LMFDB - Embedded newform 256.4.e.d.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,4,Mod(65,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("256.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	256.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.1044889615$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 242x^{12} + 13297x^{8} + 201600x^{4} + 331776 $ x^16 + 242x^12 + 13297x^8 + 201600*x^4 + 331776
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{40} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.2
Root			$-0.826679 + 0.826679i$ of defining polynomial
Character	$\chi$	$=$	256.193
Dual form			256.4.e.d.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.58521 + 3.58521i) q^{3} +(14.4583 + 14.4583i) q^{5} +31.2516i q^{7} +1.29254i q^{9} +(11.5113 + 11.5113i) q^{11} +(37.5976 - 37.5976i) q^{13} -103.672 q^{15} +38.4044 q^{17} +(14.1150 - 14.1150i) q^{19} +(-112.044 - 112.044i) q^{21} -15.4625i q^{23} +293.087i q^{25} +(-101.435 - 101.435i) q^{27} +(106.334 - 106.334i) q^{29} +55.7912 q^{31} -82.5410 q^{33} +(-451.846 + 451.846i) q^{35} +(-41.4116 - 41.4116i) q^{37} +269.591i q^{39} -4.35221i q^{41} +(109.547 + 109.547i) q^{43} +(-18.6879 + 18.6879i) q^{45} -484.096 q^{47} -633.663 q^{49} +(-137.688 + 137.688i) q^{51} +(-206.253 - 206.253i) q^{53} +332.869i q^{55} +101.210i q^{57} +(206.535 + 206.535i) q^{59} +(450.887 - 450.887i) q^{61} -40.3938 q^{63} +1087.20 q^{65} +(428.141 - 428.141i) q^{67} +(55.4364 + 55.4364i) q^{69} -848.499i q^{71} +739.630i q^{73} +(-1050.78 - 1050.78i) q^{75} +(-359.747 + 359.747i) q^{77} +331.933 q^{79} +692.431 q^{81} +(648.125 - 648.125i) q^{83} +(555.264 + 555.264i) q^{85} +762.460i q^{87} -519.978i q^{89} +(1174.99 + 1174.99i) q^{91} +(-200.023 + 200.023i) q^{93} +408.159 q^{95} -1289.64 q^{97} +(-14.8788 + 14.8788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{5} + 320 q^{13} - 384 q^{17} + 224 q^{21} + 928 q^{29} - 2432 q^{33} + 640 q^{37} + 896 q^{45} - 2832 q^{49} + 64 q^{53} + 1024 q^{61} + 2208 q^{65} + 32 q^{69} + 1056 q^{77} + 4208 q^{81}+ \cdots + 4480 q^{97}+O(q^{100}) $ 16 * q + 32 * q^5 + 320 * q^13 - 384 * q^17 + 224 * q^21 + 928 * q^29 - 2432 * q^33 + 640 * q^37 + 896 * q^45 - 2832 * q^49 + 64 * q^53 + 1024 * q^61 + 2208 * q^65 + 32 * q^69 + 1056 * q^77 + 4208 * q^81 + 1824 * q^85 - 3776 * q^93 + 4480 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.58521	+	3.58521i	−0.689974	+	0.689974i	−0.962226	−	0.272252i	$-0.912232\pi$
$3$	−3.58521	+	3.58521i	−0.689974	+	0.689974i	0.272252	+	0.962226i	$0.412232\pi$
$4$		0			0
$5$	14.4583	+	14.4583i	1.29319	+	1.29319i	0.932801	+	0.360392i	$0.117357\pi$
$5$	14.4583	+	14.4583i	1.29319	+	1.29319i	0.360392	+	0.932801i	$0.382643\pi$
$6$		0			0
$7$			31.2516i			1.68743i	0.536793	+	0.843714i	$0.319636\pi$
$7$			31.2516i			1.68743i	−0.536793	+	0.843714i	$0.680364\pi$
$8$		0			0
$9$			1.29254i			0.0478717i
$10$		0			0
$11$	11.5113	+	11.5113i	0.315527	+	0.315527i	0.847046	−	0.531519i	$-0.178379\pi$
$11$	11.5113	+	11.5113i	0.315527	+	0.315527i	−0.531519	+	0.847046i	$0.678379\pi$
$12$		0			0
$13$	37.5976	−	37.5976i	0.802131	−	0.802131i	−0.181298	−	0.983428i	$-0.558030\pi$
$13$	37.5976	−	37.5976i	0.802131	−	0.802131i	0.983428	+	0.181298i	$0.0580297\pi$
$14$		0			0
$15$	−103.672			−1.78454
$16$		0			0
$17$	38.4044			0.547908			0.273954	−	0.961743i	$-0.411668\pi$
$17$	38.4044			0.547908			0.273954	+	0.961743i	$0.411668\pi$
$18$		0			0
$19$	14.1150	−	14.1150i	0.170432	−	0.170432i	−0.616737	−	0.787169i	$-0.711546\pi$
$19$	14.1150	−	14.1150i	0.170432	−	0.170432i	0.787169	+	0.616737i	$0.211546\pi$
$20$		0			0
$21$	−112.044	−	112.044i	−1.16428	−	1.16428i
$22$		0			0
$23$		−	15.4625i		−	0.140181i	−0.997541	−	0.0700904i	$-0.977671\pi$
$23$		−	15.4625i		−	0.140181i	0.997541	−	0.0700904i	$-0.0223288\pi$
$24$		0			0
$25$			293.087i			2.34470i
$26$		0			0
$27$	−101.435	−	101.435i	−0.723004	−	0.723004i
$28$		0			0
$29$	106.334	−	106.334i	0.680888	−	0.680888i	−0.279312	−	0.960200i	$-0.590107\pi$
$29$	106.334	−	106.334i	0.680888	−	0.680888i	0.960200	+	0.279312i	$0.0901065\pi$
$30$		0			0
$31$	55.7912			0.323238			0.161619	−	0.986853i	$-0.448328\pi$
$31$	55.7912			0.323238			0.161619	+	0.986853i	$0.448328\pi$
$32$		0			0
$33$	−82.5410			−0.435411
$34$		0			0
$35$	−451.846	+	451.846i	−2.18217	+	2.18217i
$36$		0			0
$37$	−41.4116	−	41.4116i	−0.184001	−	0.184001i	0.609096	−	0.793097i	$-0.291532\pi$
$37$	−41.4116	−	41.4116i	−0.184001	−	0.184001i	−0.793097	+	0.609096i	$0.791532\pi$
$38$		0			0
$39$			269.591i			1.10690i
$40$		0			0
$41$		−	4.35221i		−	0.0165781i	−0.999966	−	0.00828903i	$-0.997361\pi$
$41$		−	4.35221i		−	0.0165781i	0.999966	−	0.00828903i	$-0.00263851\pi$
$42$		0			0
$43$	109.547	+	109.547i	0.388506	+	0.388506i	0.874154	−	0.485648i	$-0.161416\pi$
$43$	109.547	+	109.547i	0.388506	+	0.388506i	−0.485648	+	0.874154i	$0.661416\pi$
$44$		0			0
$45$	−18.6879	+	18.6879i	−0.0619073	+	0.0619073i
$46$		0			0
$47$	−484.096			−1.50240			−0.751199	−	0.660076i	$-0.770524\pi$
$47$	−484.096			−1.50240			−0.751199	+	0.660076i	$0.770524\pi$
$48$		0			0
$49$	−633.663			−1.84741
$50$		0			0
$51$	−137.688	+	137.688i	−0.378043	+	0.378043i
$52$		0			0
$53$	−206.253	−	206.253i	−0.534549	−	0.534549i	0.387374	−	0.921923i	$-0.373382\pi$
$53$	−206.253	−	206.253i	−0.534549	−	0.534549i	−0.921923	+	0.387374i	$0.873382\pi$
$54$		0			0
$55$			332.869i			0.816074i
$56$		0			0
$57$			101.210i			0.235187i
$58$		0			0
$59$	206.535	+	206.535i	0.455738	+	0.455738i	0.897254	−	0.441515i	$-0.145559\pi$
$59$	206.535	+	206.535i	0.455738	+	0.455738i	−0.441515	+	0.897254i	$0.645559\pi$
$60$		0			0
$61$	450.887	−	450.887i	0.946396	−	0.946396i	−0.0522385	−	0.998635i	$-0.516636\pi$
$61$	450.887	−	450.887i	0.946396	−	0.946396i	0.998635	+	0.0522385i	$0.0166356\pi$
$62$		0			0
$63$	−40.3938			−0.0807800
$64$		0			0
$65$	1087.20			2.07462
$66$		0			0
$67$	428.141	−	428.141i	0.780684	−	0.780684i	−0.199263	−	0.979946i	$-0.563855\pi$
$67$	428.141	−	428.141i	0.780684	−	0.780684i	0.979946	+	0.199263i	$0.0638547\pi$
$68$		0			0
$69$	55.4364	+	55.4364i	0.0967211	+	0.0967211i
$70$		0			0
$71$		−	848.499i		−	1.41829i	−0.705065	−	0.709143i	$-0.749082\pi$
$71$		−	848.499i		−	1.41829i	0.705065	−	0.709143i	$-0.250918\pi$
$72$		0			0
$73$			739.630i			1.18585i	0.805257	+	0.592926i	$0.202027\pi$
$73$			739.630i			1.18585i	−0.805257	+	0.592926i	$0.797973\pi$
$74$		0			0
$75$	−1050.78	−	1050.78i	−1.61778	−	1.61778i
$76$		0			0
$77$	−359.747	+	359.747i	−0.532429	+	0.532429i
$78$		0			0
$79$	331.933			0.472726			0.236363	−	0.971665i	$-0.424045\pi$
$79$	331.933			0.472726			0.236363	+	0.971665i	$0.424045\pi$
$80$		0			0
$81$	692.431			0.949837
$82$		0			0
$83$	648.125	−	648.125i	0.857119	−	0.857119i	−0.133878	−	0.990998i	$-0.542743\pi$
$83$	648.125	−	648.125i	0.857119	−	0.857119i	0.990998	+	0.133878i	$0.0427432\pi$
$84$		0			0
$85$	555.264	+	555.264i	0.708551	+	0.708551i
$86$		0			0
$87$			762.460i			0.939590i
$88$		0			0
$89$		−	519.978i		−	0.619299i	−0.950851	−	0.309649i	$-0.899788\pi$
$89$		−	519.978i		−	0.619299i	0.950851	−	0.309649i	$-0.100212\pi$
$90$		0			0
$91$	1174.99	+	1174.99i	1.35354	+	1.35354i
$92$		0			0
$93$	−200.023	+	200.023i	−0.223026	+	0.223026i
$94$		0			0
$95$	408.159			0.440802
$96$		0			0
$97$	−1289.64			−1.34993			−0.674966	−	0.737849i	$-0.735842\pi$
$97$	−1289.64			−1.34993			−0.674966	+	0.737849i	$0.735842\pi$
$98$		0			0
$99$	−14.8788	+	14.8788i	−0.0151048	+	0.0151048i
$100$		0			0
$101$	317.277	+	317.277i	0.312576	+	0.312576i	0.845907	−	0.533331i	$-0.179060\pi$
$101$	317.277	+	317.277i	0.312576	+	0.312576i	−0.533331	+	0.845907i	$0.679060\pi$
$102$		0			0
$103$		−	1437.94i		−	1.37558i	−0.725912	−	0.687788i	$-0.758582\pi$
$103$		−	1437.94i		−	1.37558i	0.725912	−	0.687788i	$-0.241418\pi$
$104$		0			0
$105$		−	3239.93i		−	3.01128i
$106$		0			0
$107$	338.313	+	338.313i	0.305663	+	0.305663i	0.843225	−	0.537562i	$-0.180654\pi$
$107$	338.313	+	338.313i	0.305663	+	0.305663i	−0.537562	+	0.843225i	$0.680654\pi$
$108$		0			0
$109$	−488.847	+	488.847i	−0.429569	+	0.429569i	−0.888482	−	0.458912i	$-0.848239\pi$
$109$	−488.847	+	488.847i	−0.429569	+	0.429569i	0.458912	+	0.888482i	$0.348239\pi$
$110$		0			0
$111$	296.939			0.253912
$112$		0			0
$113$	−641.182			−0.533782			−0.266891	−	0.963727i	$-0.585996\pi$
$113$	−641.182			−0.533782			−0.266891	+	0.963727i	$0.585996\pi$
$114$		0			0
$115$	223.562	−	223.562i	0.181281	−	0.181281i
$116$		0			0
$117$	48.5962	+	48.5962i	0.0383993	+	0.0383993i
$118$		0			0
$119$			1200.20i			0.924556i
$120$		0			0
$121$		−	1065.98i		−	0.800886i
$122$		0			0
$123$	15.6036	+	15.6036i	0.0114384	+	0.0114384i
$124$		0			0
$125$	−2430.26	+	2430.26i	−1.73895	+	1.73895i
$126$		0			0
$127$	2454.72			1.71513			0.857565	−	0.514376i	$-0.171976\pi$
$127$	2454.72			1.71513			0.857565	+	0.514376i	$0.171976\pi$
$128$		0			0
$129$	−785.498			−0.536118
$130$		0			0
$131$	−344.205	+	344.205i	−0.229568	+	0.229568i	−0.812512	−	0.582944i	$-0.801901\pi$
$131$	−344.205	+	344.205i	−0.229568	+	0.229568i	0.582944	+	0.812512i	$0.301901\pi$
$132$		0			0
$133$	441.117	+	441.117i	0.287591	+	0.287591i
$134$		0			0
$135$		−	2933.15i		−	1.86997i
$136$		0			0
$137$			2560.48i			1.59676i	0.602152	+	0.798382i	$0.294310\pi$
$137$			2560.48i			1.59676i	−0.602152	+	0.798382i	$0.705690\pi$
$138$		0			0
$139$	−1713.75	−	1713.75i	−1.04574	−	1.04574i	−0.998902	−	0.0468397i	$-0.985085\pi$
$139$	−1713.75	−	1713.75i	−1.04574	−	1.04574i	−0.0468397	−	0.998902i	$-0.514915\pi$
$140$		0			0
$141$	1735.59	−	1735.59i	1.03662	−	1.03662i
$142$		0			0
$143$	865.596			0.506187
$144$		0			0
$145$	3074.83			1.76104
$146$		0			0
$147$	2271.82	−	2271.82i	1.27467	−	1.27467i
$148$		0			0
$149$	−309.595	−	309.595i	−0.170222	−	0.170222i	0.616855	−	0.787077i	$-0.288406\pi$
$149$	−309.595	−	309.595i	−0.170222	−	0.170222i	−0.787077	+	0.616855i	$0.788406\pi$
$150$		0			0
$151$		−	2428.54i		−	1.30882i	−0.756139	−	0.654411i	$-0.772917\pi$
$151$		−	2428.54i		−	1.30882i	0.756139	−	0.654411i	$-0.227083\pi$
$152$		0			0
$153$			49.6391i			0.0262293i
$154$		0			0
$155$	806.648	+	806.648i	0.418010	+	0.418010i
$156$		0			0
$157$	−260.302	+	260.302i	−0.132321	+	0.132321i	−0.770165	−	0.637845i	$-0.779826\pi$
$157$	−260.302	+	260.302i	−0.132321	+	0.132321i	0.637845	+	0.770165i	$0.279826\pi$
$158$		0			0
$159$	1478.92			0.737650
$160$		0			0
$161$	483.229			0.236545
$162$		0			0
$163$	−861.313	+	861.313i	−0.413885	+	0.413885i	−0.883089	−	0.469205i	$-0.844541\pi$
$163$	−861.313	+	861.313i	−0.413885	+	0.413885i	0.469205	+	0.883089i	$0.344541\pi$
$164$		0			0
$165$	−1193.41	−	1193.41i	−0.563070	−	0.563070i
$166$		0			0
$167$			3541.18i			1.64087i	0.571742	+	0.820434i	$0.306268\pi$
$167$			3541.18i			1.64087i	−0.571742	+	0.820434i	$0.693732\pi$
$168$		0			0
$169$		−	630.160i		−	0.286827i
$170$		0			0
$171$	18.2441	+	18.2441i	0.00815885	+	0.00815885i
$172$		0			0
$173$	−160.444	+	160.444i	−0.0705106	+	0.0705106i	−0.741483	−	0.670972i	$-0.765877\pi$
$173$	−160.444	+	160.444i	−0.0705106	+	0.0705106i	0.670972	+	0.741483i	$0.265877\pi$
$174$		0			0
$175$	−9159.45			−3.95651
$176$		0			0
$177$	−1480.94			−0.628895
$178$		0			0
$179$	2085.04	−	2085.04i	0.870634	−	0.870634i	−0.121908	−	0.992541i	$-0.538901\pi$
$179$	2085.04	−	2085.04i	0.870634	−	0.870634i	0.992541	+	0.121908i	$0.0389012\pi$
$180$		0			0
$181$	1452.80	+	1452.80i	0.596607	+	0.596607i	0.939408	−	0.342801i	$-0.111376\pi$
$181$	1452.80	+	1452.80i	0.596607	+	0.596607i	−0.342801	+	0.939408i	$0.611376\pi$
$182$		0			0
$183$			3233.05i			1.30598i
$184$		0			0
$185$		−	1197.49i		−	0.475897i
$186$		0			0
$187$	442.086	+	442.086i	0.172880	+	0.172880i
$188$		0			0
$189$	3170.00	−	3170.00i	1.22002	−	1.22002i
$190$		0			0
$191$	1687.44			0.639261			0.319630	−	0.947542i	$-0.396441\pi$
$191$	1687.44			0.639261			0.319630	+	0.947542i	$0.396441\pi$
$192$		0			0
$193$	−495.873			−0.184941			−0.0924707	−	0.995715i	$-0.529476\pi$
$193$	−495.873			−0.184941			−0.0924707	+	0.995715i	$0.529476\pi$
$194$		0			0
$195$	−3897.83	+	3897.83i	−1.43143	+	1.43143i
$196$		0			0
$197$	−527.200	−	527.200i	−0.190667	−	0.190667i	0.605317	−	0.795984i	$-0.293046\pi$
$197$	−527.200	−	527.200i	−0.190667	−	0.190667i	−0.795984	+	0.605317i	$0.793046\pi$
$198$		0			0
$199$			1159.84i			0.413162i	0.978430	+	0.206581i	$0.0662336\pi$
$199$			1159.84i			0.413162i	−0.978430	+	0.206581i	$0.933766\pi$
$200$		0			0
$201$			3069.95i			1.07730i
$202$		0			0
$203$	3323.11	+	3323.11i	1.14895	+	1.14895i
$204$		0			0
$205$	62.9257	−	62.9257i	0.0214386	−	0.0214386i
$206$		0			0
$207$	19.9858			0.00671069
$208$		0			0
$209$	324.965			0.107552
$210$		0			0
$211$	−2944.23	+	2944.23i	−0.960611	+	0.960611i	−0.999253	−	0.0386422i	$-0.987697\pi$
$211$	−2944.23	+	2944.23i	−0.960611	+	0.960611i	0.0386422	+	0.999253i	$0.487697\pi$
$212$		0			0
$213$	3042.05	+	3042.05i	0.978581	+	0.978581i
$214$		0			0
$215$			3167.74i			1.00483i
$216$		0			0
$217$			1743.56i			0.545442i
$218$		0			0
$219$	−2651.73	−	2651.73i	−0.818207	−	0.818207i
$220$		0			0
$221$	1443.91	−	1443.91i	0.439494	−	0.439494i
$222$		0			0
$223$	−1645.00			−0.493980			−0.246990	−	0.969018i	$-0.579441\pi$
$223$	−1645.00			−0.493980			−0.246990	+	0.969018i	$0.579441\pi$
$224$		0			0
$225$	−378.825			−0.112245
$226$		0			0
$227$	−2652.47	+	2652.47i	−0.775555	+	0.775555i	−0.979071	−	0.203517i	$-0.934763\pi$
$227$	−2652.47	+	2652.47i	−0.775555	+	0.775555i	0.203517	+	0.979071i	$0.434763\pi$
$228$		0			0
$229$	−2840.94	−	2840.94i	−0.819802	−	0.819802i	0.166277	−	0.986079i	$-0.446825\pi$
$229$	−2840.94	−	2840.94i	−0.819802	−	0.819802i	−0.986079	+	0.166277i	$0.946825\pi$
$230$		0			0
$231$		−	2579.54i		−	0.734724i
$232$		0			0
$233$			6046.31i			1.70003i	0.526758	+	0.850015i	$0.323407\pi$
$233$			6046.31i			1.70003i	−0.526758	+	0.850015i	$0.676593\pi$
$234$		0			0
$235$	−6999.23	−	6999.23i	−1.94289	−	1.94289i
$236$		0			0
$237$	−1190.05	+	1190.05i	−0.326168	+	0.326168i
$238$		0			0
$239$	2919.88			0.790257			0.395128	−	0.918626i	$-0.370700\pi$
$239$	2919.88			0.790257			0.395128	+	0.918626i	$0.370700\pi$
$240$		0			0
$241$	−2342.75			−0.626183			−0.313091	−	0.949723i	$-0.601365\pi$
$241$	−2342.75			−0.626183			−0.313091	+	0.949723i	$0.601365\pi$
$242$		0			0
$243$	256.226	−	256.226i	0.0676416	−	0.0676416i
$244$		0			0
$245$	−9161.72	−	9161.72i	−2.38906	−	2.38906i
$246$		0			0
$247$		−	1061.38i		−	0.273417i
$248$		0			0
$249$			4647.33i			1.18278i
$250$		0			0
$251$	4127.18	+	4127.18i	1.03787	+	1.03787i	0.999254	+	0.0386151i	$0.0122946\pi$
$251$	4127.18	+	4127.18i	1.03787	+	1.03787i	0.0386151	+	0.999254i	$0.487705\pi$
$252$		0			0
$253$	177.994	−	177.994i	0.0442308	−	0.0442308i
$254$		0			0
$255$	−3981.48			−0.977764
$256$		0			0
$257$	4806.18			1.16654			0.583271	−	0.812278i	$-0.301773\pi$
$257$	4806.18			1.16654			0.583271	+	0.812278i	$0.301773\pi$
$258$		0			0
$259$	1294.18	−	1294.18i	0.310488	−	0.310488i
$260$		0			0
$261$	137.441	+	137.441i	0.0325952	+	0.0325952i
$262$		0			0
$263$		−	5267.43i		−	1.23499i	−0.786573	−	0.617497i	$-0.788147\pi$
$263$		−	5267.43i		−	1.23499i	0.786573	−	0.617497i	$-0.211853\pi$
$264$		0			0
$265$		−	5964.17i		−	1.38255i
$266$		0			0
$267$	1864.23	+	1864.23i	0.427300	+	0.427300i
$268$		0			0
$269$	4007.83	−	4007.83i	0.908408	−	0.908408i	−0.0877362	−	0.996144i	$-0.527963\pi$
$269$	4007.83	−	4007.83i	0.908408	−	0.908408i	0.996144	+	0.0877362i	$0.0279632\pi$
$270$		0			0
$271$	−97.0442			−0.0217528			−0.0108764	−	0.999941i	$-0.503462\pi$
$271$	−97.0442			−0.0217528			−0.0108764	+	0.999941i	$0.503462\pi$
$272$		0			0
$273$	−8425.14			−1.86781
$274$		0			0
$275$	−3373.82	+	3373.82i	−0.739815	+	0.739815i
$276$		0			0
$277$	−621.277	−	621.277i	−0.134761	−	0.134761i	0.636508	−	0.771270i	$-0.280378\pi$
$277$	−621.277	−	621.277i	−0.134761	−	0.134761i	−0.771270	+	0.636508i	$0.780378\pi$
$278$		0			0
$279$			72.1120i			0.0154740i
$280$		0			0
$281$		−	71.5081i		−	0.0151808i	−0.999971	−	0.00759042i	$-0.997584\pi$
$281$		−	71.5081i		−	0.0151808i	0.999971	−	0.00759042i	$-0.00241613\pi$
$282$		0			0
$283$	992.800	+	992.800i	0.208537	+	0.208537i	0.803645	−	0.595109i	$-0.202891\pi$
$283$	992.800	+	992.800i	0.208537	+	0.208537i	−0.595109	+	0.803645i	$0.702891\pi$
$284$		0			0
$285$	−1463.34	+	1463.34i	−0.304142	+	0.304142i
$286$		0			0
$287$	136.014			0.0279743
$288$		0			0
$289$	−3438.10			−0.699796
$290$		0			0
$291$	4623.64	−	4623.64i	0.931418	−	0.931418i
$292$		0			0
$293$	3877.68	+	3877.68i	0.773162	+	0.773162i	0.978658	−	0.205496i	$-0.0658807\pi$
$293$	3877.68	+	3877.68i	0.773162	+	0.773162i	−0.205496	+	0.978658i	$0.565881\pi$
$294$		0			0
$295$			5972.30i			1.17872i
$296$		0			0
$297$		−	2335.29i		−	0.456254i
$298$		0			0
$299$	−581.354	−	581.354i	−0.112443	−	0.112443i
$300$		0			0
$301$	−3423.52	+	3423.52i	−0.655576	+	0.655576i
$302$		0			0
$303$	−2275.01			−0.431339
$304$		0			0
$305$	13038.2			2.44775
$306$		0			0
$307$	−1878.23	+	1878.23i	−0.349174	+	0.349174i	−0.859802	−	0.510628i	$-0.829413\pi$
$307$	−1878.23	+	1878.23i	−0.349174	+	0.349174i	0.510628	+	0.859802i	$0.329413\pi$
$308$		0			0
$309$	5155.31	+	5155.31i	0.949111	+	0.949111i
$310$		0			0
$311$			9649.90i			1.75947i	0.475464	+	0.879735i	$0.342280\pi$
$311$			9649.90i			1.75947i	−0.475464	+	0.879735i	$0.657720\pi$
$312$		0			0
$313$			2090.02i			0.377428i	0.982032	+	0.188714i	$0.0604318\pi$
$313$			2090.02i			0.377428i	−0.982032	+	0.188714i	$0.939568\pi$
$314$		0			0
$315$	−584.027	−	584.027i	−0.104464	−	0.104464i
$316$		0			0
$317$	−2249.75	+	2249.75i	−0.398608	+	0.398608i	−0.877742	−	0.479134i	$-0.840951\pi$
$317$	−2249.75	+	2249.75i	−0.398608	+	0.398608i	0.479134	+	0.877742i	$0.340951\pi$
$318$		0			0
$319$	2448.09			0.429677
$320$		0			0
$321$	−2425.85			−0.421799
$322$		0			0
$323$	542.079	−	542.079i	0.0933810	−	0.0933810i
$324$		0			0
$325$	11019.4	+	11019.4i	1.88075	+	1.88075i
$326$		0			0
$327$		−	3505.24i		−	0.592783i
$328$		0			0
$329$		−	15128.8i		−	2.53519i
$330$		0			0
$331$	−1104.65	−	1104.65i	−0.183435	−	0.183435i	0.609416	−	0.792851i	$-0.291404\pi$
$331$	−1104.65	−	1104.65i	−0.183435	−	0.183435i	−0.792851	+	0.609416i	$0.791404\pi$
$332$		0			0
$333$	53.5260	−	53.5260i	0.00880843	−	0.00880843i
$334$		0			0
$335$	12380.4			2.01915
$336$		0			0
$337$	−1420.03			−0.229537			−0.114768	−	0.993392i	$-0.536613\pi$
$337$	−1420.03			−0.229537			−0.114768	+	0.993392i	$0.536613\pi$
$338$		0			0
$339$	2298.77	−	2298.77i	0.368295	−	0.368295i
$340$		0			0
$341$	642.230	+	642.230i	0.101990	+	0.101990i
$342$		0			0
$343$		−	9083.69i		−	1.42995i
$344$		0			0
$345$			1603.04i			0.250158i
$346$		0			0
$347$	3385.23	+	3385.23i	0.523713	+	0.523713i	0.918691	−	0.394977i	$-0.129248\pi$
$347$	3385.23	+	3385.23i	0.523713	+	0.523713i	−0.394977	+	0.918691i	$0.629248\pi$
$348$		0			0
$349$	7539.70	−	7539.70i	1.15642	−	1.15642i	0.171182	−	0.985239i	$-0.445241\pi$
$349$	7539.70	−	7539.70i	1.15642	−	1.15642i	0.985239	−	0.171182i	$-0.0547585\pi$
$350$		0			0
$351$	−7627.40			−1.15989
$352$		0			0
$353$	10875.4			1.63977			0.819886	−	0.572527i	$-0.194037\pi$
$353$	10875.4			1.63977			0.819886	+	0.572527i	$0.194037\pi$
$354$		0			0
$355$	12267.9	−	12267.9i	1.83412	−	1.83412i
$356$		0			0
$357$	−4302.97	−	4302.97i	−0.637920	−	0.637920i
$358$		0			0
$359$			1421.25i			0.208943i	0.994528	+	0.104472i	$0.0333151\pi$
$359$			1421.25i			0.208943i	−0.994528	+	0.104472i	$0.966685\pi$
$360$		0			0
$361$			6460.53i			0.941906i
$362$		0			0
$363$	3821.76	+	3821.76i	0.552590	+	0.552590i
$364$		0			0
$365$	−10693.8	+	10693.8i	−1.53353	+	1.53353i
$366$		0			0
$367$	6698.17			0.952703			0.476351	−	0.879255i	$-0.341959\pi$
$367$	6698.17			0.952703			0.476351	+	0.879255i	$0.341959\pi$
$368$		0			0
$369$	5.62538			0.000793620
$370$		0			0
$371$	6445.75	−	6445.75i	0.902013	−	0.902013i
$372$		0			0
$373$	−7317.01	−	7317.01i	−1.01571	−	1.01571i	−0.999875	−	0.0158368i	$-0.994959\pi$
$373$	−7317.01	−	7317.01i	−1.01571	−	1.01571i	−0.0158368	−	0.999875i	$-0.505041\pi$
$374$		0			0
$375$		−	17426.0i		−	2.39967i
$376$		0			0
$377$		−	7995.82i		−	1.09232i
$378$		0			0
$379$	−8591.26	−	8591.26i	−1.16439	−	1.16439i	−0.983504	−	0.180885i	$-0.942104\pi$
$379$	−8591.26	−	8591.26i	−1.16439	−	1.16439i	−0.180885	−	0.983504i	$-0.557896\pi$
$380$		0			0
$381$	−8800.70	+	8800.70i	−1.18339	+	1.18339i
$382$		0			0
$383$	−2209.21			−0.294740			−0.147370	−	0.989081i	$-0.547081\pi$
$383$	−2209.21			−0.294740			−0.147370	+	0.989081i	$0.547081\pi$
$384$		0			0
$385$	−10402.7			−1.37707
$386$		0			0
$387$	−141.593	+	141.593i	−0.0185984	+	0.0185984i
$388$		0			0
$389$	−7477.19	−	7477.19i	−0.974572	−	0.974572i	0.0251129	−	0.999685i	$-0.492005\pi$
$389$	−7477.19	−	7477.19i	−0.974572	−	0.974572i	−0.999685	+	0.0251129i	$0.992005\pi$
$390$		0			0
$391$		−	593.829i		−	0.0768062i
$392$		0			0
$393$		−	2468.10i		−	0.316791i
$394$		0			0
$395$	4799.19	+	4799.19i	0.611326	+	0.611326i
$396$		0			0
$397$	7759.12	−	7759.12i	0.980905	−	0.980905i	−0.0189162	−	0.999821i	$-0.506022\pi$
$397$	7759.12	−	7759.12i	0.980905	−	0.980905i	0.999821	+	0.0189162i	$0.00602158\pi$
$398$		0			0
$399$	−3162.99			−0.396861
$400$		0			0
$401$	−5034.84			−0.627002			−0.313501	−	0.949588i	$-0.601502\pi$
$401$	−5034.84			−0.627002			−0.313501	+	0.949588i	$0.601502\pi$
$402$		0			0
$403$	2097.61	−	2097.61i	0.259279	−	0.259279i
$404$		0			0
$405$	10011.4	+	10011.4i	1.22832	+	1.22832i
$406$		0			0
$407$		−	953.405i		−	0.116114i
$408$		0			0
$409$		−	14670.4i		−	1.77360i	−0.462149	−	0.886802i	$-0.652921\pi$
$409$		−	14670.4i		−	1.77360i	0.462149	−	0.886802i	$-0.347079\pi$
$410$		0			0
$411$	−9179.86	−	9179.86i	−1.10173	−	1.10173i
$412$		0			0
$413$	−6454.55	+	6454.55i	−0.769026	+	0.769026i
$414$		0			0
$415$	18741.6			2.21684
$416$		0			0
$417$	12288.3			1.44307
$418$		0			0
$419$	−9049.09	+	9049.09i	−1.05508	+	1.05508i	−0.0566847	+	0.998392i	$0.518053\pi$
$419$	−9049.09	+	9049.09i	−1.05508	+	1.05508i	−0.998392	+	0.0566847i	$0.981947\pi$
$420$		0			0
$421$	178.482	+	178.482i	0.0206619	+	0.0206619i	0.717362	−	0.696700i	$-0.245349\pi$
$421$	178.482	+	178.482i	0.0206619	+	0.0206619i	−0.696700	+	0.717362i	$0.745349\pi$
$422$		0			0
$423$		−	625.711i		−	0.0719223i
$424$		0			0
$425$			11255.8i			1.28468i
$426$		0			0
$427$	14090.9	+	14090.9i	1.59698	+	1.59698i
$428$		0			0
$429$	−3103.34	+	3103.34i	−0.349256	+	0.349256i
$430$		0			0
$431$	7682.25			0.858564			0.429282	−	0.903171i	$-0.358767\pi$
$431$	7682.25			0.858564			0.429282	+	0.903171i	$0.358767\pi$
$432$		0			0
$433$	−7152.63			−0.793842			−0.396921	−	0.917853i	$-0.629921\pi$
$433$	−7152.63			−0.793842			−0.396921	+	0.917853i	$0.629921\pi$
$434$		0			0
$435$	−11023.9	+	11023.9i	−1.21507	+	1.21507i
$436$		0			0
$437$	−218.253	−	218.253i	−0.0238913	−	0.0238913i
$438$		0			0
$439$		−	6415.61i		−	0.697495i	−0.937217	−	0.348747i	$-0.886607\pi$
$439$		−	6415.61i		−	0.697495i	0.937217	−	0.348747i	$-0.113393\pi$
$440$		0			0
$441$		−	819.032i		−	0.0884388i
$442$		0			0
$443$	−5614.25	−	5614.25i	−0.602124	−	0.602124i	0.338752	−	0.940876i	$-0.389995\pi$
$443$	−5614.25	−	5614.25i	−0.602124	−	0.602124i	−0.940876	+	0.338752i	$0.889995\pi$
$444$		0			0
$445$	7518.02	−	7518.02i	0.800873	−	0.800873i
$446$		0			0
$447$	2219.93			0.234897
$448$		0			0
$449$	−8911.67			−0.936676			−0.468338	−	0.883549i	$-0.655147\pi$
$449$	−8911.67			−0.936676			−0.468338	+	0.883549i	$0.655147\pi$
$450$		0			0
$451$	50.0997	−	50.0997i	0.00523082	−	0.00523082i
$452$		0			0
$453$	8706.84	+	8706.84i	0.903053	+	0.903053i
$454$		0			0
$455$			33976.7i			3.50077i
$456$		0			0
$457$			3476.75i			0.355876i	0.984042	+	0.177938i	$0.0569427\pi$
$457$			3476.75i			0.355876i	−0.984042	+	0.177938i	$0.943057\pi$
$458$		0			0
$459$	−3895.54	−	3895.54i	−0.396140	−	0.396140i
$460$		0			0
$461$	−3791.45	+	3791.45i	−0.383049	+	0.383049i	−0.872199	−	0.489150i	$-0.837307\pi$
$461$	−3791.45	+	3791.45i	−0.383049	+	0.383049i	0.489150	+	0.872199i	$0.337307\pi$
$462$		0			0
$463$	−11450.8			−1.14938			−0.574690	−	0.818371i	$-0.694877\pi$
$463$	−11450.8			−1.14938			−0.574690	+	0.818371i	$0.694877\pi$
$464$		0			0
$465$	−5784.00			−0.576832
$466$		0			0
$467$	−1190.26	+	1190.26i	−0.117942	+	0.117942i	−0.763614	−	0.645673i	$-0.776577\pi$
$467$	−1190.26	+	1190.26i	−0.117942	+	0.117942i	0.645673	+	0.763614i	$0.276577\pi$
$468$		0			0
$469$	13380.1	+	13380.1i	1.31735	+	1.31735i
$470$		0			0
$471$		−	1866.47i		−	0.182596i
$472$		0			0
$473$			2522.06i			0.245168i
$474$		0			0
$475$	4136.93	+	4136.93i	0.399611	+	0.399611i
$476$		0			0
$477$	266.590	−	266.590i	0.0255897	−	0.0255897i
$478$		0			0
$479$	−18640.5			−1.77810			−0.889048	−	0.457814i	$-0.848632\pi$
$479$	−18640.5			−1.77810			−0.889048	+	0.457814i	$0.848632\pi$
$480$		0			0
$481$	−3113.96			−0.295185
$482$		0			0
$483$	−1732.48	+	1732.48i	−0.163210	+	0.163210i
$484$		0			0
$485$	−18646.1	−	18646.1i	−1.74572	−	1.74572i
$486$		0			0
$487$			757.113i			0.0704477i	0.999379	+	0.0352239i	$0.0112144\pi$
$487$			757.113i			0.0704477i	−0.999379	+	0.0352239i	$0.988786\pi$
$488$		0			0
$489$		−	6175.97i		−	0.571139i
$490$		0			0
$491$	3595.27	+	3595.27i	0.330452	+	0.330452i	0.852758	−	0.522306i	$-0.174928\pi$
$491$	3595.27	+	3595.27i	0.330452	+	0.330452i	−0.522306	+	0.852758i	$0.674928\pi$
$492$		0			0
$493$	4083.70	−	4083.70i	0.373064	−	0.373064i
$494$		0			0
$495$	−430.245			−0.0390668
$496$		0			0
$497$	26517.0			2.39326
$498$		0			0
$499$	−5604.26	+	5604.26i	−0.502768	+	0.502768i	−0.912297	−	0.409529i	$-0.865693\pi$
$499$	−5604.26	+	5604.26i	−0.502768	+	0.502768i	0.409529	+	0.912297i	$0.365693\pi$
$500$		0			0
$501$	−12695.9	−	12695.9i	−1.13216	−	1.13216i
$502$		0			0
$503$		−	10028.1i		−	0.888926i	−0.895797	−	0.444463i	$-0.853395\pi$
$503$		−	10028.1i		−	0.888926i	0.895797	−	0.444463i	$-0.146605\pi$
$504$		0			0
$505$			9174.58i			0.808443i
$506$		0			0
$507$	2259.26	+	2259.26i	0.197904	+	0.197904i
$508$		0			0
$509$	4748.13	−	4748.13i	0.413472	−	0.413472i	−0.469474	−	0.882946i	$-0.655556\pi$
$509$	4748.13	−	4748.13i	0.413472	−	0.413472i	0.882946	+	0.469474i	$0.155556\pi$
$510$		0			0
$511$	−23114.6			−2.00104
$512$		0			0
$513$	−2863.50			−0.246446
$514$		0			0
$515$	20790.2	−	20790.2i	1.77888	−	1.77888i
$516$		0			0
$517$	−5572.59	−	5572.59i	−0.474047	−	0.474047i
$518$		0			0
$519$		−	1150.45i		−	0.0973010i
$520$		0			0
$521$			16542.9i			1.39109i	0.718481	+	0.695547i	$0.244838\pi$
$521$			16542.9i			1.39109i	−0.718481	+	0.695547i	$0.755162\pi$
$522$		0			0
$523$	−7076.26	−	7076.26i	−0.591631	−	0.591631i	0.346441	−	0.938072i	$-0.387390\pi$
$523$	−7076.26	−	7076.26i	−0.591631	−	0.591631i	−0.938072	+	0.346441i	$0.887390\pi$
$524$		0			0
$525$	32838.5	−	32838.5i	2.72989	−	2.72989i
$526$		0			0
$527$	2142.63			0.177105
$528$		0			0
$529$	11927.9			0.980349
$530$		0			0
$531$	−266.954	+	266.954i	−0.0218169	+	0.0218169i
$532$		0			0
$533$	−163.633	−	163.633i	−0.0132978	−	0.0132978i
$534$		0			0
$535$			9782.89i			0.790563i
$536$		0			0
$537$			14950.6i			1.20143i
$538$		0			0
$539$	−7294.30	−	7294.30i	−0.582909	−	0.582909i
$540$		0			0
$541$	−3432.45	+	3432.45i	−0.272778	+	0.272778i	−0.830217	−	0.557440i	$-0.811784\pi$
$541$	−3432.45	+	3432.45i	−0.272778	+	0.272778i	0.557440	+	0.830217i	$0.311784\pi$
$542$		0			0
$543$	−10417.2			−0.823287
$544$		0			0
$545$	−14135.8			−1.11103
$546$		0			0
$547$	−8378.40	+	8378.40i	−0.654908	+	0.654908i	−0.954171	−	0.299263i	$-0.903259\pi$
$547$	−8378.40	+	8378.40i	−0.654908	+	0.654908i	0.299263	+	0.954171i	$0.403259\pi$
$548$		0			0
$549$	582.787	+	582.787i	0.0453056	+	0.0453056i
$550$		0			0
$551$		−	3001.81i		−	0.232090i
$552$		0			0
$553$			10373.4i			0.797691i
$554$		0			0
$555$	4293.24	+	4293.24i	0.328357	+	0.328357i
$556$		0			0
$557$	−12185.0	+	12185.0i	−0.926923	+	0.926923i	−0.997506	−	0.0705830i	$-0.977514\pi$
$557$	−12185.0	+	12185.0i	−0.926923	+	0.926923i	0.0705830	+	0.997506i	$0.477514\pi$
$558$		0			0
$559$	8237.41			0.623265
$560$		0			0
$561$	−3169.94			−0.238565
$562$		0			0
$563$	−12700.4	+	12700.4i	−0.950727	+	0.950727i	−0.998842	−	0.0481149i	$-0.984679\pi$
$563$	−12700.4	+	12700.4i	−0.950727	+	0.950727i	0.0481149	+	0.998842i	$0.484679\pi$
$564$		0			0
$565$	−9270.43	−	9270.43i	−0.690283	−	0.690283i
$566$		0			0
$567$			21639.6i			1.60278i
$568$		0			0
$569$			14986.1i			1.10413i	0.833800	+	0.552066i	$0.186160\pi$
$569$			14986.1i			1.10413i	−0.833800	+	0.552066i	$0.813840\pi$
$570$		0			0
$571$	−9169.09	−	9169.09i	−0.672005	−	0.672005i	0.286173	−	0.958178i	$-0.407617\pi$
$571$	−9169.09	−	9169.09i	−0.672005	−	0.672005i	−0.958178	+	0.286173i	$0.907617\pi$
$572$		0			0
$573$	−6049.82	+	6049.82i	−0.441073	+	0.441073i
$574$		0			0
$575$	4531.87			0.328682
$576$		0			0
$577$	19502.4			1.40710			0.703549	−	0.710647i	$-0.251598\pi$
$577$	19502.4			1.40710			0.703549	+	0.710647i	$0.251598\pi$
$578$		0			0
$579$	1777.81	−	1777.81i	0.127605	−	0.127605i
$580$		0			0
$581$	20254.9	+	20254.9i	1.44633	+	1.44633i
$582$		0			0
$583$		−	4748.50i		−	0.337329i
$584$		0			0
$585$			1405.24i			0.0993155i
$586$		0			0
$587$	3621.91	+	3621.91i	0.254672	+	0.254672i	0.822883	−	0.568211i	$-0.192364\pi$
$587$	3621.91	+	3621.91i	0.254672	+	0.254672i	−0.568211	+	0.822883i	$0.692364\pi$
$588$		0			0
$589$	787.492	−	787.492i	0.0550901	−	0.0550901i
$590$		0			0
$591$	3780.24			0.263111
$592$		0			0
$593$	2431.22			0.168361			0.0841807	−	0.996451i	$-0.473173\pi$
$593$	2431.22			0.168361			0.0841807	+	0.996451i	$0.473173\pi$
$594$		0			0
$595$	−17352.9	+	17352.9i	−1.19563	+	1.19563i
$596$		0			0
$597$	−4158.28	−	4158.28i	−0.285071	−	0.285071i
$598$		0			0
$599$		−	2435.10i		−	0.166102i	−0.996545	−	0.0830512i	$-0.973533\pi$
$599$		−	2435.10i		−	0.166102i	0.996545	−	0.0830512i	$-0.0264665\pi$
$600$		0			0
$601$		−	13113.4i		−	0.890029i	−0.895523	−	0.445014i	$-0.853199\pi$
$601$		−	13113.4i		−	0.890029i	0.895523	−	0.445014i	$-0.146801\pi$
$602$		0			0
$603$	553.388	+	553.388i	0.0373726	+	0.0373726i
$604$		0			0
$605$	15412.3	−	15412.3i	1.03570	−	1.03570i
$606$		0			0
$607$	−13954.6			−0.933111			−0.466555	−	0.884492i	$-0.654505\pi$
$607$	−13954.6			−0.933111			−0.466555	+	0.884492i	$0.654505\pi$
$608$		0			0
$609$	−23828.1			−1.58549
$610$		0			0
$611$	−18200.9	+	18200.9i	−1.20512	+	1.20512i
$612$		0			0
$613$	3230.00	+	3230.00i	0.212820	+	0.212820i	0.805464	−	0.592644i	$-0.201916\pi$
$613$	3230.00	+	3230.00i	0.212820	+	0.212820i	−0.592644	+	0.805464i	$0.701916\pi$
$614$		0			0
$615$			451.204i			0.0295842i
$616$		0			0
$617$		−	21209.6i		−	1.38390i	−0.721944	−	0.691951i	$-0.756751\pi$
$617$		−	21209.6i		−	1.38390i	0.721944	−	0.691951i	$-0.243249\pi$
$618$		0			0
$619$	−7408.86	−	7408.86i	−0.481078	−	0.481078i	0.424398	−	0.905476i	$-0.360486\pi$
$619$	−7408.86	−	7408.86i	−0.481078	−	0.481078i	−0.905476	+	0.424398i	$0.860486\pi$
$620$		0			0
$621$	−1568.44	+	1568.44i	−0.101351	+	0.101351i
$622$		0			0
$623$	16250.2			1.04502
$624$		0			0
$625$	−33639.2			−2.15291
$626$		0			0
$627$	−1165.07	+	1165.07i	−0.0742078	+	0.0742078i
$628$		0			0
$629$	−1590.39	−	1590.39i	−0.100816	−	0.100816i
$630$		0			0
$631$			2254.96i			0.142264i	0.997467	+	0.0711319i	$0.0226611\pi$
$631$			2254.96i			0.142264i	−0.997467	+	0.0711319i	$0.977339\pi$
$632$		0			0
$633$		−	21111.3i		−	1.32559i
$634$		0			0
$635$	35491.2	+	35491.2i	2.21799	+	2.21799i
$636$		0			0
$637$	−23824.2	+	23824.2i	−1.48187	+	1.48187i
$638$		0			0
$639$	1096.71			0.0678957
$640$		0			0
$641$	−860.858			−0.0530450			−0.0265225	−	0.999648i	$-0.508443\pi$
$641$	−860.858			−0.0530450			−0.0265225	+	0.999648i	$0.508443\pi$
$642$		0			0
$643$	5562.62	−	5562.62i	0.341164	−	0.341164i	−0.515641	−	0.856805i	$-0.672446\pi$
$643$	5562.62	−	5562.62i	0.341164	−	0.341164i	0.856805	+	0.515641i	$0.172446\pi$
$644$		0			0
$645$	−11357.0	−	11357.0i	−0.693305	−	0.693305i
$646$		0			0
$647$			12046.5i			0.731990i	0.930617	+	0.365995i	$0.119271\pi$
$647$			12046.5i			0.731990i	−0.930617	+	0.365995i	$0.880729\pi$
$648$		0			0
$649$			4754.98i			0.287595i
$650$		0			0
$651$	−6251.04	−	6251.04i	−0.376341	−	0.376341i
$652$		0			0
$653$	8140.02	−	8140.02i	0.487816	−	0.487816i	−0.419801	−	0.907616i	$-0.637900\pi$
$653$	8140.02	−	8140.02i	0.487816	−	0.487816i	0.907616	+	0.419801i	$0.137900\pi$
$654$		0			0
$655$	−9953.28			−0.593751
$656$		0			0
$657$	−955.998			−0.0567687
$658$		0			0
$659$	9068.51	−	9068.51i	0.536053	−	0.536053i	−0.386314	−	0.922367i	$-0.626252\pi$
$659$	9068.51	−	9068.51i	0.536053	−	0.536053i	0.922367	+	0.386314i	$0.126252\pi$
$660$		0			0
$661$	2394.88	+	2394.88i	0.140923	+	0.140923i	0.774049	−	0.633126i	$-0.218229\pi$
$661$	2394.88	+	2394.88i	0.140923	+	0.140923i	−0.633126	+	0.774049i	$0.718229\pi$
$662$		0			0
$663$			10353.5i			0.606479i
$664$		0			0
$665$			12755.6i			0.743822i
$666$		0			0
$667$	−1644.19	−	1644.19i	−0.0954474	−	0.0954474i
$668$		0			0
$669$	5897.68	−	5897.68i	0.340833	−	0.340833i
$670$		0			0
$671$	10380.6			0.597227
$672$		0			0
$673$	7432.84			0.425728			0.212864	−	0.977082i	$-0.431721\pi$
$673$	7432.84			0.425728			0.212864	+	0.977082i	$0.431721\pi$
$674$		0			0
$675$	29729.2	−	29729.2i	1.69523	−	1.69523i
$676$		0			0
$677$	−13532.2	−	13532.2i	−0.768221	−	0.768221i	0.209572	−	0.977793i	$-0.432793\pi$
$677$	−13532.2	−	13532.2i	−0.768221	−	0.768221i	−0.977793	+	0.209572i	$0.932793\pi$
$678$		0			0
$679$		−	40303.4i		−	2.27791i
$680$		0			0
$681$		−	19019.4i		−	1.07022i
$682$		0			0
$683$	−10404.7	−	10404.7i	−0.582907	−	0.582907i	0.352794	−	0.935701i	$-0.385232\pi$
$683$	−10404.7	−	10404.7i	−0.582907	−	0.582907i	−0.935701	+	0.352794i	$0.885232\pi$
$684$		0			0
$685$	−37020.3	+	37020.3i	−2.06492	+	2.06492i
$686$		0			0
$687$	20370.7			1.13128
$688$		0			0
$689$	−15509.3			−0.857556
$690$		0			0
$691$	10759.5	−	10759.5i	0.592347	−	0.592347i	−0.345918	−	0.938265i	$-0.612432\pi$
$691$	10759.5	−	10759.5i	0.592347	−	0.592347i	0.938265	+	0.345918i	$0.112432\pi$
$692$		0			0
$693$	−464.986	−	464.986i	−0.0254883	−	0.0254883i
$694$		0			0
$695$		−	49555.9i		−	2.70469i
$696$		0			0
$697$		−	167.144i		−	0.00908326i
$698$		0			0
$699$	−21677.3	−	21677.3i	−1.17298	−	1.17298i
$700$		0			0
$701$	23974.2	−	23974.2i	1.29172	−	1.29172i	0.357990	−	0.933726i	$-0.383462\pi$
$701$	23974.2	−	23974.2i	1.29172	−	1.29172i	0.933726	−	0.357990i	$-0.116538\pi$
$702$		0			0
$703$	−1169.05			−0.0627192
$704$		0			0
$705$	50187.4			2.68109
$706$		0			0
$707$	−9915.40	+	9915.40i	−0.527450	+	0.527450i
$708$		0			0
$709$	12606.4	+	12606.4i	0.667762	+	0.667762i	0.957198	−	0.289435i	$-0.0934676\pi$
$709$	12606.4	+	12606.4i	0.667762	+	0.667762i	−0.289435	+	0.957198i	$0.593468\pi$
$710$		0			0
$711$			429.034i			0.0226302i
$712$		0			0
$713$		−	862.672i		−	0.0453118i
$714$		0			0
$715$	12515.1	+	12515.1i	0.654598	+	0.654598i
$716$		0			0
$717$	−10468.4	+	10468.4i	−0.545257	+	0.545257i
$718$		0			0
$719$	−27256.0			−1.41374			−0.706868	−	0.707345i	$-0.749893\pi$
$719$	−27256.0			−1.41374			−0.706868	+	0.707345i	$0.749893\pi$
$720$		0			0
$721$	44937.9			2.32119
$722$		0			0
$723$	8399.26	−	8399.26i	0.432050	−	0.432050i
$724$		0			0
$725$	31165.2	+	31165.2i	1.59648	+	1.59648i
$726$		0			0
$727$			20743.7i			1.05824i	0.848547	+	0.529120i	$0.177478\pi$
$727$			20743.7i			1.05824i	−0.848547	+	0.529120i	$0.822522\pi$
$728$		0			0
$729$			20532.9i			1.04318i
$730$		0			0
$731$	4207.09	+	4207.09i	0.212866	+	0.212866i
$732$		0			0
$733$	4775.28	−	4775.28i	0.240626	−	0.240626i	−0.576483	−	0.817109i	$-0.695575\pi$
$733$	4775.28	−	4775.28i	0.240626	−	0.240626i	0.817109	+	0.576483i	$0.195575\pi$
$734$		0			0
$735$	65693.4			3.29678
$736$		0			0
$737$	9856.95			0.492653
$738$		0			0
$739$	13408.3	−	13408.3i	0.667431	−	0.667431i	−0.289689	−	0.957121i	$-0.593552\pi$
$739$	13408.3	−	13408.3i	0.667431	−	0.667431i	0.957121	+	0.289689i	$0.0935520\pi$
$740$		0			0
$741$	3805.27	+	3805.27i	0.188651	+	0.188651i
$742$		0			0
$743$		−	495.531i		−	0.0244674i	−0.999925	−	0.0122337i	$-0.996106\pi$
$743$		−	495.531i		−	0.0244674i	0.999925	−	0.0122337i	$-0.00389420\pi$
$744$		0			0
$745$		−	8952.46i		−	0.440259i
$746$		0			0
$747$	837.724	+	837.724i	0.0410317	+	0.0410317i
$748$		0			0
$749$	−10572.8	+	10572.8i	−0.515784	+	0.515784i
$750$		0			0
$751$	−4249.85			−0.206497			−0.103248	−	0.994656i	$-0.532924\pi$
$751$	−4249.85			−0.206497			−0.103248	+	0.994656i	$0.532924\pi$
$752$		0			0
$753$	−29593.6			−1.43221
$754$		0			0
$755$	35112.7	−	35112.7i	1.69256	−	1.69256i
$756$		0			0
$757$	−16351.7	−	16351.7i	−0.785091	−	0.785091i	0.195594	−	0.980685i	$-0.437337\pi$
$757$	−16351.7	−	16351.7i	−0.785091	−	0.785091i	−0.980685	+	0.195594i	$0.937337\pi$
$758$		0			0
$759$			1276.29i			0.0610362i
$760$		0			0
$761$		−	29572.7i		−	1.40869i	−0.709860	−	0.704343i	$-0.751242\pi$
$761$		−	29572.7i		−	1.40869i	0.709860	−	0.704343i	$-0.248758\pi$
$762$		0			0
$763$	−15277.3	−	15277.3i	−0.724868	−	0.724868i
$764$		0			0
$765$	−717.699	+	717.699i	−0.0339195	+	0.0339195i
$766$		0			0
$767$	15530.4			0.731123
$768$		0			0
$769$	−10459.3			−0.490471			−0.245235	−	0.969464i	$-0.578865\pi$
$769$	−10459.3			−0.490471			−0.245235	+	0.969464i	$0.578865\pi$
$770$		0			0
$771$	−17231.2	+	17231.2i	−0.804884	+	0.804884i
$772$		0			0
$773$	25046.5	+	25046.5i	1.16541	+	1.16541i	0.983274	+	0.182132i	$0.0582998\pi$
$773$	25046.5	+	25046.5i	1.16541	+	1.16541i	0.182132	+	0.983274i	$0.441700\pi$
$774$		0			0
$775$			16351.7i			0.757896i
$776$		0			0
$777$			9279.82i			0.428458i
$778$		0			0
$779$	−61.4314	−	61.4314i	−0.00282543	−	0.00282543i
$780$		0			0
$781$	9767.35	−	9767.35i	0.447507	−	0.447507i
$782$		0			0
$783$	−21571.9			−0.984570
$784$		0			0
$785$	−7527.06			−0.342232
$786$		0			0
$787$	25779.4	−	25779.4i	1.16765	−	1.16765i	0.184886	−	0.982760i	$-0.440808\pi$
$787$	25779.4	−	25779.4i	1.16765	−	1.16765i	0.982760	−	0.184886i	$-0.0591917\pi$
$788$		0			0
$789$	18884.8	+	18884.8i	0.852114	+	0.852114i
$790$		0			0
$791$		−	20038.0i		−	0.900718i
$792$		0			0
$793$		−	33904.5i		−	1.51827i
$794$		0			0
$795$	21382.8	+	21382.8i	0.953924	+	0.953924i
$796$		0			0
$797$	−22655.8	+	22655.8i	−1.00691	+	1.00691i	−0.00693604	+	0.999976i	$0.502208\pi$
$797$	−22655.8	+	22655.8i	−1.00691	+	1.00691i	−0.999976	+	0.00693604i	$0.997792\pi$
$798$		0			0
$799$	−18591.4			−0.823176
$800$		0			0
$801$	672.090			0.0296469
$802$		0			0
$803$	−8514.12	+	8514.12i	−0.374168	+	0.374168i
$804$		0			0
$805$	6986.68	+	6986.68i	0.305898	+	0.305898i
$806$		0			0
$807$			28737.8i			1.25356i
$808$		0			0
$809$		−	37498.5i		−	1.62964i	−0.579715	−	0.814819i	$-0.696836\pi$
$809$		−	37498.5i		−	1.62964i	0.579715	−	0.814819i	$-0.303164\pi$
$810$		0			0
$811$	26165.2	+	26165.2i	1.13290	+	1.13290i	0.989692	+	0.143210i	$0.0457424\pi$
$811$	26165.2	+	26165.2i	1.13290	+	1.13290i	0.143210	+	0.989692i	$0.454258\pi$
$812$		0			0
$813$	347.924	−	347.924i	0.0150089	−	0.0150089i
$814$		0			0
$815$	−24906.3			−1.07047
$816$		0			0
$817$	3092.51			0.132428
$818$		0			0
$819$	−1518.71	+	1518.71i	−0.0647961	+	0.0647961i
$820$		0			0
$821$	−18365.4	−	18365.4i	−0.780701	−	0.780701i	0.199248	−	0.979949i	$-0.436150\pi$
$821$	−18365.4	−	18365.4i	−0.780701	−	0.780701i	−0.979949	+	0.199248i	$0.936150\pi$
$822$		0			0
$823$			26807.9i			1.13544i	0.823222	+	0.567719i	$0.192174\pi$
$823$			26807.9i			1.13544i	−0.823222	+	0.567719i	$0.807826\pi$
$824$		0			0
$825$		−	24191.7i		−	1.02091i
$826$		0			0
$827$	12688.0	+	12688.0i	0.533501	+	0.533501i	0.921612	−	0.388112i	$-0.126873\pi$
$827$	12688.0	+	12688.0i	0.533501	+	0.533501i	−0.388112	+	0.921612i	$0.626873\pi$
$828$		0			0
$829$	−7118.03	+	7118.03i	−0.298214	+	0.298214i	−0.840314	−	0.542100i	$-0.817629\pi$
$829$	−7118.03	+	7118.03i	−0.298214	+	0.298214i	0.542100	+	0.840314i	$0.317629\pi$
$830$		0			0
$831$	4454.82			0.185964
$832$		0			0
$833$	−24335.5			−1.01221
$834$		0			0
$835$	−51199.6	+	51199.6i	−2.12196	+	2.12196i
$836$		0			0
$837$	−5659.16	−	5659.16i	−0.233703	−	0.233703i
$838$		0			0
$839$		−	44827.5i		−	1.84460i	−0.386480	−	0.922298i	$-0.626309\pi$
$839$		−	44827.5i		−	1.84460i	0.386480	−	0.922298i	$-0.373691\pi$
$840$		0			0
$841$			1775.12i			0.0727836i
$842$		0			0
$843$	256.372	+	256.372i	0.0104744	+	0.0104744i
$844$		0			0
$845$	9111.07	−	9111.07i	0.370923	−	0.370923i
$846$		0			0
$847$	33313.6			1.35144
$848$		0			0
$849$	−7118.80			−0.287770
$850$		0			0
$851$	−640.328	+	640.328i	−0.0257934	+	0.0257934i
$852$		0			0
$853$	−10377.2	−	10377.2i	−0.416540	−	0.416540i	0.467469	−	0.884009i	$-0.345166\pi$
$853$	−10377.2	−	10377.2i	−0.416540	−	0.416540i	−0.884009	+	0.467469i	$0.845166\pi$
$854$		0			0
$855$			527.560i			0.0211019i
$856$		0			0
$857$			33750.1i			1.34525i	0.739982	+	0.672626i	$0.234834\pi$
$857$			33750.1i			1.34525i	−0.739982	+	0.672626i	$0.765166\pi$
$858$		0			0
$859$	1575.08	+	1575.08i	0.0625625	+	0.0625625i	0.737696	−	0.675133i	$-0.235914\pi$
$859$	1575.08	+	1575.08i	0.0625625	+	0.0625625i	−0.675133	+	0.737696i	$0.735914\pi$
$860$		0			0
$861$	−487.637	+	487.637i	−0.0193015	+	0.0193015i
$862$		0			0
$863$	4666.15			0.184053			0.0920264	−	0.995757i	$-0.470666\pi$
$863$	4666.15			0.184053			0.0920264	+	0.995757i	$0.470666\pi$
$864$		0			0
$865$	−4639.51			−0.182368
$866$		0			0
$867$	12326.3	−	12326.3i	0.482841	−	0.482841i
$868$		0			0
$869$	3820.98	+	3820.98i	0.149158	+	0.149158i
$870$		0			0
$871$		−	32194.2i		−	1.25242i
$872$		0			0
$873$		−	1666.91i		−	0.0646235i
$874$		0			0
$875$	−75949.6	−	75949.6i	−2.93436	−	2.93436i
$876$		0			0
$877$	5252.69	−	5252.69i	0.202247	−	0.202247i	−0.598715	−	0.800962i	$-0.704322\pi$
$877$	5252.69	−	5252.69i	0.202247	−	0.202247i	0.800962	+	0.598715i	$0.204322\pi$
$878$		0			0
$879$	−27804.6			−1.06692
$880$		0			0
$881$	68.4502			0.00261764			0.00130882	−	0.999999i	$-0.499583\pi$
$881$	68.4502			0.00261764			0.00130882	+	0.999999i	$0.499583\pi$
$882$		0			0
$883$	14434.2	−	14434.2i	0.550112	−	0.550112i	−0.376361	−	0.926473i	$-0.622825\pi$
$883$	14434.2	−	14434.2i	0.550112	−	0.550112i	0.926473	+	0.376361i	$0.122825\pi$
$884$		0			0
$885$	−21412.0	−	21412.0i	−0.813283	−	0.813283i
$886$		0			0
$887$			32526.1i			1.23125i	0.788038	+	0.615626i	$0.211097\pi$
$887$			32526.1i			1.23125i	−0.788038	+	0.615626i	$0.788903\pi$
$888$		0			0
$889$			76714.1i			2.89416i
$890$		0			0
$891$	7970.80	+	7970.80i	0.299699	+	0.299699i
$892$		0			0
$893$	−6833.02	+	6833.02i	−0.256056	+	0.256056i
$894$		0			0
$895$	60292.5			2.25180
$896$		0			0
$897$	4168.55			0.155166
$898$		0			0
$899$	5932.50	−	5932.50i	0.220089	−	0.220089i
$900$		0			0
$901$	−7921.05	−	7921.05i	−0.292884	−	0.292884i
$902$		0			0
$903$		−	24548.1i		−	0.904661i
$904$		0			0
$905$			42010.2i			1.54306i
$906$		0			0
$907$	25769.0	+	25769.0i	0.943379	+	0.943379i	0.998481	−	0.0551015i	$-0.0175483\pi$
$907$	25769.0	+	25769.0i	0.943379	+	0.943379i	−0.0551015	+	0.998481i	$0.517548\pi$
$908$		0			0
$909$	−410.091	+	410.091i	−0.0149635	+	0.0149635i
$910$		0			0
$911$	5427.50			0.197389			0.0986944	−	0.995118i	$-0.468533\pi$
$911$	5427.50			0.197389			0.0986944	+	0.995118i	$0.468533\pi$
$912$		0			0
$913$	14921.5			0.540888
$914$		0			0
$915$	−46744.5	+	46744.5i	−1.68888	+	1.68888i
$916$		0			0
$917$	−10757.0	−	10757.0i	−0.387379	−	0.387379i
$918$		0			0
$919$			5669.76i			0.203513i	0.994809	+	0.101756i	$0.0324462\pi$
$919$			5669.76i			0.203513i	−0.994809	+	0.101756i	$0.967554\pi$
$920$		0			0
$921$		−	13467.7i		−	0.481842i
$922$		0			0
$923$	−31901.5	−	31901.5i	−1.13765	−	1.13765i
$924$		0			0
$925$	12137.2	−	12137.2i	0.431426	−	0.431426i
$926$		0			0
$927$	1858.59			0.0658511
$928$		0			0
$929$	−39311.6			−1.38835			−0.694173	−	0.719808i	$-0.744230\pi$
$929$	−39311.6			−1.38835			−0.694173	+	0.719808i	$0.744230\pi$
$930$		0			0
$931$	−8944.16	+	8944.16i	−0.314858	+	0.314858i
$932$		0			0
$933$	−34596.9	−	34596.9i	−1.21399	−	1.21399i
$934$		0			0
$935$			12783.7i			0.447134i
$936$		0			0
$937$			11500.8i			0.400977i	0.979696	+	0.200489i	$0.0642530\pi$
$937$			11500.8i			0.400977i	−0.979696	+	0.200489i	$0.935747\pi$
$938$		0			0
$939$	−7493.15	−	7493.15i	−0.260415	−	0.260415i
$940$		0			0
$941$	20955.0	−	20955.0i	0.725945	−	0.725945i	−0.243865	−	0.969809i	$-0.578415\pi$
$941$	20955.0	−	20955.0i	0.725945	−	0.725945i	0.969809	+	0.243865i	$0.0784153\pi$
$942$		0			0
$943$	−67.2961			−0.00232393
$944$		0			0
$945$	91665.8			3.15544
$946$		0			0
$947$	−13425.8	+	13425.8i	−0.460698	+	0.460698i	−0.898884	−	0.438186i	$-0.855621\pi$
$947$	−13425.8	+	13425.8i	−0.460698	+	0.460698i	0.438186	+	0.898884i	$0.355621\pi$
$948$		0			0
$949$	27808.3	+	27808.3i	0.951208	+	0.951208i
$950$		0			0
$951$		−	16131.7i		−	0.550058i
$952$		0			0
$953$			9285.90i			0.315635i	0.987468	+	0.157817i	$0.0504457\pi$
$953$			9285.90i			0.315635i	−0.987468	+	0.157817i	$0.949554\pi$
$954$		0			0
$955$	24397.6	+	24397.6i	0.826688	+	0.826688i
$956$		0			0
$957$	−8776.92	+	8776.92i	−0.296466	+	0.296466i
$958$		0			0
$959$	−80019.1			−2.69442
$960$		0			0
$961$	−26678.3			−0.895517
$962$		0			0
$963$	−437.281	+	437.281i	−0.0146326	+	0.0146326i
$964$		0			0
$965$	−7169.50	−	7169.50i	−0.239165	−	0.239165i
$966$		0			0
$967$			986.542i			0.0328077i	0.999865	+	0.0164039i	$0.00522175\pi$
$967$			986.542i			0.0328077i	−0.999865	+	0.0164039i	$0.994778\pi$
$968$		0			0
$969$			3886.93i			0.128861i
$970$		0			0
$971$	−39698.5	−	39698.5i	−1.31203	−	1.31203i	−0.919914	−	0.392119i	$-0.871742\pi$
$971$	−39698.5	−	39698.5i	−1.31203	−	1.31203i	−0.392119	−	0.919914i	$-0.628258\pi$
$972$		0			0
$973$	53557.4	−	53557.4i	1.76461	−	1.76461i
$974$		0			0
$975$	−79013.6			−2.59534
$976$		0			0
$977$	−29110.8			−0.953261			−0.476630	−	0.879104i	$-0.658142\pi$
$977$	−29110.8			−0.953261			−0.476630	+	0.879104i	$0.658142\pi$
$978$		0			0
$979$	5985.64	−	5985.64i	0.195405	−	0.195405i
$980$		0			0
$981$	−631.852	−	631.852i	−0.0205642	−	0.0205642i
$982$		0			0
$983$			22518.4i			0.730646i	0.930881	+	0.365323i	$0.119041\pi$
$983$			22518.4i			0.730646i	−0.930881	+	0.365323i	$0.880959\pi$
$984$		0			0
$985$		−	15244.9i		−	0.493139i
$986$		0			0
$987$	54239.9	+	54239.9i	1.74921	+	1.74921i
$988$		0			0
$989$	1693.87	−	1693.87i	0.0544611	−	0.0544611i
$990$		0			0
$991$	1836.28			0.0588613			0.0294306	−	0.999567i	$-0.490631\pi$
$991$	1836.28			0.0588613			0.0294306	+	0.999567i	$0.490631\pi$
$992$		0			0
$993$	7920.78			0.253130
$994$		0			0
$995$	−16769.4	+	16769.4i	−0.534298	+	0.534298i
$996$		0			0
$997$	−37880.7	−	37880.7i	−1.20331	−	1.20331i	−0.973155	−	0.230150i	$-0.926078\pi$
$997$	−37880.7	−	37880.7i	−1.20331	−	1.20331i	−0.230150	−	0.973155i	$-0.573922\pi$
$998$		0			0
$999$			8401.15i			0.266067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.4.e.d.193.2	yes	16
4.3	odd	2	inner	256.4.e.d.193.7	yes	16
8.3	odd	2		256.4.e.c.193.2	yes	16
8.5	even	2		256.4.e.c.193.7	yes	16
16.3	odd	4	inner	256.4.e.d.65.7	yes	16
16.5	even	4		256.4.e.c.65.7	yes	16
16.11	odd	4		256.4.e.c.65.2	✓	16
16.13	even	4	inner	256.4.e.d.65.2	yes	16
32.3	odd	8		1024.4.a.l.1.7		8
32.5	even	8		1024.4.b.l.513.4		16
32.11	odd	8		1024.4.b.l.513.3		16
32.13	even	8		1024.4.a.l.1.8		8
32.19	odd	8		1024.4.a.k.1.2		8
32.21	even	8		1024.4.b.l.513.13		16
32.27	odd	8		1024.4.b.l.513.14		16
32.29	even	8		1024.4.a.k.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.4.e.c.65.2	✓	16	16.11	odd	4
256.4.e.c.65.7	yes	16	16.5	even	4
256.4.e.c.193.2	yes	16	8.3	odd	2
256.4.e.c.193.7	yes	16	8.5	even	2
256.4.e.d.65.2	yes	16	16.13	even	4	inner
256.4.e.d.65.7	yes	16	16.3	odd	4	inner
256.4.e.d.193.2	yes	16	1.1	even	1	trivial
256.4.e.d.193.7	yes	16	4.3	odd	2	inner
1024.4.a.k.1.1		8	32.29	even	8
1024.4.a.k.1.2		8	32.19	odd	8
1024.4.a.l.1.7		8	32.3	odd	8
1024.4.a.l.1.8		8	32.13	even	8
1024.4.b.l.513.3		16	32.11	odd	8
1024.4.b.l.513.4		16	32.5	even	8
1024.4.b.l.513.13		16	32.21	even	8
1024.4.b.l.513.14		16	32.27	odd	8

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	256.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.58521 + 3.58521i) q^{3} +(14.4583 + 14.4583i) q^{5} +31.2516i q^{7} +1.29254i q^{9} +(11.5113 + 11.5113i) q^{11} +(37.5976 - 37.5976i) q^{13} -103.672 q^{15} +38.4044 q^{17} +(14.1150 - 14.1150i) q^{19} +(-112.044 - 112.044i) q^{21} -15.4625i q^{23} +293.087i q^{25} +(-101.435 - 101.435i) q^{27} +(106.334 - 106.334i) q^{29} +55.7912 q^{31} -82.5410 q^{33} +(-451.846 + 451.846i) q^{35} +(-41.4116 - 41.4116i) q^{37} +269.591i q^{39} -4.35221i q^{41} +(109.547 + 109.547i) q^{43} +(-18.6879 + 18.6879i) q^{45} -484.096 q^{47} -633.663 q^{49} +(-137.688 + 137.688i) q^{51} +(-206.253 - 206.253i) q^{53} +332.869i q^{55} +101.210i q^{57} +(206.535 + 206.535i) q^{59} +(450.887 - 450.887i) q^{61} -40.3938 q^{63} +1087.20 q^{65} +(428.141 - 428.141i) q^{67} +(55.4364 + 55.4364i) q^{69} -848.499i q^{71} +739.630i q^{73} +(-1050.78 - 1050.78i) q^{75} +(-359.747 + 359.747i) q^{77} +331.933 q^{79} +692.431 q^{81} +(648.125 - 648.125i) q^{83} +(555.264 + 555.264i) q^{85} +762.460i q^{87} -519.978i q^{89} +(1174.99 + 1174.99i) q^{91} +(-200.023 + 200.023i) q^{93} +408.159 q^{95} -1289.64 q^{97} +(-14.8788 + 14.8788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{5} + 320 q^{13} - 384 q^{17} + 224 q^{21} + 928 q^{29} - 2432 q^{33} + 640 q^{37} + 896 q^{45} - 2832 q^{49} + 64 q^{53} + 1024 q^{61} + 2208 q^{65} + 32 q^{69} + 1056 q^{77} + 4208 q^{81}+ \cdots + 4480 q^{97}+O(q^{100}) \) 16 * q + 32 * q^5 + 320 * q^13 - 384 * q^17 + 224 * q^21 + 928 * q^29 - 2432 * q^33 + 640 * q^37 + 896 * q^45 - 2832 * q^49 + 64 * q^53 + 1024 * q^61 + 2208 * q^65 + 32 * q^69 + 1056 * q^77 + 4208 * q^81 + 1824 * q^85 - 3776 * q^93 + 4480 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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