LMFDB - Embedded newform 336.4.q.a.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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +(-3.50000 + 6.06218i) q^{5} +(17.5000 + 6.06218i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +(-3.50000 + 6.06218i) q^{5} +(17.5000 + 6.06218i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(3.50000 + 6.06218i) q^{11} -52.0000 q^{13} +21.0000 q^{15} +(-36.0000 - 62.3538i) q^{17} +(10.0000 - 17.3205i) q^{19} +(-10.5000 - 54.5596i) q^{21} +(-24.0000 + 41.5692i) q^{23} +(38.0000 + 65.8179i) q^{25} +27.0000 q^{27} -243.000 q^{29} +(47.5000 + 82.2724i) q^{31} +(10.5000 - 18.1865i) q^{33} +(-98.0000 + 84.8705i) q^{35} +(-176.000 + 304.841i) q^{37} +(78.0000 + 135.100i) q^{39} -296.000 q^{41} -158.000 q^{43} +(-31.5000 - 54.5596i) q^{45} +(-71.0000 + 122.976i) q^{47} +(269.500 + 212.176i) q^{49} +(-108.000 + 187.061i) q^{51} +(187.500 + 324.760i) q^{53} -49.0000 q^{55} -60.0000 q^{57} +(139.500 + 241.621i) q^{59} +(-123.000 + 213.042i) q^{61} +(-126.000 + 109.119i) q^{63} +(182.000 - 315.233i) q^{65} +(-365.000 - 632.199i) q^{67} +144.000 q^{69} -338.000 q^{71} +(271.000 + 469.386i) q^{73} +(114.000 - 197.454i) q^{75} +(24.5000 + 127.306i) q^{77} +(-152.500 + 264.138i) q^{79} +(-40.5000 - 70.1481i) q^{81} -1123.00 q^{83} +504.000 q^{85} +(364.500 + 631.333i) q^{87} +(213.000 - 368.927i) q^{89} +(-910.000 - 315.233i) q^{91} +(142.500 - 246.817i) q^{93} +(70.0000 + 121.244i) q^{95} -369.000 q^{97} -63.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} - 7 q^{5} + 35 q^{7} - 9 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 - 7 * q^5 + 35 * q^7 - 9 * q^9	$ 2 q - 3 q^{3} - 7 q^{5} + 35 q^{7} - 9 q^{9} + 7 q^{11} - 104 q^{13} + 42 q^{15} - 72 q^{17} + 20 q^{19} - 21 q^{21} - 48 q^{23} + 76 q^{25} + 54 q^{27} - 486 q^{29} + 95 q^{31} + 21 q^{33} - 196 q^{35} - 352 q^{37} + 156 q^{39} - 592 q^{41} - 316 q^{43} - 63 q^{45} - 142 q^{47} + 539 q^{49} - 216 q^{51} + 375 q^{53} - 98 q^{55} - 120 q^{57} + 279 q^{59} - 246 q^{61} - 252 q^{63} + 364 q^{65} - 730 q^{67} + 288 q^{69} - 676 q^{71} + 542 q^{73} + 228 q^{75} + 49 q^{77} - 305 q^{79} - 81 q^{81} - 2246 q^{83} + 1008 q^{85} + 729 q^{87} + 426 q^{89} - 1820 q^{91} + 285 q^{93} + 140 q^{95} - 738 q^{97} - 126 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 - 7 * q^5 + 35 * q^7 - 9 * q^9 + 7 * q^11 - 104 * q^13 + 42 * q^15 - 72 * q^17 + 20 * q^19 - 21 * q^21 - 48 * q^23 + 76 * q^25 + 54 * q^27 - 486 * q^29 + 95 * q^31 + 21 * q^33 - 196 * q^35 - 352 * q^37 + 156 * q^39 - 592 * q^41 - 316 * q^43 - 63 * q^45 - 142 * q^47 + 539 * q^49 - 216 * q^51 + 375 * q^53 - 98 * q^55 - 120 * q^57 + 279 * q^59 - 246 * q^61 - 252 * q^63 + 364 * q^65 - 730 * q^67 + 288 * q^69 - 676 * q^71 + 542 * q^73 + 228 * q^75 + 49 * q^77 - 305 * q^79 - 81 * q^81 - 2246 * q^83 + 1008 * q^85 + 729 * q^87 + 426 * q^89 - 1820 * q^91 + 285 * q^93 + 140 * q^95 - 738 * q^97 - 126 * 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
$5$	−3.50000	+	6.06218i	−0.313050	+	0.542218i	−0.979021	−	0.203760i	$-0.934684\pi$
$5$	−3.50000	+	6.06218i	−0.313050	+	0.542218i	0.665971	+	0.745977i	$0.268017\pi$
$6$		0			0
$7$	17.5000	+	6.06218i	0.944911	+	0.327327i
$7$	17.5000	+	6.06218i	0.944911	+	0.327327i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.50000	+	6.06218i	0.0959354	+	0.166165i	0.909999	−	0.414611i	$-0.136082\pi$
$11$	3.50000	+	6.06218i	0.0959354	+	0.166165i	−0.814063	+	0.580776i	$0.802749\pi$
$12$		0			0
$13$	−52.0000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−52.0000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	21.0000			0.361478
$16$		0			0
$17$	−36.0000	−	62.3538i	−0.513605	−	0.889590i	−0.999875	−	0.0157814i	$-0.994976\pi$
$17$	−36.0000	−	62.3538i	−0.513605	−	0.889590i	0.486271	−	0.873808i	$-0.338357\pi$
$18$		0			0
$19$	10.0000	−	17.3205i	0.120745	−	0.209137i	−0.799317	−	0.600910i	$-0.794805\pi$
$19$	10.0000	−	17.3205i	0.120745	−	0.209137i	0.920062	+	0.391773i	$0.128138\pi$
$20$		0			0
$21$	−10.5000	−	54.5596i	−0.109109	−	0.566947i
$22$		0			0
$23$	−24.0000	+	41.5692i	−0.217580	+	0.376860i	−0.954068	−	0.299591i	$-0.903150\pi$
$23$	−24.0000	+	41.5692i	−0.217580	+	0.376860i	0.736487	+	0.676451i	$0.236483\pi$
$24$		0			0
$25$	38.0000	+	65.8179i	0.304000	+	0.526543i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	−243.000			−1.55600			−0.777999	−	0.628265i	$-0.783765\pi$
$29$	−243.000			−1.55600			−0.777999	+	0.628265i	$0.783765\pi$
$30$		0			0
$31$	47.5000	+	82.2724i	0.275202	+	0.476663i	0.970186	−	0.242362i	$-0.0779220\pi$
$31$	47.5000	+	82.2724i	0.275202	+	0.476663i	−0.694984	+	0.719025i	$0.744589\pi$
$32$		0			0
$33$	10.5000	−	18.1865i	0.0553883	−	0.0959354i
$34$		0			0
$35$	−98.0000	+	84.8705i	−0.473286	+	0.409878i
$36$		0			0
$37$	−176.000	+	304.841i	−0.782006	+	1.35447i	0.148765	+	0.988873i	$0.452470\pi$
$37$	−176.000	+	304.841i	−0.782006	+	1.35447i	−0.930771	+	0.365602i	$0.880863\pi$
$38$		0			0
$39$	78.0000	+	135.100i	0.320256	+	0.554700i
$40$		0			0
$41$	−296.000			−1.12750			−0.563749	−	0.825946i	$-0.690642\pi$
$41$	−296.000			−1.12750			−0.563749	+	0.825946i	$0.690642\pi$
$42$		0			0
$43$	−158.000			−0.560344			−0.280172	−	0.959950i	$-0.590391\pi$
$43$	−158.000			−0.560344			−0.280172	+	0.959950i	$0.590391\pi$
$44$		0			0
$45$	−31.5000	−	54.5596i	−0.104350	−	0.180739i
$46$		0			0
$47$	−71.0000	+	122.976i	−0.220349	+	0.381656i	−0.954914	−	0.296882i	$-0.904053\pi$
$47$	−71.0000	+	122.976i	−0.220349	+	0.381656i	0.734565	+	0.678539i	$0.237386\pi$
$48$		0			0
$49$	269.500	+	212.176i	0.785714	+	0.618590i
$50$		0			0
$51$	−108.000	+	187.061i	−0.296530	+	0.513605i
$52$		0			0
$53$	187.500	+	324.760i	0.485945	+	0.841682i	0.999870	−	0.0161535i	$-0.00514205\pi$
$53$	187.500	+	324.760i	0.485945	+	0.841682i	−0.513924	+	0.857836i	$0.671809\pi$
$54$		0			0
$55$	−49.0000			−0.120130
$56$		0			0
$57$	−60.0000			−0.139424
$58$		0			0
$59$	139.500	+	241.621i	0.307820	+	0.533159i	0.977885	−	0.209143i	$-0.0670674\pi$
$59$	139.500	+	241.621i	0.307820	+	0.533159i	−0.670066	+	0.742302i	$0.733734\pi$
$60$		0			0
$61$	−123.000	+	213.042i	−0.258173	+	0.447168i	−0.965752	−	0.259465i	$-0.916454\pi$
$61$	−123.000	+	213.042i	−0.258173	+	0.447168i	0.707580	+	0.706634i	$0.249787\pi$
$62$		0			0
$63$	−126.000	+	109.119i	−0.251976	+	0.218218i
$64$		0			0
$65$	182.000	−	315.233i	0.347297	−	0.601536i
$66$		0			0
$67$	−365.000	−	632.199i	−0.665550	−	1.15277i	−0.979136	−	0.203207i	$-0.934864\pi$
$67$	−365.000	−	632.199i	−0.665550	−	1.15277i	0.313586	−	0.949560i	$-0.398470\pi$
$68$		0			0
$69$	144.000			0.251240
$70$		0			0
$71$	−338.000			−0.564975			−0.282487	−	0.959271i	$-0.591160\pi$
$71$	−338.000			−0.564975			−0.282487	+	0.959271i	$0.591160\pi$
$72$		0			0
$73$	271.000	+	469.386i	0.434495	+	0.752568i	0.997254	−	0.0740532i	$-0.0235935\pi$
$73$	271.000	+	469.386i	0.434495	+	0.752568i	−0.562759	+	0.826621i	$0.690260\pi$
$74$		0			0
$75$	114.000	−	197.454i	0.175514	−	0.304000i
$76$		0			0
$77$	24.5000	+	127.306i	0.0362602	+	0.188413i
$78$		0			0
$79$	−152.500	+	264.138i	−0.217185	+	0.376175i	−0.953946	−	0.299978i	$-0.903021\pi$
$79$	−152.500	+	264.138i	−0.217185	+	0.376175i	0.736761	+	0.676153i	$0.236354\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−1123.00			−1.48512			−0.742562	−	0.669778i	$-0.766389\pi$
$83$	−1123.00			−1.48512			−0.742562	+	0.669778i	$0.766389\pi$
$84$		0			0
$85$	504.000			0.643135
$86$		0			0
$87$	364.500	+	631.333i	0.449178	+	0.777999i
$88$		0			0
$89$	213.000	−	368.927i	0.253685	−	0.439395i	−0.710853	−	0.703341i	$-0.751691\pi$
$89$	213.000	−	368.927i	0.253685	−	0.439395i	0.964537	+	0.263946i	$0.0850240\pi$
$90$		0			0
$91$	−910.000	−	315.233i	−1.04828	−	0.363137i
$92$		0			0
$93$	142.500	−	246.817i	0.158888	−	0.275202i
$94$		0			0
$95$	70.0000	+	121.244i	0.0755984	+	0.130940i
$96$		0			0
$97$	−369.000			−0.386250			−0.193125	−	0.981174i	$-0.561862\pi$
$97$	−369.000			−0.386250			−0.193125	+	0.981174i	$0.561862\pi$
$98$		0			0
$99$	−63.0000			−0.0639570
$100$		0			0
$101$	−635.000	−	1099.85i	−0.625593	−	1.08356i	−0.988426	−	0.151704i	$-0.951524\pi$
$101$	−635.000	−	1099.85i	−0.625593	−	1.08356i	0.362833	−	0.931854i	$-0.381809\pi$
$102$		0			0
$103$	916.000	−	1586.56i	0.876273	−	1.51775i	0.0208734	−	0.999782i	$-0.493355\pi$
$103$	916.000	−	1586.56i	0.876273	−	1.51775i	0.855400	−	0.517968i	$-0.173311\pi$
$104$		0			0
$105$	367.500	+	127.306i	0.341565	+	0.118322i
$106$		0			0
$107$	−499.500	+	865.159i	−0.451294	+	0.781665i	−0.998467	−	0.0553553i	$-0.982371\pi$
$107$	−499.500	+	865.159i	−0.451294	+	0.781665i	0.547172	+	0.837020i	$0.315704\pi$
$108$		0			0
$109$	833.000	+	1442.80i	0.731990	+	1.26784i	0.956031	+	0.293264i	$0.0947417\pi$
$109$	833.000	+	1442.80i	0.731990	+	1.26784i	−0.224041	+	0.974580i	$0.571925\pi$
$110$		0			0
$111$	1056.00			0.902983
$112$		0			0
$113$	−1832.00			−1.52513			−0.762567	−	0.646910i	$-0.776061\pi$
$113$	−1832.00			−1.52513			−0.762567	+	0.646910i	$0.776061\pi$
$114$		0			0
$115$	−168.000	−	290.985i	−0.136227	−	0.235952i
$116$		0			0
$117$	234.000	−	405.300i	0.184900	−	0.320256i
$118$		0			0
$119$	−252.000	−	1309.43i	−0.194124	−	1.00870i
$120$		0			0
$121$	641.000	−	1110.24i	0.481593	−	0.834143i
$122$		0			0
$123$	444.000	+	769.031i	0.325481	+	0.563749i
$124$		0			0
$125$	−1407.00			−1.00677
$126$		0			0
$127$	1931.00			1.34920			0.674601	−	0.738183i	$-0.264316\pi$
$127$	1931.00			1.34920			0.674601	+	0.738183i	$0.264316\pi$
$128$		0			0
$129$	237.000	+	410.496i	0.161757	+	0.280172i
$130$		0			0
$131$	489.500	−	847.839i	0.326472	−	0.565466i	−0.655337	−	0.755336i	$-0.727473\pi$
$131$	489.500	−	847.839i	0.326472	−	0.565466i	0.981809	+	0.189871i	$0.0608068\pi$
$132$		0			0
$133$	280.000	−	242.487i	0.182549	−	0.158092i
$134$		0			0
$135$	−94.5000	+	163.679i	−0.0602464	+	0.104350i
$136$		0			0
$137$	243.000	+	420.888i	0.151539	+	0.262474i	0.931794	−	0.362989i	$-0.118244\pi$
$137$	243.000	+	420.888i	0.151539	+	0.262474i	−0.780254	+	0.625463i	$0.784910\pi$
$138$		0			0
$139$	2630.00			1.60485			0.802423	−	0.596755i	$-0.203544\pi$
$139$	2630.00			1.60485			0.802423	+	0.596755i	$0.203544\pi$
$140$		0			0
$141$	426.000			0.254437
$142$		0			0
$143$	−182.000	−	315.233i	−0.106431	−	0.184344i
$144$		0			0
$145$	850.500	−	1473.11i	0.487105	−	0.843690i
$146$		0			0
$147$	147.000	−	1018.45i	0.0824786	−	0.571429i
$148$		0			0
$149$	939.000	−	1626.40i	0.516281	−	0.894225i	−0.483540	−	0.875322i	$-0.660649\pi$
$149$	939.000	−	1626.40i	0.516281	−	0.894225i	0.999821	−	0.0189029i	$-0.00601734\pi$
$150$		0			0
$151$	1051.50	+	1821.25i	0.566688	+	0.981532i	0.996890	+	0.0787997i	$0.0251088\pi$
$151$	1051.50	+	1821.25i	0.566688	+	0.981532i	−0.430203	+	0.902732i	$0.641558\pi$
$152$		0			0
$153$	648.000			0.342403
$154$		0			0
$155$	−665.000			−0.344607
$156$		0			0
$157$	−702.000	−	1215.90i	−0.356852	−	0.618085i	0.630581	−	0.776123i	$-0.282816\pi$
$157$	−702.000	−	1215.90i	−0.356852	−	0.618085i	−0.987433	+	0.158038i	$0.949483\pi$
$158$		0			0
$159$	562.500	−	974.279i	0.280561	−	0.485945i
$160$		0			0
$161$	−672.000	+	581.969i	−0.328950	+	0.284879i
$162$		0			0
$163$	−768.000	+	1330.22i	−0.369045	+	0.639205i	−0.989417	−	0.145103i	$-0.953649\pi$
$163$	−768.000	+	1330.22i	−0.369045	+	0.639205i	0.620371	+	0.784308i	$0.286982\pi$
$164$		0			0
$165$	73.5000	+	127.306i	0.0346786	+	0.0600651i
$166$		0			0
$167$	3634.00			1.68388			0.841938	−	0.539574i	$-0.181415\pi$
$167$	3634.00			1.68388			0.841938	+	0.539574i	$0.181415\pi$
$168$		0			0
$169$	507.000			0.230769
$170$		0			0
$171$	90.0000	+	155.885i	0.0402484	+	0.0697122i
$172$		0			0
$173$	−429.000	+	743.050i	−0.188533	+	0.326549i	−0.944761	−	0.327759i	$-0.893707\pi$
$173$	−429.000	+	743.050i	−0.188533	+	0.326549i	0.756228	+	0.654308i	$0.227040\pi$
$174$		0			0
$175$	266.000	+	1382.18i	0.114901	+	0.597044i
$176$		0			0
$177$	418.500	−	724.863i	0.177720	−	0.307820i
$178$		0			0
$179$	−1210.00	−	2095.78i	−0.505249	−	0.875118i	−0.999982	−	0.00607215i	$-0.998067\pi$
$179$	−1210.00	−	2095.78i	−0.505249	−	0.875118i	0.494732	−	0.869046i	$-0.335266\pi$
$180$		0			0
$181$	−2672.00			−1.09728			−0.548641	−	0.836058i	$-0.684855\pi$
$181$	−2672.00			−1.09728			−0.548641	+	0.836058i	$0.684855\pi$
$182$		0			0
$183$	738.000			0.298112
$184$		0			0
$185$	−1232.00	−	2133.89i	−0.489613	−	0.848035i
$186$		0			0
$187$	252.000	−	436.477i	0.0985458	−	0.170686i
$188$		0			0
$189$	472.500	+	163.679i	0.181848	+	0.0629941i
$190$		0			0
$191$	−856.000	+	1482.64i	−0.324283	+	0.561674i	−0.981367	−	0.192143i	$-0.938456\pi$
$191$	−856.000	+	1482.64i	−0.324283	+	0.561674i	0.657084	+	0.753817i	$0.271790\pi$
$192$		0			0
$193$	1697.50	+	2940.16i	0.633102	+	1.09657i	0.986914	+	0.161248i	$0.0515521\pi$
$193$	1697.50	+	2940.16i	0.633102	+	1.09657i	−0.353812	+	0.935317i	$0.615115\pi$
$194$		0			0
$195$	−1092.00			−0.401024
$196$		0			0
$197$	510.000			0.184447			0.0922233	−	0.995738i	$-0.470603\pi$
$197$	510.000			0.184447			0.0922233	+	0.995738i	$0.470603\pi$
$198$		0			0
$199$	138.000	+	239.023i	0.0491586	+	0.0851452i	0.889558	−	0.456823i	$-0.151013\pi$
$199$	138.000	+	239.023i	0.0491586	+	0.0851452i	−0.840399	+	0.541968i	$0.817679\pi$
$200$		0			0
$201$	−1095.00	+	1896.60i	−0.384255	+	0.665550i
$202$		0			0
$203$	−4252.50	−	1473.11i	−1.47028	−	0.509320i
$204$		0			0
$205$	1036.00	−	1794.40i	0.352963	−	0.611350i
$206$		0			0
$207$	−216.000	−	374.123i	−0.0725268	−	0.125620i
$208$		0			0
$209$	140.000			0.0463349
$210$		0			0
$211$	−3198.00			−1.04341			−0.521705	−	0.853126i	$-0.674704\pi$
$211$	−3198.00			−1.04341			−0.521705	+	0.853126i	$0.674704\pi$
$212$		0			0
$213$	507.000	+	878.150i	0.163094	+	0.282487i
$214$		0			0
$215$	553.000	−	957.824i	0.175415	−	0.303828i
$216$		0			0
$217$	332.500	+	1727.72i	0.104016	+	0.540485i
$218$		0			0
$219$	813.000	−	1408.16i	0.250856	−	0.434495i
$220$		0			0
$221$	1872.00	+	3242.40i	0.569793	+	0.986911i
$222$		0			0
$223$	5091.00			1.52878			0.764391	−	0.644752i	$-0.223040\pi$
$223$	5091.00			1.52878			0.764391	+	0.644752i	$0.223040\pi$
$224$		0			0
$225$	−684.000			−0.202667
$226$		0			0
$227$	−1947.50	−	3373.17i	−0.569428	−	0.986278i	−0.996623	−	0.0821183i	$-0.973831\pi$
$227$	−1947.50	−	3373.17i	−0.569428	−	0.986278i	0.427195	−	0.904160i	$-0.359502\pi$
$228$		0			0
$229$	3214.00	−	5566.81i	0.927455	−	1.60640i	0.139889	−	0.990167i	$-0.455325\pi$
$229$	3214.00	−	5566.81i	0.927455	−	1.60640i	0.787565	−	0.616231i	$-0.211341\pi$
$230$		0			0
$231$	294.000	−	254.611i	0.0837393	−	0.0725204i
$232$		0			0
$233$	1912.00	−	3311.68i	0.537593	−	0.931139i	−0.461439	−	0.887172i	$-0.652667\pi$
$233$	1912.00	−	3311.68i	0.537593	−	0.931139i	0.999033	−	0.0439676i	$-0.0139998\pi$
$234$		0			0
$235$	−497.000	−	860.829i	−0.137960	−	0.238955i
$236$		0			0
$237$	915.000			0.250783
$238$		0			0
$239$	−568.000			−0.153727			−0.0768637	−	0.997042i	$-0.524491\pi$
$239$	−568.000			−0.153727			−0.0768637	+	0.997042i	$0.524491\pi$
$240$		0			0
$241$	−1767.50	−	3061.40i	−0.472426	−	0.818266i	0.527076	−	0.849818i	$-0.323288\pi$
$241$	−1767.50	−	3061.40i	−0.472426	−	0.818266i	−0.999502	+	0.0315522i	$0.989955\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−2229.50	+	891.140i	−0.581378	+	0.232379i
$246$		0			0
$247$	−520.000	+	900.666i	−0.133955	+	0.232016i
$248$		0			0
$249$	1684.50	+	2917.64i	0.428718	+	0.742562i
$250$		0			0
$251$	−4335.00			−1.09013			−0.545065	−	0.838394i	$-0.683495\pi$
$251$	−4335.00			−1.09013			−0.545065	+	0.838394i	$0.683495\pi$
$252$		0			0
$253$	−336.000			−0.0834946
$254$		0			0
$255$	−756.000	−	1309.43i	−0.185657	−	0.321568i
$256$		0			0
$257$	−1787.00	+	3095.17i	−0.433735	+	0.751252i	−0.997191	−	0.0748943i	$-0.976138\pi$
$257$	−1787.00	+	3095.17i	−0.433735	+	0.751252i	0.563456	+	0.826146i	$0.309471\pi$
$258$		0			0
$259$	−4928.00	+	4267.77i	−1.18228	+	1.02389i
$260$		0			0
$261$	1093.50	−	1894.00i	0.259333	−	0.449178i
$262$		0			0
$263$	2733.00	+	4733.69i	0.640776	+	1.10986i	0.985260	+	0.171064i	$0.0547205\pi$
$263$	2733.00	+	4733.69i	0.640776	+	1.10986i	−0.344484	+	0.938792i	$0.611946\pi$
$264$		0			0
$265$	−2625.00			−0.608500
$266$		0			0
$267$	−1278.00			−0.292930
$268$		0			0
$269$	2907.50	+	5035.94i	0.659009	+	1.14144i	0.980873	+	0.194651i	$0.0623574\pi$
$269$	2907.50	+	5035.94i	0.659009	+	1.14144i	−0.321864	+	0.946786i	$0.604309\pi$
$270$		0			0
$271$	−1618.50	+	2803.32i	−0.362793	+	0.628376i	−0.988419	−	0.151747i	$-0.951510\pi$
$271$	−1618.50	+	2803.32i	−0.362793	+	0.628376i	0.625626	+	0.780123i	$0.284843\pi$
$272$		0			0
$273$	546.000	+	2837.10i	0.121046	+	0.628971i
$274$		0			0
$275$	−266.000	+	460.726i	−0.0583287	+	0.101028i
$276$		0			0
$277$	1588.00	+	2750.50i	0.344454	+	0.596611i	0.985254	−	0.171096i	$-0.0547308\pi$
$277$	1588.00	+	2750.50i	0.344454	+	0.596611i	−0.640801	+	0.767707i	$0.721397\pi$
$278$		0			0
$279$	−855.000			−0.183468
$280$		0			0
$281$	−3282.00			−0.696753			−0.348377	−	0.937355i	$-0.613267\pi$
$281$	−3282.00			−0.696753			−0.348377	+	0.937355i	$0.613267\pi$
$282$		0			0
$283$	1091.00	+	1889.67i	0.229163	+	0.396923i	0.957560	−	0.288233i	$-0.0930677\pi$
$283$	1091.00	+	1889.67i	0.229163	+	0.396923i	−0.728397	+	0.685155i	$0.759734\pi$
$284$		0			0
$285$	210.000	−	363.731i	0.0436468	−	0.0755984i
$286$		0			0
$287$	−5180.00	−	1794.40i	−1.06539	−	0.369060i
$288$		0			0
$289$	−135.500	+	234.693i	−0.0275799	+	0.0477698i
$290$		0			0
$291$	553.500	+	958.690i	0.111501	+	0.193125i
$292$		0			0
$293$	3021.00			0.602351			0.301175	−	0.953569i	$-0.402621\pi$
$293$	3021.00			0.602351			0.301175	+	0.953569i	$0.402621\pi$
$294$		0			0
$295$	−1953.00			−0.385451
$296$		0			0
$297$	94.5000	+	163.679i	0.0184628	+	0.0319785i
$298$		0			0
$299$	1248.00	−	2161.60i	0.241384	−	0.418089i
$300$		0			0
$301$	−2765.00	−	957.824i	−0.529475	−	0.183415i
$302$		0			0
$303$	−1905.00	+	3299.56i	−0.361186	+	0.625593i
$304$		0			0
$305$	−861.000	−	1491.30i	−0.161642	−	0.279972i
$306$		0			0
$307$	1304.00			0.242421			0.121210	−	0.992627i	$-0.461322\pi$
$307$	1304.00			0.242421			0.121210	+	0.992627i	$0.461322\pi$
$308$		0			0
$309$	−5496.00			−1.01183
$310$		0			0
$311$	3104.00	+	5376.29i	0.565954	+	0.980261i	0.996960	+	0.0779121i	$0.0248254\pi$
$311$	3104.00	+	5376.29i	0.565954	+	0.980261i	−0.431006	+	0.902349i	$0.641841\pi$
$312$		0			0
$313$	−1668.50	+	2889.93i	−0.301307	+	0.521880i	−0.976432	−	0.215824i	$-0.930756\pi$
$313$	−1668.50	+	2889.93i	−0.301307	+	0.521880i	0.675125	+	0.737703i	$0.264090\pi$
$314$		0			0
$315$	−220.500	−	1145.75i	−0.0394405	−	0.204939i
$316$		0			0
$317$	−4318.50	+	7479.86i	−0.765146	+	1.32527i	0.175024	+	0.984564i	$0.444000\pi$
$317$	−4318.50	+	7479.86i	−0.765146	+	1.32527i	−0.940170	+	0.340707i	$0.889334\pi$
$318$		0			0
$319$	−850.500	−	1473.11i	−0.149275	−	0.258553i
$320$		0			0
$321$	2997.00			0.521110
$322$		0			0
$323$	−1440.00			−0.248061
$324$		0			0
$325$	−1976.00	−	3422.53i	−0.337258	−	0.584148i
$326$		0			0
$327$	2499.00	−	4328.39i	0.422615	−	0.731990i
$328$		0			0
$329$	−1988.00	+	1721.66i	−0.333137	+	0.288505i
$330$		0			0
$331$	970.000	−	1680.09i	0.161076	−	0.278991i	−0.774179	−	0.632967i	$-0.781837\pi$
$331$	970.000	−	1680.09i	0.161076	−	0.278991i	0.935255	+	0.353975i	$0.115170\pi$
$332$		0			0
$333$	−1584.00	−	2743.57i	−0.260669	−	0.451491i
$334$		0			0
$335$	5110.00			0.833400
$336$		0			0
$337$	−5527.00			−0.893397			−0.446699	−	0.894684i	$-0.647400\pi$
$337$	−5527.00			−0.893397			−0.446699	+	0.894684i	$0.647400\pi$
$338$		0			0
$339$	2748.00	+	4759.68i	0.440268	+	0.762567i
$340$		0			0
$341$	−332.500	+	575.907i	−0.0528032	+	0.0914578i
$342$		0			0
$343$	3430.00	+	5346.84i	0.539949	+	0.841698i
$344$		0			0
$345$	−504.000	+	872.954i	−0.0786506	+	0.136227i
$346$		0			0
$347$	4782.00	+	8282.67i	0.739802	+	1.28137i	0.952584	+	0.304275i	$0.0984141\pi$
$347$	4782.00	+	8282.67i	0.739802	+	1.28137i	−0.212783	+	0.977100i	$0.568253\pi$
$348$		0			0
$349$	−918.000			−0.140801			−0.0704003	−	0.997519i	$-0.522428\pi$
$349$	−918.000			−0.140801			−0.0704003	+	0.997519i	$0.522428\pi$
$350$		0			0
$351$	−1404.00			−0.213504
$352$		0			0
$353$	−5740.00	−	9941.97i	−0.865466	−	1.49903i	−0.866584	−	0.499031i	$-0.833689\pi$
$353$	−5740.00	−	9941.97i	−0.865466	−	1.49903i	0.00111843	−	0.999999i	$-0.499644\pi$
$354$		0			0
$355$	1183.00	−	2049.02i	0.176865	−	0.306339i
$356$		0			0
$357$	−3024.00	+	2618.86i	−0.448311	+	0.388249i
$358$		0			0
$359$	1827.00	−	3164.46i	0.268594	−	0.465219i	−0.699905	−	0.714236i	$-0.746774\pi$
$359$	1827.00	−	3164.46i	0.268594	−	0.465219i	0.968499	+	0.249017i	$0.0801076\pi$
$360$		0			0
$361$	3229.50	+	5593.66i	0.470841	+	0.815521i
$362$		0			0
$363$	−3846.00			−0.556095
$364$		0			0
$365$	−3794.00			−0.544074
$366$		0			0
$367$	−5033.50	−	8718.28i	−0.715931	−	1.24003i	−0.962599	−	0.270928i	$-0.912669\pi$
$367$	−5033.50	−	8718.28i	−0.715931	−	1.24003i	0.246669	−	0.969100i	$-0.420664\pi$
$368$		0			0
$369$	1332.00	−	2307.09i	0.187916	−	0.325481i
$370$		0			0
$371$	1312.50	+	6819.95i	0.183670	+	0.954378i
$372$		0			0
$373$	−4400.00	+	7621.02i	−0.610786	+	1.05791i	0.380322	+	0.924854i	$0.375813\pi$
$373$	−4400.00	+	7621.02i	−0.610786	+	1.05791i	−0.991108	+	0.133059i	$0.957520\pi$
$374$		0			0
$375$	2110.50	+	3655.49i	0.290629	+	0.503384i
$376$		0			0
$377$	12636.0			1.72623
$378$		0			0
$379$	−1136.00			−0.153964			−0.0769821	−	0.997032i	$-0.524528\pi$
$379$	−1136.00			−0.153964			−0.0769821	+	0.997032i	$0.524528\pi$
$380$		0			0
$381$	−2896.50	−	5016.89i	−0.389481	−	0.674601i
$382$		0			0
$383$	2145.00	−	3715.25i	0.286173	−	0.495667i	−0.686720	−	0.726922i	$-0.740950\pi$
$383$	2145.00	−	3715.25i	0.286173	−	0.495667i	0.972893	+	0.231256i	$0.0742834\pi$
$384$		0			0
$385$	−857.500	−	297.047i	−0.113512	−	0.0393218i
$386$		0			0
$387$	711.000	−	1231.49i	0.0933906	−	0.161757i
$388$		0			0
$389$	431.000	+	746.514i	0.0561763	+	0.0973001i	0.892746	−	0.450560i	$-0.148776\pi$
$389$	431.000	+	746.514i	0.0561763	+	0.0973001i	−0.836570	+	0.547861i	$0.815442\pi$
$390$		0			0
$391$	3456.00			0.447001
$392$		0			0
$393$	−2937.00			−0.376977
$394$		0			0
$395$	−1067.50	−	1848.96i	−0.135979	−	0.235523i
$396$		0			0
$397$	4570.00	−	7915.47i	0.577737	−	1.00067i	−0.418001	−	0.908447i	$-0.637269\pi$
$397$	4570.00	−	7915.47i	0.577737	−	1.00067i	0.995738	−	0.0922238i	$-0.0293975\pi$
$398$		0			0
$399$	−1050.00	−	363.731i	−0.131744	−	0.0456374i
$400$		0			0
$401$	7116.00	−	12325.3i	0.886175	−	1.53490i	0.0418135	−	0.999125i	$-0.486686\pi$
$401$	7116.00	−	12325.3i	0.886175	−	1.53490i	0.844361	−	0.535774i	$-0.179980\pi$
$402$		0			0
$403$	−2470.00	−	4278.17i	−0.305309	−	0.528810i
$404$		0			0
$405$	567.000			0.0695666
$406$		0			0
$407$	−2464.00			−0.300088
$408$		0			0
$409$	5000.50	+	8661.12i	0.604545	+	1.04710i	0.992123	+	0.125266i	$0.0399783\pi$
$409$	5000.50	+	8661.12i	0.604545	+	1.04710i	−0.387578	+	0.921837i	$0.626688\pi$
$410$		0			0
$411$	729.000	−	1262.67i	0.0874913	−	0.151539i
$412$		0			0
$413$	976.500	+	5074.04i	0.116345	+	0.604546i
$414$		0			0
$415$	3930.50	−	6807.83i	0.464917	−	0.805260i
$416$		0			0
$417$	−3945.00	−	6832.94i	−0.463279	−	0.802423i
$418$		0			0
$419$	10256.0			1.19580			0.597898	−	0.801572i	$-0.296003\pi$
$419$	10256.0			1.19580			0.597898	+	0.801572i	$0.296003\pi$
$420$		0			0
$421$	−4502.00			−0.521174			−0.260587	−	0.965450i	$-0.583916\pi$
$421$	−4502.00			−0.521174			−0.260587	+	0.965450i	$0.583916\pi$
$422$		0			0
$423$	−639.000	−	1106.78i	−0.0734497	−	0.127219i
$424$		0			0
$425$	2736.00	−	4738.89i	0.312272	−	0.540871i
$426$		0			0
$427$	−3444.00	+	2982.59i	−0.390320	+	0.338027i
$428$		0			0
$429$	−546.000	+	945.700i	−0.0614479	+	0.106431i
$430$		0			0
$431$	6178.00	+	10700.6i	0.690450	+	1.19589i	0.971691	+	0.236257i	$0.0759206\pi$
$431$	6178.00	+	10700.6i	0.690450	+	1.19589i	−0.281241	+	0.959637i	$0.590746\pi$
$432$		0			0
$433$	862.000			0.0956699			0.0478350	−	0.998855i	$-0.484768\pi$
$433$	862.000			0.0956699			0.0478350	+	0.998855i	$0.484768\pi$
$434$		0			0
$435$	−5103.00			−0.562460
$436$		0			0
$437$	480.000	+	831.384i	0.0525435	+	0.0910080i
$438$		0			0
$439$	−682.500	+	1182.12i	−0.0742003	+	0.128519i	−0.900738	−	0.434362i	$-0.856974\pi$
$439$	−682.500	+	1182.12i	−0.0742003	+	0.128519i	0.826538	+	0.562881i	$0.190307\pi$
$440$		0			0
$441$	−2866.50	+	1145.75i	−0.309524	+	0.123718i
$442$		0			0
$443$	4465.50	−	7734.47i	0.478922	−	0.829517i	−0.520786	−	0.853687i	$-0.674361\pi$
$443$	4465.50	−	7734.47i	0.478922	−	0.829517i	0.999708	+	0.0241705i	$0.00769445\pi$
$444$		0			0
$445$	1491.00	+	2582.49i	0.158832	+	0.275105i
$446$		0			0
$447$	−5634.00			−0.596150
$448$		0			0
$449$	11228.0			1.18014			0.590069	−	0.807353i	$-0.299100\pi$
$449$	11228.0			1.18014			0.590069	+	0.807353i	$0.299100\pi$
$450$		0			0
$451$	−1036.00	−	1794.40i	−0.108167	−	0.187351i
$452$		0			0
$453$	3154.50	−	5463.75i	0.327177	−	0.566688i
$454$		0			0
$455$	5096.00	−	4413.27i	0.525064	−	0.454719i
$456$		0			0
$457$	−6075.50	+	10523.1i	−0.621882	+	1.07713i	0.367253	+	0.930121i	$0.380298\pi$
$457$	−6075.50	+	10523.1i	−0.621882	+	1.07713i	−0.989135	+	0.147010i	$0.953035\pi$
$458$		0			0
$459$	−972.000	−	1683.55i	−0.0988433	−	0.171202i
$460$		0			0
$461$	18534.0			1.87248			0.936241	−	0.351358i	$-0.114280\pi$
$461$	18534.0			1.87248			0.936241	+	0.351358i	$0.114280\pi$
$462$		0			0
$463$	−17096.0			−1.71602			−0.858011	−	0.513631i	$-0.828300\pi$
$463$	−17096.0			−1.71602			−0.858011	+	0.513631i	$0.828300\pi$
$464$		0			0
$465$	997.500	+	1727.72i	0.0994795	+	0.172304i
$466$		0			0
$467$	−1070.00	+	1853.29i	−0.106025	+	0.183641i	−0.914157	−	0.405361i	$-0.867146\pi$
$467$	−1070.00	+	1853.29i	−0.106025	+	0.183641i	0.808131	+	0.589002i	$0.200479\pi$
$468$		0			0
$469$	−2555.00	−	13276.2i	−0.251554	−	1.30711i
$470$		0			0
$471$	−2106.00	+	3647.70i	−0.206028	+	0.356852i
$472$		0			0
$473$	−553.000	−	957.824i	−0.0537568	−	0.0931095i
$474$		0			0
$475$	1520.00			0.146826
$476$		0			0
$477$	−3375.00			−0.323964
$478$		0			0
$479$	−6633.00	−	11488.7i	−0.632713	−	1.09589i	−0.986995	−	0.160752i	$-0.948608\pi$
$479$	−6633.00	−	11488.7i	−0.632713	−	1.09589i	0.354282	−	0.935139i	$-0.384725\pi$
$480$		0			0
$481$	9152.00	−	15851.7i	0.867558	−	1.50265i
$482$		0			0
$483$	2520.00	+	872.954i	0.237400	+	0.0822376i
$484$		0			0
$485$	1291.50	−	2236.94i	0.120915	−	0.209432i
$486$		0			0
$487$	−9591.50	−	16613.0i	−0.892469	−	1.54580i	−0.836906	−	0.547346i	$-0.815638\pi$
$487$	−9591.50	−	16613.0i	−0.892469	−	1.54580i	−0.0555627	−	0.998455i	$-0.517695\pi$
$488$		0			0
$489$	4608.00			0.426137
$490$		0			0
$491$	21693.0			1.99387			0.996936	−	0.0782185i	$-0.0249232\pi$
$491$	21693.0			1.99387			0.996936	+	0.0782185i	$0.0249232\pi$
$492$		0			0
$493$	8748.00	+	15152.0i	0.799169	+	1.38420i
$494$		0			0
$495$	220.500	−	381.917i	0.0200217	−	0.0346786i
$496$		0			0
$497$	−5915.00	−	2049.02i	−0.533851	−	0.184931i
$498$		0			0
$499$	9829.00	−	17024.3i	0.881776	−	1.52728i	0.0324122	−	0.999475i	$-0.489681\pi$
$499$	9829.00	−	17024.3i	0.881776	−	1.52728i	0.849364	−	0.527807i	$-0.176986\pi$
$500$		0			0
$501$	−5451.00	−	9441.41i	−0.486093	−	0.841938i
$502$		0			0
$503$	−19436.0			−1.72288			−0.861440	−	0.507860i	$-0.830437\pi$
$503$	−19436.0			−1.72288			−0.861440	+	0.507860i	$0.830437\pi$
$504$		0			0
$505$	8890.00			0.783366
$506$		0			0
$507$	−760.500	−	1317.22i	−0.0666173	−	0.115385i
$508$		0			0
$509$	−1544.50	+	2675.15i	−0.134497	+	0.232955i	−0.925405	−	0.378980i	$-0.876275\pi$
$509$	−1544.50	+	2675.15i	−0.134497	+	0.232955i	0.790908	+	0.611934i	$0.209608\pi$
$510$		0			0
$511$	1897.00	+	9857.10i	0.164224	+	0.853332i
$512$		0			0
$513$	270.000	−	467.654i	0.0232374	−	0.0402484i
$514$		0			0
$515$	6412.00	+	11105.9i	0.548634	+	0.950262i
$516$		0			0
$517$	−994.000			−0.0845572
$518$		0			0
$519$	2574.00			0.217700
$520$		0			0
$521$	−975.000	−	1688.75i	−0.0819876	−	0.142007i	0.822116	−	0.569320i	$-0.192793\pi$
$521$	−975.000	−	1688.75i	−0.0819876	−	0.142007i	−0.904104	+	0.427313i	$0.859460\pi$
$522$		0			0
$523$	6566.00	−	11372.6i	0.548970	−	0.950843i	−0.449376	−	0.893343i	$-0.648354\pi$
$523$	6566.00	−	11372.6i	0.548970	−	0.950843i	0.998345	−	0.0575005i	$-0.0183131\pi$
$524$		0			0
$525$	3192.00	−	2764.35i	0.265353	−	0.229802i
$526$		0			0
$527$	3420.00	−	5923.61i	0.282690	−	0.489633i
$528$		0			0
$529$	4931.50	+	8541.61i	0.405318	+	0.702031i
$530$		0			0
$531$	−2511.00			−0.205213
$532$		0			0
$533$	15392.0			1.25085
$534$		0			0
$535$	−3496.50	−	6056.12i	−0.282555	−	0.489399i
$536$		0			0
$537$	−3630.00	+	6287.34i	−0.291706	+	0.505249i
$538$		0			0
$539$	−343.000	+	2376.37i	−0.0274101	+	0.189903i
$540$		0			0
$541$	−1465.00	+	2537.45i	−0.116424	+	0.201652i	−0.918348	−	0.395774i	$-0.870476\pi$
$541$	−1465.00	+	2537.45i	−0.116424	+	0.201652i	0.801924	+	0.597426i	$0.203810\pi$
$542$		0			0
$543$	4008.00	+	6942.06i	0.316758	+	0.548641i
$544$		0			0
$545$	−11662.0			−0.916597
$546$		0			0
$547$	−19824.0			−1.54957			−0.774783	−	0.632227i	$-0.782141\pi$
$547$	−19824.0			−1.54957			−0.774783	+	0.632227i	$0.782141\pi$
$548$		0			0
$549$	−1107.00	−	1917.38i	−0.0860576	−	0.149056i
$550$		0			0
$551$	−2430.00	+	4208.88i	−0.187879	+	0.325416i
$552$		0			0
$553$	−4270.00	+	3697.93i	−0.328352	+	0.284362i
$554$		0			0
$555$	−3696.00	+	6401.66i	−0.282678	+	0.489613i
$556$		0			0
$557$	9584.50	+	16600.8i	0.729099	+	1.26284i	0.957264	+	0.289215i	$0.0933941\pi$
$557$	9584.50	+	16600.8i	0.729099	+	1.26284i	−0.228165	+	0.973622i	$0.573273\pi$
$558$		0			0
$559$	8216.00			0.621645
$560$		0			0
$561$	−1512.00			−0.113791
$562$		0			0
$563$	3633.50	+	6293.41i	0.271996	+	0.471111i	0.969373	−	0.245594i	$-0.0789829\pi$
$563$	3633.50	+	6293.41i	0.271996	+	0.471111i	−0.697377	+	0.716705i	$0.745650\pi$
$564$		0			0
$565$	6412.00	−	11105.9i	0.477442	−	0.826954i
$566$		0			0
$567$	−283.500	−	1473.11i	−0.0209980	−	0.109109i
$568$		0			0
$569$	2446.00	−	4236.60i	0.180214	−	0.312139i	−0.761739	−	0.647883i	$-0.775654\pi$
$569$	2446.00	−	4236.60i	0.180214	−	0.312139i	0.941953	+	0.335744i	$0.108988\pi$
$570$		0			0
$571$	11063.0	+	19161.7i	0.810809	+	1.40436i	0.912298	+	0.409526i	$0.134306\pi$
$571$	11063.0	+	19161.7i	0.810809	+	1.40436i	−0.101489	+	0.994837i	$0.532361\pi$
$572$		0			0
$573$	5136.00			0.374449
$574$		0			0
$575$	−3648.00			−0.264578
$576$		0			0
$577$	548.500	+	950.030i	0.0395743	+	0.0685446i	0.885134	−	0.465336i	$-0.154066\pi$
$577$	548.500	+	950.030i	0.0395743	+	0.0685446i	−0.845560	+	0.533881i	$0.820733\pi$
$578$		0			0
$579$	5092.50	−	8820.47i	0.365522	−	0.633102i
$580$		0			0
$581$	−19652.5	−	6807.83i	−1.40331	−	0.486121i
$582$		0			0
$583$	−1312.50	+	2273.32i	−0.0932388	+	0.161494i
$584$		0			0
$585$	1638.00	+	2837.10i	0.115766	+	0.200512i
$586$		0			0
$587$	−9969.00			−0.700962			−0.350481	−	0.936570i	$-0.613982\pi$
$587$	−9969.00			−0.700962			−0.350481	+	0.936570i	$0.613982\pi$
$588$		0			0
$589$	1900.00			0.132917
$590$		0			0
$591$	−765.000	−	1325.02i	−0.0532452	−	0.0922233i
$592$		0			0
$593$	3212.00	−	5563.35i	0.222430	−	0.385260i	−0.733115	−	0.680104i	$-0.761934\pi$
$593$	3212.00	−	5563.35i	0.222430	−	0.385260i	0.955545	+	0.294844i	$0.0952678\pi$
$594$		0			0
$595$	8820.00	+	3055.34i	0.607705	+	0.210515i
$596$		0			0
$597$	414.000	−	717.069i	0.0283817	−	0.0491586i
$598$		0			0
$599$	8523.00	+	14762.3i	0.581370	+	1.00696i	0.995317	+	0.0966609i	$0.0308162\pi$
$599$	8523.00	+	14762.3i	0.581370	+	1.00696i	−0.413948	+	0.910301i	$0.635850\pi$
$600$		0			0
$601$	−18877.0			−1.28121			−0.640606	−	0.767869i	$-0.721317\pi$
$601$	−18877.0			−1.28121			−0.640606	+	0.767869i	$0.721317\pi$
$602$		0			0
$603$	6570.00			0.443700
$604$		0			0
$605$	4487.00	+	7771.71i	0.301525	+	0.522256i
$606$		0			0
$607$	−6891.50	+	11936.4i	−0.460819	+	0.798163i	−0.999002	−	0.0446657i	$-0.985778\pi$
$607$	−6891.50	+	11936.4i	−0.460819	+	0.798163i	0.538183	+	0.842828i	$0.319111\pi$
$608$		0			0
$609$	2551.50	+	13258.0i	0.169773	+	0.882168i
$610$		0			0
$611$	3692.00	−	6394.73i	0.244456	−	0.423409i
$612$		0			0
$613$	−9096.00	−	15754.7i	−0.599321	−	1.03806i	−0.992921	−	0.118773i	$-0.962104\pi$
$613$	−9096.00	−	15754.7i	−0.599321	−	1.03806i	0.393600	−	0.919282i	$-0.371229\pi$
$614$		0			0
$615$	−6216.00			−0.407566
$616$		0			0
$617$	−13054.0			−0.851757			−0.425879	−	0.904780i	$-0.640035\pi$
$617$	−13054.0			−0.851757			−0.425879	+	0.904780i	$0.640035\pi$
$618$		0			0
$619$	3623.00	+	6275.22i	0.235251	+	0.407468i	0.959346	−	0.282234i	$-0.0910753\pi$
$619$	3623.00	+	6275.22i	0.235251	+	0.407468i	−0.724094	+	0.689701i	$0.757742\pi$
$620$		0			0
$621$	−648.000	+	1122.37i	−0.0418733	+	0.0725268i
$622$		0			0
$623$	5964.00	−	5164.98i	0.383535	−	0.332151i
$624$		0			0
$625$	174.500	−	302.243i	0.0111680	−	0.0193435i
$626$		0			0
$627$	−210.000	−	363.731i	−0.0133757	−	0.0231675i
$628$		0			0
$629$	25344.0			1.60657
$630$		0			0
$631$	−2817.00			−0.177723			−0.0888613	−	0.996044i	$-0.528323\pi$
$631$	−2817.00			−0.177723			−0.0888613	+	0.996044i	$0.528323\pi$
$632$		0			0
$633$	4797.00	+	8308.65i	0.301206	+	0.521705i
$634$		0			0
$635$	−6758.50	+	11706.1i	−0.422367	+	0.731561i
$636$		0			0
$637$	−14014.0	−	11033.2i	−0.871672	−	0.686264i
$638$		0			0
$639$	1521.00	−	2634.45i	0.0941625	−	0.163094i
$640$		0			0
$641$	−7893.00	−	13671.1i	−0.486357	−	0.842395i	0.513520	−	0.858078i	$-0.328341\pi$
$641$	−7893.00	−	13671.1i	−0.486357	−	0.842395i	−0.999877	+	0.0156827i	$0.995008\pi$
$642$		0			0
$643$	17426.0			1.06876			0.534381	−	0.845244i	$-0.320545\pi$
$643$	17426.0			1.06876			0.534381	+	0.845244i	$0.320545\pi$
$644$		0			0
$645$	−3318.00			−0.202552
$646$		0			0
$647$	−12917.0	−	22372.9i	−0.784884	−	1.35946i	−0.929069	−	0.369907i	$-0.879389\pi$
$647$	−12917.0	−	22372.9i	−0.784884	−	1.35946i	0.144185	−	0.989551i	$-0.453944\pi$
$648$		0			0
$649$	−976.500	+	1691.35i	−0.0590616	+	0.102298i
$650$		0			0
$651$	3990.00	−	3455.44i	0.240216	−	0.208033i
$652$		0			0
$653$	−13991.5	+	24234.0i	−0.838483	+	1.45230i	0.0526789	+	0.998612i	$0.483224\pi$
$653$	−13991.5	+	24234.0i	−0.838483	+	1.45230i	−0.891162	+	0.453684i	$0.850109\pi$
$654$		0			0
$655$	3426.50	+	5934.87i	0.204404	+	0.354038i
$656$		0			0
$657$	−4878.00			−0.289663
$658$		0			0
$659$	28296.0			1.67262			0.836309	−	0.548258i	$-0.184709\pi$
$659$	28296.0			1.67262			0.836309	+	0.548258i	$0.184709\pi$
$660$		0			0
$661$	−10627.0	−	18406.5i	−0.625329	−	1.08310i	−0.988477	−	0.151370i	$-0.951631\pi$
$661$	−10627.0	−	18406.5i	−0.625329	−	1.08310i	0.363148	−	0.931731i	$-0.381702\pi$
$662$		0			0
$663$	5616.00	−	9727.20i	0.328970	−	0.569793i
$664$		0			0
$665$	490.000	+	2546.11i	0.0285735	+	0.148472i
$666$		0			0
$667$	5832.00	−	10101.3i	0.338555	−	0.586394i
$668$		0			0
$669$	−7636.50	−	13226.8i	−0.441322	−	0.764391i
$670$		0			0
$671$	−1722.00			−0.0990716
$672$		0			0
$673$	−28259.0			−1.61858			−0.809290	−	0.587409i	$-0.800148\pi$
$673$	−28259.0			−1.61858			−0.809290	+	0.587409i	$0.800148\pi$
$674$		0			0
$675$	1026.00	+	1777.08i	0.0585048	+	0.101333i
$676$		0			0
$677$	−15889.5	+	27521.4i	−0.902043	+	1.56238i	−0.0772049	+	0.997015i	$0.524600\pi$
$677$	−15889.5	+	27521.4i	−0.902043	+	1.56238i	−0.824838	+	0.565369i	$0.808734\pi$
$678$		0			0
$679$	−6457.50	−	2236.94i	−0.364972	−	0.126430i
$680$		0			0
$681$	−5842.50	+	10119.5i	−0.328759	+	0.569428i
$682$		0			0
$683$	−4873.50	−	8441.15i	−0.273030	−	0.472901i	0.696606	−	0.717453i	$-0.254692\pi$
$683$	−4873.50	−	8441.15i	−0.273030	−	0.472901i	−0.969636	+	0.244552i	$0.921359\pi$
$684$		0			0
$685$	−3402.00			−0.189757
$686$		0			0
$687$	−19284.0			−1.07093
$688$		0			0
$689$	−9750.00	−	16887.5i	−0.539108	−	0.933762i
$690$		0			0
$691$	−12256.0	+	21228.0i	−0.674733	+	1.16867i	0.301814	+	0.953367i	$0.402408\pi$
$691$	−12256.0	+	21228.0i	−0.674733	+	1.16867i	−0.976547	+	0.215304i	$0.930926\pi$
$692$		0			0
$693$	−1102.50	−	381.917i	−0.0604336	−	0.0209348i
$694$		0			0
$695$	−9205.00	+	15943.5i	−0.502396	+	0.870176i
$696$		0			0
$697$	10656.0	+	18456.7i	0.579089	+	1.00301i
$698$		0			0
$699$	−11472.0			−0.620760
$700$		0			0
$701$	14325.0			0.771823			0.385911	−	0.922536i	$-0.373887\pi$
$701$	14325.0			0.771823			0.385911	+	0.922536i	$0.373887\pi$
$702$		0			0
$703$	3520.00	+	6096.82i	0.188847	+	0.327092i
$704$		0			0
$705$	−1491.00	+	2582.49i	−0.0796515	+	0.137960i
$706$		0			0
$707$	−4445.00	−	23096.9i	−0.236452	−	1.22864i
$708$		0			0
$709$	−6039.00	+	10459.9i	−0.319886	+	0.554059i	−0.980464	−	0.196698i	$-0.936978\pi$
$709$	−6039.00	+	10459.9i	−0.319886	+	0.554059i	0.660578	+	0.750758i	$0.270311\pi$
$710$		0			0
$711$	−1372.50	−	2377.24i	−0.0723949	−	0.125392i
$712$		0			0
$713$	−4560.00			−0.239514
$714$		0			0
$715$	2548.00			0.133272
$716$		0			0
$717$	852.000	+	1475.71i	0.0443773	+	0.0768637i
$718$		0			0
$719$	−5329.00	+	9230.10i	−0.276409	+	0.478755i	−0.970490	−	0.241143i	$-0.922478\pi$
$719$	−5329.00	+	9230.10i	−0.276409	+	0.478755i	0.694081	+	0.719897i	$0.255811\pi$
$720$		0			0
$721$	25648.0	−	22211.8i	1.32480	−	1.14731i
$722$		0			0
$723$	−5302.50	+	9184.20i	−0.272755	+	0.472426i
$724$		0			0
$725$	−9234.00	−	15993.8i	−0.473024	−	0.819301i
$726$		0			0
$727$	−19099.0			−0.974337			−0.487168	−	0.873308i	$-0.661970\pi$
$727$	−19099.0			−0.974337			−0.487168	+	0.873308i	$0.661970\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	5688.00	+	9851.90i	0.287795	+	0.498476i
$732$		0			0
$733$	−703.000	+	1217.63i	−0.0354241	+	0.0613564i	−0.883194	−	0.469008i	$-0.844612\pi$
$733$	−703.000	+	1217.63i	−0.0354241	+	0.0613564i	0.847770	+	0.530364i	$0.177945\pi$
$734$		0			0
$735$	5659.50	+	4455.70i	0.284019	+	0.223607i
$736$		0			0
$737$	2555.00	−	4425.39i	0.127700	−	0.221182i
$738$		0			0
$739$	3365.00	+	5828.35i	0.167501	+	0.290121i	0.937541	−	0.347875i	$-0.113097\pi$
$739$	3365.00	+	5828.35i	0.167501	+	0.290121i	−0.770039	+	0.637996i	$0.779763\pi$
$740$		0			0
$741$	3120.00			0.154678
$742$		0			0
$743$	1166.00			0.0575725			0.0287863	−	0.999586i	$-0.490836\pi$
$743$	1166.00			0.0575725			0.0287863	+	0.999586i	$0.490836\pi$
$744$		0			0
$745$	6573.00	+	11384.8i	0.323243	+	0.559873i
$746$		0			0
$747$	5053.50	−	8752.92i	0.247521	−	0.428718i
$748$		0			0
$749$	−13986.0	+	12112.2i	−0.682293	+	0.590883i
$750$		0			0
$751$	−8483.50	+	14693.9i	−0.412207	+	0.713963i	−0.995131	−	0.0985636i	$-0.968575\pi$
$751$	−8483.50	+	14693.9i	−0.412207	+	0.713963i	0.582924	+	0.812527i	$0.301909\pi$
$752$		0			0
$753$	6502.50	+	11262.7i	0.314694	+	0.545065i
$754$		0			0
$755$	−14721.0			−0.709605
$756$		0			0
$757$	11878.0			0.570295			0.285147	−	0.958484i	$-0.407957\pi$
$757$	11878.0			0.570295			0.285147	+	0.958484i	$0.407957\pi$
$758$		0			0
$759$	504.000	+	872.954i	0.0241028	+	0.0417473i
$760$		0			0
$761$	−13662.0	+	23663.3i	−0.650785	+	1.12719i	0.332148	+	0.943227i	$0.392227\pi$
$761$	−13662.0	+	23663.3i	−0.650785	+	1.12719i	−0.982933	+	0.183965i	$0.941107\pi$
$762$		0			0
$763$	5831.00	+	30298.8i	0.276666	+	1.43760i
$764$		0			0
$765$	−2268.00	+	3928.29i	−0.107189	+	0.185657i
$766$		0			0
$767$	−7254.00	−	12564.3i	−0.341495	−	0.591487i
$768$		0			0
$769$	−11971.0			−0.561359			−0.280680	−	0.959802i	$-0.590560\pi$
$769$	−11971.0			−0.561359			−0.280680	+	0.959802i	$0.590560\pi$
$770$		0			0
$771$	10722.0			0.500834
$772$		0			0
$773$	169.000	+	292.717i	0.00786353	+	0.0136200i	0.869930	−	0.493175i	$-0.164164\pi$
$773$	169.000	+	292.717i	0.00786353	+	0.0136200i	−0.862067	+	0.506795i	$0.830830\pi$
$774$		0			0
$775$	−3610.00	+	6252.70i	−0.167323	+	0.289811i
$776$		0			0
$777$	18480.0	+	6401.66i	0.853238	+	0.295570i
$778$		0			0
$779$	−2960.00	+	5126.87i	−0.136140	+	0.235801i
$780$		0			0
$781$	−1183.00	−	2049.02i	−0.0542011	−	0.0938791i
$782$		0			0
$783$	−6561.00			−0.299452
$784$		0			0
$785$	9828.00			0.446849
$786$		0			0
$787$	7057.00	+	12223.1i	0.319638	+	0.553629i	0.980412	−	0.196956i	$-0.0631055\pi$
$787$	7057.00	+	12223.1i	0.319638	+	0.553629i	−0.660775	+	0.750584i	$0.729772\pi$
$788$		0			0
$789$	8199.00	−	14201.1i	0.369952	−	0.640776i
$790$		0			0
$791$	−32060.0	−	11105.9i	−1.44112	−	0.499217i
$792$		0			0
$793$	6396.00	−	11078.2i	0.286417	−	0.496089i
$794$		0			0
$795$	3937.50	+	6819.95i	0.175659	+	0.304250i
$796$		0			0
$797$	1563.00			0.0694659			0.0347329	−	0.999397i	$-0.488942\pi$
$797$	1563.00			0.0694659			0.0347329	+	0.999397i	$0.488942\pi$
$798$		0			0
$799$	10224.0			0.452690
$800$		0			0
$801$	1917.00	+	3320.34i	0.0845616	+	0.146465i
$802$		0			0
$803$	−1897.00	+	3285.70i	−0.0833670	+	0.144396i
$804$		0			0
$805$	−1176.00	−	6110.68i	−0.0514889	−	0.267544i
$806$		0			0
$807$	8722.50	−	15107.8i	0.380479	−	0.659009i
$808$		0			0
$809$	15784.0	+	27338.7i	0.685953	+	1.18811i	0.973136	+	0.230230i	$0.0739477\pi$
$809$	15784.0	+	27338.7i	0.685953	+	1.18811i	−0.287183	+	0.957876i	$0.592719\pi$
$810$		0			0
$811$	−2626.00			−0.113701			−0.0568504	−	0.998383i	$-0.518106\pi$
$811$	−2626.00			−0.113701			−0.0568504	+	0.998383i	$0.518106\pi$
$812$		0			0
$813$	9711.00			0.418917
$814$		0			0
$815$	−5376.00	−	9311.51i	−0.231059	−	0.400206i
$816$		0			0
$817$	−1580.00	+	2736.64i	−0.0676588	+	0.117188i
$818$		0			0
$819$	6552.00	−	5674.20i	0.279543	−	0.242091i
$820$		0			0
$821$	−180.500	+	312.635i	−0.00767295	+	0.0132899i	−0.869836	−	0.493340i	$-0.835776\pi$
$821$	−180.500	+	312.635i	−0.00767295	+	0.0132899i	0.862163	+	0.506630i	$0.169109\pi$
$822$		0			0
$823$	−14772.0	−	25585.9i	−0.625662	−	1.08368i	−0.988413	−	0.151792i	$-0.951496\pi$
$823$	−14772.0	−	25585.9i	−0.625662	−	1.08368i	0.362751	−	0.931886i	$-0.381838\pi$
$824$		0			0
$825$	1596.00			0.0673522
$826$		0			0
$827$	−24163.0			−1.01600			−0.507999	−	0.861358i	$-0.669615\pi$
$827$	−24163.0			−1.01600			−0.507999	+	0.861358i	$0.669615\pi$
$828$		0			0
$829$	19598.0	+	33944.7i	0.821070	+	1.42213i	0.904886	+	0.425653i	$0.139956\pi$
$829$	19598.0	+	33944.7i	0.821070	+	1.42213i	−0.0838169	+	0.996481i	$0.526711\pi$
$830$		0			0
$831$	4764.00	−	8251.49i	0.198870	−	0.344454i
$832$		0			0
$833$	3528.00	−	24442.7i	0.146744	−	1.01667i
$834$		0			0
$835$	−12719.0	+	22030.0i	−0.527137	+	0.913028i
$836$		0			0
$837$	1282.50	+	2221.36i	0.0529626	+	0.0917339i
$838$		0			0
$839$	−6528.00			−0.268619			−0.134310	−	0.990939i	$-0.542882\pi$
$839$	−6528.00			−0.268619			−0.134310	+	0.990939i	$0.542882\pi$
$840$		0			0
$841$	34660.0			1.42113
$842$		0			0
$843$	4923.00	+	8526.89i	0.201135	+	0.348377i
$844$		0			0
$845$	−1774.50	+	3073.52i	−0.0722422	+	0.125127i
$846$		0			0
$847$	17948.0	−	15543.4i	0.728100	−	0.630553i
$848$		0			0
$849$	3273.00	−	5669.00i	0.132308	−	0.229163i
$850$		0			0
$851$	−8448.00	−	14632.4i	−0.340298	−	0.589414i
$852$		0			0
$853$	1046.00			0.0419864			0.0209932	−	0.999780i	$-0.493317\pi$
$853$	1046.00			0.0419864			0.0209932	+	0.999780i	$0.493317\pi$
$854$		0			0
$855$	−1260.00			−0.0503989
$856$		0			0
$857$	−16455.0	−	28500.9i	−0.655883	−	1.13602i	−0.981672	−	0.190581i	$-0.938963\pi$
$857$	−16455.0	−	28500.9i	−0.655883	−	1.13602i	0.325788	−	0.945443i	$-0.394370\pi$
$858$		0			0
$859$	11341.0	−	19643.2i	0.450466	−	0.780229i	−0.547949	−	0.836512i	$-0.684591\pi$
$859$	11341.0	−	19643.2i	0.450466	−	0.780229i	0.998415	+	0.0562823i	$0.0179247\pi$
$860$		0			0
$861$	3108.00	+	16149.6i	0.123020	+	0.639231i
$862$		0			0
$863$	−3725.00	+	6451.89i	−0.146930	+	0.254490i	−0.930091	−	0.367328i	$-0.880272\pi$
$863$	−3725.00	+	6451.89i	−0.146930	+	0.254490i	0.783161	+	0.621818i	$0.213606\pi$
$864$		0			0
$865$	−3003.00	−	5201.35i	−0.118041	−	0.204452i
$866$		0			0
$867$	813.000			0.0318465
$868$		0			0
$869$	−2135.00			−0.0833428
$870$		0			0
$871$	18980.0	+	32874.3i	0.738361	+	1.27888i
$872$		0			0
$873$	1660.50	−	2876.07i	0.0643750	−	0.111501i
$874$		0			0
$875$	−24622.5	−	8529.48i	−0.951306	−	0.329542i
$876$		0			0
$877$	−5040.00	+	8729.54i	−0.194058	+	0.336118i	−0.946591	−	0.322436i	$-0.895498\pi$
$877$	−5040.00	+	8729.54i	−0.194058	+	0.336118i	0.752533	+	0.658554i	$0.228832\pi$
$878$		0			0
$879$	−4531.50	−	7848.79i	−0.173884	−	0.301175i
$880$		0			0
$881$	−32958.0			−1.26037			−0.630183	−	0.776446i	$-0.717020\pi$
$881$	−32958.0			−1.26037			−0.630183	+	0.776446i	$0.717020\pi$
$882$		0			0
$883$	19784.0			0.754003			0.377001	−	0.926213i	$-0.376955\pi$
$883$	19784.0			0.754003			0.377001	+	0.926213i	$0.376955\pi$
$884$		0			0
$885$	2929.50	+	5074.04i	0.111270	+	0.192726i
$886$		0			0
$887$	−5740.00	+	9941.97i	−0.217283	+	0.376346i	−0.953976	−	0.299881i	$-0.903053\pi$
$887$	−5740.00	+	9941.97i	−0.217283	+	0.376346i	0.736693	+	0.676227i	$0.236386\pi$
$888$		0			0
$889$	33792.5	+	11706.1i	1.27488	+	0.441630i
$890$		0			0
$891$	283.500	−	491.036i	0.0106595	−	0.0184628i
$892$		0			0
$893$	1420.00	+	2459.51i	0.0532122	+	0.0921662i
$894$		0			0
$895$	16940.0			0.632672
$896$		0			0
$897$	−7488.00			−0.278726
$898$		0			0
$899$	−11542.5	−	19992.2i	−0.428213	−	0.741688i
$900$		0			0
$901$	13500.0	−	23382.7i	0.499168	−	0.864584i
$902$		0			0
$903$	1659.00	+	8620.42i	0.0611385	+	0.317685i
$904$		0			0
$905$	9352.00	−	16198.1i	0.343504	−	0.594966i
$906$		0			0
$907$	−22676.0	−	39276.0i	−0.830148	−	1.43786i	−0.897920	−	0.440158i	$-0.854923\pi$
$907$	−22676.0	−	39276.0i	−0.830148	−	1.43786i	0.0677725	−	0.997701i	$-0.478411\pi$
$908$		0			0
$909$	11430.0			0.417062
$910$		0			0
$911$	39906.0			1.45131			0.725656	−	0.688058i	$-0.241537\pi$
$911$	39906.0			1.45131			0.725656	+	0.688058i	$0.241537\pi$
$912$		0			0
$913$	−3930.50	−	6807.83i	−0.142476	−	0.246776i
$914$		0			0
$915$	−2583.00	+	4473.89i	−0.0933239	+	0.161642i
$916$		0			0
$917$	13706.0	−	11869.7i	0.493579	−	0.427452i
$918$		0			0
$919$	8764.00	−	15179.7i	0.314579	−	0.544866i	−0.664769	−	0.747049i	$-0.731470\pi$
$919$	8764.00	−	15179.7i	0.314579	−	0.544866i	0.979348	+	0.202183i	$0.0648035\pi$
$920$		0			0
$921$	−1956.00	−	3387.89i	−0.0699809	−	0.121210i
$922$		0			0
$923$	17576.0			0.626783
$924$		0			0
$925$	−26752.0			−0.950919
$926$		0			0
$927$	8244.00	+	14279.0i	0.292091	+	0.505917i
$928$		0			0
$929$	−8533.00	+	14779.6i	−0.301355	+	0.521962i	−0.976443	−	0.215775i	$-0.930772\pi$
$929$	−8533.00	+	14779.6i	−0.301355	+	0.521962i	0.675088	+	0.737737i	$0.264106\pi$
$930$		0			0
$931$	6370.00	−	2546.11i	0.224241	−	0.0896300i
$932$		0			0
$933$	9312.00	−	16128.9i	0.326754	−	0.565954i
$934$		0			0
$935$	1764.00	+	3055.34i	0.0616994	+	0.106867i
$936$		0			0
$937$	−30821.0			−1.07458			−0.537288	−	0.843399i	$-0.680551\pi$
$937$	−30821.0			−1.07458			−0.537288	+	0.843399i	$0.680551\pi$
$938$		0			0
$939$	10011.0			0.347920
$940$		0			0
$941$	−2089.50	−	3619.12i	−0.0723866	−	0.125377i	0.827560	−	0.561377i	$-0.189728\pi$
$941$	−2089.50	−	3619.12i	−0.0723866	−	0.125377i	−0.899947	+	0.436000i	$0.856395\pi$
$942$		0			0
$943$	7104.00	−	12304.5i	0.245321	−	0.424909i
$944$		0			0
$945$	−2646.00	+	2291.50i	−0.0910840	+	0.0788811i
$946$		0			0
$947$	4888.00	−	8466.26i	0.167728	−	0.290514i	−0.769893	−	0.638174i	$-0.779690\pi$
$947$	4888.00	−	8466.26i	0.167728	−	0.290514i	0.937621	+	0.347660i	$0.113024\pi$
$948$		0			0
$949$	−14092.0	−	24408.1i	−0.482029	−	0.834899i
$950$		0			0
$951$	25911.0			0.883514
$952$		0			0
$953$	14778.0			0.502315			0.251158	−	0.967946i	$-0.419189\pi$
$953$	14778.0			0.502315			0.251158	+	0.967946i	$0.419189\pi$
$954$		0			0
$955$	−5992.00	−	10378.4i	−0.203033	−	0.351664i
$956$		0			0
$957$	−2551.50	+	4419.33i	−0.0861842	+	0.149275i
$958$		0			0
$959$	1701.00	+	8838.66i	0.0572765	+	0.297617i
$960$		0			0
$961$	10383.0	−	17983.9i	0.348528	−	0.603668i
$962$		0			0
$963$	−4495.50	−	7786.43i	−0.150431	−	0.260555i
$964$		0			0
$965$	−23765.0			−0.792769
$966$		0			0
$967$	−8759.00			−0.291283			−0.145641	−	0.989337i	$-0.546525\pi$
$967$	−8759.00			−0.291283			−0.145641	+	0.989337i	$0.546525\pi$
$968$		0			0
$969$	2160.00	+	3741.23i	0.0716091	+	0.124031i
$970$		0			0
$971$	−16789.5	+	29080.3i	−0.554893	+	0.961102i	0.443019	+	0.896512i	$0.353907\pi$
$971$	−16789.5	+	29080.3i	−0.554893	+	0.961102i	−0.997912	+	0.0645901i	$0.979426\pi$
$972$		0			0
$973$	46025.0	+	15943.5i	1.51644	+	0.525309i
$974$		0			0
$975$	−5928.00	+	10267.6i	−0.194716	+	0.337258i
$976$		0			0
$977$	−21317.0	−	36922.1i	−0.698046	−	1.20905i	−0.969143	−	0.246500i	$-0.920720\pi$
$977$	−21317.0	−	36922.1i	−0.698046	−	1.20905i	0.271097	−	0.962552i	$-0.412614\pi$
$978$		0			0
$979$	2982.00			0.0973495
$980$		0			0
$981$	−14994.0			−0.487993
$982$		0			0
$983$	14574.0	+	25242.9i	0.472877	+	0.819048i	0.999518	−	0.0310404i	$-0.00988204\pi$
$983$	14574.0	+	25242.9i	0.472877	+	0.819048i	−0.526641	+	0.850088i	$0.676549\pi$
$984$		0			0
$985$	−1785.00	+	3091.71i	−0.0577409	+	0.100010i
$986$		0			0
$987$	7455.00	+	2582.49i	0.240421	+	0.0832842i
$988$		0			0
$989$	3792.00	−	6567.94i	0.121920	−	0.211171i
$990$		0			0
$991$	−22398.5	−	38795.3i	−0.717974	−	1.24357i	−0.961801	−	0.273748i	$-0.911737\pi$
$991$	−22398.5	−	38795.3i	−0.717974	−	1.24357i	0.243828	−	0.969819i	$-0.421597\pi$
$992$		0			0
$993$	−5820.00			−0.185994
$994$		0			0
$995$	−1932.00			−0.0615563
$996$		0			0
$997$	−5327.00	−	9226.63i	−0.169215	−	0.293090i	0.768929	−	0.639334i	$-0.220790\pi$
$997$	−5327.00	−	9226.63i	−0.169215	−	0.293090i	−0.938144	+	0.346245i	$0.887457\pi$
$998$		0			0
$999$	−4752.00	+	8230.71i	−0.150497	+	0.260669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.a.289.1		2
4.3	odd	2		168.4.q.a.121.1	yes	2
7.2	even	3		2352.4.a.bg.1.1		1
7.4	even	3	inner	336.4.q.a.193.1		2
7.5	odd	6		2352.4.a.c.1.1		1
12.11	even	2		504.4.s.e.289.1		2
28.11	odd	6		168.4.q.a.25.1	✓	2
28.19	even	6		1176.4.a.i.1.1		1
28.23	odd	6		1176.4.a.f.1.1		1
84.11	even	6		504.4.s.e.361.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.a.25.1	✓	2	28.11	odd	6
168.4.q.a.121.1	yes	2	4.3	odd	2
336.4.q.a.193.1		2	7.4	even	3	inner
336.4.q.a.289.1		2	1.1	even	1	trivial
504.4.s.e.289.1		2	12.11	even	2
504.4.s.e.361.1		2	84.11	even	6
1176.4.a.f.1.1		1	28.23	odd	6
1176.4.a.i.1.1		1	28.19	even	6
2352.4.a.c.1.1		1	7.5	odd	6
2352.4.a.bg.1.1		1	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)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-3.50000 + 6.06218i) q^{5} +(17.5000 + 6.06218i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +(-3.50000 + 6.06218i) q^{5} +(17.5000 + 6.06218i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(3.50000 + 6.06218i) q^{11} -52.0000 q^{13} +21.0000 q^{15} +(-36.0000 - 62.3538i) q^{17} +(10.0000 - 17.3205i) q^{19} +(-10.5000 - 54.5596i) q^{21} +(-24.0000 + 41.5692i) q^{23} +(38.0000 + 65.8179i) q^{25} +27.0000 q^{27} -243.000 q^{29} +(47.5000 + 82.2724i) q^{31} +(10.5000 - 18.1865i) q^{33} +(-98.0000 + 84.8705i) q^{35} +(-176.000 + 304.841i) q^{37} +(78.0000 + 135.100i) q^{39} -296.000 q^{41} -158.000 q^{43} +(-31.5000 - 54.5596i) q^{45} +(-71.0000 + 122.976i) q^{47} +(269.500 + 212.176i) q^{49} +(-108.000 + 187.061i) q^{51} +(187.500 + 324.760i) q^{53} -49.0000 q^{55} -60.0000 q^{57} +(139.500 + 241.621i) q^{59} +(-123.000 + 213.042i) q^{61} +(-126.000 + 109.119i) q^{63} +(182.000 - 315.233i) q^{65} +(-365.000 - 632.199i) q^{67} +144.000 q^{69} -338.000 q^{71} +(271.000 + 469.386i) q^{73} +(114.000 - 197.454i) q^{75} +(24.5000 + 127.306i) q^{77} +(-152.500 + 264.138i) q^{79} +(-40.5000 - 70.1481i) q^{81} -1123.00 q^{83} +504.000 q^{85} +(364.500 + 631.333i) q^{87} +(213.000 - 368.927i) q^{89} +(-910.000 - 315.233i) q^{91} +(142.500 - 246.817i) q^{93} +(70.0000 + 121.244i) q^{95} -369.000 q^{97} -63.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} - 7 q^{5} + 35 q^{7} - 9 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 - 7 * q^5 + 35 * q^7 - 9 * q^9	\( 2 q - 3 q^{3} - 7 q^{5} + 35 q^{7} - 9 q^{9} + 7 q^{11} - 104 q^{13} + 42 q^{15} - 72 q^{17} + 20 q^{19} - 21 q^{21} - 48 q^{23} + 76 q^{25} + 54 q^{27} - 486 q^{29} + 95 q^{31} + 21 q^{33} - 196 q^{35} - 352 q^{37} + 156 q^{39} - 592 q^{41} - 316 q^{43} - 63 q^{45} - 142 q^{47} + 539 q^{49} - 216 q^{51} + 375 q^{53} - 98 q^{55} - 120 q^{57} + 279 q^{59} - 246 q^{61} - 252 q^{63} + 364 q^{65} - 730 q^{67} + 288 q^{69} - 676 q^{71} + 542 q^{73} + 228 q^{75} + 49 q^{77} - 305 q^{79} - 81 q^{81} - 2246 q^{83} + 1008 q^{85} + 729 q^{87} + 426 q^{89} - 1820 q^{91} + 285 q^{93} + 140 q^{95} - 738 q^{97} - 126 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 - 7 * q^5 + 35 * q^7 - 9 * q^9 + 7 * q^11 - 104 * q^13 + 42 * q^15 - 72 * q^17 + 20 * q^19 - 21 * q^21 - 48 * q^23 + 76 * q^25 + 54 * q^27 - 486 * q^29 + 95 * q^31 + 21 * q^33 - 196 * q^35 - 352 * q^37 + 156 * q^39 - 592 * q^41 - 316 * q^43 - 63 * q^45 - 142 * q^47 + 539 * q^49 - 216 * q^51 + 375 * q^53 - 98 * q^55 - 120 * q^57 + 279 * q^59 - 246 * q^61 - 252 * q^63 + 364 * q^65 - 730 * q^67 + 288 * q^69 - 676 * q^71 + 542 * q^73 + 228 * q^75 + 49 * q^77 - 305 * q^79 - 81 * q^81 - 2246 * q^83 + 1008 * q^85 + 729 * q^87 + 426 * q^89 - 1820 * q^91 + 285 * q^93 + 140 * q^95 - 738 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more