LMFDB - Embedded newform 128.4.e.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(33,128)]

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([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("128.33");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.e (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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 $ x^10 - 2x^9 - x^8 + 6x^7 + 14x^6 - 80x^5 + 56x^4 + 96x^3 - 64x^2 - 512x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.1
Root			$1.28199 - 1.53509i$ of defining polynomial
Character	$\chi$	$=$	128.97
Dual form			128.4.e.b.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.49618 + 5.49618i) q^{3} +(4.66372 + 4.66372i) q^{5} +24.8965i q^{7} -33.4160i q^{9} +O(q^{10})$	\(q+(-5.49618 + 5.49618i) q^{3} +(4.66372 + 4.66372i) q^{5} +24.8965i q^{7} -33.4160i q^{9} +(-22.3431 - 22.3431i) q^{11} +(11.2714 - 11.2714i) q^{13} -51.2653 q^{15} -88.4846 q^{17} +(-37.8187 + 37.8187i) q^{19} +(-136.836 - 136.836i) q^{21} -48.1224i q^{23} -81.4994i q^{25} +(35.2635 + 35.2635i) q^{27} +(-10.4432 + 10.4432i) q^{29} -96.9578 q^{31} +245.604 q^{33} +(-116.110 + 116.110i) q^{35} +(163.279 + 163.279i) q^{37} +123.899i q^{39} +360.519i q^{41} +(100.249 + 100.249i) q^{43} +(155.843 - 155.843i) q^{45} +220.669 q^{47} -276.837 q^{49} +(486.327 - 486.327i) q^{51} +(175.752 + 175.752i) q^{53} -208.404i q^{55} -415.717i q^{57} +(-405.008 - 405.008i) q^{59} +(-664.576 + 664.576i) q^{61} +831.942 q^{63} +105.133 q^{65} +(107.377 - 107.377i) q^{67} +(264.489 + 264.489i) q^{69} -215.050i q^{71} +668.587i q^{73} +(447.935 + 447.935i) q^{75} +(556.266 - 556.266i) q^{77} -822.956 q^{79} +514.603 q^{81} +(-326.873 + 326.873i) q^{83} +(-412.668 - 412.668i) q^{85} -114.795i q^{87} +262.733i q^{89} +(280.619 + 280.619i) q^{91} +(532.898 - 532.898i) q^{93} -352.752 q^{95} -150.801 q^{97} +(-746.618 + 746.618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{3} + 2 q^{5}+O(q^{10}) $ 10 * q + 2 * q^3 + 2 * q^5	$ 10 q + 2 q^{3} + 2 q^{5} - 18 q^{11} + 2 q^{13} - 124 q^{15} - 4 q^{17} + 26 q^{19} - 52 q^{21} - 184 q^{27} + 202 q^{29} + 368 q^{31} - 4 q^{33} - 476 q^{35} + 10 q^{37} + 838 q^{43} - 194 q^{45} - 944 q^{47} + 94 q^{49} + 1500 q^{51} + 378 q^{53} - 1706 q^{59} - 910 q^{61} + 2628 q^{63} - 492 q^{65} - 1942 q^{67} - 580 q^{69} + 2954 q^{75} + 268 q^{77} - 4416 q^{79} + 482 q^{81} + 2562 q^{83} + 12 q^{85} - 3332 q^{91} + 2192 q^{93} + 6900 q^{95} - 4 q^{97} - 4958 q^{99}+O(q^{100}) $ 10 * q + 2 * q^3 + 2 * q^5 - 18 * q^11 + 2 * q^13 - 124 * q^15 - 4 * q^17 + 26 * q^19 - 52 * q^21 - 184 * q^27 + 202 * q^29 + 368 * q^31 - 4 * q^33 - 476 * q^35 + 10 * q^37 + 838 * q^43 - 194 * q^45 - 944 * q^47 + 94 * q^49 + 1500 * q^51 + 378 * q^53 - 1706 * q^59 - 910 * q^61 + 2628 * q^63 - 492 * q^65 - 1942 * q^67 - 580 * q^69 + 2954 * q^75 + 268 * q^77 - 4416 * q^79 + 482 * q^81 + 2562 * q^83 + 12 * q^85 - 3332 * q^91 + 2192 * q^93 + 6900 * q^95 - 4 * q^97 - 4958 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−5.49618	+	5.49618i	−1.05774	+	1.05774i	−0.0595129	+	0.998228i	$0.518955\pi$
$3$	−5.49618	+	5.49618i	−1.05774	+	1.05774i	−0.998228	+	0.0595129i	$0.981045\pi$
$4$		0			0
$5$	4.66372	+	4.66372i	0.417136	+	0.417136i	0.884215	−	0.467079i	$-0.154694\pi$
$5$	4.66372	+	4.66372i	0.417136	+	0.417136i	−0.467079	+	0.884215i	$0.654694\pi$
$6$		0			0
$7$			24.8965i			1.34429i	0.740422	+	0.672143i	$0.234626\pi$
$7$			24.8965i			1.34429i	−0.740422	+	0.672143i	$0.765374\pi$
$8$		0			0
$9$		−	33.4160i		−	1.23763i
$10$		0			0
$11$	−22.3431	−	22.3431i	−0.612427	−	0.612427i	0.331151	−	0.943578i	$-0.392563\pi$
$11$	−22.3431	−	22.3431i	−0.612427	−	0.612427i	−0.943578	+	0.331151i	$0.892563\pi$
$12$		0			0
$13$	11.2714	−	11.2714i	0.240471	−	0.240471i	−0.576574	−	0.817045i	$-0.695611\pi$
$13$	11.2714	−	11.2714i	0.240471	−	0.240471i	0.817045	+	0.576574i	$0.195611\pi$
$14$		0			0
$15$	−51.2653			−0.882443
$16$		0			0
$17$	−88.4846			−1.26239			−0.631196	−	0.775623i	$-0.717436\pi$
$17$	−88.4846			−1.26239			−0.631196	+	0.775623i	$0.717436\pi$
$18$		0			0
$19$	−37.8187	+	37.8187i	−0.456643	+	0.456643i	−0.897552	−	0.440909i	$-0.854656\pi$
$19$	−37.8187	+	37.8187i	−0.456643	+	0.456643i	0.440909	+	0.897552i	$0.354656\pi$
$20$		0			0
$21$	−136.836	−	136.836i	−1.42191	−	1.42191i
$22$		0			0
$23$		−	48.1224i		−	0.436270i	−0.975919	−	0.218135i	$-0.930003\pi$
$23$		−	48.1224i		−	0.436270i	0.975919	−	0.218135i	$-0.0699973\pi$
$24$		0			0
$25$		−	81.4994i		−	0.651995i
$26$		0			0
$27$	35.2635	+	35.2635i	0.251351	+	0.251351i
$28$		0			0
$29$	−10.4432	+	10.4432i	−0.0668705	+	0.0668705i	−0.739751	−	0.672881i	$-0.765057\pi$
$29$	−10.4432	+	10.4432i	−0.0668705	+	0.0668705i	0.672881	+	0.739751i	$0.265057\pi$
$30$		0			0
$31$	−96.9578			−0.561746			−0.280873	−	0.959745i	$-0.590624\pi$
$31$	−96.9578			−0.561746			−0.280873	+	0.959745i	$0.590624\pi$
$32$		0			0
$33$	245.604			1.29558
$34$		0			0
$35$	−116.110	+	116.110i	−0.560750	+	0.560750i
$36$		0			0
$37$	163.279	+	163.279i	0.725484	+	0.725484i	0.969717	−	0.244233i	$-0.0785362\pi$
$37$	163.279	+	163.279i	0.725484	+	0.725484i	−0.244233	+	0.969717i	$0.578536\pi$
$38$		0			0
$39$			123.899i			0.508713i
$40$		0			0
$41$			360.519i			1.37326i	0.727008	+	0.686629i	$0.240910\pi$
$41$			360.519i			1.37326i	−0.727008	+	0.686629i	$0.759090\pi$
$42$		0			0
$43$	100.249	+	100.249i	0.355531	+	0.355531i	0.862163	−	0.506632i	$-0.169110\pi$
$43$	100.249	+	100.249i	0.355531	+	0.355531i	−0.506632	+	0.862163i	$0.669110\pi$
$44$		0			0
$45$	155.843	−	155.843i	0.516260	−	0.516260i
$46$		0			0
$47$	220.669			0.684849			0.342425	−	0.939545i	$-0.388752\pi$
$47$	220.669			0.684849			0.342425	+	0.939545i	$0.388752\pi$
$48$		0			0
$49$	−276.837			−0.807104
$50$		0			0
$51$	486.327	−	486.327i	1.33528	−	1.33528i
$52$		0			0
$53$	175.752	+	175.752i	0.455498	+	0.455498i	0.897174	−	0.441676i	$-0.145616\pi$
$53$	175.752	+	175.752i	0.455498	+	0.455498i	−0.441676	+	0.897174i	$0.645616\pi$
$54$		0			0
$55$		−	208.404i		−	0.510931i
$56$		0			0
$57$		−	415.717i		−	0.966019i
$58$		0			0
$59$	−405.008	−	405.008i	−0.893687	−	0.893687i	0.101181	−	0.994868i	$-0.467738\pi$
$59$	−405.008	−	405.008i	−0.893687	−	0.893687i	−0.994868	+	0.101181i	$0.967738\pi$
$60$		0			0
$61$	−664.576	+	664.576i	−1.39492	+	1.39492i	−0.581061	+	0.813860i	$0.697362\pi$
$61$	−664.576	+	664.576i	−1.39492	+	1.39492i	−0.813860	+	0.581061i	$0.802638\pi$
$62$		0			0
$63$	831.942			1.66373
$64$		0			0
$65$	105.133			0.200619
$66$		0			0
$67$	107.377	−	107.377i	0.195794	−	0.195794i	−0.602400	−	0.798194i	$-0.705789\pi$
$67$	107.377	−	107.377i	0.195794	−	0.195794i	0.798194	+	0.602400i	$0.205789\pi$
$68$		0			0
$69$	264.489	+	264.489i	0.461461	+	0.461461i
$70$		0			0
$71$		−	215.050i		−	0.359461i	−0.983716	−	0.179731i	$-0.942477\pi$
$71$		−	215.050i		−	0.359461i	0.983716	−	0.179731i	$-0.0575226\pi$
$72$		0			0
$73$			668.587i			1.07195i	0.844235	+	0.535974i	$0.180055\pi$
$73$			668.587i			1.07195i	−0.844235	+	0.535974i	$0.819945\pi$
$74$		0			0
$75$	447.935	+	447.935i	0.689642	+	0.689642i
$76$		0			0
$77$	556.266	−	556.266i	0.823277	−	0.823277i
$78$		0			0
$79$	−822.956			−1.17202			−0.586012	−	0.810303i	$-0.699303\pi$
$79$	−822.956			−1.17202			−0.586012	+	0.810303i	$0.699303\pi$
$80$		0			0
$81$	514.603			0.705902
$82$		0			0
$83$	−326.873	+	326.873i	−0.432277	+	0.432277i	−0.889402	−	0.457125i	$-0.848879\pi$
$83$	−326.873	+	326.873i	−0.432277	+	0.432277i	0.457125	+	0.889402i	$0.348879\pi$
$84$		0			0
$85$	−412.668	−	412.668i	−0.526589	−	0.526589i
$86$		0			0
$87$		−	114.795i		−	0.141463i
$88$		0			0
$89$			262.733i			0.312918i	0.987684	+	0.156459i	$0.0500079\pi$
$89$			262.733i			0.312918i	−0.987684	+	0.156459i	$0.949992\pi$
$90$		0			0
$91$	280.619	+	280.619i	0.323262	+	0.323262i
$92$		0			0
$93$	532.898	−	532.898i	0.594182	−	0.594182i
$94$		0			0
$95$	−352.752			−0.380964
$96$		0			0
$97$	−150.801			−0.157850			−0.0789251	−	0.996881i	$-0.525149\pi$
$97$	−150.801			−0.157850			−0.0789251	+	0.996881i	$0.525149\pi$
$98$		0			0
$99$	−746.618	+	746.618i	−0.757958	+	0.757958i
$100$		0			0
$101$	−487.985	−	487.985i	−0.480755	−	0.480755i	0.424617	−	0.905373i	$-0.360409\pi$
$101$	−487.985	−	487.985i	−0.480755	−	0.480755i	−0.905373	+	0.424617i	$0.860409\pi$
$102$		0			0
$103$			1840.58i			1.76075i	0.474275	+	0.880377i	$0.342710\pi$
$103$			1840.58i			1.76075i	−0.474275	+	0.880377i	$0.657290\pi$
$104$		0			0
$105$		−	1276.33i		−	1.18626i
$106$		0			0
$107$	79.4098	+	79.4098i	0.0717461	+	0.0717461i	0.742069	−	0.670323i	$-0.233845\pi$
$107$	79.4098	+	79.4098i	0.0717461	+	0.0717461i	−0.670323	+	0.742069i	$0.733845\pi$
$108$		0			0
$109$	−952.979	+	952.979i	−0.837421	+	0.837421i	−0.988519	−	0.151098i	$-0.951719\pi$
$109$	−952.979	+	952.979i	−0.837421	+	0.837421i	0.151098	+	0.988519i	$0.451719\pi$
$110$		0			0
$111$	−1794.82			−1.53475
$112$		0			0
$113$	−720.469			−0.599788			−0.299894	−	0.953973i	$-0.596951\pi$
$113$	−720.469			−0.599788			−0.299894	+	0.953973i	$0.596951\pi$
$114$		0			0
$115$	224.430	−	224.430i	0.181984	−	0.181984i
$116$		0			0
$117$	−376.646	−	376.646i	−0.297615	−	0.297615i
$118$		0			0
$119$		−	2202.96i		−	1.69702i
$120$		0			0
$121$		−	332.571i		−	0.249865i
$122$		0			0
$123$	−1981.48	−	1981.48i	−1.45255	−	1.45255i
$124$		0			0
$125$	963.056	−	963.056i	0.689107	−	0.689107i
$126$		0			0
$127$	2622.35			1.83225			0.916124	−	0.400895i	$-0.131301\pi$
$127$	2622.35			1.83225			0.916124	+	0.400895i	$0.131301\pi$
$128$		0			0
$129$	−1101.97			−0.752119
$130$		0			0
$131$	−657.574	+	657.574i	−0.438569	+	0.438569i	−0.891530	−	0.452961i	$-0.850368\pi$
$131$	−657.574	+	657.574i	−0.438569	+	0.438569i	0.452961	+	0.891530i	$0.350368\pi$
$132$		0			0
$133$	−941.555	−	941.555i	−0.613858	−	0.613858i
$134$		0			0
$135$			328.919i			0.209695i
$136$		0			0
$137$		−	2511.52i		−	1.56623i	−0.621874	−	0.783117i	$-0.713629\pi$
$137$		−	2511.52i		−	1.56623i	0.621874	−	0.783117i	$-0.286371\pi$
$138$		0			0
$139$	1086.02	+	1086.02i	0.662697	+	0.662697i	0.956015	−	0.293318i	$-0.0947595\pi$
$139$	1086.02	+	1086.02i	0.662697	+	0.662697i	−0.293318	+	0.956015i	$0.594759\pi$
$140$		0			0
$141$	−1212.84	+	1212.84i	−0.724393	+	0.724393i
$142$		0			0
$143$	−503.677			−0.294543
$144$		0			0
$145$	−97.4080			−0.0557882
$146$		0			0
$147$	1521.54	−	1521.54i	0.853706	−	0.853706i
$148$		0			0
$149$	2284.63	+	2284.63i	1.25614	+	1.25614i	0.952922	+	0.303214i	$0.0980598\pi$
$149$	2284.63	+	2284.63i	1.25614	+	1.25614i	0.303214	+	0.952922i	$0.401940\pi$
$150$		0			0
$151$			2814.39i			1.51677i	0.651809	+	0.758383i	$0.274010\pi$
$151$			2814.39i			1.51677i	−0.651809	+	0.758383i	$0.725990\pi$
$152$		0			0
$153$			2956.80i			1.56237i
$154$		0			0
$155$	−452.184	−	452.184i	−0.234325	−	0.234325i
$156$		0			0
$157$	906.308	−	906.308i	0.460709	−	0.460709i	−0.438179	−	0.898888i	$-0.644376\pi$
$157$	906.308	−	906.308i	0.460709	−	0.460709i	0.898888	+	0.438179i	$0.144376\pi$
$158$		0			0
$159$	−1931.93			−0.963598
$160$		0			0
$161$	1198.08			0.586472
$162$		0			0
$163$	−1392.36	+	1392.36i	−0.669067	+	0.669067i	−0.957500	−	0.288433i	$-0.906866\pi$
$163$	−1392.36	+	1392.36i	−0.669067	+	0.669067i	0.288433	+	0.957500i	$0.406866\pi$
$164$		0			0
$165$	1145.43	+	1145.43i	0.540433	+	0.540433i
$166$		0			0
$167$			1221.66i			0.566075i	0.959109	+	0.283038i	$0.0913421\pi$
$167$			1221.66i			0.566075i	−0.959109	+	0.283038i	$0.908658\pi$
$168$		0			0
$169$			1942.91i			0.884347i
$170$		0			0
$171$	1263.75	+	1263.75i	0.565155	+	0.565155i
$172$		0			0
$173$	563.418	−	563.418i	0.247606	−	0.247606i	−0.572381	−	0.819988i	$-0.693980\pi$
$173$	563.418	−	563.418i	0.247606	−	0.247606i	0.819988	+	0.572381i	$0.193980\pi$
$174$		0			0
$175$	2029.05			0.876468
$176$		0			0
$177$	4451.99			1.89058
$178$		0			0
$179$	2202.23	−	2202.23i	0.919565	−	0.919565i	−0.0774329	−	0.996998i	$-0.524672\pi$
$179$	2202.23	−	2202.23i	0.919565	−	0.919565i	0.996998	+	0.0774329i	$0.0246724\pi$
$180$		0			0
$181$	−121.294	−	121.294i	−0.0498104	−	0.0498104i	0.681763	−	0.731573i	$-0.261214\pi$
$181$	−121.294	−	121.294i	−0.0498104	−	0.0498104i	−0.731573	+	0.681763i	$0.761214\pi$
$182$		0			0
$183$		−	7305.26i		−	2.95093i
$184$		0			0
$185$			1522.98i			0.605251i
$186$		0			0
$187$	1977.02	+	1977.02i	0.773124	+	0.773124i
$188$		0			0
$189$	−877.939	+	877.939i	−0.337887	+	0.337887i
$190$		0			0
$191$	3927.65			1.48793			0.743966	−	0.668218i	$-0.232942\pi$
$191$	3927.65			1.48793			0.743966	+	0.668218i	$0.232942\pi$
$192$		0			0
$193$	−3249.02			−1.21176			−0.605880	−	0.795556i	$-0.707179\pi$
$193$	−3249.02			−1.21176			−0.605880	+	0.795556i	$0.707179\pi$
$194$		0			0
$195$	−577.833	+	577.833i	−0.212202	+	0.212202i
$196$		0			0
$197$	−2420.90	−	2420.90i	−0.875545	−	0.875545i	0.117525	−	0.993070i	$-0.462504\pi$
$197$	−2420.90	−	2420.90i	−0.875545	−	0.875545i	−0.993070	+	0.117525i	$0.962504\pi$
$198$		0			0
$199$		−	1371.30i		−	0.488488i	−0.969714	−	0.244244i	$-0.921460\pi$
$199$		−	1371.30i		−	0.488488i	0.969714	−	0.244244i	$-0.0785397\pi$
$200$		0			0
$201$			1180.33i			0.414198i
$202$		0			0
$203$	−259.998	−	259.998i	−0.0898931	−	0.0898931i
$204$		0			0
$205$	−1681.36	+	1681.36i	−0.572836	+	0.572836i
$206$		0			0
$207$	−1608.06			−0.539941
$208$		0			0
$209$	1689.98			0.559321
$210$		0			0
$211$	1620.50	−	1620.50i	0.528719	−	0.528719i	−0.391471	−	0.920190i	$-0.628034\pi$
$211$	1620.50	−	1620.50i	0.528719	−	0.528719i	0.920190	+	0.391471i	$0.128034\pi$
$212$		0			0
$213$	1181.95	+	1181.95i	0.380217	+	0.380217i
$214$		0			0
$215$			935.068i			0.296610i
$216$		0			0
$217$		−	2413.91i		−	0.755148i
$218$		0			0
$219$	−3674.67	−	3674.67i	−1.13384	−	1.13384i
$220$		0			0
$221$	−997.347	+	997.347i	−0.303569	+	0.303569i
$222$		0			0
$223$	−419.617			−0.126007			−0.0630036	−	0.998013i	$-0.520068\pi$
$223$	−419.617			−0.126007			−0.0630036	+	0.998013i	$0.520068\pi$
$224$		0			0
$225$	−2723.38			−0.806929
$226$		0			0
$227$	2133.64	−	2133.64i	0.623853	−	0.623853i	−0.322661	−	0.946515i	$-0.604577\pi$
$227$	2133.64	−	2133.64i	0.623853	−	0.623853i	0.946515	+	0.322661i	$0.104577\pi$
$228$		0			0
$229$	1574.42	+	1574.42i	0.454325	+	0.454325i	0.896787	−	0.442462i	$-0.145895\pi$
$229$	1574.42	+	1574.42i	0.454325	+	0.454325i	−0.442462	+	0.896787i	$0.645895\pi$
$230$		0			0
$231$			6114.67i			1.74163i
$232$		0			0
$233$		−	1194.86i		−	0.335957i	−0.985791	−	0.167978i	$-0.946276\pi$
$233$		−	1194.86i		−	0.335957i	0.985791	−	0.167978i	$-0.0537239\pi$
$234$		0			0
$235$	1029.14	+	1029.14i	0.285675	+	0.285675i
$236$		0			0
$237$	4523.12	−	4523.12i	1.23970	−	1.23970i
$238$		0			0
$239$	−4241.03			−1.14782			−0.573911	−	0.818917i	$-0.694575\pi$
$239$	−4241.03			−1.14782			−0.573911	+	0.818917i	$0.694575\pi$
$240$		0			0
$241$	−5571.19			−1.48910			−0.744548	−	0.667569i	$-0.767335\pi$
$241$	−5571.19			−1.48910			−0.744548	+	0.667569i	$0.767335\pi$
$242$		0			0
$243$	−3780.46	+	3780.46i	−0.998012	+	0.998012i
$244$		0			0
$245$	−1291.09	−	1291.09i	−0.336672	−	0.336672i
$246$		0			0
$247$			852.541i			0.219619i
$248$		0			0
$249$		−	3593.11i		−	0.914474i
$250$		0			0
$251$	482.728	+	482.728i	0.121393	+	0.121393i	0.765193	−	0.643801i	$-0.222643\pi$
$251$	482.728	+	482.728i	0.121393	+	0.121393i	−0.643801	+	0.765193i	$0.722643\pi$
$252$		0			0
$253$	−1075.20	+	1075.20i	−0.267184	+	0.267184i
$254$		0			0
$255$	4536.19			1.11399
$256$		0			0
$257$	8093.12			1.96434			0.982169	−	0.188002i	$-0.0602013\pi$
$257$	8093.12			1.96434			0.982169	+	0.188002i	$0.0602013\pi$
$258$		0			0
$259$	−4065.08	+	4065.08i	−0.975257	+	0.975257i
$260$		0			0
$261$	348.969	+	348.969i	0.0827610	+	0.0827610i
$262$		0			0
$263$			410.300i			0.0961984i	0.998843	+	0.0480992i	$0.0153164\pi$
$263$			410.300i			0.0961984i	−0.998843	+	0.0480992i	$0.984684\pi$
$264$		0			0
$265$			1639.32i			0.380009i
$266$		0			0
$267$	−1444.03	−	1444.03i	−0.330986	−	0.330986i
$268$		0			0
$269$	4.77962	−	4.77962i	0.00108334	−	0.00108334i	−0.706565	−	0.707648i	$-0.749756\pi$
$269$	4.77962	−	4.77962i	0.00108334	−	0.00108334i	0.707648	+	0.706565i	$0.249756\pi$
$270$		0			0
$271$	−2833.98			−0.635247			−0.317623	−	0.948217i	$-0.602885\pi$
$271$	−2833.98			−0.635247			−0.317623	+	0.948217i	$0.602885\pi$
$272$		0			0
$273$	−3084.67			−0.683855
$274$		0			0
$275$	−1820.95	+	1820.95i	−0.399300	+	0.399300i
$276$		0			0
$277$	−1525.80	−	1525.80i	−0.330962	−	0.330962i	0.521989	−	0.852952i	$-0.325190\pi$
$277$	−1525.80	−	1525.80i	−0.330962	−	0.330962i	−0.852952	+	0.521989i	$0.825190\pi$
$278$		0			0
$279$			3239.94i			0.695234i
$280$		0			0
$281$		−	4750.23i		−	1.00845i	−0.863572	−	0.504226i	$-0.831778\pi$
$281$		−	4750.23i		−	1.00845i	0.863572	−	0.504226i	$-0.168222\pi$
$282$		0			0
$283$	−644.104	−	644.104i	−0.135293	−	0.135293i	0.636217	−	0.771510i	$-0.280498\pi$
$283$	−644.104	−	644.104i	−0.135293	−	0.135293i	−0.771510	+	0.636217i	$0.780498\pi$
$284$		0			0
$285$	1938.79	−	1938.79i	0.402961	−	0.402961i
$286$		0			0
$287$	−8975.67			−1.84605
$288$		0			0
$289$	2916.53			0.593635
$290$		0			0
$291$	828.827	−	828.827i	0.166965	−	0.166965i
$292$		0			0
$293$	1433.16	+	1433.16i	0.285755	+	0.285755i	0.835399	−	0.549644i	$-0.185237\pi$
$293$	1433.16	+	1433.16i	0.285755	+	0.285755i	−0.549644	+	0.835399i	$0.685237\pi$
$294$		0			0
$295$		−	3777.69i		−	0.745578i
$296$		0			0
$297$		−	1575.79i		−	0.307868i
$298$		0			0
$299$	−542.407	−	542.407i	−0.104910	−	0.104910i
$300$		0			0
$301$	−2495.85	+	2495.85i	−0.477935	+	0.477935i
$302$		0			0
$303$	5364.10			1.01703
$304$		0			0
$305$	−6198.79			−1.16374
$306$		0			0
$307$	231.211	−	231.211i	0.0429834	−	0.0429834i	−0.685288	−	0.728272i	$-0.740324\pi$
$307$	231.211	−	231.211i	0.0429834	−	0.0429834i	0.728272	+	0.685288i	$0.240324\pi$
$308$		0			0
$309$	−10116.2	−	10116.2i	−1.86242	−	1.86242i
$310$		0			0
$311$		−	871.410i		−	0.158885i	−0.996839	−	0.0794423i	$-0.974686\pi$
$311$		−	871.410i		−	0.158885i	0.996839	−	0.0794423i	$-0.0253140\pi$
$312$		0			0
$313$			3515.02i			0.634762i	0.948298	+	0.317381i	$0.102803\pi$
$313$			3515.02i			0.634762i	−0.948298	+	0.317381i	$0.897197\pi$
$314$		0			0
$315$	3879.95	+	3879.95i	0.694001	+	0.694001i
$316$		0			0
$317$	−4723.77	+	4723.77i	−0.836951	+	0.836951i	−0.988456	−	0.151506i	$-0.951588\pi$
$317$	−4723.77	+	4723.77i	−0.836951	+	0.836951i	0.151506	+	0.988456i	$0.451588\pi$
$318$		0			0
$319$	466.665			0.0819067
$320$		0			0
$321$	−872.901			−0.151778
$322$		0			0
$323$	3346.38	−	3346.38i	0.576462	−	0.576462i
$324$		0			0
$325$	−918.613	−	918.613i	−0.156786	−	0.156786i
$326$		0			0
$327$		−	10475.5i		−	1.77155i
$328$		0			0
$329$			5493.90i			0.920633i
$330$		0			0
$331$	1820.26	+	1820.26i	0.302268	+	0.302268i	0.841901	−	0.539633i	$-0.181437\pi$
$331$	1820.26	+	1820.26i	0.302268	+	0.302268i	−0.539633	+	0.841901i	$0.681437\pi$
$332$		0			0
$333$	5456.13	−	5456.13i	0.897880	−	0.897880i
$334$		0			0
$335$	1001.55			0.163345
$336$		0			0
$337$	74.0970			0.0119772			0.00598861	−	0.999982i	$-0.498094\pi$
$337$	74.0970			0.0119772			0.00598861	+	0.999982i	$0.498094\pi$
$338$		0			0
$339$	3959.83	−	3959.83i	0.634420	−	0.634420i
$340$		0			0
$341$	2166.34	+	2166.34i	0.344029	+	0.344029i
$342$		0			0
$343$			1647.24i			0.259307i
$344$		0			0
$345$			2467.01i			0.384984i
$346$		0			0
$347$	−2102.73	−	2102.73i	−0.325305	−	0.325305i	0.525493	−	0.850798i	$-0.323881\pi$
$347$	−2102.73	−	2102.73i	−0.325305	−	0.325305i	−0.850798	+	0.525493i	$0.823881\pi$
$348$		0			0
$349$	6612.85	−	6612.85i	1.01426	−	1.01426i	0.0143661	−	0.999897i	$-0.495427\pi$
$349$	6612.85	−	6612.85i	1.01426	−	1.01426i	0.999897	−	0.0143661i	$-0.00457302\pi$
$350$		0			0
$351$	794.940			0.120885
$352$		0			0
$353$	2216.90			0.334259			0.167130	−	0.985935i	$-0.446550\pi$
$353$	2216.90			0.334259			0.167130	+	0.985935i	$0.446550\pi$
$354$		0			0
$355$	1002.93	−	1002.93i	0.149944	−	0.149944i
$356$		0			0
$357$	12107.9	+	12107.9i	1.79500	+	1.79500i
$358$		0			0
$359$			2082.23i			0.306117i	0.988217	+	0.153059i	$0.0489123\pi$
$359$			2082.23i			0.306117i	−0.988217	+	0.153059i	$0.951088\pi$
$360$		0			0
$361$			3998.49i			0.582955i
$362$		0			0
$363$	1827.87	+	1827.87i	0.264293	+	0.264293i
$364$		0			0
$365$	−3118.10	+	3118.10i	−0.447148	+	0.447148i
$366$		0			0
$367$	4509.22			0.641360			0.320680	−	0.947188i	$-0.396089\pi$
$367$	4509.22			0.641360			0.320680	+	0.947188i	$0.396089\pi$
$368$		0			0
$369$	12047.1			1.69959
$370$		0			0
$371$	−4375.61	+	4375.61i	−0.612320	+	0.612320i
$372$		0			0
$373$	8661.56	+	8661.56i	1.20236	+	1.20236i	0.973448	+	0.228908i	$0.0735154\pi$
$373$	8661.56	+	8661.56i	1.20236	+	1.20236i	0.228908	+	0.973448i	$0.426485\pi$
$374$		0			0
$375$			10586.3i			1.45779i
$376$		0			0
$377$			235.418i			0.0321609i
$378$		0			0
$379$	−3522.46	−	3522.46i	−0.477405	−	0.477405i	0.426896	−	0.904301i	$-0.359607\pi$
$379$	−3522.46	−	3522.46i	−0.477405	−	0.477405i	−0.904301	+	0.426896i	$0.859607\pi$
$380$		0			0
$381$	−14412.9	+	14412.9i	−1.93804	+	1.93804i
$382$		0			0
$383$	3044.88			0.406229			0.203115	−	0.979155i	$-0.434894\pi$
$383$	3044.88			0.406229			0.203115	+	0.979155i	$0.434894\pi$
$384$		0			0
$385$	5188.54			0.686837
$386$		0			0
$387$	3349.92	−	3349.92i	0.440016	−	0.440016i
$388$		0			0
$389$	−1932.73	−	1932.73i	−0.251911	−	0.251911i	0.569843	−	0.821754i	$-0.307004\pi$
$389$	−1932.73	−	1932.73i	−0.251911	−	0.251911i	−0.821754	+	0.569843i	$0.807004\pi$
$390$		0			0
$391$			4258.09i			0.550744i
$392$		0			0
$393$		−	7228.29i		−	0.927784i
$394$		0			0
$395$	−3838.04	−	3838.04i	−0.488893	−	0.488893i
$396$		0			0
$397$	672.457	−	672.457i	0.0850117	−	0.0850117i	−0.663322	−	0.748334i	$-0.730854\pi$
$397$	672.457	−	672.457i	0.0850117	−	0.0850117i	0.748334	+	0.663322i	$0.230854\pi$
$398$		0			0
$399$	10349.9			1.29861
$400$		0			0
$401$	−7606.74			−0.947288			−0.473644	−	0.880716i	$-0.657062\pi$
$401$	−7606.74			−0.947288			−0.473644	+	0.880716i	$0.657062\pi$
$402$		0			0
$403$	−1092.85	+	1092.85i	−0.135084	+	0.135084i
$404$		0			0
$405$	2399.96	+	2399.96i	0.294457	+	0.294457i
$406$		0			0
$407$		−	7296.32i		−	0.888612i
$408$		0			0
$409$		−	4981.58i		−	0.602257i	−0.953584	−	0.301129i	$-0.902637\pi$
$409$		−	4981.58i		−	0.602257i	0.953584	−	0.301129i	$-0.0973634\pi$
$410$		0			0
$411$	13803.8	+	13803.8i	1.65667	+	1.65667i
$412$		0			0
$413$	10083.3	−	10083.3i	1.20137	−	1.20137i
$414$		0			0
$415$	−3048.89			−0.360637
$416$		0			0
$417$	−11937.9			−1.40192
$418$		0			0
$419$	3433.38	−	3433.38i	0.400314	−	0.400314i	−0.478030	−	0.878344i	$-0.658649\pi$
$419$	3433.38	−	3433.38i	0.400314	−	0.400314i	0.878344	+	0.478030i	$0.158649\pi$
$420$		0			0
$421$	−7973.72	−	7973.72i	−0.923077	−	0.923077i	0.0741686	−	0.997246i	$-0.476370\pi$
$421$	−7973.72	−	7973.72i	−0.923077	−	0.923077i	−0.997246	+	0.0741686i	$0.976370\pi$
$422$		0			0
$423$		−	7373.88i		−	0.847590i
$424$		0			0
$425$			7211.44i			0.823074i
$426$		0			0
$427$	−16545.6	−	16545.6i	−1.87517	−	1.87517i
$428$		0			0
$429$	2768.30	−	2768.30i	0.311550	−	0.311550i
$430$		0			0
$431$	4800.16			0.536463			0.268232	−	0.963354i	$-0.413561\pi$
$431$	4800.16			0.536463			0.268232	+	0.963354i	$0.413561\pi$
$432$		0			0
$433$	6242.32			0.692810			0.346405	−	0.938085i	$-0.387402\pi$
$433$	6242.32			0.692810			0.346405	+	0.938085i	$0.387402\pi$
$434$		0			0
$435$	535.372	−	535.372i	0.0590095	−	0.0590095i
$436$		0			0
$437$	1819.93	+	1819.93i	0.199220	+	0.199220i
$438$		0			0
$439$		−	4929.27i		−	0.535903i	−0.963432	−	0.267951i	$-0.913653\pi$
$439$		−	4929.27i		−	0.535903i	0.963432	−	0.267951i	$-0.0863466\pi$
$440$		0			0
$441$			9250.77i			0.998896i
$442$		0			0
$443$	7670.67	+	7670.67i	0.822674	+	0.822674i	0.986491	−	0.163817i	$-0.0523807\pi$
$443$	7670.67	+	7670.67i	0.822674	+	0.822674i	−0.163817	+	0.986491i	$0.552381\pi$
$444$		0			0
$445$	−1225.32	+	1225.32i	−0.130529	+	0.130529i
$446$		0			0
$447$	−25113.5			−2.65733
$448$		0			0
$449$	−11515.2			−1.21032			−0.605162	−	0.796102i	$-0.706892\pi$
$449$	−11515.2			−1.21032			−0.605162	+	0.796102i	$0.706892\pi$
$450$		0			0
$451$	8055.12	−	8055.12i	0.841021	−	0.841021i
$452$		0			0
$453$	−15468.4	−	15468.4i	−1.60434	−	1.60434i
$454$		0			0
$455$			2617.46i			0.269689i
$456$		0			0
$457$		−	4829.89i		−	0.494383i	−0.968967	−	0.247191i	$-0.920492\pi$
$457$		−	4829.89i		−	0.494383i	0.968967	−	0.247191i	$-0.0795076\pi$
$458$		0			0
$459$	−3120.28	−	3120.28i	−0.317303	−	0.317303i
$460$		0			0
$461$	−8265.79	+	8265.79i	−0.835090	+	0.835090i	−0.988208	−	0.153118i	$-0.951069\pi$
$461$	−8265.79	+	8265.79i	−0.835090	+	0.835090i	0.153118	+	0.988208i	$0.451069\pi$
$462$		0			0
$463$	−5043.86			−0.506281			−0.253141	−	0.967430i	$-0.581464\pi$
$463$	−5043.86			−0.506281			−0.253141	+	0.967430i	$0.581464\pi$
$464$		0			0
$465$	4970.57			0.495709
$466$		0			0
$467$	−12438.8	+	12438.8i	−1.23255	+	1.23255i	−0.269564	+	0.962982i	$0.586880\pi$
$467$	−12438.8	+	12438.8i	−1.23255	+	1.23255i	−0.962982	+	0.269564i	$0.913120\pi$
$468$		0			0
$469$	2673.31	+	2673.31i	0.263203	+	0.263203i
$470$		0			0
$471$			9962.47i			0.974621i
$472$		0			0
$473$		−	4479.75i		−	0.435474i
$474$		0			0
$475$	3082.20	+	3082.20i	0.297729	+	0.297729i
$476$		0			0
$477$	5872.93	−	5872.93i	0.563738	−	0.563738i
$478$		0			0
$479$	13059.7			1.24575			0.622875	−	0.782321i	$-0.285964\pi$
$479$	13059.7			1.24575			0.622875	+	0.782321i	$0.285964\pi$
$480$		0			0
$481$	3680.77			0.348916
$482$		0			0
$483$	−6584.87	+	6584.87i	−0.620335	+	0.620335i
$484$		0			0
$485$	−703.292	−	703.292i	−0.0658450	−	0.0658450i
$486$		0			0
$487$		−	15549.3i		−	1.44683i	−0.690414	−	0.723414i	$-0.742572\pi$
$487$		−	15549.3i		−	1.44683i	0.690414	−	0.723414i	$-0.257428\pi$
$488$		0			0
$489$		−	15305.3i		−	1.41540i
$490$		0			0
$491$	8628.34	+	8628.34i	0.793058	+	0.793058i	0.981990	−	0.188932i	$-0.0605027\pi$
$491$	8628.34	+	8628.34i	0.793058	+	0.793058i	−0.188932	+	0.981990i	$0.560503\pi$
$492$		0			0
$493$	924.059	−	924.059i	0.0844169	−	0.0844169i
$494$		0			0
$495$	−6964.03			−0.632344
$496$		0			0
$497$	5354.00			0.483219
$498$		0			0
$499$	−1732.42	+	1732.42i	−0.155418	+	0.155418i	−0.780533	−	0.625115i	$-0.785052\pi$
$499$	−1732.42	+	1732.42i	−0.155418	+	0.155418i	0.625115	+	0.780533i	$0.285052\pi$
$500$		0			0
$501$	−6714.44	−	6714.44i	−0.598761	−	0.598761i
$502$		0			0
$503$			16579.6i			1.46968i	0.678241	+	0.734839i	$0.262742\pi$
$503$			16579.6i			1.46968i	−0.678241	+	0.734839i	$0.737258\pi$
$504$		0			0
$505$		−	4551.65i		−	0.401081i
$506$		0			0
$507$	−10678.6	−	10678.6i	−0.935410	−	0.935410i
$508$		0			0
$509$	7830.92	−	7830.92i	0.681924	−	0.681924i	−0.278509	−	0.960434i	$-0.589840\pi$
$509$	7830.92	−	7830.92i	0.681924	−	0.681924i	0.960434	+	0.278509i	$0.0898403\pi$
$510$		0			0
$511$	−16645.5			−1.44100
$512$		0			0
$513$	−2667.24			−0.229555
$514$		0			0
$515$	−8583.95	+	8583.95i	−0.734474	+	0.734474i
$516$		0			0
$517$	−4930.44	−	4930.44i	−0.419420	−	0.419420i
$518$		0			0
$519$			6193.30i			0.523807i
$520$		0			0
$521$			3400.02i			0.285907i	0.989729	+	0.142953i	$0.0456599\pi$
$521$			3400.02i			0.285907i	−0.989729	+	0.142953i	$0.954340\pi$
$522$		0			0
$523$	2019.50	+	2019.50i	0.168847	+	0.168847i	0.786472	−	0.617626i	$-0.211905\pi$
$523$	2019.50	+	2019.50i	0.168847	+	0.168847i	−0.617626	+	0.786472i	$0.711905\pi$
$524$		0			0
$525$	−11152.0	+	11152.0i	−0.927075	+	0.927075i
$526$		0			0
$527$	8579.28			0.709144
$528$		0			0
$529$	9851.23			0.809668
$530$		0			0
$531$	−13533.7	+	13533.7i	−1.10605	+	1.10605i
$532$		0			0
$533$	4063.56	+	4063.56i	0.330229	+	0.330229i
$534$		0			0
$535$			740.691i			0.0598558i
$536$		0			0
$537$			24207.7i			1.94532i
$538$		0			0
$539$	6185.39	+	6185.39i	0.494293	+	0.494293i
$540$		0			0
$541$	13432.6	−	13432.6i	1.06749	−	1.06749i	0.0699388	−	0.997551i	$-0.477720\pi$
$541$	13432.6	−	13432.6i	1.06749	−	1.06749i	0.997551	−	0.0699388i	$-0.0222804\pi$
$542$		0			0
$543$	1333.30			0.105373
$544$		0			0
$545$	−8888.86			−0.698637
$546$		0			0
$547$	5376.46	−	5376.46i	0.420257	−	0.420257i	−0.465035	−	0.885292i	$-0.653958\pi$
$547$	5376.46	−	5376.46i	0.420257	−	0.420257i	0.885292	+	0.465035i	$0.153958\pi$
$548$		0			0
$549$	22207.5	+	22207.5i	1.72640	+	1.72640i
$550$		0			0
$551$		−	789.894i		−	0.0610719i
$552$		0			0
$553$		−	20488.7i		−	1.57553i
$554$		0			0
$555$	−8370.55	−	8370.55i	−0.640198	−	0.640198i
$556$		0			0
$557$	2076.28	−	2076.28i	0.157944	−	0.157944i	−0.623711	−	0.781655i	$-0.714376\pi$
$557$	2076.28	−	2076.28i	0.157944	−	0.157944i	0.781655	+	0.623711i	$0.214376\pi$
$558$		0			0
$559$	2259.90			0.170990
$560$		0			0
$561$	−21732.1			−1.63553
$562$		0			0
$563$	16643.1	−	16643.1i	1.24587	−	1.24587i	0.288339	−	0.957528i	$-0.406897\pi$
$563$	16643.1	−	16643.1i	1.24587	−	1.24587i	0.957528	−	0.288339i	$-0.0931031\pi$
$564$		0			0
$565$	−3360.07	−	3360.07i	−0.250193	−	0.250193i
$566$		0			0
$567$			12811.8i			0.948934i
$568$		0			0
$569$		−	5659.60i		−	0.416982i	−0.978024	−	0.208491i	$-0.933145\pi$
$569$		−	5659.60i		−	0.416982i	0.978024	−	0.208491i	$-0.0668551\pi$
$570$		0			0
$571$	−4872.67	−	4872.67i	−0.357119	−	0.357119i	0.505631	−	0.862750i	$-0.331260\pi$
$571$	−4872.67	−	4872.67i	−0.357119	−	0.357119i	−0.862750	+	0.505631i	$0.831260\pi$
$572$		0			0
$573$	−21587.1	+	21587.1i	−1.57385	+	1.57385i
$574$		0			0
$575$	−3921.95			−0.284446
$576$		0			0
$577$	10652.2			0.768556			0.384278	−	0.923217i	$-0.374450\pi$
$577$	10652.2			0.768556			0.384278	+	0.923217i	$0.374450\pi$
$578$		0			0
$579$	17857.2	−	17857.2i	1.28173	−	1.28173i
$580$		0			0
$581$	−8138.01	−	8138.01i	−0.581104	−	0.581104i
$582$		0			0
$583$		−	7853.69i		−	0.557919i
$584$		0			0
$585$		−	3513.14i		−	0.248291i
$586$		0			0
$587$	−9903.95	−	9903.95i	−0.696388	−	0.696388i	0.267242	−	0.963630i	$-0.413888\pi$
$587$	−9903.95	−	9903.95i	−0.696388	−	0.696388i	−0.963630	+	0.267242i	$0.913888\pi$
$588$		0			0
$589$	3666.82	−	3666.82i	0.256517	−	0.256517i
$590$		0			0
$591$	26611.5			1.85220
$592$		0			0
$593$	−3528.04			−0.244316			−0.122158	−	0.992511i	$-0.538981\pi$
$593$	−3528.04			−0.244316			−0.122158	+	0.992511i	$0.538981\pi$
$594$		0			0
$595$	10274.0	−	10274.0i	0.707887	−	0.707887i
$596$		0			0
$597$	7536.93	+	7536.93i	0.516693	+	0.516693i
$598$		0			0
$599$		−	19024.9i		−	1.29772i	−0.760907	−	0.648861i	$-0.775246\pi$
$599$		−	19024.9i		−	1.29772i	0.760907	−	0.648861i	$-0.224754\pi$
$600$		0			0
$601$		−	1065.92i		−	0.0723460i	−0.999346	−	0.0361730i	$-0.988483\pi$
$601$		−	1065.92i		−	0.0723460i	0.999346	−	0.0361730i	$-0.0115167\pi$
$602$		0			0
$603$	−3588.11	−	3588.11i	−0.242320	−	0.242320i
$604$		0			0
$605$	1551.02	−	1551.02i	0.104228	−	0.104228i
$606$		0			0
$607$	12909.7			0.863242			0.431621	−	0.902055i	$-0.357942\pi$
$607$	12909.7			0.863242			0.431621	+	0.902055i	$0.357942\pi$
$608$		0			0
$609$	2858.00			0.190167
$610$		0			0
$611$	2487.25	−	2487.25i	0.164687	−	0.164687i
$612$		0			0
$613$	8763.41	+	8763.41i	0.577408	+	0.577408i	0.934188	−	0.356781i	$-0.116126\pi$
$613$	8763.41	+	8763.41i	0.577408	+	0.577408i	−0.356781	+	0.934188i	$0.616126\pi$
$614$		0			0
$615$		−	18482.1i		−	1.21182i
$616$		0			0
$617$			18921.2i			1.23459i	0.786733	+	0.617293i	$0.211771\pi$
$617$			18921.2i			1.23459i	−0.786733	+	0.617293i	$0.788229\pi$
$618$		0			0
$619$	15116.6	+	15116.6i	0.981565	+	0.981565i	0.999833	−	0.0182677i	$-0.00581513\pi$
$619$	15116.6	+	15116.6i	0.981565	+	0.981565i	−0.0182677	+	0.999833i	$0.505815\pi$
$620$		0			0
$621$	1696.97	−	1696.97i	0.109657	−	0.109657i
$622$		0			0
$623$	−6541.15			−0.420651
$624$		0			0
$625$	−1204.57			−0.0770926
$626$		0			0
$627$	−9288.42	+	9288.42i	−0.591617	+	0.591617i
$628$		0			0
$629$	−14447.7	−	14447.7i	−0.915845	−	0.915845i
$630$		0			0
$631$			9602.80i			0.605834i	0.953017	+	0.302917i	$0.0979605\pi$
$631$			9602.80i			0.605834i	−0.953017	+	0.302917i	$0.902039\pi$
$632$		0			0
$633$			17813.1i			1.11849i
$634$		0			0
$635$	12229.9	+	12229.9i	0.764297	+	0.764297i
$636$		0			0
$637$	−3120.34	+	3120.34i	−0.194085	+	0.194085i
$638$		0			0
$639$	−7186.12			−0.444880
$640$		0			0
$641$	4450.84			0.274256			0.137128	−	0.990553i	$-0.456213\pi$
$641$	4450.84			0.274256			0.137128	+	0.990553i	$0.456213\pi$
$642$		0			0
$643$	−6491.27	+	6491.27i	−0.398119	+	0.398119i	−0.877569	−	0.479450i	$-0.840836\pi$
$643$	−6491.27	+	6491.27i	−0.398119	+	0.398119i	0.479450	+	0.877569i	$0.340836\pi$
$644$		0			0
$645$	−5139.30	−	5139.30i	−0.313736	−	0.313736i
$646$		0			0
$647$			5546.17i			0.337005i	0.985701	+	0.168503i	$0.0538932\pi$
$647$			5546.17i			0.337005i	−0.985701	+	0.168503i	$0.946107\pi$
$648$		0			0
$649$			18098.3i			1.09464i
$650$		0			0
$651$	13267.3	+	13267.3i	0.798750	+	0.798750i
$652$		0			0
$653$	−6327.58	+	6327.58i	−0.379200	+	0.379200i	−0.870813	−	0.491614i	$-0.836407\pi$
$653$	−6327.58	+	6327.58i	−0.379200	+	0.379200i	0.491614	+	0.870813i	$0.336407\pi$
$654$		0			0
$655$	−6133.49			−0.365886
$656$		0			0
$657$	22341.5			1.32667
$658$		0			0
$659$	−15135.2	+	15135.2i	−0.894663	+	0.894663i	−0.994958	−	0.100294i	$-0.968022\pi$
$659$	−15135.2	+	15135.2i	−0.894663	+	0.894663i	0.100294	+	0.994958i	$0.468022\pi$
$660$		0			0
$661$	23460.1	+	23460.1i	1.38047	+	1.38047i	0.843777	+	0.536694i	$0.180327\pi$
$661$	23460.1	+	23460.1i	1.38047	+	1.38047i	0.536694	+	0.843777i	$0.319673\pi$
$662$		0			0
$663$		−	10963.2i		−	0.642195i
$664$		0			0
$665$		−	8782.30i		−	0.512125i
$666$		0			0
$667$	502.550	+	502.550i	0.0291736	+	0.0291736i
$668$		0			0
$669$	2306.29	−	2306.29i	0.133283	−	0.133283i
$670$		0			0
$671$	29697.4			1.70858
$672$		0			0
$673$	30638.5			1.75487			0.877436	−	0.479694i	$-0.159252\pi$
$673$	30638.5			1.75487			0.877436	+	0.479694i	$0.159252\pi$
$674$		0			0
$675$	2873.96	−	2873.96i	0.163879	−	0.163879i
$676$		0			0
$677$	12468.9	+	12468.9i	0.707855	+	0.707855i	0.966084	−	0.258229i	$-0.0831388\pi$
$677$	12468.9	+	12468.9i	0.707855	+	0.707855i	−0.258229	+	0.966084i	$0.583139\pi$
$678$		0			0
$679$		−	3754.41i		−	0.212196i
$680$		0			0
$681$			23453.8i			1.31975i
$682$		0			0
$683$	−13838.5	−	13838.5i	−0.775280	−	0.775280i	0.203744	−	0.979024i	$-0.434689\pi$
$683$	−13838.5	−	13838.5i	−0.775280	−	0.775280i	−0.979024	+	0.203744i	$0.934689\pi$
$684$		0			0
$685$	11713.1	−	11713.1i	0.653333	−	0.653333i
$686$		0			0
$687$	−17306.6			−0.961116
$688$		0			0
$689$	3961.95			0.219068
$690$		0			0
$691$	106.012	−	106.012i	0.00583628	−	0.00583628i	−0.704183	−	0.710019i	$-0.748686\pi$
$691$	106.012	−	106.012i	0.00583628	−	0.00583628i	0.710019	+	0.704183i	$0.248686\pi$
$692$		0			0
$693$	−18588.2	−	18588.2i	−1.01891	−	1.01891i
$694$		0			0
$695$			10129.8i			0.552870i
$696$		0			0
$697$		−	31900.4i		−	1.73359i
$698$		0			0
$699$	6567.17	+	6567.17i	0.355355	+	0.355355i
$700$		0			0
$701$	−7839.35	+	7839.35i	−0.422380	+	0.422380i	−0.886022	−	0.463643i	$-0.846542\pi$
$701$	−7839.35	+	7839.35i	−0.422380	+	0.422380i	0.463643	+	0.886022i	$0.346542\pi$
$702$		0			0
$703$	−12350.0			−0.662574
$704$		0			0
$705$	−11312.7			−0.604341
$706$		0			0
$707$	12149.1	−	12149.1i	0.646273	−	0.646273i
$708$		0			0
$709$	−2728.30	−	2728.30i	−0.144518	−	0.144518i	0.631146	−	0.775664i	$-0.282585\pi$
$709$	−2728.30	−	2728.30i	−0.144518	−	0.144518i	−0.775664	+	0.631146i	$0.782585\pi$
$710$		0			0
$711$			27499.9i			1.45053i
$712$		0			0
$713$			4665.84i			0.245073i
$714$		0			0
$715$	−2349.01	−	2349.01i	−0.122864	−	0.122864i
$716$		0			0
$717$	23309.5	−	23309.5i	1.21410	−	1.21410i
$718$		0			0
$719$	−32717.8			−1.69704			−0.848519	−	0.529166i	$-0.822505\pi$
$719$	−32717.8			−1.69704			−0.848519	+	0.529166i	$0.822505\pi$
$720$		0			0
$721$	−45824.0			−2.36696
$722$		0			0
$723$	30620.3	−	30620.3i	1.57508	−	1.57508i
$724$		0			0
$725$	851.111	+	851.111i	0.0435993	+	0.0435993i
$726$		0			0
$727$		−	25847.2i		−	1.31859i	−0.751883	−	0.659297i	$-0.770854\pi$
$727$		−	25847.2i		−	1.31859i	0.751883	−	0.659297i	$-0.229146\pi$
$728$		0			0
$729$		−	27662.0i		−	1.40537i
$730$		0			0
$731$	−8870.50	−	8870.50i	−0.448820	−	0.448820i
$732$		0			0
$733$	−10131.9	+	10131.9i	−0.510547	+	0.510547i	−0.914694	−	0.404147i	$-0.867568\pi$
$733$	−10131.9	+	10131.9i	−0.510547	+	0.510547i	0.404147	+	0.914694i	$0.367568\pi$
$734$		0			0
$735$	14192.1			0.712223
$736$		0			0
$737$	−4798.27			−0.239819
$738$		0			0
$739$	−19163.7	+	19163.7i	−0.953921	+	0.953921i	−0.998984	−	0.0450633i	$-0.985651\pi$
$739$	−19163.7	+	19163.7i	−0.953921	+	0.953921i	0.0450633	+	0.998984i	$0.485651\pi$
$740$		0			0
$741$	−4685.72	−	4685.72i	−0.232300	−	0.232300i
$742$		0			0
$743$			23322.1i			1.15155i	0.817607	+	0.575777i	$0.195301\pi$
$743$			23322.1i			1.15155i	−0.817607	+	0.575777i	$0.804699\pi$
$744$		0			0
$745$			21309.8i			1.04796i
$746$		0			0
$747$	10922.8	+	10922.8i	0.534999	+	0.534999i
$748$		0			0
$749$	−1977.03	+	1977.03i	−0.0964473	+	0.0964473i
$750$		0			0
$751$	25994.0			1.26303			0.631515	−	0.775364i	$-0.282434\pi$
$751$	25994.0			1.26303			0.631515	+	0.775364i	$0.282434\pi$
$752$		0			0
$753$	−5306.32			−0.256804
$754$		0			0
$755$	−13125.5	+	13125.5i	−0.632698	+	0.632698i
$756$		0			0
$757$	−22145.0	−	22145.0i	−1.06324	−	1.06324i	−0.997860	−	0.0653808i	$-0.979174\pi$
$757$	−22145.0	−	22145.0i	−1.06324	−	1.06324i	−0.0653808	−	0.997860i	$-0.520826\pi$
$758$		0			0
$759$		−	11819.0i		−	0.565222i
$760$		0			0
$761$		−	16497.5i		−	0.785853i	−0.919570	−	0.392926i	$-0.871463\pi$
$761$		−	16497.5i		−	0.785853i	0.919570	−	0.392926i	$-0.128537\pi$
$762$		0			0
$763$	−23725.9	−	23725.9i	−1.12573	−	1.12573i
$764$		0			0
$765$	−13789.7	+	13789.7i	−0.651723	+	0.651723i
$766$		0			0
$767$	−9130.02			−0.429812
$768$		0			0
$769$	−24867.3			−1.16611			−0.583055	−	0.812433i	$-0.698143\pi$
$769$	−24867.3			−1.16611			−0.583055	+	0.812433i	$0.698143\pi$
$770$		0			0
$771$	−44481.2	+	44481.2i	−2.07776	+	2.07776i
$772$		0			0
$773$	−1881.72	−	1881.72i	−0.0875559	−	0.0875559i	0.661972	−	0.749528i	$-0.269720\pi$
$773$	−1881.72	−	1881.72i	−0.0875559	−	0.0875559i	−0.749528	+	0.661972i	$0.769720\pi$
$774$		0			0
$775$			7902.00i			0.366256i
$776$		0			0
$777$		−	44684.8i		−	2.06314i
$778$		0			0
$779$	−13634.4	−	13634.4i	−0.627089	−	0.627089i
$780$		0			0
$781$	−4804.89	+	4804.89i	−0.220144	+	0.220144i
$782$		0			0
$783$	−736.525			−0.0336159
$784$		0			0
$785$	8453.54			0.384356
$786$		0			0
$787$	7790.94	−	7790.94i	0.352881	−	0.352881i	−0.508300	−	0.861180i	$-0.669726\pi$
$787$	7790.94	−	7790.94i	0.352881	−	0.352881i	0.861180	+	0.508300i	$0.169726\pi$
$788$		0			0
$789$	−2255.08	−	2255.08i	−0.101753	−	0.101753i
$790$		0			0
$791$		−	17937.2i		−	0.806286i
$792$		0			0
$793$			14981.4i			0.670877i
$794$		0			0
$795$	−9009.98	−	9009.98i	−0.401951	−	0.401951i
$796$		0			0
$797$	4209.84	−	4209.84i	0.187102	−	0.187102i	−0.607340	−	0.794442i	$-0.707763\pi$
$797$	4209.84	−	4209.84i	0.187102	−	0.187102i	0.794442	+	0.607340i	$0.207763\pi$
$798$		0			0
$799$	−19525.8			−0.864549
$800$		0			0
$801$	8779.50			0.387276
$802$		0			0
$803$	14938.3	−	14938.3i	0.656490	−	0.656490i
$804$		0			0
$805$	5587.51	+	5587.51i	0.244639	+	0.244639i
$806$		0			0
$807$			52.5393i			0.00229178i
$808$		0			0
$809$		−	27554.3i		−	1.19747i	−0.800946	−	0.598737i	$-0.795670\pi$
$809$		−	27554.3i		−	1.19747i	0.800946	−	0.598737i	$-0.204330\pi$
$810$		0			0
$811$	−3406.54	−	3406.54i	−0.147497	−	0.147497i	0.629502	−	0.776999i	$-0.283259\pi$
$811$	−3406.54	−	3406.54i	−0.147497	−	0.147497i	−0.776999	+	0.629502i	$0.783259\pi$
$812$		0			0
$813$	15576.1	−	15576.1i	0.671926	−	0.671926i
$814$		0			0
$815$	−12987.1			−0.558184
$816$		0			0
$817$	−7582.59			−0.324701
$818$		0			0
$819$	9377.16	−	9377.16i	0.400079	−	0.400079i
$820$		0			0
$821$	9839.14	+	9839.14i	0.418256	+	0.418256i	0.884602	−	0.466346i	$-0.154430\pi$
$821$	9839.14	+	9839.14i	0.418256	+	0.418256i	−0.466346	+	0.884602i	$0.654430\pi$
$822$		0			0
$823$			36653.5i			1.55244i	0.630461	+	0.776221i	$0.282866\pi$
$823$			36653.5i			1.55244i	−0.630461	+	0.776221i	$0.717134\pi$
$824$		0			0
$825$		−	20016.5i		−	0.844711i
$826$		0			0
$827$	22223.2	+	22223.2i	0.934431	+	0.934431i	0.997979	−	0.0635475i	$-0.0202414\pi$
$827$	22223.2	+	22223.2i	0.934431	+	0.934431i	−0.0635475	+	0.997979i	$0.520241\pi$
$828$		0			0
$829$	−14715.5	+	14715.5i	−0.616516	+	0.616516i	−0.944636	−	0.328120i	$-0.893585\pi$
$829$	−14715.5	+	14715.5i	−0.616516	+	0.616516i	0.328120	+	0.944636i	$0.393585\pi$
$830$		0			0
$831$	16772.2			0.700145
$832$		0			0
$833$	24495.8			1.01888
$834$		0			0
$835$	−5697.46	+	5697.46i	−0.236130	+	0.236130i
$836$		0			0
$837$	−3419.07	−	3419.07i	−0.141195	−	0.141195i
$838$		0			0
$839$			11010.0i			0.453050i	0.974005	+	0.226525i	$0.0727365\pi$
$839$			11010.0i			0.453050i	−0.974005	+	0.226525i	$0.927263\pi$
$840$		0			0
$841$			24170.9i			0.991057i
$842$		0			0
$843$	26108.1	+	26108.1i	1.06668	+	1.06668i
$844$		0			0
$845$	−9061.20	+	9061.20i	−0.368893	+	0.368893i
$846$		0			0
$847$	8279.85			0.335890
$848$		0			0
$849$	7080.22			0.286210
$850$		0			0
$851$	7857.37	−	7857.37i	0.316507	−	0.316507i
$852$		0			0
$853$	−12809.9	−	12809.9i	−0.514190	−	0.514190i	0.401617	−	0.915808i	$-0.368448\pi$
$853$	−12809.9	−	12809.9i	−0.514190	−	0.514190i	−0.915808	+	0.401617i	$0.868448\pi$
$854$		0			0
$855$			11787.6i			0.471493i
$856$		0			0
$857$			38510.8i			1.53501i	0.641043	+	0.767505i	$0.278502\pi$
$857$			38510.8i			1.53501i	−0.641043	+	0.767505i	$0.721498\pi$
$858$		0			0
$859$	−23234.6	−	23234.6i	−0.922882	−	0.922882i	0.0743503	−	0.997232i	$-0.476312\pi$
$859$	−23234.6	−	23234.6i	−0.922882	−	0.922882i	−0.997232	+	0.0743503i	$0.976312\pi$
$860$		0			0
$861$	49331.9	−	49331.9i	1.95264	−	1.95264i
$862$		0			0
$863$	−22079.5			−0.870911			−0.435456	−	0.900210i	$-0.643413\pi$
$863$	−22079.5			−0.870911			−0.435456	+	0.900210i	$0.643413\pi$
$864$		0			0
$865$	5255.26			0.206571
$866$		0			0
$867$	−16029.8	+	16029.8i	−0.627912	+	0.627912i
$868$		0			0
$869$	18387.4	+	18387.4i	0.717779	+	0.717779i
$870$		0			0
$871$		−	2420.58i		−	0.0941656i
$872$		0			0
$873$			5039.15i			0.195360i
$874$		0			0
$875$	23976.7	+	23976.7i	0.926356	+	0.926356i
$876$		0			0
$877$	−4082.13	+	4082.13i	−0.157176	+	0.157176i	−0.781314	−	0.624138i	$-0.785450\pi$
$877$	−4082.13	+	4082.13i	−0.157176	+	0.157176i	0.624138	+	0.781314i	$0.285450\pi$
$878$		0			0
$879$	−15753.9			−0.604510
$880$		0			0
$881$	7132.59			0.272762			0.136381	−	0.990656i	$-0.456453\pi$
$881$	7132.59			0.272762			0.136381	+	0.990656i	$0.456453\pi$
$882$		0			0
$883$	−19170.0	+	19170.0i	−0.730601	+	0.730601i	−0.970739	−	0.240138i	$-0.922807\pi$
$883$	−19170.0	+	19170.0i	−0.730601	+	0.730601i	0.240138	+	0.970739i	$0.422807\pi$
$884$		0			0
$885$	20762.9	+	20762.9i	0.788628	+	0.788628i
$886$		0			0
$887$		−	45045.7i		−	1.70517i	−0.522589	−	0.852585i	$-0.675034\pi$
$887$		−	45045.7i		−	1.70517i	0.522589	−	0.852585i	$-0.324966\pi$
$888$		0			0
$889$			65287.3i			2.46306i
$890$		0			0
$891$	−11497.8	−	11497.8i	−0.432314	−	0.432314i
$892$		0			0
$893$	−8345.43	+	8345.43i	−0.312731	+	0.312731i
$894$		0			0
$895$	20541.1			0.767167
$896$		0			0
$897$	5962.34			0.221936
$898$		0			0
$899$	1012.55	−	1012.55i	0.0375643	−	0.0375643i
$900$		0			0
$901$	−15551.4	−	15551.4i	−0.575017	−	0.575017i
$902$		0			0
$903$		−	27435.3i		−	1.01106i
$904$		0			0
$905$		−	1131.36i		−	0.0415554i
$906$		0			0
$907$	33658.2	+	33658.2i	1.23220	+	1.23220i	0.963118	+	0.269079i	$0.0867192\pi$
$907$	33658.2	+	33658.2i	1.23220	+	1.23220i	0.269079	+	0.963118i	$0.413281\pi$
$908$		0			0
$909$	−16306.5	+	16306.5i	−0.594997	+	0.594997i
$910$		0			0
$911$	−42503.8			−1.54579			−0.772895	−	0.634534i	$-0.781192\pi$
$911$	−42503.8			−1.54579			−0.772895	+	0.634534i	$0.781192\pi$
$912$		0			0
$913$	14606.7			0.529477
$914$		0			0
$915$	34069.7	−	34069.7i	1.23094	−	1.23094i
$916$		0			0
$917$	−16371.3	−	16371.3i	−0.589562	−	0.589562i
$918$		0			0
$919$		−	8819.41i		−	0.316568i	−0.987394	−	0.158284i	$-0.949404\pi$
$919$		−	8819.41i		−	0.316568i	0.987394	−	0.158284i	$-0.0505961\pi$
$920$		0			0
$921$			2541.55i			0.0909305i
$922$		0			0
$923$	−2423.92	−	2423.92i	−0.0864402	−	0.0864402i
$924$		0			0
$925$	13307.1	−	13307.1i	0.473012	−	0.473012i
$926$		0			0
$927$	61504.8			2.17916
$928$		0			0
$929$	−14155.6			−0.499925			−0.249963	−	0.968256i	$-0.580418\pi$
$929$	−14155.6			−0.499925			−0.249963	+	0.968256i	$0.580418\pi$
$930$		0			0
$931$	10469.6	−	10469.6i	0.368558	−	0.368558i
$932$		0			0
$933$	4789.43	+	4789.43i	0.168059	+	0.168059i
$934$		0			0
$935$			18440.6i			0.644996i
$936$		0			0
$937$		−	38518.7i		−	1.34296i	−0.741023	−	0.671479i	$-0.765659\pi$
$937$		−	38518.7i		−	1.34296i	0.741023	−	0.671479i	$-0.234341\pi$
$938$		0			0
$939$	−19319.2	−	19319.2i	−0.671414	−	0.671414i
$940$		0			0
$941$	−27998.2	+	27998.2i	−0.969942	+	0.969942i	−0.999561	−	0.0296196i	$-0.990570\pi$
$941$	−27998.2	+	27998.2i	−0.969942	+	0.969942i	0.0296196	+	0.999561i	$0.490570\pi$
$942$		0			0
$943$	17349.0			0.599112
$944$		0			0
$945$	−8188.93			−0.281890
$946$		0			0
$947$	32839.5	−	32839.5i	1.12687	−	1.12687i	0.136181	−	0.990684i	$-0.456517\pi$
$947$	32839.5	−	32839.5i	1.12687	−	1.12687i	0.990684	−	0.136181i	$-0.0434829\pi$
$948$		0			0
$949$	7535.92	+	7535.92i	0.257773	+	0.257773i
$950$		0			0
$951$		−	51925.4i		−	1.77055i
$952$		0			0
$953$		−	20600.1i		−	0.700211i	−0.936710	−	0.350106i	$-0.886146\pi$
$953$		−	20600.1i		−	0.700211i	0.936710	−	0.350106i	$-0.113854\pi$
$954$		0			0
$955$	18317.5	+	18317.5i	0.620670	+	0.620670i
$956$		0			0
$957$	−2564.88	+	2564.88i	−0.0866360	+	0.0866360i
$958$		0			0
$959$	62528.2			2.10547
$960$		0			0
$961$	−20390.2			−0.684441
$962$		0			0
$963$	2653.56	−	2653.56i	0.0887951	−	0.0887951i
$964$		0			0
$965$	−15152.5	−	15152.5i	−0.505469	−	0.505469i
$966$		0			0
$967$			38210.9i			1.27071i	0.772219	+	0.635356i	$0.219147\pi$
$967$			38210.9i			1.27071i	−0.772219	+	0.635356i	$0.780853\pi$
$968$		0			0
$969$			36784.6i			1.21950i
$970$		0			0
$971$	−37224.9	−	37224.9i	−1.23028	−	1.23028i	−0.963855	−	0.266427i	$-0.914157\pi$
$971$	−37224.9	−	37224.9i	−1.23028	−	1.23028i	−0.266427	−	0.963855i	$-0.585843\pi$
$972$		0			0
$973$	−27038.1	+	27038.1i	−0.890854	+	0.890854i
$974$		0			0
$975$	10097.7			0.331678
$976$		0			0
$977$	7985.95			0.261508			0.130754	−	0.991415i	$-0.458260\pi$
$977$	7985.95			0.261508			0.130754	+	0.991415i	$0.458260\pi$
$978$		0			0
$979$	5870.28	−	5870.28i	0.191639	−	0.191639i
$980$		0			0
$981$	31844.8	+	31844.8i	1.03642	+	1.03642i
$982$		0			0
$983$		−	10703.1i		−	0.347279i	−0.984809	−	0.173639i	$-0.944447\pi$
$983$		−	10703.1i		−	0.347279i	0.984809	−	0.173639i	$-0.0555527\pi$
$984$		0			0
$985$		−	22580.9i		−	0.730442i
$986$		0			0
$987$	−30195.4	−	30195.4i	−0.973791	−	0.973791i
$988$		0			0
$989$	4824.23	−	4824.23i	0.155108	−	0.155108i
$990$		0			0
$991$	−23945.4			−0.767558			−0.383779	−	0.923425i	$-0.625377\pi$
$991$	−23945.4			−0.767558			−0.383779	+	0.923425i	$0.625377\pi$
$992$		0			0
$993$	−20009.0			−0.639442
$994$		0			0
$995$	6395.37	−	6395.37i	0.203766	−	0.203766i
$996$		0			0
$997$	14292.5	+	14292.5i	0.454010	+	0.454010i	0.896683	−	0.442673i	$-0.145970\pi$
$997$	14292.5	+	14292.5i	0.454010	+	0.454010i	−0.442673	+	0.896683i	$0.645970\pi$
$998$		0			0
$999$			11515.6i			0.364702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.e.b.97.1		10
4.3	odd	2		128.4.e.a.97.5		10
8.3	odd	2		64.4.e.a.49.1		10
8.5	even	2		16.4.e.a.5.1	✓	10
16.3	odd	4		128.4.e.a.33.5		10
16.5	even	4		16.4.e.a.13.1	yes	10
16.11	odd	4		64.4.e.a.17.1		10
16.13	even	4	inner	128.4.e.b.33.1		10
24.5	odd	2		144.4.k.a.37.5		10
24.11	even	2		576.4.k.a.433.4		10
32.3	odd	8		1024.4.a.m.1.9		10
32.5	even	8		1024.4.b.j.513.2		10
32.11	odd	8		1024.4.b.k.513.2		10
32.13	even	8		1024.4.a.n.1.9		10
32.19	odd	8		1024.4.a.m.1.2		10
32.21	even	8		1024.4.b.j.513.9		10
32.27	odd	8		1024.4.b.k.513.9		10
32.29	even	8		1024.4.a.n.1.2		10
48.5	odd	4		144.4.k.a.109.5		10
48.11	even	4		576.4.k.a.145.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.4.e.a.5.1	✓	10	8.5	even	2
16.4.e.a.13.1	yes	10	16.5	even	4
64.4.e.a.17.1		10	16.11	odd	4
64.4.e.a.49.1		10	8.3	odd	2
128.4.e.a.33.5		10	16.3	odd	4
128.4.e.a.97.5		10	4.3	odd	2
128.4.e.b.33.1		10	16.13	even	4	inner
128.4.e.b.97.1		10	1.1	even	1	trivial
144.4.k.a.37.5		10	24.5	odd	2
144.4.k.a.109.5		10	48.5	odd	4
576.4.k.a.145.4		10	48.11	even	4
576.4.k.a.433.4		10	24.11	even	2
1024.4.a.m.1.2		10	32.19	odd	8
1024.4.a.m.1.9		10	32.3	odd	8
1024.4.a.n.1.2		10	32.29	even	8
1024.4.a.n.1.9		10	32.13	even	8
1024.4.b.j.513.2		10	32.5	even	8
1024.4.b.j.513.9		10	32.21	even	8
1024.4.b.k.513.2		10	32.11	odd	8
1024.4.b.k.513.9		10	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.49618 + 5.49618i) q^{3} +(4.66372 + 4.66372i) q^{5} +24.8965i q^{7} -33.4160i q^{9} +O(q^{10})\)	\(q+(-5.49618 + 5.49618i) q^{3} +(4.66372 + 4.66372i) q^{5} +24.8965i q^{7} -33.4160i q^{9} +(-22.3431 - 22.3431i) q^{11} +(11.2714 - 11.2714i) q^{13} -51.2653 q^{15} -88.4846 q^{17} +(-37.8187 + 37.8187i) q^{19} +(-136.836 - 136.836i) q^{21} -48.1224i q^{23} -81.4994i q^{25} +(35.2635 + 35.2635i) q^{27} +(-10.4432 + 10.4432i) q^{29} -96.9578 q^{31} +245.604 q^{33} +(-116.110 + 116.110i) q^{35} +(163.279 + 163.279i) q^{37} +123.899i q^{39} +360.519i q^{41} +(100.249 + 100.249i) q^{43} +(155.843 - 155.843i) q^{45} +220.669 q^{47} -276.837 q^{49} +(486.327 - 486.327i) q^{51} +(175.752 + 175.752i) q^{53} -208.404i q^{55} -415.717i q^{57} +(-405.008 - 405.008i) q^{59} +(-664.576 + 664.576i) q^{61} +831.942 q^{63} +105.133 q^{65} +(107.377 - 107.377i) q^{67} +(264.489 + 264.489i) q^{69} -215.050i q^{71} +668.587i q^{73} +(447.935 + 447.935i) q^{75} +(556.266 - 556.266i) q^{77} -822.956 q^{79} +514.603 q^{81} +(-326.873 + 326.873i) q^{83} +(-412.668 - 412.668i) q^{85} -114.795i q^{87} +262.733i q^{89} +(280.619 + 280.619i) q^{91} +(532.898 - 532.898i) q^{93} -352.752 q^{95} -150.801 q^{97} +(-746.618 + 746.618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 10 * q + 2 * q^3 + 2 * q^5	\( 10 q + 2 q^{3} + 2 q^{5} - 18 q^{11} + 2 q^{13} - 124 q^{15} - 4 q^{17} + 26 q^{19} - 52 q^{21} - 184 q^{27} + 202 q^{29} + 368 q^{31} - 4 q^{33} - 476 q^{35} + 10 q^{37} + 838 q^{43} - 194 q^{45} - 944 q^{47} + 94 q^{49} + 1500 q^{51} + 378 q^{53} - 1706 q^{59} - 910 q^{61} + 2628 q^{63} - 492 q^{65} - 1942 q^{67} - 580 q^{69} + 2954 q^{75} + 268 q^{77} - 4416 q^{79} + 482 q^{81} + 2562 q^{83} + 12 q^{85} - 3332 q^{91} + 2192 q^{93} + 6900 q^{95} - 4 q^{97} - 4958 q^{99}+O(q^{100}) \) 10 * q + 2 * q^3 + 2 * q^5 - 18 * q^11 + 2 * q^13 - 124 * q^15 - 4 * q^17 + 26 * q^19 - 52 * q^21 - 184 * q^27 + 202 * q^29 + 368 * q^31 - 4 * q^33 - 476 * q^35 + 10 * q^37 + 838 * q^43 - 194 * q^45 - 944 * q^47 + 94 * q^49 + 1500 * q^51 + 378 * q^53 - 1706 * q^59 - 910 * q^61 + 2628 * q^63 - 492 * q^65 - 1942 * q^67 - 580 * q^69 + 2954 * q^75 + 268 * q^77 - 4416 * q^79 + 482 * q^81 + 2562 * q^83 + 12 * q^85 - 3332 * q^91 + 2192 * q^93 + 6900 * q^95 - 4 * q^97 - 4958 * q^99

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