LMFDB - Embedded newform 1352.2.o.d.1161.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1352,2,Mod(361,1352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1352, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1352.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1352 = 2^{3} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1352.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,0,0,0,0,-6,0,0,0,0,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1161.1
Root			$1.35234 - 0.780776i$ of defining polynomial
Character	$\chi$	$=$	1352.1161
Dual form			1352.2.o.d.361.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28078 + 2.21837i) q^{3} -0.561553i q^{5} +(2.21837 - 1.28078i) q^{7} +(-1.78078 - 3.08440i) q^{9} +(-4.43674 - 2.56155i) q^{11} +(1.24573 + 0.719224i) q^{15} +(2.84233 + 4.92306i) q^{17} +(4.43674 - 2.56155i) q^{19} +6.56155i q^{21} +(-4.00000 + 6.92820i) q^{23} +4.68466 q^{25} +1.43845 q^{27} +(1.00000 - 1.73205i) q^{29} +4.00000i q^{31} +(11.3649 - 6.56155i) q^{33} +(-0.719224 - 1.24573i) q^{35} +(8.38716 + 4.84233i) q^{37} +(2.70469 + 1.56155i) q^{41} +(2.71922 + 4.70983i) q^{43} +(-1.73205 + 1.00000i) q^{45} +0.315342i q^{47} +(-0.219224 + 0.379706i) q^{49} -14.5616 q^{51} +3.12311 q^{53} +(-1.43845 + 2.49146i) q^{55} +13.1231i q^{57} +(-4.43674 + 2.56155i) q^{59} +(-5.56155 - 9.63289i) q^{61} +(-7.90084 - 4.56155i) q^{63} +(4.43674 + 2.56155i) q^{67} +(-10.2462 - 17.7470i) q^{69} +(-6.65511 + 3.84233i) q^{71} +6.00000i q^{73} +(-6.00000 + 10.3923i) q^{75} -13.1231 q^{77} +8.00000 q^{79} +(3.50000 - 6.06218i) q^{81} +2.24621i q^{83} +(2.76456 - 1.59612i) q^{85} +(2.56155 + 4.43674i) q^{87} +(8.66025 + 5.00000i) q^{89} +(-8.87348 - 5.12311i) q^{93} +(-1.43845 - 2.49146i) q^{95} +(-7.14143 + 4.12311i) q^{97} +18.2462i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 6 q^{9} - 2 q^{17} - 32 q^{23} - 12 q^{25} + 28 q^{27} + 8 q^{29} - 14 q^{35} + 30 q^{43} - 10 q^{49} - 100 q^{51} - 8 q^{53} - 28 q^{55} - 28 q^{61} - 16 q^{69} - 48 q^{75} - 72 q^{77}+ \cdots - 28 q^{95}+O(q^{100}) $ 8 * q - 2 * q^3 - 6 * q^9 - 2 * q^17 - 32 * q^23 - 12 * q^25 + 28 * q^27 + 8 * q^29 - 14 * q^35 + 30 * q^43 - 10 * q^49 - 100 * q^51 - 8 * q^53 - 28 * q^55 - 28 * q^61 - 16 * q^69 - 48 * q^75 - 72 * q^77 + 64 * q^79 + 28 * q^81 + 4 * q^87 - 28 * q^95

Character values

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

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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	0.213284	+	0.976990i	$0.431584\pi$
$3$	−1.28078	+	2.21837i	−0.739457	+	1.28078i	−0.952740	+	0.303786i	$0.901749\pi$
$4$		0			0
$5$		−	0.561553i		−	0.251134i	−0.992085	−	0.125567i	$-0.959925\pi$
$5$		−	0.561553i		−	0.251134i	0.992085	−	0.125567i	$-0.0400750\pi$
$6$		0			0
$7$	2.21837	−	1.28078i	0.838465	−	0.484088i	−0.0182772	−	0.999833i	$-0.505818\pi$
$7$	2.21837	−	1.28078i	0.838465	−	0.484088i	0.856742	+	0.515745i	$0.172485\pi$
$8$		0			0
$9$	−1.78078	−	3.08440i	−0.593592	−	1.02813i
$10$		0			0
$11$	−4.43674	−	2.56155i	−1.33773	−	0.772337i	−0.351257	−	0.936279i	$-0.614246\pi$
$11$	−4.43674	−	2.56155i	−1.33773	−	0.772337i	−0.986470	+	0.163942i	$0.947579\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	1.24573	+	0.719224i	0.321647	+	0.185703i
$16$		0			0
$17$	2.84233	+	4.92306i	0.689366	+	1.19402i	0.972043	+	0.234802i	$0.0754442\pi$
$17$	2.84233	+	4.92306i	0.689366	+	1.19402i	−0.282677	+	0.959215i	$0.591222\pi$
$18$		0			0
$19$	4.43674	−	2.56155i	1.01786	−	0.587661i	0.104375	−	0.994538i	$-0.466716\pi$
$19$	4.43674	−	2.56155i	1.01786	−	0.587661i	0.913483	+	0.406877i	$0.133382\pi$
$20$		0			0
$21$			6.56155i			1.43185i
$22$		0			0
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		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	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$		0			0
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$		0			0
$33$	11.3649	−	6.56155i	1.97838	−	1.14222i
$34$		0			0
$35$	−0.719224	−	1.24573i	−0.121571	−	0.210567i
$36$		0			0
$37$	8.38716	+	4.84233i	1.37884	+	0.796074i	0.992020	−	0.126081i	$-0.0402399\pi$
$37$	8.38716	+	4.84233i	1.37884	+	0.796074i	0.386821	+	0.922155i	$0.373573\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.70469	+	1.56155i	0.422401	+	0.243874i	0.696104	−	0.717941i	$-0.254915\pi$
$41$	2.70469	+	1.56155i	0.422401	+	0.243874i	−0.273703	+	0.961814i	$0.588248\pi$
$42$		0			0
$43$	2.71922	+	4.70983i	0.414678	+	0.718243i	0.995395	−	0.0958627i	$-0.0305610\pi$
$43$	2.71922	+	4.70983i	0.414678	+	0.718243i	−0.580717	+	0.814106i	$0.697228\pi$
$44$		0			0
$45$	−1.73205	+	1.00000i	−0.258199	+	0.149071i
$46$		0			0
$47$			0.315342i			0.0459973i	0.999735	+	0.0229986i	$0.00732134\pi$
$47$			0.315342i			0.0459973i	−0.999735	+	0.0229986i	$0.992679\pi$
$48$		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
$57$			13.1231i			1.73820i
$58$		0			0
$59$	−4.43674	+	2.56155i	−0.577614	+	0.333486i	−0.760185	−	0.649707i	$-0.774892\pi$
$59$	−4.43674	+	2.56155i	−0.577614	+	0.333486i	0.182570	+	0.983193i	$0.441558\pi$
$60$		0			0
$61$	−5.56155	−	9.63289i	−0.712084	−	1.23337i	−0.964074	−	0.265636i	$-0.914418\pi$
$61$	−5.56155	−	9.63289i	−0.712084	−	1.23337i	0.251990	−	0.967730i	$-0.418915\pi$
$62$		0			0
$63$	−7.90084	−	4.56155i	−0.995412	−	0.574702i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.43674	+	2.56155i	0.542034	+	0.312943i	0.745903	−	0.666055i	$-0.232018\pi$
$67$	4.43674	+	2.56155i	0.542034	+	0.312943i	−0.203869	+	0.978998i	$0.565352\pi$
$68$		0			0
$69$	−10.2462	−	17.7470i	−1.23350	−	2.13648i
$70$		0			0
$71$	−6.65511	+	3.84233i	−0.789816	+	0.456001i	−0.839898	−	0.542745i	$-0.817385\pi$
$71$	−6.65511	+	3.84233i	−0.789816	+	0.456001i	0.0500816	+	0.998745i	$0.484052\pi$
$72$		0			0
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$		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
$83$			2.24621i			0.246554i	0.992372	+	0.123277i	$0.0393403\pi$
$83$			2.24621i			0.246554i	−0.992372	+	0.123277i	$0.960660\pi$
$84$		0			0
$85$	2.76456	−	1.59612i	0.299858	−	0.173123i
$86$		0			0
$87$	2.56155	+	4.43674i	0.274627	+	0.475668i
$88$		0			0
$89$	8.66025	+	5.00000i	0.917985	+	0.529999i	0.882992	−	0.469389i	$-0.155526\pi$
$89$	8.66025	+	5.00000i	0.917985	+	0.529999i	0.0349934	+	0.999388i	$0.488859\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−8.87348	−	5.12311i	−0.920137	−	0.531241i
$94$		0			0
$95$	−1.43845	−	2.49146i	−0.147582	−	0.255619i
$96$		0			0
$97$	−7.14143	+	4.12311i	−0.725102	+	0.418638i	−0.816628	−	0.577165i	$-0.804159\pi$
$97$	−7.14143	+	4.12311i	−0.725102	+	0.418638i	0.0915255	+	0.995803i	$0.470826\pi$
$98$		0			0
$99$			18.2462i			1.83381i
$100$		0			0
$101$	−3.56155	+	6.16879i	−0.354388	+	0.613818i	−0.987013	−	0.160640i	$-0.948644\pi$
$101$	−3.56155	+	6.16879i	−0.354388	+	0.613818i	0.632625	+	0.774458i	$0.281977\pi$
$102$		0			0
$103$	−2.24621			−0.221326			−0.110663	−	0.993858i	$-0.535297\pi$
$103$	−2.24621			−0.221326			−0.110663	+	0.993858i	$0.535297\pi$
$104$		0			0
$105$	3.68466			0.359586
$106$		0			0
$107$	−2.00000	+	3.46410i	−0.193347	+	0.334887i	−0.946357	−	0.323122i	$-0.895268\pi$
$107$	−2.00000	+	3.46410i	−0.193347	+	0.334887i	0.753010	+	0.658009i	$0.228601\pi$
$108$		0			0
$109$		−	2.80776i		−	0.268935i	−0.990918	−	0.134468i	$-0.957068\pi$
$109$		−	2.80776i		−	0.268935i	0.990918	−	0.134468i	$-0.0429324\pi$
$110$		0			0
$111$	−21.4842	+	12.4039i	−2.03919	+	1.17732i
$112$		0			0
$113$	9.24621	+	16.0149i	0.869810	+	1.50656i	0.862190	+	0.506585i	$0.169092\pi$
$113$	9.24621	+	16.0149i	0.869810	+	1.50656i	0.00762026	+	0.999971i	$0.497574\pi$
$114$		0			0
$115$	3.89055	+	2.24621i	0.362796	+	0.209460i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	12.6107	+	7.28078i	1.15602	+	0.667428i
$120$		0			0
$121$	7.62311	+	13.2036i	0.693010	+	1.20033i
$122$		0			0
$123$	−6.92820	+	4.00000i	−0.624695	+	0.360668i
$124$		0			0
$125$		−	5.43845i		−	0.486430i
$126$		0			0
$127$	−5.12311	+	8.87348i	−0.454602	+	0.787394i	−0.998665	−	0.0516503i	$-0.983552\pi$
$127$	−5.12311	+	8.87348i	−0.454602	+	0.787394i	0.544063	+	0.839044i	$0.316885\pi$
$128$		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
$135$		−	0.807764i		−	0.0695213i
$136$		0			0
$137$	2.70469	−	1.56155i	0.231077	−	0.133412i	−0.379992	−	0.924990i	$-0.624073\pi$
$137$	2.70469	−	1.56155i	0.231077	−	0.133412i	0.611069	+	0.791577i	$0.290740\pi$
$138$		0			0
$139$	−3.84233	−	6.65511i	−0.325902	−	0.564479i	0.655792	−	0.754941i	$-0.272335\pi$
$139$	−3.84233	−	6.65511i	−0.325902	−	0.564479i	−0.981695	+	0.190462i	$0.939001\pi$
$140$		0			0
$141$	−0.699544	−	0.403882i	−0.0589122	−	0.0340130i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−0.972638	−	0.561553i	−0.0807732	−	0.0466344i
$146$		0			0
$147$	−0.561553	−	0.972638i	−0.0463161	−	0.0802218i
$148$		0			0
$149$	14.0696	−	8.12311i	1.15263	−	0.665471i	0.203103	−	0.979157i	$-0.434898\pi$
$149$	14.0696	−	8.12311i	1.15263	−	0.665471i	0.949527	+	0.313687i	$0.101564\pi$
$150$		0			0
$151$		−	10.5616i		−	0.859487i	−0.902951	−	0.429743i	$-0.858604\pi$
$151$		−	10.5616i		−	0.859487i	0.902951	−	0.429743i	$-0.141396\pi$
$152$		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
$161$			20.4924i			1.61503i
$162$		0			0
$163$	17.7470	−	10.2462i	1.39005	−	0.802545i	0.396729	−	0.917936i	$-0.370145\pi$
$163$	17.7470	−	10.2462i	1.39005	−	0.802545i	0.993320	+	0.115391i	$0.0368120\pi$
$164$		0			0
$165$	−3.68466	−	6.38202i	−0.286850	−	0.496839i
$166$		0			0
$167$	12.3376	+	7.12311i	0.954711	+	0.551202i	0.894541	−	0.446986i	$-0.147503\pi$
$167$	12.3376	+	7.12311i	0.954711	+	0.551202i	0.0601696	+	0.998188i	$0.480836\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−15.8017	−	9.12311i	−1.20838	−	0.697661i
$172$		0			0
$173$	−2.43845	−	4.22351i	−0.185392	−	0.321108i	0.758317	−	0.651886i	$-0.226022\pi$
$173$	−2.43845	−	4.22351i	−0.185392	−	0.321108i	−0.943708	+	0.330778i	$0.892689\pi$
$174$		0			0
$175$	10.3923	−	6.00000i	0.785584	−	0.453557i
$176$		0			0
$177$		−	13.1231i		−	0.986393i
$178$		0			0
$179$	3.84233	−	6.65511i	0.287189	−	0.497426i	−0.685949	−	0.727650i	$-0.740612\pi$
$179$	3.84233	−	6.65511i	0.287189	−	0.497426i	0.973138	+	0.230224i	$0.0739458\pi$
$180$		0			0
$181$	23.1231			1.71873			0.859363	−	0.511365i	$-0.170860\pi$
$181$	23.1231			1.71873			0.859363	+	0.511365i	$0.170860\pi$
$182$		0			0
$183$	28.4924			2.10622
$184$		0			0
$185$	2.71922	−	4.70983i	0.199921	−	0.346274i
$186$		0			0
$187$		−	29.1231i		−	2.12969i
$188$		0			0
$189$	3.19101	−	1.84233i	0.232112	−	0.134010i
$190$		0			0
$191$	−7.68466	−	13.3102i	−0.556042	−	0.963094i	−0.997822	−	0.0659698i	$-0.978986\pi$
$191$	−7.68466	−	13.3102i	−0.556042	−	0.963094i	0.441779	−	0.897124i	$-0.354347\pi$
$192$		0			0
$193$	−18.5064	−	10.6847i	−1.33212	−	0.769099i	−0.346494	−	0.938052i	$-0.612628\pi$
$193$	−18.5064	−	10.6847i	−1.33212	−	0.769099i	−0.985624	+	0.168954i	$0.945961\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.00514	−	1.15767i	−0.142861	−	0.0824806i	0.426866	−	0.904315i	$-0.359618\pi$
$197$	−2.00514	−	1.15767i	−0.142861	−	0.0824806i	−0.569727	+	0.821834i	$0.692951\pi$
$198$		0			0
$199$	2.56155	+	4.43674i	0.181584	+	0.314512i	0.942420	−	0.334432i	$-0.108544\pi$
$199$	2.56155	+	4.43674i	0.181584	+	0.314512i	−0.760836	+	0.648944i	$0.775211\pi$
$200$		0			0
$201$	−11.3649	+	6.56155i	−0.801621	+	0.462816i
$202$		0			0
$203$		−	5.12311i		−	0.359572i
$204$		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	0.459021	+	0.888425i	$0.348200\pi$
$211$	−7.84233	+	13.5833i	−0.539888	+	0.935114i	−0.998909	+	0.0466885i	$0.985133\pi$
$212$		0			0
$213$		−	19.6847i		−	1.34877i
$214$		0			0
$215$	2.64482	−	1.52699i	0.180375	−	0.104140i
$216$		0			0
$217$	5.12311	+	8.87348i	0.347779	+	0.602371i
$218$		0			0
$219$	−13.3102	−	7.68466i	−0.899421	−	0.519281i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	13.5833	+	7.84233i	0.909606	+	0.525161i	0.880304	−	0.474409i	$-0.157338\pi$
$223$	13.5833	+	7.84233i	0.909606	+	0.525161i	0.0293016	+	0.999571i	$0.490672\pi$
$224$		0			0
$225$	−8.34233	−	14.4493i	−0.556155	−	0.963289i
$226$		0			0
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	−0.711977	−	0.702202i	$-0.752200\pi$
$227$	−6.92820	+	4.00000i	−0.459841	+	0.265489i	0.252136	+	0.967692i	$0.418867\pi$
$228$		0			0
$229$		−	6.80776i		−	0.449870i	−0.974374	−	0.224935i	$-0.927783\pi$
$229$		−	6.80776i		−	0.449870i	0.974374	−	0.224935i	$-0.0722169\pi$
$230$		0			0
$231$	16.8078	−	29.1119i	1.10587	−	1.91542i
$232$		0			0
$233$	6.80776			0.445991			0.222996	−	0.974819i	$-0.428416\pi$
$233$	6.80776			0.445991			0.222996	+	0.974819i	$0.428416\pi$
$234$		0			0
$235$	0.177081			0.0115515
$236$		0			0
$237$	−10.2462	+	17.7470i	−0.665563	+	1.15279i
$238$		0			0
$239$		−	2.56155i		−	0.165693i	−0.996562	−	0.0828465i	$-0.973599\pi$
$239$		−	2.56155i		−	0.165693i	0.996562	−	0.0828465i	$-0.0264011\pi$
$240$		0			0
$241$	3.25088	−	1.87689i	0.209407	−	0.120901i	−0.391629	−	0.920123i	$-0.628088\pi$
$241$	3.25088	−	1.87689i	0.209407	−	0.120901i	0.601036	+	0.799222i	$0.294755\pi$
$242$		0			0
$243$	11.1231	+	19.2658i	0.713548	+	1.23590i
$244$		0			0
$245$	0.213225	+	0.123106i	0.0136225	+	0.00786493i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−4.98293	−	2.87689i	−0.315780	−	0.182316i
$250$		0			0
$251$	11.1231	+	19.2658i	0.702084	+	1.21605i	0.967734	+	0.251976i	$0.0810803\pi$
$251$	11.1231	+	19.2658i	0.702084	+	1.21605i	−0.265649	+	0.964070i	$0.585586\pi$
$252$		0			0
$253$	35.4939	−	20.4924i	2.23148	−	1.28835i
$254$		0			0
$255$			8.17708i			0.512069i
$256$		0			0
$257$	5.71922	−	9.90599i	0.356755	−	0.617918i	−0.630661	−	0.776058i	$-0.717216\pi$
$257$	5.71922	−	9.90599i	0.356755	−	0.617918i	0.987417	+	0.158140i	$0.0505496\pi$
$258$		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	−0.104210	−	0.994555i	$-0.533231\pi$
$263$	13.1231	−	22.7299i	0.809205	−	1.40158i	0.913415	−	0.407029i	$-0.133435\pi$
$264$		0			0
$265$		−	1.75379i		−	0.107734i
$266$		0			0
$267$	−22.1837	+	12.8078i	−1.35762	+	0.783822i
$268$		0			0
$269$	2.43845	+	4.22351i	0.148675	+	0.257512i	0.930738	−	0.365687i	$-0.119166\pi$
$269$	2.43845	+	4.22351i	0.148675	+	0.257512i	−0.782063	+	0.623199i	$0.785833\pi$
$270$		0			0
$271$	−18.0201	−	10.4039i	−1.09464	−	0.631991i	−0.159832	−	0.987144i	$-0.551095\pi$
$271$	−18.0201	−	10.4039i	−1.09464	−	0.631991i	−0.934808	+	0.355153i	$0.884429\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−20.7846	−	12.0000i	−1.25336	−	0.723627i
$276$		0			0
$277$	14.6847	+	25.4346i	0.882316	+	1.52822i	0.848760	+	0.528779i	$0.177350\pi$
$277$	14.6847	+	25.4346i	0.882316	+	1.52822i	0.0335558	+	0.999437i	$0.489317\pi$
$278$		0			0
$279$	12.3376	−	7.12311i	0.738632	−	0.426449i
$280$		0			0
$281$		−	10.0000i		−	0.596550i	−0.954480	−	0.298275i	$-0.903589\pi$
$281$		−	10.0000i		−	0.596550i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$		0			0
$283$	−4.24621	+	7.35465i	−0.252411	+	0.437189i	−0.964189	−	0.265216i	$-0.914557\pi$
$283$	−4.24621	+	7.35465i	−0.252411	+	0.437189i	0.711778	+	0.702404i	$0.247890\pi$
$284$		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
$291$		−	21.1231i		−	1.23826i
$292$		0			0
$293$	−13.3701	+	7.71922i	−0.781089	+	0.450962i	−0.836816	−	0.547484i	$-0.815586\pi$
$293$	−13.3701	+	7.71922i	−0.781089	+	0.450962i	0.0557272	+	0.998446i	$0.482252\pi$
$294$		0			0
$295$	1.43845	+	2.49146i	0.0837496	+	0.145059i
$296$		0			0
$297$	−6.38202	−	3.68466i	−0.370322	−	0.213806i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	12.0645	+	6.96543i	0.695385	+	0.401481i
$302$		0			0
$303$	−9.12311	−	15.8017i	−0.524109	−	0.907783i
$304$		0			0
$305$	−5.40938	+	3.12311i	−0.309740	+	0.178829i
$306$		0			0
$307$		−	13.1231i		−	0.748975i	−0.927232	−	0.374488i	$-0.877819\pi$
$307$		−	13.1231i		−	0.748975i	0.927232	−	0.374488i	$-0.122181\pi$
$308$		0			0
$309$	2.87689	−	4.98293i	0.163661	−	0.283469i
$310$		0			0
$311$	10.8769			0.616772			0.308386	−	0.951261i	$-0.400211\pi$
$311$	10.8769			0.616772			0.308386	+	0.951261i	$0.400211\pi$
$312$		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
$317$		−	12.2462i		−	0.687816i	−0.939003	−	0.343908i	$-0.888249\pi$
$317$		−	12.2462i		−	0.687816i	0.939003	−	0.343908i	$-0.111751\pi$
$318$		0			0
$319$	−8.87348	+	5.12311i	−0.496819	+	0.286839i
$320$		0			0
$321$	−5.12311	−	8.87348i	−0.285944	−	0.495269i
$322$		0			0
$323$	25.2213	+	14.5616i	1.40335	+	0.810226i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.22866	+	3.59612i	0.344446	+	0.198866i
$328$		0			0
$329$	0.403882	+	0.699544i	0.0222667	+	0.0385671i
$330$		0			0
$331$	−3.89055	+	2.24621i	−0.213844	+	0.123463i	−0.603097	−	0.797668i	$-0.706067\pi$
$331$	−3.89055	+	2.24621i	−0.213844	+	0.123463i	0.389253	+	0.921131i	$0.372733\pi$
$332$		0			0
$333$		−	34.4924i		−	1.89017i
$334$		0			0
$335$	1.43845	−	2.49146i	0.0785908	−	0.136123i
$336$		0			0
$337$	13.1922			0.718627			0.359313	−	0.933217i	$-0.383011\pi$
$337$	13.1922			0.718627			0.359313	+	0.933217i	$0.383011\pi$
$338$		0			0
$339$	−47.3693			−2.57275
$340$		0			0
$341$	10.2462	−	17.7470i	0.554863	−	0.961052i
$342$		0			0
$343$			19.0540i			1.02882i
$344$		0			0
$345$	−9.96585	+	5.75379i	−0.536544	+	0.309774i
$346$		0			0
$347$	−3.84233	−	6.65511i	−0.206267	−	0.357265i	0.744269	−	0.667880i	$-0.232798\pi$
$347$	−3.84233	−	6.65511i	−0.206267	−	0.357265i	−0.950536	+	0.310615i	$0.899465\pi$
$348$		0			0
$349$	10.3324	+	5.96543i	0.553083	+	0.319322i	0.750364	−	0.661024i	$-0.229878\pi$
$349$	10.3324	+	5.96543i	0.553083	+	0.319322i	−0.197282	+	0.980347i	$0.563211\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.11407	−	4.68466i	−0.431868	−	0.249339i	0.268274	−	0.963343i	$-0.413547\pi$
$353$	−8.11407	−	4.68466i	−0.431868	−	0.249339i	−0.700142	+	0.714003i	$0.746880\pi$
$354$		0			0
$355$	2.15767	+	3.73720i	0.114517	+	0.198350i
$356$		0			0
$357$	−32.3029	+	18.6501i	−1.70965	+	0.987068i
$358$		0			0
$359$		−	14.2462i		−	0.751886i	−0.926643	−	0.375943i	$-0.877319\pi$
$359$		−	14.2462i		−	0.751886i	0.926643	−	0.375943i	$-0.122681\pi$
$360$		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	−0.963791	−	0.266658i	$-0.914081\pi$
$367$	−4.80776	+	8.32729i	−0.250963	+	0.434681i	0.712828	+	0.701339i	$0.247414\pi$
$368$		0			0
$369$		−	11.1231i		−	0.579046i
$370$		0			0
$371$	6.92820	−	4.00000i	0.359694	−	0.207670i
$372$		0			0
$373$	5.80776	+	10.0593i	0.300715	+	0.520853i	0.976298	−	0.216431i	$-0.0694415\pi$
$373$	5.80776	+	10.0593i	0.300715	+	0.520853i	−0.675583	+	0.737284i	$0.736108\pi$
$374$		0			0
$375$	12.0645	+	6.96543i	0.623007	+	0.359694i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−4.98293	−	2.87689i	−0.255956	−	0.147776i	0.366533	−	0.930405i	$-0.380545\pi$
$379$	−4.98293	−	2.87689i	−0.255956	−	0.147776i	−0.622488	+	0.782629i	$0.713878\pi$
$380$		0			0
$381$	−13.1231	−	22.7299i	−0.672317	−	1.16449i
$382$		0			0
$383$	−9.69276	+	5.59612i	−0.495277	+	0.285948i	−0.726761	−	0.686890i	$-0.758975\pi$
$383$	−9.69276	+	5.59612i	−0.495277	+	0.285948i	0.231484	+	0.972839i	$0.425642\pi$
$384$		0			0
$385$			7.36932i			0.375575i
$386$		0			0
$387$	9.68466	−	16.7743i	0.492299	−	0.852687i
$388$		0			0
$389$	−20.7386			−1.05149			−0.525745	−	0.850642i	$-0.676213\pi$
$389$	−20.7386			−1.05149			−0.525745	+	0.850642i	$0.676213\pi$
$390$		0			0
$391$	−45.4773			−2.29988
$392$		0			0
$393$	6.15767	−	10.6654i	0.310613	−	0.537998i
$394$		0			0
$395$		−	4.49242i		−	0.226038i
$396$		0			0
$397$	1.73205	−	1.00000i	0.0869291	−	0.0501886i	−0.455905	−	0.890028i	$-0.650684\pi$
$397$	1.73205	−	1.00000i	0.0869291	−	0.0501886i	0.542834	+	0.839840i	$0.317351\pi$
$398$		0			0
$399$	16.8078	+	29.1119i	0.841441	+	1.45742i
$400$		0			0
$401$	3.13114	+	1.80776i	0.156362	+	0.0902754i	0.576139	−	0.817352i	$-0.304559\pi$
$401$	3.13114	+	1.80776i	0.156362	+	0.0902754i	−0.419778	+	0.907627i	$0.637892\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−3.40423	−	1.96543i	−0.169158	−	0.0976632i
$406$		0			0
$407$	−24.8078	−	42.9683i	−1.22968	−	2.12986i
$408$		0			0
$409$	11.1517	−	6.43845i	0.551417	−	0.318361i	−0.198276	−	0.980146i	$-0.563534\pi$
$409$	11.1517	−	6.43845i	0.551417	−	0.318361i	0.749693	+	0.661785i	$0.230201\pi$
$410$		0			0
$411$			8.00000i			0.394611i
$412$		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	−0.841479	−	0.540289i	$-0.818315\pi$
$419$	0.965435	−	1.67218i	0.0471646	−	0.0816914i	0.888644	+	0.458598i	$0.151648\pi$
$420$		0			0
$421$		−	6.31534i		−	0.307791i	−0.988087	−	0.153895i	$-0.950818\pi$
$421$		−	6.31534i		−	0.307791i	0.988087	−	0.153895i	$-0.0491819\pi$
$422$		0			0
$423$	0.972638	−	0.561553i	0.0472913	−	0.0273036i
$424$		0			0
$425$	13.3153	+	23.0628i	0.645889	+	1.11871i
$426$		0			0
$427$	−24.6752	−	14.2462i	−1.19411	−	0.689422i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	16.0748	+	9.28078i	0.774295	+	0.447039i	0.834405	−	0.551153i	$-0.185812\pi$
$431$	16.0748	+	9.28078i	0.774295	+	0.447039i	−0.0601098	+	0.998192i	$0.519145\pi$
$432$		0			0
$433$	−3.08854	−	5.34951i	−0.148426	−	0.257081i	0.782220	−	0.623002i	$-0.214087\pi$
$433$	−3.08854	−	5.34951i	−0.148426	−	0.257081i	−0.930646	+	0.365921i	$0.880754\pi$
$434$		0			0
$435$	2.49146	−	1.43845i	0.119457	−	0.0689683i
$436$		0			0
$437$			40.9848i			1.96057i
$438$		0			0
$439$	10.5616	−	18.2931i	0.504075	−	0.873084i	−0.495913	−	0.868372i	$-0.665167\pi$
$439$	10.5616	−	18.2931i	0.504075	−	0.873084i	0.999989	−	0.00471229i	$-0.00149997\pi$
$440$		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
$447$			41.6155i			1.96835i
$448$		0			0
$449$	−28.3525	+	16.3693i	−1.33804	+	0.772516i	−0.986516	−	0.163664i	$-0.947669\pi$
$449$	−28.3525	+	16.3693i	−1.33804	+	0.772516i	−0.351521	+	0.936180i	$0.614335\pi$
$450$		0			0
$451$	−8.00000	−	13.8564i	−0.376705	−	0.652473i
$452$		0			0
$453$	23.4294	+	13.5270i	1.10081	+	0.635553i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−21.4243	−	12.3693i	−1.00219	−	0.578612i	−0.0932915	−	0.995639i	$-0.529739\pi$
$457$	−21.4243	−	12.3693i	−1.00219	−	0.578612i	−0.908894	+	0.417027i	$0.863072\pi$
$458$		0			0
$459$	4.08854	+	7.08156i	0.190837	+	0.330539i
$460$		0			0
$461$	−30.1444	+	17.4039i	−1.40397	+	0.810580i	−0.994797	−	0.101879i	$-0.967514\pi$
$461$	−30.1444	+	17.4039i	−1.40397	+	0.810580i	−0.409168	+	0.912459i	$0.634181\pi$
$462$		0			0
$463$		−	38.2462i		−	1.77745i	−0.458439	−	0.888726i	$-0.651591\pi$
$463$		−	38.2462i		−	1.77745i	0.458439	−	0.888726i	$-0.348409\pi$
$464$		0			0
$465$	−2.87689	+	4.98293i	−0.133413	+	0.231078i
$466$		0			0
$467$	−40.4924			−1.87377			−0.936883	−	0.349643i	$-0.886303\pi$
$467$	−40.4924			−1.87377			−0.936883	+	0.349643i	$0.886303\pi$
$468$		0			0
$469$	13.1231			0.605969
$470$		0			0
$471$	28.8078	−	49.8965i	1.32739	−	2.29911i
$472$		0			0
$473$		−	27.8617i		−	1.28108i
$474$		0			0
$475$	20.7846	−	12.0000i	0.953663	−	0.550598i
$476$		0			0
$477$	−5.56155	−	9.63289i	−0.254646	−	0.441060i
$478$		0			0
$479$	9.69276	+	5.59612i	0.442874	+	0.255693i	0.704816	−	0.709390i	$-0.251030\pi$
$479$	9.69276	+	5.59612i	0.442874	+	0.255693i	−0.261942	+	0.965084i	$0.584363\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−45.4598	−	26.2462i	−2.06849	−	1.19424i
$484$		0			0
$485$	2.31534	+	4.01029i	0.105134	+	0.182098i
$486$		0			0
$487$	1.51883	−	0.876894i	0.0688246	−	0.0397359i	−0.465193	−	0.885209i	$-0.654015\pi$
$487$	1.51883	−	0.876894i	0.0688246	−	0.0397359i	0.534017	+	0.845473i	$0.320682\pi$
$488$		0			0
$489$			52.4924i			2.37379i
$490$		0			0
$491$	0.473012	−	0.819281i	0.0213467	−	0.0369737i	−0.855155	−	0.518373i	$-0.826538\pi$
$491$	0.473012	−	0.819281i	0.0213467	−	0.0369737i	0.876501	+	0.481399i	$0.159871\pi$
$492$		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
$499$			28.4924i			1.27550i	0.770245	+	0.637748i	$0.220134\pi$
$499$			28.4924i			1.27550i	−0.770245	+	0.637748i	$0.779866\pi$
$500$		0			0
$501$	−31.6034	+	18.2462i	−1.41193	+	0.815181i
$502$		0			0
$503$	3.68466	+	6.38202i	0.164291	+	0.284560i	0.936403	−	0.350926i	$-0.114133\pi$
$503$	3.68466	+	6.38202i	0.164291	+	0.284560i	−0.772112	+	0.635486i	$0.780800\pi$
$504$		0			0
$505$	3.46410	+	2.00000i	0.154150	+	0.0889988i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	15.5885	+	9.00000i	0.690946	+	0.398918i	0.803966	−	0.594675i	$-0.202719\pi$
$509$	15.5885	+	9.00000i	0.690946	+	0.398918i	−0.113020	+	0.993593i	$0.536052\pi$
$510$		0			0
$511$	7.68466	+	13.3102i	0.339949	+	0.588809i
$512$		0			0
$513$	6.38202	−	3.68466i	0.281773	−	0.162682i
$514$		0			0
$515$			1.26137i			0.0555824i
$516$		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	−0.860592	−	0.509295i	$-0.829906\pi$
$523$	0.246211	−	0.426450i	0.0107661	−	0.0186474i	0.871358	+	0.490647i	$0.163240\pi$
$524$		0			0
$525$			30.7386i			1.34154i
$526$		0			0
$527$	−19.6922	+	11.3693i	−0.857807	+	0.495255i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$	15.8017	+	9.12311i	0.685735	+	0.395909i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.94528	+	1.12311i	0.0841016	+	0.0485561i
$536$		0			0
$537$	9.84233	+	17.0474i	0.424728	+	0.735650i
$538$		0			0
$539$	1.94528	−	1.12311i	0.0837890	−	0.0483756i
$540$		0			0
$541$			5.68466i			0.244403i	0.992505	+	0.122201i	$0.0389953\pi$
$541$			5.68466i			0.244403i	−0.992505	+	0.122201i	$0.961005\pi$
$542$		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
$551$		−	10.2462i		−	0.436503i
$552$		0			0
$553$	17.7470	−	10.2462i	0.754677	−	0.435713i
$554$		0			0
$555$	6.96543	+	12.0645i	0.295666	+	0.512109i
$556$		0			0
$557$	−36.5264	−	21.0885i	−1.54767	−	0.893550i	−0.998319	−	0.0579613i	$-0.981540\pi$
$557$	−36.5264	−	21.0885i	−1.54767	−	0.893550i	−0.549355	−	0.835589i	$-0.685127\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	64.6058	+	37.3002i	2.72766	+	1.57482i
$562$		0			0
$563$	−3.52699	−	6.10892i	−0.148645	−	0.257460i	0.782082	−	0.623176i	$-0.214158\pi$
$563$	−3.52699	−	6.10892i	−0.148645	−	0.257460i	−0.930727	+	0.365715i	$0.880824\pi$
$564$		0			0
$565$	8.99322	−	5.19224i	0.378347	−	0.218439i
$566$		0			0
$567$		−	17.9309i		−	0.753026i
$568$		0			0
$569$	−20.8423	+	36.1000i	−0.873756	+	1.51339i	−0.0156737	+	0.999877i	$0.504989\pi$
$569$	−20.8423	+	36.1000i	−0.873756	+	1.51339i	−0.858082	+	0.513512i	$0.828344\pi$
$570$		0			0
$571$	−28.8078			−1.20557			−0.602784	−	0.797905i	$-0.705942\pi$
$571$	−28.8078			−1.20557			−0.602784	+	0.797905i	$0.705942\pi$
$572$		0			0
$573$	39.3693			1.64468
$574$		0			0
$575$	−18.7386	+	32.4563i	−0.781455	+	1.35352i
$576$		0			0
$577$		−	24.2462i		−	1.00938i	−0.863300	−	0.504691i	$-0.831606\pi$
$577$		−	24.2462i		−	1.00938i	0.863300	−	0.504691i	$-0.168394\pi$
$578$		0			0
$579$	47.4050	−	27.3693i	1.97009	−	1.13743i
$580$		0			0
$581$	2.87689	+	4.98293i	0.119354	+	0.206727i
$582$		0			0
$583$	−13.8564	−	8.00000i	−0.573874	−	0.331326i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.6375	+	12.4924i	0.893076	+	0.515617i	0.874947	−	0.484218i	$-0.160896\pi$
$587$	21.6375	+	12.4924i	0.893076	+	0.515617i	0.0181284	+	0.999836i	$0.494229\pi$
$588$		0			0
$589$	10.2462	+	17.7470i	0.422188	+	0.731251i
$590$		0			0
$591$	5.13628	−	2.96543i	0.211278	−	0.121982i
$592$		0			0
$593$		−	38.4924i		−	1.58069i	−0.612659	−	0.790347i	$-0.709900\pi$
$593$		−	38.4924i		−	1.58069i	0.612659	−	0.790347i	$-0.290100\pi$
$594$		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	0.272427	+	0.962177i	$0.412174\pi$
$601$	−17.0885	+	29.5982i	−0.697056	+	1.20734i	−0.969483	+	0.245160i	$0.921160\pi$
$602$		0			0
$603$		−	18.2462i		−	0.743043i
$604$		0			0
$605$	7.41452	−	4.28078i	0.301443	−	0.174038i
$606$		0			0
$607$	−7.68466	−	13.3102i	−0.311911	−	0.540245i	0.666865	−	0.745178i	$-0.267636\pi$
$607$	−7.68466	−	13.3102i	−0.311911	−	0.540245i	−0.978776	+	0.204933i	$0.934302\pi$
$608$		0			0
$609$	11.3649	+	6.56155i	0.460531	+	0.265888i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−5.19615	−	3.00000i	−0.209871	−	0.121169i	0.391381	−	0.920229i	$-0.371998\pi$
$613$	−5.19615	−	3.00000i	−0.209871	−	0.121169i	−0.601251	+	0.799060i	$0.705331\pi$
$614$		0			0
$615$	2.24621	+	3.89055i	0.0905760	+	0.156882i
$616$		0			0
$617$	18.9328	−	10.9309i	0.762207	−	0.440060i	−0.0678808	−	0.997693i	$-0.521624\pi$
$617$	18.9328	−	10.9309i	0.762207	−	0.440060i	0.830087	+	0.557633i	$0.188290\pi$
$618$		0			0
$619$			29.7538i			1.19591i	0.801531	+	0.597953i	$0.204019\pi$
$619$			29.7538i			1.19591i	−0.801531	+	0.597953i	$0.795981\pi$
$620$		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
$629$			55.0540i			2.19515i
$630$		0			0
$631$	41.2961	−	23.8423i	1.64397	−	0.949148i	0.664571	−	0.747225i	$-0.268614\pi$
$631$	41.2961	−	23.8423i	1.64397	−	0.949148i	0.979401	−	0.201923i	$-0.0647192\pi$
$632$		0			0
$633$	−20.0885	−	34.7944i	−0.798448	−	1.38295i
$634$		0			0
$635$	4.98293	+	2.87689i	0.197741	+	0.114166i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	23.7025	+	13.6847i	0.937657	+	0.541357i
$640$		0			0
$641$	−4.12311	−	7.14143i	−0.162853	−	0.282069i	0.773038	−	0.634360i	$-0.218736\pi$
$641$	−4.12311	−	7.14143i	−0.162853	−	0.282069i	−0.935891	+	0.352290i	$0.885403\pi$
$642$		0			0
$643$	31.0572	−	17.9309i	1.22478	−	0.707124i	0.258843	−	0.965919i	$-0.416659\pi$
$643$	31.0572	−	17.9309i	1.22478	−	0.707124i	0.965932	+	0.258795i	$0.0833254\pi$
$644$		0			0
$645$			7.82292i			0.308027i
$646$		0			0
$647$	2.56155	−	4.43674i	0.100705	−	0.174426i	−0.811270	−	0.584671i	$-0.801223\pi$
$647$	2.56155	−	4.43674i	0.100705	−	0.174426i	0.911975	+	0.410245i	$0.134557\pi$
$648$		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	−0.814362	−	0.580358i	$-0.802913\pi$
$653$	2.43845	−	4.22351i	0.0954238	−	0.165279i	0.909785	+	0.415079i	$0.136246\pi$
$654$		0			0
$655$			2.69981i			0.105490i
$656$		0			0
$657$	18.5064	−	10.6847i	0.722002	−	0.416848i
$658$		0			0
$659$	−8.24621	−	14.2829i	−0.321227	−	0.556381i	0.659515	−	0.751692i	$-0.270762\pi$
$659$	−8.24621	−	14.2829i	−0.321227	−	0.556381i	−0.980741	+	0.195311i	$0.937429\pi$
$660$		0			0
$661$	−35.2807	−	20.3693i	−1.37226	−	0.792275i	−0.381048	−	0.924555i	$-0.624437\pi$
$661$	−35.2807	−	20.3693i	−1.37226	−	0.792275i	−0.991212	+	0.132281i	$0.957770\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.38202	−	3.68466i	−0.247484	−	0.142885i
$666$		0			0
$667$	8.00000	+	13.8564i	0.309761	+	0.536522i
$668$		0			0
$669$	−34.7944	+	20.0885i	−1.34523	+	0.776668i
$670$		0			0
$671$			56.9848i			2.19988i
$672$		0			0
$673$	−9.65009	+	16.7145i	−0.371984	+	0.644295i	−0.989871	−	0.141972i	$-0.954656\pi$
$673$	−9.65009	+	16.7145i	−0.371984	+	0.644295i	0.617887	+	0.786267i	$0.287989\pi$
$674$		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
$681$		−	20.4924i		−	0.785271i
$682$		0			0
$683$	20.7846	−	12.0000i	0.795301	−	0.459167i	−0.0465244	−	0.998917i	$-0.514815\pi$
$683$	20.7846	−	12.0000i	0.795301	−	0.459167i	0.841825	+	0.539750i	$0.181481\pi$
$684$		0			0
$685$	−0.876894	−	1.51883i	−0.0335044	−	0.0580313i
$686$		0			0
$687$	15.1021	+	8.71922i	0.576183	+	0.332659i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−14.7093	−	8.49242i	−0.559568	−	0.323067i	0.193404	−	0.981119i	$-0.438047\pi$
$691$	−14.7093	−	8.49242i	−0.559568	−	0.323067i	−0.752972	+	0.658052i	$0.771381\pi$
$692$		0			0
$693$	23.3693	+	40.4768i	0.887727	+	1.53759i
$694$		0			0
$695$	−3.73720	+	2.15767i	−0.141760	+	0.0818451i
$696$		0			0
$697$			17.7538i			0.672473i
$698$		0			0
$699$	−8.71922	+	15.1021i	−0.329791	+	0.571215i
$700$		0			0
$701$	−22.6307			−0.854749			−0.427375	−	0.904075i	$-0.640561\pi$
$701$	−22.6307			−0.854749			−0.427375	+	0.904075i	$0.640561\pi$
$702$		0			0
$703$	49.6155			1.87129
$704$		0			0
$705$	−0.226801	+	0.392831i	−0.00854182	+	0.0147949i
$706$		0			0
$707$			18.2462i			0.686219i
$708$		0			0
$709$	21.4243	−	12.3693i	0.804606	−	0.464539i	−0.0404733	−	0.999181i	$-0.512887\pi$
$709$	21.4243	−	12.3693i	0.804606	−	0.464539i	0.845079	+	0.534641i	$0.179553\pi$
$710$		0			0
$711$	−14.2462	−	24.6752i	−0.534275	−	0.925391i
$712$		0			0
$713$	−27.7128	−	16.0000i	−1.03785	−	0.599205i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.68247	+	3.28078i	0.212216	+	0.122523i
$718$		0			0
$719$	−6.56155	−	11.3649i	−0.244705	−	0.423841i	0.717344	−	0.696719i	$-0.245358\pi$
$719$	−6.56155	−	11.3649i	−0.244705	−	0.423841i	−0.962049	+	0.272878i	$0.912024\pi$
$720$		0			0
$721$	−4.98293	+	2.87689i	−0.185574	+	0.107141i
$722$		0			0
$723$			9.61553i			0.357605i
$724$		0			0
$725$	4.68466	−	8.11407i	0.173984	−	0.301349i
$726$		0			0
$727$	46.1080			1.71005			0.855025	−	0.518587i	$-0.173542\pi$
$727$	46.1080			1.71005			0.855025	+	0.518587i	$0.173542\pi$
$728$		0			0
$729$	−35.9848			−1.33277
$730$		0			0
$731$	−15.4579	+	26.7738i	−0.571730	+	0.990265i
$732$		0			0
$733$		−	27.4384i		−	1.01346i	−0.862104	−	0.506731i	$-0.830854\pi$
$733$		−	27.4384i		−	1.01346i	0.862104	−	0.506731i	$-0.169146\pi$
$734$		0			0
$735$	−0.546188	+	0.315342i	−0.0201464	+	0.0116315i
$736$		0			0
$737$	−13.1231	−	22.7299i	−0.483396	−	0.837266i
$738$		0			0
$739$	−8.87348	−	5.12311i	−0.326416	−	0.188456i	0.327833	−	0.944736i	$-0.393682\pi$
$739$	−8.87348	−	5.12311i	−0.326416	−	0.188456i	−0.654249	+	0.756279i	$0.727015\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−44.0943	−	25.4579i	−1.61766	−	0.933958i	−0.987523	−	0.157477i	$-0.949664\pi$
$743$	−44.0943	−	25.4579i	−1.61766	−	0.933958i	−0.630140	−	0.776481i	$-0.717003\pi$
$744$		0			0
$745$	−4.56155	−	7.90084i	−0.167122	−	0.289464i
$746$		0			0
$747$	6.92820	−	4.00000i	0.253490	−	0.146352i
$748$		0			0
$749$			10.2462i			0.374388i
$750$		0			0
$751$	12.4924	−	21.6375i	0.455855	−	0.789564i	−0.542882	−	0.839809i	$-0.682667\pi$
$751$	12.4924	−	21.6375i	0.455855	−	0.789564i	0.998737	+	0.0502450i	$0.0160002\pi$
$752$		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	−0.893007	−	0.450042i	$-0.851409\pi$
$757$	−1.56155	+	2.70469i	−0.0567556	+	0.0983036i	0.836252	+	0.548346i	$0.184742\pi$
$758$		0			0
$759$			104.985i			3.81071i
$760$		0			0
$761$	−40.2636	+	23.2462i	−1.45956	+	0.842674i	−0.998989	−	0.0449510i	$-0.985687\pi$
$761$	−40.2636	+	23.2462i	−1.45956	+	0.842674i	−0.460566	+	0.887626i	$0.652353\pi$
$762$		0			0
$763$	−3.59612	−	6.22866i	−0.130188	−	0.225493i
$764$		0			0
$765$	−9.84612	−	5.68466i	−0.355987	−	0.205529i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−12.0046	−	6.93087i	−0.432898	−	0.249934i	0.267683	−	0.963507i	$-0.413742\pi$
$769$	−12.0046	−	6.93087i	−0.432898	−	0.249934i	−0.700580	+	0.713574i	$0.747075\pi$
$770$		0			0
$771$	14.6501	+	25.3747i	0.527610	+	0.913848i
$772$		0			0
$773$	39.9905	−	23.0885i	1.43836	−	0.830437i	0.440623	−	0.897692i	$-0.354757\pi$
$773$	39.9905	−	23.0885i	1.43836	−	0.830437i	0.997736	+	0.0672550i	$0.0214241\pi$
$774$		0			0
$775$			18.7386i			0.673112i
$776$		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
$785$			12.6307i			0.450808i
$786$		0			0
$787$	13.8564	−	8.00000i	0.493928	−	0.285169i	−0.232275	−	0.972650i	$-0.574617\pi$
$787$	13.8564	−	8.00000i	0.493928	−	0.285169i	0.726202	+	0.687481i	$0.241284\pi$
$788$		0			0
$789$	33.6155	+	58.2238i	1.19674	+	2.07282i
$790$		0			0
$791$	41.0230	+	23.6847i	1.45861	+	0.842130i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	3.89055	+	2.24621i	0.137984	+	0.0796649i
$796$		0			0
$797$	−6.75379	−	11.6979i	−0.239231	−	0.414361i	0.721263	−	0.692662i	$-0.243562\pi$
$797$	−6.75379	−	11.6979i	−0.239231	−	0.414361i	−0.960494	+	0.278301i	$0.910229\pi$
$798$		0			0
$799$	−1.55244	+	0.896305i	−0.0549216	+	0.0317090i
$800$		0			0
$801$		−	35.6155i		−	1.25841i
$802$		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	−0.468882	−	0.883261i	$-0.655343\pi$
$809$	15.0885	−	26.1341i	0.530485	−	0.918827i	0.999367	−	0.0355661i	$-0.0113234\pi$
$810$		0			0
$811$		−	46.7386i		−	1.64122i	−0.571492	−	0.820608i	$-0.693635\pi$
$811$		−	46.7386i		−	1.64122i	0.571492	−	0.820608i	$-0.306365\pi$
$812$		0			0
$813$	46.1593	−	26.6501i	1.61888	−	0.934660i
$814$		0			0
$815$	−5.75379	−	9.96585i	−0.201546	−	0.349089i
$816$		0			0
$817$	24.1290	+	13.9309i	0.844166	+	0.487379i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.3701	−	7.71922i	−0.466619	−	0.269403i	0.248204	−	0.968708i	$-0.420160\pi$
$821$	−13.3701	−	7.71922i	−0.466619	−	0.269403i	−0.714823	+	0.699305i	$0.753493\pi$
$822$		0			0
$823$	−4.80776	−	8.32729i	−0.167588	−	0.290271i	0.769983	−	0.638064i	$-0.220265\pi$
$823$	−4.80776	−	8.32729i	−0.167588	−	0.290271i	−0.937571	+	0.347793i	$0.886931\pi$
$824$		0			0
$825$	53.2409	−	30.7386i	1.85361	−	1.07018i
$826$		0			0
$827$			35.8617i			1.24703i	0.781809	+	0.623517i	$0.214297\pi$
$827$			35.8617i			1.24703i	−0.781809	+	0.623517i	$0.785703\pi$
$828$		0			0
$829$	9.24621	−	16.0149i	0.321134	−	0.556221i	−0.659588	−	0.751627i	$-0.729269\pi$
$829$	9.24621	−	16.0149i	0.321134	−	0.556221i	0.980722	+	0.195406i	$0.0626026\pi$
$830$		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
$837$			5.75379i			0.198880i
$838$		0			0
$839$	9.29993	−	5.36932i	0.321069	−	0.185369i	−0.330800	−	0.943701i	$-0.607318\pi$
$839$	9.29993	−	5.36932i	0.321069	−	0.185369i	0.651869	+	0.758332i	$0.273985\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$		0			0
$843$	22.1837	+	12.8078i	0.764047	+	0.441123i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	33.8217	+	19.5270i	1.16213	+	0.670955i
$848$		0			0
$849$	−10.8769	−	18.8393i	−0.373294	−	0.646564i
$850$		0			0
$851$	−67.0973	+	38.7386i	−2.30007	+	1.32794i
$852$		0			0
$853$			29.6847i			1.01638i	0.861244	+	0.508192i	$0.169686\pi$
$853$			29.6847i			1.01638i	−0.861244	+	0.508192i	$0.830314\pi$
$854$		0			0
$855$	−5.12311	+	8.87348i	−0.175207	+	0.303467i
$856$		0			0
$857$	−40.7386			−1.39161			−0.695803	−	0.718233i	$-0.744951\pi$
$857$	−40.7386			−1.39161			−0.695803	+	0.718233i	$0.744951\pi$
$858$		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
$863$		−	49.3002i		−	1.67820i	−0.543979	−	0.839099i	$-0.683083\pi$
$863$		−	49.3002i		−	1.67820i	0.543979	−	0.839099i	$-0.316917\pi$
$864$		0			0
$865$	−2.37173	+	1.36932i	−0.0806411	+	0.0465582i
$866$		0			0
$867$	−19.6155	−	33.9751i	−0.666178	−	1.15385i
$868$		0			0
$869$	−35.4939	−	20.4924i	−1.20405	−	0.695158i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	25.4346	+	14.6847i	0.860830	+	0.497000i
$874$		0			0
$875$	−6.96543	−	12.0645i	−0.235475	−	0.407854i
$876$		0			0
$877$	−32.6359	+	18.8423i	−1.10204	+	0.636260i	−0.936755	−	0.349986i	$-0.886186\pi$
$877$	−32.6359	+	18.8423i	−1.10204	+	0.636260i	−0.165280	+	0.986247i	$0.552853\pi$
$878$		0			0
$879$		−	39.5464i		−	1.33387i
$880$		0			0
$881$	−15.4039	+	26.6803i	−0.518970	+	0.898882i	0.480787	+	0.876837i	$0.340351\pi$
$881$	−15.4039	+	26.6803i	−0.518970	+	0.898882i	−0.999757	+	0.0220449i	$0.992982\pi$
$882$		0			0
$883$	−0.315342			−0.0106121			−0.00530604	−	0.999986i	$-0.501689\pi$
$883$	−0.315342			−0.0106121			−0.00530604	+	0.999986i	$0.501689\pi$
$884$		0			0
$885$	−7.36932			−0.247717
$886$		0			0
$887$	22.7386	−	39.3845i	0.763489	−	1.32240i	−0.177553	−	0.984111i	$-0.556818\pi$
$887$	22.7386	−	39.3845i	0.763489	−	1.32240i	0.941042	−	0.338290i	$-0.109848\pi$
$888$		0			0
$889$			26.2462i			0.880270i
$890$		0			0
$891$	−31.0572	+	17.9309i	−1.04045	+	0.600707i
$892$		0			0
$893$	0.807764	+	1.39909i	0.0270308	+	0.0468187i
$894$		0			0
$895$	−3.73720	−	2.15767i	−0.124921	−	0.0721230i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.92820	+	4.00000i	0.231069	+	0.133407i
$900$		0			0
$901$	8.87689	+	15.3752i	0.295732	+	0.512223i
$902$		0			0
$903$	−30.9038	+	17.8423i	−1.02841	+	0.593756i
$904$		0			0
$905$		−	12.9848i		−	0.431631i
$906$		0			0
$907$	−10.4039	+	18.0201i	−0.345455	+	0.598346i	−0.985436	−	0.170045i	$-0.945609\pi$
$907$	−10.4039	+	18.0201i	−0.345455	+	0.598346i	0.639981	+	0.768391i	$0.278942\pi$
$908$		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
$915$		−	16.0000i		−	0.528944i
$916$		0			0
$917$	−10.6654	+	6.15767i	−0.352202	+	0.203344i
$918$		0			0
$919$	−12.4924	−	21.6375i	−0.412087	−	0.713756i	0.583031	−	0.812450i	$-0.301867\pi$
$919$	−12.4924	−	21.6375i	−0.412087	−	0.713756i	−0.995118	+	0.0986944i	$0.968533\pi$
$920$		0			0
$921$	29.1119	+	16.8078i	0.959270	+	0.553835i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	39.2910	+	22.6847i	1.29188	+	0.745867i
$926$		0			0
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$		0			0
$929$	−8.54052	+	4.93087i	−0.280205	+	0.161777i	−0.633516	−	0.773729i	$-0.718389\pi$
$929$	−8.54052	+	4.93087i	−0.280205	+	0.161777i	0.353311	+	0.935506i	$0.385056\pi$
$930$		0			0
$931$			2.24621i			0.0736166i
$932$		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
$941$			55.7926i			1.81879i	0.415937	+	0.909394i	$0.363454\pi$
$941$			55.7926i			1.81879i	−0.415937	+	0.909394i	$0.636546\pi$
$942$		0			0
$943$	−21.6375	+	12.4924i	−0.704614	+	0.406809i
$944$		0			0
$945$	−1.03457	−	1.79192i	−0.0336544	−	0.0582911i
$946$		0			0
$947$	6.38202	+	3.68466i	0.207388	+	0.119735i	0.600097	−	0.799927i	$-0.295129\pi$
$947$	6.38202	+	3.68466i	0.207388	+	0.119735i	−0.392709	+	0.919663i	$0.628462\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	27.1666	+	15.6847i	0.880938	+	0.508610i
$952$		0			0
$953$	−9.33475	−	16.1683i	−0.302382	−	0.523741i	0.674293	−	0.738464i	$-0.264449\pi$
$953$	−9.33475	−	16.1683i	−0.302382	−	0.523741i	−0.976675	+	0.214723i	$0.931115\pi$
$954$		0			0
$955$	−7.47439	+	4.31534i	−0.241866	+	0.139641i
$956$		0			0
$957$		−	26.2462i		−	0.848420i
$958$		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
$967$			2.56155i			0.0823740i	0.999151	+	0.0411870i	$0.0131139\pi$
$967$			2.56155i			0.0823740i	−0.999151	+	0.0411870i	$0.986886\pi$
$968$		0			0
$969$	−64.6058	+	37.3002i	−2.07544	+	1.19825i
$970$		0			0
$971$	15.8423	+	27.4397i	0.508405	+	0.880582i	0.999953	+	0.00973207i	$0.00309786\pi$
$971$	15.8423	+	27.4397i	0.508405	+	0.880582i	−0.491548	+	0.870850i	$0.663569\pi$
$972$		0			0
$973$	−17.0474	−	9.84233i	−0.546515	−	0.315531i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−47.1918	−	27.2462i	−1.50980	−	0.871684i	−0.999935	−	0.0114294i	$-0.996362\pi$
$977$	−47.1918	−	27.2462i	−1.50980	−	0.871684i	−0.509865	−	0.860254i	$-0.670305\pi$
$978$		0			0
$979$	−25.6155	−	44.3674i	−0.818676	−	1.41799i
$980$		0			0
$981$	−8.66025	+	5.00000i	−0.276501	+	0.159638i
$982$		0			0
$983$		−	17.9309i		−	0.571906i	−0.958244	−	0.285953i	$-0.907690\pi$
$983$		−	17.9309i		−	0.571906i	0.958244	−	0.285953i	$-0.0923101\pi$
$984$		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	−0.427013	−	0.904245i	$-0.640434\pi$
$991$	17.9309	−	31.0572i	0.569593	−	0.986564i	0.996606	−	0.0823184i	$-0.0262324\pi$
$992$		0			0
$993$		−	11.5076i		−	0.365182i
$994$		0			0
$995$	2.49146	−	1.43845i	0.0789847	−	0.0456018i
$996$		0			0
$997$	−0.123106	−	0.213225i	−0.00389879	−	0.00675291i	0.864069	−	0.503373i	$-0.167908\pi$
$997$	−0.123106	−	0.213225i	−0.00389879	−	0.00675291i	−0.867968	+	0.496620i	$0.834574\pi$
$998$		0			0
$999$	12.0645	+	6.96543i	0.381703	+	0.220377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.o.d.1161.1		8
13.2	odd	12		1352.2.i.f.1329.1		4
13.3	even	3	inner	1352.2.o.d.361.1		8
13.4	even	6		1352.2.f.c.337.4		4
13.5	odd	4		1352.2.i.f.529.1		4
13.6	odd	12		104.2.a.b.1.2	✓	2
13.7	odd	12		1352.2.a.g.1.2		2
13.8	odd	4		1352.2.i.d.529.1		4
13.9	even	3		1352.2.f.c.337.3		4
13.10	even	6	inner	1352.2.o.d.361.2		8
13.11	odd	12		1352.2.i.d.1329.1		4
13.12	even	2	inner	1352.2.o.d.1161.2		8
39.32	even	12		936.2.a.j.1.2		2
52.7	even	12		2704.2.a.p.1.1		2
52.19	even	12		208.2.a.e.1.1		2
52.35	odd	6		2704.2.f.k.337.1		4
52.43	odd	6		2704.2.f.k.337.2		4
65.19	odd	12		2600.2.a.p.1.1		2
65.32	even	12		2600.2.d.k.1249.1		4
65.58	even	12		2600.2.d.k.1249.4		4
91.6	even	12		5096.2.a.m.1.1		2
104.19	even	12		832.2.a.n.1.2		2
104.45	odd	12		832.2.a.k.1.1		2
156.71	odd	12		1872.2.a.u.1.2		2
208.19	even	12		3328.2.b.w.1665.1		4
208.45	odd	12		3328.2.b.y.1665.4		4
208.123	even	12		3328.2.b.w.1665.4		4
208.149	odd	12		3328.2.b.y.1665.1		4
260.19	even	12		5200.2.a.bw.1.2		2
312.149	even	12		7488.2.a.cu.1.1		2
312.227	odd	12		7488.2.a.cv.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.a.b.1.2	✓	2	13.6	odd	12
208.2.a.e.1.1		2	52.19	even	12
832.2.a.k.1.1		2	104.45	odd	12
832.2.a.n.1.2		2	104.19	even	12
936.2.a.j.1.2		2	39.32	even	12
1352.2.a.g.1.2		2	13.7	odd	12
1352.2.f.c.337.3		4	13.9	even	3
1352.2.f.c.337.4		4	13.4	even	6
1352.2.i.d.529.1		4	13.8	odd	4
1352.2.i.d.1329.1		4	13.11	odd	12
1352.2.i.f.529.1		4	13.5	odd	4
1352.2.i.f.1329.1		4	13.2	odd	12
1352.2.o.d.361.1		8	13.3	even	3	inner
1352.2.o.d.361.2		8	13.10	even	6	inner
1352.2.o.d.1161.1		8	1.1	even	1	trivial
1352.2.o.d.1161.2		8	13.12	even	2	inner
1872.2.a.u.1.2		2	156.71	odd	12
2600.2.a.p.1.1		2	65.19	odd	12
2600.2.d.k.1249.1		4	65.32	even	12
2600.2.d.k.1249.4		4	65.58	even	12
2704.2.a.p.1.1		2	52.7	even	12
2704.2.f.k.337.1		4	52.35	odd	6
2704.2.f.k.337.2		4	52.43	odd	6
3328.2.b.w.1665.1		4	208.19	even	12
3328.2.b.w.1665.4		4	208.123	even	12
3328.2.b.y.1665.1		4	208.149	odd	12
3328.2.b.y.1665.4		4	208.45	odd	12
5096.2.a.m.1.1		2	91.6	even	12
5200.2.a.bw.1.2		2	260.19	even	12
7488.2.a.cu.1.1		2	312.149	even	12
7488.2.a.cv.1.1		2	312.227	odd	12

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28078 + 2.21837i) q^{3} -0.561553i q^{5} +(2.21837 - 1.28078i) q^{7} +(-1.78078 - 3.08440i) q^{9} +(-4.43674 - 2.56155i) q^{11} +(1.24573 + 0.719224i) q^{15} +(2.84233 + 4.92306i) q^{17} +(4.43674 - 2.56155i) q^{19} +6.56155i q^{21} +(-4.00000 + 6.92820i) q^{23} +4.68466 q^{25} +1.43845 q^{27} +(1.00000 - 1.73205i) q^{29} +4.00000i q^{31} +(11.3649 - 6.56155i) q^{33} +(-0.719224 - 1.24573i) q^{35} +(8.38716 + 4.84233i) q^{37} +(2.70469 + 1.56155i) q^{41} +(2.71922 + 4.70983i) q^{43} +(-1.73205 + 1.00000i) q^{45} +0.315342i q^{47} +(-0.219224 + 0.379706i) q^{49} -14.5616 q^{51} +3.12311 q^{53} +(-1.43845 + 2.49146i) q^{55} +13.1231i q^{57} +(-4.43674 + 2.56155i) q^{59} +(-5.56155 - 9.63289i) q^{61} +(-7.90084 - 4.56155i) q^{63} +(4.43674 + 2.56155i) q^{67} +(-10.2462 - 17.7470i) q^{69} +(-6.65511 + 3.84233i) q^{71} +6.00000i q^{73} +(-6.00000 + 10.3923i) q^{75} -13.1231 q^{77} +8.00000 q^{79} +(3.50000 - 6.06218i) q^{81} +2.24621i q^{83} +(2.76456 - 1.59612i) q^{85} +(2.56155 + 4.43674i) q^{87} +(8.66025 + 5.00000i) q^{89} +(-8.87348 - 5.12311i) q^{93} +(-1.43845 - 2.49146i) q^{95} +(-7.14143 + 4.12311i) q^{97} +18.2462i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 6 q^{9} - 2 q^{17} - 32 q^{23} - 12 q^{25} + 28 q^{27} + 8 q^{29} - 14 q^{35} + 30 q^{43} - 10 q^{49} - 100 q^{51} - 8 q^{53} - 28 q^{55} - 28 q^{61} - 16 q^{69} - 48 q^{75} - 72 q^{77}+ \cdots - 28 q^{95}+O(q^{100}) \) 8 * q - 2 * q^3 - 6 * q^9 - 2 * q^17 - 32 * q^23 - 12 * q^25 + 28 * q^27 + 8 * q^29 - 14 * q^35 + 30 * q^43 - 10 * q^49 - 100 * q^51 - 8 * q^53 - 28 * q^55 - 28 * q^61 - 16 * q^69 - 48 * q^75 - 72 * q^77 + 64 * q^79 + 28 * q^81 + 4 * q^87 - 28 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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