LMFDB - Embedded newform 128.5.f.a.95.7

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			95.7
Root			$1.03712 - 2.63142i$ of defining polynomial
Character	$\chi$	$=$	128.95
Dual form			128.5.f.a.31.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.5209 - 11.5209i) q^{3} +(14.6016 - 14.6016i) q^{5} +24.0210 q^{7} -184.461i q^{9} +O(q^{10})$	\(q+(11.5209 - 11.5209i) q^{3} +(14.6016 - 14.6016i) q^{5} +24.0210 q^{7} -184.461i q^{9} +(61.7287 + 61.7287i) q^{11} +(37.5611 + 37.5611i) q^{13} -336.446i q^{15} +96.8718 q^{17} +(-156.751 + 156.751i) q^{19} +(276.742 - 276.742i) q^{21} -959.783 q^{23} +198.587i q^{25} +(-1191.96 - 1191.96i) q^{27} +(350.180 + 350.180i) q^{29} -237.885i q^{31} +1422.34 q^{33} +(350.744 - 350.744i) q^{35} +(560.815 - 560.815i) q^{37} +865.473 q^{39} -1802.95i q^{41} +(206.090 + 206.090i) q^{43} +(-2693.42 - 2693.42i) q^{45} +1599.92i q^{47} -1823.99 q^{49} +(1116.05 - 1116.05i) q^{51} +(2234.17 - 2234.17i) q^{53} +1802.67 q^{55} +3611.82i q^{57} +(2353.11 + 2353.11i) q^{59} +(4443.45 + 4443.45i) q^{61} -4430.92i q^{63} +1096.90 q^{65} +(-3995.40 + 3995.40i) q^{67} +(-11057.5 + 11057.5i) q^{69} -4929.25 q^{71} -2651.57i q^{73} +(2287.90 + 2287.90i) q^{75} +(1482.78 + 1482.78i) q^{77} +8792.34i q^{79} -12523.4 q^{81} +(-228.231 + 228.231i) q^{83} +(1414.48 - 1414.48i) q^{85} +8068.75 q^{87} +10596.7i q^{89} +(902.254 + 902.254i) q^{91} +(-2740.64 - 2740.64i) q^{93} +4577.63i q^{95} +11048.3 q^{97} +(11386.5 - 11386.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	11.5209	−	11.5209i	1.28010	−	1.28010i	0.339485	−	0.940612i	$-0.389747\pi$
$3$	11.5209	−	11.5209i	1.28010	−	1.28010i	0.940612	−	0.339485i	$-0.110253\pi$
$4$		0			0
$5$	14.6016	−	14.6016i	0.584063	−	0.584063i	−0.351954	−	0.936017i	$-0.614483\pi$
$5$	14.6016	−	14.6016i	0.584063	−	0.584063i	0.936017	+	0.351954i	$0.114483\pi$
$6$		0			0
$7$	24.0210			0.490224			0.245112	−	0.969495i	$-0.421175\pi$
$7$	24.0210			0.490224			0.245112	+	0.969495i	$0.421175\pi$
$8$		0			0
$9$		−	184.461i		−	2.27729i
$10$		0			0
$11$	61.7287	+	61.7287i	0.510154	+	0.510154i	0.914574	−	0.404419i	$-0.132526\pi$
$11$	61.7287	+	61.7287i	0.510154	+	0.510154i	−0.404419	+	0.914574i	$0.632526\pi$
$12$		0			0
$13$	37.5611	+	37.5611i	0.222255	+	0.222255i	0.809447	−	0.587192i	$-0.199767\pi$
$13$	37.5611	+	37.5611i	0.222255	+	0.222255i	−0.587192	+	0.809447i	$0.699767\pi$
$14$		0			0
$15$		−	336.446i		−	1.49531i
$16$		0			0
$17$	96.8718			0.335197			0.167598	−	0.985855i	$-0.446399\pi$
$17$	96.8718			0.335197			0.167598	+	0.985855i	$0.446399\pi$
$18$		0			0
$19$	−156.751	+	156.751i	−0.434214	+	0.434214i	−0.890059	−	0.455845i	$-0.849337\pi$
$19$	−156.751	+	156.751i	−0.434214	+	0.434214i	0.455845	+	0.890059i	$0.349337\pi$
$20$		0			0
$21$	276.742	−	276.742i	0.627534	−	0.627534i
$22$		0			0
$23$	−959.783			−1.81433			−0.907167	−	0.420770i	$-0.861760\pi$
$23$	−959.783			−1.81433			−0.907167	+	0.420770i	$0.861760\pi$
$24$		0			0
$25$			198.587i			0.317740i
$26$		0			0
$27$	−1191.96	−	1191.96i	−1.63506	−	1.63506i
$28$		0			0
$29$	350.180	+	350.180i	0.416385	+	0.416385i	0.883956	−	0.467571i	$-0.154871\pi$
$29$	350.180	+	350.180i	0.416385	+	0.416385i	−0.467571	+	0.883956i	$0.654871\pi$
$30$		0			0
$31$		−	237.885i		−	0.247539i	−0.992311	−	0.123769i	$-0.960502\pi$
$31$		−	237.885i		−	0.247539i	0.992311	−	0.123769i	$-0.0394983\pi$
$32$		0			0
$33$	1422.34			1.30609
$34$		0			0
$35$	350.744	−	350.744i	0.286322	−	0.286322i
$36$		0			0
$37$	560.815	−	560.815i	0.409653	−	0.409653i	−0.471965	−	0.881617i	$-0.656455\pi$
$37$	560.815	−	560.815i	0.409653	−	0.409653i	0.881617	+	0.471965i	$0.156455\pi$
$38$		0			0
$39$	865.473			0.569016
$40$		0			0
$41$		−	1802.95i		−	1.07255i	−0.844044	−	0.536274i	$-0.819831\pi$
$41$		−	1802.95i		−	1.07255i	0.844044	−	0.536274i	$-0.180169\pi$
$42$		0			0
$43$	206.090	+	206.090i	0.111460	+	0.111460i	0.760637	−	0.649177i	$-0.224887\pi$
$43$	206.090	+	206.090i	0.111460	+	0.111460i	−0.649177	+	0.760637i	$0.724887\pi$
$44$		0			0
$45$	−2693.42	−	2693.42i	−1.33008	−	1.33008i
$46$		0			0
$47$			1599.92i			0.724274i	0.932125	+	0.362137i	$0.117953\pi$
$47$			1599.92i			0.724274i	−0.932125	+	0.362137i	$0.882047\pi$
$48$		0			0
$49$	−1823.99			−0.759681
$50$		0			0
$51$	1116.05	−	1116.05i	0.429084	−	0.429084i
$52$		0			0
$53$	2234.17	−	2234.17i	0.795360	−	0.795360i	−0.187000	−	0.982360i	$-0.559876\pi$
$53$	2234.17	−	2234.17i	0.795360	−	0.795360i	0.982360	+	0.187000i	$0.0598765\pi$
$54$		0			0
$55$	1802.67			0.595925
$56$		0			0
$57$			3611.82i			1.11167i
$58$		0			0
$59$	2353.11	+	2353.11i	0.675988	+	0.675988i	0.959090	−	0.283102i	$-0.0913636\pi$
$59$	2353.11	+	2353.11i	0.675988	+	0.675988i	−0.283102	+	0.959090i	$0.591364\pi$
$60$		0			0
$61$	4443.45	+	4443.45i	1.19415	+	1.19415i	0.975890	+	0.218264i	$0.0700395\pi$
$61$	4443.45	+	4443.45i	1.19415	+	1.19415i	0.218264	+	0.975890i	$0.429961\pi$
$62$		0			0
$63$		−	4430.92i		−	1.11638i
$64$		0			0
$65$	1096.90			0.259622
$66$		0			0
$67$	−3995.40	+	3995.40i	−0.890042	+	0.890042i	−0.994527	−	0.104485i	$-0.966681\pi$
$67$	−3995.40	+	3995.40i	−0.890042	+	0.890042i	0.104485	+	0.994527i	$0.466681\pi$
$68$		0			0
$69$	−11057.5	+	11057.5i	−2.32252	+	2.32252i
$70$		0			0
$71$	−4929.25			−0.977832			−0.488916	−	0.872331i	$-0.662608\pi$
$71$	−4929.25			−0.977832			−0.488916	+	0.872331i	$0.662608\pi$
$72$		0			0
$73$		−	2651.57i		−	0.497574i	−0.968558	−	0.248787i	$-0.919968\pi$
$73$		−	2651.57i		−	0.497574i	0.968558	−	0.248787i	$-0.0800319\pi$
$74$		0			0
$75$	2287.90	+	2287.90i	0.406737	+	0.406737i
$76$		0			0
$77$	1482.78	+	1482.78i	0.250090	+	0.250090i
$78$		0			0
$79$			8792.34i			1.40880i	0.709801	+	0.704402i	$0.248785\pi$
$79$			8792.34i			1.40880i	−0.709801	+	0.704402i	$0.751215\pi$
$80$		0			0
$81$	−12523.4			−1.90877
$82$		0			0
$83$	−228.231	+	228.231i	−0.0331298	+	0.0331298i	−0.723478	−	0.690348i	$-0.757458\pi$
$83$	−228.231	+	228.231i	−0.0331298	+	0.0331298i	0.690348	+	0.723478i	$0.257458\pi$
$84$		0			0
$85$	1414.48	−	1414.48i	0.195776	−	0.195776i
$86$		0			0
$87$	8068.75			1.06603
$88$		0			0
$89$			10596.7i			1.33780i	0.743353	+	0.668899i	$0.233234\pi$
$89$			10596.7i			1.33780i	−0.743353	+	0.668899i	$0.766766\pi$
$90$		0			0
$91$	902.254	+	902.254i	0.108955	+	0.108955i
$92$		0			0
$93$	−2740.64	−	2740.64i	−0.316873	−	0.316873i
$94$		0			0
$95$			4577.63i			0.507217i
$96$		0			0
$97$	11048.3			1.17422			0.587111	−	0.809506i	$-0.300265\pi$
$97$	11048.3			1.17422			0.587111	+	0.809506i	$0.300265\pi$
$98$		0			0
$99$	11386.5	−	11386.5i	1.16177	−	1.16177i
$100$		0			0
$101$	7543.12	−	7543.12i	0.739449	−	0.739449i	−0.233022	−	0.972471i	$-0.574861\pi$
$101$	7543.12	−	7543.12i	0.739449	−	0.739449i	0.972471	+	0.233022i	$0.0748615\pi$
$102$		0			0
$103$	6124.81			0.577322			0.288661	−	0.957431i	$-0.406790\pi$
$103$	6124.81			0.577322			0.288661	+	0.957431i	$0.406790\pi$
$104$		0			0
$105$		−	8081.75i		−	0.733039i
$106$		0			0
$107$	4636.79	+	4636.79i	0.404995	+	0.404995i	0.879989	−	0.474994i	$-0.157550\pi$
$107$	4636.79	+	4636.79i	0.404995	+	0.404995i	−0.474994	+	0.879989i	$0.657550\pi$
$108$		0			0
$109$	−15235.6	−	15235.6i	−1.28235	−	1.28235i	−0.939327	−	0.343022i	$-0.888549\pi$
$109$	−15235.6	−	15235.6i	−1.28235	−	1.28235i	−0.343022	−	0.939327i	$-0.611451\pi$
$110$		0			0
$111$		−	12922.1i		−	1.04879i
$112$		0			0
$113$	2902.13			0.227279			0.113639	−	0.993522i	$-0.463749\pi$
$113$	2902.13			0.227279			0.113639	+	0.993522i	$0.463749\pi$
$114$		0			0
$115$	−14014.4	+	14014.4i	−1.05969	+	1.05969i
$116$		0			0
$117$	6928.55	−	6928.55i	0.506140	−	0.506140i
$118$		0			0
$119$	2326.95			0.164321
$120$		0			0
$121$		−	7020.14i		−	0.479485i
$122$		0			0
$123$	−20771.6	−	20771.6i	−1.37296	−	1.37296i
$124$		0			0
$125$	12025.7	+	12025.7i	0.769644	+	0.769644i
$126$		0			0
$127$			3992.46i			0.247533i	0.992311	+	0.123766i	$0.0394974\pi$
$127$			3992.46i			0.247533i	−0.992311	+	0.123766i	$0.960503\pi$
$128$		0			0
$129$	4748.66			0.285359
$130$		0			0
$131$	16640.1	−	16640.1i	0.969645	−	0.969645i	−0.0299081	−	0.999553i	$-0.509521\pi$
$131$	16640.1	−	16640.1i	0.969645	−	0.969645i	0.999553	+	0.0299081i	$0.00952147\pi$
$132$		0			0
$133$	−3765.31	+	3765.31i	−0.212862	+	0.212862i
$134$		0			0
$135$	−34808.9			−1.90995
$136$		0			0
$137$			10746.6i			0.572573i	0.958144	+	0.286286i	$0.0924209\pi$
$137$			10746.6i			0.572573i	−0.958144	+	0.286286i	$0.907579\pi$
$138$		0			0
$139$	−7583.76	−	7583.76i	−0.392514	−	0.392514i	0.483069	−	0.875582i	$-0.339522\pi$
$139$	−7583.76	−	7583.76i	−0.392514	−	0.392514i	−0.875582	+	0.483069i	$0.839522\pi$
$140$		0			0
$141$	18432.5	+	18432.5i	0.927140	+	0.927140i
$142$		0			0
$143$			4637.20i			0.226769i
$144$		0			0
$145$	10226.4			0.486390
$146$		0			0
$147$	−21014.0	+	21014.0i	−0.972464	+	0.972464i
$148$		0			0
$149$	−3385.37	+	3385.37i	−0.152487	+	0.152487i	−0.779228	−	0.626741i	$-0.784389\pi$
$149$	−3385.37	+	3385.37i	−0.152487	+	0.152487i	0.626741	+	0.779228i	$0.284389\pi$
$150$		0			0
$151$	−21697.8			−0.951617			−0.475809	−	0.879549i	$-0.657845\pi$
$151$	−21697.8			−0.951617			−0.475809	+	0.879549i	$0.657845\pi$
$152$		0			0
$153$		−	17869.0i		−	0.763341i
$154$		0			0
$155$	−3473.49	−	3473.49i	−0.144578	−	0.144578i
$156$		0			0
$157$	−14212.7	−	14212.7i	−0.576603	−	0.576603i	0.357363	−	0.933966i	$-0.383676\pi$
$157$	−14212.7	−	14212.7i	−0.576603	−	0.576603i	−0.933966	+	0.357363i	$0.883676\pi$
$158$		0			0
$159$		−	51479.0i		−	2.03627i
$160$		0			0
$161$	−23054.9			−0.889430
$162$		0			0
$163$	−7450.28	+	7450.28i	−0.280412	+	0.280412i	−0.833273	−	0.552861i	$-0.813536\pi$
$163$	−7450.28	+	7450.28i	−0.280412	+	0.280412i	0.552861	+	0.833273i	$0.313536\pi$
$164$		0			0
$165$	20768.4	−	20768.4i	0.762841	−	0.762841i
$166$		0			0
$167$	3997.25			0.143327			0.0716635	−	0.997429i	$-0.477169\pi$
$167$	3997.25			0.143327			0.0716635	+	0.997429i	$0.477169\pi$
$168$		0			0
$169$		−	25739.3i		−	0.901205i
$170$		0			0
$171$	28914.4	+	28914.4i	0.988832	+	0.988832i
$172$		0			0
$173$	16996.8	+	16996.8i	0.567903	+	0.567903i	0.931540	−	0.363638i	$-0.118465\pi$
$173$	16996.8	+	16996.8i	0.567903	+	0.567903i	−0.363638	+	0.931540i	$0.618465\pi$
$174$		0			0
$175$			4770.26i			0.155764i
$176$		0			0
$177$	54219.8			1.73066
$178$		0			0
$179$	24121.3	−	24121.3i	0.752826	−	0.752826i	−0.222180	−	0.975006i	$-0.571317\pi$
$179$	24121.3	−	24121.3i	0.752826	−	0.752826i	0.975006	+	0.222180i	$0.0713173\pi$
$180$		0			0
$181$	−13837.8	+	13837.8i	−0.422386	+	0.422386i	−0.886025	−	0.463638i	$-0.846544\pi$
$181$	−13837.8	+	13837.8i	−0.422386	+	0.422386i	0.463638	+	0.886025i	$0.346544\pi$
$182$		0			0
$183$	102385.			3.05726
$184$		0			0
$185$		−	16377.6i		−	0.478526i
$186$		0			0
$187$	5979.77	+	5979.77i	0.171002	+	0.171002i
$188$		0			0
$189$	−28632.0	−	28632.0i	−0.801544	−	0.801544i
$190$		0			0
$191$		−	11717.4i		−	0.321193i	−0.987020	−	0.160596i	$-0.948658\pi$
$191$		−	11717.4i		−	0.321193i	0.987020	−	0.160596i	$-0.0513417\pi$
$192$		0			0
$193$	−68633.2			−1.84255			−0.921276	−	0.388910i	$-0.872852\pi$
$193$	−68633.2			−1.84255			−0.921276	+	0.388910i	$0.872852\pi$
$194$		0			0
$195$	12637.3	−	12637.3i	0.332341	−	0.332341i
$196$		0			0
$197$	22885.3	−	22885.3i	0.589689	−	0.589689i	−0.347858	−	0.937547i	$-0.613091\pi$
$197$	22885.3	−	22885.3i	0.589689	−	0.589689i	0.937547	+	0.347858i	$0.113091\pi$
$198$		0			0
$199$	−59936.9			−1.51352			−0.756761	−	0.653692i	$-0.773219\pi$
$199$	−59936.9			−1.51352			−0.756761	+	0.653692i	$0.773219\pi$
$200$		0			0
$201$			92060.9i			2.27868i
$202$		0			0
$203$	8411.65	+	8411.65i	0.204122	+	0.204122i
$204$		0			0
$205$	−26326.0	−	26326.0i	−0.626436	−	0.626436i
$206$		0			0
$207$			177042.i			4.13177i
$208$		0			0
$209$	−19352.1			−0.443032
$210$		0			0
$211$	−12558.8	+	12558.8i	−0.282086	+	0.282086i	−0.833941	−	0.551854i	$-0.813920\pi$
$211$	−12558.8	+	12558.8i	−0.282086	+	0.282086i	0.551854	+	0.833941i	$0.313920\pi$
$212$		0			0
$213$	−56789.2	+	56789.2i	−1.25172	+	1.25172i
$214$		0			0
$215$	6018.47			0.130199
$216$		0			0
$217$		−	5714.22i		−	0.121349i
$218$		0			0
$219$	−30548.4	−	30548.4i	−0.636943	−	0.636943i
$220$		0			0
$221$	3638.61	+	3638.61i	0.0744992	+	0.0744992i
$222$		0			0
$223$		−	22761.5i		−	0.457711i	−0.973460	−	0.228856i	$-0.926502\pi$
$223$		−	22761.5i		−	0.457711i	0.973460	−	0.228856i	$-0.0734983\pi$
$224$		0			0
$225$	36631.6			0.723586
$226$		0			0
$227$	6480.30	−	6480.30i	0.125760	−	0.125760i	−0.641425	−	0.767186i	$-0.721657\pi$
$227$	6480.30	−	6480.30i	0.125760	−	0.125760i	0.767186	+	0.641425i	$0.221657\pi$
$228$		0			0
$229$	−36068.6	+	36068.6i	−0.687795	+	0.687795i	−0.961744	−	0.273949i	$-0.911670\pi$
$229$	−36068.6	+	36068.6i	−0.687795	+	0.687795i	0.273949	+	0.961744i	$0.411670\pi$
$230$		0			0
$231$	34165.9			0.640278
$232$		0			0
$233$			68226.4i			1.25673i	0.777920	+	0.628363i	$0.216275\pi$
$233$			68226.4i			1.25673i	−0.777920	+	0.628363i	$0.783725\pi$
$234$		0			0
$235$	23361.4	+	23361.4i	0.423022	+	0.423022i
$236$		0			0
$237$	101295.	+	101295.i	1.80340	+	1.80340i
$238$		0			0
$239$		−	100556.i		−	1.76040i	−0.474599	−	0.880202i	$-0.657407\pi$
$239$		−	100556.i		−	1.76040i	0.474599	−	0.880202i	$-0.342593\pi$
$240$		0			0
$241$	−35563.1			−0.612302			−0.306151	−	0.951983i	$-0.599041\pi$
$241$	−35563.1			−0.612302			−0.306151	+	0.951983i	$0.599041\pi$
$242$		0			0
$243$	−47732.3	+	47732.3i	−0.808351	+	0.808351i
$244$		0			0
$245$	−26633.2	+	26633.2i	−0.443702	+	0.443702i
$246$		0			0
$247$	−11775.5			−0.193013
$248$		0			0
$249$			5258.84i			0.0848186i
$250$		0			0
$251$	−29206.3	−	29206.3i	−0.463585	−	0.463585i	0.436244	−	0.899829i	$-0.356309\pi$
$251$	−29206.3	−	29206.3i	−0.463585	−	0.463585i	−0.899829	+	0.436244i	$0.856309\pi$
$252$		0			0
$253$	−59246.1	−	59246.1i	−0.925591	−	0.925591i
$254$		0			0
$255$		−	32592.1i		−	0.501224i
$256$		0			0
$257$	2932.77			0.0444029			0.0222015	−	0.999754i	$-0.492932\pi$
$257$	2932.77			0.0444029			0.0222015	+	0.999754i	$0.492932\pi$
$258$		0			0
$259$	13471.3	−	13471.3i	0.200821	−	0.200821i
$260$		0			0
$261$	64594.4	−	64594.4i	0.948230	−	0.948230i
$262$		0			0
$263$	−23253.5			−0.336184			−0.168092	−	0.985771i	$-0.553761\pi$
$263$	−23253.5			−0.336184			−0.168092	+	0.985771i	$0.553761\pi$
$264$		0			0
$265$		−	65244.7i		−	0.929081i
$266$		0			0
$267$	122083.	+	122083.i	1.71251	+	1.71251i
$268$		0			0
$269$	−56836.3	−	56836.3i	−0.785455	−	0.785455i	0.195290	−	0.980745i	$-0.437435\pi$
$269$	−56836.3	−	56836.3i	−0.785455	−	0.785455i	−0.980745	+	0.195290i	$0.937435\pi$
$270$		0			0
$271$			91679.6i			1.24834i	0.781287	+	0.624172i	$0.214564\pi$
$271$			91679.6i			1.24834i	−0.781287	+	0.624172i	$0.785436\pi$
$272$		0			0
$273$	20789.5			0.278945
$274$		0			0
$275$	−12258.5	+	12258.5i	−0.162096	+	0.162096i
$276$		0			0
$277$	75831.0	−	75831.0i	0.988297	−	0.988297i	−0.0116353	−	0.999932i	$-0.503704\pi$
$277$	75831.0	−	75831.0i	0.988297	−	0.988297i	0.999932	+	0.0116353i	$0.00370370\pi$
$278$		0			0
$279$	−43880.4			−0.563718
$280$		0			0
$281$		−	77682.2i		−	0.983805i	−0.870650	−	0.491903i	$-0.836302\pi$
$281$		−	77682.2i		−	0.983805i	0.870650	−	0.491903i	$-0.163698\pi$
$282$		0			0
$283$	−43834.7	−	43834.7i	−0.547325	−	0.547325i	0.378341	−	0.925666i	$-0.376495\pi$
$283$	−43834.7	−	43834.7i	−0.547325	−	0.547325i	−0.925666	+	0.378341i	$0.876495\pi$
$284$		0			0
$285$	52738.3	+	52738.3i	0.649286	+	0.649286i
$286$		0			0
$287$		−	43308.7i		−	0.525788i
$288$		0			0
$289$	−74136.9			−0.887643
$290$		0			0
$291$	127286.	−	127286.i	1.50312	−	1.50312i
$292$		0			0
$293$	−61916.9	+	61916.9i	−0.721231	+	0.721231i	−0.968856	−	0.247625i	$-0.920350\pi$
$293$	−61916.9	+	61916.9i	−0.721231	+	0.721231i	0.247625	+	0.968856i	$0.420350\pi$
$294$		0			0
$295$	68718.4			0.789639
$296$		0			0
$297$		−	147156.i		−	1.66826i
$298$		0			0
$299$	−36050.5	−	36050.5i	−0.403245	−	0.403245i
$300$		0			0
$301$	4950.47	+	4950.47i	0.0546404	+	0.0546404i
$302$		0			0
$303$		−	173807.i		−	1.89313i
$304$		0			0
$305$	129763.			1.39492
$306$		0			0
$307$	−99698.5	+	99698.5i	−1.05782	+	1.05782i	−0.0595972	+	0.998223i	$0.518982\pi$
$307$	−99698.5	+	99698.5i	−1.05782	+	1.05782i	−0.998223	+	0.0595972i	$0.981018\pi$
$308$		0			0
$309$	70563.1	−	70563.1i	0.739028	−	0.739028i
$310$		0			0
$311$	127678.			1.32006			0.660031	−	0.751238i	$-0.270543\pi$
$311$	127678.			1.32006			0.660031	+	0.751238i	$0.270543\pi$
$312$		0			0
$313$		−	24132.5i		−	0.246328i	−0.992386	−	0.123164i	$-0.960696\pi$
$313$		−	24132.5i		−	0.246328i	0.992386	−	0.123164i	$-0.0393042\pi$
$314$		0			0
$315$	−64698.5	−	64698.5i	−0.652039	−	0.652039i
$316$		0			0
$317$	63739.0	+	63739.0i	0.634289	+	0.634289i	0.949141	−	0.314852i	$-0.101955\pi$
$317$	63739.0	+	63739.0i	0.634289	+	0.634289i	−0.314852	+	0.949141i	$0.601955\pi$
$318$		0			0
$319$			43232.3i			0.424841i
$320$		0			0
$321$	106840.			1.03687
$322$		0			0
$323$	−15184.8	+	15184.8i	−0.145547	+	0.145547i
$324$		0			0
$325$	−7459.16	+	7459.16i	−0.0706193	+	0.0706193i
$326$		0			0
$327$	−351055.			−3.28306
$328$		0			0
$329$			38431.6i			0.355056i
$330$		0			0
$331$	−111266.	−	111266.i	−1.01556	−	1.01556i	−0.999877	−	0.0156868i	$-0.995007\pi$
$331$	−111266.	−	111266.i	−1.01556	−	1.01556i	−0.0156868	−	0.999877i	$-0.504993\pi$
$332$		0			0
$333$	−103448.	−	103448.i	−0.932899	−	0.932899i
$334$		0			0
$335$			116678.i			1.03968i
$336$		0			0
$337$	−89183.5			−0.785280			−0.392640	−	0.919692i	$-0.628438\pi$
$337$	−89183.5			−0.785280			−0.392640	+	0.919692i	$0.628438\pi$
$338$		0			0
$339$	33435.0	−	33435.0i	0.290939	−	0.290939i
$340$		0			0
$341$	14684.3	−	14684.3i	0.126283	−	0.126283i
$342$		0			0
$343$	−101488.			−0.862637
$344$		0			0
$345$			322915.i			2.71300i
$346$		0			0
$347$	−17075.7	−	17075.7i	−0.141814	−	0.141814i	0.632635	−	0.774450i	$-0.281973\pi$
$347$	−17075.7	−	17075.7i	−0.141814	−	0.141814i	−0.774450	+	0.632635i	$0.781973\pi$
$348$		0			0
$349$	25961.7	+	25961.7i	0.213149	+	0.213149i	0.805604	−	0.592455i	$-0.201841\pi$
$349$	25961.7	+	25961.7i	0.213149	+	0.213149i	−0.592455	+	0.805604i	$0.701841\pi$
$350$		0			0
$351$		−	89542.5i		−	0.726800i
$352$		0			0
$353$	221897.			1.78075			0.890374	−	0.455230i	$-0.150443\pi$
$353$	221897.			1.78075			0.890374	+	0.455230i	$0.150443\pi$
$354$		0			0
$355$	−71974.9	+	71974.9i	−0.571116	+	0.571116i
$356$		0			0
$357$	26808.5	−	26808.5i	0.210347	−	0.210347i
$358$		0			0
$359$	106831.			0.828908			0.414454	−	0.910070i	$-0.363973\pi$
$359$	106831.			0.828908			0.414454	+	0.910070i	$0.363973\pi$
$360$		0			0
$361$			81179.1i			0.622917i
$362$		0			0
$363$	−80878.1	−	80878.1i	−0.613787	−	0.613787i
$364$		0			0
$365$	−38717.2	−	38717.2i	−0.290615	−	0.290615i
$366$		0			0
$367$			79074.9i			0.587093i	0.955945	+	0.293546i	$0.0948355\pi$
$367$			79074.9i			0.587093i	−0.955945	+	0.293546i	$0.905164\pi$
$368$		0			0
$369$	−332574.			−2.44250
$370$		0			0
$371$	53666.8	−	53666.8i	0.389904	−	0.389904i
$372$		0			0
$373$	86341.4	−	86341.4i	0.620585	−	0.620585i	−0.325096	−	0.945681i	$-0.605397\pi$
$373$	86341.4	−	86341.4i	0.620585	−	0.620585i	0.945681	+	0.325096i	$0.105397\pi$
$374$		0			0
$375$	277093.			1.97044
$376$		0			0
$377$			26306.3i			0.185087i
$378$		0			0
$379$	168223.	+	168223.i	1.17114	+	1.17114i	0.981939	+	0.189199i	$0.0605890\pi$
$379$	168223.	+	168223.i	1.17114	+	1.17114i	0.189199	+	0.981939i	$0.439411\pi$
$380$		0			0
$381$	45996.6	+	45996.6i	0.316866	+	0.316866i
$382$		0			0
$383$			22177.8i			0.151189i	0.997139	+	0.0755946i	$0.0240855\pi$
$383$			22177.8i			0.151189i	−0.997139	+	0.0755946i	$0.975915\pi$
$384$		0			0
$385$	43301.9			0.292137
$386$		0			0
$387$	38015.4	−	38015.4i	0.253827	−	0.253827i
$388$		0			0
$389$	−163109.	+	163109.i	−1.07790	+	1.07790i	−0.0812004	+	0.996698i	$0.525875\pi$
$389$	−163109.	+	163109.i	−1.07790	+	1.07790i	−0.996698	+	0.0812004i	$0.974125\pi$
$390$		0			0
$391$	−92975.9			−0.608159
$392$		0			0
$393$		−	383416.i		−	2.48248i
$394$		0			0
$395$	128382.	+	128382.i	0.822831	+	0.822831i
$396$		0			0
$397$	−110463.	−	110463.i	−0.700868	−	0.700868i	0.263729	−	0.964597i	$-0.415047\pi$
$397$	−110463.	−	110463.i	−0.700868	−	0.700868i	−0.964597	+	0.263729i	$0.915047\pi$
$398$		0			0
$399$			86759.4i			0.544968i
$400$		0			0
$401$	43913.8			0.273094			0.136547	−	0.990634i	$-0.456399\pi$
$401$	43913.8			0.273094			0.136547	+	0.990634i	$0.456399\pi$
$402$		0			0
$403$	8935.22	−	8935.22i	0.0550168	−	0.0550168i
$404$		0			0
$405$	−182862.	+	182862.i	−1.11484	+	1.11484i
$406$		0			0
$407$	69236.7			0.417972
$408$		0			0
$409$		−	188666.i		−	1.12784i	−0.825830	−	0.563919i	$-0.809293\pi$
$409$		−	188666.i		−	1.12784i	0.825830	−	0.563919i	$-0.190707\pi$
$410$		0			0
$411$	123810.	+	123810.i	0.732948	+	0.732948i
$412$		0			0
$413$	56524.0	+	56524.0i	0.331385	+	0.331385i
$414$		0			0
$415$			6665.07i			0.0386998i
$416$		0			0
$417$	−174743.			−1.00491
$418$		0			0
$419$	−88556.3	+	88556.3i	−0.504419	+	0.504419i	−0.912808	−	0.408389i	$-0.866091\pi$
$419$	−88556.3	+	88556.3i	−0.504419	+	0.504419i	0.408389	+	0.912808i	$0.366091\pi$
$420$		0			0
$421$	42983.4	−	42983.4i	0.242514	−	0.242514i	−0.575375	−	0.817889i	$-0.695144\pi$
$421$	42983.4	−	42983.4i	0.242514	−	0.242514i	0.817889	+	0.575375i	$0.195144\pi$
$422$		0			0
$423$	295123.			1.64938
$424$		0			0
$425$			19237.5i			0.106505i
$426$		0			0
$427$	106736.	+	106736.i	0.585403	+	0.585403i
$428$		0			0
$429$	53424.5	+	53424.5i	0.290286	+	0.290286i
$430$		0			0
$431$		−	163696.i		−	0.881219i	−0.897699	−	0.440609i	$-0.854762\pi$
$431$		−	163696.i		−	0.881219i	0.897699	−	0.440609i	$-0.145238\pi$
$432$		0			0
$433$	49710.2			0.265137			0.132568	−	0.991174i	$-0.457678\pi$
$433$	49710.2			0.265137			0.132568	+	0.991174i	$0.457678\pi$
$434$		0			0
$435$	117816.	−	117816.i	0.622626	−	0.622626i
$436$		0			0
$437$	150447.	−	150447.i	0.787809	−	0.787809i
$438$		0			0
$439$	−182166.			−0.945233			−0.472617	−	0.881268i	$-0.656690\pi$
$439$	−182166.			−0.945233			−0.472617	+	0.881268i	$0.656690\pi$
$440$		0			0
$441$			336455.i			1.73002i
$442$		0			0
$443$	−3141.28	−	3141.28i	−0.0160066	−	0.0160066i	0.699058	−	0.715065i	$-0.253603\pi$
$443$	−3141.28	−	3141.28i	−0.0160066	−	0.0160066i	−0.715065	+	0.699058i	$0.753603\pi$
$444$		0			0
$445$	154729.	+	154729.i	0.781359	+	0.781359i
$446$		0			0
$447$			78004.9i			0.390397i
$448$		0			0
$449$	−108328.			−0.537341			−0.268670	−	0.963232i	$-0.586584\pi$
$449$	−108328.			−0.537341			−0.268670	+	0.963232i	$0.586584\pi$
$450$		0			0
$451$	111294.	−	111294.i	0.547165	−	0.547165i
$452$		0			0
$453$	−249978.	+	249978.i	−1.21816	+	1.21816i
$454$		0			0
$455$	26348.7			0.127273
$456$		0			0
$457$			220908.i			1.05774i	0.848703	+	0.528870i	$0.177384\pi$
$457$			220908.i			1.05774i	−0.848703	+	0.528870i	$0.822616\pi$
$458$		0			0
$459$	−115467.	−	115467.i	−0.548066	−	0.548066i
$460$		0			0
$461$	137539.	+	137539.i	0.647176	+	0.647176i	0.952310	−	0.305133i	$-0.0987010\pi$
$461$	137539.	+	137539.i	0.647176	+	0.647176i	−0.305133	+	0.952310i	$0.598701\pi$
$462$		0			0
$463$			53332.6i			0.248789i	0.992233	+	0.124394i	$0.0396988\pi$
$463$			53332.6i			0.248789i	−0.992233	+	0.124394i	$0.960301\pi$
$464$		0			0
$465$	−80035.3			−0.370148
$466$		0			0
$467$	−207164.	+	207164.i	−0.949908	+	0.949908i	−0.998804	−	0.0488961i	$-0.984430\pi$
$467$	−207164.	+	207164.i	−0.949908	+	0.949908i	0.0488961	+	0.998804i	$0.484430\pi$
$468$		0			0
$469$	−95973.3	+	95973.3i	−0.436320	+	0.436320i
$470$		0			0
$471$	−327485.			−1.47622
$472$		0			0
$473$			25443.3i			0.113724i
$474$		0			0
$475$	−31128.8	−	31128.8i	−0.137967	−	0.137967i
$476$		0			0
$477$	−412116.	−	412116.i	−1.81127	−	1.81127i
$478$		0			0
$479$			269434.i			1.17430i	0.809477	+	0.587152i	$0.199751\pi$
$479$			269434.i			1.17430i	−0.809477	+	0.587152i	$0.800249\pi$
$480$		0			0
$481$	42129.6			0.182095
$482$		0			0
$483$	−265613.	+	265613.i	−1.13856	+	1.13856i
$484$		0			0
$485$	161322.	−	161322.i	0.685821	−	0.685821i
$486$		0			0
$487$	114893.			0.484436			0.242218	−	0.970222i	$-0.422125\pi$
$487$	114893.			0.484436			0.242218	+	0.970222i	$0.422125\pi$
$488$		0			0
$489$			171667.i			0.717910i
$490$		0			0
$491$	83485.8	+	83485.8i	0.346298	+	0.346298i	0.858728	−	0.512431i	$-0.171255\pi$
$491$	83485.8	+	83485.8i	0.346298	+	0.346298i	−0.512431	+	0.858728i	$0.671255\pi$
$492$		0			0
$493$	33922.5	+	33922.5i	0.139571	+	0.139571i
$494$		0			0
$495$		−	332522.i		−	1.35710i
$496$		0			0
$497$	−118405.			−0.479356
$498$		0			0
$499$	−8291.04	+	8291.04i	−0.0332972	+	0.0332972i	−0.723559	−	0.690262i	$-0.757495\pi$
$499$	−8291.04	+	8291.04i	−0.0332972	+	0.0332972i	0.690262	+	0.723559i	$0.257495\pi$
$500$		0			0
$501$	46051.8	−	46051.8i	0.183472	−	0.183472i
$502$		0			0
$503$	−302384.			−1.19515			−0.597575	−	0.801813i	$-0.703869\pi$
$503$	−302384.			−1.19515			−0.597575	+	0.801813i	$0.703869\pi$
$504$		0			0
$505$		−	220283.i		−	0.863770i
$506$		0			0
$507$	−296539.	−	296539.i	−1.15363	−	1.15363i
$508$		0			0
$509$	41954.6	+	41954.6i	0.161936	+	0.161936i	0.783424	−	0.621488i	$-0.213471\pi$
$509$	41954.6	+	41954.6i	0.161936	+	0.161936i	−0.621488	+	0.783424i	$0.713471\pi$
$510$		0			0
$511$		−	63693.3i		−	0.243923i
$512$		0			0
$513$	373681.			1.41993
$514$		0			0
$515$	89431.9	−	89431.9i	0.337193	−	0.337193i
$516$		0			0
$517$	−98761.0	+	98761.0i	−0.369492	+	0.369492i
$518$		0			0
$519$	391635.			1.45394
$520$		0			0
$521$			16852.7i			0.0620860i	0.999518	+	0.0310430i	$0.00988289\pi$
$521$			16852.7i			0.0620860i	−0.999518	+	0.0310430i	$0.990117\pi$
$522$		0			0
$523$	−92911.9	−	92911.9i	−0.339678	−	0.339678i	0.516568	−	0.856246i	$-0.327209\pi$
$523$	−92911.9	−	92911.9i	−0.339678	−	0.339678i	−0.856246	+	0.516568i	$0.827209\pi$
$524$		0			0
$525$	54957.5	+	54957.5i	0.199392	+	0.199392i
$526$		0			0
$527$		−	23044.3i		−	0.0829741i
$528$		0			0
$529$	641343.			2.29181
$530$		0			0
$531$	434057.	−	434057.i	1.53942	−	1.53942i
$532$		0			0
$533$	67720.9	−	67720.9i	0.238379	−	0.238379i
$534$		0			0
$535$	135409.			0.473086
$536$		0			0
$537$		−	555796.i		−	1.92738i
$538$		0			0
$539$	−112593.	−	112593.i	−0.387554	−	0.387554i
$540$		0			0
$541$	40690.8	+	40690.8i	0.139028	+	0.139028i	0.773196	−	0.634168i	$-0.218657\pi$
$541$	40690.8	+	40690.8i	0.139028	+	0.139028i	−0.634168	+	0.773196i	$0.718657\pi$
$542$		0			0
$543$			318847.i			1.08139i
$544$		0			0
$545$	−444928.			−1.49795
$546$		0			0
$547$	222264.	−	222264.i	0.742839	−	0.742839i	−0.230284	−	0.973123i	$-0.573966\pi$
$547$	222264.	−	222264.i	0.742839	−	0.742839i	0.973123	+	0.230284i	$0.0739656\pi$
$548$		0			0
$549$	819641.	−	819641.i	2.71944	−	2.71944i
$550$		0			0
$551$	−109782.			−0.361600
$552$		0			0
$553$			211201.i			0.690629i
$554$		0			0
$555$	−188684.	−	188684.i	−0.612560	−	0.612560i
$556$		0			0
$557$	−223795.	−	223795.i	−0.721341	−	0.721341i	0.247537	−	0.968878i	$-0.420379\pi$
$557$	−223795.	−	223795.i	−0.721341	−	0.721341i	−0.968878	+	0.247537i	$0.920379\pi$
$558$		0			0
$559$			15481.9i			0.0495451i
$560$		0			0
$561$	137784.			0.437798
$562$		0			0
$563$	201474.	−	201474.i	0.635626	−	0.635626i	−0.313847	−	0.949474i	$-0.601618\pi$
$563$	201474.	−	201474.i	0.635626	−	0.635626i	0.949474	+	0.313847i	$0.101618\pi$
$564$		0			0
$565$	42375.6	−	42375.6i	0.132745	−	0.132745i
$566$		0			0
$567$	−300825.			−0.935724
$568$		0			0
$569$		−	473995.i		−	1.46403i	−0.681289	−	0.732014i	$-0.738580\pi$
$569$		−	473995.i		−	1.46403i	0.681289	−	0.732014i	$-0.261420\pi$
$570$		0			0
$571$	303262.	+	303262.i	0.930133	+	0.930133i	0.997714	−	0.0675806i	$-0.0215280\pi$
$571$	303262.	+	303262.i	0.930133	+	0.930133i	−0.0675806	+	0.997714i	$0.521528\pi$
$572$		0			0
$573$	−134995.	−	134995.i	−0.411158	−	0.411158i
$574$		0			0
$575$		−	190601.i		−	0.576486i
$576$		0			0
$577$	−340809.			−1.02367			−0.511834	−	0.859084i	$-0.671034\pi$
$577$	−340809.			−1.02367			−0.511834	+	0.859084i	$0.671034\pi$
$578$		0			0
$579$	−790714.	+	790714.i	−2.35864	+	2.35864i
$580$		0			0
$581$	−5482.33	+	5482.33i	−0.0162410	+	0.0162410i
$582$		0			0
$583$	275824.			0.811512
$584$		0			0
$585$		−	202336.i		−	0.591236i
$586$		0			0
$587$	−253433.	−	253433.i	−0.735507	−	0.735507i	0.236198	−	0.971705i	$-0.424099\pi$
$587$	−253433.	−	253433.i	−0.735507	−	0.735507i	−0.971705	+	0.236198i	$0.924099\pi$
$588$		0			0
$589$	37288.7	+	37288.7i	0.107485	+	0.107485i
$590$		0			0
$591$		−	527316.i		−	1.50972i
$592$		0			0
$593$	117236.			0.333390			0.166695	−	0.986009i	$-0.446691\pi$
$593$	117236.			0.333390			0.166695	+	0.986009i	$0.446691\pi$
$594$		0			0
$595$	33977.2	−	33977.2i	0.0959741	−	0.0959741i
$596$		0			0
$597$	−690526.	+	690526.i	−1.93745	+	1.93745i
$598$		0			0
$599$	−277087.			−0.772257			−0.386129	−	0.922445i	$-0.626188\pi$
$599$	−277087.			−0.772257			−0.386129	+	0.922445i	$0.626188\pi$
$600$		0			0
$601$			323876.i			0.896665i	0.893867	+	0.448333i	$0.147982\pi$
$601$			323876.i			0.896665i	−0.893867	+	0.448333i	$0.852018\pi$
$602$		0			0
$603$	736994.	+	736994.i	2.02689	+	2.02689i
$604$		0			0
$605$	−102505.	−	102505.i	−0.280050	−	0.280050i
$606$		0			0
$607$		−	715467.i		−	1.94184i	−0.239414	−	0.970918i	$-0.576955\pi$
$607$		−	715467.i		−	1.94184i	0.239414	−	0.970918i	$-0.423045\pi$
$608$		0			0
$609$	193819.			0.522591
$610$		0			0
$611$	−60094.8	+	60094.8i	−0.160974	+	0.160974i
$612$		0			0
$613$	−137200.	+	137200.i	−0.365117	+	0.365117i	−0.865693	−	0.500576i	$-0.833122\pi$
$613$	−137200.	+	137200.i	−0.365117	+	0.365117i	0.500576	+	0.865693i	$0.333122\pi$
$614$		0			0
$615$	−606596.			−1.60380
$616$		0			0
$617$			106650.i			0.280149i	0.990141	+	0.140074i	$0.0447342\pi$
$617$			106650.i			0.280149i	−0.990141	+	0.140074i	$0.955266\pi$
$618$		0			0
$619$	−373667.	−	373667.i	−0.975221	−	0.975221i	0.0244790	−	0.999700i	$-0.492207\pi$
$619$	−373667.	−	373667.i	−0.975221	−	0.975221i	−0.999700	+	0.0244790i	$0.992207\pi$
$620$		0			0
$621$	1.14402e6	+	1.14402e6i	2.96654	+	2.96654i
$622$		0			0
$623$			254543.i			0.655820i
$624$		0			0
$625$	227071.			0.581302
$626$		0			0
$627$	−222953.	+	222953.i	−0.567124	+	0.567124i
$628$		0			0
$629$	54327.1	−	54327.1i	0.137314	−	0.137314i
$630$		0			0
$631$	445762.			1.11955			0.559777	−	0.828644i	$-0.310887\pi$
$631$	445762.			1.11955			0.559777	+	0.828644i	$0.310887\pi$
$632$		0			0
$633$			289376.i			0.722195i
$634$		0			0
$635$	58296.2	+	58296.2i	0.144575	+	0.144575i
$636$		0			0
$637$	−68511.2	−	68511.2i	−0.168843	−	0.168843i
$638$		0			0
$639$			909253.i			2.22681i
$640$		0			0
$641$	−412550.			−1.00406			−0.502031	−	0.864850i	$-0.667414\pi$
$641$	−412550.			−1.00406			−0.502031	+	0.864850i	$0.667414\pi$
$642$		0			0
$643$	−71290.0	+	71290.0i	−0.172428	+	0.172428i	−0.788045	−	0.615617i	$-0.788907\pi$
$643$	−71290.0	+	71290.0i	−0.172428	+	0.172428i	0.615617	+	0.788045i	$0.288907\pi$
$644$		0			0
$645$	69338.0	−	69338.0i	0.166668	−	0.166668i
$646$		0			0
$647$	−138722.			−0.331388			−0.165694	−	0.986177i	$-0.552986\pi$
$647$	−138722.			−0.331388			−0.165694	+	0.986177i	$0.552986\pi$
$648$		0			0
$649$			290509.i			0.689716i
$650$		0			0
$651$	−65832.7	−	65832.7i	−0.155339	−	0.155339i
$652$		0			0
$653$	−467444.	−	467444.i	−1.09623	−	1.09623i	−0.994847	−	0.101387i	$-0.967672\pi$
$653$	−467444.	−	467444.i	−1.09623	−	1.09623i	−0.101387	−	0.994847i	$-0.532328\pi$
$654$		0			0
$655$		−	485943.i		−	1.13267i
$656$		0			0
$657$	−489111.			−1.13312
$658$		0			0
$659$	180573.	−	180573.i	0.415797	−	0.415797i	−0.467955	−	0.883752i	$-0.655009\pi$
$659$	180573.	−	180573.i	0.415797	−	0.415797i	0.883752	+	0.467955i	$0.155009\pi$
$660$		0			0
$661$	−142726.	+	142726.i	−0.326664	+	0.326664i	−0.851317	−	0.524652i	$-0.824195\pi$
$661$	−142726.	+	142726.i	−0.326664	+	0.326664i	0.524652	+	0.851317i	$0.324195\pi$
$662$		0			0
$663$	83840.0			0.190732
$664$		0			0
$665$			109959.i			0.248650i
$666$		0			0
$667$	−336097.	−	336097.i	−0.755462	−	0.755462i
$668$		0			0
$669$	−262232.	−	262232.i	−0.585914	−	0.585914i
$670$		0			0
$671$			548576.i			1.21841i
$672$		0			0
$673$	−272445.			−0.601517			−0.300759	−	0.953700i	$-0.597240\pi$
$673$	−272445.			−0.601517			−0.300759	+	0.953700i	$0.597240\pi$
$674$		0			0
$675$	236708.	−	236708.i	0.519523	−	0.519523i
$676$		0			0
$677$	−285404.	+	285404.i	−0.622706	+	0.622706i	−0.946222	−	0.323517i	$-0.895135\pi$
$677$	−285404.	+	285404.i	−0.622706	+	0.622706i	0.323517	+	0.946222i	$0.395135\pi$
$678$		0			0
$679$	265390.			0.575632
$680$		0			0
$681$		−	149317.i		−	0.321970i
$682$		0			0
$683$	186551.	+	186551.i	0.399904	+	0.399904i	0.878199	−	0.478295i	$-0.158745\pi$
$683$	186551.	+	186551.i	0.399904	+	0.399904i	−0.478295	+	0.878199i	$0.658745\pi$
$684$		0			0
$685$	156918.	+	156918.i	0.334419	+	0.334419i
$686$		0			0
$687$			831084.i			1.76089i
$688$		0			0
$689$	167836.			0.353546
$690$		0			0
$691$	544261.	−	544261.i	1.13986	−	1.13986i	0.151383	−	0.988475i	$-0.451627\pi$
$691$	544261.	−	544261.i	1.13986	−	1.13986i	0.988475	−	0.151383i	$-0.0483727\pi$
$692$		0			0
$693$	273515.	−	273515.i	0.569528	−	0.569528i
$694$		0			0
$695$	−221470.			−0.458506
$696$		0			0
$697$		−	174655.i		−	0.359514i
$698$		0			0
$699$	786027.	+	786027.i	1.60873	+	1.60873i
$700$		0			0
$701$	69213.2	+	69213.2i	0.140849	+	0.140849i	0.774015	−	0.633167i	$-0.218245\pi$
$701$	69213.2	+	69213.2i	0.140849	+	0.140849i	−0.633167	+	0.774015i	$0.718245\pi$
$702$		0			0
$703$			175817.i			0.355754i
$704$		0			0
$705$	538287.			1.08302
$706$		0			0
$707$	181193.	−	181193.i	0.362496	−	0.362496i
$708$		0			0
$709$	−133745.	+	133745.i	−0.266063	+	0.266063i	−0.827512	−	0.561448i	$-0.810244\pi$
$709$	−133745.	+	133745.i	−0.266063	+	0.266063i	0.561448	+	0.827512i	$0.310244\pi$
$710$		0			0
$711$	1.62184e6			3.20826
$712$		0			0
$713$			228318.i			0.449118i
$714$		0			0
$715$	67710.4	+	67710.4i	0.132447	+	0.132447i
$716$		0			0
$717$	−1.15849e6	−	1.15849e6i	−2.25349	−	2.25349i
$718$		0			0
$719$		−	762270.i		−	1.47452i	−0.675609	−	0.737261i	$-0.736119\pi$
$719$		−	762270.i		−	1.47452i	0.675609	−	0.737261i	$-0.263881\pi$
$720$		0			0
$721$	147124.			0.283017
$722$		0			0
$723$	−409718.	+	409718.i	−0.783805	+	0.783805i
$724$		0			0
$725$	−69541.2	+	69541.2i	−0.132302	+	0.132302i
$726$		0			0
$727$	664888.			1.25800			0.628999	−	0.777406i	$-0.283465\pi$
$727$	664888.			1.25800			0.628999	+	0.777406i	$0.283465\pi$
$728$		0			0
$729$			85436.8i			0.160764i
$730$		0			0
$731$	19964.3	+	19964.3i	0.0373610	+	0.0373610i
$732$		0			0
$733$	616942.	+	616942.i	1.14825	+	1.14825i	0.986897	+	0.161352i	$0.0515856\pi$
$733$	616942.	+	616942.i	1.14825	+	1.14825i	0.161352	+	0.986897i	$0.448414\pi$
$734$		0			0
$735$			613675.i			1.13596i
$736$		0			0
$737$	−493261.			−0.908117
$738$		0			0
$739$	−204895.	+	204895.i	−0.375182	+	0.375182i	−0.869360	−	0.494179i	$-0.835469\pi$
$739$	−204895.	+	204895.i	−0.375182	+	0.375182i	0.494179	+	0.869360i	$0.335469\pi$
$740$		0			0
$741$	−135664.	+	135664.i	−0.247075	+	0.247075i
$742$		0			0
$743$	−183598.			−0.332576			−0.166288	−	0.986077i	$-0.553178\pi$
$743$	−183598.			−0.332576			−0.166288	+	0.986077i	$0.553178\pi$
$744$		0			0
$745$			98863.7i			0.178125i
$746$		0			0
$747$	42099.7	+	42099.7i	0.0754462	+	0.0754462i
$748$		0			0
$749$	111380.	+	111380.i	0.198538	+	0.198538i
$750$		0			0
$751$		−	167996.i		−	0.297864i	−0.988847	−	0.148932i	$-0.952416\pi$
$751$		−	167996.i		−	0.297864i	0.988847	−	0.148932i	$-0.0475836\pi$
$752$		0			0
$753$	−672964.			−1.18687
$754$		0			0
$755$	−316823.	+	316823.i	−0.555805	+	0.555805i
$756$		0			0
$757$	414105.	−	414105.i	0.722634	−	0.722634i	−0.246507	−	0.969141i	$-0.579283\pi$
$757$	414105.	−	414105.i	0.722634	−	0.722634i	0.969141	+	0.246507i	$0.0792828\pi$
$758$		0			0
$759$	−1.36513e6			−2.36969
$760$		0			0
$761$			315375.i			0.544575i	0.962216	+	0.272287i	$0.0877801\pi$
$761$			315375.i			0.544575i	−0.962216	+	0.272287i	$0.912220\pi$
$762$		0			0
$763$	−365974.	−	365974.i	−0.628638	−	0.628638i
$764$		0			0
$765$	−260916.	−	260916.i	−0.445839	−	0.445839i
$766$		0			0
$767$			176771.i			0.300483i
$768$		0			0
$769$	156016.			0.263825			0.131913	−	0.991261i	$-0.457888\pi$
$769$	156016.			0.263825			0.131913	+	0.991261i	$0.457888\pi$
$770$		0			0
$771$	33788.0	−	33788.0i	0.0568400	−	0.0568400i
$772$		0			0
$773$	151026.	−	151026.i	0.252751	−	0.252751i	−0.569347	−	0.822098i	$-0.692804\pi$
$773$	151026.	−	151026.i	0.252751	−	0.252751i	0.822098	+	0.569347i	$0.192804\pi$
$774$		0			0
$775$	47240.9			0.0786529
$776$		0			0
$777$		−	310402.i		−	0.514142i
$778$		0			0
$779$	282615.	+	282615.i	0.465715	+	0.465715i
$780$		0			0
$781$	−304276.	−	304276.i	−0.498845	−	0.498845i
$782$		0			0
$783$		−	834798.i		−	1.36163i
$784$		0			0
$785$	−415056.			−0.673546
$786$		0			0
$787$	95574.5	−	95574.5i	0.154310	−	0.154310i	−0.625730	−	0.780040i	$-0.715199\pi$
$787$	95574.5	−	95574.5i	0.154310	−	0.154310i	0.780040	+	0.625730i	$0.215199\pi$
$788$		0			0
$789$	−267901.	+	267901.i	−0.430348	+	0.430348i
$790$		0			0
$791$	69711.8			0.111418
$792$		0			0
$793$			333802.i			0.530814i
$794$		0			0
$795$	−751676.	−	751676.i	−1.18931	−	1.18931i
$796$		0			0
$797$	497721.	+	497721.i	0.783555	+	0.783555i	0.980429	−	0.196874i	$-0.0630790\pi$
$797$	497721.	+	497721.i	0.783555	+	0.783555i	−0.196874	+	0.980429i	$0.563079\pi$
$798$		0			0
$799$			154987.i			0.242774i
$800$		0			0
$801$	1.95467e6			3.04656
$802$		0			0
$803$	163678.	−	163678.i	0.253840	−	0.253840i
$804$		0			0
$805$	−336638.	+	336638.i	−0.519484	+	0.519484i
$806$		0			0
$807$	−1.30961e6			−2.01092
$808$		0			0
$809$		−	363878.i		−	0.555979i	−0.960584	−	0.277990i	$-0.910332\pi$
$809$		−	363878.i		−	0.555979i	0.960584	−	0.277990i	$-0.0896681\pi$
$810$		0			0
$811$	−53046.1	−	53046.1i	−0.0806513	−	0.0806513i	0.665630	−	0.746282i	$-0.268163\pi$
$811$	−53046.1	−	53046.1i	−0.0806513	−	0.0806513i	−0.746282	+	0.665630i	$0.768163\pi$
$812$		0			0
$813$	1.05623e6	+	1.05623e6i	1.59800	+	1.59800i
$814$		0			0
$815$			217572.i			0.327557i
$816$		0			0
$817$	−64609.6			−0.0967950
$818$		0			0
$819$	166430.	−	166430.i	0.248122	−	0.248122i
$820$		0			0
$821$	540562.	−	540562.i	0.801972	−	0.801972i	−0.181432	−	0.983404i	$-0.558073\pi$
$821$	540562.	−	540562.i	0.801972	−	0.801972i	0.983404	+	0.181432i	$0.0580731\pi$
$822$		0			0
$823$	−956590.			−1.41230			−0.706148	−	0.708064i	$-0.749569\pi$
$823$	−956590.			−1.41230			−0.706148	+	0.708064i	$0.749569\pi$
$824$		0			0
$825$			282458.i			0.414998i
$826$		0			0
$827$	−83207.7	−	83207.7i	−0.121661	−	0.121661i	0.643655	−	0.765316i	$-0.277417\pi$
$827$	−83207.7	−	83207.7i	−0.121661	−	0.121661i	−0.765316	+	0.643655i	$0.777417\pi$
$828$		0			0
$829$	673529.	+	673529.i	0.980048	+	0.980048i	0.999805	−	0.0197565i	$-0.00628909\pi$
$829$	673529.	+	673529.i	0.980048	+	0.980048i	−0.0197565	+	0.999805i	$0.506289\pi$
$830$		0			0
$831$		−	1.74728e6i		−	2.53023i
$832$		0			0
$833$	−176694.			−0.254642
$834$		0			0
$835$	58366.2	−	58366.2i	0.0837121	−	0.0837121i
$836$		0			0
$837$	−283548.	+	283548.i	−0.404740	+	0.404740i
$838$		0			0
$839$	488503.			0.693975			0.346987	−	0.937870i	$-0.387205\pi$
$839$	488503.			0.693975			0.346987	+	0.937870i	$0.387205\pi$
$840$		0			0
$841$		−	462029.i		−	0.653247i
$842$		0			0
$843$	−894967.	−	894967.i	−1.25937	−	1.25937i
$844$		0			0
$845$	−375835.	−	375835.i	−0.526361	−	0.526361i
$846$		0			0
$847$		−	168631.i		−	0.235055i
$848$		0			0
$849$	−1.01003e6			−1.40126
$850$		0			0
$851$	−538260.	+	538260.i	−0.743247	+	0.743247i
$852$		0			0
$853$	462565.	−	462565.i	0.635733	−	0.635733i	−0.313767	−	0.949500i	$-0.601591\pi$
$853$	462565.	−	462565.i	0.635733	−	0.635733i	0.949500	+	0.313767i	$0.101591\pi$
$854$		0			0
$855$	844393.			1.15508
$856$		0			0
$857$		−	1.08100e6i		−	1.47185i	−0.677064	−	0.735924i	$-0.736748\pi$
$857$		−	1.08100e6i		−	1.47185i	0.677064	−	0.735924i	$-0.263252\pi$
$858$		0			0
$859$	911196.	+	911196.i	1.23488	+	1.23488i	0.962066	+	0.272816i	$0.0879549\pi$
$859$	911196.	+	911196.i	1.23488	+	1.23488i	0.272816	+	0.962066i	$0.412045\pi$
$860$		0			0
$861$	−498953.	−	498953.i	−0.673060	−	0.673060i
$862$		0			0
$863$			35108.9i			0.0471406i	0.999722	+	0.0235703i	$0.00750335\pi$
$863$			35108.9i			0.0471406i	−0.999722	+	0.0235703i	$0.992497\pi$
$864$		0			0
$865$	496359.			0.663382
$866$		0			0
$867$	−854121.	+	854121.i	−1.13627	+	1.13627i
$868$		0			0
$869$	−542740.	+	542740.i	−0.718707	+	0.718707i
$870$		0			0
$871$	−300143.			−0.395633
$872$		0			0
$873$		−	2.03797e6i		−	2.67405i
$874$		0			0
$875$	288868.	+	288868.i	0.377298	+	0.377298i
$876$		0			0
$877$	−134545.	−	134545.i	−0.174931	−	0.174931i	0.614211	−	0.789142i	$-0.289474\pi$
$877$	−134545.	−	134545.i	−0.174931	−	0.174931i	−0.789142	+	0.614211i	$0.789474\pi$
$878$		0			0
$879$			1.42667e6i			1.84649i
$880$		0			0
$881$	1.27287e6			1.63995			0.819975	−	0.572399i	$-0.193987\pi$
$881$	1.27287e6			1.63995			0.819975	+	0.572399i	$0.193987\pi$
$882$		0			0
$883$	484264.	−	484264.i	0.621098	−	0.621098i	−0.324714	−	0.945812i	$-0.605268\pi$
$883$	484264.	−	484264.i	0.621098	−	0.621098i	0.945812	+	0.324714i	$0.105268\pi$
$884$		0			0
$885$	791695.	−	791695.i	1.01081	−	1.01081i
$886$		0			0
$887$	66348.3			0.0843301			0.0421650	−	0.999111i	$-0.486574\pi$
$887$	66348.3			0.0843301			0.0421650	+	0.999111i	$0.486574\pi$
$888$		0			0
$889$			95902.7i			0.121347i
$890$		0			0
$891$	−773055.	−	773055.i	−0.973767	−	0.973767i
$892$		0			0
$893$	−250790.	−	250790.i	−0.314490	−	0.314490i
$894$		0			0
$895$		−	704418.i		−	0.879396i
$896$		0			0
$897$	−830667.			−1.03239
$898$		0			0
$899$	83302.4	−	83302.4i	0.103071	−	0.103071i
$900$		0			0
$901$	216428.	−	216428.i	0.266602	−	0.266602i
$902$		0			0
$903$	114067.			0.139890
$904$		0			0
$905$			404107.i			0.493401i
$906$		0			0
$907$	846133.	+	846133.i	1.02855	+	1.02855i	0.999580	+	0.0289661i	$0.00922147\pi$
$907$	846133.	+	846133.i	1.02855	+	1.02855i	0.0289661	+	0.999580i	$0.490779\pi$
$908$		0			0
$909$	−1.39141e6	−	1.39141e6i	−1.68394	−	1.68394i
$910$		0			0
$911$		−	133938.i		−	0.161386i	−0.996739	−	0.0806932i	$-0.974287\pi$
$911$		−	133938.i		−	0.161386i	0.996739	−	0.0806932i	$-0.0257134\pi$
$912$		0			0
$913$	−28176.8			−0.0338026
$914$		0			0
$915$	1.49498e6	−	1.49498e6i	1.78564	−	1.78564i
$916$		0			0
$917$	399711.	−	399711.i	0.475343	−	0.475343i
$918$		0			0
$919$	469228.			0.555589			0.277794	−	0.960641i	$-0.410397\pi$
$919$	469228.			0.555589			0.277794	+	0.960641i	$0.410397\pi$
$920$		0			0
$921$			2.29723e6i			2.70822i
$922$		0			0
$923$	−185148.	−	185148.i	−0.217328	−	0.217328i
$924$		0			0
$925$	111371.	+	111371.i	0.130163	+	0.130163i
$926$		0			0
$927$		−	1.12979e6i		−	1.31473i
$928$		0			0
$929$	728330.			0.843911			0.421955	−	0.906617i	$-0.361344\pi$
$929$	728330.			0.843911			0.421955	+	0.906617i	$0.361344\pi$
$930$		0			0
$931$	285913.	−	285913.i	0.329864	−	0.329864i
$932$		0			0
$933$	1.47096e6	−	1.47096e6i	1.68981	−	1.68981i
$934$		0			0
$935$	174628.			0.199752
$936$		0			0
$937$			572084.i			0.651599i	0.945439	+	0.325800i	$0.105634\pi$
$937$			572084.i			0.651599i	−0.945439	+	0.325800i	$0.894366\pi$
$938$		0			0
$939$	−278028.	−	278028.i	−0.315324	−	0.315324i
$940$		0			0
$941$	270062.	+	270062.i	0.304989	+	0.304989i	0.842962	−	0.537973i	$-0.180810\pi$
$941$	270062.	+	270062.i	0.304989	+	0.304989i	−0.537973	+	0.842962i	$0.680810\pi$
$942$		0			0
$943$			1.73044e6i			1.94596i
$944$		0			0
$945$	−836144.			−0.936305
$946$		0			0
$947$	−803359.	+	803359.i	−0.895797	+	0.895797i	−0.995061	−	0.0992642i	$-0.968351\pi$
$947$	−803359.	+	803359.i	−0.895797	+	0.895797i	0.0992642	+	0.995061i	$0.468351\pi$
$948$		0			0
$949$	99596.1	−	99596.1i	0.110588	−	0.110588i
$950$		0			0
$951$	1.46866e6			1.62390
$952$		0			0
$953$			188445.i			0.207491i	0.994604	+	0.103746i	$0.0330827\pi$
$953$			188445.i			0.207491i	−0.994604	+	0.103746i	$0.966917\pi$
$954$		0			0
$955$	−171093.	−	171093.i	−0.187597	−	0.187597i
$956$		0			0
$957$	498073.	+	498073.i	0.543837	+	0.543837i
$958$		0			0
$959$			258144.i			0.280689i
$960$		0			0
$961$	866932.			0.938725
$962$		0			0
$963$	855306.	−	855306.i	0.922293	−	0.922293i
$964$		0			0
$965$	−1.00215e6	+	1.00215e6i	−1.07617	+	1.07617i
$966$		0			0
$967$	−1.17554e6			−1.25715			−0.628573	−	0.777751i	$-0.716361\pi$
$967$	−1.17554e6			−1.25715			−0.628573	+	0.777751i	$0.716361\pi$
$968$		0			0
$969$			349883.i			0.372628i
$970$		0			0
$971$	−784226.	−	784226.i	−0.831769	−	0.831769i	0.155989	−	0.987759i	$-0.450143\pi$
$971$	−784226.	−	784226.i	−0.831769	−	0.831769i	−0.987759	+	0.155989i	$0.950143\pi$
$972$		0			0
$973$	−182169.	−	182169.i	−0.192420	−	0.192420i
$974$		0			0
$975$			171872.i			0.180799i
$976$		0			0
$977$	710097.			0.743924			0.371962	−	0.928248i	$-0.378685\pi$
$977$	710097.			0.743924			0.371962	+	0.928248i	$0.378685\pi$
$978$		0			0
$979$	−654120.	+	654120.i	−0.682483	+	0.682483i
$980$		0			0
$981$	−2.81037e6	+	2.81037e6i	−2.92029	+	2.92029i
$982$		0			0
$983$	−471799.			−0.488259			−0.244129	−	0.969743i	$-0.578502\pi$
$983$	−471799.			−0.488259			−0.244129	+	0.969743i	$0.578502\pi$
$984$		0			0
$985$		−	668322.i		−	0.688832i
$986$		0			0
$987$	442766.	+	442766.i	0.454506	+	0.454506i
$988$		0			0
$989$	−197801.	−	197801.i	−0.202226	−	0.202226i
$990$		0			0
$991$			1.06681e6i			1.08627i	0.839644	+	0.543137i	$0.182763\pi$
$991$			1.06681e6i			1.08627i	−0.839644	+	0.543137i	$0.817237\pi$
$992$		0			0
$993$	−2.56377e6			−2.60004
$994$		0			0
$995$	−875175.	+	875175.i	−0.883992	+	0.883992i
$996$		0			0
$997$	303115.	−	303115.i	0.304942	−	0.304942i	−0.538002	−	0.842944i	$-0.680821\pi$
$997$	303115.	−	303115.i	0.304942	−	0.304942i	0.842944	+	0.538002i	$0.180821\pi$
$998$		0			0
$999$	−1.33693e6			−1.33961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.f.a.95.7		14
4.3	odd	2		128.5.f.b.95.1		14
8.3	odd	2		16.5.f.a.3.5	✓	14
8.5	even	2		64.5.f.a.47.1		14
16.3	odd	4		64.5.f.a.15.1		14
16.5	even	4		128.5.f.b.31.1		14
16.11	odd	4	inner	128.5.f.a.31.7		14
16.13	even	4		16.5.f.a.11.5	yes	14
24.5	odd	2		576.5.m.a.559.6		14
24.11	even	2		144.5.m.a.19.3		14
48.29	odd	4		144.5.m.a.91.3		14
48.35	even	4		576.5.m.a.271.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.5	✓	14	8.3	odd	2
16.5.f.a.11.5	yes	14	16.13	even	4
64.5.f.a.15.1		14	16.3	odd	4
64.5.f.a.47.1		14	8.5	even	2
128.5.f.a.31.7		14	16.11	odd	4	inner
128.5.f.a.95.7		14	1.1	even	1	trivial
128.5.f.b.31.1		14	16.5	even	4
128.5.f.b.95.1		14	4.3	odd	2
144.5.m.a.19.3		14	24.11	even	2
144.5.m.a.91.3		14	48.29	odd	4
576.5.m.a.271.6		14	48.35	even	4
576.5.m.a.559.6		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)

\(f(q)\)	\(=\)	\(q+(11.5209 - 11.5209i) q^{3} +(14.6016 - 14.6016i) q^{5} +24.0210 q^{7} -184.461i q^{9} +O(q^{10})\)	\(q+(11.5209 - 11.5209i) q^{3} +(14.6016 - 14.6016i) q^{5} +24.0210 q^{7} -184.461i q^{9} +(61.7287 + 61.7287i) q^{11} +(37.5611 + 37.5611i) q^{13} -336.446i q^{15} +96.8718 q^{17} +(-156.751 + 156.751i) q^{19} +(276.742 - 276.742i) q^{21} -959.783 q^{23} +198.587i q^{25} +(-1191.96 - 1191.96i) q^{27} +(350.180 + 350.180i) q^{29} -237.885i q^{31} +1422.34 q^{33} +(350.744 - 350.744i) q^{35} +(560.815 - 560.815i) q^{37} +865.473 q^{39} -1802.95i q^{41} +(206.090 + 206.090i) q^{43} +(-2693.42 - 2693.42i) q^{45} +1599.92i q^{47} -1823.99 q^{49} +(1116.05 - 1116.05i) q^{51} +(2234.17 - 2234.17i) q^{53} +1802.67 q^{55} +3611.82i q^{57} +(2353.11 + 2353.11i) q^{59} +(4443.45 + 4443.45i) q^{61} -4430.92i q^{63} +1096.90 q^{65} +(-3995.40 + 3995.40i) q^{67} +(-11057.5 + 11057.5i) q^{69} -4929.25 q^{71} -2651.57i q^{73} +(2287.90 + 2287.90i) q^{75} +(1482.78 + 1482.78i) q^{77} +8792.34i q^{79} -12523.4 q^{81} +(-228.231 + 228.231i) q^{83} +(1414.48 - 1414.48i) q^{85} +8068.75 q^{87} +10596.7i q^{89} +(902.254 + 902.254i) q^{91} +(-2740.64 - 2740.64i) q^{93} +4577.63i q^{95} +11048.3 q^{97} +(11386.5 - 11386.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 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

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