LMFDB - Embedded newform 1176.2.q.o.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(361,1176)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1176.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.q (of order $3$, degree $2$, not 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:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1176.361
Dual form			1176.2.q.o.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(1.70711 + 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(1.70711 + 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-2.41421 + 4.18154i) q^{11} -1.41421 q^{13} +3.41421 q^{15} +(-3.12132 + 5.40629i) q^{17} +(0.585786 + 1.01461i) q^{19} +(0.414214 + 0.717439i) q^{23} +(-3.32843 + 5.76500i) q^{25} -1.00000 q^{27} -8.48528 q^{29} +(5.41421 - 9.37769i) q^{31} +(2.41421 + 4.18154i) q^{33} +(4.82843 + 8.36308i) q^{37} +(-0.707107 + 1.22474i) q^{39} +3.41421 q^{41} -8.00000 q^{43} +(1.70711 - 2.95680i) q^{45} +(0.585786 + 1.01461i) q^{47} +(3.12132 + 5.40629i) q^{51} +(-4.65685 + 8.06591i) q^{53} -16.4853 q^{55} +1.17157 q^{57} +(5.41421 - 9.37769i) q^{59} +(-2.94975 - 5.10911i) q^{61} +(-2.41421 - 4.18154i) q^{65} +(4.00000 - 6.92820i) q^{67} +0.828427 q^{69} +4.82843 q^{71} +(1.53553 - 2.65962i) q^{73} +(3.32843 + 5.76500i) q^{75} +(6.82843 + 11.8272i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.31371 q^{83} -21.3137 q^{85} +(-4.24264 + 7.34847i) q^{87} +(7.36396 + 12.7548i) q^{89} +(-5.41421 - 9.37769i) q^{93} +(-2.00000 + 3.46410i) q^{95} +16.2426 q^{97} +4.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^9	$ 4 q + 2 q^{3} + 4 q^{5} - 2 q^{9} - 4 q^{11} + 8 q^{15} - 4 q^{17} + 8 q^{19} - 4 q^{23} - 2 q^{25} - 4 q^{27} + 16 q^{31} + 4 q^{33} + 8 q^{37} + 8 q^{41} - 32 q^{43} + 4 q^{45} + 8 q^{47} + 4 q^{51} + 4 q^{53} - 32 q^{55} + 16 q^{57} + 16 q^{59} + 8 q^{61} - 4 q^{65} + 16 q^{67} - 8 q^{69} + 8 q^{71} - 8 q^{73} + 2 q^{75} + 16 q^{79} - 2 q^{81} - 16 q^{83} - 40 q^{85} + 4 q^{89} - 16 q^{93} - 8 q^{95} + 48 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^9 - 4 * q^11 + 8 * q^15 - 4 * q^17 + 8 * q^19 - 4 * q^23 - 2 * q^25 - 4 * q^27 + 16 * q^31 + 4 * q^33 + 8 * q^37 + 8 * q^41 - 32 * q^43 + 4 * q^45 + 8 * q^47 + 4 * q^51 + 4 * q^53 - 32 * q^55 + 16 * q^57 + 16 * q^59 + 8 * q^61 - 4 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 8 * q^73 + 2 * q^75 + 16 * q^79 - 2 * q^81 - 16 * q^83 - 40 * q^85 + 4 * q^89 - 16 * q^93 - 8 * q^95 + 48 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	1.70711	+	2.95680i	0.763441	+	1.32232i	0.941067	+	0.338221i	$0.109825\pi$
$5$	1.70711	+	2.95680i	0.763441	+	1.32232i	−0.177625	+	0.984098i	$0.556842\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.41421	+	4.18154i	−0.727913	+	1.26078i	0.229851	+	0.973226i	$0.426176\pi$
$11$	−2.41421	+	4.18154i	−0.727913	+	1.26078i	−0.957764	+	0.287556i	$0.907157\pi$
$12$		0			0
$13$	−1.41421			−0.392232			−0.196116	−	0.980581i	$-0.562833\pi$
$13$	−1.41421			−0.392232			−0.196116	+	0.980581i	$0.562833\pi$
$14$		0			0
$15$	3.41421			0.881546
$16$		0			0
$17$	−3.12132	+	5.40629i	−0.757031	+	1.31122i	0.187327	+	0.982298i	$0.440018\pi$
$17$	−3.12132	+	5.40629i	−0.757031	+	1.31122i	−0.944358	+	0.328919i	$0.893316\pi$
$18$		0			0
$19$	0.585786	+	1.01461i	0.134389	+	0.232768i	0.925364	−	0.379080i	$-0.123760\pi$
$19$	0.585786	+	1.01461i	0.134389	+	0.232768i	−0.790975	+	0.611848i	$0.790426\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.414214	+	0.717439i	0.0863695	+	0.149596i	0.905974	−	0.423333i	$-0.139140\pi$
$23$	0.414214	+	0.717439i	0.0863695	+	0.149596i	−0.819604	+	0.572930i	$0.805807\pi$
$24$		0			0
$25$	−3.32843	+	5.76500i	−0.665685	+	1.15300i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−8.48528			−1.57568			−0.787839	−	0.615882i	$-0.788800\pi$
$29$	−8.48528			−1.57568			−0.787839	+	0.615882i	$0.788800\pi$
$30$		0			0
$31$	5.41421	−	9.37769i	0.972421	−	1.68428i	0.284227	−	0.958757i	$-0.408263\pi$
$31$	5.41421	−	9.37769i	0.972421	−	1.68428i	0.688194	−	0.725526i	$-0.258404\pi$
$32$		0			0
$33$	2.41421	+	4.18154i	0.420261	+	0.727913i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.82843	+	8.36308i	0.793789	+	1.37488i	0.923606	+	0.383344i	$0.125228\pi$
$37$	4.82843	+	8.36308i	0.793789	+	1.37488i	−0.129817	+	0.991538i	$0.541439\pi$
$38$		0			0
$39$	−0.707107	+	1.22474i	−0.113228	+	0.196116i
$40$		0			0
$41$	3.41421			0.533211			0.266605	−	0.963806i	$-0.414098\pi$
$41$	3.41421			0.533211			0.266605	+	0.963806i	$0.414098\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	1.70711	−	2.95680i	0.254480	−	0.440773i
$46$		0			0
$47$	0.585786	+	1.01461i	0.0854457	+	0.147996i	0.905581	−	0.424173i	$-0.139435\pi$
$47$	0.585786	+	1.01461i	0.0854457	+	0.147996i	−0.820135	+	0.572170i	$0.806102\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3.12132	+	5.40629i	0.437072	+	0.757031i
$52$		0			0
$53$	−4.65685	+	8.06591i	−0.639668	+	1.10794i	0.345837	+	0.938294i	$0.387595\pi$
$53$	−4.65685	+	8.06591i	−0.639668	+	1.10794i	−0.985506	+	0.169643i	$0.945738\pi$
$54$		0			0
$55$	−16.4853			−2.22287
$56$		0			0
$57$	1.17157			0.155179
$58$		0			0
$59$	5.41421	−	9.37769i	0.704871	−	1.22087i	−0.261868	−	0.965104i	$-0.584338\pi$
$59$	5.41421	−	9.37769i	0.704871	−	1.22087i	0.966738	−	0.255768i	$-0.0823283\pi$
$60$		0			0
$61$	−2.94975	−	5.10911i	−0.377676	−	0.654155i	0.613047	−	0.790046i	$-0.289944\pi$
$61$	−2.94975	−	5.10911i	−0.377676	−	0.654155i	−0.990724	+	0.135891i	$0.956610\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.41421	−	4.18154i	−0.299446	−	0.518656i
$66$		0			0
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414604\pi$
$68$		0			0
$69$	0.828427			0.0997309
$70$		0			0
$71$	4.82843			0.573029			0.286514	−	0.958076i	$-0.407503\pi$
$71$	4.82843			0.573029			0.286514	+	0.958076i	$0.407503\pi$
$72$		0			0
$73$	1.53553	−	2.65962i	0.179721	−	0.311285i	−0.762064	−	0.647501i	$-0.775814\pi$
$73$	1.53553	−	2.65962i	0.179721	−	0.311285i	0.941785	+	0.336216i	$0.109147\pi$
$74$		0			0
$75$	3.32843	+	5.76500i	0.384334	+	0.665685i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	6.82843	+	11.8272i	0.768258	+	1.33066i	0.938507	+	0.345261i	$0.112210\pi$
$79$	6.82843	+	11.8272i	0.768258	+	1.33066i	−0.170249	+	0.985401i	$0.554457\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	7.31371			0.802784			0.401392	−	0.915906i	$-0.368527\pi$
$83$	7.31371			0.802784			0.401392	+	0.915906i	$0.368527\pi$
$84$		0			0
$85$	−21.3137			−2.31180
$86$		0			0
$87$	−4.24264	+	7.34847i	−0.454859	+	0.787839i
$88$		0			0
$89$	7.36396	+	12.7548i	0.780578	+	1.35200i	0.931605	+	0.363472i	$0.118409\pi$
$89$	7.36396	+	12.7548i	0.780578	+	1.35200i	−0.151027	+	0.988530i	$0.548258\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−5.41421	−	9.37769i	−0.561428	−	0.972421i
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	16.2426			1.64919			0.824595	−	0.565723i	$-0.191403\pi$
$97$	16.2426			1.64919			0.824595	+	0.565723i	$0.191403\pi$
$98$		0			0
$99$	4.82843			0.485275
$100$		0			0
$101$	0.292893	−	0.507306i	0.0291440	−	0.0504788i	−0.851086	−	0.525027i	$-0.824055\pi$
$101$	0.292893	−	0.507306i	0.0291440	−	0.0504788i	0.880230	+	0.474548i	$0.157389\pi$
$102$		0			0
$103$	2.58579	+	4.47871i	0.254785	+	0.441301i	0.964837	−	0.262848i	$-0.0846619\pi$
$103$	2.58579	+	4.47871i	0.254785	+	0.441301i	−0.710052	+	0.704149i	$0.751329\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.24264	+	2.15232i	0.120131	+	0.208072i	0.919819	−	0.392343i	$-0.128335\pi$
$107$	1.24264	+	2.15232i	0.120131	+	0.208072i	−0.799688	+	0.600415i	$0.795002\pi$
$108$		0			0
$109$	−5.65685	+	9.79796i	−0.541828	+	0.938474i	0.456971	+	0.889482i	$0.348934\pi$
$109$	−5.65685	+	9.79796i	−0.541828	+	0.938474i	−0.998799	+	0.0489926i	$0.984399\pi$
$110$		0			0
$111$	9.65685			0.916588
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	−1.41421	+	2.44949i	−0.131876	+	0.228416i
$116$		0			0
$117$	0.707107	+	1.22474i	0.0653720	+	0.113228i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−6.15685	−	10.6640i	−0.559714	−	0.969453i
$122$		0			0
$123$	1.70711	−	2.95680i	0.153925	−	0.266605i
$124$		0			0
$125$	−5.65685			−0.505964
$126$		0			0
$127$	7.31371			0.648987			0.324493	−	0.945888i	$-0.394806\pi$
$127$	7.31371			0.648987			0.324493	+	0.945888i	$0.394806\pi$
$128$		0			0
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$		0			0
$131$	7.65685	+	13.2621i	0.668982	+	1.15871i	0.978189	+	0.207717i	$0.0666032\pi$
$131$	7.65685	+	13.2621i	0.668982	+	1.15871i	−0.309207	+	0.950995i	$0.600063\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.70711	−	2.95680i	−0.146924	−	0.254480i
$136$		0			0
$137$	6.24264	−	10.8126i	0.533345	−	0.923780i	−0.465897	−	0.884839i	$-0.654268\pi$
$137$	6.24264	−	10.8126i	0.533345	−	0.923780i	0.999242	−	0.0389412i	$-0.0123985\pi$
$138$		0			0
$139$	−9.65685			−0.819084			−0.409542	−	0.912291i	$-0.634311\pi$
$139$	−9.65685			−0.819084			−0.409542	+	0.912291i	$0.634311\pi$
$140$		0			0
$141$	1.17157			0.0986642
$142$		0			0
$143$	3.41421	−	5.91359i	0.285511	−	0.494519i
$144$		0			0
$145$	−14.4853	−	25.0892i	−1.20294	−	2.08355i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	0.828427	−	1.43488i	0.0674164	−	0.116769i	−0.830347	−	0.557247i	$-0.811858\pi$
$151$	0.828427	−	1.43488i	0.0674164	−	0.116769i	0.897763	+	0.440478i	$0.145191\pi$
$152$		0			0
$153$	6.24264			0.504688
$154$		0			0
$155$	36.9706			2.96955
$156$		0			0
$157$	2.94975	−	5.10911i	0.235415	−	0.407752i	−0.723978	−	0.689823i	$-0.757688\pi$
$157$	2.94975	−	5.10911i	0.235415	−	0.407752i	0.959393	+	0.282072i	$0.0910216\pi$
$158$		0			0
$159$	4.65685	+	8.06591i	0.369313	+	0.639668i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.17157	+	2.02922i	0.0917647	+	0.158941i	0.908254	−	0.418420i	$-0.137416\pi$
$163$	1.17157	+	2.02922i	0.0917647	+	0.158941i	−0.816489	+	0.577361i	$0.804083\pi$
$164$		0			0
$165$	−8.24264	+	14.2767i	−0.641689	+	1.11144i
$166$		0			0
$167$	−6.82843			−0.528400			−0.264200	−	0.964468i	$-0.585108\pi$
$167$	−6.82843			−0.528400			−0.264200	+	0.964468i	$0.585108\pi$
$168$		0			0
$169$	−11.0000			−0.846154
$170$		0			0
$171$	0.585786	−	1.01461i	0.0447962	−	0.0775893i
$172$		0			0
$173$	−0.292893	−	0.507306i	−0.0222683	−	0.0385698i	0.854677	−	0.519161i	$-0.173755\pi$
$173$	−0.292893	−	0.507306i	−0.0222683	−	0.0385698i	−0.876945	+	0.480591i	$0.840422\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.41421	−	9.37769i	−0.406957	−	0.704871i
$178$		0			0
$179$	10.8995	−	18.8785i	0.814667	−	1.41104i	−0.0949006	−	0.995487i	$-0.530253\pi$
$179$	10.8995	−	18.8785i	0.814667	−	1.41104i	0.909567	−	0.415557i	$-0.136413\pi$
$180$		0			0
$181$	−9.89949			−0.735824			−0.367912	−	0.929861i	$-0.619927\pi$
$181$	−9.89949			−0.735824			−0.367912	+	0.929861i	$0.619927\pi$
$182$		0			0
$183$	−5.89949			−0.436103
$184$		0			0
$185$	−16.4853	+	28.5533i	−1.21202	+	2.09928i
$186$		0			0
$187$	−15.0711	−	26.1039i	−1.10211	−	1.90890i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.4142	−	18.0379i	−0.753546	−	1.30518i	−0.946094	−	0.323892i	$-0.895008\pi$
$191$	−10.4142	−	18.0379i	−0.753546	−	1.30518i	0.192548	−	0.981288i	$-0.438325\pi$
$192$		0			0
$193$	10.3137	−	17.8639i	0.742397	−	1.28587i	−0.209004	−	0.977915i	$-0.567022\pi$
$193$	10.3137	−	17.8639i	0.742397	−	1.28587i	0.951401	−	0.307955i	$-0.0996445\pi$
$194$		0			0
$195$	−4.82843			−0.345771
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−2.82843	+	4.89898i	−0.200502	+	0.347279i	−0.948690	−	0.316207i	$-0.897591\pi$
$199$	−2.82843	+	4.89898i	−0.200502	+	0.347279i	0.748188	+	0.663486i	$0.230924\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.82843	+	10.0951i	0.407075	+	0.705075i
$206$		0			0
$207$	0.414214	−	0.717439i	0.0287898	−	0.0498655i
$208$		0			0
$209$	−5.65685			−0.391293
$210$		0			0
$211$	−25.6569			−1.76629			−0.883145	−	0.469099i	$-0.844579\pi$
$211$	−25.6569			−1.76629			−0.883145	+	0.469099i	$0.844579\pi$
$212$		0			0
$213$	2.41421	−	4.18154i	0.165419	−	0.286514i
$214$		0			0
$215$	−13.6569	−	23.6544i	−0.931390	−	1.61321i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.53553	−	2.65962i	−0.103762	−	0.179721i
$220$		0			0
$221$	4.41421	−	7.64564i	0.296932	−	0.514302i
$222$		0			0
$223$	2.34315			0.156909			0.0784543	−	0.996918i	$-0.475002\pi$
$223$	2.34315			0.156909			0.0784543	+	0.996918i	$0.475002\pi$
$224$		0			0
$225$	6.65685			0.443790
$226$		0			0
$227$	9.89949	−	17.1464i	0.657053	−	1.13805i	−0.324322	−	0.945947i	$-0.605136\pi$
$227$	9.89949	−	17.1464i	0.657053	−	1.13805i	0.981375	−	0.192102i	$-0.0615304\pi$
$228$		0			0
$229$	0.464466	+	0.804479i	0.0306928	+	0.0531615i	0.880964	−	0.473184i	$-0.156895\pi$
$229$	0.464466	+	0.804479i	0.0306928	+	0.0531615i	−0.850271	+	0.526345i	$0.823562\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.75736	+	9.97204i	0.377177	+	0.653290i	0.990650	−	0.136426i	$-0.0435615\pi$
$233$	5.75736	+	9.97204i	0.377177	+	0.653290i	−0.613473	+	0.789716i	$0.710228\pi$
$234$		0			0
$235$	−2.00000	+	3.46410i	−0.130466	+	0.225973i
$236$		0			0
$237$	13.6569			0.887108
$238$		0			0
$239$	−8.82843			−0.571063			−0.285532	−	0.958369i	$-0.592170\pi$
$239$	−8.82843			−0.571063			−0.285532	+	0.958369i	$0.592170\pi$
$240$		0			0
$241$	−1.05025	+	1.81909i	−0.0676527	+	0.117178i	−0.897868	−	0.440265i	$-0.854884\pi$
$241$	−1.05025	+	1.81909i	−0.0676527	+	0.117178i	0.830215	+	0.557443i	$0.188218\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.828427	−	1.43488i	−0.0527116	−	0.0912991i
$248$		0			0
$249$	3.65685	−	6.33386i	0.231744	−	0.401392i
$250$		0			0
$251$	8.48528			0.535586			0.267793	−	0.963476i	$-0.413706\pi$
$251$	8.48528			0.535586			0.267793	+	0.963476i	$0.413706\pi$
$252$		0			0
$253$	−4.00000			−0.251478
$254$		0			0
$255$	−10.6569	+	18.4582i	−0.667358	+	1.15590i
$256$		0			0
$257$	−10.8787	−	18.8424i	−0.678593	−	1.17536i	−0.975405	−	0.220422i	$-0.929257\pi$
$257$	−10.8787	−	18.8424i	−0.678593	−	1.17536i	0.296811	−	0.954936i	$-0.404077\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.24264	+	7.34847i	0.262613	+	0.454859i
$262$		0			0
$263$	−9.58579	+	16.6031i	−0.591085	+	1.02379i	0.403002	+	0.915199i	$0.367967\pi$
$263$	−9.58579	+	16.6031i	−0.591085	+	1.02379i	−0.994087	+	0.108590i	$0.965366\pi$
$264$		0			0
$265$	−31.7990			−1.95340
$266$		0			0
$267$	14.7279			0.901334
$268$		0			0
$269$	−9.02082	+	15.6245i	−0.550009	+	0.952643i	0.448264	+	0.893901i	$0.352042\pi$
$269$	−9.02082	+	15.6245i	−0.550009	+	0.952643i	−0.998273	+	0.0587422i	$0.981291\pi$
$270$		0			0
$271$	−9.41421	−	16.3059i	−0.571873	−	0.990513i	−0.996374	−	0.0850852i	$-0.972884\pi$
$271$	−9.41421	−	16.3059i	−0.571873	−	0.990513i	0.424501	−	0.905427i	$-0.360450\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−16.0711	−	27.8359i	−0.969122	−	1.67857i
$276$		0			0
$277$	3.00000	−	5.19615i	0.180253	−	0.312207i	−0.761714	−	0.647913i	$-0.775642\pi$
$277$	3.00000	−	5.19615i	0.180253	−	0.312207i	0.941966	+	0.335707i	$0.108975\pi$
$278$		0			0
$279$	−10.8284			−0.648281
$280$		0			0
$281$	4.48528			0.267569			0.133785	−	0.991010i	$-0.457287\pi$
$281$	4.48528			0.267569			0.133785	+	0.991010i	$0.457287\pi$
$282$		0			0
$283$	−4.58579	+	7.94282i	−0.272597	+	0.472151i	−0.969526	−	0.244989i	$-0.921216\pi$
$283$	−4.58579	+	7.94282i	−0.272597	+	0.472151i	0.696929	+	0.717140i	$0.254549\pi$
$284$		0			0
$285$	2.00000	+	3.46410i	0.118470	+	0.205196i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−10.9853	−	19.0271i	−0.646193	−	1.11924i
$290$		0			0
$291$	8.12132	−	14.0665i	0.476080	−	0.824595i
$292$		0			0
$293$	13.0711			0.763620			0.381810	−	0.924241i	$-0.375301\pi$
$293$	13.0711			0.763620			0.381810	+	0.924241i	$0.375301\pi$
$294$		0			0
$295$	36.9706			2.15251
$296$		0			0
$297$	2.41421	−	4.18154i	0.140087	−	0.242638i
$298$		0			0
$299$	−0.585786	−	1.01461i	−0.0338769	−	0.0586765i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−0.292893	−	0.507306i	−0.0168263	−	0.0291440i
$304$		0			0
$305$	10.0711	−	17.4436i	0.576668	−	0.998818i
$306$		0			0
$307$	28.4853			1.62574			0.812870	−	0.582445i	$-0.197904\pi$
$307$	28.4853			1.62574			0.812870	+	0.582445i	$0.197904\pi$
$308$		0			0
$309$	5.17157			0.294201
$310$		0			0
$311$	1.07107	−	1.85514i	0.0607347	−	0.105196i	−0.834059	−	0.551675i	$-0.813989\pi$
$311$	1.07107	−	1.85514i	0.0607347	−	0.105196i	0.894794	+	0.446479i	$0.147322\pi$
$312$		0			0
$313$	−7.29289	−	12.6317i	−0.412219	−	0.713984i	0.582913	−	0.812534i	$-0.301913\pi$
$313$	−7.29289	−	12.6317i	−0.412219	−	0.713984i	−0.995132	+	0.0985506i	$0.968579\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.656854	+	1.13770i	0.0368926	+	0.0638999i	0.883882	−	0.467710i	$-0.154921\pi$
$317$	0.656854	+	1.13770i	0.0368926	+	0.0638999i	−0.846990	+	0.531610i	$0.821587\pi$
$318$		0			0
$319$	20.4853	−	35.4815i	1.14696	−	1.98659i
$320$		0			0
$321$	2.48528			0.138715
$322$		0			0
$323$	−7.31371			−0.406946
$324$		0			0
$325$	4.70711	−	8.15295i	0.261103	−	0.452244i
$326$		0			0
$327$	5.65685	+	9.79796i	0.312825	+	0.541828i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	15.6569	+	27.1185i	0.860579	+	1.49057i	0.871371	+	0.490624i	$0.163231\pi$
$331$	15.6569	+	27.1185i	0.860579	+	1.49057i	−0.0107928	+	0.999942i	$0.503436\pi$
$332$		0			0
$333$	4.82843	−	8.36308i	0.264596	−	0.458294i
$334$		0			0
$335$	27.3137			1.49231
$336$		0			0
$337$	16.9706			0.924445			0.462223	−	0.886764i	$-0.347052\pi$
$337$	16.9706			0.924445			0.462223	+	0.886764i	$0.347052\pi$
$338$		0			0
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$		0			0
$341$	26.1421	+	45.2795i	1.41568	+	2.45202i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.41421	+	2.44949i	0.0761387	+	0.131876i
$346$		0			0
$347$	−12.0711	+	20.9077i	−0.648009	+	1.12238i	0.335589	+	0.942009i	$0.391065\pi$
$347$	−12.0711	+	20.9077i	−0.648009	+	1.12238i	−0.983598	+	0.180376i	$0.942269\pi$
$348$		0			0
$349$	6.38478			0.341769			0.170885	−	0.985291i	$-0.445337\pi$
$349$	6.38478			0.341769			0.170885	+	0.985291i	$0.445337\pi$
$350$		0			0
$351$	1.41421			0.0754851
$352$		0			0
$353$	1.94975	−	3.37706i	0.103775	−	0.179743i	−0.809462	−	0.587172i	$-0.800241\pi$
$353$	1.94975	−	3.37706i	0.103775	−	0.179743i	0.913237	+	0.407429i	$0.133575\pi$
$354$		0			0
$355$	8.24264	+	14.2767i	0.437474	+	0.757727i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.72792	−	13.3852i	−0.407864	−	0.706441i	0.586786	−	0.809742i	$-0.300393\pi$
$359$	−7.72792	−	13.3852i	−0.407864	−	0.706441i	−0.994650	+	0.103301i	$0.967060\pi$
$360$		0			0
$361$	8.81371	−	15.2658i	0.463879	−	0.803463i
$362$		0			0
$363$	−12.3137			−0.646302
$364$		0			0
$365$	10.4853			0.548825
$366$		0			0
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$		0			0
$369$	−1.70711	−	2.95680i	−0.0888684	−	0.153925i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−18.6569	−	32.3146i	−0.966015	−	1.67319i	−0.706862	−	0.707351i	$-0.749890\pi$
$373$	−18.6569	−	32.3146i	−0.966015	−	1.67319i	−0.259153	−	0.965836i	$-0.583443\pi$
$374$		0			0
$375$	−2.82843	+	4.89898i	−0.146059	+	0.252982i
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	−23.3137			−1.19754			−0.598772	−	0.800919i	$-0.704345\pi$
$379$	−23.3137			−1.19754			−0.598772	+	0.800919i	$0.704345\pi$
$380$		0			0
$381$	3.65685	−	6.33386i	0.187346	−	0.324493i
$382$		0			0
$383$	−4.48528	−	7.76874i	−0.229187	−	0.396964i	0.728380	−	0.685173i	$-0.240273\pi$
$383$	−4.48528	−	7.76874i	−0.229187	−	0.396964i	−0.957567	+	0.288209i	$0.906940\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.00000	+	6.92820i	0.203331	+	0.352180i
$388$		0			0
$389$	−7.07107	+	12.2474i	−0.358517	+	0.620970i	−0.987713	−	0.156276i	$-0.950051\pi$
$389$	−7.07107	+	12.2474i	−0.358517	+	0.620970i	0.629196	+	0.777247i	$0.283384\pi$
$390$		0			0
$391$	−5.17157			−0.261538
$392$		0			0
$393$	15.3137			0.772474
$394$		0			0
$395$	−23.3137	+	40.3805i	−1.17304	+	2.03176i
$396$		0			0
$397$	16.3640	+	28.3432i	0.821284	+	1.42251i	0.904727	+	0.425992i	$0.140075\pi$
$397$	16.3640	+	28.3432i	0.821284	+	1.42251i	−0.0834430	+	0.996513i	$0.526592\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.24264	−	3.88437i	−0.111992	−	0.193976i	0.804581	−	0.593843i	$-0.202390\pi$
$401$	−2.24264	−	3.88437i	−0.111992	−	0.193976i	−0.916573	+	0.399867i	$0.869056\pi$
$402$		0			0
$403$	−7.65685	+	13.2621i	−0.381415	+	0.660630i
$404$		0			0
$405$	−3.41421			−0.169654
$406$		0			0
$407$	−46.6274			−2.31124
$408$		0			0
$409$	3.87868	−	6.71807i	0.191788	−	0.332187i	−0.754055	−	0.656812i	$-0.771905\pi$
$409$	3.87868	−	6.71807i	0.191788	−	0.332187i	0.945843	+	0.324625i	$0.105238\pi$
$410$		0			0
$411$	−6.24264	−	10.8126i	−0.307927	−	0.533345i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	12.4853	+	21.6251i	0.612878	+	1.06154i
$416$		0			0
$417$	−4.82843	+	8.36308i	−0.236449	+	0.409542i
$418$		0			0
$419$	−5.17157			−0.252648			−0.126324	−	0.991989i	$-0.540318\pi$
$419$	−5.17157			−0.252648			−0.126324	+	0.991989i	$0.540318\pi$
$420$		0			0
$421$	29.3137			1.42866			0.714331	−	0.699808i	$-0.246731\pi$
$421$	29.3137			1.42866			0.714331	+	0.699808i	$0.246731\pi$
$422$		0			0
$423$	0.585786	−	1.01461i	0.0284819	−	0.0493321i
$424$		0			0
$425$	−20.7782	−	35.9889i	−1.00789	−	1.74572i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−3.41421	−	5.91359i	−0.164840	−	0.285511i
$430$		0			0
$431$	6.75736	−	11.7041i	0.325491	−	0.563766i	−0.656121	−	0.754656i	$-0.727804\pi$
$431$	6.75736	−	11.7041i	0.325491	−	0.563766i	0.981612	+	0.190890i	$0.0611372\pi$
$432$		0			0
$433$	10.3848			0.499061			0.249530	−	0.968367i	$-0.419724\pi$
$433$	10.3848			0.499061			0.249530	+	0.968367i	$0.419724\pi$
$434$		0			0
$435$	−28.9706			−1.38903
$436$		0			0
$437$	−0.485281	+	0.840532i	−0.0232142	+	0.0402081i
$438$		0			0
$439$	9.65685	+	16.7262i	0.460897	+	0.798296i	0.999006	−	0.0445789i	$-0.0141946\pi$
$439$	9.65685	+	16.7262i	0.460897	+	0.798296i	−0.538109	+	0.842875i	$0.680861\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.7574	−	18.6323i	−0.511098	−	0.885247i	−0.999917	−	0.0128621i	$-0.995906\pi$
$443$	−10.7574	−	18.6323i	−0.511098	−	0.885247i	0.488820	−	0.872385i	$-0.337428\pi$
$444$		0			0
$445$	−25.1421	+	43.5475i	−1.19185	+	2.06435i
$446$		0			0
$447$	10.0000			0.472984
$448$		0			0
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$		0			0
$451$	−8.24264	+	14.2767i	−0.388131	+	0.672262i
$452$		0			0
$453$	−0.828427	−	1.43488i	−0.0389229	−	0.0674164i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	12.3137	+	21.3280i	0.576011	+	0.997680i	0.995931	+	0.0901192i	$0.0287248\pi$
$457$	12.3137	+	21.3280i	0.576011	+	0.997680i	−0.419920	+	0.907561i	$0.637942\pi$
$458$		0			0
$459$	3.12132	−	5.40629i	0.145691	−	0.252344i
$460$		0			0
$461$	−9.75736			−0.454446			−0.227223	−	0.973843i	$-0.572965\pi$
$461$	−9.75736			−0.454446			−0.227223	+	0.973843i	$0.572965\pi$
$462$		0			0
$463$	−12.9706			−0.602793			−0.301397	−	0.953499i	$-0.597453\pi$
$463$	−12.9706			−0.602793			−0.301397	+	0.953499i	$0.597453\pi$
$464$		0			0
$465$	18.4853	−	32.0174i	0.857234	−	1.48477i
$466$		0			0
$467$	−2.58579	−	4.47871i	−0.119656	−	0.207250i	0.799975	−	0.600033i	$-0.204846\pi$
$467$	−2.58579	−	4.47871i	−0.119656	−	0.207250i	−0.919631	+	0.392783i	$0.871512\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.94975	−	5.10911i	−0.135917	−	0.235415i
$472$		0			0
$473$	19.3137	−	33.4523i	0.888045	−	1.53814i
$474$		0			0
$475$	−7.79899			−0.357842
$476$		0			0
$477$	9.31371			0.426445
$478$		0			0
$479$	9.55635	−	16.5521i	0.436641	−	0.756284i	−0.560787	−	0.827960i	$-0.689501\pi$
$479$	9.55635	−	16.5521i	0.436641	−	0.756284i	0.997428	+	0.0716760i	$0.0228348\pi$
$480$		0			0
$481$	−6.82843	−	11.8272i	−0.311349	−	0.539273i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	27.7279	+	48.0262i	1.25906	+	2.18076i
$486$		0			0
$487$	−6.48528	+	11.2328i	−0.293876	+	0.509008i	−0.974723	−	0.223418i	$-0.928279\pi$
$487$	−6.48528	+	11.2328i	−0.293876	+	0.509008i	0.680847	+	0.732426i	$0.261612\pi$
$488$		0			0
$489$	2.34315			0.105961
$490$		0			0
$491$	−4.14214			−0.186932			−0.0934660	−	0.995622i	$-0.529795\pi$
$491$	−4.14214			−0.186932			−0.0934660	+	0.995622i	$0.529795\pi$
$492$		0			0
$493$	26.4853	−	45.8739i	1.19284	−	2.06605i
$494$		0			0
$495$	8.24264	+	14.2767i	0.370479	+	0.641689i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−14.1421	−	24.4949i	−0.633089	−	1.09654i	−0.986917	−	0.161232i	$-0.948453\pi$
$499$	−14.1421	−	24.4949i	−0.633089	−	1.09654i	0.353828	−	0.935311i	$-0.384880\pi$
$500$		0			0
$501$	−3.41421	+	5.91359i	−0.152536	+	0.264200i
$502$		0			0
$503$	−30.6274			−1.36561			−0.682805	−	0.730601i	$-0.739240\pi$
$503$	−30.6274			−1.36561			−0.682805	+	0.730601i	$0.739240\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$		0			0
$507$	−5.50000	+	9.52628i	−0.244264	+	0.423077i
$508$		0			0
$509$	11.4645	+	19.8570i	0.508154	+	0.880148i	0.999955	+	0.00944061i	$0.00300508\pi$
$509$	11.4645	+	19.8570i	0.508154	+	0.880148i	−0.491802	+	0.870707i	$0.663662\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−0.585786	−	1.01461i	−0.0258631	−	0.0447962i
$514$		0			0
$515$	−8.82843	+	15.2913i	−0.389027	+	0.673814i
$516$		0			0
$517$	−5.65685			−0.248788
$518$		0			0
$519$	−0.585786			−0.0257132
$520$		0			0
$521$	2.63604	−	4.56575i	0.115487	−	0.200029i	−0.802487	−	0.596669i	$-0.796490\pi$
$521$	2.63604	−	4.56575i	0.115487	−	0.200029i	0.917974	+	0.396640i	$0.129824\pi$
$522$		0			0
$523$	−0.828427	−	1.43488i	−0.0362246	−	0.0627428i	0.847345	−	0.531043i	$-0.178200\pi$
$523$	−0.828427	−	1.43488i	−0.0362246	−	0.0627428i	−0.883569	+	0.468300i	$0.844867\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	33.7990	+	58.5416i	1.47231	+	2.55011i
$528$		0			0
$529$	11.1569	−	19.3242i	0.485081	−	0.840184i
$530$		0			0
$531$	−10.8284			−0.469914
$532$		0			0
$533$	−4.82843			−0.209142
$534$		0			0
$535$	−4.24264	+	7.34847i	−0.183425	+	0.317702i
$536$		0			0
$537$	−10.8995	−	18.8785i	−0.470348	−	0.814667i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.31371	+	7.47156i	0.185461	+	0.321228i	0.943732	−	0.330712i	$-0.107289\pi$
$541$	4.31371	+	7.47156i	0.185461	+	0.321228i	−0.758271	+	0.651940i	$0.773956\pi$
$542$		0			0
$543$	−4.94975	+	8.57321i	−0.212414	+	0.367912i
$544$		0			0
$545$	−38.6274			−1.65462
$546$		0			0
$547$	−4.97056			−0.212526			−0.106263	−	0.994338i	$-0.533889\pi$
$547$	−4.97056			−0.212526			−0.106263	+	0.994338i	$0.533889\pi$
$548$		0			0
$549$	−2.94975	+	5.10911i	−0.125892	+	0.218052i
$550$		0			0
$551$	−4.97056	−	8.60927i	−0.211753	−	0.366767i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	16.4853	+	28.5533i	0.699761	+	1.21202i
$556$		0			0
$557$	−21.9706	+	38.0541i	−0.930923	+	1.61241i	−0.149175	+	0.988811i	$0.547662\pi$
$557$	−21.9706	+	38.0541i	−0.930923	+	1.61241i	−0.781748	+	0.623594i	$0.785672\pi$
$558$		0			0
$559$	11.3137			0.478519
$560$		0			0
$561$	−30.1421			−1.27260
$562$		0			0
$563$	13.4142	−	23.2341i	0.565342	−	0.979201i	−0.431676	−	0.902029i	$-0.642078\pi$
$563$	13.4142	−	23.2341i	0.565342	−	0.979201i	0.997018	−	0.0771719i	$-0.0245890\pi$
$564$		0			0
$565$	10.2426	+	17.7408i	0.430911	+	0.746360i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.41421	−	5.91359i	−0.143131	−	0.247911i	0.785543	−	0.618807i	$-0.212384\pi$
$569$	−3.41421	−	5.91359i	−0.143131	−	0.247911i	−0.928674	+	0.370897i	$0.879050\pi$
$570$		0			0
$571$	−20.1421	+	34.8872i	−0.842922	+	1.45998i	0.0444914	+	0.999010i	$0.485833\pi$
$571$	−20.1421	+	34.8872i	−0.842922	+	1.45998i	−0.887414	+	0.460974i	$0.847500\pi$
$572$		0			0
$573$	−20.8284			−0.870120
$574$		0			0
$575$	−5.51472			−0.229980
$576$		0			0
$577$	−4.70711	+	8.15295i	−0.195959	+	0.339412i	−0.947215	−	0.320600i	$-0.896115\pi$
$577$	−4.70711	+	8.15295i	−0.195959	+	0.339412i	0.751255	+	0.660012i	$0.229449\pi$
$578$		0			0
$579$	−10.3137	−	17.8639i	−0.428623	−	0.742397i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−22.4853	−	38.9456i	−0.931245	−	1.61296i
$584$		0			0
$585$	−2.41421	+	4.18154i	−0.0998154	+	0.172885i
$586$		0			0
$587$	26.8284			1.10733			0.553664	−	0.832740i	$-0.313229\pi$
$587$	26.8284			1.10733			0.553664	+	0.832740i	$0.313229\pi$
$588$		0			0
$589$	12.6863			0.522730
$590$		0			0
$591$	1.00000	−	1.73205i	0.0411345	−	0.0712470i
$592$		0			0
$593$	14.5355	+	25.1763i	0.596903	+	1.03387i	0.993275	+	0.115776i	$0.0369356\pi$
$593$	14.5355	+	25.1763i	0.596903	+	1.03387i	−0.396372	+	0.918090i	$0.629731\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.82843	+	4.89898i	0.115760	+	0.200502i
$598$		0			0
$599$	−8.07107	+	13.9795i	−0.329775	+	0.571187i	−0.982467	−	0.186436i	$-0.940306\pi$
$599$	−8.07107	+	13.9795i	−0.329775	+	0.571187i	0.652692	+	0.757623i	$0.273640\pi$
$600$		0			0
$601$	12.2426			0.499388			0.249694	−	0.968325i	$-0.419670\pi$
$601$	12.2426			0.499388			0.249694	+	0.968325i	$0.419670\pi$
$602$		0			0
$603$	−8.00000			−0.325785
$604$		0			0
$605$	21.0208	−	36.4091i	0.854618	−	1.48024i
$606$		0			0
$607$	15.7990	+	27.3647i	0.641261	+	1.11070i	0.985152	+	0.171687i	$0.0549218\pi$
$607$	15.7990	+	27.3647i	0.641261	+	1.11070i	−0.343890	+	0.939010i	$0.611745\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.828427	−	1.43488i	−0.0335146	−	0.0580489i
$612$		0			0
$613$	1.17157	−	2.02922i	0.0473194	−	0.0819596i	−0.841396	−	0.540420i	$-0.818265\pi$
$613$	1.17157	−	2.02922i	0.0473194	−	0.0819596i	0.888715	+	0.458460i	$0.151599\pi$
$614$		0			0
$615$	11.6569			0.470050
$616$		0			0
$617$	21.4558			0.863780			0.431890	−	0.901926i	$-0.357847\pi$
$617$	21.4558			0.863780			0.431890	+	0.901926i	$0.357847\pi$
$618$		0			0
$619$	−20.1421	+	34.8872i	−0.809581	+	1.40224i	0.103574	+	0.994622i	$0.466972\pi$
$619$	−20.1421	+	34.8872i	−0.809581	+	1.40224i	−0.913155	+	0.407613i	$0.866361\pi$
$620$		0			0
$621$	−0.414214	−	0.717439i	−0.0166218	−	0.0287898i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$		0			0
$627$	−2.82843	+	4.89898i	−0.112956	+	0.195646i
$628$		0			0
$629$	−60.2843			−2.40369
$630$		0			0
$631$	−8.28427			−0.329792			−0.164896	−	0.986311i	$-0.552729\pi$
$631$	−8.28427			−0.329792			−0.164896	+	0.986311i	$0.552729\pi$
$632$		0			0
$633$	−12.8284	+	22.2195i	−0.509884	+	0.883145i
$634$		0			0
$635$	12.4853	+	21.6251i	0.495463	+	0.858168i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−2.41421	−	4.18154i	−0.0955048	−	0.165419i
$640$		0			0
$641$	−12.5858	+	21.7992i	−0.497109	+	0.861017i	−0.999994	−	0.00333540i	$-0.998938\pi$
$641$	−12.5858	+	21.7992i	−0.497109	+	0.861017i	0.502886	+	0.864353i	$0.332272\pi$
$642$		0			0
$643$	−19.5147			−0.769585			−0.384793	−	0.923003i	$-0.625727\pi$
$643$	−19.5147			−0.769585			−0.384793	+	0.923003i	$0.625727\pi$
$644$		0			0
$645$	−27.3137			−1.07548
$646$		0			0
$647$	7.41421	−	12.8418i	0.291483	−	0.504863i	−0.682678	−	0.730720i	$-0.739185\pi$
$647$	7.41421	−	12.8418i	0.291483	−	0.504863i	0.974161	+	0.225857i	$0.0725181\pi$
$648$		0			0
$649$	26.1421	+	45.2795i	1.02617	+	1.77738i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.41421	−	2.44949i	−0.0553425	−	0.0958559i	0.837027	−	0.547162i	$-0.184292\pi$
$653$	−1.41421	−	2.44949i	−0.0553425	−	0.0958559i	−0.892369	+	0.451306i	$0.850958\pi$
$654$		0			0
$655$	−26.1421	+	45.2795i	−1.02146	+	1.76922i
$656$		0			0
$657$	−3.07107			−0.119814
$658$		0			0
$659$	25.5147			0.993912			0.496956	−	0.867776i	$-0.334451\pi$
$659$	25.5147			0.993912			0.496956	+	0.867776i	$0.334451\pi$
$660$		0			0
$661$	−11.6777	+	20.2263i	−0.454209	+	0.786713i	−0.998642	−	0.0520914i	$-0.983411\pi$
$661$	−11.6777	+	20.2263i	−0.454209	+	0.786713i	0.544434	+	0.838804i	$0.316745\pi$
$662$		0			0
$663$	−4.41421	−	7.64564i	−0.171434	−	0.296932i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.51472	−	6.08767i	−0.136090	−	0.235716i
$668$		0			0
$669$	1.17157	−	2.02922i	0.0452956	−	0.0784543i
$670$		0			0
$671$	28.4853			1.09966
$672$		0			0
$673$	15.3137			0.590300			0.295150	−	0.955451i	$-0.404630\pi$
$673$	15.3137			0.590300			0.295150	+	0.955451i	$0.404630\pi$
$674$		0			0
$675$	3.32843	−	5.76500i	0.128111	−	0.221895i
$676$		0			0
$677$	−0.778175	−	1.34784i	−0.0299077	−	0.0518016i	0.850684	−	0.525677i	$-0.176188\pi$
$677$	−0.778175	−	1.34784i	−0.0299077	−	0.0518016i	−0.880592	+	0.473876i	$0.842855\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−9.89949	−	17.1464i	−0.379349	−	0.657053i
$682$		0			0
$683$	−6.07107	+	10.5154i	−0.232303	+	0.402361i	−0.958485	−	0.285141i	$-0.907959\pi$
$683$	−6.07107	+	10.5154i	−0.232303	+	0.402361i	0.726182	+	0.687502i	$0.241293\pi$
$684$		0			0
$685$	42.6274			1.62871
$686$		0			0
$687$	0.928932			0.0354410
$688$		0			0
$689$	6.58579	−	11.4069i	0.250898	−	0.434569i
$690$		0			0
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16.4853	−	28.5533i	−0.625322	−	1.08309i
$696$		0			0
$697$	−10.6569	+	18.4582i	−0.403657	+	0.699155i
$698$		0			0
$699$	11.5147			0.435527
$700$		0			0
$701$	−10.8284			−0.408984			−0.204492	−	0.978868i	$-0.565554\pi$
$701$	−10.8284			−0.408984			−0.204492	+	0.978868i	$0.565554\pi$
$702$		0			0
$703$	−5.65685	+	9.79796i	−0.213352	+	0.369537i
$704$		0			0
$705$	2.00000	+	3.46410i	0.0753244	+	0.130466i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	4.00000	+	6.92820i	0.150223	+	0.260194i	0.931309	−	0.364229i	$-0.118667\pi$
$709$	4.00000	+	6.92820i	0.150223	+	0.260194i	−0.781086	+	0.624423i	$0.785334\pi$
$710$		0			0
$711$	6.82843	−	11.8272i	0.256086	−	0.443554i
$712$		0			0
$713$	8.97056			0.335950
$714$		0			0
$715$	23.3137			0.871883
$716$		0			0
$717$	−4.41421	+	7.64564i	−0.164852	+	0.285532i
$718$		0			0
$719$	−13.6569	−	23.6544i	−0.509315	−	0.882159i	−0.999942	−	0.0107893i	$-0.996566\pi$
$719$	−13.6569	−	23.6544i	−0.509315	−	0.882159i	0.490627	−	0.871370i	$-0.336768\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.05025	+	1.81909i	0.0390593	+	0.0676527i
$724$		0			0
$725$	28.2426	−	48.9177i	1.04891	−	1.81676i
$726$		0			0
$727$	25.4558			0.944105			0.472052	−	0.881570i	$-0.343513\pi$
$727$	25.4558			0.944105			0.472052	+	0.881570i	$0.343513\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	24.9706	−	43.2503i	0.923570	−	1.59967i
$732$		0			0
$733$	10.1213	+	17.5306i	0.373839	+	0.647509i	0.990153	−	0.139992i	$-0.0447078\pi$
$733$	10.1213	+	17.5306i	0.373839	+	0.647509i	−0.616313	+	0.787501i	$0.711374\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.3137	+	33.4523i	0.711430	+	1.23223i
$738$		0			0
$739$	18.1421	−	31.4231i	0.667369	−	1.15592i	−0.311268	−	0.950322i	$-0.600754\pi$
$739$	18.1421	−	31.4231i	0.667369	−	1.15592i	0.978637	−	0.205595i	$-0.0659130\pi$
$740$		0			0
$741$	−1.65685			−0.0608661
$742$		0			0
$743$	−16.8284			−0.617375			−0.308688	−	0.951163i	$-0.599890\pi$
$743$	−16.8284			−0.617375			−0.308688	+	0.951163i	$0.599890\pi$
$744$		0			0
$745$	−17.0711	+	29.5680i	−0.625436	+	1.08329i
$746$		0			0
$747$	−3.65685	−	6.33386i	−0.133797	−	0.231744i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−9.17157	−	15.8856i	−0.334675	−	0.579675i	0.648747	−	0.761004i	$-0.275293\pi$
$751$	−9.17157	−	15.8856i	−0.334675	−	0.579675i	−0.983422	+	0.181329i	$0.941960\pi$
$752$		0			0
$753$	4.24264	−	7.34847i	0.154610	−	0.267793i
$754$		0			0
$755$	5.65685			0.205874
$756$		0			0
$757$	11.3137			0.411204			0.205602	−	0.978636i	$-0.434085\pi$
$757$	11.3137			0.411204			0.205602	+	0.978636i	$0.434085\pi$
$758$		0			0
$759$	−2.00000	+	3.46410i	−0.0725954	+	0.125739i
$760$		0			0
$761$	−9.12132	−	15.7986i	−0.330648	−	0.572698i	0.651991	−	0.758226i	$-0.273934\pi$
$761$	−9.12132	−	15.7986i	−0.330648	−	0.572698i	−0.982639	+	0.185528i	$0.940600\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	10.6569	+	18.4582i	0.385299	+	0.667358i
$766$		0			0
$767$	−7.65685	+	13.2621i	−0.276473	+	0.478865i
$768$		0			0
$769$	−0.928932			−0.0334982			−0.0167491	−	0.999860i	$-0.505332\pi$
$769$	−0.928932			−0.0334982			−0.0167491	+	0.999860i	$0.505332\pi$
$770$		0			0
$771$	−21.7574			−0.783572
$772$		0			0
$773$	−0.292893	+	0.507306i	−0.0105346	+	0.0182465i	−0.871245	−	0.490849i	$-0.836687\pi$
$773$	−0.292893	+	0.507306i	−0.0105346	+	0.0182465i	0.860710	+	0.509096i	$0.170020\pi$
$774$		0			0
$775$	36.0416	+	62.4259i	1.29465	+	2.24241i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.00000	+	3.46410i	0.0716574	+	0.124114i
$780$		0			0
$781$	−11.6569	+	20.1903i	−0.417115	+	0.722464i
$782$		0			0
$783$	8.48528			0.303239
$784$		0			0
$785$	20.1421			0.718904
$786$		0			0
$787$	17.3137	−	29.9882i	0.617167	−	1.06896i	−0.372833	−	0.927898i	$-0.621614\pi$
$787$	17.3137	−	29.9882i	0.617167	−	1.06896i	0.990000	−	0.141066i	$-0.0450531\pi$
$788$		0			0
$789$	9.58579	+	16.6031i	0.341263	+	0.591085i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.17157	+	7.22538i	0.148137	+	0.256581i
$794$		0			0
$795$	−15.8995	+	27.5387i	−0.563897	+	0.976698i
$796$		0			0
$797$	0.786797			0.0278698			0.0139349	−	0.999903i	$-0.495564\pi$
$797$	0.786797			0.0278698			0.0139349	+	0.999903i	$0.495564\pi$
$798$		0			0
$799$	−7.31371			−0.258740
$800$		0			0
$801$	7.36396	−	12.7548i	0.260193	−	0.450667i
$802$		0			0
$803$	7.41421	+	12.8418i	0.261642	+	0.453177i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.02082	+	15.6245i	0.317548	+	0.550009i
$808$		0			0
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$		0			0
$811$	−12.9706			−0.455458			−0.227729	−	0.973725i	$-0.573130\pi$
$811$	−12.9706			−0.455458			−0.227729	+	0.973725i	$0.573130\pi$
$812$		0			0
$813$	−18.8284			−0.660342
$814$		0			0
$815$	−4.00000	+	6.92820i	−0.140114	+	0.242684i
$816$		0			0
$817$	−4.68629	−	8.11689i	−0.163953	−	0.283974i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	0.765487	−	0.643451i	$-0.222498\pi$
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	−0.939989	+	0.341206i	$0.889165\pi$
$822$		0			0
$823$	6.82843	−	11.8272i	0.238024	−	0.412270i	−0.722123	−	0.691764i	$-0.756834\pi$
$823$	6.82843	−	11.8272i	0.238024	−	0.412270i	0.960147	+	0.279495i	$0.0901670\pi$
$824$		0			0
$825$	−32.1421			−1.11905
$826$		0			0
$827$	31.4558			1.09383			0.546913	−	0.837189i	$-0.315803\pi$
$827$	31.4558			1.09383			0.546913	+	0.837189i	$0.315803\pi$
$828$		0			0
$829$	14.3640	−	24.8791i	0.498881	−	0.864087i	−0.501118	−	0.865379i	$-0.667078\pi$
$829$	14.3640	−	24.8791i	0.498881	−	0.864087i	0.999999	+	0.00129164i	$0.000411143\pi$
$830$		0			0
$831$	−3.00000	−	5.19615i	−0.104069	−	0.180253i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−11.6569	−	20.1903i	−0.403402	−	0.698713i
$836$		0			0
$837$	−5.41421	+	9.37769i	−0.187143	+	0.324140i
$838$		0			0
$839$	−54.8284			−1.89289			−0.946444	−	0.322869i	$-0.895353\pi$
$839$	−54.8284			−1.89289			−0.946444	+	0.322869i	$0.895353\pi$
$840$		0			0
$841$	43.0000			1.48276
$842$		0			0
$843$	2.24264	−	3.88437i	0.0772406	−	0.133785i
$844$		0			0
$845$	−18.7782	−	32.5248i	−0.645989	−	1.11889i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.58579	+	7.94282i	0.157384	+	0.272597i
$850$		0			0
$851$	−4.00000	+	6.92820i	−0.137118	+	0.237496i
$852$		0			0
$853$	12.0416			0.412298			0.206149	−	0.978521i	$-0.433907\pi$
$853$	12.0416			0.412298			0.206149	+	0.978521i	$0.433907\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$		0			0
$857$	7.84924	−	13.5953i	0.268125	−	0.464406i	−0.700253	−	0.713895i	$-0.746929\pi$
$857$	7.84924	−	13.5953i	0.268125	−	0.464406i	0.968378	+	0.249489i	$0.0802626\pi$
$858$		0			0
$859$	−16.5858	−	28.7274i	−0.565900	−	0.980167i	−0.996965	−	0.0778465i	$-0.975196\pi$
$859$	−16.5858	−	28.7274i	−0.565900	−	0.980167i	0.431066	−	0.902321i	$-0.358138\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	23.2426	+	40.2574i	0.791189	+	1.37038i	0.925231	+	0.379403i	$0.123871\pi$
$863$	23.2426	+	40.2574i	0.791189	+	1.37038i	−0.134043	+	0.990976i	$0.542796\pi$
$864$		0			0
$865$	1.00000	−	1.73205i	0.0340010	−	0.0588915i
$866$		0			0
$867$	−21.9706			−0.746159
$868$		0			0
$869$	−65.9411			−2.23690
$870$		0			0
$871$	−5.65685	+	9.79796i	−0.191675	+	0.331991i
$872$		0			0
$873$	−8.12132	−	14.0665i	−0.274865	−	0.476080i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	18.1421	+	31.4231i	0.612616	+	1.06108i	0.990798	+	0.135351i	$0.0432163\pi$
$877$	18.1421	+	31.4231i	0.612616	+	1.06108i	−0.378181	+	0.925732i	$0.623450\pi$
$878$		0			0
$879$	6.53553	−	11.3199i	0.220438	−	0.381810i
$880$		0			0
$881$	10.9289			0.368205			0.184103	−	0.982907i	$-0.441062\pi$
$881$	10.9289			0.368205			0.184103	+	0.982907i	$0.441062\pi$
$882$		0			0
$883$	29.6569			0.998033			0.499016	−	0.866593i	$-0.333695\pi$
$883$	29.6569			0.998033			0.499016	+	0.866593i	$0.333695\pi$
$884$		0			0
$885$	18.4853	−	32.0174i	0.621376	−	1.07625i
$886$		0			0
$887$	−14.7279	−	25.5095i	−0.494515	−	0.856525i	0.505465	−	0.862847i	$-0.331321\pi$
$887$	−14.7279	−	25.5095i	−0.494515	−	0.856525i	−0.999980	+	0.00632174i	$0.997988\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.41421	−	4.18154i	−0.0808792	−	0.140087i
$892$		0			0
$893$	−0.686292	+	1.18869i	−0.0229659	+	0.0397781i
$894$		0			0
$895$	74.4264			2.48780
$896$		0			0
$897$	−1.17157			−0.0391177
$898$		0			0
$899$	−45.9411	+	79.5724i	−1.53222	+	2.65389i
$900$		0			0
$901$	−29.0711	−	50.3526i	−0.968498	−	1.67749i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−16.8995	−	29.2708i	−0.561758	−	0.972994i
$906$		0			0
$907$	20.4853	−	35.4815i	0.680203	−	1.17815i	−0.294716	−	0.955585i	$-0.595225\pi$
$907$	20.4853	−	35.4815i	0.680203	−	1.17815i	0.974919	−	0.222561i	$-0.0714415\pi$
$908$		0			0
$909$	−0.585786			−0.0194293
$910$		0			0
$911$	−37.5147			−1.24292			−0.621459	−	0.783447i	$-0.713460\pi$
$911$	−37.5147			−1.24292			−0.621459	+	0.783447i	$0.713460\pi$
$912$		0			0
$913$	−17.6569	+	30.5826i	−0.584357	+	1.01214i
$914$		0			0
$915$	−10.0711	−	17.4436i	−0.332939	−	0.576668i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−20.6274	−	35.7277i	−0.680436	−	1.17855i	−0.974848	−	0.222871i	$-0.928457\pi$
$919$	−20.6274	−	35.7277i	−0.680436	−	1.17855i	0.294412	−	0.955678i	$-0.404876\pi$
$920$		0			0
$921$	14.2426	−	24.6690i	0.469311	−	0.812870i
$922$		0			0
$923$	−6.82843			−0.224760
$924$		0			0
$925$	−64.2843			−2.11365
$926$		0			0
$927$	2.58579	−	4.47871i	0.0849284	−	0.147100i
$928$		0			0
$929$	3.56497	+	6.17471i	0.116963	+	0.202586i	0.918563	−	0.395275i	$-0.129351\pi$
$929$	3.56497	+	6.17471i	0.116963	+	0.202586i	−0.801600	+	0.597861i	$0.796017\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.07107	−	1.85514i	−0.0350652	−	0.0607347i
$934$		0			0
$935$	51.4558	−	89.1241i	1.68279	−	2.91467i
$936$		0			0
$937$	25.8995			0.846100			0.423050	−	0.906106i	$-0.360960\pi$
$937$	25.8995			0.846100			0.423050	+	0.906106i	$0.360960\pi$
$938$		0			0
$939$	−14.5858			−0.475989
$940$		0			0
$941$	−12.0503	+	20.8716i	−0.392827	+	0.680396i	−0.992821	−	0.119608i	$-0.961836\pi$
$941$	−12.0503	+	20.8716i	−0.392827	+	0.680396i	0.599994	+	0.800004i	$0.295170\pi$
$942$		0			0
$943$	1.41421	+	2.44949i	0.0460531	+	0.0797664i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.07107	+	7.05130i	0.132292	+	0.229136i	0.924560	−	0.381037i	$-0.124433\pi$
$947$	4.07107	+	7.05130i	0.132292	+	0.229136i	−0.792268	+	0.610174i	$0.791100\pi$
$948$		0			0
$949$	−2.17157	+	3.76127i	−0.0704922	+	0.122096i
$950$		0			0
$951$	1.31371			0.0425999
$952$		0			0
$953$	−52.6274			−1.70477			−0.852385	−	0.522915i	$-0.824844\pi$
$953$	−52.6274			−1.70477			−0.852385	+	0.522915i	$0.824844\pi$
$954$		0			0
$955$	35.5563	−	61.5854i	1.15058	−	1.99286i
$956$		0			0
$957$	−20.4853	−	35.4815i	−0.662195	−	1.14696i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−43.1274	−	74.6989i	−1.39121	−	2.40964i
$962$		0			0
$963$	1.24264	−	2.15232i	0.0400435	−	0.0693574i
$964$		0			0
$965$	70.4264			2.26711
$966$		0			0
$967$	10.6274			0.341755			0.170877	−	0.985292i	$-0.445340\pi$
$967$	10.6274			0.341755			0.170877	+	0.985292i	$0.445340\pi$
$968$		0			0
$969$	−3.65685	+	6.33386i	−0.117475	+	0.203473i
$970$		0			0
$971$	16.6274	+	28.7995i	0.533599	+	0.924221i	0.999230	+	0.0392417i	$0.0124942\pi$
$971$	16.6274	+	28.7995i	0.533599	+	0.924221i	−0.465631	+	0.884979i	$0.654172\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−4.70711	−	8.15295i	−0.150748	−	0.261103i
$976$		0			0
$977$	−25.0711	+	43.4244i	−0.802095	+	1.38927i	0.116141	+	0.993233i	$0.462948\pi$
$977$	−25.0711	+	43.4244i	−0.802095	+	1.38927i	−0.918235	+	0.396036i	$0.870386\pi$
$978$		0			0
$979$	−71.1127			−2.27277
$980$		0			0
$981$	11.3137			0.361219
$982$		0			0
$983$	15.3137	−	26.5241i	0.488431	−	0.845988i	−0.511480	−	0.859295i	$-0.670903\pi$
$983$	15.3137	−	26.5241i	0.488431	−	0.845988i	0.999911	+	0.0133071i	$0.00423590\pi$
$984$		0			0
$985$	3.41421	+	5.91359i	0.108786	+	0.188423i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.31371	−	5.73951i	−0.105370	−	0.182506i
$990$		0			0
$991$	−0.343146	+	0.594346i	−0.0109004	+	0.0188800i	−0.871424	−	0.490530i	$-0.836803\pi$
$991$	−0.343146	+	0.594346i	−0.0109004	+	0.0188800i	0.860524	+	0.509410i	$0.170136\pi$
$992$		0			0
$993$	31.3137			0.993711
$994$		0			0
$995$	−19.3137			−0.612286
$996$		0			0
$997$	−18.7071	+	32.4017i	−0.592460	+	1.02617i	0.401440	+	0.915885i	$0.368510\pi$
$997$	−18.7071	+	32.4017i	−0.592460	+	1.02617i	−0.993900	+	0.110285i	$0.964823\pi$
$998$		0			0
$999$	−4.82843	−	8.36308i	−0.152765	−	0.264596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.q.o.361.2		4
3.2	odd	2		3528.2.s.bd.361.1		4
4.3	odd	2		2352.2.q.bc.1537.2		4
7.2	even	3	inner	1176.2.q.o.961.2		4
7.3	odd	6		1176.2.a.o.1.2	yes	2
7.4	even	3		1176.2.a.j.1.1	✓	2
7.5	odd	6		1176.2.q.k.961.1		4
7.6	odd	2		1176.2.q.k.361.1		4
21.2	odd	6		3528.2.s.bd.3313.1		4
21.5	even	6		3528.2.s.bm.3313.2		4
21.11	odd	6		3528.2.a.bl.1.2		2
21.17	even	6		3528.2.a.bb.1.1		2
21.20	even	2		3528.2.s.bm.361.2		4
28.3	even	6		2352.2.a.bb.1.2		2
28.11	odd	6		2352.2.a.bd.1.1		2
28.19	even	6		2352.2.q.be.961.1		4
28.23	odd	6		2352.2.q.bc.961.2		4
28.27	even	2		2352.2.q.be.1537.1		4
56.3	even	6		9408.2.a.du.1.1		2
56.11	odd	6		9408.2.a.ds.1.2		2
56.45	odd	6		9408.2.a.dg.1.1		2
56.53	even	6		9408.2.a.ee.1.2		2
84.11	even	6		7056.2.a.cx.1.2		2
84.59	odd	6		7056.2.a.cg.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1176.2.a.j.1.1	✓	2	7.4	even	3
1176.2.a.o.1.2	yes	2	7.3	odd	6
1176.2.q.k.361.1		4	7.6	odd	2
1176.2.q.k.961.1		4	7.5	odd	6
1176.2.q.o.361.2		4	1.1	even	1	trivial
1176.2.q.o.961.2		4	7.2	even	3	inner
2352.2.a.bb.1.2		2	28.3	even	6
2352.2.a.bd.1.1		2	28.11	odd	6
2352.2.q.bc.961.2		4	28.23	odd	6
2352.2.q.bc.1537.2		4	4.3	odd	2
2352.2.q.be.961.1		4	28.19	even	6
2352.2.q.be.1537.1		4	28.27	even	2
3528.2.a.bb.1.1		2	21.17	even	6
3528.2.a.bl.1.2		2	21.11	odd	6
3528.2.s.bd.361.1		4	3.2	odd	2
3528.2.s.bd.3313.1		4	21.2	odd	6
3528.2.s.bm.361.2		4	21.20	even	2
3528.2.s.bm.3313.2		4	21.5	even	6
7056.2.a.cg.1.1		2	84.59	odd	6
7056.2.a.cx.1.2		2	84.11	even	6
9408.2.a.dg.1.1		2	56.45	odd	6
9408.2.a.ds.1.2		2	56.11	odd	6
9408.2.a.du.1.1		2	56.3	even	6
9408.2.a.ee.1.2		2	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.70711 + 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.70711 + 2.95680i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-2.41421 + 4.18154i) q^{11} -1.41421 q^{13} +3.41421 q^{15} +(-3.12132 + 5.40629i) q^{17} +(0.585786 + 1.01461i) q^{19} +(0.414214 + 0.717439i) q^{23} +(-3.32843 + 5.76500i) q^{25} -1.00000 q^{27} -8.48528 q^{29} +(5.41421 - 9.37769i) q^{31} +(2.41421 + 4.18154i) q^{33} +(4.82843 + 8.36308i) q^{37} +(-0.707107 + 1.22474i) q^{39} +3.41421 q^{41} -8.00000 q^{43} +(1.70711 - 2.95680i) q^{45} +(0.585786 + 1.01461i) q^{47} +(3.12132 + 5.40629i) q^{51} +(-4.65685 + 8.06591i) q^{53} -16.4853 q^{55} +1.17157 q^{57} +(5.41421 - 9.37769i) q^{59} +(-2.94975 - 5.10911i) q^{61} +(-2.41421 - 4.18154i) q^{65} +(4.00000 - 6.92820i) q^{67} +0.828427 q^{69} +4.82843 q^{71} +(1.53553 - 2.65962i) q^{73} +(3.32843 + 5.76500i) q^{75} +(6.82843 + 11.8272i) q^{79} +(-0.500000 + 0.866025i) q^{81} +7.31371 q^{83} -21.3137 q^{85} +(-4.24264 + 7.34847i) q^{87} +(7.36396 + 12.7548i) q^{89} +(-5.41421 - 9.37769i) q^{93} +(-2.00000 + 3.46410i) q^{95} +16.2426 q^{97} +4.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^9	\( 4 q + 2 q^{3} + 4 q^{5} - 2 q^{9} - 4 q^{11} + 8 q^{15} - 4 q^{17} + 8 q^{19} - 4 q^{23} - 2 q^{25} - 4 q^{27} + 16 q^{31} + 4 q^{33} + 8 q^{37} + 8 q^{41} - 32 q^{43} + 4 q^{45} + 8 q^{47} + 4 q^{51} + 4 q^{53} - 32 q^{55} + 16 q^{57} + 16 q^{59} + 8 q^{61} - 4 q^{65} + 16 q^{67} - 8 q^{69} + 8 q^{71} - 8 q^{73} + 2 q^{75} + 16 q^{79} - 2 q^{81} - 16 q^{83} - 40 q^{85} + 4 q^{89} - 16 q^{93} - 8 q^{95} + 48 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^5 - 2 * q^9 - 4 * q^11 + 8 * q^15 - 4 * q^17 + 8 * q^19 - 4 * q^23 - 2 * q^25 - 4 * q^27 + 16 * q^31 + 4 * q^33 + 8 * q^37 + 8 * q^41 - 32 * q^43 + 4 * q^45 + 8 * q^47 + 4 * q^51 + 4 * q^53 - 32 * q^55 + 16 * q^57 + 16 * q^59 + 8 * q^61 - 4 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 8 * q^73 + 2 * q^75 + 16 * q^79 - 2 * q^81 - 16 * q^83 - 40 * q^85 + 4 * q^89 - 16 * q^93 - 8 * q^95 + 48 * q^97 + 8 * q^99

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