LMFDB - Embedded newform 88.4.i.a.81.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,4,Mod(9,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("88.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$88 = 2^{3} \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	88.i (of order $5$ , degree $4$ , 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:	$5.19216808051$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.4
Root			$2.43785 + 7.50293i$ of defining polynomial
Character	$\chi$	$=$	88.81
Dual form			88.4.i.a.25.4

$q$ -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 $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$ .

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	1.71205	−	5.26914i	0.329484	−	1.01405i	−0.639892	−	0.768465i	$-0.721021\pi$
$3$	1.71205	−	5.26914i	0.329484	−	1.01405i	0.969376	−	0.245582i	$-0.0789791\pi$
$4$		0			0
$5$	5.02952	−	3.65416i	0.449854	−	0.326838i	−0.339684	−	0.940540i	$-0.610320\pi$
$5$	5.02952	−	3.65416i	0.449854	−	0.326838i	0.789538	+	0.613702i	$0.210320\pi$
$6$		0			0
$7$	−3.12006	−	9.60257i	−0.168468	−	0.518490i	0.830807	−	0.556560i	$-0.187879\pi$
$7$	−3.12006	−	9.60257i	−0.168468	−	0.518490i	−0.999275	+	0.0380698i	$0.987879\pi$
$8$		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	0.403238	−	0.915095i	$-0.367885\pi$
$13$	−16.0519	−	11.6624i	−0.342461	−	0.248812i	−0.745699	+	0.666282i	$0.767885\pi$
$14$		0			0
$15$	−10.6435	−	32.7574i	−0.183210	−	0.563861i
$16$		0			0
$17$	−0.0229293	+	0.0166591i	−0.000327128	+	0.000237673i	−0.587949	−	0.808898i	$-0.700064\pi$
$17$	−0.0229293	+	0.0166591i	−0.000327128	+	0.000237673i	0.587622	+	0.809136i	$0.300064\pi$
$18$		0			0
$19$	22.3778	−	68.8719i	0.270202	−	0.831595i	−0.720248	−	0.693717i	$-0.755972\pi$
$19$	22.3778	−	68.8719i	0.270202	−	0.831595i	0.990449	−	0.137878i	$-0.0440281\pi$
$20$		0			0
$21$	−55.9390			−0.581281
$22$		0			0
$23$	92.3700			0.837412			0.418706	−	0.908122i	$-0.362484\pi$
$23$	92.3700			0.837412			0.418706	+	0.908122i	$0.362484\pi$
$24$		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	0.999026	−	0.0441335i	$-0.0140527\pi$
$29$	25.7455	+	79.2365i	0.164856	+	0.507374i	−0.834170	+	0.551508i	$0.814053\pi$
$30$		0			0
$31$	139.196	+	101.132i	0.806462	+	0.585929i	0.912803	−	0.408401i	$-0.133913\pi$
$31$	139.196	+	101.132i	0.806462	+	0.585929i	−0.106341	+	0.994330i	$0.533913\pi$
$32$		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	0.995652	+	0.0931458i	$0.0296923\pi$
$37$	55.1183	+	169.637i	0.244902	+	0.753732i	−0.750750	+	0.660586i	$0.770308\pi$
$38$		0			0
$39$	−88.9324	+	64.6131i	−0.365143	+	0.265292i
$40$		0			0
$41$	−72.8262	+	224.136i	−0.277404	+	0.853761i	0.711170	+	0.703020i	$0.248166\pi$
$41$	−72.8262	+	224.136i	−0.277404	+	0.853761i	−0.988573	+	0.150740i	$0.951834\pi$
$42$		0			0
$43$	−69.3945			−0.246106			−0.123053	−	0.992400i	$-0.539269\pi$
$43$	−69.3945			−0.246106			−0.123053	+	0.992400i	$0.539269\pi$
$44$		0			0
$45$	−22.9711			−0.0760962
$46$		0			0
$47$	−133.810	+	411.825i	−0.415281	+	1.27810i	0.496719	+	0.867911i	$0.334538\pi$
$47$	−133.810	+	411.825i	−0.415281	+	1.27810i	−0.912000	+	0.410191i	$0.865462\pi$
$48$		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	0.998647	−	0.0519933i	$-0.0165574\pi$
$53$	485.316	+	352.603i	1.25780	+	0.913844i	0.259150	+	0.965837i	$0.416557\pi$
$54$		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	−0.994948	−	0.100393i	$-0.967990\pi$
$59$	−112.856	−	347.336i	−0.249028	−	0.766429i	0.745920	−	0.666035i	$-0.232010\pi$
$60$		0			0
$61$	554.647	−	402.975i	1.16418	−	0.845830i	0.173883	−	0.984766i	$-0.444368\pi$
$61$	554.647	−	402.975i	1.16418	−	0.845830i	0.990301	+	0.138937i	$0.0443685\pi$
$62$		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	$-0.434254\pi$
$67$	224.941			0.410164			0.205082	+	0.978745i	$0.434254\pi$
$68$		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	$-0.631732\pi$
$71$	206.018	−	149.681i	0.344364	−	0.250195i	0.746501	+	0.665385i	$0.231732\pi$
$72$		0			0
$73$	−272.652	−	839.136i	−0.437144	−	1.34539i	−0.890874	−	0.454251i	$-0.849907\pi$
$73$	−272.652	−	839.136i	−0.437144	−	1.34539i	0.453730	−	0.891139i	$-0.350093\pi$
$74$		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	$-0.388859\pi$
$79$	−313.056	−	227.449i	−0.445843	−	0.323924i	−0.787952	+	0.615736i	$0.788859\pi$
$80$		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	$-0.996729\pi$
$83$	−982.393	+	713.750i	−1.29918	+	0.943906i	−0.299229	+	0.954181i	$0.596729\pi$
$84$		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	0.897361	−	0.441297i	$-0.145482\pi$
$97$	721.245	+	524.015i	0.754962	+	0.548512i	−0.142399	+	0.989809i	$0.545482\pi$
$98$		0			0
$99$	−15.6453	+	133.893i	−0.0158829	+	0.135926i
$100$		0			0
$101$	249.183	+	181.042i	0.245491	+	0.178360i	0.703726	−	0.710471i	$-0.251518\pi$
$101$	249.183	+	181.042i	0.245491	+	0.178360i	−0.458235	+	0.888831i	$0.651518\pi$
$102$		0			0
$103$	−343.910	−	1058.45i	−0.328995	−	1.01254i	−0.969605	−	0.244676i	$-0.921318\pi$
$103$	−343.910	−	1058.45i	−0.328995	−	1.01254i	0.640610	−	0.767867i	$-0.278682\pi$
$104$		0			0
$105$	−281.346	+	204.410i	−0.261491	+	0.189985i
$106$		0			0
$107$	−535.793	+	1649.00i	−0.484085	+	1.48986i	0.349217	+	0.937042i	$0.386448\pi$
$107$	−535.793	+	1649.00i	−0.484085	+	1.48986i	−0.833302	+	0.552818i	$0.813552\pi$
$108$		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	−0.830501	−	0.557018i	$-0.811945\pi$
$113$	202.758	−	624.025i	0.168795	−	0.519499i	0.999296	+	0.0375191i	$0.0119455\pi$
$114$		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	−0.541811	+	0.840500i	$0.682261\pi$
$127$	−2159.14	+	1568.71i	−1.50860	+	1.09606i	−0.966792	+	0.255564i	$0.917739\pi$
$128$		0			0
$129$	−118.807	+	365.650i	−0.0810880	+	0.249563i
$130$		0			0
$131$	694.820			0.463410			0.231705	−	0.972786i	$-0.425570\pi$
$131$	694.820			0.463410			0.231705	+	0.972786i	$0.425570\pi$
$132$		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	−0.998205	−	0.0598929i	$-0.980924\pi$
$137$	−2003.96	+	1455.96i	−1.24971	+	0.907964i	−0.251501	+	0.967857i	$0.580924\pi$
$138$		0			0
$139$	−678.710	−	2088.85i	−0.414154	−	1.27463i	−0.913005	−	0.407947i	$-0.866245\pi$
$139$	−678.710	−	2088.85i	−0.414154	−	1.27463i	0.498851	−	0.866688i	$-0.333755\pi$
$140$		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	−0.510449	+	0.859908i	$0.670521\pi$
$149$	−2702.72	+	1963.64i	−1.48601	+	1.07965i	−0.975558	+	0.219740i	$0.929479\pi$
$150$		0			0
$151$	−225.119	+	692.846i	−0.121324	+	0.373398i	−0.993213	−	0.116305i	$-0.962895\pi$
$151$	−225.119	+	692.846i	−0.121324	+	0.373398i	0.871889	+	0.489703i	$0.162895\pi$
$152$		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	−0.395883	−	0.918301i	$-0.629561\pi$
$157$	913.092	−	2810.21i	0.464157	−	1.42853i	0.860040	−	0.510227i	$-0.170439\pi$
$158$		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	$-0.299514\pi$
$163$	5.14015	+	3.73454i	0.00246999	+	0.00179455i	−0.586550	+	0.809913i	$0.699514\pi$
$164$		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	$-0.245615\pi$
$167$	593.714	+	431.358i	0.275107	+	0.199877i	−0.441673	+	0.897176i	$0.645615\pi$
$168$		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	−0.926198	−	0.377038i	$-0.876943\pi$
$173$	101.780	−	313.246i	0.0447294	−	0.137663i	0.970927	+	0.239375i	$0.0769426\pi$
$174$		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	−0.617039	−	0.786932i	$-0.711668\pi$
$179$	825.515	−	2540.67i	0.344703	−	1.06089i	0.961743	−	0.273955i	$-0.0883319\pi$
$180$		0			0
$181$	1250.44	−	908.497i	0.513505	−	0.373083i	−0.300647	−	0.953736i	$-0.597202\pi$
$181$	1250.44	−	908.497i	0.513505	−	0.373083i	0.814152	+	0.580652i	$0.197202\pi$
$182$		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	$-0.0278846\pi$
$191$	366.453	+	1127.83i	0.138825	+	0.427260i	−0.857340	+	0.514750i	$0.827885\pi$
$192$		0			0
$193$	1084.84	−	788.182i	0.404603	−	0.293962i	−0.366810	−	0.930296i	$-0.619550\pi$
$193$	1084.84	−	788.182i	0.404603	−	0.293962i	0.771413	+	0.636334i	$0.219550\pi$
$194$		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	$-0.493210\pi$
$199$	119.756			0.0426597			0.0213299	+	0.999772i	$0.493210\pi$
$200$		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	$-0.355275\pi$
$211$	−856.848	−	622.536i	−0.279563	−	0.203115i	−0.718727	+	0.695293i	$0.755275\pi$
$212$		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	0.0697353	+	0.997566i	$0.477785\pi$
$223$	−1908.27	+	5873.04i	−0.573036	+	1.76362i	−0.642771	+	0.766058i	$0.722215\pi$
$224$		0			0
$225$	258.130	−	187.542i	0.0764829	−	0.0555681i
$226$		0			0
$227$	−1304.25	−	4014.07i	−0.381348	−	1.17367i	−0.939095	−	0.343658i	$-0.888334\pi$
$227$	−1304.25	−	4014.07i	−0.381348	−	1.17367i	0.557747	−	0.830011i	$-0.311666\pi$
$228$		0			0
$229$	1989.97	+	1445.80i	0.574239	+	0.417209i	0.836643	−	0.547749i	$-0.184515\pi$
$229$	1989.97	+	1445.80i	0.574239	+	0.417209i	−0.262404	+	0.964958i	$0.584515\pi$
$230$		0			0
$231$	999.835	+	1779.12i	0.284781	+	0.506742i
$232$		0			0
$233$	1006.74	+	731.437i	0.283062	+	0.205657i	0.720252	−	0.693713i	$-0.244026\pi$
$233$	1006.74	+	731.437i	0.283062	+	0.205657i	−0.437190	+	0.899369i	$0.644026\pi$
$234$		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	0.693017	+	0.720922i	$0.256281\pi$
$239$	−1076.65	+	3313.60i	−0.291393	+	0.896815i	−0.984409	+	0.175893i	$0.943719\pi$
$240$		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	$-0.0482403\pi$
$251$	4574.79	+	3323.78i	1.15043	+	0.835837i	0.161892	+	0.986808i	$0.448240\pi$
$252$		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	−0.984761	−	0.173912i	$-0.944359\pi$
$257$	−1196.02	−	3680.98i	−0.290295	−	0.893437i	0.694466	−	0.719526i	$-0.255641\pi$
$258$		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	$-0.538007\pi$
$263$	−1016.12			−0.238239			−0.119119	+	0.992880i	$0.538007\pi$
$264$		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	−0.628465	−	0.777838i	$-0.716316\pi$
$269$	−365.765	+	265.744i	−0.0829036	+	0.0602330i	0.545561	+	0.838071i	$0.316316\pi$
$270$		0			0
$271$	137.229	+	422.347i	0.0307604	+	0.0946708i	0.965258	−	0.261299i	$-0.0841507\pi$
$271$	137.229	+	422.347i	0.0307604	+	0.0946708i	−0.934498	+	0.355969i	$0.884151\pi$
$272$		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	−0.997827	−	0.0658897i	$-0.979011\pi$
$277$	−6310.61	−	4584.93i	−1.36884	−	0.994518i	−0.371010	−	0.928629i	$-0.620989\pi$
$278$		0			0
$279$	−196.455	−	604.628i	−0.0421558	−	0.129742i
$280$		0			0
$281$	3846.65	−	2794.76i	0.816626	−	0.593314i	−0.0991178	−	0.995076i	$-0.531602\pi$
$281$	3846.65	−	2794.76i	0.816626	−	0.593314i	0.915744	+	0.401762i	$0.131602\pi$
$282$		0			0
$283$	−1670.49	+	5141.25i	−0.350885	+	1.07991i	0.607472	+	0.794341i	$0.292184\pi$
$283$	−1670.49	+	5141.25i	−0.350885	+	1.07991i	−0.958357	+	0.285573i	$0.907816\pi$
$284$		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	0.962278	+	0.272067i	$0.0877074\pi$
$293$	1723.76	+	5305.18i	0.343696	+	1.05779i	−0.618582	+	0.785720i	$0.712293\pi$
$294$		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	$-0.735338\pi$
$307$	−7248.81			−1.34759			−0.673797	+	0.738916i	$0.735338\pi$
$308$		0			0
$309$	−6165.90			−1.13517
$310$		0			0
$311$	294.551	−	906.534i	0.0537056	−	0.165289i	−0.920606	−	0.390492i	$-0.872305\pi$
$311$	294.551	−	906.534i	0.0537056	−	0.165289i	0.974312	+	0.225204i	$0.0723047\pi$
$312$		0			0
$313$	−2722.92	+	1978.32i	−0.491721	+	0.357256i	−0.805846	−	0.592126i	$-0.798289\pi$
$313$	−2722.92	+	1978.32i	−0.491721	+	0.357256i	0.314125	+	0.949382i	$0.398289\pi$
$314$		0			0
$315$	71.6713	+	220.582i	0.0128197	+	0.0394551i
$316$		0			0
$317$	−7121.72	−	5174.23i	−1.26182	−	0.916763i	−0.262971	−	0.964804i	$-0.584702\pi$
$317$	−7121.72	−	5174.23i	−1.26182	−	0.916763i	−0.998845	+	0.0480404i	$0.984702\pi$
$318$		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	$-0.449986\pi$
$331$	1884.62			0.312955			0.156478	+	0.987682i	$0.449986\pi$
$332$		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	0.988248	−	0.152862i	$-0.0488491\pi$
$337$	611.773	+	1882.84i	0.0988883	+	0.304347i	−0.889359	+	0.457209i	$0.848849\pi$
$338$		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	$-0.470344\pi$
$347$	6908.05	−	5018.99i	1.06871	−	0.776466i	0.975681	+	0.219197i	$0.0703437\pi$
$348$		0			0
$349$	−291.889	+	898.341i	−0.0447692	+	0.137785i	−0.970943	−	0.239312i	$-0.923078\pi$
$349$	−291.889	+	898.341i	−0.0447692	+	0.137785i	0.926173	+	0.377098i	$0.123078\pi$
$350$		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	−0.898050	−	0.439893i	$-0.855016\pi$
$359$	−2925.40	−	9003.47i	−0.430075	−	1.32363i	0.467975	−	0.883742i	$-0.344984\pi$
$360$		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	$-0.0464770\pi$
$367$	727.199	+	2238.09i	0.103432	+	0.318330i	−0.885927	+	0.463824i	$0.846477\pi$
$368$		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	$-0.892815\pi$
$379$	−6797.44	+	4938.63i	−0.921269	+	0.669341i	0.0225706	+	0.999745i	$0.492815\pi$
$380$		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	$-0.457926\pi$
$383$	−5773.30	−	4194.55i	−0.770240	−	0.559612i	−0.902034	+	0.431665i	$0.857926\pi$
$384$		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	0.850284	+	0.526324i	$0.176430\pi$
$389$	3619.44	+	11139.5i	0.471755	+	1.45191i	−0.378529	+	0.925589i	$0.623570\pi$
$390$		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	−0.983354	−	0.181699i	$-0.941840\pi$
$401$	−8948.83	+	6501.70i	−1.11442	+	0.809675i	−0.131067	+	0.991373i	$0.541840\pi$
$402$		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	0.941925	−	0.335823i	$-0.109014\pi$
$409$	7556.94	+	5490.44i	0.913610	+	0.663776i	−0.0283153	+	0.999599i	$0.509014\pi$
$410$		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	$-0.459401\pi$
$419$	2181.92			0.254400			0.127200	+	0.991877i	$0.459401\pi$
$420$		0			0
$421$	1084.16	−	3336.70i	0.125508	−	0.386273i	−0.868486	−	0.495714i	$-0.834906\pi$
$421$	1084.16	−	3336.70i	0.125508	−	0.386273i	0.993993	+	0.109442i	$0.0349063\pi$
$422$		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	$-0.0447321\pi$
$431$	10405.4	+	7559.96i	1.16290	+	0.844896i	0.172758	+	0.984964i	$0.444732\pi$
$432$		0			0
$433$	2519.25	+	7753.44i	0.279601	+	0.860523i	0.987965	+	0.154676i	$0.0494334\pi$
$433$	2519.25	+	7753.44i	0.279601	+	0.860523i	−0.708364	+	0.705847i	$0.750567\pi$
$434$		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	$-0.471981\pi$
$439$	1617.22			0.175821			0.0879107	+	0.996128i	$0.471981\pi$
$440$		0			0
$441$	−890.698			−0.0961773
$442$		0			0
$443$	1466.63	−	4513.83i	0.157295	−	0.484105i	−0.841091	−	0.540893i	$-0.818086\pi$
$443$	1466.63	−	4513.83i	0.157295	−	0.484105i	0.998386	+	0.0567889i	$0.0180862\pi$
$444$		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	0.265453	−	0.964124i	$-0.414478\pi$
$449$	−5417.86	−	3936.30i	−0.569453	−	0.413732i	−0.834907	+	0.550392i	$0.814478\pi$
$450$		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	−0.0351900	−	0.999381i	$-0.511204\pi$
$457$	8835.61	−	6419.44i	0.904403	−	0.657087i	0.939593	+	0.342293i	$0.111204\pi$
$458$		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	$-0.451147\pi$
$463$	3046.02			0.305746			0.152873	+	0.988246i	$0.451147\pi$
$464$		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	$-0.827685\pi$
$467$	−6375.92	+	4632.37i	−0.631782	+	0.459017i	0.225235	+	0.974304i	$0.427685\pi$
$468$		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	$-0.908321\pi$
$479$	−10325.6	+	7501.99i	−0.984945	+	0.715605i	−0.0261371	+	0.999658i	$0.508321\pi$
$480$		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	$-0.963917\pi$
$487$	−1324.80	+	4077.31i	−0.123270	+	0.379385i	0.870312	+	0.492500i	$0.163917\pi$
$488$		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	$-0.125333\pi$
$491$	−534.577	−	1645.26i	−0.0491347	−	0.151221i	−0.972614	+	0.232428i	$0.925333\pi$
$492$		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	−0.948384	−	0.317125i	$-0.897283\pi$
$499$	−4096.75	−	12608.5i	−0.367526	−	1.13113i	0.580857	−	0.814005i	$-0.302717\pi$
$500$		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	$-0.898138\pi$
$503$	40.7844	−	125.521i	0.00361528	−	0.0111267i	0.952848	+	0.303448i	$0.0981380\pi$
$504$		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	−0.778952	−	0.627083i	$-0.784249\pi$
$509$	2524.36	−	7769.18i	0.219824	−	0.676548i	0.998776	−	0.0494645i	$-0.0157515\pi$
$510$		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	0.978540	−	0.206055i	$-0.0660627\pi$
$521$	782.119	+	2407.12i	0.0657683	+	0.202414i	−0.912772	+	0.408469i	$0.866063\pi$
$522$		0			0
$523$	1261.68	−	916.661i	0.105486	−	0.0766401i	−0.533792	−	0.845616i	$-0.679233\pi$
$523$	1261.68	−	916.661i	0.105486	−	0.0766401i	0.639278	+	0.768976i	$0.279233\pi$
$524$		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	−0.00236886	−	0.999997i	$-0.500754\pi$
$541$	−12006.5	−	8723.20i	−0.954155	−	0.693234i	−0.951786	+	0.306763i	$0.900754\pi$
$542$		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	$-0.843925\pi$
$547$	1385.68	−	4264.69i	0.108314	−	0.333355i	0.990494	+	0.137557i	$0.0439250\pi$
$548$		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	0.993894	−	0.110341i	$-0.0351943\pi$
$557$	1642.68	+	5055.66i	0.124960	+	0.384587i	−0.868934	+	0.494928i	$0.835194\pi$
$558$		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	$-0.355111\pi$
$563$	−3723.62	−	2705.37i	−0.278742	−	0.202518i	−0.718369	+	0.695663i	$0.755111\pi$
$564$		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	−0.823635	−	0.567120i	$-0.808058\pi$
$569$	2389.41	−	7353.85i	0.176045	−	0.541809i	0.999680	+	0.0253108i	$0.00805752\pi$
$570$		0			0
$571$	18830.2			1.38007			0.690033	−	0.723778i	$-0.257596\pi$
$571$	18830.2			1.38007			0.690033	+	0.723778i	$0.257596\pi$
$572$		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	−0.914298	−	0.405042i	$-0.867257\pi$
$577$	−11249.0	+	8172.86i	−0.811614	+	0.589672i	0.102684	+	0.994714i	$0.467257\pi$
$578$		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	0.693032	+	0.720907i	$0.256274\pi$
$587$	7908.73	+	24340.6i	0.556096	+	1.71149i	−0.136937	+	0.990580i	$0.543726\pi$
$588$		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	$-0.679651\pi$
$599$	1515.41	−	1101.01i	0.103369	−	0.0751020i	0.638269	+	0.769813i	$0.279651\pi$
$600$		0			0
$601$	−528.913	−	1627.83i	−0.0358982	−	0.110483i	0.931502	−	0.363737i	$-0.118499\pi$
$601$	−528.913	−	1627.83i	−0.0358982	−	0.110483i	−0.967400	+	0.253254i	$0.918499\pi$
$602$		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	$-0.153728\pi$
$607$	10732.2	+	7797.37i	0.717635	+	0.521393i	−0.167993	+	0.985788i	$0.553728\pi$
$608$		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	0.274644	+	0.961546i	$0.411440\pi$
$613$	−7781.79	+	23949.9i	−0.512730	+	1.57802i	−0.787374	+	0.616476i	$0.788560\pi$
$614$		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	$-0.930463\pi$
$619$	−909.502	+	2799.16i	−0.0590565	+	0.181757i	0.917176	+	0.398482i	$0.130463\pi$
$620$		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	−0.556845	−	0.830617i	$-0.687988\pi$
$631$	−9424.29	−	29005.0i	−0.594572	−	1.82990i	−0.0377276	−	0.999288i	$-0.512012\pi$
$632$		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	0.361020	+	0.932558i	$0.382429\pi$
$641$	−7776.77	+	23934.4i	−0.479195	+	1.47481i	−0.840215	+	0.542253i	$0.817571\pi$
$642$		0			0
$643$	4987.62	−	3623.72i	0.305898	−	0.222248i	−0.424236	−	0.905552i	$-0.639457\pi$
$643$	4987.62	−	3623.72i	0.305898	−	0.222248i	0.730135	+	0.683303i	$0.239457\pi$
$644$		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	$-0.170693\pi$
$647$	10522.1	+	7644.77i	0.639362	+	0.464524i	−0.220269	+	0.975439i	$0.570693\pi$
$648$		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	0.963745	+	0.266824i	$0.0859744\pi$
$653$	5688.39	+	17507.1i	0.340894	+	1.04917i	−0.622851	+	0.782341i	$0.714026\pi$
$654$		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	$-0.633904\pi$
$659$	−13817.0			−0.816745			−0.408372	+	0.912815i	$0.633904\pi$
$660$		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	0.354046	−	0.935228i	$-0.384806\pi$
$673$	−7437.64	−	5403.76i	−0.426003	−	0.309509i	−0.780049	+	0.625719i	$0.784806\pi$
$674$		0			0
$675$	3445.35	+	10603.7i	0.196462	+	0.604646i
$676$		0			0
$677$	−3603.19	+	2617.87i	−0.204552	+	0.148616i	−0.685345	−	0.728218i	$-0.740349\pi$
$677$	−3603.19	+	2617.87i	−0.204552	+	0.148616i	0.480793	+	0.876834i	$0.340349\pi$
$678$		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	$-0.617670\pi$
$683$	−12898.6			−0.722620			−0.361310	+	0.932446i	$0.617670\pi$
$684$		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	$-0.00354324\pi$
$691$	23583.5	+	17134.4i	1.29835	+	0.943306i	0.298411	+	0.954437i	$0.403543\pi$
$692$		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	−0.952334	−	0.305056i	$-0.901325\pi$
$701$	−47.7400	+	146.929i	−0.00257220	+	0.00791642i	0.949762	+	0.312973i	$0.101325\pi$
$702$		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	−0.107522	−	0.994203i	$-0.534292\pi$
$709$	15193.4	−	11038.6i	0.804794	−	0.584717i	0.912317	+	0.409485i	$0.134292\pi$
$710$		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	$-0.191366\pi$
$719$	−3373.36	−	10382.1i	−0.174972	−	0.538509i	−0.999632	+	0.0271198i	$0.991366\pi$
$720$		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	$-0.336371\pi$
$727$	19277.1			0.983424			0.491712	+	0.870758i	$0.336371\pi$
$728$		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	−0.736669	−	0.676253i	$-0.763603\pi$
$733$	−10680.4	−	32870.8i	−0.538183	−	1.65636i	0.198487	−	0.980104i	$-0.436397\pi$
$734$		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	$-0.458051\pi$
$739$	−15484.8	−	11250.4i	−0.770796	−	0.560016i	−0.902203	+	0.431312i	$0.858051\pi$
$740$		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	$-0.848320\pi$
$743$	−14722.8	+	10696.7i	−0.726953	+	0.528163i	0.161645	+	0.986849i	$0.448320\pi$
$744$		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	−0.565280	−	0.824899i	$-0.691232\pi$
$751$	7756.96	−	23873.5i	0.376905	−	1.15999i	0.942185	−	0.335094i	$-0.108768\pi$
$752$		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	−0.201994	−	0.979387i	$-0.564742\pi$
$757$	−24907.3	−	18096.2i	−1.19587	−	0.868847i	−0.993872	+	0.110539i	$0.964742\pi$
$758$		0			0
$759$	−18306.2	+	3669.66i	−0.875459	+	0.175494i
$760$		0			0
$761$	−18579.9	−	13499.1i	−0.885048	−	0.643025i	0.0495340	−	0.998772i	$-0.484226\pi$
$761$	−18579.9	−	13499.1i	−0.885048	−	0.643025i	−0.934582	+	0.355747i	$0.884226\pi$
$762$		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	0.712054	+	0.702124i	$0.247765\pi$
$773$	−5946.90	+	18302.7i	−0.276708	+	0.851620i	−0.988762	+	0.149495i	$0.952235\pi$
$774$		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	$-0.469325\pi$
$787$	23680.9	−	17205.2i	1.07260	−	0.779287i	0.976377	+	0.216073i	$0.0693249\pi$
$788$		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	−0.339222	−	0.940706i	$-0.610164\pi$
$797$	10139.0	−	7366.42i	0.450617	−	0.327393i	0.789840	+	0.613314i	$0.210164\pi$
$798$		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	−0.998933	−	0.0461861i	$-0.985293\pi$
$809$	−29078.0	+	21126.4i	−1.26369	+	0.918128i	−0.264762	+	0.964314i	$0.585293\pi$
$810$		0			0
$811$	−6684.03	+	20571.3i	−0.289406	+	0.890700i	0.695637	+	0.718393i	$0.255122\pi$
$811$	−6684.03	+	20571.3i	−0.289406	+	0.890700i	−0.985043	+	0.172307i	$0.944878\pi$
$812$		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	−0.913713	−	0.406359i	$-0.866798\pi$
$821$	−9723.86	−	29927.0i	−0.413356	−	1.27218i	0.500358	−	0.865819i	$-0.333202\pi$
$822$		0			0
$823$	28504.2	+	20709.5i	1.20728	+	0.877142i	0.994981	−	0.100062i	$-0.0319041\pi$
$823$	28504.2	+	20709.5i	1.20728	+	0.877142i	0.212302	+	0.977204i	$0.431904\pi$
$824$		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	$-0.236059\pi$
$827$	7678.07	+	5578.44i	0.322845	+	0.234560i	−0.414544	+	0.910029i	$0.636059\pi$
$828$		0			0
$829$	−11876.6	−	36552.5i	−0.497579	−	1.53139i	−0.812899	−	0.582405i	$-0.802112\pi$
$829$	−11876.6	−	36552.5i	−0.497579	−	1.53139i	0.315320	−	0.948985i	$-0.397888\pi$
$830$		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	$-0.836117\pi$
$839$	2994.13	−	9215.00i	0.123205	−	0.379186i	0.993570	+	0.113222i	$0.0361170\pi$
$840$		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	−0.911513	−	0.411272i	$-0.865085\pi$
$853$	−19981.2	+	14517.2i	−0.802043	+	0.582719i	0.109469	+	0.993990i	$0.465085\pi$
$854$		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	$-0.741225\pi$
$859$	−34609.5			−1.37469			−0.687347	+	0.726329i	$0.741225\pi$
$860$		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	$-0.682874\pi$
$863$	2205.96	−	1602.73i	0.0870126	−	0.0632183i	0.630441	+	0.776237i	$0.282874\pi$
$864$		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	−0.935348	−	0.353729i	$-0.884913\pi$
$877$	760.484	−	2340.53i	0.0292813	−	0.0901187i	0.964629	+	0.263611i	$0.0849134\pi$
$878$		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	$-0.847467\pi$
$883$	2664.16	−	8199.45i	0.101536	−	0.312495i	0.988902	+	0.148570i	$0.0474672\pi$
$884$		0			0
$885$	−10176.6	+	7393.75i	−0.386535	+	0.280834i
$886$		0			0
$887$	13158.9	+	40498.9i	0.498120	+	1.53306i	0.812038	+	0.583605i	$0.198358\pi$
$887$	13158.9	+	40498.9i	0.498120	+	1.53306i	−0.313918	+	0.949450i	$0.601642\pi$
$888$		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	$-0.755681\pi$
$907$	−7691.95	+	5588.53i	−0.281596	+	0.204591i	0.438018	+	0.898966i	$0.355681\pi$
$908$		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	$-0.366912\pi$
$911$	−9283.56	−	6744.90i	−0.337627	−	0.245300i	−0.743660	+	0.668558i	$0.766912\pi$
$912$		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	$-0.974761\pi$
$919$	−34255.3	+	24887.9i	−1.22957	+	0.893338i	−0.232716	+	0.972545i	$0.574761\pi$
$920$		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	0.220860	−	0.975306i	$-0.429114\pi$
$929$	34450.9	−	25030.0i	1.21668	−	0.883970i	0.995820	+	0.0913357i	$0.0291136\pi$
$930$		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	0.698886	−	0.715233i	$-0.253680\pi$
$937$	6729.55	+	4889.31i	0.234626	+	0.170466i	−0.464260	+	0.885699i	$0.653680\pi$
$938$		0			0
$939$	5762.27	+	17734.4i	0.200260	+	0.616338i
$940$		0			0
$941$	−25906.8	+	18822.4i	−0.897490	+	0.652064i	−0.937820	−	0.347122i	$-0.887159\pi$
$941$	−25906.8	+	18822.4i	−0.897490	+	0.652064i	0.0403304	+	0.999186i	$0.487159\pi$
$942$		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	$-0.662196\pi$
$947$	−28430.6			−0.975575			−0.487788	+	0.872962i	$0.662196\pi$
$948$		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	0.908930	−	0.416948i	$-0.136900\pi$
$953$	−2103.09	−	6472.65i	−0.0714856	−	0.220010i	−0.980416	+	0.196938i	$0.936900\pi$
$954$		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	$-0.254562\pi$
$967$	41912.2			1.39380			0.696901	+	0.717167i	$0.254562\pi$
$968$		0			0
$969$	11.3711			0.000376980
$970$		0			0
$971$	15655.9	−	48184.0i	0.517428	−	1.59248i	−0.261393	−	0.965232i	$-0.584182\pi$
$971$	15655.9	−	48184.0i	0.517428	−	1.59248i	0.778821	−	0.627246i	$-0.215818\pi$
$972$		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	0.469830	−	0.882757i	$-0.344315\pi$
$977$	−6856.91	−	4981.84i	−0.224536	−	0.163135i	−0.694366	+	0.719622i	$0.744315\pi$
$978$		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	−0.992826	−	0.119569i	$-0.961849\pi$
$983$	−8009.88	−	24651.9i	−0.259894	−	0.799871i	0.732932	−	0.680302i	$-0.238151\pi$
$984$		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	$-0.816961\pi$
$991$	−52359.2			−1.67835			−0.839174	+	0.543863i	$0.816961\pi$
$992$		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	0.846128	−	0.532980i	$-0.178928\pi$
$997$	−4775.03	−	14696.0i	−0.151682	−	0.466828i	−0.997810	+	0.0661517i	$0.978928\pi$
$998$		0			0
$999$	18631.8	+	13536.8i	0.590073	+	0.428713i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.4.i.a.81.4	yes	16
4.3	odd	2		176.4.m.e.81.1		16
11.3	even	5	inner	88.4.i.a.25.4	✓	16
11.5	even	5		968.4.a.n.1.7		8
11.6	odd	10		968.4.a.o.1.7		8
44.3	odd	10		176.4.m.e.113.1		16
44.27	odd	10		1936.4.a.bw.1.2		8
44.39	even	10		1936.4.a.bv.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.4.i.a.25.4	✓	16	11.3	even	5	inner
88.4.i.a.81.4	yes	16	1.1	even	1	trivial
176.4.m.e.81.1		16	4.3	odd	2
176.4.m.e.113.1		16	44.3	odd	10
968.4.a.n.1.7		8	11.5	even	5
968.4.a.o.1.7		8	11.6	odd	10
1936.4.a.bv.1.2		8	44.39	even	10
1936.4.a.bw.1.2		8	44.27	odd	10

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

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	88.4.i.a.81.4

Level	$88$
Weight	$4$
Character	88.81
Analytic conductor	$5.192$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$