LMFDB - Embedded newform 160.6.n.b.63.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(63,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.n (of order $4$, degree $2$, 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:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} + \cdots + 69451154208 $ x^14 - 4x^13 + 8x^12 - 4626x^11 + 149441x^10 - 2113414x^9 + 17958066x^8 - 97717112x^7 + 355171384x^6 - 910571904x^5 + 2428303248x^4 - 9166992192x^3 + 32237484304x^2 - 66916821408*x + 69451154208
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{31}\cdot 5^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.2
Root			$3.77108 + 3.77108i$ of defining polynomial
Character	$\chi$	$=$	160.63
Dual form			160.6.n.b.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.4331 + 13.4331i) q^{3} +(15.0352 + 53.8418i) q^{5} +(-76.4413 - 76.4413i) q^{7} -117.896i q^{9} +O(q^{10})$	\(q+(-13.4331 + 13.4331i) q^{3} +(15.0352 + 53.8418i) q^{5} +(-76.4413 - 76.4413i) q^{7} -117.896i q^{9} -622.995i q^{11} +(-293.552 - 293.552i) q^{13} +(-925.232 - 521.293i) q^{15} +(-1153.02 + 1153.02i) q^{17} +2003.44 q^{19} +2053.69 q^{21} +(1392.29 - 1392.29i) q^{23} +(-2672.88 + 1619.05i) q^{25} +(-1680.53 - 1680.53i) q^{27} +305.819i q^{29} +2108.06i q^{31} +(8368.75 + 8368.75i) q^{33} +(2966.43 - 5265.05i) q^{35} +(9903.12 - 9903.12i) q^{37} +7886.62 q^{39} +16996.0 q^{41} +(-2031.28 + 2031.28i) q^{43} +(6347.74 - 1772.59i) q^{45} +(-682.885 - 682.885i) q^{47} -5120.46i q^{49} -30977.2i q^{51} +(21092.5 + 21092.5i) q^{53} +(33543.2 - 9366.86i) q^{55} +(-26912.4 + 26912.4i) q^{57} +11617.4 q^{59} -1309.80 q^{61} +(-9012.12 + 9012.12i) q^{63} +(11391.8 - 20219.0i) q^{65} +(-39870.6 - 39870.6i) q^{67} +37405.7i q^{69} +25454.3i q^{71} +(1031.25 + 1031.25i) q^{73} +(14156.3 - 57653.9i) q^{75} +(-47622.5 + 47622.5i) q^{77} -11849.6 q^{79} +73798.3 q^{81} +(45180.7 - 45180.7i) q^{83} +(-79416.5 - 44744.7i) q^{85} +(-4108.09 - 4108.09i) q^{87} -143889. i q^{89} +44879.0i q^{91} +(-28317.8 - 28317.8i) q^{93} +(30122.1 + 107869. i) q^{95} +(-24390.9 + 24390.9i) q^{97} -73448.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7}+O(q^{10}) $ 14 * q + 10 * q^3 + 42 * q^5 + 66 * q^7	$ 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7} - 414 q^{13} + 278 q^{15} + 1222 q^{17} + 5672 q^{19} + 5924 q^{21} + 2902 q^{23} - 4466 q^{25} - 2168 q^{27} - 2444 q^{33} - 2618 q^{35} - 1790 q^{37} - 11076 q^{39} + 11644 q^{41} - 3982 q^{43} + 14704 q^{45} - 1278 q^{47} + 5882 q^{53} + 65608 q^{55} - 14552 q^{57} - 8504 q^{59} + 20564 q^{61} + 19422 q^{63} + 40798 q^{65} + 107926 q^{67} - 16418 q^{73} + 66586 q^{75} - 13348 q^{77} - 146544 q^{79} + 173806 q^{81} - 36398 q^{83} - 66262 q^{85} + 124384 q^{87} - 306620 q^{93} + 173768 q^{95} - 60314 q^{97} - 388628 q^{99}+O(q^{100}) $ 14 * q + 10 * q^3 + 42 * q^5 + 66 * q^7 - 414 * q^13 + 278 * q^15 + 1222 * q^17 + 5672 * q^19 + 5924 * q^21 + 2902 * q^23 - 4466 * q^25 - 2168 * q^27 - 2444 * q^33 - 2618 * q^35 - 1790 * q^37 - 11076 * q^39 + 11644 * q^41 - 3982 * q^43 + 14704 * q^45 - 1278 * q^47 + 5882 * q^53 + 65608 * q^55 - 14552 * q^57 - 8504 * q^59 + 20564 * q^61 + 19422 * q^63 + 40798 * q^65 + 107926 * q^67 - 16418 * q^73 + 66586 * q^75 - 13348 * q^77 - 146544 * q^79 + 173806 * q^81 - 36398 * q^83 - 66262 * q^85 + 124384 * q^87 - 306620 * q^93 + 173768 * q^95 - 60314 * q^97 - 388628 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−13.4331	+	13.4331i	−0.861733	+	0.861733i	−0.991539	−	0.129806i	$-0.958565\pi$
$3$	−13.4331	+	13.4331i	−0.861733	+	0.861733i	0.129806	+	0.991539i	$0.458565\pi$
$4$		0			0
$5$	15.0352	+	53.8418i	0.268958	+	0.963152i
$5$	15.0352	+	53.8418i	0.268958	+	0.963152i
$6$		0			0
$7$	−76.4413	−	76.4413i	−0.589634	−	0.589634i	0.347898	−	0.937532i	$-0.386896\pi$
$7$	−76.4413	−	76.4413i	−0.589634	−	0.589634i	−0.937532	+	0.347898i	$0.886896\pi$
$8$		0			0
$9$		−	117.896i		−	0.485169i
$10$		0			0
$11$		−	622.995i		−	1.55240i	−0.630488	−	0.776199i	$-0.717145\pi$
$11$		−	622.995i		−	1.55240i	0.630488	−	0.776199i	$-0.282855\pi$
$12$		0			0
$13$	−293.552	−	293.552i	−0.481755	−	0.481755i	0.423937	−	0.905692i	$-0.360648\pi$
$13$	−293.552	−	293.552i	−0.481755	−	0.481755i	−0.905692	+	0.423937i	$0.860648\pi$
$14$		0			0
$15$	−925.232	−	521.293i	−1.06175	−	0.598210i
$16$		0			0
$17$	−1153.02	+	1153.02i	−0.967640	+	0.967640i	−0.999493	−	0.0318524i	$-0.989859\pi$
$17$	−1153.02	+	1153.02i	−0.967640	+	0.967640i	0.0318524	+	0.999493i	$0.489859\pi$
$18$		0			0
$19$	2003.44			1.27319			0.636593	−	0.771200i	$-0.280343\pi$
$19$	2003.44			1.27319			0.636593	+	0.771200i	$0.280343\pi$
$20$		0			0
$21$	2053.69			1.01622
$22$		0			0
$23$	1392.29	−	1392.29i	0.548797	−	0.548797i	−0.377296	−	0.926093i	$-0.623146\pi$
$23$	1392.29	−	1392.29i	0.548797	−	0.548797i	0.926093	+	0.377296i	$0.123146\pi$
$24$		0			0
$25$	−2672.88	+	1619.05i	−0.855323	+	0.518095i
$26$		0			0
$27$	−1680.53	−	1680.53i	−0.443647	−	0.443647i
$28$		0			0
$29$			305.819i			0.0675257i	0.999430	+	0.0337629i	$0.0107491\pi$
$29$			305.819i			0.0675257i	−0.999430	+	0.0337629i	$0.989251\pi$
$30$		0			0
$31$			2108.06i			0.393985i	0.980405	+	0.196992i	$0.0631174\pi$
$31$			2108.06i			0.393985i	−0.980405	+	0.196992i	$0.936883\pi$
$32$		0			0
$33$	8368.75	+	8368.75i	1.33775	+	1.33775i
$34$		0			0
$35$	2966.43	−	5265.05i	0.409321	−	0.726494i
$36$		0			0
$37$	9903.12	−	9903.12i	1.18924	−	1.18924i	0.211957	−	0.977279i	$-0.432016\pi$
$37$	9903.12	−	9903.12i	1.18924	−	1.18924i	0.977279	−	0.211957i	$-0.0679835\pi$
$38$		0			0
$39$	7886.62			0.830289
$40$		0			0
$41$	16996.0			1.57902			0.789511	−	0.613736i	$-0.210334\pi$
$41$	16996.0			1.57902			0.789511	+	0.613736i	$0.210334\pi$
$42$		0			0
$43$	−2031.28	+	2031.28i	−0.167533	+	0.167533i	−0.785894	−	0.618361i	$-0.787797\pi$
$43$	−2031.28	+	2031.28i	−0.167533	+	0.167533i	0.618361	+	0.785894i	$0.287797\pi$
$44$		0			0
$45$	6347.74	−	1772.59i	0.467291	−	0.130490i
$46$		0			0
$47$	−682.885	−	682.885i	−0.0450924	−	0.0450924i	0.684201	−	0.729293i	$-0.260151\pi$
$47$	−682.885	−	682.885i	−0.0450924	−	0.0450924i	−0.729293	+	0.684201i	$0.760151\pi$
$48$		0			0
$49$		−	5120.46i		−	0.304663i
$50$		0			0
$51$		−	30977.2i		−	1.66770i
$52$		0			0
$53$	21092.5	+	21092.5i	1.03143	+	1.03143i	0.999490	+	0.0319374i	$0.0101677\pi$
$53$	21092.5	+	21092.5i	1.03143	+	1.03143i	0.0319374	+	0.999490i	$0.489832\pi$
$54$		0			0
$55$	33543.2	−	9366.86i	1.49519	−	0.417530i
$56$		0			0
$57$	−26912.4	+	26912.4i	−1.09715	+	1.09715i
$58$		0			0
$59$	11617.4			0.434490			0.217245	−	0.976117i	$-0.430293\pi$
$59$	11617.4			0.434490			0.217245	+	0.976117i	$0.430293\pi$
$60$		0			0
$61$	−1309.80			−0.0450694			−0.0225347	−	0.999746i	$-0.507174\pi$
$61$	−1309.80			−0.0450694			−0.0225347	+	0.999746i	$0.507174\pi$
$62$		0			0
$63$	−9012.12	+	9012.12i	−0.286072	+	0.286072i
$64$		0			0
$65$	11391.8	−	20219.0i	0.334432	−	0.593576i
$66$		0			0
$67$	−39870.6	−	39870.6i	−1.08509	−	1.08509i	−0.996026	−	0.0890646i	$-0.971612\pi$
$67$	−39870.6	−	39870.6i	−1.08509	−	1.08509i	−0.0890646	−	0.996026i	$-0.528388\pi$
$68$		0			0
$69$			37405.7i			0.945833i
$70$		0			0
$71$			25454.3i			0.599259i	0.954056	+	0.299630i	$0.0968631\pi$
$71$			25454.3i			0.599259i	−0.954056	+	0.299630i	$0.903137\pi$
$72$		0			0
$73$	1031.25	+	1031.25i	0.0226495	+	0.0226495i	0.718341	−	0.695691i	$-0.244902\pi$
$73$	1031.25	+	1031.25i	0.0226495	+	0.0226495i	−0.695691	+	0.718341i	$0.744902\pi$
$74$		0			0
$75$	14156.3	−	57653.9i	0.290601	−	1.18352i
$76$		0			0
$77$	−47622.5	+	47622.5i	−0.915347	+	0.915347i
$78$		0			0
$79$	−11849.6			−0.213617			−0.106808	−	0.994280i	$-0.534063\pi$
$79$	−11849.6			−0.213617			−0.106808	+	0.994280i	$0.534063\pi$
$80$		0			0
$81$	73798.3			1.24978
$82$		0			0
$83$	45180.7	−	45180.7i	0.719876	−	0.719876i	−0.248703	−	0.968580i	$-0.580004\pi$
$83$	45180.7	−	45180.7i	0.719876	−	0.719876i	0.968580	+	0.248703i	$0.0800044\pi$
$84$		0			0
$85$	−79416.5	−	44744.7i	−1.19224	−	0.671730i
$86$		0			0
$87$	−4108.09	−	4108.09i	−0.0581892	−	0.0581892i
$88$		0			0
$89$		−	143889.i		−	1.92553i	−0.270332	−	0.962767i	$-0.587133\pi$
$89$		−	143889.i		−	1.92553i	0.270332	−	0.962767i	$-0.412867\pi$
$90$		0			0
$91$			44879.0i			0.568119i
$92$		0			0
$93$	−28317.8	−	28317.8i	−0.339510	−	0.339510i
$94$		0			0
$95$	30122.1	+	107869.i	0.342434	+	1.22627i
$96$		0			0
$97$	−24390.9	+	24390.9i	−0.263207	+	0.263207i	−0.826356	−	0.563148i	$-0.809590\pi$
$97$	−24390.9	+	24390.9i	−0.263207	+	0.263207i	0.563148	+	0.826356i	$0.309590\pi$
$98$		0			0
$99$	−73448.7			−0.753175
$100$		0			0
$101$	169993.			1.65816			0.829082	−	0.559127i	$-0.188864\pi$
$101$	169993.			1.65816			0.829082	+	0.559127i	$0.188864\pi$
$102$		0			0
$103$	−116026.	+	116026.i	−1.07761	+	1.07761i	−0.0808914	+	0.996723i	$0.525777\pi$
$103$	−116026.	+	116026.i	−1.07761	+	1.07761i	−0.996723	+	0.0808914i	$0.974223\pi$
$104$		0			0
$105$	30877.6	+	110574.i	0.273319	+	0.978770i
$106$		0			0
$107$	−68471.5	−	68471.5i	−0.578163	−	0.578163i	0.356234	−	0.934397i	$-0.384061\pi$
$107$	−68471.5	−	68471.5i	−0.578163	−	0.578163i	−0.934397	+	0.356234i	$0.884061\pi$
$108$		0			0
$109$		−	20202.8i		−	0.162872i	−0.996679	−	0.0814360i	$-0.974049\pi$
$109$		−	20202.8i		−	0.162872i	0.996679	−	0.0814360i	$-0.0259506\pi$
$110$		0			0
$111$			266059.i			2.04961i
$112$		0			0
$113$	−79268.7	−	79268.7i	−0.583990	−	0.583990i	0.352007	−	0.935997i	$-0.385499\pi$
$113$	−79268.7	−	79268.7i	−0.583990	−	0.583990i	−0.935997	+	0.352007i	$0.885499\pi$
$114$		0			0
$115$	95897.1	+	54030.2i	0.676178	+	0.380971i
$116$		0			0
$117$	−34608.6	+	34608.6i	−0.233733	+	0.233733i
$118$		0			0
$119$	176276.			1.14111
$120$		0			0
$121$	−227072.			−1.40994
$122$		0			0
$123$	−228309.	+	228309.i	−1.36070	+	1.36070i
$124$		0			0
$125$	−127360.	−	119570.i	−0.729050	−	0.684460i
$126$		0			0
$127$	133983.	+	133983.i	0.737121	+	0.737121i	0.972020	−	0.234898i	$-0.0754758\pi$
$127$	133983.	+	133983.i	0.737121	+	0.737121i	−0.234898	+	0.972020i	$0.575476\pi$
$128$		0			0
$129$		−	54572.8i		−	0.288737i
$130$		0			0
$131$		−	358577.i		−	1.82559i	−0.408414	−	0.912797i	$-0.633918\pi$
$131$		−	358577.i		−	1.82559i	0.408414	−	0.912797i	$-0.366082\pi$
$132$		0			0
$133$	−153145.	−	153145.i	−0.750715	−	0.750715i
$134$		0			0
$135$	65215.8	−	115750.i	0.307977	−	0.546622i
$136$		0			0
$137$	−156028.	+	156028.i	−0.710232	+	0.710232i	−0.966584	−	0.256352i	$-0.917479\pi$
$137$	−156028.	+	156028.i	−0.710232	+	0.710232i	0.256352	+	0.966584i	$0.417479\pi$
$138$		0			0
$139$	−211815.			−0.929865			−0.464932	−	0.885346i	$-0.653921\pi$
$139$	−211815.			−0.929865			−0.464932	+	0.885346i	$0.653921\pi$
$140$		0			0
$141$	18346.5			0.0777152
$142$		0			0
$143$	−182881.	+	182881.i	−0.747876	+	0.747876i
$144$		0			0
$145$	−16465.8	+	4598.05i	−0.0650375	+	0.0181616i
$146$		0			0
$147$	68783.7	+	68783.7i	0.262538	+	0.262538i
$148$		0			0
$149$		−	55272.1i		−	0.203958i	−0.994787	−	0.101979i	$-0.967483\pi$
$149$		−	55272.1i		−	0.203958i	0.994787	−	0.101979i	$-0.0325174\pi$
$150$		0			0
$151$		−	358721.i		−	1.28031i	−0.768247	−	0.640154i	$-0.778871\pi$
$151$		−	358721.i		−	1.28031i	0.768247	−	0.640154i	$-0.221129\pi$
$152$		0			0
$153$	135936.	+	135936.i	0.469469	+	0.469469i
$154$		0			0
$155$	−113502.	+	31695.2i	−0.379467	+	0.105965i
$156$		0			0
$157$	355644.	−	355644.i	1.15151	−	1.15151i	0.165255	−	0.986251i	$-0.447155\pi$
$157$	355644.	−	355644.i	1.15151	−	1.15151i	0.986251	−	0.165255i	$-0.0528447\pi$
$158$		0			0
$159$	−566675.			−1.77763
$160$		0			0
$161$	−212858.			−0.647179
$162$		0			0
$163$	288242.	−	288242.i	0.849745	−	0.849745i	−0.140356	−	0.990101i	$-0.544825\pi$
$163$	288242.	−	288242.i	0.849745	−	0.849745i	0.990101	+	0.140356i	$0.0448248\pi$
$164$		0			0
$165$	−324763.	+	576415.i	−0.928660	+	1.64826i
$166$		0			0
$167$	78292.2	+	78292.2i	0.217234	+	0.217234i	0.807332	−	0.590098i	$-0.200911\pi$
$167$	78292.2	+	78292.2i	0.217234	+	0.217234i	−0.590098	+	0.807332i	$0.700911\pi$
$168$		0			0
$169$		−	198947.i		−	0.535823i
$170$		0			0
$171$		−	236197.i		−	0.617711i
$172$		0			0
$173$	−242048.	−	242048.i	−0.614875	−	0.614875i	0.329337	−	0.944212i	$-0.393175\pi$
$173$	−242048.	−	242048.i	−0.614875	−	0.614875i	−0.944212	+	0.329337i	$0.893175\pi$
$174$		0			0
$175$	328081.	+	80556.7i	0.809814	+	0.198841i
$176$		0			0
$177$	−156058.	+	156058.i	−0.374414	+	0.374414i
$178$		0			0
$179$	28397.8			0.0662448			0.0331224	−	0.999451i	$-0.489455\pi$
$179$	28397.8			0.0662448			0.0331224	+	0.999451i	$0.489455\pi$
$180$		0			0
$181$	637320.			1.44598			0.722988	−	0.690861i	$-0.242768\pi$
$181$	637320.			1.44598			0.722988	+	0.690861i	$0.242768\pi$
$182$		0			0
$183$	17594.7	−	17594.7i	0.0388378	−	0.0388378i
$184$		0			0
$185$	682098.	+	384307.i	1.46527	+	0.825560i
$186$		0			0
$187$	718325.	+	718325.i	1.50216	+	1.50216i
$188$		0			0
$189$			256924.i			0.523179i
$190$		0			0
$191$		−	618423.i		−	1.22660i	−0.789851	−	0.613299i	$-0.789842\pi$
$191$		−	618423.i		−	1.22660i	0.789851	−	0.613299i	$-0.210158\pi$
$192$		0			0
$193$	21641.0	+	21641.0i	0.0418199	+	0.0418199i	0.727708	−	0.685888i	$-0.240586\pi$
$193$	21641.0	+	21641.0i	0.0418199	+	0.0418199i	−0.685888	+	0.727708i	$0.740586\pi$
$194$		0			0
$195$	118577.	+	424630.i	0.223313	+	0.799695i
$196$		0			0
$197$	38033.2	−	38033.2i	0.0698227	−	0.0698227i	−0.671333	−	0.741156i	$-0.734278\pi$
$197$	38033.2	−	38033.2i	0.0698227	−	0.0698227i	0.741156	+	0.671333i	$0.234278\pi$
$198$		0			0
$199$	258481.			0.462696			0.231348	−	0.972871i	$-0.425686\pi$
$199$	258481.			0.462696			0.231348	+	0.972871i	$0.425686\pi$
$200$		0			0
$201$	1.07117e6			1.87012
$202$		0			0
$203$	23377.2	−	23377.2i	0.0398155	−	0.0398155i
$204$		0			0
$205$	255539.	+	915098.i	0.424691	+	1.52084i
$206$		0			0
$207$	−164146.	−	164146.i	−0.266259	−	0.266259i
$208$		0			0
$209$		−	1.24813e6i		−	1.97649i
$210$		0			0
$211$		−	185768.i		−	0.287253i	−0.989632	−	0.143626i	$-0.954124\pi$
$211$		−	185768.i		−	0.287253i	0.989632	−	0.143626i	$-0.0458764\pi$
$212$		0			0
$213$	−341930.	−	341930.i	−0.516402	−	0.516402i
$214$		0			0
$215$	−139909.	−	78827.2i	−0.206419	−	0.116300i
$216$		0			0
$217$	161143.	−	161143.i	0.232307	−	0.232307i
$218$		0			0
$219$	−27705.8			−0.0390356
$220$		0			0
$221$	676942.			0.932332
$222$		0			0
$223$	759885.	−	759885.i	1.02326	−	1.02326i	0.0235364	−	0.999723i	$-0.492507\pi$
$223$	759885.	−	759885.i	1.02326	−	1.02326i	0.999723	−	0.0235364i	$-0.00749255\pi$
$224$		0			0
$225$	190879.	+	315122.i	0.251363	+	0.414976i
$226$		0			0
$227$	35910.4	+	35910.4i	0.0462547	+	0.0462547i	0.729856	−	0.683601i	$-0.239587\pi$
$227$	35910.4	+	35910.4i	0.0462547	+	0.0462547i	−0.683601	+	0.729856i	$0.739587\pi$
$228$		0			0
$229$			1.54665e6i			1.94896i	0.224469	+	0.974481i	$0.427935\pi$
$229$			1.54665e6i			1.94896i	−0.224469	+	0.974481i	$0.572065\pi$
$230$		0			0
$231$		−	1.27944e6i		−	1.57757i
$232$		0			0
$233$	−389263.	−	389263.i	−0.469735	−	0.469735i	0.432093	−	0.901829i	$-0.357775\pi$
$233$	−389263.	−	389263.i	−0.469735	−	0.469735i	−0.901829	+	0.432093i	$0.857775\pi$
$234$		0			0
$235$	26500.5	−	47035.1i	0.0313028	−	0.0555587i
$236$		0			0
$237$	159176.	−	159176.i	0.184081	−	0.184081i
$238$		0			0
$239$	−823778.			−0.932858			−0.466429	−	0.884559i	$-0.654460\pi$
$239$	−823778.			−0.932858			−0.466429	+	0.884559i	$0.654460\pi$
$240$		0			0
$241$	−139658.			−0.154890			−0.0774451	−	0.996997i	$-0.524676\pi$
$241$	−139658.			−0.154890			−0.0774451	+	0.996997i	$0.524676\pi$
$242$		0			0
$243$	−582969.	+	582969.i	−0.633330	+	0.633330i
$244$		0			0
$245$	275695.	−	76987.3i	0.293436	−	0.0819415i
$246$		0			0
$247$	−588113.	−	588113.i	−0.613365	−	0.613365i
$248$		0			0
$249$			1.21383e6i			1.24068i
$250$		0			0
$251$		−	1.26857e6i		−	1.27096i	−0.772118	−	0.635480i	$-0.780802\pi$
$251$		−	1.26857e6i		−	1.27096i	0.772118	−	0.635480i	$-0.219198\pi$
$252$		0			0
$253$	−867393.	−	867393.i	−0.851951	−	0.851951i
$254$		0			0
$255$	1.66787e6	−	465749.i	1.60624	−	0.448540i
$256$		0			0
$257$	79307.5	−	79307.5i	0.0749000	−	0.0749000i	−0.668664	−	0.743564i	$-0.733134\pi$
$257$	79307.5	−	79307.5i	0.0749000	−	0.0749000i	0.743564	+	0.668664i	$0.233134\pi$
$258$		0			0
$259$	−1.51401e6			−1.40243
$260$		0			0
$261$	36054.8			0.0327614
$262$		0			0
$263$	−750568.	+	750568.i	−0.669115	+	0.669115i	−0.957511	−	0.288396i	$-0.906878\pi$
$263$	−750568.	+	750568.i	−0.669115	+	0.669115i	0.288396	+	0.957511i	$0.406878\pi$
$264$		0			0
$265$	−818529.	+	1.45279e6i	−0.716010	+	1.27083i
$266$		0			0
$267$	1.93287e6	+	1.93287e6i	1.65930	+	1.65930i
$268$		0			0
$269$		−	2.07912e6i		−	1.75186i	−0.482441	−	0.875928i	$-0.660250\pi$
$269$		−	2.07912e6i		−	1.75186i	0.482441	−	0.875928i	$-0.339750\pi$
$270$		0			0
$271$		−	826197.i		−	0.683377i	−0.939813	−	0.341689i	$-0.889001\pi$
$271$		−	826197.i		−	0.683377i	0.939813	−	0.341689i	$-0.110999\pi$
$272$		0			0
$273$	−602863.	−	602863.i	−0.489567	−	0.489567i
$274$		0			0
$275$	1.00866e6	+	1.66519e6i	0.804289	+	1.32780i
$276$		0			0
$277$	−1.13631e6	+	1.13631e6i	−0.889808	+	0.889808i	−0.994504	−	0.104696i	$-0.966613\pi$
$277$	−1.13631e6	+	1.13631e6i	−0.889808	+	0.889808i	0.104696	+	0.994504i	$0.466613\pi$
$278$		0			0
$279$	248532.			0.191149
$280$		0			0
$281$	812.516			0.000613856			0.000306928	−	1.00000i	$-0.499902\pi$
$281$	812.516			0.000613856			0.000306928		1.00000i	$0.499902\pi$
$282$		0			0
$283$	129621.	−	129621.i	0.0962076	−	0.0962076i	−0.657365	−	0.753572i	$-0.728329\pi$
$283$	129621.	−	129621.i	0.0962076	−	0.0962076i	0.753572	+	0.657365i	$0.228329\pi$
$284$		0			0
$285$	−1.85365e6	−	1.04438e6i	−1.35181	−	0.761633i
$286$		0			0
$287$	−1.29920e6	−	1.29920e6i	−0.931046	−	0.931046i
$288$		0			0
$289$		−	1.23905e6i		−	0.872655i
$290$		0			0
$291$		−	655290.i		−	0.453629i
$292$		0			0
$293$	1.81804e6	+	1.81804e6i	1.23719	+	1.23719i	0.961147	+	0.276039i	$0.0890218\pi$
$293$	1.81804e6	+	1.81804e6i	1.23719	+	1.23719i	0.276039	+	0.961147i	$0.410978\pi$
$294$		0			0
$295$	174670.	+	625503.i	0.116860	+	0.418480i
$296$		0			0
$297$	−1.04696e6	+	1.04696e6i	−0.688717	+	0.688717i
$298$		0			0
$299$	−817422.			−0.528772
$300$		0			0
$301$	310548.			0.197566
$302$		0			0
$303$	−2.28353e6	+	2.28353e6i	−1.42890	+	1.42890i
$304$		0			0
$305$	−19693.2	−	70522.2i	−0.0121218	−	0.0434087i
$306$		0			0
$307$	1.39031e6	+	1.39031e6i	0.841907	+	0.841907i	0.989107	−	0.147199i	$-0.0470259\pi$
$307$	1.39031e6	+	1.39031e6i	0.841907	+	0.841907i	−0.147199	+	0.989107i	$0.547026\pi$
$308$		0			0
$309$		−	3.11718e6i		−	1.85723i
$310$		0			0
$311$			2.77199e6i			1.62514i	0.582863	+	0.812570i	$0.301932\pi$
$311$			2.77199e6i			1.62514i	−0.582863	+	0.812570i	$0.698068\pi$
$312$		0			0
$313$	−393418.	−	393418.i	−0.226983	−	0.226983i	0.584448	−	0.811431i	$-0.301311\pi$
$313$	−393418.	−	393418.i	−0.226983	−	0.226983i	−0.811431	+	0.584448i	$0.801311\pi$
$314$		0			0
$315$	−620728.	−	349730.i	−0.352472	−	0.198590i
$316$		0			0
$317$	594016.	−	594016.i	0.332009	−	0.332009i	−0.521340	−	0.853349i	$-0.674568\pi$
$317$	594016.	−	594016.i	0.332009	−	0.332009i	0.853349	+	0.521340i	$0.174568\pi$
$318$		0			0
$319$	190524.			0.104827
$320$		0			0
$321$	1.83957e6			0.996445
$322$		0			0
$323$	−2.31000e6	+	2.31000e6i	−1.23199	+	1.23199i
$324$		0			0
$325$	1.25990e6	+	309356.i	0.661652	+	0.162462i
$326$		0			0
$327$	271387.	+	271387.i	0.140352	+	0.140352i
$328$		0			0
$329$			104401.i			0.0531760i
$330$		0			0
$331$			2.17459e6i			1.09096i	0.838124	+	0.545479i	$0.183652\pi$
$331$			2.17459e6i			1.09096i	−0.838124	+	0.545479i	$0.816348\pi$
$332$		0			0
$333$	−1.16754e6	−	1.16754e6i	−0.576980	−	0.576980i
$334$		0			0
$335$	1.54724e6	−	2.74617e6i	0.753263	−	1.33695i
$336$		0			0
$337$	−603974.	+	603974.i	−0.289696	+	0.289696i	−0.836960	−	0.547264i	$-0.815669\pi$
$337$	−603974.	+	603974.i	−0.289696	+	0.289696i	0.547264	+	0.836960i	$0.315669\pi$
$338$		0			0
$339$	2.12965e6			1.00649
$340$		0			0
$341$	1.31331e6			0.611621
$342$		0			0
$343$	−1.67616e6	+	1.67616e6i	−0.769274	+	0.769274i
$344$		0			0
$345$	−2.01399e6	+	562402.i	−0.910981	+	0.254389i
$346$		0			0
$347$	−2.94638e6	−	2.94638e6i	−1.31361	−	1.31361i	−0.918738	−	0.394869i	$-0.870790\pi$
$347$	−2.94638e6	−	2.94638e6i	−1.31361	−	1.31361i	−0.394869	−	0.918738i	$-0.629210\pi$
$348$		0			0
$349$		−	1.01585e6i		−	0.446443i	−0.974768	−	0.223221i	$-0.928343\pi$
$349$		−	1.01585e6i		−	0.446443i	0.974768	−	0.223221i	$-0.0716573\pi$
$350$		0			0
$351$			986648.i			0.427459i
$352$		0			0
$353$	−3.05696e6	−	3.05696e6i	−1.30573	−	1.30573i	−0.924468	−	0.381259i	$-0.875491\pi$
$353$	−3.05696e6	−	3.05696e6i	−1.30573	−	1.30573i	−0.381259	−	0.924468i	$-0.624509\pi$
$354$		0			0
$355$	−1.37050e6	+	382710.i	−0.577178	+	0.161176i
$356$		0			0
$357$	−2.36794e6	+	2.36794e6i	−0.983331	+	0.983331i
$358$		0			0
$359$	−1.01289e6			−0.414787			−0.207393	−	0.978258i	$-0.566498\pi$
$359$	−1.01289e6			−0.414787			−0.207393	+	0.978258i	$0.566498\pi$
$360$		0			0
$361$	1.53767e6			0.621005
$362$		0			0
$363$	3.05028e6	−	3.05028e6i	1.21499	−	1.21499i
$364$		0			0
$365$	−40019.4	+	71029.6i	−0.0157231	+	0.0279066i
$366$		0			0
$367$	1.78687e6	+	1.78687e6i	0.692511	+	0.692511i	0.962784	−	0.270272i	$-0.0871138\pi$
$367$	1.78687e6	+	1.78687e6i	0.692511	+	0.692511i	−0.270272	+	0.962784i	$0.587114\pi$
$368$		0			0
$369$		−	2.00377e6i		−	0.766092i
$370$		0			0
$371$		−	3.22468e6i		−	1.21633i
$372$		0			0
$373$	382840.	+	382840.i	0.142477	+	0.142477i	0.774748	−	0.632270i	$-0.217877\pi$
$373$	382840.	+	382840.i	0.142477	+	0.142477i	−0.632270	+	0.774748i	$0.717877\pi$
$374$		0			0
$375$	3.31704e6	−	104637.i	1.21807	−	0.0384245i
$376$		0			0
$377$	89773.7	−	89773.7i	0.0325309	−	0.0325309i
$378$		0			0
$379$	−2.37584e6			−0.849610			−0.424805	−	0.905285i	$-0.639657\pi$
$379$	−2.37584e6			−0.849610			−0.424805	+	0.905285i	$0.639657\pi$
$380$		0			0
$381$	−3.59960e6			−1.27040
$382$		0			0
$383$	−748285.	+	748285.i	−0.260657	+	0.260657i	−0.825321	−	0.564664i	$-0.809006\pi$
$383$	−748285.	+	748285.i	−0.260657	+	0.260657i	0.564664	+	0.825321i	$0.309006\pi$
$384$		0			0
$385$	−3.28010e6	−	1.84807e6i	−1.12781	−	0.635428i
$386$		0			0
$387$	239480.	+	239480.i	0.0812816	+	0.0812816i
$388$		0			0
$389$			3.04186e6i			1.01921i	0.860407	+	0.509607i	$0.170209\pi$
$389$			3.04186e6i			1.01921i	−0.860407	+	0.509607i	$0.829791\pi$
$390$		0			0
$391$			3.21068e6i			1.06208i
$392$		0			0
$393$	4.81680e6	+	4.81680e6i	1.57317	+	1.57317i
$394$		0			0
$395$	−178161.	−	638003.i	−0.0574539	−	0.205745i
$396$		0			0
$397$	−3.19165e6	+	3.19165e6i	−1.01634	+	1.01634i	−0.0164751	+	0.999864i	$0.505244\pi$
$397$	−3.19165e6	+	3.19165e6i	−1.01634	+	1.01634i	−0.999864	+	0.0164751i	$0.994756\pi$
$398$		0			0
$399$	4.11443e6			1.29383
$400$		0			0
$401$	4.27231e6			1.32679			0.663395	−	0.748270i	$-0.269115\pi$
$401$	4.27231e6			1.32679			0.663395	+	0.748270i	$0.269115\pi$
$402$		0			0
$403$	618826.	−	618826.i	0.189804	−	0.189804i
$404$		0			0
$405$	1.10957e6	+	3.97343e6i	0.336138	+	1.20373i
$406$		0			0
$407$	−6.16960e6	−	6.16960e6i	−1.84617	−	1.84617i
$408$		0			0
$409$			4.39056e6i			1.29781i	0.760869	+	0.648906i	$0.224773\pi$
$409$			4.39056e6i			1.29781i	−0.760869	+	0.648906i	$0.775227\pi$
$410$		0			0
$411$		−	4.19187e6i		−	1.22406i
$412$		0			0
$413$	−888050.	−	888050.i	−0.256190	−	0.256190i
$414$		0			0
$415$	3.11191e6	+	1.75331e6i	0.886967	+	0.499734i
$416$		0			0
$417$	2.84533e6	−	2.84533e6i	0.801295	−	0.801295i
$418$		0			0
$419$	−5.83290e6			−1.62312			−0.811558	−	0.584271i	$-0.801380\pi$
$419$	−5.83290e6			−1.62312			−0.811558	+	0.584271i	$0.801380\pi$
$420$		0			0
$421$	−741629.			−0.203930			−0.101965	−	0.994788i	$-0.532513\pi$
$421$	−741629.			−0.203930			−0.101965	+	0.994788i	$0.532513\pi$
$422$		0			0
$423$	−80509.4	+	80509.4i	−0.0218774	+	0.0218774i
$424$		0			0
$425$	1.21509e6	−	4.94868e6i	0.326316	−	1.32897i
$426$		0			0
$427$	100123.	+	100123.i	0.0265745	+	0.0265745i
$428$		0			0
$429$		−	4.91333e6i		−	1.28894i
$430$		0			0
$431$		−	12397.3i		−	0.00321464i	−0.999999	−	0.00160732i	$-0.999488\pi$
$431$		−	12397.3i		−	0.00321464i	0.999999	−	0.00160732i	$-0.000511626\pi$
$432$		0			0
$433$	−203088.	−	203088.i	−0.0520552	−	0.0520552i	0.680600	−	0.732655i	$-0.261719\pi$
$433$	−203088.	−	203088.i	−0.0520552	−	0.0520552i	−0.732655	+	0.680600i	$0.761719\pi$
$434$		0			0
$435$	159421.	−	282953.i	0.0403946	−	0.0716954i
$436$		0			0
$437$	2.78938e6	−	2.78938e6i	0.698721	−	0.698721i
$438$		0			0
$439$	6.21348e6			1.53877			0.769384	−	0.638786i	$-0.220563\pi$
$439$	6.21348e6			1.53877			0.769384	+	0.638786i	$0.220563\pi$
$440$		0			0
$441$	−603682.			−0.147813
$442$		0			0
$443$	4.93074e6	−	4.93074e6i	1.19372	−	1.19372i	0.217705	−	0.976015i	$-0.430143\pi$
$443$	4.93074e6	−	4.93074e6i	1.19372	−	1.19372i	0.976015	−	0.217705i	$-0.0698571\pi$
$444$		0			0
$445$	7.74722e6	−	2.16340e6i	1.85458	−	0.517888i
$446$		0			0
$447$	742475.	+	742475.i	0.175757	+	0.175757i
$448$		0			0
$449$			3.32541e6i			0.778449i	0.921143	+	0.389224i	$0.127257\pi$
$449$			3.32541e6i			0.778449i	−0.921143	+	0.389224i	$0.872743\pi$
$450$		0			0
$451$		−	1.05885e7i		−	2.45127i
$452$		0			0
$453$	4.81873e6	+	4.81873e6i	1.10328	+	1.10328i
$454$		0			0
$455$	−2.41637e6	+	674765.i	−0.547185	+	0.152800i
$456$		0			0
$457$	1.03786e6	−	1.03786e6i	0.232460	−	0.232460i	−0.581259	−	0.813719i	$-0.697440\pi$
$457$	1.03786e6	−	1.03786e6i	0.232460	−	0.232460i	0.813719	+	0.581259i	$0.197440\pi$
$458$		0			0
$459$	3.87537e6			0.858582
$460$		0			0
$461$	4.98358e6			1.09217			0.546083	−	0.837731i	$-0.316118\pi$
$461$	4.98358e6			1.09217			0.546083	+	0.837731i	$0.316118\pi$
$462$		0			0
$463$	−867273.	+	867273.i	−0.188020	+	0.188020i	−0.794839	−	0.606820i	$-0.792445\pi$
$463$	−867273.	+	867273.i	−0.188020	+	0.188020i	0.606820	+	0.794839i	$0.292445\pi$
$464$		0			0
$465$	1.09892e6	−	1.95045e6i	0.235686	−	0.418313i
$466$		0			0
$467$	6.21652e6	+	6.21652e6i	1.31903	+	1.31903i	0.914543	+	0.404489i	$0.132551\pi$
$467$	6.21652e6	+	6.21652e6i	1.31903	+	1.31903i	0.404489	+	0.914543i	$0.367449\pi$
$468$		0			0
$469$			6.09552e6i			1.27961i
$470$		0			0
$471$			9.55479e6i			1.98458i
$472$		0			0
$473$	1.26548e6	+	1.26548e6i	0.260077	+	0.260077i
$474$		0			0
$475$	−5.35496e6	+	3.24366e6i	−1.08899	+	0.659632i
$476$		0			0
$477$	2.48672e6	−	2.48672e6i	0.500416	−	0.500416i
$478$		0			0
$479$	−5.54732e6			−1.10470			−0.552350	−	0.833612i	$-0.686269\pi$
$479$	−5.54732e6			−1.10470			−0.552350	+	0.833612i	$0.686269\pi$
$480$		0			0
$481$	−5.81416e6			−1.14584
$482$		0			0
$483$	2.85934e6	−	2.85934e6i	0.557696	−	0.557696i
$484$		0			0
$485$	−1.67997e6	−	946528.i	−0.324300	−	0.182717i
$486$		0			0
$487$	−45082.0	−	45082.0i	−0.00861353	−	0.00861353i	0.702787	−	0.711400i	$-0.251939\pi$
$487$	−45082.0	−	45082.0i	−0.00861353	−	0.00861353i	−0.711400	+	0.702787i	$0.751939\pi$
$488$		0			0
$489$			7.74397e6i			1.46451i
$490$		0			0
$491$			4.49346e6i			0.841157i	0.907256	+	0.420579i	$0.138173\pi$
$491$			4.49346e6i			0.841157i	−0.907256	+	0.420579i	$0.861827\pi$
$492$		0			0
$493$	−352615.	−	352615.i	−0.0653406	−	0.0653406i
$494$		0			0
$495$	−1.10432e6	−	3.95461e6i	−0.202572	−	0.725422i
$496$		0			0
$497$	1.94576e6	−	1.94576e6i	0.353344	−	0.353344i
$498$		0			0
$499$	1.35470e6			0.243552			0.121776	−	0.992558i	$-0.461141\pi$
$499$	1.35470e6			0.243552			0.121776	+	0.992558i	$0.461141\pi$
$500$		0			0
$501$	−2.10341e6			−0.374395
$502$		0			0
$503$	5.30723e6	−	5.30723e6i	0.935294	−	0.935294i	−0.0627366	−	0.998030i	$-0.519983\pi$
$503$	5.30723e6	−	5.30723e6i	0.935294	−	0.935294i	0.998030	+	0.0627366i	$0.0199828\pi$
$504$		0			0
$505$	2.55588e6	+	9.15273e6i	0.445976	+	1.59706i
$506$		0			0
$507$	2.67248e6	+	2.67248e6i	0.461737	+	0.461737i
$508$		0			0
$509$		−	7.90014e6i		−	1.35158i	−0.737096	−	0.675788i	$-0.763803\pi$
$509$		−	7.90014e6i		−	1.35158i	0.737096	−	0.675788i	$-0.236197\pi$
$510$		0			0
$511$		−	157661.i		−	0.0267098i
$512$		0			0
$513$	−3.36685e6	−	3.36685e6i	−0.564846	−	0.564846i
$514$		0			0
$515$	−7.99155e6	−	4.50259e6i	−1.32774	−	0.748073i
$516$		0			0
$517$	−425434.	+	425434.i	−0.0700013	+	0.0700013i
$518$		0			0
$519$	6.50292e6			1.05972
$520$		0			0
$521$	−90092.2			−0.0145410			−0.00727048	−	0.999974i	$-0.502314\pi$
$521$	−90092.2			−0.0145410			−0.00727048	+	0.999974i	$0.502314\pi$
$522$		0			0
$523$	1.47517e6	−	1.47517e6i	0.235824	−	0.235824i	−0.579295	−	0.815118i	$-0.696672\pi$
$523$	1.47517e6	−	1.47517e6i	0.235824	−	0.235824i	0.815118	+	0.579295i	$0.196672\pi$
$524$		0			0
$525$	−5.48926e6	+	3.32501e6i	−0.869192	+	0.526496i
$526$		0			0
$527$	−2.43064e6	−	2.43064e6i	−0.381235	−	0.381235i
$528$		0			0
$529$			2.55937e6i			0.397644i
$530$		0			0
$531$		−	1.36965e6i		−	0.210801i
$532$		0			0
$533$	−4.98922e6	−	4.98922e6i	−0.760702	−	0.760702i
$534$		0			0
$535$	2.65715e6	−	4.71612e6i	0.401357	−	0.712361i
$536$		0			0
$537$	−381470.	+	381470.i	−0.0570854	+	0.0570854i
$538$		0			0
$539$	−3.19002e6			−0.472958
$540$		0			0
$541$	−1.00732e7			−1.47970			−0.739852	−	0.672769i	$-0.765105\pi$
$541$	−1.00732e7			−1.47970			−0.739852	+	0.672769i	$0.765105\pi$
$542$		0			0
$543$	−8.56118e6	+	8.56118e6i	−1.24605	+	1.24605i
$544$		0			0
$545$	1.08776e6	−	303754.i	0.156870	−	0.0438057i
$546$		0			0
$547$	−1.68628e6	−	1.68628e6i	−0.240969	−	0.240969i	0.576282	−	0.817251i	$-0.304503\pi$
$547$	−1.68628e6	−	1.68628e6i	−0.240969	−	0.240969i	−0.817251	+	0.576282i	$0.804503\pi$
$548$		0			0
$549$			154421.i			0.0218663i
$550$		0			0
$551$			612689.i			0.0859728i
$552$		0			0
$553$	905796.	+	905796.i	0.125956	+	0.125956i
$554$		0			0
$555$	−1.43251e7	+	4.00026e6i	−1.97408	+	0.551259i
$556$		0			0
$557$	5.82782e6	−	5.82782e6i	0.795917	−	0.795917i	−0.186532	−	0.982449i	$-0.559725\pi$
$557$	5.82782e6	−	5.82782e6i	0.795917	−	0.795917i	0.982449	+	0.186532i	$0.0597247\pi$
$558$		0			0
$559$	1.19257e6			0.161420
$560$		0			0
$561$	−1.92987e7			−2.58893
$562$		0			0
$563$	3.92139e6	−	3.92139e6i	0.521397	−	0.521397i	−0.396596	−	0.917993i	$-0.629809\pi$
$563$	3.92139e6	−	3.92139e6i	0.521397	−	0.521397i	0.917993	+	0.396596i	$0.129809\pi$
$564$		0			0
$565$	3.07615e6	−	5.45979e6i	0.405402	−	0.719540i
$566$		0			0
$567$	−5.64123e6	−	5.64123e6i	−0.736913	−	0.736913i
$568$		0			0
$569$		−	9.00329e6i		−	1.16579i	−0.812547	−	0.582895i	$-0.801920\pi$
$569$		−	9.00329e6i		−	1.16579i	0.812547	−	0.582895i	$-0.198080\pi$
$570$		0			0
$571$			1.33754e7i			1.71678i	0.512995	+	0.858392i	$0.328536\pi$
$571$			1.33754e7i			1.71678i	−0.512995	+	0.858392i	$0.671464\pi$
$572$		0			0
$573$	8.30734e6	+	8.30734e6i	1.05700	+	1.05700i
$574$		0			0
$575$	−1.46725e6	+	5.97563e6i	−0.185070	+	0.753727i
$576$		0			0
$577$	5.22216e6	−	5.22216e6i	0.652996	−	0.652996i	−0.300717	−	0.953713i	$-0.597226\pi$
$577$	5.22216e6	−	5.22216e6i	0.652996	−	0.652996i	0.953713	+	0.300717i	$0.0972261\pi$
$578$		0			0
$579$	−581410.			−0.0720752
$580$		0			0
$581$	−6.90734e6			−0.848928
$582$		0			0
$583$	1.31405e7	−	1.31405e7i	1.60119	−	1.60119i
$584$		0			0
$585$	−2.38374e6	−	1.34304e6i	−0.287984	−	0.162256i
$586$		0			0
$587$	3.91266e6	+	3.91266e6i	0.468680	+	0.468680i	0.901487	−	0.432807i	$-0.142477\pi$
$587$	3.91266e6	+	3.91266e6i	0.468680	+	0.468680i	−0.432807	+	0.901487i	$0.642477\pi$
$588$		0			0
$589$			4.22338e6i			0.501616i
$590$		0			0
$591$			1.02181e6i			0.120337i
$592$		0			0
$593$	−377034.	−	377034.i	−0.0440295	−	0.0440295i	0.684749	−	0.728779i	$-0.259912\pi$
$593$	−377034.	−	377034.i	−0.0440295	−	0.0440295i	−0.728779	+	0.684749i	$0.759912\pi$
$594$		0			0
$595$	2.65035e6	+	9.49104e6i	0.306910	+	1.09906i
$596$		0			0
$597$	−3.47220e6	+	3.47220e6i	−0.398721	+	0.398721i
$598$		0			0
$599$	−3.69548e6			−0.420827			−0.210413	−	0.977613i	$-0.567481\pi$
$599$	−3.69548e6			−0.420827			−0.210413	+	0.977613i	$0.567481\pi$
$600$		0			0
$601$	−5.53615e6			−0.625204			−0.312602	−	0.949884i	$-0.601201\pi$
$601$	−5.53615e6			−0.625204			−0.312602	+	0.949884i	$0.601201\pi$
$602$		0			0
$603$	−4.70059e6	+	4.70059e6i	−0.526452	+	0.526452i
$604$		0			0
$605$	−3.41408e6	−	1.22260e7i	−0.379214	−	1.35798i
$606$		0			0
$607$	−851040.	−	851040.i	−0.0937515	−	0.0937515i	0.658676	−	0.752427i	$-0.271117\pi$
$607$	−851040.	−	851040.i	−0.0937515	−	0.0937515i	−0.752427	+	0.658676i	$0.771117\pi$
$608$		0			0
$609$			628056.i			0.0686207i
$610$		0			0
$611$			400924.i			0.0434470i
$612$		0			0
$613$	−2.99552e6	−	2.99552e6i	−0.321974	−	0.321974i	0.527550	−	0.849524i	$-0.323111\pi$
$613$	−2.99552e6	−	2.99552e6i	−0.321974	−	0.321974i	−0.849524	+	0.527550i	$0.823111\pi$
$614$		0			0
$615$	−1.57253e7	−	8.85992e6i	−1.67653	−	0.944587i
$616$		0			0
$617$	2.10245e6	−	2.10245e6i	0.222337	−	0.222337i	−0.587145	−	0.809482i	$-0.699748\pi$
$617$	2.10245e6	−	2.10245e6i	0.222337	−	0.222337i	0.809482	+	0.587145i	$0.199748\pi$
$618$		0			0
$619$	4.83196e6			0.506870			0.253435	−	0.967352i	$-0.418440\pi$
$619$	4.83196e6			0.506870			0.253435	+	0.967352i	$0.418440\pi$
$620$		0			0
$621$	−4.67960e6			−0.486944
$622$		0			0
$623$	−1.09990e7	+	1.09990e7i	−1.13536	+	1.13536i
$624$		0			0
$625$	4.52300e6	−	8.65505e6i	0.463155	−	0.886277i
$626$		0			0
$627$	1.67663e7	+	1.67663e7i	1.70321	+	1.70321i
$628$		0			0
$629$			2.28370e7i			2.30150i
$630$		0			0
$631$			1.27571e7i			1.27550i	0.770244	+	0.637749i	$0.220134\pi$
$631$			1.27571e7i			1.27550i	−0.770244	+	0.637749i	$0.779866\pi$
$632$		0			0
$633$	2.49544e6	+	2.49544e6i	0.247535	+	0.247535i
$634$		0			0
$635$	−5.19941e6	+	9.22832e6i	−0.511705	+	0.908215i
$636$		0			0
$637$	−1.50312e6	+	1.50312e6i	−0.146773	+	0.146773i
$638$		0			0
$639$	3.00096e6			0.290742
$640$		0			0
$641$	7.64611e6			0.735014			0.367507	−	0.930021i	$-0.380211\pi$
$641$	7.64611e6			0.735014			0.367507	+	0.930021i	$0.380211\pi$
$642$		0			0
$643$	−2.54976e6	+	2.54976e6i	−0.243204	+	0.243204i	−0.818174	−	0.574970i	$-0.805014\pi$
$643$	−2.54976e6	+	2.54976e6i	−0.243204	+	0.243204i	0.574970	+	0.818174i	$0.305014\pi$
$644$		0			0
$645$	2.93830e6	−	820514.i	0.278098	−	0.0776581i
$646$		0			0
$647$	−3.90727e6	−	3.90727e6i	−0.366954	−	0.366954i	0.499411	−	0.866365i	$-0.333550\pi$
$647$	−3.90727e6	−	3.90727e6i	−0.366954	−	0.366954i	−0.866365	+	0.499411i	$0.833550\pi$
$648$		0			0
$649$		−	7.23760e6i		−	0.674501i
$650$		0			0
$651$			4.32930e6i			0.400373i
$652$		0			0
$653$	−4.91675e6	−	4.91675e6i	−0.451227	−	0.451227i	0.444535	−	0.895762i	$-0.353369\pi$
$653$	−4.91675e6	−	4.91675e6i	−0.451227	−	0.451227i	−0.895762	+	0.444535i	$0.853369\pi$
$654$		0			0
$655$	1.93064e7	−	5.39128e6i	1.75832	−	0.491008i
$656$		0			0
$657$	121581.	−	121581.i	0.0109888	−	0.0109888i
$658$		0			0
$659$	−1.22997e6			−0.110327			−0.0551636	−	0.998477i	$-0.517568\pi$
$659$	−1.22997e6			−0.110327			−0.0551636	+	0.998477i	$0.517568\pi$
$660$		0			0
$661$	2.50222e6			0.222752			0.111376	−	0.993778i	$-0.464474\pi$
$661$	2.50222e6			0.222752			0.111376	+	0.993778i	$0.464474\pi$
$662$		0			0
$663$	−9.09342e6	+	9.09342e6i	−0.803421	+	0.803421i
$664$		0			0
$665$	5.94306e6	−	1.05482e7i	0.521142	−	0.924963i
$666$		0			0
$667$	425790.	+	425790.i	0.0370579	+	0.0370579i
$668$		0			0
$669$			2.04152e7i			1.76355i
$670$		0			0
$671$			816001.i			0.0699656i
$672$		0			0
$673$	4.60945e6	+	4.60945e6i	0.392294	+	0.392294i	0.875504	−	0.483210i	$-0.160529\pi$
$673$	4.60945e6	+	4.60945e6i	0.392294	+	0.392294i	−0.483210	+	0.875504i	$0.660529\pi$
$674$		0			0
$675$	7.21273e6	+	1.77101e6i	0.609313	+	0.149610i
$676$		0			0
$677$	1.03990e7	−	1.03990e7i	0.872006	−	0.872006i	−0.120685	−	0.992691i	$-0.538509\pi$
$677$	1.03990e7	−	1.03990e7i	0.872006	−	0.872006i	0.992691	+	0.120685i	$0.0385091\pi$
$678$		0			0
$679$	3.72894e6			0.310392
$680$		0			0
$681$	−964776.			−0.0797185
$682$		0			0
$683$	1.39930e7	−	1.39930e7i	1.14778	−	1.14778i	0.160795	−	0.986988i	$-0.448594\pi$
$683$	1.39930e7	−	1.39930e7i	1.14778	−	1.14778i	0.986988	−	0.160795i	$-0.0514059\pi$
$684$		0			0
$685$	−1.07467e7	−	6.05490e6i	−0.875084	−	0.493038i
$686$		0			0
$687$	−2.07763e7	−	2.07763e7i	−1.67949	−	1.67949i
$688$		0			0
$689$		−	1.23835e7i		−	0.993791i
$690$		0			0
$691$			9.98056e6i			0.795169i	0.917565	+	0.397585i	$0.130152\pi$
$691$			9.98056e6i			0.795169i	−0.917565	+	0.397585i	$0.869848\pi$
$692$		0			0
$693$	5.61451e6	+	5.61451e6i	0.444098	+	0.444098i
$694$		0			0
$695$	−3.18468e6	−	1.14045e7i	−0.250095	−	0.895601i
$696$		0			0
$697$	−1.95968e7	+	1.95968e7i	−1.52793	+	1.52793i
$698$		0			0
$699$	1.04580e7			0.809573
$700$		0			0
$701$	−7.67178e6			−0.589659			−0.294830	−	0.955550i	$-0.595263\pi$
$701$	−7.67178e6			−0.589659			−0.294830	+	0.955550i	$0.595263\pi$
$702$		0			0
$703$	1.98403e7	−	1.98403e7i	1.51412	−	1.51412i
$704$		0			0
$705$	275844.	+	987810.i	0.0209021	+	0.0748515i
$706$		0			0
$707$	−1.29945e7	−	1.29945e7i	−0.977710	−	0.977710i
$708$		0			0
$709$		−	1.61069e7i		−	1.20336i	−0.798737	−	0.601681i	$-0.794498\pi$
$709$		−	1.61069e7i		−	1.20336i	0.798737	−	0.601681i	$-0.205502\pi$
$710$		0			0
$711$			1.39702e6i			0.103640i
$712$		0			0
$713$	2.93505e6	+	2.93505e6i	0.216218	+	0.216218i
$714$		0			0
$715$	−1.25963e7	−	7.09701e6i	−0.921465	−	0.519171i
$716$		0			0
$717$	1.10659e7	−	1.10659e7i	0.803874	−	0.803874i
$718$		0			0
$719$	9.25776e6			0.667857			0.333929	−	0.942598i	$-0.391626\pi$
$719$	9.25776e6			0.667857			0.333929	+	0.942598i	$0.391626\pi$
$720$		0			0
$721$	1.77384e7			1.27080
$722$		0			0
$723$	1.87604e6	−	1.87604e6i	0.133474	−	0.133474i
$724$		0			0
$725$	−495135.	−	817418.i	−0.0349847	−	0.0577563i
$726$		0			0
$727$	−1.17208e7	−	1.17208e7i	−0.822475	−	0.822475i	0.163988	−	0.986462i	$-0.447564\pi$
$727$	−1.17208e7	−	1.17208e7i	−0.822475	−	0.822475i	−0.986462	+	0.163988i	$0.947564\pi$
$728$		0			0
$729$			2.27081e6i			0.158257i
$730$		0			0
$731$		−	4.68421e6i		−	0.324223i
$732$		0			0
$733$	5.35037e6	+	5.35037e6i	0.367811	+	0.367811i	0.866678	−	0.498868i	$-0.166251\pi$
$733$	5.35037e6	+	5.35037e6i	0.367811	+	0.367811i	−0.498868	+	0.866678i	$0.666251\pi$
$734$		0			0
$735$	−2.66926e6	+	4.73762e6i	−0.182252	+	0.323476i
$736$		0			0
$737$	−2.48392e7	+	2.48392e7i	−1.68449	+	1.68449i
$738$		0			0
$739$	−2.80515e7			−1.88949			−0.944746	−	0.327803i	$-0.893692\pi$
$739$	−2.80515e7			−1.88949			−0.944746	+	0.327803i	$0.893692\pi$
$740$		0			0
$741$	1.58004e7			1.05711
$742$		0			0
$743$	3.89759e6	−	3.89759e6i	0.259014	−	0.259014i	−0.565639	−	0.824653i	$-0.691370\pi$
$743$	3.89759e6	−	3.89759e6i	0.259014	−	0.259014i	0.824653	+	0.565639i	$0.191370\pi$
$744$		0			0
$745$	2.97595e6	−	831028.i	0.196442	−	0.0548561i
$746$		0			0
$747$	−5.32663e6	−	5.32663e6i	−0.349262	−	0.349262i
$748$		0			0
$749$			1.04681e7i			0.681810i
$750$		0			0
$751$			1.33082e6i			0.0861032i	0.999073	+	0.0430516i	$0.0137080\pi$
$751$			1.33082e6i			0.0861032i	−0.999073	+	0.0430516i	$0.986292\pi$
$752$		0			0
$753$	1.70409e7	+	1.70409e7i	1.09523	+	1.09523i
$754$		0			0
$755$	1.93142e7	−	5.39344e6i	1.23313	−	0.344349i
$756$		0			0
$757$	−4.82595e6	+	4.82595e6i	−0.306085	+	0.306085i	−0.843389	−	0.537303i	$-0.819443\pi$
$757$	−4.82595e6	+	4.82595e6i	−0.306085	+	0.306085i	0.537303	+	0.843389i	$0.319443\pi$
$758$		0			0
$759$	2.33035e7			1.46831
$760$		0			0
$761$	−1.62700e7			−1.01842			−0.509210	−	0.860642i	$-0.670062\pi$
$761$	−1.62700e7			−1.01842			−0.509210	+	0.860642i	$0.670062\pi$
$762$		0			0
$763$	−1.54433e6	+	1.54433e6i	−0.0960349	+	0.0960349i
$764$		0			0
$765$	−5.27523e6	+	9.36289e6i	−0.325902	+	0.578437i
$766$		0			0
$767$	−3.41032e6	−	3.41032e6i	−0.209318	−	0.209318i
$768$		0			0
$769$			7.50924e6i			0.457910i	0.973437	+	0.228955i	$0.0735308\pi$
$769$			7.50924e6i			0.457910i	−0.973437	+	0.228955i	$0.926469\pi$
$770$		0			0
$771$			2.13069e6i			0.129088i
$772$		0			0
$773$	−2.21009e6	−	2.21009e6i	−0.133034	−	0.133034i	0.637454	−	0.770488i	$-0.279987\pi$
$773$	−2.21009e6	−	2.21009e6i	−0.133034	−	0.133034i	−0.770488	+	0.637454i	$0.779987\pi$
$774$		0			0
$775$	−3.41305e6	−	5.63461e6i	−0.204121	−	0.336984i
$776$		0			0
$777$	2.03379e7	−	2.03379e7i	1.20852	−	1.20852i
$778$		0			0
$779$	3.40505e7			2.01039
$780$		0			0
$781$	1.58579e7			0.930289
$782$		0			0
$783$	513939.	−	513939.i	0.0299576	−	0.0299576i
$784$		0			0
$785$	2.44957e7	+	1.38013e7i	1.41878	+	0.799368i
$786$		0			0
$787$	−6.25543e6	−	6.25543e6i	−0.360015	−	0.360015i	0.503803	−	0.863818i	$-0.331934\pi$
$787$	−6.25543e6	−	6.25543e6i	−0.360015	−	0.360015i	−0.863818	+	0.503803i	$0.831934\pi$
$788$		0			0
$789$		−	2.01649e7i		−	1.15320i
$790$		0			0
$791$			1.21188e7i			0.688681i
$792$		0			0
$793$	384495.	+	384495.i	0.0217124	+	0.0217124i
$794$		0			0
$795$	−8.52008e6	−	3.05108e7i	−0.478108	−	1.71213i
$796$		0			0
$797$	−6.75194e6	+	6.75194e6i	−0.376515	+	0.376515i	−0.869843	−	0.493328i	$-0.835780\pi$
$797$	−6.75194e6	+	6.75194e6i	−0.376515	+	0.376515i	0.493328	+	0.869843i	$0.335780\pi$
$798$		0			0
$799$	1.57476e6			0.0872664
$800$		0			0
$801$	−1.69639e7			−0.934209
$802$		0			0
$803$	642465.	−	642465.i	0.0351610	−	0.0351610i
$804$		0			0
$805$	−3.20036e6	−	1.14606e7i	−0.174064	−	0.623332i
$806$		0			0
$807$	2.79290e7	+	2.79290e7i	1.50963	+	1.50963i
$808$		0			0
$809$			211588.i			0.0113663i	0.999984	+	0.00568316i	$0.00180902\pi$
$809$			211588.i			0.0113663i	−0.999984	+	0.00568316i	$0.998191\pi$
$810$		0			0
$811$			9.26264e6i			0.494519i	0.968949	+	0.247259i	$0.0795300\pi$
$811$			9.26264e6i			0.494519i	−0.968949	+	0.247259i	$0.920470\pi$
$812$		0			0
$813$	1.10984e7	+	1.10984e7i	0.588889	+	0.588889i
$814$		0			0
$815$	1.98533e7	+	1.11857e7i	1.04698	+	0.589888i
$816$		0			0
$817$	−4.06955e6	+	4.06955e6i	−0.213300	+	0.213300i
$818$		0			0
$819$	5.29105e6			0.275634
$820$		0			0
$821$	2.04408e7			1.05838			0.529188	−	0.848504i	$-0.322497\pi$
$821$	2.04408e7			1.05838			0.529188	+	0.848504i	$0.322497\pi$
$822$		0			0
$823$	−1.53534e7	+	1.53534e7i	−0.790144	+	0.790144i	−0.981517	−	0.191373i	$-0.938706\pi$
$823$	−1.53534e7	+	1.53534e7i	−0.790144	+	0.790144i	0.191373	+	0.981517i	$0.438706\pi$
$824$		0			0
$825$	−3.59181e7	−	8.81931e6i	−1.83729	−	0.451128i
$826$		0			0
$827$	−2.13110e6	−	2.13110e6i	−0.108353	−	0.108353i	0.650852	−	0.759205i	$-0.274412\pi$
$827$	−2.13110e6	−	2.13110e6i	−0.108353	−	0.108353i	−0.759205	+	0.650852i	$0.774412\pi$
$828$		0			0
$829$		−	515565.i		−	0.0260554i	−0.999915	−	0.0130277i	$-0.995853\pi$
$829$		−	515565.i		−	0.0260554i	0.999915	−	0.0130277i	$-0.00414696\pi$
$830$		0			0
$831$		−	3.05282e7i		−	1.53355i
$832$		0			0
$833$	5.90399e6	+	5.90399e6i	0.294804	+	0.294804i
$834$		0			0
$835$	−3.03826e6	+	5.39254e6i	−0.150802	+	0.267656i
$836$		0			0
$837$	3.54267e6	−	3.54267e6i	0.174790	−	0.174790i
$838$		0			0
$839$	−1.95536e7			−0.959009			−0.479504	−	0.877540i	$-0.659184\pi$
$839$	−1.95536e7			−0.959009			−0.479504	+	0.877540i	$0.659184\pi$
$840$		0			0
$841$	2.04176e7			0.995440
$842$		0			0
$843$	−10914.6	+	10914.6i	−0.000528980	+	0.000528980i
$844$		0			0
$845$	1.07117e7	−	2.99122e6i	0.516079	−	0.144114i
$846$		0			0
$847$	1.73577e7	+	1.73577e7i	0.831348	+	0.831348i
$848$		0			0
$849$			3.48242e6i			0.165811i
$850$		0			0
$851$		−	2.75761e7i		−	1.30530i
$852$		0			0
$853$	−6.28522e6	−	6.28522e6i	−0.295766	−	0.295766i	0.543587	−	0.839353i	$-0.317066\pi$
$853$	−6.28522e6	−	6.28522e6i	−0.295766	−	0.295766i	−0.839353	+	0.543587i	$0.817066\pi$
$854$		0			0
$855$	1.27173e7	−	3.55128e6i	0.594949	−	0.166138i
$856$		0			0
$857$	1.66174e7	−	1.66174e7i	0.772877	−	0.772877i	−0.205731	−	0.978609i	$-0.565957\pi$
$857$	1.66174e7	−	1.66174e7i	0.772877	−	0.772877i	0.978609	+	0.205731i	$0.0659573\pi$
$858$		0			0
$859$	−1.28613e7			−0.594706			−0.297353	−	0.954768i	$-0.596104\pi$
$859$	−1.28613e7			−0.594706			−0.297353	+	0.954768i	$0.596104\pi$
$860$		0			0
$861$	3.49045e7			1.60463
$862$		0			0
$863$	−1.93783e7	+	1.93783e7i	−0.885702	+	0.885702i	−0.994107	−	0.108405i	$-0.965426\pi$
$863$	−1.93783e7	+	1.93783e7i	−0.885702	+	0.885702i	0.108405	+	0.994107i	$0.465426\pi$
$864$		0			0
$865$	9.39308e6	−	1.66716e7i	0.426843	−	0.757594i
$866$		0			0
$867$	1.66442e7	+	1.66442e7i	0.751996	+	0.751996i
$868$		0			0
$869$			7.38223e6i			0.331618i
$870$		0			0
$871$			2.34082e7i			1.04550i
$872$		0			0
$873$	2.87559e6	+	2.87559e6i	0.127700	+	0.127700i
$874$		0			0
$875$	595440.	+	1.88757e7i	0.0262917	+	0.833454i
$876$		0			0
$877$	−9.93996e6	+	9.93996e6i	−0.436401	+	0.436401i	−0.890799	−	0.454398i	$-0.849854\pi$
$877$	−9.93996e6	+	9.93996e6i	−0.436401	+	0.436401i	0.454398	+	0.890799i	$0.349854\pi$
$878$		0			0
$879$	−4.88438e7			−2.13225
$880$		0			0
$881$	−2.91928e6			−0.126717			−0.0633586	−	0.997991i	$-0.520181\pi$
$881$	−2.91928e6			−0.126717			−0.0633586	+	0.997991i	$0.520181\pi$
$882$		0			0
$883$	−1.88490e7	+	1.88490e7i	−0.813554	+	0.813554i	−0.985165	−	0.171611i	$-0.945103\pi$
$883$	−1.88490e7	+	1.88490e7i	−0.813554	+	0.813554i	0.171611	+	0.985165i	$0.445103\pi$
$884$		0			0
$885$	−1.07488e7	−	6.05608e6i	−0.461320	−	0.259916i
$886$		0			0
$887$	−3.72094e6	−	3.72094e6i	−0.158798	−	0.158798i	0.623236	−	0.782034i	$-0.285818\pi$
$887$	−3.72094e6	−	3.72094e6i	−0.158798	−	0.158798i	−0.782034	+	0.623236i	$0.785818\pi$
$888$		0			0
$889$		−	2.04836e7i		−	0.869264i
$890$		0			0
$891$		−	4.59760e7i		−	1.94016i
$892$		0			0
$893$	−1.36812e6	−	1.36812e6i	−0.0574110	−	0.0574110i
$894$		0			0
$895$	426967.	+	1.52899e6i	0.0178171	+	0.0638038i
$896$		0			0
$897$	1.09805e7	−	1.09805e7i	0.455660	−	0.455660i
$898$		0			0
$899$	−644685.			−0.0266041
$900$		0			0
$901$	−4.86401e7			−1.99610
$902$		0			0
$903$	−4.17162e6	+	4.17162e6i	−0.170249	+	0.170249i
$904$		0			0
$905$	9.58224e6	+	3.43145e7i	0.388907	+	1.39269i
$906$		0			0
$907$	−2.54494e7	−	2.54494e7i	−1.02721	−	1.02721i	−0.999619	−	0.0275916i	$-0.991216\pi$
$907$	−2.54494e7	−	2.54494e7i	−1.02721	−	1.02721i	−0.0275916	−	0.999619i	$-0.508784\pi$
$908$		0			0
$909$		−	2.00415e7i		−	0.804489i
$910$		0			0
$911$			5.37011e6i			0.214382i	0.994238	+	0.107191i	$0.0341856\pi$
$911$			5.37011e6i			0.214382i	−0.994238	+	0.107191i	$0.965814\pi$
$912$		0			0
$913$	−2.81474e7	−	2.81474e7i	−1.11753	−	1.11753i
$914$		0			0
$915$	1.21187e6	+	682791.i	0.0478524	+	0.0269610i
$916$		0			0
$917$	−2.74101e7	+	2.74101e7i	−1.07643	+	1.07643i
$918$		0			0
$919$	2.05214e7			0.801527			0.400764	−	0.916182i	$-0.368745\pi$
$919$	2.05214e7			0.801527			0.400764	+	0.916182i	$0.368745\pi$
$920$		0			0
$921$	−3.73522e7			−1.45100
$922$		0			0
$923$	7.47215e6	−	7.47215e6i	0.288696	−	0.288696i
$924$		0			0
$925$	−1.04363e7	+	4.25035e7i	−0.401044	+	1.63332i
$926$		0			0
$927$	1.36790e7	+	1.36790e7i	0.522825	+	0.522825i
$928$		0			0
$929$			3.95102e7i			1.50200i	0.660301	+	0.751001i	$0.270429\pi$
$929$			3.95102e7i			1.50200i	−0.660301	+	0.751001i	$0.729571\pi$
$930$		0			0
$931$		−	1.02585e7i		−	0.387892i
$932$		0			0
$933$	−3.72364e7	−	3.72364e7i	−1.40044	−	1.40044i
$934$		0			0
$935$	−2.78758e7	+	4.94761e7i	−1.04279	+	1.85083i
$936$		0			0
$937$	1.92190e7	−	1.92190e7i	0.715124	−	0.715124i	−0.252479	−	0.967602i	$-0.581246\pi$
$937$	1.92190e7	−	1.92190e7i	0.715124	−	0.715124i	0.967602	+	0.252479i	$0.0812457\pi$
$938$		0			0
$939$	1.05696e7			0.391198
$940$		0			0
$941$	−4.10306e7			−1.51055			−0.755274	−	0.655410i	$-0.772496\pi$
$941$	−4.10306e7			−1.51055			−0.755274	+	0.655410i	$0.772496\pi$
$942$		0			0
$943$	2.36635e7	−	2.36635e7i	0.866562	−	0.866562i
$944$		0			0
$945$	−1.38333e7	+	3.86291e6i	−0.503901	+	0.140713i
$946$		0			0
$947$	−1.98768e6	−	1.98768e6i	−0.0720229	−	0.0720229i	0.670178	−	0.742201i	$-0.266218\pi$
$947$	−1.98768e6	−	1.98768e6i	−0.0720229	−	0.0720229i	−0.742201	+	0.670178i	$0.766218\pi$
$948$		0			0
$949$		−	605453.i		−	0.0218230i
$950$		0			0
$951$			1.59590e7i			0.572207i
$952$		0			0
$953$	−2.84920e7	−	2.84920e7i	−1.01623	−	1.01623i	−0.999866	−	0.0163614i	$-0.994792\pi$
$953$	−2.84920e7	−	2.84920e7i	−1.01623	−	1.01623i	−0.0163614	−	0.999866i	$-0.505208\pi$
$954$		0			0
$955$	3.32970e7	−	9.29812e6i	1.18140	−	0.329903i
$956$		0			0
$957$	−2.55932e6	+	2.55932e6i	−0.0903327	+	0.0903327i
$958$		0			0
$959$	2.38539e7			0.837554
$960$		0			0
$961$	2.41852e7			0.844776
$962$		0			0
$963$	−8.07252e6	+	8.07252e6i	−0.280507	+	0.280507i
$964$		0			0
$965$	−839812.	+	1.49056e6i	−0.0290311	+	0.0515267i
$966$		0			0
$967$	7.76889e6	+	7.76889e6i	0.267173	+	0.267173i	0.827960	−	0.560787i	$-0.189501\pi$
$967$	7.76889e6	+	7.76889e6i	0.267173	+	0.267173i	−0.560787	+	0.827960i	$0.689501\pi$
$968$		0			0
$969$		−	6.20609e7i		−	2.12329i
$970$		0			0
$971$			3.18845e7i			1.08525i	0.839974	+	0.542627i	$0.182570\pi$
$971$			3.18845e7i			1.08525i	−0.839974	+	0.542627i	$0.817430\pi$
$972$		0			0
$973$	1.61914e7	+	1.61914e7i	0.548280	+	0.548280i
$974$		0			0
$975$	−2.10800e7	+	1.27688e7i	−0.710166	+	0.430169i
$976$		0			0
$977$	−1.76818e7	+	1.76818e7i	−0.592639	+	0.592639i	−0.938344	−	0.345704i	$-0.887640\pi$
$977$	−1.76818e7	+	1.76818e7i	−0.592639	+	0.592639i	0.345704	+	0.938344i	$0.387640\pi$
$978$		0			0
$979$	−8.96419e7			−2.98920
$980$		0			0
$981$	−2.38183e6			−0.0790204
$982$		0			0
$983$	3.50989e6	−	3.50989e6i	0.115854	−	0.115854i	−0.646803	−	0.762657i	$-0.723894\pi$
$983$	3.50989e6	−	3.50989e6i	0.115854	−	0.115854i	0.762657	+	0.646803i	$0.223894\pi$
$984$		0			0
$985$	2.61961e6	+	1.47594e6i	0.0860293	+	0.0484705i
$986$		0			0
$987$	−1.40243e6	−	1.40243e6i	−0.0458235	−	0.0458235i
$988$		0			0
$989$			5.65629e6i			0.183883i
$990$		0			0
$991$		−	3.64175e7i		−	1.17795i	−0.808152	−	0.588974i	$-0.799532\pi$
$991$		−	3.64175e7i		−	1.17795i	0.808152	−	0.588974i	$-0.200468\pi$
$992$		0			0
$993$	−2.92115e7	−	2.92115e7i	−0.940115	−	0.940115i
$994$		0			0
$995$	3.88632e6	+	1.39171e7i	0.124446	+	0.445647i
$996$		0			0
$997$	1.98847e7	−	1.98847e7i	0.633551	−	0.633551i	−0.315406	−	0.948957i	$-0.602141\pi$
$997$	1.98847e7	−	1.98847e7i	0.633551	−	0.633551i	0.948957	+	0.315406i	$0.102141\pi$
$998$		0			0
$999$	−3.32851e7			−1.05520

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.b.63.2	yes	14
4.3	odd	2		160.6.n.a.63.6	✓	14
5.2	odd	4		160.6.n.a.127.6	yes	14
20.7	even	4	inner	160.6.n.b.127.2	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.a.63.6	✓	14	4.3	odd	2
160.6.n.a.127.6	yes	14	5.2	odd	4
160.6.n.b.63.2	yes	14	1.1	even	1	trivial
160.6.n.b.127.2	yes	14	20.7	even	4	inner

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.4331 + 13.4331i) q^{3} +(15.0352 + 53.8418i) q^{5} +(-76.4413 - 76.4413i) q^{7} -117.896i q^{9} +O(q^{10})\)	\(q+(-13.4331 + 13.4331i) q^{3} +(15.0352 + 53.8418i) q^{5} +(-76.4413 - 76.4413i) q^{7} -117.896i q^{9} -622.995i q^{11} +(-293.552 - 293.552i) q^{13} +(-925.232 - 521.293i) q^{15} +(-1153.02 + 1153.02i) q^{17} +2003.44 q^{19} +2053.69 q^{21} +(1392.29 - 1392.29i) q^{23} +(-2672.88 + 1619.05i) q^{25} +(-1680.53 - 1680.53i) q^{27} +305.819i q^{29} +2108.06i q^{31} +(8368.75 + 8368.75i) q^{33} +(2966.43 - 5265.05i) q^{35} +(9903.12 - 9903.12i) q^{37} +7886.62 q^{39} +16996.0 q^{41} +(-2031.28 + 2031.28i) q^{43} +(6347.74 - 1772.59i) q^{45} +(-682.885 - 682.885i) q^{47} -5120.46i q^{49} -30977.2i q^{51} +(21092.5 + 21092.5i) q^{53} +(33543.2 - 9366.86i) q^{55} +(-26912.4 + 26912.4i) q^{57} +11617.4 q^{59} -1309.80 q^{61} +(-9012.12 + 9012.12i) q^{63} +(11391.8 - 20219.0i) q^{65} +(-39870.6 - 39870.6i) q^{67} +37405.7i q^{69} +25454.3i q^{71} +(1031.25 + 1031.25i) q^{73} +(14156.3 - 57653.9i) q^{75} +(-47622.5 + 47622.5i) q^{77} -11849.6 q^{79} +73798.3 q^{81} +(45180.7 - 45180.7i) q^{83} +(-79416.5 - 44744.7i) q^{85} +(-4108.09 - 4108.09i) q^{87} -143889. i q^{89} +44879.0i q^{91} +(-28317.8 - 28317.8i) q^{93} +(30122.1 + 107869. i) q^{95} +(-24390.9 + 24390.9i) q^{97} -73448.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7}+O(q^{10}) \) 14 * q + 10 * q^3 + 42 * q^5 + 66 * q^7	\( 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7} - 414 q^{13} + 278 q^{15} + 1222 q^{17} + 5672 q^{19} + 5924 q^{21} + 2902 q^{23} - 4466 q^{25} - 2168 q^{27} - 2444 q^{33} - 2618 q^{35} - 1790 q^{37} - 11076 q^{39} + 11644 q^{41} - 3982 q^{43} + 14704 q^{45} - 1278 q^{47} + 5882 q^{53} + 65608 q^{55} - 14552 q^{57} - 8504 q^{59} + 20564 q^{61} + 19422 q^{63} + 40798 q^{65} + 107926 q^{67} - 16418 q^{73} + 66586 q^{75} - 13348 q^{77} - 146544 q^{79} + 173806 q^{81} - 36398 q^{83} - 66262 q^{85} + 124384 q^{87} - 306620 q^{93} + 173768 q^{95} - 60314 q^{97} - 388628 q^{99}+O(q^{100}) \) 14 * q + 10 * q^3 + 42 * q^5 + 66 * q^7 - 414 * q^13 + 278 * q^15 + 1222 * q^17 + 5672 * q^19 + 5924 * q^21 + 2902 * q^23 - 4466 * q^25 - 2168 * q^27 - 2444 * q^33 - 2618 * q^35 - 1790 * q^37 - 11076 * q^39 + 11644 * q^41 - 3982 * q^43 + 14704 * q^45 - 1278 * q^47 + 5882 * q^53 + 65608 * q^55 - 14552 * q^57 - 8504 * q^59 + 20564 * q^61 + 19422 * q^63 + 40798 * q^65 + 107926 * q^67 - 16418 * q^73 + 66586 * q^75 - 13348 * q^77 - 146544 * q^79 + 173806 * q^81 - 36398 * q^83 - 66262 * q^85 + 124384 * q^87 - 306620 * q^93 + 173768 * q^95 - 60314 * q^97 - 388628 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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