LMFDB - Embedded newform 160.6.n.b.127.6

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			127.6
Root			$-2.20370 + 2.20370i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.6.n.b.63.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.9598 + 10.9598i) q^{3} +(-14.9228 + 53.8731i) q^{5} +(-75.2427 + 75.2427i) q^{7} -2.76340i q^{9} +O(q^{10})$	\(q+(10.9598 + 10.9598i) q^{3} +(-14.9228 + 53.8731i) q^{5} +(-75.2427 + 75.2427i) q^{7} -2.76340i q^{9} +207.864i q^{11} +(-233.921 + 233.921i) q^{13} +(-753.993 + 426.889i) q^{15} +(-721.173 - 721.173i) q^{17} +114.040 q^{19} -1649.30 q^{21} +(-957.212 - 957.212i) q^{23} +(-2679.62 - 1607.88i) q^{25} +(2693.53 - 2693.53i) q^{27} +4187.54i q^{29} -2744.83i q^{31} +(-2278.16 + 2278.16i) q^{33} +(-2930.73 - 5176.39i) q^{35} +(6906.15 + 6906.15i) q^{37} -5127.48 q^{39} -8458.40 q^{41} +(-13397.2 - 13397.2i) q^{43} +(148.873 + 41.2377i) q^{45} +(6672.94 - 6672.94i) q^{47} +5484.06i q^{49} -15807.9i q^{51} +(-13054.5 + 13054.5i) q^{53} +(-11198.3 - 3101.92i) q^{55} +(1249.86 + 1249.86i) q^{57} -11302.5 q^{59} -56065.4 q^{61} +(207.926 + 207.926i) q^{63} +(-9111.29 - 16092.8i) q^{65} +(35802.8 - 35802.8i) q^{67} -20981.8i q^{69} +74255.2i q^{71} +(-58806.0 + 58806.0i) q^{73} +(-11746.1 - 46990.3i) q^{75} +(-15640.3 - 15640.3i) q^{77} -65319.6 q^{79} +58369.9 q^{81} +(35508.0 + 35508.0i) q^{83} +(49613.8 - 28089.9i) q^{85} +(-45894.8 + 45894.8i) q^{87} -11119.6i q^{89} -35201.7i q^{91} +(30083.0 - 30083.0i) q^{93} +(-1701.79 + 6143.67i) q^{95} +(86604.7 + 86604.7i) q^{97} +574.413 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

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

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
$3$	10.9598	+	10.9598i	0.703075	+	0.703075i	0.965069	−	0.261995i	$-0.0843803\pi$
$3$	10.9598	+	10.9598i	0.703075	+	0.703075i	−0.261995	+	0.965069i	$0.584380\pi$
$4$		0			0
$5$	−14.9228	+	53.8731i	−0.266947	+	0.963711i
$5$	−14.9228	+	53.8731i	−0.266947	+	0.963711i
$6$		0			0
$7$	−75.2427	+	75.2427i	−0.580390	+	0.580390i	−0.935010	−	0.354621i	$-0.884610\pi$
$7$	−75.2427	+	75.2427i	−0.580390	+	0.580390i	0.354621	+	0.935010i	$0.384610\pi$
$8$		0			0
$9$		−	2.76340i		−	0.0113720i
$10$		0			0
$11$			207.864i			0.517963i	0.965882	+	0.258981i	$0.0833868\pi$
$11$			207.864i			0.517963i	−0.965882	+	0.258981i	$0.916613\pi$
$12$		0			0
$13$	−233.921	+	233.921i	−0.383894	+	0.383894i	−0.872503	−	0.488609i	$-0.837504\pi$
$13$	−233.921	+	233.921i	−0.383894	+	0.383894i	0.488609	+	0.872503i	$0.337504\pi$
$14$		0			0
$15$	−753.993	+	426.889i	−0.865245	+	0.489877i
$16$		0			0
$17$	−721.173	−	721.173i	−0.605226	−	0.605226i	0.336469	−	0.941695i	$-0.390767\pi$
$17$	−721.173	−	721.173i	−0.605226	−	0.605226i	−0.941695	+	0.336469i	$0.890767\pi$
$18$		0			0
$19$	114.040			0.0724723			0.0362361	−	0.999343i	$-0.488463\pi$
$19$	114.040			0.0724723			0.0362361	+	0.999343i	$0.488463\pi$
$20$		0			0
$21$	−1649.30			−0.816114
$22$		0			0
$23$	−957.212	−	957.212i	−0.377302	−	0.377302i	0.492826	−	0.870128i	$-0.335964\pi$
$23$	−957.212	−	957.212i	−0.377302	−	0.377302i	−0.870128	+	0.492826i	$0.835964\pi$
$24$		0			0
$25$	−2679.62	−	1607.88i	−0.857478	−	0.514520i
$26$		0			0
$27$	2693.53	−	2693.53i	0.711070	−	0.711070i
$28$		0			0
$29$			4187.54i			0.924622i	0.886718	+	0.462311i	$0.152980\pi$
$29$			4187.54i			0.924622i	−0.886718	+	0.462311i	$0.847020\pi$
$30$		0			0
$31$		−	2744.83i		−	0.512993i	−0.966545	−	0.256497i	$-0.917432\pi$
$31$		−	2744.83i		−	0.512993i	0.966545	−	0.256497i	$-0.0825683\pi$
$32$		0			0
$33$	−2278.16	+	2278.16i	−0.364166	+	0.364166i
$34$		0			0
$35$	−2930.73	−	5176.39i	−0.404394	−	0.714261i
$36$		0			0
$37$	6906.15	+	6906.15i	0.829339	+	0.829339i	0.987425	−	0.158087i	$-0.0505325\pi$
$37$	6906.15	+	6906.15i	0.829339	+	0.829339i	−0.158087	+	0.987425i	$0.550532\pi$
$38$		0			0
$39$	−5127.48			−0.539812
$40$		0			0
$41$	−8458.40			−0.785830			−0.392915	−	0.919575i	$-0.628533\pi$
$41$	−8458.40			−0.785830			−0.392915	+	0.919575i	$0.628533\pi$
$42$		0			0
$43$	−13397.2	−	13397.2i	−1.10495	−	1.10495i	−0.993804	−	0.111143i	$-0.964549\pi$
$43$	−13397.2	−	13397.2i	−1.10495	−	1.10495i	−0.111143	−	0.993804i	$-0.535451\pi$
$44$		0			0
$45$	148.873	+	41.2377i	0.0109593	+	0.00303573i
$46$		0			0
$47$	6672.94	−	6672.94i	0.440629	−	0.440629i	−0.451594	−	0.892223i	$-0.649145\pi$
$47$	6672.94	−	6672.94i	0.440629	−	0.440629i	0.892223	+	0.451594i	$0.149145\pi$
$48$		0			0
$49$			5484.06i			0.326296i
$50$		0			0
$51$		−	15807.9i		−	0.851038i
$52$		0			0
$53$	−13054.5	+	13054.5i	−0.638366	+	0.638366i	−0.950152	−	0.311786i	$-0.899073\pi$
$53$	−13054.5	+	13054.5i	−0.638366	+	0.638366i	0.311786	+	0.950152i	$0.399073\pi$
$54$		0			0
$55$	−11198.3	−	3101.92i	−0.499166	−	0.138269i
$56$		0			0
$57$	1249.86	+	1249.86i	0.0509534	+	0.0509534i
$58$		0			0
$59$	−11302.5			−0.422713			−0.211356	−	0.977409i	$-0.567788\pi$
$59$	−11302.5			−0.422713			−0.211356	+	0.977409i	$0.567788\pi$
$60$		0			0
$61$	−56065.4			−1.92917			−0.964584	−	0.263774i	$-0.915033\pi$
$61$	−56065.4			−1.92917			−0.964584	+	0.263774i	$0.915033\pi$
$62$		0			0
$63$	207.926	+	207.926i	0.00660020	+	0.00660020i
$64$		0			0
$65$	−9111.29	−	16092.8i	−0.267483	−	0.472442i
$66$		0			0
$67$	35802.8	−	35802.8i	0.974384	−	0.974384i	−0.0252960	−	0.999680i	$-0.508053\pi$
$67$	35802.8	−	35802.8i	0.974384	−	0.974384i	0.999680	+	0.0252960i	$0.00805283\pi$
$68$		0			0
$69$		−	20981.8i		−	0.530543i
$70$		0			0
$71$			74255.2i			1.74816i	0.485784	+	0.874079i	$0.338534\pi$
$71$			74255.2i			1.74816i	−0.485784	+	0.874079i	$0.661466\pi$
$72$		0			0
$73$	−58806.0	+	58806.0i	−1.29156	+	1.29156i	−0.357737	+	0.933822i	$0.616452\pi$
$73$	−58806.0	+	58806.0i	−1.29156	+	1.29156i	−0.933822	+	0.357737i	$0.883548\pi$
$74$		0			0
$75$	−11746.1	−	46990.3i	−0.241125	−	0.964617i
$76$		0			0
$77$	−15640.3	−	15640.3i	−0.300620	−	0.300620i
$78$		0			0
$79$	−65319.6			−1.17754			−0.588770	−	0.808301i	$-0.700388\pi$
$79$	−65319.6			−1.17754			−0.588770	+	0.808301i	$0.700388\pi$
$80$		0			0
$81$	58369.9			0.988499
$82$		0			0
$83$	35508.0	+	35508.0i	0.565758	+	0.565758i	0.930937	−	0.365180i	$-0.118992\pi$
$83$	35508.0	+	35508.0i	0.565758	+	0.565758i	−0.365180	+	0.930937i	$0.618992\pi$
$84$		0			0
$85$	49613.8	−	28089.9i	0.744826	−	0.421699i
$86$		0			0
$87$	−45894.8	+	45894.8i	−0.650078	+	0.650078i
$88$		0			0
$89$		−	11119.6i		−	0.148803i	−0.997228	−	0.0744017i	$-0.976295\pi$
$89$		−	11119.6i		−	0.148803i	0.997228	−	0.0744017i	$-0.0237047\pi$
$90$		0			0
$91$		−	35201.7i		−	0.445616i
$92$		0			0
$93$	30083.0	−	30083.0i	0.360673	−	0.360673i
$94$		0			0
$95$	−1701.79	+	6143.67i	−0.0193463	+	0.0698423i
$96$		0			0
$97$	86604.7	+	86604.7i	0.934571	+	0.934571i	0.997987	−	0.0634164i	$-0.0201996\pi$
$97$	86604.7	+	86604.7i	0.934571	+	0.934571i	−0.0634164	+	0.997987i	$0.520200\pi$
$98$		0			0
$99$	574.413			0.00589028
$100$		0			0
$101$	60159.9			0.586818			0.293409	−	0.955987i	$-0.405210\pi$
$101$	60159.9			0.586818			0.293409	+	0.955987i	$0.405210\pi$
$102$		0			0
$103$	96594.3	+	96594.3i	0.897136	+	0.897136i	0.995182	−	0.0980456i	$-0.0312591\pi$
$103$	96594.3	+	96594.3i	0.897136	+	0.897136i	−0.0980456	+	0.995182i	$0.531259\pi$
$104$		0			0
$105$	24612.2	−	88852.8i	0.217860	−	0.786498i
$106$		0			0
$107$	140032.	−	140032.i	1.18241	−	1.18241i	0.203292	−	0.979118i	$-0.434836\pi$
$107$	140032.	−	140032.i	1.18241	−	1.18241i	0.979118	−	0.203292i	$-0.0651641\pi$
$108$		0			0
$109$			59153.9i			0.476889i	0.971156	+	0.238445i	$0.0766375\pi$
$109$			59153.9i			0.476889i	−0.971156	+	0.238445i	$0.923362\pi$
$110$		0			0
$111$			151381.i			1.16617i
$112$		0			0
$113$	22649.2	−	22649.2i	0.166862	−	0.166862i	−0.618737	−	0.785598i	$-0.712355\pi$
$113$	22649.2	−	22649.2i	0.166862	−	0.166862i	0.785598	+	0.618737i	$0.212355\pi$
$114$		0			0
$115$	65852.3	−	37283.7i	0.464330	−	0.262890i
$116$		0			0
$117$	646.417	+	646.417i	0.00436564	+	0.00436564i
$118$		0			0
$119$	108526.			0.702533
$120$		0			0
$121$	117843.			0.731715
$122$		0			0
$123$	−92702.8	−	92702.8i	−0.552497	−	0.552497i
$124$		0			0
$125$	126609.	−	120365.i	0.724751	−	0.689011i
$126$		0			0
$127$	−44108.6	+	44108.6i	−0.242669	+	0.242669i	−0.817953	−	0.575285i	$-0.804891\pi$
$127$	−44108.6	+	44108.6i	−0.242669	+	0.242669i	0.575285	+	0.817953i	$0.304891\pi$
$128$		0			0
$129$		−	293662.i		−	1.55372i
$130$		0			0
$131$			248718.i			1.26628i	0.774038	+	0.633139i	$0.218234\pi$
$131$			248718.i			1.26628i	−0.774038	+	0.633139i	$0.781766\pi$
$132$		0			0
$133$	−8580.66	+	8580.66i	−0.0420621	+	0.0420621i
$134$		0			0
$135$	104914.	+	185304.i	0.495448	+	0.875084i
$136$		0			0
$137$	−22781.4	−	22781.4i	−0.103700	−	0.103700i	0.653353	−	0.757053i	$-0.273362\pi$
$137$	−22781.4	−	22781.4i	−0.103700	−	0.103700i	−0.757053	+	0.653353i	$0.773362\pi$
$138$		0			0
$139$	−67318.4			−0.295527			−0.147763	−	0.989023i	$-0.547207\pi$
$139$	−67318.4			−0.295527			−0.147763	+	0.989023i	$0.547207\pi$
$140$		0			0
$141$	146269.			0.619590
$142$		0			0
$143$	−48623.9	−	48623.9i	−0.198843	−	0.198843i
$144$		0			0
$145$	−225596.	−	62489.9i	−0.891069	−	0.246825i
$146$		0			0
$147$	−60104.4	+	60104.4i	−0.229410	+	0.229410i
$148$		0			0
$149$			465212.i			1.71666i	0.513096	+	0.858331i	$0.328499\pi$
$149$			465212.i			1.71666i	−0.513096	+	0.858331i	$0.671501\pi$
$150$		0			0
$151$			389781.i			1.39116i	0.718447	+	0.695582i	$0.244853\pi$
$151$			389781.i			1.39116i	−0.718447	+	0.695582i	$0.755147\pi$
$152$		0			0
$153$	−1992.89	+	1992.89i	−0.00688264	+	0.00688264i
$154$		0			0
$155$	147873.	+	40960.6i	0.494377	+	0.136942i
$156$		0			0
$157$	−134965.	−	134965.i	−0.436991	−	0.436991i	0.454007	−	0.890998i	$-0.349994\pi$
$157$	−134965.	−	134965.i	−0.436991	−	0.436991i	−0.890998	+	0.454007i	$0.849994\pi$
$158$		0			0
$159$	−286150.			−0.897638
$160$		0			0
$161$	144047.			0.437964
$162$		0			0
$163$	−38557.6	−	38557.6i	−0.113669	−	0.113669i	0.647985	−	0.761653i	$-0.275612\pi$
$163$	−38557.6	−	38557.6i	−0.113669	−	0.113669i	−0.761653	+	0.647985i	$0.775612\pi$
$164$		0			0
$165$	−88735.1	−	156728.i	−0.253738	−	0.448165i
$166$		0			0
$167$	53486.3	−	53486.3i	0.148406	−	0.148406i	−0.629000	−	0.777406i	$-0.716535\pi$
$167$	53486.3	−	53486.3i	0.148406	−	0.148406i	0.777406	+	0.629000i	$0.216535\pi$
$168$		0			0
$169$			261855.i			0.705251i
$170$		0			0
$171$		−	315.137i		−	0.000824156i
$172$		0			0
$173$	75193.4	−	75193.4i	0.191014	−	0.191014i	−0.605120	−	0.796134i	$-0.706875\pi$
$173$	75193.4	−	75193.4i	0.191014	−	0.191014i	0.796134	+	0.605120i	$0.206875\pi$
$174$		0			0
$175$	322603.	−	80640.9i	0.796294	−	0.199049i
$176$		0			0
$177$	−123874.	−	123874.i	−0.297198	−	0.297198i
$178$		0			0
$179$	168957.			0.394133			0.197066	−	0.980390i	$-0.436859\pi$
$179$	168957.			0.394133			0.197066	+	0.980390i	$0.436859\pi$
$180$		0			0
$181$	130710.			0.296561			0.148280	−	0.988945i	$-0.452626\pi$
$181$	130710.			0.296561			0.148280	+	0.988945i	$0.452626\pi$
$182$		0			0
$183$	−614468.	−	614468.i	−1.35635	−	1.35635i
$184$		0			0
$185$	−475115.	+	268997.i	−1.02063	+	0.577853i
$186$		0			0
$187$	149906.	−	149906.i	0.313484	−	0.313484i
$188$		0			0
$189$			405337.i			0.825395i
$190$		0			0
$191$		−	931440.i		−	1.84744i	−0.383063	−	0.923722i	$-0.625131\pi$
$191$		−	931440.i		−	1.84744i	0.383063	−	0.923722i	$-0.374869\pi$
$192$		0			0
$193$	−258847.	+	258847.i	−0.500207	+	0.500207i	−0.911502	−	0.411295i	$-0.865077\pi$
$193$	−258847.	+	258847.i	−0.500207	+	0.500207i	0.411295	+	0.911502i	$0.365077\pi$
$194$		0			0
$195$	76516.4	−	276233.i	0.144101	−	0.520223i
$196$		0			0
$197$	−650410.	−	650410.i	−1.19405	−	1.19405i	−0.975921	−	0.218126i	$-0.930005\pi$
$197$	−650410.	−	650410.i	−1.19405	−	1.19405i	−0.218126	−	0.975921i	$-0.569995\pi$
$198$		0			0
$199$	−55293.9			−0.0989793			−0.0494897	−	0.998775i	$-0.515759\pi$
$199$	−55293.9			−0.0989793			−0.0494897	+	0.998775i	$0.515759\pi$
$200$		0			0
$201$	784787.			1.37013
$202$		0			0
$203$	−315082.	−	315082.i	−0.536641	−	0.536641i
$204$		0			0
$205$	126223.	−	455680.i	0.209775	−	0.757313i
$206$		0			0
$207$	−2645.16	+	2645.16i	−0.00429068	+	0.00429068i
$208$		0			0
$209$			23704.8i			0.0375379i
$210$		0			0
$211$			447082.i			0.691322i	0.938359	+	0.345661i	$0.112345\pi$
$211$			447082.i			0.691322i	−0.938359	+	0.345661i	$0.887655\pi$
$212$		0			0
$213$	−813825.	+	813825.i	−1.22909	+	1.22909i
$214$		0			0
$215$	921670.	−	521823.i	1.35981	−	0.769887i
$216$		0			0
$217$	206529.	+	206529.i	0.297736	+	0.297736i
$218$		0			0
$219$	−1.28901e6			−1.81613
$220$		0			0
$221$	337395.			0.464685
$222$		0			0
$223$	−562701.	−	562701.i	−0.757732	−	0.757732i	0.218177	−	0.975909i	$-0.429989\pi$
$223$	−562701.	−	562701.i	−0.757732	−	0.757732i	−0.975909	+	0.218177i	$0.929989\pi$
$224$		0			0
$225$	−4443.21	+	7404.86i	−0.00585113	+	0.00975126i
$226$		0			0
$227$	−290103.	+	290103.i	−0.373670	+	0.373670i	−0.868812	−	0.495142i	$-0.835116\pi$
$227$	−290103.	+	290103.i	−0.373670	+	0.373670i	0.495142	+	0.868812i	$0.335116\pi$
$228$		0			0
$229$			887839.i			1.11878i	0.828904	+	0.559391i	$0.188965\pi$
$229$			887839.i			1.11878i	−0.828904	+	0.559391i	$0.811035\pi$
$230$		0			0
$231$		−	342831.i		−	0.422717i
$232$		0			0
$233$	−847028.	+	847028.i	−1.02213	+	1.02213i	−0.0223850	+	0.999749i	$0.507126\pi$
$233$	−847028.	+	847028.i	−1.02213	+	1.02213i	−0.999749	+	0.0223850i	$0.992874\pi$
$234$		0			0
$235$	259913.	+	459071.i	0.307014	+	0.542264i
$236$		0			0
$237$	−715893.	−	715893.i	−0.827899	−	0.827899i
$238$		0			0
$239$	386922.			0.438156			0.219078	−	0.975707i	$-0.429695\pi$
$239$	386922.			0.438156			0.219078	+	0.975707i	$0.429695\pi$
$240$		0			0
$241$	523763.			0.580888			0.290444	−	0.956892i	$-0.406197\pi$
$241$	523763.			0.580888			0.290444	+	0.956892i	$0.406197\pi$
$242$		0			0
$243$	−14802.9	−	14802.9i	−0.0160817	−	0.0160817i
$244$		0			0
$245$	−295443.	−	81837.6i	−0.314455	−	0.0871039i
$246$		0			0
$247$	−26676.3	+	26676.3i	−0.0278216	+	0.0278216i
$248$		0			0
$249$			778324.i			0.795540i
$250$		0			0
$251$			1.78268e6i			1.78604i	0.450022	+	0.893018i	$0.351416\pi$
$251$			1.78268e6i			1.78604i	−0.450022	+	0.893018i	$0.648584\pi$
$252$		0			0
$253$	198970.	−	198970.i	0.195428	−	0.195428i
$254$		0			0
$255$	851620.	+	235898.i	0.820154	+	0.227182i
$256$		0			0
$257$	−1.12252e6	−	1.12252e6i	−1.06013	−	1.06013i	−0.998072	−	0.0620619i	$-0.980232\pi$
$257$	−1.12252e6	−	1.12252e6i	−1.06013	−	1.06013i	−0.0620619	−	0.998072i	$-0.519768\pi$
$258$		0			0
$259$	−1.03928e6			−0.962679
$260$		0			0
$261$	11571.9			0.0105148
$262$		0			0
$263$	−829541.	−	829541.i	−0.739517	−	0.739517i	0.232967	−	0.972485i	$-0.425156\pi$
$263$	−829541.	−	829541.i	−0.739517	−	0.739517i	−0.972485	+	0.232967i	$0.925156\pi$
$264$		0			0
$265$	−508475.	−	898094.i	−0.444790	−	0.785610i
$266$		0			0
$267$	121869.	−	121869.i	0.104620	−	0.104620i
$268$		0			0
$269$		−	1.20735e6i		−	1.01731i	−0.860971	−	0.508655i	$-0.830143\pi$
$269$		−	1.20735e6i		−	1.01731i	0.860971	−	0.508655i	$-0.169857\pi$
$270$		0			0
$271$			334539.i			0.276709i	0.990383	+	0.138355i	$0.0441814\pi$
$271$			334539.i			0.276709i	−0.990383	+	0.138355i	$0.955819\pi$
$272$		0			0
$273$	385806.	−	385806.i	0.313301	−	0.313301i
$274$		0			0
$275$	334220.	−	556998.i	0.266502	−	0.444142i
$276$		0			0
$277$	1.13650e6	+	1.13650e6i	0.889956	+	0.889956i	0.994518	−	0.104562i	$-0.0333442\pi$
$277$	1.13650e6	+	1.13650e6i	0.889956	+	0.889956i	−0.104562	+	0.994518i	$0.533344\pi$
$278$		0			0
$279$	−7585.07			−0.00583377
$280$		0			0
$281$	−57687.8			−0.0435831			−0.0217916	−	0.999763i	$-0.506937\pi$
$281$	−57687.8			−0.0435831			−0.0217916	+	0.999763i	$0.506937\pi$
$282$		0			0
$283$	859732.	+	859732.i	0.638112	+	0.638112i	0.950090	−	0.311977i	$-0.100991\pi$
$283$	859732.	+	859732.i	0.638112	+	0.638112i	−0.311977	+	0.950090i	$0.600991\pi$
$284$		0			0
$285$	−85985.1	+	48682.3i	−0.0627063	+	0.0355025i
$286$		0			0
$287$	636433.	−	636433.i	0.456087	−	0.456087i
$288$		0			0
$289$		−	379675.i		−	0.267404i
$290$		0			0
$291$			1.89835e6i			1.31415i
$292$		0			0
$293$	474947.	−	474947.i	0.323204	−	0.323204i	−0.526791	−	0.849995i	$-0.676605\pi$
$293$	474947.	−	474947.i	0.323204	−	0.323204i	0.849995	+	0.526791i	$0.176605\pi$
$294$		0			0
$295$	168665.	−	608902.i	0.112842	−	0.407373i
$296$		0			0
$297$	559889.	+	559889.i	0.368308	+	0.368308i
$298$		0			0
$299$	447824.			0.289687
$300$		0			0
$301$	2.01608e6			1.28260
$302$		0			0
$303$	659343.	+	659343.i	0.412577	+	0.412577i
$304$		0			0
$305$	836653.	−	3.02042e6i	0.514987	−	1.85916i
$306$		0			0
$307$	1.52594e6	−	1.52594e6i	0.924043	−	0.924043i	−0.0732691	−	0.997312i	$-0.523343\pi$
$307$	1.52594e6	−	1.52594e6i	0.924043	−	0.924043i	0.997312	+	0.0732691i	$0.0233432\pi$
$308$		0			0
$309$			2.11732e6i			1.26151i
$310$		0			0
$311$			816321.i			0.478586i	0.970947	+	0.239293i	$0.0769157\pi$
$311$			816321.i			0.478586i	−0.970947	+	0.239293i	$0.923084\pi$
$312$		0			0
$313$	−599168.	+	599168.i	−0.345691	+	0.345691i	−0.858502	−	0.512811i	$-0.828604\pi$
$313$	−599168.	+	599168.i	−0.345691	+	0.345691i	0.512811	+	0.858502i	$0.328604\pi$
$314$		0			0
$315$	−14304.4	+	8098.77i	−0.00812259	+	0.00459878i
$316$		0			0
$317$	426253.	+	426253.i	0.238242	+	0.238242i	0.816122	−	0.577880i	$-0.196120\pi$
$317$	426253.	+	426253.i	0.238242	+	0.238242i	−0.577880	+	0.816122i	$0.696120\pi$
$318$		0			0
$319$	−870441.			−0.478920
$320$		0			0
$321$	3.06946e6			1.66265
$322$		0			0
$323$	−82242.4	−	82242.4i	−0.0438621	−	0.0438621i
$324$		0			0
$325$	1.00294e6	−	250703.i	0.526701	−	0.131659i
$326$		0			0
$327$	−648318.	+	648318.i	−0.335289	+	0.335289i
$328$		0			0
$329$			1.00418e6i			0.511473i
$330$		0			0
$331$			3.41024e6i			1.71086i	0.517915	+	0.855432i	$0.326708\pi$
$331$			3.41024e6i			1.71086i	−0.517915	+	0.855432i	$0.673292\pi$
$332$		0			0
$333$	19084.5	−	19084.5i	0.00943125	−	0.00943125i
$334$		0			0
$335$	1.39453e6	+	2.46309e6i	0.678915	+	1.19913i
$336$		0			0
$337$	461499.	+	461499.i	0.221359	+	0.221359i	0.809070	−	0.587712i	$-0.199971\pi$
$337$	461499.	+	461499.i	0.221359	+	0.221359i	−0.587712	+	0.809070i	$0.699971\pi$
$338$		0			0
$339$	496464.			0.234633
$340$		0			0
$341$	570553.			0.265711
$342$		0			0
$343$	−1.67724e6	−	1.67724e6i	−0.769768	−	0.769768i
$344$		0			0
$345$	1.13035e6	+	313108.i	0.511290	+	0.141627i
$346$		0			0
$347$	2.76855e6	−	2.76855e6i	1.23432	−	1.23432i	0.272034	−	0.962288i	$-0.412304\pi$
$347$	2.76855e6	−	2.76855e6i	1.23432	−	1.23432i	0.962288	−	0.272034i	$-0.0876965\pi$
$348$		0			0
$349$		−	2.53035e6i		−	1.11203i	−0.831172	−	0.556016i	$-0.812329\pi$
$349$		−	2.53035e6i		−	1.11203i	0.831172	−	0.556016i	$-0.187671\pi$
$350$		0			0
$351$			1.26015e6i			0.545951i
$352$		0			0
$353$	1.48632e6	−	1.48632e6i	0.634856	−	0.634856i	−0.314426	−	0.949282i	$-0.601812\pi$
$353$	1.48632e6	−	1.48632e6i	0.634856	−	0.634856i	0.949282	+	0.314426i	$0.101812\pi$
$354$		0			0
$355$	−4.00035e6	−	1.10810e6i	−1.68472	−	0.466666i
$356$		0			0
$357$	1.18943e6	+	1.18943e6i	0.493933	+	0.493933i
$358$		0			0
$359$	1.53671e6			0.629296			0.314648	−	0.949208i	$-0.398114\pi$
$359$	1.53671e6			0.629296			0.314648	+	0.949208i	$0.398114\pi$
$360$		0			0
$361$	−2.46309e6			−0.994748
$362$		0			0
$363$	1.29155e6	+	1.29155e6i	0.514450	+	0.514450i
$364$		0			0
$365$	−2.29051e6	−	4.04561e6i	−0.899912	−	1.58947i
$366$		0			0
$367$	−1.81385e6	+	1.81385e6i	−0.702970	+	0.702970i	−0.965047	−	0.262077i	$-0.915593\pi$
$367$	−1.81385e6	+	1.81385e6i	−0.702970	+	0.702970i	0.262077	+	0.965047i	$0.415593\pi$
$368$		0			0
$369$			23373.9i			0.00893647i
$370$		0			0
$371$		−	1.96451e6i		−	0.741002i
$372$		0			0
$373$	−2.79814e6	+	2.79814e6i	−1.04135	+	1.04135i	−0.0422450	+	0.999107i	$0.513451\pi$
$373$	−2.79814e6	+	2.79814e6i	−1.04135	+	1.04135i	−0.999107	+	0.0422450i	$0.986549\pi$
$374$		0			0
$375$	2.70680e6	+	68426.7i	0.993980	+	0.0251274i
$376$		0			0
$377$	−979554.	−	979554.i	−0.354957	−	0.354957i
$378$		0			0
$379$	−3.26539e6			−1.16771			−0.583857	−	0.811856i	$-0.698457\pi$
$379$	−3.26539e6			−1.16771			−0.583857	+	0.811856i	$0.698457\pi$
$380$		0			0
$381$	−966847.			−0.341228
$382$		0			0
$383$	1.43914e6	+	1.43914e6i	0.501310	+	0.501310i	0.911845	−	0.410535i	$-0.134658\pi$
$383$	1.43914e6	+	1.43914e6i	0.501310	+	0.501310i	−0.410535	+	0.911845i	$0.634658\pi$
$384$		0			0
$385$	1.07599e6	−	609194.i	0.369961	−	0.209461i
$386$		0			0
$387$	−37021.7	+	37021.7i	−0.0125655	+	0.0125655i
$388$		0			0
$389$		−	3.84322e6i		−	1.28772i	−0.765144	−	0.643859i	$-0.777332\pi$
$389$		−	3.84322e6i		−	1.28772i	0.765144	−	0.643859i	$-0.222668\pi$
$390$		0			0
$391$			1.38063e6i			0.456705i
$392$		0			0
$393$	−2.72591e6	+	2.72591e6i	−0.890288	+	0.890288i
$394$		0			0
$395$	974752.	−	3.51897e6i	0.314341	−	1.13481i
$396$		0			0
$397$	−370411.	−	370411.i	−0.117953	−	0.117953i	0.645667	−	0.763619i	$-0.276580\pi$
$397$	−370411.	−	370411.i	−0.117953	−	0.117953i	−0.763619	+	0.645667i	$0.776580\pi$
$398$		0			0
$399$	−188085.			−0.0591457
$400$		0			0
$401$	−3.33019e6			−1.03421			−0.517105	−	0.855922i	$-0.672990\pi$
$401$	−3.33019e6			−1.03421			−0.517105	+	0.855922i	$0.672990\pi$
$402$		0			0
$403$	642074.	+	642074.i	0.196935	+	0.196935i
$404$		0			0
$405$	−871043.	+	3.14456e6i	−0.263877	+	0.952627i
$406$		0			0
$407$	−1.43554e6	+	1.43554e6i	−0.429567	+	0.429567i
$408$		0			0
$409$			6.13233e6i			1.81267i	0.422565	+	0.906333i	$0.361130\pi$
$409$			6.13233e6i			1.81267i	−0.422565	+	0.906333i	$0.638870\pi$
$410$		0			0
$411$		−	499362.i		−	0.145818i
$412$		0			0
$413$	850432.	−	850432.i	0.245338	−	0.245338i
$414$		0			0
$415$	−2.44280e6	+	1.38304e6i	−0.696254	+	0.394199i
$416$		0			0
$417$	−737800.	−	737800.i	−0.207777	−	0.207777i
$418$		0			0
$419$	−217725.			−0.0605861			−0.0302931	−	0.999541i	$-0.509644\pi$
$419$	−217725.			−0.0605861			−0.0302931	+	0.999541i	$0.509644\pi$
$420$		0			0
$421$	−984530.			−0.270722			−0.135361	−	0.990796i	$-0.543219\pi$
$421$	−984530.			−0.270722			−0.135361	+	0.990796i	$0.543219\pi$
$422$		0			0
$423$	−18440.0	−	18440.0i	−0.00501084	−	0.00501084i
$424$		0			0
$425$	772912.	+	3.09203e6i	0.207567	+	0.830369i
$426$		0			0
$427$	4.21851e6	−	4.21851e6i	1.11967	−	1.11967i
$428$		0			0
$429$		−	1.06582e6i		−	0.279602i
$430$		0			0
$431$		−	4.80717e6i		−	1.24651i	−0.782018	−	0.623255i	$-0.785810\pi$
$431$		−	4.80717e6i		−	1.24651i	0.782018	−	0.623255i	$-0.214190\pi$
$432$		0			0
$433$	1.26993e6	−	1.26993e6i	0.325506	−	0.325506i	−0.525369	−	0.850875i	$-0.676073\pi$
$433$	1.26993e6	−	1.26993e6i	0.325506	−	0.325506i	0.850875	+	0.525369i	$0.176073\pi$
$434$		0			0
$435$	−1.78762e6	−	3.15738e6i	−0.452951	−	0.800024i
$436$		0			0
$437$	−109160.	−	109160.i	−0.0273439	−	0.0273439i
$438$		0			0
$439$	−4.26336e6			−1.05582			−0.527911	−	0.849300i	$-0.677024\pi$
$439$	−4.26336e6			−1.05582			−0.527911	+	0.849300i	$0.677024\pi$
$440$		0			0
$441$	15154.6			0.00371064
$442$		0			0
$443$	−2.54712e6	−	2.54712e6i	−0.616651	−	0.616651i	0.328019	−	0.944671i	$-0.393619\pi$
$443$	−2.54712e6	−	2.54712e6i	−0.616651	−	0.616651i	−0.944671	+	0.328019i	$0.893619\pi$
$444$		0			0
$445$	599045.	+	165935.i	0.143403	+	0.0397227i
$446$		0			0
$447$	−5.09865e6	+	5.09865e6i	−1.20694	+	1.20694i
$448$		0			0
$449$		−	3.41756e6i		−	0.800020i	−0.916511	−	0.400010i	$-0.869007\pi$
$449$		−	3.41756e6i		−	0.800020i	0.916511	−	0.400010i	$-0.130993\pi$
$450$		0			0
$451$		−	1.75820e6i		−	0.407031i
$452$		0			0
$453$	−4.27194e6	+	4.27194e6i	−0.978092	+	0.978092i
$454$		0			0
$455$	1.89643e6	+	525309.i	0.429445	+	0.118956i
$456$		0			0
$457$	1.39943e6	+	1.39943e6i	0.313445	+	0.313445i	0.846243	−	0.532798i	$-0.178859\pi$
$457$	1.39943e6	+	1.39943e6i	0.313445	+	0.313445i	−0.532798	+	0.846243i	$0.678859\pi$
$458$		0			0
$459$	−3.88500e6			−0.860716
$460$		0			0
$461$	1.83239e6			0.401573			0.200787	−	0.979635i	$-0.435650\pi$
$461$	1.83239e6			0.401573			0.200787	+	0.979635i	$0.435650\pi$
$462$		0			0
$463$	−4.50294e6	−	4.50294e6i	−0.976212	−	0.976212i	0.0235115	−	0.999724i	$-0.492515\pi$
$463$	−4.50294e6	−	4.50294e6i	−0.976212	−	0.976212i	−0.999724	+	0.0235115i	$0.992515\pi$
$464$		0			0
$465$	1.17174e6	+	2.06958e6i	0.251304	+	0.443865i
$466$		0			0
$467$	6.07065e6	−	6.07065e6i	1.28808	−	1.28808i	0.352131	−	0.935951i	$-0.385457\pi$
$467$	6.07065e6	−	6.07065e6i	1.28808	−	1.28808i	0.935951	−	0.352131i	$-0.114543\pi$
$468$		0			0
$469$			5.38780e6i			1.13104i
$470$		0			0
$471$		−	2.95839e6i		−	0.614474i
$472$		0			0
$473$	2.78479e6	−	2.78479e6i	0.572322	−	0.572322i
$474$		0			0
$475$	−305583.	−	183362.i	−0.0621434	−	0.0372885i
$476$		0			0
$477$	36074.7	+	36074.7i	0.00725951	+	0.00725951i
$478$		0			0
$479$	9.07331e6			1.80687			0.903435	−	0.428725i	$-0.141037\pi$
$479$	9.07331e6			1.80687			0.903435	+	0.428725i	$0.141037\pi$
$480$		0			0
$481$	−3.23099e6			−0.636756
$482$		0			0
$483$	1.57873e6	+	1.57873e6i	0.307921	+	0.307921i
$484$		0			0
$485$	−5.95805e6	+	3.37328e6i	−1.15014	+	0.651175i
$486$		0			0
$487$	−4.28896e6	+	4.28896e6i	−0.819464	+	0.819464i	−0.986030	−	0.166566i	$-0.946732\pi$
$487$	−4.28896e6	+	4.28896e6i	−0.819464	+	0.819464i	0.166566	+	0.986030i	$0.446732\pi$
$488$		0			0
$489$		−	845171.i		−	0.159835i
$490$		0			0
$491$		−	4.97918e6i		−	0.932083i	−0.884763	−	0.466041i	$-0.845680\pi$
$491$		−	4.97918e6i		−	0.932083i	0.884763	−	0.466041i	$-0.154320\pi$
$492$		0			0
$493$	3.01994e6	−	3.01994e6i	0.559605	−	0.559605i
$494$		0			0
$495$	−8571.85	+	30945.4i	−0.00157240	+	0.00567653i
$496$		0			0
$497$	−5.58716e6	−	5.58716e6i	−1.01461	−	1.01461i
$498$		0			0
$499$	8.06885e6			1.45064			0.725321	−	0.688411i	$-0.241692\pi$
$499$	8.06885e6			1.45064			0.725321	+	0.688411i	$0.241692\pi$
$500$		0			0
$501$	1.17240e6			0.208681
$502$		0			0
$503$	−351210.	−	351210.i	−0.0618938	−	0.0618938i	0.675482	−	0.737376i	$-0.263935\pi$
$503$	−351210.	−	351210.i	−0.0618938	−	0.0618938i	−0.737376	+	0.675482i	$0.763935\pi$
$504$		0			0
$505$	−897755.	+	3.24100e6i	−0.156650	+	0.565523i
$506$		0			0
$507$	−2.86989e6	+	2.86989e6i	−0.495844	+	0.495844i
$508$		0			0
$509$		−	2.07197e6i		−	0.354477i	−0.984168	−	0.177239i	$-0.943284\pi$
$509$		−	2.07197e6i		−	0.354477i	0.984168	−	0.177239i	$-0.0567164\pi$
$510$		0			0
$511$		−	8.84945e6i		−	1.49922i
$512$		0			0
$513$	307169.	−	307169.i	0.0515329	−	0.0515329i
$514$		0			0
$515$	−6.64529e6	+	3.76237e6i	−1.10407	+	0.625092i
$516$		0			0
$517$	1.38707e6	+	1.38707e6i	0.228229	+	0.228229i
$518$		0			0
$519$	1.64822e6			0.268594
$520$		0			0
$521$	−8.07892e6			−1.30394			−0.651972	−	0.758243i	$-0.726058\pi$
$521$	−8.07892e6			−1.30394			−0.651972	+	0.758243i	$0.726058\pi$
$522$		0			0
$523$	2.55559e6	+	2.55559e6i	0.408543	+	0.408543i	0.881230	−	0.472687i	$-0.156716\pi$
$523$	2.55559e6	+	2.55559e6i	0.408543	+	0.408543i	−0.472687	+	0.881230i	$0.656716\pi$
$524$		0			0
$525$	4.41949e6	+	2.65187e6i	0.699800	+	0.419907i
$526$		0			0
$527$	−1.97950e6	+	1.97950e6i	−0.310477	+	0.310477i
$528$		0			0
$529$		−	4.60383e6i		−	0.715287i
$530$		0			0
$531$			31233.4i			0.00480709i
$532$		0			0
$533$	1.97860e6	−	1.97860e6i	0.301675	−	0.301675i
$534$		0			0
$535$	5.45429e6	+	9.63363e6i	0.823860	+	1.45514i
$536$		0			0
$537$	1.85174e6	+	1.85174e6i	0.277105	+	0.277105i
$538$		0			0
$539$	−1.13994e6			−0.169009
$540$		0			0
$541$	−821557.			−0.120683			−0.0603413	−	0.998178i	$-0.519219\pi$
$541$	−821557.			−0.120683			−0.0603413	+	0.998178i	$0.519219\pi$
$542$		0			0
$543$	1.43257e6	+	1.43257e6i	0.208504	+	0.208504i
$544$		0			0
$545$	−3.18680e6	−	882743.i	−0.459583	−	0.127304i
$546$		0			0
$547$	−6.24214e6	+	6.24214e6i	−0.892000	+	0.892000i	−0.994711	−	0.102711i	$-0.967248\pi$
$547$	−6.24214e6	+	6.24214e6i	−0.892000	+	0.892000i	0.102711	+	0.994711i	$0.467248\pi$
$548$		0			0
$549$			154931.i			0.0219385i
$550$		0			0
$551$			477546.i			0.0670095i
$552$		0			0
$553$	4.91483e6	−	4.91483e6i	0.683432	−	0.683432i
$554$		0			0
$555$	−8.15535e6	−	2.25903e6i	−1.12385	−	0.311307i
$556$		0			0
$557$	−883621.	−	883621.i	−0.120678	−	0.120678i	0.644189	−	0.764867i	$-0.277195\pi$
$557$	−883621.	−	883621.i	−0.120678	−	0.120678i	−0.764867	+	0.644189i	$0.777195\pi$
$558$		0			0
$559$	6.26776e6			0.848365
$560$		0			0
$561$	3.28590e6			0.440806
$562$		0			0
$563$	9.36992e6	+	9.36992e6i	1.24585	+	1.24585i	0.957537	+	0.288310i	$0.0930934\pi$
$563$	9.36992e6	+	9.36992e6i	1.24585	+	1.24585i	0.288310	+	0.957537i	$0.406907\pi$
$564$		0			0
$565$	882193.	+	1.55817e6i	0.116263	+	0.205350i
$566$		0			0
$567$	−4.39191e6	+	4.39191e6i	−0.573714	+	0.573714i
$568$		0			0
$569$			2.55469e6i			0.330794i	0.986227	+	0.165397i	$0.0528906\pi$
$569$			2.55469e6i			0.330794i	−0.986227	+	0.165397i	$0.947109\pi$
$570$		0			0
$571$			1.27093e7i			1.63129i	0.578549	+	0.815647i	$0.303619\pi$
$571$			1.27093e7i			1.63129i	−0.578549	+	0.815647i	$0.696381\pi$
$572$		0			0
$573$	1.02084e7	−	1.02084e7i	1.29889	−	1.29889i
$574$		0			0
$575$	1.02589e6	+	4.10404e6i	0.129399	+	0.517657i
$576$		0			0
$577$	5.55174e6	+	5.55174e6i	0.694208	+	0.694208i	0.963155	−	0.268947i	$-0.0866758\pi$
$577$	5.55174e6	+	5.55174e6i	0.694208	+	0.694208i	−0.268947	+	0.963155i	$0.586676\pi$
$578$		0			0
$579$	−5.67385e6			−0.703366
$580$		0			0
$581$	−5.34343e6			−0.656720
$582$		0			0
$583$	−2.71356e6	−	2.71356e6i	−0.330650	−	0.330650i
$584$		0			0
$585$	−44470.9	+	25178.1i	−0.00537262	+	0.00304182i
$586$		0			0
$587$	1.20230e6	−	1.20230e6i	0.144019	−	0.144019i	−0.631421	−	0.775440i	$-0.717528\pi$
$587$	1.20230e6	−	1.20230e6i	0.144019	−	0.144019i	0.775440	+	0.631421i	$0.217528\pi$
$588$		0			0
$589$		−	313020.i		−	0.0371778i
$590$		0			0
$591$		−	1.42568e7i		−	1.67901i
$592$		0			0
$593$	5.12919e6	−	5.12919e6i	0.598980	−	0.598980i	−0.341061	−	0.940041i	$-0.610786\pi$
$593$	5.12919e6	−	5.12919e6i	0.598980	−	0.598980i	0.940041	+	0.341061i	$0.110786\pi$
$594$		0			0
$595$	−1.61952e6	+	5.84664e6i	−0.187539	+	0.677039i
$596$		0			0
$597$	−606013.	−	606013.i	−0.0695898	−	0.0695898i
$598$		0			0
$599$	1.19407e7			1.35976			0.679881	−	0.733322i	$-0.262031\pi$
$599$	1.19407e7			1.35976			0.679881	+	0.733322i	$0.262031\pi$
$600$		0			0
$601$	9.12810e6			1.03085			0.515423	−	0.856936i	$-0.327635\pi$
$601$	9.12810e6			1.03085			0.515423	+	0.856936i	$0.327635\pi$
$602$		0			0
$603$	−98937.5	−	98937.5i	−0.0110807	−	0.0110807i
$604$		0			0
$605$	−1.75855e6	+	6.34859e6i	−0.195329	+	0.705161i
$606$		0			0
$607$	−2.12288e6	+	2.12288e6i	−0.233859	+	0.233859i	−0.814301	−	0.580442i	$-0.802880\pi$
$607$	−2.12288e6	+	2.12288e6i	−0.233859	+	0.233859i	0.580442	+	0.814301i	$0.302880\pi$
$608$		0			0
$609$		−	6.90651e6i		−	0.754597i
$610$		0			0
$611$			3.12188e6i			0.338309i
$612$		0			0
$613$	6.53224e6	−	6.53224e6i	0.702119	−	0.702119i	−0.262746	−	0.964865i	$-0.584628\pi$
$613$	6.53224e6	−	6.53224e6i	0.702119	−	0.702119i	0.964865	+	0.262746i	$0.0846281\pi$
$614$		0			0
$615$	6.37757e6	−	3.61080e6i	0.679935	−	0.384960i
$616$		0			0
$617$	3.08121e6	+	3.08121e6i	0.325843	+	0.325843i	0.851003	−	0.525160i	$-0.175995\pi$
$617$	3.08121e6	+	3.08121e6i	0.325843	+	0.325843i	−0.525160	+	0.851003i	$0.675995\pi$
$618$		0			0
$619$	1.26926e7			1.33145			0.665724	−	0.746198i	$-0.268123\pi$
$619$	1.26926e7			1.33145			0.665724	+	0.746198i	$0.268123\pi$
$620$		0			0
$621$	−5.15656e6			−0.536576
$622$		0			0
$623$	836666.	+	836666.i	0.0863639	+	0.0863639i
$624$		0			0
$625$	4.59509e6	+	8.61699e6i	0.470538	+	0.882380i
$626$		0			0
$627$	−259801.	+	259801.i	−0.0263920	+	0.0263920i
$628$		0			0
$629$		−	9.96107e6i		−	1.00387i
$630$		0			0
$631$		−	8.30473e6i		−	0.830333i	−0.909745	−	0.415166i	$-0.863723\pi$
$631$		−	8.30473e6i		−	0.830333i	0.909745	−	0.415166i	$-0.136277\pi$
$632$		0			0
$633$	−4.89995e6	+	4.89995e6i	−0.486051	+	0.486051i
$634$		0			0
$635$	−1.71804e6	−	3.03449e6i	−0.169083	−	0.298642i
$636$		0			0
$637$	−1.28284e6	−	1.28284e6i	−0.125263	−	0.125263i
$638$		0			0
$639$	205197.			0.0198801
$640$		0			0
$641$	6.99158e6			0.672095			0.336047	−	0.941845i	$-0.390910\pi$
$641$	6.99158e6			0.672095			0.336047	+	0.941845i	$0.390910\pi$
$642$		0			0
$643$	1.28978e7	+	1.28978e7i	1.23024	+	1.23024i	0.963873	+	0.266364i	$0.0858223\pi$
$643$	1.28978e7	+	1.28978e7i	1.23024	+	1.23024i	0.266364	+	0.963873i	$0.414178\pi$
$644$		0			0
$645$	1.58205e7	+	4.38226e6i	1.49734	+	0.414762i
$646$		0			0
$647$	9.64496e6	−	9.64496e6i	0.905816	−	0.905816i	−0.0901155	−	0.995931i	$-0.528724\pi$
$647$	9.64496e6	−	9.64496e6i	0.905816	−	0.905816i	0.995931	+	0.0901155i	$0.0287236\pi$
$648$		0			0
$649$		−	2.34939e6i		−	0.218949i
$650$		0			0
$651$			4.52705e6i			0.418661i
$652$		0			0
$653$	−1.31484e6	+	1.31484e6i	−0.120667	+	0.120667i	−0.764862	−	0.644194i	$-0.777193\pi$
$653$	−1.31484e6	+	1.31484e6i	−0.120667	+	0.120667i	0.644194	+	0.764862i	$0.277193\pi$
$654$		0			0
$655$	−1.33992e7	−	3.71157e6i	−1.22033	−	0.338030i
$656$		0			0
$657$	162504.	+	162504.i	0.0146876	+	0.0146876i
$658$		0			0
$659$	533017.			0.0478109			0.0239055	−	0.999714i	$-0.492390\pi$
$659$	533017.			0.0478109			0.0239055	+	0.999714i	$0.492390\pi$
$660$		0			0
$661$	−9.93132e6			−0.884104			−0.442052	−	0.896989i	$-0.645749\pi$
$661$	−9.93132e6			−0.884104			−0.442052	+	0.896989i	$0.645749\pi$
$662$		0			0
$663$	3.69780e6	+	3.69780e6i	0.326708	+	0.326708i
$664$		0			0
$665$	−334219.	−	590314.i	−0.0293074	−	0.0517641i
$666$		0			0
$667$	4.00837e6	−	4.00837e6i	0.348861	−	0.348861i
$668$		0			0
$669$		−	1.23342e7i		−	1.06548i
$670$		0			0
$671$		−	1.16540e7i		−	0.999238i
$672$		0			0
$673$	−330472.	+	330472.i	−0.0281253	+	0.0281253i	−0.721030	−	0.692904i	$-0.756331\pi$
$673$	−330472.	+	330472.i	−0.0281253	+	0.0281253i	0.692904	+	0.721030i	$0.256331\pi$
$674$		0			0
$675$	−1.15485e7	+	2.88677e6i	−0.975587	+	0.243867i
$676$		0			0
$677$	1.88339e6	+	1.88339e6i	0.157931	+	0.157931i	0.781649	−	0.623718i	$-0.214379\pi$
$677$	1.88339e6	+	1.88339e6i	0.157931	+	0.157931i	−0.623718	+	0.781649i	$0.714379\pi$
$678$		0			0
$679$	−1.30328e7			−1.08483
$680$		0			0
$681$	−6.35898e6			−0.525436
$682$		0			0
$683$	406485.	+	406485.i	0.0333421	+	0.0333421i	0.723581	−	0.690239i	$-0.242495\pi$
$683$	406485.	+	406485.i	0.0333421	+	0.0333421i	−0.690239	+	0.723581i	$0.742495\pi$
$684$		0			0
$685$	1.56727e6	−	887342.i	0.127619	−	0.0722545i
$686$		0			0
$687$	−9.73058e6	+	9.73058e6i	−0.786587	+	0.786587i
$688$		0			0
$689$		−	6.10743e6i		−	0.490129i
$690$		0			0
$691$		−	8.41699e6i		−	0.670597i	−0.942112	−	0.335299i	$-0.891163\pi$
$691$		−	8.41699e6i		−	0.670597i	0.942112	−	0.335299i	$-0.108837\pi$
$692$		0			0
$693$	−43220.4	+	43220.4i	−0.00341866	+	0.00341866i
$694$		0			0
$695$	1.00458e6	−	3.62665e6i	0.0788901	−	0.284802i
$696$		0			0
$697$	6.09997e6	+	6.09997e6i	0.475604	+	0.475604i
$698$		0			0
$699$	−1.85666e7			−1.43727
$700$		0			0
$701$	−1.79152e7			−1.37698			−0.688490	−	0.725246i	$-0.741726\pi$
$701$	−1.79152e7			−1.37698			−0.688490	+	0.725246i	$0.741726\pi$
$702$		0			0
$703$	787575.	+	787575.i	0.0601041	+	0.0601041i
$704$		0			0
$705$	−2.18274e6	+	7.87996e6i	−0.165398	+	0.597106i
$706$		0			0
$707$	−4.52660e6	+	4.52660e6i	−0.340583	+	0.340583i
$708$		0			0
$709$			1.85631e7i			1.38686i	0.720522	+	0.693432i	$0.243902\pi$
$709$			1.85631e7i			1.38686i	−0.720522	+	0.693432i	$0.756098\pi$
$710$		0			0
$711$			180504.i			0.0133910i
$712$		0			0
$713$	−2.62739e6	+	2.62739e6i	−0.193553	+	0.193553i
$714$		0			0
$715$	3.34512e6	−	1.89391e6i	0.244707	−	0.138546i
$716$		0			0
$717$	4.24061e6	+	4.24061e6i	0.308057	+	0.308057i
$718$		0			0
$719$	1.73808e7			1.25386			0.626929	−	0.779077i	$-0.284312\pi$
$719$	1.73808e7			1.25386			0.626929	+	0.779077i	$0.284312\pi$
$720$		0			0
$721$	−1.45360e7			−1.04138
$722$		0			0
$723$	5.74036e6	+	5.74036e6i	0.408407	+	0.408407i
$724$		0			0
$725$	6.73305e6	−	1.12210e7i	0.475737	−	0.792843i
$726$		0			0
$727$	−882269.	+	882269.i	−0.0619106	+	0.0619106i	−0.737384	−	0.675474i	$-0.763939\pi$
$727$	−882269.	+	882269.i	−0.0619106	+	0.0619106i	0.675474	+	0.737384i	$0.263939\pi$
$728$		0			0
$729$		−	1.45084e7i		−	1.01111i
$730$		0			0
$731$			1.93234e7i			1.33749i
$732$		0			0
$733$	−6.82460e6	+	6.82460e6i	−0.469156	+	0.469156i	−0.901641	−	0.432485i	$-0.857637\pi$
$733$	−6.82460e6	+	6.82460e6i	−0.469156	+	0.469156i	0.432485	+	0.901641i	$0.357637\pi$
$734$		0			0
$735$	−2.34108e6	−	4.13494e6i	−0.159845	−	0.282326i
$736$		0			0
$737$	7.44213e6	+	7.44213e6i	0.504695	+	0.504695i
$738$		0			0
$739$	−6.01199e6			−0.404955			−0.202478	−	0.979287i	$-0.564899\pi$
$739$	−6.01199e6			−0.404955			−0.202478	+	0.979287i	$0.564899\pi$
$740$		0			0
$741$	−584736.			−0.0391214
$742$		0			0
$743$	−8.54128e6	−	8.54128e6i	−0.567611	−	0.567611i	0.363847	−	0.931459i	$-0.381463\pi$
$743$	−8.54128e6	−	8.54128e6i	−0.567611	−	0.567611i	−0.931459	+	0.363847i	$0.881463\pi$
$744$		0			0
$745$	−2.50624e7	−	6.94227e6i	−1.65437	−	0.458259i
$746$		0			0
$747$	98122.7	−	98122.7i	0.00643381	−	0.00643381i
$748$		0			0
$749$			2.10728e7i			1.37252i
$750$		0			0
$751$		−	9.37871e6i		−	0.606797i	−0.952864	−	0.303399i	$-0.901879\pi$
$751$		−	9.37871e6i		−	0.606797i	0.952864	−	0.303399i	$-0.0981213\pi$
$752$		0			0
$753$	−1.95379e7	+	1.95379e7i	−1.25572	+	1.25572i
$754$		0			0
$755$	−2.09987e7	−	5.81663e6i	−1.34068	−	0.371368i
$756$		0			0
$757$	−6.77063e6	−	6.77063e6i	−0.429427	−	0.429427i	0.459006	−	0.888433i	$-0.348206\pi$
$757$	−6.77063e6	−	6.77063e6i	−0.429427	−	0.429427i	−0.888433	+	0.459006i	$0.848206\pi$
$758$		0			0
$759$	4.36137e6			0.274801
$760$		0			0
$761$	−9.79369e6			−0.613035			−0.306517	−	0.951865i	$-0.599164\pi$
$761$	−9.79369e6			−0.613035			−0.306517	+	0.951865i	$0.599164\pi$
$762$		0			0
$763$	−4.45090e6	−	4.45090e6i	−0.276781	−	0.276781i
$764$		0			0
$765$	−77623.6	−	137103.i	−0.00479557	−	0.00847018i
$766$		0			0
$767$	2.64390e6	−	2.64390e6i	0.162277	−	0.162277i
$768$		0			0
$769$		−	777622.i		−	0.0474191i	−0.999719	−	0.0237095i	$-0.992452\pi$
$769$		−	777622.i		−	0.0474191i	0.999719	−	0.0237095i	$-0.00754768\pi$
$770$		0			0
$771$		−	2.46053e7i		−	1.49071i
$772$		0			0
$773$	−7.92806e6	+	7.92806e6i	−0.477220	+	0.477220i	−0.904241	−	0.427022i	$-0.859563\pi$
$773$	−7.92806e6	+	7.92806e6i	−0.477220	+	0.477220i	0.427022	+	0.904241i	$0.359563\pi$
$774$		0			0
$775$	−4.41335e6	+	7.35511e6i	−0.263945	+	0.439880i
$776$		0			0
$777$	−1.13903e7	−	1.13903e7i	−0.676835	−	0.676835i
$778$		0			0
$779$	−964593.			−0.0569509
$780$		0			0
$781$	−1.54350e7			−0.905481
$782$		0			0
$783$	1.12793e7	+	1.12793e7i	0.657471	+	0.657471i
$784$		0			0
$785$	9.28504e6	−	5.25693e6i	0.537786	−	0.304479i
$786$		0			0
$787$	1.94505e7	−	1.94505e7i	1.11942	−	1.11942i	0.127593	−	0.991827i	$-0.459275\pi$
$787$	1.94505e7	−	1.94505e7i	1.11942	−	1.11942i	0.991827	−	0.127593i	$-0.0407251\pi$
$788$		0			0
$789$		−	1.81833e7i		−	1.03987i
$790$		0			0
$791$			3.40838e6i			0.193690i
$792$		0			0
$793$	1.31149e7	−	1.31149e7i	0.740596	−	0.740596i
$794$		0			0
$795$	4.27017e6	−	1.54158e7i	0.239622	−	0.865064i
$796$		0			0
$797$	1.38207e7	+	1.38207e7i	0.770697	+	0.770697i	0.978228	−	0.207531i	$-0.0665429\pi$
$797$	1.38207e7	+	1.38207e7i	0.770697	+	0.770697i	−0.207531	+	0.978228i	$0.566543\pi$
$798$		0			0
$799$	−9.62470e6			−0.533360
$800$		0			0
$801$	−30727.8			−0.00169219
$802$		0			0
$803$	−1.22237e7	−	1.22237e7i	−0.668980	−	0.668980i
$804$		0			0
$805$	−2.14958e6	+	7.76023e6i	−0.116913	+	0.422071i
$806$		0			0
$807$	1.32324e7	−	1.32324e7i	0.715244	−	0.715244i
$808$		0			0
$809$		−	8.61846e6i		−	0.462976i	−0.972838	−	0.231488i	$-0.925641\pi$
$809$		−	8.61846e6i		−	0.462976i	0.972838	−	0.231488i	$-0.0743594\pi$
$810$		0			0
$811$		−	4.49002e6i		−	0.239715i	−0.992791	−	0.119858i	$-0.961756\pi$
$811$		−	4.49002e6i		−	0.239715i	0.992791	−	0.119858i	$-0.0382438\pi$
$812$		0			0
$813$	−3.66650e6	+	3.66650e6i	−0.194547	+	0.194547i
$814$		0			0
$815$	2.65261e6	−	1.50183e6i	0.139887	−	0.0792003i
$816$		0			0
$817$	−1.52781e6	−	1.52781e6i	−0.0800781	−	0.0800781i
$818$		0			0
$819$	−97276.4			−0.00506755
$820$		0			0
$821$	1.64704e7			0.852796			0.426398	−	0.904536i	$-0.359782\pi$
$821$	1.64704e7			0.852796			0.426398	+	0.904536i	$0.359782\pi$
$822$		0			0
$823$	−2.15186e7	−	2.15186e7i	−1.10742	−	1.10742i	−0.993488	−	0.113937i	$-0.963654\pi$
$823$	−2.15186e7	−	2.15186e7i	−1.10742	−	1.10742i	−0.113937	−	0.993488i	$-0.536346\pi$
$824$		0			0
$825$	9.76761e6	−	2.44161e6i	0.499636	−	0.124894i
$826$		0			0
$827$	5.34250e6	−	5.34250e6i	0.271632	−	0.271632i	−0.558125	−	0.829757i	$-0.688479\pi$
$827$	5.34250e6	−	5.34250e6i	0.271632	−	0.271632i	0.829757	+	0.558125i	$0.188479\pi$
$828$		0			0
$829$			3.11389e7i			1.57368i	0.617155	+	0.786842i	$0.288285\pi$
$829$			3.11389e7i			1.57368i	−0.617155	+	0.786842i	$0.711715\pi$
$830$		0			0
$831$			2.49117e7i			1.25141i
$832$		0			0
$833$	3.95496e6	−	3.95496e6i	0.197483	−	0.197483i
$834$		0			0
$835$	2.08331e6	+	3.67964e6i	0.103404	+	0.182637i
$836$		0			0
$837$	−7.39329e6	−	7.39329e6i	−0.364774	−	0.364774i
$838$		0			0
$839$	−2.37936e7			−1.16696			−0.583478	−	0.812129i	$-0.698308\pi$
$839$	−2.37936e7			−1.16696			−0.583478	+	0.812129i	$0.698308\pi$
$840$		0			0
$841$	2.97563e6			0.145074
$842$		0			0
$843$	−632250.	−	632250.i	−0.0306422	−	0.0306422i
$844$		0			0
$845$	−1.41069e7	−	3.90761e6i	−0.679659	−	0.188265i
$846$		0			0
$847$	−8.86686e6	+	8.86686e6i	−0.424679	+	0.424679i
$848$		0			0
$849$			1.88451e7i			0.897281i
$850$		0			0
$851$		−	1.32213e7i		−	0.625822i
$852$		0			0
$853$	1.29410e7	−	1.29410e7i	0.608968	−	0.608968i	−0.333708	−	0.942676i	$-0.608300\pi$
$853$	1.29410e7	−	1.29410e7i	0.608968	−	0.608968i	0.942676	+	0.333708i	$0.108300\pi$
$854$		0			0
$855$	16977.4	+	4702.73i	0.000794248	+	0.000220006i
$856$		0			0
$857$	2.40396e7	+	2.40396e7i	1.11809	+	1.11809i	0.992022	+	0.126066i	$0.0402352\pi$
$857$	2.40396e7	+	2.40396e7i	1.11809	+	1.11809i	0.126066	+	0.992022i	$0.459765\pi$
$858$		0			0
$859$	2.89624e7			1.33922			0.669610	−	0.742713i	$-0.266461\pi$
$859$	2.89624e7			1.33922			0.669610	+	0.742713i	$0.266461\pi$
$860$		0			0
$861$	1.39504e7			0.641327
$862$		0			0
$863$	5.34313e6	+	5.34313e6i	0.244213	+	0.244213i	0.818591	−	0.574377i	$-0.194756\pi$
$863$	5.34313e6	+	5.34313e6i	0.244213	+	0.244213i	−0.574377	+	0.818591i	$0.694756\pi$
$864$		0			0
$865$	2.92880e6	+	5.17300e6i	0.133091	+	0.235073i
$866$		0			0
$867$	4.16118e6	−	4.16118e6i	0.188005	−	0.188005i
$868$		0			0
$869$		−	1.35776e7i		−	0.609922i
$870$		0			0
$871$			1.67501e7i			0.748120i
$872$		0			0
$873$	239323.	−	239323.i	0.0106280	−	0.0106280i
$874$		0			0
$875$	−469770.	+	1.85830e7i	−0.0207427	+	0.820533i
$876$		0			0
$877$	−2.28059e6	−	2.28059e6i	−0.100126	−	0.100126i	0.655269	−	0.755395i	$-0.272555\pi$
$877$	−2.28059e6	−	2.28059e6i	−0.100126	−	0.100126i	−0.755395	+	0.655269i	$0.772555\pi$
$878$		0			0
$879$	1.04107e7			0.454473
$880$		0			0
$881$	−1.07166e7			−0.465174			−0.232587	−	0.972576i	$-0.574719\pi$
$881$	−1.07166e7			−0.465174			−0.232587	+	0.972576i	$0.574719\pi$
$882$		0			0
$883$	−6.80592e6	−	6.80592e6i	−0.293755	−	0.293755i	0.544807	−	0.838562i	$-0.316603\pi$
$883$	−6.80592e6	−	6.80592e6i	−0.293755	−	0.293755i	−0.838562	+	0.544807i	$0.816603\pi$
$884$		0			0
$885$	8.52202e6	−	4.82492e6i	0.365750	−	0.207077i
$886$		0			0
$887$	−8.60457e6	+	8.60457e6i	−0.367215	+	0.367215i	−0.866460	−	0.499246i	$-0.833610\pi$
$887$	−8.60457e6	+	8.60457e6i	−0.367215	+	0.367215i	0.499246	+	0.866460i	$0.333610\pi$
$888$		0			0
$889$		−	6.63770e6i		−	0.281685i
$890$		0			0
$891$			1.21330e7i			0.512005i
$892$		0			0
$893$	760980.	−	760980.i	0.0319334	−	0.0319334i
$894$		0			0
$895$	−2.52131e6	+	9.10222e6i	−0.105213	+	0.379830i
$896$		0			0
$897$	4.90809e6	+	4.90809e6i	0.203672	+	0.203672i
$898$		0			0
$899$	1.14941e7			0.474325
$900$		0			0
$901$	1.88291e7			0.772711
$902$		0			0
$903$	2.20959e7	+	2.20959e7i	0.901764	+	0.901764i
$904$		0			0
$905$	−1.95057e6	+	7.04177e6i	−0.0791661	+	0.285799i
$906$		0			0
$907$	5.32472e6	−	5.32472e6i	0.214921	−	0.214921i	−0.591433	−	0.806354i	$-0.701438\pi$
$907$	5.32472e6	−	5.32472e6i	0.214921	−	0.214921i	0.806354	+	0.591433i	$0.201438\pi$
$908$		0			0
$909$		−	166246.i		−	0.00667331i
$910$		0			0
$911$			4.68764e7i			1.87137i	0.352842	+	0.935683i	$0.385215\pi$
$911$			4.68764e7i			1.87137i	−0.352842	+	0.935683i	$0.614785\pi$
$912$		0			0
$913$	−7.38084e6	+	7.38084e6i	−0.293041	+	0.293041i
$914$		0			0
$915$	4.22729e7	−	2.39337e7i	1.66920	−	0.945055i
$916$		0			0
$917$	−1.87142e7	−	1.87142e7i	−0.734934	−	0.734934i
$918$		0			0
$919$	−3.29297e7			−1.28617			−0.643085	−	0.765794i	$-0.722346\pi$
$919$	−3.29297e7			−1.28617			−0.643085	+	0.765794i	$0.722346\pi$
$920$		0			0
$921$	3.34482e7			1.29934
$922$		0			0
$923$	−1.73698e7	−	1.73698e7i	−0.671107	−	0.671107i
$924$		0			0
$925$	−7.40162e6	−	2.96101e7i	−0.284428	−	1.13785i
$926$		0			0
$927$	266929.	−	266929.i	0.0102023	−	0.0102023i
$928$		0			0
$929$			2.68341e7i			1.02011i	0.860142	+	0.510055i	$0.170375\pi$
$929$			2.68341e7i			1.02011i	−0.860142	+	0.510055i	$0.829625\pi$
$930$		0			0
$931$			625400.i			0.0236474i
$932$		0			0
$933$	−8.94676e6	+	8.94676e6i	−0.336482	+	0.336482i
$934$		0			0
$935$	5.83889e6	+	1.03129e7i	0.218425	+	0.385792i
$936$		0			0
$937$	−3.23213e7	−	3.23213e7i	−1.20265	−	1.20265i	−0.973357	−	0.229293i	$-0.926359\pi$
$937$	−3.23213e7	−	3.23213e7i	−1.20265	−	1.20265i	−0.229293	−	0.973357i	$-0.573641\pi$
$938$		0			0
$939$	−1.31336e7			−0.486093
$940$		0			0
$941$	3.45697e7			1.27269			0.636343	−	0.771406i	$-0.280446\pi$
$941$	3.45697e7			1.27269			0.636343	+	0.771406i	$0.280446\pi$
$942$		0			0
$943$	8.09649e6	+	8.09649e6i	0.296495	+	0.296495i
$944$		0			0
$945$	−2.18368e7	−	6.04877e6i	−0.795442	−	0.220337i
$946$		0			0
$947$	−3.70980e7	+	3.70980e7i	−1.34424	+	1.34424i	−0.452444	+	0.891793i	$0.649448\pi$
$947$	−3.70980e7	+	3.70980e7i	−1.34424	+	1.34424i	−0.891793	+	0.452444i	$0.850552\pi$
$948$		0			0
$949$		−	2.75119e7i		−	0.991643i
$950$		0			0
$951$			9.34333e6i			0.335004i
$952$		0			0
$953$	3.26950e7	−	3.26950e7i	1.16614	−	1.16614i	0.183029	−	0.983108i	$-0.441410\pi$
$953$	3.26950e7	−	3.26950e7i	1.16614	−	1.16614i	0.983108	−	0.183029i	$-0.0585901\pi$
$954$		0			0
$955$	5.01795e7	+	1.38997e7i	1.78040	+	0.493171i
$956$		0			0
$957$	−9.53991e6	−	9.53991e6i	−0.336716	−	0.336716i
$958$		0			0
$959$	3.42827e6			0.120373
$960$		0			0
$961$	2.10950e7			0.736838
$962$		0			0
$963$	−386965.	−	386965.i	−0.0134464	−	0.0134464i
$964$		0			0
$965$	−1.00822e7	−	1.78076e7i	−0.348526	−	0.615584i
$966$		0			0
$967$	−9.72589e6	+	9.72589e6i	−0.334475	+	0.334475i	−0.854283	−	0.519808i	$-0.826003\pi$
$967$	−9.72589e6	+	9.72589e6i	−0.334475	+	0.334475i	0.519808	+	0.854283i	$0.326003\pi$
$968$		0			0
$969$		−	1.80273e6i		−	0.0616766i
$970$		0			0
$971$		−	4.99185e6i		−	0.169908i	−0.996385	−	0.0849539i	$-0.972926\pi$
$971$		−	4.99185e6i		−	0.169908i	0.996385	−	0.0849539i	$-0.0270743\pi$
$972$		0			0
$973$	5.06522e6	−	5.06522e6i	0.171521	−	0.171521i
$974$		0			0
$975$	1.37397e7	+	8.24435e6i	0.462877	+	0.277744i
$976$		0			0
$977$	−1.44406e7	−	1.44406e7i	−0.484005	−	0.484005i	0.422403	−	0.906408i	$-0.361187\pi$
$977$	−1.44406e7	−	1.44406e7i	−0.484005	−	0.484005i	−0.906408	+	0.422403i	$0.861187\pi$
$978$		0			0
$979$	2.31136e6			0.0770746
$980$		0			0
$981$	163466.			0.00542319
$982$		0			0
$983$	5.66330e6	+	5.66330e6i	0.186933	+	0.186933i	0.794369	−	0.607436i	$-0.207802\pi$
$983$	5.66330e6	+	5.66330e6i	0.186933	+	0.186933i	−0.607436	+	0.794369i	$0.707802\pi$
$984$		0			0
$985$	4.47455e7	−	2.53336e7i	1.46946	−	0.831969i
$986$		0			0
$987$	−1.10057e7	+	1.10057e7i	−0.359603	+	0.359603i
$988$		0			0
$989$			2.56479e7i			0.833797i
$990$		0			0
$991$		−	2.46453e7i		−	0.797167i	−0.917132	−	0.398583i	$-0.869502\pi$
$991$		−	2.46453e7i		−	0.797167i	0.917132	−	0.398583i	$-0.130498\pi$
$992$		0			0
$993$	−3.73758e7	+	3.73758e7i	−1.20286	+	1.20286i
$994$		0			0
$995$	825140.	−	2.97885e6i	0.0264223	−	0.0953874i
$996$		0			0
$997$	−1.25687e7	−	1.25687e7i	−0.400454	−	0.400454i	0.477939	−	0.878393i	$-0.341384\pi$
$997$	−1.25687e7	−	1.25687e7i	−0.400454	−	0.400454i	−0.878393	+	0.477939i	$0.841384\pi$
$998$		0			0
$999$	3.72039e7			1.17944

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.a.63.2	✓	14	5.3	odd	4
160.6.n.a.127.2	yes	14	4.3	odd	2
160.6.n.b.63.6	yes	14	20.3	even	4	inner
160.6.n.b.127.6	yes	14	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(10.9598 + 10.9598i) q^{3} +(-14.9228 + 53.8731i) q^{5} +(-75.2427 + 75.2427i) q^{7} -2.76340i q^{9} +O(q^{10})\)	\(q+(10.9598 + 10.9598i) q^{3} +(-14.9228 + 53.8731i) q^{5} +(-75.2427 + 75.2427i) q^{7} -2.76340i q^{9} +207.864i q^{11} +(-233.921 + 233.921i) q^{13} +(-753.993 + 426.889i) q^{15} +(-721.173 - 721.173i) q^{17} +114.040 q^{19} -1649.30 q^{21} +(-957.212 - 957.212i) q^{23} +(-2679.62 - 1607.88i) q^{25} +(2693.53 - 2693.53i) q^{27} +4187.54i q^{29} -2744.83i q^{31} +(-2278.16 + 2278.16i) q^{33} +(-2930.73 - 5176.39i) q^{35} +(6906.15 + 6906.15i) q^{37} -5127.48 q^{39} -8458.40 q^{41} +(-13397.2 - 13397.2i) q^{43} +(148.873 + 41.2377i) q^{45} +(6672.94 - 6672.94i) q^{47} +5484.06i q^{49} -15807.9i q^{51} +(-13054.5 + 13054.5i) q^{53} +(-11198.3 - 3101.92i) q^{55} +(1249.86 + 1249.86i) q^{57} -11302.5 q^{59} -56065.4 q^{61} +(207.926 + 207.926i) q^{63} +(-9111.29 - 16092.8i) q^{65} +(35802.8 - 35802.8i) q^{67} -20981.8i q^{69} +74255.2i q^{71} +(-58806.0 + 58806.0i) q^{73} +(-11746.1 - 46990.3i) q^{75} +(-15640.3 - 15640.3i) q^{77} -65319.6 q^{79} +58369.9 q^{81} +(35508.0 + 35508.0i) q^{83} +(49613.8 - 28089.9i) q^{85} +(-45894.8 + 45894.8i) q^{87} -11119.6i q^{89} -35201.7i q^{91} +(30083.0 - 30083.0i) q^{93} +(-1701.79 + 6143.67i) q^{95} +(86604.7 + 86604.7i) q^{97} +574.413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7}+O(q^{10}) \) 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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