LMFDB - Embedded newform 208.4.w.e.49.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,4,Mod(17,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("208.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	208.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.2723972812$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 340 x^{18} + 48278 x^{16} + 3724852 x^{14} + 170209937 x^{12} + 4703455168 x^{10} + \cdots + 549543481344 $ x^20 + 340x^18 + 48278x^16 + 3724852x^14 + 170209937x^12 + 4703455168x^10 + 76591569568x^8 + 674465272704x^6 + 2596745246976x^4 + 2244726908928*x^2 + 549543481344
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{40} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.6
Root			$-0.769882i$ of defining polynomial
Character	$\chi$	$=$	208.49
Dual form			208.4.w.e.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.884941 + 1.53276i) q^{3} +0.308172i q^{5} +(-11.0872 - 6.40118i) q^{7} +(11.9338 - 20.6699i) q^{9} +O(q^{10})$	\(q+(0.884941 + 1.53276i) q^{3} +0.308172i q^{5} +(-11.0872 - 6.40118i) q^{7} +(11.9338 - 20.6699i) q^{9} +(-19.0972 + 11.0258i) q^{11} +(10.7828 - 45.6150i) q^{13} +(-0.472354 + 0.272714i) q^{15} +(35.0294 - 60.6726i) q^{17} +(-17.4302 - 10.0633i) q^{19} -22.6587i q^{21} +(-15.5865 - 26.9966i) q^{23} +124.905 q^{25} +90.0295 q^{27} +(-42.8445 - 74.2088i) q^{29} -167.593i q^{31} +(-33.7997 - 19.5143i) q^{33} +(1.97266 - 3.41675i) q^{35} +(-19.3333 + 11.1621i) q^{37} +(79.4592 - 23.8391i) q^{39} +(-124.007 + 71.5954i) q^{41} +(170.423 - 295.181i) q^{43} +(6.36987 + 3.67765i) q^{45} -224.686i q^{47} +(-89.5497 - 155.105i) q^{49} +123.996 q^{51} +2.40240 q^{53} +(-3.39782 - 5.88520i) q^{55} -35.6218i q^{57} +(353.820 + 204.278i) q^{59} +(-231.775 + 401.446i) q^{61} +(-264.623 + 152.780i) q^{63} +(14.0573 + 3.32296i) q^{65} +(-169.791 + 98.0287i) q^{67} +(27.5862 - 47.7808i) q^{69} +(-530.234 - 306.131i) q^{71} +575.520i q^{73} +(110.534 + 191.450i) q^{75} +282.311 q^{77} -272.157 q^{79} +(-242.541 - 420.093i) q^{81} +1416.78i q^{83} +(18.6976 + 10.7951i) q^{85} +(75.8297 - 131.341i) q^{87} +(358.036 - 206.712i) q^{89} +(-411.541 + 436.719i) q^{91} +(256.880 - 148.310i) q^{93} +(3.10123 - 5.37149i) q^{95} +(726.870 + 419.659i) q^{97} +526.315i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9}+O(q^{10}) $ 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9	$ 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9} + 42 q^{11} + 24 q^{13} - 70 q^{17} + 102 q^{19} - 90 q^{23} - 628 q^{25} - 708 q^{27} + 170 q^{29} - 678 q^{33} + 544 q^{35} + 582 q^{37} - 1162 q^{39} + 438 q^{41} - 270 q^{43} + 540 q^{45} + 92 q^{49} + 444 q^{51} - 592 q^{53} + 288 q^{55} - 90 q^{59} + 746 q^{61} + 1068 q^{63} - 1412 q^{65} - 846 q^{67} + 682 q^{69} + 1038 q^{71} - 722 q^{75} + 2812 q^{77} + 1008 q^{79} + 694 q^{81} - 180 q^{85} + 338 q^{87} + 2466 q^{89} - 690 q^{91} - 4764 q^{93} + 2592 q^{95} - 846 q^{97}+O(q^{100}) $ 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9 + 42 * q^11 + 24 * q^13 - 70 * q^17 + 102 * q^19 - 90 * q^23 - 628 * q^25 - 708 * q^27 + 170 * q^29 - 678 * q^33 + 544 * q^35 + 582 * q^37 - 1162 * q^39 + 438 * q^41 - 270 * q^43 + 540 * q^45 + 92 * q^49 + 444 * q^51 - 592 * q^53 + 288 * q^55 - 90 * q^59 + 746 * q^61 + 1068 * q^63 - 1412 * q^65 - 846 * q^67 + 682 * q^69 + 1038 * q^71 - 722 * q^75 + 2812 * q^77 + 1008 * q^79 + 694 * q^81 - 180 * q^85 + 338 * q^87 + 2466 * q^89 - 690 * q^91 - 4764 * q^93 + 2592 * q^95 - 846 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	0.884941	+	1.53276i	0.170307	+	0.294980i	0.938527	−	0.345205i	$-0.112191\pi$
$3$	0.884941	+	1.53276i	0.170307	+	0.294980i	−0.768220	+	0.640186i	$0.778857\pi$
$4$		0			0
$5$			0.308172i			0.0275637i	0.999905	+	0.0137819i	$0.00438704\pi$
$5$			0.308172i			0.0275637i	−0.999905	+	0.0137819i	$0.995613\pi$
$6$		0			0
$7$	−11.0872	−	6.40118i	−0.598651	−	0.345631i	0.169860	−	0.985468i	$-0.445669\pi$
$7$	−11.0872	−	6.40118i	−0.598651	−	0.345631i	−0.768511	+	0.639837i	$0.779002\pi$
$8$		0			0
$9$	11.9338	−	20.6699i	0.441991	−	0.765551i
$10$		0			0
$11$	−19.0972	+	11.0258i	−0.523456	+	0.302217i	−0.738347	−	0.674421i	$-0.764393\pi$
$11$	−19.0972	+	11.0258i	−0.523456	+	0.302217i	0.214892	+	0.976638i	$0.431060\pi$
$12$		0			0
$13$	10.7828	−	45.6150i	0.230047	−	0.973179i
$13$	10.7828	−	45.6150i	0.230047	−	0.973179i
$14$		0			0
$15$	−0.472354	+	0.272714i	−0.00813075	+	0.00469429i
$16$		0			0
$17$	35.0294	−	60.6726i	0.499757	−	0.865605i	−0.500243	−	0.865885i	$-0.666756\pi$
$17$	35.0294	−	60.6726i	0.499757	−	0.865605i	1.00000		0.000280522i	$8.92928e-5\pi$
$18$		0			0
$19$	−17.4302	−	10.0633i	−0.210461	−	0.121510i	0.391065	−	0.920363i	$-0.372107\pi$
$19$	−17.4302	−	10.0633i	−0.210461	−	0.121510i	−0.601526	+	0.798853i	$0.705440\pi$
$20$		0			0
$21$		−	22.6587i		−	0.235454i
$22$		0			0
$23$	−15.5865	−	26.9966i	−0.141305	−	0.244747i	0.786683	−	0.617357i	$-0.211796\pi$
$23$	−15.5865	−	26.9966i	−0.141305	−	0.244747i	−0.927988	+	0.372610i	$0.878463\pi$
$24$		0			0
$25$	124.905			0.999240
$26$		0			0
$27$	90.0295			0.641710
$28$		0			0
$29$	−42.8445	−	74.2088i	−0.274346	−	0.475180i	0.695624	−	0.718406i	$-0.255128\pi$
$29$	−42.8445	−	74.2088i	−0.274346	−	0.475180i	−0.969970	+	0.243225i	$0.921795\pi$
$30$		0			0
$31$		−	167.593i		−	0.970987i	−0.874240	−	0.485493i	$-0.838640\pi$
$31$		−	167.593i		−	0.970987i	0.874240	−	0.485493i	$-0.161360\pi$
$32$		0			0
$33$	−33.7997	−	19.5143i	−0.178296	−	0.102939i
$34$		0			0
$35$	1.97266	−	3.41675i	0.00952688	−	0.0165010i
$36$		0			0
$37$	−19.3333	+	11.1621i	−0.0859021	+	0.0495956i	−0.542336	−	0.840162i	$-0.682460\pi$
$37$	−19.3333	+	11.1621i	−0.0859021	+	0.0495956i	0.456434	+	0.889757i	$0.349127\pi$
$38$		0			0
$39$	79.4592	−	23.8391i	0.326247	−	0.0978798i
$40$		0			0
$41$	−124.007	+	71.5954i	−0.472356	+	0.272715i	−0.717226	−	0.696841i	$-0.754588\pi$
$41$	−124.007	+	71.5954i	−0.472356	+	0.272715i	0.244869	+	0.969556i	$0.421255\pi$
$42$		0			0
$43$	170.423	−	295.181i	0.604401	−	1.04685i	−0.387745	−	0.921767i	$-0.626746\pi$
$43$	170.423	−	295.181i	0.604401	−	1.04685i	0.992146	−	0.125087i	$-0.0399209\pi$
$44$		0			0
$45$	6.36987	+	3.67765i	0.0211014	+	0.0121829i
$46$		0			0
$47$		−	224.686i		−	0.697314i	−0.937250	−	0.348657i	$-0.886638\pi$
$47$		−	224.686i		−	0.697314i	0.937250	−	0.348657i	$-0.113362\pi$
$48$		0			0
$49$	−89.5497	−	155.105i	−0.261078	−	0.452200i
$50$		0			0
$51$	123.996			0.340448
$52$		0			0
$53$	2.40240			0.00622632			0.00311316	−	0.999995i	$-0.499009\pi$
$53$	2.40240			0.00622632			0.00311316	+	0.999995i	$0.499009\pi$
$54$		0			0
$55$	−3.39782	−	5.88520i	−0.00833023	−	0.0144284i
$56$		0			0
$57$		−	35.6218i		−	0.0827758i
$58$		0			0
$59$	353.820	+	204.278i	0.780736	+	0.450758i	0.836691	−	0.547675i	$-0.184487\pi$
$59$	353.820	+	204.278i	0.780736	+	0.450758i	−0.0559550	+	0.998433i	$0.517820\pi$
$60$		0			0
$61$	−231.775	+	401.446i	−0.486487	+	0.842620i	−0.999879	−	0.0155338i	$-0.995055\pi$
$61$	−231.775	+	401.446i	−0.486487	+	0.842620i	0.513392	+	0.858154i	$0.328389\pi$
$62$		0			0
$63$	−264.623	+	152.780i	−0.529197	+	0.305532i
$64$		0			0
$65$	14.0573	+	3.32296i	0.0268244	+	0.00634095i
$66$		0			0
$67$	−169.791	+	98.0287i	−0.309601	+	0.178748i	−0.646748	−	0.762704i	$-0.723871\pi$
$67$	−169.791	+	98.0287i	−0.309601	+	0.178748i	0.337147	+	0.941452i	$0.390538\pi$
$68$		0			0
$69$	27.5862	−	47.7808i	0.0481303	−	0.0833642i
$70$		0			0
$71$	−530.234	−	306.131i	−0.886298	−	0.511705i	−0.0135685	−	0.999908i	$-0.504319\pi$
$71$	−530.234	−	306.131i	−0.886298	−	0.511705i	−0.872730	+	0.488203i	$0.837652\pi$
$72$		0			0
$73$			575.520i			0.922734i	0.887210	+	0.461367i	$0.152641\pi$
$73$			575.520i			0.922734i	−0.887210	+	0.461367i	$0.847359\pi$
$74$		0			0
$75$	110.534	+	191.450i	0.170178	+	0.294756i
$76$		0			0
$77$	282.311			0.417823
$78$		0			0
$79$	−272.157			−0.387595			−0.193798	−	0.981042i	$-0.562081\pi$
$79$	−272.157			−0.387595			−0.193798	+	0.981042i	$0.562081\pi$
$80$		0			0
$81$	−242.541	−	420.093i	−0.332703	−	0.576259i
$82$		0			0
$83$			1416.78i			1.87363i	0.349819	+	0.936817i	$0.386243\pi$
$83$			1416.78i			1.87363i	−0.349819	+	0.936817i	$0.613757\pi$
$84$		0			0
$85$	18.6976	+	10.7951i	0.0238593	+	0.0137752i
$86$		0			0
$87$	75.8297	−	131.341i	0.0934459	−	0.161853i
$88$		0			0
$89$	358.036	−	206.712i	0.426424	−	0.246196i	−0.271398	−	0.962467i	$-0.587486\pi$
$89$	358.036	−	206.712i	0.426424	−	0.246196i	0.697822	+	0.716271i	$0.254153\pi$
$90$		0			0
$91$	−411.541	+	436.719i	−0.474079	+	0.503083i
$92$		0			0
$93$	256.880	−	148.310i	0.286422	−	0.165366i
$94$		0			0
$95$	3.10123	−	5.37149i	0.00334926	−	0.00580109i
$96$		0			0
$97$	726.870	+	419.659i	0.760851	+	0.439277i	0.829601	−	0.558357i	$-0.188568\pi$
$97$	726.870	+	419.659i	0.760851	+	0.439277i	−0.0687504	+	0.997634i	$0.521901\pi$
$98$		0			0
$99$			526.315i			0.534309i
$100$		0			0
$101$	−47.3809	−	82.0662i	−0.0466790	−	0.0808504i	0.841742	−	0.539880i	$-0.181530\pi$
$101$	−47.3809	−	82.0662i	−0.0466790	−	0.0808504i	−0.888421	+	0.459030i	$0.848197\pi$
$102$		0			0
$103$	−894.718			−0.855915			−0.427957	−	0.903799i	$-0.640767\pi$
$103$	−894.718			−0.855915			−0.427957	+	0.903799i	$0.640767\pi$
$104$		0			0
$105$	6.98276			0.00648998
$106$		0			0
$107$	773.013	+	1338.90i	0.698411	+	1.20968i	0.969017	+	0.246994i	$0.0794427\pi$
$107$	773.013	+	1338.90i	0.698411	+	1.20968i	−0.270606	+	0.962690i	$0.587224\pi$
$108$		0			0
$109$			772.962i			0.679232i	0.940564	+	0.339616i	$0.110297\pi$
$109$			772.962i			0.679232i	−0.940564	+	0.339616i	$0.889703\pi$
$110$		0			0
$111$	−34.2177	−	19.7556i	−0.0292595	−	0.0168930i
$112$		0			0
$113$	−541.576	+	938.038i	−0.450860	+	0.780913i	−0.998440	−	0.0558408i	$-0.982216\pi$
$113$	−541.576	+	938.038i	−0.450860	+	0.780913i	0.547579	+	0.836754i	$0.315549\pi$
$114$		0			0
$115$	8.31959	−	4.80331i	0.00674613	−	0.00389488i
$116$		0			0
$117$	−814.178	−	767.238i	−0.643340	−	0.606250i
$118$		0			0
$119$	−776.753	+	448.459i	−0.598360	+	0.345463i
$120$		0			0
$121$	−422.366	+	731.559i	−0.317330	+	0.549631i
$122$		0			0
$123$	−219.477	−	126.715i	−0.160891	−	0.0928906i
$124$		0			0
$125$			77.0136i			0.0551065i
$126$		0			0
$127$	−744.855	−	1290.13i	−0.520434	−	0.901419i	−0.999718	−	0.0237586i	$-0.992437\pi$
$127$	−744.855	−	1290.13i	−0.520434	−	0.901419i	0.479283	−	0.877660i	$-0.340897\pi$
$128$		0			0
$129$	603.257			0.411735
$130$		0			0
$131$	2017.26			1.34541			0.672705	−	0.739911i	$-0.265132\pi$
$131$	2017.26			1.34541			0.672705	+	0.739911i	$0.265132\pi$
$132$		0			0
$133$	128.834	+	223.148i	0.0839952	+	0.145484i
$134$		0			0
$135$			27.7445i			0.0176879i
$136$		0			0
$137$	−1085.51	−	626.717i	−0.676942	−	0.390833i	0.121760	−	0.992560i	$-0.461146\pi$
$137$	−1085.51	−	626.717i	−0.676942	−	0.390833i	−0.798702	+	0.601727i	$0.794480\pi$
$138$		0			0
$139$	1412.92	−	2447.25i	0.862176	−	1.49333i	−0.00764755	−	0.999971i	$-0.502434\pi$
$139$	1412.92	−	2447.25i	0.862176	−	1.49333i	0.869824	−	0.493362i	$-0.164232\pi$
$140$		0			0
$141$	344.390	−	198.833i	0.205694	−	0.118757i
$142$		0			0
$143$	297.019	+	990.006i	0.173692	+	0.578940i
$144$		0			0
$145$	22.8691	−	13.2035i	0.0130977	−	0.00756198i
$146$		0			0
$147$	158.492	−	274.517i	0.0889268	−	0.154026i
$148$		0			0
$149$	2041.42	+	1178.61i	1.12241	+	0.648025i	0.942016	−	0.335569i	$-0.108929\pi$
$149$	2041.42	+	1178.61i	1.12241	+	0.648025i	0.180396	+	0.983594i	$0.442262\pi$
$150$		0			0
$151$		−	3522.71i		−	1.89851i	−0.314514	−	0.949253i	$-0.601842\pi$
$151$		−	3522.71i		−	1.89851i	0.314514	−	0.949253i	$-0.398158\pi$
$152$		0			0
$153$	−836.064	−	1448.11i	−0.441776	−	0.765179i
$154$		0			0
$155$	51.6474			0.0267640
$156$		0			0
$157$	−3294.99			−1.67496			−0.837480	−	0.546467i	$-0.815972\pi$
$157$	−3294.99			−1.67496			−0.837480	+	0.546467i	$0.815972\pi$
$158$		0			0
$159$	2.12598	+	3.68231i	0.00106038	+	0.00183664i
$160$		0			0
$161$			399.088i			0.195357i
$162$		0			0
$163$	264.163	+	152.515i	0.126938	+	0.0732875i	0.562124	−	0.827053i	$-0.309984\pi$
$163$	264.163	+	152.515i	0.126938	+	0.0732875i	−0.435187	+	0.900340i	$0.643318\pi$
$164$		0			0
$165$	6.01375	−	10.4161i	0.00283739	−	0.00491451i
$166$		0			0
$167$	745.246	−	430.268i	0.345322	−	0.199372i	−0.317301	−	0.948325i	$-0.602776\pi$
$167$	745.246	−	430.268i	0.345322	−	0.199372i	0.662623	+	0.748953i	$0.269443\pi$
$168$		0			0
$169$	−1964.46	−	983.716i	−0.894157	−	0.447754i
$170$		0			0
$171$	−416.016	+	240.187i	−0.186044	+	0.107412i
$172$		0			0
$173$	790.927	−	1369.93i	0.347590	−	0.602043i	−0.638231	−	0.769845i	$-0.720334\pi$
$173$	790.927	−	1369.93i	0.347590	−	0.602043i	0.985821	+	0.167802i	$0.0536668\pi$
$174$		0			0
$175$	−1384.84	−	799.540i	−0.598196	−	0.345369i
$176$		0			0
$177$			723.096i			0.307069i
$178$		0			0
$179$	939.937	+	1628.02i	0.392482	+	0.679798i	0.992776	−	0.119981i	$-0.0382833\pi$
$179$	939.937	+	1628.02i	0.392482	+	0.679798i	−0.600295	+	0.799779i	$0.704950\pi$
$180$		0			0
$181$	2800.78			1.15017			0.575083	−	0.818095i	$-0.304970\pi$
$181$	2800.78			1.15017			0.575083	+	0.818095i	$0.304970\pi$
$182$		0			0
$183$	−820.427			−0.331408
$184$		0			0
$185$	−3.43984	−	5.95798i	−0.00136704	−	0.00236778i
$186$		0			0
$187$			1544.90i			0.604141i
$188$		0			0
$189$	−998.173	−	576.295i	−0.384161	−	0.221795i
$190$		0			0
$191$	1792.03	−	3103.89i	0.678885	−	1.17586i	−0.296432	−	0.955054i	$-0.595797\pi$
$191$	1792.03	−	3103.89i	0.678885	−	1.17586i	0.975317	−	0.220809i	$-0.0708697\pi$
$192$		0			0
$193$	4464.23	−	2577.43i	1.66499	−	0.961280i	0.694707	−	0.719293i	$-0.255534\pi$
$193$	4464.23	−	2577.43i	1.66499	−	0.961280i	0.970279	−	0.241988i	$-0.0777994\pi$
$194$		0			0
$195$	7.34654	+	24.4871i	0.00269793	+	0.00899259i
$196$		0			0
$197$	1806.08	−	1042.74i	0.653188	−	0.377119i	−0.136488	−	0.990642i	$-0.543582\pi$
$197$	1806.08	−	1042.74i	0.653188	−	0.377119i	0.789677	+	0.613523i	$0.210248\pi$
$198$		0			0
$199$	1362.49	−	2359.91i	0.485350	−	0.840651i	−0.514508	−	0.857485i	$-0.672026\pi$
$199$	1362.49	−	2359.91i	0.485350	−	0.840651i	0.999858	+	0.0168348i	$0.00535892\pi$
$200$		0			0
$201$	−300.509	−	173.499i	−0.105454	−	0.0608840i
$202$		0			0
$203$			1097.02i			0.379290i
$204$		0			0
$205$	−22.0637	−	38.2154i	−0.00751704	−	0.0130199i
$206$		0			0
$207$	−744.022			−0.249822
$208$		0			0
$209$	443.823			0.146889
$210$		0			0
$211$	153.840	+	266.458i	0.0501931	+	0.0869370i	0.890030	−	0.455901i	$-0.150683\pi$
$211$	153.840	+	266.458i	0.0501931	+	0.0869370i	−0.839837	+	0.542838i	$0.817350\pi$
$212$		0			0
$213$		−	1083.63i		−	0.348587i
$214$		0			0
$215$	90.9664	+	52.5195i	0.0288552	+	0.0166595i
$216$		0			0
$217$	−1072.79	+	1858.13i	−0.335603	+	0.581282i
$218$		0			0
$219$	−882.136	+	509.301i	−0.272188	+	0.157148i
$220$		0			0
$221$	−2389.87	−	2252.09i	−0.727421	−	0.685483i
$222$		0			0
$223$	−4548.19	+	2625.90i	−1.36578	+	0.788535i	−0.990386	−	0.138329i	$-0.955827\pi$
$223$	−4548.19	+	2625.90i	−1.36578	+	0.788535i	−0.375397	+	0.926864i	$0.622494\pi$
$224$		0			0
$225$	1490.59	−	2581.77i	0.441655	−	0.764969i
$226$		0			0
$227$	−3156.55	−	1822.44i	−0.922942	−	0.532861i	−0.0383694	−	0.999264i	$-0.512216\pi$
$227$	−3156.55	−	1822.44i	−0.922942	−	0.532861i	−0.884572	+	0.466403i	$0.845550\pi$
$228$		0			0
$229$			1142.45i			0.329673i	0.986321	+	0.164837i	$0.0527097\pi$
$229$			1142.45i			0.329673i	−0.986321	+	0.164837i	$0.947290\pi$
$230$		0			0
$231$	249.829	+	432.716i	0.0711582	+	0.123250i
$232$		0			0
$233$	5012.43			1.40934			0.704668	−	0.709537i	$-0.251096\pi$
$233$	5012.43			1.40934			0.704668	+	0.709537i	$0.251096\pi$
$234$		0			0
$235$	69.2417			0.0192206
$236$		0			0
$237$	−240.843	−	417.152i	−0.0660102	−	0.114333i
$238$		0			0
$239$			6333.82i			1.71423i	0.515126	+	0.857114i	$0.327745\pi$
$239$			6333.82i			1.71423i	−0.515126	+	0.857114i	$0.672255\pi$
$240$		0			0
$241$	−1206.67	−	696.670i	−0.322524	−	0.186209i	0.329993	−	0.943983i	$-0.392954\pi$
$241$	−1206.67	−	696.670i	−0.322524	−	0.186209i	−0.652517	+	0.757774i	$0.726287\pi$
$242$		0			0
$243$	1644.67	−	2848.65i	0.434179	−	0.752019i
$244$		0			0
$245$	47.7989	−	27.5967i	0.0124643	−	0.00719628i
$246$		0			0
$247$	−646.985	+	686.568i	−0.166667	+	0.176863i
$248$		0			0
$249$	−2171.59	+	1253.77i	−0.552685	+	0.319093i
$250$		0			0
$251$	898.814	−	1556.79i	0.226027	−	0.391489i	−0.730600	−	0.682805i	$-0.760760\pi$
$251$	898.814	−	1556.79i	0.226027	−	0.391489i	0.956627	+	0.291316i	$0.0940931\pi$
$252$		0			0
$253$	595.316	+	343.706i	0.147933	+	0.0854094i
$254$		0			0
$255$			38.2119i			0.00938402i
$256$		0			0
$257$	691.477	+	1197.67i	0.167833	+	0.290696i	0.937658	−	0.347560i	$-0.112990\pi$
$257$	691.477	+	1197.67i	0.167833	+	0.290696i	−0.769825	+	0.638255i	$0.779656\pi$
$258$		0			0
$259$	285.803			0.0685672
$260$		0			0
$261$	−2045.18			−0.485033
$262$		0			0
$263$	2800.87	+	4851.25i	0.656688	+	1.13742i	0.981468	+	0.191628i	$0.0613765\pi$
$263$	2800.87	+	4851.25i	0.656688	+	1.13742i	−0.324780	+	0.945790i	$0.605290\pi$
$264$		0			0
$265$			0.740351i			0.000171620i
$266$		0			0
$267$	633.681	+	365.856i	0.145246	+	0.0838577i
$268$		0			0
$269$	−2213.85	+	3834.50i	−0.501788	+	0.869122i	0.498210	+	0.867056i	$0.333991\pi$
$269$	−2213.85	+	3834.50i	−0.501788	+	0.869122i	−0.999998	+	0.00206531i	$0.999343\pi$
$270$		0			0
$271$	2571.05	−	1484.39i	0.576309	−	0.332732i	−0.183356	−	0.983047i	$-0.558696\pi$
$271$	2571.05	−	1484.39i	0.576309	−	0.332732i	0.759665	+	0.650314i	$0.225363\pi$
$272$		0			0
$273$	−1033.58	−	244.324i	−0.229139	−	0.0541654i
$274$		0			0
$275$	−2385.33	+	1377.17i	−0.523058	+	0.301988i
$276$		0			0
$277$	−1072.92	+	1858.36i	−0.232728	+	0.403097i	−0.958610	−	0.284723i	$-0.908098\pi$
$277$	−1072.92	+	1858.36i	−0.232728	+	0.403097i	0.725882	+	0.687819i	$0.241432\pi$
$278$		0			0
$279$	−3464.13	−	2000.01i	−0.743340	−	0.429167i
$280$		0			0
$281$			4898.16i			1.03986i	0.854210	+	0.519928i	$0.174041\pi$
$281$			4898.16i			1.03986i	−0.854210	+	0.519928i	$0.825959\pi$
$282$		0			0
$283$	−1212.14	−	2099.48i	−0.254608	−	0.440994i	0.710181	−	0.704019i	$-0.248613\pi$
$283$	−1212.14	−	2099.48i	−0.254608	−	0.440994i	−0.964789	+	0.263025i	$0.915280\pi$
$284$		0			0
$285$	10.9776			0.00228161
$286$		0			0
$287$	1833.18			0.377036
$288$		0			0
$289$	2.38673	+	4.13394i	0.000485799	+	0.000841429i
$290$		0			0
$291$			1485.49i			0.299248i
$292$		0			0
$293$	1870.33	+	1079.84i	0.372921	+	0.215306i	0.674734	−	0.738061i	$-0.264258\pi$
$293$	1870.33	+	1079.84i	0.372921	+	0.215306i	−0.301813	+	0.953367i	$0.597592\pi$
$294$		0			0
$295$	−62.9527	+	109.037i	−0.0124246	+	0.0215200i
$296$		0			0
$297$	−1719.31	+	992.643i	−0.335907	+	0.193936i
$298$		0			0
$299$	−1399.52	+	419.879i	−0.270689	+	0.0812115i
$300$		0			0
$301$	−3779.02	+	2181.82i	−0.723651	+	0.417800i
$302$		0			0
$303$	83.8586	−	145.247i	0.0158995	−	0.0275388i
$304$		0			0
$305$	−123.714	−	71.4264i	−0.0232257	−	0.0134094i
$306$		0			0
$307$		−	885.266i		−	0.164576i	−0.996609	−	0.0822880i	$-0.973777\pi$
$307$		−	885.266i		−	0.164576i	0.996609	−	0.0822880i	$-0.0262227\pi$
$308$		0			0
$309$	−791.773	−	1371.39i	−0.145768	−	0.252478i
$310$		0			0
$311$	9880.11			1.80145			0.900723	−	0.434395i	$-0.143038\pi$
$311$	9880.11			1.80145			0.900723	+	0.434395i	$0.143038\pi$
$312$		0			0
$313$	−5644.55			−1.01933			−0.509663	−	0.860374i	$-0.670230\pi$
$313$	−5644.55			−1.01933			−0.509663	+	0.860374i	$0.670230\pi$
$314$		0			0
$315$	−47.0826	−	81.5494i	−0.00842159	−	0.0145866i
$316$		0			0
$317$			11147.7i			1.97513i	0.157202	+	0.987566i	$0.449753\pi$
$317$			11147.7i			1.97513i	−0.157202	+	0.987566i	$0.550247\pi$
$318$		0			0
$319$	1636.42	+	944.785i	0.287215	+	0.165824i
$320$		0			0
$321$	−1368.14	+	2369.69i	−0.237889	+	0.412035i
$322$		0			0
$323$	−1221.14	+	705.024i	−0.210359	+	0.121451i
$324$		0			0
$325$	1346.83	−	5697.55i	0.229872	−	0.972440i
$326$		0			0
$327$	−1184.77	+	684.025i	−0.200360	+	0.115678i
$328$		0			0
$329$	−1438.25	+	2491.13i	−0.241014	+	0.417448i
$330$		0			0
$331$	−3981.54	−	2298.74i	−0.661164	−	0.381723i	0.131556	−	0.991309i	$-0.458003\pi$
$331$	−3981.54	−	2298.74i	−0.661164	−	0.381723i	−0.792720	+	0.609585i	$0.791336\pi$
$332$		0			0
$333$			532.823i			0.0876833i
$334$		0			0
$335$	−30.2097	−	52.3247i	−0.00492696	−	0.00853374i
$336$		0			0
$337$	4309.91			0.696663			0.348332	−	0.937371i	$-0.386748\pi$
$337$	4309.91			0.696663			0.348332	+	0.937371i	$0.386748\pi$
$338$		0			0
$339$	−1917.05			−0.307139
$340$		0			0
$341$	1847.84	+	3200.55i	0.293449	+	0.508268i
$342$		0			0
$343$			6684.11i			1.05221i
$344$		0			0
$345$	14.7247	+	8.50130i	0.00229783	+	0.00132665i
$346$		0			0
$347$	932.598	−	1615.31i	0.144278	−	0.249897i	−0.784825	−	0.619717i	$-0.787247\pi$
$347$	932.598	−	1615.31i	0.144278	−	0.249897i	0.929103	+	0.369820i	$0.120581\pi$
$348$		0			0
$349$	1715.81	−	990.623i	0.263167	−	0.151939i	−0.362612	−	0.931940i	$-0.618115\pi$
$349$	1715.81	−	990.623i	0.263167	−	0.151939i	0.625778	+	0.780001i	$0.284782\pi$
$350$		0			0
$351$	970.771	−	4106.70i	0.147624	−	0.624499i
$352$		0			0
$353$	2955.95	−	1706.62i	0.445693	−	0.257321i	−0.260317	−	0.965523i	$-0.583827\pi$
$353$	2955.95	−	1706.62i	0.445693	−	0.257321i	0.706009	+	0.708202i	$0.250494\pi$
$354$		0			0
$355$	94.3408	−	163.403i	0.0141045	−	0.0244297i
$356$		0			0
$357$	−1374.76	−	793.719i	−0.203810	−	0.117670i
$358$		0			0
$359$			5042.77i			0.741357i	0.928761	+	0.370678i	$0.120875\pi$
$359$			5042.77i			0.741357i	−0.928761	+	0.370678i	$0.879125\pi$
$360$		0			0
$361$	−3226.96	−	5589.26i	−0.470471	−	0.814879i
$362$		0			0
$363$	−1495.07			−0.216174
$364$		0			0
$365$	−177.359			−0.0254340
$366$		0			0
$367$	5363.87	+	9290.49i	0.762920	+	1.32142i	0.941340	+	0.337461i	$0.109568\pi$
$367$	5363.87	+	9290.49i	0.762920	+	1.32142i	−0.178420	+	0.983954i	$0.557099\pi$
$368$		0			0
$369$			3417.61i			0.482151i
$370$		0			0
$371$	−26.6358	−	15.3782i	−0.00372739	−	0.00215201i
$372$		0			0
$373$	6338.32	−	10978.3i	0.879855	−	1.52395i	0.0283552	−	0.999598i	$-0.490973\pi$
$373$	6338.32	−	10978.3i	0.879855	−	1.52395i	0.851500	−	0.524355i	$-0.175694\pi$
$374$		0			0
$375$	−118.044	+	68.1525i	−0.0162553	+	0.00938501i
$376$		0			0
$377$	−3847.02	+	1154.17i	−0.525548	+	0.157674i
$378$		0			0
$379$	−882.953	+	509.773i	−0.119668	+	0.0690905i	−0.558639	−	0.829411i	$-0.688676\pi$
$379$	−882.953	+	509.773i	−0.119668	+	0.0690905i	0.438971	+	0.898501i	$0.355343\pi$
$380$		0			0
$381$	1318.30	−	2283.37i	0.177267	−	0.307036i
$382$		0			0
$383$	−2190.46	−	1264.66i	−0.292239	−	0.168724i	0.346712	−	0.937971i	$-0.387298\pi$
$383$	−2190.46	−	1264.66i	−0.292239	−	0.168724i	−0.638951	+	0.769247i	$0.720631\pi$
$384$		0			0
$385$			87.0004i			0.0115168i
$386$		0			0
$387$	−4067.57	−	7045.24i	−0.534280	−	0.925400i
$388$		0			0
$389$	13051.8			1.70117			0.850584	−	0.525839i	$-0.176249\pi$
$389$	13051.8			1.70117			0.850584	+	0.525839i	$0.176249\pi$
$390$		0			0
$391$	−2183.94			−0.282472
$392$		0			0
$393$	1785.15	+	3091.98i	0.229133	+	0.396869i
$394$		0			0
$395$		−	83.8710i		−	0.0106836i
$396$		0			0
$397$	−8030.23	−	4636.26i	−1.01518	−	0.586114i	−0.102475	−	0.994736i	$-0.532676\pi$
$397$	−8030.23	−	4636.26i	−1.01518	−	0.586114i	−0.912704	+	0.408622i	$0.866009\pi$
$398$		0			0
$399$	−228.022	+	394.945i	−0.0286099	+	0.0495538i
$400$		0			0
$401$	8913.94	−	5146.46i	1.11008	−	0.640903i	0.171227	−	0.985232i	$-0.445227\pi$
$401$	8913.94	−	5146.46i	1.11008	−	0.640903i	0.938849	+	0.344329i	$0.111893\pi$
$402$		0			0
$403$	−7644.76	−	1807.12i	−0.944944	−	0.223373i
$404$		0			0
$405$	129.461	−	74.7442i	0.0158838	−	0.00917054i
$406$		0			0
$407$	246.141	−	426.329i	0.0299773	−	0.0519222i
$408$		0			0
$409$	−9969.25	−	5755.75i	−1.20525	−	0.695852i	−0.243533	−	0.969893i	$-0.578306\pi$
$409$	−9969.25	−	5755.75i	−1.20525	−	0.695852i	−0.961718	+	0.274040i	$0.911640\pi$
$410$		0			0
$411$		−	2218.43i		−	0.266246i
$412$		0			0
$413$	−2615.24	−	4529.73i	−0.311592	−	0.539694i
$414$		0			0
$415$	−436.611			−0.0516443
$416$		0			0
$417$	5001.41			0.587338
$418$		0			0
$419$	−2813.49	−	4873.10i	−0.328038	−	0.568178i	0.654085	−	0.756421i	$-0.273054\pi$
$419$	−2813.49	−	4873.10i	−0.328038	−	0.568178i	−0.982122	+	0.188243i	$0.939721\pi$
$420$		0			0
$421$			2770.00i			0.320668i	0.987063	+	0.160334i	$0.0512572\pi$
$421$			2770.00i			0.320668i	−0.987063	+	0.160334i	$0.948743\pi$
$422$		0			0
$423$	−4644.22	−	2681.34i	−0.533830	−	0.308207i
$424$		0			0
$425$	4375.34	−	7578.32i	0.499377	−	0.864947i
$426$		0			0
$427$	5139.45	−	2967.26i	0.582472	−	0.336290i
$428$		0			0
$429$	−1254.60	+	1331.36i	−0.141195	+	0.149833i
$430$		0			0
$431$	11092.2	−	6404.07i	1.23966	−	0.715715i	0.270632	−	0.962683i	$-0.412767\pi$
$431$	11092.2	−	6404.07i	1.23966	−	0.715715i	0.969024	+	0.246968i	$0.0794341\pi$
$432$		0			0
$433$	5516.87	−	9555.50i	0.612295	−	1.06053i	−0.378557	−	0.925578i	$-0.623580\pi$
$433$	5516.87	−	9555.50i	0.612295	−	1.06053i	0.990853	−	0.134949i	$-0.0430870\pi$
$434$		0			0
$435$	40.4755	+	23.3686i	0.00446127	+	0.00257572i
$436$		0			0
$437$			627.408i			0.0686796i
$438$		0			0
$439$	2386.20	+	4133.02i	0.259424	+	0.449335i	0.966088	−	0.258214i	$-0.0831340\pi$
$439$	2386.20	+	4133.02i	0.259424	+	0.449335i	−0.706664	+	0.707549i	$0.749801\pi$
$440$		0			0
$441$	−4274.66			−0.461576
$442$		0			0
$443$	−12949.0			−1.38877			−0.694385	−	0.719604i	$-0.744324\pi$
$443$	−12949.0			−1.38877			−0.694385	+	0.719604i	$0.744324\pi$
$444$		0			0
$445$	63.7028	+	110.336i	0.00678607	+	0.0117538i
$446$		0			0
$447$			4172.01i			0.441452i
$448$		0			0
$449$	2773.33	+	1601.18i	0.291496	+	0.168295i	0.638616	−	0.769525i	$-0.279507\pi$
$449$	2773.33	+	1601.18i	0.291496	+	0.168295i	−0.347120	+	0.937821i	$0.612840\pi$
$450$		0			0
$451$	1578.79	−	2734.54i	0.164838	−	0.285509i
$452$		0			0
$453$	5399.48	−	3117.39i	0.560022	−	0.323329i
$454$		0			0
$455$	−134.584	−	126.825i	−0.0138668	−	0.0130674i
$456$		0			0
$457$	−4450.84	+	2569.69i	−0.455583	+	0.263031i	−0.710185	−	0.704015i	$-0.751389\pi$
$457$	−4450.84	+	2569.69i	−0.455583	+	0.263031i	0.254602	+	0.967046i	$0.418056\pi$
$458$		0			0
$459$	3153.68	−	5462.33i	0.320699	−	0.555468i
$460$		0			0
$461$	−6393.22	−	3691.13i	−0.645904	−	0.372913i	0.140981	−	0.990012i	$-0.454974\pi$
$461$	−6393.22	−	3691.13i	−0.645904	−	0.372913i	−0.786885	+	0.617099i	$0.788308\pi$
$462$		0			0
$463$			6264.13i			0.628766i	0.949296	+	0.314383i	$0.101798\pi$
$463$			6264.13i			0.628766i	−0.949296	+	0.314383i	$0.898202\pi$
$464$		0			0
$465$	45.7049	+	79.1632i	0.00455809	+	0.00789485i
$466$		0			0
$467$	14540.3			1.44078			0.720390	−	0.693569i	$-0.243963\pi$
$467$	14540.3			1.44078			0.720390	+	0.693569i	$0.243963\pi$
$468$		0			0
$469$	2510.00			0.247124
$470$		0			0
$471$	−2915.87	−	5050.44i	−0.285257	−	0.494080i
$472$		0			0
$473$			7516.16i			0.730642i
$474$		0			0
$475$	−2177.12	−	1256.96i	−0.210301	−	0.121417i
$476$		0			0
$477$	28.6696	−	49.6573i	0.00275198	−	0.00476656i
$478$		0			0
$479$	11438.9	−	6604.24i	1.09114	−	0.629970i	0.157260	−	0.987557i	$-0.449734\pi$
$479$	11438.9	−	6604.24i	1.09114	−	0.629970i	0.933880	+	0.357588i	$0.116401\pi$
$480$		0			0
$481$	300.692	+	1002.25i	0.0285039	+	0.0950075i
$482$		0			0
$483$	−611.707	+	353.169i	−0.0576266	+	0.0332707i
$484$		0			0
$485$	−129.327	+	224.001i	−0.0121081	+	0.0209719i
$486$		0			0
$487$	6333.27	+	3656.51i	0.589297	+	0.340231i	0.764820	−	0.644245i	$-0.222828\pi$
$487$	6333.27	+	3656.51i	0.589297	+	0.340231i	−0.175522	+	0.984475i	$0.556161\pi$
$488$		0			0
$489$			539.865i			0.0499255i
$490$		0			0
$491$	−4354.04	−	7541.42i	−0.400194	−	0.693156i	0.593555	−	0.804793i	$-0.297724\pi$
$491$	−4354.04	−	7541.42i	−0.400194	−	0.693156i	−0.993749	+	0.111637i	$0.964390\pi$
$492$		0			0
$493$	−6003.26			−0.548425
$494$		0			0
$495$	−162.195			−0.0147275
$496$		0			0
$497$	3919.20	+	6788.25i	0.353722	+	0.612665i
$498$		0			0
$499$		−	932.041i		−	0.0836150i	−0.999126	−	0.0418075i	$-0.986688\pi$
$499$		−	932.041i		−	0.0836150i	0.999126	−	0.0418075i	$-0.0133116\pi$
$500$		0			0
$501$	1319.00	+	761.523i	0.117622	+	0.0679088i
$502$		0			0
$503$	−1811.68	+	3137.92i	−0.160594	+	0.278157i	−0.935082	−	0.354432i	$-0.884674\pi$
$503$	−1811.68	+	3137.92i	−0.160594	+	0.278157i	0.774488	+	0.632589i	$0.218008\pi$
$504$		0			0
$505$	25.2905	−	14.6015i	0.00222854	−	0.00128665i
$506$		0			0
$507$	−230.629	−	3881.58i	−0.0202024	−	0.340014i
$508$		0			0
$509$	−11862.7	+	6848.91i	−1.03301	+	0.596410i	−0.917846	−	0.396936i	$-0.870074\pi$
$509$	−11862.7	+	6848.91i	−1.03301	+	0.596410i	−0.115167	+	0.993346i	$0.536740\pi$
$510$		0			0
$511$	3684.01	−	6380.89i	0.318926	−	0.552395i
$512$		0			0
$513$	−1569.23	−	905.996i	−0.135055	−	0.0779741i
$514$		0			0
$515$		−	275.727i		−	0.0235922i
$516$		0			0
$517$	2477.33	+	4290.86i	0.210740	+	0.365013i
$518$		0			0
$519$	2799.69			0.236788
$520$		0			0
$521$	−17030.4			−1.43209			−0.716043	−	0.698056i	$-0.754049\pi$
$521$	−17030.4			−1.43209			−0.716043	+	0.698056i	$0.754049\pi$
$522$		0			0
$523$	6084.81	+	10539.2i	0.508738	+	0.881160i	0.999949	+	0.0101193i	$0.00322114\pi$
$523$	6084.81	+	10539.2i	0.508738	+	0.881160i	−0.491211	+	0.871041i	$0.663446\pi$
$524$		0			0
$525$		−	2830.18i		−	0.235275i
$526$		0			0
$527$	−10168.3	−	5870.68i	−0.840490	−	0.485257i
$528$		0			0
$529$	5597.62	−	9695.37i	0.460066	−	0.796858i
$530$		0			0
$531$	8444.80	−	4875.61i	0.690157	−	0.398462i
$532$		0			0
$533$	1928.68	+	6428.58i	0.156737	+	0.522425i
$534$		0			0
$535$	−412.610	+	238.221i	−0.0333434	+	0.0192508i
$536$		0			0
$537$	−1663.58	+	2881.40i	−0.133685	+	0.231549i
$538$		0			0
$539$	3420.29	+	1974.71i	0.273325	+	0.157804i
$540$		0			0
$541$		−	4027.65i		−	0.320078i	−0.987111	−	0.160039i	$-0.948838\pi$
$541$		−	4027.65i		−	0.320078i	0.987111	−	0.160039i	$-0.0511620\pi$
$542$		0			0
$543$	2478.52	+	4292.92i	0.195881	+	0.339276i
$544$		0			0
$545$	−238.205			−0.0187222
$546$		0			0
$547$	−11525.4			−0.900895			−0.450447	−	0.892803i	$-0.648736\pi$
$547$	−11525.4			−0.900895			−0.450447	+	0.892803i	$0.648736\pi$
$548$		0			0
$549$	5531.89	+	9581.51i	0.430046	+	0.744861i
$550$		0			0
$551$			1724.63i			0.133343i
$552$		0			0
$553$	3017.45	+	1742.13i	0.232034	+	0.133965i
$554$		0			0
$555$	6.08811	−	10.5449i	0.000465633	−	0.000806499i
$556$		0			0
$557$	−14371.4	+	8297.31i	−1.09324	+	0.631182i	−0.934437	−	0.356129i	$-0.884096\pi$
$557$	−14371.4	+	8297.31i	−1.09324	+	0.631182i	−0.158802	+	0.987310i	$0.550763\pi$
$558$		0			0
$559$	−11627.1	−	10956.7i	−0.879736	−	0.829016i
$560$		0			0
$561$	−2367.97	+	1367.15i	−0.178210	+	0.102889i
$562$		0			0
$563$	−8891.95	+	15401.3i	−0.665633	+	1.15291i	0.313481	+	0.949595i	$0.398505\pi$
$563$	−8891.95	+	15401.3i	−0.665633	+	1.15291i	−0.979113	+	0.203315i	$0.934828\pi$
$564$		0			0
$565$	−289.077	−	166.898i	−0.0215249	−	0.0124274i
$566$		0			0
$567$			6210.19i			0.459971i
$568$		0			0
$569$	7831.97	+	13565.4i	0.577036	+	0.999455i	0.995817	+	0.0913679i	$0.0291239\pi$
$569$	7831.97	+	13565.4i	0.577036	+	0.999455i	−0.418782	+	0.908087i	$0.637543\pi$
$570$		0			0
$571$	24046.3			1.76236			0.881179	−	0.472783i	$-0.156750\pi$
$571$	24046.3			1.76236			0.881179	+	0.472783i	$0.156750\pi$
$572$		0			0
$573$	6343.37			0.462475
$574$		0			0
$575$	−1946.83	−	3372.01i	−0.141197	−	0.244561i
$576$		0			0
$577$			18975.5i			1.36908i	0.728975	+	0.684541i	$0.239997\pi$
$577$			18975.5i			1.36908i	−0.728975	+	0.684541i	$0.760003\pi$
$578$		0			0
$579$	7901.16	+	4561.74i	0.567117	+	0.327425i
$580$		0			0
$581$	9069.06	−	15708.1i	0.647587	−	1.12165i
$582$		0			0
$583$	−45.8790	+	26.4882i	−0.00325920	+	0.00188170i
$584$		0			0
$585$	236.441	−	250.906i	0.0167105	−	0.0177328i
$586$		0			0
$587$	−20733.6	+	11970.5i	−1.45786	+	0.841699i	−0.998906	−	0.0467588i	$-0.985111\pi$
$587$	−20733.6	+	11970.5i	−1.45786	+	0.841699i	−0.458959	+	0.888458i	$0.651777\pi$
$588$		0			0
$589$	−1686.54	+	2921.18i	−0.117984	+	0.204355i
$590$		0			0
$591$	3196.55	+	1845.53i	0.222485	+	0.128452i
$592$		0			0
$593$		−	16015.7i		−	1.10908i	−0.832156	−	0.554542i	$-0.812894\pi$
$593$		−	16015.7i		−	1.10908i	0.832156	−	0.554542i	$-0.187106\pi$
$594$		0			0
$595$	−138.202	−	239.373i	−0.00952225	−	0.0164930i
$596$		0			0
$597$	4822.90			0.330634
$598$		0			0
$599$	5201.91			0.354832			0.177416	−	0.984136i	$-0.443226\pi$
$599$	5201.91			0.354832			0.177416	+	0.984136i	$0.443226\pi$
$600$		0			0
$601$	408.881	+	708.203i	0.0277514	+	0.0480669i	0.879568	−	0.475774i	$-0.157832\pi$
$601$	408.881	+	708.203i	0.0277514	+	0.0480669i	−0.851816	+	0.523841i	$0.824499\pi$
$602$		0			0
$603$			4679.41i			0.316020i
$604$		0			0
$605$	−225.446	−	130.161i	−0.0151499	−	0.00874678i
$606$		0			0
$607$	−12019.2	+	20817.9i	−0.803699	+	1.39205i	0.113467	+	0.993542i	$0.463804\pi$
$607$	−12019.2	+	20817.9i	−0.803699	+	1.39205i	−0.917166	+	0.398505i	$0.869529\pi$
$608$		0			0
$609$	−1681.47	+	970.799i	−0.111883	+	0.0645957i
$610$		0			0
$611$	−10249.0	−	2422.74i	−0.678612	−	0.160415i
$612$		0			0
$613$	−4778.79	+	2759.04i	−0.314867	+	0.181789i	−0.649102	−	0.760701i	$-0.724855\pi$
$613$	−4778.79	+	2759.04i	−0.314867	+	0.181789i	0.334235	+	0.942490i	$0.391522\pi$
$614$		0			0
$615$	39.0501	−	67.6367i	0.00256041	−	0.00443476i
$616$		0			0
$617$	−15743.8	−	9089.68i	−1.02726	−	0.593090i	−0.111063	−	0.993813i	$-0.535426\pi$
$617$	−15743.8	−	9089.68i	−1.02726	−	0.593090i	−0.916199	+	0.400723i	$0.868759\pi$
$618$		0			0
$619$			25821.4i			1.67666i	0.545164	+	0.838329i	$0.316467\pi$
$619$			25821.4i			1.67666i	−0.545164	+	0.838329i	$0.683533\pi$
$620$		0			0
$621$	−1403.24	−	2430.49i	−0.0906767	−	0.157057i
$622$		0			0
$623$	−5292.81			−0.340372
$624$		0			0
$625$	15589.4			0.997721
$626$		0			0
$627$	392.757	+	680.275i	0.0250163	+	0.0433295i
$628$		0			0
$629$			1564.01i			0.0991430i
$630$		0			0
$631$	−18315.1	−	10574.2i	−1.15549	−	0.667122i	−0.205271	−	0.978705i	$-0.565807\pi$
$631$	−18315.1	−	10574.2i	−1.15549	−	0.667122i	−0.950219	+	0.311583i	$0.899141\pi$
$632$		0			0
$633$	−272.278	+	471.599i	−0.0170965	+	0.0296120i
$634$		0			0
$635$	397.580	−	229.543i	0.0248464	−	0.0143451i
$636$		0			0
$637$	−8040.70	+	2412.35i	−0.500132	+	0.150048i
$638$		0			0
$639$	−12655.4	+	7306.58i	−0.783472	+	0.452338i
$640$		0			0
$641$	8029.05	−	13906.7i	0.494740	−	0.856915i	−0.505241	−	0.862978i	$-0.668597\pi$
$641$	8029.05	−	13906.7i	0.494740	−	0.856915i	0.999982	+	0.00606294i	$0.00192991\pi$
$642$		0			0
$643$	5959.36	+	3440.64i	0.365497	+	0.211020i	0.671489	−	0.741014i	$-0.265655\pi$
$643$	5959.36	+	3440.64i	0.365497	+	0.211020i	−0.305993	+	0.952034i	$0.598988\pi$
$644$		0			0
$645$			185.907i			0.0113489i
$646$		0			0
$647$	512.640	+	887.918i	0.0311499	+	0.0539531i	0.881180	−	0.472781i	$-0.156750\pi$
$647$	512.640	+	887.918i	0.0311499	+	0.0539531i	−0.850030	+	0.526734i	$0.823416\pi$
$648$		0			0
$649$	−9009.27			−0.544908
$650$		0			0
$651$	−3797.43			−0.228622
$652$		0			0
$653$	7950.27	+	13770.3i	0.476444	+	0.825226i	0.999636	−	0.0269894i	$-0.00859205\pi$
$653$	7950.27	+	13770.3i	0.476444	+	0.825226i	−0.523191	+	0.852215i	$0.675259\pi$
$654$		0			0
$655$			621.662i			0.0370845i
$656$		0			0
$657$	11895.9	+	6868.12i	0.706400	+	0.407840i
$658$		0			0
$659$	−5361.28	+	9286.01i	−0.316913	+	0.548910i	−0.979842	−	0.199772i	$-0.935980\pi$
$659$	−5361.28	+	9286.01i	−0.316913	+	0.548910i	0.662929	+	0.748682i	$0.269313\pi$
$660$		0			0
$661$	5405.10	−	3120.64i	0.318054	−	0.183629i	−0.332471	−	0.943114i	$-0.607882\pi$
$661$	5405.10	−	3120.64i	0.318054	−	0.183629i	0.650525	+	0.759485i	$0.274549\pi$
$662$		0			0
$663$	1337.02	−	5656.07i	0.0783192	−	0.331317i
$664$		0			0
$665$	−68.7678	+	39.7031i	−0.00401008	+	0.00231522i
$666$		0			0
$667$	−1335.59	+	2313.31i	−0.0775326	+	0.134290i
$668$		0			0
$669$	−8049.76	−	4647.53i	−0.465205	−	0.268586i
$670$		0			0
$671$		−	10222.0i		−	0.588099i
$672$		0			0
$673$	393.479	+	681.526i	0.0225371	+	0.0390355i	0.877074	−	0.480355i	$-0.159492\pi$
$673$	393.479	+	681.526i	0.0225371	+	0.0390355i	−0.854537	+	0.519391i	$0.826159\pi$
$674$		0			0
$675$	11245.1			0.641223
$676$		0			0
$677$	10335.7			0.586755			0.293377	−	0.955997i	$-0.405221\pi$
$677$	10335.7			0.586755			0.293377	+	0.955997i	$0.405221\pi$
$678$		0			0
$679$	−5372.63	−	9305.66i	−0.303656	−	0.525948i
$680$		0			0
$681$		−	6450.99i		−	0.362999i
$682$		0			0
$683$	7210.96	+	4163.25i	0.403982	+	0.233239i	0.688201	−	0.725520i	$-0.258401\pi$
$683$	7210.96	+	4163.25i	0.403982	+	0.233239i	−0.284219	+	0.958759i	$0.591734\pi$
$684$		0			0
$685$	193.137	−	334.522i	0.0107728	−	0.0186590i
$686$		0			0
$687$	−1751.10	+	1011.00i	−0.0972471	+	0.0561456i
$688$		0			0
$689$	25.9046	−	109.585i	0.00143235	−	0.00605932i
$690$		0			0
$691$	25859.9	−	14930.2i	1.42367	−	0.821957i	0.427060	−	0.904223i	$-0.359549\pi$
$691$	25859.9	−	14930.2i	1.42367	−	0.821957i	0.996610	+	0.0822667i	$0.0262159\pi$
$692$		0			0
$693$	3369.04	−	5835.34i	0.184674	−	0.319865i
$694$		0			0
$695$	754.174	+	435.423i	0.0411618	+	0.0237648i
$696$		0			0
$697$			10031.8i			0.545165i
$698$		0			0
$699$	4435.71	+	7682.87i	0.240020	+	0.415726i
$700$		0			0
$701$	−9140.89			−0.492506			−0.246253	−	0.969206i	$-0.579199\pi$
$701$	−9140.89			−0.492506			−0.246253	+	0.969206i	$0.579199\pi$
$702$		0			0
$703$	449.312			0.0241054
$704$		0			0
$705$	61.2748	+	106.131i	0.00327340	+	0.00566969i
$706$		0			0
$707$			1213.18i			0.0645349i
$708$		0			0
$709$	8070.16	+	4659.31i	0.427477	+	0.246804i	0.698271	−	0.715833i	$-0.253953\pi$
$709$	8070.16	+	4659.31i	0.427477	+	0.246804i	−0.270794	+	0.962637i	$0.587286\pi$
$710$		0			0
$711$	−3247.85	+	5625.45i	−0.171314	+	0.296724i
$712$		0			0
$713$	−4524.44	+	2612.19i	−0.237646	+	0.137205i
$714$		0			0
$715$	−305.092	+	91.5328i	−0.0159577	+	0.00478760i
$716$		0			0
$717$	−9708.24	+	5605.05i	−0.505664	+	0.291945i
$718$		0			0
$719$	2452.15	−	4247.25i	0.127190	−	0.220300i	−0.795397	−	0.606089i	$-0.792737\pi$
$719$	2452.15	−	4247.25i	0.127190	−	0.220300i	0.922587	+	0.385789i	$0.126071\pi$
$720$		0			0
$721$	9919.90	+	5727.26i	0.512394	+	0.295831i
$722$		0			0
$723$		−	2466.05i		−	0.126851i
$724$		0			0
$725$	−5351.49	−	9269.06i	−0.274137	−	0.474819i
$726$		0			0
$727$	−12039.6			−0.614199			−0.307100	−	0.951677i	$-0.599358\pi$
$727$	−12039.6			−0.614199			−0.307100	+	0.951677i	$0.599358\pi$
$728$		0			0
$729$	−7275.47			−0.369632
$730$		0			0
$731$	−11939.6	−	20680.0i	−0.604107	−	1.04634i
$732$		0			0
$733$			15050.7i			0.758402i	0.925314	+	0.379201i	$0.123801\pi$
$733$			15050.7i			0.758402i	−0.925314	+	0.379201i	$0.876199\pi$
$734$		0			0
$735$	84.5983	+	48.8429i	0.00424552	+	0.00245115i
$736$		0			0
$737$	2161.68	−	3744.14i	0.108041	−	0.187133i
$738$		0			0
$739$	1357.29	−	783.630i	0.0675624	−	0.0390072i	−0.465838	−	0.884870i	$-0.654247\pi$
$739$	1357.29	−	783.630i	0.0675624	−	0.0390072i	0.533401	+	0.845863i	$0.320914\pi$
$740$		0			0
$741$	−1624.89	−	384.103i	−0.0805557	−	0.0190423i
$742$		0			0
$743$	18172.2	−	10491.7i	0.897272	−	0.518040i	0.0209580	−	0.999780i	$-0.493328\pi$
$743$	18172.2	−	10491.7i	0.897272	−	0.518040i	0.876314	+	0.481740i	$0.159995\pi$
$744$		0			0
$745$	−363.215	+	629.107i	−0.0178620	+	0.0309378i
$746$		0			0
$747$	29284.6	+	16907.5i	1.43436	+	0.828130i
$748$		0			0
$749$		−	19792.8i		−	0.965571i
$750$		0			0
$751$	−11597.6	−	20087.6i	−0.563517	−	0.976041i	−0.997186	−	0.0749681i	$-0.976115\pi$
$751$	−11597.6	−	20087.6i	−0.563517	−	0.976041i	0.433669	−	0.901072i	$-0.357219\pi$
$752$		0			0
$753$	3181.59			0.153976
$754$		0			0
$755$	1085.60			0.0523299
$756$		0			0
$757$	1357.75	+	2351.68i	0.0651890	+	0.112911i	0.896778	−	0.442481i	$-0.145902\pi$
$757$	1357.75	+	2351.68i	0.0651890	+	0.112911i	−0.831589	+	0.555392i	$0.812568\pi$
$758$		0			0
$759$			1216.64i			0.0581833i
$760$		0			0
$761$	−5511.96	−	3182.33i	−0.262561	−	0.151589i	0.362942	−	0.931812i	$-0.381772\pi$
$761$	−5511.96	−	3182.33i	−0.262561	−	0.151589i	−0.625502	+	0.780223i	$0.715106\pi$
$762$		0			0
$763$	4947.87	−	8569.96i	0.234764	−	0.406623i
$764$		0			0
$765$	446.265	−	257.651i	0.0210912	−	0.0121770i
$766$		0			0
$767$	13133.3	−	13936.8i	0.618275	−	0.656101i
$768$		0			0
$769$	−14492.8	+	8367.40i	−0.679613	+	0.392375i	−0.799709	−	0.600388i	$-0.795013\pi$
$769$	−14492.8	+	8367.40i	−0.679613	+	0.392375i	0.120096	+	0.992762i	$0.461680\pi$
$770$		0			0
$771$	−1223.83	+	2119.74i	−0.0571663	+	0.0990149i
$772$		0			0
$773$	−28226.6	−	16296.7i	−1.31338	−	0.758279i	−0.330724	−	0.943728i	$-0.607293\pi$
$773$	−28226.6	−	16296.7i	−1.31338	−	0.758279i	−0.982654	+	0.185448i	$0.940626\pi$
$774$		0			0
$775$		−	20933.2i		−	0.970249i
$776$		0			0
$777$	252.918	+	438.067i	0.0116775	+	0.0202260i
$778$		0			0
$779$	2881.95			0.132550
$780$		0			0
$781$	13501.3			0.618584
$782$		0			0
$783$	−3857.27	−	6680.98i	−0.176050	−	0.304928i
$784$		0			0
$785$		−	1015.42i		−	0.0461681i
$786$		0			0
$787$	29768.0	+	17186.6i	1.34830	+	0.778444i	0.988009	−	0.154394i	$-0.0493426\pi$
$787$	29768.0	+	17186.6i	1.34830	+	0.778444i	0.360295	+	0.932838i	$0.382676\pi$
$788$		0			0
$789$	−4957.21	+	8586.13i	−0.223677	+	0.387420i
$790$		0			0
$791$	12009.1	−	6933.46i	0.539816	−	0.311663i
$792$		0			0
$793$	15812.8	+	14901.1i	0.708106	+	0.667282i
$794$		0			0
$795$	−1.13478	+	0.655167i	−5.06246e−5	+	2.92281e-5i
$796$		0			0
$797$	1428.91	−	2474.95i	0.0635066	−	0.109997i	−0.832524	−	0.553989i	$-0.813105\pi$
$797$	1428.91	−	2474.95i	0.0635066	−	0.109997i	0.896031	+	0.443992i	$0.146438\pi$
$798$		0			0
$799$	−13632.3	−	7870.60i	−0.603598	−	0.348488i
$800$		0			0
$801$		−	9867.41i		−	0.435265i
$802$		0			0
$803$	−6345.54	−	10990.8i	−0.278866	−	0.483010i
$804$		0			0
$805$	−122.988			−0.00538477
$806$		0			0
$807$	−7836.51			−0.341832
$808$		0			0
$809$	−12203.9	−	21137.8i	−0.530366	−	0.918621i	−0.999372	−	0.0354263i	$-0.988721\pi$
$809$	−12203.9	−	21137.8i	−0.530366	−	0.918621i	0.469006	−	0.883195i	$-0.344612\pi$
$810$		0			0
$811$		−	31138.1i		−	1.34822i	−0.738631	−	0.674110i	$-0.764527\pi$
$811$		−	31138.1i		−	1.34822i	0.738631	−	0.674110i	$-0.235473\pi$
$812$		0			0
$813$	4550.45	+	2627.20i	0.196299	+	0.113333i
$814$		0			0
$815$	−47.0007	+	81.4075i	−0.00202008	+	0.00349887i
$816$		0			0
$817$	−5941.01	+	3430.04i	−0.254406	+	0.146881i
$818$		0			0
$819$	4115.70	+	13718.2i	0.175597	+	0.585290i
$820$		0			0
$821$	30329.4	−	17510.7i	1.28928	−	0.744369i	0.310758	−	0.950489i	$-0.399417\pi$
$821$	30329.4	−	17510.7i	1.28928	−	0.744369i	0.978527	+	0.206120i	$0.0660837\pi$
$822$		0			0
$823$	11993.1	−	20772.6i	0.507962	−	0.879816i	−0.491996	−	0.870598i	$-0.663732\pi$
$823$	11993.1	−	20772.6i	0.507962	−	0.879816i	0.999958	−	0.00921810i	$-0.00293425\pi$
$824$		0			0
$825$	−4221.75	−	2437.43i	−0.178161	−	0.102861i
$826$		0			0
$827$			14919.3i			0.627320i	0.949535	+	0.313660i	$0.101555\pi$
$827$			14919.3i			0.627320i	−0.949535	+	0.313660i	$0.898445\pi$
$828$		0			0
$829$	−8096.41	−	14023.4i	−0.339204	−	0.587518i	0.645079	−	0.764115i	$-0.276824\pi$
$829$	−8096.41	−	14023.4i	−0.339204	−	0.587518i	−0.984283	+	0.176597i	$0.943491\pi$
$830$		0			0
$831$	−3797.89			−0.158541
$832$		0			0
$833$	−12547.5			−0.521902
$834$		0			0
$835$	132.596	+	229.664i	0.00549543	+	0.00951836i
$836$		0			0
$837$		−	15088.3i		−	0.623092i
$838$		0			0
$839$	−37765.8	−	21804.1i	−1.55402	−	0.897213i	−0.997808	−	0.0661708i	$-0.978922\pi$
$839$	−37765.8	−	21804.1i	−1.55402	−	0.897213i	−0.556210	−	0.831042i	$-0.687745\pi$
$840$		0			0
$841$	8523.20	−	14762.6i	0.349469	−	0.605298i
$842$		0			0
$843$	−7507.72	+	4334.58i	−0.306737	+	0.177095i
$844$		0			0
$845$	303.153	−	605.391i	0.0123418	−	0.0246463i
$846$		0			0
$847$	9365.68	−	5407.28i	0.379939	−	0.219358i
$848$		0			0
$849$	2145.34	−	3715.84i	0.0867231	−	0.150209i
$850$		0			0
$851$	602.677	+	347.956i	0.0242768	+	0.0140162i
$852$		0			0
$853$			12671.8i			0.508644i	0.967120	+	0.254322i	$0.0818523\pi$
$853$			12671.8i			0.508644i	−0.967120	+	0.254322i	$0.918148\pi$
$854$		0			0
$855$	−74.0187	−	128.204i	−0.00296069	−	0.00512806i
$856$		0			0
$857$	−11021.6			−0.439314			−0.219657	−	0.975577i	$-0.570494\pi$
$857$	−11021.6			−0.439314			−0.219657	+	0.975577i	$0.570494\pi$
$858$		0			0
$859$	2679.73			0.106439			0.0532195	−	0.998583i	$-0.483052\pi$
$859$	2679.73			0.106439			0.0532195	+	0.998583i	$0.483052\pi$
$860$		0			0
$861$	1622.26	+	2809.83i	0.0642118	+	0.111218i
$862$		0			0
$863$			9500.93i			0.374757i	0.982288	+	0.187378i	$0.0599991\pi$
$863$			9500.93i			0.374757i	−0.982288	+	0.187378i	$0.940001\pi$
$864$		0			0
$865$	422.172	+	243.741i	0.0165945	+	0.00958086i
$866$		0			0
$867$	−4.22423	+	7.31658i	−0.000165470	+	0.000286602i
$868$		0			0
$869$	5197.42	−	3000.73i	0.202889	−	0.117138i
$870$		0			0
$871$	2640.76	+	8802.03i	0.102731	+	0.342417i
$872$		0			0
$873$	17348.6	−	10016.2i	0.672578	−	0.388313i
$874$		0			0
$875$	492.978	−	853.864i	0.0190465	−	0.0329896i
$876$		0			0
$877$	44593.9	+	25746.3i	1.71702	+	0.991323i	0.924235	+	0.381823i	$0.124704\pi$
$877$	44593.9	+	25746.3i	1.71702	+	0.991323i	0.792786	+	0.609499i	$0.208630\pi$
$878$		0			0
$879$			3822.37i			0.146673i
$880$		0			0
$881$	−6046.76	−	10473.3i	−0.231238	−	0.400515i	0.726935	−	0.686706i	$-0.240944\pi$
$881$	−6046.76	−	10473.3i	−0.231238	−	0.400515i	−0.958173	+	0.286191i	$0.907611\pi$
$882$		0			0
$883$	−13875.0			−0.528802			−0.264401	−	0.964413i	$-0.585174\pi$
$883$	−13875.0			−0.528802			−0.264401	+	0.964413i	$0.585174\pi$
$884$		0			0
$885$	−222.838			−0.00846396
$886$		0			0
$887$	12632.1	+	21879.4i	0.478179	+	0.828230i	0.999687	−	0.0250165i	$-0.00796384\pi$
$887$	12632.1	+	21879.4i	0.478179	+	0.828230i	−0.521508	+	0.853246i	$0.674631\pi$
$888$		0			0
$889$			19071.8i			0.719514i
$890$		0			0
$891$	9263.68	+	5348.39i	0.348311	+	0.201097i
$892$		0			0
$893$	−2261.09	+	3916.31i	−0.0847305	+	0.146758i
$894$		0			0
$895$	−501.709	+	289.662i	−0.0187378	+	0.0108182i
$896$		0			0
$897$	−1882.06	−	1773.56i	−0.0700561	−	0.0660172i
$898$		0			0
$899$	−12436.9	+	7180.43i	−0.461394	+	0.266386i
$900$		0			0
$901$	84.1545	−	145.760i	0.00311165	−	0.00538953i
$902$		0			0
$903$	−6688.41	−	3861.56i	−0.246485	−	0.142308i
$904$		0			0
$905$			863.119i			0.0317028i
$906$		0			0
$907$	−1172.04	−	2030.03i	−0.0429073	−	0.0743177i	0.843774	−	0.536698i	$-0.180329\pi$
$907$	−1172.04	−	2030.03i	−0.0429073	−	0.0743177i	−0.886682	+	0.462381i	$0.846995\pi$
$908$		0			0
$909$	−2261.73			−0.0825268
$910$		0			0
$911$	4870.47			0.177131			0.0885653	−	0.996070i	$-0.471772\pi$
$911$	4870.47			0.177131			0.0885653	+	0.996070i	$0.471772\pi$
$912$		0			0
$913$	−15621.1	−	27056.5i	−0.566245	−	0.980765i
$914$		0			0
$915$		−	252.832i		−	0.00913485i
$916$		0			0
$917$	−22365.7	−	12912.8i	−0.805431	−	0.465016i
$918$		0			0
$919$	−14502.0	+	25118.2i	−0.520541	+	0.901604i	0.479174	+	0.877720i	$0.340936\pi$
$919$	−14502.0	+	25118.2i	−0.520541	+	0.901604i	−0.999715	+	0.0238835i	$0.992397\pi$
$920$		0			0
$921$	1356.90	−	783.408i	0.0485467	−	0.0280284i
$922$		0			0
$923$	−19681.6	+	20885.7i	−0.701871	+	0.744811i
$924$		0			0
$925$	−2414.83	+	1394.20i	−0.0858369	+	0.0495579i
$926$		0			0
$927$	−10677.4	+	18493.7i	−0.378307	+	0.655246i
$928$		0			0
$929$	24834.8	+	14338.4i	0.877075	+	0.506379i	0.869693	−	0.493593i	$-0.164317\pi$
$929$	24834.8	+	14338.4i	0.877075	+	0.506379i	0.00738211	+	0.999973i	$0.497650\pi$
$930$		0			0
$931$			3604.67i			0.126894i
$932$		0			0
$933$	8743.31	+	15143.9i	0.306799	+	0.531391i
$934$		0			0
$935$	−476.095			−0.0166524
$936$		0			0
$937$	18265.9			0.636842			0.318421	−	0.947949i	$-0.396847\pi$
$937$	18265.9			0.636842			0.318421	+	0.947949i	$0.396847\pi$
$938$		0			0
$939$	−4995.10	−	8651.76i	−0.173598	−	0.300681i
$940$		0			0
$941$		−	45277.4i		−	1.56855i	−0.620415	−	0.784273i	$-0.713036\pi$
$941$		−	45277.4i		−	1.56855i	0.620415	−	0.784273i	$-0.286964\pi$
$942$		0			0
$943$	3865.66	+	2231.84i	0.133492	+	0.0770719i
$944$		0			0
$945$	177.598	−	307.608i	0.00611350	−	0.0105889i
$946$		0			0
$947$	−44615.8	+	25759.0i	−1.53096	+	0.883900i	−0.531642	+	0.846969i	$0.678425\pi$
$947$	−44615.8	+	25759.0i	−1.53096	+	0.883900i	−0.999318	+	0.0369314i	$0.988242\pi$
$948$		0			0
$949$	26252.4	+	6205.72i	0.897985	+	0.212272i
$950$		0			0
$951$	−17086.8	+	9865.05i	−0.582625	+	0.336379i
$952$		0			0
$953$	−12223.9	+	21172.4i	−0.415499	+	0.719666i	−0.995481	−	0.0949640i	$-0.969726\pi$
$953$	−12223.9	+	21172.4i	−0.415499	+	0.719666i	0.579982	+	0.814630i	$0.303060\pi$
$954$		0			0
$955$	956.532	+	552.254i	0.0324111	+	0.0187126i
$956$		0			0
$957$			3344.32i			0.112964i
$958$		0			0
$959$	8023.46	+	13897.0i	0.270168	+	0.467945i
$960$		0			0
$961$	1703.60			0.0571850
$962$		0			0
$963$	36899.8			1.23477
$964$		0			0
$965$	794.289	+	1375.75i	0.0264965	+	0.0458932i
$966$		0			0
$967$			6835.07i			0.227302i	0.993521	+	0.113651i	$0.0362546\pi$
$967$			6835.07i			0.227302i	−0.993521	+	0.113651i	$0.963745\pi$
$968$		0			0
$969$	−2161.27	−	1247.81i	−0.0716511	−	0.0413678i
$970$		0			0
$971$	14656.6	−	25386.0i	0.484400	−	0.839005i	−0.515439	−	0.856926i	$-0.672371\pi$
$971$	14656.6	−	25386.0i	0.484400	−	0.839005i	0.999839	+	0.0179207i	$0.00570464\pi$
$972$		0			0
$973$	−31330.6	+	18088.7i	−1.03229	+	0.595990i
$974$		0			0
$975$	9924.85	−	2977.63i	0.325999	−	0.0978055i
$976$		0			0
$977$	11633.2	−	6716.45i	0.380942	−	0.219937i	−0.297286	−	0.954788i	$-0.596082\pi$
$977$	11633.2	−	6716.45i	0.380942	−	0.219937i	0.678228	+	0.734852i	$0.262748\pi$
$978$		0			0
$979$	−4558.31	+	7895.23i	−0.148809	+	0.257745i
$980$		0			0
$981$	15977.0	+	9224.34i	0.519987	+	0.300215i
$982$		0			0
$983$		−	20535.8i		−	0.666316i	−0.942871	−	0.333158i	$-0.891886\pi$
$983$		−	20535.8i		−	0.666316i	0.942871	−	0.333158i	$-0.108114\pi$
$984$		0			0
$985$	321.344	+	556.584i	0.0103948	+	0.0180043i
$986$		0			0
$987$	−5091.08			−0.164185
$988$		0			0
$989$	−10625.2			−0.341619
$990$		0			0
$991$	23130.6	+	40063.4i	0.741442	+	1.28422i	0.951839	+	0.306599i	$0.0991911\pi$
$991$	23130.6	+	40063.4i	0.741442	+	1.28422i	−0.210397	+	0.977616i	$0.567476\pi$
$992$		0			0
$993$		−	8137.01i		−	0.260040i
$994$		0			0
$995$	727.257	+	419.882i	0.0231714	+	0.0133780i
$996$		0			0
$997$	−16096.9	+	27880.6i	−0.511326	+	0.885643i	0.488587	+	0.872515i	$0.337512\pi$
$997$	−16096.9	+	27880.6i	−0.511326	+	0.885643i	−0.999914	+	0.0131284i	$0.995821\pi$
$998$		0			0
$999$	−1740.57	+	1004.92i	−0.0551243	+	0.0318260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.w.e.49.6		20
4.3	odd	2		104.4.o.a.49.5	yes	20
13.4	even	6	inner	208.4.w.e.17.6		20
52.11	even	12		1352.4.a.p.1.6		10
52.15	even	12		1352.4.a.o.1.6		10
52.43	odd	6		104.4.o.a.17.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.4.o.a.17.5	✓	20	52.43	odd	6
104.4.o.a.49.5	yes	20	4.3	odd	2
208.4.w.e.17.6		20	13.4	even	6	inner
208.4.w.e.49.6		20	1.1	even	1	trivial
1352.4.a.o.1.6		10	52.15	even	12
1352.4.a.p.1.6		10	52.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.884941 + 1.53276i) q^{3} +0.308172i q^{5} +(-11.0872 - 6.40118i) q^{7} +(11.9338 - 20.6699i) q^{9} +O(q^{10})\)	\(q+(0.884941 + 1.53276i) q^{3} +0.308172i q^{5} +(-11.0872 - 6.40118i) q^{7} +(11.9338 - 20.6699i) q^{9} +(-19.0972 + 11.0258i) q^{11} +(10.7828 - 45.6150i) q^{13} +(-0.472354 + 0.272714i) q^{15} +(35.0294 - 60.6726i) q^{17} +(-17.4302 - 10.0633i) q^{19} -22.6587i q^{21} +(-15.5865 - 26.9966i) q^{23} +124.905 q^{25} +90.0295 q^{27} +(-42.8445 - 74.2088i) q^{29} -167.593i q^{31} +(-33.7997 - 19.5143i) q^{33} +(1.97266 - 3.41675i) q^{35} +(-19.3333 + 11.1621i) q^{37} +(79.4592 - 23.8391i) q^{39} +(-124.007 + 71.5954i) q^{41} +(170.423 - 295.181i) q^{43} +(6.36987 + 3.67765i) q^{45} -224.686i q^{47} +(-89.5497 - 155.105i) q^{49} +123.996 q^{51} +2.40240 q^{53} +(-3.39782 - 5.88520i) q^{55} -35.6218i q^{57} +(353.820 + 204.278i) q^{59} +(-231.775 + 401.446i) q^{61} +(-264.623 + 152.780i) q^{63} +(14.0573 + 3.32296i) q^{65} +(-169.791 + 98.0287i) q^{67} +(27.5862 - 47.7808i) q^{69} +(-530.234 - 306.131i) q^{71} +575.520i q^{73} +(110.534 + 191.450i) q^{75} +282.311 q^{77} -272.157 q^{79} +(-242.541 - 420.093i) q^{81} +1416.78i q^{83} +(18.6976 + 10.7951i) q^{85} +(75.8297 - 131.341i) q^{87} +(358.036 - 206.712i) q^{89} +(-411.541 + 436.719i) q^{91} +(256.880 - 148.310i) q^{93} +(3.10123 - 5.37149i) q^{95} +(726.870 + 419.659i) q^{97} +526.315i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9}+O(q^{10}) \) 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9	\( 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9} + 42 q^{11} + 24 q^{13} - 70 q^{17} + 102 q^{19} - 90 q^{23} - 628 q^{25} - 708 q^{27} + 170 q^{29} - 678 q^{33} + 544 q^{35} + 582 q^{37} - 1162 q^{39} + 438 q^{41} - 270 q^{43} + 540 q^{45} + 92 q^{49} + 444 q^{51} - 592 q^{53} + 288 q^{55} - 90 q^{59} + 746 q^{61} + 1068 q^{63} - 1412 q^{65} - 846 q^{67} + 682 q^{69} + 1038 q^{71} - 722 q^{75} + 2812 q^{77} + 1008 q^{79} + 694 q^{81} - 180 q^{85} + 338 q^{87} + 2466 q^{89} - 690 q^{91} - 4764 q^{93} + 2592 q^{95} - 846 q^{97}+O(q^{100}) \) 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9 + 42 * q^11 + 24 * q^13 - 70 * q^17 + 102 * q^19 - 90 * q^23 - 628 * q^25 - 708 * q^27 + 170 * q^29 - 678 * q^33 + 544 * q^35 + 582 * q^37 - 1162 * q^39 + 438 * q^41 - 270 * q^43 + 540 * q^45 + 92 * q^49 + 444 * q^51 - 592 * q^53 + 288 * q^55 - 90 * q^59 + 746 * q^61 + 1068 * q^63 - 1412 * q^65 - 846 * q^67 + 682 * q^69 + 1038 * q^71 - 722 * q^75 + 2812 * q^77 + 1008 * q^79 + 694 * q^81 - 180 * q^85 + 338 * q^87 + 2466 * q^89 - 690 * q^91 - 4764 * q^93 + 2592 * q^95 - 846 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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