LMFDB - Embedded newform 160.6.n.c.127.5

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1375 x^{14} + 743087 x^{12} + 198706725 x^{10} + 26872635188 x^{8} + 1612811892960 x^{6} + \cdots + 177426662425600 $ x^16 + 1375x^14 + 743087x^12 + 198706725x^10 + 26872635188x^8 + 1612811892960x^6 + 24971013117824x^4 + 124211190826240*x^2 + 177426662425600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{41}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.5
Root			$1.56776i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.6.n.c.63.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.56776 - 2.56776i) q^{3} +(3.91778 - 55.7642i) q^{5} +(86.5899 - 86.5899i) q^{7} -229.813i q^{9} +O(q^{10})$	\(q+(-2.56776 - 2.56776i) q^{3} +(3.91778 - 55.7642i) q^{5} +(86.5899 - 86.5899i) q^{7} -229.813i q^{9} -138.270i q^{11} +(-393.183 + 393.183i) q^{13} +(-153.249 + 133.129i) q^{15} +(724.394 + 724.394i) q^{17} +1464.48 q^{19} -444.684 q^{21} +(-2859.76 - 2859.76i) q^{23} +(-3094.30 - 436.944i) q^{25} +(-1214.07 + 1214.07i) q^{27} +2516.08i q^{29} -2965.73i q^{31} +(-355.043 + 355.043i) q^{33} +(-4489.38 - 5167.86i) q^{35} +(-1459.15 - 1459.15i) q^{37} +2019.20 q^{39} -17831.6 q^{41} +(-4660.93 - 4660.93i) q^{43} +(-12815.4 - 900.358i) q^{45} +(20752.8 - 20752.8i) q^{47} +1811.39i q^{49} -3720.15i q^{51} +(-11572.8 + 11572.8i) q^{53} +(-7710.50 - 541.710i) q^{55} +(-3760.44 - 3760.44i) q^{57} -32661.2 q^{59} -11161.0 q^{61} +(-19899.5 - 19899.5i) q^{63} +(20385.1 + 23466.0i) q^{65} +(-15320.2 + 15320.2i) q^{67} +14686.4i q^{69} -72449.6i q^{71} +(-6692.19 + 6692.19i) q^{73} +(6823.46 + 9067.40i) q^{75} +(-11972.7 - 11972.7i) q^{77} +36624.7 q^{79} -49609.7 q^{81} +(65762.8 + 65762.8i) q^{83} +(43233.3 - 37557.3i) q^{85} +(6460.70 - 6460.70i) q^{87} -55889.7i q^{89} +68091.3i q^{91} +(-7615.29 + 7615.29i) q^{93} +(5737.53 - 81665.8i) q^{95} +(50124.8 + 50124.8i) q^{97} -31776.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7}+O(q^{10}) $ 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7	$ 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7} + 536 q^{13} + 698 q^{15} - 1828 q^{17} - 2512 q^{19} - 4284 q^{21} + 7642 q^{23} + 9140 q^{25} + 12272 q^{27} + 11876 q^{33} - 10518 q^{35} - 7620 q^{37} - 11244 q^{39} - 21284 q^{41} - 20002 q^{43} + 686 q^{45} - 25298 q^{47} + 12852 q^{53} + 10584 q^{55} + 55848 q^{57} + 142704 q^{59} - 20564 q^{61} + 115282 q^{63} - 38256 q^{65} + 10506 q^{67} + 15432 q^{73} - 256226 q^{75} + 133852 q^{77} + 159344 q^{79} - 236116 q^{81} + 61222 q^{83} + 7056 q^{85} - 162176 q^{87} + 122180 q^{93} - 267512 q^{95} - 17344 q^{97} - 107332 q^{99}+O(q^{100}) $ 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7 + 536 * q^13 + 698 * q^15 - 1828 * q^17 - 2512 * q^19 - 4284 * q^21 + 7642 * q^23 + 9140 * q^25 + 12272 * q^27 + 11876 * q^33 - 10518 * q^35 - 7620 * q^37 - 11244 * q^39 - 21284 * q^41 - 20002 * q^43 + 686 * q^45 - 25298 * q^47 + 12852 * q^53 + 10584 * q^55 + 55848 * q^57 + 142704 * q^59 - 20564 * q^61 + 115282 * q^63 - 38256 * q^65 + 10506 * q^67 + 15432 * q^73 - 256226 * q^75 + 133852 * q^77 + 159344 * q^79 - 236116 * q^81 + 61222 * q^83 + 7056 * q^85 - 162176 * q^87 + 122180 * q^93 - 267512 * q^95 - 17344 * q^97 - 107332 * 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
$3$	−2.56776	−	2.56776i	−0.164722	−	0.164722i	0.619933	−	0.784655i	$-0.287160\pi$
$3$	−2.56776	−	2.56776i	−0.164722	−	0.164722i	−0.784655	+	0.619933i	$0.787160\pi$
$4$		0			0
$5$	3.91778	−	55.7642i	0.0700834	−	0.997541i
$5$	3.91778	−	55.7642i	0.0700834	−	0.997541i
$6$		0			0
$7$	86.5899	−	86.5899i	0.667916	−	0.667916i	−0.289317	−	0.957233i	$-0.593428\pi$
$7$	86.5899	−	86.5899i	0.667916	−	0.667916i	0.957233	+	0.289317i	$0.0934282\pi$
$8$		0			0
$9$		−	229.813i		−	0.945733i
$10$		0			0
$11$		−	138.270i		−	0.344544i	−0.985049	−	0.172272i	$-0.944889\pi$
$11$		−	138.270i		−	0.344544i	0.985049	−	0.172272i	$-0.0551108\pi$
$12$		0			0
$13$	−393.183	+	393.183i	−0.645262	+	0.645262i	−0.951844	−	0.306582i	$-0.900815\pi$
$13$	−393.183	+	393.183i	−0.645262	+	0.645262i	0.306582	+	0.951844i	$0.400815\pi$
$14$		0			0
$15$	−153.249	+	133.129i	−0.175861	+	0.152773i
$16$		0			0
$17$	724.394	+	724.394i	0.607929	+	0.607929i	0.942404	−	0.334476i	$-0.108559\pi$
$17$	724.394	+	724.394i	0.607929	+	0.607929i	−0.334476	+	0.942404i	$0.608559\pi$
$18$		0			0
$19$	1464.48			0.930680			0.465340	−	0.885132i	$-0.345932\pi$
$19$	1464.48			0.930680			0.465340	+	0.885132i	$0.345932\pi$
$20$		0			0
$21$	−444.684			−0.220041
$22$		0			0
$23$	−2859.76	−	2859.76i	−1.12722	−	1.12722i	−0.990627	−	0.136595i	$-0.956384\pi$
$23$	−2859.76	−	2859.76i	−1.12722	−	1.12722i	−0.136595	−	0.990627i	$-0.543616\pi$
$24$		0			0
$25$	−3094.30	−	436.944i	−0.990177	−	0.139822i
$26$		0			0
$27$	−1214.07	+	1214.07i	−0.320505	+	0.320505i
$28$		0			0
$29$			2516.08i			0.555559i	0.960645	+	0.277779i	$0.0895984\pi$
$29$			2516.08i			0.555559i	−0.960645	+	0.277779i	$0.910402\pi$
$30$		0			0
$31$		−	2965.73i		−	0.554278i	−0.960830	−	0.277139i	$-0.910614\pi$
$31$		−	2965.73i		−	0.554278i	0.960830	−	0.277139i	$-0.0893862\pi$
$32$		0			0
$33$	−355.043	+	355.043i	−0.0567540	+	0.0567540i
$34$		0			0
$35$	−4489.38	−	5167.86i	−0.619464	−	0.713084i
$36$		0			0
$37$	−1459.15	−	1459.15i	−0.175225	−	0.175225i	0.614046	−	0.789271i	$-0.289541\pi$
$37$	−1459.15	−	1459.15i	−0.175225	−	0.175225i	−0.789271	+	0.614046i	$0.789541\pi$
$38$		0			0
$39$	2019.20			0.212578
$40$		0			0
$41$	−17831.6			−1.65665			−0.828325	−	0.560247i	$-0.810706\pi$
$41$	−17831.6			−1.65665			−0.828325	+	0.560247i	$0.810706\pi$
$42$		0			0
$43$	−4660.93	−	4660.93i	−0.384416	−	0.384416i	0.488274	−	0.872690i	$-0.337627\pi$
$43$	−4660.93	−	4660.93i	−0.384416	−	0.384416i	−0.872690	+	0.488274i	$0.837627\pi$
$44$		0			0
$45$	−12815.4	−	900.358i	−0.943408	−	0.0662802i
$46$		0			0
$47$	20752.8	−	20752.8i	1.37035	−	1.37035i	0.510441	−	0.859913i	$-0.329482\pi$
$47$	20752.8	−	20752.8i	1.37035	−	1.37035i	0.859913	−	0.510441i	$-0.170518\pi$
$48$		0			0
$49$			1811.39i			0.107776i
$50$		0			0
$51$		−	3720.15i		−	0.200279i
$52$		0			0
$53$	−11572.8	+	11572.8i	−0.565911	+	0.565911i	−0.930980	−	0.365069i	$-0.881045\pi$
$53$	−11572.8	+	11572.8i	−0.565911	+	0.565911i	0.365069	+	0.930980i	$0.381045\pi$
$54$		0			0
$55$	−7710.50	−	541.710i	−0.343697	−	0.0241468i
$56$		0			0
$57$	−3760.44	−	3760.44i	−0.153303	−	0.153303i
$58$		0			0
$59$	−32661.2			−1.22152			−0.610762	−	0.791814i	$-0.709137\pi$
$59$	−32661.2			−1.22152			−0.610762	+	0.791814i	$0.709137\pi$
$60$		0			0
$61$	−11161.0			−0.384042			−0.192021	−	0.981391i	$-0.561504\pi$
$61$	−11161.0			−0.384042			−0.192021	+	0.981391i	$0.561504\pi$
$62$		0			0
$63$	−19899.5	−	19899.5i	−0.631671	−	0.631671i
$64$		0			0
$65$	20385.1	+	23466.0i	0.598454	+	0.688898i
$66$		0			0
$67$	−15320.2	+	15320.2i	−0.416943	+	0.416943i	−0.884149	−	0.467206i	$-0.845261\pi$
$67$	−15320.2	+	15320.2i	−0.416943	+	0.416943i	0.467206	+	0.884149i	$0.345261\pi$
$68$		0			0
$69$			14686.4i			0.371357i
$70$		0			0
$71$		−	72449.6i		−	1.70565i	−0.522196	−	0.852826i	$-0.674887\pi$
$71$		−	72449.6i		−	1.70565i	0.522196	−	0.852826i	$-0.325113\pi$
$72$		0			0
$73$	−6692.19	+	6692.19i	−0.146981	+	0.146981i	−0.776768	−	0.629787i	$-0.783142\pi$
$73$	−6692.19	+	6692.19i	−0.146981	+	0.146981i	0.629787	+	0.776768i	$0.283142\pi$
$74$		0			0
$75$	6823.46	+	9067.40i	0.140072	+	0.186136i
$76$		0			0
$77$	−11972.7	−	11972.7i	−0.230127	−	0.230127i
$78$		0			0
$79$	36624.7			0.660248			0.330124	−	0.943938i	$-0.392909\pi$
$79$	36624.7			0.660248			0.330124	+	0.943938i	$0.392909\pi$
$80$		0			0
$81$	−49609.7			−0.840145
$82$		0			0
$83$	65762.8	+	65762.8i	1.04782	+	1.04782i	0.998798	+	0.0490188i	$0.0156094\pi$
$83$	65762.8	+	65762.8i	1.04782	+	1.04782i	0.0490188	+	0.998798i	$0.484391\pi$
$84$		0			0
$85$	43233.3	−	37557.3i	0.649040	−	0.563828i
$86$		0			0
$87$	6460.70	−	6460.70i	0.0915128	−	0.0915128i
$88$		0			0
$89$		−	55889.7i		−	0.747922i	−0.927444	−	0.373961i	$-0.877999\pi$
$89$		−	55889.7i		−	0.747922i	0.927444	−	0.373961i	$-0.122001\pi$
$90$		0			0
$91$			68091.3i			0.861962i
$92$		0			0
$93$	−7615.29	+	7615.29i	−0.0913017	+	0.0913017i
$94$		0			0
$95$	5737.53	−	81665.8i	0.0652252	−	0.928391i
$96$		0			0
$97$	50124.8	+	50124.8i	0.540908	+	0.540908i	0.923795	−	0.382887i	$-0.125070\pi$
$97$	50124.8	+	50124.8i	0.540908	+	0.540908i	−0.382887	+	0.923795i	$0.625070\pi$
$98$		0			0
$99$	−31776.2			−0.325847
$100$		0			0
$101$	64318.2			0.627379			0.313690	−	0.949526i	$-0.398435\pi$
$101$	64318.2			0.627379			0.313690	+	0.949526i	$0.398435\pi$
$102$		0			0
$103$	68739.6	+	68739.6i	0.638431	+	0.638431i	0.950168	−	0.311737i	$-0.100911\pi$
$103$	68739.6	+	68739.6i	0.638431	+	0.638431i	−0.311737	+	0.950168i	$0.600911\pi$
$104$		0			0
$105$	−1742.18	+	24797.5i	−0.0154212	+	0.219500i
$106$		0			0
$107$	−99051.7	+	99051.7i	−0.836377	+	0.836377i	−0.988380	−	0.152003i	$-0.951428\pi$
$107$	−99051.7	+	99051.7i	−0.836377	+	0.836377i	0.152003	+	0.988380i	$0.451428\pi$
$108$		0			0
$109$		−	126068.i		−	1.01634i	−0.861258	−	0.508169i	$-0.830323\pi$
$109$		−	126068.i		−	1.01634i	0.861258	−	0.508169i	$-0.169677\pi$
$110$		0			0
$111$			7493.51i			0.0577268i
$112$		0			0
$113$	105402.	−	105402.i	0.776519	−	0.776519i	−0.202718	−	0.979237i	$-0.564977\pi$
$113$	105402.	−	105402.i	0.776519	−	0.776519i	0.979237	+	0.202718i	$0.0649775\pi$
$114$		0			0
$115$	−170676.	+	148268.i	−1.20345	+	1.04545i
$116$		0			0
$117$	90358.7	+	90358.7i	0.610246	+	0.610246i
$118$		0			0
$119$	125450.			0.812091
$120$		0			0
$121$	141933.			0.881289
$122$		0			0
$123$	45787.3	+	45787.3i	0.272887	+	0.272887i
$124$		0			0
$125$	−36488.7	+	170840.i	−0.208873	+	0.977943i
$126$		0			0
$127$	14873.2	−	14873.2i	0.0818265	−	0.0818265i	−0.665009	−	0.746835i	$-0.731572\pi$
$127$	14873.2	−	14873.2i	0.0818265	−	0.0818265i	0.746835	+	0.665009i	$0.231572\pi$
$128$		0			0
$129$			23936.3i			0.126643i
$130$		0			0
$131$			188078.i			0.957544i	0.877939	+	0.478772i	$0.158918\pi$
$131$			188078.i			0.957544i	−0.877939	+	0.478772i	$0.841082\pi$
$132$		0			0
$133$	126809.	−	126809.i	0.621616	−	0.621616i
$134$		0			0
$135$	62945.3	+	72458.3i	0.297255	+	0.342179i
$136$		0			0
$137$	−46314.7	−	46314.7i	−0.210823	−	0.210823i	0.593794	−	0.804617i	$-0.297629\pi$
$137$	−46314.7	−	46314.7i	−0.210823	−	0.210823i	−0.804617	+	0.593794i	$0.797629\pi$
$138$		0			0
$139$	237543.			1.04281			0.521406	−	0.853309i	$-0.325408\pi$
$139$	237543.			1.04281			0.521406	+	0.853309i	$0.325408\pi$
$140$		0			0
$141$	−106577.			−0.451455
$142$		0			0
$143$	54365.2	+	54365.2i	0.222321	+	0.222321i
$144$		0			0
$145$	140307.	+	9857.47i	0.554193	+	0.0389355i
$146$		0			0
$147$	4651.22	−	4651.22i	0.0177531	−	0.0177531i
$148$		0			0
$149$		−	151244.i		−	0.558099i	−0.960277	−	0.279050i	$-0.909981\pi$
$149$		−	151244.i		−	0.558099i	0.960277	−	0.279050i	$-0.0900194\pi$
$150$		0			0
$151$		−	279471.i		−	0.997457i	−0.866758	−	0.498729i	$-0.833800\pi$
$151$		−	279471.i		−	0.997457i	0.866758	−	0.498729i	$-0.166200\pi$
$152$		0			0
$153$	166475.	−	166475.i	0.574939	−	0.574939i
$154$		0			0
$155$	−165382.	−	11619.1i	−0.552915	−	0.0388457i
$156$		0			0
$157$	212711.	+	212711.i	0.688719	+	0.688719i	0.961949	−	0.273230i	$-0.0880921\pi$
$157$	212711.	+	212711.i	0.688719	+	0.688719i	−0.273230	+	0.961949i	$0.588092\pi$
$158$		0			0
$159$	59432.3			0.186436
$160$		0			0
$161$	−495252.			−1.50578
$162$		0			0
$163$	−15035.9	−	15035.9i	−0.0443262	−	0.0443262i	0.684596	−	0.728922i	$-0.259979\pi$
$163$	−15035.9	−	15035.9i	−0.0443262	−	0.0443262i	−0.728922	+	0.684596i	$0.759979\pi$
$164$		0			0
$165$	18407.7	+	21189.7i	0.0526369	+	0.0605920i
$166$		0			0
$167$	−95913.9	+	95913.9i	−0.266128	+	0.266128i	−0.827538	−	0.561410i	$-0.810259\pi$
$167$	−95913.9	+	95913.9i	−0.266128	+	0.266128i	0.561410	+	0.827538i	$0.310259\pi$
$168$		0			0
$169$			62107.2i			0.167273i
$170$		0			0
$171$		−	336558.i		−	0.880175i
$172$		0			0
$173$	292143.	−	292143.i	0.742131	−	0.742131i	−0.230856	−	0.972988i	$-0.574153\pi$
$173$	292143.	−	292143.i	0.742131	−	0.742131i	0.972988	+	0.230856i	$0.0741528\pi$
$174$		0			0
$175$	−305770.	+	230100.i	−0.754744	+	0.567965i
$176$		0			0
$177$	83866.2	+	83866.2i	0.201212	+	0.201212i
$178$		0			0
$179$	54181.2			0.126391			0.0631955	−	0.998001i	$-0.479871\pi$
$179$	54181.2			0.126391			0.0631955	+	0.998001i	$0.479871\pi$
$180$		0			0
$181$	−688743.			−1.56265			−0.781323	−	0.624126i	$-0.785455\pi$
$181$	−688743.			−1.56265			−0.781323	+	0.624126i	$0.785455\pi$
$182$		0			0
$183$	28658.8	+	28658.8i	0.0632602	+	0.0632602i
$184$		0			0
$185$	−87085.1	+	75651.8i	−0.187074	+	0.162514i
$186$		0			0
$187$	100162.	−	100162.i	0.209458	−	0.209458i
$188$		0			0
$189$			210253.i			0.428141i
$190$		0			0
$191$		−	784130.i		−	1.55527i	−0.628719	−	0.777633i	$-0.716420\pi$
$191$		−	784130.i		−	1.55527i	0.628719	−	0.777633i	$-0.283580\pi$
$192$		0			0
$193$	−471817.	+	471817.i	−0.911760	+	0.911760i	−0.996411	−	0.0846508i	$-0.973023\pi$
$193$	−471817.	+	471817.i	−0.911760	+	0.911760i	0.0846508	+	0.996411i	$0.473023\pi$
$194$		0			0
$195$	7910.79	−	112599.i	0.0148982	−	0.212055i
$196$		0			0
$197$	−313820.	−	313820.i	−0.576122	−	0.576122i	0.357710	−	0.933833i	$-0.383558\pi$
$197$	−313820.	−	313820.i	−0.576122	−	0.576122i	−0.933833	+	0.357710i	$0.883558\pi$
$198$		0			0
$199$	−265732.			−0.475675			−0.237838	−	0.971305i	$-0.576439\pi$
$199$	−265732.			−0.475675			−0.237838	+	0.971305i	$0.576439\pi$
$200$		0			0
$201$	78677.2			0.137359
$202$		0			0
$203$	217867.	+	217867.i	0.371067	+	0.371067i
$204$		0			0
$205$	−69860.4	+	994366.i	−0.116104	+	1.65258i
$206$		0			0
$207$	−657210.	+	657210.i	−1.06605	+	1.06605i
$208$		0			0
$209$		−	202493.i		−	0.320660i
$210$		0			0
$211$		−	1.22983e6i		−	1.90169i	−0.309669	−	0.950844i	$-0.600218\pi$
$211$		−	1.22983e6i		−	1.90169i	0.309669	−	0.950844i	$-0.399782\pi$
$212$		0			0
$213$	−186033.	+	186033.i	−0.280958	+	0.280958i
$214$		0			0
$215$	−278174.	+	241653.i	−0.410412	+	0.356529i
$216$		0			0
$217$	−256802.	−	256802.i	−0.370211	−	0.370211i
$218$		0			0
$219$	34367.9			0.0484220
$220$		0			0
$221$	−569639.			−0.784547
$222$		0			0
$223$	−134406.	−	134406.i	−0.180990	−	0.180990i	0.610797	−	0.791787i	$-0.290849\pi$
$223$	−134406.	−	134406.i	−0.180990	−	0.180990i	−0.791787	+	0.610797i	$0.790849\pi$
$224$		0			0
$225$	−100416.	+	711111.i	−0.132235	+	0.936443i
$226$		0			0
$227$	663217.	−	663217.i	0.854262	−	0.854262i	−0.136393	−	0.990655i	$-0.543551\pi$
$227$	663217.	−	663217.i	0.854262	−	0.854262i	0.990655	+	0.136393i	$0.0435509\pi$
$228$		0			0
$229$		−	1.36605e6i		−	1.72139i	−0.509121	−	0.860695i	$-0.670030\pi$
$229$		−	1.36605e6i		−	1.72139i	0.509121	−	0.860695i	$-0.329970\pi$
$230$		0			0
$231$			61486.3i			0.0758138i
$232$		0			0
$233$	715262.	−	715262.i	0.863128	−	0.863128i	−0.128572	−	0.991700i	$-0.541039\pi$
$233$	715262.	−	715262.i	0.863128	−	0.863128i	0.991700	+	0.128572i	$0.0410393\pi$
$234$		0			0
$235$	−1.07596e6	−	1.23857e6i	−1.27095	−	1.46302i
$236$		0			0
$237$	−94043.6	−	94043.6i	−0.108757	−	0.108757i
$238$		0			0
$239$	1.69801e6			1.92285			0.961424	−	0.275071i	$-0.0887015\pi$
$239$	1.69801e6			1.92285			0.961424	+	0.275071i	$0.0887015\pi$
$240$		0			0
$241$	−1.26836e6			−1.40669			−0.703347	−	0.710847i	$-0.748312\pi$
$241$	−1.26836e6			−1.40669			−0.703347	+	0.710847i	$0.748312\pi$
$242$		0			0
$243$	422405.	+	422405.i	0.458896	+	0.458896i
$244$		0			0
$245$	101011.	+	7096.64i	0.107511	+	0.00755331i
$246$		0			0
$247$	−575810.	+	575810.i	−0.600533	+	0.600533i
$248$		0			0
$249$		−	337727.i		−	0.345197i
$250$		0			0
$251$		−	1.01828e6i		−	1.02019i	−0.860118	−	0.510095i	$-0.829610\pi$
$251$		−	1.01828e6i		−	1.02019i	0.860118	−	0.510095i	$-0.170390\pi$
$252$		0			0
$253$	−395417.	+	395417.i	−0.388378	+	0.388378i
$254$		0			0
$255$	−207451.	−	14574.7i	−0.199786	−	0.0140362i
$256$		0			0
$257$	547963.	+	547963.i	0.517509	+	0.517509i	0.916817	−	0.399308i	$-0.130749\pi$
$257$	547963.	+	547963.i	0.517509	+	0.517509i	−0.399308	+	0.916817i	$0.630749\pi$
$258$		0			0
$259$	−252695.			−0.234071
$260$		0			0
$261$	578229.			0.525410
$262$		0			0
$263$	271982.	+	271982.i	0.242466	+	0.242466i	0.817870	−	0.575404i	$-0.195155\pi$
$263$	271982.	+	271982.i	0.242466	+	0.242466i	−0.575404	+	0.817870i	$0.695155\pi$
$264$		0			0
$265$	600008.	+	690687.i	0.524859	+	0.604181i
$266$		0			0
$267$	−143511.	+	143511.i	−0.123199	+	0.123199i
$268$		0			0
$269$			376480.i			0.317221i	0.987341	+	0.158610i	$0.0507014\pi$
$269$			376480.i			0.317221i	−0.987341	+	0.158610i	$0.949299\pi$
$270$		0			0
$271$			810637.i			0.670506i	0.942128	+	0.335253i	$0.108822\pi$
$271$			810637.i			0.670506i	−0.942128	+	0.335253i	$0.891178\pi$
$272$		0			0
$273$	174842.	−	174842.i	0.141984	−	0.141984i
$274$		0			0
$275$	−60416.1	+	427848.i	−0.0481749	+	0.341159i
$276$		0			0
$277$	1.55210e6	+	1.55210e6i	1.21540	+	1.21540i	0.969226	+	0.246173i	$0.0791732\pi$
$277$	1.55210e6	+	1.55210e6i	1.21540	+	1.21540i	0.246173	+	0.969226i	$0.420827\pi$
$278$		0			0
$279$	−681564.			−0.524199
$280$		0			0
$281$	−848494.			−0.641037			−0.320518	−	0.947242i	$-0.603857\pi$
$281$	−848494.			−0.641037			−0.320518	+	0.947242i	$0.603857\pi$
$282$		0			0
$283$	906572.	+	906572.i	0.672878	+	0.672878i	0.958378	−	0.285501i	$-0.0921600\pi$
$283$	906572.	+	906572.i	0.672878	+	0.672878i	−0.285501	+	0.958378i	$0.592160\pi$
$284$		0			0
$285$	−224431.	+	194966.i	−0.163671	+	0.142183i
$286$		0			0
$287$	−1.54404e6	+	1.54404e6i	−1.10650	+	1.10650i
$288$		0			0
$289$		−	370362.i		−	0.260845i
$290$		0			0
$291$		−	257417.i		−	0.178199i
$292$		0			0
$293$	1.85405e6	−	1.85405e6i	1.26169	−	1.26169i	0.311417	−	0.950273i	$-0.399197\pi$
$293$	1.85405e6	−	1.85405e6i	1.26169	−	1.26169i	0.950273	−	0.311417i	$-0.100803\pi$
$294$		0			0
$295$	−127960.	+	1.82133e6i	−0.0856086	+	1.21852i
$296$		0			0
$297$	167869.	+	167869.i	0.110428	+	0.110428i
$298$		0			0
$299$	2.24882e6			1.45471
$300$		0			0
$301$	−807178.			−0.513515
$302$		0			0
$303$	−165154.	−	165154.i	−0.103343	−	0.103343i
$304$		0			0
$305$	−43726.4	+	622385.i	−0.0269150	+	0.383098i
$306$		0			0
$307$	756148.	−	756148.i	0.457890	−	0.457890i	−0.440072	−	0.897962i	$-0.645047\pi$
$307$	756148.	−	756148.i	0.457890	−	0.457890i	0.897962	+	0.440072i	$0.145047\pi$
$308$		0			0
$309$		−	353014.i		−	0.210327i
$310$		0			0
$311$		−	2.78685e6i		−	1.63385i	−0.576744	−	0.816925i	$-0.695677\pi$
$311$		−	2.78685e6i		−	1.63385i	0.576744	−	0.816925i	$-0.304323\pi$
$312$		0			0
$313$	2.07387e6	−	2.07387e6i	1.19652	−	1.19652i	0.221324	−	0.975200i	$-0.428962\pi$
$313$	2.07387e6	−	2.07387e6i	1.19652	−	1.19652i	0.975200	−	0.221324i	$-0.0710379\pi$
$314$		0			0
$315$	−1.18764e6	+	1.03172e6i	−0.674387	+	0.585848i
$316$		0			0
$317$	−759404.	−	759404.i	−0.424448	−	0.424448i	0.462284	−	0.886732i	$-0.347030\pi$
$317$	−759404.	−	759404.i	−0.424448	−	0.424448i	−0.886732	+	0.462284i	$0.847030\pi$
$318$		0			0
$319$	347898.			0.191414
$320$		0			0
$321$	508682.			0.275540
$322$		0			0
$323$	1.06086e6	+	1.06086e6i	0.565787	+	0.565787i
$324$		0			0
$325$	1.38843e6	−	1.04483e6i	0.729146	−	0.548702i
$326$		0			0
$327$	−323712.	+	323712.i	−0.167413	+	0.167413i
$328$		0			0
$329$		−	3.59397e6i		−	1.83056i
$330$		0			0
$331$			3.93087e6i			1.97205i	0.166588	+	0.986027i	$0.446725\pi$
$331$			3.93087e6i			1.97205i	−0.166588	+	0.986027i	$0.553275\pi$
$332$		0			0
$333$	−335332.	+	335332.i	−0.165716	+	0.165716i
$334$		0			0
$335$	794297.	+	914339.i	0.386697	+	0.445139i
$336$		0			0
$337$	1.66349e6	+	1.66349e6i	0.797896	+	0.797896i	0.982764	−	0.184867i	$-0.0591855\pi$
$337$	1.66349e6	+	1.66349e6i	0.797896	+	0.797896i	−0.184867	+	0.982764i	$0.559185\pi$
$338$		0			0
$339$	−541294.			−0.255820
$340$		0			0
$341$	−410070.			−0.190973
$342$		0			0
$343$	1.61216e6	+	1.61216e6i	0.739901	+	0.739901i
$344$		0			0
$345$	818973.	+	57537.9i	0.370444	+	0.0260259i
$346$		0			0
$347$	1.60913e6	−	1.60913e6i	0.717411	−	0.717411i	−0.250663	−	0.968074i	$-0.580649\pi$
$347$	1.60913e6	−	1.60913e6i	0.717411	−	0.717411i	0.968074	+	0.250663i	$0.0806487\pi$
$348$		0			0
$349$			3.11197e6i			1.36764i	0.729651	+	0.683820i	$0.239683\pi$
$349$			3.11197e6i			1.36764i	−0.729651	+	0.683820i	$0.760317\pi$
$350$		0			0
$351$		−	954705.i		−	0.413620i
$352$		0			0
$353$	−883046.	+	883046.i	−0.377178	+	0.377178i	−0.870083	−	0.492905i	$-0.835935\pi$
$353$	−883046.	+	883046.i	−0.377178	+	0.377178i	0.492905	+	0.870083i	$0.335935\pi$
$354$		0			0
$355$	−4.04010e6	−	283842.i	−1.70146	−	0.119538i
$356$		0			0
$357$	−322127.	−	322127.i	−0.133769	−	0.133769i
$358$		0			0
$359$	2.78842e6			1.14188			0.570942	−	0.820991i	$-0.306578\pi$
$359$	2.78842e6			1.14188			0.570942	+	0.820991i	$0.306578\pi$
$360$		0			0
$361$	−331388.			−0.133835
$362$		0			0
$363$	−364449.	−	364449.i	−0.145168	−	0.145168i
$364$		0			0
$365$	346966.	+	399403.i	0.136319	+	0.156920i
$366$		0			0
$367$	−171952.	+	171952.i	−0.0666411	+	0.0666411i	−0.739642	−	0.673001i	$-0.765005\pi$
$367$	−171952.	+	171952.i	−0.0666411	+	0.0666411i	0.673001	+	0.739642i	$0.265005\pi$
$368$		0			0
$369$			4.09794e6i			1.56675i
$370$		0			0
$371$			2.00417e6i			0.755962i
$372$		0			0
$373$	1.43353e6	−	1.43353e6i	0.533500	−	0.533500i	−0.388112	−	0.921612i	$-0.626873\pi$
$373$	1.43353e6	−	1.43353e6i	0.533500	−	0.533500i	0.921612	+	0.388112i	$0.126873\pi$
$374$		0			0
$375$	532370.	−	344981.i	0.195495	−	0.126683i
$376$		0			0
$377$	−989281.	−	989281.i	−0.358481	−	0.358481i
$378$		0			0
$379$	−2.79105e6			−0.998090			−0.499045	−	0.866576i	$-0.666316\pi$
$379$	−2.79105e6			−0.998090			−0.499045	+	0.866576i	$0.666316\pi$
$380$		0			0
$381$	−76381.5			−0.0269573
$382$		0			0
$383$	−156048.	−	156048.i	−0.0543576	−	0.0543576i	0.679405	−	0.733763i	$-0.262238\pi$
$383$	−156048.	−	156048.i	−0.0543576	−	0.0543576i	−0.733763	+	0.679405i	$0.762238\pi$
$384$		0			0
$385$	−714557.	+	620744.i	−0.245689	+	0.213433i
$386$		0			0
$387$	−1.07114e6	+	1.07114e6i	−0.363555	+	0.363555i
$388$		0			0
$389$		−	5.09636e6i		−	1.70760i	−0.520601	−	0.853800i	$-0.674292\pi$
$389$		−	5.09636e6i		−	1.70760i	0.520601	−	0.853800i	$-0.325708\pi$
$390$		0			0
$391$		−	4.14318e6i		−	1.37054i
$392$		0			0
$393$	482938.	−	482938.i	0.157729	−	0.157729i
$394$		0			0
$395$	143488.	−	2.04235e6i	0.0462724	−	0.658624i
$396$		0			0
$397$	1.71513e6	+	1.71513e6i	0.546162	+	0.546162i	0.925329	−	0.379166i	$-0.123789\pi$
$397$	1.71513e6	+	1.71513e6i	0.546162	+	0.546162i	−0.379166	+	0.925329i	$0.623789\pi$
$398$		0			0
$399$	−651233.			−0.204788
$400$		0			0
$401$	−548874.			−0.170456			−0.0852279	−	0.996361i	$-0.527162\pi$
$401$	−548874.			−0.170456			−0.0852279	+	0.996361i	$0.527162\pi$
$402$		0			0
$403$	1.16607e6	+	1.16607e6i	0.357655	+	0.357655i
$404$		0			0
$405$	−194360.	+	2.76645e6i	−0.0588802	+	0.838079i
$406$		0			0
$407$	−201756.	+	201756.i	−0.0603727	+	0.0603727i
$408$		0			0
$409$		−	1.19568e6i		−	0.353432i	−0.984262	−	0.176716i	$-0.943453\pi$
$409$		−	1.19568e6i		−	0.353432i	0.984262	−	0.176716i	$-0.0565474\pi$
$410$		0			0
$411$			237850.i			0.0694543i
$412$		0			0
$413$	−2.82813e6	+	2.82813e6i	−0.815876	+	0.815876i
$414$		0			0
$415$	3.92486e6	−	3.40957e6i	1.11867	−	0.971806i
$416$		0			0
$417$	−609955.	−	609955.i	−0.171774	−	0.171774i
$418$		0			0
$419$	−2.17447e6			−0.605089			−0.302545	−	0.953135i	$-0.597836\pi$
$419$	−2.17447e6			−0.605089			−0.302545	+	0.953135i	$0.597836\pi$
$420$		0			0
$421$	813691.			0.223745			0.111873	−	0.993723i	$-0.464315\pi$
$421$	813691.			0.223745			0.111873	+	0.993723i	$0.464315\pi$
$422$		0			0
$423$	−4.76927e6	−	4.76927e6i	−1.29599	−	1.29599i
$424$		0			0
$425$	−1.92498e6	−	2.55802e6i	−0.516955	−	0.686959i
$426$		0			0
$427$	−966430.	+	966430.i	−0.256508	+	0.256508i
$428$		0			0
$429$		−	279194.i		−	0.0732424i
$430$		0			0
$431$		−	4.11534e6i		−	1.06712i	−0.845763	−	0.533559i	$-0.820854\pi$
$431$		−	4.11534e6i		−	1.06712i	0.845763	−	0.533559i	$-0.179146\pi$
$432$		0			0
$433$	−4.90292e6	+	4.90292e6i	−1.25671	+	1.25671i	−0.304055	+	0.952654i	$0.598341\pi$
$433$	−4.90292e6	+	4.90292e6i	−1.25671	+	1.25671i	−0.952654	+	0.304055i	$0.901659\pi$
$434$		0			0
$435$	−334965.	−	385588.i	−0.0848742	−	0.0977013i
$436$		0			0
$437$	−4.18807e6	−	4.18807e6i	−1.04908	−	1.04908i
$438$		0			0
$439$	2.45837e6			0.608816			0.304408	−	0.952542i	$-0.401541\pi$
$439$	2.45837e6			0.608816			0.304408	+	0.952542i	$0.401541\pi$
$440$		0			0
$441$	416281.			0.101927
$442$		0			0
$443$	2.32556e6	+	2.32556e6i	0.563013	+	0.563013i	0.930162	−	0.367149i	$-0.119666\pi$
$443$	2.32556e6	+	2.32556e6i	0.563013	+	0.563013i	−0.367149	+	0.930162i	$0.619666\pi$
$444$		0			0
$445$	−3.11665e6	−	218964.i	−0.746083	−	0.0524170i
$446$		0			0
$447$	−388358.	+	388358.i	−0.0919313	+	0.0919313i
$448$		0			0
$449$		−	862597.i		−	0.201926i	−0.994890	−	0.100963i	$-0.967808\pi$
$449$		−	862597.i		−	0.201926i	0.994890	−	0.100963i	$-0.0321924\pi$
$450$		0			0
$451$			2.46557e6i			0.570789i
$452$		0			0
$453$	−717615.	+	717615.i	−0.164303	+	0.164303i
$454$		0			0
$455$	3.79706e6	+	266767.i	0.859843	+	0.0604093i
$456$		0			0
$457$	1.85538e6	+	1.85538e6i	0.415569	+	0.415569i	0.883673	−	0.468104i	$-0.155063\pi$
$457$	1.85538e6	+	1.85538e6i	0.415569	+	0.415569i	−0.468104	+	0.883673i	$0.655063\pi$
$458$		0			0
$459$	−1.75893e6			−0.389689
$460$		0			0
$461$	−5.77233e6			−1.26502			−0.632512	−	0.774550i	$-0.717976\pi$
$461$	−5.77233e6			−1.26502			−0.632512	+	0.774550i	$0.717976\pi$
$462$		0			0
$463$	−4.90952e6	−	4.90952e6i	−1.06436	−	1.06436i	−0.997781	−	0.0665741i	$-0.978793\pi$
$463$	−4.90952e6	−	4.90952e6i	−1.06436	−	1.06436i	−0.0665741	−	0.997781i	$-0.521207\pi$
$464$		0			0
$465$	394826.	+	454496.i	0.0846785	+	0.0974760i
$466$		0			0
$467$	5.80856e6	−	5.80856e6i	1.23247	−	1.23247i	0.269457	−	0.963012i	$-0.413156\pi$
$467$	5.80856e6	−	5.80856e6i	1.23247	−	1.23247i	0.963012	−	0.269457i	$-0.0868443\pi$
$468$		0			0
$469$			2.65314e6i			0.556966i
$470$		0			0
$471$		−	1.09239e6i		−	0.226894i
$472$		0			0
$473$	−644464.	+	644464.i	−0.132448	+	0.132448i
$474$		0			0
$475$	−4.53155e6	−	639898.i	−0.921537	−	0.130130i
$476$		0			0
$477$	2.65958e6	+	2.65958e6i	0.535201	+	0.535201i
$478$		0			0
$479$	2.08699e6			0.415605			0.207803	−	0.978171i	$-0.433369\pi$
$479$	2.08699e6			0.415605			0.207803	+	0.978171i	$0.433369\pi$
$480$		0			0
$481$	1.14743e6			0.226132
$482$		0			0
$483$	1.27169e6	+	1.27169e6i	0.248035	+	0.248035i
$484$		0			0
$485$	2.99155e6	−	2.59879e6i	0.577486	−	0.501669i
$486$		0			0
$487$	−2.44005e6	+	2.44005e6i	−0.466204	+	0.466204i	−0.900682	−	0.434478i	$-0.856933\pi$
$487$	−2.44005e6	+	2.44005e6i	−0.466204	+	0.466204i	0.434478	+	0.900682i	$0.356933\pi$
$488$		0			0
$489$			77217.2i			0.0146030i
$490$		0			0
$491$			2.73425e6i			0.511840i	0.966698	+	0.255920i	$0.0823784\pi$
$491$			2.73425e6i			0.511840i	−0.966698	+	0.255920i	$0.917622\pi$
$492$		0			0
$493$	−1.82264e6	+	1.82264e6i	−0.337740	+	0.337740i
$494$		0			0
$495$	−124492.	+	1.77197e6i	−0.0228365	+	0.325046i
$496$		0			0
$497$	−6.27340e6	−	6.27340e6i	−1.13923	−	1.13923i
$498$		0			0
$499$	−8.35540e6			−1.50216			−0.751079	−	0.660212i	$-0.770466\pi$
$499$	−8.35540e6			−1.50216			−0.751079	+	0.660212i	$0.770466\pi$
$500$		0			0
$501$	492568.			0.0876742
$502$		0			0
$503$	−4.17030e6	−	4.17030e6i	−0.734932	−	0.734932i	0.236660	−	0.971592i	$-0.423947\pi$
$503$	−4.17030e6	−	4.17030e6i	−0.734932	−	0.734932i	−0.971592	+	0.236660i	$0.923947\pi$
$504$		0			0
$505$	251985.	−	3.58665e6i	0.0439689	−	0.625837i
$506$		0			0
$507$	159476.	−	159476.i	0.0275535	−	0.0275535i
$508$		0			0
$509$			6.82189e6i			1.16711i	0.812075	+	0.583553i	$0.198338\pi$
$509$			6.82189e6i			1.16711i	−0.812075	+	0.583553i	$0.801662\pi$
$510$		0			0
$511$			1.15895e6i			0.196342i
$512$		0			0
$513$	−1.77799e6	+	1.77799e6i	−0.298288	+	0.298288i
$514$		0			0
$515$	4.10252e6	−	3.56391e6i	0.681605	−	0.592118i
$516$		0			0
$517$	−2.86948e6	−	2.86948e6i	−0.472147	−	0.472147i
$518$		0			0
$519$	−1.50031e6			−0.244491
$520$		0			0
$521$	1.05649e7			1.70518			0.852592	−	0.522577i	$-0.175029\pi$
$521$	1.05649e7			1.70518			0.852592	+	0.522577i	$0.175029\pi$
$522$		0			0
$523$	−2.57434e6	−	2.57434e6i	−0.411540	−	0.411540i	0.470735	−	0.882275i	$-0.343989\pi$
$523$	−2.57434e6	−	2.57434e6i	−0.411540	−	0.411540i	−0.882275	+	0.470735i	$0.843989\pi$
$524$		0			0
$525$	1.37599e6	+	194302.i	0.217879	+	0.0307666i
$526$		0			0
$527$	2.14836e6	−	2.14836e6i	0.336961	−	0.336961i
$528$		0			0
$529$			9.92008e6i			1.54126i
$530$		0			0
$531$			7.50598e6i			1.15524i
$532$		0			0
$533$	7.01109e6	−	7.01109e6i	1.06897	−	1.06897i
$534$		0			0
$535$	5.13548e6	+	5.91160e6i	0.775705	+	0.892937i
$536$		0			0
$537$	−139124.	−	139124.i	−0.0208194	−	0.0208194i
$538$		0			0
$539$	250460.			0.0371336
$540$		0			0
$541$	7.45276e6			1.09477			0.547387	−	0.836880i	$-0.315623\pi$
$541$	7.45276e6			1.09477			0.547387	+	0.836880i	$0.315623\pi$
$542$		0			0
$543$	1.76853e6	+	1.76853e6i	0.257402	+	0.257402i
$544$		0			0
$545$	−7.03007e6	−	493906.i	−1.01384	−	0.0712284i
$546$		0			0
$547$	3.11940e6	−	3.11940e6i	0.445762	−	0.445762i	−0.448181	−	0.893943i	$-0.647928\pi$
$547$	3.11940e6	−	3.11940e6i	0.445762	−	0.445762i	0.893943	+	0.448181i	$0.147928\pi$
$548$		0			0
$549$			2.56495e6i			0.363201i
$550$		0			0
$551$			3.68476e6i			0.517047i
$552$		0			0
$553$	3.17133e6	−	3.17133e6i	0.440990	−	0.440990i
$554$		0			0
$555$	417870.	+	29357.9i	0.0575849	+	0.00404569i
$556$		0			0
$557$	1.09325e6	+	1.09325e6i	0.149307	+	0.149307i	0.777809	−	0.628501i	$-0.216331\pi$
$557$	1.09325e6	+	1.09325e6i	0.149307	+	0.149307i	−0.628501	+	0.777809i	$0.716331\pi$
$558$		0			0
$559$	3.66519e6			0.496098
$560$		0			0
$561$	−514383.			−0.0690048
$562$		0			0
$563$	925173.	+	925173.i	0.123013	+	0.123013i	0.765933	−	0.642920i	$-0.222277\pi$
$563$	925173.	+	925173.i	0.123013	+	0.123013i	−0.642920	+	0.765933i	$0.722277\pi$
$564$		0			0
$565$	−5.46471e6	−	6.29060e6i	−0.720189	−	0.829031i
$566$		0			0
$567$	−4.29570e6	+	4.29570e6i	−0.561146	+	0.561146i
$568$		0			0
$569$		−	1.87684e6i		−	0.243022i	−0.992590	−	0.121511i	$-0.961226\pi$
$569$		−	1.87684e6i		−	0.243022i	0.992590	−	0.121511i	$-0.0387740\pi$
$570$		0			0
$571$			1.36900e6i			0.175717i	0.996133	+	0.0878583i	$0.0280023\pi$
$571$			1.36900e6i			0.175717i	−0.996133	+	0.0878583i	$0.971998\pi$
$572$		0			0
$573$	−2.01346e6	+	2.01346e6i	−0.256187	+	0.256187i
$574$		0			0
$575$	7.59940e6	+	1.00985e7i	0.958538	+	1.27376i
$576$		0			0
$577$	570663.	+	570663.i	0.0713576	+	0.0713576i	0.741885	−	0.670527i	$-0.233932\pi$
$577$	570663.	+	570663.i	0.0713576	+	0.0713576i	−0.670527	+	0.741885i	$0.733932\pi$
$578$		0			0
$579$	2.42303e6			0.300374
$580$		0			0
$581$	1.13888e7			1.39971
$582$		0			0
$583$	1.60016e6	+	1.60016e6i	0.194981	+	0.194981i
$584$		0			0
$585$	5.39279e6	−	4.68478e6i	0.651514	−	0.565978i
$586$		0			0
$587$	1.15380e7	−	1.15380e7i	1.38209	−	1.38209i	0.541183	−	0.840905i	$-0.317977\pi$
$587$	1.15380e7	−	1.15380e7i	1.38209	−	1.38209i	0.840905	−	0.541183i	$-0.182023\pi$
$588$		0			0
$589$		−	4.34326e6i		−	0.515855i
$590$		0			0
$591$			1.61163e6i			0.189800i
$592$		0			0
$593$	6.31824e6	−	6.31824e6i	0.737835	−	0.737835i	−0.234324	−	0.972159i	$-0.575288\pi$
$593$	6.31824e6	−	6.31824e6i	0.737835	−	0.737835i	0.972159	+	0.234324i	$0.0752876\pi$
$594$		0			0
$595$	491488.	−	6.99565e6i	0.0569141	−	0.810094i
$596$		0			0
$597$	682335.	+	682335.i	0.0783542	+	0.0783542i
$598$		0			0
$599$	−2.89869e6			−0.330091			−0.165046	−	0.986286i	$-0.552777\pi$
$599$	−2.89869e6			−0.330091			−0.165046	+	0.986286i	$0.552777\pi$
$600$		0			0
$601$	−575304.			−0.0649698			−0.0324849	−	0.999472i	$-0.510342\pi$
$601$	−575304.			−0.0649698			−0.0324849	+	0.999472i	$0.510342\pi$
$602$		0			0
$603$	3.52078e6	+	3.52078e6i	0.394317	+	0.394317i
$604$		0			0
$605$	556061.	−	7.91476e6i	0.0617638	−	0.879122i
$606$		0			0
$607$	−1.08143e7	+	1.08143e7i	−1.19132	+	1.19132i	−0.214618	+	0.976698i	$0.568851\pi$
$607$	−1.08143e7	+	1.08143e7i	−1.19132	+	1.19132i	−0.976698	+	0.214618i	$0.931149\pi$
$608$		0			0
$609$		−	1.11886e6i		−	0.122246i
$610$		0			0
$611$			1.63193e7i			1.76848i
$612$		0			0
$613$	−1.04880e7	+	1.04880e7i	−1.12731	+	1.12731i	−0.136697	+	0.990613i	$0.543649\pi$
$613$	−1.04880e7	+	1.04880e7i	−1.12731	+	1.12731i	−0.990613	+	0.136697i	$0.956351\pi$
$614$		0			0
$615$	2.73268e6	−	2.37391e6i	0.291341	−	0.253091i
$616$		0			0
$617$	5.23198e6	+	5.23198e6i	0.553290	+	0.553290i	0.927389	−	0.374099i	$-0.122048\pi$
$617$	5.23198e6	+	5.23198e6i	0.553290	+	0.553290i	−0.374099	+	0.927389i	$0.622048\pi$
$618$		0			0
$619$	−5.92277e6			−0.621295			−0.310648	−	0.950525i	$-0.600546\pi$
$619$	−5.92277e6			−0.621295			−0.310648	+	0.950525i	$0.600546\pi$
$620$		0			0
$621$	6.94390e6			0.722561
$622$		0			0
$623$	−4.83948e6	−	4.83948e6i	−0.499549	−	0.499549i
$624$		0			0
$625$	9.38378e6	+	2.70408e6i	0.960900	+	0.276897i
$626$		0			0
$627$	−519955.	+	519955.i	−0.0528198	+	0.0528198i
$628$		0			0
$629$		−	2.11400e6i		−	0.213049i
$630$		0			0
$631$			1.72966e7i			1.72937i	0.502317	+	0.864684i	$0.332481\pi$
$631$			1.72966e7i			1.72937i	−0.502317	+	0.864684i	$0.667519\pi$
$632$		0			0
$633$	−3.15792e6	+	3.15792e6i	−0.313250	+	0.313250i
$634$		0			0
$635$	−771121.	−	887661.i	−0.0758907	−	0.0873600i
$636$		0			0
$637$	−712208.	−	712208.i	−0.0695438	−	0.0695438i
$638$		0			0
$639$	−1.66499e7			−1.61309
$640$		0			0
$641$	6.71337e6			0.645350			0.322675	−	0.946510i	$-0.395418\pi$
$641$	6.71337e6			0.645350			0.322675	+	0.946510i	$0.395418\pi$
$642$		0			0
$643$	−1.24589e7	−	1.24589e7i	−1.18837	−	1.18837i	−0.977517	−	0.210855i	$-0.932375\pi$
$643$	−1.24589e7	−	1.24589e7i	−1.18837	−	1.18837i	−0.210855	−	0.977517i	$-0.567625\pi$
$644$		0			0
$645$	1.33479e6	+	93777.2i	0.126332	+	0.00887561i
$646$		0			0
$647$	−7.31955e6	+	7.31955e6i	−0.687423	+	0.687423i	−0.961662	−	0.274239i	$-0.911574\pi$
$647$	−7.31955e6	+	7.31955e6i	−0.687423	+	0.687423i	0.274239	+	0.961662i	$0.411574\pi$
$648$		0			0
$649$			4.51605e6i			0.420869i
$650$		0			0
$651$			1.31881e6i			0.121964i
$652$		0			0
$653$	−2.40041e6	+	2.40041e6i	−0.220294	+	0.220294i	−0.808622	−	0.588328i	$-0.799786\pi$
$653$	−2.40041e6	+	2.40041e6i	−0.220294	+	0.220294i	0.588328	+	0.808622i	$0.299786\pi$
$654$		0			0
$655$	1.04880e7	+	736847.i	0.955189	+	0.0671079i
$656$		0			0
$657$	1.53795e6	+	1.53795e6i	0.139005	+	0.139005i
$658$		0			0
$659$	1.66675e7			1.49505			0.747527	−	0.664232i	$-0.231241\pi$
$659$	1.66675e7			1.49505			0.747527	+	0.664232i	$0.231241\pi$
$660$		0			0
$661$	1.34629e7			1.19849			0.599245	−	0.800566i	$-0.295468\pi$
$661$	1.34629e7			1.19849			0.599245	+	0.800566i	$0.295468\pi$
$662$		0			0
$663$	1.46270e6	+	1.46270e6i	0.129232	+	0.129232i
$664$		0			0
$665$	−6.57462e6	−	7.56824e6i	−0.576523	−	0.663653i
$666$		0			0
$667$	7.19539e6	−	7.19539e6i	0.626238	−	0.626238i
$668$		0			0
$669$			690244.i			0.0596262i
$670$		0			0
$671$			1.54323e6i			0.132319i
$672$		0			0
$673$	−6.51061e6	+	6.51061e6i	−0.554095	+	0.554095i	−0.927620	−	0.373525i	$-0.878149\pi$
$673$	−6.51061e6	+	6.51061e6i	−0.554095	+	0.554095i	0.373525	+	0.927620i	$0.378149\pi$
$674$		0			0
$675$	4.28719e6	−	3.22622e6i	0.362170	−	0.272543i
$676$		0			0
$677$	−6.20067e6	−	6.20067e6i	−0.519956	−	0.519956i	0.397602	−	0.917558i	$-0.369843\pi$
$677$	−6.20067e6	−	6.20067e6i	−0.519956	−	0.519956i	−0.917558	+	0.397602i	$0.869843\pi$
$678$		0			0
$679$	8.68059e6			0.722562
$680$		0			0
$681$	−3.40597e6			−0.281432
$682$		0			0
$683$	7.72258e6	+	7.72258e6i	0.633448	+	0.633448i	0.948931	−	0.315483i	$-0.102167\pi$
$683$	7.72258e6	+	7.72258e6i	0.633448	+	0.633448i	−0.315483	+	0.948931i	$0.602167\pi$
$684$		0			0
$685$	−2.76416e6	+	2.40125e6i	−0.225080	+	0.195529i
$686$		0			0
$687$	−3.50770e6	+	3.50770e6i	−0.283551	+	0.283551i
$688$		0			0
$689$		−	9.10045e6i		−	0.730322i
$690$		0			0
$691$		−	8.92136e6i		−	0.710781i	−0.934718	−	0.355391i	$-0.884348\pi$
$691$		−	8.92136e6i		−	0.710781i	0.934718	−	0.355391i	$-0.115652\pi$
$692$		0			0
$693$	−2.75149e6	+	2.75149e6i	−0.217638	+	0.217638i
$694$		0			0
$695$	930644.	−	1.32464e7i	0.0730838	−	1.04025i
$696$		0			0
$697$	−1.29171e7	−	1.29171e7i	−1.00713	−	1.00713i
$698$		0			0
$699$	−3.67325e6			−0.284353
$700$		0			0
$701$	−1.19729e7			−0.920250			−0.460125	−	0.887854i	$-0.652195\pi$
$701$	−1.19729e7			−0.920250			−0.460125	+	0.887854i	$0.652195\pi$
$702$		0			0
$703$	−2.13690e6	−	2.13690e6i	−0.163078	−	0.163078i
$704$		0			0
$705$	−417544.	+	5.94317e6i	−0.0316395	+	0.450345i
$706$		0			0
$707$	5.56930e6	−	5.56930e6i	0.419037	−	0.419037i
$708$		0			0
$709$			5.47352e6i			0.408932i	0.978874	+	0.204466i	$0.0655458\pi$
$709$			5.47352e6i			0.408932i	−0.978874	+	0.204466i	$0.934454\pi$
$710$		0			0
$711$		−	8.41685e6i		−	0.624418i
$712$		0			0
$713$	−8.48127e6	+	8.48127e6i	−0.624794	+	0.624794i
$714$		0			0
$715$	3.24463e6	−	2.81864e6i	0.237356	−	0.206194i
$716$		0			0
$717$	−4.36008e6	−	4.36008e6i	−0.316735	−	0.316735i
$718$		0			0
$719$	−1.49644e7			−1.07953			−0.539767	−	0.841815i	$-0.681488\pi$
$719$	−1.49644e7			−1.07953			−0.539767	+	0.841815i	$0.681488\pi$
$720$		0			0
$721$	1.19043e7			0.852837
$722$		0			0
$723$	3.25684e6	+	3.25684e6i	0.231713	+	0.231713i
$724$		0			0
$725$	1.09939e6	−	7.78552e6i	0.0776794	−	0.550101i
$726$		0			0
$727$	2.64630e6	−	2.64630e6i	0.185696	−	0.185696i	−0.608136	−	0.793833i	$-0.708083\pi$
$727$	2.64630e6	−	2.64630e6i	0.185696	−	0.185696i	0.793833	+	0.608136i	$0.208083\pi$
$728$		0			0
$729$			9.88589e6i			0.688964i
$730$		0			0
$731$		−	6.75270e6i		−	0.467395i
$732$		0			0
$733$	1.03631e7	−	1.03631e7i	0.712407	−	0.712407i	−0.254631	−	0.967038i	$-0.581954\pi$
$733$	1.03631e7	−	1.03631e7i	0.712407	−	0.712407i	0.967038	+	0.254631i	$0.0819540\pi$
$734$		0			0
$735$	−241149.	−	277594.i	−0.0164652	−	0.0189536i
$736$		0			0
$737$	2.11831e6	+	2.11831e6i	0.143655	+	0.143655i
$738$		0			0
$739$	−2.37399e7			−1.59907			−0.799534	−	0.600621i	$-0.794920\pi$
$739$	−2.37399e7			−1.59907			−0.799534	+	0.600621i	$0.794920\pi$
$740$		0			0
$741$	2.95709e6			0.197842
$742$		0			0
$743$	−4.48493e6	−	4.48493e6i	−0.298046	−	0.298046i	0.542202	−	0.840248i	$-0.317591\pi$
$743$	−4.48493e6	−	4.48493e6i	−0.298046	−	0.298046i	−0.840248	+	0.542202i	$0.817591\pi$
$744$		0			0
$745$	−8.43399e6	−	592540.i	−0.556727	−	0.0391135i
$746$		0			0
$747$	1.51132e7	−	1.51132e7i	0.990955	−	0.990955i
$748$		0			0
$749$			1.71537e7i			1.11726i
$750$		0			0
$751$			5.46728e6i			0.353729i	0.984235	+	0.176865i	$0.0565955\pi$
$751$			5.46728e6i			0.353729i	−0.984235	+	0.176865i	$0.943404\pi$
$752$		0			0
$753$	−2.61469e6	+	2.61469e6i	−0.168048	+	0.168048i
$754$		0			0
$755$	−1.55845e7	−	1.09491e6i	−0.995005	−	0.0699052i
$756$		0			0
$757$	7.46441e6	+	7.46441e6i	0.473430	+	0.473430i	0.903023	−	0.429593i	$-0.141343\pi$
$757$	7.46441e6	+	7.46441e6i	0.473430	+	0.473430i	−0.429593	+	0.903023i	$0.641343\pi$
$758$		0			0
$759$	2.03068e6			0.127949
$760$		0			0
$761$	−1.95302e7			−1.22249			−0.611244	−	0.791442i	$-0.709331\pi$
$761$	−1.95302e7			−1.22249			−0.611244	+	0.791442i	$0.709331\pi$
$762$		0			0
$763$	−1.09162e7	−	1.09162e7i	−0.678828	−	0.678828i
$764$		0			0
$765$	−8.63116e6	−	9.93559e6i	−0.533231	−	0.613819i
$766$		0			0
$767$	1.28418e7	−	1.28418e7i	0.788204	−	0.788204i
$768$		0			0
$769$		−	7.65143e6i		−	0.466581i	−0.972407	−	0.233290i	$-0.925051\pi$
$769$		−	7.65143e6i		−	0.466581i	0.972407	−	0.233290i	$-0.0749493\pi$
$770$		0			0
$771$		−	2.81408e6i		−	0.170490i
$772$		0			0
$773$	−1.79609e7	+	1.79609e7i	−1.08113	+	1.08113i	−0.0847295	+	0.996404i	$0.527003\pi$
$773$	−1.79609e7	+	1.79609e7i	−1.08113	+	1.08113i	−0.996404	+	0.0847295i	$0.972997\pi$
$774$		0			0
$775$	−1.29586e6	+	9.17686e6i	−0.0775003	+	0.548833i
$776$		0			0
$777$	648862.	+	648862.i	0.0385567	+	0.0385567i
$778$		0			0
$779$	−2.61141e7			−1.54181
$780$		0			0
$781$	−1.00176e7			−0.587672
$782$		0			0
$783$	−3.05471e6	−	3.05471e6i	−0.178059	−	0.178059i
$784$		0			0
$785$	1.26951e7	−	1.10283e7i	0.735293	−	0.638757i
$786$		0			0
$787$	−2.66717e6	+	2.66717e6i	−0.153502	+	0.153502i	−0.779680	−	0.626178i	$-0.784618\pi$
$787$	−2.66717e6	+	2.66717e6i	−0.153502	+	0.153502i	0.626178	+	0.779680i	$0.284618\pi$
$788$		0			0
$789$		−	1.39677e6i		−	0.0798790i
$790$		0			0
$791$		−	1.82535e7i		−	1.03730i
$792$		0			0
$793$	4.38832e6	−	4.38832e6i	0.247808	−	0.247808i
$794$		0			0
$795$	232843.	−	3.31420e6i	0.0130661	−	0.185978i
$796$		0			0
$797$	−450702.	−	450702.i	−0.0251330	−	0.0251330i	0.694429	−	0.719562i	$-0.255657\pi$
$797$	−450702.	−	450702.i	−0.0251330	−	0.0251330i	−0.719562	+	0.694429i	$0.755657\pi$
$798$		0			0
$799$	3.00665e7			1.66616
$800$		0			0
$801$	−1.28442e7			−0.707335
$802$		0			0
$803$	925326.	+	925326.i	0.0506414	+	0.0506414i
$804$		0			0
$805$	−1.94029e6	+	2.76174e7i	−0.105530	+	1.50208i
$806$		0			0
$807$	966712.	−	966712.i	0.0522532	−	0.0522532i
$808$		0			0
$809$			3.12120e7i			1.67668i	0.545147	+	0.838341i	$0.316474\pi$
$809$			3.12120e7i			1.67668i	−0.545147	+	0.838341i	$0.683526\pi$
$810$		0			0
$811$			1.23393e7i			0.658779i	0.944194	+	0.329390i	$0.106843\pi$
$811$			1.23393e7i			0.658779i	−0.944194	+	0.329390i	$0.893157\pi$
$812$		0			0
$813$	2.08152e6	−	2.08152e6i	0.110447	−	0.110447i
$814$		0			0
$815$	−897372.	+	779558.i	−0.0473237	+	0.0411106i
$816$		0			0
$817$	−6.82585e6	−	6.82585e6i	−0.357768	−	0.357768i
$818$		0			0
$819$	1.56483e7			0.815187
$820$		0			0
$821$	−2.32367e7			−1.20314			−0.601570	−	0.798820i	$-0.705458\pi$
$821$	−2.32367e7			−1.20314			−0.601570	+	0.798820i	$0.705458\pi$
$822$		0			0
$823$	−2.50932e6	−	2.50932e6i	−0.129139	−	0.129139i	0.639583	−	0.768722i	$-0.279107\pi$
$823$	−2.50932e6	−	2.50932e6i	−0.129139	−	0.129139i	−0.768722	+	0.639583i	$0.779107\pi$
$824$		0			0
$825$	1.25375e6	−	943477.i	0.0641320	−	0.0482610i
$826$		0			0
$827$	−2.63507e7	+	2.63507e7i	−1.33977	+	1.33977i	−0.443483	+	0.896283i	$0.646257\pi$
$827$	−2.63507e7	+	2.63507e7i	−1.33977	+	1.33977i	−0.896283	+	0.443483i	$0.853743\pi$
$828$		0			0
$829$		−	2.64771e7i		−	1.33809i	−0.743224	−	0.669043i	$-0.766704\pi$
$829$		−	2.64771e7i		−	1.33809i	0.743224	−	0.669043i	$-0.233296\pi$
$830$		0			0
$831$		−	7.97082e6i		−	0.400406i
$832$		0			0
$833$	−1.31216e6	+	1.31216e6i	−0.0655201	+	0.0655201i
$834$		0			0
$835$	4.97280e6	+	5.72433e6i	0.246822	+	0.284125i
$836$		0			0
$837$	3.60061e6	+	3.60061e6i	0.177649	+	0.177649i
$838$		0			0
$839$	−2.35436e6			−0.115470			−0.0577348	−	0.998332i	$-0.518388\pi$
$839$	−2.35436e6			−0.115470			−0.0577348	+	0.998332i	$0.518388\pi$
$840$		0			0
$841$	1.41805e7			0.691355
$842$		0			0
$843$	2.17873e6	+	2.17873e6i	0.105593	+	0.105593i
$844$		0			0
$845$	3.46336e6	+	243322.i	0.166861	+	0.0117230i
$846$		0			0
$847$	1.22899e7	−	1.22899e7i	0.588627	−	0.588627i
$848$		0			0
$849$		−	4.65572e6i		−	0.221676i
$850$		0			0
$851$			8.34563e6i			0.395035i
$852$		0			0
$853$	2.20809e6	−	2.20809e6i	0.103907	−	0.103907i	−0.653242	−	0.757149i	$-0.726592\pi$
$853$	2.20809e6	−	2.20809e6i	0.103907	−	0.103907i	0.757149	+	0.653242i	$0.226592\pi$
$854$		0			0
$855$	−1.87679e7	−	1.31856e6i	−0.878011	−	0.0616857i
$856$		0			0
$857$	4.75974e6	+	4.75974e6i	0.221376	+	0.221376i	0.809078	−	0.587702i	$-0.199967\pi$
$857$	4.75974e6	+	4.75974e6i	0.221376	+	0.221376i	−0.587702	+	0.809078i	$0.699967\pi$
$858$		0			0
$859$	2.97185e7			1.37418			0.687091	−	0.726572i	$-0.258888\pi$
$859$	2.97185e7			1.37418			0.687091	+	0.726572i	$0.258888\pi$
$860$		0			0
$861$	7.92944e6			0.364531
$862$		0			0
$863$	−1.61046e7	−	1.61046e7i	−0.736078	−	0.736078i	0.235738	−	0.971817i	$-0.424249\pi$
$863$	−1.61046e7	−	1.61046e7i	−0.736078	−	0.736078i	−0.971817	+	0.235738i	$0.924249\pi$
$864$		0			0
$865$	−1.51466e7	−	1.74357e7i	−0.688295	−	0.792318i
$866$		0			0
$867$	−951003.	+	951003.i	−0.0429669	+	0.0429669i
$868$		0			0
$869$		−	5.06409e6i		−	0.227484i
$870$		0			0
$871$		−	1.20473e7i		−	0.538076i
$872$		0			0
$873$	1.15193e7	−	1.15193e7i	0.511554	−	0.511554i
$874$		0			0
$875$	1.16334e7	+	1.79525e7i	0.513674	+	0.792694i
$876$		0			0
$877$	4.10327e6	+	4.10327e6i	0.180149	+	0.180149i	0.791421	−	0.611272i	$-0.209342\pi$
$877$	4.10327e6	+	4.10327e6i	0.180149	+	0.180149i	−0.611272	+	0.791421i	$0.709342\pi$
$878$		0			0
$879$	−9.52153e6			−0.415656
$880$		0			0
$881$	4.69296e6			0.203707			0.101854	−	0.994799i	$-0.467523\pi$
$881$	4.69296e6			0.203707			0.101854	+	0.994799i	$0.467523\pi$
$882$		0			0
$883$	−1.96084e6	−	1.96084e6i	−0.0846331	−	0.0846331i	0.663523	−	0.748156i	$-0.269061\pi$
$883$	−1.96084e6	−	1.96084e6i	−0.0846331	−	0.0846331i	−0.748156	+	0.663523i	$0.769061\pi$
$884$		0			0
$885$	5.00531e6	−	4.34817e6i	0.214819	−	0.186616i
$886$		0			0
$887$	1.80367e6	−	1.80367e6i	0.0769747	−	0.0769747i	−0.667571	−	0.744546i	$-0.732666\pi$
$887$	1.80367e6	−	1.80367e6i	0.0769747	−	0.0769747i	0.744546	+	0.667571i	$0.232666\pi$
$888$		0			0
$889$		−	2.57573e6i		−	0.109307i
$890$		0			0
$891$			6.85951e6i			0.289467i
$892$		0			0
$893$	3.03922e7	−	3.03922e7i	1.27536	−	1.27536i
$894$		0			0
$895$	212270.	−	3.02137e6i	0.00885791	−	0.126080i
$896$		0			0
$897$	−5.77443e6	−	5.77443e6i	−0.239623	−	0.239623i
$898$		0			0
$899$	7.46202e6			0.307934
$900$		0			0
$901$	−1.67665e7			−0.688067
$902$		0			0
$903$	2.07264e6	+	2.07264e6i	0.0845872	+	0.0845872i
$904$		0			0
$905$	−2.69835e6	+	3.84072e7i	−0.109516	+	1.55880i
$906$		0			0
$907$	−2.83458e7	+	2.83458e7i	−1.14412	+	1.14412i	−0.156430	+	0.987689i	$0.549999\pi$
$907$	−2.83458e7	+	2.83458e7i	−1.14412	+	1.14412i	−0.987689	+	0.156430i	$0.950001\pi$
$908$		0			0
$909$		−	1.47812e7i		−	0.593334i
$910$		0			0
$911$			3.85580e6i			0.153928i	0.997034	+	0.0769641i	$0.0245227\pi$
$911$			3.85580e6i			0.153928i	−0.997034	+	0.0769641i	$0.975477\pi$
$912$		0			0
$913$	9.09300e6	−	9.09300e6i	0.361019	−	0.361019i
$914$		0			0
$915$	1.71042e6	−	1.48586e6i	0.0675381	−	0.0586711i
$916$		0			0
$917$	1.62856e7	+	1.62856e7i	0.639559	+	0.639559i
$918$		0			0
$919$	2.37344e7			0.927020			0.463510	−	0.886092i	$-0.346590\pi$
$919$	2.37344e7			0.927020			0.463510	+	0.886092i	$0.346590\pi$
$920$		0			0
$921$	−3.88322e6			−0.150849
$922$		0			0
$923$	2.84860e7	+	2.84860e7i	1.10059	+	1.10059i
$924$		0			0
$925$	3.87749e6	+	5.15262e6i	0.149003	+	0.198004i
$926$		0			0
$927$	1.57973e7	−	1.57973e7i	0.603785	−	0.603785i
$928$		0			0
$929$		−	3.39945e7i		−	1.29232i	−0.763204	−	0.646158i	$-0.776375\pi$
$929$		−	3.39945e7i		−	1.29232i	0.763204	−	0.646158i	$-0.223625\pi$
$930$		0			0
$931$			2.65275e6i			0.100305i
$932$		0			0
$933$	−7.15596e6	+	7.15596e6i	−0.269131	+	0.269131i
$934$		0			0
$935$	−5.19303e6	−	5.97785e6i	−0.194264	−	0.223623i
$936$		0			0
$937$	2.97242e7	+	2.97242e7i	1.10602	+	1.10602i	0.993669	+	0.112347i	$0.0358367\pi$
$937$	2.97242e7	+	2.97242e7i	1.10602	+	1.10602i	0.112347	+	0.993669i	$0.464163\pi$
$938$		0			0
$939$	−1.06504e7			−0.394188
$940$		0			0
$941$	3.31924e7			1.22198			0.610991	−	0.791638i	$-0.290771\pi$
$941$	3.31924e7			1.22198			0.610991	+	0.791638i	$0.290771\pi$
$942$		0			0
$943$	5.09941e7	+	5.09941e7i	1.86741	+	1.86741i
$944$		0			0
$945$	1.17246e7	+	823724.i	0.427088	+	0.0300056i
$946$		0			0
$947$	−2.49692e7	+	2.49692e7i	−0.904752	+	0.904752i	−0.995843	−	0.0910904i	$-0.970965\pi$
$947$	−2.49692e7	+	2.49692e7i	−0.904752	+	0.904752i	0.0910904	+	0.995843i	$0.470965\pi$
$948$		0			0
$949$		−	5.26251e6i		−	0.189683i
$950$		0			0
$951$			3.89994e6i			0.139832i
$952$		0			0
$953$	−1.02356e7	+	1.02356e7i	−0.365072	+	0.365072i	−0.865676	−	0.500604i	$-0.833111\pi$
$953$	−1.02356e7	+	1.02356e7i	−0.365072	+	0.365072i	0.500604	+	0.865676i	$0.333111\pi$
$954$		0			0
$955$	−4.37264e7	−	3.07205e6i	−1.55144	−	0.108998i
$956$		0			0
$957$	−893318.	−	893318.i	−0.0315302	−	0.0315302i
$958$		0			0
$959$	−8.02077e6			−0.281624
$960$		0			0
$961$	1.98336e7			0.692776
$962$		0			0
$963$	2.27634e7	+	2.27634e7i	0.790990	+	0.790990i
$964$		0			0
$965$	2.44621e7	+	2.81590e7i	0.845619	+	0.973417i
$966$		0			0
$967$	3.35784e6	−	3.35784e6i	0.115477	−	0.115477i	−0.647007	−	0.762484i	$-0.723980\pi$
$967$	3.35784e6	−	3.35784e6i	0.115477	−	0.115477i	0.762484	+	0.647007i	$0.223980\pi$
$968$		0			0
$969$		−	5.44809e6i		−	0.186395i
$970$		0			0
$971$		−	2.26409e7i		−	0.770629i	−0.922785	−	0.385314i	$-0.874093\pi$
$971$		−	2.26409e7i		−	0.770629i	0.922785	−	0.385314i	$-0.125907\pi$
$972$		0			0
$973$	2.05689e7	−	2.05689e7i	0.696511	−	0.696511i
$974$		0			0
$975$	−6.24802e6	−	882279.i	−0.210490	−	0.0297231i
$976$		0			0
$977$	1.20698e7	+	1.20698e7i	0.404543	+	0.404543i	0.879830	−	0.475288i	$-0.157656\pi$
$977$	1.20698e7	+	1.20698e7i	0.404543	+	0.404543i	−0.475288	+	0.879830i	$0.657656\pi$
$978$		0			0
$979$	−7.72784e6			−0.257692
$980$		0			0
$981$	−2.89720e7			−0.961184
$982$		0			0
$983$	9.80821e6	+	9.80821e6i	0.323747	+	0.323747i	0.850203	−	0.526455i	$-0.176479\pi$
$983$	9.80821e6	+	9.80821e6i	0.323747	+	0.323747i	−0.526455	+	0.850203i	$0.676479\pi$
$984$		0			0
$985$	−1.87294e7	+	1.62704e7i	−0.615082	+	0.534329i
$986$		0			0
$987$	−9.22846e6	+	9.22846e6i	−0.301534	+	0.301534i
$988$		0			0
$989$			2.66582e7i			0.866644i
$990$		0			0
$991$		−	8.94470e6i		−	0.289322i	−0.989481	−	0.144661i	$-0.953791\pi$
$991$		−	8.94470e6i		−	0.289322i	0.989481	−	0.144661i	$-0.0462092\pi$
$992$		0			0
$993$	1.00935e7	−	1.00935e7i	0.324841	−	0.324841i
$994$		0			0
$995$	−1.04108e6	+	1.48183e7i	−0.0333369	+	0.474505i
$996$		0			0
$997$	−1.84856e7	−	1.84856e7i	−0.588975	−	0.588975i	0.348379	−	0.937354i	$-0.386732\pi$
$997$	−1.84856e7	−	1.84856e7i	−0.588975	−	0.588975i	−0.937354	+	0.348379i	$0.886732\pi$
$998$		0			0
$999$	3.54303e6			0.112321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.c.127.5	yes	16
4.3	odd	2		160.6.n.d.127.4	yes	16
5.3	odd	4		160.6.n.d.63.4	yes	16
20.3	even	4	inner	160.6.n.c.63.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.c.63.5	✓	16	20.3	even	4	inner
160.6.n.c.127.5	yes	16	1.1	even	1	trivial
160.6.n.d.63.4	yes	16	5.3	odd	4
160.6.n.d.127.4	yes	16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.56776 - 2.56776i) q^{3} +(3.91778 - 55.7642i) q^{5} +(86.5899 - 86.5899i) q^{7} -229.813i q^{9} +O(q^{10})\)	\(q+(-2.56776 - 2.56776i) q^{3} +(3.91778 - 55.7642i) q^{5} +(86.5899 - 86.5899i) q^{7} -229.813i q^{9} -138.270i q^{11} +(-393.183 + 393.183i) q^{13} +(-153.249 + 133.129i) q^{15} +(724.394 + 724.394i) q^{17} +1464.48 q^{19} -444.684 q^{21} +(-2859.76 - 2859.76i) q^{23} +(-3094.30 - 436.944i) q^{25} +(-1214.07 + 1214.07i) q^{27} +2516.08i q^{29} -2965.73i q^{31} +(-355.043 + 355.043i) q^{33} +(-4489.38 - 5167.86i) q^{35} +(-1459.15 - 1459.15i) q^{37} +2019.20 q^{39} -17831.6 q^{41} +(-4660.93 - 4660.93i) q^{43} +(-12815.4 - 900.358i) q^{45} +(20752.8 - 20752.8i) q^{47} +1811.39i q^{49} -3720.15i q^{51} +(-11572.8 + 11572.8i) q^{53} +(-7710.50 - 541.710i) q^{55} +(-3760.44 - 3760.44i) q^{57} -32661.2 q^{59} -11161.0 q^{61} +(-19899.5 - 19899.5i) q^{63} +(20385.1 + 23466.0i) q^{65} +(-15320.2 + 15320.2i) q^{67} +14686.4i q^{69} -72449.6i q^{71} +(-6692.19 + 6692.19i) q^{73} +(6823.46 + 9067.40i) q^{75} +(-11972.7 - 11972.7i) q^{77} +36624.7 q^{79} -49609.7 q^{81} +(65762.8 + 65762.8i) q^{83} +(43233.3 - 37557.3i) q^{85} +(6460.70 - 6460.70i) q^{87} -55889.7i q^{89} +68091.3i q^{91} +(-7615.29 + 7615.29i) q^{93} +(5737.53 - 81665.8i) q^{95} +(50124.8 + 50124.8i) q^{97} -31776.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7}+O(q^{10}) \) 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7	\( 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7} + 536 q^{13} + 698 q^{15} - 1828 q^{17} - 2512 q^{19} - 4284 q^{21} + 7642 q^{23} + 9140 q^{25} + 12272 q^{27} + 11876 q^{33} - 10518 q^{35} - 7620 q^{37} - 11244 q^{39} - 21284 q^{41} - 20002 q^{43} + 686 q^{45} - 25298 q^{47} + 12852 q^{53} + 10584 q^{55} + 55848 q^{57} + 142704 q^{59} - 20564 q^{61} + 115282 q^{63} - 38256 q^{65} + 10506 q^{67} + 15432 q^{73} - 256226 q^{75} + 133852 q^{77} + 159344 q^{79} - 236116 q^{81} + 61222 q^{83} + 7056 q^{85} - 162176 q^{87} + 122180 q^{93} - 267512 q^{95} - 17344 q^{97} - 107332 q^{99}+O(q^{100}) \) 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7 + 536 * q^13 + 698 * q^15 - 1828 * q^17 - 2512 * q^19 - 4284 * q^21 + 7642 * q^23 + 9140 * q^25 + 12272 * q^27 + 11876 * q^33 - 10518 * q^35 - 7620 * q^37 - 11244 * q^39 - 21284 * q^41 - 20002 * q^43 + 686 * q^45 - 25298 * q^47 + 12852 * q^53 + 10584 * q^55 + 55848 * q^57 + 142704 * q^59 - 20564 * q^61 + 115282 * q^63 - 38256 * q^65 + 10506 * q^67 + 15432 * q^73 - 256226 * q^75 + 133852 * q^77 + 159344 * q^79 - 236116 * q^81 + 61222 * q^83 + 7056 * q^85 - 162176 * q^87 + 122180 * q^93 - 267512 * q^95 - 17344 * q^97 - 107332 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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