LMFDB - Embedded newform 804.2.o.c.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.c.365.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.41421i) q^{3} -2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.41421i) q^{3} -2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 - 2.82843i) q^{9} +(-1.72474 - 2.98735i) q^{11} +(4.50000 + 2.59808i) q^{13} +(-2.00000 + 2.82843i) q^{15} +(2.17423 + 1.25529i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(0.724745 - 7.86566i) q^{21} +(-8.17423 - 4.71940i) q^{23} -1.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +(7.62372 - 4.40156i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(-5.94949 - 0.548188i) q^{33} +(-7.89898 + 4.56048i) q^{35} +(-0.0505103 + 0.0874863i) q^{37} +(8.17423 - 3.76588i) q^{39} +(0.724745 + 1.25529i) q^{41} -12.5851i q^{43} +(2.00000 + 5.65685i) q^{45} +(-2.72474 + 1.57313i) q^{47} +(6.89898 - 11.9494i) q^{49} +(3.94949 - 1.81954i) q^{51} +6.00000 q^{53} +(3.44949 + 5.97469i) q^{55} +(2.17423 + 4.71940i) q^{57} +6.29253i q^{59} +(-0.398979 - 0.230351i) q^{61} +(-10.3990 - 8.89060i) q^{63} +(-9.00000 - 5.19615i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-14.8485 + 6.84072i) q^{69} +(3.82577 - 2.20881i) q^{71} +(-1.94949 + 3.37662i) q^{73} +(-1.00000 + 1.41421i) q^{75} +(-13.6237 - 7.86566i) q^{77} +(-9.39898 + 5.42650i) q^{79} +(-7.00000 + 5.65685i) q^{81} +(7.07321 + 4.08372i) q^{83} +(-4.34847 - 2.51059i) q^{85} +(1.39898 - 15.1831i) q^{87} +16.0492i q^{89} +23.6969 q^{91} +(-0.275255 + 2.98735i) q^{93} +(3.00000 - 5.19615i) q^{95} +(-2.84847 - 1.64456i) q^{97} +(-6.72474 + 7.86566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 2 q^{21} - 18 q^{23} - 4 q^{25} - 20 q^{27} + 6 q^{29} - 6 q^{31} - 14 q^{33} - 12 q^{35} - 10 q^{37} + 18 q^{39} - 2 q^{41} + 8 q^{45} - 6 q^{47} + 8 q^{49} + 6 q^{51} + 24 q^{53} + 4 q^{55} - 6 q^{57} + 18 q^{61} - 22 q^{63} - 36 q^{65} + 32 q^{67} - 30 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} - 14 q^{87} + 36 q^{91} - 6 q^{93} + 12 q^{95} + 18 q^{97} - 22 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 - 2 * q^21 - 18 * q^23 - 4 * q^25 - 20 * q^27 + 6 * q^29 - 6 * q^31 - 14 * q^33 - 12 * q^35 - 10 * q^37 + 18 * q^39 - 2 * q^41 + 8 * q^45 - 6 * q^47 + 8 * q^49 + 6 * q^51 + 24 * q^53 + 4 * q^55 - 6 * q^57 + 18 * q^61 - 22 * q^63 - 36 * q^65 + 32 * q^67 - 30 * 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 - 14 * q^87 + 36 * q^91 - 6 * q^93 + 12 * q^95 + 18 * q^97 - 22 * 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	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$		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	$-0.992587\pi$
$11$	−1.72474	−	2.98735i	−0.520030	−	0.900719i	0.479699	−	0.877433i	$-0.340746\pi$
$12$		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	0.739928	−	0.672686i	$-0.234859\pi$
$17$	2.17423	+	1.25529i	0.527329	+	0.304454i	−0.212599	+	0.977140i	$0.568193\pi$
$18$		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
$21$	0.724745	−	7.86566i	0.158152	−	1.71643i
$22$		0			0
$23$	−8.17423	−	4.71940i	−1.70445	−	0.984062i	−0.941135	−	0.338031i	$-0.890239\pi$
$23$	−8.17423	−	4.71940i	−1.70445	−	0.984062i	−0.763311	−	0.646032i	$-0.776427\pi$
$24$		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	0.419774	−	0.907629i	$-0.362109\pi$
$29$	7.62372	−	4.40156i	1.41569	−	0.817349i	0.995916	+	0.0902798i	$0.0287761\pi$
$30$		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
$33$	−5.94949	−	0.548188i	−1.03567	−	0.0954273i
$34$		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
$39$	8.17423	−	3.76588i	1.30893	−	0.603024i
$40$		0			0
$41$	0.724745	+	1.25529i	0.113186	+	0.196044i	0.917053	−	0.398765i	$-0.130561\pi$
$41$	0.724745	+	1.25529i	0.113186	+	0.196044i	−0.803867	+	0.594809i	$0.797228\pi$
$42$		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	−0.685381	−	0.728185i	$-0.740364\pi$
$47$	−2.72474	+	1.57313i	−0.397445	+	0.229465i	0.287936	+	0.957650i	$0.407031\pi$
$48$		0			0
$49$	6.89898	−	11.9494i	0.985568	−	1.70705i
$50$		0			0
$51$	3.94949	−	1.81954i	0.553039	−	0.254786i
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	3.44949	+	5.97469i	0.465129	+	0.805627i
$56$		0			0
$57$	2.17423	+	4.71940i	0.287984	+	0.625099i
$58$		0			0
$59$			6.29253i			0.819217i	0.912261	+	0.409609i	$0.134335\pi$
$59$			6.29253i			0.819217i	−0.912261	+	0.409609i	$0.865665\pi$
$60$		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
$63$	−10.3990	−	8.89060i	−1.31015	−	1.12011i
$64$		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
$69$	−14.8485	+	6.84072i	−1.78755	+	0.823526i
$70$		0			0
$71$	3.82577	−	2.20881i	0.454035	−	0.262137i	−0.255498	−	0.966810i	$-0.582239\pi$
$71$	3.82577	−	2.20881i	0.454035	−	0.262137i	0.709533	+	0.704672i	$0.248906\pi$
$72$		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	0.835148	−	0.550025i	$-0.185382\pi$
$83$	7.07321	+	4.08372i	0.776386	+	0.448247i	−0.0587619	+	0.998272i	$0.518715\pi$
$84$		0			0
$85$	−4.34847	−	2.51059i	−0.471658	−	0.272312i
$86$		0			0
$87$	1.39898	−	15.1831i	0.149986	−	1.62780i
$88$		0			0
$89$			16.0492i			1.70121i	0.525807	+	0.850604i	$0.323763\pi$
$89$			16.0492i			1.70121i	−0.525807	+	0.850604i	$0.676237\pi$
$90$		0			0
$91$	23.6969			2.48411
$92$		0			0
$93$	−0.275255	+	2.98735i	−0.0285426	+	0.309773i
$94$		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
$99$	−6.72474	+	7.86566i	−0.675862	+	0.790529i
$100$		0			0
$101$	4.27526	+	7.40496i	0.425404	+	0.736821i	0.996458	−	0.0840913i	$-0.0267988\pi$
$101$	4.27526	+	7.40496i	0.425404	+	0.736821i	−0.571054	+	0.820912i	$0.693465\pi$
$102$		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
$105$	−1.44949	+	15.7313i	−0.141456	+	1.53522i
$106$		0			0
$107$		−	2.19275i		−	0.211981i	−0.994367	−	0.105991i	$-0.966199\pi$
$107$		−	2.19275i		−	0.211981i	0.994367	−	0.105991i	$-0.0338014\pi$
$108$		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
$111$	0.0732141	+	0.158919i	0.00694917	+	0.0150839i
$112$		0			0
$113$	5.72474	+	9.91555i	0.538539	+	0.932776i	0.998983	+	0.0450878i	$0.0143568\pi$
$113$	5.72474	+	9.91555i	0.538539	+	0.932776i	−0.460444	+	0.887689i	$0.652310\pi$
$114$		0			0
$115$	16.3485	+	9.43879i	1.52450	+	0.880172i
$116$		0			0
$117$	2.84847	−	15.3260i	0.263341	−	1.41689i
$118$		0			0
$119$	11.4495			1.04957
$120$		0			0
$121$	−0.449490	+	0.778539i	−0.0408627	+	0.0707763i
$122$		0			0
$123$	2.50000	+	0.230351i	0.225417	+	0.0207700i
$124$		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	$-0.991160\pi$
$131$		−	0.635674i		−	0.0555391i	0.999614	−	0.0277696i	$-0.00884046\pi$
$132$		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	$-0.200915\pi$
$137$	18.8990			1.61465			0.807324	+	0.590108i	$0.200915\pi$
$138$		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
$141$	−0.500000	+	5.42650i	−0.0421076	+	0.456994i
$142$		0			0
$143$		−	17.9241i		−	1.49889i
$144$		0			0
$145$	−15.2474	+	8.80312i	−1.26623	+	0.731059i
$146$		0			0
$147$	−10.0000	−	21.7060i	−0.824786	−	1.79028i
$148$		0			0
$149$		−	7.84961i		−	0.643065i	−0.946899	−	0.321532i	$-0.895802\pi$
$149$		−	7.84961i		−	0.643065i	0.946899	−	0.321532i	$-0.104198\pi$
$150$		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
$153$	1.37628	−	7.40496i	0.111265	−	0.598655i
$154$		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
$165$	11.8990	+	1.09638i	0.926334	+	0.0853528i
$166$		0			0
$167$	−4.92679	+	2.84448i	−0.381246	+	0.220113i	−0.678360	−	0.734729i	$-0.737309\pi$
$167$	−4.92679	+	2.84448i	−0.381246	+	0.220113i	0.297114	+	0.954842i	$0.403976\pi$
$168$		0			0
$169$	7.00000	+	12.1244i	0.538462	+	0.932643i
$170$		0			0
$171$	8.84847	+	1.64456i	0.676659	+	0.125763i
$172$		0			0
$173$	−1.62372	−	0.937458i	−0.123449	−	0.0712736i	0.437004	−	0.899460i	$-0.356040\pi$
$173$	−1.62372	−	0.937458i	−0.123449	−	0.0712736i	−0.560453	+	0.828186i	$0.689373\pi$
$174$		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	$-0.0941614\pi$
$179$	25.5959			1.91313			0.956564	+	0.291521i	$0.0941614\pi$
$180$		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
$183$	−0.724745	+	0.333891i	−0.0535747	+	0.0246820i
$184$		0			0
$185$	0.101021	−	0.174973i	0.00742718	−	0.0128642i
$186$		0			0
$187$		−	8.66025i		−	0.633300i
$188$		0			0
$189$	−22.9722	+	5.81577i	−1.67098	+	0.423035i
$190$		0			0
$191$	−6.27526	+	10.8691i	−0.454062	+	0.786458i	−0.998634	−	0.0522563i	$-0.983359\pi$
$191$	−6.27526	+	10.8691i	−0.454062	+	0.786458i	0.544572	+	0.838714i	$0.316692\pi$
$192$		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
$195$	−16.3485	+	7.53177i	−1.17074	+	0.539361i
$196$		0			0
$197$	−10.6237	−	18.4008i	−0.756909	−	1.31100i	−0.944420	−	0.328742i	$-0.893375\pi$
$197$	−10.6237	−	18.4008i	−0.756909	−	1.31100i	0.187511	−	0.982263i	$-0.439958\pi$
$198$		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
$201$	5.55051	−	13.0458i	0.391503	−	0.920177i
$202$		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
$207$	−5.17423	+	27.8396i	−0.359634	+	1.93499i
$208$		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
$213$	0.702041	−	7.61926i	0.0481031	−	0.522063i
$214$		0			0
$215$			25.1701i			1.71659i
$216$		0			0
$217$	−3.94949	+	6.84072i	−0.268109	+	0.464378i
$218$		0			0
$219$	2.82577	+	6.13361i	0.190948	+	0.414471i
$220$		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	−0.752731	−	0.658329i	$-0.771264\pi$
$227$	−8.42168	+	4.86226i	−0.558967	+	0.322720i	0.193764	+	0.981048i	$0.437930\pi$
$228$		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
$231$	−24.7474	+	11.4012i	−1.62826	+	0.750144i
$232$		0			0
$233$	11.7247	+	20.3079i	0.768114	+	1.33041i	0.938585	+	0.345049i	$0.112138\pi$
$233$	11.7247	+	20.3079i	0.768114	+	1.33041i	−0.170471	+	0.985363i	$0.554529\pi$
$234$		0			0
$235$	5.44949	−	3.14626i	0.355486	−	0.205240i
$236$		0			0
$237$	−1.72474	+	18.7187i	−0.112034	+	1.21591i
$238$		0			0
$239$	6.62372	+	11.4726i	0.428453	+	0.742103i	0.996736	−	0.0807307i	$-0.0257254\pi$
$239$	6.62372	+	11.4726i	0.428453	+	0.742103i	−0.568283	+	0.822833i	$0.692392\pi$
$240$		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
$249$	12.8485	−	5.91931i	0.814239	−	0.375121i
$250$		0			0
$251$	−7.07321	+	12.2512i	−0.446457	+	0.773287i	−0.998152	−	0.0607591i	$-0.980648\pi$
$251$	−7.07321	+	12.2512i	−0.446457	+	0.773287i	0.551695	+	0.834046i	$0.313981\pi$
$252$		0			0
$253$			32.5590i			2.04697i
$254$		0			0
$255$	−7.89898	+	3.63907i	−0.494653	+	0.227888i
$256$		0			0
$257$	4.07321	−	2.35167i	0.254080	−	0.146693i	−0.367551	−	0.930003i	$-0.619804\pi$
$257$	4.07321	−	2.35167i	0.254080	−	0.146693i	0.621631	+	0.783310i	$0.286470\pi$
$258$		0			0
$259$			0.460702i			0.0286266i
$260$		0			0
$261$	−20.0732	−	17.1616i	−1.24250	−	1.06228i
$262$		0			0
$263$			14.7778i			0.911239i	0.890175	+	0.455619i	$0.150582\pi$
$263$			14.7778i			0.911239i	−0.890175	+	0.455619i	$0.849418\pi$
$264$		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	$-0.662217\pi$
$269$		−	28.6342i		−	1.74586i	0.487846	−	0.872929i	$-0.337783\pi$
$270$		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
$279$	3.94949	+	3.37662i	0.236450	+	0.202153i
$280$		0			0
$281$	1.27526	−	2.20881i	0.0760753	−	0.131766i	−0.825478	−	0.564434i	$-0.809094\pi$
$281$	1.27526	−	2.20881i	0.0760753	−	0.131766i	0.901553	+	0.432668i	$0.142428\pi$
$282$		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
$285$	−4.34847	−	9.43879i	−0.257581	−	0.559106i
$286$		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
$291$	−5.17423	+	2.38378i	−0.303319	+	0.139740i
$292$		0			0
$293$			12.2993i			0.718534i	0.933235	+	0.359267i	$0.116973\pi$
$293$			12.2993i			0.718534i	−0.933235	+	0.359267i	$0.883027\pi$
$294$		0			0
$295$		−	12.5851i		−	0.732730i
$296$		0			0
$297$	4.39898	+	17.3759i	0.255255	+	1.00825i
$298$		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
$303$	14.7474	+	1.35884i	0.847219	+	0.0780630i
$304$		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
$309$	−10.1742	−	0.937458i	−0.578792	−	0.0533301i
$310$		0			0
$311$	−33.7980			−1.91651			−0.958253	−	0.285921i	$-0.907701\pi$
$311$	−33.7980			−1.91651			−0.958253	+	0.285921i	$0.907701\pi$
$312$		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
$315$	20.7980	+	17.7812i	1.17183	+	1.00186i
$316$		0			0
$317$	−25.3207	−	14.6189i	−1.42215	−	0.821079i	−0.425668	−	0.904880i	$-0.639961\pi$
$317$	−25.3207	−	14.6189i	−1.42215	−	0.821079i	−0.996483	+	0.0838009i	$0.973294\pi$
$318$		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
$333$	0.297959	+	0.0553782i	0.0163281	+	0.00303471i
$334$		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
$339$	19.7474	+	1.81954i	1.07253	+	0.0988237i
$340$		0			0
$341$	5.17423	+	2.98735i	0.280201	+	0.161774i
$342$		0			0
$343$		−	31.0019i		−	1.67395i
$344$		0			0
$345$	29.6969	−	13.6814i	1.59883	−	0.736584i
$346$		0			0
$347$	−11.0732	−	19.1794i	−0.594441	−	1.02960i	−0.993625	−	0.112732i	$-0.964040\pi$
$347$	−11.0732	−	19.1794i	−0.594441	−	1.02960i	0.399184	−	0.916871i	$-0.369293\pi$
$348$		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
$351$	−18.8258	−	19.3543i	−1.00485	−	1.03306i
$352$		0			0
$353$	4.17423	−	7.22999i	0.222172	−	0.384813i	−0.733295	−	0.679910i	$-0.762019\pi$
$353$	4.17423	−	7.22999i	0.222172	−	0.384813i	0.955467	+	0.295097i	$0.0953520\pi$
$354$		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	$-0.818708\pi$
$359$		−	20.4347i		−	1.07850i	0.842146	−	0.539250i	$-0.181292\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$		0			0
$363$	0.651531	+	1.41421i	0.0341965	+	0.0742270i
$364$		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
$369$	2.82577	−	3.30518i	0.147103	−	0.172061i
$370$		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
$381$	−18.6237	−	1.71600i	−0.954122	−	0.0879132i
$382$		0			0
$383$	−5.07321	+	8.78706i	−0.259229	+	0.448998i	−0.966036	−	0.258409i	$-0.916802\pi$
$383$	−5.07321	+	8.78706i	−0.259229	+	0.448998i	0.706806	+	0.707407i	$0.250135\pi$
$384$		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	−0.0304008	−	0.999538i	$-0.509678\pi$
$389$	−17.9722	−	10.3763i	−0.911226	−	0.526097i	−0.880826	+	0.473441i	$0.843012\pi$
$390$		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	$-0.621331\pi$
$401$	−14.8990			−0.744020			−0.372010	+	0.928229i	$0.621331\pi$
$402$		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	0.891173	−	0.453663i	$-0.149883\pi$
$419$	19.3207	+	11.1548i	0.943876	+	0.544947i	0.0527029	+	0.998610i	$0.483216\pi$
$420$		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
$423$	7.17423	+	6.13361i	0.348823	+	0.298226i
$424$		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	0.0255898	−	0.999673i	$-0.491854\pi$
$431$	18.7702	−	10.8370i	0.904126	−	0.521998i	0.878537	+	0.477675i	$0.158520\pi$
$432$		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
$435$	−2.79796	+	30.3663i	−0.134152	+	1.45595i
$436$		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
$441$	−40.6969	−	7.56388i	−1.93795	−	0.360185i
$442$		0			0
$443$	4.37628	+	7.57993i	0.207923	+	0.360133i	0.951060	−	0.309006i	$-0.0999963\pi$
$443$	4.37628	+	7.57993i	0.207923	+	0.360133i	−0.743137	+	0.669139i	$0.766663\pi$
$444$		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	−0.652341	−	0.757926i	$-0.726213\pi$
$449$	−6.82577	+	3.94086i	−0.322128	+	0.185981i	0.330213	+	0.943907i	$0.392879\pi$
$450$		0			0
$451$	2.50000	−	4.33013i	0.117720	−	0.203898i
$452$		0			0
$453$	−7.82577	−	16.9866i	−0.367687	−	0.798101i
$454$		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
$459$	−9.09592	−	9.35131i	−0.424561	−	0.436482i
$460$		0			0
$461$			14.4279i			0.671973i	0.941867	+	0.335986i	$0.109070\pi$
$461$			14.4279i			0.671973i	−0.941867	+	0.335986i	$0.890930\pi$
$462$		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
$465$	0.550510	−	5.97469i	0.0255293	−	0.277070i
$466$		0			0
$467$	27.8258	+	16.0652i	1.28762	+	0.743409i	0.978230	−	0.207525i	$-0.0665408\pi$
$467$	27.8258	+	16.0652i	1.28762	+	0.743409i	0.309393	+	0.950934i	$0.399874\pi$
$468$		0			0
$469$	27.6464	−	25.0826i	1.27659	−	1.15821i
$470$		0			0
$471$	−2.97219	−	6.45145i	−0.136951	−	0.297267i
$472$		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	0.806581	−	0.591123i	$-0.201315\pi$
$479$	15.2753	+	8.81917i	0.697944	+	0.402958i	−0.108637	+	0.994081i	$0.534649\pi$
$480$		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
$489$	28.6237	+	2.63740i	1.29441	+	0.119267i
$490$		0			0
$491$		−	22.9774i		−	1.03695i	−0.855092	−	0.518477i	$-0.826499\pi$
$491$		−	22.9774i		−	1.03695i	0.855092	−	0.518477i	$-0.173501\pi$
$492$		0			0
$493$	22.1010			0.995380
$494$		0			0
$495$	13.4495	−	15.7313i	0.604510	−	0.707070i
$496$		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
$501$	−0.904082	+	9.81201i	−0.0403914	+	0.438368i
$502$		0			0
$503$	−14.8258	−	25.6790i	−0.661048	−	1.14497i	−0.980341	−	0.197313i	$-0.936779\pi$
$503$	−14.8258	−	25.6790i	−0.661048	−	1.14497i	0.319292	−	0.947656i	$-0.396555\pi$
$504$		0			0
$505$	−8.55051	−	14.8099i	−0.380493	−	0.659033i
$506$		0			0
$507$	24.1464	+	2.22486i	1.07238	+	0.0988095i
$508$		0			0
$509$		−	2.82843i		−	0.125368i	−0.998033	−	0.0626839i	$-0.980034\pi$
$509$		−	2.82843i		−	0.125368i	0.998033	−	0.0626839i	$-0.0199660\pi$
$510$		0			0
$511$			17.7812i			0.786594i
$512$		0			0
$513$	11.1742	−	10.8691i	0.493355	−	0.479881i
$514$		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
$519$	−2.94949	+	1.35884i	−0.129468	+	0.0596463i
$520$		0			0
$521$	−28.2929			−1.23953			−0.619766	−	0.784786i	$-0.712773\pi$
$521$	−28.2929			−1.23953			−0.619766	+	0.784786i	$0.712773\pi$
$522$		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
$525$	−0.724745	+	7.86566i	−0.0316305	+	0.343286i
$526$		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
$543$	20.5227	+	1.89097i	0.880714	+	0.0811493i
$544$		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
$549$	−0.252551	+	1.35884i	−0.0107786	+	0.0579937i
$550$		0			0
$551$			26.4094i			1.12508i
$552$		0			0
$553$	−24.7474	+	42.8638i	−1.05237	+	1.82276i
$554$		0			0
$555$	−0.146428	−	0.317837i	−0.00621553	−	0.0134914i
$556$		0			0
$557$	−10.0732	+	5.81577i	−0.426816	+	0.246422i	−0.697989	−	0.716108i	$-0.745922\pi$
$557$	−10.0732	+	5.81577i	−0.426816	+	0.246422i	0.271173	+	0.962531i	$0.412588\pi$
$558$		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	$-0.686921\pi$
$563$	−26.2929			−1.10811			−0.554056	+	0.832479i	$0.686921\pi$
$564$		0			0
$565$	−11.4495	−	19.8311i	−0.481684	−	0.834301i
$566$		0			0
$567$	−14.7474	+	38.3034i	−0.619335	+	1.60859i
$568$		0			0
$569$	8.42168	−	4.86226i	0.353055	−	0.203837i	−0.312975	−	0.949761i	$-0.601326\pi$
$569$	8.42168	−	4.86226i	0.353055	−	0.203837i	0.666030	+	0.745925i	$0.267992\pi$
$570$		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
$573$	9.09592	+	19.7436i	0.379987	+	0.824801i
$574$		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
$585$	−5.69694	+	30.6520i	−0.235539	+	1.26730i
$586$		0			0
$587$	−10.7247	+	18.5758i	−0.442658	+	0.766705i	−0.997886	−	0.0649926i	$-0.979298\pi$
$587$	−10.7247	+	18.5758i	−0.442658	+	0.766705i	0.555228	+	0.831698i	$0.312631\pi$
$588$		0			0
$589$		−	5.19615i		−	0.214104i
$590$		0			0
$591$	−36.6464	−	3.37662i	−1.50743	−	0.138895i
$592$		0			0
$593$	14.9722	−	25.9326i	0.614834	−	1.06492i	−0.375579	−	0.926790i	$-0.622556\pi$
$593$	14.9722	−	25.9326i	0.614834	−	1.06492i	0.990414	−	0.138134i	$-0.0441105\pi$
$594$		0			0
$595$	−22.8990			−0.938767
$596$		0			0
$597$	−7.97219	−	17.3045i	−0.326280	−	0.708224i
$598$		0			0
$599$	0.825765	+	1.43027i	0.0337399	+	0.0584391i	0.882402	−	0.470496i	$-0.155925\pi$
$599$	0.825765	+	1.43027i	0.0337399	+	0.0584391i	−0.848662	+	0.528935i	$0.822592\pi$
$600$		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
$603$	−12.8990	−	20.8954i	−0.525287	−	0.850925i
$604$		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
$609$	−29.0959	−	63.1556i	−1.17903	−	2.55920i
$610$		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
$615$	−5.00000	−	0.460702i	−0.201619	−	0.0185773i
$616$		0			0
$617$			12.8708i			0.518158i	0.965856	+	0.259079i	$0.0834191\pi$
$617$			12.8708i			0.518158i	−0.965856	+	0.259079i	$0.916581\pi$
$618$		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
$621$	34.1969	+	35.1571i	1.37228	+	1.41081i
$622$		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
$633$	2.82577	+	6.13361i	0.112314	+	0.243789i
$634$		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
$639$	−10.0732	−	8.61209i	−0.398490	−	0.340689i
$640$		0			0
$641$	0.522704	+	0.905350i	0.0206456	+	0.0357592i	0.876164	−	0.482014i	$-0.160095\pi$
$641$	0.522704	+	0.905350i	0.0206456	+	0.0357592i	−0.855518	+	0.517773i	$0.826761\pi$
$642$		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	−0.689841	−	0.723961i	$-0.742320\pi$
$647$	7.17423	−	12.4261i	0.282048	−	0.488522i	0.971889	+	0.235439i	$0.0756528\pi$
$648$		0			0
$649$	18.7980	−	10.8530i	0.737884	−	0.426018i
$650$		0			0
$651$	5.72474	+	12.4261i	0.224370	+	0.487019i
$652$		0			0
$653$	2.62372	−	4.54442i	0.102674	−	0.177837i	−0.810111	−	0.586276i	$-0.800593\pi$
$653$	2.62372	−	4.54442i	0.102674	−	0.177837i	0.912786	+	0.408439i	$0.133927\pi$
$654$		0			0
$655$			1.27135i			0.0496757i
$656$		0			0
$657$	11.5000	+	2.13737i	0.448658	+	0.0833869i
$658$		0			0
$659$	−3.27526	+	1.89097i	−0.127586	+	0.0736617i	−0.562435	−	0.826842i	$-0.690135\pi$
$659$	−3.27526	+	1.89097i	−0.127586	+	0.0736617i	0.434849	+	0.900504i	$0.356802\pi$
$660$		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
$663$	22.5000	+	2.07316i	0.873828	+	0.0805148i
$664$		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	$-0.892803\pi$
$677$	−19.7247	−	34.1643i	−0.758084	−	1.31304i	0.185743	−	0.982598i	$-0.440531\pi$
$678$		0			0
$679$	−15.0000			−0.575647
$680$		0			0
$681$	−1.54541	+	16.7723i	−0.0592202	+	0.642717i
$682$		0			0
$683$	−8.82577	+	15.2867i	−0.337709	+	0.584928i	−0.984001	−	0.178161i	$-0.942985\pi$
$683$	−8.82577	+	15.2867i	−0.337709	+	0.584928i	0.646293	+	0.763090i	$0.276318\pi$
$684$		0			0
$685$	−37.7980			−1.44419
$686$		0			0
$687$	10.6237	−	4.89437i	0.405320	−	0.186732i
$688$		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
$693$	−8.62372	+	46.3994i	−0.327588	+	1.76257i
$694$		0			0
$695$		−	42.1407i		−	1.59849i
$696$		0			0
$697$			3.63907i			0.137840i
$698$		0			0
$699$	40.4444	+	3.72656i	1.52975	+	0.140951i
$700$		0			0
$701$	14.1742	+	24.5505i	0.535353	+	0.927259i	0.999146	+	0.0413156i	$0.0131549\pi$
$701$	14.1742	+	24.5505i	0.535353	+	0.927259i	−0.463793	+	0.885944i	$0.653512\pi$
$702$		0			0
$703$	−0.151531	−	0.262459i	−0.00571509	−	0.00989883i
$704$		0			0
$705$	1.00000	−	10.8530i	0.0376622	−	0.408748i
$706$		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
$711$	24.7474	+	21.1578i	0.928102	+	0.793480i
$712$		0			0
$713$	16.3485			0.612255
$714$		0			0
$715$			35.8481i			1.34064i
$716$		0			0
$717$	22.8485	+	2.10527i	0.853292	+	0.0786226i
$718$		0			0
$719$	−41.6691	−	24.0577i	−1.55400	−	0.897200i	−0.997810	−	0.0661425i	$-0.978931\pi$
$719$	−41.6691	−	24.0577i	−1.55400	−	0.897200i	−0.556186	−	0.831058i	$-0.687736\pi$
$720$		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
$735$	20.0000	+	43.4120i	0.737711	+	1.60128i
$736$		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
$741$	−2.47730	+	26.8861i	−0.0910057	+	0.987686i
$742$		0			0
$743$	8.72474	+	5.03723i	0.320080	+	0.184798i	0.651428	−	0.758710i	$-0.274170\pi$
$743$	8.72474	+	5.03723i	0.320080	+	0.184798i	−0.331348	+	0.943508i	$0.607504\pi$
$744$		0			0
$745$			15.6992i			0.575175i
$746$		0			0
$747$	4.47730	−	24.0898i	0.163816	−	0.881399i
$748$		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
$753$	10.2526	+	22.2542i	0.373624	+	0.810988i
$754$		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	$0.140777\pi$
$761$			23.6130i			0.855972i	−0.903785	+	0.427986i	$0.859223\pi$
$762$		0			0
$763$	27.2474	+	47.1940i	0.986424	+	1.70854i
$764$		0			0
$765$	−2.75255	+	14.8099i	−0.0995187	+	0.535454i
$766$		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
$771$	0.747449	−	8.11207i	0.0269187	−	0.292149i
$772$		0			0
$773$	23.9722	−	13.8404i	0.862220	−	0.497803i	−0.00253516	−	0.999997i	$-0.500807\pi$
$773$	23.9722	−	13.8404i	0.862220	−	0.497803i	0.864755	+	0.502194i	$0.167474\pi$
$774$		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
$783$	−44.3434	+	11.2262i	−1.58470	+	0.401192i
$784$		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	−0.566225	−	0.824251i	$-0.691597\pi$
$797$	−3.82577	+	2.20881i	−0.135516	+	0.0782399i	0.430709	+	0.902491i	$0.358263\pi$
$798$		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	$-0.746643\pi$
$809$	−39.7980			−1.39922			−0.699611	+	0.714524i	$0.746643\pi$
$810$		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	0.270259	−	0.962788i	$-0.412891\pi$
$821$	−12.2753	−	7.08712i	−0.428409	−	0.247342i	−0.698669	+	0.715445i	$0.746224\pi$
$822$		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
$825$	5.94949	+	0.548188i	0.207135	+	0.0190855i
$826$		0			0
$827$	4.32066	+	2.49454i	0.150244	+	0.0867435i	0.573237	−	0.819389i	$-0.305687\pi$
$827$	4.32066	+	2.49454i	0.150244	+	0.0867435i	−0.422993	+	0.906133i	$0.639021\pi$
$828$		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
$837$	8.72474	−	2.20881i	0.301571	−	0.0763475i
$838$		0			0
$839$	−12.5227	+	7.22999i	−0.432332	+	0.249607i	−0.700340	−	0.713810i	$-0.746968\pi$
$839$	−12.5227	+	7.22999i	−0.432332	+	0.249607i	0.268008	+	0.963417i	$0.413635\pi$
$840$		0			0
$841$	24.2474	−	41.9978i	0.836119	−	1.44820i
$842$		0			0
$843$	−1.84847	−	4.01229i	−0.0636647	−	0.138191i
$844$		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
$855$	−17.6969	−	3.28913i	−0.605223	−	0.112486i
$856$		0			0
$857$	−25.5959			−0.874340			−0.437170	−	0.899379i	$-0.644019\pi$
$857$	−25.5959			−0.874340			−0.437170	+	0.899379i	$0.644019\pi$
$858$		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
$861$	10.3990	−	4.79083i	0.354396	−	0.163271i
$862$		0			0
$863$		−	37.1195i		−	1.26356i	−0.775147	−	0.631781i	$-0.782324\pi$
$863$		−	37.1195i		−	1.26356i	0.775147	−	0.631781i	$-0.217676\pi$
$864$		0			0
$865$	3.24745	+	1.87492i	0.110417	+	0.0637490i
$866$		0			0
$867$	−18.4495	−	1.69994i	−0.626578	−	0.0577331i
$868$		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
$873$	−1.80306	+	9.70125i	−0.0610244	+	0.328338i
$874$		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	0.258532	−	0.966003i	$-0.416761\pi$
$881$	−13.3207	−	7.69069i	−0.448785	−	0.259106i	−0.707317	+	0.706897i	$0.750095\pi$
$882$		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	0.887579	−	0.460655i	$-0.152385\pi$
$887$	27.7702	+	16.0331i	0.932430	+	0.538339i	0.0448510	+	0.998994i	$0.485719\pi$
$888$		0			0
$889$	−42.6464	−	24.6219i	−1.43032	−	0.825793i
$890$		0			0
$891$	28.9722	+	11.1548i	0.970605	+	0.373700i
$892$		0			0
$893$		−	9.43879i		−	0.315857i
$894$		0			0
$895$	−51.1918			−1.71115
$896$		0			0
$897$	−84.5908	−	7.79423i	−2.82441	−	0.260242i
$898$		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
$903$	−98.9898	−	9.12096i	−3.29417	−	0.303526i
$904$		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
$909$	16.6691	−	19.4972i	0.552880	−	0.646682i
$910$		0			0
$911$		−	2.47848i		−	0.0821158i	−0.999157	−	0.0410579i	$-0.986927\pi$
$911$		−	2.47848i		−	0.0821158i	0.999157	−	0.0410579i	$-0.0130728\pi$
$912$		0			0
$913$		−	28.1735i		−	0.932407i
$914$		0			0
$915$	1.44949	−	0.667783i	0.0479187	−	0.0220762i
$916$		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
$921$	−22.1742	−	48.1314i	−0.730666	−	1.58598i
$922$		0			0
$923$	22.9546			0.755560
$924$		0			0
$925$	0.0505103	−	0.0874863i	0.00166077	−	0.00287653i
$926$		0			0
$927$	−11.5000	+	13.4511i	−0.377710	+	0.441792i
$928$		0			0
$929$	−0.494897			−0.0162371			−0.00811853	−	0.999967i	$-0.502584\pi$
$929$	−0.494897			−0.0162371			−0.00811853	+	0.999967i	$0.502584\pi$
$930$		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	$-0.347433\pi$
$941$	28.2929			0.922321			0.461160	+	0.887317i	$0.347433\pi$
$942$		0			0
$943$		−	13.6814i		−	0.445529i
$944$		0			0
$945$	45.9444	−	11.6315i	1.49457	−	0.378374i
$946$		0			0
$947$			25.5201i			0.829291i	0.909983	+	0.414645i	$0.136094\pi$
$947$			25.5201i			0.829291i	−0.909983	+	0.414645i	$0.863906\pi$
$948$		0			0
$949$	−17.5454	+	10.1298i	−0.569548	+	0.328829i
$950$		0			0
$951$	−45.9949	+	21.1899i	−1.49149	+	0.687131i
$952$		0			0
$953$			33.0197i			1.06961i	0.844974	+	0.534807i	$0.179616\pi$
$953$			33.0197i			1.06961i	−0.844974	+	0.534807i	$0.820384\pi$
$954$		0			0
$955$	12.5505	−	21.7381i	0.406125	−	0.703429i
$956$		0			0
$957$	−47.7702	+	22.0078i	−1.54419	+	0.711411i
$958$		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
$969$	−1.19694	+	12.9904i	−0.0384512	+	0.417311i
$970$		0			0
$971$	−21.2196	+	12.2512i	−0.680971	+	0.393159i	−0.800221	−	0.599706i	$-0.795284\pi$
$971$	−21.2196	+	12.2512i	−0.680971	+	0.393159i	0.119250	+	0.992864i	$0.461951\pi$
$972$		0			0
$973$	48.0454	+	83.2171i	1.54027	+	2.66782i
$974$		0			0
$975$	−8.17423	+	3.76588i	−0.261785	+	0.120605i
$976$		0			0
$977$	19.3207	+	11.1548i	0.618123	+	0.356873i	0.776138	−	0.630563i	$-0.217176\pi$
$977$	19.3207	+	11.1548i	0.618123	+	0.356873i	−0.158015	+	0.987437i	$0.550509\pi$
$978$		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	$-0.461346\pi$
$983$	7.59592			0.242272			0.121136	+	0.992636i	$0.461346\pi$
$984$		0			0
$985$	21.2474	+	36.8017i	0.677000	+	1.17260i
$986$		0			0
$987$	10.3990	+	22.5720i	0.331003	+	0.718476i
$988$		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
$993$	4.97219	−	53.9633i	0.157788	−	1.71247i
$994$		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
$999$	0.376276	−	0.365999i	0.0119048	−	0.0115797i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.41421i) q^{3} -2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.41421i) q^{3} -2.00000 q^{5} +(3.94949 - 2.28024i) q^{7} +(-1.00000 - 2.82843i) q^{9} +(-1.72474 - 2.98735i) q^{11} +(4.50000 + 2.59808i) q^{13} +(-2.00000 + 2.82843i) q^{15} +(2.17423 + 1.25529i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(0.724745 - 7.86566i) q^{21} +(-8.17423 - 4.71940i) q^{23} -1.00000 q^{25} +(-5.00000 - 1.41421i) q^{27} +(7.62372 - 4.40156i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(-5.94949 - 0.548188i) q^{33} +(-7.89898 + 4.56048i) q^{35} +(-0.0505103 + 0.0874863i) q^{37} +(8.17423 - 3.76588i) q^{39} +(0.724745 + 1.25529i) q^{41} -12.5851i q^{43} +(2.00000 + 5.65685i) q^{45} +(-2.72474 + 1.57313i) q^{47} +(6.89898 - 11.9494i) q^{49} +(3.94949 - 1.81954i) q^{51} +6.00000 q^{53} +(3.44949 + 5.97469i) q^{55} +(2.17423 + 4.71940i) q^{57} +6.29253i q^{59} +(-0.398979 - 0.230351i) q^{61} +(-10.3990 - 8.89060i) q^{63} +(-9.00000 - 5.19615i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-14.8485 + 6.84072i) q^{69} +(3.82577 - 2.20881i) q^{71} +(-1.94949 + 3.37662i) q^{73} +(-1.00000 + 1.41421i) q^{75} +(-13.6237 - 7.86566i) q^{77} +(-9.39898 + 5.42650i) q^{79} +(-7.00000 + 5.65685i) q^{81} +(7.07321 + 4.08372i) q^{83} +(-4.34847 - 2.51059i) q^{85} +(1.39898 - 15.1831i) q^{87} +16.0492i q^{89} +23.6969 q^{91} +(-0.275255 + 2.98735i) q^{93} +(3.00000 - 5.19615i) q^{95} +(-2.84847 - 1.64456i) q^{97} +(-6.72474 + 7.86566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 8 q^{5} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 8 * q^5 + 6 * q^7 - 4 * q^9	\( 4 q + 4 q^{3} - 8 q^{5} + 6 q^{7} - 4 q^{9} - 2 q^{11} + 18 q^{13} - 8 q^{15} - 6 q^{17} - 6 q^{19} - 2 q^{21} - 18 q^{23} - 4 q^{25} - 20 q^{27} + 6 q^{29} - 6 q^{31} - 14 q^{33} - 12 q^{35} - 10 q^{37} + 18 q^{39} - 2 q^{41} + 8 q^{45} - 6 q^{47} + 8 q^{49} + 6 q^{51} + 24 q^{53} + 4 q^{55} - 6 q^{57} + 18 q^{61} - 22 q^{63} - 36 q^{65} + 32 q^{67} - 30 q^{69} + 30 q^{71} + 2 q^{73} - 4 q^{75} - 30 q^{77} - 18 q^{79} - 28 q^{81} - 6 q^{83} + 12 q^{85} - 14 q^{87} + 36 q^{91} - 6 q^{93} + 12 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) \) 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 - 2 * q^21 - 18 * q^23 - 4 * q^25 - 20 * q^27 + 6 * q^29 - 6 * q^31 - 14 * q^33 - 12 * q^35 - 10 * q^37 + 18 * q^39 - 2 * q^41 + 8 * q^45 - 6 * q^47 + 8 * q^49 + 6 * q^51 + 24 * q^53 + 4 * q^55 - 6 * q^57 + 18 * q^61 - 22 * q^63 - 36 * q^65 + 32 * q^67 - 30 * 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 - 14 * q^87 + 36 * q^91 - 6 * q^93 + 12 * q^95 + 18 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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