LMFDB - Embedded newform 176.4.m.e.113.1

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 60 x^{14} - 83 x^{13} + 1685 x^{12} - 14618 x^{11} + 106543 x^{10} - 521269 x^{9} + \cdots + 2025 $ x^16 - 4x^15 + 60x^14 - 83x^13 + 1685x^12 - 14618x^11 + 106543x^10 - 521269x^9 + 3907139x^8 - 15948298x^7 + 37290102x^6 - 37052438x^5 + 40742731x^4 + 4262985x^3 + 9787185x^2 + 227475*x + 2025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			113.1
Root			$2.43785 - 7.50293i$ of defining polynomial
Character	$\chi$	$=$	176.113
Dual form			176.4.m.e.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71205 - 5.26914i) q^{3} +(5.02952 + 3.65416i) q^{5} +(3.12006 - 9.60257i) q^{7} +(-2.98931 + 2.17186i) q^{9} +(17.8737 - 31.8046i) q^{11} +(-16.0519 + 11.6624i) q^{13} +(10.6435 - 32.7574i) q^{15} +(-0.0229293 - 0.0166591i) q^{17} +(-22.3778 - 68.8719i) q^{19} -55.9390 q^{21} -92.3700 q^{23} +(-26.6839 - 82.1247i) q^{25} +(-104.458 - 75.8930i) q^{27} +(25.7455 - 79.2365i) q^{29} +(-139.196 + 101.132i) q^{31} +(-198.184 - 39.7278i) q^{33} +(50.7818 - 36.8951i) q^{35} +(55.1183 - 169.637i) q^{37} +(88.9324 + 64.6131i) q^{39} +(-72.8262 - 224.136i) q^{41} +69.3945 q^{43} -22.9711 q^{45} +(133.810 + 411.825i) q^{47} +(195.018 + 141.689i) q^{49} +(-0.0485233 + 0.149339i) q^{51} +(485.316 - 352.603i) q^{53} +(206.115 - 94.6487i) q^{55} +(-324.584 + 235.824i) q^{57} +(112.856 - 347.336i) q^{59} +(554.647 + 402.975i) q^{61} +(11.5286 + 35.4814i) q^{63} -123.349 q^{65} -224.941 q^{67} +(158.142 + 486.711i) q^{69} +(-206.018 - 149.681i) q^{71} +(-272.652 + 839.136i) q^{73} +(-387.043 + 281.203i) q^{75} +(-249.639 - 270.865i) q^{77} +(313.056 - 227.449i) q^{79} +(-251.883 + 775.217i) q^{81} +(982.393 + 713.750i) q^{83} +(-0.0544484 - 0.167575i) q^{85} -461.586 q^{87} -1236.77 q^{89} +(61.9059 + 190.527i) q^{91} +(771.188 + 560.301i) q^{93} +(139.119 - 428.165i) q^{95} +(721.245 - 524.015i) q^{97} +(15.6453 + 133.893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} - q^{5} + 13 q^{7} + 7 q^{9} - 83 q^{11} + 69 q^{13} - 93 q^{15} - 217 q^{17} - 126 q^{19} + 34 q^{21} + 92 q^{23} + 307 q^{25} - 158 q^{27} - 553 q^{29} - 205 q^{31} - 198 q^{33} - 7 q^{35}+ \cdots + 3265 q^{99}+O(q^{100}) $ 16 * q + q^3 - q^5 + 13 * q^7 + 7 * q^9 - 83 * q^11 + 69 * q^13 - 93 * q^15 - 217 * q^17 - 126 * q^19 + 34 * q^21 + 92 * q^23 + 307 * q^25 - 158 * q^27 - 553 * q^29 - 205 * q^31 - 198 * q^33 - 7 * q^35 + 127 * q^37 + 629 * q^39 - 553 * q^41 - 70 * q^43 - 1132 * q^45 - 779 * q^47 + 847 * q^49 + 2176 * q^51 + 1401 * q^53 + 385 * q^55 - 488 * q^57 - 1354 * q^59 - 1623 * q^61 - 256 * q^63 + 1674 * q^65 + 1658 * q^67 + 5470 * q^69 - 1985 * q^71 - 1245 * q^73 - 4114 * q^75 - 2645 * q^77 + 2007 * q^79 + 1966 * q^81 + 2946 * q^83 - 1543 * q^85 + 262 * q^87 - 6410 * q^89 - 3937 * q^91 + 2221 * q^93 + 8359 * q^95 + 6566 * q^97 + 3265 * q^99

Character values

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

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−1.71205	−	5.26914i	−0.329484	−	1.01405i	−0.969376	−	0.245582i	$-0.921021\pi$
$3$	−1.71205	−	5.26914i	−0.329484	−	1.01405i	0.639892	−	0.768465i	$-0.278979\pi$
$4$		0			0
$5$	5.02952	+	3.65416i	0.449854	+	0.326838i	0.789538	−	0.613702i	$-0.210320\pi$
$5$	5.02952	+	3.65416i	0.449854	+	0.326838i	−0.339684	+	0.940540i	$0.610320\pi$
$6$		0			0
$7$	3.12006	−	9.60257i	0.168468	−	0.518490i	−0.830807	−	0.556560i	$-0.812121\pi$
$7$	3.12006	−	9.60257i	0.168468	−	0.518490i	0.999275	+	0.0380698i	$0.0121209\pi$
$8$		0			0
$9$	−2.98931	+	2.17186i	−0.110715	+	0.0804392i
$10$		0			0
$11$	17.8737	−	31.8046i	0.489919	−	0.871768i
$11$	17.8737	−	31.8046i	0.489919	−	0.871768i
$12$		0			0
$13$	−16.0519	+	11.6624i	−0.342461	+	0.248812i	−0.745699	−	0.666282i	$-0.767885\pi$
$13$	−16.0519	+	11.6624i	−0.342461	+	0.248812i	0.403238	+	0.915095i	$0.367885\pi$
$14$		0			0
$15$	10.6435	−	32.7574i	0.183210	−	0.563861i
$16$		0			0
$17$	−0.0229293	−	0.0166591i	−0.000327128	−	0.000237673i	0.587622	−	0.809136i	$-0.300064\pi$
$17$	−0.0229293	−	0.0166591i	−0.000327128	−	0.000237673i	−0.587949	+	0.808898i	$0.700064\pi$
$18$		0			0
$19$	−22.3778	−	68.8719i	−0.270202	−	0.831595i	−0.990449	−	0.137878i	$-0.955972\pi$
$19$	−22.3778	−	68.8719i	−0.270202	−	0.831595i	0.720248	−	0.693717i	$-0.244028\pi$
$20$		0			0
$21$	−55.9390			−0.581281
$22$		0			0
$23$	−92.3700			−0.837412			−0.418706	−	0.908122i	$-0.637516\pi$
$23$	−92.3700			−0.837412			−0.418706	+	0.908122i	$0.637516\pi$
$24$		0			0
$25$	−26.6839	−	82.1247i	−0.213472	−	0.656998i
$26$		0			0
$27$	−104.458	−	75.8930i	−0.744552	−	0.540949i
$28$		0			0
$29$	25.7455	−	79.2365i	0.164856	−	0.507374i	−0.834170	−	0.551508i	$-0.814053\pi$
$29$	25.7455	−	79.2365i	0.164856	−	0.507374i	0.999026	+	0.0441335i	$0.0140527\pi$
$30$		0			0
$31$	−139.196	+	101.132i	−0.806462	+	0.585929i	−0.912803	−	0.408401i	$-0.866087\pi$
$31$	−139.196	+	101.132i	−0.806462	+	0.585929i	0.106341	+	0.994330i	$0.466087\pi$
$32$		0			0
$33$	−198.184	−	39.7278i	−1.04543	−	0.209567i
$34$		0			0
$35$	50.7818	−	36.8951i	0.245248	−	0.178183i
$36$		0			0
$37$	55.1183	−	169.637i	0.244902	−	0.753732i	−0.750750	−	0.660586i	$-0.770308\pi$
$37$	55.1183	−	169.637i	0.244902	−	0.753732i	0.995652	−	0.0931458i	$-0.0296923\pi$
$38$		0			0
$39$	88.9324	+	64.6131i	0.365143	+	0.265292i
$40$		0			0
$41$	−72.8262	−	224.136i	−0.277404	−	0.853761i	−0.988573	−	0.150740i	$-0.951834\pi$
$41$	−72.8262	−	224.136i	−0.277404	−	0.853761i	0.711170	−	0.703020i	$-0.248166\pi$
$42$		0			0
$43$	69.3945			0.246106			0.123053	−	0.992400i	$-0.460731\pi$
$43$	69.3945			0.246106			0.123053	+	0.992400i	$0.460731\pi$
$44$		0			0
$45$	−22.9711			−0.0760962
$46$		0			0
$47$	133.810	+	411.825i	0.415281	+	1.27810i	0.912000	+	0.410191i	$0.134538\pi$
$47$	133.810	+	411.825i	0.415281	+	1.27810i	−0.496719	+	0.867911i	$0.665462\pi$
$48$		0			0
$49$	195.018	+	141.689i	0.568566	+	0.413088i
$50$		0			0
$51$	−0.0485233	+	0.149339i	−0.000133228	+	0.000410033i
$52$		0			0
$53$	485.316	−	352.603i	1.25780	−	0.913844i	0.259150	−	0.965837i	$-0.416557\pi$
$53$	485.316	−	352.603i	1.25780	−	0.913844i	0.998647	+	0.0519933i	$0.0165574\pi$
$54$		0			0
$55$	206.115	−	94.6487i	0.505319	−	0.232044i
$56$		0			0
$57$	−324.584	+	235.824i	−0.754249	+	0.547994i
$58$		0			0
$59$	112.856	−	347.336i	0.249028	−	0.766429i	−0.745920	−	0.666035i	$-0.767990\pi$
$59$	112.856	−	347.336i	0.249028	−	0.766429i	0.994948	−	0.100393i	$-0.0320101\pi$
$60$		0			0
$61$	554.647	+	402.975i	1.16418	+	0.845830i	0.990301	−	0.138937i	$-0.0443685\pi$
$61$	554.647	+	402.975i	1.16418	+	0.845830i	0.173883	+	0.984766i	$0.444368\pi$
$62$		0			0
$63$	11.5286	+	35.4814i	0.0230550	+	0.0709561i
$64$		0			0
$65$	−123.349			−0.235379
$66$		0			0
$67$	−224.941			−0.410164			−0.205082	−	0.978745i	$-0.565746\pi$
$67$	−224.941			−0.410164			−0.205082	+	0.978745i	$0.565746\pi$
$68$		0			0
$69$	158.142	+	486.711i	0.275914	+	0.849176i
$70$		0			0
$71$	−206.018	−	149.681i	−0.344364	−	0.250195i	0.402137	−	0.915580i	$-0.368268\pi$
$71$	−206.018	−	149.681i	−0.344364	−	0.250195i	−0.746501	+	0.665385i	$0.768268\pi$
$72$		0			0
$73$	−272.652	+	839.136i	−0.437144	+	1.34539i	0.453730	+	0.891139i	$0.350093\pi$
$73$	−272.652	+	839.136i	−0.437144	+	1.34539i	−0.890874	+	0.454251i	$0.849907\pi$
$74$		0			0
$75$	−387.043	+	281.203i	−0.595891	+	0.432940i
$76$		0			0
$77$	−249.639	−	270.865i	−0.369468	−	0.400883i
$78$		0			0
$79$	313.056	−	227.449i	0.445843	−	0.323924i	−0.342110	−	0.939660i	$-0.611141\pi$
$79$	313.056	−	227.449i	0.445843	−	0.323924i	0.787952	+	0.615736i	$0.211141\pi$
$80$		0			0
$81$	−251.883	+	775.217i	−0.345519	+	1.06340i
$82$		0			0
$83$	982.393	+	713.750i	1.29918	+	0.943906i	0.999947	−	0.0102750i	$-0.00327070\pi$
$83$	982.393	+	713.750i	1.29918	+	0.943906i	0.299229	+	0.954181i	$0.403271\pi$
$84$		0			0
$85$	−0.0544484	−	0.167575i	−6.94795e−5	−	0.000213836i
$86$		0			0
$87$	−461.586			−0.568819
$88$		0			0
$89$	−1236.77			−1.47300			−0.736500	−	0.676438i	$-0.763523\pi$
$89$	−1236.77			−1.47300			−0.736500	+	0.676438i	$0.763523\pi$
$90$		0			0
$91$	61.9059	+	190.527i	0.0713132	+	0.219479i
$92$		0			0
$93$	771.188	+	560.301i	0.859876	+	0.624737i
$94$		0			0
$95$	139.119	−	428.165i	0.150246	−	0.462408i
$96$		0			0
$97$	721.245	−	524.015i	0.754962	−	0.548512i	−0.142399	−	0.989809i	$-0.545482\pi$
$97$	721.245	−	524.015i	0.754962	−	0.548512i	0.897361	+	0.441297i	$0.145482\pi$
$98$		0			0
$99$	15.6453	+	133.893i	0.0158829	+	0.135926i
$100$		0			0
$101$	249.183	−	181.042i	0.245491	−	0.178360i	−0.458235	−	0.888831i	$-0.651518\pi$
$101$	249.183	−	181.042i	0.245491	−	0.178360i	0.703726	+	0.710471i	$0.251518\pi$
$102$		0			0
$103$	343.910	−	1058.45i	0.328995	−	1.01254i	−0.640610	−	0.767867i	$-0.721318\pi$
$103$	343.910	−	1058.45i	0.328995	−	1.01254i	0.969605	−	0.244676i	$-0.0786817\pi$
$104$		0			0
$105$	−281.346	−	204.410i	−0.261491	−	0.189985i
$106$		0			0
$107$	535.793	+	1649.00i	0.484085	+	1.48986i	0.833302	+	0.552818i	$0.186448\pi$
$107$	535.793	+	1649.00i	0.484085	+	1.48986i	−0.349217	+	0.937042i	$0.613552\pi$
$108$		0			0
$109$	1565.32			1.37550			0.687752	−	0.725946i	$-0.258598\pi$
$109$	1565.32			1.37550			0.687752	+	0.725946i	$0.258598\pi$
$110$		0			0
$111$	−988.205			−0.845011
$112$		0			0
$113$	202.758	+	624.025i	0.168795	+	0.519499i	0.999296	−	0.0375191i	$-0.0119455\pi$
$113$	202.758	+	624.025i	0.168795	+	0.519499i	−0.830501	+	0.557018i	$0.811945\pi$
$114$		0			0
$115$	−464.577	−	337.535i	−0.376713	−	0.273698i
$116$		0			0
$117$	22.6550	−	69.7248i	0.0179013	−	0.0550946i
$118$		0			0
$119$	−0.231512	+	0.168203i	−0.000178341	+	0.000129573i
$120$		0			0
$121$	−692.065	−	1136.93i	−0.519959	−	0.854191i
$122$		0			0
$123$	−1056.32	+	767.464i	−0.774353	+	0.562601i
$124$		0			0
$125$	406.028	−	1249.62i	0.290530	−	0.894159i
$126$		0			0
$127$	2159.14	+	1568.71i	1.50860	+	1.09606i	0.966792	+	0.255564i	$0.0822612\pi$
$127$	2159.14	+	1568.71i	1.50860	+	1.09606i	0.541811	+	0.840500i	$0.317739\pi$
$128$		0			0
$129$	−118.807	−	365.650i	−0.0810880	−	0.249563i
$130$		0			0
$131$	−694.820			−0.463410			−0.231705	−	0.972786i	$-0.574430\pi$
$131$	−694.820			−0.463410			−0.231705	+	0.972786i	$0.574430\pi$
$132$		0			0
$133$	−731.168			−0.476694
$134$		0			0
$135$	−248.047	−	763.411i	−0.158137	−	0.486696i
$136$		0			0
$137$	−2003.96	−	1455.96i	−1.24971	−	0.907964i	−0.251501	−	0.967857i	$-0.580924\pi$
$137$	−2003.96	−	1455.96i	−1.24971	−	0.907964i	−0.998205	+	0.0598929i	$0.980924\pi$
$138$		0			0
$139$	678.710	−	2088.85i	0.414154	−	1.27463i	−0.498851	−	0.866688i	$-0.666245\pi$
$139$	678.710	−	2088.85i	0.414154	−	1.27463i	0.913005	−	0.407947i	$-0.133755\pi$
$140$		0			0
$141$	1940.87	−	1410.13i	1.15923	−	0.842228i
$142$		0			0
$143$	84.0114	+	718.973i	0.0491286	+	0.420444i
$144$		0			0
$145$	419.030	−	304.443i	0.239990	−	0.174363i
$146$		0			0
$147$	412.699	−	1270.16i	0.231557	−	0.712659i
$148$		0			0
$149$	−2702.72	−	1963.64i	−1.48601	−	1.07965i	−0.975558	−	0.219740i	$-0.929479\pi$
$149$	−2702.72	−	1963.64i	−1.48601	−	1.07965i	−0.510449	−	0.859908i	$-0.670521\pi$
$150$		0			0
$151$	225.119	+	692.846i	0.121324	+	0.373398i	0.993213	−	0.116305i	$-0.0371052\pi$
$151$	225.119	+	692.846i	0.121324	+	0.373398i	−0.871889	+	0.489703i	$0.837105\pi$
$152$		0			0
$153$	0.104724			5.53362e−5
$154$		0			0
$155$	−1069.64			−0.554294
$156$		0			0
$157$	913.092	+	2810.21i	0.464157	+	1.42853i	0.860040	+	0.510227i	$0.170439\pi$
$157$	913.092	+	2810.21i	0.464157	+	1.42853i	−0.395883	+	0.918301i	$0.629561\pi$
$158$		0			0
$159$	−2688.80	−	1953.53i	−1.34110	−	0.974370i
$160$		0			0
$161$	−288.200	+	886.990i	−0.141077	+	0.434190i
$162$		0			0
$163$	−5.14015	+	3.73454i	−0.00246999	+	0.00179455i	−0.589020	−	0.808119i	$-0.700486\pi$
$163$	−5.14015	+	3.73454i	−0.00246999	+	0.00179455i	0.586550	+	0.809913i	$0.300486\pi$
$164$		0			0
$165$	−851.596	−	924.006i	−0.401798	−	0.435962i
$166$		0			0
$167$	−593.714	+	431.358i	−0.275107	+	0.199877i	−0.716781	−	0.697299i	$-0.754385\pi$
$167$	−593.714	+	431.358i	−0.275107	+	0.199877i	0.441673	+	0.897176i	$0.354385\pi$
$168$		0			0
$169$	−557.258	+	1715.06i	−0.253645	+	0.780639i
$170$		0			0
$171$	216.474	+	157.278i	0.0968082	+	0.0703353i
$172$		0			0
$173$	101.780	+	313.246i	0.0447294	+	0.137663i	0.970927	−	0.239375i	$-0.0769426\pi$
$173$	101.780	+	313.246i	0.0447294	+	0.137663i	−0.926198	+	0.377038i	$0.876943\pi$
$174$		0			0
$175$	−871.864			−0.376610
$176$		0			0
$177$	−2023.38			−0.859245
$178$		0			0
$179$	−825.515	−	2540.67i	−0.344703	−	1.06089i	−0.961743	−	0.273955i	$-0.911668\pi$
$179$	−825.515	−	2540.67i	−0.344703	−	1.06089i	0.617039	−	0.786932i	$-0.288332\pi$
$180$		0			0
$181$	1250.44	+	908.497i	0.513505	+	0.373083i	0.814152	−	0.580652i	$-0.197202\pi$
$181$	1250.44	+	908.497i	0.513505	+	0.373083i	−0.300647	+	0.953736i	$0.597202\pi$
$182$		0			0
$183$	1173.75	−	3612.43i	0.474131	−	1.45923i
$184$		0			0
$185$	897.098	−	651.780i	0.356519	−	0.259026i
$186$		0			0
$187$	−0.939668	+	0.431499i	−0.000367462	+	0.000168740i
$188$		0			0
$189$	−1054.68	+	766.272i	−0.405910	+	0.294911i
$190$		0			0
$191$	−366.453	+	1127.83i	−0.138825	+	0.427260i	−0.996165	−	0.0874900i	$-0.972115\pi$
$191$	−366.453	+	1127.83i	−0.138825	+	0.427260i	0.857340	+	0.514750i	$0.172115\pi$
$192$		0			0
$193$	1084.84	+	788.182i	0.404603	+	0.293962i	0.771413	−	0.636334i	$-0.219550\pi$
$193$	1084.84	+	788.182i	0.404603	+	0.293962i	−0.366810	+	0.930296i	$0.619550\pi$
$194$		0			0
$195$	211.180	+	649.946i	0.0775535	+	0.238685i
$196$		0			0
$197$	797.183			0.288309			0.144155	−	0.989555i	$-0.453954\pi$
$197$	797.183			0.288309			0.144155	+	0.989555i	$0.453954\pi$
$198$		0			0
$199$	−119.756			−0.0426597			−0.0213299	−	0.999772i	$-0.506790\pi$
$199$	−119.756			−0.0426597			−0.0213299	+	0.999772i	$0.506790\pi$
$200$		0			0
$201$	385.111	+	1185.25i	0.135142	+	0.415925i
$202$		0			0
$203$	−680.547	−	494.446i	−0.235296	−	0.170952i
$204$		0			0
$205$	452.748	−	1393.42i	0.154250	−	0.474734i
$206$		0			0
$207$	276.122	−	200.615i	0.0927141	−	0.0673608i
$208$		0			0
$209$	−2590.42	−	519.274i	−0.857335	−	0.171861i
$210$		0			0
$211$	856.848	−	622.536i	0.279563	−	0.203115i	−0.439164	−	0.898407i	$-0.644725\pi$
$211$	856.848	−	622.536i	0.279563	−	0.203115i	0.718727	+	0.695293i	$0.244725\pi$
$212$		0			0
$213$	−435.977	+	1341.80i	−0.140247	+	0.431636i
$214$		0			0
$215$	349.021	+	253.579i	0.110712	+	0.0804368i
$216$		0			0
$217$	536.825	+	1652.18i	0.167936	+	0.516853i
$218$		0			0
$219$	4888.32			1.50832
$220$		0			0
$221$	0.562344			0.000171165
$222$		0			0
$223$	1908.27	+	5873.04i	0.573036	+	1.76362i	0.642771	+	0.766058i	$0.277785\pi$
$223$	1908.27	+	5873.04i	0.573036	+	1.76362i	−0.0697353	+	0.997566i	$0.522215\pi$
$224$		0			0
$225$	258.130	+	187.542i	0.0764829	+	0.0555681i
$226$		0			0
$227$	1304.25	−	4014.07i	0.381348	−	1.17367i	−0.557747	−	0.830011i	$-0.688334\pi$
$227$	1304.25	−	4014.07i	0.381348	−	1.17367i	0.939095	−	0.343658i	$-0.111666\pi$
$228$		0			0
$229$	1989.97	−	1445.80i	0.574239	−	0.417209i	−0.262404	−	0.964958i	$-0.584515\pi$
$229$	1989.97	−	1445.80i	0.574239	−	0.417209i	0.836643	+	0.547749i	$0.184515\pi$
$230$		0			0
$231$	−999.835	+	1779.12i	−0.284781	+	0.506742i
$232$		0			0
$233$	1006.74	−	731.437i	0.283062	−	0.205657i	−0.437190	−	0.899369i	$-0.644026\pi$
$233$	1006.74	−	731.437i	0.283062	−	0.205657i	0.720252	+	0.693713i	$0.244026\pi$
$234$		0			0
$235$	−831.874	+	2560.24i	−0.230917	+	0.710689i
$236$		0			0
$237$	−1734.43	−	1260.13i	−0.475372	−	0.345378i
$238$		0			0
$239$	1076.65	+	3313.60i	0.291393	+	0.896815i	0.984409	+	0.175893i	$0.0562813\pi$
$239$	1076.65	+	3313.60i	0.291393	+	0.896815i	−0.693017	+	0.720922i	$0.743719\pi$
$240$		0			0
$241$	6857.39			1.83288			0.916439	−	0.400174i	$-0.131050\pi$
$241$	6857.39			1.83288			0.916439	+	0.400174i	$0.131050\pi$
$242$		0			0
$243$	1029.81			0.271862
$244$		0			0
$245$	463.094	+	1425.26i	0.120759	+	0.371658i
$246$		0			0
$247$	1162.42	+	844.545i	0.299445	+	0.217559i
$248$		0			0
$249$	2078.95	−	6398.34i	0.529108	−	1.62843i
$250$		0			0
$251$	−4574.79	+	3323.78i	−1.15043	+	0.835837i	−0.988538	−	0.150972i	$-0.951760\pi$
$251$	−4574.79	+	3323.78i	−1.15043	+	0.835837i	−0.161892	+	0.986808i	$0.551760\pi$
$252$		0			0
$253$	−1650.99	+	2937.79i	−0.410264	+	0.730029i
$254$		0			0
$255$	−0.789758	+	0.573793i	−0.000193947	+	0.000140911i
$256$		0			0
$257$	−1196.02	+	3680.98i	−0.290295	+	0.893437i	0.694466	+	0.719526i	$0.255641\pi$
$257$	−1196.02	+	3680.98i	−0.290295	+	0.893437i	−0.984761	+	0.173912i	$0.944359\pi$
$258$		0			0
$259$	−1456.98	−	1058.55i	−0.349545	−	0.253959i
$260$		0			0
$261$	95.1293	+	292.778i	0.0225607	+	0.0694348i
$262$		0			0
$263$	1016.12			0.238239			0.119119	−	0.992880i	$-0.461993\pi$
$263$	1016.12			0.238239			0.119119	+	0.992880i	$0.461993\pi$
$264$		0			0
$265$	3729.37			0.864504
$266$		0			0
$267$	2117.40	+	6516.70i	0.485330	+	1.49369i
$268$		0			0
$269$	−365.765	−	265.744i	−0.0829036	−	0.0602330i	0.545561	−	0.838071i	$-0.316316\pi$
$269$	−365.765	−	265.744i	−0.0829036	−	0.0602330i	−0.628465	+	0.777838i	$0.716316\pi$
$270$		0			0
$271$	−137.229	+	422.347i	−0.0307604	+	0.0946708i	−0.965258	−	0.261299i	$-0.915849\pi$
$271$	−137.229	+	422.347i	−0.0307604	+	0.0946708i	0.934498	+	0.355969i	$0.115849\pi$
$272$		0			0
$273$	897.927	−	652.382i	0.199066	−	0.144630i
$274$		0			0
$275$	−3088.88	−	619.197i	−0.677333	−	0.135778i
$276$		0			0
$277$	−6310.61	+	4584.93i	−1.36884	+	0.994518i	−0.371010	+	0.928629i	$0.620989\pi$
$277$	−6310.61	+	4584.93i	−1.36884	+	0.994518i	−0.997827	+	0.0658897i	$0.979011\pi$
$278$		0			0
$279$	196.455	−	604.628i	0.0421558	−	0.129742i
$280$		0			0
$281$	3846.65	+	2794.76i	0.816626	+	0.593314i	0.915744	−	0.401762i	$-0.131602\pi$
$281$	3846.65	+	2794.76i	0.816626	+	0.593314i	−0.0991178	+	0.995076i	$0.531602\pi$
$282$		0			0
$283$	1670.49	+	5141.25i	0.350885	+	1.07991i	0.958357	+	0.285573i	$0.0921838\pi$
$283$	1670.49	+	5141.25i	0.350885	+	1.07991i	−0.607472	+	0.794341i	$0.707816\pi$
$284$		0			0
$285$	−2494.24			−0.518407
$286$		0			0
$287$	−2379.51			−0.489400
$288$		0			0
$289$	−1518.20	−	4672.54i	−0.309017	−	0.951056i
$290$		0			0
$291$	−3995.92	−	2903.20i	−0.804965	−	0.584841i
$292$		0			0
$293$	1723.76	−	5305.18i	0.343696	−	1.05779i	−0.618582	−	0.785720i	$-0.712293\pi$
$293$	1723.76	−	5305.18i	0.343696	−	1.05779i	0.962278	−	0.272067i	$-0.0877074\pi$
$294$		0			0
$295$	1836.83	−	1334.54i	0.362524	−	0.263389i
$296$		0			0
$297$	−4280.79	+	1965.75i	−0.836352	+	0.384056i
$298$		0			0
$299$	1482.71	−	1077.25i	0.286781	−	0.208359i
$300$		0			0
$301$	216.515	−	666.366i	0.0414609	−	0.127604i
$302$		0			0
$303$	−1380.55	−	1003.03i	−0.261750	−	0.190173i
$304$		0			0
$305$	1317.07	+	4053.54i	0.247264	+	0.760999i
$306$		0			0
$307$	7248.81			1.34759			0.673797	−	0.738916i	$-0.264662\pi$
$307$	7248.81			1.34759			0.673797	+	0.738916i	$0.264662\pi$
$308$		0			0
$309$	−6165.90			−1.13517
$310$		0			0
$311$	−294.551	−	906.534i	−0.0537056	−	0.165289i	0.920606	−	0.390492i	$-0.127695\pi$
$311$	−294.551	−	906.534i	−0.0537056	−	0.165289i	−0.974312	+	0.225204i	$0.927695\pi$
$312$		0			0
$313$	−2722.92	−	1978.32i	−0.491721	−	0.357256i	0.314125	−	0.949382i	$-0.398289\pi$
$313$	−2722.92	−	1978.32i	−0.491721	−	0.357256i	−0.805846	+	0.592126i	$0.798289\pi$
$314$		0			0
$315$	−71.6713	+	220.582i	−0.0128197	+	0.0394551i
$316$		0			0
$317$	−7121.72	+	5174.23i	−1.26182	+	0.916763i	−0.998845	−	0.0480404i	$-0.984702\pi$
$317$	−7121.72	+	5174.23i	−1.26182	+	0.916763i	−0.262971	+	0.964804i	$0.584702\pi$
$318$		0			0
$319$	−2059.92	−	2235.07i	−0.361547	−	0.392288i
$320$		0			0
$321$	7771.52	−	5646.34i	1.35129	−	0.981770i
$322$		0			0
$323$	−0.634238	+	1.95198i	−0.000109257	+	0.000336258i
$324$		0			0
$325$	1386.10	+	1007.06i	0.236575	+	0.171882i
$326$		0			0
$327$	−2679.90	−	8247.87i	−0.453207	−	1.39483i
$328$		0			0
$329$	4372.07			0.732645
$330$		0			0
$331$	−1884.62			−0.312955			−0.156478	−	0.987682i	$-0.550014\pi$
$331$	−1884.62			−0.312955			−0.156478	+	0.987682i	$0.550014\pi$
$332$		0			0
$333$	203.661	+	626.805i	0.0335152	+	0.103149i
$334$		0			0
$335$	−1131.35	−	821.972i	−0.184514	−	0.134057i
$336$		0			0
$337$	611.773	−	1882.84i	0.0988883	−	0.304347i	−0.889359	−	0.457209i	$-0.848849\pi$
$337$	611.773	−	1882.84i	0.0988883	−	0.304347i	0.988248	+	0.152862i	$0.0488491\pi$
$338$		0			0
$339$	2940.95	−	2136.72i	0.471181	−	0.342333i
$340$		0			0
$341$	728.516	+	6234.67i	0.115693	+	0.990106i
$342$		0			0
$343$	4770.82	−	3466.21i	0.751021	−	0.545649i
$344$		0			0
$345$	−983.141	+	3025.80i	−0.153422	+	0.472184i
$346$		0			0
$347$	−6908.05	−	5018.99i	−1.06871	−	0.776466i	−0.0930333	−	0.995663i	$-0.529656\pi$
$347$	−6908.05	−	5018.99i	−1.06871	−	0.776466i	−0.975681	+	0.219197i	$0.929656\pi$
$348$		0			0
$349$	−291.889	−	898.341i	−0.0447692	−	0.137785i	0.926173	−	0.377098i	$-0.123078\pi$
$349$	−291.889	−	898.341i	−0.0447692	−	0.137785i	−0.970943	+	0.239312i	$0.923078\pi$
$350$		0			0
$351$	2561.84			0.389575
$352$		0			0
$353$	3709.02			0.559239			0.279619	−	0.960111i	$-0.409792\pi$
$353$	3709.02			0.559239			0.279619	+	0.960111i	$0.409792\pi$
$354$		0			0
$355$	−489.213	−	1505.64i	−0.0731402	−	0.225102i
$356$		0			0
$357$	1.28265	+	0.931896i	0.000190153	+	0.000138155i
$358$		0			0
$359$	2925.40	−	9003.47i	0.430075	−	1.32363i	−0.467975	−	0.883742i	$-0.655016\pi$
$359$	2925.40	−	9003.47i	0.430075	−	1.32363i	0.898050	−	0.439893i	$-0.144984\pi$
$360$		0			0
$361$	1306.47	−	949.209i	0.190476	−	0.138389i
$362$		0			0
$363$	−4805.79	+	5593.07i	−0.694872	+	0.808705i
$364$		0			0
$365$	−4437.64	+	3224.14i	−0.636375	+	0.462354i
$366$		0			0
$367$	−727.199	+	2238.09i	−0.103432	+	0.318330i	−0.989359	−	0.145494i	$-0.953523\pi$
$367$	−727.199	+	2238.09i	−0.103432	+	0.318330i	0.885927	+	0.463824i	$0.153523\pi$
$368$		0			0
$369$	704.492	+	511.843i	0.0993886	+	0.0722100i
$370$		0			0
$371$	−1871.68	−	5760.43i	−0.261921	−	0.806109i
$372$		0			0
$373$	1447.21			0.200894			0.100447	−	0.994942i	$-0.467973\pi$
$373$	1447.21			0.200894			0.100447	+	0.994942i	$0.467973\pi$
$374$		0			0
$375$	−7279.59			−1.00244
$376$		0			0
$377$	510.822	+	1572.15i	0.0697843	+	0.214774i
$378$		0			0
$379$	6797.44	+	4938.63i	0.921269	+	0.669341i	0.943840	−	0.330404i	$-0.107185\pi$
$379$	6797.44	+	4938.63i	0.921269	+	0.669341i	−0.0225706	+	0.999745i	$0.507185\pi$
$380$		0			0
$381$	4569.19	−	14062.5i	0.614401	−	1.89093i
$382$		0			0
$383$	5773.30	−	4194.55i	0.770240	−	0.559612i	−0.131794	−	0.991277i	$-0.542074\pi$
$383$	5773.30	−	4194.55i	0.770240	−	0.559612i	0.902034	+	0.431665i	$0.142074\pi$
$384$		0			0
$385$	−265.779	−	2274.54i	−0.0351827	−	0.301095i
$386$		0			0
$387$	−207.441	+	150.715i	−0.0272476	+	0.0197966i
$388$		0			0
$389$	3619.44	−	11139.5i	0.471755	−	1.45191i	−0.378529	−	0.925589i	$-0.623570\pi$
$389$	3619.44	−	11139.5i	0.471755	−	1.45191i	0.850284	−	0.526324i	$-0.176430\pi$
$390$		0			0
$391$	2.11798	+	1.53881i	0.000273941	+	0.000199030i
$392$		0			0
$393$	1189.57	+	3661.11i	0.152686	+	0.469920i
$394$		0			0
$395$	2405.66			0.306435
$396$		0			0
$397$	−13000.5			−1.64352			−0.821759	−	0.569835i	$-0.807007\pi$
$397$	−13000.5			−1.64352			−0.821759	+	0.569835i	$0.807007\pi$
$398$		0			0
$399$	1251.79	+	3852.63i	0.157063	+	0.483390i
$400$		0			0
$401$	−8948.83	−	6501.70i	−1.11442	−	0.809675i	−0.131067	−	0.991373i	$-0.541840\pi$
$401$	−8948.83	−	6501.70i	−1.11442	−	0.809675i	−0.983354	+	0.181699i	$0.941840\pi$
$402$		0			0
$403$	1054.92	−	3246.71i	0.130395	−	0.401316i
$404$		0			0
$405$	−4099.62	+	2978.55i	−0.502992	+	0.365445i
$406$		0			0
$407$	−4410.06	−	4785.04i	−0.537097	−	0.582766i
$408$		0			0
$409$	7556.94	−	5490.44i	0.913610	−	0.663776i	−0.0283153	−	0.999599i	$-0.509014\pi$
$409$	7556.94	−	5490.44i	0.913610	−	0.663776i	0.941925	+	0.335823i	$0.109014\pi$
$410$		0			0
$411$	−4240.79	+	13051.8i	−0.508961	+	1.56642i
$412$		0			0
$413$	−2983.20	−	2167.42i	−0.355433	−	0.258237i
$414$		0			0
$415$	2332.81	+	7179.64i	0.275935	+	0.849240i
$416$		0			0
$417$	−12168.5			−1.42900
$418$		0			0
$419$	−2181.92			−0.254400			−0.127200	−	0.991877i	$-0.540599\pi$
$419$	−2181.92			−0.254400			−0.127200	+	0.991877i	$0.540599\pi$
$420$		0			0
$421$	1084.16	+	3336.70i	0.125508	+	0.386273i	0.993993	−	0.109442i	$-0.0349063\pi$
$421$	1084.16	+	3336.70i	0.125508	+	0.386273i	−0.868486	+	0.495714i	$0.834906\pi$
$422$		0			0
$423$	−1294.42	−	940.454i	−0.148787	−	0.108100i
$424$		0			0
$425$	−0.756282	+	2.32760i	−8.63178e−5	+	0.000265659i
$426$		0			0
$427$	5600.13	−	4068.73i	0.634682	−	0.461123i
$428$		0			0
$429$	3644.54	−	1673.59i	0.410163	−	0.188348i
$430$		0			0
$431$	−10405.4	+	7559.96i	−1.16290	+	0.844896i	−0.990142	−	0.140068i	$-0.955268\pi$
$431$	−10405.4	+	7559.96i	−1.16290	+	0.844896i	−0.172758	+	0.984964i	$0.555268\pi$
$432$		0			0
$433$	2519.25	−	7753.44i	0.279601	−	0.860523i	−0.708364	−	0.705847i	$-0.750567\pi$
$433$	2519.25	−	7753.44i	0.279601	−	0.860523i	0.987965	−	0.154676i	$-0.0494334\pi$
$434$		0			0
$435$	−2321.56	−	1686.71i	−0.255885	−	0.185912i
$436$		0			0
$437$	2067.04	+	6361.70i	0.226270	+	0.696388i
$438$		0			0
$439$	−1617.22			−0.175821			−0.0879107	−	0.996128i	$-0.528019\pi$
$439$	−1617.22			−0.175821			−0.0879107	+	0.996128i	$0.528019\pi$
$440$		0			0
$441$	−890.698			−0.0961773
$442$		0			0
$443$	−1466.63	−	4513.83i	−0.157295	−	0.484105i	0.841091	−	0.540893i	$-0.181914\pi$
$443$	−1466.63	−	4513.83i	−0.157295	−	0.484105i	−0.998386	+	0.0567889i	$0.981914\pi$
$444$		0			0
$445$	−6220.34	−	4519.34i	−0.662635	−	0.481432i
$446$		0			0
$447$	−5719.51	+	17602.8i	−0.605198	+	1.86261i
$448$		0			0
$449$	−5417.86	+	3936.30i	−0.569453	+	0.413732i	−0.834907	−	0.550392i	$-0.814478\pi$
$449$	−5417.86	+	3936.30i	−0.569453	+	0.413732i	0.265453	+	0.964124i	$0.414478\pi$
$450$		0			0
$451$	−8430.23	−	1689.92i	−0.880186	−	0.176442i
$452$		0			0
$453$	3265.29	−	2372.37i	0.338668	−	0.246057i
$454$		0			0
$455$	−384.858	+	1184.47i	−0.0396537	+	0.122042i
$456$		0			0
$457$	8835.61	+	6419.44i	0.904403	+	0.657087i	0.939593	−	0.342293i	$-0.111204\pi$
$457$	8835.61	+	6419.44i	0.904403	+	0.657087i	−0.0351900	+	0.999381i	$0.511204\pi$
$458$		0			0
$459$	1.13084	+	3.48035i	0.000114995	+	0.000353919i
$460$		0			0
$461$	10627.0			1.07365			0.536823	−	0.843695i	$-0.319624\pi$
$461$	10627.0			1.07365			0.536823	+	0.843695i	$0.319624\pi$
$462$		0			0
$463$	−3046.02			−0.305746			−0.152873	−	0.988246i	$-0.548853\pi$
$463$	−3046.02			−0.305746			−0.152873	+	0.988246i	$0.548853\pi$
$464$		0			0
$465$	1831.28	+	5636.09i	0.182631	+	0.562080i
$466$		0			0
$467$	6375.92	+	4632.37i	0.631782	+	0.459017i	0.857017	−	0.515288i	$-0.172315\pi$
$467$	6375.92	+	4632.37i	0.631782	+	0.459017i	−0.225235	+	0.974304i	$0.572315\pi$
$468$		0			0
$469$	−701.832	+	2160.02i	−0.0690993	+	0.212666i
$470$		0			0
$471$	13244.1	−	9622.42i	1.29566	−	0.941354i
$472$		0			0
$473$	1240.33	−	2207.06i	0.120572	−	0.214547i
$474$		0			0
$475$	−5058.96	+	3675.55i	−0.488676	+	0.355044i
$476$		0			0
$477$	−684.955	+	2108.08i	−0.0657483	+	0.202352i
$478$		0			0
$479$	10325.6	+	7501.99i	0.984945	+	0.715605i	0.958808	−	0.284054i	$-0.0916794\pi$
$479$	10325.6	+	7501.99i	0.984945	+	0.715605i	0.0261371	+	0.999658i	$0.491679\pi$
$480$		0			0
$481$	1093.61	+	3365.80i	0.103668	+	0.319059i
$482$		0			0
$483$	5167.09			0.486772
$484$		0			0
$485$	5542.35			0.518897
$486$		0			0
$487$	1324.80	+	4077.31i	0.123270	+	0.379385i	0.993582	−	0.113115i	$-0.0360830\pi$
$487$	1324.80	+	4077.31i	0.123270	+	0.379385i	−0.870312	+	0.492500i	$0.836083\pi$
$488$		0			0
$489$	28.4780	+	20.6905i	0.00263358	+	0.00191341i
$490$		0			0
$491$	534.577	−	1645.26i	0.0491347	−	0.151221i	−0.923479	−	0.383649i	$-0.874667\pi$
$491$	534.577	−	1645.26i	0.0491347	−	0.151221i	0.972614	+	0.232428i	$0.0746671\pi$
$492$		0			0
$493$	−1.91034	+	1.38794i	−0.000174518	+	0.000126795i
$494$		0			0
$495$	−410.577	+	730.586i	−0.0372810	+	0.0663382i
$496$		0			0
$497$	−2080.11	+	1511.29i	−0.187738	+	0.136399i
$498$		0			0
$499$	4096.75	−	12608.5i	0.367526	−	1.13113i	−0.580857	−	0.814005i	$-0.697283\pi$
$499$	4096.75	−	12608.5i	0.367526	−	1.13113i	0.948384	−	0.317125i	$-0.102717\pi$
$500$		0			0
$501$	3289.35	+	2389.86i	0.293328	+	0.213116i
$502$		0			0
$503$	−40.7844	−	125.521i	−0.00361528	−	0.0111267i	0.949233	−	0.314575i	$-0.101862\pi$
$503$	−40.7844	−	125.521i	−0.00361528	−	0.0111267i	−0.952848	+	0.303448i	$0.901862\pi$
$504$		0			0
$505$	1914.82			0.168730
$506$		0			0
$507$	9990.98			0.875177
$508$		0			0
$509$	2524.36	+	7769.18i	0.219824	+	0.676548i	0.998776	+	0.0494645i	$0.0157515\pi$
$509$	2524.36	+	7769.18i	0.219824	+	0.676548i	−0.778952	+	0.627083i	$0.784249\pi$
$510$		0			0
$511$	7207.17	+	5236.32i	0.623927	+	0.453309i
$512$		0			0
$513$	−2889.36	+	8892.53i	−0.248671	+	0.765331i
$514$		0			0
$515$	5597.44	−	4066.78i	0.478937	−	0.347968i
$516$		0			0
$517$	15489.6	+	3105.04i	1.31766	+	0.264138i
$518$		0			0
$519$	1476.29	−	1072.59i	0.124859	−	0.0907153i
$520$		0			0
$521$	782.119	−	2407.12i	0.0657683	−	0.202414i	−0.912772	−	0.408469i	$-0.866063\pi$
$521$	782.119	−	2407.12i	0.0657683	−	0.202414i	0.978540	+	0.206055i	$0.0660627\pi$
$522$		0			0
$523$	−1261.68	−	916.661i	−0.105486	−	0.0766401i	0.533792	−	0.845616i	$-0.320767\pi$
$523$	−1261.68	−	916.661i	−0.105486	−	0.0766401i	−0.639278	+	0.768976i	$0.720767\pi$
$524$		0			0
$525$	1492.67	+	4593.98i	0.124087	+	0.381900i
$526$		0			0
$527$	4.87644			0.000403076
$528$		0			0
$529$	−3634.78			−0.298741
$530$		0			0
$531$	417.002	+	1283.40i	0.0340798	+	0.104887i
$532$		0			0
$533$	3782.96	+	2748.48i	0.307426	+	0.223358i
$534$		0			0
$535$	−3330.93	+	10251.6i	−0.269175	+	0.828437i
$536$		0			0
$537$	−11973.9	+	8699.51i	−0.962216	+	0.699091i
$538$		0			0
$539$	7992.05	−	3669.98i	0.638668	−	0.293278i
$540$		0			0
$541$	−12006.5	+	8723.20i	−0.954155	+	0.693234i	−0.951786	−	0.306763i	$-0.900754\pi$
$541$	−12006.5	+	8723.20i	−0.954155	+	0.693234i	−0.00236886	+	0.999997i	$0.500754\pi$
$542$		0			0
$543$	2646.19	−	8144.14i	0.209132	−	0.643643i
$544$		0			0
$545$	7872.78	+	5719.91i	0.618776	+	0.449567i
$546$		0			0
$547$	−1385.68	−	4264.69i	−0.108314	−	0.333355i	0.882180	−	0.470912i	$-0.156075\pi$
$547$	−1385.68	−	4264.69i	−0.108314	−	0.333355i	−0.990494	+	0.137557i	$0.956075\pi$
$548$		0			0
$549$	−2533.21			−0.196931
$550$		0			0
$551$	−6033.30			−0.466474
$552$		0			0
$553$	−1207.34	−	3715.80i	−0.0928411	−	0.285736i
$554$		0			0
$555$	−4970.20	−	3611.06i	−0.380132	−	0.276182i
$556$		0			0
$557$	1642.68	−	5055.66i	0.124960	−	0.384587i	−0.868934	−	0.494928i	$-0.835194\pi$
$557$	1642.68	−	5055.66i	0.124960	−	0.384587i	0.993894	+	0.110341i	$0.0351943\pi$
$558$		0			0
$559$	−1113.91	+	809.305i	−0.0842817	+	0.0612343i
$560$		0			0
$561$	3.88239	+	4.21250i	0.000292183	+	0.000317027i
$562$		0			0
$563$	3723.62	−	2705.37i	0.278742	−	0.202518i	−0.439626	−	0.898181i	$-0.644889\pi$
$563$	3723.62	−	2705.37i	0.278742	−	0.202518i	0.718369	+	0.695663i	$0.244889\pi$
$564$		0			0
$565$	−1260.51	+	3879.46i	−0.0938587	+	0.288867i
$566$		0			0
$567$	6658.19	+	4837.46i	0.493153	+	0.358296i
$568$		0			0
$569$	2389.41	+	7353.85i	0.176045	+	0.541809i	0.999680	−	0.0253108i	$-0.00805752\pi$
$569$	2389.41	+	7353.85i	0.176045	+	0.541809i	−0.823635	+	0.567120i	$0.808058\pi$
$570$		0			0
$571$	−18830.2			−1.38007			−0.690033	−	0.723778i	$-0.742404\pi$
$571$	−18830.2			−1.38007			−0.690033	+	0.723778i	$0.742404\pi$
$572$		0			0
$573$	6570.07			0.479003
$574$		0			0
$575$	2464.80	+	7585.86i	0.178764	+	0.550178i
$576$		0			0
$577$	−11249.0	−	8172.86i	−0.811614	−	0.589672i	0.102684	−	0.994714i	$-0.467257\pi$
$577$	−11249.0	−	8172.86i	−0.811614	−	0.589672i	−0.914298	+	0.405042i	$0.867257\pi$
$578$		0			0
$579$	2295.75	−	7065.58i	0.164781	−	0.507142i
$580$		0			0
$581$	9918.96	−	7206.55i	0.708275	−	0.514592i
$582$		0			0
$583$	−2540.02	−	21737.6i	−0.180441	−	1.54422i
$584$		0			0
$585$	368.729	−	267.897i	0.0260600	−	0.0189337i
$586$		0			0
$587$	−7908.73	+	24340.6i	−0.556096	+	1.71149i	0.136937	+	0.990580i	$0.456274\pi$
$587$	−7908.73	+	24340.6i	−0.556096	+	1.71149i	−0.693032	+	0.720907i	$0.743726\pi$
$588$		0			0
$589$	10080.0	+	7323.58i	0.705163	+	0.512331i
$590$		0			0
$591$	−1364.82	−	4200.47i	−0.0949933	−	0.292359i
$592$		0			0
$593$	−14766.2			−1.02256			−0.511279	−	0.859415i	$-0.670828\pi$
$593$	−14766.2			−1.02256			−0.511279	+	0.859415i	$0.670828\pi$
$594$		0			0
$595$	−1.77903			−0.000122577
$596$		0			0
$597$	205.028	+	631.012i	0.0140557	+	0.0432590i
$598$		0			0
$599$	−1515.41	−	1101.01i	−0.103369	−	0.0751020i	0.534900	−	0.844915i	$-0.320349\pi$
$599$	−1515.41	−	1101.01i	−0.103369	−	0.0751020i	−0.638269	+	0.769813i	$0.720349\pi$
$600$		0			0
$601$	−528.913	+	1627.83i	−0.0358982	+	0.110483i	−0.967400	−	0.253254i	$-0.918499\pi$
$601$	−528.913	+	1627.83i	−0.0358982	+	0.110483i	0.931502	+	0.363737i	$0.118499\pi$
$602$		0			0
$603$	672.419	−	488.541i	0.0454113	−	0.0329932i
$604$		0			0
$605$	673.764	−	8247.12i	0.0452767	−	0.554204i
$606$		0			0
$607$	−10732.2	+	7797.37i	−0.717635	+	0.521393i	−0.885628	−	0.464396i	$-0.846272\pi$
$607$	−10732.2	+	7797.37i	−0.717635	+	0.521393i	0.167993	+	0.985788i	$0.446272\pi$
$608$		0			0
$609$	−1440.18	+	4432.41i	−0.0958276	+	0.294927i
$610$		0			0
$611$	−6950.76	−	5050.02i	−0.460225	−	0.334373i
$612$		0			0
$613$	−7781.79	−	23949.9i	−0.512730	−	1.57802i	−0.787374	−	0.616476i	$-0.788560\pi$
$613$	−7781.79	−	23949.9i	−0.512730	−	1.57802i	0.274644	−	0.961546i	$-0.411440\pi$
$614$		0			0
$615$	−8117.23			−0.532225
$616$		0			0
$617$	−4896.84			−0.319513			−0.159756	−	0.987156i	$-0.551071\pi$
$617$	−4896.84			−0.319513			−0.159756	+	0.987156i	$0.551071\pi$
$618$		0			0
$619$	909.502	+	2799.16i	0.0590565	+	0.181757i	0.976233	−	0.216724i	$-0.0695373\pi$
$619$	909.502	+	2799.16i	0.0590565	+	0.181757i	−0.917176	+	0.398482i	$0.869537\pi$
$620$		0			0
$621$	9648.77	+	7010.24i	0.623497	+	0.452997i
$622$		0			0
$623$	−3858.79	+	11876.1i	−0.248153	+	0.763736i
$624$		0			0
$625$	−2123.98	+	1543.16i	−0.135935	+	0.0987625i
$626$		0			0
$627$	1698.79	+	14538.3i	0.108203	+	0.926003i
$628$		0			0
$629$	−4.08983	+	2.97143i	−0.000259256	+	0.000188361i
$630$		0			0
$631$	9424.29	−	29005.0i	0.594572	−	1.82990i	0.0377276	−	0.999288i	$-0.487988\pi$
$631$	9424.29	−	29005.0i	0.594572	−	1.82990i	0.556845	−	0.830617i	$-0.312012\pi$
$632$		0			0
$633$	−4747.20	−	3449.04i	−0.298079	−	0.216567i
$634$		0			0
$635$	5127.13	+	15779.7i	0.320416	+	0.986138i
$636$		0			0
$637$	−4782.84			−0.297493
$638$		0			0
$639$	940.936			0.0582517
$640$		0			0
$641$	−7776.77	−	23934.4i	−0.479195	−	1.47481i	−0.840215	−	0.542253i	$-0.817571\pi$
$641$	−7776.77	−	23934.4i	−0.479195	−	1.47481i	0.361020	−	0.932558i	$-0.382429\pi$
$642$		0			0
$643$	−4987.62	−	3623.72i	−0.305898	−	0.222248i	0.424236	−	0.905552i	$-0.360543\pi$
$643$	−4987.62	−	3623.72i	−0.305898	−	0.222248i	−0.730135	+	0.683303i	$0.760543\pi$
$644$		0			0
$645$	738.601	−	2273.18i	0.0450890	−	0.138770i
$646$		0			0
$647$	−10522.1	+	7644.77i	−0.639362	+	0.464524i	−0.859631	−	0.510915i	$-0.829307\pi$
$647$	−10522.1	+	7644.77i	−0.639362	+	0.464524i	0.220269	+	0.975439i	$0.429307\pi$
$648$		0			0
$649$	−9029.73	−	9797.51i	−0.546144	−	0.592582i
$650$		0			0
$651$	7786.49	−	5657.21i	0.468781	−	0.340589i
$652$		0			0
$653$	5688.39	−	17507.1i	0.340894	−	1.04917i	−0.622851	−	0.782341i	$-0.714026\pi$
$653$	5688.39	−	17507.1i	0.340894	−	1.04917i	0.963745	−	0.266824i	$-0.0859744\pi$
$654$		0			0
$655$	−3494.61	−	2538.98i	−0.208467	−	0.151460i
$656$		0			0
$657$	−1007.44	−	3100.60i	−0.0598237	−	0.184118i
$658$		0			0
$659$	13817.0			0.816745			0.408372	−	0.912815i	$-0.366096\pi$
$659$	13817.0			0.816745			0.408372	+	0.912815i	$0.366096\pi$
$660$		0			0
$661$	−4130.31			−0.243042			−0.121521	−	0.992589i	$-0.538777\pi$
$661$	−4130.31			−0.243042			−0.121521	+	0.992589i	$0.538777\pi$
$662$		0			0
$663$	−0.962761	−	2.96307i	−5.63960e−5	−	0.000173569i
$664$		0			0
$665$	−3677.42	−	2671.80i	−0.214443	−	0.155802i
$666$		0			0
$667$	−2378.11	+	7319.08i	−0.138052	+	0.424881i
$668$		0			0
$669$	27678.9	−	20109.9i	1.59959	−	1.16217i
$670$		0			0
$671$	22730.0	−	10437.7i	1.30772	−	0.600511i
$672$		0			0
$673$	−7437.64	+	5403.76i	−0.426003	+	0.309509i	−0.780049	−	0.625719i	$-0.784806\pi$
$673$	−7437.64	+	5403.76i	−0.426003	+	0.309509i	0.354046	+	0.935228i	$0.384806\pi$
$674$		0			0
$675$	−3445.35	+	10603.7i	−0.196462	+	0.604646i
$676$		0			0
$677$	−3603.19	−	2617.87i	−0.204552	−	0.148616i	0.480793	−	0.876834i	$-0.340349\pi$
$677$	−3603.19	−	2617.87i	−0.204552	−	0.148616i	−0.685345	+	0.728218i	$0.740349\pi$
$678$		0			0
$679$	−2781.56	−	8560.76i	−0.157211	−	0.483847i
$680$		0			0
$681$	−23383.6			−1.31580
$682$		0			0
$683$	12898.6			0.722620			0.361310	−	0.932446i	$-0.382330\pi$
$683$	12898.6			0.722620			0.361310	+	0.932446i	$0.382330\pi$
$684$		0			0
$685$	−4758.63	−	14645.6i	−0.265428	−	0.816902i
$686$		0			0
$687$	−11025.0	−	8010.15i	−0.612272	−	0.444842i
$688$		0			0
$689$	−3678.05	+	11319.9i	−0.203371	+	0.625912i
$690$		0			0
$691$	−23583.5	+	17134.4i	−1.29835	+	0.943306i	−0.999938	−	0.0111312i	$-0.996457\pi$
$691$	−23583.5	+	17134.4i	−1.29835	+	0.943306i	−0.298411	+	0.954437i	$0.596457\pi$
$692$		0			0
$693$	1334.53	+	267.519i	0.0731523	+	0.0146641i
$694$		0			0
$695$	11046.6	−	8025.82i	0.602908	−	0.438038i
$696$		0			0
$697$	−2.06406	+	6.35252i	−0.000112169	+	0.000345221i
$698$		0			0
$699$	−5577.63	−	4052.38i	−0.301810	−	0.219278i
$700$		0			0
$701$	−47.7400	−	146.929i	−0.00257220	−	0.00791642i	0.949762	−	0.312973i	$-0.101325\pi$
$701$	−47.7400	−	146.929i	−0.00257220	−	0.00791642i	−0.952334	+	0.305056i	$0.901325\pi$
$702$		0			0
$703$	−12916.6			−0.692973
$704$		0			0
$705$	14914.5			0.796755
$706$		0			0
$707$	−961.001	−	2957.66i	−0.0511204	−	0.157333i
$708$		0			0
$709$	15193.4	+	11038.6i	0.804794	+	0.584717i	0.912317	−	0.409485i	$-0.134292\pi$
$709$	15193.4	+	11038.6i	0.804794	+	0.584717i	−0.107522	+	0.994203i	$0.534292\pi$
$710$		0			0
$711$	−441.834	+	1359.83i	−0.0233053	+	0.0717264i
$712$		0			0
$713$	12857.5	−	9341.54i	0.675341	−	0.490664i
$714$		0			0
$715$	−2204.71	+	3923.08i	−0.115317	+	0.205196i
$716$		0			0
$717$	15616.5	−	11346.1i	0.813403	−	0.590972i
$718$		0			0
$719$	3373.36	−	10382.1i	0.174972	−	0.538509i	−0.824660	−	0.565629i	$-0.808634\pi$
$719$	3373.36	−	10382.1i	0.174972	−	0.538509i	0.999632	+	0.0271198i	$0.00863355\pi$
$720$		0			0
$721$	−9090.80	−	6604.85i	−0.469569	−	0.341162i
$722$		0			0
$723$	−11740.2	−	36132.6i	−0.603904	−	1.85862i
$724$		0			0
$725$	−7194.27			−0.368536
$726$		0			0
$727$	−19277.1			−0.983424			−0.491712	−	0.870758i	$-0.663629\pi$
$727$	−19277.1			−0.983424			−0.491712	+	0.870758i	$0.663629\pi$
$728$		0			0
$729$	5037.76	+	15504.6i	0.255945	+	0.787717i
$730$		0			0
$731$	−1.59117	−	1.15605i	−8.05083e−5	−	5.84927e-5i
$732$		0			0
$733$	−10680.4	+	32870.8i	−0.538183	+	1.65636i	0.198487	+	0.980104i	$0.436397\pi$
$733$	−10680.4	+	32870.8i	−0.538183	+	1.65636i	−0.736669	+	0.676253i	$0.763603\pi$
$734$		0			0
$735$	6717.04	−	4880.21i	0.337091	−	0.244911i
$736$		0			0
$737$	−4020.52	+	7154.17i	−0.200947	+	0.357568i
$738$		0			0
$739$	15484.8	−	11250.4i	0.770796	−	0.560016i	−0.131406	−	0.991329i	$-0.541949\pi$
$739$	15484.8	−	11250.4i	0.770796	−	0.560016i	0.902203	+	0.431312i	$0.141949\pi$
$740$		0			0
$741$	2459.92	−	7570.84i	0.121953	−	0.375333i
$742$		0			0
$743$	14722.8	+	10696.7i	0.726953	+	0.528163i	0.888598	−	0.458686i	$-0.151680\pi$
$743$	14722.8	+	10696.7i	0.726953	+	0.528163i	−0.161645	+	0.986849i	$0.551680\pi$
$744$		0			0
$745$	−6417.92	−	19752.3i	−0.315616	−	0.971368i
$746$		0			0
$747$	−4486.84			−0.219765
$748$		0			0
$749$	17506.4			0.854031
$750$		0			0
$751$	−7756.96	−	23873.5i	−0.376905	−	1.15999i	−0.942185	−	0.335094i	$-0.891232\pi$
$751$	−7756.96	−	23873.5i	−0.376905	−	1.15999i	0.565280	−	0.824899i	$-0.308768\pi$
$752$		0			0
$753$	25345.7	+	18414.7i	1.22663	+	0.891196i
$754$		0			0
$755$	−1399.53	+	4307.31i	−0.0674623	+	0.207628i
$756$		0			0
$757$	−24907.3	+	18096.2i	−1.19587	+	0.868847i	−0.993872	−	0.110539i	$-0.964742\pi$
$757$	−24907.3	+	18096.2i	−1.19587	+	0.868847i	−0.201994	+	0.979387i	$0.564742\pi$
$758$		0			0
$759$	18306.2	+	3669.66i	0.875459	+	0.175494i
$760$		0			0
$761$	−18579.9	+	13499.1i	−0.885048	+	0.643025i	−0.934582	−	0.355747i	$-0.884226\pi$
$761$	−18579.9	+	13499.1i	−0.885048	+	0.643025i	0.0495340	+	0.998772i	$0.484226\pi$
$762$		0			0
$763$	4883.88	−	15031.1i	0.231728	−	0.713186i
$764$		0			0
$765$	0.526712	+	0.382679i	2.48932e−5	+	1.80860e-5i
$766$		0			0
$767$	2239.21	+	6891.57i	0.105415	+	0.324433i
$768$		0			0
$769$	28729.3			1.34721			0.673605	−	0.739091i	$-0.264745\pi$
$769$	28729.3			1.34721			0.673605	+	0.739091i	$0.264745\pi$
$770$		0			0
$771$	21443.3			1.00164
$772$		0			0
$773$	−5946.90	−	18302.7i	−0.276708	−	0.851620i	−0.988762	−	0.149495i	$-0.952235\pi$
$773$	−5946.90	−	18302.7i	−0.276708	−	0.851620i	0.712054	−	0.702124i	$-0.247765\pi$
$774$		0			0
$775$	12019.7	+	8732.84i	0.557111	+	0.404765i
$776$		0			0
$777$	−3083.26	+	9489.31i	−0.142357	+	0.438130i
$778$		0			0
$779$	−13807.0	+	10031.4i	−0.635028	+	0.461375i
$780$		0			0
$781$	−8442.83	+	3876.97i	−0.386822	+	0.177630i
$782$		0			0
$783$	−8702.82	+	6322.97i	−0.397207	+	0.288588i
$784$		0			0
$785$	−5676.53	+	17470.6i	−0.258094	+	0.794333i
$786$		0			0
$787$	−23680.9	−	17205.2i	−1.07260	−	0.779287i	−0.0962197	−	0.995360i	$-0.530675\pi$
$787$	−23680.9	−	17205.2i	−1.07260	−	0.779287i	−0.976377	+	0.216073i	$0.930675\pi$
$788$		0			0
$789$	−1739.65	−	5354.09i	−0.0784958	−	0.241585i
$790$		0			0
$791$	6624.87			0.297792
$792$		0			0
$793$	−13602.8			−0.609141
$794$		0			0
$795$	−6384.87	−	19650.6i	−0.284840	−	0.876648i
$796$		0			0
$797$	10139.0	+	7366.42i	0.450617	+	0.327393i	0.789840	−	0.613314i	$-0.210164\pi$
$797$	10139.0	+	7366.42i	0.450617	+	0.327393i	−0.339222	+	0.940706i	$0.610164\pi$
$798$		0			0
$799$	3.79247	−	11.6720i	0.000167920	−	0.000516804i
$800$		0			0
$801$	3697.07	−	2686.08i	0.163083	−	0.118487i
$802$		0			0
$803$	21815.1	+	23670.0i	0.958703	+	1.04022i
$804$		0			0
$805$	−4690.71	+	3408.00i	−0.205374	+	0.149213i
$806$		0			0
$807$	−774.034	+	2382.23i	−0.0337637	+	0.103914i
$808$		0			0
$809$	−29078.0	−	21126.4i	−1.26369	−	0.918128i	−0.264762	−	0.964314i	$-0.585293\pi$
$809$	−29078.0	−	21126.4i	−1.26369	−	0.918128i	−0.998933	+	0.0461861i	$0.985293\pi$
$810$		0			0
$811$	6684.03	+	20571.3i	0.289406	+	0.890700i	0.985043	+	0.172307i	$0.0551220\pi$
$811$	6684.03	+	20571.3i	0.289406	+	0.890700i	−0.695637	+	0.718393i	$0.744878\pi$
$812$		0			0
$813$	2460.35			0.106136
$814$		0			0
$815$	−39.4991			−0.00169766
$816$		0			0
$817$	−1552.90	−	4779.33i	−0.0664983	−	0.204661i
$818$		0			0
$819$	−598.853	−	435.092i	−0.0255502	−	0.0185633i
$820$		0			0
$821$	−9723.86	+	29927.0i	−0.413356	+	1.27218i	0.500358	+	0.865819i	$0.333202\pi$
$821$	−9723.86	+	29927.0i	−0.413356	+	1.27218i	−0.913713	+	0.406359i	$0.866798\pi$
$822$		0			0
$823$	−28504.2	+	20709.5i	−1.20728	+	0.877142i	−0.994981	−	0.100062i	$-0.968096\pi$
$823$	−28504.2	+	20709.5i	−1.20728	+	0.877142i	−0.212302	+	0.977204i	$0.568096\pi$
$824$		0			0
$825$	2025.68	+	17335.9i	0.0854851	+	0.731585i
$826$		0			0
$827$	−7678.07	+	5578.44i	−0.322845	+	0.234560i	−0.737388	−	0.675469i	$-0.763941\pi$
$827$	−7678.07	+	5578.44i	−0.322845	+	0.234560i	0.414544	+	0.910029i	$0.363941\pi$
$828$		0			0
$829$	−11876.6	+	36552.5i	−0.497579	+	1.53139i	0.315320	+	0.948985i	$0.397888\pi$
$829$	−11876.6	+	36552.5i	−0.497579	+	1.53139i	−0.812899	+	0.582405i	$0.802112\pi$
$830$		0			0
$831$	34962.7	+	25401.9i	1.45950	+	1.06039i
$832$		0			0
$833$	−2.11122	−	6.49767i	−8.78145e−5	−	0.000270265i
$834$		0			0
$835$	−4562.34			−0.189086
$836$		0			0
$837$	22215.3			0.917411
$838$		0			0
$839$	−2994.13	−	9215.00i	−0.123205	−	0.379186i	0.870365	−	0.492408i	$-0.163883\pi$
$839$	−2994.13	−	9215.00i	−0.123205	−	0.379186i	−0.993570	+	0.113222i	$0.963883\pi$
$840$		0			0
$841$	14115.5	+	10255.5i	0.578766	+	0.420498i
$842$		0			0
$843$	8140.32	−	25053.3i	0.332583	−	1.02359i
$844$		0			0
$845$	−9069.86	+	6589.64i	−0.369246	+	0.268273i
$846$		0			0
$847$	−13076.7	+	3098.31i	−0.530486	+	0.125690i
$848$		0			0
$849$	24230.0	−	17604.1i	0.979472	−	0.711628i
$850$		0			0
$851$	−5091.28	+	15669.3i	−0.205084	+	0.631185i
$852$		0			0
$853$	−19981.2	−	14517.2i	−0.802043	−	0.582719i	0.109469	−	0.993990i	$-0.465085\pi$
$853$	−19981.2	−	14517.2i	−0.802043	−	0.582719i	−0.911513	+	0.411272i	$0.865085\pi$
$854$		0			0
$855$	514.043	+	1582.06i	0.0205613	+	0.0632812i
$856$		0			0
$857$	15732.3			0.627079			0.313539	−	0.949575i	$-0.398485\pi$
$857$	15732.3			0.627079			0.313539	+	0.949575i	$0.398485\pi$
$858$		0			0
$859$	34609.5			1.37469			0.687347	−	0.726329i	$-0.258775\pi$
$859$	34609.5			1.37469			0.687347	+	0.726329i	$0.258775\pi$
$860$		0			0
$861$	4073.83	+	12538.0i	0.161249	+	0.496275i
$862$		0			0
$863$	−2205.96	−	1602.73i	−0.0870126	−	0.0632183i	0.543428	−	0.839456i	$-0.317126\pi$
$863$	−2205.96	−	1602.73i	−0.0870126	−	0.0632183i	−0.630441	+	0.776237i	$0.717126\pi$
$864$		0			0
$865$	−632.748	+	1947.40i	−0.0248718	+	0.0765474i
$866$		0			0
$867$	−22021.1	+	15999.2i	−0.862600	+	0.626716i
$868$		0			0
$869$	−1638.46	−	14022.0i	−0.0639595	−	0.547368i
$870$		0			0
$871$	3610.73	−	2623.35i	0.140465	−	0.102054i
$872$		0			0
$873$	−1017.93	+	3132.88i	−0.0394638	+	0.121457i
$874$		0			0
$875$	−10732.8	−	7797.82i	−0.414668	−	0.301274i
$876$		0			0
$877$	760.484	+	2340.53i	0.0292813	+	0.0901187i	0.964629	−	0.263611i	$-0.0849134\pi$
$877$	760.484	+	2340.53i	0.0292813	+	0.0901187i	−0.935348	+	0.353729i	$0.884913\pi$
$878$		0			0
$879$	−30904.9			−1.18589
$880$		0			0
$881$	25163.9			0.962307			0.481153	−	0.876636i	$-0.340218\pi$
$881$	25163.9			0.962307			0.481153	+	0.876636i	$0.340218\pi$
$882$		0			0
$883$	−2664.16	−	8199.45i	−0.101536	−	0.312495i	0.887366	−	0.461066i	$-0.152533\pi$
$883$	−2664.16	−	8199.45i	−0.101536	−	0.312495i	−0.988902	+	0.148570i	$0.952533\pi$
$884$		0			0
$885$	−10176.6	−	7393.75i	−0.386535	−	0.280834i
$886$		0			0
$887$	−13158.9	+	40498.9i	−0.498120	+	1.53306i	0.313918	+	0.949450i	$0.398358\pi$
$887$	−13158.9	+	40498.9i	−0.498120	+	1.53306i	−0.812038	+	0.583605i	$0.801642\pi$
$888$		0			0
$889$	21800.3	−	15838.8i	0.822450	−	0.597545i
$890$		0			0
$891$	20153.4	+	21867.0i	0.757760	+	0.822191i
$892$		0			0
$893$	25368.8	−	18431.5i	0.950654	−	0.690691i
$894$		0			0
$895$	5132.08	−	15794.9i	0.191672	−	0.589906i
$896$		0			0
$897$	−8214.68	−	5968.32i	−0.305775	−	0.222159i
$898$		0			0
$899$	4429.66	+	13633.1i	0.164335	+	0.505772i
$900$		0			0
$901$	−17.0020			−0.000628657
$902$		0			0
$903$	−3881.86			−0.143057
$904$		0			0
$905$	2969.31	+	9138.61i	0.109064	+	0.335666i
$906$		0			0
$907$	7691.95	+	5588.53i	0.281596	+	0.204591i	0.719613	−	0.694375i	$-0.244319\pi$
$907$	7691.95	+	5588.53i	0.281596	+	0.204591i	−0.438018	+	0.898966i	$0.644319\pi$
$908$		0			0
$909$	−351.686	+	1082.38i	−0.0128324	+	0.0394942i
$910$		0			0
$911$	9283.56	−	6744.90i	0.337627	−	0.245300i	−0.406033	−	0.913858i	$-0.633088\pi$
$911$	9283.56	−	6744.90i	0.337627	−	0.245300i	0.743660	+	0.668558i	$0.233088\pi$
$912$		0			0
$913$	40259.5	−	18487.3i	1.45936	−	0.670142i
$914$		0			0
$915$	19103.8	−	13879.7i	0.690220	−	0.501474i
$916$		0			0
$917$	−2167.88	+	6672.06i	−0.0780696	+	0.240274i
$918$		0			0
$919$	34255.3	+	24887.9i	1.22957	+	0.893338i	0.996858	−	0.0792073i	$-0.0252389\pi$
$919$	34255.3	+	24887.9i	1.22957	+	0.893338i	0.232716	+	0.972545i	$0.425239\pi$
$920$		0			0
$921$	−12410.3	−	38195.0i	−0.444011	−	1.36652i
$922$		0			0
$923$	5052.61			0.180183
$924$		0			0
$925$	−15402.1			−0.547480
$926$		0			0
$927$	1270.74	+	3910.95i	0.0450234	+	0.138568i
$928$		0			0
$929$	34450.9	+	25030.0i	1.21668	+	0.883970i	0.995820	−	0.0913357i	$-0.0291136\pi$
$929$	34450.9	+	25030.0i	1.21668	+	0.883970i	0.220860	+	0.975306i	$0.429114\pi$
$930$		0			0
$931$	5394.31	−	16602.0i	0.189894	−	0.584434i
$932$		0			0
$933$	−4272.37	+	3104.06i	−0.149916	+	0.108920i
$934$		0			0
$935$	−6.30284	−	1.26347i	−0.000220455	−	4.41923e-5i
$936$		0			0
$937$	6729.55	−	4889.31i	0.234626	−	0.170466i	−0.464260	−	0.885699i	$-0.653680\pi$
$937$	6729.55	−	4889.31i	0.234626	−	0.170466i	0.698886	+	0.715233i	$0.253680\pi$
$938$		0			0
$939$	−5762.27	+	17734.4i	−0.200260	+	0.616338i
$940$		0			0
$941$	−25906.8	−	18822.4i	−0.897490	−	0.652064i	0.0403304	−	0.999186i	$-0.487159\pi$
$941$	−25906.8	−	18822.4i	−0.897490	−	0.652064i	−0.937820	+	0.347122i	$0.887159\pi$
$942$		0			0
$943$	6726.96	+	20703.5i	0.232301	+	0.714950i
$944$		0			0
$945$	−8104.63			−0.278988
$946$		0			0
$947$	28430.6			0.975575			0.487788	−	0.872962i	$-0.337804\pi$
$947$	28430.6			0.975575			0.487788	+	0.872962i	$0.337804\pi$
$948$		0			0
$949$	−5409.75	−	16649.5i	−0.185045	−	0.569510i
$950$		0			0
$951$	39456.5	+	28666.8i	1.34539	+	0.977483i
$952$		0			0
$953$	−2103.09	+	6472.65i	−0.0714856	+	0.220010i	−0.980416	−	0.196938i	$-0.936900\pi$
$953$	−2103.09	+	6472.65i	−0.0714856	+	0.220010i	0.908930	+	0.416948i	$0.136900\pi$
$954$		0			0
$955$	−5964.35	+	4333.35i	−0.202096	+	0.146831i
$956$		0			0
$957$	−8250.23	+	14680.6i	−0.278675	+	0.495878i
$958$		0			0
$959$	−20233.4	+	14700.5i	−0.681306	+	0.494997i
$960$		0			0
$961$	−58.0511	+	178.663i	−0.00194861	+	0.00599721i
$962$		0			0
$963$	−5183.05	−	3765.70i	−0.173439	−	0.126011i
$964$		0			0
$965$	2576.08	+	7928.35i	0.0859346	+	0.264479i
$966$		0			0
$967$	−41912.2			−1.39380			−0.696901	−	0.717167i	$-0.745438\pi$
$967$	−41912.2			−1.39380			−0.696901	+	0.717167i	$0.745438\pi$
$968$		0			0
$969$	11.3711			0.000376980
$970$		0			0
$971$	−15655.9	−	48184.0i	−0.517428	−	1.59248i	−0.778821	−	0.627246i	$-0.784182\pi$
$971$	−15655.9	−	48184.0i	−0.517428	−	1.59248i	0.261393	−	0.965232i	$-0.415818\pi$
$972$		0			0
$973$	−17940.8	−	13034.7i	−0.591114	−	0.429470i
$974$		0			0
$975$	2933.27	−	9027.68i	0.0963486	−	0.296530i
$976$		0			0
$977$	−6856.91	+	4981.84i	−0.224536	+	0.163135i	−0.694366	−	0.719622i	$-0.744315\pi$
$977$	−6856.91	+	4981.84i	−0.224536	+	0.163135i	0.469830	+	0.882757i	$0.344315\pi$
$978$		0			0
$979$	−22105.5	+	39334.9i	−0.721651	+	1.28411i
$980$		0			0
$981$	−4679.21	+	3399.64i	−0.152289	+	0.110644i
$982$		0			0
$983$	8009.88	−	24651.9i	0.259894	−	0.799871i	−0.732932	−	0.680302i	$-0.761849\pi$
$983$	8009.88	−	24651.9i	0.259894	−	0.799871i	0.992826	−	0.119569i	$-0.0381513\pi$
$984$		0			0
$985$	4009.45	+	2913.03i	0.129697	+	0.0942304i
$986$		0			0
$987$	−7485.20	−	23037.1i	−0.241395	−	0.742937i
$988$		0			0
$989$	−6409.97			−0.206092
$990$		0			0
$991$	52359.2			1.67835			0.839174	−	0.543863i	$-0.183039\pi$
$991$	52359.2			1.67835			0.839174	+	0.543863i	$0.183039\pi$
$992$		0			0
$993$	3226.56	+	9930.34i	0.103114	+	0.317351i
$994$		0			0
$995$	−602.316	−	437.608i	−0.0191906	−	0.0139428i
$996$		0			0
$997$	−4775.03	+	14696.0i	−0.151682	+	0.466828i	−0.997810	−	0.0661517i	$-0.978928\pi$
$997$	−4775.03	+	14696.0i	−0.151682	+	0.466828i	0.846128	+	0.532980i	$0.178928\pi$
$998$		0			0
$999$	−18631.8	+	13536.8i	−0.590073	+	0.428713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.4.m.e.113.1		16
4.3	odd	2		88.4.i.a.25.4	✓	16
11.2	odd	10		1936.4.a.bv.1.2		8
11.4	even	5	inner	176.4.m.e.81.1		16
11.9	even	5		1936.4.a.bw.1.2		8
44.15	odd	10		88.4.i.a.81.4	yes	16
44.31	odd	10		968.4.a.n.1.7		8
44.35	even	10		968.4.a.o.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.4.i.a.25.4	✓	16	4.3	odd	2
88.4.i.a.81.4	yes	16	44.15	odd	10
176.4.m.e.81.1		16	11.4	even	5	inner
176.4.m.e.113.1		16	1.1	even	1	trivial
968.4.a.n.1.7		8	44.31	odd	10
968.4.a.o.1.7		8	44.35	even	10
1936.4.a.bv.1.2		8	11.2	odd	10
1936.4.a.bw.1.2		8	11.9	even	5

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)

\(f(q)\)	\(=\)	\(q+(-1.71205 - 5.26914i) q^{3} +(5.02952 + 3.65416i) q^{5} +(3.12006 - 9.60257i) q^{7} +(-2.98931 + 2.17186i) q^{9} +(17.8737 - 31.8046i) q^{11} +(-16.0519 + 11.6624i) q^{13} +(10.6435 - 32.7574i) q^{15} +(-0.0229293 - 0.0166591i) q^{17} +(-22.3778 - 68.8719i) q^{19} -55.9390 q^{21} -92.3700 q^{23} +(-26.6839 - 82.1247i) q^{25} +(-104.458 - 75.8930i) q^{27} +(25.7455 - 79.2365i) q^{29} +(-139.196 + 101.132i) q^{31} +(-198.184 - 39.7278i) q^{33} +(50.7818 - 36.8951i) q^{35} +(55.1183 - 169.637i) q^{37} +(88.9324 + 64.6131i) q^{39} +(-72.8262 - 224.136i) q^{41} +69.3945 q^{43} -22.9711 q^{45} +(133.810 + 411.825i) q^{47} +(195.018 + 141.689i) q^{49} +(-0.0485233 + 0.149339i) q^{51} +(485.316 - 352.603i) q^{53} +(206.115 - 94.6487i) q^{55} +(-324.584 + 235.824i) q^{57} +(112.856 - 347.336i) q^{59} +(554.647 + 402.975i) q^{61} +(11.5286 + 35.4814i) q^{63} -123.349 q^{65} -224.941 q^{67} +(158.142 + 486.711i) q^{69} +(-206.018 - 149.681i) q^{71} +(-272.652 + 839.136i) q^{73} +(-387.043 + 281.203i) q^{75} +(-249.639 - 270.865i) q^{77} +(313.056 - 227.449i) q^{79} +(-251.883 + 775.217i) q^{81} +(982.393 + 713.750i) q^{83} +(-0.0544484 - 0.167575i) q^{85} -461.586 q^{87} -1236.77 q^{89} +(61.9059 + 190.527i) q^{91} +(771.188 + 560.301i) q^{93} +(139.119 - 428.165i) q^{95} +(721.245 - 524.015i) q^{97} +(15.6453 + 133.893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} - q^{5} + 13 q^{7} + 7 q^{9} - 83 q^{11} + 69 q^{13} - 93 q^{15} - 217 q^{17} - 126 q^{19} + 34 q^{21} + 92 q^{23} + 307 q^{25} - 158 q^{27} - 553 q^{29} - 205 q^{31} - 198 q^{33} - 7 q^{35}+ \cdots + 3265 q^{99}+O(q^{100}) \) 16 * q + q^3 - q^5 + 13 * q^7 + 7 * q^9 - 83 * q^11 + 69 * q^13 - 93 * q^15 - 217 * q^17 - 126 * q^19 + 34 * q^21 + 92 * q^23 + 307 * q^25 - 158 * q^27 - 553 * q^29 - 205 * q^31 - 198 * q^33 - 7 * q^35 + 127 * q^37 + 629 * q^39 - 553 * q^41 - 70 * q^43 - 1132 * q^45 - 779 * q^47 + 847 * q^49 + 2176 * q^51 + 1401 * q^53 + 385 * q^55 - 488 * q^57 - 1354 * q^59 - 1623 * q^61 - 256 * q^63 + 1674 * q^65 + 1658 * q^67 + 5470 * q^69 - 1985 * q^71 - 1245 * q^73 - 4114 * q^75 - 2645 * q^77 + 2007 * q^79 + 1966 * q^81 + 2946 * q^83 - 1543 * q^85 + 262 * q^87 - 6410 * q^89 - 3937 * q^91 + 2221 * q^93 + 8359 * q^95 + 6566 * q^97 + 3265 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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