LMFDB - Embedded newform 1680.2.di.a.529.2

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			529.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1680.529
Dual form			1680.2.di.a.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{3} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-2.50000 + 4.33013i) q^{11} +1.00000i q^{13} +(-1.00000 - 2.00000i) q^{15} +(-1.73205 - 1.00000i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-2.59808 + 1.50000i) q^{23} +(1.96410 + 4.59808i) q^{25} +1.00000i q^{27} +(-3.00000 + 5.19615i) q^{31} +(-4.33013 + 2.50000i) q^{33} +(-0.767949 - 5.86603i) q^{35} +(4.33013 - 2.50000i) q^{37} +(-0.500000 + 0.866025i) q^{39} -9.00000 q^{41} -10.0000i q^{43} +(0.133975 - 2.23205i) q^{45} +(-11.2583 + 6.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(0.866025 + 0.500000i) q^{53} +(10.0000 - 5.00000i) q^{55} -7.00000i q^{57} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-0.866025 + 2.50000i) q^{63} +(1.23205 - 1.86603i) q^{65} +(-5.19615 - 3.00000i) q^{67} -3.00000 q^{69} +2.00000 q^{71} +(-3.46410 - 2.00000i) q^{73} +(-0.598076 + 4.96410i) q^{75} +(-12.9904 + 2.50000i) q^{77} +(7.00000 + 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{81} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(5.00000 + 8.66025i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(-5.19615 + 3.00000i) q^{93} +(-0.937822 + 15.6244i) q^{95} -8.00000i q^{97} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$	$1$

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
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$6$		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	0.192201	+	0.981356i	$0.438437\pi$
$11$	−2.50000	+	4.33013i	−0.753778	+	1.30558i	−0.945979	+	0.324227i	$0.894896\pi$
$12$		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	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$		0			0
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$		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	$-0.767924\pi$
$23$	−2.59808	+	1.50000i	−0.541736	+	0.312772i	0.204046	+	0.978961i	$0.434591\pi$
$24$		0			0
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$		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	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$		0			0
$33$	−4.33013	+	2.50000i	−0.753778	+	0.435194i
$34$		0			0
$35$	−0.767949	−	5.86603i	−0.129807	−	0.991539i
$36$		0			0
$37$	4.33013	−	2.50000i	0.711868	−	0.410997i	−0.0998840	−	0.994999i	$-0.531847\pi$
$37$	4.33013	−	2.50000i	0.711868	−	0.410997i	0.811752	+	0.584002i	$0.198514\pi$
$38$		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
$45$	0.133975	−	2.23205i	0.0199718	−	0.332734i
$46$		0			0
$47$	−11.2583	+	6.50000i	−1.64220	+	0.948122i	−0.662145	+	0.749375i	$0.730354\pi$
$47$	−11.2583	+	6.50000i	−1.64220	+	0.948122i	−0.980051	+	0.198747i	$0.936313\pi$
$48$		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	$-0.311454\pi$
$53$	0.866025	+	0.500000i	0.118958	+	0.0686803i	−0.439340	+	0.898321i	$0.644788\pi$
$54$		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	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$		0			0
$63$	−0.866025	+	2.50000i	−0.109109	+	0.314970i
$64$		0			0
$65$	1.23205	−	1.86603i	0.152817	−	0.231452i
$66$		0			0
$67$	−5.19615	−	3.00000i	−0.634811	−	0.366508i	0.147802	−	0.989017i	$-0.452780\pi$
$67$	−5.19615	−	3.00000i	−0.634811	−	0.366508i	−0.782613	+	0.622509i	$0.786114\pi$
$68$		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	$-0.408542\pi$
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	−0.688830	+	0.724923i	$0.741875\pi$
$74$		0			0
$75$	−0.598076	+	4.96410i	−0.0690599	+	0.573205i
$76$		0			0
$77$	−12.9904	+	2.50000i	−1.48039	+	0.284901i
$78$		0			0
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	0.927457	+	0.373930i	$0.121990\pi$
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	−0.139895	+	0.990166i	$0.544677\pi$
$80$		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	0.999388	+	0.0349934i	$0.0111410\pi$
$89$	5.00000	+	8.66025i	0.529999	+	0.917985i	−0.469389	+	0.882992i	$0.655526\pi$
$90$		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
$95$	−0.937822	+	15.6244i	−0.0962185	+	1.60303i
$96$		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	−0.993481	−	0.113998i	$-0.963634\pi$
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	0.595466	+	0.803380i	$0.296967\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$	2.26795	−	5.46410i	0.221329	−	0.533242i
$106$		0			0
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.0950377	−	0.995474i	$-0.469703\pi$
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.909624	+	0.415432i	$0.136370\pi$
$108$		0			0
$109$	−9.00000	+	15.5885i	−0.862044	+	1.49310i	0.00790932	+	0.999969i	$0.497482\pi$
$109$	−9.00000	+	15.5885i	−0.862044	+	1.49310i	−0.869953	+	0.493135i	$0.835851\pi$
$110$		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
$115$	6.69615	+	0.401924i	0.624419	+	0.0374796i
$116$		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	−0.951285	−	0.308312i	$-0.900236\pi$
$131$	−8.50000	−	14.7224i	−0.742648	−	1.28630i	0.208637	−	0.977993i	$-0.433097\pi$
$132$		0			0
$133$	6.06218	−	17.5000i	0.525657	−	1.51744i
$134$		0			0
$135$	1.23205	−	1.86603i	0.106038	−	0.160602i
$136$		0			0
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	0.344668	−	0.938725i	$-0.387992\pi$
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	−0.640626	+	0.767853i	$0.721325\pi$
$138$		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	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	−11.0000	+	19.0526i	−0.895167	+	1.55048i	−0.0615699	+	0.998103i	$0.519611\pi$
$151$	−11.0000	+	19.0526i	−0.895167	+	1.55048i	−0.833597	+	0.552372i	$0.813723\pi$
$152$		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	$-0.159728\pi$
$157$	11.2583	+	6.50000i	0.898513	+	0.518756i	0.0217953	+	0.999762i	$0.493062\pi$
$158$		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	$-0.510936\pi$
$163$	10.3923	−	6.00000i	0.813988	−	0.469956i	0.848339	+	0.529454i	$0.177603\pi$
$164$		0			0
$165$	11.1603	+	0.669873i	0.868825	+	0.0521495i
$166$		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	$-0.580932\pi$
$173$	6.06218	−	3.50000i	0.460899	−	0.266100i	0.712422	+	0.701751i	$0.247598\pi$
$174$		0			0
$175$	−5.79423	+	11.8923i	−0.438003	+	0.898974i
$176$		0			0
$177$	−3.46410	+	2.00000i	−0.260378	+	0.150329i
$178$		0			0
$179$	5.50000	−	9.52628i	0.411089	−	0.712028i	−0.583920	−	0.811811i	$-0.698482\pi$
$179$	5.50000	−	9.52628i	0.411089	−	0.712028i	0.995009	+	0.0997838i	$0.0318151\pi$
$180$		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
$185$	−11.1603	−	0.669873i	−0.820518	−	0.0492500i
$186$		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	−0.995610	−	0.0935936i	$-0.970165\pi$
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	0.416751	−	0.909021i	$-0.363169\pi$
$192$		0			0
$193$	15.5885	+	9.00000i	1.12208	+	0.647834i	0.941932	−	0.335805i	$-0.109008\pi$
$193$	15.5885	+	9.00000i	1.12208	+	0.647834i	0.180150	+	0.983639i	$0.442342\pi$
$194$		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	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$		0			0
$201$	−3.00000	−	5.19615i	−0.211604	−	0.366508i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	16.7942	+	11.0885i	1.17296	+	0.774451i
$206$		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
$215$	−12.3205	+	18.6603i	−0.840252	+	1.27262i
$216$		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	$-0.487137\pi$
$227$	−12.1244	−	7.00000i	−0.804722	−	0.464606i	−0.845120	+	0.534577i	$0.820471\pi$
$228$		0			0
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	0.792347	−	0.610071i	$-0.208859\pi$
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	−0.924510	+	0.381157i	$0.875526\pi$
$230$		0			0
$231$	−12.5000	−	4.33013i	−0.822440	−	0.284901i
$232$		0			0
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$		0			0
$235$	29.0167	+	1.74167i	1.89284	+	0.113614i
$236$		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	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	10.4019	−	11.6962i	0.664555	−	0.747240i
$246$		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
$255$	−0.267949	+	4.46410i	−0.0167796	+	0.279553i
$256$		0			0
$257$	8.66025	−	5.00000i	0.540212	−	0.311891i	−0.204953	−	0.978772i	$-0.565704\pi$
$257$	8.66025	−	5.00000i	0.540212	−	0.311891i	0.745165	+	0.666880i	$0.232371\pi$
$258$		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	$-0.0681817\pi$
$263$	20.7846	+	12.0000i	1.28163	+	0.739952i	0.304487	+	0.952517i	$0.401515\pi$
$264$		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	−0.569789	−	0.821791i	$-0.692975\pi$
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	0.996586	+	0.0825561i	$0.0263084\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$		0			0
$273$	−2.59808	+	0.500000i	−0.157243	+	0.0302614i
$274$		0			0
$275$	−24.8205	−	2.99038i	−1.49673	−	0.180327i
$276$		0			0
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	0.551131	−	0.834419i	$-0.314196\pi$
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	−0.447062	+	0.894503i	$0.647530\pi$
$278$		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	$-0.0522041\pi$
$283$	22.5167	+	13.0000i	1.33848	+	0.772770i	0.351895	+	0.936039i	$0.385537\pi$
$284$		0			0
$285$	−8.62436	+	13.0622i	−0.510863	+	0.773737i
$286$		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
$305$	0.267949	−	4.46410i	0.0153427	−	0.255614i
$306$		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	0.216606	+	0.976259i	$0.430501\pi$
$311$	−13.0000	+	22.5167i	−0.737162	+	1.27680i	−0.953768	+	0.300544i	$0.902832\pi$
$312$		0			0
$313$	−8.66025	+	5.00000i	−0.489506	+	0.282617i	−0.724370	−	0.689412i	$-0.757869\pi$
$313$	−8.66025	+	5.00000i	−0.489506	+	0.282617i	0.234863	+	0.972028i	$0.424536\pi$
$314$		0			0
$315$	4.69615	−	3.59808i	0.264598	−	0.202729i
$316$		0			0
$317$	−1.73205	+	1.00000i	−0.0972817	+	0.0561656i	−0.547852	−	0.836576i	$-0.684554\pi$
$317$	−1.73205	+	1.00000i	−0.0972817	+	0.0561656i	0.450570	+	0.892741i	$0.351221\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$			14.0000i			0.778981i
$324$		0			0
$325$	−4.59808	+	1.96410i	−0.255055	+	0.108949i
$326$		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	0.582897	−	0.812546i	$-0.301919\pi$
$331$	−7.50000	−	12.9904i	−0.412237	−	0.714016i	−0.995134	+	0.0985303i	$0.968586\pi$
$332$		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
$345$	5.59808	+	3.69615i	0.301390	+	0.198994i
$346$		0			0
$347$	13.8564	+	8.00000i	0.743851	+	0.429463i	0.823468	−	0.567363i	$-0.192036\pi$
$347$	13.8564	+	8.00000i	0.743851	+	0.429463i	−0.0796169	+	0.996826i	$0.525370\pi$
$348$		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	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$	−3.73205	−	2.46410i	−0.198077	−	0.130781i
$356$		0			0
$357$	1.73205	−	5.00000i	0.0916698	−	0.264628i
$358$		0			0
$359$	14.0000	+	24.2487i	0.738892	+	1.27980i	0.952995	+	0.302987i	$0.0979839\pi$
$359$	14.0000	+	24.2487i	0.738892	+	1.27980i	−0.214103	+	0.976811i	$0.568683\pi$
$360$		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	0.966159	+	0.257948i	$0.0830464\pi$
$367$	32.0429	+	18.5000i	1.67263	+	0.965692i	0.706469	+	0.707744i	$0.250287\pi$
$368$		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	$-0.617021\pi$
$373$	5.19615	−	3.00000i	0.269047	−	0.155334i	0.628454	+	0.777847i	$0.283688\pi$
$374$		0			0
$375$	7.23205	−	8.52628i	0.373461	−	0.440295i
$376$		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	$-0.592814\pi$
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	0.685736	+	0.727851i	$0.259481\pi$
$384$		0			0
$385$	27.3205	+	11.3397i	1.39238	+	0.577927i
$386$		0			0
$387$	8.66025	−	5.00000i	0.440225	−	0.254164i
$388$		0			0
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$		0			0
$393$		−	17.0000i		−	0.857537i
$394$		0			0
$395$	1.87564	−	31.2487i	0.0943739	−	1.57229i
$396$		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
$399$	14.0000	−	12.1244i	0.700877	−	0.606977i
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$		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	−0.715523	−	0.698589i	$-0.753812\pi$
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	0.962757	+	0.270367i	$0.0871450\pi$
$410$		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
$415$	12.3205	−	18.6603i	0.604790	−	0.915996i
$416$		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
$425$	1.19615	−	9.92820i	0.0580219	−	0.481589i
$426$		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	−0.563658	−	0.826008i	$-0.690607\pi$
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	0.997173	+	0.0751385i	$0.0239399\pi$
$432$		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	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		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	$-0.621142\pi$
$443$	5.19615	−	3.00000i	0.246877	−	0.142534i	0.618333	+	0.785916i	$0.287808\pi$
$444$		0			0
$445$	1.33975	−	22.3205i	0.0635100	−	1.05809i
$446$		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
$455$	5.86603	−	0.767949i	0.275004	−	0.0360020i
$456$		0			0
$457$	32.9090	−	19.0000i	1.53942	−	0.888783i	0.540544	−	0.841316i	$-0.318219\pi$
$457$	32.9090	−	19.0000i	1.53942	−	0.888783i	0.998873	−	0.0474665i	$-0.0151147\pi$
$458$		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
$465$	13.3923	+	0.803848i	0.621053	+	0.0372775i
$466$		0			0
$467$	1.73205	−	1.00000i	0.0801498	−	0.0462745i	−0.459390	−	0.888235i	$-0.651932\pi$
$467$	1.73205	−	1.00000i	0.0801498	−	0.0462745i	0.539539	+	0.841960i	$0.318598\pi$
$468$		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	−0.942821	−	0.333300i	$-0.891838\pi$
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	0.760056	+	0.649857i	$0.225171\pi$
$480$		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
$485$	−9.85641	+	14.9282i	−0.447556	+	0.677855i
$486$		0			0
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.0513038	−	0.998683i	$-0.516338\pi$
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.890537	+	0.454911i	$0.849671\pi$
$488$		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
$495$	9.33013	+	6.16025i	0.419358	+	0.276883i
$496$		0			0
$497$	3.46410	+	4.00000i	0.155386	+	0.179425i
$498$		0			0
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	0.988204	+	0.153141i	$0.0489388\pi$
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	−0.361478	+	0.932381i	$0.617728\pi$
$500$		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	0.978421	−	0.206623i	$-0.0662474\pi$
$509$	7.00000	+	12.1244i	0.310270	+	0.537403i	−0.668151	+	0.744026i	$0.732914\pi$
$510$		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	−0.653650	−	0.756797i	$-0.726763\pi$
$521$	7.50000	−	12.9904i	0.328581	−	0.569119i	0.982231	+	0.187678i	$0.0600963\pi$
$522$		0			0
$523$	−10.3923	+	6.00000i	−0.454424	+	0.262362i	−0.709697	−	0.704507i	$-0.751168\pi$
$523$	−10.3923	+	6.00000i	−0.454424	+	0.262362i	0.255273	+	0.966869i	$0.417835\pi$
$524$		0			0
$525$	−10.9641	+	7.40192i	−0.478513	+	0.323046i
$526$		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
$535$	−26.7846	−	1.60770i	−1.15800	−	0.0695067i
$536$		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	0.819825	−	0.572615i	$-0.194071\pi$
$541$	−2.00000	−	3.46410i	−0.0859867	−	0.148933i	−0.905811	+	0.423681i	$0.860738\pi$
$542$		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
$555$	−9.33013	−	6.16025i	−0.396042	−	0.261488i
$556$		0			0
$557$	−33.7750	−	19.5000i	−1.43109	−	0.826242i	−0.433888	−	0.900967i	$-0.642859\pi$
$557$	−33.7750	−	19.5000i	−1.43109	−	0.826242i	−0.997204	+	0.0747252i	$0.976192\pi$
$558$		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	$-0.115496\pi$
$563$	25.9808	+	15.0000i	1.09496	+	0.632175i	0.160066	+	0.987106i	$0.448829\pi$
$564$		0			0
$565$	7.39230	−	11.1962i	0.310997	−	0.471026i
$566$		0			0
$567$	−2.59808	+	0.500000i	−0.109109	+	0.0209980i
$568$		0			0
$569$	−1.50000	−	2.59808i	−0.0628833	−	0.108917i	0.832870	−	0.553469i	$-0.186696\pi$
$569$	−1.50000	−	2.59808i	−0.0628833	−	0.108917i	−0.895753	+	0.444552i	$0.853363\pi$
$570$		0			0
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	−0.937503	−	0.347977i	$-0.886869\pi$
$571$	−4.00000	+	6.92820i	−0.167395	+	0.289936i	0.770108	+	0.637913i	$0.220202\pi$
$572$		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	$-0.166826\pi$
$577$	20.7846	+	12.0000i	0.865275	+	0.499567i	−0.000500448		1.00000i	$0.500159\pi$
$578$		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
$585$	2.23205	+	0.133975i	0.0922839	+	0.00553917i
$586$		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	$-0.912640\pi$
$593$	−29.4449	+	17.0000i	−1.20916	+	0.698106i	−0.246581	+	0.969122i	$0.579307\pi$
$594$		0			0
$595$	−4.53590	+	10.9282i	−0.185954	+	0.448013i
$596$		0			0
$597$	12.1244	−	7.00000i	0.496217	−	0.286491i
$598$		0			0
$599$	14.0000	−	24.2487i	0.572024	−	0.990775i	−0.424333	−	0.905506i	$-0.639492\pi$
$599$	14.0000	−	24.2487i	0.572024	−	0.990775i	0.996358	−	0.0852695i	$-0.0271751\pi$
$600$		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
$605$	−1.87564	+	31.2487i	−0.0762558	+	1.27044i
$606$		0			0
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	−0.253804	−	0.967256i	$-0.581682\pi$
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	0.710766	+	0.703429i	$0.248349\pi$
$608$		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	$-0.458684\pi$
$613$	−16.4545	−	9.50000i	−0.664590	−	0.383701i	−0.794024	+	0.607887i	$0.792017\pi$
$614$		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	−0.976465	−	0.215677i	$-0.930804\pi$
$619$	−7.50000	+	12.9904i	−0.301450	+	0.522127i	0.675014	+	0.737805i	$0.264137\pi$
$620$		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
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$		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
$635$	11.0885	−	16.7942i	0.440032	−	0.666459i
$636$		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	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$		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	$-0.327076\pi$
$647$	0.866025	+	0.500000i	0.0340470	+	0.0196570i	−0.482880	+	0.875687i	$0.660409\pi$
$648$		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	$-0.635476\pi$
$653$	4.33013	−	2.50000i	0.169451	−	0.0978326i	0.582327	+	0.812955i	$0.302142\pi$
$654$		0			0
$655$	−2.27757	+	37.9449i	−0.0889920	+	1.48263i
$656$		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	0.155235	+	0.987878i	$0.450387\pi$
$661$	−20.0000	+	34.6410i	−0.777910	+	1.34738i	−0.933144	+	0.359502i	$0.882947\pi$
$662$		0			0
$663$	1.73205	−	1.00000i	0.0672673	−	0.0388368i
$664$		0			0
$665$	−32.8731	+	25.1865i	−1.27476	+	0.976692i
$666$		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
$675$	−4.59808	+	1.96410i	−0.176980	+	0.0755983i
$676$		0			0
$677$	−28.5788	+	16.5000i	−1.09837	+	0.634147i	−0.935793	−	0.352549i	$-0.885315\pi$
$677$	−28.5788	+	16.5000i	−1.09837	+	0.634147i	−0.162581	+	0.986695i	$0.551982\pi$
$678$		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	$-0.357717\pi$
$683$	−3.46410	−	2.00000i	−0.132550	−	0.0765279i	−0.564809	+	0.825222i	$0.691050\pi$
$684$		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	0.610704	−	0.791859i	$-0.290887\pi$
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	−0.991122	+	0.132956i	$0.957553\pi$
$692$		0			0
$693$	−8.66025	−	10.0000i	−0.328976	−	0.379869i
$694$		0			0
$695$	14.9282	+	9.85641i	0.566259	+	0.373875i
$696$		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
$705$	24.2583	+	16.0167i	0.913622	+	0.603222i
$706$		0			0
$707$	−20.7846	+	4.00000i	−0.781686	+	0.150435i
$708$		0			0
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	0.976237	−	0.216705i	$-0.0695310\pi$
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	−0.675791	+	0.737093i	$0.736198\pi$
$710$		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	0.884070	−	0.467355i	$-0.154793\pi$
$719$	1.00000	+	1.73205i	0.0372937	+	0.0645946i	−0.846776	+	0.531949i	$0.821460\pi$
$720$		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	$-0.793441\pi$
$733$	−18.1865	+	10.5000i	−0.671735	+	0.387826i	0.124999	+	0.992157i	$0.460107\pi$
$734$		0			0
$735$	14.8564	−	4.92820i	0.547987	−	0.181780i
$736$		0			0
$737$	25.9808	−	15.0000i	0.957014	−	0.552532i
$738$		0			0
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	0.00311943	+	0.999995i	$0.499007\pi$
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	−0.867581	+	0.497296i	$0.834326\pi$
$740$		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
$745$	−0.803848	+	13.3923i	−0.0294507	+	0.490656i
$746$		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	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$		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	0.891932	−	0.452170i	$-0.149350\pi$
$761$	1.50000	+	2.59808i	0.0543750	+	0.0941802i	−0.837557	+	0.546350i	$0.816017\pi$
$762$		0			0
$763$	−46.7654	+	9.00000i	−1.69302	+	0.325822i
$764$		0			0
$765$	−2.46410	+	3.73205i	−0.0890898	+	0.134933i
$766$		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	$-0.101595\pi$
$773$	32.0429	+	18.5000i	1.15250	+	0.665399i	0.203008	+	0.979177i	$0.434928\pi$
$774$		0			0
$775$	−29.7846	−	3.58846i	−1.06989	−	0.128901i
$776$		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	$-0.570173\pi$
$787$	−32.9090	−	19.0000i	−1.17308	−	0.677277i	−0.954403	+	0.298521i	$0.903507\pi$
$788$		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
$795$	0.133975	−	2.23205i	0.00475159	−	0.0791627i
$796$		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
$805$	10.7942	+	14.0885i	0.380447	+	0.496553i
$806$		0			0
$807$	12.1244	−	7.00000i	0.426798	−	0.246412i
$808$		0			0
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$		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
$815$	−26.7846	−	1.60770i	−0.938224	−	0.0563151i
$816$		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	0.808915	−	0.587925i	$-0.200055\pi$
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	−0.913616	+	0.406578i	$0.866722\pi$
$822$		0			0
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	0.374365	−	0.927281i	$-0.377861\pi$
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	−0.615867	+	0.787850i	$0.711194\pi$
$824$		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	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$		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
$835$	−23.4090	+	35.4545i	−0.810101	+	1.22695i
$836$		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
$845$	−22.3923	−	14.7846i	−0.770319	−	0.508606i
$846$		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	−0.974249	−	0.225475i	$-0.927607\pi$
$857$	−48.4974	−	28.0000i	−1.65664	−	0.956462i	−0.682391	−	0.730987i	$-0.739060\pi$
$858$		0			0
$859$	−18.0000	−	31.1769i	−0.614152	−	1.06374i	−0.990533	−	0.137277i	$-0.956165\pi$
$859$	−18.0000	−	31.1769i	−0.614152	−	1.06374i	0.376381	−	0.926465i	$-0.377169\pi$
$860$		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	$-0.748842\pi$
$863$	−12.9904	+	7.50000i	−0.442198	+	0.255303i	0.262332	+	0.964978i	$0.415509\pi$
$864$		0			0
$865$	−15.6244	−	0.937822i	−0.531244	−	0.0318869i
$866$		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
$875$	25.4641	−	15.0526i	0.860844	−	0.508869i
$876$		0			0
$877$	23.3827	−	13.5000i	0.789577	−	0.455863i	−0.0502365	−	0.998737i	$-0.515998\pi$
$877$	23.3827	−	13.5000i	0.789577	−	0.455863i	0.839814	+	0.542875i	$0.182664\pi$
$878$		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
$885$	8.92820	+	0.535898i	0.300118	+	0.0180140i
$886$		0			0
$887$	−10.3923	+	6.00000i	−0.348939	+	0.201460i	−0.664218	−	0.747539i	$-0.731235\pi$
$887$	−10.3923	+	6.00000i	−0.348939	+	0.201460i	0.315279	+	0.948999i	$0.397902\pi$
$888$		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
$905$	3.73205	+	2.46410i	0.124058	+	0.0819095i
$906$		0			0
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	0.712084	−	0.702094i	$-0.247752\pi$
$907$	13.8564	+	8.00000i	0.460094	+	0.265636i	−0.251990	+	0.967730i	$0.581085\pi$
$908$		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
$915$	2.46410	−	3.73205i	0.0814607	−	0.123378i
$916$		0			0
$917$	14.7224	−	42.5000i	0.486178	−	1.40347i
$918$		0			0
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.793742	−	0.608254i	$-0.791870\pi$
$919$	−28.0000	−	48.4974i	−0.923635	−	1.59978i	−0.129893	−	0.991528i	$-0.541463\pi$
$920$		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	0.998827	+	0.0484211i	$0.0154190\pi$
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	−0.457480	+	0.889220i	$0.651248\pi$
$930$		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
$935$	−22.3205	−	1.33975i	−0.729959	−	0.0438144i
$936$		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	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	23.3827	−	13.5000i	0.761445	−	0.439620i
$944$		0			0
$945$	5.86603	−	0.767949i	0.190822	−	0.0249814i
$946$		0			0
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	−0.321552	−	0.946892i	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$		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
$955$	−2.14359	+	35.7128i	−0.0693651	+	1.15564i
$956$		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	0.988389	+	0.151948i	$0.0485545\pi$
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	−0.362604	+	0.931943i	$0.618112\pi$
$972$		0			0
$973$	−13.8564	−	16.0000i	−0.444216	−	0.512936i
$974$		0			0
$975$	−4.96410	−	0.598076i	−0.158978	−	0.0191538i
$976$		0			0
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.952183	−	0.305530i	$-0.0988335\pi$
$977$	36.3731	+	21.0000i	1.16368	+	0.671850i	0.211495	+	0.977379i	$0.432167\pi$
$978$		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	$-0.156924\pi$
$983$	28.5788	+	16.5000i	0.911523	+	0.526268i	0.0306024	+	0.999532i	$0.490257\pi$
$984$		0			0
$985$	33.2654	−	50.3827i	1.05992	−	1.60533i
$986$		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	0.424594	+	0.905384i	$0.360417\pi$
$991$	−18.0000	+	31.1769i	−0.571789	+	0.990367i	−0.996382	+	0.0849833i	$0.972916\pi$
$992$		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	$-0.383951\pi$
$997$	−8.66025	−	5.00000i	−0.274273	−	0.158352i	−0.630828	+	0.775923i	$0.717285\pi$
$998$		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.529.2		4
4.3	odd	2		210.2.n.a.109.2	yes	4
5.4	even	2	inner	1680.2.di.a.529.1		4
7.2	even	3	inner	1680.2.di.a.289.1		4
12.11	even	2		630.2.u.c.109.1		4
20.3	even	4		1050.2.i.f.151.1		2
20.7	even	4		1050.2.i.o.151.1		2
20.19	odd	2		210.2.n.a.109.1	yes	4
28.3	even	6		1470.2.g.a.589.2		2
28.11	odd	6		1470.2.g.f.589.2		2
28.19	even	6		1470.2.n.i.79.1		4
28.23	odd	6		210.2.n.a.79.1	✓	4
28.27	even	2		1470.2.n.i.949.2		4
35.9	even	6	inner	1680.2.di.a.289.2		4
60.59	even	2		630.2.u.c.109.2		4
84.23	even	6		630.2.u.c.289.2		4
140.3	odd	12		7350.2.a.ch.1.1		1
140.19	even	6		1470.2.n.i.79.2		4
140.23	even	12		1050.2.i.f.751.1		2
140.39	odd	6		1470.2.g.f.589.1		2
140.59	even	6		1470.2.g.a.589.1		2
140.67	even	12		7350.2.a.t.1.1		1
140.79	odd	6		210.2.n.a.79.2	yes	4
140.87	odd	12		7350.2.a.b.1.1		1
140.107	even	12		1050.2.i.o.751.1		2
140.123	even	12		7350.2.a.bn.1.1		1
140.139	even	2		1470.2.n.i.949.1		4
420.359	even	6		630.2.u.c.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.a.79.1	✓	4	28.23	odd	6
210.2.n.a.79.2	yes	4	140.79	odd	6
210.2.n.a.109.1	yes	4	20.19	odd	2
210.2.n.a.109.2	yes	4	4.3	odd	2
630.2.u.c.109.1		4	12.11	even	2
630.2.u.c.109.2		4	60.59	even	2
630.2.u.c.289.1		4	420.359	even	6
630.2.u.c.289.2		4	84.23	even	6
1050.2.i.f.151.1		2	20.3	even	4
1050.2.i.f.751.1		2	140.23	even	12
1050.2.i.o.151.1		2	20.7	even	4
1050.2.i.o.751.1		2	140.107	even	12
1470.2.g.a.589.1		2	140.59	even	6
1470.2.g.a.589.2		2	28.3	even	6
1470.2.g.f.589.1		2	140.39	odd	6
1470.2.g.f.589.2		2	28.11	odd	6
1470.2.n.i.79.1		4	28.19	even	6
1470.2.n.i.79.2		4	140.19	even	6
1470.2.n.i.949.1		4	140.139	even	2
1470.2.n.i.949.2		4	28.27	even	2
1680.2.di.a.289.1		4	7.2	even	3	inner
1680.2.di.a.289.2		4	35.9	even	6	inner
1680.2.di.a.529.1		4	5.4	even	2	inner
1680.2.di.a.529.2		4	1.1	even	1	trivial
7350.2.a.b.1.1		1	140.87	odd	12
7350.2.a.t.1.1		1	140.67	even	12
7350.2.a.bn.1.1		1	140.123	even	12
7350.2.a.ch.1.1		1	140.3	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{3} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-2.50000 + 4.33013i) q^{11} +1.00000i q^{13} +(-1.00000 - 2.00000i) q^{15} +(-1.73205 - 1.00000i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(0.500000 + 2.59808i) q^{21} +(-2.59808 + 1.50000i) q^{23} +(1.96410 + 4.59808i) q^{25} +1.00000i q^{27} +(-3.00000 + 5.19615i) q^{31} +(-4.33013 + 2.50000i) q^{33} +(-0.767949 - 5.86603i) q^{35} +(4.33013 - 2.50000i) q^{37} +(-0.500000 + 0.866025i) q^{39} -9.00000 q^{41} -10.0000i q^{43} +(0.133975 - 2.23205i) q^{45} +(-11.2583 + 6.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(0.866025 + 0.500000i) q^{53} +(10.0000 - 5.00000i) q^{55} -7.00000i q^{57} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-0.866025 + 2.50000i) q^{63} +(1.23205 - 1.86603i) q^{65} +(-5.19615 - 3.00000i) q^{67} -3.00000 q^{69} +2.00000 q^{71} +(-3.46410 - 2.00000i) q^{73} +(-0.598076 + 4.96410i) q^{75} +(-12.9904 + 2.50000i) q^{77} +(7.00000 + 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{81} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(5.00000 + 8.66025i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(-5.19615 + 3.00000i) q^{93} +(-0.937822 + 15.6244i) q^{95} -8.00000i q^{97} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} + 2 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

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