LMFDB - Embedded newform 176.4.m.c.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,4,Mod(49,176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("176.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	176.m (of order $5$, degree $4$, 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:	$10.3843361610$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.29283765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 10x^{6} - 19x^{5} + 109x^{4} + 171x^{3} + 810x^{2} + 729x + 6561 $ x^8 - x^7 + 10x^6 - 19x^5 + 109x^4 + 171x^3 + 810x^2 + 729x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$-2.05602 - 1.49379i$ of defining polynomial
Character	$\chi$	$=$	176.81
Dual form			176.4.m.c.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.476313 - 1.46594i) q^{3} +(-7.05908 + 5.12872i) q^{5} +(-0.239524 - 0.737179i) q^{7} +(19.9214 + 14.4737i) q^{9} +O(q^{10})$	\(q+(0.476313 - 1.46594i) q^{3} +(-7.05908 + 5.12872i) q^{5} +(-0.239524 - 0.737179i) q^{7} +(19.9214 + 14.4737i) q^{9} +(-32.3688 - 16.8303i) q^{11} +(-52.2644 - 37.9723i) q^{13} +(4.15607 + 12.7911i) q^{15} +(-56.7325 + 41.2186i) q^{17} +(-40.0535 + 123.272i) q^{19} -1.19475 q^{21} -103.308 q^{23} +(-15.1003 + 46.4740i) q^{25} +(64.3755 - 46.7715i) q^{27} +(-21.2472 - 65.3921i) q^{29} +(4.63339 + 3.36636i) q^{31} +(-40.0899 + 39.4343i) q^{33} +(5.47160 + 3.97535i) q^{35} +(53.2416 + 163.861i) q^{37} +(-80.5593 + 58.5298i) q^{39} +(-65.3332 + 201.075i) q^{41} -300.793 q^{43} -214.858 q^{45} +(59.0277 - 181.669i) q^{47} +(277.007 - 201.257i) q^{49} +(33.4015 + 102.799i) q^{51} +(-519.068 - 377.125i) q^{53} +(314.812 - 47.2041i) q^{55} +(161.632 + 117.432i) q^{57} +(-16.0697 - 49.4574i) q^{59} +(398.663 - 289.646i) q^{61} +(5.89807 - 18.1524i) q^{63} +563.687 q^{65} +320.988 q^{67} +(-49.2068 + 151.443i) q^{69} +(-147.737 + 107.337i) q^{71} +(-64.2516 - 197.746i) q^{73} +(60.9357 + 44.2724i) q^{75} +(-4.65384 + 27.8929i) q^{77} +(528.180 + 383.745i) q^{79} +(167.549 + 515.663i) q^{81} +(972.740 - 706.737i) q^{83} +(189.080 - 581.930i) q^{85} -105.981 q^{87} +716.942 q^{89} +(-15.4738 + 47.6234i) q^{91} +(7.14183 - 5.18884i) q^{93} +(-349.487 - 1075.61i) q^{95} +(508.361 + 369.346i) q^{97} +(-401.234 - 803.779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} - 7 q^{5} + 35 q^{7} + 31 q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 - 7 * q^5 + 35 * q^7 + 31 * q^9	$ 8 q + 3 q^{3} - 7 q^{5} + 35 q^{7} + 31 q^{9} - 67 q^{11} - 65 q^{13} + 121 q^{15} - 31 q^{17} - 148 q^{19} + 334 q^{21} + 12 q^{23} - 201 q^{25} - 72 q^{27} - 199 q^{29} + 361 q^{31} - 232 q^{33} - 237 q^{35} + 81 q^{37} - 365 q^{39} - 31 q^{41} + 650 q^{43} + 452 q^{45} - 857 q^{47} + 1375 q^{49} + 246 q^{51} - 1493 q^{53} + 1583 q^{55} + 102 q^{57} - 676 q^{59} - 525 q^{61} + 68 q^{63} + 1790 q^{65} - 86 q^{67} - 42 q^{69} - 1143 q^{71} - 2155 q^{73} + 160 q^{75} - 2015 q^{77} + 861 q^{79} - 26 q^{81} - 52 q^{83} + 2383 q^{85} - 2310 q^{87} + 3782 q^{89} - 135 q^{91} - 2077 q^{93} + 1317 q^{95} - 1344 q^{97} - 2099 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 - 7 * q^5 + 35 * q^7 + 31 * q^9 - 67 * q^11 - 65 * q^13 + 121 * q^15 - 31 * q^17 - 148 * q^19 + 334 * q^21 + 12 * q^23 - 201 * q^25 - 72 * q^27 - 199 * q^29 + 361 * q^31 - 232 * q^33 - 237 * q^35 + 81 * q^37 - 365 * q^39 - 31 * q^41 + 650 * q^43 + 452 * q^45 - 857 * q^47 + 1375 * q^49 + 246 * q^51 - 1493 * q^53 + 1583 * q^55 + 102 * q^57 - 676 * q^59 - 525 * q^61 + 68 * q^63 + 1790 * q^65 - 86 * q^67 - 42 * q^69 - 1143 * q^71 - 2155 * q^73 + 160 * q^75 - 2015 * q^77 + 861 * q^79 - 26 * q^81 - 52 * q^83 + 2383 * q^85 - 2310 * q^87 + 3782 * q^89 - 135 * q^91 - 2077 * q^93 + 1317 * q^95 - 1344 * q^97 - 2099 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	0.476313	−	1.46594i	0.0916665	−	0.282120i	−0.894704	−	0.446659i	$-0.852614\pi$
$3$	0.476313	−	1.46594i	0.0916665	−	0.282120i	0.986371	+	0.164539i	$0.0526136\pi$
$4$		0			0
$5$	−7.05908	+	5.12872i	−0.631383	+	0.458727i	−0.856879	−	0.515518i	$-0.827600\pi$
$5$	−7.05908	+	5.12872i	−0.631383	+	0.458727i	0.225496	+	0.974244i	$0.427600\pi$
$6$		0			0
$7$	−0.239524	−	0.737179i	−0.0129331	−	0.0398039i	0.944382	−	0.328851i	$-0.106661\pi$
$7$	−0.239524	−	0.737179i	−0.0129331	−	0.0398039i	−0.957315	+	0.289047i	$0.906661\pi$
$8$		0			0
$9$	19.9214	+	14.4737i	0.737828	+	0.536063i
$10$		0			0
$11$	−32.3688	−	16.8303i	−0.887233	−	0.461321i
$11$	−32.3688	−	16.8303i	−0.887233	−	0.461321i
$12$		0			0
$13$	−52.2644	−	37.9723i	−1.11504	−	0.810124i	−0.131590	−	0.991304i	$-0.542008\pi$
$13$	−52.2644	−	37.9723i	−1.11504	−	0.810124i	−0.983450	+	0.181180i	$0.942008\pi$
$14$		0			0
$15$	4.15607	+	12.7911i	0.0715395	+	0.220176i
$16$		0			0
$17$	−56.7325	+	41.2186i	−0.809391	+	0.588057i	−0.913654	−	0.406493i	$-0.866752\pi$
$17$	−56.7325	+	41.2186i	−0.809391	+	0.588057i	0.104263	+	0.994550i	$0.466752\pi$
$18$		0			0
$19$	−40.0535	+	123.272i	−0.483627	+	1.48845i	0.350333	+	0.936625i	$0.386068\pi$
$19$	−40.0535	+	123.272i	−0.483627	+	1.48845i	−0.833960	+	0.551825i	$0.813932\pi$
$20$		0			0
$21$	−1.19475			−0.0124150
$22$		0			0
$23$	−103.308			−0.936572			−0.468286	−	0.883577i	$-0.655128\pi$
$23$	−103.308			−0.936572			−0.468286	+	0.883577i	$0.655128\pi$
$24$		0			0
$25$	−15.1003	+	46.4740i	−0.120803	+	0.371792i
$26$		0			0
$27$	64.3755	−	46.7715i	0.458854	−	0.333377i
$28$		0			0
$29$	−21.2472	−	65.3921i	−0.136052	−	0.418724i	0.859700	−	0.510799i	$-0.170650\pi$
$29$	−21.2472	−	65.3921i	−0.136052	−	0.418724i	−0.995752	+	0.0920744i	$0.970650\pi$
$30$		0			0
$31$	4.63339	+	3.36636i	0.0268446	+	0.0195037i	0.601127	−	0.799154i	$-0.294719\pi$
$31$	4.63339	+	3.36636i	0.0268446	+	0.0195037i	−0.574282	+	0.818658i	$0.694719\pi$
$32$		0			0
$33$	−40.0899	+	39.4343i	−0.211478	+	0.208019i
$34$		0			0
$35$	5.47160	+	3.97535i	0.0264248	+	0.0191988i
$36$		0			0
$37$	53.2416	+	163.861i	0.236564	+	0.728069i	0.996910	+	0.0785508i	$0.0250293\pi$
$37$	53.2416	+	163.861i	0.236564	+	0.728069i	−0.760346	+	0.649518i	$0.774971\pi$
$38$		0			0
$39$	−80.5593	+	58.5298i	−0.330764	+	0.240314i
$40$		0			0
$41$	−65.3332	+	201.075i	−0.248862	+	0.765917i	0.746116	+	0.665816i	$0.231917\pi$
$41$	−65.3332	+	201.075i	−0.248862	+	0.765917i	−0.994977	+	0.100101i	$0.968083\pi$
$42$		0			0
$43$	−300.793			−1.06676			−0.533378	−	0.845877i	$-0.679078\pi$
$43$	−300.793			−1.06676			−0.533378	+	0.845877i	$0.679078\pi$
$44$		0			0
$45$	−214.858			−0.711758
$46$		0			0
$47$	59.0277	−	181.669i	0.183193	−	0.563811i	−0.816719	−	0.577035i	$-0.804210\pi$
$47$	59.0277	−	181.669i	0.183193	−	0.563811i	0.999913	+	0.0132245i	$0.00420961\pi$
$48$		0			0
$49$	277.007	−	201.257i	0.807600	−	0.586756i
$50$		0			0
$51$	33.4015	+	102.799i	0.0917089	+	0.282251i
$52$		0			0
$53$	−519.068	−	377.125i	−1.34527	−	0.977398i	−0.999232	−	0.0391779i	$-0.987526\pi$
$53$	−519.068	−	377.125i	−1.34527	−	0.977398i	−0.346040	−	0.938220i	$-0.612474\pi$
$54$		0			0
$55$	314.812	−	47.2041i	0.771804	−	0.115727i
$56$		0			0
$57$	161.632	+	117.432i	0.375590	+	0.272882i
$58$		0			0
$59$	−16.0697	−	49.4574i	−0.0354592	−	0.109132i	0.931760	−	0.363074i	$-0.118273\pi$
$59$	−16.0697	−	49.4574i	−0.0354592	−	0.109132i	−0.967219	+	0.253942i	$0.918273\pi$
$60$		0			0
$61$	398.663	−	289.646i	0.836780	−	0.607956i	−0.0846894	−	0.996407i	$-0.526990\pi$
$61$	398.663	−	289.646i	0.836780	−	0.607956i	0.921469	+	0.388451i	$0.126990\pi$
$62$		0			0
$63$	5.89807	−	18.1524i	0.0117950	−	0.0363014i
$64$		0			0
$65$	563.687			1.07564
$66$		0			0
$67$	320.988			0.585298			0.292649	−	0.956220i	$-0.405463\pi$
$67$	320.988			0.585298			0.292649	+	0.956220i	$0.405463\pi$
$68$		0			0
$69$	−49.2068	+	151.443i	−0.0858523	+	0.264226i
$70$		0			0
$71$	−147.737	+	107.337i	−0.246945	+	0.179416i	−0.704372	−	0.709831i	$-0.748771\pi$
$71$	−147.737	+	107.337i	−0.246945	+	0.179416i	0.457427	+	0.889247i	$0.348771\pi$
$72$		0			0
$73$	−64.2516	−	197.746i	−0.103015	−	0.317047i	0.886245	−	0.463218i	$-0.153305\pi$
$73$	−64.2516	−	197.746i	−0.103015	−	0.317047i	−0.989259	+	0.146171i	$0.953305\pi$
$74$		0			0
$75$	60.9357	+	44.2724i	0.0938167	+	0.0681618i
$76$		0			0
$77$	−4.65384	+	27.8929i	−0.00688772	+	0.0412817i
$78$		0			0
$79$	528.180	+	383.745i	0.752214	+	0.546516i	0.896512	−	0.443019i	$-0.146092\pi$
$79$	528.180	+	383.745i	0.752214	+	0.546516i	−0.144298	+	0.989534i	$0.546092\pi$
$80$		0			0
$81$	167.549	+	515.663i	0.229834	+	0.707357i
$82$		0			0
$83$	972.740	−	706.737i	1.28641	−	0.934632i	0.286684	−	0.958025i	$-0.407447\pi$
$83$	972.740	−	706.737i	1.28641	−	0.934632i	0.999726	+	0.0233931i	$0.00744694\pi$
$84$		0			0
$85$	189.080	−	581.930i	0.241278	−	0.742578i
$86$		0			0
$87$	−105.981			−0.130602
$88$		0			0
$89$	716.942			0.853885			0.426942	−	0.904279i	$-0.359591\pi$
$89$	716.942			0.853885			0.426942	+	0.904279i	$0.359591\pi$
$90$		0			0
$91$	−15.4738	+	47.6234i	−0.0178252	+	0.0548603i
$92$		0			0
$93$	7.14183	−	5.18884i	0.00796315	−	0.00578557i
$94$		0			0
$95$	−349.487	−	1075.61i	−0.377438	−	1.16163i
$96$		0			0
$97$	508.361	+	369.346i	0.532126	+	0.386612i	0.821152	−	0.570709i	$-0.193332\pi$
$97$	508.361	+	369.346i	0.532126	+	0.386612i	−0.289026	+	0.957321i	$0.593332\pi$
$98$		0			0
$99$	−401.234	−	803.779i	−0.407328	−	0.815989i
$100$		0			0
$101$	−411.960	−	299.307i	−0.405857	−	0.294872i	0.366065	−	0.930589i	$-0.380705\pi$
$101$	−411.960	−	299.307i	−0.405857	−	0.294872i	−0.771922	+	0.635717i	$0.780705\pi$
$102$		0			0
$103$	54.0555	+	166.366i	0.0517111	+	0.159150i	0.973577	−	0.228358i	$-0.0733357\pi$
$103$	54.0555	+	166.366i	0.0517111	+	0.159150i	−0.921866	+	0.387509i	$0.873336\pi$
$104$		0			0
$105$	8.43382	−	6.12753i	0.00783863	−	0.00569510i
$106$		0			0
$107$	−546.753	+	1682.73i	−0.493987	+	1.52034i	0.324543	+	0.945871i	$0.394790\pi$
$107$	−546.753	+	1682.73i	−0.493987	+	1.52034i	−0.818530	+	0.574464i	$0.805210\pi$
$108$		0			0
$109$	−823.593			−0.723724			−0.361862	−	0.932232i	$-0.617859\pi$
$109$	−823.593			−0.723724			−0.361862	+	0.932232i	$0.617859\pi$
$110$		0			0
$111$	265.570			0.227088
$112$		0			0
$113$	−336.492	+	1035.62i	−0.280128	+	0.862146i	0.707689	+	0.706525i	$0.249738\pi$
$113$	−336.492	+	1035.62i	−0.280128	+	0.862146i	−0.987817	+	0.155621i	$0.950262\pi$
$114$		0			0
$115$	729.257	−	529.837i	0.591336	−	0.429631i
$116$		0			0
$117$	−491.577	−	1512.92i	−0.388430	−	1.19546i
$118$		0			0
$119$	43.9742	+	31.9491i	0.0338749	+	0.0246115i
$120$		0			0
$121$	764.481	+	1089.55i	0.574366	+	0.818599i
$122$		0			0
$123$	263.645	+	191.549i	0.193269	+	0.140418i
$124$		0			0
$125$	−468.799	−	1442.81i	−0.335445	−	1.03239i
$126$		0			0
$127$	−1015.52	+	737.819i	−0.709551	+	0.515519i	−0.883029	−	0.469319i	$-0.844499\pi$
$127$	−1015.52	+	737.819i	−0.709551	+	0.515519i	0.173478	+	0.984838i	$0.444499\pi$
$128$		0			0
$129$	−143.272	+	440.945i	−0.0977858	+	0.300954i
$130$		0			0
$131$	−1401.18			−0.934519			−0.467259	−	0.884120i	$-0.654759\pi$
$131$	−1401.18			−0.934519			−0.467259	+	0.884120i	$0.654759\pi$
$132$		0			0
$133$	100.467			0.0655009
$134$		0			0
$135$	−214.553	+	660.328i	−0.136784	+	0.420977i
$136$		0			0
$137$	331.158	−	240.600i	0.206516	−	0.150043i	−0.479720	−	0.877422i	$-0.659262\pi$
$137$	331.158	−	240.600i	0.206516	−	0.150043i	0.686236	+	0.727379i	$0.259262\pi$
$138$		0			0
$139$	−183.982	−	566.240i	−0.112268	−	0.345524i	0.879100	−	0.476638i	$-0.158145\pi$
$139$	−183.982	−	566.240i	−0.112268	−	0.345524i	−0.991367	+	0.131114i	$0.958145\pi$
$140$		0			0
$141$	−238.200	−	173.062i	−0.142270	−	0.103365i
$142$		0			0
$143$	1052.65	+	2108.74i	0.615574	+	1.23316i
$144$		0			0
$145$	485.363	+	352.637i	0.277981	+	0.201965i
$146$		0			0
$147$	−163.089	−	501.937i	−0.0915059	−	0.281626i
$148$		0			0
$149$	−1755.64	+	1275.54i	−0.965283	+	0.701319i	−0.954372	−	0.298621i	$-0.903473\pi$
$149$	−1755.64	+	1275.54i	−0.965283	+	0.701319i	−0.0109117	+	0.999940i	$0.503473\pi$
$150$		0			0
$151$	555.847	−	1710.72i	0.299564	−	0.921963i	−0.682086	−	0.731272i	$-0.738927\pi$
$151$	555.847	−	1710.72i	0.299564	−	0.921963i	0.981650	−	0.190691i	$-0.0610729\pi$
$152$		0			0
$153$	−1726.77			−0.912427
$154$		0			0
$155$	−49.9726			−0.0258961
$156$		0			0
$157$	−24.2312	+	74.5758i	−0.0123176	+	0.0379095i	−0.957026	−	0.290001i	$-0.906344\pi$
$157$	−24.2312	+	74.5758i	−0.0123176	+	0.0379095i	0.944709	+	0.327910i	$0.106344\pi$
$158$		0			0
$159$	−800.081	+	581.293i	−0.399060	+	0.289934i
$160$		0			0
$161$	24.7447	+	76.1563i	0.0121128	+	0.0372792i
$162$		0			0
$163$	266.032	+	193.283i	0.127836	+	0.0928780i	0.649866	−	0.760049i	$-0.274825\pi$
$163$	266.032	+	193.283i	0.127836	+	0.0928780i	−0.522030	+	0.852927i	$0.674825\pi$
$164$		0			0
$165$	80.7505	−	483.980i	0.0380995	−	0.228350i
$166$		0			0
$167$	−2850.77	−	2071.21i	−1.32095	−	0.959729i	−0.999920	−	0.0126616i	$-0.995970\pi$
$167$	−2850.77	−	2071.21i	−1.32095	−	0.959729i	−0.321034	−	0.947068i	$-0.604030\pi$
$168$		0			0
$169$	610.758	+	1879.72i	0.277997	+	0.855585i
$170$		0			0
$171$	−2582.12	+	1876.02i	−1.15474	+	0.838965i
$172$		0			0
$173$	−836.578	+	2574.72i	−0.367652	+	1.13152i	0.580651	+	0.814152i	$0.302798\pi$
$173$	−836.578	+	2574.72i	−0.367652	+	1.13152i	−0.948304	+	0.317365i	$0.897202\pi$
$174$		0			0
$175$	37.8766			0.0163611
$176$		0			0
$177$	−80.1558			−0.0340389
$178$		0			0
$179$	−455.234	+	1401.07i	−0.190088	+	0.585032i	−0.999999	−	0.00152166i	$-0.999516\pi$
$179$	−455.234	+	1401.07i	−0.190088	+	0.585032i	0.809910	+	0.586554i	$0.199516\pi$
$180$		0			0
$181$	398.134	−	289.261i	0.163498	−	0.118788i	−0.503028	−	0.864270i	$-0.667781\pi$
$181$	398.134	−	289.261i	0.163498	−	0.118788i	0.666526	+	0.745482i	$0.267781\pi$
$182$		0			0
$183$	−234.715	−	722.378i	−0.0948122	−	0.291802i
$184$		0			0
$185$	−1216.23	−	883.644i	−0.483347	−	0.351172i
$186$		0			0
$187$	2530.08	−	379.371i	0.989402	−	0.148355i
$188$		0			0
$189$	−49.8984	−	36.2533i	−0.0192041	−	0.0139526i
$190$		0			0
$191$	399.844	+	1230.59i	0.151475	+	0.466192i	0.997787	−	0.0664961i	$-0.0211820\pi$
$191$	399.844	+	1230.59i	0.151475	+	0.466192i	−0.846312	+	0.532688i	$0.821182\pi$
$192$		0			0
$193$	424.037	−	308.081i	0.158149	−	0.114902i	−0.505896	−	0.862594i	$-0.668838\pi$
$193$	424.037	−	308.081i	0.158149	−	0.114902i	0.664046	+	0.747692i	$0.268838\pi$
$194$		0			0
$195$	268.491	−	826.332i	0.0986004	−	0.303461i
$196$		0			0
$197$	−1177.35			−0.425801			−0.212900	−	0.977074i	$-0.568291\pi$
$197$	−1177.35			−0.425801			−0.212900	+	0.977074i	$0.568291\pi$
$198$		0			0
$199$	3054.83			1.08820			0.544098	−	0.839022i	$-0.316872\pi$
$199$	3054.83			1.08820			0.544098	+	0.839022i	$0.316872\pi$
$200$		0			0
$201$	152.891	−	470.550i	0.0536522	−	0.165125i
$202$		0			0
$203$	−43.1164	+	31.3259i	−0.0149073	+	0.0108308i
$204$		0			0
$205$	−570.064	−	1754.48i	−0.194220	−	0.597747i
$206$		0			0
$207$	−2058.03	−	1495.25i	−0.691029	−	0.502062i
$208$		0			0
$209$	3371.19	−	3316.06i	1.11574	−	1.09750i
$210$		0			0
$211$	1379.08	+	1001.96i	0.449953	+	0.326910i	0.789577	−	0.613651i	$-0.210300\pi$
$211$	1379.08	+	1001.96i	0.449953	+	0.326910i	−0.339624	+	0.940561i	$0.610300\pi$
$212$		0			0
$213$	86.9808	+	267.699i	0.0279804	+	0.0861148i
$214$		0			0
$215$	2123.32	−	1542.68i	0.673532	−	0.489349i
$216$		0			0
$217$	1.37180	−	4.22196i	0.000429142	−	0.00132076i
$218$		0			0
$219$	−320.488			−0.0988884
$220$		0			0
$221$	4530.25			1.37890
$222$		0			0
$223$	−1422.26	+	4377.26i	−0.427092	+	1.31445i	0.473886	+	0.880586i	$0.342851\pi$
$223$	−1422.26	+	4377.26i	−0.427092	+	1.31445i	−0.900977	+	0.433866i	$0.857149\pi$
$224$		0			0
$225$	−973.471	+	707.268i	−0.288436	+	0.209561i
$226$		0			0
$227$	−1015.88	−	3126.56i	−0.297032	−	0.914171i	−0.982531	−	0.186097i	$-0.940416\pi$
$227$	−1015.88	−	3126.56i	−0.297032	−	0.914171i	0.685499	−	0.728073i	$-0.259584\pi$
$228$		0			0
$229$	2387.40	+	1734.55i	0.688925	+	0.500533i	0.876307	−	0.481754i	$-0.160000\pi$
$229$	2387.40	+	1734.55i	0.688925	+	0.500533i	−0.187382	+	0.982287i	$0.560000\pi$
$230$		0			0
$231$	38.6726	+	20.1080i	0.0110150	+	0.00572731i
$232$		0			0
$233$	−2283.62	−	1659.14i	−0.642080	−	0.466498i	0.218484	−	0.975840i	$-0.429889\pi$
$233$	−2283.62	−	1659.14i	−0.642080	−	0.466498i	−0.860564	+	0.509342i	$0.829889\pi$
$234$		0			0
$235$	515.046	+	1585.15i	0.142970	+	0.440016i
$236$		0			0
$237$	814.127	−	591.498i	0.223136	−	0.162118i
$238$		0			0
$239$	−636.935	+	1960.28i	−0.172385	+	0.530545i	−0.999504	−	0.0314806i	$-0.989978\pi$
$239$	−636.935	+	1960.28i	−0.172385	+	0.530545i	0.827120	+	0.562026i	$0.189978\pi$
$240$		0			0
$241$	−3089.45			−0.825763			−0.412881	−	0.910785i	$-0.635478\pi$
$241$	−3089.45			−0.825763			−0.412881	+	0.910785i	$0.635478\pi$
$242$		0			0
$243$	2984.19			0.787803
$244$		0			0
$245$	−923.220	+	2841.38i	−0.240744	+	0.740935i
$246$		0			0
$247$	6774.29	−	4921.81i	1.74509	−	1.26788i
$248$		0			0
$249$	−572.706	−	1762.61i	−0.145758	−	0.448597i
$250$		0			0
$251$	−3259.66	−	2368.28i	−0.819712	−	0.595555i	0.0969183	−	0.995292i	$-0.469101\pi$
$251$	−3259.66	−	2368.28i	−0.819712	−	0.595555i	−0.916630	+	0.399737i	$0.869101\pi$
$252$		0			0
$253$	3343.95	+	1738.70i	0.830958	+	0.432060i
$254$		0			0
$255$	−763.013	−	554.362i	−0.187379	−	0.136139i
$256$		0			0
$257$	−1358.89	−	4182.25i	−0.329827	−	1.01510i	−0.969215	−	0.246218i	$-0.920812\pi$
$257$	−1358.89	−	4182.25i	−0.329827	−	1.01510i	0.639388	−	0.768884i	$-0.279188\pi$
$258$		0			0
$259$	108.042	−	78.4971i	0.0259205	−	0.0188323i
$260$		0			0
$261$	523.194	−	1610.22i	0.124080	−	0.381879i
$262$		0			0
$263$	914.661			0.214450			0.107225	−	0.994235i	$-0.465803\pi$
$263$	914.661			0.214450			0.107225	+	0.994235i	$0.465803\pi$
$264$		0			0
$265$	5598.31			1.29774
$266$		0			0
$267$	341.489	−	1051.00i	0.0782726	−	0.240898i
$268$		0			0
$269$	1430.97	−	1039.66i	0.324341	−	0.235648i	−0.413685	−	0.910420i	$-0.635758\pi$
$269$	1430.97	−	1039.66i	0.324341	−	0.235648i	0.738026	+	0.674773i	$0.235758\pi$
$270$		0			0
$271$	−1241.80	−	3821.86i	−0.278353	−	0.856684i	−0.988313	−	0.152441i	$-0.951287\pi$
$271$	−1241.80	−	3821.86i	−0.278353	−	0.856684i	0.709959	−	0.704243i	$-0.248713\pi$
$272$		0			0
$273$	62.4428	+	45.3673i	0.0138433	+	0.0100577i
$274$		0			0
$275$	1270.95	−	1250.17i	0.278696	−	0.274138i
$276$		0			0
$277$	5376.57	+	3906.30i	1.16623	+	0.847318i	0.990553	−	0.137129i	$-0.0437876\pi$
$277$	5376.57	+	3906.30i	1.16623	+	0.847318i	0.175680	+	0.984447i	$0.443788\pi$
$278$		0			0
$279$	43.5798	+	134.125i	0.00935145	+	0.0287808i
$280$		0			0
$281$	−3545.96	+	2576.29i	−0.752792	+	0.546935i	−0.896691	−	0.442657i	$-0.854036\pi$
$281$	−3545.96	+	2576.29i	−0.752792	+	0.546935i	0.143899	+	0.989592i	$0.454036\pi$
$282$		0			0
$283$	−1154.14	+	3552.07i	−0.242425	+	0.746108i	0.753624	+	0.657306i	$0.228304\pi$
$283$	−1154.14	+	3552.07i	−0.242425	+	0.746108i	−0.996049	+	0.0888023i	$0.971696\pi$
$284$		0			0
$285$	−1743.25			−0.362319
$286$		0			0
$287$	163.877			0.0337050
$288$		0			0
$289$	1.40440	−	4.32230i	0.000285854	−	0.000879768i
$290$		0			0
$291$	783.578	−	569.303i	0.157849	−	0.114684i
$292$		0			0
$293$	−690.705	−	2125.77i	−0.137718	−	0.423853i	0.858285	−	0.513174i	$-0.171530\pi$
$293$	−690.705	−	2125.77i	−0.137718	−	0.423853i	−0.996003	+	0.0893208i	$0.971530\pi$
$294$		0			0
$295$	367.090	+	266.707i	0.0724502	+	0.0526382i
$296$		0			0
$297$	−2870.94	+	430.480i	−0.560905	+	0.0841043i
$298$		0			0
$299$	5399.31	+	3922.83i	1.04432	+	0.758740i
$300$		0			0
$301$	72.0471	+	221.738i	0.0137964	+	0.0424611i
$302$		0			0
$303$	−634.988	+	461.345i	−0.120393	+	0.0874706i
$304$		0			0
$305$	−1328.68	+	4089.26i	−0.249443	+	0.767706i
$306$		0			0
$307$	−1022.51			−0.190090			−0.0950451	−	0.995473i	$-0.530300\pi$
$307$	−1022.51			−0.190090			−0.0950451	+	0.995473i	$0.530300\pi$
$308$		0			0
$309$	269.629			0.0496398
$310$		0			0
$311$	−1643.78	+	5059.04i	−0.299711	+	0.922417i	0.681887	+	0.731458i	$0.261160\pi$
$311$	−1643.78	+	5059.04i	−0.299711	+	0.922417i	−0.981598	+	0.190959i	$0.938840\pi$
$312$		0			0
$313$	5657.83	−	4110.65i	1.02172	−	0.742325i	0.0550879	−	0.998482i	$-0.482456\pi$
$313$	5657.83	−	4110.65i	1.02172	−	0.742325i	0.966635	+	0.256156i	$0.0824561\pi$
$314$		0			0
$315$	51.4636	+	158.389i	0.00920522	+	0.0283308i
$316$		0			0
$317$	−3490.64	−	2536.10i	−0.618467	−	0.449343i	0.233919	−	0.972256i	$-0.424845\pi$
$317$	−3490.64	−	2536.10i	−0.618467	−	0.449343i	−0.852386	+	0.522913i	$0.824845\pi$
$318$		0			0
$319$	−412.823	+	2474.26i	−0.0724566	+	0.434270i
$320$		0			0
$321$	2206.36	+	1603.01i	0.383636	+	0.278728i
$322$		0			0
$323$	−2808.76	−	8644.48i	−0.483850	−	1.48914i
$324$		0			0
$325$	2553.93	−	1855.54i	0.435898	−	0.316698i
$326$		0			0
$327$	−392.288	+	1207.34i	−0.0663412	+	0.204177i
$328$		0			0
$329$	−148.061			−0.0248111
$330$		0			0
$331$	3886.73			0.645420			0.322710	−	0.946498i	$-0.395406\pi$
$331$	3886.73			0.645420			0.322710	+	0.946498i	$0.395406\pi$
$332$		0			0
$333$	−1311.03	+	4034.93i	−0.215748	+	0.664003i
$334$		0			0
$335$	−2265.88	+	1646.26i	−0.369547	+	0.268492i
$336$		0			0
$337$	−2812.70	−	8656.61i	−0.454652	−	1.39928i	−0.871543	−	0.490319i	$-0.836880\pi$
$337$	−2812.70	−	8656.61i	−0.454652	−	1.39928i	0.416891	−	0.908956i	$-0.363120\pi$
$338$		0			0
$339$	1357.88	+	986.554i	0.217551	+	0.158060i
$340$		0			0
$341$	−93.3207	−	186.947i	−0.0148199	−	0.0296883i
$342$		0			0
$343$	−429.801	−	312.269i	−0.0676591	−	0.0491572i
$344$		0			0
$345$	−429.354	−	1321.42i	−0.0670019	−	0.206211i
$346$		0			0
$347$	−8213.72	+	5967.62i	−1.27071	+	0.923223i	−0.999231	−	0.0392218i	$-0.987512\pi$
$347$	−8213.72	+	5967.62i	−1.27071	+	0.923223i	−0.271477	+	0.962445i	$0.587512\pi$
$348$		0			0
$349$	−3297.87	+	10149.8i	−0.505820	+	1.55675i	0.293568	+	0.955938i	$0.405157\pi$
$349$	−3297.87	+	10149.8i	−0.505820	+	1.55675i	−0.799388	+	0.600815i	$0.794843\pi$
$350$		0			0
$351$	−5140.56			−0.781718
$352$		0			0
$353$	−9301.69			−1.40249			−0.701245	−	0.712920i	$-0.747372\pi$
$353$	−9301.69			−1.40249			−0.701245	+	0.712920i	$0.747372\pi$
$354$		0			0
$355$	492.383	−	1515.40i	0.0736141	−	0.226561i
$356$		0			0
$357$	67.7811	−	49.2458i	0.0100486	−	0.00730074i
$358$		0			0
$359$	−2594.94	−	7986.40i	−0.381492	−	1.17411i	−0.938993	−	0.343936i	$-0.888240\pi$
$359$	−2594.94	−	7986.40i	−0.381492	−	1.17411i	0.557501	−	0.830176i	$-0.311760\pi$
$360$		0			0
$361$	−8042.67	−	5843.34i	−1.17257	−	0.851924i
$362$		0			0
$363$	1961.35	−	601.715i	0.283593	−	0.0870024i
$364$		0			0
$365$	1467.74	+	1066.38i	0.210480	+	0.152922i
$366$		0			0
$367$	2894.86	+	8909.46i	0.411745	+	1.26722i	0.915130	+	0.403158i	$0.132088\pi$
$367$	2894.86	+	8909.46i	0.411745	+	1.26722i	−0.503385	+	0.864062i	$0.667912\pi$
$368$		0			0
$369$	−4211.82	+	3060.07i	−0.594197	+	0.431710i
$370$		0			0
$371$	−153.679	+	472.976i	−0.0215057	+	0.0661879i
$372$		0			0
$373$	2639.31			0.366376			0.183188	−	0.983078i	$-0.441358\pi$
$373$	2639.31			0.366376			0.183188	+	0.983078i	$0.441358\pi$
$374$		0			0
$375$	−2338.38			−0.322008
$376$		0			0
$377$	−1372.62	+	4224.48i	−0.187515	+	0.577113i
$378$		0			0
$379$	−5959.64	+	4329.93i	−0.807721	+	0.586843i	−0.913169	−	0.407581i	$-0.866372\pi$
$379$	−5959.64	+	4329.93i	−0.807721	+	0.586843i	0.105448	+	0.994425i	$0.466372\pi$
$380$		0			0
$381$	597.893	+	1840.13i	0.0803963	+	0.247434i
$382$		0			0
$383$	−2605.34	−	1892.89i	−0.347589	−	0.252538i	0.400268	−	0.916398i	$-0.368917\pi$
$383$	−2605.34	−	1892.89i	−0.347589	−	0.252538i	−0.747857	+	0.663860i	$0.768917\pi$
$384$		0			0
$385$	−110.203	−	220.766i	−0.0145882	−	0.0292241i
$386$		0			0
$387$	−5992.20	−	4353.59i	−0.787082	−	0.571849i
$388$		0			0
$389$	3778.65	+	11629.5i	0.492507	+	1.51578i	0.820807	+	0.571206i	$0.193524\pi$
$389$	3778.65	+	11629.5i	0.492507	+	1.51578i	−0.328300	+	0.944574i	$0.606476\pi$
$390$		0			0
$391$	5860.91	−	4258.20i	0.758053	−	0.550758i
$392$		0			0
$393$	−667.402	+	2054.05i	−0.0856640	+	0.263647i
$394$		0			0
$395$	−5696.59			−0.725636
$396$		0			0
$397$	8381.55			1.05959			0.529796	−	0.848125i	$-0.322269\pi$
$397$	8381.55			1.05959			0.529796	+	0.848125i	$0.322269\pi$
$398$		0			0
$399$	47.8539	−	147.279i	0.00600424	−	0.0184791i
$400$		0			0
$401$	3503.32	−	2545.31i	0.436279	−	0.316975i	−0.347876	−	0.937541i	$-0.613097\pi$
$401$	3503.32	−	2545.31i	0.436279	−	0.316975i	0.784154	+	0.620566i	$0.213097\pi$
$402$		0			0
$403$	−114.333	−	351.881i	−0.0141323	−	0.0434949i
$404$		0			0
$405$	−3827.43	−	2780.79i	−0.469597	−	0.341182i
$406$		0			0
$407$	1034.46	−	6200.05i	0.125986	−	0.755099i
$408$		0			0
$409$	−9657.95	−	7016.91i	−1.16762	−	0.848323i	−0.176895	−	0.984230i	$-0.556605\pi$
$409$	−9657.95	−	7016.91i	−1.16762	−	0.848323i	−0.990722	+	0.135907i	$0.956605\pi$
$410$		0			0
$411$	−194.971	−	600.059i	−0.0233995	−	0.0720164i
$412$		0			0
$413$	−32.6099	+	23.6924i	−0.00388529	+	0.00282283i
$414$		0			0
$415$	−3241.99	+	9977.82i	−0.383477	+	1.18022i
$416$		0			0
$417$	−917.707			−0.107770
$418$		0			0
$419$	11888.5			1.38614			0.693070	−	0.720870i	$-0.256257\pi$
$419$	11888.5			1.38614			0.693070	+	0.720870i	$0.256257\pi$
$420$		0			0
$421$	−2622.15	+	8070.15i	−0.303553	+	0.934240i	0.676660	+	0.736295i	$0.263427\pi$
$421$	−2622.15	+	8070.15i	−0.303553	+	0.934240i	−0.980213	+	0.197944i	$0.936573\pi$
$422$		0			0
$423$	3805.33	−	2764.73i	0.437403	−	0.317792i
$424$		0			0
$425$	−1058.91	−	3259.00i	−0.120859	−	0.371964i
$426$		0			0
$427$	−309.010	−	224.509i	−0.0350212	−	0.0254444i
$428$		0			0
$429$	3592.68	−	538.701i	0.404327	−	0.0606264i
$430$		0			0
$431$	9271.93	+	6736.45i	1.03623	+	0.752862i	0.969545	−	0.244913i	$-0.0787593\pi$
$431$	9271.93	+	6736.45i	1.03623	+	0.752862i	0.0666800	+	0.997774i	$0.478759\pi$
$432$		0			0
$433$	1019.16	+	3136.66i	0.113113	+	0.348125i	0.991549	−	0.129735i	$-0.0414126\pi$
$433$	1019.16	+	3136.66i	0.113113	+	0.348125i	−0.878436	+	0.477860i	$0.841413\pi$
$434$		0			0
$435$	748.129	−	543.548i	0.0824599	−	0.0599106i
$436$		0			0
$437$	4137.84	−	12735.0i	0.452951	−	1.39404i
$438$		0			0
$439$	−5549.93			−0.603380			−0.301690	−	0.953406i	$-0.597551\pi$
$439$	−5549.93			−0.603380			−0.301690	+	0.953406i	$0.597551\pi$
$440$		0			0
$441$	8431.29			0.910408
$442$		0			0
$443$	−3362.36	+	10348.3i	−0.360611	+	1.10985i	0.592073	+	0.805884i	$0.298310\pi$
$443$	−3362.36	+	10348.3i	−0.360611	+	1.10985i	−0.952684	+	0.303962i	$0.901690\pi$
$444$		0			0
$445$	−5060.95	+	3677.00i	−0.539128	+	0.391700i
$446$		0			0
$447$	1033.64	+	3181.21i	0.109372	+	0.336614i
$448$		0			0
$449$	6104.61	+	4435.26i	0.641636	+	0.466176i	0.860412	−	0.509599i	$-0.170206\pi$
$449$	6104.61	+	4435.26i	0.641636	+	0.466176i	−0.218776	+	0.975775i	$0.570206\pi$
$450$		0			0
$451$	5498.91	−	5408.98i	0.574132	−	0.564742i
$452$		0			0
$453$	−2243.06	−	1629.68i	−0.232645	−	0.169026i
$454$		0			0
$455$	−135.017	−	415.538i	−0.0139114	−	0.0428148i
$456$		0			0
$457$	2620.61	−	1903.98i	0.268242	−	0.194890i	−0.445530	−	0.895267i	$-0.646985\pi$
$457$	2620.61	−	1903.98i	0.268242	−	0.194890i	0.713773	+	0.700377i	$0.246985\pi$
$458$		0			0
$459$	−1724.33	+	5306.93i	−0.175348	+	0.539665i
$460$		0			0
$461$	−4837.43			−0.488724			−0.244362	−	0.969684i	$-0.578578\pi$
$461$	−4837.43			−0.488724			−0.244362	+	0.969684i	$0.578578\pi$
$462$		0			0
$463$	−14089.7			−1.41427			−0.707133	−	0.707081i	$-0.750012\pi$
$463$	−14089.7			−1.41427			−0.707133	+	0.707081i	$0.750012\pi$
$464$		0			0
$465$	−23.8026	+	73.2568i	−0.00237380	+	0.00730582i
$466$		0			0
$467$	11767.4	−	8549.52i	1.16602	−	0.847162i	0.175491	−	0.984481i	$-0.443849\pi$
$467$	11767.4	−	8549.52i	1.16602	−	0.847162i	0.990527	+	0.137319i	$0.0438486\pi$
$468$		0			0
$469$	−76.8844	−	236.626i	−0.00756970	−	0.0232971i
$470$		0			0
$471$	97.7821	+	71.0429i	0.00956595	+	0.00695007i
$472$		0			0
$473$	9736.32	+	5062.44i	0.946462	+	0.492117i
$474$		0			0
$475$	−5124.13	−	3722.90i	−0.494971	−	0.359617i
$476$		0			0
$477$	−4882.14	−	15025.7i	−0.468632	−	1.44230i
$478$		0			0
$479$	2289.58	−	1663.47i	0.218400	−	0.158677i	−0.473206	−	0.880952i	$-0.656904\pi$
$479$	2289.58	−	1663.47i	0.218400	−	0.158677i	0.691606	+	0.722275i	$0.256904\pi$
$480$		0			0
$481$	3439.53	−	10585.8i	0.326048	−	1.00347i
$482$		0			0
$483$	123.427			0.0116276
$484$		0			0
$485$	−5482.83			−0.513325
$486$		0			0
$487$	5912.90	−	18198.0i	0.550183	−	1.69329i	−0.158155	−	0.987414i	$-0.550555\pi$
$487$	5912.90	−	18198.0i	0.550183	−	1.69329i	0.708338	−	0.705874i	$-0.249445\pi$
$488$		0			0
$489$	410.056	−	297.923i	0.0379210	−	0.0275512i
$490$		0			0
$491$	3489.95	+	10740.9i	0.320772	+	0.987235i	0.973313	+	0.229481i	$0.0737030\pi$
$491$	3489.95	+	10740.9i	0.320772	+	0.987235i	−0.652541	+	0.757753i	$0.726297\pi$
$492$		0			0
$493$	3900.77	+	2834.08i	0.356353	+	0.258906i
$494$		0			0
$495$	6954.70	+	3616.13i	0.631496	+	0.328349i
$496$		0			0
$497$	114.513	+	83.1986i	0.0103352	+	0.00750899i
$498$		0			0
$499$	−267.665	−	823.790i	−0.0240127	−	0.0739036i	0.938332	−	0.345735i	$-0.112371\pi$
$499$	−267.665	−	823.790i	−0.0240127	−	0.0739036i	−0.962345	+	0.271832i	$0.912371\pi$
$500$		0			0
$501$	−4394.13	+	3192.52i	−0.391846	+	0.284693i
$502$		0			0
$503$	1849.01	−	5690.65i	0.163903	−	0.504441i	−0.835051	−	0.550173i	$-0.814562\pi$
$503$	1849.01	−	5690.65i	0.163903	−	0.504441i	0.998954	+	0.0457317i	$0.0145619\pi$
$504$		0			0
$505$	4443.12			0.391517
$506$		0			0
$507$	3046.47			0.266861
$508$		0			0
$509$	3419.92	−	10525.4i	0.297810	−	0.916566i	−0.684453	−	0.729057i	$-0.739959\pi$
$509$	3419.92	−	10525.4i	0.297810	−	0.916566i	0.982263	−	0.187509i	$-0.0600412\pi$
$510$		0			0
$511$	−130.384	+	94.7298i	−0.0112874	+	0.00820078i
$512$		0			0
$513$	3187.16	+	9809.07i	0.274301	+	0.844212i
$514$		0			0
$515$	−1234.82	−	897.152i	−0.105656	−	0.0767636i
$516$		0			0
$517$	−4968.20	+	4886.95i	−0.422633	+	0.415721i
$518$		0			0
$519$	3375.92	+	2452.75i	0.285523	+	0.207444i
$520$		0			0
$521$	4605.23	+	14173.4i	0.387253	+	1.19184i	0.934833	+	0.355088i	$0.115549\pi$
$521$	4605.23	+	14173.4i	0.387253	+	1.19184i	−0.547580	+	0.836753i	$0.684451\pi$
$522$		0			0
$523$	−1204.98	+	875.470i	−0.100746	+	0.0731963i	−0.637018	−	0.770849i	$-0.719832\pi$
$523$	−1204.98	+	875.470i	−0.100746	+	0.0731963i	0.536272	+	0.844045i	$0.319832\pi$
$524$		0			0
$525$	18.0411	−	55.5248i	0.00149977	−	0.00461581i
$526$		0			0
$527$	−401.620			−0.0331971
$528$		0			0
$529$	−1494.50			−0.122832
$530$		0			0
$531$	395.702	−	1217.85i	0.0323390	−	0.0995292i
$532$		0			0
$533$	11049.9	−	8028.20i	0.897979	−	0.652420i
$534$		0			0
$535$	−4770.69	−	14682.7i	−0.385523	−	1.18652i
$536$		0			0
$537$	1837.05	+	1334.69i	0.147625	+	0.107256i
$538$		0			0
$539$	−12353.6	+	1852.35i	−0.987212	+	0.148027i
$540$		0			0
$541$	−431.634	−	313.600i	−0.0343020	−	0.0249219i	0.570502	−	0.821296i	$-0.306749\pi$
$541$	−431.634	−	313.600i	−0.0343020	−	0.0249219i	−0.604804	+	0.796374i	$0.706749\pi$
$542$		0			0
$543$	−234.404	−	721.420i	−0.0185253	−	0.0570149i
$544$		0			0
$545$	5813.81	−	4223.98i	0.456947	−	0.331991i
$546$		0			0
$547$	5716.57	−	17593.8i	0.446842	−	1.37524i	−0.433609	−	0.901101i	$-0.642760\pi$
$547$	5716.57	−	17593.8i	0.446842	−	1.37524i	0.880451	−	0.474138i	$-0.157240\pi$
$548$		0			0
$549$	12134.2			0.943302
$550$		0			0
$551$	8912.04			0.689049
$552$		0			0
$553$	156.377	−	481.279i	0.0120250	−	0.0370092i
$554$		0			0
$555$	−1874.68	+	1362.03i	−0.143380	+	0.104171i
$556$		0			0
$557$	−4865.09	−	14973.2i	−0.370091	−	1.13902i	−0.946732	−	0.322024i	$-0.895637\pi$
$557$	−4865.09	−	14973.2i	−0.370091	−	1.13902i	0.576641	−	0.816998i	$-0.304363\pi$
$558$		0			0
$559$	15720.8	+	11421.8i	1.18948	+	0.864205i
$560$		0			0
$561$	648.977	−	3889.65i	0.0488410	−	0.292730i
$562$		0			0
$563$	4880.11	+	3545.61i	0.365314	+	0.265416i	0.755265	−	0.655419i	$-0.227508\pi$
$563$	4880.11	+	3545.61i	0.365314	+	0.265416i	−0.389951	+	0.920836i	$0.627508\pi$
$564$		0			0
$565$	−2936.06	−	9036.26i	−0.218621	−	0.672846i
$566$		0			0
$567$	340.004	−	247.027i	0.0251831	−	0.0182966i
$568$		0			0
$569$	−4829.81	+	14864.6i	−0.355845	+	1.09518i	0.599672	+	0.800246i	$0.295298\pi$
$569$	−4829.81	+	14864.6i	−0.355845	+	1.09518i	−0.955518	+	0.294934i	$0.904702\pi$
$570$		0			0
$571$	7252.67			0.531550			0.265775	−	0.964035i	$-0.414372\pi$
$571$	7252.67			0.531550			0.265775	+	0.964035i	$0.414372\pi$
$572$		0			0
$573$	1994.43			0.145407
$574$		0			0
$575$	1559.98	−	4801.13i	0.113140	−	0.348210i
$576$		0			0
$577$	−10515.4	+	7639.85i	−0.758683	+	0.551215i	−0.898506	−	0.438961i	$-0.855347\pi$
$577$	−10515.4	+	7639.85i	−0.758683	+	0.551215i	0.139823	+	0.990176i	$0.455347\pi$
$578$		0			0
$579$	−249.654	−	768.355i	−0.0179193	−	0.0551498i
$580$		0			0
$581$	−753.986	−	547.803i	−0.0538392	−	0.0391165i
$582$		0			0
$583$	10454.5	+	20943.2i	0.742677	+	1.48778i
$584$		0			0
$585$	11229.4	+	8158.64i	0.793639	+	0.576613i
$586$		0			0
$587$	−3131.18	−	9636.79i	−0.220166	−	0.677603i	−0.998746	−	0.0500572i	$-0.984060\pi$
$587$	−3131.18	−	9636.79i	−0.220166	−	0.677603i	0.778580	−	0.627546i	$-0.215940\pi$
$588$		0			0
$589$	−600.562	+	436.334i	−0.0420131	+	0.0305243i
$590$		0			0
$591$	−560.787	+	1725.93i	−0.0390317	+	0.120127i
$592$		0			0
$593$	−838.751			−0.0580833			−0.0290416	−	0.999578i	$-0.509246\pi$
$593$	−838.751			−0.0580833			−0.0290416	+	0.999578i	$0.509246\pi$
$594$		0			0
$595$	−474.276			−0.0326780
$596$		0			0
$597$	1455.05	−	4478.20i	0.0997511	−	0.307002i
$598$		0			0
$599$	−20801.8	+	15113.4i	−1.41893	+	1.03091i	−0.426978	+	0.904262i	$0.640422\pi$
$599$	−20801.8	+	15113.4i	−1.41893	+	1.03091i	−0.991948	+	0.126648i	$0.959578\pi$
$600$		0			0
$601$	−439.880	−	1353.81i	−0.0298554	−	0.0918853i	0.935019	−	0.354599i	$-0.115383\pi$
$601$	−439.880	−	1353.81i	−0.0298554	−	0.0918853i	−0.964874	+	0.262714i	$0.915383\pi$
$602$		0			0
$603$	6394.52	+	4645.89i	0.431849	+	0.313757i
$604$		0			0
$605$	−10984.6	−	3770.44i	−0.738158	−	0.253372i
$606$		0			0
$607$	−20688.0	−	15030.7i	−1.38336	−	1.00507i	−0.996557	−	0.0829067i	$-0.973580\pi$
$607$	−20688.0	−	15030.7i	−1.38336	−	1.00507i	−0.386802	−	0.922163i	$-0.626420\pi$
$608$		0			0
$609$	25.3850	+	78.1271i	0.00168909	+	0.00519847i
$610$		0			0
$611$	−9983.42	+	7253.38i	−0.661024	+	0.480262i
$612$		0			0
$613$	−1499.35	+	4614.51i	−0.0987895	+	0.304043i	−0.988223	−	0.153022i	$-0.951099\pi$
$613$	−1499.35	+	4614.51i	−0.0987895	+	0.304043i	0.889433	+	0.457065i	$0.151099\pi$
$614$		0			0
$615$	−2843.49			−0.186440
$616$		0			0
$617$	3850.99			0.251272			0.125636	−	0.992076i	$-0.459903\pi$
$617$	3850.99			0.251272			0.125636	+	0.992076i	$0.459903\pi$
$618$		0			0
$619$	−7443.43	+	22908.5i	−0.483323	+	1.48751i	0.351073	+	0.936348i	$0.385817\pi$
$619$	−7443.43	+	22908.5i	−0.483323	+	1.48751i	−0.834396	+	0.551166i	$0.814183\pi$
$620$		0			0
$621$	−6650.49	+	4831.86i	−0.429750	+	0.312232i
$622$		0			0
$623$	−171.725	−	528.515i	−0.0110434	−	0.0339880i
$624$		0			0
$625$	5767.43	+	4190.28i	0.369115	+	0.268178i
$626$		0			0
$627$	−3255.40	−	6521.45i	−0.207350	−	0.415377i
$628$		0			0
$629$	−9774.63	−	7101.69i	−0.619619	−	0.450179i
$630$		0			0
$631$	899.970	+	2769.82i	0.0567785	+	0.174746i	0.975424	−	0.220337i	$-0.0707157\pi$
$631$	899.970	+	2769.82i	0.0567785	+	0.174746i	−0.918645	+	0.395083i	$0.870716\pi$
$632$		0			0
$633$	2125.69	−	1544.41i	0.133474	−	0.0969742i
$634$		0			0
$635$	3384.57	−	10416.6i	0.211516	−	0.650979i
$636$		0			0
$637$	−22119.8			−1.37585
$638$		0			0
$639$	−4496.68			−0.278382
$640$		0			0
$641$	1900.65	−	5849.60i	0.117116	−	0.360445i	−0.875267	−	0.483641i	$-0.839314\pi$
$641$	1900.65	−	5849.60i	0.117116	−	0.360445i	0.992382	+	0.123195i	$0.0393142\pi$
$642$		0			0
$643$	−7892.25	+	5734.05i	−0.484043	+	0.351678i	−0.802889	−	0.596129i	$-0.796705\pi$
$643$	−7892.25	+	5734.05i	−0.484043	+	0.351678i	0.318846	+	0.947807i	$0.396705\pi$
$644$		0			0
$645$	−1250.12	−	3847.46i	−0.0763152	−	0.234874i
$646$		0			0
$647$	−1473.76	−	1070.75i	−0.0895507	−	0.0650624i	0.542109	−	0.840308i	$-0.317626\pi$
$647$	−1473.76	−	1070.75i	−0.0895507	−	0.0650624i	−0.631660	+	0.775246i	$0.717626\pi$
$648$		0			0
$649$	−312.227	+	1871.34i	−0.0188844	+	0.113184i
$650$		0			0
$651$	−5.53574	−	4.02195i	−0.000333276	−	0.000242139i
$652$		0			0
$653$	1971.95	+	6069.03i	0.118175	+	0.363705i	0.992596	−	0.121463i	$-0.0387585\pi$
$653$	1971.95	+	6069.03i	0.118175	+	0.363705i	−0.874421	+	0.485168i	$0.838759\pi$
$654$		0			0
$655$	9891.06	−	7186.27i	0.590039	−	0.428689i
$656$		0			0
$657$	1582.14	−	4869.33i	0.0939501	−	0.289149i
$658$		0			0
$659$	27285.6			1.61289			0.806445	−	0.591309i	$-0.201389\pi$
$659$	27285.6			1.61289			0.806445	+	0.591309i	$0.201389\pi$
$660$		0			0
$661$	−23925.0			−1.40783			−0.703913	−	0.710286i	$-0.748566\pi$
$661$	−23925.0			−1.40783			−0.703913	+	0.710286i	$0.748566\pi$
$662$		0			0
$663$	2157.82	−	6641.08i	0.126399	−	0.389017i
$664$		0			0
$665$	−709.206	+	515.269i	−0.0413562	+	0.0300470i
$666$		0			0
$667$	2195.00	+	6755.51i	0.127422	+	0.392166i
$668$		0			0
$669$	5739.36	+	4169.89i	0.331684	+	0.240982i
$670$		0			0
$671$	−17779.1	+	2665.87i	−1.02288	+	0.153375i
$672$		0			0
$673$	6744.56	+	4900.21i	0.386306	+	0.280667i	0.763940	−	0.645287i	$-0.223262\pi$
$673$	6744.56	+	4900.21i	0.386306	+	0.280667i	−0.377634	+	0.925955i	$0.623262\pi$
$674$		0			0
$675$	1201.57	+	3698.06i	0.0685163	+	0.210871i
$676$		0			0
$677$	898.252	−	652.618i	0.0509935	−	0.0370490i	−0.561997	−	0.827140i	$-0.689967\pi$
$677$	898.252	−	652.618i	0.0509935	−	0.0370490i	0.612990	+	0.790091i	$0.289967\pi$
$678$		0			0
$679$	150.509	−	463.220i	0.00850665	−	0.0261808i
$680$		0			0
$681$	−5067.22			−0.285134
$682$		0			0
$683$	−8337.88			−0.467116			−0.233558	−	0.972343i	$-0.575037\pi$
$683$	−8337.88			−0.467116			−0.233558	+	0.972343i	$0.575037\pi$
$684$		0			0
$685$	−1103.70	+	3396.83i	−0.0615622	+	0.189469i
$686$		0			0
$687$	3679.89	−	2673.60i	0.204362	−	0.148478i
$688$		0			0
$689$	12808.5	+	39420.4i	0.708219	+	2.17968i
$690$		0			0
$691$	−26998.5	−	19615.5i	−1.48635	−	1.07990i	−0.975440	−	0.220266i	$-0.929307\pi$
$691$	−26998.5	−	19615.5i	−1.48635	−	1.07990i	−0.510913	−	0.859632i	$-0.670693\pi$
$692$		0			0
$693$	−496.424	+	488.305i	−0.0272115	+	0.0267665i
$694$		0			0
$695$	4202.83	+	3053.53i	0.229385	+	0.166658i
$696$		0			0
$697$	−4581.50	−	14100.4i	−0.248977	−	0.766272i
$698$		0			0
$699$	−3519.92	+	2557.37i	−0.190466	+	0.138382i
$700$		0			0
$701$	2413.07	−	7426.67i	0.130015	−	0.400145i	−0.864767	−	0.502174i	$-0.832534\pi$
$701$	2413.07	−	7426.67i	0.130015	−	0.400145i	0.994781	+	0.102030i	$0.0325336\pi$
$702$		0			0
$703$	−22332.0			−1.19810
$704$		0			0
$705$	2569.06			0.137243
$706$		0			0
$707$	−121.968	+	375.379i	−0.00648809	+	0.0199683i
$708$		0			0
$709$	−22613.7	+	16429.8i	−1.19785	+	0.870288i	−0.994071	−	0.108730i	$-0.965322\pi$
$709$	−22613.7	+	16429.8i	−1.19785	+	0.870288i	−0.203777	+	0.979017i	$0.565322\pi$
$710$		0			0
$711$	4967.84	+	15289.5i	0.262038	+	0.806469i
$712$		0			0
$713$	−478.666	−	347.771i	−0.0251419	−	0.0182667i
$714$		0			0
$715$	−18245.9	−	9487.03i	−0.954346	−	0.496216i
$716$		0			0
$717$	2570.28	+	1867.42i	0.133876	+	0.0972664i
$718$		0			0
$719$	7720.14	+	23760.2i	0.400435	+	1.23241i	0.924647	+	0.380824i	$0.124360\pi$
$719$	7720.14	+	23760.2i	0.400435	+	1.23241i	−0.524212	+	0.851588i	$0.675640\pi$
$720$		0			0
$721$	109.694	−	79.6971i	0.00566602	−	0.00411661i
$722$		0			0
$723$	−1471.54	+	4528.95i	−0.0756948	+	0.232965i
$724$		0			0
$725$	3359.87			0.172114
$726$		0			0
$727$	−31671.2			−1.61571			−0.807855	−	0.589381i	$-0.799372\pi$
$727$	−31671.2			−1.61571			−0.807855	+	0.589381i	$0.799372\pi$
$728$		0			0
$729$	−3102.42	+	9548.25i	−0.157619	+	0.485102i
$730$		0			0
$731$	17064.7	−	12398.3i	0.863423	−	0.627314i
$732$		0			0
$733$	3656.22	+	11252.7i	0.184237	+	0.567023i	0.999934	−	0.0114559i	$-0.00364661\pi$
$733$	3656.22	+	11252.7i	0.184237	+	0.567023i	−0.815698	+	0.578479i	$0.803647\pi$
$734$		0			0
$735$	3725.55	+	2706.77i	0.186965	+	0.135838i
$736$		0			0
$737$	−10390.0	−	5402.33i	−0.519296	−	0.270010i
$738$		0			0
$739$	4490.16	+	3262.29i	0.223509	+	0.162389i	0.693905	−	0.720067i	$-0.255889\pi$
$739$	4490.16	+	3262.29i	0.223509	+	0.162389i	−0.470396	+	0.882456i	$0.655889\pi$
$740$		0			0
$741$	−3988.40	−	12275.0i	−0.197729	−	0.608549i
$742$		0			0
$743$	30176.1	−	21924.2i	1.48998	−	1.08253i	0.515813	−	0.856701i	$-0.327490\pi$
$743$	30176.1	−	21924.2i	1.48998	−	1.08253i	0.974166	−	0.225832i	$-0.0725101\pi$
$744$		0			0
$745$	5851.26	−	18008.3i	0.287750	−	0.885602i
$746$		0			0
$747$	29607.4			1.45017
$748$		0			0
$749$	1371.43			0.0669041
$750$		0			0
$751$	1606.66	−	4944.80i	0.0780665	−	0.240264i	−0.904406	−	0.426674i	$-0.859685\pi$
$751$	1606.66	−	4944.80i	0.0780665	−	0.240264i	0.982472	+	0.186410i	$0.0596852\pi$
$752$		0			0
$753$	−5024.37	+	3650.42i	−0.243158	+	0.176665i
$754$		0			0
$755$	4850.04	+	14926.9i	0.233789	+	0.719530i
$756$		0			0
$757$	−127.874	−	92.9061i	−0.00613959	−	0.00446067i	0.584711	−	0.811242i	$-0.301208\pi$
$757$	−127.874	−	92.9061i	−0.00613959	−	0.00446067i	−0.590851	+	0.806781i	$0.701208\pi$
$758$		0			0
$759$	4141.60	−	4073.87i	0.198064	−	0.194825i
$760$		0			0
$761$	−5383.00	−	3910.98i	−0.256417	−	0.186298i	0.452149	−	0.891943i	$-0.350658\pi$
$761$	−5383.00	−	3910.98i	−0.256417	−	0.186298i	−0.708566	+	0.705644i	$0.750658\pi$
$762$		0			0
$763$	197.270	+	607.135i	0.00935998	+	0.0288070i
$764$		0			0
$765$	12189.4	−	8856.13i	0.576091	−	0.418554i
$766$		0			0
$767$	−1038.14	+	3195.06i	−0.0488722	+	0.150413i
$768$		0			0
$769$	5519.26			0.258816			0.129408	−	0.991591i	$-0.458692\pi$
$769$	5519.26			0.258816			0.129408	+	0.991591i	$0.458692\pi$
$770$		0			0
$771$	−6778.18			−0.316615
$772$		0			0
$773$	9540.72	−	29363.3i	0.443927	−	1.36627i	−0.439729	−	0.898131i	$-0.644925\pi$
$773$	9540.72	−	29363.3i	0.443927	−	1.36627i	0.883656	−	0.468137i	$-0.155075\pi$
$774$		0			0
$775$	−226.414	+	164.499i	−0.0104942	+	0.00762451i
$776$		0			0
$777$	−63.6103	−	195.772i	−0.00293695	−	0.00903899i
$778$		0			0
$779$	−22170.1	−	16107.5i	−1.01967	−	0.740836i
$780$		0			0
$781$	6588.58	−	987.918i	0.301867	−	0.0452631i
$782$		0			0
$783$	−4426.29	−	3215.88i	−0.202021	−	0.146777i
$784$		0			0
$785$	−211.429	−	650.711i	−0.00961302	−	0.0295858i
$786$		0			0
$787$	−20220.4	+	14690.9i	−0.915855	+	0.665408i	−0.942489	−	0.334238i	$-0.891521\pi$
$787$	−20220.4	+	14690.9i	−0.915855	+	0.665408i	0.0266338	+	0.999645i	$0.491521\pi$
$788$		0			0
$789$	435.665	−	1340.84i	0.0196579	−	0.0605008i
$790$		0			0
$791$	844.031			0.0379397
$792$		0			0
$793$	−31834.4			−1.42556
$794$		0			0
$795$	2666.55	−	8206.78i	0.118959	−	0.366119i
$796$		0			0
$797$	16563.4	−	12034.0i	0.736141	−	0.534838i	−0.155359	−	0.987858i	$-0.549654\pi$
$797$	16563.4	−	12034.0i	0.736141	−	0.534838i	0.891500	+	0.453020i	$0.149654\pi$
$798$		0			0
$799$	4139.33	+	12739.6i	0.183278	+	0.564071i
$800$		0			0
$801$	14282.5	+	10376.8i	0.630020	+	0.457736i
$802$		0			0
$803$	−1248.38	+	7482.18i	−0.0548622	+	0.328818i
$804$		0			0
$805$	−565.259	−	410.685i	−0.0247488	−	0.0179810i
$806$		0			0
$807$	−842.491	−	2592.92i	−0.0367498	−	0.113104i
$808$		0			0
$809$	−11872.0	+	8625.48i	−0.515941	+	0.374853i	−0.815072	−	0.579359i	$-0.803303\pi$
$809$	−11872.0	+	8625.48i	−0.515941	+	0.374853i	0.299132	+	0.954212i	$0.403303\pi$
$810$		0			0
$811$	−1459.87	+	4493.01i	−0.0632095	+	0.194539i	−0.977674	−	0.210127i	$-0.932612\pi$
$811$	−1459.87	+	4493.01i	−0.0632095	+	0.194539i	0.914465	+	0.404666i	$0.132612\pi$
$812$		0			0
$813$	−6194.10			−0.267204
$814$		0			0
$815$	−2869.23			−0.123319
$816$		0			0
$817$	12047.8	−	37079.4i	0.515912	−	1.58781i
$818$		0			0
$819$	−997.546	+	724.760i	−0.0425606	+	0.0309221i
$820$		0			0
$821$	13881.5	+	42723.0i	0.590097	+	1.81613i	0.577760	+	0.816207i	$0.303927\pi$
$821$	13881.5	+	42723.0i	0.590097	+	1.81613i	0.0123363	+	0.999924i	$0.496073\pi$
$822$		0			0
$823$	32002.7	+	23251.3i	1.35546	+	0.984800i	0.998719	+	0.0505967i	$0.0161123\pi$
$823$	32002.7	+	23251.3i	1.35546	+	0.984800i	0.356742	+	0.934203i	$0.383888\pi$
$824$		0			0
$825$	−1227.30	−	2458.61i	−0.0517928	−	0.103755i
$826$		0			0
$827$	12752.3	+	9265.07i	0.536203	+	0.389574i	0.822673	−	0.568515i	$-0.192482\pi$
$827$	12752.3	+	9265.07i	0.536203	+	0.389574i	−0.286470	+	0.958089i	$0.592482\pi$
$828$		0			0
$829$	6977.80	+	21475.5i	0.292339	+	0.899727i	0.984102	+	0.177603i	$0.0568342\pi$
$829$	6977.80	+	21475.5i	0.292339	+	0.899727i	−0.691763	+	0.722124i	$0.743166\pi$
$830$		0			0
$831$	8287.34	−	6021.10i	0.345950	−	0.251348i
$832$		0			0
$833$	−7419.75	+	22835.6i	−0.308618	+	0.949830i
$834$		0			0
$835$	30746.4			1.27428
$836$		0			0
$837$	455.727			0.0188199
$838$		0			0
$839$	7245.74	−	22300.1i	0.298153	−	0.917621i	−0.683991	−	0.729491i	$-0.739757\pi$
$839$	7245.74	−	22300.1i	0.298153	−	0.917621i	0.982144	−	0.188131i	$-0.0602428\pi$
$840$		0			0
$841$	15906.4	−	11556.7i	0.652197	−	0.473849i
$842$		0			0
$843$	2087.71	+	6425.30i	0.0852958	+	0.262514i
$844$		0			0
$845$	−13952.0	−	10136.7i	−0.568002	−	0.412678i
$846$		0			0
$847$	620.085	−	824.534i	0.0251551	−	0.0334490i
$848$		0			0
$849$	4657.39	+	3383.79i	0.188270	+	0.136786i
$850$		0			0
$851$	−5500.27	−	16928.1i	−0.221559	−	0.681889i
$852$		0			0
$853$	12132.7	−	8814.90i	0.487004	−	0.353829i	−0.317027	−	0.948417i	$-0.602685\pi$
$853$	12132.7	−	8814.90i	0.487004	−	0.353829i	0.804031	+	0.594587i	$0.202685\pi$
$854$		0			0
$855$	8605.82	−	26486.0i	0.344225	−	1.05942i
$856$		0			0
$857$	46121.7			1.83838			0.919188	−	0.393819i	$-0.128846\pi$
$857$	46121.7			1.83838			0.919188	+	0.393819i	$0.128846\pi$
$858$		0			0
$859$	17398.7			0.691080			0.345540	−	0.938404i	$-0.387696\pi$
$859$	17398.7			0.691080			0.345540	+	0.938404i	$0.387696\pi$
$860$		0			0
$861$	78.0567	−	240.234i	0.00308962	−	0.00950888i
$862$		0			0
$863$	−8989.57	+	6531.30i	−0.354587	+	0.257622i	−0.750791	−	0.660540i	$-0.770327\pi$
$863$	−8989.57	+	6531.30i	−0.354587	+	0.257622i	0.396204	+	0.918163i	$0.370327\pi$
$864$		0			0
$865$	−7299.56	−	22465.7i	−0.286928	−	0.883072i
$866$		0			0
$867$	−5.66730	−	4.11754i	−0.000221997	−	0.000161291i
$868$		0			0
$869$	−10638.0	−	21310.8i	−0.415270	−	0.831899i
$870$		0			0
$871$	−16776.2	−	12188.7i	−0.652631	−	0.474164i
$872$		0			0
$873$	4781.43	+	14715.7i	0.185369	+	0.570507i
$874$		0			0
$875$	−951.323	+	691.177i	−0.0367550	+	0.0267040i
$876$		0			0
$877$	493.384	−	1518.48i	0.0189970	−	0.0584668i	−0.941109	−	0.338104i	$-0.890214\pi$
$877$	493.384	−	1518.48i	0.0189970	−	0.0584668i	0.960106	+	0.279638i	$0.0902143\pi$
$878$		0			0
$879$	−3445.25			−0.132202
$880$		0			0
$881$	4924.45			0.188319			0.0941594	−	0.995557i	$-0.469984\pi$
$881$	4924.45			0.188319			0.0941594	+	0.995557i	$0.469984\pi$
$882$		0			0
$883$	6665.86	−	20515.4i	0.254048	−	0.781878i	−0.739968	−	0.672642i	$-0.765159\pi$
$883$	6665.86	−	20515.4i	0.254048	−	0.781878i	0.994016	−	0.109236i	$-0.0348406\pi$
$884$		0			0
$885$	565.826	−	411.097i	0.0214916	−	0.0156145i
$886$		0			0
$887$	−6836.67	−	21041.1i	−0.258797	−	0.796495i	−0.993058	−	0.117628i	$-0.962471\pi$
$887$	−6836.67	−	21041.1i	−0.258797	−	0.796495i	0.734261	−	0.678868i	$-0.237529\pi$
$888$		0			0
$889$	787.146	+	571.895i	0.0296963	+	0.0215756i
$890$		0			0
$891$	3255.40	−	19511.3i	0.122402	−	0.733618i
$892$		0			0
$893$	20030.4	+	14552.9i	0.750607	+	0.545348i
$894$		0			0
$895$	−3972.15	−	12225.0i	−0.148351	−	0.456578i
$896$		0			0
$897$	8322.40	−	6046.58i	0.309785	−	0.225072i
$898$		0			0
$899$	121.687	−	374.513i	0.00451443	−	0.0138940i
$900$		0			0
$901$	44992.5			1.66362
$902$		0			0
$903$	359.372			0.0132438
$904$		0			0
$905$	−1326.92	+	4083.83i	−0.0487384	+	0.150001i
$906$		0			0
$907$	−1648.63	+	1197.80i	−0.0603548	+	0.0438504i	−0.617554	−	0.786529i	$-0.711876\pi$
$907$	−1648.63	+	1197.80i	−0.0603548	+	0.0438504i	0.557199	+	0.830379i	$0.311876\pi$
$908$		0			0
$909$	−3874.73	−	11925.2i	−0.141382	−	0.435130i
$910$		0			0
$911$	35177.4	+	25557.9i	1.27934	+	0.929495i	0.999533	−	0.0305606i	$-0.00972926\pi$
$911$	35177.4	+	25557.9i	1.27934	+	0.929495i	0.279808	+	0.960056i	$0.409729\pi$
$912$		0			0
$913$	−43381.0	+	6504.73i	−1.57251	+	0.235789i
$914$		0			0
$915$	5361.75	+	3895.54i	0.193720	+	0.140746i
$916$		0			0
$917$	335.617	+	1032.92i	0.0120862	+	0.0371975i
$918$		0			0
$919$	−7796.33	+	5664.36i	−0.279845	+	0.203319i	−0.718850	−	0.695166i	$-0.755331\pi$
$919$	−7796.33	+	5664.36i	−0.279845	+	0.203319i	0.439005	+	0.898485i	$0.355331\pi$
$920$		0			0
$921$	−487.035	+	1498.94i	−0.0174249	+	0.0536283i
$922$		0			0
$923$	11797.2			0.420704
$924$		0			0
$925$	−8419.24			−0.299268
$926$		0			0
$927$	−1331.07	+	4096.61i	−0.0471608	+	0.145146i
$928$		0			0
$929$	−5085.28	+	3694.67i	−0.179594	+	0.130482i	−0.673950	−	0.738777i	$-0.735404\pi$
$929$	−5085.28	+	3694.67i	−0.179594	+	0.130482i	0.494356	+	0.869259i	$0.335404\pi$
$930$		0			0
$931$	13714.3	+	42208.3i	0.482780	+	1.48584i
$932$		0			0
$933$	6633.29	+	4819.37i	0.232759	+	0.169109i
$934$		0			0
$935$	−15914.4	+	15654.1i	−0.556637	+	0.547534i
$936$		0			0
$937$	−19912.9	−	14467.6i	−0.694266	−	0.504413i	0.183794	−	0.982965i	$-0.441162\pi$
$937$	−19912.9	−	14467.6i	−0.694266	−	0.504413i	−0.878060	+	0.478551i	$0.841162\pi$
$938$		0			0
$939$	−3331.08	−	10252.0i	−0.115767	−	0.356295i
$940$		0			0
$941$	−15898.0	+	11550.6i	−0.550754	+	0.400146i	−0.828063	−	0.560635i	$-0.810557\pi$
$941$	−15898.0	+	11550.6i	−0.550754	+	0.400146i	0.277310	+	0.960781i	$0.410557\pi$
$942$		0			0
$943$	6749.43	−	20772.6i	0.233077	−	0.717337i
$944$		0			0
$945$	538.170			0.0185256
$946$		0			0
$947$	−3025.82			−0.103829			−0.0519144	−	0.998652i	$-0.516532\pi$
$947$	−3025.82			−0.103829			−0.0519144	+	0.998652i	$0.516532\pi$
$948$		0			0
$949$	−4150.80	+	12774.9i	−0.141982	+	0.436975i
$950$		0			0
$951$	−5380.41	+	3909.10i	−0.183461	+	0.133293i
$952$		0			0
$953$	−3617.77	−	11134.3i	−0.122971	−	0.378465i	0.870555	−	0.492071i	$-0.163760\pi$
$953$	−3617.77	−	11134.3i	−0.122971	−	0.378465i	−0.993526	+	0.113606i	$0.963760\pi$
$954$		0			0
$955$	−9133.90	−	6636.16i	−0.309493	−	0.224860i
$956$		0			0
$957$	3430.49	+	1783.70i	0.115875	+	0.0602495i
$958$		0			0
$959$	−256.686	−	186.493i	−0.00864319	−	0.00627964i
$960$		0			0
$961$	−9195.79	−	28301.7i	−0.308677	−	0.950009i
$962$		0			0
$963$	−35247.4	+	25608.8i	−1.17947	+	0.856938i
$964$		0			0
$965$	−1413.25	+	4349.53i	−0.0471441	+	0.145095i
$966$		0			0
$967$	−12352.3			−0.410779			−0.205390	−	0.978680i	$-0.565846\pi$
$967$	−12352.3			−0.410779			−0.205390	+	0.978680i	$0.565846\pi$
$968$		0			0
$969$	−14010.1			−0.464469
$970$		0			0
$971$	5225.07	−	16081.1i	0.172688	−	0.531481i	−0.826832	−	0.562449i	$-0.809859\pi$
$971$	5225.07	−	16081.1i	0.172688	−	0.531481i	0.999520	+	0.0309686i	$0.00985920\pi$
$972$		0			0
$973$	−373.352	+	271.256i	−0.0123012	+	0.00893737i
$974$		0			0
$975$	−1503.64	−	4627.73i	−0.0493898	−	0.152006i
$976$		0			0
$977$	−19980.0	−	14516.3i	−0.654266	−	0.475352i	0.210456	−	0.977603i	$-0.432505\pi$
$977$	−19980.0	−	14516.3i	−0.654266	−	0.475352i	−0.864722	+	0.502251i	$0.832505\pi$
$978$		0			0
$979$	−23206.6	−	12066.4i	−0.757595	−	0.393915i
$980$		0			0
$981$	−16407.1	−	11920.4i	−0.533984	−	0.387962i
$982$		0			0
$983$	9496.51	+	29227.2i	0.308130	+	0.948326i	0.978491	+	0.206291i	$0.0661392\pi$
$983$	9496.51	+	29227.2i	0.308130	+	0.948326i	−0.670361	+	0.742035i	$0.733861\pi$
$984$		0			0
$985$	8311.01	−	6038.30i	0.268843	−	0.195326i
$986$		0			0
$987$	−70.5233	+	217.048i	−0.00227435	+	0.00699972i
$988$		0			0
$989$	31074.3			0.999094
$990$		0			0
$991$	−40862.5			−1.30983			−0.654915	−	0.755703i	$-0.727295\pi$
$991$	−40862.5			−1.30983			−0.654915	+	0.755703i	$0.727295\pi$
$992$		0			0
$993$	1851.30	−	5697.71i	0.0591633	−	0.182086i
$994$		0			0
$995$	−21564.3	+	15667.3i	−0.687068	+	0.499184i
$996$		0			0
$997$	17934.9	+	55198.1i	0.569715	+	1.75340i	0.653509	+	0.756918i	$0.273296\pi$
$997$	17934.9	+	55198.1i	0.569715	+	1.75340i	−0.0837946	+	0.996483i	$0.526704\pi$
$998$		0			0
$999$	11091.5	+	8058.43i	0.351270	+	0.255213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.4.m.c.81.2		8
4.3	odd	2		11.4.c.a.4.2	yes	8
11.3	even	5	inner	176.4.m.c.113.2		8
11.5	even	5		1936.4.a.bk.1.4		4
11.6	odd	10		1936.4.a.bl.1.4		4
12.11	even	2		99.4.f.c.37.1		8
44.3	odd	10		11.4.c.a.3.2	✓	8
44.7	even	10		121.4.c.b.9.2		8
44.15	odd	10		121.4.c.h.9.1		8
44.19	even	10		121.4.c.i.3.1		8
44.27	odd	10		121.4.a.g.1.2		4
44.31	odd	10		121.4.c.h.27.1		8
44.35	even	10		121.4.c.b.27.2		8
44.39	even	10		121.4.a.f.1.3		4
44.43	even	2		121.4.c.i.81.1		8
132.47	even	10		99.4.f.c.91.1		8
132.71	even	10		1089.4.a.y.1.3		4
132.83	odd	10		1089.4.a.bh.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.c.a.3.2	✓	8	44.3	odd	10
11.4.c.a.4.2	yes	8	4.3	odd	2
99.4.f.c.37.1		8	12.11	even	2
99.4.f.c.91.1		8	132.47	even	10
121.4.a.f.1.3		4	44.39	even	10
121.4.a.g.1.2		4	44.27	odd	10
121.4.c.b.9.2		8	44.7	even	10
121.4.c.b.27.2		8	44.35	even	10
121.4.c.h.9.1		8	44.15	odd	10
121.4.c.h.27.1		8	44.31	odd	10
121.4.c.i.3.1		8	44.19	even	10
121.4.c.i.81.1		8	44.43	even	2
176.4.m.c.81.2		8	1.1	even	1	trivial
176.4.m.c.113.2		8	11.3	even	5	inner
1089.4.a.y.1.3		4	132.71	even	10
1089.4.a.bh.1.2		4	132.83	odd	10
1936.4.a.bk.1.4		4	11.5	even	5
1936.4.a.bl.1.4		4	11.6	odd	10

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:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	176.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.476313 - 1.46594i) q^{3} +(-7.05908 + 5.12872i) q^{5} +(-0.239524 - 0.737179i) q^{7} +(19.9214 + 14.4737i) q^{9} +O(q^{10})\)	\(q+(0.476313 - 1.46594i) q^{3} +(-7.05908 + 5.12872i) q^{5} +(-0.239524 - 0.737179i) q^{7} +(19.9214 + 14.4737i) q^{9} +(-32.3688 - 16.8303i) q^{11} +(-52.2644 - 37.9723i) q^{13} +(4.15607 + 12.7911i) q^{15} +(-56.7325 + 41.2186i) q^{17} +(-40.0535 + 123.272i) q^{19} -1.19475 q^{21} -103.308 q^{23} +(-15.1003 + 46.4740i) q^{25} +(64.3755 - 46.7715i) q^{27} +(-21.2472 - 65.3921i) q^{29} +(4.63339 + 3.36636i) q^{31} +(-40.0899 + 39.4343i) q^{33} +(5.47160 + 3.97535i) q^{35} +(53.2416 + 163.861i) q^{37} +(-80.5593 + 58.5298i) q^{39} +(-65.3332 + 201.075i) q^{41} -300.793 q^{43} -214.858 q^{45} +(59.0277 - 181.669i) q^{47} +(277.007 - 201.257i) q^{49} +(33.4015 + 102.799i) q^{51} +(-519.068 - 377.125i) q^{53} +(314.812 - 47.2041i) q^{55} +(161.632 + 117.432i) q^{57} +(-16.0697 - 49.4574i) q^{59} +(398.663 - 289.646i) q^{61} +(5.89807 - 18.1524i) q^{63} +563.687 q^{65} +320.988 q^{67} +(-49.2068 + 151.443i) q^{69} +(-147.737 + 107.337i) q^{71} +(-64.2516 - 197.746i) q^{73} +(60.9357 + 44.2724i) q^{75} +(-4.65384 + 27.8929i) q^{77} +(528.180 + 383.745i) q^{79} +(167.549 + 515.663i) q^{81} +(972.740 - 706.737i) q^{83} +(189.080 - 581.930i) q^{85} -105.981 q^{87} +716.942 q^{89} +(-15.4738 + 47.6234i) q^{91} +(7.14183 - 5.18884i) q^{93} +(-349.487 - 1075.61i) q^{95} +(508.361 + 369.346i) q^{97} +(-401.234 - 803.779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} - 7 q^{5} + 35 q^{7} + 31 q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 - 7 * q^5 + 35 * q^7 + 31 * q^9	\( 8 q + 3 q^{3} - 7 q^{5} + 35 q^{7} + 31 q^{9} - 67 q^{11} - 65 q^{13} + 121 q^{15} - 31 q^{17} - 148 q^{19} + 334 q^{21} + 12 q^{23} - 201 q^{25} - 72 q^{27} - 199 q^{29} + 361 q^{31} - 232 q^{33} - 237 q^{35} + 81 q^{37} - 365 q^{39} - 31 q^{41} + 650 q^{43} + 452 q^{45} - 857 q^{47} + 1375 q^{49} + 246 q^{51} - 1493 q^{53} + 1583 q^{55} + 102 q^{57} - 676 q^{59} - 525 q^{61} + 68 q^{63} + 1790 q^{65} - 86 q^{67} - 42 q^{69} - 1143 q^{71} - 2155 q^{73} + 160 q^{75} - 2015 q^{77} + 861 q^{79} - 26 q^{81} - 52 q^{83} + 2383 q^{85} - 2310 q^{87} + 3782 q^{89} - 135 q^{91} - 2077 q^{93} + 1317 q^{95} - 1344 q^{97} - 2099 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 - 7 * q^5 + 35 * q^7 + 31 * q^9 - 67 * q^11 - 65 * q^13 + 121 * q^15 - 31 * q^17 - 148 * q^19 + 334 * q^21 + 12 * q^23 - 201 * q^25 - 72 * q^27 - 199 * q^29 + 361 * q^31 - 232 * q^33 - 237 * q^35 + 81 * q^37 - 365 * q^39 - 31 * q^41 + 650 * q^43 + 452 * q^45 - 857 * q^47 + 1375 * q^49 + 246 * q^51 - 1493 * q^53 + 1583 * q^55 + 102 * q^57 - 676 * q^59 - 525 * q^61 + 68 * q^63 + 1790 * q^65 - 86 * q^67 - 42 * q^69 - 1143 * q^71 - 2155 * q^73 + 160 * q^75 - 2015 * q^77 + 861 * q^79 - 26 * q^81 - 52 * q^83 + 2383 * q^85 - 2310 * q^87 + 3782 * q^89 - 135 * q^91 - 2077 * q^93 + 1317 * q^95 - 1344 * q^97 - 2099 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more