - 8 * q^40 + 14 * q^43 - 6 * q^46 + 14 * q^49 - 6 * q^52 - 16 * q^53 - 2 * q^55 - 2 * q^56 - 6 * q^58 - 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 + 6 * q^65 + 24 * q^67 + 16 * q^68 + 12 * q^71 - 10 * q^74 - 6 * q^76 - 16 * q^77 - 20 * q^79 + 4 * q^82 - 2 * q^88 - 42 * q^89 - 10 * q^91 - 8 * q^92 - 8 * q^94 - 24 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−2.01141	−	1.16129i	−0.760243	−	0.438926i	0.0691402	−	0.997607i	$-0.477974\pi$
$7$	−2.01141	−	1.16129i	−0.760243	−	0.438926i	−0.829383	+	0.558681i	$0.811308\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−4.62926	+	2.67270i	−1.39577	+	0.805850i	−0.993946	−	0.109865i	$-0.964958\pi$
$11$	−4.62926	+	2.67270i	−1.39577	+	0.805850i	−0.401827	+	0.915716i	$0.631625\pi$
$12$		0			0
$13$	−3.60194	−	0.161290i	−0.998999	−	0.0447338i
$13$	−3.60194	−	0.161290i	−0.998999	−	0.0447338i
$14$	−2.32258			−0.620736
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	−3.48387	−	2.01141i	−0.799254	−	0.461450i	0.0439559	−	0.999033i	$-0.486004\pi$
$19$	−3.48387	−	2.01141i	−0.799254	−	0.461450i	−0.843210	+	0.537584i	$0.819337\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		0			0
$22$	−2.67270	+	4.62926i	−0.569822	+	0.986961i
$23$	2.46797	+	4.27464i	0.514607	+	0.891325i	0.999856	+	0.0169494i	$0.00539541\pi$
$23$	2.46797	+	4.27464i	0.514607	+	0.891325i	−0.485250	+	0.874376i	$0.661271\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−3.20002	+	1.66129i	−0.627575	+	0.325806i
$27$		0			0
$28$	−2.01141	+	1.16129i	−0.380121	+	0.219463i
$29$	2.14539	+	3.71592i	0.398388	+	0.690029i	0.993527	−	0.113594i	$-0.0362363\pi$
$29$	2.14539	+	3.71592i	0.398388	+	0.690029i	−0.595139	+	0.803623i	$0.702903\pi$
$30$		0			0
$31$		−	3.47183i		−	0.623560i	−0.950154	−	0.311780i	$-0.899075\pi$
$31$		−	3.47183i		−	0.623560i	0.950154	−	0.311780i	$-0.100925\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			4.00000i			0.685994i
$35$	−1.16129	+	2.01141i	−0.196294	+	0.339991i
$36$		0			0
$37$	−2.72733	+	1.57463i	−0.448371	+	0.258867i	−0.707142	−	0.707072i	$-0.750016\pi$
$37$	−2.72733	+	1.57463i	−0.448371	+	0.258867i	0.258771	+	0.965939i	$0.416682\pi$
$38$	−4.02283			−0.652589
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−2.29078	+	1.32258i	−0.357759	+	0.206552i	−0.668097	−	0.744074i	$-0.732891\pi$
$41$	−2.29078	+	1.32258i	−0.357759	+	0.206552i	0.310338	+	0.950626i	$0.399558\pi$
$42$		0			0
$43$	6.12539	−	10.6095i	0.934113	−	1.61793i	0.157906	−	0.987454i	$-0.449526\pi$
$43$	6.12539	−	10.6095i	0.934113	−	1.61793i	0.776207	−	0.630478i	$-0.217141\pi$
$44$			5.34541i			0.805850i
$45$		0			0
$46$	4.27464	+	2.46797i	0.630262	+	0.363882i
$47$		−	1.81894i		−	0.265320i	−0.991162	−	0.132660i	$-0.957648\pi$
$47$		−	1.81894i		−	0.265320i	0.991162	−	0.132660i	$-0.0423518\pi$
$48$		0			0
$49$	−0.802812	−	1.39051i	−0.114687	−	0.198644i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	−1.94065	+	3.03873i	−0.269120	+	0.421396i
$53$	5.48693			0.753687			0.376844	−	0.926277i	$-0.377009\pi$
$53$	5.48693			0.753687			0.376844	+	0.926277i	$0.377009\pi$
$54$		0			0
$55$	2.67270	+	4.62926i	0.360387	+	0.624209i
$56$	−1.16129	+	2.01141i	−0.155184	+	0.268786i
$57$		0			0
$58$	3.71592	+	2.14539i	0.487924	+	0.281703i
$59$	−5.87744	−	3.39334i	−0.765177	−	0.441775i	0.0659742	−	0.997821i	$-0.478984\pi$
$59$	−5.87744	−	3.39334i	−0.765177	−	0.441775i	−0.831152	+	0.556046i	$0.812318\pi$
$60$		0			0
$61$	−0.267949	+	0.464102i	−0.0343074	+	0.0594221i	−0.882669	−	0.469995i	$-0.844256\pi$
$61$	−0.267949	+	0.464102i	−0.0343074	+	0.0594221i	0.848362	+	0.529417i	$0.177589\pi$
$62$	−1.73592	−	3.00670i	−0.220462	−	0.381851i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.161290	+	3.60194i	−0.0200055	+	0.446766i
$66$		0			0
$67$	3.55872	−	2.05463i	0.434767	−	0.251013i	−0.266608	−	0.963805i	$-0.585903\pi$
$67$	3.55872	−	2.05463i	0.434767	−	0.251013i	0.701376	+	0.712792i	$0.252570\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$		0			0
$70$			2.32258i			0.277601i
$71$	−13.7454	−	7.93593i	−1.63128	−	0.941822i	−0.983698	−	0.179830i	$-0.942445\pi$
$71$	−13.7454	−	7.93593i	−1.63128	−	0.941822i	−0.647586	−	0.761992i	$-0.724221\pi$
$72$		0			0
$73$			13.5734i			1.58864i	0.607498	+	0.794321i	$0.292173\pi$
$73$			13.5734i			1.58864i	−0.607498	+	0.794321i	$0.707827\pi$
$74$	−1.57463	+	2.72733i	−0.183047	+	0.317046i
$75$		0			0
$76$	−3.48387	+	2.01141i	−0.399627	+	0.230725i
$77$	12.4151			1.41484
$78$		0			0
$79$	−7.96774			−0.896441			−0.448220	−	0.893923i	$-0.647942\pi$
$79$	−7.96774			−0.896441			−0.448220	+	0.893923i	$0.647942\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$		0			0
$82$	−1.32258	+	2.29078i	−0.146054	+	0.252974i
$83$		−	11.3360i		−	1.24428i	−0.782904	−	0.622142i	$-0.786263\pi$
$83$		−	11.3360i		−	1.24428i	0.782904	−	0.622142i	$-0.213737\pi$
$84$		0			0
$85$	3.46410	+	2.00000i	0.375735	+	0.216930i
$86$		−	12.2508i		−	1.32104i
$87$		0			0
$88$	2.67270	+	4.62926i	0.284911	+	0.493480i
$89$	1.50670	−	0.869891i	0.159709	−	0.0922083i	−0.418015	−	0.908440i	$-0.637274\pi$
$89$	1.50670	−	0.869891i	0.159709	−	0.0922083i	0.577725	+	0.816232i	$0.303941\pi$
$90$		0			0
$91$	7.05769	+	4.50732i	0.739847	+	0.472495i
$92$	4.93593			0.514607
$93$		0			0
$94$	−0.909471	−	1.57525i	−0.0938048	−	0.162475i
$95$	−2.01141	+	3.48387i	−0.206367	+	0.357437i
$96$		0			0
$97$	−13.9510	−	8.05463i	−1.41651	−	0.817824i	−0.420522	−	0.907282i	$-0.638153\pi$
$97$	−13.9510	−	8.05463i	−1.41651	−	0.817824i	−0.995991	+	0.0894586i	$0.971486\pi$
$98$	−1.39051	−	0.802812i	−0.140463	−	0.0810962i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−6.34541	−	10.9906i	−0.631391	−	1.09360i	−0.987267	−	0.159069i	$-0.949151\pi$
$101$	−6.34541	−	10.9906i	−0.631391	−	1.09360i	0.355876	−	0.934533i	$-0.384183\pi$
$102$		0			0
$103$	−4.79612			−0.472575			−0.236288	−	0.971683i	$-0.575931\pi$
$103$	−4.79612			−0.472575			−0.236288	+	0.971683i	$0.575931\pi$
$104$	−0.161290	+	3.60194i	−0.0158158	+	0.353199i
$105$		0			0
$106$	4.75182	−	2.74346i	0.461537	−	0.266469i
$107$	1.53590	+	2.66025i	0.148481	+	0.257176i	0.930666	−	0.365869i	$-0.119228\pi$
$107$	1.53590	+	2.66025i	0.148481	+	0.257176i	−0.782185	+	0.623046i	$0.785895\pi$
$108$		0			0
$109$			6.69081i			0.640864i	0.947272	+	0.320432i	$0.103828\pi$
$109$			6.69081i			0.640864i	−0.947272	+	0.320432i	$0.896172\pi$
$110$	4.62926	+	2.67270i	0.441382	+	0.254832i
$111$		0			0
$112$			2.32258i			0.219463i
$113$	−3.55486	+	6.15720i	−0.334413	+	0.579220i	−0.983372	−	0.181603i	$-0.941871\pi$
$113$	−3.55486	+	6.15720i	−0.334413	+	0.579220i	0.648959	+	0.760823i	$0.275205\pi$
$114$		0			0
$115$	4.27464	−	2.46797i	0.398613	−	0.230139i
$116$	4.29078			0.398388
$117$		0			0
$118$	−6.78668			−0.624765
$119$	8.04565	−	4.64516i	0.737544	−	0.425821i
$120$		0			0
$121$	8.78668	−	15.2190i	0.798789	−	1.38354i
$122$			0.535898i			0.0485180i
$123$		0			0
$124$	−3.00670	−	1.73592i	−0.270009	−	0.155890i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−1.06604	−	1.84644i	−0.0945961	−	0.163845i	0.814844	−	0.579680i	$-0.196823\pi$
$127$	−1.06604	−	1.84644i	−0.0945961	−	0.163845i	−0.909440	+	0.415835i	$0.863489\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.66129	+	3.20002i	0.145705	+	0.280660i
$131$	−1.25851			−0.109957			−0.0549785	−	0.998488i	$-0.517509\pi$
$131$	−1.25851			−0.109957			−0.0549785	+	0.998488i	$0.517509\pi$
$132$		0			0
$133$	4.67167	+	8.09156i	0.405085	+	0.701628i
$134$	2.05463	−	3.55872i	0.177493	−	0.307427i
$135$		0			0
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	−17.0736	−	9.85744i	−1.45870	−	0.842178i	−0.459748	−	0.888049i	$-0.652060\pi$
$137$	−17.0736	−	9.85744i	−1.45870	−	0.842178i	−0.998947	+	0.0458713i	$0.985394\pi$
$138$		0			0
$139$	−2.83871	+	4.91679i	−0.240776	+	0.417037i	−0.960936	−	0.276772i	$-0.910735\pi$
$139$	−2.83871	+	4.91679i	−0.240776	+	0.417037i	0.720159	+	0.693809i	$0.244069\pi$
$140$	1.16129	+	2.01141i	0.0981469	+	0.169995i
$141$		0			0
$142$	−15.8719			−1.33194
$143$	17.1054	−	8.88027i	1.43043	−	0.742605i
$144$		0			0
$145$	3.71592	−	2.14539i	0.308590	−	0.178165i
$146$	6.78668	+	11.7549i	0.561670	+	0.972841i
$147$		0			0
$148$			3.14925i			0.258867i
$149$	16.8680	+	9.73875i	1.38188	+	0.797829i	0.992382	−	0.123198i	$-0.0393150\pi$
$149$	16.8680	+	9.73875i	1.38188	+	0.797829i	0.389499	+	0.921027i	$0.372648\pi$
$150$		0			0
$151$		−	14.5170i		−	1.18138i	−0.806899	−	0.590690i	$-0.798856\pi$
$151$		−	14.5170i		−	1.18138i	0.806899	−	0.590690i	$-0.201144\pi$
$152$	−2.01141	+	3.48387i	−0.163147	+	0.282579i
$153$		0			0
$154$	10.7518	−	6.20757i	0.866406	−	0.500220i
$155$	−3.47183			−0.278864
$156$		0			0
$157$	24.3829			1.94596			0.972982	−	0.230879i	$-0.0741602\pi$
$157$	24.3829			1.94596			0.972982	+	0.230879i	$0.0741602\pi$
$158$	−6.90026	+	3.98387i	−0.548956	+	0.316940i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		−	11.4641i		−	0.903498i
$162$		0			0
$163$	20.4614	+	11.8134i	1.60266	+	0.925295i	0.990953	+	0.134208i	$0.0428492\pi$
$163$	20.4614	+	11.8134i	1.60266	+	0.925295i	0.611704	+	0.791086i	$0.290484\pi$
$164$			2.64516i			0.206552i
$165$		0			0
$166$	−5.66799	−	9.81724i	−0.439921	−	0.761966i
$167$	−14.5035	+	8.37357i	−1.12231	+	0.647967i	−0.941990	−	0.335641i	$-0.891047\pi$
$167$	−14.5035	+	8.37357i	−1.12231	+	0.647967i	−0.180321	+	0.983608i	$0.557714\pi$
$168$		0			0
$169$	12.9480	+	1.16191i	0.995998	+	0.0893780i
$170$	4.00000			0.306786
$171$		0			0
$172$	−6.12539	−	10.6095i	−0.467057	−	0.808966i
$173$	−8.06604	+	13.9708i	−0.613250	+	1.06218i	0.377439	+	0.926034i	$0.376805\pi$
$173$	−8.06604	+	13.9708i	−0.613250	+	1.06218i	−0.990689	+	0.136146i	$0.956529\pi$
$174$		0			0
$175$	2.01141	+	1.16129i	0.152049	+	0.0877853i
$176$	4.62926	+	2.67270i	0.348943	+	0.201463i
$177$		0			0
$178$	0.869891	−	1.50670i	0.0652011	−	0.112932i
$179$	−3.66412	−	6.34644i	−0.273869	−	0.474355i	0.695980	−	0.718061i	$-0.254970\pi$
$179$	−3.66412	−	6.34644i	−0.273869	−	0.474355i	−0.969849	+	0.243706i	$0.921637\pi$
$180$		0			0
$181$	−19.5734			−1.45488			−0.727438	−	0.686173i	$-0.759289\pi$
$181$	−19.5734			−1.45488			−0.727438	+	0.686173i	$0.759289\pi$
$182$	8.36580	+	0.374609i	0.620114	+	0.0277678i
$183$		0			0
$184$	4.27464	−	2.46797i	0.315131	−	0.181941i
$185$	1.57463	+	2.72733i	0.115769	+	0.200518i
$186$		0			0
$187$		−	21.3816i		−	1.56358i
$188$	−1.57525	−	0.909471i	−0.114887	−	0.0663300i
$189$		0			0
$190$			4.02283i			0.291846i
$191$	−8.51873	+	14.7549i	−0.616394	+	1.06763i	0.373744	+	0.927532i	$0.378074\pi$
$191$	−8.51873	+	14.7549i	−0.616394	+	1.06763i	−0.990138	+	0.140094i	$0.955260\pi$
$192$		0			0
$193$	5.33031	−	3.07746i	0.383684	−	0.221520i	−0.295736	−	0.955270i	$-0.595565\pi$
$193$	5.33031	−	3.07746i	0.383684	−	0.221520i	0.679420	+	0.733750i	$0.262231\pi$
$194$	−16.1093			−1.15658
$195$		0			0
$196$	−1.60562			−0.114687
$197$	11.9396	−	6.89334i	0.850662	−	0.491130i	−0.0102119	−	0.999948i	$-0.503251\pi$
$197$	11.9396	−	6.89334i	0.850662	−	0.491130i	0.860874	+	0.508818i	$0.169917\pi$
$198$		0			0
$199$	1.14152	−	1.97717i	0.0809203	−	0.140158i	−0.822725	−	0.568439i	$-0.807547\pi$
$199$	1.14152	−	1.97717i	0.0809203	−	0.140158i	0.903646	+	0.428281i	$0.140881\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−10.9906	−	6.34541i	−0.773293	−	0.446461i
$203$		−	9.96567i		−	0.699453i
$204$		0			0
$205$	1.32258	+	2.29078i	0.0923730	+	0.159995i
$206$	−4.15356	+	2.39806i	−0.289392	+	0.167081i
$207$		0			0
$208$	1.66129	+	3.20002i	0.115190	+	0.221881i
$209$	21.5036			1.48744
$210$		0			0
$211$	−11.2387	−	19.4661i	−0.773707	−	1.34010i	−0.935518	−	0.353278i	$-0.885067\pi$
$211$	−11.2387	−	19.4661i	−0.773707	−	1.34010i	0.161811	−	0.986822i	$-0.448267\pi$
$212$	2.74346	−	4.75182i	0.188422	−	0.326356i
$213$		0			0
$214$	2.66025	+	1.53590i	0.181851	+	0.104992i
$215$	−10.6095	−	6.12539i	−0.723561	−	0.417748i
$216$		0			0
$217$	−4.03180	+	6.98329i	−0.273697	+	0.474057i
$218$	3.34541	+	5.79441i	0.226579	+	0.392447i
$219$		0			0
$220$	5.34541			0.360387
$221$	7.76261	−	12.1549i	0.522170	−	0.817628i
$222$		0			0
$223$	1.19417	−	0.689457i	0.0799678	−	0.0461694i	−0.459483	−	0.888187i	$-0.651965\pi$
$223$	1.19417	−	0.689457i	0.0799678	−	0.0461694i	0.539451	+	0.842017i	$0.318632\pi$
$224$	1.16129	+	2.01141i	0.0775919	+	0.134393i
$225$		0			0
$226$			7.10972i			0.472931i
$227$	16.7321	+	9.66025i	1.11055	+	0.641174i	0.938971	−	0.343998i	$-0.111781\pi$
$227$	16.7321	+	9.66025i	1.11055	+	0.641174i	0.171575	+	0.985171i	$0.445115\pi$
$228$		0			0
$229$			15.7626i			1.04162i	0.853672	+	0.520811i	$0.174370\pi$
$229$			15.7626i			1.04162i	−0.853672	+	0.520811i	$0.825630\pi$
$230$	2.46797	−	4.27464i	0.162733	−	0.281862i
$231$		0			0
$232$	3.71592	−	2.14539i	0.243962	−	0.140852i
$233$	16.5549			1.08455			0.542275	−	0.840201i	$-0.317563\pi$
$233$	16.5549			1.08455			0.542275	+	0.840201i	$0.317563\pi$
$234$		0			0
$235$	−1.81894			−0.118655
$236$	−5.87744	+	3.39334i	−0.382589	+	0.220888i
$237$		0			0
$238$	4.64516	−	8.04565i	0.301101	−	0.521522i
$239$			26.2006i			1.69477i	0.530976	+	0.847387i	$0.321825\pi$
$239$			26.2006i			1.69477i	−0.530976	+	0.847387i	$0.678175\pi$
$240$		0			0
$241$	−13.5529	−	7.82479i	−0.873021	−	0.504039i	−0.00466988	−	0.999989i	$-0.501486\pi$
$241$	−13.5529	−	7.82479i	−0.873021	−	0.504039i	−0.868351	+	0.495950i	$0.834820\pi$
$242$		−	17.5734i		−	1.12966i
$243$		0			0
$244$	0.267949	+	0.464102i	0.0171537	+	0.0297111i
$245$	−1.39051	+	0.802812i	−0.0888365	+	0.0512898i
$246$		0			0
$247$	12.2243	+	7.80691i	0.777812	+	0.496742i
$248$	−3.47183			−0.220462
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	14.1708	−	24.5446i	0.894454	−	1.54924i	0.0599750	−	0.998200i	$-0.480898\pi$
$251$	14.1708	−	24.5446i	0.894454	−	1.54924i	0.834479	−	0.551040i	$-0.185769\pi$
$252$		0			0
$253$	−22.8497	−	13.1923i	−1.43655	−	0.829392i
$254$	−1.84644	−	1.06604i	−0.115856	−	0.0668895i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.25465	+	10.8334i	0.390154	+	0.675767i	0.992470	−	0.122491i	$-0.0390883\pi$
$257$	6.25465	+	10.8334i	0.390154	+	0.675767i	−0.602315	+	0.798258i	$0.705755\pi$
$258$		0			0
$259$	7.31439			0.454494
$260$	3.03873	+	1.94065i	0.188454	+	0.120354i
$261$		0			0
$262$	−1.08991	+	0.629257i	−0.0673346	+	0.0388756i
$263$	−5.35295	−	9.27159i	−0.330077	−	0.571711i	0.652449	−	0.757832i	$-0.273741\pi$
$263$	−5.35295	−	9.27159i	−0.330077	−	0.571711i	−0.982527	+	0.186122i	$0.940408\pi$
$264$		0			0
$265$		−	5.48693i		−	0.337059i
$266$	8.09156	+	4.67167i	0.496126	+	0.286438i
$267$		0			0
$268$		−	4.10926i		−	0.251013i
$269$	3.76261	−	6.51703i	0.229410	−	0.397350i	−0.728223	−	0.685340i	$-0.759654\pi$
$269$	3.76261	−	6.51703i	0.229410	−	0.397350i	0.957633	+	0.287990i	$0.0929869\pi$
$270$		0			0
$271$	8.52920	−	4.92434i	0.518112	−	0.299132i	−0.218050	−	0.975938i	$-0.569970\pi$
$271$	8.52920	−	4.92434i	0.518112	−	0.299132i	0.736162	+	0.676805i	$0.236636\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−19.7149			−1.19102
$275$	4.62926	−	2.67270i	0.279155	−	0.161170i
$276$		0			0
$277$	0.476550	−	0.825410i	0.0286331	−	0.0495941i	−0.851354	−	0.524592i	$-0.824218\pi$
$277$	0.476550	−	0.825410i	0.0286331	−	0.0495941i	0.879987	+	0.474998i	$0.157551\pi$
$278$			5.67742i			0.340509i
$279$		0			0
$280$	2.01141	+	1.16129i	0.120205	+	0.0694003i
$281$		−	5.57336i		−	0.332479i	−0.986085	−	0.166239i	$-0.946838\pi$
$281$		−	5.57336i		−	0.332479i	0.986085	−	0.166239i	$-0.0531625\pi$
$282$		0			0
$283$	11.0067	+	19.0642i	0.654280	+	1.13325i	0.982074	+	0.188497i	$0.0603616\pi$
$283$	11.0067	+	19.0642i	0.654280	+	1.13325i	−0.327794	+	0.944749i	$0.606305\pi$
$284$	−13.7454	+	7.93593i	−0.815642	+	0.470911i
$285$		0			0
$286$	10.3736	−	16.2432i	0.613402	−	0.960483i
$287$	6.14359			0.362645
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	2.14539	−	3.71592i	0.125981	−	0.218206i
$291$		0			0
$292$	11.7549	+	6.78668i	0.687902	+	0.397160i
$293$	−5.92623	−	3.42151i	−0.346214	−	0.199887i	0.316803	−	0.948491i	$-0.397391\pi$
$293$	−5.92623	−	3.42151i	−0.346214	−	0.199887i	−0.663016	+	0.748605i	$0.730724\pi$
$294$		0			0
$295$	−3.39334	+	5.87744i	−0.197568	+	0.342198i
$296$	1.57463	+	2.72733i	0.0915233	+	0.158523i
$297$		0			0
$298$	19.4775			1.12830
$299$	−8.20002	−	15.7951i	−0.474219	−	0.913453i
$300$		0			0
$301$	−24.6414	+	14.2267i	−1.42031	+	0.820014i
$302$	−7.25851	−	12.5721i	−0.417681	−	0.723444i
$303$		0			0
$304$			4.02283i			0.230725i
$305$	0.464102	+	0.267949i	0.0265744	+	0.0153427i
$306$		0			0
$307$			4.75442i			0.271349i	0.990753	+	0.135675i	$0.0433202\pi$
$307$			4.75442i			0.271349i	−0.990753	+	0.135675i	$0.956680\pi$
$308$	6.20757	−	10.7518i	0.353709	−	0.612642i
$309$		0			0
$310$	−3.00670	+	1.73592i	−0.170769	+	0.0985934i
$311$	−1.93639			−0.109803			−0.0549013	−	0.998492i	$-0.517484\pi$
$311$	−1.93639			−0.109803			−0.0549013	+	0.998492i	$0.517484\pi$
$312$		0			0
$313$	25.5545			1.44443			0.722213	−	0.691671i	$-0.243125\pi$
$313$	25.5545			1.44443			0.722213	+	0.691671i	$0.243125\pi$
$314$	21.1162	−	12.1914i	1.19166	−	0.688002i
$315$		0			0
$316$	−3.98387	+	6.90026i	−0.224110	+	0.388170i
$317$		−	12.6667i		−	0.711435i	−0.934594	−	0.355717i	$-0.884237\pi$
$317$		−	12.6667i		−	0.711435i	0.934594	−	0.355717i	$-0.115763\pi$
$318$		0			0
$319$	−19.8631	−	11.4680i	−1.11212	−	0.642083i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	−5.73205	−	9.92820i	−0.319435	−	0.553277i
$323$	13.9355	−	8.04565i	0.775391	−	0.447672i
$324$		0			0
$325$	3.60194	+	0.161290i	0.199800	+	0.00894675i
$326$	23.6267			1.30856
$327$		0			0
$328$	1.32258	+	2.29078i	0.0730272	+	0.126487i
$329$	−2.11232	+	3.65864i	−0.116456	+	0.201708i
$330$		0			0
$331$	−20.5231	−	11.8490i	−1.12805	−	0.651282i	−0.184609	−	0.982812i	$-0.559102\pi$
$331$	−20.5231	−	11.8490i	−1.12805	−	0.651282i	−0.943445	+	0.331530i	$0.892435\pi$
$332$	−9.81724	−	5.66799i	−0.538791	−	0.311071i
$333$		0			0
$334$	−8.37357	+	14.5035i	−0.458182	+	0.793594i
$335$	−2.05463	−	3.55872i	−0.112256	−	0.194434i
$336$		0			0
$337$	19.5554			1.06525			0.532625	−	0.846351i	$-0.321205\pi$
$337$	19.5554			1.06525			0.532625	+	0.846351i	$0.321205\pi$
$338$	11.7942	−	5.46774i	0.641521	−	0.297406i
$339$		0			0
$340$	3.46410	−	2.00000i	0.187867	−	0.108465i
$341$	9.27918	+	16.0720i	0.502496	+	0.870348i
$342$		0			0
$343$			19.9872i			1.07921i
$344$	−10.6095	−	6.12539i	−0.572025	−	0.330259i
$345$		0			0
$346$			16.1321i			0.867266i
$347$	−11.5187	+	19.9510i	−0.618358	+	1.07103i	0.371427	+	0.928462i	$0.378868\pi$
$347$	−11.5187	+	19.9510i	−0.618358	+	1.07103i	−0.989785	+	0.142565i	$0.954465\pi$
$348$		0			0
$349$	13.2679	−	7.66025i	0.710217	−	0.410044i	−0.100924	−	0.994894i	$-0.532180\pi$
$349$	13.2679	−	7.66025i	0.710217	−	0.410044i	0.811141	+	0.584850i	$0.198847\pi$
$350$	2.32258			0.124147
$351$		0			0
$352$	5.34541			0.284911
$353$	−24.6018	+	14.2039i	−1.30942	+	0.755996i	−0.982000	−	0.188881i	$-0.939514\pi$
$353$	−24.6018	+	14.2039i	−1.30942	+	0.755996i	−0.327424	+	0.944877i	$0.606181\pi$
$354$		0			0
$355$	−7.93593	+	13.7454i	−0.421196	+	0.729532i
$356$		−	1.73978i		−	0.0922083i
$357$		0			0
$358$	−6.34644	−	3.66412i	−0.335420	−	0.193655i
$359$			23.5734i			1.24415i	0.782956	+	0.622077i	$0.213711\pi$
$359$			23.5734i			1.24415i	−0.782956	+	0.622077i	$0.786289\pi$
$360$		0			0
$361$	−1.40844	−	2.43948i	−0.0741282	−	0.128394i
$362$	−16.9510	+	9.78668i	−0.890926	+	0.514377i
$363$		0			0
$364$	7.43230	−	3.85848i	0.389558	−	0.202239i
$365$	13.5734			0.710462
$366$		0			0
$367$	−13.7454	−	23.8078i	−0.717506	−	1.24276i	−0.961985	−	0.273103i	$-0.911950\pi$
$367$	−13.7454	−	23.8078i	−0.717506	−	1.24276i	0.244479	−	0.969655i	$-0.421383\pi$
$368$	2.46797	−	4.27464i	0.128652	−	0.222831i
$369$		0			0
$370$	2.72733	+	1.57463i	0.141787	+	0.0818609i
$371$	−11.0365	−	6.37191i	−0.572985	−	0.330813i
$372$		0			0
$373$	−13.1710	+	22.8129i	−0.681971	+	1.18121i	0.292408	+	0.956294i	$0.405544\pi$
$373$	−13.1710	+	22.8129i	−0.681971	+	1.18121i	−0.974379	+	0.224914i	$0.927790\pi$
$374$	−10.6908	−	18.5170i	−0.552809	−	0.957493i
$375$		0			0
$376$	−1.81894			−0.0938048
$377$	−7.12822	−	13.7306i	−0.367122	−	0.707160i
$378$		0			0
$379$	0.388456	−	0.224275i	0.0199537	−	0.0115202i	−0.489990	−	0.871728i	$-0.663000\pi$
$379$	0.388456	−	0.224275i	0.0199537	−	0.0115202i	0.509944	+	0.860208i	$0.329666\pi$
$380$	2.01141	+	3.48387i	0.103183	+	0.178719i
$381$		0			0
$382$			17.0375i			0.871713i
$383$	−10.4985	−	6.06133i	−0.536450	−	0.309719i	0.207189	−	0.978301i	$-0.433568\pi$
$383$	−10.4985	−	6.06133i	−0.536450	−	0.309719i	−0.743639	+	0.668582i	$0.766902\pi$
$384$		0			0
$385$		−	12.4151i		−	0.632734i
$386$	3.07746	−	5.33031i	0.156638	−	0.271306i
$387$		0			0
$388$	−13.9510	+	8.05463i	−0.708256	+	0.408912i
$389$	−18.6195			−0.944045			−0.472022	−	0.881587i	$-0.656476\pi$
$389$	−18.6195			−0.944045			−0.472022	+	0.881587i	$0.656476\pi$
$390$		0			0
$391$	−19.7437			−0.998484
$392$	−1.39051	+	0.802812i	−0.0702314	+	0.0405481i
$393$		0			0
$394$	6.89334	−	11.9396i	0.347281	−	0.601509i
$395$			7.96774i			0.400900i
$396$		0			0
$397$	9.78970	+	5.65208i	0.491331	+	0.283670i	0.725126	−	0.688616i	$-0.241781\pi$
$397$	9.78970	+	5.65208i	0.491331	+	0.283670i	−0.233796	+	0.972286i	$0.575115\pi$
$398$		−	2.28304i		−	0.114439i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	1.30406	−	0.752899i	0.0651216	−	0.0375980i	−0.467086	−	0.884212i	$-0.654696\pi$
$401$	1.30406	−	0.752899i	0.0651216	−	0.0375980i	0.532207	+	0.846614i	$0.321363\pi$
$402$		0			0
$403$	−0.559971	+	12.5053i	−0.0278942	+	0.622935i
$404$	−12.6908			−0.631391
$405$		0			0
$406$	−4.98283	−	8.63052i	−0.247294	−	0.428326i
$407$	8.41702	−	14.5787i	0.417216	−	0.722640i
$408$		0			0
$409$	9.64697	+	5.56968i	0.477012	+	0.275403i	0.719170	−	0.694834i	$-0.244522\pi$
$409$	9.64697	+	5.56968i	0.477012	+	0.275403i	−0.242158	+	0.970237i	$0.577855\pi$
$410$	2.29078	+	1.32258i	0.113133	+	0.0653176i
$411$		0			0
$412$	−2.39806	+	4.15356i	−0.118144	+	0.204631i
$413$	7.88130	+	13.6508i	0.387814	+	0.671713i
$414$		0			0
$415$	−11.3360			−0.556461
$416$	3.03873	+	1.94065i	0.148986	+	0.0951483i
$417$		0			0
$418$	18.6227	−	10.7518i	0.910866	−	0.525889i
$419$	−7.75488	−	13.4318i	−0.378851	−	0.656188i	0.612045	−	0.790823i	$-0.290347\pi$
$419$	−7.75488	−	13.4318i	−0.378851	−	0.656188i	−0.990895	+	0.134635i	$0.957014\pi$
$420$		0			0
$421$			39.4452i			1.92244i	0.275778	+	0.961221i	$0.411065\pi$
$421$			39.4452i			1.92244i	−0.275778	+	0.961221i	$0.588935\pi$
$422$	−19.4661	−	11.2387i	−0.947594	−	0.547094i
$423$		0			0
$424$		−	5.48693i		−	0.266469i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$	1.07791	−	0.622333i	0.0521639	−	0.0301168i
$428$	3.07180			0.148481
$429$		0			0
$430$	−12.2508			−0.590785
$431$	−1.86621	+	1.07746i	−0.0898921	+	0.0518993i	−0.544272	−	0.838909i	$-0.683194\pi$
$431$	−1.86621	+	1.07746i	−0.0898921	+	0.0518993i	0.454380	+	0.890808i	$0.349861\pi$
$432$		0			0
$433$	0.669689	−	1.15994i	0.0321832	−	0.0557429i	−0.849485	−	0.527612i	$-0.823087\pi$
$433$	0.669689	−	1.15994i	0.0321832	−	0.0557429i	0.881668	+	0.471870i	$0.156421\pi$
$434$			8.06361i			0.387066i
$435$		0			0
$436$	5.79441	+	3.34541i	0.277502	+	0.160216i
$437$		−	19.8564i		−	0.949861i
$438$		0			0
$439$	−15.8490	−	27.4513i	−0.756434	−	1.31018i	−0.944658	−	0.328055i	$-0.893607\pi$
$439$	−15.8490	−	27.4513i	−0.756434	−	1.31018i	0.188225	−	0.982126i	$-0.439727\pi$
$440$	4.62926	−	2.67270i	0.220691	−	0.127416i
$441$		0			0
$442$	0.645159	−	14.4078i	0.0306871	−	0.685308i
$443$	28.0904			1.33461			0.667307	−	0.744782i	$-0.267447\pi$
$443$	28.0904			1.33461			0.667307	+	0.744782i	$0.267447\pi$
$444$		0			0
$445$	−0.869891	−	1.50670i	−0.0412368	−	0.0714242i
$446$	0.689457	−	1.19417i	0.0326467	−	0.0565458i
$447$		0			0
$448$	2.01141	+	1.16129i	0.0950303	+	0.0548658i
$449$	−25.0426	−	14.4583i	−1.18183	−	0.682332i	−0.225395	−	0.974267i	$-0.572367\pi$
$449$	−25.0426	−	14.4583i	−1.18183	−	0.682332i	−0.956438	+	0.291936i	$0.905701\pi$
$450$		0			0
$451$	7.06973	−	12.2451i	0.332900	−	0.576600i
$452$	3.55486	+	6.15720i	0.167206	+	0.289610i
$453$		0			0
$454$	19.3205			0.906756
$455$	4.50732	−	7.05769i	0.211306	−	0.330870i
$456$		0			0
$457$	8.39958	−	4.84950i	0.392916	−	0.226850i	−0.290507	−	0.956873i	$-0.593824\pi$
$457$	8.39958	−	4.84950i	0.392916	−	0.226850i	0.683423	+	0.730023i	$0.260491\pi$
$458$	7.88130	+	13.6508i	0.368269	+	0.637861i
$459$		0			0
$460$		−	4.93593i		−	0.230139i
$461$	−10.3905	−	5.99896i	−0.483934	−	0.279400i	0.238120	−	0.971236i	$-0.423469\pi$
$461$	−10.3905	−	5.99896i	−0.483934	−	0.279400i	−0.722055	+	0.691836i	$0.756802\pi$
$462$		0			0
$463$		−	6.42664i		−	0.298671i	−0.988787	−	0.149336i	$-0.952287\pi$
$463$		−	6.42664i		−	0.298671i	0.988787	−	0.149336i	$-0.0477135\pi$
$464$	2.14539	−	3.71592i	0.0995971	−	0.172507i
$465$		0			0
$466$	14.3370	−	8.27747i	0.664149	−	0.383447i
$467$	−26.2642			−1.21536			−0.607681	−	0.794182i	$-0.707900\pi$
$467$	−26.2642			−1.21536			−0.607681	+	0.794182i	$0.707900\pi$
$468$		0			0
$469$	−9.54409			−0.440705
$470$	−1.57525	+	0.909471i	−0.0726609	+	0.0419508i
$471$		0			0
$472$	−3.39334	+	5.87744i	−0.156191	+	0.270531i
$473$			65.4854i			3.01102i
$474$		0			0
$475$	3.48387	+	2.01141i	0.159851	+	0.0922900i
$476$		−	9.29032i		−	0.425821i
$477$		0			0
$478$	13.1003	+	22.6904i	0.599193	+	1.03783i
$479$	22.2418	−	12.8413i	1.01625	−	0.586735i	0.103237	−	0.994657i	$-0.467080\pi$
$479$	22.2418	−	12.8413i	1.01625	−	0.586735i	0.913017	+	0.407922i	$0.133747\pi$
$480$		0			0
$481$	10.0777	−	5.23182i	0.459502	−	0.238551i
$482$	−15.6496			−0.712818
$483$		0			0
$484$	−8.78668	−	15.2190i	−0.399395	−	0.691772i
$485$	−8.05463	+	13.9510i	−0.365742	+	0.633484i
$486$		0			0
$487$	−8.12238	−	4.68946i	−0.368060	−	0.212500i	0.304551	−	0.952496i	$-0.401494\pi$
$487$	−8.12238	−	4.68946i	−0.368060	−	0.212500i	−0.672611	+	0.739997i	$0.734827\pi$
$488$	0.464102	+	0.267949i	0.0210089	+	0.0121295i
$489$		0			0
$490$	−0.802812	+	1.39051i	−0.0362673	+	0.0628169i
$491$	3.86927	+	6.70177i	0.174618	+	0.302447i	0.940029	−	0.341095i	$-0.110798\pi$
$491$	3.86927	+	6.70177i	0.174618	+	0.302447i	−0.765411	+	0.643541i	$0.777464\pi$
$492$		0			0
$493$	−17.1631			−0.772987
$494$	14.4900	+	0.648841i	0.651935	+	0.0291927i
$495$		0			0
$496$	−3.00670	+	1.73592i	−0.135005	+	0.0779450i
$497$	18.4318	+	31.9249i	0.826781	+	1.43203i
$498$		0			0
$499$		−	3.18106i		−	0.142404i	−0.997462	−	0.0712019i	$-0.977317\pi$
$499$		−	3.18106i		−	0.142404i	0.997462	−	0.0712019i	$-0.0226834\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$		0			0
$502$		−	28.3416i		−	1.26495i
$503$	−17.5379	+	30.3765i	−0.781975	+	1.35442i	0.148814	+	0.988865i	$0.452454\pi$
$503$	−17.5379	+	30.3765i	−0.781975	+	1.35442i	−0.930789	+	0.365556i	$0.880879\pi$
$504$		0			0
$505$	−10.9906	+	6.34541i	−0.489074	+	0.282367i
$506$	−26.3846			−1.17294
$507$		0			0
$508$	−2.13209			−0.0945961
$509$	16.2697	−	9.39334i	0.721144	−	0.416353i	−0.0940298	−	0.995569i	$-0.529975\pi$
$509$	16.2697	−	9.39334i	0.721144	−	0.416353i	0.815173	+	0.579217i	$0.196642\pi$
$510$		0			0
$511$	15.7626	−	27.3016i	0.697297	−	1.20775i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	10.8334	+	6.25465i	0.477839	+	0.275881i
$515$			4.79612i			0.211342i
$516$		0			0
$517$	4.86149	+	8.42035i	0.213808	+	0.370327i
$518$	6.33445	−	3.65720i	0.278320	−	0.160688i
$519$		0			0
$520$	3.60194	+	0.161290i	0.157956	+	0.00707303i
$521$	−5.28512			−0.231545			−0.115773	−	0.993276i	$-0.536934\pi$
$521$	−5.28512			−0.231545			−0.115773	+	0.993276i	$0.536934\pi$
$522$		0			0
$523$	10.3762	+	17.9721i	0.453718	+	0.785863i	0.998614	−	0.0526409i	$-0.0167639\pi$
$523$	10.3762	+	17.9721i	0.453718	+	0.785863i	−0.544895	+	0.838504i	$0.683431\pi$
$524$	−0.629257	+	1.08991i	−0.0274892	+	0.0476127i
$525$		0			0
$526$	−9.27159	−	5.35295i	−0.404260	−	0.233400i
$527$	12.0268	+	6.94367i	0.523895	+	0.302471i
$528$		0			0
$529$	−0.681725	+	1.18078i	−0.0296402	+	0.0513384i
$530$	−2.74346	−	4.75182i	−0.119168	−	0.206406i
$531$		0			0
$532$	9.34333			0.405085
$533$	8.46456	−	4.39438i	0.366641	−	0.190342i
$534$		0			0
$535$	2.66025	−	1.53590i	0.115013	−	0.0664027i
$536$	−2.05463	−	3.55872i	−0.0887465	−	0.153713i
$537$		0			0
$538$		−	7.52522i		−	0.324435i
$539$	7.43284	+	4.29135i	0.320155	+	0.184842i
$540$		0			0
$541$			28.7365i			1.23548i	0.786384	+	0.617739i	$0.211951\pi$
$541$			28.7365i			1.23548i	−0.786384	+	0.617739i	$0.788049\pi$
$542$	4.92434	−	8.52920i	0.211518	−	0.366361i
$543$		0			0
$544$	3.46410	−	2.00000i	0.148522	−	0.0857493i
$545$	6.69081			0.286603
$546$		0			0
$547$	18.3768			0.785737			0.392869	−	0.919595i	$-0.371483\pi$
$547$	18.3768			0.785737			0.392869	+	0.919595i	$0.371483\pi$
$548$	−17.0736	+	9.85744i	−0.729348	+	0.421089i
$549$		0			0
$550$	2.67270	−	4.62926i	0.113964	−	0.197392i
$551$		−	17.2610i		−	0.735345i
$552$		0			0
$553$	16.0264	+	9.25285i	0.681512	+	0.393471i
$554$		−	0.953101i		−	0.0404934i
$555$		0			0
$556$	2.83871	+	4.91679i	0.120388	+	0.208518i
$557$	−22.9831	+	13.2693i	−0.973826	+	0.562238i	−0.900400	−	0.435062i	$-0.856726\pi$
$557$	−22.9831	+	13.2693i	−0.973826	+	0.562238i	−0.0734252	+	0.997301i	$0.523393\pi$
$558$		0			0
$559$	−23.7745	+	37.2268i	−1.00555	+	1.57453i
$560$	2.32258			0.0981469
$561$		0			0
$562$	−2.78668	−	4.82667i	−0.117549	−	0.203601i
$563$	3.03056	−	5.24908i	0.127723	−	0.221222i	−0.795071	−	0.606516i	$-0.792567\pi$
$563$	3.03056	−	5.24908i	0.127723	−	0.221222i	0.922794	+	0.385294i	$0.125900\pi$
$564$		0			0
$565$	6.15720	+	3.55486i	0.259035	+	0.149554i
$566$	19.0642	+	11.0067i	0.801326	+	0.462646i
$567$		0			0
$568$	−7.93593	+	13.7454i	−0.332984	+	0.576746i
$569$	7.24818	+	12.5542i	0.303860	+	0.526300i	0.977007	−	0.213208i	$-0.0683913\pi$
$569$	7.24818	+	12.5542i	0.303860	+	0.526300i	−0.673147	+	0.739509i	$0.735058\pi$
$570$		0			0
$571$	−2.90413			−0.121534			−0.0607670	−	0.998152i	$-0.519355\pi$
$571$	−2.90413			−0.121534			−0.0607670	+	0.998152i	$0.519355\pi$
$572$	0.862160	−	19.2538i	0.0360487	−	0.805044i
$573$		0			0
$574$	5.32051	−	3.07180i	0.222074	−	0.128214i
$575$	−2.46797	−	4.27464i	−0.102921	−	0.178265i
$576$		0			0
$577$			18.8180i			0.783405i	0.920092	+	0.391702i	$0.128114\pi$
$577$			18.8180i			0.783405i	−0.920092	+	0.391702i	$0.871886\pi$
$578$	0.866025	+	0.500000i	0.0360219	+	0.0207973i
$579$		0			0
$580$		−	4.29078i		−	0.178165i
$581$	−13.1643	+	22.8013i	−0.546149	+	0.945958i
$582$		0			0
$583$	−25.4004	+	14.6649i	−1.05198	+	0.607359i
$584$	13.5734			0.561670
$585$		0			0
$586$	−6.84302			−0.282682
$587$	3.40901	−	1.96820i	0.140705	−	0.0812361i	−0.427995	−	0.903781i	$-0.640780\pi$
$587$	3.40901	−	1.96820i	0.140705	−	0.0812361i	0.568700	+	0.822545i	$0.307447\pi$
$588$		0			0
$589$	−6.98329	+	12.0954i	−0.287741	+	0.498383i
$590$			6.78668i			0.279403i
$591$		0			0
$592$	2.72733	+	1.57463i	0.112093	+	0.0647168i
$593$			20.1227i			0.826338i	0.910654	+	0.413169i	$0.135578\pi$
$593$			20.1227i			0.826338i	−0.910654	+	0.413169i	$0.864422\pi$
$594$		0			0
$595$	−4.64516	−	8.04565i	−0.190433	−	0.329840i
$596$	16.8680	−	9.73875i	0.690940	−	0.398915i
$597$		0			0
$598$	−14.9990	−	9.57893i	−0.613353	−	0.391712i
$599$	−48.1172			−1.96601			−0.983007	−	0.183567i	$-0.941236\pi$
$599$	−48.1172			−1.96601			−0.983007	+	0.183567i	$0.941236\pi$
$600$		0			0
$601$	2.12109	+	3.67383i	0.0865209	+	0.149859i	0.906038	−	0.423196i	$-0.139092\pi$
$601$	2.12109	+	3.67383i	0.0865209	+	0.149859i	−0.819517	+	0.573054i	$0.805758\pi$
$602$	−14.2267	+	24.6414i	−0.579837	+	1.00431i
$603$		0			0
$604$	−12.5721	−	7.25851i	−0.511552	−	0.295345i
$605$	−15.2190	−	8.78668i	−0.618739	−	0.357229i
$606$		0			0
$607$	−6.03424	+	10.4516i	−0.244922	+	0.424218i	−0.962110	−	0.272663i	$-0.912096\pi$
$607$	−6.03424	+	10.4516i	−0.244922	+	0.424218i	0.717188	+	0.696880i	$0.245429\pi$
$608$	2.01141	+	3.48387i	0.0815736	+	0.141290i
$609$		0			0
$610$	0.535898			0.0216979
$611$	−0.293377	+	6.55172i	−0.0118688	+	0.265054i
$612$		0			0
$613$	36.1497	−	20.8711i	1.46007	−	0.842974i	0.461060	−	0.887369i	$-0.347469\pi$
$613$	36.1497	−	20.8711i	1.46007	−	0.842974i	0.999014	+	0.0443946i	$0.0141359\pi$
$614$	2.37721	+	4.11745i	0.0959364	+	0.166167i
$615$		0			0
$616$		−	12.4151i		−	0.500220i
$617$	28.9760	+	16.7293i	1.16653	+	0.673497i	0.952860	−	0.303409i	$-0.0981249\pi$
$617$	28.9760	+	16.7293i	1.16653	+	0.673497i	0.213670	+	0.976906i	$0.431458\pi$
$618$		0			0
$619$		−	38.0978i		−	1.53128i	−0.643270	−	0.765639i	$-0.722423\pi$
$619$		−	38.0978i		−	1.53128i	0.643270	−	0.765639i	$-0.277577\pi$
$620$	−1.73592	+	3.00670i	−0.0697161	+	0.120752i
$621$		0			0
$622$	−1.67696	+	0.968196i	−0.0672401	+	0.0388211i
$623$	−4.04078			−0.161891
$624$		0			0
$625$	1.00000			0.0400000
$626$	22.1308	−	12.7772i	0.884526	−	0.510681i
$627$		0			0
$628$	12.1914	−	21.1162i	0.486491	−	0.842628i
$629$		−	12.5970i		−	0.502276i
$630$		0			0
$631$	−21.4775	−	12.4000i	−0.855005	−	0.493638i	0.00733109	−	0.999973i	$-0.497666\pi$
$631$	−21.4775	−	12.4000i	−0.855005	−	0.493638i	−0.862337	+	0.506335i	$0.831000\pi$
$632$			7.96774i			0.316940i
$633$		0			0
$634$	−6.33337	−	10.9697i	−0.251530	−	0.435663i
$635$	−1.84644	+	1.06604i	−0.0732738	+	0.0423046i
$636$		0			0
$637$	2.66741	+	5.13802i	0.105686	+	0.203576i
$638$	−22.9359			−0.908042
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−2.04259	+	3.53788i	−0.0806776	+	0.139738i	−0.903541	−	0.428501i	$-0.859042\pi$
$641$	−2.04259	+	3.53788i	−0.0806776	+	0.139738i	0.822864	+	0.568239i	$0.192375\pi$
$642$		0			0
$643$	−31.6806	−	18.2908i	−1.24936	−	0.721318i	−0.278377	−	0.960472i	$-0.589797\pi$
$643$	−31.6806	−	18.2908i	−1.24936	−	0.721318i	−0.970982	+	0.239154i	$0.923130\pi$
$644$	−9.92820	−	5.73205i	−0.391226	−	0.225874i
$645$		0			0
$646$	8.04565	−	13.9355i	0.316552	−	0.548284i
$647$	−8.61704	−	14.9251i	−0.338771	−	0.586768i	0.645431	−	0.763818i	$-0.276678\pi$
$647$	−8.61704	−	14.9251i	−0.338771	−	0.586768i	−0.984202	+	0.177050i	$0.943344\pi$
$648$		0			0
$649$	36.2776			1.42402
$650$	3.20002	−	1.66129i	0.125515	−	0.0651611i
$651$		0			0
$652$	20.4614	−	11.8134i	0.801329	−	0.462647i
$653$	−10.9637	−	18.9897i	−0.429042	−	0.743123i	0.567746	−	0.823204i	$-0.307816\pi$
$653$	−10.9637	−	18.9897i	−0.429042	−	0.743123i	−0.996788	+	0.0800806i	$0.974482\pi$
$654$		0			0
$655$			1.25851i			0.0491742i
$656$	2.29078	+	1.32258i	0.0894397	+	0.0516381i
$657$		0			0
$658$			4.22464i			0.164694i
$659$	−24.2379	+	41.9813i	−0.944176	+	1.63536i	−0.186783	+	0.982401i	$0.559806\pi$
$659$	−24.2379	+	41.9813i	−0.944176	+	1.63536i	−0.757393	+	0.652960i	$0.773527\pi$
$660$		0			0
$661$	−25.8267	+	14.9110i	−1.00454	+	0.579972i	−0.909589	−	0.415510i	$-0.863603\pi$
$661$	−25.8267	+	14.9110i	−1.00454	+	0.579972i	−0.0949524	+	0.995482i	$0.530270\pi$
$662$	−23.6981			−0.921052
$663$		0			0
$664$	−11.3360			−0.439921
$665$	8.09156	−	4.67167i	0.313777	−	0.181159i
$666$		0			0
$667$	−10.5895	+	18.3415i	−0.410027	+	0.710187i
$668$			16.7471i			0.647967i
$669$		0			0
$670$	−3.55872	−	2.05463i	−0.137486	−	0.0793773i
$671$		−	2.86459i		−	0.110586i
$672$		0			0
$673$	−15.3360	−	26.5627i	−0.591158	−	1.02392i	−0.994077	−	0.108680i	$-0.965338\pi$
$673$	−15.3360	−	26.5627i	−0.591158	−	1.02392i	0.402919	−	0.915236i	$-0.367996\pi$
$674$	16.9355	−	9.77770i	0.652330	−	0.376623i
$675$		0			0
$676$	7.48023	−	10.6323i	0.287701	−	0.408935i
$677$	−21.0831			−0.810290			−0.405145	−	0.914252i	$-0.632779\pi$
$677$	−21.0831			−0.810290			−0.405145	+	0.914252i	$0.632779\pi$
$678$		0			0
$679$	18.7075	+	32.4024i	0.717929	+	1.24349i
$680$	2.00000	−	3.46410i	0.0766965	−	0.132842i
$681$		0			0
$682$	16.0720	+	9.27918i	0.615429	+	0.355318i
$683$	11.5493	+	6.66799i	0.441921	+	0.255143i	0.704412	−	0.709791i	$-0.251211\pi$
$683$	11.5493	+	6.66799i	0.441921	+	0.255143i	−0.262491	+	0.964934i	$0.584544\pi$
$684$		0			0
$685$	−9.85744	+	17.0736i	−0.376634	+	0.652348i
$686$	9.99362	+	17.3095i	0.381558	+	0.660878i
$687$		0			0
$688$	−12.2508			−0.467057
$689$	−19.7636	−	0.884986i	−0.752933	−	0.0337153i
$690$		0			0
$691$	−30.2289	+	17.4527i	−1.14996	+	0.663932i	−0.948878	−	0.315642i	$-0.897780\pi$
$691$	−30.2289	+	17.4527i	−1.14996	+	0.663932i	−0.201085	+	0.979574i	$0.564447\pi$
$692$	8.06604	+	13.9708i	0.306625	+	0.531090i
$693$		0			0
$694$			23.0375i			0.874490i
$695$	4.91679	+	2.83871i	0.186504	+	0.107678i
$696$		0			0
$697$		−	10.5806i		−	0.400770i
$698$	7.66025	−	13.2679i	0.289945	−	0.502199i
$699$		0			0
$700$	2.01141	−	1.16129i	0.0760243	−	0.0438926i
$701$	−39.6715			−1.49837			−0.749186	−	0.662360i	$-0.769555\pi$
$701$	−39.6715			−1.49837			−0.749186	+	0.662360i	$0.769555\pi$
$702$		0			0
$703$	12.6689			0.477817
$704$	4.62926	−	2.67270i	0.174472	−	0.100731i
$705$		0			0
$706$	−14.2039	+	24.6018i	−0.534570	+	0.925903i
$707$			29.4754i			1.10854i
$708$		0			0
$709$	2.45467	+	1.41720i	0.0921869	+	0.0532242i	0.545385	−	0.838186i	$-0.316384\pi$
$709$	2.45467	+	1.41720i	0.0921869	+	0.0532242i	−0.453198	+	0.891410i	$0.649717\pi$
$710$			15.8719i			0.595661i
$711$		0			0
$712$	−0.869891	−	1.50670i	−0.0326005	−	0.0564658i
$713$	14.8409	−	8.56837i	0.555794	−	0.320888i
$714$		0			0
$715$	−8.88027	−	17.1054i	−0.332103	−	0.639706i
$716$	−7.32824			−0.273869
$717$		0			0
$718$	11.7867	+	20.4151i	0.439875	+	0.761886i
$719$	21.8564	−	37.8564i	0.815106	−	1.41181i	−0.0941451	−	0.995558i	$-0.530012\pi$
$719$	21.8564	−	37.8564i	0.815106	−	1.41181i	0.909251	−	0.416247i	$-0.136655\pi$
$720$		0			0
$721$	9.64697	+	5.56968i	0.359272	+	0.207426i
$722$	−2.43948	−	1.40844i	−0.0907881	−	0.0524165i
$723$		0			0
$724$	−9.78668	+	16.9510i	−0.363719	+	0.629980i
$725$	−2.14539	−	3.71592i	−0.0796777	−	0.138006i
$726$		0			0
$727$	−16.2568			−0.602932			−0.301466	−	0.953477i	$-0.597476\pi$
$727$	−16.2568			−0.602932			−0.301466	+	0.953477i	$0.597476\pi$
$728$	4.50732	−	7.05769i	0.167052	−	0.261575i
$729$		0			0
$730$	11.7549	−	6.78668i	0.435068	−	0.251186i
$731$	24.5016	+	42.4380i	0.906223	+	1.56962i
$732$		0			0
$733$		−	4.96774i		−	0.183488i	−0.995783	−	0.0917438i	$-0.970756\pi$
$733$		−	4.96774i		−	0.183488i	0.995783	−	0.0917438i	$-0.0292441\pi$
$734$	−23.8078	−	13.7454i	−0.878762	−	0.507354i
$735$		0			0
$736$		−	4.93593i		−	0.181941i
$737$	−10.9828	+	19.0228i	−0.404558	+	0.700715i
$738$		0			0
$739$	43.0306	−	24.8437i	1.58291	−	0.913892i	0.588475	−	0.808515i	$-0.299729\pi$
$739$	43.0306	−	24.8437i	1.58291	−	0.913892i	0.994432	−	0.105377i	$-0.0336048\pi$
$740$	3.14925			0.115769
$741$		0			0
$742$	−12.7438			−0.467841
$743$	−18.6559	+	10.7710i	−0.684420	+	0.395150i	−0.801518	−	0.597970i	$-0.795974\pi$
$743$	−18.6559	+	10.7710i	−0.684420	+	0.395150i	0.117098	+	0.993120i	$0.462641\pi$
$744$		0			0
$745$	9.73875	−	16.8680i	0.356800	−	0.617996i
$746$			26.3421i			0.964452i
$747$		0			0
$748$	−18.5170	−	10.6908i	−0.677050	−	0.390895i
$749$		−	7.13449i		−	0.260689i
$750$		0			0
$751$	−3.17436	−	5.49816i	−0.115834	−	0.200631i	0.802279	−	0.596950i	$-0.203621\pi$
$751$	−3.17436	−	5.49816i	−0.115834	−	0.200631i	−0.918113	+	0.396319i	$0.870287\pi$
$752$	−1.57525	+	0.909471i	−0.0574435	+	0.0331650i
$753$		0			0
$754$	−13.0385	−	8.32690i	−0.474834	−	0.303248i
$755$	−14.5170			−0.528329
$756$		0			0
$757$	24.0554	+	41.6651i	0.874307	+	1.51434i	0.857499	+	0.514485i	$0.172017\pi$
$757$	24.0554	+	41.6651i	0.874307	+	1.51434i	0.0168078	+	0.999859i	$0.494650\pi$
$758$	0.224275	−	0.388456i	0.00814604	−	0.0141094i
$759$		0			0
$760$	3.48387	+	2.01141i	0.126373	+	0.0729616i
$761$	−29.1734	−	16.8433i	−1.05754	−	0.610569i	−0.132786	−	0.991145i	$-0.542392\pi$
$761$	−29.1734	−	16.8433i	−1.05754	−	0.610569i	−0.924750	+	0.380576i	$0.875726\pi$
$762$		0			0
$763$	7.76997	−	13.4580i	0.281292	−	0.487212i
$764$	8.51873	+	14.7549i	0.308197	+	0.533813i
$765$		0			0
$766$	−12.1227			−0.438009
$767$	20.6229	+	13.1706i	0.744649	+	0.475562i
$768$		0			0
$769$	−5.18651	+	2.99443i	−0.187030	+	0.107982i	−0.590592	−	0.806971i	$-0.701106\pi$
$769$	−5.18651	+	2.99443i	−0.187030	+	0.107982i	0.403561	+	0.914953i	$0.367772\pi$
$770$	−6.20757	−	10.7518i	−0.223705	−	0.387469i
$771$		0			0
$772$		−	6.15491i		−	0.221520i
$773$	−11.6811	−	6.74409i	−0.420140	−	0.242568i	0.274997	−	0.961445i	$-0.411323\pi$
$773$	−11.6811	−	6.74409i	−0.420140	−	0.242568i	−0.695137	+	0.718877i	$0.744656\pi$
$774$		0			0
$775$			3.47183i			0.124712i
$776$	−8.05463	+	13.9510i	−0.289144	+	0.500813i
$777$		0			0
$778$	−16.1249	+	9.30974i	−0.578107	+	0.333770i
$779$	10.6410			0.381254
$780$		0			0
$781$	84.8416			3.03587
$782$	−17.0986	+	9.87187i	−0.611444	+	0.353017i
$783$		0			0
$784$	−0.802812	+	1.39051i	−0.0286718	+	0.0496611i
$785$		−	24.3829i		−	0.870262i
$786$		0			0
$787$	−47.3272	−	27.3244i	−1.68703	−	0.974009i	−0.956772	−	0.290841i	$-0.906065\pi$
$787$	−47.3272	−	27.3244i	−1.68703	−	0.974009i	−0.730261	−	0.683168i	$-0.760602\pi$
$788$		−	13.7867i		−	0.491130i
$789$		0			0
$790$	3.98387	+	6.90026i	0.141740	+	0.245500i
$791$	14.3006	−	8.25644i	0.508470	−	0.293565i
$792$		0			0
$793$	1.03999	−	1.62845i	0.0369312	−	0.0578279i
$794$	11.3042			0.401170
$795$		0			0
$796$	−1.14152	−	1.97717i	−0.0404602	−	0.0700791i
$797$	19.1622	−	33.1899i	0.678760	−	1.17565i	−0.296595	−	0.955003i	$-0.595851\pi$
$797$	19.1622	−	33.1899i	0.678760	−	1.17565i	0.975355	−	0.220643i	$-0.0708155\pi$
$798$		0			0
$799$	6.30100	+	3.63788i	0.222913	+	0.128699i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	0.752899	−	1.30406i	0.0265858	−	0.0460479i
$803$	−36.2776	−	62.8346i	−1.28021	−	2.21738i
$804$		0			0
$805$	−11.4641			−0.404056
$806$	5.76772	+	11.1099i	0.203159	+	0.391331i
$807$		0			0
$808$	−10.9906	+	6.34541i	−0.386647	+	0.223231i
$809$	5.69081	+	9.85677i	0.200078	+	0.346546i	0.948553	−	0.316617i	$-0.102547\pi$
$809$	5.69081	+	9.85677i	0.200078	+	0.346546i	−0.748475	+	0.663163i	$0.769214\pi$
$810$		0			0
$811$			10.8899i			0.382397i	0.981551	+	0.191198i	$0.0612374\pi$
$811$			10.8899i			0.382397i	−0.981551	+	0.191198i	$0.938763\pi$
$812$	−8.63052	−	4.98283i	−0.302872	−	0.174863i
$813$		0			0
$814$		−	16.8340i		−	0.590033i
$815$	11.8134	−	20.4614i	0.413804	−	0.716730i
$816$		0			0
$817$	−42.6801	+	24.6414i	−1.49319	+	0.862093i
$818$	11.1394			0.389479
$819$		0			0
$820$	2.64516			0.0923730
$821$	1.46194	−	0.844051i	0.0510220	−	0.0294576i	−0.474272	−	0.880378i	$-0.657289\pi$
$821$	1.46194	−	0.844051i	0.0510220	−	0.0294576i	0.525294	+	0.850921i	$0.323955\pi$
$822$		0			0
$823$	3.38908	−	5.87006i	0.118136	−	0.204617i	−0.800893	−	0.598807i	$-0.795641\pi$
$823$	3.38908	−	5.87006i	0.118136	−	0.204617i	0.919029	+	0.394190i	$0.128975\pi$
$824$			4.79612i			0.167081i
$825$		0			0
$826$	13.6508	+	7.88130i	0.474973	+	0.274226i
$827$		−	30.2298i		−	1.05119i	−0.850733	−	0.525597i	$-0.823842\pi$
$827$		−	30.2298i		−	1.05119i	0.850733	−	0.525597i	$-0.176158\pi$
$828$		0			0
$829$	−5.22023	−	9.04170i	−0.181306	−	0.314031i	0.761020	−	0.648729i	$-0.224699\pi$
$829$	−5.22023	−	9.04170i	−0.181306	−	0.314031i	−0.942326	+	0.334698i	$0.891366\pi$
$830$	−9.81724	+	5.66799i	−0.340761	+	0.196739i
$831$		0			0
$832$	3.60194	+	0.161290i	0.124875	+	0.00559172i
$833$	6.42249			0.222526
$834$		0			0
$835$	8.37357	+	14.5035i	0.289779	+	0.501913i
$836$	10.7518	−	18.6227i	0.371859	−	0.644079i
$837$		0			0
$838$	−13.4318	−	7.75488i	−0.463995	−	0.267888i
$839$	−9.69647	−	5.59826i	−0.334759	−	0.193273i	0.323193	−	0.946333i	$-0.395244\pi$
$839$	−9.69647	−	5.59826i	−0.334759	−	0.193273i	−0.657952	+	0.753060i	$0.728577\pi$
$840$		0			0
$841$	5.29462	−	9.17056i	0.182573	−	0.316226i
$842$	19.7226	+	34.1606i	0.679686	+	1.17725i
$843$		0			0
$844$	−22.4775			−0.773707
$845$	1.16191	−	12.9480i	0.0399710	−	0.445424i
$846$		0			0
$847$	−35.3473	+	20.4078i	−1.21455	+	0.701219i
$848$	−2.74346	−	4.75182i	−0.0942109	−	0.163178i
$849$		0			0
$850$		−	4.00000i		−	0.137199i
$851$	−13.4619	−	7.77225i	−0.461469	−	0.266429i
$852$		0			0
$853$		−	21.8185i		−	0.747051i	−0.927620	−	0.373525i	$-0.878149\pi$
$853$		−	21.8185i		−	0.747051i	0.927620	−	0.373525i	$-0.121851\pi$
$854$	0.622333	−	1.07791i	0.0212958	−	0.0368854i
$855$		0			0
$856$	2.66025	−	1.53590i	0.0909256	−	0.0524959i
$857$	9.42369			0.321907			0.160954	−	0.986962i	$-0.448543\pi$
$857$	9.42369			0.321907			0.160954	+	0.986962i	$0.448543\pi$
$858$		0			0
$859$	24.4775			0.835161			0.417581	−	0.908640i	$-0.362878\pi$
$859$	24.4775			0.835161			0.417581	+	0.908640i	$0.362878\pi$
$860$	−10.6095	+	6.12539i	−0.361781	+	0.208874i
$861$		0			0
$862$	−1.07746	+	1.86621i	−0.0366983	+	0.0635633i
$863$		−	29.7873i		−	1.01397i	−0.861954	−	0.506986i	$-0.830760\pi$
$863$		−	29.7873i		−	1.01397i	0.861954	−	0.506986i	$-0.169240\pi$
$864$		0			0
$865$	13.9708	+	8.06604i	0.475021	+	0.274254i
$866$		−	1.33938i		−	0.0455139i
$867$		0			0
$868$	4.03180	+	6.98329i	0.136848	+	0.237028i
$869$	36.8847	−	21.2954i	1.25123	−	0.722397i
$870$		0			0
$871$	−13.1497	+	6.82667i	−0.445561	+	0.231313i
$872$	6.69081			0.226579
$873$		0			0
$874$	−9.92820	−	17.1962i	−0.335826	−	0.581669i
$875$	1.16129	−	2.01141i	0.0392588	−	0.0679982i
$876$		0			0
$877$	1.65393	+	0.954895i	0.0558491	+	0.0322445i	0.527665	−	0.849453i	$-0.323068\pi$
$877$	1.65393	+	0.954895i	0.0558491	+	0.0322445i	−0.471815	+	0.881697i	$0.656401\pi$
$878$	−27.4513	−	15.8490i	−0.926438	−	0.534879i
$879$		0			0
$880$	2.67270	−	4.62926i	0.0900968	−	0.156052i
$881$	−3.18412	−	5.51505i	−0.107276	−	0.185807i	0.807390	−	0.590018i	$-0.200879\pi$
$881$	−3.18412	−	5.51505i	−0.107276	−	0.185807i	−0.914666	+	0.404211i	$0.867546\pi$
$882$		0			0
$883$	−34.9897			−1.17750			−0.588749	−	0.808316i	$-0.700379\pi$
$883$	−34.9897			−1.17750			−0.588749	+	0.808316i	$0.700379\pi$
$884$	−6.64516	−	12.8001i	−0.223501	−	0.430513i
$885$		0			0
$886$	24.3270	−	14.0452i	0.817281	−	0.471858i
$887$	10.7001	+	18.5331i	0.359273	+	0.622279i	0.987840	−	0.155477i	$-0.0496914\pi$
$887$	10.7001	+	18.5331i	0.359273	+	0.622279i	−0.628567	+	0.777756i	$0.716358\pi$
$888$		0			0
$889$			4.95194i			0.166083i
$890$	−1.50670	−	0.869891i	−0.0505046	−	0.0291588i
$891$		0			0
$892$		−	1.37891i		−	0.0461694i
$893$	−3.65864	+	6.33696i	−0.122432	+	0.212058i
$894$		0			0
$895$	−6.34644	+	3.66412i	−0.212138	+	0.122478i
$896$	2.32258			0.0775919
$897$		0			0
$898$	−28.9167			−0.964963
$899$	12.9011	−	7.44843i	0.430274	−	0.248419i
$900$		0			0
$901$	−10.9739	+	19.0073i	−0.365592	+	0.633224i
$902$		−	14.1395i		−	0.470792i
$903$		0			0
$904$	6.15720	+	3.55486i	0.204785	+	0.118233i
$905$			19.5734i			0.650641i
$906$		0			0
$907$	16.2347	+	28.1192i	0.539063	+	0.933684i	0.998955	+	0.0457093i	$0.0145548\pi$
$907$	16.2347	+	28.1192i	0.539063	+	0.933684i	−0.459892	+	0.887975i	$0.652112\pi$
$908$	16.7321	−	9.66025i	0.555273	−	0.320587i
$909$		0			0
$910$	0.374609	−	8.36580i	0.0124182	−	0.277323i
$911$	−34.4380			−1.14098			−0.570490	−	0.821304i	$-0.693247\pi$
$911$	−34.4380			−1.14098			−0.570490	+	0.821304i	$0.693247\pi$
$912$		0			0
$913$	30.2977	+	52.4771i	1.00271	+	1.73674i
$914$	4.84950	−	8.39958i	0.160407	−	0.277833i
$915$		0			0
$916$	13.6508	+	7.88130i	0.451036	+	0.260406i
$917$	2.53139	+	1.46150i	0.0835939	+	0.0482630i
$918$		0			0
$919$	−18.2413	+	31.5949i	−0.601727	+	1.04222i	0.390833	+	0.920462i	$0.372187\pi$
$919$	−18.2413	+	31.5949i	−0.601727	+	1.04222i	−0.992560	+	0.121759i	$0.961146\pi$
$920$	−2.46797	−	4.27464i	−0.0813665	−	0.140931i
$921$		0			0
$922$	−11.9979			−0.395131
$923$	48.2303	+	30.8018i	1.58752	+	1.01385i
$924$		0			0
$925$	2.72733	−	1.57463i	0.0896742	−	0.0517734i
$926$	−3.21332	−	5.56563i	−0.105596	−	0.182898i
$927$		0			0
$928$		−	4.29078i		−	0.140852i
$929$	−43.2233	−	24.9550i	−1.41811	−	0.818747i	−0.421978	−	0.906606i	$-0.638664\pi$
$929$	−43.2233	−	24.9550i	−1.41811	−	0.818747i	−0.996133	+	0.0878597i	$0.971997\pi$
$930$		0			0
$931$			6.45914i			0.211690i
$932$	8.27747	−	14.3370i	0.271138	−	0.469624i
$933$		0			0
$934$	−22.7454	+	13.1321i	−0.744254	+	0.429695i
$935$	−21.3816			−0.699254
$936$		0			0
$937$	−15.8873			−0.519017			−0.259508	−	0.965741i	$-0.583560\pi$
$937$	−15.8873			−0.519017			−0.259508	+	0.965741i	$0.583560\pi$
$938$	−8.26542	+	4.77204i	−0.269876	+	0.155813i
$939$		0			0
$940$	−0.909471	+	1.57525i	−0.0296637	+	0.0513790i
$941$			6.99273i			0.227956i	0.993483	+	0.113978i	$0.0363594\pi$
$941$			6.99273i			0.227956i	−0.993483	+	0.113978i	$0.963641\pi$
$942$		0			0
$943$	−11.3071	−	6.52817i	−0.368210	−	0.212586i
$944$			6.78668i			0.220888i
$945$		0			0
$946$	32.7427	+	56.7120i	1.06456	+	1.84387i
$947$	45.2987	−	26.1532i	1.47201	−	0.849865i	0.472505	−	0.881328i	$-0.343350\pi$
$947$	45.2987	−	26.1532i	1.47201	−	0.849865i	0.999505	+	0.0314631i	$0.0100167\pi$
$948$		0			0
$949$	2.18925	−	48.8905i	0.0710659	−	1.58705i
$950$	4.02283			0.130518
$951$		0			0
$952$	−4.64516	−	8.04565i	−0.150550	−	0.260761i
$953$	−14.4414	+	25.0132i	−0.467802	+	0.810256i	−0.999323	−	0.0367885i	$-0.988287\pi$
$953$	−14.4414	+	25.0132i	−0.467802	+	0.810256i	0.531521	+	0.847045i	$0.321621\pi$
$954$		0			0
$955$	14.7549	+	8.51873i	0.477457	+	0.275660i
$956$	22.6904	+	13.1003i	0.733859	+	0.423693i
$957$		0			0
$958$	12.8413	−	22.2418i	0.414884	−	0.718600i
$959$	22.8947	+	39.6548i	0.739308	+	1.28052i
$960$		0			0
$961$	18.9464			0.611173
$962$	6.11160	−	9.56973i	0.197046	−	0.308540i
$963$		0			0
$964$	−13.5529	+	7.82479i	−0.436510	+	0.252019i
$965$	−3.07746	−	5.33031i	−0.0990668	−	0.171589i
$966$		0			0
$967$		−	10.8610i		−	0.349265i	−0.984634	−	0.174633i	$-0.944126\pi$
$967$		−	10.8610i		−	0.349265i	0.984634	−	0.174633i	$-0.0558738\pi$
$968$	−15.2190	−	8.78668i	−0.489156	−	0.282415i
$969$		0			0
$970$			16.1093i			0.517237i
$971$	−12.4990	+	21.6488i	−0.401111	+	0.694744i	−0.993860	−	0.110643i	$-0.964709\pi$
$971$	−12.4990	+	21.6488i	−0.401111	+	0.694744i	0.592749	+	0.805387i	$0.298042\pi$
$972$		0			0
$973$	11.4196	−	6.59313i	0.366097	−	0.211366i
$974$	−9.37891			−0.300520
$975$		0			0
$976$	0.535898			0.0171537
$977$	37.0359	−	21.3827i	1.18488	−	0.684092i	0.227743	−	0.973721i	$-0.426865\pi$
$977$	37.0359	−	21.3827i	1.18488	−	0.684092i	0.957139	+	0.289629i	$0.0935321\pi$
$978$		0			0
$979$	−4.64992	+	8.05390i	−0.148612	+	0.257404i
$980$			1.60562i			0.0512898i
$981$		0			0
$982$	6.70177	+	3.86927i	0.213862	+	0.123473i
$983$		−	10.1288i		−	0.323058i	−0.986868	−	0.161529i	$-0.948358\pi$
$983$		−	10.1288i		−	0.323058i	0.986868	−	0.161529i	$-0.0516425\pi$
$984$		0			0
$985$	−6.89334	−	11.9396i	−0.219640	−	0.380428i
$986$	−14.8637	+	8.58155i	−0.473356	+	0.273292i
$987$		0			0
$988$	12.8731	−	6.68308i	0.409548	−	0.212617i
$989$	60.4691			1.92280
$990$		0			0
$991$	−10.1241	−	17.5355i	−0.321604	−	0.557035i	0.659215	−	0.751954i	$-0.270889\pi$
$991$	−10.1241	−	17.5355i	−0.321604	−	0.557035i	−0.980819	+	0.194920i	$0.937555\pi$
$992$	−1.73592	+	3.00670i	−0.0551154	+	0.0954627i
$993$		0			0
$994$	31.9249	+	18.4318i	1.01260	+	0.584622i
$995$	−1.97717	−	1.14152i	−0.0626806	−	0.0361887i
$996$		0			0
$997$	10.3981	−	18.0100i	0.329310	−	0.570381i	−0.653065	−	0.757302i	$-0.726517\pi$
$997$	10.3981	−	18.0100i	0.329310	−	0.570381i	0.982375	+	0.186920i	$0.0598506\pi$
$998$	−1.59053	−	2.75488i	−0.0503473	−	0.0872041i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.f.361.3		8
3.2	odd	2		390.2.bb.c.361.1	yes	8
13.4	even	6	inner	1170.2.bs.f.901.3		8
15.2	even	4		1950.2.y.j.49.2		8
15.8	even	4		1950.2.y.k.49.3		8
15.14	odd	2		1950.2.bc.g.751.4		8
39.2	even	12		5070.2.a.bz.1.2		4
39.11	even	12		5070.2.a.ca.1.3		4
39.17	odd	6		390.2.bb.c.121.1	✓	8
39.23	odd	6		5070.2.b.ba.1351.6		8
39.29	odd	6		5070.2.b.ba.1351.3		8
195.17	even	12		1950.2.y.k.199.3		8
195.134	odd	6		1950.2.bc.g.901.4		8
195.173	even	12		1950.2.y.j.199.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.1	✓	8	39.17	odd	6
390.2.bb.c.361.1	yes	8	3.2	odd	2
1170.2.bs.f.361.3		8	1.1	even	1	trivial
1170.2.bs.f.901.3		8	13.4	even	6	inner
1950.2.y.j.49.2		8	15.2	even	4
1950.2.y.j.199.2		8	195.173	even	12
1950.2.y.k.49.3		8	15.8	even	4
1950.2.y.k.199.3		8	195.17	even	12
1950.2.bc.g.751.4		8	15.14	odd	2
1950.2.bc.g.901.4		8	195.134	odd	6
5070.2.a.bz.1.2		4	39.2	even	12
5070.2.a.ca.1.3		4	39.11	even	12
5070.2.b.ba.1351.3		8	39.29	odd	6
5070.2.b.ba.1351.6		8	39.23	odd	6

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-2.01141 - 1.16129i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-2.01141 - 1.16129i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-4.62926 + 2.67270i) q^{11} +(-3.60194 - 0.161290i) q^{13} -2.32258 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-3.48387 - 2.01141i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-2.67270 + 4.62926i) q^{22} +(2.46797 + 4.27464i) q^{23} -1.00000 q^{25} +(-3.20002 + 1.66129i) q^{26} +(-2.01141 + 1.16129i) q^{28} +(2.14539 + 3.71592i) q^{29} -3.47183i q^{31} +(-0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(-1.16129 + 2.01141i) q^{35} +(-2.72733 + 1.57463i) q^{37} -4.02283 q^{38} -1.00000 q^{40} +(-2.29078 + 1.32258i) q^{41} +(6.12539 - 10.6095i) q^{43} +5.34541i q^{44} +(4.27464 + 2.46797i) q^{46} -1.81894i q^{47} +(-0.802812 - 1.39051i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-1.94065 + 3.03873i) q^{52} +5.48693 q^{53} +(2.67270 + 4.62926i) q^{55} +(-1.16129 + 2.01141i) q^{56} +(3.71592 + 2.14539i) q^{58} +(-5.87744 - 3.39334i) q^{59} +(-0.267949 + 0.464102i) q^{61} +(-1.73592 - 3.00670i) q^{62} -1.00000 q^{64} +(-0.161290 + 3.60194i) q^{65} +(3.55872 - 2.05463i) q^{67} +(2.00000 + 3.46410i) q^{68} +2.32258i q^{70} +(-13.7454 - 7.93593i) q^{71} +13.5734i q^{73} +(-1.57463 + 2.72733i) q^{74} +(-3.48387 + 2.01141i) q^{76} +12.4151 q^{77} -7.96774 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-1.32258 + 2.29078i) q^{82} -11.3360i q^{83} +(3.46410 + 2.00000i) q^{85} -12.2508i q^{86} +(2.67270 + 4.62926i) q^{88} +(1.50670 - 0.869891i) q^{89} +(7.05769 + 4.50732i) q^{91} +4.93593 q^{92} +(-0.909471 - 1.57525i) q^{94} +(-2.01141 + 3.48387i) q^{95} +(-13.9510 - 8.05463i) q^{97} +(-1.39051 - 0.802812i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 4 q^{10} - 6 q^{11} - 12 q^{13} - 4 q^{14} - 4 q^{16} - 16 q^{17} - 6 q^{19} + 2 q^{22} - 4 q^{23} - 8 q^{25} + 12 q^{26} + 8 q^{29} - 2 q^{35} + 30 q^{37} - 8 q^{40} + 14 q^{43} - 6 q^{46} + 14 q^{49} - 6 q^{52} - 16 q^{53} - 2 q^{55} - 2 q^{56} - 6 q^{58} - 24 q^{59} - 16 q^{61} - 4 q^{62} - 8 q^{64} + 6 q^{65} + 24 q^{67} + 16 q^{68} + 12 q^{71} - 10 q^{74} - 6 q^{76} - 16 q^{77} - 20 q^{79} + 4 q^{82} - 2 q^{88} - 42 q^{89} - 10 q^{91} - 8 q^{92} - 8 q^{94} - 24 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^10 - 6 * q^11 - 12 * q^13 - 4 * q^14 - 4 * q^16 - 16 * q^17 - 6 * q^19 + 2 * q^22 - 4 * q^23 - 8 * q^25 + 12 * q^26 + 8 * q^29 - 2 * q^35 + 30 * q^37 - 8 * q^40 + 14 * q^43 - 6 * q^46 + 14 * q^49 - 6 * q^52 - 16 * q^53 - 2 * q^55 - 2 * q^56 - 6 * q^58 - 24 * q^59 - 16 * q^61 - 4 * q^62 - 8 * q^64 + 6 * q^65 + 24 * q^67 + 16 * q^68 + 12 * q^71 - 10 * q^74 - 6 * q^76 - 16 * q^77 - 20 * q^79 + 4 * q^82 - 2 * q^88 - 42 * q^89 - 10 * q^91 - 8 * q^92 - 8 * q^94 - 24 * q^97 - 48 * q^98

Introduction

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