LMFDB - Embedded newform 336.4.q.g.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{505})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 127x^{2} + 126x + 15876 $ x^4 - x^3 + 127x^2 + 126x + 15876
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$5.86805 + 10.1638i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.4.q.g.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{3} +(-7.86805 - 13.6279i) q^{5} +(-11.2361 + 14.7224i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{3} +(-7.86805 - 13.6279i) q^{5} +(-11.2361 + 14.7224i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(29.3403 - 50.8188i) q^{11} -20.7361 q^{13} +47.2083 q^{15} +(-21.4722 + 37.1910i) q^{17} +(68.5764 + 118.778i) q^{19} +(-21.3958 - 51.2759i) q^{21} +(14.5278 + 25.1629i) q^{23} +(-61.3125 + 106.196i) q^{25} +27.0000 q^{27} +8.68051 q^{29} +(-101.236 + 175.346i) q^{31} +(88.0208 + 152.456i) q^{33} +(289.042 + 37.2872i) q^{35} +(7.63195 + 13.2189i) q^{37} +(31.1042 - 53.8740i) q^{39} +117.250 q^{41} +101.875 q^{43} +(-70.8125 + 122.651i) q^{45} +(294.250 + 509.656i) q^{47} +(-90.5000 - 330.846i) q^{49} +(-64.4166 - 111.573i) q^{51} +(-202.340 + 350.464i) q^{53} -923.403 q^{55} -411.458 q^{57} +(5.43738 - 9.41783i) q^{59} +(447.305 + 774.756i) q^{61} +(165.312 + 21.3258i) q^{63} +(163.153 + 282.589i) q^{65} +(-351.868 + 609.453i) q^{67} -87.1668 q^{69} -1161.94 q^{71} +(558.187 - 966.809i) q^{73} +(-183.937 - 318.589i) q^{75} +(418.506 + 1002.97i) q^{77} +(69.1665 + 119.800i) q^{79} +(-40.5000 + 70.1481i) q^{81} +894.319 q^{83} +675.778 q^{85} +(-13.0208 + 22.5526i) q^{87} +(340.903 + 590.461i) q^{89} +(232.993 - 305.286i) q^{91} +(-303.708 - 526.038i) q^{93} +(1079.12 - 1869.10i) q^{95} +246.514 q^{97} -528.125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 9 q^{5} - 18 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 - 9 * q^5 - 18 * q^9	$ 4 q - 6 q^{3} - 9 q^{5} - 18 q^{9} + 5 q^{11} - 38 q^{13} + 54 q^{15} + 4 q^{17} + 117 q^{19} - 153 q^{21} + 148 q^{23} - 43 q^{25} + 108 q^{27} - 190 q^{29} - 360 q^{31} + 15 q^{33} + 482 q^{35} + 53 q^{37} + 57 q^{39} - 340 q^{41} - 806 q^{43} - 81 q^{45} + 368 q^{47} - 362 q^{49} + 12 q^{51} - 697 q^{53} - 2570 q^{55} - 702 q^{57} - 585 q^{59} + 1160 q^{61} + 459 q^{63} + 338 q^{65} + 233 q^{67} - 888 q^{69} - 1232 q^{71} + 817 q^{73} - 129 q^{75} - 1135 q^{77} - 802 q^{79} - 162 q^{81} + 566 q^{83} + 1984 q^{85} + 285 q^{87} + 1858 q^{89} + 505 q^{91} - 1080 q^{93} + 2294 q^{95} + 3458 q^{97} - 90 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 9 * q^5 - 18 * q^9 + 5 * q^11 - 38 * q^13 + 54 * q^15 + 4 * q^17 + 117 * q^19 - 153 * q^21 + 148 * q^23 - 43 * q^25 + 108 * q^27 - 190 * q^29 - 360 * q^31 + 15 * q^33 + 482 * q^35 + 53 * q^37 + 57 * q^39 - 340 * q^41 - 806 * q^43 - 81 * q^45 + 368 * q^47 - 362 * q^49 + 12 * q^51 - 697 * q^53 - 2570 * q^55 - 702 * q^57 - 585 * q^59 + 1160 * q^61 + 459 * q^63 + 338 * q^65 + 233 * q^67 - 888 * q^69 - 1232 * q^71 + 817 * q^73 - 129 * q^75 - 1135 * q^77 - 802 * q^79 - 162 * q^81 + 566 * q^83 + 1984 * q^85 + 285 * q^87 + 1858 * q^89 + 505 * q^91 - 1080 * q^93 + 2294 * q^95 + 3458 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−7.86805	−	13.6279i	−0.703740	−	1.21891i	−0.967144	−	0.254228i	$-0.918179\pi$
$5$	−7.86805	−	13.6279i	−0.703740	−	1.21891i	0.263404	−	0.964685i	$-0.415155\pi$
$6$		0			0
$7$	−11.2361	+	14.7224i	−0.606693	+	0.794937i
$7$	−11.2361	+	14.7224i	−0.606693	+	0.794937i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	29.3403	−	50.8188i	0.804220	−	1.39295i	−0.112596	−	0.993641i	$-0.535917\pi$
$11$	29.3403	−	50.8188i	0.804220	−	1.39295i	0.916816	−	0.399309i	$-0.130750\pi$
$12$		0			0
$13$	−20.7361			−0.442397			−0.221198	−	0.975229i	$-0.570997\pi$
$13$	−20.7361			−0.442397			−0.221198	+	0.975229i	$0.570997\pi$
$14$		0			0
$15$	47.2083			0.812609
$16$		0			0
$17$	−21.4722	+	37.1910i	−0.306340	+	0.530596i	−0.977559	−	0.210663i	$-0.932438\pi$
$17$	−21.4722	+	37.1910i	−0.306340	+	0.530596i	0.671219	+	0.741259i	$0.265771\pi$
$18$		0			0
$19$	68.5764	+	118.778i	0.828026	+	1.43418i	0.899584	+	0.436747i	$0.143869\pi$
$19$	68.5764	+	118.778i	0.828026	+	1.43418i	−0.0715584	+	0.997436i	$0.522797\pi$
$20$		0			0
$21$	−21.3958	−	51.2759i	−0.222331	−	0.532825i
$22$		0			0
$23$	14.5278	+	25.1629i	0.131707	+	0.228123i	0.924335	−	0.381583i	$-0.124621\pi$
$23$	14.5278	+	25.1629i	0.131707	+	0.228123i	−0.792628	+	0.609706i	$0.791288\pi$
$24$		0			0
$25$	−61.3125	+	106.196i	−0.490500	+	0.849570i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	8.68051			0.0555838			0.0277919	−	0.999614i	$-0.491152\pi$
$29$	8.68051			0.0555838			0.0277919	+	0.999614i	$0.491152\pi$
$30$		0			0
$31$	−101.236	+	175.346i	−0.586534	+	1.01591i	0.408149	+	0.912915i	$0.366174\pi$
$31$	−101.236	+	175.346i	−0.586534	+	1.01591i	−0.994682	+	0.102991i	$0.967159\pi$
$32$		0			0
$33$	88.0208	+	152.456i	0.464317	+	0.804220i
$34$		0			0
$35$	289.042	+	37.2872i	1.39591	+	0.180077i
$36$		0			0
$37$	7.63195	+	13.2189i	0.0339104	+	0.0587345i	0.882483	−	0.470345i	$-0.155871\pi$
$37$	7.63195	+	13.2189i	0.0339104	+	0.0587345i	−0.848572	+	0.529080i	$0.822537\pi$
$38$		0			0
$39$	31.1042	−	53.8740i	0.127709	−	0.221198i
$40$		0			0
$41$	117.250			0.446618			0.223309	−	0.974748i	$-0.428314\pi$
$41$	117.250			0.446618			0.223309	+	0.974748i	$0.428314\pi$
$42$		0			0
$43$	101.875			0.361297			0.180648	−	0.983548i	$-0.442180\pi$
$43$	101.875			0.361297			0.180648	+	0.983548i	$0.442180\pi$
$44$		0			0
$45$	−70.8125	+	122.651i	−0.234580	+	0.406304i
$46$		0			0
$47$	294.250	+	509.656i	0.913207	+	1.58172i	0.809505	+	0.587113i	$0.199736\pi$
$47$	294.250	+	509.656i	0.913207	+	1.58172i	0.103703	+	0.994608i	$0.466931\pi$
$48$		0			0
$49$	−90.5000	−	330.846i	−0.263848	−	0.964564i
$50$		0			0
$51$	−64.4166	−	111.573i	−0.176865	−	0.306340i
$52$		0			0
$53$	−202.340	+	350.464i	−0.524407	+	0.908300i	0.475189	+	0.879884i	$0.342380\pi$
$53$	−202.340	+	350.464i	−0.524407	+	0.908300i	−0.999596	+	0.0284159i	$0.990954\pi$
$54$		0			0
$55$	−923.403			−2.26385
$56$		0			0
$57$	−411.458			−0.956122
$58$		0			0
$59$	5.43738	−	9.41783i	0.0119981	−	0.0207813i	−0.859964	−	0.510355i	$-0.829514\pi$
$59$	5.43738	−	9.41783i	0.0119981	−	0.0207813i	0.871962	+	0.489573i	$0.162847\pi$
$60$		0			0
$61$	447.305	+	774.756i	0.938879	+	1.62619i	0.767567	+	0.640968i	$0.221467\pi$
$61$	447.305	+	774.756i	0.938879	+	1.62619i	0.171311	+	0.985217i	$0.445200\pi$
$62$		0			0
$63$	165.312	+	21.3258i	0.330594	+	0.0426476i
$64$		0			0
$65$	163.153	+	282.589i	0.311332	+	0.539243i
$66$		0			0
$67$	−351.868	+	609.453i	−0.641604	+	1.11129i	0.343470	+	0.939164i	$0.388398\pi$
$67$	−351.868	+	609.453i	−0.641604	+	1.11129i	−0.985075	+	0.172128i	$0.944936\pi$
$68$		0			0
$69$	−87.1668			−0.152082
$70$		0			0
$71$	−1161.94			−1.94222			−0.971108	−	0.238640i	$-0.923298\pi$
$71$	−1161.94			−1.94222			−0.971108	+	0.238640i	$0.923298\pi$
$72$		0			0
$73$	558.187	−	966.809i	0.894943	−	1.55009i	0.0610689	−	0.998134i	$-0.480549\pi$
$73$	558.187	−	966.809i	0.894943	−	1.55009i	0.833875	−	0.551954i	$-0.186118\pi$
$74$		0			0
$75$	−183.937	−	318.589i	−0.283190	−	0.490500i
$76$		0			0
$77$	418.506	+	1002.97i	0.619393	+	1.48440i
$78$		0			0
$79$	69.1665	+	119.800i	0.0985042	+	0.170614i	0.911066	−	0.412261i	$-0.135261\pi$
$79$	69.1665	+	119.800i	0.0985042	+	0.170614i	−0.812561	+	0.582875i	$0.801928\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	894.319			1.18270			0.591351	−	0.806414i	$-0.298595\pi$
$83$	894.319			1.18270			0.591351	+	0.806414i	$0.298595\pi$
$84$		0			0
$85$	675.778			0.862334
$86$		0			0
$87$	−13.0208	+	22.5526i	−0.0160457	+	0.0277919i
$88$		0			0
$89$	340.903	+	590.461i	0.406018	+	0.703244i	0.994439	−	0.105310i	$-0.0335836\pi$
$89$	340.903	+	590.461i	0.406018	+	0.703244i	−0.588421	+	0.808555i	$0.700250\pi$
$90$		0			0
$91$	232.993	−	305.286i	0.268399	−	0.351678i
$92$		0			0
$93$	−303.708	−	526.038i	−0.338635	−	0.586534i
$94$		0			0
$95$	1079.12	−	1869.10i	1.16543	−	2.01858i
$96$		0			0
$97$	246.514			0.258039			0.129019	−	0.991642i	$-0.458817\pi$
$97$	246.514			0.258039			0.129019	+	0.991642i	$0.458817\pi$
$98$		0			0
$99$	−528.125			−0.536147
$100$		0			0
$101$	544.972	−	943.919i	0.536898	−	0.929935i	−0.462171	−	0.886791i	$-0.652929\pi$
$101$	544.972	−	943.919i	0.536898	−	0.929935i	0.999069	−	0.0431441i	$-0.0137375\pi$
$102$		0			0
$103$	−15.1182	−	26.1855i	−0.0144625	−	0.0250498i	0.858704	−	0.512473i	$-0.171270\pi$
$103$	−15.1182	−	26.1855i	−0.0144625	−	0.0250498i	−0.873166	+	0.487423i	$0.837937\pi$
$104$		0			0
$105$	−530.437	+	695.021i	−0.493004	+	0.645973i
$106$		0			0
$107$	943.812	+	1634.73i	0.852727	+	1.47697i	0.878738	+	0.477305i	$0.158386\pi$
$107$	943.812	+	1634.73i	0.852727	+	1.47697i	−0.0260107	+	0.999662i	$0.508280\pi$
$108$		0			0
$109$	482.298	−	835.365i	0.423815	−	0.734069i	−0.572494	−	0.819909i	$-0.694024\pi$
$109$	482.298	−	835.365i	0.423815	−	0.734069i	0.996309	+	0.0858401i	$0.0273574\pi$
$110$		0			0
$111$	−45.7917			−0.0391564
$112$		0			0
$113$	119.806			0.0997378			0.0498689	−	0.998756i	$-0.484120\pi$
$113$	119.806			0.0997378			0.0498689	+	0.998756i	$0.484120\pi$
$114$		0			0
$115$	228.611	−	395.966i	0.185375	−	0.321078i
$116$		0			0
$117$	93.3125	+	161.622i	0.0737328	+	0.127709i
$118$		0			0
$119$	−306.277	−	734.004i	−0.235936	−	0.565429i
$120$		0			0
$121$	−1056.20	−	1829.39i	−0.793540	−	1.37445i
$122$		0			0
$123$	−175.875	+	304.624i	−0.128928	+	0.223309i
$124$		0			0
$125$	−37.3745			−0.0267430
$126$		0			0
$127$	−683.722			−0.477721			−0.238860	−	0.971054i	$-0.576774\pi$
$127$	−683.722			−0.477721			−0.238860	+	0.971054i	$0.576774\pi$
$128$		0			0
$129$	−152.812	+	264.678i	−0.104297	+	0.180648i
$130$		0			0
$131$	130.119	+	225.372i	0.0867825	+	0.150312i	0.906149	−	0.422958i	$-0.139008\pi$
$131$	130.119	+	225.372i	0.0867825	+	0.150312i	−0.819367	+	0.573269i	$0.805675\pi$
$132$		0			0
$133$	−2519.23	−	324.988i	−1.64244	−	0.211880i
$134$		0			0
$135$	−212.437	−	367.952i	−0.135435	−	0.234580i
$136$		0			0
$137$	365.847	−	633.666i	0.228149	−	0.395166i	−0.729110	−	0.684396i	$-0.760066\pi$
$137$	365.847	−	633.666i	0.228149	−	0.395166i	0.957260	+	0.289230i	$0.0933993\pi$
$138$		0			0
$139$	−2287.74			−1.39599			−0.697997	−	0.716101i	$-0.745925\pi$
$139$	−2287.74			−1.39599			−0.697997	+	0.716101i	$0.745925\pi$
$140$		0			0
$141$	−1765.50			−1.05448
$142$		0			0
$143$	−608.403	+	1053.78i	−0.355784	+	0.616237i
$144$		0			0
$145$	−68.2987	−	118.297i	−0.0391166	−	0.0677519i
$146$		0			0
$147$	995.312	+	261.142i	0.558449	+	0.146521i
$148$		0			0
$149$	−1719.60	−	2978.43i	−0.945469	−	1.63760i	−0.754810	−	0.655944i	$-0.772271\pi$
$149$	−1719.60	−	2978.43i	−0.945469	−	1.63760i	−0.190659	−	0.981656i	$-0.561063\pi$
$150$		0			0
$151$	1425.88	−	2469.70i	0.768455	−	1.33100i	−0.169946	−	0.985453i	$-0.554359\pi$
$151$	1425.88	−	2469.70i	0.768455	−	1.33100i	0.938401	−	0.345549i	$-0.112307\pi$
$152$		0			0
$153$	386.500			0.204226
$154$		0			0
$155$	3186.12			1.65107
$156$		0			0
$157$	−1220.12	+	2113.32i	−0.620232	+	1.07427i	0.369210	+	0.929346i	$0.379628\pi$
$157$	−1220.12	+	2113.32i	−0.620232	+	1.07427i	−0.989442	+	0.144928i	$0.953705\pi$
$158$		0			0
$159$	−607.021	−	1051.39i	−0.302767	−	0.524407i
$160$		0			0
$161$	−533.695	−	68.8482i	−0.261249	−	0.0337019i
$162$		0			0
$163$	120.695	+	209.050i	0.0579974	+	0.100454i	0.893566	−	0.448931i	$-0.148195\pi$
$163$	120.695	+	209.050i	0.0579974	+	0.100454i	−0.835569	+	0.549386i	$0.814862\pi$
$164$		0			0
$165$	1385.10	−	2399.07i	0.653516	−	1.13192i
$166$		0			0
$167$	−326.445			−0.151264			−0.0756319	−	0.997136i	$-0.524097\pi$
$167$	−326.445			−0.151264			−0.0756319	+	0.997136i	$0.524097\pi$
$168$		0			0
$169$	−1767.01			−0.804285
$170$		0			0
$171$	617.187	−	1069.00i	0.276009	−	0.478061i
$172$		0			0
$173$	797.847	+	1381.91i	0.350631	+	0.607311i	0.986360	−	0.164601i	$-0.0526337\pi$
$173$	797.847	+	1381.91i	0.350631	+	0.607311i	−0.635729	+	0.771912i	$0.719300\pi$
$174$		0			0
$175$	−874.555	−	2095.90i	−0.377772	−	0.905344i
$176$		0			0
$177$	16.3122	+	28.2535i	0.00692710	+	0.0119981i
$178$		0			0
$179$	1441.43	−	2496.63i	0.601886	−	1.04250i	−0.390650	−	0.920539i	$-0.627750\pi$
$179$	1441.43	−	2496.63i	0.601886	−	1.04250i	0.992535	−	0.121957i	$-0.0389171\pi$
$180$		0			0
$181$	1128.60			0.463470			0.231735	−	0.972779i	$-0.425560\pi$
$181$	1128.60			0.463470			0.231735	+	0.972779i	$0.425560\pi$
$182$		0			0
$183$	−2683.83			−1.08412
$184$		0			0
$185$	120.097	−	208.014i	0.0477282	−	0.0826677i
$186$		0			0
$187$	1260.00	+	2182.38i	0.492729	+	0.853432i
$188$		0			0
$189$	−303.375	+	397.506i	−0.116758	+	0.152986i
$190$		0			0
$191$	1102.62	+	1909.80i	0.417713	+	0.723500i	0.995709	−	0.0925397i	$-0.0294985\pi$
$191$	1102.62	+	1909.80i	0.417713	+	0.723500i	−0.577996	+	0.816039i	$0.696165\pi$
$192$		0			0
$193$	−1897.68	+	3286.88i	−0.707761	+	1.22588i	0.257924	+	0.966165i	$0.416962\pi$
$193$	−1897.68	+	3286.88i	−0.707761	+	1.22588i	−0.965686	+	0.259714i	$0.916372\pi$
$194$		0			0
$195$	−978.916			−0.359496
$196$		0			0
$197$	3701.25			1.33859			0.669297	−	0.742995i	$-0.266595\pi$
$197$	3701.25			1.33859			0.669297	+	0.742995i	$0.266595\pi$
$198$		0			0
$199$	−1800.19	+	3118.03i	−0.641268	+	1.11071i	0.343882	+	0.939013i	$0.388258\pi$
$199$	−1800.19	+	3118.03i	−0.641268	+	1.11071i	−0.985150	+	0.171696i	$0.945075\pi$
$200$		0			0
$201$	−1055.60	−	1828.36i	−0.370430	−	0.641604i
$202$		0			0
$203$	−97.5351	+	127.798i	−0.0337223	+	0.0441856i
$204$		0			0
$205$	−922.528	−	1597.87i	−0.314303	−	0.544389i
$206$		0			0
$207$	130.750	−	226.466i	0.0439022	−	0.0760409i
$208$		0			0
$209$	8048.19			2.66366
$210$		0			0
$211$	4137.64			1.34998			0.674992	−	0.737825i	$-0.264147\pi$
$211$	4137.64			1.34998			0.674992	+	0.737825i	$0.264147\pi$
$212$		0			0
$213$	1742.92	−	3018.82i	0.560670	−	0.971108i
$214$		0			0
$215$	−801.556	−	1388.34i	−0.254259	−	0.440389i
$216$		0			0
$217$	−1444.02	−	3460.65i	−0.451735	−	1.08260i
$218$		0			0
$219$	1674.56	+	2900.43i	0.516696	+	0.894943i
$220$		0			0
$221$	445.250	−	771.195i	0.135524	−	0.234734i
$222$		0			0
$223$	−4261.62			−1.27973			−0.639864	−	0.768488i	$-0.721009\pi$
$223$	−4261.62			−1.27973			−0.639864	+	0.768488i	$0.721009\pi$
$224$		0			0
$225$	1103.62			0.327000
$226$		0			0
$227$	−767.063	+	1328.59i	−0.224281	+	0.388466i	−0.956103	−	0.293029i	$-0.905337\pi$
$227$	−767.063	+	1328.59i	−0.224281	+	0.388466i	0.731823	+	0.681495i	$0.238670\pi$
$228$		0			0
$229$	287.452	+	497.881i	0.0829491	+	0.143672i	0.904515	−	0.426441i	$-0.140233\pi$
$229$	287.452	+	497.881i	0.0829491	+	0.143672i	−0.821566	+	0.570113i	$0.806899\pi$
$230$		0			0
$231$	−3233.54	−	417.136i	−0.921001	−	0.118812i
$232$		0			0
$233$	2076.07	+	3595.86i	0.583724	+	1.01104i	0.995033	+	0.0995443i	$0.0317385\pi$
$233$	2076.07	+	3595.86i	0.583724	+	1.01104i	−0.411309	+	0.911496i	$0.634928\pi$
$234$		0			0
$235$	4630.35	−	8019.99i	1.28532	−	2.22624i
$236$		0			0
$237$	−414.999			−0.113743
$238$		0			0
$239$	−4548.36			−1.23100			−0.615500	−	0.788137i	$-0.711046\pi$
$239$	−4548.36			−1.23100			−0.615500	+	0.788137i	$0.711046\pi$
$240$		0			0
$241$	−3504.39	+	6069.79i	−0.936672	+	1.62236i	−0.165046	+	0.986286i	$0.552777\pi$
$241$	−3504.39	+	6069.79i	−0.936672	+	1.62236i	−0.771625	+	0.636077i	$0.780556\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−3796.66	+	3836.43i	−0.990039	+	1.00041i
$246$		0			0
$247$	−1422.01	−	2462.99i	−0.366316	−	0.634478i
$248$		0			0
$249$	−1341.48	+	2323.51i	−0.341417	+	0.591351i
$250$		0			0
$251$	−682.819			−0.171710			−0.0858548	−	0.996308i	$-0.527362\pi$
$251$	−682.819			−0.171710			−0.0858548	+	0.996308i	$0.527362\pi$
$252$		0			0
$253$	1705.00			0.423685
$254$		0			0
$255$	−1013.67	+	1755.72i	−0.248934	+	0.431167i
$256$		0			0
$257$	−851.276	−	1474.45i	−0.206619	−	0.357875i	0.744028	−	0.668148i	$-0.232913\pi$
$257$	−851.276	−	1474.45i	−0.206619	−	0.357875i	−0.950647	+	0.310273i	$0.899579\pi$
$258$		0			0
$259$	−280.368	−	36.1683i	−0.0672634	−	0.00867718i
$260$		0			0
$261$	−39.0623	−	67.6579i	−0.00926397	−	0.0160457i
$262$		0			0
$263$	−1462.12	+	2532.47i	−0.342808	+	0.593760i	−0.984953	−	0.172823i	$-0.944711\pi$
$263$	−1462.12	+	2532.47i	−0.342808	+	0.593760i	0.642145	+	0.766583i	$0.278045\pi$
$264$		0			0
$265$	6368.09			1.47618
$266$		0			0
$267$	−2045.42			−0.468830
$268$		0			0
$269$	−686.910	+	1189.76i	−0.155694	+	0.269670i	−0.933311	−	0.359068i	$-0.883095\pi$
$269$	−686.910	+	1189.76i	−0.155694	+	0.269670i	0.777618	+	0.628738i	$0.216428\pi$
$270$		0			0
$271$	−390.756	−	676.809i	−0.0875894	−	0.151709i	0.818902	−	0.573933i	$-0.194583\pi$
$271$	−390.756	−	676.809i	−0.0875894	−	0.151709i	−0.906492	+	0.422224i	$0.861250\pi$
$272$		0			0
$273$	443.666	+	1063.26i	0.0983587	+	0.235720i
$274$		0			0
$275$	3597.85	+	6231.65i	0.788939	+	1.36648i
$276$		0			0
$277$	1075.81	−	1863.36i	0.233355	−	0.404182i	−0.725439	−	0.688287i	$-0.758363\pi$
$277$	1075.81	−	1863.36i	0.233355	−	0.404182i	0.958793	+	0.284105i	$0.0916964\pi$
$278$		0			0
$279$	1822.25			0.391022
$280$		0			0
$281$	−2388.25			−0.507014			−0.253507	−	0.967334i	$-0.581584\pi$
$281$	−2388.25			−0.507014			−0.253507	+	0.967334i	$0.581584\pi$
$282$		0			0
$283$	−1647.33	+	2853.25i	−0.346019	+	0.599322i	−0.985538	−	0.169453i	$-0.945800\pi$
$283$	−1647.33	+	2853.25i	−0.346019	+	0.599322i	0.639519	+	0.768775i	$0.279133\pi$
$284$		0			0
$285$	3237.37	+	5607.30i	0.672861	+	1.16543i
$286$		0			0
$287$	−1317.43	+	1726.20i	−0.270960	+	0.355033i
$288$		0			0
$289$	1534.39	+	2657.64i	0.312312	+	0.540940i
$290$		0			0
$291$	−369.772	+	640.463i	−0.0744893	+	0.129019i
$292$		0			0
$293$	−4355.37			−0.868408			−0.434204	−	0.900815i	$-0.642970\pi$
$293$	−4355.37			−0.868408			−0.434204	+	0.900815i	$0.642970\pi$
$294$		0			0
$295$	−171.126			−0.0337741
$296$		0			0
$297$	792.187	−	1372.11i	0.154772	−	0.268073i
$298$		0			0
$299$	−301.250	−	521.780i	−0.0582667	−	0.100921i
$300$		0			0
$301$	−1144.68	+	1499.84i	−0.219196	+	0.287208i
$302$		0			0
$303$	1634.92	+	2831.76i	0.309978	+	0.536898i
$304$		0			0
$305$	7038.84	−	12191.6i	1.32145	−	2.28882i
$306$		0			0
$307$	8189.87			1.52254			0.761271	−	0.648434i	$-0.224576\pi$
$307$	8189.87			1.52254			0.761271	+	0.648434i	$0.224576\pi$
$308$		0			0
$309$	90.7092			0.0166999
$310$		0			0
$311$	582.651	−	1009.18i	0.106235	−	0.184004i	−0.808007	−	0.589173i	$-0.799454\pi$
$311$	582.651	−	1009.18i	0.106235	−	0.184004i	0.914242	+	0.405168i	$0.132787\pi$
$312$		0			0
$313$	2892.26	+	5009.54i	0.522301	+	0.904652i	0.999663	+	0.0259457i	$0.00825969\pi$
$313$	2892.26	+	5009.54i	0.522301	+	0.904652i	−0.477362	+	0.878707i	$0.658407\pi$
$314$		0			0
$315$	−1010.06	−	2420.65i	−0.180668	−	0.432978i
$316$		0			0
$317$	2283.69	+	3955.46i	0.404620	+	0.700822i	0.994277	−	0.106831i	$-0.0340705\pi$
$317$	2283.69	+	3955.46i	0.404620	+	0.700822i	−0.589657	+	0.807654i	$0.700737\pi$
$318$		0			0
$319$	254.688	−	441.133i	0.0447016	−	0.0774255i
$320$		0			0
$321$	−5662.87			−0.984644
$322$		0			0
$323$	−5889.94			−1.01463
$324$		0			0
$325$	1271.38	−	2202.10i	0.216996	−	0.375847i
$326$		0			0
$327$	1446.90	+	2506.10i	0.244690	+	0.423815i
$328$		0			0
$329$	−10809.6	−	1394.47i	−1.81140	−	0.233677i
$330$		0			0
$331$	1770.31	+	3066.27i	0.293973	+	0.509177i	0.974746	−	0.223319i	$-0.0716890\pi$
$331$	1770.31	+	3066.27i	0.293973	+	0.509177i	−0.680772	+	0.732495i	$0.738356\pi$
$332$		0			0
$333$	68.6875	−	118.970i	0.0113035	−	0.0195782i
$334$		0			0
$335$	11074.1			1.80609
$336$		0			0
$337$	−9183.50			−1.48444			−0.742221	−	0.670155i	$-0.766227\pi$
$337$	−9183.50			−1.48444			−0.742221	+	0.670155i	$0.766227\pi$
$338$		0			0
$339$	−179.709	+	311.264i	−0.0287918	+	0.0498689i
$340$		0			0
$341$	5940.59	+	10289.4i	0.943404	+	1.63402i
$342$		0			0
$343$	5887.72	+	2385.03i	0.926842	+	0.375451i
$344$		0			0
$345$	685.833	+	1187.90i	0.107026	+	0.185375i
$346$		0			0
$347$	−2977.50	+	5157.18i	−0.460636	+	0.797844i	−0.998993	−	0.0448726i	$-0.985712\pi$
$347$	−2977.50	+	5157.18i	−0.460636	+	0.797844i	0.538357	+	0.842717i	$0.319045\pi$
$348$		0			0
$349$	2816.11			0.431929			0.215964	−	0.976401i	$-0.430711\pi$
$349$	2816.11			0.431929			0.215964	+	0.976401i	$0.430711\pi$
$350$		0			0
$351$	−559.875			−0.0851393
$352$		0			0
$353$	190.653	−	330.221i	0.0287463	−	0.0497900i	−0.851294	−	0.524688i	$-0.824182\pi$
$353$	190.653	−	330.221i	0.0287463	−	0.0497900i	0.880041	+	0.474898i	$0.157515\pi$
$354$		0			0
$355$	9142.23	+	15834.8i	1.36682	+	2.36739i
$356$		0			0
$357$	2366.42	+	305.275i	0.350823	+	0.0452573i
$358$		0			0
$359$	−1497.38	−	2593.53i	−0.220135	−	0.381285i	0.734714	−	0.678377i	$-0.237316\pi$
$359$	−1497.38	−	2593.53i	−0.220135	−	0.381285i	−0.954849	+	0.297092i	$0.903983\pi$
$360$		0			0
$361$	−5975.93	+	10350.6i	−0.871254	+	1.50906i
$362$		0			0
$363$	6337.21			0.916301
$364$		0			0
$365$	−17567.4			−2.51923
$366$		0			0
$367$	−2325.01	+	4027.04i	−0.330694	+	0.572779i	−0.982648	−	0.185479i	$-0.940616\pi$
$367$	−2325.01	+	4027.04i	−0.330694	+	0.572779i	0.651954	+	0.758259i	$0.273950\pi$
$368$		0			0
$369$	−527.624	−	913.872i	−0.0744364	−	0.128928i
$370$		0			0
$371$	−2886.16	−	6916.79i	−0.403887	−	0.967929i
$372$		0			0
$373$	−2414.17	−	4181.47i	−0.335123	−	0.580451i	0.648385	−	0.761312i	$-0.275445\pi$
$373$	−2414.17	−	4181.47i	−0.335123	−	0.580451i	−0.983509	+	0.180862i	$0.942111\pi$
$374$		0			0
$375$	56.0617	−	97.1017i	0.00772004	−	0.0133715i
$376$		0			0
$377$	−180.000			−0.0245901
$378$		0			0
$379$	−13230.5			−1.79315			−0.896577	−	0.442887i	$-0.853954\pi$
$379$	−13230.5			−1.79315			−0.896577	+	0.442887i	$0.853954\pi$
$380$		0			0
$381$	1025.58	−	1776.36i	0.137906	−	0.238860i
$382$		0			0
$383$	−2204.87	−	3818.95i	−0.294161	−	0.509502i	0.680628	−	0.732629i	$-0.261707\pi$
$383$	−2204.87	−	3818.95i	−0.294161	−	0.509502i	−0.974789	+	0.223127i	$0.928374\pi$
$384$		0			0
$385$	10375.4	−	13594.7i	1.37346	−	1.79961i
$386$		0			0
$387$	−458.436	−	794.035i	−0.0602161	−	0.104297i
$388$		0			0
$389$	−287.691	+	498.296i	−0.0374975	+	0.0649476i	−0.884165	−	0.467175i	$-0.845272\pi$
$389$	−287.691	+	498.296i	−0.0374975	+	0.0649476i	0.846668	+	0.532122i	$0.178605\pi$
$390$		0			0
$391$	−1247.78			−0.161388
$392$		0			0
$393$	−780.711			−0.100208
$394$		0			0
$395$	1088.41	−	1885.18i	0.138643	−	0.240136i
$396$		0			0
$397$	−3620.81	−	6271.43i	−0.457741	−	0.792831i	0.541100	−	0.840958i	$-0.318008\pi$
$397$	−3620.81	−	6271.43i	−0.457741	−	0.792831i	−0.998841	+	0.0481274i	$0.984675\pi$
$398$		0			0
$399$	4623.19	−	6057.66i	0.580072	−	0.760057i
$400$		0			0
$401$	−1123.50	−	1945.96i	−0.139912	−	0.242335i	0.787551	−	0.616250i	$-0.211349\pi$
$401$	−1123.50	−	1945.96i	−0.139912	−	0.242335i	−0.927463	+	0.373914i	$0.878015\pi$
$402$		0			0
$403$	2099.24	−	3635.99i	0.259481	−	0.449434i
$404$		0			0
$405$	1274.62			0.156387
$406$		0			0
$407$	895.693			0.109086
$408$		0			0
$409$	825.318	−	1429.49i	0.0997784	−	0.172821i	−0.811814	−	0.583915i	$-0.801520\pi$
$409$	825.318	−	1429.49i	0.0997784	−	0.172821i	0.911593	+	0.411094i	$0.134853\pi$
$410$		0			0
$411$	1097.54	+	1901.00i	0.131722	+	0.228149i
$412$		0			0
$413$	77.5583	+	185.871i	0.00924066	+	0.0221456i
$414$		0			0
$415$	−7036.55	−	12187.7i	−0.832314	−	1.44161i
$416$		0			0
$417$	3431.60	−	5943.71i	0.402989	−	0.697997i
$418$		0			0
$419$	3178.64			0.370613			0.185307	−	0.982681i	$-0.440672\pi$
$419$	3178.64			0.370613			0.185307	+	0.982681i	$0.440672\pi$
$420$		0			0
$421$	8781.12			1.01655			0.508273	−	0.861196i	$-0.330284\pi$
$421$	8781.12			1.01655			0.508273	+	0.861196i	$0.330284\pi$
$422$		0			0
$423$	2648.25	−	4586.90i	0.304402	−	0.527241i
$424$		0			0
$425$	−2633.03	−	4560.54i	−0.300519	−	0.520514i
$426$		0			0
$427$	−16432.3	−	2119.81i	−1.86232	−	0.240246i
$428$		0			0
$429$	−1825.21	−	3161.35i	−0.205412	−	0.355784i
$430$		0			0
$431$	4543.35	−	7869.31i	0.507762	−	0.879469i	−0.492198	−	0.870483i	$-0.663806\pi$
$431$	4543.35	−	7869.31i	0.507762	−	0.879469i	0.999960	−	0.00898583i	$-0.00286032\pi$
$432$		0			0
$433$	3150.88			0.349703			0.174852	−	0.984595i	$-0.444055\pi$
$433$	3150.88			0.349703			0.174852	+	0.984595i	$0.444055\pi$
$434$		0			0
$435$	409.792			0.0451679
$436$		0			0
$437$	−1992.53	+	3451.16i	−0.218113	+	0.377783i
$438$		0			0
$439$	5165.69	+	8947.23i	0.561605	+	0.972729i	0.997357	+	0.0726619i	$0.0231494\pi$
$439$	5165.69	+	8947.23i	0.561605	+	0.972729i	−0.435751	+	0.900067i	$0.643517\pi$
$440$		0			0
$441$	−2171.44	+	2194.18i	−0.234471	+	0.236927i
$442$		0			0
$443$	−4136.03	−	7163.82i	−0.443587	−	0.768315i	0.554366	−	0.832273i	$-0.312961\pi$
$443$	−4136.03	−	7163.82i	−0.443587	−	0.768315i	−0.997953	+	0.0639584i	$0.979627\pi$
$444$		0			0
$445$	5364.48	−	9291.56i	0.571463	−	0.989802i
$446$		0			0
$447$	10317.6			1.09173
$448$		0			0
$449$	10111.1			1.06275			0.531374	−	0.847137i	$-0.321676\pi$
$449$	10111.1			1.06275			0.531374	+	0.847137i	$0.321676\pi$
$450$		0			0
$451$	3440.14	−	5958.50i	0.359179	−	0.622117i
$452$		0			0
$453$	4277.65	+	7409.10i	0.443667	+	0.768455i
$454$		0			0
$455$	−5993.59	−	773.192i	−0.617547	−	0.0796655i
$456$		0			0
$457$	8920.37	+	15450.5i	0.913080	+	1.58150i	0.809688	+	0.586860i	$0.199636\pi$
$457$	8920.37	+	15450.5i	0.913080	+	1.58150i	0.103392	+	0.994641i	$0.467031\pi$
$458$		0			0
$459$	−579.750	+	1004.16i	−0.0589551	+	0.102113i
$460$		0			0
$461$	−15787.7			−1.59503			−0.797515	−	0.603299i	$-0.793852\pi$
$461$	−15787.7			−1.59503			−0.797515	+	0.603299i	$0.793852\pi$
$462$		0			0
$463$	5960.87			0.598326			0.299163	−	0.954202i	$-0.403293\pi$
$463$	5960.87			0.598326			0.299163	+	0.954202i	$0.403293\pi$
$464$		0			0
$465$	−4779.19	+	8277.79i	−0.476622	+	0.825534i
$466$		0			0
$467$	−5529.15	−	9576.78i	−0.547877	−	0.948951i	−0.998420	−	0.0561964i	$-0.982103\pi$
$467$	−5529.15	−	9576.78i	−0.547877	−	0.948951i	0.450542	−	0.892755i	$-0.351231\pi$
$468$		0			0
$469$	−5019.01	−	12028.2i	−0.494150	−	1.18425i
$470$		0			0
$471$	−3660.37	−	6339.95i	−0.358091	−	0.620232i
$472$		0			0
$473$	2989.03	−	5177.15i	0.290562	−	0.503268i
$474$		0			0
$475$	−16818.3			−1.62459
$476$		0			0
$477$	3642.12			0.349605
$478$		0			0
$479$	−5931.90	+	10274.3i	−0.565836	+	0.980056i	0.431136	+	0.902287i	$0.358113\pi$
$479$	−5931.90	+	10274.3i	−0.565836	+	0.980056i	−0.996971	+	0.0777692i	$0.975220\pi$
$480$		0			0
$481$	−158.257	−	274.109i	−0.0150019	−	0.0259840i
$482$		0			0
$483$	979.415	−	1283.31i	0.0922669	−	0.120895i
$484$		0			0
$485$	−1939.59	−	3359.46i	−0.181592	−	0.314527i
$486$		0			0
$487$	−2962.48	+	5131.17i	−0.275653	+	0.477445i	−0.970300	−	0.241906i	$-0.922227\pi$
$487$	−2962.48	+	5131.17i	−0.275653	+	0.477445i	0.694647	+	0.719351i	$0.255561\pi$
$488$		0			0
$489$	−724.171			−0.0669696
$490$		0			0
$491$	9203.12			0.845888			0.422944	−	0.906156i	$-0.360997\pi$
$491$	9203.12			0.845888			0.422944	+	0.906156i	$0.360997\pi$
$492$		0			0
$493$	−186.390	+	322.837i	−0.0170275	+	0.0294925i
$494$		0			0
$495$	4155.31	+	7197.21i	0.377308	+	0.653516i
$496$		0			0
$497$	13055.7	−	17106.6i	1.17833	−	1.54394i
$498$		0			0
$499$	−4903.80	−	8493.63i	−0.439928	−	0.761978i	0.557755	−	0.830006i	$-0.311663\pi$
$499$	−4903.80	−	8493.63i	−0.439928	−	0.761978i	−0.997683	+	0.0680273i	$0.978329\pi$
$500$		0			0
$501$	489.667	−	848.128i	0.0436661	−	0.0756319i
$502$		0			0
$503$	−10462.6			−0.927446			−0.463723	−	0.885980i	$-0.653487\pi$
$503$	−10462.6			−0.927446			−0.463723	+	0.885980i	$0.653487\pi$
$504$		0			0
$505$	−17151.5			−1.51135
$506$		0			0
$507$	2650.52	−	4590.84i	0.232177	−	0.402142i
$508$		0			0
$509$	−2670.91	−	4626.16i	−0.232586	−	0.402850i	0.725983	−	0.687713i	$-0.241385\pi$
$509$	−2670.91	−	4626.16i	−0.232586	−	0.402850i	−0.958568	+	0.284863i	$0.908052\pi$
$510$		0			0
$511$	7961.93	+	19081.0i	0.689266	+	1.65185i
$512$		0			0
$513$	1851.56	+	3207.00i	0.159354	+	0.276009i
$514$		0			0
$515$	−237.902	+	412.058i	−0.0203557	+	0.0352572i
$516$		0			0
$517$	34533.5			2.93768
$518$		0			0
$519$	−4787.08			−0.404874
$520$		0			0
$521$	−5776.63	+	10005.4i	−0.485755	+	0.841353i	−0.999866	−	0.0163709i	$-0.994789\pi$
$521$	−5776.63	+	10005.4i	−0.485755	+	0.841353i	0.514111	+	0.857724i	$0.328122\pi$
$522$		0			0
$523$	2625.76	+	4547.94i	0.219534	+	0.380244i	0.954666	−	0.297680i	$-0.0962129\pi$
$523$	2625.76	+	4547.94i	0.219534	+	0.380244i	−0.735132	+	0.677925i	$0.762880\pi$
$524$		0			0
$525$	6757.14	+	871.692i	0.561725	+	0.0724643i
$526$		0			0
$527$	−4347.52	−	7530.13i	−0.359357	−	0.622425i
$528$		0			0
$529$	5661.39	−	9805.81i	0.465307	−	0.805935i
$530$		0			0
$531$	−97.8729			−0.00799872
$532$		0			0
$533$	−2431.30			−0.197583
$534$		0			0
$535$	14851.9	−	25724.3i	1.20020	−	2.07880i
$536$		0			0
$537$	4324.29	+	7489.89i	0.347499	+	0.601886i
$538$		0			0
$539$	−19468.5	−	5107.99i	−1.55578	−	0.408194i
$540$		0			0
$541$	10308.8	+	17855.4i	0.819241	+	1.41897i	0.906242	+	0.422759i	$0.138938\pi$
$541$	10308.8	+	17855.4i	0.819241	+	1.41897i	−0.0870006	+	0.996208i	$0.527728\pi$
$542$		0			0
$543$	−1692.90	+	2932.18i	−0.133792	+	0.231735i
$544$		0			0
$545$	−15179.0			−1.19302
$546$		0			0
$547$	−10669.4			−0.833985			−0.416993	−	0.908910i	$-0.636916\pi$
$547$	−10669.4			−0.833985			−0.416993	+	0.908910i	$0.636916\pi$
$548$		0			0
$549$	4025.75	−	6972.80i	0.312960	−	0.542062i
$550$		0			0
$551$	595.278	+	1031.05i	0.0460249	+	0.0797174i
$552$		0			0
$553$	−2540.91	−	327.785i	−0.195389	−	0.0252058i
$554$		0			0
$555$	360.291	+	624.043i	0.0275559	+	0.0477282i
$556$		0			0
$557$	2688.94	−	4657.38i	0.204549	−	0.354290i	−0.745440	−	0.666573i	$-0.767760\pi$
$557$	2688.94	−	4657.38i	0.204549	−	0.354290i	0.949989	+	0.312283i	$0.101094\pi$
$558$		0			0
$559$	−2112.49			−0.159837
$560$		0			0
$561$	−7560.00			−0.568954
$562$		0			0
$563$	−1759.44	+	3047.43i	−0.131708	+	0.228124i	−0.924335	−	0.381582i	$-0.875379\pi$
$563$	−1759.44	+	3047.43i	−0.131708	+	0.228124i	0.792627	+	0.609706i	$0.208713\pi$
$564$		0			0
$565$	−942.638	−	1632.70i	−0.0701895	−	0.121572i
$566$		0			0
$567$	−577.688	−	1384.45i	−0.0427877	−	0.102542i
$568$		0			0
$569$	−1275.15	−	2208.63i	−0.0939492	−	0.162725i	0.815220	−	0.579151i	$-0.196616\pi$
$569$	−1275.15	−	2208.63i	−0.0939492	−	0.162725i	−0.909170	+	0.416426i	$0.863282\pi$
$570$		0			0
$571$	6827.67	−	11825.9i	0.500401	−	0.866721i	−0.499599	−	0.866257i	$-0.666519\pi$
$571$	6827.67	−	11825.9i	0.500401	−	0.866721i	1.00000		0.000463542i	$-0.000147550\pi$
$572$		0			0
$573$	−6615.75			−0.482333
$574$		0			0
$575$	−3562.94			−0.258408
$576$		0			0
$577$	8347.94	−	14459.1i	0.602304	−	1.04322i	−0.390168	−	0.920744i	$-0.627583\pi$
$577$	8347.94	−	14459.1i	0.602304	−	1.04322i	0.992471	−	0.122477i	$-0.0390837\pi$
$578$		0			0
$579$	−5693.04	−	9860.63i	−0.408626	−	0.707761i
$580$		0			0
$581$	−10048.7	+	13166.5i	−0.717536	+	0.940173i
$582$		0			0
$583$	11873.4	+	20565.4i	0.843477	+	1.46095i
$584$		0			0
$585$	1468.37	−	2543.30i	0.103777	−	0.179748i
$586$		0			0
$587$	16341.4			1.14903			0.574517	−	0.818493i	$-0.305190\pi$
$587$	16341.4			1.14903			0.574517	+	0.818493i	$0.305190\pi$
$588$		0			0
$589$	−27769.6			−1.94266
$590$		0			0
$591$	−5551.87	+	9616.13i	−0.386419	+	0.669297i
$592$		0			0
$593$	−9962.59	−	17255.7i	−0.689906	−	1.19495i	−0.971868	−	0.235527i	$-0.924318\pi$
$593$	−9962.59	−	17255.7i	−0.689906	−	1.19495i	0.281961	−	0.959426i	$-0.409015\pi$
$594$		0			0
$595$	−7593.11	+	9949.09i	−0.523171	+	0.685501i
$596$		0			0
$597$	−5400.58	−	9354.08i	−0.370236	−	0.641268i
$598$		0			0
$599$	7390.84	−	12801.3i	0.504143	−	0.873201i	−0.495846	−	0.868411i	$-0.665142\pi$
$599$	7390.84	−	12801.3i	0.504143	−	0.873201i	0.999989	−	0.00479026i	$-0.00152479\pi$
$600$		0			0
$601$	−20487.7			−1.39054			−0.695268	−	0.718751i	$-0.744714\pi$
$601$	−20487.7			−1.39054			−0.695268	+	0.718751i	$0.744714\pi$
$602$		0			0
$603$	6333.62			0.427736
$604$		0			0
$605$	−16620.5	+	28787.5i	−1.11689	+	1.93451i
$606$		0			0
$607$	3762.02	+	6516.01i	0.251558	+	0.435711i	0.963955	−	0.266066i	$-0.0857238\pi$
$607$	3762.02	+	6516.01i	0.251558	+	0.435711i	−0.712397	+	0.701777i	$0.752390\pi$
$608$		0			0
$609$	−185.727	−	445.101i	−0.0123580	−	0.0296164i
$610$		0			0
$611$	−6101.59	−	10568.3i	−0.404000	−	0.699749i
$612$		0			0
$613$	−1707.32	+	2957.16i	−0.112493	+	0.194843i	−0.916775	−	0.399405i	$-0.869217\pi$
$613$	−1707.32	+	2957.16i	−0.112493	+	0.194843i	0.804282	+	0.594248i	$0.202550\pi$
$614$		0			0
$615$	5535.17			0.362926
$616$		0			0
$617$	22219.4			1.44979			0.724895	−	0.688859i	$-0.241888\pi$
$617$	22219.4			1.44979			0.724895	+	0.688859i	$0.241888\pi$
$618$		0			0
$619$	10931.7	−	18934.3i	0.709828	−	1.22946i	−0.255092	−	0.966917i	$-0.582106\pi$
$619$	10931.7	−	18934.3i	0.709828	−	1.22946i	0.964921	−	0.262542i	$-0.0845608\pi$
$620$		0			0
$621$	392.250	+	679.398i	0.0253470	+	0.0439022i
$622$		0			0
$623$	−12523.4	−	1615.56i	−0.805363	−	0.103894i
$624$		0			0
$625$	7958.12	+	13783.9i	0.509320	+	0.882168i
$626$		0			0
$627$	−12072.3	+	20909.8i	−0.768933	+	1.33183i
$628$		0			0
$629$	−655.499			−0.0415524
$630$		0			0
$631$	16080.8			1.01452			0.507262	−	0.861792i	$-0.330658\pi$
$631$	16080.8			1.01452			0.507262	+	0.861792i	$0.330658\pi$
$632$		0			0
$633$	−6206.46	+	10749.9i	−0.389707	+	0.674992i
$634$		0			0
$635$	5379.56	+	9317.67i	0.336191	+	0.582300i
$636$		0			0
$637$	1876.62	+	6860.45i	0.116726	+	0.426720i
$638$		0			0
$639$	5228.75	+	9056.46i	0.323703	+	0.560670i
$640$		0			0
$641$	9231.90	−	15990.1i	0.568858	−	0.985292i	−0.427821	−	0.903864i	$-0.640719\pi$
$641$	9231.90	−	15990.1i	0.568858	−	0.985292i	0.996679	−	0.0814280i	$-0.0259481\pi$
$642$		0			0
$643$	3110.87			0.190794			0.0953971	−	0.995439i	$-0.469588\pi$
$643$	3110.87			0.190794			0.0953971	+	0.995439i	$0.469588\pi$
$644$		0			0
$645$	4809.34			0.293593
$646$		0			0
$647$	−12364.5	+	21416.0i	−0.751313	+	1.30131i	0.195873	+	0.980629i	$0.437246\pi$
$647$	−12364.5	+	21416.0i	−0.751313	+	1.30131i	−0.947186	+	0.320683i	$0.896087\pi$
$648$		0			0
$649$	−319.068	−	552.643i	−0.0192982	−	0.0334255i
$650$		0			0
$651$	11157.1	+	1439.29i	0.671705	+	0.0866519i
$652$		0			0
$653$	−3526.32	−	6107.76i	−0.211325	−	0.366026i	0.740804	−	0.671721i	$-0.234445\pi$
$653$	−3526.32	−	6107.76i	−0.211325	−	0.366026i	−0.952130	+	0.305695i	$0.901111\pi$
$654$		0			0
$655$	2047.56	−	3546.47i	0.122145	−	0.211561i
$656$		0			0
$657$	−10047.4			−0.596629
$658$		0			0
$659$	−7895.55			−0.466718			−0.233359	−	0.972391i	$-0.574972\pi$
$659$	−7895.55			−0.466718			−0.233359	+	0.972391i	$0.574972\pi$
$660$		0			0
$661$	6550.56	−	11345.9i	0.385457	−	0.667631i	−0.606375	−	0.795179i	$-0.707377\pi$
$661$	6550.56	−	11345.9i	0.385457	−	0.667631i	0.991833	+	0.127547i	$0.0407104\pi$
$662$		0			0
$663$	1335.75	+	2313.59i	0.0782447	+	0.135524i
$664$		0			0
$665$	15392.5	+	36888.7i	0.897589	+	2.15110i
$666$		0			0
$667$	126.109	+	218.427i	0.00732076	+	0.0126799i
$668$		0			0
$669$	6392.44	−	11072.0i	0.369426	−	0.639864i
$670$		0			0
$671$	52496.2			3.02026
$672$		0			0
$673$	−9128.25			−0.522836			−0.261418	−	0.965226i	$-0.584190\pi$
$673$	−9128.25			−0.522836			−0.261418	+	0.965226i	$0.584190\pi$
$674$		0			0
$675$	−1655.44	+	2867.30i	−0.0943967	+	0.163500i
$676$		0			0
$677$	−8014.93	−	13882.3i	−0.455006	−	0.788093i	0.543683	−	0.839291i	$-0.317029\pi$
$677$	−8014.93	−	13882.3i	−0.455006	−	0.788093i	−0.998689	+	0.0511978i	$0.983696\pi$
$678$		0			0
$679$	−2769.86	+	3629.29i	−0.156550	+	0.205124i
$680$		0			0
$681$	−2301.19	−	3985.78i	−0.129489	−	0.224281i
$682$		0			0
$683$	−11088.2	+	19205.3i	−0.621197	+	1.07594i	0.368066	+	0.929800i	$0.380020\pi$
$683$	−11088.2	+	19205.3i	−0.621197	+	1.07594i	−0.989263	+	0.146145i	$0.953313\pi$
$684$		0			0
$685$	−11514.0			−0.642231
$686$		0			0
$687$	−1724.71			−0.0957814
$688$		0			0
$689$	4195.75	−	7267.25i	0.231996	−	0.401829i
$690$		0			0
$691$	−592.072	−	1025.50i	−0.0325955	−	0.0564570i	0.849267	−	0.527963i	$-0.177044\pi$
$691$	−592.072	−	1025.50i	−0.0325955	−	0.0564570i	−0.881863	+	0.471506i	$0.843711\pi$
$692$		0			0
$693$	5934.06	−	7775.28i	0.325276	−	0.426203i
$694$		0			0
$695$	18000.0	+	31176.9i	0.982417	+	1.70160i
$696$		0			0
$697$	−2517.61	+	4360.63i	−0.136817	+	0.236974i
$698$		0			0
$699$	−12456.4			−0.674027
$700$		0			0
$701$	31064.6			1.67374			0.836870	−	0.547401i	$-0.184383\pi$
$701$	31064.6			1.67374			0.836870	+	0.547401i	$0.184383\pi$
$702$		0			0
$703$	−1046.74	+	1813.01i	−0.0561574	+	0.0972674i
$704$		0			0
$705$	13891.0	+	24060.0i	0.742080	+	1.28532i
$706$		0			0
$707$	7773.42	+	18629.3i	0.413507	+	0.990985i
$708$		0			0
$709$	−287.946	−	498.736i	−0.0152525	−	0.0264181i	0.858298	−	0.513151i	$-0.171522\pi$
$709$	−287.946	−	498.736i	−0.0152525	−	0.0264181i	−0.873551	+	0.486733i	$0.838189\pi$
$710$		0			0
$711$	622.498	−	1078.20i	0.0328347	−	0.0568714i
$712$		0			0
$713$	−5882.95			−0.309002
$714$		0			0
$715$	19147.8			1.00152
$716$		0			0
$717$	6822.54	−	11817.0i	0.355359	−	0.615500i
$718$		0			0
$719$	2417.77	+	4187.70i	0.125407	+	0.217211i	0.921892	−	0.387447i	$-0.126643\pi$
$719$	2417.77	+	4187.70i	0.125407	+	0.217211i	−0.796485	+	0.604658i	$0.793310\pi$
$720$		0			0
$721$	555.384	+	71.6462i	0.0286874	+	0.00370076i
$722$		0			0
$723$	−10513.2	−	18209.4i	−0.540788	−	0.936672i
$724$		0			0
$725$	−532.224	+	921.838i	−0.0272638	+	0.0472224i
$726$		0			0
$727$	17999.8			0.918259			0.459129	−	0.888369i	$-0.348161\pi$
$727$	17999.8			0.918259			0.459129	+	0.888369i	$0.348161\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−2187.48	+	3788.82i	−0.110680	+	0.191703i
$732$		0			0
$733$	−2556.70	−	4428.33i	−0.128832	−	0.223144i	0.794392	−	0.607405i	$-0.207789\pi$
$733$	−2556.70	−	4428.33i	−0.128832	−	0.223144i	−0.923224	+	0.384261i	$0.874456\pi$
$734$		0			0
$735$	−4272.35	−	15618.7i	−0.214406	−	0.783813i
$736$		0			0
$737$	20647.8	+	35763.0i	1.03198	+	1.78745i
$738$		0			0
$739$	6528.06	−	11306.9i	0.324951	−	0.562831i	−0.656552	−	0.754281i	$-0.727986\pi$
$739$	6528.06	−	11306.9i	0.324951	−	0.562831i	0.981502	+	0.191450i	$0.0613189\pi$
$740$		0			0
$741$	8532.04			0.422986
$742$		0			0
$743$	28402.9			1.40242			0.701212	−	0.712953i	$-0.252643\pi$
$743$	28402.9			1.40242			0.701212	+	0.712953i	$0.252643\pi$
$744$		0			0
$745$	−27059.8	+	46868.9i	−1.33073	+	2.30489i
$746$		0			0
$747$	−4024.43	−	6970.53i	−0.197117	−	0.341417i
$748$		0			0
$749$	−34672.0	−	4472.79i	−1.69144	−	0.218201i
$750$		0			0
$751$	−16635.1	−	28812.9i	−0.808288	−	1.40000i	−0.914049	−	0.405605i	$-0.867061\pi$
$751$	−16635.1	−	28812.9i	−0.808288	−	1.40000i	0.105760	−	0.994392i	$-0.466272\pi$
$752$		0			0
$753$	1024.23	−	1774.01i	0.0495683	−	0.0858548i
$754$		0			0
$755$	−44875.7			−2.16317
$756$		0			0
$757$	18331.2			0.880129			0.440064	−	0.897966i	$-0.354956\pi$
$757$	18331.2			0.880129			0.440064	+	0.897966i	$0.354956\pi$
$758$		0			0
$759$	−2557.50	+	4429.71i	−0.122307	+	0.211842i
$760$		0			0
$761$	−2498.50	−	4327.53i	−0.119015	−	0.206141i	0.800362	−	0.599517i	$-0.204640\pi$
$761$	−2498.50	−	4327.53i	−0.119015	−	0.206141i	−0.919378	+	0.393376i	$0.871307\pi$
$762$		0			0
$763$	6879.46	+	16486.9i	0.326413	+	0.782260i
$764$		0			0
$765$	−3041.00	−	5267.17i	−0.143722	−	0.248934i
$766$		0			0
$767$	−112.750	+	195.289i	−0.00530792	+	0.00919358i
$768$		0			0
$769$	−9834.47			−0.461171			−0.230585	−	0.973052i	$-0.574064\pi$
$769$	−9834.47			−0.461171			−0.230585	+	0.973052i	$0.574064\pi$
$770$		0			0
$771$	5107.66			0.238583
$772$		0			0
$773$	6991.49	−	12109.6i	0.325312	−	0.563458i	−0.656263	−	0.754532i	$-0.727864\pi$
$773$	6991.49	−	12109.6i	0.325312	−	0.563458i	0.981576	+	0.191074i	$0.0611972\pi$
$774$		0			0
$775$	−12414.1	−	21501.8i	−0.575389	−	0.996603i
$776$		0			0
$777$	514.520	−	674.165i	0.0237559	−	0.0311268i
$778$		0			0
$779$	8040.57	+	13926.7i	0.369812	+	0.640532i
$780$		0			0
$781$	−34091.7	+	59048.6i	−1.56197	+	2.70541i
$782$		0			0
$783$	234.374			0.0106971
$784$		0			0
$785$	38400.0			1.74593
$786$		0			0
$787$	−15639.3	+	27088.1i	−0.708362	+	1.22692i	0.257102	+	0.966384i	$0.417232\pi$
$787$	−15639.3	+	27088.1i	−0.708362	+	1.22692i	−0.965464	+	0.260535i	$0.916101\pi$
$788$		0			0
$789$	−4386.37	−	7597.42i	−0.197920	−	0.342808i
$790$		0			0
$791$	−1346.15	+	1763.83i	−0.0605102	+	0.0792853i
$792$		0			0
$793$	−9275.37	−	16065.4i	−0.415357	−	0.719419i
$794$		0			0
$795$	−9552.14	+	16544.8i	−0.426138	+	0.738092i
$796$		0			0
$797$	30546.9			1.35762			0.678811	−	0.734313i	$-0.262495\pi$
$797$	30546.9			1.35762			0.678811	+	0.734313i	$0.262495\pi$
$798$		0			0
$799$	−25272.8			−1.11901
$800$		0			0
$801$	3068.13	−	5314.15i	0.135339	−	0.234415i
$802$		0			0
$803$	−32754.7	−	56732.8i	−1.43946	−	2.49322i
$804$		0			0
$805$	3260.88	+	7814.82i	0.142771	+	0.342157i
$806$		0			0
$807$	−2060.73	−	3569.29i	−0.0898899	−	0.155694i
$808$		0			0
$809$	14786.3	−	25610.7i	0.642596	−	1.11301i	−0.342256	−	0.939607i	$-0.611191\pi$
$809$	14786.3	−	25610.7i	0.642596	−	1.11301i	0.984851	−	0.173401i	$-0.0554758\pi$
$810$		0			0
$811$	−45069.0			−1.95140			−0.975701	−	0.219107i	$-0.929686\pi$
$811$	−45069.0			−1.95140			−0.975701	+	0.219107i	$0.929686\pi$
$812$		0			0
$813$	2344.53			0.101139
$814$		0			0
$815$	1899.27	−	3289.64i	0.0816302	−	0.141388i
$816$		0			0
$817$	6986.20	+	12100.5i	0.299163	+	0.518166i
$818$		0			0
$819$	−3427.94	−	442.214i	−0.146254	−	0.0188672i
$820$		0			0
$821$	−4700.47	−	8141.45i	−0.199814	−	0.346088i	0.748654	−	0.662961i	$-0.230701\pi$
$821$	−4700.47	−	8141.45i	−0.199814	−	0.346088i	−0.948468	+	0.316873i	$0.897367\pi$
$822$		0			0
$823$	−14004.4	+	24256.4i	−0.593152	+	1.02737i	0.400653	+	0.916230i	$0.368783\pi$
$823$	−14004.4	+	24256.4i	−0.593152	+	1.02737i	−0.993805	+	0.111139i	$0.964550\pi$
$824$		0			0
$825$	−21587.1			−0.910989
$826$		0			0
$827$	28650.8			1.20470			0.602349	−	0.798232i	$-0.294231\pi$
$827$	28650.8			1.20470			0.602349	+	0.798232i	$0.294231\pi$
$828$		0			0
$829$	2124.82	−	3680.29i	0.0890205	−	0.154188i	−0.818077	−	0.575109i	$-0.804960\pi$
$829$	2124.82	−	3680.29i	0.0890205	−	0.154188i	0.907097	+	0.420921i	$0.138293\pi$
$830$		0			0
$831$	3227.43	+	5590.08i	0.134727	+	0.233355i
$832$		0			0
$833$	14247.7	+	3738.20i	0.592621	+	0.155487i
$834$		0			0
$835$	2568.48	+	4448.74i	0.106450	+	0.184377i
$836$		0			0
$837$	−2733.37	+	4734.34i	−0.112878	+	0.195511i
$838$		0			0
$839$	−9265.50			−0.381264			−0.190632	−	0.981662i	$-0.561054\pi$
$839$	−9265.50			−0.381264			−0.190632	+	0.981662i	$0.561054\pi$
$840$		0			0
$841$	−24313.6			−0.996910
$842$		0			0
$843$	3582.37	−	6204.85i	0.146362	−	0.253507i
$844$		0			0
$845$	13903.0	+	24080.6i	0.566007	+	0.980354i
$846$		0			0
$847$	38800.7	+	5005.41i	1.57404	+	0.203055i
$848$		0			0
$849$	−4941.98	−	8559.76i	−0.199774	−	0.346019i
$850$		0			0
$851$	−221.751	+	384.084i	−0.00893245	+	0.0154715i
$852$		0			0
$853$	36321.1			1.45793			0.728964	−	0.684552i	$-0.240002\pi$
$853$	36321.1			1.45793			0.728964	+	0.684552i	$0.240002\pi$
$854$		0			0
$855$	−19424.2			−0.776953
$856$		0			0
$857$	11838.1	−	20504.2i	0.471858	−	0.817282i	−0.527623	−	0.849478i	$-0.676917\pi$
$857$	11838.1	−	20504.2i	0.471858	−	0.817282i	0.999482	+	0.0321962i	$0.0102501\pi$
$858$		0			0
$859$	13706.2	+	23739.8i	0.544410	+	0.942946i	0.998644	+	0.0520636i	$0.0165799\pi$
$859$	13706.2	+	23739.8i	0.544410	+	0.942946i	−0.454233	+	0.890883i	$0.650087\pi$
$860$		0			0
$861$	−2508.66	−	6012.09i	−0.0992972	−	0.237969i
$862$		0			0
$863$	−11362.7	−	19680.9i	−0.448195	−	0.776297i	0.550074	−	0.835116i	$-0.314600\pi$
$863$	−11362.7	−	19680.9i	−0.448195	−	0.776297i	−0.998269	+	0.0588195i	$0.981266\pi$
$864$		0			0
$865$	12555.0	−	21745.9i	0.493506	−	0.854778i
$866$		0			0
$867$	−9206.33			−0.360627
$868$		0			0
$869$	8117.45			0.316876
$870$		0			0
$871$	7296.37	−	12637.7i	0.283844	−	0.491632i
$872$		0			0
$873$	−1109.31	−	1921.39i	−0.0430064	−	0.0744893i
$874$		0			0
$875$	419.943	−	550.243i	0.0162248	−	0.0212590i
$876$		0			0
$877$	−5990.93	−	10376.6i	−0.230672	−	0.399536i	0.727334	−	0.686284i	$-0.240759\pi$
$877$	−5990.93	−	10376.6i	−0.230672	−	0.399536i	−0.958006	+	0.286748i	$0.907426\pi$
$878$		0			0
$879$	6533.06	−	11315.6i	0.250688	−	0.434204i
$880$		0			0
$881$	−22891.8			−0.875419			−0.437709	−	0.899117i	$-0.644210\pi$
$881$	−22891.8			−0.875419			−0.437709	+	0.899117i	$0.644210\pi$
$882$		0			0
$883$	−36489.6			−1.39068			−0.695341	−	0.718680i	$-0.744747\pi$
$883$	−36489.6			−1.39068			−0.695341	+	0.718680i	$0.744747\pi$
$884$		0			0
$885$	256.690	−	444.600i	0.00974975	−	0.0168871i
$886$		0			0
$887$	12052.9	+	20876.2i	0.456253	+	0.790254i	0.998759	−	0.0497981i	$-0.0158578\pi$
$887$	12052.9	+	20876.2i	0.456253	+	0.790254i	−0.542506	+	0.840052i	$0.682524\pi$
$888$		0			0
$889$	7682.37	−	10066.1i	0.289830	−	0.379758i
$890$		0			0
$891$	2376.56	+	4116.32i	0.0893578	+	0.154772i
$892$		0			0
$893$	−40357.2	+	69900.7i	−1.51232	+	2.61941i
$894$		0			0
$895$	−45365.0			−1.69428
$896$		0			0
$897$	1807.50			0.0672805
$898$		0			0
$899$	−878.781	+	1522.09i	−0.0326018	+	0.0564679i
$900$		0			0
$901$	−8689.38	−	15050.5i	−0.321293	−	0.556496i
$902$		0			0
$903$	−2179.70	−	5223.72i	−0.0803275	−	0.192508i
$904$		0			0
$905$	−8879.87	−	15380.4i	−0.326162	−	0.564929i
$906$		0			0
$907$	11181.6	−	19367.2i	0.409350	−	0.709014i	−0.585467	−	0.810696i	$-0.699089\pi$
$907$	11181.6	−	19367.2i	0.409350	−	0.709014i	0.994817	+	0.101682i	$0.0324223\pi$
$908$		0			0
$909$	−9809.49			−0.357932
$910$		0			0
$911$	21426.3			0.779238			0.389619	−	0.920976i	$-0.372607\pi$
$911$	21426.3			0.779238			0.389619	+	0.920976i	$0.372607\pi$
$912$		0			0
$913$	26239.5	−	45448.2i	0.951152	−	1.64744i
$914$		0			0
$915$	21116.5	+	36574.9i	0.762941	+	1.32145i
$916$		0			0
$917$	−4780.05	−	616.641i	−0.172139	−	0.0222064i
$918$		0			0
$919$	−15263.0	−	26436.4i	−0.547858	−	0.948917i	−0.998421	−	0.0561730i	$-0.982110\pi$
$919$	−15263.0	−	26436.4i	−0.547858	−	0.948917i	0.450563	−	0.892744i	$-0.351223\pi$
$920$		0			0
$921$	−12284.8	+	21277.9i	−0.439520	+	0.761271i
$922$		0			0
$923$	24094.2			0.859231
$924$		0			0
$925$	−1871.73			−0.0665322
$926$		0			0
$927$	−136.064	+	235.670i	−0.00482084	+	0.00834995i
$928$		0			0
$929$	−2319.45	−	4017.40i	−0.0819146	−	0.141880i	0.822158	−	0.569260i	$-0.192770\pi$
$929$	−2319.45	−	4017.40i	−0.0819146	−	0.141880i	−0.904072	+	0.427380i	$0.859437\pi$
$930$		0			0
$931$	33090.9	−	33437.6i	1.16489	−	1.17709i
$932$		0			0
$933$	1747.95	+	3027.54i	0.0613348	+	0.106235i
$934$		0			0
$935$	19827.5	−	34342.2i	0.693506	−	1.20119i
$936$		0			0
$937$	−7713.38			−0.268928			−0.134464	−	0.990919i	$-0.542931\pi$
$937$	−7713.38			−0.268928			−0.134464	+	0.990919i	$0.542931\pi$
$938$		0			0
$939$	−17353.6			−0.603102
$940$		0			0
$941$	3745.31	−	6487.07i	0.129749	−	0.224732i	−0.793830	−	0.608139i	$-0.791916\pi$
$941$	3745.31	−	6487.07i	0.129749	−	0.224732i	0.923579	+	0.383408i	$0.125250\pi$
$942$		0			0
$943$	1703.38	+	2950.34i	0.0588226	+	0.101884i
$944$		0			0
$945$	7804.12	+	1006.76i	0.268643	+	0.0346558i
$946$		0			0
$947$	12569.6	+	21771.1i	0.431316	+	0.747061i	0.996987	−	0.0775698i	$-0.0247161\pi$
$947$	12569.6	+	21771.1i	0.431316	+	0.747061i	−0.565671	+	0.824631i	$0.691383\pi$
$948$		0			0
$949$	−11574.6	+	20047.8i	−0.395920	+	0.685754i
$950$		0			0
$951$	−13702.1			−0.467215
$952$		0			0
$953$	−2505.29			−0.0851568			−0.0425784	−	0.999093i	$-0.513557\pi$
$953$	−2505.29			−0.0851568			−0.0425784	+	0.999093i	$0.513557\pi$
$954$		0			0
$955$	17351.0	−	30052.8i	0.587922	−	1.01831i
$956$		0			0
$957$	764.065	+	1323.40i	0.0258085	+	0.0447016i
$958$		0			0
$959$	5218.41	+	12506.1i	0.175716	+	0.421108i
$960$		0			0
$961$	−5602.00	−	9702.94i	−0.188043	−	0.325700i
$962$		0			0
$963$	8494.31	−	14712.6i	0.284242	−	0.492322i
$964$		0			0
$965$	59724.2			1.99232
$966$		0			0
$967$	9331.61			0.310325			0.155162	−	0.987889i	$-0.450410\pi$
$967$	9331.61			0.310325			0.155162	+	0.987889i	$0.450410\pi$
$968$		0			0
$969$	8834.91	−	15302.5i	0.292898	−	0.507315i
$970$		0			0
$971$	−20993.0	−	36360.9i	−0.693817	−	1.20173i	−0.970578	−	0.240787i	$-0.922594\pi$
$971$	−20993.0	−	36360.9i	−0.693817	−	1.20173i	0.276761	−	0.960939i	$-0.410739\pi$
$972$		0			0
$973$	25705.2	−	33681.0i	0.846939	−	1.10973i
$974$		0			0
$975$	3814.14	+	6606.29i	0.125282	+	0.216996i
$976$		0			0
$977$	3975.47	−	6885.72i	0.130181	−	0.225480i	−0.793565	−	0.608485i	$-0.791778\pi$
$977$	3975.47	−	6885.72i	0.130181	−	0.225480i	0.923746	+	0.383005i	$0.125111\pi$
$978$		0			0
$979$	40008.7			1.30611
$980$		0			0
$981$	−8681.37			−0.282543
$982$		0			0
$983$	5269.74	−	9127.47i	0.170986	−	0.296156i	−0.767779	−	0.640715i	$-0.778638\pi$
$983$	5269.74	−	9127.47i	0.170986	−	0.296156i	0.938765	+	0.344559i	$0.111972\pi$
$984$		0			0
$985$	−29121.6	−	50440.1i	−0.942022	−	1.63163i
$986$		0			0
$987$	19837.3	−	25992.4i	0.639746	−	0.838246i
$988$		0			0
$989$	1480.02	+	2563.46i	0.0475852	+	0.0824200i
$990$		0			0
$991$	−2215.93	+	3838.10i	−0.0710306	+	0.123029i	−0.899353	−	0.437223i	$-0.855962\pi$
$991$	−2215.93	+	3838.10i	−0.0710306	+	0.123029i	0.828323	+	0.560251i	$0.189295\pi$
$992$		0			0
$993$	−10621.9			−0.339451
$994$		0			0
$995$	56656.0			1.80514
$996$		0			0
$997$	19707.8	−	34134.9i	0.626031	−	1.08432i	−0.362310	−	0.932058i	$-0.618012\pi$
$997$	19707.8	−	34134.9i	0.626031	−	1.08432i	0.988341	−	0.152259i	$-0.0486548\pi$
$998$		0			0
$999$	206.063	+	356.911i	0.00652606	+	0.0113035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.g.193.1		4
4.3	odd	2		168.4.q.d.25.1	✓	4
7.2	even	3	inner	336.4.q.g.289.1		4
7.3	odd	6		2352.4.a.bo.1.1		2
7.4	even	3		2352.4.a.cc.1.2		2
12.11	even	2		504.4.s.f.361.2		4
28.3	even	6		1176.4.a.u.1.1		2
28.11	odd	6		1176.4.a.r.1.2		2
28.23	odd	6		168.4.q.d.121.1	yes	4
84.23	even	6		504.4.s.f.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.d.25.1	✓	4	4.3	odd	2
168.4.q.d.121.1	yes	4	28.23	odd	6
336.4.q.g.193.1		4	1.1	even	1	trivial
336.4.q.g.289.1		4	7.2	even	3	inner
504.4.s.f.289.2		4	84.23	even	6
504.4.s.f.361.2		4	12.11	even	2
1176.4.a.r.1.2		2	28.11	odd	6
1176.4.a.u.1.1		2	28.3	even	6
2352.4.a.bo.1.1		2	7.3	odd	6
2352.4.a.cc.1.2		2	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +(-7.86805 - 13.6279i) q^{5} +(-11.2361 + 14.7224i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{3} +(-7.86805 - 13.6279i) q^{5} +(-11.2361 + 14.7224i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(29.3403 - 50.8188i) q^{11} -20.7361 q^{13} +47.2083 q^{15} +(-21.4722 + 37.1910i) q^{17} +(68.5764 + 118.778i) q^{19} +(-21.3958 - 51.2759i) q^{21} +(14.5278 + 25.1629i) q^{23} +(-61.3125 + 106.196i) q^{25} +27.0000 q^{27} +8.68051 q^{29} +(-101.236 + 175.346i) q^{31} +(88.0208 + 152.456i) q^{33} +(289.042 + 37.2872i) q^{35} +(7.63195 + 13.2189i) q^{37} +(31.1042 - 53.8740i) q^{39} +117.250 q^{41} +101.875 q^{43} +(-70.8125 + 122.651i) q^{45} +(294.250 + 509.656i) q^{47} +(-90.5000 - 330.846i) q^{49} +(-64.4166 - 111.573i) q^{51} +(-202.340 + 350.464i) q^{53} -923.403 q^{55} -411.458 q^{57} +(5.43738 - 9.41783i) q^{59} +(447.305 + 774.756i) q^{61} +(165.312 + 21.3258i) q^{63} +(163.153 + 282.589i) q^{65} +(-351.868 + 609.453i) q^{67} -87.1668 q^{69} -1161.94 q^{71} +(558.187 - 966.809i) q^{73} +(-183.937 - 318.589i) q^{75} +(418.506 + 1002.97i) q^{77} +(69.1665 + 119.800i) q^{79} +(-40.5000 + 70.1481i) q^{81} +894.319 q^{83} +675.778 q^{85} +(-13.0208 + 22.5526i) q^{87} +(340.903 + 590.461i) q^{89} +(232.993 - 305.286i) q^{91} +(-303.708 - 526.038i) q^{93} +(1079.12 - 1869.10i) q^{95} +246.514 q^{97} -528.125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 9 q^{5} - 18 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 - 9 * q^5 - 18 * q^9	\( 4 q - 6 q^{3} - 9 q^{5} - 18 q^{9} + 5 q^{11} - 38 q^{13} + 54 q^{15} + 4 q^{17} + 117 q^{19} - 153 q^{21} + 148 q^{23} - 43 q^{25} + 108 q^{27} - 190 q^{29} - 360 q^{31} + 15 q^{33} + 482 q^{35} + 53 q^{37} + 57 q^{39} - 340 q^{41} - 806 q^{43} - 81 q^{45} + 368 q^{47} - 362 q^{49} + 12 q^{51} - 697 q^{53} - 2570 q^{55} - 702 q^{57} - 585 q^{59} + 1160 q^{61} + 459 q^{63} + 338 q^{65} + 233 q^{67} - 888 q^{69} - 1232 q^{71} + 817 q^{73} - 129 q^{75} - 1135 q^{77} - 802 q^{79} - 162 q^{81} + 566 q^{83} + 1984 q^{85} + 285 q^{87} + 1858 q^{89} + 505 q^{91} - 1080 q^{93} + 2294 q^{95} + 3458 q^{97} - 90 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 9 * q^5 - 18 * q^9 + 5 * q^11 - 38 * q^13 + 54 * q^15 + 4 * q^17 + 117 * q^19 - 153 * q^21 + 148 * q^23 - 43 * q^25 + 108 * q^27 - 190 * q^29 - 360 * q^31 + 15 * q^33 + 482 * q^35 + 53 * q^37 + 57 * q^39 - 340 * q^41 - 806 * q^43 - 81 * q^45 + 368 * q^47 - 362 * q^49 + 12 * q^51 - 697 * q^53 - 2570 * q^55 - 702 * q^57 - 585 * q^59 + 1160 * q^61 + 459 * q^63 + 338 * q^65 + 233 * q^67 - 888 * q^69 - 1232 * q^71 + 817 * q^73 - 129 * q^75 - 1135 * q^77 - 802 * q^79 - 162 * q^81 + 566 * q^83 + 1984 * q^85 + 285 * q^87 + 1858 * q^89 + 505 * q^91 - 1080 * q^93 + 2294 * q^95 + 3458 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

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Database

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