LMFDB - Embedded newform 336.4.q.f.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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.4.q.f.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(3.00000 - 5.19615i) q^{5} +(3.50000 + 18.1865i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +(3.00000 - 5.19615i) q^{5} +(3.50000 + 18.1865i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-15.0000 - 25.9808i) q^{11} +53.0000 q^{13} +18.0000 q^{15} +(42.0000 + 72.7461i) q^{17} +(-48.5000 + 84.0045i) q^{19} +(-42.0000 + 36.3731i) q^{21} +(42.0000 - 72.7461i) q^{23} +(44.5000 + 77.0763i) q^{25} -27.0000 q^{27} -180.000 q^{29} +(89.5000 + 155.019i) q^{31} +(45.0000 - 77.9423i) q^{33} +(105.000 + 36.3731i) q^{35} +(72.5000 - 125.574i) q^{37} +(79.5000 + 137.698i) q^{39} +126.000 q^{41} +325.000 q^{43} +(27.0000 + 46.7654i) q^{45} +(-183.000 + 316.965i) q^{47} +(-318.500 + 127.306i) q^{49} +(-126.000 + 218.238i) q^{51} +(384.000 + 665.108i) q^{53} -180.000 q^{55} -291.000 q^{57} +(-132.000 - 228.631i) q^{59} +(-409.000 + 708.409i) q^{61} +(-157.500 - 54.5596i) q^{63} +(159.000 - 275.396i) q^{65} +(-261.500 - 452.931i) q^{67} +252.000 q^{69} +342.000 q^{71} +(21.5000 + 37.2391i) q^{73} +(-133.500 + 231.229i) q^{75} +(420.000 - 363.731i) q^{77} +(-585.500 + 1014.12i) q^{79} +(-40.5000 - 70.1481i) q^{81} +810.000 q^{83} +504.000 q^{85} +(-270.000 - 467.654i) q^{87} +(300.000 - 519.615i) q^{89} +(185.500 + 963.886i) q^{91} +(-268.500 + 465.056i) q^{93} +(291.000 + 504.027i) q^{95} +386.000 q^{97} +270.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 6 q^{5} + 7 q^{7} - 9 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 6 * q^5 + 7 * q^7 - 9 * q^9	$ 2 q + 3 q^{3} + 6 q^{5} + 7 q^{7} - 9 q^{9} - 30 q^{11} + 106 q^{13} + 36 q^{15} + 84 q^{17} - 97 q^{19} - 84 q^{21} + 84 q^{23} + 89 q^{25} - 54 q^{27} - 360 q^{29} + 179 q^{31} + 90 q^{33} + 210 q^{35} + 145 q^{37} + 159 q^{39} + 252 q^{41} + 650 q^{43} + 54 q^{45} - 366 q^{47} - 637 q^{49} - 252 q^{51} + 768 q^{53} - 360 q^{55} - 582 q^{57} - 264 q^{59} - 818 q^{61} - 315 q^{63} + 318 q^{65} - 523 q^{67} + 504 q^{69} + 684 q^{71} + 43 q^{73} - 267 q^{75} + 840 q^{77} - 1171 q^{79} - 81 q^{81} + 1620 q^{83} + 1008 q^{85} - 540 q^{87} + 600 q^{89} + 371 q^{91} - 537 q^{93} + 582 q^{95} + 772 q^{97} + 540 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 6 * q^5 + 7 * q^7 - 9 * q^9 - 30 * q^11 + 106 * q^13 + 36 * q^15 + 84 * q^17 - 97 * q^19 - 84 * q^21 + 84 * q^23 + 89 * q^25 - 54 * q^27 - 360 * q^29 + 179 * q^31 + 90 * q^33 + 210 * q^35 + 145 * q^37 + 159 * q^39 + 252 * q^41 + 650 * q^43 + 54 * q^45 - 366 * q^47 - 637 * q^49 - 252 * q^51 + 768 * q^53 - 360 * q^55 - 582 * q^57 - 264 * q^59 - 818 * q^61 - 315 * q^63 + 318 * q^65 - 523 * q^67 + 504 * q^69 + 684 * q^71 + 43 * q^73 - 267 * q^75 + 840 * q^77 - 1171 * q^79 - 81 * q^81 + 1620 * q^83 + 1008 * q^85 - 540 * q^87 + 600 * q^89 + 371 * q^91 - 537 * q^93 + 582 * q^95 + 772 * q^97 + 540 * 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
$5$	3.00000	−	5.19615i	0.268328	−	0.464758i	−0.700102	−	0.714043i	$-0.746862\pi$
$5$	3.00000	−	5.19615i	0.268328	−	0.464758i	0.968430	+	0.249285i	$0.0801955\pi$
$6$		0			0
$7$	3.50000	+	18.1865i	0.188982	+	0.981981i
$7$	3.50000	+	18.1865i	0.188982	+	0.981981i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−15.0000	−	25.9808i	−0.411152	−	0.712136i	0.583864	−	0.811851i	$-0.301540\pi$
$11$	−15.0000	−	25.9808i	−0.411152	−	0.712136i	−0.995016	+	0.0997155i	$0.968207\pi$
$12$		0			0
$13$	53.0000			1.13074			0.565368	−	0.824839i	$-0.308734\pi$
$13$	53.0000			1.13074			0.565368	+	0.824839i	$0.308734\pi$
$14$		0			0
$15$	18.0000			0.309839
$16$		0			0
$17$	42.0000	+	72.7461i	0.599206	+	1.03785i	0.992939	+	0.118630i	$0.0378502\pi$
$17$	42.0000	+	72.7461i	0.599206	+	1.03785i	−0.393733	+	0.919225i	$0.628817\pi$
$18$		0			0
$19$	−48.5000	+	84.0045i	−0.585614	+	1.01431i	0.409185	+	0.912452i	$0.365813\pi$
$19$	−48.5000	+	84.0045i	−0.585614	+	1.01431i	−0.994799	+	0.101861i	$0.967520\pi$
$20$		0			0
$21$	−42.0000	+	36.3731i	−0.436436	+	0.377964i
$22$		0			0
$23$	42.0000	−	72.7461i	0.380765	−	0.659505i	−0.610406	−	0.792088i	$-0.708994\pi$
$23$	42.0000	−	72.7461i	0.380765	−	0.659505i	0.991172	+	0.132583i	$0.0423272\pi$
$24$		0			0
$25$	44.5000	+	77.0763i	0.356000	+	0.616610i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−180.000			−1.15259			−0.576296	−	0.817241i	$-0.695502\pi$
$29$	−180.000			−1.15259			−0.576296	+	0.817241i	$0.695502\pi$
$30$		0			0
$31$	89.5000	+	155.019i	0.518538	+	0.898134i	0.999768	+	0.0215397i	$0.00685682\pi$
$31$	89.5000	+	155.019i	0.518538	+	0.898134i	−0.481230	+	0.876594i	$0.659810\pi$
$32$		0			0
$33$	45.0000	−	77.9423i	0.237379	−	0.411152i
$34$		0			0
$35$	105.000	+	36.3731i	0.507093	+	0.175662i
$36$		0			0
$37$	72.5000	−	125.574i	0.322133	−	0.557951i	−0.658795	−	0.752323i	$-0.728933\pi$
$37$	72.5000	−	125.574i	0.322133	−	0.557951i	0.980928	+	0.194372i	$0.0622668\pi$
$38$		0			0
$39$	79.5000	+	137.698i	0.326415	+	0.565368i
$40$		0			0
$41$	126.000			0.479949			0.239974	−	0.970779i	$-0.422861\pi$
$41$	126.000			0.479949			0.239974	+	0.970779i	$0.422861\pi$
$42$		0			0
$43$	325.000			1.15261			0.576303	−	0.817236i	$-0.304495\pi$
$43$	325.000			1.15261			0.576303	+	0.817236i	$0.304495\pi$
$44$		0			0
$45$	27.0000	+	46.7654i	0.0894427	+	0.154919i
$46$		0			0
$47$	−183.000	+	316.965i	−0.567942	+	0.983705i	0.428827	+	0.903387i	$0.358927\pi$
$47$	−183.000	+	316.965i	−0.567942	+	0.983705i	−0.996769	+	0.0803184i	$0.974406\pi$
$48$		0			0
$49$	−318.500	+	127.306i	−0.928571	+	0.371154i
$50$		0			0
$51$	−126.000	+	218.238i	−0.345952	+	0.599206i
$52$		0			0
$53$	384.000	+	665.108i	0.995216	+	1.72376i	0.582217	+	0.813034i	$0.302186\pi$
$53$	384.000	+	665.108i	0.995216	+	1.72376i	0.413000	+	0.910731i	$0.364481\pi$
$54$		0			0
$55$	−180.000			−0.441294
$56$		0			0
$57$	−291.000			−0.676209
$58$		0			0
$59$	−132.000	−	228.631i	−0.291270	−	0.504495i	0.682840	−	0.730568i	$-0.260745\pi$
$59$	−132.000	−	228.631i	−0.291270	−	0.504495i	−0.974110	+	0.226073i	$0.927411\pi$
$60$		0			0
$61$	−409.000	+	708.409i	−0.858477	+	1.48693i	0.0149048	+	0.999889i	$0.495255\pi$
$61$	−409.000	+	708.409i	−0.858477	+	1.48693i	−0.873382	+	0.487036i	$0.838078\pi$
$62$		0			0
$63$	−157.500	−	54.5596i	−0.314970	−	0.109109i
$64$		0			0
$65$	159.000	−	275.396i	0.303408	−	0.525518i
$66$		0			0
$67$	−261.500	−	452.931i	−0.476826	−	0.825886i	0.522822	−	0.852442i	$-0.324879\pi$
$67$	−261.500	−	452.931i	−0.476826	−	0.825886i	−0.999647	+	0.0265560i	$0.991546\pi$
$68$		0			0
$69$	252.000			0.439670
$70$		0			0
$71$	342.000			0.571661			0.285831	−	0.958280i	$-0.407731\pi$
$71$	342.000			0.571661			0.285831	+	0.958280i	$0.407731\pi$
$72$		0			0
$73$	21.5000	+	37.2391i	0.0344710	+	0.0597056i	0.882746	−	0.469850i	$-0.155692\pi$
$73$	21.5000	+	37.2391i	0.0344710	+	0.0597056i	−0.848275	+	0.529556i	$0.822359\pi$
$74$		0			0
$75$	−133.500	+	231.229i	−0.205537	+	0.356000i
$76$		0			0
$77$	420.000	−	363.731i	0.621603	−	0.538324i
$78$		0			0
$79$	−585.500	+	1014.12i	−0.833847	+	1.44427i	0.0611191	+	0.998130i	$0.480533\pi$
$79$	−585.500	+	1014.12i	−0.833847	+	1.44427i	−0.894966	+	0.446135i	$0.852800\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	810.000			1.07119			0.535597	−	0.844474i	$-0.320087\pi$
$83$	810.000			1.07119			0.535597	+	0.844474i	$0.320087\pi$
$84$		0			0
$85$	504.000			0.643135
$86$		0			0
$87$	−270.000	−	467.654i	−0.332725	−	0.576296i
$88$		0			0
$89$	300.000	−	519.615i	0.357303	−	0.618866i	−0.630207	−	0.776428i	$-0.717030\pi$
$89$	300.000	−	519.615i	0.357303	−	0.618866i	0.987509	+	0.157561i	$0.0503631\pi$
$90$		0			0
$91$	185.500	+	963.886i	0.213689	+	1.11036i
$92$		0			0
$93$	−268.500	+	465.056i	−0.299378	+	0.518538i
$94$		0			0
$95$	291.000	+	504.027i	0.314273	+	0.544337i
$96$		0			0
$97$	386.000			0.404045			0.202022	−	0.979381i	$-0.435249\pi$
$97$	386.000			0.404045			0.202022	+	0.979381i	$0.435249\pi$
$98$		0			0
$99$	270.000			0.274101
$100$		0			0
$101$	−309.000	−	535.204i	−0.304422	−	0.527275i	0.672710	−	0.739906i	$-0.265130\pi$
$101$	−309.000	−	535.204i	−0.304422	−	0.527275i	−0.977133	+	0.212631i	$0.931797\pi$
$102$		0			0
$103$	737.500	−	1277.39i	0.705515	−	1.22199i	−0.260991	−	0.965341i	$-0.584049\pi$
$103$	737.500	−	1277.39i	0.705515	−	1.22199i	0.966505	−	0.256646i	$-0.0826175\pi$
$104$		0			0
$105$	63.0000	+	327.358i	0.0585540	+	0.304256i
$106$		0			0
$107$	942.000	−	1631.59i	0.851090	−	1.47413i	−0.0291364	−	0.999575i	$-0.509276\pi$
$107$	942.000	−	1631.59i	0.851090	−	1.47413i	0.880226	−	0.474555i	$-0.157391\pi$
$108$		0			0
$109$	−206.500	−	357.668i	−0.181460	−	0.314298i	0.760918	−	0.648848i	$-0.224749\pi$
$109$	−206.500	−	357.668i	−0.181460	−	0.314298i	−0.942378	+	0.334550i	$0.891416\pi$
$110$		0			0
$111$	435.000			0.371967
$112$		0			0
$113$	−882.000			−0.734262			−0.367131	−	0.930169i	$-0.619660\pi$
$113$	−882.000			−0.734262			−0.367131	+	0.930169i	$0.619660\pi$
$114$		0			0
$115$	−252.000	−	436.477i	−0.204340	−	0.353928i
$116$		0			0
$117$	−238.500	+	413.094i	−0.188456	+	0.326415i
$118$		0			0
$119$	−1176.00	+	1018.45i	−0.905914	+	0.784544i
$120$		0			0
$121$	215.500	−	373.257i	0.161908	−	0.280433i
$122$		0			0
$123$	189.000	+	327.358i	0.138549	+	0.239974i
$124$		0			0
$125$	1284.00			0.918756
$126$		0			0
$127$	−2483.00			−1.73489			−0.867443	−	0.497536i	$-0.834238\pi$
$127$	−2483.00			−1.73489			−0.867443	+	0.497536i	$0.834238\pi$
$128$		0			0
$129$	487.500	+	844.375i	0.332729	+	0.576303i
$130$		0			0
$131$	1059.00	−	1834.24i	0.706300	−	1.22335i	−0.259921	−	0.965630i	$-0.583696\pi$
$131$	1059.00	−	1834.24i	0.706300	−	1.22335i	0.966220	−	0.257717i	$-0.0829702\pi$
$132$		0			0
$133$	−1697.50	−	588.031i	−1.10671	−	0.383374i
$134$		0			0
$135$	−81.0000	+	140.296i	−0.0516398	+	0.0894427i
$136$		0			0
$137$	−1506.00	−	2608.47i	−0.939170	−	1.62669i	−0.767024	−	0.641618i	$-0.778263\pi$
$137$	−1506.00	−	2608.47i	−0.939170	−	1.62669i	−0.172146	−	0.985071i	$-0.555070\pi$
$138$		0			0
$139$	37.0000			0.0225777			0.0112888	−	0.999936i	$-0.496407\pi$
$139$	37.0000			0.0225777			0.0112888	+	0.999936i	$0.496407\pi$
$140$		0			0
$141$	−1098.00			−0.655803
$142$		0			0
$143$	−795.000	−	1376.98i	−0.464904	−	0.805237i
$144$		0			0
$145$	−540.000	+	935.307i	−0.309273	+	0.535676i
$146$		0			0
$147$	−808.500	−	636.529i	−0.453632	−	0.357143i
$148$		0			0
$149$	822.000	−	1423.75i	0.451952	−	0.782804i	−0.546555	−	0.837423i	$-0.684061\pi$
$149$	822.000	−	1423.75i	0.451952	−	0.782804i	0.998507	+	0.0546191i	$0.0173945\pi$
$150$		0			0
$151$	544.000	+	942.236i	0.293179	+	0.507802i	0.974560	−	0.224128i	$-0.0719533\pi$
$151$	544.000	+	942.236i	0.293179	+	0.507802i	−0.681380	+	0.731930i	$0.738620\pi$
$152$		0			0
$153$	−756.000			−0.399470
$154$		0			0
$155$	1074.00			0.556553
$156$		0			0
$157$	−253.000	−	438.209i	−0.128609	−	0.222757i	0.794529	−	0.607226i	$-0.207718\pi$
$157$	−253.000	−	438.209i	−0.128609	−	0.222757i	−0.923138	+	0.384469i	$0.874385\pi$
$158$		0			0
$159$	−1152.00	+	1995.32i	−0.574588	+	0.995216i
$160$		0			0
$161$	1470.00	+	509.223i	0.719579	+	0.249270i
$162$		0			0
$163$	922.000	−	1596.95i	0.443047	−	0.767379i	−0.554867	−	0.831939i	$-0.687231\pi$
$163$	922.000	−	1596.95i	0.443047	−	0.767379i	0.997914	+	0.0645596i	$0.0205642\pi$
$164$		0			0
$165$	−270.000	−	467.654i	−0.127391	−	0.220647i
$166$		0			0
$167$	−162.000			−0.0750655			−0.0375327	−	0.999295i	$-0.511950\pi$
$167$	−162.000			−0.0750655			−0.0375327	+	0.999295i	$0.511950\pi$
$168$		0			0
$169$	612.000			0.278562
$170$		0			0
$171$	−436.500	−	756.040i	−0.195205	−	0.338104i
$172$		0			0
$173$	1362.00	−	2359.05i	0.598560	−	1.03674i	−0.394473	−	0.918907i	$-0.629073\pi$
$173$	1362.00	−	2359.05i	0.598560	−	1.03674i	0.993034	−	0.117830i	$-0.0375937\pi$
$174$		0			0
$175$	−1246.00	+	1079.07i	−0.538221	+	0.466113i
$176$		0			0
$177$	396.000	−	685.892i	0.168165	−	0.291270i
$178$		0			0
$179$	−627.000	−	1086.00i	−0.261811	−	0.453470i	0.704912	−	0.709295i	$-0.250986\pi$
$179$	−627.000	−	1086.00i	−0.261811	−	0.453470i	−0.966723	+	0.255825i	$0.917653\pi$
$180$		0			0
$181$	−1807.00			−0.742062			−0.371031	−	0.928620i	$-0.620996\pi$
$181$	−1807.00			−0.742062			−0.371031	+	0.928620i	$0.620996\pi$
$182$		0			0
$183$	−2454.00			−0.991284
$184$		0			0
$185$	−435.000	−	753.442i	−0.172875	−	0.299428i
$186$		0			0
$187$	1260.00	−	2182.38i	0.492729	−	0.853432i
$188$		0			0
$189$	−94.5000	−	491.036i	−0.0363696	−	0.188982i
$190$		0			0
$191$	357.000	−	618.342i	0.135244	−	0.234250i	−0.790447	−	0.612531i	$-0.790151\pi$
$191$	357.000	−	618.342i	0.135244	−	0.234250i	0.925691	+	0.378281i	$0.123485\pi$
$192$		0			0
$193$	1854.50	+	3212.09i	0.691657	+	1.19799i	0.971295	+	0.237880i	$0.0764524\pi$
$193$	1854.50	+	3212.09i	0.691657	+	1.19799i	−0.279637	+	0.960106i	$0.590214\pi$
$194$		0			0
$195$	954.000			0.350345
$196$		0			0
$197$	−1044.00			−0.377573			−0.188787	−	0.982018i	$-0.560455\pi$
$197$	−1044.00			−0.377573			−0.188787	+	0.982018i	$0.560455\pi$
$198$		0			0
$199$	−68.0000	−	117.779i	−0.0242231	−	0.0419556i	0.853660	−	0.520831i	$-0.174378\pi$
$199$	−68.0000	−	117.779i	−0.0242231	−	0.0419556i	−0.877883	+	0.478875i	$0.841045\pi$
$200$		0			0
$201$	784.500	−	1358.79i	0.275295	−	0.476826i
$202$		0			0
$203$	−630.000	−	3273.58i	−0.217819	−	1.13182i
$204$		0			0
$205$	378.000	−	654.715i	0.128784	−	0.223060i
$206$		0			0
$207$	378.000	+	654.715i	0.126922	+	0.219835i
$208$		0			0
$209$	2910.00			0.963105
$210$		0			0
$211$	−1484.00			−0.484184			−0.242092	−	0.970253i	$-0.577834\pi$
$211$	−1484.00			−0.484184			−0.242092	+	0.970253i	$0.577834\pi$
$212$		0			0
$213$	513.000	+	888.542i	0.165024	+	0.285831i
$214$		0			0
$215$	975.000	−	1688.75i	0.309277	−	0.535683i
$216$		0			0
$217$	−2506.00	+	2170.26i	−0.783956	+	0.678925i
$218$		0			0
$219$	−64.5000	+	111.717i	−0.0199019	+	0.0344710i
$220$		0			0
$221$	2226.00	+	3855.55i	0.677543	+	1.17354i
$222$		0			0
$223$	2032.00			0.610192			0.305096	−	0.952322i	$-0.401311\pi$
$223$	2032.00			0.610192			0.305096	+	0.952322i	$0.401311\pi$
$224$		0			0
$225$	−801.000			−0.237333
$226$		0			0
$227$	3099.00	+	5367.63i	0.906114	+	1.56944i	0.819415	+	0.573201i	$0.194298\pi$
$227$	3099.00	+	5367.63i	0.906114	+	1.56944i	0.0866989	+	0.996235i	$0.472368\pi$
$228$		0			0
$229$	2295.50	−	3975.92i	0.662406	−	1.14732i	−0.317576	−	0.948233i	$-0.602869\pi$
$229$	2295.50	−	3975.92i	0.662406	−	1.14732i	0.979982	−	0.199088i	$-0.0637978\pi$
$230$		0			0
$231$	1575.00	+	545.596i	0.448603	+	0.155401i
$232$		0			0
$233$	−2265.00	+	3923.10i	−0.636846	+	1.10305i	0.349275	+	0.937020i	$0.386428\pi$
$233$	−2265.00	+	3923.10i	−0.636846	+	1.10305i	−0.986121	+	0.166029i	$0.946905\pi$
$234$		0			0
$235$	1098.00	+	1901.79i	0.304790	+	0.527912i
$236$		0			0
$237$	−3513.00			−0.962843
$238$		0			0
$239$	−1530.00			−0.414090			−0.207045	−	0.978331i	$-0.566385\pi$
$239$	−1530.00			−0.414090			−0.207045	+	0.978331i	$0.566385\pi$
$240$		0			0
$241$	−2767.00	−	4792.58i	−0.739577	−	1.28099i	−0.952686	−	0.303957i	$-0.901692\pi$
$241$	−2767.00	−	4792.58i	−0.739577	−	1.28099i	0.213108	−	0.977029i	$-0.431641\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−294.000	+	2036.89i	−0.0766652	+	0.531152i
$246$		0			0
$247$	−2570.50	+	4452.24i	−0.662174	+	1.14692i
$248$		0			0
$249$	1215.00	+	2104.44i	0.309227	+	0.535597i
$250$		0			0
$251$	468.000			0.117689			0.0588444	−	0.998267i	$-0.481258\pi$
$251$	468.000			0.117689			0.0588444	+	0.998267i	$0.481258\pi$
$252$		0			0
$253$	−2520.00			−0.626210
$254$		0			0
$255$	756.000	+	1309.43i	0.185657	+	0.321568i
$256$		0			0
$257$	1245.00	−	2156.40i	0.302183	−	0.523396i	−0.674447	−	0.738323i	$-0.735618\pi$
$257$	1245.00	−	2156.40i	0.302183	−	0.523396i	0.976630	+	0.214927i	$0.0689514\pi$
$258$		0			0
$259$	2537.50	+	879.016i	0.608774	+	0.210886i
$260$		0			0
$261$	810.000	−	1402.96i	0.192099	−	0.332725i
$262$		0			0
$263$	786.000	+	1361.39i	0.184285	+	0.319190i	0.943335	−	0.331841i	$-0.107670\pi$
$263$	786.000	+	1361.39i	0.184285	+	0.319190i	−0.759051	+	0.651032i	$0.774337\pi$
$264$		0			0
$265$	4608.00			1.06818
$266$		0			0
$267$	1800.00			0.412578
$268$		0			0
$269$	−903.000	−	1564.04i	−0.204672	−	0.354503i	0.745356	−	0.666667i	$-0.232280\pi$
$269$	−903.000	−	1564.04i	−0.204672	−	0.354503i	−0.950028	+	0.312164i	$0.898946\pi$
$270$		0			0
$271$	−3056.00	+	5293.15i	−0.685014	+	1.18648i	0.288418	+	0.957504i	$0.406871\pi$
$271$	−3056.00	+	5293.15i	−0.685014	+	1.18648i	−0.973432	+	0.228975i	$0.926463\pi$
$272$		0			0
$273$	−2226.00	+	1927.77i	−0.493493	+	0.427378i
$274$		0			0
$275$	1335.00	−	2312.29i	0.292740	−	0.507041i
$276$		0			0
$277$	2115.50	+	3664.15i	0.458874	+	0.794793i	0.998902	−	0.0468542i	$-0.0149196\pi$
$277$	2115.50	+	3664.15i	0.458874	+	0.794793i	−0.540028	+	0.841647i	$0.681586\pi$
$278$		0			0
$279$	−1611.00			−0.345692
$280$		0			0
$281$	−3816.00			−0.810119			−0.405060	−	0.914290i	$-0.632749\pi$
$281$	−3816.00			−0.810119			−0.405060	+	0.914290i	$0.632749\pi$
$282$		0			0
$283$	−1998.50	−	3461.50i	−0.419783	−	0.727085i	0.576135	−	0.817355i	$-0.304560\pi$
$283$	−1998.50	−	3461.50i	−0.419783	−	0.727085i	−0.995917	+	0.0902699i	$0.971227\pi$
$284$		0			0
$285$	−873.000	+	1512.08i	−0.181446	+	0.314273i
$286$		0			0
$287$	441.000	+	2291.50i	0.0907018	+	0.471300i
$288$		0			0
$289$	−1071.50	+	1855.89i	−0.218095	+	0.377751i
$290$		0			0
$291$	579.000	+	1002.86i	0.116638	+	0.202022i
$292$		0			0
$293$	4608.00			0.918779			0.459389	−	0.888235i	$-0.348068\pi$
$293$	4608.00			0.918779			0.459389	+	0.888235i	$0.348068\pi$
$294$		0			0
$295$	−1584.00			−0.312624
$296$		0			0
$297$	405.000	+	701.481i	0.0791262	+	0.137051i
$298$		0			0
$299$	2226.00	−	3855.55i	0.430545	−	0.745726i
$300$		0			0
$301$	1137.50	+	5910.62i	0.217822	+	1.13184i
$302$		0			0
$303$	927.000	−	1605.61i	0.175758	−	0.304422i
$304$		0			0
$305$	2454.00	+	4250.45i	0.460707	+	0.797968i
$306$		0			0
$307$	631.000			0.117306			0.0586532	−	0.998278i	$-0.481319\pi$
$307$	631.000			0.117306			0.0586532	+	0.998278i	$0.481319\pi$
$308$		0			0
$309$	4425.00			0.814658
$310$		0			0
$311$	1947.00	+	3372.30i	0.354998	+	0.614874i	0.987118	−	0.159997i	$-0.0511484\pi$
$311$	1947.00	+	3372.30i	0.354998	+	0.614874i	−0.632120	+	0.774871i	$0.717815\pi$
$312$		0			0
$313$	1092.50	−	1892.27i	0.197290	−	0.341716i	−0.750359	−	0.661031i	$-0.770119\pi$
$313$	1092.50	−	1892.27i	0.197290	−	0.341716i	0.947649	+	0.319314i	$0.103453\pi$
$314$		0			0
$315$	−756.000	+	654.715i	−0.135225	+	0.117108i
$316$		0			0
$317$	−1752.00	+	3034.55i	−0.310417	+	0.537658i	−0.978453	−	0.206471i	$-0.933802\pi$
$317$	−1752.00	+	3034.55i	−0.310417	+	0.537658i	0.668036	+	0.744129i	$0.267135\pi$
$318$		0			0
$319$	2700.00	+	4676.54i	0.473890	+	0.820802i
$320$		0			0
$321$	5652.00			0.982754
$322$		0			0
$323$	−8148.00			−1.40361
$324$		0			0
$325$	2358.50	+	4085.04i	0.402542	+	0.697223i
$326$		0			0
$327$	619.500	−	1073.01i	0.104766	−	0.181460i
$328$		0			0
$329$	−6405.00	−	2218.76i	−1.07331	−	0.371806i
$330$		0			0
$331$	1472.50	−	2550.44i	0.244519	−	0.423520i	−0.717477	−	0.696582i	$-0.754703\pi$
$331$	1472.50	−	2550.44i	0.244519	−	0.423520i	0.961996	+	0.273062i	$0.0880365\pi$
$332$		0			0
$333$	652.500	+	1130.16i	0.107378	+	0.185984i
$334$		0			0
$335$	−3138.00			−0.511783
$336$		0			0
$337$	4277.00			0.691344			0.345672	−	0.938355i	$-0.387651\pi$
$337$	4277.00			0.691344			0.345672	+	0.938355i	$0.387651\pi$
$338$		0			0
$339$	−1323.00	−	2291.50i	−0.211963	−	0.367131i
$340$		0			0
$341$	2685.00	−	4650.56i	0.426396	−	0.738539i
$342$		0			0
$343$	−3430.00	−	5346.84i	−0.539949	−	0.841698i
$344$		0			0
$345$	756.000	−	1309.43i	0.117976	−	0.204340i
$346$		0			0
$347$	3594.00	+	6224.99i	0.556012	+	0.963040i	0.997824	+	0.0659329i	$0.0210023\pi$
$347$	3594.00	+	6224.99i	0.556012	+	0.963040i	−0.441812	+	0.897107i	$0.645664\pi$
$348$		0			0
$349$	−9406.00			−1.44267			−0.721335	−	0.692587i	$-0.756471\pi$
$349$	−9406.00			−1.44267			−0.721335	+	0.692587i	$0.756471\pi$
$350$		0			0
$351$	−1431.00			−0.217610
$352$		0			0
$353$	−1695.00	−	2935.83i	−0.255569	−	0.442658i	0.709481	−	0.704724i	$-0.248929\pi$
$353$	−1695.00	−	2935.83i	−0.255569	−	0.442658i	−0.965050	+	0.262066i	$0.915596\pi$
$354$		0			0
$355$	1026.00	−	1777.08i	0.153393	−	0.265684i
$356$		0			0
$357$	−4410.00	−	1527.67i	−0.653787	−	0.226478i
$358$		0			0
$359$	−2406.00	+	4167.31i	−0.353715	+	0.612653i	−0.986897	−	0.161350i	$-0.948415\pi$
$359$	−2406.00	+	4167.31i	−0.353715	+	0.612653i	0.633182	+	0.774003i	$0.281749\pi$
$360$		0			0
$361$	−1275.00	−	2208.36i	−0.185887	−	0.321966i
$362$		0			0
$363$	1293.00			0.186956
$364$		0			0
$365$	258.000			0.0369982
$366$		0			0
$367$	−3549.50	−	6147.91i	−0.504857	−	0.874437i	−0.999984	−	0.00561709i	$-0.998212\pi$
$367$	−3549.50	−	6147.91i	−0.504857	−	0.874437i	0.495128	−	0.868820i	$-0.335121\pi$
$368$		0			0
$369$	−567.000	+	982.073i	−0.0799914	+	0.138549i
$370$		0			0
$371$	−10752.0	+	9311.51i	−1.50463	+	1.30304i
$372$		0			0
$373$	−1481.50	+	2566.03i	−0.205655	+	0.356204i	−0.950341	−	0.311210i	$-0.899266\pi$
$373$	−1481.50	+	2566.03i	−0.205655	+	0.356204i	0.744687	+	0.667414i	$0.232599\pi$
$374$		0			0
$375$	1926.00	+	3335.93i	0.265222	+	0.459378i
$376$		0			0
$377$	−9540.00			−1.30328
$378$		0			0
$379$	11899.0			1.61269			0.806346	−	0.591444i	$-0.201442\pi$
$379$	11899.0			1.61269			0.806346	+	0.591444i	$0.201442\pi$
$380$		0			0
$381$	−3724.50	−	6451.02i	−0.500819	−	0.867443i
$382$		0			0
$383$	1284.00	−	2223.95i	0.171304	−	0.296707i	−0.767572	−	0.640963i	$-0.778535\pi$
$383$	1284.00	−	2223.95i	0.171304	−	0.296707i	0.938876	+	0.344256i	$0.111869\pi$
$384$		0			0
$385$	−630.000	−	3273.58i	−0.0833968	−	0.433343i
$386$		0			0
$387$	−1462.50	+	2533.12i	−0.192101	+	0.332729i
$388$		0			0
$389$	5073.00	+	8786.69i	0.661212	+	1.14525i	0.980298	+	0.197526i	$0.0632908\pi$
$389$	5073.00	+	8786.69i	0.661212	+	1.14525i	−0.319086	+	0.947726i	$0.603376\pi$
$390$		0			0
$391$	7056.00			0.912627
$392$		0			0
$393$	6354.00			0.815565
$394$		0			0
$395$	3513.00	+	6084.69i	0.447489	+	0.775074i
$396$		0			0
$397$	3114.50	−	5394.47i	0.393734	−	0.681967i	−0.599205	−	0.800596i	$-0.704517\pi$
$397$	3114.50	−	5394.47i	0.393734	−	0.681967i	0.992939	+	0.118629i	$0.0378499\pi$
$398$		0			0
$399$	−1018.50	−	5292.28i	−0.127791	−	0.664024i
$400$		0			0
$401$	1236.00	−	2140.81i	0.153922	−	0.266601i	−0.778744	−	0.627342i	$-0.784143\pi$
$401$	1236.00	−	2140.81i	0.153922	−	0.266601i	0.932666	+	0.360741i	$0.117476\pi$
$402$		0			0
$403$	4743.50	+	8215.98i	0.586329	+	1.01555i
$404$		0			0
$405$	−486.000			−0.0596285
$406$		0			0
$407$	−4350.00			−0.529783
$408$		0			0
$409$	3537.50	+	6127.13i	0.427673	+	0.740751i	0.996666	−	0.0815915i	$-0.0260003\pi$
$409$	3537.50	+	6127.13i	0.427673	+	0.740751i	−0.568993	+	0.822342i	$0.692667\pi$
$410$		0			0
$411$	4518.00	−	7825.41i	0.542230	−	0.939170i
$412$		0			0
$413$	3696.00	−	3200.83i	0.440359	−	0.381362i
$414$		0			0
$415$	2430.00	−	4208.88i	0.287431	−	0.497846i
$416$		0			0
$417$	55.5000	+	96.1288i	0.00651762	+	0.0112888i
$418$		0			0
$419$	4158.00			0.484801			0.242400	−	0.970176i	$-0.422065\pi$
$419$	4158.00			0.484801			0.242400	+	0.970176i	$0.422065\pi$
$420$		0			0
$421$	−6595.00			−0.763469			−0.381735	−	0.924272i	$-0.624673\pi$
$421$	−6595.00			−0.763469			−0.381735	+	0.924272i	$0.624673\pi$
$422$		0			0
$423$	−1647.00	−	2852.69i	−0.189314	−	0.327902i
$424$		0			0
$425$	−3738.00	+	6474.41i	−0.426634	+	0.738953i
$426$		0			0
$427$	−14315.0	−	4958.86i	−1.62237	−	0.562005i
$428$		0			0
$429$	2385.00	−	4130.94i	0.268412	−	0.464904i
$430$		0			0
$431$	759.000	+	1314.63i	0.0848254	+	0.146922i	0.905317	−	0.424737i	$-0.139633\pi$
$431$	759.000	+	1314.63i	0.0848254	+	0.146922i	−0.820491	+	0.571659i	$0.806300\pi$
$432$		0			0
$433$	8567.00			0.950817			0.475408	−	0.879765i	$-0.342300\pi$
$433$	8567.00			0.950817			0.475408	+	0.879765i	$0.342300\pi$
$434$		0			0
$435$	−3240.00			−0.357117
$436$		0			0
$437$	4074.00	+	7056.37i	0.445963	+	0.772431i
$438$		0			0
$439$	5320.00	−	9214.51i	0.578382	−	1.00179i	−0.417283	−	0.908777i	$-0.637018\pi$
$439$	5320.00	−	9214.51i	0.578382	−	1.00179i	0.995665	−	0.0930106i	$-0.0296491\pi$
$440$		0			0
$441$	441.000	−	3055.34i	0.0476190	−	0.329914i
$442$		0			0
$443$	3516.00	−	6089.89i	0.377088	−	0.653136i	−0.613549	−	0.789657i	$-0.710259\pi$
$443$	3516.00	−	6089.89i	0.377088	−	0.653136i	0.990637	+	0.136520i	$0.0435919\pi$
$444$		0			0
$445$	−1800.00	−	3117.69i	−0.191749	−	0.332119i
$446$		0			0
$447$	4932.00			0.521869
$448$		0			0
$449$	−14814.0			−1.55705			−0.778525	−	0.627613i	$-0.784032\pi$
$449$	−14814.0			−1.55705			−0.778525	+	0.627613i	$0.784032\pi$
$450$		0			0
$451$	−1890.00	−	3273.58i	−0.197332	−	0.341789i
$452$		0			0
$453$	−1632.00	+	2826.71i	−0.169267	+	0.293179i
$454$		0			0
$455$	5565.00	+	1927.77i	0.573387	+	0.198627i
$456$		0			0
$457$	5625.50	−	9743.65i	0.575820	−	0.997350i	−0.420132	−	0.907463i	$-0.638016\pi$
$457$	5625.50	−	9743.65i	0.575820	−	0.997350i	0.995952	−	0.0898866i	$-0.0286505\pi$
$458$		0			0
$459$	−1134.00	−	1964.15i	−0.115317	−	0.199735i
$460$		0			0
$461$	−3852.00			−0.389166			−0.194583	−	0.980886i	$-0.562335\pi$
$461$	−3852.00			−0.389166			−0.194583	+	0.980886i	$0.562335\pi$
$462$		0			0
$463$	475.000			0.0476784			0.0238392	−	0.999716i	$-0.492411\pi$
$463$	475.000			0.0476784			0.0238392	+	0.999716i	$0.492411\pi$
$464$		0			0
$465$	1611.00	+	2790.33i	0.160663	+	0.278277i
$466$		0			0
$467$	2967.00	−	5138.99i	0.293997	−	0.509217i	−0.680754	−	0.732512i	$-0.738348\pi$
$467$	2967.00	−	5138.99i	0.293997	−	0.509217i	0.974751	+	0.223295i	$0.0716812\pi$
$468$		0			0
$469$	7322.00	−	6341.04i	0.720892	−	0.624311i
$470$		0			0
$471$	759.000	−	1314.63i	0.0742524	−	0.128609i
$472$		0			0
$473$	−4875.00	−	8443.75i	−0.473896	−	0.820812i
$474$		0			0
$475$	−8633.00			−0.833914
$476$		0			0
$477$	−6912.00			−0.663477
$478$		0			0
$479$	−6684.00	−	11577.0i	−0.637578	−	1.10432i	−0.985963	−	0.166966i	$-0.946603\pi$
$479$	−6684.00	−	11577.0i	−0.637578	−	1.10432i	0.348385	−	0.937352i	$-0.386730\pi$
$480$		0			0
$481$	3842.50	−	6655.41i	0.364247	−	0.630895i
$482$		0			0
$483$	882.000	+	4583.01i	0.0830898	+	0.431747i
$484$		0			0
$485$	1158.00	−	2005.71i	0.108417	−	0.187783i
$486$		0			0
$487$	3326.50	+	5761.67i	0.309524	+	0.536111i	0.978258	−	0.207390i	$-0.0664970\pi$
$487$	3326.50	+	5761.67i	0.309524	+	0.536111i	−0.668734	+	0.743501i	$0.733164\pi$
$488$		0			0
$489$	5532.00			0.511586
$490$		0			0
$491$	−15444.0			−1.41951			−0.709754	−	0.704450i	$-0.751194\pi$
$491$	−15444.0			−1.41951			−0.709754	+	0.704450i	$0.751194\pi$
$492$		0			0
$493$	−7560.00	−	13094.3i	−0.690640	−	1.19622i
$494$		0			0
$495$	810.000	−	1402.96i	0.0735491	−	0.127391i
$496$		0			0
$497$	1197.00	+	6219.79i	0.108034	+	0.561360i
$498$		0			0
$499$	341.500	−	591.495i	0.0306366	−	0.0530641i	−0.850301	−	0.526297i	$-0.823580\pi$
$499$	341.500	−	591.495i	0.0306366	−	0.0530641i	0.880937	+	0.473233i	$0.156913\pi$
$500$		0			0
$501$	−243.000	−	420.888i	−0.0216695	−	0.0375327i
$502$		0			0
$503$	−9882.00			−0.875977			−0.437989	−	0.898980i	$-0.644309\pi$
$503$	−9882.00			−0.875977			−0.437989	+	0.898980i	$0.644309\pi$
$504$		0			0
$505$	−3708.00			−0.326740
$506$		0			0
$507$	918.000	+	1590.02i	0.0804138	+	0.139281i
$508$		0			0
$509$	−2103.00	+	3642.50i	−0.183131	+	0.317193i	−0.942945	−	0.332948i	$-0.891957\pi$
$509$	−2103.00	+	3642.50i	−0.183131	+	0.317193i	0.759814	+	0.650141i	$0.225290\pi$
$510$		0			0
$511$	−602.000	+	521.347i	−0.0521153	+	0.0451332i
$512$		0			0
$513$	1309.50	−	2268.12i	0.112701	−	0.195205i
$514$		0			0
$515$	−4425.00	−	7664.32i	−0.378619	−	0.655787i
$516$		0			0
$517$	10980.0			0.934042
$518$		0			0
$519$	8172.00			0.691158
$520$		0			0
$521$	−4530.00	−	7846.19i	−0.380927	−	0.659785i	0.610268	−	0.792195i	$-0.291062\pi$
$521$	−4530.00	−	7846.19i	−0.380927	−	0.659785i	−0.991195	+	0.132410i	$0.957728\pi$
$522$		0			0
$523$	−7839.50	+	13578.4i	−0.655444	+	1.13526i	0.326338	+	0.945253i	$0.394185\pi$
$523$	−7839.50	+	13578.4i	−0.655444	+	1.13526i	−0.981782	+	0.190010i	$0.939148\pi$
$524$		0			0
$525$	−4672.50	−	1618.60i	−0.388428	−	0.134555i
$526$		0			0
$527$	−7518.00	+	13021.6i	−0.621422	+	1.07633i
$528$		0			0
$529$	2555.50	+	4426.26i	0.210035	+	0.363792i
$530$		0			0
$531$	2376.00			0.194180
$532$		0			0
$533$	6678.00			0.542695
$534$		0			0
$535$	−5652.00	−	9789.55i	−0.456743	−	0.791101i
$536$		0			0
$537$	1881.00	−	3257.99i	0.151157	−	0.261811i
$538$		0			0
$539$	8085.00	+	6365.29i	0.646096	+	0.508668i
$540$		0			0
$541$	3855.50	−	6677.92i	0.306397	−	0.530696i	−0.671174	−	0.741300i	$-0.734210\pi$
$541$	3855.50	−	6677.92i	0.306397	−	0.530696i	0.977571	+	0.210604i	$0.0675431\pi$
$542$		0			0
$543$	−2710.50	−	4694.72i	−0.214215	−	0.371031i
$544$		0			0
$545$	−2478.00			−0.194763
$546$		0			0
$547$	−4292.00			−0.335489			−0.167745	−	0.985830i	$-0.553648\pi$
$547$	−4292.00			−0.335489			−0.167745	+	0.985830i	$0.553648\pi$
$548$		0			0
$549$	−3681.00	−	6375.68i	−0.286159	−	0.495642i
$550$		0			0
$551$	8730.00	−	15120.8i	0.674974	−	1.16909i
$552$		0			0
$553$	−20492.5	−	7098.81i	−1.57582	−	0.545881i
$554$		0			0
$555$	1305.00	−	2260.33i	0.0998093	−	0.172875i
$556$		0			0
$557$	4929.00	+	8537.28i	0.374952	+	0.649436i	0.990320	−	0.138804i	$-0.0443258\pi$
$557$	4929.00	+	8537.28i	0.374952	+	0.649436i	−0.615368	+	0.788240i	$0.710992\pi$
$558$		0			0
$559$	17225.0			1.30329
$560$		0			0
$561$	7560.00			0.568954
$562$		0			0
$563$	−6945.00	−	12029.1i	−0.519888	−	0.900472i	−0.999733	−	0.0231188i	$-0.992640\pi$
$563$	−6945.00	−	12029.1i	−0.519888	−	0.900472i	0.479845	−	0.877353i	$-0.340693\pi$
$564$		0			0
$565$	−2646.00	+	4583.01i	−0.197023	+	0.341254i
$566$		0			0
$567$	1134.00	−	982.073i	0.0839921	−	0.0727393i
$568$		0			0
$569$	−9519.00	+	16487.4i	−0.701331	+	1.21474i	0.266669	+	0.963788i	$0.414077\pi$
$569$	−9519.00	+	16487.4i	−0.701331	+	1.21474i	−0.967999	+	0.250952i	$0.919256\pi$
$570$		0			0
$571$	−4026.50	−	6974.10i	−0.295103	−	0.511133i	0.679906	−	0.733299i	$-0.262021\pi$
$571$	−4026.50	−	6974.10i	−0.295103	−	0.511133i	−0.975009	+	0.222166i	$0.928687\pi$
$572$		0			0
$573$	2142.00			0.156166
$574$		0			0
$575$	7476.00			0.542210
$576$		0			0
$577$	8568.50	+	14841.1i	0.618217	+	1.07078i	0.989811	+	0.142388i	$0.0454781\pi$
$577$	8568.50	+	14841.1i	0.618217	+	1.07078i	−0.371594	+	0.928395i	$0.621189\pi$
$578$		0			0
$579$	−5563.50	+	9636.26i	−0.399328	+	0.691657i
$580$		0			0
$581$	2835.00	+	14731.1i	0.202437	+	1.05189i
$582$		0			0
$583$	11520.0	−	19953.2i	0.818370	−	1.41746i
$584$		0			0
$585$	1431.00	+	2478.56i	0.101136	+	0.175173i
$586$		0			0
$587$	−18144.0			−1.27578			−0.637890	−	0.770127i	$-0.720193\pi$
$587$	−18144.0			−1.27578			−0.637890	+	0.770127i	$0.720193\pi$
$588$		0			0
$589$	−17363.0			−1.21465
$590$		0			0
$591$	−1566.00	−	2712.39i	−0.108996	−	0.188787i
$592$		0			0
$593$	12351.0	−	21392.6i	0.855303	−	1.48143i	−0.0210603	−	0.999778i	$-0.506704\pi$
$593$	12351.0	−	21392.6i	0.855303	−	1.48143i	0.876363	−	0.481650i	$-0.159962\pi$
$594$		0			0
$595$	1764.00	+	9166.01i	0.121541	+	0.631546i
$596$		0			0
$597$	204.000	−	353.338i	0.0139852	−	0.0242231i
$598$		0			0
$599$	−1086.00	−	1881.01i	−0.0740781	−	0.128307i	0.826607	−	0.562780i	$-0.190268\pi$
$599$	−1086.00	−	1881.01i	−0.0740781	−	0.128307i	−0.900685	+	0.434473i	$0.856935\pi$
$600$		0			0
$601$	4175.00			0.283364			0.141682	−	0.989912i	$-0.454749\pi$
$601$	4175.00			0.283364			0.141682	+	0.989912i	$0.454749\pi$
$602$		0			0
$603$	4707.00			0.317884
$604$		0			0
$605$	−1293.00	−	2239.54i	−0.0868891	−	0.150496i
$606$		0			0
$607$	1130.50	−	1958.08i	0.0755940	−	0.130933i	−0.825750	−	0.564036i	$-0.809248\pi$
$607$	1130.50	−	1958.08i	0.0755940	−	0.130933i	0.901344	+	0.433103i	$0.142581\pi$
$608$		0			0
$609$	7560.00	−	6547.15i	0.503032	−	0.435639i
$610$		0			0
$611$	−9699.00	+	16799.2i	−0.642192	+	1.11231i
$612$		0			0
$613$	8159.00	+	14131.8i	0.537584	+	0.931123i	0.999033	+	0.0439561i	$0.0139962\pi$
$613$	8159.00	+	14131.8i	0.537584	+	0.931123i	−0.461450	+	0.887166i	$0.652670\pi$
$614$		0			0
$615$	2268.00			0.148707
$616$		0			0
$617$	−26550.0			−1.73235			−0.866177	−	0.499737i	$-0.833430\pi$
$617$	−26550.0			−1.73235			−0.866177	+	0.499737i	$0.833430\pi$
$618$		0			0
$619$	9962.50	+	17255.6i	0.646893	+	1.12045i	0.983861	+	0.178935i	$0.0572652\pi$
$619$	9962.50	+	17255.6i	0.646893	+	1.12045i	−0.336968	+	0.941516i	$0.609401\pi$
$620$		0			0
$621$	−1134.00	+	1964.15i	−0.0732783	+	0.126922i
$622$		0			0
$623$	10500.0	+	3637.31i	0.675239	+	0.233909i
$624$		0			0
$625$	−1710.50	+	2962.67i	−0.109472	+	0.189611i
$626$		0			0
$627$	4365.00	+	7560.40i	0.278024	+	0.481552i
$628$		0			0
$629$	12180.0			0.772096
$630$		0			0
$631$	6832.00			0.431026			0.215513	−	0.976501i	$-0.430858\pi$
$631$	6832.00			0.431026			0.215513	+	0.976501i	$0.430858\pi$
$632$		0			0
$633$	−2226.00	−	3855.55i	−0.139772	−	0.242092i
$634$		0			0
$635$	−7449.00	+	12902.0i	−0.465519	+	0.806303i
$636$		0			0
$637$	−16880.5	+	6747.20i	−1.04997	+	0.419677i
$638$		0			0
$639$	−1539.00	+	2665.63i	−0.0952768	+	0.165024i
$640$		0			0
$641$	−5106.00	−	8843.85i	−0.314625	−	0.544947i	0.664732	−	0.747082i	$-0.268546\pi$
$641$	−5106.00	−	8843.85i	−0.314625	−	0.544947i	−0.979358	+	0.202134i	$0.935212\pi$
$642$		0			0
$643$	−3779.00			−0.231772			−0.115886	−	0.993263i	$-0.536971\pi$
$643$	−3779.00			−0.231772			−0.115886	+	0.993263i	$0.536971\pi$
$644$		0			0
$645$	5850.00			0.357122
$646$		0			0
$647$	8499.00	+	14720.7i	0.516430	+	0.894483i	0.999818	+	0.0190767i	$0.00607268\pi$
$647$	8499.00	+	14720.7i	0.516430	+	0.894483i	−0.483388	+	0.875406i	$0.660594\pi$
$648$		0			0
$649$	−3960.00	+	6858.92i	−0.239512	+	0.414848i
$650$		0			0
$651$	−9397.50	−	3255.39i	−0.565771	−	0.195989i
$652$		0			0
$653$	10875.0	−	18836.1i	0.651718	−	1.12881i	−0.330988	−	0.943635i	$-0.607382\pi$
$653$	10875.0	−	18836.1i	0.651718	−	1.12881i	0.982706	−	0.185173i	$-0.0592846\pi$
$654$		0			0
$655$	−6354.00	−	11005.5i	−0.379040	−	0.656517i
$656$		0			0
$657$	−387.000			−0.0229807
$658$		0			0
$659$	10944.0			0.646916			0.323458	−	0.946243i	$-0.395155\pi$
$659$	10944.0			0.646916			0.323458	+	0.946243i	$0.395155\pi$
$660$		0			0
$661$	−5477.50	−	9487.31i	−0.322315	−	0.558266i	0.658650	−	0.752449i	$-0.271128\pi$
$661$	−5477.50	−	9487.31i	−0.322315	−	0.558266i	−0.980965	+	0.194184i	$0.937794\pi$
$662$		0			0
$663$	−6678.00	+	11566.6i	−0.391180	+	0.677543i
$664$		0			0
$665$	−8148.00	+	7056.37i	−0.475137	+	0.411480i
$666$		0			0
$667$	−7560.00	+	13094.3i	−0.438867	+	0.760140i
$668$		0			0
$669$	3048.00	+	5279.29i	0.176147	+	0.305096i
$670$		0			0
$671$	24540.0			1.41186
$672$		0			0
$673$	25103.0			1.43782			0.718908	−	0.695106i	$-0.244642\pi$
$673$	25103.0			1.43782			0.718908	+	0.695106i	$0.244642\pi$
$674$		0			0
$675$	−1201.50	−	2081.06i	−0.0685122	−	0.118667i
$676$		0			0
$677$	2802.00	−	4853.21i	0.159069	−	0.275515i	−0.775464	−	0.631391i	$-0.782484\pi$
$677$	2802.00	−	4853.21i	0.159069	−	0.275515i	0.934533	+	0.355876i	$0.115817\pi$
$678$		0			0
$679$	1351.00	+	7020.00i	0.0763573	+	0.396764i
$680$		0			0
$681$	−9297.00	+	16102.9i	−0.523145	+	0.906114i
$682$		0			0
$683$	5484.00	+	9498.57i	0.307232	+	0.532141i	0.977756	−	0.209747i	$-0.0672639\pi$
$683$	5484.00	+	9498.57i	0.307232	+	0.532141i	−0.670524	+	0.741888i	$0.733931\pi$
$684$		0			0
$685$	−18072.0			−1.00802
$686$		0			0
$687$	13773.0			0.764880
$688$		0			0
$689$	20352.0	+	35250.7i	1.12533	+	1.94912i
$690$		0			0
$691$	4202.50	−	7278.94i	0.231361	−	0.400729i	−0.726848	−	0.686799i	$-0.759015\pi$
$691$	4202.50	−	7278.94i	0.231361	−	0.400729i	0.958209	+	0.286069i	$0.0923487\pi$
$692$		0			0
$693$	945.000	+	4910.36i	0.0518003	+	0.269162i
$694$		0			0
$695$	111.000	−	192.258i	0.00605823	−	0.0104932i
$696$		0			0
$697$	5292.00	+	9166.01i	0.287588	+	0.498117i
$698$		0			0
$699$	−13590.0			−0.735366
$700$		0			0
$701$	468.000			0.0252156			0.0126078	−	0.999921i	$-0.495987\pi$
$701$	468.000			0.0252156			0.0126078	+	0.999921i	$0.495987\pi$
$702$		0			0
$703$	7032.50	+	12180.6i	0.377291	+	0.653488i
$704$		0			0
$705$	−3294.00	+	5705.38i	−0.175971	+	0.304790i
$706$		0			0
$707$	8652.00	−	7492.85i	0.460243	−	0.398582i
$708$		0			0
$709$	12533.0	−	21707.8i	0.663874	−	1.14986i	−0.315715	−	0.948854i	$-0.602244\pi$
$709$	12533.0	−	21707.8i	0.663874	−	1.14986i	0.979589	−	0.201010i	$-0.0644222\pi$
$710$		0			0
$711$	−5269.50	−	9127.04i	−0.277949	−	0.481422i
$712$		0			0
$713$	15036.0			0.789765
$714$		0			0
$715$	−9540.00			−0.498987
$716$		0			0
$717$	−2295.00	−	3975.06i	−0.119537	−	0.207045i
$718$		0			0
$719$	5541.00	−	9597.29i	0.287405	−	0.497801i	−0.685784	−	0.727805i	$-0.740541\pi$
$719$	5541.00	−	9597.29i	0.287405	−	0.497801i	0.973190	+	0.230004i	$0.0738740\pi$
$720$		0			0
$721$	25812.5	+	8941.71i	1.33330	+	0.461868i
$722$		0			0
$723$	8301.00	−	14377.8i	0.426995	−	0.739577i
$724$		0			0
$725$	−8010.00	−	13873.7i	−0.410323	−	0.710700i
$726$		0			0
$727$	−13481.0			−0.687734			−0.343867	−	0.939018i	$-0.611737\pi$
$727$	−13481.0			−0.687734			−0.343867	+	0.939018i	$0.611737\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	13650.0	+	23642.5i	0.690648	+	1.19624i
$732$		0			0
$733$	−12158.5	+	21059.1i	−0.612666	+	1.06117i	0.378123	+	0.925755i	$0.376570\pi$
$733$	−12158.5	+	21059.1i	−0.612666	+	1.06117i	−0.990789	+	0.135414i	$0.956764\pi$
$734$		0			0
$735$	−5733.00	+	2291.50i	−0.287707	+	0.114998i
$736$		0			0
$737$	−7845.00	+	13587.9i	−0.392095	+	0.679129i
$738$		0			0
$739$	−9108.50	−	15776.4i	−0.453399	−	0.785309i	0.545196	−	0.838309i	$-0.316455\pi$
$739$	−9108.50	−	15776.4i	−0.453399	−	0.785309i	−0.998595	+	0.0529992i	$0.983122\pi$
$740$		0			0
$741$	−15423.0			−0.764613
$742$		0			0
$743$	−19782.0			−0.976758			−0.488379	−	0.872632i	$-0.662412\pi$
$743$	−19782.0			−0.976758			−0.488379	+	0.872632i	$0.662412\pi$
$744$		0			0
$745$	−4932.00	−	8542.47i	−0.242543	−	0.420097i
$746$		0			0
$747$	−3645.00	+	6313.33i	−0.178532	+	0.309227i
$748$		0			0
$749$	32970.0	+	11421.1i	1.60841	+	0.557169i
$750$		0			0
$751$	−2460.50	+	4261.71i	−0.119554	+	0.207073i	−0.919591	−	0.392877i	$-0.871480\pi$
$751$	−2460.50	+	4261.71i	−0.119554	+	0.207073i	0.800037	+	0.599951i	$0.204813\pi$
$752$		0			0
$753$	702.000	+	1215.90i	0.0339738	+	0.0588444i
$754$		0			0
$755$	6528.00			0.314673
$756$		0			0
$757$	18098.0			0.868934			0.434467	−	0.900688i	$-0.356937\pi$
$757$	18098.0			0.868934			0.434467	+	0.900688i	$0.356937\pi$
$758$		0			0
$759$	−3780.00	−	6547.15i	−0.180771	−	0.313105i
$760$		0			0
$761$	12234.0	−	21189.9i	0.582762	−	1.00937i	−0.412388	−	0.911008i	$-0.635305\pi$
$761$	12234.0	−	21189.9i	0.582762	−	1.00937i	0.995150	−	0.0983657i	$-0.0313615\pi$
$762$		0			0
$763$	5782.00	−	5007.36i	0.274341	−	0.237587i
$764$		0			0
$765$	−2268.00	+	3928.29i	−0.107189	+	0.185657i
$766$		0			0
$767$	−6996.00	−	12117.4i	−0.329349	−	0.570450i
$768$		0			0
$769$	21719.0			1.01847			0.509237	−	0.860626i	$-0.329928\pi$
$769$	21719.0			1.01847			0.509237	+	0.860626i	$0.329928\pi$
$770$		0			0
$771$	7470.00			0.348931
$772$		0			0
$773$	15153.0	+	26245.8i	0.705065	+	1.22121i	0.966668	+	0.256033i	$0.0824157\pi$
$773$	15153.0	+	26245.8i	0.705065	+	1.22121i	−0.261603	+	0.965176i	$0.584251\pi$
$774$		0			0
$775$	−7965.50	+	13796.7i	−0.369199	+	0.639471i
$776$		0			0
$777$	1522.50	+	7911.14i	0.0702952	+	0.365265i
$778$		0			0
$779$	−6111.00	+	10584.6i	−0.281065	+	0.486818i
$780$		0			0
$781$	−5130.00	−	8885.42i	−0.235039	−	0.407100i
$782$		0			0
$783$	4860.00			0.221816
$784$		0			0
$785$	−3036.00			−0.138038
$786$		0			0
$787$	13648.0	+	23639.0i	0.618169	+	1.07070i	0.989820	+	0.142327i	$0.0454584\pi$
$787$	13648.0	+	23639.0i	0.618169	+	1.07070i	−0.371651	+	0.928372i	$0.621208\pi$
$788$		0			0
$789$	−2358.00	+	4084.18i	−0.106397	+	0.184285i
$790$		0			0
$791$	−3087.00	−	16040.5i	−0.138762	−	0.721031i
$792$		0			0
$793$	−21677.0	+	37545.7i	−0.970710	+	1.68132i
$794$		0			0
$795$	6912.00	+	11971.9i	0.308356	+	0.534089i
$796$		0			0
$797$	−35100.0			−1.55998			−0.779991	−	0.625791i	$-0.784776\pi$
$797$	−35100.0			−1.55998			−0.779991	+	0.625791i	$0.784776\pi$
$798$		0			0
$799$	−30744.0			−1.36126
$800$		0			0
$801$	2700.00	+	4676.54i	0.119101	+	0.206289i
$802$		0			0
$803$	645.000	−	1117.17i	0.0283456	−	0.0490961i
$804$		0			0
$805$	7056.00	−	6110.68i	0.308933	−	0.267544i
$806$		0			0
$807$	2709.00	−	4692.13i	0.118168	−	0.204672i
$808$		0			0
$809$	−22197.0	−	38446.3i	−0.964654	−	1.67083i	−0.710542	−	0.703655i	$-0.751550\pi$
$809$	−22197.0	−	38446.3i	−0.964654	−	1.67083i	−0.254112	−	0.967175i	$-0.581783\pi$
$810$		0			0
$811$	8584.00			0.371671			0.185835	−	0.982581i	$-0.440501\pi$
$811$	8584.00			0.371671			0.185835	+	0.982581i	$0.440501\pi$
$812$		0			0
$813$	−18336.0			−0.790986
$814$		0			0
$815$	−5532.00	−	9581.71i	−0.237764	−	0.411819i
$816$		0			0
$817$	−15762.5	+	27301.5i	−0.674982	+	1.16910i
$818$		0			0
$819$	−8347.50	−	2891.66i	−0.356148	−	0.123373i
$820$		0			0
$821$	4917.00	−	8516.49i	0.209019	−	0.362031i	−0.742387	−	0.669971i	$-0.766306\pi$
$821$	4917.00	−	8516.49i	0.209019	−	0.362031i	0.951406	+	0.307940i	$0.0996397\pi$
$822$		0			0
$823$	21928.0	+	37980.4i	0.928751	+	1.60864i	0.785415	+	0.618970i	$0.212450\pi$
$823$	21928.0	+	37980.4i	0.928751	+	1.60864i	0.143336	+	0.989674i	$0.454217\pi$
$824$		0			0
$825$	8010.00			0.338027
$826$		0			0
$827$	−13266.0			−0.557804			−0.278902	−	0.960320i	$-0.589970\pi$
$827$	−13266.0			−0.557804			−0.278902	+	0.960320i	$0.589970\pi$
$828$		0			0
$829$	−8726.50	−	15114.7i	−0.365602	−	0.633241i	0.623271	−	0.782006i	$-0.285803\pi$
$829$	−8726.50	−	15114.7i	−0.365602	−	0.633241i	−0.988873	+	0.148765i	$0.952470\pi$
$830$		0			0
$831$	−6346.50	+	10992.5i	−0.264931	+	0.458874i
$832$		0			0
$833$	−22638.0	−	17822.8i	−0.941609	−	0.741325i
$834$		0			0
$835$	−486.000	+	841.777i	−0.0201422	+	0.0348873i
$836$		0			0
$837$	−2416.50	−	4185.50i	−0.0997927	−	0.172846i
$838$		0			0
$839$	35172.0			1.44729			0.723643	−	0.690175i	$-0.242466\pi$
$839$	35172.0			1.44729			0.723643	+	0.690175i	$0.242466\pi$
$840$		0			0
$841$	8011.00			0.328468
$842$		0			0
$843$	−5724.00	−	9914.26i	−0.233861	−	0.405060i
$844$		0			0
$845$	1836.00	−	3180.05i	0.0747459	−	0.129464i
$846$		0			0
$847$	7542.50	+	2612.80i	0.305978	+	0.105994i
$848$		0			0
$849$	5995.50	−	10384.5i	0.242362	−	0.419783i
$850$		0			0
$851$	−6090.00	−	10548.2i	−0.245314	−	0.424897i
$852$		0			0
$853$	3503.00			0.140610			0.0703051	−	0.997526i	$-0.477603\pi$
$853$	3503.00			0.140610			0.0703051	+	0.997526i	$0.477603\pi$
$854$		0			0
$855$	−5238.00			−0.209516
$856$		0			0
$857$	−11424.0	−	19786.9i	−0.455352	−	0.788692i	0.543357	−	0.839502i	$-0.317153\pi$
$857$	−11424.0	−	19786.9i	−0.455352	−	0.788692i	−0.998708	+	0.0508097i	$0.983820\pi$
$858$		0			0
$859$	−6728.00	+	11653.2i	−0.267237	+	0.462868i	−0.968147	−	0.250382i	$-0.919444\pi$
$859$	−6728.00	+	11653.2i	−0.267237	+	0.462868i	0.700910	+	0.713249i	$0.252777\pi$
$860$		0			0
$861$	−5292.00	+	4583.01i	−0.209467	+	0.181404i
$862$		0			0
$863$	20355.0	−	35255.9i	0.802888	−	1.39064i	−0.114820	−	0.993386i	$-0.536629\pi$
$863$	20355.0	−	35255.9i	0.802888	−	1.39064i	0.917708	−	0.397256i	$-0.130038\pi$
$864$		0			0
$865$	−8172.00	−	14154.3i	−0.321221	−	0.556371i
$866$		0			0
$867$	−6429.00			−0.251834
$868$		0			0
$869$	35130.0			1.37135
$870$		0			0
$871$	−13859.5	−	24005.4i	−0.539163	−	0.933858i
$872$		0			0
$873$	−1737.00	+	3008.57i	−0.0673408	+	0.116638i
$874$		0			0
$875$	4494.00	+	23351.5i	0.173628	+	0.902200i
$876$		0			0
$877$	−1453.00	+	2516.67i	−0.0559456	+	0.0969007i	−0.892642	−	0.450767i	$-0.851151\pi$
$877$	−1453.00	+	2516.67i	−0.0559456	+	0.0969007i	0.836696	+	0.547667i	$0.184484\pi$
$878$		0			0
$879$	6912.00	+	11971.9i	0.265229	+	0.459389i
$880$		0			0
$881$	−19188.0			−0.733780			−0.366890	−	0.930264i	$-0.619577\pi$
$881$	−19188.0			−0.733780			−0.366890	+	0.930264i	$0.619577\pi$
$882$		0			0
$883$	17251.0			0.657466			0.328733	−	0.944423i	$-0.393378\pi$
$883$	17251.0			0.657466			0.328733	+	0.944423i	$0.393378\pi$
$884$		0			0
$885$	−2376.00	−	4115.35i	−0.0902467	−	0.156312i
$886$		0			0
$887$	−1047.00	+	1813.46i	−0.0396334	+	0.0686471i	−0.885162	−	0.465284i	$-0.845952\pi$
$887$	−1047.00	+	1813.46i	−0.0396334	+	0.0686471i	0.845528	+	0.533931i	$0.179286\pi$
$888$		0			0
$889$	−8690.50	−	45157.2i	−0.327863	−	1.70362i
$890$		0			0
$891$	−1215.00	+	2104.44i	−0.0456835	+	0.0791262i
$892$		0			0
$893$	−17751.0	−	30745.6i	−0.665190	−	1.15214i
$894$		0			0
$895$	−7524.00			−0.281005
$896$		0			0
$897$	13356.0			0.497150
$898$		0			0
$899$	−16110.0	−	27903.3i	−0.597662	−	1.03518i
$900$		0			0
$901$	−32256.0	+	55869.0i	−1.19268	+	2.06578i
$902$		0			0
$903$	−13650.0	+	11821.2i	−0.503038	+	0.435644i
$904$		0			0
$905$	−5421.00	+	9389.45i	−0.199116	+	0.344879i
$906$		0			0
$907$	−20133.5	−	34872.2i	−0.737069	−	1.27664i	−0.953809	−	0.300412i	$-0.902876\pi$
$907$	−20133.5	−	34872.2i	−0.737069	−	1.27664i	0.216740	−	0.976229i	$-0.430458\pi$
$908$		0			0
$909$	5562.00			0.202948
$910$		0			0
$911$	−17604.0			−0.640227			−0.320113	−	0.947379i	$-0.603721\pi$
$911$	−17604.0			−0.640227			−0.320113	+	0.947379i	$0.603721\pi$
$912$		0			0
$913$	−12150.0	−	21044.4i	−0.440423	−	0.762835i
$914$		0			0
$915$	−7362.00	+	12751.4i	−0.265989	+	0.460707i
$916$		0			0
$917$	37065.0	+	12839.7i	1.33478	+	0.462382i
$918$		0			0
$919$	1754.50	−	3038.88i	0.0629767	−	0.109079i	−0.832818	−	0.553547i	$-0.813274\pi$
$919$	1754.50	−	3038.88i	0.0629767	−	0.109079i	0.895795	+	0.444468i	$0.146607\pi$
$920$		0			0
$921$	946.500	+	1639.39i	0.0338634	+	0.0586532i
$922$		0			0
$923$	18126.0			0.646397
$924$		0			0
$925$	12905.0			0.458718
$926$		0			0
$927$	6637.50	+	11496.5i	0.235172	+	0.407329i
$928$		0			0
$929$	17319.0	−	29997.4i	0.611645	−	1.05940i	−0.379319	−	0.925266i	$-0.623842\pi$
$929$	17319.0	−	29997.4i	0.611645	−	1.05940i	0.990963	−	0.134134i	$-0.0428251\pi$
$930$		0			0
$931$	4753.00	−	32929.7i	0.167318	−	1.15921i
$932$		0			0
$933$	−5841.00	+	10116.9i	−0.204958	+	0.354998i
$934$		0			0
$935$	−7560.00	−	13094.3i	−0.264426	−	0.458000i
$936$		0			0
$937$	−17353.0			−0.605014			−0.302507	−	0.953147i	$-0.597824\pi$
$937$	−17353.0			−0.605014			−0.302507	+	0.953147i	$0.597824\pi$
$938$		0			0
$939$	6555.00			0.227811
$940$		0			0
$941$	23460.0	+	40633.9i	0.812725	+	1.40768i	0.910950	+	0.412517i	$0.135350\pi$
$941$	23460.0	+	40633.9i	0.812725	+	1.40768i	−0.0982252	+	0.995164i	$0.531317\pi$
$942$		0			0
$943$	5292.00	−	9166.01i	0.182748	−	0.316529i
$944$		0			0
$945$	−2835.00	−	982.073i	−0.0975900	−	0.0338062i
$946$		0			0
$947$	9177.00	−	15895.0i	0.314902	−	0.545427i	−0.664514	−	0.747275i	$-0.731362\pi$
$947$	9177.00	−	15895.0i	0.314902	−	0.545427i	0.979417	+	0.201849i	$0.0646949\pi$
$948$		0			0
$949$	1139.50	+	1973.67i	0.0389776	+	0.0675112i
$950$		0			0
$951$	−10512.0			−0.358438
$952$		0			0
$953$	35568.0			1.20898			0.604491	−	0.796612i	$-0.293376\pi$
$953$	35568.0			1.20898			0.604491	+	0.796612i	$0.293376\pi$
$954$		0			0
$955$	−2142.00	−	3710.05i	−0.0725796	−	0.125712i
$956$		0			0
$957$	−8100.00	+	14029.6i	−0.273601	+	0.473890i
$958$		0			0
$959$	42168.0	−	36518.6i	1.41989	−	1.22966i
$960$		0			0
$961$	−1125.00	+	1948.56i	−0.0377631	+	0.0654076i
$962$		0			0
$963$	8478.00	+	14684.3i	0.283697	+	0.491377i
$964$		0			0
$965$	22254.0			0.742364
$966$		0			0
$967$	27343.0			0.909298			0.454649	−	0.890671i	$-0.349765\pi$
$967$	27343.0			0.909298			0.454649	+	0.890671i	$0.349765\pi$
$968$		0			0
$969$	−12222.0	−	21169.1i	−0.405188	−	0.701806i
$970$		0			0
$971$	25512.0	−	44188.1i	0.843171	−	1.46042i	−0.0440291	−	0.999030i	$-0.514019\pi$
$971$	25512.0	−	44188.1i	0.843171	−	1.46042i	0.887200	−	0.461385i	$-0.152647\pi$
$972$		0			0
$973$	129.500	+	672.902i	0.00426678	+	0.0221709i
$974$		0			0
$975$	−7075.50	+	12255.1i	−0.232408	+	0.402542i
$976$		0			0
$977$	1113.00	+	1927.77i	0.0364463	+	0.0631268i	0.883673	−	0.468104i	$-0.155063\pi$
$977$	1113.00	+	1927.77i	0.0364463	+	0.0631268i	−0.847227	+	0.531231i	$0.821730\pi$
$978$		0			0
$979$	−18000.0			−0.587623
$980$		0			0
$981$	3717.00			0.120973
$982$		0			0
$983$	17652.0	+	30574.2i	0.572748	+	0.992029i	0.996282	+	0.0861487i	$0.0274560\pi$
$983$	17652.0	+	30574.2i	0.572748	+	0.992029i	−0.423534	+	0.905880i	$0.639211\pi$
$984$		0			0
$985$	−3132.00	+	5424.78i	−0.101314	+	0.175480i
$986$		0			0
$987$	−3843.00	−	19968.8i	−0.123935	−	0.643986i
$988$		0			0
$989$	13650.0	−	23642.5i	0.438872	−	0.760149i
$990$		0			0
$991$	−1170.50	−	2027.37i	−0.0375198	−	0.0649863i	0.846656	−	0.532141i	$-0.178612\pi$
$991$	−1170.50	−	2027.37i	−0.0375198	−	0.0649863i	−0.884176	+	0.467155i	$0.845279\pi$
$992$		0			0
$993$	8835.00			0.282347
$994$		0			0
$995$	−816.000			−0.0259989
$996$		0			0
$997$	−14507.5	−	25127.7i	−0.460840	−	0.798198i	0.538163	−	0.842841i	$-0.319118\pi$
$997$	−14507.5	−	25127.7i	−0.460840	−	0.798198i	−0.999003	+	0.0446429i	$0.985785\pi$
$998$		0			0
$999$	−1957.50	+	3390.49i	−0.0619946	+	0.107378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.f.289.1		2
4.3	odd	2		42.4.e.a.37.1	yes	2
7.2	even	3		2352.4.a.f.1.1		1
7.4	even	3	inner	336.4.q.f.193.1		2
7.5	odd	6		2352.4.a.bf.1.1		1
12.11	even	2		126.4.g.b.37.1		2
28.3	even	6		294.4.e.i.67.1		2
28.11	odd	6		42.4.e.a.25.1	✓	2
28.19	even	6		294.4.a.c.1.1		1
28.23	odd	6		294.4.a.d.1.1		1
28.27	even	2		294.4.e.i.79.1		2
84.11	even	6		126.4.g.b.109.1		2
84.23	even	6		882.4.a.o.1.1		1
84.47	odd	6		882.4.a.l.1.1		1
84.59	odd	6		882.4.g.g.361.1		2
84.83	odd	2		882.4.g.g.667.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.a.25.1	✓	2	28.11	odd	6
42.4.e.a.37.1	yes	2	4.3	odd	2
126.4.g.b.37.1		2	12.11	even	2
126.4.g.b.109.1		2	84.11	even	6
294.4.a.c.1.1		1	28.19	even	6
294.4.a.d.1.1		1	28.23	odd	6
294.4.e.i.67.1		2	28.3	even	6
294.4.e.i.79.1		2	28.27	even	2
336.4.q.f.193.1		2	7.4	even	3	inner
336.4.q.f.289.1		2	1.1	even	1	trivial
882.4.a.l.1.1		1	84.47	odd	6
882.4.a.o.1.1		1	84.23	even	6
882.4.g.g.361.1		2	84.59	odd	6
882.4.g.g.667.1		2	84.83	odd	2
2352.4.a.f.1.1		1	7.2	even	3
2352.4.a.bf.1.1		1	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(3.00000 - 5.19615i) q^{5} +(3.50000 + 18.1865i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(3.00000 - 5.19615i) q^{5} +(3.50000 + 18.1865i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-15.0000 - 25.9808i) q^{11} +53.0000 q^{13} +18.0000 q^{15} +(42.0000 + 72.7461i) q^{17} +(-48.5000 + 84.0045i) q^{19} +(-42.0000 + 36.3731i) q^{21} +(42.0000 - 72.7461i) q^{23} +(44.5000 + 77.0763i) q^{25} -27.0000 q^{27} -180.000 q^{29} +(89.5000 + 155.019i) q^{31} +(45.0000 - 77.9423i) q^{33} +(105.000 + 36.3731i) q^{35} +(72.5000 - 125.574i) q^{37} +(79.5000 + 137.698i) q^{39} +126.000 q^{41} +325.000 q^{43} +(27.0000 + 46.7654i) q^{45} +(-183.000 + 316.965i) q^{47} +(-318.500 + 127.306i) q^{49} +(-126.000 + 218.238i) q^{51} +(384.000 + 665.108i) q^{53} -180.000 q^{55} -291.000 q^{57} +(-132.000 - 228.631i) q^{59} +(-409.000 + 708.409i) q^{61} +(-157.500 - 54.5596i) q^{63} +(159.000 - 275.396i) q^{65} +(-261.500 - 452.931i) q^{67} +252.000 q^{69} +342.000 q^{71} +(21.5000 + 37.2391i) q^{73} +(-133.500 + 231.229i) q^{75} +(420.000 - 363.731i) q^{77} +(-585.500 + 1014.12i) q^{79} +(-40.5000 - 70.1481i) q^{81} +810.000 q^{83} +504.000 q^{85} +(-270.000 - 467.654i) q^{87} +(300.000 - 519.615i) q^{89} +(185.500 + 963.886i) q^{91} +(-268.500 + 465.056i) q^{93} +(291.000 + 504.027i) q^{95} +386.000 q^{97} +270.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 6 q^{5} + 7 q^{7} - 9 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 6 * q^5 + 7 * q^7 - 9 * q^9	\( 2 q + 3 q^{3} + 6 q^{5} + 7 q^{7} - 9 q^{9} - 30 q^{11} + 106 q^{13} + 36 q^{15} + 84 q^{17} - 97 q^{19} - 84 q^{21} + 84 q^{23} + 89 q^{25} - 54 q^{27} - 360 q^{29} + 179 q^{31} + 90 q^{33} + 210 q^{35} + 145 q^{37} + 159 q^{39} + 252 q^{41} + 650 q^{43} + 54 q^{45} - 366 q^{47} - 637 q^{49} - 252 q^{51} + 768 q^{53} - 360 q^{55} - 582 q^{57} - 264 q^{59} - 818 q^{61} - 315 q^{63} + 318 q^{65} - 523 q^{67} + 504 q^{69} + 684 q^{71} + 43 q^{73} - 267 q^{75} + 840 q^{77} - 1171 q^{79} - 81 q^{81} + 1620 q^{83} + 1008 q^{85} - 540 q^{87} + 600 q^{89} + 371 q^{91} - 537 q^{93} + 582 q^{95} + 772 q^{97} + 540 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 6 * q^5 + 7 * q^7 - 9 * q^9 - 30 * q^11 + 106 * q^13 + 36 * q^15 + 84 * q^17 - 97 * q^19 - 84 * q^21 + 84 * q^23 + 89 * q^25 - 54 * q^27 - 360 * q^29 + 179 * q^31 + 90 * q^33 + 210 * q^35 + 145 * q^37 + 159 * q^39 + 252 * q^41 + 650 * q^43 + 54 * q^45 - 366 * q^47 - 637 * q^49 - 252 * q^51 + 768 * q^53 - 360 * q^55 - 582 * q^57 - 264 * q^59 - 818 * q^61 - 315 * q^63 + 318 * q^65 - 523 * q^67 + 504 * q^69 + 684 * q^71 + 43 * q^73 - 267 * q^75 + 840 * q^77 - 1171 * q^79 - 81 * q^81 + 1620 * q^83 + 1008 * q^85 - 540 * q^87 + 600 * q^89 + 371 * q^91 - 537 * q^93 + 582 * q^95 + 772 * q^97 + 540 * q^99

Introduction

L-functions

Modular forms

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Database

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