LMFDB - Embedded newform 336.4.q.k.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.9924270768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 $ x^6 - x^5 + 25x^4 + 12x^3 + 582x^2 - 144x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-2.27818 + 3.94593i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.4.q.k.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +(-8.93660 + 15.4786i) q^{5} +(-2.26047 + 18.3818i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +(-8.93660 + 15.4786i) q^{5} +(-2.26047 + 18.3818i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-5.69708 - 9.86762i) q^{11} -13.0987 q^{13} +53.6196 q^{15} +(-26.6337 - 46.1309i) q^{17} +(-21.2111 + 36.7388i) q^{19} +(51.1480 - 21.6998i) q^{21} +(76.0427 - 131.710i) q^{23} +(-97.2257 - 168.400i) q^{25} +27.0000 q^{27} +186.493 q^{29} +(-78.9369 - 136.723i) q^{31} +(-17.0912 + 29.6029i) q^{33} +(-264.324 - 199.260i) q^{35} +(-1.87294 + 3.24403i) q^{37} +(19.6480 + 34.0313i) q^{39} -39.3230 q^{41} -429.439 q^{43} +(-80.4294 - 139.308i) q^{45} +(10.5934 - 18.3484i) q^{47} +(-332.781 - 83.1031i) q^{49} +(-79.9010 + 138.393i) q^{51} +(-182.952 - 316.882i) q^{53} +203.650 q^{55} +127.267 q^{57} +(-113.289 - 196.222i) q^{59} +(-325.987 + 564.626i) q^{61} +(-133.100 - 100.337i) q^{63} +(117.058 - 202.750i) q^{65} +(72.7166 + 125.949i) q^{67} -456.256 q^{69} +368.962 q^{71} +(-304.453 - 527.328i) q^{73} +(-291.677 + 505.200i) q^{75} +(194.263 - 82.4170i) q^{77} +(455.119 - 788.289i) q^{79} +(-40.5000 - 70.1481i) q^{81} +327.929 q^{83} +952.058 q^{85} +(-279.740 - 484.524i) q^{87} +(18.8059 - 32.5728i) q^{89} +(29.6092 - 240.777i) q^{91} +(-236.811 + 410.168i) q^{93} +(-379.111 - 656.640i) q^{95} +722.013 q^{97} +102.547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 11 q^{5} + 13 q^{7} - 27 q^{9}+O(q^{10}) $ 6 * q - 9 * q^3 - 11 * q^5 + 13 * q^7 - 27 * q^9	$ 6 q - 9 q^{3} - 11 q^{5} + 13 q^{7} - 27 q^{9} + 35 q^{11} + 124 q^{13} + 66 q^{15} - 48 q^{17} - 202 q^{19} + 3 q^{21} + 216 q^{23} - 130 q^{25} + 162 q^{27} + 106 q^{29} - 95 q^{31} + 105 q^{33} - 56 q^{35} - 262 q^{37} - 186 q^{39} + 488 q^{41} - 720 q^{43} - 99 q^{45} - 210 q^{47} - 303 q^{49} - 144 q^{51} - 393 q^{53} + 2062 q^{55} + 1212 q^{57} + 1143 q^{59} + 70 q^{61} - 126 q^{63} + 472 q^{65} - 628 q^{67} - 1296 q^{69} - 636 q^{71} - 988 q^{73} - 390 q^{75} + 1073 q^{77} + 861 q^{79} - 243 q^{81} - 1038 q^{83} + 3600 q^{85} - 159 q^{87} - 1766 q^{89} + 654 q^{91} - 285 q^{93} - 736 q^{95} + 38 q^{97} - 630 q^{99}+O(q^{100}) $ 6 * q - 9 * q^3 - 11 * q^5 + 13 * q^7 - 27 * q^9 + 35 * q^11 + 124 * q^13 + 66 * q^15 - 48 * q^17 - 202 * q^19 + 3 * q^21 + 216 * q^23 - 130 * q^25 + 162 * q^27 + 106 * q^29 - 95 * q^31 + 105 * q^33 - 56 * q^35 - 262 * q^37 - 186 * q^39 + 488 * q^41 - 720 * q^43 - 99 * q^45 - 210 * q^47 - 303 * q^49 - 144 * q^51 - 393 * q^53 + 2062 * q^55 + 1212 * q^57 + 1143 * q^59 + 70 * q^61 - 126 * q^63 + 472 * q^65 - 628 * q^67 - 1296 * q^69 - 636 * q^71 - 988 * q^73 - 390 * q^75 + 1073 * q^77 + 861 * q^79 - 243 * q^81 - 1038 * q^83 + 3600 * q^85 - 159 * q^87 - 1766 * q^89 + 654 * q^91 - 285 * q^93 - 736 * q^95 + 38 * q^97 - 630 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$		0			0
$5$	−8.93660	+	15.4786i	−0.799314	+	1.38445i	0.120749	+	0.992683i	$0.461470\pi$
$5$	−8.93660	+	15.4786i	−0.799314	+	1.38445i	−0.920063	+	0.391769i	$0.871863\pi$
$6$		0			0
$7$	−2.26047	+	18.3818i	−0.122054	+	0.992523i
$7$	−2.26047	+	18.3818i	−0.122054	+	0.992523i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−5.69708	−	9.86762i	−0.156158	−	0.270473i	0.777322	−	0.629102i	$-0.216577\pi$
$11$	−5.69708	−	9.86762i	−0.156158	−	0.270473i	−0.933480	+	0.358630i	$0.883244\pi$
$12$		0			0
$13$	−13.0987			−0.279455			−0.139728	−	0.990190i	$-0.544623\pi$
$13$	−13.0987			−0.279455			−0.139728	+	0.990190i	$0.544623\pi$
$14$		0			0
$15$	53.6196			0.922968
$16$		0			0
$17$	−26.6337	−	46.1309i	−0.379977	−	0.658140i	0.611081	−	0.791568i	$-0.290735\pi$
$17$	−26.6337	−	46.1309i	−0.379977	−	0.658140i	−0.991059	+	0.133428i	$0.957402\pi$
$18$		0			0
$19$	−21.2111	+	36.7388i	−0.256114	+	0.443603i	−0.965198	−	0.261522i	$-0.915776\pi$
$19$	−21.2111	+	36.7388i	−0.256114	+	0.443603i	0.709083	+	0.705125i	$0.249109\pi$
$20$		0			0
$21$	51.1480	−	21.6998i	0.531496	−	0.225490i
$22$		0			0
$23$	76.0427	−	131.710i	0.689391	−	1.19406i	−0.282644	−	0.959225i	$-0.591211\pi$
$23$	76.0427	−	131.710i	0.689391	−	1.19406i	0.972035	−	0.234836i	$-0.0754553\pi$
$24$		0			0
$25$	−97.2257	−	168.400i	−0.777806	−	1.34720i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	186.493			1.19417			0.597085	−	0.802178i	$-0.296325\pi$
$29$	186.493			1.19417			0.597085	+	0.802178i	$0.296325\pi$
$30$		0			0
$31$	−78.9369	−	136.723i	−0.457338	−	0.792133i	0.541481	−	0.840713i	$-0.317864\pi$
$31$	−78.9369	−	136.723i	−0.457338	−	0.792133i	−0.998819	+	0.0485801i	$0.984530\pi$
$32$		0			0
$33$	−17.0912	+	29.6029i	−0.0901576	+	0.156158i
$34$		0			0
$35$	−264.324	−	199.260i	−1.27654	−	0.962316i
$36$		0			0
$37$	−1.87294	+	3.24403i	−0.00832188	+	0.0144139i	−0.870156	−	0.492776i	$-0.835982\pi$
$37$	−1.87294	+	3.24403i	−0.00832188	+	0.0144139i	0.861834	+	0.507190i	$0.169316\pi$
$38$		0			0
$39$	19.6480	+	34.0313i	0.0806718	+	0.139728i
$40$		0			0
$41$	−39.3230			−0.149786			−0.0748930	−	0.997192i	$-0.523862\pi$
$41$	−39.3230			−0.149786			−0.0748930	+	0.997192i	$0.523862\pi$
$42$		0			0
$43$	−429.439			−1.52300			−0.761498	−	0.648168i	$-0.775536\pi$
$43$	−429.439			−1.52300			−0.761498	+	0.648168i	$0.775536\pi$
$44$		0			0
$45$	−80.4294	−	139.308i	−0.266438	−	0.461484i
$46$		0			0
$47$	10.5934	−	18.3484i	0.0328768	−	0.0569444i	−0.849119	−	0.528202i	$-0.822866\pi$
$47$	10.5934	−	18.3484i	0.0328768	−	0.0569444i	0.881996	+	0.471258i	$0.156200\pi$
$48$		0			0
$49$	−332.781	−	83.1031i	−0.970206	−	0.242283i
$50$		0			0
$51$	−79.9010	+	138.393i	−0.219380	+	0.379977i
$52$		0			0
$53$	−182.952	−	316.882i	−0.474158	−	0.821266i	0.525404	−	0.850853i	$-0.323914\pi$
$53$	−182.952	−	316.882i	−0.474158	−	0.821266i	−0.999562	+	0.0295866i	$0.990581\pi$
$54$		0			0
$55$	203.650			0.499276
$56$		0			0
$57$	127.267			0.295735
$58$		0			0
$59$	−113.289	−	196.222i	−0.249982	−	0.432982i	0.713538	−	0.700616i	$-0.247091\pi$
$59$	−113.289	−	196.222i	−0.249982	−	0.432982i	−0.963521	+	0.267634i	$0.913758\pi$
$60$		0			0
$61$	−325.987	+	564.626i	−0.684235	+	1.18513i	0.289442	+	0.957196i	$0.406530\pi$
$61$	−325.987	+	564.626i	−0.684235	+	1.18513i	−0.973677	+	0.227934i	$0.926803\pi$
$62$		0			0
$63$	−133.100	−	100.337i	−0.266174	−	0.200655i
$64$		0			0
$65$	117.058	−	202.750i	0.223372	−	0.386892i
$66$		0			0
$67$	72.7166	+	125.949i	0.132593	+	0.229658i	0.924675	−	0.380756i	$-0.124336\pi$
$67$	72.7166	+	125.949i	0.132593	+	0.229658i	−0.792082	+	0.610414i	$0.791003\pi$
$68$		0			0
$69$	−456.256			−0.796041
$70$		0			0
$71$	368.962			0.616728			0.308364	−	0.951268i	$-0.400218\pi$
$71$	368.962			0.616728			0.308364	+	0.951268i	$0.400218\pi$
$72$		0			0
$73$	−304.453	−	527.328i	−0.488130	−	0.845466i	0.511777	−	0.859119i	$-0.328988\pi$
$73$	−304.453	−	527.328i	−0.488130	−	0.845466i	−0.999907	+	0.0136522i	$0.995654\pi$
$74$		0			0
$75$	−291.677	+	505.200i	−0.449066	+	0.777806i
$76$		0			0
$77$	194.263	−	82.4170i	0.287510	−	0.121978i
$78$		0			0
$79$	455.119	−	788.289i	0.648163	−	1.12265i	−0.335399	−	0.942076i	$-0.608871\pi$
$79$	455.119	−	788.289i	0.648163	−	1.12265i	0.983561	−	0.180574i	$-0.0577957\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	327.929			0.433674			0.216837	−	0.976208i	$-0.430426\pi$
$83$	327.929			0.433674			0.216837	+	0.976208i	$0.430426\pi$
$84$		0			0
$85$	952.058			1.21489
$86$		0			0
$87$	−279.740	−	484.524i	−0.344727	−	0.597085i
$88$		0			0
$89$	18.8059	−	32.5728i	0.0223980	−	0.0387945i	−0.854609	−	0.519272i	$-0.826203\pi$
$89$	18.8059	−	32.5728i	0.0223980	−	0.0387945i	0.877007	+	0.480477i	$0.159537\pi$
$90$		0			0
$91$	29.6092	−	240.777i	0.0341086	−	0.277366i
$92$		0			0
$93$	−236.811	+	410.168i	−0.264044	+	0.457338i
$94$		0			0
$95$	−379.111	−	656.640i	−0.409431	−	0.709156i
$96$		0			0
$97$	722.013			0.755766			0.377883	−	0.925853i	$-0.376652\pi$
$97$	722.013			0.755766			0.377883	+	0.925853i	$0.376652\pi$
$98$		0			0
$99$	102.547			0.104105
$100$		0			0
$101$	−759.336	−	1315.21i	−0.748087	−	1.29572i	−0.948739	−	0.316062i	$-0.897639\pi$
$101$	−759.336	−	1315.21i	−0.748087	−	1.29572i	0.200652	−	0.979663i	$-0.435694\pi$
$102$		0			0
$103$	−525.942	+	910.957i	−0.503132	+	0.871450i	0.496862	+	0.867830i	$0.334486\pi$
$103$	−525.942	+	910.957i	−0.503132	+	0.871450i	−0.999993	+	0.00361990i	$0.998848\pi$
$104$		0			0
$105$	−121.206	+	985.625i	−0.112652	+	0.916068i
$106$		0			0
$107$	383.260	−	663.826i	0.346273	−	0.599762i	−0.639312	−	0.768948i	$-0.720781\pi$
$107$	383.260	−	663.826i	0.346273	−	0.599762i	0.985584	+	0.169186i	$0.0541139\pi$
$108$		0			0
$109$	713.524	+	1235.86i	0.627002	+	1.08600i	0.988150	+	0.153491i	$0.0490516\pi$
$109$	713.524	+	1235.86i	0.627002	+	1.08600i	−0.361148	+	0.932509i	$0.617615\pi$
$110$		0			0
$111$	11.2376			0.00960928
$112$		0			0
$113$	362.564			0.301833			0.150917	−	0.988546i	$-0.451778\pi$
$113$	362.564			0.301833			0.150917	+	0.988546i	$0.451778\pi$
$114$		0			0
$115$	1359.13	+	2354.08i	1.10208	+	1.90886i
$116$		0			0
$117$	58.9440	−	102.094i	0.0465759	−	0.0806718i
$118$		0			0
$119$	908.173	−	385.297i	0.699597	−	0.296808i
$120$		0			0
$121$	600.587	−	1040.25i	0.451230	−	0.781553i
$122$		0			0
$123$	58.9845	+	102.164i	0.0432395	+	0.0748930i
$124$		0			0
$125$	1241.32			0.888216
$126$		0			0
$127$	−974.777			−0.681082			−0.340541	−	0.940230i	$-0.610610\pi$
$127$	−974.777			−0.681082			−0.340541	+	0.940230i	$0.610610\pi$
$128$		0			0
$129$	644.158	+	1115.71i	0.439651	+	0.761498i
$130$		0			0
$131$	−896.351	+	1552.53i	−0.597821	+	1.03546i	0.395321	+	0.918543i	$0.370633\pi$
$131$	−896.351	+	1552.53i	−0.597821	+	1.03546i	−0.993142	+	0.116914i	$0.962700\pi$
$132$		0			0
$133$	−627.377	−	472.946i	−0.409026	−	0.308343i
$134$		0			0
$135$	−241.288	+	417.924i	−0.153828	+	0.266438i
$136$		0			0
$137$	−842.208	−	1458.75i	−0.525217	−	0.909702i	−0.999569	−	0.0293665i	$-0.990651\pi$
$137$	−842.208	−	1458.75i	−0.525217	−	0.909702i	0.474352	−	0.880335i	$-0.342682\pi$
$138$		0			0
$139$	−315.089			−0.192270			−0.0961350	−	0.995368i	$-0.530648\pi$
$139$	−315.089			−0.192270			−0.0961350	+	0.995368i	$0.530648\pi$
$140$		0			0
$141$	−63.5606			−0.0379629
$142$		0			0
$143$	74.6241	+	129.253i	0.0436390	+	0.0755850i
$144$		0			0
$145$	−1666.62	+	2886.67i	−0.954517	+	1.65327i
$146$		0			0
$147$	283.263	+	989.244i	0.158933	+	0.555044i
$148$		0			0
$149$	−946.887	+	1640.06i	−0.520617	+	0.901736i	0.479095	+	0.877763i	$0.340965\pi$
$149$	−946.887	+	1640.06i	−0.520617	+	0.901736i	−0.999713	+	0.0239729i	$0.992368\pi$
$150$		0			0
$151$	−1005.92	−	1742.31i	−0.542124	−	0.938986i	−0.998782	−	0.0493434i	$-0.984287\pi$
$151$	−1005.92	−	1742.31i	−0.542124	−	0.938986i	0.456658	−	0.889642i	$-0.349046\pi$
$152$		0			0
$153$	479.406			0.253318
$154$		0			0
$155$	2821.71			1.46223
$156$		0			0
$157$	1914.25	+	3315.58i	0.973082	+	1.68543i	0.686125	+	0.727483i	$0.259310\pi$
$157$	1914.25	+	3315.58i	0.973082	+	1.68543i	0.286956	+	0.957944i	$0.407357\pi$
$158$		0			0
$159$	−548.856	+	950.647i	−0.273755	+	0.474158i
$160$		0			0
$161$	2249.17	+	1695.53i	1.10099	+	0.829977i
$162$		0			0
$163$	−1754.63	+	3039.11i	−0.843148	+	1.46038i	0.0440718	+	0.999028i	$0.485967\pi$
$163$	−1754.63	+	3039.11i	−0.843148	+	1.46038i	−0.887220	+	0.461347i	$0.847366\pi$
$164$		0			0
$165$	−305.475	−	529.098i	−0.144128	−	0.249638i
$166$		0			0
$167$	343.008			0.158939			0.0794694	−	0.996837i	$-0.474677\pi$
$167$	343.008			0.158939			0.0794694	+	0.996837i	$0.474677\pi$
$168$		0			0
$169$	−2025.42			−0.921905
$170$		0			0
$171$	−190.900	−	330.649i	−0.0853714	−	0.147868i
$172$		0			0
$173$	2093.61	−	3626.23i	0.920081	−	1.59363i	0.120793	−	0.992678i	$-0.461456\pi$
$173$	2093.61	−	3626.23i	0.920081	−	1.59363i	0.799288	−	0.600949i	$-0.205210\pi$
$174$		0			0
$175$	3315.27	−	1406.52i	1.43206	−	0.607559i
$176$		0			0
$177$	−339.866	+	588.666i	−0.144327	+	0.249982i
$178$		0			0
$179$	−985.143	−	1706.32i	−0.411358	−	0.712493i	0.583681	−	0.811983i	$-0.301612\pi$
$179$	−985.143	−	1706.32i	−0.411358	−	0.712493i	−0.995039	+	0.0994906i	$0.968279\pi$
$180$		0			0
$181$	−3613.10			−1.48376			−0.741878	−	0.670535i	$-0.766065\pi$
$181$	−3613.10			−1.48376			−0.741878	+	0.670535i	$0.766065\pi$
$182$		0			0
$183$	1955.92			0.790086
$184$		0			0
$185$	−33.4755	−	57.9812i	−0.0133036	−	0.0230425i
$186$		0			0
$187$	−303.468	+	525.622i	−0.118673	+	0.205547i
$188$		0			0
$189$	−61.0328	+	496.308i	−0.0234893	+	0.191011i
$190$		0			0
$191$	953.884	−	1652.18i	0.361365	−	0.625902i	−0.626821	−	0.779163i	$-0.715644\pi$
$191$	953.884	−	1652.18i	0.361365	−	0.625902i	0.988186	+	0.153261i	$0.0489776\pi$
$192$		0			0
$193$	−1199.96	−	2078.40i	−0.447540	−	0.775162i	0.550685	−	0.834713i	$-0.314366\pi$
$193$	−1199.96	−	2078.40i	−0.447540	−	0.775162i	−0.998225	+	0.0595509i	$0.981033\pi$
$194$		0			0
$195$	−702.346			−0.257928
$196$		0			0
$197$	1514.32			0.547668			0.273834	−	0.961777i	$-0.411708\pi$
$197$	1514.32			0.547668			0.273834	+	0.961777i	$0.411708\pi$
$198$		0			0
$199$	683.889	+	1184.53i	0.243616	+	0.421955i	0.961742	−	0.273958i	$-0.0883330\pi$
$199$	683.889	+	1184.53i	0.243616	+	0.421955i	−0.718126	+	0.695914i	$0.755000\pi$
$200$		0			0
$201$	218.150	−	377.847i	0.0765527	−	0.132593i
$202$		0			0
$203$	−421.563	+	3428.08i	−0.145753	+	1.18524i
$204$		0			0
$205$	351.414	−	608.667i	0.119726	−	0.207371i
$206$		0			0
$207$	684.384	+	1185.39i	0.229797	+	0.398020i
$208$		0			0
$209$	483.366			0.159977
$210$		0			0
$211$	−4302.52			−1.40378			−0.701891	−	0.712285i	$-0.747661\pi$
$211$	−4302.52			−1.40378			−0.701891	+	0.712285i	$0.747661\pi$
$212$		0			0
$213$	−553.443	−	958.591i	−0.178034	−	0.308364i
$214$		0			0
$215$	3837.72	−	6647.13i	1.21735	−	2.10851i
$216$		0			0
$217$	2691.64	−	1141.94i	0.842030	−	0.357236i
$218$		0			0
$219$	−913.359	+	1581.98i	−0.281822	+	0.488130i
$220$		0			0
$221$	348.866	+	604.253i	0.106187	+	0.183921i
$222$		0			0
$223$	1497.19			0.449592			0.224796	−	0.974406i	$-0.427828\pi$
$223$	1497.19			0.449592			0.224796	+	0.974406i	$0.427828\pi$
$224$		0			0
$225$	1750.06			0.518537
$226$		0			0
$227$	801.662	+	1388.52i	0.234397	+	0.405988i	0.959097	−	0.283076i	$-0.0913550\pi$
$227$	801.662	+	1388.52i	0.234397	+	0.405988i	−0.724700	+	0.689065i	$0.758022\pi$
$228$		0			0
$229$	−505.261	+	875.137i	−0.145802	+	0.252536i	−0.929672	−	0.368389i	$-0.879909\pi$
$229$	−505.261	+	875.137i	−0.145802	+	0.252536i	0.783870	+	0.620925i	$0.213243\pi$
$230$		0			0
$231$	−505.520	−	381.084i	−0.143986	−	0.108543i
$232$		0			0
$233$	−99.1084	+	171.661i	−0.0278661	+	0.0482656i	−0.879622	−	0.475673i	$-0.842205\pi$
$233$	−99.1084	+	171.661i	−0.0278661	+	0.0482656i	0.851756	+	0.523939i	$0.175538\pi$
$234$		0			0
$235$	189.339	+	327.944i	0.0525578	+	0.0910329i
$236$		0			0
$237$	−2730.71			−0.748434
$238$		0			0
$239$	1201.19			0.325098			0.162549	−	0.986700i	$-0.448028\pi$
$239$	1201.19			0.325098			0.162549	+	0.986700i	$0.448028\pi$
$240$		0			0
$241$	1366.35	+	2366.58i	0.365204	+	0.632551i	0.988809	−	0.149188i	$-0.0476660\pi$
$241$	1366.35	+	2366.58i	0.365204	+	0.632551i	−0.623605	+	0.781739i	$0.714333\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	4260.25	−	4408.33i	1.11093	−	1.14954i
$246$		0			0
$247$	277.838	−	481.229i	0.0715724	−	0.123967i
$248$		0			0
$249$	−491.894	−	851.985i	−0.125191	−	0.216837i
$250$		0			0
$251$	−7565.82			−1.90259			−0.951295	−	0.308281i	$-0.900246\pi$
$251$	−7565.82			−1.90259			−0.951295	+	0.308281i	$0.900246\pi$
$252$		0			0
$253$	−1732.88			−0.430615
$254$		0			0
$255$	−1428.09	−	2473.52i	−0.350707	−	0.607443i
$256$		0			0
$257$	−2504.34	+	4337.64i	−0.607846	+	1.05282i	0.383749	+	0.923437i	$0.374633\pi$
$257$	−2504.34	+	4337.64i	−0.607846	+	1.05282i	−0.991595	+	0.129382i	$0.958701\pi$
$258$		0			0
$259$	−55.3973	−	41.7610i	−0.0132904	−	0.0100189i
$260$		0			0
$261$	−839.220	+	1453.57i	−0.199028	+	0.344727i
$262$		0			0
$263$	−3124.40	−	5411.63i	−0.732544	−	1.26880i	−0.955793	−	0.294042i	$-0.905000\pi$
$263$	−3124.40	−	5411.63i	−0.732544	−	1.26880i	0.223249	−	0.974761i	$-0.428334\pi$
$264$		0			0
$265$	6539.88			1.51601
$266$		0			0
$267$	−112.835			−0.0258630
$268$		0			0
$269$	1794.22	+	3107.69i	0.406676	+	0.704383i	0.994515	−	0.104595i	$-0.0333546\pi$
$269$	1794.22	+	3107.69i	0.406676	+	0.704383i	−0.587839	+	0.808978i	$0.700021\pi$
$270$		0			0
$271$	−991.571	+	1717.45i	−0.222264	+	0.384973i	−0.955495	−	0.295007i	$-0.904678\pi$
$271$	−991.571	+	1717.45i	−0.222264	+	0.384973i	0.733231	+	0.679980i	$0.238012\pi$
$272$		0			0
$273$	−669.971	+	284.239i	−0.148529	+	0.0630143i
$274$		0			0
$275$	−1107.80	+	1918.77i	−0.242920	+	0.420751i
$276$		0			0
$277$	−3681.96	−	6377.33i	−0.798654	−	1.38331i	−0.920493	−	0.390760i	$-0.872212\pi$
$277$	−3681.96	−	6377.33i	−0.798654	−	1.38331i	0.121838	−	0.992550i	$-0.461121\pi$
$278$		0			0
$279$	1420.86			0.304892
$280$		0			0
$281$	−5312.05			−1.12772			−0.563861	−	0.825869i	$-0.690685\pi$
$281$	−5312.05			−1.12772			−0.563861	+	0.825869i	$0.690685\pi$
$282$		0			0
$283$	−545.882	−	945.495i	−0.114662	−	0.198600i	0.802983	−	0.596002i	$-0.203245\pi$
$283$	−545.882	−	945.495i	−0.114662	−	0.198600i	−0.917645	+	0.397402i	$0.869912\pi$
$284$		0			0
$285$	−1137.33	+	1969.92i	−0.236385	+	0.409431i
$286$		0			0
$287$	88.8886	−	722.827i	0.0182820	−	0.148666i
$288$		0			0
$289$	1037.79	−	1797.51i	0.211234	−	0.365869i
$290$		0			0
$291$	−1083.02	−	1875.84i	−0.218171	−	0.377883i
$292$		0			0
$293$	−7191.86			−1.43397			−0.716985	−	0.697089i	$-0.754478\pi$
$293$	−7191.86			−1.43397			−0.716985	+	0.697089i	$0.754478\pi$
$294$		0			0
$295$	4049.67			0.799257
$296$		0			0
$297$	−153.821	−	266.426i	−0.0300525	−	0.0520525i
$298$		0			0
$299$	−996.058	+	1725.22i	−0.192654	+	0.333687i
$300$		0			0
$301$	970.735	−	7893.85i	0.185888	−	1.51161i
$302$		0			0
$303$	−2278.01	+	3945.63i	−0.431908	+	0.748087i
$304$		0			0
$305$	−5826.43	−	10091.7i	−1.09384	−	1.89458i
$306$		0			0
$307$	−541.355			−0.100641			−0.0503204	−	0.998733i	$-0.516024\pi$
$307$	−541.355			−0.100641			−0.0503204	+	0.998733i	$0.516024\pi$
$308$		0			0
$309$	3155.65			0.580966
$310$		0			0
$311$	27.0084	+	46.7799i	0.00492446	+	0.00852941i	0.868477	−	0.495729i	$-0.165099\pi$
$311$	27.0084	+	46.7799i	0.00492446	+	0.00852941i	−0.863553	+	0.504259i	$0.831766\pi$
$312$		0			0
$313$	−1886.47	+	3267.46i	−0.340670	+	0.590058i	−0.984557	−	0.175063i	$-0.943987\pi$
$313$	−1886.47	+	3267.46i	−0.340670	+	0.590058i	0.643887	+	0.765120i	$0.277321\pi$
$314$		0			0
$315$	2742.54	−	1163.54i	0.490554	−	0.208120i
$316$		0			0
$317$	−859.618	+	1488.90i	−0.152306	+	0.263802i	−0.932075	−	0.362266i	$-0.882003\pi$
$317$	−859.618	+	1488.90i	−0.152306	+	0.263802i	0.779769	+	0.626068i	$0.215337\pi$
$318$		0			0
$319$	−1062.47	−	1840.25i	−0.186479	−	0.322991i
$320$		0			0
$321$	−2299.56			−0.399841
$322$		0			0
$323$	2259.72			0.389270
$324$		0			0
$325$	1273.53	+	2205.81i	0.217362	+	0.376482i
$326$		0			0
$327$	2140.57	−	3707.58i	0.362000	−	0.627002i
$328$		0			0
$329$	313.330	+	236.202i	0.0525059	+	0.0395813i
$330$		0			0
$331$	4204.11	−	7281.73i	0.698123	−	1.20918i	−0.270994	−	0.962581i	$-0.587352\pi$
$331$	4204.11	−	7281.73i	0.698123	−	1.20918i	0.969117	−	0.246603i	$-0.0793143\pi$
$332$		0			0
$333$	−16.8565	−	29.1963i	−0.00277396	−	0.00480464i
$334$		0			0
$335$	−2599.36			−0.423935
$336$		0			0
$337$	2789.46			0.450894			0.225447	−	0.974255i	$-0.427616\pi$
$337$	2789.46			0.450894			0.225447	+	0.974255i	$0.427616\pi$
$338$		0			0
$339$	−543.846	−	941.969i	−0.0871317	−	0.150917i
$340$		0			0
$341$	−899.419	+	1557.84i	−0.142834	+	0.247395i
$342$		0			0
$343$	2279.82	−	5929.25i	0.358889	−	0.933380i
$344$		0			0
$345$	4077.38	−	7062.23i	0.636286	−	1.10208i
$346$		0			0
$347$	−1735.98	−	3006.81i	−0.268566	−	0.465170i	0.699926	−	0.714216i	$-0.253216\pi$
$347$	−1735.98	−	3006.81i	−0.268566	−	0.465170i	−0.968492	+	0.249046i	$0.919883\pi$
$348$		0			0
$349$	−6626.12			−1.01630			−0.508149	−	0.861269i	$-0.669670\pi$
$349$	−6626.12			−1.01630			−0.508149	+	0.861269i	$0.669670\pi$
$350$		0			0
$351$	−353.664			−0.0537812
$352$		0			0
$353$	−4734.20	−	8199.87i	−0.713813	−	1.23636i	−0.963416	−	0.268012i	$-0.913633\pi$
$353$	−4734.20	−	8199.87i	−0.713813	−	1.23636i	0.249603	−	0.968348i	$-0.419700\pi$
$354$		0			0
$355$	−3297.27	+	5711.03i	−0.492960	+	0.853831i
$356$		0			0
$357$	−2363.29	−	1781.56i	−0.350360	−	0.264118i
$358$		0			0
$359$	−3139.78	+	5438.25i	−0.461591	+	0.799499i	−0.999040	−	0.0437971i	$-0.986054\pi$
$359$	−3139.78	+	5438.25i	−0.461591	+	0.799499i	0.537450	+	0.843296i	$0.319388\pi$
$360$		0			0
$361$	2529.68	+	4381.53i	0.368811	+	0.638800i
$362$		0			0
$363$	−3603.52			−0.521035
$364$		0			0
$365$	10883.1			1.56068
$366$		0			0
$367$	−5413.91	−	9377.17i	−0.770038	−	1.33374i	−0.937542	−	0.347873i	$-0.886904\pi$
$367$	−5413.91	−	9377.17i	−0.770038	−	1.33374i	0.167504	−	0.985871i	$-0.446429\pi$
$368$		0			0
$369$	176.954	−	306.493i	0.0249643	−	0.0432395i
$370$		0			0
$371$	6238.42	−	2646.68i	0.872999	−	0.370374i
$372$		0			0
$373$	−2619.61	+	4537.30i	−0.363642	+	0.629846i	−0.988557	−	0.150846i	$-0.951800\pi$
$373$	−2619.61	+	4537.30i	−0.363642	+	0.629846i	0.624915	+	0.780693i	$0.285134\pi$
$374$		0			0
$375$	−1861.98	−	3225.04i	−0.256406	−	0.444108i
$376$		0			0
$377$	−2442.81			−0.333717
$378$		0			0
$379$	11050.4			1.49768			0.748839	−	0.662751i	$-0.230611\pi$
$379$	11050.4			1.49768			0.748839	+	0.662751i	$0.230611\pi$
$380$		0			0
$381$	1462.16	+	2532.54i	0.196611	+	0.340541i
$382$		0			0
$383$	−5234.02	+	9065.59i	−0.698292	+	1.20948i	0.270766	+	0.962645i	$0.412723\pi$
$383$	−5234.02	+	9065.59i	−0.698292	+	1.20948i	−0.969058	+	0.246832i	$0.920610\pi$
$384$		0			0
$385$	−460.345	+	3743.45i	−0.0609386	+	0.495543i
$386$		0			0
$387$	1932.47	−	3347.14i	0.253833	−	0.439651i
$388$		0			0
$389$	5807.02	+	10058.1i	0.756884	+	1.31096i	0.944432	+	0.328705i	$0.106612\pi$
$389$	5807.02	+	10058.1i	0.756884	+	1.31096i	−0.187549	+	0.982255i	$0.560054\pi$
$390$		0			0
$391$	−8101.19			−1.04781
$392$		0			0
$393$	5378.11			0.690304
$394$		0			0
$395$	8134.43	+	14089.2i	1.03617	+	1.79470i
$396$		0			0
$397$	3353.65	−	5808.69i	0.423967	−	0.734332i	−0.572356	−	0.820005i	$-0.693971\pi$
$397$	3353.65	−	5808.69i	0.423967	−	0.734332i	0.996323	+	0.0856726i	$0.0273039\pi$
$398$		0			0
$399$	−287.683	+	2339.39i	−0.0360957	+	0.293524i
$400$		0			0
$401$	−2763.19	+	4785.98i	−0.344107	+	0.596011i	−0.985191	−	0.171459i	$-0.945152\pi$
$401$	−2763.19	+	4785.98i	−0.344107	+	0.596011i	0.641084	+	0.767471i	$0.278485\pi$
$402$		0			0
$403$	1033.97	+	1790.89i	0.127805	+	0.221366i
$404$		0			0
$405$	1447.73			0.177625
$406$		0			0
$407$	42.6811			0.00519810
$408$		0			0
$409$	659.453	+	1142.21i	0.0797258	+	0.138089i	0.903132	−	0.429364i	$-0.141262\pi$
$409$	659.453	+	1142.21i	0.0797258	+	0.138089i	−0.823406	+	0.567453i	$0.807929\pi$
$410$		0			0
$411$	−2526.62	+	4376.24i	−0.303234	+	0.525217i
$412$		0			0
$413$	3863.00	−	1638.90i	0.460256	−	0.195266i
$414$		0			0
$415$	−2930.57	+	5075.90i	−0.346641	+	0.600401i
$416$		0			0
$417$	472.634	+	818.626i	0.0555036	+	0.0961350i
$418$		0			0
$419$	−3656.13			−0.426286			−0.213143	−	0.977021i	$-0.568370\pi$
$419$	−3656.13			−0.426286			−0.213143	+	0.977021i	$0.568370\pi$
$420$		0			0
$421$	−135.389			−0.0156733			−0.00783663	−	0.999969i	$-0.502495\pi$
$421$	−135.389			−0.0156733			−0.00783663	+	0.999969i	$0.502495\pi$
$422$		0			0
$423$	95.3409	+	165.135i	0.0109589	+	0.0189815i
$424$		0			0
$425$	−5178.96	+	8970.22i	−0.591097	+	1.02381i
$426$		0			0
$427$	−9641.94	−	7268.54i	−1.09276	−	0.823769i
$428$		0			0
$429$	223.872	−	387.758i	0.0251950	−	0.0436390i
$430$		0			0
$431$	4194.58	+	7265.23i	0.468784	+	0.811958i	0.999363	−	0.0356776i	$-0.0113589\pi$
$431$	4194.58	+	7265.23i	0.468784	+	0.811958i	−0.530579	+	0.847635i	$0.678026\pi$
$432$		0			0
$433$	−8243.02			−0.914859			−0.457430	−	0.889246i	$-0.651230\pi$
$433$	−8243.02			−0.914859			−0.457430	+	0.889246i	$0.651230\pi$
$434$		0			0
$435$	9999.70			1.10218
$436$		0			0
$437$	3225.91	+	5587.43i	0.353126	+	0.611632i
$438$		0			0
$439$	−9141.59	+	15833.7i	−0.993859	+	1.72142i	−0.401104	+	0.916032i	$0.631374\pi$
$439$	−9141.59	+	15833.7i	−0.993859	+	1.72142i	−0.592755	+	0.805383i	$0.701960\pi$
$440$		0			0
$441$	2145.24	−	2219.80i	0.231642	−	0.239694i
$442$		0			0
$443$	605.218	−	1048.27i	0.0649092	−	0.112426i	−0.831745	−	0.555159i	$-0.812658\pi$
$443$	605.218	−	1048.27i	0.0649092	−	0.112426i	0.896654	+	0.442733i	$0.145991\pi$
$444$		0			0
$445$	336.122	+	582.180i	0.0358061	+	0.0620179i
$446$		0			0
$447$	5681.32			0.601157
$448$		0			0
$449$	−8301.16			−0.872508			−0.436254	−	0.899824i	$-0.643695\pi$
$449$	−8301.16			−0.872508			−0.436254	+	0.899824i	$0.643695\pi$
$450$		0			0
$451$	224.026	+	388.025i	0.0233902	+	0.0405130i
$452$		0			0
$453$	−3017.76	+	5226.92i	−0.312995	+	0.542124i
$454$		0			0
$455$	3462.30	+	2610.04i	0.356736	+	0.268924i
$456$		0			0
$457$	6146.88	−	10646.7i	0.629188	−	1.08979i	−0.358527	−	0.933519i	$-0.616721\pi$
$457$	6146.88	−	10646.7i	0.629188	−	1.08979i	0.987715	−	0.156266i	$-0.0499458\pi$
$458$		0			0
$459$	−719.109	−	1245.53i	−0.0731267	−	0.126659i
$460$		0			0
$461$	19434.2			1.96343			0.981717	−	0.190346i	$-0.0609609\pi$
$461$	19434.2			1.96343			0.981717	+	0.190346i	$0.0609609\pi$
$462$		0			0
$463$	12491.1			1.25380			0.626902	−	0.779098i	$-0.284322\pi$
$463$	12491.1			1.25380			0.626902	+	0.779098i	$0.284322\pi$
$464$		0			0
$465$	−4232.56	−	7331.02i	−0.422109	−	0.731113i
$466$		0			0
$467$	1692.59	−	2931.65i	0.167716	−	0.290493i	−0.769900	−	0.638164i	$-0.779694\pi$
$467$	1692.59	−	2931.65i	0.167716	−	0.290493i	0.937617	+	0.347671i	$0.113027\pi$
$468$		0			0
$469$	−2479.54	+	1051.96i	−0.244125	+	0.103571i
$470$		0			0
$471$	5742.75	−	9946.74i	0.561809	−	0.973082i
$472$		0			0
$473$	2446.54	+	4237.54i	0.237827	+	0.411929i
$474$		0			0
$475$	8249.07			0.796828
$476$		0			0
$477$	3293.14			0.316106
$478$		0			0
$479$	2989.71	+	5178.32i	0.285184	+	0.493953i	0.972654	−	0.232260i	$-0.0746120\pi$
$479$	2989.71	+	5178.32i	0.285184	+	0.493953i	−0.687470	+	0.726213i	$0.741279\pi$
$480$		0			0
$481$	24.5330	−	42.4925i	0.00232559	−	0.00402804i
$482$		0			0
$483$	1031.35	−	8386.81i	0.0971600	−	0.790089i
$484$		0			0
$485$	−6452.34	+	11175.8i	−0.604094	+	1.04632i
$486$		0			0
$487$	−557.481	−	965.586i	−0.0518725	−	0.0898457i	0.838923	−	0.544250i	$-0.183186\pi$
$487$	−557.481	−	965.586i	−0.0518725	−	0.0898457i	−0.890796	+	0.454404i	$0.849852\pi$
$488$		0			0
$489$	10527.8			0.973583
$490$		0			0
$491$	−1086.23			−0.0998387			−0.0499194	−	0.998753i	$-0.515896\pi$
$491$	−1086.23			−0.0998387			−0.0499194	+	0.998753i	$0.515896\pi$
$492$		0			0
$493$	−4967.00	−	8603.10i	−0.453758	−	0.785932i
$494$		0			0
$495$	−916.425	+	1587.29i	−0.0832126	+	0.144128i
$496$		0			0
$497$	−834.028	+	6782.18i	−0.0752742	+	0.612117i
$498$		0			0
$499$	−1106.75	+	1916.95i	−0.0992884	+	0.171973i	−0.911390	−	0.411543i	$-0.864990\pi$
$499$	−1106.75	+	1916.95i	−0.0992884	+	0.171973i	0.812102	+	0.583516i	$0.198323\pi$
$500$		0			0
$501$	−514.512	−	891.162i	−0.0458817	−	0.0794694i
$502$		0			0
$503$	2643.32			0.234314			0.117157	−	0.993113i	$-0.462622\pi$
$503$	2643.32			0.234314			0.117157	+	0.993113i	$0.462622\pi$
$504$		0			0
$505$	27143.5			2.39183
$506$		0			0
$507$	3038.14	+	5262.21i	0.266131	+	0.460952i
$508$		0			0
$509$	332.584	−	576.053i	0.0289618	−	0.0501633i	−0.851181	−	0.524872i	$-0.824113\pi$
$509$	332.584	−	576.053i	0.0289618	−	0.0501633i	0.880143	+	0.474709i	$0.157447\pi$
$510$		0			0
$511$	10381.4	−	4404.38i	0.898724	−	0.381288i
$512$		0			0
$513$	−572.701	+	991.947i	−0.0492892	+	0.0853714i
$514$		0			0
$515$	−9400.26	−	16281.7i	−0.804320	−	1.39312i
$516$		0			0
$517$	−241.406			−0.0205359
$518$		0			0
$519$	−12561.6			−1.06242
$520$		0			0
$521$	5880.99	+	10186.2i	0.494531	+	0.856554i	0.999980	−	0.00630307i	$-0.00200634\pi$
$521$	5880.99	+	10186.2i	0.494531	+	0.856554i	−0.505449	+	0.862857i	$0.668673\pi$
$522$		0			0
$523$	5061.30	−	8766.43i	0.423165	−	0.732943i	−0.573082	−	0.819498i	$-0.694252\pi$
$523$	5061.30	−	8766.43i	0.423165	−	0.732943i	0.996247	+	0.0865547i	$0.0275857\pi$
$524$		0			0
$525$	−8627.15	−	6503.54i	−0.717180	−	0.540643i
$526$		0			0
$527$	−4204.76	+	7282.85i	−0.347556	+	0.601985i
$528$		0			0
$529$	−5481.49	−	9494.22i	−0.450521	−	0.780325i
$530$		0			0
$531$	2039.20			0.166655
$532$		0			0
$533$	515.079			0.0418585
$534$		0			0
$535$	6850.09	+	11864.7i	0.553561	+	0.958796i
$536$		0			0
$537$	−2955.43	+	5118.95i	−0.237498	+	0.411358i
$538$		0			0
$539$	1075.85	+	3757.20i	0.0859740	+	0.300249i
$540$		0			0
$541$	−8058.98	+	13958.6i	−0.640449	+	1.10929i	0.344884	+	0.938645i	$0.387918\pi$
$541$	−8058.98	+	13958.6i	−0.640449	+	1.10929i	−0.985333	+	0.170644i	$0.945415\pi$
$542$		0			0
$543$	5419.65	+	9387.11i	0.428323	+	0.741878i
$544$		0			0
$545$	−25505.9			−2.00469
$546$		0			0
$547$	626.100			0.0489399			0.0244699	−	0.999701i	$-0.492210\pi$
$547$	626.100			0.0489399			0.0244699	+	0.999701i	$0.492210\pi$
$548$		0			0
$549$	−2933.88	−	5081.63i	−0.228078	−	0.395043i
$550$		0			0
$551$	−3955.74	+	6851.54i	−0.305844	+	0.529737i
$552$		0			0
$553$	13461.4	+	10147.8i	1.03515	+	0.780341i
$554$		0			0
$555$	−100.426	+	173.944i	−0.00768083	+	0.0133036i
$556$		0			0
$557$	−10385.6	−	17988.4i	−0.790039	−	1.36839i	−0.925942	−	0.377665i	$-0.876727\pi$
$557$	−10385.6	−	17988.4i	−0.790039	−	1.36839i	0.135903	−	0.990722i	$-0.456606\pi$
$558$		0			0
$559$	5625.08			0.425609
$560$		0			0
$561$	1820.81			0.137031
$562$		0			0
$563$	−2760.86	−	4781.95i	−0.206672	−	0.357966i	0.743992	−	0.668188i	$-0.232930\pi$
$563$	−2760.86	−	4781.95i	−0.206672	−	0.357966i	−0.950664	+	0.310222i	$0.899597\pi$
$564$		0			0
$565$	−3240.09	+	5612.00i	−0.241260	+	0.417874i
$566$		0			0
$567$	1381.00	−	585.895i	0.102286	−	0.0433955i
$568$		0			0
$569$	−3787.40	+	6559.97i	−0.279044	+	0.483319i	−0.971147	−	0.238480i	$-0.923351\pi$
$569$	−3787.40	+	6559.97i	−0.279044	+	0.483319i	0.692103	+	0.721799i	$0.256684\pi$
$570$		0			0
$571$	−165.624	−	286.869i	−0.0121386	−	0.0210247i	0.859892	−	0.510476i	$-0.170531\pi$
$571$	−165.624	−	286.869i	−0.0121386	−	0.0210247i	−0.872031	+	0.489451i	$0.837197\pi$
$572$		0			0
$573$	−5723.31			−0.417268
$574$		0			0
$575$	−29573.2			−2.14485
$576$		0			0
$577$	−1019.06	−	1765.06i	−0.0735248	−	0.127349i	0.826919	−	0.562321i	$-0.190091\pi$
$577$	−1019.06	−	1765.06i	−0.0735248	−	0.127349i	−0.900444	+	0.434972i	$0.856758\pi$
$578$		0			0
$579$	−3599.89	+	6235.19i	−0.258387	+	0.447540i
$580$		0			0
$581$	−741.275	+	6027.93i	−0.0529316	+	0.430431i
$582$		0			0
$583$	−2084.58	+	3610.60i	−0.148087	+	0.256494i
$584$		0			0
$585$	1053.52	+	1824.75i	0.0744575	+	0.128964i
$586$		0			0
$587$	−5232.90			−0.367947			−0.183973	−	0.982931i	$-0.558896\pi$
$587$	−5232.90			−0.367947			−0.183973	+	0.982931i	$0.558896\pi$
$588$		0			0
$589$	6697.36			0.468523
$590$		0			0
$591$	−2271.47	−	3934.31i	−0.158098	−	0.273834i
$592$		0			0
$593$	2860.12	−	4953.87i	0.198062	−	0.343054i	−0.749838	−	0.661622i	$-0.769868\pi$
$593$	2860.12	−	4953.87i	0.198062	−	0.343054i	0.947900	+	0.318568i	$0.103202\pi$
$594$		0			0
$595$	−2152.10	+	17500.5i	−0.148282	+	1.20580i
$596$		0			0
$597$	2051.67	−	3553.59i	0.140652	−	0.243616i
$598$		0			0
$599$	9044.21	+	15665.0i	0.616922	+	1.06854i	0.990044	+	0.140758i	$0.0449540\pi$
$599$	9044.21	+	15665.0i	0.616922	+	1.06854i	−0.373122	+	0.927782i	$0.621713\pi$
$600$		0			0
$601$	−1821.43			−0.123623			−0.0618117	−	0.998088i	$-0.519688\pi$
$601$	−1821.43			−0.123623			−0.0618117	+	0.998088i	$0.519688\pi$
$602$		0			0
$603$	−1308.90			−0.0883955
$604$		0			0
$605$	10734.4	+	18592.5i	0.721348	+	1.24941i
$606$		0			0
$607$	1186.10	−	2054.39i	0.0793120	−	0.137372i	−0.823641	−	0.567111i	$-0.808061\pi$
$607$	1186.10	−	2054.39i	0.0793120	−	0.137372i	0.902953	+	0.429739i	$0.141394\pi$
$608$		0			0
$609$	9538.76	−	4046.87i	0.634696	−	0.269273i
$610$		0			0
$611$	−138.760	+	240.339i	−0.00918760	+	0.0159134i
$612$		0			0
$613$	−4862.54	−	8422.16i	−0.320385	−	0.554923i	0.660182	−	0.751105i	$-0.270479\pi$
$613$	−4862.54	−	8422.16i	−0.320385	−	0.554923i	−0.980567	+	0.196182i	$0.937146\pi$
$614$		0			0
$615$	−2108.48			−0.138248
$616$		0			0
$617$	−5329.51			−0.347744			−0.173872	−	0.984768i	$-0.555628\pi$
$617$	−5329.51			−0.347744			−0.173872	+	0.984768i	$0.555628\pi$
$618$		0			0
$619$	−7988.29	−	13836.1i	−0.518702	−	0.898418i	−0.999764	−	0.0217314i	$-0.993082\pi$
$619$	−7988.29	−	13836.1i	−0.518702	−	0.898418i	0.481062	−	0.876687i	$-0.340251\pi$
$620$		0			0
$621$	2053.15	−	3556.17i	0.132673	−	0.229797i
$622$		0			0
$623$	556.236	+	419.316i	0.0357706	+	0.0269656i
$624$		0			0
$625$	1060.03	−	1836.03i	0.0678420	−	0.117506i
$626$		0			0
$627$	−725.049	−	1255.82i	−0.0461813	−	0.0799883i
$628$		0			0
$629$	199.533			0.0126485
$630$		0			0
$631$	4199.98			0.264974			0.132487	−	0.991185i	$-0.457704\pi$
$631$	4199.98			0.264974			0.132487	+	0.991185i	$0.457704\pi$
$632$		0			0
$633$	6453.78	+	11178.3i	0.405237	+	0.701891i
$634$		0			0
$635$	8711.19	−	15088.2i	0.544399	−	0.942926i
$636$		0			0
$637$	4358.98	+	1088.54i	0.271129	+	0.0677072i
$638$		0			0
$639$	−1660.33	+	2875.77i	−0.102788	+	0.178034i
$640$		0			0
$641$	−1324.25	−	2293.67i	−0.0815988	−	0.141333i	0.822338	−	0.568999i	$-0.192669\pi$
$641$	−1324.25	−	2293.67i	−0.0815988	−	0.141333i	−0.903937	+	0.427666i	$0.859336\pi$
$642$		0			0
$643$	−13.4305			−0.000823715			−0.000411857	−	1.00000i	$-0.500131\pi$
$643$	−13.4305			−0.000823715			−0.000411857		1.00000i	$0.500131\pi$
$644$		0			0
$645$	−23026.3			−1.40568
$646$		0			0
$647$	5812.07	+	10066.8i	0.353162	+	0.611695i	0.986802	−	0.161934i	$-0.0517730\pi$
$647$	5812.07	+	10066.8i	0.353162	+	0.611695i	−0.633639	+	0.773628i	$0.718440\pi$
$648$		0			0
$649$	−1290.83	+	2235.78i	−0.0780732	+	0.135227i
$650$		0			0
$651$	−7004.32	−	5280.18i	−0.421691	−	0.317890i
$652$		0			0
$653$	14258.3	−	24696.1i	0.854471	−	1.47999i	−0.0226638	−	0.999743i	$-0.507215\pi$
$653$	14258.3	−	24696.1i	0.854471	−	1.47999i	0.877135	−	0.480244i	$-0.159452\pi$
$654$		0			0
$655$	−16020.7	−	27748.6i	−0.955694	−	1.65531i
$656$		0			0
$657$	5480.15			0.325420
$658$		0			0
$659$	−18048.6			−1.06688			−0.533440	−	0.845838i	$-0.679101\pi$
$659$	−18048.6			−1.06688			−0.533440	+	0.845838i	$0.679101\pi$
$660$		0			0
$661$	−8920.72	−	15451.1i	−0.524926	−	0.909198i	−0.999579	−	0.0290250i	$-0.990760\pi$
$661$	−8920.72	−	15451.1i	−0.524926	−	0.909198i	0.474653	−	0.880173i	$-0.342574\pi$
$662$		0			0
$663$	1046.60	−	1812.76i	0.0613069	−	0.106187i
$664$		0			0
$665$	12927.2	−	5484.42i	0.753826	−	0.319815i
$666$		0			0
$667$	14181.5	−	24563.0i	0.823251	−	1.42591i
$668$		0			0
$669$	−2245.78	−	3889.80i	−0.129786	−	0.224796i
$670$		0			0
$671$	7428.68			0.427394
$672$		0			0
$673$	−6826.13			−0.390978			−0.195489	−	0.980706i	$-0.562629\pi$
$673$	−6826.13			−0.390978			−0.195489	+	0.980706i	$0.562629\pi$
$674$		0			0
$675$	−2625.09	−	4546.80i	−0.149689	−	0.259269i
$676$		0			0
$677$	10643.4	−	18435.0i	0.604225	−	1.04655i	−0.387949	−	0.921681i	$-0.626816\pi$
$677$	10643.4	−	18435.0i	0.604225	−	1.04655i	0.992173	−	0.124867i	$-0.0398505\pi$
$678$		0			0
$679$	−1632.09	+	13271.9i	−0.0922443	+	0.750115i
$680$		0			0
$681$	2404.99	−	4165.56i	0.135329	−	0.234397i
$682$		0			0
$683$	−10348.4	−	17924.0i	−0.579753	−	1.00416i	−0.995507	−	0.0946842i	$-0.969816\pi$
$683$	−10348.4	−	17924.0i	−0.579753	−	1.00416i	0.415755	−	0.909477i	$-0.363517\pi$
$684$		0			0
$685$	30105.9			1.67925
$686$		0			0
$687$	3031.56			0.168357
$688$		0			0
$689$	2396.43	+	4150.74i	0.132506	+	0.229507i
$690$		0			0
$691$	15671.0	−	27142.9i	0.862738	−	1.49431i	−0.00653825	−	0.999979i	$-0.502081\pi$
$691$	15671.0	−	27142.9i	0.862738	−	1.49431i	0.869276	−	0.494327i	$-0.164585\pi$
$692$		0			0
$693$	−231.805	+	1885.00i	−0.0127064	+	0.103327i
$694$		0			0
$695$	2815.83	−	4877.16i	0.153684	−	0.266189i
$696$		0			0
$697$	1047.32	+	1814.01i	0.0569153	+	0.0985801i
$698$		0			0
$699$	594.651			0.0321770
$700$		0			0
$701$	−9213.32			−0.496408			−0.248204	−	0.968708i	$-0.579840\pi$
$701$	−9213.32			−0.496408			−0.248204	+	0.968708i	$0.579840\pi$
$702$		0			0
$703$	−79.4544	−	137.619i	−0.00426270	−	0.00738322i
$704$		0			0
$705$	568.016	−	983.833i	0.0303443	−	0.0525578i
$706$		0			0
$707$	25892.4	−	10985.0i	1.37734	−	0.584345i
$708$		0			0
$709$	−7258.27	+	12571.7i	−0.384471	+	0.665923i	−0.991696	−	0.128607i	$-0.958949\pi$
$709$	−7258.27	+	12571.7i	−0.384471	+	0.665923i	0.607225	+	0.794530i	$0.292283\pi$
$710$		0			0
$711$	4096.07	+	7094.60i	0.216054	+	0.374217i
$712$		0			0
$713$	−24010.3			−1.26114
$714$		0			0
$715$	−2667.54			−0.139525
$716$		0			0
$717$	−1801.78	−	3120.78i	−0.0938477	−	0.162549i
$718$		0			0
$719$	12941.2	−	22414.8i	0.671246	−	1.16263i	−0.306306	−	0.951933i	$-0.599093\pi$
$719$	12941.2	−	22414.8i	0.671246	−	1.16263i	0.977551	−	0.210698i	$-0.0675737\pi$
$720$		0			0
$721$	−15556.2	−	11726.9i	−0.803525	−	0.605734i
$722$		0			0
$723$	4099.04	−	7099.74i	0.210850	−	0.365204i
$724$		0			0
$725$	−18132.0	−	31405.5i	−0.928833	−	1.60879i
$726$		0			0
$727$	−32181.2			−1.64172			−0.820862	−	0.571127i	$-0.806506\pi$
$727$	−32181.2			−1.64172			−0.820862	+	0.571127i	$0.806506\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	11437.5	+	19810.4i	0.578704	+	1.00234i
$732$		0			0
$733$	−10418.1	+	18044.6i	−0.524966	+	0.909268i	0.474611	+	0.880195i	$0.342589\pi$
$733$	−10418.1	+	18044.6i	−0.524966	+	0.909268i	−0.999577	+	0.0290722i	$0.990745\pi$
$734$		0			0
$735$	−17843.6	−	4455.95i	−0.895469	−	0.223620i
$736$		0			0
$737$	828.544	−	1435.08i	0.0414109	−	0.0717257i
$738$		0			0
$739$	13217.4	+	22893.3i	0.657931	+	1.13957i	0.981150	+	0.193246i	$0.0619016\pi$
$739$	13217.4	+	22893.3i	0.657931	+	1.13957i	−0.323219	+	0.946324i	$0.604765\pi$
$740$		0			0
$741$	−1667.03			−0.0826447
$742$		0			0
$743$	−9954.69			−0.491524			−0.245762	−	0.969330i	$-0.579038\pi$
$743$	−9954.69			−0.491524			−0.245762	+	0.969330i	$0.579038\pi$
$744$		0			0
$745$	−16923.9	−	29313.1i	−0.832274	−	1.44154i
$746$		0			0
$747$	−1475.68	+	2555.96i	−0.0722790	+	0.125191i
$748$		0			0
$749$	11336.0	+	8545.57i	0.553014	+	0.416887i
$750$		0			0
$751$	−16602.3	+	28756.0i	−0.806692	+	1.39723i	0.108451	+	0.994102i	$0.465411\pi$
$751$	−16602.3	+	28756.0i	−0.806692	+	1.39723i	−0.915143	+	0.403129i	$0.867923\pi$
$752$		0			0
$753$	11348.7	+	19656.6i	0.549231	+	0.951295i
$754$		0			0
$755$	35958.1			1.73331
$756$		0			0
$757$	1964.06			0.0942998			0.0471499	−	0.998888i	$-0.484986\pi$
$757$	1964.06			0.0942998			0.0471499	+	0.998888i	$0.484986\pi$
$758$		0			0
$759$	2599.33	+	4502.17i	0.124308	+	0.215307i
$760$		0			0
$761$	19276.9	−	33388.6i	0.918248	−	1.59045i	0.116174	−	0.993229i	$-0.462937\pi$
$761$	19276.9	−	33388.6i	0.918248	−	1.59045i	0.802075	−	0.597224i	$-0.203730\pi$
$762$		0			0
$763$	−24330.2	+	10322.2i	−1.15441	+	0.489764i
$764$		0			0
$765$	−4284.26	+	7420.56i	−0.202481	+	0.350707i
$766$		0			0
$767$	1483.93	+	2570.25i	0.0698588	+	0.120999i
$768$		0			0
$769$	−19715.0			−0.924501			−0.462251	−	0.886749i	$-0.652958\pi$
$769$	−19715.0			−0.924501			−0.462251	+	0.886749i	$0.652958\pi$
$770$		0			0
$771$	15026.0			0.701880
$772$		0			0
$773$	7350.34	+	12731.2i	0.342010	+	0.592378i	0.984806	−	0.173659i	$-0.0555591\pi$
$773$	7350.34	+	12731.2i	0.342010	+	0.592378i	−0.642796	+	0.766037i	$0.722226\pi$
$774$		0			0
$775$	−15349.4	+	26585.9i	−0.711440	+	1.23225i
$776$		0			0
$777$	−25.4024	+	206.568i	−0.00117285	+	0.00953744i
$778$		0			0
$779$	834.086	−	1444.68i	0.0383623	−	0.0664454i
$780$		0			0
$781$	−2102.00	−	3640.78i	−0.0963068	−	0.166808i
$782$		0			0
$783$	5035.32			0.229818
$784$		0			0
$785$	−68427.6			−3.11119
$786$		0			0
$787$	−11959.3	−	20714.1i	−0.541681	−	0.938218i	−0.998808	−	0.0488169i	$-0.984455\pi$
$787$	−11959.3	−	20714.1i	−0.541681	−	0.938218i	0.457127	−	0.889401i	$-0.348878\pi$
$788$		0			0
$789$	−9373.21	+	16234.9i	−0.422934	+	0.732544i
$790$		0			0
$791$	−819.566	+	6664.58i	−0.0368400	+	0.299577i
$792$		0			0
$793$	4269.99	−	7395.84i	0.191213	−	0.331191i
$794$		0			0
$795$	−9809.82	−	16991.1i	−0.437633	−	0.758003i
$796$		0			0
$797$	38252.7			1.70010			0.850051	−	0.526700i	$-0.176571\pi$
$797$	38252.7			1.70010			0.850051	+	0.526700i	$0.176571\pi$
$798$		0			0
$799$	−1128.57			−0.0499698
$800$		0			0
$801$	169.253	+	293.155i	0.00746600	+	0.0129315i
$802$		0			0
$803$	−3468.98	+	6008.45i	−0.152450	+	0.264052i
$804$		0			0
$805$	−46344.4	+	19661.9i	−2.02910	+	0.860857i
$806$		0			0
$807$	5382.67	−	9323.06i	0.234794	−	0.406676i
$808$		0			0
$809$	15717.8	+	27224.0i	0.683075	+	1.18312i	0.974038	+	0.226386i	$0.0726912\pi$
$809$	15717.8	+	27224.0i	0.683075	+	1.18312i	−0.290962	+	0.956734i	$0.593975\pi$
$810$		0			0
$811$	−11467.0			−0.496501			−0.248250	−	0.968696i	$-0.579856\pi$
$811$	−11467.0			−0.496501			−0.248250	+	0.968696i	$0.579856\pi$
$812$		0			0
$813$	5949.43			0.256649
$814$		0			0
$815$	−31360.8	−	54318.6i	−1.34788	−	2.33460i
$816$		0			0
$817$	9108.88	−	15777.1i	0.390061	−	0.675605i
$818$		0			0
$819$	1743.43	+	1314.28i	0.0743838	+	0.0560740i
$820$		0			0
$821$	2515.29	−	4356.60i	0.106923	−	0.185197i	−0.807599	−	0.589732i	$-0.799233\pi$
$821$	2515.29	−	4356.60i	0.106923	−	0.185197i	0.914522	+	0.404535i	$0.132567\pi$
$822$		0			0
$823$	−6992.59	−	12111.5i	−0.296168	−	0.512978i	0.679088	−	0.734057i	$-0.262375\pi$
$823$	−6992.59	−	12111.5i	−0.296168	−	0.512978i	−0.975256	+	0.221079i	$0.929042\pi$
$824$		0			0
$825$	6646.83			0.280500
$826$		0			0
$827$	13939.5			0.586125			0.293063	−	0.956093i	$-0.405326\pi$
$827$	13939.5			0.586125			0.293063	+	0.956093i	$0.405326\pi$
$828$		0			0
$829$	10052.2	+	17410.9i	0.421143	+	0.729441i	0.996052	−	0.0887769i	$-0.0282958\pi$
$829$	10052.2	+	17410.9i	0.421143	+	0.729441i	−0.574909	+	0.818218i	$0.694962\pi$
$830$		0			0
$831$	−11045.9	+	19132.0i	−0.461103	+	0.798654i
$832$		0			0
$833$	5029.55	+	17564.8i	0.209200	+	0.730593i
$834$		0			0
$835$	−3065.33	+	5309.31i	−0.127042	+	0.220043i
$836$		0			0
$837$	−2131.30	−	3691.51i	−0.0880148	−	0.152446i
$838$		0			0
$839$	−15949.5			−0.656302			−0.328151	−	0.944625i	$-0.606425\pi$
$839$	−15949.5			−0.656302			−0.328151	+	0.944625i	$0.606425\pi$
$840$		0			0
$841$	10390.8			0.426043
$842$		0			0
$843$	7968.07	+	13801.1i	0.325546	+	0.563861i
$844$		0			0
$845$	18100.4	−	31350.8i	0.736891	−	1.27633i
$846$		0			0
$847$	17764.0	+	13391.3i	0.720635	+	0.543248i
$848$		0			0
$849$	−1637.65	+	2836.49i	−0.0662001	+	0.114662i
$850$		0			0
$851$	284.847	+	493.369i	0.0114741	+	0.0198737i
$852$		0			0
$853$	11802.0			0.473730			0.236865	−	0.971543i	$-0.423880\pi$
$853$	11802.0			0.473730			0.236865	+	0.971543i	$0.423880\pi$
$854$		0			0
$855$	6824.00			0.272954
$856$		0			0
$857$	−4797.64	−	8309.76i	−0.191230	−	0.331220i	0.754428	−	0.656383i	$-0.227914\pi$
$857$	−4797.64	−	8309.76i	−0.191230	−	0.331220i	−0.945658	+	0.325162i	$0.894581\pi$
$858$		0			0
$859$	10920.4	−	18914.7i	0.433760	−	0.751295i	−0.563433	−	0.826162i	$-0.690520\pi$
$859$	10920.4	−	18914.7i	0.433760	−	0.751295i	0.997194	+	0.0748666i	$0.0238531\pi$
$860$		0			0
$861$	−2011.29	+	853.302i	−0.0796106	+	0.0337752i
$862$		0			0
$863$	−13265.8	+	22977.1i	−0.523260	+	0.906313i	0.476374	+	0.879243i	$0.341951\pi$
$863$	−13265.8	+	22977.1i	−0.523260	+	0.906313i	−0.999634	+	0.0270699i	$0.991382\pi$
$864$		0			0
$865$	37419.5	+	64812.4i	1.47087	+	2.54762i
$866$		0			0
$867$	−6226.77			−0.243912
$868$		0			0
$869$	−10371.4			−0.404862
$870$		0			0
$871$	−952.491	−	1649.76i	−0.0370539	−	0.0641792i
$872$		0			0
$873$	−3249.06	+	5627.53i	−0.125961	+	0.218171i
$874$		0			0
$875$	−2805.97	+	22817.7i	−0.108410	+	0.881576i
$876$		0			0
$877$	3416.23	−	5917.09i	0.131537	−	0.227829i	−0.792732	−	0.609570i	$-0.791342\pi$
$877$	3416.23	−	5917.09i	0.131537	−	0.227829i	0.924269	+	0.381741i	$0.124675\pi$
$878$		0			0
$879$	10787.8	+	18685.0i	0.413951	+	0.716985i
$880$		0			0
$881$	−3994.77			−0.152766			−0.0763832	−	0.997079i	$-0.524337\pi$
$881$	−3994.77			−0.152766			−0.0763832	+	0.997079i	$0.524337\pi$
$882$		0			0
$883$	−13727.0			−0.523161			−0.261580	−	0.965182i	$-0.584244\pi$
$883$	−13727.0			−0.523161			−0.261580	+	0.965182i	$0.584244\pi$
$884$		0			0
$885$	−6074.50	−	10521.3i	−0.230726	−	0.399628i
$886$		0			0
$887$	22059.7	−	38208.5i	0.835054	−	1.44636i	−0.0589333	−	0.998262i	$-0.518770\pi$
$887$	22059.7	−	38208.5i	0.835054	−	1.44636i	0.893987	−	0.448093i	$-0.147897\pi$
$888$		0			0
$889$	2203.46	−	17918.1i	0.0831288	−	0.675990i
$890$		0			0
$891$	−461.463	+	799.278i	−0.0173508	+	0.0300525i
$892$		0			0
$893$	449.398	+	778.380i	0.0168405	+	0.0291685i
$894$		0			0
$895$	35215.3			1.31522
$896$		0			0
$897$	5976.35			0.222458
$898$		0			0
$899$	−14721.2	−	25497.9i	−0.546140	−	0.945942i
$900$		0			0
$901$	−9745.37	+	16879.5i	−0.360339	+	0.624125i
$902$		0			0
$903$	−21964.9	+	9318.74i	−0.809465	+	0.343420i
$904$		0			0
$905$	32288.9	−	55925.9i	1.18599	−	2.05419i
$906$		0			0
$907$	18452.9	+	31961.4i	0.675545	+	1.17008i	0.976309	+	0.216380i	$0.0694249\pi$
$907$	18452.9	+	31961.4i	0.675545	+	1.17008i	−0.300764	+	0.953698i	$0.597242\pi$
$908$		0			0
$909$	13668.1			0.498725
$910$		0			0
$911$	3169.56			0.115271			0.0576356	−	0.998338i	$-0.481644\pi$
$911$	3169.56			0.115271			0.0576356	+	0.998338i	$0.481644\pi$
$912$		0			0
$913$	−1868.24	−	3235.88i	−0.0677214	−	0.117297i
$914$		0			0
$915$	−17479.3	+	30275.0i	−0.631527	+	1.09384i
$916$		0			0
$917$	−26512.0	−	19986.0i	−0.954749	−	0.719733i
$918$		0			0
$919$	4363.50	−	7557.80i	0.156625	−	0.271283i	−0.777024	−	0.629470i	$-0.783272\pi$
$919$	4363.50	−	7557.80i	0.156625	−	0.271283i	0.933650	+	0.358188i	$0.116605\pi$
$920$		0			0
$921$	812.032	+	1406.48i	0.0290525	+	0.0503204i
$922$		0			0
$923$	−4832.91			−0.172348
$924$		0			0
$925$	728.392			0.0258912
$926$		0			0
$927$	−4733.47	−	8198.62i	−0.167711	−	0.290483i
$928$		0			0
$929$	−9702.54	+	16805.3i	−0.342659	+	0.593502i	−0.984926	−	0.172979i	$-0.944661\pi$
$929$	−9702.54	+	16805.3i	−0.342659	+	0.593502i	0.642267	+	0.766481i	$0.277994\pi$
$930$		0			0
$931$	10111.8	−	10463.2i	0.355961	−	0.368334i
$932$		0			0
$933$	81.0252	−	140.340i	0.00284314	−	0.00492446i
$934$		0			0
$935$	−5423.95	−	9394.55i	−0.189713	−	0.328593i
$936$		0			0
$937$	−615.692			−0.0214662			−0.0107331	−	0.999942i	$-0.503417\pi$
$937$	−615.692			−0.0214662			−0.0107331	+	0.999942i	$0.503417\pi$
$938$		0			0
$939$	11318.8			0.393372
$940$		0			0
$941$	14801.0	+	25636.1i	0.512751	+	0.888111i	0.999891	+	0.0147865i	$0.00470687\pi$
$941$	14801.0	+	25636.1i	0.512751	+	0.888111i	−0.487140	+	0.873324i	$0.661960\pi$
$942$		0			0
$943$	−2990.23	+	5179.23i	−0.103261	+	0.178854i
$944$		0			0
$945$	−7136.76	−	5380.02i	−0.245671	−	0.185198i
$946$		0			0
$947$	6768.71	−	11723.8i	0.232264	−	0.402292i	−0.726210	−	0.687473i	$-0.758720\pi$
$947$	6768.71	−	11723.8i	0.232264	−	0.402292i	0.958474	+	0.285180i	$0.0920535\pi$
$948$		0			0
$949$	3987.93	+	6907.29i	0.136411	+	0.236270i
$950$		0			0
$951$	5157.71			0.175868
$952$		0			0
$953$	33468.5			1.13762			0.568810	−	0.822469i	$-0.307404\pi$
$953$	33468.5			1.13762			0.568810	+	0.822469i	$0.307404\pi$
$954$		0			0
$955$	17049.0	+	29529.7i	0.577688	+	1.00058i
$956$		0			0
$957$	−3187.40	+	5520.74i	−0.107664	+	0.186479i
$958$		0			0
$959$	28718.2	−	12183.8i	0.967005	−	0.410257i
$960$		0			0
$961$	2433.44	−	4214.85i	0.0816838	−	0.141480i
$962$		0			0
$963$	3449.34	+	5974.44i	0.115424	+	0.199921i
$964$		0			0
$965$	42894.4			1.43090
$966$		0			0
$967$	55733.5			1.85343			0.926715	−	0.375764i	$-0.122620\pi$
$967$	55733.5			1.85343			0.926715	+	0.375764i	$0.122620\pi$
$968$		0			0
$969$	−3389.58	−	5870.93i	−0.112373	−	0.194635i
$970$		0			0
$971$	−9745.65	+	16880.0i	−0.322094	+	0.557882i	−0.980920	−	0.194413i	$-0.937720\pi$
$971$	−9745.65	+	16880.0i	−0.322094	+	0.557882i	0.658826	+	0.752295i	$0.271053\pi$
$972$		0			0
$973$	712.251	−	5791.91i	0.0234673	−	0.190832i
$974$		0			0
$975$	3820.58	−	6617.44i	0.125494	−	0.217362i
$976$		0			0
$977$	3120.78	+	5405.35i	0.102193	+	0.177004i	0.912588	−	0.408881i	$-0.134081\pi$
$977$	3120.78	+	5405.35i	0.102193	+	0.177004i	−0.810395	+	0.585884i	$0.800747\pi$
$978$		0			0
$979$	−428.554			−0.0139905
$980$		0			0
$981$	−12843.4			−0.418001
$982$		0			0
$983$	29847.3	+	51697.0i	0.968444	+	1.67739i	0.700062	+	0.714082i	$0.253155\pi$
$983$	29847.3	+	51697.0i	0.968444	+	1.67739i	0.268382	+	0.963313i	$0.413511\pi$
$984$		0			0
$985$	−13532.8	+	23439.6i	−0.437758	+	0.758220i
$986$		0			0
$987$	143.677	−	1168.36i	0.00463353	−	0.0376791i
$988$		0			0
$989$	−32655.7	+	56561.3i	−1.04994	+	1.81855i
$990$		0			0
$991$	7780.82	+	13476.8i	0.249411	+	0.431992i	0.963362	−	0.268203i	$-0.0864298\pi$
$991$	7780.82	+	13476.8i	0.249411	+	0.431992i	−0.713952	+	0.700195i	$0.753096\pi$
$992$		0			0
$993$	−25224.6			−0.806123
$994$		0			0
$995$	−24446.6			−0.778903
$996$		0			0
$997$	−9942.47	−	17220.9i	−0.315829	−	0.547031i	0.663785	−	0.747924i	$-0.268949\pi$
$997$	−9942.47	−	17220.9i	−0.315829	−	0.547031i	−0.979613	+	0.200892i	$0.935616\pi$
$998$		0			0
$999$	−50.5694	+	87.5888i	−0.00160155	+	0.00277396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.k.289.1		6
4.3	odd	2		21.4.e.b.16.3	yes	6
7.2	even	3		2352.4.a.ci.1.3		3
7.4	even	3	inner	336.4.q.k.193.1		6
7.5	odd	6		2352.4.a.cg.1.1		3
12.11	even	2		63.4.e.c.37.1		6
28.3	even	6		147.4.e.n.67.3		6
28.11	odd	6		21.4.e.b.4.3	✓	6
28.19	even	6		147.4.a.m.1.1		3
28.23	odd	6		147.4.a.l.1.1		3
28.27	even	2		147.4.e.n.79.3		6
84.11	even	6		63.4.e.c.46.1		6
84.23	even	6		441.4.a.s.1.3		3
84.47	odd	6		441.4.a.t.1.3		3
84.59	odd	6		441.4.e.w.361.1		6
84.83	odd	2		441.4.e.w.226.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.3	✓	6	28.11	odd	6
21.4.e.b.16.3	yes	6	4.3	odd	2
63.4.e.c.37.1		6	12.11	even	2
63.4.e.c.46.1		6	84.11	even	6
147.4.a.l.1.1		3	28.23	odd	6
147.4.a.m.1.1		3	28.19	even	6
147.4.e.n.67.3		6	28.3	even	6
147.4.e.n.79.3		6	28.27	even	2
336.4.q.k.193.1		6	7.4	even	3	inner
336.4.q.k.289.1		6	1.1	even	1	trivial
441.4.a.s.1.3		3	84.23	even	6
441.4.a.t.1.3		3	84.47	odd	6
441.4.e.w.226.1		6	84.83	odd	2
441.4.e.w.361.1		6	84.59	odd	6
2352.4.a.cg.1.1		3	7.5	odd	6
2352.4.a.ci.1.3		3	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-8.93660 + 15.4786i) q^{5} +(-2.26047 + 18.3818i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-8.93660 + 15.4786i) q^{5} +(-2.26047 + 18.3818i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-5.69708 - 9.86762i) q^{11} -13.0987 q^{13} +53.6196 q^{15} +(-26.6337 - 46.1309i) q^{17} +(-21.2111 + 36.7388i) q^{19} +(51.1480 - 21.6998i) q^{21} +(76.0427 - 131.710i) q^{23} +(-97.2257 - 168.400i) q^{25} +27.0000 q^{27} +186.493 q^{29} +(-78.9369 - 136.723i) q^{31} +(-17.0912 + 29.6029i) q^{33} +(-264.324 - 199.260i) q^{35} +(-1.87294 + 3.24403i) q^{37} +(19.6480 + 34.0313i) q^{39} -39.3230 q^{41} -429.439 q^{43} +(-80.4294 - 139.308i) q^{45} +(10.5934 - 18.3484i) q^{47} +(-332.781 - 83.1031i) q^{49} +(-79.9010 + 138.393i) q^{51} +(-182.952 - 316.882i) q^{53} +203.650 q^{55} +127.267 q^{57} +(-113.289 - 196.222i) q^{59} +(-325.987 + 564.626i) q^{61} +(-133.100 - 100.337i) q^{63} +(117.058 - 202.750i) q^{65} +(72.7166 + 125.949i) q^{67} -456.256 q^{69} +368.962 q^{71} +(-304.453 - 527.328i) q^{73} +(-291.677 + 505.200i) q^{75} +(194.263 - 82.4170i) q^{77} +(455.119 - 788.289i) q^{79} +(-40.5000 - 70.1481i) q^{81} +327.929 q^{83} +952.058 q^{85} +(-279.740 - 484.524i) q^{87} +(18.8059 - 32.5728i) q^{89} +(29.6092 - 240.777i) q^{91} +(-236.811 + 410.168i) q^{93} +(-379.111 - 656.640i) q^{95} +722.013 q^{97} +102.547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 11 q^{5} + 13 q^{7} - 27 q^{9}+O(q^{10}) \) 6 * q - 9 * q^3 - 11 * q^5 + 13 * q^7 - 27 * q^9	\( 6 q - 9 q^{3} - 11 q^{5} + 13 q^{7} - 27 q^{9} + 35 q^{11} + 124 q^{13} + 66 q^{15} - 48 q^{17} - 202 q^{19} + 3 q^{21} + 216 q^{23} - 130 q^{25} + 162 q^{27} + 106 q^{29} - 95 q^{31} + 105 q^{33} - 56 q^{35} - 262 q^{37} - 186 q^{39} + 488 q^{41} - 720 q^{43} - 99 q^{45} - 210 q^{47} - 303 q^{49} - 144 q^{51} - 393 q^{53} + 2062 q^{55} + 1212 q^{57} + 1143 q^{59} + 70 q^{61} - 126 q^{63} + 472 q^{65} - 628 q^{67} - 1296 q^{69} - 636 q^{71} - 988 q^{73} - 390 q^{75} + 1073 q^{77} + 861 q^{79} - 243 q^{81} - 1038 q^{83} + 3600 q^{85} - 159 q^{87} - 1766 q^{89} + 654 q^{91} - 285 q^{93} - 736 q^{95} + 38 q^{97} - 630 q^{99}+O(q^{100}) \) 6 * q - 9 * q^3 - 11 * q^5 + 13 * q^7 - 27 * q^9 + 35 * q^11 + 124 * q^13 + 66 * q^15 - 48 * q^17 - 202 * q^19 + 3 * q^21 + 216 * q^23 - 130 * q^25 + 162 * q^27 + 106 * q^29 - 95 * q^31 + 105 * q^33 - 56 * q^35 - 262 * q^37 - 186 * q^39 + 488 * q^41 - 720 * q^43 - 99 * q^45 - 210 * q^47 - 303 * q^49 - 144 * q^51 - 393 * q^53 + 2062 * q^55 + 1212 * q^57 + 1143 * q^59 + 70 * q^61 - 126 * q^63 + 472 * q^65 - 628 * q^67 - 1296 * q^69 - 636 * q^71 - 988 * q^73 - 390 * q^75 + 1073 * q^77 + 861 * q^79 - 243 * q^81 - 1038 * q^83 + 3600 * q^85 - 159 * q^87 - 1766 * q^89 + 654 * q^91 - 285 * q^93 - 736 * q^95 + 38 * q^97 - 630 * q^99

Introduction

L-functions

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