LMFDB - Embedded newform 1680.2.di.a.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(289,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 3, 2]))

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

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

chi := DirichletCharacter("1680.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.di (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1680.289
Dual form			1680.2.di.a.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(-0.133975 + 2.23205i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{3} +(-0.133975 + 2.23205i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.50000 - 4.33013i) q^{11} +1.00000i q^{13} +(-1.00000 - 2.00000i) q^{15} +(1.73205 - 1.00000i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(0.500000 - 2.59808i) q^{21} +(2.59808 + 1.50000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +1.00000i q^{27} +(-3.00000 - 5.19615i) q^{31} +(4.33013 + 2.50000i) q^{33} +(-4.23205 - 4.13397i) q^{35} +(-4.33013 - 2.50000i) q^{37} +(-0.500000 - 0.866025i) q^{39} -9.00000 q^{41} -10.0000i q^{43} +(1.86603 + 1.23205i) q^{45} +(11.2583 + 6.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-0.866025 + 0.500000i) q^{53} +(10.0000 - 5.00000i) q^{55} -7.00000i q^{57} +(-2.00000 - 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +(0.866025 + 2.50000i) q^{63} +(-2.23205 - 0.133975i) q^{65} +(5.19615 - 3.00000i) q^{67} -3.00000 q^{69} +2.00000 q^{71} +(3.46410 - 2.00000i) q^{73} +(4.59808 - 1.96410i) q^{75} +(12.9904 + 2.50000i) q^{77} +(7.00000 - 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(5.00000 - 8.66025i) q^{89} +(-2.00000 - 1.73205i) q^{91} +(5.19615 + 3.00000i) q^{93} +(-13.0622 - 8.62436i) q^{95} -8.00000i q^{97} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^5 + 2 * q^9	$ 4 q - 4 q^{5} + 2 q^{9} - 10 q^{11} - 4 q^{15} - 14 q^{19} + 2 q^{21} - 6 q^{25} - 12 q^{31} - 10 q^{35} - 2 q^{39} - 36 q^{41} + 4 q^{45} - 4 q^{49} - 4 q^{51} + 40 q^{55} - 8 q^{59} + 4 q^{61} - 2 q^{65} - 12 q^{69} + 8 q^{71} + 8 q^{75} + 28 q^{79} - 2 q^{81} + 8 q^{85} + 20 q^{89} - 8 q^{91} - 28 q^{95} - 20 q^{99}+O(q^{100}) $ 4 * q - 4 * q^5 + 2 * q^9 - 10 * q^11 - 4 * q^15 - 14 * q^19 + 2 * q^21 - 6 * q^25 - 12 * q^31 - 10 * q^35 - 2 * q^39 - 36 * q^41 + 4 * q^45 - 4 * q^49 - 4 * q^51 + 40 * q^55 - 8 * q^59 + 4 * q^61 - 2 * q^65 - 12 * q^69 + 8 * q^71 + 8 * q^75 + 28 * q^79 - 2 * q^81 + 8 * q^85 + 20 * q^89 - 8 * q^91 - 28 * q^95 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		0			0
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$6$		0			0
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$		0			0
$15$	−1.00000	−	2.00000i	−0.258199	−	0.516398i
$16$		0			0
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	−0.275029	−	0.961436i	$-0.588688\pi$
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	0.695113	+	0.718900i	$0.255354\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	0.500000	−	2.59808i	0.109109	−	0.566947i
$22$		0			0
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	0.745782	−	0.666190i	$-0.232076\pi$
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	−0.204046	+	0.978961i	$0.565409\pi$
$24$		0			0
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$		0			0
$33$	4.33013	+	2.50000i	0.753778	+	0.435194i
$34$		0			0
$35$	−4.23205	−	4.13397i	−0.715347	−	0.698769i
$36$		0			0
$37$	−4.33013	−	2.50000i	−0.711868	−	0.410997i	0.0998840	−	0.994999i	$-0.468153\pi$
$37$	−4.33013	−	2.50000i	−0.711868	−	0.410997i	−0.811752	+	0.584002i	$0.801486\pi$
$38$		0			0
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$		−	10.0000i		−	1.52499i	−0.646997	−	0.762493i	$-0.723975\pi$
$43$		−	10.0000i		−	1.52499i	0.646997	−	0.762493i	$-0.276025\pi$
$44$		0			0
$45$	1.86603	+	1.23205i	0.278171	+	0.183663i
$46$		0			0
$47$	11.2583	+	6.50000i	1.64220	+	0.948122i	0.980051	+	0.198747i	$0.0636872\pi$
$47$	11.2583	+	6.50000i	1.64220	+	0.948122i	0.662145	+	0.749375i	$0.269646\pi$
$48$		0			0
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$		0			0
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$		0			0
$53$	−0.866025	+	0.500000i	−0.118958	+	0.0686803i	−0.558298	−	0.829640i	$-0.688546\pi$
$53$	−0.866025	+	0.500000i	−0.118958	+	0.0686803i	0.439340	+	0.898321i	$0.355212\pi$
$54$		0			0
$55$	10.0000	−	5.00000i	1.34840	−	0.674200i
$56$		0			0
$57$		−	7.00000i		−	0.927173i
$58$		0			0
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$		0			0
$63$	0.866025	+	2.50000i	0.109109	+	0.314970i
$64$		0			0
$65$	−2.23205	−	0.133975i	−0.276852	−	0.0166175i
$66$		0			0
$67$	5.19615	−	3.00000i	0.634811	−	0.366508i	−0.147802	−	0.989017i	$-0.547220\pi$
$67$	5.19615	−	3.00000i	0.634811	−	0.366508i	0.782613	+	0.622509i	$0.213886\pi$
$68$		0			0
$69$	−3.00000			−0.361158
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	−0.283387	−	0.959006i	$-0.591458\pi$
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	0.688830	+	0.724923i	$0.258125\pi$
$74$		0			0
$75$	4.59808	−	1.96410i	0.530940	−	0.226795i
$76$		0			0
$77$	12.9904	+	2.50000i	1.48039	+	0.284901i
$78$		0			0
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	−0.139895	−	0.990166i	$-0.544677\pi$
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	0.927457	−	0.373930i	$-0.121990\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			10.0000i			1.09764i	0.835940	+	0.548821i	$0.184923\pi$
$83$			10.0000i			1.09764i	−0.835940	+	0.548821i	$0.815077\pi$
$84$		0			0
$85$	2.00000	+	4.00000i	0.216930	+	0.433861i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	−0.469389	−	0.882992i	$-0.655526\pi$
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	0.999388	−	0.0349934i	$-0.0111410\pi$
$90$		0			0
$91$	−2.00000	−	1.73205i	−0.209657	−	0.181568i
$92$		0			0
$93$	5.19615	+	3.00000i	0.538816	+	0.311086i
$94$		0			0
$95$	−13.0622	−	8.62436i	−1.34015	−	0.884840i
$96$		0			0
$97$		−	8.00000i		−	0.812277i	−0.913812	−	0.406138i	$-0.866875\pi$
$97$		−	8.00000i		−	0.812277i	0.913812	−	0.406138i	$-0.133125\pi$
$98$		0			0
$99$	−5.00000			−0.502519
$100$		0			0
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	0.595466	−	0.803380i	$-0.296967\pi$
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	−0.993481	+	0.113998i	$0.963634\pi$
$102$		0			0
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$		0			0
$105$	5.73205	+	1.46410i	0.559391	+	0.142882i
$106$		0			0
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.0950377	−	0.995474i	$-0.530297\pi$
$107$	−10.3923	−	6.00000i	−1.00466	−	0.580042i	−0.909624	+	0.415432i	$0.863630\pi$
$108$		0			0
$109$	−9.00000	−	15.5885i	−0.862044	−	1.49310i	−0.869953	−	0.493135i	$-0.835851\pi$
$109$	−9.00000	−	15.5885i	−0.862044	−	1.49310i	0.00790932	−	0.999969i	$-0.497482\pi$
$110$		0			0
$111$	5.00000			0.474579
$112$		0			0
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$	−3.69615	+	5.59808i	−0.344668	+	0.522023i
$116$		0			0
$117$	0.866025	+	0.500000i	0.0800641	+	0.0462250i
$118$		0			0
$119$	−1.00000	+	5.19615i	−0.0916698	+	0.476331i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$	7.79423	−	4.50000i	0.702782	−	0.405751i
$124$		0			0
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$			9.00000i			0.798621i	0.916816	+	0.399310i	$0.130750\pi$
$127$			9.00000i			0.798621i	−0.916816	+	0.399310i	$0.869250\pi$
$128$		0			0
$129$	5.00000	+	8.66025i	0.440225	+	0.762493i
$130$		0			0
$131$	−8.50000	+	14.7224i	−0.742648	+	1.28630i	0.208637	+	0.977993i	$0.433097\pi$
$131$	−8.50000	+	14.7224i	−0.742648	+	1.28630i	−0.951285	+	0.308312i	$0.900236\pi$
$132$		0			0
$133$	−6.06218	−	17.5000i	−0.525657	−	1.51744i
$134$		0			0
$135$	−2.23205	−	0.133975i	−0.192104	−	0.0115307i
$136$		0			0
$137$	3.46410	−	2.00000i	0.295958	−	0.170872i	−0.344668	−	0.938725i	$-0.612008\pi$
$137$	3.46410	−	2.00000i	0.295958	−	0.170872i	0.640626	+	0.767853i	$0.278675\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−13.0000			−1.09480
$142$		0			0
$143$	4.33013	−	2.50000i	0.362103	−	0.209061i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.33013	+	5.50000i	0.357143	+	0.453632i
$148$		0			0
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−11.0000	−	19.0526i	−0.895167	−	1.55048i	−0.833597	−	0.552372i	$-0.813723\pi$
$151$	−11.0000	−	19.0526i	−0.895167	−	1.55048i	−0.0615699	−	0.998103i	$-0.519611\pi$
$152$		0			0
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	12.0000	−	6.00000i	0.963863	−	0.481932i
$156$		0			0
$157$	−11.2583	+	6.50000i	−0.898513	+	0.518756i	−0.876717	−	0.481006i	$-0.840272\pi$
$157$	−11.2583	+	6.50000i	−0.898513	+	0.518756i	−0.0217953	+	0.999762i	$0.506938\pi$
$158$		0			0
$159$	0.500000	−	0.866025i	0.0396526	−	0.0686803i
$160$		0			0
$161$	−7.50000	+	2.59808i	−0.591083	+	0.204757i
$162$		0			0
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	0.0343508	−	0.999410i	$-0.489064\pi$
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	−0.848339	+	0.529454i	$0.822397\pi$
$164$		0			0
$165$	−6.16025	+	9.33013i	−0.479575	+	0.726349i
$166$		0			0
$167$		−	19.0000i		−	1.47026i	−0.677924	−	0.735132i	$-0.737120\pi$
$167$		−	19.0000i		−	1.47026i	0.677924	−	0.735132i	$-0.262880\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	3.50000	+	6.06218i	0.267652	+	0.463586i
$172$		0			0
$173$	−6.06218	−	3.50000i	−0.460899	−	0.266100i	0.251523	−	0.967851i	$-0.419068\pi$
$173$	−6.06218	−	3.50000i	−0.460899	−	0.266100i	−0.712422	+	0.701751i	$0.752402\pi$
$174$		0			0
$175$	9.79423	−	8.89230i	0.740374	−	0.672195i
$176$		0			0
$177$	3.46410	+	2.00000i	0.260378	+	0.150329i
$178$		0			0
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	0.995009	−	0.0997838i	$-0.0318151\pi$
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	−0.583920	+	0.811811i	$0.698482\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$			2.00000i			0.147844i
$184$		0			0
$185$	6.16025	−	9.33013i	0.452911	−	0.685965i
$186$		0			0
$187$	−8.66025	−	5.00000i	−0.633300	−	0.365636i
$188$		0			0
$189$	−2.00000	−	1.73205i	−0.145479	−	0.125988i
$190$		0			0
$191$	−8.00000	+	13.8564i	−0.578860	+	1.00261i	0.416751	+	0.909021i	$0.363169\pi$
$191$	−8.00000	+	13.8564i	−0.578860	+	1.00261i	−0.995610	+	0.0935936i	$0.970165\pi$
$192$		0			0
$193$	−15.5885	+	9.00000i	−1.12208	+	0.647834i	−0.941932	−	0.335805i	$-0.890992\pi$
$193$	−15.5885	+	9.00000i	−1.12208	+	0.647834i	−0.180150	+	0.983639i	$0.557658\pi$
$194$		0			0
$195$	2.00000	−	1.00000i	0.143223	−	0.0716115i
$196$		0			0
$197$			27.0000i			1.92367i	0.273629	+	0.961835i	$0.411776\pi$
$197$			27.0000i			1.92367i	−0.273629	+	0.961835i	$0.588224\pi$
$198$		0			0
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	0.999990	−	0.00436292i	$-0.00138876\pi$
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	−0.503774	+	0.863836i	$0.668055\pi$
$200$		0			0
$201$	−3.00000	+	5.19615i	−0.211604	+	0.366508i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.20577	−	20.0885i	0.0842147	−	1.40304i
$206$		0			0
$207$	2.59808	−	1.50000i	0.180579	−	0.104257i
$208$		0			0
$209$	35.0000			2.42100
$210$		0			0
$211$	−19.0000			−1.30801			−0.654007	−	0.756489i	$-0.726913\pi$
$211$	−19.0000			−1.30801			−0.654007	+	0.756489i	$0.726913\pi$
$212$		0			0
$213$	−1.73205	+	1.00000i	−0.118678	+	0.0685189i
$214$		0			0
$215$	22.3205	+	1.33975i	1.52225	+	0.0913699i
$216$		0			0
$217$	15.5885	+	3.00000i	1.05821	+	0.203653i
$218$		0			0
$219$	−2.00000	+	3.46410i	−0.135147	+	0.234082i
$220$		0			0
$221$	1.00000	+	1.73205i	0.0672673	+	0.116510i
$222$		0			0
$223$		−	16.0000i		−	1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$		−	16.0000i		−	1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$224$		0			0
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$		0			0
$227$	12.1244	−	7.00000i	0.804722	−	0.464606i	−0.0403978	−	0.999184i	$-0.512863\pi$
$227$	12.1244	−	7.00000i	0.804722	−	0.464606i	0.845120	+	0.534577i	$0.179529\pi$
$228$		0			0
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	−0.924510	−	0.381157i	$-0.875526\pi$
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	0.792347	+	0.610071i	$0.208859\pi$
$230$		0			0
$231$	−12.5000	+	4.33013i	−0.822440	+	0.284901i
$232$		0			0
$233$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$233$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$234$		0			0
$235$	−16.0167	+	24.2583i	−1.04481	+	1.58244i
$236$		0			0
$237$			14.0000i			0.909398i
$238$		0			0
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$	15.5981	−	1.30385i	0.996525	−	0.0832998i
$246$		0			0
$247$	−6.06218	−	3.50000i	−0.385727	−	0.222700i
$248$		0			0
$249$	−5.00000	−	8.66025i	−0.316862	−	0.548821i
$250$		0			0
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$		−	15.0000i		−	0.943042i
$254$		0			0
$255$	−3.73205	−	2.46410i	−0.233710	−	0.154308i
$256$		0			0
$257$	−8.66025	−	5.00000i	−0.540212	−	0.311891i	0.204953	−	0.978772i	$-0.434296\pi$
$257$	−8.66025	−	5.00000i	−0.540212	−	0.311891i	−0.745165	+	0.666880i	$0.767629\pi$
$258$		0			0
$259$	12.5000	−	4.33013i	0.776712	−	0.269061i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.977147	−	0.212565i	$-0.931818\pi$
$263$	−20.7846	+	12.0000i	−1.28163	+	0.739952i	−0.304487	+	0.952517i	$0.598485\pi$
$264$		0			0
$265$	−1.00000	−	2.00000i	−0.0614295	−	0.122859i
$266$		0			0
$267$			10.0000i			0.611990i
$268$		0			0
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	−0.718580	−	0.695444i	$-0.755208\pi$
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	0.961563	+	0.274586i	$0.0885408\pi$
$272$		0			0
$273$	2.59808	+	0.500000i	0.157243	+	0.0302614i
$274$		0			0
$275$	9.82051	+	22.9904i	0.592199	+	1.38637i
$276$		0			0
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	−0.551131	−	0.834419i	$-0.685804\pi$
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	0.447062	+	0.894503i	$0.352470\pi$
$278$		0			0
$279$	−6.00000			−0.359211
$280$		0			0
$281$	−11.0000			−0.656205			−0.328102	−	0.944642i	$-0.606409\pi$
$281$	−11.0000			−0.656205			−0.328102	+	0.944642i	$0.606409\pi$
$282$		0			0
$283$	−22.5167	+	13.0000i	−1.33848	+	0.772770i	−0.986581	−	0.163270i	$-0.947796\pi$
$283$	−22.5167	+	13.0000i	−1.33848	+	0.772770i	−0.351895	+	0.936039i	$0.614463\pi$
$284$		0			0
$285$	15.6244	+	0.937822i	0.925507	+	0.0555518i
$286$		0			0
$287$	15.5885	−	18.0000i	0.920158	−	1.06251i
$288$		0			0
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$		0			0
$291$	4.00000	+	6.92820i	0.234484	+	0.406138i
$292$		0			0
$293$			1.00000i			0.0584206i	0.999573	+	0.0292103i	$0.00929925\pi$
$293$			1.00000i			0.0584206i	−0.999573	+	0.0292103i	$0.990701\pi$
$294$		0			0
$295$	8.00000	−	4.00000i	0.465778	−	0.232889i
$296$		0			0
$297$	4.33013	−	2.50000i	0.251259	−	0.145065i
$298$		0			0
$299$	−1.50000	+	2.59808i	−0.0867472	+	0.150251i
$300$		0			0
$301$	20.0000	+	17.3205i	1.15278	+	0.998337i
$302$		0			0
$303$	6.92820	+	4.00000i	0.398015	+	0.229794i
$304$		0			0
$305$	3.73205	+	2.46410i	0.213697	+	0.141094i
$306$		0			0
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−13.0000	−	22.5167i	−0.737162	−	1.27680i	−0.953768	−	0.300544i	$-0.902832\pi$
$311$	−13.0000	−	22.5167i	−0.737162	−	1.27680i	0.216606	−	0.976259i	$-0.430501\pi$
$312$		0			0
$313$	8.66025	+	5.00000i	0.489506	+	0.282617i	0.724370	−	0.689412i	$-0.242131\pi$
$313$	8.66025	+	5.00000i	0.489506	+	0.282617i	−0.234863	+	0.972028i	$0.575464\pi$
$314$		0			0
$315$	−5.69615	+	1.59808i	−0.320942	+	0.0900414i
$316$		0			0
$317$	1.73205	+	1.00000i	0.0972817	+	0.0561656i	0.547852	−	0.836576i	$-0.315446\pi$
$317$	1.73205	+	1.00000i	0.0972817	+	0.0561656i	−0.450570	+	0.892741i	$0.648779\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$			14.0000i			0.778981i
$324$		0			0
$325$	0.598076	−	4.96410i	0.0331753	−	0.275359i
$326$		0			0
$327$	15.5885	+	9.00000i	0.862044	+	0.497701i
$328$		0			0
$329$	−32.5000	+	11.2583i	−1.79178	+	0.620692i
$330$		0			0
$331$	−7.50000	+	12.9904i	−0.412237	+	0.714016i	−0.995134	−	0.0985303i	$-0.968586\pi$
$331$	−7.50000	+	12.9904i	−0.412237	+	0.714016i	0.582897	+	0.812546i	$0.301919\pi$
$332$		0			0
$333$	−4.33013	+	2.50000i	−0.237289	+	0.136999i
$334$		0			0
$335$	6.00000	+	12.0000i	0.327815	+	0.655630i
$336$		0			0
$337$			14.0000i			0.762629i	0.924445	+	0.381314i	$0.124528\pi$
$337$			14.0000i			0.762629i	−0.924445	+	0.381314i	$0.875472\pi$
$338$		0			0
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$	−15.0000	+	25.9808i	−0.812296	+	1.40694i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$	0.401924	−	6.69615i	0.0216388	−	0.360509i
$346$		0			0
$347$	−13.8564	+	8.00000i	−0.743851	+	0.429463i	−0.823468	−	0.567363i	$-0.807964\pi$
$347$	−13.8564	+	8.00000i	−0.743851	+	0.429463i	0.0796169	+	0.996826i	$0.474630\pi$
$348$		0			0
$349$	24.0000			1.28469			0.642345	−	0.766415i	$-0.277962\pi$
$349$	24.0000			1.28469			0.642345	+	0.766415i	$0.277962\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$	−0.267949	+	4.46410i	−0.0142213	+	0.236930i
$356$		0			0
$357$	−1.73205	−	5.00000i	−0.0916698	−	0.264628i
$358$		0			0
$359$	14.0000	−	24.2487i	0.738892	−	1.27980i	−0.214103	−	0.976811i	$-0.568683\pi$
$359$	14.0000	−	24.2487i	0.738892	−	1.27980i	0.952995	−	0.302987i	$-0.0979839\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$		−	14.0000i		−	0.734809i
$364$		0			0
$365$	4.00000	+	8.00000i	0.209370	+	0.418739i
$366$		0			0
$367$	−32.0429	+	18.5000i	−1.67263	+	0.965692i	−0.706469	+	0.707744i	$0.749713\pi$
$367$	−32.0429	+	18.5000i	−1.67263	+	0.965692i	−0.966159	+	0.257948i	$0.916954\pi$
$368$		0			0
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$		0			0
$371$	0.500000	−	2.59808i	0.0259587	−	0.134885i
$372$		0			0
$373$	−5.19615	−	3.00000i	−0.269047	−	0.155334i	0.359408	−	0.933181i	$-0.382979\pi$
$373$	−5.19615	−	3.00000i	−0.269047	−	0.155334i	−0.628454	+	0.777847i	$0.716312\pi$
$374$		0			0
$375$	3.76795	+	10.5263i	0.194576	+	0.543575i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$		0			0
$381$	−4.50000	−	7.79423i	−0.230542	−	0.399310i
$382$		0			0
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	0.287469	−	0.957790i	$-0.407186\pi$
$383$	−7.79423	−	4.50000i	−0.398266	−	0.229939i	−0.685736	+	0.727851i	$0.740519\pi$
$384$		0			0
$385$	−7.32051	+	28.6603i	−0.373088	+	1.46066i
$386$		0			0
$387$	−8.66025	−	5.00000i	−0.440225	−	0.254164i
$388$		0			0
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$		0			0
$393$		−	17.0000i		−	0.857537i
$394$		0			0
$395$	26.1244	+	17.2487i	1.31446	+	0.867877i
$396$		0			0
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	0.455905	−	0.890028i	$-0.349316\pi$
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	−0.542834	+	0.839840i	$0.682649\pi$
$398$		0			0
$399$	14.0000	+	12.1244i	0.700877	+	0.606977i
$400$		0			0
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$		0			0
$403$	5.19615	−	3.00000i	0.258839	−	0.149441i
$404$		0			0
$405$	2.00000	−	1.00000i	0.0993808	−	0.0496904i
$406$		0			0
$407$			25.0000i			1.23920i
$408$		0			0
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$		0			0
$411$	−2.00000	+	3.46410i	−0.0986527	+	0.170872i
$412$		0			0
$413$	10.3923	+	2.00000i	0.511372	+	0.0984136i
$414$		0			0
$415$	−22.3205	−	1.33975i	−1.09567	−	0.0657655i
$416$		0			0
$417$	6.92820	−	4.00000i	0.339276	−	0.195881i
$418$		0			0
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$		0			0
$423$	11.2583	−	6.50000i	0.547399	−	0.316041i
$424$		0			0
$425$	−9.19615	+	3.92820i	−0.446079	+	0.190546i
$426$		0			0
$427$	1.73205	+	5.00000i	0.0838198	+	0.241967i
$428$		0			0
$429$	−2.50000	+	4.33013i	−0.120701	+	0.209061i
$430$		0			0
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$		0			0
$433$			4.00000i			0.192228i	0.995370	+	0.0961139i	$0.0306413\pi$
$433$			4.00000i			0.192228i	−0.995370	+	0.0961139i	$0.969359\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−18.1865	+	10.5000i	−0.869980	+	0.502283i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	−5.19615	−	3.00000i	−0.246877	−	0.142534i	0.371457	−	0.928450i	$-0.378858\pi$
$443$	−5.19615	−	3.00000i	−0.246877	−	0.142534i	−0.618333	+	0.785916i	$0.712192\pi$
$444$		0			0
$445$	18.6603	+	12.3205i	0.884581	+	0.584048i
$446$		0			0
$447$		−	6.00000i		−	0.283790i
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	22.5000	+	38.9711i	1.05948	+	1.83508i
$452$		0			0
$453$	19.0526	+	11.0000i	0.895167	+	0.516825i
$454$		0			0
$455$	4.13397	−	4.23205i	0.193804	−	0.198402i
$456$		0			0
$457$	−32.9090	−	19.0000i	−1.53942	−	0.888783i	−0.998873	−	0.0474665i	$-0.984885\pi$
$457$	−32.9090	−	19.0000i	−1.53942	−	0.888783i	−0.540544	−	0.841316i	$-0.681781\pi$
$458$		0			0
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$		0			0
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$			15.0000i			0.697109i	0.937288	+	0.348555i	$0.113327\pi$
$463$			15.0000i			0.697109i	−0.937288	+	0.348555i	$0.886673\pi$
$464$		0			0
$465$	−7.39230	+	11.1962i	−0.342810	+	0.519209i
$466$		0			0
$467$	−1.73205	−	1.00000i	−0.0801498	−	0.0462745i	0.459390	−	0.888235i	$-0.348068\pi$
$467$	−1.73205	−	1.00000i	−0.0801498	−	0.0462745i	−0.539539	+	0.841960i	$0.681402\pi$
$468$		0			0
$469$	−3.00000	+	15.5885i	−0.138527	+	0.719808i
$470$		0			0
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$		0			0
$473$	−43.3013	+	25.0000i	−1.99099	+	1.14950i
$474$		0			0
$475$	21.0000	−	28.0000i	0.963546	−	1.28473i
$476$		0			0
$477$			1.00000i			0.0457869i
$478$		0			0
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	0.760056	−	0.649857i	$-0.225171\pi$
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	−0.942821	+	0.333300i	$0.891838\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$		0			0
$483$	5.19615	−	6.00000i	0.236433	−	0.273009i
$484$		0			0
$485$	17.8564	+	1.07180i	0.810818	+	0.0486678i
$486$		0			0
$487$	20.7846	−	12.0000i	0.941841	−	0.543772i	0.0513038	−	0.998683i	$-0.483662\pi$
$487$	20.7846	−	12.0000i	0.941841	−	0.543772i	0.890537	+	0.454911i	$0.150329\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	−24.0000			−1.08310			−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000			−1.08310			−0.541552	+	0.840667i	$0.682163\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.669873	−	11.1603i	0.0301086	−	0.501616i
$496$		0			0
$497$	−3.46410	+	4.00000i	−0.155386	+	0.179425i
$498$		0			0
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$		0			0
$501$	9.50000	+	16.4545i	0.424429	+	0.735132i
$502$		0			0
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$		0			0
$505$	16.0000	−	8.00000i	0.711991	−	0.355995i
$506$		0			0
$507$	−10.3923	+	6.00000i	−0.461538	+	0.266469i
$508$		0			0
$509$	7.00000	−	12.1244i	0.310270	−	0.537403i	−0.668151	−	0.744026i	$-0.732914\pi$
$509$	7.00000	−	12.1244i	0.310270	−	0.537403i	0.978421	+	0.206623i	$0.0662474\pi$
$510$		0			0
$511$	−2.00000	+	10.3923i	−0.0884748	+	0.459728i
$512$		0			0
$513$	−6.06218	−	3.50000i	−0.267652	−	0.154529i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	65.0000i		−	2.85870i
$518$		0			0
$519$	7.00000			0.307266
$520$		0			0
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	0.982231	−	0.187678i	$-0.0600963\pi$
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	−0.653650	+	0.756797i	$0.726763\pi$
$522$		0			0
$523$	10.3923	+	6.00000i	0.454424	+	0.262362i	0.709697	−	0.704507i	$-0.248832\pi$
$523$	10.3923	+	6.00000i	0.454424	+	0.262362i	−0.255273	+	0.966869i	$0.582165\pi$
$524$		0			0
$525$	−4.03590	+	12.5981i	−0.176141	+	0.549825i
$526$		0			0
$527$	−10.3923	−	6.00000i	−0.452696	−	0.261364i
$528$		0			0
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$		−	9.00000i		−	0.389833i
$534$		0			0
$535$	14.7846	−	22.3923i	0.639194	−	0.968104i
$536$		0			0
$537$	−9.52628	−	5.50000i	−0.411089	−	0.237343i
$538$		0			0
$539$	−27.5000	+	21.6506i	−1.18451	+	0.932559i
$540$		0			0
$541$	−2.00000	+	3.46410i	−0.0859867	+	0.148933i	−0.905811	−	0.423681i	$-0.860738\pi$
$541$	−2.00000	+	3.46410i	−0.0859867	+	0.148933i	0.819825	+	0.572615i	$0.194071\pi$
$542$		0			0
$543$	1.73205	−	1.00000i	0.0743294	−	0.0429141i
$544$		0			0
$545$	36.0000	−	18.0000i	1.54207	−	0.771035i
$546$		0			0
$547$		−	14.0000i		−	0.598597i	−0.954160	−	0.299298i	$-0.903247\pi$
$547$		−	14.0000i		−	0.598597i	0.954160	−	0.299298i	$-0.0967526\pi$
$548$		0			0
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	12.1244	+	35.0000i	0.515580	+	1.48835i
$554$		0			0
$555$	−0.669873	+	11.1603i	−0.0284345	+	0.473726i
$556$		0			0
$557$	33.7750	−	19.5000i	1.43109	−	0.826242i	0.433888	−	0.900967i	$-0.357141\pi$
$557$	33.7750	−	19.5000i	1.43109	−	0.826242i	0.997204	+	0.0747252i	$0.0238080\pi$
$558$		0			0
$559$	10.0000			0.422955
$560$		0			0
$561$	10.0000			0.422200
$562$		0			0
$563$	−25.9808	+	15.0000i	−1.09496	+	0.632175i	−0.934892	−	0.354932i	$-0.884504\pi$
$563$	−25.9808	+	15.0000i	−1.09496	+	0.632175i	−0.160066	+	0.987106i	$0.551171\pi$
$564$		0			0
$565$	−13.3923	−	0.803848i	−0.563418	−	0.0338181i
$566$		0			0
$567$	2.59808	+	0.500000i	0.109109	+	0.0209980i
$568$		0			0
$569$	−1.50000	+	2.59808i	−0.0628833	+	0.108917i	−0.895753	−	0.444552i	$-0.853363\pi$
$569$	−1.50000	+	2.59808i	−0.0628833	+	0.108917i	0.832870	+	0.553469i	$0.186696\pi$
$570$		0			0
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	0.770108	−	0.637913i	$-0.220202\pi$
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	−0.937503	+	0.347977i	$0.886869\pi$
$572$		0			0
$573$		−	16.0000i		−	0.668410i
$574$		0			0
$575$	−12.0000	−	9.00000i	−0.500435	−	0.375326i
$576$		0			0
$577$	−20.7846	+	12.0000i	−0.865275	+	0.499567i	−0.865775	−	0.500433i	$-0.833174\pi$
$577$	−20.7846	+	12.0000i	−0.865275	+	0.499567i	0.000500448		1.00000i	$0.499841\pi$
$578$		0			0
$579$	9.00000	−	15.5885i	0.374027	−	0.647834i
$580$		0			0
$581$	−20.0000	−	17.3205i	−0.829740	−	0.718576i
$582$		0			0
$583$	4.33013	+	2.50000i	0.179336	+	0.103539i
$584$		0			0
$585$	−1.23205	+	1.86603i	−0.0509390	+	0.0771507i
$586$		0			0
$587$			2.00000i			0.0825488i	0.999148	+	0.0412744i	$0.0131418\pi$
$587$			2.00000i			0.0825488i	−0.999148	+	0.0412744i	$0.986858\pi$
$588$		0			0
$589$	42.0000			1.73058
$590$		0			0
$591$	−13.5000	−	23.3827i	−0.555316	−	0.961835i
$592$		0			0
$593$	29.4449	+	17.0000i	1.20916	+	0.698106i	0.962575	−	0.271016i	$-0.0873596\pi$
$593$	29.4449	+	17.0000i	1.20916	+	0.698106i	0.246581	+	0.969122i	$0.420693\pi$
$594$		0			0
$595$	−11.4641	−	2.92820i	−0.469982	−	0.120045i
$596$		0			0
$597$	−12.1244	−	7.00000i	−0.496217	−	0.286491i
$598$		0			0
$599$	14.0000	+	24.2487i	0.572024	+	0.990775i	0.996358	+	0.0852695i	$0.0271751\pi$
$599$	14.0000	+	24.2487i	0.572024	+	0.990775i	−0.424333	+	0.905506i	$0.639492\pi$
$600$		0			0
$601$	−30.0000			−1.22373			−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000			−1.22373			−0.611863	+	0.790964i	$0.709580\pi$
$602$		0			0
$603$		−	6.00000i		−	0.244339i
$604$		0			0
$605$	−26.1244	−	17.2487i	−1.06211	−	0.701260i
$606$		0			0
$607$	−11.2583	−	6.50000i	−0.456962	−	0.263827i	0.253804	−	0.967256i	$-0.418318\pi$
$607$	−11.2583	−	6.50000i	−0.456962	−	0.263827i	−0.710766	+	0.703429i	$0.751651\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.50000	+	11.2583i	−0.262962	+	0.455463i
$612$		0			0
$613$	16.4545	−	9.50000i	0.664590	−	0.383701i	−0.129433	−	0.991588i	$-0.541316\pi$
$613$	16.4545	−	9.50000i	0.664590	−	0.383701i	0.794024	+	0.607887i	$0.207983\pi$
$614$		0			0
$615$	9.00000	+	18.0000i	0.362915	+	0.725830i
$616$		0			0
$617$		−	30.0000i		−	1.20775i	−0.797077	−	0.603877i	$-0.793622\pi$
$617$		−	30.0000i		−	1.20775i	0.797077	−	0.603877i	$-0.206378\pi$
$618$		0			0
$619$	−7.50000	−	12.9904i	−0.301450	−	0.522127i	0.675014	−	0.737805i	$-0.264137\pi$
$619$	−7.50000	−	12.9904i	−0.301450	−	0.522127i	−0.976465	+	0.215677i	$0.930804\pi$
$620$		0			0
$621$	−1.50000	+	2.59808i	−0.0601929	+	0.104257i
$622$		0			0
$623$	8.66025	+	25.0000i	0.346966	+	1.00160i
$624$		0			0
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$		0			0
$627$	−30.3109	+	17.5000i	−1.21050	+	0.698883i
$628$		0			0
$629$	−10.0000			−0.398726
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$		0			0
$633$	16.4545	−	9.50000i	0.654007	−	0.377591i
$634$		0			0
$635$	−20.0885	−	1.20577i	−0.797186	−	0.0478496i
$636$		0			0
$637$	6.92820	−	1.00000i	0.274505	−	0.0396214i
$638$		0			0
$639$	1.00000	−	1.73205i	0.0395594	−	0.0685189i
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$		0			0
$643$		−	38.0000i		−	1.49857i	−0.662246	−	0.749287i	$-0.730396\pi$
$643$		−	38.0000i		−	1.49857i	0.662246	−	0.749287i	$-0.269604\pi$
$644$		0			0
$645$	−20.0000	+	10.0000i	−0.787499	+	0.393750i
$646$		0			0
$647$	−0.866025	+	0.500000i	−0.0340470	+	0.0196570i	−0.516927	−	0.856030i	$-0.672924\pi$
$647$	−0.866025	+	0.500000i	−0.0340470	+	0.0196570i	0.482880	+	0.875687i	$0.339591\pi$
$648$		0			0
$649$	−10.0000	+	17.3205i	−0.392534	+	0.679889i
$650$		0			0
$651$	−15.0000	+	5.19615i	−0.587896	+	0.203653i
$652$		0			0
$653$	−4.33013	−	2.50000i	−0.169451	−	0.0978326i	0.412876	−	0.910787i	$-0.364524\pi$
$653$	−4.33013	−	2.50000i	−0.169451	−	0.0978326i	−0.582327	+	0.812955i	$0.697858\pi$
$654$		0			0
$655$	−31.7224	−	20.9449i	−1.23950	−	0.818384i
$656$		0			0
$657$		−	4.00000i		−	0.156055i
$658$		0			0
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−20.0000	−	34.6410i	−0.777910	−	1.34738i	−0.933144	−	0.359502i	$-0.882947\pi$
$661$	−20.0000	−	34.6410i	−0.777910	−	1.34738i	0.155235	−	0.987878i	$-0.450387\pi$
$662$		0			0
$663$	−1.73205	−	1.00000i	−0.0672673	−	0.0388368i
$664$		0			0
$665$	39.8731	−	11.1865i	1.54621	−	0.433795i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$		0			0
$671$	−10.0000			−0.386046
$672$		0			0
$673$			36.0000i			1.38770i	0.720121	+	0.693849i	$0.244086\pi$
$673$			36.0000i			1.38770i	−0.720121	+	0.693849i	$0.755914\pi$
$674$		0			0
$675$	0.598076	−	4.96410i	0.0230200	−	0.191068i
$676$		0			0
$677$	28.5788	+	16.5000i	1.09837	+	0.634147i	0.935793	−	0.352549i	$-0.114685\pi$
$677$	28.5788	+	16.5000i	1.09837	+	0.634147i	0.162581	+	0.986695i	$0.448018\pi$
$678$		0			0
$679$	16.0000	+	13.8564i	0.614024	+	0.531760i
$680$		0			0
$681$	−7.00000	+	12.1244i	−0.268241	+	0.464606i
$682$		0			0
$683$	3.46410	−	2.00000i	0.132550	−	0.0765279i	−0.432259	−	0.901750i	$-0.642283\pi$
$683$	3.46410	−	2.00000i	0.132550	−	0.0765279i	0.564809	+	0.825222i	$0.308950\pi$
$684$		0			0
$685$	4.00000	+	8.00000i	0.152832	+	0.305664i
$686$		0			0
$687$		−	4.00000i		−	0.152610i
$688$		0			0
$689$	−0.500000	−	0.866025i	−0.0190485	−	0.0329929i
$690$		0			0
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$		0			0
$693$	8.66025	−	10.0000i	0.328976	−	0.379869i
$694$		0			0
$695$	1.07180	−	17.8564i	0.0406556	−	0.677332i
$696$		0			0
$697$	−15.5885	+	9.00000i	−0.590455	+	0.340899i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	30.3109	−	17.5000i	1.14320	−	0.660025i
$704$		0			0
$705$	1.74167	−	29.0167i	0.0655951	−	1.09283i
$706$		0			0
$707$	20.7846	+	4.00000i	0.781686	+	0.150435i
$708$		0			0
$709$	8.00000	−	13.8564i	0.300446	−	0.520388i	−0.675791	−	0.737093i	$-0.736198\pi$
$709$	8.00000	−	13.8564i	0.300446	−	0.520388i	0.976237	+	0.216705i	$0.0695310\pi$
$710$		0			0
$711$	−7.00000	−	12.1244i	−0.262521	−	0.454699i
$712$		0			0
$713$		−	18.0000i		−	0.674105i
$714$		0			0
$715$	5.00000	+	10.0000i	0.186989	+	0.373979i
$716$		0			0
$717$	−17.3205	+	10.0000i	−0.646846	+	0.373457i
$718$		0			0
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	−0.846776	−	0.531949i	$-0.821460\pi$
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	0.884070	+	0.467355i	$0.154793\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−0.866025	−	0.500000i	−0.0322078	−	0.0185952i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			53.0000i			1.96566i	0.184510	+	0.982831i	$0.440930\pi$
$727$			53.0000i			1.96566i	−0.184510	+	0.982831i	$0.559070\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−10.0000	−	17.3205i	−0.369863	−	0.640622i
$732$		0			0
$733$	18.1865	+	10.5000i	0.671735	+	0.387826i	0.796734	−	0.604331i	$-0.206559\pi$
$733$	18.1865	+	10.5000i	0.671735	+	0.387826i	−0.124999	+	0.992157i	$0.539893\pi$
$734$		0			0
$735$	−12.8564	+	8.92820i	−0.474216	+	0.329322i
$736$		0			0
$737$	−25.9808	−	15.0000i	−0.957014	−	0.552532i
$738$		0			0
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	−0.867581	−	0.497296i	$-0.834326\pi$
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	0.00311943	−	0.999995i	$-0.499007\pi$
$740$		0			0
$741$	7.00000			0.257151
$742$		0			0
$743$			31.0000i			1.13728i	0.822587	+	0.568640i	$0.192530\pi$
$743$			31.0000i			1.13728i	−0.822587	+	0.568640i	$0.807470\pi$
$744$		0			0
$745$	−11.1962	−	7.39230i	−0.410195	−	0.270833i
$746$		0			0
$747$	8.66025	+	5.00000i	0.316862	+	0.182940i
$748$		0			0
$749$	30.0000	−	10.3923i	1.09618	−	0.379727i
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$		0			0
$753$	−2.59808	+	1.50000i	−0.0946792	+	0.0546630i
$754$		0			0
$755$	44.0000	−	22.0000i	1.60132	−	0.800662i
$756$		0			0
$757$			26.0000i			0.944986i	0.881334	+	0.472493i	$0.156646\pi$
$757$			26.0000i			0.944986i	−0.881334	+	0.472493i	$0.843354\pi$
$758$		0			0
$759$	7.50000	+	12.9904i	0.272233	+	0.471521i
$760$		0			0
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	−0.837557	−	0.546350i	$-0.816017\pi$
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	0.891932	+	0.452170i	$0.149350\pi$
$762$		0			0
$763$	46.7654	+	9.00000i	1.69302	+	0.325822i
$764$		0			0
$765$	4.46410	+	0.267949i	0.161400	+	0.00968772i
$766$		0			0
$767$	3.46410	−	2.00000i	0.125081	−	0.0722158i
$768$		0			0
$769$	−51.0000			−1.83911			−0.919554	−	0.392965i	$-0.871449\pi$
$769$	−51.0000			−1.83911			−0.919554	+	0.392965i	$0.871449\pi$
$770$		0			0
$771$	10.0000			0.360141
$772$		0			0
$773$	−32.0429	+	18.5000i	−1.15250	+	0.665399i	−0.949496	−	0.313778i	$-0.898405\pi$
$773$	−32.0429	+	18.5000i	−1.15250	+	0.665399i	−0.203008	+	0.979177i	$0.565072\pi$
$774$		0			0
$775$	11.7846	+	27.5885i	0.423316	+	0.991007i
$776$		0			0
$777$	−8.66025	+	10.0000i	−0.310685	+	0.358748i
$778$		0			0
$779$	31.5000	−	54.5596i	1.12860	−	1.95480i
$780$		0			0
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−13.0000	−	26.0000i	−0.463990	−	0.927980i
$786$		0			0
$787$	32.9090	−	19.0000i	1.17308	−	0.677277i	0.218675	−	0.975798i	$-0.429827\pi$
$787$	32.9090	−	19.0000i	1.17308	−	0.677277i	0.954403	+	0.298521i	$0.0964933\pi$
$788$		0			0
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$		0			0
$791$	−12.0000	−	10.3923i	−0.426671	−	0.369508i
$792$		0			0
$793$	1.73205	+	1.00000i	0.0615069	+	0.0355110i
$794$		0			0
$795$	1.86603	+	1.23205i	0.0661811	+	0.0436963i
$796$		0			0
$797$			30.0000i			1.06265i	0.847167	+	0.531327i	$0.178307\pi$
$797$			30.0000i			1.06265i	−0.847167	+	0.531327i	$0.821693\pi$
$798$		0			0
$799$	26.0000			0.919814
$800$		0			0
$801$	−5.00000	−	8.66025i	−0.176666	−	0.305995i
$802$		0			0
$803$	−17.3205	−	10.0000i	−0.611227	−	0.352892i
$804$		0			0
$805$	−4.79423	−	17.0885i	−0.168974	−	0.602289i
$806$		0			0
$807$	−12.1244	−	7.00000i	−0.426798	−	0.246412i
$808$		0			0
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	0.776012	−	0.630718i	$-0.217239\pi$
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	−0.934224	+	0.356687i	$0.883906\pi$
$810$		0			0
$811$	−11.0000			−0.386262			−0.193131	−	0.981173i	$-0.561864\pi$
$811$	−11.0000			−0.386262			−0.193131	+	0.981173i	$0.561864\pi$
$812$		0			0
$813$			8.00000i			0.280572i
$814$		0			0
$815$	14.7846	−	22.3923i	0.517882	−	0.784368i
$816$		0			0
$817$	60.6218	+	35.0000i	2.12089	+	1.22449i
$818$		0			0
$819$	−2.50000	+	0.866025i	−0.0873571	+	0.0302614i
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$		0			0
$823$	6.92820	−	4.00000i	0.241502	−	0.139431i	−0.374365	−	0.927281i	$-0.622139\pi$
$823$	6.92820	−	4.00000i	0.241502	−	0.139431i	0.615867	+	0.787850i	$0.288806\pi$
$824$		0			0
$825$	−20.0000	−	15.0000i	−0.696311	−	0.522233i
$826$		0			0
$827$		−	42.0000i		−	1.46048i	−0.683189	−	0.730242i	$-0.739408\pi$
$827$		−	42.0000i		−	1.46048i	0.683189	−	0.730242i	$-0.260592\pi$
$828$		0			0
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$		0			0
$831$	1.00000	−	1.73205i	0.0346896	−	0.0600842i
$832$		0			0
$833$	−8.66025	−	11.0000i	−0.300060	−	0.381127i
$834$		0			0
$835$	42.4090	+	2.54552i	1.46762	+	0.0880913i
$836$		0			0
$837$	5.19615	−	3.00000i	0.179605	−	0.103695i
$838$		0			0
$839$	2.00000			0.0690477			0.0345238	−	0.999404i	$-0.489009\pi$
$839$	2.00000			0.0690477			0.0345238	+	0.999404i	$0.489009\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		0			0
$843$	9.52628	−	5.50000i	0.328102	−	0.189430i
$844$		0			0
$845$	−1.60770	+	26.7846i	−0.0553064	+	0.921419i
$846$		0			0
$847$	−12.1244	−	35.0000i	−0.416598	−	1.20261i
$848$		0			0
$849$	13.0000	−	22.5167i	0.446159	−	0.772770i
$850$		0			0
$851$	−7.50000	−	12.9904i	−0.257097	−	0.445305i
$852$		0			0
$853$		−	49.0000i		−	1.67773i	−0.544341	−	0.838864i	$-0.683220\pi$
$853$		−	49.0000i		−	1.67773i	0.544341	−	0.838864i	$-0.316780\pi$
$854$		0			0
$855$	−14.0000	+	7.00000i	−0.478790	+	0.239395i
$856$		0			0
$857$	48.4974	−	28.0000i	1.65664	−	0.956462i	0.682391	−	0.730987i	$-0.260940\pi$
$857$	48.4974	−	28.0000i	1.65664	−	0.956462i	0.974249	−	0.225475i	$-0.0723933\pi$
$858$		0			0
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	0.376381	+	0.926465i	$0.377169\pi$
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	−0.990533	+	0.137277i	$0.956165\pi$
$860$		0			0
$861$	−4.50000	+	23.3827i	−0.153360	+	0.796880i
$862$		0			0
$863$	12.9904	+	7.50000i	0.442198	+	0.255303i	0.704529	−	0.709675i	$-0.251158\pi$
$863$	12.9904	+	7.50000i	0.442198	+	0.255303i	−0.262332	+	0.964978i	$0.584491\pi$
$864$		0			0
$865$	8.62436	−	13.0622i	0.293237	−	0.444127i
$866$		0			0
$867$		−	13.0000i		−	0.441503i
$868$		0			0
$869$	−70.0000			−2.37459
$870$		0			0
$871$	3.00000	+	5.19615i	0.101651	+	0.176065i
$872$		0			0
$873$	−6.92820	−	4.00000i	−0.234484	−	0.135379i
$874$		0			0
$875$	18.5359	+	23.0526i	0.626628	+	0.779319i
$876$		0			0
$877$	−23.3827	−	13.5000i	−0.789577	−	0.455863i	0.0502365	−	0.998737i	$-0.484002\pi$
$877$	−23.3827	−	13.5000i	−0.789577	−	0.455863i	−0.839814	+	0.542875i	$0.817336\pi$
$878$		0			0
$879$	−0.500000	−	0.866025i	−0.0168646	−	0.0292103i
$880$		0			0
$881$	−3.00000			−0.101073			−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000			−0.101073			−0.0505363	+	0.998722i	$0.516093\pi$
$882$		0			0
$883$			52.0000i			1.74994i	0.484178	+	0.874970i	$0.339119\pi$
$883$			52.0000i			1.74994i	−0.484178	+	0.874970i	$0.660881\pi$
$884$		0			0
$885$	−4.92820	+	7.46410i	−0.165660	+	0.250903i
$886$		0			0
$887$	10.3923	+	6.00000i	0.348939	+	0.201460i	0.664218	−	0.747539i	$-0.268765\pi$
$887$	10.3923	+	6.00000i	0.348939	+	0.201460i	−0.315279	+	0.948999i	$0.602098\pi$
$888$		0			0
$889$	−18.0000	−	15.5885i	−0.603701	−	0.522820i
$890$		0			0
$891$	−2.50000	+	4.33013i	−0.0837532	+	0.145065i
$892$		0			0
$893$	−78.8083	+	45.5000i	−2.63722	+	1.52260i
$894$		0			0
$895$	−22.0000	+	11.0000i	−0.735379	+	0.367689i
$896$		0			0
$897$		−	3.00000i		−	0.100167i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−1.00000	+	1.73205i	−0.0333148	+	0.0577030i
$902$		0			0
$903$	−25.9808	−	5.00000i	−0.864586	−	0.166390i
$904$		0			0
$905$	0.267949	−	4.46410i	0.00890693	−	0.148392i
$906$		0			0
$907$	−13.8564	+	8.00000i	−0.460094	+	0.265636i	−0.712084	−	0.702094i	$-0.752248\pi$
$907$	−13.8564	+	8.00000i	−0.460094	+	0.265636i	0.251990	+	0.967730i	$0.418915\pi$
$908$		0			0
$909$	−8.00000			−0.265343
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$		0			0
$913$	43.3013	−	25.0000i	1.43306	−	0.827379i
$914$		0			0
$915$	−4.46410	−	0.267949i	−0.147579	−	0.00885813i
$916$		0			0
$917$	−14.7224	−	42.5000i	−0.486178	−	1.40347i
$918$		0			0
$919$	−28.0000	+	48.4974i	−0.923635	+	1.59978i	−0.129893	+	0.991528i	$0.541463\pi$
$919$	−28.0000	+	48.4974i	−0.923635	+	1.59978i	−0.793742	+	0.608254i	$0.791870\pi$
$920$		0			0
$921$	−1.00000	−	1.73205i	−0.0329511	−	0.0570730i
$922$		0			0
$923$			2.00000i			0.0658308i
$924$		0			0
$925$	20.0000	+	15.0000i	0.657596	+	0.493197i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	16.5000	−	28.5788i	0.541347	−	0.937641i	−0.457480	−	0.889220i	$-0.651248\pi$
$929$	16.5000	−	28.5788i	0.541347	−	0.937641i	0.998827	−	0.0484211i	$-0.0154190\pi$
$930$		0			0
$931$	45.5000	+	18.1865i	1.49120	+	0.596040i
$932$		0			0
$933$	22.5167	+	13.0000i	0.737162	+	0.425601i
$934$		0			0
$935$	12.3205	−	18.6603i	0.402924	−	0.610256i
$936$		0			0
$937$			34.0000i			1.11073i	0.831606	+	0.555366i	$0.187422\pi$
$937$			34.0000i			1.11073i	−0.831606	+	0.555366i	$0.812578\pi$
$938$		0			0
$939$	−10.0000			−0.326338
$940$		0			0
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$		0			0
$943$	−23.3827	−	13.5000i	−0.761445	−	0.439620i
$944$		0			0
$945$	4.13397	−	4.23205i	0.134478	−	0.137669i
$946$		0			0
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	0.321552	−	0.946892i	$-0.395796\pi$
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	−0.659256	+	0.751918i	$0.729129\pi$
$948$		0			0
$949$	2.00000	+	3.46410i	0.0649227	+	0.112449i
$950$		0			0
$951$	−2.00000			−0.0648544
$952$		0			0
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$		0			0
$955$	−29.8564	−	19.7128i	−0.966131	−	0.637892i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.00000	+	10.3923i	−0.0645834	+	0.335585i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$	−10.3923	+	6.00000i	−0.334887	+	0.193347i
$964$		0			0
$965$	−18.0000	−	36.0000i	−0.579441	−	1.15888i
$966$		0			0
$967$		−	24.0000i		−	0.771788i	−0.922543	−	0.385894i	$-0.873893\pi$
$967$		−	24.0000i		−	0.771788i	0.922543	−	0.385894i	$-0.126107\pi$
$968$		0			0
$969$	−7.00000	−	12.1244i	−0.224872	−	0.389490i
$970$		0			0
$971$	19.5000	−	33.7750i	0.625785	−	1.08389i	−0.362604	−	0.931943i	$-0.618112\pi$
$971$	19.5000	−	33.7750i	0.625785	−	1.08389i	0.988389	−	0.151948i	$-0.0485545\pi$
$972$		0			0
$973$	13.8564	−	16.0000i	0.444216	−	0.512936i
$974$		0			0
$975$	1.96410	+	4.59808i	0.0629016	+	0.147256i
$976$		0			0
$977$	−36.3731	+	21.0000i	−1.16368	+	0.671850i	−0.952183	−	0.305530i	$-0.901167\pi$
$977$	−36.3731	+	21.0000i	−1.16368	+	0.671850i	−0.211495	+	0.977379i	$0.567833\pi$
$978$		0			0
$979$	−50.0000			−1.59801
$980$		0			0
$981$	−18.0000			−0.574696
$982$		0			0
$983$	−28.5788	+	16.5000i	−0.911523	+	0.526268i	−0.880921	−	0.473263i	$-0.843076\pi$
$983$	−28.5788	+	16.5000i	−0.911523	+	0.526268i	−0.0306024	+	0.999532i	$0.509743\pi$
$984$		0			0
$985$	−60.2654	−	3.61731i	−1.92021	−	0.115257i
$986$		0			0
$987$	22.5167	−	26.0000i	0.716713	−	0.827589i
$988$		0			0
$989$	15.0000	−	25.9808i	0.476972	−	0.826140i
$990$		0			0
$991$	−18.0000	−	31.1769i	−0.571789	−	0.990367i	−0.996382	−	0.0849833i	$-0.972916\pi$
$991$	−18.0000	−	31.1769i	−0.571789	−	0.990367i	0.424594	−	0.905384i	$-0.360417\pi$
$992$		0			0
$993$		−	15.0000i		−	0.476011i
$994$		0			0
$995$	−28.0000	+	14.0000i	−0.887660	+	0.443830i
$996$		0			0
$997$	8.66025	−	5.00000i	0.274273	−	0.158352i	−0.356555	−	0.934274i	$-0.616049\pi$
$997$	8.66025	−	5.00000i	0.274273	−	0.158352i	0.630828	+	0.775923i	$0.282715\pi$
$998$		0			0
$999$	2.50000	−	4.33013i	0.0790965	−	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.di.a.289.1		4
4.3	odd	2		210.2.n.a.79.1	✓	4
5.4	even	2	inner	1680.2.di.a.289.2		4
7.4	even	3	inner	1680.2.di.a.529.2		4
12.11	even	2		630.2.u.c.289.2		4
20.3	even	4		1050.2.i.f.751.1		2
20.7	even	4		1050.2.i.o.751.1		2
20.19	odd	2		210.2.n.a.79.2	yes	4
28.3	even	6		1470.2.n.i.949.2		4
28.11	odd	6		210.2.n.a.109.2	yes	4
28.19	even	6		1470.2.g.a.589.2		2
28.23	odd	6		1470.2.g.f.589.2		2
28.27	even	2		1470.2.n.i.79.1		4
35.4	even	6	inner	1680.2.di.a.529.1		4
60.59	even	2		630.2.u.c.289.1		4
84.11	even	6		630.2.u.c.109.1		4
140.19	even	6		1470.2.g.a.589.1		2
140.23	even	12		7350.2.a.bn.1.1		1
140.39	odd	6		210.2.n.a.109.1	yes	4
140.47	odd	12		7350.2.a.b.1.1		1
140.59	even	6		1470.2.n.i.949.1		4
140.67	even	12		1050.2.i.o.151.1		2
140.79	odd	6		1470.2.g.f.589.1		2
140.103	odd	12		7350.2.a.ch.1.1		1
140.107	even	12		7350.2.a.t.1.1		1
140.123	even	12		1050.2.i.f.151.1		2
140.139	even	2		1470.2.n.i.79.2		4
420.179	even	6		630.2.u.c.109.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.a.79.1	✓	4	4.3	odd	2
210.2.n.a.79.2	yes	4	20.19	odd	2
210.2.n.a.109.1	yes	4	140.39	odd	6
210.2.n.a.109.2	yes	4	28.11	odd	6
630.2.u.c.109.1		4	84.11	even	6
630.2.u.c.109.2		4	420.179	even	6
630.2.u.c.289.1		4	60.59	even	2
630.2.u.c.289.2		4	12.11	even	2
1050.2.i.f.151.1		2	140.123	even	12
1050.2.i.f.751.1		2	20.3	even	4
1050.2.i.o.151.1		2	140.67	even	12
1050.2.i.o.751.1		2	20.7	even	4
1470.2.g.a.589.1		2	140.19	even	6
1470.2.g.a.589.2		2	28.19	even	6
1470.2.g.f.589.1		2	140.79	odd	6
1470.2.g.f.589.2		2	28.23	odd	6
1470.2.n.i.79.1		4	28.27	even	2
1470.2.n.i.79.2		4	140.139	even	2
1470.2.n.i.949.1		4	140.59	even	6
1470.2.n.i.949.2		4	28.3	even	6
1680.2.di.a.289.1		4	1.1	even	1	trivial
1680.2.di.a.289.2		4	5.4	even	2	inner
1680.2.di.a.529.1		4	35.4	even	6	inner
1680.2.di.a.529.2		4	7.4	even	3	inner
7350.2.a.b.1.1		1	140.47	odd	12
7350.2.a.t.1.1		1	140.107	even	12
7350.2.a.bn.1.1		1	140.23	even	12
7350.2.a.ch.1.1		1	140.103	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.di (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-0.133975 + 2.23205i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-0.133975 + 2.23205i) q^{5} +(-1.73205 + 2.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.50000 - 4.33013i) q^{11} +1.00000i q^{13} +(-1.00000 - 2.00000i) q^{15} +(1.73205 - 1.00000i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(0.500000 - 2.59808i) q^{21} +(2.59808 + 1.50000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +1.00000i q^{27} +(-3.00000 - 5.19615i) q^{31} +(4.33013 + 2.50000i) q^{33} +(-4.23205 - 4.13397i) q^{35} +(-4.33013 - 2.50000i) q^{37} +(-0.500000 - 0.866025i) q^{39} -9.00000 q^{41} -10.0000i q^{43} +(1.86603 + 1.23205i) q^{45} +(11.2583 + 6.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-0.866025 + 0.500000i) q^{53} +(10.0000 - 5.00000i) q^{55} -7.00000i q^{57} +(-2.00000 - 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +(0.866025 + 2.50000i) q^{63} +(-2.23205 - 0.133975i) q^{65} +(5.19615 - 3.00000i) q^{67} -3.00000 q^{69} +2.00000 q^{71} +(3.46410 - 2.00000i) q^{73} +(4.59808 - 1.96410i) q^{75} +(12.9904 + 2.50000i) q^{77} +(7.00000 - 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(5.00000 - 8.66025i) q^{89} +(-2.00000 - 1.73205i) q^{91} +(5.19615 + 3.00000i) q^{93} +(-13.0622 - 8.62436i) q^{95} -8.00000i q^{97} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^5 + 2 * q^9	\( 4 q - 4 q^{5} + 2 q^{9} - 10 q^{11} - 4 q^{15} - 14 q^{19} + 2 q^{21} - 6 q^{25} - 12 q^{31} - 10 q^{35} - 2 q^{39} - 36 q^{41} + 4 q^{45} - 4 q^{49} - 4 q^{51} + 40 q^{55} - 8 q^{59} + 4 q^{61} - 2 q^{65} - 12 q^{69} + 8 q^{71} + 8 q^{75} + 28 q^{79} - 2 q^{81} + 8 q^{85} + 20 q^{89} - 8 q^{91} - 28 q^{95} - 20 q^{99}+O(q^{100}) \) 4 * q - 4 * q^5 + 2 * q^9 - 10 * q^11 - 4 * q^15 - 14 * q^19 + 2 * q^21 - 6 * q^25 - 12 * q^31 - 10 * q^35 - 2 * q^39 - 36 * q^41 + 4 * q^45 - 4 * q^49 - 4 * q^51 + 40 * q^55 - 8 * q^59 + 4 * q^61 - 2 * q^65 - 12 * q^69 + 8 * q^71 + 8 * q^75 + 28 * q^79 - 2 * q^81 + 8 * q^85 + 20 * q^89 - 8 * q^91 - 28 * q^95 - 20 * q^99

Introduction

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