LMFDB - Embedded newform 160.6.n.a.63.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 8 x^{12} - 4626 x^{11} + 149441 x^{10} - 2113414 x^{9} + 17958066 x^{8} + \cdots + 69451154208 $ x^14 - 4x^13 + 8x^12 - 4626x^11 + 149441x^10 - 2113414x^9 + 17958066x^8 - 97717112x^7 + 355171384x^6 - 910571904x^5 + 2428303248x^4 - 9166992192x^3 + 32237484304x^2 - 66916821408*x + 69451154208
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{31}\cdot 5^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.1
Root			$2.75256 + 2.75256i$ of defining polynomial
Character	$\chi$	$=$	160.63
Dual form			160.6.n.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.9245 + 18.9245i) q^{3} +(-36.4318 + 42.3996i) q^{5} +(-112.521 - 112.521i) q^{7} -473.272i q^{9} +O(q^{10})$	\(q+(-18.9245 + 18.9245i) q^{3} +(-36.4318 + 42.3996i) q^{5} +(-112.521 - 112.521i) q^{7} -473.272i q^{9} +269.371i q^{11} +(-403.647 - 403.647i) q^{13} +(-112.936 - 1491.84i) q^{15} +(1098.68 - 1098.68i) q^{17} -1802.73 q^{19} +4258.82 q^{21} +(-2833.05 + 2833.05i) q^{23} +(-470.444 - 3089.39i) q^{25} +(4357.78 + 4357.78i) q^{27} +7856.77i q^{29} +4682.69i q^{31} +(-5097.71 - 5097.71i) q^{33} +(8870.22 - 671.497i) q^{35} +(5157.30 - 5157.30i) q^{37} +15277.6 q^{39} +1658.51 q^{41} +(3231.92 - 3231.92i) q^{43} +(20066.5 + 17242.2i) q^{45} +(6001.67 + 6001.67i) q^{47} +8515.15i q^{49} +41583.7i q^{51} +(-6075.77 - 6075.77i) q^{53} +(-11421.2 - 9813.69i) q^{55} +(34115.8 - 34115.8i) q^{57} +39361.1 q^{59} -11975.4 q^{61} +(-53253.2 + 53253.2i) q^{63} +(31820.1 - 2408.86i) q^{65} +(-43638.2 - 43638.2i) q^{67} -107228. i q^{69} -7043.28i q^{71} +(24461.9 + 24461.9i) q^{73} +(67367.9 + 49562.1i) q^{75} +(30310.1 - 30310.1i) q^{77} -30620.5 q^{79} -49932.2 q^{81} +(25676.6 - 25676.6i) q^{83} +(6556.60 + 86610.2i) q^{85} +(-148685. - 148685. i) q^{87} +137436. i q^{89} +90838.0i q^{91} +(-88617.5 - 88617.5i) q^{93} +(65676.9 - 76435.1i) q^{95} +(47906.2 - 47906.2i) q^{97} +127486. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7}+O(q^{10}) $ 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7	$ 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7} - 414 q^{13} - 278 q^{15} + 1222 q^{17} - 5672 q^{19} + 5924 q^{21} - 2902 q^{23} - 4466 q^{25} + 2168 q^{27} - 2444 q^{33} + 2618 q^{35} - 1790 q^{37} + 11076 q^{39} + 11644 q^{41} + 3982 q^{43} + 14704 q^{45} + 1278 q^{47} + 5882 q^{53} - 65608 q^{55} - 14552 q^{57} + 8504 q^{59} + 20564 q^{61} - 19422 q^{63} + 40798 q^{65} - 107926 q^{67} - 16418 q^{73} - 66586 q^{75} - 13348 q^{77} + 146544 q^{79} + 173806 q^{81} + 36398 q^{83} - 66262 q^{85} - 124384 q^{87} - 306620 q^{93} - 173768 q^{95} - 60314 q^{97} + 388628 q^{99}+O(q^{100}) $ 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7 - 414 * q^13 - 278 * q^15 + 1222 * q^17 - 5672 * q^19 + 5924 * q^21 - 2902 * q^23 - 4466 * q^25 + 2168 * q^27 - 2444 * q^33 + 2618 * q^35 - 1790 * q^37 + 11076 * q^39 + 11644 * q^41 + 3982 * q^43 + 14704 * q^45 + 1278 * q^47 + 5882 * q^53 - 65608 * q^55 - 14552 * q^57 + 8504 * q^59 + 20564 * q^61 - 19422 * q^63 + 40798 * q^65 - 107926 * q^67 - 16418 * q^73 - 66586 * q^75 - 13348 * q^77 + 146544 * q^79 + 173806 * q^81 + 36398 * q^83 - 66262 * q^85 - 124384 * q^87 - 306620 * q^93 - 173768 * q^95 - 60314 * q^97 + 388628 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−18.9245	+	18.9245i	−1.21401	+	1.21401i	−0.244308	+	0.969698i	$0.578561\pi$
$3$	−18.9245	+	18.9245i	−1.21401	+	1.21401i	−0.969698	+	0.244308i	$0.921439\pi$
$4$		0			0
$5$	−36.4318	+	42.3996i	−0.651712	+	0.758466i
$5$	−36.4318	+	42.3996i	−0.651712	+	0.758466i
$6$		0			0
$7$	−112.521	−	112.521i	−0.867941	−	0.867941i	0.124303	−	0.992244i	$-0.460330\pi$
$7$	−112.521	−	112.521i	−0.867941	−	0.867941i	−0.992244	+	0.124303i	$0.960330\pi$
$8$		0			0
$9$		−	473.272i		−	1.94762i
$10$		0			0
$11$			269.371i			0.671228i	0.942000	+	0.335614i	$0.108944\pi$
$11$			269.371i			0.671228i	−0.942000	+	0.335614i	$0.891056\pi$
$12$		0			0
$13$	−403.647	−	403.647i	−0.662436	−	0.662436i	0.293518	−	0.955954i	$-0.405174\pi$
$13$	−403.647	−	403.647i	−0.662436	−	0.662436i	−0.955954	+	0.293518i	$0.905174\pi$
$14$		0			0
$15$	−112.936	−	1491.84i	−0.129600	−	1.71197i
$16$		0			0
$17$	1098.68	−	1098.68i	0.922035	−	0.922035i	−0.0751382	−	0.997173i	$-0.523940\pi$
$17$	1098.68	−	1098.68i	0.922035	−	0.922035i	0.997173	+	0.0751382i	$0.0239398\pi$
$18$		0			0
$19$	−1802.73			−1.14564			−0.572819	−	0.819682i	$-0.694150\pi$
$19$	−1802.73			−1.14564			−0.572819	+	0.819682i	$0.694150\pi$
$20$		0			0
$21$	4258.82			2.10737
$22$		0			0
$23$	−2833.05	+	2833.05i	−1.11670	+	1.11670i	−0.124474	+	0.992223i	$0.539724\pi$
$23$	−2833.05	+	2833.05i	−1.11670	+	1.11670i	−0.992223	+	0.124474i	$0.960276\pi$
$24$		0			0
$25$	−470.444	−	3089.39i	−0.150542	−	0.988604i
$26$		0			0
$27$	4357.78	+	4357.78i	1.15042	+	1.15042i
$28$		0			0
$29$			7856.77i			1.73480i	0.497612	+	0.867400i	$0.334210\pi$
$29$			7856.77i			1.73480i	−0.497612	+	0.867400i	$0.665790\pi$
$30$		0			0
$31$			4682.69i			0.875167i	0.899178	+	0.437584i	$0.144166\pi$
$31$			4682.69i			0.875167i	−0.899178	+	0.437584i	$0.855834\pi$
$32$		0			0
$33$	−5097.71	−	5097.71i	−0.814874	−	0.814874i
$34$		0			0
$35$	8870.22	−	671.497i	1.22395	−	0.0926561i
$36$		0			0
$37$	5157.30	−	5157.30i	0.619324	−	0.619324i	−0.326034	−	0.945358i	$-0.605712\pi$
$37$	5157.30	−	5157.30i	0.619324	−	0.619324i	0.945358	+	0.326034i	$0.105712\pi$
$38$		0			0
$39$	15277.6			1.60840
$40$		0			0
$41$	1658.51			0.154084			0.0770421	−	0.997028i	$-0.475452\pi$
$41$	1658.51			0.154084			0.0770421	+	0.997028i	$0.475452\pi$
$42$		0			0
$43$	3231.92	−	3231.92i	0.266557	−	0.266557i	−0.561154	−	0.827711i	$-0.689643\pi$
$43$	3231.92	−	3231.92i	0.266557	−	0.266557i	0.827711	+	0.561154i	$0.189643\pi$
$44$		0			0
$45$	20066.5	+	17242.2i	1.47720	+	1.26929i
$46$		0			0
$47$	6001.67	+	6001.67i	0.396303	+	0.396303i	0.876927	−	0.480624i	$-0.159590\pi$
$47$	6001.67	+	6001.67i	0.396303	+	0.396303i	−0.480624	+	0.876927i	$0.659590\pi$
$48$		0			0
$49$			8515.15i			0.506643i
$50$		0			0
$51$			41583.7i			2.23871i
$52$		0			0
$53$	−6075.77	−	6075.77i	−0.297106	−	0.297106i	0.542773	−	0.839879i	$-0.317374\pi$
$53$	−6075.77	−	6075.77i	−0.297106	−	0.297106i	−0.839879	+	0.542773i	$0.817374\pi$
$54$		0			0
$55$	−11421.2	−	9813.69i	−0.509103	−	0.437447i
$56$		0			0
$57$	34115.8	−	34115.8i	1.39081	−	1.39081i
$58$		0			0
$59$	39361.1			1.47210			0.736050	−	0.676927i	$-0.236689\pi$
$59$	39361.1			1.47210			0.736050	+	0.676927i	$0.236689\pi$
$60$		0			0
$61$	−11975.4			−0.412063			−0.206032	−	0.978545i	$-0.566055\pi$
$61$	−11975.4			−0.412063			−0.206032	+	0.978545i	$0.566055\pi$
$62$		0			0
$63$	−53253.2	+	53253.2i	−1.69042	+	1.69042i
$64$		0			0
$65$	31820.1	−	2408.86i	0.934153	−	0.0707176i
$66$		0			0
$67$	−43638.2	−	43638.2i	−1.18763	−	1.18763i	−0.977722	−	0.209904i	$-0.932685\pi$
$67$	−43638.2	−	43638.2i	−1.18763	−	1.18763i	−0.209904	−	0.977722i	$-0.567315\pi$
$68$		0			0
$69$		−	107228.i		−	2.71135i
$70$		0			0
$71$		−	7043.28i		−	0.165817i	−0.996557	−	0.0829086i	$-0.973579\pi$
$71$		−	7043.28i		−	0.165817i	0.996557	−	0.0829086i	$-0.0264209\pi$
$72$		0			0
$73$	24461.9	+	24461.9i	0.537257	+	0.537257i	0.922722	−	0.385465i	$-0.125959\pi$
$73$	24461.9	+	24461.9i	0.537257	+	0.537257i	−0.385465	+	0.922722i	$0.625959\pi$
$74$		0			0
$75$	67367.9	+	49562.1i	1.38293	+	1.01741i
$76$		0			0
$77$	30310.1	−	30310.1i	0.582586	−	0.582586i
$78$		0			0
$79$	−30620.5			−0.552007			−0.276003	−	0.961157i	$-0.589010\pi$
$79$	−30620.5			−0.552007			−0.276003	+	0.961157i	$0.589010\pi$
$80$		0			0
$81$	−49932.2			−0.845606
$82$		0			0
$83$	25676.6	−	25676.6i	0.409112	−	0.409112i	−0.472317	−	0.881429i	$-0.656582\pi$
$83$	25676.6	−	25676.6i	0.409112	−	0.409112i	0.881429	+	0.472317i	$0.156582\pi$
$84$		0			0
$85$	6556.60	+	86610.2i	0.0984309	+	1.30023i
$86$		0			0
$87$	−148685.	−	148685.i	−2.10606	−	2.10606i
$88$		0			0
$89$			137436.i			1.83919i	0.392868	+	0.919595i	$0.371483\pi$
$89$			137436.i			1.83919i	−0.392868	+	0.919595i	$0.628517\pi$
$90$		0			0
$91$			90838.0i			1.14991i
$92$		0			0
$93$	−88617.5	−	88617.5i	−1.06246	−	1.06246i
$94$		0			0
$95$	65676.9	−	76435.1i	0.746627	−	0.868928i
$96$		0			0
$97$	47906.2	−	47906.2i	0.516967	−	0.516967i	−0.399685	−	0.916652i	$-0.630881\pi$
$97$	47906.2	−	47906.2i	0.516967	−	0.516967i	0.916652	+	0.399685i	$0.130881\pi$
$98$		0			0
$99$	127486.			1.30730
$100$		0			0
$101$	−49807.9			−0.485842			−0.242921	−	0.970046i	$-0.578106\pi$
$101$	−49807.9			−0.485842			−0.242921	+	0.970046i	$0.578106\pi$
$102$		0			0
$103$	76305.7	−	76305.7i	0.708703	−	0.708703i	−0.257560	−	0.966262i	$-0.582918\pi$
$103$	76305.7	−	76305.7i	0.708703	−	0.708703i	0.966262	+	0.257560i	$0.0829184\pi$
$104$		0			0
$105$	−155157.	+	180572.i	−1.37340	+	1.59837i
$106$		0			0
$107$	86325.0	+	86325.0i	0.728916	+	0.728916i	0.970404	−	0.241488i	$-0.0776355\pi$
$107$	86325.0	+	86325.0i	0.728916	+	0.728916i	−0.241488	+	0.970404i	$0.577635\pi$
$108$		0			0
$109$			85263.0i			0.687376i	0.939084	+	0.343688i	$0.111676\pi$
$109$			85263.0i			0.687376i	−0.939084	+	0.343688i	$0.888324\pi$
$110$		0			0
$111$			195198.i			1.50373i
$112$		0			0
$113$	−150561.	−	150561.i	−1.10922	−	1.10922i	−0.993254	−	0.115962i	$-0.963005\pi$
$113$	−150561.	−	150561.i	−1.10922	−	1.10922i	−0.115962	−	0.993254i	$-0.536995\pi$
$114$		0			0
$115$	−16906.9	−	223334.i	−0.119212	−	1.57474i
$116$		0			0
$117$	−191035.	+	191035.i	−1.29017	+	1.29017i
$118$		0			0
$119$	−247249.			−1.60054
$120$		0			0
$121$	88490.1			0.549454
$122$		0			0
$123$	−31386.4	+	31386.4i	−0.187059	+	0.187059i
$124$		0			0
$125$	148128.	+	92605.4i	0.847933	+	0.530104i
$126$		0			0
$127$	−61749.1	−	61749.1i	−0.339720	−	0.339720i	0.516542	−	0.856262i	$-0.327219\pi$
$127$	−61749.1	−	61749.1i	−0.339720	−	0.339720i	−0.856262	+	0.516542i	$0.827219\pi$
$128$		0			0
$129$			122325.i			0.647203i
$130$		0			0
$131$		−	228440.i		−	1.16304i	−0.813532	−	0.581520i	$-0.802458\pi$
$131$		−	228440.i		−	1.16304i	0.813532	−	0.581520i	$-0.197542\pi$
$132$		0			0
$133$	202846.	+	202846.i	0.994346	+	0.994346i
$134$		0			0
$135$	−343529.	+	26006.0i	−1.62229	+	0.122812i
$136$		0			0
$137$	201798.	−	201798.i	0.918579	−	0.918579i	−0.0783472	−	0.996926i	$-0.524964\pi$
$137$	201798.	−	201798.i	0.918579	−	0.918579i	0.996926	+	0.0783472i	$0.0249643\pi$
$138$		0			0
$139$	122666.			0.538503			0.269252	−	0.963070i	$-0.413224\pi$
$139$	122666.			0.538503			0.269252	+	0.963070i	$0.413224\pi$
$140$		0			0
$141$	−227157.			−0.962229
$142$		0			0
$143$	108731.	−	108731.i	0.444645	−	0.444645i
$144$		0			0
$145$	−333124.	−	286237.i	−1.31579	−	1.13059i
$146$		0			0
$147$	−161145.	−	161145.i	−0.615067	−	0.615067i
$148$		0			0
$149$		−	385846.i		−	1.42380i	−0.702281	−	0.711900i	$-0.747835\pi$
$149$		−	385846.i		−	1.42380i	0.702281	−	0.711900i	$-0.252165\pi$
$150$		0			0
$151$		−	325566.i		−	1.16198i	−0.813912	−	0.580988i	$-0.802666\pi$
$151$		−	325566.i		−	1.16198i	0.813912	−	0.580988i	$-0.197334\pi$
$152$		0			0
$153$	−519973.	−	519973.i	−1.79577	−	1.79577i
$154$		0			0
$155$	−198544.	−	170599.i	−0.663785	−	0.570357i
$156$		0			0
$157$	−217734.	+	217734.i	−0.704981	+	0.704981i	−0.965475	−	0.260495i	$-0.916114\pi$
$157$	−217734.	+	217734.i	−0.704981	+	0.704981i	0.260495	+	0.965475i	$0.416114\pi$
$158$		0			0
$159$	229962.			0.721377
$160$		0			0
$161$	637559.			1.93845
$162$		0			0
$163$	−128681.	+	128681.i	−0.379353	+	0.379353i	−0.870869	−	0.491515i	$-0.836443\pi$
$163$	−128681.	+	128681.i	−0.379353	+	0.379353i	0.491515	+	0.870869i	$0.336443\pi$
$164$		0			0
$165$	401860.	−	30421.8i	1.14912	−	0.0869910i
$166$		0			0
$167$	−84402.8	−	84402.8i	−0.234189	−	0.234189i	0.580250	−	0.814438i	$-0.302955\pi$
$167$	−84402.8	−	84402.8i	−0.234189	−	0.234189i	−0.814438	+	0.580250i	$0.802955\pi$
$168$		0			0
$169$		−	45430.5i		−	0.122358i
$170$		0			0
$171$			853183.i			2.23127i
$172$		0			0
$173$	66342.8	+	66342.8i	0.168530	+	0.168530i	0.786333	−	0.617803i	$-0.211977\pi$
$173$	66342.8	+	66342.8i	0.168530	+	0.168530i	−0.617803	+	0.786333i	$0.711977\pi$
$174$		0			0
$175$	−294687.	+	400557.i	−0.727388	+	0.988711i
$176$		0			0
$177$	−744888.	+	744888.i	−1.78714	+	1.78714i
$178$		0			0
$179$	393894.			0.918855			0.459427	−	0.888215i	$-0.348055\pi$
$179$	393894.			0.918855			0.459427	+	0.888215i	$0.348055\pi$
$180$		0			0
$181$	589531.			1.33755			0.668775	−	0.743465i	$-0.266819\pi$
$181$	589531.			1.33755			0.668775	+	0.743465i	$0.266819\pi$
$182$		0			0
$183$	226627.	−	226627.i	0.500247	−	0.500247i
$184$		0			0
$185$	30777.3	+	406557.i	0.0661153	+	0.873357i
$186$		0			0
$187$	295952.	+	295952.i	0.618895	+	0.618895i
$188$		0			0
$189$		−	980686.i		−	1.99699i
$190$		0			0
$191$			146556.i			0.290683i	0.989382	+	0.145342i	$0.0464281\pi$
$191$			146556.i			0.290683i	−0.989382	+	0.145342i	$0.953572\pi$
$192$		0			0
$193$	649988.	+	649988.i	1.25606	+	1.25606i	0.952956	+	0.303109i	$0.0980246\pi$
$193$	649988.	+	649988.i	1.25606	+	1.25606i	0.303109	+	0.952956i	$0.401975\pi$
$194$		0			0
$195$	−556592.	+	647765.i	−1.04822	+	1.21992i
$196$		0			0
$197$	−484881.	+	484881.i	−0.890163	+	0.890163i	−0.994538	−	0.104375i	$-0.966716\pi$
$197$	−484881.	+	484881.i	−0.890163	+	0.890163i	0.104375	+	0.994538i	$0.466716\pi$
$198$		0			0
$199$	728394.			1.30387			0.651934	−	0.758275i	$-0.273958\pi$
$199$	728394.			1.30387			0.651934	+	0.758275i	$0.273958\pi$
$200$		0			0
$201$	1.65166e6			2.88357
$202$		0			0
$203$	884055.	−	884055.i	1.50570	−	1.50570i
$204$		0			0
$205$	−60422.5	+	70320.0i	−0.100419	+	0.116868i
$206$		0			0
$207$	1.34080e6	+	1.34080e6i	2.17490	+	2.17490i
$208$		0			0
$209$		−	485605.i		−	0.768984i
$210$		0			0
$211$		−	396241.i		−	0.612708i	−0.951918	−	0.306354i	$-0.900891\pi$
$211$		−	396241.i		−	0.612708i	0.951918	−	0.306354i	$-0.0991091\pi$
$212$		0			0
$213$	133290.	+	133290.i	0.201303	+	0.201303i
$214$		0			0
$215$	19287.2	+	254777.i	0.0284560	+	0.375893i
$216$		0			0
$217$	526903.	−	526903.i	0.759593	−	0.759593i
$218$		0			0
$219$	−925856.			−1.30447
$220$		0			0
$221$	−886956.			−1.22158
$222$		0			0
$223$	382870.	−	382870.i	0.515572	−	0.515572i	−0.400657	−	0.916228i	$-0.631218\pi$
$223$	382870.	−	382870.i	0.515572	−	0.515572i	0.916228	+	0.400657i	$0.131218\pi$
$224$		0			0
$225$	−1.46212e6	+	222648.i	−1.92543	+	0.293199i
$226$		0			0
$227$	−420420.	−	420420.i	−0.541525	−	0.541525i	0.382451	−	0.923976i	$-0.375080\pi$
$227$	−420420.	−	420420.i	−0.541525	−	0.541525i	−0.923976	+	0.382451i	$0.875080\pi$
$228$		0			0
$229$		−	842886.i		−	1.06214i	−0.847329	−	0.531068i	$-0.821791\pi$
$229$		−	842886.i		−	1.06214i	0.847329	−	0.531068i	$-0.178209\pi$
$230$		0			0
$231$			1.14720e6i			1.41453i
$232$		0			0
$233$	−36169.3	−	36169.3i	−0.0436466	−	0.0436466i	0.684947	−	0.728593i	$-0.259825\pi$
$233$	−36169.3	−	36169.3i	−0.0436466	−	0.0436466i	−0.728593	+	0.684947i	$0.759825\pi$
$234$		0			0
$235$	−473120.	+	35816.3i	−0.558858	+	0.0423069i
$236$		0			0
$237$	579477.	−	579477.i	0.670139	−	0.670139i
$238$		0			0
$239$	−273532.			−0.309751			−0.154876	−	0.987934i	$-0.549498\pi$
$239$	−273532.			−0.309751			−0.154876	+	0.987934i	$0.549498\pi$
$240$		0			0
$241$	901321.			0.999624			0.499812	−	0.866134i	$-0.333402\pi$
$241$	901321.			0.999624			0.499812	+	0.866134i	$0.333402\pi$
$242$		0			0
$243$	−113998.	+	113998.i	−0.123846	+	0.123846i
$244$		0			0
$245$	−361038.	−	310222.i	−0.384272	−	0.330185i
$246$		0			0
$247$	727669.	+	727669.i	0.758912	+	0.758912i
$248$		0			0
$249$			971832.i			0.993329i
$250$		0			0
$251$			1.31819e6i			1.32067i	0.750973	+	0.660333i	$0.229585\pi$
$251$			1.31819e6i			1.32067i	−0.750973	+	0.660333i	$0.770415\pi$
$252$		0			0
$253$	−763144.	−	763144.i	−0.749558	−	0.749558i
$254$		0			0
$255$	−1.76313e6	−	1.51497e6i	−1.69799	−	1.45900i
$256$		0			0
$257$	684108.	−	684108.i	0.646088	−	0.646088i	−0.305957	−	0.952045i	$-0.598976\pi$
$257$	684108.	−	684108.i	0.646088	−	0.646088i	0.952045	+	0.305957i	$0.0989764\pi$
$258$		0			0
$259$	−1.16061e6			−1.07507
$260$		0			0
$261$	3.71839e6			3.37873
$262$		0			0
$263$	974703.	−	974703.i	0.868926	−	0.868926i	−0.123427	−	0.992354i	$-0.539389\pi$
$263$	974703.	−	974703.i	0.868926	−	0.868926i	0.992354	+	0.123427i	$0.0393886\pi$
$264$		0			0
$265$	478961.	−	36258.5i	0.418973	−	0.0317173i
$266$		0			0
$267$	−2.60091e6	−	2.60091e6i	−2.23279	−	2.23279i
$268$		0			0
$269$		−	775071.i		−	0.653072i	−0.945185	−	0.326536i	$-0.894119\pi$
$269$		−	775071.i		−	0.653072i	0.945185	−	0.326536i	$-0.105881\pi$
$270$		0			0
$271$		−	102988.i		−	0.0851848i	−0.999093	−	0.0425924i	$-0.986438\pi$
$271$		−	102988.i		−	0.0851848i	0.999093	−	0.0425924i	$-0.0135617\pi$
$272$		0			0
$273$	−1.71906e6	−	1.71906e6i	−1.39600	−	1.39600i
$274$		0			0
$275$	832192.	−	126724.i	0.663578	−	0.101048i
$276$		0			0
$277$	−1.46313e6	+	1.46313e6i	−1.14573	+	1.14573i	−0.158347	+	0.987384i	$0.550616\pi$
$277$	−1.46313e6	+	1.46313e6i	−1.14573	+	1.14573i	−0.987384	+	0.158347i	$0.949384\pi$
$278$		0			0
$279$	2.21619e6			1.70449
$280$		0			0
$281$	−1.69321e6			−1.27922			−0.639611	−	0.768699i	$-0.720905\pi$
$281$	−1.69321e6			−1.27922			−0.639611	+	0.768699i	$0.720905\pi$
$282$		0			0
$283$	−67338.9	+	67338.9i	−0.0499804	+	0.0499804i	−0.731655	−	0.681675i	$-0.761252\pi$
$283$	−67338.9	+	67338.9i	−0.0499804	+	0.0499804i	0.681675	+	0.731655i	$0.261252\pi$
$284$		0			0
$285$	203594.	+	2.68940e6i	0.148475	+	1.96129i
$286$		0			0
$287$	−186618.	−	186618.i	−0.133736	−	0.133736i
$288$		0			0
$289$		−	994321.i		−	0.700297i
$290$		0			0
$291$			1.81320e6i			1.25520i
$292$		0			0
$293$	342591.	+	342591.i	0.233135	+	0.233135i	0.814000	−	0.580865i	$-0.197286\pi$
$293$	342591.	+	342591.i	0.233135	+	0.233135i	−0.580865	+	0.814000i	$0.697286\pi$
$294$		0			0
$295$	−1.43400e6	+	1.66889e6i	−0.959385	+	1.11654i
$296$		0			0
$297$	−1.17386e6	+	1.17386e6i	−0.772192	+	0.772192i
$298$		0			0
$299$	2.28711e6			1.47948
$300$		0			0
$301$	−727321.			−0.462711
$302$		0			0
$303$	942588.	−	942588.i	0.589815	−	0.589815i
$304$		0			0
$305$	436284.	−	507750.i	0.268547	−	0.312536i
$306$		0			0
$307$	−8371.33	−	8371.33i	−0.00506931	−	0.00506931i	0.704568	−	0.709637i	$-0.251141\pi$
$307$	−8371.33	−	8371.33i	−0.00506931	−	0.00506931i	−0.709637	+	0.704568i	$0.751141\pi$
$308$		0			0
$309$			2.88809e6i			1.72074i
$310$		0			0
$311$		−	112470.i		−	0.0659383i	−0.999456	−	0.0329691i	$-0.989504\pi$
$311$		−	112470.i		−	0.0659383i	0.999456	−	0.0329691i	$-0.0104963\pi$
$312$		0			0
$313$	932889.	+	932889.i	0.538232	+	0.538232i	0.923009	−	0.384778i	$-0.125722\pi$
$313$	932889.	+	932889.i	0.538232	+	0.538232i	−0.384778	+	0.923009i	$0.625722\pi$
$314$		0			0
$315$	−317801.	−	4.19803e6i	−0.180459	−	2.38379i
$316$		0			0
$317$	−1.24528e6	+	1.24528e6i	−0.696018	+	0.696018i	−0.963549	−	0.267531i	$-0.913792\pi$
$317$	−1.24528e6	+	1.24528e6i	−0.696018	+	0.696018i	0.267531	+	0.963549i	$0.413792\pi$
$318$		0			0
$319$	−2.11639e6			−1.16445
$320$		0			0
$321$	−3.26731e6			−1.76982
$322$		0			0
$323$	−1.98062e6	+	1.98062e6i	−1.05632	+	1.05632i
$324$		0			0
$325$	−1.05713e6	+	1.43692e6i	−0.555162	+	0.754611i
$326$		0			0
$327$	−1.61356e6	−	1.61356e6i	−0.834478	−	0.834478i
$328$		0			0
$329$		−	1.35063e6i		−	0.687936i
$330$		0			0
$331$		−	558197.i		−	0.280038i	−0.990149	−	0.140019i	$-0.955284\pi$
$331$		−	558197.i		−	0.280038i	0.990149	−	0.140019i	$-0.0447164\pi$
$332$		0			0
$333$	−2.44080e6	−	2.44080e6i	−1.20621	−	1.20621i
$334$		0			0
$335$	3.44006e6	−	260421.i	1.67477	−	0.126784i
$336$		0			0
$337$	−2.10837e6	+	2.10837e6i	−1.01128	+	1.01128i	−0.0113470	+	0.999936i	$0.503612\pi$
$337$	−2.10837e6	+	2.10837e6i	−1.01128	+	1.01128i	−0.999936	+	0.0113470i	$0.996388\pi$
$338$		0			0
$339$	5.69857e6			2.69319
$340$		0			0
$341$	−1.26138e6			−0.587436
$342$		0			0
$343$	−933011.	+	933011.i	−0.428205	+	0.428205i
$344$		0			0
$345$	4.54643e6	+	3.90652e6i	2.05647	+	1.76702i
$346$		0			0
$347$	−1.22415e6	−	1.22415e6i	−0.545773	−	0.545773i	0.379442	−	0.925215i	$-0.376116\pi$
$347$	−1.22415e6	−	1.22415e6i	−0.545773	−	0.545773i	−0.925215	+	0.379442i	$0.876116\pi$
$348$		0			0
$349$			1.81586e6i			0.798027i	0.916945	+	0.399014i	$0.130647\pi$
$349$			1.81586e6i			0.798027i	−0.916945	+	0.399014i	$0.869353\pi$
$350$		0			0
$351$		−	3.51801e6i		−	1.52416i
$352$		0			0
$353$	−2.92561e6	−	2.92561e6i	−1.24963	−	1.24963i	−0.955885	−	0.293740i	$-0.905100\pi$
$353$	−2.92561e6	−	2.92561e6i	−1.24963	−	1.24963i	−0.293740	−	0.955885i	$-0.594900\pi$
$354$		0			0
$355$	298632.	+	256600.i	0.125767	+	0.108065i
$356$		0			0
$357$	4.67906e6	−	4.67906e6i	1.94307	−	1.94307i
$358$		0			0
$359$	2.12540e6			0.870372			0.435186	−	0.900341i	$-0.356683\pi$
$359$	2.12540e6			0.870372			0.435186	+	0.900341i	$0.356683\pi$
$360$		0			0
$361$	773749.			0.312487
$362$		0			0
$363$	−1.67463e6	+	1.67463e6i	−0.667040	+	0.667040i
$364$		0			0
$365$	−1.92836e6	+	145982.i	−0.757629	+	0.0573544i
$366$		0			0
$367$	−2.48776e6	−	2.48776e6i	−0.964149	−	0.964149i	0.0352305	−	0.999379i	$-0.488783\pi$
$367$	−2.48776e6	−	2.48776e6i	−0.964149	−	0.964149i	−0.999379	+	0.0352305i	$0.988783\pi$
$368$		0			0
$369$		−	784925.i		−	0.300097i
$370$		0			0
$371$			1.36731e6i			0.515741i
$372$		0			0
$373$	−1.03845e6	−	1.03845e6i	−0.386469	−	0.386469i	0.486957	−	0.873426i	$-0.338107\pi$
$373$	−1.03845e6	−	1.03845e6i	−0.386469	−	0.386469i	−0.873426	+	0.486957i	$0.838107\pi$
$374$		0			0
$375$	−4.55575e6	+	1.05073e6i	−1.67294	+	0.385846i
$376$		0			0
$377$	3.17137e6	−	3.17137e6i	1.14919	−	1.14919i
$378$		0			0
$379$	−2.06631e6			−0.738921			−0.369461	−	0.929246i	$-0.620458\pi$
$379$	−2.06631e6			−0.738921			−0.369461	+	0.929246i	$0.620458\pi$
$380$		0			0
$381$	2.33714e6			0.824845
$382$		0			0
$383$	413143.	−	413143.i	0.143914	−	0.143914i	−0.631479	−	0.775393i	$-0.717552\pi$
$383$	413143.	−	413143.i	0.143914	−	0.143914i	0.775393	+	0.631479i	$0.217552\pi$
$384$		0			0
$385$	180882.	+	2.38938e6i	0.0621933	+	0.821550i
$386$		0			0
$387$	−1.52958e6	−	1.52958e6i	−0.519152	−	0.519152i
$388$		0			0
$389$		−	2.20146e6i		−	0.737628i	−0.929503	−	0.368814i	$-0.879764\pi$
$389$		−	2.20146e6i		−	0.737628i	0.929503	−	0.368814i	$-0.120236\pi$
$390$		0			0
$391$			6.22522e6i			2.05927i
$392$		0			0
$393$	4.32312e6	+	4.32312e6i	1.41194	+	1.41194i
$394$		0			0
$395$	1.11556e6	−	1.29829e6i	0.359749	−	0.418678i
$396$		0			0
$397$	1.35037e6	−	1.35037e6i	0.430007	−	0.430007i	−0.458624	−	0.888630i	$-0.651657\pi$
$397$	1.35037e6	−	1.35037e6i	0.430007	−	0.430007i	0.888630	+	0.458624i	$0.151657\pi$
$398$		0			0
$399$	−7.67752e6			−2.41428
$400$		0			0
$401$	−478159.			−0.148495			−0.0742474	−	0.997240i	$-0.523655\pi$
$401$	−478159.			−0.148495			−0.0742474	+	0.997240i	$0.523655\pi$
$402$		0			0
$403$	1.89016e6	−	1.89016e6i	0.579742	−	0.579742i
$404$		0			0
$405$	1.81912e6	−	2.11710e6i	0.551092	−	0.641364i
$406$		0			0
$407$	1.38923e6	+	1.38923e6i	0.415707	+	0.415707i
$408$		0			0
$409$		−	1.52948e6i		−	0.452101i	−0.974116	−	0.226051i	$-0.927419\pi$
$409$		−	1.52948e6i		−	0.452101i	0.974116	−	0.226051i	$-0.0725815\pi$
$410$		0			0
$411$			7.63786e6i			2.23032i
$412$		0			0
$413$	−4.42897e6	−	4.42897e6i	−1.27770	−	1.27770i
$414$		0			0
$415$	153231.	+	2.02412e6i	0.0436743	+	0.576921i
$416$		0			0
$417$	−2.32140e6	+	2.32140e6i	−0.653746	+	0.653746i
$418$		0			0
$419$	430992.			0.119932			0.0599658	−	0.998200i	$-0.480901\pi$
$419$	430992.			0.119932			0.0599658	+	0.998200i	$0.480901\pi$
$420$		0			0
$421$	532919.			0.146540			0.0732700	−	0.997312i	$-0.476657\pi$
$421$	532919.			0.146540			0.0732700	+	0.997312i	$0.476657\pi$
$422$		0			0
$423$	2.84042e6	−	2.84042e6i	0.771849	−	0.771849i
$424$		0			0
$425$	−3.91110e6	−	2.87737e6i	−1.05033	−	0.772722i
$426$		0			0
$427$	1.34748e6	+	1.34748e6i	0.357647	+	0.357647i
$428$		0			0
$429$			4.11536e6i			1.07960i
$430$		0			0
$431$		−	2.91761e6i		−	0.756544i	−0.925695	−	0.378272i	$-0.876518\pi$
$431$		−	2.91761e6i		−	0.756544i	0.925695	−	0.378272i	$-0.123482\pi$
$432$		0			0
$433$	2.83132e6	+	2.83132e6i	0.725719	+	0.725719i	0.969764	−	0.244045i	$-0.0784744\pi$
$433$	2.83132e6	+	2.83132e6i	0.725719	+	0.725719i	−0.244045	+	0.969764i	$0.578474\pi$
$434$		0			0
$435$	1.17211e7	−	887314.i	2.96992	−	0.224830i
$436$		0			0
$437$	5.10724e6	−	5.10724e6i	1.27933	−	1.27933i
$438$		0			0
$439$	−3.88608e6			−0.962389			−0.481195	−	0.876614i	$-0.659797\pi$
$439$	−3.88608e6			−0.962389			−0.481195	+	0.876614i	$0.659797\pi$
$440$		0			0
$441$	4.02998e6			0.986748
$442$		0			0
$443$	2.65811e6	−	2.65811e6i	0.643523	−	0.643523i	−0.307897	−	0.951420i	$-0.599625\pi$
$443$	2.65811e6	−	2.65811e6i	0.643523	−	0.643523i	0.951420	+	0.307897i	$0.0996251\pi$
$444$		0			0
$445$	−5.82724e6	−	5.00706e6i	−1.39496	−	1.19862i
$446$		0			0
$447$	7.30194e6	+	7.30194e6i	1.72850	+	1.72850i
$448$		0			0
$449$		−	2.36957e6i		−	0.554695i	−0.960770	−	0.277347i	$-0.910545\pi$
$449$		−	2.36957e6i		−	0.554695i	0.960770	−	0.277347i	$-0.0894553\pi$
$450$		0			0
$451$			446755.i			0.103425i
$452$		0			0
$453$	6.16117e6	+	6.16117e6i	1.41065	+	1.41065i
$454$		0			0
$455$	−3.85149e6	−	3.30939e6i	−0.872168	−	0.749411i
$456$		0			0
$457$	−522790.	+	522790.i	−0.117095	+	0.117095i	−0.763226	−	0.646132i	$-0.776386\pi$
$457$	−522790.	+	522790.i	−0.117095	+	0.117095i	0.646132	+	0.763226i	$0.276386\pi$
$458$		0			0
$459$	9.57557e6			2.12145
$460$		0			0
$461$	−2.50003e6			−0.547890			−0.273945	−	0.961745i	$-0.588329\pi$
$461$	−2.50003e6			−0.547890			−0.273945	+	0.961745i	$0.588329\pi$
$462$		0			0
$463$	−1.66673e6	+	1.66673e6i	−0.361338	+	0.361338i	−0.864306	−	0.502967i	$-0.832242\pi$
$463$	−1.66673e6	+	1.66673e6i	−0.361338	+	0.361338i	0.502967	+	0.864306i	$0.332242\pi$
$464$		0			0
$465$	6.98584e6	−	528845.i	1.49826	−	0.113422i
$466$		0			0
$467$	694126.	+	694126.i	0.147281	+	0.147281i	0.776902	−	0.629621i	$-0.216790\pi$
$467$	694126.	+	694126.i	0.147281	+	0.147281i	−0.629621	+	0.776902i	$0.716790\pi$
$468$		0			0
$469$			9.82047e6i			2.06158i
$470$		0			0
$471$		−	8.24101e6i		−	1.71170i
$472$		0			0
$473$	870588.	+	870588.i	0.178920	+	0.178920i
$474$		0			0
$475$	848085.	+	5.56934e6i	0.172467	+	1.13258i
$476$		0			0
$477$	−2.87549e6	+	2.87549e6i	−0.578650	+	0.578650i
$478$		0			0
$479$	2.67104e6			0.531914			0.265957	−	0.963985i	$-0.414312\pi$
$479$	2.67104e6			0.531914			0.265957	+	0.963985i	$0.414312\pi$
$480$		0			0
$481$	−4.16346e6			−0.820525
$482$		0			0
$483$	−1.20655e7	+	1.20655e7i	−2.35329	+	2.35329i
$484$		0			0
$485$	285891.	+	3.77652e6i	0.0551883	+	0.729016i
$486$		0			0
$487$	3.46493e6	+	3.46493e6i	0.662021	+	0.662021i	0.955856	−	0.293835i	$-0.0949317\pi$
$487$	3.46493e6	+	3.46493e6i	0.662021	+	0.662021i	−0.293835	+	0.955856i	$0.594932\pi$
$488$		0			0
$489$		−	4.87043e6i		−	0.921075i
$490$		0			0
$491$			4.65929e6i			0.872199i	0.899898	+	0.436100i	$0.143640\pi$
$491$			4.65929e6i			0.872199i	−0.899898	+	0.436100i	$0.856360\pi$
$492$		0			0
$493$	8.63205e6	+	8.63205e6i	1.59955	+	1.59955i
$494$		0			0
$495$	−4.64454e6	+	5.40535e6i	−0.851981	+	0.991541i
$496$		0			0
$497$	−792520.	+	792520.i	−0.143919	+	0.143919i
$498$		0			0
$499$	−5.22603e6			−0.939551			−0.469776	−	0.882786i	$-0.655665\pi$
$499$	−5.22603e6			−0.939551			−0.469776	+	0.882786i	$0.655665\pi$
$500$		0			0
$501$	3.19456e6			0.568613
$502$		0			0
$503$	3.92987e6	−	3.92987e6i	0.692561	−	0.692561i	−0.270234	−	0.962795i	$-0.587101\pi$
$503$	3.92987e6	−	3.92987e6i	0.692561	−	0.692561i	0.962795	+	0.270234i	$0.0871010\pi$
$504$		0			0
$505$	1.81459e6	−	2.11183e6i	0.316629	−	0.368494i
$506$		0			0
$507$	859749.	+	859749.i	0.148543	+	0.148543i
$508$		0			0
$509$		−	7.30782e6i		−	1.25024i	−0.780529	−	0.625120i	$-0.785050\pi$
$509$		−	7.30782e6i		−	1.25024i	0.780529	−	0.625120i	$-0.214950\pi$
$510$		0			0
$511$		−	5.50497e6i		−	0.932615i
$512$		0			0
$513$	−7.85591e6	−	7.85591e6i	−1.31796	−	1.31796i
$514$		0			0
$515$	455372.	+	6.01529e6i	0.0756568	+	0.999398i
$516$		0			0
$517$	−1.61668e6	+	1.61668e6i	−0.266010	+	0.266010i
$518$		0			0
$519$	−2.51100e6			−0.409194
$520$		0			0
$521$	3.41968e6			0.551940			0.275970	−	0.961166i	$-0.411001\pi$
$521$	3.41968e6			0.551940			0.275970	+	0.961166i	$0.411001\pi$
$522$		0			0
$523$	7.89585e6	−	7.89585e6i	1.26225	−	1.26225i	0.312248	−	0.950001i	$-0.398918\pi$
$523$	7.89585e6	−	7.89585e6i	1.26225	−	1.26225i	0.950001	−	0.312248i	$-0.101082\pi$
$524$		0			0
$525$	−2.00354e6	−	1.31571e7i	−0.317248	−	2.08335i
$526$		0			0
$527$	5.14476e6	+	5.14476e6i	0.806935	+	0.806935i
$528$		0			0
$529$		−	9.61605e6i		−	1.49402i
$530$		0			0
$531$		−	1.86285e7i		−	2.86709i
$532$		0			0
$533$	−669452.	−	669452.i	−0.102071	−	0.102071i
$534$		0			0
$535$	−6.80512e6	+	515164.i	−1.02790	+	0.0778146i
$536$		0			0
$537$	−7.45424e6	+	7.45424e6i	−1.11550	+	1.11550i
$538$		0			0
$539$	−2.29374e6			−0.340073
$540$		0			0
$541$	3.77154e6			0.554020			0.277010	−	0.960867i	$-0.410656\pi$
$541$	3.77154e6			0.554020			0.277010	+	0.960867i	$0.410656\pi$
$542$		0			0
$543$	−1.11566e7	+	1.11566e7i	−1.62379	+	1.62379i
$544$		0			0
$545$	−3.61511e6	−	3.10629e6i	−0.521351	−	0.447971i
$546$		0			0
$547$	−8.30474e6	−	8.30474e6i	−1.18675	−	1.18675i	−0.977962	−	0.208783i	$-0.933050\pi$
$547$	−8.30474e6	−	8.30474e6i	−1.18675	−	1.18675i	−0.208783	−	0.977962i	$-0.566950\pi$
$548$		0			0
$549$			5.66760e6i			0.802543i
$550$		0			0
$551$		−	1.41637e7i		−	1.98745i
$552$		0			0
$553$	3.44546e6	+	3.44546e6i	0.479109	+	0.479109i
$554$		0			0
$555$	−8.27632e6	−	7.11143e6i	−1.14053	−	0.979996i
$556$		0			0
$557$	−3.82357e6	+	3.82357e6i	−0.522193	+	0.522193i	−0.918233	−	0.396040i	$-0.870384\pi$
$557$	−3.82357e6	+	3.82357e6i	−0.522193	+	0.522193i	0.396040	+	0.918233i	$0.370384\pi$
$558$		0			0
$559$	−2.60912e6			−0.353154
$560$		0			0
$561$	−1.12015e7			−1.50269
$562$		0			0
$563$	7.83668e6	−	7.83668e6i	1.04198	−	1.04198i	0.0429050	−	0.999079i	$-0.486339\pi$
$563$	7.83668e6	−	7.83668e6i	1.04198	−	1.04198i	0.999079	−	0.0429050i	$-0.0136613\pi$
$564$		0			0
$565$	1.18689e7	−	898506.i	1.56419	−	0.118413i
$566$		0			0
$567$	5.61844e6	+	5.61844e6i	0.733936	+	0.733936i
$568$		0			0
$569$			1.06662e7i			1.38111i	0.723280	+	0.690555i	$0.242634\pi$
$569$			1.06662e7i			1.38111i	−0.723280	+	0.690555i	$0.757366\pi$
$570$		0			0
$571$			103844.i			0.0133288i	0.999978	+	0.00666439i	$0.00212136\pi$
$571$			103844.i			0.0133288i	−0.999978	+	0.00666439i	$0.997879\pi$
$572$		0			0
$573$	−2.77349e6	−	2.77349e6i	−0.352891	−	0.352891i
$574$		0			0
$575$	1.00852e7	+	7.41960e6i	1.27208	+	0.935861i
$576$		0			0
$577$	5.35378e6	−	5.35378e6i	0.669455	−	0.669455i	−0.288135	−	0.957590i	$-0.593035\pi$
$577$	5.35378e6	−	5.35378e6i	0.669455	−	0.669455i	0.957590	+	0.288135i	$0.0930352\pi$
$578$		0			0
$579$	−2.46014e7			−3.04974
$580$		0			0
$581$	−5.77833e6			−0.710170
$582$		0			0
$583$	1.63664e6	−	1.63664e6i	0.199426	−	0.199426i
$584$		0			0
$585$	−1.14004e6	−	1.50596e7i	−0.137731	−	1.81938i
$586$		0			0
$587$	−3.02584e6	−	3.02584e6i	−0.362453	−	0.362453i	0.502263	−	0.864715i	$-0.332501\pi$
$587$	−3.02584e6	−	3.02584e6i	−0.362453	−	0.362453i	−0.864715	+	0.502263i	$0.832501\pi$
$588$		0			0
$589$		−	8.44164e6i		−	1.00263i
$590$		0			0
$591$		−	1.83522e7i		−	2.16133i
$592$		0			0
$593$	7.77341e6	+	7.77341e6i	0.907768	+	0.907768i	0.996092	−	0.0883240i	$-0.0281511\pi$
$593$	7.77341e6	+	7.77341e6i	0.907768	+	0.907768i	−0.0883240	+	0.996092i	$0.528151\pi$
$594$		0			0
$595$	9.00774e6	−	1.04833e7i	1.04309	−	1.21396i
$596$		0			0
$597$	−1.37845e7	+	1.37845e7i	−1.58290	+	1.58290i
$598$		0			0
$599$	396440.			0.0451451			0.0225726	−	0.999745i	$-0.492814\pi$
$599$	396440.			0.0451451			0.0225726	+	0.999745i	$0.492814\pi$
$600$		0			0
$601$	−3.27167e6			−0.369474			−0.184737	−	0.982788i	$-0.559143\pi$
$601$	−3.27167e6			−0.369474			−0.184737	+	0.982788i	$0.559143\pi$
$602$		0			0
$603$	−2.06527e7	+	2.06527e7i	−2.31305	+	2.31305i
$604$		0			0
$605$	−3.22385e6	+	3.75194e6i	−0.358086	+	0.416742i
$606$		0			0
$607$	7.39370e6	+	7.39370e6i	0.814498	+	0.814498i	0.985305	−	0.170807i	$-0.0546374\pi$
$607$	7.39370e6	+	7.39370e6i	0.814498	+	0.814498i	−0.170807	+	0.985305i	$0.554637\pi$
$608$		0			0
$609$			3.34606e7i			3.65587i
$610$		0			0
$611$		−	4.84512e6i		−	0.525051i
$612$		0			0
$613$	−3.55531e6	−	3.55531e6i	−0.382143	−	0.382143i	0.489730	−	0.871874i	$-0.337095\pi$
$613$	−3.55531e6	−	3.55531e6i	−0.382143	−	0.382143i	−0.871874	+	0.489730i	$0.837095\pi$
$614$		0			0
$615$	−187305.	−	2.47423e6i	−0.0199693	−	0.263787i
$616$		0			0
$617$	3.25539e6	−	3.25539e6i	0.344263	−	0.344263i	−0.513704	−	0.857967i	$-0.671727\pi$
$617$	3.25539e6	−	3.25539e6i	0.344263	−	0.344263i	0.857967	+	0.513704i	$0.171727\pi$
$618$		0			0
$619$	1.78255e7			1.86989			0.934943	−	0.354798i	$-0.115450\pi$
$619$	1.78255e7			1.86989			0.934943	+	0.354798i	$0.115450\pi$
$620$		0			0
$621$	−2.46916e7			−2.56933
$622$		0			0
$623$	1.54645e7	−	1.54645e7i	1.59631	−	1.59631i
$624$		0			0
$625$	−9.32299e6	+	2.90677e6i	−0.954674	+	0.297653i
$626$		0			0
$627$	9.18982e6	+	9.18982e6i	0.933551	+	0.933551i
$628$		0			0
$629$		−	1.13324e7i		−	1.14208i
$630$		0			0
$631$			1.77949e7i			1.77919i	0.456754	+	0.889593i	$0.349012\pi$
$631$			1.77949e7i			1.77919i	−0.456754	+	0.889593i	$0.650988\pi$
$632$		0			0
$633$	7.49866e6	+	7.49866e6i	0.743831	+	0.743831i
$634$		0			0
$635$	4.86777e6	−	368502.i	0.479066	−	0.0362665i
$636$		0			0
$637$	3.43712e6	−	3.43712e6i	0.335618	−	0.335618i
$638$		0			0
$639$	−3.33339e6			−0.322949
$640$		0			0
$641$	−3.48962e6			−0.335454			−0.167727	−	0.985833i	$-0.553643\pi$
$641$	−3.48962e6			−0.335454			−0.167727	+	0.985833i	$0.553643\pi$
$642$		0			0
$643$	−9.79073e6	+	9.79073e6i	−0.933873	+	0.933873i	−0.997945	−	0.0640725i	$-0.979591\pi$
$643$	−9.79073e6	+	9.79073e6i	−0.933873	+	0.933873i	0.0640725	+	0.997945i	$0.479591\pi$
$644$		0			0
$645$	−5.18652e6	−	4.45652e6i	−0.490882	−	0.421790i
$646$		0			0
$647$	−9.53507e6	−	9.53507e6i	−0.895495	−	0.895495i	0.0995389	−	0.995034i	$-0.468263\pi$
$647$	−9.53507e6	−	9.53507e6i	−0.895495	−	0.895495i	−0.995034	+	0.0995389i	$0.968263\pi$
$648$		0			0
$649$			1.06028e7i			0.988114i
$650$		0			0
$651$			1.99427e7i			1.84430i
$652$		0			0
$653$	1.15953e7	+	1.15953e7i	1.06414	+	1.06414i	0.997797	+	0.0663484i	$0.0211349\pi$
$653$	1.15953e7	+	1.15953e7i	1.06414	+	1.06414i	0.0663484	+	0.997797i	$0.478865\pi$
$654$		0			0
$655$	9.68577e6	+	8.32250e6i	0.882127	+	0.757968i
$656$		0			0
$657$	1.15771e7	−	1.15771e7i	1.04637	−	1.04637i
$658$		0			0
$659$	−6.06117e6			−0.543679			−0.271840	−	0.962343i	$-0.587632\pi$
$659$	−6.06117e6			−0.543679			−0.271840	+	0.962343i	$0.587632\pi$
$660$		0			0
$661$	4.27293e6			0.380384			0.190192	−	0.981747i	$-0.439089\pi$
$661$	4.27293e6			0.380384			0.190192	+	0.981747i	$0.439089\pi$
$662$		0			0
$663$	1.67852e7	−	1.67852e7i	1.48300	−	1.48300i
$664$		0			0
$665$	−1.59906e7	+	1.21053e6i	−1.40221	+	0.106150i
$666$		0			0
$667$	−2.22587e7	−	2.22587e7i	−1.93724	−	1.93724i
$668$		0			0
$669$			1.44912e7i			1.25181i
$670$		0			0
$671$		−	3.22582e6i		−	0.276588i
$672$		0			0
$673$	5.55486e6	+	5.55486e6i	0.472755	+	0.472755i	0.902805	−	0.430050i	$-0.141504\pi$
$673$	5.55486e6	+	5.55486e6i	0.472755	+	0.472755i	−0.430050	+	0.902805i	$0.641504\pi$
$674$		0			0
$675$	1.14128e7	−	1.55129e7i	0.964121	−	1.31049i
$676$		0			0
$677$	1.30293e7	−	1.30293e7i	1.09257	−	1.09257i	0.0973148	−	0.995254i	$-0.468975\pi$
$677$	1.30293e7	−	1.30293e7i	1.09257	−	1.09257i	0.995254	−	0.0973148i	$-0.0310253\pi$
$678$		0			0
$679$	−1.07810e7			−0.897393
$680$		0			0
$681$	1.59124e7			1.31483
$682$		0			0
$683$	−378888.	+	378888.i	−0.0310784	+	0.0310784i	−0.722475	−	0.691397i	$-0.756996\pi$
$683$	−378888.	+	378888.i	−0.0310784	+	0.0310784i	0.691397	+	0.722475i	$0.256996\pi$
$684$		0			0
$685$	1.20428e6	+	1.59081e7i	0.0980619	+	1.29536i
$686$		0			0
$687$	1.59512e7	+	1.59512e7i	1.28944	+	1.28944i
$688$		0			0
$689$			4.90494e6i			0.393628i
$690$		0			0
$691$		−	2.01178e7i		−	1.60282i	−0.598113	−	0.801412i	$-0.704083\pi$
$691$		−	2.01178e7i		−	1.60282i	0.598113	−	0.801412i	$-0.295917\pi$
$692$		0			0
$693$	−1.43449e7	−	1.43449e7i	−1.13466	−	1.13466i
$694$		0			0
$695$	−4.46896e6	+	5.20100e6i	−0.350949	+	0.408437i
$696$		0			0
$697$	1.82216e6	−	1.82216e6i	0.142071	−	0.142071i
$698$		0			0
$699$	1.36897e6			0.105974
$700$		0			0
$701$	891657.			0.0685335			0.0342667	−	0.999413i	$-0.489090\pi$
$701$	891657.			0.0685335			0.0342667	+	0.999413i	$0.489090\pi$
$702$		0			0
$703$	−9.29723e6	+	9.29723e6i	−0.709521	+	0.709521i
$704$		0			0
$705$	8.27575e6	−	9.63136e6i	0.627097	−	0.729818i
$706$		0			0
$707$	5.60445e6	+	5.60445e6i	0.421682	+	0.421682i
$708$		0			0
$709$		−	1.98980e7i		−	1.48660i	−0.668959	−	0.743299i	$-0.733260\pi$
$709$		−	1.98980e7i		−	1.48660i	0.668959	−	0.743299i	$-0.266740\pi$
$710$		0			0
$711$			1.44918e7i			1.07510i
$712$		0			0
$713$	−1.32663e7	−	1.32663e7i	−0.977296	−	0.977296i
$714$		0			0
$715$	648877.	+	8.57142e6i	0.0474676	+	0.627029i
$716$		0			0
$717$	5.17644e6	−	5.17644e6i	0.376040	−	0.376040i
$718$		0			0
$719$	−1.06358e7			−0.767272			−0.383636	−	0.923484i	$-0.625328\pi$
$719$	−1.06358e7			−0.767272			−0.383636	+	0.923484i	$0.625328\pi$
$720$		0			0
$721$	−1.71721e7			−1.23022
$722$		0			0
$723$	−1.70570e7	+	1.70570e7i	−1.21355	+	1.21355i
$724$		0			0
$725$	2.42726e7	−	3.69617e6i	1.71503	−	0.261160i
$726$		0			0
$727$	−3.76230e6	−	3.76230e6i	−0.264008	−	0.264008i	0.562672	−	0.826680i	$-0.309773\pi$
$727$	−3.76230e6	−	3.76230e6i	−0.264008	−	0.264008i	−0.826680	+	0.562672i	$0.809773\pi$
$728$		0			0
$729$		−	1.64482e7i		−	1.14631i
$730$		0			0
$731$		−	7.10167e6i		−	0.491550i
$732$		0			0
$733$	1.16678e7	+	1.16678e7i	0.802104	+	0.802104i	0.983424	−	0.181320i	$-0.0580369\pi$
$733$	1.16678e7	+	1.16678e7i	0.802104	+	0.802104i	−0.181320	+	0.983424i	$0.558037\pi$
$734$		0			0
$735$	1.27033e7	−	961668.i	0.867355	−	0.0656609i
$736$		0			0
$737$	1.17549e7	−	1.17549e7i	0.797167	−	0.797167i
$738$		0			0
$739$	−1.52408e6			−0.102659			−0.0513296	−	0.998682i	$-0.516346\pi$
$739$	−1.52408e6			−0.102659			−0.0513296	+	0.998682i	$0.516346\pi$
$740$		0			0
$741$	−2.75415e7			−1.84265
$742$		0			0
$743$	−5.92734e6	+	5.92734e6i	−0.393901	+	0.393901i	−0.876075	−	0.482174i	$-0.839847\pi$
$743$	−5.92734e6	+	5.92734e6i	−0.393901	+	0.393901i	0.482174	+	0.876075i	$0.339847\pi$
$744$		0			0
$745$	1.63597e7	+	1.40571e7i	1.07990	+	0.927907i
$746$		0			0
$747$	−1.21520e7	−	1.21520e7i	−0.796795	−	0.796795i
$748$		0			0
$749$		−	1.94268e7i		−	1.26531i
$750$		0			0
$751$		−	1.28380e7i		−	0.830614i	−0.909681	−	0.415307i	$-0.863674\pi$
$751$		−	1.28380e7i		−	0.830614i	0.909681	−	0.415307i	$-0.136326\pi$
$752$		0			0
$753$	−2.49460e7	−	2.49460e7i	−1.60330	−	1.60330i
$754$		0			0
$755$	1.38039e7	+	1.18610e7i	0.881319	+	0.757274i
$756$		0			0
$757$	9.71886e6	−	9.71886e6i	0.616418	−	0.616418i	−0.328192	−	0.944611i	$-0.606439\pi$
$757$	9.71886e6	−	9.71886e6i	0.616418	−	0.616418i	0.944611	+	0.328192i	$0.106439\pi$
$758$		0			0
$759$	2.88842e7			1.81993
$760$		0			0
$761$	−2.02827e7			−1.26959			−0.634795	−	0.772680i	$-0.718916\pi$
$761$	−2.02827e7			−1.26959			−0.634795	+	0.772680i	$0.718916\pi$
$762$		0			0
$763$	9.59391e6	−	9.59391e6i	0.596602	−	0.596602i
$764$		0			0
$765$	4.09902e7	−	3.10305e6i	2.53236	−	0.191706i
$766$		0			0
$767$	−1.58880e7	−	1.58880e7i	−0.975171	−	0.975171i
$768$		0			0
$769$			4.07161e6i			0.248285i	0.992264	+	0.124142i	$0.0396180\pi$
$769$			4.07161e6i			0.248285i	−0.992264	+	0.124142i	$0.960382\pi$
$770$		0			0
$771$			2.58928e7i			1.56871i
$772$		0			0
$773$	1.88515e7	+	1.88515e7i	1.13474	+	1.13474i	0.989378	+	0.145362i	$0.0464348\pi$
$773$	1.88515e7	+	1.88515e7i	1.13474	+	1.13474i	0.145362	+	0.989378i	$0.453565\pi$
$774$		0			0
$775$	1.44666e7	−	2.20294e6i	0.865194	−	0.131750i
$776$		0			0
$777$	2.19640e7	−	2.19640e7i	1.30514	−	1.30514i
$778$		0			0
$779$	−2.98985e6			−0.176525
$780$		0			0
$781$	1.89726e6			0.111301
$782$		0			0
$783$	−3.42381e7	+	3.42381e7i	−1.99574	+	1.99574i
$784$		0			0
$785$	−1.29938e6	−	1.71643e7i	−0.0752595	−	0.994148i
$786$		0			0
$787$	1.81274e6	+	1.81274e6i	0.104327	+	0.104327i	0.757344	−	0.653016i	$-0.226497\pi$
$787$	1.81274e6	+	1.81274e6i	0.104327	+	0.104327i	−0.653016	+	0.757344i	$0.726497\pi$
$788$		0			0
$789$			3.68915e7i			2.10976i
$790$		0			0
$791$			3.38826e7i			1.92547i
$792$		0			0
$793$	4.83382e6	+	4.83382e6i	0.272966	+	0.272966i
$794$		0			0
$795$	−8.37792e6	+	9.75027e6i	−0.470130	+	0.547140i
$796$		0			0
$797$	−1.40418e7	+	1.40418e7i	−0.783027	+	0.783027i	−0.980341	−	0.197313i	$-0.936778\pi$
$797$	−1.40418e7	+	1.40418e7i	−0.783027	+	0.783027i	0.197313	+	0.980341i	$0.436778\pi$
$798$		0			0
$799$	1.31878e7			0.730811
$800$		0			0
$801$	6.50448e7			3.58204
$802$		0			0
$803$	−6.58933e6	+	6.58933e6i	−0.360622	+	0.360622i
$804$		0			0
$805$	−2.32274e7	+	2.70322e7i	−1.26331	+	1.47025i
$806$		0			0
$807$	1.46678e7	+	1.46678e7i	0.792833	+	0.792833i
$808$		0			0
$809$			5.17254e6i			0.277864i	0.990302	+	0.138932i	$0.0443670\pi$
$809$			5.17254e6i			0.277864i	−0.990302	+	0.138932i	$0.955633\pi$
$810$		0			0
$811$			7.42351e6i			0.396330i	0.980169	+	0.198165i	$0.0634982\pi$
$811$			7.42351e6i			0.396330i	−0.980169	+	0.198165i	$0.936502\pi$
$812$		0			0
$813$	1.94899e6	+	1.94899e6i	0.103415	+	0.103415i
$814$		0			0
$815$	−767931.	−	1.01441e7i	−0.0404975	−	0.534956i
$816$		0			0
$817$	−5.82630e6	+	5.82630e6i	−0.305378	+	0.305378i
$818$		0			0
$819$	4.29911e7			2.23959
$820$		0			0
$821$	8.07068e6			0.417881			0.208940	−	0.977928i	$-0.432999\pi$
$821$	8.07068e6			0.417881			0.208940	+	0.977928i	$0.432999\pi$
$822$		0			0
$823$	−4.89931e6	+	4.89931e6i	−0.252136	+	0.252136i	−0.821846	−	0.569710i	$-0.807056\pi$
$823$	−4.89931e6	+	4.89931e6i	−0.252136	+	0.252136i	0.569710	+	0.821846i	$0.307056\pi$
$824$		0			0
$825$	−1.33506e7	+	1.81470e7i	−0.682915	+	0.928260i
$826$		0			0
$827$	1.10433e7	+	1.10433e7i	0.561482	+	0.561482i	0.929728	−	0.368247i	$-0.120042\pi$
$827$	1.10433e7	+	1.10433e7i	0.561482	+	0.561482i	−0.368247	+	0.929728i	$0.620042\pi$
$828$		0			0
$829$		−	9.14531e6i		−	0.462181i	−0.972932	−	0.231091i	$-0.925771\pi$
$829$		−	9.14531e6i		−	0.462181i	0.972932	−	0.231091i	$-0.0742294\pi$
$830$		0			0
$831$		−	5.53778e7i		−	2.78185i
$832$		0			0
$833$	9.35539e6	+	9.35539e6i	0.467142	+	0.467142i
$834$		0			0
$835$	6.65359e6	−	503693.i	0.330248	−	0.0250005i
$836$		0			0
$837$	−2.04061e7	+	2.04061e7i	−1.00681	+	1.00681i
$838$		0			0
$839$	6.10920e6			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$839$	6.10920e6			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$840$		0			0
$841$	−4.12177e7			−2.00953
$842$		0			0
$843$	3.20432e7	−	3.20432e7i	1.55298	−	1.55298i
$844$		0			0
$845$	1.92623e6	+	1.65512e6i	0.0928041	+	0.0797419i
$846$		0			0
$847$	−9.95703e6	−	9.95703e6i	−0.476893	−	0.476893i
$848$		0			0
$849$		−	2.54871e6i		−	0.121353i
$850$		0			0
$851$			2.92218e7i			1.38319i
$852$		0			0
$853$	−1.91716e7	−	1.91716e7i	−0.902162	−	0.902162i	0.0934606	−	0.995623i	$-0.470207\pi$
$853$	−1.91716e7	−	1.91716e7i	−0.902162	−	0.902162i	−0.995623	+	0.0934606i	$0.970207\pi$
$854$		0			0
$855$	−3.61746e7	−	3.10830e7i	−1.69234	−	1.45415i
$856$		0			0
$857$	−6.93923e6	+	6.93923e6i	−0.322745	+	0.322745i	−0.849819	−	0.527074i	$-0.823289\pi$
$857$	−6.93923e6	+	6.93923e6i	−0.322745	+	0.322745i	0.527074	+	0.849819i	$0.323289\pi$
$858$		0			0
$859$	2.45235e7			1.13396			0.566981	−	0.823731i	$-0.308111\pi$
$859$	2.45235e7			1.13396			0.566981	+	0.823731i	$0.308111\pi$
$860$		0			0
$861$	7.06328e6			0.324712
$862$		0			0
$863$	6.42655e6	−	6.42655e6i	0.293732	−	0.293732i	−0.544821	−	0.838552i	$-0.683402\pi$
$863$	6.42655e6	−	6.42655e6i	0.293732	−	0.293732i	0.838552	+	0.544821i	$0.183402\pi$
$864$		0			0
$865$	−5.22989e6	+	395916.i	−0.237658	+	0.0179913i
$866$		0			0
$867$	1.88170e7	+	1.88170e7i	0.850165	+	0.850165i
$868$		0			0
$869$		−	8.24828e6i		−	0.370522i
$870$		0			0
$871$			3.52289e7i			1.57345i
$872$		0			0
$873$	−2.26727e7	−	2.26727e7i	−1.00686	−	1.00686i
$874$		0			0
$875$	−6.24746e6	−	2.70876e7i	−0.275856	−	1.19605i
$876$		0			0
$877$	2.15276e7	−	2.15276e7i	0.945142	−	0.945142i	−0.0534292	−	0.998572i	$-0.517015\pi$
$877$	2.15276e7	−	2.15276e7i	0.945142	−	0.945142i	0.998572	+	0.0534292i	$0.0170151\pi$
$878$		0			0
$879$	−1.29667e7			−0.566055
$880$		0			0
$881$	3.72835e7			1.61836			0.809182	−	0.587558i	$-0.199910\pi$
$881$	3.72835e7			1.61836			0.809182	+	0.587558i	$0.199910\pi$
$882$		0			0
$883$	6.55054e6	−	6.55054e6i	0.282732	−	0.282732i	−0.551465	−	0.834198i	$-0.685931\pi$
$883$	6.55054e6	−	6.55054e6i	0.282732	−	0.282732i	0.834198	+	0.551465i	$0.185931\pi$
$884$		0			0
$885$	−4.44529e6	−	5.87206e7i	−0.190784	−	2.52018i
$886$		0			0
$887$	3.51685e6	+	3.51685e6i	0.150087	+	0.150087i	0.778157	−	0.628070i	$-0.216155\pi$
$887$	3.51685e6	+	3.51685e6i	0.150087	+	0.150087i	−0.628070	+	0.778157i	$0.716155\pi$
$888$		0			0
$889$			1.38962e7i			0.589714i
$890$		0			0
$891$		−	1.34503e7i		−	0.567594i
$892$		0			0
$893$	−1.08194e7	−	1.08194e7i	−0.454020	−	0.454020i
$894$		0			0
$895$	−1.43503e7	+	1.67009e7i	−0.598829	+	0.696920i
$896$		0			0
$897$	−4.32824e7	+	4.32824e7i	−1.79610	+	1.79610i
$898$		0			0
$899$	−3.67908e7			−1.51824
$900$		0			0
$901$	−1.33506e7			−0.547884
$902$		0			0
$903$	1.37642e7	−	1.37642e7i	0.561734	−	0.561734i
$904$		0			0
$905$	−2.14777e7	+	2.49958e7i	−0.871698	+	1.01449i
$906$		0			0
$907$	−7.47394e6	−	7.47394e6i	−0.301670	−	0.301670i	0.539997	−	0.841667i	$-0.318425\pi$
$907$	−7.47394e6	−	7.47394e6i	−0.301670	−	0.301670i	−0.841667	+	0.539997i	$0.818425\pi$
$908$		0			0
$909$			2.35727e7i			0.946235i
$910$		0			0
$911$		−	2.11403e6i		−	0.0843949i	−0.999109	−	0.0421974i	$-0.986564\pi$
$911$		−	2.11403e6i		−	0.0843949i	0.999109	−	0.0421974i	$-0.0134358\pi$
$912$		0			0
$913$	6.91654e6	+	6.91654e6i	0.274607	+	0.274607i
$914$		0			0
$915$	1.35245e6	+	1.78654e7i	0.0534034	+	0.705438i
$916$		0			0
$917$	−2.57044e7	+	2.57044e7i	−1.00945	+	1.00945i
$918$		0			0
$919$	−3.25445e7			−1.27113			−0.635564	−	0.772049i	$-0.719232\pi$
$919$	−3.25445e7			−1.27113			−0.635564	+	0.772049i	$0.719232\pi$
$920$		0			0
$921$	316846.			0.0123083
$922$		0			0
$923$	−2.84300e6	+	2.84300e6i	−0.109843	+	0.109843i
$924$		0			0
$925$	−1.83591e7	−	1.35067e7i	−0.705500	−	0.519031i
$926$		0			0
$927$	−3.61134e7	−	3.61134e7i	−1.38028	−	1.38028i
$928$		0			0
$929$			3.59514e6i			0.136671i	0.997662	+	0.0683354i	$0.0217688\pi$
$929$			3.59514e6i			0.136671i	−0.997662	+	0.0683354i	$0.978231\pi$
$930$		0			0
$931$		−	1.53505e7i		−	0.580430i
$932$		0			0
$933$	2.12845e6	+	2.12845e6i	0.0800494	+	0.0800494i
$934$		0			0
$935$	−2.33303e7	+	1.76616e6i	−0.872753	+	0.0660695i
$936$		0			0
$937$	2.34165e7	−	2.34165e7i	0.871312	−	0.871312i	−0.121303	−	0.992616i	$-0.538707\pi$
$937$	2.34165e7	−	2.34165e7i	0.871312	−	0.871312i	0.992616	+	0.121303i	$0.0387073\pi$
$938$		0			0
$939$	−3.53089e7			−1.30683
$940$		0			0
$941$	2.41809e7			0.890221			0.445111	−	0.895476i	$-0.353164\pi$
$941$	2.41809e7			0.890221			0.445111	+	0.895476i	$0.353164\pi$
$942$		0			0
$943$	−4.69864e6	+	4.69864e6i	−0.172065	+	0.172065i
$944$		0			0
$945$	4.15807e7	+	3.57282e7i	1.51465	+	1.30146i
$946$		0			0
$947$	4.13320e6	+	4.13320e6i	0.149765	+	0.149765i	0.778013	−	0.628248i	$-0.216228\pi$
$947$	4.13320e6	+	4.13320e6i	0.149765	+	0.149765i	−0.628248	+	0.778013i	$0.716228\pi$
$948$		0			0
$949$		−	1.97479e7i		−	0.711797i
$950$		0			0
$951$		−	4.71327e7i		−	1.68994i
$952$		0			0
$953$	2.17837e7	+	2.17837e7i	0.776961	+	0.776961i	0.979313	−	0.202352i	$-0.0648584\pi$
$953$	2.17837e7	+	2.17837e7i	0.776961	+	0.776961i	−0.202352	+	0.979313i	$0.564858\pi$
$954$		0			0
$955$	−6.21390e6	−	5.33930e6i	−0.220473	−	0.189442i
$956$		0			0
$957$	4.00516e7	−	4.00516e7i	1.41364	−	1.41364i
$958$		0			0
$959$	−4.54133e7			−1.59454
$960$		0			0
$961$	6.70158e6			0.234082
$962$		0			0
$963$	4.08552e7	−	4.08552e7i	1.41965	−	1.41965i
$964$		0			0
$965$	−5.12394e7	+	3.87895e6i	−1.77128	+	0.134090i
$966$		0			0
$967$	−1.19376e7	−	1.19376e7i	−0.410537	−	0.410537i	0.471389	−	0.881925i	$-0.343753\pi$
$967$	−1.19376e7	−	1.19376e7i	−0.410537	−	0.410537i	−0.881925	+	0.471389i	$0.843753\pi$
$968$		0			0
$969$		−	7.49644e7i		−	2.56475i
$970$		0			0
$971$			3.44007e7i			1.17090i	0.810709	+	0.585449i	$0.199082\pi$
$971$			3.44007e7i			1.17090i	−0.810709	+	0.585449i	$0.800918\pi$
$972$		0			0
$973$	−1.38026e7	−	1.38026e7i	−0.467389	−	0.467389i
$974$		0			0
$975$	−7.18727e6	−	4.71985e7i	−0.242132	−	1.59007i
$976$		0			0
$977$	−2.17722e7	+	2.17722e7i	−0.729735	+	0.729735i	−0.970567	−	0.240832i	$-0.922580\pi$
$977$	−2.17722e7	+	2.17722e7i	−0.729735	+	0.729735i	0.240832	+	0.970567i	$0.422580\pi$
$978$		0			0
$979$	−3.70214e7			−1.23451
$980$		0			0
$981$	4.03526e7			1.33875
$982$		0			0
$983$	2.19706e7	−	2.19706e7i	0.725202	−	0.725202i	−0.244458	−	0.969660i	$-0.578610\pi$
$983$	2.19706e7	−	2.19706e7i	0.725202	−	0.725202i	0.969660	+	0.244458i	$0.0786100\pi$
$984$		0			0
$985$	−2.89364e6	−	3.82238e7i	−0.0950284	−	1.25529i
$986$		0			0
$987$	2.55600e7	+	2.55600e7i	0.835158	+	0.835158i
$988$		0			0
$989$			1.83124e7i			0.595326i
$990$		0			0
$991$			4.31203e7i			1.39475i	0.716704	+	0.697377i	$0.245650\pi$
$991$			4.31203e7i			1.39475i	−0.716704	+	0.697377i	$0.754350\pi$
$992$		0			0
$993$	1.05636e7	+	1.05636e7i	0.339968	+	0.339968i
$994$		0			0
$995$	−2.65367e7	+	3.08836e7i	−0.849747	+	0.988940i
$996$		0			0
$997$	−2.23176e7	+	2.23176e7i	−0.711065	+	0.711065i	−0.966758	−	0.255693i	$-0.917696\pi$
$997$	−2.23176e7	+	2.23176e7i	−0.711065	+	0.711065i	0.255693	+	0.966758i	$0.417696\pi$
$998$		0			0
$999$	4.49487e7			1.42496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.a.63.1	✓	14
4.3	odd	2		160.6.n.b.63.7	yes	14
5.2	odd	4		160.6.n.b.127.7	yes	14
20.7	even	4	inner	160.6.n.a.127.1	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.a.63.1	✓	14	1.1	even	1	trivial
160.6.n.a.127.1	yes	14	20.7	even	4	inner
160.6.n.b.63.7	yes	14	4.3	odd	2
160.6.n.b.127.7	yes	14	5.2	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-18.9245 + 18.9245i) q^{3} +(-36.4318 + 42.3996i) q^{5} +(-112.521 - 112.521i) q^{7} -473.272i q^{9} +O(q^{10})\)	\(q+(-18.9245 + 18.9245i) q^{3} +(-36.4318 + 42.3996i) q^{5} +(-112.521 - 112.521i) q^{7} -473.272i q^{9} +269.371i q^{11} +(-403.647 - 403.647i) q^{13} +(-112.936 - 1491.84i) q^{15} +(1098.68 - 1098.68i) q^{17} -1802.73 q^{19} +4258.82 q^{21} +(-2833.05 + 2833.05i) q^{23} +(-470.444 - 3089.39i) q^{25} +(4357.78 + 4357.78i) q^{27} +7856.77i q^{29} +4682.69i q^{31} +(-5097.71 - 5097.71i) q^{33} +(8870.22 - 671.497i) q^{35} +(5157.30 - 5157.30i) q^{37} +15277.6 q^{39} +1658.51 q^{41} +(3231.92 - 3231.92i) q^{43} +(20066.5 + 17242.2i) q^{45} +(6001.67 + 6001.67i) q^{47} +8515.15i q^{49} +41583.7i q^{51} +(-6075.77 - 6075.77i) q^{53} +(-11421.2 - 9813.69i) q^{55} +(34115.8 - 34115.8i) q^{57} +39361.1 q^{59} -11975.4 q^{61} +(-53253.2 + 53253.2i) q^{63} +(31820.1 - 2408.86i) q^{65} +(-43638.2 - 43638.2i) q^{67} -107228. i q^{69} -7043.28i q^{71} +(24461.9 + 24461.9i) q^{73} +(67367.9 + 49562.1i) q^{75} +(30310.1 - 30310.1i) q^{77} -30620.5 q^{79} -49932.2 q^{81} +(25676.6 - 25676.6i) q^{83} +(6556.60 + 86610.2i) q^{85} +(-148685. - 148685. i) q^{87} +137436. i q^{89} +90838.0i q^{91} +(-88617.5 - 88617.5i) q^{93} +(65676.9 - 76435.1i) q^{95} +(47906.2 - 47906.2i) q^{97} +127486. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7}+O(q^{10}) \) 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7	\( 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7} - 414 q^{13} - 278 q^{15} + 1222 q^{17} - 5672 q^{19} + 5924 q^{21} - 2902 q^{23} - 4466 q^{25} + 2168 q^{27} - 2444 q^{33} + 2618 q^{35} - 1790 q^{37} + 11076 q^{39} + 11644 q^{41} + 3982 q^{43} + 14704 q^{45} + 1278 q^{47} + 5882 q^{53} - 65608 q^{55} - 14552 q^{57} + 8504 q^{59} + 20564 q^{61} - 19422 q^{63} + 40798 q^{65} - 107926 q^{67} - 16418 q^{73} - 66586 q^{75} - 13348 q^{77} + 146544 q^{79} + 173806 q^{81} + 36398 q^{83} - 66262 q^{85} - 124384 q^{87} - 306620 q^{93} - 173768 q^{95} - 60314 q^{97} + 388628 q^{99}+O(q^{100}) \) 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7 - 414 * q^13 - 278 * q^15 + 1222 * q^17 - 5672 * q^19 + 5924 * q^21 - 2902 * q^23 - 4466 * q^25 + 2168 * q^27 - 2444 * q^33 + 2618 * q^35 - 1790 * q^37 + 11076 * q^39 + 11644 * q^41 + 3982 * q^43 + 14704 * q^45 + 1278 * q^47 + 5882 * q^53 - 65608 * q^55 - 14552 * q^57 + 8504 * q^59 + 20564 * q^61 - 19422 * q^63 + 40798 * q^65 - 107926 * q^67 - 16418 * q^73 - 66586 * q^75 - 13348 * q^77 + 146544 * q^79 + 173806 * q^81 + 36398 * q^83 - 66262 * q^85 - 124384 * q^87 - 306620 * q^93 - 173768 * q^95 - 60314 * q^97 + 388628 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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