LMFDB - Embedded newform 100.3.d.b.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,3,Mod(99,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("100.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	100.d (of order $2$, degree $1$, 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:	$2.72480264360$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.3
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	100.99
Dual form			100.3.d.b.99.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17557 - 1.61803i) q^{2} +3.80423 q^{3} +(-1.23607 + 3.80423i) q^{4} +(-4.47214 - 6.15537i) q^{6} +8.50651 q^{7} +(7.60845 - 2.47214i) q^{8} +5.47214 q^{9} +O(q^{10})$	\(q+(-1.17557 - 1.61803i) q^{2} +3.80423 q^{3} +(-1.23607 + 3.80423i) q^{4} +(-4.47214 - 6.15537i) q^{6} +8.50651 q^{7} +(7.60845 - 2.47214i) q^{8} +5.47214 q^{9} +1.79611i q^{11} +(-4.70228 + 14.4721i) q^{12} -0.472136i q^{13} +(-10.0000 - 13.7638i) q^{14} +(-12.9443 - 9.40456i) q^{16} -23.8885i q^{17} +(-6.43288 - 8.85410i) q^{18} +9.40456i q^{19} +32.3607 q^{21} +(2.90617 - 2.11146i) q^{22} -16.1150 q^{23} +(28.9443 - 9.40456i) q^{24} +(-0.763932 + 0.555029i) q^{26} -13.4208 q^{27} +(-10.5146 + 32.3607i) q^{28} -6.94427 q^{29} +47.4468i q^{31} +32.0000i q^{32} +6.83282i q^{33} +(-38.6525 + 28.0827i) q^{34} +(-6.76393 + 20.8172i) q^{36} +26.3607i q^{37} +(15.2169 - 11.0557i) q^{38} -1.79611i q^{39} -41.4164 q^{41} +(-38.0423 - 52.3607i) q^{42} -2.00811 q^{43} +(-6.83282 - 2.22012i) q^{44} +(18.9443 + 26.0746i) q^{46} +35.3481 q^{47} +(-49.2429 - 35.7771i) q^{48} +23.3607 q^{49} -90.8774i q^{51} +(1.79611 + 0.583592i) q^{52} +21.6393i q^{53} +(15.7771 + 21.7153i) q^{54} +(64.7214 - 21.0292i) q^{56} +35.7771i q^{57} +(8.16348 + 11.2361i) q^{58} -73.8644i q^{59} -26.1378 q^{61} +(76.7706 - 55.7771i) q^{62} +46.5488 q^{63} +(51.7771 - 37.6183i) q^{64} +(11.0557 - 8.03246i) q^{66} -88.8693 q^{67} +(90.8774 + 29.5279i) q^{68} -61.3050 q^{69} -39.4144i q^{71} +(41.6345 - 13.5279i) q^{72} -137.554i q^{73} +(42.6525 - 30.9888i) q^{74} +(-35.7771 - 11.6247i) q^{76} +15.2786i q^{77} +(-2.90617 + 2.11146i) q^{78} +113.703i q^{79} -100.305 q^{81} +(48.6879 + 67.0132i) q^{82} +21.2412 q^{83} +(-40.0000 + 123.107i) q^{84} +(2.36068 + 3.24920i) q^{86} -26.4176 q^{87} +(4.44023 + 13.6656i) q^{88} -67.4427 q^{89} -4.01623i q^{91} +(19.9192 - 61.3050i) q^{92} +180.498i q^{93} +(-41.5542 - 57.1944i) q^{94} +121.735i q^{96} -39.1672i q^{97} +(-27.4621 - 37.7984i) q^{98} +9.82857i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 + 8 * q^9	$ 8 q + 8 q^{4} + 8 q^{9} - 80 q^{14} - 32 q^{16} + 80 q^{21} + 160 q^{24} - 24 q^{26} + 16 q^{29} - 184 q^{34} - 72 q^{36} - 224 q^{41} + 160 q^{44} + 80 q^{46} + 8 q^{49} - 160 q^{54} + 160 q^{56} + 256 q^{61} + 128 q^{64} + 160 q^{66} - 240 q^{69} + 216 q^{74} - 552 q^{81} - 320 q^{84} - 160 q^{86} + 176 q^{89} + 240 q^{94}+O(q^{100}) $ 8 * q + 8 * q^4 + 8 * q^9 - 80 * q^14 - 32 * q^16 + 80 * q^21 + 160 * q^24 - 24 * q^26 + 16 * q^29 - 184 * q^34 - 72 * q^36 - 224 * q^41 + 160 * q^44 + 80 * q^46 + 8 * q^49 - 160 * q^54 + 160 * q^56 + 256 * q^61 + 128 * q^64 + 160 * q^66 - 240 * q^69 + 216 * q^74 - 552 * q^81 - 320 * q^84 - 160 * q^86 + 176 * q^89 + 240 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.17557	−	1.61803i	−0.587785	−	0.809017i
$2$	−1.17557	−	1.61803i	−0.587785	−	0.809017i
$3$	3.80423			1.26808			0.634038	−	0.773302i	$-0.281396\pi$
$3$	3.80423			1.26808			0.634038	+	0.773302i	$0.281396\pi$
$4$	−1.23607	+	3.80423i	−0.309017	+	0.951057i
$5$		0			0
$5$		0			0
$6$	−4.47214	−	6.15537i	−0.745356	−	1.02589i
$7$	8.50651			1.21522			0.607608	−	0.794237i	$-0.292129\pi$
$7$	8.50651			1.21522			0.607608	+	0.794237i	$0.292129\pi$
$8$	7.60845	−	2.47214i	0.951057	−	0.309017i
$9$	5.47214			0.608015
$10$		0			0
$11$			1.79611i			0.163283i	0.996662	+	0.0816415i	$0.0260162\pi$
$11$			1.79611i			0.163283i	−0.996662	+	0.0816415i	$0.973984\pi$
$12$	−4.70228	+	14.4721i	−0.391857	+	1.20601i
$13$		−	0.472136i		−	0.0363182i	−0.999835	−	0.0181591i	$-0.994219\pi$
$13$		−	0.472136i		−	0.0363182i	0.999835	−	0.0181591i	$-0.00578053\pi$
$14$	−10.0000	−	13.7638i	−0.714286	−	0.983130i
$15$		0			0
$16$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$17$		−	23.8885i		−	1.40521i	−0.711581	−	0.702604i	$-0.752020\pi$
$17$		−	23.8885i		−	1.40521i	0.711581	−	0.702604i	$-0.247980\pi$
$18$	−6.43288	−	8.85410i	−0.357382	−	0.491895i
$19$			9.40456i			0.494977i	0.968891	+	0.247489i	$0.0796053\pi$
$19$			9.40456i			0.494977i	−0.968891	+	0.247489i	$0.920395\pi$
$20$		0			0
$21$	32.3607			1.54098
$22$	2.90617	−	2.11146i	0.132099	−	0.0959753i
$23$	−16.1150			−0.700650			−0.350325	−	0.936628i	$-0.613929\pi$
$23$	−16.1150			−0.700650			−0.350325	+	0.936628i	$0.613929\pi$
$24$	28.9443	−	9.40456i	1.20601	−	0.391857i
$25$		0			0
$26$	−0.763932	+	0.555029i	−0.0293820	+	0.0213473i
$27$	−13.4208			−0.497066
$28$	−10.5146	+	32.3607i	−0.375522	+	1.15574i
$29$	−6.94427			−0.239458			−0.119729	−	0.992807i	$-0.538203\pi$
$29$	−6.94427			−0.239458			−0.119729	+	0.992807i	$0.538203\pi$
$30$		0			0
$31$			47.4468i			1.53054i	0.643708	+	0.765271i	$0.277395\pi$
$31$			47.4468i			1.53054i	−0.643708	+	0.765271i	$0.722605\pi$
$32$			32.0000i			1.00000i
$33$			6.83282i			0.207055i
$34$	−38.6525	+	28.0827i	−1.13684	+	0.825961i
$35$		0			0
$36$	−6.76393	+	20.8172i	−0.187887	+	0.578257i
$37$			26.3607i			0.712451i	0.934400	+	0.356225i	$0.115936\pi$
$37$			26.3607i			0.712451i	−0.934400	+	0.356225i	$0.884064\pi$
$38$	15.2169	−	11.0557i	0.400445	−	0.290940i
$39$		−	1.79611i		−	0.0460542i
$40$		0			0
$41$	−41.4164			−1.01016			−0.505078	−	0.863074i	$-0.668536\pi$
$41$	−41.4164			−1.01016			−0.505078	+	0.863074i	$0.668536\pi$
$42$	−38.0423	−	52.3607i	−0.905768	−	1.24668i
$43$	−2.00811			−0.0467003			−0.0233502	−	0.999727i	$-0.507433\pi$
$43$	−2.00811			−0.0467003			−0.0233502	+	0.999727i	$0.507433\pi$
$44$	−6.83282	−	2.22012i	−0.155291	−	0.0504572i
$45$		0			0
$46$	18.9443	+	26.0746i	0.411832	+	0.566838i
$47$	35.3481			0.752087			0.376044	−	0.926602i	$-0.377284\pi$
$47$	35.3481			0.752087			0.376044	+	0.926602i	$0.377284\pi$
$48$	−49.2429	−	35.7771i	−1.02589	−	0.745356i
$49$	23.3607			0.476749
$50$		0			0
$51$		−	90.8774i		−	1.78191i
$52$	1.79611	+	0.583592i	0.0345406	+	0.0112229i
$53$			21.6393i			0.408289i	0.978941	+	0.204145i	$0.0654413\pi$
$53$			21.6393i			0.408289i	−0.978941	+	0.204145i	$0.934559\pi$
$54$	15.7771	+	21.7153i	0.292168	+	0.402135i
$55$		0			0
$56$	64.7214	−	21.0292i	1.15574	−	0.375522i
$57$			35.7771i			0.627668i
$58$	8.16348	+	11.2361i	0.140750	+	0.193725i
$59$		−	73.8644i		−	1.25194i	−0.779848	−	0.625970i	$-0.784703\pi$
$59$		−	73.8644i		−	1.25194i	0.779848	−	0.625970i	$-0.215297\pi$
$60$		0			0
$61$	−26.1378			−0.428488			−0.214244	−	0.976780i	$-0.568729\pi$
$61$	−26.1378			−0.428488			−0.214244	+	0.976780i	$0.568729\pi$
$62$	76.7706	−	55.7771i	1.23824	−	0.899630i
$63$	46.5488			0.738869
$64$	51.7771	−	37.6183i	0.809017	−	0.587785i
$65$		0			0
$66$	11.0557	−	8.03246i	0.167511	−	0.121704i
$67$	−88.8693			−1.32641			−0.663204	−	0.748439i	$-0.730804\pi$
$67$	−88.8693			−1.32641			−0.663204	+	0.748439i	$0.730804\pi$
$68$	90.8774	+	29.5279i	1.33643	+	0.434233i
$69$	−61.3050			−0.888478
$70$		0			0
$71$		−	39.4144i		−	0.555132i	−0.960707	−	0.277566i	$-0.910472\pi$
$71$		−	39.4144i		−	0.555132i	0.960707	−	0.277566i	$-0.0895277\pi$
$72$	41.6345	−	13.5279i	0.578257	−	0.187887i
$73$		−	137.554i		−	1.88430i	−0.335186	−	0.942152i	$-0.608799\pi$
$73$		−	137.554i		−	1.88430i	0.335186	−	0.942152i	$-0.391201\pi$
$74$	42.6525	−	30.9888i	0.576385	−	0.418768i
$75$		0			0
$76$	−35.7771	−	11.6247i	−0.470751	−	0.152956i
$77$			15.2786i			0.198424i
$78$	−2.90617	+	2.11146i	−0.0372586	+	0.0270700i
$79$			113.703i			1.43928i	0.694350	+	0.719638i	$0.255692\pi$
$79$			113.703i			1.43928i	−0.694350	+	0.719638i	$0.744308\pi$
$80$		0			0
$81$	−100.305			−1.23833
$82$	48.6879	+	67.0132i	0.593755	+	0.817234i
$83$	21.2412			0.255919			0.127959	−	0.991779i	$-0.459157\pi$
$83$	21.2412			0.255919			0.127959	+	0.991779i	$0.459157\pi$
$84$	−40.0000	+	123.107i	−0.476190	+	1.46556i
$85$		0			0
$86$	2.36068	+	3.24920i	0.0274498	+	0.0377814i
$87$	−26.4176			−0.303650
$88$	4.44023	+	13.6656i	0.0504572	+	0.155291i
$89$	−67.4427			−0.757783			−0.378892	−	0.925441i	$-0.623695\pi$
$89$	−67.4427			−0.757783			−0.378892	+	0.925441i	$0.623695\pi$
$90$		0			0
$91$		−	4.01623i		−	0.0441344i
$92$	19.9192	−	61.3050i	0.216513	−	0.666358i
$93$			180.498i			1.94084i
$94$	−41.5542	−	57.1944i	−0.442066	−	0.608451i
$95$		0			0
$96$			121.735i			1.26808i
$97$		−	39.1672i		−	0.403785i	−0.979408	−	0.201893i	$-0.935291\pi$
$97$		−	39.1672i		−	0.403785i	0.979408	−	0.201893i	$-0.0647092\pi$
$98$	−27.4621	−	37.7984i	−0.280226	−	0.385698i
$99$			9.82857i			0.0992785i
$100$		0			0
$101$	99.8885			0.988995			0.494498	−	0.869179i	$-0.335352\pi$
$101$	99.8885			0.988995			0.494498	+	0.869179i	$0.335352\pi$
$102$	−147.043	+	106.833i	−1.44160	+	1.04738i
$103$	−35.7721			−0.347302			−0.173651	−	0.984807i	$-0.555556\pi$
$103$	−35.7721			−0.347302			−0.173651	+	0.984807i	$0.555556\pi$
$104$	−1.16718	−	3.59222i	−0.0112229	−	0.0345406i
$105$		0			0
$106$	35.0132	−	25.4385i	0.330313	−	0.239986i
$107$	121.099			1.13177			0.565884	−	0.824485i	$-0.308535\pi$
$107$	121.099			1.13177			0.565884	+	0.824485i	$0.308535\pi$
$108$	16.5890	−	51.0557i	0.153602	−	0.472738i
$109$	197.469			1.81164			0.905821	−	0.423660i	$-0.139255\pi$
$109$	197.469			1.81164			0.905821	+	0.423660i	$0.139255\pi$
$110$		0			0
$111$			100.282i			0.903441i
$112$	−110.111	−	80.0000i	−0.983130	−	0.714286i
$113$		−	81.2786i		−	0.719280i	−0.933091	−	0.359640i	$-0.882900\pi$
$113$		−	81.2786i		−	0.719280i	0.933091	−	0.359640i	$-0.117100\pi$
$114$	57.8885	−	42.0585i	0.507794	−	0.368934i
$115$		0			0
$116$	8.58359	−	26.4176i	0.0739965	−	0.227738i
$117$		−	2.58359i		−	0.0220820i
$118$	−119.515	+	86.8328i	−1.01284	+	0.735871i
$119$		−	203.208i		−	1.70763i
$120$		0			0
$121$	117.774			0.973339
$122$	30.7268	+	42.2918i	0.251859	+	0.346654i
$123$	−157.557			−1.28095
$124$	−180.498	−	58.6475i	−1.45563	−	0.472964i
$125$		0			0
$126$	−54.7214	−	75.3175i	−0.434297	−	0.597758i
$127$	1.84616			0.0145367			0.00726834	−	0.999974i	$-0.497686\pi$
$127$	1.84616			0.0145367			0.00726834	+	0.999974i	$0.497686\pi$
$128$	−121.735	−	39.5542i	−0.951057	−	0.309017i
$129$	−7.63932			−0.0592195
$130$		0			0
$131$			225.609i			1.72221i	0.508428	+	0.861105i	$0.330227\pi$
$131$			225.609i			1.72221i	−0.508428	+	0.861105i	$0.669773\pi$
$132$	−25.9936	−	8.44582i	−0.196921	−	0.0639835i
$133$			80.0000i			0.601504i
$134$	104.472	+	143.794i	0.779643	+	1.07309i
$135$		0			0
$136$	−59.0557	−	181.755i	−0.434233	−	1.33643i
$137$		−	52.8328i		−	0.385641i	−0.981234	−	0.192820i	$-0.938236\pi$
$137$		−	52.8328i		−	0.385641i	0.981234	−	0.192820i	$-0.0617635\pi$
$138$	72.0683	+	99.1935i	0.522234	+	0.718793i
$139$			125.852i			0.905407i	0.891661	+	0.452703i	$0.149540\pi$
$139$			125.852i			0.905407i	−0.891661	+	0.452703i	$0.850460\pi$
$140$		0			0
$141$	134.472			0.953703
$142$	−63.7738	+	46.3344i	−0.449111	+	0.326298i
$143$	0.848009			0.00593013
$144$	−70.8328	−	51.4631i	−0.491895	−	0.357382i
$145$		0			0
$146$	−222.567	+	161.705i	−1.52443	+	1.10757i
$147$	88.8693			0.604553
$148$	−100.282	−	32.5836i	−0.677581	−	0.220159i
$149$	−132.971			−0.892420			−0.446210	−	0.894928i	$-0.647227\pi$
$149$	−132.971			−0.892420			−0.446210	+	0.894928i	$0.647227\pi$
$150$		0			0
$151$		−	151.221i		−	1.00146i	−0.865603	−	0.500732i	$-0.833064\pi$
$151$		−	151.221i		−	1.00146i	0.865603	−	0.500732i	$-0.166936\pi$
$152$	23.2494	+	71.5542i	0.152956	+	0.470751i
$153$		−	130.721i		−	0.854388i
$154$	24.7214	−	17.9611i	0.160528	−	0.116631i
$155$		0			0
$156$	6.83282	+	2.22012i	0.0438001	+	0.0142315i
$157$		−	36.7477i		−	0.234062i	−0.993128	−	0.117031i	$-0.962662\pi$
$157$		−	36.7477i		−	0.234062i	0.993128	−	0.117031i	$-0.0373376\pi$
$158$	183.975	−	133.666i	1.16440	−	0.845985i
$159$			82.3209i			0.517741i
$160$		0			0
$161$	−137.082			−0.851441
$162$	117.916	+	162.297i	0.727874	+	1.00183i
$163$	302.854			1.85800			0.929000	−	0.370079i	$-0.120669\pi$
$163$	302.854			1.85800			0.929000	+	0.370079i	$0.120669\pi$
$164$	51.1935	−	157.557i	0.312155	−	0.960716i
$165$		0			0
$166$	−24.9706	−	34.3691i	−0.150425	−	0.207043i
$167$	−99.3839			−0.595113			−0.297557	−	0.954704i	$-0.596172\pi$
$167$	−99.3839			−0.595113			−0.297557	+	0.954704i	$0.596172\pi$
$168$	246.215	−	80.0000i	1.46556	−	0.476190i
$169$	168.777			0.998681
$170$		0			0
$171$			51.4631i			0.300954i
$172$	2.48217	−	7.63932i	0.0144312	−	0.0444147i
$173$			181.639i			1.04994i	0.851121	+	0.524969i	$0.175923\pi$
$173$			181.639i			1.04994i	−0.851121	+	0.524969i	$0.824077\pi$
$174$	31.0557	+	42.7445i	0.178481	+	0.245658i
$175$		0			0
$176$	16.8916	−	23.2494i	0.0959753	−	0.132099i
$177$		−	280.997i		−	1.58755i
$178$	79.2837	+	109.125i	0.445414	+	0.613060i
$179$			260.907i			1.45758i	0.684735	+	0.728792i	$0.259918\pi$
$179$			260.907i			1.45758i	−0.684735	+	0.728792i	$0.740082\pi$
$180$		0			0
$181$	157.777			0.871697			0.435848	−	0.900020i	$-0.356448\pi$
$181$	157.777			0.871697			0.435848	+	0.900020i	$0.356448\pi$
$182$	−6.49839	+	4.72136i	−0.0357055	+	0.0259415i
$183$	−99.4340			−0.543355
$184$	−122.610	+	39.8384i	−0.666358	+	0.216513i
$185$		0			0
$186$	292.053	−	212.189i	1.57018	−	1.14080i
$187$	42.9065			0.229447
$188$	−43.6926	+	134.472i	−0.232408	+	0.715277i
$189$	−114.164			−0.604043
$190$		0			0
$191$		−	324.095i		−	1.69683i	−0.529328	−	0.848417i	$-0.677556\pi$
$191$		−	324.095i		−	1.69683i	0.529328	−	0.848417i	$-0.322444\pi$
$192$	196.972	−	143.108i	1.02589	−	0.745356i
$193$		−	181.777i		−	0.941850i	−0.882173	−	0.470925i	$-0.843920\pi$
$193$		−	181.777i		−	0.941850i	0.882173	−	0.470925i	$-0.156080\pi$
$194$	−63.3738	+	46.0438i	−0.326669	+	0.237339i
$195$		0			0
$196$	−28.8754	+	88.8693i	−0.147323	+	0.453415i
$197$			140.525i			0.713324i	0.934234	+	0.356662i	$0.116085\pi$
$197$			140.525i			0.713324i	−0.934234	+	0.356662i	$0.883915\pi$
$198$	15.9030	−	11.5542i	0.0803180	−	0.0583544i
$199$		−	168.234i		−	0.845397i	−0.906270	−	0.422698i	$-0.861083\pi$
$199$		−	168.234i		−	0.845397i	0.906270	−	0.422698i	$-0.138917\pi$
$200$		0			0
$201$	−338.079			−1.68198
$202$	−117.426	−	161.623i	−0.581317	−	0.800114i
$203$	−59.0715			−0.290993
$204$	345.718	+	112.331i	1.69470	+	0.550641i
$205$		0			0
$206$	42.0526	+	57.8805i	0.204139	+	0.280973i
$207$	−88.1833			−0.426006
$208$	−4.44023	+	6.11146i	−0.0213473	+	0.0293820i
$209$	−16.8916			−0.0808213
$210$		0			0
$211$			93.9455i			0.445240i	0.974905	+	0.222620i	$0.0714608\pi$
$211$			93.9455i			0.445240i	−0.974905	+	0.222620i	$0.928539\pi$
$212$	−82.3209	−	26.7477i	−0.388306	−	0.126168i
$213$		−	149.941i		−	0.703949i
$214$	−142.361	−	195.943i	−0.665237	−	0.915620i
$215$		0			0
$216$	−102.111	+	33.1780i	−0.472738	+	0.153602i
$217$			403.607i			1.85994i
$218$	−232.139	−	319.512i	−1.06486	−	1.46565i
$219$		−	523.287i		−	2.38944i
$220$		0			0
$221$	−11.2786			−0.0510346
$222$	162.260	−	117.889i	0.730899	−	0.531029i
$223$	214.035			0.959797			0.479899	−	0.877324i	$-0.340673\pi$
$223$	214.035			0.959797			0.479899	+	0.877324i	$0.340673\pi$
$224$			272.208i			1.21522i
$225$		0			0
$226$	−131.512	+	95.5488i	−0.581910	+	0.422782i
$227$	41.4225			0.182478			0.0912389	−	0.995829i	$-0.470917\pi$
$227$	41.4225			0.182478			0.0912389	+	0.995829i	$0.470917\pi$
$228$	−136.104	−	44.2229i	−0.596948	−	0.193960i
$229$	−73.2786			−0.319994			−0.159997	−	0.987117i	$-0.551148\pi$
$229$	−73.2786			−0.319994			−0.159997	+	0.987117i	$0.551148\pi$
$230$		0			0
$231$			58.1234i			0.251616i
$232$	−52.8352	+	17.1672i	−0.227738	+	0.0739965i
$233$			307.050i			1.31781i	0.752227	+	0.658905i	$0.228980\pi$
$233$			307.050i			1.31781i	−0.752227	+	0.658905i	$0.771020\pi$
$234$	−4.18034	+	3.03719i	−0.0178647	+	0.0129795i
$235$		0			0
$236$	280.997	+	91.3014i	1.19066	+	0.386870i
$237$			432.551i			1.82511i
$238$	−328.798	+	238.885i	−1.38150	+	1.00372i
$239$			42.9065i			0.179525i	0.995963	+	0.0897625i	$0.0286108\pi$
$239$			42.9065i			0.179525i	−0.995963	+	0.0897625i	$0.971389\pi$
$240$		0			0
$241$	−135.082			−0.560506			−0.280253	−	0.959926i	$-0.590418\pi$
$241$	−135.082			−0.560506			−0.280253	+	0.959926i	$0.590418\pi$
$242$	−138.452	−	190.562i	−0.572114	−	0.787448i
$243$	−260.796			−1.07323
$244$	32.3081	−	99.4340i	0.132410	−	0.407516i
$245$		0			0
$246$	185.220	+	254.933i	0.752926	+	1.03631i
$247$	4.44023			0.0179767
$248$	117.295	+	360.997i	0.472964	+	1.45563i
$249$	80.8065			0.324524
$250$		0			0
$251$		−	221.169i		−	0.881152i	−0.897715	−	0.440576i	$-0.854774\pi$
$251$		−	221.169i		−	0.881152i	0.897715	−	0.440576i	$-0.145226\pi$
$252$	−57.5374	+	177.082i	−0.228323	+	0.702707i
$253$		−	28.9443i		−	0.114404i
$254$	−2.17029	−	2.98715i	−0.00854445	−	0.0117604i
$255$		0			0
$256$	79.1084	+	243.470i	0.309017	+	0.951057i
$257$		−	257.056i		−	1.00022i	−0.865963	−	0.500108i	$-0.833293\pi$
$257$		−	257.056i		−	1.00022i	0.865963	−	0.500108i	$-0.166707\pi$
$258$	8.98056	+	12.3607i	0.0348084	+	0.0479096i
$259$			224.237i			0.865781i
$260$		0			0
$261$	−38.0000			−0.145594
$262$	365.044	−	265.220i	1.39330	−	1.01229i
$263$	−164.168			−0.624212			−0.312106	−	0.950047i	$-0.601034\pi$
$263$	−164.168			−0.624212			−0.312106	+	0.950047i	$0.601034\pi$
$264$	16.8916	+	51.9872i	0.0639835	+	0.196921i
$265$		0			0
$266$	129.443	−	94.0456i	0.486627	−	0.353555i
$267$	−256.567			−0.960926
$268$	109.849	−	338.079i	0.409882	−	1.26149i
$269$	35.4752			0.131878			0.0659391	−	0.997824i	$-0.478996\pi$
$269$	35.4752			0.131878			0.0659391	+	0.997824i	$0.478996\pi$
$270$		0			0
$271$			298.950i			1.10314i	0.834130	+	0.551568i	$0.185970\pi$
$271$			298.950i			1.10314i	−0.834130	+	0.551568i	$0.814030\pi$
$272$	−224.661	+	309.220i	−0.825961	+	1.13684i
$273$		−	15.2786i		−	0.0559657i
$274$	−85.4853	+	62.1087i	−0.311990	+	0.226674i
$275$		0			0
$276$	75.7771	−	233.218i	0.274555	−	0.844992i
$277$		−	457.246i		−	1.65071i	−0.564616	−	0.825354i	$-0.690976\pi$
$277$		−	457.246i		−	1.65071i	0.564616	−	0.825354i	$-0.309024\pi$
$278$	203.632	−	147.947i	0.732490	−	0.532185i
$279$			259.635i			0.930593i
$280$		0			0
$281$	−5.63932			−0.0200688			−0.0100344	−	0.999950i	$-0.503194\pi$
$281$	−5.63932			−0.0200688			−0.0100344	+	0.999950i	$0.503194\pi$
$282$	−158.081	−	217.580i	−0.560573	−	0.771562i
$283$	−169.918			−0.600418			−0.300209	−	0.953874i	$-0.597056\pi$
$283$	−169.918			−0.600418			−0.300209	+	0.953874i	$0.597056\pi$
$284$	149.941	+	48.7188i	0.527962	+	0.171545i
$285$		0			0
$286$	−0.996894	−	1.37211i	−0.00348564	−	0.00479758i
$287$	−352.309			−1.22756
$288$			175.108i			0.608015i
$289$	−281.663			−0.974611
$290$		0			0
$291$		−	149.001i		−	0.512030i
$292$	523.287	+	170.026i	1.79208	+	0.582282i
$293$			26.8591i			0.0916694i	0.998949	+	0.0458347i	$0.0145947\pi$
$293$			26.8591i			0.0916694i	−0.998949	+	0.0458347i	$0.985405\pi$
$294$	−104.472	−	143.794i	−0.355347	−	0.489094i
$295$		0			0
$296$	65.1672	+	200.564i	0.220159	+	0.677581i
$297$		−	24.1052i		−	0.0811624i
$298$	156.316	+	215.151i	0.524551	+	0.721983i
$299$			7.60845i			0.0254463i
$300$		0			0
$301$	−17.0820			−0.0567510
$302$	−244.681	+	177.771i	−0.810201	+	0.588645i
$303$	379.999			1.25412
$304$	88.4458	−	121.735i	0.290940	−	0.400445i
$305$		0			0
$306$	−211.512	+	153.672i	−0.691214	+	0.502197i
$307$	118.031			0.384466			0.192233	−	0.981349i	$-0.438427\pi$
$307$	118.031			0.384466			0.192233	+	0.981349i	$0.438427\pi$
$308$	−58.1234	−	18.8854i	−0.188712	−	0.0613164i
$309$	−136.085			−0.440405
$310$		0			0
$311$			121.835i			0.391753i	0.980629	+	0.195877i	$0.0627552\pi$
$311$			121.835i			0.391753i	−0.980629	+	0.195877i	$0.937245\pi$
$312$	−4.44023	−	13.6656i	−0.0142315	−	0.0438001i
$313$		−	219.548i		−	0.701431i	−0.936482	−	0.350716i	$-0.885938\pi$
$313$		−	219.548i		−	0.701431i	0.936482	−	0.350716i	$-0.114062\pi$
$314$	−59.4590	+	43.1995i	−0.189360	+	0.137578i
$315$		0			0
$316$	−432.551	−	140.544i	−1.36883	−	0.444761i
$317$			366.859i			1.15728i	0.815582	+	0.578642i	$0.196417\pi$
$317$			366.859i			1.15728i	−0.815582	+	0.578642i	$0.803583\pi$
$318$	133.198	−	96.7740i	0.418862	−	0.304321i
$319$		−	12.4727i		−	0.0390993i
$320$		0			0
$321$	460.689			1.43517
$322$	161.150	+	221.803i	0.500465	+	0.688830i
$323$	224.661			0.695546
$324$	123.984	−	381.583i	0.382666	−	1.17772i
$325$		0			0
$326$	−356.026	−	490.028i	−1.09211	−	1.50315i
$327$	751.217			2.29730
$328$	−315.115	+	102.387i	−0.960716	+	0.312155i
$329$	300.689			0.913948
$330$		0			0
$331$		−	162.846i		−	0.491981i	−0.969272	−	0.245990i	$-0.920887\pi$
$331$		−	162.846i		−	0.491981i	0.969272	−	0.245990i	$-0.0791132\pi$
$332$	−26.2556	+	80.8065i	−0.0790832	+	0.243393i
$333$			144.249i			0.433181i
$334$	116.833	+	160.807i	0.349799	+	0.481457i
$335$		0			0
$336$	−418.885	−	304.338i	−1.24668	−	0.905768i
$337$			17.1084i			0.0507666i	0.999678	+	0.0253833i	$0.00808063\pi$
$337$			17.1084i			0.0507666i	−0.999678	+	0.0253833i	$0.991919\pi$
$338$	−198.409	−	273.087i	−0.587010	−	0.807950i
$339$		−	309.202i		−	0.912101i
$340$		0			0
$341$	−85.2198			−0.249911
$342$	83.2690	−	60.4984i	0.243477	−	0.176896i
$343$	−218.101			−0.635863
$344$	−15.2786	+	4.96433i	−0.0444147	+	0.0144312i
$345$		0			0
$346$	293.899	−	213.530i	0.849418	−	0.617138i
$347$	−167.498			−0.482703			−0.241351	−	0.970438i	$-0.577591\pi$
$347$	−167.498			−0.482703			−0.241351	+	0.970438i	$0.577591\pi$
$348$	32.6539	−	100.498i	0.0938331	−	0.288789i
$349$	483.495			1.38537			0.692687	−	0.721239i	$-0.256427\pi$
$349$	483.495			1.38537			0.692687	+	0.721239i	$0.256427\pi$
$350$		0			0
$351$			6.33644i			0.0180525i
$352$	−57.4756			−0.163283
$353$		−	307.994i		−	0.872504i	−0.899825	−	0.436252i	$-0.856306\pi$
$353$		−	307.994i		−	0.872504i	0.899825	−	0.436252i	$-0.143694\pi$
$354$	−454.663	+	330.332i	−1.28436	+	0.933140i
$355$		0			0
$356$	83.3638	−	256.567i	0.234168	−	0.720695i
$357$		−	773.050i		−	2.16540i
$358$	422.157	−	306.715i	1.17921	−	0.856746i
$359$			23.2494i			0.0647615i	0.999476	+	0.0323807i	$0.0103089\pi$
$359$			23.2494i			0.0647615i	−0.999476	+	0.0323807i	$0.989691\pi$
$360$		0			0
$361$	272.554			0.754998
$362$	−185.478	−	255.289i	−0.512370	−	0.705217i
$363$	448.039			1.23427
$364$	15.2786	+	4.96433i	0.0419743	+	0.0136383i
$365$		0			0
$366$	116.892	+	160.888i	0.319376	+	0.439583i
$367$	517.325			1.40960			0.704802	−	0.709404i	$-0.251036\pi$
$367$	517.325			1.40960			0.704802	+	0.709404i	$0.251036\pi$
$368$	208.596	+	151.554i	0.566838	+	0.411832i
$369$	−226.636			−0.614190
$370$		0			0
$371$			184.075i			0.496159i
$372$	−686.657	−	223.108i	−1.84585	−	0.599754i
$373$			88.3545i			0.236875i	0.992961	+	0.118438i	$0.0377886\pi$
$373$			88.3545i			0.236875i	−0.992961	+	0.118438i	$0.962211\pi$
$374$	−50.4396	−	69.4242i	−0.134865	−	0.185626i
$375$		0			0
$376$	268.944	−	87.3853i	0.715277	−	0.232408i
$377$			3.27864i			0.00869666i
$378$	134.208	+	184.721i	0.355047	+	0.488681i
$379$		−	19.3332i		−	0.0510112i	−0.999675	−	0.0255056i	$-0.991880\pi$
$379$		−	19.3332i		−	0.0510112i	0.999675	−	0.0255056i	$-0.00811956\pi$
$380$		0			0
$381$	7.02321			0.0184336
$382$	−524.397	+	380.997i	−1.37277	+	0.997374i
$383$	−431.612			−1.12692			−0.563462	−	0.826142i	$-0.690531\pi$
$383$	−431.612			−1.12692			−0.563462	+	0.826142i	$0.690531\pi$
$384$	−463.108	−	150.473i	−1.20601	−	0.391857i
$385$		0			0
$386$	−294.122	+	213.692i	−0.761973	+	0.553606i
$387$	−10.9887			−0.0283945
$388$	149.001	+	48.4133i	0.384023	+	0.124777i
$389$	296.354			0.761837			0.380918	−	0.924609i	$-0.375608\pi$
$389$	296.354			0.761837			0.380918	+	0.924609i	$0.375608\pi$
$390$		0			0
$391$			384.963i			0.984560i
$392$	177.739	−	57.7508i	0.453415	−	0.147323i
$393$			858.269i			2.18389i
$394$	227.374	−	165.197i	0.577091	−	0.419281i
$395$		0			0
$396$	−37.3901	−	12.1488i	−0.0944194	−	0.0306787i
$397$		−	86.1904i		−	0.217104i	−0.994091	−	0.108552i	$-0.965379\pi$
$397$		−	86.1904i		−	0.217104i	0.994091	−	0.108552i	$-0.0346214\pi$
$398$	−272.208	+	197.771i	−0.683940	+	0.496912i
$399$			304.338i			0.762752i
$400$		0			0
$401$	442.997			1.10473			0.552365	−	0.833602i	$-0.313725\pi$
$401$	442.997			1.10473			0.552365	+	0.833602i	$0.313725\pi$
$402$	397.436	+	547.023i	0.988646	+	1.36075i
$403$	22.4014			0.0555865
$404$	−123.469	+	379.999i	−0.305616	+	0.940591i
$405$		0			0
$406$	69.4427	+	95.5797i	0.171041	+	0.235418i
$407$	−47.3467			−0.116331
$408$	−224.661	−	691.437i	−0.550641	−	1.69470i
$409$	−63.4102			−0.155037			−0.0775186	−	0.996991i	$-0.524700\pi$
$409$	−63.4102			−0.155037			−0.0775186	+	0.996991i	$0.524700\pi$
$410$		0			0
$411$		−	200.988i		−	0.489022i
$412$	44.2167	−	136.085i	0.107322	−	0.330304i
$413$		−	628.328i		−	1.52138i
$414$	103.666	+	142.684i	0.250400	+	0.344646i
$415$		0			0
$416$	15.1084			0.0363182
$417$			478.768i			1.14812i
$418$	19.8573	+	27.3313i	0.0475056	+	0.0653858i
$419$			435.678i			1.03980i	0.854226	+	0.519902i	$0.174032\pi$
$419$			435.678i			1.03980i	−0.854226	+	0.519902i	$0.825968\pi$
$420$		0			0
$421$	−582.912			−1.38459			−0.692294	−	0.721615i	$-0.743400\pi$
$421$	−582.912			−1.38459			−0.692294	+	0.721615i	$0.743400\pi$
$422$	152.007	−	110.440i	0.360206	−	0.261705i
$423$	193.430			0.457280
$424$	53.4953	+	164.642i	0.126168	+	0.388306i
$425$		0			0
$426$	−242.610	+	176.266i	−0.569507	+	0.413771i
$427$	−222.341			−0.520705
$428$	−149.687	+	460.689i	−0.349736	+	1.07638i
$429$	3.22602			0.00751986
$430$		0			0
$431$			375.882i			0.872117i	0.899918	+	0.436058i	$0.143626\pi$
$431$			375.882i			0.872117i	−0.899918	+	0.436058i	$0.856374\pi$
$432$	173.722	+	126.217i	0.402135	+	0.292168i
$433$			368.164i			0.850263i	0.905131	+	0.425132i	$0.139772\pi$
$433$			368.164i			0.850263i	−0.905131	+	0.425132i	$0.860228\pi$
$434$	653.050	−	474.468i	1.50472	−	1.09324i
$435$		0			0
$436$	−244.085	+	751.217i	−0.559828	+	1.72297i
$437$		−	151.554i		−	0.346806i
$438$	−846.696	+	615.161i	−1.93310	+	1.40448i
$439$		−	483.549i		−	1.10148i	−0.834677	−	0.550739i	$-0.814346\pi$
$439$		−	483.549i		−	1.10148i	0.834677	−	0.550739i	$-0.185654\pi$
$440$		0			0
$441$	127.833			0.289870
$442$	13.2588	+	18.2492i	0.0299974	+	0.0412878i
$443$	−279.181			−0.630205			−0.315102	−	0.949058i	$-0.602039\pi$
$443$	−279.181			−0.630205			−0.315102	+	0.949058i	$0.602039\pi$
$444$	−381.495	−	123.955i	−0.859224	−	0.279179i
$445$		0			0
$446$	−251.613	−	346.316i	−0.564155	−	0.776492i
$447$	−505.850			−1.13166
$448$	440.442	−	320.000i	0.983130	−	0.714286i
$449$	−756.079			−1.68392			−0.841959	−	0.539542i	$-0.818597\pi$
$449$	−756.079			−1.68392			−0.841959	+	0.539542i	$0.818597\pi$
$450$		0			0
$451$		−	74.3885i		−	0.164941i
$452$	309.202	+	100.466i	0.684076	+	0.222270i
$453$		−	575.279i		−	1.26993i
$454$	−48.6950	−	67.0230i	−0.107258	−	0.147628i
$455$		0			0
$456$	88.4458	+	272.208i	0.193960	+	0.596948i
$457$			285.672i			0.625103i	0.949901	+	0.312551i	$0.101184\pi$
$457$			285.672i			0.625103i	−0.949901	+	0.312551i	$0.898816\pi$
$458$	86.1442	+	118.567i	0.188088	+	0.258881i
$459$			320.603i			0.698482i
$460$		0			0
$461$	−99.1146			−0.214999			−0.107500	−	0.994205i	$-0.534284\pi$
$461$	−99.1146			−0.214999			−0.107500	+	0.994205i	$0.534284\pi$
$462$	94.0456	−	68.3282i	0.203562	−	0.147896i
$463$	−630.603			−1.36199			−0.680997	−	0.732286i	$-0.738453\pi$
$463$	−630.603			−1.36199			−0.680997	+	0.732286i	$0.738453\pi$
$464$	89.8885	+	65.3078i	0.193725	+	0.140750i
$465$		0			0
$466$	496.817	−	360.958i	1.06613	−	0.774589i
$467$	−496.010			−1.06212			−0.531060	−	0.847334i	$-0.678206\pi$
$467$	−496.010			−1.06212			−0.531060	+	0.847334i	$0.678206\pi$
$468$	9.82857	+	3.19350i	0.0210012	+	0.00682371i
$469$	−755.967			−1.61187
$470$		0			0
$471$		−	139.796i		−	0.296808i
$472$	−182.603	−	561.994i	−0.386870	−	1.19066i
$473$		−	3.60680i		−	0.00762537i
$474$	699.882	−	508.494i	1.47655	−	1.07277i
$475$		0			0
$476$	773.050	+	251.179i	1.62405	+	0.527687i
$477$			118.413i			0.248246i
$478$	69.4242	−	50.4396i	0.145239	−	0.105522i
$479$		−	579.090i		−	1.20896i	−0.796621	−	0.604478i	$-0.793382\pi$
$479$		−	579.090i		−	1.20896i	0.796621	−	0.604478i	$-0.206618\pi$
$480$		0			0
$481$	12.4458			0.0258749
$482$	158.798	+	218.567i	0.329457	+	0.453459i
$483$	−521.491			−1.07969
$484$	−145.577	+	448.039i	−0.300778	+	0.925700i
$485$		0			0
$486$	306.584	+	421.976i	0.630830	+	0.868264i
$487$	−626.363			−1.28617			−0.643084	−	0.765796i	$-0.722345\pi$
$487$	−626.363			−1.28617			−0.643084	+	0.765796i	$0.722345\pi$
$488$	−198.868	+	64.6161i	−0.407516	+	0.132410i
$489$	1152.13			2.35608
$490$		0			0
$491$			22.3013i			0.0454201i	0.999742	+	0.0227100i	$0.00722945\pi$
$491$			22.3013i			0.0454201i	−0.999742	+	0.0227100i	$0.992771\pi$
$492$	194.752	−	599.384i	0.395837	−	1.21826i
$493$			165.889i			0.336488i
$494$	−5.21981	−	7.18445i	−0.0105664	−	0.0145434i
$495$		0			0
$496$	446.217	−	614.165i	0.899630	−	1.23824i
$497$		−	335.279i		−	0.674605i
$498$	−94.9937	−	130.748i	−0.190750	−	0.262546i
$499$		−	627.362i		−	1.25724i	−0.777714	−	0.628619i	$-0.783621\pi$
$499$		−	627.362i		−	1.25724i	0.777714	−	0.628619i	$-0.216379\pi$
$500$		0			0
$501$	−378.079			−0.754649
$502$	−357.859	+	260.000i	−0.712867	+	0.517928i
$503$	780.853			1.55239			0.776196	−	0.630492i	$-0.217147\pi$
$503$	780.853			1.55239			0.776196	+	0.630492i	$0.217147\pi$
$504$	354.164	−	115.075i	0.702707	−	0.228323i
$505$		0			0
$506$	−46.8328	+	34.0260i	−0.0925550	+	0.0672451i
$507$	642.066			1.26640
$508$	−2.28198	+	7.02321i	−0.00449208	+	0.0138252i
$509$	288.950			0.567683			0.283841	−	0.958871i	$-0.408391\pi$
$509$	288.950			0.567683			0.283841	+	0.958871i	$0.408391\pi$
$510$		0			0
$511$		−	1170.11i		−	2.28984i
$512$	300.946	−	414.217i	0.587785	−	0.809017i
$513$		−	126.217i		−	0.246036i
$514$	−415.925	+	302.187i	−0.809192	+	0.587913i
$515$		0			0
$516$	9.44272	−	29.0617i	0.0182998	−	0.0563211i
$517$			63.4891i			0.122803i
$518$	362.824	−	263.607i	0.700432	−	0.508893i
$519$			690.997i			1.33140i
$520$		0			0
$521$	−602.984			−1.15736			−0.578680	−	0.815555i	$-0.696432\pi$
$521$	−602.984			−1.15736			−0.578680	+	0.815555i	$0.696432\pi$
$522$	44.6717	+	61.4853i	0.0855779	+	0.117788i
$523$	367.962			0.703560			0.351780	−	0.936083i	$-0.385577\pi$
$523$	367.962			0.703560			0.351780	+	0.936083i	$0.385577\pi$
$524$	−858.269	−	278.869i	−1.63792	−	0.532192i
$525$		0			0
$526$	192.991	+	265.629i	0.366902	+	0.504998i
$527$	1133.44			2.15073
$528$	64.2597	−	88.4458i	0.121704	−	0.167511i
$529$	−269.308			−0.509089
$530$		0			0
$531$		−	404.196i		−	0.761198i
$532$	−304.338	−	98.8854i	−0.572064	−	0.185875i
$533$			19.5542i			0.0366870i
$534$	301.613	+	415.135i	0.564818	+	0.777406i
$535$		0			0
$536$	−676.158	+	219.697i	−1.26149	+	0.409882i
$537$			992.551i			1.84833i
$538$	−41.7036	−	57.4001i	−0.0775161	−	0.106692i
$539$			41.9584i			0.0778449i
$540$		0			0
$541$	−616.885			−1.14027			−0.570134	−	0.821551i	$-0.693109\pi$
$541$	−616.885			−1.14027			−0.570134	+	0.821551i	$0.693109\pi$
$542$	483.711	−	351.437i	0.892455	−	0.648407i
$543$	600.220			1.10538
$544$	764.433			1.40521
$545$		0			0
$546$	−24.7214	+	17.9611i	−0.0452772	+	0.0328958i
$547$	97.8499			0.178885			0.0894423	−	0.995992i	$-0.471492\pi$
$547$	97.8499			0.178885			0.0894423	+	0.995992i	$0.471492\pi$
$548$	200.988	+	65.3050i	0.366766	+	0.119170i
$549$	−143.029			−0.260527
$550$		0			0
$551$		−	65.3078i		−	0.118526i
$552$	−466.436	+	151.554i	−0.844992	+	0.274555i
$553$			967.214i			1.74903i
$554$	−739.840	+	537.525i	−1.33545	+	0.970262i
$555$		0			0
$556$	−478.768	−	155.561i	−0.861093	−	0.279786i
$557$			896.302i			1.60916i	0.593845	+	0.804580i	$0.297609\pi$
$557$			896.302i			1.60916i	−0.593845	+	0.804580i	$0.702391\pi$
$558$	420.099	−	305.220i	0.752866	−	0.546989i
$559$			0.948103i			0.00169607i
$560$		0			0
$561$	163.226			0.290955
$562$	6.62942	+	9.12461i	0.0117961	+	0.0162360i
$563$	771.186			1.36978			0.684890	−	0.728647i	$-0.259850\pi$
$563$	771.186			1.36978			0.684890	+	0.728647i	$0.259850\pi$
$564$	−166.217	+	511.562i	−0.294710	+	0.907026i
$565$		0			0
$566$	199.751	+	274.933i	0.352917	+	0.485748i
$567$	−853.245			−1.50484
$568$	−97.4377	−	299.882i	−0.171545	−	0.527962i
$569$	−8.74767			−0.0153738			−0.00768688	−	0.999970i	$-0.502447\pi$
$569$	−8.74767			−0.0153738			−0.00768688	+	0.999970i	$0.502447\pi$
$570$		0			0
$571$			511.138i			0.895164i	0.894243	+	0.447582i	$0.147715\pi$
$571$			511.138i			0.895164i	−0.894243	+	0.447582i	$0.852285\pi$
$572$	−1.04820	+	3.22602i	−0.00183251	+	0.00563989i
$573$		−	1232.93i		−	2.15171i
$574$	414.164	+	570.048i	0.721540	+	0.993115i
$575$		0			0
$576$	283.331	−	205.852i	0.491895	−	0.357382i
$577$		−	713.712i		−	1.23694i	−0.785810	−	0.618468i	$-0.787754\pi$
$577$		−	713.712i		−	1.23694i	0.785810	−	0.618468i	$-0.212246\pi$
$578$	331.114	+	455.740i	0.572862	+	0.788477i
$579$		−	691.521i		−	1.19434i
$580$		0			0
$581$	180.689			0.310996
$582$	−241.088	+	175.161i	−0.414241	+	0.300964i
$583$	−38.8666			−0.0666666
$584$	−340.053	−	1046.57i	−0.582282	−	1.79208i
$585$		0			0
$586$	43.4590	−	31.5748i	0.0741621	−	0.0538819i
$587$	422.169			0.719198			0.359599	−	0.933107i	$-0.382914\pi$
$587$	422.169			0.719198			0.359599	+	0.933107i	$0.382914\pi$
$588$	−109.849	+	338.079i	−0.186817	+	0.574964i
$589$	−446.217			−0.757584
$590$		0			0
$591$			534.588i			0.904548i
$592$	247.911	−	341.220i	0.418768	−	0.576385i
$593$			308.663i			0.520510i	0.965540	+	0.260255i	$0.0838067\pi$
$593$			308.663i			0.520510i	−0.965540	+	0.260255i	$0.916193\pi$
$594$	−39.0031	+	28.3374i	−0.0656618	+	0.0477061i
$595$		0			0
$596$	164.361	−	505.850i	0.275773	−	0.848742i
$597$		−	640.000i		−	1.07203i
$598$	12.3107	−	8.94427i	0.0205865	−	0.0149570i
$599$			462.196i			0.771612i	0.922580	+	0.385806i	$0.126077\pi$
$599$			462.196i			0.771612i	−0.922580	+	0.385806i	$0.873923\pi$
$600$		0			0
$601$	355.358			0.591277			0.295639	−	0.955300i	$-0.404468\pi$
$601$	355.358			0.591277			0.295639	+	0.955300i	$0.404468\pi$
$602$	20.0811	+	27.6393i	0.0333574	+	0.0459125i
$603$	−486.305			−0.806476
$604$	575.279	+	186.919i	0.952448	+	0.309469i
$605$		0			0
$606$	−446.715	−	614.851i	−0.737154	−	1.01461i
$607$	−630.403			−1.03856			−0.519278	−	0.854605i	$-0.673799\pi$
$607$	−630.403			−1.03856			−0.519278	+	0.854605i	$0.673799\pi$
$608$	−300.946			−0.494977
$609$	−224.721			−0.369001
$610$		0			0
$611$		−	16.6891i		−	0.0273144i
$612$	497.294	+	161.580i	0.812571	+	0.264020i
$613$		−	812.525i		−	1.32549i	−0.748846	−	0.662745i	$-0.769392\pi$
$613$		−	812.525i		−	1.32549i	0.748846	−	0.662745i	$-0.230608\pi$
$614$	−138.754	−	190.978i	−0.225984	−	0.311040i
$615$		0			0
$616$	37.7709	+	116.247i	0.0613164	+	0.188712i
$617$		−	437.935i		−	0.709781i	−0.934908	−	0.354891i	$-0.884518\pi$
$617$		−	437.935i		−	0.709781i	0.934908	−	0.354891i	$-0.115482\pi$
$618$	159.978	+	220.190i	0.258864	+	0.356295i
$619$			770.250i			1.24435i	0.782880	+	0.622173i	$0.213750\pi$
$619$			770.250i			1.24435i	−0.782880	+	0.622173i	$0.786250\pi$
$620$		0			0
$621$	216.276			0.348270
$622$	197.134	−	143.226i	0.316935	−	0.230267i
$623$	−573.702			−0.920870
$624$	−16.8916	+	23.2494i	−0.0270700	+	0.0372586i
$625$		0			0
$626$	−355.236	+	258.094i	−0.567470	+	0.412291i
$627$	−64.2597			−0.102487
$628$	139.796	+	45.4226i	0.222606	+	0.0723290i
$629$	629.718			1.00114
$630$		0			0
$631$		−	875.496i		−	1.38747i	−0.720228	−	0.693737i	$-0.755963\pi$
$631$		−	875.496i		−	1.38747i	0.720228	−	0.693737i	$-0.244037\pi$
$632$	281.089	+	865.102i	0.444761	+	1.36883i
$633$			357.390i			0.564597i
$634$	593.591	−	431.269i	0.936263	−	0.680235i
$635$		0			0
$636$	−313.167	−	101.754i	−0.492401	−	0.159991i
$637$		−	11.0294i		−	0.0173146i
$638$	−20.1812	+	14.6625i	−0.0316320	+	0.0229820i
$639$		−	215.681i		−	0.337529i
$640$		0			0
$641$	842.571			1.31446			0.657232	−	0.753689i	$-0.271727\pi$
$641$	842.571			1.31446			0.657232	+	0.753689i	$0.271727\pi$
$642$	−541.572	−	745.410i	−0.843570	−	1.16108i
$643$	−1153.20			−1.79348			−0.896738	−	0.442563i	$-0.854069\pi$
$643$	−1153.20			−1.79348			−0.896738	+	0.442563i	$0.854069\pi$
$644$	169.443	−	521.491i	0.263110	−	0.809769i
$645$		0			0
$646$	−264.105	−	363.510i	−0.408832	−	0.562708i
$647$	355.751			0.549847			0.274924	−	0.961466i	$-0.411347\pi$
$647$	355.751			0.549847			0.274924	+	0.961466i	$0.411347\pi$
$648$	−763.165	+	247.967i	−1.17772	+	0.382666i
$649$	132.669			0.204420
$650$		0			0
$651$			1535.41i			2.35854i
$652$	−374.348	+	1152.13i	−0.574154	+	1.76706i
$653$			557.915i			0.854387i	0.904160	+	0.427194i	$0.140498\pi$
$653$			557.915i			0.854387i	−0.904160	+	0.427194i	$0.859502\pi$
$654$	−883.108	−	1215.49i	−1.35032	−	1.85855i
$655$		0			0
$656$	536.105	+	389.503i	0.817234	+	0.593755i
$657$		−	752.715i		−	1.14569i
$658$	−353.481	−	486.525i	−0.537205	−	0.739399i
$659$		−	284.157i		−	0.431194i	−0.976482	−	0.215597i	$-0.930830\pi$
$659$		−	284.157i		−	0.431194i	0.976482	−	0.215597i	$-0.0691697\pi$
$660$		0			0
$661$	716.735			1.08432			0.542160	−	0.840275i	$-0.317607\pi$
$661$	716.735			1.08432			0.542160	+	0.840275i	$0.317607\pi$
$662$	−263.490	+	191.437i	−0.398021	+	0.289179i
$663$	−42.9065			−0.0647157
$664$	161.613	−	52.5112i	0.243393	−	0.0790832i
$665$		0			0
$666$	233.400	−	169.575i	0.350451	−	0.254617i
$667$	111.907			0.167776
$668$	122.845	−	378.079i	0.183900	−	0.565986i
$669$	814.237			1.21710
$670$		0			0
$671$		−	46.9464i		−	0.0699648i
$672$			1035.54i			1.54098i
$673$			695.378i			1.03325i	0.856212	+	0.516625i	$0.172812\pi$
$673$			695.378i			1.03325i	−0.856212	+	0.516625i	$0.827188\pi$
$674$	27.6819	−	20.1121i	0.0410711	−	0.0298399i
$675$		0			0
$676$	−208.620	+	642.066i	−0.308609	+	0.949802i
$677$		−	820.237i		−	1.21158i	−0.795626	−	0.605788i	$-0.792858\pi$
$677$		−	820.237i		−	1.21158i	0.795626	−	0.605788i	$-0.207142\pi$
$678$	−500.300	+	363.489i	−0.737905	+	0.536120i
$679$		−	333.176i		−	0.490686i
$680$		0			0
$681$	157.580			0.231396
$682$	100.182	+	137.889i	0.146894	+	0.202183i
$683$	335.508			0.491227			0.245613	−	0.969368i	$-0.421011\pi$
$683$	335.508			0.491227			0.245613	+	0.969368i	$0.421011\pi$
$684$	−195.777	−	63.6118i	−0.286224	−	0.0929998i
$685$		0			0
$686$	256.393	+	352.895i	0.373751	+	0.514424i
$687$	−278.769			−0.405777
$688$	25.9936	+	18.8854i	0.0377814	+	0.0274498i
$689$	10.2167			0.0148283
$690$		0			0
$691$			336.568i			0.487074i	0.969892	+	0.243537i	$0.0783077\pi$
$691$			336.568i			0.487074i	−0.969892	+	0.243537i	$0.921692\pi$
$692$	−690.997	−	224.519i	−0.998551	−	0.324449i
$693$			83.6068i			0.120645i
$694$	196.906	+	271.017i	0.283726	+	0.390515i
$695$		0			0
$696$	−200.997	+	65.3078i	−0.288789	+	0.0938331i
$697$			989.378i			1.41948i
$698$	−568.383	−	782.312i	−0.814302	−	1.12079i
$699$			1168.09i			1.67108i
$700$		0			0
$701$	−429.364			−0.612502			−0.306251	−	0.951951i	$-0.599075\pi$
$701$	−429.364			−0.612502			−0.306251	+	0.951951i	$0.599075\pi$
$702$	10.2526	−	7.44893i	0.0146048	−	0.0106110i
$703$	−247.911			−0.352647
$704$	67.5666	+	92.9974i	0.0959753	+	0.132099i
$705$		0			0
$706$	−498.344	+	362.068i	−0.705870	+	0.512845i
$707$	849.703			1.20184
$708$	1068.98	+	347.331i	1.50985	+	0.490581i
$709$	−1224.60			−1.72722			−0.863609	−	0.504162i	$-0.831801\pi$
$709$	−1224.60			−1.72722			−0.863609	+	0.504162i	$0.831801\pi$
$710$		0			0
$711$			622.197i			0.875101i
$712$	−513.135	+	166.728i	−0.720695	+	0.234168i
$713$		−	764.604i		−	1.07238i
$714$	−1250.82	+	908.774i	−1.75185	+	1.27279i
$715$		0			0
$716$	−992.551	−	322.499i	−1.38624	−	0.450418i
$717$			163.226i			0.227651i
$718$	37.6183	−	27.3313i	0.0523931	−	0.0380658i
$719$		−	496.022i		−	0.689877i	−0.938625	−	0.344939i	$-0.887900\pi$
$719$		−	496.022i		−	0.689877i	0.938625	−	0.344939i	$-0.112100\pi$
$720$		0			0
$721$	−304.296			−0.422047
$722$	−320.407	−	441.002i	−0.443777	−	0.610806i
$723$	−513.883			−0.710764
$724$	−195.023	+	600.220i	−0.269369	+	0.829033i
$725$		0			0
$726$	−526.701	−	724.942i	−0.725484	−	0.998543i
$727$	152.843			0.210238			0.105119	−	0.994460i	$-0.466478\pi$
$727$	152.843			0.210238			0.105119	+	0.994460i	$0.466478\pi$
$728$	−9.92866	−	30.5573i	−0.0136383	−	0.0419743i
$729$	−89.3808			−0.122607
$730$		0			0
$731$			47.9709i			0.0656237i
$732$	122.907	−	378.269i	0.167906	−	0.516761i
$733$			761.286i			1.03859i	0.854595	+	0.519295i	$0.173805\pi$
$733$			761.286i			1.03859i	−0.854595	+	0.519295i	$0.826195\pi$
$734$	−608.152	−	837.049i	−0.828544	−	1.14039i
$735$		0			0
$736$		−	515.679i		−	0.700650i
$737$		−	159.619i		−	0.216580i
$738$	266.427	+	366.705i	0.361012	+	0.496890i
$739$			183.975i			0.248951i	0.992223	+	0.124476i	$0.0397249\pi$
$739$			183.975i			0.248951i	−0.992223	+	0.124476i	$0.960275\pi$
$740$		0			0
$741$	16.8916			0.0227957
$742$	297.840	−	216.393i	0.401401	−	0.291635i
$743$	495.247			0.666551			0.333275	−	0.942830i	$-0.391846\pi$
$743$	495.247			0.666551			0.333275	+	0.942830i	$0.391846\pi$
$744$	446.217	+	1373.31i	0.599754	+	1.84585i
$745$		0			0
$746$	142.961	−	103.867i	0.191636	−	0.139232i
$747$	116.235			0.155602
$748$	−53.0353	+	163.226i	−0.0709029	+	0.218217i
$749$	1030.13			1.37534
$750$		0			0
$751$			800.059i			1.06533i	0.846328	+	0.532663i	$0.178809\pi$
$751$			800.059i			1.06533i	−0.846328	+	0.532663i	$0.821191\pi$
$752$	−457.555	−	332.433i	−0.608451	−	0.442066i
$753$		−	841.378i		−	1.11737i
$754$	5.30495	−	3.85427i	0.00703574	−	0.00511177i
$755$		0			0
$756$	141.115	−	434.306i	0.186659	−	0.574479i
$757$		−	276.367i		−	0.365082i	−0.983198	−	0.182541i	$-0.941568\pi$
$757$		−	276.367i		−	0.365082i	0.983198	−	0.182541i	$-0.0584322\pi$
$758$	−31.2818	+	22.7276i	−0.0412689	+	0.0299836i
$759$		−	110.111i		−	0.145073i
$760$		0			0
$761$	891.207			1.17110			0.585550	−	0.810636i	$-0.300879\pi$
$761$	891.207			1.17110			0.585550	+	0.810636i	$0.300879\pi$
$762$	−8.25627	−	11.3638i	−0.0108350	−	0.0149131i
$763$	1679.77			2.20154
$764$	1232.93	+	400.604i	1.61379	+	0.524351i
$765$		0			0
$766$	507.390	+	698.363i	0.662389	+	0.911700i
$767$	−34.8740			−0.0454681
$768$	300.946	+	926.217i	0.391857	+	1.20601i
$769$	835.430			1.08639			0.543193	−	0.839608i	$-0.317215\pi$
$769$	835.430			1.08639			0.543193	+	0.839608i	$0.317215\pi$
$770$		0			0
$771$		−	977.898i		−	1.26835i
$772$	691.521	+	224.689i	0.895753	+	0.291048i
$773$		−	213.522i		−	0.276225i	−0.990417	−	0.138112i	$-0.955897\pi$
$773$		−	213.522i		−	0.276225i	0.990417	−	0.138112i	$-0.0441035\pi$
$774$	12.9180	+	17.7800i	0.0166899	+	0.0229716i
$775$		0			0
$776$	−96.8266	−	298.002i	−0.124777	−	0.384023i
$777$			853.050i			1.09788i
$778$	−348.386	−	479.512i	−0.447796	−	0.616339i
$779$		−	389.503i		−	0.500004i
$780$		0			0
$781$	70.7926			0.0906436
$782$	622.883	−	452.551i	0.796526	−	0.578710i
$783$	93.1976			0.119026
$784$	−302.387	−	219.697i	−0.385698	−	0.280226i
$785$		0			0
$786$	1388.71	−	1008.96i	1.76681	−	1.28366i
$787$	370.182			0.470371			0.235185	−	0.971951i	$-0.424430\pi$
$787$	370.182			0.470371			0.235185	+	0.971951i	$0.424430\pi$
$788$	−534.588	−	173.698i	−0.678411	−	0.220429i
$789$	−624.531			−0.791547
$790$		0			0
$791$		−	691.397i		−	0.874080i
$792$	24.2976	+	74.7802i	0.0306787	+	0.0944194i
$793$			12.3406i			0.0155619i
$794$	−139.459	+	101.323i	−0.175641	+	0.127611i
$795$		0			0
$796$	640.000	+	207.949i	0.804020	+	0.261242i
$797$			274.426i			0.344323i	0.985069	+	0.172162i	$0.0550752\pi$
$797$			274.426i			0.344323i	−0.985069	+	0.172162i	$0.944925\pi$
$798$	492.429	−	357.771i	0.617079	−	0.448334i
$799$		−	844.414i		−	1.05684i
$800$		0			0
$801$	−369.056			−0.460744
$802$	−520.774	−	716.784i	−0.649344	−	0.893746i
$803$	247.063			0.307675
$804$	417.889	−	1286.13i	0.519762	−	1.59966i
$805$		0			0
$806$	−26.3344	−	36.2461i	−0.0326729	−	0.0449704i
$807$	134.956			0.167232
$808$	759.997	−	246.938i	0.940591	−	0.305616i
$809$	−665.214			−0.822266			−0.411133	−	0.911575i	$-0.634867\pi$
$809$	−665.214			−0.822266			−0.411133	+	0.911575i	$0.634867\pi$
$810$		0			0
$811$		−	360.665i		−	0.444717i	−0.974965	−	0.222358i	$-0.928624\pi$
$811$		−	360.665i		−	0.444717i	0.974965	−	0.222358i	$-0.0713755\pi$
$812$	73.0164	−	224.721i	0.0899217	−	0.276750i
$813$			1137.27i			1.39886i
$814$	55.6594	+	76.6086i	0.0683777	+	0.0941138i
$815$		0			0
$816$	−854.663	+	1176.34i	−1.04738	+	1.44160i
$817$		−	18.8854i		−	0.0231156i
$818$	74.5432	+	102.600i	0.0911286	+	0.125428i
$819$		−	21.9773i		−	0.0268344i
$820$		0			0
$821$	−666.899			−0.812301			−0.406151	−	0.913806i	$-0.633129\pi$
$821$	−666.899			−0.812301			−0.406151	+	0.913806i	$0.633129\pi$
$822$	−325.205	+	236.276i	−0.395627	+	0.287440i
$823$	−122.433			−0.148764			−0.0743822	−	0.997230i	$-0.523698\pi$
$823$	−122.433			−0.148764			−0.0743822	+	0.997230i	$0.523698\pi$
$824$	−272.170	+	88.4335i	−0.330304	+	0.107322i
$825$		0			0
$826$	−1016.66	+	738.644i	−1.23082	+	0.894242i
$827$	−1532.98			−1.85366			−0.926832	−	0.375477i	$-0.877479\pi$
$827$	−1532.98			−1.85366			−0.926832	+	0.375477i	$0.877479\pi$
$828$	109.000	−	335.469i	0.131643	−	0.405156i
$829$	195.475			0.235796			0.117898	−	0.993026i	$-0.462384\pi$
$829$	195.475			0.235796			0.117898	+	0.993026i	$0.462384\pi$
$830$		0			0
$831$		−	1739.47i		−	2.09322i
$832$	−17.7609	−	24.4458i	−0.0213473	−	0.0293820i
$833$		−	558.053i		−	0.669931i
$834$	774.663	−	562.825i	0.928852	−	0.674850i
$835$		0			0
$836$	20.8792	−	64.2597i	0.0249752	−	0.0768656i
$837$		−	636.774i		−	0.760781i
$838$	704.942	−	512.170i	0.841219	−	0.611182i
$839$			1325.97i			1.58041i	0.612840	+	0.790207i	$0.290027\pi$
$839$			1325.97i			1.58041i	−0.612840	+	0.790207i	$0.709973\pi$
$840$		0			0
$841$	−792.777			−0.942660
$842$	685.254	+	943.171i	0.813841	+	1.12016i
$843$	−21.4532			−0.0254487
$844$	−357.390	−	116.123i	−0.423448	−	0.137587i
$845$		0			0
$846$	−227.390	−	312.976i	−0.268783	−	0.369948i
$847$	1001.85			1.18282
$848$	203.508	−	280.105i	0.239986	−	0.330313i
$849$	−646.407			−0.761375
$850$		0			0
$851$		−	424.801i		−	0.499179i
$852$	570.410	+	185.337i	0.669495	+	0.217532i
$853$		−	1055.28i		−	1.23714i	−0.785730	−	0.618570i	$-0.787712\pi$
$853$		−	1055.28i		−	1.23714i	0.785730	−	0.618570i	$-0.212288\pi$
$854$	261.378	+	359.756i	0.306063	+	0.421259i
$855$		0			0
$856$	921.378	−	299.374i	1.07638	−	0.349736i
$857$			155.378i			0.181304i	0.995883	+	0.0906521i	$0.0288951\pi$
$857$			155.378i			0.181304i	−0.995883	+	0.0906521i	$0.971105\pi$
$858$	−3.79241	−	5.21981i	−0.00442006	−	0.00608369i
$859$		−	226.033i		−	0.263136i	−0.991307	−	0.131568i	$-0.957999\pi$
$859$		−	226.033i		−	0.263136i	0.991307	−	0.131568i	$-0.0420011\pi$
$860$		0			0
$861$	−1340.26			−1.55664
$862$	608.190	−	441.876i	0.705557	−	0.512617i
$863$	−930.702			−1.07845			−0.539225	−	0.842162i	$-0.681283\pi$
$863$	−930.702			−1.07845			−0.539225	+	0.842162i	$0.681283\pi$
$864$		−	429.465i		−	0.497066i
$865$		0			0
$866$	595.702	−	432.803i	0.687878	−	0.499772i
$867$	−1071.51			−1.23588
$868$	−1535.41	−	498.885i	−1.76891	−	0.574753i
$869$	−204.223			−0.235009
$870$		0			0
$871$			41.9584i			0.0481727i
$872$	1502.43	−	488.170i	1.72297	−	0.559828i
$873$		−	214.328i		−	0.245508i
$874$	−245.220	+	178.163i	−0.280572	+	0.203847i
$875$		0			0
$876$	1990.70	+	646.819i	2.27249	+	0.738377i
$877$		−	33.5217i		−	0.0382231i	−0.999817	−	0.0191115i	$-0.993916\pi$
$877$		−	33.5217i		−	0.0382231i	0.999817	−	0.0191115i	$-0.00608376\pi$
$878$	−782.399	+	568.446i	−0.891115	+	0.647433i
$879$			102.178i			0.116244i
$880$		0			0
$881$	−933.850			−1.05999			−0.529994	−	0.848001i	$-0.677806\pi$
$881$	−933.850			−1.05999			−0.529994	+	0.848001i	$0.677806\pi$
$882$	−150.276	−	206.838i	−0.170382	−	0.234510i
$883$	−542.308			−0.614166			−0.307083	−	0.951683i	$-0.599353\pi$
$883$	−542.308			−0.614166			−0.307083	+	0.951683i	$0.599353\pi$
$884$	13.9412	−	42.9065i	0.0157706	−	0.0485368i
$885$		0			0
$886$	328.197	+	451.724i	0.370425	+	0.509846i
$887$	−714.720			−0.805773			−0.402886	−	0.915250i	$-0.631993\pi$
$887$	−714.720			−0.805773			−0.402886	+	0.915250i	$0.631993\pi$
$888$	247.911	+	762.991i	0.279179	+	0.859224i
$889$	15.7044			0.0176652
$890$		0			0
$891$		−	180.159i		−	0.202199i
$892$	−264.562	+	814.237i	−0.296594	+	0.912822i
$893$			332.433i			0.372266i
$894$	594.663	+	818.483i	0.665171	+	0.915529i
$895$		0			0
$896$	−1035.54	−	336.468i	−1.15574	−	0.375522i
$897$			28.9443i			0.0322679i
$898$	888.824	+	1223.36i	0.989782	+	1.36232i
$899$		−	329.484i		−	0.366500i
$900$		0			0
$901$	516.932			0.573731
$902$	−120.363	+	87.4489i	−0.133440	+	0.0969500i
$903$	−64.9839			−0.0719645
$904$	−200.932	−	618.405i	−0.222270	−	0.684076i
$905$		0			0
$906$	−930.820	+	676.281i	−1.02740	+	0.746447i
$907$	−347.233			−0.382837			−0.191418	−	0.981509i	$-0.561309\pi$
$907$	−347.233			−0.382837			−0.191418	+	0.981509i	$0.561309\pi$
$908$	−51.2010	+	157.580i	−0.0563888	+	0.173547i
$909$	546.604			0.601324
$910$		0			0
$911$			1427.54i			1.56701i	0.621386	+	0.783504i	$0.286570\pi$
$911$			1427.54i			1.56701i	−0.621386	+	0.783504i	$0.713430\pi$
$912$	336.468	−	463.108i	0.368934	−	0.507794i
$913$			38.1517i			0.0417871i
$914$	462.227	−	335.827i	0.505719	−	0.367426i
$915$		0			0
$916$	90.5774	−	278.769i	0.0988836	−	0.304332i
$917$			1919.15i			2.09286i
$918$	518.747	−	376.892i	0.565084	−	0.410557i
$919$			569.162i			0.619327i	0.950846	+	0.309664i	$0.100216\pi$
$919$			569.162i			0.619327i	−0.950846	+	0.309664i	$0.899784\pi$
$920$		0			0
$921$	449.017			0.487532
$922$	116.516	+	160.371i	0.126373	+	0.173938i
$923$	−18.6089			−0.0201614
$924$	−221.115	−	71.8445i	−0.239301	−	0.0777538i
$925$		0			0
$926$	741.319	+	1020.34i	0.800560	+	1.10188i
$927$	−195.750			−0.211165
$928$		−	222.217i		−	0.239458i
$929$	−1535.96			−1.65335			−0.826675	−	0.562680i	$-0.809770\pi$
$929$	−1535.96			−1.65335			−0.826675	+	0.562680i	$0.809770\pi$
$930$		0			0
$931$			219.697i			0.235980i
$932$	−1168.09	−	379.534i	−1.25331	−	0.407225i
$933$			463.489i			0.496773i
$934$	583.094	+	802.561i	0.624298	+	0.859273i
$935$		0			0
$936$	−6.38699	−	19.6571i	−0.00682371	−	0.0210012i
$937$			338.721i			0.361496i	0.983529	+	0.180748i	$0.0578518\pi$
$937$			338.721i			0.361496i	−0.983529	+	0.180748i	$0.942148\pi$
$938$	888.693	+	1223.18i	0.947434	+	1.30403i
$939$		−	835.210i		−	0.889468i
$940$		0			0
$941$	1439.77			1.53004			0.765022	−	0.644004i	$-0.222728\pi$
$941$	1439.77			1.53004			0.765022	+	0.644004i	$0.222728\pi$
$942$	−226.195	+	164.341i	−0.240123	+	0.174459i
$943$	667.424			0.707766
$944$	−694.663	+	956.121i	−0.735871	+	1.01284i
$945$		0			0
$946$	−5.83592	+	4.24005i	−0.00616905	+	0.00448208i
$947$	−656.135			−0.692856			−0.346428	−	0.938077i	$-0.612606\pi$
$947$	−656.135			−0.692856			−0.346428	+	0.938077i	$0.612606\pi$
$948$	−1645.52	−	534.663i	−1.73578	−	0.563990i
$949$	−64.9443			−0.0684344
$950$		0			0
$951$			1395.62i			1.46752i
$952$	−502.358	−	1546.10i	−0.527687	−	1.62405i
$953$		−	436.675i		−	0.458211i	−0.973402	−	0.229105i	$-0.926420\pi$
$953$		−	436.675i		−	0.458211i	0.973402	−	0.229105i	$-0.0735801\pi$
$954$	191.597	−	139.203i	0.200835	−	0.145915i
$955$		0			0
$956$	−163.226	−	53.0353i	−0.170739	−	0.0554763i
$957$		−	47.4489i		−	0.0495809i
$958$	−936.988	+	680.762i	−0.978067	+	0.710607i
$959$		−	449.423i		−	0.468637i
$960$		0			0
$961$	−1290.20			−1.34256
$962$	−14.6309	−	20.1378i	−0.0152089	−	0.0209332i
$963$	662.671			0.688132
$964$	166.971	−	513.883i	0.173206	−	0.533073i
$965$		0			0
$966$	613.050	+	843.790i	0.634627	+	0.873489i
$967$	903.436			0.934267			0.467133	−	0.884187i	$-0.345287\pi$
$967$	903.436			0.934267			0.467133	+	0.884187i	$0.345287\pi$
$968$	896.078	−	291.153i	0.925700	−	0.300778i
$969$	854.663			0.882005
$970$		0			0
$971$		−	1866.89i		−	1.92265i	−0.275420	−	0.961324i	$-0.588817\pi$
$971$		−	1866.89i		−	1.92265i	0.275420	−	0.961324i	$-0.411183\pi$
$972$	322.361	−	992.125i	0.331647	−	1.02071i
$973$			1070.56i			1.10026i
$974$	736.334	+	1013.48i	0.755990	+	1.04053i
$975$		0			0
$976$	338.334	+	245.814i	0.346654	+	0.251859i
$977$		−	1073.95i		−	1.09923i	−0.835418	−	0.549615i	$-0.814774\pi$
$977$		−	1073.95i		−	1.09923i	0.835418	−	0.549615i	$-0.185226\pi$
$978$	−1354.40	−	1864.18i	−1.38487	−	1.90611i
$979$		−	121.135i		−	0.123733i
$980$		0			0
$981$	1080.58			1.10151
$982$	36.0842	−	26.2167i	0.0367456	−	0.0266973i
$983$	534.114			0.543351			0.271675	−	0.962389i	$-0.412422\pi$
$983$	534.114			0.543351			0.271675	+	0.962389i	$0.412422\pi$
$984$	−1198.77	+	389.503i	−1.21826	+	0.395837i
$985$		0			0
$986$	268.413	−	195.014i	0.272224	−	0.197783i
$987$	1143.89			1.15895
$988$	−5.48843	+	16.8916i	−0.00555509	+	0.0170968i
$989$	32.3607			0.0327206
$990$		0			0
$991$			520.419i			0.525146i	0.964912	+	0.262573i	$0.0845710\pi$
$991$			520.419i			0.525146i	−0.964912	+	0.262573i	$0.915429\pi$
$992$	−1518.30			−1.53054
$993$		−	619.502i		−	0.623869i
$994$	−542.492	+	394.144i	−0.545767	+	0.396523i
$995$		0			0
$996$	−99.8823	+	307.406i	−0.100283	+	0.308641i
$997$			457.680i			0.459057i	0.973302	+	0.229528i	$0.0737184\pi$
$997$			457.680i			0.459057i	−0.973302	+	0.229528i	$0.926282\pi$
$998$	−1015.09	+	737.508i	−1.01713	+	0.738986i
$999$		−	353.781i		−	0.354135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.3.d.b.99.3		8
3.2	odd	2		900.3.f.e.199.6		8
4.3	odd	2	inner	100.3.d.b.99.5		8
5.2	odd	4		100.3.b.f.51.3		4
5.3	odd	4		20.3.b.a.11.2	yes	4
5.4	even	2	inner	100.3.d.b.99.6		8
8.3	odd	2		1600.3.h.n.1599.8		8
8.5	even	2		1600.3.h.n.1599.1		8
12.11	even	2		900.3.f.e.199.4		8
15.2	even	4		900.3.c.k.451.2		4
15.8	even	4		180.3.c.a.91.3		4
15.14	odd	2		900.3.f.e.199.3		8
20.3	even	4		20.3.b.a.11.1	✓	4
20.7	even	4		100.3.b.f.51.4		4
20.19	odd	2	inner	100.3.d.b.99.4		8
40.3	even	4		320.3.b.c.191.4		4
40.13	odd	4		320.3.b.c.191.1		4
40.19	odd	2		1600.3.h.n.1599.2		8
40.27	even	4		1600.3.b.s.1151.1		4
40.29	even	2		1600.3.h.n.1599.7		8
40.37	odd	4		1600.3.b.s.1151.4		4
60.23	odd	4		180.3.c.a.91.4		4
60.47	odd	4		900.3.c.k.451.1		4
60.59	even	2		900.3.f.e.199.5		8
80.3	even	4		1280.3.g.e.1151.7		8
80.13	odd	4		1280.3.g.e.1151.1		8
80.43	even	4		1280.3.g.e.1151.2		8
80.53	odd	4		1280.3.g.e.1151.8		8
120.53	even	4		2880.3.e.e.2431.3		4
120.83	odd	4		2880.3.e.e.2431.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.b.a.11.1	✓	4	20.3	even	4
20.3.b.a.11.2	yes	4	5.3	odd	4
100.3.b.f.51.3		4	5.2	odd	4
100.3.b.f.51.4		4	20.7	even	4
100.3.d.b.99.3		8	1.1	even	1	trivial
100.3.d.b.99.4		8	20.19	odd	2	inner
100.3.d.b.99.5		8	4.3	odd	2	inner
100.3.d.b.99.6		8	5.4	even	2	inner
180.3.c.a.91.3		4	15.8	even	4
180.3.c.a.91.4		4	60.23	odd	4
320.3.b.c.191.1		4	40.13	odd	4
320.3.b.c.191.4		4	40.3	even	4
900.3.c.k.451.1		4	60.47	odd	4
900.3.c.k.451.2		4	15.2	even	4
900.3.f.e.199.3		8	15.14	odd	2
900.3.f.e.199.4		8	12.11	even	2
900.3.f.e.199.5		8	60.59	even	2
900.3.f.e.199.6		8	3.2	odd	2
1280.3.g.e.1151.1		8	80.13	odd	4
1280.3.g.e.1151.2		8	80.43	even	4
1280.3.g.e.1151.7		8	80.3	even	4
1280.3.g.e.1151.8		8	80.53	odd	4
1600.3.b.s.1151.1		4	40.27	even	4
1600.3.b.s.1151.4		4	40.37	odd	4
1600.3.h.n.1599.1		8	8.5	even	2
1600.3.h.n.1599.2		8	40.19	odd	2
1600.3.h.n.1599.7		8	40.29	even	2
1600.3.h.n.1599.8		8	8.3	odd	2
2880.3.e.e.2431.3		4	120.53	even	4
2880.3.e.e.2431.4		4	120.83	odd	4

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.17557 - 1.61803i) q^{2} +3.80423 q^{3} +(-1.23607 + 3.80423i) q^{4} +(-4.47214 - 6.15537i) q^{6} +8.50651 q^{7} +(7.60845 - 2.47214i) q^{8} +5.47214 q^{9} +O(q^{10})\)	\(q+(-1.17557 - 1.61803i) q^{2} +3.80423 q^{3} +(-1.23607 + 3.80423i) q^{4} +(-4.47214 - 6.15537i) q^{6} +8.50651 q^{7} +(7.60845 - 2.47214i) q^{8} +5.47214 q^{9} +1.79611i q^{11} +(-4.70228 + 14.4721i) q^{12} -0.472136i q^{13} +(-10.0000 - 13.7638i) q^{14} +(-12.9443 - 9.40456i) q^{16} -23.8885i q^{17} +(-6.43288 - 8.85410i) q^{18} +9.40456i q^{19} +32.3607 q^{21} +(2.90617 - 2.11146i) q^{22} -16.1150 q^{23} +(28.9443 - 9.40456i) q^{24} +(-0.763932 + 0.555029i) q^{26} -13.4208 q^{27} +(-10.5146 + 32.3607i) q^{28} -6.94427 q^{29} +47.4468i q^{31} +32.0000i q^{32} +6.83282i q^{33} +(-38.6525 + 28.0827i) q^{34} +(-6.76393 + 20.8172i) q^{36} +26.3607i q^{37} +(15.2169 - 11.0557i) q^{38} -1.79611i q^{39} -41.4164 q^{41} +(-38.0423 - 52.3607i) q^{42} -2.00811 q^{43} +(-6.83282 - 2.22012i) q^{44} +(18.9443 + 26.0746i) q^{46} +35.3481 q^{47} +(-49.2429 - 35.7771i) q^{48} +23.3607 q^{49} -90.8774i q^{51} +(1.79611 + 0.583592i) q^{52} +21.6393i q^{53} +(15.7771 + 21.7153i) q^{54} +(64.7214 - 21.0292i) q^{56} +35.7771i q^{57} +(8.16348 + 11.2361i) q^{58} -73.8644i q^{59} -26.1378 q^{61} +(76.7706 - 55.7771i) q^{62} +46.5488 q^{63} +(51.7771 - 37.6183i) q^{64} +(11.0557 - 8.03246i) q^{66} -88.8693 q^{67} +(90.8774 + 29.5279i) q^{68} -61.3050 q^{69} -39.4144i q^{71} +(41.6345 - 13.5279i) q^{72} -137.554i q^{73} +(42.6525 - 30.9888i) q^{74} +(-35.7771 - 11.6247i) q^{76} +15.2786i q^{77} +(-2.90617 + 2.11146i) q^{78} +113.703i q^{79} -100.305 q^{81} +(48.6879 + 67.0132i) q^{82} +21.2412 q^{83} +(-40.0000 + 123.107i) q^{84} +(2.36068 + 3.24920i) q^{86} -26.4176 q^{87} +(4.44023 + 13.6656i) q^{88} -67.4427 q^{89} -4.01623i q^{91} +(19.9192 - 61.3050i) q^{92} +180.498i q^{93} +(-41.5542 - 57.1944i) q^{94} +121.735i q^{96} -39.1672i q^{97} +(-27.4621 - 37.7984i) q^{98} +9.82857i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 + 8 * q^9	\( 8 q + 8 q^{4} + 8 q^{9} - 80 q^{14} - 32 q^{16} + 80 q^{21} + 160 q^{24} - 24 q^{26} + 16 q^{29} - 184 q^{34} - 72 q^{36} - 224 q^{41} + 160 q^{44} + 80 q^{46} + 8 q^{49} - 160 q^{54} + 160 q^{56} + 256 q^{61} + 128 q^{64} + 160 q^{66} - 240 q^{69} + 216 q^{74} - 552 q^{81} - 320 q^{84} - 160 q^{86} + 176 q^{89} + 240 q^{94}+O(q^{100}) \) 8 * q + 8 * q^4 + 8 * q^9 - 80 * q^14 - 32 * q^16 + 80 * q^21 + 160 * q^24 - 24 * q^26 + 16 * q^29 - 184 * q^34 - 72 * q^36 - 224 * q^41 + 160 * q^44 + 80 * q^46 + 8 * q^49 - 160 * q^54 + 160 * q^56 + 256 * q^61 + 128 * q^64 + 160 * q^66 - 240 * q^69 + 216 * q^74 - 552 * q^81 - 320 * q^84 - 160 * q^86 + 176 * q^89 + 240 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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