LMFDB - Embedded newform 128.4.g.a.113.1

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			113.1
Character	$\chi$	$=$	128.113
Dual form			128.4.g.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.54796 - 8.56554i) q^{3} +(-7.55322 - 3.12865i) q^{5} +(-7.16166 - 7.16166i) q^{7} +(-41.6886 + 41.6886i) q^{9} +O(q^{10})$	\(q+(-3.54796 - 8.56554i) q^{3} +(-7.55322 - 3.12865i) q^{5} +(-7.16166 - 7.16166i) q^{7} +(-41.6886 + 41.6886i) q^{9} +(-0.758120 + 1.83026i) q^{11} +(71.0832 - 29.4436i) q^{13} +75.7978i q^{15} +98.5470i q^{17} +(-89.5748 + 37.1031i) q^{19} +(-35.9342 + 86.7528i) q^{21} +(-24.9355 + 24.9355i) q^{23} +(-41.1256 - 41.1256i) q^{25} +(273.726 + 113.381i) q^{27} +(-57.8528 - 139.669i) q^{29} -58.0545 q^{31} +18.3670 q^{33} +(31.6873 + 76.4999i) q^{35} +(-202.968 - 84.0720i) q^{37} +(-504.401 - 504.401i) q^{39} +(-45.3618 + 45.3618i) q^{41} +(-89.7175 + 216.597i) q^{43} +(445.312 - 184.454i) q^{45} -4.38416i q^{47} -240.421i q^{49} +(844.109 - 349.641i) q^{51} +(8.98141 - 21.6830i) q^{53} +(11.4525 - 11.4525i) q^{55} +(635.616 + 635.616i) q^{57} +(-287.366 - 119.031i) q^{59} +(-28.2072 - 68.0983i) q^{61} +597.119 q^{63} -629.026 q^{65} +(-293.521 - 708.622i) q^{67} +(302.057 + 125.116i) q^{69} +(579.730 + 579.730i) q^{71} +(-258.894 + 258.894i) q^{73} +(-206.351 + 498.176i) q^{75} +(18.5371 - 7.67833i) q^{77} -834.510i q^{79} -1155.05i q^{81} +(-234.905 + 97.3009i) q^{83} +(308.319 - 744.347i) q^{85} +(-991.082 + 991.082i) q^{87} +(179.539 + 179.539i) q^{89} +(-719.939 - 298.208i) q^{91} +(205.975 + 497.268i) q^{93} +792.661 q^{95} -624.033 q^{97} +(-44.6962 - 107.906i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

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

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
$3$	−3.54796	−	8.56554i	−0.682806	−	1.64844i	−0.758794	−	0.651331i	$-0.774211\pi$
$3$	−3.54796	−	8.56554i	−0.682806	−	1.64844i	0.0759878	−	0.997109i	$-0.475789\pi$
$4$		0			0
$5$	−7.55322	−	3.12865i	−0.675581	−	0.279835i	0.0183975	−	0.999831i	$-0.494144\pi$
$5$	−7.55322	−	3.12865i	−0.675581	−	0.279835i	−0.693978	+	0.719996i	$0.744144\pi$
$6$		0			0
$7$	−7.16166	−	7.16166i	−0.386693	−	0.386693i	0.486813	−	0.873506i	$-0.338159\pi$
$7$	−7.16166	−	7.16166i	−0.386693	−	0.386693i	−0.873506	+	0.486813i	$0.838159\pi$
$8$		0			0
$9$	−41.6886	+	41.6886i	−1.54402	+	1.54402i
$10$		0			0
$11$	−0.758120	+	1.83026i	−0.0207802	+	0.0501678i	−0.933929	−	0.357458i	$-0.883643\pi$
$11$	−0.758120	+	1.83026i	−0.0207802	+	0.0501678i	0.913149	+	0.407626i	$0.133643\pi$
$12$		0			0
$13$	71.0832	−	29.4436i	1.51653	−	0.628168i	0.539639	−	0.841896i	$-0.318561\pi$
$13$	71.0832	−	29.4436i	1.51653	−	0.628168i	0.976893	+	0.213728i	$0.0685606\pi$
$14$		0			0
$15$			75.7978i			1.30473i
$16$		0			0
$17$			98.5470i			1.40595i	0.711214	+	0.702975i	$0.248146\pi$
$17$			98.5470i			1.40595i	−0.711214	+	0.702975i	$0.751854\pi$
$18$		0			0
$19$	−89.5748	+	37.1031i	−1.08157	+	0.448002i	−0.851060	−	0.525068i	$-0.824040\pi$
$19$	−89.5748	+	37.1031i	−1.08157	+	0.448002i	−0.230512	+	0.973070i	$0.574040\pi$
$20$		0			0
$21$	−35.9342	+	86.7528i	−0.373404	+	0.901477i
$22$		0			0
$23$	−24.9355	+	24.9355i	−0.226062	+	0.226062i	−0.811045	−	0.584984i	$-0.801101\pi$
$23$	−24.9355	+	24.9355i	−0.226062	+	0.226062i	0.584984	+	0.811045i	$0.301101\pi$
$24$		0			0
$25$	−41.1256	−	41.1256i	−0.329005	−	0.329005i
$26$		0			0
$27$	273.726	+	113.381i	1.95106	+	0.808154i
$28$		0			0
$29$	−57.8528	−	139.669i	−0.370448	−	0.894341i	−0.993674	−	0.112299i	$-0.964178\pi$
$29$	−57.8528	−	139.669i	−0.370448	−	0.894341i	0.623226	−	0.782042i	$-0.285822\pi$
$30$		0			0
$31$	−58.0545			−0.336351			−0.168176	−	0.985757i	$-0.553788\pi$
$31$	−58.0545			−0.336351			−0.168176	+	0.985757i	$0.553788\pi$
$32$		0			0
$33$	18.3670			0.0968874
$34$		0			0
$35$	31.6873	+	76.4999i	0.153032	+	0.369453i
$36$		0			0
$37$	−202.968	−	84.0720i	−0.901829	−	0.373550i	−0.116906	−	0.993143i	$-0.537298\pi$
$37$	−202.968	−	84.0720i	−0.901829	−	0.373550i	−0.784923	+	0.619593i	$0.787298\pi$
$38$		0			0
$39$	−504.401	−	504.401i	−2.07100	−	2.07100i
$40$		0			0
$41$	−45.3618	+	45.3618i	−0.172788	+	0.172788i	−0.788203	−	0.615415i	$-0.788988\pi$
$41$	−45.3618	+	45.3618i	−0.172788	+	0.172788i	0.615415	+	0.788203i	$0.288988\pi$
$42$		0			0
$43$	−89.7175	+	216.597i	−0.318181	+	0.768157i	0.681170	+	0.732126i	$0.261472\pi$
$43$	−89.7175	+	216.597i	−0.318181	+	0.768157i	−0.999351	+	0.0360314i	$0.988528\pi$
$44$		0			0
$45$	445.312	−	184.454i	1.47518	−	0.611041i
$46$		0			0
$47$		−	4.38416i		−	0.0136063i	−0.999977	−	0.00680315i	$-0.997834\pi$
$47$		−	4.38416i		−	0.0136063i	0.999977	−	0.00680315i	$-0.00216553\pi$
$48$		0			0
$49$		−	240.421i		−	0.700937i
$50$		0			0
$51$	844.109	−	349.641i	2.31762	−	0.959992i
$52$		0			0
$53$	8.98141	−	21.6830i	0.0232772	−	0.0561961i	−0.911814	−	0.410604i	$-0.865318\pi$
$53$	8.98141	−	21.6830i	0.0232772	−	0.0561961i	0.935091	+	0.354408i	$0.115318\pi$
$54$		0			0
$55$	11.4525	−	11.4525i	0.0280774	−	0.0280774i
$56$		0			0
$57$	635.616	+	635.616i	1.47701	+	1.47701i
$58$		0			0
$59$	−287.366	−	119.031i	−0.634099	−	0.262652i	0.0423945	−	0.999101i	$-0.486501\pi$
$59$	−287.366	−	119.031i	−0.634099	−	0.262652i	−0.676494	+	0.736448i	$0.736501\pi$
$60$		0			0
$61$	−28.2072	−	68.0983i	−0.0592060	−	0.142936i	0.891508	−	0.453005i	$-0.149648\pi$
$61$	−28.2072	−	68.0983i	−0.0592060	−	0.142936i	−0.950714	+	0.310069i	$0.899648\pi$
$62$		0			0
$63$	597.119			1.19413
$64$		0			0
$65$	−629.026			−1.20032
$66$		0			0
$67$	−293.521	−	708.622i	−0.535213	−	1.29212i	−0.928031	−	0.372502i	$-0.878500\pi$
$67$	−293.521	−	708.622i	−0.535213	−	1.29212i	0.392818	−	0.919616i	$-0.371500\pi$
$68$		0			0
$69$	302.057	+	125.116i	0.527005	+	0.218293i
$70$		0			0
$71$	579.730	+	579.730i	0.969032	+	0.969032i	0.999535	−	0.0305030i	$-0.00971091\pi$
$71$	579.730	+	579.730i	0.969032	+	0.969032i	−0.0305030	+	0.999535i	$0.509711\pi$
$72$		0			0
$73$	−258.894	+	258.894i	−0.415085	+	0.415085i	−0.883506	−	0.468420i	$-0.844823\pi$
$73$	−258.894	+	258.894i	−0.415085	+	0.415085i	0.468420	+	0.883506i	$0.344823\pi$
$74$		0			0
$75$	−206.351	+	498.176i	−0.317698	+	0.766991i
$76$		0			0
$77$	18.5371	−	7.67833i	0.0274351	−	0.0113640i
$78$		0			0
$79$		−	834.510i		−	1.18848i	−0.804289	−	0.594239i	$-0.797453\pi$
$79$		−	834.510i		−	1.18848i	0.804289	−	0.594239i	$-0.202547\pi$
$80$		0			0
$81$		−	1155.05i		−	1.58443i
$82$		0			0
$83$	−234.905	+	97.3009i	−0.310653	+	0.128677i	−0.532563	−	0.846391i	$-0.678771\pi$
$83$	−234.905	+	97.3009i	−0.310653	+	0.128677i	0.221910	+	0.975067i	$0.428771\pi$
$84$		0			0
$85$	308.319	−	744.347i	0.393434	−	0.949833i
$86$		0			0
$87$	−991.082	+	991.082i	−1.22132	+	1.22132i
$88$		0			0
$89$	179.539	+	179.539i	0.213833	+	0.213833i	0.805893	−	0.592061i	$-0.201685\pi$
$89$	179.539	+	179.539i	0.213833	+	0.213833i	−0.592061	+	0.805893i	$0.701685\pi$
$90$		0			0
$91$	−719.939	−	298.208i	−0.829342	−	0.343525i
$92$		0			0
$93$	205.975	+	497.268i	0.229663	+	0.554455i
$94$		0			0
$95$	792.661			0.856056
$96$		0			0
$97$	−624.033			−0.653205			−0.326603	−	0.945162i	$-0.605904\pi$
$97$	−624.033			−0.653205			−0.326603	+	0.945162i	$0.605904\pi$
$98$		0			0
$99$	−44.6962	−	107.906i	−0.0453751	−	0.109545i
$100$		0			0
$101$	−1513.83	−	627.049i	−1.49140	−	0.617760i	−0.519782	−	0.854299i	$-0.673987\pi$
$101$	−1513.83	−	627.049i	−1.49140	−	0.617760i	−0.971622	+	0.236540i	$0.923987\pi$
$102$		0			0
$103$	−146.406	−	146.406i	−0.140056	−	0.140056i	0.633603	−	0.773659i	$-0.281575\pi$
$103$	−146.406	−	146.406i	−0.140056	−	0.140056i	−0.773659	+	0.633603i	$0.781575\pi$
$104$		0			0
$105$	542.838	−	542.838i	0.504529	−	0.504529i
$106$		0			0
$107$	−375.001	+	905.331i	−0.338810	+	0.817960i	0.659021	+	0.752125i	$0.270971\pi$
$107$	−375.001	+	905.331i	−0.338810	+	0.817960i	−0.997831	+	0.0658347i	$0.979029\pi$
$108$		0			0
$109$	−330.443	+	136.874i	−0.290373	+	0.120277i	−0.523115	−	0.852262i	$-0.675230\pi$
$109$	−330.443	+	136.874i	−0.290373	+	0.120277i	0.232742	+	0.972539i	$0.425230\pi$
$110$		0			0
$111$			2036.81i			1.74167i
$112$		0			0
$113$		−	743.066i		−	0.618600i	−0.950965	−	0.309300i	$-0.899905\pi$
$113$		−	743.066i		−	0.618600i	0.950965	−	0.309300i	$-0.100095\pi$
$114$		0			0
$115$	266.358	−	110.329i	0.215983	−	0.0894630i
$116$		0			0
$117$	−1735.89	+	4190.82i	−1.37165	+	3.31147i
$118$		0			0
$119$	705.760	−	705.760i	0.543672	−	0.543672i
$120$		0			0
$121$	938.384	+	938.384i	0.705022	+	0.705022i
$122$		0			0
$123$	549.491	+	227.606i	0.402812	+	0.166850i
$124$		0			0
$125$	573.044	+	1383.45i	0.410037	+	0.989917i
$126$		0			0
$127$	316.036			0.220816			0.110408	−	0.993886i	$-0.464784\pi$
$127$	316.036			0.220816			0.110408	+	0.993886i	$0.464784\pi$
$128$		0			0
$129$	2173.59			1.48352
$130$		0			0
$131$	126.926	+	306.426i	0.0846532	+	0.204371i	0.960538	−	0.278150i	$-0.0897212\pi$
$131$	126.926	+	306.426i	0.0846532	+	0.204371i	−0.875884	+	0.482521i	$0.839721\pi$
$132$		0			0
$133$	907.224	+	375.785i	0.591476	+	0.244997i
$134$		0			0
$135$	−1712.78	−	1712.78i	−1.09195	−	1.09195i
$136$		0			0
$137$	−465.127	+	465.127i	−0.290062	+	0.290062i	−0.837105	−	0.547043i	$-0.815754\pi$
$137$	−465.127	+	465.127i	−0.290062	+	0.290062i	0.547043	+	0.837105i	$0.315754\pi$
$138$		0			0
$139$	−158.069	+	381.612i	−0.0964548	+	0.232863i	−0.964741	−	0.263201i	$-0.915222\pi$
$139$	−158.069	+	381.612i	−0.0964548	+	0.232863i	0.868286	+	0.496064i	$0.165222\pi$
$140$		0			0
$141$	−37.5528	+	15.5549i	−0.0224292	+	0.00929046i
$142$		0			0
$143$			152.423i			0.0891345i
$144$		0			0
$145$			1235.95i			0.707864i
$146$		0			0
$147$	−2059.34	+	853.006i	−1.15545	+	0.478604i
$148$		0			0
$149$	316.900	−	765.063i	0.174238	−	0.420647i	−0.812502	−	0.582959i	$-0.801895\pi$
$149$	316.900	−	765.063i	0.174238	−	0.420647i	0.986740	+	0.162312i	$0.0518949\pi$
$150$		0			0
$151$	1447.99	−	1447.99i	0.780369	−	0.780369i	−0.199524	−	0.979893i	$-0.563940\pi$
$151$	1447.99	−	1447.99i	0.780369	−	0.780369i	0.979893	+	0.199524i	$0.0639397\pi$
$152$		0			0
$153$	−4108.29	−	4108.29i	−2.17082	−	2.17082i
$154$		0			0
$155$	438.498	+	181.632i	0.227233	+	0.0941228i
$156$		0			0
$157$	−1154.08	−	2786.21i	−0.586662	−	1.41633i	−0.886675	−	0.462393i	$-0.846991\pi$
$157$	−1154.08	−	2786.21i	−0.586662	−	1.41633i	0.300013	−	0.953935i	$-0.403009\pi$
$158$		0			0
$159$	−217.593			−0.108530
$160$		0			0
$161$	357.160			0.174833
$162$		0			0
$163$	−1315.01	−	3174.72i	−0.631899	−	1.52554i	−0.837232	−	0.546848i	$-0.815828\pi$
$163$	−1315.01	−	3174.72i	−0.631899	−	1.52554i	0.205333	−	0.978692i	$-0.434172\pi$
$164$		0			0
$165$	−138.730	−	57.4638i	−0.0654552	−	0.0271125i
$166$		0			0
$167$	2616.84	+	2616.84i	1.21256	+	1.21256i	0.970182	+	0.242376i	$0.0779268\pi$
$167$	2616.84	+	2616.84i	1.21256	+	1.21256i	0.242376	+	0.970182i	$0.422073\pi$
$168$		0			0
$169$	2632.38	−	2632.38i	1.19817	−	1.19817i
$170$		0			0
$171$	2187.47	−	5281.03i	0.978247	−	2.36170i
$172$		0			0
$173$	1699.43	−	703.925i	0.746849	−	0.309355i	0.0233941	−	0.999726i	$-0.492553\pi$
$173$	1699.43	−	703.925i	0.746849	−	0.309355i	0.723455	+	0.690371i	$0.242553\pi$
$174$		0			0
$175$			589.055i			0.254448i
$176$		0			0
$177$			2883.76i			1.22461i
$178$		0			0
$179$	−1726.10	+	714.972i	−0.720751	+	0.298545i	−0.712745	−	0.701423i	$-0.752548\pi$
$179$	−1726.10	+	714.972i	−0.720751	+	0.298545i	−0.00800596	+	0.999968i	$0.502548\pi$
$180$		0			0
$181$	1087.42	−	2625.26i	0.446559	−	1.07809i	−0.527043	−	0.849839i	$-0.676699\pi$
$181$	1087.42	−	2625.26i	0.446559	−	1.07809i	0.973602	−	0.228251i	$-0.0733006\pi$
$182$		0			0
$183$	−483.221	+	483.221i	−0.195195	+	0.195195i
$184$		0			0
$185$	1270.03	+	1270.03i	0.504726	+	0.504726i
$186$		0			0
$187$	−180.367	−	74.7105i	−0.0705334	−	0.0292159i
$188$		0			0
$189$	−1148.33	−	2772.32i	−0.441953	−	1.06697i
$190$		0			0
$191$	−1649.64			−0.624940			−0.312470	−	0.949928i	$-0.601156\pi$
$191$	−1649.64			−0.624940			−0.312470	+	0.949928i	$0.601156\pi$
$192$		0			0
$193$	−1928.59			−0.719291			−0.359645	−	0.933089i	$-0.617102\pi$
$193$	−1928.59			−0.719291			−0.359645	+	0.933089i	$0.617102\pi$
$194$		0			0
$195$	2231.76	+	5387.95i	0.819588	+	1.97866i
$196$		0			0
$197$	3725.06	+	1542.97i	1.34720	+	0.558030i	0.935513	−	0.353293i	$-0.114938\pi$
$197$	3725.06	+	1542.97i	1.34720	+	0.558030i	0.411692	+	0.911323i	$0.364938\pi$
$198$		0			0
$199$	−361.648	−	361.648i	−0.128827	−	0.128827i	0.639753	−	0.768580i	$-0.279036\pi$
$199$	−361.648	−	361.648i	−0.128827	−	0.128827i	−0.768580	+	0.639753i	$0.779036\pi$
$200$		0			0
$201$	−5028.33	+	5028.33i	−1.76453	+	1.76453i
$202$		0			0
$203$	−585.940	+	1414.58i	−0.202586	+	0.489086i
$204$		0			0
$205$	484.549	−	200.707i	0.165085	−	0.0683803i
$206$		0			0
$207$		−	2079.06i		−	0.698089i
$208$		0			0
$209$		−	192.074i		−	0.0635696i
$210$		0			0
$211$	5549.04	−	2298.49i	1.81048	−	0.749927i	0.828762	−	0.559601i	$-0.189046\pi$
$211$	5549.04	−	2298.49i	1.81048	−	0.749927i	0.981721	−	0.190325i	$-0.0609543\pi$
$212$		0			0
$213$	2908.84	−	7022.56i	0.935730	−	2.25905i
$214$		0			0
$215$	1355.31	−	1355.31i	0.429914	−	0.429914i
$216$		0			0
$217$	415.767	+	415.767i	0.130065	+	0.130065i
$218$		0			0
$219$	3136.11	+	1299.02i	0.967666	+	0.400820i
$220$		0			0
$221$	2901.58	+	7005.03i	0.883174	+	2.13217i
$222$		0			0
$223$	−2968.26			−0.891344			−0.445672	−	0.895196i	$-0.647035\pi$
$223$	−2968.26			−0.891344			−0.445672	+	0.895196i	$0.647035\pi$
$224$		0			0
$225$	3428.94			1.01598
$226$		0			0
$227$	947.980	+	2288.63i	0.277179	+	0.669169i	0.999755	−	0.0221219i	$-0.00704218\pi$
$227$	947.980	+	2288.63i	0.277179	+	0.669169i	−0.722576	+	0.691291i	$0.757042\pi$
$228$		0			0
$229$	−5763.17	−	2387.18i	−1.66306	−	0.688862i	−0.664756	−	0.747061i	$-0.731464\pi$
$229$	−5763.17	−	2387.18i	−1.66306	−	0.688862i	−0.998305	+	0.0581984i	$0.981464\pi$
$230$		0			0
$231$	−131.538	−	131.538i	−0.0374657	−	0.0374657i
$232$		0			0
$233$	3036.23	−	3036.23i	0.853691	−	0.853691i	−0.136895	−	0.990586i	$-0.543712\pi$
$233$	3036.23	−	3036.23i	0.853691	−	0.853691i	0.990586	+	0.136895i	$0.0437122\pi$
$234$		0			0
$235$	−13.7165	+	33.1146i	−0.00380751	+	0.00919215i
$236$		0			0
$237$	−7148.03	+	2960.81i	−1.95913	+	0.811500i
$238$		0			0
$239$		−	6291.50i		−	1.70278i	−0.524537	−	0.851388i	$-0.675761\pi$
$239$		−	6291.50i		−	1.70278i	0.524537	−	0.851388i	$-0.324239\pi$
$240$		0			0
$241$		−	795.320i		−	0.212577i	−0.994335	−	0.106289i	$-0.966103\pi$
$241$		−	795.320i		−	0.212577i	0.994335	−	0.106289i	$-0.0338967\pi$
$242$		0			0
$243$	−2503.05	+	1036.80i	−0.660786	+	0.273706i
$244$		0			0
$245$	−752.193	+	1815.95i	−0.196146	+	0.473539i
$246$		0			0
$247$	−5274.81	+	5274.81i	−1.35882	+	1.35882i
$248$		0			0
$249$	1666.87	+	1666.87i	0.424231	+	0.424231i
$250$		0			0
$251$	−6040.73	−	2502.15i	−1.51907	−	0.629221i	−0.541668	−	0.840593i	$-0.682207\pi$
$251$	−6040.73	−	2502.15i	−1.51907	−	0.629221i	−0.977406	+	0.211372i	$0.932207\pi$
$252$		0			0
$253$	−26.7345	−	64.5428i	−0.00664341	−	0.0160386i
$254$		0			0
$255$	−7469.64			−1.83438
$256$		0			0
$257$	−3591.20			−0.871645			−0.435823	−	0.900033i	$-0.643543\pi$
$257$	−3591.20			−0.871645			−0.435823	+	0.900033i	$0.643543\pi$
$258$		0			0
$259$	851.491	+	2055.68i	0.204282	+	0.493181i
$260$		0			0
$261$	8234.41	+	3410.80i	1.95286	+	0.808902i
$262$		0			0
$263$	2616.63	+	2616.63i	0.613491	+	0.613491i	0.943854	−	0.330363i	$-0.107171\pi$
$263$	2616.63	+	2616.63i	0.613491	+	0.613491i	−0.330363	+	0.943854i	$0.607171\pi$
$264$		0			0
$265$	−135.677	+	135.677i	−0.0314513	+	0.0314513i
$266$		0			0
$267$	900.853	−	2174.85i	0.206484	−	0.498497i
$268$		0			0
$269$	−6877.53	+	2848.77i	−1.55885	+	0.645697i	−0.984889	−	0.173186i	$-0.944594\pi$
$269$	−6877.53	+	2848.77i	−1.55885	+	0.645697i	−0.573961	+	0.818883i	$0.694594\pi$
$270$		0			0
$271$		−	6338.06i		−	1.42070i	−0.703848	−	0.710350i	$-0.748537\pi$
$271$		−	6338.06i		−	1.42070i	0.703848	−	0.710350i	$-0.251463\pi$
$272$		0			0
$273$			7224.70i			1.60168i
$274$		0			0
$275$	106.449	−	44.0926i	0.0233422	−	0.00966867i
$276$		0			0
$277$	655.560	−	1582.66i	0.142198	−	0.343296i	−0.836695	−	0.547669i	$-0.815515\pi$
$277$	655.560	−	1582.66i	0.142198	−	0.343296i	0.978893	+	0.204373i	$0.0655155\pi$
$278$		0			0
$279$	2420.21	−	2420.21i	0.519334	−	0.519334i
$280$		0			0
$281$	−3436.47	−	3436.47i	−0.729547	−	0.729547i	0.240983	−	0.970529i	$-0.422530\pi$
$281$	−3436.47	−	3436.47i	−0.729547	−	0.729547i	−0.970529	+	0.240983i	$0.922530\pi$
$282$		0			0
$283$	5101.55	+	2113.13i	1.07158	+	0.443861i	0.847546	−	0.530722i	$-0.178079\pi$
$283$	5101.55	+	2113.13i	1.07158	+	0.443861i	0.224029	+	0.974582i	$0.428079\pi$
$284$		0			0
$285$	−2812.33	−	6789.57i	−0.584520	−	1.41116i
$286$		0			0
$287$	649.732			0.133632
$288$		0			0
$289$	−4798.52			−0.976698
$290$		0			0
$291$	2214.05	+	5345.18i	0.446013	+	1.07677i
$292$		0			0
$293$	2820.64	+	1168.35i	0.562402	+	0.232954i	0.645727	−	0.763568i	$-0.276554\pi$
$293$	2820.64	+	1168.35i	0.562402	+	0.232954i	−0.0833258	+	0.996522i	$0.526554\pi$
$294$		0			0
$295$	1798.13	+	1798.13i	0.354886	+	0.354886i
$296$		0			0
$297$	−415.034	+	415.034i	−0.0810866	+	0.0810866i
$298$		0			0
$299$	−1038.30	+	2506.69i	−0.200825	+	0.484835i
$300$		0			0
$301$	2193.72	−	908.669i	0.420080	−	0.174003i
$302$		0			0
$303$			15191.5i			2.88030i
$304$		0			0
$305$			602.612i			0.113133i
$306$		0			0
$307$	−424.120	+	175.676i	−0.0788463	+	0.0326592i	−0.421758	−	0.906708i	$-0.638587\pi$
$307$	−424.120	+	175.676i	−0.0788463	+	0.0326592i	0.342912	+	0.939368i	$0.388587\pi$
$308$		0			0
$309$	−734.603	+	1773.49i	−0.135243	+	0.326506i
$310$		0			0
$311$	3761.67	−	3761.67i	0.685868	−	0.685868i	−0.275448	−	0.961316i	$-0.588826\pi$
$311$	3761.67	−	3761.67i	0.685868	−	0.685868i	0.961316	+	0.275448i	$0.0888262\pi$
$312$		0			0
$313$	718.221	+	718.221i	0.129700	+	0.129700i	0.768977	−	0.639277i	$-0.220766\pi$
$313$	718.221	+	718.221i	0.129700	+	0.129700i	−0.639277	+	0.768977i	$0.720766\pi$
$314$		0			0
$315$	−4510.17	−	1868.18i	−0.806729	−	0.334158i
$316$		0			0
$317$	1315.47	+	3175.83i	0.233073	+	0.562689i	0.996536	−	0.0831634i	$-0.0265023\pi$
$317$	1315.47	+	3175.83i	0.233073	+	0.562689i	−0.763463	+	0.645852i	$0.776502\pi$
$318$		0			0
$319$	299.491			0.0525651
$320$		0			0
$321$	9085.14			1.57970
$322$		0			0
$323$	−3656.40	−	8827.33i	−0.629869	−	1.52064i
$324$		0			0
$325$	−4134.23	−	1712.45i	−0.705617	−	0.292276i
$326$		0			0
$327$	2344.80	+	2344.80i	0.396537	+	0.396537i
$328$		0			0
$329$	−31.3979	+	31.3979i	−0.00526147	+	0.00526147i
$330$		0			0
$331$	−515.566	+	1244.69i	−0.0856136	+	0.206689i	−0.960888	−	0.276937i	$-0.910681\pi$
$331$	−515.566	+	1244.69i	−0.0856136	+	0.206689i	0.875274	+	0.483626i	$0.160681\pi$
$332$		0			0
$333$	11966.3	−	4956.60i	1.96921	−	0.815675i
$334$		0			0
$335$			6270.70i			1.02270i
$336$		0			0
$337$		−	4770.86i		−	0.771173i	−0.922672	−	0.385587i	$-0.873999\pi$
$337$		−	4770.86i		−	0.771173i	0.922672	−	0.385587i	$-0.126001\pi$
$338$		0			0
$339$	−6364.77	+	2636.37i	−1.01972	+	0.422384i
$340$		0			0
$341$	44.0123	−	106.255i	0.00698944	−	0.0168740i
$342$		0			0
$343$	−4178.26	+	4178.26i	−0.657741	+	0.657741i
$344$		0			0
$345$	−1890.06	−	1890.06i	−0.294949	−	0.294949i
$346$		0			0
$347$	−2534.53	−	1049.84i	−0.392105	−	0.162415i	0.177915	−	0.984046i	$-0.443065\pi$
$347$	−2534.53	−	1049.84i	−0.392105	−	0.162415i	−0.570021	+	0.821630i	$0.693065\pi$
$348$		0			0
$349$	1115.54	+	2693.15i	0.171099	+	0.413069i	0.986048	−	0.166464i	$-0.0532349\pi$
$349$	1115.54	+	2693.15i	0.171099	+	0.413069i	−0.814949	+	0.579533i	$0.803235\pi$
$350$		0			0
$351$	22795.6			3.46650
$352$		0			0
$353$	2416.71			0.364387			0.182193	−	0.983263i	$-0.441680\pi$
$353$	2416.71			0.364387			0.182193	+	0.983263i	$0.441680\pi$
$354$		0			0
$355$	−2565.06	−	6192.60i	−0.383490	−	0.925828i
$356$		0			0
$357$	−8549.23	−	3541.21i	−1.26743	−	0.524988i
$358$		0			0
$359$	−8445.07	−	8445.07i	−1.24154	−	1.24154i	−0.959361	−	0.282182i	$-0.908942\pi$
$359$	−8445.07	−	8445.07i	−1.24154	−	1.24154i	−0.282182	−	0.959361i	$-0.591058\pi$
$360$		0			0
$361$	1796.96	−	1796.96i	0.261986	−	0.261986i
$362$		0			0
$363$	4708.42	−	11367.1i	0.680793	−	1.64358i
$364$		0			0
$365$	2765.47	−	1145.49i	0.396579	−	0.164268i
$366$		0			0
$367$		−	1632.32i		−	0.232170i	−0.993239	−	0.116085i	$-0.962966\pi$
$367$		−	1632.32i		−	0.232170i	0.993239	−	0.116085i	$-0.0370345\pi$
$368$		0			0
$369$		−	3782.14i		−	0.533578i
$370$		0			0
$371$	−219.608	+	90.9648i	−0.0307318	+	0.0127295i
$372$		0			0
$373$	−5198.39	+	12550.0i	−0.721615	+	1.74213i	−0.0529149	+	0.998599i	$0.516851\pi$
$373$	−5198.39	+	12550.0i	−0.721615	+	1.74213i	−0.668700	+	0.743533i	$0.733149\pi$
$374$		0			0
$375$	9816.87	−	9816.87i	1.35184	−	1.35184i
$376$		0			0
$377$	−8224.72	−	8224.72i	−1.12359	−	1.12359i
$378$		0			0
$379$	4404.78	+	1824.52i	0.596987	+	0.247280i	0.660653	−	0.750691i	$-0.270279\pi$
$379$	4404.78	+	1824.52i	0.596987	+	0.247280i	−0.0636663	+	0.997971i	$0.520279\pi$
$380$		0			0
$381$	−1121.28	−	2707.02i	−0.150775	−	0.364002i
$382$		0			0
$383$	−7295.56			−0.973331			−0.486665	−	0.873589i	$-0.661787\pi$
$383$	−7295.56			−0.973331			−0.486665	+	0.873589i	$0.661787\pi$
$384$		0			0
$385$	−164.038			−0.0217147
$386$		0			0
$387$	−5289.44	−	12769.8i	−0.694773	−	1.67733i
$388$		0			0
$389$	−2614.79	−	1083.08i	−0.340810	−	0.141168i	0.205712	−	0.978612i	$-0.434049\pi$
$389$	−2614.79	−	1083.08i	−0.340810	−	0.141168i	−0.546523	+	0.837444i	$0.684049\pi$
$390$		0			0
$391$	−2457.32	−	2457.32i	−0.317832	−	0.317832i
$392$		0			0
$393$	2174.38	−	2174.38i	0.279091	−	0.279091i
$394$		0			0
$395$	−2610.89	+	6303.24i	−0.332577	+	0.802913i
$396$		0			0
$397$	−1867.07	+	773.367i	−0.236034	+	0.0977687i	−0.497566	−	0.867426i	$-0.665773\pi$
$397$	−1867.07	+	773.367i	−0.236034	+	0.0977687i	0.261531	+	0.965195i	$0.415773\pi$
$398$		0			0
$399$		−	9104.14i		−	1.14230i
$400$		0			0
$401$		−	12147.1i		−	1.51271i	−0.654162	−	0.756354i	$-0.726979\pi$
$401$		−	12147.1i		−	1.51271i	0.654162	−	0.756354i	$-0.273021\pi$
$402$		0			0
$403$	−4126.70	+	1709.33i	−0.510088	+	0.211285i
$404$		0			0
$405$	−3613.75	+	8724.36i	−0.443379	+	1.07041i
$406$		0			0
$407$	307.748	−	307.748i	0.0374803	−	0.0374803i
$408$		0			0
$409$	9049.93	+	9049.93i	1.09411	+	1.09411i	0.995085	+	0.0990235i	$0.0315719\pi$
$409$	9049.93	+	9049.93i	1.09411	+	1.09411i	0.0990235	+	0.995085i	$0.468428\pi$
$410$		0			0
$411$	5634.32	+	2333.81i	0.676206	+	0.280094i
$412$		0			0
$413$	1205.56	+	2910.48i	0.143636	+	0.346768i
$414$		0			0
$415$	2078.71			0.245879
$416$		0			0
$417$	3829.54			0.449720
$418$		0			0
$419$	5216.15	+	12592.9i	0.608176	+	1.46827i	0.864982	+	0.501803i	$0.167330\pi$
$419$	5216.15	+	12592.9i	0.608176	+	1.46827i	−0.256806	+	0.966463i	$0.582670\pi$
$420$		0			0
$421$	12044.9	+	4989.15i	1.39437	+	0.577568i	0.948285	−	0.317421i	$-0.102817\pi$
$421$	12044.9	+	4989.15i	1.39437	+	0.577568i	0.446088	+	0.894989i	$0.352817\pi$
$422$		0			0
$423$	182.770	+	182.770i	0.0210084	+	0.0210084i
$424$		0			0
$425$	4052.81	−	4052.81i	0.462565	−	0.462565i
$426$		0			0
$427$	−285.686	+	689.708i	−0.0323778	+	0.0781670i
$428$		0			0
$429$	1305.58	−	540.791i	0.146933	−	0.0608616i
$430$		0			0
$431$			3074.64i			0.343620i	0.985130	+	0.171810i	$0.0549615\pi$
$431$			3074.64i			0.343620i	−0.985130	+	0.171810i	$0.945039\pi$
$432$		0			0
$433$			3478.83i			0.386101i	0.981189	+	0.193051i	$0.0618381\pi$
$433$			3478.83i			0.386101i	−0.981189	+	0.193051i	$0.938162\pi$
$434$		0			0
$435$	10586.6	−	4385.12i	1.16687	−	0.483334i
$436$		0			0
$437$	1308.41	−	3158.78i	0.143226	−	0.345778i
$438$		0			0
$439$	−6595.03	+	6595.03i	−0.717001	+	0.717001i	−0.967990	−	0.250989i	$-0.919244\pi$
$439$	−6595.03	+	6595.03i	−0.717001	+	0.717001i	0.250989	+	0.967990i	$0.419244\pi$
$440$		0			0
$441$	10022.8	+	10022.8i	1.08226	+	1.08226i
$442$		0			0
$443$	−1177.46	−	487.720i	−0.126282	−	0.0523076i	0.318648	−	0.947873i	$-0.396771\pi$
$443$	−1177.46	−	487.720i	−0.126282	−	0.0523076i	−0.444930	+	0.895566i	$0.646771\pi$
$444$		0			0
$445$	−794.385	−	1917.82i	−0.0846235	−	0.204299i
$446$		0			0
$447$	−7677.53			−0.812382
$448$		0			0
$449$	−517.491			−0.0543918			−0.0271959	−	0.999630i	$-0.508658\pi$
$449$	−517.491			−0.0543918			−0.0271959	+	0.999630i	$0.508658\pi$
$450$		0			0
$451$	−48.6344	−	117.414i	−0.00507784	−	0.0122590i
$452$		0			0
$453$	−17540.2	−	7265.40i	−1.81923	−	0.753550i
$454$		0			0
$455$	4504.87	+	4504.87i	0.464157	+	0.464157i
$456$		0			0
$457$	1142.85	−	1142.85i	0.116981	−	0.116981i	−0.646193	−	0.763174i	$-0.723640\pi$
$457$	1142.85	−	1142.85i	0.116981	−	0.116981i	0.763174	+	0.646193i	$0.223640\pi$
$458$		0			0
$459$	−11173.3	+	26974.8i	−1.13622	+	2.74309i
$460$		0			0
$461$	−7860.73	+	3256.02i	−0.794166	+	0.328954i	−0.742617	−	0.669716i	$-0.766416\pi$
$461$	−7860.73	+	3256.02i	−0.794166	+	0.328954i	−0.0515489	+	0.998670i	$0.516416\pi$
$462$		0			0
$463$			2545.63i			0.255519i	0.991805	+	0.127760i	$0.0407786\pi$
$463$			2545.63i			0.255519i	−0.991805	+	0.127760i	$0.959221\pi$
$464$		0			0
$465$		−	4400.40i		−	0.438847i
$466$		0			0
$467$	7269.46	−	3011.11i	0.720322	−	0.298367i	0.00775364	−	0.999970i	$-0.497532\pi$
$467$	7269.46	−	3011.11i	0.720322	−	0.298367i	0.712568	+	0.701603i	$0.247532\pi$
$468$		0			0
$469$	−2972.81	+	7177.01i	−0.292690	+	0.706617i
$470$		0			0
$471$	−19770.7	+	19770.7i	−1.93415	+	1.93415i
$472$		0			0
$473$	−328.413	−	328.413i	−0.0319249	−	0.0319249i
$474$		0			0
$475$	5209.71	+	2157.93i	0.503237	+	0.208448i
$476$		0			0
$477$	529.513	+	1278.36i	0.0508276	+	0.122709i
$478$		0			0
$479$	19071.7			1.81922			0.909612	−	0.415459i	$-0.136379\pi$
$479$	19071.7			1.81922			0.909612	+	0.415459i	$0.136379\pi$
$480$		0			0
$481$	−16903.0			−1.60231
$482$		0			0
$483$	−1267.19	−	3059.27i	−0.119377	−	0.288202i
$484$		0			0
$485$	4713.46	+	1952.38i	0.441293	+	0.182790i
$486$		0			0
$487$	−4422.93	−	4422.93i	−0.411544	−	0.411544i	0.470732	−	0.882276i	$-0.343990\pi$
$487$	−4422.93	−	4422.93i	−0.411544	−	0.411544i	−0.882276	+	0.470732i	$0.843990\pi$
$488$		0			0
$489$	−22527.6	+	22527.6i	−2.08330	+	2.08330i
$490$		0			0
$491$	1908.12	−	4606.60i	0.175381	−	0.423408i	−0.811606	−	0.584205i	$-0.801407\pi$
$491$	1908.12	−	4606.60i	0.175381	−	0.423408i	0.986987	+	0.160797i	$0.0514065\pi$
$492$		0			0
$493$	13764.0	−	5701.22i	1.25740	−	0.520832i
$494$		0			0
$495$			954.878i			0.0867042i
$496$		0			0
$497$		−	8303.65i		−	0.749436i
$498$		0			0
$499$	9996.34	−	4140.62i	0.896789	−	0.371462i	0.113804	−	0.993503i	$-0.463696\pi$
$499$	9996.34	−	4140.62i	0.896789	−	0.371462i	0.782985	+	0.622041i	$0.213696\pi$
$500$		0			0
$501$	13130.2	−	31699.1i	1.17089	−	2.82677i
$502$		0			0
$503$	6186.59	−	6186.59i	0.548402	−	0.548402i	−0.377576	−	0.925978i	$-0.623242\pi$
$503$	6186.59	−	6186.59i	0.548402	−	0.548402i	0.925978	+	0.377576i	$0.123242\pi$
$504$		0			0
$505$	9472.48	+	9472.48i	0.834693	+	0.834693i
$506$		0			0
$507$	−31887.3	−	13208.2i	−2.79323	−	1.15699i
$508$		0			0
$509$	1472.42	+	3554.75i	0.128220	+	0.309551i	0.974933	−	0.222500i	$-0.0714216\pi$
$509$	1472.42	+	3554.75i	0.128220	+	0.309551i	−0.846713	+	0.532051i	$0.821422\pi$
$510$		0			0
$511$	3708.22			0.321021
$512$		0			0
$513$	−28725.7			−2.47226
$514$		0			0
$515$	647.783	+	1563.89i	0.0554267	+	0.133812i
$516$		0			0
$517$	8.02418	+	3.32372i	0.000682598	+	0.000282741i
$518$		0			0
$519$	−12059.0	−	12059.0i	−1.01991	−	1.01991i
$520$		0			0
$521$	−41.6914	+	41.6914i	−0.00350582	+	0.00350582i	−0.708858	−	0.705352i	$-0.750789\pi$
$521$	−41.6914	+	41.6914i	−0.00350582	+	0.00350582i	0.705352	+	0.708858i	$0.250789\pi$
$522$		0			0
$523$	−6675.06	+	16115.0i	−0.558088	+	1.34734i	0.353191	+	0.935551i	$0.385097\pi$
$523$	−6675.06	+	16115.0i	−0.558088	+	1.34734i	−0.911278	+	0.411791i	$0.864903\pi$
$524$		0			0
$525$	5045.58	−	2089.95i	0.419442	−	0.173739i
$526$		0			0
$527$		−	5721.10i		−	0.472894i
$528$		0			0
$529$			10923.4i			0.897792i
$530$		0			0
$531$	16942.1	−	7017.65i	1.38460	−	0.573522i
$532$		0			0
$533$	−1888.85	+	4560.08i	−0.153499	+	0.370579i
$534$		0			0
$535$	5664.92	−	5664.92i	0.457787	−	0.457787i
$536$		0			0
$537$	12248.3	+	12248.3i	0.984266	+	0.984266i
$538$		0			0
$539$	440.035	+	182.268i	0.0351644	+	0.0145656i
$540$		0			0
$541$	−5953.02	−	14371.9i	−0.473087	−	1.14213i	−0.962792	−	0.270245i	$-0.912895\pi$
$541$	−5953.02	−	14371.9i	−0.473087	−	1.14213i	0.489704	−	0.871889i	$-0.337105\pi$
$542$		0			0
$543$	−26344.9			−2.08208
$544$		0			0
$545$	2924.14			0.229828
$546$		0			0
$547$	−2956.49	−	7137.60i	−0.231098	−	0.557919i	0.765209	−	0.643782i	$-0.222635\pi$
$547$	−2956.49	−	7137.60i	−0.231098	−	0.557919i	−0.996307	+	0.0858625i	$0.972635\pi$
$548$		0			0
$549$	4014.84	+	1663.00i	0.312112	+	0.129281i
$550$		0			0
$551$	10364.3	+	10364.3i	0.801333	+	0.801333i
$552$		0			0
$553$	−5976.48	+	5976.48i	−0.459576	+	0.459576i
$554$		0			0
$555$	6372.47	−	15384.5i	0.487381	−	1.17664i
$556$		0			0
$557$	−6601.43	+	2734.40i	−0.502176	+	0.208008i	−0.619367	−	0.785101i	$-0.712611\pi$
$557$	−6601.43	+	2734.40i	−0.502176	+	0.208008i	0.117192	+	0.993109i	$0.462611\pi$
$558$		0			0
$559$			18038.0i			1.36481i
$560$		0			0
$561$			1810.01i			0.136219i
$562$		0			0
$563$	−17608.4	+	7293.65i	−1.31813	+	0.545987i	−0.927246	−	0.374453i	$-0.877830\pi$
$563$	−17608.4	+	7293.65i	−1.31813	+	0.545987i	−0.390883	+	0.920440i	$0.627830\pi$
$564$		0			0
$565$	−2324.79	+	5612.54i	−0.173106	+	0.417914i
$566$		0			0
$567$	−8272.09	+	8272.09i	−0.612690	+	0.612690i
$568$		0			0
$569$	−13651.2	−	13651.2i	−1.00578	−	1.00578i	−0.999983	−	0.00579351i	$-0.998156\pi$
$569$	−13651.2	−	13651.2i	−1.00578	−	1.00578i	−0.00579351	−	0.999983i	$-0.501844\pi$
$570$		0			0
$571$	15023.6	+	6222.97i	1.10108	+	0.456083i	0.857858	−	0.513887i	$-0.171795\pi$
$571$	15023.6	+	6222.97i	1.10108	+	0.456083i	0.243224	+	0.969970i	$0.421795\pi$
$572$		0			0
$573$	5852.85	+	14130.0i	0.426713	+	1.03018i
$574$		0			0
$575$	2050.98			0.148751
$576$		0			0
$577$	17031.0			1.22879			0.614394	−	0.788999i	$-0.289400\pi$
$577$	17031.0			1.22879			0.614394	+	0.788999i	$0.289400\pi$
$578$		0			0
$579$	6842.58	+	16519.4i	0.491136	+	1.18571i
$580$		0			0
$581$	2379.15	+	985.475i	0.169886	+	0.0703690i
$582$		0			0
$583$	32.8767	+	32.8767i	0.00233553	+	0.00233553i
$584$		0			0
$585$	26223.2	−	26223.2i	1.85333	−	1.85333i
$586$		0			0
$587$	6926.72	−	16722.6i	0.487046	−	1.17583i	−0.469153	−	0.883117i	$-0.655441\pi$
$587$	6926.72	−	16722.6i	0.487046	−	1.17583i	0.956199	−	0.292717i	$-0.0945594\pi$
$588$		0			0
$589$	5200.22	−	2154.00i	0.363788	−	0.150686i
$590$		0			0
$591$		−	37381.5i		−	2.60181i
$592$		0			0
$593$			23359.0i			1.61760i	0.588082	+	0.808801i	$0.299883\pi$
$593$			23359.0i			1.61760i	−0.588082	+	0.808801i	$0.700117\pi$
$594$		0			0
$595$	−7538.84	+	3122.69i	−0.519432	+	0.215156i
$596$		0			0
$597$	−1814.60	+	4380.82i	−0.124399	+	0.300327i
$598$		0			0
$599$	8027.34	−	8027.34i	0.547559	−	0.547559i	−0.378175	−	0.925734i	$-0.623448\pi$
$599$	8027.34	−	8027.34i	0.547559	−	0.547559i	0.925734	+	0.378175i	$0.123448\pi$
$600$		0			0
$601$	11725.6	+	11725.6i	0.795837	+	0.795837i	0.982436	−	0.186599i	$-0.0597466\pi$
$601$	11725.6	+	11725.6i	0.795837	+	0.795837i	−0.186599	+	0.982436i	$0.559747\pi$
$602$		0			0
$603$	41777.9	+	17305.0i	2.82144	+	1.16868i
$604$		0			0
$605$	−4151.95	−	10023.7i	−0.279010	−	0.673589i
$606$		0			0
$607$	25799.6			1.72516			0.862580	−	0.505920i	$-0.168847\pi$
$607$	25799.6			1.72516			0.862580	+	0.505920i	$0.168847\pi$
$608$		0			0
$609$	14195.6			0.944555
$610$		0			0
$611$	−129.086	−	311.640i	−0.00854705	−	0.0206344i
$612$		0			0
$613$	8320.05	+	3446.28i	0.548195	+	0.227070i	0.639551	−	0.768748i	$-0.279120\pi$
$613$	8320.05	+	3446.28i	0.548195	+	0.227070i	−0.0913562	+	0.995818i	$0.529120\pi$
$614$		0			0
$615$	−3438.32	−	3438.32i	−0.225442	−	0.225442i
$616$		0			0
$617$	−14643.0	+	14643.0i	−0.955437	+	0.955437i	−0.999049	−	0.0436114i	$-0.986114\pi$
$617$	−14643.0	+	14643.0i	−0.955437	+	0.955437i	0.0436114	+	0.999049i	$0.486114\pi$
$618$		0			0
$619$	842.686	−	2034.42i	0.0547180	−	0.132101i	−0.894156	−	0.447755i	$-0.852224\pi$
$619$	842.686	−	2034.42i	0.0547180	−	0.132101i	0.948874	+	0.315654i	$0.102224\pi$
$620$		0			0
$621$	−9652.70	+	3998.28i	−0.623751	+	0.258366i
$622$		0			0
$623$		−	2571.60i		−	0.165376i
$624$		0			0
$625$		−	4972.32i		−	0.318228i
$626$		0			0
$627$	−1645.22	+	681.473i	−0.104791	+	0.0434057i
$628$		0			0
$629$	8285.04	−	20001.9i	0.525193	−	1.26793i
$630$		0			0
$631$	−16113.6	+	16113.6i	−1.01660	+	1.01660i	−0.0167358	+	0.999860i	$0.505327\pi$
$631$	−16113.6	+	16113.6i	−1.01660	+	1.01660i	−0.999860	+	0.0167358i	$0.994673\pi$
$632$		0			0
$633$	−39375.6	−	39375.6i	−2.47242	−	2.47242i
$634$		0			0
$635$	−2387.09	−	988.765i	−0.149179	−	0.0617921i
$636$		0			0
$637$	−7078.87	−	17089.9i	−0.440306	−	1.06299i
$638$		0			0
$639$	−48336.2			−2.99241
$640$		0			0
$641$	21358.0			1.31605			0.658026	−	0.752995i	$-0.271392\pi$
$641$	21358.0			1.31605			0.658026	+	0.752995i	$0.271392\pi$
$642$		0			0
$643$	1217.22	+	2938.63i	0.0746540	+	0.180231i	0.956801	−	0.290743i	$-0.0939026\pi$
$643$	1217.22	+	2938.63i	0.0746540	+	0.180231i	−0.882147	+	0.470974i	$0.843903\pi$
$644$		0			0
$645$	−16417.6	−	6800.39i	−1.00224	−	0.415139i
$646$		0			0
$647$	−16654.8	−	16654.8i	−1.01200	−	1.01200i	−0.999927	−	0.0120763i	$-0.996156\pi$
$647$	−16654.8	−	16654.8i	−1.01200	−	1.01200i	−0.0120763	−	0.999927i	$-0.503844\pi$
$648$		0			0
$649$	435.716	−	435.716i	0.0263534	−	0.0263534i
$650$		0			0
$651$	2086.14	−	5036.39i	0.125595	−	0.303213i
$652$		0			0
$653$	20645.8	−	8551.79i	1.23727	−	0.512492i	0.334406	−	0.942429i	$-0.391464\pi$
$653$	20645.8	−	8551.79i	1.23727	−	0.512492i	0.902859	+	0.429937i	$0.141464\pi$
$654$		0			0
$655$		−	2711.61i		−	0.161758i
$656$		0			0
$657$		−	21585.8i		−	1.28180i
$658$		0			0
$659$	−3783.98	+	1567.37i	−0.223676	+	0.0926498i	−0.491707	−	0.870760i	$-0.663627\pi$
$659$	−3783.98	+	1567.37i	−0.223676	+	0.0926498i	0.268031	+	0.963410i	$0.413627\pi$
$660$		0			0
$661$	−9874.75	+	23839.8i	−0.581064	+	1.40281i	0.310785	+	0.950480i	$0.399408\pi$
$661$	−9874.75	+	23839.8i	−0.581064	+	1.40281i	−0.891849	+	0.452333i	$0.850592\pi$
$662$		0			0
$663$	49707.2	−	49707.2i	2.91172	−	2.91172i
$664$		0			0
$665$	−5676.77	−	5676.77i	−0.331031	−	0.331031i
$666$		0			0
$667$	4925.31	+	2040.13i	0.285920	+	0.118432i
$668$		0			0
$669$	10531.3	+	25424.8i	0.608615	+	1.46933i
$670$		0			0
$671$	146.022			0.00840109
$672$		0			0
$673$	8888.42			0.509099			0.254549	−	0.967060i	$-0.418073\pi$
$673$	8888.42			0.509099			0.254549	+	0.967060i	$0.418073\pi$
$674$		0			0
$675$	−6594.28	−	15920.0i	−0.376020	−	0.907794i
$676$		0			0
$677$	−12382.5	−	5128.98i	−0.702949	−	0.291171i	0.00243434	−	0.999997i	$-0.499225\pi$
$677$	−12382.5	−	5128.98i	−0.702949	−	0.291171i	−0.705383	+	0.708826i	$0.749225\pi$
$678$		0			0
$679$	4469.11	+	4469.11i	0.252590	+	0.252590i
$680$		0			0
$681$	16239.9	−	16239.9i	0.913826	−	0.913826i
$682$		0			0
$683$	3359.39	−	8110.29i	0.188204	−	0.454365i	−0.801410	−	0.598116i	$-0.795916\pi$
$683$	3359.39	−	8110.29i	0.188204	−	0.454365i	0.989614	+	0.143751i	$0.0459163\pi$
$684$		0			0
$685$	4968.43	−	2057.99i	0.277130	−	0.114791i
$686$		0			0
$687$			57834.3i			3.21181i
$688$		0			0
$689$		−	1805.74i		−	0.0998453i
$690$		0			0
$691$	−19614.8	+	8124.74i	−1.07986	+	0.447293i	−0.850460	−	0.526039i	$-0.823677\pi$
$691$	−19614.8	+	8124.74i	−1.07986	+	0.447293i	−0.229401	+	0.973332i	$0.573677\pi$
$692$		0			0
$693$	−452.688	+	1092.89i	−0.0248142	+	0.0599067i
$694$		0			0
$695$	2387.86	−	2387.86i	0.130326	−	0.130326i
$696$		0			0
$697$	−4470.27	−	4470.27i	−0.242932	−	0.242932i
$698$		0			0
$699$	−36779.4	−	15234.5i	−1.99016	−	0.824353i
$700$		0			0
$701$	−7415.56	−	17902.8i	−0.399546	−	0.964590i	−0.987774	−	0.155895i	$-0.950174\pi$
$701$	−7415.56	−	17902.8i	−0.399546	−	0.964590i	0.588227	−	0.808696i	$-0.299826\pi$
$702$		0			0
$703$	21300.1			1.14274
$704$		0			0
$705$	332.310			0.0177525
$706$		0			0
$707$	6350.83	+	15332.3i	0.337832	+	0.815599i
$708$		0			0
$709$	−4168.86	−	1726.80i	−0.220825	−	0.0914686i	0.269528	−	0.962992i	$-0.413132\pi$
$709$	−4168.86	−	1726.80i	−0.220825	−	0.0914686i	−0.490353	+	0.871524i	$0.663132\pi$
$710$		0			0
$711$	34789.6	+	34789.6i	1.83504	+	1.83504i
$712$		0			0
$713$	1447.62	−	1447.62i	0.0760362	−	0.0760362i
$714$		0			0
$715$	476.877	−	1151.28i	0.0249429	−	0.0602176i
$716$		0			0
$717$	−53890.1	+	22322.0i	−2.80692	+	1.16267i
$718$		0			0
$719$			13109.2i			0.679961i	0.940432	+	0.339981i	$0.110420\pi$
$719$			13109.2i			0.679961i	−0.940432	+	0.339981i	$0.889580\pi$
$720$		0			0
$721$			2097.02i			0.108318i
$722$		0			0
$723$	−6812.35	+	2821.77i	−0.350420	+	0.145149i
$724$		0			0
$725$	−3364.74	+	8123.21i	−0.172363	+	0.416122i
$726$		0			0
$727$	−19846.0	+	19846.0i	−1.01245	+	1.01245i	−0.0125242	+	0.999922i	$0.503987\pi$
$727$	−19846.0	+	19846.0i	−1.01245	+	1.01245i	−0.999922	+	0.0125242i	$0.996013\pi$
$728$		0			0
$729$	−4290.62	−	4290.62i	−0.217986	−	0.217986i
$730$		0			0
$731$	−21345.0	−	8841.39i	−1.07999	−	0.447347i
$732$		0			0
$733$	−1724.21	−	4162.60i	−0.0868827	−	0.209753i	0.874466	−	0.485086i	$-0.161212\pi$
$733$	−1724.21	−	4162.60i	−0.0868827	−	0.209753i	−0.961349	+	0.275333i	$0.911212\pi$
$734$		0			0
$735$	18223.4			0.914531
$736$		0			0
$737$	1519.49			0.0759445
$738$		0			0
$739$	−6958.79	−	16800.0i	−0.346391	−	0.836263i	−0.997040	−	0.0768839i	$-0.975503\pi$
$739$	−6958.79	−	16800.0i	−0.346391	−	0.836263i	0.650649	−	0.759379i	$-0.274497\pi$
$740$		0			0
$741$	63896.5	+	26466.8i	3.16774	+	1.31212i
$742$		0			0
$743$	1100.04	+	1100.04i	0.0543157	+	0.0543157i	0.733743	−	0.679427i	$-0.237772\pi$
$743$	1100.04	+	1100.04i	0.0543157	+	0.0543157i	−0.679427	+	0.733743i	$0.737772\pi$
$744$		0			0
$745$	−4787.23	+	4787.23i	−0.235423	+	0.235423i
$746$		0			0
$747$	5736.53	−	13849.2i	0.280975	−	0.678335i
$748$		0			0
$749$	9169.30	−	3798.05i	0.447315	−	0.185284i
$750$		0			0
$751$		−	22547.4i		−	1.09556i	−0.836623	−	0.547780i	$-0.815473\pi$
$751$		−	22547.4i		−	1.09556i	0.836623	−	0.547780i	$-0.184527\pi$
$752$		0			0
$753$			60619.7i			2.93374i
$754$		0			0
$755$	−15467.2	+	6406.73i	−0.745576	+	0.308828i
$756$		0			0
$757$	1904.46	−	4597.78i	0.0914383	−	0.220752i	−0.871543	−	0.490318i	$-0.836880\pi$
$757$	1904.46	−	4597.78i	0.0914383	−	0.220752i	0.962982	+	0.269567i	$0.0868805\pi$
$758$		0			0
$759$	−457.991	+	457.991i	−0.0219025	+	0.0219025i
$760$		0			0
$761$	7703.17	+	7703.17i	0.366938	+	0.366938i	0.866359	−	0.499421i	$-0.166454\pi$
$761$	7703.17	+	7703.17i	0.366938	+	0.366938i	−0.499421	+	0.866359i	$0.666454\pi$
$762$		0			0
$763$	3346.76	+	1386.28i	0.158796	+	0.0657753i
$764$		0			0
$765$	18177.4	+	43884.2i	0.859093	+	2.07403i
$766$		0			0
$767$	−23931.6			−1.12662
$768$		0			0
$769$	−29833.1			−1.39897			−0.699485	−	0.714648i	$-0.746587\pi$
$769$	−29833.1			−1.39897			−0.699485	+	0.714648i	$0.746587\pi$
$770$		0			0
$771$	12741.4	+	30760.6i	0.595165	+	1.43685i
$772$		0			0
$773$	736.895	+	305.232i	0.0342876	+	0.0142024i	0.399761	−	0.916619i	$-0.369093\pi$
$773$	736.895	+	305.232i	0.0342876	+	0.0142024i	−0.365474	+	0.930822i	$0.619093\pi$
$774$		0			0
$775$	2387.53	+	2387.53i	0.110661	+	0.110661i
$776$		0			0
$777$	14587.0	−	14587.0i	0.673493	−	0.673493i
$778$		0			0
$779$	2380.21	−	5746.34i	0.109474	−	0.264293i
$780$		0			0
$781$	−1500.56	+	621.554i	−0.0687508	+	0.0284775i
$782$		0			0
$783$		−	44790.4i		−	2.04429i
$784$		0			0
$785$			24655.6i			1.12101i
$786$		0			0
$787$	−23884.7	+	9893.38i	−1.08183	+	0.448108i	−0.851150	−	0.524922i	$-0.824094\pi$
$787$	−23884.7	+	9893.38i	−1.08183	+	0.448108i	−0.230678	+	0.973030i	$0.574094\pi$
$788$		0			0
$789$	13129.1	−	31696.5i	0.592408	−	1.43020i
$790$		0			0
$791$	−5321.59	+	5321.59i	−0.239208	+	0.239208i
$792$		0			0
$793$	−4010.12	−	4010.12i	−0.179576	−	0.179576i
$794$		0			0
$795$	1643.53	+	680.771i	0.0733206	+	0.0303704i
$796$		0			0
$797$	5927.29	+	14309.7i	0.263432	+	0.635981i	0.999146	−	0.0413107i	$-0.0131534\pi$
$797$	5927.29	+	14309.7i	0.263432	+	0.635981i	−0.735714	+	0.677292i	$0.763153\pi$
$798$		0			0
$799$	432.046			0.0191298
$800$		0			0
$801$	−14969.5			−0.660326
$802$		0			0
$803$	−277.571	−	670.117i	−0.0121984	−	0.0294494i
$804$		0			0
$805$	−2697.71	−	1117.43i	−0.118114	−	0.0489244i
$806$		0			0
$807$	48802.5	+	48802.5i	2.12878	+	2.12878i
$808$		0			0
$809$	−15747.5	+	15747.5i	−0.684367	+	0.684367i	−0.960981	−	0.276614i	$-0.910788\pi$
$809$	−15747.5	+	15747.5i	−0.684367	+	0.684367i	0.276614	+	0.960981i	$0.410788\pi$
$810$		0			0
$811$	4881.91	−	11786.0i	0.211377	−	0.510310i	−0.782258	−	0.622955i	$-0.785932\pi$
$811$	4881.91	−	11786.0i	0.211377	−	0.510310i	0.993635	+	0.112644i	$0.0359321\pi$
$812$		0			0
$813$	−54289.0	+	22487.2i	−2.34194	+	0.970063i
$814$		0			0
$815$			28093.5i			1.20745i
$816$		0			0
$817$		−	22730.4i		−	0.973363i
$818$		0			0
$819$	42445.1	−	17581.3i	1.81093	−	0.750112i
$820$		0			0
$821$	417.068	−	1006.89i	0.0177293	−	0.0428024i	−0.914767	−	0.403982i	$-0.867626\pi$
$821$	417.068	−	1006.89i	0.0177293	−	0.0428024i	0.932496	+	0.361180i	$0.117626\pi$
$822$		0			0
$823$	12509.6	−	12509.6i	0.529837	−	0.529837i	−0.390687	−	0.920524i	$-0.627763\pi$
$823$	12509.6	−	12509.6i	0.529837	−	0.529837i	0.920524	+	0.390687i	$0.127763\pi$
$824$		0			0
$825$	−755.354	−	755.354i	−0.0318764	−	0.0318764i
$826$		0			0
$827$	−25130.3	−	10409.3i	−1.05667	−	0.437687i	−0.214401	−	0.976746i	$-0.568780\pi$
$827$	−25130.3	−	10409.3i	−1.05667	−	0.437687i	−0.842268	+	0.539059i	$0.818780\pi$
$828$		0			0
$829$	−10061.9	−	24291.6i	−0.421549	−	1.01771i	−0.981891	−	0.189448i	$-0.939330\pi$
$829$	−10061.9	−	24291.6i	−0.421549	−	1.01771i	0.560341	−	0.828262i	$-0.310670\pi$
$830$		0			0
$831$	−15882.3			−0.662996
$832$		0			0
$833$	23692.8			0.985482
$834$		0			0
$835$	−11578.4	−	27952.8i	−0.479865	−	1.15850i
$836$		0			0
$837$	−15891.0	−	6582.27i	−0.656240	−	0.271824i
$838$		0			0
$839$	997.866	+	997.866i	0.0410610	+	0.0410610i	0.727339	−	0.686278i	$-0.240757\pi$
$839$	997.866	+	997.866i	0.0410610	+	0.0410610i	−0.686278	+	0.727339i	$0.740757\pi$
$840$		0			0
$841$	1085.13	−	1085.13i	0.0444926	−	0.0444926i
$842$		0			0
$843$	−17242.8	+	41627.7i	−0.704475	+	1.70075i
$844$		0			0
$845$	−28118.7	+	11647.1i	−1.14475	+	0.474171i
$846$		0			0
$847$		−	13440.8i		−	0.545254i
$848$		0			0
$849$		−	51194.9i		−	2.06950i
$850$		0			0
$851$	7157.49	−	2964.73i	0.288314	−	0.119424i
$852$		0			0
$853$	−3356.26	+	8102.73i	−0.134720	+	0.325243i	−0.976815	−	0.214087i	$-0.931322\pi$
$853$	−3356.26	+	8102.73i	−0.134720	+	0.325243i	0.842095	+	0.539330i	$0.181322\pi$
$854$		0			0
$855$	−33044.9	+	33044.9i	−1.32177	+	1.32177i
$856$		0			0
$857$	22839.3	+	22839.3i	0.910357	+	0.910357i	0.996300	−	0.0859432i	$-0.0273904\pi$
$857$	22839.3	+	22839.3i	0.910357	+	0.910357i	−0.0859432	+	0.996300i	$0.527390\pi$
$858$		0			0
$859$	−7527.54	−	3118.01i	−0.298994	−	0.123848i	0.228143	−	0.973628i	$-0.426735\pi$
$859$	−7527.54	−	3118.01i	−0.298994	−	0.123848i	−0.527137	+	0.849780i	$0.676735\pi$
$860$		0			0
$861$	−2305.23	−	5565.31i	−0.0912449	−	0.220285i
$862$		0			0
$863$	−29479.1			−1.16278			−0.581392	−	0.813624i	$-0.697492\pi$
$863$	−29479.1			−1.16278			−0.581392	+	0.813624i	$0.697492\pi$
$864$		0			0
$865$	−15038.5			−0.591125
$866$		0			0
$867$	17025.0	+	41101.9i	0.666895	+	1.61003i
$868$		0			0
$869$	1527.37	+	632.659i	0.0596233	+	0.0246968i
$870$		0			0
$871$	−41728.8	−	41728.8i	−1.62334	−	1.62334i
$872$		0			0
$873$	26015.1	−	26015.1i	1.00856	−	1.00856i
$874$		0			0
$875$	5803.86	−	14011.8i	0.224236	−	0.541353i
$876$		0			0
$877$	−35.5671	+	14.7324i	−0.00136946	+	0.000567248i	−0.383368	−	0.923596i	$-0.625236\pi$
$877$	−35.5671	+	14.7324i	−0.00136946	+	0.000567248i	0.381999	+	0.924163i	$0.375236\pi$
$878$		0			0
$879$		−	28305.6i		−	1.08615i
$880$		0			0
$881$		−	50541.0i		−	1.93277i	−0.257100	−	0.966385i	$-0.582767\pi$
$881$		−	50541.0i		−	1.93277i	0.257100	−	0.966385i	$-0.417233\pi$
$882$		0			0
$883$	17247.2	−	7144.04i	0.657323	−	0.272272i	−0.0289887	−	0.999580i	$-0.509229\pi$
$883$	17247.2	−	7144.04i	0.657323	−	0.272272i	0.686312	+	0.727308i	$0.259229\pi$
$884$		0			0
$885$	9022.27	−	21781.7i	0.342690	−	0.827326i
$886$		0			0
$887$	10744.8	−	10744.8i	0.406736	−	0.406736i	−0.473863	−	0.880599i	$-0.657141\pi$
$887$	10744.8	−	10744.8i	0.406736	−	0.406736i	0.880599	+	0.473863i	$0.157141\pi$
$888$		0			0
$889$	−2263.34	−	2263.34i	−0.0853882	−	0.0853882i
$890$		0			0
$891$	2114.05	+	875.668i	0.0794875	+	0.0329248i
$892$		0			0
$893$	162.666	+	392.711i	0.00609565	+	0.0147162i
$894$		0			0
$895$	15274.5			0.570469
$896$		0			0
$897$	25155.0			0.936345
$898$		0			0
$899$	3358.62	+	8108.42i	0.124601	+	0.300813i
$900$		0			0
$901$	2136.80	+	885.091i	0.0790090	+	0.0327266i
$902$		0			0
$903$	−15566.5	−	15566.5i	−0.573666	−	0.573666i
$904$		0			0
$905$	−16427.0	+	16427.0i	−0.603374	+	0.603374i
$906$		0			0
$907$	−15317.6	+	36980.0i	−0.560764	+	1.35380i	0.348393	+	0.937349i	$0.386727\pi$
$907$	−15317.6	+	36980.0i	−0.560764	+	1.35380i	−0.909157	+	0.416454i	$0.863273\pi$
$908$		0			0
$909$	89250.3	−	36968.7i	3.25659	−	1.34893i
$910$		0			0
$911$		−	18795.0i		−	0.683540i	−0.939784	−	0.341770i	$-0.888974\pi$
$911$		−	18795.0i		−	0.683540i	0.939784	−	0.341770i	$-0.111026\pi$
$912$		0			0
$913$		−	503.705i		−	0.0182587i
$914$		0			0
$915$	5161.70	−	2138.05i	0.186492	−	0.0772477i
$916$		0			0
$917$	1285.52	−	3103.52i	0.0462940	−	0.111764i
$918$		0			0
$919$	6027.61	−	6027.61i	0.216358	−	0.216358i	−0.590604	−	0.806962i	$-0.701110\pi$
$919$	6027.61	−	6027.61i	0.216358	−	0.216358i	0.806962	+	0.590604i	$0.201110\pi$
$920$		0			0
$921$	3009.52	+	3009.52i	0.107673	+	0.107673i
$922$		0			0
$923$	58278.4	+	24139.7i	2.07828	+	0.860853i
$924$		0			0
$925$	4889.66	+	11804.7i	0.173807	+	0.419606i
$926$		0			0
$927$	12206.9			0.432500
$928$		0			0
$929$	5213.50			0.184122			0.0920611	−	0.995753i	$-0.470654\pi$
$929$	5213.50			0.184122			0.0920611	+	0.995753i	$0.470654\pi$
$930$		0			0
$931$	8920.37	+	21535.7i	0.314021	+	0.758113i
$932$		0			0
$933$	−45567.1	−	18874.5i	−1.59893	−	0.662297i
$934$		0			0
$935$	1128.61	+	1128.61i	0.0394754	+	0.0394754i
$936$		0			0
$937$	18034.8	−	18034.8i	0.628783	−	0.628783i	−0.318979	−	0.947762i	$-0.603340\pi$
$937$	18034.8	−	18034.8i	0.628783	−	0.628783i	0.947762	+	0.318979i	$0.103340\pi$
$938$		0			0
$939$	3603.73	−	8700.17i	0.125243	−	0.302363i
$940$		0			0
$941$	−1253.64	+	519.275i	−0.0434299	+	0.0179892i	−0.404293	−	0.914630i	$-0.632482\pi$
$941$	−1253.64	+	519.275i	−0.0434299	+	0.0179892i	0.360863	+	0.932619i	$0.382482\pi$
$942$		0			0
$943$		−	2262.24i		−	0.0781217i
$944$		0			0
$945$			24532.7i			0.844497i
$946$		0			0
$947$	25052.1	−	10376.9i	0.859646	−	0.356077i	0.0910771	−	0.995844i	$-0.470969\pi$
$947$	25052.1	−	10376.9i	0.859646	−	0.356077i	0.768569	+	0.639767i	$0.220969\pi$
$948$		0			0
$949$	−10780.2	+	26025.8i	−0.368747	+	0.890234i
$950$		0			0
$951$	22535.4	−	22535.4i	0.768414	−	0.768414i
$952$		0			0
$953$	9648.15	+	9648.15i	0.327948	+	0.327948i	0.851806	−	0.523858i	$-0.175508\pi$
$953$	9648.15	+	9648.15i	0.327948	+	0.327948i	−0.523858	+	0.851806i	$0.675508\pi$
$954$		0			0
$955$	12460.1	+	5161.13i	0.422197	+	0.174880i
$956$		0			0
$957$	−1062.58	−	2565.30i	−0.0358918	−	0.0866504i
$958$		0			0
$959$	6662.17			0.224330
$960$		0			0
$961$	−26420.7			−0.886868
$962$		0			0
$963$	−22108.8	−	53375.2i	−0.739818	−	1.78608i
$964$		0			0
$965$	14567.1	+	6033.88i	0.485939	+	0.201283i
$966$		0			0
$967$	12684.4	+	12684.4i	0.421824	+	0.421824i	0.885831	−	0.464007i	$-0.153589\pi$
$967$	12684.4	+	12684.4i	0.421824	+	0.421824i	−0.464007	+	0.885831i	$0.653589\pi$
$968$		0			0
$969$	−62638.1	+	62638.1i	−2.07660	+	2.07660i
$970$		0			0
$971$	10462.9	−	25259.7i	0.345799	−	0.834832i	−0.651308	−	0.758814i	$-0.725779\pi$
$971$	10462.9	−	25259.7i	0.345799	−	0.834832i	0.997106	−	0.0760183i	$-0.0242208\pi$
$972$		0			0
$973$	3865.01	−	1600.94i	0.127345	−	0.0527480i
$974$		0			0
$975$			41487.6i			1.36274i
$976$		0			0
$977$			60560.6i			1.98312i	0.129654	+	0.991559i	$0.458613\pi$
$977$			60560.6i			1.98312i	−0.129654	+	0.991559i	$0.541387\pi$
$978$		0			0
$979$	−464.717	+	192.492i	−0.0151710	+	0.00628404i
$980$		0			0
$981$	8069.62	−	19481.8i	0.262633	−	0.634053i
$982$		0			0
$983$	−36767.4	+	36767.4i	−1.19298	+	1.19298i	−0.216751	+	0.976227i	$0.569546\pi$
$983$	−36767.4	+	36767.4i	−1.19298	+	1.19298i	−0.976227	+	0.216751i	$0.930454\pi$
$984$		0			0
$985$	−23308.8	−	23308.8i	−0.753989	−	0.753989i
$986$		0			0
$987$	380.339	+	157.541i	0.0122658	+	0.00508065i
$988$		0			0
$989$	−3163.81	−	7638.12i	−0.101722	−	0.245579i
$990$		0			0
$991$	38103.0			1.22137			0.610687	−	0.791872i	$-0.290893\pi$
$991$	38103.0			1.22137			0.610687	+	0.791872i	$0.290893\pi$
$992$		0			0
$993$	12490.6			0.399173
$994$		0			0
$995$	1600.14	+	3863.07i	0.0509827	+	0.123083i
$996$		0			0
$997$	967.156	+	400.609i	0.0307223	+	0.0127256i	0.397992	−	0.917389i	$-0.369707\pi$
$997$	967.156	+	400.609i	0.0307223	+	0.0127256i	−0.367269	+	0.930115i	$0.619707\pi$
$998$		0			0
$999$	−46025.3	−	46025.3i	−1.45763	−	1.45763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.113.1		44
4.3	odd	2		32.4.g.a.5.4	✓	44
8.3	odd	2		256.4.g.b.225.1		44
8.5	even	2		256.4.g.a.225.11		44
32.3	odd	8		256.4.g.b.33.1		44
32.13	even	8	inner	128.4.g.a.17.1		44
32.19	odd	8		32.4.g.a.13.4	yes	44
32.29	even	8		256.4.g.a.33.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.5.4	✓	44	4.3	odd	2
32.4.g.a.13.4	yes	44	32.19	odd	8
128.4.g.a.17.1		44	32.13	even	8	inner
128.4.g.a.113.1		44	1.1	even	1	trivial
256.4.g.a.33.11		44	32.29	even	8
256.4.g.a.225.11		44	8.5	even	2
256.4.g.b.33.1		44	32.3	odd	8
256.4.g.b.225.1		44	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.54796 - 8.56554i) q^{3} +(-7.55322 - 3.12865i) q^{5} +(-7.16166 - 7.16166i) q^{7} +(-41.6886 + 41.6886i) q^{9} +O(q^{10})\)	\(q+(-3.54796 - 8.56554i) q^{3} +(-7.55322 - 3.12865i) q^{5} +(-7.16166 - 7.16166i) q^{7} +(-41.6886 + 41.6886i) q^{9} +(-0.758120 + 1.83026i) q^{11} +(71.0832 - 29.4436i) q^{13} +75.7978i q^{15} +98.5470i q^{17} +(-89.5748 + 37.1031i) q^{19} +(-35.9342 + 86.7528i) q^{21} +(-24.9355 + 24.9355i) q^{23} +(-41.1256 - 41.1256i) q^{25} +(273.726 + 113.381i) q^{27} +(-57.8528 - 139.669i) q^{29} -58.0545 q^{31} +18.3670 q^{33} +(31.6873 + 76.4999i) q^{35} +(-202.968 - 84.0720i) q^{37} +(-504.401 - 504.401i) q^{39} +(-45.3618 + 45.3618i) q^{41} +(-89.7175 + 216.597i) q^{43} +(445.312 - 184.454i) q^{45} -4.38416i q^{47} -240.421i q^{49} +(844.109 - 349.641i) q^{51} +(8.98141 - 21.6830i) q^{53} +(11.4525 - 11.4525i) q^{55} +(635.616 + 635.616i) q^{57} +(-287.366 - 119.031i) q^{59} +(-28.2072 - 68.0983i) q^{61} +597.119 q^{63} -629.026 q^{65} +(-293.521 - 708.622i) q^{67} +(302.057 + 125.116i) q^{69} +(579.730 + 579.730i) q^{71} +(-258.894 + 258.894i) q^{73} +(-206.351 + 498.176i) q^{75} +(18.5371 - 7.67833i) q^{77} -834.510i q^{79} -1155.05i q^{81} +(-234.905 + 97.3009i) q^{83} +(308.319 - 744.347i) q^{85} +(-991.082 + 991.082i) q^{87} +(179.539 + 179.539i) q^{89} +(-719.939 - 298.208i) q^{91} +(205.975 + 497.268i) q^{93} +792.661 q^{95} -624.033 q^{97} +(-44.6962 - 107.906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 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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