LMFDB - Embedded newform 168.4.q.d.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(25,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, 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("168.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.q (of order $3$, degree $2$, 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:	$9.91232088096$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-5.36805 + 9.29774i$ of defining polynomial
Character	$\chi$	$=$	168.121
Dual form			168.4.q.d.25.1

$q$-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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		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	0.263404	+	0.964685i	$0.415155\pi$
$5$	−7.86805	+	13.6279i	−0.703740	+	1.21891i	−0.967144	+	0.254228i	$0.918179\pi$
$6$		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	−0.916816	−	0.399309i	$-0.869250\pi$
$11$	−29.3403	−	50.8188i	−0.804220	−	1.39295i	0.112596	−	0.993641i	$-0.464083\pi$
$12$		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	0.671219	−	0.741259i	$-0.265771\pi$
$17$	−21.4722	−	37.1910i	−0.306340	−	0.530596i	−0.977559	+	0.210663i	$0.932438\pi$
$18$		0			0
$19$	−68.5764	+	118.778i	−0.828026	+	1.43418i	0.0715584	+	0.997436i	$0.477203\pi$
$19$	−68.5764	+	118.778i	−0.828026	+	1.43418i	−0.899584	+	0.436747i	$0.856131\pi$
$20$		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	$-0.875379\pi$
$23$	−14.5278	+	25.1629i	−0.131707	+	0.228123i	0.792628	+	0.609706i	$0.208712\pi$
$24$		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	0.994682	+	0.102991i	$0.0328411\pi$
$31$	101.236	+	175.346i	0.586534	+	1.01591i	−0.408149	+	0.912915i	$0.633826\pi$
$32$		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	−0.848572	−	0.529080i	$-0.822537\pi$
$37$	7.63195	−	13.2189i	0.0339104	−	0.0587345i	0.882483	+	0.470345i	$0.155871\pi$
$38$		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	$-0.557820\pi$
$43$	−101.875			−0.361297			−0.180648	+	0.983548i	$0.557820\pi$
$44$		0			0
$45$	−70.8125	−	122.651i	−0.234580	−	0.406304i
$46$		0			0
$47$	−294.250	+	509.656i	−0.913207	+	1.58172i	−0.103703	+	0.994608i	$0.533069\pi$
$47$	−294.250	+	509.656i	−0.913207	+	1.58172i	−0.809505	+	0.587113i	$0.800264\pi$
$48$		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	−0.999596	−	0.0284159i	$-0.990954\pi$
$53$	−202.340	−	350.464i	−0.524407	−	0.908300i	0.475189	−	0.879884i	$-0.342380\pi$
$54$		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	$-0.170486\pi$
$59$	−5.43738	−	9.41783i	−0.0119981	−	0.0207813i	−0.871962	+	0.489573i	$0.837153\pi$
$60$		0			0
$61$	447.305	−	774.756i	0.938879	−	1.62619i	0.171311	−	0.985217i	$-0.445200\pi$
$61$	447.305	−	774.756i	0.938879	−	1.62619i	0.767567	−	0.640968i	$-0.221467\pi$
$62$		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	0.985075	+	0.172128i	$0.0550642\pi$
$67$	351.868	+	609.453i	0.641604	+	1.11129i	−0.343470	+	0.939164i	$0.611602\pi$
$68$		0			0
$69$	−87.1668			−0.152082
$70$		0			0
$71$	1161.94			1.94222			0.971108	−	0.238640i	$-0.0767015\pi$
$71$	1161.94			1.94222			0.971108	+	0.238640i	$0.0767015\pi$
$72$		0			0
$73$	558.187	+	966.809i	0.894943	+	1.55009i	0.833875	+	0.551954i	$0.186118\pi$
$73$	558.187	+	966.809i	0.894943	+	1.55009i	0.0610689	+	0.998134i	$0.480549\pi$
$74$		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	$-0.864739\pi$
$79$	−69.1665	+	119.800i	−0.0985042	+	0.170614i	0.812561	+	0.582875i	$0.198072\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−894.319			−1.18270			−0.591351	−	0.806414i	$-0.701405\pi$
$83$	−894.319			−1.18270			−0.591351	+	0.806414i	$0.701405\pi$
$84$		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	−0.588421	−	0.808555i	$-0.700250\pi$
$89$	340.903	−	590.461i	0.406018	−	0.703244i	0.994439	+	0.105310i	$0.0335836\pi$
$90$		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	0.999069	+	0.0431441i	$0.0137375\pi$
$101$	544.972	+	943.919i	0.536898	+	0.929935i	−0.462171	+	0.886791i	$0.652929\pi$
$102$		0			0
$103$	15.1182	−	26.1855i	0.0144625	−	0.0250498i	−0.858704	−	0.512473i	$-0.828730\pi$
$103$	15.1182	−	26.1855i	0.0144625	−	0.0250498i	0.873166	+	0.487423i	$0.162063\pi$
$104$		0			0
$105$	−530.437	−	695.021i	−0.493004	−	0.645973i
$106$		0			0
$107$	−943.812	+	1634.73i	−0.852727	+	1.47697i	0.0260107	+	0.999662i	$0.491720\pi$
$107$	−943.812	+	1634.73i	−0.852727	+	1.47697i	−0.878738	+	0.477305i	$0.841614\pi$
$108$		0			0
$109$	482.298	+	835.365i	0.423815	+	0.734069i	0.996309	−	0.0858401i	$-0.0273574\pi$
$109$	482.298	+	835.365i	0.423815	+	0.734069i	−0.572494	+	0.819909i	$0.694024\pi$
$110$		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	$-0.423226\pi$
$127$	683.722			0.477721			0.238860	+	0.971054i	$0.423226\pi$
$128$		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	$-0.860992\pi$
$131$	−130.119	+	225.372i	−0.0867825	+	0.150312i	0.819367	+	0.573269i	$0.194325\pi$
$132$		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	0.957260	−	0.289230i	$-0.0933993\pi$
$137$	365.847	+	633.666i	0.228149	+	0.395166i	−0.729110	+	0.684396i	$0.760066\pi$
$138$		0			0
$139$	2287.74			1.39599			0.697997	−	0.716101i	$-0.254075\pi$
$139$	2287.74			1.39599			0.697997	+	0.716101i	$0.254075\pi$
$140$		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	−0.190659	+	0.981656i	$0.561063\pi$
$149$	−1719.60	+	2978.43i	−0.945469	+	1.63760i	−0.754810	+	0.655944i	$0.772271\pi$
$150$		0			0
$151$	−1425.88	−	2469.70i	−0.768455	−	1.33100i	−0.938401	−	0.345549i	$-0.887693\pi$
$151$	−1425.88	−	2469.70i	−0.768455	−	1.33100i	0.169946	−	0.985453i	$-0.445641\pi$
$152$		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	−0.989442	−	0.144928i	$-0.953705\pi$
$157$	−1220.12	−	2113.32i	−0.620232	−	1.07427i	0.369210	−	0.929346i	$-0.379628\pi$
$158$		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	$-0.851805\pi$
$163$	−120.695	+	209.050i	−0.0579974	+	0.100454i	0.835569	+	0.549386i	$0.185138\pi$
$164$		0			0
$165$	1385.10	+	2399.07i	0.653516	+	1.13192i
$166$		0			0
$167$	326.445			0.151264			0.0756319	−	0.997136i	$-0.475903\pi$
$167$	326.445			0.151264			0.0756319	+	0.997136i	$0.475903\pi$
$168$		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	−0.635729	−	0.771912i	$-0.719300\pi$
$173$	797.847	−	1381.91i	0.350631	−	0.607311i	0.986360	+	0.164601i	$0.0526337\pi$
$174$		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	−0.992535	−	0.121957i	$-0.961083\pi$
$179$	−1441.43	−	2496.63i	−0.601886	−	1.04250i	0.390650	−	0.920539i	$-0.372250\pi$
$180$		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	$-0.970501\pi$
$191$	−1102.62	+	1909.80i	−0.417713	+	0.723500i	0.577996	+	0.816039i	$0.303835\pi$
$192$		0			0
$193$	−1897.68	−	3286.88i	−0.707761	−	1.22588i	−0.965686	−	0.259714i	$-0.916372\pi$
$193$	−1897.68	−	3286.88i	−0.707761	−	1.22588i	0.257924	−	0.966165i	$-0.416962\pi$
$194$		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	0.985150	+	0.171696i	$0.0549246\pi$
$199$	1800.19	+	3118.03i	0.641268	+	1.11071i	−0.343882	+	0.939013i	$0.611742\pi$
$200$		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	$-0.735853\pi$
$211$	−4137.64			−1.34998			−0.674992	+	0.737825i	$0.735853\pi$
$212$		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	$-0.278991\pi$
$223$	4261.62			1.27973			0.639864	+	0.768488i	$0.278991\pi$
$224$		0			0
$225$	1103.62			0.327000
$226$		0			0
$227$	767.063	+	1328.59i	0.224281	+	0.388466i	0.956103	−	0.293029i	$-0.0946634\pi$
$227$	767.063	+	1328.59i	0.224281	+	0.388466i	−0.731823	+	0.681495i	$0.761330\pi$
$228$		0			0
$229$	287.452	−	497.881i	0.0829491	−	0.143672i	−0.821566	−	0.570113i	$-0.806899\pi$
$229$	287.452	−	497.881i	0.0829491	−	0.143672i	0.904515	+	0.426441i	$0.140233\pi$
$230$		0			0
$231$	3233.54	−	417.136i	0.921001	−	0.118812i
$232$		0			0
$233$	2076.07	−	3595.86i	0.583724	−	1.01104i	−0.411309	−	0.911496i	$-0.634928\pi$
$233$	2076.07	−	3595.86i	0.583724	−	1.01104i	0.995033	−	0.0995443i	$-0.0317385\pi$
$234$		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	$-0.288954\pi$
$239$	4548.36			1.23100			0.615500	+	0.788137i	$0.288954\pi$
$240$		0			0
$241$	−3504.39	−	6069.79i	−0.936672	−	1.62236i	−0.771625	−	0.636077i	$-0.780556\pi$
$241$	−3504.39	−	6069.79i	−0.936672	−	1.62236i	−0.165046	−	0.986286i	$-0.552777\pi$
$242$		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	$-0.472638\pi$
$251$	682.819			0.171710			0.0858548	+	0.996308i	$0.472638\pi$
$252$		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	−0.950647	−	0.310273i	$-0.899579\pi$
$257$	−851.276	+	1474.45i	−0.206619	+	0.357875i	0.744028	+	0.668148i	$0.232913\pi$
$258$		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	$-0.0552888\pi$
$263$	1462.12	+	2532.47i	0.342808	+	0.593760i	−0.642145	+	0.766583i	$0.721955\pi$
$264$		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	0.777618	−	0.628738i	$-0.216428\pi$
$269$	−686.910	−	1189.76i	−0.155694	−	0.269670i	−0.933311	+	0.359068i	$0.883095\pi$
$270$		0			0
$271$	390.756	−	676.809i	0.0875894	−	0.151709i	−0.818902	−	0.573933i	$-0.805417\pi$
$271$	390.756	−	676.809i	0.0875894	−	0.151709i	0.906492	+	0.422224i	$0.138750\pi$
$272$		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	0.958793	−	0.284105i	$-0.0916964\pi$
$277$	1075.81	+	1863.36i	0.233355	+	0.404182i	−0.725439	+	0.688287i	$0.758363\pi$
$278$		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	$-0.0542000\pi$
$283$	1647.33	+	2853.25i	0.346019	+	0.599322i	−0.639519	+	0.768775i	$0.720867\pi$
$284$		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	$-0.775424\pi$
$307$	−8189.87			−1.52254			−0.761271	+	0.648434i	$0.775424\pi$
$308$		0			0
$309$	90.7092			0.0166999
$310$		0			0
$311$	−582.651	−	1009.18i	−0.106235	−	0.184004i	0.808007	−	0.589173i	$-0.200546\pi$
$311$	−582.651	−	1009.18i	−0.106235	−	0.184004i	−0.914242	+	0.405168i	$0.867213\pi$
$312$		0			0
$313$	2892.26	−	5009.54i	0.522301	−	0.904652i	−0.477362	−	0.878707i	$-0.658407\pi$
$313$	2892.26	−	5009.54i	0.522301	−	0.904652i	0.999663	−	0.0259457i	$-0.00825969\pi$
$314$		0			0
$315$	1010.06	−	2420.65i	0.180668	−	0.432978i
$316$		0			0
$317$	2283.69	−	3955.46i	0.404620	−	0.700822i	−0.589657	−	0.807654i	$-0.700737\pi$
$317$	2283.69	−	3955.46i	0.404620	−	0.700822i	0.994277	+	0.106831i	$0.0340705\pi$
$318$		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	$-0.928311\pi$
$331$	−1770.31	+	3066.27i	−0.293973	+	0.509177i	0.680772	+	0.732495i	$0.261644\pi$
$332$		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	$-0.0142882\pi$
$347$	2977.50	+	5157.18i	0.460636	+	0.797844i	−0.538357	+	0.842717i	$0.680955\pi$
$348$		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	0.880041	−	0.474898i	$-0.157515\pi$
$353$	190.653	+	330.221i	0.0287463	+	0.0497900i	−0.851294	+	0.524688i	$0.824182\pi$
$354$		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	$-0.762684\pi$
$359$	1497.38	−	2593.53i	0.220135	−	0.381285i	0.954849	+	0.297092i	$0.0960169\pi$
$360$		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	$-0.0593838\pi$
$367$	2325.01	+	4027.04i	0.330694	+	0.572779i	−0.651954	+	0.758259i	$0.726050\pi$
$368$		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	−0.983509	−	0.180862i	$-0.942111\pi$
$373$	−2414.17	+	4181.47i	−0.335123	+	0.580451i	0.648385	+	0.761312i	$0.275445\pi$
$374$		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	$-0.146046\pi$
$379$	13230.5			1.79315			0.896577	+	0.442887i	$0.146046\pi$
$380$		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	$-0.738293\pi$
$383$	2204.87	−	3818.95i	0.294161	−	0.509502i	0.974789	+	0.223127i	$0.0716264\pi$
$384$		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	0.846668	−	0.532122i	$-0.178605\pi$
$389$	−287.691	−	498.296i	−0.0374975	−	0.0649476i	−0.884165	+	0.467175i	$0.845272\pi$
$390$		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	−0.998841	−	0.0481274i	$-0.984675\pi$
$397$	−3620.81	+	6271.43i	−0.457741	+	0.792831i	0.541100	+	0.840958i	$0.318008\pi$
$398$		0			0
$399$	−4623.19	−	6057.66i	−0.580072	−	0.760057i
$400$		0			0
$401$	−1123.50	+	1945.96i	−0.139912	+	0.242335i	−0.927463	−	0.373914i	$-0.878015\pi$
$401$	−1123.50	+	1945.96i	−0.139912	+	0.242335i	0.787551	+	0.616250i	$0.211349\pi$
$402$		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	0.911593	−	0.411094i	$-0.134853\pi$
$409$	825.318	+	1429.49i	0.0997784	+	0.172821i	−0.811814	+	0.583915i	$0.801520\pi$
$410$		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	$-0.559328\pi$
$419$	−3178.64			−0.370613			−0.185307	+	0.982681i	$0.559328\pi$
$420$		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	−0.999960	−	0.00898583i	$-0.997140\pi$
$431$	−4543.35	−	7869.31i	−0.507762	−	0.879469i	0.492198	−	0.870483i	$-0.336194\pi$
$432$		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	0.435751	+	0.900067i	$0.356483\pi$
$439$	−5165.69	+	8947.23i	−0.561605	+	0.972729i	−0.997357	+	0.0726619i	$0.976851\pi$
$440$		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	$-0.687039\pi$
$443$	4136.03	−	7163.82i	0.443587	−	0.768315i	0.997953	+	0.0639584i	$0.0203725\pi$
$444$		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	0.103392	−	0.994641i	$-0.467031\pi$
$457$	8920.37	−	15450.5i	0.913080	−	1.58150i	0.809688	−	0.586860i	$-0.199636\pi$
$458$		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	$-0.596707\pi$
$463$	−5960.87			−0.598326			−0.299163	+	0.954202i	$0.596707\pi$
$464$		0			0
$465$	−4779.19	−	8277.79i	−0.476622	−	0.825534i
$466$		0			0
$467$	5529.15	−	9576.78i	0.547877	−	0.948951i	−0.450542	−	0.892755i	$-0.648769\pi$
$467$	5529.15	−	9576.78i	0.547877	−	0.948951i	0.998420	−	0.0561964i	$-0.0178973\pi$
$468$		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	0.996971	+	0.0777692i	$0.0247797\pi$
$479$	5931.90	+	10274.3i	0.565836	+	0.980056i	−0.431136	+	0.902287i	$0.641887\pi$
$480$		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	$-0.0777727\pi$
$487$	2962.48	+	5131.17i	0.275653	+	0.477445i	−0.694647	+	0.719351i	$0.744439\pi$
$488$		0			0
$489$	−724.171			−0.0669696
$490$		0			0
$491$	−9203.12			−0.845888			−0.422944	−	0.906156i	$-0.639003\pi$
$491$	−9203.12			−0.845888			−0.422944	+	0.906156i	$0.639003\pi$
$492$		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	$-0.688337\pi$
$499$	4903.80	−	8493.63i	0.439928	−	0.761978i	0.997683	+	0.0680273i	$0.0216705\pi$
$500$		0			0
$501$	489.667	+	848.128i	0.0436661	+	0.0756319i
$502$		0			0
$503$	10462.6			0.927446			0.463723	−	0.885980i	$-0.346513\pi$
$503$	10462.6			0.927446			0.463723	+	0.885980i	$0.346513\pi$
$504$		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	−0.958568	−	0.284863i	$-0.908052\pi$
$509$	−2670.91	+	4626.16i	−0.232586	+	0.402850i	0.725983	+	0.687713i	$0.241385\pi$
$510$		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	0.514111	−	0.857724i	$-0.328122\pi$
$521$	−5776.63	−	10005.4i	−0.485755	−	0.841353i	−0.999866	+	0.0163709i	$0.994789\pi$
$522$		0			0
$523$	−2625.76	+	4547.94i	−0.219534	+	0.380244i	−0.954666	−	0.297680i	$-0.903787\pi$
$523$	−2625.76	+	4547.94i	−0.219534	+	0.380244i	0.735132	+	0.677925i	$0.237120\pi$
$524$		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	−0.0870006	−	0.996208i	$-0.527728\pi$
$541$	10308.8	−	17855.4i	0.819241	−	1.41897i	0.906242	−	0.422759i	$-0.138938\pi$
$542$		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	$-0.363084\pi$
$547$	10669.4			0.833985			0.416993	+	0.908910i	$0.363084\pi$
$548$		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	0.949989	−	0.312283i	$-0.101094\pi$
$557$	2688.94	+	4657.38i	0.204549	+	0.354290i	−0.745440	+	0.666573i	$0.767760\pi$
$558$		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	$-0.124621\pi$
$563$	1759.44	+	3047.43i	0.131708	+	0.228124i	−0.792627	+	0.609706i	$0.791287\pi$
$564$		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	−0.909170	−	0.416426i	$-0.863282\pi$
$569$	−1275.15	+	2208.63i	−0.0939492	+	0.162725i	0.815220	+	0.579151i	$0.196616\pi$
$570$		0			0
$571$	−6827.67	−	11825.9i	−0.500401	−	0.866721i	−1.00000		0.000463542i	$-0.999852\pi$
$571$	−6827.67	−	11825.9i	−0.500401	−	0.866721i	0.499599	−	0.866257i	$-0.333481\pi$
$572$		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	0.992471	+	0.122477i	$0.0390837\pi$
$577$	8347.94	+	14459.1i	0.602304	+	1.04322i	−0.390168	+	0.920744i	$0.627583\pi$
$578$		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	$-0.694810\pi$
$587$	−16341.4			−1.14903			−0.574517	+	0.818493i	$0.694810\pi$
$588$		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	0.281961	+	0.959426i	$0.409015\pi$
$593$	−9962.59	+	17255.7i	−0.689906	+	1.19495i	−0.971868	+	0.235527i	$0.924318\pi$
$594$		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	−0.999989	−	0.00479026i	$-0.998475\pi$
$599$	−7390.84	−	12801.3i	−0.504143	−	0.873201i	0.495846	−	0.868411i	$-0.334858\pi$
$600$		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	$-0.914276\pi$
$607$	−3762.02	+	6516.01i	−0.251558	+	0.435711i	0.712397	+	0.701777i	$0.247610\pi$
$608$		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	0.804282	−	0.594248i	$-0.202550\pi$
$613$	−1707.32	−	2957.16i	−0.112493	−	0.194843i	−0.916775	+	0.399405i	$0.869217\pi$
$614$		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	−0.964921	−	0.262542i	$-0.915439\pi$
$619$	−10931.7	−	18934.3i	−0.709828	−	1.22946i	0.255092	−	0.966917i	$-0.417894\pi$
$620$		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	$-0.669342\pi$
$631$	−16080.8			−1.01452			−0.507262	+	0.861792i	$0.669342\pi$
$632$		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	0.996679	+	0.0814280i	$0.0259481\pi$
$641$	9231.90	+	15990.1i	0.568858	+	0.985292i	−0.427821	+	0.903864i	$0.640719\pi$
$642$		0			0
$643$	−3110.87			−0.190794			−0.0953971	−	0.995439i	$-0.530412\pi$
$643$	−3110.87			−0.190794			−0.0953971	+	0.995439i	$0.530412\pi$
$644$		0			0
$645$	4809.34			0.293593
$646$		0			0
$647$	12364.5	+	21416.0i	0.751313	+	1.30131i	0.947186	+	0.320683i	$0.103913\pi$
$647$	12364.5	+	21416.0i	0.751313	+	1.30131i	−0.195873	+	0.980629i	$0.562754\pi$
$648$		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	−0.952130	−	0.305695i	$-0.901111\pi$
$653$	−3526.32	+	6107.76i	−0.211325	+	0.366026i	0.740804	+	0.671721i	$0.234445\pi$
$654$		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	$-0.425028\pi$
$659$	7895.55			0.466718			0.233359	+	0.972391i	$0.425028\pi$
$660$		0			0
$661$	6550.56	+	11345.9i	0.385457	+	0.667631i	0.991833	−	0.127547i	$-0.0407104\pi$
$661$	6550.56	+	11345.9i	0.385457	+	0.667631i	−0.606375	+	0.795179i	$0.707377\pi$
$662$		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	−0.998689	−	0.0511978i	$-0.983696\pi$
$677$	−8014.93	+	13882.3i	−0.455006	+	0.788093i	0.543683	+	0.839291i	$0.317029\pi$
$678$		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	0.989263	+	0.146145i	$0.0466866\pi$
$683$	11088.2	+	19205.3i	0.621197	+	1.07594i	−0.368066	+	0.929800i	$0.619980\pi$
$684$		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	$-0.822956\pi$
$691$	592.072	−	1025.50i	0.0325955	−	0.0564570i	0.881863	+	0.471506i	$0.156289\pi$
$692$		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	−0.873551	−	0.486733i	$-0.838189\pi$
$709$	−287.946	+	498.736i	−0.0152525	+	0.0264181i	0.858298	+	0.513151i	$0.171522\pi$
$710$		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	$-0.873357\pi$
$719$	−2417.77	+	4187.70i	−0.125407	+	0.217211i	0.796485	+	0.604658i	$0.206690\pi$
$720$		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	$-0.651839\pi$
$727$	−17999.8			−0.918259			−0.459129	+	0.888369i	$0.651839\pi$
$728$		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	−0.923224	−	0.384261i	$-0.874456\pi$
$733$	−2556.70	+	4428.33i	−0.128832	+	0.223144i	0.794392	+	0.607405i	$0.207789\pi$
$734$		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	$-0.272014\pi$
$739$	−6528.06	−	11306.9i	−0.324951	−	0.562831i	−0.981502	+	0.191450i	$0.938681\pi$
$740$		0			0
$741$	8532.04			0.422986
$742$		0			0
$743$	−28402.9			−1.40242			−0.701212	−	0.712953i	$-0.747357\pi$
$743$	−28402.9			−1.40242			−0.701212	+	0.712953i	$0.747357\pi$
$744$		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	−0.105760	−	0.994392i	$-0.533728\pi$
$751$	16635.1	−	28812.9i	0.808288	−	1.40000i	0.914049	−	0.405605i	$-0.132939\pi$
$752$		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	−0.919378	−	0.393376i	$-0.871307\pi$
$761$	−2498.50	+	4327.53i	−0.119015	+	0.206141i	0.800362	+	0.599517i	$0.204640\pi$
$762$		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	0.981576	−	0.191074i	$-0.0611972\pi$
$773$	6991.49	+	12109.6i	0.325312	+	0.563458i	−0.656263	+	0.754532i	$0.727864\pi$
$774$		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	0.965464	+	0.260535i	$0.0838990\pi$
$787$	15639.3	+	27088.1i	0.708362	+	1.22692i	−0.257102	+	0.966384i	$0.582768\pi$
$788$		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	0.984851	+	0.173401i	$0.0554758\pi$
$809$	14786.3	+	25610.7i	0.642596	+	1.11301i	−0.342256	+	0.939607i	$0.611191\pi$
$810$		0			0
$811$	45069.0			1.95140			0.975701	−	0.219107i	$-0.0703144\pi$
$811$	45069.0			1.95140			0.975701	+	0.219107i	$0.0703144\pi$
$812$		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	−0.948468	−	0.316873i	$-0.897367\pi$
$821$	−4700.47	+	8141.45i	−0.199814	+	0.346088i	0.748654	+	0.662961i	$0.230701\pi$
$822$		0			0
$823$	14004.4	+	24256.4i	0.593152	+	1.02737i	0.993805	+	0.111139i	$0.0354499\pi$
$823$	14004.4	+	24256.4i	0.593152	+	1.02737i	−0.400653	+	0.916230i	$0.631217\pi$
$824$		0			0
$825$	−21587.1			−0.910989
$826$		0			0
$827$	−28650.8			−1.20470			−0.602349	−	0.798232i	$-0.705769\pi$
$827$	−28650.8			−1.20470			−0.602349	+	0.798232i	$0.705769\pi$
$828$		0			0
$829$	2124.82	+	3680.29i	0.0890205	+	0.154188i	0.907097	−	0.420921i	$-0.138293\pi$
$829$	2124.82	+	3680.29i	0.0890205	+	0.154188i	−0.818077	+	0.575109i	$0.804960\pi$
$830$		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	$-0.438946\pi$
$839$	9265.50			0.381264			0.190632	+	0.981662i	$0.438946\pi$
$840$		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	0.999482	−	0.0321962i	$-0.0102501\pi$
$857$	11838.1	+	20504.2i	0.471858	+	0.817282i	−0.527623	+	0.849478i	$0.676917\pi$
$858$		0			0
$859$	−13706.2	+	23739.8i	−0.544410	+	0.942946i	0.454233	+	0.890883i	$0.349913\pi$
$859$	−13706.2	+	23739.8i	−0.544410	+	0.942946i	−0.998644	+	0.0520636i	$0.983420\pi$
$860$		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	$-0.685400\pi$
$863$	11362.7	−	19680.9i	0.448195	−	0.776297i	0.998269	+	0.0588195i	$0.0187337\pi$
$864$		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	−0.958006	−	0.286748i	$-0.907426\pi$
$877$	−5990.93	+	10376.6i	−0.230672	+	0.399536i	0.727334	+	0.686284i	$0.240759\pi$
$878$		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	$-0.255253\pi$
$883$	36489.6			1.39068			0.695341	+	0.718680i	$0.255253\pi$
$884$		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	$-0.984142\pi$
$887$	−12052.9	+	20876.2i	−0.456253	+	0.790254i	0.542506	+	0.840052i	$0.317476\pi$
$888$		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	$-0.300911\pi$
$907$	−11181.6	−	19367.2i	−0.409350	−	0.709014i	−0.994817	+	0.101682i	$0.967578\pi$
$908$		0			0
$909$	−9809.49			−0.357932
$910$		0			0
$911$	−21426.3			−0.779238			−0.389619	−	0.920976i	$-0.627393\pi$
$911$	−21426.3			−0.779238			−0.389619	+	0.920976i	$0.627393\pi$
$912$		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	−0.450563	−	0.892744i	$-0.648777\pi$
$919$	15263.0	−	26436.4i	0.547858	−	0.948917i	0.998421	−	0.0561730i	$-0.0178898\pi$
$920$		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	−0.904072	−	0.427380i	$-0.859437\pi$
$929$	−2319.45	+	4017.40i	−0.0819146	+	0.141880i	0.822158	+	0.569260i	$0.192770\pi$
$930$		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	0.923579	−	0.383408i	$-0.125250\pi$
$941$	3745.31	+	6487.07i	0.129749	+	0.224732i	−0.793830	+	0.608139i	$0.791916\pi$
$942$		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	$-0.975284\pi$
$947$	−12569.6	+	21771.1i	−0.431316	+	0.747061i	0.565671	+	0.824631i	$0.308617\pi$
$948$		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	$-0.549590\pi$
$967$	−9331.61			−0.310325			−0.155162	+	0.987889i	$0.549590\pi$
$968$		0			0
$969$	8834.91	+	15302.5i	0.292898	+	0.507315i
$970$		0			0
$971$	20993.0	−	36360.9i	0.693817	−	1.20173i	−0.276761	−	0.960939i	$-0.589261\pi$
$971$	20993.0	−	36360.9i	0.693817	−	1.20173i	0.970578	−	0.240787i	$-0.0774055\pi$
$972$		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	0.923746	−	0.383005i	$-0.125111\pi$
$977$	3975.47	+	6885.72i	0.130181	+	0.225480i	−0.793565	+	0.608485i	$0.791778\pi$
$978$		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	$-0.221362\pi$
$983$	−5269.74	−	9127.47i	−0.170986	−	0.296156i	−0.938765	+	0.344559i	$0.888028\pi$
$984$		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	$-0.144038\pi$
$991$	2215.93	+	3838.10i	0.0710306	+	0.123029i	−0.828323	+	0.560251i	$0.810705\pi$
$992$		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	0.988341	+	0.152259i	$0.0486548\pi$
$997$	19707.8	+	34134.9i	0.626031	+	1.08432i	−0.362310	+	0.932058i	$0.618012\pi$
$998$		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	168.4.q.d.121.1	yes	4
3.2	odd	2		504.4.s.f.289.2		4
4.3	odd	2		336.4.q.g.289.1		4
7.2	even	3		1176.4.a.r.1.2		2
7.4	even	3	inner	168.4.q.d.25.1	✓	4
7.5	odd	6		1176.4.a.u.1.1		2
21.11	odd	6		504.4.s.f.361.2		4
28.11	odd	6		336.4.q.g.193.1		4
28.19	even	6		2352.4.a.bo.1.1		2
28.23	odd	6		2352.4.a.cc.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.d.25.1	✓	4	7.4	even	3	inner
168.4.q.d.121.1	yes	4	1.1	even	1	trivial
336.4.q.g.193.1		4	28.11	odd	6
336.4.q.g.289.1		4	4.3	odd	2
504.4.s.f.289.2		4	3.2	odd	2
504.4.s.f.361.2		4	21.11	odd	6
1176.4.a.r.1.2		2	7.2	even	3
1176.4.a.u.1.1		2	7.5	odd	6
2352.4.a.bo.1.1		2	28.19	even	6
2352.4.a.cc.1.2		2	28.23	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.q (of order \(3\), degree \(2\), 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

Varieties

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Representations

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Database

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