LMFDB - Embedded newform 624.4.bv.h.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,4,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, 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:	$36.8171918436$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-2.04224i$ of defining polynomial
Character	$\chi$	$=$	624.49
Dual form			624.4.bv.h.433.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} -12.0825i q^{5} +(25.7533 + 14.8686i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} -12.0825i q^{5} +(25.7533 + 14.8686i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-24.3038 + 14.0318i) q^{11} +(-40.9717 + 22.7667i) q^{13} +(31.3911 - 18.1237i) q^{15} +(-25.3278 + 43.8690i) q^{17} +(-91.0612 - 52.5742i) q^{19} +89.2119i q^{21} +(80.2961 + 139.077i) q^{23} -20.9857 q^{25} -27.0000 q^{27} +(-70.0525 - 121.334i) q^{29} +223.593i q^{31} +(-72.9113 - 42.0954i) q^{33} +(179.650 - 311.163i) q^{35} +(-197.759 + 114.176i) q^{37} +(-120.607 - 72.2975i) q^{39} +(256.259 - 147.951i) q^{41} +(-96.0517 + 166.366i) q^{43} +(94.1734 + 54.3710i) q^{45} -36.9300i q^{47} +(270.653 + 468.785i) q^{49} -151.967 q^{51} +149.102 q^{53} +(169.538 + 293.649i) q^{55} -315.445i q^{57} +(380.070 + 219.433i) q^{59} +(-143.073 + 247.809i) q^{61} +(-231.779 + 133.818i) q^{63} +(275.077 + 495.038i) q^{65} +(-465.166 + 268.564i) q^{67} +(-240.888 + 417.231i) q^{69} +(-88.9656 - 51.3643i) q^{71} -75.5209i q^{73} +(-31.4786 - 54.5225i) q^{75} -834.535 q^{77} -17.5526 q^{79} +(-40.5000 - 70.1481i) q^{81} +1463.08i q^{83} +(530.045 + 306.022i) q^{85} +(210.157 - 364.003i) q^{87} +(-290.036 + 167.453i) q^{89} +(-1393.66 - 22.8773i) q^{91} +(-580.912 + 335.390i) q^{93} +(-635.225 + 1100.24i) q^{95} +(-648.442 - 374.378i) q^{97} -252.572i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$		−	12.0825i		−	1.08069i	−0.841444	−	0.540344i	$-0.818294\pi$
$5$		−	12.0825i		−	1.08069i	0.841444	−	0.540344i	$-0.181706\pi$
$6$		0			0
$7$	25.7533	+	14.8686i	1.39055	+	0.802832i	0.993375	−	0.114914i	$-0.0366591\pi$
$7$	25.7533	+	14.8686i	1.39055	+	0.802832i	0.397170	+	0.917745i	$0.369992\pi$
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−24.3038	+	14.0318i	−0.666169	+	0.384613i	−0.794624	−	0.607102i	$-0.792332\pi$
$11$	−24.3038	+	14.0318i	−0.666169	+	0.384613i	0.128454	+	0.991715i	$0.458998\pi$
$12$		0			0
$13$	−40.9717	+	22.7667i	−0.874115	+	0.485719i
$13$	−40.9717	+	22.7667i	−0.874115	+	0.485719i
$14$		0			0
$15$	31.3911	−	18.1237i	0.540344	−	0.311968i
$16$		0			0
$17$	−25.3278	+	43.8690i	−0.361347	+	0.625871i	−0.988183	−	0.153280i	$-0.951016\pi$
$17$	−25.3278	+	43.8690i	−0.361347	+	0.625871i	0.626836	+	0.779151i	$0.284350\pi$
$18$		0			0
$19$	−91.0612	−	52.5742i	−1.09952	−	0.634808i	−0.163425	−	0.986556i	$-0.552254\pi$
$19$	−91.0612	−	52.5742i	−1.09952	−	0.634808i	−0.936095	+	0.351748i	$0.885587\pi$
$20$		0			0
$21$			89.2119i			0.927030i
$22$		0			0
$23$	80.2961	+	139.077i	0.727951	+	1.26085i	0.957748	+	0.287610i	$0.0928607\pi$
$23$	80.2961	+	139.077i	0.727951	+	1.26085i	−0.229796	+	0.973239i	$0.573806\pi$
$24$		0			0
$25$	−20.9857			−0.167886
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−70.0525	−	121.334i	−0.448566	−	0.776939i	0.549727	−	0.835344i	$-0.314732\pi$
$29$	−70.0525	−	121.334i	−0.448566	−	0.776939i	−0.998293	+	0.0584051i	$0.981398\pi$
$30$		0			0
$31$			223.593i			1.29544i	0.761880	+	0.647718i	$0.224276\pi$
$31$			223.593i			1.29544i	−0.761880	+	0.647718i	$0.775724\pi$
$32$		0			0
$33$	−72.9113	−	42.0954i	−0.384613	−	0.222056i
$34$		0			0
$35$	179.650	−	311.163i	0.867610	−	1.50274i
$36$		0			0
$37$	−197.759	+	114.176i	−0.878684	+	0.507308i	−0.870224	−	0.492656i	$-0.836026\pi$
$37$	−197.759	+	114.176i	−0.878684	+	0.507308i	−0.00845956	+	0.999964i	$0.502693\pi$
$38$		0			0
$39$	−120.607	−	72.2975i	−0.495195	−	0.296843i
$40$		0			0
$41$	256.259	−	147.951i	0.976119	−	0.563563i	0.0750227	−	0.997182i	$-0.476097\pi$
$41$	256.259	−	147.951i	0.976119	−	0.563563i	0.901096	+	0.433619i	$0.142764\pi$
$42$		0			0
$43$	−96.0517	+	166.366i	−0.340645	+	0.590015i	−0.984553	−	0.175088i	$-0.943979\pi$
$43$	−96.0517	+	166.366i	−0.340645	+	0.590015i	0.643907	+	0.765103i	$0.277312\pi$
$44$		0			0
$45$	94.1734	+	54.3710i	0.311968	+	0.180115i
$46$		0			0
$47$		−	36.9300i		−	0.114613i	−0.998357	−	0.0573063i	$-0.981749\pi$
$47$		−	36.9300i		−	0.114613i	0.998357	−	0.0573063i	$-0.0182512\pi$
$48$		0			0
$49$	270.653	+	468.785i	0.789077	+	1.36672i
$50$		0			0
$51$	−151.967			−0.417247
$52$		0			0
$53$	149.102			0.386429			0.193214	−	0.981157i	$-0.438109\pi$
$53$	149.102			0.386429			0.193214	+	0.981157i	$0.438109\pi$
$54$		0			0
$55$	169.538	+	293.649i	0.415647	+	0.719921i
$56$		0			0
$57$		−	315.445i		−	0.733013i
$58$		0			0
$59$	380.070	+	219.433i	0.838659	+	0.484200i	0.856808	−	0.515635i	$-0.172444\pi$
$59$	380.070	+	219.433i	0.838659	+	0.484200i	−0.0181492	+	0.999835i	$0.505777\pi$
$60$		0			0
$61$	−143.073	+	247.809i	−0.300305	+	0.520143i	−0.976205	−	0.216850i	$-0.930422\pi$
$61$	−143.073	+	247.809i	−0.300305	+	0.520143i	0.675900	+	0.736993i	$0.263755\pi$
$62$		0			0
$63$	−231.779	+	133.818i	−0.463515	+	0.267611i
$64$		0			0
$65$	275.077	+	495.038i	0.524910	+	0.944645i
$66$		0			0
$67$	−465.166	+	268.564i	−0.848195	+	0.489706i	−0.860042	−	0.510224i	$-0.829562\pi$
$67$	−465.166	+	268.564i	−0.848195	+	0.489706i	0.0118462	+	0.999930i	$0.496229\pi$
$68$		0			0
$69$	−240.888	+	417.231i	−0.420283	+	0.727951i
$70$		0			0
$71$	−88.9656	−	51.3643i	−0.148708	−	0.0858567i	0.423800	−	0.905756i	$-0.360696\pi$
$71$	−88.9656	−	51.3643i	−0.148708	−	0.0858567i	−0.572508	+	0.819899i	$0.694029\pi$
$72$		0			0
$73$		−	75.5209i		−	0.121083i	−0.998166	−	0.0605414i	$-0.980717\pi$
$73$		−	75.5209i		−	0.121083i	0.998166	−	0.0605414i	$-0.0192827\pi$
$74$		0			0
$75$	−31.4786	−	54.5225i	−0.0484644	−	0.0839428i
$76$		0			0
$77$	−834.535			−1.23512
$78$		0			0
$79$	−17.5526			−0.0249978			−0.0124989	−	0.999922i	$-0.503979\pi$
$79$	−17.5526			−0.0249978			−0.0124989	+	0.999922i	$0.503979\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			1463.08i			1.93487i	0.253122	+	0.967434i	$0.418543\pi$
$83$			1463.08i			1.93487i	−0.253122	+	0.967434i	$0.581457\pi$
$84$		0			0
$85$	530.045	+	306.022i	0.676371	+	0.390503i
$86$		0			0
$87$	210.157	−	364.003i	0.258980	−	0.448566i
$88$		0			0
$89$	−290.036	+	167.453i	−0.345436	+	0.199438i	−0.662673	−	0.748909i	$-0.730578\pi$
$89$	−290.036	+	167.453i	−0.345436	+	0.199438i	0.317237	+	0.948346i	$0.397245\pi$
$90$		0			0
$91$	−1393.66	−	22.8773i	−1.60545	−	0.0263538i
$92$		0			0
$93$	−580.912	+	335.390i	−0.647718	+	0.373960i
$94$		0			0
$95$	−635.225	+	1100.24i	−0.686029	+	1.18824i
$96$		0			0
$97$	−648.442	−	374.378i	−0.678756	−	0.391880i	0.120630	−	0.992697i	$-0.461508\pi$
$97$	−648.442	−	374.378i	−0.678756	−	0.391880i	−0.799386	+	0.600818i	$0.794842\pi$
$98$		0			0
$99$		−	252.572i		−	0.256409i
$100$		0			0
$101$	−392.001	−	678.966i	−0.386194	−	0.668907i	0.605740	−	0.795662i	$-0.292877\pi$
$101$	−392.001	−	678.966i	−0.386194	−	0.668907i	−0.991934	+	0.126755i	$0.959544\pi$
$102$		0			0
$103$	396.040			0.378864			0.189432	−	0.981894i	$-0.439335\pi$
$103$	396.040			0.378864			0.189432	+	0.981894i	$0.439335\pi$
$104$		0			0
$105$	1077.90			1.00183
$106$		0			0
$107$	−718.296	−	1244.12i	−0.648974	−	1.12406i	−0.983368	−	0.181623i	$-0.941865\pi$
$107$	−718.296	−	1244.12i	−0.648974	−	1.12406i	0.334394	−	0.942433i	$-0.391468\pi$
$108$		0			0
$109$			1977.92i			1.73807i	0.494746	+	0.869037i	$0.335261\pi$
$109$			1977.92i			1.73807i	−0.494746	+	0.869037i	$0.664739\pi$
$110$		0			0
$111$	−593.276	−	342.528i	−0.507308	−	0.292895i
$112$		0			0
$113$	−61.2026	+	106.006i	−0.0509509	+	0.0882496i	−0.890376	−	0.455226i	$-0.849559\pi$
$113$	−61.2026	+	106.006i	−0.0509509	+	0.0882496i	0.839425	+	0.543475i	$0.182892\pi$
$114$		0			0
$115$	1680.39	−	970.173i	1.36258	−	0.786688i
$116$		0			0
$117$	6.92382	−	421.793i	0.00547100	−	0.333288i
$118$		0			0
$119$	−1304.55	+	753.180i	−1.00494	+	0.580201i
$120$		0			0
$121$	−271.718	+	470.629i	−0.204146	+	0.353591i
$122$		0			0
$123$	768.776	+	443.853i	0.563563	+	0.325373i
$124$		0			0
$125$		−	1256.75i		−	0.899256i
$126$		0			0
$127$	−1154.80	−	2000.18i	−0.806868	−	1.39754i	−0.915022	−	0.403403i	$-0.867827\pi$
$127$	−1154.80	−	2000.18i	−0.806868	−	1.39754i	0.108154	−	0.994134i	$-0.465506\pi$
$128$		0			0
$129$	−576.310			−0.393343
$130$		0			0
$131$	1444.26			0.963250			0.481625	−	0.876377i	$-0.340047\pi$
$131$	1444.26			0.963250			0.481625	+	0.876377i	$0.340047\pi$
$132$		0			0
$133$	−1563.41	−	2707.91i	−1.01929	−	1.76546i
$134$		0			0
$135$			326.226i			0.207978i
$136$		0			0
$137$	637.324	+	367.959i	0.397447	+	0.229466i	0.685382	−	0.728184i	$-0.259635\pi$
$137$	637.324	+	367.959i	0.397447	+	0.229466i	−0.287935	+	0.957650i	$0.592969\pi$
$138$		0			0
$139$	−752.571	+	1303.49i	−0.459225	+	0.795400i	−0.998920	−	0.0464599i	$-0.985206\pi$
$139$	−752.571	+	1303.49i	−0.459225	+	0.795400i	0.539696	+	0.841860i	$0.318539\pi$
$140$		0			0
$141$	95.9469	−	55.3950i	0.0573063	−	0.0330858i
$142$		0			0
$143$	676.309	−	1128.22i	0.395495	−	0.659767i
$144$		0			0
$145$	−1466.02	+	846.406i	−0.839629	+	0.484760i
$146$		0			0
$147$	−811.960	+	1406.36i	−0.455574	+	0.789077i
$148$		0			0
$149$	370.523	+	213.921i	0.203721	+	0.117618i	0.598390	−	0.801205i	$-0.295807\pi$
$149$	370.523	+	213.921i	0.203721	+	0.117618i	−0.394669	+	0.918823i	$0.629141\pi$
$150$		0			0
$151$			1601.83i			0.863278i	0.902046	+	0.431639i	$0.142065\pi$
$151$			1601.83i			0.863278i	−0.902046	+	0.431639i	$0.857935\pi$
$152$		0			0
$153$	−227.950	−	394.821i	−0.120449	−	0.208624i
$154$		0			0
$155$	2701.55			1.39996
$156$		0			0
$157$	−730.346			−0.371261			−0.185631	−	0.982620i	$-0.559433\pi$
$157$	−730.346			−0.371261			−0.185631	+	0.982620i	$0.559433\pi$
$158$		0			0
$159$	223.653	+	387.378i	0.111552	+	0.193214i
$160$		0			0
$161$			4775.58i			2.33769i
$162$		0			0
$163$	1644.03	+	949.180i	0.790001	+	0.456107i	0.839963	−	0.542644i	$-0.182577\pi$
$163$	1644.03	+	949.180i	0.790001	+	0.456107i	−0.0499619	+	0.998751i	$0.515910\pi$
$164$		0			0
$165$	−508.615	+	880.948i	−0.239974	+	0.415647i
$166$		0			0
$167$	−1236.25	+	713.751i	−0.572839	+	0.330729i	−0.758282	−	0.651926i	$-0.773961\pi$
$167$	−1236.25	+	713.751i	−0.572839	+	0.330729i	0.185444	+	0.982655i	$0.440628\pi$
$168$		0			0
$169$	1160.36	−	1865.58i	0.528155	−	0.849148i
$170$		0			0
$171$	819.551	−	473.168i	0.366507	−	0.211603i
$172$		0			0
$173$	−1022.20	+	1770.50i	−0.449227	+	0.778084i	−0.998336	−	0.0576667i	$-0.981634\pi$
$173$	−1022.20	+	1770.50i	−0.449227	+	0.778084i	0.549109	+	0.835751i	$0.314967\pi$
$174$		0			0
$175$	−540.450	−	312.029i	−0.233453	−	0.134784i
$176$		0			0
$177$			1316.60i			0.559106i
$178$		0			0
$179$	1944.86	+	3368.59i	0.812098	+	1.40660i	0.911393	+	0.411537i	$0.135008\pi$
$179$	1944.86	+	3368.59i	0.812098	+	1.40660i	−0.0992948	+	0.995058i	$0.531659\pi$
$180$		0			0
$181$	2477.02			1.01721			0.508606	−	0.861000i	$-0.330161\pi$
$181$	2477.02			1.01721			0.508606	+	0.861000i	$0.330161\pi$
$182$		0			0
$183$	−858.437			−0.346762
$184$		0			0
$185$	1379.53	+	2389.41i	0.548242	+	0.949583i
$186$		0			0
$187$		−	1421.58i		−	0.555914i
$188$		0			0
$189$	−695.338	−	401.454i	−0.267611	−	0.154505i
$190$		0			0
$191$	1138.40	−	1971.78i	0.431267	−	0.746977i	−0.565715	−	0.824601i	$-0.691400\pi$
$191$	1138.40	−	1971.78i	0.431267	−	0.746977i	0.996983	+	0.0776235i	$0.0247332\pi$
$192$		0			0
$193$	3396.92	−	1961.21i	1.26692	−	0.731456i	0.292515	−	0.956261i	$-0.405508\pi$
$193$	3396.92	−	1961.21i	1.26692	−	0.731456i	0.974404	+	0.224805i	$0.0721744\pi$
$194$		0			0
$195$	−873.531	+	1457.23i	−0.320794	+	0.535151i
$196$		0			0
$197$	4384.88	−	2531.61i	1.58584	−	0.915584i	0.591855	−	0.806045i	$-0.298396\pi$
$197$	4384.88	−	2531.61i	1.58584	−	0.915584i	0.993982	−	0.109539i	$-0.0349375\pi$
$198$		0			0
$199$	−1635.03	+	2831.95i	−0.582433	+	1.00880i	0.412757	+	0.910841i	$0.364566\pi$
$199$	−1635.03	+	2831.95i	−0.582433	+	1.00880i	−0.995190	+	0.0979624i	$0.968767\pi$
$200$		0			0
$201$	−1395.50	−	805.691i	−0.489706	−	0.282732i
$202$		0			0
$203$		−	4166.34i		−	1.44049i
$204$		0			0
$205$	−1787.61	−	3096.23i	−0.609035	−	1.05488i
$206$		0			0
$207$	−1445.33			−0.485301
$208$		0			0
$209$	2950.84			0.976622
$210$		0			0
$211$	−1406.09	−	2435.42i	−0.458764	−	0.794602i	0.540132	−	0.841580i	$-0.318374\pi$
$211$	−1406.09	−	2435.42i	−0.458764	−	0.794602i	−0.998896	+	0.0469781i	$0.985041\pi$
$212$		0			0
$213$		−	308.186i		−	0.0991388i
$214$		0			0
$215$	2010.12	+	1160.54i	0.637622	+	0.368131i
$216$		0			0
$217$	−3324.53	+	5758.25i	−1.04002	+	1.80136i
$218$		0			0
$219$	196.209	−	113.281i	0.0605414	−	0.0349536i
$220$		0			0
$221$	38.9700	−	2374.02i	0.0118616	−	0.722596i
$222$		0			0
$223$	−794.783	+	458.868i	−0.238666	+	0.137794i	−0.614564	−	0.788867i	$-0.710668\pi$
$223$	−794.783	+	458.868i	−0.238666	+	0.137794i	0.375897	+	0.926661i	$0.377335\pi$
$224$		0			0
$225$	94.4357	−	163.567i	0.0279809	−	0.0484644i
$226$		0			0
$227$	1157.35	+	668.194i	0.338396	+	0.195373i	0.659562	−	0.751650i	$-0.270742\pi$
$227$	1157.35	+	668.194i	0.338396	+	0.195373i	−0.321167	+	0.947023i	$0.604075\pi$
$228$		0			0
$229$			164.820i			0.0475617i	0.999717	+	0.0237808i	$0.00757039\pi$
$229$			164.820i			0.0475617i	−0.999717	+	0.0237808i	$0.992430\pi$
$230$		0			0
$231$	−1251.80	−	2168.19i	−0.356548	−	0.617559i
$232$		0			0
$233$	4243.42			1.19312			0.596558	−	0.802570i	$-0.296535\pi$
$233$	4243.42			1.19312			0.596558	+	0.802570i	$0.296535\pi$
$234$		0			0
$235$	−446.205			−0.123860
$236$		0			0
$237$	−26.3289	−	45.6031i	−0.00721624	−	0.0124989i
$238$		0			0
$239$		−	2491.07i		−	0.674200i	−0.941469	−	0.337100i	$-0.890554\pi$
$239$		−	2491.07i		−	0.674200i	0.941469	−	0.337100i	$-0.109446\pi$
$240$		0			0
$241$	−2526.54	−	1458.70i	−0.675306	−	0.389888i	0.122778	−	0.992434i	$-0.460820\pi$
$241$	−2526.54	−	1458.70i	−0.675306	−	0.389888i	−0.798084	+	0.602546i	$0.794153\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	5664.08	−	3270.16i	1.47700	−	0.852746i
$246$		0			0
$247$	4927.87	+	80.8921i	1.26944	+	0.0208382i
$248$		0			0
$249$	−3801.20	+	2194.62i	−0.967434	+	0.558549i
$250$		0			0
$251$	656.939	−	1137.85i	0.165202	−	0.286138i	−0.771525	−	0.636199i	$-0.780506\pi$
$251$	656.939	−	1137.85i	0.165202	−	0.286138i	0.936727	+	0.350061i	$0.113839\pi$
$252$		0			0
$253$	−3902.99	−	2253.39i	−0.969878	−	0.559959i
$254$		0			0
$255$			1836.13i			0.450914i
$256$		0			0
$257$	−493.791	−	855.271i	−0.119851	−	0.207589i	0.799857	−	0.600190i	$-0.204909\pi$
$257$	−493.791	−	855.271i	−0.119851	−	0.207589i	−0.919709	+	0.392601i	$0.871575\pi$
$258$		0			0
$259$	−6790.57			−1.62913
$260$		0			0
$261$	1260.94			0.299044
$262$		0			0
$263$	−3493.23	−	6050.44i	−0.819017	−	1.41858i	−0.906407	−	0.422405i	$-0.861186\pi$
$263$	−3493.23	−	6050.44i	−0.819017	−	1.41858i	0.0873899	−	0.996174i	$-0.472147\pi$
$264$		0			0
$265$		−	1801.52i		−	0.417609i
$266$		0			0
$267$	−870.109	−	502.358i	−0.199438	−	0.115145i
$268$		0			0
$269$	2952.17	−	5113.31i	0.669134	−	1.15897i	−0.309013	−	0.951058i	$-0.599999\pi$
$269$	2952.17	−	5113.31i	0.669134	−	1.15897i	0.978147	−	0.207916i	$-0.0666681\pi$
$270$		0			0
$271$	1845.97	−	1065.77i	0.413781	−	0.238897i	−0.278632	−	0.960398i	$-0.589881\pi$
$271$	1845.97	−	1065.77i	0.413781	−	0.238897i	0.692413	+	0.721501i	$0.256548\pi$
$272$		0			0
$273$	−2031.06	−	3655.16i	−0.450276	−	0.810331i
$274$		0			0
$275$	510.032	−	294.467i	0.111840	−	0.0645710i
$276$		0			0
$277$	2016.21	−	3492.17i	0.437336	−	0.757489i	−0.560147	−	0.828393i	$-0.689255\pi$
$277$	2016.21	−	3492.17i	0.437336	−	0.757489i	0.997483	+	0.0709046i	$0.0225886\pi$
$278$		0			0
$279$	−1742.74	−	1006.17i	−0.373960	−	0.215906i
$280$		0			0
$281$		−	2298.29i		−	0.487916i	−0.969786	−	0.243958i	$-0.921554\pi$
$281$		−	2298.29i		−	0.487916i	0.969786	−	0.243958i	$-0.0784459\pi$
$282$		0			0
$283$	−3328.40	−	5764.96i	−0.699127	−	1.21092i	−0.968770	−	0.247963i	$-0.920239\pi$
$283$	−3328.40	−	5764.96i	−0.699127	−	1.21092i	0.269643	−	0.962960i	$-0.413094\pi$
$284$		0			0
$285$	−3811.35			−0.792158
$286$		0			0
$287$	8799.33			1.80978
$288$		0			0
$289$	1173.51	+	2032.57i	0.238857	+	0.413713i
$290$		0			0
$291$		−	2246.27i		−	0.452504i
$292$		0			0
$293$	−6466.60	−	3733.49i	−1.28936	−	0.744413i	−0.310821	−	0.950468i	$-0.600604\pi$
$293$	−6466.60	−	3733.49i	−1.28936	−	0.744413i	−0.978540	+	0.206055i	$0.933937\pi$
$294$		0			0
$295$	2651.29	−	4592.18i	0.523269	−	0.906328i
$296$		0			0
$297$	656.202	−	378.858i	0.128204	−	0.0740188i
$298$		0			0
$299$	−6456.18	−	3870.14i	−1.24873	−	0.748548i
$300$		0			0
$301$	−4947.29	+	2856.32i	−0.947365	+	0.546962i
$302$		0			0
$303$	1176.00	−	2036.90i	0.222969	−	0.386194i
$304$		0			0
$305$	2994.14	+	1728.67i	0.562112	+	0.324536i
$306$		0			0
$307$			3965.99i			0.737299i	0.929568	+	0.368650i	$0.120180\pi$
$307$			3965.99i			0.737299i	−0.929568	+	0.368650i	$0.879820\pi$
$308$		0			0
$309$	594.060	+	1028.94i	0.109369	+	0.189432i
$310$		0			0
$311$	7372.29			1.34419			0.672097	−	0.740463i	$-0.265394\pi$
$311$	7372.29			1.34419			0.672097	+	0.740463i	$0.265394\pi$
$312$		0			0
$313$	8249.55			1.48975			0.744875	−	0.667204i	$-0.232509\pi$
$313$	8249.55			1.48975			0.744875	+	0.667204i	$0.232509\pi$
$314$		0			0
$315$	1616.85	+	2800.46i	0.289203	+	0.500915i
$316$		0			0
$317$			5575.26i			0.987817i	0.869514	+	0.493909i	$0.164432\pi$
$317$			5575.26i			0.987817i	−0.869514	+	0.493909i	$0.835568\pi$
$318$		0			0
$319$	3405.08	+	1965.92i	0.597642	+	0.345049i
$320$		0			0
$321$	2154.89	−	3732.37i	0.374686	−	0.648974i
$322$		0			0
$323$	4612.76	−	2663.18i	0.794615	−	0.458771i
$324$		0			0
$325$	859.819	−	477.775i	0.146751	−	0.0815452i
$326$		0			0
$327$	−5138.78	+	2966.88i	−0.869037	+	0.501739i
$328$		0			0
$329$	549.099	−	951.068i	0.0920146	−	0.159374i
$330$		0			0
$331$	3600.38	+	2078.68i	0.597870	+	0.345180i	0.768203	−	0.640206i	$-0.221151\pi$
$331$	3600.38	+	2078.68i	0.597870	+	0.345180i	−0.170333	+	0.985387i	$0.554484\pi$
$332$		0			0
$333$		−	2055.17i		−	0.338206i
$334$		0			0
$335$	3244.91	+	5620.35i	0.529219	+	0.916634i
$336$		0			0
$337$	−3225.18			−0.521326			−0.260663	−	0.965430i	$-0.583941\pi$
$337$	−3225.18			−0.521326			−0.260663	+	0.965430i	$0.583941\pi$
$338$		0			0
$339$	−367.215			−0.0588330
$340$		0			0
$341$	−3137.41	−	5434.15i	−0.498241	−	0.862979i
$342$		0			0
$343$			5897.11i			0.928321i
$344$		0			0
$345$	5041.17	+	2910.52i	0.786688	+	0.454195i
$346$		0			0
$347$	1645.25	−	2849.65i	0.254529	−	0.440856i	−0.710239	−	0.703961i	$-0.751413\pi$
$347$	1645.25	−	2849.65i	0.254529	−	0.440856i	0.964767	+	0.263104i	$0.0847464\pi$
$348$		0			0
$349$	−3889.77	+	2245.76i	−0.596604	+	0.344449i	−0.767704	−	0.640804i	$-0.778601\pi$
$349$	−3889.77	+	2245.76i	−0.596604	+	0.344449i	0.171101	+	0.985254i	$0.445268\pi$
$350$		0			0
$351$	1106.24	−	614.700i	0.168224	−	0.0934766i
$352$		0			0
$353$	−5107.71	+	2948.94i	−0.770130	+	0.444635i	−0.832921	−	0.553392i	$-0.813333\pi$
$353$	−5107.71	+	2948.94i	−0.770130	+	0.444635i	0.0627907	+	0.998027i	$0.480000\pi$
$354$		0			0
$355$	−620.607	+	1074.92i	−0.0927843	+	0.160707i
$356$		0			0
$357$	−3913.64	−	2259.54i	−0.580201	−	0.334979i
$358$		0			0
$359$			9277.20i			1.36388i	0.731410	+	0.681938i	$0.238863\pi$
$359$			9277.20i			1.36388i	−0.731410	+	0.681938i	$0.761137\pi$
$360$		0			0
$361$	2098.59	+	3634.87i	0.305962	+	0.529942i
$362$		0			0
$363$	−1630.31			−0.235727
$364$		0			0
$365$	−912.477			−0.130853
$366$		0			0
$367$	−3287.18	−	5693.56i	−0.467546	−	0.809814i	0.531766	−	0.846891i	$-0.321529\pi$
$367$	−3287.18	−	5693.56i	−0.467546	−	0.809814i	−0.999312	+	0.0370774i	$0.988195\pi$
$368$		0			0
$369$			2663.12i			0.375708i
$370$		0			0
$371$	3839.86	+	2216.94i	0.537347	+	0.310237i
$372$		0			0
$373$	2672.77	−	4629.38i	0.371021	−	0.642628i	−0.618702	−	0.785626i	$-0.712341\pi$
$373$	2672.77	−	4629.38i	0.371021	−	0.642628i	0.989723	+	0.142998i	$0.0456743\pi$
$374$		0			0
$375$	3265.13	−	1885.12i	0.449628	−	0.259593i
$376$		0			0
$377$	5632.55	+	3376.41i	0.769472	+	0.461258i
$378$		0			0
$379$	−899.378	+	519.256i	−0.121894	+	0.0703757i	−0.559707	−	0.828690i	$-0.689086\pi$
$379$	−899.378	+	519.256i	−0.121894	+	0.0703757i	0.437813	+	0.899066i	$0.355753\pi$
$380$		0			0
$381$	3464.41	−	6000.54i	0.465846	−	0.806868i
$382$		0			0
$383$	−5844.97	−	3374.59i	−0.779801	−	0.450219i	0.0565585	−	0.998399i	$-0.481987\pi$
$383$	−5844.97	−	3374.59i	−0.779801	−	0.450219i	−0.836360	+	0.548181i	$0.815321\pi$
$384$		0			0
$385$			10083.2i			1.33478i
$386$		0			0
$387$	−864.465	−	1497.30i	−0.113548	−	0.196672i
$388$		0			0
$389$	1246.11			0.162417			0.0812083	−	0.996697i	$-0.474122\pi$
$389$	1246.11			0.162417			0.0812083	+	0.996697i	$0.474122\pi$
$390$		0			0
$391$	−8134.89			−1.05217
$392$		0			0
$393$	2166.39	+	3752.30i	0.278066	+	0.481625i
$394$		0			0
$395$			212.079i			0.0270148i
$396$		0			0
$397$	−7236.24	−	4177.85i	−0.914802	−	0.528161i	−0.0328293	−	0.999461i	$-0.510452\pi$
$397$	−7236.24	−	4177.85i	−0.914802	−	0.528161i	−0.881973	+	0.471300i	$0.843785\pi$
$398$		0			0
$399$	4690.24	−	8123.74i	0.588486	−	1.01929i
$400$		0			0
$401$	2843.73	−	1641.83i	0.354137	−	0.204461i	−0.312369	−	0.949961i	$-0.601122\pi$
$401$	2843.73	−	1641.83i	0.354137	−	0.204461i	0.666506	+	0.745500i	$0.267789\pi$
$402$		0			0
$403$	−5090.47	−	9160.98i	−0.629217	−	1.13236i
$404$		0			0
$405$	−847.561	+	489.339i	−0.103989	+	0.0600382i
$406$		0			0
$407$	3204.18	−	5549.81i	0.390235	−	0.675906i
$408$		0			0
$409$	9464.72	+	5464.46i	1.14426	+	0.660636i	0.947481	−	0.319813i	$-0.103620\pi$
$409$	9464.72	+	5464.46i	1.14426	+	0.660636i	0.196775	+	0.980449i	$0.436953\pi$
$410$		0			0
$411$			2207.75i			0.264965i
$412$		0			0
$413$	6525.36	+	11302.3i	0.777462	+	1.34660i
$414$		0			0
$415$	17677.6			2.09099
$416$		0			0
$417$	−4515.43			−0.530267
$418$		0			0
$419$	3651.47	+	6324.53i	0.425742	+	0.737407i	0.996489	−	0.0837185i	$-0.0266796\pi$
$419$	3651.47	+	6324.53i	0.425742	+	0.737407i	−0.570747	+	0.821126i	$0.693346\pi$
$420$		0			0
$421$		−	7580.99i		−	0.877612i	−0.898582	−	0.438806i	$-0.855401\pi$
$421$		−	7580.99i		−	0.877612i	0.898582	−	0.438806i	$-0.144599\pi$
$422$		0			0
$423$	287.841	+	166.185i	0.0330858	+	0.0191021i
$424$		0			0
$425$	531.521	−	920.622i	0.0606649	−	0.105075i
$426$		0			0
$427$	−7369.18	+	4254.60i	−0.835175	+	0.482188i
$428$		0			0
$429$	3945.67	+	64.7690i	0.444053	+	0.00728923i
$430$		0			0
$431$	−8709.40	+	5028.37i	−0.973357	+	0.561968i	−0.900258	−	0.435357i	$-0.856622\pi$
$431$	−8709.40	+	5028.37i	−0.973357	+	0.561968i	−0.0730993	+	0.997325i	$0.523289\pi$
$432$		0			0
$433$	1366.69	−	2367.18i	0.151683	−	0.262723i	−0.780163	−	0.625576i	$-0.784864\pi$
$433$	1366.69	−	2367.18i	0.151683	−	0.262723i	0.931846	+	0.362853i	$0.118197\pi$
$434$		0			0
$435$	−4398.05	−	2539.22i	−0.484760	−	0.279876i
$436$		0			0
$437$		−	16886.0i		−	1.84844i
$438$		0			0
$439$	−3372.12	−	5840.68i	−0.366611	−	0.634989i	0.622422	−	0.782682i	$-0.286149\pi$
$439$	−3372.12	−	5840.68i	−0.366611	−	0.634989i	−0.989033	+	0.147692i	$0.952815\pi$
$440$		0			0
$441$	−4871.76			−0.526051
$442$		0			0
$443$	−8655.69			−0.928317			−0.464158	−	0.885752i	$-0.653643\pi$
$443$	−8655.69			−0.928317			−0.464158	+	0.885752i	$0.653643\pi$
$444$		0			0
$445$	2023.24	+	3504.35i	0.215530	+	0.373308i
$446$		0			0
$447$			1283.53i			0.135814i
$448$		0			0
$449$	5648.62	+	3261.23i	0.593708	+	0.342777i	0.766562	−	0.642170i	$-0.221966\pi$
$449$	5648.62	+	3261.23i	0.593708	+	0.342777i	−0.172854	+	0.984947i	$0.555299\pi$
$450$		0			0
$451$	−4152.03	+	7191.53i	−0.433507	+	0.750856i
$452$		0			0
$453$	−4161.67	+	2402.74i	−0.431639	+	0.249207i
$454$		0			0
$455$	−276.414	+	16838.9i	−0.0284802	+	1.73499i
$456$		0			0
$457$	−1343.40	+	775.613i	−0.137509	+	0.0793909i	−0.567176	−	0.823596i	$-0.691964\pi$
$457$	−1343.40	+	775.613i	−0.137509	+	0.0793909i	0.429667	+	0.902987i	$0.358631\pi$
$458$		0			0
$459$	683.850	−	1184.46i	0.0695412	−	0.120449i
$460$		0			0
$461$	−6725.77	−	3883.12i	−0.679501	−	0.392310i	0.120166	−	0.992754i	$-0.461657\pi$
$461$	−6725.77	−	3883.12i	−0.679501	−	0.392310i	−0.799667	+	0.600444i	$0.794991\pi$
$462$		0			0
$463$		−	2004.52i		−	0.201205i	−0.994927	−	0.100603i	$-0.967923\pi$
$463$		−	2004.52i		−	0.201205i	0.994927	−	0.100603i	$-0.0320771\pi$
$464$		0			0
$465$	4052.33	+	7018.84i	0.404134	+	0.699980i
$466$		0			0
$467$	18674.3			1.85042			0.925209	−	0.379458i	$-0.123889\pi$
$467$	18674.3			1.85042			0.925209	+	0.379458i	$0.123889\pi$
$468$		0			0
$469$	−15972.7			−1.57261
$470$		0			0
$471$	−1095.52	−	1897.50i	−0.107174	−	0.185631i
$472$		0			0
$473$		−	5391.11i		−	0.524067i
$474$		0			0
$475$	1910.98	+	1103.31i	0.184594	+	0.106575i
$476$		0			0
$477$	−670.959	+	1162.13i	−0.0644048	+	0.111552i
$478$		0			0
$479$	−8065.31	+	4656.51i	−0.769340	+	0.444178i	−0.832639	−	0.553816i	$-0.813171\pi$
$479$	−8065.31	+	4656.51i	−0.769340	+	0.444178i	0.0632994	+	0.997995i	$0.479838\pi$
$480$		0			0
$481$	5503.09	−	9180.28i	0.521662	−	0.870239i
$482$		0			0
$483$	−12407.3	+	7163.36i	−1.16884	+	0.674833i
$484$		0			0
$485$	−4523.41	+	7834.77i	−0.423500	+	0.733523i
$486$		0			0
$487$	−3062.96	−	1768.40i	−0.285002	−	0.164546i	0.350684	−	0.936494i	$-0.385949\pi$
$487$	−3062.96	−	1768.40i	−0.285002	−	0.164546i	−0.635686	+	0.771948i	$0.719283\pi$
$488$		0			0
$489$			5695.08i			0.526667i
$490$		0			0
$491$	1680.89	+	2911.39i	0.154496	+	0.267595i	0.932875	−	0.360199i	$-0.117291\pi$
$491$	1680.89	+	2911.39i	0.154496	+	0.267595i	−0.778379	+	0.627794i	$0.783958\pi$
$492$		0			0
$493$	7097.10			0.648351
$494$		0			0
$495$	−3051.69			−0.277098
$496$		0			0
$497$	−1527.44	−	2645.60i	−0.137857	−	0.238775i
$498$		0			0
$499$		−	4027.43i		−	0.361308i	−0.983547	−	0.180654i	$-0.942179\pi$
$499$		−	4027.43i		−	0.361308i	0.983547	−	0.180654i	$-0.0578214\pi$
$500$		0			0
$501$	−3708.76	−	2141.25i	−0.330729	−	0.190946i
$502$		0			0
$503$	883.336	−	1529.98i	0.0783022	−	0.135623i	−0.824215	−	0.566277i	$-0.808383\pi$
$503$	883.336	−	1529.98i	0.0783022	−	0.135623i	0.902518	+	0.430653i	$0.141717\pi$
$504$		0			0
$505$	−8203.57	+	4736.33i	−0.722880	+	0.417355i
$506$		0			0
$507$	6587.45	+	216.327i	0.577039	+	0.0189496i
$508$		0			0
$509$	−5903.06	+	3408.13i	−0.514044	+	0.296784i	−0.734495	−	0.678615i	$-0.762581\pi$
$509$	−5903.06	+	3408.13i	−0.514044	+	0.296784i	0.220450	+	0.975398i	$0.429247\pi$
$510$		0			0
$511$	1122.89	−	1944.91i	0.0972091	−	0.168371i
$512$		0			0
$513$	2458.65	+	1419.50i	0.211603	+	0.122169i
$514$		0			0
$515$		−	4785.13i		−	0.409433i
$516$		0			0
$517$	518.194	+	897.538i	0.0440815	+	0.0763514i
$518$		0			0
$519$	−6133.19			−0.518723
$520$		0			0
$521$	−5442.27			−0.457640			−0.228820	−	0.973469i	$-0.573487\pi$
$521$	−5442.27			−0.457640			−0.228820	+	0.973469i	$0.573487\pi$
$522$		0			0
$523$	10364.3	+	17951.4i	0.866535	+	1.50088i	0.865515	+	0.500883i	$0.166991\pi$
$523$	10364.3	+	17951.4i	0.866535	+	1.50088i	0.00101984	+	0.999999i	$0.499675\pi$
$524$		0			0
$525$		−	1872.17i		−	0.155635i
$526$		0			0
$527$	−9808.81	−	5663.12i	−0.810775	−	0.468101i
$528$		0			0
$529$	−6811.41	+	11797.7i	−0.559827	+	0.969648i
$530$		0			0
$531$	−3420.63	+	1974.90i	−0.279553	+	0.161400i
$532$		0			0
$533$	−7130.99	+	11896.0i	−0.579508	+	0.966738i
$534$		0			0
$535$	−15032.1	+	8678.77i	−1.21475	+	0.701339i
$536$		0			0
$537$	−5834.58	+	10105.8i	−0.468865	+	0.812098i
$538$		0			0
$539$	−13155.8	−	7595.50i	−1.05132	−	0.606979i
$540$		0			0
$541$			8577.44i			0.681651i	0.940127	+	0.340825i	$0.110706\pi$
$541$			8577.44i			0.681651i	−0.940127	+	0.340825i	$0.889294\pi$
$542$		0			0
$543$	3715.53	+	6435.48i	0.293644	+	0.508606i
$544$		0			0
$545$	23898.1			1.87832
$546$		0			0
$547$	−8723.99			−0.681921			−0.340961	−	0.940078i	$-0.610752\pi$
$547$	−8723.99			−0.681921			−0.340961	+	0.940078i	$0.610752\pi$
$548$		0			0
$549$	−1287.65	−	2230.28i	−0.100102	−	0.173381i
$550$		0			0
$551$			14731.8i			1.13901i
$552$		0			0
$553$	−452.037	−	260.984i	−0.0347606	−	0.0200690i
$554$		0			0
$555$	−4138.58	+	7168.22i	−0.316528	+	0.548242i
$556$		0			0
$557$	−835.720	+	482.503i	−0.0635738	+	0.0367043i	−0.531450	−	0.847090i	$-0.678353\pi$
$557$	−835.720	+	482.503i	−0.0635738	+	0.0367043i	0.467876	+	0.883794i	$0.345019\pi$
$558$		0			0
$559$	147.788	−	9003.09i	0.0111820	−	0.681199i
$560$		0			0
$561$	3693.36	−	2132.37i	0.277957	−	0.160479i
$562$		0			0
$563$	7302.60	−	12648.5i	0.546657	−	0.946837i	−0.451844	−	0.892097i	$-0.649234\pi$
$563$	7302.60	−	12648.5i	0.546657	−	0.946837i	0.998501	−	0.0547402i	$-0.0174331\pi$
$564$		0			0
$565$	1280.81	+	739.477i	0.0953702	+	0.0550620i
$566$		0			0
$567$		−	2408.72i		−	0.178407i
$568$		0			0
$569$	3901.24	+	6757.15i	0.287432	+	0.497846i	0.973196	−	0.229977i	$-0.0738653\pi$
$569$	3901.24	+	6757.15i	0.287432	+	0.497846i	−0.685764	+	0.727824i	$0.740532\pi$
$570$		0			0
$571$	11988.2			0.878618			0.439309	−	0.898336i	$-0.355223\pi$
$571$	11988.2			0.878618			0.439309	+	0.898336i	$0.355223\pi$
$572$		0			0
$573$	6830.43			0.497985
$574$		0			0
$575$	−1685.07	−	2918.63i	−0.122213	−	0.211678i
$576$		0			0
$577$		−	5576.90i		−	0.402374i	−0.979553	−	0.201187i	$-0.935520\pi$
$577$		−	5576.90i		−	0.402374i	0.979553	−	0.201187i	$-0.0644798\pi$
$578$		0			0
$579$	10190.8	+	5883.63i	0.731456	+	0.422306i
$580$		0			0
$581$	−21754.1	+	37679.1i	−1.55337	+	2.69052i
$582$		0			0
$583$	−3623.74	+	2092.17i	−0.257427	+	0.148626i
$584$		0			0
$585$	−5096.29	−	83.6567i	−0.360181	−	0.00591245i
$586$		0			0
$587$	23169.7	−	13377.0i	1.62916	−	0.940593i	0.644810	−	0.764343i	$-0.276936\pi$
$587$	23169.7	−	13377.0i	1.62916	−	0.940593i	0.984345	−	0.176251i	$-0.0563969\pi$
$588$		0			0
$589$	11755.2	−	20360.6i	0.822353	−	1.42436i
$590$		0			0
$591$	13154.6	+	7594.84i	0.915584	+	0.528612i
$592$		0			0
$593$		−	3589.40i		−	0.248565i	−0.992247	−	0.124283i	$-0.960337\pi$
$593$		−	3589.40i		−	0.248565i	0.992247	−	0.124283i	$-0.0396629\pi$
$594$		0			0
$595$	9100.26	+	15762.1i	0.627016	+	1.08602i
$596$		0			0
$597$	−9810.18			−0.672536
$598$		0			0
$599$	7462.78			0.509050			0.254525	−	0.967066i	$-0.418081\pi$
$599$	7462.78			0.509050			0.254525	+	0.967066i	$0.418081\pi$
$600$		0			0
$601$	8255.52	+	14299.0i	0.560316	+	0.970495i	0.997469	+	0.0711081i	$0.0226535\pi$
$601$	8255.52	+	14299.0i	0.560316	+	0.970495i	−0.437153	+	0.899387i	$0.644013\pi$
$602$		0			0
$603$		−	4834.15i		−	0.326471i
$604$		0			0
$605$	5686.35	+	3283.02i	0.382121	+	0.220618i
$606$		0			0
$607$	−5976.78	+	10352.1i	−0.399654	+	0.692222i	−0.993683	−	0.112222i	$-0.964203\pi$
$607$	−5976.78	+	10352.1i	−0.399654	+	0.692222i	0.594029	+	0.804444i	$0.297536\pi$
$608$		0			0
$609$	10824.5	−	6249.51i	0.720246	−	0.415834i
$610$		0			0
$611$	840.773	+	1513.08i	0.0556695	+	0.100185i
$612$		0			0
$613$	3962.63	−	2287.82i	0.261091	−	0.150741i	−0.363741	−	0.931500i	$-0.618501\pi$
$613$	3962.63	−	2287.82i	0.261091	−	0.150741i	0.624832	+	0.780759i	$0.285167\pi$
$614$		0			0
$615$	5362.83	−	9288.70i	0.351627	−	0.609035i
$616$		0			0
$617$	−16654.6	−	9615.51i	−1.08669	−	0.627400i	−0.153996	−	0.988071i	$-0.549214\pi$
$617$	−16654.6	−	9615.51i	−1.08669	−	0.627400i	−0.932693	+	0.360671i	$0.882548\pi$
$618$		0			0
$619$			11715.6i			0.760727i	0.924837	+	0.380363i	$0.124201\pi$
$619$			11715.6i			0.760727i	−0.924837	+	0.380363i	$0.875799\pi$
$620$		0			0
$621$	−2167.99	−	3755.07i	−0.140094	−	0.242650i
$622$		0			0
$623$	−9959.17			−0.640459
$624$		0			0
$625$	−17807.8			−1.13970
$626$		0			0
$627$	4426.26	+	7666.51i	0.281926	+	0.488311i
$628$		0			0
$629$		−	11567.3i		−	0.733256i
$630$		0			0
$631$	−7603.78	−	4390.04i	−0.479717	−	0.276965i	0.240581	−	0.970629i	$-0.422662\pi$
$631$	−7603.78	−	4390.04i	−0.479717	−	0.276965i	−0.720299	+	0.693664i	$0.755995\pi$
$632$		0			0
$633$	4218.27	−	7306.25i	0.264867	−	0.458764i
$634$		0			0
$635$	−24167.1	+	13952.9i	−1.51030	+	0.871973i
$636$		0			0
$637$	−21761.8	−	13045.0i	−1.35359	−	0.811403i
$638$		0			0
$639$	800.691	−	462.279i	0.0495694	−	0.0286189i
$640$		0			0
$641$	12495.9	−	21643.5i	0.769980	−	1.33364i	−0.167593	−	0.985856i	$-0.553599\pi$
$641$	12495.9	−	21643.5i	0.769980	−	1.33364i	0.937573	−	0.347789i	$-0.113067\pi$
$642$		0			0
$643$	2038.50	+	1176.93i	0.125024	+	0.0721827i	0.561208	−	0.827675i	$-0.310337\pi$
$643$	2038.50	+	1176.93i	0.125024	+	0.0721827i	−0.436184	+	0.899858i	$0.643670\pi$
$644$		0			0
$645$			6963.24i			0.425081i
$646$		0			0
$647$	2955.40	+	5118.90i	0.179581	+	0.311043i	0.941737	−	0.336350i	$-0.109193\pi$
$647$	2955.40	+	5118.90i	0.179581	+	0.311043i	−0.762156	+	0.647393i	$0.775859\pi$
$648$		0			0
$649$	−12316.2			−0.744918
$650$		0			0
$651$	−19947.2			−1.20091
$652$		0			0
$653$	−2962.17	−	5130.63i	−0.177517	−	0.307469i	0.763512	−	0.645793i	$-0.223473\pi$
$653$	−2962.17	−	5130.63i	−0.177517	−	0.307469i	−0.941029	+	0.338325i	$0.890140\pi$
$654$		0			0
$655$		−	17450.2i		−	1.04097i
$656$		0			0
$657$	588.627	+	339.844i	0.0349536	+	0.0201805i
$658$		0			0
$659$	−6419.77	+	11119.4i	−0.379482	+	0.657282i	−0.990987	−	0.133958i	$-0.957231\pi$
$659$	−6419.77	+	11119.4i	−0.379482	+	0.657282i	0.611505	+	0.791241i	$0.290564\pi$
$660$		0			0
$661$	8890.18	−	5132.75i	0.523129	−	0.302028i	−0.215085	−	0.976595i	$-0.569003\pi$
$661$	8890.18	−	5132.75i	0.523129	−	0.302028i	0.738214	+	0.674567i	$0.235670\pi$
$662$		0			0
$663$	6226.33	−	3459.78i	0.364722	−	0.202665i
$664$		0			0
$665$	−32718.2	+	18889.9i	−1.90791	+	1.10153i
$666$		0			0
$667$	11249.9	−	19485.4i	0.653069	−	1.13115i
$668$		0			0
$669$	−2384.35	−	1376.60i	−0.137794	−	0.0795555i
$670$		0			0
$671$		−	8030.27i		−	0.462004i
$672$		0			0
$673$	4931.41	+	8541.45i	0.282454	+	0.489225i	0.971989	−	0.235028i	$-0.0755181\pi$
$673$	4931.41	+	8541.45i	0.282454	+	0.489225i	−0.689534	+	0.724253i	$0.742185\pi$
$674$		0			0
$675$	566.614			0.0323096
$676$		0			0
$677$	32615.5			1.85158			0.925788	−	0.378043i	$-0.123403\pi$
$677$	32615.5			1.85158			0.925788	+	0.378043i	$0.123403\pi$
$678$		0			0
$679$	−11133.0	−	19282.9i	−0.629227	−	1.08985i
$680$		0			0
$681$			4009.17i			0.225597i
$682$		0			0
$683$	−18729.9	−	10813.7i	−1.04931	−	0.605820i	−0.126854	−	0.991921i	$-0.540488\pi$
$683$	−18729.9	−	10813.7i	−1.04931	−	0.605820i	−0.922456	+	0.386102i	$0.873821\pi$
$684$		0			0
$685$	4445.85	−	7700.44i	0.247981	−	0.429516i
$686$		0			0
$687$	−428.215	+	247.230i	−0.0237808	+	0.0137299i
$688$		0			0
$689$	−6108.95	+	3394.56i	−0.337783	+	0.187696i
$690$		0			0
$691$	12326.3	−	7116.57i	0.678601	−	0.391790i	−0.120727	−	0.992686i	$-0.538523\pi$
$691$	12326.3	−	7116.57i	0.678601	−	0.391790i	0.799328	+	0.600896i	$0.205189\pi$
$692$		0			0
$693$	3755.41	−	6504.56i	0.205853	−	0.356548i
$694$		0			0
$695$	15749.4	+	9092.90i	0.859579	+	0.496278i
$696$		0			0
$697$			14989.1i			0.814566i
$698$		0			0
$699$	6365.13	+	11024.7i	0.344423	+	0.596558i
$700$		0			0
$701$	28747.0			1.54887			0.774437	−	0.632651i	$-0.218033\pi$
$701$	28747.0			1.54887			0.774437	+	0.632651i	$0.218033\pi$
$702$		0			0
$703$	24010.8			1.28817
$704$		0			0
$705$	−669.307	−	1159.27i	−0.0357554	−	0.0619302i
$706$		0			0
$707$		−	23314.1i		−	1.24019i
$708$		0			0
$709$	1575.00	+	909.324i	0.0834276	+	0.0481670i	0.541133	−	0.840937i	$-0.317995\pi$
$709$	1575.00	+	909.324i	0.0834276	+	0.0481670i	−0.457706	+	0.889104i	$0.651329\pi$
$710$		0			0
$711$	78.9868	−	136.809i	0.00416630	−	0.00721624i
$712$		0			0
$713$	−31096.6	+	17953.6i	−1.63335	+	0.943014i
$714$		0			0
$715$	−13631.7	−	8171.47i	−0.713002	−	0.427407i
$716$		0			0
$717$	6471.98	−	3736.60i	0.337100	−	0.194625i
$718$		0			0
$719$	−13070.9	+	22639.5i	−0.677973	+	1.17428i	0.297617	+	0.954685i	$0.403808\pi$
$719$	−13070.9	+	22639.5i	−0.677973	+	1.17428i	−0.975590	+	0.219599i	$0.929525\pi$
$720$		0			0
$721$	10199.3	+	5888.58i	0.526827	+	0.304164i
$722$		0			0
$723$		−	8752.19i		−	0.450204i
$724$		0			0
$725$	1470.10	+	2546.29i	0.0753078	+	0.130437i
$726$		0			0
$727$	−1340.10			−0.0683652			−0.0341826	−	0.999416i	$-0.510883\pi$
$727$	−1340.10			−0.0683652			−0.0341826	+	0.999416i	$0.510883\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−4865.56	−	8427.39i	−0.246182	−	0.426400i
$732$		0			0
$733$			32517.1i			1.63854i	0.573409	+	0.819269i	$0.305620\pi$
$733$			32517.1i			1.63854i	−0.573409	+	0.819269i	$0.694380\pi$
$734$		0			0
$735$	16992.2	+	9810.47i	0.852746	+	0.492333i
$736$		0			0
$737$	7536.86	−	13054.2i	0.376694	−	0.652454i
$738$		0			0
$739$	19200.2	−	11085.3i	0.955741	−	0.551797i	0.0608813	−	0.998145i	$-0.480609\pi$
$739$	19200.2	−	11085.3i	0.955741	−	0.551797i	0.894860	+	0.446348i	$0.147276\pi$
$740$		0			0
$741$	7181.64	+	12924.3i	0.356038	+	0.640738i
$742$		0			0
$743$	−26316.6	+	15193.9i	−1.29941	+	0.750216i	−0.980303	−	0.197502i	$-0.936717\pi$
$743$	−26316.6	+	15193.9i	−1.29941	+	0.750216i	−0.319110	+	0.947718i	$0.603384\pi$
$744$		0			0
$745$	2584.70	−	4476.83i	0.127109	−	0.220159i
$746$		0			0
$747$	−11403.6	−	6583.87i	−0.558549	−	0.322478i
$748$		0			0
$749$		−	42720.3i		−	2.08407i
$750$		0			0
$751$	8449.17	+	14634.4i	0.410539	+	0.711074i	0.994949	−	0.100385i	$-0.0320074\pi$
$751$	8449.17	+	14634.4i	0.410539	+	0.711074i	−0.584410	+	0.811459i	$0.698674\pi$
$752$		0			0
$753$	3941.63			0.190758
$754$		0			0
$755$	19354.0			0.932934
$756$		0			0
$757$	−16462.9	−	28514.6i	−0.790428	−	1.36906i	−0.925702	−	0.378253i	$-0.876525\pi$
$757$	−16462.9	−	28514.6i	−0.790428	−	1.36906i	0.135275	−	0.990808i	$-0.456808\pi$
$758$		0			0
$759$		−	13520.4i		−	0.646585i
$760$		0			0
$761$	14542.3	+	8396.01i	0.692718	+	0.399941i	0.804630	−	0.593777i	$-0.202364\pi$
$761$	14542.3	+	8396.01i	0.692718	+	0.399941i	−0.111911	+	0.993718i	$0.535697\pi$
$762$		0			0
$763$	−29409.0	+	50937.8i	−1.39538	+	2.41687i
$764$		0			0
$765$	−4770.41	+	2754.20i	−0.225457	+	0.130168i
$766$		0			0
$767$	−20567.9	−	337.626i	−0.968270	−	0.0158944i
$768$		0			0
$769$	1335.04	−	770.783i	0.0626042	−	0.0361445i	−0.468371	−	0.883532i	$-0.655159\pi$
$769$	1335.04	−	770.783i	0.0626042	−	0.0361445i	0.530975	+	0.847387i	$0.321826\pi$
$770$		0			0
$771$	1481.37	−	2565.81i	0.0691963	−	0.119851i
$772$		0			0
$773$	−32970.6	−	19035.6i	−1.53411	−	0.885721i	−0.999166	−	0.0408357i	$-0.986998\pi$
$773$	−32970.6	−	19035.6i	−1.53411	−	0.885721i	−0.534948	−	0.844885i	$-0.679669\pi$
$774$		0			0
$775$		−	4692.26i		−	0.217485i
$776$		0			0
$777$	−10185.9	−	17642.4i	−0.470290	−	0.814566i
$778$		0			0
$779$	−31113.6			−1.43102
$780$		0			0
$781$	2882.93			0.132086
$782$		0			0
$783$	1891.42	+	3276.03i	0.0863266	+	0.149522i
$784$		0			0
$785$			8824.38i			0.401217i
$786$		0			0
$787$	17363.6	+	10024.9i	0.786463	+	0.454065i	0.838716	−	0.544569i	$-0.183307\pi$
$787$	17363.6	+	10024.9i	0.786463	+	0.454065i	−0.0522528	+	0.998634i	$0.516640\pi$
$788$		0			0
$789$	10479.7	−	18151.3i	0.472860	−	0.819017i
$790$		0			0
$791$	−3152.33	+	1820.00i	−0.141699	+	0.0818100i
$792$		0			0
$793$	220.136	−	13410.5i	0.00985781	−	0.600529i
$794$		0			0
$795$	4680.48	−	2702.28i	0.208804	−	0.120553i
$796$		0			0
$797$	−11200.9	+	19400.6i	−0.497813	+	0.862238i	−0.999997	−	0.00252302i	$-0.999197\pi$
$797$	−11200.9	+	19400.6i	−0.497813	+	0.862238i	0.502183	+	0.864761i	$0.332530\pi$
$798$		0			0
$799$	1620.08	+	935.355i	0.0717327	+	0.0414149i
$800$		0			0
$801$		−	3014.15i		−	0.132958i
$802$		0			0
$803$	1059.69	+	1835.44i	0.0465700	+	0.0806617i
$804$		0			0
$805$	57700.7			2.52631
$806$		0			0
$807$	17713.0			0.772649
$808$		0			0
$809$	20983.2	+	36343.9i	0.911903	+	1.57946i	0.811373	+	0.584528i	$0.198720\pi$
$809$	20983.2	+	36343.9i	0.911903	+	1.57946i	0.100530	+	0.994934i	$0.467946\pi$
$810$		0			0
$811$		−	13029.1i		−	0.564133i	−0.959395	−	0.282067i	$-0.908980\pi$
$811$		−	13029.1i		−	0.564133i	0.959395	−	0.282067i	$-0.0910199\pi$
$812$		0			0
$813$	5537.91	+	3197.31i	0.238897	+	0.137927i
$814$		0			0
$815$	11468.4	−	19863.9i	0.492909	−	0.853744i
$816$		0			0
$817$	17493.2	−	10099.7i	0.749092	−	0.432489i
$818$		0			0
$819$	6449.80	−	10759.6i	0.275182	−	0.459060i
$820$		0			0
$821$	−7706.01	+	4449.07i	−0.327578	+	0.189127i	−0.654765	−	0.755832i	$-0.727233\pi$
$821$	−7706.01	+	4449.07i	−0.327578	+	0.189127i	0.327187	+	0.944960i	$0.393899\pi$
$822$		0			0
$823$	−11361.8	+	19679.2i	−0.481224	+	0.833504i	−0.999768	−	0.0215466i	$-0.993141\pi$
$823$	−11361.8	+	19679.2i	−0.481224	+	0.833504i	0.518544	+	0.855051i	$0.326474\pi$
$824$		0			0
$825$	1530.09	+	883.401i	0.0645710	+	0.0372801i
$826$		0			0
$827$		−	19073.3i		−	0.801989i	−0.916081	−	0.400994i	$-0.868665\pi$
$827$		−	19073.3i		−	0.801989i	0.916081	−	0.400994i	$-0.131335\pi$
$828$		0			0
$829$	21251.9	+	36809.4i	0.890361	+	1.54215i	0.839443	+	0.543448i	$0.182881\pi$
$829$	21251.9	+	36809.4i	0.890361	+	1.54215i	0.0509178	+	0.998703i	$0.483785\pi$
$830$		0			0
$831$	12097.2			0.504992
$832$		0			0
$833$	−27420.2			−1.14052
$834$		0			0
$835$	8623.86	+	14937.0i	0.357414	+	0.619060i
$836$		0			0
$837$		−	6037.01i		−	0.249307i
$838$		0			0
$839$	−16824.5	−	9713.62i	−0.692307	−	0.399704i	0.112168	−	0.993689i	$-0.464220\pi$
$839$	−16824.5	−	9713.62i	−0.692307	−	0.399704i	−0.804476	+	0.593985i	$0.797554\pi$
$840$		0			0
$841$	2379.80	−	4121.94i	0.0975768	−	0.169008i
$842$		0			0
$843$	5971.13	−	3447.43i	0.243958	−	0.140849i
$844$		0			0
$845$	−22540.8	−	14020.0i	−0.917664	−	0.570770i
$846$		0			0
$847$	−13995.2	+	8080.15i	−0.567747	+	0.327789i
$848$		0			0
$849$	9985.20	−	17294.9i	0.403641	−	0.699127i
$850$		0			0
$851$	−31758.5	−	18335.8i	−1.27928	−	0.738592i
$852$		0			0
$853$			26851.8i			1.07783i	0.842361	+	0.538914i	$0.181165\pi$
$853$			26851.8i			1.07783i	−0.842361	+	0.538914i	$0.818835\pi$
$854$		0			0
$855$	−5717.03	−	9902.18i	−0.228676	−	0.396079i
$856$		0			0
$857$	−41539.4			−1.65573			−0.827864	−	0.560929i	$-0.810444\pi$
$857$	−41539.4			−1.65573			−0.827864	+	0.560929i	$0.810444\pi$
$858$		0			0
$859$	11936.2			0.474107			0.237054	−	0.971497i	$-0.423818\pi$
$859$	11936.2			0.474107			0.237054	+	0.971497i	$0.423818\pi$
$860$		0			0
$861$	13199.0	+	22861.3i	0.522439	+	0.904892i
$862$		0			0
$863$			41128.6i			1.62229i	0.584848	+	0.811143i	$0.301154\pi$
$863$			41128.6i			1.62229i	−0.584848	+	0.811143i	$0.698846\pi$
$864$		0			0
$865$	21392.0	+	12350.7i	0.840866	+	0.485474i
$866$		0			0
$867$	−3520.52	+	6097.72i	−0.137904	+	0.238857i
$868$		0			0
$869$	426.595	−	246.295i	0.0166528	−	0.00961448i
$870$		0			0
$871$	12944.3	−	21593.8i	0.503561	−	0.840044i
$872$		0			0
$873$	5835.98	−	3369.40i	0.226252	−	0.130627i
$874$		0			0
$875$	18686.1	−	32365.4i	0.721951	−	1.25046i
$876$		0			0
$877$	−5548.50	−	3203.43i	−0.213637	−	0.123343i	0.389364	−	0.921084i	$-0.372695\pi$
$877$	−5548.50	−	3203.43i	−0.213637	−	0.123343i	−0.603001	+	0.797741i	$0.706028\pi$
$878$		0			0
$879$		−	22401.0i		−	0.859574i
$880$		0			0
$881$	−1469.04	−	2544.45i	−0.0561783	−	0.0973037i	0.836569	−	0.547862i	$-0.184558\pi$
$881$	−1469.04	−	2544.45i	−0.0561783	−	0.0973037i	−0.892747	+	0.450559i	$0.851225\pi$
$882$		0			0
$883$	3022.06			0.115176			0.0575881	−	0.998340i	$-0.481659\pi$
$883$	3022.06			0.115176			0.0575881	+	0.998340i	$0.481659\pi$
$884$		0			0
$885$	15907.8			0.604219
$886$		0			0
$887$	−5030.22	−	8712.59i	−0.190415	−	0.329809i	0.754973	−	0.655756i	$-0.227650\pi$
$887$	−5030.22	−	8712.59i	−0.190415	−	0.329809i	−0.945388	+	0.325948i	$0.894317\pi$
$888$		0			0
$889$		−	68681.5i		−	2.59112i
$890$		0			0
$891$	1968.61	+	1136.57i	0.0740188	+	0.0427348i
$892$		0			0
$893$	−1941.57	+	3362.89i	−0.0727570	+	0.126019i
$894$		0			0
$895$	40700.9	−	23498.7i	1.52009	−	0.877624i
$896$		0			0
$897$	370.637	−	22578.9i	0.0137962	−	0.840453i
$898$		0			0
$899$	27129.5	−	15663.2i	1.00647	−	0.581088i
$900$		0			0
$901$	−3776.42	+	6540.95i	−0.139635	+	0.241854i
$902$		0			0
$903$	−14841.9	−	8568.96i	−0.546962	−	0.315788i
$904$		0			0
$905$		−	29928.4i		−	1.09929i
$906$		0			0
$907$	21579.3	+	37376.5i	0.789999	+	1.36832i	0.925967	+	0.377606i	$0.123252\pi$
$907$	21579.3	+	37376.5i	0.789999	+	1.36832i	−0.135967	+	0.990713i	$0.543414\pi$
$908$		0			0
$909$	7056.02			0.257462
$910$		0			0
$911$	32665.9			1.18800			0.594001	−	0.804464i	$-0.297547\pi$
$911$	32665.9			1.18800			0.594001	+	0.804464i	$0.297547\pi$
$912$		0			0
$913$	−20529.7	−	35558.4i	−0.744176	−	1.28895i
$914$		0			0
$915$			10372.0i			0.374741i
$916$		0			0
$917$	37194.4	+	21474.2i	1.33944	+	0.773327i
$918$		0			0
$919$	9494.97	−	16445.8i	0.340816	−	0.590311i	−0.643768	−	0.765221i	$-0.722630\pi$
$919$	9494.97	−	16445.8i	0.340816	−	0.590311i	0.984585	+	0.174909i	$0.0559632\pi$
$920$		0			0
$921$	−10303.9	+	5948.98i	−0.368650	+	0.212840i
$922$		0			0
$923$	4814.47	+	79.0305i	0.171690	+	0.00281833i
$924$		0			0
$925$	4150.10	−	2396.06i	0.147518	−	0.0851698i
$926$		0			0
$927$	−1782.18	+	3086.83i	−0.0631440	+	0.109369i
$928$		0			0
$929$	−4846.98	−	2798.40i	−0.171178	−	0.0988295i	0.411963	−	0.911200i	$-0.364843\pi$
$929$	−4846.98	−	2798.40i	−0.171178	−	0.0988295i	−0.583141	+	0.812371i	$0.698177\pi$
$930$		0			0
$931$		−	56917.6i		−	2.00365i
$932$		0			0
$933$	11058.4	+	19153.8i	0.388035	+	0.672097i
$934$		0			0
$935$	−17176.1			−0.600770
$936$		0			0
$937$	40294.4			1.40487			0.702433	−	0.711750i	$-0.252097\pi$
$937$	40294.4			1.40487			0.702433	+	0.711750i	$0.252097\pi$
$938$		0			0
$939$	12374.3	+	21432.9i	0.430054	+	0.744875i
$940$		0			0
$941$		−	43648.8i		−	1.51213i	−0.654499	−	0.756063i	$-0.727120\pi$
$941$		−	43648.8i		−	1.51213i	0.654499	−	0.756063i	$-0.272880\pi$
$942$		0			0
$943$	41153.1	+	23759.8i	1.42113	+	0.820492i
$944$		0			0
$945$	−4850.54	+	8401.39i	−0.166972	+	0.289203i
$946$		0			0
$947$	9081.62	−	5243.28i	0.311629	−	0.179919i	−0.336026	−	0.941853i	$-0.609083\pi$
$947$	9081.62	−	5243.28i	0.311629	−	0.179919i	0.647655	+	0.761933i	$0.275750\pi$
$948$		0			0
$949$	1719.36	+	3094.22i	0.0588122	+	0.105840i
$950$		0			0
$951$	−14485.0	+	8362.90i	−0.493909	+	0.285158i
$952$		0			0
$953$	16529.4	−	28629.7i	0.561846	−	0.973145i	−0.435490	−	0.900194i	$-0.643425\pi$
$953$	16529.4	−	28629.7i	0.561846	−	0.973145i	0.997335	−	0.0729517i	$-0.0232419\pi$
$954$		0			0
$955$	−23823.9	−	13754.7i	−0.807249	−	0.466065i
$956$		0			0
$957$			11795.5i			0.398428i
$958$		0			0
$959$	10942.1	+	18952.3i	0.368445	+	0.638166i
$960$		0			0
$961$	−20202.8			−0.678152
$962$		0			0
$963$	12929.3			0.432650
$964$		0			0
$965$	−23696.2	−	41043.1i	−0.790476	−	1.36914i
$966$		0			0
$967$		−	53634.9i		−	1.78364i	−0.452389	−	0.891821i	$-0.649428\pi$
$967$		−	53634.9i		−	1.78364i	0.452389	−	0.891821i	$-0.350572\pi$
$968$		0			0
$969$	13838.3	+	7989.53i	0.458771	+	0.264872i
$970$		0			0
$971$	−2043.40	+	3539.27i	−0.0675344	+	0.116973i	−0.897815	−	0.440372i	$-0.854847\pi$
$971$	−2043.40	+	3539.27i	−0.0675344	+	0.116973i	0.830281	+	0.557345i	$0.188180\pi$
$972$		0			0
$973$	−38762.3	+	22379.4i	−1.27715	+	0.737360i
$974$		0			0
$975$	2531.02	+	1517.21i	0.0831361	+	0.0498356i
$976$		0			0
$977$	−12454.3	+	7190.48i	−0.407827	+	0.235459i	−0.689856	−	0.723947i	$-0.742326\pi$
$977$	−12454.3	+	7190.48i	−0.407827	+	0.235459i	0.282028	+	0.959406i	$0.408993\pi$
$978$		0			0
$979$	4699.32	−	8139.46i	0.153413	−	0.265718i
$980$		0			0
$981$	−15416.3	−	8900.63i	−0.501739	−	0.289679i
$982$		0			0
$983$			12916.5i			0.419099i	0.977798	+	0.209549i	$0.0671997\pi$
$983$			12916.5i			0.419099i	−0.977798	+	0.209549i	$0.932800\pi$
$984$		0			0
$985$	−30588.1	−	52980.1i	−0.989460	−	1.71379i
$986$		0			0
$987$	3294.59			0.106249
$988$		0			0
$989$	−30850.3			−0.991893
$990$		0			0
$991$	−2919.49	−	5056.71i	−0.0935829	−	0.162090i	0.815433	−	0.578851i	$-0.196499\pi$
$991$	−2919.49	−	5056.71i	−0.0935829	−	0.162090i	−0.909016	+	0.416761i	$0.863165\pi$
$992$		0			0
$993$			12472.1i			0.398580i
$994$		0			0
$995$	34217.0	+	19755.2i	1.09020	+	0.629428i
$996$		0			0
$997$	−22145.1	+	38356.4i	−0.703452	+	1.21841i	0.263796	+	0.964579i	$0.415026\pi$
$997$	−22145.1	+	38356.4i	−0.703452	+	1.21841i	−0.967247	+	0.253835i	$0.918308\pi$
$998$		0			0
$999$	5339.48	−	3082.75i	0.169103	−	0.0976315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.bv.h.49.2		10
4.3	odd	2		39.4.j.c.10.2	yes	10
12.11	even	2		117.4.q.e.10.4		10
13.4	even	6	inner	624.4.bv.h.433.4		10
52.3	odd	6		507.4.b.i.337.4		10
52.11	even	12		507.4.a.r.1.7		10
52.15	even	12		507.4.a.r.1.4		10
52.23	odd	6		507.4.b.i.337.7		10
52.43	odd	6		39.4.j.c.4.2	✓	10
156.11	odd	12		1521.4.a.bk.1.4		10
156.95	even	6		117.4.q.e.82.4		10
156.119	odd	12		1521.4.a.bk.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.2	✓	10	52.43	odd	6
39.4.j.c.10.2	yes	10	4.3	odd	2
117.4.q.e.10.4		10	12.11	even	2
117.4.q.e.82.4		10	156.95	even	6
507.4.a.r.1.4		10	52.15	even	12
507.4.a.r.1.7		10	52.11	even	12
507.4.b.i.337.4		10	52.3	odd	6
507.4.b.i.337.7		10	52.23	odd	6
624.4.bv.h.49.2		10	1.1	even	1	trivial
624.4.bv.h.433.4		10	13.4	even	6	inner
1521.4.a.bk.1.4		10	156.11	odd	12
1521.4.a.bk.1.7		10	156.119	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} -12.0825i q^{5} +(25.7533 + 14.8686i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} -12.0825i q^{5} +(25.7533 + 14.8686i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-24.3038 + 14.0318i) q^{11} +(-40.9717 + 22.7667i) q^{13} +(31.3911 - 18.1237i) q^{15} +(-25.3278 + 43.8690i) q^{17} +(-91.0612 - 52.5742i) q^{19} +89.2119i q^{21} +(80.2961 + 139.077i) q^{23} -20.9857 q^{25} -27.0000 q^{27} +(-70.0525 - 121.334i) q^{29} +223.593i q^{31} +(-72.9113 - 42.0954i) q^{33} +(179.650 - 311.163i) q^{35} +(-197.759 + 114.176i) q^{37} +(-120.607 - 72.2975i) q^{39} +(256.259 - 147.951i) q^{41} +(-96.0517 + 166.366i) q^{43} +(94.1734 + 54.3710i) q^{45} -36.9300i q^{47} +(270.653 + 468.785i) q^{49} -151.967 q^{51} +149.102 q^{53} +(169.538 + 293.649i) q^{55} -315.445i q^{57} +(380.070 + 219.433i) q^{59} +(-143.073 + 247.809i) q^{61} +(-231.779 + 133.818i) q^{63} +(275.077 + 495.038i) q^{65} +(-465.166 + 268.564i) q^{67} +(-240.888 + 417.231i) q^{69} +(-88.9656 - 51.3643i) q^{71} -75.5209i q^{73} +(-31.4786 - 54.5225i) q^{75} -834.535 q^{77} -17.5526 q^{79} +(-40.5000 - 70.1481i) q^{81} +1463.08i q^{83} +(530.045 + 306.022i) q^{85} +(210.157 - 364.003i) q^{87} +(-290.036 + 167.453i) q^{89} +(-1393.66 - 22.8773i) q^{91} +(-580.912 + 335.390i) q^{93} +(-635.225 + 1100.24i) q^{95} +(-648.442 - 374.378i) q^{97} -252.572i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Introduction

L-functions

Modular forms

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Database

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