LMFDB - Embedded newform 560.4.q.l.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,4,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$33.0410696032$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 22x^{2} + 484 $ x^4 + 22*x^2 + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			401.1
Root			$-2.34521 - 4.06202i$ of defining polynomial
Character	$\chi$	$=$	560.401
Dual form			560.4.q.l.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.154792 + 0.268108i) q^{3} +(-2.50000 + 4.33013i) q^{5} +(15.8452 - 9.58798i) q^{7} +(13.4521 - 23.2997i) q^{9} +O(q^{10})$	\(q+(0.154792 + 0.268108i) q^{3} +(-2.50000 + 4.33013i) q^{5} +(15.8452 - 9.58798i) q^{7} +(13.4521 - 23.2997i) q^{9} +(8.30958 + 14.3926i) q^{11} -91.6658 q^{13} -1.54792 q^{15} +(-13.8329 - 23.9593i) q^{17} +(39.3096 - 68.0862i) q^{19} +(5.02333 + 2.76408i) q^{21} +(18.4644 - 31.9812i) q^{23} +(-12.5000 - 21.6506i) q^{25} +16.6879 q^{27} -209.285 q^{29} +(89.1425 + 154.399i) q^{31} +(-2.57252 + 4.45573i) q^{33} +(1.90416 + 92.5817i) q^{35} +(-68.5700 + 118.767i) q^{37} +(-14.1891 - 24.5763i) q^{39} +225.806 q^{41} -502.589 q^{43} +(67.2604 + 116.498i) q^{45} +(225.904 - 391.277i) q^{47} +(159.141 - 303.847i) q^{49} +(4.28245 - 7.41742i) q^{51} +(-253.595 - 439.239i) q^{53} -83.0958 q^{55} +24.3393 q^{57} +(-343.118 - 594.298i) q^{59} +(275.950 - 477.959i) q^{61} +(-10.2460 - 498.167i) q^{63} +(229.165 - 396.925i) q^{65} +(-90.7960 - 157.263i) q^{67} +11.4326 q^{69} -832.801 q^{71} +(170.781 + 295.802i) q^{73} +(3.86980 - 6.70270i) q^{75} +(269.663 + 148.382i) q^{77} +(89.6930 - 155.353i) q^{79} +(-360.623 - 624.617i) q^{81} +708.108 q^{83} +138.329 q^{85} +(-32.3957 - 56.1109i) q^{87} +(-434.446 + 752.482i) q^{89} +(-1452.46 + 878.890i) q^{91} +(-27.5971 + 47.7996i) q^{93} +(196.548 + 340.431i) q^{95} -801.145 q^{97} +447.125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{3} - 10 q^{5} + 54 q^{7} - 40 q^{9}+O(q^{10}) $ 4 * q + 10 * q^3 - 10 * q^5 + 54 * q^7 - 40 * q^9	$ 4 q + 10 q^{3} - 10 q^{5} + 54 q^{7} - 40 q^{9} + 52 q^{11} - 104 q^{13} - 100 q^{15} + 76 q^{17} + 176 q^{19} - 130 q^{21} + 102 q^{23} - 50 q^{25} - 740 q^{27} - 612 q^{29} + 244 q^{31} - 348 q^{33} - 180 q^{35} + 176 q^{37} + 356 q^{39} - 260 q^{41} - 228 q^{43} - 200 q^{45} + 716 q^{47} + 130 q^{49} - 996 q^{51} - 808 q^{53} - 520 q^{55} + 1936 q^{57} - 1016 q^{59} + 222 q^{61} - 2480 q^{63} + 260 q^{65} + 134 q^{67} + 1284 q^{69} - 592 q^{71} - 724 q^{73} + 250 q^{75} + 28 q^{77} + 1128 q^{79} - 2662 q^{81} - 676 q^{83} - 760 q^{85} - 1002 q^{87} + 326 q^{89} - 2020 q^{91} - 692 q^{93} + 880 q^{95} - 3880 q^{97} - 3840 q^{99}+O(q^{100}) $ 4 * q + 10 * q^3 - 10 * q^5 + 54 * q^7 - 40 * q^9 + 52 * q^11 - 104 * q^13 - 100 * q^15 + 76 * q^17 + 176 * q^19 - 130 * q^21 + 102 * q^23 - 50 * q^25 - 740 * q^27 - 612 * q^29 + 244 * q^31 - 348 * q^33 - 180 * q^35 + 176 * q^37 + 356 * q^39 - 260 * q^41 - 228 * q^43 - 200 * q^45 + 716 * q^47 + 130 * q^49 - 996 * q^51 - 808 * q^53 - 520 * q^55 + 1936 * q^57 - 1016 * q^59 + 222 * q^61 - 2480 * q^63 + 260 * q^65 + 134 * q^67 + 1284 * q^69 - 592 * q^71 - 724 * q^73 + 250 * q^75 + 28 * q^77 + 1128 * q^79 - 2662 * q^81 - 676 * q^83 - 760 * q^85 - 1002 * q^87 + 326 * q^89 - 2020 * q^91 - 692 * q^93 + 880 * q^95 - 3880 * q^97 - 3840 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$3$	0.154792	+	0.268108i	0.0297898	+	0.0515974i	0.880536	−	0.473979i	$-0.157183\pi$
$3$	0.154792	+	0.268108i	0.0297898	+	0.0515974i	−0.850746	+	0.525577i	$0.823850\pi$
$4$		0			0
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	15.8452	−	9.58798i	0.855561	−	0.517702i
$7$	15.8452	−	9.58798i	0.855561	−	0.517702i
$8$		0			0
$9$	13.4521	−	23.2997i	0.498225	−	0.862951i
$10$		0			0
$11$	8.30958	+	14.3926i	0.227767	+	0.394504i	0.957146	−	0.289606i	$-0.0935243\pi$
$11$	8.30958	+	14.3926i	0.227767	+	0.394504i	−0.729379	+	0.684110i	$0.760191\pi$
$12$		0			0
$13$	−91.6658			−1.95566			−0.977828	−	0.209410i	$-0.932846\pi$
$13$	−91.6658			−1.95566			−0.977828	+	0.209410i	$0.932846\pi$
$14$		0			0
$15$	−1.54792			−0.0266448
$16$		0			0
$17$	−13.8329	−	23.9593i	−0.197351	−	0.341823i	0.750317	−	0.661078i	$-0.229901\pi$
$17$	−13.8329	−	23.9593i	−0.197351	−	0.341823i	−0.947669	+	0.319255i	$0.896567\pi$
$18$		0			0
$19$	39.3096	−	68.0862i	0.474644	−	0.822108i	−0.524934	−	0.851143i	$-0.675910\pi$
$19$	39.3096	−	68.0862i	0.474644	−	0.822108i	0.999578	+	0.0290351i	$0.00924346\pi$
$20$		0			0
$21$	5.02333	+	2.76408i	0.0521990	+	0.0287225i
$22$		0			0
$23$	18.4644	−	31.9812i	0.167395	−	0.289937i	−0.770108	−	0.637913i	$-0.779798\pi$
$23$	18.4644	−	31.9812i	0.167395	−	0.289937i	0.937503	+	0.347976i	$0.113131\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$		0			0
$27$	16.6879			0.118948
$28$		0			0
$29$	−209.285			−1.34011			−0.670056	−	0.742311i	$-0.733730\pi$
$29$	−209.285			−1.34011			−0.670056	+	0.742311i	$0.733730\pi$
$30$		0			0
$31$	89.1425	+	154.399i	0.516467	+	0.894546i	0.999817	+	0.0191195i	$0.00608631\pi$
$31$	89.1425	+	154.399i	0.516467	+	0.894546i	−0.483351	+	0.875427i	$0.660580\pi$
$32$		0			0
$33$	−2.57252	+	4.45573i	−0.0135702	+	0.0235043i
$34$		0			0
$35$	1.90416	+	92.5817i	0.00919604	+	0.447119i
$36$		0			0
$37$	−68.5700	+	118.767i	−0.304671	+	0.527706i	−0.977188	−	0.212376i	$-0.931880\pi$
$37$	−68.5700	+	118.767i	−0.304671	+	0.527706i	0.672517	+	0.740082i	$0.265213\pi$
$38$		0			0
$39$	−14.1891	−	24.5763i	−0.0582585	−	0.100907i
$40$		0			0
$41$	225.806			0.860120			0.430060	−	0.902800i	$-0.358492\pi$
$41$	225.806			0.860120			0.430060	+	0.902800i	$0.358492\pi$
$42$		0			0
$43$	−502.589			−1.78242			−0.891211	−	0.453588i	$-0.850144\pi$
$43$	−502.589			−1.78242			−0.891211	+	0.453588i	$0.850144\pi$
$44$		0			0
$45$	67.2604	+	116.498i	0.222813	+	0.385924i
$46$		0			0
$47$	225.904	−	391.277i	0.701096	−	1.21433i	−0.266986	−	0.963700i	$-0.586028\pi$
$47$	225.904	−	391.277i	0.701096	−	1.21433i	0.968082	−	0.250633i	$-0.0806389\pi$
$48$		0			0
$49$	159.141	−	303.847i	0.463969	−	0.885852i
$50$		0			0
$51$	4.28245	−	7.41742i	0.0117581	−	0.0203656i
$52$		0			0
$53$	−253.595	−	439.239i	−0.657243	−	1.13838i	−0.981326	−	0.192350i	$-0.938389\pi$
$53$	−253.595	−	439.239i	−0.657243	−	1.13838i	0.324083	−	0.946029i	$-0.394944\pi$
$54$		0			0
$55$	−83.0958			−0.203721
$56$		0			0
$57$	24.3393			0.0565581
$58$		0			0
$59$	−343.118	−	594.298i	−0.757121	−	1.31137i	−0.944313	−	0.329049i	$-0.893272\pi$
$59$	−343.118	−	594.298i	−0.757121	−	1.31137i	0.187192	−	0.982323i	$-0.440061\pi$
$60$		0			0
$61$	275.950	−	477.959i	0.579208	−	1.00322i	−0.416362	−	0.909199i	$-0.636695\pi$
$61$	275.950	−	477.959i	0.579208	−	1.00322i	0.995570	−	0.0940196i	$-0.0299716\pi$
$62$		0			0
$63$	−10.2460	−	498.167i	−0.0204900	−	0.996240i
$64$		0			0
$65$	229.165	−	396.925i	0.437298	−	0.757422i
$66$		0			0
$67$	−90.7960	−	157.263i	−0.165560	−	0.286758i	0.771294	−	0.636479i	$-0.219610\pi$
$67$	−90.7960	−	157.263i	−0.165560	−	0.286758i	−0.936854	+	0.349721i	$0.886276\pi$
$68$		0			0
$69$	11.4326			0.0199466
$70$		0			0
$71$	−832.801			−1.39205			−0.696023	−	0.718020i	$-0.745049\pi$
$71$	−832.801			−1.39205			−0.696023	+	0.718020i	$0.745049\pi$
$72$		0			0
$73$	170.781	+	295.802i	0.273814	+	0.474260i	0.969835	−	0.243761i	$-0.0783814\pi$
$73$	170.781	+	295.802i	0.273814	+	0.474260i	−0.696021	+	0.718021i	$0.745048\pi$
$74$		0			0
$75$	3.86980	−	6.70270i	0.00595795	−	0.0103195i
$76$		0			0
$77$	269.663	+	148.382i	0.399104	+	0.219606i
$78$		0			0
$79$	89.6930	−	155.353i	0.127737	−	0.221247i	−0.795062	−	0.606528i	$-0.792562\pi$
$79$	89.6930	−	155.353i	0.127737	−	0.221247i	0.922800	+	0.385280i	$0.125895\pi$
$80$		0			0
$81$	−360.623	−	624.617i	−0.494682	−	0.856814i
$82$		0			0
$83$	708.108			0.936445			0.468222	−	0.883611i	$-0.344895\pi$
$83$	708.108			0.936445			0.468222	+	0.883611i	$0.344895\pi$
$84$		0			0
$85$	138.329			0.176516
$86$		0			0
$87$	−32.3957	−	56.1109i	−0.0399216	−	0.0691463i
$88$		0			0
$89$	−434.446	+	752.482i	−0.517429	+	0.896213i	0.482366	+	0.875970i	$0.339777\pi$
$89$	−434.446	+	752.482i	−0.517429	+	0.896213i	−0.999795	+	0.0202433i	$0.993556\pi$
$90$		0			0
$91$	−1452.46	+	878.890i	−1.67318	+	1.01245i
$92$		0			0
$93$	−27.5971	+	47.7996i	−0.0307708	+	0.0532966i
$94$		0			0
$95$	196.548	+	340.431i	0.212267	+	0.367658i
$96$		0			0
$97$	−801.145			−0.838597			−0.419299	−	0.907848i	$-0.637724\pi$
$97$	−801.145			−0.838597			−0.419299	+	0.907848i	$0.637724\pi$
$98$		0			0
$99$	447.125			0.453916
$100$		0			0
$101$	−471.777	−	817.142i	−0.464788	−	0.805037i	0.534404	−	0.845229i	$-0.320536\pi$
$101$	−471.777	−	817.142i	−0.464788	−	0.805037i	−0.999192	+	0.0401926i	$0.987203\pi$
$102$		0			0
$103$	84.5848	−	146.505i	0.0809164	−	0.140151i	−0.822727	−	0.568436i	$-0.807549\pi$
$103$	84.5848	−	146.505i	0.0809164	−	0.140151i	0.903644	+	0.428285i	$0.140882\pi$
$104$		0			0
$105$	−24.5271	+	14.8414i	−0.0227962	+	0.0137941i
$106$		0			0
$107$	787.533	−	1364.05i	0.711530	−	1.23241i	−0.252753	−	0.967531i	$-0.581336\pi$
$107$	787.533	−	1364.05i	0.711530	−	1.23241i	0.964283	−	0.264875i	$-0.0853307\pi$
$108$		0			0
$109$	−458.525	−	794.188i	−0.402924	−	0.697884i	0.591154	−	0.806559i	$-0.298673\pi$
$109$	−458.525	−	794.188i	−0.402924	−	0.697884i	−0.994077	+	0.108675i	$0.965339\pi$
$110$		0			0
$111$	−42.4564			−0.0363043
$112$		0			0
$113$	−90.9042			−0.0756774			−0.0378387	−	0.999284i	$-0.512047\pi$
$113$	−90.9042			−0.0756774			−0.0378387	+	0.999284i	$0.512047\pi$
$114$		0			0
$115$	92.3219	+	159.906i	0.0748614	+	0.129664i
$116$		0			0
$117$	−1233.10	+	2135.78i	−0.974357	+	1.68764i
$118$		0			0
$119$	−448.907	−	247.010i	−0.345808	−	0.190281i
$120$		0			0
$121$	527.402	−	913.486i	0.396245	−	0.686316i
$122$		0			0
$123$	34.9530	+	60.5403i	0.0256228	+	0.0443800i
$124$		0			0
$125$	125.000			0.0894427
$126$		0			0
$127$	300.762			0.210144			0.105072	−	0.994465i	$-0.466493\pi$
$127$	300.762			0.210144			0.105072	+	0.994465i	$0.466493\pi$
$128$		0			0
$129$	−77.7969	−	134.748i	−0.0530979	−	0.0919683i
$130$		0			0
$131$	460.472	−	797.560i	0.307111	−	0.531933i	−0.670618	−	0.741803i	$-0.733971\pi$
$131$	460.472	−	797.560i	0.307111	−	0.531933i	0.977729	+	0.209871i	$0.0673043\pi$
$132$		0			0
$133$	−29.9407	−	1455.74i	−0.0195202	−	0.949087i
$134$		0			0
$135$	−41.7197	+	72.2606i	−0.0265975	+	0.0460682i
$136$		0			0
$137$	−1383.27	−	2395.90i	−0.862635	−	1.49413i	−0.869377	−	0.494150i	$-0.835480\pi$
$137$	−1383.27	−	2395.90i	−0.862635	−	1.49413i	0.00674241	−	0.999977i	$-0.497854\pi$
$138$		0			0
$139$	2735.74			1.66937			0.834686	−	0.550726i	$-0.185649\pi$
$139$	2735.74			1.66937			0.834686	+	0.550726i	$0.185649\pi$
$140$		0			0
$141$	139.873			0.0835419
$142$		0			0
$143$	−761.705	−	1319.31i	−0.445433	−	0.771513i
$144$		0			0
$145$	523.212	−	906.231i	0.299658	−	0.519023i
$146$		0			0
$147$	106.098	−	4.36613i	0.0595291	−	0.00244975i
$148$		0			0
$149$	−1334.14	+	2310.80i	−0.733538	+	1.27052i	0.221824	+	0.975087i	$0.428799\pi$
$149$	−1334.14	+	2310.80i	−0.733538	+	1.27052i	−0.955362	+	0.295438i	$0.904534\pi$
$150$		0			0
$151$	1153.28	+	1997.54i	0.621540	+	1.07654i	0.989199	+	0.146579i	$0.0468261\pi$
$151$	1153.28	+	1997.54i	0.621540	+	1.07654i	−0.367659	+	0.929961i	$0.619841\pi$
$152$		0			0
$153$	−744.326			−0.393302
$154$		0			0
$155$	−891.425			−0.461942
$156$		0			0
$157$	990.808	+	1716.13i	0.503663	+	0.872370i	0.999991	+	0.00423500i	$0.00134805\pi$
$157$	990.808	+	1716.13i	0.503663	+	0.872370i	−0.496328	+	0.868135i	$0.665319\pi$
$158$		0			0
$159$	78.5089	−	135.981i	0.0391582	−	0.0678241i
$160$		0			0
$161$	−14.0636	−	683.785i	−0.00688428	−	0.334720i
$162$		0			0
$163$	−541.580	+	938.044i	−0.260244	+	0.450756i	−0.966307	−	0.257393i	$-0.917136\pi$
$163$	−541.580	+	938.044i	−0.260244	+	0.450756i	0.706062	+	0.708150i	$0.250470\pi$
$164$		0			0
$165$	−12.8626	−	22.2786i	−0.00606879	−	0.0105115i
$166$		0			0
$167$	−1203.77			−0.557789			−0.278895	−	0.960322i	$-0.589968\pi$
$167$	−1203.77			−0.557789			−0.278895	+	0.960322i	$0.589968\pi$
$168$		0			0
$169$	6205.62			2.82459
$170$		0			0
$171$	−1057.59	−	1831.80i	−0.472959	−	0.819189i
$172$		0			0
$173$	−1341.90	+	2324.23i	−0.589725	+	1.02143i	0.404543	+	0.914519i	$0.367431\pi$
$173$	−1341.90	+	2324.23i	−0.589725	+	1.02143i	−0.994268	+	0.106915i	$0.965903\pi$
$174$		0			0
$175$	−405.651	−	223.209i	−0.175225	−	0.0964172i
$176$		0			0
$177$	106.224	−	183.985i	0.0451089	−	0.0781309i
$178$		0			0
$179$	31.1425	+	53.9404i	0.0130039	+	0.0225234i	0.872454	−	0.488696i	$-0.162527\pi$
$179$	31.1425	+	53.9404i	0.0130039	+	0.0225234i	−0.859450	+	0.511219i	$0.829194\pi$
$180$		0			0
$181$	680.223			0.279340			0.139670	−	0.990198i	$-0.455396\pi$
$181$	680.223			0.279340			0.139670	+	0.990198i	$0.455396\pi$
$182$		0			0
$183$	170.859			0.0690179
$184$		0			0
$185$	−342.850	−	593.833i	−0.136253	−	0.235997i
$186$		0			0
$187$	229.891	−	398.184i	0.0899002	−	0.155712i
$188$		0			0
$189$	264.423	−	160.003i	0.101767	−	0.0615794i
$190$		0			0
$191$	−972.059	+	1683.65i	−0.368250	+	0.637827i	−0.989292	−	0.145950i	$-0.953376\pi$
$191$	−972.059	+	1683.65i	−0.368250	+	0.637827i	0.621042	+	0.783777i	$0.286710\pi$
$192$		0			0
$193$	−340.435	−	589.651i	−0.126969	−	0.219917i	0.795532	−	0.605912i	$-0.207192\pi$
$193$	−340.435	−	589.651i	−0.126969	−	0.219917i	−0.922501	+	0.385995i	$0.873858\pi$
$194$		0			0
$195$	141.891			0.0521080
$196$		0			0
$197$	323.259			0.116910			0.0584549	−	0.998290i	$-0.481383\pi$
$197$	323.259			0.116910			0.0584549	+	0.998290i	$0.481383\pi$
$198$		0			0
$199$	1415.28	+	2451.34i	0.504154	+	0.873221i	0.999988	+	0.00480368i	$0.00152906\pi$
$199$	1415.28	+	2451.34i	0.504154	+	0.873221i	−0.495834	+	0.868417i	$0.665138\pi$
$200$		0			0
$201$	28.1090	−	48.6862i	0.00986397	−	0.0170849i
$202$		0			0
$203$	−3316.16	+	2006.62i	−1.14655	+	0.693779i
$204$		0			0
$205$	−564.514	+	977.768i	−0.192329	+	0.333123i
$206$		0			0
$207$	−496.768	−	860.428i	−0.166801	−	0.288908i
$208$		0			0
$209$	1306.59			0.432432
$210$		0			0
$211$	−2488.78			−0.812013			−0.406006	−	0.913870i	$-0.633079\pi$
$211$	−2488.78			−0.812013			−0.406006	+	0.913870i	$0.633079\pi$
$212$		0			0
$213$	−128.911	−	223.280i	−0.0414687	−	0.0718259i
$214$		0			0
$215$	1256.47	−	2176.28i	0.398562	−	0.690329i
$216$		0			0
$217$	2892.86	+	1591.79i	0.904977	+	0.497963i
$218$		0			0
$219$	−52.8712	+	91.5755i	−0.0163137	+	0.0282562i
$220$		0			0
$221$	1268.01	+	2196.25i	0.385951	+	0.668487i
$222$		0			0
$223$	−1994.33			−0.598881			−0.299440	−	0.954115i	$-0.596800\pi$
$223$	−1994.33			−0.598881			−0.299440	+	0.954115i	$0.596800\pi$
$224$		0			0
$225$	−672.604			−0.199290
$226$		0			0
$227$	889.192	+	1540.13i	0.259990	+	0.450316i	0.966239	−	0.257648i	$-0.0829474\pi$
$227$	889.192	+	1540.13i	0.259990	+	0.450316i	−0.706249	+	0.707964i	$0.749614\pi$
$228$		0			0
$229$	505.826	−	876.116i	0.145965	−	0.252818i	−0.783768	−	0.621054i	$-0.786705\pi$
$229$	505.826	−	876.116i	0.145965	−	0.252818i	0.929732	+	0.368236i	$0.120038\pi$
$230$		0			0
$231$	1.95939	+	95.2672i	0.000558088	+	0.0271347i
$232$		0			0
$233$	−1642.61	+	2845.09i	−0.461851	+	0.799949i	−0.999053	−	0.0435046i	$-0.986148\pi$
$233$	−1642.61	+	2845.09i	−0.461851	+	0.799949i	0.537203	+	0.843453i	$0.319481\pi$
$234$		0			0
$235$	1129.52	+	1956.39i	0.313540	+	0.543067i
$236$		0			0
$237$	55.5350			0.0152211
$238$		0			0
$239$	3355.78			0.908231			0.454116	−	0.890943i	$-0.349955\pi$
$239$	3355.78			0.908231			0.454116	+	0.890943i	$0.349955\pi$
$240$		0			0
$241$	1446.38	+	2505.21i	0.386596	+	0.669604i	0.991989	−	0.126323i	$-0.0403175\pi$
$241$	1446.38	+	2505.21i	0.386596	+	0.669604i	−0.605393	+	0.795926i	$0.706984\pi$
$242$		0			0
$243$	336.930	−	583.579i	0.0889467	−	0.154060i
$244$		0			0
$245$	917.844	+	1448.72i	0.239342	+	0.377777i
$246$		0			0
$247$	−3603.35	+	6241.18i	−0.928240	+	1.60776i
$248$		0			0
$249$	109.609	+	189.849i	0.0278965	+	0.0483181i
$250$		0			0
$251$	6497.64			1.63397			0.816987	−	0.576656i	$-0.195643\pi$
$251$	6497.64			1.63397			0.816987	+	0.576656i	$0.195643\pi$
$252$		0			0
$253$	613.725			0.152508
$254$		0			0
$255$	21.4123	+	37.0871i	0.00525838	+	0.00910778i
$256$		0			0
$257$	1129.37	−	1956.12i	0.274116	−	0.474783i	−0.695795	−	0.718240i	$-0.744948\pi$
$257$	1129.37	−	1956.12i	0.274116	−	0.474783i	0.969912	+	0.243457i	$0.0782813\pi$
$258$		0			0
$259$	52.2272	+	2539.33i	0.0125299	+	0.609214i
$260$		0			0
$261$	−2815.32	+	4876.27i	−0.667677	+	1.15645i
$262$		0			0
$263$	67.4499	+	116.827i	0.0158142	+	0.0273910i	0.873824	−	0.486242i	$-0.161633\pi$
$263$	67.4499	+	116.827i	0.0158142	+	0.0273910i	−0.858010	+	0.513633i	$0.828299\pi$
$264$		0			0
$265$	2535.95			0.587856
$266$		0			0
$267$	−268.995			−0.0616563
$268$		0			0
$269$	3265.28	+	5655.63i	0.740102	+	1.28190i	0.952448	+	0.304700i	$0.0985563\pi$
$269$	3265.28	+	5655.63i	0.740102	+	1.28190i	−0.212346	+	0.977195i	$0.568110\pi$
$270$		0			0
$271$	1073.74	−	1859.78i	0.240683	−	0.416876i	−0.720226	−	0.693740i	$-0.755962\pi$
$271$	1073.74	−	1859.78i	0.240683	−	0.416876i	0.960909	+	0.276864i	$0.0892951\pi$
$272$		0			0
$273$	−460.467	−	253.372i	−0.102083	−	0.0561712i
$274$		0			0
$275$	207.740	−	359.816i	0.0455533	−	0.0789007i
$276$		0			0
$277$	−3914.02	−	6779.28i	−0.848991	−	1.47050i	−0.882109	−	0.471045i	$-0.843877\pi$
$277$	−3914.02	−	6779.28i	−0.848991	−	1.47050i	0.0331177	−	0.999451i	$-0.489456\pi$
$278$		0			0
$279$	4796.61			1.02927
$280$		0			0
$281$	−5934.49			−1.25987			−0.629933	−	0.776650i	$-0.716917\pi$
$281$	−5934.49			−1.25987			−0.629933	+	0.776650i	$0.716917\pi$
$282$		0			0
$283$	2619.14	+	4536.48i	0.550147	+	0.952882i	0.998263	+	0.0589072i	$0.0187616\pi$
$283$	2619.14	+	4536.48i	0.550147	+	0.952882i	−0.448117	+	0.893975i	$0.647905\pi$
$284$		0			0
$285$	−60.8481	+	105.392i	−0.0126468	+	0.0219049i
$286$		0			0
$287$	3577.94	−	2165.02i	0.735885	−	0.445286i
$288$		0			0
$289$	2073.80	−	3591.93i	0.422105	−	0.731107i
$290$		0			0
$291$	−124.011	−	214.793i	−0.0249816	−	0.0432694i
$292$		0			0
$293$	−3564.95			−0.710808			−0.355404	−	0.934713i	$-0.615657\pi$
$293$	−3564.95			−0.710808			−0.355404	+	0.934713i	$0.615657\pi$
$294$		0			0
$295$	3431.18			0.677190
$296$		0			0
$297$	138.669	+	240.182i	0.0270923	+	0.0469252i
$298$		0			0
$299$	−1692.55	+	2931.59i	−0.327367	+	0.567017i
$300$		0			0
$301$	−7963.64	+	4818.82i	−1.52497	+	0.922764i
$302$		0			0
$303$	146.055	−	252.974i	0.0276919	−	0.0479637i
$304$		0			0
$305$	1379.75	+	2389.79i	0.259030	+	0.448653i
$306$		0			0
$307$	−5809.11			−1.07995			−0.539973	−	0.841682i	$-0.681566\pi$
$307$	−5809.11			−1.07995			−0.539973	+	0.841682i	$0.681566\pi$
$308$		0			0
$309$	52.3723			0.00964192
$310$		0			0
$311$	697.216	+	1207.61i	0.127124	+	0.220185i	0.922561	−	0.385851i	$-0.126092\pi$
$311$	697.216	+	1207.61i	0.127124	+	0.220185i	−0.795437	+	0.606036i	$0.792759\pi$
$312$		0			0
$313$	2971.29	−	5146.43i	0.536573	−	0.929372i	−0.462512	−	0.886613i	$-0.653052\pi$
$313$	2971.29	−	5146.43i	0.536573	−	0.929372i	0.999085	−	0.0427590i	$-0.0136148\pi$
$314$		0			0
$315$	2182.74	+	1201.05i	0.390424	+	0.214830i
$316$		0			0
$317$	−721.455	+	1249.60i	−0.127826	+	0.221402i	−0.922834	−	0.385197i	$-0.874133\pi$
$317$	−721.455	+	1249.60i	−0.127826	+	0.221402i	0.795008	+	0.606599i	$0.207467\pi$
$318$		0			0
$319$	−1739.07	−	3012.16i	−0.305233	−	0.528679i
$320$		0			0
$321$	487.616			0.0847852
$322$		0			0
$323$	−2175.06			−0.374687
$324$		0			0
$325$	1145.82	+	1984.62i	0.195566	+	0.338730i
$326$		0			0
$327$	141.952	−	245.868i	0.0240060	−	0.0415796i
$328$		0			0
$329$	−172.063	−	8365.84i	−0.0288332	−	1.40190i
$330$		0			0
$331$	2945.46	−	5101.68i	0.489115	−	0.847171i	−0.510807	−	0.859695i	$-0.670653\pi$
$331$	2945.46	−	5101.68i	0.489115	−	0.847171i	0.999922	+	0.0125241i	$0.00398666\pi$
$332$		0			0
$333$	1844.82	+	3195.32i	0.303590	+	0.525833i
$334$		0			0
$335$	907.960			0.148081
$336$		0			0
$337$	−1326.63			−0.214439			−0.107220	−	0.994235i	$-0.534195\pi$
$337$	−1326.63			−0.214439			−0.107220	+	0.994235i	$0.534195\pi$
$338$		0			0
$339$	−14.0712	−	24.3721i	−0.00225441	−	0.00390475i
$340$		0			0
$341$	−1481.47	+	2565.99i	−0.235268	+	0.407496i
$342$		0			0
$343$	−391.655	−	6340.36i	−0.0616541	−	0.998098i
$344$		0			0
$345$	−28.5814	+	49.5044i	−0.00446021	+	0.00772530i
$346$		0			0
$347$	1102.49	+	1909.57i	0.170562	+	0.295421i	0.938616	−	0.344963i	$-0.112109\pi$
$347$	1102.49	+	1909.57i	0.170562	+	0.295421i	−0.768055	+	0.640384i	$0.778775\pi$
$348$		0			0
$349$	1792.52			0.274933			0.137466	−	0.990506i	$-0.456104\pi$
$349$	1792.52			0.274933			0.137466	+	0.990506i	$0.456104\pi$
$350$		0			0
$351$	−1529.71			−0.232620
$352$		0			0
$353$	−3070.75	−	5318.70i	−0.463002	−	0.801943i	0.536107	−	0.844150i	$-0.319894\pi$
$353$	−3070.75	−	5318.70i	−0.463002	−	0.801943i	−0.999109	+	0.0422071i	$0.986561\pi$
$354$		0			0
$355$	2082.00	−	3606.13i	0.311271	−	0.539137i
$356$		0			0
$357$	−3.26178	−	158.591i	−0.000483563	−	0.0235112i
$358$		0			0
$359$	67.6039	−	117.093i	0.00993872	−	0.0172144i	−0.861013	−	0.508582i	$-0.830170\pi$
$359$	67.6039	−	117.093i	0.00993872	−	0.0172144i	0.870952	+	0.491368i	$0.163503\pi$
$360$		0			0
$361$	339.013	+	587.188i	0.0494260	+	0.0856084i
$362$		0			0
$363$	326.550			0.0472161
$364$		0			0
$365$	−1707.81			−0.244907
$366$		0			0
$367$	4566.68	+	7909.72i	0.649533	+	1.12502i	0.983234	+	0.182346i	$0.0583690\pi$
$367$	4566.68	+	7909.72i	0.649533	+	1.12502i	−0.333701	+	0.942679i	$0.608298\pi$
$368$		0			0
$369$	3037.56	−	5261.20i	0.428534	−	0.742242i
$370$		0			0
$371$	−8229.67	−	4528.37i	−1.15165	−	0.633696i
$372$		0			0
$373$	−3775.01	+	6538.50i	−0.524028	+	0.907643i	0.475581	+	0.879672i	$0.342238\pi$
$373$	−3775.01	+	6538.50i	−0.524028	+	0.907643i	−0.999609	+	0.0279712i	$0.991095\pi$
$374$		0			0
$375$	19.3490	+	33.5135i	0.00266448	+	0.00461501i
$376$		0			0
$377$	19184.3			2.62080
$378$		0			0
$379$	8444.21			1.14446			0.572229	−	0.820094i	$-0.306079\pi$
$379$	8444.21			1.14446			0.572229	+	0.820094i	$0.306079\pi$
$380$		0			0
$381$	46.5555	+	80.6366i	0.00626014	+	0.0108429i
$382$		0			0
$383$	−6313.53	+	10935.3i	−0.842314	+	1.45893i	0.0456204	+	0.998959i	$0.485474\pi$
$383$	−6313.53	+	10935.3i	−0.842314	+	1.45893i	−0.887934	+	0.459971i	$0.847860\pi$
$384$		0			0
$385$	−1316.67	+	796.721i	−0.174295	+	0.105467i
$386$		0			0
$387$	−6760.87	+	11710.2i	−0.888048	+	1.53814i
$388$		0			0
$389$	7180.32	+	12436.7i	0.935878	+	1.62099i	0.773060	+	0.634333i	$0.218725\pi$
$389$	7180.32	+	12436.7i	0.935878	+	1.62099i	0.162818	+	0.986656i	$0.447942\pi$
$390$		0			0
$391$	−1021.66			−0.132143
$392$		0			0
$393$	285.109			0.0365951
$394$		0			0
$395$	448.465	+	776.764i	0.0571259	+	0.0989449i
$396$		0			0
$397$	711.358	−	1232.11i	0.0899296	−	0.155763i	−0.817552	−	0.575855i	$-0.804669\pi$
$397$	711.358	−	1232.11i	0.0899296	−	0.155763i	0.907481	+	0.420093i	$0.138002\pi$
$398$		0			0
$399$	385.661	−	233.364i	0.0483889	−	0.0292803i
$400$		0			0
$401$	2004.64	−	3472.14i	0.249643	−	0.432395i	−0.713783	−	0.700366i	$-0.753020\pi$
$401$	2004.64	−	3472.14i	0.249643	−	0.432395i	0.963427	+	0.267971i	$0.0863533\pi$
$402$		0			0
$403$	−8171.32	−	14153.1i	−1.01003	−	1.74942i
$404$		0			0
$405$	3606.23			0.442457
$406$		0			0
$407$	−2279.15			−0.277576
$408$		0			0
$409$	−84.2472	−	145.920i	−0.0101852	−	0.0176413i	0.860888	−	0.508795i	$-0.169909\pi$
$409$	−84.2472	−	145.920i	−0.0101852	−	0.0176413i	−0.871073	+	0.491153i	$0.836575\pi$
$410$		0			0
$411$	428.239	−	741.732i	0.0513953	−	0.0890193i
$412$		0			0
$413$	−11134.9	−	6126.96i	−1.32666	−	0.729995i
$414$		0			0
$415$	−1770.27	+	3066.20i	−0.209395	+	0.362684i
$416$		0			0
$417$	423.472	+	733.474i	0.0497302	+	0.0861352i
$418$		0			0
$419$	2861.16			0.333596			0.166798	−	0.985991i	$-0.446657\pi$
$419$	2861.16			0.333596			0.166798	+	0.985991i	$0.446657\pi$
$420$		0			0
$421$	1135.73			0.131477			0.0657387	−	0.997837i	$-0.479060\pi$
$421$	1135.73			0.131477			0.0657387	+	0.997837i	$0.479060\pi$
$422$		0			0
$423$	−6077.76	−	10527.0i	−0.698607	−	1.21002i
$424$		0			0
$425$	−345.823	+	598.983i	−0.0394703	+	0.0683645i
$426$		0			0
$427$	−210.181	−	10219.2i	−0.0238205	−	1.15817i
$428$		0			0
$429$	235.812	−	408.438i	0.0265387	−	0.0459664i
$430$		0			0
$431$	−8150.59	−	14117.2i	−0.910905	−	1.57773i	−0.812788	−	0.582560i	$-0.802051\pi$
$431$	−8150.59	−	14117.2i	−0.910905	−	1.57773i	−0.0981175	−	0.995175i	$-0.531282\pi$
$432$		0			0
$433$	−5065.77			−0.562230			−0.281115	−	0.959674i	$-0.590704\pi$
$433$	−5065.77			−0.562230			−0.281115	+	0.959674i	$0.590704\pi$
$434$		0			0
$435$	323.957			0.0357070
$436$		0			0
$437$	−1451.65	−	2514.34i	−0.158906	−	0.275234i
$438$		0			0
$439$	−5026.07	+	8705.41i	−0.546427	+	0.946439i	0.452089	+	0.891973i	$0.350679\pi$
$439$	−5026.07	+	8705.41i	−0.546427	+	0.946439i	−0.998516	+	0.0544661i	$0.982654\pi$
$440$		0			0
$441$	−4938.76	−	7795.32i	−0.533286	−	0.841736i
$442$		0			0
$443$	−8646.73	+	14976.6i	−0.927356	+	1.60623i	−0.139628	+	0.990204i	$0.544591\pi$
$443$	−8646.73	+	14976.6i	−0.927356	+	1.60623i	−0.787728	+	0.616024i	$0.788743\pi$
$444$		0			0
$445$	−2172.23	−	3762.41i	−0.231401	−	0.400799i
$446$		0			0
$447$	−826.058			−0.0874076
$448$		0			0
$449$	10414.5			1.09463			0.547315	−	0.836927i	$-0.315650\pi$
$449$	10414.5			1.09463			0.547315	+	0.836927i	$0.315650\pi$
$450$		0			0
$451$	1876.35	+	3249.94i	0.195907	+	0.339321i
$452$		0			0
$453$	−357.037	+	618.407i	−0.0370311	+	0.0641397i
$454$		0			0
$455$	−174.546	−	8486.58i	−0.0179843	−	0.874411i
$456$		0			0
$457$	−849.474	+	1471.33i	−0.0869513	+	0.150604i	−0.906221	−	0.422804i	$-0.861046\pi$
$457$	−849.474	+	1471.33i	−0.0869513	+	0.150604i	0.819270	+	0.573408i	$0.194379\pi$
$458$		0			0
$459$	−230.842	−	399.830i	−0.0234745	−	0.0406590i
$460$		0			0
$461$	−3640.68			−0.367817			−0.183908	−	0.982943i	$-0.558875\pi$
$461$	−3640.68			−0.367817			−0.183908	+	0.982943i	$0.558875\pi$
$462$		0			0
$463$	−2701.96			−0.271211			−0.135605	−	0.990763i	$-0.543298\pi$
$463$	−2701.96			−0.271211			−0.135605	+	0.990763i	$0.543298\pi$
$464$		0			0
$465$	−137.986	−	238.998i	−0.0137611	−	0.0238350i
$466$		0			0
$467$	6223.49	−	10779.4i	0.616678	−	1.06812i	−0.373409	−	0.927667i	$-0.621811\pi$
$467$	6223.49	−	10779.4i	0.616678	−	1.06812i	0.990088	−	0.140452i	$-0.0448554\pi$
$468$		0			0
$469$	−2946.52	−	1621.32i	−0.290102	−	0.159628i
$470$		0			0
$471$	−306.739	+	531.287i	−0.0300080	+	0.0519754i
$472$		0			0
$473$	−4176.31	−	7233.58i	−0.405977	−	0.703172i
$474$		0			0
$475$	−1965.48			−0.189858
$476$		0			0
$477$	−13645.5			−1.30982
$478$		0			0
$479$	111.809	+	193.659i	0.0106653	+	0.0184729i	0.871309	−	0.490735i	$-0.163272\pi$
$479$	111.809	+	193.659i	0.0106653	+	0.0184729i	−0.860643	+	0.509208i	$0.829938\pi$
$480$		0			0
$481$	6285.52	−	10886.8i	0.595832	−	1.03201i
$482$		0			0
$483$	181.151	−	109.615i	0.0170656	−	0.0103264i
$484$		0			0
$485$	2002.86	−	3469.06i	0.187516	−	0.324787i
$486$		0			0
$487$	−3070.46	−	5318.18i	−0.285699	−	0.494846i	0.687079	−	0.726583i	$-0.258893\pi$
$487$	−3070.46	−	5318.18i	−0.285699	−	0.494846i	−0.972779	+	0.231737i	$0.925559\pi$
$488$		0			0
$489$	−335.329			−0.0310105
$490$		0			0
$491$	16011.3			1.47165			0.735827	−	0.677170i	$-0.236794\pi$
$491$	16011.3			1.47165			0.735827	+	0.677170i	$0.236794\pi$
$492$		0			0
$493$	2895.02	+	5014.32i	0.264473	+	0.458081i
$494$		0			0
$495$	−1117.81	+	1936.11i	−0.101499	+	0.175801i
$496$		0			0
$497$	−13195.9	+	7984.88i	−1.19098	+	0.720665i
$498$		0			0
$499$	9323.69	−	16149.1i	0.836444	−	1.44876i	−0.0564050	−	0.998408i	$-0.517964\pi$
$499$	9323.69	−	16149.1i	0.836444	−	1.44876i	0.892849	−	0.450356i	$-0.148703\pi$
$500$		0			0
$501$	−186.335	−	322.741i	−0.0166164	−	0.0287805i
$502$		0			0
$503$	149.768			0.0132760			0.00663800	−	0.999978i	$-0.497887\pi$
$503$	149.768			0.0132760			0.00663800	+	0.999978i	$0.497887\pi$
$504$		0			0
$505$	4717.77			0.415719
$506$		0			0
$507$	960.581	+	1663.78i	0.0841438	+	0.145741i
$508$		0			0
$509$	6014.68	−	10417.7i	0.523764	−	0.907186i	−0.475853	−	0.879525i	$-0.657861\pi$
$509$	6014.68	−	10417.7i	0.523764	−	0.907186i	0.999617	−	0.0276612i	$-0.00880594\pi$
$510$		0			0
$511$	5542.20	+	3049.59i	0.479790	+	0.264004i
$512$		0			0
$513$	655.994	−	1136.21i	0.0564577	−	0.0977877i
$514$		0			0
$515$	422.924	+	732.526i	0.0361869	+	0.0626776i
$516$		0			0
$517$	7508.68			0.638745
$518$		0			0
$519$	−830.860			−0.0702711
$520$		0			0
$521$	−6052.09	−	10482.5i	−0.508919	−	0.881474i	−0.999947	−	0.0103300i	$-0.996712\pi$
$521$	−6052.09	−	10482.5i	−0.508919	−	0.881474i	0.491027	−	0.871144i	$-0.336622\pi$
$522$		0			0
$523$	2081.15	−	3604.65i	0.174000	−	0.301377i	−0.765815	−	0.643061i	$-0.777664\pi$
$523$	2081.15	−	3604.65i	0.174000	−	0.301377i	0.939815	+	0.341684i	$0.110997\pi$
$524$		0			0
$525$	−2.94749	−	143.309i	−0.000245026	−	0.0119134i
$526$		0			0
$527$	2466.20	−	4271.58i	0.203851	−	0.353080i
$528$		0			0
$529$	5401.63	+	9355.90i	0.443958	+	0.768957i
$530$		0			0
$531$	−18462.6			−1.50887
$532$		0			0
$533$	−20698.7			−1.68210
$534$		0			0
$535$	3937.67	+	6820.24i	0.318206	+	0.551149i
$536$		0			0
$537$	−9.64123	+	16.6991i	−0.000774766	+	0.00134193i
$538$		0			0
$539$	5695.55	−	234.384i	0.455148	−	0.0187303i
$540$		0			0
$541$	−5551.37	+	9615.26i	−0.441168	+	0.764126i	−0.997776	−	0.0666491i	$-0.978769\pi$
$541$	−5551.37	+	9615.26i	−0.441168	+	0.764126i	0.556608	+	0.830775i	$0.312103\pi$
$542$		0			0
$543$	105.293	+	182.373i	0.00832148	+	0.0144132i
$544$		0			0
$545$	4585.25			0.360386
$546$		0			0
$547$	17160.3			1.34135			0.670677	−	0.741749i	$-0.266004\pi$
$547$	17160.3			1.34135			0.670677	+	0.741749i	$0.266004\pi$
$548$		0			0
$549$	−7424.19	−	12859.1i	−0.577152	−	0.999657i
$550$		0			0
$551$	−8226.91	+	14249.4i	−0.636076	+	1.10172i
$552$		0			0
$553$	−68.3158	−	3321.57i	−0.00525332	−	0.255421i
$554$		0			0
$555$	106.141	−	183.841i	0.00811789	−	0.0140606i
$556$		0			0
$557$	−11108.1	−	19239.7i	−0.844997	−	1.46358i	−0.885624	−	0.464403i	$-0.846269\pi$
$557$	−11108.1	−	19239.7i	−0.844997	−	1.46358i	0.0406273	−	0.999174i	$-0.487064\pi$
$558$		0			0
$559$	46070.3			3.48581
$560$		0			0
$561$	142.342			0.0107124
$562$		0			0
$563$	−4431.18	−	7675.03i	−0.331709	−	0.574536i	0.651138	−	0.758959i	$-0.274292\pi$
$563$	−4431.18	−	7675.03i	−0.331709	−	0.574536i	−0.982847	+	0.184423i	$0.940958\pi$
$564$		0			0
$565$	227.260	−	393.627i	0.0169220	−	0.0293097i
$566$		0			0
$567$	−11703.0	−	6439.54i	−0.866805	−	0.476958i
$568$		0			0
$569$	−10475.3	+	18143.8i	−0.771789	+	1.33678i	0.164793	+	0.986328i	$0.447304\pi$
$569$	−10475.3	+	18143.8i	−0.771789	+	1.33678i	−0.936582	+	0.350449i	$0.886029\pi$
$570$		0			0
$571$	−3895.39	−	6747.02i	−0.285494	−	0.494490i	0.687235	−	0.726435i	$-0.258824\pi$
$571$	−3895.39	−	6747.02i	−0.285494	−	0.494490i	−0.972729	+	0.231945i	$0.925491\pi$
$572$		0			0
$573$	−601.868			−0.0438803
$574$		0			0
$575$	−923.219			−0.0669581
$576$		0			0
$577$	1231.40	+	2132.84i	0.0888454	+	0.153885i	0.907023	−	0.421080i	$-0.138349\pi$
$577$	1231.40	+	2132.84i	0.0888454	+	0.153885i	−0.818178	+	0.574965i	$0.805016\pi$
$578$		0			0
$579$	105.393	−	182.547i	0.00756476	−	0.0131026i
$580$		0			0
$581$	11220.1	−	6789.32i	0.801186	−	0.484800i
$582$		0			0
$583$	4214.53	−	7299.78i	0.299396	−	0.518570i
$584$		0			0
$585$	−6165.48	−	10678.9i	−0.435746	−	0.754734i
$586$		0			0
$587$	−20438.3			−1.43710			−0.718551	−	0.695475i	$-0.755194\pi$
$587$	−20438.3			−1.43710			−0.718551	+	0.695475i	$0.755194\pi$
$588$		0			0
$589$	14016.6			0.980551
$590$		0			0
$591$	50.0379	+	86.6682i	0.00348271	+	0.00603224i
$592$		0			0
$593$	1341.34	−	2323.27i	0.0928873	−	0.160886i	−0.815838	−	0.578281i	$-0.803724\pi$
$593$	1341.34	−	2323.27i	0.0928873	−	0.160886i	0.908725	+	0.417396i	$0.137057\pi$
$594$		0			0
$595$	2191.85	−	1326.30i	0.151021	−	0.0913830i
$596$		0			0
$597$	−438.149	+	758.897i	−0.0300373	+	0.0520261i
$598$		0			0
$599$	−12842.9	−	22244.6i	−0.876039	−	1.51734i	−0.855652	−	0.517552i	$-0.826843\pi$
$599$	−12842.9	−	22244.6i	−0.876039	−	1.51734i	−0.0203871	−	0.999792i	$-0.506490\pi$
$600$		0			0
$601$	6960.19			0.472400			0.236200	−	0.971705i	$-0.424098\pi$
$601$	6960.19			0.472400			0.236200	+	0.971705i	$0.424098\pi$
$602$		0			0
$603$	−4885.58			−0.329944
$604$		0			0
$605$	2637.01	+	4567.43i	0.177206	+	0.306930i
$606$		0			0
$607$	13746.5	−	23809.7i	0.919199	−	1.59210i	0.118565	−	0.992946i	$-0.462171\pi$
$607$	13746.5	−	23809.7i	0.919199	−	1.59210i	0.800634	−	0.599153i	$-0.204496\pi$
$608$		0			0
$609$	−1051.31	−	578.480i	−0.0699525	−	0.0384913i
$610$		0			0
$611$	−20707.7	+	35866.8i	−1.37110	+	2.37482i
$612$		0			0
$613$	7280.71	+	12610.6i	0.479715	+	0.830890i	0.999729	−	0.0232673i	$-0.00740687\pi$
$613$	7280.71	+	12610.6i	0.479715	+	0.830890i	−0.520015	+	0.854157i	$0.674074\pi$
$614$		0			0
$615$	−349.530			−0.0229177
$616$		0			0
$617$	−15433.9			−1.00704			−0.503522	−	0.863983i	$-0.667963\pi$
$617$	−15433.9			−1.00704			−0.503522	+	0.863983i	$0.667963\pi$
$618$		0			0
$619$	3792.25	+	6568.37i	0.246241	+	0.426503i	0.962480	−	0.271353i	$-0.0874710\pi$
$619$	3792.25	+	6568.37i	0.246241	+	0.426503i	−0.716238	+	0.697856i	$0.754138\pi$
$620$		0			0
$621$	308.131	−	533.699i	0.0199112	−	0.0344873i
$622$		0			0
$623$	330.901	+	16088.7i	0.0212797	+	1.03464i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	202.249	+	350.306i	0.0128821	+	0.0223124i
$628$		0			0
$629$	3794.09			0.240509
$630$		0			0
$631$	−14755.4			−0.930905			−0.465453	−	0.885073i	$-0.654108\pi$
$631$	−14755.4			−0.930905			−0.465453	+	0.885073i	$0.654108\pi$
$632$		0			0
$633$	−385.244	−	667.261i	−0.0241897	−	0.0418977i
$634$		0			0
$635$	−751.904	+	1302.34i	−0.0469896	+	0.0813884i
$636$		0			0
$637$	−14587.8	+	27852.4i	−0.907363	+	1.73242i
$638$		0			0
$639$	−11202.9	+	19404.0i	−0.693552	+	1.20127i
$640$		0			0
$641$	−14418.3	−	24973.2i	−0.888438	−	1.53882i	−0.841722	−	0.539911i	$-0.818458\pi$
$641$	−14418.3	−	24973.2i	−0.888438	−	1.53882i	−0.0467161	−	0.998908i	$-0.514876\pi$
$642$		0			0
$643$	24838.4			1.52338			0.761689	−	0.647943i	$-0.224371\pi$
$643$	24838.4			1.52338			0.761689	+	0.647943i	$0.224371\pi$
$644$		0			0
$645$	777.969			0.0474922
$646$		0			0
$647$	−3594.13	−	6225.22i	−0.218392	−	0.378267i	0.735924	−	0.677064i	$-0.236748\pi$
$647$	−3594.13	−	6225.22i	−0.218392	−	0.378267i	−0.954317	+	0.298797i	$0.903415\pi$
$648$		0			0
$649$	5702.33	−	9876.73i	0.344894	−	0.597374i
$650$		0			0
$651$	21.0197	+	1022.00i	0.00126548	+	0.0615286i
$652$		0			0
$653$	−3585.82	+	6210.83i	−0.214891	+	0.372203i	−0.953239	−	0.302218i	$-0.902273\pi$
$653$	−3585.82	+	6210.83i	−0.214891	+	0.372203i	0.738348	+	0.674420i	$0.235606\pi$
$654$		0			0
$655$	2302.36	+	3987.80i	0.137344	+	0.237887i
$656$		0			0
$657$	9189.45			0.545684
$658$		0			0
$659$	−8236.07			−0.486847			−0.243423	−	0.969920i	$-0.578270\pi$
$659$	−8236.07			−0.486847			−0.243423	+	0.969920i	$0.578270\pi$
$660$		0			0
$661$	8487.12	+	14700.1i	0.499411	+	0.865005i	1.00000		0.000680243i	$-0.000216528\pi$
$661$	8487.12	+	14700.1i	0.499411	+	0.865005i	−0.500589	+	0.865685i	$0.666883\pi$
$662$		0			0
$663$	−392.554	+	679.924i	−0.0229948	+	0.0398282i
$664$		0			0
$665$	6378.39	+	3509.70i	0.371945	+	0.204662i
$666$		0			0
$667$	−3864.32	+	6693.19i	−0.224328	+	0.388548i
$668$		0			0
$669$	−308.707	−	534.696i	−0.0178405	−	0.0309007i
$670$		0			0
$671$	9172.10			0.527698
$672$		0			0
$673$	16220.1			0.929032			0.464516	−	0.885565i	$-0.346228\pi$
$673$	16220.1			0.929032			0.464516	+	0.885565i	$0.346228\pi$
$674$		0			0
$675$	−208.598	−	361.303i	−0.0118948	−	0.0206023i
$676$		0			0
$677$	−3200.14	+	5542.80i	−0.181671	+	0.314664i	−0.942450	−	0.334348i	$-0.891484\pi$
$677$	−3200.14	+	5542.80i	−0.181671	+	0.314664i	0.760779	+	0.649011i	$0.224817\pi$
$678$		0			0
$679$	−12694.3	+	7681.36i	−0.717471	+	0.434144i
$680$		0			0
$681$	−275.280	+	476.798i	−0.0154901	+	0.0268296i
$682$		0			0
$683$	−8278.16	−	14338.2i	−0.463770	−	0.803273i	0.535375	−	0.844614i	$-0.320170\pi$
$683$	−8278.16	−	14338.2i	−0.463770	−	0.803273i	−0.999145	+	0.0413413i	$0.986837\pi$
$684$		0			0
$685$	13832.7			0.771564
$686$		0			0
$687$	313.192			0.0173930
$688$		0			0
$689$	23246.0	+	40263.2i	1.28534	+	2.22628i
$690$		0			0
$691$	−3728.61	+	6458.15i	−0.205272	+	0.355542i	−0.950219	−	0.311581i	$-0.899141\pi$
$691$	−3728.61	+	6458.15i	−0.205272	+	0.355542i	0.744947	+	0.667124i	$0.232475\pi$
$692$		0			0
$693$	7084.78	−	4287.02i	0.388353	−	0.234994i
$694$		0			0
$695$	−6839.36	+	11846.1i	−0.373283	+	0.646545i
$696$		0			0
$697$	−3123.55	−	5410.15i	−0.169746	−	0.294009i
$698$		0			0
$699$	−1017.05			−0.0550337
$700$		0			0
$701$	26830.5			1.44561			0.722807	−	0.691050i	$-0.242852\pi$
$701$	26830.5			1.44561			0.722807	+	0.691050i	$0.242852\pi$
$702$		0			0
$703$	5390.91	+	9337.34i	0.289221	+	0.500945i
$704$		0			0
$705$	−349.682	+	605.667i	−0.0186805	+	0.0323556i
$706$		0			0
$707$	−15310.2	−	8424.40i	−0.814424	−	0.448136i
$708$		0			0
$709$	−3604.94	+	6243.95i	−0.190954	+	0.330742i	−0.945567	−	0.325428i	$-0.894492\pi$
$709$	−3604.94	+	6243.95i	−0.190954	+	0.330742i	0.754613	+	0.656171i	$0.227825\pi$
$710$		0			0
$711$	−2413.11	−	4179.63i	−0.127284	−	0.220462i
$712$		0			0
$713$	6583.84			0.345816
$714$		0			0
$715$	7617.05			0.398408
$716$		0			0
$717$	519.448	+	899.710i	0.0270560	+	0.0468623i
$718$		0			0
$719$	13975.8	−	24206.8i	0.724908	−	1.25558i	−0.234104	−	0.972211i	$-0.575216\pi$
$719$	13975.8	−	24206.8i	0.724908	−	1.25558i	0.959012	−	0.283365i	$-0.0914509\pi$
$720$		0			0
$721$	−64.4251	−	3132.40i	−0.00332776	−	0.161799i
$722$		0			0
$723$	−447.777	+	775.572i	−0.0230332	+	0.0398947i
$724$		0			0
$725$	2616.06	+	4531.15i	0.134011	+	0.232114i
$726$		0			0
$727$	2492.55			0.127158			0.0635788	−	0.997977i	$-0.479749\pi$
$727$	2492.55			0.127158			0.0635788	+	0.997977i	$0.479749\pi$
$728$		0			0
$729$	−19265.0			−0.978765
$730$		0			0
$731$	6952.28	+	12041.7i	0.351764	+	0.609272i
$732$		0			0
$733$	5065.28	−	8773.32i	0.255239	−	0.442087i	−0.709721	−	0.704483i	$-0.751179\pi$
$733$	5065.28	−	8773.32i	0.255239	−	0.442087i	0.964960	+	0.262395i	$0.0845125\pi$
$734$		0			0
$735$	−246.338	+	470.331i	−0.0123623	+	0.0236033i
$736$		0			0
$737$	1508.95	−	2613.59i	0.0754180	−	0.130628i
$738$		0			0
$739$	3660.25	+	6339.73i	0.182198	+	0.315576i	0.942629	−	0.333843i	$-0.108345\pi$
$739$	3660.25	+	6339.73i	0.182198	+	0.315576i	−0.760431	+	0.649419i	$0.775012\pi$
$740$		0			0
$741$	−2231.08			−0.110608
$742$		0			0
$743$	−16974.1			−0.838116			−0.419058	−	0.907959i	$-0.637640\pi$
$743$	−16974.1			−0.838116			−0.419058	+	0.907959i	$0.637640\pi$
$744$		0			0
$745$	−6670.71	−	11554.0i	−0.328048	−	0.568196i
$746$		0			0
$747$	9525.52	−	16498.7i	0.466560	−	0.808106i
$748$		0			0
$749$	−599.835	−	29164.5i	−0.0292623	−	1.42276i
$750$		0			0
$751$	8857.32	−	15341.3i	0.430370	−	0.745423i	−0.566535	−	0.824038i	$-0.691716\pi$
$751$	8857.32	−	15341.3i	0.430370	−	0.745423i	0.996905	+	0.0786146i	$0.0250496\pi$
$752$		0			0
$753$	1005.78	+	1742.07i	0.0486757	+	0.0843088i
$754$		0			0
$755$	−11532.8			−0.555923
$756$		0			0
$757$	30171.9			1.44864			0.724318	−	0.689467i	$-0.242155\pi$
$757$	30171.9			1.44864			0.724318	+	0.689467i	$0.242155\pi$
$758$		0			0
$759$	94.9998	+	164.545i	0.00454318	+	0.00786902i
$760$		0			0
$761$	−7211.78	+	12491.2i	−0.343531	+	0.595013i	−0.985086	−	0.172064i	$-0.944956\pi$
$761$	−7211.78	+	12491.2i	−0.343531	+	0.595013i	0.641555	+	0.767077i	$0.278290\pi$
$762$		0			0
$763$	−14880.1	−	8187.75i	−0.706022	−	0.388488i
$764$		0			0
$765$	1860.81	−	3223.02i	0.0879449	−	0.152325i
$766$		0			0
$767$	31452.2	+	54476.8i	1.48067	+	2.56459i
$768$		0			0
$769$	−21410.8			−1.00402			−0.502010	−	0.864862i	$-0.667406\pi$
$769$	−21410.8			−1.00402			−0.502010	+	0.864862i	$0.667406\pi$
$770$		0			0
$771$	699.268			0.0326634
$772$		0			0
$773$	−13566.1	−	23497.1i	−0.631227	−	1.09332i	−0.987301	−	0.158859i	$-0.949218\pi$
$773$	−13566.1	−	23497.1i	−0.631227	−	1.09332i	0.356075	−	0.934457i	$-0.384115\pi$
$774$		0			0
$775$	2228.56	−	3859.98i	0.103293	−	0.178909i
$776$		0			0
$777$	−672.730	+	407.071i	−0.0310606	+	0.0187948i
$778$		0			0
$779$	8876.33	−	15374.3i	0.408251	−	0.707112i
$780$		0			0
$781$	−6920.23	−	11986.2i	−0.317062	−	0.549167i
$782$		0			0
$783$	−3492.52			−0.159403
$784$		0			0
$785$	−9908.08			−0.450490
$786$		0			0
$787$	6543.76	+	11334.1i	0.296391	+	0.513364i	0.975308	−	0.220851i	$-0.0708835\pi$
$787$	6543.76	+	11334.1i	0.296391	+	0.513364i	−0.678917	+	0.734215i	$0.737550\pi$
$788$		0			0
$789$	−20.8814	+	36.1677i	−0.000942204	+	0.00163194i
$790$		0			0
$791$	−1440.40	+	871.587i	−0.0647466	+	0.0391784i
$792$		0			0
$793$	−25295.1	+	43812.5i	−1.13273	+	1.96195i
$794$		0			0
$795$	392.544	+	679.907i	0.0175121	+	0.0303318i
$796$		0			0
$797$	19398.5			0.862147			0.431074	−	0.902317i	$-0.358135\pi$
$797$	19398.5			0.862147			0.431074	+	0.902317i	$0.358135\pi$
$798$		0			0
$799$	−12499.6			−0.553449
$800$		0			0
$801$	11688.4	+	20244.9i	0.515592	+	0.893032i
$802$		0			0
$803$	−2838.24	+	4915.98i	−0.124731	+	0.216041i
$804$		0			0
$805$	2996.04	+	1648.57i	0.131176	+	0.0721793i
$806$		0			0
$807$	−1010.88	+	1750.89i	−0.0440949	+	0.0763747i
$808$		0			0
$809$	10792.0	+	18692.4i	0.469008	+	0.812346i	0.999372	−	0.0354238i	$-0.0112781\pi$
$809$	10792.0	+	18692.4i	0.469008	+	0.812346i	−0.530364	+	0.847770i	$0.677945\pi$
$810$		0			0
$811$	26798.2			1.16031			0.580156	−	0.814505i	$-0.302991\pi$
$811$	26798.2			1.16031			0.580156	+	0.814505i	$0.302991\pi$
$812$		0			0
$813$	664.827			0.0286796
$814$		0			0
$815$	−2707.90	−	4690.22i	−0.116385	−	0.201584i
$816$		0			0
$817$	−19756.6	+	34219.4i	−0.846016	+	1.46534i
$818$		0			0
$819$	939.204	+	45664.9i	0.0400713	+	1.94830i
$820$		0			0
$821$	−1115.88	+	1932.75i	−0.0474352	+	0.0821602i	−0.888768	−	0.458357i	$-0.848438\pi$
$821$	−1115.88	+	1932.75i	−0.0474352	+	0.0821602i	0.841333	+	0.540517i	$0.181771\pi$
$822$		0			0
$823$	15084.3	+	26126.7i	0.638888	+	1.10659i	0.985677	+	0.168643i	$0.0539386\pi$
$823$	15084.3	+	26126.7i	0.638888	+	1.10659i	−0.346789	+	0.937943i	$0.612728\pi$
$824$		0			0
$825$	128.626			0.00542809
$826$		0			0
$827$	18201.0			0.765310			0.382655	−	0.923891i	$-0.375010\pi$
$827$	18201.0			0.765310			0.382655	+	0.923891i	$0.375010\pi$
$828$		0			0
$829$	−2428.84	−	4206.87i	−0.101758	−	0.176249i	0.810651	−	0.585529i	$-0.199113\pi$
$829$	−2428.84	−	4206.87i	−0.101758	−	0.176249i	−0.912409	+	0.409280i	$0.865780\pi$
$830$		0			0
$831$	1211.72	−	2098.76i	0.0505825	−	0.0876115i
$832$		0			0
$833$	−9481.35	+	390.177i	−0.394369	+	0.0162291i
$834$		0			0
$835$	3009.43	−	5212.49i	0.124725	−	0.216031i
$836$		0			0
$837$	1487.60	+	2576.60i	0.0614324	+	0.106404i
$838$		0			0
$839$	27903.8			1.14821			0.574104	−	0.818783i	$-0.305351\pi$
$839$	27903.8			1.14821			0.574104	+	0.818783i	$0.305351\pi$
$840$		0			0
$841$	19411.2			0.795900
$842$		0			0
$843$	−918.613	−	1591.08i	−0.0375311	−	0.0650057i
$844$		0			0
$845$	−15514.1	+	26871.1i	−0.631597	+	1.09396i
$846$		0			0
$847$	−401.702	−	19531.1i	−0.0162959	−	0.792322i
$848$		0			0
$849$	−810.844	+	1404.42i	−0.0327775	+	0.0567723i
$850$		0			0
$851$	2532.20	+	4385.91i	0.102001	+	0.176671i
$852$		0			0
$853$	14219.1			0.570755			0.285377	−	0.958415i	$-0.407881\pi$
$853$	14219.1			0.570755			0.285377	+	0.958415i	$0.407881\pi$
$854$		0			0
$855$	10575.9			0.423028
$856$		0			0
$857$	7293.37	+	12632.5i	0.290708	+	0.503521i	0.973977	−	0.226646i	$-0.0727759\pi$
$857$	7293.37	+	12632.5i	0.290708	+	0.503521i	−0.683269	+	0.730166i	$0.739443\pi$
$858$		0			0
$859$	−13305.2	+	23045.2i	−0.528482	+	0.915358i	0.470966	+	0.882151i	$0.343905\pi$
$859$	−13305.2	+	23045.2i	−0.528482	+	0.915358i	−0.999448	+	0.0332070i	$0.989428\pi$
$860$		0			0
$861$	1134.30	+	624.145i	0.0448975	+	0.0247048i
$862$		0			0
$863$	−2530.39	+	4382.77i	−0.0998095	+	0.172875i	−0.911606	−	0.411066i	$-0.865157\pi$
$863$	−2530.39	+	4382.77i	−0.0998095	+	0.172875i	0.811796	+	0.583941i	$0.198490\pi$
$864$		0			0
$865$	−6709.48	−	11621.2i	−0.263733	−	0.456799i
$866$		0			0
$867$	1284.03			0.0502976
$868$		0			0
$869$	2981.24			0.116377
$870$		0			0
$871$	8322.89	+	14415.7i	0.323778	+	0.560800i
$872$		0			0
$873$	−10777.1	+	18666.4i	−0.417810	+	0.723669i
$874$		0			0
$875$	1980.65	−	1198.50i	0.0765237	−	0.0463047i
$876$		0			0
$877$	13807.6	−	23915.5i	0.531643	−	0.920832i	−0.467675	−	0.883900i	$-0.654908\pi$
$877$	13807.6	−	23915.5i	0.531643	−	0.920832i	0.999318	−	0.0369317i	$-0.0117584\pi$
$878$		0			0
$879$	−551.827	−	955.792i	−0.0211748	−	0.0366758i
$880$		0			0
$881$	−40580.4			−1.55186			−0.775931	−	0.630818i	$-0.782719\pi$
$881$	−40580.4			−1.55186			−0.775931	+	0.630818i	$0.782719\pi$
$882$		0			0
$883$	−1567.20			−0.0597289			−0.0298645	−	0.999554i	$-0.509508\pi$
$883$	−1567.20			−0.0597289			−0.0298645	+	0.999554i	$0.509508\pi$
$884$		0			0
$885$	531.119	+	919.926i	0.0201733	+	0.0349412i
$886$		0			0
$887$	−7576.55	+	13123.0i	−0.286805	+	0.496760i	−0.973045	−	0.230614i	$-0.925926\pi$
$887$	−7576.55	+	13123.0i	−0.286805	+	0.496760i	0.686241	+	0.727375i	$0.259260\pi$
$888$		0			0
$889$	4765.63	−	2883.70i	0.179791	−	0.108792i
$890$		0			0
$891$	5993.25	−	10380.6i	0.225344	−	0.390307i
$892$		0			0
$893$	−17760.4	−	30761.9i	−0.665542	−	1.15275i
$894$		0			0
$895$	−311.425			−0.0116310
$896$		0			0
$897$	−1047.97			−0.0390088
$898$		0			0
$899$	−18656.2	−	32313.5i	−0.692123	−	1.19879i
$900$		0			0
$901$	−7015.90	+	12151.9i	−0.259416	+	0.449321i
$902$		0			0
$903$	−2524.67	−	1389.20i	−0.0930407	−	0.0511956i
$904$		0			0
$905$	−1700.56	+	2945.45i	−0.0624624	+	0.108188i
$906$		0			0
$907$	22828.8	+	39540.6i	0.835741	+	1.44755i	0.893425	+	0.449212i	$0.148295\pi$
$907$	22828.8	+	39540.6i	0.835741	+	1.44755i	−0.0576841	+	0.998335i	$0.518372\pi$
$908$		0			0
$909$	−25385.5			−0.926277
$910$		0			0
$911$	12137.4			0.441417			0.220709	−	0.975340i	$-0.429163\pi$
$911$	12137.4			0.441417			0.220709	+	0.975340i	$0.429163\pi$
$912$		0			0
$913$	5884.08	+	10191.5i	0.213291	+	0.369431i
$914$		0			0
$915$	−427.148	+	739.842i	−0.0154329	+	0.0267305i
$916$		0			0
$917$	−350.724	−	17052.5i	−0.0126302	−	0.614093i
$918$		0			0
$919$	−11352.0	+	19662.2i	−0.407473	+	0.705763i	−0.994606	−	0.103727i	$-0.966923\pi$
$919$	−11352.0	+	19662.2i	−0.407473	+	0.705763i	0.587133	+	0.809490i	$0.300256\pi$
$920$		0			0
$921$	−899.204	−	1557.47i	−0.0321713	−	0.0557224i
$922$		0			0
$923$	76339.4			2.72236
$924$		0			0
$925$	3428.50			0.121868
$926$		0			0
$927$	−2275.68	−	3941.60i	−0.0806292	−	0.139654i
$928$		0			0
$929$	5669.56	−	9819.97i	0.200229	−	0.346806i	−0.748373	−	0.663278i	$-0.769165\pi$
$929$	5669.56	−	9819.97i	0.200229	−	0.346806i	0.948602	+	0.316472i	$0.102498\pi$
$930$		0			0
$931$	−14432.0	−	22779.4i	−0.508045	−	0.801896i
$932$		0			0
$933$	−215.847	+	373.858i	−0.00757398	+	0.0131185i
$934$		0			0
$935$	1149.46	+	1990.92i	0.0402046	+	0.0696364i
$936$		0			0
$937$	52101.8			1.81653			0.908267	−	0.418391i	$-0.137406\pi$
$937$	52101.8			1.81653			0.908267	+	0.418391i	$0.137406\pi$
$938$		0			0
$939$	1839.73			0.0639375
$940$		0			0
$941$	22432.9	+	38855.0i	0.777144	+	1.34605i	0.933582	+	0.358365i	$0.116666\pi$
$941$	22432.9	+	38855.0i	0.777144	+	1.34605i	−0.156438	+	0.987688i	$0.550001\pi$
$942$		0			0
$943$	4169.36	−	7221.55i	0.143980	−	0.249381i
$944$		0			0
$945$	31.7763	+	1544.99i	0.00109385	+	0.0531837i
$946$		0			0
$947$	−16044.2	+	27789.4i	−0.550547	+	0.953575i	0.447688	+	0.894190i	$0.352247\pi$
$947$	−16044.2	+	27789.4i	−0.550547	+	0.953575i	−0.998235	+	0.0593855i	$0.981086\pi$
$948$		0			0
$949$	−15654.8	−	27114.9i	−0.535486	−	0.927489i
$950$		0			0
$951$	−446.702			−0.0152317
$952$		0			0
$953$	17825.8			0.605913			0.302957	−	0.953004i	$-0.402026\pi$
$953$	17825.8			0.605913			0.302957	+	0.953004i	$0.402026\pi$
$954$		0			0
$955$	−4860.29	−	8418.27i	−0.164686	−	0.285245i
$956$		0			0
$957$	538.389	−	932.517i	0.0181856	−	0.0314984i
$958$		0			0
$959$	−44890.1	−	24700.7i	−1.51155	−	0.831728i
$960$		0			0
$961$	−997.269	+	1727.32i	−0.0334755	+	0.0579813i
$962$		0			0
$963$	−21187.9	−	36698.5i	−0.709004	−	1.22803i
$964$		0			0
$965$	3404.35			0.113565
$966$		0			0
$967$	−34128.6			−1.13495			−0.567477	−	0.823389i	$-0.692080\pi$
$967$	−34128.6			−1.13495			−0.567477	+	0.823389i	$0.692080\pi$
$968$		0			0
$969$	−336.683	−	583.152i	−0.0111618	−	0.0193328i
$970$		0			0
$971$	21040.9	−	36443.9i	0.695401	−	1.20447i	−0.274645	−	0.961546i	$-0.588560\pi$
$971$	21040.9	−	36443.9i	0.695401	−	1.20447i	0.970045	−	0.242924i	$-0.0781065\pi$
$972$		0			0
$973$	43348.4	−	26230.3i	1.42825	−	0.864238i
$974$		0			0
$975$	−354.729	+	614.408i	−0.0116517	+	0.0201813i
$976$		0			0
$977$	400.588	+	693.839i	0.0131177	+	0.0227204i	0.872510	−	0.488597i	$-0.162491\pi$
$977$	400.588	+	693.839i	0.0131177	+	0.0227204i	−0.859392	+	0.511317i	$0.829158\pi$
$978$		0			0
$979$	−14440.3			−0.471412
$980$		0			0
$981$	−24672.4			−0.802987
$982$		0			0
$983$	4.48329	+	7.76529i	0.000145468	+	0.000251957i	0.866098	−	0.499874i	$-0.166620\pi$
$983$	4.48329	+	7.76529i	0.000145468	+	0.000251957i	−0.865953	+	0.500126i	$0.833287\pi$
$984$		0			0
$985$	−808.147	+	1399.75i	−0.0261418	+	0.0452790i
$986$		0			0
$987$	2216.31	−	1341.10i	0.0714752	−	0.0432498i
$988$		0			0
$989$	−9280.00	+	16073.4i	−0.298369	+	0.516790i
$990$		0			0
$991$	−4405.91	−	7631.26i	−0.141229	−	0.244617i	0.786730	−	0.617297i	$-0.211772\pi$
$991$	−4405.91	−	7631.26i	−0.141229	−	0.244617i	−0.927960	+	0.372680i	$0.878439\pi$
$992$		0			0
$993$	1823.73			0.0582824
$994$		0			0
$995$	−14152.8			−0.450929
$996$		0			0
$997$	−28762.5	−	49818.1i	−0.913658	−	1.58250i	−0.808854	−	0.588009i	$-0.799912\pi$
$997$	−28762.5	−	49818.1i	−0.913658	−	1.58250i	−0.104804	−	0.994493i	$-0.533422\pi$
$998$		0			0
$999$	−1144.29	+	1981.96i	−0.0362399	+	0.0627693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.4.q.l.401.1		4
4.3	odd	2		140.4.i.c.121.2	yes	4
7.4	even	3	inner	560.4.q.l.81.1		4
12.11	even	2		1260.4.s.e.541.1		4
20.3	even	4		700.4.r.f.149.3		8
20.7	even	4		700.4.r.f.149.2		8
20.19	odd	2		700.4.i.h.401.1		4
28.3	even	6		980.4.i.w.361.1		4
28.11	odd	6		140.4.i.c.81.2	✓	4
28.19	even	6		980.4.a.n.1.2		2
28.23	odd	6		980.4.a.u.1.1		2
28.27	even	2		980.4.i.w.961.1		4
84.11	even	6		1260.4.s.e.361.1		4
140.39	odd	6		700.4.i.h.501.1		4
140.67	even	12		700.4.r.f.249.3		8
140.123	even	12		700.4.r.f.249.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.4.i.c.81.2	✓	4	28.11	odd	6
140.4.i.c.121.2	yes	4	4.3	odd	2
560.4.q.l.81.1		4	7.4	even	3	inner
560.4.q.l.401.1		4	1.1	even	1	trivial
700.4.i.h.401.1		4	20.19	odd	2
700.4.i.h.501.1		4	140.39	odd	6
700.4.r.f.149.2		8	20.7	even	4
700.4.r.f.149.3		8	20.3	even	4
700.4.r.f.249.2		8	140.123	even	12
700.4.r.f.249.3		8	140.67	even	12
980.4.a.n.1.2		2	28.19	even	6
980.4.a.u.1.1		2	28.23	odd	6
980.4.i.w.361.1		4	28.3	even	6
980.4.i.w.961.1		4	28.27	even	2
1260.4.s.e.361.1		4	84.11	even	6
1260.4.s.e.541.1		4	12.11	even	2

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.154792 + 0.268108i) q^{3} +(-2.50000 + 4.33013i) q^{5} +(15.8452 - 9.58798i) q^{7} +(13.4521 - 23.2997i) q^{9} +O(q^{10})\)	\(q+(0.154792 + 0.268108i) q^{3} +(-2.50000 + 4.33013i) q^{5} +(15.8452 - 9.58798i) q^{7} +(13.4521 - 23.2997i) q^{9} +(8.30958 + 14.3926i) q^{11} -91.6658 q^{13} -1.54792 q^{15} +(-13.8329 - 23.9593i) q^{17} +(39.3096 - 68.0862i) q^{19} +(5.02333 + 2.76408i) q^{21} +(18.4644 - 31.9812i) q^{23} +(-12.5000 - 21.6506i) q^{25} +16.6879 q^{27} -209.285 q^{29} +(89.1425 + 154.399i) q^{31} +(-2.57252 + 4.45573i) q^{33} +(1.90416 + 92.5817i) q^{35} +(-68.5700 + 118.767i) q^{37} +(-14.1891 - 24.5763i) q^{39} +225.806 q^{41} -502.589 q^{43} +(67.2604 + 116.498i) q^{45} +(225.904 - 391.277i) q^{47} +(159.141 - 303.847i) q^{49} +(4.28245 - 7.41742i) q^{51} +(-253.595 - 439.239i) q^{53} -83.0958 q^{55} +24.3393 q^{57} +(-343.118 - 594.298i) q^{59} +(275.950 - 477.959i) q^{61} +(-10.2460 - 498.167i) q^{63} +(229.165 - 396.925i) q^{65} +(-90.7960 - 157.263i) q^{67} +11.4326 q^{69} -832.801 q^{71} +(170.781 + 295.802i) q^{73} +(3.86980 - 6.70270i) q^{75} +(269.663 + 148.382i) q^{77} +(89.6930 - 155.353i) q^{79} +(-360.623 - 624.617i) q^{81} +708.108 q^{83} +138.329 q^{85} +(-32.3957 - 56.1109i) q^{87} +(-434.446 + 752.482i) q^{89} +(-1452.46 + 878.890i) q^{91} +(-27.5971 + 47.7996i) q^{93} +(196.548 + 340.431i) q^{95} -801.145 q^{97} +447.125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{3} - 10 q^{5} + 54 q^{7} - 40 q^{9}+O(q^{10}) \) 4 * q + 10 * q^3 - 10 * q^5 + 54 * q^7 - 40 * q^9	\( 4 q + 10 q^{3} - 10 q^{5} + 54 q^{7} - 40 q^{9} + 52 q^{11} - 104 q^{13} - 100 q^{15} + 76 q^{17} + 176 q^{19} - 130 q^{21} + 102 q^{23} - 50 q^{25} - 740 q^{27} - 612 q^{29} + 244 q^{31} - 348 q^{33} - 180 q^{35} + 176 q^{37} + 356 q^{39} - 260 q^{41} - 228 q^{43} - 200 q^{45} + 716 q^{47} + 130 q^{49} - 996 q^{51} - 808 q^{53} - 520 q^{55} + 1936 q^{57} - 1016 q^{59} + 222 q^{61} - 2480 q^{63} + 260 q^{65} + 134 q^{67} + 1284 q^{69} - 592 q^{71} - 724 q^{73} + 250 q^{75} + 28 q^{77} + 1128 q^{79} - 2662 q^{81} - 676 q^{83} - 760 q^{85} - 1002 q^{87} + 326 q^{89} - 2020 q^{91} - 692 q^{93} + 880 q^{95} - 3880 q^{97} - 3840 q^{99}+O(q^{100}) \) 4 * q + 10 * q^3 - 10 * q^5 + 54 * q^7 - 40 * q^9 + 52 * q^11 - 104 * q^13 - 100 * q^15 + 76 * q^17 + 176 * q^19 - 130 * q^21 + 102 * q^23 - 50 * q^25 - 740 * q^27 - 612 * q^29 + 244 * q^31 - 348 * q^33 - 180 * q^35 + 176 * q^37 + 356 * q^39 - 260 * q^41 - 228 * q^43 - 200 * q^45 + 716 * q^47 + 130 * q^49 - 996 * q^51 - 808 * q^53 - 520 * q^55 + 1936 * q^57 - 1016 * q^59 + 222 * q^61 - 2480 * q^63 + 260 * q^65 + 134 * q^67 + 1284 * q^69 - 592 * q^71 - 724 * q^73 + 250 * q^75 + 28 * q^77 + 1128 * q^79 - 2662 * q^81 - 676 * q^83 - 760 * q^85 - 1002 * q^87 + 326 * q^89 - 2020 * q^91 - 692 * q^93 + 880 * q^95 - 3880 * q^97 - 3840 * q^99

Introduction

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