LMFDB - Embedded newform 160.6.n.d.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$16$
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			127.2
Root			$14.0500i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.6.n.d.63.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.0500 - 13.0500i) q^{3} +(-30.1056 + 47.1026i) q^{5} +(-150.919 + 150.919i) q^{7} +97.6048i q^{9} +O(q^{10})$	\(q+(-13.0500 - 13.0500i) q^{3} +(-30.1056 + 47.1026i) q^{5} +(-150.919 + 150.919i) q^{7} +97.6048i q^{9} +579.815i q^{11} +(649.369 - 649.369i) q^{13} +(1007.57 - 221.810i) q^{15} +(-106.515 - 106.515i) q^{17} -1205.80 q^{19} +3938.97 q^{21} +(-609.294 - 609.294i) q^{23} +(-1312.30 - 2836.10i) q^{25} +(-1897.41 + 1897.41i) q^{27} +6019.46i q^{29} -6416.45i q^{31} +(7566.58 - 7566.58i) q^{33} +(-2565.15 - 11652.1i) q^{35} +(-2856.48 - 2856.48i) q^{37} -16948.5 q^{39} -12989.8 q^{41} +(3195.40 + 3195.40i) q^{43} +(-4597.44 - 2938.45i) q^{45} +(14942.0 - 14942.0i) q^{47} -28745.8i q^{49} +2780.04i q^{51} +(23529.1 - 23529.1i) q^{53} +(-27310.8 - 17455.7i) q^{55} +(15735.7 + 15735.7i) q^{57} -16943.1 q^{59} +51250.5 q^{61} +(-14730.4 - 14730.4i) q^{63} +(11037.3 + 50136.6i) q^{65} +(-4751.63 + 4751.63i) q^{67} +15902.6i q^{69} -9191.35i q^{71} +(29486.5 - 29486.5i) q^{73} +(-19885.6 + 54136.7i) q^{75} +(-87504.8 - 87504.8i) q^{77} +21056.6 q^{79} +73240.3 q^{81} +(21862.0 + 21862.0i) q^{83} +(8223.83 - 1810.43i) q^{85} +(78553.9 - 78553.9i) q^{87} -10293.5i q^{89} +196004. i q^{91} +(-83734.6 + 83734.6i) q^{93} +(36301.3 - 56796.1i) q^{95} +(-54038.8 - 54038.8i) q^{97} -56592.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−13.0500	−	13.0500i	−0.837158	−	0.837158i	0.151326	−	0.988484i	$-0.451646\pi$
$3$	−13.0500	−	13.0500i	−0.837158	−	0.837158i	−0.988484	+	0.151326i	$0.951646\pi$
$4$		0			0
$5$	−30.1056	+	47.1026i	−0.538546	+	0.842596i
$5$	−30.1056	+	47.1026i	−0.538546	+	0.842596i
$6$		0			0
$7$	−150.919	+	150.919i	−1.16412	+	1.16412i	−0.180554	+	0.983565i	$0.557789\pi$
$7$	−150.919	+	150.919i	−1.16412	+	1.16412i	−0.983565	+	0.180554i	$0.942211\pi$
$8$		0			0
$9$			97.6048i			0.401666i
$10$		0			0
$11$			579.815i			1.44480i	0.691476	+	0.722400i	$0.256961\pi$
$11$			579.815i			1.44480i	−0.691476	+	0.722400i	$0.743039\pi$
$12$		0			0
$13$	649.369	−	649.369i	1.06570	−	1.06570i	0.0680108	−	0.997685i	$-0.478335\pi$
$13$	649.369	−	649.369i	1.06570	−	1.06570i	0.997685	−	0.0680108i	$-0.0216652\pi$
$14$		0			0
$15$	1007.57	−	221.810i	1.15623	−	0.254538i
$16$		0			0
$17$	−106.515	−	106.515i	−0.0893899	−	0.0893899i	0.660998	−	0.750388i	$-0.270133\pi$
$17$	−106.515	−	106.515i	−0.0893899	−	0.0893899i	−0.750388	+	0.660998i	$0.770133\pi$
$18$		0			0
$19$	−1205.80			−0.766285			−0.383142	−	0.923689i	$-0.625158\pi$
$19$	−1205.80			−0.766285			−0.383142	+	0.923689i	$0.625158\pi$
$20$		0			0
$21$	3938.97			1.94910
$22$		0			0
$23$	−609.294	−	609.294i	−0.240164	−	0.240164i	0.576754	−	0.816918i	$-0.304319\pi$
$23$	−609.294	−	609.294i	−0.240164	−	0.240164i	−0.816918	+	0.576754i	$0.804319\pi$
$24$		0			0
$25$	−1312.30	−	2836.10i	−0.419937	−	0.907553i
$26$		0			0
$27$	−1897.41	+	1897.41i	−0.500900	+	0.500900i
$28$		0			0
$29$			6019.46i			1.32912i	0.747237	+	0.664558i	$0.231380\pi$
$29$			6019.46i			1.32912i	−0.747237	+	0.664558i	$0.768620\pi$
$30$		0			0
$31$		−	6416.45i		−	1.19920i	−0.800301	−	0.599598i	$-0.795327\pi$
$31$		−	6416.45i		−	1.19920i	0.800301	−	0.599598i	$-0.204673\pi$
$32$		0			0
$33$	7566.58	−	7566.58i	1.20952	−	1.20952i
$34$		0			0
$35$	−2565.15	−	11652.1i	−0.353951	−	1.60781i
$36$		0			0
$37$	−2856.48	−	2856.48i	−0.343026	−	0.343026i	0.514478	−	0.857504i	$-0.327986\pi$
$37$	−2856.48	−	2856.48i	−0.343026	−	0.343026i	−0.857504	+	0.514478i	$0.827986\pi$
$38$		0			0
$39$	−16948.5			−1.78431
$40$		0			0
$41$	−12989.8			−1.20682			−0.603411	−	0.797431i	$-0.706192\pi$
$41$	−12989.8			−1.20682			−0.603411	+	0.797431i	$0.706192\pi$
$42$		0			0
$43$	3195.40	+	3195.40i	0.263545	+	0.263545i	0.826493	−	0.562948i	$-0.190333\pi$
$43$	3195.40	+	3195.40i	0.263545	+	0.263545i	−0.562948	+	0.826493i	$0.690333\pi$
$44$		0			0
$45$	−4597.44	−	2938.45i	−0.338442	−	0.216316i
$46$		0			0
$47$	14942.0	−	14942.0i	0.986654	−	0.986654i	−0.0132586	−	0.999912i	$-0.504220\pi$
$47$	14942.0	−	14942.0i	0.986654	−	0.986654i	0.999912	+	0.0132586i	$0.00422046\pi$
$48$		0			0
$49$		−	28745.8i		−	1.71035i
$50$		0			0
$51$			2780.04i			0.149667i
$52$		0			0
$53$	23529.1	−	23529.1i	1.15058	−	1.15058i	0.164142	−	0.986437i	$-0.447514\pi$
$53$	23529.1	−	23529.1i	1.15058	−	1.15058i	0.986437	−	0.164142i	$-0.0524856\pi$
$54$		0			0
$55$	−27310.8	−	17455.7i	−1.21738	−	0.778091i
$56$		0			0
$57$	15735.7	+	15735.7i	0.641501	+	0.641501i
$58$		0			0
$59$	−16943.1			−0.633670			−0.316835	−	0.948481i	$-0.602620\pi$
$59$	−16943.1			−0.633670			−0.316835	+	0.948481i	$0.602620\pi$
$60$		0			0
$61$	51250.5			1.76349			0.881746	−	0.471725i	$-0.156369\pi$
$61$	51250.5			1.76349			0.881746	+	0.471725i	$0.156369\pi$
$62$		0			0
$63$	−14730.4	−	14730.4i	−0.467587	−	0.467587i
$64$		0			0
$65$	11037.3	+	50136.6i	0.324025	+	1.47188i
$66$		0			0
$67$	−4751.63	+	4751.63i	−0.129317	+	0.129317i	−0.768803	−	0.639486i	$-0.779147\pi$
$67$	−4751.63	+	4751.63i	−0.129317	+	0.129317i	0.639486	+	0.768803i	$0.279147\pi$
$68$		0			0
$69$			15902.6i			0.402110i
$70$		0			0
$71$		−	9191.35i		−	0.216388i	−0.994130	−	0.108194i	$-0.965493\pi$
$71$		−	9191.35i		−	0.216388i	0.994130	−	0.108194i	$-0.0345068\pi$
$72$		0			0
$73$	29486.5	−	29486.5i	0.647614	−	0.647614i	−0.304802	−	0.952416i	$-0.598590\pi$
$73$	29486.5	−	29486.5i	0.647614	−	0.647614i	0.952416	+	0.304802i	$0.0985903\pi$
$74$		0			0
$75$	−19885.6	+	54136.7i	−0.408212	+	1.11132i
$76$		0			0
$77$	−87504.8	−	87504.8i	−1.68192	−	1.68192i
$78$		0			0
$79$	21056.6			0.379595			0.189797	−	0.981823i	$-0.439217\pi$
$79$	21056.6			0.379595			0.189797	+	0.981823i	$0.439217\pi$
$80$		0			0
$81$	73240.3			1.24033
$82$		0			0
$83$	21862.0	+	21862.0i	0.348333	+	0.348333i	0.859488	−	0.511155i	$-0.170782\pi$
$83$	21862.0	+	21862.0i	0.348333	+	0.348333i	−0.511155	+	0.859488i	$0.670782\pi$
$84$		0			0
$85$	8223.83	−	1810.43i	0.123460	−	0.0271790i
$86$		0			0
$87$	78553.9	−	78553.9i	1.11268	−	1.11268i
$88$		0			0
$89$		−	10293.5i		−	0.137749i	−0.997625	−	0.0688744i	$-0.978059\pi$
$89$		−	10293.5i		−	0.137749i	0.997625	−	0.0688744i	$-0.0219408\pi$
$90$		0			0
$91$			196004.i			2.48119i
$92$		0			0
$93$	−83734.6	+	83734.6i	−1.00392	+	1.00392i
$94$		0			0
$95$	36301.3	−	56796.1i	0.412680	−	0.645669i
$96$		0			0
$97$	−54038.8	−	54038.8i	−0.583145	−	0.583145i	0.352621	−	0.935766i	$-0.385290\pi$
$97$	−54038.8	−	54038.8i	−0.583145	−	0.583145i	−0.935766	+	0.352621i	$0.885290\pi$
$98$		0			0
$99$	−56592.7			−0.580327
$100$		0			0
$101$	−98592.7			−0.961704			−0.480852	−	0.876802i	$-0.659673\pi$
$101$	−98592.7			−0.961704			−0.480852	+	0.876802i	$0.659673\pi$
$102$		0			0
$103$	−106125.	−	106125.i	−0.985652	−	0.985652i	0.0142461	−	0.999899i	$-0.495465\pi$
$103$	−106125.	−	106125.i	−0.985652	−	0.985652i	−0.999899	+	0.0142461i	$0.995465\pi$
$104$		0			0
$105$	−118585.	+	185536.i	−1.04968	+	1.64231i
$106$		0			0
$107$	98108.2	−	98108.2i	0.828411	−	0.828411i	−0.158886	−	0.987297i	$-0.550790\pi$
$107$	98108.2	−	98108.2i	0.828411	−	0.828411i	0.987297	+	0.158886i	$0.0507903\pi$
$108$		0			0
$109$			99013.0i			0.798226i	0.916902	+	0.399113i	$0.130682\pi$
$109$			99013.0i			0.798226i	−0.916902	+	0.399113i	$0.869318\pi$
$110$		0			0
$111$			74554.2i			0.574334i
$112$		0			0
$113$	−42242.2	+	42242.2i	−0.311208	+	0.311208i	−0.845377	−	0.534169i	$-0.820624\pi$
$113$	−42242.2	+	42242.2i	−0.311208	+	0.311208i	0.534169	+	0.845377i	$0.320624\pi$
$114$		0			0
$115$	47042.5	−	10356.1i	0.331700	−	0.0730219i
$116$		0			0
$117$	63381.5	+	63381.5i	0.428054	+	0.428054i
$118$		0			0
$119$	32150.2			0.208121
$120$		0			0
$121$	−175134.			−1.08745
$122$		0			0
$123$	169517.	+	169517.i	1.01030	+	1.01030i
$124$		0			0
$125$	173095.	+	23569.9i	0.990856	+	0.134922i
$126$		0			0
$127$	44240.0	−	44240.0i	0.243392	−	0.243392i	−0.574860	−	0.818252i	$-0.694943\pi$
$127$	44240.0	−	44240.0i	0.243392	−	0.243392i	0.818252	+	0.574860i	$0.194943\pi$
$128$		0			0
$129$		−	83400.0i		−	0.441257i
$130$		0			0
$131$			145388.i			0.740202i	0.928991	+	0.370101i	$0.120677\pi$
$131$			145388.i			0.740202i	−0.928991	+	0.370101i	$0.879323\pi$
$132$		0			0
$133$	181977.	−	181977.i	0.892047	−	0.892047i
$134$		0			0
$135$	−32250.1	−	146495.i	−0.152299	−	0.691814i
$136$		0			0
$137$	154789.	+	154789.i	0.704594	+	0.704594i	0.965393	−	0.260799i	$-0.0839859\pi$
$137$	154789.	+	154789.i	0.704594	+	0.704594i	−0.260799	+	0.965393i	$0.583986\pi$
$138$		0			0
$139$	212054.			0.930914			0.465457	−	0.885071i	$-0.345890\pi$
$139$	212054.			0.930914			0.465457	+	0.885071i	$0.345890\pi$
$140$		0			0
$141$	−389987.			−1.65197
$142$		0			0
$143$	376514.	+	376514.i	1.53972	+	1.53972i
$144$		0			0
$145$	−283532.	−	181220.i	−1.11991	−	0.715789i
$146$		0			0
$147$	−375133.	+	375133.i	−1.43183	+	1.43183i
$148$		0			0
$149$			262414.i			0.968327i	0.874978	+	0.484163i	$0.160876\pi$
$149$			262414.i			0.968327i	−0.874978	+	0.484163i	$0.839124\pi$
$150$		0			0
$151$			7909.13i			0.0282284i	0.999900	+	0.0141142i	$0.00449284\pi$
$151$			7909.13i			0.0282284i	−0.999900	+	0.0141142i	$0.995507\pi$
$152$		0			0
$153$	10396.4	−	10396.4i	0.0359049	−	0.0359049i
$154$		0			0
$155$	302231.	+	193171.i	1.01044	+	0.645822i
$156$		0			0
$157$	166849.	+	166849.i	0.540225	+	0.540225i	0.923595	−	0.383370i	$-0.125237\pi$
$157$	166849.	+	166849.i	0.540225	+	0.540225i	−0.383370	+	0.923595i	$0.625237\pi$
$158$		0			0
$159$	−614110.			−1.92643
$160$		0			0
$161$	183908.			0.559158
$162$		0			0
$163$	−360227.	−	360227.i	−1.06196	−	1.06196i	−0.997949	−	0.0640087i	$-0.979611\pi$
$163$	−360227.	−	360227.i	−1.06196	−	1.06196i	−0.0640087	−	0.997949i	$-0.520389\pi$
$164$		0			0
$165$	128609.	+	584202.i	0.367757	+	1.67053i
$166$		0			0
$167$	66411.6	−	66411.6i	0.184269	−	0.184269i	−0.608944	−	0.793213i	$-0.708407\pi$
$167$	66411.6	−	66411.6i	0.184269	−	0.184269i	0.793213	+	0.608944i	$0.208407\pi$
$168$		0			0
$169$		−	472067.i		−	1.27141i
$170$		0			0
$171$		−	117692.i		−	0.307791i
$172$		0			0
$173$	550711.	−	550711.i	1.39897	−	1.39897i	0.595940	−	0.803029i	$-0.296779\pi$
$173$	550711.	−	550711.i	1.39897	−	1.39897i	0.803029	−	0.595940i	$-0.203221\pi$
$174$		0			0
$175$	626071.	+	229970.i	1.54536	+	0.567644i
$176$		0			0
$177$	221108.	+	221108.i	0.530482	+	0.530482i
$178$		0			0
$179$	−241860.			−0.564199			−0.282099	−	0.959385i	$-0.591031\pi$
$179$	−241860.			−0.564199			−0.282099	+	0.959385i	$0.591031\pi$
$180$		0			0
$181$	−774574.			−1.75738			−0.878691	−	0.477390i	$-0.841583\pi$
$181$	−774574.			−1.75738			−0.878691	+	0.477390i	$0.841583\pi$
$182$		0			0
$183$	−668818.	−	668818.i	−1.47632	−	1.47632i
$184$		0			0
$185$	220544.	−	48551.5i	0.473768	−	0.104297i
$186$		0			0
$187$	61758.9	−	61758.9i	0.129150	−	0.129150i
$188$		0			0
$189$		−	572708.i		−	1.16621i
$190$		0			0
$191$		−	39522.0i		−	0.0783891i	−0.999232	−	0.0391946i	$-0.987521\pi$
$191$		−	39522.0i		−	0.0783891i	0.999232	−	0.0391946i	$-0.0124792\pi$
$192$		0			0
$193$	−265806.	+	265806.i	−0.513655	+	0.513655i	−0.915644	−	0.401989i	$-0.868319\pi$
$193$	−265806.	+	265806.i	−0.513655	+	0.513655i	0.401989	+	0.915644i	$0.368319\pi$
$194$		0			0
$195$	510246.	−	798319.i	0.960933	−	1.50345i
$196$		0			0
$197$	−255657.	−	255657.i	−0.469345	−	0.469345i	0.432357	−	0.901702i	$-0.357682\pi$
$197$	−255657.	−	255657.i	−0.469345	−	0.469345i	−0.901702	+	0.432357i	$0.857682\pi$
$198$		0			0
$199$	402296.			0.720134			0.360067	−	0.932926i	$-0.382754\pi$
$199$	402296.			0.720134			0.360067	+	0.932926i	$0.382754\pi$
$200$		0			0
$201$	124017.			0.216517
$202$		0			0
$203$	−908448.	−	908448.i	−1.54725	−	1.54725i
$204$		0			0
$205$	391066.	−	611853.i	0.649929	−	1.01686i
$206$		0			0
$207$	59470.1	−	59470.1i	0.0964656	−	0.0964656i
$208$		0			0
$209$		−	699139.i		−	1.10713i
$210$		0			0
$211$		−	233095.i		−	0.360435i	−0.983627	−	0.180217i	$-0.942320\pi$
$211$		−	233095.i		−	0.360435i	0.983627	−	0.180217i	$-0.0576801\pi$
$212$		0			0
$213$	−119947.	+	119947.i	−0.181151	+	0.181151i
$214$		0			0
$215$	−246711.	+	54312.0i	−0.363993	+	0.0801309i
$216$		0			0
$217$	968361.	+	968361.i	1.39601	+	1.39601i
$218$		0			0
$219$	−769598.			−1.08431
$220$		0			0
$221$	−138335.			−0.190525
$222$		0			0
$223$	−509006.	−	509006.i	−0.685427	−	0.685427i	0.275791	−	0.961218i	$-0.411060\pi$
$223$	−509006.	−	509006.i	−0.685427	−	0.685427i	−0.961218	+	0.275791i	$0.911060\pi$
$224$		0			0
$225$	276817.	−	128087.i	0.364533	−	0.168674i
$226$		0			0
$227$	705428.	−	705428.i	0.908632	−	0.908632i	−0.0875296	−	0.996162i	$-0.527897\pi$
$227$	705428.	−	705428.i	0.908632	−	0.908632i	0.996162	+	0.0875296i	$0.0278972\pi$
$228$		0			0
$229$		−	743272.i		−	0.936611i	−0.883567	−	0.468305i	$-0.844865\pi$
$229$		−	743272.i		−	0.936611i	0.883567	−	0.468305i	$-0.155135\pi$
$230$		0			0
$231$			2.28387e6i			2.81606i
$232$		0			0
$233$	−170776.	+	170776.i	−0.206081	+	0.206081i	−0.802599	−	0.596518i	$-0.796550\pi$
$233$	−170776.	+	170776.i	−0.206081	+	0.206081i	0.596518	+	0.802599i	$0.296550\pi$
$234$		0			0
$235$	253969.	+	1.15365e6i	0.299992	+	1.36271i
$236$		0			0
$237$	−274788.	−	274788.i	−0.317781	−	0.317781i
$238$		0			0
$239$	−729826.			−0.826465			−0.413232	−	0.910626i	$-0.635600\pi$
$239$	−729826.			−0.826465			−0.413232	+	0.910626i	$0.635600\pi$
$240$		0			0
$241$	−798526.			−0.885618			−0.442809	−	0.896616i	$-0.646018\pi$
$241$	−798526.			−0.885618			−0.442809	+	0.896616i	$0.646018\pi$
$242$		0			0
$243$	−494716.	−	494716.i	−0.537452	−	0.537452i
$244$		0			0
$245$	1.35400e6	+	865410.i	1.44113	+	0.921100i
$246$		0			0
$247$	−783007.	+	783007.i	−0.816626	+	0.816626i
$248$		0			0
$249$		−	570598.i		−	0.583219i
$250$		0			0
$251$		−	1.40849e6i		−	1.41113i	−0.708643	−	0.705567i	$-0.750692\pi$
$251$		−	1.40849e6i		−	1.41113i	0.708643	−	0.705567i	$-0.249308\pi$
$252$		0			0
$253$	353278.	−	353278.i	0.346988	−	0.346988i
$254$		0			0
$255$	−130947.	−	83694.8i	−0.126109	−	0.0806024i
$256$		0			0
$257$	−109090.	−	109090.i	−0.103027	−	0.103027i	0.653714	−	0.756742i	$-0.273210\pi$
$257$	−109090.	−	109090.i	−0.103027	−	0.103027i	−0.756742	+	0.653714i	$0.773210\pi$
$258$		0			0
$259$	862192.			0.798647
$260$		0			0
$261$	−587528.			−0.533860
$262$		0			0
$263$	761476.	+	761476.i	0.678839	+	0.678839i	0.959737	−	0.280899i	$-0.0906325\pi$
$263$	761476.	+	761476.i	0.678839	+	0.678839i	−0.280899	+	0.959737i	$0.590632\pi$
$264$		0			0
$265$	399923.	+	1.81664e6i	0.349834	+	1.58911i
$266$		0			0
$267$	−134330.	+	134330.i	−0.115317	+	0.115317i
$268$		0			0
$269$			180038.i			0.151699i	0.997119	+	0.0758497i	$0.0241669\pi$
$269$			180038.i			0.151699i	−0.997119	+	0.0758497i	$0.975833\pi$
$270$		0			0
$271$			1.52319e6i			1.25988i	0.776642	+	0.629942i	$0.216921\pi$
$271$			1.52319e6i			1.25988i	−0.776642	+	0.629942i	$0.783079\pi$
$272$		0			0
$273$	2.55785e6	−	2.55785e6i	2.07715	−	2.07715i
$274$		0			0
$275$	1.64442e6	−	760892.i	1.31123	−	0.606724i
$276$		0			0
$277$	1.55349e6	+	1.55349e6i	1.21649	+	1.21649i	0.968852	+	0.247639i	$0.0796546\pi$
$277$	1.55349e6	+	1.55349e6i	1.21649	+	1.21649i	0.247639	+	0.968852i	$0.420345\pi$
$278$		0			0
$279$	626276.			0.481677
$280$		0			0
$281$	−1.40212e6			−1.05930			−0.529651	−	0.848216i	$-0.677677\pi$
$281$	−1.40212e6			−1.05930			−0.529651	+	0.848216i	$0.677677\pi$
$282$		0			0
$283$	−649894.	−	649894.i	−0.482366	−	0.482366i	0.423521	−	0.905886i	$-0.360794\pi$
$283$	−649894.	−	649894.i	−0.482366	−	0.482366i	−0.905886	+	0.423521i	$0.860794\pi$
$284$		0			0
$285$	−1.21492e6	+	267458.i	−0.886004	+	0.195049i
$286$		0			0
$287$	1.96040e6	−	1.96040e6i	1.40488	−	1.40488i
$288$		0			0
$289$		−	1.39717e6i		−	0.984019i
$290$		0			0
$291$			1.41041e6i			0.976369i
$292$		0			0
$293$	−632027.	+	632027.i	−0.430097	+	0.430097i	−0.888661	−	0.458564i	$-0.848364\pi$
$293$	−632027.	+	632027.i	−0.430097	+	0.430097i	0.458564	+	0.888661i	$0.348364\pi$
$294$		0			0
$295$	510083.	−	798064.i	0.341260	−	0.533928i
$296$		0			0
$297$	−1.10014e6	−	1.10014e6i	−0.723700	−	0.723700i
$298$		0			0
$299$	−791313.			−0.511883
$300$		0			0
$301$	−964491.			−0.613595
$302$		0			0
$303$	1.28663e6	+	1.28663e6i	0.805098	+	0.805098i
$304$		0			0
$305$	−1.54293e6	+	2.41403e6i	−0.949721	+	1.48591i
$306$		0			0
$307$	−2.18716e6	+	2.18716e6i	−1.32445	+	1.32445i	−0.414309	+	0.910136i	$0.635977\pi$
$307$	−2.18716e6	+	2.18716e6i	−1.32445	+	1.32445i	−0.910136	+	0.414309i	$0.864023\pi$
$308$		0			0
$309$			2.76986e6i			1.65029i
$310$		0			0
$311$			509764.i			0.298860i	0.988772	+	0.149430i	$0.0477439\pi$
$311$			509764.i			0.298860i	−0.988772	+	0.149430i	$0.952256\pi$
$312$		0			0
$313$	−1.27372e6	+	1.27372e6i	−0.734873	+	0.734873i	−0.971581	−	0.236708i	$-0.923932\pi$
$313$	−1.27372e6	+	1.27372e6i	−0.734873	+	0.734873i	0.236708	+	0.971581i	$0.423932\pi$
$314$		0			0
$315$	1.13731e6	−	250371.i	0.645804	−	0.142170i
$316$		0			0
$317$	7587.55	+	7587.55i	0.00424086	+	0.00424086i	0.709224	−	0.704983i	$-0.249045\pi$
$317$	7587.55	+	7587.55i	0.00424086	+	0.00424086i	−0.704983	+	0.709224i	$0.749045\pi$
$318$		0			0
$319$	−3.49017e6			−1.92030
$320$		0			0
$321$	−2.56062e6			−1.38702
$322$		0			0
$323$	128435.	+	128435.i	0.0684981	+	0.0684981i
$324$		0			0
$325$	−2.69385e6	−	989509.i	−1.41470	−	0.519651i
$326$		0			0
$327$	1.29212e6	−	1.29212e6i	0.668241	−	0.668241i
$328$		0			0
$329$			4.51005e6i			2.29716i
$330$		0			0
$331$		−	641322.i		−	0.321741i	−0.986976	−	0.160870i	$-0.948570\pi$
$331$		−	641322.i		−	0.321741i	0.986976	−	0.160870i	$-0.0514301\pi$
$332$		0			0
$333$	278807.	−	278807.i	0.137782	−	0.137782i
$334$		0			0
$335$	−80763.1	−	366865.i	−0.0393189	−	0.178605i
$336$		0			0
$337$	−1.66910e6	−	1.66910e6i	−0.800585	−	0.800585i	0.182602	−	0.983187i	$-0.441548\pi$
$337$	−1.66910e6	−	1.66910e6i	−0.800585	−	0.800585i	−0.983187	+	0.182602i	$0.941548\pi$
$338$		0			0
$339$	1.10252e6			0.521061
$340$		0			0
$341$	3.72035e6			1.73260
$342$		0			0
$343$	1.80179e6	+	1.80179e6i	0.826928	+	0.826928i
$344$		0			0
$345$	−749052.	−	478757.i	−0.338816	−	0.216555i
$346$		0			0
$347$	2.20487e6	−	2.20487e6i	0.983014	−	0.983014i	−0.0168446	−	0.999858i	$-0.505362\pi$
$347$	2.20487e6	−	2.20487e6i	0.983014	−	0.983014i	0.999858	+	0.0168446i	$0.00536206\pi$
$348$		0			0
$349$		−	3.76721e6i		−	1.65560i	−0.561021	−	0.827802i	$-0.689591\pi$
$349$		−	3.76721e6i		−	1.65560i	0.561021	−	0.827802i	$-0.310409\pi$
$350$		0			0
$351$			2.46423e6i			1.06761i
$352$		0			0
$353$	1.42291e6	−	1.42291e6i	0.607774	−	0.607774i	−0.334590	−	0.942364i	$-0.608598\pi$
$353$	1.42291e6	−	1.42291e6i	0.607774	−	0.607774i	0.942364	+	0.334590i	$0.108598\pi$
$354$		0			0
$355$	432936.	+	276711.i	0.182328	+	0.116535i
$356$		0			0
$357$	−419559.	−	419559.i	−0.174230	−	0.174230i
$358$		0			0
$359$	314544.			0.128809			0.0644045	−	0.997924i	$-0.479485\pi$
$359$	314544.			0.128809			0.0644045	+	0.997924i	$0.479485\pi$
$360$		0			0
$361$	−1.02215e6			−0.412807
$362$		0			0
$363$	2.28550e6	+	2.28550e6i	0.910363	+	0.910363i
$364$		0			0
$365$	501180.	+	2.27660e6i	0.196907	+	0.894447i
$366$		0			0
$367$	2.32082e6	−	2.32082e6i	0.899450	−	0.899450i	−0.0959375	−	0.995387i	$-0.530585\pi$
$367$	2.32082e6	−	2.32082e6i	0.899450	−	0.899450i	0.995387	+	0.0959375i	$0.0305849\pi$
$368$		0			0
$369$		−	1.26787e6i		−	0.484739i
$370$		0			0
$371$			7.10197e6i			2.67882i
$372$		0			0
$373$	−885760.	+	885760.i	−0.329643	+	0.329643i	−0.852451	−	0.522808i	$-0.824885\pi$
$373$	−885760.	+	885760.i	−0.329643	+	0.329643i	0.522808	+	0.852451i	$0.324885\pi$
$374$		0			0
$375$	−1.95131e6	−	2.56648e6i	−0.716552	−	0.942454i
$376$		0			0
$377$	3.90885e6	+	3.90885e6i	1.41643	+	1.41643i
$378$		0			0
$379$	−1.46575e6			−0.524158			−0.262079	−	0.965046i	$-0.584408\pi$
$379$	−1.46575e6			−0.524158			−0.262079	+	0.965046i	$0.584408\pi$
$380$		0			0
$381$	−1.15466e6			−0.407515
$382$		0			0
$383$	−2.57386e6	−	2.57386e6i	−0.896577	−	0.896577i	0.0985545	−	0.995132i	$-0.468578\pi$
$383$	−2.57386e6	−	2.57386e6i	−0.896577	−	0.896577i	−0.995132	+	0.0985545i	$0.968578\pi$
$384$		0			0
$385$	6.75609e6	−	1.48731e6i	2.32297	−	0.511388i
$386$		0			0
$387$	−311887.	+	311887.i	−0.105857	+	0.105857i
$388$		0			0
$389$			1.22343e6i			0.409925i	0.978770	+	0.204962i	$0.0657072\pi$
$389$			1.22343e6i			0.409925i	−0.978770	+	0.204962i	$0.934293\pi$
$390$		0			0
$391$			129798.i			0.0429364i
$392$		0			0
$393$	1.89731e6	−	1.89731e6i	0.619666	−	0.619666i
$394$		0			0
$395$	−633922.	+	991819.i	−0.204429	+	0.319845i
$396$		0			0
$397$	−2.04714e6	−	2.04714e6i	−0.651887	−	0.651887i	0.301560	−	0.953447i	$-0.402493\pi$
$397$	−2.04714e6	−	2.04714e6i	−0.651887	−	0.651887i	−0.953447	+	0.301560i	$0.902493\pi$
$398$		0			0
$399$	−4.74960e6			−1.49357
$400$		0			0
$401$	4.02347e6			1.24951			0.624755	−	0.780821i	$-0.285199\pi$
$401$	4.02347e6			1.24951			0.624755	+	0.780821i	$0.285199\pi$
$402$		0			0
$403$	−4.16664e6	−	4.16664e6i	−1.27798	−	1.27798i
$404$		0			0
$405$	−2.20494e6	+	3.44980e6i	−0.667975	+	1.04510i
$406$		0			0
$407$	1.65623e6	−	1.65623e6i	0.495604	−	0.495604i
$408$		0			0
$409$			3.19667e6i			0.944909i	0.881355	+	0.472455i	$0.156632\pi$
$409$			3.19667e6i			0.944909i	−0.881355	+	0.472455i	$0.843368\pi$
$410$		0			0
$411$		−	4.04000e6i		−	1.17971i
$412$		0			0
$413$	2.55703e6	−	2.55703e6i	0.737668	−	0.737668i
$414$		0			0
$415$	−1.68792e6	+	371587.i	−0.481097	+	0.105911i
$416$		0			0
$417$	−2.76730e6	−	2.76730e6i	−0.779322	−	0.779322i
$418$		0			0
$419$	5.65821e6			1.57451			0.787253	−	0.616630i	$-0.211503\pi$
$419$	5.65821e6			1.57451			0.787253	+	0.616630i	$0.211503\pi$
$420$		0			0
$421$	421244.			0.115832			0.0579160	−	0.998321i	$-0.481554\pi$
$421$	421244.			0.115832			0.0579160	+	0.998321i	$0.481554\pi$
$422$		0			0
$423$	1.45841e6	+	1.45841e6i	0.396305	+	0.396305i
$424$		0			0
$425$	−162308.	+	441867.i	−0.0435880	+	0.118664i
$426$		0			0
$427$	−7.73464e6	+	7.73464e6i	−2.05291	+	2.05291i
$428$		0			0
$429$		−	9.82700e6i		−	2.57797i
$430$		0			0
$431$		−	3.25489e6i		−	0.844002i	−0.906595	−	0.422001i	$-0.861328\pi$
$431$		−	3.25489e6i		−	0.844002i	0.906595	−	0.422001i	$-0.138672\pi$
$432$		0			0
$433$	−3.31185e6	+	3.31185e6i	−0.848890	+	0.848890i	−0.989995	−	0.141105i	$-0.954935\pi$
$433$	−3.31185e6	+	3.31185e6i	−0.848890	+	0.848890i	0.141105	+	0.989995i	$0.454935\pi$
$434$		0			0
$435$	1.33518e6	+	6.06501e6i	0.338310	+	1.53677i
$436$		0			0
$437$	734685.	+	734685.i	0.184034	+	0.184034i
$438$		0			0
$439$	4.01407e6			0.994086			0.497043	−	0.867726i	$-0.334419\pi$
$439$	4.01407e6			0.994086			0.497043	+	0.867726i	$0.334419\pi$
$440$		0			0
$441$	2.80573e6			0.686988
$442$		0			0
$443$	−400968.	−	400968.i	−0.0970733	−	0.0970733i	0.656902	−	0.753976i	$-0.271866\pi$
$443$	−400968.	−	400968.i	−0.0970733	−	0.0970733i	−0.753976	+	0.656902i	$0.771866\pi$
$444$		0			0
$445$	484850.	+	309892.i	0.116067	+	0.0741840i
$446$		0			0
$447$	3.42451e6	−	3.42451e6i	0.810642	−	0.810642i
$448$		0			0
$449$		−	2.60937e6i		−	0.610829i	−0.952219	−	0.305415i	$-0.901205\pi$
$449$		−	2.60937e6i		−	0.610829i	0.952219	−	0.305415i	$-0.0987951\pi$
$450$		0			0
$451$		−	7.53168e6i		−	1.74361i
$452$		0			0
$453$	103214.	−	103214.i	0.0236316	−	0.0236316i
$454$		0			0
$455$	−9.23227e6	−	5.90081e6i	−2.09064	−	1.33624i
$456$		0			0
$457$	−5.59866e6	−	5.59866e6i	−1.25399	−	1.25399i	−0.953916	−	0.300073i	$-0.902989\pi$
$457$	−5.59866e6	−	5.59866e6i	−1.25399	−	1.25399i	−0.300073	−	0.953916i	$-0.597011\pi$
$458$		0			0
$459$	404204.			0.0895507
$460$		0			0
$461$	2.59843e6			0.569454			0.284727	−	0.958609i	$-0.408097\pi$
$461$	2.59843e6			0.569454			0.284727	+	0.958609i	$0.408097\pi$
$462$		0			0
$463$	−4.24793e6	−	4.24793e6i	−0.920927	−	0.920927i	0.0761683	−	0.997095i	$-0.475731\pi$
$463$	−4.24793e6	−	4.24793e6i	−0.920927	−	0.920927i	−0.997095	+	0.0761683i	$0.975731\pi$
$464$		0			0
$465$	−1.42323e6	−	6.46500e6i	−0.305241	−	1.38655i
$466$		0			0
$467$	−1.09729e6	+	1.09729e6i	−0.232825	+	0.232825i	−0.813871	−	0.581046i	$-0.802644\pi$
$467$	−1.09729e6	+	1.09729e6i	−0.232825	+	0.232825i	0.581046	+	0.813871i	$0.302644\pi$
$468$		0			0
$469$		−	1.43422e6i		−	0.301081i
$470$		0			0
$471$		−	4.35476e6i		−	0.904507i
$472$		0			0
$473$	−1.85274e6	+	1.85274e6i	−0.380769	+	0.380769i
$474$		0			0
$475$	1.58237e6	+	3.41977e6i	0.321791	+	0.695444i
$476$		0			0
$477$	2.29656e6	+	2.29656e6i	0.462148	+	0.462148i
$478$		0			0
$479$	7.71704e6			1.53678			0.768391	−	0.639981i	$-0.221058\pi$
$479$	7.71704e6			1.53678			0.768391	+	0.639981i	$0.221058\pi$
$480$		0			0
$481$	−3.70982e6			−0.731123
$482$		0			0
$483$	−2.39999e6	−	2.39999e6i	−0.468104	−	0.468104i
$484$		0			0
$485$	4.17224e6	−	918494.i	0.805406	−	0.177305i
$486$		0			0
$487$	1.79262e6	−	1.79262e6i	0.342504	−	0.342504i	−0.514804	−	0.857308i	$-0.672135\pi$
$487$	1.79262e6	−	1.79262e6i	0.342504	−	0.342504i	0.857308	+	0.514804i	$0.172135\pi$
$488$		0			0
$489$			9.40193e6i			1.77805i
$490$		0			0
$491$		−	6.83120e6i		−	1.27877i	−0.768886	−	0.639386i	$-0.779189\pi$
$491$		−	6.83120e6i		−	1.27877i	0.768886	−	0.639386i	$-0.220811\pi$
$492$		0			0
$493$	641163.	−	641163.i	0.118809	−	0.118809i
$494$		0			0
$495$	1.70376e6	−	2.66566e6i	0.312533	−	0.488981i
$496$		0			0
$497$	1.38715e6	+	1.38715e6i	0.251902	+	0.251902i
$498$		0			0
$499$	−1.09519e7			−1.96896			−0.984482	−	0.175483i	$-0.943851\pi$
$499$	−1.09519e7			−1.96896			−0.984482	+	0.175483i	$0.943851\pi$
$500$		0			0
$501$	−1.73334e6			−0.308525
$502$		0			0
$503$	97058.2	+	97058.2i	0.0171046	+	0.0171046i	0.715607	−	0.698503i	$-0.246150\pi$
$503$	97058.2	+	97058.2i	0.0171046	+	0.0171046i	−0.698503	+	0.715607i	$0.746150\pi$
$504$		0			0
$505$	2.96820e6	−	4.64397e6i	0.517922	−	0.810328i
$506$		0			0
$507$	−6.16047e6	+	6.16047e6i	−1.06437	+	1.06437i
$508$		0			0
$509$			6.15863e6i			1.05363i	0.849979	+	0.526817i	$0.176615\pi$
$509$			6.15863e6i			1.05363i	−0.849979	+	0.526817i	$0.823385\pi$
$510$		0			0
$511$			8.90012e6i			1.50780i
$512$		0			0
$513$	2.28789e6	−	2.28789e6i	0.383832	−	0.383832i
$514$		0			0
$515$	8.19370e6	−	1.80380e6i	1.36133	−	0.299688i
$516$		0			0
$517$	8.66360e6	+	8.66360e6i	1.42552	+	1.42552i
$518$		0			0
$519$	−1.43735e7			−2.34232
$520$		0			0
$521$	6.30417e6			1.01750			0.508749	−	0.860915i	$-0.330108\pi$
$521$	6.30417e6			1.01750			0.508749	+	0.860915i	$0.330108\pi$
$522$		0			0
$523$	5.94369e6	+	5.94369e6i	0.950171	+	0.950171i	0.998816	−	0.0486450i	$-0.0154903\pi$
$523$	5.94369e6	+	5.94369e6i	0.950171	+	0.950171i	−0.0486450	+	0.998816i	$0.515490\pi$
$524$		0			0
$525$	−5.16912e6	−	1.11713e7i	−0.818500	−	1.76891i
$526$		0			0
$527$	−683448.	+	683448.i	−0.107196	+	0.107196i
$528$		0			0
$529$		−	5.69386e6i		−	0.884643i
$530$		0			0
$531$		−	1.65373e6i		−	0.254524i
$532$		0			0
$533$	−8.43517e6	+	8.43517e6i	−1.28610	+	1.28610i
$534$		0			0
$535$	1.66754e6	+	7.57475e6i	0.251879	+	1.14415i
$536$		0			0
$537$	3.15628e6	+	3.15628e6i	0.472323	+	0.472323i
$538$		0			0
$539$	1.66672e7			2.47111
$540$		0			0
$541$	4.08733e6			0.600409			0.300204	−	0.953875i	$-0.402945\pi$
$541$	4.08733e6			0.600409			0.300204	+	0.953875i	$0.402945\pi$
$542$		0			0
$543$	1.01082e7	+	1.01082e7i	1.47121	+	1.47121i
$544$		0			0
$545$	−4.66377e6	−	2.98085e6i	−0.672582	−	0.429881i
$546$		0			0
$547$	767768.	−	767768.i	0.109714	−	0.109714i	−0.650119	−	0.759833i	$-0.725281\pi$
$547$	767768.	−	767768.i	0.109714	−	0.109714i	0.759833	+	0.650119i	$0.225281\pi$
$548$		0			0
$549$			5.00229e6i			0.708334i
$550$		0			0
$551$		−	7.25825e6i		−	1.01848i
$552$		0			0
$553$	−3.17783e6	+	3.17783e6i	−0.441894	+	0.441894i
$554$		0			0
$555$	−3.51169e6	−	2.24450e6i	−0.483932	−	0.309305i
$556$		0			0
$557$	998573.	+	998573.i	0.136377	+	0.136377i	0.772000	−	0.635623i	$-0.219257\pi$
$557$	998573.	+	998573.i	0.136377	+	0.136377i	−0.635623	+	0.772000i	$0.719257\pi$
$558$		0			0
$559$	4.14999e6			0.561717
$560$		0			0
$561$	−1.61191e6			−0.216239
$562$		0			0
$563$	−2.68618e6	−	2.68618e6i	−0.357161	−	0.357161i	0.505605	−	0.862765i	$-0.331269\pi$
$563$	−2.68618e6	−	2.68618e6i	−0.357161	−	0.357161i	−0.862765	+	0.505605i	$0.831269\pi$
$564$		0			0
$565$	−717989.	−	3.26145e6i	−0.0946230	−	0.429823i
$566$		0			0
$567$	−1.10533e7	+	1.10533e7i	−1.44389	+	1.44389i
$568$		0			0
$569$		−	5.71067e6i		−	0.739446i	−0.929142	−	0.369723i	$-0.879453\pi$
$569$		−	5.71067e6i		−	0.739446i	0.929142	−	0.369723i	$-0.120547\pi$
$570$		0			0
$571$			747077.i			0.0958904i	0.998850	+	0.0479452i	$0.0152673\pi$
$571$			747077.i			0.0958904i	−0.998850	+	0.0479452i	$0.984733\pi$
$572$		0			0
$573$	−515762.	+	515762.i	−0.0656241	+	0.0656241i
$574$		0			0
$575$	−928444.	+	2.52760e6i	−0.117108	+	0.318815i
$576$		0			0
$577$	−2.38245e6	−	2.38245e6i	−0.297909	−	0.297909i	0.542285	−	0.840194i	$-0.317559\pi$
$577$	−2.38245e6	−	2.38245e6i	−0.297909	−	0.297909i	−0.840194	+	0.542285i	$0.817559\pi$
$578$		0			0
$579$	6.93753e6			0.860020
$580$		0			0
$581$	−6.59876e6			−0.811002
$582$		0			0
$583$	1.36425e7	+	1.36425e7i	1.66236	+	1.66236i
$584$		0			0
$585$	−4.89357e6	+	1.07729e6i	−0.591203	+	0.130150i
$586$		0			0
$587$	−5.16997e6	+	5.16997e6i	−0.619288	+	0.619288i	−0.945349	−	0.326061i	$-0.894279\pi$
$587$	−5.16997e6	+	5.16997e6i	−0.619288	+	0.619288i	0.326061	+	0.945349i	$0.394279\pi$
$588$		0			0
$589$			7.73694e6i			0.918927i
$590$		0			0
$591$			6.67264e6i			0.785831i
$592$		0			0
$593$	−4.89288e6	+	4.89288e6i	−0.571383	+	0.571383i	−0.932515	−	0.361132i	$-0.882391\pi$
$593$	−4.89288e6	+	4.89288e6i	−0.571383	+	0.571383i	0.361132	+	0.932515i	$0.382391\pi$
$594$		0			0
$595$	−967901.	+	1.51435e6i	−0.112083	+	0.175362i
$596$		0			0
$597$	−5.24997e6	−	5.24997e6i	−0.602866	−	0.602866i
$598$		0			0
$599$	4.49261e6			0.511602			0.255801	−	0.966730i	$-0.417661\pi$
$599$	4.49261e6			0.511602			0.255801	+	0.966730i	$0.417661\pi$
$600$		0			0
$601$	−1.13732e6			−0.128439			−0.0642194	−	0.997936i	$-0.520456\pi$
$601$	−1.13732e6			−0.128439			−0.0642194	+	0.997936i	$0.520456\pi$
$602$		0			0
$603$	−463782.	−	463782.i	−0.0519422	−	0.0519422i
$604$		0			0
$605$	5.27252e6	−	8.24927e6i	0.585639	−	0.916277i
$606$		0			0
$607$	5.38282e6	−	5.38282e6i	0.592977	−	0.592977i	−0.345457	−	0.938434i	$-0.612276\pi$
$607$	5.38282e6	−	5.38282e6i	0.592977	−	0.592977i	0.938434	+	0.345457i	$0.112276\pi$
$608$		0			0
$609$			2.37105e7i			2.59058i
$610$		0			0
$611$		−	1.94058e7i		−	2.10294i
$612$		0			0
$613$	−6.95830e6	+	6.95830e6i	−0.747914	+	0.747914i	−0.974087	−	0.226173i	$-0.927379\pi$
$613$	−6.95830e6	+	6.95830e6i	−0.747914	+	0.747914i	0.226173	+	0.974087i	$0.427379\pi$
$614$		0			0
$615$	−1.30881e7	+	2.88127e6i	−1.39537	+	0.307182i
$616$		0			0
$617$	6.70551e6	+	6.70551e6i	0.709118	+	0.709118i	0.966350	−	0.257232i	$-0.0828103\pi$
$617$	6.70551e6	+	6.70551e6i	0.709118	+	0.709118i	−0.257232	+	0.966350i	$0.582810\pi$
$618$		0			0
$619$	1.62651e7			1.70620			0.853099	−	0.521749i	$-0.174720\pi$
$619$	1.62651e7			1.70620			0.853099	+	0.521749i	$0.174720\pi$
$620$		0			0
$621$	2.31216e6			0.240596
$622$		0			0
$623$	1.55348e6	+	1.55348e6i	0.160356	+	0.160356i
$624$		0			0
$625$	−6.32135e6	+	7.44365e6i	−0.647306	+	0.762230i
$626$		0			0
$627$	−9.12376e6	+	9.12376e6i	−0.926841	+	0.926841i
$628$		0			0
$629$			608516.i			0.0613261i
$630$		0			0
$631$		−	1.04712e7i		−	1.04694i	−0.852044	−	0.523470i	$-0.824637\pi$
$631$		−	1.04712e7i		−	1.04694i	0.852044	−	0.523470i	$-0.175363\pi$
$632$		0			0
$633$	−3.04189e6	+	3.04189e6i	−0.301741	+	0.301741i
$634$		0			0
$635$	751945.	+	3.41569e6i	0.0740034	+	0.336159i
$636$		0			0
$637$	−1.86666e7	−	1.86666e7i	−1.82271	−	1.82271i
$638$		0			0
$639$	897120.			0.0869158
$640$		0			0
$641$	1.02364e7			0.984020			0.492010	−	0.870589i	$-0.336262\pi$
$641$	1.02364e7			0.984020			0.492010	+	0.870589i	$0.336262\pi$
$642$		0			0
$643$	−8.21318e6	−	8.21318e6i	−0.783400	−	0.783400i	0.197003	−	0.980403i	$-0.436879\pi$
$643$	−8.21318e6	−	8.21318e6i	−0.783400	−	0.783400i	−0.980403	+	0.197003i	$0.936879\pi$
$644$		0			0
$645$	3.92835e6	+	2.51081e6i	0.371802	+	0.237637i
$646$		0			0
$647$	1.26993e7	−	1.26993e7i	1.19267	−	1.19267i	0.216356	−	0.976315i	$-0.430583\pi$
$647$	1.26993e7	−	1.26993e7i	1.19267	−	1.19267i	0.976315	−	0.216356i	$-0.0694171\pi$
$648$		0			0
$649$		−	9.82387e6i		−	0.915526i
$650$		0			0
$651$		−	2.52742e7i		−	2.33736i
$652$		0			0
$653$	−3.68109e6	+	3.68109e6i	−0.337827	+	0.337827i	−0.855549	−	0.517722i	$-0.826780\pi$
$653$	−3.68109e6	+	3.68109e6i	−0.337827	+	0.337827i	0.517722	+	0.855549i	$0.326780\pi$
$654$		0			0
$655$	−6.84815e6	−	4.37700e6i	−0.623692	−	0.398633i
$656$		0			0
$657$	2.87803e6	+	2.87803e6i	0.260124	+	0.260124i
$658$		0			0
$659$	−7.29404e6			−0.654267			−0.327133	−	0.944978i	$-0.606083\pi$
$659$	−7.29404e6			−0.654267			−0.327133	+	0.944978i	$0.606083\pi$
$660$		0			0
$661$	1.20221e7			1.07023			0.535113	−	0.844781i	$-0.320269\pi$
$661$	1.20221e7			1.07023			0.535113	+	0.844781i	$0.320269\pi$
$662$		0			0
$663$	1.80527e6	+	1.80527e6i	0.159499	+	0.159499i
$664$		0			0
$665$	3.09305e6	+	1.40501e7i	0.271227	+	1.23204i
$666$		0			0
$667$	3.66762e6	−	3.66762e6i	0.319205	−	0.319205i
$668$		0			0
$669$			1.32851e7i			1.14762i
$670$		0			0
$671$			2.97158e7i			2.54789i
$672$		0			0
$673$	3.57322e6	−	3.57322e6i	0.304104	−	0.304104i	−0.538513	−	0.842617i	$-0.681014\pi$
$673$	3.57322e6	−	3.57322e6i	0.304104	−	0.304104i	0.842617	+	0.538513i	$0.181014\pi$
$674$		0			0
$675$	7.87121e6	+	2.89127e6i	0.664940	+	0.244247i
$676$		0			0
$677$	−1.59000e7	−	1.59000e7i	−1.33329	−	1.33329i	−0.902408	−	0.430883i	$-0.858202\pi$
$677$	−1.59000e7	−	1.59000e7i	−1.33329	−	1.33329i	−0.430883	−	0.902408i	$-0.641798\pi$
$678$		0			0
$679$	1.63109e7			1.35770
$680$		0			0
$681$	−1.84117e7			−1.52134
$682$		0			0
$683$	−3.93608e6	−	3.93608e6i	−0.322859	−	0.322859i	0.527004	−	0.849863i	$-0.323315\pi$
$683$	−3.93608e6	−	3.93608e6i	−0.322859	−	0.322859i	−0.849863	+	0.527004i	$0.823315\pi$
$684$		0			0
$685$	−1.19510e7	+	2.63094e6i	−0.973145	+	0.214232i
$686$		0			0
$687$	−9.69970e6	+	9.69970e6i	−0.784091	+	0.784091i
$688$		0			0
$689$		−	3.05582e7i		−	2.45233i
$690$		0			0
$691$			1.54457e7i			1.23059i	0.788297	+	0.615294i	$0.210963\pi$
$691$			1.54457e7i			1.23059i	−0.788297	+	0.615294i	$0.789037\pi$
$692$		0			0
$693$	8.54089e6	−	8.54089e6i	0.675569	−	0.675569i
$694$		0			0
$695$	−6.38402e6	+	9.98829e6i	−0.501340	+	0.784385i
$696$		0			0
$697$	1.38361e6	+	1.38361e6i	0.107878	+	0.107878i
$698$		0			0
$699$	4.45727e6			0.345045
$700$		0			0
$701$	6.96247e6			0.535141			0.267570	−	0.963538i	$-0.413779\pi$
$701$	6.96247e6			0.535141			0.267570	+	0.963538i	$0.413779\pi$
$702$		0			0
$703$	3.44434e6	+	3.44434e6i	0.262856	+	0.262856i
$704$		0			0
$705$	1.17408e7	−	1.83694e7i	0.889661	−	1.39194i
$706$		0			0
$707$	1.48795e7	−	1.48795e7i	1.11954	−	1.11954i
$708$		0			0
$709$			3.88418e6i			0.290191i	0.989418	+	0.145096i	$0.0463490\pi$
$709$			3.88418e6i			0.290191i	−0.989418	+	0.145096i	$0.953651\pi$
$710$		0			0
$711$			2.05522e6i			0.152470i
$712$		0			0
$713$	−3.90951e6	+	3.90951e6i	−0.288004	+	0.288004i
$714$		0			0
$715$	−2.90699e7	+	6.39958e6i	−2.12657	+	0.468151i
$716$		0			0
$717$	9.52422e6	+	9.52422e6i	0.691881	+	0.691881i
$718$		0			0
$719$	−1.89296e7			−1.36559			−0.682794	−	0.730611i	$-0.739235\pi$
$719$	−1.89296e7			−1.36559			−0.682794	+	0.730611i	$0.739235\pi$
$720$		0			0
$721$	3.20324e7			2.29483
$722$		0			0
$723$	1.04208e7	+	1.04208e7i	0.741402	+	0.741402i
$724$		0			0
$725$	1.70718e7	−	7.89935e6i	1.20624	−	0.558144i
$726$		0			0
$727$	1.02585e7	−	1.02585e7i	0.719860	−	0.719860i	−0.248716	−	0.968576i	$-0.580009\pi$
$727$	1.02585e7	−	1.02585e7i	0.719860	−	0.719860i	0.968576	+	0.248716i	$0.0800087\pi$
$728$		0			0
$729$		−	4.88531e6i		−	0.340466i
$730$		0			0
$731$		−	680716.i		−	0.0471165i
$732$		0			0
$733$	−1.84548e6	+	1.84548e6i	−0.126867	+	0.126867i	−0.767689	−	0.640822i	$-0.778594\pi$
$733$	−1.84548e6	+	1.84548e6i	−0.126867	+	0.126867i	0.640822	+	0.767689i	$0.278594\pi$
$734$		0			0
$735$	−6.37610e6	−	2.89633e7i	−0.435348	−	1.97756i
$736$		0			0
$737$	−2.75506e6	−	2.75506e6i	−0.186837	−	0.186837i
$738$		0			0
$739$	−2.52035e7			−1.69766			−0.848828	−	0.528669i	$-0.822691\pi$
$739$	−2.52035e7			−1.69766			−0.848828	+	0.528669i	$0.822691\pi$
$740$		0			0
$741$	2.04365e7			1.36729
$742$		0			0
$743$	3.48728e6	+	3.48728e6i	0.231748	+	0.231748i	0.813422	−	0.581674i	$-0.197602\pi$
$743$	3.48728e6	+	3.48728e6i	0.231748	+	0.231748i	−0.581674	+	0.813422i	$0.697602\pi$
$744$		0			0
$745$	−1.23604e7	−	7.90015e6i	−0.815908	−	0.521488i
$746$		0			0
$747$	−2.13384e6	+	2.13384e6i	−0.139913	+	0.139913i
$748$		0			0
$749$			2.96127e7i			1.92874i
$750$		0			0
$751$			1.38646e6i			0.0897029i	0.998994	+	0.0448514i	$0.0142815\pi$
$751$			1.38646e6i			0.0897029i	−0.998994	+	0.0448514i	$0.985719\pi$
$752$		0			0
$753$	−1.83807e7	+	1.83807e7i	−1.18134	+	1.18134i
$754$		0			0
$755$	−372540.	−	238109.i	−0.0237851	−	0.0152023i
$756$		0			0
$757$	−4.65475e6	−	4.65475e6i	−0.295227	−	0.295227i	0.543914	−	0.839141i	$-0.316942\pi$
$757$	−4.65475e6	−	4.65475e6i	−0.295227	−	0.295227i	−0.839141	+	0.543914i	$0.816942\pi$
$758$		0			0
$759$	−9.22055e6			−0.580968
$760$		0			0
$761$	2.54119e7			1.59066			0.795328	−	0.606179i	$-0.207299\pi$
$761$	2.54119e7			1.59066			0.795328	+	0.606179i	$0.207299\pi$
$762$		0			0
$763$	−1.49429e7	−	1.49429e7i	−0.929230	−	0.929230i
$764$		0			0
$765$	176706.	+	802685.i	0.0109169	+	0.0495897i
$766$		0			0
$767$	−1.10023e7	+	1.10023e7i	−0.675299	+	0.675299i
$768$		0			0
$769$			6.85765e6i			0.418176i	0.977897	+	0.209088i	$0.0670496\pi$
$769$			6.85765e6i			0.418176i	−0.977897	+	0.209088i	$0.932950\pi$
$770$		0			0
$771$			2.84725e6i			0.172500i
$772$		0			0
$773$	1.58202e7	−	1.58202e7i	0.952277	−	0.952277i	−0.0466349	−	0.998912i	$-0.514850\pi$
$773$	1.58202e7	−	1.58202e7i	0.952277	−	0.952277i	0.998912	+	0.0466349i	$0.0148497\pi$
$774$		0			0
$775$	−1.81977e7	+	8.42032e6i	−1.08834	+	0.503587i
$776$		0			0
$777$	−1.12516e7	−	1.12516e7i	−0.668593	−	0.668593i
$778$		0			0
$779$	1.56631e7			0.924769
$780$		0			0
$781$	5.32928e6			0.312637
$782$		0			0
$783$	−1.14214e7	−	1.14214e7i	−0.665754	−	0.665754i
$784$		0			0
$785$	−1.28821e7	+	2.83592e6i	−0.746127	+	0.164256i
$786$		0			0
$787$	1.34058e7	−	1.34058e7i	0.771538	−	0.771538i	−0.206837	−	0.978375i	$-0.566317\pi$
$787$	1.34058e7	−	1.34058e7i	0.771538	−	0.771538i	0.978375	+	0.206837i	$0.0663170\pi$
$788$		0			0
$789$		−	1.98745e7i		−	1.13659i
$790$		0			0
$791$		−	1.27503e7i		−	0.724567i
$792$		0			0
$793$	3.32805e7	−	3.32805e7i	1.87934	−	1.87934i
$794$		0			0
$795$	1.84882e7	−	2.89262e7i	1.03747	−	1.62320i
$796$		0			0
$797$	4.58811e6	+	4.58811e6i	0.255852	+	0.255852i	0.823365	−	0.567513i	$-0.192094\pi$
$797$	4.58811e6	+	4.58811e6i	0.255852	+	0.255852i	−0.567513	+	0.823365i	$0.692094\pi$
$798$		0			0
$799$	−3.18310e6			−0.176394
$800$		0			0
$801$	1.00469e6			0.0553290
$802$		0			0
$803$	1.70967e7	+	1.70967e7i	0.935672	+	0.935672i
$804$		0			0
$805$	−5.53665e6	+	8.66252e6i	−0.301132	+	0.471145i
$806$		0			0
$807$	2.34950e6	−	2.34950e6i	0.126996	−	0.126996i
$808$		0			0
$809$			5.02809e6i			0.270104i	0.990838	+	0.135052i	$0.0431202\pi$
$809$			5.02809e6i			0.270104i	−0.990838	+	0.135052i	$0.956880\pi$
$810$		0			0
$811$		−	6.77890e6i		−	0.361915i	−0.983491	−	0.180958i	$-0.942080\pi$
$811$		−	6.77890e6i		−	0.361915i	0.983491	−	0.180958i	$-0.0579197\pi$
$812$		0			0
$813$	1.98776e7	−	1.98776e7i	1.05472	−	1.05472i
$814$		0			0
$815$	2.78125e7	−	6.12276e6i	1.46671	−	0.322889i
$816$		0			0
$817$	−3.85301e6	−	3.85301e6i	−0.201950	−	0.201950i
$818$		0			0
$819$	−1.91309e7			−0.996611
$820$		0			0
$821$	−3.05125e7			−1.57987			−0.789933	−	0.613194i	$-0.789885\pi$
$821$	−3.05125e7			−1.57987			−0.789933	+	0.613194i	$0.789885\pi$
$822$		0			0
$823$	−357891.	−	357891.i	−0.0184184	−	0.0184184i	0.697838	−	0.716256i	$-0.254146\pi$
$823$	−357891.	−	357891.i	−0.0184184	−	0.0184184i	−0.716256	+	0.697838i	$0.754146\pi$
$824$		0			0
$825$	−3.13893e7	−	1.15300e7i	−1.60563	−	0.589784i
$826$		0			0
$827$	−1.47785e7	+	1.47785e7i	−0.751391	+	0.751391i	−0.974739	−	0.223348i	$-0.928301\pi$
$827$	−1.47785e7	+	1.47785e7i	−0.751391	+	0.751391i	0.223348	+	0.974739i	$0.428301\pi$
$828$		0			0
$829$		−	2.59329e7i		−	1.31059i	−0.755375	−	0.655293i	$-0.772545\pi$
$829$		−	2.59329e7i		−	1.31059i	0.755375	−	0.655293i	$-0.227455\pi$
$830$		0			0
$831$		−	4.05461e7i		−	2.03679i
$832$		0			0
$833$	−3.06186e6	+	3.06186e6i	−0.152888	+	0.152888i
$834$		0			0
$835$	1.12879e6	+	5.12752e6i	0.0560271	+	0.254502i
$836$		0			0
$837$	1.21746e7	+	1.21746e7i	0.600678	+	0.600678i
$838$		0			0
$839$	−7.43726e6			−0.364761			−0.182380	−	0.983228i	$-0.558380\pi$
$839$	−7.43726e6			−0.364761			−0.182380	+	0.983228i	$0.558380\pi$
$840$		0			0
$841$	−1.57228e7			−0.766547
$842$		0			0
$843$	1.82977e7	+	1.82977e7i	0.886802	+	0.886802i
$844$		0			0
$845$	2.22356e7	+	1.42119e7i	1.07129	+	0.684714i
$846$		0			0
$847$	2.64310e7	−	2.64310e7i	1.26592	−	1.26592i
$848$		0			0
$849$			1.69622e7i			0.807632i
$850$		0			0
$851$			3.48088e6i			0.164765i
$852$		0			0
$853$	−809973.	+	809973.i	−0.0381152	+	0.0381152i	−0.725908	−	0.687792i	$-0.758580\pi$
$853$	−809973.	+	809973.i	−0.0381152	+	0.0381152i	0.687792	+	0.725908i	$0.258580\pi$
$854$		0			0
$855$	5.54358e6	+	3.54318e6i	0.259343	+	0.165759i
$856$		0			0
$857$	−6.77429e6	−	6.77429e6i	−0.315074	−	0.315074i	0.531798	−	0.846871i	$-0.321517\pi$
$857$	−6.77429e6	−	6.77429e6i	−0.315074	−	0.315074i	−0.846871	+	0.531798i	$0.821517\pi$
$858$		0			0
$859$	−2.95020e7			−1.36417			−0.682086	−	0.731272i	$-0.738927\pi$
$859$	−2.95020e7			−1.36417			−0.682086	+	0.731272i	$0.738927\pi$
$860$		0			0
$861$	−5.11665e7			−2.35222
$862$		0			0
$863$	−2.22127e7	−	2.22127e7i	−1.01525	−	1.01525i	−0.999882	−	0.0153701i	$-0.995107\pi$
$863$	−2.22127e7	−	2.22127e7i	−1.01525	−	1.01525i	−0.0153701	−	0.999882i	$-0.504893\pi$
$864$		0			0
$865$	9.36039e6	+	4.25194e7i	0.425357	+	1.93218i
$866$		0			0
$867$	−1.82330e7	+	1.82330e7i	−0.823779	+	0.823779i
$868$		0			0
$869$			1.22089e7i			0.548438i
$870$		0			0
$871$			6.17112e6i			0.275625i
$872$		0			0
$873$	5.27445e6	−	5.27445e6i	0.234230	−	0.234230i
$874$		0			0
$875$	−2.96804e7	+	2.25662e7i	−1.31054	+	0.996410i
$876$		0			0
$877$	1.07450e7	+	1.07450e7i	0.471744	+	0.471744i	0.902479	−	0.430735i	$-0.141746\pi$
$877$	1.07450e7	+	1.07450e7i	0.471744	+	0.471744i	−0.430735	+	0.902479i	$0.641746\pi$
$878$		0			0
$879$	1.64959e7			0.720118
$880$		0			0
$881$	−3.06659e7			−1.33112			−0.665559	−	0.746346i	$-0.731807\pi$
$881$	−3.06659e7			−1.33112			−0.665559	+	0.746346i	$0.731807\pi$
$882$		0			0
$883$	−5.50118e6	−	5.50118e6i	−0.237440	−	0.237440i	0.578349	−	0.815789i	$-0.303697\pi$
$883$	−5.50118e6	−	5.50118e6i	−0.237440	−	0.237440i	−0.815789	+	0.578349i	$0.803697\pi$
$884$		0			0
$885$	−1.70713e7	+	3.75815e6i	−0.732671	+	0.161293i
$886$		0			0
$887$	−1.66597e7	+	1.66597e7i	−0.710983	+	0.710983i	−0.966741	−	0.255758i	$-0.917675\pi$
$887$	−1.66597e7	+	1.66597e7i	−0.710983	+	0.710983i	0.255758	+	0.966741i	$0.417675\pi$
$888$		0			0
$889$			1.33533e7i			0.566674i
$890$		0			0
$891$			4.24658e7i			1.79203i
$892$		0			0
$893$	−1.80170e7	+	1.80170e7i	−0.756058	+	0.756058i
$894$		0			0
$895$	7.28136e6	−	1.13922e7i	0.303847	−	0.475392i
$896$		0			0
$897$	1.03266e7	+	1.03266e7i	0.428527	+	0.428527i
$898$		0			0
$899$	3.86236e7			1.59387
$900$		0			0
$901$	−5.01241e6			−0.205700
$902$		0			0
$903$	1.25866e7	+	1.25866e7i	0.513676	+	0.513676i
$904$		0			0
$905$	2.33190e7	−	3.64844e7i	0.946431	−	1.48076i
$906$		0			0
$907$	−2.20921e7	+	2.20921e7i	−0.891702	+	0.891702i	−0.994683	−	0.102981i	$-0.967162\pi$
$907$	−2.20921e7	+	2.20921e7i	−0.891702	+	0.891702i	0.102981	+	0.994683i	$0.467162\pi$
$908$		0			0
$909$		−	9.62313e6i		−	0.386284i
$910$		0			0
$911$			6.41906e6i			0.256257i	0.991758	+	0.128128i	$0.0408970\pi$
$911$			6.41906e6i			0.256257i	−0.991758	+	0.128128i	$0.959103\pi$
$912$		0			0
$913$	−1.26759e7	+	1.26759e7i	−0.503271	+	0.503271i
$914$		0			0
$915$	5.16383e7	−	1.13679e7i	2.03901	−	0.448876i
$916$		0			0
$917$	−2.19417e7	−	2.19417e7i	−0.861684	−	0.861684i
$918$		0			0
$919$	2.61369e7			1.02086			0.510428	−	0.859920i	$-0.329487\pi$
$919$	2.61369e7			1.02086			0.510428	+	0.859920i	$0.329487\pi$
$920$		0			0
$921$	5.70848e7			2.21754
$922$		0			0
$923$	−5.96858e6	−	5.96858e6i	−0.230604	−	0.230604i
$924$		0			0
$925$	−4.35271e6	+	1.18499e7i	−0.167265	+	0.455364i
$926$		0			0
$927$	1.03583e7	−	1.03583e7i	0.395903	−	0.395903i
$928$		0			0
$929$		−	5.63201e6i		−	0.214104i	−0.994253	−	0.107052i	$-0.965859\pi$
$929$		−	5.63201e6i		−	0.214104i	0.994253	−	0.107052i	$-0.0341411\pi$
$930$		0			0
$931$			3.46616e7i			1.31061i
$932$		0			0
$933$	6.65242e6	−	6.65242e6i	0.250193	−	0.250193i
$934$		0			0
$935$	1.04971e6	+	4.76830e6i	0.0392682	+	0.178375i
$936$		0			0
$937$	2.00140e7	+	2.00140e7i	0.744707	+	0.744707i	0.973480	−	0.228773i	$-0.0734714\pi$
$937$	2.00140e7	+	2.00140e7i	0.744707	+	0.744707i	−0.228773	+	0.973480i	$0.573471\pi$
$938$		0			0
$939$	3.32440e7			1.23041
$940$		0			0
$941$	−1.14203e7			−0.420439			−0.210220	−	0.977654i	$-0.567418\pi$
$941$	−1.14203e7			−0.420439			−0.210220	+	0.977654i	$0.567418\pi$
$942$		0			0
$943$	7.91461e6	+	7.91461e6i	0.289835	+	0.289835i
$944$		0			0
$945$	2.69760e7	+	1.72417e7i	0.982648	+	0.628060i
$946$		0			0
$947$	−3.41208e6	+	3.41208e6i	−0.123636	+	0.123636i	−0.766217	−	0.642582i	$-0.777863\pi$
$947$	−3.41208e6	+	3.41208e6i	−0.123636	+	0.123636i	0.642582	+	0.766217i	$0.277863\pi$
$948$		0			0
$949$		−	3.82952e7i		−	1.38032i
$950$		0			0
$951$		−	198035.i		−	0.00710053i
$952$		0			0
$953$	−2.95198e6	+	2.95198e6i	−0.105289	+	0.105289i	−0.757789	−	0.652500i	$-0.773720\pi$
$953$	−2.95198e6	+	2.95198e6i	−0.105289	+	0.105289i	0.652500	+	0.757789i	$0.273720\pi$
$954$		0			0
$955$	1.86159e6	+	1.18984e6i	0.0660504	+	0.0422161i
$956$		0			0
$957$	4.55467e7	+	4.55467e7i	1.60760	+	1.60760i
$958$		0			0
$959$	−4.67211e7			−1.64046
$960$		0			0
$961$	−1.25417e7			−0.438073
$962$		0			0
$963$	9.57583e6	+	9.57583e6i	0.332744	+	0.332744i
$964$		0			0
$965$	−4.51789e6	−	2.05224e7i	−0.156177	−	0.709430i
$966$		0			0
$967$	1.54121e7	−	1.54121e7i	0.530024	−	0.530024i	−0.390555	−	0.920580i	$-0.627717\pi$
$967$	1.54121e7	−	1.54121e7i	0.530024	−	0.530024i	0.920580	+	0.390555i	$0.127717\pi$
$968$		0			0
$969$		−	3.35216e6i		−	0.114687i
$970$		0			0
$971$			2.20583e7i			0.750800i	0.926863	+	0.375400i	$0.122495\pi$
$971$			2.20583e7i			0.750800i	−0.926863	+	0.375400i	$0.877505\pi$
$972$		0			0
$973$	−3.20029e7	+	3.20029e7i	−1.08369	+	1.08369i
$974$		0			0
$975$	2.22416e7	+	4.80678e7i	0.749297	+	1.61936i
$976$		0			0
$977$	6.28253e6	+	6.28253e6i	0.210571	+	0.210571i	0.804510	−	0.593939i	$-0.202428\pi$
$977$	6.28253e6	+	6.28253e6i	0.210571	+	0.210571i	−0.593939	+	0.804510i	$0.702428\pi$
$978$		0			0
$979$	5.96832e6			0.199019
$980$		0			0
$981$	−9.66415e6			−0.320620
$982$		0			0
$983$	−2.92505e7	−	2.92505e7i	−0.965493	−	0.965493i	0.0339308	−	0.999424i	$-0.489197\pi$
$983$	−2.92505e7	−	2.92505e7i	−0.965493	−	0.965493i	−0.999424	+	0.0339308i	$0.989197\pi$
$984$		0			0
$985$	1.97388e7	−	4.34538e6i	0.648232	−	0.142704i
$986$		0			0
$987$	5.88562e7	−	5.88562e7i	1.92309	−	1.92309i
$988$		0			0
$989$		−	3.89388e6i		−	0.126588i
$990$		0			0
$991$			1.52850e7i			0.494404i	0.968964	+	0.247202i	$0.0795111\pi$
$991$			1.52850e7i			0.494404i	−0.968964	+	0.247202i	$0.920489\pi$
$992$		0			0
$993$	−8.36925e6	+	8.36925e6i	−0.269348	+	0.269348i
$994$		0			0
$995$	−1.21114e7	+	1.89492e7i	−0.387825	+	0.606783i
$996$		0			0
$997$	−672720.	−	672720.i	−0.0214337	−	0.0214337i	0.696309	−	0.717742i	$-0.254824\pi$
$997$	−672720.	−	672720.i	−0.0214337	−	0.0214337i	−0.717742	+	0.696309i	$0.754824\pi$
$998$		0			0
$999$	1.08398e7			0.343644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.d.127.2	yes	16
4.3	odd	2		160.6.n.c.127.7	yes	16
5.3	odd	4		160.6.n.c.63.7	✓	16
20.3	even	4	inner	160.6.n.d.63.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.c.63.7	✓	16	5.3	odd	4
160.6.n.c.127.7	yes	16	4.3	odd	2
160.6.n.d.63.2	yes	16	20.3	even	4	inner
160.6.n.d.127.2	yes	16	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)

\(f(q)\)	\(=\)	\(q+(-13.0500 - 13.0500i) q^{3} +(-30.1056 + 47.1026i) q^{5} +(-150.919 + 150.919i) q^{7} +97.6048i q^{9} +O(q^{10})\)	\(q+(-13.0500 - 13.0500i) q^{3} +(-30.1056 + 47.1026i) q^{5} +(-150.919 + 150.919i) q^{7} +97.6048i q^{9} +579.815i q^{11} +(649.369 - 649.369i) q^{13} +(1007.57 - 221.810i) q^{15} +(-106.515 - 106.515i) q^{17} -1205.80 q^{19} +3938.97 q^{21} +(-609.294 - 609.294i) q^{23} +(-1312.30 - 2836.10i) q^{25} +(-1897.41 + 1897.41i) q^{27} +6019.46i q^{29} -6416.45i q^{31} +(7566.58 - 7566.58i) q^{33} +(-2565.15 - 11652.1i) q^{35} +(-2856.48 - 2856.48i) q^{37} -16948.5 q^{39} -12989.8 q^{41} +(3195.40 + 3195.40i) q^{43} +(-4597.44 - 2938.45i) q^{45} +(14942.0 - 14942.0i) q^{47} -28745.8i q^{49} +2780.04i q^{51} +(23529.1 - 23529.1i) q^{53} +(-27310.8 - 17455.7i) q^{55} +(15735.7 + 15735.7i) q^{57} -16943.1 q^{59} +51250.5 q^{61} +(-14730.4 - 14730.4i) q^{63} +(11037.3 + 50136.6i) q^{65} +(-4751.63 + 4751.63i) q^{67} +15902.6i q^{69} -9191.35i q^{71} +(29486.5 - 29486.5i) q^{73} +(-19885.6 + 54136.7i) q^{75} +(-87504.8 - 87504.8i) q^{77} +21056.6 q^{79} +73240.3 q^{81} +(21862.0 + 21862.0i) q^{83} +(8223.83 - 1810.43i) q^{85} +(78553.9 - 78553.9i) q^{87} -10293.5i q^{89} +196004. i q^{91} +(-83734.6 + 83734.6i) q^{93} +(36301.3 - 56796.1i) q^{95} +(-54038.8 - 54038.8i) q^{97} -56592.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{3} - 42 q^{5} - 86 q^{7}+O(q^{10}) \) 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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