LMFDB - Embedded newform 1352.2.i.f.1329.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1352,2,Mod(529,1352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,0,-1,0,6,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
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			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	1352.1329
Dual form			1352.2.i.f.529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28078 - 2.21837i) q^{3} -0.561553 q^{5} +(1.28078 - 2.21837i) q^{7} +(-1.78078 + 3.08440i) q^{9} +(2.56155 + 4.43674i) q^{11} +(0.719224 + 1.24573i) q^{15} +(-2.84233 + 4.92306i) q^{17} +(-2.56155 + 4.43674i) q^{19} -6.56155 q^{21} +(4.00000 + 6.92820i) q^{23} -4.68466 q^{25} +1.43845 q^{27} +(1.00000 + 1.73205i) q^{29} +4.00000 q^{31} +(6.56155 - 11.3649i) q^{33} +(-0.719224 + 1.24573i) q^{35} +(-4.84233 - 8.38716i) q^{37} +(1.56155 + 2.70469i) q^{41} +(-2.71922 + 4.70983i) q^{43} +(1.00000 - 1.73205i) q^{45} -0.315342 q^{47} +(0.219224 + 0.379706i) q^{49} +14.5616 q^{51} +3.12311 q^{53} +(-1.43845 - 2.49146i) q^{55} +13.1231 q^{57} +(-2.56155 + 4.43674i) q^{59} +(-5.56155 + 9.63289i) q^{61} +(4.56155 + 7.90084i) q^{63} +(2.56155 + 4.43674i) q^{67} +(10.2462 - 17.7470i) q^{69} +(3.84233 - 6.65511i) q^{71} -6.00000 q^{73} +(6.00000 + 10.3923i) q^{75} +13.1231 q^{77} +8.00000 q^{79} +(3.50000 + 6.06218i) q^{81} +2.24621 q^{83} +(1.59612 - 2.76456i) q^{85} +(2.56155 - 4.43674i) q^{87} +(-5.00000 - 8.66025i) q^{89} +(-5.12311 - 8.87348i) q^{93} +(1.43845 - 2.49146i) q^{95} +(4.12311 - 7.14143i) q^{97} -18.2462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 6 q^{5} + q^{7} - 3 q^{9} + 2 q^{11} + 7 q^{15} + q^{17} - 2 q^{19} - 18 q^{21} + 16 q^{23} + 6 q^{25} + 14 q^{27} + 4 q^{29} + 16 q^{31} + 18 q^{33} - 7 q^{35} - 7 q^{37} - 2 q^{41} - 15 q^{43}+ \cdots - 40 q^{99}+O(q^{100}) $ 4 * q - q^3 + 6 * q^5 + q^7 - 3 * q^9 + 2 * q^11 + 7 * q^15 + q^17 - 2 * q^19 - 18 * q^21 + 16 * q^23 + 6 * q^25 + 14 * q^27 + 4 * q^29 + 16 * q^31 + 18 * q^33 - 7 * q^35 - 7 * q^37 - 2 * q^41 - 15 * q^43 + 4 * q^45 - 26 * q^47 + 5 * q^49 + 50 * q^51 - 4 * q^53 - 14 * q^55 + 36 * q^57 - 2 * q^59 - 14 * q^61 + 10 * q^63 + 2 * q^67 + 8 * q^69 + 3 * q^71 - 24 * q^73 + 24 * q^75 + 36 * q^77 + 32 * q^79 + 14 * q^81 - 24 * q^83 + 27 * q^85 + 2 * q^87 - 20 * q^89 - 4 * q^93 + 14 * q^95 - 40 * 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
$3$	−1.28078	−	2.21837i	−0.739457	−	1.28078i	−0.952740	−	0.303786i	$-0.901749\pi$
$3$	−1.28078	−	2.21837i	−0.739457	−	1.28078i	0.213284	−	0.976990i	$-0.431584\pi$
$4$		0			0
$5$	−0.561553			−0.251134			−0.125567	−	0.992085i	$-0.540075\pi$
$5$	−0.561553			−0.251134			−0.125567	+	0.992085i	$0.540075\pi$
$6$		0			0
$7$	1.28078	−	2.21837i	0.484088	−	0.838465i	−0.515745	−	0.856742i	$-0.672485\pi$
$7$	1.28078	−	2.21837i	0.484088	−	0.838465i	0.999833	+	0.0182772i	$0.00581813\pi$
$8$		0			0
$9$	−1.78078	+	3.08440i	−0.593592	+	1.02813i
$10$		0			0
$11$	2.56155	+	4.43674i	0.772337	+	1.33773i	0.936279	+	0.351257i	$0.114246\pi$
$11$	2.56155	+	4.43674i	0.772337	+	1.33773i	−0.163942	+	0.986470i	$0.552421\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	0.719224	+	1.24573i	0.185703	+	0.321647i
$16$		0			0
$17$	−2.84233	+	4.92306i	−0.689366	+	1.19402i	0.282677	+	0.959215i	$0.408778\pi$
$17$	−2.84233	+	4.92306i	−0.689366	+	1.19402i	−0.972043	+	0.234802i	$0.924556\pi$
$18$		0			0
$19$	−2.56155	+	4.43674i	−0.587661	+	1.01786i	0.406877	+	0.913483i	$0.366618\pi$
$19$	−2.56155	+	4.43674i	−0.587661	+	1.01786i	−0.994538	+	0.104375i	$0.966716\pi$
$20$		0			0
$21$	−6.56155			−1.43185
$22$		0			0
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	0.894795	+	0.446476i	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$		0			0
$25$	−4.68466			−0.936932
$26$		0			0
$27$	1.43845			0.276829
$28$		0			0
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	0.943811	−	0.330487i	$-0.107213\pi$
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	−0.758115	+	0.652121i	$0.773880\pi$
$30$		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
$33$	6.56155	−	11.3649i	1.14222	−	1.97838i
$34$		0			0
$35$	−0.719224	+	1.24573i	−0.121571	+	0.210567i
$36$		0			0
$37$	−4.84233	−	8.38716i	−0.796074	−	1.37884i	−0.922155	−	0.386821i	$-0.873573\pi$
$37$	−4.84233	−	8.38716i	−0.796074	−	1.37884i	0.126081	−	0.992020i	$-0.459760\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.56155	+	2.70469i	0.243874	+	0.422401i	0.961814	−	0.273703i	$-0.0882485\pi$
$41$	1.56155	+	2.70469i	0.243874	+	0.422401i	−0.717941	+	0.696104i	$0.754915\pi$
$42$		0			0
$43$	−2.71922	+	4.70983i	−0.414678	+	0.718243i	−0.995395	−	0.0958627i	$-0.969439\pi$
$43$	−2.71922	+	4.70983i	−0.414678	+	0.718243i	0.580717	+	0.814106i	$0.302772\pi$
$44$		0			0
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$		0			0
$47$	−0.315342			−0.0459973			−0.0229986	−	0.999735i	$-0.507321\pi$
$47$	−0.315342			−0.0459973			−0.0229986	+	0.999735i	$0.507321\pi$
$48$		0			0
$49$	0.219224	+	0.379706i	0.0313177	+	0.0542438i
$50$		0			0
$51$	14.5616			2.03903
$52$		0			0
$53$	3.12311			0.428992			0.214496	−	0.976725i	$-0.431189\pi$
$53$	3.12311			0.428992			0.214496	+	0.976725i	$0.431189\pi$
$54$		0			0
$55$	−1.43845	−	2.49146i	−0.193960	−	0.335949i
$56$		0			0
$57$	13.1231			1.73820
$58$		0			0
$59$	−2.56155	+	4.43674i	−0.333486	+	0.577614i	−0.983193	−	0.182570i	$-0.941558\pi$
$59$	−2.56155	+	4.43674i	−0.333486	+	0.577614i	0.649707	+	0.760185i	$0.274892\pi$
$60$		0			0
$61$	−5.56155	+	9.63289i	−0.712084	+	1.23337i	0.251990	+	0.967730i	$0.418915\pi$
$61$	−5.56155	+	9.63289i	−0.712084	+	1.23337i	−0.964074	+	0.265636i	$0.914418\pi$
$62$		0			0
$63$	4.56155	+	7.90084i	0.574702	+	0.995412i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.56155	+	4.43674i	0.312943	+	0.542034i	0.978998	−	0.203869i	$-0.0653516\pi$
$67$	2.56155	+	4.43674i	0.312943	+	0.542034i	−0.666055	+	0.745903i	$0.732018\pi$
$68$		0			0
$69$	10.2462	−	17.7470i	1.23350	−	2.13648i
$70$		0			0
$71$	3.84233	−	6.65511i	0.456001	−	0.789816i	−0.542745	−	0.839898i	$-0.682615\pi$
$71$	3.84233	−	6.65511i	0.456001	−	0.789816i	0.998745	+	0.0500816i	$0.0159482\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$		0			0
$75$	6.00000	+	10.3923i	0.692820	+	1.20000i
$76$		0			0
$77$	13.1231			1.49552
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$		0			0
$83$	2.24621			0.246554			0.123277	−	0.992372i	$-0.460660\pi$
$83$	2.24621			0.246554			0.123277	+	0.992372i	$0.460660\pi$
$84$		0			0
$85$	1.59612	−	2.76456i	0.173123	−	0.299858i
$86$		0			0
$87$	2.56155	−	4.43674i	0.274627	−	0.475668i
$88$		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
$93$	−5.12311	−	8.87348i	−0.531241	−	0.920137i
$94$		0			0
$95$	1.43845	−	2.49146i	0.147582	−	0.255619i
$96$		0			0
$97$	4.12311	−	7.14143i	0.418638	−	0.725102i	−0.577165	−	0.816628i	$-0.695841\pi$
$97$	4.12311	−	7.14143i	0.418638	−	0.725102i	0.995803	+	0.0915255i	$0.0291743\pi$
$98$		0			0
$99$	−18.2462			−1.83381
$100$		0			0
$101$	3.56155	+	6.16879i	0.354388	+	0.613818i	0.987013	−	0.160640i	$-0.0513560\pi$
$101$	3.56155	+	6.16879i	0.354388	+	0.613818i	−0.632625	+	0.774458i	$0.718023\pi$
$102$		0			0
$103$	2.24621			0.221326			0.110663	−	0.993858i	$-0.464703\pi$
$103$	2.24621			0.221326			0.110663	+	0.993858i	$0.464703\pi$
$104$		0			0
$105$	3.68466			0.359586
$106$		0			0
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	0.753010	−	0.658009i	$-0.228601\pi$
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	−0.946357	+	0.323122i	$0.895268\pi$
$108$		0			0
$109$	−2.80776			−0.268935			−0.134468	−	0.990918i	$-0.542932\pi$
$109$	−2.80776			−0.268935			−0.134468	+	0.990918i	$0.542932\pi$
$110$		0			0
$111$	−12.4039	+	21.4842i	−1.17732	+	2.03919i
$112$		0			0
$113$	9.24621	−	16.0149i	0.869810	−	1.50656i	0.00762026	−	0.999971i	$-0.497574\pi$
$113$	9.24621	−	16.0149i	0.869810	−	1.50656i	0.862190	−	0.506585i	$-0.169092\pi$
$114$		0			0
$115$	−2.24621	−	3.89055i	−0.209460	−	0.362796i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.28078	+	12.6107i	0.667428	+	1.15602i
$120$		0			0
$121$	−7.62311	+	13.2036i	−0.693010	+	1.20033i
$122$		0			0
$123$	4.00000	−	6.92820i	0.360668	−	0.624695i
$124$		0			0
$125$	5.43845			0.486430
$126$		0			0
$127$	5.12311	+	8.87348i	0.454602	+	0.787394i	0.998665	−	0.0516503i	$-0.0164481\pi$
$127$	5.12311	+	8.87348i	0.454602	+	0.787394i	−0.544063	+	0.839044i	$0.683115\pi$
$128$		0			0
$129$	13.9309			1.22654
$130$		0			0
$131$	−4.80776			−0.420056			−0.210028	−	0.977695i	$-0.567356\pi$
$131$	−4.80776			−0.420056			−0.210028	+	0.977695i	$0.567356\pi$
$132$		0			0
$133$	6.56155	+	11.3649i	0.568959	+	0.985466i
$134$		0			0
$135$	−0.807764			−0.0695213
$136$		0			0
$137$	1.56155	−	2.70469i	0.133412	−	0.231077i	−0.791577	−	0.611069i	$-0.790740\pi$
$137$	1.56155	−	2.70469i	0.133412	−	0.231077i	0.924990	+	0.379992i	$0.124073\pi$
$138$		0			0
$139$	−3.84233	+	6.65511i	−0.325902	+	0.564479i	−0.981695	−	0.190462i	$-0.939001\pi$
$139$	−3.84233	+	6.65511i	−0.325902	+	0.564479i	0.655792	+	0.754941i	$0.272335\pi$
$140$		0			0
$141$	0.403882	+	0.699544i	0.0340130	+	0.0589122i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−0.561553	−	0.972638i	−0.0466344	−	0.0807732i
$146$		0			0
$147$	0.561553	−	0.972638i	0.0463161	−	0.0802218i
$148$		0			0
$149$	−8.12311	+	14.0696i	−0.665471	+	1.15263i	0.313687	+	0.949527i	$0.398436\pi$
$149$	−8.12311	+	14.0696i	−0.665471	+	1.15263i	−0.979157	+	0.203103i	$0.934898\pi$
$150$		0			0
$151$	10.5616			0.859487			0.429743	−	0.902951i	$-0.358604\pi$
$151$	10.5616			0.859487			0.429743	+	0.902951i	$0.358604\pi$
$152$		0			0
$153$	−10.1231	−	17.5337i	−0.818405	−	1.41752i
$154$		0			0
$155$	−2.24621			−0.180420
$156$		0			0
$157$	−22.4924			−1.79509			−0.897545	−	0.440922i	$-0.854651\pi$
$157$	−22.4924			−1.79509			−0.897545	+	0.440922i	$0.854651\pi$
$158$		0			0
$159$	−4.00000	−	6.92820i	−0.317221	−	0.549442i
$160$		0			0
$161$	20.4924			1.61503
$162$		0			0
$163$	10.2462	−	17.7470i	0.802545	−	1.39005i	−0.115391	−	0.993320i	$-0.536812\pi$
$163$	10.2462	−	17.7470i	0.802545	−	1.39005i	0.917936	−	0.396729i	$-0.129855\pi$
$164$		0			0
$165$	−3.68466	+	6.38202i	−0.286850	+	0.496839i
$166$		0			0
$167$	−7.12311	−	12.3376i	−0.551202	−	0.954711i	−0.998188	−	0.0601696i	$-0.980836\pi$
$167$	−7.12311	−	12.3376i	−0.551202	−	0.954711i	0.446986	−	0.894541i	$-0.352497\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−9.12311	−	15.8017i	−0.697661	−	1.20838i
$172$		0			0
$173$	2.43845	−	4.22351i	0.185392	−	0.321108i	−0.758317	−	0.651886i	$-0.773978\pi$
$173$	2.43845	−	4.22351i	0.185392	−	0.321108i	0.943708	+	0.330778i	$0.107311\pi$
$174$		0			0
$175$	−6.00000	+	10.3923i	−0.453557	+	0.785584i
$176$		0			0
$177$	13.1231			0.986393
$178$		0			0
$179$	−3.84233	−	6.65511i	−0.287189	−	0.497426i	0.685949	−	0.727650i	$-0.259388\pi$
$179$	−3.84233	−	6.65511i	−0.287189	−	0.497426i	−0.973138	+	0.230224i	$0.926054\pi$
$180$		0			0
$181$	−23.1231			−1.71873			−0.859363	−	0.511365i	$-0.829140\pi$
$181$	−23.1231			−1.71873			−0.859363	+	0.511365i	$0.829140\pi$
$182$		0			0
$183$	28.4924			2.10622
$184$		0			0
$185$	2.71922	+	4.70983i	0.199921	+	0.346274i
$186$		0			0
$187$	−29.1231			−2.12969
$188$		0			0
$189$	1.84233	−	3.19101i	0.134010	−	0.232112i
$190$		0			0
$191$	−7.68466	+	13.3102i	−0.556042	+	0.963094i	0.441779	+	0.897124i	$0.354347\pi$
$191$	−7.68466	+	13.3102i	−0.556042	+	0.963094i	−0.997822	+	0.0659698i	$0.978986\pi$
$192$		0			0
$193$	10.6847	+	18.5064i	0.769099	+	1.33212i	0.938052	+	0.346494i	$0.112628\pi$
$193$	10.6847	+	18.5064i	0.769099	+	1.33212i	−0.168954	+	0.985624i	$0.554039\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.15767	−	2.00514i	−0.0824806	−	0.142861i	0.821834	−	0.569727i	$-0.192951\pi$
$197$	−1.15767	−	2.00514i	−0.0824806	−	0.142861i	−0.904315	+	0.426866i	$0.859618\pi$
$198$		0			0
$199$	−2.56155	+	4.43674i	−0.181584	+	0.314512i	−0.942420	−	0.334432i	$-0.891456\pi$
$199$	−2.56155	+	4.43674i	−0.181584	+	0.314512i	0.760836	+	0.648944i	$0.224789\pi$
$200$		0			0
$201$	6.56155	−	11.3649i	0.462816	−	0.801621i
$202$		0			0
$203$	5.12311			0.359572
$204$		0			0
$205$	−0.876894	−	1.51883i	−0.0612450	−	0.106079i
$206$		0			0
$207$	−28.4924			−1.98036
$208$		0			0
$209$	−26.2462			−1.81549
$210$		0			0
$211$	−7.84233	−	13.5833i	−0.539888	−	0.935114i	−0.998909	−	0.0466885i	$-0.985133\pi$
$211$	−7.84233	−	13.5833i	−0.539888	−	0.935114i	0.459021	−	0.888425i	$-0.348200\pi$
$212$		0			0
$213$	−19.6847			−1.34877
$214$		0			0
$215$	1.52699	−	2.64482i	0.104140	−	0.180375i
$216$		0			0
$217$	5.12311	−	8.87348i	0.347779	−	0.602371i
$218$		0			0
$219$	7.68466	+	13.3102i	0.519281	+	0.899421i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	7.84233	+	13.5833i	0.525161	+	0.909606i	0.999571	+	0.0293016i	$0.00932831\pi$
$223$	7.84233	+	13.5833i	0.525161	+	0.909606i	−0.474409	+	0.880304i	$0.657338\pi$
$224$		0			0
$225$	8.34233	−	14.4493i	0.556155	−	0.963289i
$226$		0			0
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	−0.702202	−	0.711977i	$-0.747800\pi$
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	0.967692	+	0.252136i	$0.0811332\pi$
$228$		0			0
$229$	6.80776			0.449870			0.224935	−	0.974374i	$-0.427783\pi$
$229$	6.80776			0.449870			0.224935	+	0.974374i	$0.427783\pi$
$230$		0			0
$231$	−16.8078	−	29.1119i	−1.10587	−	1.91542i
$232$		0			0
$233$	−6.80776			−0.445991			−0.222996	−	0.974819i	$-0.571584\pi$
$233$	−6.80776			−0.445991			−0.222996	+	0.974819i	$0.571584\pi$
$234$		0			0
$235$	0.177081			0.0115515
$236$		0			0
$237$	−10.2462	−	17.7470i	−0.665563	−	1.15279i
$238$		0			0
$239$	−2.56155			−0.165693			−0.0828465	−	0.996562i	$-0.526401\pi$
$239$	−2.56155			−0.165693			−0.0828465	+	0.996562i	$0.526401\pi$
$240$		0			0
$241$	1.87689	−	3.25088i	0.120901	−	0.209407i	−0.799222	−	0.601036i	$-0.794755\pi$
$241$	1.87689	−	3.25088i	0.120901	−	0.209407i	0.920123	+	0.391629i	$0.128088\pi$
$242$		0			0
$243$	11.1231	−	19.2658i	0.713548	−	1.23590i
$244$		0			0
$245$	−0.123106	−	0.213225i	−0.00786493	−	0.0136225i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−2.87689	−	4.98293i	−0.182316	−	0.315780i
$250$		0			0
$251$	−11.1231	+	19.2658i	−0.702084	+	1.21605i	0.265649	+	0.964070i	$0.414414\pi$
$251$	−11.1231	+	19.2658i	−0.702084	+	1.21605i	−0.967734	+	0.251976i	$0.918920\pi$
$252$		0			0
$253$	−20.4924	+	35.4939i	−1.28835	+	2.23148i
$254$		0			0
$255$	−8.17708			−0.512069
$256$		0			0
$257$	−5.71922	−	9.90599i	−0.356755	−	0.617918i	0.630661	−	0.776058i	$-0.282784\pi$
$257$	−5.71922	−	9.90599i	−0.356755	−	0.617918i	−0.987417	+	0.158140i	$0.949450\pi$
$258$		0			0
$259$	−24.8078			−1.54148
$260$		0			0
$261$	−7.12311			−0.440909
$262$		0			0
$263$	13.1231	+	22.7299i	0.809205	+	1.40158i	0.913415	+	0.407029i	$0.133435\pi$
$263$	13.1231	+	22.7299i	0.809205	+	1.40158i	−0.104210	+	0.994555i	$0.533231\pi$
$264$		0			0
$265$	−1.75379			−0.107734
$266$		0			0
$267$	−12.8078	+	22.1837i	−0.783822	+	1.35762i
$268$		0			0
$269$	2.43845	−	4.22351i	0.148675	−	0.257512i	−0.782063	−	0.623199i	$-0.785833\pi$
$269$	2.43845	−	4.22351i	0.148675	−	0.257512i	0.930738	+	0.365687i	$0.119166\pi$
$270$		0			0
$271$	10.4039	+	18.0201i	0.631991	+	1.09464i	0.987144	+	0.159832i	$0.0510953\pi$
$271$	10.4039	+	18.0201i	0.631991	+	1.09464i	−0.355153	+	0.934808i	$0.615571\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−12.0000	−	20.7846i	−0.723627	−	1.25336i
$276$		0			0
$277$	−14.6847	+	25.4346i	−0.882316	+	1.52822i	−0.0335558	+	0.999437i	$0.510683\pi$
$277$	−14.6847	+	25.4346i	−0.882316	+	1.52822i	−0.848760	+	0.528779i	$0.822650\pi$
$278$		0			0
$279$	−7.12311	+	12.3376i	−0.426449	+	0.738632i
$280$		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
$283$	4.24621	+	7.35465i	0.252411	+	0.437189i	0.964189	−	0.265216i	$-0.0854432\pi$
$283$	4.24621	+	7.35465i	0.252411	+	0.437189i	−0.711778	+	0.702404i	$0.752110\pi$
$284$		0			0
$285$	−7.36932			−0.436521
$286$		0			0
$287$	8.00000			0.472225
$288$		0			0
$289$	−7.65767	−	13.2635i	−0.450451	−	0.780204i
$290$		0			0
$291$	−21.1231			−1.23826
$292$		0			0
$293$	−7.71922	+	13.3701i	−0.450962	+	0.781089i	−0.998446	−	0.0557272i	$-0.982252\pi$
$293$	−7.71922	+	13.3701i	−0.450962	+	0.781089i	0.547484	+	0.836816i	$0.315586\pi$
$294$		0			0
$295$	1.43845	−	2.49146i	0.0837496	−	0.145059i
$296$		0			0
$297$	3.68466	+	6.38202i	0.213806	+	0.370322i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	6.96543	+	12.0645i	0.401481	+	0.695385i
$302$		0			0
$303$	9.12311	−	15.8017i	0.524109	−	0.907783i
$304$		0			0
$305$	3.12311	−	5.40938i	0.178829	−	0.309740i
$306$		0			0
$307$	13.1231			0.748975			0.374488	−	0.927232i	$-0.377819\pi$
$307$	13.1231			0.748975			0.374488	+	0.927232i	$0.377819\pi$
$308$		0			0
$309$	−2.87689	−	4.98293i	−0.163661	−	0.283469i
$310$		0			0
$311$	−10.8769			−0.616772			−0.308386	−	0.951261i	$-0.599789\pi$
$311$	−10.8769			−0.616772			−0.308386	+	0.951261i	$0.599789\pi$
$312$		0			0
$313$	26.8078			1.51526			0.757632	−	0.652682i	$-0.226356\pi$
$313$	26.8078			1.51526			0.757632	+	0.652682i	$0.226356\pi$
$314$		0			0
$315$	−2.56155	−	4.43674i	−0.144327	−	0.249982i
$316$		0			0
$317$	−12.2462			−0.687816			−0.343908	−	0.939003i	$-0.611751\pi$
$317$	−12.2462			−0.687816			−0.343908	+	0.939003i	$0.611751\pi$
$318$		0			0
$319$	−5.12311	+	8.87348i	−0.286839	+	0.496819i
$320$		0			0
$321$	−5.12311	+	8.87348i	−0.285944	+	0.495269i
$322$		0			0
$323$	−14.5616	−	25.2213i	−0.810226	−	1.40335i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.59612	+	6.22866i	0.198866	+	0.344446i
$328$		0			0
$329$	−0.403882	+	0.699544i	−0.0222667	+	0.0385671i
$330$		0			0
$331$	2.24621	−	3.89055i	0.123463	−	0.213844i	−0.797668	−	0.603097i	$-0.793933\pi$
$331$	2.24621	−	3.89055i	0.123463	−	0.213844i	0.921131	+	0.389253i	$0.127267\pi$
$332$		0			0
$333$	34.4924			1.89017
$334$		0			0
$335$	−1.43845	−	2.49146i	−0.0785908	−	0.136123i
$336$		0			0
$337$	−13.1922			−0.718627			−0.359313	−	0.933217i	$-0.616989\pi$
$337$	−13.1922			−0.718627			−0.359313	+	0.933217i	$0.616989\pi$
$338$		0			0
$339$	−47.3693			−2.57275
$340$		0			0
$341$	10.2462	+	17.7470i	0.554863	+	0.961052i
$342$		0			0
$343$	19.0540			1.02882
$344$		0			0
$345$	−5.75379	+	9.96585i	−0.309774	+	0.536544i
$346$		0			0
$347$	−3.84233	+	6.65511i	−0.206267	+	0.357265i	−0.950536	−	0.310615i	$-0.899465\pi$
$347$	−3.84233	+	6.65511i	−0.206267	+	0.357265i	0.744269	+	0.667880i	$0.232798\pi$
$348$		0			0
$349$	−5.96543	−	10.3324i	−0.319322	−	0.553083i	0.661024	−	0.750364i	$-0.270122\pi$
$349$	−5.96543	−	10.3324i	−0.319322	−	0.553083i	−0.980347	+	0.197282i	$0.936789\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.68466	−	8.11407i	−0.249339	−	0.431868i	0.714003	−	0.700142i	$-0.246880\pi$
$353$	−4.68466	−	8.11407i	−0.249339	−	0.431868i	−0.963343	+	0.268274i	$0.913547\pi$
$354$		0			0
$355$	−2.15767	+	3.73720i	−0.114517	+	0.198350i
$356$		0			0
$357$	18.6501	−	32.3029i	0.987068	−	1.70965i
$358$		0			0
$359$	14.2462			0.751886			0.375943	−	0.926643i	$-0.377319\pi$
$359$	14.2462			0.751886			0.375943	+	0.926643i	$0.377319\pi$
$360$		0			0
$361$	−3.62311	−	6.27540i	−0.190690	−	0.330284i
$362$		0			0
$363$	39.0540			2.04980
$364$		0			0
$365$	3.36932			0.176358
$366$		0			0
$367$	−4.80776	−	8.32729i	−0.250963	−	0.434681i	0.712828	−	0.701339i	$-0.247414\pi$
$367$	−4.80776	−	8.32729i	−0.250963	−	0.434681i	−0.963791	+	0.266658i	$0.914081\pi$
$368$		0			0
$369$	−11.1231			−0.579046
$370$		0			0
$371$	4.00000	−	6.92820i	0.207670	−	0.359694i
$372$		0			0
$373$	5.80776	−	10.0593i	0.300715	−	0.520853i	−0.675583	−	0.737284i	$-0.736108\pi$
$373$	5.80776	−	10.0593i	0.300715	−	0.520853i	0.976298	+	0.216431i	$0.0694415\pi$
$374$		0			0
$375$	−6.96543	−	12.0645i	−0.359694	−	0.623007i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−2.87689	−	4.98293i	−0.147776	−	0.255956i	0.782629	−	0.622488i	$-0.213878\pi$
$379$	−2.87689	−	4.98293i	−0.147776	−	0.255956i	−0.930405	+	0.366533i	$0.880545\pi$
$380$		0			0
$381$	13.1231	−	22.7299i	0.672317	−	1.16449i
$382$		0			0
$383$	5.59612	−	9.69276i	0.285948	−	0.495277i	−0.686890	−	0.726761i	$-0.741025\pi$
$383$	5.59612	−	9.69276i	0.285948	−	0.495277i	0.972839	+	0.231484i	$0.0743581\pi$
$384$		0			0
$385$	−7.36932			−0.375575
$386$		0			0
$387$	−9.68466	−	16.7743i	−0.492299	−	0.852687i
$388$		0			0
$389$	20.7386			1.05149			0.525745	−	0.850642i	$-0.323787\pi$
$389$	20.7386			1.05149			0.525745	+	0.850642i	$0.323787\pi$
$390$		0			0
$391$	−45.4773			−2.29988
$392$		0			0
$393$	6.15767	+	10.6654i	0.310613	+	0.537998i
$394$		0			0
$395$	−4.49242			−0.226038
$396$		0			0
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$		0			0
$399$	16.8078	−	29.1119i	0.841441	−	1.45742i
$400$		0			0
$401$	−1.80776	−	3.13114i	−0.0902754	−	0.156362i	0.817352	−	0.576139i	$-0.195441\pi$
$401$	−1.80776	−	3.13114i	−0.0902754	−	0.156362i	−0.907627	+	0.419778i	$0.862108\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.96543	−	3.40423i	−0.0976632	−	0.169158i
$406$		0			0
$407$	24.8078	−	42.9683i	1.22968	−	2.12986i
$408$		0			0
$409$	−6.43845	+	11.1517i	−0.318361	+	0.551417i	−0.980146	−	0.198276i	$-0.936466\pi$
$409$	−6.43845	+	11.1517i	−0.318361	+	0.551417i	0.661785	+	0.749693i	$0.269799\pi$
$410$		0			0
$411$	−8.00000			−0.394611
$412$		0			0
$413$	6.56155	+	11.3649i	0.322873	+	0.559232i
$414$		0			0
$415$	−1.26137			−0.0619180
$416$		0			0
$417$	19.6847			0.963962
$418$		0			0
$419$	0.965435	+	1.67218i	0.0471646	+	0.0816914i	0.888644	−	0.458598i	$-0.151648\pi$
$419$	0.965435	+	1.67218i	0.0471646	+	0.0816914i	−0.841479	+	0.540289i	$0.818315\pi$
$420$		0			0
$421$	−6.31534			−0.307791			−0.153895	−	0.988087i	$-0.549182\pi$
$421$	−6.31534			−0.307791			−0.153895	+	0.988087i	$0.549182\pi$
$422$		0			0
$423$	0.561553	−	0.972638i	0.0273036	−	0.0472913i
$424$		0			0
$425$	13.3153	−	23.0628i	0.645889	−	1.11871i
$426$		0			0
$427$	14.2462	+	24.6752i	0.689422	+	1.19411i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.28078	+	16.0748i	0.447039	+	0.774295i	0.998192	−	0.0601098i	$-0.0191451\pi$
$431$	9.28078	+	16.0748i	0.447039	+	0.774295i	−0.551153	+	0.834405i	$0.685812\pi$
$432$		0			0
$433$	3.08854	−	5.34951i	0.148426	−	0.257081i	−0.782220	−	0.623002i	$-0.785913\pi$
$433$	3.08854	−	5.34951i	0.148426	−	0.257081i	0.930646	+	0.365921i	$0.119246\pi$
$434$		0			0
$435$	−1.43845	+	2.49146i	−0.0689683	+	0.119457i
$436$		0			0
$437$	−40.9848			−1.96057
$438$		0			0
$439$	−10.5616	−	18.2931i	−0.504075	−	0.873084i	−0.999989	−	0.00471229i	$-0.998500\pi$
$439$	−10.5616	−	18.2931i	−0.504075	−	0.873084i	0.495913	−	0.868372i	$-0.334833\pi$
$440$		0			0
$441$	−1.56155			−0.0743597
$442$		0			0
$443$	20.8078			0.988607			0.494303	−	0.869289i	$-0.335423\pi$
$443$	20.8078			0.988607			0.494303	+	0.869289i	$0.335423\pi$
$444$		0			0
$445$	2.80776	+	4.86319i	0.133101	+	0.230537i
$446$		0			0
$447$	41.6155			1.96835
$448$		0			0
$449$	−16.3693	+	28.3525i	−0.772516	+	1.33804i	0.163664	+	0.986516i	$0.447669\pi$
$449$	−16.3693	+	28.3525i	−0.772516	+	1.33804i	−0.936180	+	0.351521i	$0.885665\pi$
$450$		0			0
$451$	−8.00000	+	13.8564i	−0.376705	+	0.652473i
$452$		0			0
$453$	−13.5270	−	23.4294i	−0.635553	−	1.10081i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−12.3693	−	21.4243i	−0.578612	−	1.00219i	−0.995639	−	0.0932915i	$-0.970261\pi$
$457$	−12.3693	−	21.4243i	−0.578612	−	1.00219i	0.417027	−	0.908894i	$-0.363072\pi$
$458$		0			0
$459$	−4.08854	+	7.08156i	−0.190837	+	0.330539i
$460$		0			0
$461$	17.4039	−	30.1444i	0.810580	−	1.40397i	−0.101879	−	0.994797i	$-0.532486\pi$
$461$	17.4039	−	30.1444i	0.810580	−	1.40397i	0.912459	−	0.409168i	$-0.134181\pi$
$462$		0			0
$463$	38.2462			1.77745			0.888726	−	0.458439i	$-0.151591\pi$
$463$	38.2462			1.77745			0.888726	+	0.458439i	$0.151591\pi$
$464$		0			0
$465$	2.87689	+	4.98293i	0.133413	+	0.231078i
$466$		0			0
$467$	40.4924			1.87377			0.936883	−	0.349643i	$-0.113697\pi$
$467$	40.4924			1.87377			0.936883	+	0.349643i	$0.113697\pi$
$468$		0			0
$469$	13.1231			0.605969
$470$		0			0
$471$	28.8078	+	49.8965i	1.32739	+	2.29911i
$472$		0			0
$473$	−27.8617			−1.28108
$474$		0			0
$475$	12.0000	−	20.7846i	0.550598	−	0.953663i
$476$		0			0
$477$	−5.56155	+	9.63289i	−0.254646	+	0.441060i
$478$		0			0
$479$	−5.59612	−	9.69276i	−0.255693	−	0.442874i	0.709390	−	0.704816i	$-0.248970\pi$
$479$	−5.59612	−	9.69276i	−0.255693	−	0.442874i	−0.965084	+	0.261942i	$0.915637\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−26.2462	−	45.4598i	−1.19424	−	2.06849i
$484$		0			0
$485$	−2.31534	+	4.01029i	−0.105134	+	0.182098i
$486$		0			0
$487$	−0.876894	+	1.51883i	−0.0397359	+	0.0688246i	−0.885209	−	0.465193i	$-0.845985\pi$
$487$	−0.876894	+	1.51883i	−0.0397359	+	0.0688246i	0.845473	+	0.534017i	$0.179318\pi$
$488$		0			0
$489$	−52.4924			−2.37379
$490$		0			0
$491$	−0.473012	−	0.819281i	−0.0213467	−	0.0369737i	0.855155	−	0.518373i	$-0.173462\pi$
$491$	−0.473012	−	0.819281i	−0.0213467	−	0.0369737i	−0.876501	+	0.481399i	$0.840129\pi$
$492$		0			0
$493$	−11.3693			−0.512048
$494$		0			0
$495$	10.2462			0.460533
$496$		0			0
$497$	−9.84233	−	17.0474i	−0.441489	−	0.764681i
$498$		0			0
$499$	28.4924			1.27550			0.637748	−	0.770245i	$-0.279866\pi$
$499$	28.4924			1.27550			0.637748	+	0.770245i	$0.279866\pi$
$500$		0			0
$501$	−18.2462	+	31.6034i	−0.815181	+	1.41193i
$502$		0			0
$503$	3.68466	−	6.38202i	0.164291	−	0.284560i	−0.772112	−	0.635486i	$-0.780800\pi$
$503$	3.68466	−	6.38202i	0.164291	−	0.284560i	0.936403	+	0.350926i	$0.114133\pi$
$504$		0			0
$505$	−2.00000	−	3.46410i	−0.0889988	−	0.154150i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	−7.68466	+	13.3102i	−0.339949	+	0.588809i
$512$		0			0
$513$	−3.68466	+	6.38202i	−0.162682	+	0.281773i
$514$		0			0
$515$	−1.26137			−0.0555824
$516$		0			0
$517$	−0.807764	−	1.39909i	−0.0355254	−	0.0615318i
$518$		0			0
$519$	−12.4924			−0.548356
$520$		0			0
$521$	−9.68466			−0.424293			−0.212146	−	0.977238i	$-0.568045\pi$
$521$	−9.68466			−0.424293			−0.212146	+	0.977238i	$0.568045\pi$
$522$		0			0
$523$	0.246211	+	0.426450i	0.0107661	+	0.0186474i	0.871358	−	0.490647i	$-0.163240\pi$
$523$	0.246211	+	0.426450i	0.0107661	+	0.0186474i	−0.860592	+	0.509295i	$0.829906\pi$
$524$		0			0
$525$	30.7386			1.34154
$526$		0			0
$527$	−11.3693	+	19.6922i	−0.495255	+	0.857807i
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$		0			0
$531$	−9.12311	−	15.8017i	−0.395909	−	0.685735i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.12311	+	1.94528i	0.0485561	+	0.0841016i
$536$		0			0
$537$	−9.84233	+	17.0474i	−0.424728	+	0.735650i
$538$		0			0
$539$	−1.12311	+	1.94528i	−0.0483756	+	0.0837890i
$540$		0			0
$541$	−5.68466			−0.244403			−0.122201	−	0.992505i	$-0.538995\pi$
$541$	−5.68466			−0.244403			−0.122201	+	0.992505i	$0.538995\pi$
$542$		0			0
$543$	29.6155	+	51.2956i	1.27092	+	2.20130i
$544$		0			0
$545$	1.57671			0.0675387
$546$		0			0
$547$	−29.4384			−1.25870			−0.629349	−	0.777123i	$-0.716678\pi$
$547$	−29.4384			−1.25870			−0.629349	+	0.777123i	$0.716678\pi$
$548$		0			0
$549$	−19.8078	−	34.3081i	−0.845375	−	1.46423i
$550$		0			0
$551$	−10.2462			−0.436503
$552$		0			0
$553$	10.2462	−	17.7470i	0.435713	−	0.754677i
$554$		0			0
$555$	6.96543	−	12.0645i	0.295666	−	0.512109i
$556$		0			0
$557$	21.0885	+	36.5264i	0.893550	+	1.54767i	0.835589	+	0.549355i	$0.185127\pi$
$557$	21.0885	+	36.5264i	0.893550	+	1.54767i	0.0579613	+	0.998319i	$0.481540\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	37.3002	+	64.6058i	1.57482	+	2.72766i
$562$		0			0
$563$	3.52699	−	6.10892i	0.148645	−	0.257460i	−0.782082	−	0.623176i	$-0.785842\pi$
$563$	3.52699	−	6.10892i	0.148645	−	0.257460i	0.930727	+	0.365715i	$0.119176\pi$
$564$		0			0
$565$	−5.19224	+	8.99322i	−0.218439	+	0.378347i
$566$		0			0
$567$	17.9309			0.753026
$568$		0			0
$569$	20.8423	+	36.1000i	0.873756	+	1.51339i	0.858082	+	0.513512i	$0.171656\pi$
$569$	20.8423	+	36.1000i	0.873756	+	1.51339i	0.0156737	+	0.999877i	$0.495011\pi$
$570$		0			0
$571$	28.8078			1.20557			0.602784	−	0.797905i	$-0.294058\pi$
$571$	28.8078			1.20557			0.602784	+	0.797905i	$0.294058\pi$
$572$		0			0
$573$	39.3693			1.64468
$574$		0			0
$575$	−18.7386	−	32.4563i	−0.781455	−	1.35352i
$576$		0			0
$577$	−24.2462			−1.00938			−0.504691	−	0.863300i	$-0.668394\pi$
$577$	−24.2462			−1.00938			−0.504691	+	0.863300i	$0.668394\pi$
$578$		0			0
$579$	27.3693	−	47.4050i	1.13743	−	1.97009i
$580$		0			0
$581$	2.87689	−	4.98293i	0.119354	−	0.206727i
$582$		0			0
$583$	8.00000	+	13.8564i	0.331326	+	0.573874i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.4924	+	21.6375i	0.515617	+	0.893076i	0.999836	+	0.0181284i	$0.00577075\pi$
$587$	12.4924	+	21.6375i	0.515617	+	0.893076i	−0.484218	+	0.874947i	$0.660896\pi$
$588$		0			0
$589$	−10.2462	+	17.7470i	−0.422188	+	0.731251i
$590$		0			0
$591$	−2.96543	+	5.13628i	−0.121982	+	0.211278i
$592$		0			0
$593$	38.4924			1.58069			0.790347	−	0.612659i	$-0.209900\pi$
$593$	38.4924			1.58069			0.790347	+	0.612659i	$0.209900\pi$
$594$		0			0
$595$	−4.08854	−	7.08156i	−0.167614	−	0.290316i
$596$		0			0
$597$	13.1231			0.537093
$598$		0			0
$599$	23.3693			0.954844			0.477422	−	0.878674i	$-0.341571\pi$
$599$	23.3693			0.954844			0.477422	+	0.878674i	$0.341571\pi$
$600$		0			0
$601$	−17.0885	−	29.5982i	−0.697056	−	1.20734i	−0.969483	−	0.245160i	$-0.921160\pi$
$601$	−17.0885	−	29.5982i	−0.697056	−	1.20734i	0.272427	−	0.962177i	$-0.412174\pi$
$602$		0			0
$603$	−18.2462			−0.743043
$604$		0			0
$605$	4.28078	−	7.41452i	0.174038	−	0.301443i
$606$		0			0
$607$	−7.68466	+	13.3102i	−0.311911	+	0.540245i	−0.978776	−	0.204933i	$-0.934302\pi$
$607$	−7.68466	+	13.3102i	−0.311911	+	0.540245i	0.666865	+	0.745178i	$0.267636\pi$
$608$		0			0
$609$	−6.56155	−	11.3649i	−0.265888	−	0.460531i
$610$		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
$615$	−2.24621	+	3.89055i	−0.0905760	+	0.156882i
$616$		0			0
$617$	−10.9309	+	18.9328i	−0.440060	+	0.762207i	−0.997693	−	0.0678808i	$-0.978376\pi$
$617$	−10.9309	+	18.9328i	−0.440060	+	0.762207i	0.557633	+	0.830087i	$0.311710\pi$
$618$		0			0
$619$	−29.7538			−1.19591			−0.597953	−	0.801531i	$-0.704019\pi$
$619$	−29.7538			−1.19591			−0.597953	+	0.801531i	$0.704019\pi$
$620$		0			0
$621$	5.75379	+	9.96585i	0.230892	+	0.399916i
$622$		0			0
$623$	−25.6155			−1.02626
$624$		0			0
$625$	20.3693			0.814773
$626$		0			0
$627$	33.6155	+	58.2238i	1.34247	+	2.32523i
$628$		0			0
$629$	55.0540			2.19515
$630$		0			0
$631$	23.8423	−	41.2961i	0.949148	−	1.64397i	0.201923	−	0.979401i	$-0.435281\pi$
$631$	23.8423	−	41.2961i	0.949148	−	1.64397i	0.747225	−	0.664571i	$-0.231386\pi$
$632$		0			0
$633$	−20.0885	+	34.7944i	−0.798448	+	1.38295i
$634$		0			0
$635$	−2.87689	−	4.98293i	−0.114166	−	0.197741i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	13.6847	+	23.7025i	0.541357	+	0.937657i
$640$		0			0
$641$	4.12311	−	7.14143i	0.162853	−	0.282069i	−0.773038	−	0.634360i	$-0.781264\pi$
$641$	4.12311	−	7.14143i	0.162853	−	0.282069i	0.935891	+	0.352290i	$0.114597\pi$
$642$		0			0
$643$	−17.9309	+	31.0572i	−0.707124	+	1.22478i	0.258795	+	0.965932i	$0.416675\pi$
$643$	−17.9309	+	31.0572i	−0.707124	+	1.22478i	−0.965919	+	0.258843i	$0.916659\pi$
$644$		0			0
$645$	−7.82292			−0.308027
$646$		0			0
$647$	−2.56155	−	4.43674i	−0.100705	−	0.174426i	0.811270	−	0.584671i	$-0.198777\pi$
$647$	−2.56155	−	4.43674i	−0.100705	−	0.174426i	−0.911975	+	0.410245i	$0.865443\pi$
$648$		0			0
$649$	−26.2462			−1.03025
$650$		0			0
$651$	−26.2462			−1.02867
$652$		0			0
$653$	2.43845	+	4.22351i	0.0954238	+	0.165279i	0.909785	−	0.415079i	$-0.136246\pi$
$653$	2.43845	+	4.22351i	0.0954238	+	0.165279i	−0.814362	+	0.580358i	$0.802913\pi$
$654$		0			0
$655$	2.69981			0.105490
$656$		0			0
$657$	10.6847	−	18.5064i	0.416848	−	0.722002i
$658$		0			0
$659$	−8.24621	+	14.2829i	−0.321227	+	0.556381i	−0.980741	−	0.195311i	$-0.937429\pi$
$659$	−8.24621	+	14.2829i	−0.321227	+	0.556381i	0.659515	+	0.751692i	$0.270762\pi$
$660$		0			0
$661$	20.3693	+	35.2807i	0.792275	+	1.37226i	0.924555	+	0.381048i	$0.124437\pi$
$661$	20.3693	+	35.2807i	0.792275	+	1.37226i	−0.132281	+	0.991212i	$0.542230\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.68466	−	6.38202i	−0.142885	−	0.247484i
$666$		0			0
$667$	−8.00000	+	13.8564i	−0.309761	+	0.536522i
$668$		0			0
$669$	20.0885	−	34.7944i	0.776668	−	1.34523i
$670$		0			0
$671$	−56.9848			−2.19988
$672$		0			0
$673$	9.65009	+	16.7145i	0.371984	+	0.644295i	0.989871	−	0.141972i	$-0.0453444\pi$
$673$	9.65009	+	16.7145i	0.371984	+	0.644295i	−0.617887	+	0.786267i	$0.712011\pi$
$674$		0			0
$675$	−6.73863			−0.259370
$676$		0			0
$677$	−1.36932			−0.0526271			−0.0263136	−	0.999654i	$-0.508377\pi$
$677$	−1.36932			−0.0526271			−0.0263136	+	0.999654i	$0.508377\pi$
$678$		0			0
$679$	−10.5616	−	18.2931i	−0.405315	−	0.702027i
$680$		0			0
$681$	−20.4924			−0.785271
$682$		0			0
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	−0.539750	−	0.841825i	$-0.681481\pi$
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	0.998917	+	0.0465244i	$0.0148145\pi$
$684$		0			0
$685$	−0.876894	+	1.51883i	−0.0335044	+	0.0580313i
$686$		0			0
$687$	−8.71922	−	15.1021i	−0.332659	−	0.576183i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−8.49242	−	14.7093i	−0.323067	−	0.559568i	0.658052	−	0.752972i	$-0.271381\pi$
$691$	−8.49242	−	14.7093i	−0.323067	−	0.559568i	−0.981119	+	0.193404i	$0.938047\pi$
$692$		0			0
$693$	−23.3693	+	40.4768i	−0.887727	+	1.53759i
$694$		0			0
$695$	2.15767	−	3.73720i	0.0818451	−	0.141760i
$696$		0			0
$697$	−17.7538			−0.672473
$698$		0			0
$699$	8.71922	+	15.1021i	0.329791	+	0.571215i
$700$		0			0
$701$	22.6307			0.854749			0.427375	−	0.904075i	$-0.359439\pi$
$701$	22.6307			0.854749			0.427375	+	0.904075i	$0.359439\pi$
$702$		0			0
$703$	49.6155			1.87129
$704$		0			0
$705$	−0.226801	−	0.392831i	−0.00854182	−	0.0147949i
$706$		0			0
$707$	18.2462			0.686219
$708$		0			0
$709$	12.3693	−	21.4243i	0.464539	−	0.804606i	−0.534641	−	0.845079i	$-0.679553\pi$
$709$	12.3693	−	21.4243i	0.464539	−	0.804606i	0.999181	+	0.0404733i	$0.0128866\pi$
$710$		0			0
$711$	−14.2462	+	24.6752i	−0.534275	+	0.925391i
$712$		0			0
$713$	16.0000	+	27.7128i	0.599205	+	1.03785i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.28078	+	5.68247i	0.122523	+	0.212216i
$718$		0			0
$719$	6.56155	−	11.3649i	0.244705	−	0.423841i	−0.717344	−	0.696719i	$-0.754642\pi$
$719$	6.56155	−	11.3649i	0.244705	−	0.423841i	0.962049	+	0.272878i	$0.0879757\pi$
$720$		0			0
$721$	2.87689	−	4.98293i	0.107141	−	0.185574i
$722$		0			0
$723$	−9.61553			−0.357605
$724$		0			0
$725$	−4.68466	−	8.11407i	−0.173984	−	0.301349i
$726$		0			0
$727$	−46.1080			−1.71005			−0.855025	−	0.518587i	$-0.826458\pi$
$727$	−46.1080			−1.71005			−0.855025	+	0.518587i	$0.826458\pi$
$728$		0			0
$729$	−35.9848			−1.33277
$730$		0			0
$731$	−15.4579	−	26.7738i	−0.571730	−	0.990265i
$732$		0			0
$733$	−27.4384			−1.01346			−0.506731	−	0.862104i	$-0.669146\pi$
$733$	−27.4384			−1.01346			−0.506731	+	0.862104i	$0.669146\pi$
$734$		0			0
$735$	−0.315342	+	0.546188i	−0.0116315	+	0.0201464i
$736$		0			0
$737$	−13.1231	+	22.7299i	−0.483396	+	0.837266i
$738$		0			0
$739$	5.12311	+	8.87348i	0.188456	+	0.326416i	0.944736	−	0.327833i	$-0.106318\pi$
$739$	5.12311	+	8.87348i	0.188456	+	0.326416i	−0.756279	+	0.654249i	$0.772985\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−25.4579	−	44.0943i	−0.933958	−	1.61766i	−0.776481	−	0.630140i	$-0.782997\pi$
$743$	−25.4579	−	44.0943i	−0.933958	−	1.61766i	−0.157477	−	0.987523i	$-0.550336\pi$
$744$		0			0
$745$	4.56155	−	7.90084i	0.167122	−	0.289464i
$746$		0			0
$747$	−4.00000	+	6.92820i	−0.146352	+	0.253490i
$748$		0			0
$749$	−10.2462			−0.374388
$750$		0			0
$751$	−12.4924	−	21.6375i	−0.455855	−	0.789564i	0.542882	−	0.839809i	$-0.317333\pi$
$751$	−12.4924	−	21.6375i	−0.455855	−	0.789564i	−0.998737	+	0.0502450i	$0.984000\pi$
$752$		0			0
$753$	56.9848			2.07664
$754$		0			0
$755$	−5.93087			−0.215846
$756$		0			0
$757$	−1.56155	−	2.70469i	−0.0567556	−	0.0983036i	0.836252	−	0.548346i	$-0.184742\pi$
$757$	−1.56155	−	2.70469i	−0.0567556	−	0.0983036i	−0.893007	+	0.450042i	$0.851409\pi$
$758$		0			0
$759$	104.985			3.81071
$760$		0			0
$761$	−23.2462	+	40.2636i	−0.842674	+	1.45956i	0.0449510	+	0.998989i	$0.485687\pi$
$761$	−23.2462	+	40.2636i	−0.842674	+	1.45956i	−0.887626	+	0.460566i	$0.847647\pi$
$762$		0			0
$763$	−3.59612	+	6.22866i	−0.130188	+	0.225493i
$764$		0			0
$765$	5.68466	+	9.84612i	0.205529	+	0.355987i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−6.93087	−	12.0046i	−0.249934	−	0.432898i	0.713574	−	0.700580i	$-0.247075\pi$
$769$	−6.93087	−	12.0046i	−0.249934	−	0.432898i	−0.963507	+	0.267683i	$0.913742\pi$
$770$		0			0
$771$	−14.6501	+	25.3747i	−0.527610	+	0.913848i
$772$		0			0
$773$	−23.0885	+	39.9905i	−0.830437	+	1.43836i	0.0672550	+	0.997736i	$0.478576\pi$
$773$	−23.0885	+	39.9905i	−0.830437	+	1.43836i	−0.897692	+	0.440623i	$0.854757\pi$
$774$		0			0
$775$	−18.7386			−0.673112
$776$		0			0
$777$	31.7732	+	55.0328i	1.13986	+	1.97429i
$778$		0			0
$779$	−16.0000			−0.573259
$780$		0			0
$781$	39.3693			1.40874
$782$		0			0
$783$	1.43845	+	2.49146i	0.0514059	+	0.0890376i
$784$		0			0
$785$	12.6307			0.450808
$786$		0			0
$787$	8.00000	−	13.8564i	0.285169	−	0.493928i	−0.687481	−	0.726202i	$-0.741284\pi$
$787$	8.00000	−	13.8564i	0.285169	−	0.493928i	0.972650	+	0.232275i	$0.0746169\pi$
$788$		0			0
$789$	33.6155	−	58.2238i	1.19674	−	2.07282i
$790$		0			0
$791$	−23.6847	−	41.0230i	−0.842130	−	1.45861i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	2.24621	+	3.89055i	0.0796649	+	0.137984i
$796$		0			0
$797$	6.75379	−	11.6979i	0.239231	−	0.414361i	−0.721263	−	0.692662i	$-0.756438\pi$
$797$	6.75379	−	11.6979i	0.239231	−	0.414361i	0.960494	+	0.278301i	$0.0897712\pi$
$798$		0			0
$799$	0.896305	−	1.55244i	0.0317090	−	0.0549216i
$800$		0			0
$801$	35.6155			1.25841
$802$		0			0
$803$	−15.3693	−	26.6204i	−0.542371	−	0.939415i
$804$		0			0
$805$	−11.5076			−0.405589
$806$		0			0
$807$	−12.4924			−0.439754
$808$		0			0
$809$	15.0885	+	26.1341i	0.530485	+	0.918827i	0.999367	+	0.0355661i	$0.0113234\pi$
$809$	15.0885	+	26.1341i	0.530485	+	0.918827i	−0.468882	+	0.883261i	$0.655343\pi$
$810$		0			0
$811$	−46.7386			−1.64122			−0.820608	−	0.571492i	$-0.806365\pi$
$811$	−46.7386			−1.64122			−0.820608	+	0.571492i	$0.806365\pi$
$812$		0			0
$813$	26.6501	−	46.1593i	0.934660	−	1.61888i
$814$		0			0
$815$	−5.75379	+	9.96585i	−0.201546	+	0.349089i
$816$		0			0
$817$	−13.9309	−	24.1290i	−0.487379	−	0.844166i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.71922	−	13.3701i	−0.269403	−	0.466619i	0.699305	−	0.714823i	$-0.253493\pi$
$821$	−7.71922	−	13.3701i	−0.269403	−	0.466619i	−0.968708	+	0.248204i	$0.920160\pi$
$822$		0			0
$823$	4.80776	−	8.32729i	0.167588	−	0.290271i	−0.769983	−	0.638064i	$-0.779735\pi$
$823$	4.80776	−	8.32729i	0.167588	−	0.290271i	0.937571	+	0.347793i	$0.113069\pi$
$824$		0			0
$825$	−30.7386	+	53.2409i	−1.07018	+	1.85361i
$826$		0			0
$827$	−35.8617			−1.24703			−0.623517	−	0.781809i	$-0.714297\pi$
$827$	−35.8617			−1.24703			−0.623517	+	0.781809i	$0.714297\pi$
$828$		0			0
$829$	−9.24621	−	16.0149i	−0.321134	−	0.556221i	0.659588	−	0.751627i	$-0.270731\pi$
$829$	−9.24621	−	16.0149i	−0.321134	−	0.556221i	−0.980722	+	0.195406i	$0.937397\pi$
$830$		0			0
$831$	75.2311			2.60974
$832$		0			0
$833$	−2.49242			−0.0863573
$834$		0			0
$835$	4.00000	+	6.92820i	0.138426	+	0.239760i
$836$		0			0
$837$	5.75379			0.198880
$838$		0			0
$839$	5.36932	−	9.29993i	0.185369	−	0.321069i	−0.758332	−	0.651869i	$-0.773985\pi$
$839$	5.36932	−	9.29993i	0.185369	−	0.321069i	0.943701	+	0.330800i	$0.107318\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$		0			0
$843$	−12.8078	−	22.1837i	−0.441123	−	0.764047i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	19.5270	+	33.8217i	0.670955	+	1.16213i
$848$		0			0
$849$	10.8769	−	18.8393i	0.373294	−	0.646564i
$850$		0			0
$851$	38.7386	−	67.0973i	1.32794	−	2.30007i
$852$		0			0
$853$	−29.6847			−1.01638			−0.508192	−	0.861244i	$-0.669686\pi$
$853$	−29.6847			−1.01638			−0.508192	+	0.861244i	$0.669686\pi$
$854$		0			0
$855$	5.12311	+	8.87348i	0.175207	+	0.303467i
$856$		0			0
$857$	40.7386			1.39161			0.695803	−	0.718233i	$-0.255049\pi$
$857$	40.7386			1.39161			0.695803	+	0.718233i	$0.255049\pi$
$858$		0			0
$859$	12.9848			0.443037			0.221519	−	0.975156i	$-0.428899\pi$
$859$	12.9848			0.443037			0.221519	+	0.975156i	$0.428899\pi$
$860$		0			0
$861$	−10.2462	−	17.7470i	−0.349190	−	0.604815i
$862$		0			0
$863$	−49.3002			−1.67820			−0.839099	−	0.543979i	$-0.816917\pi$
$863$	−49.3002			−1.67820			−0.839099	+	0.543979i	$0.816917\pi$
$864$		0			0
$865$	−1.36932	+	2.37173i	−0.0465582	+	0.0806411i
$866$		0			0
$867$	−19.6155	+	33.9751i	−0.666178	+	1.15385i
$868$		0			0
$869$	20.4924	+	35.4939i	0.695158	+	1.20405i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	14.6847	+	25.4346i	0.497000	+	0.860830i
$874$		0			0
$875$	6.96543	−	12.0645i	0.235475	−	0.407854i
$876$		0			0
$877$	18.8423	−	32.6359i	0.636260	−	1.10204i	−0.349986	−	0.936755i	$-0.613814\pi$
$877$	18.8423	−	32.6359i	0.636260	−	1.10204i	0.986247	−	0.165280i	$-0.0528529\pi$
$878$		0			0
$879$	39.5464			1.33387
$880$		0			0
$881$	15.4039	+	26.6803i	0.518970	+	0.898882i	0.999757	+	0.0220449i	$0.00701769\pi$
$881$	15.4039	+	26.6803i	0.518970	+	0.898882i	−0.480787	+	0.876837i	$0.659649\pi$
$882$		0			0
$883$	0.315342			0.0106121			0.00530604	−	0.999986i	$-0.498311\pi$
$883$	0.315342			0.0106121			0.00530604	+	0.999986i	$0.498311\pi$
$884$		0			0
$885$	−7.36932			−0.247717
$886$		0			0
$887$	22.7386	+	39.3845i	0.763489	+	1.32240i	0.941042	+	0.338290i	$0.109848\pi$
$887$	22.7386	+	39.3845i	0.763489	+	1.32240i	−0.177553	+	0.984111i	$0.556818\pi$
$888$		0			0
$889$	26.2462			0.880270
$890$		0			0
$891$	−17.9309	+	31.0572i	−0.600707	+	1.04045i
$892$		0			0
$893$	0.807764	−	1.39909i	0.0270308	−	0.0468187i
$894$		0			0
$895$	2.15767	+	3.73720i	0.0721230	+	0.124921i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	4.00000	+	6.92820i	0.133407	+	0.231069i
$900$		0			0
$901$	−8.87689	+	15.3752i	−0.295732	+	0.512223i
$902$		0			0
$903$	17.8423	−	30.9038i	0.593756	−	1.02841i
$904$		0			0
$905$	12.9848			0.431631
$906$		0			0
$907$	10.4039	+	18.0201i	0.345455	+	0.598346i	0.985436	−	0.170045i	$-0.0543912\pi$
$907$	10.4039	+	18.0201i	0.345455	+	0.598346i	−0.639981	+	0.768391i	$0.721058\pi$
$908$		0			0
$909$	−25.3693			−0.841447
$910$		0			0
$911$	15.3693			0.509208			0.254604	−	0.967045i	$-0.418055\pi$
$911$	15.3693			0.509208			0.254604	+	0.967045i	$0.418055\pi$
$912$		0			0
$913$	5.75379	+	9.96585i	0.190423	+	0.329822i
$914$		0			0
$915$	−16.0000			−0.528944
$916$		0			0
$917$	−6.15767	+	10.6654i	−0.203344	+	0.352202i
$918$		0			0
$919$	−12.4924	+	21.6375i	−0.412087	+	0.713756i	−0.995118	−	0.0986944i	$-0.968533\pi$
$919$	−12.4924	+	21.6375i	−0.412087	+	0.713756i	0.583031	+	0.812450i	$0.301867\pi$
$920$		0			0
$921$	−16.8078	−	29.1119i	−0.553835	−	0.959270i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	22.6847	+	39.2910i	0.745867	+	1.29188i
$926$		0			0
$927$	−4.00000	+	6.92820i	−0.131377	+	0.227552i
$928$		0			0
$929$	4.93087	−	8.54052i	0.161777	−	0.280205i	−0.773729	−	0.633516i	$-0.781611\pi$
$929$	4.93087	−	8.54052i	0.161777	−	0.280205i	0.935506	+	0.353311i	$0.114944\pi$
$930$		0			0
$931$	−2.24621			−0.0736166
$932$		0			0
$933$	13.9309	+	24.1290i	0.456076	+	0.789947i
$934$		0			0
$935$	16.3542			0.534838
$936$		0			0
$937$	−36.7386			−1.20020			−0.600099	−	0.799925i	$-0.704872\pi$
$937$	−36.7386			−1.20020			−0.600099	+	0.799925i	$0.704872\pi$
$938$		0			0
$939$	−34.3348	−	59.4695i	−1.12047	−	1.94071i
$940$		0			0
$941$	55.7926			1.81879			0.909394	−	0.415937i	$-0.136546\pi$
$941$	55.7926			1.81879			0.909394	+	0.415937i	$0.136546\pi$
$942$		0			0
$943$	−12.4924	+	21.6375i	−0.406809	+	0.704614i
$944$		0			0
$945$	−1.03457	+	1.79192i	−0.0336544	+	0.0582911i
$946$		0			0
$947$	−3.68466	−	6.38202i	−0.119735	−	0.207388i	0.799927	−	0.600097i	$-0.204871\pi$
$947$	−3.68466	−	6.38202i	−0.119735	−	0.207388i	−0.919663	+	0.392709i	$0.871538\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	15.6847	+	27.1666i	0.508610	+	0.880938i
$952$		0			0
$953$	9.33475	−	16.1683i	0.302382	−	0.523741i	−0.674293	−	0.738464i	$-0.735551\pi$
$953$	9.33475	−	16.1683i	0.302382	−	0.523741i	0.976675	+	0.214723i	$0.0688848\pi$
$954$		0			0
$955$	4.31534	−	7.47439i	0.139641	−	0.241866i
$956$		0			0
$957$	26.2462			0.848420
$958$		0			0
$959$	−4.00000	−	6.92820i	−0.129167	−	0.223723i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	14.2462			0.459078
$964$		0			0
$965$	−6.00000	−	10.3923i	−0.193147	−	0.334540i
$966$		0			0
$967$	2.56155			0.0823740			0.0411870	−	0.999151i	$-0.486886\pi$
$967$	2.56155			0.0823740			0.0411870	+	0.999151i	$0.486886\pi$
$968$		0			0
$969$	−37.3002	+	64.6058i	−1.19825	+	2.07544i
$970$		0			0
$971$	15.8423	−	27.4397i	0.508405	−	0.880582i	−0.491548	−	0.870850i	$-0.663569\pi$
$971$	15.8423	−	27.4397i	0.508405	−	0.880582i	0.999953	−	0.00973207i	$-0.00309786\pi$
$972$		0			0
$973$	9.84233	+	17.0474i	0.315531	+	0.546515i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−27.2462	−	47.1918i	−0.871684	−	1.50980i	−0.860254	−	0.509865i	$-0.829695\pi$
$977$	−27.2462	−	47.1918i	−0.871684	−	1.50980i	−0.0114294	−	0.999935i	$-0.503638\pi$
$978$		0			0
$979$	25.6155	−	44.3674i	0.818676	−	1.41799i
$980$		0			0
$981$	5.00000	−	8.66025i	0.159638	−	0.276501i
$982$		0			0
$983$	17.9309			0.571906			0.285953	−	0.958244i	$-0.407690\pi$
$983$	17.9309			0.571906			0.285953	+	0.958244i	$0.407690\pi$
$984$		0			0
$985$	0.650093	+	1.12599i	0.0207137	+	0.0358772i
$986$		0			0
$987$	2.06913			0.0658611
$988$		0			0
$989$	−43.5076			−1.38346
$990$		0			0
$991$	17.9309	+	31.0572i	0.569593	+	0.986564i	0.996606	+	0.0823184i	$0.0262324\pi$
$991$	17.9309	+	31.0572i	0.569593	+	0.986564i	−0.427013	+	0.904245i	$0.640434\pi$
$992$		0			0
$993$	−11.5076			−0.365182
$994$		0			0
$995$	1.43845	−	2.49146i	0.0456018	−	0.0789847i
$996$		0			0
$997$	−0.123106	+	0.213225i	−0.00389879	+	0.00675291i	−0.867968	−	0.496620i	$-0.834574\pi$
$997$	−0.123106	+	0.213225i	−0.00389879	+	0.00675291i	0.864069	+	0.503373i	$0.167908\pi$
$998$		0			0
$999$	−6.96543	−	12.0645i	−0.220377	−	0.381703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.i.f.1329.1		4
13.2	odd	12		1352.2.f.c.337.4		4
13.3	even	3		104.2.a.b.1.2	✓	2
13.4	even	6		1352.2.i.d.529.1		4
13.5	odd	4		1352.2.o.d.361.2		8
13.6	odd	12		1352.2.o.d.1161.2		8
13.7	odd	12		1352.2.o.d.1161.1		8
13.8	odd	4		1352.2.o.d.361.1		8
13.9	even	3	inner	1352.2.i.f.529.1		4
13.10	even	6		1352.2.a.g.1.2		2
13.11	odd	12		1352.2.f.c.337.3		4
13.12	even	2		1352.2.i.d.1329.1		4
39.29	odd	6		936.2.a.j.1.2		2
52.3	odd	6		208.2.a.e.1.1		2
52.11	even	12		2704.2.f.k.337.1		4
52.15	even	12		2704.2.f.k.337.2		4
52.23	odd	6		2704.2.a.p.1.1		2
65.3	odd	12		2600.2.d.k.1249.4		4
65.29	even	6		2600.2.a.p.1.1		2
65.42	odd	12		2600.2.d.k.1249.1		4
91.55	odd	6		5096.2.a.m.1.1		2
104.3	odd	6		832.2.a.n.1.2		2
104.29	even	6		832.2.a.k.1.1		2
156.107	even	6		1872.2.a.u.1.2		2
208.3	odd	12		3328.2.b.w.1665.1		4
208.29	even	12		3328.2.b.y.1665.4		4
208.107	odd	12		3328.2.b.w.1665.4		4
208.133	even	12		3328.2.b.y.1665.1		4
260.159	odd	6		5200.2.a.bw.1.2		2
312.29	odd	6		7488.2.a.cu.1.1		2
312.107	even	6		7488.2.a.cv.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.a.b.1.2	✓	2	13.3	even	3
208.2.a.e.1.1		2	52.3	odd	6
832.2.a.k.1.1		2	104.29	even	6
832.2.a.n.1.2		2	104.3	odd	6
936.2.a.j.1.2		2	39.29	odd	6
1352.2.a.g.1.2		2	13.10	even	6
1352.2.f.c.337.3		4	13.11	odd	12
1352.2.f.c.337.4		4	13.2	odd	12
1352.2.i.d.529.1		4	13.4	even	6
1352.2.i.d.1329.1		4	13.12	even	2
1352.2.i.f.529.1		4	13.9	even	3	inner
1352.2.i.f.1329.1		4	1.1	even	1	trivial
1352.2.o.d.361.1		8	13.8	odd	4
1352.2.o.d.361.2		8	13.5	odd	4
1352.2.o.d.1161.1		8	13.7	odd	12
1352.2.o.d.1161.2		8	13.6	odd	12
1872.2.a.u.1.2		2	156.107	even	6
2600.2.a.p.1.1		2	65.29	even	6
2600.2.d.k.1249.1		4	65.42	odd	12
2600.2.d.k.1249.4		4	65.3	odd	12
2704.2.a.p.1.1		2	52.23	odd	6
2704.2.f.k.337.1		4	52.11	even	12
2704.2.f.k.337.2		4	52.15	even	12
3328.2.b.w.1665.1		4	208.3	odd	12
3328.2.b.w.1665.4		4	208.107	odd	12
3328.2.b.y.1665.1		4	208.133	even	12
3328.2.b.y.1665.4		4	208.29	even	12
5096.2.a.m.1.1		2	91.55	odd	6
5200.2.a.bw.1.2		2	260.159	odd	6
7488.2.a.cu.1.1		2	312.29	odd	6
7488.2.a.cv.1.1		2	312.107	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28078 - 2.21837i) q^{3} -0.561553 q^{5} +(1.28078 - 2.21837i) q^{7} +(-1.78078 + 3.08440i) q^{9} +(2.56155 + 4.43674i) q^{11} +(0.719224 + 1.24573i) q^{15} +(-2.84233 + 4.92306i) q^{17} +(-2.56155 + 4.43674i) q^{19} -6.56155 q^{21} +(4.00000 + 6.92820i) q^{23} -4.68466 q^{25} +1.43845 q^{27} +(1.00000 + 1.73205i) q^{29} +4.00000 q^{31} +(6.56155 - 11.3649i) q^{33} +(-0.719224 + 1.24573i) q^{35} +(-4.84233 - 8.38716i) q^{37} +(1.56155 + 2.70469i) q^{41} +(-2.71922 + 4.70983i) q^{43} +(1.00000 - 1.73205i) q^{45} -0.315342 q^{47} +(0.219224 + 0.379706i) q^{49} +14.5616 q^{51} +3.12311 q^{53} +(-1.43845 - 2.49146i) q^{55} +13.1231 q^{57} +(-2.56155 + 4.43674i) q^{59} +(-5.56155 + 9.63289i) q^{61} +(4.56155 + 7.90084i) q^{63} +(2.56155 + 4.43674i) q^{67} +(10.2462 - 17.7470i) q^{69} +(3.84233 - 6.65511i) q^{71} -6.00000 q^{73} +(6.00000 + 10.3923i) q^{75} +13.1231 q^{77} +8.00000 q^{79} +(3.50000 + 6.06218i) q^{81} +2.24621 q^{83} +(1.59612 - 2.76456i) q^{85} +(2.56155 - 4.43674i) q^{87} +(-5.00000 - 8.66025i) q^{89} +(-5.12311 - 8.87348i) q^{93} +(1.43845 - 2.49146i) q^{95} +(4.12311 - 7.14143i) q^{97} -18.2462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 6 q^{5} + q^{7} - 3 q^{9} + 2 q^{11} + 7 q^{15} + q^{17} - 2 q^{19} - 18 q^{21} + 16 q^{23} + 6 q^{25} + 14 q^{27} + 4 q^{29} + 16 q^{31} + 18 q^{33} - 7 q^{35} - 7 q^{37} - 2 q^{41} - 15 q^{43}+ \cdots - 40 q^{99}+O(q^{100}) \) 4 * q - q^3 + 6 * q^5 + q^7 - 3 * q^9 + 2 * q^11 + 7 * q^15 + q^17 - 2 * q^19 - 18 * q^21 + 16 * q^23 + 6 * q^25 + 14 * q^27 + 4 * q^29 + 16 * q^31 + 18 * q^33 - 7 * q^35 - 7 * q^37 - 2 * q^41 - 15 * q^43 + 4 * q^45 - 26 * q^47 + 5 * q^49 + 50 * q^51 - 4 * q^53 - 14 * q^55 + 36 * q^57 - 2 * q^59 - 14 * q^61 + 10 * q^63 + 2 * q^67 + 8 * q^69 + 3 * q^71 - 24 * q^73 + 24 * q^75 + 36 * q^77 + 32 * q^79 + 14 * q^81 - 24 * q^83 + 27 * q^85 + 2 * q^87 - 20 * q^89 - 4 * q^93 + 14 * q^95 - 40 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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