LMFDB - Embedded newform 804.2.o.b.641.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(365,804)]

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, 3, 5]))

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

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

chi := DirichletCharacter("804.365");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			641.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	804.641
Dual form			804.2.o.b.365.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.41421i) q^{3} +2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.41421i) q^{3} +2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 + 2.82843i) q^{9} +(1.72474 + 2.98735i) q^{11} +(4.50000 + 2.59808i) q^{13} +(-2.00000 - 2.82843i) q^{15} +(-2.17423 - 1.25529i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(-7.17423 - 3.30518i) q^{21} +(8.17423 + 4.71940i) q^{23} -1.00000 q^{25} +(5.00000 - 1.41421i) q^{27} +(-7.62372 + 4.40156i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(2.50000 - 5.42650i) q^{33} +(7.89898 - 4.56048i) q^{35} +(-0.0505103 + 0.0874863i) q^{37} +(-0.825765 - 8.96204i) q^{39} +(-0.724745 - 1.25529i) q^{41} -12.5851i q^{43} +(-2.00000 + 5.65685i) q^{45} +(2.72474 - 1.57313i) q^{47} +(6.89898 - 11.9494i) q^{49} +(0.398979 + 4.33013i) q^{51} -6.00000 q^{53} +(3.44949 + 5.97469i) q^{55} +(5.17423 - 0.476756i) q^{57} -6.29253i q^{59} +(-0.398979 - 0.230351i) q^{61} +(2.50000 + 13.4511i) q^{63} +(9.00000 + 5.19615i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-1.50000 - 16.2795i) q^{69} +(-3.82577 + 2.20881i) q^{71} +(-1.94949 + 3.37662i) q^{73} +(1.00000 + 1.41421i) q^{75} +(13.6237 + 7.86566i) q^{77} +(-9.39898 + 5.42650i) q^{79} +(-7.00000 - 5.65685i) q^{81} +(-7.07321 - 4.08372i) q^{83} +(-4.34847 - 2.51059i) q^{85} +(13.8485 + 6.38002i) q^{87} -16.0492i q^{89} +23.6969 q^{91} +(2.72474 + 1.25529i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(-2.84847 - 1.64456i) q^{97} +(-10.1742 + 1.89097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 8 q^{5} + 6 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 8 * q^5 + 6 * q^7 - 4 * q^9	$ 4 q - 4 q^{3} + 8 q^{5} + 6 q^{7} - 4 q^{9} + 2 q^{11} + 18 q^{13} - 8 q^{15} + 6 q^{17} - 6 q^{19} - 14 q^{21} + 18 q^{23} - 4 q^{25} + 20 q^{27} - 6 q^{29} - 6 q^{31} + 10 q^{33} + 12 q^{35} - 10 q^{37} - 18 q^{39} + 2 q^{41} - 8 q^{45} + 6 q^{47} + 8 q^{49} - 18 q^{51} - 24 q^{53} + 4 q^{55} + 6 q^{57} + 18 q^{61} + 10 q^{63} + 36 q^{65} + 32 q^{67} - 6 q^{69} - 30 q^{71} + 2 q^{73} + 4 q^{75} + 30 q^{77} - 18 q^{79} - 28 q^{81} + 6 q^{83} + 12 q^{85} + 26 q^{87} + 36 q^{91} + 6 q^{93} - 12 q^{95} + 18 q^{97} - 26 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 8 * q^5 + 6 * q^7 - 4 * q^9 + 2 * q^11 + 18 * q^13 - 8 * q^15 + 6 * q^17 - 6 * q^19 - 14 * q^21 + 18 * q^23 - 4 * q^25 + 20 * q^27 - 6 * q^29 - 6 * q^31 + 10 * q^33 + 12 * q^35 - 10 * q^37 - 18 * q^39 + 2 * q^41 - 8 * q^45 + 6 * q^47 + 8 * q^49 - 18 * q^51 - 24 * q^53 + 4 * q^55 + 6 * q^57 + 18 * q^61 + 10 * q^63 + 36 * q^65 + 32 * q^67 - 6 * q^69 - 30 * q^71 + 2 * q^73 + 4 * q^75 + 30 * q^77 - 18 * q^79 - 28 * q^81 + 6 * q^83 + 12 * q^85 + 26 * q^87 + 36 * q^91 + 6 * q^93 - 12 * q^95 + 18 * q^97 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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	−	1.41421i	−0.577350	−	0.816497i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$4$		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
$7$	3.94949	−	2.28024i	1.49277	−	0.861849i	0.492801	−	0.870142i	$-0.335973\pi$
$7$	3.94949	−	2.28024i	1.49277	−	0.861849i	0.999966	+	0.00829261i	$0.00263965\pi$
$8$		0			0
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$		0			0
$11$	1.72474	+	2.98735i	0.520030	+	0.900719i	0.999729	+	0.0232854i	$0.00741263\pi$
$11$	1.72474	+	2.98735i	0.520030	+	0.900719i	−0.479699	+	0.877433i	$0.659254\pi$
$12$		0			0
$13$	4.50000	+	2.59808i	1.24808	+	0.720577i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	4.50000	+	2.59808i	1.24808	+	0.720577i	0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	−2.00000	−	2.82843i	−0.516398	−	0.730297i
$16$		0			0
$17$	−2.17423	−	1.25529i	−0.527329	−	0.304454i	0.212599	−	0.977140i	$-0.431807\pi$
$17$	−2.17423	−	1.25529i	−0.527329	−	0.304454i	−0.739928	+	0.672686i	$0.765141\pi$
$18$		0			0
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	−0.985194	−	0.171442i	$-0.945157\pi$
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	0.641071	+	0.767482i	$0.278491\pi$
$20$		0			0
$21$	−7.17423	−	3.30518i	−1.56555	−	0.721250i
$22$		0			0
$23$	8.17423	+	4.71940i	1.70445	+	0.984062i	0.941135	+	0.338031i	$0.109761\pi$
$23$	8.17423	+	4.71940i	1.70445	+	0.984062i	0.763311	+	0.646032i	$0.223573\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$		0			0
$29$	−7.62372	+	4.40156i	−1.41569	+	0.817349i	−0.995916	−	0.0902798i	$-0.971224\pi$
$29$	−7.62372	+	4.40156i	−1.41569	+	0.817349i	−0.419774	+	0.907629i	$0.637891\pi$
$30$		0			0
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	2.50000	−	5.42650i	0.435194	−	0.944633i
$34$		0			0
$35$	7.89898	−	4.56048i	1.33517	−	0.770861i
$36$		0			0
$37$	−0.0505103	+	0.0874863i	−0.00830384	+	0.0143827i	−0.870147	−	0.492791i	$-0.835977\pi$
$37$	−0.0505103	+	0.0874863i	−0.00830384	+	0.0143827i	0.861844	+	0.507174i	$0.169310\pi$
$38$		0			0
$39$	−0.825765	−	8.96204i	−0.132228	−	1.43507i
$40$		0			0
$41$	−0.724745	−	1.25529i	−0.113186	−	0.196044i	0.803867	−	0.594809i	$-0.202772\pi$
$41$	−0.724745	−	1.25529i	−0.113186	−	0.196044i	−0.917053	+	0.398765i	$0.869439\pi$
$42$		0			0
$43$		−	12.5851i		−	1.91920i	−0.281362	−	0.959602i	$-0.590786\pi$
$43$		−	12.5851i		−	1.91920i	0.281362	−	0.959602i	$-0.409214\pi$
$44$		0			0
$45$	−2.00000	+	5.65685i	−0.298142	+	0.843274i
$46$		0			0
$47$	2.72474	−	1.57313i	0.397445	−	0.229465i	−0.287936	−	0.957650i	$-0.592969\pi$
$47$	2.72474	−	1.57313i	0.397445	−	0.229465i	0.685381	+	0.728185i	$0.259636\pi$
$48$		0			0
$49$	6.89898	−	11.9494i	0.985568	−	1.70705i
$50$		0			0
$51$	0.398979	+	4.33013i	0.0558683	+	0.606339i
$52$		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
$55$	3.44949	+	5.97469i	0.465129	+	0.805627i
$56$		0			0
$57$	5.17423	−	0.476756i	0.685344	−	0.0631479i
$58$		0			0
$59$		−	6.29253i		−	0.819217i	−0.912261	−	0.409609i	$-0.865665\pi$
$59$		−	6.29253i		−	0.819217i	0.912261	−	0.409609i	$-0.134335\pi$
$60$		0			0
$61$	−0.398979	−	0.230351i	−0.0510841	−	0.0294934i	0.474240	−	0.880395i	$-0.342723\pi$
$61$	−0.398979	−	0.230351i	−0.0510841	−	0.0294934i	−0.525325	+	0.850902i	$0.676056\pi$
$62$		0			0
$63$	2.50000	+	13.4511i	0.314970	+	1.69468i
$64$		0			0
$65$	9.00000	+	5.19615i	1.11631	+	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	−	16.2795i	−0.180579	−	1.95982i
$70$		0			0
$71$	−3.82577	+	2.20881i	−0.454035	+	0.262137i	−0.709533	−	0.704672i	$-0.751094\pi$
$71$	−3.82577	+	2.20881i	−0.454035	+	0.262137i	0.255498	+	0.966810i	$0.417761\pi$
$72$		0			0
$73$	−1.94949	+	3.37662i	−0.228171	+	0.395203i	−0.957266	−	0.289209i	$-0.906608\pi$
$73$	−1.94949	+	3.37662i	−0.228171	+	0.395203i	0.729095	+	0.684412i	$0.239941\pi$
$74$		0			0
$75$	1.00000	+	1.41421i	0.115470	+	0.163299i
$76$		0			0
$77$	13.6237	+	7.86566i	1.55257	+	0.896375i
$78$		0			0
$79$	−9.39898	+	5.42650i	−1.05747	+	0.610529i	−0.924731	−	0.380622i	$-0.875710\pi$
$79$	−9.39898	+	5.42650i	−1.05747	+	0.610529i	−0.132737	+	0.991151i	$0.542377\pi$
$80$		0			0
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$		0			0
$83$	−7.07321	−	4.08372i	−0.776386	−	0.448247i	0.0587619	−	0.998272i	$-0.481285\pi$
$83$	−7.07321	−	4.08372i	−0.776386	−	0.448247i	−0.835148	+	0.550025i	$0.814618\pi$
$84$		0			0
$85$	−4.34847	−	2.51059i	−0.471658	−	0.272312i
$86$		0			0
$87$	13.8485	+	6.38002i	1.48471	+	0.684009i
$88$		0			0
$89$		−	16.0492i		−	1.70121i	−0.525807	−	0.850604i	$-0.676237\pi$
$89$		−	16.0492i		−	1.70121i	0.525807	−	0.850604i	$-0.323763\pi$
$90$		0			0
$91$	23.6969			2.48411
$92$		0			0
$93$	2.72474	+	1.25529i	0.282543	+	0.130168i
$94$		0			0
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	−2.84847	−	1.64456i	−0.289218	−	0.166980i	0.348371	−	0.937357i	$-0.386735\pi$
$97$	−2.84847	−	1.64456i	−0.289218	−	0.166980i	−0.637589	+	0.770377i	$0.720068\pi$
$98$		0			0
$99$	−10.1742	+	1.89097i	−1.02255	+	0.190050i
$100$		0			0
$101$	−4.27526	−	7.40496i	−0.425404	−	0.736821i	0.571054	−	0.820912i	$-0.306535\pi$
$101$	−4.27526	−	7.40496i	−0.425404	−	0.736821i	−0.996458	+	0.0840913i	$0.973201\pi$
$102$		0			0
$103$	−2.94949	−	5.10867i	−0.290622	−	0.503372i	0.683335	−	0.730105i	$-0.260529\pi$
$103$	−2.94949	−	5.10867i	−0.290622	−	0.503372i	−0.973957	+	0.226733i	$0.927195\pi$
$104$		0			0
$105$	−14.3485	−	6.61037i	−1.40027	−	0.645106i
$106$		0			0
$107$			2.19275i			0.211981i	0.994367	+	0.105991i	$0.0338014\pi$
$107$			2.19275i			0.211981i	−0.994367	+	0.105991i	$0.966199\pi$
$108$		0			0
$109$			11.9494i			1.14454i	0.820064	+	0.572272i	$0.193938\pi$
$109$			11.9494i			1.14454i	−0.820064	+	0.572272i	$0.806062\pi$
$110$		0			0
$111$	0.174235	−	0.0160540i	0.0165376	−	0.00152378i
$112$		0			0
$113$	−5.72474	−	9.91555i	−0.538539	−	0.932776i	−0.998983	−	0.0450878i	$-0.985643\pi$
$113$	−5.72474	−	9.91555i	−0.538539	−	0.932776i	0.460444	−	0.887689i	$-0.347690\pi$
$114$		0			0
$115$	16.3485	+	9.43879i	1.52450	+	0.880172i
$116$		0			0
$117$	−11.8485	+	10.1298i	−1.09539	+	0.936505i
$118$		0			0
$119$	−11.4495			−1.04957
$120$		0			0
$121$	−0.449490	+	0.778539i	−0.0408627	+	0.0707763i
$122$		0			0
$123$	−1.05051	+	2.28024i	−0.0947213	+	0.205602i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−5.39898	−	9.35131i	−0.479082	−	0.829794i	0.520630	−	0.853782i	$-0.325697\pi$
$127$	−5.39898	−	9.35131i	−0.479082	−	0.829794i	−0.999712	+	0.0239879i	$0.992364\pi$
$128$		0			0
$129$	−17.7980	+	12.5851i	−1.56702	+	1.10805i
$130$		0			0
$131$			0.635674i			0.0555391i	0.999614	+	0.0277696i	$0.00884046\pi$
$131$			0.635674i			0.0555391i	−0.999614	+	0.0277696i	$0.991160\pi$
$132$		0			0
$133$			13.6814i			1.18633i
$134$		0			0
$135$	10.0000	−	2.82843i	0.860663	−	0.243432i
$136$		0			0
$137$	−18.8990			−1.61465			−0.807324	−	0.590108i	$-0.799085\pi$
$137$	−18.8990			−1.61465			−0.807324	+	0.590108i	$0.799085\pi$
$138$		0			0
$139$			21.0703i			1.78716i	0.448901	+	0.893581i	$0.351816\pi$
$139$			21.0703i			1.78716i	−0.448901	+	0.893581i	$0.648184\pi$
$140$		0			0
$141$	−4.94949	−	2.28024i	−0.416822	−	0.192031i
$142$		0			0
$143$			17.9241i			1.49889i
$144$		0			0
$145$	−15.2474	+	8.80312i	−1.26623	+	0.731059i
$146$		0			0
$147$	−23.7980	+	2.19275i	−1.96282	+	0.180855i
$148$		0			0
$149$			7.84961i			0.643065i	0.946899	+	0.321532i	$0.104198\pi$
$149$			7.84961i			0.643065i	−0.946899	+	0.321532i	$0.895802\pi$
$150$		0			0
$151$	5.39898	−	9.35131i	0.439363	−	0.760999i	−0.558278	−	0.829654i	$-0.688538\pi$
$151$	5.39898	−	9.35131i	0.439363	−	0.760999i	0.997640	+	0.0686556i	$0.0218710\pi$
$152$		0			0
$153$	5.72474	−	4.89437i	0.462818	−	0.395686i
$154$		0			0
$155$	−3.00000	+	1.73205i	−0.240966	+	0.139122i
$156$		0			0
$157$	2.05051	−	3.55159i	0.163649	−	0.283448i	−0.772526	−	0.634983i	$-0.781007\pi$
$157$	2.05051	−	3.55159i	0.163649	−	0.283448i	0.936175	+	0.351536i	$0.114340\pi$
$158$		0			0
$159$	6.00000	+	8.48528i	0.475831	+	0.672927i
$160$		0			0
$161$	43.0454			3.39245
$162$		0			0
$163$	8.29796	+	14.3725i	0.649946	+	1.12574i	0.983135	+	0.182880i	$0.0585420\pi$
$163$	8.29796	+	14.3725i	0.649946	+	1.12574i	−0.333189	+	0.942860i	$0.608125\pi$
$164$		0			0
$165$	5.00000	−	10.8530i	0.389249	−	0.844905i
$166$		0			0
$167$	4.92679	−	2.84448i	0.381246	−	0.220113i	−0.297114	−	0.954842i	$-0.596024\pi$
$167$	4.92679	−	2.84448i	0.381246	−	0.220113i	0.678360	+	0.734729i	$0.262691\pi$
$168$		0			0
$169$	7.00000	+	12.1244i	0.538462	+	0.932643i
$170$		0			0
$171$	−5.84847	−	6.84072i	−0.447244	−	0.523123i
$172$		0			0
$173$	1.62372	+	0.937458i	0.123449	+	0.0712736i	0.560453	−	0.828186i	$-0.310627\pi$
$173$	1.62372	+	0.937458i	0.123449	+	0.0712736i	−0.437004	+	0.899460i	$0.643960\pi$
$174$		0			0
$175$	−3.94949	+	2.28024i	−0.298553	+	0.172370i
$176$		0			0
$177$	−8.89898	+	6.29253i	−0.668888	+	0.472975i
$178$		0			0
$179$	−25.5959			−1.91313			−0.956564	−	0.291521i	$-0.905839\pi$
$179$	−25.5959			−1.91313			−0.956564	+	0.291521i	$0.905839\pi$
$180$		0			0
$181$	5.94949	+	10.3048i	0.442222	+	0.765951i	0.997854	−	0.0654772i	$-0.0208570\pi$
$181$	5.94949	+	10.3048i	0.442222	+	0.765951i	−0.555632	+	0.831428i	$0.687524\pi$
$182$		0			0
$183$	0.0732141	+	0.794593i	0.00541214	+	0.0587380i
$184$		0			0
$185$	−0.101021	+	0.174973i	−0.00742718	+	0.0128642i
$186$		0			0
$187$		−	8.66025i		−	0.633300i
$188$		0			0
$189$	16.5227	−	16.9866i	1.20185	−	1.23559i
$190$		0			0
$191$	6.27526	−	10.8691i	0.454062	−	0.786458i	−0.544572	−	0.838714i	$-0.683308\pi$
$191$	6.27526	−	10.8691i	0.454062	−	0.786458i	0.998634	+	0.0522563i	$0.0166413\pi$
$192$		0			0
$193$	−3.10102			−0.223216			−0.111608	−	0.993752i	$-0.535600\pi$
$193$	−3.10102			−0.223216			−0.111608	+	0.993752i	$0.535600\pi$
$194$		0			0
$195$	−1.65153	−	17.9241i	−0.118269	−	1.28357i
$196$		0			0
$197$	10.6237	+	18.4008i	0.756909	+	1.31100i	0.944420	+	0.328742i	$0.106625\pi$
$197$	10.6237	+	18.4008i	0.756909	+	1.31100i	−0.187511	+	0.982263i	$0.560042\pi$
$198$		0			0
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	0.992434	+	0.122782i	$0.0391815\pi$
$200$		0			0
$201$	−10.4495	−	9.58166i	−0.737050	−	0.675838i
$202$		0			0
$203$	−20.0732	+	34.7678i	−1.40886	+	2.44022i
$204$		0			0
$205$	−1.44949	−	2.51059i	−0.101237	−	0.175347i
$206$		0			0
$207$	−21.5227	+	18.4008i	−1.49593	+	1.27895i
$208$		0			0
$209$	−10.3485			−0.715819
$210$		0			0
$211$	−1.94949	+	3.37662i	−0.134208	+	0.232456i	−0.925295	−	0.379249i	$-0.876182\pi$
$211$	−1.94949	+	3.37662i	−0.134208	+	0.232456i	0.791086	+	0.611704i	$0.209516\pi$
$212$		0			0
$213$	6.94949	+	3.20164i	0.476171	+	0.219373i
$214$		0			0
$215$		−	25.1701i		−	1.71659i
$216$		0			0
$217$	−3.94949	+	6.84072i	−0.268109	+	0.464378i
$218$		0			0
$219$	6.72474	−	0.619620i	0.454416	−	0.0418701i
$220$		0			0
$221$	−6.52270	−	11.2977i	−0.438765	−	0.759962i
$222$		0			0
$223$	−8.69694			−0.582390			−0.291195	−	0.956664i	$-0.594053\pi$
$223$	−8.69694			−0.582390			−0.291195	+	0.956664i	$0.594053\pi$
$224$		0			0
$225$	1.00000	−	2.82843i	0.0666667	−	0.188562i
$226$		0			0
$227$	8.42168	−	4.86226i	0.558967	−	0.322720i	−0.193764	−	0.981048i	$-0.562070\pi$
$227$	8.42168	−	4.86226i	0.558967	−	0.322720i	0.752731	+	0.658329i	$0.228736\pi$
$228$		0			0
$229$	5.84847	+	3.37662i	0.386478	+	0.223133i	0.680633	−	0.732625i	$-0.261705\pi$
$229$	5.84847	+	3.37662i	0.386478	+	0.223133i	−0.294155	+	0.955758i	$0.595038\pi$
$230$		0			0
$231$	−2.50000	−	27.1325i	−0.164488	−	1.78519i
$232$		0			0
$233$	−11.7247	−	20.3079i	−0.768114	−	1.33041i	−0.938585	−	0.345049i	$-0.887862\pi$
$233$	−11.7247	−	20.3079i	−0.768114	−	1.33041i	0.170471	−	0.985363i	$-0.445471\pi$
$234$		0			0
$235$	5.44949	−	3.14626i	0.355486	−	0.205240i
$236$		0			0
$237$	17.0732	+	7.86566i	1.10902	+	0.510930i
$238$		0			0
$239$	−6.62372	−	11.4726i	−0.428453	−	0.742103i	0.568283	−	0.822833i	$-0.307608\pi$
$239$	−6.62372	−	11.4726i	−0.428453	−	0.742103i	−0.996736	+	0.0807307i	$0.974275\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$		0			0
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$		0			0
$245$	13.7980	−	23.8988i	0.881519	−	1.52684i
$246$		0			0
$247$	−13.5000	+	7.79423i	−0.858984	+	0.495935i
$248$		0			0
$249$	1.29796	+	14.0868i	0.0822548	+	0.892712i
$250$		0			0
$251$	7.07321	−	12.2512i	0.446457	−	0.773287i	−0.551695	−	0.834046i	$-0.686019\pi$
$251$	7.07321	−	12.2512i	0.446457	−	0.773287i	0.998152	+	0.0607591i	$0.0193521\pi$
$252$		0			0
$253$			32.5590i			2.04697i
$254$		0			0
$255$	0.797959	+	8.66025i	0.0499701	+	0.542326i
$256$		0			0
$257$	−4.07321	+	2.35167i	−0.254080	+	0.146693i	−0.621631	−	0.783310i	$-0.713530\pi$
$257$	−4.07321	+	2.35167i	−0.254080	+	0.146693i	0.367551	+	0.930003i	$0.380196\pi$
$258$		0			0
$259$			0.460702i			0.0286266i
$260$		0			0
$261$	−4.82577	−	25.9647i	−0.298707	−	1.60718i
$262$		0			0
$263$		−	14.7778i		−	0.911239i	−0.890175	−	0.455619i	$-0.849418\pi$
$263$		−	14.7778i		−	0.911239i	0.890175	−	0.455619i	$-0.150582\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	−22.6969	+	16.0492i	−1.38903	+	0.982193i
$268$		0			0
$269$			28.6342i			1.74586i	0.487846	+	0.872929i	$0.337783\pi$
$269$			28.6342i			1.74586i	−0.487846	+	0.872929i	$0.662217\pi$
$270$		0			0
$271$			4.09978i			0.249044i	0.992217	+	0.124522i	$0.0397397\pi$
$271$			4.09978i			0.249044i	−0.992217	+	0.124522i	$0.960260\pi$
$272$		0			0
$273$	−23.6969	−	33.5125i	−1.43420	−	2.02827i
$274$		0			0
$275$	−1.72474	−	2.98735i	−0.104006	−	0.180144i
$276$		0			0
$277$	6.20204			0.372645			0.186322	−	0.982489i	$-0.440343\pi$
$277$	6.20204			0.372645			0.186322	+	0.982489i	$0.440343\pi$
$278$		0			0
$279$	−0.949490	−	5.10867i	−0.0568445	−	0.305848i
$280$		0			0
$281$	−1.27526	+	2.20881i	−0.0760753	+	0.131766i	−0.901553	−	0.432668i	$-0.857572\pi$
$281$	−1.27526	+	2.20881i	−0.0760753	+	0.131766i	0.825478	+	0.564434i	$0.190906\pi$
$282$		0			0
$283$	11.7980			0.701316			0.350658	−	0.936504i	$-0.385958\pi$
$283$	11.7980			0.701316			0.350658	+	0.936504i	$0.385958\pi$
$284$		0			0
$285$	10.3485	−	0.953512i	0.612990	−	0.0564812i
$286$		0			0
$287$	−5.72474	−	3.30518i	−0.337921	−	0.195099i
$288$		0			0
$289$	−5.34847	−	9.26382i	−0.314616	−	0.544931i
$290$		0			0
$291$	0.522704	+	5.67291i	0.0306414	+	0.332552i
$292$		0			0
$293$		−	12.2993i		−	0.718534i	−0.933235	−	0.359267i	$-0.883027\pi$
$293$		−	12.2993i		−	0.718534i	0.933235	−	0.359267i	$-0.116973\pi$
$294$		0			0
$295$		−	12.5851i		−	0.732730i
$296$		0			0
$297$	12.8485	+	12.4976i	0.745544	+	0.725183i
$298$		0			0
$299$	24.5227	+	42.4746i	1.41818	+	2.45637i
$300$		0			0
$301$	−28.6969	−	49.7046i	−1.65406	−	2.86492i
$302$		0			0
$303$	−6.19694	+	13.4511i	−0.356005	+	0.772745i
$304$		0			0
$305$	−0.797959	−	0.460702i	−0.0456910	−	0.0263797i
$306$		0			0
$307$	15.2980	−	26.4968i	0.873101	−	1.51225i	0.0143283	−	0.999897i	$-0.495439\pi$
$307$	15.2980	−	26.4968i	0.873101	−	1.51225i	0.858772	−	0.512357i	$-0.171228\pi$
$308$		0			0
$309$	−4.27526	+	9.27987i	−0.243211	+	0.527914i
$310$		0			0
$311$	33.7980			1.91651			0.958253	−	0.285921i	$-0.0922995\pi$
$311$	33.7980			1.91651			0.958253	+	0.285921i	$0.0922995\pi$
$312$		0			0
$313$			22.9774i			1.29876i	0.760465	+	0.649379i	$0.224971\pi$
$313$			22.9774i			1.29876i	−0.760465	+	0.649379i	$0.775029\pi$
$314$		0			0
$315$	5.00000	+	26.9022i	0.281718	+	1.51577i
$316$		0			0
$317$	25.3207	+	14.6189i	1.42215	+	0.821079i	0.996483	−	0.0838009i	$-0.0267060\pi$
$317$	25.3207	+	14.6189i	1.42215	+	0.821079i	0.425668	+	0.904880i	$0.360039\pi$
$318$		0			0
$319$	−26.2980	−	15.1831i	−1.47240	−	0.850092i
$320$		0			0
$321$	3.10102	−	2.19275i	0.173082	−	0.122388i
$322$		0			0
$323$	6.52270	−	3.76588i	0.362933	−	0.209539i
$324$		0			0
$325$	−4.50000	−	2.59808i	−0.249615	−	0.144115i
$326$		0			0
$327$	16.8990	−	11.9494i	0.934516	−	0.660802i
$328$		0			0
$329$	7.17423	−	12.4261i	0.395528	−	0.685075i
$330$		0			0
$331$	27.0959	−	15.6438i	1.48933	−	0.859863i	0.489401	−	0.872059i	$-0.337216\pi$
$331$	27.0959	−	15.6438i	1.48933	−	0.859863i	0.999926	+	0.0121961i	$0.00388222\pi$
$332$		0			0
$333$	−0.196938	−	0.230351i	−0.0107922	−	0.0126232i
$334$		0			0
$335$	16.0000	−	3.46410i	0.874173	−	0.189264i
$336$		0			0
$337$	−11.0505	−	6.38002i	−0.601960	−	0.347542i	0.167852	−	0.985812i	$-0.446317\pi$
$337$	−11.0505	−	6.38002i	−0.601960	−	0.347542i	−0.769812	+	0.638271i	$0.779650\pi$
$338$		0			0
$339$	−8.29796	+	18.0116i	−0.450683	+	0.978254i
$340$		0			0
$341$	−5.17423	−	2.98735i	−0.280201	−	0.161774i
$342$		0			0
$343$		−	31.0019i		−	1.67395i
$344$		0			0
$345$	−3.00000	−	32.5590i	−0.161515	−	1.75292i
$346$		0			0
$347$	11.0732	+	19.1794i	0.594441	+	1.02960i	0.993625	+	0.112732i	$0.0359601\pi$
$347$	11.0732	+	19.1794i	0.594441	+	1.02960i	−0.399184	+	0.916871i	$0.630707\pi$
$348$		0			0
$349$	21.7980			1.16682			0.583409	−	0.812179i	$-0.301718\pi$
$349$	21.7980			1.16682			0.583409	+	0.812179i	$0.301718\pi$
$350$		0			0
$351$	26.1742	+	6.62642i	1.39708	+	0.353692i
$352$		0			0
$353$	−4.17423	+	7.22999i	−0.222172	+	0.384813i	−0.955467	−	0.295097i	$-0.904648\pi$
$353$	−4.17423	+	7.22999i	−0.222172	+	0.384813i	0.733295	+	0.679910i	$0.237981\pi$
$354$		0			0
$355$	−7.65153	+	4.41761i	−0.406101	+	0.234463i
$356$		0			0
$357$	11.4495	+	16.1920i	0.605971	+	0.856973i
$358$		0			0
$359$			20.4347i			1.07850i	0.842146	+	0.539250i	$0.181292\pi$
$359$			20.4347i			1.07850i	−0.842146	+	0.539250i	$0.818708\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$		0			0
$363$	1.55051	−	0.142865i	0.0813807	−	0.00749845i
$364$		0			0
$365$	−3.89898	+	6.75323i	−0.204082	+	0.353480i
$366$		0			0
$367$	13.5000	−	7.79423i	0.704694	−	0.406855i	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	13.5000	−	7.79423i	0.704694	−	0.406855i	0.809093	+	0.587680i	$0.199959\pi$
$368$		0			0
$369$	4.27526	−	0.794593i	0.222561	−	0.0413649i
$370$		0			0
$371$	−23.6969	+	13.6814i	−1.23028	+	0.710305i
$372$		0			0
$373$	−9.39898	+	5.42650i	−0.486661	+	0.280974i	−0.723188	−	0.690651i	$-0.757324\pi$
$373$	−9.39898	+	5.42650i	−0.486661	+	0.280974i	0.236527	+	0.971625i	$0.423991\pi$
$374$		0			0
$375$	12.0000	+	16.9706i	0.619677	+	0.876356i
$376$		0			0
$377$	−45.7423			−2.35585
$378$		0			0
$379$	−30.3990	−	17.5509i	−1.56149	−	0.901527i	−0.997107	−	0.0760147i	$-0.975780\pi$
$379$	−30.3990	−	17.5509i	−1.56149	−	0.901527i	−0.564384	−	0.825512i	$-0.690886\pi$
$380$		0			0
$381$	−7.82577	+	16.9866i	−0.400926	+	0.870251i
$382$		0			0
$383$	5.07321	−	8.78706i	0.259229	−	0.448998i	−0.706806	−	0.707407i	$-0.749865\pi$
$383$	5.07321	−	8.78706i	0.259229	−	0.448998i	0.966036	+	0.258409i	$0.0831982\pi$
$384$		0			0
$385$	27.2474	+	15.7313i	1.38866	+	0.801742i
$386$		0			0
$387$	35.5959	+	12.5851i	1.80944	+	0.639734i
$388$		0			0
$389$	17.9722	+	10.3763i	0.911226	+	0.526097i	0.880826	−	0.473441i	$-0.156988\pi$
$389$	17.9722	+	10.3763i	0.911226	+	0.526097i	0.0304008	+	0.999538i	$0.490322\pi$
$390$		0			0
$391$	−11.8485	−	20.5222i	−0.599203	−	1.03785i
$392$		0			0
$393$	0.898979	−	0.635674i	0.0453475	−	0.0320655i
$394$		0			0
$395$	−18.7980	+	10.8530i	−0.945828	+	0.546074i
$396$		0			0
$397$	2.69694			0.135355			0.0676777	−	0.997707i	$-0.478441\pi$
$397$	2.69694			0.135355			0.0676777	+	0.997707i	$0.478441\pi$
$398$		0			0
$399$	19.3485	−	13.6814i	0.968635	−	0.684928i
$400$		0			0
$401$	14.8990			0.744020			0.372010	−	0.928229i	$-0.378669\pi$
$401$	14.8990			0.744020			0.372010	+	0.928229i	$0.378669\pi$
$402$		0			0
$403$	−9.00000			−0.448322
$404$		0			0
$405$	−14.0000	−	11.3137i	−0.695666	−	0.562183i
$406$		0			0
$407$	−0.348469			−0.0172730
$408$		0			0
$409$	−16.5000	+	9.52628i	−0.815872	+	0.471044i	−0.848991	−	0.528407i	$-0.822789\pi$
$409$	−16.5000	+	9.52628i	−0.815872	+	0.471044i	0.0331186	+	0.999451i	$0.489456\pi$
$410$		0			0
$411$	18.8990	+	26.7272i	0.932218	+	1.31836i
$412$		0			0
$413$	−14.3485	−	24.8523i	−0.706042	−	1.22290i
$414$		0			0
$415$	−14.1464	−	8.16744i	−0.694421	−	0.400924i
$416$		0			0
$417$	29.7980	−	21.0703i	1.45921	−	1.03182i
$418$		0			0
$419$	−19.3207	−	11.1548i	−0.943876	−	0.544947i	−0.0527029	−	0.998610i	$-0.516784\pi$
$419$	−19.3207	−	11.1548i	−0.943876	−	0.544947i	−0.891173	+	0.453663i	$0.850117\pi$
$420$		0			0
$421$	−6.50000	+	11.2583i	−0.316791	+	0.548697i	−0.979817	−	0.199899i	$-0.935939\pi$
$421$	−6.50000	+	11.2583i	−0.316791	+	0.548697i	0.663026	+	0.748596i	$0.269272\pi$
$422$		0			0
$423$	1.72474	+	9.27987i	0.0838600	+	0.451203i
$424$		0			0
$425$	2.17423	+	1.25529i	0.105466	+	0.0608907i
$426$		0			0
$427$	−2.10102			−0.101676
$428$		0			0
$429$	25.3485	−	17.9241i	1.22384	−	0.865382i
$430$		0			0
$431$	−18.7702	+	10.8370i	−0.904126	+	0.521998i	−0.878537	−	0.477675i	$-0.841480\pi$
$431$	−18.7702	+	10.8370i	−0.904126	+	0.521998i	−0.0255898	+	0.999673i	$0.508146\pi$
$432$		0			0
$433$	−13.5000	+	7.79423i	−0.648769	+	0.374567i	−0.787984	−	0.615695i	$-0.788875\pi$
$433$	−13.5000	+	7.79423i	−0.648769	+	0.374567i	0.139216	+	0.990262i	$0.455542\pi$
$434$		0			0
$435$	27.6969	+	12.7600i	1.32797	+	0.611797i
$436$		0			0
$437$	−24.5227	+	14.1582i	−1.17308	+	0.677278i
$438$		0			0
$439$	−14.3990	+	24.9398i	−0.687226	+	1.19031i	0.285506	+	0.958377i	$0.407838\pi$
$439$	−14.3990	+	24.9398i	−0.687226	+	1.19031i	−0.972732	+	0.231933i	$0.925495\pi$
$440$		0			0
$441$	26.8990	+	31.4626i	1.28090	+	1.49822i
$442$		0			0
$443$	−4.37628	−	7.57993i	−0.207923	−	0.360133i	0.743137	−	0.669139i	$-0.233337\pi$
$443$	−4.37628	−	7.57993i	−0.207923	−	0.360133i	−0.951060	+	0.309006i	$0.900004\pi$
$444$		0			0
$445$		−	32.0983i		−	1.52161i
$446$		0			0
$447$	11.1010	−	7.84961i	0.525060	−	0.371274i
$448$		0			0
$449$	6.82577	−	3.94086i	0.322128	−	0.185981i	−0.330213	−	0.943907i	$-0.607121\pi$
$449$	6.82577	−	3.94086i	0.322128	−	0.185981i	0.652341	+	0.757926i	$0.273787\pi$
$450$		0			0
$451$	2.50000	−	4.33013i	0.117720	−	0.203898i
$452$		0			0
$453$	−18.6237	+	1.71600i	−0.875019	+	0.0806246i
$454$		0			0
$455$	47.3939			2.22186
$456$		0			0
$457$	−11.1969	−	19.3937i	−0.523771	−	0.907197i	−0.999617	−	0.0276691i	$-0.991192\pi$
$457$	−11.1969	−	19.3937i	−0.523771	−	0.907197i	0.475846	−	0.879528i	$-0.342142\pi$
$458$		0			0
$459$	−12.6464	−	3.20164i	−0.590285	−	0.149440i
$460$		0			0
$461$		−	14.4279i		−	0.671973i	−0.941867	−	0.335986i	$-0.890930\pi$
$461$		−	14.4279i		−	0.671973i	0.941867	−	0.335986i	$-0.109070\pi$
$462$		0			0
$463$	22.1969	+	12.8154i	1.03158	+	0.595583i	0.917437	−	0.397882i	$-0.130255\pi$
$463$	22.1969	+	12.8154i	1.03158	+	0.595583i	0.114143	+	0.993464i	$0.463588\pi$
$464$		0			0
$465$	5.44949	+	2.51059i	0.252714	+	0.116426i
$466$		0			0
$467$	−27.8258	−	16.0652i	−1.28762	−	0.743409i	−0.309393	−	0.950934i	$-0.600126\pi$
$467$	−27.8258	−	16.0652i	−1.28762	−	0.743409i	−0.978230	+	0.207525i	$0.933459\pi$
$468$		0			0
$469$	27.6464	−	25.0826i	1.27659	−	1.15821i
$470$		0			0
$471$	−7.07321	+	0.651729i	−0.325917	+	0.0300301i
$472$		0			0
$473$	37.5959	−	21.7060i	1.72866	−	0.998044i
$474$		0			0
$475$	1.50000	−	2.59808i	0.0688247	−	0.119208i
$476$		0			0
$477$	6.00000	−	16.9706i	0.274721	−	0.777029i
$478$		0			0
$479$	−15.2753	−	8.81917i	−0.697944	−	0.402958i	0.108637	−	0.994081i	$-0.465351\pi$
$479$	−15.2753	−	8.81917i	−0.697944	−	0.402958i	−0.806581	+	0.591123i	$0.798685\pi$
$480$		0			0
$481$	−0.454592	+	0.262459i	−0.0207276	+	0.0119671i
$482$		0			0
$483$	−43.0454	−	60.8754i	−1.95863	−	2.76993i
$484$		0			0
$485$	−5.69694	−	3.28913i	−0.258685	−	0.149352i
$486$		0			0
$487$	−18.3990	−	10.6227i	−0.833737	−	0.481358i	0.0213932	−	0.999771i	$-0.493190\pi$
$487$	−18.3990	−	10.6227i	−0.833737	−	0.481358i	−0.855131	+	0.518413i	$0.826523\pi$
$488$		0			0
$489$	12.0278	−	26.1076i	0.543916	−	1.18063i
$490$		0			0
$491$			22.9774i			1.03695i	0.855092	+	0.518477i	$0.173501\pi$
$491$			22.9774i			1.03695i	−0.855092	+	0.518477i	$0.826499\pi$
$492$		0			0
$493$	22.1010			0.995380
$494$		0			0
$495$	−20.3485	+	3.78194i	−0.914596	+	0.169986i
$496$		0			0
$497$	−10.0732	+	17.4473i	−0.451845	+	0.782619i
$498$		0			0
$499$	6.39898	+	3.69445i	0.286458	+	0.165386i	0.636343	−	0.771406i	$-0.280446\pi$
$499$	6.39898	+	3.69445i	0.286458	+	0.165386i	−0.349886	+	0.936792i	$0.613780\pi$
$500$		0			0
$501$	−8.94949	−	4.12305i	−0.399834	−	0.184204i
$502$		0			0
$503$	14.8258	+	25.6790i	0.661048	+	1.14497i	0.980341	+	0.197313i	$0.0632215\pi$
$503$	14.8258	+	25.6790i	0.661048	+	1.14497i	−0.319292	+	0.947656i	$0.603445\pi$
$504$		0			0
$505$	−8.55051	−	14.8099i	−0.380493	−	0.659033i
$506$		0			0
$507$	10.1464	−	22.0239i	0.450619	−	0.978114i
$508$		0			0
$509$			2.82843i			0.125368i	0.998033	+	0.0626839i	$0.0199660\pi$
$509$			2.82843i			0.125368i	−0.998033	+	0.0626839i	$0.980034\pi$
$510$		0			0
$511$			17.7812i			0.786594i
$512$		0			0
$513$	−3.82577	+	15.1117i	−0.168912	+	0.667198i
$514$		0			0
$515$	−5.89898	−	10.2173i	−0.259940	−	0.450229i
$516$		0			0
$517$	9.39898	+	5.42650i	0.413367	+	0.238657i
$518$		0			0
$519$	−0.297959	−	3.23375i	−0.0130789	−	0.141946i
$520$		0			0
$521$	28.2929			1.23953			0.619766	−	0.784786i	$-0.287227\pi$
$521$	28.2929			1.23953			0.619766	+	0.784786i	$0.287227\pi$
$522$		0			0
$523$	−11.6464	+	20.1722i	−0.509263	+	0.882069i	0.490680	+	0.871340i	$0.336749\pi$
$523$	−11.6464	+	20.1722i	−0.509263	+	0.882069i	−0.999942	+	0.0107289i	$0.996585\pi$
$524$		0			0
$525$	7.17423	+	3.30518i	0.313109	+	0.144250i
$526$		0			0
$527$	4.34847			0.189422
$528$		0			0
$529$	33.0454	+	57.2363i	1.43676	+	2.48854i
$530$		0			0
$531$	17.7980	+	6.29253i	0.772366	+	0.273072i
$532$		0			0
$533$		−	7.53177i		−	0.326237i
$534$		0			0
$535$			4.38551i			0.189602i
$536$		0			0
$537$	25.5959	+	36.1981i	1.10455	+	1.56206i
$538$		0			0
$539$	47.5959			2.05010
$540$		0			0
$541$		−	17.8920i		−	0.769236i	−0.923076	−	0.384618i	$-0.874333\pi$
$541$		−	17.8920i		−	0.769236i	0.923076	−	0.384618i	$-0.125667\pi$
$542$		0			0
$543$	8.62372	−	18.7187i	0.370079	−	0.803295i
$544$		0			0
$545$			23.8988i			1.02371i
$546$		0			0
$547$	3.15153	−	1.81954i	0.134750	−	0.0777978i	−0.431110	−	0.902300i	$-0.641878\pi$
$547$	3.15153	−	1.81954i	0.134750	−	0.0777978i	0.565859	+	0.824502i	$0.308544\pi$
$548$		0			0
$549$	1.05051	−	0.898133i	0.0448347	−	0.0383314i
$550$		0			0
$551$		−	26.4094i		−	1.12508i
$552$		0			0
$553$	−24.7474	+	42.8638i	−1.05237	+	1.82276i
$554$		0			0
$555$	0.348469	−	0.0321081i	0.0147917	−	0.00136291i
$556$		0			0
$557$	10.0732	−	5.81577i	0.426816	−	0.246422i	−0.271173	−	0.962531i	$-0.587412\pi$
$557$	10.0732	−	5.81577i	0.426816	−	0.246422i	0.697989	+	0.716108i	$0.254078\pi$
$558$		0			0
$559$	32.6969	−	56.6328i	1.38293	−	2.39531i
$560$		0			0
$561$	−12.2474	+	8.66025i	−0.517088	+	0.365636i
$562$		0			0
$563$	26.2929			1.10811			0.554056	−	0.832479i	$-0.313079\pi$
$563$	26.2929			1.10811			0.554056	+	0.832479i	$0.313079\pi$
$564$		0			0
$565$	−11.4495	−	19.8311i	−0.481684	−	0.834301i
$566$		0			0
$567$	−40.5454	−	6.38002i	−1.70275	−	0.267935i
$568$		0			0
$569$	−8.42168	+	4.86226i	−0.353055	+	0.203837i	−0.666030	−	0.745925i	$-0.732008\pi$
$569$	−8.42168	+	4.86226i	−0.353055	+	0.203837i	0.312975	+	0.949761i	$0.398674\pi$
$570$		0			0
$571$	−4.15153	−	7.19066i	−0.173736	−	0.300920i	0.765987	−	0.642856i	$-0.222251\pi$
$571$	−4.15153	−	7.19066i	−0.173736	−	0.300920i	−0.939723	+	0.341936i	$0.888917\pi$
$572$		0			0
$573$	−21.6464	+	1.99451i	−0.904293	+	0.0833218i
$574$		0			0
$575$	−8.17423	−	4.71940i	−0.340889	−	0.196812i
$576$		0			0
$577$	−12.1515	+	7.01569i	−0.505875	+	0.292067i	−0.731136	−	0.682231i	$-0.761010\pi$
$577$	−12.1515	+	7.01569i	−0.505875	+	0.292067i	0.225262	+	0.974298i	$0.427676\pi$
$578$		0			0
$579$	3.10102	+	4.38551i	0.128874	+	0.182255i
$580$		0			0
$581$	−37.2474			−1.54528
$582$		0			0
$583$	−10.3485	−	17.9241i	−0.428590	−	0.742339i
$584$		0			0
$585$	−23.6969	+	20.2597i	−0.979748	+	0.837635i
$586$		0			0
$587$	10.7247	−	18.5758i	0.442658	−	0.766705i	−0.555228	−	0.831698i	$-0.687369\pi$
$587$	10.7247	−	18.5758i	0.442658	−	0.766705i	0.997886	+	0.0649926i	$0.0207024\pi$
$588$		0			0
$589$		−	5.19615i		−	0.214104i
$590$		0			0
$591$	15.3990	−	33.4250i	0.633429	−	1.37492i
$592$		0			0
$593$	−14.9722	+	25.9326i	−0.614834	+	1.06492i	0.375579	+	0.926790i	$0.377444\pi$
$593$	−14.9722	+	25.9326i	−0.614834	+	1.06492i	−0.990414	+	0.138134i	$0.955890\pi$
$594$		0			0
$595$	−22.8990			−0.938767
$596$		0			0
$597$	−18.9722	+	1.74810i	−0.776480	+	0.0715452i
$598$		0			0
$599$	−0.825765	−	1.43027i	−0.0337399	−	0.0584391i	0.848662	−	0.528935i	$-0.177408\pi$
$599$	−0.825765	−	1.43027i	−0.0337399	−	0.0584391i	−0.882402	+	0.470496i	$0.844075\pi$
$600$		0			0
$601$	8.39898	−	14.5475i	0.342602	−	0.593403i	−0.642313	−	0.766442i	$-0.722025\pi$
$601$	8.39898	−	14.5475i	0.342602	−	0.593403i	0.984915	+	0.173039i	$0.0553586\pi$
$602$		0			0
$603$	−3.10102	+	24.3595i	−0.126283	+	0.991994i
$604$		0			0
$605$	−0.898979	+	1.55708i	−0.0365487	+	0.0633042i
$606$		0			0
$607$	4.84847	+	8.39780i	0.196793	+	0.340856i	0.947487	−	0.319795i	$-0.103614\pi$
$607$	4.84847	+	8.39780i	0.196793	+	0.340856i	−0.750694	+	0.660650i	$0.770281\pi$
$608$		0			0
$609$	69.2423	−	6.38002i	2.80584	−	0.258531i
$610$		0			0
$611$	16.3485			0.661388
$612$		0			0
$613$	−16.1969	+	28.0539i	−0.654188	+	1.13309i	0.327908	+	0.944709i	$0.393656\pi$
$613$	−16.1969	+	28.0539i	−0.654188	+	1.13309i	−0.982097	+	0.188378i	$0.939677\pi$
$614$		0			0
$615$	−2.10102	+	4.56048i	−0.0847213	+	0.183896i
$616$		0			0
$617$		−	12.8708i		−	0.518158i	−0.965856	−	0.259079i	$-0.916581\pi$
$617$		−	12.8708i		−	0.518158i	0.965856	−	0.259079i	$-0.0834191\pi$
$618$		0			0
$619$	1.94949	−	3.37662i	0.0783566	−	0.135718i	−0.824184	−	0.566322i	$-0.808366\pi$
$619$	1.94949	−	3.37662i	0.0783566	−	0.135718i	0.902541	+	0.430604i	$0.141699\pi$
$620$		0			0
$621$	47.5454	+	12.0369i	1.90793	+	0.483023i
$622$		0			0
$623$	−36.5959	−	63.3860i	−1.46618	−	2.53951i
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$	10.3485	+	14.6349i	0.413278	+	0.584463i
$628$		0			0
$629$	0.219642	−	0.126811i	0.00875771	−	0.00505627i
$630$		0			0
$631$	−20.5454	−	11.8619i	−0.817900	−	0.472215i	0.0317919	−	0.999495i	$-0.489879\pi$
$631$	−20.5454	−	11.8619i	−0.817900	−	0.472215i	−0.849692	+	0.527280i	$0.823212\pi$
$632$		0			0
$633$	6.72474	−	0.619620i	0.267285	−	0.0246277i
$634$		0			0
$635$	−10.7980	−	18.7026i	−0.428504	−	0.742191i
$636$		0			0
$637$	62.0908	−	35.8481i	2.46013	−	1.42036i
$638$		0			0
$639$	−2.42168	−	13.0297i	−0.0958003	−	0.515447i
$640$		0			0
$641$	−0.522704	−	0.905350i	−0.0206456	−	0.0357592i	0.855518	−	0.517773i	$-0.173239\pi$
$641$	−0.522704	−	0.905350i	−0.0206456	−	0.0357592i	−0.876164	+	0.482014i	$0.839905\pi$
$642$		0			0
$643$	−49.1918			−1.93994			−0.969968	−	0.243231i	$-0.921793\pi$
$643$	−49.1918			−1.93994			−0.969968	+	0.243231i	$0.921793\pi$
$644$		0			0
$645$	−35.5959	+	25.1701i	−1.40159	+	0.991072i
$646$		0			0
$647$	−7.17423	+	12.4261i	−0.282048	+	0.488522i	−0.971889	−	0.235439i	$-0.924347\pi$
$647$	−7.17423	+	12.4261i	−0.282048	+	0.488522i	0.689841	+	0.723961i	$0.257680\pi$
$648$		0			0
$649$	18.7980	−	10.8530i	0.737884	−	0.426018i
$650$		0			0
$651$	13.6237	−	1.25529i	0.533956	−	0.0491989i
$652$		0			0
$653$	−2.62372	+	4.54442i	−0.102674	+	0.177837i	−0.912786	−	0.408439i	$-0.866073\pi$
$653$	−2.62372	+	4.54442i	−0.102674	+	0.177837i	0.810111	+	0.586276i	$0.199407\pi$
$654$		0			0
$655$			1.27135i			0.0496757i
$656$		0			0
$657$	−7.60102	−	8.89060i	−0.296544	−	0.346856i
$658$		0			0
$659$	3.27526	−	1.89097i	0.127586	−	0.0736617i	−0.434849	−	0.900504i	$-0.643198\pi$
$659$	3.27526	−	1.89097i	0.127586	−	0.0736617i	0.562435	+	0.826842i	$0.309865\pi$
$660$		0			0
$661$			2.47848i			0.0964018i	0.998838	+	0.0482009i	$0.0153488\pi$
$661$			2.47848i			0.0964018i	−0.998838	+	0.0482009i	$0.984651\pi$
$662$		0			0
$663$	−9.45459	+	20.5222i	−0.367186	+	0.797014i
$664$		0			0
$665$			27.3629i			1.06109i
$666$		0			0
$667$	−83.0908			−3.21729
$668$		0			0
$669$	8.69694	+	12.2993i	0.336243	+	0.475520i
$670$		0			0
$671$		−	1.58919i		−	0.0613499i
$672$		0			0
$673$			18.2419i			0.703174i	0.936155	+	0.351587i	$0.114358\pi$
$673$			18.2419i			0.703174i	−0.936155	+	0.351587i	$0.885642\pi$
$674$		0			0
$675$	−5.00000	+	1.41421i	−0.192450	+	0.0544331i
$676$		0			0
$677$	19.7247	+	34.1643i	0.758084	+	1.31304i	0.943827	+	0.330441i	$0.107197\pi$
$677$	19.7247	+	34.1643i	0.758084	+	1.31304i	−0.185743	+	0.982598i	$0.559469\pi$
$678$		0			0
$679$	−15.0000			−0.575647
$680$		0			0
$681$	−15.2980	−	7.04780i	−0.586219	−	0.270072i
$682$		0			0
$683$	8.82577	−	15.2867i	0.337709	−	0.584928i	−0.646293	−	0.763090i	$-0.723682\pi$
$683$	8.82577	−	15.2867i	0.337709	−	0.584928i	0.984001	+	0.178161i	$0.0570149\pi$
$684$		0			0
$685$	−37.7980			−1.44419
$686$		0			0
$687$	−1.07321	−	11.6476i	−0.0409457	−	0.444384i
$688$		0			0
$689$	−27.0000	−	15.5885i	−1.02862	−	0.593873i
$690$		0			0
$691$	20.6464	+	35.7607i	0.785427	+	1.36040i	0.928744	+	0.370723i	$0.120890\pi$
$691$	20.6464	+	35.7607i	0.785427	+	1.36040i	−0.143316	+	0.989677i	$0.545777\pi$
$692$		0			0
$693$	−35.8712	+	30.6681i	−1.36263	+	1.16498i
$694$		0			0
$695$			42.1407i			1.59849i
$696$		0			0
$697$			3.63907i			0.137840i
$698$		0			0
$699$	−16.9949	+	36.8891i	−0.642806	+	1.39528i
$700$		0			0
$701$	−14.1742	−	24.5505i	−0.535353	−	0.927259i	−0.999146	−	0.0413156i	$-0.986845\pi$
$701$	−14.1742	−	24.5505i	−0.535353	−	0.927259i	0.463793	−	0.885944i	$-0.346488\pi$
$702$		0			0
$703$	−0.151531	−	0.262459i	−0.00571509	−	0.00989883i
$704$		0			0
$705$	−9.89898	−	4.56048i	−0.372817	−	0.171758i
$706$		0			0
$707$	−33.7702	−	19.4972i	−1.27006	−	0.733268i
$708$		0			0
$709$	−11.7474	+	20.3472i	−0.441185	+	0.764154i	−0.997778	−	0.0666310i	$-0.978775\pi$
$709$	−11.7474	+	20.3472i	−0.441185	+	0.764154i	0.556593	+	0.830785i	$0.312108\pi$
$710$		0			0
$711$	−5.94949	−	32.0108i	−0.223123	−	1.20050i
$712$		0			0
$713$	−16.3485			−0.612255
$714$		0			0
$715$			35.8481i			1.34064i
$716$		0			0
$717$	−9.60102	+	20.8400i	−0.358557	+	0.778284i
$718$		0			0
$719$	41.6691	+	24.0577i	1.55400	+	0.897200i	0.997810	+	0.0661425i	$0.0210692\pi$
$719$	41.6691	+	24.0577i	1.55400	+	0.897200i	0.556186	+	0.831058i	$0.312264\pi$
$720$		0			0
$721$	−23.2980	−	13.4511i	−0.867661	−	0.500945i
$722$		0			0
$723$	−4.00000	−	5.65685i	−0.148762	−	0.210381i
$724$		0			0
$725$	7.62372	−	4.40156i	0.283138	−	0.163470i
$726$		0			0
$727$	−12.8939	−	7.44428i	−0.478207	−	0.276093i	0.241462	−	0.970410i	$-0.422373\pi$
$727$	−12.8939	−	7.44428i	−0.478207	−	0.276093i	−0.719669	+	0.694317i	$0.755707\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		0			0
$731$	−15.7980	+	27.3629i	−0.584309	+	1.01205i
$732$		0			0
$733$	18.9495	−	10.9405i	0.699915	−	0.404096i	−0.107401	−	0.994216i	$-0.534253\pi$
$733$	18.9495	−	10.9405i	0.699915	−	0.404096i	0.807316	+	0.590120i	$0.200919\pi$
$734$		0			0
$735$	−47.5959	+	4.38551i	−1.75560	+	0.161762i
$736$		0			0
$737$	18.9722	+	20.9114i	0.698850	+	0.770282i
$738$		0			0
$739$	−2.35357	−	1.35884i	−0.0865775	−	0.0499856i	0.456086	−	0.889936i	$-0.349251\pi$
$739$	−2.35357	−	1.35884i	−0.0865775	−	0.0499856i	−0.542664	+	0.839950i	$0.682584\pi$
$740$		0			0
$741$	24.5227	+	11.2977i	0.900864	+	0.415030i
$742$		0			0
$743$	−8.72474	−	5.03723i	−0.320080	−	0.184798i	0.331348	−	0.943508i	$-0.392496\pi$
$743$	−8.72474	−	5.03723i	−0.320080	−	0.184798i	−0.651428	+	0.758710i	$0.725830\pi$
$744$		0			0
$745$			15.6992i			0.575175i
$746$		0			0
$747$	18.6237	−	15.9223i	0.681406	−	0.582568i
$748$		0			0
$749$	5.00000	+	8.66025i	0.182696	+	0.316439i
$750$		0			0
$751$	−43.3939			−1.58347			−0.791733	−	0.610868i	$-0.790821\pi$
$751$	−43.3939			−1.58347			−0.791733	+	0.610868i	$0.790821\pi$
$752$		0			0
$753$	−24.3990	+	2.24813i	−0.889148	+	0.0819264i
$754$		0			0
$755$	10.7980	−	18.7026i	0.392978	−	0.680658i
$756$		0			0
$757$	−21.9495	+	12.6725i	−0.797768	+	0.460591i	−0.842690	−	0.538399i	$-0.819029\pi$
$757$	−21.9495	+	12.6725i	−0.797768	+	0.460591i	0.0449222	+	0.998990i	$0.485696\pi$
$758$		0			0
$759$	46.0454	−	32.5590i	1.67134	−	1.18182i
$760$		0			0
$761$		−	23.6130i		−	0.855972i	−0.903785	−	0.427986i	$-0.859223\pi$
$761$		−	23.6130i		−	0.855972i	0.903785	−	0.427986i	$-0.140777\pi$
$762$		0			0
$763$	27.2474	+	47.1940i	0.986424	+	1.70854i
$764$		0			0
$765$	11.4495	−	9.78874i	0.413957	−	0.353913i
$766$		0			0
$767$	16.3485	−	28.3164i	0.590309	−	1.02245i
$768$		0			0
$769$	13.7474	−	7.93709i	0.495746	−	0.286219i	−0.231209	−	0.972904i	$-0.574268\pi$
$769$	13.7474	−	7.93709i	0.495746	−	0.286219i	0.726955	+	0.686685i	$0.240935\pi$
$770$		0			0
$771$	7.39898	+	3.40872i	0.266468	+	0.122762i
$772$		0			0
$773$	−23.9722	+	13.8404i	−0.862220	+	0.497803i	−0.864755	−	0.502194i	$-0.832526\pi$
$773$	−23.9722	+	13.8404i	−0.862220	+	0.497803i	0.00253516	+	0.999997i	$0.499193\pi$
$774$		0			0
$775$	1.50000	−	0.866025i	0.0538816	−	0.0311086i
$776$		0			0
$777$	0.651531	−	0.460702i	0.0233735	−	0.0165276i
$778$		0			0
$779$	4.34847			0.155800
$780$		0			0
$781$	−13.1969	−	7.61926i	−0.472224	−	0.272638i
$782$		0			0
$783$	−31.8939	+	32.7894i	−1.13979	+	1.17180i
$784$		0			0
$785$	4.10102	−	7.10318i	0.146372	−	0.253523i
$786$		0			0
$787$	−15.6464	−	9.03347i	−0.557735	−	0.322008i	0.194501	−	0.980902i	$-0.437691\pi$
$787$	−15.6464	−	9.03347i	−0.557735	−	0.322008i	−0.752236	+	0.658894i	$0.771025\pi$
$788$		0			0
$789$	−20.8990	+	14.7778i	−0.744023	+	0.526104i
$790$		0			0
$791$	−45.2196	−	26.1076i	−1.60783	−	0.928278i
$792$		0			0
$793$	−1.19694	−	2.07316i	−0.0425045	−	0.0736200i
$794$		0			0
$795$	12.0000	+	16.9706i	0.425596	+	0.601884i
$796$		0			0
$797$	3.82577	−	2.20881i	0.135516	−	0.0782399i	−0.430709	−	0.902491i	$-0.641737\pi$
$797$	3.82577	−	2.20881i	0.135516	−	0.0782399i	0.566225	+	0.824251i	$0.308403\pi$
$798$		0			0
$799$	−7.89898			−0.279446
$800$		0			0
$801$	45.3939	+	16.0492i	1.60391	+	0.567069i
$802$		0			0
$803$	−13.4495			−0.474622
$804$		0			0
$805$	86.0908			3.03430
$806$		0			0
$807$	40.4949	−	28.6342i	1.42549	−	1.00797i
$808$		0			0
$809$	39.7980			1.39922			0.699611	−	0.714524i	$-0.253357\pi$
$809$	39.7980			1.39922			0.699611	+	0.714524i	$0.253357\pi$
$810$		0			0
$811$	−6.15153	+	3.55159i	−0.216009	+	0.124713i	−0.604101	−	0.796908i	$-0.706468\pi$
$811$	−6.15153	+	3.55159i	−0.216009	+	0.124713i	0.388092	+	0.921621i	$0.373134\pi$
$812$		0			0
$813$	5.79796	−	4.09978i	0.203343	−	0.143785i
$814$		0			0
$815$	16.5959	+	28.7450i	0.581330	+	1.00689i
$816$		0			0
$817$	32.6969	+	18.8776i	1.14392	+	0.660443i
$818$		0			0
$819$	−23.6969	+	67.0251i	−0.828038	+	2.34205i
$820$		0			0
$821$	12.2753	+	7.08712i	0.428409	+	0.247342i	0.698669	−	0.715445i	$-0.253776\pi$
$821$	12.2753	+	7.08712i	0.428409	+	0.247342i	−0.270259	+	0.962788i	$0.587109\pi$
$822$		0			0
$823$	10.6010	−	18.3615i	0.369528	−	0.640042i	−0.619963	−	0.784631i	$-0.712853\pi$
$823$	10.6010	−	18.3615i	0.369528	−	0.640042i	0.989492	+	0.144589i	$0.0461859\pi$
$824$		0			0
$825$	−2.50000	+	5.42650i	−0.0870388	+	0.188927i
$826$		0			0
$827$	−4.32066	−	2.49454i	−0.150244	−	0.0867435i	0.422993	−	0.906133i	$-0.360979\pi$
$827$	−4.32066	−	2.49454i	−0.150244	−	0.0867435i	−0.573237	+	0.819389i	$0.694313\pi$
$828$		0			0
$829$	−39.3939			−1.36821			−0.684103	−	0.729385i	$-0.739806\pi$
$829$	−39.3939			−1.36821			−0.684103	+	0.729385i	$0.739806\pi$
$830$		0			0
$831$	−6.20204	−	8.77101i	−0.215146	−	0.304263i
$832$		0			0
$833$	−30.0000	+	17.3205i	−1.03944	+	0.600120i
$834$		0			0
$835$	9.85357	−	5.68896i	0.340997	−	0.196875i
$836$		0			0
$837$	−6.27526	+	6.45145i	−0.216905	+	0.222995i
$838$		0			0
$839$	12.5227	−	7.22999i	0.432332	−	0.249607i	−0.268008	−	0.963417i	$-0.586365\pi$
$839$	12.5227	−	7.22999i	0.432332	−	0.249607i	0.700340	+	0.713810i	$0.253032\pi$
$840$		0			0
$841$	24.2474	−	41.9978i	0.836119	−	1.44820i
$842$		0			0
$843$	4.39898	−	0.405324i	0.151509	−	0.0139601i
$844$		0			0
$845$	14.0000	+	24.2487i	0.481615	+	0.834181i
$846$		0			0
$847$			4.09978i			0.140870i
$848$		0			0
$849$	−11.7980	−	16.6848i	−0.404905	−	0.572622i
$850$		0			0
$851$	−0.825765	+	0.476756i	−0.0283069	+	0.0163430i
$852$		0			0
$853$	−12.6464	+	21.9043i	−0.433005	+	0.749987i	−0.997130	−	0.0757019i	$-0.975880\pi$
$853$	−12.6464	+	21.9043i	−0.433005	+	0.749987i	0.564125	+	0.825689i	$0.309214\pi$
$854$		0			0
$855$	−11.6969	−	13.6814i	−0.400027	−	0.467895i
$856$		0			0
$857$	25.5959			0.874340			0.437170	−	0.899379i	$-0.355981\pi$
$857$	25.5959			0.874340			0.437170	+	0.899379i	$0.355981\pi$
$858$		0			0
$859$	12.8485	+	22.2542i	0.438384	+	0.759304i	0.997565	−	0.0697421i	$-0.0222176\pi$
$859$	12.8485	+	22.2542i	0.438384	+	0.759304i	−0.559181	+	0.829046i	$0.688884\pi$
$860$		0			0
$861$	1.05051	+	11.4012i	0.0358013	+	0.388552i
$862$		0			0
$863$			37.1195i			1.26356i	0.775147	+	0.631781i	$0.217676\pi$
$863$			37.1195i			1.26356i	−0.775147	+	0.631781i	$0.782324\pi$
$864$		0			0
$865$	3.24745	+	1.87492i	0.110417	+	0.0637490i
$866$		0			0
$867$	−7.75255	+	16.8277i	−0.263290	+	0.571499i
$868$		0			0
$869$	−32.4217	−	18.7187i	−1.09983	−	0.634987i
$870$		0			0
$871$	40.5000	+	12.9904i	1.37229	+	0.440162i
$872$		0			0
$873$	7.50000	−	6.41212i	0.253837	−	0.217017i
$874$		0			0
$875$	−47.3939	+	27.3629i	−1.60221	+	0.925034i
$876$		0			0
$877$	9.64643	−	16.7081i	0.325737	−	0.564193i	−0.655924	−	0.754827i	$-0.727721\pi$
$877$	9.64643	−	16.7081i	0.325737	−	0.564193i	0.981661	+	0.190634i	$0.0610544\pi$
$878$		0			0
$879$	−17.3939	+	12.2993i	−0.586681	+	0.414846i
$880$		0			0
$881$	13.3207	+	7.69069i	0.448785	+	0.259106i	0.707317	−	0.706897i	$-0.249905\pi$
$881$	13.3207	+	7.69069i	0.448785	+	0.259106i	−0.258532	+	0.966003i	$0.583239\pi$
$882$		0			0
$883$	38.5454	−	22.2542i	1.29716	−	0.748914i	0.317244	−	0.948344i	$-0.397242\pi$
$883$	38.5454	−	22.2542i	1.29716	−	0.748914i	0.979912	+	0.199430i	$0.0639092\pi$
$884$		0			0
$885$	−17.7980	+	12.5851i	−0.598272	+	0.423042i
$886$		0			0
$887$	−27.7702	−	16.0331i	−0.932430	−	0.538339i	−0.0448510	−	0.998994i	$-0.514281\pi$
$887$	−27.7702	−	16.0331i	−0.932430	−	0.538339i	−0.887579	+	0.460655i	$0.847615\pi$
$888$		0			0
$889$	−42.6464	−	24.6219i	−1.43032	−	0.825793i
$890$		0			0
$891$	4.82577	−	30.6681i	0.161669	−	1.02742i
$892$		0			0
$893$			9.43879i			0.315857i
$894$		0			0
$895$	−51.1918			−1.71115
$896$		0			0
$897$	35.5454	−	77.1549i	1.18683	−	2.57613i
$898$		0			0
$899$	7.62372	−	13.2047i	0.254265	−	0.440401i
$900$		0			0
$901$	13.0454	+	7.53177i	0.434606	+	0.250920i
$902$		0			0
$903$	−41.5959	+	90.2882i	−1.38423	+	3.00460i
$904$		0			0
$905$	11.8990	+	20.6096i	0.395535	+	0.685088i
$906$		0			0
$907$	27.3990	+	47.4564i	0.909768	+	1.57576i	0.814386	+	0.580324i	$0.197074\pi$
$907$	27.3990	+	47.4564i	0.909768	+	1.57576i	0.0953825	+	0.995441i	$0.469593\pi$
$908$		0			0
$909$	25.2196	−	4.68729i	0.836483	−	0.155468i
$910$		0			0
$911$			2.47848i			0.0821158i	0.999157	+	0.0410579i	$0.0130728\pi$
$911$			2.47848i			0.0821158i	−0.999157	+	0.0410579i	$0.986927\pi$
$912$		0			0
$913$		−	28.1735i		−	0.932407i
$914$		0			0
$915$	0.146428	+	1.58919i	0.00484077	+	0.0525369i
$916$		0			0
$917$	1.44949	+	2.51059i	0.0478664	+	0.0829070i
$918$		0			0
$919$	−11.8485	−	6.84072i	−0.390845	−	0.225654i	0.291681	−	0.956516i	$-0.405785\pi$
$919$	−11.8485	−	6.84072i	−0.390845	−	0.225654i	−0.682526	+	0.730861i	$0.739119\pi$
$920$		0			0
$921$	−52.7702	+	4.86226i	−1.73884	+	0.160217i
$922$		0			0
$923$	−22.9546			−0.755560
$924$		0			0
$925$	0.0505103	−	0.0874863i	0.00166077	−	0.00287653i
$926$		0			0
$927$	17.3990	−	3.23375i	0.571457	−	0.106210i
$928$		0			0
$929$	0.494897			0.0162371			0.00811853	−	0.999967i	$-0.497416\pi$
$929$	0.494897			0.0162371			0.00811853	+	0.999967i	$0.497416\pi$
$930$		0			0
$931$	20.6969	+	35.8481i	0.678315	+	1.17488i
$932$		0			0
$933$	−33.7980	−	47.7975i	−1.10650	−	1.56482i
$934$		0			0
$935$		−	17.3205i		−	0.566441i
$936$		0			0
$937$		−	10.1066i		−	0.330167i	−0.986280	−	0.165084i	$-0.947211\pi$
$937$		−	10.1066i		−	0.330167i	0.986280	−	0.165084i	$-0.0527894\pi$
$938$		0			0
$939$	32.4949	−	22.9774i	1.06043	−	0.749838i
$940$		0			0
$941$	−28.2929			−0.922321			−0.461160	−	0.887317i	$-0.652567\pi$
$941$	−28.2929			−0.922321			−0.461160	+	0.887317i	$0.652567\pi$
$942$		0			0
$943$		−	13.6814i		−	0.445529i
$944$		0			0
$945$	33.0454	−	33.9732i	1.07497	−	1.10515i
$946$		0			0
$947$		−	25.5201i		−	0.829291i	−0.909983	−	0.414645i	$-0.863906\pi$
$947$		−	25.5201i		−	0.829291i	0.909983	−	0.414645i	$-0.136094\pi$
$948$		0			0
$949$	−17.5454	+	10.1298i	−0.569548	+	0.328829i
$950$		0			0
$951$	−4.64643	−	50.4277i	−0.150671	−	1.63523i
$952$		0			0
$953$		−	33.0197i		−	1.06961i	−0.844974	−	0.534807i	$-0.820384\pi$
$953$		−	33.0197i		−	1.06961i	0.844974	−	0.534807i	$-0.179616\pi$
$954$		0			0
$955$	12.5505	−	21.7381i	0.406125	−	0.703429i
$956$		0			0
$957$	4.82577	+	52.3741i	0.155995	+	1.69301i
$958$		0			0
$959$	−74.6413	+	43.0942i	−2.41029	+	1.39158i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$		0			0
$963$	−6.20204	−	2.19275i	−0.199858	−	0.0706605i
$964$		0			0
$965$	−6.20204			−0.199651
$966$		0			0
$967$	−7.84847	−	13.5939i	−0.252390	−	0.437152i	0.711794	−	0.702389i	$-0.247883\pi$
$967$	−7.84847	−	13.5939i	−0.252390	−	0.437152i	−0.964183	+	0.265237i	$0.914550\pi$
$968$		0			0
$969$	−11.8485	−	5.45861i	−0.380628	−	0.175356i
$970$		0			0
$971$	21.2196	−	12.2512i	0.680971	−	0.393159i	−0.119250	−	0.992864i	$-0.538049\pi$
$971$	21.2196	−	12.2512i	0.680971	−	0.393159i	0.800221	+	0.599706i	$0.204716\pi$
$972$		0			0
$973$	48.0454	+	83.2171i	1.54027	+	2.66782i
$974$		0			0
$975$	0.825765	+	8.96204i	0.0264457	+	0.287015i
$976$		0			0
$977$	−19.3207	−	11.1548i	−0.618123	−	0.356873i	0.158015	−	0.987437i	$-0.449491\pi$
$977$	−19.3207	−	11.1548i	−0.618123	−	0.356873i	−0.776138	+	0.630563i	$0.782824\pi$
$978$		0			0
$979$	47.9444	−	27.6807i	1.53231	−	0.884679i
$980$		0			0
$981$	−33.7980	−	11.9494i	−1.07909	−	0.381514i
$982$		0			0
$983$	−7.59592			−0.242272			−0.121136	−	0.992636i	$-0.538654\pi$
$983$	−7.59592			−0.242272			−0.121136	+	0.992636i	$0.538654\pi$
$984$		0			0
$985$	21.2474	+	36.8017i	0.677000	+	1.17260i
$986$		0			0
$987$	−24.7474	+	2.28024i	−0.787720	+	0.0725808i
$988$		0			0
$989$	59.3939	−	102.873i	1.88862	−	3.27118i
$990$		0			0
$991$		−	32.3840i		−	1.02871i	−0.857576	−	0.514357i	$-0.828031\pi$
$991$		−	32.3840i		−	1.02871i	0.857576	−	0.514357i	$-0.171969\pi$
$992$		0			0
$993$	−49.2196	−	22.6756i	−1.56194	−	0.719588i
$994$		0			0
$995$	11.0000	−	19.0526i	0.348723	−	0.604007i
$996$		0			0
$997$	34.2929			1.08607			0.543033	−	0.839711i	$-0.317276\pi$
$997$	34.2929			1.08607			0.543033	+	0.839711i	$0.317276\pi$
$998$		0			0
$999$	−0.128827	+	0.508864i	−0.00407590	+	0.0160997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.b.641.1	yes	4
3.2	odd	2		804.2.o.c.641.1	yes	4
67.30	odd	6		804.2.o.c.365.2	yes	4
201.164	even	6	inner	804.2.o.b.365.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.b.365.2	✓	4	201.164	even	6	inner
804.2.o.b.641.1	yes	4	1.1	even	1	trivial
804.2.o.c.365.2	yes	4	67.30	odd	6
804.2.o.c.641.1	yes	4	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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.41421i) q^{3} +2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.41421i) q^{3} +2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 + 2.82843i) q^{9} +(1.72474 + 2.98735i) q^{11} +(4.50000 + 2.59808i) q^{13} +(-2.00000 - 2.82843i) q^{15} +(-2.17423 - 1.25529i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(-7.17423 - 3.30518i) q^{21} +(8.17423 + 4.71940i) q^{23} -1.00000 q^{25} +(5.00000 - 1.41421i) q^{27} +(-7.62372 + 4.40156i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(2.50000 - 5.42650i) q^{33} +(7.89898 - 4.56048i) q^{35} +(-0.0505103 + 0.0874863i) q^{37} +(-0.825765 - 8.96204i) q^{39} +(-0.724745 - 1.25529i) q^{41} -12.5851i q^{43} +(-2.00000 + 5.65685i) q^{45} +(2.72474 - 1.57313i) q^{47} +(6.89898 - 11.9494i) q^{49} +(0.398979 + 4.33013i) q^{51} -6.00000 q^{53} +(3.44949 + 5.97469i) q^{55} +(5.17423 - 0.476756i) q^{57} -6.29253i q^{59} +(-0.398979 - 0.230351i) q^{61} +(2.50000 + 13.4511i) q^{63} +(9.00000 + 5.19615i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-1.50000 - 16.2795i) q^{69} +(-3.82577 + 2.20881i) q^{71} +(-1.94949 + 3.37662i) q^{73} +(1.00000 + 1.41421i) q^{75} +(13.6237 + 7.86566i) q^{77} +(-9.39898 + 5.42650i) q^{79} +(-7.00000 - 5.65685i) q^{81} +(-7.07321 - 4.08372i) q^{83} +(-4.34847 - 2.51059i) q^{85} +(13.8485 + 6.38002i) q^{87} -16.0492i q^{89} +23.6969 q^{91} +(2.72474 + 1.25529i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(-2.84847 - 1.64456i) q^{97} +(-10.1742 + 1.89097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 8 q^{5} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 8 * q^5 + 6 * q^7 - 4 * q^9	\( 4 q - 4 q^{3} + 8 q^{5} + 6 q^{7} - 4 q^{9} + 2 q^{11} + 18 q^{13} - 8 q^{15} + 6 q^{17} - 6 q^{19} - 14 q^{21} + 18 q^{23} - 4 q^{25} + 20 q^{27} - 6 q^{29} - 6 q^{31} + 10 q^{33} + 12 q^{35} - 10 q^{37} - 18 q^{39} + 2 q^{41} - 8 q^{45} + 6 q^{47} + 8 q^{49} - 18 q^{51} - 24 q^{53} + 4 q^{55} + 6 q^{57} + 18 q^{61} + 10 q^{63} + 36 q^{65} + 32 q^{67} - 6 q^{69} - 30 q^{71} + 2 q^{73} + 4 q^{75} + 30 q^{77} - 18 q^{79} - 28 q^{81} + 6 q^{83} + 12 q^{85} + 26 q^{87} + 36 q^{91} + 6 q^{93} - 12 q^{95} + 18 q^{97} - 26 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 8 * q^5 + 6 * q^7 - 4 * q^9 + 2 * q^11 + 18 * q^13 - 8 * q^15 + 6 * q^17 - 6 * q^19 - 14 * q^21 + 18 * q^23 - 4 * q^25 + 20 * q^27 - 6 * q^29 - 6 * q^31 + 10 * q^33 + 12 * q^35 - 10 * q^37 - 18 * q^39 + 2 * q^41 - 8 * q^45 + 6 * q^47 + 8 * q^49 - 18 * q^51 - 24 * q^53 + 4 * q^55 + 6 * q^57 + 18 * q^61 + 10 * q^63 + 36 * q^65 + 32 * q^67 - 6 * q^69 - 30 * q^71 + 2 * q^73 + 4 * q^75 + 30 * q^77 - 18 * q^79 - 28 * q^81 + 6 * q^83 + 12 * q^85 + 26 * q^87 + 36 * q^91 + 6 * q^93 - 12 * q^95 + 18 * q^97 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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