LMFDB - Embedded newform 336.4.bl.f.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(31,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.31"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-9,0,12] 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:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.633537072.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 13x^{4} - 16x^{3} + 158x^{2} - 168x + 196 $ x^6 - x^5 + 13x^4 - 16x^3 + 158x^2 - 168x + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$0.594460 - 1.02964i$ of defining polynomial
Character	$\chi$	$=$	336.31
Dual form			336.4.bl.f.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 2.59808i) q^{3} +(-8.37970 + 4.83802i) q^{5} +(-15.8619 - 9.56041i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(10.0800 + 5.81968i) q^{11} +17.6819i q^{13} -29.0281i q^{15} +(-34.7594 - 20.0684i) q^{17} +(-19.0102 - 32.9266i) q^{19} +(48.6315 - 26.8697i) q^{21} +(157.957 - 91.1965i) q^{23} +(-15.6871 + 27.1708i) q^{25} +27.0000 q^{27} +114.011 q^{29} +(111.695 - 193.461i) q^{31} +(-30.2400 + 17.4590i) q^{33} +(179.171 + 3.37338i) q^{35} +(174.270 + 301.844i) q^{37} +(-45.9388 - 26.5228i) q^{39} +134.358i q^{41} -56.1966i q^{43} +(75.4173 + 43.5422i) q^{45} +(-110.328 - 191.094i) q^{47} +(160.197 + 303.292i) q^{49} +(104.278 - 60.2051i) q^{51} +(272.718 - 472.361i) q^{53} -112.623 q^{55} +114.061 q^{57} +(268.762 - 465.509i) q^{59} +(342.122 - 197.524i) q^{61} +(-3.13769 + 166.653i) q^{63} +(-85.5453 - 148.169i) q^{65} +(376.317 + 217.267i) q^{67} +547.179i q^{69} -349.854i q^{71} +(-430.764 - 248.702i) q^{73} +(-47.0612 - 81.5123i) q^{75} +(-104.249 - 188.680i) q^{77} +(361.339 - 208.619i) q^{79} +(-40.5000 + 70.1481i) q^{81} +41.2728 q^{83} +388.365 q^{85} +(-171.017 + 296.210i) q^{87} +(-72.2561 + 41.7171i) q^{89} +(169.046 - 280.467i) q^{91} +(335.084 + 580.382i) q^{93} +(318.600 + 183.944i) q^{95} +1095.15i q^{97} -104.754i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} + 12 q^{5} - 7 q^{7} - 27 q^{9} - 48 q^{11} - 84 q^{17} - 77 q^{19} + 42 q^{21} + 108 q^{23} - 141 q^{25} + 162 q^{27} + 372 q^{29} + 11 q^{31} + 144 q^{33} + 546 q^{35} + 159 q^{37} - 135 q^{39}+ \cdots - 258 q^{95}+O(q^{100}) $ 6 * q - 9 * q^3 + 12 * q^5 - 7 * q^7 - 27 * q^9 - 48 * q^11 - 84 * q^17 - 77 * q^19 + 42 * q^21 + 108 * q^23 - 141 * q^25 + 162 * q^27 + 372 * q^29 + 11 * q^31 + 144 * q^33 + 546 * q^35 + 159 * q^37 - 135 * q^39 - 108 * q^45 - 378 * q^47 - 567 * q^49 + 252 * q^51 + 78 * q^53 - 1044 * q^55 + 462 * q^57 - 150 * q^59 + 1608 * q^61 - 63 * q^63 - 78 * q^65 - 339 * q^67 - 273 * q^73 - 423 * q^75 - 2394 * q^77 + 3429 * q^79 - 243 * q^81 - 1464 * q^83 + 648 * q^85 - 558 * q^87 + 768 * q^89 + 1029 * q^91 + 33 * q^93 - 258 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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
$5$	−8.37970	+	4.83802i	−0.749503	+	0.432726i	−0.825514	−	0.564381i	$-0.809115\pi$
$5$	−8.37970	+	4.83802i	−0.749503	+	0.432726i	0.0760111	+	0.997107i	$0.475782\pi$
$6$		0			0
$7$	−15.8619	−	9.56041i	−0.856460	−	0.516214i
$7$	−15.8619	−	9.56041i	−0.856460	−	0.516214i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	10.0800	+	5.81968i	0.276294	+	0.159518i	0.631744	−	0.775177i	$-0.282339\pi$
$11$	10.0800	+	5.81968i	0.276294	+	0.159518i	−0.355451	+	0.934695i	$0.615673\pi$
$12$		0			0
$13$			17.6819i			0.377236i	0.982051	+	0.188618i	$0.0604008\pi$
$13$			17.6819i			0.377236i	−0.982051	+	0.188618i	$0.939599\pi$
$14$		0			0
$15$		−	29.0281i		−	0.499669i
$16$		0			0
$17$	−34.7594	−	20.0684i	−0.495906	−	0.286311i	0.231116	−	0.972926i	$-0.425762\pi$
$17$	−34.7594	−	20.0684i	−0.495906	−	0.286311i	−0.727021	+	0.686615i	$0.759096\pi$
$18$		0			0
$19$	−19.0102	−	32.9266i	−0.229539	−	0.397573i	0.728133	−	0.685436i	$-0.240388\pi$
$19$	−19.0102	−	32.9266i	−0.229539	−	0.397573i	−0.957672	+	0.287863i	$0.907055\pi$
$20$		0			0
$21$	48.6315	−	26.8697i	0.505346	−	0.279212i
$22$		0			0
$23$	157.957	−	91.1965i	1.43201	−	0.826773i	0.434739	−	0.900556i	$-0.356841\pi$
$23$	157.957	−	91.1965i	1.43201	−	0.826773i	0.997274	+	0.0737830i	$0.0235072\pi$
$24$		0			0
$25$	−15.6871	+	27.1708i	−0.125496	+	0.217366i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	114.011			0.730046			0.365023	−	0.930998i	$-0.381061\pi$
$29$	114.011			0.730046			0.365023	+	0.930998i	$0.381061\pi$
$30$		0			0
$31$	111.695	−	193.461i	0.647127	−	1.12086i	−0.336679	−	0.941620i	$-0.609304\pi$
$31$	111.695	−	193.461i	0.647127	−	1.12086i	0.983806	−	0.179237i	$-0.0573630\pi$
$32$		0			0
$33$	−30.2400	+	17.4590i	−0.159518	+	0.0920979i
$34$		0			0
$35$	179.171	+	3.37338i	0.865299	+	0.0162916i
$36$		0			0
$37$	174.270	+	301.844i	0.774319	+	1.34116i	0.935176	+	0.354182i	$0.115241\pi$
$37$	174.270	+	301.844i	0.774319	+	1.34116i	−0.160858	+	0.986978i	$0.551426\pi$
$38$		0			0
$39$	−45.9388	−	26.5228i	−0.188618	−	0.108899i
$40$		0			0
$41$			134.358i			0.511786i	0.966705	+	0.255893i	$0.0823694\pi$
$41$			134.358i			0.511786i	−0.966705	+	0.255893i	$0.917631\pi$
$42$		0			0
$43$		−	56.1966i		−	0.199300i	−0.995023	−	0.0996500i	$-0.968228\pi$
$43$		−	56.1966i		−	0.199300i	0.995023	−	0.0996500i	$-0.0317723\pi$
$44$		0			0
$45$	75.4173	+	43.5422i	0.249834	+	0.144242i
$46$		0			0
$47$	−110.328	−	191.094i	−0.342405	−	0.593063i	0.642474	−	0.766308i	$-0.277908\pi$
$47$	−110.328	−	191.094i	−0.342405	−	0.593063i	−0.984879	+	0.173245i	$0.944575\pi$
$48$		0			0
$49$	160.197	+	303.292i	0.467047	+	0.884233i
$50$		0			0
$51$	104.278	−	60.2051i	0.286311	−	0.165302i
$52$		0			0
$53$	272.718	−	472.361i	0.706805	−	1.22422i	−0.259231	−	0.965815i	$-0.583469\pi$
$53$	272.718	−	472.361i	0.706805	−	1.22422i	0.966036	−	0.258407i	$-0.0831976\pi$
$54$		0			0
$55$	−112.623			−0.276111
$56$		0			0
$57$	114.061			0.265049
$58$		0			0
$59$	268.762	−	465.509i	0.593047	−	1.02719i	−0.400772	−	0.916178i	$-0.631258\pi$
$59$	268.762	−	465.509i	0.593047	−	1.02719i	0.993819	−	0.111010i	$-0.0354087\pi$
$60$		0			0
$61$	342.122	−	197.524i	0.718103	−	0.414597i	−0.0959510	−	0.995386i	$-0.530589\pi$
$61$	342.122	−	197.524i	0.718103	−	0.414597i	0.814054	+	0.580789i	$0.197256\pi$
$62$		0			0
$63$	−3.13769	+	166.653i	−0.00627479	+	0.333274i
$64$		0			0
$65$	−85.5453	−	148.169i	−0.163240	−	0.282740i
$66$		0			0
$67$	376.317	+	217.267i	0.686186	+	0.396170i	0.802182	−	0.597080i	$-0.203672\pi$
$67$	376.317	+	217.267i	0.686186	+	0.396170i	−0.115995	+	0.993250i	$0.537006\pi$
$68$		0			0
$69$			547.179i			0.954676i
$70$		0			0
$71$		−	349.854i		−	0.584789i	−0.956298	−	0.292394i	$-0.905548\pi$
$71$		−	349.854i		−	0.584789i	0.956298	−	0.292394i	$-0.0944520\pi$
$72$		0			0
$73$	−430.764	−	248.702i	−0.690645	−	0.398744i	0.113209	−	0.993571i	$-0.463887\pi$
$73$	−430.764	−	248.702i	−0.690645	−	0.398744i	−0.803854	+	0.594827i	$0.797221\pi$
$74$		0			0
$75$	−47.0612	−	81.5123i	−0.0724554	−	0.125496i
$76$		0			0
$77$	−104.249	−	188.680i	−0.154289	−	0.279248i
$78$		0			0
$79$	361.339	−	208.619i	0.514606	−	0.297108i	−0.220119	−	0.975473i	$-0.570645\pi$
$79$	361.339	−	208.619i	0.514606	−	0.297108i	0.734725	+	0.678365i	$0.237311\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	41.2728			0.0545817			0.0272909	−	0.999628i	$-0.491312\pi$
$83$	41.2728			0.0545817			0.0272909	+	0.999628i	$0.491312\pi$
$84$		0			0
$85$	388.365			0.495577
$86$		0			0
$87$	−171.017	+	296.210i	−0.210746	+	0.365023i
$88$		0			0
$89$	−72.2561	+	41.7171i	−0.0860576	+	0.0496854i	−0.542411	−	0.840113i	$-0.682489\pi$
$89$	−72.2561	+	41.7171i	−0.0860576	+	0.0496854i	0.456354	+	0.889798i	$0.349155\pi$
$90$		0			0
$91$	169.046	−	280.467i	0.194734	−	0.323087i
$92$		0			0
$93$	335.084	+	580.382i	0.373619	+	0.647127i
$94$		0			0
$95$	318.600	+	183.944i	0.344080	+	0.198655i
$96$		0			0
$97$			1095.15i			1.14634i	0.819436	+	0.573171i	$0.194287\pi$
$97$			1095.15i			1.14634i	−0.819436	+	0.573171i	$0.805713\pi$
$98$		0			0
$99$		−	104.754i		−	0.106345i
$100$		0			0
$101$	−1022.84	−	590.537i	−1.00769	−	0.581788i	−0.0971729	−	0.995268i	$-0.530980\pi$
$101$	−1022.84	−	590.537i	−1.00769	−	0.581788i	−0.910513	+	0.413480i	$0.864313\pi$
$102$		0			0
$103$	−729.351	−	1263.27i	−0.697719	−	1.20848i	−0.969255	−	0.246057i	$-0.920865\pi$
$103$	−729.351	−	1263.27i	−0.697719	−	1.20848i	0.271537	−	0.962428i	$-0.412468\pi$
$104$		0			0
$105$	−277.521	+	460.440i	−0.257936	+	0.427946i
$106$		0			0
$107$	799.428	−	461.550i	0.722277	−	0.417007i	−0.0933134	−	0.995637i	$-0.529746\pi$
$107$	799.428	−	461.550i	0.722277	−	0.417007i	0.815590	+	0.578630i	$0.196413\pi$
$108$		0			0
$109$	206.498	−	357.665i	0.181458	−	0.314294i	−0.760919	−	0.648846i	$-0.775252\pi$
$109$	206.498	−	357.665i	0.181458	−	0.314294i	0.942377	+	0.334552i	$0.108585\pi$
$110$		0			0
$111$	−1045.62			−0.894107
$112$		0			0
$113$	−1058.21			−0.880953			−0.440477	−	0.897764i	$-0.645191\pi$
$113$	−1058.21			−0.880953			−0.440477	+	0.897764i	$0.645191\pi$
$114$		0			0
$115$	−882.422	+	1528.40i	−0.715533	+	1.23934i
$116$		0			0
$117$	137.816	−	79.5684i	0.108899	−	0.0628726i
$118$		0			0
$119$	359.487	+	650.636i	0.276925	+	0.501207i
$120$		0			0
$121$	−597.763	−	1035.36i	−0.449108	−	0.777878i
$122$		0			0
$123$	−349.073	−	201.537i	−0.255893	−	0.147740i
$124$		0			0
$125$		−	1513.08i		−	1.08267i
$126$		0			0
$127$			2586.01i			1.80686i	0.428734	+	0.903431i	$0.358960\pi$
$127$			2586.01i			1.80686i	−0.428734	+	0.903431i	$0.641040\pi$
$128$		0			0
$129$	146.003	+	84.2949i	0.0996500	+	0.0575329i
$130$		0			0
$131$	393.132	+	680.925i	0.262199	+	0.454143i	0.966826	−	0.255436i	$-0.0822189\pi$
$131$	393.132	+	680.925i	0.262199	+	0.454143i	−0.704627	+	0.709578i	$0.748886\pi$
$132$		0			0
$133$	−13.2551	+	704.023i	−0.00864185	+	0.458997i
$134$		0			0
$135$	−226.252	+	130.627i	−0.144242	+	0.0832782i
$136$		0			0
$137$	734.739	−	1272.61i	0.458197	−	0.793620i	−0.540669	−	0.841236i	$-0.681829\pi$
$137$	734.739	−	1272.61i	0.458197	−	0.793620i	0.998866	+	0.0476151i	$0.0151621\pi$
$138$		0			0
$139$	−1587.08			−0.968451			−0.484225	−	0.874943i	$-0.660899\pi$
$139$	−1587.08			−0.968451			−0.484225	+	0.874943i	$0.660899\pi$
$140$		0			0
$141$	661.970			0.395375
$142$		0			0
$143$	−102.903	+	178.233i	−0.0601760	+	0.104228i
$144$		0			0
$145$	−955.380	+	551.589i	−0.547172	+	0.315910i
$146$		0			0
$147$	−1028.27	−	38.7337i	−0.576941	−	0.0217326i
$148$		0			0
$149$	−1464.84	−	2537.17i	−0.805397	−	1.39499i	−0.916023	−	0.401126i	$-0.868619\pi$
$149$	−1464.84	−	2537.17i	−0.805397	−	1.39499i	0.110626	−	0.993862i	$-0.464714\pi$
$150$		0			0
$151$	−438.340	−	253.075i	−0.236236	−	0.136391i	0.377210	−	0.926128i	$-0.376884\pi$
$151$	−438.340	−	253.075i	−0.236236	−	0.136391i	−0.613445	+	0.789737i	$0.710217\pi$
$152$		0			0
$153$			361.230i			0.190874i
$154$		0			0
$155$			2161.52i			1.12011i
$156$		0			0
$157$	1037.80	+	599.173i	0.527550	+	0.304581i	0.740018	−	0.672587i	$-0.234817\pi$
$157$	1037.80	+	599.173i	0.527550	+	0.304581i	−0.212468	+	0.977168i	$0.568150\pi$
$158$		0			0
$159$	818.154	+	1417.08i	0.408074	+	0.706805i
$160$		0			0
$161$	−3377.37	−	63.5881i	−1.65325	−	0.0311270i
$162$		0			0
$163$	−2394.00	+	1382.18i	−1.15038	+	0.664174i	−0.948981	−	0.315335i	$-0.897883\pi$
$163$	−2394.00	+	1382.18i	−1.15038	+	0.664174i	−0.201402	+	0.979509i	$0.564550\pi$
$164$		0			0
$165$	168.935	−	292.603i	0.0797063	−	0.138055i
$166$		0			0
$167$	−1807.47			−0.837522			−0.418761	−	0.908097i	$-0.637535\pi$
$167$	−1807.47			−0.837522			−0.418761	+	0.908097i	$0.637535\pi$
$168$		0			0
$169$	1884.35			0.857693
$170$		0			0
$171$	−171.092	+	296.340i	−0.0765130	+	0.132524i
$172$		0			0
$173$	2493.46	−	1439.60i	1.09580	−	0.632663i	0.160689	−	0.987005i	$-0.448628\pi$
$173$	2493.46	−	1439.60i	1.09580	−	0.632663i	0.935116	+	0.354342i	$0.115295\pi$
$174$		0			0
$175$	508.590	−	281.004i	0.219690	−	0.121382i
$176$		0			0
$177$	806.285	+	1396.53i	0.342396	+	0.593047i
$178$		0			0
$179$	478.529	+	276.279i	0.199815	+	0.115363i	0.596569	−	0.802562i	$-0.296530\pi$
$179$	478.529	+	276.279i	0.199815	+	0.115363i	−0.396754	+	0.917925i	$0.629863\pi$
$180$		0			0
$181$			2276.63i			0.934921i	0.884014	+	0.467460i	$0.154831\pi$
$181$			2276.63i			0.934921i	−0.884014	+	0.467460i	$0.845169\pi$
$182$		0			0
$183$			1185.15i			0.478735i
$184$		0			0
$185$	−2920.66	−	1686.24i	−1.16071	−	0.670136i
$186$		0			0
$187$	−233.583	−	404.577i	−0.0913437	−	0.158212i
$188$		0			0
$189$	−428.270	−	258.131i	−0.164826	−	0.0993454i
$190$		0			0
$191$	4096.66	−	2365.21i	1.55196	−	0.896024i	0.553977	−	0.832532i	$-0.313109\pi$
$191$	4096.66	−	2365.21i	1.55196	−	0.896024i	0.997982	−	0.0634923i	$-0.0202238\pi$
$192$		0			0
$193$	−1771.75	+	3068.76i	−0.660795	+	1.14453i	0.319612	+	0.947548i	$0.396447\pi$
$193$	−1771.75	+	3068.76i	−0.660795	+	1.14453i	−0.980407	+	0.196982i	$0.936886\pi$
$194$		0			0
$195$	513.272			0.188493
$196$		0			0
$197$	3478.40			1.25800			0.628999	−	0.777406i	$-0.283465\pi$
$197$	3478.40			1.25800			0.628999	+	0.777406i	$0.283465\pi$
$198$		0			0
$199$	−1036.76	+	1795.72i	−0.369316	+	0.639674i	−0.989459	−	0.144815i	$-0.953741\pi$
$199$	−1036.76	+	1795.72i	−0.369316	+	0.639674i	0.620143	+	0.784489i	$0.287075\pi$
$200$		0			0
$201$	−1128.95	+	651.801i	−0.396170	+	0.228729i
$202$		0			0
$203$	−1808.43	−	1089.99i	−0.625255	−	0.376860i
$204$		0			0
$205$	−650.028	−	1125.88i	−0.221463	−	0.383585i
$206$		0			0
$207$	−1421.61	−	820.769i	−0.477338	−	0.275591i
$208$		0			0
$209$		−	442.533i		−	0.146463i
$210$		0			0
$211$		−	239.803i		−	0.0782404i	−0.999235	−	0.0391202i	$-0.987544\pi$
$211$		−	239.803i		−	0.0782404i	0.999235	−	0.0391202i	$-0.0124555\pi$
$212$		0			0
$213$	908.947	+	524.781i	0.292394	+	0.168814i
$214$		0			0
$215$	271.880	+	470.911i	0.0862423	+	0.149376i
$216$		0			0
$217$	−3621.25	+	2000.80i	−1.13284	+	0.625913i
$218$		0			0
$219$	1292.29	−	746.105i	0.398744	−	0.230215i
$220$		0			0
$221$	354.846	−	614.611i	0.108007	−	0.187073i
$222$		0			0
$223$	974.175			0.292536			0.146268	−	0.989245i	$-0.453274\pi$
$223$	974.175			0.292536			0.146268	+	0.989245i	$0.453274\pi$
$224$		0			0
$225$	282.367			0.0836643
$226$		0			0
$227$	823.400	−	1426.17i	0.240753	−	0.416997i	−0.720176	−	0.693792i	$-0.755939\pi$
$227$	823.400	−	1426.17i	0.240753	−	0.416997i	0.960929	+	0.276795i	$0.0892722\pi$
$228$		0			0
$229$	5149.33	−	2972.97i	1.48593	−	0.857900i	0.486055	−	0.873928i	$-0.338435\pi$
$229$	5149.33	−	2972.97i	1.48593	−	0.857900i	0.999872	+	0.0160278i	$0.00510203\pi$
$230$		0			0
$231$	646.578	+	12.1736i	0.184163	+	0.00346737i
$232$		0			0
$233$	−2179.86	−	3775.63i	−0.612907	−	1.06159i	−0.990748	−	0.135715i	$-0.956667\pi$
$233$	−2179.86	−	3775.63i	−0.612907	−	1.06159i	0.377841	−	0.925870i	$-0.376667\pi$
$234$		0			0
$235$	1849.04	+	1067.54i	0.513267	+	0.296335i
$236$		0			0
$237$			1251.72i			0.343070i
$238$		0			0
$239$		−	2369.30i		−	0.641245i	−0.947207	−	0.320623i	$-0.896108\pi$
$239$		−	2369.30i		−	0.641245i	0.947207	−	0.320623i	$-0.103892\pi$
$240$		0			0
$241$	−1558.34	−	899.707i	−0.416520	−	0.240478i	0.277067	−	0.960851i	$-0.410638\pi$
$241$	−1558.34	−	899.707i	−0.416520	−	0.240478i	−0.693587	+	0.720372i	$0.743971\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−2809.74	−	1766.46i	−0.732683	−	0.460632i
$246$		0			0
$247$	582.204	−	336.136i	0.149979	−	0.0865903i
$248$		0			0
$249$	−61.9092	+	107.230i	−0.0157564	+	0.0272909i
$250$		0			0
$251$	−498.383			−0.125329			−0.0626646	−	0.998035i	$-0.519960\pi$
$251$	−498.383			−0.125329			−0.0626646	+	0.998035i	$0.519960\pi$
$252$		0			0
$253$	2122.94			0.527542
$254$		0			0
$255$	−582.547	+	1009.00i	−0.143061	+	0.247789i
$256$		0			0
$257$	−3817.20	+	2203.86i	−0.926501	+	0.534915i	−0.885703	−	0.464252i	$-0.846323\pi$
$257$	−3817.20	+	2203.86i	−0.926501	+	0.534915i	−0.0407975	+	0.999167i	$0.512990\pi$
$258$		0			0
$259$	121.512	−	6453.91i	0.0291521	−	1.54836i
$260$		0			0
$261$	−513.050	−	888.629i	−0.121674	−	0.210746i
$262$		0			0
$263$	675.576	+	390.044i	0.158395	+	0.0914493i	0.577102	−	0.816672i	$-0.304183\pi$
$263$	675.576	+	390.044i	0.158395	+	0.0914493i	−0.418707	+	0.908121i	$0.637517\pi$
$264$		0			0
$265$			5277.66i			1.22341i
$266$		0			0
$267$		−	250.302i		−	0.0573718i
$268$		0			0
$269$	5380.70	+	3106.55i	1.21958	+	0.704125i	0.964828	−	0.262881i	$-0.0846727\pi$
$269$	5380.70	+	3106.55i	1.21958	+	0.704125i	0.254752	+	0.967006i	$0.418006\pi$
$270$		0			0
$271$	−224.863	−	389.475i	−0.0504040	−	0.0873022i	0.839723	−	0.543016i	$-0.182718\pi$
$271$	−224.863	−	389.475i	−0.0504040	−	0.0873022i	−0.890127	+	0.455713i	$0.849384\pi$
$272$		0			0
$273$	475.106	+	859.895i	0.105329	+	0.190634i
$274$		0			0
$275$	−316.251	+	182.587i	−0.0693478	+	0.0400379i
$276$		0			0
$277$	2917.57	−	5053.39i	0.632852	−	1.09613i	−0.354114	−	0.935202i	$-0.615217\pi$
$277$	2917.57	−	5053.39i	0.632852	−	1.09613i	0.986966	−	0.160930i	$-0.0514492\pi$
$278$		0			0
$279$	−2010.50			−0.431418
$280$		0			0
$281$	6938.33			1.47298			0.736488	−	0.676451i	$-0.236483\pi$
$281$	6938.33			1.47298			0.736488	+	0.676451i	$0.236483\pi$
$282$		0			0
$283$	3741.01	−	6479.62i	0.785795	−	1.36104i	−0.142728	−	0.989762i	$-0.545587\pi$
$283$	3741.01	−	6479.62i	0.785795	−	1.36104i	0.928523	−	0.371275i	$-0.121079\pi$
$284$		0			0
$285$	−955.799	+	551.831i	−0.198655	+	0.114693i
$286$		0			0
$287$	1284.52	−	2131.17i	0.264191	−	0.438324i
$288$		0			0
$289$	−1651.02	−	2859.65i	−0.336052	−	0.582059i
$290$		0			0
$291$	−2845.27	−	1642.72i	−0.573171	−	0.330921i
$292$		0			0
$293$			9235.64i			1.84147i	0.390183	+	0.920737i	$0.372412\pi$
$293$			9235.64i			1.84147i	−0.390183	+	0.920737i	$0.627588\pi$
$294$		0			0
$295$			5201.10i			1.02651i
$296$		0			0
$297$	272.160	+	157.131i	0.0531727	+	0.0306993i
$298$		0			0
$299$	1612.52	+	2792.97i	0.311889	+	0.540207i
$300$		0			0
$301$	−537.263	+	891.382i	−0.102881	+	0.170692i
$302$		0			0
$303$	3068.52	−	1771.61i	0.581788	−	0.335895i
$304$		0			0
$305$	−1911.26	+	3310.39i	−0.358814	+	0.621484i
$306$		0			0
$307$	1275.94			0.237204			0.118602	−	0.992942i	$-0.462159\pi$
$307$	1275.94			0.237204			0.118602	+	0.992942i	$0.462159\pi$
$308$		0			0
$309$	4376.10			0.805656
$310$		0			0
$311$	4768.42	−	8259.14i	0.869428	−	1.50589i	0.00684646	−	0.999977i	$-0.497821\pi$
$311$	4768.42	−	8259.14i	0.869428	−	1.50589i	0.862582	−	0.505917i	$-0.168846\pi$
$312$		0			0
$313$	2908.28	−	1679.09i	0.525193	−	0.303220i	−0.213864	−	0.976864i	$-0.568605\pi$
$313$	2908.28	−	1679.09i	0.525193	−	0.303220i	0.739057	+	0.673643i	$0.235272\pi$
$314$		0			0
$315$	−779.977	−	1411.68i	−0.139513	−	0.252505i
$316$		0			0
$317$	307.211	+	532.105i	0.0544312	+	0.0942775i	0.891957	−	0.452120i	$-0.149332\pi$
$317$	307.211	+	532.105i	0.0544312	+	0.0942775i	−0.837526	+	0.546398i	$0.815999\pi$
$318$		0			0
$319$	1149.23	+	663.509i	0.201707	+	0.116456i
$320$		0			0
$321$			2769.30i			0.481518i
$322$		0			0
$323$			1526.01i			0.262878i
$324$		0			0
$325$	−480.430	−	277.376i	−0.0819983	−	0.0473418i
$326$		0			0
$327$	619.493	+	1072.99i	0.104765	+	0.181458i
$328$		0			0
$329$	−76.9279	+	4085.89i	−0.0128911	+	0.684689i
$330$		0			0
$331$	4203.73	−	2427.02i	0.698060	−	0.403025i	−0.108564	−	0.994089i	$-0.534625\pi$
$331$	4203.73	−	2427.02i	0.698060	−	0.403025i	0.806624	+	0.591064i	$0.201292\pi$
$332$		0			0
$333$	1568.43	−	2716.60i	0.258106	−	0.447053i
$334$		0			0
$335$	−4204.57			−0.685732
$336$		0			0
$337$	5807.46			0.938732			0.469366	−	0.883004i	$-0.344482\pi$
$337$	5807.46			0.938732			0.469366	+	0.883004i	$0.344482\pi$
$338$		0			0
$339$	1587.31	−	2749.30i	0.254309	−	0.440477i
$340$		0			0
$341$	2251.76	−	1300.05i	0.357594	−	0.206457i
$342$		0			0
$343$	358.573	−	6342.32i	0.0564464	−	0.998406i
$344$		0			0
$345$	−2647.27	−	4585.20i	−0.413113	−	0.715533i
$346$		0			0
$347$	9692.95	+	5596.23i	1.49955	+	0.865767i	1.00000		0.000516671i	$-0.000164462\pi$
$347$	9692.95	+	5596.23i	1.49955	+	0.865767i	0.499552	+	0.866284i	$0.333498\pi$
$348$		0			0
$349$			5155.92i			0.790802i	0.918509	+	0.395401i	$0.129394\pi$
$349$			5155.92i			0.790802i	−0.918509	+	0.395401i	$0.870606\pi$
$350$		0			0
$351$			477.410i			0.0725991i
$352$		0			0
$353$	2631.52	+	1519.31i	0.396776	+	0.229079i	0.685092	−	0.728457i	$-0.259762\pi$
$353$	2631.52	+	1519.31i	0.396776	+	0.229079i	−0.288316	+	0.957535i	$0.593095\pi$
$354$		0			0
$355$	1692.60	+	2931.67i	0.253053	+	0.438301i
$356$		0			0
$357$	−2229.63	−	41.9788i	−0.330545	−	0.00622340i
$358$		0			0
$359$	−538.963	+	311.170i	−0.0792350	+	0.0457463i	−0.539094	−	0.842246i	$-0.681233\pi$
$359$	−538.963	+	311.170i	−0.0792350	+	0.0457463i	0.459859	+	0.887992i	$0.347900\pi$
$360$		0			0
$361$	2706.72	−	4688.18i	0.394624	−	0.683508i
$362$		0			0
$363$	3586.58			0.518585
$364$		0			0
$365$	4812.90			0.690188
$366$		0			0
$367$	−1037.16	+	1796.41i	−0.147518	+	0.255509i	−0.930310	−	0.366775i	$-0.880462\pi$
$367$	−1037.16	+	1796.41i	−0.147518	+	0.255509i	0.782791	+	0.622284i	$0.213795\pi$
$368$		0			0
$369$	1047.22	−	604.612i	0.147740	−	0.0852976i
$370$		0			0
$371$	−8841.78	+	4885.23i	−1.23731	+	0.683635i
$372$		0			0
$373$	−3695.78	−	6401.28i	−0.513030	−	0.888594i	−0.999886	−	0.0151118i	$-0.995190\pi$
$373$	−3695.78	−	6401.28i	−0.513030	−	0.888594i	0.486856	−	0.873482i	$-0.338144\pi$
$374$		0			0
$375$	3931.11	+	2269.62i	0.541337	+	0.312541i
$376$		0			0
$377$			2015.93i			0.275400i
$378$		0			0
$379$		−	3265.03i		−	0.442515i	−0.975215	−	0.221258i	$-0.928984\pi$
$379$		−	3265.03i		−	0.442515i	0.975215	−	0.221258i	$-0.0710162\pi$
$380$		0			0
$381$	−6718.66	−	3879.02i	−0.903431	−	0.521596i
$382$		0			0
$383$	−5541.74	−	9598.58i	−0.739347	−	1.28059i	−0.952790	−	0.303630i	$-0.901801\pi$
$383$	−5541.74	−	9598.58i	−0.739347	−	1.28059i	0.213443	−	0.976955i	$-0.431532\pi$
$384$		0			0
$385$	1786.41	+	1076.72i	0.236478	+	0.142532i
$386$		0			0
$387$	−438.009	+	252.885i	−0.0575329	+	0.0332167i
$388$		0			0
$389$	2739.46	−	4744.89i	0.357060	−	0.618445i	−0.630409	−	0.776263i	$-0.717113\pi$
$389$	2739.46	−	4744.89i	0.357060	−	0.618445i	0.987468	+	0.157818i	$0.0504460\pi$
$390$		0			0
$391$	−7320.65			−0.946858
$392$		0			0
$393$	−2358.79			−0.302762
$394$		0			0
$395$	−2018.61	+	3496.33i	−0.257132	+	0.445366i
$396$		0			0
$397$	−10548.3	+	6090.06i	−1.33351	+	0.769903i	−0.985836	−	0.167712i	$-0.946362\pi$
$397$	−10548.3	+	6090.06i	−1.33351	+	0.769903i	−0.347675	+	0.937615i	$0.613029\pi$
$398$		0			0
$399$	−1809.22	−	1090.47i	−0.227004	−	0.136822i
$400$		0			0
$401$	1770.00	+	3065.73i	0.220423	+	0.381783i	0.954936	−	0.296811i	$-0.0959230\pi$
$401$	1770.00	+	3065.73i	0.220423	+	0.381783i	−0.734514	+	0.678594i	$0.762590\pi$
$402$		0			0
$403$	3420.74	+	1974.97i	0.422827	+	0.244120i
$404$		0			0
$405$		−	783.760i		−	0.0961613i
$406$		0			0
$407$			4056.78i			0.494072i
$408$		0			0
$409$	−8286.58	−	4784.26i	−1.00182	−	0.578402i	−0.0930351	−	0.995663i	$-0.529657\pi$
$409$	−8286.58	−	4784.26i	−1.00182	−	0.578402i	−0.908787	+	0.417261i	$0.862990\pi$
$410$		0			0
$411$	2204.22	+	3817.82i	0.264540	+	0.458197i
$412$		0			0
$413$	−8713.52	+	4814.36i	−1.03817	+	0.573606i
$414$		0			0
$415$	−345.854	+	199.679i	−0.0409092	+	0.0236189i
$416$		0			0
$417$	2380.63	−	4123.36i	0.279568	−	0.484225i
$418$		0			0
$419$	−14604.7			−1.70284			−0.851418	−	0.524488i	$-0.824257\pi$
$419$	−14604.7			−1.70284			−0.851418	+	0.524488i	$0.824257\pi$
$420$		0			0
$421$	−1561.17			−0.180729			−0.0903645	−	0.995909i	$-0.528803\pi$
$421$	−1561.17			−0.180729			−0.0903645	+	0.995909i	$0.528803\pi$
$422$		0			0
$423$	−992.954	+	1719.85i	−0.114135	+	0.197688i
$424$		0			0
$425$	1090.55	−	629.627i	0.124469	−	0.0718621i
$426$		0			0
$427$	−7315.11	−	137.727i	−0.829047	−	0.0156090i
$428$		0			0
$429$	−308.708	−	534.699i	−0.0347426	−	0.0601760i
$430$		0			0
$431$	−5340.58	−	3083.39i	−0.596861	−	0.344598i	0.170945	−	0.985281i	$-0.445318\pi$
$431$	−5340.58	−	3083.39i	−0.596861	−	0.344598i	−0.767806	+	0.640683i	$0.778651\pi$
$432$		0			0
$433$			10063.2i			1.11688i	0.829545	+	0.558439i	$0.188600\pi$
$433$			10063.2i			1.11688i	−0.829545	+	0.558439i	$0.811400\pi$
$434$		0			0
$435$		−	3309.53i		−	0.364781i
$436$		0			0
$437$	−6005.59	−	3467.33i	−0.657406	−	0.379553i
$438$		0			0
$439$	4671.71	+	8091.64i	0.507901	+	0.879710i	0.999958	+	0.00914752i	$0.00291179\pi$
$439$	4671.71	+	8091.64i	0.507901	+	0.879710i	−0.492057	+	0.870563i	$0.663755\pi$
$440$		0			0
$441$	1643.04	−	2613.43i	0.177415	−	0.282197i
$442$		0			0
$443$	−11420.3	+	6593.53i	−1.22482	+	0.707152i	−0.965942	−	0.258758i	$-0.916687\pi$
$443$	−11420.3	+	6593.53i	−1.22482	+	0.707152i	−0.258881	+	0.965909i	$0.583354\pi$
$444$		0			0
$445$	403.656	−	699.153i	0.0430003	−	0.0744788i
$446$		0			0
$447$	8789.02			0.929992
$448$		0			0
$449$	9537.25			1.00243			0.501215	−	0.865323i	$-0.332887\pi$
$449$	9537.25			1.00243			0.501215	+	0.865323i	$0.332887\pi$
$450$		0			0
$451$	−781.922	+	1354.33i	−0.0816392	+	0.141403i
$452$		0			0
$453$	1315.02	−	759.226i	0.136391	−	0.0787452i
$454$		0			0
$455$	−59.6476	+	3168.08i	−0.00614577	+	0.326422i
$456$		0			0
$457$	−7608.39	−	13178.1i	−0.778787	−	1.34890i	−0.932641	−	0.360804i	$-0.882502\pi$
$457$	−7608.39	−	13178.1i	−0.778787	−	1.34890i	0.153855	−	0.988093i	$-0.450831\pi$
$458$		0			0
$459$	−938.504	−	541.845i	−0.0954371	−	0.0551006i
$460$		0			0
$461$			18561.3i			1.87524i	0.347666	+	0.937618i	$0.386974\pi$
$461$			18561.3i			1.87524i	−0.347666	+	0.937618i	$0.613026\pi$
$462$		0			0
$463$			11389.0i			1.14318i	0.820540	+	0.571589i	$0.193673\pi$
$463$			11389.0i			1.14318i	−0.820540	+	0.571589i	$0.806327\pi$
$464$		0			0
$465$	−5615.80	−	3242.29i	−0.560057	−	0.323349i
$466$		0			0
$467$	6437.45	+	11150.0i	0.637880	+	1.10484i	0.985897	+	0.167352i	$0.0535217\pi$
$467$	6437.45	+	11150.0i	0.637880	+	1.10484i	−0.348017	+	0.937488i	$0.613145\pi$
$468$		0			0
$469$	−3891.93	−	7044.01i	−0.383183	−	0.693523i
$470$		0			0
$471$	−3113.39	+	1797.52i	−0.304581	+	0.175850i
$472$		0			0
$473$	327.046	−	566.461i	0.0317920	−	0.0550653i
$474$		0			0
$475$	1192.86			0.115225
$476$		0			0
$477$	−4908.92			−0.471204
$478$		0			0
$479$	7612.67	−	13185.5i	0.726163	−	1.25775i	−0.232331	−	0.972637i	$-0.574635\pi$
$479$	7612.67	−	13185.5i	0.726163	−	1.25775i	0.958494	−	0.285114i	$-0.0920315\pi$
$480$		0			0
$481$	−5337.17	+	3081.42i	−0.505934	+	0.292101i
$482$		0			0
$483$	5231.26	−	8679.28i	0.492817	−	0.817641i
$484$		0			0
$485$	−5298.34	−	9177.00i	−0.496052	−	0.859187i
$486$		0			0
$487$	−7146.25	−	4125.89i	−0.664943	−	0.383905i	0.129215	−	0.991617i	$-0.458754\pi$
$487$	−7146.25	−	4125.89i	−0.664943	−	0.383905i	−0.794158	+	0.607711i	$0.792088\pi$
$488$		0			0
$489$		−	8293.05i		−	0.766922i
$490$		0			0
$491$			11192.2i			1.02871i	0.857576	+	0.514357i	$0.171969\pi$
$491$			11192.2i			1.02871i	−0.857576	+	0.514357i	$0.828031\pi$
$492$		0			0
$493$	−3962.96	−	2288.02i	−0.362034	−	0.209020i
$494$		0			0
$495$	506.804	+	877.810i	0.0460184	+	0.0797063i
$496$		0			0
$497$	−3344.75	+	5549.33i	−0.301876	+	0.500848i
$498$		0			0
$499$	8448.83	−	4877.93i	0.757959	−	0.437608i	−0.0706035	−	0.997504i	$-0.522493\pi$
$499$	8448.83	−	4877.93i	0.757959	−	0.437608i	0.828562	+	0.559897i	$0.189159\pi$
$500$		0			0
$501$	2711.20	−	4695.94i	0.241772	−	0.418761i
$502$		0			0
$503$	−16561.4			−1.46806			−0.734031	−	0.679116i	$-0.762363\pi$
$503$	−16561.4			−1.46806			−0.734031	+	0.679116i	$0.762363\pi$
$504$		0			0
$505$	11428.1			1.00702
$506$		0			0
$507$	−2826.53	+	4895.69i	−0.247595	+	0.428847i
$508$		0			0
$509$	2806.22	−	1620.17i	0.244368	−	0.141086i	−0.372815	−	0.927906i	$-0.621607\pi$
$509$	2806.22	−	1620.17i	0.244368	−	0.141086i	0.617183	+	0.786820i	$0.288274\pi$
$510$		0			0
$511$	4455.02	+	8063.15i	0.385673	+	0.698029i
$512$		0			0
$513$	−513.276	−	889.019i	−0.0441748	−	0.0765130i
$514$		0			0
$515$	12223.5	+	7057.23i	1.04589	+	0.603842i
$516$		0			0
$517$		−	2568.30i		−	0.218479i
$518$		0			0
$519$			8637.60i			0.730537i
$520$		0			0
$521$	13536.7	+	7815.42i	1.13830	+	0.657197i	0.946009	−	0.324141i	$-0.105075\pi$
$521$	13536.7	+	7815.42i	1.13830	+	0.657197i	0.192290	+	0.981338i	$0.438409\pi$
$522$		0			0
$523$	−4745.38	−	8219.24i	−0.396751	−	0.687194i	0.596572	−	0.802560i	$-0.296529\pi$
$523$	−4745.38	−	8219.24i	−0.396751	−	0.687194i	−0.993323	+	0.115366i	$0.963196\pi$
$524$		0			0
$525$	−32.8141	+	1742.86i	−0.00272785	+	0.144885i
$526$		0			0
$527$	−7764.87	+	4483.05i	−0.641828	+	0.370559i
$528$		0			0
$529$	10550.1	−	18273.3i	0.867108	−	1.50188i
$530$		0			0
$531$	−4837.71			−0.395365
$532$		0			0
$533$	−2375.70			−0.193064
$534$		0			0
$535$	−4465.98	+	7735.30i	−0.360899	+	0.625096i
$536$		0			0
$537$	−1435.59	+	828.837i	−0.115363	+	0.0666051i
$538$		0			0
$539$	−150.278	+	3989.47i	−0.0120092	+	0.318810i
$540$		0			0
$541$	3936.37	+	6818.00i	0.312824	+	0.541827i	0.978973	−	0.203992i	$-0.0653916\pi$
$541$	3936.37	+	6818.00i	0.312824	+	0.541827i	−0.666148	+	0.745819i	$0.732058\pi$
$542$		0			0
$543$	−5914.86	−	3414.95i	−0.467460	−	0.269888i
$544$		0			0
$545$			3996.16i			0.314086i
$546$		0			0
$547$		−	208.051i		−	0.0162626i	−0.999967	−	0.00813129i	$-0.997412\pi$
$547$		−	208.051i		−	0.0162626i	0.999967	−	0.00813129i	$-0.00258830\pi$
$548$		0			0
$549$	−3079.10	−	1777.72i	−0.239368	−	0.138199i
$550$		0			0
$551$	−2167.38	−	3754.00i	−0.167574	−	0.290247i
$552$		0			0
$553$	−7726.00	−	145.463i	−0.594110	−	0.0111857i
$554$		0			0
$555$	8761.98	−	5058.73i	0.670136	−	0.386903i
$556$		0			0
$557$	−12417.6	+	21508.0i	−0.944618	+	1.63613i	−0.188104	+	0.982149i	$0.560234\pi$
$557$	−12417.6	+	21508.0i	−0.944618	+	1.63613i	−0.756514	+	0.653977i	$0.773099\pi$
$558$		0			0
$559$	993.660			0.0751831
$560$		0			0
$561$	1401.50			0.105475
$562$		0			0
$563$	−7475.61	+	12948.1i	−0.559608	+	0.969269i	0.437921	+	0.899013i	$0.355715\pi$
$563$	−7475.61	+	12948.1i	−0.559608	+	0.969269i	−0.997529	+	0.0702559i	$0.977618\pi$
$564$		0			0
$565$	8867.46	−	5119.63i	0.660278	−	0.381211i
$566$		0			0
$567$	1313.05	−	725.482i	0.0972538	−	0.0537343i
$568$		0			0
$569$	1192.58	+	2065.60i	0.0878655	+	0.152187i	0.906609	−	0.421972i	$-0.138662\pi$
$569$	1192.58	+	2065.60i	0.0878655	+	0.152187i	−0.818743	+	0.574160i	$0.805329\pi$
$570$		0			0
$571$	−8201.71	−	4735.26i	−0.601105	−	0.347048i	0.168371	−	0.985724i	$-0.446149\pi$
$571$	−8201.71	−	4735.26i	−0.601105	−	0.347048i	−0.769476	+	0.638676i	$0.779483\pi$
$572$		0			0
$573$			14191.3i			1.03464i
$574$		0			0
$575$			5722.42i			0.415029i
$576$		0			0
$577$	−6291.15	−	3632.20i	−0.453907	−	0.262063i	0.255572	−	0.966790i	$-0.417736\pi$
$577$	−6291.15	−	3632.20i	−0.453907	−	0.262063i	−0.709479	+	0.704727i	$0.751070\pi$
$578$		0			0
$579$	−5315.25	−	9206.29i	−0.381510	−	0.660795i
$580$		0			0
$581$	−654.664	−	394.585i	−0.0467470	−	0.0281758i
$582$		0			0
$583$	5497.98	−	3174.26i	0.390572	−	0.225497i
$584$		0			0
$585$	−769.907	+	1333.52i	−0.0544132	+	0.0942465i
$586$		0			0
$587$	−9116.08			−0.640990			−0.320495	−	0.947250i	$-0.603849\pi$
$587$	−9116.08			−0.640990			−0.320495	+	0.947250i	$0.603849\pi$
$588$		0			0
$589$	−8493.35			−0.594163
$590$		0			0
$591$	−5217.59	+	9037.14i	−0.363153	+	0.628999i
$592$		0			0
$593$	8328.11	−	4808.23i	0.576719	−	0.332969i	−0.183109	−	0.983093i	$-0.558616\pi$
$593$	8328.11	−	4808.23i	0.576719	−	0.332969i	0.759828	+	0.650124i	$0.225283\pi$
$594$		0			0
$595$	−6160.18	−	3712.93i	−0.424442	−	0.255824i
$596$		0			0
$597$	−3110.28	−	5387.15i	−0.213225	−	0.369316i
$598$		0			0
$599$	11917.3	+	6880.48i	0.812904	+	0.469330i	0.847963	−	0.530055i	$-0.177829\pi$
$599$	11917.3	+	6880.48i	0.812904	+	0.469330i	−0.0350594	+	0.999385i	$0.511162\pi$
$600$		0			0
$601$		−	21447.9i		−	1.45570i	−0.685735	−	0.727851i	$-0.740519\pi$
$601$		−	21447.9i		−	1.45570i	0.685735	−	0.727851i	$-0.259481\pi$
$602$		0			0
$603$		−	3910.81i		−	0.264113i
$604$		0			0
$605$	10018.1	+	5783.98i	0.673216	+	0.388681i
$606$		0			0
$607$	9809.66	+	16990.8i	0.655950	+	1.13614i	0.981655	+	0.190668i	$0.0610652\pi$
$607$	9809.66	+	16990.8i	0.655950	+	1.13614i	−0.325704	+	0.945472i	$0.605601\pi$
$608$		0			0
$609$	5544.53	−	3063.45i	0.368926	−	0.203838i
$610$		0			0
$611$	3378.90	−	1950.81i	0.223725	−	0.129167i
$612$		0			0
$613$	−4758.18	+	8241.41i	−0.313509	+	0.543013i	−0.979119	−	0.203286i	$-0.934838\pi$
$613$	−4758.18	+	8241.41i	−0.313509	+	0.543013i	0.665610	+	0.746299i	$0.268171\pi$
$614$		0			0
$615$	3900.17			0.255723
$616$		0			0
$617$	5047.07			0.329315			0.164658	−	0.986351i	$-0.447348\pi$
$617$	5047.07			0.329315			0.164658	+	0.986351i	$0.447348\pi$
$618$		0			0
$619$	−1926.89	+	3337.47i	−0.125118	+	0.216711i	−0.921779	−	0.387715i	$-0.873264\pi$
$619$	−1926.89	+	3337.47i	−0.125118	+	0.216711i	0.796661	+	0.604426i	$0.206598\pi$
$620$		0			0
$621$	4264.84	−	2462.31i	0.275591	−	0.159113i
$622$		0			0
$623$	1544.95	+	29.0878i	0.0993532	+	0.00187059i
$624$		0			0
$625$	5359.45	+	9282.84i	0.343005	+	0.594102i
$626$		0			0
$627$	1149.74	+	663.800i	0.0732313	+	0.0422801i
$628$		0			0
$629$		−	13989.2i		−	0.886785i
$630$		0			0
$631$		−	13161.7i		−	0.830365i	−0.909738	−	0.415182i	$-0.863718\pi$
$631$		−	13161.7i		−	0.830365i	0.909738	−	0.415182i	$-0.136282\pi$
$632$		0			0
$633$	623.027	+	359.705i	0.0391202	+	0.0225861i
$634$		0			0
$635$	−12511.2	−	21670.0i	−0.781876	−	1.35425i
$636$		0			0
$637$	−5362.76	+	2832.58i	−0.333564	+	0.176187i
$638$		0			0
$639$	−2726.84	+	1574.34i	−0.168814	+	0.0974648i
$640$		0			0
$641$	−7786.29	+	13486.2i	−0.479781	+	0.831006i	−0.999731	−	0.0231911i	$-0.992617\pi$
$641$	−7786.29	+	13486.2i	−0.479781	+	0.831006i	0.519950	+	0.854197i	$0.325951\pi$
$642$		0			0
$643$	16136.6			0.989681			0.494840	−	0.868984i	$-0.335227\pi$
$643$	16136.6			0.989681			0.494840	+	0.868984i	$0.335227\pi$
$644$		0			0
$645$	−1631.28			−0.0995840
$646$		0			0
$647$	15768.6	−	27311.9i	0.958155	−	1.65957i	0.231177	−	0.972912i	$-0.425742\pi$
$647$	15768.6	−	27311.9i	0.958155	−	1.65957i	0.726978	−	0.686661i	$-0.240924\pi$
$648$		0			0
$649$	5418.23	−	3128.22i	0.327710	−	0.189204i
$650$		0			0
$651$	233.642	−	12409.5i	0.0140663	−	0.747105i
$652$		0			0
$653$	−762.710	−	1321.05i	−0.0457077	−	0.0791681i	0.842266	−	0.539061i	$-0.181221\pi$
$653$	−762.710	−	1321.05i	−0.0457077	−	0.0791681i	−0.887974	+	0.459893i	$0.847888\pi$
$654$		0			0
$655$	−6588.66	−	3803.96i	−0.393039	−	0.226921i
$656$		0			0
$657$			4476.63i			0.265829i
$658$		0			0
$659$		−	18237.7i		−	1.07806i	−0.842288	−	0.539028i	$-0.818792\pi$
$659$		−	18237.7i		−	1.07806i	0.842288	−	0.539028i	$-0.181208\pi$
$660$		0			0
$661$	−8986.00	−	5188.07i	−0.528767	−	0.305284i	0.211747	−	0.977324i	$-0.432085\pi$
$661$	−8986.00	−	5188.07i	−0.528767	−	0.305284i	−0.740514	+	0.672041i	$0.765418\pi$
$662$		0			0
$663$	1064.54	+	1843.83i	0.0623578	+	0.108007i
$664$		0			0
$665$	−3295.01	−	5963.63i	−0.192143	−	0.347759i
$666$		0			0
$667$	18008.9	−	10397.4i	1.04544	−	0.603583i
$668$		0			0
$669$	−1461.26	+	2530.98i	−0.0844480	+	0.146268i
$670$		0			0
$671$	4598.12			0.264543
$672$		0			0
$673$	25836.8			1.47984			0.739922	−	0.672692i	$-0.234862\pi$
$673$	25836.8			1.47984			0.739922	+	0.672692i	$0.234862\pi$
$674$		0			0
$675$	−423.551	+	733.611i	−0.0241518	+	0.0418322i
$676$		0			0
$677$	−1617.08	+	933.621i	−0.0918012	+	0.0530014i	−0.545198	−	0.838307i	$-0.683545\pi$
$677$	−1617.08	+	933.621i	−0.0918012	+	0.0530014i	0.453397	+	0.891309i	$0.350212\pi$
$678$		0			0
$679$	10470.0	−	17371.0i	0.591758	−	0.981796i
$680$		0			0
$681$	2470.20	+	4278.51i	0.138999	+	0.240753i
$682$		0			0
$683$	8719.37	+	5034.13i	0.488488	+	0.282029i	0.723947	−	0.689856i	$-0.242326\pi$
$683$	8719.37	+	5034.13i	0.488488	+	0.282029i	−0.235459	+	0.971884i	$0.575659\pi$
$684$		0			0
$685$			14218.7i			0.793095i
$686$		0			0
$687$			17837.8i			0.990618i
$688$		0			0
$689$	8352.23	+	4822.16i	0.461821	+	0.266632i
$690$		0			0
$691$	3390.20	+	5872.00i	0.186642	+	0.323273i	0.944128	−	0.329578i	$-0.106906\pi$
$691$	3390.20	+	5872.00i	0.186642	+	0.323273i	−0.757487	+	0.652850i	$0.773573\pi$
$692$		0			0
$693$	−1001.49	+	1661.60i	−0.0548970	+	0.0910806i
$694$		0			0
$695$	13299.3	−	7678.35i	0.725857	−	0.419074i
$696$		0			0
$697$	2696.35	−	4670.21i	0.146530	−	0.253797i
$698$		0			0
$699$	13079.2			0.707724
$700$		0			0
$701$	−7053.80			−0.380054			−0.190027	−	0.981779i	$-0.560858\pi$
$701$	−7053.80			−0.380054			−0.190027	+	0.981779i	$0.560858\pi$
$702$		0			0
$703$	6625.81	−	11476.2i	0.355473	−	0.615697i
$704$		0			0
$705$	−5547.11	+	3202.62i	−0.296335	+	0.171089i
$706$		0			0
$707$	10578.4	+	19145.8i	0.562716	+	1.01846i
$708$		0			0
$709$	10813.0	+	18728.6i	0.572763	+	0.992055i	0.996281	+	0.0861673i	$0.0274620\pi$
$709$	10813.0	+	18728.6i	0.572763	+	0.992055i	−0.423517	+	0.905888i	$0.639205\pi$
$710$		0			0
$711$	−3252.05	−	1877.57i	−0.171535	−	0.0990359i
$712$		0			0
$713$		−	40744.6i		−	2.14011i
$714$		0			0
$715$		−	1991.39i		−	0.104159i
$716$		0			0
$717$	6155.63	+	3553.96i	0.320623	+	0.185112i
$718$		0			0
$719$	−15990.5	−	27696.4i	−0.829410	−	1.43658i	−0.898502	−	0.438970i	$-0.855343\pi$
$719$	−15990.5	−	27696.4i	−0.829410	−	1.43658i	0.0690914	−	0.997610i	$-0.477990\pi$
$720$		0			0
$721$	−508.550	+	27010.7i	−0.0262682	+	1.39519i
$722$		0			0
$723$	4675.02	−	2699.12i	0.240478	−	0.138840i
$724$		0			0
$725$	−1788.50	+	3097.77i	−0.0916182	+	0.158687i
$726$		0			0
$727$	14884.7			0.759342			0.379671	−	0.925122i	$-0.376037\pi$
$727$	14884.7			0.759342			0.379671	+	0.925122i	$0.376037\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−1127.77	+	1953.36i	−0.0570618	+	0.0988340i
$732$		0			0
$733$	−11723.4	+	6768.50i	−0.590741	+	0.341064i	−0.765390	−	0.643566i	$-0.777454\pi$
$733$	−11723.4	+	6768.50i	−0.590741	+	0.341064i	0.174650	+	0.984631i	$0.444121\pi$
$734$		0			0
$735$	8804.00	−	4650.22i	0.441824	−	0.233369i
$736$		0			0
$737$	2528.85	+	4380.10i	0.126393	+	0.218918i
$738$		0			0
$739$	−28810.2	−	16633.6i	−1.43410	−	0.827979i	−0.436671	−	0.899621i	$-0.643842\pi$
$739$	−28810.2	−	16633.6i	−1.43410	−	0.827979i	−0.997430	+	0.0716429i	$0.977176\pi$
$740$		0			0
$741$			2016.81i			0.0999859i
$742$		0			0
$743$		−	22712.5i		−	1.12145i	−0.828001	−	0.560726i	$-0.810522\pi$
$743$		−	22712.5i		−	1.12145i	0.828001	−	0.560726i	$-0.189478\pi$
$744$		0			0
$745$	24549.8	+	14173.8i	1.20729	+	0.697032i
$746$		0			0
$747$	−185.728	−	321.690i	−0.00909695	−	0.0157564i
$748$		0			0
$749$	−17093.0	−	321.822i	−0.833865	−	0.0156998i
$750$		0			0
$751$	753.214	−	434.868i	0.0365981	−	0.0211299i	−0.481589	−	0.876397i	$-0.659940\pi$
$751$	753.214	−	434.868i	0.0365981	−	0.0211299i	0.518187	+	0.855267i	$0.326607\pi$
$752$		0			0
$753$	747.574	−	1294.84i	0.0361794	−	0.0626646i
$754$		0			0
$755$	4897.54			0.236079
$756$		0			0
$757$	−31483.2			−1.51159			−0.755797	−	0.654806i	$-0.772750\pi$
$757$	−31483.2			−1.51159			−0.755797	+	0.654806i	$0.772750\pi$
$758$		0			0
$759$	−3184.41	+	5515.56i	−0.152288	+	0.263771i
$760$		0			0
$761$	29232.2	−	16877.2i	1.39247	−	0.803940i	0.398878	−	0.917004i	$-0.369400\pi$
$761$	29232.2	−	16877.2i	1.39247	−	0.803940i	0.993588	+	0.113064i	$0.0360664\pi$
$762$		0			0
$763$	−6694.86	+	3699.02i	−0.317654	+	0.175509i
$764$		0			0
$765$	−1747.64	−	3027.00i	−0.0825962	−	0.143061i
$766$		0			0
$767$	8231.06	+	4752.21i	0.387492	+	0.223719i
$768$		0			0
$769$			23724.6i			1.11252i	0.831007	+	0.556262i	$0.187765\pi$
$769$			23724.6i			1.11252i	−0.831007	+	0.556262i	$0.812235\pi$
$770$		0			0
$771$		−	13223.2i		−	0.617667i
$772$		0			0
$773$	11462.1	+	6617.65i	0.533329	+	0.307917i	0.742371	−	0.669989i	$-0.233701\pi$
$773$	11462.1	+	6617.65i	0.533329	+	0.307917i	−0.209042	+	0.977907i	$0.567035\pi$
$774$		0			0
$775$	3504.32	+	6069.66i	0.162424	+	0.281327i
$776$		0			0
$777$	16585.5	+	9996.56i	0.765766	+	0.461550i
$778$		0			0
$779$	4423.96	−	2554.18i	0.203472	−	0.117475i
$780$		0			0
$781$	2036.04	−	3526.52i	0.0932845	−	0.161573i
$782$		0			0
$783$	3078.30			0.140497
$784$		0			0
$785$	−11595.3			−0.527200
$786$		0			0
$787$	−20103.4	+	34820.2i	−0.910559	+	1.57713i	−0.0972819	+	0.995257i	$0.531015\pi$
$787$	−20103.4	+	34820.2i	−0.910559	+	1.57713i	−0.813277	+	0.581877i	$0.802319\pi$
$788$		0			0
$789$	−2026.73	+	1170.13i	−0.0914493	+	0.0527983i
$790$		0			0
$791$	16785.1	+	10116.9i	0.754501	+	0.454760i
$792$		0			0
$793$	3492.60	+	6049.36i	0.156401	+	0.270894i
$794$		0			0
$795$	−13711.8	−	7916.49i	−0.611706	−	0.353169i
$796$		0			0
$797$		−	19842.4i		−	0.881874i	−0.897538	−	0.440937i	$-0.854646\pi$
$797$		−	19842.4i		−	0.881874i	0.897538	−	0.440937i	$-0.145354\pi$
$798$		0			0
$799$			8856.43i			0.392137i
$800$		0			0
$801$	650.305	+	375.454i	0.0286859	+	0.0165618i
$802$		0			0
$803$	−2894.73	−	5013.82i	−0.127214	−	0.220341i
$804$		0			0
$805$	28609.0	−	15806.9i	1.25259	−	0.692076i
$806$		0			0
$807$	−16142.1	+	9319.65i	−0.704125	+	0.406527i
$808$		0			0
$809$	5697.97	−	9869.17i	0.247626	−	0.428902i	−0.715240	−	0.698879i	$-0.753683\pi$
$809$	5697.97	−	9869.17i	0.247626	−	0.428902i	0.962867	+	0.269977i	$0.0870161\pi$
$810$		0			0
$811$	−8614.59			−0.372995			−0.186498	−	0.982455i	$-0.559714\pi$
$811$	−8614.59			−0.372995			−0.186498	+	0.982455i	$0.559714\pi$
$812$		0			0
$813$	1349.18			0.0582015
$814$		0			0
$815$	13374.0	−	23164.4i	0.574811	−	0.995601i
$816$		0			0
$817$	−1850.36	+	1068.31i	−0.0792363	+	0.0457471i
$818$		0			0
$819$	−2946.73	−	55.4802i	−0.125723	−	0.00236707i
$820$		0			0
$821$	−5237.17	−	9071.05i	−0.222629	−	0.385605i	0.732976	−	0.680254i	$-0.238131\pi$
$821$	−5237.17	−	9071.05i	−0.222629	−	0.385605i	−0.955606	+	0.294649i	$0.904797\pi$
$822$		0			0
$823$	−33091.3	−	19105.3i	−1.40157	−	0.809195i	−0.407013	−	0.913422i	$-0.633430\pi$
$823$	−33091.3	−	19105.3i	−1.40157	−	0.809195i	−0.994554	+	0.104227i	$0.966763\pi$
$824$		0			0
$825$		−	1095.52i		−	0.0462318i
$826$		0			0
$827$			11066.3i			0.465311i	0.972559	+	0.232656i	$0.0747415\pi$
$827$			11066.3i			0.465311i	−0.972559	+	0.232656i	$0.925259\pi$
$828$		0			0
$829$	10825.0	+	6249.82i	0.453520	+	0.261840i	0.709316	−	0.704891i	$-0.249004\pi$
$829$	10825.0	+	6249.82i	0.453520	+	0.261840i	−0.255796	+	0.966731i	$0.582337\pi$
$830$		0			0
$831$	8752.72	+	15160.2i	0.365377	+	0.632852i
$832$		0			0
$833$	518.214	−	13757.1i	0.0215547	−	0.572217i
$834$		0			0
$835$	15146.1	−	8744.58i	0.627725	−	0.362417i
$836$		0			0
$837$	3015.75	−	5223.44i	0.124540	−	0.215709i
$838$		0			0
$839$	−6337.87			−0.260796			−0.130398	−	0.991462i	$-0.541625\pi$
$839$	−6337.87			−0.260796			−0.130398	+	0.991462i	$0.541625\pi$
$840$		0			0
$841$	−11390.5			−0.467032
$842$		0			0
$843$	−10407.5	+	18026.3i	−0.425211	+	0.736488i
$844$		0			0
$845$	−15790.3	+	9116.54i	−0.642844	+	0.371146i
$846$		0			0
$847$	−416.798	+	22137.5i	−0.0169083	+	0.898057i
$848$		0			0
$849$	11223.0	+	19438.9i	0.453679	+	0.785795i
$850$		0			0
$851$	55054.3	+	31785.6i	2.21767	+	1.28037i
$852$		0			0
$853$		−	39868.4i		−	1.60032i	−0.599789	−	0.800158i	$-0.704749\pi$
$853$		−	39868.4i		−	1.60032i	0.599789	−	0.800158i	$-0.295251\pi$
$854$		0			0
$855$		−	3310.99i		−	0.132437i
$856$		0			0
$857$	−30182.6	−	17425.9i	−1.20305	−	0.694584i	−0.241821	−	0.970321i	$-0.577745\pi$
$857$	−30182.6	−	17425.9i	−1.20305	−	0.694584i	−0.961233	+	0.275737i	$0.911078\pi$
$858$		0			0
$859$	−13997.5	−	24244.3i	−0.555981	−	0.962987i	−0.997826	−	0.0658962i	$-0.979009\pi$
$859$	−13997.5	−	24244.3i	−0.555981	−	0.962987i	0.441845	−	0.897091i	$-0.354324\pi$
$860$		0			0
$861$	3610.16	+	6534.03i	0.142897	+	0.258629i
$862$		0			0
$863$	−19275.3	+	11128.6i	−0.760300	+	0.438960i	−0.829404	−	0.558650i	$-0.811320\pi$
$863$	−19275.3	+	11128.6i	−0.760300	+	0.438960i	0.0691032	+	0.997610i	$0.477986\pi$
$864$		0			0
$865$	−13929.6	+	24126.8i	−0.547540	+	0.948366i
$866$		0			0
$867$	9906.14			0.388039
$868$		0			0
$869$	4856.39			0.189576
$870$		0			0
$871$	−3841.68	+	6653.99i	−0.149450	+	0.258854i
$872$		0			0
$873$	8535.82	−	4928.16i	0.330921	−	0.191057i
$874$		0			0
$875$	−14465.7	+	24000.3i	−0.558891	+	0.927267i
$876$		0			0
$877$	19876.7	+	34427.5i	0.765325	+	1.32558i	0.940075	+	0.340969i	$0.110755\pi$
$877$	19876.7	+	34427.5i	0.765325	+	1.32558i	−0.174749	+	0.984613i	$0.555912\pi$
$878$		0			0
$879$	−23994.9	−	13853.5i	−0.920737	−	0.531588i
$880$		0			0
$881$		−	16721.9i		−	0.639473i	−0.947506	−	0.319737i	$-0.896406\pi$
$881$		−	16721.9i		−	0.639473i	0.947506	−	0.319737i	$-0.103594\pi$
$882$		0			0
$883$		−	30714.2i		−	1.17057i	−0.810826	−	0.585287i	$-0.800982\pi$
$883$		−	30714.2i		−	1.17057i	0.810826	−	0.585287i	$-0.199018\pi$
$884$		0			0
$885$	−13512.9	−	7801.65i	−0.513254	−	0.296327i
$886$		0			0
$887$	14302.2	+	24772.1i	0.541398	+	0.937729i	0.998824	+	0.0484811i	$0.0154381\pi$
$887$	14302.2	+	24772.1i	0.541398	+	0.937729i	−0.457426	+	0.889248i	$0.651229\pi$
$888$		0			0
$889$	24723.3	−	41019.0i	0.932727	−	1.54750i
$890$		0			0
$891$	−816.479	+	471.394i	−0.0306993	+	0.0177242i
$892$		0			0
$893$	−4194.73	+	7265.48i	−0.157191	+	0.272262i
$894$		0			0
$895$	−5346.57			−0.199683
$896$		0			0
$897$	−9675.14			−0.360138
$898$		0			0
$899$	12734.4	−	22056.7i	0.472433	−	0.818277i
$900$		0			0
$901$	−18959.0	+	10946.0i	−0.701017	+	0.404733i
$902$		0			0
$903$	−1509.98	−	2732.92i	−0.0556469	−	0.100715i
$904$		0			0
$905$	−11014.4	−	19077.5i	−0.404564	−	0.700726i
$906$		0			0
$907$	44227.6	+	25534.8i	1.61913	+	0.934807i	0.987145	+	0.159828i	$0.0510940\pi$
$907$	44227.6	+	25534.8i	1.61913	+	0.934807i	0.631988	+	0.774979i	$0.282239\pi$
$908$		0			0
$909$			10629.7i			0.387859i
$910$		0			0
$911$		−	20799.6i		−	0.756444i	−0.925715	−	0.378222i	$-0.876536\pi$
$911$		−	20799.6i		−	0.756444i	0.925715	−	0.378222i	$-0.123464\pi$
$912$		0			0
$913$	416.030	+	240.195i	0.0150806	+	0.00870678i
$914$		0			0
$915$	−5733.77	−	9931.18i	−0.207161	−	0.358814i
$916$		0			0
$917$	274.117	−	14559.2i	0.00987147	−	0.524306i
$918$		0			0
$919$	−37548.2	+	21678.5i	−1.34777	+	0.778136i	−0.987933	−	0.154879i	$-0.950501\pi$
$919$	−37548.2	+	21678.5i	−1.34777	+	0.778136i	−0.359838	+	0.933015i	$0.617168\pi$
$920$		0			0
$921$	−1913.91	+	3314.98i	−0.0684749	+	0.118602i
$922$		0			0
$923$	6186.07			0.220603
$924$		0			0
$925$	−10935.1			−0.388697
$926$		0			0
$927$	−6564.16	+	11369.5i	−0.232573	+	0.402828i
$928$		0			0
$929$	−6972.50	+	4025.58i	−0.246244	+	0.142169i	−0.618043	−	0.786144i	$-0.712074\pi$
$929$	−6972.50	+	4025.58i	−0.246244	+	0.142169i	0.371799	+	0.928313i	$0.378741\pi$
$930$		0			0
$931$	6941.00	−	11040.4i	0.244342	−	0.388651i
$932$		0			0
$933$	14305.3	+	24777.4i	0.501965	+	0.869428i
$934$		0			0
$935$	3914.71	+	2260.16i	0.136925	+	0.0790536i
$936$		0			0
$937$			23098.3i			0.805325i	0.915349	+	0.402663i	$0.131915\pi$
$937$			23098.3i			0.805325i	−0.915349	+	0.402663i	$0.868085\pi$
$938$		0			0
$939$			10074.6i			0.350129i
$940$		0			0
$941$	5766.38	+	3329.22i	0.199765	+	0.115334i	0.596546	−	0.802579i	$-0.296539\pi$
$941$	5766.38	+	3329.22i	0.199765	+	0.115334i	−0.396781	+	0.917913i	$0.629873\pi$
$942$		0			0
$943$	12253.0	+	21222.8i	0.423131	+	0.732884i
$944$		0			0
$945$	4837.62	+	91.0813i	0.166527	+	0.00313532i
$946$		0			0
$947$	−20067.6	+	11586.0i	−0.688604	+	0.397566i	−0.803089	−	0.595859i	$-0.796812\pi$
$947$	−20067.6	+	11586.0i	−0.688604	+	0.397566i	0.114485	+	0.993425i	$0.463478\pi$
$948$		0			0
$949$	4397.51	−	7616.71i	0.150421	−	0.260536i
$950$		0			0
$951$	−1843.26			−0.0628517
$952$		0			0
$953$	−53982.2			−1.83490			−0.917448	−	0.397855i	$-0.869755\pi$
$953$	−53982.2			−1.83490			−0.917448	+	0.397855i	$0.869755\pi$
$954$		0			0
$955$	−22885.9	+	39639.5i	−0.775466	+	1.34315i
$956$		0			0
$957$	−3447.69	+	1990.53i	−0.116456	+	0.0672357i
$958$		0			0
$959$	−23821.0	+	13161.5i	−0.802105	+	0.443176i
$960$		0			0
$961$	−10055.9	−	17417.3i	−0.337547	−	0.584648i
$962$		0			0
$963$	−7194.85	−	4153.95i	−0.240759	−	0.139002i
$964$		0			0
$965$		−	34287.1i		−	1.14377i
$966$		0			0
$967$			38714.9i			1.28748i	0.765246	+	0.643738i	$0.222617\pi$
$967$			38714.9i			1.28748i	−0.765246	+	0.643738i	$0.777383\pi$
$968$		0			0
$969$	−3964.70	−	2289.02i	−0.131439	−	0.0758864i
$970$		0			0
$971$	−8881.95	−	15384.0i	−0.293548	−	0.508440i	0.681098	−	0.732192i	$-0.261503\pi$
$971$	−8881.95	−	15384.0i	−0.293548	−	0.508440i	−0.974646	+	0.223752i	$0.928169\pi$
$972$		0			0
$973$	25174.1	+	15173.2i	0.829439	+	0.499928i
$974$		0			0
$975$	1441.29	−	832.129i	0.0473418	−	0.0273328i
$976$		0			0
$977$	−20708.6	+	35868.3i	−0.678123	+	1.17454i	0.297422	+	0.954746i	$0.403873\pi$
$977$	−20708.6	+	35868.3i	−0.678123	+	1.17454i	−0.975545	+	0.219798i	$0.929460\pi$
$978$		0			0
$979$	−971.121			−0.0317029
$980$		0			0
$981$	−3716.96			−0.120972
$982$		0			0
$983$	21845.1	−	37836.8i	0.708800	−	1.22768i	−0.256502	−	0.966544i	$-0.582570\pi$
$983$	21845.1	−	37836.8i	0.708800	−	1.22768i	0.965302	−	0.261135i	$-0.0840967\pi$
$984$		0			0
$985$	−29147.9	+	16828.6i	−0.942873	+	0.544368i
$986$		0			0
$987$	−10500.1	−	6328.70i	−0.338623	−	0.204098i
$988$		0			0
$989$	−5124.93	−	8876.64i	−0.164776	−	0.285400i
$990$		0			0
$991$	−30670.9	−	17707.8i	−0.983141	−	0.567617i	−0.0799239	−	0.996801i	$-0.525468\pi$
$991$	−30670.9	−	17707.8i	−0.983141	−	0.567617i	−0.903217	+	0.429184i	$0.858801\pi$
$992$		0			0
$993$			14562.1i			0.465373i
$994$		0			0
$995$		−	20063.4i		−	0.639250i
$996$		0			0
$997$	−22448.8	−	12960.8i	−0.713100	−	0.411708i	0.0991081	−	0.995077i	$-0.468401\pi$
$997$	−22448.8	−	12960.8i	−0.713100	−	0.411708i	−0.812208	+	0.583368i	$0.801734\pi$
$998$		0			0
$999$	4705.29	+	8149.80i	0.149018	+	0.258106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bl.f.31.1	✓	6
4.3	odd	2		336.4.bl.h.31.1	yes	6
7.5	odd	6		336.4.bl.h.271.1	yes	6
28.19	even	6	inner	336.4.bl.f.271.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bl.f.31.1	✓	6	1.1	even	1	trivial
336.4.bl.f.271.1	yes	6	28.19	even	6	inner
336.4.bl.h.31.1	yes	6	4.3	odd	2
336.4.bl.h.271.1	yes	6	7.5	odd	6

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +(-8.37970 + 4.83802i) q^{5} +(-15.8619 - 9.56041i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(10.0800 + 5.81968i) q^{11} +17.6819i q^{13} -29.0281i q^{15} +(-34.7594 - 20.0684i) q^{17} +(-19.0102 - 32.9266i) q^{19} +(48.6315 - 26.8697i) q^{21} +(157.957 - 91.1965i) q^{23} +(-15.6871 + 27.1708i) q^{25} +27.0000 q^{27} +114.011 q^{29} +(111.695 - 193.461i) q^{31} +(-30.2400 + 17.4590i) q^{33} +(179.171 + 3.37338i) q^{35} +(174.270 + 301.844i) q^{37} +(-45.9388 - 26.5228i) q^{39} +134.358i q^{41} -56.1966i q^{43} +(75.4173 + 43.5422i) q^{45} +(-110.328 - 191.094i) q^{47} +(160.197 + 303.292i) q^{49} +(104.278 - 60.2051i) q^{51} +(272.718 - 472.361i) q^{53} -112.623 q^{55} +114.061 q^{57} +(268.762 - 465.509i) q^{59} +(342.122 - 197.524i) q^{61} +(-3.13769 + 166.653i) q^{63} +(-85.5453 - 148.169i) q^{65} +(376.317 + 217.267i) q^{67} +547.179i q^{69} -349.854i q^{71} +(-430.764 - 248.702i) q^{73} +(-47.0612 - 81.5123i) q^{75} +(-104.249 - 188.680i) q^{77} +(361.339 - 208.619i) q^{79} +(-40.5000 + 70.1481i) q^{81} +41.2728 q^{83} +388.365 q^{85} +(-171.017 + 296.210i) q^{87} +(-72.2561 + 41.7171i) q^{89} +(169.046 - 280.467i) q^{91} +(335.084 + 580.382i) q^{93} +(318.600 + 183.944i) q^{95} +1095.15i q^{97} -104.754i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} + 12 q^{5} - 7 q^{7} - 27 q^{9} - 48 q^{11} - 84 q^{17} - 77 q^{19} + 42 q^{21} + 108 q^{23} - 141 q^{25} + 162 q^{27} + 372 q^{29} + 11 q^{31} + 144 q^{33} + 546 q^{35} + 159 q^{37} - 135 q^{39}+ \cdots - 258 q^{95}+O(q^{100}) \) 6 * q - 9 * q^3 + 12 * q^5 - 7 * q^7 - 27 * q^9 - 48 * q^11 - 84 * q^17 - 77 * q^19 + 42 * q^21 + 108 * q^23 - 141 * q^25 + 162 * q^27 + 372 * q^29 + 11 * q^31 + 144 * q^33 + 546 * q^35 + 159 * q^37 - 135 * q^39 - 108 * q^45 - 378 * q^47 - 567 * q^49 + 252 * q^51 + 78 * q^53 - 1044 * q^55 + 462 * q^57 - 150 * q^59 + 1608 * q^61 - 63 * q^63 - 78 * q^65 - 339 * q^67 - 273 * q^73 - 423 * q^75 - 2394 * q^77 + 3429 * q^79 - 243 * q^81 - 1464 * q^83 + 648 * q^85 - 558 * q^87 + 768 * q^89 + 1029 * q^91 + 33 * q^93 - 258 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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