LMFDB - Embedded newform 160.6.n.a.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			127.3
Root			$4.57273 - 4.57273i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.6.n.a.63.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.28112 - 9.28112i) q^{3} +(42.6946 - 36.0856i) q^{5} +(105.819 - 105.819i) q^{7} -70.7216i q^{9} +O(q^{10})$	\(q+(-9.28112 - 9.28112i) q^{3} +(42.6946 - 36.0856i) q^{5} +(105.819 - 105.819i) q^{7} -70.7216i q^{9} +344.770i q^{11} +(707.360 - 707.360i) q^{13} +(-731.169 - 61.3385i) q^{15} +(1263.06 + 1263.06i) q^{17} -438.382 q^{19} -1964.24 q^{21} +(1722.78 + 1722.78i) q^{23} +(520.655 - 3081.32i) q^{25} +(-2911.69 + 2911.69i) q^{27} -2513.02i q^{29} -7145.63i q^{31} +(3199.85 - 3199.85i) q^{33} +(699.354 - 8336.45i) q^{35} +(-3361.24 - 3361.24i) q^{37} -13130.2 q^{39} +6969.83 q^{41} +(-16311.3 - 16311.3i) q^{43} +(-2552.03 - 3019.43i) q^{45} +(-13020.0 + 13020.0i) q^{47} -5588.36i q^{49} -23445.3i q^{51} +(20029.3 - 20029.3i) q^{53} +(12441.2 + 14719.8i) q^{55} +(4068.67 + 4068.67i) q^{57} -8416.00 q^{59} -2293.72 q^{61} +(-7483.70 - 7483.70i) q^{63} +(4674.91 - 55725.9i) q^{65} +(-395.619 + 395.619i) q^{67} -31978.6i q^{69} +40844.5i q^{71} +(-45689.8 + 45689.8i) q^{73} +(-33430.4 + 23765.9i) q^{75} +(36483.2 + 36483.2i) q^{77} +58457.5 q^{79} +36862.1 q^{81} +(-26914.9 - 26914.9i) q^{83} +(99504.4 + 8347.53i) q^{85} +(-23323.6 + 23323.6i) q^{87} -61939.2i q^{89} -149704. i q^{91} +(-66319.5 + 66319.5i) q^{93} +(-18716.5 + 15819.3i) q^{95} +(-11097.0 - 11097.0i) q^{97} +24382.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7}+O(q^{10}) $ 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7	$ 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7} - 414 q^{13} - 278 q^{15} + 1222 q^{17} - 5672 q^{19} + 5924 q^{21} - 2902 q^{23} - 4466 q^{25} + 2168 q^{27} - 2444 q^{33} + 2618 q^{35} - 1790 q^{37} + 11076 q^{39} + 11644 q^{41} + 3982 q^{43} + 14704 q^{45} + 1278 q^{47} + 5882 q^{53} - 65608 q^{55} - 14552 q^{57} + 8504 q^{59} + 20564 q^{61} - 19422 q^{63} + 40798 q^{65} - 107926 q^{67} - 16418 q^{73} - 66586 q^{75} - 13348 q^{77} + 146544 q^{79} + 173806 q^{81} + 36398 q^{83} - 66262 q^{85} - 124384 q^{87} - 306620 q^{93} - 173768 q^{95} - 60314 q^{97} + 388628 q^{99}+O(q^{100}) $ 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7 - 414 * q^13 - 278 * q^15 + 1222 * q^17 - 5672 * q^19 + 5924 * q^21 - 2902 * q^23 - 4466 * q^25 + 2168 * q^27 - 2444 * q^33 + 2618 * q^35 - 1790 * q^37 + 11076 * q^39 + 11644 * q^41 + 3982 * q^43 + 14704 * q^45 + 1278 * q^47 + 5882 * q^53 - 65608 * q^55 - 14552 * q^57 + 8504 * q^59 + 20564 * q^61 - 19422 * q^63 + 40798 * q^65 - 107926 * q^67 - 16418 * q^73 - 66586 * q^75 - 13348 * q^77 + 146544 * q^79 + 173806 * q^81 + 36398 * q^83 - 66262 * q^85 - 124384 * q^87 - 306620 * q^93 - 173768 * q^95 - 60314 * q^97 + 388628 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−9.28112	−	9.28112i	−0.595384	−	0.595384i	0.343697	−	0.939081i	$-0.388321\pi$
$3$	−9.28112	−	9.28112i	−0.595384	−	0.595384i	−0.939081	+	0.343697i	$0.888321\pi$
$4$		0			0
$5$	42.6946	−	36.0856i	0.763744	−	0.645519i
$5$	42.6946	−	36.0856i	0.763744	−	0.645519i
$6$		0			0
$7$	105.819	−	105.819i	0.816242	−	0.816242i	−0.169319	−	0.985561i	$-0.554157\pi$
$7$	105.819	−	105.819i	0.816242	−	0.816242i	0.985561	+	0.169319i	$0.0541569\pi$
$8$		0			0
$9$		−	70.7216i		−	0.291035i
$10$		0			0
$11$			344.770i			0.859108i	0.903041	+	0.429554i	$0.141329\pi$
$11$			344.770i			0.859108i	−0.903041	+	0.429554i	$0.858671\pi$
$12$		0			0
$13$	707.360	−	707.360i	1.16087	−	1.16087i	0.176579	−	0.984286i	$-0.443497\pi$
$13$	707.360	−	707.360i	1.16087	−	1.16087i	0.984286	−	0.176579i	$-0.0565031\pi$
$14$		0			0
$15$	−731.169	−	61.3385i	−0.839053	−	0.0703891i
$16$		0			0
$17$	1263.06	+	1263.06i	1.05999	+	1.05999i	0.998082	+	0.0619108i	$0.0197194\pi$
$17$	1263.06	+	1263.06i	1.05999	+	1.05999i	0.0619108	+	0.998082i	$0.480281\pi$
$18$		0			0
$19$	−438.382			−0.278592			−0.139296	−	0.990251i	$-0.544484\pi$
$19$	−438.382			−0.278592			−0.139296	+	0.990251i	$0.544484\pi$
$20$		0			0
$21$	−1964.24			−0.971955
$22$		0			0
$23$	1722.78	+	1722.78i	0.679063	+	0.679063i	0.959788	−	0.280725i	$-0.0905750\pi$
$23$	1722.78	+	1722.78i	0.679063	+	0.679063i	−0.280725	+	0.959788i	$0.590575\pi$
$24$		0			0
$25$	520.655	−	3081.32i	0.166610	−	0.986023i
$26$		0			0
$27$	−2911.69	+	2911.69i	−0.768662	+	0.768662i
$28$		0			0
$29$		−	2513.02i		−	0.554881i	−0.960743	−	0.277441i	$-0.910514\pi$
$29$		−	2513.02i		−	0.554881i	0.960743	−	0.277441i	$-0.0894862\pi$
$30$		0			0
$31$		−	7145.63i		−	1.33548i	−0.744396	−	0.667739i	$-0.767262\pi$
$31$		−	7145.63i		−	1.33548i	0.744396	−	0.667739i	$-0.232738\pi$
$32$		0			0
$33$	3199.85	−	3199.85i	0.511499	−	0.511499i
$34$		0			0
$35$	699.354	−	8336.45i	0.0964999	−	1.15030i
$36$		0			0
$37$	−3361.24	−	3361.24i	−0.403641	−	0.403641i	0.475873	−	0.879514i	$-0.342132\pi$
$37$	−3361.24	−	3361.24i	−0.403641	−	0.403641i	−0.879514	+	0.475873i	$0.842132\pi$
$38$		0			0
$39$	−13130.2			−1.38232
$40$		0			0
$41$	6969.83			0.647534			0.323767	−	0.946137i	$-0.395051\pi$
$41$	6969.83			0.647534			0.323767	+	0.946137i	$0.395051\pi$
$42$		0			0
$43$	−16311.3	−	16311.3i	−1.34530	−	1.34530i	−0.890695	−	0.454602i	$-0.849781\pi$
$43$	−16311.3	−	16311.3i	−1.34530	−	1.34530i	−0.454602	−	0.890695i	$-0.650219\pi$
$44$		0			0
$45$	−2552.03	−	3019.43i	−0.187869	−	0.222277i
$46$		0			0
$47$	−13020.0	+	13020.0i	−0.859740	+	0.859740i	−0.991307	−	0.131567i	$-0.957999\pi$
$47$	−13020.0	+	13020.0i	−0.859740	+	0.859740i	0.131567	+	0.991307i	$0.457999\pi$
$48$		0			0
$49$		−	5588.36i		−	0.332502i
$50$		0			0
$51$		−	23445.3i		−	1.26221i
$52$		0			0
$53$	20029.3	−	20029.3i	0.979436	−	0.979436i	−0.0203564	−	0.999793i	$-0.506480\pi$
$53$	20029.3	−	20029.3i	0.979436	−	0.979436i	0.999793	+	0.0203564i	$0.00648008\pi$
$54$		0			0
$55$	12441.2	+	14719.8i	0.554571	+	0.656138i
$56$		0			0
$57$	4068.67	+	4068.67i	0.165869	+	0.165869i
$58$		0			0
$59$	−8416.00			−0.314757			−0.157379	−	0.987538i	$-0.550304\pi$
$59$	−8416.00			−0.314757			−0.157379	+	0.987538i	$0.550304\pi$
$60$		0			0
$61$	−2293.72			−0.0789254			−0.0394627	−	0.999221i	$-0.512565\pi$
$61$	−2293.72			−0.0789254			−0.0394627	+	0.999221i	$0.512565\pi$
$62$		0			0
$63$	−7483.70	−	7483.70i	−0.237555	−	0.237555i
$64$		0			0
$65$	4674.91	−	55725.9i	0.137243	−	1.63596i
$66$		0			0
$67$	−395.619	+	395.619i	−0.0107669	+	0.0107669i	−0.712470	−	0.701703i	$-0.752423\pi$
$67$	−395.619	+	395.619i	−0.0107669	+	0.0107669i	0.701703	+	0.712470i	$0.252423\pi$
$68$		0			0
$69$		−	31978.6i		−	0.808606i
$70$		0			0
$71$			40844.5i			0.961585i	0.876834	+	0.480793i	$0.159651\pi$
$71$			40844.5i			0.961585i	−0.876834	+	0.480793i	$0.840349\pi$
$72$		0			0
$73$	−45689.8	+	45689.8i	−1.00349	+	1.00349i	−0.00349408	+	0.999994i	$0.501112\pi$
$73$	−45689.8	+	45689.8i	−1.00349	+	1.00349i	−0.999994	+	0.00349408i	$0.998888\pi$
$74$		0			0
$75$	−33430.4	+	23765.9i	−0.686259	+	0.487866i
$76$		0			0
$77$	36483.2	+	36483.2i	0.701240	+	0.701240i
$78$		0			0
$79$	58457.5			1.05383			0.526917	−	0.849916i	$-0.323348\pi$
$79$	58457.5			1.05383			0.526917	+	0.849916i	$0.323348\pi$
$80$		0			0
$81$	36862.1			0.624263
$82$		0			0
$83$	−26914.9	−	26914.9i	−0.428843	−	0.428843i	0.459391	−	0.888234i	$-0.348068\pi$
$83$	−26914.9	−	26914.9i	−0.428843	−	0.428843i	−0.888234	+	0.459391i	$0.848068\pi$
$84$		0			0
$85$	99504.4	+	8347.53i	1.49381	+	0.125317i
$86$		0			0
$87$	−23323.6	+	23323.6i	−0.330368	+	0.330368i
$88$		0			0
$89$		−	61939.2i		−	0.828878i	−0.910077	−	0.414439i	$-0.863978\pi$
$89$		−	61939.2i		−	0.828878i	0.910077	−	0.414439i	$-0.136022\pi$
$90$		0			0
$91$		−	149704.i		−	1.89509i
$92$		0			0
$93$	−66319.5	+	66319.5i	−0.795122	+	0.795122i
$94$		0			0
$95$	−18716.5	+	15819.3i	−0.212773	+	0.179836i
$96$		0			0
$97$	−11097.0	−	11097.0i	−0.119751	−	0.119751i	0.644692	−	0.764442i	$-0.276986\pi$
$97$	−11097.0	−	11097.0i	−0.119751	−	0.119751i	−0.764442	+	0.644692i	$0.776986\pi$
$98$		0			0
$99$	24382.7			0.250031
$100$		0			0
$101$	−137921.			−1.34533			−0.672664	−	0.739948i	$-0.734850\pi$
$101$	−137921.			−1.34533			−0.672664	+	0.739948i	$0.734850\pi$
$102$		0			0
$103$	106930.	+	106930.i	0.993132	+	0.993132i	0.999977	−	0.00684431i	$-0.00217863\pi$
$103$	106930.	+	106930.i	0.993132	+	0.993132i	−0.00684431	+	0.999977i	$0.502179\pi$
$104$		0			0
$105$	−83862.4	+	70880.8i	−0.742325	+	0.627416i
$106$		0			0
$107$	19347.9	−	19347.9i	0.163371	−	0.163371i	−0.620687	−	0.784058i	$-0.713146\pi$
$107$	19347.9	−	19347.9i	0.163371	−	0.163371i	0.784058	+	0.620687i	$0.213146\pi$
$108$		0			0
$109$			155519.i			1.25376i	0.779114	+	0.626882i	$0.215669\pi$
$109$			155519.i			1.25376i	−0.779114	+	0.626882i	$0.784331\pi$
$110$		0			0
$111$			62392.1i			0.480643i
$112$		0			0
$113$	−88859.9	+	88859.9i	−0.654651	+	0.654651i	−0.954109	−	0.299459i	$-0.903194\pi$
$113$	−88859.9	+	88859.9i	−0.654651	+	0.654651i	0.299459	+	0.954109i	$0.403194\pi$
$114$		0			0
$115$	135721.	+	11385.8i	0.956978	+	0.0802819i
$116$		0			0
$117$	−50025.6	−	50025.6i	−0.337853	−	0.337853i
$118$		0			0
$119$	267312.			1.73042
$120$		0			0
$121$	42184.7			0.261934
$122$		0			0
$123$	−64687.9	−	64687.9i	−0.385532	−	0.385532i
$124$		0			0
$125$	−88962.3	−	150344.i	−0.509250	−	0.860619i
$126$		0			0
$127$	−147966.	+	147966.i	−0.814052	+	0.814052i	−0.985239	−	0.171186i	$-0.945240\pi$
$127$	−147966.	+	147966.i	−0.814052	+	0.814052i	0.171186	+	0.985239i	$0.445240\pi$
$128$		0			0
$129$			302775.i			1.60194i
$130$		0			0
$131$		−	103447.i		−	0.526670i	−0.964704	−	0.263335i	$-0.915178\pi$
$131$		−	103447.i		−	0.526670i	0.964704	−	0.263335i	$-0.0848225\pi$
$132$		0			0
$133$	−46389.1	+	46389.1i	−0.227398	+	0.227398i
$134$		0			0
$135$	−19243.2	+	229383.i	−0.0908748	+	1.08325i
$136$		0			0
$137$	142659.	+	142659.i	0.649380	+	0.649380i	0.952843	−	0.303463i	$-0.0981430\pi$
$137$	142659.	+	142659.i	0.649380	+	0.649380i	−0.303463	+	0.952843i	$0.598143\pi$
$138$		0			0
$139$	147275.			0.646534			0.323267	−	0.946308i	$-0.395219\pi$
$139$	147275.			0.646534			0.323267	+	0.946308i	$0.395219\pi$
$140$		0			0
$141$	241681.			1.02375
$142$		0			0
$143$	243876.	+	243876.i	0.997309	+	0.997309i
$144$		0			0
$145$	−90683.7	−	107292.i	−0.358187	−	0.423787i
$146$		0			0
$147$	−51866.2	+	51866.2i	−0.197966	+	0.197966i
$148$		0			0
$149$			312656.i			1.15372i	0.816842	+	0.576861i	$0.195723\pi$
$149$			312656.i			1.15372i	−0.816842	+	0.576861i	$0.804277\pi$
$150$		0			0
$151$		−	91450.6i		−	0.326396i	−0.986593	−	0.163198i	$-0.947819\pi$
$151$		−	91450.6i		−	0.326396i	0.986593	−	0.163198i	$-0.0521809\pi$
$152$		0			0
$153$	89325.9	−	89325.9i	0.308495	−	0.308495i
$154$		0			0
$155$	−257855.	−	305080.i	−0.862076	−	1.01996i
$156$		0			0
$157$	−215386.	−	215386.i	−0.697377	−	0.697377i	0.266467	−	0.963844i	$-0.414144\pi$
$157$	−215386.	−	215386.i	−0.697377	−	0.697377i	−0.963844	+	0.266467i	$0.914144\pi$
$158$		0			0
$159$	−371789.			−1.16628
$160$		0			0
$161$	364606.			1.10856
$162$		0			0
$163$	419280.	+	419280.i	1.23605	+	1.23605i	0.961603	+	0.274444i	$0.0884939\pi$
$163$	419280.	+	419280.i	1.23605	+	1.23605i	0.274444	+	0.961603i	$0.411506\pi$
$164$		0			0
$165$	21147.7	−	252085.i	0.0604718	−	0.720837i
$166$		0			0
$167$	396893.	−	396893.i	1.10124	−	1.10124i	0.106978	−	0.994261i	$-0.465883\pi$
$167$	396893.	−	396893.i	1.10124	−	1.10124i	0.994261	−	0.106978i	$-0.0341174\pi$
$168$		0			0
$169$		−	629422.i		−	1.69522i
$170$		0			0
$171$			31003.1i			0.0810801i
$172$		0			0
$173$	−46145.1	+	46145.1i	−0.117222	+	0.117222i	−0.763285	−	0.646062i	$-0.776415\pi$
$173$	−46145.1	+	46145.1i	−0.117222	+	0.117222i	0.646062	+	0.763285i	$0.276415\pi$
$174$		0			0
$175$	−270967.	−	381158.i	−0.668840	−	0.940827i
$176$		0			0
$177$	78109.9	+	78109.9i	0.187401	+	0.187401i
$178$		0			0
$179$	−18040.3			−0.0420834			−0.0210417	−	0.999779i	$-0.506698\pi$
$179$	−18040.3			−0.0420834			−0.0210417	+	0.999779i	$0.506698\pi$
$180$		0			0
$181$	125468.			0.284667			0.142333	−	0.989819i	$-0.454540\pi$
$181$	125468.			0.284667			0.142333	+	0.989819i	$0.454540\pi$
$182$		0			0
$183$	21288.3	+	21288.3i	0.0469909	+	0.0469909i
$184$		0			0
$185$	−264799.	−	22214.3i	−0.568836	−	0.0477203i
$186$		0			0
$187$	−435466.	+	435466.i	−0.910648	+	0.910648i
$188$		0			0
$189$			616224.i			1.25483i
$190$		0			0
$191$		−	474723.i		−	0.941579i	−0.882246	−	0.470789i	$-0.843969\pi$
$191$		−	474723.i		−	0.941579i	0.882246	−	0.470789i	$-0.156031\pi$
$192$		0			0
$193$	−345560.	+	345560.i	−0.667776	+	0.667776i	−0.957201	−	0.289425i	$-0.906536\pi$
$193$	−345560.	+	345560.i	−0.667776	+	0.667776i	0.289425	+	0.957201i	$0.406536\pi$
$194$		0			0
$195$	−560588.	+	473811.i	−1.05574	+	0.892315i
$196$		0			0
$197$	−458847.	−	458847.i	−0.842370	−	0.842370i	0.146797	−	0.989167i	$-0.453104\pi$
$197$	−458847.	−	458847.i	−0.842370	−	0.842370i	−0.989167	+	0.146797i	$0.953104\pi$
$198$		0			0
$199$	−362349.			−0.648627			−0.324313	−	0.945950i	$-0.605133\pi$
$199$	−362349.			−0.648627			−0.324313	+	0.945950i	$0.605133\pi$
$200$		0			0
$201$	7343.57			0.0128209
$202$		0			0
$203$	−265925.	−	265925.i	−0.452917	−	0.452917i
$204$		0			0
$205$	297574.	−	251511.i	0.494550	−	0.417996i
$206$		0			0
$207$	121838.	−	121838.i	0.197631	−	0.197631i
$208$		0			0
$209$		−	151141.i		−	0.239340i
$210$		0			0
$211$		−	931084.i		−	1.43974i	−0.694111	−	0.719868i	$-0.744202\pi$
$211$		−	931084.i		−	1.43974i	0.694111	−	0.719868i	$-0.255798\pi$
$212$		0			0
$213$	379083.	−	379083.i	0.572513	−	0.572513i
$214$		0			0
$215$	−1.28501e6	−	107801.i	−1.89588	−	0.159047i
$216$		0			0
$217$	−756144.	−	756144.i	−1.09007	−	1.09007i
$218$		0			0
$219$	848105.			1.19492
$220$		0			0
$221$	1.78688e6			2.46102
$222$		0			0
$223$	−517823.	−	517823.i	−0.697299	−	0.697299i	0.266528	−	0.963827i	$-0.414123\pi$
$223$	−517823.	−	517823.i	−0.697299	−	0.697299i	−0.963827	+	0.266528i	$0.914123\pi$
$224$		0			0
$225$	−217916.	−	36821.6i	−0.286968	−	0.0484893i
$226$		0			0
$227$	62975.3	−	62975.3i	0.0811158	−	0.0811158i	−0.665385	−	0.746501i	$-0.731732\pi$
$227$	62975.3	−	62975.3i	0.0811158	−	0.0811158i	0.746501	+	0.665385i	$0.231732\pi$
$228$		0			0
$229$		−	300417.i		−	0.378560i	−0.981923	−	0.189280i	$-0.939385\pi$
$229$		−	300417.i		−	0.378560i	0.981923	−	0.189280i	$-0.0606155\pi$
$230$		0			0
$231$		−	677211.i		−	0.835014i
$232$		0			0
$233$	488904.	−	488904.i	0.589975	−	0.589975i	−0.347649	−	0.937625i	$-0.613020\pi$
$233$	488904.	−	488904.i	0.589975	−	0.589975i	0.937625	+	0.347649i	$0.113020\pi$
$234$		0			0
$235$	−86048.8	+	1.02572e6i	−0.101642	+	1.21160i
$236$		0			0
$237$	−542551.	−	542551.i	−0.627437	−	0.627437i
$238$		0			0
$239$	1.06439e6			1.20533			0.602663	−	0.797996i	$-0.294106\pi$
$239$	1.06439e6			1.20533			0.602663	+	0.797996i	$0.294106\pi$
$240$		0			0
$241$	1.37049e6			1.51996			0.759981	−	0.649946i	$-0.225208\pi$
$241$	1.37049e6			1.51996			0.759981	+	0.649946i	$0.225208\pi$
$242$		0			0
$243$	365419.	+	365419.i	0.396986	+	0.396986i
$244$		0			0
$245$	−201659.	−	238593.i	−0.214636	−	0.253946i
$246$		0			0
$247$	−310093.	+	310093.i	−0.323408	+	0.323408i
$248$		0			0
$249$			499602.i			0.510652i
$250$		0			0
$251$			483364.i			0.484272i	0.970242	+	0.242136i	$0.0778481\pi$
$251$			483364.i			0.484272i	−0.970242	+	0.242136i	$0.922152\pi$
$252$		0			0
$253$	−593962.	+	593962.i	−0.583388	+	0.583388i
$254$		0			0
$255$	−846038.	−	1.00099e6i	−0.814778	−	0.964002i
$256$		0			0
$257$	244037.	+	244037.i	0.230474	+	0.230474i	0.812891	−	0.582416i	$-0.197893\pi$
$257$	244037.	+	244037.i	0.230474	+	0.230474i	−0.582416	+	0.812891i	$0.697893\pi$
$258$		0			0
$259$	−711366.			−0.658937
$260$		0			0
$261$	−177724.			−0.161490
$262$		0			0
$263$	660423.	+	660423.i	0.588752	+	0.588752i	0.937293	−	0.348541i	$-0.113323\pi$
$263$	660423.	+	660423.i	0.588752	+	0.588752i	−0.348541	+	0.937293i	$0.613323\pi$
$264$		0			0
$265$	132373.	−	1.57791e6i	0.115793	−	1.38028i
$266$		0			0
$267$	−574865.	+	574865.i	−0.493501	+	0.493501i
$268$		0			0
$269$			1.08159e6i			0.911344i	0.890148	+	0.455672i	$0.150601\pi$
$269$			1.08159e6i			0.911344i	−0.890148	+	0.455672i	$0.849399\pi$
$270$		0			0
$271$			343393.i			0.284032i	0.989864	+	0.142016i	$0.0453585\pi$
$271$			343393.i			0.284032i	−0.989864	+	0.142016i	$0.954642\pi$
$272$		0			0
$273$	−1.38942e6	+	1.38942e6i	−1.12831	+	1.12831i
$274$		0			0
$275$	1.06235e6	+	179506.i	0.847100	+	0.143136i
$276$		0			0
$277$	335813.	+	335813.i	0.262965	+	0.262965i	0.826258	−	0.563292i	$-0.190465\pi$
$277$	335813.	+	335813.i	0.262965	+	0.262965i	−0.563292	+	0.826258i	$0.690465\pi$
$278$		0			0
$279$	−505351.			−0.388671
$280$		0			0
$281$	1.59679e6			1.20637			0.603187	−	0.797600i	$-0.293897\pi$
$281$	1.59679e6			1.20637			0.603187	+	0.797600i	$0.293897\pi$
$282$		0			0
$283$	1.31343e6	+	1.31343e6i	0.974859	+	0.974859i	0.999692	−	0.0248326i	$-0.00790527\pi$
$283$	1.31343e6	+	1.31343e6i	0.974859	+	0.974859i	−0.0248326	+	0.999692i	$0.507905\pi$
$284$		0			0
$285$	320531.	+	26889.7i	0.233753	+	0.0196098i
$286$		0			0
$287$	737541.	−	737541.i	0.528545	−	0.528545i
$288$		0			0
$289$			1.77080e6i			1.24717i
$290$		0			0
$291$			205986.i			0.142595i
$292$		0			0
$293$	−979199.	+	979199.i	−0.666350	+	0.666350i	−0.956869	−	0.290520i	$-0.906172\pi$
$293$	−979199.	+	979199.i	−0.666350	+	0.666350i	0.290520	+	0.956869i	$0.406172\pi$
$294$		0			0
$295$	−359318.	+	303697.i	−0.240394	+	0.203182i
$296$		0			0
$297$	−1.00386e6	−	1.00386e6i	−0.660364	−	0.660364i
$298$		0			0
$299$	2.43725e6			1.57660
$300$		0			0
$301$	−3.45210e6			−2.19618
$302$		0			0
$303$	1.28006e6	+	1.28006e6i	0.800986	+	0.800986i
$304$		0			0
$305$	−97929.6	+	82770.5i	−0.0602788	+	0.0509478i
$306$		0			0
$307$	−1.37916e6	+	1.37916e6i	−0.835159	+	0.835159i	−0.988217	−	0.153058i	$-0.951088\pi$
$307$	−1.37916e6	+	1.37916e6i	−0.835159	+	0.835159i	0.153058	+	0.988217i	$0.451088\pi$
$308$		0			0
$309$		−	1.98486e6i		−	1.18259i
$310$		0			0
$311$		−	3.40266e6i		−	1.99488i	−0.0714984	−	0.997441i	$-0.522778\pi$
$311$		−	3.40266e6i		−	1.99488i	0.0714984	−	0.997441i	$-0.477222\pi$
$312$		0			0
$313$	−1.12834e6	+	1.12834e6i	−0.650997	+	0.650997i	−0.953233	−	0.302236i	$-0.902267\pi$
$313$	−1.12834e6	+	1.12834e6i	−0.650997	+	0.650997i	0.302236	+	0.953233i	$0.402267\pi$
$314$		0			0
$315$	−589567.	−	49459.4i	−0.334778	−	0.0280849i
$316$		0			0
$317$	2.46256e6	+	2.46256e6i	1.37638	+	1.37638i	0.850657	+	0.525722i	$0.176205\pi$
$317$	2.46256e6	+	2.46256e6i	1.37638	+	1.37638i	0.525722	+	0.850657i	$0.323795\pi$
$318$		0			0
$319$	866412.			0.476703
$320$		0			0
$321$	−359141.			−0.194537
$322$		0			0
$323$	−553704.	−	553704.i	−0.295305	−	0.295305i
$324$		0			0
$325$	−1.81131e6	−	2.54789e6i	−0.951229	−	1.33805i
$326$		0			0
$327$	1.44339e6	−	1.44339e6i	0.746471	−	0.746471i
$328$		0			0
$329$			2.75554e6i			1.40351i
$330$		0			0
$331$		−	3.84785e6i		−	1.93041i	−0.261503	−	0.965203i	$-0.584218\pi$
$331$		−	3.84785e6i		−	1.93041i	0.261503	−	0.965203i	$-0.415782\pi$
$332$		0			0
$333$	−237712.	+	237712.i	−0.117474	+	0.117474i
$334$		0			0
$335$	−2614.63	+	31166.9i	−0.00127291	+	0.0151734i
$336$		0			0
$337$	2.14771e6	+	2.14771e6i	1.03015	+	1.03015i	0.999531	+	0.0306217i	$0.00974872\pi$
$337$	2.14771e6	+	2.14771e6i	1.03015	+	1.03015i	0.0306217	+	0.999531i	$0.490251\pi$
$338$		0			0
$339$	1.64944e6			0.779537
$340$		0			0
$341$	2.46360e6			1.14732
$342$		0			0
$343$	1.18715e6	+	1.18715e6i	0.544840	+	0.544840i
$344$		0			0
$345$	−1.15397e6	−	1.36531e6i	−0.521971	−	0.617568i
$346$		0			0
$347$	−2.44660e6	+	2.44660e6i	−1.09078	+	1.09078i	−0.0953396	+	0.995445i	$0.530394\pi$
$347$	−2.44660e6	+	2.44660e6i	−1.09078	+	1.09078i	−0.995445	+	0.0953396i	$0.969606\pi$
$348$		0			0
$349$			3.21607e6i			1.41339i	0.707519	+	0.706694i	$0.249814\pi$
$349$			3.21607e6i			1.41339i	−0.707519	+	0.706694i	$0.750186\pi$
$350$		0			0
$351$			4.11922e6i			1.78463i
$352$		0			0
$353$	1.20920e6	−	1.20920e6i	0.516490	−	0.516490i	−0.400017	−	0.916508i	$-0.630996\pi$
$353$	1.20920e6	−	1.20920e6i	0.516490	−	0.516490i	0.916508	+	0.400017i	$0.130996\pi$
$354$		0			0
$355$	1.47390e6	+	1.74384e6i	0.620722	+	0.734405i
$356$		0			0
$357$	−2.48096e6	−	2.48096e6i	−1.03027	−	1.03027i
$358$		0			0
$359$	−1.56580e6			−0.641211			−0.320606	−	0.947213i	$-0.603886\pi$
$359$	−1.56580e6			−0.641211			−0.320606	+	0.947213i	$0.603886\pi$
$360$		0			0
$361$	−2.28392e6			−0.922387
$362$		0			0
$363$	−391521.	−	391521.i	−0.155951	−	0.155951i
$364$		0			0
$365$	−301962.	+	3.59945e6i	−0.118637	+	1.41418i
$366$		0			0
$367$	−1.29136e6	+	1.29136e6i	−0.500475	+	0.500475i	−0.911585	−	0.411111i	$-0.865141\pi$
$367$	−1.29136e6	+	1.29136e6i	−0.500475	+	0.500475i	0.411111	+	0.911585i	$0.365141\pi$
$368$		0			0
$369$		−	492918.i		−	0.188455i
$370$		0			0
$371$		−	4.23897e6i		−	1.59891i
$372$		0			0
$373$	−20034.2	+	20034.2i	−0.00745588	+	0.00745588i	−0.710825	−	0.703369i	$-0.751678\pi$
$373$	−20034.2	+	20034.2i	−0.00745588	+	0.00745588i	0.703369	+	0.710825i	$0.251678\pi$
$374$		0			0
$375$	−569690.	+	2.22103e6i	−0.209200	+	0.815598i
$376$		0			0
$377$	−1.77761e6	−	1.77761e6i	−0.644143	−	0.644143i
$378$		0			0
$379$	3.86453e6			1.38197			0.690985	−	0.722869i	$-0.257177\pi$
$379$	3.86453e6			1.38197			0.690985	+	0.722869i	$0.257177\pi$
$380$		0			0
$381$	2.74658e6			0.969348
$382$		0			0
$383$	1.42232e6	+	1.42232e6i	0.495452	+	0.495452i	0.910019	−	0.414567i	$-0.136067\pi$
$383$	1.42232e6	+	1.42232e6i	0.495452	+	0.495452i	−0.414567	+	0.910019i	$0.636067\pi$
$384$		0			0
$385$	2.87416e6	+	241116.i	0.988232	+	0.0829038i
$386$		0			0
$387$	−1.15356e6	+	1.15356e6i	−0.391529	+	0.391529i
$388$		0			0
$389$		−	3.06571e6i		−	1.02720i	−0.858029	−	0.513602i	$-0.828311\pi$
$389$		−	3.06571e6i		−	1.02720i	0.858029	−	0.513602i	$-0.171689\pi$
$390$		0			0
$391$			4.35196e6i			1.43960i
$392$		0			0
$393$	−960102.	+	960102.i	−0.313571	+	0.313571i
$394$		0			0
$395$	2.49582e6	−	2.10948e6i	0.804860	−	0.680271i
$396$		0			0
$397$	2.86964e6	+	2.86964e6i	0.913800	+	0.913800i	0.996569	−	0.0827685i	$-0.0263762\pi$
$397$	2.86964e6	+	2.86964e6i	0.913800	+	0.913800i	−0.0827685	+	0.996569i	$0.526376\pi$
$398$		0			0
$399$	861086.			0.270779
$400$		0			0
$401$	−1.30150e6			−0.404187			−0.202093	−	0.979366i	$-0.564774\pi$
$401$	−1.30150e6			−0.404187			−0.202093	+	0.979366i	$0.564774\pi$
$402$		0			0
$403$	−5.05453e6	−	5.05453e6i	−1.55031	−	1.55031i
$404$		0			0
$405$	1.57381e6	−	1.33019e6i	0.476777	−	0.402974i
$406$		0			0
$407$	1.15885e6	−	1.15885e6i	0.346771	−	0.346771i
$408$		0			0
$409$		−	5.91742e6i		−	1.74914i	−0.484902	−	0.874569i	$-0.661145\pi$
$409$		−	5.91742e6i		−	1.74914i	0.484902	−	0.874569i	$-0.338855\pi$
$410$		0			0
$411$		−	2.64808e6i		−	0.773261i
$412$		0			0
$413$	−890573.	+	890573.i	−0.256918	+	0.256918i
$414$		0			0
$415$	−2.12036e6	−	177880.i	−0.604352	−	0.0506998i
$416$		0			0
$417$	−1.36687e6	−	1.36687e6i	−0.384936	−	0.384936i
$418$		0			0
$419$	−5.36914e6			−1.49407			−0.747033	−	0.664788i	$-0.768522\pi$
$419$	−5.36914e6			−1.49407			−0.747033	+	0.664788i	$0.768522\pi$
$420$		0			0
$421$	2.11924e6			0.582740			0.291370	−	0.956610i	$-0.405889\pi$
$421$	2.11924e6			0.582740			0.291370	+	0.956610i	$0.405889\pi$
$422$		0			0
$423$	920798.	+	920798.i	0.250215	+	0.250215i
$424$		0			0
$425$	4.54952e6	−	3.23428e6i	1.22178	−	0.868572i
$426$		0			0
$427$	−242720.	+	242720.i	−0.0644222	+	0.0644222i
$428$		0			0
$429$		−	4.52689e6i		−	1.18756i
$430$		0			0
$431$			469972.i			0.121865i	0.998142	+	0.0609325i	$0.0194074\pi$
$431$			469972.i			0.121865i	−0.998142	+	0.0609325i	$0.980593\pi$
$432$		0			0
$433$	630785.	−	630785.i	0.161682	−	0.161682i	−0.621629	−	0.783311i	$-0.713529\pi$
$433$	630785.	−	630785.i	0.161682	−	0.161682i	0.783311	+	0.621629i	$0.213529\pi$
$434$		0			0
$435$	−154145.	+	1.83744e6i	−0.0390576	+	0.465575i
$436$		0			0
$437$	−755235.	−	755235.i	−0.189181	−	0.189181i
$438$		0			0
$439$	−798304.			−0.197700			−0.0988501	−	0.995102i	$-0.531516\pi$
$439$	−798304.			−0.197700			−0.0988501	+	0.995102i	$0.531516\pi$
$440$		0			0
$441$	−395218.			−0.0967698
$442$		0			0
$443$	−3.62223e6	−	3.62223e6i	−0.876934	−	0.876934i	0.116282	−	0.993216i	$-0.462902\pi$
$443$	−3.62223e6	−	3.62223e6i	−0.876934	−	0.876934i	−0.993216	+	0.116282i	$0.962902\pi$
$444$		0			0
$445$	−2.23512e6	−	2.64447e6i	−0.535057	−	0.633051i
$446$		0			0
$447$	2.90180e6	−	2.90180e6i	0.686908	−	0.686908i
$448$		0			0
$449$			7.51152e6i			1.75838i	0.476474	+	0.879188i	$0.341915\pi$
$449$			7.51152e6i			1.75838i	−0.476474	+	0.879188i	$0.658085\pi$
$450$		0			0
$451$			2.40299e6i			0.556302i
$452$		0			0
$453$	−848764.	+	848764.i	−0.194331	+	0.194331i
$454$		0			0
$455$	−5.40217e6	−	6.39156e6i	−1.22332	−	1.44737i
$456$		0			0
$457$	−994327.	−	994327.i	−0.222710	−	0.222710i	0.586929	−	0.809638i	$-0.300337\pi$
$457$	−994327.	−	994327.i	−0.222710	−	0.222710i	−0.809638	+	0.586929i	$0.800337\pi$
$458$		0			0
$459$	−7.35529e6			−1.62955
$460$		0			0
$461$	3.47063e6			0.760600			0.380300	−	0.924863i	$-0.375821\pi$
$461$	3.47063e6			0.760600			0.380300	+	0.924863i	$0.375821\pi$
$462$		0			0
$463$	−2.81963e6	−	2.81963e6i	−0.611280	−	0.611280i	0.332000	−	0.943279i	$-0.392277\pi$
$463$	−2.81963e6	−	2.81963e6i	−0.611280	−	0.611280i	−0.943279	+	0.332000i	$0.892277\pi$
$464$		0			0
$465$	−438303.	+	5.22466e6i	−0.0940030	+	1.12054i
$466$		0			0
$467$	5.53855e6	−	5.53855e6i	1.17518	−	1.17518i	0.194221	−	0.980958i	$-0.437782\pi$
$467$	5.53855e6	−	5.53855e6i	1.17518	−	1.17518i	0.980958	−	0.194221i	$-0.0622178\pi$
$468$		0			0
$469$			83728.0i			0.0175768i
$470$		0			0
$471$			3.99804e6i			0.830415i
$472$		0			0
$473$	5.62365e6	−	5.62365e6i	1.15575	−	1.15575i
$474$		0			0
$475$	−228246.	+	1.35079e6i	−0.0464161	+	0.274698i
$476$		0			0
$477$	−1.41650e6	−	1.41650e6i	−0.285051	−	0.285051i
$478$		0			0
$479$	−2.72200e6			−0.542063			−0.271031	−	0.962571i	$-0.587365\pi$
$479$	−2.72200e6			−0.542063			−0.271031	+	0.962571i	$0.587365\pi$
$480$		0			0
$481$	−4.75521e6			−0.937145
$482$		0			0
$483$	−3.38395e6	−	3.38395e6i	−0.660018	−	0.660018i
$484$		0			0
$485$	−874227.	−	73339.8i	−0.168760	−	0.0141575i
$486$		0			0
$487$	−1.53481e6	+	1.53481e6i	−0.293246	+	0.293246i	−0.838361	−	0.545115i	$-0.816486\pi$
$487$	−1.53481e6	+	1.53481e6i	−0.293246	+	0.293246i	0.545115	+	0.838361i	$0.316486\pi$
$488$		0			0
$489$		−	7.78278e6i		−	1.47185i
$490$		0			0
$491$		−	4.17663e6i		−	0.781848i	−0.920423	−	0.390924i	$-0.872156\pi$
$491$		−	4.17663e6i		−	0.781848i	0.920423	−	0.390924i	$-0.127844\pi$
$492$		0			0
$493$	3.17410e6	−	3.17410e6i	0.588170	−	0.588170i
$494$		0			0
$495$	1.04101e6	−	879865.i	0.190960	−	0.161400i
$496$		0			0
$497$	4.32213e6	+	4.32213e6i	0.784886	+	0.784886i
$498$		0			0
$499$	5.43895e6			0.977830			0.488915	−	0.872331i	$-0.337393\pi$
$499$	5.43895e6			0.977830			0.488915	+	0.872331i	$0.337393\pi$
$500$		0			0
$501$	−7.36721e6			−1.31132
$502$		0			0
$503$	6.20134e6	+	6.20134e6i	1.09286	+	1.09286i	0.995222	+	0.0976412i	$0.0311298\pi$
$503$	6.20134e6	+	6.20134e6i	1.09286	+	1.09286i	0.0976412	+	0.995222i	$0.468870\pi$
$504$		0			0
$505$	−5.88849e6	+	4.97698e6i	−1.02749	+	0.868435i
$506$		0			0
$507$	−5.84174e6	+	5.84174e6i	−1.00931	+	1.00931i
$508$		0			0
$509$			1.07552e6i			0.184003i	0.995759	+	0.0920015i	$0.0293265\pi$
$509$			1.07552e6i			0.184003i	−0.995759	+	0.0920015i	$0.970674\pi$
$510$		0			0
$511$			9.66971e6i			1.63818i
$512$		0			0
$513$	1.27643e6	−	1.27643e6i	0.214143	−	0.214143i
$514$		0			0
$515$	8.42398e6	+	706697.i	1.39958	+	0.117413i
$516$		0			0
$517$	−4.48892e6	−	4.48892e6i	−0.738610	−	0.738610i
$518$		0			0
$519$	856557.			0.139585
$520$		0			0
$521$	512247.			0.0826770			0.0413385	−	0.999145i	$-0.486838\pi$
$521$	512247.			0.0826770			0.0413385	+	0.999145i	$0.486838\pi$
$522$		0			0
$523$	1.62407e6	+	1.62407e6i	0.259627	+	0.259627i	0.824902	−	0.565275i	$-0.191230\pi$
$523$	1.62407e6	+	1.62407e6i	0.259627	+	0.259627i	−0.565275	+	0.824902i	$0.691230\pi$
$524$		0			0
$525$	−1.02269e6	+	6.05245e6i	−0.161937	+	0.958370i
$526$		0			0
$527$	9.02539e6	−	9.02539e6i	1.41560	−	1.41560i
$528$		0			0
$529$		−	500411.i		−	0.0777477i
$530$		0			0
$531$			595193.i			0.0916055i
$532$		0			0
$533$	4.93018e6	−	4.93018e6i	0.751700	−	0.751700i
$534$		0			0
$535$	127870.	−	1.52423e6i	0.0193145	−	0.230233i
$536$		0			0
$537$	167434.	+	167434.i	0.0250558	+	0.0250558i
$538$		0			0
$539$	1.92670e6			0.285655
$540$		0			0
$541$	−2.18839e6			−0.321464			−0.160732	−	0.986998i	$-0.551385\pi$
$541$	−2.18839e6			−0.321464			−0.160732	+	0.986998i	$0.551385\pi$
$542$		0			0
$543$	−1.16448e6	−	1.16448e6i	−0.169486	−	0.169486i
$544$		0			0
$545$	5.61198e6	+	6.63980e6i	0.809329	+	0.957555i
$546$		0			0
$547$	−7.08793e6	+	7.08793e6i	−1.01286	+	1.01286i	−0.0129482	+	0.999916i	$0.504122\pi$
$547$	−7.08793e6	+	7.08793e6i	−1.01286	+	1.01286i	−0.999916	+	0.0129482i	$0.995878\pi$
$548$		0			0
$549$			162216.i			0.0229701i
$550$		0			0
$551$			1.10166e6i			0.154585i
$552$		0			0
$553$	6.18592e6	−	6.18592e6i	0.860184	−	0.860184i
$554$		0			0
$555$	2.25146e6	+	2.66381e6i	0.310264	+	0.367088i
$556$		0			0
$557$	8.47008e6	+	8.47008e6i	1.15678	+	1.15678i	0.985165	+	0.171612i	$0.0548975\pi$
$557$	8.47008e6	+	8.47008e6i	1.15678	+	1.15678i	0.171612	+	0.985165i	$0.445102\pi$
$558$		0			0
$559$	−2.30759e7			−3.12342
$560$		0			0
$561$	8.08323e6			1.08437
$562$		0			0
$563$	3.30786e6	+	3.30786e6i	0.439821	+	0.439821i	0.891952	−	0.452131i	$-0.149336\pi$
$563$	3.30786e6	+	3.30786e6i	0.439821	+	0.439821i	−0.452131	+	0.891952i	$0.649336\pi$
$564$		0			0
$565$	−587271.	+	7.00040e6i	−0.0773958	+	0.922575i
$566$		0			0
$567$	3.90071e6	−	3.90071e6i	0.509550	−	0.509550i
$568$		0			0
$569$			5.57983e6i			0.722504i	0.932468	+	0.361252i	$0.117651\pi$
$569$			5.57983e6i			0.722504i	−0.932468	+	0.361252i	$0.882349\pi$
$570$		0			0
$571$		−	119122.i		−	0.0152898i	−0.999971	−	0.00764491i	$-0.997567\pi$
$571$		−	119122.i		−	0.0152898i	0.999971	−	0.00764491i	$-0.00243348\pi$
$572$		0			0
$573$	−4.40596e6	+	4.40596e6i	−0.560601	+	0.560601i
$574$		0			0
$575$	6.20541e6	−	4.41146e6i	0.782710	−	0.556433i
$576$		0			0
$577$	−5.74821e6	−	5.74821e6i	−0.718775	−	0.718775i	0.249579	−	0.968354i	$-0.419708\pi$
$577$	−5.74821e6	−	5.74821e6i	−0.718775	−	0.718775i	−0.968354	+	0.249579i	$0.919708\pi$
$578$		0			0
$579$	6.41438e6			0.795166
$580$		0			0
$581$	−5.69623e6			−0.700079
$582$		0			0
$583$	6.90550e6	+	6.90550e6i	0.841442	+	0.841442i
$584$		0			0
$585$	−3.94103e6	−	330617.i	−0.476124	−	0.0399425i
$586$		0			0
$587$	1.01460e6	−	1.01460e6i	0.121535	−	0.121535i	−0.643724	−	0.765258i	$-0.722611\pi$
$587$	1.01460e6	−	1.01460e6i	0.121535	−	0.121535i	0.765258	+	0.643724i	$0.222611\pi$
$588$		0			0
$589$			3.13252e6i			0.372053i
$590$		0			0
$591$			8.51724e6i			1.00307i
$592$		0			0
$593$	−5.72430e6	+	5.72430e6i	−0.668476	+	0.668476i	−0.957363	−	0.288887i	$-0.906715\pi$
$593$	−5.72430e6	+	5.72430e6i	−0.668476	+	0.668476i	0.288887	+	0.957363i	$0.406715\pi$
$594$		0			0
$595$	1.14128e7	−	9.64614e6i	1.32160	−	1.11702i
$596$		0			0
$597$	3.36301e6	+	3.36301e6i	0.386182	+	0.386182i
$598$		0			0
$599$	5.13903e6			0.585213			0.292606	−	0.956233i	$-0.405477\pi$
$599$	5.13903e6			0.585213			0.292606	+	0.956233i	$0.405477\pi$
$600$		0			0
$601$	−1.24740e7			−1.40871			−0.704353	−	0.709850i	$-0.748763\pi$
$601$	−1.24740e7			−1.40871			−0.704353	+	0.709850i	$0.748763\pi$
$602$		0			0
$603$	27978.8	+	27978.8i	0.00313354	+	0.00313354i
$604$		0			0
$605$	1.80106e6	−	1.52226e6i	0.200050	−	0.169083i
$606$		0			0
$607$	9.43385e6	−	9.43385e6i	1.03924	−	1.03924i	0.0400449	−	0.999198i	$-0.487250\pi$
$607$	9.43385e6	−	9.43385e6i	1.03924	−	1.03924i	0.999198	−	0.0400449i	$-0.0127501\pi$
$608$		0			0
$609$			4.93616e6i			0.539320i
$610$		0			0
$611$			1.84197e7i			1.99609i
$612$		0			0
$613$	5.01442e6	−	5.01442e6i	0.538976	−	0.538976i	−0.384252	−	0.923228i	$-0.625541\pi$
$613$	5.01442e6	−	5.01442e6i	0.538976	−	0.538976i	0.923228	+	0.384252i	$0.125541\pi$
$614$		0			0
$615$	−5.09612e6	−	427519.i	−0.543316	−	0.0455793i
$616$		0			0
$617$	4.22945e6	+	4.22945e6i	0.447272	+	0.447272i	0.894446	−	0.447175i	$-0.147570\pi$
$617$	4.22945e6	+	4.22945e6i	0.447272	+	0.447272i	−0.447175	+	0.894446i	$0.647570\pi$
$618$		0			0
$619$	6.02116e6			0.631617			0.315808	−	0.948823i	$-0.397724\pi$
$619$	6.02116e6			0.631617			0.315808	+	0.948823i	$0.397724\pi$
$620$		0			0
$621$	−1.00324e7			−1.04394
$622$		0			0
$623$	−6.55435e6	−	6.55435e6i	−0.676565	−	0.676565i
$624$		0			0
$625$	−9.22346e6	−	3.20861e6i	−0.944482	−	0.328562i
$626$		0			0
$627$	−1.40276e6	+	1.40276e6i	−0.142499	+	0.142499i
$628$		0			0
$629$		−	8.49092e6i		−	0.855713i
$630$		0			0
$631$		−	2.59184e6i		−	0.259141i	−0.991570	−	0.129570i	$-0.958640\pi$
$631$		−	2.59184e6i		−	0.259141i	0.991570	−	0.129570i	$-0.0413598\pi$
$632$		0			0
$633$	−8.64150e6	+	8.64150e6i	−0.857196	+	0.857196i
$634$		0			0
$635$	−977900.	+	1.16568e7i	−0.0962410	+	1.14721i
$636$		0			0
$637$	−3.95298e6	−	3.95298e6i	−0.385990	−	0.385990i
$638$		0			0
$639$	2.88859e6			0.279855
$640$		0			0
$641$	−5.99741e6			−0.576526			−0.288263	−	0.957551i	$-0.593078\pi$
$641$	−5.99741e6			−0.576526			−0.288263	+	0.957551i	$0.593078\pi$
$642$		0			0
$643$	−841642.	−	841642.i	−0.0802786	−	0.0802786i	0.665827	−	0.746106i	$-0.268079\pi$
$643$	−841642.	−	841642.i	−0.0802786	−	0.0802786i	−0.746106	+	0.665827i	$0.768079\pi$
$644$		0			0
$645$	1.09258e7	+	1.29268e7i	1.03408	+	1.22347i
$646$		0			0
$647$	1.18127e7	−	1.18127e7i	1.10940	−	1.10940i	0.116170	−	0.993229i	$-0.462938\pi$
$647$	1.18127e7	−	1.18127e7i	1.10940	−	1.10940i	0.993229	−	0.116170i	$-0.0370618\pi$
$648$		0			0
$649$		−	2.90158e6i		−	0.270410i
$650$		0			0
$651$			1.40357e7i			1.29802i
$652$		0			0
$653$	1.22862e6	−	1.22862e6i	0.112755	−	0.112755i	−0.648478	−	0.761233i	$-0.724594\pi$
$653$	1.22862e6	−	1.22862e6i	0.112755	−	0.112755i	0.761233	+	0.648478i	$0.224594\pi$
$654$		0			0
$655$	−3.73294e6	−	4.41662e6i	−0.339976	−	0.402241i
$656$		0			0
$657$	3.23126e6	+	3.23126e6i	0.292051	+	0.292051i
$658$		0			0
$659$	−4.69732e6			−0.421343			−0.210672	−	0.977557i	$-0.567565\pi$
$659$	−4.69732e6			−0.421343			−0.210672	+	0.977557i	$0.567565\pi$
$660$		0			0
$661$	−1.07325e7			−0.955423			−0.477712	−	0.878517i	$-0.658534\pi$
$661$	−1.07325e7			−0.955423			−0.477712	+	0.878517i	$0.658534\pi$
$662$		0			0
$663$	−1.65842e7	−	1.65842e7i	−1.46525	−	1.46525i
$664$		0			0
$665$	−306584.	+	3.65455e6i	−0.0268841	+	0.320464i
$666$		0			0
$667$	4.32937e6	−	4.32937e6i	0.376799	−	0.376799i
$668$		0			0
$669$			9.61195e6i			0.830322i
$670$		0			0
$671$		−	790807.i		−	0.0678054i
$672$		0			0
$673$	−6.62488e6	+	6.62488e6i	−0.563820	+	0.563820i	−0.930390	−	0.366571i	$-0.880532\pi$
$673$	−6.62488e6	+	6.62488e6i	−0.563820	+	0.563820i	0.366571	+	0.930390i	$0.380532\pi$
$674$		0			0
$675$	7.45586e6	+	1.04878e7i	0.629852	+	0.885985i
$676$		0			0
$677$	5.62424e6	+	5.62424e6i	0.471620	+	0.471620i	0.902438	−	0.430819i	$-0.141775\pi$
$677$	5.62424e6	+	5.62424e6i	0.471620	+	0.471620i	−0.430819	+	0.902438i	$0.641775\pi$
$678$		0			0
$679$	−2.34856e6			−0.195491
$680$		0			0
$681$	−1.16896e6			−0.0965902
$682$		0			0
$683$	−6.92168e6	−	6.92168e6i	−0.567754	−	0.567754i	0.363745	−	0.931499i	$-0.381498\pi$
$683$	−6.92168e6	−	6.92168e6i	−0.567754	−	0.567754i	−0.931499	+	0.363745i	$0.881498\pi$
$684$		0			0
$685$	1.12387e7	+	942829.i	0.915147	+	0.0767727i
$686$		0			0
$687$	−2.78820e6	+	2.78820e6i	−0.225389	+	0.225389i
$688$		0			0
$689$		−	2.83358e7i		−	2.27399i
$690$		0			0
$691$			9.49915e6i			0.756815i	0.925639	+	0.378407i	$0.123528\pi$
$691$			9.49915e6i			0.756815i	−0.925639	+	0.378407i	$0.876472\pi$
$692$		0			0
$693$	2.58015e6	−	2.58015e6i	0.204086	−	0.204086i
$694$		0			0
$695$	6.28783e6	−	5.31450e6i	0.493786	−	0.417350i
$696$		0			0
$697$	8.80334e6	+	8.80334e6i	0.686381	+	0.686381i
$698$		0			0
$699$	−9.07516e6			−0.702524
$700$		0			0
$701$	1.94148e6			0.149224			0.0746120	−	0.997213i	$-0.476228\pi$
$701$	1.94148e6			0.149224			0.0746120	+	0.997213i	$0.476228\pi$
$702$		0			0
$703$	1.47351e6	+	1.47351e6i	0.112451	+	0.112451i
$704$		0			0
$705$	1.03185e7	−	8.72121e6i	0.781884	−	0.660852i
$706$		0			0
$707$	−1.45947e7	+	1.45947e7i	−1.09811	+	1.09811i
$708$		0			0
$709$		−	2.89625e6i		−	0.216382i	−0.994130	−	0.108191i	$-0.965494\pi$
$709$		−	2.89625e6i		−	0.216382i	0.994130	−	0.108191i	$-0.0345057\pi$
$710$		0			0
$711$		−	4.13421e6i		−	0.306703i
$712$		0			0
$713$	1.23103e7	−	1.23103e7i	0.906873	−	0.906873i
$714$		0			0
$715$	1.92126e7	+	1.61177e6i	1.40547	+	0.117906i
$716$		0			0
$717$	−9.87870e6	−	9.87870e6i	−0.717632	−	0.717632i
$718$		0			0
$719$	751266.			0.0541965			0.0270983	−	0.999633i	$-0.491373\pi$
$719$	751266.			0.0541965			0.0270983	+	0.999633i	$0.491373\pi$
$720$		0			0
$721$	2.26305e7			1.62127
$722$		0			0
$723$	−1.27197e7	−	1.27197e7i	−0.904961	−	0.904961i
$724$		0			0
$725$	−7.74341e6	−	1.30841e6i	−0.547126	−	0.0924486i
$726$		0			0
$727$	−1.73454e7	+	1.73454e7i	−1.21716	+	1.21716i	−0.248536	+	0.968623i	$0.579949\pi$
$727$	−1.73454e7	+	1.73454e7i	−1.21716	+	1.21716i	−0.968623	+	0.248536i	$0.920051\pi$
$728$		0			0
$729$		−	1.57405e7i		−	1.09698i
$730$		0			0
$731$		−	4.12045e7i		−	2.85201i
$732$		0			0
$733$	1.21536e7	−	1.21536e7i	0.835496	−	0.835496i	−0.152766	−	0.988262i	$-0.548818\pi$
$733$	1.21536e7	−	1.21536e7i	0.835496	−	0.835496i	0.988262	+	0.152766i	$0.0488181\pi$
$734$		0			0
$735$	−342782.	+	4.08603e6i	−0.0234045	+	0.278987i
$736$		0			0
$737$	−136397.	−	136397.i	−0.00924991	−	0.00924991i
$738$		0			0
$739$	−888631.			−0.0598564			−0.0299282	−	0.999552i	$-0.509528\pi$
$739$	−888631.			−0.0598564			−0.0299282	+	0.999552i	$0.509528\pi$
$740$		0			0
$741$	5.75603e6			0.385104
$742$		0			0
$743$	−3.63933e6	−	3.63933e6i	−0.241852	−	0.241852i	0.575764	−	0.817616i	$-0.304705\pi$
$743$	−3.63933e6	−	3.63933e6i	−0.241852	−	0.241852i	−0.817616	+	0.575764i	$0.804705\pi$
$744$		0			0
$745$	1.12824e7	+	1.33487e7i	0.744750	+	0.881148i
$746$		0			0
$747$	−1.90347e6	+	1.90347e6i	−0.124808	+	0.124808i
$748$		0			0
$749$		−	4.09476e6i		−	0.266700i
$750$		0			0
$751$		−	202134.i		−	0.0130779i	−0.999979	−	0.00653897i	$-0.997919\pi$
$751$		−	202134.i		−	0.0130779i	0.999979	−	0.00653897i	$-0.00208143\pi$
$752$		0			0
$753$	4.48616e6	−	4.48616e6i	0.288328	−	0.288328i
$754$		0			0
$755$	−3.30005e6	−	3.90445e6i	−0.210695	−	0.249283i
$756$		0			0
$757$	−8.73504e6	−	8.73504e6i	−0.554020	−	0.554020i	0.373579	−	0.927599i	$-0.378131\pi$
$757$	−8.73504e6	−	8.73504e6i	−0.554020	−	0.554020i	−0.927599	+	0.373579i	$0.878131\pi$
$758$		0			0
$759$	1.10253e7			0.694680
$760$		0			0
$761$	−1.57714e7			−0.987208			−0.493604	−	0.869687i	$-0.664321\pi$
$761$	−1.57714e7			−0.987208			−0.493604	+	0.869687i	$0.664321\pi$
$762$		0			0
$763$	1.64568e7	+	1.64568e7i	1.02337	+	1.02337i
$764$		0			0
$765$	590351.	−	7.03711e6i	0.0364717	−	0.434751i
$766$		0			0
$767$	−5.95314e6	+	5.95314e6i	−0.365391	+	0.365391i
$768$		0			0
$769$		−	5.82867e6i		−	0.355430i	−0.984082	−	0.177715i	$-0.943130\pi$
$769$		−	5.82867e6i		−	0.355430i	0.984082	−	0.177715i	$-0.0568705\pi$
$770$		0			0
$771$		−	4.52986e6i		−	0.274441i
$772$		0			0
$773$	−3.64656e6	+	3.64656e6i	−0.219500	+	0.219500i	−0.808288	−	0.588788i	$-0.799605\pi$
$773$	−3.64656e6	+	3.64656e6i	−0.219500	+	0.219500i	0.588788	+	0.808288i	$0.299605\pi$
$774$		0			0
$775$	−2.20180e7	−	3.72041e6i	−1.31681	−	0.222503i
$776$		0			0
$777$	6.60228e6	+	6.60228e6i	0.392321	+	0.392321i
$778$		0			0
$779$	−3.05545e6			−0.180398
$780$		0			0
$781$	−1.40820e7			−0.826105
$782$		0			0
$783$	7.31712e6	+	7.31712e6i	0.426516	+	0.426516i
$784$		0			0
$785$	−1.69681e7	−	1.42348e6i	−0.982788	−	0.0824472i
$786$		0			0
$787$	1.07036e7	−	1.07036e7i	0.616016	−	0.616016i	−0.328491	−	0.944507i	$-0.606540\pi$
$787$	1.07036e7	−	1.07036e7i	0.616016	−	0.616016i	0.944507	+	0.328491i	$0.106540\pi$
$788$		0			0
$789$		−	1.22589e7i		−	0.701068i
$790$		0			0
$791$			1.88061e7i			1.06871i
$792$		0			0
$793$	−1.62249e6	+	1.62249e6i	−0.0916217	+	0.0916217i
$794$		0			0
$795$	−1.58734e7	+	1.34162e7i	−0.890741	+	0.752857i
$796$		0			0
$797$	3.51227e6	+	3.51227e6i	0.195858	+	0.195858i	0.798222	−	0.602364i	$-0.205774\pi$
$797$	3.51227e6	+	3.51227e6i	0.195858	+	0.195858i	−0.602364	+	0.798222i	$0.705774\pi$
$798$		0			0
$799$	−3.28902e7			−1.82264
$800$		0			0
$801$	−4.38044e6			−0.241233
$802$		0			0
$803$	−1.57525e7	−	1.57525e7i	−0.862104	−	0.862104i
$804$		0			0
$805$	1.55667e7	−	1.31570e7i	0.846655	−	0.715596i
$806$		0			0
$807$	1.00384e7	−	1.00384e7i	0.542600	−	0.542600i
$808$		0			0
$809$			3.21162e7i			1.72525i	0.505840	+	0.862627i	$0.331183\pi$
$809$			3.21162e7i			1.72525i	−0.505840	+	0.862627i	$0.668817\pi$
$810$		0			0
$811$		−	6.71193e6i		−	0.358340i	−0.983818	−	0.179170i	$-0.942659\pi$
$811$		−	6.71193e6i		−	0.358340i	0.983818	−	0.179170i	$-0.0573412\pi$
$812$		0			0
$813$	3.18707e6	−	3.18707e6i	0.169108	−	0.169108i
$814$		0			0
$815$	3.30310e7	+	2.77100e6i	1.74192	+	0.146131i
$816$		0			0
$817$	7.15059e6	+	7.15059e6i	0.374789	+	0.374789i
$818$		0			0
$819$	−1.05873e7			−0.551540
$820$		0			0
$821$	2.61048e6			0.135164			0.0675821	−	0.997714i	$-0.478472\pi$
$821$	2.61048e6			0.135164			0.0675821	+	0.997714i	$0.478472\pi$
$822$		0			0
$823$	−7.89694e6	−	7.89694e6i	−0.406405	−	0.406405i	0.474078	−	0.880483i	$-0.342782\pi$
$823$	−7.89694e6	−	7.89694e6i	−0.406405	−	0.406405i	−0.880483	+	0.474078i	$0.842782\pi$
$824$		0			0
$825$	−8.19375e6	−	1.15258e7i	−0.419129	−	0.589571i
$826$		0			0
$827$	−1.87602e7	+	1.87602e7i	−0.953834	+	0.953834i	−0.998980	−	0.0451462i	$-0.985625\pi$
$827$	−1.87602e7	+	1.87602e7i	−0.953834	+	0.953834i	0.0451462	+	0.998980i	$0.485625\pi$
$828$		0			0
$829$			3.06101e6i			0.154696i	0.997004	+	0.0773480i	$0.0246452\pi$
$829$			3.06101e6i			0.154696i	−0.997004	+	0.0773480i	$0.975355\pi$
$830$		0			0
$831$		−	6.23345e6i		−	0.313131i
$832$		0			0
$833$	7.05845e6	−	7.05845e6i	0.352449	−	0.352449i
$834$		0			0
$835$	2.62305e6	−	3.12673e7i	0.130194	−	1.55194i
$836$		0			0
$837$	2.08059e7	+	2.08059e7i	1.02653	+	1.02653i
$838$		0			0
$839$	−2.88579e6			−0.141534			−0.0707668	−	0.997493i	$-0.522545\pi$
$839$	−2.88579e6			−0.141534			−0.0707668	+	0.997493i	$0.522545\pi$
$840$		0			0
$841$	1.41959e7			0.692107
$842$		0			0
$843$	−1.48200e7	−	1.48200e7i	−0.718256	−	0.718256i
$844$		0			0
$845$	−2.27131e7	−	2.68729e7i	−1.09430	−	1.29471i
$846$		0			0
$847$	4.46395e6	−	4.46395e6i	0.213801	−	0.213801i
$848$		0			0
$849$		−	2.43803e7i		−	1.16083i
$850$		0			0
$851$		−	1.15813e7i		−	0.548195i
$852$		0			0
$853$	−2.27693e7	+	2.27693e7i	−1.07146	+	1.07146i	−0.0742217	+	0.997242i	$0.523647\pi$
$853$	−2.27693e7	+	2.27693e7i	−1.07146	+	1.07146i	−0.997242	+	0.0742217i	$0.976353\pi$
$854$		0			0
$855$	1.11876e6	+	1.32366e6i	0.0523388	+	0.0619244i
$856$		0			0
$857$	709645.	+	709645.i	0.0330057	+	0.0330057i	0.723417	−	0.690411i	$-0.242570\pi$
$857$	709645.	+	709645.i	0.0330057	+	0.0330057i	−0.690411	+	0.723417i	$0.742570\pi$
$858$		0			0
$859$	2.46778e7			1.14110			0.570549	−	0.821264i	$-0.306731\pi$
$859$	2.46778e7			1.14110			0.570549	+	0.821264i	$0.306731\pi$
$860$		0			0
$861$	−1.36904e7			−0.629374
$862$		0			0
$863$	1.20888e7	+	1.20888e7i	0.552532	+	0.552532i	0.927171	−	0.374639i	$-0.122233\pi$
$863$	1.20888e7	+	1.20888e7i	0.552532	+	0.552532i	−0.374639	+	0.927171i	$0.622233\pi$
$864$		0			0
$865$	−304971.	+	3.63532e6i	−0.0138586	+	0.165197i
$866$		0			0
$867$	1.64350e7	−	1.64350e7i	0.742544	−	0.742544i
$868$		0			0
$869$			2.01544e7i			0.905358i
$870$		0			0
$871$			559690.i			0.0249978i
$872$		0			0
$873$	−784800.	+	784800.i	−0.0348517	+	0.0348517i
$874$		0			0
$875$	−2.53232e7	−	6.49535e6i	−1.11814	−	0.286802i
$876$		0			0
$877$	−5.57595e6	−	5.57595e6i	−0.244805	−	0.244805i	0.574030	−	0.818834i	$-0.305379\pi$
$877$	−5.57595e6	−	5.57595e6i	−0.244805	−	0.244805i	−0.818834	+	0.574030i	$0.805379\pi$
$878$		0			0
$879$	1.81761e7			0.793468
$880$		0			0
$881$	−3.00694e7			−1.30522			−0.652611	−	0.757693i	$-0.726326\pi$
$881$	−3.00694e7			−1.30522			−0.652611	+	0.757693i	$0.726326\pi$
$882$		0			0
$883$	9.38514e6	+	9.38514e6i	0.405078	+	0.405078i	0.880018	−	0.474940i	$-0.157530\pi$
$883$	9.38514e6	+	9.38514e6i	0.405078	+	0.405078i	−0.474940	+	0.880018i	$0.657530\pi$
$884$		0			0
$885$	6.15351e6	+	516225.i	0.264098	+	0.0221555i
$886$		0			0
$887$	−1.96936e7	+	1.96936e7i	−0.840458	+	0.840458i	−0.988918	−	0.148461i	$-0.952568\pi$
$887$	−1.96936e7	+	1.96936e7i	−0.840458	+	0.840458i	0.148461	+	0.988918i	$0.452568\pi$
$888$		0			0
$889$			3.13152e7i			1.32893i
$890$		0			0
$891$			1.27089e7i			0.536309i
$892$		0			0
$893$	5.70774e6	−	5.70774e6i	0.239517	−	0.239517i
$894$		0			0
$895$	−770222.	+	650995.i	−0.0321409	+	0.0271656i
$896$		0			0
$897$	−2.26204e7	−	2.26204e7i	−0.938683	−	0.938683i
$898$		0			0
$899$	−1.79571e7			−0.741032
$900$		0			0
$901$	5.05966e7			2.07639
$902$		0			0
$903$	3.20393e7	+	3.20393e7i	1.30757	+	1.30757i
$904$		0			0
$905$	5.35680e6	−	4.52759e6i	0.217412	−	0.183758i
$906$		0			0
$907$	2.14154e7	−	2.14154e7i	0.864388	−	0.864388i	−0.127456	−	0.991844i	$-0.540681\pi$
$907$	2.14154e7	−	2.14154e7i	0.864388	−	0.864388i	0.991844	+	0.127456i	$0.0406813\pi$
$908$		0			0
$909$			9.75402e6i			0.391538i
$910$		0			0
$911$			3.69457e6i			0.147492i	0.997277	+	0.0737459i	$0.0234954\pi$
$911$			3.69457e6i			0.147492i	−0.997277	+	0.0737459i	$0.976505\pi$
$912$		0			0
$913$	9.27946e6	−	9.27946e6i	0.368422	−	0.368422i
$914$		0			0
$915$	1.67710e6	+	140694.i	0.0662226	+	0.00555548i
$916$		0			0
$917$	−1.09466e7	−	1.09466e7i	−0.429890	−	0.429890i
$918$		0			0
$919$	2.06290e7			0.805731			0.402865	−	0.915259i	$-0.368014\pi$
$919$	2.06290e7			0.805731			0.402865	+	0.915259i	$0.368014\pi$
$920$		0			0
$921$	2.56003e7			0.994481
$922$		0			0
$923$	2.88918e7	+	2.88918e7i	1.11627	+	1.11627i
$924$		0			0
$925$	−1.21071e7	+	8.60701e6i	−0.465250	+	0.330749i
$926$		0			0
$927$	7.56227e6	−	7.56227e6i	0.289037	−	0.289037i
$928$		0			0
$929$		−	7.31010e6i		−	0.277897i	−0.990300	−	0.138948i	$-0.955628\pi$
$929$		−	7.31010e6i		−	0.277897i	0.990300	−	0.138948i	$-0.0443722\pi$
$930$		0			0
$931$			2.44983e6i			0.0926323i
$932$		0			0
$933$	−3.15805e7	+	3.15805e7i	−1.18772	+	1.18772i
$934$		0			0
$935$	−2.87798e6	+	3.43061e7i	−0.107661	+	1.28334i
$936$		0			0
$937$	−6.32850e6	−	6.32850e6i	−0.235479	−	0.235479i	0.579496	−	0.814975i	$-0.303249\pi$
$937$	−6.32850e6	−	6.32850e6i	−0.235479	−	0.235479i	−0.814975	+	0.579496i	$0.803249\pi$
$938$		0			0
$939$	2.09445e7			0.775187
$940$		0			0
$941$	4.14005e7			1.52416			0.762082	−	0.647481i	$-0.224177\pi$
$941$	4.14005e7			1.52416			0.762082	+	0.647481i	$0.224177\pi$
$942$		0			0
$943$	1.20075e7	+	1.20075e7i	0.439716	+	0.439716i
$944$		0			0
$945$	2.22368e7	+	2.63094e7i	0.810016	+	0.958368i
$946$		0			0
$947$	−2.01051e7	+	2.01051e7i	−0.728503	+	0.728503i	−0.970322	−	0.241818i	$-0.922256\pi$
$947$	−2.01051e7	+	2.01051e7i	−0.728503	+	0.728503i	0.241818	+	0.970322i	$0.422256\pi$
$948$		0			0
$949$			6.46382e7i			2.32983i
$950$		0			0
$951$		−	4.57105e7i		−	1.63895i
$952$		0			0
$953$	−2.97014e7	+	2.97014e7i	−1.05936	+	1.05936i	−0.0612391	+	0.998123i	$0.519505\pi$
$953$	−2.97014e7	+	2.97014e7i	−1.05936	+	1.05936i	−0.998123	+	0.0612391i	$0.980495\pi$
$954$		0			0
$955$	−1.71307e7	−	2.02681e7i	−0.607807	−	0.719125i
$956$		0			0
$957$	−8.04127e6	−	8.04127e6i	−0.283821	−	0.283821i
$958$		0			0
$959$	3.01922e7			1.06010
$960$		0			0
$961$	−2.24309e7			−0.783500
$962$		0			0
$963$	−1.36832e6	−	1.36832e6i	−0.0475467	−	0.0475467i
$964$		0			0
$965$	−2.28379e6	+	2.72233e7i	−0.0789475	+	0.941072i
$966$		0			0
$967$	−3.21695e7	+	3.21695e7i	−1.10631	+	1.10631i	−0.112681	+	0.993631i	$0.535944\pi$
$967$	−3.21695e7	+	3.21695e7i	−1.10631	+	1.10631i	−0.993631	+	0.112681i	$0.964056\pi$
$968$		0			0
$969$			1.02780e7i			0.351640i
$970$		0			0
$971$			3.27877e7i			1.11600i	0.829842	+	0.557998i	$0.188430\pi$
$971$			3.27877e7i			1.11600i	−0.829842	+	0.557998i	$0.811570\pi$
$972$		0			0
$973$	1.55845e7	−	1.55845e7i	0.527728	−	0.527728i
$974$		0			0
$975$	−6.83629e6	+	4.04583e7i	−0.230308	+	1.36300i
$976$		0			0
$977$	−2.68706e7	−	2.68706e7i	−0.900618	−	0.900618i	0.0948719	−	0.995489i	$-0.469756\pi$
$977$	−2.68706e7	−	2.68706e7i	−0.900618	−	0.900618i	−0.995489	+	0.0948719i	$0.969756\pi$
$978$		0			0
$979$	2.13548e7			0.712096
$980$		0			0
$981$	1.09985e7			0.364890
$982$		0			0
$983$	1.96745e7	+	1.96745e7i	0.649412	+	0.649412i	0.952851	−	0.303439i	$-0.0981349\pi$
$983$	1.96745e7	+	1.96745e7i	0.649412	+	0.649412i	−0.303439	+	0.952851i	$0.598135\pi$
$984$		0			0
$985$	−3.61481e7	−	3.03250e6i	−1.18712	−	0.0995888i
$986$		0			0
$987$	2.55745e7	−	2.55745e7i	0.835629	−	0.835629i
$988$		0			0
$989$		−	5.62016e7i		−	1.82708i
$990$		0			0
$991$			3.01223e7i			0.974324i	0.873312	+	0.487162i	$0.161968\pi$
$991$			3.01223e7i			0.974324i	−0.873312	+	0.487162i	$0.838032\pi$
$992$		0			0
$993$	−3.57124e7	+	3.57124e7i	−1.14933	+	1.14933i
$994$		0			0
$995$	−1.54704e7	+	1.30756e7i	−0.495385	+	0.418701i
$996$		0			0
$997$	−4.86509e6	−	4.86509e6i	−0.155008	−	0.155008i	0.625343	−	0.780350i	$-0.284959\pi$
$997$	−4.86509e6	−	4.86509e6i	−0.155008	−	0.155008i	−0.780350	+	0.625343i	$0.784959\pi$
$998$		0			0
$999$	1.95738e7			0.620527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.a.127.3	yes	14
4.3	odd	2		160.6.n.b.127.5	yes	14
5.3	odd	4		160.6.n.b.63.5	yes	14
20.3	even	4	inner	160.6.n.a.63.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.a.63.3	✓	14	20.3	even	4	inner
160.6.n.a.127.3	yes	14	1.1	even	1	trivial
160.6.n.b.63.5	yes	14	5.3	odd	4
160.6.n.b.127.5	yes	14	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-9.28112 - 9.28112i) q^{3} +(42.6946 - 36.0856i) q^{5} +(105.819 - 105.819i) q^{7} -70.7216i q^{9} +O(q^{10})\)	\(q+(-9.28112 - 9.28112i) q^{3} +(42.6946 - 36.0856i) q^{5} +(105.819 - 105.819i) q^{7} -70.7216i q^{9} +344.770i q^{11} +(707.360 - 707.360i) q^{13} +(-731.169 - 61.3385i) q^{15} +(1263.06 + 1263.06i) q^{17} -438.382 q^{19} -1964.24 q^{21} +(1722.78 + 1722.78i) q^{23} +(520.655 - 3081.32i) q^{25} +(-2911.69 + 2911.69i) q^{27} -2513.02i q^{29} -7145.63i q^{31} +(3199.85 - 3199.85i) q^{33} +(699.354 - 8336.45i) q^{35} +(-3361.24 - 3361.24i) q^{37} -13130.2 q^{39} +6969.83 q^{41} +(-16311.3 - 16311.3i) q^{43} +(-2552.03 - 3019.43i) q^{45} +(-13020.0 + 13020.0i) q^{47} -5588.36i q^{49} -23445.3i q^{51} +(20029.3 - 20029.3i) q^{53} +(12441.2 + 14719.8i) q^{55} +(4068.67 + 4068.67i) q^{57} -8416.00 q^{59} -2293.72 q^{61} +(-7483.70 - 7483.70i) q^{63} +(4674.91 - 55725.9i) q^{65} +(-395.619 + 395.619i) q^{67} -31978.6i q^{69} +40844.5i q^{71} +(-45689.8 + 45689.8i) q^{73} +(-33430.4 + 23765.9i) q^{75} +(36483.2 + 36483.2i) q^{77} +58457.5 q^{79} +36862.1 q^{81} +(-26914.9 - 26914.9i) q^{83} +(99504.4 + 8347.53i) q^{85} +(-23323.6 + 23323.6i) q^{87} -61939.2i q^{89} -149704. i q^{91} +(-66319.5 + 66319.5i) q^{93} +(-18716.5 + 15819.3i) q^{95} +(-11097.0 - 11097.0i) q^{97} +24382.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7}+O(q^{10}) \) 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7	\( 14 q - 10 q^{3} + 42 q^{5} - 66 q^{7} - 414 q^{13} - 278 q^{15} + 1222 q^{17} - 5672 q^{19} + 5924 q^{21} - 2902 q^{23} - 4466 q^{25} + 2168 q^{27} - 2444 q^{33} + 2618 q^{35} - 1790 q^{37} + 11076 q^{39} + 11644 q^{41} + 3982 q^{43} + 14704 q^{45} + 1278 q^{47} + 5882 q^{53} - 65608 q^{55} - 14552 q^{57} + 8504 q^{59} + 20564 q^{61} - 19422 q^{63} + 40798 q^{65} - 107926 q^{67} - 16418 q^{73} - 66586 q^{75} - 13348 q^{77} + 146544 q^{79} + 173806 q^{81} + 36398 q^{83} - 66262 q^{85} - 124384 q^{87} - 306620 q^{93} - 173768 q^{95} - 60314 q^{97} + 388628 q^{99}+O(q^{100}) \) 14 * q - 10 * q^3 + 42 * q^5 - 66 * q^7 - 414 * q^13 - 278 * q^15 + 1222 * q^17 - 5672 * q^19 + 5924 * q^21 - 2902 * q^23 - 4466 * q^25 + 2168 * q^27 - 2444 * q^33 + 2618 * q^35 - 1790 * q^37 + 11076 * q^39 + 11644 * q^41 + 3982 * q^43 + 14704 * q^45 + 1278 * q^47 + 5882 * q^53 - 65608 * q^55 - 14552 * q^57 + 8504 * q^59 + 20564 * q^61 - 19422 * q^63 + 40798 * q^65 - 107926 * q^67 - 16418 * q^73 - 66586 * q^75 - 13348 * q^77 + 146544 * q^79 + 173806 * q^81 + 36398 * q^83 - 66262 * q^85 - 124384 * q^87 - 306620 * q^93 - 173768 * q^95 - 60314 * q^97 + 388628 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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