LMFDB - Embedded newform 804.2.i.c.37.1

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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	804.37
Dual form			804.2.i.c.565.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +2.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +2.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +(-0.500000 + 0.866025i) q^{11} +(2.50000 + 4.33013i) q^{13} +2.00000 q^{15} +(0.500000 + 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{19} +(1.50000 - 2.59808i) q^{21} +(-3.50000 - 6.06218i) q^{23} -1.00000 q^{25} +1.00000 q^{27} +(2.50000 - 4.33013i) q^{29} +(1.50000 - 2.59808i) q^{31} +(-0.500000 + 0.866025i) q^{33} +(3.00000 - 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(2.50000 + 4.33013i) q^{39} +(-3.50000 + 6.06218i) q^{41} +4.00000 q^{43} +2.00000 q^{45} +(-4.50000 + 7.79423i) q^{47} +(-1.00000 - 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{51} +2.00000 q^{53} +(-1.00000 + 1.73205i) q^{55} +(0.500000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{61} +(1.50000 - 2.59808i) q^{63} +(5.00000 + 8.66025i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-3.50000 - 6.06218i) q^{69} +(-2.50000 + 4.33013i) q^{71} +(4.50000 + 7.79423i) q^{73} -1.00000 q^{75} +(1.50000 + 2.59808i) q^{77} +(7.50000 - 12.9904i) q^{79} +1.00000 q^{81} +(-5.50000 - 9.52628i) q^{83} +(1.00000 + 1.73205i) q^{85} +(2.50000 - 4.33013i) q^{87} -18.0000 q^{89} +15.0000 q^{91} +(1.50000 - 2.59808i) q^{93} +(1.00000 + 1.73205i) q^{95} +(-7.50000 - 12.9904i) q^{97} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 4 q^{5} + 3 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 4 * q^5 + 3 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} + 4 q^{5} + 3 q^{7} + 2 q^{9} - q^{11} + 5 q^{13} + 4 q^{15} + q^{17} + q^{19} + 3 q^{21} - 7 q^{23} - 2 q^{25} + 2 q^{27} + 5 q^{29} + 3 q^{31} - q^{33} + 6 q^{35} - 3 q^{37} + 5 q^{39} - 7 q^{41} + 8 q^{43} + 4 q^{45} - 9 q^{47} - 2 q^{49} + q^{51} + 4 q^{53} - 2 q^{55} + q^{57} + q^{61} + 3 q^{63} + 10 q^{65} + 16 q^{67} - 7 q^{69} - 5 q^{71} + 9 q^{73} - 2 q^{75} + 3 q^{77} + 15 q^{79} + 2 q^{81} - 11 q^{83} + 2 q^{85} + 5 q^{87} - 36 q^{89} + 30 q^{91} + 3 q^{93} + 2 q^{95} - 15 q^{97} - q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 4 * q^5 + 3 * q^7 + 2 * q^9 - q^11 + 5 * q^13 + 4 * q^15 + q^17 + q^19 + 3 * q^21 - 7 * q^23 - 2 * q^25 + 2 * q^27 + 5 * q^29 + 3 * q^31 - q^33 + 6 * q^35 - 3 * q^37 + 5 * q^39 - 7 * q^41 + 8 * q^43 + 4 * q^45 - 9 * q^47 - 2 * q^49 + q^51 + 4 * q^53 - 2 * q^55 + q^57 + q^61 + 3 * q^63 + 10 * q^65 + 16 * q^67 - 7 * q^69 - 5 * q^71 + 9 * q^73 - 2 * q^75 + 3 * q^77 + 15 * q^79 + 2 * q^81 - 11 * q^83 + 2 * q^85 + 5 * q^87 - 36 * q^89 + 30 * q^91 + 3 * q^93 + 2 * q^95 - 15 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	−0.429919	−	0.902867i	$-0.641458\pi$
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	0.996866	−	0.0791130i	$-0.0252088\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		0			0
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		0			0
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	0.920268	−	0.391289i	$-0.127971\pi$
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	−0.799000	+	0.601331i	$0.794637\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	1.50000	−	2.59808i	0.327327	−	0.566947i
$22$		0			0
$23$	−3.50000	−	6.06218i	−0.729800	−	1.26405i	−0.956967	−	0.290196i	$-0.906280\pi$
$23$	−3.50000	−	6.06218i	−0.729800	−	1.26405i	0.227167	−	0.973856i	$-0.427054\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	−0.534928	−	0.844897i	$-0.679661\pi$
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	0.999167	+	0.0408130i	$0.0129948\pi$
$30$		0			0
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	−0.699301	−	0.714827i	$-0.746505\pi$
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	0.968709	+	0.248199i	$0.0798387\pi$
$32$		0			0
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$		0			0
$35$	3.00000	−	5.19615i	0.507093	−	0.878310i
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$		0			0
$39$	2.50000	+	4.33013i	0.400320	+	0.693375i
$40$		0			0
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	0.451896	+	0.892071i	$0.350748\pi$
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	−0.998504	+	0.0546823i	$0.982585\pi$
$42$		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
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	0.325150	+	0.945662i	$0.394585\pi$
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	−0.981543	+	0.191243i	$0.938748\pi$
$48$		0			0
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$		0			0
$51$	0.500000	+	0.866025i	0.0700140	+	0.121268i
$52$		0			0
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$		0			0
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$		0			0
$57$	0.500000	+	0.866025i	0.0662266	+	0.114708i
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	1.50000	−	2.59808i	0.188982	−	0.327327i
$64$		0			0
$65$	5.00000	+	8.66025i	0.620174	+	1.07417i
$66$		0			0
$67$	8.00000	−	1.73205i	0.977356	−	0.211604i
$67$	8.00000	−	1.73205i	0.977356	−	0.211604i
$68$		0			0
$69$	−3.50000	−	6.06218i	−0.421350	−	0.729800i
$70$		0			0
$71$	−2.50000	+	4.33013i	−0.296695	+	0.513892i	−0.975378	−	0.220540i	$-0.929218\pi$
$71$	−2.50000	+	4.33013i	−0.296695	+	0.513892i	0.678682	+	0.734432i	$0.262551\pi$
$72$		0			0
$73$	4.50000	+	7.79423i	0.526685	+	0.912245i	0.999517	+	0.0310925i	$0.00989865\pi$
$73$	4.50000	+	7.79423i	0.526685	+	0.912245i	−0.472831	+	0.881153i	$0.656768\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	1.50000	+	2.59808i	0.170941	+	0.296078i
$78$		0			0
$79$	7.50000	−	12.9904i	0.843816	−	1.46153i	−0.0428296	−	0.999082i	$-0.513637\pi$
$79$	7.50000	−	12.9904i	0.843816	−	1.46153i	0.886646	−	0.462450i	$-0.153029\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−5.50000	−	9.52628i	−0.603703	−	1.04565i	−0.992255	−	0.124218i	$-0.960358\pi$
$83$	−5.50000	−	9.52628i	−0.603703	−	1.04565i	0.388552	−	0.921427i	$-0.372976\pi$
$84$		0			0
$85$	1.00000	+	1.73205i	0.108465	+	0.187867i
$86$		0			0
$87$	2.50000	−	4.33013i	0.268028	−	0.464238i
$88$		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
$93$	1.50000	−	2.59808i	0.155543	−	0.269408i
$94$		0			0
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$		0			0
$97$	−7.50000	−	12.9904i	−0.761510	−	1.31897i	−0.942072	−	0.335410i	$-0.891125\pi$
$97$	−7.50000	−	12.9904i	−0.761510	−	1.31897i	0.180563	−	0.983563i	$-0.442208\pi$
$98$		0			0
$99$	−0.500000	+	0.866025i	−0.0502519	+	0.0870388i
$100$		0			0
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$		0			0
$103$	−8.50000	+	14.7224i	−0.837530	+	1.45064i	0.0544240	+	0.998518i	$0.482668\pi$
$103$	−8.50000	+	14.7224i	−0.837530	+	1.45064i	−0.891954	+	0.452126i	$0.850666\pi$
$104$		0			0
$105$	3.00000	−	5.19615i	0.292770	−	0.507093i
$106$		0			0
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	−1.50000	−	2.59808i	−0.142374	−	0.246598i
$112$		0			0
$113$	−3.50000	+	6.06218i	−0.329252	+	0.570282i	−0.982364	−	0.186980i	$-0.940130\pi$
$113$	−3.50000	+	6.06218i	−0.329252	+	0.570282i	0.653111	+	0.757262i	$0.273463\pi$
$114$		0			0
$115$	−7.00000	−	12.1244i	−0.652753	−	1.13060i
$116$		0			0
$117$	2.50000	+	4.33013i	0.231125	+	0.400320i
$118$		0			0
$119$	3.00000			0.275010
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$	−3.50000	+	6.06218i	−0.315584	+	0.546608i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	3.50000	−	6.06218i	0.310575	−	0.537931i	−0.667912	−	0.744240i	$-0.732812\pi$
$127$	3.50000	−	6.06218i	0.310575	−	0.537931i	0.978487	+	0.206309i	$0.0661452\pi$
$128$		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
$133$	3.00000			0.260133
$134$		0			0
$135$	2.00000			0.172133
$136$		0			0
$137$	6.00000			0.512615			0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000			0.512615			0.256307	+	0.966595i	$0.417494\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$	−4.50000	+	7.79423i	−0.378968	+	0.656392i
$142$		0			0
$143$	−5.00000			−0.418121
$144$		0			0
$145$	5.00000	−	8.66025i	0.415227	−	0.719195i
$146$		0			0
$147$	−1.00000	−	1.73205i	−0.0824786	−	0.142857i
$148$		0			0
$149$	−14.0000			−1.14692			−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000			−1.14692			−0.573462	+	0.819232i	$0.694400\pi$
$150$		0			0
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	0.949637	−	0.313353i	$-0.101452\pi$
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	−0.746190	+	0.665733i	$0.768119\pi$
$152$		0			0
$153$	0.500000	+	0.866025i	0.0404226	+	0.0700140i
$154$		0			0
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$		0			0
$159$	2.00000			0.158610
$160$		0			0
$161$	−21.0000			−1.65503
$162$		0			0
$163$	−2.50000	+	4.33013i	−0.195815	+	0.339162i	−0.947167	−	0.320740i	$-0.896069\pi$
$163$	−2.50000	+	4.33013i	−0.195815	+	0.339162i	0.751352	+	0.659901i	$0.229402\pi$
$164$		0			0
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$		0			0
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	−0.802135	−	0.597143i	$-0.796303\pi$
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	0.918208	+	0.396098i	$0.129636\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$		0			0
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$		0			0
$175$	−1.50000	+	2.59808i	−0.113389	+	0.196396i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	0.706129	+	0.708083i	$0.250440\pi$
$182$		0			0
$183$	0.500000	+	0.866025i	0.0369611	+	0.0640184i
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$	−1.00000			−0.0731272
$188$		0			0
$189$	1.50000	−	2.59808i	0.109109	−	0.188982i
$190$		0			0
$191$	−5.50000	−	9.52628i	−0.397966	−	0.689297i	0.595509	−	0.803349i	$-0.296950\pi$
$191$	−5.50000	−	9.52628i	−0.397966	−	0.689297i	−0.993475	+	0.114051i	$0.963617\pi$
$192$		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
$195$	5.00000	+	8.66025i	0.358057	+	0.620174i
$196$		0			0
$197$	−3.50000	+	6.06218i	−0.249365	+	0.431912i	−0.963350	−	0.268249i	$-0.913555\pi$
$197$	−3.50000	+	6.06218i	−0.249365	+	0.431912i	0.713985	+	0.700161i	$0.246888\pi$
$198$		0			0
$199$	−3.50000	−	6.06218i	−0.248108	−	0.429736i	0.714893	−	0.699234i	$-0.246476\pi$
$199$	−3.50000	−	6.06218i	−0.248108	−	0.429736i	−0.963001	+	0.269498i	$0.913142\pi$
$200$		0			0
$201$	8.00000	−	1.73205i	0.564276	−	0.122169i
$202$		0			0
$203$	−7.50000	−	12.9904i	−0.526397	−	0.911746i
$204$		0			0
$205$	−7.00000	+	12.1244i	−0.488901	+	0.846802i
$206$		0			0
$207$	−3.50000	−	6.06218i	−0.243267	−	0.421350i
$208$		0			0
$209$	−1.00000			−0.0691714
$210$		0			0
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$		0			0
$213$	−2.50000	+	4.33013i	−0.171297	+	0.296695i
$214$		0			0
$215$	8.00000			0.545595
$216$		0			0
$217$	−4.50000	−	7.79423i	−0.305480	−	0.529107i
$218$		0			0
$219$	4.50000	+	7.79423i	0.304082	+	0.526685i
$220$		0			0
$221$	−2.50000	+	4.33013i	−0.168168	+	0.291276i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$		0			0
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	0.882073	−	0.471113i	$-0.156147\pi$
$229$	0.500000	+	0.866025i	0.0330409	+	0.0572286i	−0.849032	+	0.528341i	$0.822814\pi$
$230$		0			0
$231$	1.50000	+	2.59808i	0.0986928	+	0.170941i
$232$		0			0
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	−0.988013	−	0.154371i	$-0.950665\pi$
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	0.627696	+	0.778459i	$0.283998\pi$
$234$		0			0
$235$	−9.00000	+	15.5885i	−0.587095	+	1.01688i
$236$		0			0
$237$	7.50000	−	12.9904i	0.487177	−	0.843816i
$238$		0			0
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	−0.514719	−	0.857359i	$-0.672104\pi$
$239$	7.50000	−	12.9904i	0.485135	−	0.840278i	0.999854	+	0.0170808i	$0.00543724\pi$
$240$		0			0
$241$	−26.0000			−1.67481			−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000			−1.67481			−0.837404	+	0.546585i	$0.815928\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−2.00000	−	3.46410i	−0.127775	−	0.221313i
$246$		0			0
$247$	−2.50000	+	4.33013i	−0.159071	+	0.275519i
$248$		0			0
$249$	−5.50000	−	9.52628i	−0.348548	−	0.603703i
$250$		0			0
$251$	4.50000	+	7.79423i	0.284037	+	0.491967i	0.972375	−	0.233423i	$-0.0749927\pi$
$251$	4.50000	+	7.79423i	0.284037	+	0.491967i	−0.688338	+	0.725390i	$0.741659\pi$
$252$		0			0
$253$	7.00000			0.440086
$254$		0			0
$255$	1.00000	+	1.73205i	0.0626224	+	0.108465i
$256$		0			0
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$		0			0
$259$	−9.00000			−0.559233
$260$		0			0
$261$	2.50000	−	4.33013i	0.154746	−	0.268028i
$262$		0			0
$263$	−8.00000			−0.493301			−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000			−0.493301			−0.246651	+	0.969104i	$0.579330\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$		0			0
$267$	−18.0000			−1.10158
$268$		0			0
$269$	10.0000			0.609711			0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000			0.609711			0.304855	+	0.952399i	$0.401392\pi$
$270$		0			0
$271$	24.0000			1.45790			0.728948	−	0.684569i	$-0.240010\pi$
$271$	24.0000			1.45790			0.728948	+	0.684569i	$0.240010\pi$
$272$		0			0
$273$	15.0000			0.907841
$274$		0			0
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		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
$279$	1.50000	−	2.59808i	0.0898027	−	0.155543i
$280$		0			0
$281$	6.50000	+	11.2583i	0.387757	+	0.671616i	0.992148	−	0.125073i	$-0.0399165\pi$
$281$	6.50000	+	11.2583i	0.387757	+	0.671616i	−0.604390	+	0.796689i	$0.706583\pi$
$282$		0			0
$283$	−28.0000			−1.66443			−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000			−1.66443			−0.832214	+	0.554455i	$0.812927\pi$
$284$		0			0
$285$	1.00000	+	1.73205i	0.0592349	+	0.102598i
$286$		0			0
$287$	10.5000	+	18.1865i	0.619795	+	1.07352i
$288$		0			0
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$		0			0
$291$	−7.50000	−	12.9904i	−0.439658	−	0.761510i
$292$		0			0
$293$	−22.0000			−1.28525			−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000			−1.28525			−0.642627	+	0.766179i	$0.722155\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$		0			0
$299$	17.5000	−	30.3109i	1.01205	−	1.75292i
$300$		0			0
$301$	6.00000	−	10.3923i	0.345834	−	0.599002i
$302$		0			0
$303$	−1.50000	+	2.59808i	−0.0861727	+	0.149256i
$304$		0			0
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$		0			0
$307$	−5.50000	−	9.52628i	−0.313902	−	0.543693i	0.665302	−	0.746575i	$-0.268303\pi$
$307$	−5.50000	−	9.52628i	−0.313902	−	0.543693i	−0.979203	+	0.202881i	$0.934970\pi$
$308$		0			0
$309$	−8.50000	+	14.7224i	−0.483548	+	0.837530i
$310$		0			0
$311$	28.0000			1.58773			0.793867	−	0.608091i	$-0.208065\pi$
$311$	28.0000			1.58773			0.793867	+	0.608091i	$0.208065\pi$
$312$		0			0
$313$	−18.0000			−1.01742			−0.508710	−	0.860938i	$-0.669877\pi$
$313$	−18.0000			−1.01742			−0.508710	+	0.860938i	$0.669877\pi$
$314$		0			0
$315$	3.00000	−	5.19615i	0.169031	−	0.292770i
$316$		0			0
$317$	8.50000	+	14.7224i	0.477408	+	0.826894i	0.999665	−	0.0258939i	$-0.00824321\pi$
$317$	8.50000	+	14.7224i	0.477408	+	0.826894i	−0.522257	+	0.852788i	$0.674910\pi$
$318$		0			0
$319$	2.50000	+	4.33013i	0.139973	+	0.242441i
$320$		0			0
$321$	−4.00000			−0.223258
$322$		0			0
$323$	−0.500000	+	0.866025i	−0.0278207	+	0.0481869i
$324$		0			0
$325$	−2.50000	−	4.33013i	−0.138675	−	0.240192i
$326$		0			0
$327$	−2.00000			−0.110600
$328$		0			0
$329$	13.5000	+	23.3827i	0.744279	+	1.28913i
$330$		0			0
$331$	1.50000	−	2.59808i	0.0824475	−	0.142803i	−0.821853	−	0.569699i	$-0.807060\pi$
$331$	1.50000	−	2.59808i	0.0824475	−	0.142803i	0.904301	+	0.426896i	$0.140393\pi$
$332$		0			0
$333$	−1.50000	−	2.59808i	−0.0821995	−	0.142374i
$334$		0			0
$335$	16.0000	−	3.46410i	0.874173	−	0.189264i
$336$		0			0
$337$	−5.50000	−	9.52628i	−0.299604	−	0.518930i	0.676441	−	0.736497i	$-0.263521\pi$
$337$	−5.50000	−	9.52628i	−0.299604	−	0.518930i	−0.976045	+	0.217567i	$0.930188\pi$
$338$		0			0
$339$	−3.50000	+	6.06218i	−0.190094	+	0.329252i
$340$		0			0
$341$	1.50000	+	2.59808i	0.0812296	+	0.140694i
$342$		0			0
$343$	15.0000			0.809924
$344$		0			0
$345$	−7.00000	−	12.1244i	−0.376867	−	0.652753i
$346$		0			0
$347$	7.50000	−	12.9904i	0.402621	−	0.697360i	−0.591420	−	0.806363i	$-0.701433\pi$
$347$	7.50000	−	12.9904i	0.402621	−	0.697360i	0.994041	+	0.109003i	$0.0347659\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	2.50000	+	4.33013i	0.133440	+	0.231125i
$352$		0			0
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	0.594441	−	0.804139i	$-0.297373\pi$
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	−0.993626	+	0.112731i	$0.964040\pi$
$354$		0			0
$355$	−5.00000	+	8.66025i	−0.265372	+	0.459639i
$356$		0			0
$357$	3.00000			0.158777
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	5.00000	+	8.66025i	0.262432	+	0.454545i
$364$		0			0
$365$	9.00000	+	15.5885i	0.471082	+	0.815937i
$366$		0			0
$367$	−12.5000	+	21.6506i	−0.652495	+	1.13015i	0.330021	+	0.943974i	$0.392944\pi$
$367$	−12.5000	+	21.6506i	−0.652495	+	1.13015i	−0.982516	+	0.186180i	$0.940389\pi$
$368$		0			0
$369$	−3.50000	+	6.06218i	−0.182203	+	0.315584i
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	0.398036	+	0.917370i	$0.369692\pi$
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	−0.993484	+	0.113975i	$0.963641\pi$
$374$		0			0
$375$	−12.0000			−0.619677
$376$		0			0
$377$	25.0000			1.28757
$378$		0			0
$379$	14.5000	+	25.1147i	0.744815	+	1.29006i	0.950281	+	0.311393i	$0.100796\pi$
$379$	14.5000	+	25.1147i	0.744815	+	1.29006i	−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	3.50000	−	6.06218i	0.179310	−	0.310575i
$382$		0			0
$383$	0.500000	+	0.866025i	0.0255488	+	0.0442518i	0.878517	−	0.477711i	$-0.158533\pi$
$383$	0.500000	+	0.866025i	0.0255488	+	0.0442518i	−0.852968	+	0.521963i	$0.825200\pi$
$384$		0			0
$385$	3.00000	+	5.19615i	0.152894	+	0.264820i
$386$		0			0
$387$	4.00000			0.203331
$388$		0			0
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$		0			0
$391$	3.50000	−	6.06218i	0.177003	−	0.306578i
$392$		0			0
$393$	−12.0000			−0.605320
$394$		0			0
$395$	15.0000	−	25.9808i	0.754732	−	1.30723i
$396$		0			0
$397$	34.0000			1.70641			0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000			1.70641			0.853206	+	0.521575i	$0.174655\pi$
$398$		0			0
$399$	3.00000			0.150188
$400$		0			0
$401$	34.0000			1.69788			0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000			1.69788			0.848939	+	0.528490i	$0.177242\pi$
$402$		0			0
$403$	15.0000			0.747203
$404$		0			0
$405$	2.00000			0.0993808
$406$		0			0
$407$	3.00000			0.148704
$408$		0			0
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	−0.797574	−	0.603220i	$-0.793884\pi$
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	0.921192	+	0.389109i	$0.127217\pi$
$410$		0			0
$411$	6.00000			0.295958
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−11.0000	−	19.0526i	−0.539969	−	0.935253i
$416$		0			0
$417$	−4.00000			−0.195881
$418$		0			0
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	0.622601	−	0.782540i	$-0.286076\pi$
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	−0.989000	+	0.147918i	$0.952743\pi$
$420$		0			0
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	0.877952	−	0.478748i	$-0.158909\pi$
$421$	0.500000	+	0.866025i	0.0243685	+	0.0422075i	−0.853584	+	0.520955i	$0.825576\pi$
$422$		0			0
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$		0			0
$425$	−0.500000	−	0.866025i	−0.0242536	−	0.0420084i
$426$		0			0
$427$	3.00000			0.145180
$428$		0			0
$429$	−5.00000			−0.241402
$430$		0			0
$431$	11.5000	−	19.9186i	0.553936	−	0.959444i	−0.444050	−	0.896002i	$-0.646459\pi$
$431$	11.5000	−	19.9186i	0.553936	−	0.959444i	0.997985	−	0.0634424i	$-0.0202079\pi$
$432$		0			0
$433$	14.5000	−	25.1147i	0.696826	−	1.20694i	−0.272736	−	0.962089i	$-0.587929\pi$
$433$	14.5000	−	25.1147i	0.696826	−	1.20694i	0.969561	−	0.244848i	$-0.0787382\pi$
$434$		0			0
$435$	5.00000	−	8.66025i	0.239732	−	0.415227i
$436$		0			0
$437$	3.50000	−	6.06218i	0.167428	−	0.289993i
$438$		0			0
$439$	18.5000	+	32.0429i	0.882957	+	1.52933i	0.848038	+	0.529936i	$0.177784\pi$
$439$	18.5000	+	32.0429i	0.882957	+	1.52933i	0.0349192	+	0.999390i	$0.488883\pi$
$440$		0			0
$441$	−1.00000	−	1.73205i	−0.0476190	−	0.0824786i
$442$		0			0
$443$	19.5000	−	33.7750i	0.926473	−	1.60470i	0.137298	−	0.990530i	$-0.456158\pi$
$443$	19.5000	−	33.7750i	0.926473	−	1.60470i	0.789175	−	0.614168i	$-0.210508\pi$
$444$		0			0
$445$	−36.0000			−1.70656
$446$		0			0
$447$	−14.0000			−0.662177
$448$		0			0
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	−0.740087	−	0.672511i	$-0.765216\pi$
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	0.952455	+	0.304679i	$0.0985491\pi$
$450$		0			0
$451$	−3.50000	−	6.06218i	−0.164809	−	0.285457i
$452$		0			0
$453$	2.50000	+	4.33013i	0.117460	+	0.203447i
$454$		0			0
$455$	30.0000			1.40642
$456$		0			0
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$		0			0
$459$	0.500000	+	0.866025i	0.0233380	+	0.0404226i
$460$		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
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	0.877410	−	0.479741i	$-0.159269\pi$
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	−0.854173	+	0.519989i	$0.825936\pi$
$464$		0			0
$465$	3.00000	−	5.19615i	0.139122	−	0.240966i
$466$		0			0
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	0.773611	−	0.633661i	$-0.218448\pi$
$467$	−3.50000	−	6.06218i	−0.161961	−	0.280524i	−0.935572	+	0.353137i	$0.885115\pi$
$468$		0			0
$469$	7.50000	−	23.3827i	0.346318	−	1.07971i
$470$		0			0
$471$	6.50000	+	11.2583i	0.299504	+	0.518756i
$472$		0			0
$473$	−2.00000	+	3.46410i	−0.0919601	+	0.159280i
$474$		0			0
$475$	−0.500000	−	0.866025i	−0.0229416	−	0.0397360i
$476$		0			0
$477$	2.00000			0.0915737
$478$		0			0
$479$	14.5000	+	25.1147i	0.662522	+	1.14752i	0.979951	+	0.199240i	$0.0638472\pi$
$479$	14.5000	+	25.1147i	0.662522	+	1.14752i	−0.317429	+	0.948282i	$0.602819\pi$
$480$		0			0
$481$	7.50000	−	12.9904i	0.341971	−	0.592310i
$482$		0			0
$483$	−21.0000			−0.955533
$484$		0			0
$485$	−15.0000	−	25.9808i	−0.681115	−	1.17973i
$486$		0			0
$487$	16.5000	+	28.5788i	0.747686	+	1.29503i	0.948929	+	0.315489i	$0.102169\pi$
$487$	16.5000	+	28.5788i	0.747686	+	1.29503i	−0.201243	+	0.979541i	$0.564498\pi$
$488$		0			0
$489$	−2.50000	+	4.33013i	−0.113054	+	0.195815i
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	5.00000			0.225189
$494$		0			0
$495$	−1.00000	+	1.73205i	−0.0449467	+	0.0778499i
$496$		0			0
$497$	7.50000	+	12.9904i	0.336421	+	0.582698i
$498$		0			0
$499$	−1.50000	−	2.59808i	−0.0671492	−	0.116306i	0.830496	−	0.557024i	$-0.188057\pi$
$499$	−1.50000	−	2.59808i	−0.0671492	−	0.116306i	−0.897645	+	0.440719i	$0.854724\pi$
$500$		0			0
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$		0			0
$503$	−4.50000	+	7.79423i	−0.200645	+	0.347527i	−0.948736	−	0.316068i	$-0.897637\pi$
$503$	−4.50000	+	7.79423i	−0.200645	+	0.347527i	0.748091	+	0.663596i	$0.230970\pi$
$504$		0			0
$505$	−3.00000	+	5.19615i	−0.133498	+	0.231226i
$506$		0			0
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$		0			0
$509$	18.0000			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$510$		0			0
$511$	27.0000			1.19441
$512$		0			0
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$		0			0
$515$	−17.0000	+	29.4449i	−0.749110	+	1.29750i
$516$		0			0
$517$	−4.50000	−	7.79423i	−0.197910	−	0.342790i
$518$		0			0
$519$	4.50000	+	7.79423i	0.197528	+	0.342129i
$520$		0			0
$521$	38.0000			1.66481			0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000			1.66481			0.832405	+	0.554168i	$0.186963\pi$
$522$		0			0
$523$	−9.50000	−	16.4545i	−0.415406	−	0.719504i	0.580065	−	0.814570i	$-0.303027\pi$
$523$	−9.50000	−	16.4545i	−0.415406	−	0.719504i	−0.995471	+	0.0950659i	$0.969694\pi$
$524$		0			0
$525$	−1.50000	+	2.59808i	−0.0654654	+	0.113389i
$526$		0			0
$527$	3.00000			0.130682
$528$		0			0
$529$	−13.0000	+	22.5167i	−0.565217	+	0.978985i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−35.0000			−1.51602
$534$		0			0
$535$	−8.00000			−0.345870
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.00000			0.0861461
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$		0			0
$543$	−3.50000	+	6.06218i	−0.150199	+	0.260153i
$544$		0			0
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−4.50000	+	7.79423i	−0.192406	+	0.333257i	−0.946047	−	0.324029i	$-0.894962\pi$
$547$	−4.50000	+	7.79423i	−0.192406	+	0.333257i	0.753641	+	0.657286i	$0.228296\pi$
$548$		0			0
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$	5.00000			0.213007
$552$		0			0
$553$	−22.5000	−	38.9711i	−0.956797	−	1.65722i
$554$		0			0
$555$	−3.00000	−	5.19615i	−0.127343	−	0.220564i
$556$		0			0
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	−0.145802	−	0.989314i	$-0.546576\pi$
$557$	18.5000	−	32.0429i	0.783870	−	1.35770i	0.929672	−	0.368389i	$-0.120091\pi$
$558$		0			0
$559$	10.0000	+	17.3205i	0.422955	+	0.732579i
$560$		0			0
$561$	−1.00000			−0.0422200
$562$		0			0
$563$	−36.0000			−1.51722			−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000			−1.51722			−0.758610	+	0.651546i	$0.774121\pi$
$564$		0			0
$565$	−7.00000	+	12.1244i	−0.294492	+	0.510075i
$566$		0			0
$567$	1.50000	−	2.59808i	0.0629941	−	0.109109i
$568$		0			0
$569$	4.50000	−	7.79423i	0.188650	−	0.326751i	−0.756151	−	0.654398i	$-0.772922\pi$
$569$	4.50000	−	7.79423i	0.188650	−	0.326751i	0.944800	+	0.327647i	$0.106256\pi$
$570$		0			0
$571$	−18.5000	+	32.0429i	−0.774201	+	1.34096i	0.161042	+	0.986948i	$0.448515\pi$
$571$	−18.5000	+	32.0429i	−0.774201	+	1.34096i	−0.935243	+	0.354008i	$0.884819\pi$
$572$		0			0
$573$	−5.50000	−	9.52628i	−0.229766	−	0.397966i
$574$		0			0
$575$	3.50000	+	6.06218i	0.145960	+	0.252810i
$576$		0			0
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	−0.633062	−	0.774101i	$-0.718202\pi$
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	0.986922	+	0.161198i	$0.0515357\pi$
$578$		0			0
$579$	2.00000			0.0831172
$580$		0			0
$581$	−33.0000			−1.36907
$582$		0			0
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$		0			0
$585$	5.00000	+	8.66025i	0.206725	+	0.358057i
$586$		0			0
$587$	12.5000	+	21.6506i	0.515930	+	0.893617i	0.999829	+	0.0184934i	$0.00588696\pi$
$587$	12.5000	+	21.6506i	0.515930	+	0.893617i	−0.483899	+	0.875124i	$0.660780\pi$
$588$		0			0
$589$	3.00000			0.123613
$590$		0			0
$591$	−3.50000	+	6.06218i	−0.143971	+	0.249365i
$592$		0			0
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	0.996976	−	0.0777165i	$-0.0247629\pi$
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	−0.565792	+	0.824548i	$0.691430\pi$
$594$		0			0
$595$	6.00000			0.245976
$596$		0			0
$597$	−3.50000	−	6.06218i	−0.143245	−	0.248108i
$598$		0			0
$599$	−2.50000	+	4.33013i	−0.102147	+	0.176924i	−0.912569	−	0.408923i	$-0.865905\pi$
$599$	−2.50000	+	4.33013i	−0.102147	+	0.176924i	0.810422	+	0.585847i	$0.199238\pi$
$600$		0			0
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	0.604601	−	0.796528i	$-0.293332\pi$
$601$	−9.50000	−	16.4545i	−0.387513	−	0.671192i	−0.992114	+	0.125336i	$0.959999\pi$
$602$		0			0
$603$	8.00000	−	1.73205i	0.325785	−	0.0705346i
$604$		0			0
$605$	10.0000	+	17.3205i	0.406558	+	0.704179i
$606$		0			0
$607$	−18.5000	+	32.0429i	−0.750892	+	1.30058i	0.196499	+	0.980504i	$0.437043\pi$
$607$	−18.5000	+	32.0429i	−0.750892	+	1.30058i	−0.947391	+	0.320079i	$0.896291\pi$
$608$		0			0
$609$	−7.50000	−	12.9904i	−0.303915	−	0.526397i
$610$		0			0
$611$	−45.0000			−1.82051
$612$		0			0
$613$	6.50000	+	11.2583i	0.262533	+	0.454720i	0.966914	−	0.255102i	$-0.0821090\pi$
$613$	6.50000	+	11.2583i	0.262533	+	0.454720i	−0.704382	+	0.709821i	$0.748776\pi$
$614$		0			0
$615$	−7.00000	+	12.1244i	−0.282267	+	0.488901i
$616$		0			0
$617$	38.0000			1.52982			0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000			1.52982			0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$	−7.50000	−	12.9904i	−0.301450	−	0.522127i	0.675014	−	0.737805i	$-0.264137\pi$
$619$	−7.50000	−	12.9904i	−0.301450	−	0.522127i	−0.976465	+	0.215677i	$0.930804\pi$
$620$		0			0
$621$	−3.50000	−	6.06218i	−0.140450	−	0.243267i
$622$		0			0
$623$	−27.0000	+	46.7654i	−1.08173	+	1.87362i
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$	−1.00000			−0.0399362
$628$		0			0
$629$	1.50000	−	2.59808i	0.0598089	−	0.103592i
$630$		0			0
$631$	10.5000	+	18.1865i	0.417998	+	0.723994i	0.995738	−	0.0922266i	$-0.0293984\pi$
$631$	10.5000	+	18.1865i	0.417998	+	0.723994i	−0.577740	+	0.816221i	$0.696065\pi$
$632$		0			0
$633$	−11.5000	−	19.9186i	−0.457084	−	0.791693i
$634$		0			0
$635$	7.00000	−	12.1244i	0.277787	−	0.481140i
$636$		0			0
$637$	5.00000	−	8.66025i	0.198107	−	0.343132i
$638$		0			0
$639$	−2.50000	+	4.33013i	−0.0988985	+	0.171297i
$640$		0			0
$641$	12.5000	−	21.6506i	0.493720	−	0.855149i	−0.506254	−	0.862385i	$-0.668970\pi$
$641$	12.5000	−	21.6506i	0.493720	−	0.855149i	0.999974	+	0.00723604i	$0.00230332\pi$
$642$		0			0
$643$	−36.0000			−1.41970			−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000			−1.41970			−0.709851	+	0.704352i	$0.751238\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	0.500000	+	0.866025i	0.0196570	+	0.0340470i	0.875687	−	0.482880i	$-0.160409\pi$
$647$	0.500000	+	0.866025i	0.0196570	+	0.0340470i	−0.856030	+	0.516927i	$0.827076\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−4.50000	−	7.79423i	−0.176369	−	0.305480i
$652$		0			0
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	−0.941248	−	0.337715i	$-0.890346\pi$
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	0.178154	−	0.984003i	$-0.442987\pi$
$654$		0			0
$655$	−24.0000			−0.937758
$656$		0			0
$657$	4.50000	+	7.79423i	0.175562	+	0.304082i
$658$		0			0
$659$	25.5000	−	44.1673i	0.993339	−	1.72051i	0.396878	−	0.917871i	$-0.370093\pi$
$659$	25.5000	−	44.1673i	0.993339	−	1.72051i	0.596461	−	0.802642i	$-0.296573\pi$
$660$		0			0
$661$	−10.0000			−0.388955			−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000			−0.388955			−0.194477	+	0.980907i	$0.562301\pi$
$662$		0			0
$663$	−2.50000	+	4.33013i	−0.0970920	+	0.168168i
$664$		0			0
$665$	6.00000			0.232670
$666$		0			0
$667$	−35.0000			−1.35521
$668$		0			0
$669$	−4.00000			−0.154649
$670$		0			0
$671$	−1.00000			−0.0386046
$672$		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
$677$	14.5000	−	25.1147i	0.557280	−	0.965238i	−0.440442	−	0.897781i	$-0.645178\pi$
$677$	14.5000	−	25.1147i	0.557280	−	0.965238i	0.997722	−	0.0674566i	$-0.0214884\pi$
$678$		0			0
$679$	−45.0000			−1.72694
$680$		0			0
$681$	1.50000	−	2.59808i	0.0574801	−	0.0995585i
$682$		0			0
$683$	4.50000	+	7.79423i	0.172188	+	0.298238i	0.939184	−	0.343413i	$-0.111583\pi$
$683$	4.50000	+	7.79423i	0.172188	+	0.298238i	−0.766997	+	0.641651i	$0.778250\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	0.500000	+	0.866025i	0.0190762	+	0.0330409i
$688$		0			0
$689$	5.00000	+	8.66025i	0.190485	+	0.329929i
$690$		0			0
$691$	−0.500000	+	0.866025i	−0.0190209	+	0.0329452i	−0.875379	−	0.483437i	$-0.839388\pi$
$691$	−0.500000	+	0.866025i	−0.0190209	+	0.0329452i	0.856358	+	0.516382i	$0.172722\pi$
$692$		0			0
$693$	1.50000	+	2.59808i	0.0569803	+	0.0986928i
$694$		0			0
$695$	−8.00000			−0.303457
$696$		0			0
$697$	−7.00000			−0.265144
$698$		0			0
$699$	−5.50000	+	9.52628i	−0.208029	+	0.360317i
$700$		0			0
$701$	16.5000	−	28.5788i	0.623196	−	1.07941i	−0.365690	−	0.930737i	$-0.619167\pi$
$701$	16.5000	−	28.5788i	0.623196	−	1.07941i	0.988887	−	0.148671i	$-0.0474996\pi$
$702$		0			0
$703$	1.50000	−	2.59808i	0.0565736	−	0.0979883i
$704$		0			0
$705$	−9.00000	+	15.5885i	−0.338960	+	0.587095i
$706$		0			0
$707$	4.50000	+	7.79423i	0.169240	+	0.293132i
$708$		0			0
$709$	20.5000	+	35.5070i	0.769894	+	1.33349i	0.937620	+	0.347661i	$0.113024\pi$
$709$	20.5000	+	35.5070i	0.769894	+	1.33349i	−0.167727	+	0.985834i	$0.553643\pi$
$710$		0			0
$711$	7.50000	−	12.9904i	0.281272	−	0.487177i
$712$		0			0
$713$	−21.0000			−0.786456
$714$		0			0
$715$	−10.0000			−0.373979
$716$		0			0
$717$	7.50000	−	12.9904i	0.280093	−	0.485135i
$718$		0			0
$719$	8.50000	+	14.7224i	0.316997	+	0.549054i	0.979860	−	0.199686i	$-0.0639923\pi$
$719$	8.50000	+	14.7224i	0.316997	+	0.549054i	−0.662863	+	0.748740i	$0.730659\pi$
$720$		0			0
$721$	25.5000	+	44.1673i	0.949670	+	1.64488i
$722$		0			0
$723$	−26.0000			−0.966950
$724$		0			0
$725$	−2.50000	+	4.33013i	−0.0928477	+	0.160817i
$726$		0			0
$727$	−15.5000	−	26.8468i	−0.574863	−	0.995692i	−0.996056	−	0.0887213i	$-0.971722\pi$
$727$	−15.5000	−	26.8468i	−0.574863	−	0.995692i	0.421193	−	0.906971i	$-0.361611\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.00000	+	3.46410i	0.0739727	+	0.128124i
$732$		0			0
$733$	18.5000	−	32.0429i	0.683313	−	1.18353i	−0.290651	−	0.956829i	$-0.593872\pi$
$733$	18.5000	−	32.0429i	0.683313	−	1.18353i	0.973964	−	0.226704i	$-0.0727949\pi$
$734$		0			0
$735$	−2.00000	−	3.46410i	−0.0737711	−	0.127775i
$736$		0			0
$737$	−2.50000	+	7.79423i	−0.0920887	+	0.287104i
$738$		0			0
$739$	−7.50000	−	12.9904i	−0.275892	−	0.477859i	0.694468	−	0.719524i	$-0.255640\pi$
$739$	−7.50000	−	12.9904i	−0.275892	−	0.477859i	−0.970360	+	0.241665i	$0.922307\pi$
$740$		0			0
$741$	−2.50000	+	4.33013i	−0.0918398	+	0.159071i
$742$		0			0
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	0.991798	−	0.127815i	$-0.0407965\pi$
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	−0.606590	+	0.795015i	$0.707463\pi$
$744$		0			0
$745$	−28.0000			−1.02584
$746$		0			0
$747$	−5.50000	−	9.52628i	−0.201234	−	0.348548i
$748$		0			0
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$		0			0
$751$	−24.0000			−0.875772			−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000			−0.875772			−0.437886	+	0.899030i	$0.644273\pi$
$752$		0			0
$753$	4.50000	+	7.79423i	0.163989	+	0.284037i
$754$		0			0
$755$	5.00000	+	8.66025i	0.181969	+	0.315179i
$756$		0			0
$757$	10.5000	−	18.1865i	0.381629	−	0.661001i	−0.609666	−	0.792658i	$-0.708697\pi$
$757$	10.5000	−	18.1865i	0.381629	−	0.661001i	0.991295	+	0.131657i	$0.0420299\pi$
$758$		0			0
$759$	7.00000			0.254084
$760$		0			0
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$		0			0
$763$	−3.00000	+	5.19615i	−0.108607	+	0.188113i
$764$		0			0
$765$	1.00000	+	1.73205i	0.0361551	+	0.0626224i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	10.5000	−	18.1865i	0.378640	−	0.655823i	−0.612225	−	0.790684i	$-0.709725\pi$
$769$	10.5000	−	18.1865i	0.378640	−	0.655823i	0.990865	+	0.134860i	$0.0430586\pi$
$770$		0			0
$771$	−7.50000	+	12.9904i	−0.270106	+	0.467837i
$772$		0			0
$773$	−7.50000	+	12.9904i	−0.269756	+	0.467232i	−0.968799	−	0.247849i	$-0.920276\pi$
$773$	−7.50000	+	12.9904i	−0.269756	+	0.467232i	0.699043	+	0.715080i	$0.253610\pi$
$774$		0			0
$775$	−1.50000	+	2.59808i	−0.0538816	+	0.0933257i
$776$		0			0
$777$	−9.00000			−0.322873
$778$		0			0
$779$	−7.00000			−0.250801
$780$		0			0
$781$	−2.50000	−	4.33013i	−0.0894570	−	0.154944i
$782$		0			0
$783$	2.50000	−	4.33013i	0.0893427	−	0.154746i
$784$		0			0
$785$	13.0000	+	22.5167i	0.463990	+	0.803654i
$786$		0			0
$787$	8.50000	+	14.7224i	0.302992	+	0.524798i	0.976812	−	0.214097i	$-0.0686810\pi$
$787$	8.50000	+	14.7224i	0.302992	+	0.524798i	−0.673820	+	0.738896i	$0.735348\pi$
$788$		0			0
$789$	−8.00000			−0.284808
$790$		0			0
$791$	10.5000	+	18.1865i	0.373337	+	0.646639i
$792$		0			0
$793$	−2.50000	+	4.33013i	−0.0887776	+	0.153767i
$794$		0			0
$795$	4.00000			0.141865
$796$		0			0
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	−0.617933	−	0.786231i	$-0.712030\pi$
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	0.989862	+	0.142031i	$0.0453631\pi$
$798$		0			0
$799$	−9.00000			−0.318397
$800$		0			0
$801$	−18.0000			−0.635999
$802$		0			0
$803$	−9.00000			−0.317603
$804$		0			0
$805$	−42.0000			−1.48031
$806$		0			0
$807$	10.0000			0.352017
$808$		0			0
$809$	46.0000			1.61727			0.808637	−	0.588308i	$-0.200206\pi$
$809$	46.0000			1.61727			0.808637	+	0.588308i	$0.200206\pi$
$810$		0			0
$811$	3.50000	−	6.06218i	0.122902	−	0.212872i	−0.798009	−	0.602645i	$-0.794113\pi$
$811$	3.50000	−	6.06218i	0.122902	−	0.212872i	0.920911	+	0.389774i	$0.127447\pi$
$812$		0			0
$813$	24.0000			0.841717
$814$		0			0
$815$	−5.00000	+	8.66025i	−0.175142	+	0.303355i
$816$		0			0
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$		0			0
$819$	15.0000			0.524142
$820$		0			0
$821$	−23.5000	−	40.7032i	−0.820156	−	1.42055i	−0.905566	−	0.424205i	$-0.860553\pi$
$821$	−23.5000	−	40.7032i	−0.820156	−	1.42055i	0.0854103	−	0.996346i	$-0.472780\pi$
$822$		0			0
$823$	10.5000	+	18.1865i	0.366007	+	0.633943i	0.988937	−	0.148335i	$-0.0473913\pi$
$823$	10.5000	+	18.1865i	0.366007	+	0.633943i	−0.622930	+	0.782277i	$0.714058\pi$
$824$		0			0
$825$	0.500000	−	0.866025i	0.0174078	−	0.0301511i
$826$		0			0
$827$	−13.5000	−	23.3827i	−0.469441	−	0.813096i	0.529949	−	0.848030i	$-0.322211\pi$
$827$	−13.5000	−	23.3827i	−0.469441	−	0.813096i	−0.999390	+	0.0349341i	$0.988878\pi$
$828$		0			0
$829$	26.0000			0.903017			0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000			0.903017			0.451509	+	0.892267i	$0.350886\pi$
$830$		0			0
$831$	26.0000			0.901930
$832$		0			0
$833$	1.00000	−	1.73205i	0.0346479	−	0.0600120i
$834$		0			0
$835$	3.00000	−	5.19615i	0.103819	−	0.179820i
$836$		0			0
$837$	1.50000	−	2.59808i	0.0518476	−	0.0898027i
$838$		0			0
$839$	21.5000	−	37.2391i	0.742262	−	1.28564i	−0.209200	−	0.977873i	$-0.567086\pi$
$839$	21.5000	−	37.2391i	0.742262	−	1.28564i	0.951463	−	0.307763i	$-0.0995805\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$		0			0
$843$	6.50000	+	11.2583i	0.223872	+	0.387757i
$844$		0			0
$845$	−12.0000	+	20.7846i	−0.412813	+	0.715012i
$846$		0			0
$847$	30.0000			1.03081
$848$		0			0
$849$	−28.0000			−0.960958
$850$		0			0
$851$	−10.5000	+	18.1865i	−0.359935	+	0.623426i
$852$		0			0
$853$	−9.50000	−	16.4545i	−0.325274	−	0.563391i	0.656294	−	0.754505i	$-0.272123\pi$
$853$	−9.50000	−	16.4545i	−0.325274	−	0.563391i	−0.981568	+	0.191115i	$0.938790\pi$
$854$		0			0
$855$	1.00000	+	1.73205i	0.0341993	+	0.0592349i
$856$		0			0
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$		0			0
$859$	5.50000	−	9.52628i	0.187658	−	0.325032i	−0.756811	−	0.653633i	$-0.773244\pi$
$859$	5.50000	−	9.52628i	0.187658	−	0.325032i	0.944469	+	0.328601i	$0.106577\pi$
$860$		0			0
$861$	10.5000	+	18.1865i	0.357839	+	0.619795i
$862$		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
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$		0			0
$867$	8.00000	−	13.8564i	0.271694	−	0.470588i
$868$		0			0
$869$	7.50000	+	12.9904i	0.254420	+	0.440668i
$870$		0			0
$871$	27.5000	+	30.3109i	0.931802	+	1.02705i
$872$		0			0
$873$	−7.50000	−	12.9904i	−0.253837	−	0.439658i
$874$		0			0
$875$	−18.0000	+	31.1769i	−0.608511	+	1.05397i
$876$		0			0
$877$	−15.5000	−	26.8468i	−0.523398	−	0.906552i	−0.999629	−	0.0272316i	$-0.991331\pi$
$877$	−15.5000	−	26.8468i	−0.523398	−	0.906552i	0.476231	−	0.879320i	$-0.342002\pi$
$878$		0			0
$879$	−22.0000			−0.742042
$880$		0			0
$881$	18.5000	+	32.0429i	0.623281	+	1.07955i	0.988871	+	0.148778i	$0.0475340\pi$
$881$	18.5000	+	32.0429i	0.623281	+	1.07955i	−0.365590	+	0.930776i	$0.619133\pi$
$882$		0			0
$883$	−12.5000	+	21.6506i	−0.420658	+	0.728602i	−0.996004	−	0.0893086i	$-0.971534\pi$
$883$	−12.5000	+	21.6506i	−0.420658	+	0.728602i	0.575346	+	0.817910i	$0.304868\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.50000	−	2.59808i	−0.0503651	−	0.0872349i	0.839744	−	0.542983i	$-0.182705\pi$
$887$	−1.50000	−	2.59808i	−0.0503651	−	0.0872349i	−0.890109	+	0.455748i	$0.849372\pi$
$888$		0			0
$889$	−10.5000	−	18.1865i	−0.352159	−	0.609957i
$890$		0			0
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$		0			0
$893$	−9.00000			−0.301174
$894$		0			0
$895$		0			0
$896$		0			0
$897$	17.5000	−	30.3109i	0.584308	−	1.01205i
$898$		0			0
$899$	−7.50000	−	12.9904i	−0.250139	−	0.433253i
$900$		0			0
$901$	1.00000	+	1.73205i	0.0333148	+	0.0577030i
$902$		0			0
$903$	6.00000	−	10.3923i	0.199667	−	0.345834i
$904$		0			0
$905$	−7.00000	+	12.1244i	−0.232688	+	0.403027i
$906$		0			0
$907$	27.5000	−	47.6314i	0.913123	−	1.58157i	0.103495	−	0.994630i	$-0.466997\pi$
$907$	27.5000	−	47.6314i	0.913123	−	1.58157i	0.809627	−	0.586945i	$-0.199669\pi$
$908$		0			0
$909$	−1.50000	+	2.59808i	−0.0497519	+	0.0861727i
$910$		0			0
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$		0			0
$913$	11.0000			0.364047
$914$		0			0
$915$	1.00000	+	1.73205i	0.0330590	+	0.0572598i
$916$		0			0
$917$	−18.0000	+	31.1769i	−0.594412	+	1.02955i
$918$		0			0
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	0.715402	−	0.698713i	$-0.246244\pi$
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	−0.962804	+	0.270200i	$0.912910\pi$
$920$		0			0
$921$	−5.50000	−	9.52628i	−0.181231	−	0.313902i
$922$		0			0
$923$	−25.0000			−0.822885
$924$		0			0
$925$	1.50000	+	2.59808i	0.0493197	+	0.0854242i
$926$		0			0
$927$	−8.50000	+	14.7224i	−0.279177	+	0.483548i
$928$		0			0
$929$	18.0000			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$930$		0			0
$931$	1.00000	−	1.73205i	0.0327737	−	0.0567657i
$932$		0			0
$933$	28.0000			0.916679
$934$		0			0
$935$	−2.00000			−0.0654070
$936$		0			0
$937$	−50.0000			−1.63343			−0.816714	−	0.577042i	$-0.804207\pi$
$937$	−50.0000			−1.63343			−0.816714	+	0.577042i	$0.804207\pi$
$938$		0			0
$939$	−18.0000			−0.587408
$940$		0			0
$941$	14.0000			0.456387			0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000			0.456387			0.228193	+	0.973616i	$0.426718\pi$
$942$		0			0
$943$	49.0000			1.59566
$944$		0			0
$945$	3.00000	−	5.19615i	0.0975900	−	0.169031i
$946$		0			0
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$		0			0
$949$	−22.5000	+	38.9711i	−0.730381	+	1.26506i
$950$		0			0
$951$	8.50000	+	14.7224i	0.275631	+	0.477408i
$952$		0			0
$953$	−38.0000			−1.23094			−0.615470	−	0.788160i	$-0.711034\pi$
$953$	−38.0000			−1.23094			−0.615470	+	0.788160i	$0.711034\pi$
$954$		0			0
$955$	−11.0000	−	19.0526i	−0.355952	−	0.616526i
$956$		0			0
$957$	2.50000	+	4.33013i	0.0808135	+	0.139973i
$958$		0			0
$959$	9.00000	−	15.5885i	0.290625	−	0.503378i
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$		0			0
$963$	−4.00000			−0.128898
$964$		0			0
$965$	4.00000			0.128765
$966$		0			0
$967$	−18.5000	+	32.0429i	−0.594920	+	1.03043i	0.398638	+	0.917108i	$0.369483\pi$
$967$	−18.5000	+	32.0429i	−0.594920	+	1.03043i	−0.993558	+	0.113323i	$0.963850\pi$
$968$		0			0
$969$	−0.500000	+	0.866025i	−0.0160623	+	0.0278207i
$970$		0			0
$971$	−14.5000	+	25.1147i	−0.465327	+	0.805970i	−0.999216	−	0.0395843i	$-0.987397\pi$
$971$	−14.5000	+	25.1147i	−0.465327	+	0.805970i	0.533889	+	0.845555i	$0.320730\pi$
$972$		0			0
$973$	−6.00000	+	10.3923i	−0.192351	+	0.333162i
$974$		0			0
$975$	−2.50000	−	4.33013i	−0.0800641	−	0.138675i
$976$		0			0
$977$	−19.5000	−	33.7750i	−0.623860	−	1.08056i	−0.988760	−	0.149511i	$-0.952230\pi$
$977$	−19.5000	−	33.7750i	−0.623860	−	1.08056i	0.364900	−	0.931047i	$-0.381103\pi$
$978$		0			0
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$	−2.00000			−0.0638551
$982$		0			0
$983$	−52.0000			−1.65854			−0.829271	−	0.558846i	$-0.811244\pi$
$983$	−52.0000			−1.65854			−0.829271	+	0.558846i	$0.811244\pi$
$984$		0			0
$985$	−7.00000	+	12.1244i	−0.223039	+	0.386314i
$986$		0			0
$987$	13.5000	+	23.3827i	0.429710	+	0.744279i
$988$		0			0
$989$	−14.0000	−	24.2487i	−0.445174	−	0.771064i
$990$		0			0
$991$	52.0000			1.65183			0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000			1.65183			0.825917	+	0.563791i	$0.190658\pi$
$992$		0			0
$993$	1.50000	−	2.59808i	0.0476011	−	0.0824475i
$994$		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
$999$	−1.50000	−	2.59808i	−0.0474579	−	0.0821995i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.c.37.1	✓	2	1.1	even	1	trivial
804.2.i.c.565.1	yes	2	67.29	even	3	inner
2412.2.l.b.37.1		2	3.2	odd	2
2412.2.l.b.1369.1		2	201.29	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +2.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +2.00000 q^{5} +(1.50000 - 2.59808i) q^{7} +1.00000 q^{9} +(-0.500000 + 0.866025i) q^{11} +(2.50000 + 4.33013i) q^{13} +2.00000 q^{15} +(0.500000 + 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{19} +(1.50000 - 2.59808i) q^{21} +(-3.50000 - 6.06218i) q^{23} -1.00000 q^{25} +1.00000 q^{27} +(2.50000 - 4.33013i) q^{29} +(1.50000 - 2.59808i) q^{31} +(-0.500000 + 0.866025i) q^{33} +(3.00000 - 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(2.50000 + 4.33013i) q^{39} +(-3.50000 + 6.06218i) q^{41} +4.00000 q^{43} +2.00000 q^{45} +(-4.50000 + 7.79423i) q^{47} +(-1.00000 - 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{51} +2.00000 q^{53} +(-1.00000 + 1.73205i) q^{55} +(0.500000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{61} +(1.50000 - 2.59808i) q^{63} +(5.00000 + 8.66025i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-3.50000 - 6.06218i) q^{69} +(-2.50000 + 4.33013i) q^{71} +(4.50000 + 7.79423i) q^{73} -1.00000 q^{75} +(1.50000 + 2.59808i) q^{77} +(7.50000 - 12.9904i) q^{79} +1.00000 q^{81} +(-5.50000 - 9.52628i) q^{83} +(1.00000 + 1.73205i) q^{85} +(2.50000 - 4.33013i) q^{87} -18.0000 q^{89} +15.0000 q^{91} +(1.50000 - 2.59808i) q^{93} +(1.00000 + 1.73205i) q^{95} +(-7.50000 - 12.9904i) q^{97} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 4 q^{5} + 3 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 4 * q^5 + 3 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 4 q^{5} + 3 q^{7} + 2 q^{9} - q^{11} + 5 q^{13} + 4 q^{15} + q^{17} + q^{19} + 3 q^{21} - 7 q^{23} - 2 q^{25} + 2 q^{27} + 5 q^{29} + 3 q^{31} - q^{33} + 6 q^{35} - 3 q^{37} + 5 q^{39} - 7 q^{41} + 8 q^{43} + 4 q^{45} - 9 q^{47} - 2 q^{49} + q^{51} + 4 q^{53} - 2 q^{55} + q^{57} + q^{61} + 3 q^{63} + 10 q^{65} + 16 q^{67} - 7 q^{69} - 5 q^{71} + 9 q^{73} - 2 q^{75} + 3 q^{77} + 15 q^{79} + 2 q^{81} - 11 q^{83} + 2 q^{85} + 5 q^{87} - 36 q^{89} + 30 q^{91} + 3 q^{93} + 2 q^{95} - 15 q^{97} - q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 4 * q^5 + 3 * q^7 + 2 * q^9 - q^11 + 5 * q^13 + 4 * q^15 + q^17 + q^19 + 3 * q^21 - 7 * q^23 - 2 * q^25 + 2 * q^27 + 5 * q^29 + 3 * q^31 - q^33 + 6 * q^35 - 3 * q^37 + 5 * q^39 - 7 * q^41 + 8 * q^43 + 4 * q^45 - 9 * q^47 - 2 * q^49 + q^51 + 4 * q^53 - 2 * q^55 + q^57 + q^61 + 3 * q^63 + 10 * q^65 + 16 * q^67 - 7 * q^69 - 5 * q^71 + 9 * q^73 - 2 * q^75 + 3 * q^77 + 15 * q^79 + 2 * q^81 - 11 * q^83 + 2 * q^85 + 5 * q^87 - 36 * q^89 + 30 * q^91 + 3 * q^93 + 2 * q^95 - 15 * q^97 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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