LMFDB - Embedded newform 1352.2.i.c.1329.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1352,2,Mod(529,1352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1352.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1352 = 2^{3} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1352.i (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:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1329.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1352.1329
Dual form			1352.2.i.c.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(2.50000 - 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{19} -5.00000 q^{21} +(-2.00000 - 3.46410i) q^{23} -4.00000 q^{25} -5.00000 q^{27} +(3.00000 + 5.19615i) q^{29} +4.00000 q^{31} +(-1.00000 + 1.73205i) q^{33} +(2.50000 - 4.33013i) q^{35} +(5.50000 + 9.52628i) q^{37} +(4.00000 + 6.92820i) q^{41} +(0.500000 - 0.866025i) q^{43} +(1.00000 - 1.73205i) q^{45} -9.00000 q^{47} +(-9.00000 - 15.5885i) q^{49} -3.00000 q^{51} -12.0000 q^{53} +(-1.00000 - 1.73205i) q^{55} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-5.00000 - 8.66025i) q^{63} +(3.00000 + 5.19615i) q^{67} +(-2.00000 + 3.46410i) q^{69} +(3.50000 - 6.06218i) q^{71} +2.00000 q^{73} +(2.00000 + 3.46410i) q^{75} -10.0000 q^{77} +12.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +16.0000 q^{83} +(1.50000 - 2.59808i) q^{85} +(3.00000 - 5.19615i) q^{87} +(-5.00000 - 8.66025i) q^{89} +(-2.00000 - 3.46410i) q^{93} +(-1.00000 + 1.73205i) q^{95} +(-5.00000 + 8.66025i) q^{97} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 2 q^{5} + 5 q^{7} + 2 q^{9} - 2 q^{11} - q^{15} + 3 q^{17} - 2 q^{19} - 10 q^{21} - 4 q^{23} - 8 q^{25} - 10 q^{27} + 6 q^{29} + 8 q^{31} - 2 q^{33} + 5 q^{35} + 11 q^{37} + 8 q^{41} + q^{43}+ \cdots - 8 q^{99}+O(q^{100}) $ 2 * q - q^3 + 2 * q^5 + 5 * q^7 + 2 * q^9 - 2 * q^11 - q^15 + 3 * q^17 - 2 * q^19 - 10 * q^21 - 4 * q^23 - 8 * q^25 - 10 * q^27 + 6 * q^29 + 8 * q^31 - 2 * q^33 + 5 * q^35 + 11 * q^37 + 8 * q^41 + q^43 + 2 * q^45 - 18 * q^47 - 18 * q^49 - 6 * q^51 - 24 * q^53 - 2 * q^55 + 4 * q^57 + 6 * q^59 - 10 * q^63 + 6 * q^67 - 4 * q^69 + 7 * q^71 + 4 * q^73 + 4 * q^75 - 20 * q^77 + 24 * q^79 - q^81 + 32 * q^83 + 3 * q^85 + 6 * q^87 - 10 * q^89 - 4 * q^93 - 2 * q^95 - 10 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$		0			0
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$		0			0
$7$	2.50000	−	4.33013i	0.944911	−	1.63663i	0.188982	−	0.981981i	$-0.439481\pi$
$7$	2.50000	−	4.33013i	0.944911	−	1.63663i	0.755929	−	0.654654i	$-0.227186\pi$
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$	−5.00000			−1.09109
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$		0			0
$35$	2.50000	−	4.33013i	0.422577	−	0.731925i
$36$		0			0
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.821995	+	0.569495i	$0.192861\pi$
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.0821995	+	0.996616i	$0.473806\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	0.988600	+	0.150567i	$0.0481100\pi$
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	−0.363905	+	0.931436i	$0.618557\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$		0			0
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$		0			0
$47$	−9.00000			−1.31278			−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000			−1.31278			−0.656392	+	0.754420i	$0.727918\pi$
$48$		0			0
$49$	−9.00000	−	15.5885i	−1.28571	−	2.22692i
$50$		0			0
$51$	−3.00000			−0.420084
$52$		0			0
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$		0			0
$55$	−1.00000	−	1.73205i	−0.134840	−	0.233550i
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$		0			0
$63$	−5.00000	−	8.66025i	−0.629941	−	1.09109i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.00000	+	5.19615i	0.366508	+	0.634811i	0.989017	−	0.147802i	$-0.0472198\pi$
$67$	3.00000	+	5.19615i	0.366508	+	0.634811i	−0.622509	+	0.782613i	$0.713886\pi$
$68$		0			0
$69$	−2.00000	+	3.46410i	−0.240772	+	0.417029i
$70$		0			0
$71$	3.50000	−	6.06218i	0.415374	−	0.719448i	−0.580094	−	0.814550i	$-0.696984\pi$
$71$	3.50000	−	6.06218i	0.415374	−	0.719448i	0.995468	+	0.0951014i	$0.0303175\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$		0			0
$77$	−10.0000			−1.13961
$78$		0			0
$79$	12.0000			1.35011			0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000			1.35011			0.675053	+	0.737769i	$0.264121\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	16.0000			1.75623			0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000			1.75623			0.878114	+	0.478451i	$0.158802\pi$
$84$		0			0
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$		0			0
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$		0			0
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$		0			0
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$		0			0
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	0.492287	+	0.870433i	$0.336161\pi$
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	−0.999961	+	0.00888289i	$0.997172\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$		0			0
$101$	−2.00000	−	3.46410i	−0.199007	−	0.344691i	0.749199	−	0.662344i	$-0.230438\pi$
$101$	−2.00000	−	3.46410i	−0.199007	−	0.344691i	−0.948207	+	0.317653i	$0.897105\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$		0			0
$105$	−5.00000			−0.487950
$106$		0			0
$107$	−10.0000	−	17.3205i	−0.966736	−	1.67444i	−0.704875	−	0.709331i	$-0.748997\pi$
$107$	−10.0000	−	17.3205i	−0.966736	−	1.67444i	−0.261861	−	0.965106i	$-0.584336\pi$
$108$		0			0
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$		0			0
$111$	5.50000	−	9.52628i	0.522037	−	0.904194i
$112$		0			0
$113$	−1.00000	+	1.73205i	−0.0940721	+	0.162938i	−0.909221	−	0.416314i	$-0.863322\pi$
$113$	−1.00000	+	1.73205i	−0.0940721	+	0.162938i	0.815149	+	0.579252i	$0.196655\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.50000	−	12.9904i	−0.687524	−	1.19083i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	4.00000	−	6.92820i	0.360668	−	0.624695i
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	0.987108	−	0.160055i	$-0.0511671\pi$
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	−0.632166	+	0.774833i	$0.717834\pi$
$128$		0			0
$129$	−1.00000			−0.0880451
$130$		0			0
$131$	3.00000			0.262111			0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000			0.262111			0.131056	+	0.991375i	$0.458163\pi$
$132$		0			0
$133$	5.00000	+	8.66025i	0.433555	+	0.750939i
$134$		0			0
$135$	−5.00000			−0.430331
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	−1.50000	+	2.59808i	−0.127228	+	0.220366i	−0.922602	−	0.385754i	$-0.873941\pi$
$139$	−1.50000	+	2.59808i	−0.127228	+	0.220366i	0.795373	+	0.606120i	$0.207275\pi$
$140$		0			0
$141$	4.50000	+	7.79423i	0.378968	+	0.656392i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$		0			0
$147$	−9.00000	+	15.5885i	−0.742307	+	1.28571i
$148$		0			0
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	−0.422744	−	0.906249i	$-0.638933\pi$
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	0.996207	−	0.0870170i	$-0.0277334\pi$
$150$		0			0
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$		0			0
$153$	−3.00000	−	5.19615i	−0.242536	−	0.420084i
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$		0			0
$159$	6.00000	+	10.3923i	0.475831	+	0.824163i
$160$		0			0
$161$	−20.0000			−1.57622
$162$		0			0
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$		0			0
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$		0			0
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	0.978259	−	0.207385i	$-0.0664952\pi$
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	−0.668730	+	0.743505i	$0.733162\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$		0			0
$173$	6.00000	−	10.3923i	0.456172	−	0.790112i	−0.542583	−	0.840002i	$-0.682554\pi$
$173$	6.00000	−	10.3923i	0.456172	−	0.790112i	0.998755	+	0.0498898i	$0.0158870\pi$
$174$		0			0
$175$	−10.0000	+	17.3205i	−0.755929	+	1.30931i
$176$		0			0
$177$	−6.00000			−0.450988
$178$		0			0
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$		0			0
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.50000	+	9.52628i	0.404368	+	0.700386i
$186$		0			0
$187$	−6.00000			−0.438763
$188$		0			0
$189$	−12.5000	+	21.6506i	−0.909241	+	1.57485i
$190$		0			0
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	−0.988255	−	0.152813i	$-0.951167\pi$
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	0.626468	+	0.779447i	$0.284500\pi$
$192$		0			0
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	0.995948	+	0.0899262i	$0.0286631\pi$
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.50000	+	14.7224i	0.605600	+	1.04893i	0.991956	+	0.126580i	$0.0404001\pi$
$197$	8.50000	+	14.7224i	0.605600	+	1.04893i	−0.386356	+	0.922350i	$0.626267\pi$
$198$		0			0
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	−0.347879	−	0.937539i	$-0.613098\pi$
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	0.985873	−	0.167497i	$-0.0535685\pi$
$200$		0			0
$201$	3.00000	−	5.19615i	0.211604	−	0.366508i
$202$		0			0
$203$	30.0000			2.10559
$204$		0			0
$205$	4.00000	+	6.92820i	0.279372	+	0.483887i
$206$		0			0
$207$	−8.00000			−0.556038
$208$		0			0
$209$	4.00000			0.276686
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$		0			0
$213$	−7.00000			−0.479632
$214$		0			0
$215$	0.500000	−	0.866025i	0.0340997	−	0.0590624i
$216$		0			0
$217$	10.0000	−	17.3205i	0.678844	−	1.17579i
$218$		0			0
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−8.50000	−	14.7224i	−0.569202	−	0.985887i	−0.996645	−	0.0818447i	$-0.973919\pi$
$223$	−8.50000	−	14.7224i	−0.569202	−	0.985887i	0.427443	−	0.904042i	$-0.359414\pi$
$224$		0			0
$225$	−4.00000	+	6.92820i	−0.266667	+	0.461880i
$226$		0			0
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	0.468368	+	0.883534i	$0.344842\pi$
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	−0.999346	+	0.0361484i	$0.988491\pi$
$228$		0			0
$229$	15.0000			0.991228			0.495614	−	0.868543i	$-0.334943\pi$
$229$	15.0000			0.991228			0.495614	+	0.868543i	$0.334943\pi$
$230$		0			0
$231$	5.00000	+	8.66025i	0.328976	+	0.569803i
$232$		0			0
$233$	13.0000			0.851658			0.425829	−	0.904804i	$-0.359982\pi$
$233$	13.0000			0.851658			0.425829	+	0.904804i	$0.359982\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$		0			0
$237$	−6.00000	−	10.3923i	−0.389742	−	0.675053i
$238$		0			0
$239$	3.00000			0.194054			0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000			0.194054			0.0970269	+	0.995282i	$0.469067\pi$
$240$		0			0
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	−0.832019	−	0.554747i	$-0.812815\pi$
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	0.896435	+	0.443176i	$0.146148\pi$
$242$		0			0
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$		0			0
$245$	−9.00000	−	15.5885i	−0.574989	−	0.995910i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−8.00000	−	13.8564i	−0.506979	−	0.878114i
$250$		0			0
$251$	−4.00000	+	6.92820i	−0.252478	+	0.437304i	−0.964207	−	0.265149i	$-0.914579\pi$
$251$	−4.00000	+	6.92820i	−0.252478	+	0.437304i	0.711730	+	0.702454i	$0.247912\pi$
$252$		0			0
$253$	−4.00000	+	6.92820i	−0.251478	+	0.435572i
$254$		0			0
$255$	−3.00000			−0.187867
$256$		0			0
$257$	15.5000	+	26.8468i	0.966863	+	1.67466i	0.704523	+	0.709681i	$0.251161\pi$
$257$	15.5000	+	26.8468i	0.966863	+	1.67466i	0.262341	+	0.964975i	$0.415506\pi$
$258$		0			0
$259$	55.0000			3.41753
$260$		0			0
$261$	12.0000			0.742781
$262$		0			0
$263$	−10.0000	−	17.3205i	−0.616626	−	1.06803i	−0.990097	−	0.140386i	$-0.955166\pi$
$263$	−10.0000	−	17.3205i	−0.616626	−	1.06803i	0.373470	−	0.927642i	$-0.378168\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	−5.00000	+	8.66025i	−0.305995	+	0.529999i
$268$		0			0
$269$	−8.00000	+	13.8564i	−0.487769	+	0.844840i	−0.999901	−	0.0140665i	$-0.995522\pi$
$269$	−8.00000	+	13.8564i	−0.487769	+	0.844840i	0.512132	+	0.858906i	$0.328856\pi$
$270$		0			0
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	0.739921	−	0.672694i	$-0.234863\pi$
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	−0.952531	+	0.304443i	$0.901530\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.00000	+	6.92820i	0.241209	+	0.417786i
$276$		0			0
$277$	6.00000	−	10.3923i	0.360505	−	0.624413i	−0.627539	−	0.778585i	$-0.715938\pi$
$277$	6.00000	−	10.3923i	0.360505	−	0.624413i	0.988044	+	0.154172i	$0.0492710\pi$
$278$		0			0
$279$	4.00000	−	6.92820i	0.239474	−	0.414781i
$280$		0			0
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	0.993626	+	0.112728i	$0.0359589\pi$
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	−0.399188	+	0.916869i	$0.630708\pi$
$284$		0			0
$285$	2.00000			0.118470
$286$		0			0
$287$	40.0000			2.36113
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	10.0000			0.586210
$292$		0			0
$293$	7.50000	−	12.9904i	0.438155	−	0.758906i	−0.559393	−	0.828903i	$-0.688966\pi$
$293$	7.50000	−	12.9904i	0.438155	−	0.758906i	0.997547	+	0.0699967i	$0.0222989\pi$
$294$		0			0
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$		0			0
$297$	5.00000	+	8.66025i	0.290129	+	0.502519i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−2.50000	−	4.33013i	−0.144098	−	0.249584i
$302$		0			0
$303$	−2.00000	+	3.46410i	−0.114897	+	0.199007i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$		0			0
$309$	4.00000	+	6.92820i	0.227552	+	0.394132i
$310$		0			0
$311$	−22.0000			−1.24751			−0.623753	−	0.781622i	$-0.714393\pi$
$311$	−22.0000			−1.24751			−0.623753	+	0.781622i	$0.714393\pi$
$312$		0			0
$313$	−9.00000			−0.508710			−0.254355	−	0.967111i	$-0.581863\pi$
$313$	−9.00000			−0.508710			−0.254355	+	0.967111i	$0.581863\pi$
$314$		0			0
$315$	−5.00000	−	8.66025i	−0.281718	−	0.487950i
$316$		0			0
$317$	2.00000			0.112331			0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000			0.112331			0.0561656	+	0.998421i	$0.482113\pi$
$318$		0			0
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$	−10.0000	+	17.3205i	−0.558146	+	0.966736i
$322$		0			0
$323$	3.00000	+	5.19615i	0.166924	+	0.289122i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.50000	−	4.33013i	−0.138250	−	0.239457i
$328$		0			0
$329$	−22.5000	+	38.9711i	−1.24047	+	2.14855i
$330$		0			0
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	−0.652680	−	0.757634i	$-0.726355\pi$
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	0.982470	+	0.186421i	$0.0596888\pi$
$332$		0			0
$333$	22.0000			1.20559
$334$		0			0
$335$	3.00000	+	5.19615i	0.163908	+	0.283896i
$336$		0			0
$337$	15.0000			0.817102			0.408551	−	0.912735i	$-0.366034\pi$
$337$	15.0000			0.817102			0.408551	+	0.912735i	$0.366034\pi$
$338$		0			0
$339$	2.00000			0.108625
$340$		0			0
$341$	−4.00000	−	6.92820i	−0.216612	−	0.375183i
$342$		0			0
$343$	−55.0000			−2.96972
$344$		0			0
$345$	−2.00000	+	3.46410i	−0.107676	+	0.186501i
$346$		0			0
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	−0.903475	−	0.428640i	$-0.858993\pi$
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	0.822951	+	0.568112i	$0.192326\pi$
$348$		0			0
$349$	−4.50000	−	7.79423i	−0.240879	−	0.417215i	0.720086	−	0.693885i	$-0.244103\pi$
$349$	−4.50000	−	7.79423i	−0.240879	−	0.417215i	−0.960965	+	0.276670i	$0.910769\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.0000	−	24.2487i	−0.745145	−	1.29063i	−0.950127	−	0.311863i	$-0.899047\pi$
$353$	−14.0000	−	24.2487i	−0.745145	−	1.29063i	0.204982	−	0.978766i	$-0.434286\pi$
$354$		0			0
$355$	3.50000	−	6.06218i	0.185761	−	0.321747i
$356$		0			0
$357$	−7.50000	+	12.9904i	−0.396942	+	0.687524i
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$	2.00000			0.104685
$366$		0			0
$367$	9.00000	+	15.5885i	0.469796	+	0.813711i	0.999404	−	0.0345320i	$-0.0109941\pi$
$367$	9.00000	+	15.5885i	0.469796	+	0.813711i	−0.529607	+	0.848243i	$0.677661\pi$
$368$		0			0
$369$	16.0000			0.832927
$370$		0			0
$371$	−30.0000	+	51.9615i	−1.55752	+	2.69771i
$372$		0			0
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$	4.50000	+	7.79423i	0.232379	+	0.402492i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	12.0000	+	20.7846i	0.616399	+	1.06763i	0.990137	+	0.140100i	$0.0447423\pi$
$379$	12.0000	+	20.7846i	0.616399	+	1.06763i	−0.373739	+	0.927534i	$0.621924\pi$
$380$		0			0
$381$	4.00000	−	6.92820i	0.204926	−	0.354943i
$382$		0			0
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$		0			0
$385$	−10.0000			−0.509647
$386$		0			0
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$		0			0
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$		0			0
$393$	−1.50000	−	2.59808i	−0.0756650	−	0.131056i
$394$		0			0
$395$	12.0000			0.603786
$396$		0			0
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	−0.712843	−	0.701324i	$-0.752593\pi$
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	0.963786	+	0.266678i	$0.0859261\pi$
$398$		0			0
$399$	5.00000	−	8.66025i	0.250313	−	0.433555i
$400$		0			0
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$		0			0
$407$	11.0000	−	19.0526i	0.545250	−	0.944400i
$408$		0			0
$409$	−2.00000	+	3.46410i	−0.0988936	+	0.171289i	−0.911227	−	0.411905i	$-0.864864\pi$
$409$	−2.00000	+	3.46410i	−0.0988936	+	0.171289i	0.812333	+	0.583193i	$0.198197\pi$
$410$		0			0
$411$	12.0000			0.591916
$412$		0			0
$413$	−15.0000	−	25.9808i	−0.738102	−	1.27843i
$414$		0			0
$415$	16.0000			0.785409
$416$		0			0
$417$	3.00000			0.146911
$418$		0			0
$419$	19.5000	+	33.7750i	0.952637	+	1.65002i	0.739685	+	0.672954i	$0.234975\pi$
$419$	19.5000	+	33.7750i	0.952637	+	1.65002i	0.212953	+	0.977062i	$0.431692\pi$
$420$		0			0
$421$	−11.0000			−0.536107			−0.268054	−	0.963404i	$-0.586380\pi$
$421$	−11.0000			−0.536107			−0.268054	+	0.963404i	$0.586380\pi$
$422$		0			0
$423$	−9.00000	+	15.5885i	−0.437595	+	0.757937i
$424$		0			0
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.50000	−	9.52628i	−0.264926	−	0.458865i	0.702618	−	0.711567i	$-0.252014\pi$
$431$	−5.50000	−	9.52628i	−0.264926	−	0.458865i	−0.967544	+	0.252702i	$0.918681\pi$
$432$		0			0
$433$	8.50000	−	14.7224i	0.408484	−	0.707515i	−0.586236	−	0.810140i	$-0.699391\pi$
$433$	8.50000	−	14.7224i	0.408484	−	0.707515i	0.994720	+	0.102625i	$0.0327243\pi$
$434$		0			0
$435$	3.00000	−	5.19615i	0.143839	−	0.249136i
$436$		0			0
$437$	8.00000			0.382692
$438$		0			0
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$	−36.0000			−1.71429
$442$		0			0
$443$	−27.0000			−1.28281			−0.641404	−	0.767203i	$-0.721648\pi$
$443$	−27.0000			−1.28281			−0.641404	+	0.767203i	$0.721648\pi$
$444$		0			0
$445$	−5.00000	−	8.66025i	−0.237023	−	0.410535i
$446$		0			0
$447$	−14.0000			−0.662177
$448$		0			0
$449$	−9.00000	+	15.5885i	−0.424736	+	0.735665i	−0.996396	−	0.0848262i	$-0.972967\pi$
$449$	−9.00000	+	15.5885i	−0.424736	+	0.735665i	0.571660	+	0.820491i	$0.306300\pi$
$450$		0			0
$451$	8.00000	−	13.8564i	0.376705	−	0.652473i
$452$		0			0
$453$	−2.50000	−	4.33013i	−0.117460	−	0.203447i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$		0			0
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$		0			0
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	−0.828978	−	0.559281i	$-0.811077\pi$
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	0.898840	+	0.438276i	$0.144411\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$		0			0
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$		0			0
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$		0			0
$469$	30.0000			1.38527
$470$		0			0
$471$	1.00000	+	1.73205i	0.0460776	+	0.0798087i
$472$		0			0
$473$	−2.00000			−0.0919601
$474$		0			0
$475$	4.00000	−	6.92820i	0.183533	−	0.317888i
$476$		0			0
$477$	−12.0000	+	20.7846i	−0.549442	+	0.951662i
$478$		0			0
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	0.950327	−	0.311253i	$-0.100749\pi$
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	−0.744717	+	0.667381i	$0.767415\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	10.0000	+	17.3205i	0.455016	+	0.788110i
$484$		0			0
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$		0			0
$487$	4.00000	−	6.92820i	0.181257	−	0.313947i	−0.761052	−	0.648691i	$-0.775317\pi$
$487$	4.00000	−	6.92820i	0.181257	−	0.313947i	0.942309	+	0.334744i	$0.108650\pi$
$488$		0			0
$489$	−4.00000			−0.180886
$490$		0			0
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	0.645675	−	0.763612i	$-0.276576\pi$
$491$	−7.50000	−	12.9904i	−0.338470	−	0.586248i	−0.984145	+	0.177365i	$0.943243\pi$
$492$		0			0
$493$	18.0000			0.810679
$494$		0			0
$495$	−4.00000			−0.179787
$496$		0			0
$497$	−17.5000	−	30.3109i	−0.784982	−	1.35963i
$498$		0			0
$499$	24.0000			1.07439			0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000			1.07439			0.537194	+	0.843459i	$0.319484\pi$
$500$		0			0
$501$	4.00000	−	6.92820i	0.178707	−	0.309529i
$502$		0			0
$503$	−13.0000	+	22.5167i	−0.579641	+	1.00397i	0.415879	+	0.909420i	$0.363474\pi$
$503$	−13.0000	+	22.5167i	−0.579641	+	1.00397i	−0.995520	+	0.0945483i	$0.969859\pi$
$504$		0			0
$505$	−2.00000	−	3.46410i	−0.0889988	−	0.154150i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	0.887336	−	0.461123i	$-0.152553\pi$
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	−0.843012	+	0.537895i	$0.819220\pi$
$510$		0			0
$511$	5.00000	−	8.66025i	0.221187	−	0.383107i
$512$		0			0
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$		0			0
$515$	−8.00000			−0.352522
$516$		0			0
$517$	9.00000	+	15.5885i	0.395820	+	0.685580i
$518$		0			0
$519$	−12.0000			−0.526742
$520$		0			0
$521$	15.0000			0.657162			0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000			0.657162			0.328581	+	0.944476i	$0.393430\pi$
$522$		0			0
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$		0			0
$525$	20.0000			0.872872
$526$		0			0
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−10.0000	−	17.3205i	−0.432338	−	0.748831i
$536$		0			0
$537$	−1.50000	+	2.59808i	−0.0647298	+	0.112115i
$538$		0			0
$539$	−18.0000	+	31.1769i	−0.775315	+	1.34288i
$540$		0			0
$541$	−9.00000			−0.386940			−0.193470	−	0.981106i	$-0.561974\pi$
$541$	−9.00000			−0.386940			−0.193470	+	0.981106i	$0.561974\pi$
$542$		0			0
$543$	−8.00000	−	13.8564i	−0.343313	−	0.594635i
$544$		0			0
$545$	5.00000			0.214176
$546$		0			0
$547$	−39.0000			−1.66752			−0.833760	−	0.552127i	$-0.813816\pi$
$547$	−39.0000			−1.66752			−0.833760	+	0.552127i	$0.813816\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.0000			−0.511217
$552$		0			0
$553$	30.0000	−	51.9615i	1.27573	−	2.20963i
$554$		0			0
$555$	5.50000	−	9.52628i	0.233462	−	0.404368i
$556$		0			0
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	0.512622	−	0.858614i	$-0.328674\pi$
$557$	−11.5000	−	19.9186i	−0.487271	−	0.843978i	−0.999893	+	0.0146368i	$0.995341\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	3.00000	+	5.19615i	0.126660	+	0.219382i
$562$		0			0
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	0.0824933	+	0.996592i	$0.473712\pi$
$563$	−19.5000	+	33.7750i	−0.821827	+	1.42345i	−0.904320	+	0.426855i	$0.859622\pi$
$564$		0			0
$565$	−1.00000	+	1.73205i	−0.0420703	+	0.0728679i
$566$		0			0
$567$	−5.00000			−0.209980
$568$		0			0
$569$	8.50000	+	14.7224i	0.356339	+	0.617196i	0.987346	−	0.158580i	$-0.0506917\pi$
$569$	8.50000	+	14.7224i	0.356339	+	0.617196i	−0.631008	+	0.775777i	$0.717358\pi$
$570$		0			0
$571$	37.0000			1.54840			0.774201	−	0.632940i	$-0.218152\pi$
$571$	37.0000			1.54840			0.774201	+	0.632940i	$0.218152\pi$
$572$		0			0
$573$	10.0000			0.417756
$574$		0			0
$575$	8.00000	+	13.8564i	0.333623	+	0.577852i
$576$		0			0
$577$	38.0000			1.58196			0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000			1.58196			0.790980	+	0.611842i	$0.209571\pi$
$578$		0			0
$579$	8.00000	−	13.8564i	0.332469	−	0.575853i
$580$		0			0
$581$	40.0000	−	69.2820i	1.65948	−	2.87430i
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$		0			0
$589$	−4.00000	+	6.92820i	−0.164817	+	0.285472i
$590$		0			0
$591$	8.50000	−	14.7224i	0.349643	−	0.605600i
$592$		0			0
$593$	−2.00000			−0.0821302			−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000			−0.0821302			−0.0410651	+	0.999156i	$0.513075\pi$
$594$		0			0
$595$	−7.50000	−	12.9904i	−0.307470	−	0.532554i
$596$		0			0
$597$	−18.0000			−0.736691
$598$		0			0
$599$	−2.00000			−0.0817178			−0.0408589	−	0.999165i	$-0.513009\pi$
$599$	−2.00000			−0.0817178			−0.0408589	+	0.999165i	$0.513009\pi$
$600$		0			0
$601$	1.50000	+	2.59808i	0.0611863	+	0.105978i	0.894996	−	0.446074i	$-0.147178\pi$
$601$	1.50000	+	2.59808i	0.0611863	+	0.105978i	−0.833810	+	0.552052i	$0.813845\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$		0			0
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$		0			0
$607$	5.00000	−	8.66025i	0.202944	−	0.351509i	−0.746532	−	0.665350i	$-0.768282\pi$
$607$	5.00000	−	8.66025i	0.202944	−	0.351509i	0.949476	+	0.313841i	$0.101616\pi$
$608$		0			0
$609$	−15.0000	−	25.9808i	−0.607831	−	1.05279i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	0.799060	−	0.601251i	$-0.205331\pi$
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	−0.920229	+	0.391381i	$0.871998\pi$
$614$		0			0
$615$	4.00000	−	6.92820i	0.161296	−	0.279372i
$616$		0			0
$617$	16.0000	−	27.7128i	0.644136	−	1.11568i	−0.340365	−	0.940294i	$-0.610551\pi$
$617$	16.0000	−	27.7128i	0.644136	−	1.11568i	0.984500	−	0.175382i	$-0.0561162\pi$
$618$		0			0
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$		0			0
$621$	10.0000	+	17.3205i	0.401286	+	0.695048i
$622$		0			0
$623$	−50.0000			−2.00321
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$	−2.00000	−	3.46410i	−0.0798723	−	0.138343i
$628$		0			0
$629$	33.0000			1.31580
$630$		0			0
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	−0.677239	−	0.735763i	$-0.736824\pi$
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	0.975809	+	0.218624i	$0.0701569\pi$
$632$		0			0
$633$	2.50000	−	4.33013i	0.0993661	−	0.172107i
$634$		0			0
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−7.00000	−	12.1244i	−0.276916	−	0.479632i
$640$		0			0
$641$	17.0000	−	29.4449i	0.671460	−	1.16300i	−0.306031	−	0.952022i	$-0.599001\pi$
$641$	17.0000	−	29.4449i	0.671460	−	1.16300i	0.977490	−	0.210981i	$-0.0676657\pi$
$642$		0			0
$643$	−13.0000	+	22.5167i	−0.512670	+	0.887970i	0.487222	+	0.873278i	$0.338010\pi$
$643$	−13.0000	+	22.5167i	−0.512670	+	0.887970i	−0.999892	+	0.0146923i	$0.995323\pi$
$644$		0			0
$645$	−1.00000			−0.0393750
$646$		0			0
$647$	−21.0000	−	36.3731i	−0.825595	−	1.42997i	−0.901464	−	0.432855i	$-0.857506\pi$
$647$	−21.0000	−	36.3731i	−0.825595	−	1.42997i	0.0758684	−	0.997118i	$-0.475827\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$		0			0
$651$	−20.0000			−0.783862
$652$		0			0
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$		0			0
$655$	3.00000			0.117220
$656$		0			0
$657$	2.00000	−	3.46410i	0.0780274	−	0.135147i
$658$		0			0
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	0.453221	+	0.891398i	$0.350275\pi$
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	−0.998584	+	0.0531977i	$0.983059\pi$
$660$		0			0
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	0.952940	+	0.303160i	$0.0980418\pi$
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	−0.213925	+	0.976850i	$0.568625\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.00000	+	8.66025i	0.193892	+	0.335830i
$666$		0			0
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$		0			0
$669$	−8.50000	+	14.7224i	−0.328629	+	0.569202i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−10.5000	−	18.1865i	−0.404745	−	0.701039i	0.589547	−	0.807734i	$-0.299306\pi$
$673$	−10.5000	−	18.1865i	−0.404745	−	0.701039i	−0.994292	+	0.106695i	$0.965973\pi$
$674$		0			0
$675$	20.0000			0.769800
$676$		0			0
$677$	−36.0000			−1.38359			−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000			−1.38359			−0.691796	+	0.722093i	$0.743180\pi$
$678$		0			0
$679$	25.0000	+	43.3013i	0.959412	+	1.66175i
$680$		0			0
$681$	16.0000			0.613121
$682$		0			0
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$		0			0
$685$	−6.00000	+	10.3923i	−0.229248	+	0.397070i
$686$		0			0
$687$	−7.50000	−	12.9904i	−0.286143	−	0.495614i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	0.942420	+	0.334431i	$0.108544\pi$
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	−0.181584	+	0.983375i	$0.558123\pi$
$692$		0			0
$693$	−10.0000	+	17.3205i	−0.379869	+	0.657952i
$694$		0			0
$695$	−1.50000	+	2.59808i	−0.0568982	+	0.0985506i
$696$		0			0
$697$	24.0000			0.909065
$698$		0			0
$699$	−6.50000	−	11.2583i	−0.245853	−	0.425829i
$700$		0			0
$701$	−4.00000			−0.151078			−0.0755390	−	0.997143i	$-0.524068\pi$
$701$	−4.00000			−0.151078			−0.0755390	+	0.997143i	$0.524068\pi$
$702$		0			0
$703$	−22.0000			−0.829746
$704$		0			0
$705$	4.50000	+	7.79423i	0.169480	+	0.293548i
$706$		0			0
$707$	−20.0000			−0.752177
$708$		0			0
$709$	11.0000	−	19.0526i	0.413114	−	0.715534i	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	11.0000	−	19.0526i	0.413114	−	0.715534i	0.995228	+	0.0975728i	$0.0311079\pi$
$710$		0			0
$711$	12.0000	−	20.7846i	0.450035	−	0.779484i
$712$		0			0
$713$	−8.00000	−	13.8564i	−0.299602	−	0.518927i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.50000	−	2.59808i	−0.0560185	−	0.0970269i
$718$		0			0
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	−0.438141	−	0.898906i	$-0.644363\pi$
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	0.997546	−	0.0700124i	$-0.0223039\pi$
$720$		0			0
$721$	−20.0000	+	34.6410i	−0.744839	+	1.29010i
$722$		0			0
$723$	−2.00000			−0.0743808
$724$		0			0
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$		0			0
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$		0			0
$733$	−37.0000			−1.36663			−0.683313	−	0.730125i	$-0.739462\pi$
$733$	−37.0000			−1.36663			−0.683313	+	0.730125i	$0.739462\pi$
$734$		0			0
$735$	−9.00000	+	15.5885i	−0.331970	+	0.574989i
$736$		0			0
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$		0			0
$739$	26.0000	+	45.0333i	0.956425	+	1.65658i	0.731072	+	0.682300i	$0.239020\pi$
$739$	26.0000	+	45.0333i	0.956425	+	1.65658i	0.225354	+	0.974277i	$0.427646\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	14.5000	+	25.1147i	0.531953	+	0.921370i	0.999304	+	0.0372984i	$0.0118752\pi$
$743$	14.5000	+	25.1147i	0.531953	+	0.921370i	−0.467351	+	0.884072i	$0.654791\pi$
$744$		0			0
$745$	7.00000	−	12.1244i	0.256460	−	0.444202i
$746$		0			0
$747$	16.0000	−	27.7128i	0.585409	−	1.01396i
$748$		0			0
$749$	−100.000			−3.65392
$750$		0			0
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	−0.995018	−	0.0996961i	$-0.968213\pi$
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	0.411170	−	0.911559i	$-0.365120\pi$
$752$		0			0
$753$	8.00000			0.291536
$754$		0			0
$755$	5.00000			0.181969
$756$		0			0
$757$	26.0000	+	45.0333i	0.944986	+	1.63676i	0.755779	+	0.654827i	$0.227258\pi$
$757$	26.0000	+	45.0333i	0.944986	+	1.63676i	0.189207	+	0.981937i	$0.439408\pi$
$758$		0			0
$759$	8.00000			0.290382
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$		0			0
$763$	12.5000	−	21.6506i	0.452530	−	0.783806i
$764$		0			0
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	8.00000	+	13.8564i	0.288487	+	0.499675i	0.973449	−	0.228904i	$-0.0735143\pi$
$769$	8.00000	+	13.8564i	0.288487	+	0.499675i	−0.684962	+	0.728579i	$0.740181\pi$
$770$		0			0
$771$	15.5000	−	26.8468i	0.558219	−	0.966863i
$772$		0			0
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	−0.514301	−	0.857610i	$-0.671949\pi$
$773$	13.5000	−	23.3827i	0.485561	−	0.841017i	0.999862	+	0.0165929i	$0.00528194\pi$
$774$		0			0
$775$	−16.0000			−0.574737
$776$		0			0
$777$	−27.5000	−	47.6314i	−0.986557	−	1.70877i
$778$		0			0
$779$	−16.0000			−0.573259
$780$		0			0
$781$	−14.0000			−0.500959
$782$		0			0
$783$	−15.0000	−	25.9808i	−0.536056	−	0.928477i
$784$		0			0
$785$	−2.00000			−0.0713831
$786$		0			0
$787$	−12.0000	+	20.7846i	−0.427754	+	0.740891i	−0.996673	−	0.0815020i	$-0.974028\pi$
$787$	−12.0000	+	20.7846i	−0.427754	+	0.740891i	0.568919	+	0.822393i	$0.307362\pi$
$788$		0			0
$789$	−10.0000	+	17.3205i	−0.356009	+	0.616626i
$790$		0			0
$791$	5.00000	+	8.66025i	0.177780	+	0.307923i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	6.00000	+	10.3923i	0.212798	+	0.368577i
$796$		0			0
$797$	−19.0000	+	32.9090i	−0.673015	+	1.16570i	0.304030	+	0.952662i	$0.401668\pi$
$797$	−19.0000	+	32.9090i	−0.673015	+	1.16570i	−0.977045	+	0.213033i	$0.931666\pi$
$798$		0			0
$799$	−13.5000	+	23.3827i	−0.477596	+	0.827220i
$800$		0			0
$801$	−20.0000			−0.706665
$802$		0			0
$803$	−2.00000	−	3.46410i	−0.0705785	−	0.122245i
$804$		0			0
$805$	−20.0000			−0.704907
$806$		0			0
$807$	16.0000			0.563227
$808$		0			0
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	0.703533	−	0.710663i	$-0.251605\pi$
$809$	−7.50000	−	12.9904i	−0.263686	−	0.456717i	−0.967219	+	0.253946i	$0.918272\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	−3.50000	+	6.06218i	−0.122750	+	0.212610i
$814$		0			0
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	1.00000	+	1.73205i	0.0349856	+	0.0605968i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−20.5000	−	35.5070i	−0.715455	−	1.23920i	−0.962784	−	0.270273i	$-0.912886\pi$
$821$	−20.5000	−	35.5070i	−0.715455	−	1.23920i	0.247329	−	0.968932i	$-0.420447\pi$
$822$		0			0
$823$	13.0000	−	22.5167i	0.453152	−	0.784881i	−0.545428	−	0.838157i	$-0.683633\pi$
$823$	13.0000	−	22.5167i	0.453152	−	0.784881i	0.998580	+	0.0532760i	$0.0169663\pi$
$824$		0			0
$825$	4.00000	−	6.92820i	0.139262	−	0.241209i
$826$		0			0
$827$	10.0000			0.347734			0.173867	−	0.984769i	$-0.444374\pi$
$827$	10.0000			0.347734			0.173867	+	0.984769i	$0.444374\pi$
$828$		0			0
$829$	3.00000	+	5.19615i	0.104194	+	0.180470i	0.913409	−	0.407044i	$-0.133440\pi$
$829$	3.00000	+	5.19615i	0.104194	+	0.180470i	−0.809214	+	0.587513i	$0.800107\pi$
$830$		0			0
$831$	−12.0000			−0.416275
$832$		0			0
$833$	−54.0000			−1.87099
$834$		0			0
$835$	4.00000	+	6.92820i	0.138426	+	0.239760i
$836$		0			0
$837$	−20.0000			−0.691301
$838$		0			0
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$	−5.00000	−	8.66025i	−0.172209	−	0.298275i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−17.5000	−	30.3109i	−0.601307	−	1.04149i
$848$		0			0
$849$	10.0000	−	17.3205i	0.343199	−	0.594438i
$850$		0			0
$851$	22.0000	−	38.1051i	0.754150	−	1.30623i
$852$		0			0
$853$	47.0000			1.60925			0.804625	−	0.593784i	$-0.202367\pi$
$853$	47.0000			1.60925			0.804625	+	0.593784i	$0.202367\pi$
$854$		0			0
$855$	2.00000	+	3.46410i	0.0683986	+	0.118470i
$856$		0			0
$857$	30.0000			1.02478			0.512390	−	0.858753i	$-0.328760\pi$
$857$	30.0000			1.02478			0.512390	+	0.858753i	$0.328760\pi$
$858$		0			0
$859$	44.0000			1.50126			0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000			1.50126			0.750630	+	0.660722i	$0.229750\pi$
$860$		0			0
$861$	−20.0000	−	34.6410i	−0.681598	−	1.18056i
$862$		0			0
$863$	7.00000			0.238283			0.119141	−	0.992877i	$-0.461986\pi$
$863$	7.00000			0.238283			0.119141	+	0.992877i	$0.461986\pi$
$864$		0			0
$865$	6.00000	−	10.3923i	0.204006	−	0.353349i
$866$		0			0
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$		0			0
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	10.0000	+	17.3205i	0.338449	+	0.586210i
$874$		0			0
$875$	−22.5000	+	38.9711i	−0.760639	+	1.31747i
$876$		0			0
$877$	−3.50000	+	6.06218i	−0.118187	+	0.204705i	−0.919049	−	0.394143i	$-0.871041\pi$
$877$	−3.50000	+	6.06218i	−0.118187	+	0.204705i	0.800862	+	0.598848i	$0.204375\pi$
$878$		0			0
$879$	−15.0000			−0.505937
$880$		0			0
$881$	13.5000	+	23.3827i	0.454827	+	0.787783i	0.998678	−	0.0513987i	$-0.0163679\pi$
$881$	13.5000	+	23.3827i	0.454827	+	0.787783i	−0.543852	+	0.839181i	$0.683035\pi$
$882$		0			0
$883$	−51.0000			−1.71629			−0.858143	−	0.513410i	$-0.828382\pi$
$883$	−51.0000			−1.71629			−0.858143	+	0.513410i	$0.828382\pi$
$884$		0			0
$885$	−6.00000			−0.201688
$886$		0			0
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	0.915722	+	0.401813i	$0.131620\pi$
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	−0.109881	+	0.993945i	$0.535047\pi$
$888$		0			0
$889$	40.0000			1.34156
$890$		0			0
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$		0			0
$893$	9.00000	−	15.5885i	0.301174	−	0.521648i
$894$		0			0
$895$	−1.50000	−	2.59808i	−0.0501395	−	0.0868441i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$	−2.50000	+	4.33013i	−0.0831948	+	0.144098i
$904$		0			0
$905$	16.0000			0.531858
$906$		0			0
$907$	2.50000	+	4.33013i	0.0830111	+	0.143780i	0.904542	−	0.426385i	$-0.140213\pi$
$907$	2.50000	+	4.33013i	0.0830111	+	0.143780i	−0.821531	+	0.570164i	$0.806880\pi$
$908$		0			0
$909$	−8.00000			−0.265343
$910$		0			0
$911$	26.0000			0.861418			0.430709	−	0.902491i	$-0.358263\pi$
$911$	26.0000			0.861418			0.430709	+	0.902491i	$0.358263\pi$
$912$		0			0
$913$	−16.0000	−	27.7128i	−0.529523	−	0.917160i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.50000	−	12.9904i	0.247672	−	0.428980i
$918$		0			0
$919$	12.0000	−	20.7846i	0.395843	−	0.685621i	−0.597365	−	0.801970i	$-0.703786\pi$
$919$	12.0000	−	20.7846i	0.395843	−	0.685621i	0.993208	+	0.116348i	$0.0371189\pi$
$920$		0			0
$921$	−1.00000	−	1.73205i	−0.0329511	−	0.0570730i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−22.0000	−	38.1051i	−0.723356	−	1.25289i
$926$		0			0
$927$	−8.00000	+	13.8564i	−0.262754	+	0.455104i
$928$		0			0
$929$	−10.0000	+	17.3205i	−0.328089	+	0.568267i	−0.982133	−	0.188190i	$-0.939738\pi$
$929$	−10.0000	+	17.3205i	−0.328089	+	0.568267i	0.654043	+	0.756457i	$0.273071\pi$
$930$		0			0
$931$	36.0000			1.17985
$932$		0			0
$933$	11.0000	+	19.0526i	0.360124	+	0.623753i
$934$		0			0
$935$	−6.00000			−0.196221
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$		0			0
$939$	4.50000	+	7.79423i	0.146852	+	0.254355i
$940$		0			0
$941$	7.00000			0.228193			0.114097	−	0.993470i	$-0.463603\pi$
$941$	7.00000			0.228193			0.114097	+	0.993470i	$0.463603\pi$
$942$		0			0
$943$	16.0000	−	27.7128i	0.521032	−	0.902453i
$944$		0			0
$945$	−12.5000	+	21.6506i	−0.406625	+	0.704295i
$946$		0			0
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−1.00000	−	1.73205i	−0.0324272	−	0.0561656i
$952$		0			0
$953$	4.50000	−	7.79423i	0.145769	−	0.252480i	−0.783890	−	0.620899i	$-0.786768\pi$
$953$	4.50000	−	7.79423i	0.145769	−	0.252480i	0.929660	+	0.368419i	$0.120101\pi$
$954$		0			0
$955$	−5.00000	+	8.66025i	−0.161796	+	0.280239i
$956$		0			0
$957$	−12.0000			−0.387905
$958$		0			0
$959$	30.0000	+	51.9615i	0.968751	+	1.67793i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−40.0000			−1.28898
$964$		0			0
$965$	8.00000	+	13.8564i	0.257529	+	0.446054i
$966$		0			0
$967$	13.0000			0.418052			0.209026	−	0.977910i	$-0.432971\pi$
$967$	13.0000			0.418052			0.209026	+	0.977910i	$0.432971\pi$
$968$		0			0
$969$	3.00000	−	5.19615i	0.0963739	−	0.166924i
$970$		0			0
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	0.238114	+	0.971237i	$0.423471\pi$
$971$	−22.5000	+	38.9711i	−0.722059	+	1.25064i	−0.960173	+	0.279406i	$0.909862\pi$
$972$		0			0
$973$	7.50000	+	12.9904i	0.240439	+	0.416452i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$		0			0
$979$	−10.0000	+	17.3205i	−0.319601	+	0.553566i
$980$		0			0
$981$	5.00000	−	8.66025i	0.159638	−	0.276501i
$982$		0			0
$983$	−5.00000			−0.159475			−0.0797376	−	0.996816i	$-0.525408\pi$
$983$	−5.00000			−0.159475			−0.0797376	+	0.996816i	$0.525408\pi$
$984$		0			0
$985$	8.50000	+	14.7224i	0.270833	+	0.469096i
$986$		0			0
$987$	45.0000			1.43237
$988$		0			0
$989$	−4.00000			−0.127193
$990$		0			0
$991$	−29.0000	−	50.2295i	−0.921215	−	1.59559i	−0.797537	−	0.603269i	$-0.793864\pi$
$991$	−29.0000	−	50.2295i	−0.921215	−	1.59559i	−0.123678	−	0.992322i	$-0.539469\pi$
$992$		0			0
$993$	−12.0000			−0.380808
$994$		0			0
$995$	9.00000	−	15.5885i	0.285319	−	0.494187i
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$		0			0
$999$	−27.5000	−	47.6314i	−0.870061	−	1.50699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.i.c.1329.1		2
13.2	odd	12		1352.2.f.b.337.1		2
13.3	even	3		1352.2.a.b.1.1		1
13.4	even	6		1352.2.i.b.529.1		2
13.5	odd	4		1352.2.o.a.361.1		4
13.6	odd	12		1352.2.o.a.1161.1		4
13.7	odd	12		1352.2.o.a.1161.2		4
13.8	odd	4		1352.2.o.a.361.2		4
13.9	even	3	inner	1352.2.i.c.529.1		2
13.10	even	6		104.2.a.a.1.1	✓	1
13.11	odd	12		1352.2.f.b.337.2		2
13.12	even	2		1352.2.i.b.1329.1		2
39.23	odd	6		936.2.a.f.1.1		1
52.3	odd	6		2704.2.a.d.1.1		1
52.11	even	12		2704.2.f.e.337.2		2
52.15	even	12		2704.2.f.e.337.1		2
52.23	odd	6		208.2.a.b.1.1		1
65.23	odd	12		2600.2.d.f.1249.2		2
65.49	even	6		2600.2.a.e.1.1		1
65.62	odd	12		2600.2.d.f.1249.1		2
91.62	odd	6		5096.2.a.c.1.1		1
104.75	odd	6		832.2.a.h.1.1		1
104.101	even	6		832.2.a.c.1.1		1
156.23	even	6		1872.2.a.l.1.1		1
208.75	odd	12		3328.2.b.t.1665.2		2
208.101	even	12		3328.2.b.a.1665.1		2
208.179	odd	12		3328.2.b.t.1665.1		2
208.205	even	12		3328.2.b.a.1665.2		2
260.179	odd	6		5200.2.a.bb.1.1		1
312.101	odd	6		7488.2.a.x.1.1		1
312.179	even	6		7488.2.a.u.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.a.a.1.1	✓	1	13.10	even	6
208.2.a.b.1.1		1	52.23	odd	6
832.2.a.c.1.1		1	104.101	even	6
832.2.a.h.1.1		1	104.75	odd	6
936.2.a.f.1.1		1	39.23	odd	6
1352.2.a.b.1.1		1	13.3	even	3
1352.2.f.b.337.1		2	13.2	odd	12
1352.2.f.b.337.2		2	13.11	odd	12
1352.2.i.b.529.1		2	13.4	even	6
1352.2.i.b.1329.1		2	13.12	even	2
1352.2.i.c.529.1		2	13.9	even	3	inner
1352.2.i.c.1329.1		2	1.1	even	1	trivial
1352.2.o.a.361.1		4	13.5	odd	4
1352.2.o.a.361.2		4	13.8	odd	4
1352.2.o.a.1161.1		4	13.6	odd	12
1352.2.o.a.1161.2		4	13.7	odd	12
1872.2.a.l.1.1		1	156.23	even	6
2600.2.a.e.1.1		1	65.49	even	6
2600.2.d.f.1249.1		2	65.62	odd	12
2600.2.d.f.1249.2		2	65.23	odd	12
2704.2.a.d.1.1		1	52.3	odd	6
2704.2.f.e.337.1		2	52.15	even	12
2704.2.f.e.337.2		2	52.11	even	12
3328.2.b.a.1665.1		2	208.101	even	12
3328.2.b.a.1665.2		2	208.205	even	12
3328.2.b.t.1665.1		2	208.179	odd	12
3328.2.b.t.1665.2		2	208.75	odd	12
5096.2.a.c.1.1		1	91.62	odd	6
5200.2.a.bb.1.1		1	260.179	odd	6
7488.2.a.u.1.1		1	312.179	even	6
7488.2.a.x.1.1		1	312.101	odd	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:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +1.00000 q^{5} +(2.50000 - 4.33013i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{15} +(1.50000 - 2.59808i) q^{17} +(-1.00000 + 1.73205i) q^{19} -5.00000 q^{21} +(-2.00000 - 3.46410i) q^{23} -4.00000 q^{25} -5.00000 q^{27} +(3.00000 + 5.19615i) q^{29} +4.00000 q^{31} +(-1.00000 + 1.73205i) q^{33} +(2.50000 - 4.33013i) q^{35} +(5.50000 + 9.52628i) q^{37} +(4.00000 + 6.92820i) q^{41} +(0.500000 - 0.866025i) q^{43} +(1.00000 - 1.73205i) q^{45} -9.00000 q^{47} +(-9.00000 - 15.5885i) q^{49} -3.00000 q^{51} -12.0000 q^{53} +(-1.00000 - 1.73205i) q^{55} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-5.00000 - 8.66025i) q^{63} +(3.00000 + 5.19615i) q^{67} +(-2.00000 + 3.46410i) q^{69} +(3.50000 - 6.06218i) q^{71} +2.00000 q^{73} +(2.00000 + 3.46410i) q^{75} -10.0000 q^{77} +12.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +16.0000 q^{83} +(1.50000 - 2.59808i) q^{85} +(3.00000 - 5.19615i) q^{87} +(-5.00000 - 8.66025i) q^{89} +(-2.00000 - 3.46410i) q^{93} +(-1.00000 + 1.73205i) q^{95} +(-5.00000 + 8.66025i) q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 2 q^{5} + 5 q^{7} + 2 q^{9} - 2 q^{11} - q^{15} + 3 q^{17} - 2 q^{19} - 10 q^{21} - 4 q^{23} - 8 q^{25} - 10 q^{27} + 6 q^{29} + 8 q^{31} - 2 q^{33} + 5 q^{35} + 11 q^{37} + 8 q^{41} + q^{43}+ \cdots - 8 q^{99}+O(q^{100}) \) 2 * q - q^3 + 2 * q^5 + 5 * q^7 + 2 * q^9 - 2 * q^11 - q^15 + 3 * q^17 - 2 * q^19 - 10 * q^21 - 4 * q^23 - 8 * q^25 - 10 * q^27 + 6 * q^29 + 8 * q^31 - 2 * q^33 + 5 * q^35 + 11 * q^37 + 8 * q^41 + q^43 + 2 * q^45 - 18 * q^47 - 18 * q^49 - 6 * q^51 - 24 * q^53 - 2 * q^55 + 4 * q^57 + 6 * q^59 - 10 * q^63 + 6 * q^67 - 4 * q^69 + 7 * q^71 + 4 * q^73 + 4 * q^75 - 20 * q^77 + 24 * q^79 - q^81 + 32 * q^83 + 3 * q^85 + 6 * q^87 - 10 * q^89 - 4 * q^93 - 2 * q^95 - 10 * q^97 - 8 * q^99

Introduction

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