LMFDB - Embedded newform 128.5.f.a.95.5

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			95.5
Root			$-2.15805 + 1.82834i$ of defining polynomial
Character	$\chi$	$=$	128.95
Dual form			128.5.f.a.31.5

$q$-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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.91498	−	3.91498i	0.434998	−	0.434998i	−0.455327	−	0.890324i	$-0.650477\pi$
$3$	3.91498	−	3.91498i	0.434998	−	0.434998i	0.890324	+	0.455327i	$0.150477\pi$
$4$		0			0
$5$	−4.72348	+	4.72348i	−0.188939	+	0.188939i	−0.795237	−	0.606298i	$-0.792654\pi$
$5$	−4.72348	+	4.72348i	−0.188939	+	0.188939i	0.606298	+	0.795237i	$0.292654\pi$
$6$		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	0.996349	−	0.0853752i	$-0.0272089\pi$
$11$	110.228	+	110.228i	0.910974	+	0.910974i	−0.0853752	+	0.996349i	$0.527209\pi$
$12$		0			0
$13$	157.128	+	157.128i	0.929754	+	0.929754i	0.997690	−	0.0679357i	$-0.0216413\pi$
$13$	157.128	+	157.128i	0.929754	+	0.929754i	−0.0679357	+	0.997690i	$0.521641\pi$
$14$		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	−0.367388	−	0.930068i	$-0.619748\pi$
$19$	203.127	−	203.127i	0.562680	−	0.562680i	0.930068	+	0.367388i	$0.119748\pi$
$20$		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	0.656276	−	0.754521i	$-0.272131\pi$
$29$	−82.6244	−	82.6244i	−0.0982455	−	0.0982455i	−0.754521	+	0.656276i	$0.772131\pi$
$30$		0			0
$31$			286.217i			0.297833i	0.988850	+	0.148916i	$0.0475785\pi$
$31$			286.217i			0.297833i	−0.988850	+	0.148916i	$0.952421\pi$
$32$		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	−0.0770352	+	0.997028i	$0.524545\pi$
$37$	−1470.39	+	1470.39i	−1.07406	+	1.07406i	−0.997028	+	0.0770352i	$0.975455\pi$
$38$		0			0
$39$	1230.31			0.808882
$40$		0			0
$41$			1301.21i			0.774070i	0.922065	+	0.387035i	$0.126501\pi$
$41$			1301.21i			0.774070i	−0.922065	+	0.387035i	$0.873499\pi$
$42$		0			0
$43$	−366.979	−	366.979i	−0.198474	−	0.198474i	0.600871	−	0.799346i	$-0.294820\pi$
$43$	−366.979	−	366.979i	−0.198474	−	0.198474i	−0.799346	+	0.600871i	$0.794820\pi$
$44$		0			0
$45$	−237.808	−	237.808i	−0.117436	−	0.117436i
$46$		0			0
$47$			751.307i			0.340112i	0.985434	+	0.170056i	$0.0543948\pi$
$47$			751.307i			0.340112i	−0.985434	+	0.170056i	$0.945605\pi$
$48$		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	−0.274693	−	0.961532i	$-0.588576\pi$
$53$	1929.33	−	1929.33i	0.686838	−	0.686838i	0.961532	+	0.274693i	$0.0885764\pi$
$54$		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	0.484691	−	0.874685i	$-0.338932\pi$
$59$	−1357.57	−	1357.57i	−0.389994	−	0.389994i	−0.874685	+	0.484691i	$0.838932\pi$
$60$		0			0
$61$	1835.78	+	1835.78i	0.493356	+	0.493356i	0.909362	−	0.416006i	$-0.136570\pi$
$61$	1835.78	+	1835.78i	0.493356	+	0.493356i	−0.416006	+	0.909362i	$0.636570\pi$
$62$		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	−0.417481	−	0.908686i	$-0.637087\pi$
$67$	2205.02	−	2205.02i	0.491204	−	0.491204i	0.908686	+	0.417481i	$0.137087\pi$
$68$		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	$-0.659330\pi$
$73$		−	9350.46i		−	1.75464i	0.479909	−	0.877318i	$-0.340670\pi$
$74$		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	$-0.926410\pi$
$79$		−	2860.08i		−	0.458273i	0.973394	−	0.229137i	$-0.0735903\pi$
$80$		0			0
$81$	−51.7173			−0.00788253
$82$		0			0
$83$	−1036.63	+	1036.63i	−0.150477	+	0.150477i	−0.778331	−	0.627854i	$-0.783933\pi$
$83$	−1036.63	+	1036.63i	−0.150477	+	0.150477i	0.627854	+	0.778331i	$0.283933\pi$
$84$		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	$0.105841\pi$
$89$			5171.06i			0.652830i	−0.945227	+	0.326415i	$0.894159\pi$
$90$		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	−0.732968	−	0.680263i	$-0.761866\pi$
$101$	−537.642	+	537.642i	−0.0527049	+	0.0527049i	0.680263	+	0.732968i	$0.261866\pi$
$102$		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	0.564387	−	0.825510i	$-0.309113\pi$
$107$	−2989.60	−	2989.60i	−0.261123	−	0.261123i	−0.825510	+	0.564387i	$0.809113\pi$
$108$		0			0
$109$	3353.83	+	3353.83i	0.282285	+	0.282285i	0.834020	−	0.551734i	$-0.186034\pi$
$109$	3353.83	+	3353.83i	0.282285	+	0.282285i	−0.551734	+	0.834020i	$0.686034\pi$
$110$		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	$-0.748733\pi$
$127$		−	22900.5i		−	1.41983i	0.704287	−	0.709915i	$-0.251267\pi$
$128$		0			0
$129$	−2873.43			−0.172672
$130$		0			0
$131$	19255.9	−	19255.9i	1.12207	−	1.12207i	0.130644	−	0.991429i	$-0.458296\pi$
$131$	19255.9	−	19255.9i	1.12207	−	1.12207i	0.991429	−	0.130644i	$-0.0417045\pi$
$132$		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	$0.178239\pi$
$137$			19938.2i			1.06229i	−0.847280	+	0.531147i	$0.821761\pi$
$138$		0			0
$139$	25175.4	+	25175.4i	1.30301	+	1.30301i	0.926356	+	0.376649i	$0.122924\pi$
$139$	25175.4	+	25175.4i	1.30301	+	1.30301i	0.376649	+	0.926356i	$0.377076\pi$
$140$		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	−0.630934	−	0.775837i	$-0.717328\pi$
$149$	3216.99	−	3216.99i	0.144903	−	0.144903i	0.775837	+	0.630934i	$0.217328\pi$
$150$		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	0.970787	−	0.239942i	$-0.0771284\pi$
$157$	18014.6	+	18014.6i	0.730845	+	0.730845i	−0.239942	+	0.970787i	$0.577128\pi$
$158$		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	−0.363784	−	0.931483i	$-0.618515\pi$
$163$	15083.2	−	15083.2i	0.567700	−	0.567700i	0.931483	+	0.363784i	$0.118515\pi$
$164$		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	0.879416	−	0.476053i	$-0.157933\pi$
$173$	12072.3	+	12072.3i	0.403363	+	0.403363i	−0.476053	+	0.879416i	$0.657933\pi$
$174$		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	−0.993261	−	0.115900i	$-0.963025\pi$
$179$	−28111.5	+	28111.5i	−0.877361	+	0.877361i	0.115900	+	0.993261i	$0.463025\pi$
$180$		0			0
$181$	15906.7	−	15906.7i	0.485539	−	0.485539i	−0.421356	−	0.906895i	$-0.638446\pi$
$181$	15906.7	−	15906.7i	0.485539	−	0.485539i	0.906895	+	0.421356i	$0.138446\pi$
$182$		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	$0.125554\pi$
$191$			28038.6i			0.768581i	−0.923212	+	0.384290i	$0.874446\pi$
$192$		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	−0.563692	−	0.825985i	$-0.690620\pi$
$197$	10179.3	−	10179.3i	0.262292	−	0.262292i	0.825985	+	0.563692i	$0.190620\pi$
$198$		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	−0.816988	−	0.576655i	$-0.804358\pi$
$211$	−10699.8	+	10699.8i	−0.240332	+	0.240332i	0.576655	+	0.816988i	$0.304358\pi$
$212$		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	$-0.626553\pi$
$223$		−	91700.4i		−	1.84400i	0.387187	−	0.922001i	$-0.373447\pi$
$224$		0			0
$225$	−29219.6			−0.577177
$226$		0			0
$227$	17499.5	−	17499.5i	0.339605	−	0.339605i	−0.516614	−	0.856218i	$-0.672808\pi$
$227$	17499.5	−	17499.5i	0.339605	−	0.339605i	0.856218	+	0.516614i	$0.172808\pi$
$228$		0			0
$229$	63859.8	−	63859.8i	1.21775	−	1.21775i	0.249326	−	0.968420i	$-0.419791\pi$
$229$	63859.8	−	63859.8i	1.21775	−	1.21775i	0.968420	−	0.249326i	$-0.0802091\pi$
$230$		0			0
$231$	−39159.0			−0.733850
$232$		0			0
$233$		−	63891.7i		−	1.17688i	−0.808540	−	0.588441i	$-0.799742\pi$
$233$		−	63891.7i		−	1.17688i	0.808540	−	0.588441i	$-0.200258\pi$
$234$		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	$0.0337672\pi$
$239$			12096.4i			0.211768i	−0.994378	+	0.105884i	$0.966233\pi$
$240$		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	0.722771	−	0.691088i	$-0.242868\pi$
$251$	1996.06	+	1996.06i	0.0316830	+	0.0316830i	−0.691088	+	0.722771i	$0.742868\pi$
$252$		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	0.803446	−	0.595377i	$-0.202997\pi$
$269$	15056.1	+	15056.1i	0.208069	+	0.208069i	−0.595377	+	0.803446i	$0.702997\pi$
$270$		0			0
$271$			104320.i			1.42046i	0.703968	+	0.710232i	$0.251410\pi$
$271$			104320.i			1.42046i	−0.703968	+	0.710232i	$0.748590\pi$
$272$		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	−0.720891	−	0.693048i	$-0.756267\pi$
$277$	−2136.36	+	2136.36i	−0.0278430	+	0.0278430i	0.693048	+	0.720891i	$0.256267\pi$
$278$		0			0
$279$	−14409.8			−0.185119
$280$		0			0
$281$			36783.7i			0.465846i	0.972495	+	0.232923i	$0.0748290\pi$
$281$			36783.7i			0.465846i	−0.972495	+	0.232923i	$0.925171\pi$
$282$		0			0
$283$	14172.0	+	14172.0i	0.176953	+	0.176953i	0.790026	−	0.613073i	$-0.210067\pi$
$283$	14172.0	+	14172.0i	0.176953	+	0.176953i	−0.613073	+	0.790026i	$0.710067\pi$
$284$		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	−0.998314	−	0.0580384i	$-0.981515\pi$
$293$	−80721.8	+	80721.8i	−0.940276	+	0.940276i	0.0580384	+	0.998314i	$0.481515\pi$
$294$		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	0.234389	−	0.972143i	$-0.424691\pi$
$307$	113714.	−	113714.i	1.20653	−	1.20653i	0.972143	−	0.234389i	$-0.0753090\pi$
$308$		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	$0.0149993\pi$
$313$			9229.52i			0.0942086i	−0.998890	+	0.0471043i	$0.985001\pi$
$314$		0			0
$315$	10789.6	+	10789.6i	0.108739	+	0.108739i
$316$		0			0
$317$	8447.44	+	8447.44i	0.0840634	+	0.0840634i	0.747888	−	0.663825i	$-0.231068\pi$
$317$	8447.44	+	8447.44i	0.0840634	+	0.0840634i	−0.663825	+	0.747888i	$0.731068\pi$
$318$		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	0.464746	−	0.885444i	$-0.346146\pi$
$331$	−46092.1	−	46092.1i	−0.420698	−	0.420698i	−0.885444	+	0.464746i	$0.846146\pi$
$332$		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	0.367731	−	0.929932i	$-0.380135\pi$
$347$	−67694.0	−	67694.0i	−0.562201	−	0.562201i	−0.929932	+	0.367731i	$0.880135\pi$
$348$		0			0
$349$	7662.83	+	7662.83i	0.0629127	+	0.0629127i	0.737863	−	0.674950i	$-0.235835\pi$
$349$	7662.83	+	7662.83i	0.0629127	+	0.0629127i	−0.674950	+	0.737863i	$0.735835\pi$
$350$		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	$-0.900802\pi$
$367$		−	82596.4i		−	0.613238i	0.951832	−	0.306619i	$-0.0991977\pi$
$368$		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	−0.375878	−	0.926669i	$-0.622659\pi$
$373$	76631.0	−	76631.0i	0.550791	−	0.550791i	0.926669	+	0.375878i	$0.122659\pi$
$374$		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	0.289340	−	0.957226i	$-0.406564\pi$
$379$	−95935.8	−	95935.8i	−0.667886	−	0.667886i	−0.957226	+	0.289340i	$0.906564\pi$
$380$		0			0
$381$	−89654.8	−	89654.8i	−0.617623	−	0.617623i
$382$		0			0
$383$		−	168708.i		−	1.15011i	−0.818116	−	0.575054i	$-0.804981\pi$
$383$		−	168708.i		−	1.15011i	0.818116	−	0.575054i	$-0.195019\pi$
$384$		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	−0.891809	−	0.452412i	$-0.850564\pi$
$389$	−66490.0	+	66490.0i	−0.439397	+	0.439397i	0.452412	+	0.891809i	$0.350564\pi$
$390$		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	0.645706	−	0.763586i	$-0.276563\pi$
$397$	−18578.8	−	18578.8i	−0.117879	−	0.117879i	−0.763586	+	0.645706i	$0.776563\pi$
$398$		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	$0.0170885\pi$
$409$			17952.4i			0.107319i	−0.998559	+	0.0536594i	$0.982911\pi$
$410$		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	−0.526280	−	0.850311i	$-0.676414\pi$
$419$	56887.3	−	56887.3i	0.324031	−	0.324031i	0.850311	+	0.526280i	$0.176414\pi$
$420$		0			0
$421$	144162.	−	144162.i	0.813365	−	0.813365i	−0.171772	−	0.985137i	$-0.554949\pi$
$421$	144162.	−	144162.i	0.813365	−	0.813365i	0.985137	+	0.171772i	$0.0549492\pi$
$422$		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	$0.0159782\pi$
$431$			18641.5i			0.100352i	−0.998740	+	0.0501760i	$0.984022\pi$
$432$		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	0.797013	−	0.603963i	$-0.206412\pi$
$443$	37885.8	+	37885.8i	0.193050	+	0.193050i	−0.603963	+	0.797013i	$0.706412\pi$
$444$		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	$0.0745502\pi$
$457$			96935.7i			0.464142i	−0.972699	+	0.232071i	$0.925450\pi$
$458$		0			0
$459$	−194678.	−	194678.i	−0.924042	−	0.924042i
$460$		0			0
$461$	−295014.	−	295014.i	−1.38816	−	1.38816i	−0.829176	−	0.558988i	$-0.811190\pi$
$461$	−295014.	−	295014.i	−1.38816	−	1.38816i	−0.558988	−	0.829176i	$-0.688810\pi$
$462$		0			0
$463$		−	224348.i		−	1.04655i	−0.852164	−	0.523275i	$-0.824710\pi$
$463$		−	224348.i		−	1.04655i	0.852164	−	0.523275i	$-0.175290\pi$
$464$		0			0
$465$	−10585.7			−0.0489567
$466$		0			0
$467$	189556.	−	189556.i	0.869168	−	0.869168i	−0.123212	−	0.992380i	$-0.539320\pi$
$467$	189556.	−	189556.i	0.869168	−	0.869168i	0.992380	+	0.123212i	$0.0393196\pi$
$468$		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	$0.0934526\pi$
$479$			132796.i			0.578781i	−0.957211	+	0.289390i	$0.906547\pi$
$480$		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	0.436345	−	0.899780i	$-0.356273\pi$
$491$	−111725.	−	111725.i	−0.463435	−	0.463435i	−0.899780	+	0.436345i	$0.856273\pi$
$492$		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	−0.572521	−	0.819890i	$-0.694035\pi$
$499$	61595.1	−	61595.1i	0.247369	−	0.247369i	0.819890	+	0.572521i	$0.194035\pi$
$500$		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	0.909800	−	0.415046i	$-0.136235\pi$
$509$	128181.	+	128181.i	0.494754	+	0.494754i	−0.415046	+	0.909800i	$0.636235\pi$
$510$		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	$0.364241\pi$
$521$			494250.i			1.82084i	−0.413688	+	0.910419i	$0.635759\pi$
$522$		0			0
$523$	179670.	+	179670.i	0.656859	+	0.656859i	0.954636	−	0.297776i	$-0.0962450\pi$
$523$	179670.	+	179670.i	0.656859	+	0.656859i	−0.297776	+	0.954636i	$0.596245\pi$
$524$		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	−0.999588	−	0.0287034i	$-0.990862\pi$
$541$	−300961.	−	300961.i	−1.02829	−	1.02829i	−0.0287034	−	0.999588i	$-0.509138\pi$
$542$		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	−0.921046	−	0.389455i	$-0.872663\pi$
$547$	−159057.	+	159057.i	−0.531591	+	0.531591i	0.389455	+	0.921046i	$0.372663\pi$
$548$		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	0.945229	+	0.326409i	$0.105839\pi$
$557$	394524.	+	394524.i	1.27164	+	1.27164i	0.326409	+	0.945229i	$0.394161\pi$
$558$		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	−0.387636	−	0.921813i	$-0.626708\pi$
$563$	169317.	−	169317.i	0.534177	−	0.534177i	0.921813	+	0.387636i	$0.126708\pi$
$564$		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	$0.0823432\pi$
$569$			165645.i			0.511626i	−0.966726	+	0.255813i	$0.917657\pi$
$570$		0			0
$571$	335641.	+	335641.i	1.02945	+	1.02945i	0.999553	+	0.0298925i	$0.00951651\pi$
$571$	335641.	+	335641.i	1.02945	+	1.02945i	0.0298925	+	0.999553i	$0.490483\pi$
$572$		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	0.638748	−	0.769416i	$-0.279452\pi$
$587$	−45023.9	−	45023.9i	−0.130667	−	0.130667i	−0.769416	+	0.638748i	$0.779452\pi$
$588$		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	$-0.747033\pi$
$601$		−	515555.i		−	1.42734i	0.700484	−	0.713668i	$-0.252967\pi$
$602$		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	$0.0130889\pi$
$607$			30292.7i			0.0822167i	−0.999155	+	0.0411084i	$0.986911\pi$
$608$		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	−0.561726	−	0.827324i	$-0.689862\pi$
$613$	99803.4	−	99803.4i	0.265598	−	0.265598i	0.827324	+	0.561726i	$0.189862\pi$
$614$		0			0
$615$	−48124.9			−0.127239
$616$		0			0
$617$			102196.i			0.268451i	0.990951	+	0.134226i	$0.0428547\pi$
$617$			102196.i			0.268451i	−0.990951	+	0.134226i	$0.957145\pi$
$618$		0			0
$619$	−105904.	−	105904.i	−0.276395	−	0.276395i	0.555273	−	0.831668i	$-0.312614\pi$
$619$	−105904.	−	105904.i	−0.276395	−	0.276395i	−0.831668	+	0.555273i	$0.812614\pi$
$620$		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	−0.878330	−	0.478054i	$-0.841342\pi$
$643$	−165494.	+	165494.i	−0.400276	+	0.400276i	0.478054	+	0.878330i	$0.341342\pi$
$644$		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	−0.996379	−	0.0850198i	$-0.972905\pi$
$653$	−461118.	−	461118.i	−1.08140	−	1.08140i	−0.0850198	−	0.996379i	$-0.527095\pi$
$654$		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	−0.222284	−	0.974982i	$-0.571351\pi$
$659$	326883.	−	326883.i	0.752698	−	0.752698i	0.974982	+	0.222284i	$0.0713511\pi$
$660$		0			0
$661$	−549615.	+	549615.i	−1.25793	+	1.25793i	−0.305848	+	0.952080i	$0.598940\pi$
$661$	−549615.	+	549615.i	−1.25793	+	1.25793i	−0.952080	+	0.305848i	$0.901060\pi$
$662$		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	0.209564	−	0.977795i	$-0.432796\pi$
$677$	544201.	−	544201.i	1.18736	−	1.18736i	0.977795	−	0.209564i	$-0.0672043\pi$
$678$		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	−0.966364	−	0.257179i	$-0.917207\pi$
$683$	−570769.	−	570769.i	−1.22354	−	1.22354i	−0.257179	−	0.966364i	$-0.582793\pi$
$684$		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	−0.964067	−	0.265658i	$-0.914411\pi$
$691$	−333477.	+	333477.i	−0.698409	+	0.698409i	0.265658	+	0.964067i	$0.414411\pi$
$692$		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	0.674325	−	0.738434i	$-0.264435\pi$
$701$	−31503.2	−	31503.2i	−0.0641089	−	0.0641089i	−0.738434	+	0.674325i	$0.764435\pi$
$702$		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	−0.242847	+	0.970064i	$0.578081\pi$
$709$	−609708.	+	609708.i	−1.21291	+	1.21291i	−0.970064	+	0.242847i	$0.921919\pi$
$710$		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	$-0.754404\pi$
$719$		−	720908.i		−	1.39451i	0.716823	−	0.697256i	$-0.245596\pi$
$720$		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	0.910080	−	0.414432i	$-0.136020\pi$
$733$	266306.	+	266306.i	0.495648	+	0.495648i	−0.414432	+	0.910080i	$0.636020\pi$
$734$		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	−0.0938378	+	0.995587i	$0.529914\pi$
$739$	−594958.	+	594958.i	−1.08943	+	1.08943i	−0.995587	+	0.0938378i	$0.970086\pi$
$740$		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	$0.311434\pi$
$751$			935795.i			1.65921i	−0.558352	+	0.829604i	$0.688566\pi$
$752$		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	0.0989818	−	0.995089i	$-0.468441\pi$
$757$	626956.	−	626956.i	1.09407	−	1.09407i	0.995089	−	0.0989818i	$-0.0315586\pi$
$758$		0			0
$759$	639062.			1.10933
$760$		0			0
$761$		−	253505.i		−	0.437741i	−0.975754	−	0.218871i	$-0.929763\pi$
$761$		−	253505.i		−	0.437741i	0.975754	−	0.218871i	$-0.0702372\pi$
$762$		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	−0.965763	−	0.259426i	$-0.916467\pi$
$773$	−422057.	+	422057.i	−0.706337	+	0.706337i	0.259426	+	0.965763i	$0.416467\pi$
$774$		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	0.0647134	−	0.997904i	$-0.479387\pi$
$787$	658152.	−	658152.i	1.06262	−	1.06262i	0.997904	−	0.0647134i	$-0.0206133\pi$
$788$		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	0.995709	−	0.0925382i	$-0.0294980\pi$
$797$	573702.	+	573702.i	0.903171	+	0.903171i	−0.0925382	+	0.995709i	$0.529498\pi$
$798$		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	$0.0729575\pi$
$809$			297398.i			0.454402i	−0.973848	+	0.227201i	$0.927043\pi$
$810$		0			0
$811$	481203.	+	481203.i	0.731621	+	0.731621i	0.970941	−	0.239320i	$-0.0769243\pi$
$811$	481203.	+	481203.i	0.731621	+	0.731621i	−0.239320	+	0.970941i	$0.576924\pi$
$812$		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	−0.974847	−	0.222876i	$-0.928456\pi$
$821$	−506859.	+	506859.i	−0.751971	+	0.751971i	0.222876	+	0.974847i	$0.428456\pi$
$822$		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	0.940239	−	0.340515i	$-0.110601\pi$
$827$	410169.	+	410169.i	0.599725	+	0.599725i	−0.340515	+	0.940239i	$0.610601\pi$
$828$		0			0
$829$	328989.	+	328989.i	0.478710	+	0.478710i	0.904719	−	0.426009i	$-0.140081\pi$
$829$	328989.	+	328989.i	0.478710	+	0.478710i	−0.426009	+	0.904719i	$0.640081\pi$
$830$		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	−0.759689	−	0.650286i	$-0.774649\pi$
$853$	−79602.6	+	79602.6i	−0.109403	+	0.109403i	0.650286	+	0.759689i	$0.274649\pi$
$854$		0			0
$855$	−96610.5			−0.132158
$856$		0			0
$857$			556304.i			0.757444i	0.925510	+	0.378722i	$0.123636\pi$
$857$			556304.i			0.757444i	−0.925510	+	0.378722i	$0.876364\pi$
$858$		0			0
$859$	825505.	+	825505.i	1.11875	+	1.11875i	0.991925	+	0.126825i	$0.0404788\pi$
$859$	825505.	+	825505.i	1.11875	+	1.11875i	0.126825	+	0.991925i	$0.459521\pi$
$860$		0			0
$861$	−231131.	−	231131.i	−0.311782	−	0.311782i
$862$		0			0
$863$			800580.i			1.07494i	0.843284	+	0.537469i	$0.180619\pi$
$863$			800580.i			1.07494i	−0.843284	+	0.537469i	$0.819381\pi$
$864$		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	0.994485	−	0.104876i	$-0.0334445\pi$
$877$	684224.	+	684224.i	0.889609	+	0.889609i	−0.104876	+	0.994485i	$0.533445\pi$
$878$		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	−0.662500	−	0.749062i	$-0.730505\pi$
$883$	67491.2	−	67491.2i	0.0865617	−	0.0865617i	0.749062	+	0.662500i	$0.230505\pi$
$884$		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	−0.995917	−	0.0902686i	$-0.971227\pi$
$907$	−893550.	−	893550.i	−1.08619	−	1.08619i	−0.0902686	−	0.995917i	$-0.528773\pi$
$908$		0			0
$909$	−27068.1	−	27068.1i	−0.0327589	−	0.0327589i
$910$		0			0
$911$		−	638798.i		−	0.769709i	−0.922977	−	0.384855i	$-0.874252\pi$
$911$		−	638798.i		−	0.769709i	0.922977	−	0.384855i	$-0.125748\pi$
$912$		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	$0.0711389\pi$
$937$			389175.i			0.443267i	−0.975130	+	0.221634i	$0.928861\pi$
$938$		0			0
$939$	36133.4	+	36133.4i	0.0409805	+	0.0409805i
$940$		0			0
$941$	481044.	+	481044.i	0.543257	+	0.543257i	0.924482	−	0.381225i	$-0.124498\pi$
$941$	481044.	+	481044.i	0.543257	+	0.543257i	−0.381225	+	0.924482i	$0.624498\pi$
$942$		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	−0.893872	−	0.448321i	$-0.852022\pi$
$947$	−399574.	+	399574.i	−0.445551	+	0.445551i	0.448321	+	0.893872i	$0.352022\pi$
$948$		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	$-0.755658\pi$
$953$		−	1.26137e6i		−	1.38885i	0.719564	−	0.694427i	$-0.244342\pi$
$954$		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	0.992277	−	0.124044i	$-0.0395864\pi$
$971$	818605.	+	818605.i	0.868233	+	0.868233i	−0.124044	+	0.992277i	$0.539586\pi$
$972$		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	$-0.798626\pi$
$991$		−	1.16135e6i		−	1.18254i	0.806472	−	0.591272i	$-0.201374\pi$
$992$		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	−0.830447	−	0.557098i	$-0.811915\pi$
$997$	−271712.	+	271712.i	−0.273349	+	0.273349i	0.557098	+	0.830447i	$0.311915\pi$
$998$		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.95.5		14
4.3	odd	2		128.5.f.b.95.3		14
8.3	odd	2		16.5.f.a.3.4	✓	14
8.5	even	2		64.5.f.a.47.3		14
16.3	odd	4		64.5.f.a.15.3		14
16.5	even	4		128.5.f.b.31.3		14
16.11	odd	4	inner	128.5.f.a.31.5		14
16.13	even	4		16.5.f.a.11.4	yes	14
24.5	odd	2		576.5.m.a.559.3		14
24.11	even	2		144.5.m.a.19.4		14
48.29	odd	4		144.5.m.a.91.4		14
48.35	even	4		576.5.m.a.271.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.4	✓	14	8.3	odd	2
16.5.f.a.11.4	yes	14	16.13	even	4
64.5.f.a.15.3		14	16.3	odd	4
64.5.f.a.47.3		14	8.5	even	2
128.5.f.a.31.5		14	16.11	odd	4	inner
128.5.f.a.95.5		14	1.1	even	1	trivial
128.5.f.b.31.3		14	16.5	even	4
128.5.f.b.95.3		14	4.3	odd	2
144.5.m.a.19.4		14	24.11	even	2
144.5.m.a.91.4		14	48.29	odd	4
576.5.m.a.271.3		14	48.35	even	4
576.5.m.a.559.3		14	24.5	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
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

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