LMFDB - Embedded newform 804.2.o.c.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.c.365.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.41421i) q^{3} -2.00000 q^{5} +(-0.949490 + 0.548188i) q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.41421i) q^{3} -2.00000 q^{5} +(-0.949490 + 0.548188i) q^{7} +(-1.00000 + 2.82843i) q^{9} +(0.724745 + 1.25529i) q^{11} +(4.50000 + 2.59808i) q^{13} +(-2.00000 - 2.82843i) q^{15} +(-5.17423 - 2.98735i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(-1.72474 - 0.794593i) q^{21} +(-0.825765 - 0.476756i) q^{23} -1.00000 q^{25} +(-5.00000 + 1.41421i) q^{27} +(-4.62372 + 2.66951i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(-1.05051 + 2.28024i) q^{33} +(1.89898 - 1.09638i) q^{35} +(-4.94949 + 8.57277i) q^{37} +(0.825765 + 8.96204i) q^{39} +(-1.72474 - 2.98735i) q^{41} -1.27135i q^{43} +(2.00000 - 5.65685i) q^{45} +(-0.275255 + 0.158919i) q^{47} +(-2.89898 + 5.02118i) q^{49} +(-0.949490 - 10.3048i) q^{51} +6.00000 q^{53} +(-1.44949 - 2.51059i) q^{55} +(-5.17423 + 0.476756i) q^{57} +0.635674i q^{59} +(9.39898 + 5.42650i) q^{61} +(-0.601021 - 3.23375i) q^{63} +(-9.00000 - 5.19615i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-0.151531 - 1.64456i) q^{69} +(11.1742 - 6.45145i) q^{71} +(2.94949 - 5.10867i) q^{73} +(-1.00000 - 1.41421i) q^{75} +(-1.37628 - 0.794593i) q^{77} +(0.398979 - 0.230351i) q^{79} +(-7.00000 - 5.65685i) q^{81} +(-10.0732 - 5.81577i) q^{83} +(10.3485 + 5.97469i) q^{85} +(-8.39898 - 3.86943i) q^{87} +4.73545i q^{89} -5.69694 q^{91} +(-2.72474 - 1.25529i) q^{93} +(3.00000 - 5.19615i) q^{95} +(11.8485 + 6.84072i) q^{97} +(-4.27526 + 0.794593i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−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	0.954355	−	0.298674i	$-0.0965442\pi$
$11$	0.724745	+	1.25529i	0.218519	+	0.378486i	−0.735837	+	0.677159i	$0.763211\pi$
$12$		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	−0.282851	−	0.959164i	$-0.591280\pi$
$17$	−5.17423	−	2.98735i	−1.25494	−	0.724538i	−0.972086	+	0.234626i	$0.924613\pi$
$18$		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
$21$	−1.72474	−	0.794593i	−0.376370	−	0.173394i
$22$		0			0
$23$	−0.825765	−	0.476756i	−0.172184	−	0.0994105i	0.411431	−	0.911441i	$-0.365029\pi$
$23$	−0.825765	−	0.476756i	−0.172184	−	0.0994105i	−0.583615	+	0.812030i	$0.698362\pi$
$24$		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	−0.863545	−	0.504273i	$-0.831761\pi$
$29$	−4.62372	+	2.66951i	−0.858604	+	0.495715i	0.00494052	+	0.999988i	$0.498427\pi$
$30$		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
$33$	−1.05051	+	2.28024i	−0.182870	+	0.396939i
$34$		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
$39$	0.825765	+	8.96204i	0.132228	+	1.43507i
$40$		0			0
$41$	−1.72474	−	2.98735i	−0.269360	−	0.466545i	0.699337	−	0.714792i	$-0.253479\pi$
$41$	−1.72474	−	2.98735i	−0.269360	−	0.466545i	−0.968697	+	0.248247i	$0.920145\pi$
$42$		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	−0.519941	−	0.854202i	$-0.674046\pi$
$47$	−0.275255	+	0.158919i	−0.0401501	+	0.0231807i	0.479791	+	0.877383i	$0.340713\pi$
$48$		0			0
$49$	−2.89898	+	5.02118i	−0.414140	+	0.717311i
$50$		0			0
$51$	−0.949490	−	10.3048i	−0.132955	−	1.44296i
$52$		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
$55$	−1.44949	−	2.51059i	−0.195449	−	0.338528i
$56$		0			0
$57$	−5.17423	+	0.476756i	−0.685344	+	0.0631479i
$58$		0			0
$59$			0.635674i			0.0827578i	0.999144	+	0.0413789i	$0.0131751\pi$
$59$			0.635674i			0.0827578i	−0.999144	+	0.0413789i	$0.986825\pi$
$60$		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
$63$	−0.601021	−	3.23375i	−0.0757215	−	0.407414i
$64$		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
$69$	−0.151531	−	1.64456i	−0.0182422	−	0.197982i
$70$		0			0
$71$	11.1742	−	6.45145i	1.32614	−	0.765646i	0.341438	−	0.939904i	$-0.389086\pi$
$71$	11.1742	−	6.45145i	1.32614	−	0.765646i	0.984700	+	0.174258i	$0.0557528\pi$
$72$		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	−0.167972	−	0.985792i	$-0.553722\pi$
$83$	−10.0732	−	5.81577i	−1.10568	−	0.638364i	−0.937707	+	0.347428i	$0.887055\pi$
$84$		0			0
$85$	10.3485	+	5.97469i	1.12245	+	0.648046i
$86$		0			0
$87$	−8.39898	−	3.86943i	−0.900465	−	0.414846i
$88$		0			0
$89$			4.73545i			0.501957i	0.967993	+	0.250978i	$0.0807523\pi$
$89$			4.73545i			0.501957i	−0.967993	+	0.250978i	$0.919248\pi$
$90$		0			0
$91$	−5.69694			−0.597201
$92$		0			0
$93$	−2.72474	−	1.25529i	−0.282543	−	0.130168i
$94$		0			0
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	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
$99$	−4.27526	+	0.794593i	−0.429679	+	0.0798596i
$100$		0			0
$101$	6.72474	+	11.6476i	0.669137	+	1.15898i	0.978146	+	0.207920i	$0.0666695\pi$
$101$	6.72474	+	11.6476i	0.669137	+	1.15898i	−0.309009	+	0.951059i	$0.599997\pi$
$102$		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
$105$	3.44949	+	1.58919i	0.336636	+	0.155089i
$106$		0			0
$107$			9.12096i			0.881756i	0.897567	+	0.440878i	$0.145333\pi$
$107$			9.12096i			0.881756i	−0.897567	+	0.440878i	$0.854667\pi$
$108$		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
$111$	−17.0732	+	1.57313i	−1.62052	+	0.149315i
$112$		0			0
$113$	3.27526	+	5.67291i	0.308110	+	0.533662i	0.977949	−	0.208844i	$-0.0669702\pi$
$113$	3.27526	+	5.67291i	0.308110	+	0.533662i	−0.669839	+	0.742507i	$0.733637\pi$
$114$		0			0
$115$	1.65153	+	0.953512i	0.154006	+	0.0889154i
$116$		0			0
$117$	−11.8485	+	10.1298i	−1.09539	+	0.936505i
$118$		0			0
$119$	6.55051			0.600484
$120$		0			0
$121$	4.44949	−	7.70674i	0.404499	−	0.700613i
$122$		0			0
$123$	2.50000	−	5.42650i	0.225417	−	0.489291i
$124$		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	$-0.911358\pi$
$131$		−	6.29253i		−	0.549781i	0.961476	−	0.274890i	$-0.0886416\pi$
$132$		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	$-0.372898\pi$
$137$	9.10102			0.777553			0.388776	+	0.921332i	$0.372898\pi$
$138$		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
$141$	−0.500000	−	0.230351i	−0.0421076	−	0.0193990i
$142$		0			0
$143$			7.53177i			0.629838i
$144$		0			0
$145$	9.24745	−	5.33902i	0.767959	−	0.443381i
$146$		0			0
$147$	−10.0000	+	0.921404i	−0.824786	+	0.0759961i
$148$		0			0
$149$			14.7778i			1.21065i	0.795980	+	0.605323i	$0.206956\pi$
$149$			14.7778i			1.21065i	−0.795980	+	0.605323i	$0.793044\pi$
$150$		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
$153$	13.6237	−	11.6476i	1.10141	−	0.941653i
$154$		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
$165$	2.10102	−	4.56048i	0.163564	−	0.355033i
$166$		0			0
$167$	−22.0732	+	12.7440i	−1.70808	+	0.986158i	−0.771136	+	0.636671i	$0.780311\pi$
$167$	−22.0732	+	12.7440i	−1.70808	+	0.986158i	−0.936941	+	0.349487i	$0.886356\pi$
$168$		0			0
$169$	7.00000	+	12.1244i	0.538462	+	0.932643i
$170$		0			0
$171$	−5.84847	−	6.84072i	−0.447244	−	0.523123i
$172$		0			0
$173$	10.6237	+	6.13361i	0.807707	+	0.466330i	0.846159	−	0.532931i	$-0.178909\pi$
$173$	10.6237	+	6.13361i	0.807707	+	0.466330i	−0.0384521	+	0.999260i	$0.512243\pi$
$174$		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	$-0.669653\pi$
$179$	−13.5959			−1.01621			−0.508103	+	0.861296i	$0.669653\pi$
$180$		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
$183$	1.72474	+	18.7187i	0.127497	+	1.38372i
$184$		0			0
$185$	9.89898	−	17.1455i	0.727787	−	1.26056i
$186$		0			0
$187$		−	8.66025i		−	0.633300i
$188$		0			0
$189$	3.97219	−	4.08372i	0.288935	−	0.297047i
$190$		0			0
$191$	−8.72474	+	15.1117i	−0.631300	+	1.09344i	0.355986	+	0.934491i	$0.384145\pi$
$191$	−8.72474	+	15.1117i	−0.631300	+	1.09344i	−0.987286	+	0.158953i	$0.949188\pi$
$192$		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
$195$	−1.65153	−	17.9241i	−0.118269	−	1.28357i
$196$		0			0
$197$	1.62372	+	2.81237i	0.115686	+	0.200373i	0.918054	−	0.396456i	$-0.129760\pi$
$197$	1.62372	+	2.81237i	0.115686	+	0.200373i	−0.802368	+	0.596830i	$0.796427\pi$
$198$		0			0
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	0.992434	+	0.122782i	$0.0391815\pi$
$200$		0			0
$201$	10.4495	+	9.58166i	0.737050	+	0.675838i
$202$		0			0
$203$	2.92679	−	5.06934i	0.205420	−	0.355798i
$204$		0			0
$205$	3.44949	+	5.97469i	0.240923	+	0.417291i
$206$		0			0
$207$	2.17423	−	1.85886i	0.151120	−	0.129200i
$208$		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
$213$	20.2980	+	9.35131i	1.39079	+	0.640741i
$214$		0			0
$215$			2.54270i			0.173411i
$216$		0			0
$217$	0.949490	−	1.64456i	0.0644556	−	0.111640i
$218$		0			0
$219$	10.1742	−	0.937458i	0.687511	−	0.0633475i
$220$		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	$-0.312033\pi$
$227$	23.4217	−	13.5225i	1.55455	−	0.897521i	0.997762	−	0.0668675i	$-0.0213005\pi$
$228$		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
$231$	−0.252551	−	2.74094i	−0.0166167	−	0.180341i
$232$		0			0
$233$	9.27526	+	16.0652i	0.607642	+	1.05247i	0.991628	+	0.129128i	$0.0412178\pi$
$233$	9.27526	+	16.0652i	0.607642	+	1.05247i	−0.383986	+	0.923339i	$0.625449\pi$
$234$		0			0
$235$	0.550510	−	0.317837i	0.0359113	−	0.0207334i
$236$		0			0
$237$	0.724745	+	0.333891i	0.0470772	+	0.0216886i
$238$		0			0
$239$	−5.62372	−	9.74058i	−0.363768	−	0.630066i	0.624809	−	0.780777i	$-0.285177\pi$
$239$	−5.62372	−	9.74058i	−0.363768	−	0.630066i	−0.988578	+	0.150712i	$0.951843\pi$
$240$		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
$249$	−1.84847	−	20.0614i	−0.117142	−	1.27134i
$250$		0			0
$251$	10.0732	−	17.4473i	0.635816	−	1.10126i	−0.350526	−	0.936553i	$-0.613997\pi$
$251$	10.0732	−	17.4473i	0.635816	−	1.10126i	0.986342	−	0.164712i	$-0.0526695\pi$
$252$		0			0
$253$		−	1.38211i		−	0.0868922i
$254$		0			0
$255$	1.89898	+	20.6096i	0.118919	+	1.29063i
$256$		0			0
$257$	−13.0732	+	7.54782i	−0.815485	+	0.470820i	−0.848857	−	0.528623i	$-0.822709\pi$
$257$	−13.0732	+	7.54782i	−0.815485	+	0.470820i	0.0333722	+	0.999443i	$0.489375\pi$
$258$		0			0
$259$		−	10.8530i		−	0.674373i
$260$		0			0
$261$	−2.92679	−	15.7474i	−0.181163	−	0.974738i
$262$		0			0
$263$		−	7.84961i		−	0.484027i	−0.970273	−	0.242014i	$-0.922192\pi$
$263$		−	7.84961i		−	0.484027i	0.970273	−	0.242014i	$-0.0778079\pi$
$264$		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	$-0.941380\pi$
$269$		−	6.00680i		−	0.366241i	0.983090	−	0.183121i	$-0.0586199\pi$
$270$		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
$279$	−0.949490	−	5.10867i	−0.0568445	−	0.305848i
$280$		0			0
$281$	3.72474	−	6.45145i	0.222200	−	0.384861i	−0.733276	−	0.679931i	$-0.762010\pi$
$281$	3.72474	−	6.45145i	0.222200	−	0.384861i	0.955476	+	0.295070i	$0.0953430\pi$
$282$		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
$285$	10.3485	−	0.953512i	0.612990	−	0.0564812i
$286$		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
$291$	2.17423	+	23.5970i	0.127456	+	1.38328i
$292$		0			0
$293$			29.2699i			1.70997i	0.518657	+	0.854983i	$0.326432\pi$
$293$			29.2699i			1.70997i	−0.518657	+	0.854983i	$0.673568\pi$
$294$		0			0
$295$		−	1.27135i		−	0.0740208i
$296$		0			0
$297$	−5.39898	−	5.25153i	−0.313281	−	0.304725i
$298$		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
$303$	−9.74745	+	21.1578i	−0.559976	+	1.21549i
$304$		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
$309$	−2.82577	+	6.13361i	−0.160752	+	0.348929i
$310$		0			0
$311$	−14.2020			−0.805324			−0.402662	−	0.915349i	$-0.631915\pi$
$311$	−14.2020			−0.805324			−0.402662	+	0.915349i	$0.631915\pi$
$312$		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
$315$	1.20204	+	6.46750i	0.0677273	+	0.364402i
$316$		0			0
$317$	16.3207	+	9.42274i	0.916660	+	0.529234i	0.882568	−	0.470185i	$-0.155813\pi$
$317$	16.3207	+	9.42274i	0.916660	+	0.529234i	0.0340918	+	0.999419i	$0.489146\pi$
$318$		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
$333$	−19.2980	−	22.5720i	−1.05752	−	1.23694i
$334$		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
$339$	−4.74745	+	10.3048i	−0.257846	+	0.559681i
$340$		0			0
$341$	−2.17423	−	1.25529i	−0.117741	−	0.0679780i
$342$		0			0
$343$		−	14.0314i		−	0.757623i
$344$		0			0
$345$	0.303062	+	3.28913i	0.0163163	+	0.177081i
$346$		0			0
$347$	6.07321	+	10.5191i	0.326027	+	0.564696i	0.981720	−	0.190332i	$-0.0609566\pi$
$347$	6.07321	+	10.5191i	0.326027	+	0.564696i	−0.655693	+	0.755028i	$0.727623\pi$
$348$		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
$351$	−26.1742	−	6.62642i	−1.39708	−	0.353692i
$352$		0			0
$353$	−3.17423	+	5.49794i	−0.168947	+	0.292626i	−0.938050	−	0.346500i	$-0.887370\pi$
$353$	−3.17423	+	5.49794i	−0.168947	+	0.292626i	0.769103	+	0.639125i	$0.220703\pi$
$354$		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	$0.116003\pi$
$359$			13.5065i			0.712844i	−0.934325	+	0.356422i	$0.883997\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$		0			0
$363$	15.3485	−	1.41421i	0.805586	−	0.0742270i
$364$		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
$369$	10.1742	−	1.89097i	0.529649	−	0.0984399i
$370$		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
$381$	−6.37628	+	13.8404i	−0.326666	+	0.709063i
$382$		0			0
$383$	12.0732	−	20.9114i	0.616912	−	1.06852i	−0.373133	−	0.927778i	$-0.621717\pi$
$383$	12.0732	−	20.9114i	0.616912	−	1.06852i	0.990046	−	0.140746i	$-0.0449501\pi$
$384$		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	0.709901	−	0.704302i	$-0.248740\pi$
$389$	8.97219	+	5.18010i	0.454908	+	0.262641i	−0.254993	+	0.966943i	$0.582073\pi$
$390$		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	$-0.540652\pi$
$401$	−5.10102			−0.254733			−0.127366	+	0.991856i	$0.540652\pi$
$402$		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	−0.156743	−	0.987639i	$-0.550100\pi$
$419$	−22.3207	−	12.8868i	−1.09044	−	0.629563i	−0.933692	+	0.358076i	$0.883433\pi$
$420$		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
$423$	−0.174235	−	0.937458i	−0.00847158	−	0.0455808i
$424$		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	−0.986457	−	0.164019i	$-0.947554\pi$
$431$	−27.7702	+	16.0331i	−1.33764	+	0.772287i	−0.351184	+	0.936306i	$0.614221\pi$
$432$		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
$435$	16.7980	+	7.73885i	0.805400	+	0.371049i
$436$		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
$441$	−11.3031	−	13.2207i	−0.538241	−	0.629559i
$442$		0			0
$443$	16.6237	+	28.7931i	0.789817	+	1.36800i	0.926079	+	0.377330i	$0.123158\pi$
$443$	16.6237	+	28.7931i	0.789817	+	1.36800i	−0.136262	+	0.990673i	$0.543509\pi$
$444$		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	−0.795669	−	0.605732i	$-0.792880\pi$
$449$	−14.1742	+	8.18350i	−0.668923	+	0.386203i	0.126745	+	0.991935i	$0.459547\pi$
$450$		0			0
$451$	2.50000	−	4.33013i	0.117720	−	0.203898i
$452$		0			0
$453$	−15.1742	+	1.39816i	−0.712948	+	0.0656913i
$454$		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
$459$	30.0959	+	7.61926i	1.40476	+	0.355636i
$460$		0			0
$461$		−	42.1407i		−	1.96269i	−0.192263	−	0.981344i	$-0.561583\pi$
$461$		−	42.1407i		−	1.96269i	0.192263	−	0.981344i	$-0.438417\pi$
$462$		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
$465$	5.44949	+	2.51059i	0.252714	+	0.116426i
$466$		0			0
$467$	35.1742	+	20.3079i	1.62767	+	0.939735i	0.984786	+	0.173771i	$0.0555954\pi$
$467$	35.1742	+	20.3079i	1.62767	+	0.939735i	0.642883	+	0.765964i	$0.277738\pi$
$468$		0			0
$469$	−6.64643	+	6.03007i	−0.306904	+	0.278443i
$470$		0			0
$471$	23.9722	−	2.20881i	1.10458	−	0.101776i
$472$		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	0.846909	−	0.531738i	$-0.178461\pi$
$479$	17.7247	+	10.2334i	0.809864	+	0.467575i	−0.0370445	+	0.999314i	$0.511794\pi$
$480$		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
$489$	16.3763	−	35.5464i	0.740561	−	1.60746i
$490$		0			0
$491$		−	11.6637i		−	0.526373i	−0.964745	−	0.263187i	$-0.915226\pi$
$491$		−	11.6637i		−	0.526373i	0.964745	−	0.263187i	$-0.0847735\pi$
$492$		0			0
$493$	31.8990			1.43666
$494$		0			0
$495$	8.55051	−	1.58919i	0.384317	−	0.0714286i
$496$		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
$501$	−40.0959	−	18.4723i	−1.79135	−	0.825280i
$502$		0			0
$503$	−22.1742	−	38.4069i	−0.988700	−	1.71248i	−0.624173	−	0.781287i	$-0.714564\pi$
$503$	−22.1742	−	38.4069i	−0.988700	−	1.71248i	−0.364528	−	0.931193i	$-0.618770\pi$
$504$		0			0
$505$	−13.4495	−	23.2952i	−0.598494	−	1.03662i
$506$		0			0
$507$	−10.1464	+	22.0239i	−0.450619	+	0.978114i
$508$		0			0
$509$			2.82843i			0.125368i	0.998033	+	0.0626839i	$0.0199660\pi$
$509$			2.82843i			0.125368i	−0.998033	+	0.0626839i	$0.980034\pi$
$510$		0			0
$511$			6.46750i			0.286105i
$512$		0			0
$513$	3.82577	−	15.1117i	0.168912	−	0.667198i
$514$		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
$519$	1.94949	+	21.1578i	0.0855731	+	0.928725i
$520$		0			0
$521$	40.2929			1.76526			0.882631	−	0.470066i	$-0.155770\pi$
$521$	40.2929			1.76526			0.882631	+	0.470066i	$0.155770\pi$
$522$		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
$525$	1.72474	+	0.794593i	0.0752740	+	0.0346789i
$526$		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
$543$	−1.52270	+	3.30518i	−0.0653455	+	0.141839i
$544$		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
$549$	−24.7474	+	21.1578i	−1.05620	+	0.902994i
$550$		0			0
$551$		−	16.0171i		−	0.682349i
$552$		0			0
$553$	−0.252551	+	0.437432i	−0.0107396	+	0.0186015i
$554$		0			0
$555$	34.1464	−	3.14626i	1.44944	−	0.133551i
$556$		0			0
$557$	7.07321	−	4.08372i	0.299702	−	0.173033i	−0.342607	−	0.939479i	$-0.611310\pi$
$557$	7.07321	−	4.08372i	0.299702	−	0.173033i	0.642309	+	0.766446i	$0.277977\pi$
$558$		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	$-0.149853\pi$
$563$	42.2929			1.78243			0.891216	+	0.453580i	$0.149853\pi$
$564$		0			0
$565$	−6.55051	−	11.3458i	−0.275582	−	0.477322i
$566$		0			0
$567$	9.74745	+	1.53381i	0.409354	+	0.0644139i
$568$		0			0
$569$	−23.4217	+	13.5225i	−0.981888	+	0.566893i	−0.902840	−	0.429977i	$-0.858522\pi$
$569$	−23.4217	+	13.5225i	−0.981888	+	0.566893i	−0.0790484	+	0.996871i	$0.525188\pi$
$570$		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
$573$	−30.0959	+	2.77305i	−1.25728	+	0.115846i
$574$		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
$585$	23.6969	−	20.2597i	0.979748	−	0.837635i
$586$		0			0
$587$	−8.27526	+	14.3332i	−0.341556	+	0.591593i	−0.984722	−	0.174134i	$-0.944287\pi$
$587$	−8.27526	+	14.3332i	−0.341556	+	0.591593i	0.643166	+	0.765727i	$0.277621\pi$
$588$		0			0
$589$		−	5.19615i		−	0.214104i
$590$		0			0
$591$	−2.35357	+	5.10867i	−0.0968130	+	0.210142i
$592$		0			0
$593$	−11.9722	+	20.7364i	−0.491639	+	0.851544i	−0.999954	−	0.00962762i	$-0.996935\pi$
$593$	−11.9722	+	20.7364i	−0.491639	+	0.851544i	0.508315	+	0.861171i	$0.330269\pi$
$594$		0			0
$595$	−13.1010			−0.537089
$596$		0			0
$597$	18.9722	−	1.74810i	0.776480	−	0.0715452i
$598$		0			0
$599$	8.17423	+	14.1582i	0.333990	+	0.578488i	0.983290	−	0.182044i	$-0.0582714\pi$
$599$	8.17423	+	14.1582i	0.333990	+	0.578488i	−0.649300	+	0.760532i	$0.724938\pi$
$600$		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
$603$	−3.10102	+	24.3595i	−0.126283	+	0.991994i
$604$		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
$609$	10.0959	−	0.930242i	0.409107	−	0.0376953i
$610$		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
$615$	−5.00000	+	10.8530i	−0.201619	+	0.437635i
$616$		0			0
$617$		−	26.7272i		−	1.07600i	−0.842946	−	0.537998i	$-0.819181\pi$
$617$		−	26.7272i		−	1.07600i	0.842946	−	0.537998i	$-0.180819\pi$
$618$		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
$621$	4.80306	+	1.21597i	0.192740	+	0.0487952i
$622$		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
$633$	10.1742	−	0.937458i	0.404390	−	0.0372606i
$634$		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
$639$	7.07321	+	38.0570i	0.279812	+	1.50551i
$640$		0			0
$641$	−21.5227	−	37.2784i	−0.850096	−	1.47241i	−0.881121	−	0.472890i	$-0.843211\pi$
$641$	−21.5227	−	37.2784i	−0.850096	−	1.47241i	0.0310256	−	0.999519i	$-0.490123\pi$
$642$		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	−0.869430	−	0.494056i	$-0.835514\pi$
$647$	−0.174235	+	0.301783i	−0.00684987	+	0.0118643i	0.862580	+	0.505920i	$0.168847\pi$
$648$		0			0
$649$	−0.797959	+	0.460702i	−0.0313226	+	0.0180841i
$650$		0			0
$651$	3.27526	−	0.301783i	0.128367	−	0.0118278i
$652$		0			0
$653$	−9.62372	+	16.6688i	−0.376605	+	0.652300i	−0.990566	−	0.137037i	$-0.956242\pi$
$653$	−9.62372	+	16.6688i	−0.376605	+	0.652300i	0.613960	+	0.789337i	$0.289575\pi$
$654$		0			0
$655$			12.5851i			0.491739i
$656$		0			0
$657$	11.5000	+	13.4511i	0.448658	+	0.524777i
$658$		0			0
$659$	−5.72474	+	3.30518i	−0.223004	+	0.128752i	−0.607341	−	0.794442i	$-0.707764\pi$
$659$	−5.72474	+	3.30518i	−0.223004	+	0.128752i	0.384336	+	0.923193i	$0.374430\pi$
$660$		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
$663$	22.5000	−	48.8385i	0.873828	−	1.89673i
$664$		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	$-0.935549\pi$
$677$	−17.2753	−	29.9216i	−0.663942	−	1.14998i	0.315629	−	0.948883i	$-0.397784\pi$
$678$		0			0
$679$	−15.0000			−0.575647
$680$		0			0
$681$	42.5454	+	19.6007i	1.63034	+	0.751102i
$682$		0			0
$683$	−16.1742	+	28.0146i	−0.618890	+	1.07195i	0.370799	+	0.928713i	$0.379084\pi$
$683$	−16.1742	+	28.0146i	−0.618890	+	1.07195i	−0.989689	+	0.143235i	$0.954249\pi$
$684$		0			0
$685$	−18.2020			−0.695464
$686$		0			0
$687$	−1.62372	−	17.6223i	−0.0619489	−	0.672332i
$688$		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
$693$	3.62372	−	3.09810i	0.137654	−	0.117687i
$694$		0			0
$695$			14.4279i			0.547280i
$696$		0			0
$697$			20.6096i			0.780646i
$698$		0			0
$699$	−13.4444	+	29.1824i	−0.508513	+	1.10378i
$700$		0			0
$701$	6.82577	+	11.8226i	0.257806	+	0.446532i	0.965654	−	0.259832i	$-0.0836673\pi$
$701$	6.82577	+	11.8226i	0.257806	+	0.446532i	−0.707848	+	0.706365i	$0.750334\pi$
$702$		0			0
$703$	−14.8485	−	25.7183i	−0.560021	−	0.969984i
$704$		0			0
$705$	1.00000	+	0.460702i	0.0376622	+	0.0173510i
$706$		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
$711$	0.252551	+	1.35884i	0.00947141	+	0.0509603i
$712$		0			0
$713$	1.65153			0.0618503
$714$		0			0
$715$		−	15.0635i		−	0.563344i
$716$		0			0
$717$	8.15153	−	17.6937i	0.304424	−	0.660784i
$718$		0			0
$719$	14.6691	+	8.46923i	0.547066	+	0.315849i	0.747938	−	0.663769i	$-0.231044\pi$
$719$	14.6691	+	8.46923i	0.547066	+	0.315849i	−0.200872	+	0.979618i	$0.564377\pi$
$720$		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
$735$	20.0000	−	1.84281i	0.737711	−	0.0679730i
$736$		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
$741$	−24.5227	−	11.2977i	−0.900864	−	0.415030i
$742$		0			0
$743$	6.27526	+	3.62302i	0.230217	+	0.132916i	0.610672	−	0.791884i	$-0.290899\pi$
$743$	6.27526	+	3.62302i	0.230217	+	0.132916i	−0.380455	+	0.924799i	$0.624233\pi$
$744$		0			0
$745$		−	29.5556i		−	1.08283i
$746$		0			0
$747$	26.5227	−	22.6756i	0.970415	−	0.829656i
$748$		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
$753$	34.7474	−	3.20164i	1.26627	−	0.116674i
$754$		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	$0.105518\pi$
$761$			17.9562i			0.650911i	−0.945557	+	0.325456i	$0.894482\pi$
$762$		0			0
$763$	2.75255	+	4.76756i	0.0996490	+	0.172597i
$764$		0			0
$765$	−27.2474	+	23.2952i	−0.985134	+	0.842240i
$766$		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
$771$	−23.7474	−	10.9405i	−0.855243	−	0.394012i
$772$		0			0
$773$	−2.97219	+	1.71600i	−0.106902	+	0.0617201i	−0.552498	−	0.833514i	$-0.686325\pi$
$773$	−2.97219	+	1.71600i	−0.106902	+	0.0617201i	0.445596	+	0.895234i	$0.352992\pi$
$774$		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
$783$	19.3434	−	19.8865i	0.691276	−	0.710685i
$784$		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	−0.684675	−	0.728848i	$-0.740056\pi$
$797$	−11.1742	+	6.45145i	−0.395812	+	0.228522i	0.288864	+	0.957370i	$0.406723\pi$
$798$		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	$-0.615564\pi$
$809$	−20.2020			−0.710266			−0.355133	+	0.934816i	$0.615564\pi$
$810$		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	0.220537	−	0.975379i	$-0.429219\pi$
$821$	−14.7247	−	8.50134i	−0.513897	−	0.296699i	−0.734434	+	0.678680i	$0.762552\pi$
$822$		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
$825$	1.05051	−	2.28024i	0.0365741	−	0.0793877i
$826$		0			0
$827$	−37.3207	−	21.5471i	−1.29777	−	0.749266i	−0.317749	−	0.948175i	$-0.602927\pi$
$827$	−37.3207	−	21.5471i	−1.29777	−	0.749266i	−0.980018	+	0.198909i	$0.936260\pi$
$828$		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
$837$	6.27526	−	6.45145i	0.216905	−	0.222995i
$838$		0			0
$839$	9.52270	−	5.49794i	0.328760	−	0.189810i	−0.326530	−	0.945187i	$-0.605880\pi$
$839$	9.52270	−	5.49794i	0.328760	−	0.189810i	0.655291	+	0.755377i	$0.272546\pi$
$840$		0			0
$841$	−0.247449	+	0.428594i	−0.00853271	+	0.0147791i
$842$		0			0
$843$	12.8485	−	1.18386i	0.442525	−	0.0407744i
$844$		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
$855$	11.6969	+	13.6814i	0.400027	+	0.467895i
$856$		0			0
$857$	13.5959			0.464428			0.232214	−	0.972665i	$-0.425403\pi$
$857$	13.5959			0.464428			0.232214	+	0.972665i	$0.425403\pi$
$858$		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
$861$	0.601021	+	6.52288i	0.0204827	+	0.222299i
$862$		0			0
$863$			2.47848i			0.0843685i	0.999110	+	0.0421843i	$0.0134316\pi$
$863$			2.47848i			0.0843685i	−0.999110	+	0.0421843i	$0.986568\pi$
$864$		0			0
$865$	−21.2474	−	12.2672i	−0.722435	−	0.417098i
$866$		0			0
$867$	−13.5505	+	29.4128i	−0.460199	+	0.998910i
$868$		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
$873$	−31.1969	+	26.6718i	−1.05586	+	0.902704i
$874$		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	0.894367	−	0.447334i	$-0.147627\pi$
$881$	28.3207	+	16.3509i	0.954147	+	0.550877i	0.0597805	+	0.998212i	$0.480960\pi$
$882$		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	0.150605	−	0.988594i	$-0.451878\pi$
$887$	−18.7702	−	10.8370i	−0.630240	−	0.363869i	−0.780845	+	0.624725i	$0.785211\pi$
$888$		0			0
$889$	−8.35357	−	4.82294i	−0.280170	−	0.161756i
$890$		0			0
$891$	2.02781	−	12.8868i	0.0679341	−	0.431725i
$892$		0			0
$893$		−	0.953512i		−	0.0319081i
$894$		0			0
$895$	27.1918			0.908923
$896$		0			0
$897$	3.59082	−	7.79423i	0.119894	−	0.260242i
$898$		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
$903$	−1.01021	+	2.19275i	−0.0336175	+	0.0729702i
$904$		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
$909$	−39.6691	+	7.37285i	−1.31574	+	0.244542i
$910$		0			0
$911$			37.1195i			1.22982i	0.788596	+	0.614912i	$0.210808\pi$
$911$			37.1195i			1.22982i	−0.788596	+	0.614912i	$0.789192\pi$
$912$		0			0
$913$		−	16.8598i		−	0.557978i
$914$		0			0
$915$	−3.44949	−	37.4373i	−0.114037	−	1.23764i
$916$		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
$921$	−14.8258	+	1.36605i	−0.488526	+	0.0450129i
$922$		0			0
$923$	67.0454			2.20683
$924$		0			0
$925$	4.94949	−	8.57277i	0.162738	−	0.281871i
$926$		0			0
$927$	−11.5000	+	2.13737i	−0.377710	+	0.0702006i
$928$		0			0
$929$	48.4949			1.59107			0.795533	−	0.605910i	$-0.207191\pi$
$929$	48.4949			1.59107			0.795533	+	0.605910i	$0.207191\pi$
$930$		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	$-0.728071\pi$
$941$	−40.2929			−1.31351			−0.656755	+	0.754104i	$0.728071\pi$
$942$		0			0
$943$			3.28913i			0.107109i
$944$		0			0
$945$	−7.94439	+	8.16744i	−0.258431	+	0.265687i
$946$		0			0
$947$			36.8338i			1.19694i	0.801146	+	0.598468i	$0.204224\pi$
$947$			36.8338i			1.19694i	−0.801146	+	0.598468i	$0.795776\pi$
$948$		0			0
$949$	26.5454	−	15.3260i	0.861700	−	0.497503i
$950$		0			0
$951$	2.99490	+	32.5036i	0.0971162	+	1.05400i
$952$		0			0
$953$		−	12.2351i		−	0.396334i	−0.980168	−	0.198167i	$-0.936501\pi$
$953$		−	12.2351i		−	0.396334i	0.980168	−	0.198167i	$-0.0634989\pi$
$954$		0			0
$955$	17.4495	−	30.2234i	0.564652	−	0.978006i
$956$		0			0
$957$	−1.22985	−	13.3475i	−0.0397553	−	0.431465i
$958$		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
$969$	28.1969	+	12.9904i	0.905816	+	0.417311i
$970$		0			0
$971$	30.2196	−	17.4473i	0.969794	−	0.559911i	0.0706209	−	0.997503i	$-0.477502\pi$
$971$	30.2196	−	17.4473i	0.969794	−	0.559911i	0.899174	+	0.437592i	$0.144169\pi$
$972$		0			0
$973$	3.95459	+	6.84955i	0.126778	+	0.219587i
$974$		0			0
$975$	−0.825765	−	8.96204i	−0.0264457	−	0.287015i
$976$		0			0
$977$	−22.3207	−	12.8868i	−0.714101	−	0.412287i	0.0984765	−	0.995139i	$-0.468603\pi$
$977$	−22.3207	−	12.8868i	−0.714101	−	0.412287i	−0.812578	+	0.582853i	$0.801936\pi$
$978$		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	$-0.668093\pi$
$983$	−31.5959			−1.00775			−0.503877	+	0.863776i	$0.668093\pi$
$984$		0			0
$985$	−3.24745	−	5.62475i	−0.103472	−	0.179219i
$986$		0			0
$987$	0.601021	−	0.0553782i	0.0191307	−	0.00176271i
$988$		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
$993$	−21.9722	−	10.1226i	−0.697266	−	0.321232i
$994$		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
$999$	12.6237	−	49.8635i	0.399397	−	1.57761i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.b.365.1	✓	4	67.30	odd	6
804.2.o.b.641.2	yes	4	3.2	odd	2
804.2.o.c.365.1	yes	4	201.164	even	6	inner
804.2.o.c.641.2	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.41421i) q^{3} -2.00000 q^{5} +(-0.949490 + 0.548188i) q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.41421i) q^{3} -2.00000 q^{5} +(-0.949490 + 0.548188i) q^{7} +(-1.00000 + 2.82843i) q^{9} +(0.724745 + 1.25529i) q^{11} +(4.50000 + 2.59808i) q^{13} +(-2.00000 - 2.82843i) q^{15} +(-5.17423 - 2.98735i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(-1.72474 - 0.794593i) q^{21} +(-0.825765 - 0.476756i) q^{23} -1.00000 q^{25} +(-5.00000 + 1.41421i) q^{27} +(-4.62372 + 2.66951i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(-1.05051 + 2.28024i) q^{33} +(1.89898 - 1.09638i) q^{35} +(-4.94949 + 8.57277i) q^{37} +(0.825765 + 8.96204i) q^{39} +(-1.72474 - 2.98735i) q^{41} -1.27135i q^{43} +(2.00000 - 5.65685i) q^{45} +(-0.275255 + 0.158919i) q^{47} +(-2.89898 + 5.02118i) q^{49} +(-0.949490 - 10.3048i) q^{51} +6.00000 q^{53} +(-1.44949 - 2.51059i) q^{55} +(-5.17423 + 0.476756i) q^{57} +0.635674i q^{59} +(9.39898 + 5.42650i) q^{61} +(-0.601021 - 3.23375i) q^{63} +(-9.00000 - 5.19615i) q^{65} +(8.00000 - 1.73205i) q^{67} +(-0.151531 - 1.64456i) q^{69} +(11.1742 - 6.45145i) q^{71} +(2.94949 - 5.10867i) q^{73} +(-1.00000 - 1.41421i) q^{75} +(-1.37628 - 0.794593i) q^{77} +(0.398979 - 0.230351i) q^{79} +(-7.00000 - 5.65685i) q^{81} +(-10.0732 - 5.81577i) q^{83} +(10.3485 + 5.97469i) q^{85} +(-8.39898 - 3.86943i) q^{87} +4.73545i q^{89} -5.69694 q^{91} +(-2.72474 - 1.25529i) q^{93} +(3.00000 - 5.19615i) q^{95} +(11.8485 + 6.84072i) q^{97} +(-4.27526 + 0.794593i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 8 q^{5} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 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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