LMFDB - Embedded newform 804.2.o.b.641.2

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			641.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	804.641
Dual form			804.2.o.b.365.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.41421i) q^{3} +2.00000 q^{5} +(-0.949490 + 0.548188i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.41421i) q^{3} +2.00000 q^{5} +(-0.949490 + 0.548188i) q^{7} +(-1.00000 - 2.82843i) q^{9} +(-0.724745 - 1.25529i) q^{11} +(4.50000 + 2.59808i) q^{13} +(-2.00000 + 2.82843i) q^{15} +(5.17423 + 2.98735i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(0.174235 - 1.89097i) q^{21} +(0.825765 + 0.476756i) q^{23} -1.00000 q^{25} +(5.00000 + 1.41421i) q^{27} +(4.62372 - 2.66951i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(2.50000 + 0.230351i) q^{33} +(-1.89898 + 1.09638i) q^{35} +(-4.94949 + 8.57277i) q^{37} +(-8.17423 + 3.76588i) q^{39} +(1.72474 + 2.98735i) q^{41} -1.27135i q^{43} +(-2.00000 - 5.65685i) q^{45} +(0.275255 - 0.158919i) q^{47} +(-2.89898 + 5.02118i) q^{49} +(-9.39898 + 4.33013i) q^{51} -6.00000 q^{53} +(-1.44949 - 2.51059i) q^{55} +(-2.17423 - 4.71940i) q^{57} -0.635674i q^{59} +(9.39898 + 5.42650i) q^{61} +(2.50000 + 2.13737i) q^{63} +(9.00000 + 5.19615i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-1.50000 + 0.691053i) q^{69} +(-11.1742 + 6.45145i) q^{71} +(2.94949 - 5.10867i) q^{73} +(1.00000 - 1.41421i) q^{75} +(1.37628 + 0.794593i) q^{77} +(0.398979 - 0.230351i) q^{79} +(-7.00000 + 5.65685i) q^{81} +(10.0732 + 5.81577i) q^{83} +(10.3485 + 5.97469i) q^{85} +(-0.848469 + 9.20844i) q^{87} -4.73545i q^{89} -5.69694 q^{91} +(0.275255 - 2.98735i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(11.8485 + 6.84072i) q^{97} +(-2.82577 + 3.30518i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−0.949490	+	0.548188i	−0.358873	+	0.207196i	−0.668586	−	0.743634i	$-0.733100\pi$
$7$	−0.949490	+	0.548188i	−0.358873	+	0.207196i	0.309713	+	0.950830i	$0.399767\pi$
$8$		0			0
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$		0			0
$11$	−0.724745	−	1.25529i	−0.218519	−	0.378486i	0.735837	−	0.677159i	$-0.236789\pi$
$11$	−0.724745	−	1.25529i	−0.218519	−	0.378486i	−0.954355	+	0.298674i	$0.903456\pi$
$12$		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
$17$	5.17423	+	2.98735i	1.25494	+	0.724538i	0.972086	−	0.234626i	$-0.0753866\pi$
$17$	5.17423	+	2.98735i	1.25494	+	0.724538i	0.282851	+	0.959164i	$0.408720\pi$
$18$		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
$21$	0.174235	−	1.89097i	0.0380211	−	0.412643i
$22$		0			0
$23$	0.825765	+	0.476756i	0.172184	+	0.0994105i	0.583615	−	0.812030i	$-0.301638\pi$
$23$	0.825765	+	0.476756i	0.172184	+	0.0994105i	−0.411431	+	0.911441i	$0.634971\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$		0			0
$29$	4.62372	−	2.66951i	0.858604	−	0.495715i	−0.00494052	−	0.999988i	$-0.501573\pi$
$29$	4.62372	−	2.66951i	0.858604	−	0.495715i	0.863545	+	0.504273i	$0.168239\pi$
$30$		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	+	0.230351i	0.435194	+	0.0400989i
$34$		0			0
$35$	−1.89898	+	1.09638i	−0.320986	+	0.185321i
$36$		0			0
$37$	−4.94949	+	8.57277i	−0.813691	+	1.40935i	0.0965729	+	0.995326i	$0.469212\pi$
$37$	−4.94949	+	8.57277i	−0.813691	+	1.40935i	−0.910264	+	0.414028i	$0.864121\pi$
$38$		0			0
$39$	−8.17423	+	3.76588i	−1.30893	+	0.603024i
$40$		0			0
$41$	1.72474	+	2.98735i	0.269360	+	0.466545i	0.968697	−	0.248247i	$-0.0798546\pi$
$41$	1.72474	+	2.98735i	0.269360	+	0.466545i	−0.699337	+	0.714792i	$0.746521\pi$
$42$		0			0
$43$		−	1.27135i		−	0.193879i	−0.995290	−	0.0969395i	$-0.969095\pi$
$43$		−	1.27135i		−	0.193879i	0.995290	−	0.0969395i	$-0.0309053\pi$
$44$		0			0
$45$	−2.00000	−	5.65685i	−0.298142	−	0.843274i
$46$		0			0
$47$	0.275255	−	0.158919i	0.0401501	−	0.0231807i	−0.479791	−	0.877383i	$-0.659287\pi$
$47$	0.275255	−	0.158919i	0.0401501	−	0.0231807i	0.519941	+	0.854202i	$0.325954\pi$
$48$		0			0
$49$	−2.89898	+	5.02118i	−0.414140	+	0.717311i
$50$		0			0
$51$	−9.39898	+	4.33013i	−1.31612	+	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
$55$	−1.44949	−	2.51059i	−0.195449	−	0.338528i
$56$		0			0
$57$	−2.17423	−	4.71940i	−0.287984	−	0.625099i
$58$		0			0
$59$		−	0.635674i		−	0.0827578i	−0.999144	−	0.0413789i	$-0.986825\pi$
$59$		−	0.635674i		−	0.0827578i	0.999144	−	0.0413789i	$-0.0131751\pi$
$60$		0			0
$61$	9.39898	+	5.42650i	1.20342	+	0.694793i	0.961313	−	0.275458i	$-0.0888295\pi$
$61$	9.39898	+	5.42650i	1.20342	+	0.694793i	0.242103	+	0.970251i	$0.422163\pi$
$62$		0			0
$63$	2.50000	+	2.13737i	0.314970	+	0.269284i
$64$		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	+	0.691053i	−0.180579	+	0.0831930i
$70$		0			0
$71$	−11.1742	+	6.45145i	−1.32614	+	0.765646i	−0.984700	−	0.174258i	$-0.944247\pi$
$71$	−11.1742	+	6.45145i	−1.32614	+	0.765646i	−0.341438	+	0.939904i	$0.610914\pi$
$72$		0			0
$73$	2.94949	−	5.10867i	0.345212	−	0.597924i	−0.640181	−	0.768224i	$-0.721140\pi$
$73$	2.94949	−	5.10867i	0.345212	−	0.597924i	0.985392	+	0.170300i	$0.0544738\pi$
$74$		0			0
$75$	1.00000	−	1.41421i	0.115470	−	0.163299i
$76$		0			0
$77$	1.37628	+	0.794593i	0.156841	+	0.0905523i
$78$		0			0
$79$	0.398979	−	0.230351i	0.0448887	−	0.0259165i	−0.477388	−	0.878693i	$-0.658416\pi$
$79$	0.398979	−	0.230351i	0.0448887	−	0.0259165i	0.522276	+	0.852776i	$0.325083\pi$
$80$		0			0
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$		0			0
$83$	10.0732	+	5.81577i	1.10568	+	0.638364i	0.937707	−	0.347428i	$-0.112945\pi$
$83$	10.0732	+	5.81577i	1.10568	+	0.638364i	0.167972	+	0.985792i	$0.446278\pi$
$84$		0			0
$85$	10.3485	+	5.97469i	1.12245	+	0.648046i
$86$		0			0
$87$	−0.848469	+	9.20844i	−0.0909654	+	0.987249i
$88$		0			0
$89$		−	4.73545i		−	0.501957i	−0.967993	−	0.250978i	$-0.919248\pi$
$89$		−	4.73545i		−	0.501957i	0.967993	−	0.250978i	$-0.0807523\pi$
$90$		0			0
$91$	−5.69694			−0.597201
$92$		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
$97$	11.8485	+	6.84072i	1.20303	+	0.694570i	0.961228	−	0.275756i	$-0.0889282\pi$
$97$	11.8485	+	6.84072i	1.20303	+	0.694570i	0.241802	+	0.970326i	$0.422262\pi$
$98$		0			0
$99$	−2.82577	+	3.30518i	−0.284000	+	0.332183i
$100$		0			0
$101$	−6.72474	−	11.6476i	−0.669137	−	1.15898i	−0.978146	−	0.207920i	$-0.933331\pi$
$101$	−6.72474	−	11.6476i	−0.669137	−	1.15898i	0.309009	−	0.951059i	$-0.400003\pi$
$102$		0			0
$103$	1.94949	+	3.37662i	0.192089	+	0.332708i	0.945942	−	0.324335i	$-0.105140\pi$
$103$	1.94949	+	3.37662i	0.192089	+	0.332708i	−0.753853	+	0.657043i	$0.771807\pi$
$104$		0			0
$105$	0.348469	−	3.78194i	0.0340071	−	0.369079i
$106$		0			0
$107$		−	9.12096i		−	0.881756i	−0.897567	−	0.440878i	$-0.854667\pi$
$107$		−	9.12096i		−	0.881756i	0.897567	−	0.440878i	$-0.145333\pi$
$108$		0			0
$109$		−	5.02118i		−	0.480942i	−0.970656	−	0.240471i	$-0.922698\pi$
$109$		−	5.02118i		−	0.480942i	0.970656	−	0.240471i	$-0.0773019\pi$
$110$		0			0
$111$	−7.17423	−	15.5724i	−0.680948	−	1.47807i
$112$		0			0
$113$	−3.27526	−	5.67291i	−0.308110	−	0.533662i	0.669839	−	0.742507i	$-0.266363\pi$
$113$	−3.27526	−	5.67291i	−0.308110	−	0.533662i	−0.977949	+	0.208844i	$0.933030\pi$
$114$		0			0
$115$	1.65153	+	0.953512i	0.154006	+	0.0889154i
$116$		0			0
$117$	2.84847	−	15.3260i	0.263341	−	1.41689i
$118$		0			0
$119$	−6.55051			−0.600484
$120$		0			0
$121$	4.44949	−	7.70674i	0.404499	−	0.700613i
$122$		0			0
$123$	−5.94949	−	0.548188i	−0.536447	−	0.0494285i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	4.39898	+	7.61926i	0.390346	+	0.676100i	0.992495	−	0.122284i	$-0.0390219\pi$
$127$	4.39898	+	7.61926i	0.390346	+	0.676100i	−0.602149	+	0.798384i	$0.705689\pi$
$128$		0			0
$129$	1.79796	+	1.27135i	0.158301	+	0.111936i
$130$		0			0
$131$			6.29253i			0.549781i	0.961476	+	0.274890i	$0.0886416\pi$
$131$			6.29253i			0.549781i	−0.961476	+	0.274890i	$0.911358\pi$
$132$		0			0
$133$		−	3.28913i		−	0.285204i
$134$		0			0
$135$	10.0000	+	2.82843i	0.860663	+	0.243432i
$136$		0			0
$137$	−9.10102			−0.777553			−0.388776	−	0.921332i	$-0.627102\pi$
$137$	−9.10102			−0.777553			−0.388776	+	0.921332i	$0.627102\pi$
$138$		0			0
$139$		−	7.21393i		−	0.611878i	−0.952051	−	0.305939i	$-0.901030\pi$
$139$		−	7.21393i		−	0.611878i	0.952051	−	0.305939i	$-0.0989703\pi$
$140$		0			0
$141$	−0.0505103	+	0.548188i	−0.00425373	+	0.0461658i
$142$		0			0
$143$		−	7.53177i		−	0.629838i
$144$		0			0
$145$	9.24745	−	5.33902i	0.767959	−	0.443381i
$146$		0			0
$147$	−4.20204	−	9.12096i	−0.346579	−	0.752284i
$148$		0			0
$149$		−	14.7778i		−	1.21065i	−0.795980	−	0.605323i	$-0.793044\pi$
$149$		−	14.7778i		−	1.21065i	0.795980	−	0.605323i	$-0.206956\pi$
$150$		0			0
$151$	−4.39898	+	7.61926i	−0.357984	+	0.620046i	−0.987624	−	0.156841i	$-0.949869\pi$
$151$	−4.39898	+	7.61926i	−0.357984	+	0.620046i	0.629640	+	0.776887i	$0.283202\pi$
$152$		0			0
$153$	3.27526	−	17.6223i	0.264789	−	1.42468i
$154$		0			0
$155$	−3.00000	+	1.73205i	−0.240966	+	0.139122i
$156$		0			0
$157$	6.94949	−	12.0369i	0.554630	−	0.960647i	−0.443303	−	0.896372i	$-0.646193\pi$
$157$	6.94949	−	12.0369i	0.554630	−	0.960647i	0.997932	−	0.0642747i	$-0.0204734\pi$
$158$		0			0
$159$	6.00000	−	8.48528i	0.475831	−	0.672927i
$160$		0			0
$161$	−1.04541			−0.0823897
$162$		0			0
$163$	−11.2980	−	19.5686i	−0.884924	−	1.53273i	−0.845800	−	0.533500i	$-0.820877\pi$
$163$	−11.2980	−	19.5686i	−0.884924	−	1.53273i	−0.0391242	−	0.999234i	$-0.512457\pi$
$164$		0			0
$165$	5.00000	+	0.460702i	0.389249	+	0.0358656i
$166$		0			0
$167$	22.0732	−	12.7440i	1.70808	−	0.986158i	0.771136	−	0.636671i	$-0.219689\pi$
$167$	22.0732	−	12.7440i	1.70808	−	0.986158i	0.936941	−	0.349487i	$-0.113644\pi$
$168$		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
$173$	−10.6237	−	6.13361i	−0.807707	−	0.466330i	0.0384521	−	0.999260i	$-0.487757\pi$
$173$	−10.6237	−	6.13361i	−0.807707	−	0.466330i	−0.846159	+	0.532931i	$0.821091\pi$
$174$		0			0
$175$	0.949490	−	0.548188i	0.0717747	−	0.0414391i
$176$		0			0
$177$	0.898979	+	0.635674i	0.0675714	+	0.0477802i
$178$		0			0
$179$	13.5959			1.01621			0.508103	−	0.861296i	$-0.330347\pi$
$179$	13.5959			1.01621			0.508103	+	0.861296i	$0.330347\pi$
$180$		0			0
$181$	1.05051	+	1.81954i	0.0780838	+	0.135245i	0.902423	−	0.430851i	$-0.141786\pi$
$181$	1.05051	+	1.81954i	0.0780838	+	0.135245i	−0.824339	+	0.566096i	$0.808453\pi$
$182$		0			0
$183$	−17.0732	+	7.86566i	−1.26209	+	0.581446i
$184$		0			0
$185$	−9.89898	+	17.1455i	−0.727787	+	1.26056i
$186$		0			0
$187$		−	8.66025i		−	0.633300i
$188$		0			0
$189$	−5.52270	+	1.39816i	−0.401718	+	0.101701i
$190$		0			0
$191$	8.72474	−	15.1117i	0.631300	−	1.09344i	−0.355986	−	0.934491i	$-0.615855\pi$
$191$	8.72474	−	15.1117i	0.631300	−	1.09344i	0.987286	−	0.158953i	$-0.0508118\pi$
$192$		0			0
$193$	−12.8990			−0.928489			−0.464244	−	0.885707i	$-0.653674\pi$
$193$	−12.8990			−0.928489			−0.464244	+	0.885707i	$0.653674\pi$
$194$		0			0
$195$	−16.3485	+	7.53177i	−1.17074	+	0.539361i
$196$		0			0
$197$	−1.62372	−	2.81237i	−0.115686	−	0.200373i	0.802368	−	0.596830i	$-0.203573\pi$
$197$	−1.62372	−	2.81237i	−0.115686	−	0.200373i	−0.918054	+	0.396456i	$0.870240\pi$
$198$		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
$203$	−2.92679	+	5.06934i	−0.205420	+	0.355798i
$204$		0			0
$205$	3.44949	+	5.97469i	0.240923	+	0.417291i
$206$		0			0
$207$	0.522704	−	2.81237i	0.0363304	−	0.195473i
$208$		0			0
$209$	4.34847			0.300790
$210$		0			0
$211$	2.94949	−	5.10867i	0.203051	−	0.351695i	−0.746459	−	0.665432i	$-0.768248\pi$
$211$	2.94949	−	5.10867i	0.203051	−	0.351695i	0.949510	+	0.313737i	$0.101581\pi$
$212$		0			0
$213$	2.05051	−	22.2542i	0.140499	−	1.52483i
$214$		0			0
$215$		−	2.54270i		−	0.173411i
$216$		0			0
$217$	0.949490	−	1.64456i	0.0644556	−	0.111640i
$218$		0			0
$219$	4.27526	+	9.27987i	0.288895	+	0.627076i
$220$		0			0
$221$	15.5227	+	26.8861i	1.04417	+	1.80856i
$222$		0			0
$223$	20.6969			1.38597			0.692985	−	0.720952i	$-0.256295\pi$
$223$	20.6969			1.38597			0.692985	+	0.720952i	$0.256295\pi$
$224$		0			0
$225$	1.00000	+	2.82843i	0.0666667	+	0.188562i
$226$		0			0
$227$	−23.4217	+	13.5225i	−1.55455	+	0.897521i	−0.556790	+	0.830653i	$0.687967\pi$
$227$	−23.4217	+	13.5225i	−1.55455	+	0.897521i	−0.997762	+	0.0668675i	$0.978700\pi$
$228$		0			0
$229$	−8.84847	−	5.10867i	−0.584723	−	0.337590i	0.178285	−	0.983979i	$-0.442945\pi$
$229$	−8.84847	−	5.10867i	−0.584723	−	0.337590i	−0.763008	+	0.646389i	$0.776278\pi$
$230$		0			0
$231$	−2.50000	+	1.15175i	−0.164488	+	0.0757799i
$232$		0			0
$233$	−9.27526	−	16.0652i	−0.607642	−	1.05247i	−0.991628	−	0.129128i	$-0.958782\pi$
$233$	−9.27526	−	16.0652i	−0.607642	−	1.05247i	0.383986	−	0.923339i	$-0.374551\pi$
$234$		0			0
$235$	0.550510	−	0.317837i	0.0359113	−	0.0207334i
$236$		0			0
$237$	−0.0732141	+	0.794593i	−0.00475577	+	0.0516144i
$238$		0			0
$239$	5.62372	+	9.74058i	0.363768	+	0.630066i	0.988578	−	0.150712i	$-0.0481566\pi$
$239$	5.62372	+	9.74058i	0.363768	+	0.630066i	−0.624809	+	0.780777i	$0.714823\pi$
$240$		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
$245$	−5.79796	+	10.0424i	−0.370418	+	0.641583i
$246$		0			0
$247$	−13.5000	+	7.79423i	−0.858984	+	0.495935i
$248$		0			0
$249$	−18.2980	+	8.42990i	−1.15959	+	0.534223i
$250$		0			0
$251$	−10.0732	+	17.4473i	−0.635816	+	1.10126i	0.350526	+	0.936553i	$0.386003\pi$
$251$	−10.0732	+	17.4473i	−0.635816	+	1.10126i	−0.986342	+	0.164712i	$0.947331\pi$
$252$		0			0
$253$		−	1.38211i		−	0.0868922i
$254$		0			0
$255$	−18.7980	+	8.66025i	−1.17717	+	0.542326i
$256$		0			0
$257$	13.0732	−	7.54782i	0.815485	−	0.470820i	−0.0333722	−	0.999443i	$-0.510625\pi$
$257$	13.0732	−	7.54782i	0.815485	−	0.470820i	0.848857	+	0.528623i	$0.177291\pi$
$258$		0			0
$259$		−	10.8530i		−	0.674373i
$260$		0			0
$261$	−12.1742	−	10.4084i	−0.753566	−	0.644261i
$262$		0			0
$263$			7.84961i			0.484027i	0.970273	+	0.242014i	$0.0778079\pi$
$263$			7.84961i			0.484027i	−0.970273	+	0.242014i	$0.922192\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	6.69694	+	4.73545i	0.409846	+	0.289805i
$268$		0			0
$269$			6.00680i			0.366241i	0.983090	+	0.183121i	$0.0586199\pi$
$269$			6.00680i			0.366241i	−0.983090	+	0.183121i	$0.941380\pi$
$270$		0			0
$271$			9.75663i			0.592673i	0.955084	+	0.296337i	$0.0957650\pi$
$271$			9.75663i			0.592673i	−0.955084	+	0.296337i	$0.904235\pi$
$272$		0			0
$273$	5.69694	−	8.05669i	0.344794	−	0.487613i
$274$		0			0
$275$	0.724745	+	1.25529i	0.0437038	+	0.0756971i
$276$		0			0
$277$	25.7980			1.55005			0.775025	−	0.631931i	$-0.217737\pi$
$277$	25.7980			1.55005			0.775025	+	0.631931i	$0.217737\pi$
$278$		0			0
$279$	3.94949	+	3.37662i	0.236450	+	0.202153i
$280$		0			0
$281$	−3.72474	+	6.45145i	−0.222200	+	0.384861i	−0.955476	−	0.295070i	$-0.904657\pi$
$281$	−3.72474	+	6.45145i	−0.222200	+	0.384861i	0.733276	+	0.679931i	$0.237990\pi$
$282$		0			0
$283$	−7.79796			−0.463541			−0.231770	−	0.972771i	$-0.574452\pi$
$283$	−7.79796			−0.463541			−0.231770	+	0.972771i	$0.574452\pi$
$284$		0			0
$285$	−4.34847	−	9.43879i	−0.257581	−	0.559106i
$286$		0			0
$287$	−3.27526	−	1.89097i	−0.193332	−	0.111620i
$288$		0			0
$289$	9.34847	+	16.1920i	0.549910	+	0.952472i
$290$		0			0
$291$	−21.5227	+	9.91555i	−1.26168	+	0.581260i
$292$		0			0
$293$		−	29.2699i		−	1.70997i	−0.518657	−	0.854983i	$-0.673568\pi$
$293$		−	29.2699i		−	1.70997i	0.518657	−	0.854983i	$-0.326432\pi$
$294$		0			0
$295$		−	1.27135i		−	0.0740208i
$296$		0			0
$297$	−1.84847	−	7.30142i	−0.107259	−	0.423671i
$298$		0			0
$299$	2.47730	+	4.29080i	0.143266	+	0.248144i
$300$		0			0
$301$	0.696938	+	1.20713i	0.0401709	+	0.0695780i
$302$		0			0
$303$	23.1969	+	2.13737i	1.33263	+	0.122789i
$304$		0			0
$305$	18.7980	+	10.8530i	1.07637	+	0.621441i
$306$		0			0
$307$	−4.29796	+	7.44428i	−0.245297	+	0.424868i	−0.962215	−	0.272290i	$-0.912219\pi$
$307$	−4.29796	+	7.44428i	−0.245297	+	0.424868i	0.716918	+	0.697158i	$0.245552\pi$
$308$		0			0
$309$	−6.72474	−	0.619620i	−0.382557	−	0.0352490i
$310$		0			0
$311$	14.2020			0.805324			0.402662	−	0.915349i	$-0.368085\pi$
$311$	14.2020			0.805324			0.402662	+	0.915349i	$0.368085\pi$
$312$		0			0
$313$			11.6637i			0.659269i	0.944109	+	0.329634i	$0.106925\pi$
$313$			11.6637i			0.659269i	−0.944109	+	0.329634i	$0.893075\pi$
$314$		0			0
$315$	5.00000	+	4.27475i	0.281718	+	0.240855i
$316$		0			0
$317$	−16.3207	−	9.42274i	−0.916660	−	0.529234i	−0.0340918	−	0.999419i	$-0.510854\pi$
$317$	−16.3207	−	9.42274i	−0.916660	−	0.529234i	−0.882568	+	0.470185i	$0.844187\pi$
$318$		0			0
$319$	−6.70204	−	3.86943i	−0.375242	−	0.216646i
$320$		0			0
$321$	12.8990	+	9.12096i	0.719951	+	0.509082i
$322$		0			0
$323$	−15.5227	+	8.96204i	−0.863706	+	0.498661i
$324$		0			0
$325$	−4.50000	−	2.59808i	−0.249615	−	0.144115i
$326$		0			0
$327$	7.10102	+	5.02118i	0.392687	+	0.277672i
$328$		0			0
$329$	−0.174235	+	0.301783i	−0.00960587	+	0.0166378i
$330$		0			0
$331$	−12.0959	+	6.98358i	−0.664852	+	0.383852i	−0.794123	−	0.607757i	$-0.792070\pi$
$331$	−12.0959	+	6.98358i	−0.664852	+	0.383852i	0.129271	+	0.991609i	$0.458736\pi$
$332$		0			0
$333$	29.1969	+	5.42650i	1.59998	+	0.297371i
$334$		0			0
$335$	16.0000	−	3.46410i	0.874173	−	0.189264i
$336$		0			0
$337$	−15.9495	−	9.20844i	−0.868824	−	0.501616i	−0.00186678	−	0.999998i	$-0.500594\pi$
$337$	−15.9495	−	9.20844i	−0.868824	−	0.501616i	−0.866957	+	0.498382i	$0.833928\pi$
$338$		0			0
$339$	11.2980	+	1.04100i	0.613621	+	0.0565393i
$340$		0			0
$341$	2.17423	+	1.25529i	0.117741	+	0.0679780i
$342$		0			0
$343$		−	14.0314i		−	0.757623i
$344$		0			0
$345$	−3.00000	+	1.38211i	−0.161515	+	0.0744101i
$346$		0			0
$347$	−6.07321	−	10.5191i	−0.326027	−	0.564696i	0.655693	−	0.755028i	$-0.272377\pi$
$347$	−6.07321	−	10.5191i	−0.326027	−	0.564696i	−0.981720	+	0.190332i	$0.939043\pi$
$348$		0			0
$349$	2.20204			0.117873			0.0589363	−	0.998262i	$-0.481229\pi$
$349$	2.20204			0.117873			0.0589363	+	0.998262i	$0.481229\pi$
$350$		0			0
$351$	18.8258	+	19.3543i	1.00485	+	1.03306i
$352$		0			0
$353$	3.17423	−	5.49794i	0.168947	−	0.292626i	−0.769103	−	0.639125i	$-0.779297\pi$
$353$	3.17423	−	5.49794i	0.168947	−	0.292626i	0.938050	+	0.346500i	$0.112630\pi$
$354$		0			0
$355$	−22.3485	+	12.9029i	−1.18613	+	0.684815i
$356$		0			0
$357$	6.55051	−	9.26382i	0.346690	−	0.490293i
$358$		0			0
$359$		−	13.5065i		−	0.712844i	−0.934325	−	0.356422i	$-0.883997\pi$
$359$		−	13.5065i		−	0.712844i	0.934325	−	0.356422i	$-0.116003\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$		0			0
$363$	6.44949	+	13.9993i	0.338510	+	0.734771i
$364$		0			0
$365$	5.89898	−	10.2173i	0.308767	−	0.534800i
$366$		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
$369$	6.72474	−	7.86566i	0.350076	−	0.409470i
$370$		0			0
$371$	5.69694	−	3.28913i	0.295770	−	0.170763i
$372$		0			0
$373$	0.398979	−	0.230351i	0.0206584	−	0.0119271i	−0.489635	−	0.871927i	$-0.662870\pi$
$373$	0.398979	−	0.230351i	0.0206584	−	0.0119271i	0.510294	+	0.860000i	$0.329537\pi$
$374$		0			0
$375$	12.0000	−	16.9706i	0.619677	−	0.876356i
$376$		0			0
$377$	27.7423			1.42880
$378$		0			0
$379$	−20.6010	−	11.8940i	−1.05820	−	0.610954i	−0.133269	−	0.991080i	$-0.542547\pi$
$379$	−20.6010	−	11.8940i	−1.05820	−	0.610954i	−0.924935	+	0.380126i	$0.875881\pi$
$380$		0			0
$381$	−15.1742	−	1.39816i	−0.777400	−	0.0716299i
$382$		0			0
$383$	−12.0732	+	20.9114i	−0.616912	+	1.06852i	0.373133	+	0.927778i	$0.378283\pi$
$383$	−12.0732	+	20.9114i	−0.616912	+	1.06852i	−0.990046	+	0.140746i	$0.955050\pi$
$384$		0			0
$385$	2.75255	+	1.58919i	0.140283	+	0.0809924i
$386$		0			0
$387$	−3.59592	+	1.27135i	−0.182791	+	0.0646263i
$388$		0			0
$389$	−8.97219	−	5.18010i	−0.454908	−	0.262641i	0.254993	−	0.966943i	$-0.417927\pi$
$389$	−8.97219	−	5.18010i	−0.454908	−	0.262641i	−0.709901	+	0.704302i	$0.751260\pi$
$390$		0			0
$391$	2.84847	+	4.93369i	0.144053	+	0.249508i
$392$		0			0
$393$	−8.89898	−	6.29253i	−0.448894	−	0.317416i
$394$		0			0
$395$	0.797959	−	0.460702i	0.0401497	−	0.0231804i
$396$		0			0
$397$	−26.6969			−1.33988			−0.669940	−	0.742415i	$-0.733680\pi$
$397$	−26.6969			−1.33988			−0.669940	+	0.742415i	$0.733680\pi$
$398$		0			0
$399$	4.65153	+	3.28913i	0.232868	+	0.164662i
$400$		0			0
$401$	5.10102			0.254733			0.127366	−	0.991856i	$-0.459348\pi$
$401$	5.10102			0.254733			0.127366	+	0.991856i	$0.459348\pi$
$402$		0			0
$403$	−9.00000			−0.448322
$404$		0			0
$405$	−14.0000	+	11.3137i	−0.695666	+	0.562183i
$406$		0			0
$407$	14.3485			0.711227
$408$		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
$411$	9.10102	−	12.8708i	0.448920	−	0.634869i
$412$		0			0
$413$	0.348469	+	0.603566i	0.0171470	+	0.0296996i
$414$		0			0
$415$	20.1464	+	11.6315i	0.988949	+	0.570970i
$416$		0			0
$417$	10.2020	+	7.21393i	0.499596	+	0.353268i
$418$		0			0
$419$	22.3207	+	12.8868i	1.09044	+	0.629563i	0.933692	−	0.358076i	$-0.116567\pi$
$419$	22.3207	+	12.8868i	1.09044	+	0.629563i	0.156743	+	0.987639i	$0.449900\pi$
$420$		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
$423$	−0.724745	−	0.619620i	−0.0352383	−	0.0301270i
$424$		0			0
$425$	−5.17423	−	2.98735i	−0.250987	−	0.144908i
$426$		0			0
$427$	−11.8990			−0.575832
$428$		0			0
$429$	10.6515	+	7.53177i	0.514261	+	0.363637i
$430$		0			0
$431$	27.7702	−	16.0331i	1.33764	−	0.772287i	0.351184	−	0.936306i	$-0.385779\pi$
$431$	27.7702	−	16.0331i	1.33764	−	0.772287i	0.986457	+	0.164019i	$0.0524458\pi$
$432$		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
$435$	−1.69694	+	18.4169i	−0.0813620	+	0.883022i
$436$		0			0
$437$	−2.47730	+	1.43027i	−0.118505	+	0.0684190i
$438$		0			0
$439$	−4.60102	+	7.96920i	−0.219595	+	0.380349i	−0.954684	−	0.297621i	$-0.903807\pi$
$439$	−4.60102	+	7.96920i	−0.219595	+	0.380349i	0.735089	+	0.677970i	$0.237140\pi$
$440$		0			0
$441$	17.1010	+	3.17837i	0.814334	+	0.151351i
$442$		0			0
$443$	−16.6237	−	28.7931i	−0.789817	−	1.36800i	−0.926079	−	0.377330i	$-0.876842\pi$
$443$	−16.6237	−	28.7931i	−0.789817	−	1.36800i	0.136262	−	0.990673i	$-0.456491\pi$
$444$		0			0
$445$		−	9.47090i		−	0.448964i
$446$		0			0
$447$	20.8990	+	14.7778i	0.988488	+	0.698966i
$448$		0			0
$449$	14.1742	−	8.18350i	0.668923	−	0.386203i	−0.126745	−	0.991935i	$-0.540453\pi$
$449$	14.1742	−	8.18350i	0.668923	−	0.386203i	0.795669	+	0.605732i	$0.207120\pi$
$450$		0			0
$451$	2.50000	−	4.33013i	0.117720	−	0.203898i
$452$		0			0
$453$	−6.37628	−	13.8404i	−0.299584	−	0.650276i
$454$		0			0
$455$	−11.3939			−0.534153
$456$		0			0
$457$	18.1969	+	31.5180i	0.851217	+	1.47435i	0.880111	+	0.474768i	$0.157468\pi$
$457$	18.1969	+	31.5180i	0.851217	+	1.47435i	−0.0288939	+	0.999582i	$0.509198\pi$
$458$		0			0
$459$	21.6464	+	22.2542i	1.01037	+	1.03874i
$460$		0			0
$461$			42.1407i			1.96269i	0.192263	+	0.981344i	$0.438417\pi$
$461$			42.1407i			1.96269i	−0.192263	+	0.981344i	$0.561583\pi$
$462$		0			0
$463$	−7.19694	−	4.15515i	−0.334470	−	0.193106i	0.323354	−	0.946278i	$-0.395190\pi$
$463$	−7.19694	−	4.15515i	−0.334470	−	0.193106i	−0.657824	+	0.753172i	$0.728523\pi$
$464$		0			0
$465$	0.550510	−	5.97469i	0.0255293	−	0.277070i
$466$		0			0
$467$	−35.1742	−	20.3079i	−1.62767	−	0.939735i	−0.984786	−	0.173771i	$-0.944405\pi$
$467$	−35.1742	−	20.3079i	−1.62767	−	0.939735i	−0.642883	−	0.765964i	$-0.722262\pi$
$468$		0			0
$469$	−6.64643	+	6.03007i	−0.306904	+	0.278443i
$470$		0			0
$471$	10.0732	+	21.8649i	0.464149	+	1.00748i
$472$		0			0
$473$	−1.59592	+	0.921404i	−0.0733804	+	0.0423662i
$474$		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
$479$	−17.7247	−	10.2334i	−0.809864	−	0.467575i	0.0370445	−	0.999314i	$-0.488206\pi$
$479$	−17.7247	−	10.2334i	−0.809864	−	0.467575i	−0.846909	+	0.531738i	$0.821539\pi$
$480$		0			0
$481$	−44.5454	+	25.7183i	−2.03110	+	1.17265i
$482$		0			0
$483$	1.04541	−	1.47843i	0.0475677	−	0.0672709i
$484$		0			0
$485$	23.6969	+	13.6814i	1.07602	+	0.621242i
$486$		0			0
$487$	−8.60102	−	4.96580i	−0.389749	−	0.225022i	0.292302	−	0.956326i	$-0.405579\pi$
$487$	−8.60102	−	4.96580i	−0.389749	−	0.225022i	−0.682052	+	0.731304i	$0.738912\pi$
$488$		0			0
$489$	38.9722	+	3.59091i	1.76238	+	0.162387i
$490$		0			0
$491$			11.6637i			0.526373i	0.964745	+	0.263187i	$0.0847735\pi$
$491$			11.6637i			0.526373i	−0.964745	+	0.263187i	$0.915226\pi$
$492$		0			0
$493$	31.8990			1.43666
$494$		0			0
$495$	−5.65153	+	6.61037i	−0.254017	+	0.297114i
$496$		0			0
$497$	7.07321	−	12.2512i	0.317277	−	0.549540i
$498$		0			0
$499$	−3.39898	−	1.96240i	−0.152159	−	0.0878492i	0.421987	−	0.906602i	$-0.361333\pi$
$499$	−3.39898	−	1.96240i	−0.152159	−	0.0878492i	−0.574147	+	0.818753i	$0.694666\pi$
$500$		0			0
$501$	−4.05051	+	43.9602i	−0.180963	+	1.96400i
$502$		0			0
$503$	22.1742	+	38.4069i	0.988700	+	1.71248i	0.624173	+	0.781287i	$0.285436\pi$
$503$	22.1742	+	38.4069i	0.988700	+	1.71248i	0.364528	+	0.931193i	$0.381230\pi$
$504$		0			0
$505$	−13.4495	−	23.2952i	−0.598494	−	1.03662i
$506$		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
$511$			6.46750i			0.286105i
$512$		0			0
$513$	−11.1742	+	10.8691i	−0.493355	+	0.479881i
$514$		0			0
$515$	3.89898	+	6.75323i	0.171810	+	0.297583i
$516$		0			0
$517$	−0.398979	−	0.230351i	−0.0175471	−	0.0101308i
$518$		0			0
$519$	19.2980	−	8.89060i	0.847086	−	0.390254i
$520$		0			0
$521$	−40.2929			−1.76526			−0.882631	−	0.470066i	$-0.844230\pi$
$521$	−40.2929			−1.76526			−0.882631	+	0.470066i	$0.844230\pi$
$522$		0			0
$523$	22.6464	−	39.2248i	0.990259	−	1.71518i	0.374547	−	0.927208i	$-0.377798\pi$
$523$	22.6464	−	39.2248i	0.990259	−	1.71518i	0.615712	−	0.787971i	$-0.288869\pi$
$524$		0			0
$525$	−0.174235	+	1.89097i	−0.00760422	+	0.0825287i
$526$		0			0
$527$	−10.3485			−0.450786
$528$		0			0
$529$	−11.0454	−	19.1312i	−0.480235	−	0.831792i
$530$		0			0
$531$	−1.79796	+	0.635674i	−0.0780248	+	0.0275859i
$532$		0			0
$533$			17.9241i			0.776378i
$534$		0			0
$535$		−	18.2419i		−	0.788667i
$536$		0			0
$537$	−13.5959	+	19.2275i	−0.586707	+	0.829729i
$538$		0			0
$539$	8.40408			0.361989
$540$		0			0
$541$			38.6766i			1.66284i	0.555648	+	0.831418i	$0.312470\pi$
$541$			38.6766i			1.66284i	−0.555648	+	0.831418i	$0.687530\pi$
$542$		0			0
$543$	−3.62372	−	0.333891i	−0.155509	−	0.0143286i
$544$		0			0
$545$		−	10.0424i		−	0.430167i
$546$		0			0
$547$	17.8485	−	10.3048i	0.763145	−	0.440602i	−0.0672785	−	0.997734i	$-0.521432\pi$
$547$	17.8485	−	10.3048i	0.763145	−	0.440602i	0.830424	+	0.557132i	$0.188098\pi$
$548$		0			0
$549$	5.94949	−	32.0108i	0.253918	−	1.36619i
$550$		0			0
$551$			16.0171i			0.682349i
$552$		0			0
$553$	−0.252551	+	0.437432i	−0.0107396	+	0.0186015i
$554$		0			0
$555$	−14.3485	−	31.1448i	−0.609059	−	1.32202i
$556$		0			0
$557$	−7.07321	+	4.08372i	−0.299702	+	0.173033i	−0.642309	−	0.766446i	$-0.722023\pi$
$557$	−7.07321	+	4.08372i	−0.299702	+	0.173033i	0.342607	+	0.939479i	$0.388690\pi$
$558$		0			0
$559$	3.30306	−	5.72107i	0.139705	−	0.241975i
$560$		0			0
$561$	12.2474	+	8.66025i	0.517088	+	0.365636i
$562$		0			0
$563$	−42.2929			−1.78243			−0.891216	−	0.453580i	$-0.850147\pi$
$563$	−42.2929			−1.78243			−0.891216	+	0.453580i	$0.850147\pi$
$564$		0			0
$565$	−6.55051	−	11.3458i	−0.275582	−	0.477322i
$566$		0			0
$567$	3.54541	−	9.20844i	0.148893	−	0.386718i
$568$		0			0
$569$	23.4217	−	13.5225i	0.981888	−	0.566893i	0.0790484	−	0.996871i	$-0.474812\pi$
$569$	23.4217	−	13.5225i	0.981888	−	0.566893i	0.902840	+	0.429977i	$0.141478\pi$
$570$		0			0
$571$	−18.8485	−	32.6465i	−0.788784	−	1.36621i	−0.926712	−	0.375772i	$-0.877378\pi$
$571$	−18.8485	−	32.6465i	−0.788784	−	1.36621i	0.137928	−	0.990442i	$-0.455956\pi$
$572$		0			0
$573$	12.6464	+	27.4504i	0.528312	+	1.14675i
$574$		0			0
$575$	−0.825765	−	0.476756i	−0.0344368	−	0.0198821i
$576$		0			0
$577$	−26.8485	+	15.5010i	−1.11772	+	0.645314i	−0.940817	−	0.338915i	$-0.889940\pi$
$577$	−26.8485	+	15.5010i	−1.11772	+	0.645314i	−0.176899	+	0.984229i	$0.556607\pi$
$578$		0			0
$579$	12.8990	−	18.2419i	0.536063	−	0.758108i
$580$		0			0
$581$	−12.7526			−0.529065
$582$		0			0
$583$	4.34847	+	7.53177i	0.180095	+	0.311934i
$584$		0			0
$585$	5.69694	−	30.6520i	0.235539	−	1.26730i
$586$		0			0
$587$	8.27526	−	14.3332i	0.341556	−	0.591593i	−0.643166	−	0.765727i	$-0.722379\pi$
$587$	8.27526	−	14.3332i	0.341556	−	0.591593i	0.984722	+	0.174134i	$0.0557127\pi$
$588$		0			0
$589$		−	5.19615i		−	0.214104i
$590$		0			0
$591$	5.60102	+	0.516080i	0.230395	+	0.0212287i
$592$		0			0
$593$	11.9722	−	20.7364i	0.491639	−	0.851544i	−0.508315	−	0.861171i	$-0.669731\pi$
$593$	11.9722	−	20.7364i	0.491639	−	0.851544i	0.999954	+	0.00962762i	$0.00306461\pi$
$594$		0			0
$595$	−13.1010			−0.537089
$596$		0			0
$597$	7.97219	+	17.3045i	0.326280	+	0.708224i
$598$		0			0
$599$	−8.17423	−	14.1582i	−0.333990	−	0.578488i	0.649300	−	0.760532i	$-0.275062\pi$
$599$	−8.17423	−	14.1582i	−0.333990	−	0.578488i	−0.983290	+	0.182044i	$0.941729\pi$
$600$		0			0
$601$	−1.39898	+	2.42310i	−0.0570656	+	0.0988405i	−0.893147	−	0.449765i	$-0.851508\pi$
$601$	−1.39898	+	2.42310i	−0.0570656	+	0.0988405i	0.836081	+	0.548605i	$0.184841\pi$
$602$		0			0
$603$	−12.8990	−	20.8954i	−0.525287	−	0.850925i
$604$		0			0
$605$	8.89898	−	15.4135i	0.361795	−	0.626647i
$606$		0			0
$607$	−9.84847	−	17.0580i	−0.399737	−	0.692365i	0.593956	−	0.804497i	$-0.297565\pi$
$607$	−9.84847	−	17.0580i	−0.399737	−	0.692365i	−0.993693	+	0.112133i	$0.964232\pi$
$608$		0			0
$609$	−4.24235	−	9.20844i	−0.171909	−	0.373145i
$610$		0			0
$611$	1.65153			0.0668138
$612$		0			0
$613$	13.1969	−	22.8578i	0.533019	−	0.923217i	−0.466237	−	0.884660i	$-0.654391\pi$
$613$	13.1969	−	22.8578i	0.533019	−	0.923217i	0.999256	−	0.0385567i	$-0.0122760\pi$
$614$		0			0
$615$	−11.8990	−	1.09638i	−0.479813	−	0.0442102i
$616$		0			0
$617$			26.7272i			1.07600i	0.842946	+	0.537998i	$0.180819\pi$
$617$			26.7272i			1.07600i	−0.842946	+	0.537998i	$0.819181\pi$
$618$		0			0
$619$	−2.94949	+	5.10867i	−0.118550	+	0.205335i	−0.919193	−	0.393807i	$-0.871158\pi$
$619$	−2.94949	+	5.10867i	−0.118550	+	0.205335i	0.800643	+	0.599141i	$0.204491\pi$
$620$		0			0
$621$	3.45459	+	3.55159i	0.138628	+	0.142520i
$622$		0			0
$623$	2.59592	+	4.49626i	0.104003	+	0.180139i
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$	−4.34847	+	6.14966i	−0.173661	+	0.245594i
$628$		0			0
$629$	−51.2196	+	29.5717i	−2.04226	+	1.17910i
$630$		0			0
$631$	23.5454	+	13.5939i	0.937328	+	0.541167i	0.889122	−	0.457671i	$-0.151316\pi$
$631$	23.5454	+	13.5939i	0.937328	+	0.541167i	0.0482062	+	0.998837i	$0.484650\pi$
$632$		0			0
$633$	4.27526	+	9.27987i	0.169926	+	0.368842i
$634$		0			0
$635$	8.79796	+	15.2385i	0.349136	+	0.604722i
$636$		0			0
$637$	−26.0908	+	15.0635i	−1.03376	+	0.596839i
$638$		0			0
$639$	29.4217	+	25.1541i	1.16390	+	0.995079i
$640$		0			0
$641$	21.5227	+	37.2784i	0.850096	+	1.47241i	0.881121	+	0.472890i	$0.156789\pi$
$641$	21.5227	+	37.2784i	0.850096	+	1.47241i	−0.0310256	+	0.999519i	$0.509877\pi$
$642$		0			0
$643$	29.1918			1.15121			0.575607	−	0.817727i	$-0.304766\pi$
$643$	29.1918			1.15121			0.575607	+	0.817727i	$0.304766\pi$
$644$		0			0
$645$	3.59592	+	2.54270i	0.141589	+	0.100119i
$646$		0			0
$647$	0.174235	−	0.301783i	0.00684987	−	0.0118643i	−0.862580	−	0.505920i	$-0.831153\pi$
$647$	0.174235	−	0.301783i	0.00684987	−	0.0118643i	0.869430	+	0.494056i	$0.164486\pi$
$648$		0			0
$649$	−0.797959	+	0.460702i	−0.0313226	+	0.0180841i
$650$		0			0
$651$	1.37628	+	2.98735i	0.0539405	+	0.117083i
$652$		0			0
$653$	9.62372	−	16.6688i	0.376605	−	0.652300i	−0.613960	−	0.789337i	$-0.710425\pi$
$653$	9.62372	−	16.6688i	0.376605	−	0.652300i	0.990566	+	0.137037i	$0.0437579\pi$
$654$		0			0
$655$			12.5851i			0.491739i
$656$		0			0
$657$	−17.3990	−	3.23375i	−0.678799	−	0.126161i
$658$		0			0
$659$	5.72474	−	3.30518i	0.223004	−	0.128752i	−0.384336	−	0.923193i	$-0.625570\pi$
$659$	5.72474	−	3.30518i	0.223004	−	0.128752i	0.607341	+	0.794442i	$0.292236\pi$
$660$		0			0
$661$		−	37.1195i		−	1.44378i	−0.692007	−	0.721891i	$-0.743273\pi$
$661$		−	37.1195i		−	1.44378i	0.692007	−	0.721891i	$-0.256727\pi$
$662$		0			0
$663$	−53.5454	−	4.93369i	−2.07953	−	0.191609i
$664$		0			0
$665$		−	6.57826i		−	0.255094i
$666$		0			0
$667$	5.09082			0.197117
$668$		0			0
$669$	−20.6969	+	29.2699i	−0.800190	+	1.13164i
$670$		0			0
$671$		−	15.7313i		−	0.607301i
$672$		0			0
$673$		−	4.38551i		−	0.169049i	−0.996421	−	0.0845244i	$-0.973063\pi$
$673$		−	4.38551i		−	0.169049i	0.996421	−	0.0845244i	$-0.0269371\pi$
$674$		0			0
$675$	−5.00000	−	1.41421i	−0.192450	−	0.0544331i
$676$		0			0
$677$	17.2753	+	29.9216i	0.663942	+	1.14998i	0.979571	+	0.201099i	$0.0644512\pi$
$677$	17.2753	+	29.9216i	0.663942	+	1.14998i	−0.315629	+	0.948883i	$0.602216\pi$
$678$		0			0
$679$	−15.0000			−0.575647
$680$		0			0
$681$	4.29796	−	46.6458i	0.164698	−	1.78747i
$682$		0			0
$683$	16.1742	−	28.0146i	0.618890	−	1.07195i	−0.370799	−	0.928713i	$-0.620916\pi$
$683$	16.1742	−	28.0146i	0.618890	−	1.07195i	0.989689	−	0.143235i	$-0.0457506\pi$
$684$		0			0
$685$	−18.2020			−0.695464
$686$		0			0
$687$	16.0732	−	7.40496i	0.613231	−	0.282517i
$688$		0			0
$689$	−27.0000	−	15.5885i	−1.02862	−	0.593873i
$690$		0			0
$691$	−13.6464	−	23.6363i	−0.519135	−	0.899167i	−0.999753	−	0.0222375i	$-0.992921\pi$
$691$	−13.6464	−	23.6363i	−0.519135	−	0.899167i	0.480618	−	0.876930i	$-0.340412\pi$
$692$		0			0
$693$	0.871173	−	4.68729i	0.0330931	−	0.178055i
$694$		0			0
$695$		−	14.4279i		−	0.547280i
$696$		0			0
$697$			20.6096i			0.780646i
$698$		0			0
$699$	31.9949	+	2.94802i	1.21016	+	0.111504i
$700$		0			0
$701$	−6.82577	−	11.8226i	−0.257806	−	0.446532i	0.707848	−	0.706365i	$-0.249666\pi$
$701$	−6.82577	−	11.8226i	−0.257806	−	0.446532i	−0.965654	+	0.259832i	$0.916333\pi$
$702$		0			0
$703$	−14.8485	−	25.7183i	−0.560021	−	0.969984i
$704$		0			0
$705$	−0.101021	+	1.09638i	−0.00380465	+	0.0412919i
$706$		0			0
$707$	12.7702	+	7.37285i	0.480271	+	0.277285i
$708$		0			0
$709$	12.7474	−	22.0792i	0.478740	−	0.829203i	−0.520962	−	0.853580i	$-0.674427\pi$
$709$	12.7474	−	22.0792i	0.478740	−	0.829203i	0.999703	+	0.0243768i	$0.00776015\pi$
$710$		0			0
$711$	−1.05051	−	0.898133i	−0.0393972	−	0.0336826i
$712$		0			0
$713$	−1.65153			−0.0618503
$714$		0			0
$715$		−	15.0635i		−	0.563344i
$716$		0			0
$717$	−19.3990	−	1.78743i	−0.724468	−	0.0667528i
$718$		0			0
$719$	−14.6691	−	8.46923i	−0.547066	−	0.315849i	0.200872	−	0.979618i	$-0.435623\pi$
$719$	−14.6691	−	8.46923i	−0.547066	−	0.315849i	−0.747938	+	0.663769i	$0.768956\pi$
$720$		0			0
$721$	−3.70204	−	2.13737i	−0.137871	−	0.0796000i
$722$		0			0
$723$	−4.00000	+	5.65685i	−0.148762	+	0.210381i
$724$		0			0
$725$	−4.62372	+	2.66951i	−0.171721	+	0.0991431i
$726$		0			0
$727$	45.8939	+	26.4968i	1.70211	+	0.982713i	0.943621	+	0.331027i	$0.107395\pi$
$727$	45.8939	+	26.4968i	1.70211	+	0.982713i	0.758488	+	0.651687i	$0.225938\pi$
$728$		0			0
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$	3.79796	−	6.57826i	0.140473	−	0.243306i
$732$		0			0
$733$	14.0505	−	8.11207i	0.518967	−	0.299626i	−0.217545	−	0.976050i	$-0.569805\pi$
$733$	14.0505	−	8.11207i	0.518967	−	0.299626i	0.736512	+	0.676424i	$0.236471\pi$
$734$		0			0
$735$	−8.40408	−	18.2419i	−0.309989	−	0.672863i
$736$		0			0
$737$	−7.97219	−	8.78706i	−0.293660	−	0.323676i
$738$		0			0
$739$	−36.6464	−	21.1578i	−1.34806	−	0.778303i	−0.360086	−	0.932919i	$-0.617253\pi$
$739$	−36.6464	−	21.1578i	−1.34806	−	0.778303i	−0.987975	+	0.154616i	$0.950586\pi$
$740$		0			0
$741$	2.47730	−	26.8861i	0.0910057	−	0.987686i
$742$		0			0
$743$	−6.27526	−	3.62302i	−0.230217	−	0.132916i	0.380455	−	0.924799i	$-0.375767\pi$
$743$	−6.27526	−	3.62302i	−0.230217	−	0.132916i	−0.610672	+	0.791884i	$0.709101\pi$
$744$		0			0
$745$		−	29.5556i		−	1.08283i
$746$		0			0
$747$	6.37628	−	34.3071i	0.233296	−	1.25523i
$748$		0			0
$749$	5.00000	+	8.66025i	0.182696	+	0.316439i
$750$		0			0
$751$	15.3939			0.561731			0.280865	−	0.959747i	$-0.409379\pi$
$751$	15.3939			0.561731			0.280865	+	0.959747i	$0.409379\pi$
$752$		0			0
$753$	−14.6010	−	31.6930i	−0.532091	−	1.15496i
$754$		0			0
$755$	−8.79796	+	15.2385i	−0.320191	+	0.554586i
$756$		0			0
$757$	−17.0505	+	9.84412i	−0.619711	+	0.357791i	−0.776757	−	0.629801i	$-0.783136\pi$
$757$	−17.0505	+	9.84412i	−0.619711	+	0.357791i	0.157045	+	0.987591i	$0.449803\pi$
$758$		0			0
$759$	1.95459	+	1.38211i	0.0709472	+	0.0501673i
$760$		0			0
$761$		−	17.9562i		−	0.650911i	−0.945557	−	0.325456i	$-0.894482\pi$
$761$		−	17.9562i		−	0.650911i	0.945557	−	0.325456i	$-0.105518\pi$
$762$		0			0
$763$	2.75255	+	4.76756i	0.0996490	+	0.172597i
$764$		0			0
$765$	6.55051	−	35.2446i	0.236834	−	1.27427i
$766$		0			0
$767$	1.65153	−	2.86054i	0.0596333	−	0.103288i
$768$		0			0
$769$	−10.7474	+	6.20504i	−0.387563	+	0.223760i	−0.681104	−	0.732187i	$-0.738500\pi$
$769$	−10.7474	+	6.20504i	−0.387563	+	0.223760i	0.293541	+	0.955947i	$0.405166\pi$
$770$		0			0
$771$	−2.39898	+	26.0361i	−0.0863971	+	0.937669i
$772$		0			0
$773$	2.97219	−	1.71600i	0.106902	−	0.0617201i	−0.445596	−	0.895234i	$-0.647008\pi$
$773$	2.97219	−	1.71600i	0.106902	−	0.0617201i	0.552498	+	0.833514i	$0.313675\pi$
$774$		0			0
$775$	1.50000	−	0.866025i	0.0538816	−	0.0311086i
$776$		0			0
$777$	15.3485	+	10.8530i	0.550623	+	0.389349i
$778$		0			0
$779$	−10.3485			−0.370772
$780$		0			0
$781$	16.1969	+	9.35131i	0.579572	+	0.334616i
$782$		0			0
$783$	26.8939	−	6.80861i	0.961109	−	0.243320i
$784$		0			0
$785$	13.8990	−	24.0737i	0.496076	−	0.859229i
$786$		0			0
$787$	18.6464	+	10.7655i	0.664673	+	0.383749i	0.794055	−	0.607845i	$-0.207966\pi$
$787$	18.6464	+	10.7655i	0.664673	+	0.383749i	−0.129382	+	0.991595i	$0.541299\pi$
$788$		0			0
$789$	−11.1010	−	7.84961i	−0.395207	−	0.279453i
$790$		0			0
$791$	6.21964	+	3.59091i	0.221145	+	0.127678i
$792$		0			0
$793$	28.1969	+	48.8385i	1.00130	+	1.73431i
$794$		0			0
$795$	12.0000	−	16.9706i	0.425596	−	0.601884i
$796$		0			0
$797$	11.1742	−	6.45145i	0.395812	−	0.228522i	−0.288864	−	0.957370i	$-0.593277\pi$
$797$	11.1742	−	6.45145i	0.395812	−	0.228522i	0.684675	+	0.728848i	$0.259944\pi$
$798$		0			0
$799$	1.89898			0.0671811
$800$		0			0
$801$	−13.3939	+	4.73545i	−0.473249	+	0.167319i
$802$		0			0
$803$	−8.55051			−0.301741
$804$		0			0
$805$	−2.09082			−0.0736916
$806$		0			0
$807$	−8.49490	−	6.00680i	−0.299035	−	0.211449i
$808$		0			0
$809$	20.2020			0.710266			0.355133	−	0.934816i	$-0.384436\pi$
$809$	20.2020			0.710266			0.355133	+	0.934816i	$0.384436\pi$
$810$		0			0
$811$	−20.8485	+	12.0369i	−0.732089	+	0.422672i	−0.819186	−	0.573528i	$-0.805574\pi$
$811$	−20.8485	+	12.0369i	−0.732089	+	0.422672i	0.0870971	+	0.996200i	$0.472241\pi$
$812$		0			0
$813$	−13.7980	−	9.75663i	−0.483916	−	0.342180i
$814$		0			0
$815$	−22.5959	−	39.1373i	−0.791500	−	1.37092i
$816$		0			0
$817$	3.30306	+	1.90702i	0.115559	+	0.0667183i
$818$		0			0
$819$	5.69694	+	16.1134i	0.199067	+	0.563047i
$820$		0			0
$821$	14.7247	+	8.50134i	0.513897	+	0.296699i	0.734434	−	0.678680i	$-0.237448\pi$
$821$	14.7247	+	8.50134i	0.513897	+	0.296699i	−0.220537	+	0.975379i	$0.570781\pi$
$822$		0			0
$823$	20.3990	−	35.3321i	0.711064	−	1.23160i	−0.253394	−	0.967363i	$-0.581547\pi$
$823$	20.3990	−	35.3321i	0.711064	−	1.23160i	0.964458	−	0.264235i	$-0.0851196\pi$
$824$		0			0
$825$	−2.50000	−	0.230351i	−0.0870388	−	0.00801979i
$826$		0			0
$827$	37.3207	+	21.5471i	1.29777	+	0.749266i	0.980018	−	0.198909i	$-0.0637398\pi$
$827$	37.3207	+	21.5471i	1.29777	+	0.749266i	0.317749	+	0.948175i	$0.397073\pi$
$828$		0			0
$829$	19.3939			0.673577			0.336789	−	0.941580i	$-0.390659\pi$
$829$	19.3939			0.673577			0.336789	+	0.941580i	$0.390659\pi$
$830$		0			0
$831$	−25.7980	+	36.4838i	−0.894921	+	1.26561i
$832$		0			0
$833$	−30.0000	+	17.3205i	−1.03944	+	0.600120i
$834$		0			0
$835$	44.1464	−	25.4880i	1.52775	−	0.882047i
$836$		0			0
$837$	−8.72474	+	2.20881i	−0.301571	+	0.0763475i
$838$		0			0
$839$	−9.52270	+	5.49794i	−0.328760	+	0.189810i	−0.655291	−	0.755377i	$-0.727454\pi$
$839$	−9.52270	+	5.49794i	−0.328760	+	0.189810i	0.326530	+	0.945187i	$0.394120\pi$
$840$		0			0
$841$	−0.247449	+	0.428594i	−0.00853271	+	0.0147791i
$842$		0			0
$843$	−5.39898	−	11.7190i	−0.185951	−	0.403625i
$844$		0			0
$845$	14.0000	+	24.2487i	0.481615	+	0.834181i
$846$		0			0
$847$			9.75663i			0.335242i
$848$		0			0
$849$	7.79796	−	11.0280i	0.267625	−	0.378479i
$850$		0			0
$851$	−8.17423	+	4.71940i	−0.280209	+	0.161779i
$852$		0			0
$853$	21.6464	−	37.4927i	0.741160	−	1.28373i	−0.210808	−	0.977527i	$-0.567610\pi$
$853$	21.6464	−	37.4927i	0.741160	−	1.28373i	0.951968	−	0.306199i	$-0.0990572\pi$
$854$		0			0
$855$	17.6969	+	3.28913i	0.605223	+	0.112486i
$856$		0			0
$857$	−13.5959			−0.464428			−0.232214	−	0.972665i	$-0.574597\pi$
$857$	−13.5959			−0.464428			−0.232214	+	0.972665i	$0.574597\pi$
$858$		0			0
$859$	−1.84847	−	3.20164i	−0.0630690	−	0.109239i	0.832767	−	0.553624i	$-0.186755\pi$
$859$	−1.84847	−	3.20164i	−0.0630690	−	0.109239i	−0.895836	+	0.444385i	$0.853422\pi$
$860$		0			0
$861$	5.94949	−	2.74094i	0.202758	−	0.0934110i
$862$		0			0
$863$		−	2.47848i		−	0.0843685i	−0.999110	−	0.0421843i	$-0.986568\pi$
$863$		−	2.47848i		−	0.0843685i	0.999110	−	0.0421843i	$-0.0134316\pi$
$864$		0			0
$865$	−21.2474	−	12.2672i	−0.722435	−	0.417098i
$866$		0			0
$867$	−32.2474	−	2.97129i	−1.09518	−	0.100910i
$868$		0			0
$869$	−0.578317	−	0.333891i	−0.0196180	−	0.0113265i
$870$		0			0
$871$	40.5000	+	12.9904i	1.37229	+	0.440162i
$872$		0			0
$873$	7.50000	−	40.3532i	0.253837	−	1.36575i
$874$		0			0
$875$	11.3939	−	6.57826i	0.385183	−	0.222386i
$876$		0			0
$877$	−24.6464	+	42.6889i	−0.832251	+	1.44150i	0.0639986	+	0.997950i	$0.479615\pi$
$877$	−24.6464	+	42.6889i	−0.832251	+	1.44150i	−0.896249	+	0.443551i	$0.853719\pi$
$878$		0			0
$879$	41.3939	+	29.2699i	1.39618	+	0.987249i
$880$		0			0
$881$	−28.3207	−	16.3509i	−0.954147	−	0.550877i	−0.0597805	−	0.998212i	$-0.519040\pi$
$881$	−28.3207	−	16.3509i	−0.954147	−	0.550877i	−0.894367	+	0.447334i	$0.852373\pi$
$882$		0			0
$883$	−5.54541	+	3.20164i	−0.186618	+	0.107744i	−0.590398	−	0.807112i	$-0.701029\pi$
$883$	−5.54541	+	3.20164i	−0.186618	+	0.107744i	0.403780	+	0.914856i	$0.367696\pi$
$884$		0			0
$885$	1.79796	+	1.27135i	0.0604377	+	0.0427359i
$886$		0			0
$887$	18.7702	+	10.8370i	0.630240	+	0.363869i	0.780845	−	0.624725i	$-0.214789\pi$
$887$	18.7702	+	10.8370i	0.630240	+	0.363869i	−0.150605	+	0.988594i	$0.548122\pi$
$888$		0			0
$889$	−8.35357	−	4.82294i	−0.280170	−	0.161756i
$890$		0			0
$891$	12.1742	+	4.68729i	0.407852	+	0.157030i
$892$		0			0
$893$			0.953512i			0.0319081i
$894$		0			0
$895$	27.1918			0.908923
$896$		0			0
$897$	−8.54541	−	0.787377i	−0.285323	−	0.0262898i
$898$		0			0
$899$	−4.62372	+	8.00853i	−0.154210	+	0.267099i
$900$		0			0
$901$	−31.0454	−	17.9241i	−1.03427	−	0.597137i
$902$		0			0
$903$	−2.40408	−	0.221513i	−0.0800028	−	0.00737149i
$904$		0			0
$905$	2.10102	+	3.63907i	0.0698403	+	0.120967i
$906$		0			0
$907$	17.6010	+	30.4859i	0.584432	+	1.01227i	0.994946	+	0.100412i	$0.0320161\pi$
$907$	17.6010	+	30.4859i	0.584432	+	1.01227i	−0.410514	+	0.911854i	$0.634651\pi$
$908$		0			0
$909$	−26.2196	+	30.6681i	−0.869651	+	1.01720i
$910$		0			0
$911$		−	37.1195i		−	1.22982i	−0.788596	−	0.614912i	$-0.789192\pi$
$911$		−	37.1195i		−	1.22982i	0.788596	−	0.614912i	$-0.210808\pi$
$912$		0			0
$913$		−	16.8598i		−	0.557978i
$914$		0			0
$915$	−34.1464	+	15.7313i	−1.12885	+	0.520061i
$916$		0			0
$917$	−3.44949	−	5.97469i	−0.113912	−	0.197302i
$918$		0			0
$919$	2.84847	+	1.64456i	0.0939623	+	0.0542492i	0.546245	−	0.837626i	$-0.316057\pi$
$919$	2.84847	+	1.64456i	0.0939623	+	0.0542492i	−0.452283	+	0.891875i	$0.649390\pi$
$920$		0			0
$921$	−6.22985	−	13.5225i	−0.205280	−	0.445582i
$922$		0			0
$923$	−67.0454			−2.20683
$924$		0			0
$925$	4.94949	−	8.57277i	0.162738	−	0.281871i
$926$		0			0
$927$	7.60102	−	8.89060i	0.249650	−	0.292006i
$928$		0			0
$929$	−48.4949			−1.59107			−0.795533	−	0.605910i	$-0.792809\pi$
$929$	−48.4949			−1.59107			−0.795533	+	0.605910i	$0.792809\pi$
$930$		0			0
$931$	−8.69694	−	15.0635i	−0.285031	−	0.493688i
$932$		0			0
$933$	−14.2020	+	20.0847i	−0.464954	+	0.657544i
$934$		0			0
$935$		−	17.3205i		−	0.566441i
$936$		0			0
$937$		−	38.3908i		−	1.25417i	−0.778949	−	0.627087i	$-0.784247\pi$
$937$		−	38.3908i		−	1.25417i	0.778949	−	0.627087i	$-0.215753\pi$
$938$		0			0
$939$	−16.4949	−	11.6637i	−0.538291	−	0.380629i
$940$		0			0
$941$	40.2929			1.31351			0.656755	−	0.754104i	$-0.271929\pi$
$941$	40.2929			1.31351			0.656755	+	0.754104i	$0.271929\pi$
$942$		0			0
$943$			3.28913i			0.107109i
$944$		0			0
$945$	−11.0454	+	2.79632i	−0.359307	+	0.0909643i
$946$		0			0
$947$		−	36.8338i		−	1.19694i	−0.801146	−	0.598468i	$-0.795776\pi$
$947$		−	36.8338i		−	1.19694i	0.801146	−	0.598468i	$-0.204224\pi$
$948$		0			0
$949$	26.5454	−	15.3260i	0.861700	−	0.497503i
$950$		0			0
$951$	29.6464	−	13.6582i	0.961351	−	0.442896i
$952$		0			0
$953$			12.2351i			0.396334i	0.980168	+	0.198167i	$0.0634989\pi$
$953$			12.2351i			0.396334i	−0.980168	+	0.198167i	$0.936501\pi$
$954$		0			0
$955$	17.4495	−	30.2234i	0.564652	−	0.978006i
$956$		0			0
$957$	12.1742	−	5.60869i	0.393537	−	0.181303i
$958$		0			0
$959$	8.64133	−	4.98907i	0.279043	−	0.161106i
$960$		0			0
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$		0			0
$963$	−25.7980	+	9.12096i	−0.831328	+	0.293919i
$964$		0			0
$965$	−25.7980			−0.830466
$966$		0			0
$967$	6.84847	+	11.8619i	0.220232	+	0.381453i	0.954878	−	0.296997i	$-0.0959852\pi$
$967$	6.84847	+	11.8619i	0.220232	+	0.381453i	−0.734646	+	0.678450i	$0.762652\pi$
$968$		0			0
$969$	2.84847	−	30.9145i	0.0915060	−	0.993115i
$970$		0			0
$971$	−30.2196	+	17.4473i	−0.969794	+	0.559911i	−0.899174	−	0.437592i	$-0.855831\pi$
$971$	−30.2196	+	17.4473i	−0.969794	+	0.559911i	−0.0706209	+	0.997503i	$0.522498\pi$
$972$		0			0
$973$	3.95459	+	6.84955i	0.126778	+	0.219587i
$974$		0			0
$975$	8.17423	−	3.76588i	0.261785	−	0.120605i
$976$		0			0
$977$	22.3207	+	12.8868i	0.714101	+	0.412287i	0.812578	−	0.582853i	$-0.198064\pi$
$977$	22.3207	+	12.8868i	0.714101	+	0.412287i	−0.0984765	+	0.995139i	$0.531397\pi$
$978$		0			0
$979$	−5.94439	+	3.43199i	−0.189983	+	0.109687i
$980$		0			0
$981$	−14.2020	+	5.02118i	−0.453436	+	0.160314i
$982$		0			0
$983$	31.5959			1.00775			0.503877	−	0.863776i	$-0.331907\pi$
$983$	31.5959			1.00775			0.503877	+	0.863776i	$0.331907\pi$
$984$		0			0
$985$	−3.24745	−	5.62475i	−0.103472	−	0.179219i
$986$		0			0
$987$	−0.252551	−	0.548188i	−0.00803880	−	0.0174490i
$988$		0			0
$989$	0.606123	−	1.04984i	0.0192736	−	0.0333828i
$990$		0			0
$991$			18.5276i			0.588550i	0.955721	+	0.294275i	$0.0950781\pi$
$991$			18.5276i			0.588550i	−0.955721	+	0.294275i	$0.904922\pi$
$992$		0			0
$993$	2.21964	−	24.0898i	0.0704382	−	0.764466i
$994$		0			0
$995$	11.0000	−	19.0526i	0.348723	−	0.604007i
$996$		0			0
$997$	−34.2929			−1.08607			−0.543033	−	0.839711i	$-0.682724\pi$
$997$	−34.2929			−1.08607			−0.543033	+	0.839711i	$0.682724\pi$
$998$		0			0
$999$	−36.8712	+	35.8642i	−1.16655	+	1.13469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.b.641.2	yes	4
3.2	odd	2		804.2.o.c.641.2	yes	4
67.30	odd	6		804.2.o.c.365.1	yes	4
201.164	even	6	inner	804.2.o.b.365.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.b.365.1	✓	4	201.164	even	6	inner
804.2.o.b.641.2	yes	4	1.1	even	1	trivial
804.2.o.c.365.1	yes	4	67.30	odd	6
804.2.o.c.641.2	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.41421i) q^{3} +2.00000 q^{5} +(-0.949490 + 0.548188i) q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.41421i) q^{3} +2.00000 q^{5} +(-0.949490 + 0.548188i) q^{7} +(-1.00000 - 2.82843i) q^{9} +(-0.724745 - 1.25529i) q^{11} +(4.50000 + 2.59808i) q^{13} +(-2.00000 + 2.82843i) q^{15} +(5.17423 + 2.98735i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(0.174235 - 1.89097i) q^{21} +(0.825765 + 0.476756i) q^{23} -1.00000 q^{25} +(5.00000 + 1.41421i) q^{27} +(4.62372 - 2.66951i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(2.50000 + 0.230351i) q^{33} +(-1.89898 + 1.09638i) q^{35} +(-4.94949 + 8.57277i) q^{37} +(-8.17423 + 3.76588i) q^{39} +(1.72474 + 2.98735i) q^{41} -1.27135i q^{43} +(-2.00000 - 5.65685i) q^{45} +(0.275255 - 0.158919i) q^{47} +(-2.89898 + 5.02118i) q^{49} +(-9.39898 + 4.33013i) q^{51} -6.00000 q^{53} +(-1.44949 - 2.51059i) q^{55} +(-2.17423 - 4.71940i) q^{57} -0.635674i q^{59} +(9.39898 + 5.42650i) q^{61} +(2.50000 + 2.13737i) q^{63} +(9.00000 + 5.19615i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-1.50000 + 0.691053i) q^{69} +(-11.1742 + 6.45145i) q^{71} +(2.94949 - 5.10867i) q^{73} +(1.00000 - 1.41421i) q^{75} +(1.37628 + 0.794593i) q^{77} +(0.398979 - 0.230351i) q^{79} +(-7.00000 + 5.65685i) q^{81} +(10.0732 + 5.81577i) q^{83} +(10.3485 + 5.97469i) q^{85} +(-0.848469 + 9.20844i) q^{87} -4.73545i q^{89} -5.69694 q^{91} +(0.275255 - 2.98735i) q^{93} +(-3.00000 + 5.19615i) q^{95} +(11.8485 + 6.84072i) q^{97} +(-2.82577 + 3.30518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 8 q^{5} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 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

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