LMFDB - Embedded newform 128.5.f.a.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,5,Mod(31,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("128.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	128.f (of order $4$, degree $2$, not 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:	$13.2313552747$
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} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{42} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.5
Root			$-2.15805 - 1.82834i$ of defining polynomial
Character	$\chi$	$=$	128.31
Dual form			128.5.f.a.95.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.91498 + 3.91498i) q^{3} +(-4.72348 - 4.72348i) q^{5} -45.3712 q^{7} -50.3458i q^{9} +O(q^{10})$	\(q+(3.91498 + 3.91498i) q^{3} +(-4.72348 - 4.72348i) q^{5} -45.3712 q^{7} -50.3458i q^{9} +(110.228 - 110.228i) q^{11} +(157.128 - 157.128i) q^{13} -36.9847i q^{15} -378.592 q^{17} +(203.127 + 203.127i) q^{19} +(-177.627 - 177.627i) q^{21} +740.444 q^{23} -580.377i q^{25} +(514.217 - 514.217i) q^{27} +(-82.6244 + 82.6244i) q^{29} -286.217i q^{31} +863.080 q^{33} +(214.310 + 214.310i) q^{35} +(-1470.39 - 1470.39i) q^{37} +1230.31 q^{39} -1301.21i q^{41} +(-366.979 + 366.979i) q^{43} +(-237.808 + 237.808i) q^{45} -751.307i q^{47} -342.455 q^{49} +(-1482.18 - 1482.18i) q^{51} +(1929.33 + 1929.33i) q^{53} -1041.32 q^{55} +1590.48i q^{57} +(-1357.57 + 1357.57i) q^{59} +(1835.78 - 1835.78i) q^{61} +2284.25i q^{63} -1484.39 q^{65} +(2205.02 + 2205.02i) q^{67} +(2898.83 + 2898.83i) q^{69} -8970.40 q^{71} +9350.46i q^{73} +(2272.17 - 2272.17i) q^{75} +(-5001.17 + 5001.17i) q^{77} +2860.08i q^{79} -51.7173 q^{81} +(-1036.63 - 1036.63i) q^{83} +(1788.27 + 1788.27i) q^{85} -646.946 q^{87} -5171.06i q^{89} +(-7129.10 + 7129.10i) q^{91} +(1120.54 - 1120.54i) q^{93} -1918.94i q^{95} +8539.92 q^{97} +(-5549.51 - 5549.51i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	$ 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 94 q^{11} + 2 q^{13} - 4 q^{17} - 706 q^{19} + 164 q^{21} - 1148 q^{23} - 1664 q^{27} - 862 q^{29} - 4 q^{33} + 1340 q^{35} + 1826 q^{37} - 2684 q^{39} + 1694 q^{43} - 1410 q^{45} + 682 q^{49} - 3012 q^{51} + 482 q^{53} + 11780 q^{55} - 2786 q^{59} + 3778 q^{61} - 2020 q^{65} + 7998 q^{67} - 9628 q^{69} - 19964 q^{71} + 17570 q^{75} + 9508 q^{77} + 1454 q^{81} - 17282 q^{83} - 9948 q^{85} + 49284 q^{87} - 28036 q^{91} - 8896 q^{93} - 4 q^{97} + 49214 q^{99}+O(q^{100}) $ 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 + 94 * q^11 + 2 * q^13 - 4 * q^17 - 706 * q^19 + 164 * q^21 - 1148 * q^23 - 1664 * q^27 - 862 * q^29 - 4 * q^33 + 1340 * q^35 + 1826 * q^37 - 2684 * q^39 + 1694 * q^43 - 1410 * q^45 + 682 * q^49 - 3012 * q^51 + 482 * q^53 + 11780 * q^55 - 2786 * q^59 + 3778 * q^61 - 2020 * q^65 + 7998 * q^67 - 9628 * q^69 - 19964 * q^71 + 17570 * q^75 + 9508 * q^77 + 1454 * q^81 - 17282 * q^83 - 9948 * q^85 + 49284 * q^87 - 28036 * q^91 - 8896 * q^93 - 4 * q^97 + 49214 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$	3.91498	+	3.91498i	0.434998	+	0.434998i	0.890324	−	0.455327i	$-0.150477\pi$
$3$	3.91498	+	3.91498i	0.434998	+	0.434998i	−0.455327	+	0.890324i	$0.650477\pi$
$4$		0			0
$5$	−4.72348	−	4.72348i	−0.188939	−	0.188939i	0.606298	−	0.795237i	$-0.292654\pi$
$5$	−4.72348	−	4.72348i	−0.188939	−	0.188939i	−0.795237	+	0.606298i	$0.792654\pi$
$6$		0			0
$7$	−45.3712			−0.925943			−0.462971	−	0.886373i	$-0.653217\pi$
$7$	−45.3712			−0.925943			−0.462971	+	0.886373i	$0.653217\pi$
$8$		0			0
$9$		−	50.3458i		−	0.621554i
$10$		0			0
$11$	110.228	−	110.228i	0.910974	−	0.910974i	−0.0853752	−	0.996349i	$-0.527209\pi$
$11$	110.228	−	110.228i	0.910974	−	0.910974i	0.996349	+	0.0853752i	$0.0272089\pi$
$12$		0			0
$13$	157.128	−	157.128i	0.929754	−	0.929754i	−0.0679357	−	0.997690i	$-0.521641\pi$
$13$	157.128	−	157.128i	0.929754	−	0.929754i	0.997690	+	0.0679357i	$0.0216413\pi$
$14$		0			0
$15$		−	36.9847i		−	0.164376i
$16$		0			0
$17$	−378.592			−1.31001			−0.655003	−	0.755626i	$-0.727333\pi$
$17$	−378.592			−1.31001			−0.655003	+	0.755626i	$0.727333\pi$
$18$		0			0
$19$	203.127	+	203.127i	0.562680	+	0.562680i	0.930068	−	0.367388i	$-0.119748\pi$
$19$	203.127	+	203.127i	0.562680	+	0.562680i	−0.367388	+	0.930068i	$0.619748\pi$
$20$		0			0
$21$	−177.627	−	177.627i	−0.402783	−	0.402783i
$22$		0			0
$23$	740.444			1.39971			0.699853	−	0.714287i	$-0.253249\pi$
$23$	740.444			1.39971			0.699853	+	0.714287i	$0.253249\pi$
$24$		0			0
$25$		−	580.377i		−	0.928604i
$26$		0			0
$27$	514.217	−	514.217i	0.705372	−	0.705372i
$28$		0			0
$29$	−82.6244	+	82.6244i	−0.0982455	+	0.0982455i	−0.754521	−	0.656276i	$-0.772131\pi$
$29$	−82.6244	+	82.6244i	−0.0982455	+	0.0982455i	0.656276	+	0.754521i	$0.272131\pi$
$30$		0			0
$31$		−	286.217i		−	0.297833i	−0.988850	−	0.148916i	$-0.952421\pi$
$31$		−	286.217i		−	0.297833i	0.988850	−	0.148916i	$-0.0475785\pi$
$32$		0			0
$33$	863.080			0.792543
$34$		0			0
$35$	214.310	+	214.310i	0.174947	+	0.174947i
$36$		0			0
$37$	−1470.39	−	1470.39i	−1.07406	−	1.07406i	−0.997028	−	0.0770352i	$-0.975455\pi$
$37$	−1470.39	−	1470.39i	−1.07406	−	1.07406i	−0.0770352	−	0.997028i	$-0.524545\pi$
$38$		0			0
$39$	1230.31			0.808882
$40$		0			0
$41$		−	1301.21i		−	0.774070i	−0.922065	−	0.387035i	$-0.873499\pi$
$41$		−	1301.21i		−	0.774070i	0.922065	−	0.387035i	$-0.126501\pi$
$42$		0			0
$43$	−366.979	+	366.979i	−0.198474	+	0.198474i	−0.799346	−	0.600871i	$-0.794820\pi$
$43$	−366.979	+	366.979i	−0.198474	+	0.198474i	0.600871	+	0.799346i	$0.294820\pi$
$44$		0			0
$45$	−237.808	+	237.808i	−0.117436	+	0.117436i
$46$		0			0
$47$		−	751.307i		−	0.340112i	−0.985434	−	0.170056i	$-0.945605\pi$
$47$		−	751.307i		−	0.340112i	0.985434	−	0.170056i	$-0.0543948\pi$
$48$		0			0
$49$	−342.455			−0.142630
$50$		0			0
$51$	−1482.18	−	1482.18i	−0.569850	−	0.569850i
$52$		0			0
$53$	1929.33	+	1929.33i	0.686838	+	0.686838i	0.961532	−	0.274693i	$-0.0885764\pi$
$53$	1929.33	+	1929.33i	0.686838	+	0.686838i	−0.274693	+	0.961532i	$0.588576\pi$
$54$		0			0
$55$	−1041.32			−0.344238
$56$		0			0
$57$			1590.48i			0.489529i
$58$		0			0
$59$	−1357.57	+	1357.57i	−0.389994	+	0.389994i	−0.874685	−	0.484691i	$-0.838932\pi$
$59$	−1357.57	+	1357.57i	−0.389994	+	0.389994i	0.484691	+	0.874685i	$0.338932\pi$
$60$		0			0
$61$	1835.78	−	1835.78i	0.493356	−	0.493356i	−0.416006	−	0.909362i	$-0.636570\pi$
$61$	1835.78	−	1835.78i	0.493356	−	0.493356i	0.909362	+	0.416006i	$0.136570\pi$
$62$		0			0
$63$			2284.25i			0.575523i
$64$		0			0
$65$	−1484.39			−0.351334
$66$		0			0
$67$	2205.02	+	2205.02i	0.491204	+	0.491204i	0.908686	−	0.417481i	$-0.137087\pi$
$67$	2205.02	+	2205.02i	0.491204	+	0.491204i	−0.417481	+	0.908686i	$0.637087\pi$
$68$		0			0
$69$	2898.83	+	2898.83i	0.608869	+	0.608869i
$70$		0			0
$71$	−8970.40			−1.77949			−0.889744	−	0.456460i	$-0.849117\pi$
$71$	−8970.40			−1.77949			−0.889744	+	0.456460i	$0.849117\pi$
$72$		0			0
$73$			9350.46i			1.75464i	0.479909	+	0.877318i	$0.340670\pi$
$73$			9350.46i			1.75464i	−0.479909	+	0.877318i	$0.659330\pi$
$74$		0			0
$75$	2272.17	−	2272.17i	0.403941	−	0.403941i
$76$		0			0
$77$	−5001.17	+	5001.17i	−0.843509	+	0.843509i
$78$		0			0
$79$			2860.08i			0.458273i	0.973394	+	0.229137i	$0.0735903\pi$
$79$			2860.08i			0.458273i	−0.973394	+	0.229137i	$0.926410\pi$
$80$		0			0
$81$	−51.7173			−0.00788253
$82$		0			0
$83$	−1036.63	−	1036.63i	−0.150477	−	0.150477i	0.627854	−	0.778331i	$-0.283933\pi$
$83$	−1036.63	−	1036.63i	−0.150477	−	0.150477i	−0.778331	+	0.627854i	$0.783933\pi$
$84$		0			0
$85$	1788.27	+	1788.27i	0.247512	+	0.247512i
$86$		0			0
$87$	−646.946			−0.0854731
$88$		0			0
$89$		−	5171.06i		−	0.652830i	−0.945227	−	0.326415i	$-0.894159\pi$
$89$		−	5171.06i		−	0.652830i	0.945227	−	0.326415i	$-0.105841\pi$
$90$		0			0
$91$	−7129.10	+	7129.10i	−0.860899	+	0.860899i
$92$		0			0
$93$	1120.54	−	1120.54i	0.129557	−	0.129557i
$94$		0			0
$95$		−	1918.94i		−	0.212625i
$96$		0			0
$97$	8539.92			0.907633			0.453817	−	0.891095i	$-0.350062\pi$
$97$	8539.92			0.907633			0.453817	+	0.891095i	$0.350062\pi$
$98$		0			0
$99$	−5549.51	−	5549.51i	−0.566219	−	0.566219i
$100$		0			0
$101$	−537.642	−	537.642i	−0.0527049	−	0.0527049i	0.680263	−	0.732968i	$-0.261866\pi$
$101$	−537.642	−	537.642i	−0.0527049	−	0.0527049i	−0.732968	+	0.680263i	$0.761866\pi$
$102$		0			0
$103$	5543.86			0.522562			0.261281	−	0.965263i	$-0.415855\pi$
$103$	5543.86			0.522562			0.261281	+	0.965263i	$0.415855\pi$
$104$		0			0
$105$			1678.04i			0.152203i
$106$		0			0
$107$	−2989.60	+	2989.60i	−0.261123	+	0.261123i	−0.825510	−	0.564387i	$-0.809113\pi$
$107$	−2989.60	+	2989.60i	−0.261123	+	0.261123i	0.564387	+	0.825510i	$0.309113\pi$
$108$		0			0
$109$	3353.83	−	3353.83i	0.282285	−	0.282285i	−0.551734	−	0.834020i	$-0.686034\pi$
$109$	3353.83	−	3353.83i	0.282285	−	0.282285i	0.834020	+	0.551734i	$0.186034\pi$
$110$		0			0
$111$		−	11513.1i		−	0.934431i
$112$		0			0
$113$	−3193.81			−0.250122			−0.125061	−	0.992149i	$-0.539913\pi$
$113$	−3193.81			−0.250122			−0.125061	+	0.992149i	$0.539913\pi$
$114$		0			0
$115$	−3497.48	−	3497.48i	−0.264459	−	0.264459i
$116$		0			0
$117$	−7910.76	−	7910.76i	−0.577892	−	0.577892i
$118$		0			0
$119$	17177.2			1.21299
$120$		0			0
$121$		−	9659.34i		−	0.659746i
$122$		0			0
$123$	5094.22	−	5094.22i	0.336719	−	0.336719i
$124$		0			0
$125$	−5693.58	+	5693.58i	−0.364389	+	0.364389i
$126$		0			0
$127$			22900.5i			1.41983i	0.704287	+	0.709915i	$0.251267\pi$
$127$			22900.5i			1.41983i	−0.704287	+	0.709915i	$0.748733\pi$
$128$		0			0
$129$	−2873.43			−0.172672
$130$		0			0
$131$	19255.9	+	19255.9i	1.12207	+	1.12207i	0.991429	+	0.130644i	$0.0417045\pi$
$131$	19255.9	+	19255.9i	1.12207	+	1.12207i	0.130644	+	0.991429i	$0.458296\pi$
$132$		0			0
$133$	−9216.13	−	9216.13i	−0.521009	−	0.521009i
$134$		0			0
$135$	−4857.79			−0.266545
$136$		0			0
$137$		−	19938.2i		−	1.06229i	−0.847280	−	0.531147i	$-0.821761\pi$
$137$		−	19938.2i		−	1.06229i	0.847280	−	0.531147i	$-0.178239\pi$
$138$		0			0
$139$	25175.4	−	25175.4i	1.30301	−	1.30301i	0.376649	−	0.926356i	$-0.377076\pi$
$139$	25175.4	−	25175.4i	1.30301	−	1.30301i	0.926356	−	0.376649i	$-0.122924\pi$
$140$		0			0
$141$	2941.35	−	2941.35i	0.147948	−	0.147948i
$142$		0			0
$143$		−	34639.8i		−	1.69396i
$144$		0			0
$145$	780.550			0.0371249
$146$		0			0
$147$	−1340.70	−	1340.70i	−0.0620438	−	0.0620438i
$148$		0			0
$149$	3216.99	+	3216.99i	0.144903	+	0.144903i	0.775837	−	0.630934i	$-0.217328\pi$
$149$	3216.99	+	3216.99i	0.144903	+	0.144903i	−0.630934	+	0.775837i	$0.717328\pi$
$150$		0			0
$151$	14770.5			0.647802			0.323901	−	0.946091i	$-0.395006\pi$
$151$	14770.5			0.647802			0.323901	+	0.946091i	$0.395006\pi$
$152$		0			0
$153$			19060.5i			0.814239i
$154$		0			0
$155$	−1351.94	+	1351.94i	−0.0562723	+	0.0562723i
$156$		0			0
$157$	18014.6	−	18014.6i	0.730845	−	0.730845i	−0.239942	−	0.970787i	$-0.577128\pi$
$157$	18014.6	−	18014.6i	0.730845	−	0.730845i	0.970787	+	0.239942i	$0.0771284\pi$
$158$		0			0
$159$			15106.6i			0.597547i
$160$		0			0
$161$	−33594.8			−1.29605
$162$		0			0
$163$	15083.2	+	15083.2i	0.567700	+	0.567700i	0.931483	−	0.363784i	$-0.118515\pi$
$163$	15083.2	+	15083.2i	0.567700	+	0.567700i	−0.363784	+	0.931483i	$0.618515\pi$
$164$		0			0
$165$	−4076.74	−	4076.74i	−0.149743	−	0.149743i
$166$		0			0
$167$	−23733.6			−0.851001			−0.425501	−	0.904958i	$-0.639902\pi$
$167$	−23733.6			−0.851001			−0.425501	+	0.904958i	$0.639902\pi$
$168$		0			0
$169$		−	20817.7i		−	0.728885i
$170$		0			0
$171$	10226.6	−	10226.6i	0.349736	−	0.349736i
$172$		0			0
$173$	12072.3	−	12072.3i	0.403363	−	0.403363i	−0.476053	−	0.879416i	$-0.657933\pi$
$173$	12072.3	−	12072.3i	0.403363	−	0.403363i	0.879416	+	0.476053i	$0.157933\pi$
$174$		0			0
$175$			26332.4i			0.859834i
$176$		0			0
$177$	−10629.7			−0.339293
$178$		0			0
$179$	−28111.5	−	28111.5i	−0.877361	−	0.877361i	0.115900	−	0.993261i	$-0.463025\pi$
$179$	−28111.5	−	28111.5i	−0.877361	−	0.877361i	−0.993261	+	0.115900i	$0.963025\pi$
$180$		0			0
$181$	15906.7	+	15906.7i	0.485539	+	0.485539i	0.906895	−	0.421356i	$-0.138446\pi$
$181$	15906.7	+	15906.7i	0.485539	+	0.485539i	−0.421356	+	0.906895i	$0.638446\pi$
$182$		0			0
$183$	14374.1			0.429218
$184$		0			0
$185$			13890.8i			0.405866i
$186$		0			0
$187$	−41731.4	+	41731.4i	−1.19338	+	1.19338i
$188$		0			0
$189$	−23330.6	+	23330.6i	−0.653134	+	0.653134i
$190$		0			0
$191$		−	28038.6i		−	0.768581i	−0.923212	−	0.384290i	$-0.874446\pi$
$191$		−	28038.6i		−	0.768581i	0.923212	−	0.384290i	$-0.125554\pi$
$192$		0			0
$193$	56713.1			1.52254			0.761270	−	0.648436i	$-0.224576\pi$
$193$	56713.1			1.52254			0.761270	+	0.648436i	$0.224576\pi$
$194$		0			0
$195$	−5811.35	−	5811.35i	−0.152830	−	0.152830i
$196$		0			0
$197$	10179.3	+	10179.3i	0.262292	+	0.262292i	0.825985	−	0.563692i	$-0.190620\pi$
$197$	10179.3	+	10179.3i	0.262292	+	0.262292i	−0.563692	+	0.825985i	$0.690620\pi$
$198$		0			0
$199$	−31787.3			−0.802689			−0.401344	−	0.915927i	$-0.631457\pi$
$199$	−31787.3			−0.802689			−0.401344	+	0.915927i	$0.631457\pi$
$200$		0			0
$201$			17265.2i			0.427346i
$202$		0			0
$203$	3748.77	−	3748.77i	0.0909697	−	0.0909697i
$204$		0			0
$205$	−6146.25	+	6146.25i	−0.146252	+	0.146252i
$206$		0			0
$207$		−	37278.3i		−	0.869992i
$208$		0			0
$209$	44780.6			1.02517
$210$		0			0
$211$	−10699.8	−	10699.8i	−0.240332	−	0.240332i	0.576655	−	0.816988i	$-0.304358\pi$
$211$	−10699.8	−	10699.8i	−0.240332	−	0.240332i	−0.816988	+	0.576655i	$0.804358\pi$
$212$		0			0
$213$	−35118.9	−	35118.9i	−0.774073	−	0.774073i
$214$		0			0
$215$	3466.84			0.0749992
$216$		0			0
$217$			12986.0i			0.275776i
$218$		0			0
$219$	−36606.9	+	36606.9i	−0.763263	+	0.763263i
$220$		0			0
$221$	−59487.5	+	59487.5i	−1.21798	+	1.21798i
$222$		0			0
$223$			91700.4i			1.84400i	0.387187	+	0.922001i	$0.373447\pi$
$223$			91700.4i			1.84400i	−0.387187	+	0.922001i	$0.626553\pi$
$224$		0			0
$225$	−29219.6			−0.577177
$226$		0			0
$227$	17499.5	+	17499.5i	0.339605	+	0.339605i	0.856218	−	0.516614i	$-0.172808\pi$
$227$	17499.5	+	17499.5i	0.339605	+	0.339605i	−0.516614	+	0.856218i	$0.672808\pi$
$228$		0			0
$229$	63859.8	+	63859.8i	1.21775	+	1.21775i	0.968420	+	0.249326i	$0.0802091\pi$
$229$	63859.8	+	63859.8i	1.21775	+	1.21775i	0.249326	+	0.968420i	$0.419791\pi$
$230$		0			0
$231$	−39159.0			−0.733850
$232$		0			0
$233$			63891.7i			1.17688i	0.808540	+	0.588441i	$0.200258\pi$
$233$			63891.7i			1.17688i	−0.808540	+	0.588441i	$0.799742\pi$
$234$		0			0
$235$	−3548.79	+	3548.79i	−0.0642605	+	0.0642605i
$236$		0			0
$237$	−11197.2	+	11197.2i	−0.199348	+	0.199348i
$238$		0			0
$239$		−	12096.4i		−	0.211768i	−0.994378	−	0.105884i	$-0.966233\pi$
$239$		−	12096.4i		−	0.211768i	0.994378	−	0.105884i	$-0.0337672\pi$
$240$		0			0
$241$	27978.6			0.481717			0.240859	−	0.970560i	$-0.422571\pi$
$241$	27978.6			0.481717			0.240859	+	0.970560i	$0.422571\pi$
$242$		0			0
$243$	−41854.0	−	41854.0i	−0.708801	−	0.708801i
$244$		0			0
$245$	1617.58	+	1617.58i	0.0269484	+	0.0269484i
$246$		0			0
$247$	63834.2			1.04631
$248$		0			0
$249$		−	8116.80i		−	0.130914i
$250$		0			0
$251$	1996.06	−	1996.06i	0.0316830	−	0.0316830i	−0.691088	−	0.722771i	$-0.742868\pi$
$251$	1996.06	−	1996.06i	0.0316830	−	0.0316830i	0.722771	+	0.691088i	$0.242868\pi$
$252$		0			0
$253$	81617.5	−	81617.5i	1.27509	−	1.27509i
$254$		0			0
$255$			14002.1i			0.215334i
$256$		0			0
$257$	−73510.4			−1.11297			−0.556484	−	0.830859i	$-0.687850\pi$
$257$	−73510.4			−1.11297			−0.556484	+	0.830859i	$0.687850\pi$
$258$		0			0
$259$	66713.5	+	66713.5i	0.994521	+	0.994521i
$260$		0			0
$261$	4159.80	+	4159.80i	0.0610648	+	0.0610648i
$262$		0			0
$263$	−68109.3			−0.984680			−0.492340	−	0.870403i	$-0.663858\pi$
$263$	−68109.3			−0.984680			−0.492340	+	0.870403i	$0.663858\pi$
$264$		0			0
$265$		−	18226.3i		−	0.259542i
$266$		0			0
$267$	20244.6	−	20244.6i	0.283980	−	0.283980i
$268$		0			0
$269$	15056.1	−	15056.1i	0.208069	−	0.208069i	−0.595377	−	0.803446i	$-0.702997\pi$
$269$	15056.1	−	15056.1i	0.208069	−	0.208069i	0.803446	+	0.595377i	$0.202997\pi$
$270$		0			0
$271$		−	104320.i		−	1.42046i	−0.703968	−	0.710232i	$-0.748590\pi$
$271$		−	104320.i		−	1.42046i	0.703968	−	0.710232i	$-0.251410\pi$
$272$		0			0
$273$	−55820.6			−0.748979
$274$		0			0
$275$	−63973.7	−	63973.7i	−0.845934	−	0.845934i
$276$		0			0
$277$	−2136.36	−	2136.36i	−0.0278430	−	0.0278430i	0.693048	−	0.720891i	$-0.256267\pi$
$277$	−2136.36	−	2136.36i	−0.0278430	−	0.0278430i	−0.720891	+	0.693048i	$0.756267\pi$
$278$		0			0
$279$	−14409.8			−0.185119
$280$		0			0
$281$		−	36783.7i		−	0.465846i	−0.972495	−	0.232923i	$-0.925171\pi$
$281$		−	36783.7i		−	0.465846i	0.972495	−	0.232923i	$-0.0748290\pi$
$282$		0			0
$283$	14172.0	−	14172.0i	0.176953	−	0.176953i	−0.613073	−	0.790026i	$-0.710067\pi$
$283$	14172.0	−	14172.0i	0.176953	−	0.176953i	0.790026	+	0.613073i	$0.210067\pi$
$284$		0			0
$285$	7512.60	−	7512.60i	0.0924913	−	0.0924913i
$286$		0			0
$287$			59037.5i			0.716744i
$288$		0			0
$289$	59810.8			0.716117
$290$		0			0
$291$	33433.6	+	33433.6i	0.394819	+	0.394819i
$292$		0			0
$293$	−80721.8	−	80721.8i	−0.940276	−	0.940276i	0.0580384	−	0.998314i	$-0.481515\pi$
$293$	−80721.8	−	80721.8i	−0.940276	−	0.940276i	−0.998314	+	0.0580384i	$0.981515\pi$
$294$		0			0
$295$	12824.9			0.147370
$296$		0			0
$297$		−	113362.i		−	1.28515i
$298$		0			0
$299$	116345.	−	116345.i	1.30138	−	1.30138i
$300$		0			0
$301$	16650.3	−	16650.3i	0.183776	−	0.183776i
$302$		0			0
$303$		−	4209.72i		−	0.0458530i
$304$		0			0
$305$	−17342.5			−0.186429
$306$		0			0
$307$	113714.	+	113714.i	1.20653	+	1.20653i	0.972143	+	0.234389i	$0.0753090\pi$
$307$	113714.	+	113714.i	1.20653	+	1.20653i	0.234389	+	0.972143i	$0.424691\pi$
$308$		0			0
$309$	21704.1	+	21704.1i	0.227313	+	0.227313i
$310$		0			0
$311$	93801.8			0.969819			0.484909	−	0.874564i	$-0.338853\pi$
$311$	93801.8			0.969819			0.484909	+	0.874564i	$0.338853\pi$
$312$		0			0
$313$		−	9229.52i		−	0.0942086i	−0.998890	−	0.0471043i	$-0.985001\pi$
$313$		−	9229.52i		−	0.0942086i	0.998890	−	0.0471043i	$-0.0149993\pi$
$314$		0			0
$315$	10789.6	−	10789.6i	0.108739	−	0.108739i
$316$		0			0
$317$	8447.44	−	8447.44i	0.0840634	−	0.0840634i	−0.663825	−	0.747888i	$-0.731068\pi$
$317$	8447.44	−	8447.44i	0.0840634	−	0.0840634i	0.747888	+	0.663825i	$0.231068\pi$
$318$		0			0
$319$			18215.0i			0.178998i
$320$		0			0
$321$	−23408.5			−0.227176
$322$		0			0
$323$	−76902.4	−	76902.4i	−0.737114	−	0.737114i
$324$		0			0
$325$	−91193.8	−	91193.8i	−0.863373	−	0.863373i
$326$		0			0
$327$	26260.4			0.245587
$328$		0			0
$329$			34087.7i			0.314924i
$330$		0			0
$331$	−46092.1	+	46092.1i	−0.420698	+	0.420698i	−0.885444	−	0.464746i	$-0.846146\pi$
$331$	−46092.1	+	46092.1i	−0.420698	+	0.420698i	0.464746	+	0.885444i	$0.346146\pi$
$332$		0			0
$333$	−74028.2	+	74028.2i	−0.667588	+	0.667588i
$334$		0			0
$335$		−	20830.7i		−	0.185616i
$336$		0			0
$337$	39317.8			0.346201			0.173101	−	0.984904i	$-0.444621\pi$
$337$	39317.8			0.346201			0.173101	+	0.984904i	$0.444621\pi$
$338$		0			0
$339$	−12503.7	−	12503.7i	−0.108803	−	0.108803i
$340$		0			0
$341$	−31549.1	−	31549.1i	−0.271318	−	0.271318i
$342$		0			0
$343$	124474.			1.05801
$344$		0			0
$345$		−	27385.1i		−	0.230079i
$346$		0			0
$347$	−67694.0	+	67694.0i	−0.562201	+	0.562201i	−0.929932	−	0.367731i	$-0.880135\pi$
$347$	−67694.0	+	67694.0i	−0.562201	+	0.562201i	0.367731	+	0.929932i	$0.380135\pi$
$348$		0			0
$349$	7662.83	−	7662.83i	0.0629127	−	0.0629127i	−0.674950	−	0.737863i	$-0.735835\pi$
$349$	7662.83	−	7662.83i	0.0629127	−	0.0629127i	0.737863	+	0.674950i	$0.235835\pi$
$350$		0			0
$351$		−	161596.i		−	1.31165i
$352$		0			0
$353$	70618.0			0.566716			0.283358	−	0.959014i	$-0.408551\pi$
$353$	70618.0			0.566716			0.283358	+	0.959014i	$0.408551\pi$
$354$		0			0
$355$	42371.5	+	42371.5i	0.336215	+	0.336215i
$356$		0			0
$357$	67248.3	+	67248.3i	0.527649	+	0.527649i
$358$		0			0
$359$	168144.			1.30465			0.652323	−	0.757941i	$-0.273794\pi$
$359$	168144.			1.30465			0.652323	+	0.757941i	$0.273794\pi$
$360$		0			0
$361$		−	47799.6i		−	0.366783i
$362$		0			0
$363$	37816.1	−	37816.1i	0.286988	−	0.286988i
$364$		0			0
$365$	44166.7	−	44166.7i	0.331520	−	0.331520i
$366$		0			0
$367$			82596.4i			0.613238i	0.951832	+	0.306619i	$0.0991977\pi$
$367$			82596.4i			0.613238i	−0.951832	+	0.306619i	$0.900802\pi$
$368$		0			0
$369$	−65510.6			−0.481126
$370$		0			0
$371$	−87536.0	−	87536.0i	−0.635973	−	0.635973i
$372$		0			0
$373$	76631.0	+	76631.0i	0.550791	+	0.550791i	0.926669	−	0.375878i	$-0.122659\pi$
$373$	76631.0	+	76631.0i	0.550791	+	0.550791i	−0.375878	+	0.926669i	$0.622659\pi$
$374$		0			0
$375$	−44580.5			−0.317017
$376$		0			0
$377$			25965.3i			0.182688i
$378$		0			0
$379$	−95935.8	+	95935.8i	−0.667886	+	0.667886i	−0.957226	−	0.289340i	$-0.906564\pi$
$379$	−95935.8	+	95935.8i	−0.667886	+	0.667886i	0.289340	+	0.957226i	$0.406564\pi$
$380$		0			0
$381$	−89654.8	+	89654.8i	−0.617623	+	0.617623i
$382$		0			0
$383$			168708.i			1.15011i	0.818116	+	0.575054i	$0.195019\pi$
$383$			168708.i			1.15011i	−0.818116	+	0.575054i	$0.804981\pi$
$384$		0			0
$385$	47245.9			0.318744
$386$		0			0
$387$	18475.9	+	18475.9i	0.123362	+	0.123362i
$388$		0			0
$389$	−66490.0	−	66490.0i	−0.439397	−	0.439397i	0.452412	−	0.891809i	$-0.350564\pi$
$389$	−66490.0	−	66490.0i	−0.439397	−	0.439397i	−0.891809	+	0.452412i	$0.850564\pi$
$390$		0			0
$391$	−280326.			−1.83362
$392$		0			0
$393$			150773.i			0.976199i
$394$		0			0
$395$	13509.6	−	13509.6i	0.0865859	−	0.0865859i
$396$		0			0
$397$	−18578.8	+	18578.8i	−0.117879	+	0.117879i	−0.763586	−	0.645706i	$-0.776563\pi$
$397$	−18578.8	+	18578.8i	−0.117879	+	0.117879i	0.645706	+	0.763586i	$0.276563\pi$
$398$		0			0
$399$		−	72162.0i		−	0.453276i
$400$		0			0
$401$	−129108.			−0.802908			−0.401454	−	0.915879i	$-0.631495\pi$
$401$	−129108.			−0.802908			−0.401454	+	0.915879i	$0.631495\pi$
$402$		0			0
$403$	−44972.9	−	44972.9i	−0.276911	−	0.276911i
$404$		0			0
$405$	244.286	+	244.286i	0.00148932	+	0.00148932i
$406$		0			0
$407$	−324156.			−1.95689
$408$		0			0
$409$		−	17952.4i		−	0.107319i	−0.998559	−	0.0536594i	$-0.982911\pi$
$409$		−	17952.4i		−	0.107319i	0.998559	−	0.0536594i	$-0.0170885\pi$
$410$		0			0
$411$	78057.7	−	78057.7i	0.462096	−	0.462096i
$412$		0			0
$413$	61594.5	−	61594.5i	0.361112	−	0.361112i
$414$		0			0
$415$			9793.04i			0.0568619i
$416$		0			0
$417$	197122.			1.13361
$418$		0			0
$419$	56887.3	+	56887.3i	0.324031	+	0.324031i	0.850311	−	0.526280i	$-0.176414\pi$
$419$	56887.3	+	56887.3i	0.324031	+	0.324031i	−0.526280	+	0.850311i	$0.676414\pi$
$420$		0			0
$421$	144162.	+	144162.i	0.813365	+	0.813365i	0.985137	−	0.171772i	$-0.0549492\pi$
$421$	144162.	+	144162.i	0.813365	+	0.813365i	−0.171772	+	0.985137i	$0.554949\pi$
$422$		0			0
$423$	−37825.2			−0.211398
$424$		0			0
$425$			219726.i			1.21648i
$426$		0			0
$427$	−83291.4	+	83291.4i	−0.456819	+	0.456819i
$428$		0			0
$429$	135614.	−	135614.i	0.736870	−	0.736870i
$430$		0			0
$431$		−	18641.5i		−	0.100352i	−0.998740	−	0.0501760i	$-0.984022\pi$
$431$		−	18641.5i		−	0.100352i	0.998740	−	0.0501760i	$-0.0159782\pi$
$432$		0			0
$433$	2193.97			0.0117019			0.00585094	−	0.999983i	$-0.498138\pi$
$433$	2193.97			0.0117019			0.00585094	+	0.999983i	$0.498138\pi$
$434$		0			0
$435$	3055.84	+	3055.84i	0.0161492	+	0.0161492i
$436$		0			0
$437$	150404.	+	150404.i	0.787586	+	0.787586i
$438$		0			0
$439$	−118115.			−0.612880			−0.306440	−	0.951890i	$-0.599138\pi$
$439$	−118115.			−0.612880			−0.306440	+	0.951890i	$0.599138\pi$
$440$		0			0
$441$			17241.2i			0.0886523i
$442$		0			0
$443$	37885.8	−	37885.8i	0.193050	−	0.193050i	−0.603963	−	0.797013i	$-0.706412\pi$
$443$	37885.8	−	37885.8i	0.193050	−	0.193050i	0.797013	+	0.603963i	$0.206412\pi$
$444$		0			0
$445$	−24425.4	+	24425.4i	−0.123345	+	0.123345i
$446$		0			0
$447$			25188.9i			0.126065i
$448$		0			0
$449$	−85186.6			−0.422550			−0.211275	−	0.977427i	$-0.567762\pi$
$449$	−85186.6			−0.422550			−0.211275	+	0.977427i	$0.567762\pi$
$450$		0			0
$451$	−143430.	−	143430.i	−0.705157	−	0.705157i
$452$		0			0
$453$	57826.4	+	57826.4i	0.281793	+	0.281793i
$454$		0			0
$455$	67348.4			0.325315
$456$		0			0
$457$		−	96935.7i		−	0.464142i	−0.972699	−	0.232071i	$-0.925450\pi$
$457$		−	96935.7i		−	0.464142i	0.972699	−	0.232071i	$-0.0745502\pi$
$458$		0			0
$459$	−194678.	+	194678.i	−0.924042	+	0.924042i
$460$		0			0
$461$	−295014.	+	295014.i	−1.38816	+	1.38816i	−0.558988	+	0.829176i	$0.688810\pi$
$461$	−295014.	+	295014.i	−1.38816	+	1.38816i	−0.829176	+	0.558988i	$0.811190\pi$
$462$		0			0
$463$			224348.i			1.04655i	0.852164	+	0.523275i	$0.175290\pi$
$463$			224348.i			1.04655i	−0.852164	+	0.523275i	$0.824710\pi$
$464$		0			0
$465$	−10585.7			−0.0489567
$466$		0			0
$467$	189556.	+	189556.i	0.869168	+	0.869168i	0.992380	−	0.123212i	$-0.0393196\pi$
$467$	189556.	+	189556.i	0.869168	+	0.869168i	−0.123212	+	0.992380i	$0.539320\pi$
$468$		0			0
$469$	−100044.	−	100044.i	−0.454827	−	0.454827i
$470$		0			0
$471$	141054.			0.635832
$472$		0			0
$473$			80902.6i			0.361610i
$474$		0			0
$475$	117891.	−	117891.i	0.522506	−	0.522506i
$476$		0			0
$477$	97133.7	−	97133.7i	0.426907	−	0.426907i
$478$		0			0
$479$		−	132796.i		−	0.578781i	−0.957211	−	0.289390i	$-0.906547\pi$
$479$		−	132796.i		−	0.578781i	0.957211	−	0.289390i	$-0.0934526\pi$
$480$		0			0
$481$	−462081.			−1.99723
$482$		0			0
$483$	−131523.	−	131523.i	−0.563778	−	0.563778i
$484$		0			0
$485$	−40338.2	−	40338.2i	−0.171488	−	0.171488i
$486$		0			0
$487$	283936.			1.19719			0.598595	−	0.801052i	$-0.295726\pi$
$487$	283936.			1.19719			0.598595	+	0.801052i	$0.295726\pi$
$488$		0			0
$489$			118101.i			0.493896i
$490$		0			0
$491$	−111725.	+	111725.i	−0.463435	+	0.463435i	−0.899780	−	0.436345i	$-0.856273\pi$
$491$	−111725.	+	111725.i	−0.463435	+	0.463435i	0.436345	+	0.899780i	$0.356273\pi$
$492$		0			0
$493$	31280.9	−	31280.9i	0.128702	−	0.128702i
$494$		0			0
$495$			52426.1i			0.213962i
$496$		0			0
$497$	406998.			1.64770
$498$		0			0
$499$	61595.1	+	61595.1i	0.247369	+	0.247369i	0.819890	−	0.572521i	$-0.194035\pi$
$499$	61595.1	+	61595.1i	0.247369	+	0.247369i	−0.572521	+	0.819890i	$0.694035\pi$
$500$		0			0
$501$	−92916.5	−	92916.5i	−0.370184	−	0.370184i
$502$		0			0
$503$	70874.1			0.280125			0.140062	−	0.990143i	$-0.455270\pi$
$503$	70874.1			0.280125			0.140062	+	0.990143i	$0.455270\pi$
$504$		0			0
$505$			5079.09i			0.0199160i
$506$		0			0
$507$	81500.9	−	81500.9i	0.317064	−	0.317064i
$508$		0			0
$509$	128181.	−	128181.i	0.494754	−	0.494754i	−0.415046	−	0.909800i	$-0.636235\pi$
$509$	128181.	−	128181.i	0.494754	−	0.494754i	0.909800	+	0.415046i	$0.136235\pi$
$510$		0			0
$511$		−	424241.i		−	1.62469i
$512$		0			0
$513$	208903.			0.793797
$514$		0			0
$515$	−26186.3	−	26186.3i	−0.0987324	−	0.0987324i
$516$		0			0
$517$	−82814.9	−	82814.9i	−0.309833	−	0.309833i
$518$		0			0
$519$	94525.3			0.350924
$520$		0			0
$521$		−	494250.i		−	1.82084i	−0.413688	−	0.910419i	$-0.635759\pi$
$521$		−	494250.i		−	1.82084i	0.413688	−	0.910419i	$-0.364241\pi$
$522$		0			0
$523$	179670.	−	179670.i	0.656859	−	0.656859i	−0.297776	−	0.954636i	$-0.596245\pi$
$523$	179670.	−	179670.i	0.656859	−	0.656859i	0.954636	+	0.297776i	$0.0962450\pi$
$524$		0			0
$525$	−103091.	+	103091.i	−0.374026	+	0.374026i
$526$		0			0
$527$			108360.i			0.390163i
$528$		0			0
$529$	268417.			0.959175
$530$		0			0
$531$	68347.9	+	68347.9i	0.242402	+	0.242402i
$532$		0			0
$533$	−204457.	−	204457.i	−0.719694	−	0.719694i
$534$		0			0
$535$	28242.7			0.0986729
$536$		0			0
$537$		−	220112.i		−	0.763300i
$538$		0			0
$539$	−37748.1	+	37748.1i	−0.129932	+	0.129932i
$540$		0			0
$541$	−300961.	+	300961.i	−1.02829	+	1.02829i	−0.0287034	+	0.999588i	$0.509138\pi$
$541$	−300961.	+	300961.i	−1.02829	+	1.02829i	−0.999588	+	0.0287034i	$0.990862\pi$
$542$		0			0
$543$			124549.i			0.422417i
$544$		0			0
$545$	−31683.6			−0.106670
$546$		0			0
$547$	−159057.	−	159057.i	−0.531591	−	0.531591i	0.389455	−	0.921046i	$-0.372663\pi$
$547$	−159057.	−	159057.i	−0.531591	−	0.531591i	−0.921046	+	0.389455i	$0.872663\pi$
$548$		0			0
$549$	−92423.8	−	92423.8i	−0.306647	−	0.306647i
$550$		0			0
$551$	−33566.6			−0.110561
$552$		0			0
$553$		−	129765.i		−	0.424335i
$554$		0			0
$555$	−54382.0	+	54382.0i	−0.176551	+	0.176551i
$556$		0			0
$557$	394524.	−	394524.i	1.27164	−	1.27164i	0.326409	−	0.945229i	$-0.394161\pi$
$557$	394524.	−	394524.i	1.27164	−	1.27164i	0.945229	−	0.326409i	$-0.105839\pi$
$558$		0			0
$559$			115326.i			0.369065i
$560$		0			0
$561$	−326755.			−1.03824
$562$		0			0
$563$	169317.	+	169317.i	0.534177	+	0.534177i	0.921813	−	0.387636i	$-0.126708\pi$
$563$	169317.	+	169317.i	0.534177	+	0.534177i	−0.387636	+	0.921813i	$0.626708\pi$
$564$		0			0
$565$	15085.9	+	15085.9i	0.0472579	+	0.0472579i
$566$		0			0
$567$	2346.48			0.00729877
$568$		0			0
$569$		−	165645.i		−	0.511626i	−0.966726	−	0.255813i	$-0.917657\pi$
$569$		−	165645.i		−	0.511626i	0.966726	−	0.255813i	$-0.0823432\pi$
$570$		0			0
$571$	335641.	−	335641.i	1.02945	−	1.02945i	0.0298925	−	0.999553i	$-0.490483\pi$
$571$	335641.	−	335641.i	1.02945	−	1.02945i	0.999553	−	0.0298925i	$-0.00951651\pi$
$572$		0			0
$573$	109771.	−	109771.i	0.334331	−	0.334331i
$574$		0			0
$575$		−	429737.i		−	1.29977i
$576$		0			0
$577$	−99615.9			−0.299211			−0.149605	−	0.988746i	$-0.547800\pi$
$577$	−99615.9			−0.299211			−0.149605	+	0.988746i	$0.547800\pi$
$578$		0			0
$579$	222031.	+	222031.i	0.662301	+	0.662301i
$580$		0			0
$581$	47033.3	+	47033.3i	0.139333	+	0.139333i
$582$		0			0
$583$	425331.			1.25138
$584$		0			0
$585$			74732.7i			0.218373i
$586$		0			0
$587$	−45023.9	+	45023.9i	−0.130667	+	0.130667i	−0.769416	−	0.638748i	$-0.779452\pi$
$587$	−45023.9	+	45023.9i	−0.130667	+	0.130667i	0.638748	+	0.769416i	$0.279452\pi$
$588$		0			0
$589$	58138.5	−	58138.5i	0.167584	−	0.167584i
$590$		0			0
$591$			79703.6i			0.228193i
$592$		0			0
$593$	−385101.			−1.09513			−0.547564	−	0.836764i	$-0.684445\pi$
$593$	−385101.			−1.09513			−0.547564	+	0.836764i	$0.684445\pi$
$594$		0			0
$595$	−81136.1	−	81136.1i	−0.229182	−	0.229182i
$596$		0			0
$597$	−124447.	−	124447.i	−0.349168	−	0.349168i
$598$		0			0
$599$	−209331.			−0.583417			−0.291709	−	0.956507i	$-0.594224\pi$
$599$	−209331.			−0.583417			−0.291709	+	0.956507i	$0.594224\pi$
$600$		0			0
$601$			515555.i			1.42734i	0.700484	+	0.713668i	$0.252967\pi$
$601$			515555.i			1.42734i	−0.700484	+	0.713668i	$0.747033\pi$
$602$		0			0
$603$	111013.	−	111013.i	0.305310	−	0.305310i
$604$		0			0
$605$	−45625.7	+	45625.7i	−0.124652	+	0.124652i
$606$		0			0
$607$		−	30292.7i		−	0.0822167i	−0.999155	−	0.0411084i	$-0.986911\pi$
$607$		−	30292.7i		−	0.0822167i	0.999155	−	0.0411084i	$-0.0130889\pi$
$608$		0			0
$609$	29352.7			0.0791432
$610$		0			0
$611$	−118052.	−	118052.i	−0.316220	−	0.316220i
$612$		0			0
$613$	99803.4	+	99803.4i	0.265598	+	0.265598i	0.827324	−	0.561726i	$-0.189862\pi$
$613$	99803.4	+	99803.4i	0.265598	+	0.265598i	−0.561726	+	0.827324i	$0.689862\pi$
$614$		0			0
$615$	−48124.9			−0.127239
$616$		0			0
$617$		−	102196.i		−	0.268451i	−0.990951	−	0.134226i	$-0.957145\pi$
$617$		−	102196.i		−	0.268451i	0.990951	−	0.134226i	$-0.0428547\pi$
$618$		0			0
$619$	−105904.	+	105904.i	−0.276395	+	0.276395i	−0.831668	−	0.555273i	$-0.812614\pi$
$619$	−105904.	+	105904.i	−0.276395	+	0.276395i	0.555273	+	0.831668i	$0.312614\pi$
$620$		0			0
$621$	380749.	−	380749.i	0.987314	−	0.987314i
$622$		0			0
$623$			234617.i			0.604483i
$624$		0			0
$625$	−308949.			−0.790909
$626$		0			0
$627$	175315.	+	175315.i	0.445948	+	0.445948i
$628$		0			0
$629$	556679.	+	556679.i	1.40703	+	1.40703i
$630$		0			0
$631$	−692480.			−1.73920			−0.869598	−	0.493760i	$-0.835622\pi$
$631$	−692480.			−1.73920			−0.869598	+	0.493760i	$0.835622\pi$
$632$		0			0
$633$		−	83779.3i		−	0.209088i
$634$		0			0
$635$	108170.	−	108170.i	0.268262	−	0.268262i
$636$		0			0
$637$	−53809.4	+	53809.4i	−0.132611	+	0.132611i
$638$		0			0
$639$			451622.i			1.10605i
$640$		0			0
$641$	49519.0			0.120519			0.0602595	−	0.998183i	$-0.480807\pi$
$641$	49519.0			0.120519			0.0602595	+	0.998183i	$0.480807\pi$
$642$		0			0
$643$	−165494.	−	165494.i	−0.400276	−	0.400276i	0.478054	−	0.878330i	$-0.341342\pi$
$643$	−165494.	−	165494.i	−0.400276	−	0.400276i	−0.878330	+	0.478054i	$0.841342\pi$
$644$		0			0
$645$	13572.6	+	13572.6i	0.0326245	+	0.0326245i
$646$		0			0
$647$	666565.			1.59233			0.796166	−	0.605078i	$-0.206858\pi$
$647$	666565.			1.59233			0.796166	+	0.605078i	$0.206858\pi$
$648$		0			0
$649$			299284.i			0.710548i
$650$		0			0
$651$	−50840.0	+	50840.0i	−0.119962	+	0.119962i
$652$		0			0
$653$	−461118.	+	461118.i	−1.08140	+	1.08140i	−0.0850198	+	0.996379i	$0.527095\pi$
$653$	−461118.	+	461118.i	−1.08140	+	1.08140i	−0.996379	+	0.0850198i	$0.972905\pi$
$654$		0			0
$655$		−	181910.i		−	0.424008i
$656$		0			0
$657$	470757.			1.09060
$658$		0			0
$659$	326883.	+	326883.i	0.752698	+	0.752698i	0.974982	−	0.222284i	$-0.0713511\pi$
$659$	326883.	+	326883.i	0.752698	+	0.752698i	−0.222284	+	0.974982i	$0.571351\pi$
$660$		0			0
$661$	−549615.	−	549615.i	−1.25793	−	1.25793i	−0.952080	−	0.305848i	$-0.901060\pi$
$661$	−549615.	−	549615.i	−1.25793	−	1.25793i	−0.305848	−	0.952080i	$-0.598940\pi$
$662$		0			0
$663$	−465785.			−1.05964
$664$		0			0
$665$			87064.5i			0.196878i
$666$		0			0
$667$	−61178.8	+	61178.8i	−0.137515	+	0.137515i
$668$		0			0
$669$	−359005.	+	359005.i	−0.802137	+	0.802137i
$670$		0			0
$671$		−	404708.i		−	0.898869i
$672$		0			0
$673$	191664.			0.423166			0.211583	−	0.977360i	$-0.432138\pi$
$673$	191664.			0.423166			0.211583	+	0.977360i	$0.432138\pi$
$674$		0			0
$675$	−298440.	−	298440.i	−0.655012	−	0.655012i
$676$		0			0
$677$	544201.	+	544201.i	1.18736	+	1.18736i	0.977795	+	0.209564i	$0.0672043\pi$
$677$	544201.	+	544201.i	1.18736	+	1.18736i	0.209564	+	0.977795i	$0.432796\pi$
$678$		0			0
$679$	−387466.			−0.840416
$680$		0			0
$681$			137020.i			0.295455i
$682$		0			0
$683$	−570769.	+	570769.i	−1.22354	+	1.22354i	−0.257179	+	0.966364i	$0.582793\pi$
$683$	−570769.	+	570769.i	−1.22354	+	1.22354i	−0.966364	+	0.257179i	$0.917207\pi$
$684$		0			0
$685$	−94177.8	+	94177.8i	−0.200709	+	0.200709i
$686$		0			0
$687$			500020.i			1.05943i
$688$		0			0
$689$	606305.			1.27718
$690$		0			0
$691$	−333477.	−	333477.i	−0.698409	−	0.698409i	0.265658	−	0.964067i	$-0.414411\pi$
$691$	−333477.	−	333477.i	−0.698409	−	0.698409i	−0.964067	+	0.265658i	$0.914411\pi$
$692$		0			0
$693$	251788.	+	251788.i	0.524286	+	0.524286i
$694$		0			0
$695$	−237831.			−0.492378
$696$		0			0
$697$			492628.i			1.01404i
$698$		0			0
$699$	−250135.	+	250135.i	−0.511941	+	0.511941i
$700$		0			0
$701$	−31503.2	+	31503.2i	−0.0641089	+	0.0641089i	−0.738434	−	0.674325i	$-0.764435\pi$
$701$	−31503.2	+	31503.2i	−0.0641089	+	0.0641089i	0.674325	+	0.738434i	$0.264435\pi$
$702$		0			0
$703$		−	597354.i		−	1.20871i
$704$		0			0
$705$	−27786.9			−0.0559064
$706$		0			0
$707$	24393.5	+	24393.5i	0.0488017	+	0.0488017i
$708$		0			0
$709$	−609708.	−	609708.i	−1.21291	−	1.21291i	−0.970064	−	0.242847i	$-0.921919\pi$
$709$	−609708.	−	609708.i	−1.21291	−	1.21291i	−0.242847	−	0.970064i	$-0.578081\pi$
$710$		0			0
$711$	143993.			0.284841
$712$		0			0
$713$		−	211928.i		−	0.416878i
$714$		0			0
$715$	−163621.	+	163621.i	−0.320056	+	0.320056i
$716$		0			0
$717$	47357.2	−	47357.2i	0.0921187	−	0.0921187i
$718$		0			0
$719$			720908.i			1.39451i	0.716823	+	0.697256i	$0.245596\pi$
$719$			720908.i			1.39451i	−0.716823	+	0.697256i	$0.754404\pi$
$720$		0			0
$721$	−251531.			−0.483862
$722$		0			0
$723$	109536.	+	109536.i	0.209546	+	0.209546i
$724$		0			0
$725$	47953.4	+	47953.4i	0.0912311	+	0.0912311i
$726$		0			0
$727$	279904.			0.529591			0.264796	−	0.964305i	$-0.414696\pi$
$727$	279904.			0.529591			0.264796	+	0.964305i	$0.414696\pi$
$728$		0			0
$729$		−	323526.i		−	0.608772i
$730$		0			0
$731$	138935.	−	138935.i	0.260003	−	0.260003i
$732$		0			0
$733$	266306.	−	266306.i	0.495648	−	0.495648i	−0.414432	−	0.910080i	$-0.636020\pi$
$733$	266306.	−	266306.i	0.495648	−	0.495648i	0.910080	+	0.414432i	$0.136020\pi$
$734$		0			0
$735$			12665.6i			0.0234450i
$736$		0			0
$737$	486108.			0.894948
$738$		0			0
$739$	−594958.	−	594958.i	−1.08943	−	1.08943i	−0.995587	−	0.0938378i	$-0.970086\pi$
$739$	−594958.	−	594958.i	−1.08943	−	1.08943i	−0.0938378	−	0.995587i	$-0.529914\pi$
$740$		0			0
$741$	249910.	+	249910.i	0.455142	+	0.455142i
$742$		0			0
$743$	−289367.			−0.524170			−0.262085	−	0.965045i	$-0.584410\pi$
$743$	−289367.			−0.524170			−0.262085	+	0.965045i	$0.584410\pi$
$744$		0			0
$745$		−	30390.8i		−	0.0547557i
$746$		0			0
$747$	−52190.2	+	52190.2i	−0.0935293	+	0.0935293i
$748$		0			0
$749$	135642.	−	135642.i	0.241785	−	0.241785i
$750$		0			0
$751$		−	935795.i		−	1.65921i	−0.558352	−	0.829604i	$-0.688566\pi$
$751$		−	935795.i		−	1.65921i	0.558352	−	0.829604i	$-0.311434\pi$
$752$		0			0
$753$	15629.1			0.0275641
$754$		0			0
$755$	−69768.4	−	69768.4i	−0.122395	−	0.122395i
$756$		0			0
$757$	626956.	+	626956.i	1.09407	+	1.09407i	0.995089	+	0.0989818i	$0.0315586\pi$
$757$	626956.	+	626956.i	1.09407	+	1.09407i	0.0989818	+	0.995089i	$0.468441\pi$
$758$		0			0
$759$	639062.			1.10933
$760$		0			0
$761$			253505.i			0.437741i	0.975754	+	0.218871i	$0.0702372\pi$
$761$			253505.i			0.437741i	−0.975754	+	0.218871i	$0.929763\pi$
$762$		0			0
$763$	−152167.	+	152167.i	−0.261380	+	0.261380i
$764$		0			0
$765$	90032.1	−	90032.1i	0.153842	−	0.153842i
$766$		0			0
$767$			426625.i			0.725197i
$768$		0			0
$769$	−740462.			−1.25213			−0.626066	−	0.779770i	$-0.715336\pi$
$769$	−740462.			−1.25213			−0.626066	+	0.779770i	$0.715336\pi$
$770$		0			0
$771$	−287792.	−	287792.i	−0.484138	−	0.484138i
$772$		0			0
$773$	−422057.	−	422057.i	−0.706337	−	0.706337i	0.259426	−	0.965763i	$-0.416467\pi$
$773$	−422057.	−	422057.i	−0.706337	−	0.706337i	−0.965763	+	0.259426i	$0.916467\pi$
$774$		0			0
$775$	−166114.			−0.276569
$776$		0			0
$777$			522364.i			0.865229i
$778$		0			0
$779$	264312.	−	264312.i	0.435553	−	0.435553i
$780$		0			0
$781$	−988787.	+	988787.i	−1.62107	+	1.62107i
$782$		0			0
$783$			84973.7i			0.138599i
$784$		0			0
$785$	−170183.			−0.276171
$786$		0			0
$787$	658152.	+	658152.i	1.06262	+	1.06262i	0.997904	+	0.0647134i	$0.0206133\pi$
$787$	658152.	+	658152.i	1.06262	+	1.06262i	0.0647134	+	0.997904i	$0.479387\pi$
$788$		0			0
$789$	−266647.	−	266647.i	−0.428334	−	0.428334i
$790$		0			0
$791$	144907.			0.231599
$792$		0			0
$793$		−	576906.i		−	0.917400i
$794$		0			0
$795$	71355.7	−	71355.7i	0.112900	−	0.112900i
$796$		0			0
$797$	573702.	−	573702.i	0.903171	−	0.903171i	−0.0925382	−	0.995709i	$-0.529498\pi$
$797$	573702.	−	573702.i	0.903171	−	0.903171i	0.995709	+	0.0925382i	$0.0294980\pi$
$798$		0			0
$799$			284439.i			0.445549i
$800$		0			0
$801$	−260342.			−0.405769
$802$		0			0
$803$	1.03068e6	+	1.03068e6i	1.59843	+	1.59843i
$804$		0			0
$805$	158685.	+	158685.i	0.244874	+	0.244874i
$806$		0			0
$807$	117889.			0.181019
$808$		0			0
$809$		−	297398.i		−	0.454402i	−0.973848	−	0.227201i	$-0.927043\pi$
$809$		−	297398.i		−	0.454402i	0.973848	−	0.227201i	$-0.0729575\pi$
$810$		0			0
$811$	481203.	−	481203.i	0.731621	−	0.731621i	−0.239320	−	0.970941i	$-0.576924\pi$
$811$	481203.	−	481203.i	0.731621	−	0.731621i	0.970941	+	0.239320i	$0.0769243\pi$
$812$		0			0
$813$	408412.	−	408412.i	0.617899	−	0.617899i
$814$		0			0
$815$		−	142491.i		−	0.214522i
$816$		0			0
$817$	−149087.			−0.223355
$818$		0			0
$819$	358921.	+	358921.i	0.535095	+	0.535095i
$820$		0			0
$821$	−506859.	−	506859.i	−0.751971	−	0.751971i	0.222876	−	0.974847i	$-0.428456\pi$
$821$	−506859.	−	506859.i	−0.751971	−	0.751971i	−0.974847	+	0.222876i	$0.928456\pi$
$822$		0			0
$823$	−401221.			−0.592357			−0.296179	−	0.955133i	$-0.595712\pi$
$823$	−401221.			−0.592357			−0.296179	+	0.955133i	$0.595712\pi$
$824$		0			0
$825$		−	500912.i		−	0.735959i
$826$		0			0
$827$	410169.	−	410169.i	0.599725	−	0.599725i	−0.340515	−	0.940239i	$-0.610601\pi$
$827$	410169.	−	410169.i	0.599725	−	0.599725i	0.940239	+	0.340515i	$0.110601\pi$
$828$		0			0
$829$	328989.	−	328989.i	0.478710	−	0.478710i	−0.426009	−	0.904719i	$-0.640081\pi$
$829$	328989.	−	328989.i	0.478710	−	0.478710i	0.904719	+	0.426009i	$0.140081\pi$
$830$		0			0
$831$		−	16727.6i		−	0.0242233i
$832$		0			0
$833$	129651.			0.186846
$834$		0			0
$835$	112105.	+	112105.i	0.160788	+	0.160788i
$836$		0			0
$837$	−147178.	−	147178.i	−0.210083	−	0.210083i
$838$		0			0
$839$	114596.			0.162797			0.0813985	−	0.996682i	$-0.474061\pi$
$839$	114596.			0.162797			0.0813985	+	0.996682i	$0.474061\pi$
$840$		0			0
$841$			693627.i			0.980696i
$842$		0			0
$843$	144007.	−	144007.i	0.202642	−	0.202642i
$844$		0			0
$845$	−98332.0	+	98332.0i	−0.137715	+	0.137715i
$846$		0			0
$847$			438256.i			0.610887i
$848$		0			0
$849$	110966.			0.153949
$850$		0			0
$851$	−1.08874e6	−	1.08874e6i	−1.50337	−	1.50337i
$852$		0			0
$853$	−79602.6	−	79602.6i	−0.109403	−	0.109403i	0.650286	−	0.759689i	$-0.274649\pi$
$853$	−79602.6	−	79602.6i	−0.109403	−	0.109403i	−0.759689	+	0.650286i	$0.774649\pi$
$854$		0			0
$855$	−96610.5			−0.132158
$856$		0			0
$857$		−	556304.i		−	0.757444i	−0.925510	−	0.378722i	$-0.876364\pi$
$857$		−	556304.i		−	0.757444i	0.925510	−	0.378722i	$-0.123636\pi$
$858$		0			0
$859$	825505.	−	825505.i	1.11875	−	1.11875i	0.126825	−	0.991925i	$-0.459521\pi$
$859$	825505.	−	825505.i	1.11875	−	1.11875i	0.991925	−	0.126825i	$-0.0404788\pi$
$860$		0			0
$861$	−231131.	+	231131.i	−0.311782	+	0.311782i
$862$		0			0
$863$		−	800580.i		−	1.07494i	−0.843284	−	0.537469i	$-0.819381\pi$
$863$		−	800580.i		−	1.07494i	0.843284	−	0.537469i	$-0.180619\pi$
$864$		0			0
$865$	−114046.			−0.152422
$866$		0			0
$867$	234158.	+	234158.i	0.311509	+	0.311509i
$868$		0			0
$869$	315261.	+	315261.i	0.417475	+	0.417475i
$870$		0			0
$871$	692941.			0.913398
$872$		0			0
$873$		−	429949.i		−	0.564143i
$874$		0			0
$875$	258325.	−	258325.i	0.337403	−	0.337403i
$876$		0			0
$877$	684224.	−	684224.i	0.889609	−	0.889609i	−0.104876	−	0.994485i	$-0.533445\pi$
$877$	684224.	−	684224.i	0.889609	−	0.889609i	0.994485	+	0.104876i	$0.0334445\pi$
$878$		0			0
$879$		−	632048.i		−	0.818036i
$880$		0			0
$881$	−995272.			−1.28230			−0.641150	−	0.767415i	$-0.721542\pi$
$881$	−995272.			−1.28230			−0.641150	+	0.767415i	$0.721542\pi$
$882$		0			0
$883$	67491.2	+	67491.2i	0.0865617	+	0.0865617i	0.749062	−	0.662500i	$-0.230505\pi$
$883$	67491.2	+	67491.2i	0.0865617	+	0.0865617i	−0.662500	+	0.749062i	$0.730505\pi$
$884$		0			0
$885$	50209.3	+	50209.3i	0.0641058	+	0.0641058i
$886$		0			0
$887$	−180136.			−0.228957			−0.114479	−	0.993426i	$-0.536520\pi$
$887$	−180136.			−0.228957			−0.114479	+	0.993426i	$0.536520\pi$
$888$		0			0
$889$		−	1.03902e6i		−	1.31468i
$890$		0			0
$891$	−5700.68	+	5700.68i	−0.00718078	+	0.00718078i
$892$		0			0
$893$	152611.	−	152611.i	0.191374	−	0.191374i
$894$		0			0
$895$			265569.i			0.331536i
$896$		0			0
$897$	910976.			1.13220
$898$		0			0
$899$	23648.5	+	23648.5i	0.0292607	+	0.0292607i
$900$		0			0
$901$	−730428.	−	730428.i	−0.899763	−	0.899763i
$902$		0			0
$903$	130371.			0.159884
$904$		0			0
$905$		−	150271.i		−	0.183475i
$906$		0			0
$907$	−893550.	+	893550.i	−1.08619	+	1.08619i	−0.0902686	+	0.995917i	$0.528773\pi$
$907$	−893550.	+	893550.i	−1.08619	+	1.08619i	−0.995917	+	0.0902686i	$0.971227\pi$
$908$		0			0
$909$	−27068.1	+	27068.1i	−0.0327589	+	0.0327589i
$910$		0			0
$911$			638798.i			0.769709i	0.922977	+	0.384855i	$0.125748\pi$
$911$			638798.i			0.769709i	−0.922977	+	0.384855i	$0.874252\pi$
$912$		0			0
$913$	−228532.			−0.274160
$914$		0			0
$915$	−67895.7	−	67895.7i	−0.0810961	−	0.0810961i
$916$		0			0
$917$	−873663.	−	873663.i	−1.03898	−	1.03898i
$918$		0			0
$919$	1.28409e6			1.52043			0.760213	−	0.649674i	$-0.225095\pi$
$919$	1.28409e6			1.52043			0.760213	+	0.649674i	$0.225095\pi$
$920$		0			0
$921$			890380.i			1.04968i
$922$		0			0
$923$	−1.40950e6	+	1.40950e6i	−1.65449	+	1.65449i
$924$		0			0
$925$	−853383.	+	853383.i	−0.997380	+	0.997380i
$926$		0			0
$927$		−	279110.i		−	0.324800i
$928$		0			0
$929$	198494.			0.229994			0.114997	−	0.993366i	$-0.463314\pi$
$929$	198494.			0.229994			0.114997	+	0.993366i	$0.463314\pi$
$930$		0			0
$931$	−69562.0	−	69562.0i	−0.0802551	−	0.0802551i
$932$		0			0
$933$	367232.	+	367232.i	0.421869	+	0.421869i
$934$		0			0
$935$	394235.			0.450953
$936$		0			0
$937$		−	389175.i		−	0.443267i	−0.975130	−	0.221634i	$-0.928861\pi$
$937$		−	389175.i		−	0.443267i	0.975130	−	0.221634i	$-0.0711389\pi$
$938$		0			0
$939$	36133.4	−	36133.4i	0.0409805	−	0.0409805i
$940$		0			0
$941$	481044.	−	481044.i	0.543257	−	0.543257i	−0.381225	−	0.924482i	$-0.624498\pi$
$941$	481044.	−	481044.i	0.543257	−	0.543257i	0.924482	+	0.381225i	$0.124498\pi$
$942$		0			0
$943$		−	963474.i		−	1.08347i
$944$		0			0
$945$	220404.			0.246806
$946$		0			0
$947$	−399574.	−	399574.i	−0.445551	−	0.445551i	0.448321	−	0.893872i	$-0.352022\pi$
$947$	−399574.	−	399574.i	−0.445551	−	0.445551i	−0.893872	+	0.448321i	$0.852022\pi$
$948$		0			0
$949$	1.46922e6	+	1.46922e6i	1.63138	+	1.63138i
$950$		0			0
$951$	66143.2			0.0731348
$952$		0			0
$953$			1.26137e6i			1.38885i	0.719564	+	0.694427i	$0.244342\pi$
$953$			1.26137e6i			1.38885i	−0.719564	+	0.694427i	$0.755658\pi$
$954$		0			0
$955$	−132440.	+	132440.i	−0.145215	+	0.145215i
$956$		0			0
$957$	−71311.5	+	71311.5i	−0.0778638	+	0.0778638i
$958$		0			0
$959$			904620.i			0.983624i
$960$		0			0
$961$	841601.			0.911296
$962$		0			0
$963$	150514.	+	150514.i	0.162302	+	0.162302i
$964$		0			0
$965$	−267883.	−	267883.i	−0.287668	−	0.287668i
$966$		0			0
$967$	−1.50478e6			−1.60924			−0.804619	−	0.593791i	$-0.797630\pi$
$967$	−1.50478e6			−1.60924			−0.804619	+	0.593791i	$0.797630\pi$
$968$		0			0
$969$		−	602143.i		−	0.641286i
$970$		0			0
$971$	818605.	−	818605.i	0.868233	−	0.868233i	−0.124044	−	0.992277i	$-0.539586\pi$
$971$	818605.	−	818605.i	0.868233	−	0.868233i	0.992277	+	0.124044i	$0.0395864\pi$
$972$		0			0
$973$	−1.14224e6	+	1.14224e6i	−1.20651	+	1.20651i
$974$		0			0
$975$		−	714044.i		−	0.751131i
$976$		0			0
$977$	753210.			0.789091			0.394545	−	0.918876i	$-0.370902\pi$
$977$	753210.			0.789091			0.394545	+	0.918876i	$0.370902\pi$
$978$		0			0
$979$	−569995.	−	569995.i	−0.594711	−	0.594711i
$980$		0			0
$981$	−168852.	−	168852.i	−0.175456	−	0.175456i
$982$		0			0
$983$	460098.			0.476149			0.238075	−	0.971247i	$-0.423484\pi$
$983$	460098.			0.476149			0.238075	+	0.971247i	$0.423484\pi$
$984$		0			0
$985$		−	96163.6i		−	0.0991147i
$986$		0			0
$987$	−133453.	+	133453.i	−0.136991	+	0.136991i
$988$		0			0
$989$	−271727.	+	271727.i	−0.277806	+	0.277806i
$990$		0			0
$991$			1.16135e6i			1.18254i	0.806472	+	0.591272i	$0.201374\pi$
$991$			1.16135e6i			1.18254i	−0.806472	+	0.591272i	$0.798626\pi$
$992$		0			0
$993$	−360899.			−0.366005
$994$		0			0
$995$	150147.	+	150147.i	0.151659	+	0.151659i
$996$		0			0
$997$	−271712.	−	271712.i	−0.273349	−	0.273349i	0.557098	−	0.830447i	$-0.311915\pi$
$997$	−271712.	−	271712.i	−0.273349	−	0.273349i	−0.830447	+	0.557098i	$0.811915\pi$
$998$		0			0
$999$	−1.51220e6			−1.51523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.f.a.31.5		14
4.3	odd	2		128.5.f.b.31.3		14
8.3	odd	2		16.5.f.a.11.4	yes	14
8.5	even	2		64.5.f.a.15.3		14
16.3	odd	4	inner	128.5.f.a.95.5		14
16.5	even	4		16.5.f.a.3.4	✓	14
16.11	odd	4		64.5.f.a.47.3		14
16.13	even	4		128.5.f.b.95.3		14
24.5	odd	2		576.5.m.a.271.3		14
24.11	even	2		144.5.m.a.91.4		14
48.5	odd	4		144.5.m.a.19.4		14
48.11	even	4		576.5.m.a.559.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.4	✓	14	16.5	even	4
16.5.f.a.11.4	yes	14	8.3	odd	2
64.5.f.a.15.3		14	8.5	even	2
64.5.f.a.47.3		14	16.11	odd	4
128.5.f.a.31.5		14	1.1	even	1	trivial
128.5.f.a.95.5		14	16.3	odd	4	inner
128.5.f.b.31.3		14	4.3	odd	2
128.5.f.b.95.3		14	16.13	even	4
144.5.m.a.19.4		14	48.5	odd	4
144.5.m.a.91.4		14	24.11	even	2
576.5.m.a.271.3		14	24.5	odd	2
576.5.m.a.559.3		14	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.91498 + 3.91498i) q^{3} +(-4.72348 - 4.72348i) q^{5} -45.3712 q^{7} -50.3458i q^{9} +O(q^{10})\)	\(q+(3.91498 + 3.91498i) q^{3} +(-4.72348 - 4.72348i) q^{5} -45.3712 q^{7} -50.3458i q^{9} +(110.228 - 110.228i) q^{11} +(157.128 - 157.128i) q^{13} -36.9847i q^{15} -378.592 q^{17} +(203.127 + 203.127i) q^{19} +(-177.627 - 177.627i) q^{21} +740.444 q^{23} -580.377i q^{25} +(514.217 - 514.217i) q^{27} +(-82.6244 + 82.6244i) q^{29} -286.217i q^{31} +863.080 q^{33} +(214.310 + 214.310i) q^{35} +(-1470.39 - 1470.39i) q^{37} +1230.31 q^{39} -1301.21i q^{41} +(-366.979 + 366.979i) q^{43} +(-237.808 + 237.808i) q^{45} -751.307i q^{47} -342.455 q^{49} +(-1482.18 - 1482.18i) q^{51} +(1929.33 + 1929.33i) q^{53} -1041.32 q^{55} +1590.48i q^{57} +(-1357.57 + 1357.57i) q^{59} +(1835.78 - 1835.78i) q^{61} +2284.25i q^{63} -1484.39 q^{65} +(2205.02 + 2205.02i) q^{67} +(2898.83 + 2898.83i) q^{69} -8970.40 q^{71} +9350.46i q^{73} +(2272.17 - 2272.17i) q^{75} +(-5001.17 + 5001.17i) q^{77} +2860.08i q^{79} -51.7173 q^{81} +(-1036.63 - 1036.63i) q^{83} +(1788.27 + 1788.27i) q^{85} -646.946 q^{87} -5171.06i q^{89} +(-7129.10 + 7129.10i) q^{91} +(1120.54 - 1120.54i) q^{93} -1918.94i q^{95} +8539.92 q^{97} +(-5549.51 - 5549.51i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	\( 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 94 q^{11} + 2 q^{13} - 4 q^{17} - 706 q^{19} + 164 q^{21} - 1148 q^{23} - 1664 q^{27} - 862 q^{29} - 4 q^{33} + 1340 q^{35} + 1826 q^{37} - 2684 q^{39} + 1694 q^{43} - 1410 q^{45} + 682 q^{49} - 3012 q^{51} + 482 q^{53} + 11780 q^{55} - 2786 q^{59} + 3778 q^{61} - 2020 q^{65} + 7998 q^{67} - 9628 q^{69} - 19964 q^{71} + 17570 q^{75} + 9508 q^{77} + 1454 q^{81} - 17282 q^{83} - 9948 q^{85} + 49284 q^{87} - 28036 q^{91} - 8896 q^{93} - 4 q^{97} + 49214 q^{99}+O(q^{100}) \) 14 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 + 94 * q^11 + 2 * q^13 - 4 * q^17 - 706 * q^19 + 164 * q^21 - 1148 * q^23 - 1664 * q^27 - 862 * q^29 - 4 * q^33 + 1340 * q^35 + 1826 * q^37 - 2684 * q^39 + 1694 * q^43 - 1410 * q^45 + 682 * q^49 - 3012 * q^51 + 482 * q^53 + 11780 * q^55 - 2786 * q^59 + 3778 * q^61 - 2020 * q^65 + 7998 * q^67 - 9628 * q^69 - 19964 * q^71 + 17570 * q^75 + 9508 * q^77 + 1454 * q^81 - 17282 * q^83 - 9948 * q^85 + 49284 * q^87 - 28036 * q^91 - 8896 * q^93 - 4 * q^97 + 49214 * q^99

Introduction

L-functions

Modular forms

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