LMFDB - Embedded newform 160.6.n.b.127.4

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			127.4
Root			$6.86993 - 6.86993i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.6.n.b.63.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47740 + 1.47740i) q^{3} +(55.2474 + 8.52775i) q^{5} +(156.265 - 156.265i) q^{7} -238.635i q^{9} +O(q^{10})$	\(q+(1.47740 + 1.47740i) q^{3} +(55.2474 + 8.52775i) q^{5} +(156.265 - 156.265i) q^{7} -238.635i q^{9} -35.4820i q^{11} +(-247.384 + 247.384i) q^{13} +(69.0238 + 94.2216i) q^{15} +(-1193.47 - 1193.47i) q^{17} -1010.27 q^{19} +461.733 q^{21} +(2033.39 + 2033.39i) q^{23} +(2979.55 + 942.273i) q^{25} +(711.568 - 711.568i) q^{27} -2206.91i q^{29} -6179.11i q^{31} +(52.4213 - 52.4213i) q^{33} +(9965.84 - 7300.66i) q^{35} +(-9466.02 - 9466.02i) q^{37} -730.972 q^{39} -9004.04 q^{41} +(15902.9 + 15902.9i) q^{43} +(2035.02 - 13183.9i) q^{45} +(7193.64 - 7193.64i) q^{47} -32030.6i q^{49} -3526.47i q^{51} +(-12995.3 + 12995.3i) q^{53} +(302.582 - 1960.29i) q^{55} +(-1492.57 - 1492.57i) q^{57} +40515.4 q^{59} +29233.6 q^{61} +(-37290.3 - 37290.3i) q^{63} +(-15777.0 + 11557.7i) q^{65} +(18221.2 - 18221.2i) q^{67} +6008.26i q^{69} +26609.8i q^{71} +(36402.4 - 36402.4i) q^{73} +(3009.89 + 5794.12i) q^{75} +(-5544.61 - 5544.61i) q^{77} -5089.11 q^{79} -55885.7 q^{81} +(20395.0 + 20395.0i) q^{83} +(-55758.6 - 76113.8i) q^{85} +(3260.49 - 3260.49i) q^{87} +59348.0i q^{89} +77315.1i q^{91} +(9129.03 - 9129.03i) q^{93} +(-55814.6 - 8615.30i) q^{95} +(69542.4 + 69542.4i) q^{97} -8467.24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.47740	+	1.47740i	0.0947754	+	0.0947754i	0.752905	−	0.658129i	$-0.228652\pi$
$3$	1.47740	+	1.47740i	0.0947754	+	0.0947754i	−0.658129	+	0.752905i	$0.728652\pi$
$4$		0			0
$5$	55.2474	+	8.52775i	0.988296	+	0.152549i
$5$	55.2474	+	8.52775i	0.988296	+	0.152549i
$6$		0			0
$7$	156.265	−	156.265i	1.20536	−	1.20536i	0.232848	−	0.972513i	$-0.425196\pi$
$7$	156.265	−	156.265i	1.20536	−	1.20536i	0.972513	−	0.232848i	$-0.0748044\pi$
$8$		0			0
$9$		−	238.635i		−	0.982035i
$10$		0			0
$11$		−	35.4820i		−	0.0884152i	−0.999022	−	0.0442076i	$-0.985924\pi$
$11$		−	35.4820i		−	0.0884152i	0.999022	−	0.0442076i	$-0.0140763\pi$
$12$		0			0
$13$	−247.384	+	247.384i	−0.405988	+	0.405988i	−0.880337	−	0.474349i	$-0.842684\pi$
$13$	−247.384	+	247.384i	−0.405988	+	0.405988i	0.474349	+	0.880337i	$0.342684\pi$
$14$		0			0
$15$	69.0238	+	94.2216i	0.0792083	+	0.108124i
$16$		0			0
$17$	−1193.47	−	1193.47i	−1.00159	−	1.00159i	−0.999999	−	0.00159016i	$-0.999494\pi$
$17$	−1193.47	−	1193.47i	−1.00159	−	1.00159i	−0.00159016	−	0.999999i	$-0.500506\pi$
$18$		0			0
$19$	−1010.27			−0.642025			−0.321012	−	0.947075i	$-0.604023\pi$
$19$	−1010.27			−0.642025			−0.321012	+	0.947075i	$0.604023\pi$
$20$		0			0
$21$	461.733			0.228477
$22$		0			0
$23$	2033.39	+	2033.39i	0.801494	+	0.801494i	0.983329	−	0.181835i	$-0.0582036\pi$
$23$	2033.39	+	2033.39i	0.801494	+	0.801494i	−0.181835	+	0.983329i	$0.558204\pi$
$24$		0			0
$25$	2979.55	+	942.273i	0.953458	+	0.301527i
$26$		0			0
$27$	711.568	−	711.568i	0.187848	−	0.187848i
$28$		0			0
$29$		−	2206.91i		−	0.487291i	−0.969864	−	0.243646i	$-0.921657\pi$
$29$		−	2206.91i		−	0.487291i	0.969864	−	0.243646i	$-0.0783434\pi$
$30$		0			0
$31$		−	6179.11i		−	1.15484i	−0.816448	−	0.577419i	$-0.804060\pi$
$31$		−	6179.11i		−	1.15484i	0.816448	−	0.577419i	$-0.195940\pi$
$32$		0			0
$33$	52.4213	−	52.4213i	0.00837959	−	0.00837959i
$34$		0			0
$35$	9965.84	−	7300.66i	1.37513	−	1.00738i
$36$		0			0
$37$	−9466.02	−	9466.02i	−1.13674	−	1.13674i	−0.989030	−	0.147715i	$-0.952808\pi$
$37$	−9466.02	−	9466.02i	−1.13674	−	1.13674i	−0.147715	−	0.989030i	$-0.547192\pi$
$38$		0			0
$39$	−730.972			−0.0769554
$40$		0			0
$41$	−9004.04			−0.836523			−0.418261	−	0.908327i	$-0.637360\pi$
$41$	−9004.04			−0.836523			−0.418261	+	0.908327i	$0.637360\pi$
$42$		0			0
$43$	15902.9	+	15902.9i	1.31161	+	1.31161i	0.920228	+	0.391383i	$0.128003\pi$
$43$	15902.9	+	15902.9i	1.31161	+	1.31161i	0.391383	+	0.920228i	$0.371997\pi$
$44$		0			0
$45$	2035.02	−	13183.9i	0.149809	−	0.970541i
$46$		0			0
$47$	7193.64	−	7193.64i	0.475011	−	0.475011i	−0.428521	−	0.903532i	$-0.640965\pi$
$47$	7193.64	−	7193.64i	0.475011	−	0.475011i	0.903532	+	0.428521i	$0.140965\pi$
$48$		0			0
$49$		−	32030.6i		−	1.90579i
$50$		0			0
$51$		−	3526.47i		−	0.189852i
$52$		0			0
$53$	−12995.3	+	12995.3i	−0.635474	+	0.635474i	−0.949436	−	0.313962i	$-0.898344\pi$
$53$	−12995.3	+	12995.3i	−0.635474	+	0.635474i	0.313962	+	0.949436i	$0.398344\pi$
$54$		0			0
$55$	302.582	−	1960.29i	0.0134877	−	0.0873804i
$56$		0			0
$57$	−1492.57	−	1492.57i	−0.0608482	−	0.0608482i
$58$		0			0
$59$	40515.4			1.51527			0.757636	−	0.652677i	$-0.226354\pi$
$59$	40515.4			1.51527			0.757636	+	0.652677i	$0.226354\pi$
$60$		0			0
$61$	29233.6			1.00591			0.502954	−	0.864313i	$-0.332247\pi$
$61$	29233.6			1.00591			0.502954	+	0.864313i	$0.332247\pi$
$62$		0			0
$63$	−37290.3	−	37290.3i	−1.18371	−	1.18371i
$64$		0			0
$65$	−15777.0	+	11557.7i	−0.463170	+	0.339303i
$66$		0			0
$67$	18221.2	−	18221.2i	0.495894	−	0.495894i	−0.414263	−	0.910157i	$-0.635961\pi$
$67$	18221.2	−	18221.2i	0.495894	−	0.495894i	0.910157	+	0.414263i	$0.135961\pi$
$68$		0			0
$69$			6008.26i			0.151924i
$70$		0			0
$71$			26609.8i			0.626463i	0.949677	+	0.313232i	$0.101412\pi$
$71$			26609.8i			0.626463i	−0.949677	+	0.313232i	$0.898588\pi$
$72$		0			0
$73$	36402.4	−	36402.4i	0.799507	−	0.799507i	−0.183511	−	0.983018i	$-0.558746\pi$
$73$	36402.4	−	36402.4i	0.799507	−	0.799507i	0.983018	+	0.183511i	$0.0587462\pi$
$74$		0			0
$75$	3009.89	+	5794.12i	0.0617870	+	0.118942i
$76$		0			0
$77$	−5544.61	−	5544.61i	−0.106572	−	0.106572i
$78$		0			0
$79$	−5089.11			−0.0917432			−0.0458716	−	0.998947i	$-0.514607\pi$
$79$	−5089.11			−0.0917432			−0.0458716	+	0.998947i	$0.514607\pi$
$80$		0			0
$81$	−55885.7			−0.946428
$82$		0			0
$83$	20395.0	+	20395.0i	0.324958	+	0.324958i	0.850666	−	0.525707i	$-0.176199\pi$
$83$	20395.0	+	20395.0i	0.324958	+	0.324958i	−0.525707	+	0.850666i	$0.676199\pi$
$84$		0			0
$85$	−55758.6	−	76113.8i	−0.837075	−	1.14266i
$86$		0			0
$87$	3260.49	−	3260.49i	0.0461832	−	0.0461832i
$88$		0			0
$89$			59348.0i			0.794202i	0.917775	+	0.397101i	$0.129984\pi$
$89$			59348.0i			0.794202i	−0.917775	+	0.397101i	$0.870016\pi$
$90$		0			0
$91$			77315.1i			0.978725i
$92$		0			0
$93$	9129.03	−	9129.03i	0.109450	−	0.109450i
$94$		0			0
$95$	−55814.6	−	8615.30i	−0.634511	−	0.0979403i
$96$		0			0
$97$	69542.4	+	69542.4i	0.750447	+	0.750447i	0.974563	−	0.224115i	$-0.0719492\pi$
$97$	69542.4	+	69542.4i	0.750447	+	0.750447i	−0.224115	+	0.974563i	$0.571949\pi$
$98$		0			0
$99$	−8467.24			−0.0868268
$100$		0			0
$101$	51962.3			0.506857			0.253428	−	0.967354i	$-0.418442\pi$
$101$	51962.3			0.506857			0.253428	+	0.967354i	$0.418442\pi$
$102$		0			0
$103$	−95475.1	−	95475.1i	−0.886742	−	0.886742i	0.107467	−	0.994209i	$-0.465726\pi$
$103$	−95475.1	−	95475.1i	−0.886742	−	0.886742i	−0.994209	+	0.107467i	$0.965726\pi$
$104$		0			0
$105$	25509.6	+	3937.55i	0.225803	+	0.0348540i
$106$		0			0
$107$	47628.0	−	47628.0i	0.402164	−	0.402164i	−0.476831	−	0.878995i	$-0.658215\pi$
$107$	47628.0	−	47628.0i	0.402164	−	0.402164i	0.878995	+	0.476831i	$0.158215\pi$
$108$		0			0
$109$			207149.i			1.67000i	0.550249	+	0.835000i	$0.314533\pi$
$109$			207149.i			1.67000i	−0.550249	+	0.835000i	$0.685467\pi$
$110$		0			0
$111$		−	27970.2i		−	0.215471i
$112$		0			0
$113$	−69766.1	+	69766.1i	−0.513983	+	0.513983i	−0.915744	−	0.401762i	$-0.868398\pi$
$113$	−69766.1	+	69766.1i	−0.513983	+	0.513983i	0.401762	+	0.915744i	$0.368398\pi$
$114$		0			0
$115$	94999.2	+	129680.i	0.669846	+	0.914381i
$116$		0			0
$117$	59034.4	+	59034.4i	0.398695	+	0.398695i
$118$		0			0
$119$	−372996.			−2.41455
$120$		0			0
$121$	159792.			0.992183
$122$		0			0
$123$	−13302.6	−	13302.6i	−0.0792818	−	0.0792818i
$124$		0			0
$125$	156577.	+	77467.0i	0.896301	+	0.443447i
$126$		0			0
$127$	−211933.	+	211933.i	−1.16598	+	1.16598i	−0.182831	+	0.983144i	$0.558526\pi$
$127$	−211933.	+	211933.i	−1.16598	+	1.16598i	−0.983144	+	0.182831i	$0.941474\pi$
$128$		0			0
$129$			46990.0i			0.248617i
$130$		0			0
$131$			231312.i			1.17766i	0.808258	+	0.588829i	$0.200411\pi$
$131$			231312.i			1.17766i	−0.808258	+	0.588829i	$0.799589\pi$
$132$		0			0
$133$	−157869.	+	157869.i	−0.773872	+	0.773872i
$134$		0			0
$135$	45380.4	−	33244.2i	0.214306	−	0.156994i
$136$		0			0
$137$	−148753.	−	148753.i	−0.677119	−	0.677119i	0.282228	−	0.959347i	$-0.408926\pi$
$137$	−148753.	−	148753.i	−0.677119	−	0.677119i	−0.959347	+	0.282228i	$0.908926\pi$
$138$		0			0
$139$	−28622.8			−0.125653			−0.0628267	−	0.998024i	$-0.520012\pi$
$139$	−28622.8			−0.125653			−0.0628267	+	0.998024i	$0.520012\pi$
$140$		0			0
$141$	21255.8			0.0900388
$142$		0			0
$143$	8777.70	+	8777.70i	0.0358955	+	0.0358955i
$144$		0			0
$145$	18819.9	−	121926.i	0.0743358	−	0.481588i
$146$		0			0
$147$	47322.1	−	47322.1i	0.180622	−	0.180622i
$148$		0			0
$149$		−	168468.i		−	0.621658i	−0.950466	−	0.310829i	$-0.899393\pi$
$149$		−	168468.i		−	0.621658i	0.950466	−	0.310829i	$-0.100607\pi$
$150$		0			0
$151$		−	114484.i		−	0.408604i	−0.978908	−	0.204302i	$-0.934508\pi$
$151$		−	114484.i		−	0.408604i	0.978908	−	0.204302i	$-0.0654924\pi$
$152$		0			0
$153$	−284803.	+	284803.i	−0.983596	+	0.983596i
$154$		0			0
$155$	52693.9	−	341380.i	0.176170	−	1.14132i
$156$		0			0
$157$	−148793.	−	148793.i	−0.481762	−	0.481762i	0.423932	−	0.905694i	$-0.360650\pi$
$157$	−148793.	−	148793.i	−0.481762	−	0.481762i	−0.905694	+	0.423932i	$0.860650\pi$
$158$		0			0
$159$	−38398.7			−0.120455
$160$		0			0
$161$	635495.			1.93218
$162$		0			0
$163$	−14195.8	−	14195.8i	−0.0418496	−	0.0418496i	0.685872	−	0.727722i	$-0.259421\pi$
$163$	−14195.8	−	14195.8i	−0.0418496	−	0.0418496i	−0.727722	+	0.685872i	$0.759421\pi$
$164$		0			0
$165$	3343.17	−	2449.10i	0.00955981	−	0.00700321i
$166$		0			0
$167$	129380.	−	129380.i	0.358985	−	0.358985i	−0.504453	−	0.863439i	$-0.668306\pi$
$167$	129380.	−	129380.i	0.358985	−	0.358985i	0.863439	+	0.504453i	$0.168306\pi$
$168$		0			0
$169$			248895.i			0.670347i
$170$		0			0
$171$			241084.i			0.630491i
$172$		0			0
$173$	152149.	−	152149.i	0.386505	−	0.386505i	−0.486934	−	0.873439i	$-0.661885\pi$
$173$	152149.	−	152149.i	0.386505	−	0.386505i	0.873439	+	0.486934i	$0.161885\pi$
$174$		0			0
$175$	612845.	−	318356.i	1.51271	−	0.785811i
$176$		0			0
$177$	59857.6	+	59857.6i	0.143611	+	0.143611i
$178$		0			0
$179$	−293286.			−0.684161			−0.342081	−	0.939671i	$-0.611132\pi$
$179$	−293286.			−0.684161			−0.342081	+	0.939671i	$0.611132\pi$
$180$		0			0
$181$	−35244.3			−0.0799635			−0.0399818	−	0.999200i	$-0.512730\pi$
$181$	−35244.3			−0.0799635			−0.0399818	+	0.999200i	$0.512730\pi$
$182$		0			0
$183$	43189.8	+	43189.8i	0.0953353	+	0.0953353i
$184$		0			0
$185$	−442249.	−	603697.i	−0.950031	−	1.29685i
$186$		0			0
$187$	−42346.8	+	42346.8i	−0.0885557	+	0.0885557i
$188$		0			0
$189$		−	222387.i		−	0.452850i
$190$		0			0
$191$			862350.i			1.71041i	0.518291	+	0.855204i	$0.326568\pi$
$191$			862350.i			1.71041i	−0.518291	+	0.855204i	$0.673432\pi$
$192$		0			0
$193$	−87253.9	+	87253.9i	−0.168613	+	0.168613i	−0.786370	−	0.617756i	$-0.788042\pi$
$193$	−87253.9	+	87253.9i	−0.168613	+	0.168613i	0.617756	+	0.786370i	$0.288042\pi$
$194$		0			0
$195$	−40384.3	−	6233.55i	−0.0760547	−	0.0117395i
$196$		0			0
$197$	−113501.	−	113501.i	−0.208369	−	0.208369i	0.595205	−	0.803574i	$-0.297071\pi$
$197$	−113501.	−	113501.i	−0.208369	−	0.208369i	−0.803574	+	0.595205i	$0.797071\pi$
$198$		0			0
$199$	497444.			0.890455			0.445227	−	0.895418i	$-0.353123\pi$
$199$	497444.			0.890455			0.445227	+	0.895418i	$0.353123\pi$
$200$		0			0
$201$	53840.0			0.0939971
$202$		0			0
$203$	−344863.	−	344863.i	−0.587362	−	0.587362i
$204$		0			0
$205$	−497450.	−	76784.2i	−0.826732	−	0.127611i
$206$		0			0
$207$	485236.	−	485236.i	0.787096	−	0.787096i
$208$		0			0
$209$			35846.3i			0.0567648i
$210$		0			0
$211$		−	359007.i		−	0.555133i	−0.960706	−	0.277566i	$-0.910472\pi$
$211$		−	359007.i		−	0.555133i	0.960706	−	0.277566i	$-0.0895278\pi$
$212$		0			0
$213$	−39313.4	+	39313.4i	−0.0593733	+	0.0593733i
$214$		0			0
$215$	742978.	+	1.01421e6i	1.09617	+	1.49634i
$216$		0			0
$217$	−965579.	−	965579.i	−1.39200	−	1.39200i
$218$		0			0
$219$	107562.			0.151547
$220$		0			0
$221$	590492.			0.813267
$222$		0			0
$223$	−927233.	−	927233.i	−1.24861	−	1.24861i	−0.956334	−	0.292276i	$-0.905587\pi$
$223$	−927233.	−	927233.i	−1.24861	−	1.24861i	−0.292276	−	0.956334i	$-0.594413\pi$
$224$		0			0
$225$	224859.	−	711025.i	0.296110	−	0.936329i
$226$		0			0
$227$	1.02849e6	−	1.02849e6i	1.32475	−	1.32475i	0.414871	−	0.909880i	$-0.363827\pi$
$227$	1.02849e6	−	1.02849e6i	1.32475	−	1.32475i	0.909880	−	0.414871i	$-0.136173\pi$
$228$		0			0
$229$			624395.i			0.786812i	0.919365	+	0.393406i	$0.128703\pi$
$229$			624395.i			0.786812i	−0.919365	+	0.393406i	$0.871297\pi$
$230$		0			0
$231$		−	16383.2i		−	0.0202009i
$232$		0			0
$233$	73769.5	−	73769.5i	0.0890199	−	0.0890199i	−0.661195	−	0.750214i	$-0.729950\pi$
$233$	73769.5	−	73769.5i	0.0890199	−	0.0890199i	0.750214	+	0.661195i	$0.229950\pi$
$234$		0			0
$235$	458776.	−	336084.i	0.541914	−	0.396989i
$236$		0			0
$237$	−7518.66	−	7518.66i	−0.00869500	−	0.00869500i
$238$		0			0
$239$	1.58693e6			1.79706			0.898529	−	0.438914i	$-0.144637\pi$
$239$	1.58693e6			1.79706			0.898529	+	0.438914i	$0.144637\pi$
$240$		0			0
$241$	217448.			0.241165			0.120582	−	0.992703i	$-0.461524\pi$
$241$	217448.			0.241165			0.120582	+	0.992703i	$0.461524\pi$
$242$		0			0
$243$	−255477.	−	255477.i	−0.277546	−	0.277546i
$244$		0			0
$245$	273149.	−	1.76961e6i	0.290727	−	1.88349i
$246$		0			0
$247$	249924.	−	249924.i	0.260655	−	0.260655i
$248$		0			0
$249$			60263.1i			0.0615961i
$250$		0			0
$251$			1.84448e6i			1.84794i	0.382460	+	0.923972i	$0.375077\pi$
$251$			1.84448e6i			1.84794i	−0.382460	+	0.923972i	$0.624923\pi$
$252$		0			0
$253$	72148.7	−	72148.7i	0.0708643	−	0.0708643i
$254$		0			0
$255$	30072.9	−	194829.i	0.0289617	−	0.187630i
$256$		0			0
$257$	934464.	+	934464.i	0.882531	+	0.882531i	0.993791	−	0.111261i	$-0.0354888\pi$
$257$	934464.	+	934464.i	0.882531	+	0.882531i	−0.111261	+	0.993791i	$0.535489\pi$
$258$		0			0
$259$	−2.95842e6			−2.74038
$260$		0			0
$261$	−526644.			−0.478537
$262$		0			0
$263$	545731.	+	545731.i	0.486508	+	0.486508i	0.907202	−	0.420695i	$-0.138214\pi$
$263$	545731.	+	545731.i	0.486508	+	0.486508i	−0.420695	+	0.907202i	$0.638214\pi$
$264$		0			0
$265$	−828779.	+	607137.i	−0.724977	+	0.531095i
$266$		0			0
$267$	−87680.8	+	87680.8i	−0.0752708	+	0.0752708i
$268$		0			0
$269$			1.62710e6i			1.37099i	0.728078	+	0.685495i	$0.240414\pi$
$269$			1.62710e6i			1.37099i	−0.728078	+	0.685495i	$0.759586\pi$
$270$		0			0
$271$			344866.i			0.285251i	0.989777	+	0.142626i	$0.0455545\pi$
$271$			344866.i			0.285251i	−0.989777	+	0.142626i	$0.954446\pi$
$272$		0			0
$273$	−114225.	+	114225.i	−0.0927591	+	0.0927591i
$274$		0			0
$275$	33433.8	−	105721.i	0.0266596	−	0.0843001i
$276$		0			0
$277$	−1.31320e6	−	1.31320e6i	−1.02833	−	1.02833i	−0.999587	−	0.0287441i	$-0.990849\pi$
$277$	−1.31320e6	−	1.31320e6i	−1.02833	−	1.02833i	−0.0287441	−	0.999587i	$-0.509151\pi$
$278$		0			0
$279$	−1.47455e6			−1.13409
$280$		0			0
$281$	592433.			0.447583			0.223791	−	0.974637i	$-0.428157\pi$
$281$	592433.			0.447583			0.223791	+	0.974637i	$0.428157\pi$
$282$		0			0
$283$	−898854.	−	898854.i	−0.667149	−	0.667149i	0.289906	−	0.957055i	$-0.406376\pi$
$283$	−898854.	−	898854.i	−0.667149	−	0.667149i	−0.957055	+	0.289906i	$0.906376\pi$
$284$		0			0
$285$	−69732.4	−	95188.9i	−0.0508537	−	0.0694183i
$286$		0			0
$287$	−1.40702e6	+	1.40702e6i	−1.00831	+	1.00831i
$288$		0			0
$289$			1.42889e6i			1.00636i
$290$		0			0
$291$			205484.i			0.142248i
$292$		0			0
$293$	−1.69674e6	+	1.69674e6i	−1.15464	+	1.15464i	−0.169032	+	0.985611i	$0.554064\pi$
$293$	−1.69674e6	+	1.69674e6i	−1.15464	+	1.15464i	−0.985611	+	0.169032i	$0.945936\pi$
$294$		0			0
$295$	2.23837e6	+	345506.i	1.49754	+	0.231153i
$296$		0			0
$297$	−25247.9	−	25247.9i	−0.0166086	−	0.0166086i
$298$		0			0
$299$	−1.00606e6			−0.650795
$300$		0			0
$301$	4.97014e6			3.16193
$302$		0			0
$303$	76769.3	+	76769.3i	0.0480375	+	0.0480375i
$304$		0			0
$305$	1.61508e6	+	249297.i	0.994135	+	0.153450i
$306$		0			0
$307$	149779.	−	149779.i	0.0906992	−	0.0906992i	−0.660301	−	0.751001i	$-0.729571\pi$
$307$	149779.	−	149779.i	0.0906992	−	0.0906992i	0.751001	+	0.660301i	$0.229571\pi$
$308$		0			0
$309$		−	282110.i		−	0.168083i
$310$		0			0
$311$			384127.i			0.225203i	0.993640	+	0.112601i	$0.0359183\pi$
$311$			384127.i			0.225203i	−0.993640	+	0.112601i	$0.964082\pi$
$312$		0			0
$313$	−661386.	+	661386.i	−0.381588	+	0.381588i	−0.871674	−	0.490086i	$-0.836965\pi$
$313$	−661386.	+	661386.i	−0.381588	+	0.381588i	0.490086	+	0.871674i	$0.336965\pi$
$314$		0			0
$315$	−1.74219e6	−	2.37819e6i	−0.989279	−	1.35043i
$316$		0			0
$317$	1.48199e6	+	1.48199e6i	0.828319	+	0.828319i	0.987284	−	0.158965i	$-0.0508159\pi$
$317$	1.48199e6	+	1.48199e6i	0.828319	+	0.828319i	−0.158965	+	0.987284i	$0.550816\pi$
$318$		0			0
$319$	−78305.5			−0.0430840
$320$		0			0
$321$	140732.			0.0762305
$322$		0			0
$323$	1.20572e6	+	1.20572e6i	0.643045	+	0.643045i
$324$		0			0
$325$	−970198.	+	503991.i	−0.509509	+	0.264676i
$326$		0			0
$327$	−306042.	+	306042.i	−0.158275	+	0.158275i
$328$		0			0
$329$		−	2.24823e6i		−	1.14512i
$330$		0			0
$331$			1.76606e6i			0.886004i	0.896521	+	0.443002i	$0.146087\pi$
$331$			1.76606e6i			0.886004i	−0.896521	+	0.443002i	$0.853913\pi$
$332$		0			0
$333$	−2.25892e6	+	2.25892e6i	−1.11632	+	1.11632i
$334$		0			0
$335$	1.16206e6	−	851286.i	0.565738	−	0.414442i
$336$		0			0
$337$	−239492.	−	239492.i	−0.114872	−	0.114872i	0.647334	−	0.762206i	$-0.275884\pi$
$337$	−239492.	−	239492.i	−0.114872	−	0.114872i	−0.762206	+	0.647334i	$0.775884\pi$
$338$		0			0
$339$	−206145.			−0.0974258
$340$		0			0
$341$	−219247.			−0.102105
$342$		0			0
$343$	−2.37892e6	−	2.37892e6i	−1.09180	−	1.09180i
$344$		0			0
$345$	−51237.0	+	331941.i	−0.0231758	+	0.150146i
$346$		0			0
$347$	111547.	−	111547.i	0.0497316	−	0.0497316i	−0.681804	−	0.731535i	$-0.738804\pi$
$347$	111547.	−	111547.i	0.0497316	−	0.0497316i	0.731535	+	0.681804i	$0.238804\pi$
$348$		0			0
$349$			726170.i			0.319135i	0.987187	+	0.159568i	$0.0510100\pi$
$349$			726170.i			0.319135i	−0.987187	+	0.159568i	$0.948990\pi$
$350$		0			0
$351$			352061.i			0.152528i
$352$		0			0
$353$	−254625.	+	254625.i	−0.108759	+	0.108759i	−0.759392	−	0.650633i	$-0.774504\pi$
$353$	−254625.	+	254625.i	−0.108759	+	0.108759i	0.650633	+	0.759392i	$0.274504\pi$
$354$		0			0
$355$	−226922.	+	1.47012e6i	−0.0955664	+	0.619131i
$356$		0			0
$357$	−551065.	−	551065.i	−0.228840	−	0.228840i
$358$		0			0
$359$	−3.35115e6			−1.37233			−0.686163	−	0.727447i	$-0.740707\pi$
$359$	−3.35115e6			−1.37233			−0.686163	+	0.727447i	$0.740707\pi$
$360$		0			0
$361$	−1.45546e6			−0.587804
$362$		0			0
$363$	236077.	+	236077.i	0.0940345	+	0.0940345i
$364$		0			0
$365$	2.32157e6	−	1.70071e6i	0.912114	−	0.668186i
$366$		0			0
$367$	−2.84683e6	+	2.84683e6i	−1.10331	+	1.10331i	−0.109299	+	0.994009i	$0.534861\pi$
$367$	−2.84683e6	+	2.84683e6i	−1.10331	+	1.10331i	−0.994009	+	0.109299i	$0.965139\pi$
$368$		0			0
$369$			2.14868e6i			0.821495i
$370$		0			0
$371$			4.06144e6i			1.53195i
$372$		0			0
$373$	450340.	−	450340.i	0.167598	−	0.167598i	−0.618325	−	0.785923i	$-0.712188\pi$
$373$	450340.	−	450340.i	0.167598	−	0.167598i	0.785923	+	0.618325i	$0.212188\pi$
$374$		0			0
$375$	116878.	+	345778.i	0.0429194	+	0.126975i
$376$		0			0
$377$	545954.	+	545954.i	0.197835	+	0.197835i
$378$		0			0
$379$	3.33522e6			1.19269			0.596343	−	0.802729i	$-0.296620\pi$
$379$	3.33522e6			1.19269			0.596343	+	0.802729i	$0.296620\pi$
$380$		0			0
$381$	−626221.			−0.221012
$382$		0			0
$383$	−1.03183e6	−	1.03183e6i	−0.359427	−	0.359427i	0.504175	−	0.863602i	$-0.331797\pi$
$383$	−1.03183e6	−	1.03183e6i	−0.359427	−	0.359427i	−0.863602	+	0.504175i	$0.831797\pi$
$384$		0			0
$385$	−259042.	−	353608.i	−0.0890674	−	0.121582i
$386$		0			0
$387$	3.79498e6	−	3.79498e6i	1.28805	−	1.28805i
$388$		0			0
$389$		−	695763.i		−	0.233124i	−0.993183	−	0.116562i	$-0.962813\pi$
$389$		−	695763.i		−	0.233124i	0.993183	−	0.116562i	$-0.0371874\pi$
$390$		0			0
$391$		−	4.85358e6i		−	1.60554i
$392$		0			0
$393$	−341740.	+	341740.i	−0.111613	+	0.111613i
$394$		0			0
$395$	−281160.	−	43398.6i	−0.0906694	−	0.0139953i
$396$		0			0
$397$	752665.	+	752665.i	0.239677	+	0.239677i	0.816716	−	0.577040i	$-0.195792\pi$
$397$	752665.	+	752665.i	0.239677	+	0.239677i	−0.577040	+	0.816716i	$0.695792\pi$
$398$		0			0
$399$	−466473.			−0.146688
$400$		0			0
$401$	5.46256e6			1.69643			0.848214	−	0.529654i	$-0.177678\pi$
$401$	5.46256e6			1.69643			0.848214	+	0.529654i	$0.177678\pi$
$402$		0			0
$403$	1.52861e6	+	1.52861e6i	0.468851	+	0.468851i
$404$		0			0
$405$	−3.08754e6	−	476579.i	−0.935351	−	0.144377i
$406$		0			0
$407$	−335874.	+	335874.i	−0.100506	+	0.100506i
$408$		0			0
$409$			2.57791e6i			0.762008i	0.924573	+	0.381004i	$0.124422\pi$
$409$			2.57791e6i			0.762008i	−0.924573	+	0.381004i	$0.875578\pi$
$410$		0			0
$411$		−	439537.i		−	0.128348i
$412$		0			0
$413$	6.33115e6	−	6.33115e6i	1.82645	−	1.82645i
$414$		0			0
$415$	952846.	+	1.30069e6i	0.271583	+	0.370727i
$416$		0			0
$417$	−42287.3	−	42287.3i	−0.0119089	−	0.0119089i
$418$		0			0
$419$	1.48123e6			0.412181			0.206090	−	0.978533i	$-0.433926\pi$
$419$	1.48123e6			0.412181			0.206090	+	0.978533i	$0.433926\pi$
$420$		0			0
$421$	−6.15274e6			−1.69186			−0.845928	−	0.533297i	$-0.820953\pi$
$421$	−6.15274e6			−1.69186			−0.845928	+	0.533297i	$0.820953\pi$
$422$		0			0
$423$	−1.71665e6	−	1.71665e6i	−0.466478	−	0.466478i
$424$		0			0
$425$	−2.43144e6	−	4.68059e6i	−0.652966	−	1.25698i
$426$		0			0
$427$	4.56820e6	−	4.56820e6i	1.21248	−	1.21248i
$428$		0			0
$429$			25936.4i			0.00680403i
$430$		0			0
$431$		−	3.08017e6i		−	0.798695i	−0.916800	−	0.399348i	$-0.869237\pi$
$431$		−	3.08017e6i		−	0.798695i	0.916800	−	0.399348i	$-0.130763\pi$
$432$		0			0
$433$	1.51152e6	−	1.51152e6i	0.387430	−	0.387430i	−0.486340	−	0.873770i	$-0.661668\pi$
$433$	1.51152e6	−	1.51152e6i	0.387430	−	0.387430i	0.873770	+	0.486340i	$0.161668\pi$
$434$		0			0
$435$	207938.	−	152329.i	0.0526879	−	0.0385975i
$436$		0			0
$437$	−2.05426e6	−	2.05426e6i	−0.514579	−	0.514579i
$438$		0			0
$439$	5.41400e6			1.34078			0.670389	−	0.742010i	$-0.266127\pi$
$439$	5.41400e6			1.34078			0.670389	+	0.742010i	$0.266127\pi$
$440$		0			0
$441$	−7.64361e6			−1.87155
$442$		0			0
$443$	5.09102e6	+	5.09102e6i	1.23252	+	1.23252i	0.962991	+	0.269533i	$0.0868693\pi$
$443$	5.09102e6	+	5.09102e6i	1.23252	+	1.23252i	0.269533	+	0.962991i	$0.413131\pi$
$444$		0			0
$445$	−506105.	+	3.27882e6i	−0.121155	+	0.784906i
$446$		0			0
$447$	248895.	−	248895.i	0.0589179	−	0.0589179i
$448$		0			0
$449$		−	3.85655e6i		−	0.902783i	−0.892326	−	0.451392i	$-0.850928\pi$
$449$		−	3.85655e6i		−	0.902783i	0.892326	−	0.451392i	$-0.149072\pi$
$450$		0			0
$451$			319482.i			0.0739613i
$452$		0			0
$453$	169139.	−	169139.i	0.0387256	−	0.0387256i
$454$		0			0
$455$	−659324.	+	4.27146e6i	−0.149304	+	0.967270i
$456$		0			0
$457$	−5.72418e6	−	5.72418e6i	−1.28210	−	1.28210i	−0.939469	−	0.342634i	$-0.888681\pi$
$457$	−5.72418e6	−	5.72418e6i	−1.28210	−	1.28210i	−0.342634	−	0.939469i	$-0.611319\pi$
$458$		0			0
$459$	−1.69847e6			−0.376293
$460$		0			0
$461$	−1.28502e6			−0.281615			−0.140808	−	0.990037i	$-0.544970\pi$
$461$	−1.28502e6			−0.281615			−0.140808	+	0.990037i	$0.544970\pi$
$462$		0			0
$463$	−3.79316e6	−	3.79316e6i	−0.822334	−	0.822334i	0.164108	−	0.986442i	$-0.447525\pi$
$463$	−3.79316e6	−	3.79316e6i	−0.822334	−	0.822334i	−0.986442	+	0.164108i	$0.947525\pi$
$464$		0			0
$465$	582205.	−	426505.i	0.124866	−	0.0914728i
$466$		0			0
$467$	2.71510e6	−	2.71510e6i	0.576095	−	0.576095i	−0.357730	−	0.933825i	$-0.616449\pi$
$467$	2.71510e6	−	2.71510e6i	0.576095	−	0.576095i	0.933825	+	0.357730i	$0.116449\pi$
$468$		0			0
$469$		−	5.69467e6i		−	1.19546i
$470$		0			0
$471$		−	439653.i		−	0.0913184i
$472$		0			0
$473$	564267.	−	564267.i	0.115966	−	0.115966i
$474$		0			0
$475$	−3.01014e6	−	951946.i	−0.612143	−	0.193588i
$476$		0			0
$477$	3.10113e6	+	3.10113e6i	0.624058	+	0.624058i
$478$		0			0
$479$	7.87712e6			1.56866			0.784329	−	0.620345i	$-0.213007\pi$
$479$	7.87712e6			1.56866			0.784329	+	0.620345i	$0.213007\pi$
$480$		0			0
$481$	4.68349e6			0.923010
$482$		0			0
$483$	938882.	+	938882.i	0.183123	+	0.183123i
$484$		0			0
$485$	3.24900e6	+	4.43508e6i	0.627184	+	0.856144i
$486$		0			0
$487$	−2.23639e6	+	2.23639e6i	−0.427292	+	0.427292i	−0.887705	−	0.460413i	$-0.847701\pi$
$487$	−2.23639e6	+	2.23639e6i	−0.427292	+	0.427292i	0.460413	+	0.887705i	$0.347701\pi$
$488$		0			0
$489$		−	41945.9i		−	0.00793263i
$490$		0			0
$491$			5.93940e6i			1.11183i	0.831239	+	0.555916i	$0.187632\pi$
$491$			5.93940e6i			1.11183i	−0.831239	+	0.555916i	$0.812368\pi$
$492$		0			0
$493$	−2.63388e6	+	2.63388e6i	−0.488066	+	0.488066i
$494$		0			0
$495$	−467793.	−	72206.5i	−0.0858106	−	0.0132454i
$496$		0			0
$497$	4.15818e6	+	4.15818e6i	0.755114	+	0.755114i
$498$		0			0
$499$	−41191.0			−0.00740545			−0.00370272	−	0.999993i	$-0.501179\pi$
$499$	−41191.0			−0.00740545			−0.00370272	+	0.999993i	$0.501179\pi$
$500$		0			0
$501$	382293.			0.0680460
$502$		0			0
$503$	1.52979e6	+	1.52979e6i	0.269596	+	0.269596i	0.828937	−	0.559342i	$-0.188946\pi$
$503$	1.52979e6	+	1.52979e6i	0.269596	+	0.269596i	−0.559342	+	0.828937i	$0.688946\pi$
$504$		0			0
$505$	2.87078e6	+	443122.i	0.500924	+	0.0773205i
$506$		0			0
$507$	−367718.	+	367718.i	−0.0635324	+	0.0635324i
$508$		0			0
$509$		−	2.48052e6i		−	0.424374i	−0.977229	−	0.212187i	$-0.931941\pi$
$509$		−	2.48052e6i		−	0.424374i	0.977229	−	0.212187i	$-0.0680586\pi$
$510$		0			0
$511$		−	1.13768e7i		−	1.92739i
$512$		0			0
$513$	−718873.	+	718873.i	−0.120603	+	0.120603i
$514$		0			0
$515$	−4.46057e6	−	6.08894e6i	−0.741092	−	1.01163i
$516$		0			0
$517$	−255245.	−	255245.i	−0.0419982	−	0.0419982i
$518$		0			0
$519$	449572.			0.0732624
$520$		0			0
$521$	−949964.			−0.153325			−0.0766624	−	0.997057i	$-0.524426\pi$
$521$	−949964.			−0.153325			−0.0766624	+	0.997057i	$0.524426\pi$
$522$		0			0
$523$	3.91973e6	+	3.91973e6i	0.626617	+	0.626617i	0.947215	−	0.320598i	$-0.103884\pi$
$523$	3.91973e6	+	3.91973e6i	0.626617	+	0.626617i	−0.320598	+	0.947215i	$0.603884\pi$
$524$		0			0
$525$	1.37576e6	+	435079.i	0.217843	+	0.0688921i
$526$		0			0
$527$	−7.37458e6	+	7.37458e6i	−1.15667	+	1.15667i
$528$		0			0
$529$			1.83298e6i			0.284786i
$530$		0			0
$531$		−	9.66839e6i		−	1.48805i
$532$		0			0
$533$	2.22746e6	−	2.22746e6i	0.339619	−	0.339619i
$534$		0			0
$535$	3.03749e6	−	2.22517e6i	0.458807	−	0.336107i
$536$		0			0
$537$	−433301.	−	433301.i	−0.0648416	−	0.0648416i
$538$		0			0
$539$	−1.13651e6			−0.168501
$540$		0			0
$541$	−7.07953e6			−1.03995			−0.519973	−	0.854182i	$-0.674058\pi$
$541$	−7.07953e6			−1.03995			−0.519973	+	0.854182i	$0.674058\pi$
$542$		0			0
$543$	−52070.0	−	52070.0i	−0.00757858	−	0.00757858i
$544$		0			0
$545$	−1.76652e6	+	1.14444e7i	−0.254757	+	1.65045i
$546$		0			0
$547$	−8.01896e6	+	8.01896e6i	−1.14591	+	1.14591i	−0.158559	+	0.987350i	$0.550685\pi$
$547$	−8.01896e6	+	8.01896e6i	−1.14591	+	1.14591i	−0.987350	+	0.158559i	$0.949315\pi$
$548$		0			0
$549$		−	6.97616e6i		−	0.987837i
$550$		0			0
$551$			2.22956e6i			0.312853i
$552$		0			0
$553$	−795250.	+	795250.i	−0.110584	+	0.110584i
$554$		0			0
$555$	238523.	−	1.54528e6i	0.0328699	−	0.212949i
$556$		0			0
$557$	687054.	+	687054.i	0.0938324	+	0.0938324i	0.752465	−	0.658632i	$-0.228865\pi$
$557$	687054.	+	687054.i	0.0938324	+	0.0938324i	−0.658632	+	0.752465i	$0.728865\pi$
$558$		0			0
$559$	−7.86825e6			−1.06500
$560$		0			0
$561$	−125126.			−0.0167858
$562$		0			0
$563$	7.17411e6	+	7.17411e6i	0.953888	+	0.953888i	0.998983	−	0.0450948i	$-0.0143590\pi$
$563$	7.17411e6	+	7.17411e6i	0.953888	+	0.953888i	−0.0450948	+	0.998983i	$0.514359\pi$
$564$		0			0
$565$	−4.44935e6	+	3.25945e6i	−0.586375	+	0.429559i
$566$		0			0
$567$	−8.73298e6	+	8.73298e6i	−1.14079	+	1.14079i
$568$		0			0
$569$		−	8.08487e6i		−	1.04687i	−0.852066	−	0.523435i	$-0.824650\pi$
$569$		−	8.08487e6i		−	1.04687i	0.852066	−	0.523435i	$-0.175350\pi$
$570$		0			0
$571$		−	3.00555e6i		−	0.385774i	−0.981221	−	0.192887i	$-0.938215\pi$
$571$		−	3.00555e6i		−	0.385774i	0.981221	−	0.192887i	$-0.0617851\pi$
$572$		0			0
$573$	−1.27404e6	+	1.27404e6i	−0.162105	+	0.162105i
$574$		0			0
$575$	4.14258e6	+	7.97459e6i	0.522518	+	1.00586i
$576$		0			0
$577$	4.07557e6	+	4.07557e6i	0.509622	+	0.509622i	0.914410	−	0.404788i	$-0.132655\pi$
$577$	4.07557e6	+	4.07557e6i	0.509622	+	0.509622i	−0.404788	+	0.914410i	$0.632655\pi$
$578$		0			0
$579$	−257818.			−0.0319608
$580$		0			0
$581$	6.37405e6			0.783384
$582$		0			0
$583$	461101.	+	461101.i	0.0561855	+	0.0561855i
$584$		0			0
$585$	2.75807e6	+	3.76493e6i	0.333208	+	0.454849i
$586$		0			0
$587$	3.45341e6	−	3.45341e6i	0.413669	−	0.413669i	−0.469346	−	0.883014i	$-0.655510\pi$
$587$	3.45341e6	−	3.45341e6i	0.413669	−	0.413669i	0.883014	+	0.469346i	$0.155510\pi$
$588$		0			0
$589$			6.24254e6i			0.741435i
$590$		0			0
$591$		−	335373.i		−	0.0394965i
$592$		0			0
$593$	4.96777e6	−	4.96777e6i	0.580129	−	0.580129i	−0.354810	−	0.934939i	$-0.615454\pi$
$593$	4.96777e6	−	4.96777e6i	0.580129	−	0.580129i	0.934939	+	0.354810i	$0.115454\pi$
$594$		0			0
$595$	−2.06071e7	−	3.18082e6i	−2.38629	−	0.368338i
$596$		0			0
$597$	734926.	+	734926.i	0.0843932	+	0.0843932i
$598$		0			0
$599$	8.61814e6			0.981401			0.490701	−	0.871328i	$-0.336741\pi$
$599$	8.61814e6			0.981401			0.490701	+	0.871328i	$0.336741\pi$
$600$		0			0
$601$	−1.36092e7			−1.53690			−0.768451	−	0.639909i	$-0.778972\pi$
$601$	−1.36092e7			−1.53690			−0.768451	+	0.639909i	$0.778972\pi$
$602$		0			0
$603$	−4.34820e6	−	4.34820e6i	−0.486986	−	0.486986i
$604$		0			0
$605$	8.82810e6	+	1.36267e6i	0.980570	+	0.151357i
$606$		0			0
$607$	7.54202e6	−	7.54202e6i	0.830837	−	0.830837i	−0.156794	−	0.987631i	$-0.550116\pi$
$607$	7.54202e6	−	7.54202e6i	0.830837	−	0.830837i	0.987631	+	0.156794i	$0.0501159\pi$
$608$		0			0
$609$		−	1.01900e6i		−	0.111335i
$610$		0			0
$611$			3.55918e6i			0.385698i
$612$		0			0
$613$	−2.33571e6	+	2.33571e6i	−0.251054	+	0.251054i	−0.821403	−	0.570349i	$-0.806808\pi$
$613$	−2.33571e6	+	2.33571e6i	−0.251054	+	0.251054i	0.570349	+	0.821403i	$0.306808\pi$
$614$		0			0
$615$	−621493.	−	848375.i	−0.0662595	−	0.0904483i
$616$		0			0
$617$	9.52103e6	+	9.52103e6i	1.00686	+	1.00686i	0.999976	+	0.00688826i	$0.00219262\pi$
$617$	9.52103e6	+	9.52103e6i	1.00686	+	1.00686i	0.00688826	+	0.999976i	$0.497807\pi$
$618$		0			0
$619$	−1.71115e7			−1.79499			−0.897494	−	0.441027i	$-0.854614\pi$
$619$	−1.71115e7			−1.79499			−0.897494	+	0.441027i	$0.854614\pi$
$620$		0			0
$621$	2.89379e6			0.301119
$622$		0			0
$623$	9.27402e6	+	9.27402e6i	0.957300	+	0.957300i
$624$		0			0
$625$	7.98987e6	+	5.61511e6i	0.818163	+	0.574987i
$626$		0			0
$627$	−52959.4	+	52959.4i	−0.00537990	+	0.00537990i
$628$		0			0
$629$			2.25948e7i			2.27710i
$630$		0			0
$631$		−	1.54863e7i		−	1.54837i	−0.632958	−	0.774186i	$-0.718159\pi$
$631$		−	1.54863e7i		−	1.54837i	0.632958	−	0.774186i	$-0.281841\pi$
$632$		0			0
$633$	530398.	−	530398.i	0.0526129	−	0.0526129i
$634$		0			0
$635$	−1.35161e7	+	9.90144e6i	−1.33020	+	0.974460i
$636$		0			0
$637$	7.92387e6	+	7.92387e6i	0.773729	+	0.773729i
$638$		0			0
$639$	6.35001e6			0.615209
$640$		0			0
$641$	−8.16308e6			−0.784709			−0.392355	−	0.919814i	$-0.628339\pi$
$641$	−8.16308e6			−0.784709			−0.392355	+	0.919814i	$0.628339\pi$
$642$		0			0
$643$	−6.82289e6	−	6.82289e6i	−0.650791	−	0.650791i	0.302393	−	0.953183i	$-0.402215\pi$
$643$	−6.82289e6	−	6.82289e6i	−0.650791	−	0.650791i	−0.953183	+	0.302393i	$0.902215\pi$
$644$		0			0
$645$	−400719.	+	2.59607e6i	−0.0379263	+	0.245707i
$646$		0			0
$647$	−1.04574e7	+	1.04574e7i	−0.982113	+	0.982113i	−0.999843	−	0.0177299i	$-0.994356\pi$
$647$	−1.04574e7	+	1.04574e7i	−0.982113	+	0.982113i	0.0177299	+	0.999843i	$0.494356\pi$
$648$		0			0
$649$		−	1.43757e6i		−	0.133973i
$650$		0			0
$651$		−	2.85310e6i		−	0.263854i
$652$		0			0
$653$	8.91308e6	−	8.91308e6i	0.817984	−	0.817984i	−0.167831	−	0.985816i	$-0.553676\pi$
$653$	8.91308e6	−	8.91308e6i	0.817984	−	0.817984i	0.985816	+	0.167831i	$0.0536764\pi$
$654$		0			0
$655$	−1.97257e6	+	1.27794e7i	−0.179651	+	1.16387i
$656$		0			0
$657$	−8.68686e6	−	8.68686e6i	−0.785144	−	0.785144i
$658$		0			0
$659$	4.26560e6			0.382619			0.191310	−	0.981530i	$-0.438727\pi$
$659$	4.26560e6			0.382619			0.191310	+	0.981530i	$0.438727\pi$
$660$		0			0
$661$	−5.64640e6			−0.502653			−0.251326	−	0.967902i	$-0.580867\pi$
$661$	−5.64640e6			−0.502653			−0.251326	+	0.967902i	$0.580867\pi$
$662$		0			0
$663$	872394.	+	872394.i	0.0770777	+	0.0770777i
$664$		0			0
$665$	−1.00682e7	+	7.37561e6i	−0.882868	+	0.646761i
$666$		0			0
$667$	4.48749e6	−	4.48749e6i	0.390561	−	0.390561i
$668$		0			0
$669$		−	2.73979e6i		−	0.236675i
$670$		0			0
$671$		−	1.03727e6i		−	0.0889376i
$672$		0			0
$673$	6.79083e6	−	6.79083e6i	0.577943	−	0.577943i	−0.356393	−	0.934336i	$-0.615994\pi$
$673$	6.79083e6	−	6.79083e6i	0.577943	−	0.577943i	0.934336	+	0.356393i	$0.115994\pi$
$674$		0			0
$675$	2.79065e6	−	1.44967e6i	0.235747	−	0.122464i
$676$		0			0
$677$	−1.14580e7	−	1.14580e7i	−0.960807	−	0.960807i	0.0384535	−	0.999260i	$-0.487757\pi$
$677$	−1.14580e7	−	1.14580e7i	−0.960807	−	0.960807i	−0.999260	+	0.0384535i	$0.987757\pi$
$678$		0			0
$679$	2.17341e7			1.80912
$680$		0			0
$681$	3.03898e6			0.251108
$682$		0			0
$683$	−9.47517e6	−	9.47517e6i	−0.777204	−	0.777204i	0.202150	−	0.979354i	$-0.435207\pi$
$683$	−9.47517e6	−	9.47517e6i	−0.777204	−	0.777204i	−0.979354	+	0.202150i	$0.935207\pi$
$684$		0			0
$685$	−6.94970e6	−	9.48676e6i	−0.565900	−	0.772488i
$686$		0			0
$687$	−922483.	+	922483.i	−0.0745704	+	0.0745704i
$688$		0			0
$689$		−	6.42968e6i		−	0.515990i
$690$		0			0
$691$			2.19649e7i			1.74998i	0.484137	+	0.874992i	$0.339133\pi$
$691$			2.19649e7i			1.74998i	−0.484137	+	0.874992i	$0.660867\pi$
$692$		0			0
$693$	−1.32314e6	+	1.32314e6i	−0.104658	+	0.104658i
$694$		0			0
$695$	−1.58133e6	−	244088.i	−0.124183	−	0.0191683i
$696$		0			0
$697$	1.07461e7	+	1.07461e7i	0.837852	+	0.837852i
$698$		0			0
$699$	217975.			0.0168738
$700$		0			0
$701$	−9.21992e6			−0.708651			−0.354325	−	0.935122i	$-0.615289\pi$
$701$	−9.21992e6			−0.708651			−0.354325	+	0.935122i	$0.615289\pi$
$702$		0			0
$703$	9.56320e6	+	9.56320e6i	0.729818	+	0.729818i
$704$		0			0
$705$	1.17433e6	+	181264.i	0.0889850	+	0.0137353i
$706$		0			0
$707$	8.11990e6	−	8.11990e6i	0.610945	−	0.610945i
$708$		0			0
$709$		−	2.13169e7i		−	1.59260i	−0.604900	−	0.796301i	$-0.706787\pi$
$709$		−	2.13169e7i		−	1.59260i	0.604900	−	0.796301i	$-0.293213\pi$
$710$		0			0
$711$			1.21444e6i			0.0900951i
$712$		0			0
$713$	1.25645e7	−	1.25645e7i	0.925597	−	0.925597i
$714$		0			0
$715$	410091.	+	559799.i	0.0299996	+	0.0409512i
$716$		0			0
$717$	2.34453e6	+	2.34453e6i	0.170317	+	0.170317i
$718$		0			0
$719$	5.27347e6			0.380430			0.190215	−	0.981742i	$-0.439082\pi$
$719$	5.27347e6			0.380430			0.190215	+	0.981742i	$0.439082\pi$
$720$		0			0
$721$	−2.98389e7			−2.13769
$722$		0			0
$723$	321259.	+	321259.i	0.0228565	+	0.0228565i
$724$		0			0
$725$	2.07951e6	−	6.57560e6i	0.146932	−	0.464612i
$726$		0			0
$727$	8.91293e6	−	8.91293e6i	0.625438	−	0.625438i	−0.321479	−	0.946917i	$-0.604180\pi$
$727$	8.91293e6	−	8.91293e6i	0.625438	−	0.625438i	0.946917	+	0.321479i	$0.104180\pi$
$728$		0			0
$729$			1.28253e7i			0.893819i
$730$		0			0
$731$		−	3.79593e7i		−	2.62739i
$732$		0			0
$733$	3.62320e6	−	3.62320e6i	0.249076	−	0.249076i	−0.571515	−	0.820591i	$-0.693644\pi$
$733$	3.62320e6	−	3.62320e6i	0.249076	−	0.249076i	0.820591	+	0.571515i	$0.193644\pi$
$734$		0			0
$735$	3.01798e6	−	2.21087e6i	0.206062	−	0.150954i
$736$		0			0
$737$	−646524.	−	646524.i	−0.0438446	−	0.0438446i
$738$		0			0
$739$	8.18176e6			0.551106			0.275553	−	0.961286i	$-0.411139\pi$
$739$	8.18176e6			0.551106			0.275553	+	0.961286i	$0.411139\pi$
$740$		0			0
$741$	738476.			0.0494073
$742$		0			0
$743$	−1.12407e7	−	1.12407e7i	−0.747004	−	0.747004i	0.226911	−	0.973915i	$-0.427137\pi$
$743$	−1.12407e7	−	1.12407e7i	−0.747004	−	0.747004i	−0.973915	+	0.226911i	$0.927137\pi$
$744$		0			0
$745$	1.43665e6	−	9.30742e6i	0.0948333	−	0.614382i
$746$		0			0
$747$	4.86694e6	−	4.86694e6i	0.319121	−	0.319121i
$748$		0			0
$749$		−	1.48852e7i		−	0.969506i
$750$		0			0
$751$		−	1.89630e7i		−	1.22689i	−0.789736	−	0.613447i	$-0.789783\pi$
$751$		−	1.89630e7i		−	1.22689i	0.789736	−	0.613447i	$-0.210217\pi$
$752$		0			0
$753$	−2.72503e6	+	2.72503e6i	−0.175140	+	0.175140i
$754$		0			0
$755$	976291.	−	6.32495e6i	0.0623321	−	0.403822i
$756$		0			0
$757$	9.61677e6	+	9.61677e6i	0.609943	+	0.609943i	0.942931	−	0.332988i	$-0.108057\pi$
$757$	9.61677e6	+	9.61677e6i	0.609943	+	0.609943i	−0.332988	+	0.942931i	$0.608057\pi$
$758$		0			0
$759$	213185.			0.0134324
$760$		0			0
$761$	2.07945e7			1.30163			0.650814	−	0.759238i	$-0.274428\pi$
$761$	2.07945e7			1.30163			0.650814	+	0.759238i	$0.274428\pi$
$762$		0			0
$763$	3.23702e7	+	3.23702e7i	2.01295	+	2.01295i
$764$		0			0
$765$	−1.81634e7	+	1.33059e7i	−1.12213	+	0.822037i
$766$		0			0
$767$	−1.00229e7	+	1.00229e7i	−0.615183	+	0.615183i
$768$		0			0
$769$		−	1.39172e7i		−	0.848667i	−0.905506	−	0.424334i	$-0.860508\pi$
$769$		−	1.39172e7i		−	0.848667i	0.905506	−	0.424334i	$-0.139492\pi$
$770$		0			0
$771$			2.76116e6i			0.167284i
$772$		0			0
$773$	−3.19729e6	+	3.19729e6i	−0.192457	+	0.192457i	−0.796757	−	0.604300i	$-0.793453\pi$
$773$	−3.19729e6	+	3.19729e6i	−0.192457	+	0.192457i	0.604300	+	0.796757i	$0.293453\pi$
$774$		0			0
$775$	5.82240e6	−	1.84110e7i	0.348215	−	1.10109i
$776$		0			0
$777$	−4.37077e6	−	4.37077e6i	−0.259720	−	0.259720i
$778$		0			0
$779$	9.09648e6			0.537069
$780$		0			0
$781$	944170.			0.0553889
$782$		0			0
$783$	−1.57036e6	−	1.57036e6i	−0.0915368	−	0.0915368i
$784$		0			0
$785$	−6.95154e6	−	9.48928e6i	−0.402631	−	0.549616i
$786$		0			0
$787$	−5.00799e6	+	5.00799e6i	−0.288222	+	0.288222i	−0.836377	−	0.548155i	$-0.815330\pi$
$787$	−5.00799e6	+	5.00799e6i	−0.288222	+	0.288222i	0.548155	+	0.836377i	$0.315330\pi$
$788$		0			0
$789$			1.61253e6i			0.0922179i
$790$		0			0
$791$			2.18040e7i			1.23907i
$792$		0			0
$793$	−7.23194e6	+	7.23194e6i	−0.408387	+	0.408387i
$794$		0			0
$795$	−2.12143e6	−	327454.i	−0.119045	−	0.0183752i
$796$		0			0
$797$	−1.15915e7	−	1.15915e7i	−0.646391	−	0.646391i	0.305728	−	0.952119i	$-0.401100\pi$
$797$	−1.15915e7	−	1.15915e7i	−0.646391	−	0.646391i	−0.952119	+	0.305728i	$0.901100\pi$
$798$		0			0
$799$	−1.71708e7			−0.951532
$800$		0			0
$801$	1.41625e7			0.779934
$802$		0			0
$803$	−1.29163e6	−	1.29163e6i	−0.0706886	−	0.0706886i
$804$		0			0
$805$	3.51095e7	+	5.41935e6i	1.90957	+	0.294752i
$806$		0			0
$807$	−2.40388e6	+	2.40388e6i	−0.129936	+	0.129936i
$808$		0			0
$809$		−	3.00176e7i		−	1.61252i	−0.591564	−	0.806258i	$-0.701489\pi$
$809$		−	3.00176e7i		−	1.61252i	0.591564	−	0.806258i	$-0.298511\pi$
$810$		0			0
$811$			3.56109e7i			1.90121i	0.310401	+	0.950606i	$0.399537\pi$
$811$			3.56109e7i			1.90121i	−0.310401	+	0.950606i	$0.600463\pi$
$812$		0			0
$813$	−509506.	+	509506.i	−0.0270348	+	0.0270348i
$814$		0			0
$815$	−663224.	−	905341.i	−0.0349757	−	0.0477439i
$816$		0			0
$817$	−1.60662e7	−	1.60662e7i	−0.842087	−	0.842087i
$818$		0			0
$819$	1.84501e7			0.961143
$820$		0			0
$821$	−1.88846e7			−0.977798			−0.488899	−	0.872340i	$-0.662601\pi$
$821$	−1.88846e7			−0.977798			−0.488899	+	0.872340i	$0.662601\pi$
$822$		0			0
$823$	−1.66837e6	−	1.66837e6i	−0.0858605	−	0.0858605i	0.662872	−	0.748733i	$-0.269337\pi$
$823$	−1.66837e6	−	1.66837e6i	−0.0858605	−	0.0858605i	−0.748733	+	0.662872i	$0.769337\pi$
$824$		0			0
$825$	205587.	−	106797.i	0.0105163	−	0.00546291i
$826$		0			0
$827$	−4.64308e6	+	4.64308e6i	−0.236071	+	0.236071i	−0.815221	−	0.579150i	$-0.803384\pi$
$827$	−4.64308e6	+	4.64308e6i	−0.236071	+	0.236071i	0.579150	+	0.815221i	$0.303384\pi$
$828$		0			0
$829$			5.94731e6i			0.300562i	0.988643	+	0.150281i	$0.0480179\pi$
$829$			5.94731e6i			0.300562i	−0.988643	+	0.150281i	$0.951982\pi$
$830$		0			0
$831$		−	3.88026e6i		−	0.194921i
$832$		0			0
$833$	−3.82276e7	+	3.82276e7i	−1.90882	+	1.90882i
$834$		0			0
$835$	8.25125e6	−	6.04460e6i	0.409547	−	0.300021i
$836$		0			0
$837$	−4.39685e6	−	4.39685e6i	−0.216934	−	0.216934i
$838$		0			0
$839$	−5.50020e6			−0.269758			−0.134879	−	0.990862i	$-0.543065\pi$
$839$	−5.50020e6			−0.269758			−0.134879	+	0.990862i	$0.543065\pi$
$840$		0			0
$841$	1.56407e7			0.762547
$842$		0			0
$843$	875262.	+	875262.i	0.0424199	+	0.0424199i
$844$		0			0
$845$	−2.12252e6	+	1.37508e7i	−0.102261	+	0.662501i
$846$		0			0
$847$	2.49699e7	−	2.49699e7i	1.19594	−	1.19594i
$848$		0			0
$849$		−	2.65594e6i		−	0.126459i
$850$		0			0
$851$		−	3.84961e7i		−	1.82219i
$852$		0			0
$853$	9.08999e6	−	9.08999e6i	0.427751	−	0.427751i	−0.460111	−	0.887861i	$-0.652190\pi$
$853$	9.08999e6	−	9.08999e6i	0.427751	−	0.427751i	0.887861	+	0.460111i	$0.152190\pi$
$854$		0			0
$855$	−2.05591e6	+	1.33193e7i	−0.0961808	+	0.623112i
$856$		0			0
$857$	−5.51829e6	−	5.51829e6i	−0.256656	−	0.256656i	0.567036	−	0.823693i	$-0.308090\pi$
$857$	−5.51829e6	−	5.51829e6i	−0.256656	−	0.256656i	−0.823693	+	0.567036i	$0.808090\pi$
$858$		0			0
$859$	−1.76624e7			−0.816710			−0.408355	−	0.912823i	$-0.633897\pi$
$859$	−1.76624e7			−0.816710			−0.408355	+	0.912823i	$0.633897\pi$
$860$		0			0
$861$	−4.15747e6			−0.191126
$862$		0			0
$863$	−1.56489e7	−	1.56489e7i	−0.715247	−	0.715247i	0.252381	−	0.967628i	$-0.418786\pi$
$863$	−1.56489e7	−	1.56489e7i	−0.715247	−	0.715247i	−0.967628	+	0.252381i	$0.918786\pi$
$864$		0			0
$865$	9.70336e6	−	7.10837e6i	0.440942	−	0.323020i
$866$		0			0
$867$	−2.11104e6	+	2.11104e6i	−0.0953782	+	0.0953782i
$868$		0			0
$869$			180572.i			0.00811149i
$870$		0			0
$871$			9.01525e6i			0.402654i
$872$		0			0
$873$	1.65952e7	−	1.65952e7i	0.736966	−	0.736966i
$874$		0			0
$875$	3.65730e7	−	1.23622e7i	1.61488	−	0.545852i
$876$		0			0
$877$	−1.20911e7	−	1.20911e7i	−0.530842	−	0.530842i	0.389981	−	0.920823i	$-0.372482\pi$
$877$	−1.20911e7	−	1.20911e7i	−0.530842	−	0.530842i	−0.920823	+	0.389981i	$0.872482\pi$
$878$		0			0
$879$	−5.01355e6			−0.218863
$880$		0			0
$881$	2.36084e7			1.02477			0.512386	−	0.858755i	$-0.328762\pi$
$881$	2.36084e7			1.02477			0.512386	+	0.858755i	$0.328762\pi$
$882$		0			0
$883$	1.03875e7	+	1.03875e7i	0.448341	+	0.448341i	0.894803	−	0.446462i	$-0.147316\pi$
$883$	1.03875e7	+	1.03875e7i	0.448341	+	0.448341i	−0.446462	+	0.894803i	$0.647316\pi$
$884$		0			0
$885$	2.79653e6	+	3.81743e6i	0.120022	+	0.163837i
$886$		0			0
$887$	−1.88440e6	+	1.88440e6i	−0.0804199	+	0.0804199i	−0.746173	−	0.665753i	$-0.768111\pi$
$887$	−1.88440e6	+	1.88440e6i	−0.0804199	+	0.0804199i	0.665753	+	0.746173i	$0.268111\pi$
$888$		0			0
$889$			6.62355e7i			2.81084i
$890$		0			0
$891$			1.98294e6i			0.0836787i
$892$		0			0
$893$	−7.26749e6	+	7.26749e6i	−0.304969	+	0.304969i
$894$		0			0
$895$	−1.62033e7	−	2.50107e6i	−0.676154	−	0.104368i
$896$		0			0
$897$	−1.48635e6	−	1.48635e6i	−0.0616793	−	0.0616793i
$898$		0			0
$899$	−1.36367e7			−0.562743
$900$		0			0
$901$	3.10191e7			1.27297
$902$		0			0
$903$	7.34289e6	+	7.34289e6i	0.299673	+	0.299673i
$904$		0			0
$905$	−1.94715e6	−	300554.i	−0.0790276	−	0.0121984i
$906$		0			0
$907$	−2.10664e6	+	2.10664e6i	−0.0850301	+	0.0850301i	−0.748343	−	0.663312i	$-0.769150\pi$
$907$	−2.10664e6	+	2.10664e6i	−0.0850301	+	0.0850301i	0.663312	+	0.748343i	$0.269150\pi$
$908$		0			0
$909$		−	1.24000e7i		−	0.497751i
$910$		0			0
$911$		−	2.18101e6i		−	0.0870688i	−0.999052	−	0.0435344i	$-0.986138\pi$
$911$		−	2.18101e6i		−	0.0870688i	0.999052	−	0.0435344i	$-0.0138618\pi$
$912$		0			0
$913$	723655.	−	723655.i	0.0287313	−	0.0287313i
$914$		0			0
$915$	2.01782e6	+	2.75444e6i	0.0796762	+	0.108763i
$916$		0			0
$917$	3.61460e7	+	3.61460e7i	1.41950	+	1.41950i
$918$		0			0
$919$	−3.80005e7			−1.48423			−0.742113	−	0.670274i	$-0.766176\pi$
$919$	−3.80005e7			−1.48423			−0.742113	+	0.670274i	$0.766176\pi$
$920$		0			0
$921$	442566.			0.0171921
$922$		0			0
$923$	−6.58284e6	−	6.58284e6i	−0.254337	−	0.254337i
$924$		0			0
$925$	−1.92849e7	−	3.71241e7i	−0.741078	−	1.42660i
$926$		0			0
$927$	−2.27837e7	+	2.27837e7i	−0.870812	+	0.870812i
$928$		0			0
$929$			3.64144e7i			1.38431i	0.721747	+	0.692156i	$0.243339\pi$
$929$			3.64144e7i			1.38431i	−0.721747	+	0.692156i	$0.756661\pi$
$930$		0			0
$931$			3.23595e7i			1.22357i
$932$		0			0
$933$	−567510.	+	567510.i	−0.0213437	+	0.0213437i
$934$		0			0
$935$	−2.70067e6	+	1.97843e6i	−0.101028	+	0.0740101i
$936$		0			0
$937$	1.58634e7	+	1.58634e7i	0.590266	+	0.590266i	0.937703	−	0.347437i	$-0.112948\pi$
$937$	1.58634e7	+	1.58634e7i	0.590266	+	0.590266i	−0.347437	+	0.937703i	$0.612948\pi$
$938$		0			0
$939$	−1.95427e6			−0.0723303
$940$		0			0
$941$	−2.94325e7			−1.08356			−0.541780	−	0.840521i	$-0.682249\pi$
$941$	−2.94325e7			−1.08356			−0.541780	+	0.840521i	$0.682249\pi$
$942$		0			0
$943$	−1.83087e7	−	1.83087e7i	−0.670468	−	0.670468i
$944$		0			0
$945$	1.89646e6	−	1.22863e7i	0.0690818	−	0.447550i
$946$		0			0
$947$	−9.53732e6	+	9.53732e6i	−0.345582	+	0.345582i	−0.858461	−	0.512879i	$-0.828579\pi$
$947$	−9.53732e6	+	9.53732e6i	−0.345582	+	0.345582i	0.512879	+	0.858461i	$0.328579\pi$
$948$		0			0
$949$			1.80107e7i			0.649181i
$950$		0			0
$951$			4.37899e6i			0.157008i
$952$		0			0
$953$	−9.60341e6	+	9.60341e6i	−0.342526	+	0.342526i	−0.857316	−	0.514790i	$-0.827870\pi$
$953$	−9.60341e6	+	9.60341e6i	−0.342526	+	0.342526i	0.514790	+	0.857316i	$0.327870\pi$
$954$		0			0
$955$	−7.35390e6	+	4.76426e7i	−0.260921	+	1.69039i
$956$		0			0
$957$	−115689.	−	115689.i	−0.00408330	−	0.00408330i
$958$		0			0
$959$	−4.64899e7			−1.63235
$960$		0			0
$961$	−9.55220e6			−0.333653
$962$		0			0
$963$	−1.13657e7	−	1.13657e7i	−0.394939	−	0.394939i
$964$		0			0
$965$	−5.56463e6	+	4.07647e6i	−0.192362	+	0.140918i
$966$		0			0
$967$	1.47143e7	−	1.47143e7i	0.506027	−	0.506027i	−0.407277	−	0.913305i	$-0.633522\pi$
$967$	1.47143e7	−	1.47143e7i	0.506027	−	0.506027i	0.913305	+	0.407277i	$0.133522\pi$
$968$		0			0
$969$			3.56268e6i			0.121890i
$970$		0			0
$971$			4.63072e7i			1.57616i	0.615571	+	0.788081i	$0.288925\pi$
$971$			4.63072e7i			1.57616i	−0.615571	+	0.788081i	$0.711075\pi$
$972$		0			0
$973$	−4.47274e6	+	4.47274e6i	−0.151458	+	0.151458i
$974$		0			0
$975$	−2.17797e6	−	688775.i	−0.0733737	−	0.0232042i
$976$		0			0
$977$	−733830.	−	733830.i	−0.0245957	−	0.0245957i	0.694702	−	0.719298i	$-0.255536\pi$
$977$	−733830.	−	733830.i	−0.0245957	−	0.0245957i	−0.719298	+	0.694702i	$0.755536\pi$
$978$		0			0
$979$	2.10579e6			0.0702195
$980$		0			0
$981$	4.94329e7			1.64000
$982$		0			0
$983$	−1.77154e7	−	1.77154e7i	−0.584747	−	0.584747i	0.351457	−	0.936204i	$-0.385686\pi$
$983$	−1.77154e7	−	1.77154e7i	−0.584747	−	0.584747i	−0.936204	+	0.351457i	$0.885686\pi$
$984$		0			0
$985$	−5.30272e6	−	7.23853e6i	−0.174144	−	0.237717i
$986$		0			0
$987$	3.32154e6	−	3.32154e6i	0.108529	−	0.108529i
$988$		0			0
$989$			6.46735e7i			2.10250i
$990$		0			0
$991$			3.29330e7i			1.06524i	0.846355	+	0.532619i	$0.178792\pi$
$991$			3.29330e7i			1.06524i	−0.846355	+	0.532619i	$0.821208\pi$
$992$		0			0
$993$	−2.60918e6	+	2.60918e6i	−0.0839714	+	0.0839714i
$994$		0			0
$995$	2.74825e7	+	4.24208e6i	0.880033	+	0.135838i
$996$		0			0
$997$	9.40492e6	+	9.40492e6i	0.299652	+	0.299652i	0.840878	−	0.541225i	$-0.182039\pi$
$997$	9.40492e6	+	9.40492e6i	0.299652	+	0.299652i	−0.541225	+	0.840878i	$0.682039\pi$
$998$		0			0
$999$	−1.34714e7			−0.427071

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.b.127.4	yes	14
4.3	odd	2		160.6.n.a.127.4	yes	14
5.3	odd	4		160.6.n.a.63.4	✓	14
20.3	even	4	inner	160.6.n.b.63.4	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.a.63.4	✓	14	5.3	odd	4
160.6.n.a.127.4	yes	14	4.3	odd	2
160.6.n.b.63.4	yes	14	20.3	even	4	inner
160.6.n.b.127.4	yes	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.47740 + 1.47740i) q^{3} +(55.2474 + 8.52775i) q^{5} +(156.265 - 156.265i) q^{7} -238.635i q^{9} +O(q^{10})\)	\(q+(1.47740 + 1.47740i) q^{3} +(55.2474 + 8.52775i) q^{5} +(156.265 - 156.265i) q^{7} -238.635i q^{9} -35.4820i q^{11} +(-247.384 + 247.384i) q^{13} +(69.0238 + 94.2216i) q^{15} +(-1193.47 - 1193.47i) q^{17} -1010.27 q^{19} +461.733 q^{21} +(2033.39 + 2033.39i) q^{23} +(2979.55 + 942.273i) q^{25} +(711.568 - 711.568i) q^{27} -2206.91i q^{29} -6179.11i q^{31} +(52.4213 - 52.4213i) q^{33} +(9965.84 - 7300.66i) q^{35} +(-9466.02 - 9466.02i) q^{37} -730.972 q^{39} -9004.04 q^{41} +(15902.9 + 15902.9i) q^{43} +(2035.02 - 13183.9i) q^{45} +(7193.64 - 7193.64i) q^{47} -32030.6i q^{49} -3526.47i q^{51} +(-12995.3 + 12995.3i) q^{53} +(302.582 - 1960.29i) q^{55} +(-1492.57 - 1492.57i) q^{57} +40515.4 q^{59} +29233.6 q^{61} +(-37290.3 - 37290.3i) q^{63} +(-15777.0 + 11557.7i) q^{65} +(18221.2 - 18221.2i) q^{67} +6008.26i q^{69} +26609.8i q^{71} +(36402.4 - 36402.4i) q^{73} +(3009.89 + 5794.12i) q^{75} +(-5544.61 - 5544.61i) q^{77} -5089.11 q^{79} -55885.7 q^{81} +(20395.0 + 20395.0i) q^{83} +(-55758.6 - 76113.8i) q^{85} +(3260.49 - 3260.49i) q^{87} +59348.0i q^{89} +77315.1i q^{91} +(9129.03 - 9129.03i) q^{93} +(-55814.6 - 8615.30i) q^{95} +(69542.4 + 69542.4i) q^{97} -8467.24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 10 q^{3} + 42 q^{5} + 66 q^{7}+O(q^{10}) \) 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

Related objects

Downloads

Learn more