LMFDB - Embedded newform 804.2.i.b.565.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(37,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("804.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.i (of order $3$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			565.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	804.565
Dual form			804.2.i.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +2.00000 q^{5} +(-2.50000 - 4.33013i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +2.00000 q^{5} +(-2.50000 - 4.33013i) q^{7} +1.00000 q^{9} +(-2.50000 - 4.33013i) q^{11} +(-1.50000 + 2.59808i) q^{13} -2.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(2.50000 + 4.33013i) q^{21} +(-1.50000 + 2.59808i) q^{23} -1.00000 q^{25} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +(-2.50000 - 4.33013i) q^{31} +(2.50000 + 4.33013i) q^{33} +(-5.00000 - 8.66025i) q^{35} +(2.50000 - 4.33013i) q^{37} +(1.50000 - 2.59808i) q^{39} +(-5.50000 - 9.52628i) q^{41} +4.00000 q^{43} +2.00000 q^{45} +(1.50000 + 2.59808i) q^{47} +(-9.00000 + 15.5885i) q^{49} +(1.50000 - 2.59808i) q^{51} -6.00000 q^{53} +(-5.00000 - 8.66025i) q^{55} +(3.50000 - 6.06218i) q^{57} -8.00000 q^{59} +(0.500000 - 0.866025i) q^{61} +(-2.50000 - 4.33013i) q^{63} +(-3.00000 + 5.19615i) q^{65} +(8.00000 + 1.73205i) q^{67} +(1.50000 - 2.59808i) q^{69} +(-0.500000 - 0.866025i) q^{71} +(4.50000 - 7.79423i) q^{73} +1.00000 q^{75} +(-12.5000 + 21.6506i) q^{77} +(-0.500000 - 0.866025i) q^{79} +1.00000 q^{81} +(4.50000 - 7.79423i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-0.500000 - 0.866025i) q^{87} -18.0000 q^{89} +15.0000 q^{91} +(2.50000 + 4.33013i) q^{93} +(-7.00000 + 12.1244i) q^{95} +(8.50000 - 14.7224i) q^{97} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 4 q^{5} - 5 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 4 * q^5 - 5 * q^7 + 2 * q^9	$ 2 q - 2 q^{3} + 4 q^{5} - 5 q^{7} + 2 q^{9} - 5 q^{11} - 3 q^{13} - 4 q^{15} - 3 q^{17} - 7 q^{19} + 5 q^{21} - 3 q^{23} - 2 q^{25} - 2 q^{27} + q^{29} - 5 q^{31} + 5 q^{33} - 10 q^{35} + 5 q^{37} + 3 q^{39} - 11 q^{41} + 8 q^{43} + 4 q^{45} + 3 q^{47} - 18 q^{49} + 3 q^{51} - 12 q^{53} - 10 q^{55} + 7 q^{57} - 16 q^{59} + q^{61} - 5 q^{63} - 6 q^{65} + 16 q^{67} + 3 q^{69} - q^{71} + 9 q^{73} + 2 q^{75} - 25 q^{77} - q^{79} + 2 q^{81} + 9 q^{83} - 6 q^{85} - q^{87} - 36 q^{89} + 30 q^{91} + 5 q^{93} - 14 q^{95} + 17 q^{97} - 5 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 4 * q^5 - 5 * q^7 + 2 * q^9 - 5 * q^11 - 3 * q^13 - 4 * q^15 - 3 * q^17 - 7 * q^19 + 5 * q^21 - 3 * q^23 - 2 * q^25 - 2 * q^27 + q^29 - 5 * q^31 + 5 * q^33 - 10 * q^35 + 5 * q^37 + 3 * q^39 - 11 * q^41 + 8 * q^43 + 4 * q^45 + 3 * q^47 - 18 * q^49 + 3 * q^51 - 12 * q^53 - 10 * q^55 + 7 * q^57 - 16 * q^59 + q^61 - 5 * q^63 - 6 * q^65 + 16 * q^67 + 3 * q^69 - q^71 + 9 * q^73 + 2 * q^75 - 25 * q^77 - q^79 + 2 * q^81 + 9 * q^83 - 6 * q^85 - q^87 - 36 * q^89 + 30 * q^91 + 5 * q^93 - 14 * q^95 + 17 * q^97 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$		0			0
$7$	−2.50000	−	4.33013i	−0.944911	−	1.63663i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−2.50000	−	4.33013i	−0.944911	−	1.63663i	−0.188982	−	0.981981i	$-0.560519\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	−0.995535	−	0.0943882i	$-0.969911\pi$
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	0.579510	+	0.814965i	$0.303244\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	2.50000	+	4.33013i	0.545545	+	0.944911i
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$		0			0
$33$	2.50000	+	4.33013i	0.435194	+	0.753778i
$34$		0			0
$35$	−5.00000	−	8.66025i	−0.845154	−	1.46385i
$36$		0			0
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	−0.584002	−	0.811752i	$-0.698514\pi$
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	0.994999	+	0.0998840i	$0.0318472\pi$
$38$		0			0
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$		0			0
$41$	−5.50000	−	9.52628i	−0.858956	−	1.48775i	−0.872926	−	0.487852i	$-0.837780\pi$
$41$	−5.50000	−	9.52628i	−0.858956	−	1.48775i	0.0139704	−	0.999902i	$-0.495553\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$		0			0
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$		0			0
$49$	−9.00000	+	15.5885i	−1.28571	+	2.22692i
$50$		0			0
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	−5.00000	−	8.66025i	−0.674200	−	1.16775i
$56$		0			0
$57$	3.50000	−	6.06218i	0.463586	−	0.802955i
$58$		0			0
$59$	−8.00000			−1.04151			−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000			−1.04151			−0.520756	+	0.853706i	$0.674350\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	−2.50000	−	4.33013i	−0.314970	−	0.545545i
$64$		0			0
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		0			0
$67$	8.00000	+	1.73205i	0.977356	+	0.211604i
$67$	8.00000	+	1.73205i	0.977356	+	0.211604i
$68$		0			0
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		0			0
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	0.834830	−	0.550508i	$-0.185566\pi$
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	−0.894169	+	0.447730i	$0.852233\pi$
$72$		0			0
$73$	4.50000	−	7.79423i	0.526685	−	0.912245i	−0.472831	−	0.881153i	$-0.656768\pi$
$73$	4.50000	−	7.79423i	0.526685	−	0.912245i	0.999517	−	0.0310925i	$-0.00989865\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−12.5000	+	21.6506i	−1.42451	+	2.46732i
$78$		0			0
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$		0			0
$87$	−0.500000	−	0.866025i	−0.0536056	−	0.0928477i
$88$		0			0
$89$	−18.0000			−1.90800			−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000			−1.90800			−0.953998	+	0.299813i	$0.903076\pi$
$90$		0			0
$91$	15.0000			1.57243
$92$		0			0
$93$	2.50000	+	4.33013i	0.259238	+	0.449013i
$94$		0			0
$95$	−7.00000	+	12.1244i	−0.718185	+	1.24393i
$96$		0			0
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	−0.00593185	−	0.999982i	$-0.501888\pi$
$97$	8.50000	−	14.7224i	0.863044	−	1.49484i	0.868976	−	0.494854i	$-0.164778\pi$
$98$		0			0
$99$	−2.50000	−	4.33013i	−0.251259	−	0.435194i
$100$		0			0
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$		0			0
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	0.840341	−	0.542059i	$-0.182355\pi$
$103$	−0.500000	−	0.866025i	−0.0492665	−	0.0853320i	−0.889607	+	0.456727i	$0.849022\pi$
$104$		0			0
$105$	5.00000	+	8.66025i	0.487950	+	0.845154i
$106$		0			0
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	−2.50000	+	4.33013i	−0.237289	+	0.410997i
$112$		0			0
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	0.786806	−	0.617200i	$-0.211733\pi$
$113$	−1.50000	−	2.59808i	−0.141108	−	0.244406i	−0.927914	+	0.372794i	$0.878400\pi$
$114$		0			0
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$		0			0
$117$	−1.50000	+	2.59808i	−0.138675	+	0.240192i
$118$		0			0
$119$	15.0000			1.37505
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$	5.50000	+	9.52628i	0.495918	+	0.858956i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	3.50000	+	6.06218i	0.310575	+	0.537931i	0.978487	−	0.206309i	$-0.0661452\pi$
$127$	3.50000	+	6.06218i	0.310575	+	0.537931i	−0.667912	+	0.744240i	$0.732812\pi$
$128$		0			0
$129$	−4.00000			−0.352180
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$	35.0000			3.03488
$134$		0			0
$135$	−2.00000			−0.172133
$136$		0			0
$137$	14.0000			1.19610			0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000			1.19610			0.598050	+	0.801459i	$0.295942\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$		0			0
$141$	−1.50000	−	2.59808i	−0.126323	−	0.218797i
$142$		0			0
$143$	15.0000			1.25436
$144$		0			0
$145$	1.00000	+	1.73205i	0.0830455	+	0.143839i
$146$		0			0
$147$	9.00000	−	15.5885i	0.742307	−	1.28571i
$148$		0			0
$149$	18.0000			1.47462			0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000			1.47462			0.737309	+	0.675556i	$0.236096\pi$
$150$		0			0
$151$	6.50000	−	11.2583i	0.528962	−	0.916190i	−0.470467	−	0.882418i	$-0.655915\pi$
$151$	6.50000	−	11.2583i	0.528962	−	0.916190i	0.999430	−	0.0337724i	$-0.0107521\pi$
$152$		0			0
$153$	−1.50000	+	2.59808i	−0.121268	+	0.210042i
$154$		0			0
$155$	−5.00000	−	8.66025i	−0.401610	−	0.695608i
$156$		0			0
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	−0.919654	−	0.392730i	$-0.871531\pi$
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	0.799941	+	0.600079i	$0.204864\pi$
$158$		0			0
$159$	6.00000			0.475831
$160$		0			0
$161$	15.0000			1.18217
$162$		0			0
$163$	1.50000	+	2.59808i	0.117489	+	0.203497i	0.918772	−	0.394789i	$-0.129182\pi$
$163$	1.50000	+	2.59808i	0.117489	+	0.203497i	−0.801283	+	0.598286i	$0.795849\pi$
$164$		0			0
$165$	5.00000	+	8.66025i	0.389249	+	0.674200i
$166$		0			0
$167$	−0.500000	−	0.866025i	−0.0386912	−	0.0670151i	0.846031	−	0.533133i	$-0.178986\pi$
$167$	−0.500000	−	0.866025i	−0.0386912	−	0.0670151i	−0.884723	+	0.466118i	$0.845652\pi$
$168$		0			0
$169$	2.00000	+	3.46410i	0.153846	+	0.266469i
$170$		0			0
$171$	−3.50000	+	6.06218i	−0.267652	+	0.463586i
$172$		0			0
$173$	6.50000	−	11.2583i	0.494186	−	0.855955i	−0.505792	−	0.862656i	$-0.668800\pi$
$173$	6.50000	−	11.2583i	0.494186	−	0.855955i	0.999978	+	0.00670064i	$0.00213290\pi$
$174$		0			0
$175$	2.50000	+	4.33013i	0.188982	+	0.327327i
$176$		0			0
$177$	8.00000			0.601317
$178$		0			0
$179$	−8.00000			−0.597948			−0.298974	−	0.954261i	$-0.596644\pi$
$179$	−8.00000			−0.597948			−0.298974	+	0.954261i	$0.596644\pi$
$180$		0			0
$181$	8.50000	+	14.7224i	0.631800	+	1.09431i	0.987184	+	0.159589i	$0.0510169\pi$
$181$	8.50000	+	14.7224i	0.631800	+	1.09431i	−0.355383	+	0.934721i	$0.615650\pi$
$182$		0			0
$183$	−0.500000	+	0.866025i	−0.0369611	+	0.0640184i
$184$		0			0
$185$	5.00000	−	8.66025i	0.367607	−	0.636715i
$186$		0			0
$187$	15.0000			1.09691
$188$		0			0
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$		0			0
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$		0			0
$193$	2.00000			0.143963			0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000			0.143963			0.0719816	+	0.997406i	$0.477068\pi$
$194$		0			0
$195$	3.00000	−	5.19615i	0.214834	−	0.372104i
$196$		0			0
$197$	−9.50000	−	16.4545i	−0.676847	−	1.17233i	−0.975925	−	0.218105i	$-0.930013\pi$
$197$	−9.50000	−	16.4545i	−0.676847	−	1.17233i	0.299078	−	0.954229i	$-0.403321\pi$
$198$		0			0
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	−0.963001	−	0.269498i	$-0.913142\pi$
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	0.714893	+	0.699234i	$0.246476\pi$
$200$		0			0
$201$	−8.00000	−	1.73205i	−0.564276	−	0.122169i
$202$		0			0
$203$	2.50000	−	4.33013i	0.175466	−	0.303915i
$204$		0			0
$205$	−11.0000	−	19.0526i	−0.768273	−	1.33069i
$206$		0			0
$207$	−1.50000	+	2.59808i	−0.104257	+	0.180579i
$208$		0			0
$209$	35.0000			2.42100
$210$		0			0
$211$	8.50000	−	14.7224i	0.585164	−	1.01353i	−0.409691	−	0.912224i	$-0.634363\pi$
$211$	8.50000	−	14.7224i	0.585164	−	1.01353i	0.994855	−	0.101310i	$-0.0323033\pi$
$212$		0			0
$213$	0.500000	+	0.866025i	0.0342594	+	0.0593391i
$214$		0			0
$215$	8.00000			0.545595
$216$		0			0
$217$	−12.5000	+	21.6506i	−0.848555	+	1.46974i
$218$		0			0
$219$	−4.50000	+	7.79423i	−0.304082	+	0.526685i
$220$		0			0
$221$	−4.50000	−	7.79423i	−0.302703	−	0.524297i
$222$		0			0
$223$	−20.0000			−1.33930			−0.669650	−	0.742677i	$-0.733556\pi$
$223$	−20.0000			−1.33930			−0.669650	+	0.742677i	$0.733556\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	0.999997	−	0.00254715i	$-0.000810783\pi$
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	−0.502204	+	0.864749i	$0.667477\pi$
$228$		0			0
$229$	−11.5000	+	19.9186i	−0.759941	+	1.31626i	0.182939	+	0.983124i	$0.441439\pi$
$229$	−11.5000	+	19.9186i	−0.759941	+	1.31626i	−0.942880	+	0.333133i	$0.891894\pi$
$230$		0			0
$231$	12.5000	−	21.6506i	0.822440	−	1.42451i
$232$		0			0
$233$	0.500000	+	0.866025i	0.0327561	+	0.0567352i	0.881939	−	0.471364i	$-0.156238\pi$
$233$	0.500000	+	0.866025i	0.0327561	+	0.0567352i	−0.849183	+	0.528099i	$0.822905\pi$
$234$		0			0
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$		0			0
$237$	0.500000	+	0.866025i	0.0324785	+	0.0562544i
$238$		0			0
$239$	−2.50000	−	4.33013i	−0.161712	−	0.280093i	0.773771	−	0.633465i	$-0.218368\pi$
$239$	−2.50000	−	4.33013i	−0.161712	−	0.280093i	−0.935483	+	0.353373i	$0.885035\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−18.0000	+	31.1769i	−1.14998	+	1.99182i
$246$		0			0
$247$	−10.5000	−	18.1865i	−0.668099	−	1.15718i
$248$		0			0
$249$	−4.50000	+	7.79423i	−0.285176	+	0.493939i
$250$		0			0
$251$	10.5000	−	18.1865i	0.662754	−	1.14792i	−0.317135	−	0.948380i	$-0.602721\pi$
$251$	10.5000	−	18.1865i	0.662754	−	1.14792i	0.979889	−	0.199543i	$-0.0639459\pi$
$252$		0			0
$253$	15.0000			0.943042
$254$		0			0
$255$	3.00000	−	5.19615i	0.187867	−	0.325396i
$256$		0			0
$257$	−9.50000	−	16.4545i	−0.592594	−	1.02640i	−0.993882	−	0.110450i	$-0.964771\pi$
$257$	−9.50000	−	16.4545i	−0.592594	−	1.02640i	0.401288	−	0.915952i	$-0.368563\pi$
$258$		0			0
$259$	−25.0000			−1.55342
$260$		0			0
$261$	0.500000	+	0.866025i	0.0309492	+	0.0536056i
$262$		0			0
$263$	−24.0000			−1.47990			−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000			−1.47990			−0.739952	+	0.672660i	$0.765152\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	18.0000			1.10158
$268$		0			0
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$		0			0
$273$	−15.0000			−0.907841
$274$		0			0
$275$	2.50000	+	4.33013i	0.150756	+	0.261116i
$276$		0			0
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$		0			0
$279$	−2.50000	−	4.33013i	−0.149671	−	0.259238i
$280$		0			0
$281$	−11.5000	+	19.9186i	−0.686032	+	1.18824i	0.287079	+	0.957907i	$0.407316\pi$
$281$	−11.5000	+	19.9186i	−0.686032	+	1.18824i	−0.973111	+	0.230336i	$0.926017\pi$
$282$		0			0
$283$	−12.0000			−0.713326			−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000			−0.713326			−0.356663	+	0.934233i	$0.616086\pi$
$284$		0			0
$285$	7.00000	−	12.1244i	0.414644	−	0.718185i
$286$		0			0
$287$	−27.5000	+	47.6314i	−1.62327	+	2.81159i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−8.50000	+	14.7224i	−0.498279	+	0.863044i
$292$		0			0
$293$	26.0000			1.51894			0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000			1.51894			0.759468	+	0.650545i	$0.225459\pi$
$294$		0			0
$295$	−16.0000			−0.931556
$296$		0			0
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$		0			0
$299$	−4.50000	−	7.79423i	−0.260242	−	0.450752i
$300$		0			0
$301$	−10.0000	−	17.3205i	−0.576390	−	0.998337i
$302$		0			0
$303$	7.50000	+	12.9904i	0.430864	+	0.746278i
$304$		0			0
$305$	1.00000	−	1.73205i	0.0572598	−	0.0991769i
$306$		0			0
$307$	14.5000	−	25.1147i	0.827559	−	1.43337i	−0.0723893	−	0.997376i	$-0.523062\pi$
$307$	14.5000	−	25.1147i	0.827559	−	1.43337i	0.899948	−	0.435997i	$-0.143604\pi$
$308$		0			0
$309$	0.500000	+	0.866025i	0.0284440	+	0.0492665i
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$		0			0
$313$	22.0000			1.24351			0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000			1.24351			0.621757	+	0.783210i	$0.286419\pi$
$314$		0			0
$315$	−5.00000	−	8.66025i	−0.281718	−	0.487950i
$316$		0			0
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	−0.905071	−	0.425261i	$-0.860182\pi$
$317$	−1.50000	+	2.59808i	−0.0842484	+	0.145922i	0.820822	+	0.571184i	$0.193516\pi$
$318$		0			0
$319$	2.50000	−	4.33013i	0.139973	−	0.242441i
$320$		0			0
$321$	−4.00000			−0.223258
$322$		0			0
$323$	−10.5000	−	18.1865i	−0.584236	−	1.01193i
$324$		0			0
$325$	1.50000	−	2.59808i	0.0832050	−	0.144115i
$326$		0			0
$327$	−14.0000			−0.774202
$328$		0			0
$329$	7.50000	−	12.9904i	0.413488	−	0.716183i
$330$		0			0
$331$	−2.50000	−	4.33013i	−0.137412	−	0.238005i	0.789104	−	0.614260i	$-0.210545\pi$
$331$	−2.50000	−	4.33013i	−0.137412	−	0.238005i	−0.926516	+	0.376254i	$0.877212\pi$
$332$		0			0
$333$	2.50000	−	4.33013i	0.136999	−	0.237289i
$334$		0			0
$335$	16.0000	+	3.46410i	0.874173	+	0.189264i
$336$		0			0
$337$	−1.50000	+	2.59808i	−0.0817102	+	0.141526i	−0.903985	−	0.427565i	$-0.859372\pi$
$337$	−1.50000	+	2.59808i	−0.0817102	+	0.141526i	0.822274	+	0.569091i	$0.192705\pi$
$338$		0			0
$339$	1.50000	+	2.59808i	0.0814688	+	0.141108i
$340$		0			0
$341$	−12.5000	+	21.6506i	−0.676913	+	1.17245i
$342$		0			0
$343$	55.0000			2.96972
$344$		0			0
$345$	3.00000	−	5.19615i	0.161515	−	0.279751i
$346$		0			0
$347$	9.50000	+	16.4545i	0.509987	+	0.883323i	0.999933	+	0.0115703i	$0.00368303\pi$
$347$	9.50000	+	16.4545i	0.509987	+	0.883323i	−0.489946	+	0.871753i	$0.662984\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	1.50000	−	2.59808i	0.0800641	−	0.138675i
$352$		0			0
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$		0			0
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$		0			0
$357$	−15.0000			−0.793884
$358$		0			0
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$	7.00000	−	12.1244i	0.367405	−	0.636364i
$364$		0			0
$365$	9.00000	−	15.5885i	0.471082	−	0.815937i
$366$		0			0
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$		0			0
$369$	−5.50000	−	9.52628i	−0.286319	−	0.495918i
$370$		0			0
$371$	15.0000	+	25.9808i	0.778761	+	1.34885i
$372$		0			0
$373$	−15.5000	−	26.8468i	−0.802560	−	1.39007i	−0.917926	−	0.396751i	$-0.870138\pi$
$373$	−15.5000	−	26.8468i	−0.802560	−	1.39007i	0.115367	−	0.993323i	$-0.463196\pi$
$374$		0			0
$375$	12.0000			0.619677
$376$		0			0
$377$	−3.00000			−0.154508
$378$		0			0
$379$	6.50000	−	11.2583i	0.333883	−	0.578302i	−0.649387	−	0.760458i	$-0.724974\pi$
$379$	6.50000	−	11.2583i	0.333883	−	0.578302i	0.983270	+	0.182157i	$0.0583078\pi$
$380$		0			0
$381$	−3.50000	−	6.06218i	−0.179310	−	0.310575i
$382$		0			0
$383$	−17.5000	+	30.3109i	−0.894208	+	1.54881i	−0.0594268	+	0.998233i	$0.518927\pi$
$383$	−17.5000	+	30.3109i	−0.894208	+	1.54881i	−0.834781	+	0.550581i	$0.814406\pi$
$384$		0			0
$385$	−25.0000	+	43.3013i	−1.27412	+	2.20684i
$386$		0			0
$387$	4.00000			0.203331
$388$		0			0
$389$	18.5000	−	32.0429i	0.937987	−	1.62464i	0.168769	−	0.985656i	$-0.446021\pi$
$389$	18.5000	−	32.0429i	0.937987	−	1.62464i	0.769218	−	0.638986i	$-0.220646\pi$
$390$		0			0
$391$	−4.50000	−	7.79423i	−0.227575	−	0.394171i
$392$		0			0
$393$	12.0000			0.605320
$394$		0			0
$395$	−1.00000	−	1.73205i	−0.0503155	−	0.0871489i
$396$		0			0
$397$	−22.0000			−1.10415			−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000			−1.10415			−0.552074	+	0.833795i	$0.686163\pi$
$398$		0			0
$399$	−35.0000			−1.75219
$400$		0			0
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$		0			0
$403$	15.0000			0.747203
$404$		0			0
$405$	2.00000			0.0993808
$406$		0			0
$407$	−25.0000			−1.23920
$408$		0			0
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$		0			0
$411$	−14.0000			−0.690569
$412$		0			0
$413$	20.0000	+	34.6410i	0.984136	+	1.70457i
$414$		0			0
$415$	9.00000	−	15.5885i	0.441793	−	0.765207i
$416$		0			0
$417$	12.0000			0.587643
$418$		0			0
$419$	14.5000	−	25.1147i	0.708371	−	1.22694i	−0.257090	−	0.966388i	$-0.582764\pi$
$419$	14.5000	−	25.1147i	0.708371	−	1.22694i	0.965461	−	0.260548i	$-0.0839031\pi$
$420$		0			0
$421$	−15.5000	+	26.8468i	−0.755424	+	1.30843i	0.189740	+	0.981834i	$0.439236\pi$
$421$	−15.5000	+	26.8468i	−0.755424	+	1.30843i	−0.945163	+	0.326598i	$0.894098\pi$
$422$		0			0
$423$	1.50000	+	2.59808i	0.0729325	+	0.126323i
$424$		0			0
$425$	1.50000	−	2.59808i	0.0727607	−	0.126025i
$426$		0			0
$427$	−5.00000			−0.241967
$428$		0			0
$429$	−15.0000			−0.724207
$430$		0			0
$431$	−2.50000	−	4.33013i	−0.120421	−	0.208575i	0.799513	−	0.600649i	$-0.205091\pi$
$431$	−2.50000	−	4.33013i	−0.120421	−	0.208575i	−0.919934	+	0.392074i	$0.871758\pi$
$432$		0			0
$433$	14.5000	+	25.1147i	0.696826	+	1.20694i	0.969561	+	0.244848i	$0.0787382\pi$
$433$	14.5000	+	25.1147i	0.696826	+	1.20694i	−0.272736	+	0.962089i	$0.587929\pi$
$434$		0			0
$435$	−1.00000	−	1.73205i	−0.0479463	−	0.0830455i
$436$		0			0
$437$	−10.5000	−	18.1865i	−0.502283	−	0.869980i
$438$		0			0
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	0.0586141	+	0.998281i	$0.481332\pi$
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	−0.893843	+	0.448379i	$0.852001\pi$
$440$		0			0
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$		0			0
$443$	−14.5000	−	25.1147i	−0.688916	−	1.19324i	−0.972189	−	0.234198i	$-0.924754\pi$
$443$	−14.5000	−	25.1147i	−0.688916	−	1.19324i	0.283273	−	0.959039i	$-0.408580\pi$
$444$		0			0
$445$	−36.0000			−1.70656
$446$		0			0
$447$	−18.0000			−0.851371
$448$		0			0
$449$	6.50000	+	11.2583i	0.306754	+	0.531313i	0.977650	−	0.210238i	$-0.0674238\pi$
$449$	6.50000	+	11.2583i	0.306754	+	0.531313i	−0.670896	+	0.741551i	$0.734090\pi$
$450$		0			0
$451$	−27.5000	+	47.6314i	−1.29492	+	2.24287i
$452$		0			0
$453$	−6.50000	+	11.2583i	−0.305397	+	0.528962i
$454$		0			0
$455$	30.0000			1.40642
$456$		0			0
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	0.993431	−	0.114433i	$-0.0365053\pi$
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	−0.595818	+	0.803120i	$0.703172\pi$
$458$		0			0
$459$	1.50000	−	2.59808i	0.0700140	−	0.121268i
$460$		0			0
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	0.464739	+	0.885448i	$0.346148\pi$
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$		0			0
$465$	5.00000	+	8.66025i	0.231869	+	0.401610i
$466$		0			0
$467$	−9.50000	+	16.4545i	−0.439608	+	0.761423i	−0.997659	−	0.0683836i	$-0.978216\pi$
$467$	−9.50000	+	16.4545i	−0.439608	+	0.761423i	0.558052	+	0.829806i	$0.311549\pi$
$468$		0			0
$469$	−12.5000	−	38.9711i	−0.577196	−	1.79952i
$470$		0			0
$471$	1.50000	−	2.59808i	0.0691164	−	0.119713i
$472$		0			0
$473$	−10.0000	−	17.3205i	−0.459800	−	0.796398i
$474$		0			0
$475$	3.50000	−	6.06218i	0.160591	−	0.278152i
$476$		0			0
$477$	−6.00000			−0.274721
$478$		0			0
$479$	−11.5000	+	19.9186i	−0.525448	+	0.910103i	0.474112	+	0.880464i	$0.342769\pi$
$479$	−11.5000	+	19.9186i	−0.525448	+	0.910103i	−0.999561	+	0.0296389i	$0.990564\pi$
$480$		0			0
$481$	7.50000	+	12.9904i	0.341971	+	0.592310i
$482$		0			0
$483$	−15.0000			−0.682524
$484$		0			0
$485$	17.0000	−	29.4449i	0.771930	−	1.33702i
$486$		0			0
$487$	−3.50000	+	6.06218i	−0.158600	+	0.274703i	−0.934364	−	0.356320i	$-0.884031\pi$
$487$	−3.50000	+	6.06218i	−0.158600	+	0.274703i	0.775764	+	0.631023i	$0.217365\pi$
$488$		0			0
$489$	−1.50000	−	2.59808i	−0.0678323	−	0.117489i
$490$		0			0
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$		0			0
$493$	−3.00000			−0.135113
$494$		0			0
$495$	−5.00000	−	8.66025i	−0.224733	−	0.389249i
$496$		0			0
$497$	−2.50000	+	4.33013i	−0.112140	+	0.194233i
$498$		0			0
$499$	10.5000	−	18.1865i	0.470045	−	0.814141i	−0.529369	−	0.848392i	$-0.677571\pi$
$499$	10.5000	−	18.1865i	0.470045	−	0.814141i	0.999413	+	0.0342508i	$0.0109045\pi$
$500$		0			0
$501$	0.500000	+	0.866025i	0.0223384	+	0.0386912i
$502$		0			0
$503$	−10.5000	−	18.1865i	−0.468172	−	0.810897i	0.531167	−	0.847267i	$-0.321754\pi$
$503$	−10.5000	−	18.1865i	−0.468172	−	0.810897i	−0.999338	+	0.0363700i	$0.988421\pi$
$504$		0			0
$505$	−15.0000	−	25.9808i	−0.667491	−	1.15613i
$506$		0			0
$507$	−2.00000	−	3.46410i	−0.0888231	−	0.153846i
$508$		0			0
$509$	−6.00000			−0.265945			−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000			−0.265945			−0.132973	+	0.991120i	$0.542452\pi$
$510$		0			0
$511$	−45.0000			−1.99068
$512$		0			0
$513$	3.50000	−	6.06218i	0.154529	−	0.267652i
$514$		0			0
$515$	−1.00000	−	1.73205i	−0.0440653	−	0.0763233i
$516$		0			0
$517$	7.50000	−	12.9904i	0.329850	−	0.571316i
$518$		0			0
$519$	−6.50000	+	11.2583i	−0.285318	+	0.494186i
$520$		0			0
$521$	−34.0000			−1.48957			−0.744784	−	0.667306i	$-0.767447\pi$
$521$	−34.0000			−1.48957			−0.744784	+	0.667306i	$0.767447\pi$
$522$		0			0
$523$	6.50000	−	11.2583i	0.284225	−	0.492292i	−0.688196	−	0.725525i	$-0.741597\pi$
$523$	6.50000	−	11.2583i	0.284225	−	0.492292i	0.972421	+	0.233233i	$0.0749303\pi$
$524$		0			0
$525$	−2.50000	−	4.33013i	−0.109109	−	0.188982i
$526$		0			0
$527$	15.0000			0.653410
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	−8.00000			−0.347170
$532$		0			0
$533$	33.0000			1.42939
$534$		0			0
$535$	8.00000			0.345870
$536$		0			0
$537$	8.00000			0.345225
$538$		0			0
$539$	90.0000			3.87657
$540$		0			0
$541$	−6.00000			−0.257960			−0.128980	−	0.991647i	$-0.541170\pi$
$541$	−6.00000			−0.257960			−0.128980	+	0.991647i	$0.541170\pi$
$542$		0			0
$543$	−8.50000	−	14.7224i	−0.364770	−	0.631800i
$544$		0			0
$545$	28.0000			1.19939
$546$		0			0
$547$	−4.50000	−	7.79423i	−0.192406	−	0.333257i	0.753641	−	0.657286i	$-0.228296\pi$
$547$	−4.50000	−	7.79423i	−0.192406	−	0.333257i	−0.946047	+	0.324029i	$0.894962\pi$
$548$		0			0
$549$	0.500000	−	0.866025i	0.0213395	−	0.0369611i
$550$		0			0
$551$	−7.00000			−0.298210
$552$		0			0
$553$	−2.50000	+	4.33013i	−0.106311	+	0.184136i
$554$		0			0
$555$	−5.00000	+	8.66025i	−0.212238	+	0.367607i
$556$		0			0
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	0.512622	−	0.858614i	$-0.328674\pi$
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	−0.999893	+	0.0146368i	$0.995341\pi$
$558$		0			0
$559$	−6.00000	+	10.3923i	−0.253773	+	0.439548i
$560$		0			0
$561$	−15.0000			−0.633300
$562$		0			0
$563$	36.0000			1.51722			0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000			1.51722			0.758610	+	0.651546i	$0.225879\pi$
$564$		0			0
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$		0			0
$567$	−2.50000	−	4.33013i	−0.104990	−	0.181848i
$568$		0			0
$569$	−5.50000	−	9.52628i	−0.230572	−	0.399362i	0.727405	−	0.686209i	$-0.240726\pi$
$569$	−5.50000	−	9.52628i	−0.230572	−	0.399362i	−0.957977	+	0.286846i	$0.907393\pi$
$570$		0			0
$571$	−22.5000	−	38.9711i	−0.941596	−	1.63089i	−0.762428	−	0.647073i	$-0.775993\pi$
$571$	−22.5000	−	38.9711i	−0.941596	−	1.63089i	−0.179168	−	0.983819i	$-0.557340\pi$
$572$		0			0
$573$	7.50000	−	12.9904i	0.313317	−	0.542681i
$574$		0			0
$575$	1.50000	−	2.59808i	0.0625543	−	0.108347i
$576$		0			0
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	0.876245	−	0.481865i	$-0.160040\pi$
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	−0.855430	+	0.517918i	$0.826707\pi$
$578$		0			0
$579$	−2.00000			−0.0831172
$580$		0			0
$581$	−45.0000			−1.86691
$582$		0			0
$583$	15.0000	+	25.9808i	0.621237	+	1.07601i
$584$		0			0
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$		0			0
$587$	18.5000	−	32.0429i	0.763577	−	1.32255i	−0.177419	−	0.984135i	$-0.556775\pi$
$587$	18.5000	−	32.0429i	0.763577	−	1.32255i	0.940996	−	0.338418i	$-0.109892\pi$
$588$		0			0
$589$	35.0000			1.44215
$590$		0			0
$591$	9.50000	+	16.4545i	0.390778	+	0.676847i
$592$		0			0
$593$	20.5000	−	35.5070i	0.841834	−	1.45810i	−0.0465084	−	0.998918i	$-0.514809\pi$
$593$	20.5000	−	35.5070i	0.841834	−	1.45810i	0.888342	−	0.459182i	$-0.151857\pi$
$594$		0			0
$595$	30.0000			1.22988
$596$		0			0
$597$	3.50000	−	6.06218i	0.143245	−	0.248108i
$598$		0			0
$599$	7.50000	+	12.9904i	0.306442	+	0.530773i	0.977581	−	0.210558i	$-0.0675282\pi$
$599$	7.50000	+	12.9904i	0.306442	+	0.530773i	−0.671140	+	0.741331i	$0.734195\pi$
$600$		0			0
$601$	6.50000	−	11.2583i	0.265141	−	0.459237i	−0.702460	−	0.711723i	$-0.747915\pi$
$601$	6.50000	−	11.2583i	0.265141	−	0.459237i	0.967600	+	0.252486i	$0.0812483\pi$
$602$		0			0
$603$	8.00000	+	1.73205i	0.325785	+	0.0705346i
$604$		0			0
$605$	−14.0000	+	24.2487i	−0.569181	+	0.985850i
$606$		0			0
$607$	1.50000	+	2.59808i	0.0608831	+	0.105453i	0.894860	−	0.446346i	$-0.147275\pi$
$607$	1.50000	+	2.59808i	0.0608831	+	0.105453i	−0.833977	+	0.551799i	$0.813942\pi$
$608$		0			0
$609$	−2.50000	+	4.33013i	−0.101305	+	0.175466i
$610$		0			0
$611$	−9.00000			−0.364101
$612$		0			0
$613$	2.50000	−	4.33013i	0.100974	−	0.174892i	−0.811112	−	0.584891i	$-0.801137\pi$
$613$	2.50000	−	4.33013i	0.100974	−	0.174892i	0.912086	+	0.409998i	$0.134471\pi$
$614$		0			0
$615$	11.0000	+	19.0526i	0.443563	+	0.768273i
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$		0			0
$619$	8.50000	−	14.7224i	0.341644	−	0.591744i	−0.643094	−	0.765787i	$-0.722350\pi$
$619$	8.50000	−	14.7224i	0.341644	−	0.591744i	0.984738	+	0.174042i	$0.0556830\pi$
$620$		0			0
$621$	1.50000	−	2.59808i	0.0601929	−	0.104257i
$622$		0			0
$623$	45.0000	+	77.9423i	1.80289	+	3.12269i
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$	−35.0000			−1.39777
$628$		0			0
$629$	7.50000	+	12.9904i	0.299045	+	0.517960i
$630$		0			0
$631$	2.50000	−	4.33013i	0.0995234	−	0.172380i	−0.811964	−	0.583707i	$-0.801602\pi$
$631$	2.50000	−	4.33013i	0.0995234	−	0.172380i	0.911487	+	0.411328i	$0.134935\pi$
$632$		0			0
$633$	−8.50000	+	14.7224i	−0.337845	+	0.585164i
$634$		0			0
$635$	7.00000	+	12.1244i	0.277787	+	0.481140i
$636$		0			0
$637$	−27.0000	−	46.7654i	−1.06978	−	1.85291i
$638$		0			0
$639$	−0.500000	−	0.866025i	−0.0197797	−	0.0342594i
$640$		0			0
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	0.911165	−	0.412042i	$-0.135184\pi$
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	−0.812421	+	0.583071i	$0.801851\pi$
$642$		0			0
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$		0			0
$647$	−21.5000	+	37.2391i	−0.845252	+	1.46402i	0.0401498	+	0.999194i	$0.487216\pi$
$647$	−21.5000	+	37.2391i	−0.845252	+	1.46402i	−0.885402	+	0.464826i	$0.846117\pi$
$648$		0			0
$649$	20.0000	+	34.6410i	0.785069	+	1.35978i
$650$		0			0
$651$	12.5000	−	21.6506i	0.489914	−	0.848555i
$652$		0			0
$653$	−21.5000	+	37.2391i	−0.841360	+	1.45728i	0.0473852	+	0.998877i	$0.484911\pi$
$653$	−21.5000	+	37.2391i	−0.841360	+	1.45728i	−0.888745	+	0.458402i	$0.848422\pi$
$654$		0			0
$655$	−24.0000			−0.937758
$656$		0			0
$657$	4.50000	−	7.79423i	0.175562	−	0.304082i
$658$		0			0
$659$	−0.500000	−	0.866025i	−0.0194772	−	0.0337356i	0.856123	−	0.516773i	$-0.172867\pi$
$659$	−0.500000	−	0.866025i	−0.0194772	−	0.0337356i	−0.875600	+	0.483037i	$0.839534\pi$
$660$		0			0
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$		0			0
$663$	4.50000	+	7.79423i	0.174766	+	0.302703i
$664$		0			0
$665$	70.0000			2.71448
$666$		0			0
$667$	−3.00000			−0.116160
$668$		0			0
$669$	20.0000			0.773245
$670$		0			0
$671$	−5.00000			−0.193023
$672$		0			0
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−11.5000	−	19.9186i	−0.441981	−	0.765533i	0.555856	−	0.831279i	$-0.312391\pi$
$677$	−11.5000	−	19.9186i	−0.441981	−	0.765533i	−0.997836	+	0.0657455i	$0.979057\pi$
$678$		0			0
$679$	−85.0000			−3.26200
$680$		0			0
$681$	−7.50000	−	12.9904i	−0.287401	−	0.497792i
$682$		0			0
$683$	−17.5000	+	30.3109i	−0.669619	+	1.15981i	0.308392	+	0.951259i	$0.400209\pi$
$683$	−17.5000	+	30.3109i	−0.669619	+	1.15981i	−0.978011	+	0.208555i	$0.933124\pi$
$684$		0			0
$685$	28.0000			1.06983
$686$		0			0
$687$	11.5000	−	19.9186i	0.438752	−	0.759941i
$688$		0			0
$689$	9.00000	−	15.5885i	0.342873	−	0.593873i
$690$		0			0
$691$	7.50000	+	12.9904i	0.285313	+	0.494177i	0.972685	−	0.232128i	$-0.0745690\pi$
$691$	7.50000	+	12.9904i	0.285313	+	0.494177i	−0.687372	+	0.726306i	$0.741236\pi$
$692$		0			0
$693$	−12.5000	+	21.6506i	−0.474836	+	0.822440i
$694$		0			0
$695$	−24.0000			−0.910372
$696$		0			0
$697$	33.0000			1.24996
$698$		0			0
$699$	−0.500000	−	0.866025i	−0.0189117	−	0.0327561i
$700$		0			0
$701$	−13.5000	−	23.3827i	−0.509888	−	0.883152i	−0.999934	−	0.0114555i	$-0.996354\pi$
$701$	−13.5000	−	23.3827i	−0.509888	−	0.883152i	0.490046	−	0.871696i	$-0.336980\pi$
$702$		0			0
$703$	17.5000	+	30.3109i	0.660025	+	1.14320i
$704$		0			0
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$		0			0
$707$	−37.5000	+	64.9519i	−1.41033	+	2.44277i
$708$		0			0
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	−0.529943	−	0.848034i	$-0.677787\pi$
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	0.999390	+	0.0349269i	$0.0111198\pi$
$710$		0			0
$711$	−0.500000	−	0.866025i	−0.0187515	−	0.0324785i
$712$		0			0
$713$	15.0000			0.561754
$714$		0			0
$715$	30.0000			1.12194
$716$		0			0
$717$	2.50000	+	4.33013i	0.0933642	+	0.161712i
$718$		0			0
$719$	10.5000	−	18.1865i	0.391584	−	0.678243i	−0.601075	−	0.799193i	$-0.705261\pi$
$719$	10.5000	−	18.1865i	0.391584	−	0.678243i	0.992659	+	0.120950i	$0.0385939\pi$
$720$		0			0
$721$	−2.50000	+	4.33013i	−0.0931049	+	0.161262i
$722$		0			0
$723$	18.0000			0.669427
$724$		0			0
$725$	−0.500000	−	0.866025i	−0.0185695	−	0.0321634i
$726$		0			0
$727$	−23.5000	+	40.7032i	−0.871567	+	1.50960i	−0.0111912	+	0.999937i	$0.503562\pi$
$727$	−23.5000	+	40.7032i	−0.871567	+	1.50960i	−0.860376	+	0.509661i	$0.829771\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−6.00000	+	10.3923i	−0.221918	+	0.384373i
$732$		0			0
$733$	10.5000	+	18.1865i	0.387826	+	0.671735i	0.992157	−	0.124999i	$-0.0398927\pi$
$733$	10.5000	+	18.1865i	0.387826	+	0.671735i	−0.604331	+	0.796734i	$0.706559\pi$
$734$		0			0
$735$	18.0000	−	31.1769i	0.663940	−	1.14998i
$736$		0			0
$737$	−12.5000	−	38.9711i	−0.460443	−	1.43552i
$738$		0			0
$739$	20.5000	−	35.5070i	0.754105	−	1.30615i	−0.191714	−	0.981451i	$-0.561404\pi$
$739$	20.5000	−	35.5070i	0.754105	−	1.30615i	0.945818	−	0.324697i	$-0.105262\pi$
$740$		0			0
$741$	10.5000	+	18.1865i	0.385727	+	0.668099i
$742$		0			0
$743$	0.500000	−	0.866025i	0.0183432	−	0.0317714i	−0.856708	−	0.515802i	$-0.827494\pi$
$743$	0.500000	−	0.866025i	0.0183432	−	0.0317714i	0.875051	+	0.484030i	$0.160828\pi$
$744$		0			0
$745$	36.0000			1.31894
$746$		0			0
$747$	4.50000	−	7.79423i	0.164646	−	0.285176i
$748$		0			0
$749$	−10.0000	−	17.3205i	−0.365392	−	0.632878i
$750$		0			0
$751$	40.0000			1.45962			0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000			1.45962			0.729810	+	0.683650i	$0.239608\pi$
$752$		0			0
$753$	−10.5000	+	18.1865i	−0.382641	+	0.662754i
$754$		0			0
$755$	13.0000	−	22.5167i	0.473118	−	0.819465i
$756$		0			0
$757$	10.5000	+	18.1865i	0.381629	+	0.661001i	0.991295	−	0.131657i	$-0.0420299\pi$
$757$	10.5000	+	18.1865i	0.381629	+	0.661001i	−0.609666	+	0.792658i	$0.708697\pi$
$758$		0			0
$759$	−15.0000			−0.544466
$760$		0			0
$761$	38.0000			1.37750			0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000			1.37750			0.688749	+	0.724999i	$0.258160\pi$
$762$		0			0
$763$	−35.0000	−	60.6218i	−1.26709	−	2.19466i
$764$		0			0
$765$	−3.00000	+	5.19615i	−0.108465	+	0.187867i
$766$		0			0
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$		0			0
$769$	−21.5000	−	37.2391i	−0.775310	−	1.34288i	−0.934620	−	0.355647i	$-0.884260\pi$
$769$	−21.5000	−	37.2391i	−0.775310	−	1.34288i	0.159310	−	0.987229i	$-0.449073\pi$
$770$		0			0
$771$	9.50000	+	16.4545i	0.342134	+	0.592594i
$772$		0			0
$773$	26.5000	+	45.8993i	0.953139	+	1.65088i	0.738571	+	0.674176i	$0.235501\pi$
$773$	26.5000	+	45.8993i	0.953139	+	1.65088i	0.214568	+	0.976709i	$0.431166\pi$
$774$		0			0
$775$	2.50000	+	4.33013i	0.0898027	+	0.155543i
$776$		0			0
$777$	25.0000			0.896870
$778$		0			0
$779$	77.0000			2.75881
$780$		0			0
$781$	−2.50000	+	4.33013i	−0.0894570	+	0.154944i
$782$		0			0
$783$	−0.500000	−	0.866025i	−0.0178685	−	0.0309492i
$784$		0			0
$785$	−3.00000	+	5.19615i	−0.107075	+	0.185459i
$786$		0			0
$787$	−11.5000	+	19.9186i	−0.409931	+	0.710021i	−0.994882	−	0.101048i	$-0.967780\pi$
$787$	−11.5000	+	19.9186i	−0.409931	+	0.710021i	0.584951	+	0.811069i	$0.301114\pi$
$788$		0			0
$789$	24.0000			0.854423
$790$		0			0
$791$	−7.50000	+	12.9904i	−0.266669	+	0.461885i
$792$		0			0
$793$	1.50000	+	2.59808i	0.0532666	+	0.0922604i
$794$		0			0
$795$	12.0000			0.425596
$796$		0			0
$797$	−3.50000	−	6.06218i	−0.123976	−	0.214733i	0.797356	−	0.603509i	$-0.206231\pi$
$797$	−3.50000	−	6.06218i	−0.123976	−	0.214733i	−0.921332	+	0.388776i	$0.872898\pi$
$798$		0			0
$799$	−9.00000			−0.318397
$800$		0			0
$801$	−18.0000			−0.635999
$802$		0			0
$803$	−45.0000			−1.58802
$804$		0			0
$805$	30.0000			1.05736
$806$		0			0
$807$	6.00000			0.211210
$808$		0			0
$809$	−34.0000			−1.19538			−0.597688	−	0.801729i	$-0.703914\pi$
$809$	−34.0000			−1.19538			−0.597688	+	0.801729i	$0.703914\pi$
$810$		0			0
$811$	23.5000	+	40.7032i	0.825197	+	1.42928i	0.901769	+	0.432218i	$0.142269\pi$
$811$	23.5000	+	40.7032i	0.825197	+	1.42928i	−0.0765723	+	0.997064i	$0.524398\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.00000	+	5.19615i	0.105085	+	0.182013i
$816$		0			0
$817$	−14.0000	+	24.2487i	−0.489798	+	0.848355i
$818$		0			0
$819$	15.0000			0.524142
$820$		0			0
$821$	18.5000	−	32.0429i	0.645654	−	1.11831i	−0.338495	−	0.940968i	$-0.609918\pi$
$821$	18.5000	−	32.0429i	0.645654	−	1.11831i	0.984150	−	0.177338i	$-0.0567487\pi$
$822$		0			0
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	−0.730215	−	0.683217i	$-0.760580\pi$
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	0.956791	+	0.290776i	$0.0939136\pi$
$824$		0			0
$825$	−2.50000	−	4.33013i	−0.0870388	−	0.150756i
$826$		0			0
$827$	0.500000	−	0.866025i	0.0173867	−	0.0301147i	−0.857201	−	0.514982i	$-0.827799\pi$
$827$	0.500000	−	0.866025i	0.0173867	−	0.0301147i	0.874588	+	0.484867i	$0.161132\pi$
$828$		0			0
$829$	−54.0000			−1.87550			−0.937749	−	0.347314i	$-0.887094\pi$
$829$	−54.0000			−1.87550			−0.937749	+	0.347314i	$0.887094\pi$
$830$		0			0
$831$	−26.0000			−0.901930
$832$		0			0
$833$	−27.0000	−	46.7654i	−0.935495	−	1.62032i
$834$		0			0
$835$	−1.00000	−	1.73205i	−0.0346064	−	0.0599401i
$836$		0			0
$837$	2.50000	+	4.33013i	0.0864126	+	0.149671i
$838$		0			0
$839$	−4.50000	−	7.79423i	−0.155357	−	0.269087i	0.777832	−	0.628473i	$-0.216320\pi$
$839$	−4.50000	−	7.79423i	−0.155357	−	0.269087i	−0.933189	+	0.359386i	$0.882986\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$		0			0
$843$	11.5000	−	19.9186i	0.396081	−	0.686032i
$844$		0			0
$845$	4.00000	+	6.92820i	0.137604	+	0.238337i
$846$		0			0
$847$	70.0000			2.40523
$848$		0			0
$849$	12.0000			0.411839
$850$		0			0
$851$	7.50000	+	12.9904i	0.257097	+	0.445305i
$852$		0			0
$853$	−25.5000	+	44.1673i	−0.873103	+	1.51226i	−0.0143339	+	0.999897i	$0.504563\pi$
$853$	−25.5000	+	44.1673i	−0.873103	+	1.51226i	−0.858769	+	0.512362i	$0.828771\pi$
$854$		0			0
$855$	−7.00000	+	12.1244i	−0.239395	+	0.414644i
$856$		0			0
$857$	−2.00000			−0.0683187			−0.0341593	−	0.999416i	$-0.510875\pi$
$857$	−2.00000			−0.0683187			−0.0341593	+	0.999416i	$0.510875\pi$
$858$		0			0
$859$	−10.5000	−	18.1865i	−0.358255	−	0.620517i	0.629414	−	0.777070i	$-0.283295\pi$
$859$	−10.5000	−	18.1865i	−0.358255	−	0.620517i	−0.987669	+	0.156554i	$0.949962\pi$
$860$		0			0
$861$	27.5000	−	47.6314i	0.937197	−	1.62327i
$862$		0			0
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	13.0000	−	22.5167i	0.442013	−	0.765589i
$866$		0			0
$867$	−4.00000	−	6.92820i	−0.135847	−	0.235294i
$868$		0			0
$869$	−2.50000	+	4.33013i	−0.0848067	+	0.146889i
$870$		0			0
$871$	−16.5000	+	18.1865i	−0.559081	+	0.616227i
$872$		0			0
$873$	8.50000	−	14.7224i	0.287681	−	0.498279i
$874$		0			0
$875$	30.0000	+	51.9615i	1.01419	+	1.75662i
$876$		0			0
$877$	−7.50000	+	12.9904i	−0.253257	+	0.438654i	−0.964421	−	0.264373i	$-0.914835\pi$
$877$	−7.50000	+	12.9904i	−0.253257	+	0.438654i	0.711164	+	0.703027i	$0.248168\pi$
$878$		0			0
$879$	−26.0000			−0.876958
$880$		0			0
$881$	16.5000	−	28.5788i	0.555899	−	0.962846i	−0.441934	−	0.897048i	$-0.645707\pi$
$881$	16.5000	−	28.5788i	0.555899	−	0.962846i	0.997833	−	0.0657979i	$-0.0209593\pi$
$882$		0			0
$883$	23.5000	+	40.7032i	0.790838	+	1.36977i	0.925449	+	0.378873i	$0.123688\pi$
$883$	23.5000	+	40.7032i	0.790838	+	1.36977i	−0.134611	+	0.990899i	$0.542978\pi$
$884$		0			0
$885$	16.0000			0.537834
$886$		0			0
$887$	−3.50000	+	6.06218i	−0.117518	+	0.203548i	−0.918784	−	0.394761i	$-0.870827\pi$
$887$	−3.50000	+	6.06218i	−0.117518	+	0.203548i	0.801265	+	0.598309i	$0.204161\pi$
$888$		0			0
$889$	17.5000	−	30.3109i	0.586931	−	1.01659i
$890$		0			0
$891$	−2.50000	−	4.33013i	−0.0837532	−	0.145065i
$892$		0			0
$893$	−21.0000			−0.702738
$894$		0			0
$895$	−16.0000			−0.534821
$896$		0			0
$897$	4.50000	+	7.79423i	0.150251	+	0.260242i
$898$		0			0
$899$	2.50000	−	4.33013i	0.0833797	−	0.144418i
$900$		0			0
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$		0			0
$903$	10.0000	+	17.3205i	0.332779	+	0.576390i
$904$		0			0
$905$	17.0000	+	29.4449i	0.565099	+	0.978780i
$906$		0			0
$907$	−0.500000	−	0.866025i	−0.0166022	−	0.0287559i	0.857605	−	0.514309i	$-0.171952\pi$
$907$	−0.500000	−	0.866025i	−0.0166022	−	0.0287559i	−0.874207	+	0.485553i	$0.838618\pi$
$908$		0			0
$909$	−7.50000	−	12.9904i	−0.248759	−	0.430864i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−45.0000			−1.48928
$914$		0			0
$915$	−1.00000	+	1.73205i	−0.0330590	+	0.0572598i
$916$		0			0
$917$	30.0000	+	51.9615i	0.990687	+	1.71592i
$918$		0			0
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	−0.782210	−	0.623015i	$-0.785908\pi$
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	0.930652	+	0.365907i	$0.119241\pi$
$920$		0			0
$921$	−14.5000	+	25.1147i	−0.477791	+	0.827559i
$922$		0			0
$923$	3.00000			0.0987462
$924$		0			0
$925$	−2.50000	+	4.33013i	−0.0821995	+	0.142374i
$926$		0			0
$927$	−0.500000	−	0.866025i	−0.0164222	−	0.0284440i
$928$		0			0
$929$	2.00000			0.0656179			0.0328089	−	0.999462i	$-0.489555\pi$
$929$	2.00000			0.0656179			0.0328089	+	0.999462i	$0.489555\pi$
$930$		0			0
$931$	−63.0000	−	109.119i	−2.06474	−	3.57624i
$932$		0			0
$933$	−4.00000			−0.130954
$934$		0			0
$935$	30.0000			0.981105
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$		0			0
$939$	−22.0000			−0.717943
$940$		0			0
$941$	−50.0000			−1.62995			−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000			−1.62995			−0.814977	+	0.579494i	$0.803250\pi$
$942$		0			0
$943$	33.0000			1.07463
$944$		0			0
$945$	5.00000	+	8.66025i	0.162650	+	0.281718i
$946$		0			0
$947$	4.00000			0.129983			0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000			0.129983			0.0649913	+	0.997886i	$0.479298\pi$
$948$		0			0
$949$	13.5000	+	23.3827i	0.438229	+	0.759034i
$950$		0			0
$951$	1.50000	−	2.59808i	0.0486408	−	0.0842484i
$952$		0			0
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$		0			0
$955$	−15.0000	+	25.9808i	−0.485389	+	0.840718i
$956$		0			0
$957$	−2.50000	+	4.33013i	−0.0808135	+	0.139973i
$958$		0			0
$959$	−35.0000	−	60.6218i	−1.13021	−	1.95758i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$	4.00000			0.128898
$964$		0			0
$965$	4.00000			0.128765
$966$		0			0
$967$	9.50000	+	16.4545i	0.305499	+	0.529140i	0.977372	−	0.211526i	$-0.0678433\pi$
$967$	9.50000	+	16.4545i	0.305499	+	0.529140i	−0.671873	+	0.740666i	$0.734510\pi$
$968$		0			0
$969$	10.5000	+	18.1865i	0.337309	+	0.584236i
$970$		0			0
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	0.988389	+	0.151948i	$0.0485545\pi$
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	−0.362604	+	0.931943i	$0.618112\pi$
$972$		0			0
$973$	30.0000	+	51.9615i	0.961756	+	1.66581i
$974$		0			0
$975$	−1.50000	+	2.59808i	−0.0480384	+	0.0832050i
$976$		0			0
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	−0.647737	−	0.761864i	$-0.724285\pi$
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	0.983662	+	0.180025i	$0.0576179\pi$
$978$		0			0
$979$	45.0000	+	77.9423i	1.43821	+	2.49105i
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	−12.0000			−0.382741			−0.191370	−	0.981518i	$-0.561293\pi$
$983$	−12.0000			−0.382741			−0.191370	+	0.981518i	$0.561293\pi$
$984$		0			0
$985$	−19.0000	−	32.9090i	−0.605390	−	1.04857i
$986$		0			0
$987$	−7.50000	+	12.9904i	−0.238728	+	0.413488i
$988$		0			0
$989$	−6.00000	+	10.3923i	−0.190789	+	0.330456i
$990$		0			0
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$		0			0
$993$	2.50000	+	4.33013i	0.0793351	+	0.137412i
$994$		0			0
$995$	−7.00000	+	12.1244i	−0.221915	+	0.384368i
$996$		0			0
$997$	6.00000			0.190022			0.0950110	−	0.995476i	$-0.469711\pi$
$997$	6.00000			0.190022			0.0950110	+	0.995476i	$0.469711\pi$
$998$		0			0
$999$	−2.50000	+	4.33013i	−0.0790965	+	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.i.b.565.1	yes	2
3.2	odd	2		2412.2.l.a.1369.1		2
67.37	even	3	inner	804.2.i.b.37.1	✓	2
201.104	odd	6		2412.2.l.a.37.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.b.37.1	✓	2	67.37	even	3	inner
804.2.i.b.565.1	yes	2	1.1	even	1	trivial
2412.2.l.a.37.1		2	201.104	odd	6
2412.2.l.a.1369.1		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +2.00000 q^{5} +(-2.50000 - 4.33013i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +2.00000 q^{5} +(-2.50000 - 4.33013i) q^{7} +1.00000 q^{9} +(-2.50000 - 4.33013i) q^{11} +(-1.50000 + 2.59808i) q^{13} -2.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(2.50000 + 4.33013i) q^{21} +(-1.50000 + 2.59808i) q^{23} -1.00000 q^{25} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{29} +(-2.50000 - 4.33013i) q^{31} +(2.50000 + 4.33013i) q^{33} +(-5.00000 - 8.66025i) q^{35} +(2.50000 - 4.33013i) q^{37} +(1.50000 - 2.59808i) q^{39} +(-5.50000 - 9.52628i) q^{41} +4.00000 q^{43} +2.00000 q^{45} +(1.50000 + 2.59808i) q^{47} +(-9.00000 + 15.5885i) q^{49} +(1.50000 - 2.59808i) q^{51} -6.00000 q^{53} +(-5.00000 - 8.66025i) q^{55} +(3.50000 - 6.06218i) q^{57} -8.00000 q^{59} +(0.500000 - 0.866025i) q^{61} +(-2.50000 - 4.33013i) q^{63} +(-3.00000 + 5.19615i) q^{65} +(8.00000 + 1.73205i) q^{67} +(1.50000 - 2.59808i) q^{69} +(-0.500000 - 0.866025i) q^{71} +(4.50000 - 7.79423i) q^{73} +1.00000 q^{75} +(-12.5000 + 21.6506i) q^{77} +(-0.500000 - 0.866025i) q^{79} +1.00000 q^{81} +(4.50000 - 7.79423i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-0.500000 - 0.866025i) q^{87} -18.0000 q^{89} +15.0000 q^{91} +(2.50000 + 4.33013i) q^{93} +(-7.00000 + 12.1244i) q^{95} +(8.50000 - 14.7224i) q^{97} +(-2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 4 q^{5} - 5 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 4 * q^5 - 5 * q^7 + 2 * q^9	\( 2 q - 2 q^{3} + 4 q^{5} - 5 q^{7} + 2 q^{9} - 5 q^{11} - 3 q^{13} - 4 q^{15} - 3 q^{17} - 7 q^{19} + 5 q^{21} - 3 q^{23} - 2 q^{25} - 2 q^{27} + q^{29} - 5 q^{31} + 5 q^{33} - 10 q^{35} + 5 q^{37} + 3 q^{39} - 11 q^{41} + 8 q^{43} + 4 q^{45} + 3 q^{47} - 18 q^{49} + 3 q^{51} - 12 q^{53} - 10 q^{55} + 7 q^{57} - 16 q^{59} + q^{61} - 5 q^{63} - 6 q^{65} + 16 q^{67} + 3 q^{69} - q^{71} + 9 q^{73} + 2 q^{75} - 25 q^{77} - q^{79} + 2 q^{81} + 9 q^{83} - 6 q^{85} - q^{87} - 36 q^{89} + 30 q^{91} + 5 q^{93} - 14 q^{95} + 17 q^{97} - 5 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 4 * q^5 - 5 * q^7 + 2 * q^9 - 5 * q^11 - 3 * q^13 - 4 * q^15 - 3 * q^17 - 7 * q^19 + 5 * q^21 - 3 * q^23 - 2 * q^25 - 2 * q^27 + q^29 - 5 * q^31 + 5 * q^33 - 10 * q^35 + 5 * q^37 + 3 * q^39 - 11 * q^41 + 8 * q^43 + 4 * q^45 + 3 * q^47 - 18 * q^49 + 3 * q^51 - 12 * q^53 - 10 * q^55 + 7 * q^57 - 16 * q^59 + q^61 - 5 * q^63 - 6 * q^65 + 16 * q^67 + 3 * q^69 - q^71 + 9 * q^73 + 2 * q^75 - 25 * q^77 - q^79 + 2 * q^81 + 9 * q^83 - 6 * q^85 - q^87 - 36 * q^89 + 30 * q^91 + 5 * q^93 - 14 * q^95 + 17 * q^97 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more