LMFDB - Embedded newform 624.4.q.m.289.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [624,4,Mod(289,624)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("624.289"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(624, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	624.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,15,0,-22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$36.8171918436$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 120 x^{8} - 979 x^{7} + 14252 x^{6} - 68003 x^{5} + 352315 x^{4} - 602502 x^{3} + \cdots + 12873744 $ x^10 - x^9 + 120x^8 - 979x^7 + 14252x^6 - 68003x^5 + 352315x^4 - 602502x^3 + 2179576x^2 - 1643304x + 12873744
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$-6.06267 - 10.5009i$ of defining polynomial
Character	$\chi$	$=$	624.289
Dual form			624.4.q.m.529.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 2.59808i) q^{3} -3.53523 q^{5} +(0.928779 - 1.60869i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(21.0289 + 36.4231i) q^{11} +(20.1361 + 42.3266i) q^{13} +(-5.30284 - 9.18479i) q^{15} +(5.33140 - 9.23425i) q^{17} +(35.8148 - 62.0331i) q^{19} +5.57267 q^{21} +(-47.1837 - 81.7246i) q^{23} -112.502 q^{25} -27.0000 q^{27} +(50.0368 + 86.6662i) q^{29} -118.087 q^{31} +(-63.0867 + 109.269i) q^{33} +(-3.28345 + 5.68709i) q^{35} +(69.2279 + 119.906i) q^{37} +(-79.7634 + 115.805i) q^{39} +(252.422 + 437.208i) q^{41} +(36.2359 - 62.7624i) q^{43} +(15.9085 - 27.5544i) q^{45} -228.606 q^{47} +(169.775 + 294.058i) q^{49} +31.9884 q^{51} -267.285 q^{53} +(-74.3419 - 128.764i) q^{55} +214.889 q^{57} +(-183.243 + 317.386i) q^{59} +(-415.082 + 718.943i) q^{61} +(8.35901 + 14.4782i) q^{63} +(-71.1857 - 149.634i) q^{65} +(-120.245 - 208.271i) q^{67} +(141.551 - 245.174i) q^{69} +(-7.29803 + 12.6406i) q^{71} -955.859 q^{73} +(-168.753 - 292.289i) q^{75} +78.1248 q^{77} -711.069 q^{79} +(-40.5000 - 70.1481i) q^{81} +111.954 q^{83} +(-18.8477 + 32.6452i) q^{85} +(-150.110 + 259.999i) q^{87} +(452.016 + 782.914i) q^{89} +(86.7924 + 6.91921i) q^{91} +(-177.131 - 306.799i) q^{93} +(-126.614 + 219.301i) q^{95} +(-210.964 + 365.400i) q^{97} -378.520 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 15 q^{3} - 22 q^{5} + 4 q^{7} - 45 q^{9} - 46 q^{11} - 31 q^{13} - 33 q^{15} - 11 q^{17} - 158 q^{19} + 24 q^{21} + 26 q^{23} + 340 q^{25} - 270 q^{27} - 125 q^{29} + 396 q^{31} + 138 q^{33} + 230 q^{35}+ \cdots + 828 q^{99}+O(q^{100}) $ 10 * q + 15 * q^3 - 22 * q^5 + 4 * q^7 - 45 * q^9 - 46 * q^11 - 31 * q^13 - 33 * q^15 - 11 * q^17 - 158 * q^19 + 24 * q^21 + 26 * q^23 + 340 * q^25 - 270 * q^27 - 125 * q^29 + 396 * q^31 + 138 * q^33 + 230 * q^35 + 261 * q^37 - 141 * q^39 - 151 * q^41 - 264 * q^43 + 99 * q^45 + 332 * q^47 + 293 * q^49 - 66 * q^51 + 1178 * q^53 + 106 * q^55 - 948 * q^57 + 72 * q^59 - 157 * q^61 + 36 * q^63 + 1137 * q^65 - 1120 * q^67 - 78 * q^69 - 898 * q^71 + 470 * q^73 + 510 * q^75 + 192 * q^77 + 148 * q^79 - 405 * q^81 + 2036 * q^83 - 2249 * q^85 + 375 * q^87 - 170 * q^89 - 334 * q^91 + 594 * q^93 - 1810 * q^95 + 2620 * q^97 + 828 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$	−3.53523			−0.316200			−0.158100	−	0.987423i	$-0.550537\pi$
$5$	−3.53523			−0.316200			−0.158100	+	0.987423i	$0.550537\pi$
$6$		0			0
$7$	0.928779	−	1.60869i	0.0501493	−	0.0868612i	−0.839861	−	0.542801i	$-0.817364\pi$
$7$	0.928779	−	1.60869i	0.0501493	−	0.0868612i	0.890010	+	0.455940i	$0.150697\pi$
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	21.0289	+	36.4231i	0.576405	+	0.998362i	0.995887	+	0.0905988i	$0.0288781\pi$
$11$	21.0289	+	36.4231i	0.576405	+	0.998362i	−0.419483	+	0.907763i	$0.637789\pi$
$12$		0			0
$13$	20.1361	+	42.3266i	0.429596	+	0.903021i
$13$	20.1361	+	42.3266i	0.429596	+	0.903021i
$14$		0			0
$15$	−5.30284	−	9.18479i	−0.0912792	−	0.158100i
$16$		0			0
$17$	5.33140	−	9.23425i	0.0760620	−	0.131743i	−0.825486	−	0.564423i	$-0.809099\pi$
$17$	5.33140	−	9.23425i	0.0760620	−	0.131743i	0.901548	+	0.432680i	$0.142432\pi$
$18$		0			0
$19$	35.8148	−	62.0331i	0.432446	−	0.749019i	−0.564637	−	0.825339i	$-0.690984\pi$
$19$	35.8148	−	62.0331i	0.432446	−	0.749019i	0.997083	+	0.0763203i	$0.0243172\pi$
$20$		0			0
$21$	5.57267			0.0579075
$22$		0			0
$23$	−47.1837	−	81.7246i	−0.427760	−	0.740903i	0.568913	−	0.822397i	$-0.307364\pi$
$23$	−47.1837	−	81.7246i	−0.427760	−	0.740903i	−0.996674	+	0.0814948i	$0.974031\pi$
$24$		0			0
$25$	−112.502			−0.900017
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	50.0368	+	86.6662i	0.320400	+	0.554949i	0.980571	−	0.196167i	$-0.0628494\pi$
$29$	50.0368	+	86.6662i	0.320400	+	0.554949i	−0.660171	+	0.751116i	$0.729516\pi$
$30$		0			0
$31$	−118.087			−0.684163			−0.342082	−	0.939670i	$-0.611132\pi$
$31$	−118.087			−0.684163			−0.342082	+	0.939670i	$0.611132\pi$
$32$		0			0
$33$	−63.0867	+	109.269i	−0.332787	+	0.576405i
$34$		0			0
$35$	−3.28345	+	5.68709i	−0.0158572	+	0.0274656i
$36$		0			0
$37$	69.2279	+	119.906i	0.307594	+	0.532769i	0.977836	−	0.209374i	$-0.0671427\pi$
$37$	69.2279	+	119.906i	0.307594	+	0.532769i	−0.670241	+	0.742143i	$0.733809\pi$
$38$		0			0
$39$	−79.7634	+	115.805i	−0.327497	+	0.475478i
$40$		0			0
$41$	252.422	+	437.208i	0.961504	+	1.66537i	0.718727	+	0.695293i	$0.244725\pi$
$41$	252.422	+	437.208i	0.961504	+	1.66537i	0.242778	+	0.970082i	$0.421941\pi$
$42$		0			0
$43$	36.2359	−	62.7624i	0.128510	−	0.222585i	−0.794590	−	0.607147i	$-0.792314\pi$
$43$	36.2359	−	62.7624i	0.128510	−	0.222585i	0.923099	+	0.384561i	$0.125647\pi$
$44$		0			0
$45$	15.9085	−	27.5544i	0.0527001	−	0.0912792i
$46$		0			0
$47$	−228.606			−0.709482			−0.354741	−	0.934965i	$-0.615431\pi$
$47$	−228.606			−0.709482			−0.354741	+	0.934965i	$0.615431\pi$
$48$		0			0
$49$	169.775	+	294.058i	0.494970	+	0.857313i
$50$		0			0
$51$	31.9884			0.0878288
$52$		0			0
$53$	−267.285			−0.692724			−0.346362	−	0.938101i	$-0.612583\pi$
$53$	−267.285			−0.692724			−0.346362	+	0.938101i	$0.612583\pi$
$54$		0			0
$55$	−74.3419	−	128.764i	−0.182259	−	0.315683i
$56$		0			0
$57$	214.889			0.499346
$58$		0			0
$59$	−183.243	+	317.386i	−0.404342	+	0.700341i	−0.994245	−	0.107133i	$-0.965833\pi$
$59$	−183.243	+	317.386i	−0.404342	+	0.700341i	0.589903	+	0.807474i	$0.299166\pi$
$60$		0			0
$61$	−415.082	+	718.943i	−0.871243	+	1.50904i	−0.0105312	+	0.999945i	$0.503352\pi$
$61$	−415.082	+	718.943i	−0.871243	+	1.50904i	−0.860712	+	0.509093i	$0.829981\pi$
$62$		0			0
$63$	8.35901	+	14.4782i	0.0167164	+	0.0289537i
$64$		0			0
$65$	−71.1857	−	149.634i	−0.135839	−	0.285536i
$66$		0			0
$67$	−120.245	−	208.271i	−0.219258	−	0.379766i	0.735323	−	0.677716i	$-0.237030\pi$
$67$	−120.245	−	208.271i	−0.219258	−	0.379766i	−0.954581	+	0.297951i	$0.903697\pi$
$68$		0			0
$69$	141.551	−	245.174i	0.246968	−	0.427760i
$70$		0			0
$71$	−7.29803	+	12.6406i	−0.0121988	+	0.0211290i	−0.872060	−	0.489398i	$-0.837216\pi$
$71$	−7.29803	+	12.6406i	−0.0121988	+	0.0211290i	0.859862	+	0.510527i	$0.170550\pi$
$72$		0			0
$73$	−955.859			−1.53253			−0.766266	−	0.642523i	$-0.777888\pi$
$73$	−955.859			−1.53253			−0.766266	+	0.642523i	$0.777888\pi$
$74$		0			0
$75$	−168.753	−	292.289i	−0.259813	−	0.450009i
$76$		0			0
$77$	78.1248			0.115625
$78$		0			0
$79$	−711.069			−1.01268			−0.506338	−	0.862335i	$-0.669001\pi$
$79$	−711.069			−1.01268			−0.506338	+	0.862335i	$0.669001\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	111.954			0.148055			0.0740273	−	0.997256i	$-0.476415\pi$
$83$	111.954			0.148055			0.0740273	+	0.997256i	$0.476415\pi$
$84$		0			0
$85$	−18.8477	+	32.6452i	−0.0240508	+	0.0416573i
$86$		0			0
$87$	−150.110	+	259.999i	−0.184983	+	0.320400i
$88$		0			0
$89$	452.016	+	782.914i	0.538355	+	0.932457i	0.998993	+	0.0448695i	$0.0142872\pi$
$89$	452.016	+	782.914i	0.538355	+	0.932457i	−0.460638	+	0.887588i	$0.652379\pi$
$90$		0			0
$91$	86.7924	+	6.91921i	0.0999815	+	0.00797066i
$92$		0			0
$93$	−177.131	−	306.799i	−0.197501	−	0.342082i
$94$		0			0
$95$	−126.614	+	219.301i	−0.136740	+	0.236840i
$96$		0			0
$97$	−210.964	+	365.400i	−0.220826	+	0.382482i	−0.955059	−	0.296416i	$-0.904209\pi$
$97$	−210.964	+	365.400i	−0.220826	+	0.382482i	0.734233	+	0.678898i	$0.237542\pi$
$98$		0			0
$99$	−378.520			−0.384270
$100$		0			0
$101$	−543.914	−	942.087i	−0.535856	−	0.928130i	−0.999121	−	0.0419104i	$-0.986656\pi$
$101$	−543.914	−	942.087i	−0.535856	−	0.928130i	0.463265	−	0.886220i	$-0.346678\pi$
$102$		0			0
$103$	854.216			0.817169			0.408584	−	0.912721i	$-0.366023\pi$
$103$	854.216			0.817169			0.408584	+	0.912721i	$0.366023\pi$
$104$		0			0
$105$	−19.7007			−0.0183104
$106$		0			0
$107$	640.871	+	1110.02i	0.579022	+	1.00290i	0.995592	+	0.0937914i	$0.0298987\pi$
$107$	640.871	+	1110.02i	0.579022	+	1.00290i	−0.416570	+	0.909104i	$0.636768\pi$
$108$		0			0
$109$	−1532.31			−1.34650			−0.673250	−	0.739415i	$-0.735102\pi$
$109$	−1532.31			−1.34650			−0.673250	+	0.739415i	$0.735102\pi$
$110$		0			0
$111$	−207.684	+	359.719i	−0.177590	+	0.307594i
$112$		0			0
$113$	119.330	−	206.686i	0.0993419	−	0.172065i	−0.812071	−	0.583559i	$-0.801660\pi$
$113$	119.330	−	206.686i	0.0993419	−	0.172065i	0.911412	+	0.411494i	$0.134993\pi$
$114$		0			0
$115$	166.805	+	288.915i	0.135258	+	0.234274i
$116$		0			0
$117$	−420.515	−	33.5241i	−0.332279	−	0.0264897i
$118$		0			0
$119$	−9.90337	−	17.1531i	−0.00762892	−	0.0132137i
$120$		0			0
$121$	−218.929	+	379.196i	−0.164484	+	0.284895i
$122$		0			0
$123$	−757.266	+	1311.62i	−0.555125	+	0.961504i
$124$		0			0
$125$	839.624			0.600786
$126$		0			0
$127$	167.209	+	289.614i	0.116830	+	0.202355i	0.918510	−	0.395398i	$-0.129393\pi$
$127$	167.209	+	289.614i	0.116830	+	0.202355i	−0.801680	+	0.597754i	$0.796060\pi$
$128$		0			0
$129$	217.415			0.148390
$130$		0			0
$131$	−329.101			−0.219494			−0.109747	−	0.993960i	$-0.535004\pi$
$131$	−329.101			−0.219494			−0.109747	+	0.993960i	$0.535004\pi$
$132$		0			0
$133$	−66.5281	−	115.230i	−0.0433738	−	0.0751256i
$134$		0			0
$135$	95.4512			0.0608528
$136$		0			0
$137$	−107.789	+	186.697i	−0.0672194	+	0.116428i	−0.897676	−	0.440655i	$-0.854746\pi$
$137$	−107.789	+	186.697i	−0.0672194	+	0.116428i	0.830457	+	0.557083i	$0.188079\pi$
$138$		0			0
$139$	−279.826	+	484.673i	−0.170752	+	0.295752i	−0.938683	−	0.344781i	$-0.887953\pi$
$139$	−279.826	+	484.673i	−0.170752	+	0.295752i	0.767931	+	0.640533i	$0.221286\pi$
$140$		0			0
$141$	−342.909	−	593.937i	−0.204810	−	0.354741i
$142$		0			0
$143$	−1118.22	+	1623.50i	−0.653921	+	0.949398i
$144$		0			0
$145$	−176.891	−	306.385i	−0.101311	−	0.175475i
$146$		0			0
$147$	−509.324	+	882.175i	−0.285771	+	0.494970i
$148$		0			0
$149$	1338.13	−	2317.72i	0.735733	−	1.27433i	−0.218668	−	0.975799i	$-0.570171\pi$
$149$	1338.13	−	2317.72i	0.735733	−	1.27433i	0.954401	−	0.298528i	$-0.0964955\pi$
$150$		0			0
$151$	161.987			0.0873003			0.0436502	−	0.999047i	$-0.486101\pi$
$151$	161.987			0.0873003			0.0436502	+	0.999047i	$0.486101\pi$
$152$		0			0
$153$	47.9826	+	83.1082i	0.0253540	+	0.0439144i
$154$		0			0
$155$	417.465			0.216333
$156$		0			0
$157$	97.3557			0.0494894			0.0247447	−	0.999694i	$-0.492123\pi$
$157$	97.3557			0.0494894			0.0247447	+	0.999694i	$0.492123\pi$
$158$		0			0
$159$	−400.927	−	694.426i	−0.199972	−	0.346362i
$160$		0			0
$161$	−175.293			−0.0858076
$162$		0			0
$163$	1697.58	−	2940.29i	0.815733	−	1.41289i	−0.0930670	−	0.995660i	$-0.529667\pi$
$163$	1697.58	−	2940.29i	0.815733	−	1.41289i	0.908800	−	0.417232i	$-0.137000\pi$
$164$		0			0
$165$	223.026	−	386.292i	0.105228	−	0.182259i
$166$		0			0
$167$	470.913	+	815.644i	0.218205	+	0.377943i	0.954259	−	0.298980i	$-0.0966464\pi$
$167$	470.913	+	815.644i	0.218205	+	0.377943i	−0.736054	+	0.676923i	$0.763313\pi$
$168$		0			0
$169$	−1386.07	+	1704.58i	−0.630894	+	0.775869i
$170$		0			0
$171$	322.333	+	558.298i	0.144149	+	0.249673i
$172$		0			0
$173$	280.748	−	486.269i	0.123381	−	0.213702i	−0.797718	−	0.603031i	$-0.793960\pi$
$173$	280.748	−	486.269i	0.123381	−	0.213702i	0.921099	+	0.389329i	$0.127293\pi$
$174$		0			0
$175$	−104.490	+	180.981i	−0.0451353	+	0.0781766i
$176$		0			0
$177$	−1099.46			−0.466894
$178$		0			0
$179$	2038.23	+	3530.32i	0.851088	+	1.47413i	0.880228	+	0.474552i	$0.157390\pi$
$179$	2038.23	+	3530.32i	0.851088	+	1.47413i	−0.0291399	+	0.999575i	$0.509277\pi$
$180$		0			0
$181$	−1140.76			−0.468463			−0.234231	−	0.972181i	$-0.575257\pi$
$181$	−1140.76			−0.468463			−0.234231	+	0.972181i	$0.575257\pi$
$182$		0			0
$183$	−2490.49			−1.00602
$184$		0			0
$185$	−244.736	−	423.896i	−0.0972615	−	0.168462i
$186$		0			0
$187$	448.453			0.175370
$188$		0			0
$189$	−25.0770	+	43.4347i	−0.00965125	+	0.0167164i
$190$		0			0
$191$	−50.3932	+	87.2835i	−0.0190907	+	0.0330660i	−0.875413	−	0.483376i	$-0.839410\pi$
$191$	−50.3932	+	87.2835i	−0.0190907	+	0.0330660i	0.856322	+	0.516442i	$0.172744\pi$
$192$		0			0
$193$	870.796	+	1508.26i	0.324774	+	0.562524i	0.981467	−	0.191634i	$-0.0613786\pi$
$193$	870.796	+	1508.26i	0.324774	+	0.562524i	−0.656693	+	0.754158i	$0.728045\pi$
$194$		0			0
$195$	281.982	−	409.397i	0.103555	−	0.150346i
$196$		0			0
$197$	1695.55	+	2936.78i	0.613212	+	1.06211i	0.990695	+	0.136098i	$0.0434563\pi$
$197$	1695.55	+	2936.78i	0.613212	+	1.06211i	−0.377483	+	0.926016i	$0.623210\pi$
$198$		0			0
$199$	−506.865	+	877.915i	−0.180556	+	0.312732i	−0.942070	−	0.335416i	$-0.891123\pi$
$199$	−506.865	+	877.915i	−0.180556	+	0.312732i	0.761514	+	0.648149i	$0.224456\pi$
$200$		0			0
$201$	360.735	−	624.812i	0.126589	−	0.219258i
$202$		0			0
$203$	185.892			0.0642714
$204$		0			0
$205$	−892.369	−	1545.63i	−0.304028	−	0.526592i
$206$		0			0
$207$	849.307			0.285174
$208$		0			0
$209$	3012.58			0.997056
$210$		0			0
$211$	819.232	+	1418.95i	0.267290	+	0.462961i	0.968161	−	0.250328i	$-0.0805384\pi$
$211$	819.232	+	1418.95i	0.267290	+	0.462961i	−0.700871	+	0.713288i	$0.747205\pi$
$212$		0			0
$213$	−43.7882			−0.0140860
$214$		0			0
$215$	−128.102	+	221.879i	−0.0406348	+	0.0703816i
$216$		0			0
$217$	−109.677	+	189.966i	−0.0343103	+	0.0594273i
$218$		0			0
$219$	−1433.79	−	2483.40i	−0.442404	−	0.766266i
$220$		0			0
$221$	498.207	+	39.7178i	0.151643	+	0.0120892i
$222$		0			0
$223$	−2623.97	−	4544.85i	−0.787956	−	1.36478i	−0.927217	−	0.374524i	$-0.877806\pi$
$223$	−2623.97	−	4544.85i	−0.787956	−	1.36478i	0.139262	−	0.990256i	$-0.455527\pi$
$224$		0			0
$225$	506.260	−	876.868i	0.150003	−	0.259813i
$226$		0			0
$227$	1871.66	−	3241.81i	0.547254	−	0.947871i	−0.451208	−	0.892419i	$-0.649007\pi$
$227$	1871.66	−	3241.81i	0.547254	−	0.947871i	0.998461	−	0.0554520i	$-0.0176600\pi$
$228$		0			0
$229$	−2355.28			−0.679656			−0.339828	−	0.940488i	$-0.610369\pi$
$229$	−2355.28			−0.679656			−0.339828	+	0.940488i	$0.610369\pi$
$230$		0			0
$231$	117.187	+	202.974i	0.0333781	+	0.0578126i
$232$		0			0
$233$	1631.80			0.458809			0.229405	−	0.973331i	$-0.426322\pi$
$233$	1631.80			0.458809			0.229405	+	0.973331i	$0.426322\pi$
$234$		0			0
$235$	808.176			0.224339
$236$		0			0
$237$	−1066.60	−	1847.41i	−0.292335	−	0.506338i
$238$		0			0
$239$	5544.73			1.50067			0.750333	−	0.661061i	$-0.229893\pi$
$239$	5544.73			1.50067			0.750333	+	0.661061i	$0.229893\pi$
$240$		0			0
$241$	−447.461	+	775.025i	−0.119599	+	0.207152i	−0.919609	−	0.392835i	$-0.871494\pi$
$241$	−447.461	+	775.025i	−0.119599	+	0.207152i	0.800010	+	0.599987i	$0.204828\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−600.192	−	1039.56i	−0.156510	−	0.271083i
$246$		0			0
$247$	3346.82	+	266.813i	0.862157	+	0.0687324i
$248$		0			0
$249$	167.931	+	290.865i	0.0427397	+	0.0740273i
$250$		0			0
$251$	1773.30	−	3071.45i	0.445935	−	0.772383i	−0.552181	−	0.833724i	$-0.686204\pi$
$251$	1773.30	−	3071.45i	0.445935	−	0.772383i	0.998117	+	0.0613411i	$0.0195377\pi$
$252$		0			0
$253$	1984.44	−	3437.16i	0.493126	−	0.854119i
$254$		0			0
$255$	−113.086			−0.0277715
$256$		0			0
$257$	3052.86	+	5287.71i	0.740981	+	1.28342i	0.952049	+	0.305946i	$0.0989726\pi$
$257$	3052.86	+	5287.71i	0.740981	+	1.28342i	−0.211068	+	0.977471i	$0.567694\pi$
$258$		0			0
$259$	257.190			0.0617026
$260$		0			0
$261$	−900.662			−0.213600
$262$		0			0
$263$	−1859.09	−	3220.04i	−0.435881	−	0.754967i	0.561487	−	0.827486i	$-0.310230\pi$
$263$	−1859.09	−	3220.04i	−0.435881	−	0.754967i	−0.997367	+	0.0725187i	$0.976896\pi$
$264$		0			0
$265$	944.912			0.219040
$266$		0			0
$267$	−1356.05	+	2348.74i	−0.310819	+	0.538355i
$268$		0			0
$269$	2102.84	−	3642.22i	0.476626	−	0.825540i	−0.523015	−	0.852323i	$-0.675193\pi$
$269$	2102.84	−	3642.22i	0.476626	−	0.825540i	0.999641	+	0.0267830i	$0.00852631\pi$
$270$		0			0
$271$	−3480.50	−	6028.41i	−0.780168	−	1.35129i	−0.931844	−	0.362860i	$-0.881800\pi$
$271$	−3480.50	−	6028.41i	−0.780168	−	1.35129i	0.151676	−	0.988430i	$-0.451533\pi$
$272$		0			0
$273$	112.212	+	235.872i	0.0248768	+	0.0522917i
$274$		0			0
$275$	−2365.80	−	4097.68i	−0.518774	−	0.898543i
$276$		0			0
$277$	90.6830	−	157.068i	0.0196701	−	0.0340696i	−0.856023	−	0.516938i	$-0.827072\pi$
$277$	90.6830	−	157.068i	0.0196701	−	0.0340696i	0.875693	+	0.482868i	$0.160405\pi$
$278$		0			0
$279$	531.392	−	920.398i	0.114027	−	0.197501i
$280$		0			0
$281$	3831.89			0.813493			0.406747	−	0.913541i	$-0.366663\pi$
$281$	3831.89			0.813493			0.406747	+	0.913541i	$0.366663\pi$
$282$		0			0
$283$	−1987.19	−	3441.91i	−0.417406	−	0.722969i	0.578271	−	0.815844i	$-0.303727\pi$
$283$	−1987.19	−	3441.91i	−0.417406	−	0.722969i	−0.995678	+	0.0928755i	$0.970394\pi$
$284$		0			0
$285$	−759.681			−0.157893
$286$		0			0
$287$	937.777			0.192875
$288$		0			0
$289$	2399.65	+	4156.32i	0.488429	+	0.845984i
$290$		0			0
$291$	−1265.78			−0.254988
$292$		0			0
$293$	479.577	−	830.652i	0.0956219	−	0.165622i	−0.814246	−	0.580520i	$-0.802849\pi$
$293$	479.577	−	830.652i	0.0956219	−	0.165622i	0.909868	+	0.414898i	$0.136183\pi$
$294$		0			0
$295$	647.805	−	1122.03i	0.127853	−	0.221448i
$296$		0			0
$297$	−567.780	−	983.424i	−0.110929	−	0.192135i
$298$		0			0
$299$	2509.02	−	3642.74i	0.485286	−	0.704566i
$300$		0			0
$301$	−67.3102	−	116.585i	−0.0128894	−	0.0223250i
$302$		0			0
$303$	1631.74	−	2826.26i	0.309377	−	0.535856i
$304$		0			0
$305$	1467.41	−	2541.63i	0.275487	−	0.477158i
$306$		0			0
$307$	−9414.17			−1.75015			−0.875074	−	0.483990i	$-0.839187\pi$
$307$	−9414.17			−1.75015			−0.875074	+	0.483990i	$0.839187\pi$
$308$		0			0
$309$	1281.32	+	2219.32i	0.235896	+	0.408584i
$310$		0			0
$311$	10059.1			1.83408			0.917041	−	0.398794i	$-0.130571\pi$
$311$	10059.1			1.83408			0.917041	+	0.398794i	$0.130571\pi$
$312$		0			0
$313$	8964.67			1.61889			0.809446	−	0.587194i	$-0.199768\pi$
$313$	8964.67			1.61889			0.809446	+	0.587194i	$0.199768\pi$
$314$		0			0
$315$	−29.5510	−	51.1838i	−0.00528575	−	0.00915518i
$316$		0			0
$317$	2956.07			0.523752			0.261876	−	0.965102i	$-0.415659\pi$
$317$	2956.07			0.523752			0.261876	+	0.965102i	$0.415659\pi$
$318$		0			0
$319$	−2104.44	+	3644.99i	−0.369360	+	0.639750i
$320$		0			0
$321$	−1922.61	+	3330.06i	−0.334298	+	0.579022i
$322$		0			0
$323$	−381.886	−	661.446i	−0.0657854	−	0.113944i
$324$		0			0
$325$	−2265.36	−	4761.83i	−0.386644	−	0.812735i
$326$		0			0
$327$	−2298.46	−	3981.05i	−0.388701	−	0.673250i
$328$		0			0
$329$	−212.325	+	367.757i	−0.0355801	+	0.0616265i
$330$		0			0
$331$	253.451	−	438.990i	0.0420874	−	0.0728975i	−0.844214	−	0.536006i	$-0.819933\pi$
$331$	253.451	−	438.990i	0.0420874	−	0.0728975i	0.886302	+	0.463108i	$0.153266\pi$
$332$		0			0
$333$	−1246.10			−0.205063
$334$		0			0
$335$	425.094	+	736.284i	0.0693295	+	0.120082i
$336$		0			0
$337$	−8692.65			−1.40510			−0.702550	−	0.711634i	$-0.747955\pi$
$337$	−8692.65			−1.40510			−0.702550	+	0.711634i	$0.747955\pi$
$338$		0			0
$339$	715.981			0.114710
$340$		0			0
$341$	−2483.24	−	4301.10i	−0.394355	−	0.683043i
$342$		0			0
$343$	1267.88			0.199588
$344$		0			0
$345$	−500.416	+	866.745i	−0.0780912	+	0.135258i
$346$		0			0
$347$	668.244	−	1157.43i	0.103381	−	0.179061i	−0.809695	−	0.586852i	$-0.800367\pi$
$347$	668.244	−	1157.43i	0.103381	−	0.179061i	0.913076	+	0.407790i	$0.133701\pi$
$348$		0			0
$349$	−3289.31	−	5697.26i	−0.504507	−	0.873832i	−0.999986	−	0.00521198i	$-0.998341\pi$
$349$	−3289.31	−	5697.26i	−0.504507	−	0.873832i	0.495480	−	0.868620i	$-0.334992\pi$
$350$		0			0
$351$	−543.675	−	1142.82i	−0.0826758	−	0.173786i
$352$		0			0
$353$	5036.06	+	8722.71i	0.759326	+	1.31519i	0.943194	+	0.332241i	$0.107805\pi$
$353$	5036.06	+	8722.71i	0.759326	+	1.31519i	−0.183868	+	0.982951i	$0.558862\pi$
$354$		0			0
$355$	25.8002	−	44.6873i	0.00385727	−	0.00668100i
$356$		0			0
$357$	29.7101	−	51.4594i	0.00440456	−	0.00762892i
$358$		0			0
$359$	4323.09			0.635555			0.317777	−	0.948165i	$-0.397064\pi$
$359$	4323.09			0.635555			0.317777	+	0.948165i	$0.397064\pi$
$360$		0			0
$361$	864.099	+	1496.66i	0.125980	+	0.218204i
$362$		0			0
$363$	−1313.57			−0.189930
$364$		0			0
$365$	3379.18			0.484587
$366$		0			0
$367$	3331.55	+	5770.42i	0.473857	+	0.820745i	0.999552	−	0.0299284i	$-0.00952793\pi$
$367$	3331.55	+	5770.42i	0.473857	+	0.820745i	−0.525695	+	0.850673i	$0.676195\pi$
$368$		0			0
$369$	−4543.59			−0.641003
$370$		0			0
$371$	−248.248	+	429.979i	−0.0347396	+	0.0601708i
$372$		0			0
$373$	4460.55	−	7725.89i	0.619191	−	1.07247i	−0.370442	−	0.928855i	$-0.620794\pi$
$373$	4460.55	−	7725.89i	0.619191	−	1.07247i	0.989634	−	0.143615i	$-0.0458728\pi$
$374$		0			0
$375$	1259.44	+	2181.41i	0.173432	+	0.300393i
$376$		0			0
$377$	−2660.74	+	3863.00i	−0.363488	+	0.527732i
$378$		0			0
$379$	1303.56	+	2257.82i	0.176673	+	0.306007i	0.940739	−	0.339131i	$-0.110133\pi$
$379$	1303.56	+	2257.82i	0.176673	+	0.306007i	−0.764066	+	0.645138i	$0.776800\pi$
$380$		0			0
$381$	−501.627	+	868.843i	−0.0674518	+	0.116830i
$382$		0			0
$383$	−3404.29	+	5896.40i	−0.454180	+	0.786663i	−0.998641	−	0.0521237i	$-0.983401\pi$
$383$	−3404.29	+	5896.40i	−0.454180	+	0.786663i	0.544461	+	0.838786i	$0.316734\pi$
$384$		0			0
$385$	−276.189			−0.0365608
$386$		0			0
$387$	326.123	+	564.861i	0.0428366	+	0.0741951i
$388$		0			0
$389$	−5307.62			−0.691792			−0.345896	−	0.938273i	$-0.612425\pi$
$389$	−5307.62			−0.691792			−0.345896	+	0.938273i	$0.612425\pi$
$390$		0			0
$391$	−1006.22			−0.130145
$392$		0			0
$393$	−493.651	−	855.029i	−0.0633624	−	0.109747i
$394$		0			0
$395$	2513.79			0.320209
$396$		0			0
$397$	4729.31	−	8191.40i	0.597877	−	1.03555i	−0.395257	−	0.918571i	$-0.629344\pi$
$397$	4729.31	−	8191.40i	0.597877	−	1.03555i	0.993134	−	0.116983i	$-0.0373223\pi$
$398$		0			0
$399$	199.584	−	345.690i	0.0250419	−	0.0433738i
$400$		0			0
$401$	−189.750	−	328.656i	−0.0236300	−	0.0409284i	0.853969	−	0.520325i	$-0.174189\pi$
$401$	−189.750	−	328.656i	−0.0236300	−	0.0409284i	−0.877599	+	0.479396i	$0.840856\pi$
$402$		0			0
$403$	−2377.81	−	4998.22i	−0.293914	−	0.617814i
$404$		0			0
$405$	143.177	+	247.989i	0.0175667	+	0.0304264i
$406$		0			0
$407$	−2911.57	+	5042.99i	−0.354598	+	0.614181i
$408$		0			0
$409$	6048.61	−	10476.5i	0.731259	−	1.26658i	−0.225087	−	0.974339i	$-0.572267\pi$
$409$	6048.61	−	10476.5i	0.731259	−	1.26658i	0.956346	−	0.292238i	$-0.0944000\pi$
$410$		0			0
$411$	−646.736			−0.0776183
$412$		0			0
$413$	340.384	+	589.563i	0.0405550	+	0.0702433i
$414$		0			0
$415$	−395.783			−0.0468149
$416$		0			0
$417$	−1678.96			−0.197168
$418$		0			0
$419$	5703.41	+	9878.60i	0.664988	+	1.15179i	0.979289	+	0.202469i	$0.0648965\pi$
$419$	5703.41	+	9878.60i	0.664988	+	1.15179i	−0.314301	+	0.949323i	$0.601770\pi$
$420$		0			0
$421$	−3068.96			−0.355278			−0.177639	−	0.984096i	$-0.556846\pi$
$421$	−3068.96			−0.355278			−0.177639	+	0.984096i	$0.556846\pi$
$422$		0			0
$423$	1028.73	−	1781.81i	0.118247	−	0.204810i
$424$		0			0
$425$	−599.794	+	1038.87i	−0.0684571	+	0.118571i
$426$		0			0
$427$	771.039	+	1335.48i	0.0873845	+	0.151354i
$428$		0			0
$429$	−5895.31	−	469.983i	−0.663470	−	0.0528927i
$430$		0			0
$431$	−1109.01	−	1920.86i	−0.123942	−	0.214674i	0.797377	−	0.603482i	$-0.206220\pi$
$431$	−1109.01	−	1920.86i	−0.123942	−	0.214674i	−0.921319	+	0.388808i	$0.872887\pi$
$432$		0			0
$433$	−4330.44	+	7500.54i	−0.480618	+	0.832455i	−0.999753	−	0.0222375i	$-0.992921\pi$
$433$	−4330.44	+	7500.54i	−0.480618	+	0.832455i	0.519135	+	0.854692i	$0.326254\pi$
$434$		0			0
$435$	530.674	−	919.155i	0.0584917	−	0.101311i
$436$		0			0
$437$	−6759.50			−0.739933
$438$		0			0
$439$	7757.19	+	13435.8i	0.843349	+	1.46072i	0.887047	+	0.461679i	$0.152753\pi$
$439$	7757.19	+	13435.8i	0.843349	+	1.46072i	−0.0436981	+	0.999045i	$0.513914\pi$
$440$		0			0
$441$	−3055.95			−0.329980
$442$		0			0
$443$	9100.19			0.975989			0.487994	−	0.872847i	$-0.337729\pi$
$443$	9100.19			0.975989			0.487994	+	0.872847i	$0.337729\pi$
$444$		0			0
$445$	−1597.98	−	2767.78i	−0.170228	−	0.294843i
$446$		0			0
$447$	8028.81			0.849551
$448$		0			0
$449$	−3758.43	+	6509.78i	−0.395036	+	0.684222i	−0.993106	−	0.117222i	$-0.962601\pi$
$449$	−3758.43	+	6509.78i	−0.395036	+	0.684222i	0.598070	+	0.801444i	$0.295934\pi$
$450$		0			0
$451$	−10616.3	+	18388.0i	−1.10843	+	1.91986i
$452$		0			0
$453$	242.981	+	420.856i	0.0252014	+	0.0436502i
$454$		0			0
$455$	−306.831	−	24.4610i	−0.0316142	−	0.00252033i
$456$		0			0
$457$	3859.77	+	6685.31i	0.395082	+	0.684301i	0.993112	−	0.117172i	$-0.0373830\pi$
$457$	3859.77	+	6685.31i	0.395082	+	0.684301i	−0.598030	+	0.801474i	$0.704050\pi$
$458$		0			0
$459$	−143.948	+	249.325i	−0.0146381	+	0.0253540i
$460$		0			0
$461$	5633.65	−	9757.78i	0.569166	−	0.985824i	−0.427483	−	0.904023i	$-0.640600\pi$
$461$	5633.65	−	9757.78i	0.569166	−	0.985824i	0.996649	−	0.0818007i	$-0.0260671\pi$
$462$		0			0
$463$	−11503.9			−1.15471			−0.577355	−	0.816493i	$-0.695915\pi$
$463$	−11503.9			−1.15471			−0.577355	+	0.816493i	$0.695915\pi$
$464$		0			0
$465$	626.197	+	1084.61i	0.0624499	+	0.108166i
$466$		0			0
$467$	10583.1			1.04867			0.524333	−	0.851513i	$-0.324315\pi$
$467$	10583.1			1.04867			0.524333	+	0.851513i	$0.324315\pi$
$468$		0			0
$469$	−446.725			−0.0439826
$470$		0			0
$471$	146.034	+	252.938i	0.0142864	+	0.0247447i
$472$		0			0
$473$	3048.00			0.296294
$474$		0			0
$475$	−4029.24	+	6978.85i	−0.389209	+	0.674130i
$476$		0			0
$477$	1202.78	−	2083.28i	0.115454	−	0.199972i
$478$		0			0
$479$	−6145.51	−	10644.3i	−0.586212	−	1.01535i	−0.994723	−	0.102595i	$-0.967285\pi$
$479$	−6145.51	−	10644.3i	−0.586212	−	1.01535i	0.408511	−	0.912753i	$-0.366048\pi$
$480$		0			0
$481$	−3681.24	+	5344.62i	−0.348960	+	0.506640i
$482$		0			0
$483$	−262.939	−	455.425i	−0.0247705	−	0.0429038i
$484$		0			0
$485$	745.805	−	1291.77i	0.0698253	−	0.120941i
$486$		0			0
$487$	417.296	−	722.778i	0.0388285	−	0.0672530i	−0.845958	−	0.533249i	$-0.820971\pi$
$487$	417.296	−	722.778i	0.0388285	−	0.0672530i	0.884787	+	0.465996i	$0.154304\pi$
$488$		0			0
$489$	10185.5			0.941928
$490$		0			0
$491$	−4135.70	−	7163.25i	−0.380126	−	0.658397i	0.610954	−	0.791666i	$-0.290786\pi$
$491$	−4135.70	−	7163.25i	−0.380126	−	0.658397i	−0.991080	+	0.133269i	$0.957453\pi$
$492$		0			0
$493$	1067.06			0.0974809
$494$		0			0
$495$	1338.16			0.121506
$496$		0			0
$497$	13.5565	+	23.4806i	0.00122353	+	0.00211921i
$498$		0			0
$499$	−3466.25			−0.310964			−0.155482	−	0.987839i	$-0.549693\pi$
$499$	−3466.25			−0.310964			−0.155482	+	0.987839i	$0.549693\pi$
$500$		0			0
$501$	−1412.74	+	2446.93i	−0.125981	+	0.218205i
$502$		0			0
$503$	−8964.24	+	15526.5i	−0.794623	+	1.37633i	0.128455	+	0.991715i	$0.458998\pi$
$503$	−8964.24	+	15526.5i	−0.794623	+	1.37633i	−0.923078	+	0.384613i	$0.874335\pi$
$504$		0			0
$505$	1922.86	+	3330.49i	0.169438	+	0.293475i
$506$		0			0
$507$	−6507.75	−	1044.25i	−0.570058	−	0.0914730i
$508$		0			0
$509$	−4688.80	−	8121.24i	−0.408305	−	0.707206i	0.586395	−	0.810026i	$-0.300547\pi$
$509$	−4688.80	−	8121.24i	−0.408305	−	0.707206i	−0.994700	+	0.102820i	$0.967214\pi$
$510$		0			0
$511$	−887.782	+	1537.68i	−0.0768555	+	0.133118i
$512$		0			0
$513$	−967.000	+	1674.89i	−0.0832243	+	0.144149i
$514$		0			0
$515$	−3019.85			−0.258389
$516$		0			0
$517$	−4807.34	−	8326.55i	−0.408949	−	0.708320i
$518$		0			0
$519$	1684.49			0.142468
$520$		0			0
$521$	−4889.72			−0.411176			−0.205588	−	0.978639i	$-0.565911\pi$
$521$	−4889.72			−0.411176			−0.205588	+	0.978639i	$0.565911\pi$
$522$		0			0
$523$	8142.08	+	14102.5i	0.680743	+	1.17908i	0.974755	+	0.223279i	$0.0716761\pi$
$523$	8142.08	+	14102.5i	0.680743	+	1.17908i	−0.294012	+	0.955802i	$0.594991\pi$
$524$		0			0
$525$	−626.938			−0.0521177
$526$		0			0
$527$	−629.569	+	1090.45i	−0.0520388	+	0.0901339i
$528$		0			0
$529$	1630.89	−	2824.79i	0.134042	−	0.232168i
$530$		0			0
$531$	−1649.19	−	2856.47i	−0.134781	−	0.233447i
$532$		0			0
$533$	−13422.7	+	19487.8i	−1.09081	+	1.58370i
$534$		0			0
$535$	−2265.62	−	3924.18i	−0.183087	−	0.317116i
$536$		0			0
$537$	−6114.70	+	10591.0i	−0.491376	+	0.851088i
$538$		0			0
$539$	−7140.35	+	12367.4i	−0.570606	+	0.988319i
$540$		0			0
$541$	−1972.77			−0.156776			−0.0783881	−	0.996923i	$-0.524977\pi$
$541$	−1972.77			−0.156776			−0.0783881	+	0.996923i	$0.524977\pi$
$542$		0			0
$543$	−1711.13	−	2963.77i	−0.135233	−	0.234231i
$544$		0			0
$545$	5417.06			0.425764
$546$		0			0
$547$	−20991.9			−1.64086			−0.820430	−	0.571747i	$-0.806266\pi$
$547$	−20991.9			−1.64086			−0.820430	+	0.571747i	$0.806266\pi$
$548$		0			0
$549$	−3735.74	−	6470.49i	−0.290414	−	0.503012i
$550$		0			0
$551$	7168.23			0.554223
$552$		0			0
$553$	−660.426	+	1143.89i	−0.0507851	+	0.0879623i
$554$		0			0
$555$	734.209	−	1271.69i	0.0561539	−	0.0972615i
$556$		0			0
$557$	−2502.08	−	4333.73i	−0.190335	−	0.329670i	0.755026	−	0.655695i	$-0.227624\pi$
$557$	−2502.08	−	4333.73i	−0.190335	−	0.329670i	−0.945361	+	0.326025i	$0.894291\pi$
$558$		0			0
$559$	3386.16	+	269.950i	0.256207	+	0.0204251i
$560$		0			0
$561$	672.680	+	1165.12i	0.0506249	+	0.0876849i
$562$		0			0
$563$	7631.61	−	13218.3i	0.571286	−	0.989496i	−0.425148	−	0.905124i	$-0.639778\pi$
$563$	7631.61	−	13218.3i	0.571286	−	0.989496i	0.996434	−	0.0843727i	$-0.0268886\pi$
$564$		0			0
$565$	−421.859	+	730.682i	−0.0314120	+	0.0544071i
$566$		0			0
$567$	−150.462			−0.0111443
$568$		0			0
$569$	5171.63	+	8957.53i	0.381030	+	0.659963i	0.991210	−	0.132300i	$-0.0422362\pi$
$569$	5171.63	+	8957.53i	0.381030	+	0.659963i	−0.610180	+	0.792263i	$0.708903\pi$
$570$		0			0
$571$	14885.6			1.09097			0.545483	−	0.838122i	$-0.316346\pi$
$571$	14885.6			1.09097			0.545483	+	0.838122i	$0.316346\pi$
$572$		0			0
$573$	−302.359			−0.0220440
$574$		0			0
$575$	5308.27	+	9194.20i	0.384992	+	0.666825i
$576$		0			0
$577$	8542.00			0.616305			0.308153	−	0.951337i	$-0.400289\pi$
$577$	8542.00			0.616305			0.308153	+	0.951337i	$0.400289\pi$
$578$		0			0
$579$	−2612.39	+	4524.79i	−0.187508	+	0.324774i
$580$		0			0
$581$	103.980	−	180.099i	0.00742484	−	0.0128602i
$582$		0			0
$583$	−5620.70	−	9735.34i	−0.399289	−	0.691589i
$584$		0			0
$585$	1486.62	+	118.515i	0.105067	+	0.00837607i
$586$		0			0
$587$	−6315.34	−	10938.5i	−0.444058	−	0.769131i	0.553928	−	0.832565i	$-0.313128\pi$
$587$	−6315.34	−	10938.5i	−0.444058	−	0.769131i	−0.997986	+	0.0634335i	$0.979795\pi$
$588$		0			0
$589$	−4229.27	+	7325.30i	−0.295864	+	0.512451i
$590$		0			0
$591$	−5086.64	+	8810.33i	−0.354038	+	0.613212i
$592$		0			0
$593$	−11659.6			−0.807423			−0.403712	−	0.914886i	$-0.632280\pi$
$593$	−11659.6			−0.807423			−0.403712	+	0.914886i	$0.632280\pi$
$594$		0			0
$595$	35.0107	+	60.6403i	0.00241227	+	0.00417817i
$596$		0			0
$597$	−3041.19			−0.208488
$598$		0			0
$599$	−18282.4			−1.24708			−0.623539	−	0.781792i	$-0.714306\pi$
$599$	−18282.4			−1.24708			−0.623539	+	0.781792i	$0.714306\pi$
$600$		0			0
$601$	−4771.23	−	8264.01i	−0.323831	−	0.560892i	0.657444	−	0.753503i	$-0.271638\pi$
$601$	−4771.23	−	8264.01i	−0.323831	−	0.560892i	−0.981275	+	0.192611i	$0.938304\pi$
$602$		0			0
$603$	2164.41			0.146172
$604$		0			0
$605$	773.963	−	1340.54i	0.0520101	−	0.0900841i
$606$		0			0
$607$	−806.399	+	1396.72i	−0.0539221	+	0.0933959i	−0.891727	−	0.452575i	$-0.850506\pi$
$607$	−806.399	+	1396.72i	−0.0539221	+	0.0933959i	0.837804	+	0.545971i	$0.183839\pi$
$608$		0			0
$609$	278.839	+	482.962i	0.0185535	+	0.0321357i
$610$		0			0
$611$	−4603.24	−	9676.12i	−0.304791	−	0.640677i
$612$		0			0
$613$	9245.77	+	16014.1i	0.609190	+	1.05515i	0.991374	+	0.131061i	$0.0418385\pi$
$613$	9245.77	+	16014.1i	0.609190	+	1.05515i	−0.382185	+	0.924086i	$0.624828\pi$
$614$		0			0
$615$	2677.11	−	4636.89i	0.175531	−	0.304028i
$616$		0			0
$617$	−652.242	+	1129.72i	−0.0425580	+	0.0737126i	−0.886520	−	0.462691i	$-0.846884\pi$
$617$	−652.242	+	1129.72i	−0.0425580	+	0.0737126i	0.843962	+	0.536403i	$0.180217\pi$
$618$		0			0
$619$	−10100.7			−0.655865			−0.327932	−	0.944701i	$-0.606352\pi$
$619$	−10100.7			−0.655865			−0.327932	+	0.944701i	$0.606352\pi$
$620$		0			0
$621$	1273.96	+	2206.56i	0.0823225	+	0.142587i
$622$		0			0
$623$	1679.29			0.107993
$624$		0			0
$625$	11094.5			0.710048
$626$		0			0
$627$	4518.87	+	7826.92i	0.287825	+	0.498528i
$628$		0			0
$629$	1476.32			0.0935849
$630$		0			0
$631$	8027.22	−	13903.6i	0.506432	−	0.877166i	−0.493540	−	0.869723i	$-0.664297\pi$
$631$	8027.22	−	13903.6i	0.506432	−	0.877166i	0.999972	−	0.00744325i	$-0.00236928\pi$
$632$		0			0
$633$	−2457.70	+	4256.86i	−0.154320	+	0.267290i
$634$		0			0
$635$	−591.122	−	1023.85i	−0.0369417	−	0.0639848i
$636$		0			0
$637$	−9027.88	+	13107.2i	−0.561535	+	0.815267i
$638$		0			0
$639$	−65.6823	−	113.765i	−0.00406628	−	0.00704300i
$640$		0			0
$641$	−13041.3	+	22588.2i	−0.803588	+	1.39186i	0.113652	+	0.993521i	$0.463745\pi$
$641$	−13041.3	+	22588.2i	−0.803588	+	1.39186i	−0.917240	+	0.398335i	$0.869588\pi$
$642$		0			0
$643$	9647.37	−	16709.7i	0.591688	−	1.02483i	−0.402318	−	0.915500i	$-0.631795\pi$
$643$	9647.37	−	16709.7i	0.591688	−	1.02483i	0.994005	−	0.109333i	$-0.0348714\pi$
$644$		0			0
$645$	−768.613			−0.0469211
$646$		0			0
$647$	−3128.43	−	5418.60i	−0.190095	−	0.329254i	0.755187	−	0.655510i	$-0.227546\pi$
$647$	−3128.43	−	5418.60i	−0.190095	−	0.329254i	−0.945281	+	0.326256i	$0.894213\pi$
$648$		0			0
$649$	−15413.6			−0.932259
$650$		0			0
$651$	−658.061			−0.0396182
$652$		0			0
$653$	3713.39	+	6431.79i	0.222536	+	0.385444i	0.955578	−	0.294740i	$-0.0952330\pi$
$653$	3713.39	+	6431.79i	0.222536	+	0.385444i	−0.733041	+	0.680184i	$0.761900\pi$
$654$		0			0
$655$	1163.45			0.0694040
$656$		0			0
$657$	4301.37	−	7450.19i	0.255422	−	0.442404i
$658$		0			0
$659$	30.9243	−	53.5625i	0.00182798	−	0.00316616i	−0.865110	−	0.501582i	$-0.832751\pi$
$659$	30.9243	−	53.5625i	0.00182798	−	0.00316616i	0.866938	+	0.498416i	$0.166085\pi$
$660$		0			0
$661$	3365.00	+	5828.36i	0.198008	+	0.342961i	0.947883	−	0.318620i	$-0.103219\pi$
$661$	3365.00	+	5828.36i	0.198008	+	0.342961i	−0.749874	+	0.661580i	$0.769886\pi$
$662$		0			0
$663$	644.121	+	1353.96i	0.0377309	+	0.0793112i
$664$		0			0
$665$	235.192	+	407.364i	0.0137148	+	0.0237548i
$666$		0			0
$667$	4721.84	−	8178.47i	0.274109	−	0.474770i
$668$		0			0
$669$	7871.91	−	13634.6i	0.454926	−	0.787956i
$670$		0			0
$671$	−34914.9			−2.00875
$672$		0			0
$673$	−1614.32	−	2796.09i	−0.0924629	−	0.160150i	0.816084	−	0.577933i	$-0.196141\pi$
$673$	−1614.32	−	2796.09i	−0.0924629	−	0.160150i	−0.908547	+	0.417783i	$0.862807\pi$
$674$		0			0
$675$	3037.56			0.173208
$676$		0			0
$677$	831.739			0.0472176			0.0236088	−	0.999721i	$-0.492484\pi$
$677$	831.739			0.0472176			0.0236088	+	0.999721i	$0.492484\pi$
$678$		0			0
$679$	391.878	+	678.752i	0.0221486	+	0.0383624i
$680$		0			0
$681$	11230.0			0.631914
$682$		0			0
$683$	−1918.37	+	3322.71i	−0.107473	+	0.186149i	−0.914746	−	0.404029i	$-0.867609\pi$
$683$	−1918.37	+	3322.71i	−0.107473	+	0.186149i	0.807273	+	0.590179i	$0.200943\pi$
$684$		0			0
$685$	381.060	−	660.015i	0.0212548	−	0.0368144i
$686$		0			0
$687$	−3532.92	−	6119.20i	−0.196200	−	0.339828i
$688$		0			0
$689$	−5382.07	−	11313.2i	−0.297592	−	0.625544i
$690$		0			0
$691$	2113.21	+	3660.20i	0.116339	+	0.201506i	0.918314	−	0.395852i	$-0.129551\pi$
$691$	2113.21	+	3660.20i	0.116339	+	0.201506i	−0.801975	+	0.597358i	$0.796217\pi$
$692$		0			0
$693$	−351.561	+	608.922i	−0.0192709	+	0.0333781i
$694$		0			0
$695$	989.250	−	1713.43i	0.0539919	−	0.0935168i
$696$		0			0
$697$	5383.04			0.292536
$698$		0			0
$699$	2447.70	+	4239.53i	0.132447	+	0.229405i
$700$		0			0
$701$	−15196.5			−0.818777			−0.409389	−	0.912360i	$-0.634258\pi$
$701$	−15196.5			−0.818777			−0.409389	+	0.912360i	$0.634258\pi$
$702$		0			0
$703$	9917.53			0.532072
$704$		0			0
$705$	1212.26	+	2099.70i	0.0647610	+	0.112169i
$706$		0			0
$707$	−2020.70			−0.107491
$708$		0			0
$709$	−9767.94	+	16918.6i	−0.517408	+	0.896178i	0.482387	+	0.875958i	$0.339770\pi$
$709$	−9767.94	+	16918.6i	−0.517408	+	0.896178i	−0.999796	+	0.0202195i	$0.993563\pi$
$710$		0			0
$711$	3199.81	−	5542.23i	0.168779	−	0.292335i
$712$		0			0
$713$	5571.79	+	9650.62i	0.292658	+	0.506898i
$714$		0			0
$715$	3953.18	−	5739.44i	0.206770	−	0.300200i
$716$		0			0
$717$	8317.10	+	14405.6i	0.433205	+	0.750333i
$718$		0			0
$719$	−13777.7	+	23863.7i	−0.714633	+	1.23778i	0.248468	+	0.968640i	$0.420073\pi$
$719$	−13777.7	+	23863.7i	−0.714633	+	1.23778i	−0.963101	+	0.269141i	$0.913260\pi$
$720$		0			0
$721$	793.377	−	1374.17i	0.0409805	−	0.0709803i
$722$		0			0
$723$	−2684.76			−0.138102
$724$		0			0
$725$	−5629.24	−	9750.14i	−0.288365	−	0.499463i
$726$		0			0
$727$	30722.6			1.56732			0.783658	−	0.621193i	$-0.213352\pi$
$727$	30722.6			1.56732			0.783658	+	0.621193i	$0.213352\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−386.376	−	669.222i	−0.0195494	−	0.0338606i
$732$		0			0
$733$	35290.8			1.77830			0.889152	−	0.457612i	$-0.151295\pi$
$733$	35290.8			1.77830			0.889152	+	0.457612i	$0.151295\pi$
$734$		0			0
$735$	1800.58	−	3118.69i	0.0903610	−	0.156510i
$736$		0			0
$737$	5057.24	−	8759.40i	0.252763	−	0.437798i
$738$		0			0
$739$	−5151.72	−	8923.04i	−0.256440	−	0.444167i	0.708846	−	0.705364i	$-0.249216\pi$
$739$	−5151.72	−	8923.04i	−0.256440	−	0.444167i	−0.965286	+	0.261197i	$0.915883\pi$
$740$		0			0
$741$	4327.03	+	9095.50i	0.214517	+	0.450920i
$742$		0			0
$743$	−3251.06	−	5631.00i	−0.160525	−	0.278037i	0.774532	−	0.632534i	$-0.217985\pi$
$743$	−3251.06	−	5631.00i	−0.160525	−	0.278037i	−0.935057	+	0.354498i	$0.884652\pi$
$744$		0			0
$745$	−4730.61	+	8193.66i	−0.232639	+	0.402943i
$746$		0			0
$747$	−503.792	+	872.594i	−0.0246758	+	0.0427397i
$748$		0			0
$749$	2380.91			0.116150
$750$		0			0
$751$	−13460.8	−	23314.7i	−0.654048	−	1.13284i	−0.982131	−	0.188196i	$-0.939736\pi$
$751$	−13460.8	−	23314.7i	−0.654048	−	1.13284i	0.328083	−	0.944649i	$-0.393597\pi$
$752$		0			0
$753$	10639.8			0.514922
$754$		0			0
$755$	−572.662			−0.0276044
$756$		0			0
$757$	1475.76	+	2556.09i	0.0708551	+	0.122725i	0.899276	−	0.437381i	$-0.144094\pi$
$757$	1475.76	+	2556.09i	0.0708551	+	0.122725i	−0.828421	+	0.560106i	$0.810761\pi$
$758$		0			0
$759$	11906.7			0.569413
$760$		0			0
$761$	6261.20	−	10844.7i	0.298250	−	0.516585i	−0.677486	−	0.735536i	$-0.736930\pi$
$761$	6261.20	−	10844.7i	0.298250	−	0.516585i	0.975736	+	0.218952i	$0.0702637\pi$
$762$		0			0
$763$	−1423.17	+	2465.01i	−0.0675261	+	0.116959i
$764$		0			0
$765$	−169.629	−	293.807i	−0.00801694	−	0.0138858i
$766$		0			0
$767$	−17123.7	−	1365.12i	−0.806127	−	0.0642655i
$768$		0			0
$769$	9098.11	+	15758.4i	0.426640	+	0.738962i	0.996572	−	0.0827295i	$-0.0263638\pi$
$769$	9098.11	+	15758.4i	0.426640	+	0.738962i	−0.569932	+	0.821692i	$0.693030\pi$
$770$		0			0
$771$	−9158.58	+	15863.1i	−0.427806	+	0.740981i
$772$		0			0
$773$	19464.0	−	33712.6i	0.905655	−	1.56864i	0.0856199	−	0.996328i	$-0.472713\pi$
$773$	19464.0	−	33712.6i	0.905655	−	1.56864i	0.820035	−	0.572313i	$-0.193954\pi$
$774$		0			0
$775$	13285.1			0.615759
$776$		0			0
$777$	385.784	+	668.198i	0.0178120	+	0.0308513i
$778$		0			0
$779$	36161.8			1.66320
$780$		0			0
$781$	−613.878			−0.0281258
$782$		0			0
$783$	−1350.99	−	2339.99i	−0.0616610	−	0.106800i
$784$		0			0
$785$	−344.175			−0.0156486
$786$		0			0
$787$	−12199.3	+	21129.9i	−0.552554	+	0.957051i	0.445536	+	0.895264i	$0.353013\pi$
$787$	−12199.3	+	21129.9i	−0.552554	+	0.957051i	−0.998089	+	0.0617870i	$0.980320\pi$
$788$		0			0
$789$	5577.28	−	9660.13i	0.251656	−	0.435881i
$790$		0			0
$791$	−221.663	−	383.931i	−0.00996386	−	0.0172579i
$792$		0			0
$793$	−38788.5	−	3092.28i	−1.73698	−	0.138474i
$794$		0			0
$795$	1417.37	+	2454.95i	0.0632313	+	0.109520i
$796$		0			0
$797$	−7276.60	+	12603.4i	−0.323401	+	0.560147i	−0.981187	−	0.193058i	$-0.938160\pi$
$797$	−7276.60	+	12603.4i	−0.323401	+	0.560147i	0.657787	+	0.753204i	$0.271493\pi$
$798$		0			0
$799$	−1218.79	+	2111.01i	−0.0539646	+	0.0934694i
$800$		0			0
$801$	−8136.28			−0.358903
$802$		0			0
$803$	−20100.7	−	34815.4i	−0.883359	−	1.53002i
$804$		0			0
$805$	619.701			0.0271324
$806$		0			0
$807$	12617.0			0.550360
$808$		0			0
$809$	−21894.4	−	37922.2i	−0.951504	−	1.64805i	−0.742173	−	0.670208i	$-0.766205\pi$
$809$	−21894.4	−	37922.2i	−0.951504	−	1.64805i	−0.209331	−	0.977845i	$-0.567129\pi$
$810$		0			0
$811$	10303.9			0.446139			0.223069	−	0.974803i	$-0.428392\pi$
$811$	10303.9			0.446139			0.223069	+	0.974803i	$0.428392\pi$
$812$		0			0
$813$	10441.5	−	18085.2i	0.450430	−	0.780168i
$814$		0			0
$815$	−6001.32	+	10394.6i	−0.257935	+	0.446757i
$816$		0			0
$817$	−2595.56	−	4495.65i	−0.111147	−	0.192513i
$818$		0			0
$819$	−444.496	+	645.343i	−0.0189645	+	0.0275337i
$820$		0			0
$821$	20143.6	+	34889.7i	0.856291	+	1.48314i	0.875442	+	0.483323i	$0.160570\pi$
$821$	20143.6	+	34889.7i	0.856291	+	1.48314i	−0.0191506	+	0.999817i	$0.506096\pi$
$822$		0			0
$823$	12813.6	−	22193.8i	0.542715	−	0.940011i	−0.456032	−	0.889964i	$-0.650730\pi$
$823$	12813.6	−	22193.8i	0.542715	−	0.940011i	0.998747	−	0.0500469i	$-0.0159371\pi$
$824$		0			0
$825$	7097.39	−	12293.0i	0.299514	−	0.518774i
$826$		0			0
$827$	19038.4			0.800520			0.400260	−	0.916402i	$-0.368920\pi$
$827$	19038.4			0.800520			0.400260	+	0.916402i	$0.368920\pi$
$828$		0			0
$829$	−5998.36	−	10389.5i	−0.251305	−	0.435272i	0.712581	−	0.701590i	$-0.247526\pi$
$829$	−5998.36	−	10389.5i	−0.251305	−	0.435272i	−0.963885	+	0.266318i	$0.914193\pi$
$830$		0			0
$831$	544.098			0.0227131
$832$		0			0
$833$	3620.55			0.150594
$834$		0			0
$835$	−1664.78	−	2883.49i	−0.0689966	−	0.119506i
$836$		0			0
$837$	3188.35			0.131667
$838$		0			0
$839$	−13001.9	+	22519.9i	−0.535011	+	0.926667i	0.464152	+	0.885756i	$0.346359\pi$
$839$	−13001.9	+	22519.9i	−0.535011	+	0.926667i	−0.999163	+	0.0409109i	$0.986974\pi$
$840$		0			0
$841$	7187.14	−	12448.5i	0.294688	−	0.510415i
$842$		0			0
$843$	5747.84	+	9955.55i	0.234835	+	0.406747i
$844$		0			0
$845$	4900.09	−	6026.09i	0.199489	−	0.245330i
$846$		0			0
$847$	406.673	+	704.378i	0.0164976	+	0.0285746i
$848$		0			0
$849$	5961.56	−	10325.7i	0.240990	−	0.417406i
$850$		0			0
$851$	6532.86	−	11315.2i	0.263153	−	0.455795i
$852$		0			0
$853$	12837.4			0.515291			0.257646	−	0.966239i	$-0.417053\pi$
$853$	12837.4			0.515291			0.257646	+	0.966239i	$0.417053\pi$
$854$		0			0
$855$	−1139.52	−	1973.71i	−0.0455799	−	0.0789467i
$856$		0			0
$857$	16611.0			0.662100			0.331050	−	0.943613i	$-0.392597\pi$
$857$	16611.0			0.662100			0.331050	+	0.943613i	$0.392597\pi$
$858$		0			0
$859$	28847.1			1.14581			0.572904	−	0.819623i	$-0.305817\pi$
$859$	28847.1			1.14581			0.572904	+	0.819623i	$0.305817\pi$
$860$		0			0
$861$	1406.66	+	2436.42i	0.0556783	+	0.0964376i
$862$		0			0
$863$	−8997.99			−0.354919			−0.177460	−	0.984128i	$-0.556788\pi$
$863$	−8997.99			−0.354919			−0.177460	+	0.984128i	$0.556788\pi$
$864$		0			0
$865$	−992.508	+	1719.07i	−0.0390130	+	0.0675725i
$866$		0			0
$867$	−7198.96	+	12469.0i	−0.281995	+	0.488429i
$868$		0			0
$869$	−14953.0	−	25899.3i	−0.583712	−	1.01102i
$870$		0			0
$871$	6394.11	−	9283.32i	0.248744	−	0.361141i
$872$		0			0
$873$	−1898.67	−	3288.60i	−0.0736087	−	0.127494i
$874$		0			0
$875$	779.825	−	1350.70i	0.0301290	−	0.0521850i
$876$		0			0
$877$	−13091.7	+	22675.4i	−0.504075	+	0.873084i	0.495913	+	0.868372i	$0.334833\pi$
$877$	−13091.7	+	22675.4i	−0.504075	+	0.873084i	−0.999989	+	0.00471237i	$0.998500\pi$
$878$		0			0
$879$	2877.46			0.110415
$880$		0			0
$881$	−21805.7	−	37768.5i	−0.833884	−	1.44433i	−0.894936	−	0.446194i	$-0.852779\pi$
$881$	−21805.7	−	37768.5i	−0.833884	−	1.44433i	0.0610524	−	0.998135i	$-0.480554\pi$
$882$		0			0
$883$	19797.8			0.754531			0.377265	−	0.926105i	$-0.376864\pi$
$883$	19797.8			0.754531			0.377265	+	0.926105i	$0.376864\pi$
$884$		0			0
$885$	3886.83			0.147632
$886$		0			0
$887$	23170.3	+	40132.2i	0.877096	+	1.51917i	0.854513	+	0.519430i	$0.173856\pi$
$887$	23170.3	+	40132.2i	0.877096	+	1.51917i	0.0225828	+	0.999745i	$0.492811\pi$
$888$		0			0
$889$	621.201			0.0234358
$890$		0			0
$891$	1703.34	−	2950.27i	0.0640450	−	0.110929i
$892$		0			0
$893$	−8187.49	+	14181.2i	−0.306813	+	0.531416i
$894$		0			0
$895$	−7205.62	−	12480.5i	−0.269114	−	0.466120i
$896$		0			0
$897$	13227.7	+	1054.53i	0.492373	+	0.0392526i
$898$		0			0
$899$	−5908.70	−	10234.2i	−0.219206	−	0.379676i
$900$		0			0
$901$	−1425.00	+	2468.17i	−0.0526899	+	0.0912616i
$902$		0			0
$903$	201.931	−	349.754i	0.00744168	−	0.0128894i
$904$		0			0
$905$	4032.83			0.148128
$906$		0			0
$907$	22467.8	+	38915.4i	0.822526	+	1.42466i	0.903795	+	0.427965i	$0.140769\pi$
$907$	22467.8	+	38915.4i	0.822526	+	1.42466i	−0.0812690	+	0.996692i	$0.525897\pi$
$908$		0			0
$909$	9790.45			0.357237
$910$		0			0
$911$	−3792.66			−0.137933			−0.0689663	−	0.997619i	$-0.521970\pi$
$911$	−3792.66			−0.137933			−0.0689663	+	0.997619i	$0.521970\pi$
$912$		0			0
$913$	2354.27	+	4077.71i	0.0853394	+	0.147812i
$914$		0			0
$915$	8804.46			0.318105
$916$		0			0
$917$	−305.662	+	529.422i	−0.0110075	+	0.0190655i
$918$		0			0
$919$	−13505.8	+	23392.8i	−0.484784	+	0.839670i	−0.999847	−	0.0174822i	$-0.994435\pi$
$919$	−13505.8	+	23392.8i	−0.484784	+	0.839670i	0.515064	+	0.857152i	$0.327768\pi$
$920$		0			0
$921$	−14121.3	−	24458.7i	−0.505224	−	0.875074i
$922$		0			0
$923$	−681.985	−	54.3688i	−0.0243205	−	0.00193886i
$924$		0			0
$925$	−7788.29	−	13489.7i	−0.276840	−	0.479501i
$926$		0			0
$927$	−3843.97	+	6657.95i	−0.136195	+	0.235896i
$928$		0			0
$929$	19630.8	−	34001.5i	0.693288	−	1.20081i	−0.277467	−	0.960735i	$-0.589495\pi$
$929$	19630.8	−	34001.5i	0.693288	−	1.20081i	0.970755	−	0.240074i	$-0.0771718\pi$
$930$		0			0
$931$	24321.8			0.856192
$932$		0			0
$933$	15088.7	+	26134.3i	0.529454	+	0.917041i
$934$		0			0
$935$	−1585.39			−0.0554520
$936$		0			0
$937$	49675.0			1.73192			0.865961	−	0.500111i	$-0.166708\pi$
$937$	49675.0			1.73192			0.865961	+	0.500111i	$0.166708\pi$
$938$		0			0
$939$	13447.0	+	23290.9i	0.467334	+	0.809446i
$940$		0			0
$941$	−34045.1			−1.17942			−0.589712	−	0.807613i	$-0.700759\pi$
$941$	−34045.1			−1.17942			−0.589712	+	0.807613i	$0.700759\pi$
$942$		0			0
$943$	23820.4	−	41258.2i	0.822587	−	1.42476i
$944$		0			0
$945$	88.6530	−	153.552i	0.00305173	−	0.00528575i
$946$		0			0
$947$	−14324.6	−	24810.9i	−0.491538	−	0.851369i	0.508414	−	0.861113i	$-0.330232\pi$
$947$	−14324.6	−	24810.9i	−0.491538	−	0.851369i	−0.999953	+	0.00974338i	$0.996899\pi$
$948$		0			0
$949$	−19247.3	−	40458.2i	−0.658370	−	1.38391i
$950$		0			0
$951$	4434.10	+	7680.09i	0.151194	+	0.261876i
$952$		0			0
$953$	−11924.7	+	20654.2i	−0.405329	+	0.702050i	−0.994360	−	0.106060i	$-0.966176\pi$
$953$	−11924.7	+	20654.2i	−0.405329	+	0.702050i	0.589031	+	0.808111i	$0.299510\pi$
$954$		0			0
$955$	178.151	−	308.567i	0.00603648	−	0.0104555i
$956$		0			0
$957$	−12626.6			−0.426500
$958$		0			0
$959$	200.225	+	346.800i	0.00674202	+	0.0116775i
$960$		0			0
$961$	−15846.4			−0.531920
$962$		0			0
$963$	−11535.7			−0.386014
$964$		0			0
$965$	−3078.46	−	5332.06i	−0.102694	−	0.177870i
$966$		0			0
$967$	10638.5			0.353787			0.176894	−	0.984230i	$-0.443395\pi$
$967$	10638.5			0.353787			0.176894	+	0.984230i	$0.443395\pi$
$968$		0			0
$969$	1145.66	−	1984.34i	0.0379812	−	0.0657854i
$970$		0			0
$971$	10904.0	−	18886.3i	0.360377	−	0.624192i	−0.627646	−	0.778499i	$-0.715981\pi$
$971$	10904.0	−	18886.3i	0.360377	−	0.624192i	0.988023	+	0.154308i	$0.0493147\pi$
$972$		0			0
$973$	519.794	+	900.309i	0.0171262	+	0.0296635i
$974$		0			0
$975$	8973.56	−	13028.3i	0.294753	−	0.427938i
$976$		0			0
$977$	−13464.9	−	23321.9i	−0.440922	−	0.763700i	0.556836	−	0.830623i	$-0.312015\pi$
$977$	−13464.9	−	23321.9i	−0.440922	−	0.763700i	−0.997758	+	0.0669226i	$0.978682\pi$
$978$		0			0
$979$	−19010.8	+	32927.6i	−0.620620	+	1.07495i
$980$		0			0
$981$	6895.38	−	11943.2i	0.224417	−	0.388701i
$982$		0			0
$983$	−36458.9			−1.18297			−0.591484	−	0.806317i	$-0.701458\pi$
$983$	−36458.9			−1.18297			−0.591484	+	0.806317i	$0.701458\pi$
$984$		0			0
$985$	−5994.15	−	10382.2i	−0.193898	−	0.335841i
$986$		0			0
$987$	−1273.95			−0.0410843
$988$		0			0
$989$	−6838.97			−0.219885
$990$		0			0
$991$	−9011.19	−	15607.8i	−0.288850	−	0.500302i	0.684686	−	0.728838i	$-0.259939\pi$
$991$	−9011.19	−	15607.8i	−0.288850	−	0.500302i	−0.973535	+	0.228536i	$0.926606\pi$
$992$		0			0
$993$	1520.71			0.0485984
$994$		0			0
$995$	1791.88	−	3103.63i	0.0570919	−	0.0988862i
$996$		0			0
$997$	776.102	−	1344.25i	0.0246534	−	0.0427009i	−0.853436	−	0.521198i	$-0.825485\pi$
$997$	776.102	−	1344.25i	0.0246534	−	0.0427009i	0.878089	+	0.478498i	$0.158818\pi$
$998$		0			0
$999$	−1869.15	−	3237.47i	−0.0591966	−	0.102531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.q.m.289.3		10
4.3	odd	2		312.4.q.d.289.3	yes	10
13.9	even	3	inner	624.4.q.m.529.3		10
52.35	odd	6		312.4.q.d.217.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.4.q.d.217.3	✓	10	52.35	odd	6
312.4.q.d.289.3	yes	10	4.3	odd	2
624.4.q.m.289.3		10	1.1	even	1	trivial
624.4.q.m.529.3		10	13.9	even	3	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	624.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} -3.53523 q^{5} +(0.928779 - 1.60869i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(21.0289 + 36.4231i) q^{11} +(20.1361 + 42.3266i) q^{13} +(-5.30284 - 9.18479i) q^{15} +(5.33140 - 9.23425i) q^{17} +(35.8148 - 62.0331i) q^{19} +5.57267 q^{21} +(-47.1837 - 81.7246i) q^{23} -112.502 q^{25} -27.0000 q^{27} +(50.0368 + 86.6662i) q^{29} -118.087 q^{31} +(-63.0867 + 109.269i) q^{33} +(-3.28345 + 5.68709i) q^{35} +(69.2279 + 119.906i) q^{37} +(-79.7634 + 115.805i) q^{39} +(252.422 + 437.208i) q^{41} +(36.2359 - 62.7624i) q^{43} +(15.9085 - 27.5544i) q^{45} -228.606 q^{47} +(169.775 + 294.058i) q^{49} +31.9884 q^{51} -267.285 q^{53} +(-74.3419 - 128.764i) q^{55} +214.889 q^{57} +(-183.243 + 317.386i) q^{59} +(-415.082 + 718.943i) q^{61} +(8.35901 + 14.4782i) q^{63} +(-71.1857 - 149.634i) q^{65} +(-120.245 - 208.271i) q^{67} +(141.551 - 245.174i) q^{69} +(-7.29803 + 12.6406i) q^{71} -955.859 q^{73} +(-168.753 - 292.289i) q^{75} +78.1248 q^{77} -711.069 q^{79} +(-40.5000 - 70.1481i) q^{81} +111.954 q^{83} +(-18.8477 + 32.6452i) q^{85} +(-150.110 + 259.999i) q^{87} +(452.016 + 782.914i) q^{89} +(86.7924 + 6.91921i) q^{91} +(-177.131 - 306.799i) q^{93} +(-126.614 + 219.301i) q^{95} +(-210.964 + 365.400i) q^{97} -378.520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 15 q^{3} - 22 q^{5} + 4 q^{7} - 45 q^{9} - 46 q^{11} - 31 q^{13} - 33 q^{15} - 11 q^{17} - 158 q^{19} + 24 q^{21} + 26 q^{23} + 340 q^{25} - 270 q^{27} - 125 q^{29} + 396 q^{31} + 138 q^{33} + 230 q^{35}+ \cdots + 828 q^{99}+O(q^{100}) \) 10 * q + 15 * q^3 - 22 * q^5 + 4 * q^7 - 45 * q^9 - 46 * q^11 - 31 * q^13 - 33 * q^15 - 11 * q^17 - 158 * q^19 + 24 * q^21 + 26 * q^23 + 340 * q^25 - 270 * q^27 - 125 * q^29 + 396 * q^31 + 138 * q^33 + 230 * q^35 + 261 * q^37 - 141 * q^39 - 151 * q^41 - 264 * q^43 + 99 * q^45 + 332 * q^47 + 293 * q^49 - 66 * q^51 + 1178 * q^53 + 106 * q^55 - 948 * q^57 + 72 * q^59 - 157 * q^61 + 36 * q^63 + 1137 * q^65 - 1120 * q^67 - 78 * q^69 - 898 * q^71 + 470 * q^73 + 510 * q^75 + 192 * q^77 + 148 * q^79 - 405 * q^81 + 2036 * q^83 - 2249 * q^85 + 375 * q^87 - 170 * q^89 - 334 * q^91 + 594 * q^93 - 1810 * q^95 + 2620 * q^97 + 828 * q^99

Introduction

L-functions

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