LMFDB - Embedded newform 208.4.i.d.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [208,4,Mod(81,208)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(208, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("208.81"); S:= CuspForms(chi, 4); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [4,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2723972812$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{217})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 55x^{2} + 54x + 2916 $ x^4 - x^3 + 55x^2 + 54x + 2916
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$3.93273 - 6.81169i$ of defining polynomial
Character	$\chi$	$=$	208.81
Dual form			208.4.i.d.113.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.43273 - 7.67771i) q^{3} +3.86546 q^{5} +(-7.56727 + 13.1069i) q^{7} +(-25.7982 + 44.6838i) q^{9} +(27.0291 + 46.8158i) q^{11} +(-19.7982 + 42.4857i) q^{13} +(-17.1345 - 29.6779i) q^{15} +(61.9618 - 107.321i) q^{17} +(4.43273 - 7.67771i) q^{19} +134.175 q^{21} +(19.2982 + 33.4254i) q^{23} -110.058 q^{25} +218.058 q^{27} +(93.6928 + 162.281i) q^{29} +36.7710 q^{31} +(239.625 - 415.044i) q^{33} +(-29.2510 + 50.6642i) q^{35} +(160.769 + 278.460i) q^{37} +(413.953 - 36.3226i) q^{39} +(13.1546 + 22.7844i) q^{41} +(68.8182 - 119.197i) q^{43} +(-99.7219 + 172.723i) q^{45} +300.466 q^{47} +(56.9728 + 98.6799i) q^{49} -1098.64 q^{51} -260.135 q^{53} +(104.480 + 180.965i) q^{55} -78.5964 q^{57} +(-123.029 + 213.093i) q^{59} +(-45.6526 + 79.0727i) q^{61} +(-390.444 - 676.268i) q^{63} +(-76.5291 + 164.227i) q^{65} +(205.262 + 355.524i) q^{67} +(171.087 - 296.332i) q^{69} +(-212.222 + 367.579i) q^{71} -421.982 q^{73} +(487.858 + 844.995i) q^{75} -818.146 q^{77} -733.542 q^{79} +(-270.042 - 467.727i) q^{81} +616.843 q^{83} +(239.511 - 414.845i) q^{85} +(830.629 - 1438.69i) q^{87} +(103.585 + 179.415i) q^{89} +(-407.037 - 580.993i) q^{91} +(-162.996 - 282.317i) q^{93} +(17.1345 - 29.6779i) q^{95} +(370.742 - 642.144i) q^{97} -2789.21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{3} - 14 q^{5} - 45 q^{7} - 59 q^{9} + 5 q^{11} - 35 q^{13} - 98 q^{15} + 130 q^{17} + 3 q^{19} - 82 q^{21} + 33 q^{23} - 234 q^{25} + 666 q^{27} + 198 q^{29} - 560 q^{31} + 767 q^{33} + 266 q^{35}+ \cdots - 4852 q^{99}+O(q^{100}) $ 4 * q - 3 * q^3 - 14 * q^5 - 45 * q^7 - 59 * q^9 + 5 * q^11 - 35 * q^13 - 98 * q^15 + 130 * q^17 + 3 * q^19 - 82 * q^21 + 33 * q^23 - 234 * q^25 + 666 * q^27 + 198 * q^29 - 560 * q^31 + 767 * q^33 + 266 * q^35 + 702 * q^37 + 1317 * q^39 - 242 * q^41 - 93 * q^43 - 119 * q^45 - 448 * q^47 - 435 * q^49 - 2126 * q^51 - 1070 * q^53 + 742 * q^55 - 226 * q^57 - 389 * q^59 - 654 * q^61 - 1002 * q^63 - 203 * q^65 - 107 * q^67 + 375 * q^69 - 569 * q^71 - 1246 * q^73 + 935 * q^75 + 1294 * q^77 - 1520 * q^79 + 334 * q^81 + 3528 * q^83 + 413 * q^85 + 1599 * q^87 + 871 * q^89 + 1539 * q^91 - 2184 * q^93 + 98 * q^95 + 879 * q^97 - 4852 * q^99

Character values

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

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−4.43273	−	7.67771i	−0.853079	−	1.47758i	−0.878416	−	0.477898i	$-0.841399\pi$
$3$	−4.43273	−	7.67771i	−0.853079	−	1.47758i	0.0253362	−	0.999679i	$-0.491934\pi$
$4$		0			0
$5$	3.86546			0.345737			0.172869	−	0.984945i	$-0.444696\pi$
$5$	3.86546			0.345737			0.172869	+	0.984945i	$0.444696\pi$
$6$		0			0
$7$	−7.56727	+	13.1069i	−0.408594	+	0.707706i	−0.994732	−	0.102505i	$-0.967314\pi$
$7$	−7.56727	+	13.1069i	−0.408594	+	0.707706i	0.586138	+	0.810211i	$0.300648\pi$
$8$		0			0
$9$	−25.7982	+	44.6838i	−0.955489	+	1.65495i
$10$		0			0
$11$	27.0291	+	46.8158i	0.740871	+	1.28323i	0.952099	+	0.305790i	$0.0989205\pi$
$11$	27.0291	+	46.8158i	0.740871	+	1.28323i	−0.211228	+	0.977437i	$0.567746\pi$
$12$		0			0
$13$	−19.7982	+	42.4857i	−0.422387	+	0.906416i
$13$	−19.7982	+	42.4857i	−0.422387	+	0.906416i
$14$		0			0
$15$	−17.1345	−	29.6779i	−0.294941	−	0.510853i
$16$		0			0
$17$	61.9618	−	107.321i	0.883997	−	1.53113i	0.0371386	−	0.999310i	$-0.488176\pi$
$17$	61.9618	−	107.321i	0.883997	−	1.53113i	0.846859	−	0.531818i	$-0.178491\pi$
$18$		0			0
$19$	4.43273	−	7.67771i	0.0535231	−	0.0927046i	−0.838023	−	0.545636i	$-0.816288\pi$
$19$	4.43273	−	7.67771i	0.0535231	−	0.0927046i	0.891546	+	0.452931i	$0.149622\pi$
$20$		0			0
$21$	134.175			1.39425
$22$		0			0
$23$	19.2982	+	33.4254i	0.174954	+	0.303030i	0.940145	−	0.340773i	$-0.110689\pi$
$23$	19.2982	+	33.4254i	0.174954	+	0.303030i	−0.765191	+	0.643803i	$0.777356\pi$
$24$		0			0
$25$	−110.058			−0.880466
$26$		0			0
$27$	218.058			1.55427
$28$		0			0
$29$	93.6928	+	162.281i	0.599942	+	1.03913i	0.992829	+	0.119543i	$0.0381429\pi$
$29$	93.6928	+	162.281i	0.599942	+	1.03913i	−0.392887	+	0.919587i	$0.628524\pi$
$30$		0			0
$31$	36.7710			0.213041			0.106521	−	0.994311i	$-0.466029\pi$
$31$	36.7710			0.213041			0.106521	+	0.994311i	$0.466029\pi$
$32$		0			0
$33$	239.625	−	415.044i	1.26404	−	2.18939i
$34$		0			0
$35$	−29.2510	+	50.6642i	−0.141266	+	0.244680i
$36$		0			0
$37$	160.769	+	278.460i	0.714332	+	1.23726i	0.963217	+	0.268726i	$0.0866025\pi$
$37$	160.769	+	278.460i	0.714332	+	1.23726i	−0.248885	+	0.968533i	$0.580064\pi$
$38$		0			0
$39$	413.953	−	36.3226i	1.69963	−	0.149135i
$40$		0			0
$41$	13.1546	+	22.7844i	0.0501074	+	0.0867886i	0.889991	−	0.455978i	$-0.150710\pi$
$41$	13.1546	+	22.7844i	0.0501074	+	0.0867886i	−0.839884	+	0.542766i	$0.817377\pi$
$42$		0			0
$43$	68.8182	−	119.197i	0.244062	−	0.422729i	−0.717805	−	0.696244i	$-0.754853\pi$
$43$	68.8182	−	119.197i	0.244062	−	0.422729i	0.961868	+	0.273515i	$0.0881865\pi$
$44$		0			0
$45$	−99.7219	+	172.723i	−0.330348	+	0.572179i
$46$		0			0
$47$	300.466			0.932499			0.466249	−	0.884653i	$-0.345605\pi$
$47$	300.466			0.932499			0.466249	+	0.884653i	$0.345605\pi$
$48$		0			0
$49$	56.9728	+	98.6799i	0.166102	+	0.287696i
$50$		0			0
$51$	−1098.64			−3.01648
$52$		0			0
$53$	−260.135			−0.674193			−0.337096	−	0.941470i	$-0.609445\pi$
$53$	−260.135			−0.674193			−0.337096	+	0.941470i	$0.609445\pi$
$54$		0			0
$55$	104.480	+	180.965i	0.256147	+	0.443659i
$56$		0			0
$57$	−78.5964			−0.182638
$58$		0			0
$59$	−123.029	+	213.093i	−0.271475	+	0.470209i	−0.969240	−	0.246118i	$-0.920845\pi$
$59$	−123.029	+	213.093i	−0.271475	+	0.470209i	0.697765	+	0.716327i	$0.254178\pi$
$60$		0			0
$61$	−45.6526	+	79.0727i	−0.0958233	+	0.165971i	−0.909952	−	0.414714i	$-0.863882\pi$
$61$	−45.6526	+	79.0727i	−0.0958233	+	0.165971i	0.814129	+	0.580685i	$0.197215\pi$
$62$		0			0
$63$	−390.444	−	676.268i	−0.780814	−	1.35241i
$64$		0			0
$65$	−76.5291	+	164.227i	−0.146035	+	0.313382i
$66$		0			0
$67$	205.262	+	355.524i	0.374280	+	0.648272i	0.990219	−	0.139522i	$-0.0445566\pi$
$67$	205.262	+	355.524i	0.374280	+	0.648272i	−0.615939	+	0.787794i	$0.711223\pi$
$68$		0			0
$69$	171.087	−	296.332i	0.298500	−	0.517017i
$70$		0			0
$71$	−212.222	+	367.579i	−0.354734	+	0.614417i	−0.987072	−	0.160275i	$-0.948762\pi$
$71$	−212.222	+	367.579i	−0.354734	+	0.614417i	0.632339	+	0.774692i	$0.282095\pi$
$72$		0			0
$73$	−421.982			−0.676565			−0.338283	−	0.941045i	$-0.609846\pi$
$73$	−421.982			−0.676565			−0.338283	+	0.941045i	$0.609846\pi$
$74$		0			0
$75$	487.858	+	844.995i	0.751107	+	1.30096i
$76$		0			0
$77$	−818.146			−1.21086
$78$		0			0
$79$	−733.542			−1.04468			−0.522341	−	0.852736i	$-0.674941\pi$
$79$	−733.542			−1.04468			−0.522341	+	0.852736i	$0.674941\pi$
$80$		0			0
$81$	−270.042	−	467.727i	−0.370428	−	0.641600i
$82$		0			0
$83$	616.843			0.815751			0.407876	−	0.913037i	$-0.366270\pi$
$83$	616.843			0.815751			0.407876	+	0.913037i	$0.366270\pi$
$84$		0			0
$85$	239.511	−	414.845i	0.305631	−	0.529368i
$86$		0			0
$87$	830.629	−	1438.69i	1.02360	−	1.77292i
$88$		0			0
$89$	103.585	+	179.415i	0.123371	+	0.213685i	0.921095	−	0.389338i	$-0.127296\pi$
$89$	103.585	+	179.415i	0.123371	+	0.213685i	−0.797724	+	0.603023i	$0.793963\pi$
$90$		0			0
$91$	−407.037	−	580.993i	−0.468891	−	0.669282i
$92$		0			0
$93$	−162.996	−	282.317i	−0.181741	−	0.314785i
$94$		0			0
$95$	17.1345	−	29.6779i	0.0185049	−	0.0320514i
$96$		0			0
$97$	370.742	−	642.144i	0.388074	−	0.672163i	−0.604117	−	0.796896i	$-0.706474\pi$
$97$	370.742	−	642.144i	0.388074	−	0.672163i	0.992190	+	0.124733i	$0.0398073\pi$
$98$		0			0
$99$	−2789.21			−2.83158
$100$		0			0
$101$	206.653	+	357.933i	0.203591	+	0.352630i	0.949683	−	0.313213i	$-0.101405\pi$
$101$	206.653	+	357.933i	0.203591	+	0.352630i	−0.746092	+	0.665843i	$0.768072\pi$
$102$		0			0
$103$	3.76712			0.00360374			0.00180187	−	0.999998i	$-0.499426\pi$
$103$	3.76712			0.00360374			0.00180187	+	0.999998i	$0.499426\pi$
$104$		0			0
$105$	518.647			0.482045
$106$		0			0
$107$	56.9127	+	98.5756i	0.0514201	+	0.0890623i	0.890590	−	0.454807i	$-0.150292\pi$
$107$	56.9127	+	98.5756i	0.0514201	+	0.0890623i	−0.839170	+	0.543870i	$0.816959\pi$
$108$		0			0
$109$	1935.63			1.70092			0.850458	−	0.526044i	$-0.176325\pi$
$109$	1935.63			1.70092			0.850458	+	0.526044i	$0.176325\pi$
$110$		0			0
$111$	1425.29	−	2468.68i	1.21876	−	2.11096i
$112$		0			0
$113$	−949.391	+	1644.39i	−0.790365	+	1.36895i	0.135376	+	0.990794i	$0.456776\pi$
$113$	−949.391	+	1644.39i	−0.790365	+	1.36895i	−0.925741	+	0.378158i	$0.876558\pi$
$114$		0			0
$115$	74.5964	+	129.205i	0.0604882	+	0.104769i
$116$		0			0
$117$	−1387.66	−	1980.71i	−1.09649	−	1.56510i
$118$		0			0
$119$	937.764	+	1624.25i	0.722392	+	1.25122i
$120$		0			0
$121$	−795.646	+	1378.10i	−0.597780	+	1.03539i
$122$		0			0
$123$	116.622	−	201.994i	0.0854912	−	0.148075i
$124$		0			0
$125$	−908.608			−0.650147
$126$		0			0
$127$	122.302	+	211.833i	0.0854532	+	0.148009i	0.905584	−	0.424166i	$-0.139433\pi$
$127$	122.302	+	211.833i	0.0854532	+	0.148009i	−0.820131	+	0.572176i	$0.806100\pi$
$128$		0			0
$129$	−1220.21			−0.832818
$130$		0			0
$131$	−1615.62			−1.07754			−0.538769	−	0.842453i	$-0.681111\pi$
$131$	−1615.62			−1.07754			−0.538769	+	0.842453i	$0.681111\pi$
$132$		0			0
$133$	67.0873	+	116.199i	0.0437384	+	0.0757572i
$134$		0			0
$135$	842.895			0.537369
$136$		0			0
$137$	1150.97	−	1993.54i	0.717769	−	1.24321i	−0.244113	−	0.969747i	$-0.578497\pi$
$137$	1150.97	−	1993.54i	0.717769	−	1.24321i	0.961882	−	0.273465i	$-0.0881698\pi$
$138$		0			0
$139$	−1404.53	+	2432.73i	−0.857058	+	1.48447i	0.0176640	+	0.999844i	$0.494377\pi$
$139$	−1404.53	+	2432.73i	−0.857058	+	1.48447i	−0.874722	+	0.484625i	$0.838956\pi$
$140$		0			0
$141$	−1331.88	−	2306.89i	−0.795495	−	1.37784i
$142$		0			0
$143$	−2524.13	+	221.482i	−1.47607	+	0.129519i
$144$		0			0
$145$	362.166	+	627.289i	0.207422	+	0.359266i
$146$		0			0
$147$	505.091	−	874.842i	0.283396	−	0.490856i
$148$		0			0
$149$	−1266.58	+	2193.79i	−0.696393	+	1.20619i	0.273315	+	0.961925i	$0.411880\pi$
$149$	−1266.58	+	2193.79i	−0.696393	+	1.20619i	−0.969709	+	0.244264i	$0.921454\pi$
$150$		0			0
$151$	2391.10			1.28864			0.644321	−	0.764755i	$-0.277140\pi$
$151$	2391.10			1.28864			0.644321	+	0.764755i	$0.277140\pi$
$152$		0			0
$153$	3197.01	+	5537.38i	1.68930	+	2.92595i
$154$		0			0
$155$	142.137			0.0736562
$156$		0			0
$157$	1927.49			0.979811			0.489905	−	0.871776i	$-0.337031\pi$
$157$	1927.49			0.979811			0.489905	+	0.871776i	$0.337031\pi$
$158$		0			0
$159$	1153.11	+	1997.24i	0.575140	+	0.996172i
$160$		0			0
$161$	−584.138			−0.285941
$162$		0			0
$163$	−1109.26	+	1921.30i	−0.533031	+	0.923237i	0.466225	+	0.884666i	$0.345614\pi$
$163$	−1109.26	+	1921.30i	−0.533031	+	0.923237i	−0.999256	+	0.0385709i	$0.987719\pi$
$164$		0			0
$165$	926.263	−	1604.33i	0.437027	−	0.756953i
$166$		0			0
$167$	−754.135	−	1306.20i	−0.349442	−	0.605251i	0.636709	−	0.771104i	$-0.280295\pi$
$167$	−754.135	−	1306.20i	−0.349442	−	0.605251i	−0.986150	+	0.165854i	$0.946962\pi$
$168$		0			0
$169$	−1413.06	−	1682.28i	−0.643179	−	0.765716i
$170$		0			0
$171$	228.713	+	396.142i	0.102281	+	0.177156i
$172$		0			0
$173$	853.236	−	1477.85i	0.374973	−	0.649472i	−0.615350	−	0.788254i	$-0.710985\pi$
$173$	853.236	−	1477.85i	0.374973	−	0.649472i	0.990323	+	0.138782i	$0.0443186\pi$
$174$		0			0
$175$	832.840	−	1442.52i	0.359753	−	0.623111i
$176$		0			0
$177$	2181.42			0.926359
$178$		0			0
$179$	297.611	+	515.478i	0.124271	+	0.215244i	0.921448	−	0.388502i	$-0.127007\pi$
$179$	297.611	+	515.478i	0.124271	+	0.215244i	−0.797177	+	0.603746i	$0.793674\pi$
$180$		0			0
$181$	403.006			0.165498			0.0827492	−	0.996570i	$-0.473630\pi$
$181$	403.006			0.165498			0.0827492	+	0.996570i	$0.473630\pi$
$182$		0			0
$183$	809.463			0.326980
$184$		0			0
$185$	621.446	+	1076.38i	0.246971	+	0.427766i
$186$		0			0
$187$	6699.09			2.61971
$188$		0			0
$189$	−1650.11	+	2858.07i	−0.635066	+	1.09997i
$190$		0			0
$191$	−306.848	+	531.476i	−0.116245	+	0.201342i	−0.918277	−	0.395939i	$-0.870419\pi$
$191$	−306.848	+	531.476i	−0.116245	+	0.201342i	0.802032	+	0.597281i	$0.203752\pi$
$192$		0			0
$193$	−1002.66	−	1736.67i	−0.373955	−	0.647709i	0.616215	−	0.787578i	$-0.288665\pi$
$193$	−1002.66	−	1736.67i	−0.373955	−	0.647709i	−0.990170	+	0.139869i	$0.955332\pi$
$194$		0			0
$195$	1600.12	−	140.404i	0.587625	−	0.0515616i
$196$		0			0
$197$	278.750	+	482.809i	0.100813	+	0.174613i	0.912020	−	0.410146i	$-0.134522\pi$
$197$	278.750	+	482.809i	0.100813	+	0.174613i	−0.811207	+	0.584759i	$0.801189\pi$
$198$		0			0
$199$	2766.99	−	4792.56i	0.985661	−	1.70721i	0.346698	−	0.937977i	$-0.387303\pi$
$199$	2766.99	−	4792.56i	0.985661	−	1.70721i	0.638963	−	0.769237i	$-0.279364\pi$
$200$		0			0
$201$	1819.74	−	3151.89i	0.638581	−	1.10605i
$202$		0			0
$203$	−2835.99			−0.980531
$204$		0			0
$205$	50.8486	+	88.0723i	0.0173240	+	0.0300060i
$206$		0			0
$207$	−1991.43			−0.668668
$208$		0			0
$209$	479.251			0.158615
$210$		0			0
$211$	−2341.87	−	4056.23i	−0.764079	−	1.32342i	−0.940732	−	0.339151i	$-0.889860\pi$
$211$	−2341.87	−	4056.23i	−0.764079	−	1.32342i	0.176653	−	0.984273i	$-0.443473\pi$
$212$		0			0
$213$	3762.89			1.21046
$214$		0			0
$215$	266.014	−	460.750i	0.0843815	−	0.146153i
$216$		0			0
$217$	−278.256	+	481.954i	−0.0870473	+	0.150770i
$218$		0			0
$219$	1870.53	+	3239.86i	0.577164	+	0.999677i
$220$		0			0
$221$	3332.87	+	4757.25i	1.01445	+	1.44800i
$222$		0			0
$223$	−1191.93	−	2064.48i	−0.357926	−	0.619947i	0.629688	−	0.776848i	$-0.283183\pi$
$223$	−1191.93	−	2064.48i	−0.357926	−	0.619947i	−0.987614	+	0.156902i	$0.949849\pi$
$224$		0			0
$225$	2839.30	−	4917.82i	0.841275	−	1.45713i
$226$		0			0
$227$	−777.037	+	1345.87i	−0.227197	+	0.393517i	−0.956976	−	0.290166i	$-0.906290\pi$
$227$	−777.037	+	1345.87i	−0.227197	+	0.393517i	0.729779	+	0.683683i	$0.239623\pi$
$228$		0			0
$229$	−2915.60			−0.841346			−0.420673	−	0.907212i	$-0.638206\pi$
$229$	−2915.60			−0.841346			−0.420673	+	0.907212i	$0.638206\pi$
$230$		0			0
$231$	3626.62	+	6281.49i	1.03296	+	1.78914i
$232$		0			0
$233$	−4233.93			−1.19045			−0.595223	−	0.803561i	$-0.702936\pi$
$233$	−4233.93			−1.19045			−0.595223	+	0.803561i	$0.702936\pi$
$234$		0			0
$235$	1161.44			0.322400
$236$		0			0
$237$	3251.59	+	5631.93i	0.891197	+	1.54360i
$238$		0			0
$239$	−2372.55			−0.642124			−0.321062	−	0.947058i	$-0.604040\pi$
$239$	−2372.55			−0.642124			−0.321062	+	0.947058i	$0.604040\pi$
$240$		0			0
$241$	−162.882	+	282.119i	−0.0435358	+	0.0754062i	−0.886972	−	0.461823i	$-0.847196\pi$
$241$	−162.882	+	282.119i	−0.0435358	+	0.0754062i	0.843436	+	0.537229i	$0.180529\pi$
$242$		0			0
$243$	549.739	−	952.175i	0.145127	−	0.251367i
$244$		0			0
$245$	220.226	+	381.443i	0.0574275	+	0.0994674i
$246$		0			0
$247$	238.433	+	340.332i	0.0614215	+	0.0876714i
$248$		0			0
$249$	−2734.30	−	4735.95i	−0.695901	−	1.20534i
$250$		0			0
$251$	−1300.88	+	2253.20i	−0.327136	+	0.566616i	−0.981942	−	0.189181i	$-0.939417\pi$
$251$	−1300.88	+	2253.20i	−0.327136	+	0.566616i	0.654806	+	0.755797i	$0.272750\pi$
$252$		0			0
$253$	−1043.23	+	1806.92i	−0.259237	+	0.449012i
$254$		0			0
$255$	−4246.75			−1.04291
$256$		0			0
$257$	−2108.55	−	3652.11i	−0.511781	−	0.886430i	−0.999907	−	0.0136569i	$-0.995653\pi$
$257$	−2108.55	−	3652.11i	−0.511781	−	0.886430i	0.488126	−	0.872773i	$-0.337681\pi$
$258$		0			0
$259$	−4866.33			−1.16749
$260$		0			0
$261$	−9668.41			−2.29295
$262$		0			0
$263$	3237.16	+	5606.93i	0.758981	+	1.31459i	0.943371	+	0.331740i	$0.107636\pi$
$263$	3237.16	+	5606.93i	0.758981	+	1.31459i	−0.184390	+	0.982853i	$0.559031\pi$
$264$		0			0
$265$	−1005.54			−0.233094
$266$		0			0
$267$	918.332	−	1590.60i	0.210491	−	0.364580i
$268$		0			0
$269$	650.517	−	1126.73i	0.147445	−	0.255382i	−0.782837	−	0.622226i	$-0.786228\pi$
$269$	650.517	−	1126.73i	0.147445	−	0.255382i	0.930282	+	0.366844i	$0.119562\pi$
$270$		0			0
$271$	−1539.82	−	2667.05i	−0.345157	−	0.597829i	0.640225	−	0.768187i	$-0.278841\pi$
$271$	−1539.82	−	2667.05i	−0.345157	−	0.597829i	−0.985382	+	0.170358i	$0.945508\pi$
$272$		0			0
$273$	−2656.42	+	5700.50i	−0.588914	+	1.26377i
$274$		0			0
$275$	−2974.78	−	5152.46i	−0.652312	−	1.12984i
$276$		0			0
$277$	3143.95	−	5445.48i	0.681955	−	1.18118i	−0.292428	−	0.956288i	$-0.594463\pi$
$277$	3143.95	−	5445.48i	0.681955	−	1.18118i	0.974383	−	0.224894i	$-0.0722034\pi$
$278$		0			0
$279$	−948.626	+	1643.07i	−0.203558	+	0.352573i
$280$		0			0
$281$	−3226.00			−0.684864			−0.342432	−	0.939543i	$-0.611251\pi$
$281$	−3226.00			−0.684864			−0.342432	+	0.939543i	$0.611251\pi$
$282$		0			0
$283$	−193.292	−	334.791i	−0.0406007	−	0.0703225i	0.845011	−	0.534749i	$-0.179594\pi$
$283$	−193.292	−	334.791i	−0.0406007	−	0.0703225i	−0.885612	+	0.464426i	$0.846261\pi$
$284$		0			0
$285$	−303.811			−0.0631446
$286$		0			0
$287$	−398.178			−0.0818944
$288$		0			0
$289$	−5222.04	−	9044.84i	−1.06290	−	1.84100i
$290$		0			0
$291$	−6573.60			−1.32423
$292$		0			0
$293$	−1096.41	+	1899.04i	−0.218611	+	0.378645i	−0.954384	−	0.298583i	$-0.903486\pi$
$293$	−1096.41	+	1899.04i	−0.218611	+	0.378645i	0.735773	+	0.677229i	$0.236819\pi$
$294$		0			0
$295$	−475.564	+	823.701i	−0.0938590	+	0.162569i
$296$		0			0
$297$	5893.92	+	10208.6i	1.15151	+	1.99448i
$298$		0			0
$299$	−1802.17	+	158.133i	−0.348569	+	0.0305855i
$300$		0			0
$301$	1041.53	+	1803.99i	0.199445	+	0.345449i
$302$		0			0
$303$	1832.07	−	3173.24i	0.347359	−	0.601643i
$304$		0			0
$305$	−176.468	+	305.652i	−0.0331297	+	0.0573823i
$306$		0			0
$307$	8083.96			1.50285			0.751427	−	0.659817i	$-0.229366\pi$
$307$	8083.96			1.50285			0.751427	+	0.659817i	$0.229366\pi$
$308$		0			0
$309$	−16.6986	−	28.9229i	−0.00307428	−	0.00532481i
$310$		0			0
$311$	−244.409			−0.0445632			−0.0222816	−	0.999752i	$-0.507093\pi$
$311$	−244.409			−0.0445632			−0.0222816	+	0.999752i	$0.507093\pi$
$312$		0			0
$313$	4444.13			0.802546			0.401273	−	0.915958i	$-0.368568\pi$
$313$	4444.13			0.802546			0.401273	+	0.915958i	$0.368568\pi$
$314$		0			0
$315$	−1509.24	−	2614.09i	−0.269957	−	0.467578i
$316$		0			0
$317$	930.597			0.164882			0.0824409	−	0.996596i	$-0.473728\pi$
$317$	930.597			0.164882			0.0824409	+	0.996596i	$0.473728\pi$
$318$		0			0
$319$	−5064.86	+	8772.60i	−0.888959	+	1.53972i
$320$		0			0
$321$	504.557	−	873.918i	0.0877309	−	0.151954i
$322$		0			0
$323$	−549.320	−	951.451i	−0.0946285	−	0.163901i
$324$		0			0
$325$	2178.95	−	4675.90i	0.371897	−	0.798068i
$326$		0			0
$327$	−8580.13	−	14861.2i	−1.45102	−	2.51323i
$328$		0			0
$329$	−2273.71	+	3938.17i	−0.381014	+	0.659935i
$330$		0			0
$331$	2413.68	−	4180.61i	0.400809	−	0.694221i	−0.593015	−	0.805191i	$-0.702063\pi$
$331$	2413.68	−	4180.61i	0.400809	−	0.694221i	0.993824	+	0.110970i	$0.0353958\pi$
$332$		0			0
$333$	−16590.2			−2.73014
$334$		0			0
$335$	793.432	+	1374.26i	0.129402	+	0.224132i
$336$		0			0
$337$	10709.7			1.73115			0.865573	−	0.500782i	$-0.166954\pi$
$337$	10709.7			1.73115			0.865573	+	0.500782i	$0.166954\pi$
$338$		0			0
$339$	16833.6			2.69698
$340$		0			0
$341$	993.888	+	1721.47i	0.157836	+	0.273380i
$342$		0			0
$343$	−6915.66			−1.08866
$344$		0			0
$345$	661.331	−	1145.46i	0.103203	−	0.178752i
$346$		0			0
$347$	3200.54	−	5543.51i	0.495142	−	0.857611i	−0.504842	−	0.863211i	$-0.668449\pi$
$347$	3200.54	−	5543.51i	0.495142	−	0.857611i	0.999984	+	0.00560066i	$0.00178275\pi$
$348$		0			0
$349$	1215.01	+	2104.46i	0.186355	+	0.322777i	0.944032	−	0.329853i	$-0.106999\pi$
$349$	1215.01	+	2104.46i	0.186355	+	0.322777i	−0.757677	+	0.652630i	$0.773666\pi$
$350$		0			0
$351$	−4317.16	+	9264.35i	−0.656504	+	1.40882i
$352$		0			0
$353$	−4040.01	−	6997.51i	−0.609145	−	1.05507i	−0.991382	−	0.131006i	$-0.958179\pi$
$353$	−4040.01	−	6997.51i	−0.609145	−	1.05507i	0.382237	−	0.924064i	$-0.375154\pi$
$354$		0			0
$355$	−820.335	+	1420.86i	−0.122645	+	0.212427i
$356$		0			0
$357$	8313.71	−	14399.8i	1.23252	−	2.13478i
$358$		0			0
$359$	−8715.23			−1.28126			−0.640630	−	0.767850i	$-0.721327\pi$
$359$	−8715.23			−1.28126			−0.640630	+	0.767850i	$0.721327\pi$
$360$		0			0
$361$	3390.20	+	5872.00i	0.494271	+	0.856102i
$362$		0			0
$363$	14107.5			2.03982
$364$		0			0
$365$	−1631.15			−0.233914
$366$		0			0
$367$	1410.44	+	2442.95i	0.200611	+	0.347469i	0.948726	−	0.316101i	$-0.102374\pi$
$367$	1410.44	+	2442.95i	0.200611	+	0.347469i	−0.748114	+	0.663570i	$0.769041\pi$
$368$		0			0
$369$	−1357.46			−0.191508
$370$		0			0
$371$	1968.51	−	3409.56i	0.275471	−	0.477130i
$372$		0			0
$373$	6464.84	−	11197.4i	0.897418	−	1.55437i	0.0666351	−	0.997777i	$-0.478774\pi$
$373$	6464.84	−	11197.4i	0.897418	−	1.55437i	0.830783	−	0.556596i	$-0.187893\pi$
$374$		0			0
$375$	4027.61	+	6976.03i	0.554627	+	0.960642i
$376$		0			0
$377$	−8749.55	+	767.737i	−1.19529	+	0.104882i
$378$		0			0
$379$	−1144.02	−	1981.51i	−0.155052	−	0.268557i	0.778026	−	0.628232i	$-0.216221\pi$
$379$	−1144.02	−	1981.51i	−0.155052	−	0.268557i	−0.933078	+	0.359675i	$0.882888\pi$
$380$		0			0
$381$	1084.26	−	1878.00i	0.145797	−	0.252527i
$382$		0			0
$383$	6078.10	−	10527.6i	0.810904	−	1.40453i	−0.101328	−	0.994853i	$-0.532309\pi$
$383$	6078.10	−	10527.6i	0.810904	−	1.40453i	0.912232	−	0.409674i	$-0.134358\pi$
$384$		0			0
$385$	−3162.51			−0.418640
$386$		0			0
$387$	3550.77	+	6150.12i	0.466398	+	0.807825i
$388$		0			0
$389$	−1479.71			−0.192864			−0.0964322	−	0.995340i	$-0.530743\pi$
$389$	−1479.71			−0.192864			−0.0964322	+	0.995340i	$0.530743\pi$
$390$		0			0
$391$	4783.01			0.618637
$392$		0			0
$393$	7161.62	+	12404.3i	0.919226	+	1.59215i
$394$		0			0
$395$	−2835.48			−0.361186
$396$		0			0
$397$	−7635.63	+	13225.3i	−0.965292	+	1.67194i	−0.256465	+	0.966554i	$0.582558\pi$
$397$	−7635.63	+	13225.3i	−0.965292	+	1.67194i	−0.708827	+	0.705382i	$0.750775\pi$
$398$		0			0
$399$	594.760	−	1030.15i	0.0746247	−	0.129254i
$400$		0			0
$401$	−1282.27	−	2220.96i	−0.159685	−	0.276582i	0.775070	−	0.631875i	$-0.217714\pi$
$401$	−1282.27	−	2220.96i	−0.159685	−	0.276582i	−0.934755	+	0.355293i	$0.884381\pi$
$402$		0			0
$403$	−728.000	+	1562.24i	−0.0899858	+	0.193104i
$404$		0			0
$405$	−1043.84	−	1807.98i	−0.128071	−	0.221825i
$406$		0			0
$407$	−8690.89	+	15053.1i	−1.05846	+	1.83330i
$408$		0			0
$409$	−526.235	+	911.465i	−0.0636201	+	0.110193i	−0.896081	−	0.443890i	$-0.853598\pi$
$409$	−526.235	+	911.465i	−0.0636201	+	0.110193i	0.832461	+	0.554084i	$0.186931\pi$
$410$		0			0
$411$	−20407.8			−2.44925
$412$		0			0
$413$	−1861.99	−	3225.06i	−0.221846	−	0.384249i
$414$		0			0
$415$	2384.38			0.282036
$416$		0			0
$417$	24903.7			2.92455
$418$		0			0
$419$	4355.81	+	7544.48i	0.507864	+	0.879647i	0.999959	+	0.00910485i	$0.00289820\pi$
$419$	4355.81	+	7544.48i	0.507864	+	0.879647i	−0.492094	+	0.870542i	$0.663768\pi$
$420$		0			0
$421$	213.335			0.0246967			0.0123484	−	0.999924i	$-0.496069\pi$
$421$	213.335			0.0246967			0.0123484	+	0.999924i	$0.496069\pi$
$422$		0			0
$423$	−7751.47	+	13425.9i	−0.890992	+	1.54324i
$424$		0			0
$425$	−6819.41	+	11811.6i	−0.778329	+	1.34811i
$426$		0			0
$427$	−690.932	−	1196.73i	−0.0783057	−	0.135629i
$428$		0			0
$429$	12889.2	+	18397.8i	1.45058	+	2.07052i
$430$		0			0
$431$	4476.72	+	7753.91i	0.500316	+	0.866573i	1.00000		0.000364932i	$0.000116162\pi$
$431$	4476.72	+	7753.91i	0.500316	+	0.866573i	−0.499684	+	0.866208i	$0.666551\pi$
$432$		0			0
$433$	−2930.72	+	5076.16i	−0.325269	+	0.563382i	−0.981567	−	0.191120i	$-0.938788\pi$
$433$	−2930.72	+	5076.16i	−0.325269	+	0.563382i	0.656298	+	0.754502i	$0.272122\pi$
$434$		0			0
$435$	3210.76	−	5561.21i	0.353895	−	0.612964i
$436$		0			0
$437$	342.175			0.0374564
$438$		0			0
$439$	−5221.77	−	9044.36i	−0.567702	−	0.983289i	−0.996793	−	0.0800275i	$-0.974499\pi$
$439$	−5221.77	−	9044.36i	−0.567702	−	0.983289i	0.429090	−	0.903262i	$-0.358834\pi$
$440$		0			0
$441$	−5879.19			−0.634833
$442$		0			0
$443$	−8789.73			−0.942692			−0.471346	−	0.881948i	$-0.656232\pi$
$443$	−8789.73			−0.942692			−0.471346	+	0.881948i	$0.656232\pi$
$444$		0			0
$445$	400.405	+	693.522i	0.0426540	+	0.0738789i
$446$		0			0
$447$	22457.7			2.37632
$448$		0			0
$449$	−4318.06	+	7479.09i	−0.453857	+	0.786103i	−0.998622	−	0.0524857i	$-0.983286\pi$
$449$	−4318.06	+	7479.09i	−0.453857	+	0.786103i	0.544765	+	0.838589i	$0.316619\pi$
$450$		0			0
$451$	−711.114	+	1231.69i	−0.0742463	+	0.128598i
$452$		0			0
$453$	−10599.1	−	18358.2i	−1.09931	−	1.90407i
$454$		0			0
$455$	−1573.38	−	2245.81i	−0.162113	−	0.231396i
$456$		0			0
$457$	−2438.48	−	4223.57i	−0.249600	−	0.432320i	0.713815	−	0.700335i	$-0.246966\pi$
$457$	−2438.48	−	4223.57i	−0.249600	−	0.432320i	−0.963415	+	0.268014i	$0.913633\pi$
$458$		0			0
$459$	13511.3	−	23402.2i	1.37397	−	2.37979i
$460$		0			0
$461$	5901.96	−	10222.5i	0.596272	−	1.03277i	−0.397094	−	0.917778i	$-0.629981\pi$
$461$	5901.96	−	10222.5i	0.596272	−	1.03277i	0.993366	−	0.114996i	$-0.0366855\pi$
$462$		0			0
$463$	4797.53			0.481555			0.240777	−	0.970580i	$-0.422598\pi$
$463$	4797.53			0.481555			0.240777	+	0.970580i	$0.422598\pi$
$464$		0			0
$465$	−630.055	−	1091.29i	−0.0628346	−	0.108833i
$466$		0			0
$467$	13188.7			1.30686			0.653428	−	0.756989i	$-0.273330\pi$
$467$	13188.7			1.30686			0.653428	+	0.756989i	$0.273330\pi$
$468$		0			0
$469$	−6213.09			−0.611714
$470$		0			0
$471$	−8544.03	−	14798.7i	−0.835856	−	1.44775i
$472$		0			0
$473$	7440.38			0.723275
$474$		0			0
$475$	−487.858	+	844.995i	−0.0471252	+	0.0816233i
$476$		0			0
$477$	6711.00	−	11623.8i	0.644184	−	1.11576i
$478$		0			0
$479$	9024.41	+	15630.7i	0.860827	+	1.49100i	0.871132	+	0.491049i	$0.163386\pi$
$479$	9024.41	+	15630.7i	0.860827	+	1.49100i	−0.0103054	+	0.999947i	$0.503280\pi$
$480$		0			0
$481$	−15013.5	+	1317.37i	−1.42320	+	0.124879i
$482$		0			0
$483$	2589.33	+	4484.85i	0.243931	+	0.422500i
$484$		0			0
$485$	1433.09	−	2482.18i	0.134171	−	0.232392i
$486$		0			0
$487$	5750.62	−	9960.37i	0.535084	−	0.926792i	−0.464076	−	0.885796i	$-0.653613\pi$
$487$	5750.62	−	9960.37i	0.535084	−	0.926792i	0.999159	−	0.0409963i	$-0.0130532\pi$
$488$		0			0
$489$	19668.2			1.81887
$490$		0			0
$491$	−2000.33	−	3464.67i	−0.183856	−	0.318449i	0.759334	−	0.650701i	$-0.225525\pi$
$491$	−2000.33	−	3464.67i	−0.183856	−	0.318449i	−0.943191	+	0.332252i	$0.892191\pi$
$492$		0			0
$493$	23221.5			2.12139
$494$		0			0
$495$	−10781.6			−0.978981
$496$		0			0
$497$	−3211.88	−	5563.14i	−0.289884	−	0.502094i
$498$		0			0
$499$	8322.72			0.746645			0.373323	−	0.927702i	$-0.378218\pi$
$499$	8322.72			0.746645			0.373323	+	0.927702i	$0.378218\pi$
$500$		0			0
$501$	−6685.76	+	11580.1i	−0.596203	+	1.03265i
$502$		0			0
$503$	−3563.74	+	6172.58i	−0.315903	+	0.547160i	−0.979629	−	0.200816i	$-0.935641\pi$
$503$	−3563.74	+	6172.58i	−0.315903	+	0.547160i	0.663726	+	0.747976i	$0.268974\pi$
$504$		0			0
$505$	798.808	+	1383.58i	0.0703890	+	0.121917i
$506$		0			0
$507$	−6652.32	+	18306.2i	−0.582722	+	1.60356i
$508$		0			0
$509$	7174.46	+	12426.5i	0.624759	+	1.08211i	0.988587	+	0.150649i	$0.0481362\pi$
$509$	7174.46	+	12426.5i	0.624759	+	1.08211i	−0.363828	+	0.931466i	$0.618530\pi$
$510$		0			0
$511$	3193.25	−	5530.87i	0.276441	−	0.478809i
$512$		0			0
$513$	966.593	−	1674.19i	0.0831893	−	0.144088i
$514$		0			0
$515$	14.5617			0.00124595
$516$		0			0
$517$	8121.32	+	14066.5i	0.690861	+	1.19661i
$518$		0			0
$519$	−15128.7			−1.27953
$520$		0			0
$521$	3535.86			0.297329			0.148665	−	0.988888i	$-0.452502\pi$
$521$	3535.86			0.297329			0.148665	+	0.988888i	$0.452502\pi$
$522$		0			0
$523$	6982.44	+	12093.9i	0.583787	+	1.01115i	0.995025	+	0.0996211i	$0.0317631\pi$
$523$	6982.44	+	12093.9i	0.583787	+	1.01115i	−0.411238	+	0.911528i	$0.634904\pi$
$524$		0			0
$525$	−14767.0			−1.22759
$526$		0			0
$527$	2278.40	−	3946.31i	0.188328	−	0.326193i
$528$		0			0
$529$	5338.66	−	9246.83i	0.438782	−	0.759993i
$530$		0			0
$531$	−6347.86	−	10994.8i	−0.518783	−	0.898558i
$532$		0			0
$533$	−1228.45	+	107.791i	−0.0998312	+	0.00875978i
$534$		0			0
$535$	219.994	+	381.040i	0.0177779	+	0.0307922i
$536$		0			0
$537$	2638.46	−	4569.95i	0.212026	−	0.367240i
$538$		0			0
$539$	−3079.85	+	5334.46i	−0.246120	+	0.426292i
$540$		0			0
$541$	−10661.6			−0.847277			−0.423638	−	0.905831i	$-0.639247\pi$
$541$	−10661.6			−0.847277			−0.423638	+	0.905831i	$0.639247\pi$
$542$		0			0
$543$	−1786.42	−	3094.17i	−0.141183	−	0.244537i
$544$		0			0
$545$	7482.10			0.588070
$546$		0			0
$547$	3393.59			0.265264			0.132632	−	0.991165i	$-0.457657\pi$
$547$	3393.59			0.265264			0.132632	+	0.991165i	$0.457657\pi$
$548$		0			0
$549$	−2355.51	−	4079.86i	−0.183116	−	0.317166i
$550$		0			0
$551$	1661.26			0.128443
$552$		0			0
$553$	5550.91	−	9614.46i	0.426851	−	0.739328i
$554$		0			0
$555$	5509.41	−	9542.58i	0.421372	−	0.729837i
$556$		0			0
$557$	4124.51	+	7143.87i	0.313754	+	0.543439i	0.979172	−	0.203033i	$-0.0650798\pi$
$557$	4124.51	+	7143.87i	0.313754	+	0.543439i	−0.665418	+	0.746471i	$0.731746\pi$
$558$		0			0
$559$	3701.67	+	5283.67i	0.280079	+	0.399777i
$560$		0			0
$561$	−29695.3	−	51433.7i	−2.23482	−	3.87083i
$562$		0			0
$563$	4434.39	−	7680.59i	0.331949	−	0.574953i	−0.650945	−	0.759125i	$-0.725627\pi$
$563$	4434.39	−	7680.59i	0.331949	−	0.574953i	0.982894	+	0.184172i	$0.0589604\pi$
$564$		0			0
$565$	−3669.83	+	6356.34i	−0.273259	+	0.473298i
$566$		0			0
$567$	8173.93			0.605419
$568$		0			0
$569$	3204.24	+	5549.91i	0.236079	+	0.408901i	0.959586	−	0.281417i	$-0.0908043\pi$
$569$	3204.24	+	5549.91i	0.236079	+	0.408901i	−0.723507	+	0.690317i	$0.757471\pi$
$570$		0			0
$571$	−10045.2			−0.736212			−0.368106	−	0.929784i	$-0.619994\pi$
$571$	−10045.2			−0.736212			−0.368106	+	0.929784i	$0.619994\pi$
$572$		0			0
$573$	5440.70			0.396664
$574$		0			0
$575$	−2123.92	−	3678.75i	−0.154041	−	0.266807i
$576$		0			0
$577$	−24528.9			−1.76976			−0.884880	−	0.465818i	$-0.845760\pi$
$577$	−24528.9			−1.76976			−0.884880	+	0.465818i	$0.845760\pi$
$578$		0			0
$579$	−8889.08	+	15396.3i	−0.638027	+	1.10510i
$580$		0			0
$581$	−4667.82	+	8084.90i	−0.333311	+	0.577312i
$582$		0			0
$583$	−7031.21	−	12178.4i	−0.499490	−	0.865142i
$584$		0			0
$585$	−5363.95	−	7656.36i	−0.379098	−	0.541114i
$586$		0			0
$587$	−7951.88	−	13773.1i	−0.559130	−	0.968441i	−0.997569	−	0.0696803i	$-0.977802\pi$
$587$	−7951.88	−	13773.1i	−0.559130	−	0.968441i	0.438440	−	0.898761i	$-0.355531\pi$
$588$		0			0
$589$	162.996	−	282.317i	0.0114026	−	0.0197499i
$590$		0			0
$591$	2471.24	−	4280.32i	0.172002	−	0.297917i
$592$		0			0
$593$	−5436.51			−0.376477			−0.188238	−	0.982123i	$-0.560278\pi$
$593$	−5436.51			−0.376477			−0.188238	+	0.982123i	$0.560278\pi$
$594$		0			0
$595$	3624.89	+	6278.49i	0.249758	+	0.432593i
$596$		0			0
$597$	−49061.2			−3.36339
$598$		0			0
$599$	−6872.46			−0.468783			−0.234392	−	0.972142i	$-0.575310\pi$
$599$	−6872.46			−0.468783			−0.234392	+	0.972142i	$0.575310\pi$
$600$		0			0
$601$	708.911	+	1227.87i	0.0481149	+	0.0833375i	0.889080	−	0.457752i	$-0.151345\pi$
$601$	708.911	+	1227.87i	0.0481149	+	0.0833375i	−0.840965	+	0.541090i	$0.818012\pi$
$602$		0			0
$603$	−21181.6			−1.43048
$604$		0			0
$605$	−3075.54	+	5326.98i	−0.206675	+	0.357971i
$606$		0			0
$607$	−6796.67	+	11772.2i	−0.454478	+	0.787180i	−0.998658	−	0.0517890i	$-0.983508\pi$
$607$	−6796.67	+	11772.2i	−0.454478	+	0.787180i	0.544180	+	0.838969i	$0.316841\pi$
$608$		0			0
$609$	12571.2	+	21773.9i	0.836470	+	1.44881i
$610$		0			0
$611$	−5948.68	+	12765.5i	−0.393875	+	0.845231i
$612$		0			0
$613$	8639.71	+	14964.4i	0.569257	+	0.985982i	0.996640	+	0.0819112i	$0.0261024\pi$
$613$	8639.71	+	14964.4i	0.569257	+	0.985982i	−0.427383	+	0.904071i	$0.640564\pi$
$614$		0			0
$615$	450.796	−	780.802i	0.0295575	−	0.0511951i
$616$		0			0
$617$	1088.54	−	1885.40i	0.0710256	−	0.123020i	−0.828325	−	0.560247i	$-0.810706\pi$
$617$	1088.54	−	1885.40i	0.0710256	−	0.123020i	0.899351	+	0.437227i	$0.144039\pi$
$618$		0			0
$619$	−17067.5			−1.10824			−0.554121	−	0.832436i	$-0.686945\pi$
$619$	−17067.5			−1.10824			−0.554121	+	0.832436i	$0.686945\pi$
$620$		0			0
$621$	4208.13	+	7288.69i	0.271927	+	0.470991i
$622$		0			0
$623$	−3135.43			−0.201635
$624$		0			0
$625$	10245.1			0.655686
$626$		0			0
$627$	−2124.39	−	3679.55i	−0.135311	−	0.234365i
$628$		0			0
$629$	39846.2			2.52587
$630$		0			0
$631$	−3964.98	+	6867.55i	−0.250148	+	0.433269i	−0.963566	−	0.267469i	$-0.913813\pi$
$631$	−3964.98	+	6867.55i	−0.250148	+	0.433269i	0.713418	+	0.700738i	$0.247146\pi$
$632$		0			0
$633$	−20761.7	+	35960.4i	−1.30364	+	2.25797i
$634$		0			0
$635$	472.754	+	818.834i	0.0295444	+	0.0511723i
$636$		0			0
$637$	−5320.44	+	466.847i	−0.330932	+	0.0290379i
$638$		0			0
$639$	−10949.9	−	18965.7i	−0.677888	−	1.17414i
$640$		0			0
$641$	2919.53	−	5056.77i	0.179898	−	0.311592i	−0.761948	−	0.647639i	$-0.775757\pi$
$641$	2919.53	−	5056.77i	0.179898	−	0.311592i	0.941845	+	0.336047i	$0.109090\pi$
$642$		0			0
$643$	−8511.42	+	14742.2i	−0.522018	+	0.904161i	0.477654	+	0.878548i	$0.341487\pi$
$643$	−8511.42	+	14742.2i	−0.522018	+	0.904161i	−0.999672	+	0.0256134i	$0.991846\pi$
$644$		0			0
$645$	−4716.68			−0.287936
$646$		0			0
$647$	10889.6	+	18861.4i	0.661694	+	1.14609i	0.980170	+	0.198157i	$0.0634956\pi$
$647$	10889.6	+	18861.4i	0.661694	+	1.14609i	−0.318476	+	0.947931i	$0.603171\pi$
$648$		0			0
$649$	−13301.5			−0.804512
$650$		0			0
$651$	4933.74			0.297033
$652$		0			0
$653$	−8520.81	−	14758.5i	−0.510636	−	0.884447i	−0.999924	−	0.0123250i	$-0.996077\pi$
$653$	−8520.81	−	14758.5i	−0.510636	−	0.884447i	0.489288	−	0.872122i	$-0.337257\pi$
$654$		0			0
$655$	−6245.12			−0.372545
$656$		0			0
$657$	10886.4	−	18855.7i	0.646450	−	1.11968i
$658$		0			0
$659$	15382.9	−	26644.0i	0.909306	−	1.57496i	0.0942763	−	0.995546i	$-0.469946\pi$
$659$	15382.9	−	26644.0i	0.909306	−	1.57496i	0.815030	−	0.579419i	$-0.196720\pi$
$660$		0			0
$661$	−3872.35	−	6707.11i	−0.227862	−	0.394669i	0.729312	−	0.684181i	$-0.239840\pi$
$661$	−3872.35	−	6707.11i	−0.227862	−	0.394669i	−0.957174	+	0.289512i	$0.906507\pi$
$662$		0			0
$663$	21751.1	−	46676.5i	1.27412	−	2.73418i
$664$		0			0
$665$	259.323	+	449.161i	0.0151220	+	0.0261921i
$666$		0			0
$667$	−3616.20	+	6263.44i	−0.209925	+	0.363601i
$668$		0			0
$669$	−10567.0	+	18302.6i	−0.610679	+	1.05773i
$670$		0			0
$671$	−4935.80			−0.283971
$672$		0			0
$673$	1151.23	+	1993.98i	0.0659384	+	0.114209i	0.897110	−	0.441808i	$-0.145663\pi$
$673$	1151.23	+	1993.98i	0.0659384	+	0.114209i	−0.831171	+	0.556016i	$0.812329\pi$
$674$		0			0
$675$	−23999.1			−1.36848
$676$		0			0
$677$	−15932.6			−0.904488			−0.452244	−	0.891894i	$-0.649376\pi$
$677$	−15932.6			−0.904488			−0.452244	+	0.891894i	$0.649376\pi$
$678$		0			0
$679$	5611.01	+	9718.55i	0.317129	+	0.549284i
$680$		0			0
$681$	13777.6			0.775269
$682$		0			0
$683$	9229.29	−	15985.6i	0.517055	−	0.895566i	−0.482748	−	0.875759i	$-0.660361\pi$
$683$	9229.29	−	15985.6i	0.517055	−	0.895566i	0.999804	−	0.0198072i	$-0.00630523\pi$
$684$		0			0
$685$	4449.04	−	7705.97i	0.248159	−	0.429825i
$686$		0			0
$687$	12924.1	+	22385.1i	0.717735	+	1.24315i
$688$		0			0
$689$	5150.19	−	11052.0i	0.284770	−	0.611099i
$690$		0			0
$691$	11489.7	+	19900.7i	0.632544	+	1.09560i	0.987030	+	0.160537i	$0.0513226\pi$
$691$	11489.7	+	19900.7i	0.632544	+	1.09560i	−0.354486	+	0.935061i	$0.615344\pi$
$692$		0			0
$693$	21106.7	−	36557.9i	1.15697	−	2.00392i
$694$		0			0
$695$	−5429.17	+	9403.60i	−0.296317	+	0.513236i
$696$		0			0
$697$	3260.33			0.177179
$698$		0			0
$699$	18767.9	+	32506.9i	1.01554	+	1.75897i
$700$		0			0
$701$	8633.81			0.465185			0.232592	−	0.972574i	$-0.425279\pi$
$701$	8633.81			0.465185			0.232592	+	0.972574i	$0.425279\pi$
$702$		0			0
$703$	2850.58			0.152933
$704$		0			0
$705$	−5148.34	−	8917.19i	−0.275032	−	0.476370i
$706$		0			0
$707$	−6255.19			−0.332745
$708$		0			0
$709$	12811.2	−	22189.7i	0.678612	−	1.17539i	−0.296787	−	0.954944i	$-0.595915\pi$
$709$	12811.2	−	22189.7i	0.678612	−	1.17539i	0.975399	−	0.220447i	$-0.0707515\pi$
$710$		0			0
$711$	18924.1	−	32777.4i	0.998182	−	1.72890i
$712$		0			0
$713$	709.614	+	1229.09i	0.0372725	+	0.0645578i
$714$		0			0
$715$	−9756.91	+	856.129i	−0.510333	+	0.0447796i
$716$		0			0
$717$	10516.9	+	18215.8i	0.547783	+	0.948788i
$718$		0			0
$719$	17477.4	−	30271.7i	0.906532	−	1.57016i	0.0876845	−	0.996148i	$-0.472053\pi$
$719$	17477.4	−	30271.7i	0.906532	−	1.57016i	0.818847	−	0.574011i	$-0.194613\pi$
$720$		0			0
$721$	−28.5068	+	49.3753i	−0.00147247	+	0.00255039i
$722$		0			0
$723$	2888.04			0.148558
$724$		0			0
$725$	−10311.7	−	17860.3i	−0.528228	−	0.914918i
$726$		0			0
$727$	23397.0			1.19360			0.596800	−	0.802390i	$-0.296438\pi$
$727$	23397.0			1.19360			0.596800	+	0.802390i	$0.296438\pi$
$728$		0			0
$729$	−24329.6			−1.23607
$730$		0			0
$731$	−8528.21	−	14771.3i	−0.431501	−	0.747382i
$732$		0			0
$733$	−3541.17			−0.178440			−0.0892198	−	0.996012i	$-0.528437\pi$
$733$	−3541.17			−0.178440			−0.0892198	+	0.996012i	$0.528437\pi$
$734$		0			0
$735$	1952.41	−	3381.67i	0.0979804	−	0.169707i
$736$		0			0
$737$	−11096.1	+	19219.0i	−0.554586	+	0.960571i
$738$		0			0
$739$	−19616.5	−	33976.8i	−0.976460	−	1.69128i	−0.675029	−	0.737791i	$-0.735869\pi$
$739$	−19616.5	−	33976.8i	−0.976460	−	1.69128i	−0.301431	−	0.953488i	$-0.597464\pi$
$740$		0			0
$741$	1556.07	−	3339.22i	0.0771437	−	0.165546i
$742$		0			0
$743$	19099.4	+	33081.1i	0.943052	+	1.63341i	0.759606	+	0.650383i	$0.225392\pi$
$743$	19099.4	+	33081.1i	0.943052	+	1.63341i	0.183446	+	0.983030i	$0.441275\pi$
$744$		0			0
$745$	−4895.93	+	8480.00i	−0.240769	+	0.417024i
$746$		0			0
$747$	−15913.4	+	27562.9i	−0.779441	+	1.35003i
$748$		0			0
$749$	−1722.69			−0.0840399
$750$		0			0
$751$	−835.377	−	1446.92i	−0.0405903	−	0.0703045i	0.845017	−	0.534740i	$-0.179591\pi$
$751$	−835.377	−	1446.92i	−0.0405903	−	0.0703045i	−0.885607	+	0.464436i	$0.846257\pi$
$752$		0			0
$753$	23065.9			1.11629
$754$		0			0
$755$	9242.70			0.445532
$756$		0			0
$757$	18974.3	+	32864.4i	0.911007	+	1.57791i	0.812645	+	0.582759i	$0.198027\pi$
$757$	18974.3	+	32864.4i	0.911007	+	1.57791i	0.0983617	+	0.995151i	$0.468640\pi$
$758$		0			0
$759$	18497.4			0.884600
$760$		0			0
$761$	18886.4	−	32712.1i	0.899645	−	1.55823i	0.0716969	−	0.997426i	$-0.477159\pi$
$761$	18886.4	−	32712.1i	0.899645	−	1.55823i	0.827948	−	0.560805i	$-0.189508\pi$
$762$		0			0
$763$	−14647.4	+	25370.1i	−0.694984	+	1.20375i
$764$		0			0
$765$	12357.9	+	21404.5i	0.584053	+	1.01161i
$766$		0			0
$767$	−6617.63	−	9445.82i	−0.311537	−	0.444679i
$768$		0			0
$769$	6536.64	+	11321.8i	0.306524	+	0.530916i	0.977600	−	0.210474i	$-0.0675006\pi$
$769$	6536.64	+	11321.8i	0.306524	+	0.530916i	−0.671075	+	0.741389i	$0.734167\pi$
$770$		0			0
$771$	−18693.2	+	32377.7i	−0.873179	+	1.51239i
$772$		0			0
$773$	12571.5	−	21774.6i	0.584951	−	1.01316i	−0.409931	−	0.912117i	$-0.634447\pi$
$773$	12571.5	−	21774.6i	0.584951	−	1.01316i	0.994882	−	0.101048i	$-0.0322196\pi$
$774$		0			0
$775$	−4046.96			−0.187575
$776$		0			0
$777$	21571.1	+	37362.3i	0.995959	+	1.72505i
$778$		0			0
$779$	233.243			0.0107276
$780$		0			0
$781$	−22944.7			−1.05125
$782$		0			0
$783$	20430.5	+	35386.6i	0.932472	+	1.61509i
$784$		0			0
$785$	7450.63			0.338757
$786$		0			0
$787$	9582.29	−	16597.0i	0.434017	−	0.751740i	−0.563197	−	0.826322i	$-0.690429\pi$
$787$	9582.29	−	16597.0i	0.434017	−	0.751740i	0.997215	+	0.0745822i	$0.0237623\pi$
$788$		0			0
$789$	28698.9	−	49708.0i	1.29494	−	2.24290i
$790$		0			0
$791$	−14368.6	−	24887.1i	−0.645877	−	1.11869i
$792$		0			0
$793$	−2455.62	−	3505.08i	−0.109964	−	0.156960i
$794$		0			0
$795$	4457.29	+	7720.25i	0.198847	+	0.344414i
$796$		0			0
$797$	−14495.7	+	25107.3i	−0.644246	+	1.11587i	0.340229	+	0.940343i	$0.389496\pi$
$797$	−14495.7	+	25107.3i	−0.644246	+	1.11587i	−0.984475	+	0.175525i	$0.943838\pi$
$798$		0			0
$799$	18617.4	−	32246.3i	0.824326	−	1.42777i
$800$		0			0
$801$	−10689.3			−0.471519
$802$		0			0
$803$	−11405.8	−	19755.4i	−0.501248	−	0.868186i
$804$		0			0
$805$	−2257.96			−0.0988606
$806$		0			0
$807$	−11534.3			−0.503129
$808$		0			0
$809$	8446.41	+	14629.6i	0.367070	+	0.635784i	0.989106	−	0.147204i	$-0.0470275\pi$
$809$	8446.41	+	14629.6i	0.367070	+	0.635784i	−0.622036	+	0.782989i	$0.713694\pi$
$810$		0			0
$811$	42182.9			1.82644			0.913220	−	0.407466i	$-0.133587\pi$
$811$	42182.9			1.82644			0.913220	+	0.407466i	$0.133587\pi$
$812$		0			0
$813$	−13651.2	+	23644.6i	−0.588892	+	1.01999i
$814$		0			0
$815$	−4287.81	+	7426.70i	−0.184289	+	0.319198i
$816$		0			0
$817$	−610.105	−	1056.73i	−0.0261259	−	0.0452514i
$818$		0			0
$819$	36461.8	−	3199.37i	1.55565	−	0.136502i
$820$		0			0
$821$	9250.39	+	16022.1i	0.393229	+	0.681092i	0.992873	−	0.119174i	$-0.0380247\pi$
$821$	9250.39	+	16022.1i	0.393229	+	0.681092i	−0.599645	+	0.800266i	$0.704691\pi$
$822$		0			0
$823$	−13934.4	+	24135.0i	−0.590184	+	1.02223i	0.404024	+	0.914749i	$0.367611\pi$
$823$	−13934.4	+	24135.0i	−0.590184	+	1.02223i	−0.994207	+	0.107480i	$0.965722\pi$
$824$		0			0
$825$	−26372.8	+	45679.0i	−1.11295	+	1.92768i
$826$		0			0
$827$	−2541.96			−0.106884			−0.0534418	−	0.998571i	$-0.517019\pi$
$827$	−2541.96			−0.106884			−0.0534418	+	0.998571i	$0.517019\pi$
$828$		0			0
$829$	−14785.0	−	25608.4i	−0.619427	−	1.07288i	−0.989590	−	0.143912i	$-0.954032\pi$
$829$	−14785.0	−	25608.4i	−0.619427	−	1.07288i	0.370164	−	0.928967i	$-0.379302\pi$
$830$		0			0
$831$	−55745.1			−2.32705
$832$		0			0
$833$	14120.6			0.587333
$834$		0			0
$835$	−2915.08	−	5049.07i	−0.120815	−	0.209258i
$836$		0			0
$837$	8018.23			0.331124
$838$		0			0
$839$	10803.7	−	18712.6i	0.444561	−	0.770002i	−0.553460	−	0.832875i	$-0.686693\pi$
$839$	10803.7	−	18712.6i	0.444561	−	0.770002i	0.998022	+	0.0628731i	$0.0200263\pi$
$840$		0			0
$841$	−5362.17	+	9287.54i	−0.219860	+	0.380809i
$842$		0			0
$843$	14300.0	+	24768.3i	0.584244	+	1.01194i
$844$		0			0
$845$	−5462.14	−	6502.78i	−0.222371	−	0.264737i
$846$		0			0
$847$	−12041.7	−	20856.9i	−0.488499	−	0.846105i
$848$		0			0
$849$	−1713.62	+	2968.08i	−0.0692713	+	0.119981i
$850$		0			0
$851$	−6205.10	+	10747.6i	−0.249951	+	0.432928i
$852$		0			0
$853$	−28695.1			−1.15182			−0.575910	−	0.817513i	$-0.695352\pi$
$853$	−28695.1			−1.15182			−0.575910	+	0.817513i	$0.695352\pi$
$854$		0			0
$855$	884.080	+	1531.27i	0.0353625	+	0.0612496i
$856$		0			0
$857$	8720.01			0.347573			0.173786	−	0.984783i	$-0.444400\pi$
$857$	8720.01			0.347573			0.173786	+	0.984783i	$0.444400\pi$
$858$		0			0
$859$	1750.23			0.0695191			0.0347596	−	0.999396i	$-0.488933\pi$
$859$	1750.23			0.0695191			0.0347596	+	0.999396i	$0.488933\pi$
$860$		0			0
$861$	1765.01	+	3057.09i	0.0698624	+	0.121005i
$862$		0			0
$863$	35493.3			1.40001			0.700004	−	0.714139i	$-0.253181\pi$
$863$	35493.3			1.40001			0.700004	+	0.714139i	$0.253181\pi$
$864$		0			0
$865$	3298.15	−	5712.56i	0.129642	−	0.224547i
$866$		0			0
$867$	−46295.8	+	80186.6i	−1.81348	+	3.14104i
$868$		0			0
$869$	−19827.0	−	34341.4i	−0.773975	−	1.34056i
$870$		0			0
$871$	−19168.5	+	1681.96i	−0.745694	+	0.0654316i
$872$		0			0
$873$	19128.9	+	33132.3i	0.741600	+	1.28449i
$874$		0			0
$875$	6875.68	−	11909.0i	0.265646	−	0.460113i
$876$		0			0
$877$	13213.9	−	22887.2i	0.508782	−	0.881237i	−0.491166	−	0.871066i	$-0.663429\pi$
$877$	13213.9	−	22887.2i	0.508782	−	0.881237i	0.999948	−	0.0101709i	$-0.00323754\pi$
$878$		0			0
$879$	19440.4			0.745970
$880$		0			0
$881$	−383.063	−	663.484i	−0.0146489	−	0.0253727i	0.858608	−	0.512633i	$-0.171330\pi$
$881$	−383.063	−	663.484i	−0.0146489	−	0.0253727i	−0.873257	+	0.487260i	$0.837996\pi$
$882$		0			0
$883$	−6521.89			−0.248561			−0.124280	−	0.992247i	$-0.539662\pi$
$883$	−6521.89			−0.248561			−0.124280	+	0.992247i	$0.539662\pi$
$884$		0			0
$885$	8432.19			0.320277
$886$		0			0
$887$	12675.8	+	21955.2i	0.479834	+	0.831097i	0.999732	−	0.0231313i	$-0.00736359\pi$
$887$	12675.8	+	21955.2i	0.479834	+	0.831097i	−0.519899	+	0.854228i	$0.674030\pi$
$888$		0			0
$889$	−3701.97			−0.139663
$890$		0			0
$891$	14598.0	−	25284.5i	0.548879	−	0.950686i
$892$		0			0
$893$	1331.88	−	2306.89i	0.0499102	−	0.0864470i
$894$		0			0
$895$	1150.40	+	1992.56i	0.0429651	+	0.0744178i
$896$		0			0
$897$	9202.64	+	13135.6i	0.342550	+	0.488946i
$898$		0			0
$899$	3445.18	+	5967.23i	0.127812	+	0.221377i
$900$		0			0
$901$	−16118.4	+	27917.9i	−0.595985	+	1.03228i
$902$		0			0
$903$	9233.67	−	15993.2i	0.340285	−	0.589390i
$904$		0			0
$905$	1557.80			0.0572190
$906$		0			0
$907$	−4752.28	−	8231.20i	−0.173977	−	0.301337i	0.765830	−	0.643043i	$-0.222328\pi$
$907$	−4752.28	−	8231.20i	−0.173977	−	0.301337i	−0.939807	+	0.341707i	$0.888995\pi$
$908$		0			0
$909$	−21325.1			−0.778116
$910$		0			0
$911$	−6435.82			−0.234059			−0.117030	−	0.993128i	$-0.537337\pi$
$911$	−6435.82			−0.234059			−0.117030	+	0.993128i	$0.537337\pi$
$912$		0			0
$913$	16672.7	+	28878.0i	0.604367	+	1.04679i
$914$		0			0
$915$	3128.95			0.113049
$916$		0			0
$917$	12225.9	−	21175.8i	0.440276	−	0.762581i
$918$		0			0
$919$	7476.96	−	12950.5i	0.268381	−	0.464849i	−0.700063	−	0.714081i	$-0.746845\pi$
$919$	7476.96	−	12950.5i	0.268381	−	0.464849i	0.968444	+	0.249232i	$0.0801781\pi$
$920$		0			0
$921$	−35834.0	−	62066.3i	−1.28205	−	2.22058i
$922$		0			0
$923$	−11415.2	−	16293.8i	−0.407082	−	0.581058i
$924$		0			0
$925$	−17694.0	−	30646.8i	−0.628945	−	1.08936i
$926$		0			0
$927$	−97.1849	+	168.329i	−0.00344334	+	0.00596403i
$928$		0			0
$929$	19030.9	−	32962.5i	0.672103	−	1.16412i	−0.305204	−	0.952287i	$-0.598725\pi$
$929$	19030.9	−	32962.5i	0.672103	−	1.16412i	0.977307	−	0.211829i	$-0.0679419\pi$
$930$		0			0
$931$	1010.18			0.0355611
$932$		0			0
$933$	1083.40	+	1876.50i	0.0380160	+	0.0658456i
$934$		0			0
$935$	25895.1			0.905732
$936$		0			0
$937$	14572.5			0.508072			0.254036	−	0.967195i	$-0.418242\pi$
$937$	14572.5			0.508072			0.254036	+	0.967195i	$0.418242\pi$
$938$		0			0
$939$	−19699.6	−	34120.7i	−0.684635	−	1.18582i
$940$		0			0
$941$	32190.2			1.11516			0.557582	−	0.830122i	$-0.311729\pi$
$941$	32190.2			1.11516			0.557582	+	0.830122i	$0.311729\pi$
$942$		0			0
$943$	−507.720	+	879.397i	−0.0175330	+	0.0303681i
$944$		0			0
$945$	−6378.42	+	11047.7i	−0.219566	+	0.380300i
$946$		0			0
$947$	−21115.5	−	36573.1i	−0.724563	−	1.25498i	−0.959154	−	0.282886i	$-0.908708\pi$
$947$	−21115.5	−	36573.1i	−0.724563	−	1.25498i	0.234590	−	0.972094i	$-0.424625\pi$
$948$		0			0
$949$	8354.48	−	17928.2i	0.285772	−	0.613249i
$950$		0			0
$951$	−4125.09	−	7144.86i	−0.140657	−	0.243626i
$952$		0			0
$953$	4084.22	−	7074.07i	0.138826	−	0.240453i	−0.788227	−	0.615385i	$-0.789001\pi$
$953$	4084.22	−	7074.07i	0.138826	−	0.240453i	0.927052	+	0.374932i	$0.122334\pi$
$954$		0			0
$955$	−1186.11	+	2054.40i	−0.0401901	+	0.0696114i
$956$		0			0
$957$	89804.7			3.03341
$958$		0			0
$959$	17419.5	+	30171.4i	0.586552	+	1.01594i
$960$		0			0
$961$	−28438.9			−0.954613
$962$		0			0
$963$	−5872.98			−0.196525
$964$		0			0
$965$	−3875.76	−	6713.01i	−0.129290	−	0.223937i
$966$		0			0
$967$	−52022.1			−1.73001			−0.865003	−	0.501766i	$-0.832684\pi$
$967$	−52022.1			−1.73001			−0.865003	+	0.501766i	$0.832684\pi$
$968$		0			0
$969$	−4869.98	+	8435.05i	−0.161451	+	0.279642i
$970$		0			0
$971$	−5972.47	+	10344.6i	−0.197390	+	0.341890i	−0.947681	−	0.319218i	$-0.896580\pi$
$971$	−5972.47	+	10344.6i	−0.197390	+	0.341890i	0.750291	+	0.661107i	$0.229913\pi$
$972$		0			0
$973$	−21257.0	−	36818.2i	−0.700378	−	1.21309i
$974$		0			0
$975$	−45558.9	+	3997.61i	−1.49646	+	0.131309i
$976$		0			0
$977$	−9494.95	−	16445.7i	−0.310922	−	0.538532i	0.667640	−	0.744484i	$-0.267304\pi$
$977$	−9494.95	−	16445.7i	−0.310922	−	0.538532i	−0.978562	+	0.205952i	$0.933971\pi$
$978$		0			0
$979$	−5599.64	+	9698.86i	−0.182804	+	0.316626i
$980$		0			0
$981$	−49935.8	+	86491.3i	−1.62520	+	2.81494i
$982$		0			0
$983$	47187.4			1.53107			0.765537	−	0.643392i	$-0.222474\pi$
$983$	47187.4			1.53107			0.765537	+	0.643392i	$0.222474\pi$
$984$		0			0
$985$	1077.50	+	1866.28i	0.0348547	+	0.0603701i
$986$		0			0
$987$	40314.9			1.30014
$988$		0			0
$989$	5312.27			0.170799
$990$		0			0
$991$	−15379.7	−	26638.5i	−0.492991	−	0.853885i	0.506977	−	0.861960i	$-0.330763\pi$
$991$	−15379.7	−	26638.5i	−0.492991	−	0.853885i	−0.999967	+	0.00807499i	$0.997430\pi$
$992$		0			0
$993$	−42796.7			−1.36769
$994$		0			0
$995$	10695.7	−	18525.5i	0.340780	−	0.590248i
$996$		0			0
$997$	−24666.1	+	42722.9i	−0.783533	+	1.35712i	0.146338	+	0.989235i	$0.453251\pi$
$997$	−24666.1	+	42722.9i	−0.783533	+	1.35712i	−0.929871	+	0.367885i	$0.880082\pi$
$998$		0			0
$999$	35057.0	+	60720.5i	1.11027	+	1.92304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.i.d.81.1		4
4.3	odd	2		26.4.c.b.3.2	✓	4
12.11	even	2		234.4.h.h.55.1		4
13.9	even	3	inner	208.4.i.d.113.1		4
52.3	odd	6		338.4.a.h.1.1		2
52.7	even	12		338.4.e.f.147.2		8
52.11	even	12		338.4.b.e.337.3		4
52.15	even	12		338.4.b.e.337.1		4
52.19	even	12		338.4.e.f.147.4		8
52.23	odd	6		338.4.a.g.1.1		2
52.31	even	4		338.4.e.f.23.2		8
52.35	odd	6		26.4.c.b.9.2	yes	4
52.43	odd	6		338.4.c.j.191.2		4
52.47	even	4		338.4.e.f.23.4		8
52.51	odd	2		338.4.c.j.315.2		4
156.35	even	6		234.4.h.h.217.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.c.b.3.2	✓	4	4.3	odd	2
26.4.c.b.9.2	yes	4	52.35	odd	6
208.4.i.d.81.1		4	1.1	even	1	trivial
208.4.i.d.113.1		4	13.9	even	3	inner
234.4.h.h.55.1		4	12.11	even	2
234.4.h.h.217.1		4	156.35	even	6
338.4.a.g.1.1		2	52.23	odd	6
338.4.a.h.1.1		2	52.3	odd	6
338.4.b.e.337.1		4	52.15	even	12
338.4.b.e.337.3		4	52.11	even	12
338.4.c.j.191.2		4	52.43	odd	6
338.4.c.j.315.2		4	52.51	odd	2
338.4.e.f.23.2		8	52.31	even	4
338.4.e.f.23.4		8	52.47	even	4
338.4.e.f.147.2		8	52.7	even	12
338.4.e.f.147.4		8	52.19	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-4.43273 - 7.67771i) q^{3} +3.86546 q^{5} +(-7.56727 + 13.1069i) q^{7} +(-25.7982 + 44.6838i) q^{9} +(27.0291 + 46.8158i) q^{11} +(-19.7982 + 42.4857i) q^{13} +(-17.1345 - 29.6779i) q^{15} +(61.9618 - 107.321i) q^{17} +(4.43273 - 7.67771i) q^{19} +134.175 q^{21} +(19.2982 + 33.4254i) q^{23} -110.058 q^{25} +218.058 q^{27} +(93.6928 + 162.281i) q^{29} +36.7710 q^{31} +(239.625 - 415.044i) q^{33} +(-29.2510 + 50.6642i) q^{35} +(160.769 + 278.460i) q^{37} +(413.953 - 36.3226i) q^{39} +(13.1546 + 22.7844i) q^{41} +(68.8182 - 119.197i) q^{43} +(-99.7219 + 172.723i) q^{45} +300.466 q^{47} +(56.9728 + 98.6799i) q^{49} -1098.64 q^{51} -260.135 q^{53} +(104.480 + 180.965i) q^{55} -78.5964 q^{57} +(-123.029 + 213.093i) q^{59} +(-45.6526 + 79.0727i) q^{61} +(-390.444 - 676.268i) q^{63} +(-76.5291 + 164.227i) q^{65} +(205.262 + 355.524i) q^{67} +(171.087 - 296.332i) q^{69} +(-212.222 + 367.579i) q^{71} -421.982 q^{73} +(487.858 + 844.995i) q^{75} -818.146 q^{77} -733.542 q^{79} +(-270.042 - 467.727i) q^{81} +616.843 q^{83} +(239.511 - 414.845i) q^{85} +(830.629 - 1438.69i) q^{87} +(103.585 + 179.415i) q^{89} +(-407.037 - 580.993i) q^{91} +(-162.996 - 282.317i) q^{93} +(17.1345 - 29.6779i) q^{95} +(370.742 - 642.144i) q^{97} -2789.21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{3} - 14 q^{5} - 45 q^{7} - 59 q^{9} + 5 q^{11} - 35 q^{13} - 98 q^{15} + 130 q^{17} + 3 q^{19} - 82 q^{21} + 33 q^{23} - 234 q^{25} + 666 q^{27} + 198 q^{29} - 560 q^{31} + 767 q^{33} + 266 q^{35}+ \cdots - 4852 q^{99}+O(q^{100}) \) 4 * q - 3 * q^3 - 14 * q^5 - 45 * q^7 - 59 * q^9 + 5 * q^11 - 35 * q^13 - 98 * q^15 + 130 * q^17 + 3 * q^19 - 82 * q^21 + 33 * q^23 - 234 * q^25 + 666 * q^27 + 198 * q^29 - 560 * q^31 + 767 * q^33 + 266 * q^35 + 702 * q^37 + 1317 * q^39 - 242 * q^41 - 93 * q^43 - 119 * q^45 - 448 * q^47 - 435 * q^49 - 2126 * q^51 - 1070 * q^53 + 742 * q^55 - 226 * q^57 - 389 * q^59 - 654 * q^61 - 1002 * q^63 - 203 * q^65 - 107 * q^67 + 375 * q^69 - 569 * q^71 - 1246 * q^73 + 935 * q^75 + 1294 * q^77 - 1520 * q^79 + 334 * q^81 + 3528 * q^83 + 413 * q^85 + 1599 * q^87 + 871 * q^89 + 1539 * q^91 - 2184 * q^93 + 98 * q^95 + 879 * q^97 - 4852 * q^99

Introduction

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