LMFDB - Embedded newform 160.6.n.c.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1375 x^{14} + 743087 x^{12} + 198706725 x^{10} + 26872635188 x^{8} + 1612811892960 x^{6} + \cdots + 177426662425600 $ x^16 + 1375x^14 + 743087x^12 + 198706725x^10 + 26872635188x^8 + 1612811892960x^6 + 24971013117824x^4 + 124211190826240*x^2 + 177426662425600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{41}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.1
Root			$19.8299i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.6.n.c.63.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-20.8299 - 20.8299i) q^{3} +(-55.6057 + 5.74531i) q^{5} +(135.906 - 135.906i) q^{7} +624.772i q^{9} +O(q^{10})$	\(q+(-20.8299 - 20.8299i) q^{3} +(-55.6057 + 5.74531i) q^{5} +(135.906 - 135.906i) q^{7} +624.772i q^{9} +629.190i q^{11} +(-2.08659 + 2.08659i) q^{13} +(1277.94 + 1038.59i) q^{15} +(-241.044 - 241.044i) q^{17} -372.104 q^{19} -5661.81 q^{21} +(2034.55 + 2034.55i) q^{23} +(3058.98 - 638.944i) q^{25} +(7952.27 - 7952.27i) q^{27} +55.2453i q^{29} -1844.67i q^{31} +(13106.0 - 13106.0i) q^{33} +(-6776.31 + 8337.95i) q^{35} +(-61.7891 - 61.7891i) q^{37} +86.9270 q^{39} -4808.22 q^{41} +(-10658.2 - 10658.2i) q^{43} +(-3589.51 - 34740.8i) q^{45} +(12121.5 - 12121.5i) q^{47} -20133.7i q^{49} +10041.9i q^{51} +(-21384.1 + 21384.1i) q^{53} +(-3614.89 - 34986.5i) q^{55} +(7750.90 + 7750.90i) q^{57} +50708.8 q^{59} +16164.0 q^{61} +(84910.0 + 84910.0i) q^{63} +(104.038 - 128.014i) q^{65} +(24888.6 - 24888.6i) q^{67} -84759.2i q^{69} +58597.1i q^{71} +(-42184.9 + 42184.9i) q^{73} +(-77027.5 - 50409.2i) q^{75} +(85510.5 + 85510.5i) q^{77} +32362.8 q^{79} -179471. q^{81} +(-10165.1 - 10165.1i) q^{83} +(14788.3 + 12018.6i) q^{85} +(1150.76 - 1150.76i) q^{87} -32266.2i q^{89} +567.158i q^{91} +(-38424.3 + 38424.3i) q^{93} +(20691.1 - 2137.85i) q^{95} +(24499.5 + 24499.5i) q^{97} -393100. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7}+O(q^{10}) $ 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7	$ 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7} + 536 q^{13} + 698 q^{15} - 1828 q^{17} - 2512 q^{19} - 4284 q^{21} + 7642 q^{23} + 9140 q^{25} + 12272 q^{27} + 11876 q^{33} - 10518 q^{35} - 7620 q^{37} - 11244 q^{39} - 21284 q^{41} - 20002 q^{43} + 686 q^{45} - 25298 q^{47} + 12852 q^{53} + 10584 q^{55} + 55848 q^{57} + 142704 q^{59} - 20564 q^{61} + 115282 q^{63} - 38256 q^{65} + 10506 q^{67} + 15432 q^{73} - 256226 q^{75} + 133852 q^{77} + 159344 q^{79} - 236116 q^{81} + 61222 q^{83} + 7056 q^{85} - 162176 q^{87} + 122180 q^{93} - 267512 q^{95} - 17344 q^{97} - 107332 q^{99}+O(q^{100}) $ 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7 + 536 * q^13 + 698 * q^15 - 1828 * q^17 - 2512 * q^19 - 4284 * q^21 + 7642 * q^23 + 9140 * q^25 + 12272 * q^27 + 11876 * q^33 - 10518 * q^35 - 7620 * q^37 - 11244 * q^39 - 21284 * q^41 - 20002 * q^43 + 686 * q^45 - 25298 * q^47 + 12852 * q^53 + 10584 * q^55 + 55848 * q^57 + 142704 * q^59 - 20564 * q^61 + 115282 * q^63 - 38256 * q^65 + 10506 * q^67 + 15432 * q^73 - 256226 * q^75 + 133852 * q^77 + 159344 * q^79 - 236116 * q^81 + 61222 * q^83 + 7056 * q^85 - 162176 * q^87 + 122180 * q^93 - 267512 * q^95 - 17344 * q^97 - 107332 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−20.8299	−	20.8299i	−1.33624	−	1.33624i	−0.899670	−	0.436570i	$-0.856193\pi$
$3$	−20.8299	−	20.8299i	−1.33624	−	1.33624i	−0.436570	−	0.899670i	$-0.643807\pi$
$4$		0			0
$5$	−55.6057	+	5.74531i	−0.994705	+	0.102775i
$5$	−55.6057	+	5.74531i	−0.994705	+	0.102775i
$6$		0			0
$7$	135.906	−	135.906i	1.04832	−	1.04832i	0.0495445	−	0.998772i	$-0.484223\pi$
$7$	135.906	−	135.906i	1.04832	−	1.04832i	0.998772	−	0.0495445i	$-0.0157770\pi$
$8$		0			0
$9$			624.772i			2.57108i
$10$		0			0
$11$			629.190i			1.56783i	0.620866	+	0.783917i	$0.286781\pi$
$11$			629.190i			1.56783i	−0.620866	+	0.783917i	$0.713219\pi$
$12$		0			0
$13$	−2.08659	+	2.08659i	−0.00342435	+	0.00342435i	−0.708817	−	0.705393i	$-0.750771\pi$
$13$	−2.08659	+	2.08659i	−0.00342435	+	0.00342435i	0.705393	+	0.708817i	$0.250771\pi$
$14$		0			0
$15$	1277.94	+	1038.59i	1.46650	+	1.19183i
$16$		0			0
$17$	−241.044	−	241.044i	−0.202290	−	0.202290i	0.598690	−	0.800981i	$-0.295688\pi$
$17$	−241.044	−	241.044i	−0.202290	−	0.202290i	−0.800981	+	0.598690i	$0.795688\pi$
$18$		0			0
$19$	−372.104			−0.236472			−0.118236	−	0.992986i	$-0.537724\pi$
$19$	−372.104			−0.236472			−0.118236	+	0.992986i	$0.537724\pi$
$20$		0			0
$21$	−5661.81			−2.80161
$22$		0			0
$23$	2034.55	+	2034.55i	0.801954	+	0.801954i	0.983401	−	0.181447i	$-0.0580781\pi$
$23$	2034.55	+	2034.55i	0.801954	+	0.801954i	−0.181447	+	0.983401i	$0.558078\pi$
$24$		0			0
$25$	3058.98	−	638.944i	0.978874	−	0.204462i
$26$		0			0
$27$	7952.27	−	7952.27i	2.09934	−	2.09934i
$28$		0			0
$29$			55.2453i			0.0121983i	0.999981	+	0.00609916i	$0.00194144\pi$
$29$			55.2453i			0.0121983i	−0.999981	+	0.00609916i	$0.998059\pi$
$30$		0			0
$31$		−	1844.67i		−	0.344757i	−0.985031	−	0.172379i	$-0.944855\pi$
$31$		−	1844.67i		−	0.344757i	0.985031	−	0.172379i	$-0.0551453\pi$
$32$		0			0
$33$	13106.0	−	13106.0i	2.09500	−	2.09500i
$34$		0			0
$35$	−6776.31	+	8337.95i	−0.935024	+	1.15051i
$36$		0			0
$37$	−61.7891	−	61.7891i	−0.00742006	−	0.00742006i	0.703387	−	0.710807i	$-0.251670\pi$
$37$	−61.7891	−	61.7891i	−0.00742006	−	0.00742006i	−0.710807	+	0.703387i	$0.751670\pi$
$38$		0			0
$39$	86.9270			0.00915152
$40$		0			0
$41$	−4808.22			−0.446709			−0.223355	−	0.974737i	$-0.571701\pi$
$41$	−4808.22			−0.446709			−0.223355	+	0.974737i	$0.571701\pi$
$42$		0			0
$43$	−10658.2	−	10658.2i	−0.879048	−	0.879048i	0.114388	−	0.993436i	$-0.463509\pi$
$43$	−10658.2	−	10658.2i	−0.879048	−	0.879048i	−0.993436	+	0.114388i	$0.963509\pi$
$44$		0			0
$45$	−3589.51	−	34740.8i	−0.264243	−	2.55746i
$46$		0			0
$47$	12121.5	−	12121.5i	0.800410	−	0.800410i	−0.182750	−	0.983159i	$-0.558500\pi$
$47$	12121.5	−	12121.5i	0.800410	−	0.800410i	0.983159	+	0.182750i	$0.0584998\pi$
$48$		0			0
$49$		−	20133.7i		−	1.19793i
$50$		0			0
$51$			10041.9i			0.540617i
$52$		0			0
$53$	−21384.1	+	21384.1i	−1.04569	+	1.04569i	−0.0467821	+	0.998905i	$0.514897\pi$
$53$	−21384.1	+	21384.1i	−1.04569	+	1.04569i	−0.998905	+	0.0467821i	$0.985103\pi$
$54$		0			0
$55$	−3614.89	−	34986.5i	−0.161135	−	1.55953i
$56$		0			0
$57$	7750.90	+	7750.90i	0.315984	+	0.315984i
$58$		0			0
$59$	50708.8			1.89650			0.948252	−	0.317519i	$-0.102850\pi$
$59$	50708.8			1.89650			0.948252	+	0.317519i	$0.102850\pi$
$60$		0			0
$61$	16164.0			0.556191			0.278095	−	0.960554i	$-0.410297\pi$
$61$	16164.0			0.556191			0.278095	+	0.960554i	$0.410297\pi$
$62$		0			0
$63$	84910.0	+	84910.0i	2.69530	+	2.69530i
$64$		0			0
$65$	104.038	−	128.014i	0.00305428	−	0.00375816i
$66$		0			0
$67$	24888.6	−	24888.6i	0.677350	−	0.677350i	−0.282050	−	0.959400i	$-0.591014\pi$
$67$	24888.6	−	24888.6i	0.677350	−	0.677350i	0.959400	+	0.282050i	$0.0910143\pi$
$68$		0			0
$69$		−	84759.2i		−	2.14321i
$70$		0			0
$71$			58597.1i			1.37953i	0.724034	+	0.689764i	$0.242286\pi$
$71$			58597.1i			1.37953i	−0.724034	+	0.689764i	$0.757714\pi$
$72$		0			0
$73$	−42184.9	+	42184.9i	−0.926509	+	0.926509i	−0.997478	−	0.0709698i	$-0.977391\pi$
$73$	−42184.9	+	42184.9i	−0.926509	+	0.926509i	0.0709698	+	0.997478i	$0.477391\pi$
$74$		0			0
$75$	−77027.5	−	50409.2i	−1.58122	−	1.03480i
$76$		0			0
$77$	85510.5	+	85510.5i	1.64359	+	1.64359i
$78$		0			0
$79$	32362.8			0.583417			0.291708	−	0.956507i	$-0.405776\pi$
$79$	32362.8			0.583417			0.291708	+	0.956507i	$0.405776\pi$
$80$		0			0
$81$	−179471.			−3.03936
$82$		0			0
$83$	−10165.1	−	10165.1i	−0.161963	−	0.161963i	0.621473	−	0.783436i	$-0.286535\pi$
$83$	−10165.1	−	10165.1i	−0.161963	−	0.161963i	−0.783436	+	0.621473i	$0.786535\pi$
$84$		0			0
$85$	14788.3	+	12018.6i	0.222009	+	0.180429i
$86$		0			0
$87$	1150.76	−	1150.76i	0.0162999	−	0.0162999i
$88$		0			0
$89$		−	32266.2i		−	0.431790i	−0.976417	−	0.215895i	$-0.930733\pi$
$89$		−	32266.2i		−	0.431790i	0.976417	−	0.215895i	$-0.0692669\pi$
$90$		0			0
$91$			567.158i			0.00717961i
$92$		0			0
$93$	−38424.3	+	38424.3i	−0.460679	+	0.460679i
$94$		0			0
$95$	20691.1	−	2137.85i	0.235220	−	0.0243035i
$96$		0			0
$97$	24499.5	+	24499.5i	0.264379	+	0.264379i	0.826830	−	0.562451i	$-0.190142\pi$
$97$	24499.5	+	24499.5i	0.264379	+	0.264379i	−0.562451	+	0.826830i	$0.690142\pi$
$98$		0			0
$99$	−393100.			−4.03102
$100$		0			0
$101$	128187.			1.25037			0.625186	−	0.780476i	$-0.285023\pi$
$101$	128187.			1.25037			0.625186	+	0.780476i	$0.285023\pi$
$102$		0			0
$103$	−8402.08	−	8402.08i	−0.0780358	−	0.0780358i	0.667012	−	0.745047i	$-0.267573\pi$
$103$	−8402.08	−	8402.08i	−0.0780358	−	0.0780358i	−0.745047	+	0.667012i	$0.767573\pi$
$104$		0			0
$105$	314829.	−	32528.9i	2.78677	−	0.287936i
$106$		0			0
$107$	54744.5	−	54744.5i	0.462254	−	0.462254i	−0.437139	−	0.899394i	$-0.644008\pi$
$107$	54744.5	−	54744.5i	0.462254	−	0.462254i	0.899394	+	0.437139i	$0.144008\pi$
$108$		0			0
$109$		−	17456.0i		−	0.140728i	−0.997521	−	0.0703638i	$-0.977584\pi$
$109$		−	17456.0i		−	0.140728i	0.997521	−	0.0703638i	$-0.0224160\pi$
$110$		0			0
$111$			2574.13i			0.0198300i
$112$		0			0
$113$	85583.2	−	85583.2i	0.630511	−	0.630511i	−0.317686	−	0.948196i	$-0.602906\pi$
$113$	85583.2	−	85583.2i	0.630511	−	0.630511i	0.948196	+	0.317686i	$0.102906\pi$
$114$		0			0
$115$	−124822.	−	101444.i	−0.880128	−	0.715286i
$116$		0			0
$117$	−1303.64	−	1303.64i	−0.00880427	−	0.00880427i
$118$		0			0
$119$	−65518.6			−0.424128
$120$		0			0
$121$	−234829.			−1.45810
$122$		0			0
$123$	100155.	+	100155.i	0.596911	+	0.596911i
$124$		0			0
$125$	−166426.	+	53103.7i	−0.952677	+	0.303984i
$126$		0			0
$127$	96993.9	−	96993.9i	0.533624	−	0.533624i	−0.388025	−	0.921649i	$-0.626843\pi$
$127$	96993.9	−	96993.9i	0.533624	−	0.533624i	0.921649	+	0.388025i	$0.126843\pi$
$128$		0			0
$129$			444019.i			2.34924i
$130$		0			0
$131$		−	272784.i		−	1.38880i	−0.719588	−	0.694402i	$-0.755669\pi$
$131$		−	272784.i		−	1.38880i	0.719588	−	0.694402i	$-0.244331\pi$
$132$		0			0
$133$	−50571.0	+	50571.0i	−0.247898	+	0.247898i
$134$		0			0
$135$	−396503.	+	487880.i	−1.87246	+	2.30398i
$136$		0			0
$137$	164113.	+	164113.i	0.747037	+	0.747037i	0.973922	−	0.226885i	$-0.0728541\pi$
$137$	164113.	+	164113.i	0.747037	+	0.747037i	−0.226885	+	0.973922i	$0.572854\pi$
$138$		0			0
$139$	244627.			1.07391			0.536955	−	0.843611i	$-0.319574\pi$
$139$	244627.			1.07391			0.536955	+	0.843611i	$0.319574\pi$
$140$		0			0
$141$	−504981.			−2.13908
$142$		0			0
$143$	−1312.86	−	1312.86i	−0.00536882	−	0.00536882i
$144$		0			0
$145$	−317.402	−	3071.95i	−0.00125369	−	0.0121337i
$146$		0			0
$147$	−419383.	+	419383.i	−1.60073	+	1.60073i
$148$		0			0
$149$		−	130589.i		−	0.481883i	−0.970540	−	0.240941i	$-0.922544\pi$
$149$		−	130589.i		−	0.481883i	0.970540	−	0.240941i	$-0.0774562\pi$
$150$		0			0
$151$		−	12502.0i		−	0.0446208i	−0.999751	−	0.0223104i	$-0.992898\pi$
$151$		−	12502.0i		−	0.0446208i	0.999751	−	0.0223104i	$-0.00710221\pi$
$152$		0			0
$153$	150598.	−	150598.i	0.520104	−	0.520104i
$154$		0			0
$155$	10598.2	+	102574.i	0.0354326	+	0.342932i
$156$		0			0
$157$	402134.	+	402134.i	1.30203	+	1.30203i	0.927020	+	0.375012i	$0.122362\pi$
$157$	402134.	+	402134.i	1.30203	+	1.30203i	0.375012	+	0.927020i	$0.377638\pi$
$158$		0			0
$159$	890859.			2.79458
$160$		0			0
$161$	553014.			1.68140
$162$		0			0
$163$	−6089.60	−	6089.60i	−0.0179523	−	0.0179523i	0.698074	−	0.716026i	$-0.254041\pi$
$163$	−6089.60	−	6089.60i	−0.0179523	−	0.0179523i	−0.716026	+	0.698074i	$0.754041\pi$
$164$		0			0
$165$	−653469.	+	804065.i	−1.86859	+	2.29922i
$166$		0			0
$167$	−179899.	+	179899.i	−0.499156	+	0.499156i	−0.911175	−	0.412019i	$-0.864824\pi$
$167$	−179899.	+	179899.i	−0.499156	+	0.499156i	0.412019	+	0.911175i	$0.364824\pi$
$168$		0			0
$169$			371284.i			0.999977i
$170$		0			0
$171$		−	232480.i		−	0.607988i
$172$		0			0
$173$	85872.0	−	85872.0i	0.218140	−	0.218140i	−0.589574	−	0.807714i	$-0.700704\pi$
$173$	85872.0	−	85872.0i	0.218140	−	0.218140i	0.807714	+	0.589574i	$0.200704\pi$
$174$		0			0
$175$	328897.	−	502569.i	0.811829	−	1.24051i
$176$		0			0
$177$	−1.05626e6	−	1.05626e6i	−2.53418	−	2.53418i
$178$		0			0
$179$	230684.			0.538127			0.269064	−	0.963122i	$-0.413286\pi$
$179$	230684.			0.538127			0.269064	+	0.963122i	$0.413286\pi$
$180$		0			0
$181$	601745.			1.36526			0.682631	−	0.730763i	$-0.260836\pi$
$181$	601745.			1.36526			0.682631	+	0.730763i	$0.260836\pi$
$182$		0			0
$183$	−336694.	−	336694.i	−0.743204	−	0.743204i
$184$		0			0
$185$	3790.82	+	3080.83i	0.00814337	+	0.00661817i
$186$		0			0
$187$	151663.	−	151663.i	0.317157	−	0.317157i
$188$		0			0
$189$		−	2.16152e6i		−	4.40154i
$190$		0			0
$191$		−	573479.i		−	1.13746i	−0.822526	−	0.568728i	$-0.807436\pi$
$191$		−	573479.i		−	1.13746i	0.822526	−	0.568728i	$-0.192564\pi$
$192$		0			0
$193$	617099.	−	617099.i	1.19251	−	1.19251i	0.216148	−	0.976361i	$-0.430651\pi$
$193$	617099.	−	617099.i	1.19251	−	1.19251i	0.976361	−	0.216148i	$-0.0693494\pi$
$194$		0			0
$195$	−4833.63	+	499.423i	−0.00910306	+	0.000940550i
$196$		0			0
$197$	283085.	+	283085.i	0.519698	+	0.519698i	0.917480	−	0.397782i	$-0.130220\pi$
$197$	283085.	+	283085.i	0.519698	+	0.519698i	−0.397782	+	0.917480i	$0.630220\pi$
$198$		0			0
$199$	−125350.			−0.224385			−0.112192	−	0.993687i	$-0.535787\pi$
$199$	−125350.			−0.224385			−0.112192	+	0.993687i	$0.535787\pi$
$200$		0			0
$201$	−1.03685e6			−1.81020
$202$		0			0
$203$	7508.15	+	7508.15i	0.0127877	+	0.0127877i
$204$		0			0
$205$	267364.	−	27624.7i	0.444344	−	0.0459107i
$206$		0			0
$207$	−1.27113e6	+	1.27113e6i	−2.06188	+	2.06188i
$208$		0			0
$209$		−	234124.i		−	0.370749i
$210$		0			0
$211$			4378.03i			0.00676974i	0.999994	+	0.00338487i	$0.00107744\pi$
$211$			4378.03i			0.00676974i	−0.999994	+	0.00338487i	$0.998923\pi$
$212$		0			0
$213$	1.22057e6	−	1.22057e6i	1.84338	−	1.84338i
$214$		0			0
$215$	653891.	+	531421.i	0.964737	+	0.784048i
$216$		0			0
$217$	−250701.	−	250701.i	−0.361415	−	0.361415i
$218$		0			0
$219$	1.75742e6			2.47608
$220$		0			0
$221$	1005.92			0.00138543
$222$		0			0
$223$	298702.	+	298702.i	0.402231	+	0.402231i	0.879019	−	0.476787i	$-0.158199\pi$
$223$	298702.	+	298702.i	0.402231	+	0.402231i	−0.476787	+	0.879019i	$0.658199\pi$
$224$		0			0
$225$	399194.	+	1.91117e6i	0.525688	+	2.51676i
$226$		0			0
$227$	605799.	−	605799.i	0.780304	−	0.780304i	−0.199578	−	0.979882i	$-0.563957\pi$
$227$	605799.	−	605799.i	0.780304	−	0.780304i	0.979882	+	0.199578i	$0.0639572\pi$
$228$		0			0
$229$			527570.i			0.664801i	0.943138	+	0.332400i	$0.107859\pi$
$229$			527570.i			0.664801i	−0.943138	+	0.332400i	$0.892141\pi$
$230$		0			0
$231$		−	3.56235e6i		−	4.39245i
$232$		0			0
$233$	214988.	−	214988.i	0.259432	−	0.259432i	−0.565391	−	0.824823i	$-0.691275\pi$
$233$	214988.	−	214988.i	0.259432	−	0.259432i	0.824823	+	0.565391i	$0.191275\pi$
$234$		0			0
$235$	−604383.	+	743667.i	−0.713909	+	0.878434i
$236$		0			0
$237$	−674116.	−	674116.i	−0.779585	−	0.779585i
$238$		0			0
$239$	−1.17211e6			−1.32731			−0.663656	−	0.748038i	$-0.730996\pi$
$239$	−1.17211e6			−1.32731			−0.663656	+	0.748038i	$0.730996\pi$
$240$		0			0
$241$	−1.37526e6			−1.52525			−0.762625	−	0.646841i	$-0.776090\pi$
$241$	−1.37526e6			−1.52525			−0.762625	+	0.646841i	$0.776090\pi$
$242$		0			0
$243$	1.80597e6	+	1.80597e6i	1.96198	+	1.96198i
$244$		0			0
$245$	115674.	+	1.11955e6i	0.123118	+	1.19159i
$246$		0			0
$247$	776.428	−	776.428i	0.000809765	−	0.000809765i
$248$		0			0
$249$			423476.i			0.432843i
$250$		0			0
$251$			305774.i			0.306349i	0.988199	+	0.153174i	$0.0489496\pi$
$251$			305774.i			0.306349i	−0.988199	+	0.153174i	$0.951050\pi$
$252$		0			0
$253$	−1.28012e6	+	1.28012e6i	−1.25733	+	1.25733i
$254$		0			0
$255$	−57693.7	−	558385.i	−0.0555620	−	0.537754i
$256$		0			0
$257$	−964285.	−	964285.i	−0.910694	−	0.910694i	0.0856328	−	0.996327i	$-0.472709\pi$
$257$	−964285.	−	964285.i	−0.910694	−	0.910694i	−0.996327	+	0.0856328i	$0.972709\pi$
$258$		0			0
$259$	−16795.0			−0.0155572
$260$		0			0
$261$	−34515.7			−0.0313628
$262$		0			0
$263$	1.19814e6	+	1.19814e6i	1.06812	+	1.06812i	0.997504	+	0.0706129i	$0.0224955\pi$
$263$	1.19814e6	+	1.19814e6i	1.06812	+	1.06812i	0.0706129	+	0.997504i	$0.477504\pi$
$264$		0			0
$265$	1.06622e6	−	1.31194e6i	0.932679	−	1.14762i
$266$		0			0
$267$	−672102.	+	672102.i	−0.576975	+	0.576975i
$268$		0			0
$269$			1.22133e6i			1.02909i	0.857463	+	0.514546i	$0.172039\pi$
$269$			1.22133e6i			1.02909i	−0.857463	+	0.514546i	$0.827961\pi$
$270$		0			0
$271$			501303.i			0.414646i	0.978273	+	0.207323i	$0.0664751\pi$
$271$			501303.i			0.414646i	−0.978273	+	0.207323i	$0.933525\pi$
$272$		0			0
$273$	11813.9	−	11813.9i	0.00959369	−	0.00959369i
$274$		0			0
$275$	402017.	+	1.92468e6i	0.320563	+	1.53471i
$276$		0			0
$277$	−314343.	−	314343.i	−0.246153	−	0.246153i	0.573237	−	0.819390i	$-0.305687\pi$
$277$	−314343.	−	314343.i	−0.246153	−	0.246153i	−0.819390	+	0.573237i	$0.805687\pi$
$278$		0			0
$279$	1.15250e6			0.886398
$280$		0			0
$281$	1.00305e6			0.757807			0.378904	−	0.925436i	$-0.376301\pi$
$281$	1.00305e6			0.757807			0.378904	+	0.925436i	$0.376301\pi$
$282$		0			0
$283$	−575269.	−	575269.i	−0.426977	−	0.426977i	0.460620	−	0.887597i	$-0.347627\pi$
$283$	−575269.	−	575269.i	−0.426977	−	0.426977i	−0.887597	+	0.460620i	$0.847627\pi$
$284$		0			0
$285$	−475525.	−	386463.i	−0.346786	−	0.281835i
$286$		0			0
$287$	−653465.	+	653465.i	−0.468293	+	0.468293i
$288$		0			0
$289$		−	1.30365e6i		−	0.918157i
$290$		0			0
$291$		−	1.02064e6i		−	0.706548i
$292$		0			0
$293$	738761.	−	738761.i	0.502730	−	0.502730i	−0.409555	−	0.912285i	$-0.634316\pi$
$293$	738761.	−	738761.i	0.502730	−	0.502730i	0.912285	+	0.409555i	$0.134316\pi$
$294$		0			0
$295$	−2.81970e6	+	291338.i	−1.88646	+	0.194914i
$296$		0			0
$297$	5.00349e6	+	5.00349e6i	3.29141	+	3.29141i
$298$		0			0
$299$	−8490.55			−0.00549235
$300$		0			0
$301$	−2.89702e6			−1.84304
$302$		0			0
$303$	−2.67012e6	−	2.67012e6i	−1.67080	−	1.67080i
$304$		0			0
$305$	−898809.	+	92867.1i	−0.553245	+	0.0571626i
$306$		0			0
$307$	2.06010e6	−	2.06010e6i	1.24750	−	1.24750i	0.290686	−	0.956819i	$-0.406117\pi$
$307$	2.06010e6	−	2.06010e6i	1.24750	−	1.24750i	0.956819	−	0.290686i	$-0.0938834\pi$
$308$		0			0
$309$			350030.i			0.208549i
$310$		0			0
$311$			891640.i			0.522744i	0.965238	+	0.261372i	$0.0841749\pi$
$311$			891640.i			0.522744i	−0.965238	+	0.261372i	$0.915825\pi$
$312$		0			0
$313$	910965.	−	910965.i	0.525582	−	0.525582i	−0.393670	−	0.919252i	$-0.628795\pi$
$313$	910965.	−	910965.i	0.525582	−	0.525582i	0.919252	+	0.393670i	$0.128795\pi$
$314$		0			0
$315$	−5.20931e6	−	4.23364e6i	−2.95804	−	2.40402i
$316$		0			0
$317$	1.21076e6	+	1.21076e6i	0.676721	+	0.676721i	0.959257	−	0.282536i	$-0.0911757\pi$
$317$	1.21076e6	+	1.21076e6i	0.676721	+	0.676721i	−0.282536	+	0.959257i	$0.591176\pi$
$318$		0			0
$319$	−34759.8			−0.0191249
$320$		0			0
$321$	−2.28065e6			−1.23537
$322$		0			0
$323$	89693.6	+	89693.6i	0.0478360	+	0.0478360i
$324$		0			0
$325$	−5049.63	+	7716.05i	−0.00265186	+	0.00405216i
$326$		0			0
$327$	−363608.	+	363608.i	−0.188046	+	0.188046i
$328$		0			0
$329$		−	3.29477e6i		−	1.67817i
$330$		0			0
$331$			1.52738e6i			0.766262i	0.923694	+	0.383131i	$0.125154\pi$
$331$			1.52738e6i			0.766262i	−0.923694	+	0.383131i	$0.874846\pi$
$332$		0			0
$333$	38604.1	−	38604.1i	0.0190776	−	0.0190776i
$334$		0			0
$335$	−1.24095e6	+	1.52694e6i	−0.604148	+	0.743378i
$336$		0			0
$337$	2.27407e6	+	2.27407e6i	1.09076	+	1.09076i	0.995447	+	0.0953146i	$0.0303857\pi$
$337$	2.27407e6	+	2.27407e6i	1.09076	+	1.09076i	0.0953146	+	0.995447i	$0.469614\pi$
$338$		0			0
$339$	−3.56538e6			−1.68503
$340$		0			0
$341$	1.16065e6			0.540522
$342$		0			0
$343$	−452116.	−	452116.i	−0.207498	−	0.207498i
$344$		0			0
$345$	486968.	+	4.71309e6i	0.220269	+	2.13186i
$346$		0			0
$347$	−2.68164e6	+	2.68164e6i	−1.19558	+	1.19558i	−0.220097	+	0.975478i	$0.570637\pi$
$347$	−2.68164e6	+	2.68164e6i	−1.19558	+	1.19558i	−0.975478	+	0.220097i	$0.929363\pi$
$348$		0			0
$349$		−	951948.i		−	0.418359i	−0.977877	−	0.209180i	$-0.932921\pi$
$349$		−	951948.i		−	0.418359i	0.977877	−	0.209180i	$-0.0670794\pi$
$350$		0			0
$351$			33186.2i			0.0143777i
$352$		0			0
$353$	4882.13	−	4882.13i	0.00208532	−	0.00208532i	−0.706063	−	0.708149i	$-0.749531\pi$
$353$	4882.13	−	4882.13i	0.00208532	−	0.00208532i	0.708149	+	0.706063i	$0.249531\pi$
$354$		0			0
$355$	−336659.	−	3.25833e6i	−0.141781	−	1.37222i
$356$		0			0
$357$	1.36475e6	+	1.36475e6i	0.566737	+	0.566737i
$358$		0			0
$359$	3.85803e6			1.57990			0.789951	−	0.613170i	$-0.210106\pi$
$359$	3.85803e6			1.57990			0.789951	+	0.613170i	$0.210106\pi$
$360$		0			0
$361$	−2.33764e6			−0.944081
$362$		0			0
$363$	4.89147e6	+	4.89147e6i	1.94838	+	1.94838i
$364$		0			0
$365$	2.10335e6	−	2.58808e6i	0.826380	−	1.01682i
$366$		0			0
$367$	701915.	−	701915.i	0.272032	−	0.272032i	−0.557886	−	0.829918i	$-0.688387\pi$
$367$	701915.	−	701915.i	0.272032	−	0.272032i	0.829918	+	0.557886i	$0.188387\pi$
$368$		0			0
$369$		−	3.00404e6i		−	1.14852i
$370$		0			0
$371$			5.81245e6i			2.19242i
$372$		0			0
$373$	−2.74504e6	+	2.74504e6i	−1.02159	+	1.02159i	−0.0218283	+	0.999762i	$0.506949\pi$
$373$	−2.74504e6	+	2.74504e6i	−1.02159	+	1.02159i	−0.999762	+	0.0218283i	$0.993051\pi$
$374$		0			0
$375$	4.57279e6	+	2.36049e6i	1.67920	+	0.866811i
$376$		0			0
$377$	−115.274	−	115.274i	−4.17714e−5	−	4.17714e-5i
$378$		0			0
$379$	−2.26919e6			−0.811472			−0.405736	−	0.913990i	$-0.632985\pi$
$379$	−2.26919e6			−0.811472			−0.405736	+	0.913990i	$0.632985\pi$
$380$		0			0
$381$	−4.04075e6			−1.42610
$382$		0			0
$383$	−1.29183e6	−	1.29183e6i	−0.449997	−	0.449997i	0.445356	−	0.895353i	$-0.353077\pi$
$383$	−1.29183e6	−	1.29183e6i	−0.449997	−	0.449997i	−0.895353	+	0.445356i	$0.853077\pi$
$384$		0			0
$385$	−5.24615e6	−	4.26358e6i	−1.80380	−	1.46596i
$386$		0			0
$387$	6.65894e6	−	6.65894e6i	2.26010	−	2.26010i
$388$		0			0
$389$			5.08803e6i			1.70481i	0.522884	+	0.852404i	$0.324856\pi$
$389$			5.08803e6i			1.70481i	−0.522884	+	0.852404i	$0.675144\pi$
$390$		0			0
$391$		−	980835.i		−	0.324455i
$392$		0			0
$393$	−5.68207e6	+	5.68207e6i	−1.85578	+	1.85578i
$394$		0			0
$395$	−1.79956e6	+	185935.i	−0.580327	+	0.0599608i
$396$		0			0
$397$	−424803.	−	424803.i	−0.135273	−	0.135273i	0.636228	−	0.771501i	$-0.280494\pi$
$397$	−424803.	−	424803.i	−0.135273	−	0.135273i	−0.771501	+	0.636228i	$0.780494\pi$
$398$		0			0
$399$	2.10678e6			0.662502
$400$		0			0
$401$	1.57875e6			0.490289			0.245145	−	0.969487i	$-0.421165\pi$
$401$	1.57875e6			0.490289			0.245145	+	0.969487i	$0.421165\pi$
$402$		0			0
$403$	3849.06	+	3849.06i	0.00118057	+	0.00118057i
$404$		0			0
$405$	9.97961e6	−	1.03112e6i	3.02326	−	0.312371i
$406$		0			0
$407$	38877.1	−	38877.1i	0.0116334	−	0.0116334i
$408$		0			0
$409$			2.15206e6i			0.636130i	0.948069	+	0.318065i	$0.103033\pi$
$409$			2.15206e6i			0.636130i	−0.948069	+	0.318065i	$0.896967\pi$
$410$		0			0
$411$		−	6.83693e6i		−	1.99644i
$412$		0			0
$413$	6.89162e6	−	6.89162e6i	1.98814	−	1.98814i
$414$		0			0
$415$	623639.	+	506835.i	0.177751	+	0.144460i
$416$		0			0
$417$	−5.09557e6	−	5.09557e6i	−1.43500	−	1.43500i
$418$		0			0
$419$	−2.70273e6			−0.752087			−0.376043	−	0.926602i	$-0.622716\pi$
$419$	−2.70273e6			−0.752087			−0.376043	+	0.926602i	$0.622716\pi$
$420$		0			0
$421$	−3.60276e6			−0.990673			−0.495337	−	0.868701i	$-0.664955\pi$
$421$	−3.60276e6			−0.990673			−0.495337	+	0.868701i	$0.664955\pi$
$422$		0			0
$423$	7.57318e6	+	7.57318e6i	2.05791	+	2.05791i
$424$		0			0
$425$	−891365.	−	583337.i	−0.239377	−	0.156656i
$426$		0			0
$427$	2.19678e6	−	2.19678e6i	0.583064	−	0.583064i
$428$		0			0
$429$			54693.6i			0.0143481i
$430$		0			0
$431$			3.84787e6i			0.997763i	0.866670	+	0.498882i	$0.166256\pi$
$431$			3.84787e6i			0.997763i	−0.866670	+	0.498882i	$0.833744\pi$
$432$		0			0
$433$	−1.93938e6	+	1.93938e6i	−0.497100	+	0.497100i	−0.910534	−	0.413434i	$-0.864329\pi$
$433$	−1.93938e6	+	1.93938e6i	−0.497100	+	0.497100i	0.413434	+	0.910534i	$0.364329\pi$
$434$		0			0
$435$	−57377.1	+	70600.0i	−0.0145384	+	0.0178888i
$436$		0			0
$437$	−757065.	−	757065.i	−0.189640	−	0.189640i
$438$		0			0
$439$	−1.92588e6			−0.476945			−0.238472	−	0.971149i	$-0.576647\pi$
$439$	−1.92588e6			−0.476945			−0.238472	+	0.971149i	$0.576647\pi$
$440$		0			0
$441$	1.25790e7			3.07998
$442$		0			0
$443$	655444.	+	655444.i	0.158681	+	0.158681i	0.781982	−	0.623301i	$-0.214209\pi$
$443$	655444.	+	655444.i	0.158681	+	0.158681i	−0.623301	+	0.781982i	$0.714209\pi$
$444$		0			0
$445$	185379.	+	1.79418e6i	0.0443774	+	0.429504i
$446$		0			0
$447$	−2.72016e6	+	2.72016e6i	−0.643911	+	0.643911i
$448$		0			0
$449$		−	4.59016e6i		−	1.07451i	−0.843418	−	0.537257i	$-0.819460\pi$
$449$		−	4.59016e6i		−	1.07451i	0.843418	−	0.537257i	$-0.180540\pi$
$450$		0			0
$451$		−	3.02528e6i		−	0.700366i
$452$		0			0
$453$	−260416.	+	260416.i	−0.0596241	+	0.0596241i
$454$		0			0
$455$	−3258.50	−	31537.2i	−0.000737887	−	0.00714159i
$456$		0			0
$457$	−2.50178e6	−	2.50178e6i	−0.560349	−	0.560349i	0.369057	−	0.929407i	$-0.379681\pi$
$457$	−2.50178e6	−	2.50178e6i	−0.560349	−	0.560349i	−0.929407	+	0.369057i	$0.879681\pi$
$458$		0			0
$459$	−3.83370e6			−0.849350
$460$		0			0
$461$	−2.98032e6			−0.653145			−0.326573	−	0.945172i	$-0.605894\pi$
$461$	−2.98032e6			−0.653145			−0.326573	+	0.945172i	$0.605894\pi$
$462$		0			0
$463$	−268149.	−	268149.i	−0.0581331	−	0.0581331i	0.677443	−	0.735576i	$-0.263088\pi$
$463$	−268149.	−	268149.i	−0.0581331	−	0.0581331i	−0.735576	+	0.677443i	$0.763088\pi$
$464$		0			0
$465$	1.91585e6	−	2.35737e6i	0.410893	−	0.505586i
$466$		0			0
$467$	−4.69656e6	+	4.69656e6i	−0.996525	+	0.996525i	−0.999994	−	0.00346931i	$-0.998896\pi$
$467$	−4.69656e6	+	4.69656e6i	−0.996525	+	0.996525i	0.00346931	+	0.999994i	$0.498896\pi$
$468$		0			0
$469$		−	6.76500e6i		−	1.42015i
$470$		0			0
$471$		−	1.67528e7i		−	3.47966i
$472$		0			0
$473$	6.70603e6	−	6.70603e6i	1.37820	−	1.37820i
$474$		0			0
$475$	−1.13826e6	+	237754.i	−0.231477	+	0.0483496i
$476$		0			0
$477$	−1.33602e7	−	1.33602e7i	−2.68854	−	2.68854i
$478$		0			0
$479$	5.68594e6			1.13231			0.566153	−	0.824300i	$-0.308431\pi$
$479$	5.68594e6			1.13231			0.566153	+	0.824300i	$0.308431\pi$
$480$		0			0
$481$	257.857			5.08178e−5
$482$		0			0
$483$	−1.15192e7	−	1.15192e7i	−2.24676	−	2.24676i
$484$		0			0
$485$	−1.50307e6	−	1.22155e6i	−0.290151	−	0.235807i
$486$		0			0
$487$	−4.35039e6	+	4.35039e6i	−0.831200	+	0.831200i	−0.987681	−	0.156481i	$-0.949985\pi$
$487$	−4.35039e6	+	4.35039e6i	−0.831200	+	0.831200i	0.156481	+	0.987681i	$0.449985\pi$
$488$		0			0
$489$			253692.i			0.0479772i
$490$		0			0
$491$			3.84948e6i			0.720606i	0.932835	+	0.360303i	$0.117327\pi$
$491$			3.84948e6i			0.720606i	−0.932835	+	0.360303i	$0.882673\pi$
$492$		0			0
$493$	13316.6	−	13316.6i	0.00246760	−	0.00246760i
$494$		0			0
$495$	2.18586e7	−	2.25848e6i	4.00967	−	0.414289i
$496$		0			0
$497$	7.96368e6	+	7.96368e6i	1.44618	+	1.44618i
$498$		0			0
$499$	8.16271e6			1.46752			0.733758	−	0.679411i	$-0.237765\pi$
$499$	8.16271e6			1.46752			0.733758	+	0.679411i	$0.237765\pi$
$500$		0			0
$501$	7.49455e6			1.33399
$502$		0			0
$503$	−2.68480e6	−	2.68480e6i	−0.473143	−	0.473143i	0.429787	−	0.902930i	$-0.358589\pi$
$503$	−2.68480e6	−	2.68480e6i	−0.473143	−	0.473143i	−0.902930	+	0.429787i	$0.858589\pi$
$504$		0			0
$505$	−7.12790e6	+	736472.i	−1.24375	+	0.128507i
$506$		0			0
$507$	7.73382e6	−	7.73382e6i	1.33621	−	1.33621i
$508$		0			0
$509$			9.38152e6i			1.60501i	0.596643	+	0.802507i	$0.296501\pi$
$509$			9.38152e6i			1.60501i	−0.596643	+	0.802507i	$0.703499\pi$
$510$		0			0
$511$			1.14663e7i			1.94255i
$512$		0			0
$513$	−2.95907e6	+	2.95907e6i	−0.496435	+	0.496435i
$514$		0			0
$515$	515476.	+	418931.i	0.0856427	+	0.0696024i
$516$		0			0
$517$	7.62674e6	+	7.62674e6i	1.25491	+	1.25491i
$518$		0			0
$519$	−3.57741e6			−0.582976
$520$		0			0
$521$	1.02177e7			1.64914			0.824572	−	0.565757i	$-0.191416\pi$
$521$	1.02177e7			1.64914			0.824572	+	0.565757i	$0.191416\pi$
$522$		0			0
$523$	−638202.	−	638202.i	−0.102024	−	0.102024i	0.654252	−	0.756277i	$-0.272984\pi$
$523$	−638202.	−	638202.i	−0.102024	−	0.102024i	−0.756277	+	0.654252i	$0.772984\pi$
$524$		0			0
$525$	−1.73194e7	+	3.61758e6i	−2.74242	+	0.572822i
$526$		0			0
$527$	−444647.	+	444647.i	−0.0697411	+	0.0697411i
$528$		0			0
$529$			1.84246e6i			0.286260i
$530$		0			0
$531$			3.16814e7i			4.87606i
$532$		0			0
$533$	10032.8	−	10032.8i	0.00152969	−	0.00152969i
$534$		0			0
$535$	−2.72958e6	+	3.35863e6i	−0.412298	+	0.507315i
$536$		0			0
$537$	−4.80513e6	−	4.80513e6i	−0.719068	−	0.719068i
$538$		0			0
$539$	1.26679e7			1.87816
$540$		0			0
$541$	7.81061e6			1.14734			0.573669	−	0.819087i	$-0.305519\pi$
$541$	7.81061e6			1.14734			0.573669	+	0.819087i	$0.305519\pi$
$542$		0			0
$543$	−1.25343e7	−	1.25343e7i	−1.82432	−	1.82432i
$544$		0			0
$545$	100290.	+	970655.i	0.0144633	+	0.139982i
$546$		0			0
$547$	4.78434e6	−	4.78434e6i	0.683682	−	0.683682i	−0.277146	−	0.960828i	$-0.589389\pi$
$547$	4.78434e6	−	4.78434e6i	0.683682	−	0.683682i	0.960828	+	0.277146i	$0.0893886\pi$
$548$		0			0
$549$			1.00988e7i			1.43001i
$550$		0			0
$551$		−	20557.0i		−	0.00288457i
$552$		0			0
$553$	4.39829e6	−	4.39829e6i	0.611605	−	0.611605i
$554$		0			0
$555$	−14789.2	−	143136.i	−0.00203803	−	0.0197250i
$556$		0			0
$557$	−5.45559e6	−	5.45559e6i	−0.745082	−	0.745082i	0.228469	−	0.973551i	$-0.426628\pi$
$557$	−5.45559e6	−	5.45559e6i	−0.745082	−	0.745082i	−0.973551	+	0.228469i	$0.926628\pi$
$558$		0			0
$559$	44478.5			0.00602034
$560$		0			0
$561$	−6.31825e6			−0.847597
$562$		0			0
$563$	970144.	+	970144.i	0.128993	+	0.128993i	0.768656	−	0.639663i	$-0.220926\pi$
$563$	970144.	+	970144.i	0.128993	+	0.128993i	−0.639663	+	0.768656i	$0.720926\pi$
$564$		0			0
$565$	−4.26721e6	+	5.25061e6i	−0.562371	+	0.691973i
$566$		0			0
$567$	−2.43911e7	+	2.43911e7i	−3.18621	+	3.18621i
$568$		0			0
$569$			1.24295e7i			1.60943i	0.593661	+	0.804715i	$0.297682\pi$
$569$			1.24295e7i			1.60943i	−0.593661	+	0.804715i	$0.702318\pi$
$570$		0			0
$571$		−	1.36788e7i		−	1.75573i	−0.478909	−	0.877864i	$-0.658968\pi$
$571$		−	1.36788e7i		−	1.75573i	0.478909	−	0.877864i	$-0.341032\pi$
$572$		0			0
$573$	−1.19455e7	+	1.19455e7i	−1.51991	+	1.51991i
$574$		0			0
$575$	7.52363e6	+	4.92370e6i	0.948981	+	0.621043i
$576$		0			0
$577$	1.07760e6	+	1.07760e6i	0.134747	+	0.134747i	0.771263	−	0.636516i	$-0.219625\pi$
$577$	1.07760e6	+	1.07760e6i	0.134747	+	0.134747i	−0.636516	+	0.771263i	$0.719625\pi$
$578$		0			0
$579$	−2.57083e7			−3.18696
$580$		0			0
$581$	−2.76299e6			−0.339577
$582$		0			0
$583$	−1.34547e7	−	1.34547e7i	−1.63946	−	1.63946i
$584$		0			0
$585$	79979.7	+	65000.0i	0.00966251	+	0.00785279i
$586$		0			0
$587$	−998920.	+	998920.i	−0.119656	+	0.119656i	−0.764399	−	0.644743i	$-0.776964\pi$
$587$	−998920.	+	998920.i	−0.119656	+	0.119656i	0.644743	+	0.764399i	$0.276964\pi$
$588$		0			0
$589$			686408.i			0.0815256i
$590$		0			0
$591$		−	1.17933e7i		−	1.38888i
$592$		0			0
$593$	−9.60583e6	+	9.60583e6i	−1.12176	+	1.12176i	−0.130278	+	0.991478i	$0.541587\pi$
$593$	−9.60583e6	+	9.60583e6i	−1.12176	+	1.12176i	−0.991478	+	0.130278i	$0.958413\pi$
$594$		0			0
$595$	3.64321e6	−	376425.i	0.421882	−	0.0435899i
$596$		0			0
$597$	2.61104e6	+	2.61104e6i	0.299832	+	0.299832i
$598$		0			0
$599$	9.45847e6			1.07709			0.538547	−	0.842595i	$-0.318973\pi$
$599$	9.45847e6			1.07709			0.538547	+	0.842595i	$0.318973\pi$
$600$		0			0
$601$	−1.44386e6			−0.163057			−0.0815287	−	0.996671i	$-0.525980\pi$
$601$	−1.44386e6			−0.163057			−0.0815287	+	0.996671i	$0.525980\pi$
$602$		0			0
$603$	1.55497e7	+	1.55497e7i	1.74152	+	1.74152i
$604$		0			0
$605$	1.30578e7	−	1.34917e6i	1.45038	−	0.149857i
$606$		0			0
$607$	1.07148e7	−	1.07148e7i	1.18036	−	1.18036i	0.200707	−	0.979651i	$-0.435676\pi$
$607$	1.07148e7	−	1.07148e7i	1.18036	−	1.18036i	0.979651	−	0.200707i	$-0.0643240\pi$
$608$		0			0
$609$		−	312788.i		−	0.0341749i
$610$		0			0
$611$			50585.3i			0.00548177i
$612$		0			0
$613$	1.16515e7	−	1.16515e7i	1.25237	−	1.25237i	0.297711	−	0.954656i	$-0.403777\pi$
$613$	1.16515e7	−	1.16515e7i	1.25237	−	1.25237i	0.954656	−	0.297711i	$-0.0962233\pi$
$614$		0			0
$615$	−6.14460e6	−	4.99376e6i	−0.655098	−	0.532402i
$616$		0			0
$617$	−250447.	−	250447.i	−0.0264852	−	0.0264852i	0.693740	−	0.720225i	$-0.255962\pi$
$617$	−250447.	−	250447.i	−0.0264852	−	0.0264852i	−0.720225	+	0.693740i	$0.755962\pi$
$618$		0			0
$619$	2.33339e6			0.244771			0.122386	−	0.992483i	$-0.460946\pi$
$619$	2.33339e6			0.244771			0.122386	+	0.992483i	$0.460946\pi$
$620$		0			0
$621$	3.23586e7			3.36714
$622$		0			0
$623$	−4.38516e6	−	4.38516e6i	−0.452653	−	0.452653i
$624$		0			0
$625$	8.94913e6	−	3.90904e6i	0.916390	−	0.400286i
$626$		0			0
$627$	−4.87679e6	+	4.87679e6i	−0.495410	+	0.495410i
$628$		0			0
$629$			29787.9i			0.00300201i
$630$		0			0
$631$		−	5.87636e6i		−	0.587536i	−0.955877	−	0.293768i	$-0.905091\pi$
$631$		−	5.87636e6i		−	0.587536i	0.955877	−	0.293768i	$-0.0949094\pi$
$632$		0			0
$633$	91194.0	−	91194.0i	0.00904601	−	0.00904601i
$634$		0			0
$635$	−4.83615e6	+	5.95067e6i	−0.475954	+	0.585641i
$636$		0			0
$637$	42010.7	+	42010.7i	0.00410215	+	0.00410215i
$638$		0			0
$639$	−3.66098e7			−3.54687
$640$		0			0
$641$	1.87093e6			0.179851			0.0899254	−	0.995949i	$-0.471337\pi$
$641$	1.87093e6			0.179851			0.0899254	+	0.995949i	$0.471337\pi$
$642$		0			0
$643$	−8.11386e6	−	8.11386e6i	−0.773927	−	0.773927i	0.204864	−	0.978791i	$-0.434325\pi$
$643$	−8.11386e6	−	8.11386e6i	−0.773927	−	0.773927i	−0.978791	+	0.204864i	$0.934325\pi$
$644$		0			0
$645$	−2.55103e6	−	2.46900e7i	−0.241444	−	2.33680i
$646$		0			0
$647$	1.28000e7	−	1.28000e7i	1.20213	−	1.20213i	0.228610	−	0.973518i	$-0.426582\pi$
$647$	1.28000e7	−	1.28000e7i	1.20213	−	1.20213i	0.973518	−	0.228610i	$-0.0734179\pi$
$648$		0			0
$649$			3.19055e7i			2.97340i
$650$		0			0
$651$			1.04442e7i			0.965874i
$652$		0			0
$653$	7.18312e6	−	7.18312e6i	0.659220	−	0.659220i	−0.295975	−	0.955196i	$-0.595645\pi$
$653$	7.18312e6	−	7.18312e6i	0.659220	−	0.659220i	0.955196	+	0.295975i	$0.0956447\pi$
$654$		0			0
$655$	1.56723e6	+	1.51683e7i	0.142735	+	1.38145i
$656$		0			0
$657$	−2.63559e7	−	2.63559e7i	−2.38212	−	2.38212i
$658$		0			0
$659$	−1.69340e7			−1.51895			−0.759477	−	0.650534i	$-0.774545\pi$
$659$	−1.69340e7			−1.51895			−0.759477	+	0.650534i	$0.774545\pi$
$660$		0			0
$661$	1.24863e7			1.11156			0.555778	−	0.831331i	$-0.312421\pi$
$661$	1.24863e7			1.11156			0.555778	+	0.831331i	$0.312421\pi$
$662$		0			0
$663$	−20953.3	−	20953.3i	−0.00185126	−	0.00185126i
$664$		0			0
$665$	2.52149e6	−	3.10258e6i	0.221107	−	0.272063i
$666$		0			0
$667$	−112399.	+	112399.i	−0.00978249	+	0.00978249i
$668$		0			0
$669$		−	1.24439e7i		−	1.07496i
$670$		0			0
$671$			1.01702e7i			0.872014i
$672$		0			0
$673$	2.56500e6	−	2.56500e6i	0.218298	−	0.218298i	−0.589483	−	0.807781i	$-0.700668\pi$
$673$	2.56500e6	−	2.56500e6i	0.218298	−	0.218298i	0.807781	+	0.589483i	$0.200668\pi$
$674$		0			0
$675$	1.92448e7	−	2.94069e7i	1.62575	−	2.48422i
$676$		0			0
$677$	6.86486e6	+	6.86486e6i	0.575652	+	0.575652i	0.933702	−	0.358050i	$-0.116558\pi$
$677$	6.86486e6	+	6.86486e6i	0.575652	+	0.575652i	−0.358050	+	0.933702i	$0.616558\pi$
$678$		0			0
$679$	6.65923e6			0.554306
$680$		0			0
$681$	−2.52375e7			−2.08535
$682$		0			0
$683$	9.80708e6	+	9.80708e6i	0.804430	+	0.804430i	0.983784	−	0.179355i	$-0.0574010\pi$
$683$	9.80708e6	+	9.80708e6i	0.804430	+	0.804430i	−0.179355	+	0.983784i	$0.557401\pi$
$684$		0			0
$685$	−1.00685e7	−	8.18274e6i	−0.819858	−	0.666304i
$686$		0			0
$687$	1.09892e7	−	1.09892e7i	0.888334	−	0.888334i
$688$		0			0
$689$		−	89239.8i		−	0.00716160i
$690$		0			0
$691$			5.31783e6i			0.423681i	0.977304	+	0.211841i	$0.0679458\pi$
$691$			5.31783e6i			0.423681i	−0.977304	+	0.211841i	$0.932054\pi$
$692$		0			0
$693$	−5.34245e7	+	5.34245e7i	−4.22579	+	4.22579i
$694$		0			0
$695$	−1.36027e7	+	1.40546e6i	−1.06822	+	0.110371i
$696$		0			0
$697$	1.15900e6	+	1.15900e6i	0.0903649	+	0.0903649i
$698$		0			0
$699$	−8.95636e6			−0.693328
$700$		0			0
$701$	−9.52528e6			−0.732121			−0.366060	−	0.930591i	$-0.619294\pi$
$701$	−9.52528e6			−0.732121			−0.366060	+	0.930591i	$0.619294\pi$
$702$		0			0
$703$	22992.0	+	22992.0i	0.00175464	+	0.00175464i
$704$		0			0
$705$	2.80798e7	−	2.90127e6i	2.12775	−	0.219845i
$706$		0			0
$707$	1.74213e7	−	1.74213e7i	1.31078	−	1.31078i
$708$		0			0
$709$		−	9.71196e6i		−	0.725590i	−0.931869	−	0.362795i	$-0.881823\pi$
$709$		−	9.71196e6i		−	0.725590i	0.931869	−	0.362795i	$-0.118177\pi$
$710$		0			0
$711$			2.02194e7i			1.50001i
$712$		0			0
$713$	3.75307e6	−	3.75307e6i	0.276480	−	0.276480i
$714$		0			0
$715$	80545.3	+	65459.7i	0.00589217	+	0.00478860i
$716$		0			0
$717$	2.44149e7	+	2.44149e7i	1.77361	+	1.77361i
$718$		0			0
$719$	−9.73163e6			−0.702042			−0.351021	−	0.936368i	$-0.614165\pi$
$719$	−9.73163e6			−0.702042			−0.351021	+	0.936368i	$0.614165\pi$
$720$		0			0
$721$	−2.28378e6			−0.163612
$722$		0			0
$723$	2.86465e7	+	2.86465e7i	2.03810	+	2.03810i
$724$		0			0
$725$	35298.7	+	168994.i	0.00249410	+	0.0119406i
$726$		0			0
$727$	−1.43193e7	+	1.43193e7i	−1.00482	+	1.00482i	−0.00482795	+	0.999988i	$0.501537\pi$
$727$	−1.43193e7	+	1.43193e7i	−1.00482	+	1.00482i	−0.999988	+	0.00482795i	$0.998463\pi$
$728$		0			0
$729$		−	3.16248e7i		−	2.20399i
$730$		0			0
$731$			5.13820e6i			0.355646i
$732$		0			0
$733$	−6.05150e6	+	6.05150e6i	−0.416009	+	0.416009i	−0.883826	−	0.467816i	$-0.845041\pi$
$733$	−6.05150e6	+	6.05150e6i	−0.416009	+	0.416009i	0.467816	+	0.883826i	$0.345041\pi$
$734$		0			0
$735$	2.09106e7	−	2.57296e7i	1.42774	−	1.75677i
$736$		0			0
$737$	1.56596e7	+	1.56596e7i	1.06197	+	1.06197i
$738$		0			0
$739$	2.40664e7			1.62107			0.810533	−	0.585693i	$-0.199178\pi$
$739$	2.40664e7			1.62107			0.810533	+	0.585693i	$0.199178\pi$
$740$		0			0
$741$	−32345.9			−0.00216408
$742$		0			0
$743$	−431915.	−	431915.i	−0.0287029	−	0.0287029i	0.692610	−	0.721313i	$-0.256461\pi$
$743$	−431915.	−	431915.i	−0.0287029	−	0.0287029i	−0.721313	+	0.692610i	$0.756461\pi$
$744$		0			0
$745$	750276.	+	7.26150e6i	0.0495257	+	0.479331i
$746$		0			0
$747$	6.35086e6	−	6.35086e6i	0.416420	−	0.416420i
$748$		0			0
$749$		−	1.48802e7i		−	0.969178i
$750$		0			0
$751$			6.74056e6i			0.436110i	0.975936	+	0.218055i	$0.0699712\pi$
$751$			6.74056e6i			0.436110i	−0.975936	+	0.218055i	$0.930029\pi$
$752$		0			0
$753$	6.36925e6	−	6.36925e6i	0.409355	−	0.409355i
$754$		0			0
$755$	71827.9	+	695182.i	0.00458591	+	0.0443845i
$756$		0			0
$757$	−1.62480e7	−	1.62480e7i	−1.03053	−	1.03053i	−0.999519	−	0.0310107i	$-0.990127\pi$
$757$	−1.62480e7	−	1.62480e7i	−1.03053	−	1.03053i	−0.0310107	−	0.999519i	$-0.509873\pi$
$758$		0			0
$759$	5.33296e7			3.36019
$760$		0			0
$761$	1.16648e6			0.0730156			0.0365078	−	0.999333i	$-0.488377\pi$
$761$	1.16648e6			0.0730156			0.0365078	+	0.999333i	$0.488377\pi$
$762$		0			0
$763$	−2.37237e6	−	2.37237e6i	−0.147527	−	0.147527i
$764$		0			0
$765$	−7.50886e6	+	9.23932e6i	−0.463896	+	0.570803i
$766$		0			0
$767$	−105809.	+	105809.i	−0.00649430	+	0.00649430i
$768$		0			0
$769$			1.27850e7i			0.779626i	0.920894	+	0.389813i	$0.127460\pi$
$769$			1.27850e7i			0.779626i	−0.920894	+	0.389813i	$0.872540\pi$
$770$		0			0
$771$			4.01720e7i			2.43381i
$772$		0			0
$773$	2.30426e7	−	2.30426e7i	1.38702	−	1.38702i	0.555504	−	0.831514i	$-0.312525\pi$
$773$	2.30426e7	−	2.30426e7i	1.38702	−	1.38702i	0.831514	−	0.555504i	$-0.187475\pi$
$774$		0			0
$775$	−1.17864e6	−	5.64280e6i	−0.0704898	−	0.337474i
$776$		0			0
$777$	349838.	+	349838.i	0.0207881	+	0.0207881i
$778$		0			0
$779$	1.78916e6			0.105634
$780$		0			0
$781$	−3.68687e7			−2.16287
$782$		0			0
$783$	439326.	+	439326.i	0.0256084	+	0.0256084i
$784$		0			0
$785$	−2.46713e7	−	2.00505e7i	−1.42895	−	1.16132i
$786$		0			0
$787$	1.89243e7	−	1.89243e7i	1.08914	−	1.08914i	0.0935222	−	0.995617i	$-0.470187\pi$
$787$	1.89243e7	−	1.89243e7i	1.08914	−	1.08914i	0.995617	−	0.0935222i	$-0.0298126\pi$
$788$		0			0
$789$		−	4.99144e7i		−	2.85452i
$790$		0			0
$791$		−	2.32625e7i		−	1.32195i
$792$		0			0
$793$	−33727.6	+	33727.6i	−0.00190459	+	0.00190459i
$794$		0			0
$795$	−4.95368e7	+	5.11827e6i	−2.77978	+	0.287214i
$796$		0			0
$797$	1.83940e7	+	1.83940e7i	1.02572	+	1.02572i	0.999660	+	0.0260618i	$0.00829668\pi$
$797$	1.83940e7	+	1.83940e7i	1.02572	+	1.02572i	0.0260618	+	0.999660i	$0.491703\pi$
$798$		0			0
$799$	−5.84365e6			−0.323830
$800$		0			0
$801$	2.01590e7			1.11017
$802$		0			0
$803$	−2.65423e7	−	2.65423e7i	−1.45261	−	1.45261i
$804$		0			0
$805$	−3.07507e7	+	3.17724e6i	−1.67250	+	0.172807i
$806$		0			0
$807$	2.54403e7	−	2.54403e7i	1.37511	−	1.37511i
$808$		0			0
$809$			2.81220e6i			0.151069i	0.997143	+	0.0755344i	$0.0240663\pi$
$809$			2.81220e6i			0.151069i	−0.997143	+	0.0755344i	$0.975934\pi$
$810$		0			0
$811$		−	5.65169e6i		−	0.301736i	−0.988554	−	0.150868i	$-0.951793\pi$
$811$		−	5.65169e6i		−	0.301736i	0.988554	−	0.150868i	$-0.0482068\pi$
$812$		0			0
$813$	1.04421e7	−	1.04421e7i	0.554067	−	0.554067i
$814$		0			0
$815$	373603.	+	303630.i	0.0197023	+	0.0160122i
$816$		0			0
$817$	3.96596e6	+	3.96596e6i	0.207870	+	0.207870i
$818$		0			0
$819$	−354344.			−0.0184593
$820$		0			0
$821$	−1.26086e7			−0.652844			−0.326422	−	0.945224i	$-0.605843\pi$
$821$	−1.26086e7			−0.652844			−0.326422	+	0.945224i	$0.605843\pi$
$822$		0			0
$823$	1.12950e7	+	1.12950e7i	0.581282	+	0.581282i	0.935255	−	0.353974i	$-0.115170\pi$
$823$	1.12950e7	+	1.12950e7i	0.581282	+	0.581282i	−0.353974	+	0.935255i	$0.615170\pi$
$824$		0			0
$825$	3.17170e7	−	4.84650e7i	1.62240	−	2.47909i
$826$		0			0
$827$	8.08514e6	−	8.08514e6i	0.411078	−	0.411078i	−0.471036	−	0.882114i	$-0.656120\pi$
$827$	8.08514e6	−	8.08514e6i	0.411078	−	0.411078i	0.882114	+	0.471036i	$0.156120\pi$
$828$		0			0
$829$			7.84537e6i			0.396485i	0.980153	+	0.198243i	$0.0635234\pi$
$829$			7.84537e6i			0.396485i	−0.980153	+	0.198243i	$0.936477\pi$
$830$		0			0
$831$			1.30955e7i			0.657839i
$832$		0			0
$833$	−4.85312e6	+	4.85312e6i	−0.242331	+	0.242331i
$834$		0			0
$835$	8.96981e6	−	1.10370e7i	0.445212	−	0.547814i
$836$		0			0
$837$	−1.46693e7	−	1.46693e7i	−0.723762	−	0.723762i
$838$		0			0
$839$	−2.47278e7			−1.21278			−0.606389	−	0.795168i	$-0.707383\pi$
$839$	−2.47278e7			−1.21278			−0.606389	+	0.795168i	$0.707383\pi$
$840$		0			0
$841$	2.05081e7			0.999851
$842$		0			0
$843$	−2.08936e7	−	2.08936e7i	−1.01261	−	1.01261i
$844$		0			0
$845$	−2.13314e6	−	2.06455e7i	−0.102773	−	0.994681i
$846$		0			0
$847$	−3.19146e7	+	3.19146e7i	−1.52855	+	1.52855i
$848$		0			0
$849$			2.39656e7i			1.14109i
$850$		0			0
$851$		−	251426.i		−	0.0119011i
$852$		0			0
$853$	1.59901e7	−	1.59901e7i	0.752452	−	0.752452i	−0.222484	−	0.974936i	$-0.571417\pi$
$853$	1.59901e7	−	1.59901e7i	0.752452	−	0.752452i	0.974936	+	0.222484i	$0.0714166\pi$
$854$		0			0
$855$	1.33567e6	+	1.29272e7i	0.0624862	+	0.604769i
$856$		0			0
$857$	2.17808e6	+	2.17808e6i	0.101303	+	0.101303i	0.755942	−	0.654639i	$-0.227179\pi$
$857$	2.17808e6	+	2.17808e6i	0.101303	+	0.101303i	−0.654639	+	0.755942i	$0.727179\pi$
$858$		0			0
$859$	1.18655e7			0.548659			0.274329	−	0.961636i	$-0.411544\pi$
$859$	1.18655e7			0.548659			0.274329	+	0.961636i	$0.411544\pi$
$860$		0			0
$861$	2.72232e7			1.25150
$862$		0			0
$863$	1.71183e7	+	1.71183e7i	0.782411	+	0.782411i	0.980237	−	0.197827i	$-0.0633883\pi$
$863$	1.71183e7	+	1.71183e7i	0.782411	+	0.782411i	−0.197827	+	0.980237i	$0.563388\pi$
$864$		0			0
$865$	−4.28161e6	+	5.26833e6i	−0.194566	+	0.239405i
$866$		0			0
$867$	−2.71550e7	+	2.71550e7i	−1.22688	+	1.22688i
$868$		0			0
$869$			2.03624e7i			0.914701i
$870$		0			0
$871$			103864.i			0.00463897i
$872$		0			0
$873$	−1.53066e7	+	1.53066e7i	−0.679739	+	0.679739i
$874$		0			0
$875$	−1.54011e7	+	2.98353e7i	−0.680036	+	1.31738i
$876$		0			0
$877$	2.01657e7	+	2.01657e7i	0.885347	+	0.885347i	0.994072	−	0.108725i	$-0.0346769\pi$
$877$	2.01657e7	+	2.01657e7i	0.885347	+	0.885347i	−0.108725	+	0.994072i	$0.534677\pi$
$878$		0			0
$879$	−3.07767e7			−1.34354
$880$		0			0
$881$	−7.91597e6			−0.343609			−0.171804	−	0.985131i	$-0.554960\pi$
$881$	−7.91597e6			−0.343609			−0.171804	+	0.985131i	$0.554960\pi$
$882$		0			0
$883$	−3.14814e7	−	3.14814e7i	−1.35879	−	1.35879i	−0.875410	−	0.483380i	$-0.839409\pi$
$883$	−3.14814e7	−	3.14814e7i	−1.35879	−	1.35879i	−0.483380	−	0.875410i	$-0.660591\pi$
$884$		0			0
$885$	6.48027e7	+	5.26656e7i	2.78122	+	2.26031i
$886$		0			0
$887$	1.71941e7	−	1.71941e7i	0.733787	−	0.733787i	−0.237581	−	0.971368i	$-0.576354\pi$
$887$	1.71941e7	−	1.71941e7i	0.733787	−	0.733787i	0.971368	+	0.237581i	$0.0763545\pi$
$888$		0			0
$889$		−	2.63640e7i		−	1.11881i
$890$		0			0
$891$		−	1.12921e8i		−	4.76521i
$892$		0			0
$893$	−4.51047e6	+	4.51047e6i	−0.189275	+	0.189275i
$894$		0			0
$895$	−1.28273e7	+	1.32535e6i	−0.535278	+	0.0553062i
$896$		0			0
$897$	176858.	+	176858.i	0.00733909	+	0.00733909i
$898$		0			0
$899$	101909.			0.00420546
$900$		0			0
$901$	1.03091e7			0.423065
$902$		0			0
$903$	6.03446e7	+	6.03446e7i	2.46274	+	2.46274i
$904$		0			0
$905$	−3.34605e7	+	3.45722e6i	−1.35803	+	0.140315i
$906$		0			0
$907$	−1.12763e7	+	1.12763e7i	−0.455143	+	0.455143i	−0.897057	−	0.441914i	$-0.854300\pi$
$907$	−1.12763e7	+	1.12763e7i	−0.455143	+	0.455143i	0.441914	+	0.897057i	$0.354300\pi$
$908$		0			0
$909$			8.00873e7i			3.21480i
$910$		0			0
$911$			5.86631e6i			0.234190i	0.993121	+	0.117095i	$0.0373583\pi$
$911$			5.86631e6i			0.234190i	−0.993121	+	0.117095i	$0.962642\pi$
$912$		0			0
$913$	6.39578e6	−	6.39578e6i	0.253931	−	0.253931i
$914$		0			0
$915$	2.06565e7	+	1.67877e7i	0.815652	+	0.662886i
$916$		0			0
$917$	−3.70729e7	−	3.70729e7i	−1.45591	−	1.45591i
$918$		0			0
$919$	2.68789e7			1.04984			0.524919	−	0.851152i	$-0.324096\pi$
$919$	2.68789e7			1.04984			0.524919	+	0.851152i	$0.324096\pi$
$920$		0			0
$921$	−8.58234e7			−3.33393
$922$		0			0
$923$	−122268.	−	122268.i	−0.00472399	−	0.00472399i
$924$		0			0
$925$	−228492.	−	149532.i	−0.00878043	−	0.00574619i
$926$		0			0
$927$	5.24938e6	−	5.24938e6i	0.200636	−	0.200636i
$928$		0			0
$929$			2.10476e7i			0.800134i	0.916486	+	0.400067i	$0.131013\pi$
$929$			2.10476e7i			0.800134i	−0.916486	+	0.400067i	$0.868987\pi$
$930$		0			0
$931$			7.49183e6i			0.283278i
$932$		0			0
$933$	1.85728e7	−	1.85728e7i	0.698511	−	0.698511i
$934$		0			0
$935$	−7.56196e6	+	9.30466e6i	−0.282882	+	0.348074i
$936$		0			0
$937$	−2.37746e7	−	2.37746e7i	−0.884637	−	0.884637i	0.109365	−	0.994002i	$-0.465118\pi$
$937$	−2.37746e7	−	2.37746e7i	−0.884637	−	0.884637i	−0.994002	+	0.109365i	$0.965118\pi$
$938$		0			0
$939$	−3.79507e7			−1.40461
$940$		0			0
$941$	−2.62621e7			−0.966843			−0.483421	−	0.875388i	$-0.660606\pi$
$941$	−2.62621e7			−0.966843			−0.483421	+	0.875388i	$0.660606\pi$
$942$		0			0
$943$	−9.78258e6	−	9.78258e6i	−0.358240	−	0.358240i
$944$		0			0
$945$	1.24186e7	+	1.20193e8i	0.452369	+	4.37823i
$946$		0			0
$947$	−1.23513e7	+	1.23513e7i	−0.447545	+	0.447545i	−0.894538	−	0.446993i	$-0.852495\pi$
$947$	−1.23513e7	+	1.23513e7i	−0.447545	+	0.447545i	0.446993	+	0.894538i	$0.352495\pi$
$948$		0			0
$949$		−	176045.i		−	0.00634539i
$950$		0			0
$951$		−	5.04400e7i		−	1.80852i
$952$		0			0
$953$	−1.58367e7	+	1.58367e7i	−0.564850	+	0.564850i	−0.930681	−	0.365831i	$-0.880785\pi$
$953$	−1.58367e7	+	1.58367e7i	−0.564850	+	0.564850i	0.365831	+	0.930681i	$0.380785\pi$
$954$		0			0
$955$	3.29482e6	+	3.18887e7i	0.116902	+	1.13143i
$956$		0			0
$957$	724044.	+	724044.i	0.0255555	+	0.0255555i
$958$		0			0
$959$	4.46078e7			1.56626
$960$		0			0
$961$	2.52264e7			0.881142
$962$		0			0
$963$	3.42028e7	+	3.42028e7i	1.18849	+	1.18849i
$964$		0			0
$965$	−3.07688e7	+	3.78596e7i	−1.06363	+	1.30875i
$966$		0			0
$967$	−3.52477e7	+	3.52477e7i	−1.21217	+	1.21217i	−0.241862	+	0.970311i	$0.577758\pi$
$967$	−3.52477e7	+	3.52477e7i	−1.21217	+	1.21217i	−0.970311	+	0.241862i	$0.922242\pi$
$968$		0			0
$969$		−	3.73662e6i		−	0.127841i
$970$		0			0
$971$			3.28671e7i			1.11870i	0.828932	+	0.559350i	$0.188949\pi$
$971$			3.28671e7i			1.11870i	−0.828932	+	0.559350i	$0.811051\pi$
$972$		0			0
$973$	3.32462e7	−	3.32462e7i	1.12580	−	1.12580i
$974$		0			0
$975$	265908.	−	55541.5i	0.00895819	−	0.00187114i
$976$		0			0
$977$	−4.09369e6	−	4.09369e6i	−0.137208	−	0.137208i	0.635167	−	0.772375i	$-0.280931\pi$
$977$	−4.09369e6	−	4.09369e6i	−0.137208	−	0.137208i	−0.772375	+	0.635167i	$0.780931\pi$
$978$		0			0
$979$	2.03016e7			0.676975
$980$		0			0
$981$	1.09060e7			0.361821
$982$		0			0
$983$	−2.92387e7	−	2.92387e7i	−0.965105	−	0.965105i	0.0343062	−	0.999411i	$-0.489078\pi$
$983$	−2.92387e7	−	2.92387e7i	−0.965105	−	0.965105i	−0.999411	+	0.0343062i	$0.989078\pi$
$984$		0			0
$985$	−1.73675e7	−	1.41147e7i	−0.570358	−	0.463534i
$986$		0			0
$987$	−6.86297e7	+	6.86297e7i	−2.24243	+	2.24243i
$988$		0			0
$989$		−	4.33693e7i		−	1.40991i
$990$		0			0
$991$			4.98205e7i			1.61148i	0.592271	+	0.805739i	$0.298232\pi$
$991$			4.98205e7i			1.61148i	−0.592271	+	0.805739i	$0.701768\pi$
$992$		0			0
$993$	3.18152e7	−	3.18152e7i	1.02391	−	1.02391i
$994$		0			0
$995$	6.97019e6	−	720177.i	0.223196	−	0.0230612i
$996$		0			0
$997$	1.22401e7	+	1.22401e7i	0.389985	+	0.389985i	0.874682	−	0.484697i	$-0.161070\pi$
$997$	1.22401e7	+	1.22401e7i	0.389985	+	0.389985i	−0.484697	+	0.874682i	$0.661070\pi$
$998$		0			0
$999$	−982728.			−0.0311544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.c.127.1	yes	16
4.3	odd	2		160.6.n.d.127.8	yes	16
5.3	odd	4		160.6.n.d.63.8	yes	16
20.3	even	4	inner	160.6.n.c.63.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.c.63.1	✓	16	20.3	even	4	inner
160.6.n.c.127.1	yes	16	1.1	even	1	trivial
160.6.n.d.63.8	yes	16	5.3	odd	4
160.6.n.d.127.8	yes	16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-20.8299 - 20.8299i) q^{3} +(-55.6057 + 5.74531i) q^{5} +(135.906 - 135.906i) q^{7} +624.772i q^{9} +O(q^{10})\)	\(q+(-20.8299 - 20.8299i) q^{3} +(-55.6057 + 5.74531i) q^{5} +(135.906 - 135.906i) q^{7} +624.772i q^{9} +629.190i q^{11} +(-2.08659 + 2.08659i) q^{13} +(1277.94 + 1038.59i) q^{15} +(-241.044 - 241.044i) q^{17} -372.104 q^{19} -5661.81 q^{21} +(2034.55 + 2034.55i) q^{23} +(3058.98 - 638.944i) q^{25} +(7952.27 - 7952.27i) q^{27} +55.2453i q^{29} -1844.67i q^{31} +(13106.0 - 13106.0i) q^{33} +(-6776.31 + 8337.95i) q^{35} +(-61.7891 - 61.7891i) q^{37} +86.9270 q^{39} -4808.22 q^{41} +(-10658.2 - 10658.2i) q^{43} +(-3589.51 - 34740.8i) q^{45} +(12121.5 - 12121.5i) q^{47} -20133.7i q^{49} +10041.9i q^{51} +(-21384.1 + 21384.1i) q^{53} +(-3614.89 - 34986.5i) q^{55} +(7750.90 + 7750.90i) q^{57} +50708.8 q^{59} +16164.0 q^{61} +(84910.0 + 84910.0i) q^{63} +(104.038 - 128.014i) q^{65} +(24888.6 - 24888.6i) q^{67} -84759.2i q^{69} +58597.1i q^{71} +(-42184.9 + 42184.9i) q^{73} +(-77027.5 - 50409.2i) q^{75} +(85510.5 + 85510.5i) q^{77} +32362.8 q^{79} -179471. q^{81} +(-10165.1 - 10165.1i) q^{83} +(14788.3 + 12018.6i) q^{85} +(1150.76 - 1150.76i) q^{87} -32266.2i q^{89} +567.158i q^{91} +(-38424.3 + 38424.3i) q^{93} +(20691.1 - 2137.85i) q^{95} +(24499.5 + 24499.5i) q^{97} -393100. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7}+O(q^{10}) \) 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7	\( 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7} + 536 q^{13} + 698 q^{15} - 1828 q^{17} - 2512 q^{19} - 4284 q^{21} + 7642 q^{23} + 9140 q^{25} + 12272 q^{27} + 11876 q^{33} - 10518 q^{35} - 7620 q^{37} - 11244 q^{39} - 21284 q^{41} - 20002 q^{43} + 686 q^{45} - 25298 q^{47} + 12852 q^{53} + 10584 q^{55} + 55848 q^{57} + 142704 q^{59} - 20564 q^{61} + 115282 q^{63} - 38256 q^{65} + 10506 q^{67} + 15432 q^{73} - 256226 q^{75} + 133852 q^{77} + 159344 q^{79} - 236116 q^{81} + 61222 q^{83} + 7056 q^{85} - 162176 q^{87} + 122180 q^{93} - 267512 q^{95} - 17344 q^{97} - 107332 q^{99}+O(q^{100}) \) 16 * q - 10 * q^3 - 42 * q^5 + 86 * q^7 + 536 * q^13 + 698 * q^15 - 1828 * q^17 - 2512 * q^19 - 4284 * q^21 + 7642 * q^23 + 9140 * q^25 + 12272 * q^27 + 11876 * q^33 - 10518 * q^35 - 7620 * q^37 - 11244 * q^39 - 21284 * q^41 - 20002 * q^43 + 686 * q^45 - 25298 * q^47 + 12852 * q^53 + 10584 * q^55 + 55848 * q^57 + 142704 * q^59 - 20564 * q^61 + 115282 * q^63 - 38256 * q^65 + 10506 * q^67 + 15432 * q^73 - 256226 * q^75 + 133852 * q^77 + 159344 * q^79 - 236116 * q^81 + 61222 * q^83 + 7056 * q^85 - 162176 * q^87 + 122180 * q^93 - 267512 * q^95 - 17344 * q^97 - 107332 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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