LMFDB - Embedded newform 360.4.m.c.179.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(179,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.179");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.m (of order $2$, degree $1$, 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:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.17
Character	$\chi$	$=$	360.179
Dual form			360.4.m.c.179.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15135 - 1.83622i) q^{2} +(1.25659 + 7.90069i) q^{4} +(-10.3208 + 4.29888i) q^{5} -31.9386 q^{7} +(11.8040 - 19.3045i) q^{8} +O(q^{10})$	\(q+(-2.15135 - 1.83622i) q^{2} +(1.25659 + 7.90069i) q^{4} +(-10.3208 + 4.29888i) q^{5} -31.9386 q^{7} +(11.8040 - 19.3045i) q^{8} +(30.0974 + 9.70292i) q^{10} +4.25616i q^{11} -74.7376 q^{13} +(68.7110 + 58.6462i) q^{14} +(-60.8419 + 19.8559i) q^{16} +11.4153 q^{17} -41.6766 q^{19} +(-46.9333 - 76.1398i) q^{20} +(7.81525 - 9.15648i) q^{22} -80.4383i q^{23} +(88.0392 - 88.7361i) q^{25} +(160.787 + 137.235i) q^{26} +(-40.1338 - 252.337i) q^{28} +142.612 q^{29} +293.514i q^{31} +(167.352 + 69.0022i) q^{32} +(-24.5582 - 20.9609i) q^{34} +(329.633 - 137.300i) q^{35} +80.0444 q^{37} +(89.6609 + 76.5274i) q^{38} +(-38.8396 + 249.983i) q^{40} +221.256i q^{41} -78.5904i q^{43} +(-33.6266 + 5.34827i) q^{44} +(-147.702 + 173.051i) q^{46} -319.651i q^{47} +677.073 q^{49} +(-352.342 + 29.2430i) q^{50} +(-93.9148 - 590.479i) q^{52} +234.142i q^{53} +(-18.2967 - 43.9271i) q^{55} +(-377.004 + 616.559i) q^{56} +(-306.807 - 261.866i) q^{58} -69.6092i q^{59} -390.739i q^{61} +(538.957 - 631.452i) q^{62} +(-233.329 - 455.743i) q^{64} +(771.354 - 321.288i) q^{65} +600.238i q^{67} +(14.3443 + 90.1885i) q^{68} +(-961.268 - 309.898i) q^{70} +554.269 q^{71} -491.603i q^{73} +(-172.203 - 146.979i) q^{74} +(-52.3705 - 329.274i) q^{76} -135.936i q^{77} -1140.16i q^{79} +(542.581 - 466.482i) q^{80} +(406.274 - 475.998i) q^{82} +188.475 q^{83} +(-117.815 + 49.0729i) q^{85} +(-144.309 + 169.075i) q^{86} +(82.1632 + 50.2399i) q^{88} -1298.28i q^{89} +2387.01 q^{91} +(635.518 - 101.078i) q^{92} +(-586.950 + 687.682i) q^{94} +(430.137 - 179.163i) q^{95} +547.916i q^{97} +(-1456.62 - 1243.25i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 76 q^{4}+O(q^{10}) $ 64 * q + 76 * q^4	$ 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) $ 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−2.15135	−	1.83622i	−0.760616	−	0.649202i
$2$	−2.15135	−	1.83622i	−0.760616	−	0.649202i
$3$		0			0
$3$		0			0
$4$	1.25659	+	7.90069i	0.157074	+	0.987587i
$5$	−10.3208	+	4.29888i	−0.923123	+	0.384504i
$5$	−10.3208	+	4.29888i	−0.923123	+	0.384504i
$6$		0			0
$7$	−31.9386			−1.72452			−0.862260	−	0.506465i	$-0.830952\pi$
$7$	−31.9386			−1.72452			−0.862260	+	0.506465i	$0.830952\pi$
$8$	11.8040	−	19.3045i	0.521670	−	0.853147i
$9$		0			0
$10$	30.0974	+	9.70292i	0.951763	+	0.306833i
$11$			4.25616i			0.116662i	0.998297	+	0.0583310i	$0.0185779\pi$
$11$			4.25616i			0.116662i	−0.998297	+	0.0583310i	$0.981422\pi$
$12$		0			0
$13$	−74.7376			−1.59450			−0.797249	−	0.603651i	$-0.793712\pi$
$13$	−74.7376			−1.59450			−0.797249	+	0.603651i	$0.793712\pi$
$14$	68.7110	+	58.6462i	1.31170	+	1.11956i
$15$		0			0
$16$	−60.8419	+	19.8559i	−0.950655	+	0.310249i
$17$	11.4153			0.162859			0.0814296	−	0.996679i	$-0.474051\pi$
$17$	11.4153			0.162859			0.0814296	+	0.996679i	$0.474051\pi$
$18$		0			0
$19$	−41.6766			−0.503225			−0.251612	−	0.967828i	$-0.580961\pi$
$19$	−41.6766			−0.503225			−0.251612	+	0.967828i	$0.580961\pi$
$20$	−46.9333	−	76.1398i	−0.524730	−	0.851269i
$21$		0			0
$22$	7.81525	−	9.15648i	0.0757371	−	0.0887350i
$23$		−	80.4383i		−	0.729241i	−0.931156	−	0.364620i	$-0.881199\pi$
$23$		−	80.4383i		−	0.729241i	0.931156	−	0.364620i	$-0.118801\pi$
$24$		0			0
$25$	88.0392	−	88.7361i	0.704313	−	0.709889i
$26$	160.787	+	137.235i	1.21280	+	1.03515i
$27$		0			0
$28$	−40.1338	−	252.337i	−0.270878	−	1.70311i
$29$	142.612			0.913183			0.456592	−	0.889676i	$-0.349070\pi$
$29$	142.612			0.913183			0.456592	+	0.889676i	$0.349070\pi$
$30$		0			0
$31$			293.514i			1.70054i	0.526346	+	0.850270i	$0.323562\pi$
$31$			293.514i			1.70054i	−0.526346	+	0.850270i	$0.676438\pi$
$32$	167.352	+	69.0022i	0.924498	+	0.381187i
$33$		0			0
$34$	−24.5582	−	20.9609i	−0.123873	−	0.105729i
$35$	329.633	−	137.300i	1.59195	−	0.663085i
$36$		0			0
$37$	80.0444			0.355655			0.177827	−	0.984062i	$-0.443093\pi$
$37$	80.0444			0.355655			0.177827	+	0.984062i	$0.443093\pi$
$38$	89.6609	+	76.5274i	0.382761	+	0.326694i
$39$		0			0
$40$	−38.8396	+	249.983i	−0.153527	+	0.988144i
$41$			221.256i			0.842789i	0.906878	+	0.421394i	$0.138459\pi$
$41$			221.256i			0.842789i	−0.906878	+	0.421394i	$0.861541\pi$
$42$		0			0
$43$		−	78.5904i		−	0.278719i	−0.990242	−	0.139360i	$-0.955496\pi$
$43$		−	78.5904i		−	0.278719i	0.990242	−	0.139360i	$-0.0445044\pi$
$44$	−33.6266	+	5.34827i	−0.115214	+	0.0183246i
$45$		0			0
$46$	−147.702	+	173.051i	−0.473424	+	0.554672i
$47$		−	319.651i		−	0.992042i	−0.868311	−	0.496021i	$-0.834794\pi$
$47$		−	319.651i		−	0.992042i	0.868311	−	0.496021i	$-0.165206\pi$
$48$		0			0
$49$	677.073			1.97397
$50$	−352.342	+	29.2430i	−0.996574	+	0.0827117i
$51$		0			0
$52$	−93.9148	−	590.479i	−0.250454	−	1.57471i
$53$			234.142i			0.606829i	0.952859	+	0.303414i	$0.0981266\pi$
$53$			234.142i			0.606829i	−0.952859	+	0.303414i	$0.901873\pi$
$54$		0			0
$55$	−18.2967	−	43.9271i	−0.0448570	−	0.107693i
$56$	−377.004	+	616.559i	−0.899631	+	1.47127i
$57$		0			0
$58$	−306.807	−	261.866i	−0.694582	−	0.592840i
$59$		−	69.6092i		−	0.153599i	−0.997047	−	0.0767996i	$-0.975530\pi$
$59$		−	69.6092i		−	0.153599i	0.997047	−	0.0767996i	$-0.0244702\pi$
$60$		0			0
$61$		−	390.739i		−	0.820148i	−0.912052	−	0.410074i	$-0.865503\pi$
$61$		−	390.739i		−	0.820148i	0.912052	−	0.410074i	$-0.134497\pi$
$62$	538.957	−	631.452i	1.10399	−	1.29346i
$63$		0			0
$64$	−233.329	−	455.743i	−0.455721	−	0.890123i
$65$	771.354	−	321.288i	1.47192	−	0.613091i
$66$		0			0
$67$			600.238i			1.09449i	0.836973	+	0.547244i	$0.184323\pi$
$67$			600.238i			1.09449i	−0.836973	+	0.547244i	$0.815677\pi$
$68$	14.3443	+	90.1885i	0.0255810	+	0.160838i
$69$		0			0
$70$	−961.268	−	309.898i	−1.64134	−	0.529141i
$71$	554.269			0.926474			0.463237	−	0.886234i	$-0.346688\pi$
$71$	554.269			0.926474			0.463237	+	0.886234i	$0.346688\pi$
$72$		0			0
$73$		−	491.603i		−	0.788189i	−0.919070	−	0.394095i	$-0.871058\pi$
$73$		−	491.603i		−	0.788189i	0.919070	−	0.394095i	$-0.128942\pi$
$74$	−172.203	−	146.979i	−0.270517	−	0.230892i
$75$		0			0
$76$	−52.3705	−	329.274i	−0.0790436	−	0.496978i
$77$		−	135.936i		−	0.201186i
$78$		0			0
$79$		−	1140.16i		−	1.62378i	−0.583812	−	0.811889i	$-0.698439\pi$
$79$		−	1140.16i		−	1.62378i	0.583812	−	0.811889i	$-0.301561\pi$
$80$	542.581	−	466.482i	0.758280	−	0.651929i
$81$		0			0
$82$	406.274	−	475.998i	0.547140	−	0.641039i
$83$	188.475			0.249250			0.124625	−	0.992204i	$-0.460227\pi$
$83$	188.475			0.249250			0.124625	+	0.992204i	$0.460227\pi$
$84$		0			0
$85$	−117.815	+	49.0729i	−0.150339	+	0.0626200i
$86$	−144.309	+	169.075i	−0.180945	+	0.211998i
$87$		0			0
$88$	82.1632	+	50.2399i	0.0995298	+	0.0608590i
$89$		−	1298.28i		−	1.54626i	−0.634248	−	0.773129i	$-0.718690\pi$
$89$		−	1298.28i		−	1.54626i	0.634248	−	0.773129i	$-0.281310\pi$
$90$		0			0
$91$	2387.01			2.74975
$92$	635.518	−	101.078i	0.720189	−	0.114545i
$93$		0			0
$94$	−586.950	+	687.682i	−0.644035	+	0.754563i
$95$	430.137	−	179.163i	0.464538	−	0.193492i
$96$		0			0
$97$			547.916i			0.573531i	0.958001	+	0.286765i	$0.0925800\pi$
$97$			547.916i			0.573531i	−0.958001	+	0.286765i	$0.907420\pi$
$98$	−1456.62	−	1243.25i	−1.50144	−	1.28151i
$99$		0			0
$100$	811.707	+	584.065i	0.811707	+	0.584065i
$101$	−1619.83			−1.59583			−0.797914	−	0.602771i	$-0.794063\pi$
$101$	−1619.83			−1.59583			−0.797914	+	0.602771i	$0.794063\pi$
$102$		0			0
$103$	−1285.37			−1.22963			−0.614813	−	0.788673i	$-0.710768\pi$
$103$	−1285.37			−1.22963			−0.614813	+	0.788673i	$0.710768\pi$
$104$	−882.206	+	1442.77i	−0.831802	+	1.36034i
$105$		0			0
$106$	429.937	−	503.721i	0.393954	−	0.461564i
$107$	−1733.97			−1.56663			−0.783316	−	0.621623i	$-0.786473\pi$
$107$	−1733.97			−1.56663			−0.783316	+	0.621623i	$0.786473\pi$
$108$		0			0
$109$			2080.39i			1.82812i	0.405576	+	0.914061i	$0.367071\pi$
$109$			2080.39i			1.82812i	−0.405576	+	0.914061i	$0.632929\pi$
$110$	−41.2972	+	128.099i	−0.0357958	+	0.111035i
$111$		0			0
$112$	1943.21	−	634.170i	1.63943	−	0.535031i
$113$	1829.17			1.52278			0.761388	−	0.648296i	$-0.224518\pi$
$113$	1829.17			1.52278			0.761388	+	0.648296i	$0.224518\pi$
$114$		0			0
$115$	345.795	+	830.190i	0.280396	+	0.673179i
$116$	179.205	+	1126.73i	0.143438	+	0.901848i
$117$		0			0
$118$	−127.818	+	149.754i	−0.0997168	+	0.116830i
$119$	−364.587			−0.280854
$120$		0			0
$121$	1312.89			0.986390
$122$	−717.483	+	840.616i	−0.532441	+	0.623818i
$123$		0			0
$124$	−2318.97	+	368.828i	−1.67943	+	0.267111i
$125$	−527.171	+	1294.30i	−0.377213	+	0.926127i
$126$		0			0
$127$	219.783			0.153564			0.0767818	−	0.997048i	$-0.475536\pi$
$127$	219.783			0.153564			0.0767818	+	0.997048i	$0.475536\pi$
$128$	−334.872	+	1408.90i	−0.231240	+	0.972897i
$129$		0			0
$130$	−2249.41	−	725.173i	−1.51758	−	0.489245i
$131$		−	1698.07i		−	1.13253i	−0.824224	−	0.566263i	$-0.808389\pi$
$131$		−	1698.07i		−	1.13253i	0.824224	−	0.566263i	$-0.191611\pi$
$132$		0			0
$133$	1331.09			0.867821
$134$	1102.17	−	1291.32i	0.710543	−	0.832485i
$135$		0			0
$136$	134.746	−	220.366i	0.0849588	−	0.138943i
$137$	−158.329			−0.0987368			−0.0493684	−	0.998781i	$-0.515721\pi$
$137$	−158.329			−0.0987368			−0.0493684	+	0.998781i	$0.515721\pi$
$138$		0			0
$139$	−1492.99			−0.911033			−0.455517	−	0.890227i	$-0.650545\pi$
$139$	−1492.99			−0.911033			−0.455517	+	0.890227i	$0.650545\pi$
$140$	1498.98	+	2431.80i	0.904908	+	1.46803i
$141$		0			0
$142$	−1192.43	−	1017.76i	−0.704691	−	0.601468i
$143$		−	318.095i		−	0.186017i
$144$		0			0
$145$	−1471.87	+	613.071i	−0.842981	+	0.351123i
$146$	−902.691	+	1057.61i	−0.511694	+	0.599509i
$147$		0			0
$148$	100.583	+	632.406i	0.0558641	+	0.351240i
$149$	3072.98			1.68958			0.844792	−	0.535094i	$-0.179724\pi$
$149$	3072.98			1.68958			0.844792	+	0.535094i	$0.179724\pi$
$150$		0			0
$151$			1388.77i			0.748452i	0.927338	+	0.374226i	$0.122092\pi$
$151$			1388.77i			0.748452i	−0.927338	+	0.374226i	$0.877908\pi$
$152$	−491.952	+	804.547i	−0.262517	+	0.429325i
$153$		0			0
$154$	−249.608	+	292.445i	−0.130610	+	0.153025i
$155$	−1261.78	−	3029.31i	−0.653864	−	1.56981i
$156$		0			0
$157$	3177.64			1.61531			0.807655	−	0.589656i	$-0.200737\pi$
$157$	3177.64			1.61531			0.807655	+	0.589656i	$0.200737\pi$
$158$	−2093.59	+	2452.89i	−1.05416	+	1.23507i
$159$		0			0
$160$	−2023.84	+	7.26690i	−0.999994	+	0.00359062i
$161$			2569.08i			1.25759i
$162$		0			0
$163$			2226.14i			1.06972i	0.844941	+	0.534860i	$0.179636\pi$
$163$			2226.14i			1.06972i	−0.844941	+	0.534860i	$0.820364\pi$
$164$	−1748.07	+	278.028i	−0.832327	+	0.132380i
$165$		0			0
$166$	−405.474	−	346.081i	−0.189584	−	0.161814i
$167$		−	3096.64i		−	1.43488i	−0.696620	−	0.717441i	$-0.745313\pi$
$167$		−	3096.64i		−	1.43488i	0.696620	−	0.717441i	$-0.254687\pi$
$168$		0			0
$169$	3388.71			1.54242
$170$	343.570	+	110.761i	0.155003	+	0.0499707i
$171$		0			0
$172$	620.919	−	98.7562i	0.275259	−	0.0437796i
$173$			3178.07i			1.39667i	0.715771	+	0.698335i	$0.246075\pi$
$173$			3178.07i			1.39667i	−0.715771	+	0.698335i	$0.753925\pi$
$174$		0			0
$175$	−2811.85	+	2834.11i	−1.21460	+	1.22422i
$176$	−84.5100	−	258.953i	−0.0361942	−	0.110905i
$177$		0			0
$178$	−2383.92	+	2793.04i	−1.00383	+	1.17611i
$179$		−	883.450i		−	0.368895i	−0.982842	−	0.184447i	$-0.940950\pi$
$179$		−	883.450i		−	0.368895i	0.982842	−	0.184447i	$-0.0590495\pi$
$180$		0			0
$181$			1968.99i			0.808587i	0.914629	+	0.404293i	$0.132482\pi$
$181$			1968.99i			0.808587i	−0.914629	+	0.404293i	$0.867518\pi$
$182$	−5135.29	−	4383.08i	−2.09150	−	1.78514i
$183$		0			0
$184$	−1552.82	−	949.497i	−0.622150	−	0.380423i
$185$	−826.125	+	344.102i	−0.328313	+	0.136751i
$186$		0			0
$187$			48.5852i			0.0189995i
$188$	2525.47	−	401.672i	0.979727	−	0.155824i
$189$		0			0
$190$	−1254.36	−	404.385i	−0.478951	−	0.154406i
$191$	−673.714			−0.255226			−0.127613	−	0.991824i	$-0.540732\pi$
$191$	−673.714			−0.255226			−0.127613	+	0.991824i	$0.540732\pi$
$192$		0			0
$193$			3885.22i			1.44904i	0.689255	+	0.724519i	$0.257938\pi$
$193$			3885.22i			1.44904i	−0.689255	+	0.724519i	$0.742062\pi$
$194$	1006.09	−	1178.76i	0.372337	−	0.436237i
$195$		0			0
$196$	850.805	+	5349.34i	0.310060	+	1.94947i
$197$			3232.03i			1.16890i	0.811431	+	0.584448i	$0.198689\pi$
$197$			3232.03i			1.16890i	−0.811431	+	0.584448i	$0.801311\pi$
$198$		0			0
$199$		−	5043.25i		−	1.79651i	−0.439470	−	0.898257i	$-0.644834\pi$
$199$		−	5043.25i		−	1.79651i	0.439470	−	0.898257i	$-0.355166\pi$
$200$	−673.791	−	2747.00i	−0.238221	−	0.971211i
$201$		0			0
$202$	3484.81	+	2974.36i	1.21381	+	1.03601i
$203$	−4554.81			−1.57480
$204$		0			0
$205$	−951.153	−	2283.54i	−0.324056	−	0.777998i
$206$	2765.28	+	2360.22i	0.935273	+	0.798275i
$207$		0			0
$208$	4547.18	−	1483.98i	1.51582	−	0.494691i
$209$		−	177.382i		−	0.0587072i
$210$		0			0
$211$	−3744.17			−1.22161			−0.610804	−	0.791782i	$-0.709154\pi$
$211$	−3744.17			−1.22161			−0.610804	+	0.791782i	$0.709154\pi$
$212$	−1849.89	+	294.222i	−0.599296	+	0.0953171i
$213$		0			0
$214$	3730.38	+	3183.96i	1.19161	+	1.01706i
$215$	337.851	+	811.119i	0.107169	+	0.257292i
$216$		0			0
$217$		−	9374.43i		−	2.93262i
$218$	3820.06	−	4475.64i	1.18682	−	1.39050i
$219$		0			0
$220$	324.063	−	199.756i	0.0993107	−	0.0612160i
$221$	−853.149			−0.259679
$222$		0			0
$223$	−2038.68			−0.612197			−0.306099	−	0.952000i	$-0.599024\pi$
$223$	−2038.68			−0.612197			−0.306099	+	0.952000i	$0.599024\pi$
$224$	−5344.98	−	2203.83i	−1.59432	−	0.657365i
$225$		0			0
$226$	−3935.18	−	3358.76i	−1.15825	−	0.988589i
$227$	401.230			0.117315			0.0586576	−	0.998278i	$-0.481318\pi$
$227$	401.230			0.117315			0.0586576	+	0.998278i	$0.481318\pi$
$228$		0			0
$229$		−	2201.68i		−	0.635332i	−0.948203	−	0.317666i	$-0.897101\pi$
$229$		−	2201.68i		−	0.635332i	0.948203	−	0.317666i	$-0.102899\pi$
$230$	780.486	−	2420.98i	0.223755	−	0.694065i
$231$		0			0
$232$	1683.39	−	2753.05i	0.476380	−	0.779080i
$233$	900.008			0.253053			0.126527	−	0.991963i	$-0.459617\pi$
$233$	900.008			0.253053			0.126527	+	0.991963i	$0.459617\pi$
$234$		0			0
$235$	1374.14	+	3299.07i	0.381444	+	0.915777i
$236$	549.961	−	87.4705i	0.151692	−	0.0241265i
$237$		0			0
$238$	784.354	+	669.462i	0.213622	+	0.182331i
$239$	5295.58			1.43323			0.716617	−	0.697467i	$-0.245690\pi$
$239$	5295.58			1.43323			0.716617	+	0.697467i	$0.245690\pi$
$240$		0			0
$241$	−188.408			−0.0503586			−0.0251793	−	0.999683i	$-0.508016\pi$
$241$	−188.408			−0.0503586			−0.0251793	+	0.999683i	$0.508016\pi$
$242$	−2824.47	−	2410.75i	−0.750264	−	0.640366i
$243$		0			0
$244$	3087.11	−	491.000i	0.809967	−	0.128824i
$245$	−6987.95	+	2910.66i	−1.82222	+	0.759000i
$246$		0			0
$247$	3114.81			0.802391
$248$	5666.16	+	3464.66i	1.45081	+	0.887121i
$249$		0			0
$250$	3510.75	−	1816.49i	0.888157	−	0.459540i
$251$			5469.28i			1.37537i	0.726009	+	0.687685i	$0.241373\pi$
$251$			5469.28i			1.37537i	−0.726009	+	0.687685i	$0.758627\pi$
$252$		0			0
$253$	342.358			0.0850746
$254$	−472.829	−	403.569i	−0.116803	−	0.0996937i
$255$		0			0
$256$	3307.48	−	2416.15i	0.807491	−	0.589879i
$257$	5966.94			1.44828			0.724139	−	0.689654i	$-0.242237\pi$
$257$	5966.94			1.44828			0.724139	+	0.689654i	$0.242237\pi$
$258$		0			0
$259$	−2556.50			−0.613334
$260$	3507.68	+	5690.50i	0.836681	+	1.35735i
$261$		0			0
$262$	−3118.03	+	3653.14i	−0.735238	+	0.861418i
$263$		−	4595.41i		−	1.07743i	−0.842487	−	0.538717i	$-0.818909\pi$
$263$		−	4595.41i		−	1.07743i	0.842487	−	0.538717i	$-0.181091\pi$
$264$		0			0
$265$	−1006.55	−	2416.54i	−0.233328	−	0.560178i
$266$	−2863.64	−	2444.18i	−0.660079	−	0.563391i
$267$		0			0
$268$	−4742.29	+	754.255i	−1.08090	+	0.171916i
$269$	−1974.63			−0.447567			−0.223783	−	0.974639i	$-0.571841\pi$
$269$	−1974.63			−0.447567			−0.223783	+	0.974639i	$0.571841\pi$
$270$		0			0
$271$		−	3724.40i		−	0.834839i	−0.908714	−	0.417419i	$-0.862935\pi$
$271$		−	3724.40i		−	0.834839i	0.908714	−	0.417419i	$-0.137065\pi$
$272$	−694.527	+	226.661i	−0.154823	+	0.0505269i
$273$		0			0
$274$	340.620	+	290.727i	0.0751008	+	0.0641001i
$275$	377.675	+	374.709i	0.0828170	+	0.0821666i
$276$		0			0
$277$	5185.67			1.12483			0.562413	−	0.826857i	$-0.309873\pi$
$277$	5185.67			1.12483			0.562413	+	0.826857i	$0.309873\pi$
$278$	3211.94	+	2741.45i	0.692947	+	0.591444i
$279$		0			0
$280$	1240.48	−	7984.10i	0.264761	−	1.70408i
$281$		−	3196.71i		−	0.678646i	−0.940670	−	0.339323i	$-0.889802\pi$
$281$		−	3196.71i		−	0.678646i	0.940670	−	0.339323i	$-0.110198\pi$
$282$		0			0
$283$			2872.47i			0.603360i	0.953409	+	0.301680i	$0.0975474\pi$
$283$			2872.47i			0.603360i	−0.953409	+	0.301680i	$0.902453\pi$
$284$	696.491	+	4379.11i	0.145525	+	0.914973i
$285$		0			0
$286$	−584.093	+	684.333i	−0.120763	+	0.141488i
$287$		−	7066.59i		−	1.45341i
$288$		0			0
$289$	−4782.69			−0.973477
$290$	4292.24	+	1383.75i	0.869134	+	0.280195i
$291$		0			0
$292$	3884.01	−	617.745i	0.778405	−	0.123804i
$293$		−	1721.81i		−	0.343308i	−0.985157	−	0.171654i	$-0.945089\pi$
$293$		−	1721.81i		−	0.343308i	0.985157	−	0.171654i	$-0.0549112\pi$
$294$		0			0
$295$	299.242	+	718.425i	0.0590595	+	0.141791i
$296$	944.847	−	1545.22i	0.185534	−	0.303426i
$297$		0			0
$298$	−6611.04	−	5642.66i	−1.28513	−	1.09688i
$299$			6011.76i			1.16277i
$300$		0			0
$301$			2510.07i			0.480657i
$302$	2550.08	−	2987.72i	0.485896	−	0.569285i
$303$		0			0
$304$	2535.69	−	827.527i	0.478393	−	0.156125i
$305$	1679.74	+	4032.75i	0.315350	+	0.757098i
$306$		0			0
$307$		−	7795.23i		−	1.44918i	−0.689182	−	0.724588i	$-0.742030\pi$
$307$		−	7795.23i		−	1.44918i	0.689182	−	0.724588i	$-0.257970\pi$
$308$	1073.99	−	170.816i	0.198689	−	0.0316011i
$309$		0			0
$310$	−2847.95	+	8834.02i	−0.521783	+	1.61851i
$311$	−1738.75			−0.317027			−0.158514	−	0.987357i	$-0.550670\pi$
$311$	−1738.75			−0.317027			−0.158514	+	0.987357i	$0.550670\pi$
$312$		0			0
$313$		−	7247.51i		−	1.30880i	−0.756150	−	0.654398i	$-0.772922\pi$
$313$		−	7247.51i		−	1.30880i	0.756150	−	0.654398i	$-0.227078\pi$
$314$	−6836.21	−	5834.85i	−1.22863	−	1.04866i
$315$		0			0
$316$	9008.09	−	1432.72i	1.60362	−	0.255054i
$317$		−	6041.25i		−	1.07038i	−0.844732	−	0.535190i	$-0.820240\pi$
$317$		−	6041.25i		−	1.07038i	0.844732	−	0.535190i	$-0.179760\pi$
$318$		0			0
$319$			606.978i			0.106534i
$320$	4367.34	+	3700.59i	0.762942	+	0.646466i
$321$		0			0
$322$	4717.40	−	5526.99i	0.816430	−	0.956544i
$323$	−475.749			−0.0819548
$324$		0			0
$325$	−6579.84	+	6631.92i	−1.12303	+	1.13192i
$326$	4087.67	−	4789.19i	0.694464	−	0.813646i
$327$		0			0
$328$	4271.24	+	2611.71i	0.719023	+	0.439657i
$329$			10209.2i			1.71080i
$330$		0			0
$331$	−6159.28			−1.02279			−0.511396	−	0.859345i	$-0.670872\pi$
$331$	−6159.28			−1.02279			−0.511396	+	0.859345i	$0.670872\pi$
$332$	236.836	+	1489.08i	0.0391508	+	0.246156i
$333$		0			0
$334$	−5686.11	+	6661.95i	−0.931527	+	1.09139i
$335$	−2580.35	−	6194.95i	−0.420835	−	1.01035i
$336$		0			0
$337$		−	1473.95i		−	0.238253i	−0.992879	−	0.119127i	$-0.961991\pi$
$337$		−	1473.95i		−	0.238253i	0.992879	−	0.119127i	$-0.0380094\pi$
$338$	−7290.28	−	6222.41i	−1.17319	−	1.00134i
$339$		0			0
$340$	−535.755	−	869.156i	−0.0854571	−	0.138637i
$341$	−1249.25			−0.198388
$342$		0			0
$343$	−10669.8			−1.67964
$344$	−1517.15	−	927.685i	−0.237789	−	0.145399i
$345$		0			0
$346$	5835.63	−	6837.13i	0.906721	−	1.06233i
$347$	−4771.59			−0.738191			−0.369095	−	0.929392i	$-0.620332\pi$
$347$	−4771.59			−0.738191			−0.369095	+	0.929392i	$0.620332\pi$
$348$		0			0
$349$		−	6991.09i		−	1.07228i	−0.844130	−	0.536138i	$-0.819883\pi$
$349$		−	6991.09i		−	1.07228i	0.844130	−	0.536138i	$-0.180117\pi$
$350$	11253.3	−	933.980i	1.71861	−	0.142638i
$351$		0			0
$352$	−293.685	+	712.277i	−0.0444700	+	0.107854i
$353$	7893.57			1.19018			0.595088	−	0.803660i	$-0.297117\pi$
$353$	7893.57			1.19018			0.595088	+	0.803660i	$0.297117\pi$
$354$		0			0
$355$	−5720.52	+	2382.74i	−0.855250	+	0.356233i
$356$	10257.3	−	1631.41i	1.52706	−	0.242877i
$357$		0			0
$358$	−1622.21	+	1900.61i	−0.239487	+	0.280587i
$359$	8832.42			1.29849			0.649244	−	0.760580i	$-0.275085\pi$
$359$	8832.42			1.29849			0.649244	+	0.760580i	$0.275085\pi$
$360$		0			0
$361$	−5122.06			−0.746765
$362$	3615.51	−	4235.99i	0.524936	−	0.615024i
$363$		0			0
$364$	2999.50	+	18859.1i	0.431914	+	2.71561i
$365$	2113.35	+	5073.75i	0.303062	+	0.727596i
$366$		0			0
$367$	1142.28			0.162470			0.0812348	−	0.996695i	$-0.474114\pi$
$367$	1142.28			0.162470			0.0812348	+	0.996695i	$0.474114\pi$
$368$	1597.18	+	4894.02i	0.226246	+	0.693257i
$369$		0			0
$370$	2409.13	+	776.665i	0.338499	+	0.109127i
$371$		−	7478.17i		−	1.04649i
$372$		0			0
$373$	4341.48			0.602664			0.301332	−	0.953519i	$-0.402569\pi$
$373$	4341.48			0.602664			0.301332	+	0.953519i	$0.402569\pi$
$374$	89.2131	−	104.524i	0.0123345	−	0.0144513i
$375$		0			0
$376$	−6170.72	−	3773.18i	−0.846358	−	0.517518i
$377$	−10658.4			−1.45607
$378$		0			0
$379$	4733.85			0.641587			0.320793	−	0.947149i	$-0.396051\pi$
$379$	4733.85			0.641587			0.320793	+	0.947149i	$0.396051\pi$
$380$	1956.02	+	3173.25i	0.264057	+	0.428379i
$381$		0			0
$382$	1449.39	+	1237.09i	0.194129	+	0.165693i
$383$			13768.4i			1.83689i	0.395546	+	0.918446i	$0.370555\pi$
$383$			13768.4i			1.83689i	−0.395546	+	0.918446i	$0.629445\pi$
$384$		0			0
$385$	584.372	+	1402.97i	0.0773568	+	0.185719i
$386$	7134.12	−	8358.46i	0.940718	−	1.10216i
$387$		0			0
$388$	−4328.92	+	688.508i	−0.566411	+	0.0900868i
$389$	11815.6			1.54003			0.770017	−	0.638024i	$-0.220248\pi$
$389$	11815.6			1.54003			0.770017	+	0.638024i	$0.220248\pi$
$390$		0			0
$391$		−	918.224i		−	0.118764i
$392$	7992.19	−	13070.6i	1.02976	−	1.68409i
$393$		0			0
$394$	5934.71	−	6953.22i	0.758849	−	0.889081i
$395$	4901.43	+	11767.4i	0.624349	+	1.49895i
$396$		0			0
$397$	−1683.65			−0.212846			−0.106423	−	0.994321i	$-0.533940\pi$
$397$	−1683.65			−0.212846			−0.106423	+	0.994321i	$0.533940\pi$
$398$	−9260.51	+	10849.8i	−1.16630	+	1.36646i
$399$		0			0
$400$	−3594.54	+	7146.98i	−0.449317	+	0.893372i
$401$			1328.96i			0.165499i	0.996570	+	0.0827494i	$0.0263701\pi$
$401$			1328.96i			0.165499i	−0.996570	+	0.0827494i	$0.973630\pi$
$402$		0			0
$403$		−	21936.6i		−	2.71151i
$404$	−2035.46	−	12797.7i	−0.250663	−	1.57602i
$405$		0			0
$406$	9798.99	+	8363.64i	1.19782	+	1.02237i
$407$			340.682i			0.0414913i
$408$		0			0
$409$	−5943.61			−0.718564			−0.359282	−	0.933229i	$-0.616978\pi$
$409$	−5943.61			−0.718564			−0.359282	+	0.933229i	$0.616978\pi$
$410$	−2146.83	+	6659.22i	−0.258596	+	0.802135i
$411$		0			0
$412$	−1615.19	−	10155.3i	−0.193142	−	1.21436i
$413$			2223.22i			0.264885i
$414$		0			0
$415$	−1945.22	+	810.231i	−0.230089	+	0.0958377i
$416$	−12507.5	−	5157.06i	−1.47411	−	0.607802i
$417$		0			0
$418$	−325.713	+	381.611i	−0.0381128	+	0.0446536i
$419$		−	5960.18i		−	0.694926i	−0.937694	−	0.347463i	$-0.887043\pi$
$419$		−	5960.18i		−	0.694926i	0.937694	−	0.347463i	$-0.112957\pi$
$420$		0			0
$421$		−	162.920i		−	0.0188604i	−0.999956	−	0.00943021i	$-0.996998\pi$
$421$		−	162.920i		−	0.0188604i	0.999956	−	0.00943021i	$-0.00300177\pi$
$422$	8055.01	+	6875.12i	0.929174	+	0.793070i
$423$		0			0
$424$	4520.01	+	2763.83i	0.517714	+	0.316564i
$425$	1004.99	−	1012.95i	0.114704	−	0.115612i
$426$		0			0
$427$			12479.6i			1.41436i
$428$	−2178.90	−	13699.6i	−0.246078	−	1.54719i
$429$		0			0
$430$	762.557	−	2365.37i	0.0855204	−	0.265275i
$431$	−3767.56			−0.421060			−0.210530	−	0.977587i	$-0.567519\pi$
$431$	−3767.56			−0.421060			−0.210530	+	0.977587i	$0.567519\pi$
$432$		0			0
$433$			6294.32i			0.698582i	0.937014	+	0.349291i	$0.113577\pi$
$433$			6294.32i			0.698582i	−0.937014	+	0.349291i	$0.886423\pi$
$434$	−17213.5	+	20167.7i	−1.90386	+	2.23060i
$435$		0			0
$436$	−16436.5	+	2614.21i	−1.80543	+	0.287151i
$437$			3352.39i			0.366972i
$438$		0			0
$439$		−	3541.41i		−	0.385017i	−0.981295	−	0.192509i	$-0.938338\pi$
$439$		−	3541.41i		−	0.385017i	0.981295	−	0.192509i	$-0.0616623\pi$
$440$	−1063.97	−	165.308i	−0.115279	−	0.0179108i
$441$		0			0
$442$	1835.42	+	1566.57i	0.197516	+	0.168584i
$443$	−3317.48			−0.355797			−0.177898	−	0.984049i	$-0.556930\pi$
$443$	−3317.48			−0.355797			−0.177898	+	0.984049i	$0.556930\pi$
$444$		0			0
$445$	5581.14	+	13399.3i	0.594543	+	1.42739i
$446$	4385.91	+	3743.46i	0.465647	+	0.397440i
$447$		0			0
$448$	7452.20	+	14555.8i	0.785900	+	1.53504i
$449$			9186.24i			0.965536i	0.875748	+	0.482768i	$0.160369\pi$
$449$			9186.24i			0.965536i	−0.875748	+	0.482768i	$0.839631\pi$
$450$		0			0
$451$	−941.700			−0.0983213
$452$	2298.52	+	14451.7i	0.239189	+	1.50387i
$453$		0			0
$454$	−863.185	−	736.747i	−0.0892319	−	0.0761613i
$455$	−24636.0	+	10261.5i	−2.53835	+	1.05729i
$456$		0			0
$457$			11292.7i			1.15591i	0.816068	+	0.577955i	$0.196149\pi$
$457$			11292.7i			1.15591i	−0.816068	+	0.577955i	$0.803851\pi$
$458$	−4042.77	+	4736.58i	−0.412459	+	0.483244i
$459$		0			0
$460$	−6124.55	+	3775.23i	−0.620780	+	0.382654i
$461$	−2955.57			−0.298600			−0.149300	−	0.988792i	$-0.547702\pi$
$461$	−2955.57			−0.298600			−0.149300	+	0.988792i	$0.547702\pi$
$462$		0			0
$463$	3971.35			0.398627			0.199313	−	0.979936i	$-0.436129\pi$
$463$	3971.35			0.398627			0.199313	+	0.979936i	$0.436129\pi$
$464$	−8676.77	+	2831.69i	−0.868123	+	0.283314i
$465$		0			0
$466$	−1936.23	−	1652.61i	−0.192477	−	0.164283i
$467$	−5536.85			−0.548640			−0.274320	−	0.961638i	$-0.588453\pi$
$467$	−5536.85			−0.548640			−0.274320	+	0.961638i	$0.588453\pi$
$468$		0			0
$469$		−	19170.7i		−	1.88747i
$470$	3101.55	−	9620.68i	0.304391	−	0.944189i
$471$		0			0
$472$	−1343.77	−	821.670i	−0.131043	−	0.0801280i
$473$	334.494			0.0325159
$474$		0			0
$475$	−3669.17	+	3698.22i	−0.354428	+	0.357234i
$476$	−458.138	−	2880.49i	−0.0441149	−	0.277368i
$477$		0			0
$478$	−11392.6	−	9723.85i	−1.09014	−	0.930457i
$479$	13557.0			1.29318			0.646591	−	0.762837i	$-0.276194\pi$
$479$	13557.0			1.29318			0.646591	+	0.762837i	$0.276194\pi$
$480$		0			0
$481$	−5982.32			−0.567090
$482$	405.331	+	345.959i	0.0383036	+	0.0326929i
$483$		0			0
$484$	1649.76	+	10372.7i	0.154936	+	0.974146i
$485$	−2355.43	−	5654.95i	−0.220525	−	0.529439i
$486$		0			0
$487$	9905.19			0.921658			0.460829	−	0.887489i	$-0.347552\pi$
$487$	9905.19			0.921658			0.460829	+	0.887489i	$0.347552\pi$
$488$	−7543.03	−	4612.30i	−0.699707	−	0.427846i
$489$		0			0
$490$	20378.1	+	6569.58i	1.87875	+	0.605681i
$491$		−	12743.3i		−	1.17128i	−0.810573	−	0.585638i	$-0.800844\pi$
$491$		−	12743.3i		−	1.17128i	0.810573	−	0.585638i	$-0.199156\pi$
$492$		0			0
$493$	1627.95			0.148720
$494$	−6701.04	−	5719.47i	−0.610311	−	0.520913i
$495$		0			0
$496$	−5828.00	−	17858.0i	−0.527591	−	1.61663i
$497$	−17702.6			−1.59772
$498$		0			0
$499$	10350.5			0.928558			0.464279	−	0.885689i	$-0.346314\pi$
$499$	10350.5			0.928558			0.464279	+	0.885689i	$0.346314\pi$
$500$	−10888.3	−	2538.61i	−0.973881	−	0.227060i
$501$		0			0
$502$	10042.8	−	11766.3i	0.892893	−	1.04613i
$503$		−	5518.18i		−	0.489152i	−0.969630	−	0.244576i	$-0.921351\pi$
$503$		−	5518.18i		−	0.489152i	0.969630	−	0.244576i	$-0.0786488\pi$
$504$		0			0
$505$	16717.9	−	6963.44i	1.47315	−	0.613602i
$506$	−736.532	−	628.645i	−0.0647091	−	0.0552306i
$507$		0			0
$508$	276.178	+	1736.44i	0.0241209	+	0.151657i
$509$	6937.62			0.604135			0.302067	−	0.953287i	$-0.402323\pi$
$509$	6937.62			0.604135			0.302067	+	0.953287i	$0.402323\pi$
$510$		0			0
$511$			15701.1i			1.35925i
$512$	−11552.1	−	875.299i	−0.997142	−	0.0755530i
$513$		0			0
$514$	−12837.0	−	10956.6i	−1.10158	−	0.940225i
$515$	13266.1	−	5525.66i	1.13510	−	0.472796i
$516$		0			0
$517$	1360.49			0.115733
$518$	5499.93	+	4694.30i	0.466512	+	0.398177i
$519$		0			0
$520$	2902.78	−	18683.1i	0.244799	−	1.57559i
$521$		−	9876.27i		−	0.830493i	−0.909709	−	0.415247i	$-0.863695\pi$
$521$		−	9876.27i		−	0.830493i	0.909709	−	0.415247i	$-0.136305\pi$
$522$		0			0
$523$		−	3022.02i		−	0.252665i	−0.991988	−	0.126333i	$-0.959679\pi$
$523$		−	3022.02i		−	0.252665i	0.991988	−	0.126333i	$-0.0403206\pi$
$524$	13415.9	−	2133.78i	1.11847	−	0.177891i
$525$		0			0
$526$	−8438.18	+	9886.32i	−0.699472	+	0.819513i
$527$			3350.54i			0.276949i
$528$		0			0
$529$	5696.69			0.468208
$530$	−2271.86	+	7047.07i	−0.186195	+	0.577557i
$531$		0			0
$532$	1672.64	+	10516.5i	0.136312	+	0.857049i
$533$		−	16536.1i		−	1.34382i
$534$		0			0
$535$	17896.1	−	7454.16i	1.44620	−	0.602376i
$536$	11587.3	+	7085.23i	0.933760	+	0.570961i
$537$		0			0
$538$	4248.12	+	3625.86i	0.340427	+	0.290561i
$539$			2881.73i			0.230287i
$540$		0			0
$541$			684.787i			0.0544201i	0.999630	+	0.0272101i	$0.00866230\pi$
$541$			684.787i			0.0544201i	−0.999630	+	0.0272101i	$0.991338\pi$
$542$	−6838.82	+	8012.48i	−0.541979	+	0.634992i
$543$		0			0
$544$	1910.37	+	787.678i	0.150563	+	0.0620798i
$545$	−8943.36	−	21471.4i	−0.702920	−	1.68758i
$546$		0			0
$547$			9141.42i			0.714550i	0.933999	+	0.357275i	$0.116294\pi$
$547$			9141.42i			0.714550i	−0.933999	+	0.357275i	$0.883706\pi$
$548$	−198.955	−	1250.91i	−0.0155090	−	0.0975112i
$549$		0			0
$550$	−124.463	−	1499.62i	−0.00964930	−	0.116262i
$551$	−5943.57			−0.459536
$552$		0			0
$553$			36415.2i			2.80024i
$554$	−11156.2	−	9522.03i	−0.855560	−	0.730239i
$555$		0			0
$556$	−1876.08	−	11795.6i	−0.143100	−	0.899724i
$557$		−	9201.05i		−	0.699930i	−0.936763	−	0.349965i	$-0.886193\pi$
$557$		−	9201.05i		−	0.699930i	0.936763	−	0.349965i	$-0.113807\pi$
$558$		0			0
$559$			5873.66i			0.444417i
$560$	−17329.3	+	14898.8i	−1.30767	+	1.12426i
$561$		0			0
$562$	−5869.85	+	6877.23i	−0.440578	+	0.516189i
$563$	−1579.08			−0.118207			−0.0591033	−	0.998252i	$-0.518824\pi$
$563$	−1579.08			−0.118207			−0.0591033	+	0.998252i	$0.518824\pi$
$564$		0			0
$565$	−18878.6	+	7863.39i	−1.40571	+	0.585514i
$566$	5274.50	−	6179.69i	0.391702	−	0.458925i
$567$		0			0
$568$	6542.62	−	10699.9i	0.483314	−	0.790419i
$569$		−	18088.3i		−	1.33269i	−0.745643	−	0.666345i	$-0.767858\pi$
$569$		−	18088.3i		−	1.33269i	0.745643	−	0.666345i	$-0.232142\pi$
$570$		0			0
$571$	4521.90			0.331411			0.165705	−	0.986175i	$-0.447010\pi$
$571$	4521.90			0.331411			0.165705	+	0.986175i	$0.447010\pi$
$572$	2513.17	−	399.716i	0.183708	−	0.0292185i
$573$		0			0
$574$	−12975.8	+	15202.7i	−0.943554	+	1.10548i
$575$	−7137.78	−	7081.72i	−0.517680	−	0.513614i
$576$		0			0
$577$		−	7328.50i		−	0.528751i	−0.964420	−	0.264376i	$-0.914834\pi$
$577$		−	7328.50i		−	0.528751i	0.964420	−	0.264376i	$-0.0851659\pi$
$578$	10289.2	+	8782.07i	0.740442	+	0.631983i
$579$		0			0
$580$	−6693.23	−	10858.4i	−0.479175	−	0.777365i
$581$	−6019.61			−0.429837
$582$		0			0
$583$	−996.548			−0.0707938
$584$	−9490.16	−	5802.90i	−0.672441	−	0.411174i
$585$		0			0
$586$	−3161.63	+	3704.22i	−0.222876	+	0.261126i
$587$	18074.5			1.27089			0.635445	−	0.772146i	$-0.280816\pi$
$587$	18074.5			1.27089			0.635445	+	0.772146i	$0.280816\pi$
$588$		0			0
$589$		−	12232.7i		−	0.855754i
$590$	675.413	−	2095.06i	0.0471293	−	0.146190i
$591$		0			0
$592$	−4870.06	+	1589.36i	−0.338105	+	0.110341i
$593$	−11920.6			−0.825501			−0.412751	−	0.910844i	$-0.635432\pi$
$593$	−11920.6			−0.825501			−0.412751	+	0.910844i	$0.635432\pi$
$594$		0			0
$595$	3762.84	−	1567.32i	0.259263	−	0.107990i
$596$	3861.48	+	24278.7i	0.265390	+	1.66861i
$597$		0			0
$598$	11038.9	−	12933.4i	0.754874	−	0.884424i
$599$	10650.0			0.726455			0.363227	−	0.931701i	$-0.381675\pi$
$599$	10650.0			0.726455			0.363227	+	0.931701i	$0.381675\pi$
$600$		0			0
$601$	1765.62			0.119836			0.0599178	−	0.998203i	$-0.480916\pi$
$601$	1765.62			0.119836			0.0599178	+	0.998203i	$0.480916\pi$
$602$	4609.03	−	5400.02i	0.312043	−	0.365596i
$603$		0			0
$604$	−10972.2	+	1745.12i	−0.739161	+	0.117562i
$605$	−13550.1	+	5643.94i	−0.910560	+	0.379271i
$606$		0			0
$607$	−1595.41			−0.106682			−0.0533408	−	0.998576i	$-0.516987\pi$
$607$	−1595.41			−0.106682			−0.0533408	+	0.998576i	$0.516987\pi$
$608$	−6974.66	−	2875.78i	−0.465230	−	0.191823i
$609$		0			0
$610$	3791.31	−	11760.2i	0.251649	−	0.780586i
$611$			23890.0i			1.58181i
$612$		0			0
$613$	4272.44			0.281505			0.140752	−	0.990045i	$-0.455048\pi$
$613$	4272.44			0.281505			0.140752	+	0.990045i	$0.455048\pi$
$614$	−14313.8	+	16770.2i	−0.940808	+	1.10227i
$615$		0			0
$616$	−2624.17	−	1604.59i	−0.171641	−	0.104953i
$617$	13024.1			0.849809			0.424905	−	0.905238i	$-0.360308\pi$
$617$	13024.1			0.849809			0.424905	+	0.905238i	$0.360308\pi$
$618$		0			0
$619$	24627.5			1.59913			0.799567	−	0.600577i	$-0.205062\pi$
$619$	24627.5			1.59913			0.799567	+	0.600577i	$0.205062\pi$
$620$	22348.1	−	13775.6i	1.44762	−	0.892324i
$621$		0			0
$622$	3740.66	+	3192.73i	0.241136	+	0.205815i
$623$			41465.1i			2.66656i
$624$		0			0
$625$	−123.205	−	15624.5i	−0.00788514	−	0.999969i
$626$	−13308.0	+	15591.9i	−0.849673	+	0.995492i
$627$		0			0
$628$	3993.01	+	25105.6i	0.253723	+	1.59526i
$629$	913.728			0.0579216
$630$		0			0
$631$		−	1363.03i		−	0.0859929i	−0.999075	−	0.0429965i	$-0.986310\pi$
$631$		−	1363.03i		−	0.0859929i	0.999075	−	0.0429965i	$-0.0136904\pi$
$632$	−22010.3	−	13458.5i	−1.38532	−	0.847076i
$633$		0			0
$634$	−11093.1	+	12996.8i	−0.694893	+	0.814148i
$635$	−2268.34	+	944.821i	−0.141758	+	0.0590458i
$636$		0			0
$637$	−50602.8			−3.14750
$638$	1114.55	−	1305.82i	0.0691619	−	0.0810313i
$639$		0			0
$640$	−2600.56	−	15980.6i	−0.160619	−	0.987016i
$641$		−	15846.4i		−	0.976434i	−0.872722	−	0.488217i	$-0.837647\pi$
$641$		−	15846.4i		−	0.976434i	0.872722	−	0.488217i	$-0.162353\pi$
$642$		0			0
$643$			15056.7i			0.923451i	0.887023	+	0.461725i	$0.152769\pi$
$643$			15056.7i			0.923451i	−0.887023	+	0.461725i	$0.847231\pi$
$644$	−20297.5	+	3228.29i	−1.24198	+	0.197535i
$645$		0			0
$646$	1023.50	+	873.580i	0.0623361	+	0.0532052i
$647$			23210.8i			1.41037i	0.709022	+	0.705187i	$0.249137\pi$
$647$			23210.8i			1.41037i	−0.709022	+	0.705187i	$0.750863\pi$
$648$		0			0
$649$	296.268			0.0179192
$650$	26333.2	−	2185.55i	1.58903	−	0.131884i
$651$		0			0
$652$	−17588.0	+	2797.35i	−1.05644	+	0.168025i
$653$		−	21282.4i		−	1.27542i	−0.770278	−	0.637708i	$-0.779883\pi$
$653$		−	21282.4i		−	1.27542i	0.770278	−	0.637708i	$-0.220117\pi$
$654$		0			0
$655$	7299.80	+	17525.5i	0.435461	+	1.04546i
$656$	−4393.24	−	13461.6i	−0.261474	−	0.801202i
$657$		0			0
$658$	18746.4	−	21963.6i	1.11065	−	1.30126i
$659$		−	308.293i		−	0.0182236i	−0.999958	−	0.00911182i	$-0.997100\pi$
$659$		−	308.293i		−	0.0182236i	0.999958	−	0.00911182i	$-0.00290042\pi$
$660$		0			0
$661$			7209.40i			0.424226i	0.977245	+	0.212113i	$0.0680345\pi$
$661$			7209.40i			0.424226i	−0.977245	+	0.212113i	$0.931966\pi$
$662$	13250.7	+	11309.8i	0.777953	+	0.663999i
$663$		0			0
$664$	2224.76	−	3638.41i	0.130026	−	0.212647i
$665$	−13738.0	+	5722.21i	−0.801106	+	0.333681i
$666$		0			0
$667$		−	11471.4i		−	0.665931i
$668$	24465.6	−	3891.22i	1.41707	−	0.225383i
$669$		0			0
$670$	−5824.06	+	18065.6i	−0.335825	+	1.04169i
$671$	1663.05			0.0956800
$672$		0			0
$673$			4006.93i			0.229503i	0.993394	+	0.114752i	$0.0366072\pi$
$673$			4006.93i			0.229503i	−0.993394	+	0.114752i	$0.963393\pi$
$674$	−2706.50	+	3170.98i	−0.154674	+	0.181219i
$675$		0			0
$676$	4258.23	+	26773.1i	0.242275	+	1.52328i
$677$			24267.9i			1.37768i	0.724911	+	0.688842i	$0.241881\pi$
$677$			24267.9i			1.37768i	−0.724911	+	0.688842i	$0.758119\pi$
$678$		0			0
$679$		−	17499.7i		−	0.989065i
$680$	−443.365	+	2853.62i	−0.0250033	+	0.160928i
$681$		0			0
$682$	2687.56	+	2293.89i	0.150897	+	0.128794i
$683$	2683.04			0.150313			0.0751565	−	0.997172i	$-0.476054\pi$
$683$	2683.04			0.150313			0.0751565	+	0.997172i	$0.476054\pi$
$684$		0			0
$685$	1634.09	−	680.637i	0.0911463	−	0.0379647i
$686$	22954.5	+	19592.1i	1.27756	+	1.09042i
$687$		0			0
$688$	1560.49	+	4781.59i	0.0864723	+	0.264966i
$689$		−	17499.2i		−	0.967587i
$690$		0			0
$691$	25584.4			1.40850			0.704251	−	0.709951i	$-0.251283\pi$
$691$	25584.4			1.40850			0.704251	+	0.709951i	$0.251283\pi$
$692$	−25108.9	+	3993.54i	−1.37933	+	0.219381i
$693$		0			0
$694$	10265.3	+	8761.68i	0.561480	+	0.479235i
$695$	15408.9	−	6418.18i	0.840996	−	0.350296i
$696$		0			0
$697$			2525.69i			0.137256i
$698$	−12837.2	+	15040.3i	−0.696124	+	0.815591i
$699$		0			0
$700$	−25924.8	−	18654.2i	−1.39981	−	1.00723i
$701$	10270.6			0.553376			0.276688	−	0.960960i	$-0.410763\pi$
$701$	10270.6			0.553376			0.276688	+	0.960960i	$0.410763\pi$
$702$		0			0
$703$	−3335.98			−0.178974
$704$	1939.72	−	993.087i	0.103843	−	0.0531653i
$705$		0			0
$706$	−16981.8	−	14494.3i	−0.905268	−	0.772665i
$707$	51734.9			2.75204
$708$		0			0
$709$			4424.27i			0.234354i	0.993111	+	0.117177i	$0.0373845\pi$
$709$			4424.27i			0.234354i	−0.993111	+	0.117177i	$0.962616\pi$
$710$	16682.1	+	5378.03i	0.881784	+	0.284273i
$711$		0			0
$712$	−25062.6	−	15324.9i	−1.31919	−	0.806637i
$713$	23609.8			1.24010
$714$		0			0
$715$	1367.45	+	3283.01i	0.0715244	+	0.171717i
$716$	6979.87	−	1110.14i	0.364316	−	0.0579439i
$717$		0			0
$718$	−19001.6	−	16218.3i	−0.987651	−	0.842981i
$719$	20863.0			1.08214			0.541070	−	0.840977i	$-0.318019\pi$
$719$	20863.0			1.08214			0.541070	+	0.840977i	$0.318019\pi$
$720$		0			0
$721$	41052.9			2.12051
$722$	11019.3	+	9405.23i	0.568002	+	0.484801i
$723$		0			0
$724$	−15556.4	+	2474.22i	−0.798549	+	0.127008i
$725$	12555.4	−	12654.8i	0.643167	−	0.648259i
$726$		0			0
$727$	14584.9			0.744049			0.372024	−	0.928223i	$-0.378664\pi$
$727$	14584.9			0.744049			0.372024	+	0.928223i	$0.378664\pi$
$728$	28176.4	−	46080.1i	1.43446	−	2.34594i
$729$		0			0
$730$	4769.99	−	14796.0i	0.241843	−	0.750169i
$731$		−	897.130i		−	0.0453920i
$732$		0			0
$733$	29746.9			1.49895			0.749474	−	0.662034i	$-0.230307\pi$
$733$	29746.9			1.49895			0.749474	+	0.662034i	$0.230307\pi$
$734$	−2457.43	−	2097.47i	−0.123577	−	0.105475i
$735$		0			0
$736$	5550.42	−	13461.5i	0.277977	−	0.674182i
$737$	−2554.71			−0.127685
$738$		0			0
$739$	−23680.1			−1.17873			−0.589367	−	0.807865i	$-0.700623\pi$
$739$	−23680.1			−1.17873			−0.589367	+	0.807865i	$0.700623\pi$
$740$	−3756.74	−	6094.56i	−0.186623	−	0.302758i
$741$		0			0
$742$	−13731.6	+	16088.1i	−0.679382	+	0.795976i
$743$		−	21315.5i		−	1.05247i	−0.850338	−	0.526237i	$-0.823602\pi$
$743$		−	21315.5i		−	1.05247i	0.850338	−	0.526237i	$-0.176398\pi$
$744$		0			0
$745$	−31715.7	+	13210.4i	−1.55970	+	0.649652i
$746$	−9340.04	−	7971.92i	−0.458396	−	0.391250i
$747$		0			0
$748$	−383.857	+	61.0518i	−0.0187636	+	0.00298433i
$749$	55380.7			2.70169
$750$		0			0
$751$			19166.0i			0.931260i	0.884979	+	0.465630i	$0.154172\pi$
$751$			19166.0i			0.931260i	−0.884979	+	0.465630i	$0.845828\pi$
$752$	6346.98	+	19448.2i	0.307780	+	0.943090i
$753$		0			0
$754$	22930.0	+	19571.3i	1.10751	+	0.945283i
$755$	−5970.15	−	14333.2i	−0.287783	−	0.690914i
$756$		0			0
$757$	2422.26			0.116299			0.0581496	−	0.998308i	$-0.481480\pi$
$757$	2422.26			0.116299			0.0581496	+	0.998308i	$0.481480\pi$
$758$	−10184.1	−	8692.38i	−0.488001	−	0.416519i
$759$		0			0
$760$	1618.70	−	10418.4i	0.0772586	−	0.497259i
$761$			14275.8i			0.680021i	0.940422	+	0.340010i	$0.110431\pi$
$761$			14275.8i			0.680021i	−0.940422	+	0.340010i	$0.889569\pi$
$762$		0			0
$763$		−	66444.7i		−	3.15264i
$764$	−846.585	−	5322.81i	−0.0400895	−	0.252058i
$765$		0			0
$766$	25281.7	−	29620.5i	1.19251	−	1.39717i
$767$			5202.42i			0.244913i
$768$		0			0
$769$	18004.1			0.844273			0.422137	−	0.906532i	$-0.361280\pi$
$769$	18004.1			0.844273			0.422137	+	0.906532i	$0.361280\pi$
$770$	1318.97	−	4091.31i	0.0617306	−	0.191481i
$771$		0			0
$772$	−30695.9	+	4882.14i	−1.43105	+	0.227606i
$773$		−	37113.1i		−	1.72686i	−0.504467	−	0.863431i	$-0.668311\pi$
$773$		−	37113.1i		−	1.72686i	0.504467	−	0.863431i	$-0.331689\pi$
$774$		0			0
$775$	26045.3	+	25840.8i	1.20720	+	1.19771i
$776$	10577.3	+	6467.63i	0.489306	+	0.299194i
$777$		0			0
$778$	−25419.4	−	21696.0i	−1.17137	−	0.999792i
$779$		−	9221.18i		−	0.424112i
$780$		0			0
$781$			2359.06i			0.108084i
$782$	−1686.06	+	1975.42i	−0.0771015	+	0.0903335i
$783$		0			0
$784$	−41194.4	+	13443.9i	−1.87657	+	0.612423i
$785$	−32795.9	+	13660.3i	−1.49113	+	0.621093i
$786$		0			0
$787$		−	1036.34i		−	0.0469397i	−0.999725	−	0.0234699i	$-0.992529\pi$
$787$		−	1036.34i		−	0.0469397i	0.999725	−	0.0234699i	$-0.00747138\pi$
$788$	−25535.3	+	4061.35i	−1.15439	+	0.183603i
$789$		0			0
$790$	11062.9	−	34316.0i	0.498229	−	1.54545i
$791$	−58421.1			−2.62606
$792$		0			0
$793$			29202.9i			1.30772i
$794$	3622.11	+	3091.54i	0.161894	+	0.138180i
$795$		0			0
$796$	39845.2	−	6337.31i	1.77421	−	0.282186i
$797$		−	34984.2i		−	1.55484i	−0.628984	−	0.777418i	$-0.716529\pi$
$797$		−	34984.2i		−	1.55484i	0.628984	−	0.777418i	$-0.283471\pi$
$798$		0			0
$799$		−	3648.91i		−	0.161563i
$800$	20856.5	−	8775.28i	0.921737	−	0.387816i
$801$		0			0
$802$	2440.26	−	2859.05i	0.107442	−	0.125881i
$803$	2092.34			0.0919516
$804$		0			0
$805$	−11044.2	−	26515.1i	−0.483549	−	1.16091i
$806$	−40280.3	+	47193.2i	−1.76032	+	2.06242i
$807$		0			0
$808$	−19120.5	+	31270.0i	−0.832496	+	1.36148i
$809$			38174.4i			1.65901i	0.558497	+	0.829507i	$0.311378\pi$
$809$			38174.4i			1.65901i	−0.558497	+	0.829507i	$0.688622\pi$
$810$		0			0
$811$	6350.80			0.274977			0.137489	−	0.990503i	$-0.456097\pi$
$811$	6350.80			0.274977			0.137489	+	0.990503i	$0.456097\pi$
$812$	−5723.55	−	35986.2i	−0.247361	−	1.55526i
$813$		0			0
$814$	625.567	−	732.925i	0.0269363	−	0.0315590i
$815$	−9569.90	−	22975.6i	−0.411312	−	0.987484i
$816$		0			0
$817$			3275.38i			0.140258i
$818$	12786.8	+	10913.8i	0.546551	+	0.466493i
$819$		0			0
$820$	16846.4	−	10384.3i	0.717440	−	0.442236i
$821$	8736.22			0.371372			0.185686	−	0.982609i	$-0.440549\pi$
$821$	8736.22			0.371372			0.185686	+	0.982609i	$0.440549\pi$
$822$		0			0
$823$	−31090.6			−1.31683			−0.658415	−	0.752655i	$-0.728773\pi$
$823$	−31090.6			−1.31683			−0.658415	+	0.752655i	$0.728773\pi$
$824$	−15172.6	+	24813.5i	−0.641458	+	1.04905i
$825$		0			0
$826$	4082.32	−	4782.92i	0.171964	−	0.201476i
$827$	14582.7			0.613169			0.306585	−	0.951843i	$-0.400814\pi$
$827$	14582.7			0.613169			0.306585	+	0.951843i	$0.400814\pi$
$828$		0			0
$829$		−	13515.4i		−	0.566237i	−0.959085	−	0.283118i	$-0.908631\pi$
$829$		−	13515.4i		−	0.566237i	0.959085	−	0.283118i	$-0.0913690\pi$
$830$	5672.60	+	1828.75i	0.237227	+	0.0764783i
$831$		0			0
$832$	17438.5	+	34061.1i	0.726646	+	1.41930i
$833$	7728.96			0.321480
$834$		0			0
$835$	13312.1	+	31959.9i	0.551717	+	1.32457i
$836$	1401.44	−	222.898i	0.0579784	−	0.00922138i
$837$		0			0
$838$	−10944.2	+	12822.4i	−0.451147	+	0.528572i
$839$	−36481.5			−1.50117			−0.750585	−	0.660774i	$-0.770228\pi$
$839$	−36481.5			−1.50117			−0.750585	+	0.660774i	$0.770228\pi$
$840$		0			0
$841$	−4050.92			−0.166096
$842$	−299.157	+	350.498i	−0.0122442	+	0.0143455i
$843$		0			0
$844$	−4704.90	−	29581.5i	−0.191883	−	1.20644i
$845$	−34974.3	+	14567.7i	−1.42385	+	0.593068i
$846$		0			0
$847$	−41931.7			−1.70105
$848$	−4649.11	−	14245.7i	−0.188268	−	0.576885i
$849$		0			0
$850$	−4022.08	+	333.816i	−0.162301	+	0.0134704i
$851$		−	6438.63i		−	0.259358i
$852$		0			0
$853$	−8546.50			−0.343056			−0.171528	−	0.985179i	$-0.554870\pi$
$853$	−8546.50			−0.343056			−0.171528	+	0.985179i	$0.554870\pi$
$854$	22915.4	−	26848.1i	0.918206	−	1.07579i
$855$		0			0
$856$	−20467.9	+	33473.6i	−0.817265	+	1.33657i
$857$	24433.9			0.973915			0.486957	−	0.873426i	$-0.338107\pi$
$857$	24433.9			0.973915			0.486957	+	0.873426i	$0.338107\pi$
$858$		0			0
$859$	−16705.4			−0.663540			−0.331770	−	0.943360i	$-0.607646\pi$
$859$	−16705.4			−0.663540			−0.331770	+	0.943360i	$0.607646\pi$
$860$	−5983.86	+	3688.50i	−0.237265	+	0.146252i
$861$		0			0
$862$	8105.33	+	6918.07i	0.320265	+	0.273353i
$863$			27872.2i			1.09940i	0.835363	+	0.549698i	$0.185257\pi$
$863$			27872.2i			1.09940i	−0.835363	+	0.549698i	$0.814743\pi$
$864$		0			0
$865$	−13662.1	−	32800.3i	−0.537025	−	1.28930i
$866$	11557.8	−	13541.3i	0.453520	−	0.531353i
$867$		0			0
$868$	74064.5	−	11779.9i	2.89621	−	0.460639i
$869$	4852.72			0.189433
$870$		0			0
$871$		−	44860.3i		−	1.74516i
$872$	40161.0	+	24557.0i	1.55966	+	0.953676i
$873$		0			0
$874$	6155.73	−	7212.16i	0.238239	−	0.279125i
$875$	16837.1	−	41338.1i	0.650512	−	1.59712i
$876$		0			0
$877$	−19230.0			−0.740422			−0.370211	−	0.928948i	$-0.620715\pi$
$877$	−19230.0			−0.740422			−0.370211	+	0.928948i	$0.620715\pi$
$878$	−6502.81	+	7618.81i	−0.249954	+	0.292850i
$879$		0			0
$880$	1985.42	+	2309.31i	0.0760552	+	0.0884624i
$881$			27428.7i			1.04892i	0.851436	+	0.524458i	$0.175732\pi$
$881$			27428.7i			1.04892i	−0.851436	+	0.524458i	$0.824268\pi$
$882$		0			0
$883$		−	40783.4i		−	1.55433i	−0.629299	−	0.777163i	$-0.716658\pi$
$883$		−	40783.4i		−	1.55433i	0.629299	−	0.777163i	$-0.283342\pi$
$884$	−1072.06	−	6740.47i	−0.0407888	−	0.256455i
$885$		0			0
$886$	7137.04	+	6091.61i	0.270625	+	0.230984i
$887$			5179.73i			0.196075i	0.995183	+	0.0980375i	$0.0312565\pi$
$887$			5179.73i			0.196075i	−0.995183	+	0.0980375i	$0.968743\pi$
$888$		0			0
$889$	−7019.55			−0.264823
$890$	12597.1	−	39074.7i	0.474444	−	1.47167i
$891$		0			0
$892$	−2561.79	−	16107.0i	−0.0961604	−	0.604598i
$893$			13322.0i			0.499220i
$894$		0			0
$895$	3797.85	+	9117.94i	0.141842	+	0.340535i
$896$	10695.3	−	44998.4i	0.398779	−	1.67778i
$897$		0			0
$898$	16868.0	−	19762.8i	0.626828	−	0.734402i
$899$			41858.6i			1.55291i
$900$		0			0
$901$			2672.80i			0.0988277i
$902$	2025.92	+	1729.17i	0.0747848	+	0.0638304i
$903$		0			0
$904$	21591.6	−	35311.2i	0.794387	−	1.29915i
$905$	−8464.48	−	20321.7i	−0.310905	−	0.746425i
$906$		0			0
$907$			10040.2i			0.367562i	0.982967	+	0.183781i	$0.0588337\pi$
$907$			10040.2i			0.367562i	−0.982967	+	0.183781i	$0.941166\pi$
$908$	504.183	+	3170.00i	0.0184272	+	0.115859i
$909$		0			0
$910$	71842.8	+	23161.0i	2.61711	+	0.843714i
$911$	34682.6			1.26134			0.630672	−	0.776049i	$-0.282779\pi$
$911$	34682.6			1.26134			0.630672	+	0.776049i	$0.282779\pi$
$912$		0			0
$913$			802.179i			0.0290780i
$914$	20735.9	−	24294.6i	0.750419	−	0.879205i
$915$		0			0
$916$	17394.8	−	2766.62i	0.627446	−	0.0997943i
$917$			54233.9i			1.95307i
$918$		0			0
$919$		−	52040.2i		−	1.86795i	−0.357334	−	0.933977i	$-0.616314\pi$
$919$		−	52040.2i		−	1.86795i	0.357334	−	0.933977i	$-0.383686\pi$
$920$	20108.2	+	3124.19i	0.720595	+	0.111958i
$921$		0			0
$922$	6358.45	+	5427.07i	0.227120	+	0.193851i
$923$	−41424.7			−1.47726
$924$		0			0
$925$	7047.04	−	7102.83i	0.250492	−	0.252475i
$926$	−8543.75	−	7292.27i	−0.303202	−	0.258789i
$927$		0			0
$928$	23866.3	+	9840.52i	0.844236	+	0.348094i
$929$		−	43993.9i		−	1.55371i	−0.629682	−	0.776853i	$-0.716815\pi$
$929$		−	43993.9i		−	1.55371i	0.629682	−	0.776853i	$-0.283185\pi$
$930$		0			0
$931$	−28218.1			−0.993352
$932$	1130.94	+	7110.69i	0.0397482	+	0.249912i
$933$		0			0
$934$	11911.7	+	10166.9i	0.417304	+	0.356178i
$935$	−208.862	−	501.440i	−0.00730537	−	0.0175389i
$936$		0			0
$937$			12605.3i			0.439485i	0.975558	+	0.219743i	$0.0705217\pi$
$937$			12605.3i			0.439485i	−0.975558	+	0.219743i	$0.929478\pi$
$938$	−35201.7	+	41242.9i	−1.22535	+	1.43564i
$939$		0			0
$940$	−24338.2	+	15002.3i	−0.844494	+	0.520554i
$941$	−53167.1			−1.84187			−0.920934	−	0.389719i	$-0.872572\pi$
$941$	−53167.1			−1.84187			−0.920934	+	0.389719i	$0.872572\pi$
$942$		0			0
$943$	17797.4			0.614596
$944$	1382.16	+	4235.16i	0.0476539	+	0.146020i
$945$		0			0
$946$	−719.612	−	614.204i	−0.0247321	−	0.0211094i
$947$	−45425.5			−1.55874			−0.779371	−	0.626563i	$-0.784461\pi$
$947$	−45425.5			−1.55874			−0.779371	+	0.626563i	$0.784461\pi$
$948$		0			0
$949$			36741.2i			1.25677i
$950$	14684.4	−	1218.75i	0.501500	−	0.0416226i
$951$		0			0
$952$	−4303.60	+	7038.18i	−0.146513	+	0.239610i
$953$	6962.93			0.236675			0.118338	−	0.992973i	$-0.462244\pi$
$953$	6962.93			0.236675			0.118338	+	0.992973i	$0.462244\pi$
$954$		0			0
$955$	6953.29	−	2896.22i	0.235606	−	0.0981356i
$956$	6654.39	+	41838.8i	0.225124	+	1.41544i
$957$		0			0
$958$	−29165.8	−	24893.6i	−0.983616	−	0.839536i
$959$	5056.80			0.170274
$960$		0			0
$961$	−56359.7			−1.89184
$962$	12870.1	+	10984.9i	0.431338	+	0.368156i
$963$		0			0
$964$	−236.752	−	1488.55i	−0.00791004	−	0.0497335i
$965$	−16702.1	−	40098.7i	−0.557161	−	1.33764i
$966$		0			0
$967$	10419.0			0.346488			0.173244	−	0.984879i	$-0.444575\pi$
$967$	10419.0			0.346488			0.173244	+	0.984879i	$0.444575\pi$
$968$	15497.4	−	25344.6i	0.514570	−	0.841536i
$969$		0			0
$970$	−5316.39	+	16490.9i	−0.175978	+	0.545865i
$971$			49841.1i			1.64725i	0.567137	+	0.823623i	$0.308051\pi$
$971$			49841.1i			1.64725i	−0.567137	+	0.823623i	$0.691949\pi$
$972$		0			0
$973$	47683.9			1.57110
$974$	−21309.5	−	18188.1i	−0.701028	−	0.598342i
$975$		0			0
$976$	7758.48	+	23773.3i	0.254450	+	0.779678i
$977$	−28971.3			−0.948693			−0.474347	−	0.880338i	$-0.657316\pi$
$977$	−28971.3			−0.948693			−0.474347	+	0.880338i	$0.657316\pi$
$978$		0			0
$979$	5525.68			0.180390
$980$	−31777.2	−	51552.2i	−1.03580	−	1.68038i
$981$		0			0
$982$	−23399.5	+	27415.2i	−0.760394	+	0.890891i
$983$			16936.3i			0.549525i	0.961512	+	0.274762i	$0.0885992\pi$
$983$			16936.3i			0.549525i	−0.961512	+	0.274762i	$0.911401\pi$
$984$		0			0
$985$	−13894.1	−	33357.2i	−0.449445	−	1.07904i
$986$	−3502.28	−	2989.27i	−0.113119	−	0.0965495i
$987$		0			0
$988$	3914.05	+	24609.1i	0.126035	+	0.792431i
$989$	−6321.68			−0.203253
$990$		0			0
$991$			53391.5i			1.71144i	0.517440	+	0.855719i	$0.326885\pi$
$991$			53391.5i			1.71144i	−0.517440	+	0.855719i	$0.673115\pi$
$992$	−20253.1	+	49120.2i	−0.648224	+	1.57215i
$993$		0			0
$994$	38084.4	+	32505.8i	1.21525	+	1.03724i
$995$	21680.3	+	52050.5i	0.690767	+	1.65840i
$996$		0			0
$997$	2722.62			0.0864856			0.0432428	−	0.999065i	$-0.486231\pi$
$997$	2722.62			0.0864856			0.0432428	+	0.999065i	$0.486231\pi$
$998$	−22267.4	−	19005.7i	−0.706276	−	0.602821i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.m.c.179.17	✓	64
3.2	odd	2	inner	360.4.m.c.179.48	yes	64
4.3	odd	2		1440.4.m.c.719.12		64
5.4	even	2	inner	360.4.m.c.179.47	yes	64
8.3	odd	2	inner	360.4.m.c.179.20	yes	64
8.5	even	2		1440.4.m.c.719.53		64
12.11	even	2		1440.4.m.c.719.54		64
15.14	odd	2	inner	360.4.m.c.179.18	yes	64
20.19	odd	2		1440.4.m.c.719.9		64
24.5	odd	2		1440.4.m.c.719.11		64
24.11	even	2	inner	360.4.m.c.179.45	yes	64
40.19	odd	2	inner	360.4.m.c.179.46	yes	64
40.29	even	2		1440.4.m.c.719.56		64
60.59	even	2		1440.4.m.c.719.55		64
120.29	odd	2		1440.4.m.c.719.10		64
120.59	even	2	inner	360.4.m.c.179.19	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.4.m.c.179.17	✓	64	1.1	even	1	trivial
360.4.m.c.179.18	yes	64	15.14	odd	2	inner
360.4.m.c.179.19	yes	64	120.59	even	2	inner
360.4.m.c.179.20	yes	64	8.3	odd	2	inner
360.4.m.c.179.45	yes	64	24.11	even	2	inner
360.4.m.c.179.46	yes	64	40.19	odd	2	inner
360.4.m.c.179.47	yes	64	5.4	even	2	inner
360.4.m.c.179.48	yes	64	3.2	odd	2	inner
1440.4.m.c.719.9		64	20.19	odd	2
1440.4.m.c.719.10		64	120.29	odd	2
1440.4.m.c.719.11		64	24.5	odd	2
1440.4.m.c.719.12		64	4.3	odd	2
1440.4.m.c.719.53		64	8.5	even	2
1440.4.m.c.719.54		64	12.11	even	2
1440.4.m.c.719.55		64	60.59	even	2
1440.4.m.c.719.56		64	40.29	even	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15135 - 1.83622i) q^{2} +(1.25659 + 7.90069i) q^{4} +(-10.3208 + 4.29888i) q^{5} -31.9386 q^{7} +(11.8040 - 19.3045i) q^{8} +O(q^{10})\)	\(q+(-2.15135 - 1.83622i) q^{2} +(1.25659 + 7.90069i) q^{4} +(-10.3208 + 4.29888i) q^{5} -31.9386 q^{7} +(11.8040 - 19.3045i) q^{8} +(30.0974 + 9.70292i) q^{10} +4.25616i q^{11} -74.7376 q^{13} +(68.7110 + 58.6462i) q^{14} +(-60.8419 + 19.8559i) q^{16} +11.4153 q^{17} -41.6766 q^{19} +(-46.9333 - 76.1398i) q^{20} +(7.81525 - 9.15648i) q^{22} -80.4383i q^{23} +(88.0392 - 88.7361i) q^{25} +(160.787 + 137.235i) q^{26} +(-40.1338 - 252.337i) q^{28} +142.612 q^{29} +293.514i q^{31} +(167.352 + 69.0022i) q^{32} +(-24.5582 - 20.9609i) q^{34} +(329.633 - 137.300i) q^{35} +80.0444 q^{37} +(89.6609 + 76.5274i) q^{38} +(-38.8396 + 249.983i) q^{40} +221.256i q^{41} -78.5904i q^{43} +(-33.6266 + 5.34827i) q^{44} +(-147.702 + 173.051i) q^{46} -319.651i q^{47} +677.073 q^{49} +(-352.342 + 29.2430i) q^{50} +(-93.9148 - 590.479i) q^{52} +234.142i q^{53} +(-18.2967 - 43.9271i) q^{55} +(-377.004 + 616.559i) q^{56} +(-306.807 - 261.866i) q^{58} -69.6092i q^{59} -390.739i q^{61} +(538.957 - 631.452i) q^{62} +(-233.329 - 455.743i) q^{64} +(771.354 - 321.288i) q^{65} +600.238i q^{67} +(14.3443 + 90.1885i) q^{68} +(-961.268 - 309.898i) q^{70} +554.269 q^{71} -491.603i q^{73} +(-172.203 - 146.979i) q^{74} +(-52.3705 - 329.274i) q^{76} -135.936i q^{77} -1140.16i q^{79} +(542.581 - 466.482i) q^{80} +(406.274 - 475.998i) q^{82} +188.475 q^{83} +(-117.815 + 49.0729i) q^{85} +(-144.309 + 169.075i) q^{86} +(82.1632 + 50.2399i) q^{88} -1298.28i q^{89} +2387.01 q^{91} +(635.518 - 101.078i) q^{92} +(-586.950 + 687.682i) q^{94} +(430.137 - 179.163i) q^{95} +547.916i q^{97} +(-1456.62 - 1243.25i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 76 q^{4}+O(q^{10}) \) 64 * q + 76 * q^4	\( 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) \) 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Introduction

L-functions

Modular forms

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