LMFDB - Embedded newform 208.3.bd.d.145.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [208,3,Mod(33,208)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(208, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("208.33"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	208.bd (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2,0,-14,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.66758949869$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	208.145
Dual form			208.3.bd.d.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 0.633975i) q^{3} +(-2.63397 + 2.63397i) q^{5} +(-5.73205 + 1.53590i) q^{7} +(4.23205 - 7.33013i) q^{9} +(4.19615 - 15.6603i) q^{11} +(-6.50000 - 11.2583i) q^{13} +(2.63397 + 0.705771i) q^{15} +(-15.9904 - 9.23205i) q^{17} +(-1.63397 - 6.09808i) q^{19} +(3.07180 + 3.07180i) q^{21} +(-17.4904 + 10.0981i) q^{23} +11.1244i q^{25} -12.7846 q^{27} +(-4.69615 - 8.13397i) q^{29} +(11.9282 - 11.9282i) q^{31} +(-11.4641 + 3.07180i) q^{33} +(11.0526 - 19.1436i) q^{35} +(8.11474 - 30.2846i) q^{37} +(-4.75833 + 8.24167i) q^{39} +(44.9186 + 12.0359i) q^{41} +(-45.0000 - 25.9808i) q^{43} +(8.16025 + 30.4545i) q^{45} +(34.3205 + 34.3205i) q^{47} +(-11.9378 + 6.89230i) q^{49} +13.5167i q^{51} -14.7654 q^{53} +(30.1962 + 52.3013i) q^{55} +(-3.26795 + 3.26795i) q^{57} +(92.9615 - 24.9090i) q^{59} +(-12.8135 + 22.1936i) q^{61} +(-13.0000 + 48.5167i) q^{63} +(46.7750 + 12.5333i) q^{65} +(-39.0263 - 10.4571i) q^{67} +(12.8038 + 7.39230i) q^{69} +(11.9737 + 44.6865i) q^{71} +(-19.2750 - 19.2750i) q^{73} +(7.05256 - 4.07180i) q^{75} +96.2102i q^{77} -62.7461 q^{79} +(-33.4090 - 57.8660i) q^{81} +(24.4833 - 24.4833i) q^{83} +(66.4352 - 17.8013i) q^{85} +(-3.43782 + 5.95448i) q^{87} +(-23.1699 + 86.4711i) q^{89} +(54.5500 + 54.5500i) q^{91} +(-11.9282 - 3.19615i) q^{93} +(20.3660 + 11.7583i) q^{95} +(14.1891 + 52.9545i) q^{97} +(-97.0333 - 97.0333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 14 q^{5} - 16 q^{7} + 10 q^{9} - 4 q^{11} - 26 q^{13} + 14 q^{15} - 12 q^{17} - 10 q^{19} + 40 q^{21} - 18 q^{23} + 32 q^{27} + 2 q^{29} + 20 q^{31} - 32 q^{33} - 32 q^{35} - 68 q^{37} + 26 q^{39}+ \cdots - 208 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 14 * q^5 - 16 * q^7 + 10 * q^9 - 4 * q^11 - 26 * q^13 + 14 * q^15 - 12 * q^17 - 10 * q^19 + 40 * q^21 - 18 * q^23 + 32 * q^27 + 2 * q^29 + 20 * q^31 - 32 * q^33 - 32 * q^35 - 68 * q^37 + 26 * q^39 + 100 * q^41 - 180 * q^43 - 2 * q^45 + 68 * q^47 - 72 * q^49 + 128 * q^53 + 100 * q^55 - 20 * q^57 + 164 * q^59 - 124 * q^61 - 52 * q^63 + 52 * q^65 - 118 * q^67 + 72 * q^69 + 86 * q^71 + 58 * q^73 - 48 * q^75 + 40 * q^79 - 2 * q^81 + 188 * q^83 + 96 * q^85 - 38 * q^87 - 110 * q^89 - 52 * q^91 - 20 * q^93 + 78 * q^95 + 178 * q^97 - 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.366025	−	0.633975i	−0.122008	−	0.211325i	0.798551	−	0.601927i	$-0.205600\pi$
$3$	−0.366025	−	0.633975i	−0.122008	−	0.211325i	−0.920560	+	0.390602i	$0.872267\pi$
$4$		0			0
$5$	−2.63397	+	2.63397i	−0.526795	+	0.526795i	−0.919615	−	0.392820i	$-0.871499\pi$
$5$	−2.63397	+	2.63397i	−0.526795	+	0.526795i	0.392820	+	0.919615i	$0.371499\pi$
$6$		0			0
$7$	−5.73205	+	1.53590i	−0.818864	+	0.219414i	−0.643850	−	0.765152i	$-0.722664\pi$
$7$	−5.73205	+	1.53590i	−0.818864	+	0.219414i	−0.175014	+	0.984566i	$0.555997\pi$
$8$		0			0
$9$	4.23205	−	7.33013i	0.470228	−	0.814459i
$10$		0			0
$11$	4.19615	−	15.6603i	0.381468	−	1.42366i	−0.462191	−	0.886780i	$-0.652937\pi$
$11$	4.19615	−	15.6603i	0.381468	−	1.42366i	0.843659	−	0.536879i	$-0.180397\pi$
$12$		0			0
$13$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$13$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$14$		0			0
$15$	2.63397	+	0.705771i	0.175598	+	0.0470514i
$16$		0			0
$17$	−15.9904	−	9.23205i	−0.940611	−	0.543062i	−0.0504590	−	0.998726i	$-0.516068\pi$
$17$	−15.9904	−	9.23205i	−0.940611	−	0.543062i	−0.890152	+	0.455664i	$0.849402\pi$
$18$		0			0
$19$	−1.63397	−	6.09808i	−0.0859987	−	0.320951i	0.909503	−	0.415698i	$-0.136463\pi$
$19$	−1.63397	−	6.09808i	−0.0859987	−	0.320951i	−0.995501	+	0.0947465i	$0.969796\pi$
$20$		0			0
$21$	3.07180	+	3.07180i	0.146276	+	0.146276i
$22$		0			0
$23$	−17.4904	+	10.0981i	−0.760451	+	0.439047i	−0.829458	−	0.558569i	$-0.811350\pi$
$23$	−17.4904	+	10.0981i	−0.760451	+	0.439047i	0.0690064	+	0.997616i	$0.478017\pi$
$24$		0			0
$25$			11.1244i			0.444974i
$26$		0			0
$27$	−12.7846			−0.473504
$28$		0			0
$29$	−4.69615	−	8.13397i	−0.161936	−	0.280482i	0.773627	−	0.633642i	$-0.218441\pi$
$29$	−4.69615	−	8.13397i	−0.161936	−	0.280482i	−0.935563	+	0.353160i	$0.885107\pi$
$30$		0			0
$31$	11.9282	−	11.9282i	0.384781	−	0.384781i	−0.488040	−	0.872821i	$-0.662288\pi$
$31$	11.9282	−	11.9282i	0.384781	−	0.384781i	0.872821	+	0.488040i	$0.162288\pi$
$32$		0			0
$33$	−11.4641	+	3.07180i	−0.347397	+	0.0930848i
$34$		0			0
$35$	11.0526	−	19.1436i	0.315787	−	0.546960i
$36$		0			0
$37$	8.11474	−	30.2846i	0.219317	−	0.818503i	−0.765285	−	0.643692i	$-0.777402\pi$
$37$	8.11474	−	30.2846i	0.219317	−	0.818503i	0.984602	−	0.174811i	$-0.0559315\pi$
$38$		0			0
$39$	−4.75833	+	8.24167i	−0.122008	+	0.211325i
$40$		0			0
$41$	44.9186	+	12.0359i	1.09558	+	0.293558i	0.760962	−	0.648797i	$-0.224728\pi$
$41$	44.9186	+	12.0359i	1.09558	+	0.293558i	0.334614	+	0.942355i	$0.391394\pi$
$42$		0			0
$43$	−45.0000	−	25.9808i	−1.04651	−	0.604204i	−0.124841	−	0.992177i	$-0.539842\pi$
$43$	−45.0000	−	25.9808i	−1.04651	−	0.604204i	−0.921671	+	0.387973i	$0.873175\pi$
$44$		0			0
$45$	8.16025	+	30.4545i	0.181339	+	0.676766i
$46$		0			0
$47$	34.3205	+	34.3205i	0.730224	+	0.730224i	0.970664	−	0.240440i	$-0.0772918\pi$
$47$	34.3205	+	34.3205i	0.730224	+	0.730224i	−0.240440	+	0.970664i	$0.577292\pi$
$48$		0			0
$49$	−11.9378	+	6.89230i	−0.243629	+	0.140659i
$50$		0			0
$51$			13.5167i			0.265033i
$52$		0			0
$53$	−14.7654			−0.278592			−0.139296	−	0.990251i	$-0.544484\pi$
$53$	−14.7654			−0.278592			−0.139296	+	0.990251i	$0.544484\pi$
$54$		0			0
$55$	30.1962	+	52.3013i	0.549021	+	0.950932i
$56$		0			0
$57$	−3.26795	+	3.26795i	−0.0573324	+	0.0573324i
$58$		0			0
$59$	92.9615	−	24.9090i	1.57562	−	0.422186i	0.638053	−	0.769993i	$-0.279740\pi$
$59$	92.9615	−	24.9090i	1.57562	−	0.422186i	0.937566	+	0.347807i	$0.113073\pi$
$60$		0			0
$61$	−12.8135	+	22.1936i	−0.210057	+	0.363829i	−0.951732	−	0.306930i	$-0.900698\pi$
$61$	−12.8135	+	22.1936i	−0.210057	+	0.363829i	0.741675	+	0.670759i	$0.234032\pi$
$62$		0			0
$63$	−13.0000	+	48.5167i	−0.206349	+	0.770106i
$64$		0			0
$65$	46.7750	+	12.5333i	0.719615	+	0.192820i
$66$		0			0
$67$	−39.0263	−	10.4571i	−0.582482	−	0.156076i	−0.0444669	−	0.999011i	$-0.514159\pi$
$67$	−39.0263	−	10.4571i	−0.582482	−	0.156076i	−0.538015	+	0.842935i	$0.680826\pi$
$68$		0			0
$69$	12.8038	+	7.39230i	0.185563	+	0.107135i
$70$		0			0
$71$	11.9737	+	44.6865i	0.168644	+	0.629388i	0.997547	+	0.0699959i	$0.0222986\pi$
$71$	11.9737	+	44.6865i	0.168644	+	0.629388i	−0.828903	+	0.559392i	$0.811035\pi$
$72$		0			0
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	0.562653	−	0.826693i	$-0.309781\pi$
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	−0.826693	+	0.562653i	$0.809781\pi$
$74$		0			0
$75$	7.05256	−	4.07180i	0.0940341	−	0.0542906i
$76$		0			0
$77$			96.2102i			1.24948i
$78$		0			0
$79$	−62.7461			−0.794255			−0.397127	−	0.917763i	$-0.629993\pi$
$79$	−62.7461			−0.794255			−0.397127	+	0.917763i	$0.629993\pi$
$80$		0			0
$81$	−33.4090	−	57.8660i	−0.412456	−	0.714395i
$82$		0			0
$83$	24.4833	−	24.4833i	0.294980	−	0.294980i	−0.544064	−	0.839044i	$-0.683115\pi$
$83$	24.4833	−	24.4833i	0.294980	−	0.294980i	0.839044	+	0.544064i	$0.183115\pi$
$84$		0			0
$85$	66.4352	−	17.8013i	0.781591	−	0.209427i
$86$		0			0
$87$	−3.43782	+	5.95448i	−0.0395152	+	0.0684423i
$88$		0			0
$89$	−23.1699	+	86.4711i	−0.260336	+	0.971586i	0.704708	+	0.709497i	$0.251078\pi$
$89$	−23.1699	+	86.4711i	−0.260336	+	0.971586i	−0.965044	+	0.262089i	$0.915589\pi$
$90$		0			0
$91$	54.5500	+	54.5500i	0.599450	+	0.599450i
$92$		0			0
$93$	−11.9282	−	3.19615i	−0.128260	−	0.0343672i
$94$		0			0
$95$	20.3660	+	11.7583i	0.214379	+	0.123772i
$96$		0			0
$97$	14.1891	+	52.9545i	0.146279	+	0.545923i	0.999695	+	0.0246915i	$0.00786034\pi$
$97$	14.1891	+	52.9545i	0.146279	+	0.545923i	−0.853416	+	0.521231i	$0.825473\pi$
$98$		0			0
$99$	−97.0333	−	97.0333i	−0.980135	−	0.980135i
$100$		0			0
$101$	138.560	−	79.9974i	1.37188	−	0.792054i	0.380713	−	0.924693i	$-0.375679\pi$
$101$	138.560	−	79.9974i	1.37188	−	0.792054i	0.991164	+	0.132640i	$0.0423453\pi$
$102$		0			0
$103$			78.7705i			0.764762i	0.924005	+	0.382381i	$0.124896\pi$
$103$			78.7705i			0.764762i	−0.924005	+	0.382381i	$0.875104\pi$
$104$		0			0
$105$	−16.1821			−0.154115
$106$		0			0
$107$	−47.6673	−	82.5622i	−0.445489	−	0.771609i	0.552597	−	0.833448i	$-0.313637\pi$
$107$	−47.6673	−	82.5622i	−0.445489	−	0.771609i	−0.998086	+	0.0618392i	$0.980303\pi$
$108$		0			0
$109$	−51.9808	+	51.9808i	−0.476888	+	0.476888i	−0.904135	−	0.427247i	$-0.859483\pi$
$109$	−51.9808	+	51.9808i	−0.476888	+	0.476888i	0.427247	+	0.904135i	$0.359483\pi$
$110$		0			0
$111$	−22.1699	+	5.94040i	−0.199729	+	0.0535171i
$112$		0			0
$113$	71.9904	−	124.691i	0.637083	−	1.10346i	−0.348987	−	0.937128i	$-0.613474\pi$
$113$	71.9904	−	124.691i	0.637083	−	1.10346i	0.986070	−	0.166332i	$-0.0531925\pi$
$114$		0			0
$115$	19.4711	−	72.6673i	0.169314	−	0.631890i
$116$		0			0
$117$	−110.033			−0.940456
$118$		0			0
$119$	105.837	+	28.3590i	0.889388	+	0.238311i
$120$		0			0
$121$	−122.847	−	70.9256i	−1.01526	−	0.586162i
$122$		0			0
$123$	−8.81089	−	32.8827i	−0.0716332	−	0.267339i
$124$		0			0
$125$	−95.1506	−	95.1506i	−0.761205	−	0.761205i
$126$		0			0
$127$	24.6673	−	14.2417i	0.194231	−	0.112139i	−0.399731	−	0.916633i	$-0.630896\pi$
$127$	24.6673	−	14.2417i	0.194231	−	0.112139i	0.593962	+	0.804493i	$0.297563\pi$
$128$		0			0
$129$			38.0385i			0.294872i
$130$		0			0
$131$	2.98076			0.0227539			0.0113770	−	0.999935i	$-0.496379\pi$
$131$	2.98076			0.0227539			0.0113770	+	0.999935i	$0.496379\pi$
$132$		0			0
$133$	18.7321	+	32.4449i	0.140842	+	0.243946i
$134$		0			0
$135$	33.6743	−	33.6743i	0.249440	−	0.249440i
$136$		0			0
$137$	94.6051	−	25.3494i	0.690548	−	0.185032i	0.103555	−	0.994624i	$-0.466978\pi$
$137$	94.6051	−	25.3494i	0.690548	−	0.185032i	0.586993	+	0.809592i	$0.300312\pi$
$138$		0			0
$139$	16.2154	−	28.0859i	0.116657	−	0.202057i	−0.801784	−	0.597614i	$-0.796115\pi$
$139$	16.2154	−	28.0859i	0.116657	−	0.202057i	0.918441	+	0.395558i	$0.129449\pi$
$140$		0			0
$141$	9.19615	−	34.3205i	0.0652209	−	0.243408i
$142$		0			0
$143$	−203.583	+	54.5500i	−1.42366	+	0.381468i
$144$		0			0
$145$	33.7942	+	9.05514i	0.233064	+	0.0624492i
$146$		0			0
$147$	8.73909	+	5.04552i	0.0594496	+	0.0343232i
$148$		0			0
$149$	−33.0903	−	123.495i	−0.222083	−	0.828824i	−0.983552	−	0.180624i	$-0.942188\pi$
$149$	−33.0903	−	123.495i	−0.222083	−	0.828824i	0.761469	−	0.648201i	$-0.224478\pi$
$150$		0			0
$151$	−127.995	−	127.995i	−0.847648	−	0.847648i	0.142191	−	0.989839i	$-0.454585\pi$
$151$	−127.995	−	127.995i	−0.847648	−	0.847648i	−0.989839	+	0.142191i	$0.954585\pi$
$152$		0			0
$153$	−135.344	+	78.1410i	−0.884603	+	0.510726i
$154$		0			0
$155$			62.8372i			0.405401i
$156$		0			0
$157$	−97.7461			−0.622587			−0.311293	−	0.950314i	$-0.600762\pi$
$157$	−97.7461			−0.622587			−0.311293	+	0.950314i	$0.600762\pi$
$158$		0			0
$159$	5.40450	+	9.36087i	0.0339906	+	0.0588734i
$160$		0			0
$161$	84.7461	−	84.7461i	0.526374	−	0.526374i
$162$		0			0
$163$	122.282	−	32.7654i	0.750197	−	0.201015i	0.136591	−	0.990627i	$-0.456385\pi$
$163$	122.282	−	32.7654i	0.750197	−	0.201015i	0.613605	+	0.789613i	$0.289719\pi$
$164$		0			0
$165$	22.1051	−	38.2872i	0.133970	−	0.232044i
$166$		0			0
$167$	13.5936	−	50.7321i	0.0813989	−	0.303785i	−0.913209	−	0.407491i	$-0.866404\pi$
$167$	13.5936	−	50.7321i	0.0813989	−	0.303785i	0.994608	+	0.103707i	$0.0330703\pi$
$168$		0			0
$169$	−84.5000	+	146.358i	−0.500000	+	0.866025i
$170$		0			0
$171$	−51.6147	−	13.8301i	−0.301841	−	0.0808779i
$172$		0			0
$173$	118.865	+	68.6269i	0.687083	+	0.396687i	0.802518	−	0.596628i	$-0.203493\pi$
$173$	118.865	+	68.6269i	0.687083	+	0.396687i	−0.115435	+	0.993315i	$0.536826\pi$
$174$		0			0
$175$	−17.0859	−	63.7654i	−0.0976336	−	0.364374i
$176$		0			0
$177$	−49.8179	−	49.8179i	−0.281457	−	0.281457i
$178$		0			0
$179$	−0.903811	+	0.521815i	−0.00504922	+	0.00291517i	−0.502522	−	0.864564i	$-0.667595\pi$
$179$	−0.903811	+	0.521815i	−0.00504922	+	0.00291517i	0.497473	+	0.867479i	$0.334261\pi$
$180$		0			0
$181$		−	23.0807i		−	0.127518i	−0.997965	−	0.0637589i	$-0.979691\pi$
$181$		−	23.0807i		−	0.127518i	0.997965	−	0.0637589i	$-0.0203089\pi$
$182$		0			0
$183$	18.7602			0.102515
$184$		0			0
$185$	58.3949	+	101.143i	0.315648	+	0.546718i
$186$		0			0
$187$	−211.674	+	211.674i	−1.13195	+	1.13195i
$188$		0			0
$189$	73.2820	−	19.6359i	0.387736	−	0.103893i
$190$		0			0
$191$	147.002	−	254.615i	0.769643	−	1.33306i	−0.168113	−	0.985768i	$-0.553767\pi$
$191$	147.002	−	254.615i	0.769643	−	1.33306i	0.937756	−	0.347294i	$-0.112899\pi$
$192$		0			0
$193$	85.5507	−	319.279i	0.443268	−	1.65430i	−0.277202	−	0.960812i	$-0.589407\pi$
$193$	85.5507	−	319.279i	0.443268	−	1.65430i	0.720470	−	0.693486i	$-0.243926\pi$
$194$		0			0
$195$	−9.17503	−	34.2417i	−0.0470514	−	0.175598i
$196$		0			0
$197$	85.1122	+	22.8057i	0.432041	+	0.115765i	0.468284	−	0.883578i	$-0.344872\pi$
$197$	85.1122	+	22.8057i	0.432041	+	0.115765i	−0.0362429	+	0.999343i	$0.511539\pi$
$198$		0			0
$199$	−174.452	−	100.720i	−0.876643	−	0.506130i	−0.00709275	−	0.999975i	$-0.502258\pi$
$199$	−174.452	−	100.720i	−0.876643	−	0.506130i	−0.869550	+	0.493845i	$0.835591\pi$
$200$		0			0
$201$	7.65510	+	28.5692i	0.0380851	+	0.142135i
$202$		0			0
$203$	39.4115	+	39.4115i	0.194146	+	0.194146i
$204$		0			0
$205$	−150.017	+	86.6122i	−0.731789	+	0.422498i
$206$		0			0
$207$			170.942i			0.825808i
$208$		0			0
$209$	−102.354			−0.489731
$210$		0			0
$211$	36.6481	+	63.4763i	0.173687	+	0.300836i	0.939706	−	0.341983i	$-0.111098\pi$
$211$	36.6481	+	63.4763i	0.173687	+	0.300836i	−0.766019	+	0.642818i	$0.777765\pi$
$212$		0			0
$213$	23.9474	−	23.9474i	0.112429	−	0.112429i
$214$		0			0
$215$	186.962	−	50.0962i	0.869588	−	0.233006i
$216$		0			0
$217$	−50.0526	+	86.6936i	−0.230657	+	0.399510i
$218$		0			0
$219$	−5.16472	+	19.2750i	−0.0235832	+	0.0880137i
$220$		0			0
$221$			240.033i			1.08612i
$222$		0			0
$223$	367.533	+	98.4801i	1.64813	+	0.441615i	0.959088	−	0.283108i	$-0.0913656\pi$
$223$	367.533	+	98.4801i	1.64813	+	0.441615i	0.689040	+	0.724723i	$0.258032\pi$
$224$		0			0
$225$	81.5429	+	47.0788i	0.362413	+	0.209239i
$226$		0			0
$227$	108.280	+	404.107i	0.477005	+	1.78021i	0.613640	+	0.789586i	$0.289704\pi$
$227$	108.280	+	404.107i	0.477005	+	1.78021i	−0.136635	+	0.990621i	$0.543629\pi$
$228$		0			0
$229$	−72.2679	−	72.2679i	−0.315581	−	0.315581i	0.531486	−	0.847067i	$-0.321634\pi$
$229$	−72.2679	−	72.2679i	−0.315581	−	0.315581i	−0.847067	+	0.531486i	$0.821634\pi$
$230$		0			0
$231$	60.9948	−	35.2154i	0.264047	−	0.152448i
$232$		0			0
$233$			256.592i			1.10125i	0.834751	+	0.550627i	$0.185611\pi$
$233$			256.592i			1.10125i	−0.834751	+	0.550627i	$0.814389\pi$
$234$		0			0
$235$	−180.799			−0.769356
$236$		0			0
$237$	22.9667	+	39.7795i	0.0969058	+	0.167846i
$238$		0			0
$239$	−39.3449	+	39.3449i	−0.164623	+	0.164623i	−0.784611	−	0.619988i	$-0.787137\pi$
$239$	−39.3449	+	39.3449i	−0.164623	+	0.164623i	0.619988	+	0.784611i	$0.287137\pi$
$240$		0			0
$241$	233.351	−	62.5263i	0.968262	−	0.259445i	0.260168	−	0.965563i	$-0.416222\pi$
$241$	233.351	−	62.5263i	0.968262	−	0.259445i	0.708094	+	0.706118i	$0.249555\pi$
$242$		0			0
$243$	−81.9878	+	142.007i	−0.337398	+	0.584391i
$244$		0			0
$245$	13.2898	−	49.5981i	0.0542439	−	0.202441i
$246$		0			0
$247$	−58.0333	+	58.0333i	−0.234953	+	0.234953i
$248$		0			0
$249$	−24.4833	−	6.56029i	−0.0983267	−	0.0263466i
$250$		0			0
$251$	221.375	+	127.811i	0.881972	+	0.509207i	0.871308	−	0.490736i	$-0.163272\pi$
$251$	221.375	+	127.811i	0.881972	+	0.509207i	0.0106638	+	0.999943i	$0.496606\pi$
$252$		0			0
$253$	84.7461	+	316.277i	0.334965	+	1.25011i
$254$		0			0
$255$	−35.6025	−	35.6025i	−0.139618	−	0.139618i
$256$		0			0
$257$	85.7731	−	49.5211i	0.333747	−	0.192689i	−0.323756	−	0.946141i	$-0.604946\pi$
$257$	85.7731	−	49.5211i	0.333747	−	0.192689i	0.657504	+	0.753451i	$0.271612\pi$
$258$		0			0
$259$			186.056i			0.718364i
$260$		0			0
$261$	−79.4974			−0.304588
$262$		0			0
$263$	−127.669	−	221.130i	−0.485434	−	0.840797i	0.514426	−	0.857535i	$-0.328005\pi$
$263$	−127.669	−	221.130i	−0.485434	−	0.840797i	−0.999860	+	0.0167383i	$0.994672\pi$
$264$		0			0
$265$	38.8916	−	38.8916i	0.146761	−	0.146761i
$266$		0			0
$267$	63.3013	−	16.9615i	0.237083	−	0.0635263i
$268$		0			0
$269$	46.3538	−	80.2872i	0.172319	−	0.298465i	−0.766911	−	0.641753i	$-0.778207\pi$
$269$	46.3538	−	80.2872i	0.172319	−	0.298465i	0.939230	+	0.343288i	$0.111541\pi$
$270$		0			0
$271$	113.133	−	422.219i	0.417466	−	1.55800i	−0.362379	−	0.932031i	$-0.618035\pi$
$271$	113.133	−	422.219i	0.417466	−	1.55800i	0.779845	−	0.625973i	$-0.215298\pi$
$272$		0			0
$273$	14.6166	−	54.5500i	0.0535407	−	0.199817i
$274$		0			0
$275$	174.210	+	46.6795i	0.633492	+	0.169744i
$276$		0			0
$277$	−302.110	−	174.423i	−1.09065	−	0.629686i	−0.156899	−	0.987615i	$-0.550150\pi$
$277$	−302.110	−	174.423i	−1.09065	−	0.629686i	−0.933749	+	0.357929i	$0.883483\pi$
$278$		0			0
$279$	−36.9545	−	137.916i	−0.132453	−	0.494323i
$280$		0			0
$281$	91.9737	+	91.9737i	0.327309	+	0.327309i	0.851562	−	0.524254i	$-0.175656\pi$
$281$	91.9737	+	91.9737i	0.327309	+	0.327309i	−0.524254	+	0.851562i	$0.675656\pi$
$282$		0			0
$283$	30.8038	−	17.7846i	0.108848	−	0.0628431i	−0.444588	−	0.895735i	$-0.646650\pi$
$283$	30.8038	−	17.7846i	0.108848	−	0.0628431i	0.553435	+	0.832892i	$0.313317\pi$
$284$		0			0
$285$		−	17.2154i		−	0.0604049i
$286$		0			0
$287$	−275.962			−0.961538
$288$		0			0
$289$	25.9615	+	44.9667i	0.0898323	+	0.155594i
$290$		0			0
$291$	28.3782	−	28.3782i	0.0975197	−	0.0975197i
$292$		0			0
$293$	386.758	−	103.631i	1.31999	−	0.353691i	0.471017	−	0.882124i	$-0.343887\pi$
$293$	386.758	−	103.631i	1.31999	−	0.353691i	0.848975	+	0.528433i	$0.177220\pi$
$294$		0			0
$295$	−179.249	+	310.468i	−0.607623	+	1.05243i
$296$		0			0
$297$	−53.6462	+	200.210i	−0.180627	+	0.674109i
$298$		0			0
$299$	227.375	+	131.275i	0.760451	+	0.439047i
$300$		0			0
$301$	297.846	+	79.8076i	0.989522	+	0.265142i
$302$		0			0
$303$	−101.433	−	58.5622i	−0.334761	−	0.193275i
$304$		0			0
$305$	−24.7070	−	92.2077i	−0.0810065	−	0.302320i
$306$		0			0
$307$	−260.219	−	260.219i	−0.847619	−	0.847619i	0.142216	−	0.989836i	$-0.454577\pi$
$307$	−260.219	−	260.219i	−0.847619	−	0.847619i	−0.989836	+	0.142216i	$0.954577\pi$
$308$		0			0
$309$	49.9385	−	28.8320i	0.161613	−	0.0933075i
$310$		0			0
$311$			71.4782i			0.229833i	0.993375	+	0.114917i	$0.0366601\pi$
$311$			71.4782i			0.229833i	−0.993375	+	0.114917i	$0.963340\pi$
$312$		0			0
$313$	−394.315			−1.25979			−0.629897	−	0.776679i	$-0.716903\pi$
$313$	−394.315			−1.25979			−0.629897	+	0.776679i	$0.716903\pi$
$314$		0			0
$315$	−93.5500	−	162.033i	−0.296984	−	0.514391i
$316$		0			0
$317$	−206.054	+	206.054i	−0.650014	+	0.650014i	−0.952996	−	0.302982i	$-0.902018\pi$
$317$	−206.054	+	206.054i	−0.650014	+	0.650014i	0.302982	+	0.952996i	$0.402018\pi$
$318$		0			0
$319$	−147.086	+	39.4115i	−0.461084	+	0.123547i
$320$		0			0
$321$	−34.8949	+	60.4397i	−0.108707	+	0.188286i
$322$		0			0
$323$	−30.1699	+	112.595i	−0.0934052	+	0.348593i
$324$		0			0
$325$	125.242	−	72.3083i	0.385359	−	0.222487i
$326$		0			0
$327$	51.9808	+	13.9282i	0.158963	+	0.0425939i
$328$		0			0
$329$	−249.440	−	144.014i	−0.758175	−	0.437733i
$330$		0			0
$331$	119.397	+	445.597i	0.360717	+	1.34622i	0.873135	+	0.487479i	$0.162083\pi$
$331$	119.397	+	445.597i	0.360717	+	1.34622i	−0.512417	+	0.858737i	$0.671250\pi$
$332$		0			0
$333$	−187.648	−	187.648i	−0.563508	−	0.563508i
$334$		0			0
$335$	130.338	−	75.2506i	0.389068	−	0.224629i
$336$		0			0
$337$			144.779i			0.429613i	0.976657	+	0.214806i	$0.0689120\pi$
$337$			144.779i			0.429613i	−0.976657	+	0.214806i	$0.931088\pi$
$338$		0			0
$339$	−105.401			−0.310918
$340$		0			0
$341$	−136.746	−	236.851i	−0.401015	−	0.694578i
$342$		0			0
$343$	263.454	−	263.454i	0.768087	−	0.768087i
$344$		0			0
$345$	−53.1962	+	14.2539i	−0.154192	+	0.0413156i
$346$		0			0
$347$	243.590	−	421.911i	0.701989	−	1.21588i	−0.265778	−	0.964034i	$-0.585629\pi$
$347$	243.590	−	421.911i	0.701989	−	1.21588i	0.967767	−	0.251847i	$-0.0810380\pi$
$348$		0			0
$349$	−3.04036	+	11.3468i	−0.00871164	+	0.0325123i	−0.970145	−	0.242526i	$-0.922024\pi$
$349$	−3.04036	+	11.3468i	−0.00871164	+	0.0325123i	0.961433	+	0.275039i	$0.0886906\pi$
$350$		0			0
$351$	83.1000	+	143.933i	0.236752	+	0.410067i
$352$		0			0
$353$	−276.169	−	73.9993i	−0.782349	−	0.209630i	−0.154529	−	0.987988i	$-0.549386\pi$
$353$	−276.169	−	73.9993i	−0.782349	−	0.209630i	−0.627820	+	0.778358i	$0.716053\pi$
$354$		0			0
$355$	−149.242	−	86.1647i	−0.420399	−	0.242718i
$356$		0			0
$357$	−20.7602	−	77.4782i	−0.0581519	−	0.217026i
$358$		0			0
$359$	−92.0770	−	92.0770i	−0.256482	−	0.256482i	0.567140	−	0.823622i	$-0.308050\pi$
$359$	−92.0770	−	92.0770i	−0.256482	−	0.256482i	−0.823622	+	0.567140i	$0.808050\pi$
$360$		0			0
$361$	278.119	−	160.572i	0.770411	−	0.444797i
$362$		0			0
$363$			103.842i			0.286067i
$364$		0			0
$365$	101.540			0.278191
$366$		0			0
$367$	6.27499	+	10.8686i	0.0170981	+	0.0296147i	0.874448	−	0.485120i	$-0.161224\pi$
$367$	6.27499	+	10.8686i	0.0170981	+	0.0296147i	−0.857350	+	0.514734i	$0.827891\pi$
$368$		0			0
$369$	278.322	−	278.322i	0.754261	−	0.754261i
$370$		0			0
$371$	84.6359	−	22.6781i	0.228129	−	0.0611270i
$372$		0			0
$373$	155.638	−	269.574i	0.417261	−	0.722718i	−0.578402	−	0.815752i	$-0.696323\pi$
$373$	155.638	−	269.574i	0.417261	−	0.722718i	0.995663	+	0.0930345i	$0.0296567\pi$
$374$		0			0
$375$	−25.4955	+	95.1506i	−0.0679881	+	0.253735i
$376$		0			0
$377$	−61.0500	+	105.742i	−0.161936	+	0.280482i
$378$		0			0
$379$	−379.858	−	101.783i	−1.00226	−	0.268556i	−0.279871	−	0.960038i	$-0.590292\pi$
$379$	−379.858	−	101.783i	−1.00226	−	0.268556i	−0.722394	+	0.691482i	$0.756958\pi$
$380$		0			0
$381$	−18.0577	−	10.4256i	−0.0473956	−	0.0273638i
$382$		0			0
$383$	−191.061	−	713.051i	−0.498855	−	1.86175i	−0.507269	−	0.861788i	$-0.669345\pi$
$383$	−191.061	−	713.051i	−0.498855	−	1.86175i	0.00841386	−	0.999965i	$-0.497322\pi$
$384$		0			0
$385$	−253.415	−	253.415i	−0.658222	−	0.658222i
$386$		0			0
$387$	−380.885	+	219.904i	−0.984198	+	0.568227i
$388$		0			0
$389$			344.478i			0.885548i	0.896633	+	0.442774i	$0.146006\pi$
$389$			344.478i			0.885548i	−0.896633	+	0.442774i	$0.853994\pi$
$390$		0			0
$391$	372.904			0.953718
$392$		0			0
$393$	−1.09103	−	1.88973i	−0.00277617	−	0.00480847i
$394$		0			0
$395$	165.272	−	165.272i	0.418409	−	0.418409i
$396$		0			0
$397$	−678.422	+	181.783i	−1.70887	+	0.457891i	−0.975148	−	0.221556i	$-0.928886\pi$
$397$	−678.422	+	181.783i	−1.70887	+	0.457891i	−0.733725	+	0.679447i	$0.762220\pi$
$398$		0			0
$399$	13.7128	−	23.7513i	0.0343680	−	0.0595270i
$400$		0			0
$401$	146.833	−	547.989i	0.366168	−	1.36656i	−0.499663	−	0.866220i	$-0.666543\pi$
$401$	146.833	−	547.989i	0.366168	−	1.36656i	0.865831	−	0.500336i	$-0.166790\pi$
$402$		0			0
$403$	−211.825	−	56.7583i	−0.525620	−	0.140840i
$404$		0			0
$405$	240.416	+	64.4193i	0.593620	+	0.159060i
$406$		0			0
$407$	−440.214	−	254.158i	−1.08161	−	0.624466i
$408$		0			0
$409$	26.3212	+	98.2321i	0.0643550	+	0.240176i	0.990609	−	0.136723i	$-0.0436570\pi$
$409$	26.3212	+	98.2321i	0.0643550	+	0.240176i	−0.926254	+	0.376899i	$0.876990\pi$
$410$		0			0
$411$	−50.6987	−	50.6987i	−0.123355	−	0.123355i
$412$		0			0
$413$	−494.603	+	285.559i	−1.19758	+	0.691426i
$414$		0			0
$415$			128.977i			0.310788i
$416$		0			0
$417$	−23.7410			−0.0569328
$418$		0			0
$419$	322.279	+	558.203i	0.769162	+	1.33223i	0.938018	+	0.346587i	$0.112659\pi$
$419$	322.279	+	558.203i	0.769162	+	1.33223i	−0.168856	+	0.985641i	$0.554007\pi$
$420$		0			0
$421$	346.619	−	346.619i	0.823322	−	0.823322i	−0.163261	−	0.986583i	$-0.552201\pi$
$421$	346.619	−	346.619i	0.823322	−	0.823322i	0.986583	+	0.163261i	$0.0522013\pi$
$422$		0			0
$423$	396.820	−	106.328i	0.938108	−	0.251365i
$424$		0			0
$425$	102.701	−	177.883i	0.241649	−	0.418547i
$426$		0			0
$427$	39.3604	−	146.895i	0.0921788	−	0.344016i
$428$		0			0
$429$	109.100	+	109.100i	0.254312	+	0.254312i
$430$		0			0
$431$	−101.699	−	27.2501i	−0.235960	−	0.0632253i	0.138901	−	0.990306i	$-0.455643\pi$
$431$	−101.699	−	27.2501i	−0.235960	−	0.0632253i	−0.374861	+	0.927081i	$0.622310\pi$
$432$		0			0
$433$	596.892	+	344.616i	1.37850	+	0.795880i	0.991979	−	0.126399i	$-0.0403421\pi$
$433$	596.892	+	344.616i	1.37850	+	0.795880i	0.386525	+	0.922279i	$0.373675\pi$
$434$		0			0
$435$	−6.62882	−	24.7391i	−0.0152387	−	0.0568715i
$436$		0			0
$437$	90.1577	+	90.1577i	0.206310	+	0.206310i
$438$		0			0
$439$	−78.0577	+	45.0666i	−0.177808	+	0.102657i	−0.586262	−	0.810121i	$-0.699401\pi$
$439$	−78.0577	+	45.0666i	−0.177808	+	0.102657i	0.408454	+	0.912779i	$0.366068\pi$
$440$		0			0
$441$			116.674i			0.264568i
$442$		0			0
$443$	−642.277			−1.44983			−0.724917	−	0.688836i	$-0.758122\pi$
$443$	−642.277			−1.44983			−0.724917	+	0.688836i	$0.758122\pi$
$444$		0			0
$445$	−166.734	−	288.792i	−0.374683	−	0.648970i
$446$		0			0
$447$	−66.1807	+	66.1807i	−0.148055	+	0.148055i
$448$		0			0
$449$	22.6007	−	6.05583i	0.0503355	−	0.0134874i	−0.233563	−	0.972342i	$-0.575039\pi$
$449$	22.6007	−	6.05583i	0.0503355	−	0.0134874i	0.283899	+	0.958854i	$0.408372\pi$
$450$		0			0
$451$	376.970	−	652.932i	0.835855	−	1.44774i
$452$		0			0
$453$	−34.2961	+	127.995i	−0.0757089	+	0.282549i
$454$		0			0
$455$	−287.367			−0.631575
$456$		0			0
$457$	228.698	+	61.2795i	0.500433	+	0.134091i	0.500201	−	0.865909i	$-0.333259\pi$
$457$	228.698	+	61.2795i	0.500433	+	0.134091i	0.000232237		1.00000i	$0.499926\pi$
$458$		0			0
$459$	204.431	+	118.028i	0.445383	+	0.257142i
$460$		0			0
$461$	−12.6032	−	47.0359i	−0.0273389	−	0.102030i	0.950908	−	0.309473i	$-0.100153\pi$
$461$	−12.6032	−	47.0359i	−0.0273389	−	0.102030i	−0.978247	+	0.207443i	$0.933486\pi$
$462$		0			0
$463$	521.191	+	521.191i	1.12568	+	1.12568i	0.990871	+	0.134811i	$0.0430428\pi$
$463$	521.191	+	521.191i	1.12568	+	1.12568i	0.134811	+	0.990871i	$0.456957\pi$
$464$		0			0
$465$	39.8372	−	23.0000i	0.0856713	−	0.0494624i
$466$		0			0
$467$			141.415i			0.302817i	0.988471	+	0.151408i	$0.0483808\pi$
$467$			141.415i			0.302817i	−0.988471	+	0.151408i	$0.951619\pi$
$468$		0			0
$469$	239.762			0.511219
$470$		0			0
$471$	35.7776	+	61.9686i	0.0759609	+	0.131568i
$472$		0			0
$473$	−595.692	+	595.692i	−1.25939	+	1.25939i
$474$		0			0
$475$	67.8372	−	18.1769i	0.142815	−	0.0382672i
$476$		0			0
$477$	−62.4878	+	108.232i	−0.131002	+	0.226902i
$478$		0			0
$479$	−193.783	+	723.207i	−0.404557	+	1.50983i	0.400315	+	0.916378i	$0.368901\pi$
$479$	−193.783	+	723.207i	−0.404557	+	1.50983i	−0.804872	+	0.593449i	$0.797766\pi$
$480$		0			0
$481$	−393.700	+	105.492i	−0.818503	+	0.219317i
$482$		0			0
$483$	−84.7461	−	22.7077i	−0.175458	−	0.0470138i
$484$		0			0
$485$	−176.855	−	102.107i	−0.364648	−	0.210530i
$486$		0			0
$487$	62.9371	+	234.885i	0.129234	+	0.482309i	0.999955	−	0.00946847i	$-0.00301395\pi$
$487$	62.9371	+	234.885i	0.129234	+	0.482309i	−0.870721	+	0.491778i	$0.836347\pi$
$488$		0			0
$489$	−65.5307	−	65.5307i	−0.134010	−	0.134010i
$490$		0			0
$491$	73.3191	−	42.3308i	0.149326	−	0.0862135i	−0.423475	−	0.905908i	$-0.639190\pi$
$491$	73.3191	−	42.3308i	0.149326	−	0.0862135i	0.572801	+	0.819694i	$0.305857\pi$
$492$		0			0
$493$			173.420i			0.351766i
$494$		0			0
$495$	511.167			1.03266
$496$		0			0
$497$	−137.268	−	237.755i	−0.276193	−	0.478380i
$498$		0			0
$499$	134.397	−	134.397i	0.269334	−	0.269334i	−0.559498	−	0.828832i	$-0.689006\pi$
$499$	134.397	−	134.397i	0.269334	−	0.269334i	0.828832	+	0.559498i	$0.189006\pi$
$500$		0			0
$501$	−37.1384	+	9.95121i	−0.0741286	+	0.0198627i
$502$		0			0
$503$	−398.200	+	689.703i	−0.791650	+	1.37118i	0.133295	+	0.991076i	$0.457444\pi$
$503$	−398.200	+	689.703i	−0.791650	+	1.37118i	−0.924945	+	0.380102i	$0.875889\pi$
$504$		0			0
$505$	−154.251	+	575.674i	−0.305448	+	1.13995i
$506$		0			0
$507$	123.717			0.244017
$508$		0			0
$509$	79.6051	+	21.3301i	0.156395	+	0.0419059i	0.336167	−	0.941802i	$-0.390869\pi$
$509$	79.6051	+	21.3301i	0.156395	+	0.0419059i	−0.179772	+	0.983708i	$0.557536\pi$
$510$		0			0
$511$	140.090	+	80.8808i	0.274148	+	0.158279i
$512$		0			0
$513$	20.8897	+	77.9615i	0.0407207	+	0.151972i
$514$		0			0
$515$	−207.480	−	207.480i	−0.402873	−	0.402873i
$516$		0			0
$517$	681.482	−	393.454i	1.31815	−	0.761032i
$518$		0			0
$519$		−	100.477i		−	0.193597i
$520$		0			0
$521$	677.011			1.29945			0.649723	−	0.760171i	$-0.274885\pi$
$521$	677.011			1.29945			0.649723	+	0.760171i	$0.274885\pi$
$522$		0			0
$523$	−91.8269	−	159.049i	−0.175577	−	0.304109i	0.764784	−	0.644287i	$-0.222846\pi$
$523$	−91.8269	−	159.049i	−0.175577	−	0.304109i	−0.940361	+	0.340179i	$0.889512\pi$
$524$		0			0
$525$	−34.1718	+	34.1718i	−0.0650891	+	0.0650891i
$526$		0			0
$527$	−300.858	+	80.6147i	−0.570889	+	0.152969i
$528$		0			0
$529$	−60.5577	+	104.889i	−0.114476	+	0.198278i
$530$		0			0
$531$	210.832	−	786.836i	0.397047	−	1.48180i
$532$		0			0
$533$	−156.467	−	583.942i	−0.293558	−	1.09558i
$534$		0			0
$535$	343.021	+	91.9122i	0.641161	+	0.171799i
$536$		0			0
$537$	0.661635	+	0.381995i	0.00123210	+	0.000711351i
$538$		0			0
$539$	57.8423	+	215.870i	0.107314	+	0.400502i
$540$		0			0
$541$	317.629	+	317.629i	0.587114	+	0.587114i	0.936849	−	0.349735i	$-0.113728\pi$
$541$	317.629	+	317.629i	0.587114	+	0.587114i	−0.349735	+	0.936849i	$0.613728\pi$
$542$		0			0
$543$	−14.6326	+	8.44813i	−0.0269477	+	0.0155583i
$544$		0			0
$545$		−	273.832i		−	0.502444i
$546$		0			0
$547$	724.904			1.32524			0.662618	−	0.748958i	$-0.269445\pi$
$547$	724.904			1.32524			0.662618	+	0.748958i	$0.269445\pi$
$548$		0			0
$549$	108.454	+	187.849i	0.197549	+	0.342165i
$550$		0			0
$551$	−41.9282	+	41.9282i	−0.0760947	+	0.0760947i
$552$		0			0
$553$	359.664	−	96.3717i	0.650387	−	0.174271i
$554$		0			0
$555$	42.7480	−	74.0417i	0.0770235	−	0.133409i
$556$		0			0
$557$	−31.0641	+	115.933i	−0.0557703	+	0.208138i	−0.988188	−	0.153244i	$-0.951028\pi$
$557$	−31.0641	+	115.933i	−0.0557703	+	0.208138i	0.932418	+	0.361381i	$0.117695\pi$
$558$		0			0
$559$			675.500i			1.20841i
$560$		0			0
$561$	211.674	+	56.7180i	0.377316	+	0.101102i
$562$		0			0
$563$	534.888	+	308.818i	0.950068	+	0.548522i	0.893102	−	0.449854i	$-0.148524\pi$
$563$	534.888	+	308.818i	0.950068	+	0.548522i	0.0569660	+	0.998376i	$0.481857\pi$
$564$		0			0
$565$	138.812	+	518.054i	0.245685	+	0.916909i
$566$		0			0
$567$	280.378	+	280.378i	0.494494	+	0.494494i
$568$		0			0
$569$	−381.315	+	220.153i	−0.670150	+	0.386911i	−0.796133	−	0.605121i	$-0.793125\pi$
$569$	−381.315	+	220.153i	−0.670150	+	0.386911i	0.125983	+	0.992032i	$0.459791\pi$
$570$		0			0
$571$		−	618.249i		−	1.08275i	−0.840782	−	0.541374i	$-0.817904\pi$
$571$		−	618.249i		−	1.08275i	0.840782	−	0.541374i	$-0.182096\pi$
$572$		0			0
$573$	−215.226			−0.375612
$574$		0			0
$575$	−112.335	−	194.569i	−0.195365	−	0.338381i
$576$		0			0
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	−0.899119	−	0.437704i	$-0.855792\pi$
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	0.437704	+	0.899119i	$0.355792\pi$
$578$		0			0
$579$	−233.729	+	62.6274i	−0.403677	+	0.108165i
$580$		0			0
$581$	−102.736	+	177.944i	−0.176826	+	0.306271i
$582$		0			0
$583$	−61.9578	+	231.229i	−0.106274	+	0.396620i
$584$		0			0
$585$	289.825	−	289.825i	0.495427	−	0.495427i
$586$		0			0
$587$	−465.123	−	124.629i	−0.792373	−	0.212316i	−0.160140	−	0.987094i	$-0.551195\pi$
$587$	−465.123	−	124.629i	−0.792373	−	0.212316i	−0.632233	+	0.774779i	$0.717861\pi$
$588$		0			0
$589$	−92.2295	−	53.2487i	−0.156587	−	0.0904053i
$590$		0			0
$591$	−16.6950	−	62.3064i	−0.0282487	−	0.105425i
$592$		0			0
$593$	389.671	+	389.671i	0.657118	+	0.657118i	0.954697	−	0.297579i	$-0.0961792\pi$
$593$	389.671	+	389.671i	0.657118	+	0.657118i	−0.297579	+	0.954697i	$0.596179\pi$
$594$		0			0
$595$	−353.469	+	204.076i	−0.594066	+	0.342984i
$596$		0			0
$597$			147.464i			0.247009i
$598$		0			0
$599$	−808.596			−1.34991			−0.674955	−	0.737859i	$-0.735837\pi$
$599$	−808.596			−1.34991			−0.674955	+	0.737859i	$0.735837\pi$
$600$		0			0
$601$	221.344	+	383.379i	0.368293	+	0.637903i	0.989299	−	0.145904i	$-0.0466089\pi$
$601$	221.344	+	383.379i	0.368293	+	0.637903i	−0.621006	+	0.783806i	$0.713276\pi$
$602$		0			0
$603$	−241.813	+	241.813i	−0.401016	+	0.401016i
$604$		0			0
$605$	510.392	−	136.759i	0.843623	−	0.226048i
$606$		0			0
$607$	−471.398	+	816.485i	−0.776603	+	1.34512i	0.157286	+	0.987553i	$0.449725\pi$
$607$	−471.398	+	816.485i	−0.776603	+	1.34512i	−0.933889	+	0.357563i	$0.883608\pi$
$608$		0			0
$609$	10.5603	−	39.4115i	0.0173404	−	0.0647152i
$610$		0			0
$611$	163.308	−	609.475i	0.267280	−	0.997504i
$612$		0			0
$613$	−973.161	−	260.758i	−1.58754	−	0.425380i	−0.646289	−	0.763093i	$-0.723680\pi$
$613$	−973.161	−	260.758i	−1.58754	−	0.425380i	−0.941249	+	0.337713i	$0.890347\pi$
$614$		0			0
$615$	109.820	+	63.4045i	0.178569	+	0.103097i
$616$		0			0
$617$	−71.9115	−	268.378i	−0.116550	−	0.434972i	0.882848	−	0.469659i	$-0.155623\pi$
$617$	−71.9115	−	268.378i	−0.116550	−	0.434972i	−0.999398	+	0.0346873i	$0.988956\pi$
$618$		0			0
$619$	−206.483	−	206.483i	−0.333576	−	0.333576i	0.520367	−	0.853943i	$-0.325795\pi$
$619$	−206.483	−	206.483i	−0.333576	−	0.333576i	−0.853943	+	0.520367i	$0.825795\pi$
$620$		0			0
$621$	223.608	−	129.100i	0.360077	−	0.207890i
$622$		0			0
$623$		−	531.244i		−	0.852718i
$624$		0			0
$625$	223.140			0.357024
$626$		0			0
$627$	37.4641	+	64.8897i	0.0597514	+	0.103492i
$628$		0			0
$629$	−409.347	+	409.347i	−0.650790	+	0.650790i
$630$		0			0
$631$	428.813	−	114.900i	0.679577	−	0.182092i	0.0975117	−	0.995234i	$-0.468912\pi$
$631$	428.813	−	114.900i	0.679577	−	0.182092i	0.582065	+	0.813142i	$0.302245\pi$
$632$		0			0
$633$	26.8282	−	46.4679i	0.0423827	−	0.0734090i
$634$		0			0
$635$	−27.4608	+	102.485i	−0.0432454	+	0.161394i
$636$		0			0
$637$	155.192	+	89.6000i	0.243629	+	0.140659i
$638$		0			0
$639$	378.231	+	101.347i	0.591911	+	0.158602i
$640$		0			0
$641$	−471.717	−	272.346i	−0.735908	−	0.424877i	0.0846714	−	0.996409i	$-0.473016\pi$
$641$	−471.717	−	272.346i	−0.735908	−	0.424877i	−0.820580	+	0.571532i	$0.806349\pi$
$642$		0			0
$643$	−100.073	−	373.478i	−0.155635	−	0.580837i	−0.999050	−	0.0435749i	$-0.986125\pi$
$643$	−100.073	−	373.478i	−0.155635	−	0.580837i	0.843415	−	0.537262i	$-0.180541\pi$
$644$		0			0
$645$	−100.192	−	100.192i	−0.155337	−	0.155337i
$646$		0			0
$647$	436.056	−	251.757i	0.673966	−	0.389114i	−0.123612	−	0.992331i	$-0.539448\pi$
$647$	436.056	−	251.757i	0.673966	−	0.389114i	0.797578	+	0.603216i	$0.206114\pi$
$648$		0			0
$649$		−	1560.32i		−	2.40420i
$650$		0			0
$651$	73.2820			0.112568
$652$		0			0
$653$	−15.5692	−	26.9667i	−0.0238426	−	0.0412966i	0.853858	−	0.520506i	$-0.174257\pi$
$653$	−15.5692	−	26.9667i	−0.0238426	−	0.0412966i	−0.877701	+	0.479210i	$0.840923\pi$
$654$		0			0
$655$	−7.85125	+	7.85125i	−0.0119866	+	0.0119866i
$656$		0			0
$657$	−222.861	+	59.7154i	−0.339210	+	0.0908910i
$658$		0			0
$659$	379.488	−	657.293i	0.575855	−	0.997410i	−0.420093	−	0.907481i	$-0.638003\pi$
$659$	379.488	−	657.293i	0.575855	−	0.997410i	0.995948	−	0.0899292i	$-0.0286641\pi$
$660$		0			0
$661$	67.8083	−	253.064i	0.102584	−	0.382850i	−0.895475	−	0.445111i	$-0.853164\pi$
$661$	67.8083	−	253.064i	0.102584	−	0.382850i	0.998060	+	0.0622605i	$0.0198310\pi$
$662$		0			0
$663$	152.175	−	87.8583i	0.229525	−	0.132516i
$664$		0			0
$665$	−134.799	−	36.1192i	−0.202705	−	0.0543146i
$666$		0			0
$667$	164.275	+	94.8442i	0.246289	+	0.142195i
$668$		0			0
$669$	−72.0924	−	269.053i	−0.107761	−	0.402171i
$670$		0			0
$671$	293.790	+	293.790i	0.437839	+	0.437839i
$672$		0			0
$673$	−272.210	+	157.160i	−0.404472	+	0.233522i	−0.688412	−	0.725320i	$-0.741692\pi$
$673$	−272.210	+	157.160i	−0.404472	+	0.233522i	0.283940	+	0.958842i	$0.408358\pi$
$674$		0			0
$675$		−	142.221i		−	0.210697i
$676$		0			0
$677$	−547.384			−0.808544			−0.404272	−	0.914639i	$-0.632475\pi$
$677$	−547.384			−0.808544			−0.404272	+	0.914639i	$0.632475\pi$
$678$		0			0
$679$	−162.665	−	281.745i	−0.239566	−	0.414941i
$680$		0			0
$681$	216.560	−	216.560i	0.318003	−	0.318003i
$682$		0			0
$683$	−252.954	+	67.7789i	−0.370358	+	0.0992371i	−0.439197	−	0.898391i	$-0.644737\pi$
$683$	−252.954	+	67.7789i	−0.370358	+	0.0992371i	0.0688393	+	0.997628i	$0.478070\pi$
$684$		0			0
$685$	−182.418	+	315.957i	−0.266303	+	0.461251i
$686$		0			0
$687$	−19.3641	+	72.2679i	−0.0281865	+	0.105194i
$688$		0			0
$689$	95.9749	+	166.233i	0.139296	+	0.241268i
$690$		0			0
$691$	−1062.75	−	284.764i	−1.53799	−	0.412104i	−0.612377	−	0.790566i	$-0.709786\pi$
$691$	−1062.75	−	284.764i	−1.53799	−	0.412104i	−0.925617	+	0.378462i	$0.876453\pi$
$692$		0			0
$693$	705.233	+	407.167i	1.01765	+	0.587542i
$694$		0			0
$695$	31.2666	+	116.688i	0.0449879	+	0.167897i
$696$		0			0
$697$	−607.149	−	607.149i	−0.871089	−	0.871089i
$698$		0			0
$699$	162.673	−	93.9193i	0.232722	−	0.134362i
$700$		0			0
$701$		−	638.323i		−	0.910589i	−0.890341	−	0.455295i	$-0.849534\pi$
$701$		−	638.323i		−	0.910589i	0.890341	−	0.455295i	$-0.150466\pi$
$702$		0			0
$703$	−197.937			−0.281561
$704$		0			0
$705$	66.1769	+	114.622i	0.0938680	+	0.162584i
$706$		0			0
$707$	−671.363	+	671.363i	−0.949594	+	0.949594i
$708$		0			0
$709$	−625.185	+	167.518i	−0.881784	+	0.236273i	−0.671177	−	0.741297i	$-0.734211\pi$
$709$	−625.185	+	167.518i	−0.881784	+	0.236273i	−0.210608	+	0.977571i	$0.567544\pi$
$710$		0			0
$711$	−265.545	+	459.937i	−0.373481	+	0.646888i
$712$		0			0
$713$	−88.1769	+	329.081i	−0.123670	+	0.461544i
$714$		0			0
$715$	392.550	−	679.917i	0.549021	−	0.950932i
$716$		0			0
$717$	39.3449	+	10.5424i	0.0548743	+	0.0147035i
$718$		0			0
$719$	−1058.38	−	611.056i	−1.47202	−	0.849870i	−0.472512	−	0.881324i	$-0.656653\pi$
$719$	−1058.38	−	611.056i	−1.47202	−	0.849870i	−0.999505	+	0.0314543i	$0.989986\pi$
$720$		0			0
$721$	−120.984	−	451.517i	−0.167800	−	0.626237i
$722$		0			0
$723$	−125.053	−	125.053i	−0.172963	−	0.172963i
$724$		0			0
$725$	90.4852	−	52.2417i	0.124807	−	0.0720575i
$726$		0			0
$727$		−	508.974i		−	0.700102i	−0.936731	−	0.350051i	$-0.886164\pi$
$727$		−	508.974i		−	0.700102i	0.936731	−	0.350051i	$-0.113836\pi$
$728$		0			0
$729$	−481.323			−0.660251
$730$		0			0
$731$	479.711	+	830.885i	0.656240	+	1.13664i
$732$		0			0
$733$	861.681	−	861.681i	1.17555	−	1.17555i	0.194689	−	0.980865i	$-0.437630\pi$
$733$	861.681	−	861.681i	1.17555	−	1.17555i	0.980865	−	0.194689i	$-0.0623699\pi$
$734$		0			0
$735$	−36.3083	+	9.72878i	−0.0493991	+	0.0132364i
$736$		0			0
$737$	−327.520	+	567.282i	−0.444397	+	0.769718i
$738$		0			0
$739$	−40.4242	+	150.865i	−0.0547013	+	0.204148i	−0.987868	−	0.155296i	$-0.950367\pi$
$739$	−40.4242	+	150.865i	−0.0547013	+	0.204148i	0.933167	+	0.359444i	$0.117034\pi$
$740$		0			0
$741$	58.0333	+	15.5500i	0.0783176	+	0.0209851i
$742$		0			0
$743$	369.252	+	98.9409i	0.496975	+	0.133164i	0.498596	−	0.866835i	$-0.333849\pi$
$743$	369.252	+	98.9409i	0.496975	+	0.133164i	−0.00162070	+	0.999999i	$0.500516\pi$
$744$		0			0
$745$	412.441	+	238.123i	0.553613	+	0.319628i
$746$		0			0
$747$	−75.8513	−	283.081i	−0.101541	−	0.378957i
$748$		0			0
$749$	400.038	+	400.038i	0.534097	+	0.534097i
$750$		0			0
$751$	906.415	−	523.319i	1.20694	−	0.696830i	0.244854	−	0.969560i	$-0.421260\pi$
$751$	906.415	−	523.319i	1.20694	−	0.696830i	0.962091	+	0.272730i	$0.0879267\pi$
$752$		0			0
$753$		−	187.128i		−	0.248510i
$754$		0			0
$755$	674.270			0.893073
$756$		0			0
$757$	188.415	+	326.345i	0.248897	+	0.431103i	0.963220	−	0.268713i	$-0.0865985\pi$
$757$	188.415	+	326.345i	0.248897	+	0.431103i	−0.714323	+	0.699816i	$0.753265\pi$
$758$		0			0
$759$	169.492	−	169.492i	0.223310	−	0.223310i
$760$		0			0
$761$	−742.044	+	198.830i	−0.975091	+	0.261275i	−0.710976	−	0.703216i	$-0.751747\pi$
$761$	−742.044	+	198.830i	−0.975091	+	0.261275i	−0.264115	+	0.964491i	$0.585080\pi$
$762$		0			0
$763$	218.119	−	377.794i	0.285871	−	0.495142i
$764$		0			0
$765$	150.672	−	562.315i	0.196957	−	0.735052i
$766$		0			0
$767$	−884.683	−	884.683i	−1.15343	−	1.15343i
$768$		0			0
$769$	−65.7006	−	17.6044i	−0.0854364	−	0.0228926i	0.215848	−	0.976427i	$-0.430749\pi$
$769$	−65.7006	−	17.6044i	−0.0854364	−	0.0228926i	−0.301284	+	0.953534i	$0.597415\pi$
$770$		0			0
$771$	−62.7903	−	36.2520i	−0.0814400	−	0.0470194i
$772$		0			0
$773$	−238.681	−	890.771i	−0.308773	−	1.15236i	−0.929649	−	0.368447i	$-0.879890\pi$
$773$	−238.681	−	890.771i	−0.308773	−	1.15236i	0.620876	−	0.783909i	$-0.286777\pi$
$774$		0			0
$775$	132.694	+	132.694i	0.171218	+	0.171218i
$776$		0			0
$777$	117.955	−	68.1013i	0.151808	−	0.0876465i
$778$		0			0
$779$		−	293.583i		−	0.376872i
$780$		0			0
$781$	750.046			0.960366
$782$		0			0
$783$	60.0385	+	103.990i	0.0766775	+	0.132809i
$784$		0			0
$785$	257.461	−	257.461i	0.327976	−	0.327976i
$786$		0			0
$787$	−1188.62	+	318.489i	−1.51031	+	0.404687i	−0.916540	−	0.399944i	$-0.869030\pi$
$787$	−1188.62	+	318.489i	−1.51031	+	0.404687i	−0.593774	+	0.804632i	$0.702363\pi$
$788$		0			0
$789$	−93.4603	+	161.878i	−0.118454	+	0.205169i
$790$		0			0
$791$	−221.140	+	825.305i	−0.279570	+	1.04337i
$792$		0			0
$793$	333.150			0.420114
$794$		0			0
$795$	−38.8916	−	10.4210i	−0.0489203	−	0.0131081i
$796$		0			0
$797$	−22.0615	−	12.7372i	−0.0276807	−	0.0159814i	0.486096	−	0.873906i	$-0.338421\pi$
$797$	−22.0615	−	12.7372i	−0.0276807	−	0.0159814i	−0.513776	+	0.857924i	$0.671754\pi$
$798$		0			0
$799$	−231.949	−	865.647i	−0.290300	−	1.08341i
$800$		0			0
$801$	535.788	+	535.788i	0.668899	+	0.668899i
$802$		0			0
$803$	−382.732	+	220.970i	−0.476628	+	0.275181i
$804$		0			0
$805$			446.438i			0.554582i
$806$		0			0
$807$	−67.8667			−0.0840975
$808$		0			0
$809$	351.463	+	608.752i	0.434442	+	0.752475i	0.997250	−	0.0741123i	$-0.0236123\pi$
$809$	351.463	+	608.752i	0.434442	+	0.752475i	−0.562808	+	0.826588i	$0.690279\pi$
$810$		0			0
$811$	−506.292	+	506.292i	−0.624282	+	0.624282i	−0.946623	−	0.322342i	$-0.895530\pi$
$811$	−506.292	+	506.292i	−0.624282	+	0.624282i	0.322342	+	0.946623i	$0.395530\pi$
$812$		0			0
$813$	−309.086	+	82.8193i	−0.380179	+	0.101869i
$814$		0			0
$815$	−235.785	+	408.391i	−0.289306	+	0.501093i
$816$		0			0
$817$	−84.9038	+	316.865i	−0.103921	+	0.387840i
$818$		0			0
$819$	630.717	−	169.000i	0.770106	−	0.206349i
$820$		0			0
$821$	−1090.79	−	292.276i	−1.32861	−	0.356000i	−0.476414	−	0.879221i	$-0.658064\pi$
$821$	−1090.79	−	292.276i	−1.32861	−	0.356000i	−0.852197	+	0.523220i	$0.824730\pi$
$822$		0			0
$823$	449.858	+	259.726i	0.546607	+	0.315584i	0.747752	−	0.663978i	$-0.231133\pi$
$823$	449.858	+	259.726i	0.546607	+	0.315584i	−0.201145	+	0.979561i	$0.564466\pi$
$824$		0			0
$825$	−34.1718	−	127.531i	−0.0414203	−	0.154583i
$826$		0			0
$827$	571.769	+	571.769i	0.691377	+	0.691377i	0.962535	−	0.271158i	$-0.0874064\pi$
$827$	571.769	+	571.769i	0.691377	+	0.691377i	−0.271158	+	0.962535i	$0.587406\pi$
$828$		0			0
$829$	−848.094	+	489.647i	−1.02303	+	0.590648i	−0.914981	−	0.403497i	$-0.867795\pi$
$829$	−848.094	+	489.647i	−1.02303	+	0.590648i	−0.108052	+	0.994145i	$0.534461\pi$
$830$		0			0
$831$			255.373i			0.307308i
$832$		0			0
$833$	254.520			0.305547
$834$		0			0
$835$	97.8217	+	169.432i	0.117152	+	0.202913i
$836$		0			0
$837$	−152.497	+	152.497i	−0.182195	+	0.182195i
$838$		0			0
$839$	−513.757	+	137.661i	−0.612344	+	0.164077i	−0.551645	−	0.834079i	$-0.686000\pi$
$839$	−513.757	+	137.661i	−0.612344	+	0.164077i	−0.0606993	+	0.998156i	$0.519333\pi$
$840$		0			0
$841$	376.392	−	651.931i	0.447553	−	0.775185i
$842$		0			0
$843$	24.6443	−	91.9737i	0.0292340	−	0.109103i
$844$		0			0
$845$	−162.933	−	608.075i	−0.192820	−	0.719615i
$846$		0			0
$847$	813.099	+	217.869i	0.959975	+	0.257224i
$848$		0			0
$849$	−22.5500	−	13.0192i	−0.0265606	−	0.0153348i
$850$		0			0
$851$	163.886	+	611.633i	0.192581	+	0.718722i
$852$		0			0
$853$	713.043	+	713.043i	0.835924	+	0.835924i	0.988320	−	0.152396i	$-0.0486989\pi$
$853$	713.043	+	713.043i	0.835924	+	0.835924i	−0.152396	+	0.988320i	$0.548699\pi$
$854$		0			0
$855$	172.380	−	99.5237i	0.201614	−	0.116402i
$856$		0			0
$857$			311.663i			0.363667i	0.983329	+	0.181834i	$0.0582032\pi$
$857$			311.663i			0.363667i	−0.983329	+	0.181834i	$0.941797\pi$
$858$		0			0
$859$	1475.02			1.71714			0.858568	−	0.512700i	$-0.171355\pi$
$859$	1475.02			1.71714			0.858568	+	0.512700i	$0.171355\pi$
$860$		0			0
$861$	101.009	+	174.953i	0.117316	+	0.203197i
$862$		0			0
$863$	700.396	−	700.396i	0.811583	−	0.811583i	−0.173288	−	0.984871i	$-0.555439\pi$
$863$	700.396	−	700.396i	0.811583	−	0.811583i	0.984871	+	0.173288i	$0.0554392\pi$
$864$		0			0
$865$	−493.850	+	132.327i	−0.570925	+	0.152979i
$866$		0			0
$867$	19.0052	−	32.9179i	0.0219206	−	0.0379676i
$868$		0			0
$869$	−263.292	+	982.620i	−0.302983	+	1.13075i
$870$		0			0
$871$	135.942	+	507.342i	0.156076	+	0.582482i
$872$		0			0
$873$	448.212	+	120.098i	0.513416	+	0.137569i
$874$		0			0
$875$	691.550	+	399.267i	0.790343	+	0.456305i
$876$		0			0
$877$	−35.4498	−	132.301i	−0.0404217	−	0.150856i	0.942765	−	0.333457i	$-0.108215\pi$
$877$	−35.4498	−	132.301i	−0.0404217	−	0.150856i	−0.983187	+	0.182601i	$0.941548\pi$
$878$		0			0
$879$	−207.263	−	207.263i	−0.235794	−	0.235794i
$880$		0			0
$881$	383.677	−	221.516i	0.435502	−	0.251437i	−0.266186	−	0.963922i	$-0.585764\pi$
$881$	383.677	−	221.516i	0.435502	−	0.251437i	0.701688	+	0.712485i	$0.252430\pi$
$882$		0			0
$883$			1305.20i			1.47814i	0.673630	+	0.739069i	$0.264734\pi$
$883$			1305.20i			1.47814i	−0.673630	+	0.739069i	$0.735266\pi$
$884$		0			0
$885$	262.438			0.296540
$886$		0			0
$887$	−861.377	−	1491.95i	−0.971113	−	1.68202i	−0.692209	−	0.721697i	$-0.743362\pi$
$887$	−861.377	−	1491.95i	−0.971113	−	1.68202i	−0.278904	−	0.960319i	$-0.589971\pi$
$888$		0			0
$889$	−119.520	+	119.520i	−0.134444	+	0.134444i
$890$		0			0
$891$	−1046.39	+	280.378i	−1.17439	+	0.314678i
$892$		0			0
$893$	153.210	−	265.368i	0.171568	−	0.297165i
$894$		0			0
$895$	1.00617	−	3.75506i	0.00112421	−	0.00419560i
$896$		0			0
$897$		−	192.200i		−	0.214270i
$898$		0			0
$899$	−153.040	−	41.0070i	−0.170234	−	0.0456141i
$900$		0			0
$901$	236.104	+	136.315i	0.262047	+	0.151293i
$902$		0			0
$903$	−58.4232	−	218.038i	−0.0646990	−	0.241460i
$904$		0			0
$905$	60.7940	+	60.7940i	0.0671757	+	0.0671757i
$906$		0			0
$907$	−758.800	+	438.093i	−0.836604	+	0.483014i	−0.856109	−	0.516796i	$-0.827125\pi$
$907$	−758.800	+	438.093i	−0.836604	+	0.483014i	0.0195043	+	0.999810i	$0.493791\pi$
$908$		0			0
$909$		−	1354.21i		−	1.48978i
$910$		0			0
$911$	1103.35			1.21114			0.605569	−	0.795793i	$-0.292946\pi$
$911$	1103.35			1.21114			0.605569	+	0.795793i	$0.292946\pi$
$912$		0			0
$913$	−280.679	−	486.151i	−0.307426	−	0.532477i
$914$		0			0
$915$	−49.4139	+	49.4139i	−0.0540043	+	0.0540043i
$916$		0			0
$917$	−17.0859	+	4.57815i	−0.0186324	+	0.00499253i
$918$		0			0
$919$	−328.160	+	568.389i	−0.357083	+	0.618486i	−0.987472	−	0.157793i	$-0.949562\pi$
$919$	−328.160	+	568.389i	−0.357083	+	0.618486i	0.630389	+	0.776279i	$0.282895\pi$
$920$		0			0
$921$	−69.7255	+	260.219i	−0.0757063	+	0.282540i
$922$		0			0
$923$	425.267	−	425.267i	0.460744	−	0.460744i
$924$		0			0
$925$	336.897	+	90.2712i	0.364213	+	0.0975905i
$926$		0			0
$927$	577.398	+	333.361i	0.622867	+	0.359613i
$928$		0			0
$929$	219.574	+	819.460i	0.236355	+	0.882088i	0.977533	+	0.210780i	$0.0676005\pi$
$929$	219.574	+	819.460i	0.236355	+	0.882088i	−0.741179	+	0.671308i	$0.765733\pi$
$930$		0			0
$931$	61.5359	+	61.5359i	0.0660966	+	0.0660966i
$932$		0			0
$933$	45.3154	−	26.1628i	0.0485695	−	0.0280416i
$934$		0			0
$935$		−	1115.09i		−	1.19261i
$936$		0			0
$937$	842.615			0.899269			0.449635	−	0.893213i	$-0.351554\pi$
$937$	842.615			0.899269			0.449635	+	0.893213i	$0.351554\pi$
$938$		0			0
$939$	144.329	+	249.986i	0.153705	+	0.266226i
$940$		0			0
$941$	−471.659	+	471.659i	−0.501232	+	0.501232i	−0.911821	−	0.410589i	$-0.865323\pi$
$941$	−471.659	+	471.659i	−0.501232	+	0.501232i	0.410589	+	0.911821i	$0.365323\pi$
$942$		0			0
$943$	−907.183	+	243.079i	−0.962018	+	0.257772i
$944$		0			0
$945$	−141.303	+	244.743i	−0.149527	+	0.258988i
$946$		0			0
$947$	131.110	−	489.308i	0.138447	−	0.516693i	−0.861512	−	0.507737i	$-0.830482\pi$
$947$	131.110	−	489.308i	0.138447	−	0.516693i	0.999960	−	0.00895652i	$-0.00285099\pi$
$948$		0			0
$949$	−91.7168	+	342.292i	−0.0966457	+	0.360687i
$950$		0			0
$951$	206.054	+	55.2121i	0.216671	+	0.0580569i
$952$		0			0
$953$	−770.092	−	444.613i	−0.808071	−	0.466540i	0.0382143	−	0.999270i	$-0.487833\pi$
$953$	−770.092	−	444.613i	−0.808071	−	0.466540i	−0.846286	+	0.532729i	$0.821166\pi$
$954$		0			0
$955$	283.450	+	1057.85i	0.296806	+	1.10769i
$956$		0			0
$957$	78.8231	+	78.8231i	0.0823648	+	0.0823648i
$958$		0			0
$959$	−503.347	+	290.608i	−0.524867	+	0.303032i
$960$		0			0
$961$			676.436i			0.703888i
$962$		0			0
$963$	−806.922			−0.837925
$964$		0			0
$965$	615.636	+	1066.31i	0.637964	+	1.10499i
$966$		0			0
$967$	384.317	−	384.317i	0.397432	−	0.397432i	−0.479894	−	0.877326i	$-0.659325\pi$
$967$	384.317	−	384.317i	0.397432	−	0.397432i	0.877326	+	0.479894i	$0.159325\pi$
$968$		0			0
$969$	82.4256	−	22.0859i	0.0850626	−	0.0227924i
$970$		0			0
$971$	−121.863	+	211.074i	−0.125503	+	0.217378i	−0.921929	−	0.387358i	$-0.873388\pi$
$971$	−121.863	+	211.074i	−0.125503	+	0.217378i	0.796426	+	0.604735i	$0.206721\pi$
$972$		0			0
$973$	−49.8104	+	185.895i	−0.0511926	+	0.191053i
$974$		0			0
$975$	−91.6833	−	52.9334i	−0.0940341	−	0.0542906i
$976$		0			0
$977$	−1110.01	−	297.426i	−1.13614	−	0.304428i	−0.358742	−	0.933437i	$-0.616794\pi$
$977$	−1110.01	−	297.426i	−1.13614	−	0.304428i	−0.777398	+	0.629009i	$0.783461\pi$
$978$		0			0
$979$	1256.94	+	725.692i	1.28390	+	0.741259i
$980$		0			0
$981$	161.040	+	601.011i	0.164159	+	0.612651i
$982$		0			0
$983$	774.213	+	774.213i	0.787602	+	0.787602i	0.981101	−	0.193499i	$-0.0619835\pi$
$983$	774.213	+	774.213i	0.787602	+	0.787602i	−0.193499	+	0.981101i	$0.561984\pi$
$984$		0			0
$985$	−284.253	+	164.114i	−0.288582	+	0.166613i
$986$		0			0
$987$			210.851i			0.213628i
$988$		0			0
$989$	1049.42			1.06109
$990$		0			0
$991$	−391.733	−	678.501i	−0.395290	−	0.684663i	0.597848	−	0.801609i	$-0.296023\pi$
$991$	−391.733	−	678.501i	−0.395290	−	0.684663i	−0.993138	+	0.116947i	$0.962689\pi$
$992$		0			0
$993$	238.795	−	238.795i	0.240478	−	0.240478i
$994$		0			0
$995$	724.795	−	194.208i	0.728438	−	0.195184i
$996$		0			0
$997$	−250.817	+	434.428i	−0.251572	+	0.435735i	−0.963959	−	0.266052i	$-0.914281\pi$
$997$	−250.817	+	434.428i	−0.251572	+	0.435735i	0.712387	+	0.701787i	$0.247614\pi$
$998$		0			0
$999$	−103.744	+	387.177i	−0.103848	+	0.387564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.3.bd.d.145.1		4
4.3	odd	2		13.3.f.a.2.1	✓	4
12.11	even	2		117.3.bd.b.28.1		4
13.7	odd	12	inner	208.3.bd.d.33.1		4
20.3	even	4		325.3.w.a.249.1		4
20.7	even	4		325.3.w.b.249.1		4
20.19	odd	2		325.3.t.a.301.1		4
52.3	odd	6		169.3.d.a.70.2		4
52.7	even	12		13.3.f.a.7.1	yes	4
52.11	even	12		169.3.d.a.99.2		4
52.15	even	12		169.3.d.c.99.1		4
52.19	even	12		169.3.f.b.150.1		4
52.23	odd	6		169.3.d.c.70.1		4
52.31	even	4		169.3.f.a.89.1		4
52.35	odd	6		169.3.f.c.19.1		4
52.43	odd	6		169.3.f.a.19.1		4
52.47	even	4		169.3.f.c.89.1		4
52.51	odd	2		169.3.f.b.80.1		4
156.59	odd	12		117.3.bd.b.46.1		4
260.7	odd	12		325.3.w.a.124.1		4
260.59	even	12		325.3.t.a.176.1		4
260.163	odd	12		325.3.w.b.124.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.f.a.2.1	✓	4	4.3	odd	2
13.3.f.a.7.1	yes	4	52.7	even	12
117.3.bd.b.28.1		4	12.11	even	2
117.3.bd.b.46.1		4	156.59	odd	12
169.3.d.a.70.2		4	52.3	odd	6
169.3.d.a.99.2		4	52.11	even	12
169.3.d.c.70.1		4	52.23	odd	6
169.3.d.c.99.1		4	52.15	even	12
169.3.f.a.19.1		4	52.43	odd	6
169.3.f.a.89.1		4	52.31	even	4
169.3.f.b.80.1		4	52.51	odd	2
169.3.f.b.150.1		4	52.19	even	12
169.3.f.c.19.1		4	52.35	odd	6
169.3.f.c.89.1		4	52.47	even	4
208.3.bd.d.33.1		4	13.7	odd	12	inner
208.3.bd.d.145.1		4	1.1	even	1	trivial
325.3.t.a.176.1		4	260.59	even	12
325.3.t.a.301.1		4	20.19	odd	2
325.3.w.a.124.1		4	260.7	odd	12
325.3.w.a.249.1		4	20.3	even	4
325.3.w.b.124.1		4	260.163	odd	12
325.3.w.b.249.1		4	20.7	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	208.bd (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 0.633975i) q^{3} +(-2.63397 + 2.63397i) q^{5} +(-5.73205 + 1.53590i) q^{7} +(4.23205 - 7.33013i) q^{9} +(4.19615 - 15.6603i) q^{11} +(-6.50000 - 11.2583i) q^{13} +(2.63397 + 0.705771i) q^{15} +(-15.9904 - 9.23205i) q^{17} +(-1.63397 - 6.09808i) q^{19} +(3.07180 + 3.07180i) q^{21} +(-17.4904 + 10.0981i) q^{23} +11.1244i q^{25} -12.7846 q^{27} +(-4.69615 - 8.13397i) q^{29} +(11.9282 - 11.9282i) q^{31} +(-11.4641 + 3.07180i) q^{33} +(11.0526 - 19.1436i) q^{35} +(8.11474 - 30.2846i) q^{37} +(-4.75833 + 8.24167i) q^{39} +(44.9186 + 12.0359i) q^{41} +(-45.0000 - 25.9808i) q^{43} +(8.16025 + 30.4545i) q^{45} +(34.3205 + 34.3205i) q^{47} +(-11.9378 + 6.89230i) q^{49} +13.5167i q^{51} -14.7654 q^{53} +(30.1962 + 52.3013i) q^{55} +(-3.26795 + 3.26795i) q^{57} +(92.9615 - 24.9090i) q^{59} +(-12.8135 + 22.1936i) q^{61} +(-13.0000 + 48.5167i) q^{63} +(46.7750 + 12.5333i) q^{65} +(-39.0263 - 10.4571i) q^{67} +(12.8038 + 7.39230i) q^{69} +(11.9737 + 44.6865i) q^{71} +(-19.2750 - 19.2750i) q^{73} +(7.05256 - 4.07180i) q^{75} +96.2102i q^{77} -62.7461 q^{79} +(-33.4090 - 57.8660i) q^{81} +(24.4833 - 24.4833i) q^{83} +(66.4352 - 17.8013i) q^{85} +(-3.43782 + 5.95448i) q^{87} +(-23.1699 + 86.4711i) q^{89} +(54.5500 + 54.5500i) q^{91} +(-11.9282 - 3.19615i) q^{93} +(20.3660 + 11.7583i) q^{95} +(14.1891 + 52.9545i) q^{97} +(-97.0333 - 97.0333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 14 q^{5} - 16 q^{7} + 10 q^{9} - 4 q^{11} - 26 q^{13} + 14 q^{15} - 12 q^{17} - 10 q^{19} + 40 q^{21} - 18 q^{23} + 32 q^{27} + 2 q^{29} + 20 q^{31} - 32 q^{33} - 32 q^{35} - 68 q^{37} + 26 q^{39}+ \cdots - 208 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 14 * q^5 - 16 * q^7 + 10 * q^9 - 4 * q^11 - 26 * q^13 + 14 * q^15 - 12 * q^17 - 10 * q^19 + 40 * q^21 - 18 * q^23 + 32 * q^27 + 2 * q^29 + 20 * q^31 - 32 * q^33 - 32 * q^35 - 68 * q^37 + 26 * q^39 + 100 * q^41 - 180 * q^43 - 2 * q^45 + 68 * q^47 - 72 * q^49 + 128 * q^53 + 100 * q^55 - 20 * q^57 + 164 * q^59 - 124 * q^61 - 52 * q^63 + 52 * q^65 - 118 * q^67 + 72 * q^69 + 86 * q^71 + 58 * q^73 - 48 * q^75 + 40 * q^79 - 2 * q^81 + 188 * q^83 + 96 * q^85 - 38 * q^87 - 110 * q^89 - 52 * q^91 - 20 * q^93 + 78 * q^95 + 178 * q^97 - 208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more