LMFDB - Embedded newform 128.4.g.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, 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:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	128.17
Dual form			128.4.g.a.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.92731 + 7.06715i) q^{3} +(13.5234 - 5.60159i) q^{5} +(23.0737 - 23.0737i) q^{7} +(-22.2836 - 22.2836i) q^{9} +O(q^{10})$	\(q+(-2.92731 + 7.06715i) q^{3} +(13.5234 - 5.60159i) q^{5} +(23.0737 - 23.0737i) q^{7} +(-22.2836 - 22.2836i) q^{9} +(7.41078 + 17.8912i) q^{11} +(14.8121 + 6.13537i) q^{13} +111.970i q^{15} +27.7996i q^{17} +(82.2959 + 34.0881i) q^{19} +(95.5216 + 230.610i) q^{21} +(-39.2456 - 39.2456i) q^{23} +(63.1173 - 63.1173i) q^{25} +(31.8994 - 13.2132i) q^{27} +(5.57538 - 13.4602i) q^{29} -155.853 q^{31} -148.133 q^{33} +(182.787 - 441.286i) q^{35} +(188.743 - 78.1798i) q^{37} +(-86.7192 + 86.7192i) q^{39} +(113.814 + 113.814i) q^{41} +(24.6509 + 59.5126i) q^{43} +(-426.174 - 176.527i) q^{45} +217.464i q^{47} -721.795i q^{49} +(-196.464 - 81.3779i) q^{51} +(-35.7808 - 86.3826i) q^{53} +(200.438 + 200.438i) q^{55} +(-481.811 + 481.811i) q^{57} +(116.586 - 48.2914i) q^{59} +(-197.015 + 475.636i) q^{61} -1028.33 q^{63} +234.678 q^{65} +(-144.765 + 349.494i) q^{67} +(392.239 - 162.471i) q^{69} +(523.475 - 523.475i) q^{71} +(-718.521 - 718.521i) q^{73} +(261.296 + 630.823i) q^{75} +(583.811 + 241.822i) q^{77} -958.779i q^{79} -586.755i q^{81} +(-1241.90 - 514.414i) q^{83} +(155.722 + 375.946i) q^{85} +(78.8041 + 78.8041i) q^{87} +(-808.016 + 808.016i) q^{89} +(483.336 - 200.204i) q^{91} +(456.231 - 1101.44i) q^{93} +1303.87 q^{95} +1399.29 q^{97} +(233.541 - 563.819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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
$3$	−2.92731	+	7.06715i	−0.563361	+	1.36007i	0.343702	+	0.939079i	$0.388319\pi$
$3$	−2.92731	+	7.06715i	−0.563361	+	1.36007i	−0.907063	+	0.420995i	$0.861681\pi$
$4$		0			0
$5$	13.5234	−	5.60159i	1.20957	−	0.501022i	0.315493	−	0.948928i	$-0.397830\pi$
$5$	13.5234	−	5.60159i	1.20957	−	0.501022i	0.894081	+	0.447906i	$0.147830\pi$
$6$		0			0
$7$	23.0737	−	23.0737i	1.24586	−	1.24586i	0.288335	−	0.957530i	$-0.406898\pi$
$7$	23.0737	−	23.0737i	1.24586	−	1.24586i	0.957530	−	0.288335i	$-0.0931017\pi$
$8$		0			0
$9$	−22.2836	−	22.2836i	−0.825318	−	0.825318i
$10$		0			0
$11$	7.41078	+	17.8912i	0.203130	+	0.490400i	0.992312	−	0.123760i	$-0.0394951\pi$
$11$	7.41078	+	17.8912i	0.203130	+	0.490400i	−0.789182	+	0.614159i	$0.789495\pi$
$12$		0			0
$13$	14.8121	+	6.13537i	0.316010	+	0.130896i	0.535051	−	0.844820i	$-0.320293\pi$
$13$	14.8121	+	6.13537i	0.316010	+	0.130896i	−0.219040	+	0.975716i	$0.570293\pi$
$14$		0			0
$15$			111.970i			1.92737i
$16$		0			0
$17$			27.7996i			0.396611i	0.980140	+	0.198305i	$0.0635438\pi$
$17$			27.7996i			0.396611i	−0.980140	+	0.198305i	$0.936456\pi$
$18$		0			0
$19$	82.2959	+	34.0881i	0.993683	+	0.411597i	0.819477	−	0.573112i	$-0.194264\pi$
$19$	82.2959	+	34.0881i	0.993683	+	0.411597i	0.174206	+	0.984709i	$0.444264\pi$
$20$		0			0
$21$	95.5216	+	230.610i	0.992596	+	2.39634i
$22$		0			0
$23$	−39.2456	−	39.2456i	−0.355795	−	0.355795i	0.506466	−	0.862260i	$-0.330952\pi$
$23$	−39.2456	−	39.2456i	−0.355795	−	0.355795i	−0.862260	+	0.506466i	$0.830952\pi$
$24$		0			0
$25$	63.1173	−	63.1173i	0.504938	−	0.504938i
$26$		0			0
$27$	31.8994	−	13.2132i	0.227372	−	0.0941805i
$28$		0			0
$29$	5.57538	−	13.4602i	0.0357008	−	0.0861892i	−0.905024	−	0.425362i	$-0.860147\pi$
$29$	5.57538	−	13.4602i	0.0357008	−	0.0861892i	0.940724	+	0.339172i	$0.110147\pi$
$30$		0			0
$31$	−155.853			−0.902970			−0.451485	−	0.892279i	$-0.649106\pi$
$31$	−155.853			−0.902970			−0.451485	+	0.892279i	$0.649106\pi$
$32$		0			0
$33$	−148.133			−0.781416
$34$		0			0
$35$	182.787	−	441.286i	0.882760	−	2.13117i
$36$		0			0
$37$	188.743	−	78.1798i	0.838625	−	0.347370i	0.0783139	−	0.996929i	$-0.475046\pi$
$37$	188.743	−	78.1798i	0.838625	−	0.347370i	0.760311	+	0.649559i	$0.225046\pi$
$38$		0			0
$39$	−86.7192	+	86.7192i	−0.356056	+	0.356056i
$40$		0			0
$41$	113.814	+	113.814i	0.433530	+	0.433530i	0.889827	−	0.456297i	$-0.150825\pi$
$41$	113.814	+	113.814i	0.433530	+	0.433530i	−0.456297	+	0.889827i	$0.650825\pi$
$42$		0			0
$43$	24.6509	+	59.5126i	0.0874240	+	0.211060i	0.961545	−	0.274649i	$-0.0885615\pi$
$43$	24.6509	+	59.5126i	0.0874240	+	0.211060i	−0.874121	+	0.485709i	$0.838562\pi$
$44$		0			0
$45$	−426.174	−	176.527i	−1.41179	−	0.584781i
$46$		0			0
$47$			217.464i			0.674902i	0.941343	+	0.337451i	$0.109565\pi$
$47$			217.464i			0.674902i	−0.941343	+	0.337451i	$0.890435\pi$
$48$		0			0
$49$		−	721.795i		−	2.10436i
$50$		0			0
$51$	−196.464	−	81.3779i	−0.539420	−	0.223435i
$52$		0			0
$53$	−35.7808	−	86.3826i	−0.0927335	−	0.223879i	0.870706	−	0.491803i	$-0.163662\pi$
$53$	−35.7808	−	86.3826i	−0.0927335	−	0.223879i	−0.963440	+	0.267925i	$0.913662\pi$
$54$		0			0
$55$	200.438	+	200.438i	0.491402	+	0.491402i
$56$		0			0
$57$	−481.811	+	481.811i	−1.11960	+	1.11960i
$58$		0			0
$59$	116.586	−	48.2914i	0.257257	−	0.106559i	−0.250328	−	0.968161i	$-0.580538\pi$
$59$	116.586	−	48.2914i	0.257257	−	0.106559i	0.507585	+	0.861602i	$0.330538\pi$
$60$		0			0
$61$	−197.015	+	475.636i	−0.413528	+	0.998344i	0.570655	+	0.821190i	$0.306689\pi$
$61$	−197.015	+	475.636i	−0.413528	+	0.998344i	−0.984183	+	0.177155i	$0.943311\pi$
$62$		0			0
$63$	−1028.33			−2.05647
$64$		0			0
$65$	234.678			0.447819
$66$		0			0
$67$	−144.765	+	349.494i	−0.263968	+	0.637276i	−0.999177	−	0.0405648i	$-0.987084\pi$
$67$	−144.765	+	349.494i	−0.263968	+	0.637276i	0.735208	+	0.677841i	$0.237084\pi$
$68$		0			0
$69$	392.239	−	162.471i	0.684348	−	0.283466i
$70$		0			0
$71$	523.475	−	523.475i	0.875001	−	0.875001i	−0.118011	−	0.993012i	$-0.537652\pi$
$71$	523.475	−	523.475i	0.875001	−	0.875001i	0.993012	+	0.118011i	$0.0376519\pi$
$72$		0			0
$73$	−718.521	−	718.521i	−1.15201	−	1.15201i	−0.986150	−	0.165856i	$-0.946961\pi$
$73$	−718.521	−	718.521i	−1.15201	−	1.15201i	−0.165856	−	0.986150i	$-0.553039\pi$
$74$		0			0
$75$	261.296	+	630.823i	0.402291	+	0.971216i
$76$		0			0
$77$	583.811	+	241.822i	0.864045	+	0.357899i
$78$		0			0
$79$		−	958.779i		−	1.36546i	−0.730673	−	0.682728i	$-0.760793\pi$
$79$		−	958.779i		−	1.36546i	0.730673	−	0.682728i	$-0.239207\pi$
$80$		0			0
$81$		−	586.755i		−	0.804876i
$82$		0			0
$83$	−1241.90	−	514.414i	−1.64237	−	0.680292i	−0.645836	−	0.763476i	$-0.723491\pi$
$83$	−1241.90	−	514.414i	−1.64237	−	0.680292i	−0.996534	+	0.0831842i	$0.973491\pi$
$84$		0			0
$85$	155.722	+	375.946i	0.198711	+	0.479730i
$86$		0			0
$87$	78.8041	+	78.8041i	0.0971113	+	0.0971113i
$88$		0			0
$89$	−808.016	+	808.016i	−0.962354	+	0.962354i	−0.999317	−	0.0369622i	$-0.988232\pi$
$89$	−808.016	+	808.016i	−0.962354	+	0.962354i	0.0369622	+	0.999317i	$0.488232\pi$
$90$		0			0
$91$	483.336	−	200.204i	0.556785	−	0.230628i
$92$		0			0
$93$	456.231	−	1101.44i	0.508698	−	1.22811i
$94$		0			0
$95$	1303.87			1.40815
$96$		0			0
$97$	1399.29			1.46471			0.732354	−	0.680924i	$-0.238422\pi$
$97$	1399.29			1.46471			0.732354	+	0.680924i	$0.238422\pi$
$98$		0			0
$99$	233.541	−	563.819i	0.237089	−	0.572383i
$100$		0			0
$101$	−1024.11	+	424.200i	−1.00894	+	0.417916i	−0.825067	−	0.565035i	$-0.808863\pi$
$101$	−1024.11	+	424.200i	−1.00894	+	0.417916i	−0.183871	+	0.982950i	$0.558863\pi$
$102$		0			0
$103$	483.862	−	483.862i	0.462877	−	0.462877i	−0.436720	−	0.899597i	$-0.643860\pi$
$103$	483.862	−	483.862i	0.462877	−	0.462877i	0.899597	+	0.436720i	$0.143860\pi$
$104$		0			0
$105$	2583.56	+	2583.56i	2.40124	+	2.40124i
$106$		0			0
$107$	682.420	+	1647.51i	0.616561	+	1.48851i	0.855673	+	0.517517i	$0.173144\pi$
$107$	682.420	+	1647.51i	0.616561	+	1.48851i	−0.239112	+	0.970992i	$0.576856\pi$
$108$		0			0
$109$	−1813.85	−	751.322i	−1.59390	−	0.660217i	−0.603367	−	0.797463i	$-0.706175\pi$
$109$	−1813.85	−	751.322i	−1.59390	−	0.660217i	−0.990537	+	0.137247i	$0.956175\pi$
$110$		0			0
$111$			1562.73i			1.33629i
$112$		0			0
$113$			1392.34i			1.15912i	0.814931	+	0.579558i	$0.196775\pi$
$113$			1392.34i			1.15912i	−0.814931	+	0.579558i	$0.803225\pi$
$114$		0			0
$115$	−750.574	−	310.898i	−0.608621	−	0.252099i
$116$		0			0
$117$	−193.349	−	466.785i	−0.152778	−	0.368840i
$118$		0			0
$119$	641.440	+	641.440i	0.494123	+	0.494123i
$120$		0			0
$121$	675.984	−	675.984i	0.507877	−	0.507877i
$122$		0			0
$123$	−1137.51	+	471.171i	−0.833867	+	0.345399i
$124$		0			0
$125$	−200.193	+	483.310i	−0.143247	+	0.345828i
$126$		0			0
$127$	−909.845			−0.635714			−0.317857	−	0.948139i	$-0.602963\pi$
$127$	−909.845			−0.635714			−0.317857	+	0.948139i	$0.602963\pi$
$128$		0			0
$129$	−492.746			−0.336309
$130$		0			0
$131$	−375.465	+	906.452i	−0.250416	+	0.604558i	−0.998238	−	0.0593418i	$-0.981100\pi$
$131$	−375.465	+	906.452i	−0.250416	+	0.604558i	0.747822	+	0.663900i	$0.231100\pi$
$132$		0			0
$133$	2685.41	−	1112.34i	1.75079	−	0.725201i
$134$		0			0
$135$	357.375	−	357.375i	0.227837	−	0.227837i
$136$		0			0
$137$	−821.434	−	821.434i	−0.512262	−	0.512262i	0.402957	−	0.915219i	$-0.367982\pi$
$137$	−821.434	−	821.434i	−0.512262	−	0.512262i	−0.915219	+	0.402957i	$0.867982\pi$
$138$		0			0
$139$	−673.401	−	1625.73i	−0.410915	−	0.992036i	−0.984893	−	0.173165i	$-0.944600\pi$
$139$	−673.401	−	1625.73i	−0.410915	−	0.992036i	0.573978	−	0.818871i	$-0.305400\pi$
$140$		0			0
$141$	−1536.85	−	636.584i	−0.917916	−	0.380213i
$142$		0			0
$143$			310.474i			0.181560i
$144$		0			0
$145$		−	213.259i		−	0.122139i
$146$		0			0
$147$	5101.03	+	2112.92i	2.86208	+	1.18551i
$148$		0			0
$149$	247.105	+	596.564i	0.135863	+	0.328003i	0.977138	−	0.212604i	$-0.0681946\pi$
$149$	247.105	+	596.564i	0.135863	+	0.328003i	−0.841275	+	0.540607i	$0.818195\pi$
$150$		0			0
$151$	−373.703	−	373.703i	−0.201401	−	0.201401i	0.599199	−	0.800600i	$-0.295486\pi$
$151$	−373.703	−	373.703i	−0.201401	−	0.201401i	−0.800600	+	0.599199i	$0.795486\pi$
$152$		0			0
$153$	619.474	−	619.474i	0.327330	−	0.327330i
$154$		0			0
$155$	−2107.67	+	873.027i	−1.09221	+	0.452408i
$156$		0			0
$157$	−186.690	+	450.709i	−0.0949011	+	0.229112i	−0.964200	−	0.265174i	$-0.914570\pi$
$157$	−186.690	+	450.709i	−0.0949011	+	0.229112i	0.869299	+	0.494286i	$0.164570\pi$
$158$		0			0
$159$	715.220			0.356734
$160$		0			0
$161$	−1811.09			−0.886544
$162$		0			0
$163$	495.962	−	1197.36i	0.238324	−	0.575364i	−0.758786	−	0.651340i	$-0.774207\pi$
$163$	495.962	−	1197.36i	0.238324	−	0.575364i	0.997110	+	0.0759758i	$0.0242072\pi$
$164$		0			0
$165$	−2003.27	+	829.783i	−0.945180	+	0.391506i
$166$		0			0
$167$	644.684	−	644.684i	0.298725	−	0.298725i	−0.541789	−	0.840514i	$-0.682253\pi$
$167$	644.684	−	644.684i	0.298725	−	0.298725i	0.840514	+	0.541789i	$0.182253\pi$
$168$		0			0
$169$	−1371.76	−	1371.76i	−0.624378	−	0.624378i
$170$		0			0
$171$	−1074.24	−	2593.45i	−0.480406	−	1.15980i
$172$		0			0
$173$	2383.01	+	987.076i	1.04727	+	0.433792i	0.838915	−	0.544262i	$-0.183190\pi$
$173$	2383.01	+	987.076i	1.04727	+	0.433792i	0.208351	+	0.978054i	$0.433190\pi$
$174$		0			0
$175$		−	2912.70i		−	1.25817i
$176$		0			0
$177$			965.293i			0.409920i
$178$		0			0
$179$	−3184.86	−	1319.21i	−1.32987	−	0.550852i	−0.399254	−	0.916840i	$-0.630731\pi$
$179$	−3184.86	−	1319.21i	−1.32987	−	0.550852i	−0.930619	+	0.365988i	$0.880731\pi$
$180$		0			0
$181$	−820.433	−	1980.70i	−0.336919	−	0.813394i	−0.998008	−	0.0630866i	$-0.979906\pi$
$181$	−820.433	−	1980.70i	−0.336919	−	0.813394i	0.661089	−	0.750307i	$-0.270094\pi$
$182$		0			0
$183$	−2784.67	−	2784.67i	−1.12486	−	1.12486i
$184$		0			0
$185$	2114.52	−	2114.52i	0.840339	−	0.840339i
$186$		0			0
$187$	−497.368	+	206.016i	−0.194498	+	0.0805637i
$188$		0			0
$189$	431.161	−	1040.92i	0.165938	−	0.400611i
$190$		0			0
$191$	330.108			0.125056			0.0625282	−	0.998043i	$-0.480084\pi$
$191$	330.108			0.125056			0.0625282	+	0.998043i	$0.480084\pi$
$192$		0			0
$193$	−914.905			−0.341224			−0.170612	−	0.985338i	$-0.554575\pi$
$193$	−914.905			−0.341224			−0.170612	+	0.985338i	$0.554575\pi$
$194$		0			0
$195$	−686.976	+	1658.51i	−0.252284	+	0.609068i
$196$		0			0
$197$	−41.3093	+	17.1109i	−0.0149399	+	0.00618832i	−0.390141	−	0.920755i	$-0.627574\pi$
$197$	−41.3093	+	17.1109i	−0.0149399	+	0.00618832i	0.375201	+	0.926943i	$0.377574\pi$
$198$		0			0
$199$	−2946.98	+	2946.98i	−1.04978	+	1.04978i	−0.0510831	+	0.998694i	$0.516267\pi$
$199$	−2946.98	+	2946.98i	−1.04978	+	1.04978i	−0.998694	+	0.0510831i	$0.983733\pi$
$200$		0			0
$201$	−2046.16	−	2046.16i	−0.718033	−	0.718033i
$202$		0			0
$203$	−181.931	−	439.221i	−0.0629018	−	0.151858i
$204$		0			0
$205$	2176.69	+	901.616i	0.741594	+	0.307178i
$206$		0			0
$207$			1749.07i			0.587288i
$208$		0			0
$209$			1724.99i			0.570910i
$210$		0			0
$211$	−1661.58	−	688.250i	−0.542124	−	0.224555i	0.0947802	−	0.995498i	$-0.469785\pi$
$211$	−1661.58	−	688.250i	−0.542124	−	0.224555i	−0.636904	+	0.770943i	$0.719785\pi$
$212$		0			0
$213$	2167.10	+	5231.85i	0.697124	+	1.68301i
$214$		0			0
$215$	666.731	+	666.731i	0.211492	+	0.211492i
$216$		0			0
$217$	−3596.12	+	3596.12i	−1.12498	+	1.12498i
$218$		0			0
$219$	7181.22	−	2974.56i	2.21581	−	0.917818i
$220$		0			0
$221$	−170.561	+	411.770i	−0.0519147	+	0.125333i
$222$		0			0
$223$	2657.54			0.798035			0.399018	−	0.916943i	$-0.369351\pi$
$223$	2657.54			0.798035			0.399018	+	0.916943i	$0.369351\pi$
$224$		0			0
$225$	−2812.96			−0.833470
$226$		0			0
$227$	−833.769	+	2012.90i	−0.243785	+	0.588549i	−0.997653	−	0.0684772i	$-0.978186\pi$
$227$	−833.769	+	2012.90i	−0.243785	+	0.588549i	0.753868	+	0.657026i	$0.228186\pi$
$228$		0			0
$229$	−5607.23	+	2322.59i	−1.61806	+	0.670224i	−0.993820	−	0.111006i	$-0.964593\pi$
$229$	−5607.23	+	2322.59i	−1.61806	+	0.670224i	−0.624244	+	0.781230i	$0.714593\pi$
$230$		0			0
$231$	−3417.99	+	3417.99i	−0.973538	+	0.973538i
$232$		0			0
$233$	132.710	+	132.710i	0.0373138	+	0.0373138i	0.725518	−	0.688204i	$-0.241600\pi$
$233$	132.710	+	132.710i	0.0373138	+	0.0373138i	−0.688204	+	0.725518i	$0.741600\pi$
$234$		0			0
$235$	1218.14	+	2940.86i	0.338140	+	0.816343i
$236$		0			0
$237$	6775.83	+	2806.64i	1.85712	+	0.769245i
$238$		0			0
$239$			138.825i			0.0375727i	0.999824	+	0.0187863i	$0.00598023\pi$
$239$			138.825i			0.0375727i	−0.999824	+	0.0187863i	$0.994020\pi$
$240$		0			0
$241$		−	4825.11i		−	1.28968i	−0.764318	−	0.644839i	$-0.776924\pi$
$241$		−	4825.11i		−	1.28968i	0.764318	−	0.644839i	$-0.223076\pi$
$242$		0			0
$243$	5007.97	+	2074.37i	1.32206	+	0.547616i
$244$		0			0
$245$	−4043.20	−	9761.15i	−1.05433	−	2.54537i
$246$		0			0
$247$	1009.83	+	1009.83i	0.260138	+	0.260138i
$248$		0			0
$249$	7270.88	−	7270.88i	1.85049	−	1.85049i
$250$		0			0
$251$	3296.58	−	1365.49i	0.828996	−	0.343381i	0.0724909	−	0.997369i	$-0.476905\pi$
$251$	3296.58	−	1365.49i	0.828996	−	0.343381i	0.756505	+	0.653988i	$0.226905\pi$
$252$		0			0
$253$	411.311	−	992.992i	0.102209	−	0.246754i
$254$		0			0
$255$	−3112.71			−0.764414
$256$		0			0
$257$	6601.51			1.60230			0.801149	−	0.598465i	$-0.204222\pi$
$257$	6601.51			1.60230			0.801149	+	0.598465i	$0.204222\pi$
$258$		0			0
$259$	2551.10	−	6158.90i	0.612038	−	1.47759i
$260$		0			0
$261$	−424.180	+	175.701i	−0.100598	+	0.0416691i
$262$		0			0
$263$	−4812.19	+	4812.19i	−1.12826	+	1.12826i	−0.137799	+	0.990460i	$0.544003\pi$
$263$	−4812.19	+	4812.19i	−1.12826	+	1.12826i	−0.990460	+	0.137799i	$0.955997\pi$
$264$		0			0
$265$	−967.760	−	967.760i	−0.224336	−	0.224336i
$266$		0			0
$267$	−3345.06	−	8075.69i	−0.766720	−	1.85103i
$268$		0			0
$269$	952.102	+	394.374i	0.215802	+	0.0893880i	0.487965	−	0.872863i	$-0.337739\pi$
$269$	952.102	+	394.374i	0.215802	+	0.0893880i	−0.272164	+	0.962251i	$0.587739\pi$
$270$		0			0
$271$		−	134.675i		−	0.0301880i	−0.999886	−	0.0150940i	$-0.995195\pi$
$271$		−	134.675i		−	0.0301880i	0.999886	−	0.0150940i	$-0.00480475\pi$
$272$		0			0
$273$			4001.87i			0.887195i
$274$		0			0
$275$	1596.99	+	661.496i	0.350190	+	0.145053i
$276$		0			0
$277$	196.577	+	474.579i	0.0426396	+	0.102941i	0.943764	−	0.330619i	$-0.107257\pi$
$277$	196.577	+	474.579i	0.0426396	+	0.102941i	−0.901125	+	0.433560i	$0.857257\pi$
$278$		0			0
$279$	3472.97	+	3472.97i	0.745238	+	0.745238i
$280$		0			0
$281$	−5752.69	+	5752.69i	−1.22127	+	1.22127i	−0.254087	+	0.967181i	$0.581775\pi$
$281$	−5752.69	+	5752.69i	−1.22127	+	1.22127i	−0.967181	+	0.254087i	$0.918225\pi$
$282$		0			0
$283$	30.6153	−	12.6813i	0.00643071	−	0.00266369i	−0.379466	−	0.925206i	$-0.623892\pi$
$283$	30.6153	−	12.6813i	0.00643071	−	0.00266369i	0.385896	+	0.922542i	$0.373892\pi$
$284$		0			0
$285$	−3816.84	+	9214.66i	−0.793298	+	1.91519i
$286$		0			0
$287$	5252.22			1.08024
$288$		0			0
$289$	4140.18			0.842700
$290$		0			0
$291$	−4096.16	+	9889.01i	−0.825159	+	1.99211i
$292$		0			0
$293$	6083.38	−	2519.82i	1.21295	−	0.502421i	0.317790	−	0.948161i	$-0.397059\pi$
$293$	6083.38	−	2519.82i	1.21295	−	0.502421i	0.895163	+	0.445740i	$0.147059\pi$
$294$		0			0
$295$	1306.13	−	1306.13i	0.257783	−	0.257783i
$296$		0			0
$297$	472.799	+	472.799i	0.0923722	+	0.0923722i
$298$		0			0
$299$	−340.523	−	822.096i	−0.0658628	−	0.159007i
$300$		0			0
$301$	1941.97	+	804.390i	0.371871	+	0.154034i
$302$		0			0
$303$		−	8479.30i		−	1.60767i
$304$		0			0
$305$			7535.84i			1.41476i
$306$		0			0
$307$	5493.47	+	2275.47i	1.02127	+	0.423022i	0.829553	−	0.558428i	$-0.188595\pi$
$307$	5493.47	+	2275.47i	1.02127	+	0.423022i	0.191714	+	0.981451i	$0.438595\pi$
$308$		0			0
$309$	2003.11	+	4835.94i	0.368780	+	0.890314i
$310$		0			0
$311$	640.062	+	640.062i	0.116703	+	0.116703i	0.763047	−	0.646344i	$-0.223703\pi$
$311$	640.062	+	640.062i	0.116703	+	0.116703i	−0.646344	+	0.763047i	$0.723703\pi$
$312$		0			0
$313$	571.963	−	571.963i	0.103288	−	0.103288i	−0.653574	−	0.756862i	$-0.726731\pi$
$313$	571.963	−	571.963i	0.103288	−	0.103288i	0.756862	+	0.653574i	$0.226731\pi$
$314$		0			0
$315$	−13906.6	+	5760.29i	−2.48745	+	1.03034i
$316$		0			0
$317$	1686.24	−	4070.95i	0.298766	−	0.721284i	−0.701200	−	0.712965i	$-0.747352\pi$
$317$	1686.24	−	4070.95i	0.298766	−	0.721284i	0.999965	−	0.00831921i	$-0.00264812\pi$
$318$		0			0
$319$	282.136			0.0495191
$320$		0			0
$321$	−13640.8			−2.37183
$322$		0			0
$323$	−947.634	+	2287.79i	−0.163244	+	0.394106i
$324$		0			0
$325$	1322.15	−	547.651i	0.225660	−	0.0934715i
$326$		0			0
$327$	10619.4	−	10619.4i	1.79589	−	1.79589i
$328$		0			0
$329$	5017.70	+	5017.70i	0.840836	+	0.840836i
$330$		0			0
$331$	2604.99	+	6288.99i	0.432577	+	1.04433i	0.978453	+	0.206467i	$0.0661968\pi$
$331$	2604.99	+	6288.99i	0.432577	+	1.04433i	−0.545877	+	0.837866i	$0.683803\pi$
$332$		0			0
$333$	−5948.00	−	2463.74i	−0.978823	−	0.405442i
$334$		0			0
$335$			5537.28i			0.903086i
$336$		0			0
$337$		−	5051.39i		−	0.816518i	−0.912866	−	0.408259i	$-0.866136\pi$
$337$		−	5051.39i		−	0.816518i	0.912866	−	0.408259i	$-0.133864\pi$
$338$		0			0
$339$	−9839.85	−	4075.80i	−1.57648	−	0.653000i
$340$		0			0
$341$	−1154.99	−	2788.40i	−0.183421	−	0.442817i
$342$		0			0
$343$	−8740.21	−	8740.21i	−1.37588	−	1.37588i
$344$		0			0
$345$	4394.32	−	4394.32i	0.685746	−	0.685746i
$346$		0			0
$347$	−1548.08	+	641.238i	−0.239497	+	0.0992030i	−0.499204	−	0.866485i	$-0.666374\pi$
$347$	−1548.08	+	641.238i	−0.239497	+	0.0992030i	0.259707	+	0.965688i	$0.416374\pi$
$348$		0			0
$349$	3012.90	−	7273.78i	0.462111	−	1.11563i	−0.505418	−	0.862875i	$-0.668662\pi$
$349$	3012.90	−	7273.78i	0.462111	−	1.11563i	0.967529	−	0.252760i	$-0.0813383\pi$
$350$		0			0
$351$	553.564			0.0841797
$352$		0			0
$353$	−3877.72			−0.584675			−0.292337	−	0.956315i	$-0.594433\pi$
$353$	−3877.72			−0.584675			−0.292337	+	0.956315i	$0.594433\pi$
$354$		0			0
$355$	4146.89	−	10011.5i	0.619983	−	1.49677i
$356$		0			0
$357$	−6410.84	+	2655.46i	−0.950414	+	0.393674i
$358$		0			0
$359$	80.3532	−	80.3532i	0.0118130	−	0.0118130i	−0.701176	−	0.712989i	$-0.747341\pi$
$359$	80.3532	−	80.3532i	0.0118130	−	0.0118130i	0.712989	+	0.701176i	$0.247341\pi$
$360$		0			0
$361$	760.577	+	760.577i	0.110887	+	0.110887i
$362$		0			0
$363$	2798.47	+	6756.09i	0.404632	+	0.976867i
$364$		0			0
$365$	−13741.7	−	5692.01i	−1.97062	−	0.816256i
$366$		0			0
$367$		−	2569.61i		−	0.365484i	−0.983161	−	0.182742i	$-0.941503\pi$
$367$		−	2569.61i		−	0.365484i	0.983161	−	0.182742i	$-0.0584973\pi$
$368$		0			0
$369$		−	5072.36i		−	0.715601i
$370$		0			0
$371$	−2818.77	−	1167.57i	−0.394456	−	0.163389i
$372$		0			0
$373$	3461.88	+	8357.71i	0.480561	+	1.16018i	0.959343	+	0.282243i	$0.0910785\pi$
$373$	3461.88	+	8357.71i	0.480561	+	1.16018i	−0.478782	+	0.877934i	$0.658922\pi$
$374$		0			0
$375$	−2829.60	−	2829.60i	−0.389652	−	0.389652i
$376$		0			0
$377$	165.166	−	165.166i	0.0225636	−	0.0225636i
$378$		0			0
$379$	−200.232	+	82.9388i	−0.0271378	+	0.0112408i	−0.396211	−	0.918159i	$-0.629675\pi$
$379$	−200.232	+	82.9388i	−0.0271378	+	0.0112408i	0.369073	+	0.929400i	$0.379675\pi$
$380$		0			0
$381$	2663.40	−	6430.01i	0.358136	−	0.864618i
$382$		0			0
$383$	4511.40			0.601885			0.300942	−	0.953642i	$-0.402699\pi$
$383$	4511.40			0.601885			0.300942	+	0.953642i	$0.402699\pi$
$384$		0			0
$385$	9249.73			1.22444
$386$		0			0
$387$	776.844	−	1875.47i	0.102039	−	0.246345i
$388$		0			0
$389$	4993.23	−	2068.26i	0.650814	−	0.269576i	−0.0327533	−	0.999463i	$-0.510428\pi$
$389$	4993.23	−	2068.26i	0.650814	−	0.269576i	0.683567	+	0.729887i	$0.260428\pi$
$390$		0			0
$391$	1091.01	−	1091.01i	0.141112	−	0.141112i
$392$		0			0
$393$	−5306.93	−	5306.93i	−0.681169	−	0.681169i
$394$		0			0
$395$	−5370.69	−	12966.0i	−0.684123	−	1.65162i
$396$		0			0
$397$	−7615.39	−	3154.40i	−0.962734	−	0.398778i	−0.154732	−	0.987957i	$-0.549451\pi$
$397$	−7615.39	−	3154.40i	−0.962734	−	0.398778i	−0.808003	+	0.589179i	$0.799451\pi$
$398$		0			0
$399$			22234.4i			2.78975i
$400$		0			0
$401$			5161.80i			0.642813i	0.946941	+	0.321407i	$0.104156\pi$
$401$			5161.80i			0.642813i	−0.946941	+	0.321407i	$0.895844\pi$
$402$		0			0
$403$	−2308.51	−	956.218i	−0.285348	−	0.118195i
$404$		0			0
$405$	−3286.76	−	7934.94i	−0.403260	−	0.973557i
$406$		0			0
$407$	2797.46	+	2797.46i	0.340700	+	0.340700i
$408$		0			0
$409$	554.377	−	554.377i	0.0670225	−	0.0670225i	−0.672801	−	0.739823i	$-0.734909\pi$
$409$	554.377	−	554.377i	0.0670225	−	0.0670225i	0.739823	+	0.672801i	$0.234909\pi$
$410$		0			0
$411$	8209.79	−	3400.61i	0.985302	−	0.408125i
$412$		0			0
$413$	1575.81	−	3804.33i	0.187749	−	0.453266i
$414$		0			0
$415$	−19676.4			−2.32741
$416$		0			0
$417$	13460.6			1.58074
$418$		0			0
$419$	−1812.51	+	4375.80i	−0.211330	+	0.510195i	−0.993628	−	0.112709i	$-0.964047\pi$
$419$	−1812.51	+	4375.80i	−0.211330	+	0.510195i	0.782298	+	0.622904i	$0.214047\pi$
$420$		0			0
$421$	−4077.46	+	1688.94i	−0.472026	+	0.195520i	−0.605999	−	0.795465i	$-0.707226\pi$
$421$	−4077.46	+	1688.94i	−0.472026	+	0.195520i	0.133973	+	0.990985i	$0.457226\pi$
$422$		0			0
$423$	4845.88	−	4845.88i	0.557008	−	0.557008i
$424$		0			0
$425$	1754.63	+	1754.63i	0.200264	+	0.200264i
$426$		0			0
$427$	6428.84	+	15520.6i	0.728602	+	1.75900i
$428$		0			0
$429$	−2194.17	−	908.853i	−0.246936	−	0.102284i
$430$		0			0
$431$		−	17343.8i		−	1.93833i	−0.246418	−	0.969164i	$-0.579254\pi$
$431$		−	17343.8i		−	1.93833i	0.246418	−	0.969164i	$-0.420746\pi$
$432$		0			0
$433$			10223.8i			1.13469i	0.823479	+	0.567347i	$0.192030\pi$
$433$			10223.8i			1.13469i	−0.823479	+	0.567347i	$0.807970\pi$
$434$		0			0
$435$	1507.13	+	624.274i	0.166118	+	0.0688084i
$436$		0			0
$437$	−1891.95	−	4567.56i	−0.207103	−	0.499991i
$438$		0			0
$439$	12436.5	+	12436.5i	1.35208	+	1.35208i	0.883335	+	0.468742i	$0.155293\pi$
$439$	12436.5	+	12436.5i	1.35208	+	1.35208i	0.468742	+	0.883335i	$0.344707\pi$
$440$		0			0
$441$	−16084.2	+	16084.2i	−1.73676	+	1.73676i
$442$		0			0
$443$	−9677.23	+	4008.44i	−1.03788	+	0.429902i	−0.835549	−	0.549416i	$-0.814850\pi$
$443$	−9677.23	+	4008.44i	−1.03788	+	0.429902i	−0.202327	+	0.979318i	$0.564850\pi$
$444$		0			0
$445$	−6400.98	+	15453.3i	−0.681878	+	1.64620i
$446$		0			0
$447$	−4939.36			−0.522648
$448$		0			0
$449$	−2416.16			−0.253954			−0.126977	−	0.991906i	$-0.540527\pi$
$449$	−2416.16			−0.253954			−0.126977	+	0.991906i	$0.540527\pi$
$450$		0			0
$451$	−1192.82	+	2879.71i	−0.124540	+	0.300666i
$452$		0			0
$453$	3734.96	−	1547.07i	0.387381	−	0.160458i
$454$		0			0
$455$	5414.91	−	5414.91i	0.557922	−	0.557922i
$456$		0			0
$457$	6285.99	+	6285.99i	0.643427	+	0.643427i	0.951396	−	0.307969i	$-0.0996493\pi$
$457$	6285.99	+	6285.99i	0.643427	+	0.643427i	−0.307969	+	0.951396i	$0.599649\pi$
$458$		0			0
$459$	367.320	+	886.789i	0.0373530	+	0.0901782i
$460$		0			0
$461$	8841.89	+	3662.43i	0.893292	+	0.370014i	0.781637	−	0.623733i	$-0.214385\pi$
$461$	8841.89	+	3662.43i	0.893292	+	0.370014i	0.111655	+	0.993747i	$0.464385\pi$
$462$		0			0
$463$			7744.43i			0.777353i	0.921374	+	0.388676i	$0.127068\pi$
$463$			7744.43i			0.777353i	−0.921374	+	0.388676i	$0.872932\pi$
$464$		0			0
$465$		−	17450.9i		−	1.74035i
$466$		0			0
$467$	−7032.30	−	2912.87i	−0.696822	−	0.288633i	0.00601716	−	0.999982i	$-0.498085\pi$
$467$	−7032.30	−	2912.87i	−0.696822	−	0.288633i	−0.702839	+	0.711349i	$0.748085\pi$
$468$		0			0
$469$	4723.86	+	11404.4i	0.465091	+	1.12283i
$470$		0			0
$471$	−2638.73	−	2638.73i	−0.258145	−	0.258145i
$472$		0			0
$473$	−882.070	+	882.070i	−0.0857455	+	0.0857455i
$474$		0			0
$475$	7345.84	−	3042.75i	0.709580	−	0.293918i
$476$		0			0
$477$	−1127.59	+	2722.24i	−0.108236	+	0.261306i
$478$		0			0
$479$	19364.6			1.84716			0.923580	−	0.383405i	$-0.125249\pi$
$479$	19364.6			1.84716			0.923580	+	0.383405i	$0.125249\pi$
$480$		0			0
$481$	3275.34			0.310484
$482$		0			0
$483$	5301.61	−	12799.2i	0.499444	−	1.20577i
$484$		0			0
$485$	18923.3	−	7838.27i	1.77167	−	0.733850i
$486$		0			0
$487$	−2799.10	+	2799.10i	−0.260450	+	0.260450i	−0.825237	−	0.564787i	$-0.808958\pi$
$487$	−2799.10	+	2799.10i	−0.260450	+	0.260450i	0.564787	+	0.825237i	$0.308958\pi$
$488$		0			0
$489$	7010.08	+	7010.08i	0.648276	+	0.648276i
$490$		0			0
$491$	935.299	+	2258.01i	0.0859663	+	0.207541i	0.961016	−	0.276491i	$-0.0891717\pi$
$491$	935.299	+	2258.01i	0.0859663	+	0.207541i	−0.875050	+	0.484032i	$0.839172\pi$
$492$		0			0
$493$	374.186	+	154.993i	0.0341836	+	0.0141593i
$494$		0			0
$495$		−	8932.98i		−	0.811126i
$496$		0			0
$497$		−	24157.1i		−	2.18027i
$498$		0			0
$499$	552.418	+	228.819i	0.0495583	+	0.0205277i	0.407325	−	0.913283i	$-0.366462\pi$
$499$	552.418	+	228.819i	0.0495583	+	0.0205277i	−0.357767	+	0.933811i	$0.616462\pi$
$500$		0			0
$501$	2668.89	+	6443.27i	0.237998	+	0.574579i
$502$		0			0
$503$	254.724	+	254.724i	0.0225797	+	0.0225797i	0.718307	−	0.695727i	$-0.244918\pi$
$503$	254.724	+	254.724i	0.0225797	+	0.0225797i	−0.695727	+	0.718307i	$0.744918\pi$
$504$		0			0
$505$	−11473.3	+	11473.3i	−1.01100	+	1.01100i
$506$		0			0
$507$	13710.0	−	5678.86i	1.20095	−	0.497450i
$508$		0			0
$509$	−5370.63	+	12965.8i	−0.467680	+	1.12908i	0.497494	+	0.867468i	$0.334254\pi$
$509$	−5370.63	+	12965.8i	−0.467680	+	1.12908i	−0.965173	+	0.261611i	$0.915746\pi$
$510$		0			0
$511$	−33157.9			−2.87049
$512$		0			0
$513$	3075.60			0.264700
$514$		0			0
$515$	3833.08	−	9253.88i	0.327972	−	0.791796i
$516$		0			0
$517$	−3890.69	+	1611.58i	−0.330972	+	0.137093i
$518$		0			0
$519$	−13951.6	+	13951.6i	−1.17998	+	1.17998i
$520$		0			0
$521$	2418.86	+	2418.86i	0.203402	+	0.203402i	0.801456	−	0.598054i	$-0.204059\pi$
$521$	2418.86	+	2418.86i	0.203402	+	0.203402i	−0.598054	+	0.801456i	$0.704059\pi$
$522$		0			0
$523$	3061.70	+	7391.60i	0.255982	+	0.617996i	0.998665	−	0.0516471i	$-0.0164471\pi$
$523$	3061.70	+	7391.60i	0.255982	+	0.617996i	−0.742683	+	0.669643i	$0.766447\pi$
$524$		0			0
$525$	20584.5	+	8526.38i	1.71120	+	0.708804i
$526$		0			0
$527$		−	4332.65i		−	0.358128i
$528$		0			0
$529$		−	9086.56i		−	0.746820i
$530$		0			0
$531$	−3674.06	−	1521.84i	−0.300264	−	0.124374i
$532$		0			0
$533$	987.531	+	2384.11i	0.0802528	+	0.193747i
$534$		0			0
$535$	18457.3	+	18457.3i	1.49155	+	1.49155i
$536$		0			0
$537$	18646.1	−	18646.1i	1.49840	−	1.49840i
$538$		0			0
$539$	12913.8	−	5349.06i	1.03198	−	0.427459i
$540$		0			0
$541$	4520.94	−	10914.5i	0.359280	−	0.867379i	−0.636121	−	0.771589i	$-0.719462\pi$
$541$	4520.94	−	10914.5i	0.359280	−	0.867379i	0.995402	−	0.0957899i	$-0.0305377\pi$
$542$		0			0
$543$	16399.6			1.29608
$544$		0			0
$545$	−28738.1			−2.25873
$546$		0			0
$547$	−4726.46	+	11410.7i	−0.369450	+	0.891930i	0.624391	+	0.781112i	$0.285347\pi$
$547$	−4726.46	+	11410.7i	−0.369450	+	0.891930i	−0.993841	+	0.110818i	$0.964653\pi$
$548$		0			0
$549$	14989.1	−	6208.68i	1.16524	−	0.482660i
$550$		0			0
$551$	917.662	−	917.662i	0.0709505	−	0.0709505i
$552$		0			0
$553$	−22122.6	−	22122.6i	−1.70117	−	1.70117i
$554$		0			0
$555$	8753.78	+	21133.5i	0.669509	+	1.61634i
$556$		0			0
$557$	−2303.67	−	954.213i	−0.175242	−	0.0725876i	0.293337	−	0.956009i	$-0.405234\pi$
$557$	−2303.67	−	954.213i	−0.175242	−	0.0725876i	−0.468579	+	0.883421i	$0.655234\pi$
$558$		0			0
$559$			1032.75i			0.0781407i
$560$		0			0
$561$		−	4118.04i		−	0.309918i
$562$		0			0
$563$	2533.84	+	1049.55i	0.189677	+	0.0785670i	0.475501	−	0.879715i	$-0.342267\pi$
$563$	2533.84	+	1049.55i	0.189677	+	0.0785670i	−0.285823	+	0.958282i	$0.592267\pi$
$564$		0			0
$565$	7799.30	+	18829.2i	0.580742	+	1.40204i
$566$		0			0
$567$	−13538.6	−	13538.6i	−1.00277	−	1.00277i
$568$		0			0
$569$	−10461.9	+	10461.9i	−0.770801	+	0.770801i	−0.978247	−	0.207445i	$-0.933485\pi$
$569$	−10461.9	+	10461.9i	−0.770801	+	0.770801i	0.207445	+	0.978247i	$0.433485\pi$
$570$		0			0
$571$	−21510.2	+	8909.80i	−1.57648	+	0.653001i	−0.987852	−	0.155400i	$-0.950333\pi$
$571$	−21510.2	+	8909.80i	−1.57648	+	0.653001i	−0.588632	+	0.808401i	$0.700333\pi$
$572$		0			0
$573$	−966.329	+	2332.92i	−0.0704519	+	0.170086i
$574$		0			0
$575$	−4954.16			−0.359309
$576$		0			0
$577$	8321.88			0.600424			0.300212	−	0.953873i	$-0.402943\pi$
$577$	8321.88			0.600424			0.300212	+	0.953873i	$0.402943\pi$
$578$		0			0
$579$	2678.21	−	6465.77i	0.192232	−	0.464090i
$580$		0			0
$581$	−40524.8	+	16785.9i	−2.89372	+	1.19862i
$582$		0			0
$583$	1280.32	−	1280.32i	0.0909530	−	0.0909530i
$584$		0			0
$585$	−5229.48	−	5229.48i	−0.369594	−	0.369594i
$586$		0			0
$587$	−7994.94	−	19301.5i	−0.562158	−	1.35717i	−0.908037	−	0.418890i	$-0.862419\pi$
$587$	−7994.94	−	19301.5i	−0.562158	−	1.35717i	0.345880	−	0.938279i	$-0.387581\pi$
$588$		0			0
$589$	−12826.1	−	5312.74i	−0.897266	−	0.371660i
$590$		0			0
$591$		−	342.028i		−	0.0238057i
$592$		0			0
$593$			17757.1i			1.22968i	0.788654	+	0.614838i	$0.210778\pi$
$593$			17757.1i			1.22968i	−0.788654	+	0.614838i	$0.789222\pi$
$594$		0			0
$595$	12267.6	+	5081.39i	0.845245	+	0.350112i
$596$		0			0
$597$	−12200.0	−	29453.5i	−0.836371	−	2.01918i
$598$		0			0
$599$	−17544.2	−	17544.2i	−1.19672	−	1.19672i	−0.975143	−	0.221578i	$-0.928879\pi$
$599$	−17544.2	−	17544.2i	−1.19672	−	1.19672i	−0.221578	−	0.975143i	$-0.571121\pi$
$600$		0			0
$601$	16.0607	−	16.0607i	0.00109006	−	0.00109006i	−0.706562	−	0.707652i	$-0.749755\pi$
$601$	16.0607	−	16.0607i	0.00109006	−	0.00109006i	0.707652	+	0.706562i	$0.249755\pi$
$602$		0			0
$603$	11013.9	−	4562.10i	0.743814	−	0.308098i
$604$		0			0
$605$	5355.04	−	12928.2i	0.359857	−	0.868771i
$606$		0			0
$607$	15461.8			1.03390			0.516950	−	0.856016i	$-0.327067\pi$
$607$	15461.8			1.03390			0.516950	+	0.856016i	$0.327067\pi$
$608$		0			0
$609$	3636.61			0.241975
$610$		0			0
$611$	−1334.22	+	3221.10i	−0.0883418	+	0.213276i
$612$		0			0
$613$	13837.1	−	5731.53i	0.911708	−	0.377642i	0.122998	−	0.992407i	$-0.460749\pi$
$613$	13837.1	−	5731.53i	0.911708	−	0.377642i	0.788710	+	0.614765i	$0.210749\pi$
$614$		0			0
$615$	−12743.7	+	12743.7i	−0.835571	+	0.835571i
$616$		0			0
$617$	6349.72	+	6349.72i	0.414312	+	0.414312i	0.883238	−	0.468926i	$-0.155359\pi$
$617$	6349.72	+	6349.72i	0.414312	+	0.414312i	−0.468926	+	0.883238i	$0.655359\pi$
$618$		0			0
$619$	−7640.34	−	18445.4i	−0.496109	−	1.19771i	−0.951563	−	0.307453i	$-0.900523\pi$
$619$	−7640.34	−	18445.4i	−0.496109	−	1.19771i	0.455455	−	0.890259i	$-0.349477\pi$
$620$		0			0
$621$	−1770.47	−	733.353i	−0.114407	−	0.0473888i
$622$		0			0
$623$			37287.9i			2.39793i
$624$		0			0
$625$			18815.1i			1.20417i
$626$		0			0
$627$	−12190.8	−	5049.59i	−0.776480	−	0.321628i
$628$		0			0
$629$	2173.37	+	5246.97i	0.137771	+	0.332608i
$630$		0			0
$631$	3471.86	+	3471.86i	0.219037	+	0.219037i	0.808093	−	0.589055i	$-0.200500\pi$
$631$	3471.86	+	3471.86i	0.219037	+	0.219037i	−0.589055	+	0.808093i	$0.700500\pi$
$632$		0			0
$633$	9727.94	−	9727.94i	0.610823	−	0.610823i
$634$		0			0
$635$	−12304.2	+	5096.58i	−0.768943	+	0.318506i
$636$		0			0
$637$	4428.48	−	10691.3i	0.275452	−	0.664999i
$638$		0			0
$639$	−23329.8			−1.44431
$640$		0			0
$641$	7666.55			0.472403			0.236202	−	0.971704i	$-0.424097\pi$
$641$	7666.55			0.472403			0.236202	+	0.971704i	$0.424097\pi$
$642$		0			0
$643$	3146.10	−	7595.36i	0.192955	−	0.465835i	−0.797560	−	0.603240i	$-0.793876\pi$
$643$	3146.10	−	7595.36i	0.192955	−	0.465835i	0.990515	+	0.137405i	$0.0438761\pi$
$644$		0			0
$645$	−6663.62	+	2760.16i	−0.406790	+	0.168498i
$646$		0			0
$647$	10868.8	−	10868.8i	0.660428	−	0.660428i	−0.295053	−	0.955481i	$-0.595337\pi$
$647$	10868.8	−	10868.8i	0.660428	−	0.660428i	0.955481	+	0.295053i	$0.0953372\pi$
$648$		0			0
$649$	1727.98	+	1727.98i	0.104513	+	0.104513i
$650$		0			0
$651$	−14887.4	−	35941.3i	−0.896285	−	2.16382i
$652$		0			0
$653$	−2635.05	−	1091.47i	−0.157914	−	0.0654099i	0.302327	−	0.953204i	$-0.402237\pi$
$653$	−2635.05	−	1091.47i	−0.157914	−	0.0654099i	−0.460240	+	0.887794i	$0.652237\pi$
$654$		0			0
$655$			14361.6i			0.856721i
$656$		0			0
$657$			32022.4i			1.90154i
$658$		0			0
$659$	19323.7	+	8004.13i	1.14225	+	0.473136i	0.871928	−	0.489633i	$-0.162869\pi$
$659$	19323.7	+	8004.13i	1.14225	+	0.473136i	0.270323	+	0.962770i	$0.412869\pi$
$660$		0			0
$661$	67.1965	+	162.227i	0.00395407	+	0.00954598i	0.925844	−	0.377905i	$-0.123356\pi$
$661$	67.1965	+	162.227i	0.00395407	+	0.00954598i	−0.921890	+	0.387451i	$0.873356\pi$
$662$		0			0
$663$	−2410.76	−	2410.76i	−0.141216	−	0.141216i
$664$		0			0
$665$	30085.2	−	30085.2i	1.75437	−	1.75437i
$666$		0			0
$667$	−747.061	+	309.443i	−0.0433678	+	0.0179635i
$668$		0			0
$669$	−7779.43	+	18781.2i	−0.449582	+	1.08539i
$670$		0			0
$671$	−9969.74			−0.573588
$672$		0			0
$673$	3444.70			0.197301			0.0986503	−	0.995122i	$-0.468547\pi$
$673$	3444.70			0.197301			0.0986503	+	0.995122i	$0.468547\pi$
$674$		0			0
$675$	1179.42	−	2847.38i	0.0672534	−	0.162364i
$676$		0			0
$677$	−4665.73	+	1932.61i	−0.264872	+	0.109714i	−0.511167	−	0.859481i	$-0.670787\pi$
$677$	−4665.73	+	1932.61i	−0.264872	+	0.109714i	0.246295	+	0.969195i	$0.420787\pi$
$678$		0			0
$679$	32286.9	−	32286.9i	1.82483	−	1.82483i
$680$		0			0
$681$	−11784.7	−	11784.7i	−0.663131	−	0.663131i
$682$		0			0
$683$	−537.141	−	1296.77i	−0.0300924	−	0.0726496i	0.908119	−	0.418712i	$-0.137518\pi$
$683$	−537.141	−	1296.77i	−0.0300924	−	0.0726496i	−0.938211	+	0.346063i	$0.887518\pi$
$684$		0			0
$685$	−15710.0	−	6507.27i	−0.876272	−	0.362964i
$686$		0			0
$687$		−	46426.1i		−	2.57826i
$688$		0			0
$689$		−	1499.04i		−	0.0828864i
$690$		0			0
$691$	−10591.5	−	4387.14i	−0.583097	−	0.241526i	0.0715810	−	0.997435i	$-0.477196\pi$
$691$	−10591.5	−	4387.14i	−0.583097	−	0.241526i	−0.654678	+	0.755908i	$0.727196\pi$
$692$		0			0
$693$	−7620.73	−	18398.1i	−0.417731	−	1.00849i
$694$		0			0
$695$	−18213.4	−	18213.4i	−0.994063	−	0.994063i
$696$		0			0
$697$	−3163.97	+	3163.97i	−0.171943	+	0.171943i
$698$		0			0
$699$	−1326.36	+	549.398i	−0.0717706	+	0.0297284i
$700$		0			0
$701$	2339.32	−	5647.61i	0.126041	−	0.304290i	−0.848245	−	0.529604i	$-0.822341\pi$
$701$	2339.32	−	5647.61i	0.126041	−	0.304290i	0.974286	+	0.225314i	$0.0723406\pi$
$702$		0			0
$703$	18197.8			0.976304
$704$		0			0
$705$	−24349.4			−1.30078
$706$		0			0
$707$	−13842.2	+	33417.9i	−0.736334	+	1.77767i
$708$		0			0
$709$	13955.2	−	5780.42i	0.739207	−	0.306189i	0.0188776	−	0.999822i	$-0.493991\pi$
$709$	13955.2	−	5780.42i	0.739207	−	0.306189i	0.720329	+	0.693632i	$0.243991\pi$
$710$		0			0
$711$	−21365.0	+	21365.0i	−1.12694	+	1.12694i
$712$		0			0
$713$	6116.56	+	6116.56i	0.321272	+	0.321272i
$714$		0			0
$715$	1739.15	+	4198.68i	0.0909657	+	0.219611i
$716$		0			0
$717$	−981.100	−	406.385i	−0.0511016	−	0.0211670i
$718$		0			0
$719$		−	153.579i		−	0.00796595i	−0.999992	−	0.00398298i	$-0.998732\pi$
$719$		−	153.579i		−	0.00796595i	0.999992	−	0.00398298i	$-0.00126782\pi$
$720$		0			0
$721$		−	22329.0i		−	1.15336i
$722$		0			0
$723$	34099.7	+	14124.6i	1.75406	+	0.726554i
$724$		0			0
$725$	−497.666	−	1201.47i	−0.0254936	−	0.0615469i
$726$		0			0
$727$	5550.98	+	5550.98i	0.283184	+	0.283184i	0.834377	−	0.551194i	$-0.185827\pi$
$727$	5550.98	+	5550.98i	0.283184	+	0.283184i	−0.551194	+	0.834377i	$0.685827\pi$
$728$		0			0
$729$	−18117.5	+	18117.5i	−0.920464	+	0.920464i
$730$		0			0
$731$	−1654.43	+	685.286i	−0.0837088	+	0.0346733i
$732$		0			0
$733$	−827.485	+	1997.73i	−0.0416969	+	0.100665i	−0.943356	−	0.331782i	$-0.892350\pi$
$733$	−827.485	+	1997.73i	−0.0416969	+	0.100665i	0.901659	+	0.432448i	$0.142350\pi$
$734$		0			0
$735$	80819.2			4.05587
$736$		0			0
$737$	−7325.69			−0.366140
$738$		0			0
$739$	1375.10	−	3319.78i	0.0684489	−	0.165250i	−0.885953	−	0.463775i	$-0.846495\pi$
$739$	1375.10	−	3319.78i	0.0684489	−	0.165250i	0.954402	+	0.298525i	$0.0964946\pi$
$740$		0			0
$741$	−10092.7	+	4180.54i	−0.500358	+	0.207255i
$742$		0			0
$743$	−22288.2	+	22288.2i	−1.10051	+	1.10051i	−0.106156	+	0.994349i	$0.533854\pi$
$743$	−22288.2	+	22288.2i	−1.10051	+	1.10051i	−0.994349	+	0.106156i	$0.966146\pi$
$744$		0			0
$745$	6683.41	+	6683.41i	0.328673	+	0.328673i
$746$		0			0
$747$	16211.1	+	39137.1i	0.794021	+	1.91694i
$748$		0			0
$749$	53760.1	+	22268.2i	2.62263	+	1.08633i
$750$		0			0
$751$		−	24467.3i		−	1.18885i	−0.804151	−	0.594424i	$-0.797380\pi$
$751$		−	24467.3i		−	1.18885i	0.804151	−	0.594424i	$-0.202620\pi$
$752$		0			0
$753$			27294.6i			1.32094i
$754$		0			0
$755$	−7147.08	−	2960.42i	−0.344515	−	0.142703i
$756$		0			0
$757$	13698.7	+	33071.6i	0.657712	+	1.58786i	0.801328	+	0.598225i	$0.204127\pi$
$757$	13698.7	+	33071.6i	0.657712	+	1.58786i	−0.143616	+	0.989633i	$0.545873\pi$
$758$		0			0
$759$	5813.59	+	5813.59i	0.278024	+	0.278024i
$760$		0			0
$761$	23068.9	−	23068.9i	1.09888	−	1.09888i	0.104338	−	0.994542i	$-0.466728\pi$
$761$	23068.9	−	23068.9i	1.09888	−	1.09888i	0.994542	−	0.104338i	$-0.0332725\pi$
$762$		0			0
$763$	−59188.2	+	24516.5i	−2.80833	+	1.16325i
$764$		0			0
$765$	4907.38	−	11847.5i	0.231930	−	0.559929i
$766$		0			0
$767$	2023.17			0.0952441
$768$		0			0
$769$	−22615.1			−1.06050			−0.530249	−	0.847842i	$-0.677902\pi$
$769$	−22615.1			−1.06050			−0.530249	+	0.847842i	$0.677902\pi$
$770$		0			0
$771$	−19324.7	+	46653.8i	−0.902672	+	2.17924i
$772$		0			0
$773$	−5061.63	+	2096.60i	−0.235516	+	0.0975541i	−0.497320	−	0.867567i	$-0.665683\pi$
$773$	−5061.63	+	2096.60i	−0.235516	+	0.0975541i	0.261804	+	0.965121i	$0.415683\pi$
$774$		0			0
$775$	−9837.04	+	9837.04i	−0.455944	+	0.455944i
$776$		0			0
$777$	36058.0	+	36058.0i	1.66483	+	1.66483i
$778$		0			0
$779$	5486.72	+	13246.1i	0.252352	+	0.609231i
$780$		0			0
$781$	13245.0	+	5486.24i	0.606840	+	0.251361i
$782$		0			0
$783$		−	503.039i		−	0.0229593i
$784$		0			0
$785$			7140.90i			0.324675i
$786$		0			0
$787$	4514.92	+	1870.14i	0.204497	+	0.0847056i	0.482581	−	0.875851i	$-0.339699\pi$
$787$	4514.92	+	1870.14i	0.204497	+	0.0847056i	−0.278084	+	0.960557i	$0.589699\pi$
$788$		0			0
$789$	−19921.7	−	48095.2i	−0.898899	−	2.17013i
$790$		0			0
$791$	32126.4	+	32126.4i	1.44410	+	1.44410i
$792$		0			0
$793$	−5836.41	+	5836.41i	−0.261358	+	0.261358i
$794$		0			0
$795$	9672.24	−	4006.37i	0.431496	−	0.178731i
$796$		0			0
$797$	−3175.58	+	7666.53i	−0.141135	+	0.340731i	−0.978603	−	0.205755i	$-0.934035\pi$
$797$	−3175.58	+	7666.53i	−0.141135	+	0.340731i	0.837468	+	0.546486i	$0.184035\pi$
$798$		0			0
$799$	−6045.40			−0.267673
$800$		0			0
$801$	36011.0			1.58850
$802$		0			0
$803$	7530.40	−	18180.0i	0.330936	−	0.798951i
$804$		0			0
$805$	−24492.1	+	10145.0i	−1.07234	+	0.444178i
$806$		0			0
$807$	−5574.19	+	5574.19i	−0.243149	+	0.243149i
$808$		0			0
$809$	−24242.4	−	24242.4i	−1.05355	−	1.05355i	−0.998483	−	0.0550636i	$-0.982464\pi$
$809$	−24242.4	−	24242.4i	−1.05355	−	1.05355i	−0.0550636	−	0.998483i	$-0.517536\pi$
$810$		0			0
$811$	−8971.75	−	21659.7i	−0.388460	−	0.937825i	−0.990267	−	0.139183i	$-0.955552\pi$
$811$	−8971.75	−	21659.7i	−0.388460	−	0.937825i	0.601807	−	0.798642i	$-0.294448\pi$
$812$		0			0
$813$	951.771	+	394.236i	0.0410579	+	0.0170067i
$814$		0			0
$815$		−	18970.6i		−	0.815351i
$816$		0			0
$817$			5737.95i			0.245711i
$818$		0			0
$819$	−15231.7	−	6309.19i	−0.649866	−	0.269183i
$820$		0			0
$821$	−13914.2	−	33592.0i	−0.591486	−	1.42797i	−0.882067	−	0.471124i	$-0.843848\pi$
$821$	−13914.2	−	33592.0i	−0.591486	−	1.42797i	0.290580	−	0.956851i	$-0.406152\pi$
$822$		0			0
$823$	16528.3	+	16528.3i	0.700050	+	0.700050i	0.964421	−	0.264371i	$-0.0851643\pi$
$823$	16528.3	+	16528.3i	0.700050	+	0.700050i	−0.264371	+	0.964421i	$0.585164\pi$
$824$		0			0
$825$	−9349.78	+	9349.78i	−0.394567	+	0.394567i
$826$		0			0
$827$	42195.4	−	17477.9i	1.77422	−	0.734905i	0.780219	−	0.625506i	$-0.215107\pi$
$827$	42195.4	−	17477.9i	1.77422	−	0.734905i	0.993998	−	0.109399i	$-0.0348925\pi$
$828$		0			0
$829$	10495.1	−	25337.5i	0.439699	−	1.06153i	−0.536353	−	0.843994i	$-0.680198\pi$
$829$	10495.1	−	25337.5i	0.439699	−	1.06153i	0.976053	−	0.217535i	$-0.0698015\pi$
$830$		0			0
$831$	−3929.37			−0.164029
$832$		0			0
$833$	20065.6			0.834611
$834$		0			0
$835$	5107.09	−	12329.6i	0.211662	−	0.510998i
$836$		0			0
$837$	−4971.63	+	2059.31i	−0.205310	+	0.0850422i
$838$		0			0
$839$	24243.8	−	24243.8i	0.997605	−	0.997605i	−0.00239210	−	0.999997i	$-0.500761\pi$
$839$	24243.8	−	24243.8i	0.997605	−	0.997605i	0.999997	+	0.00239210i	$0.000761430\pi$
$840$		0			0
$841$	17095.5	+	17095.5i	0.700953	+	0.700953i
$842$		0			0
$843$	−23815.2	−	57495.0i	−0.973000	−	2.34903i
$844$		0			0
$845$	−26234.9	−	10866.9i	−1.06806	−	0.442404i
$846$		0			0
$847$		−	31194.9i		−	1.26549i
$848$		0			0
$849$			253.485i			0.0102469i
$850$		0			0
$851$	−10475.5	−	4339.11i	−0.421971	−	0.174786i
$852$		0			0
$853$	−2422.60	−	5848.66i	−0.0972428	−	0.234765i	0.867771	−	0.496965i	$-0.165552\pi$
$853$	−2422.60	−	5848.66i	−0.0972428	−	0.234765i	−0.965014	+	0.262200i	$0.915552\pi$
$854$		0			0
$855$	−29054.9	−	29054.9i	−1.16217	−	1.16217i
$856$		0			0
$857$	9164.60	−	9164.60i	0.365294	−	0.365294i	−0.500464	−	0.865758i	$-0.666837\pi$
$857$	9164.60	−	9164.60i	0.365294	−	0.365294i	0.865758	+	0.500464i	$0.166837\pi$
$858$		0			0
$859$	35659.4	−	14770.6i	1.41639	−	0.586689i	0.462442	−	0.886650i	$-0.346973\pi$
$859$	35659.4	−	14770.6i	1.41639	−	0.586689i	0.953952	+	0.299960i	$0.0969735\pi$
$860$		0			0
$861$	−15374.9	+	37118.2i	−0.608565	+	1.46921i
$862$		0			0
$863$	2066.31			0.0815043			0.0407521	−	0.999169i	$-0.487025\pi$
$863$	2066.31			0.0815043			0.0407521	+	0.999169i	$0.487025\pi$
$864$		0			0
$865$	37755.7			1.48409
$866$		0			0
$867$	−12119.6	+	29259.3i	−0.474744	+	1.14613i
$868$		0			0
$869$	17153.7	−	7105.29i	0.669619	−	0.277365i
$870$		0			0
$871$	−4288.55	+	4288.55i	−0.166834	+	0.166834i
$872$		0			0
$873$	−31181.3	−	31181.3i	−1.20885	−	1.20885i
$874$		0			0
$875$	6532.55	+	15771.0i	0.252389	+	0.609321i
$876$		0			0
$877$	−218.985	−	90.7068i	−0.00843172	−	0.00349253i	0.378464	−	0.925616i	$-0.376453\pi$
$877$	−218.985	−	90.7068i	−0.00843172	−	0.00349253i	−0.386895	+	0.922124i	$0.626453\pi$
$878$		0			0
$879$			50368.5i			1.93275i
$880$		0			0
$881$		−	6300.18i		−	0.240929i	−0.992718	−	0.120464i	$-0.961562\pi$
$881$		−	6300.18i		−	0.240929i	0.992718	−	0.120464i	$-0.0384384\pi$
$882$		0			0
$883$	16904.8	+	7002.21i	0.644272	+	0.266866i	0.680803	−	0.732466i	$-0.261631\pi$
$883$	16904.8	+	7002.21i	0.644272	+	0.266866i	−0.0365310	+	0.999333i	$0.511631\pi$
$884$		0			0
$885$	5407.18	+	13054.1i	0.205379	+	0.495829i
$886$		0			0
$887$	−8766.03	−	8766.03i	−0.331832	−	0.331832i	0.521450	−	0.853282i	$-0.325391\pi$
$887$	−8766.03	−	8766.03i	−0.331832	−	0.331832i	−0.853282	+	0.521450i	$0.825391\pi$
$888$		0			0
$889$	−20993.5	+	20993.5i	−0.792013	+	0.792013i
$890$		0			0
$891$	10497.7	−	4348.31i	0.394711	−	0.163495i
$892$		0			0
$893$	−7412.93	+	17896.4i	−0.277787	+	0.670638i
$894$		0			0
$895$	−50459.9			−1.88457
$896$		0			0
$897$	6806.70			0.253366
$898$		0			0
$899$	−868.941	+	2097.81i	−0.0322367	+	0.0778263i
$900$		0			0
$901$	2401.40	−	994.692i	0.0887927	−	0.0367791i
$902$		0			0
$903$	−11369.5	+	11369.5i	−0.418995	+	0.418995i
$904$		0			0
$905$	−22190.2	−	22190.2i	−0.815056	−	0.815056i
$906$		0			0
$907$	10784.4	+	26035.9i	0.394808	+	0.953150i	0.988877	+	0.148736i	$0.0475206\pi$
$907$	10784.4	+	26035.9i	0.394808	+	0.953150i	−0.594069	+	0.804414i	$0.702479\pi$
$908$		0			0
$909$	32273.5	+	13368.1i	1.17761	+	0.487781i
$910$		0			0
$911$			39106.7i			1.42224i	0.703070	+	0.711121i	$0.251812\pi$
$911$			39106.7i			1.42224i	−0.703070	+	0.711121i	$0.748188\pi$
$912$		0			0
$913$		−	26031.4i		−	0.943606i
$914$		0			0
$915$	−53256.9	−	22059.7i	−1.92417	−	0.797019i
$916$		0			0
$917$	12251.9	+	29578.6i	0.441213	+	1.06518i
$918$		0			0
$919$	−22104.3	−	22104.3i	−0.793422	−	0.793422i	0.188626	−	0.982049i	$-0.439596\pi$
$919$	−22104.3	−	22104.3i	−0.793422	−	0.793422i	−0.982049	+	0.188626i	$0.939596\pi$
$920$		0			0
$921$	−32162.2	+	32162.2i	−1.15068	+	1.15068i
$922$		0			0
$923$	10965.5	−	4542.05i	0.391043	−	0.161975i
$924$		0			0
$925$	6978.44	−	16847.4i	0.248054	−	0.598854i
$926$		0			0
$927$	−21564.4			−0.764042
$928$		0			0
$929$	−48663.4			−1.71862			−0.859308	−	0.511459i	$-0.829105\pi$
$929$	−48663.4			−1.71862			−0.859308	+	0.511459i	$0.829105\pi$
$930$		0			0
$931$	24604.6	−	59400.8i	0.866147	−	2.09106i
$932$		0			0
$933$	−6397.08	+	2649.76i	−0.224470	+	0.0929787i
$934$		0			0
$935$	−5572.10	+	5572.10i	−0.194895	+	0.194895i
$936$		0			0
$937$	16318.9	+	16318.9i	0.568960	+	0.568960i	0.931837	−	0.362877i	$-0.118205\pi$
$937$	16318.9	+	16318.9i	0.568960	+	0.568960i	−0.362877	+	0.931837i	$0.618205\pi$
$938$		0			0
$939$	2367.83	+	5716.46i	0.0822911	+	0.198668i
$940$		0			0
$941$	16638.7	+	6891.96i	0.576414	+	0.238758i	0.651793	−	0.758397i	$-0.274017\pi$
$941$	16638.7	+	6891.96i	0.576414	+	0.238758i	−0.0753798	+	0.997155i	$0.524017\pi$
$942$		0			0
$943$		−	8933.39i		−	0.308495i
$944$		0			0
$945$		−	16491.9i		−	0.567707i
$946$		0			0
$947$	22740.2	+	9419.31i	0.780315	+	0.323217i	0.737043	−	0.675846i	$-0.236222\pi$
$947$	22740.2	+	9419.31i	0.780315	+	0.323217i	0.0432725	+	0.999063i	$0.486222\pi$
$948$		0			0
$949$	−6234.40	−	15051.2i	−0.213253	−	0.514839i
$950$		0			0
$951$	23833.8	+	23833.8i	0.812687	+	0.812687i
$952$		0			0
$953$	36291.7	−	36291.7i	1.23358	−	1.23358i	0.271005	−	0.962578i	$-0.412644\pi$
$953$	36291.7	−	36291.7i	1.23358	−	1.23358i	0.962578	−	0.271005i	$-0.0873560\pi$
$954$		0			0
$955$	4464.20	−	1849.13i	0.151265	−	0.0626560i
$956$		0			0
$957$	−825.900	+	1993.90i	−0.0278971	+	0.0673496i
$958$		0			0
$959$	−37907.1			−1.27642
$960$		0			0
$961$	−5500.75			−0.184645
$962$		0			0
$963$	21505.6	−	51919.1i	0.719635	−	1.73735i
$964$		0			0
$965$	−12372.7	+	5124.92i	−0.412736	+	0.170961i
$966$		0			0
$967$	7129.16	−	7129.16i	0.237082	−	0.237082i	−0.578559	−	0.815641i	$-0.696385\pi$
$967$	7129.16	−	7129.16i	0.237082	−	0.237082i	0.815641	+	0.578559i	$0.196385\pi$
$968$		0			0
$969$	−13394.1	−	13394.1i	−0.444047	−	0.444047i
$970$		0			0
$971$	−3934.25	−	9498.11i	−0.130027	−	0.313912i	0.845436	−	0.534077i	$-0.179341\pi$
$971$	−3934.25	−	9498.11i	−0.130027	−	0.313912i	−0.975463	+	0.220164i	$0.929341\pi$
$972$		0			0
$973$	−53049.7	−	21973.9i	−1.74789	−	0.723999i
$974$		0			0
$975$			10947.0i			0.359573i
$976$		0			0
$977$			16541.9i			0.541682i	0.962624	+	0.270841i	$0.0873018\pi$
$977$			16541.9i			0.541682i	−0.962624	+	0.270841i	$0.912698\pi$
$978$		0			0
$979$	−20444.4	−	8468.35i	−0.667422	−	0.276455i
$980$		0			0
$981$	23677.0	+	57161.3i	0.770589	+	1.86037i
$982$		0			0
$983$	−20577.7	−	20577.7i	−0.667678	−	0.667678i	0.289500	−	0.957178i	$-0.406511\pi$
$983$	−20577.7	−	20577.7i	−0.667678	−	0.667678i	−0.957178	+	0.289500i	$0.906511\pi$
$984$		0			0
$985$	−462.796	+	462.796i	−0.0149705	+	0.0149705i
$986$		0			0
$987$	−50149.3	+	20772.5i	−1.61729	+	0.669905i
$988$		0			0
$989$	1368.17	−	3303.05i	0.0439891	−	0.106199i
$990$		0			0
$991$	31319.0			1.00392			0.501958	−	0.864892i	$-0.332613\pi$
$991$	31319.0			1.00392			0.501958	+	0.864892i	$0.332613\pi$
$992$		0			0
$993$	−52070.9			−1.66407
$994$		0			0
$995$	−23345.5	+	56361.1i	−0.743822	+	1.79574i
$996$		0			0
$997$	−12142.4	+	5029.56i	−0.385712	+	0.159767i	−0.567109	−	0.823643i	$-0.691938\pi$
$997$	−12142.4	+	5029.56i	−0.385712	+	0.159767i	0.181397	+	0.983410i	$0.441938\pi$
$998$		0			0
$999$	4987.78	−	4987.78i	0.157964	−	0.157964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.17.2		44
4.3	odd	2		32.4.g.a.13.8	yes	44
8.3	odd	2		256.4.g.b.33.2		44
8.5	even	2		256.4.g.a.33.10		44
32.5	even	8	inner	128.4.g.a.113.2		44
32.11	odd	8		256.4.g.b.225.2		44
32.21	even	8		256.4.g.a.225.10		44
32.27	odd	8		32.4.g.a.5.8	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.8	✓	44	32.27	odd	8
32.4.g.a.13.8	yes	44	4.3	odd	2
128.4.g.a.17.2		44	1.1	even	1	trivial
128.4.g.a.113.2		44	32.5	even	8	inner
256.4.g.a.33.10		44	8.5	even	2
256.4.g.a.225.10		44	32.21	even	8
256.4.g.b.33.2		44	8.3	odd	2
256.4.g.b.225.2		44	32.11	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.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.92731 + 7.06715i) q^{3} +(13.5234 - 5.60159i) q^{5} +(23.0737 - 23.0737i) q^{7} +(-22.2836 - 22.2836i) q^{9} +O(q^{10})\)	\(q+(-2.92731 + 7.06715i) q^{3} +(13.5234 - 5.60159i) q^{5} +(23.0737 - 23.0737i) q^{7} +(-22.2836 - 22.2836i) q^{9} +(7.41078 + 17.8912i) q^{11} +(14.8121 + 6.13537i) q^{13} +111.970i q^{15} +27.7996i q^{17} +(82.2959 + 34.0881i) q^{19} +(95.5216 + 230.610i) q^{21} +(-39.2456 - 39.2456i) q^{23} +(63.1173 - 63.1173i) q^{25} +(31.8994 - 13.2132i) q^{27} +(5.57538 - 13.4602i) q^{29} -155.853 q^{31} -148.133 q^{33} +(182.787 - 441.286i) q^{35} +(188.743 - 78.1798i) q^{37} +(-86.7192 + 86.7192i) q^{39} +(113.814 + 113.814i) q^{41} +(24.6509 + 59.5126i) q^{43} +(-426.174 - 176.527i) q^{45} +217.464i q^{47} -721.795i q^{49} +(-196.464 - 81.3779i) q^{51} +(-35.7808 - 86.3826i) q^{53} +(200.438 + 200.438i) q^{55} +(-481.811 + 481.811i) q^{57} +(116.586 - 48.2914i) q^{59} +(-197.015 + 475.636i) q^{61} -1028.33 q^{63} +234.678 q^{65} +(-144.765 + 349.494i) q^{67} +(392.239 - 162.471i) q^{69} +(523.475 - 523.475i) q^{71} +(-718.521 - 718.521i) q^{73} +(261.296 + 630.823i) q^{75} +(583.811 + 241.822i) q^{77} -958.779i q^{79} -586.755i q^{81} +(-1241.90 - 514.414i) q^{83} +(155.722 + 375.946i) q^{85} +(78.8041 + 78.8041i) q^{87} +(-808.016 + 808.016i) q^{89} +(483.336 - 200.204i) q^{91} +(456.231 - 1101.44i) q^{93} +1303.87 q^{95} +1399.29 q^{97} +(233.541 - 563.819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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