LMFDB - Embedded newform 208.4.i.b.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,4,Mod(81,208)]

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, 2]))

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

//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: 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			113.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	208.113
Dual form			208.4.i.b.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{3} +17.0000 q^{5} +(10.0000 + 17.3205i) q^{7} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{3} +17.0000 q^{5} +(10.0000 + 17.3205i) q^{7} +(11.5000 + 19.9186i) q^{9} +(-16.0000 + 27.7128i) q^{11} +(-45.5000 - 11.2583i) q^{13} +(17.0000 - 29.4449i) q^{15} +(6.50000 + 11.2583i) q^{17} +(15.0000 + 25.9808i) q^{19} +40.0000 q^{21} +(39.0000 - 67.5500i) q^{23} +164.000 q^{25} +100.000 q^{27} +(-98.5000 + 170.607i) q^{29} +74.0000 q^{31} +(32.0000 + 55.4256i) q^{33} +(170.000 + 294.449i) q^{35} +(113.500 - 196.588i) q^{37} +(-65.0000 + 67.5500i) q^{39} +(82.5000 - 142.894i) q^{41} +(-78.0000 - 135.100i) q^{43} +(195.500 + 338.616i) q^{45} +162.000 q^{47} +(-28.5000 + 49.3634i) q^{49} +26.0000 q^{51} +93.0000 q^{53} +(-272.000 + 471.118i) q^{55} +60.0000 q^{57} +(-432.000 - 748.246i) q^{59} +(-72.5000 - 125.574i) q^{61} +(-230.000 + 398.372i) q^{63} +(-773.500 - 191.392i) q^{65} +(431.000 - 746.514i) q^{67} +(-78.0000 - 135.100i) q^{69} +(327.000 + 566.381i) q^{71} +215.000 q^{73} +(164.000 - 284.056i) q^{75} -640.000 q^{77} +76.0000 q^{79} +(-210.500 + 364.597i) q^{81} -628.000 q^{83} +(110.500 + 191.392i) q^{85} +(197.000 + 341.214i) q^{87} +(133.000 - 230.363i) q^{89} +(-260.000 - 900.666i) q^{91} +(74.0000 - 128.172i) q^{93} +(255.000 + 441.673i) q^{95} +(-119.000 - 206.114i) q^{97} -736.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 34 q^{5} + 20 q^{7} + 23 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 34 * q^5 + 20 * q^7 + 23 * q^9	$ 2 q + 2 q^{3} + 34 q^{5} + 20 q^{7} + 23 q^{9} - 32 q^{11} - 91 q^{13} + 34 q^{15} + 13 q^{17} + 30 q^{19} + 80 q^{21} + 78 q^{23} + 328 q^{25} + 200 q^{27} - 197 q^{29} + 148 q^{31} + 64 q^{33} + 340 q^{35} + 227 q^{37} - 130 q^{39} + 165 q^{41} - 156 q^{43} + 391 q^{45} + 324 q^{47} - 57 q^{49} + 52 q^{51} + 186 q^{53} - 544 q^{55} + 120 q^{57} - 864 q^{59} - 145 q^{61} - 460 q^{63} - 1547 q^{65} + 862 q^{67} - 156 q^{69} + 654 q^{71} + 430 q^{73} + 328 q^{75} - 1280 q^{77} + 152 q^{79} - 421 q^{81} - 1256 q^{83} + 221 q^{85} + 394 q^{87} + 266 q^{89} - 520 q^{91} + 148 q^{93} + 510 q^{95} - 238 q^{97} - 1472 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 34 * q^5 + 20 * q^7 + 23 * q^9 - 32 * q^11 - 91 * q^13 + 34 * q^15 + 13 * q^17 + 30 * q^19 + 80 * q^21 + 78 * q^23 + 328 * q^25 + 200 * q^27 - 197 * q^29 + 148 * q^31 + 64 * q^33 + 340 * q^35 + 227 * q^37 - 130 * q^39 + 165 * q^41 - 156 * q^43 + 391 * q^45 + 324 * q^47 - 57 * q^49 + 52 * q^51 + 186 * q^53 - 544 * q^55 + 120 * q^57 - 864 * q^59 - 145 * q^61 - 460 * q^63 - 1547 * q^65 + 862 * q^67 - 156 * q^69 + 654 * q^71 + 430 * q^73 + 328 * q^75 - 1280 * q^77 + 152 * q^79 - 421 * q^81 - 1256 * q^83 + 221 * q^85 + 394 * q^87 + 266 * q^89 - 520 * q^91 + 148 * q^93 + 510 * q^95 - 238 * q^97 - 1472 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.00000	−	1.73205i	0.192450	−	0.333333i	−0.753612	−	0.657320i	$-0.771690\pi$
$3$	1.00000	−	1.73205i	0.192450	−	0.333333i	0.946062	+	0.323987i	$0.105023\pi$
$4$		0			0
$5$	17.0000			1.52053			0.760263	−	0.649615i	$-0.225070\pi$
$5$	17.0000			1.52053			0.760263	+	0.649615i	$0.225070\pi$
$6$		0			0
$7$	10.0000	+	17.3205i	0.539949	+	0.935220i	0.998906	+	0.0467610i	$0.0148899\pi$
$7$	10.0000	+	17.3205i	0.539949	+	0.935220i	−0.458957	+	0.888459i	$0.651777\pi$
$8$		0			0
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$		0			0
$11$	−16.0000	+	27.7128i	−0.438562	+	0.759612i	−0.997579	−	0.0695447i	$-0.977845\pi$
$11$	−16.0000	+	27.7128i	−0.438562	+	0.759612i	0.559017	+	0.829156i	$0.311179\pi$
$12$		0			0
$13$	−45.5000	−	11.2583i	−0.970725	−	0.240192i
$13$	−45.5000	−	11.2583i	−0.970725	−	0.240192i
$14$		0			0
$15$	17.0000	−	29.4449i	0.292625	−	0.506842i
$16$		0			0
$17$	6.50000	+	11.2583i	0.0927342	+	0.160620i	0.908661	−	0.417535i	$-0.137106\pi$
$17$	6.50000	+	11.2583i	0.0927342	+	0.160620i	−0.815927	+	0.578156i	$0.803773\pi$
$18$		0			0
$19$	15.0000	+	25.9808i	0.181118	+	0.313705i	0.942261	−	0.334878i	$-0.108695\pi$
$19$	15.0000	+	25.9808i	0.181118	+	0.313705i	−0.761144	+	0.648583i	$0.775362\pi$
$20$		0			0
$21$	40.0000			0.415653
$22$		0			0
$23$	39.0000	−	67.5500i	0.353568	−	0.612398i	−0.633304	−	0.773903i	$-0.718302\pi$
$23$	39.0000	−	67.5500i	0.353568	−	0.612398i	0.986872	+	0.161506i	$0.0516350\pi$
$24$		0			0
$25$	164.000			1.31200
$26$		0			0
$27$	100.000			0.712778
$28$		0			0
$29$	−98.5000	+	170.607i	−0.630724	+	1.09245i	0.356680	+	0.934227i	$0.383909\pi$
$29$	−98.5000	+	170.607i	−0.630724	+	1.09245i	−0.987404	+	0.158219i	$0.949425\pi$
$30$		0			0
$31$	74.0000			0.428735			0.214368	−	0.976753i	$-0.431231\pi$
$31$	74.0000			0.428735			0.214368	+	0.976753i	$0.431231\pi$
$32$		0			0
$33$	32.0000	+	55.4256i	0.168803	+	0.292375i
$34$		0			0
$35$	170.000	+	294.449i	0.821007	+	1.42203i
$36$		0			0
$37$	113.500	−	196.588i	0.504305	−	0.873482i	−0.495683	−	0.868504i	$-0.665082\pi$
$37$	113.500	−	196.588i	0.504305	−	0.873482i	0.999988	−	0.00497814i	$-0.00158460\pi$
$38$		0			0
$39$	−65.0000	+	67.5500i	−0.266880	+	0.277350i
$40$		0			0
$41$	82.5000	−	142.894i	0.314252	−	0.544301i	−0.665026	−	0.746820i	$-0.731580\pi$
$41$	82.5000	−	142.894i	0.314252	−	0.544301i	0.979278	+	0.202520i	$0.0649130\pi$
$42$		0			0
$43$	−78.0000	−	135.100i	−0.276625	−	0.479129i	0.693919	−	0.720053i	$-0.255883\pi$
$43$	−78.0000	−	135.100i	−0.276625	−	0.479129i	−0.970544	+	0.240924i	$0.922549\pi$
$44$		0			0
$45$	195.500	+	338.616i	0.647632	+	1.12173i
$46$		0			0
$47$	162.000			0.502769			0.251384	−	0.967887i	$-0.419114\pi$
$47$	162.000			0.502769			0.251384	+	0.967887i	$0.419114\pi$
$48$		0			0
$49$	−28.5000	+	49.3634i	−0.0830904	+	0.143917i
$50$		0			0
$51$	26.0000			0.0713868
$52$		0			0
$53$	93.0000			0.241029			0.120514	−	0.992712i	$-0.461546\pi$
$53$	93.0000			0.241029			0.120514	+	0.992712i	$0.461546\pi$
$54$		0			0
$55$	−272.000	+	471.118i	−0.666845	+	1.15501i
$56$		0			0
$57$	60.0000			0.139424
$58$		0			0
$59$	−432.000	−	748.246i	−0.953248	−	1.65107i	−0.738328	−	0.674442i	$-0.764384\pi$
$59$	−432.000	−	748.246i	−0.953248	−	1.65107i	−0.214919	−	0.976632i	$-0.568949\pi$
$60$		0			0
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	0.779852	−	0.625964i	$-0.215294\pi$
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	−0.932027	+	0.362389i	$0.881961\pi$
$62$		0			0
$63$	−230.000	+	398.372i	−0.459957	+	0.796668i
$64$		0			0
$65$	−773.500	−	191.392i	−1.47601	−	0.365219i
$66$		0			0
$67$	431.000	−	746.514i	0.785896	−	1.36121i	−0.142566	−	0.989785i	$-0.545535\pi$
$67$	431.000	−	746.514i	0.785896	−	1.36121i	0.928462	−	0.371427i	$-0.121131\pi$
$68$		0			0
$69$	−78.0000	−	135.100i	−0.136088	−	0.235712i
$70$		0			0
$71$	327.000	+	566.381i	0.546588	+	0.946718i	0.998505	+	0.0546585i	$0.0174070\pi$
$71$	327.000	+	566.381i	0.546588	+	0.946718i	−0.451917	+	0.892060i	$0.649260\pi$
$72$		0			0
$73$	215.000			0.344710			0.172355	−	0.985035i	$-0.444862\pi$
$73$	215.000			0.344710			0.172355	+	0.985035i	$0.444862\pi$
$74$		0			0
$75$	164.000	−	284.056i	0.252495	−	0.437333i
$76$		0			0
$77$	−640.000			−0.947205
$78$		0			0
$79$	76.0000			0.108236			0.0541182	−	0.998535i	$-0.482765\pi$
$79$	76.0000			0.108236			0.0541182	+	0.998535i	$0.482765\pi$
$80$		0			0
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$		0			0
$83$	−628.000			−0.830505			−0.415253	−	0.909706i	$-0.636307\pi$
$83$	−628.000			−0.830505			−0.415253	+	0.909706i	$0.636307\pi$
$84$		0			0
$85$	110.500	+	191.392i	0.141005	+	0.244227i
$86$		0			0
$87$	197.000	+	341.214i	0.242766	+	0.420483i
$88$		0			0
$89$	133.000	−	230.363i	0.158404	−	0.274364i	−0.775889	−	0.630869i	$-0.782698\pi$
$89$	133.000	−	230.363i	0.158404	−	0.274364i	0.934293	+	0.356505i	$0.116032\pi$
$90$		0			0
$91$	−260.000	−	900.666i	−0.299510	−	1.03753i
$92$		0			0
$93$	74.0000	−	128.172i	0.0825101	−	0.142912i
$94$		0			0
$95$	255.000	+	441.673i	0.275394	+	0.476997i
$96$		0			0
$97$	−119.000	−	206.114i	−0.124563	−	0.215750i	0.796999	−	0.603981i	$-0.206420\pi$
$97$	−119.000	−	206.114i	−0.124563	−	0.215750i	−0.921562	+	0.388231i	$0.873086\pi$
$98$		0			0
$99$	−736.000			−0.747180
$100$		0			0
$101$	409.500	−	709.275i	0.403433	−	0.698767i	−0.590704	−	0.806888i	$-0.701150\pi$
$101$	409.500	−	709.275i	0.403433	−	0.698767i	0.994138	+	0.108121i	$0.0344834\pi$
$102$		0			0
$103$	−1638.00			−1.56696			−0.783480	−	0.621417i	$-0.786557\pi$
$103$	−1638.00			−1.56696			−0.783480	+	0.621417i	$0.786557\pi$
$104$		0			0
$105$	680.000			0.632011
$106$		0			0
$107$	261.000	−	452.065i	0.235811	−	0.408437i	−0.723697	−	0.690118i	$-0.757559\pi$
$107$	261.000	−	452.065i	0.235811	−	0.408437i	0.959508	+	0.281681i	$0.0908919\pi$
$108$		0			0
$109$	−1634.00			−1.43586			−0.717930	−	0.696115i	$-0.754910\pi$
$109$	−1634.00			−1.43586			−0.717930	+	0.696115i	$0.754910\pi$
$110$		0			0
$111$	−227.000	−	393.176i	−0.194107	−	0.336203i
$112$		0			0
$113$	−163.500	−	283.190i	−0.136113	−	0.235755i	0.789909	−	0.613224i	$-0.210128\pi$
$113$	−163.500	−	283.190i	−0.136113	−	0.235755i	−0.926022	+	0.377469i	$0.876794\pi$
$114$		0			0
$115$	663.000	−	1148.35i	0.537609	−	0.931167i
$116$		0			0
$117$	−299.000	−	1035.77i	−0.236261	−	0.818433i
$118$		0			0
$119$	−130.000	+	225.167i	−0.100144	+	0.173454i
$120$		0			0
$121$	153.500	+	265.870i	0.115327	+	0.199752i
$122$		0			0
$123$	−165.000	−	285.788i	−0.120956	−	0.209501i
$124$		0			0
$125$	663.000			0.474404
$126$		0			0
$127$	−1079.00	+	1868.88i	−0.753904	+	1.30580i	0.192014	+	0.981392i	$0.438498\pi$
$127$	−1079.00	+	1868.88i	−0.753904	+	1.30580i	−0.945918	+	0.324407i	$0.894835\pi$
$128$		0			0
$129$	−312.000			−0.212946
$130$		0			0
$131$	−730.000			−0.486873			−0.243437	−	0.969917i	$-0.578275\pi$
$131$	−730.000			−0.486873			−0.243437	+	0.969917i	$0.578275\pi$
$132$		0			0
$133$	−300.000	+	519.615i	−0.195589	+	0.338770i
$134$		0			0
$135$	1700.00			1.08380
$136$		0			0
$137$	−835.500	−	1447.13i	−0.521033	−	0.902456i	−0.999701	−	0.0244601i	$-0.992213\pi$
$137$	−835.500	−	1447.13i	−0.521033	−	0.902456i	0.478667	−	0.877996i	$-0.341120\pi$
$138$		0			0
$139$	456.000	+	789.815i	0.278255	+	0.481951i	0.970951	−	0.239278i	$-0.0769107\pi$
$139$	456.000	+	789.815i	0.278255	+	0.481951i	−0.692696	+	0.721229i	$0.743577\pi$
$140$		0			0
$141$	162.000	−	280.592i	0.0967579	−	0.167590i
$142$		0			0
$143$	1040.00	−	1080.80i	0.608176	−	0.632035i
$144$		0			0
$145$	−1674.50	+	2900.32i	−0.959032	+	1.66109i
$146$		0			0
$147$	57.0000	+	98.7269i	0.0319815	+	0.0553936i
$148$		0			0
$149$	1057.50	+	1831.64i	0.581435	+	1.00707i	0.995310	+	0.0967407i	$0.0308418\pi$
$149$	1057.50	+	1831.64i	0.581435	+	1.00707i	−0.413875	+	0.910334i	$0.635825\pi$
$150$		0			0
$151$	−514.000			−0.277011			−0.138506	−	0.990362i	$-0.544230\pi$
$151$	−514.000			−0.277011			−0.138506	+	0.990362i	$0.544230\pi$
$152$		0			0
$153$	−149.500	+	258.942i	−0.0789958	+	0.136825i
$154$		0			0
$155$	1258.00			0.651903
$156$		0			0
$157$	2901.00			1.47468			0.737341	−	0.675521i	$-0.236081\pi$
$157$	2901.00			1.47468			0.737341	+	0.675521i	$0.236081\pi$
$158$		0			0
$159$	93.0000	−	161.081i	0.0463860	−	0.0803430i
$160$		0			0
$161$	1560.00			0.763635
$162$		0			0
$163$	1180.00	+	2043.82i	0.567023	+	0.982112i	0.996858	+	0.0792052i	$0.0252382\pi$
$163$	1180.00	+	2043.82i	0.567023	+	0.982112i	−0.429835	+	0.902907i	$0.641428\pi$
$164$		0			0
$165$	544.000	+	942.236i	0.256669	+	0.444563i
$166$		0			0
$167$	140.000	−	242.487i	0.0648714	−	0.112361i	−0.831766	−	0.555127i	$-0.812670\pi$
$167$	140.000	−	242.487i	0.0648714	−	0.112361i	0.896637	+	0.442767i	$0.146003\pi$
$168$		0			0
$169$	1943.50	+	1024.51i	0.884615	+	0.466321i
$170$		0			0
$171$	−345.000	+	597.558i	−0.154285	+	0.267230i
$172$		0			0
$173$	−663.000	−	1148.35i	−0.291370	−	0.504667i	0.682764	−	0.730639i	$-0.260778\pi$
$173$	−663.000	−	1148.35i	−0.291370	−	0.504667i	−0.974134	+	0.225972i	$0.927444\pi$
$174$		0			0
$175$	1640.00	+	2840.56i	0.708413	+	1.22701i
$176$		0			0
$177$	−1728.00			−0.733810
$178$		0			0
$179$	2132.00	−	3692.73i	0.890241	−	1.54194i	0.0506550	−	0.998716i	$-0.483869\pi$
$179$	2132.00	−	3692.73i	0.890241	−	1.54194i	0.839586	−	0.543227i	$-0.182798\pi$
$180$		0			0
$181$	−403.000			−0.165496			−0.0827479	−	0.996571i	$-0.526370\pi$
$181$	−403.000			−0.165496			−0.0827479	+	0.996571i	$0.526370\pi$
$182$		0			0
$183$	−290.000			−0.117144
$184$		0			0
$185$	1929.50	−	3341.99i	0.766809	−	1.32815i
$186$		0			0
$187$	−416.000			−0.162679
$188$		0			0
$189$	1000.00	+	1732.05i	0.384864	+	0.666604i
$190$		0			0
$191$	−623.000	−	1079.07i	−0.236014	−	0.408788i	0.723553	−	0.690269i	$-0.242508\pi$
$191$	−623.000	−	1079.07i	−0.236014	−	0.408788i	−0.959567	+	0.281481i	$0.909174\pi$
$192$		0			0
$193$	−133.500	+	231.229i	−0.0497904	+	0.0862394i	−0.889846	−	0.456260i	$-0.849189\pi$
$193$	−133.500	+	231.229i	−0.0497904	+	0.0862394i	0.840056	+	0.542500i	$0.182522\pi$
$194$		0			0
$195$	−1105.00	+	1148.35i	−0.405798	+	0.421718i
$196$		0			0
$197$	−639.000	+	1106.78i	−0.231101	+	0.400278i	−0.958132	−	0.286326i	$-0.907566\pi$
$197$	−639.000	+	1106.78i	−0.231101	+	0.400278i	0.727032	+	0.686604i	$0.240899\pi$
$198$		0			0
$199$	2119.00	+	3670.22i	0.754834	+	1.30741i	0.945457	+	0.325747i	$0.105616\pi$
$199$	2119.00	+	3670.22i	0.754834	+	1.30741i	−0.190623	+	0.981663i	$0.561051\pi$
$200$		0			0
$201$	−862.000	−	1493.03i	−0.302492	−	0.523931i
$202$		0			0
$203$	−3940.00			−1.36224
$204$		0			0
$205$	1402.50	−	2429.20i	0.477829	−	0.827623i
$206$		0			0
$207$	1794.00			0.602375
$208$		0			0
$209$	−960.000			−0.317725
$210$		0			0
$211$	1535.00	−	2658.70i	0.500823	−	0.867452i	−0.499176	−	0.866501i	$-0.666364\pi$
$211$	1535.00	−	2658.70i	0.500823	−	0.867452i	1.00000		0.000951154i	$-0.000302762\pi$
$212$		0			0
$213$	1308.00			0.420764
$214$		0			0
$215$	−1326.00	−	2296.70i	−0.420616	−	0.728528i
$216$		0			0
$217$	740.000	+	1281.72i	0.231495	+	0.400962i
$218$		0			0
$219$	215.000	−	372.391i	0.0663395	−	0.114903i
$220$		0			0
$221$	−169.000	−	585.433i	−0.0514397	−	0.178192i
$222$		0			0
$223$	−2689.00	+	4657.48i	−0.807483	+	1.39860i	0.107119	+	0.994246i	$0.465838\pi$
$223$	−2689.00	+	4657.48i	−0.807483	+	1.39860i	−0.914602	+	0.404356i	$0.867496\pi$
$224$		0			0
$225$	1886.00	+	3266.65i	0.558815	+	0.967896i
$226$		0			0
$227$	−1987.00	−	3441.58i	−0.580977	−	1.00628i	−0.995364	−	0.0961811i	$-0.969337\pi$
$227$	−1987.00	−	3441.58i	−0.580977	−	1.00628i	0.414387	−	0.910101i	$-0.363996\pi$
$228$		0			0
$229$	−6298.00			−1.81740			−0.908698	−	0.417455i	$-0.862922\pi$
$229$	−6298.00			−1.81740			−0.908698	+	0.417455i	$0.862922\pi$
$230$		0			0
$231$	−640.000	+	1108.51i	−0.182290	+	0.315735i
$232$		0			0
$233$	4030.00			1.13311			0.566554	−	0.824025i	$-0.308276\pi$
$233$	4030.00			1.13311			0.566554	+	0.824025i	$0.308276\pi$
$234$		0			0
$235$	2754.00			0.764473
$236$		0			0
$237$	76.0000	−	131.636i	0.0208301	−	0.0360788i
$238$		0			0
$239$	984.000			0.266317			0.133158	−	0.991095i	$-0.457488\pi$
$239$	984.000			0.266317			0.133158	+	0.991095i	$0.457488\pi$
$240$		0			0
$241$	−471.500	−	816.662i	−0.126025	−	0.218281i	0.796108	−	0.605154i	$-0.206889\pi$
$241$	−471.500	−	816.662i	−0.126025	−	0.218281i	−0.922133	+	0.386873i	$0.873555\pi$
$242$		0			0
$243$	1771.00	+	3067.46i	0.467530	+	0.809785i
$244$		0			0
$245$	−484.500	+	839.179i	−0.126341	+	0.218829i
$246$		0			0
$247$	−390.000	−	1351.00i	−0.100466	−	0.348024i
$248$		0			0
$249$	−628.000	+	1087.73i	−0.159831	+	0.276835i
$250$		0			0
$251$	−1365.00	−	2364.25i	−0.343259	−	0.594542i	0.641777	−	0.766891i	$-0.278198\pi$
$251$	−1365.00	−	2364.25i	−0.343259	−	0.594542i	−0.985036	+	0.172349i	$0.944864\pi$
$252$		0			0
$253$	1248.00	+	2161.60i	0.310123	+	0.537149i
$254$		0			0
$255$	442.000			0.108546
$256$		0			0
$257$	942.500	−	1632.46i	0.228761	−	0.396225i	−0.728680	−	0.684854i	$-0.759866\pi$
$257$	942.500	−	1632.46i	0.228761	−	0.396225i	0.957441	+	0.288629i	$0.0931993\pi$
$258$		0			0
$259$	4540.00			1.08920
$260$		0			0
$261$	−4531.00			−1.07457
$262$		0			0
$263$	2016.00	−	3491.81i	0.472669	−	0.818686i	−0.526842	−	0.849963i	$-0.676624\pi$
$263$	2016.00	−	3491.81i	0.472669	−	0.818686i	0.999511	+	0.0312769i	$0.00995738\pi$
$264$		0			0
$265$	1581.00			0.366491
$266$		0			0
$267$	−266.000	−	460.726i	−0.0609698	−	0.105603i
$268$		0			0
$269$	−2003.00	−	3469.30i	−0.453997	−	0.786345i	0.544633	−	0.838674i	$-0.316669\pi$
$269$	−2003.00	−	3469.30i	−0.453997	−	0.786345i	−0.998630	+	0.0523292i	$0.983335\pi$
$270$		0			0
$271$	−2148.00	+	3720.45i	−0.481482	+	0.833952i	−0.999774	−	0.0212520i	$-0.993235\pi$
$271$	−2148.00	+	3720.45i	−0.481482	+	0.833952i	0.518292	+	0.855204i	$0.326568\pi$
$272$		0			0
$273$	−1820.00	−	450.333i	−0.403485	−	0.0998367i
$274$		0			0
$275$	−2624.00	+	4544.90i	−0.575393	+	0.996610i
$276$		0			0
$277$	2775.50	+	4807.31i	0.602035	+	1.04275i	0.992513	+	0.122142i	$0.0389765\pi$
$277$	2775.50	+	4807.31i	0.602035	+	1.04275i	−0.390478	+	0.920612i	$0.627690\pi$
$278$		0			0
$279$	851.000	+	1473.98i	0.182609	+	0.316289i
$280$		0			0
$281$	−5557.00			−1.17973			−0.589863	−	0.807504i	$-0.700818\pi$
$281$	−5557.00			−1.17973			−0.589863	+	0.807504i	$0.700818\pi$
$282$		0			0
$283$	1560.00	−	2702.00i	0.327676	−	0.567552i	−0.654374	−	0.756171i	$-0.727068\pi$
$283$	1560.00	−	2702.00i	0.327676	−	0.567552i	0.982050	+	0.188619i	$0.0604012\pi$
$284$		0			0
$285$	1020.00			0.211999
$286$		0			0
$287$	3300.00			0.678721
$288$		0			0
$289$	2372.00	−	4108.42i	0.482801	−	0.836235i
$290$		0			0
$291$	−476.000			−0.0958887
$292$		0			0
$293$	−4150.50	−	7188.88i	−0.827559	−	1.43337i	−0.899948	−	0.435998i	$-0.856396\pi$
$293$	−4150.50	−	7188.88i	−0.827559	−	1.43337i	0.0723887	−	0.997376i	$-0.476938\pi$
$294$		0			0
$295$	−7344.00	−	12720.2i	−1.44944	−	2.51050i
$296$		0			0
$297$	−1600.00	+	2771.28i	−0.312597	+	0.541435i
$298$		0			0
$299$	−2535.00	+	2634.45i	−0.490310	+	0.509546i
$300$		0			0
$301$	1560.00	−	2702.00i	0.298727	−	0.517411i
$302$		0			0
$303$	−819.000	−	1418.55i	−0.155282	−	0.268956i
$304$		0			0
$305$	−1232.50	−	2134.75i	−0.231386	−	0.400772i
$306$		0			0
$307$	−8678.00			−1.61329			−0.806644	−	0.591037i	$-0.798719\pi$
$307$	−8678.00			−1.61329			−0.806644	+	0.591037i	$0.798719\pi$
$308$		0			0
$309$	−1638.00	+	2837.10i	−0.301562	+	0.522320i
$310$		0			0
$311$	−8658.00			−1.57862			−0.789309	−	0.613996i	$-0.789561\pi$
$311$	−8658.00			−1.57862			−0.789309	+	0.613996i	$0.789561\pi$
$312$		0			0
$313$	−5250.00			−0.948075			−0.474038	−	0.880505i	$-0.657204\pi$
$313$	−5250.00			−0.948075			−0.474038	+	0.880505i	$0.657204\pi$
$314$		0			0
$315$	−3910.00	+	6772.32i	−0.699376	+	1.21136i
$316$		0			0
$317$	6413.00			1.13625			0.568123	−	0.822944i	$-0.307670\pi$
$317$	6413.00			1.13625			0.568123	+	0.822944i	$0.307670\pi$
$318$		0			0
$319$	−3152.00	−	5459.42i	−0.553223	−	0.958210i
$320$		0			0
$321$	−522.000	−	904.131i	−0.0907639	−	0.157208i
$322$		0			0
$323$	−195.000	+	337.750i	−0.0335916	+	0.0581824i
$324$		0			0
$325$	−7462.00	−	1846.37i	−1.27359	−	0.315132i
$326$		0			0
$327$	−1634.00	+	2830.17i	−0.276332	+	0.478620i
$328$		0			0
$329$	1620.00	+	2805.92i	0.271470	+	0.470199i
$330$		0			0
$331$	1744.00	+	3020.70i	0.289604	+	0.501609i	0.973715	−	0.227769i	$-0.0731431\pi$
$331$	1744.00	+	3020.70i	0.289604	+	0.501609i	−0.684111	+	0.729378i	$0.739810\pi$
$332$		0			0
$333$	5221.00			0.859186
$334$		0			0
$335$	7327.00	−	12690.7i	1.19498	−	2.06976i
$336$		0			0
$337$	−1833.00			−0.296290			−0.148145	−	0.988966i	$-0.547330\pi$
$337$	−1833.00			−0.296290			−0.148145	+	0.988966i	$0.547330\pi$
$338$		0			0
$339$	−654.000			−0.104780
$340$		0			0
$341$	−1184.00	+	2050.75i	−0.188027	+	0.325672i
$342$		0			0
$343$	5720.00			0.900440
$344$		0			0
$345$	−1326.00	−	2296.70i	−0.206926	−	0.358406i
$346$		0			0
$347$	3615.00	+	6261.36i	0.559260	+	0.968667i	0.997558	+	0.0698377i	$0.0222481\pi$
$347$	3615.00	+	6261.36i	0.559260	+	0.968667i	−0.438298	+	0.898830i	$0.644419\pi$
$348$		0			0
$349$	2629.00	−	4553.56i	0.403230	−	0.698414i	−0.590884	−	0.806757i	$-0.701221\pi$
$349$	2629.00	−	4553.56i	0.403230	−	0.698414i	0.994114	+	0.108342i	$0.0345543\pi$
$350$		0			0
$351$	−4550.00	−	1125.83i	−0.691912	−	0.171204i
$352$		0			0
$353$	−1581.50	+	2739.24i	−0.238455	+	0.413017i	−0.960271	−	0.279068i	$-0.909974\pi$
$353$	−1581.50	+	2739.24i	−0.238455	+	0.413017i	0.721816	+	0.692085i	$0.243308\pi$
$354$		0			0
$355$	5559.00	+	9628.47i	0.831102	+	1.43951i
$356$		0			0
$357$	260.000	+	450.333i	0.0385453	+	0.0667624i
$358$		0			0
$359$	10068.0			1.48014			0.740068	−	0.672532i	$-0.234793\pi$
$359$	10068.0			1.48014			0.740068	+	0.672532i	$0.234793\pi$
$360$		0			0
$361$	2979.50	−	5160.65i	0.434393	−	0.752390i
$362$		0			0
$363$	614.000			0.0887786
$364$		0			0
$365$	3655.00			0.524141
$366$		0			0
$367$	3719.00	−	6441.50i	0.528965	−	0.916195i	−0.470464	−	0.882419i	$-0.655914\pi$
$367$	3719.00	−	6441.50i	0.528965	−	0.916195i	0.999429	−	0.0337755i	$-0.0107531\pi$
$368$		0			0
$369$	3795.00			0.535392
$370$		0			0
$371$	930.000	+	1610.81i	0.130143	+	0.225415i
$372$		0			0
$373$	4841.50	+	8385.72i	0.672073	+	1.16407i	0.977315	+	0.211790i	$0.0679294\pi$
$373$	4841.50	+	8385.72i	0.672073	+	1.16407i	−0.305242	+	0.952275i	$0.598737\pi$
$374$		0			0
$375$	663.000	−	1148.35i	0.0912991	−	0.158135i
$376$		0			0
$377$	6402.50	−	6653.67i	0.874657	−	0.908970i
$378$		0			0
$379$	−531.000	+	919.719i	−0.0719674	+	0.124651i	−0.899763	−	0.436378i	$-0.856261\pi$
$379$	−531.000	+	919.719i	−0.0719674	+	0.124651i	0.827796	+	0.561029i	$0.189594\pi$
$380$		0			0
$381$	2158.00	+	3737.77i	0.290178	+	0.502602i
$382$		0			0
$383$	−1766.00	−	3058.80i	−0.235609	−	0.408087i	0.723840	−	0.689968i	$-0.242375\pi$
$383$	−1766.00	−	3058.80i	−0.235609	−	0.408087i	−0.959450	+	0.281880i	$0.909042\pi$
$384$		0			0
$385$	−10880.0			−1.44025
$386$		0			0
$387$	1794.00	−	3107.30i	0.235644	−	0.408147i
$388$		0			0
$389$	−11063.0			−1.44194			−0.720972	−	0.692964i	$-0.756304\pi$
$389$	−11063.0			−1.44194			−0.720972	+	0.692964i	$0.756304\pi$
$390$		0			0
$391$	1014.00			0.131151
$392$		0			0
$393$	−730.000	+	1264.40i	−0.0936988	+	0.162291i
$394$		0			0
$395$	1292.00			0.164576
$396$		0			0
$397$	2993.00	+	5184.03i	0.378374	+	0.655362i	0.990826	−	0.135145i	$-0.0431501\pi$
$397$	2993.00	+	5184.03i	0.378374	+	0.655362i	−0.612452	+	0.790508i	$0.709817\pi$
$398$		0			0
$399$	600.000	+	1039.23i	0.0752821	+	0.130392i
$400$		0			0
$401$	−2967.50	+	5139.86i	−0.369551	+	0.640081i	−0.989495	−	0.144565i	$-0.953822\pi$
$401$	−2967.50	+	5139.86i	−0.369551	+	0.640081i	0.619945	+	0.784646i	$0.287155\pi$
$402$		0			0
$403$	−3367.00	−	833.116i	−0.416184	−	0.102979i
$404$		0			0
$405$	−3578.50	+	6198.14i	−0.439055	+	0.760465i
$406$		0			0
$407$	3632.00	+	6290.81i	0.442338	+	0.766152i
$408$		0			0
$409$	7544.50	+	13067.5i	0.912106	+	1.57981i	0.811083	+	0.584931i	$0.198878\pi$
$409$	7544.50	+	13067.5i	0.912106	+	1.57981i	0.101023	+	0.994884i	$0.467788\pi$
$410$		0			0
$411$	−3342.00			−0.401092
$412$		0			0
$413$	8640.00	−	14964.9i	1.02941	−	1.78299i
$414$		0			0
$415$	−10676.0			−1.26281
$416$		0			0
$417$	1824.00			0.214201
$418$		0			0
$419$	−5407.00	+	9365.20i	−0.630428	+	1.09193i	0.357037	+	0.934090i	$0.383787\pi$
$419$	−5407.00	+	9365.20i	−0.630428	+	1.09193i	−0.987464	+	0.157843i	$0.949546\pi$
$420$		0			0
$421$	−6535.00			−0.756524			−0.378262	−	0.925699i	$-0.623478\pi$
$421$	−6535.00			−0.756524			−0.378262	+	0.925699i	$0.623478\pi$
$422$		0			0
$423$	1863.00	+	3226.81i	0.214142	+	0.370905i
$424$		0			0
$425$	1066.00	+	1846.37i	0.121667	+	0.210734i
$426$		0			0
$427$	1450.00	−	2511.47i	0.164334	−	0.284634i
$428$		0			0
$429$	−832.000	−	2882.13i	−0.0936348	−	0.324361i
$430$		0			0
$431$	990.000	−	1714.73i	0.110642	−	0.191637i	−0.805387	−	0.592749i	$-0.798043\pi$
$431$	990.000	−	1714.73i	0.110642	−	0.191637i	0.916029	+	0.401112i	$0.131376\pi$
$432$		0			0
$433$	3464.50	+	6000.69i	0.384511	+	0.665993i	0.991701	−	0.128564i	$-0.0410368\pi$
$433$	3464.50	+	6000.69i	0.384511	+	0.665993i	−0.607190	+	0.794556i	$0.707703\pi$
$434$		0			0
$435$	3349.00	+	5800.64i	0.369132	+	0.639355i
$436$		0			0
$437$	2340.00			0.256150
$438$		0			0
$439$	−2288.00	+	3962.93i	−0.248748	+	0.430844i	−0.963179	−	0.268862i	$-0.913352\pi$
$439$	−2288.00	+	3962.93i	−0.248748	+	0.430844i	0.714431	+	0.699706i	$0.246686\pi$
$440$		0			0
$441$	−1311.00			−0.141561
$442$		0			0
$443$	8812.00			0.945081			0.472540	−	0.881309i	$-0.343337\pi$
$443$	8812.00			0.945081			0.472540	+	0.881309i	$0.343337\pi$
$444$		0			0
$445$	2261.00	−	3916.17i	0.240858	−	0.417178i
$446$		0			0
$447$	4230.00			0.447589
$448$		0			0
$449$	−959.000	−	1661.04i	−0.100797	−	0.174586i	0.811216	−	0.584747i	$-0.198806\pi$
$449$	−959.000	−	1661.04i	−0.100797	−	0.174586i	−0.912013	+	0.410160i	$0.865473\pi$
$450$		0			0
$451$	2640.00	+	4572.61i	0.275638	+	0.477419i
$452$		0			0
$453$	−514.000	+	890.274i	−0.0533109	+	0.0923371i
$454$		0			0
$455$	−4420.00	−	15311.3i	−0.455413	−	1.57760i
$456$		0			0
$457$	5880.50	−	10185.3i	0.601922	−	1.04256i	−0.390608	−	0.920557i	$-0.627735\pi$
$457$	5880.50	−	10185.3i	0.601922	−	1.04256i	0.992530	−	0.122002i	$-0.0389314\pi$
$458$		0			0
$459$	650.000	+	1125.83i	0.0660989	+	0.114487i
$460$		0			0
$461$	−450.500	−	780.289i	−0.0455138	−	0.0788323i	0.842371	−	0.538898i	$-0.181159\pi$
$461$	−450.500	−	780.289i	−0.0455138	−	0.0788323i	−0.887885	+	0.460066i	$0.847826\pi$
$462$		0			0
$463$	−1372.00			−0.137715			−0.0688577	−	0.997626i	$-0.521935\pi$
$463$	−1372.00			−0.137715			−0.0688577	+	0.997626i	$0.521935\pi$
$464$		0			0
$465$	1258.00	−	2178.92i	0.125459	−	0.217301i
$466$		0			0
$467$	6396.00			0.633772			0.316886	−	0.948464i	$-0.397363\pi$
$467$	6396.00			0.633772			0.316886	+	0.948464i	$0.397363\pi$
$468$		0			0
$469$	17240.0			1.69738
$470$		0			0
$471$	2901.00	−	5024.68i	0.283803	−	0.491561i
$472$		0			0
$473$	4992.00			0.485269
$474$		0			0
$475$	2460.00	+	4260.84i	0.237626	+	0.411581i
$476$		0			0
$477$	1069.50	+	1852.43i	0.102660	+	0.177813i
$478$		0			0
$479$	1635.00	−	2831.90i	0.155960	−	0.270131i	−0.777448	−	0.628947i	$-0.783486\pi$
$479$	1635.00	−	2831.90i	0.155960	−	0.270131i	0.933408	+	0.358816i	$0.116819\pi$
$480$		0			0
$481$	−7377.50	+	7666.92i	−0.699345	+	0.726781i
$482$		0			0
$483$	1560.00	−	2702.00i	0.146962	−	0.254545i
$484$		0			0
$485$	−2023.00	−	3503.94i	−0.189401	−	0.328053i
$486$		0			0
$487$	9960.00	+	17251.2i	0.926757	+	1.60519i	0.788711	+	0.614765i	$0.210749\pi$
$487$	9960.00	+	17251.2i	0.926757	+	1.60519i	0.138046	+	0.990426i	$0.455918\pi$
$488$		0			0
$489$	4720.00			0.436494
$490$		0			0
$491$	3276.00	−	5674.20i	0.301108	−	0.521534i	−0.675280	−	0.737562i	$-0.735977\pi$
$491$	3276.00	−	5674.20i	0.301108	−	0.521534i	0.976387	+	0.216028i	$0.0693103\pi$
$492$		0			0
$493$	−2561.00			−0.233959
$494$		0			0
$495$	−12512.0			−1.13611
$496$		0			0
$497$	−6540.00	+	11327.6i	−0.590260	+	1.02236i
$498$		0			0
$499$	−1746.00			−0.156637			−0.0783183	−	0.996928i	$-0.524955\pi$
$499$	−1746.00			−0.156637			−0.0783183	+	0.996928i	$0.524955\pi$
$500$		0			0
$501$	−280.000	−	484.974i	−0.0249690	−	0.0432476i
$502$		0			0
$503$	7346.00	+	12723.6i	0.651177	+	1.12787i	0.982838	+	0.184473i	$0.0590577\pi$
$503$	7346.00	+	12723.6i	0.651177	+	1.12787i	−0.331661	+	0.943399i	$0.607609\pi$
$504$		0			0
$505$	6961.50	−	12057.7i	0.613431	−	1.06249i
$506$		0			0
$507$	3718.00	−	2341.73i	0.325685	−	0.205128i
$508$		0			0
$509$	−4038.50	+	6994.89i	−0.351677	+	0.609122i	−0.986543	−	0.163500i	$-0.947722\pi$
$509$	−4038.50	+	6994.89i	−0.351677	+	0.609122i	0.634867	+	0.772622i	$0.281055\pi$
$510$		0			0
$511$	2150.00	+	3723.91i	0.186126	+	0.322380i
$512$		0			0
$513$	1500.00	+	2598.08i	0.129097	+	0.223602i
$514$		0			0
$515$	−27846.0			−2.38260
$516$		0			0
$517$	−2592.00	+	4489.48i	−0.220495	+	0.381909i
$518$		0			0
$519$	−2652.00			−0.224296
$520$		0			0
$521$	11247.0			0.945758			0.472879	−	0.881127i	$-0.343215\pi$
$521$	11247.0			0.945758			0.472879	+	0.881127i	$0.343215\pi$
$522$		0			0
$523$	1366.00	−	2365.98i	0.114208	−	0.197815i	−0.803255	−	0.595636i	$-0.796900\pi$
$523$	1366.00	−	2365.98i	0.114208	−	0.197815i	0.917463	+	0.397821i	$0.130233\pi$
$524$		0			0
$525$	6560.00			0.545337
$526$		0			0
$527$	481.000	+	833.116i	0.0397584	+	0.0688636i
$528$		0			0
$529$	3041.50	+	5268.03i	0.249979	+	0.432977i
$530$		0			0
$531$	9936.00	−	17209.7i	0.812026	−	1.40647i
$532$		0			0
$533$	−5362.50	+	5572.87i	−0.435789	+	0.452885i
$534$		0			0
$535$	4437.00	−	7685.11i	0.358557	−	0.621040i
$536$		0			0
$537$	−4264.00	−	7385.46i	−0.342654	−	0.593494i
$538$		0			0
$539$	−912.000	−	1579.63i	−0.0728806	−	0.126233i
$540$		0			0
$541$	−18375.0			−1.46026			−0.730132	−	0.683306i	$-0.760542\pi$
$541$	−18375.0			−1.46026			−0.730132	+	0.683306i	$0.760542\pi$
$542$		0			0
$543$	−403.000	+	698.016i	−0.0318497	+	0.0551653i
$544$		0			0
$545$	−27778.0			−2.18326
$546$		0			0
$547$	10346.0			0.808708			0.404354	−	0.914603i	$-0.367496\pi$
$547$	10346.0			0.808708			0.404354	+	0.914603i	$0.367496\pi$
$548$		0			0
$549$	1667.50	−	2888.19i	0.129631	−	0.224527i
$550$		0			0
$551$	−5910.00			−0.456941
$552$		0			0
$553$	760.000	+	1316.36i	0.0584421	+	0.101225i
$554$		0			0
$555$	−3859.00	−	6683.98i	−0.295145	−	0.511206i
$556$		0			0
$557$	−172.500	+	298.779i	−0.0131222	+	0.0227283i	−0.872512	−	0.488593i	$-0.837510\pi$
$557$	−172.500	+	298.779i	−0.0131222	+	0.0227283i	0.859390	+	0.511321i	$0.170844\pi$
$558$		0			0
$559$	2028.00	+	7025.20i	0.153444	+	0.531546i
$560$		0			0
$561$	−416.000	+	720.533i	−0.0313075	+	0.0542263i
$562$		0			0
$563$	−4290.00	−	7430.50i	−0.321140	−	0.556231i	0.659583	−	0.751631i	$-0.270733\pi$
$563$	−4290.00	−	7430.50i	−0.321140	−	0.556231i	−0.980724	+	0.195400i	$0.937399\pi$
$564$		0			0
$565$	−2779.50	−	4814.24i	−0.206964	−	0.358472i
$566$		0			0
$567$	−8420.00			−0.623645
$568$		0			0
$569$	9841.00	−	17045.1i	0.725055	−	1.25583i	−0.233897	−	0.972261i	$-0.575148\pi$
$569$	9841.00	−	17045.1i	0.725055	−	1.25583i	0.958951	−	0.283570i	$-0.0915189\pi$
$570$		0			0
$571$	−26624.0			−1.95128			−0.975639	−	0.219382i	$-0.929596\pi$
$571$	−26624.0			−1.95128			−0.975639	+	0.219382i	$0.929596\pi$
$572$		0			0
$573$	−2492.00			−0.181684
$574$		0			0
$575$	6396.00	−	11078.2i	0.463881	−	0.803466i
$576$		0			0
$577$	−14101.0			−1.01739			−0.508694	−	0.860948i	$-0.669871\pi$
$577$	−14101.0			−1.01739			−0.508694	+	0.860948i	$0.669871\pi$
$578$		0			0
$579$	267.000	+	462.458i	0.0191643	+	0.0331936i
$580$		0			0
$581$	−6280.00	−	10877.3i	−0.448431	−	0.776705i
$582$		0			0
$583$	−1488.00	+	2577.29i	−0.105706	+	0.183088i
$584$		0			0
$585$	−5083.00	−	17608.0i	−0.359241	−	1.24445i
$586$		0			0
$587$	704.000	−	1219.36i	0.0495012	−	0.0857386i	−0.840213	−	0.542256i	$-0.817570\pi$
$587$	704.000	−	1219.36i	0.0495012	−	0.0857386i	0.889714	+	0.456518i	$0.150904\pi$
$588$		0			0
$589$	1110.00	+	1922.58i	0.0776515	+	0.134496i
$590$		0			0
$591$	1278.00	+	2213.56i	0.0889508	+	0.154067i
$592$		0			0
$593$	−1241.00			−0.0859389			−0.0429694	−	0.999076i	$-0.513682\pi$
$593$	−1241.00			−0.0859389			−0.0429694	+	0.999076i	$0.513682\pi$
$594$		0			0
$595$	−2210.00	+	3827.83i	−0.152271	+	0.263741i
$596$		0			0
$597$	8476.00			0.581071
$598$		0			0
$599$	−11078.0			−0.755651			−0.377825	−	0.925877i	$-0.623328\pi$
$599$	−11078.0			−0.755651			−0.377825	+	0.925877i	$0.623328\pi$
$600$		0			0
$601$	6908.50	−	11965.9i	0.468891	−	0.812143i	−0.530477	−	0.847700i	$-0.677987\pi$
$601$	6908.50	−	11965.9i	0.468891	−	0.812143i	0.999368	+	0.0355563i	$0.0113203\pi$
$602$		0			0
$603$	19826.0			1.33893
$604$		0			0
$605$	2609.50	+	4519.79i	0.175357	+	0.303728i
$606$		0			0
$607$	4135.00	+	7162.03i	0.276498	+	0.478909i	0.970512	−	0.241053i	$-0.0774926\pi$
$607$	4135.00	+	7162.03i	0.276498	+	0.478909i	−0.694014	+	0.719962i	$0.744159\pi$
$608$		0			0
$609$	−3940.00	+	6824.28i	−0.262162	+	0.454078i
$610$		0			0
$611$	−7371.00	−	1823.85i	−0.488050	−	0.120761i
$612$		0			0
$613$	−11136.5	+	19289.0i	−0.733767	+	1.27092i	0.221496	+	0.975161i	$0.428906\pi$
$613$	−11136.5	+	19289.0i	−0.733767	+	1.27092i	−0.955262	+	0.295760i	$0.904427\pi$
$614$		0			0
$615$	−2805.00	−	4858.40i	−0.183916	−	0.318552i
$616$		0			0
$617$	9494.50	+	16445.0i	0.619504	+	1.07301i	0.989576	+	0.144010i	$0.0459997\pi$
$617$	9494.50	+	16445.0i	0.619504	+	1.07301i	−0.370072	+	0.929003i	$0.620667\pi$
$618$		0			0
$619$	−72.0000			−0.00467516			−0.00233758	−	0.999997i	$-0.500744\pi$
$619$	−72.0000			−0.00467516			−0.00233758	+	0.999997i	$0.500744\pi$
$620$		0			0
$621$	3900.00	−	6755.00i	0.252015	−	0.436504i
$622$		0			0
$623$	5320.00			0.342121
$624$		0			0
$625$	−9229.00			−0.590656
$626$		0			0
$627$	−960.000	+	1662.77i	−0.0611463	+	0.105908i
$628$		0			0
$629$	2951.00			0.187065
$630$		0			0
$631$	−11690.0	−	20247.7i	−0.737514	−	1.27741i	−0.953611	−	0.301040i	$-0.902666\pi$
$631$	−11690.0	−	20247.7i	−0.737514	−	1.27741i	0.216097	−	0.976372i	$-0.430667\pi$
$632$		0			0
$633$	−3070.00	−	5317.40i	−0.192767	−	0.333882i
$634$		0			0
$635$	−18343.0	+	31771.0i	−1.14633	+	1.98550i
$636$		0			0
$637$	1852.50	−	1925.17i	0.115226	−	0.119746i
$638$		0			0
$639$	−7521.00	+	13026.8i	−0.465612	+	0.806464i
$640$		0			0
$641$	−3191.50	−	5527.84i	−0.196656	−	0.340619i	0.750786	−	0.660546i	$-0.229675\pi$
$641$	−3191.50	−	5527.84i	−0.196656	−	0.340619i	−0.947442	+	0.319927i	$0.896342\pi$
$642$		0			0
$643$	−8552.00	−	14812.5i	−0.524507	−	0.908473i	−0.999593	−	0.0285332i	$-0.990916\pi$
$643$	−8552.00	−	14812.5i	−0.524507	−	0.908473i	0.475086	−	0.879939i	$-0.342417\pi$
$644$		0			0
$645$	−5304.00			−0.323790
$646$		0			0
$647$	3497.00	−	6056.98i	0.212490	−	0.368044i	−0.740003	−	0.672604i	$-0.765176\pi$
$647$	3497.00	−	6056.98i	0.212490	−	0.368044i	0.952493	+	0.304560i	$0.0985093\pi$
$648$		0			0
$649$	27648.0			1.67223
$650$		0			0
$651$	2960.00			0.178205
$652$		0			0
$653$	2625.00	−	4546.63i	0.157311	−	0.272471i	−0.776587	−	0.630010i	$-0.783051\pi$
$653$	2625.00	−	4546.63i	0.157311	−	0.272471i	0.933898	+	0.357539i	$0.116384\pi$
$654$		0			0
$655$	−12410.0			−0.740304
$656$		0			0
$657$	2472.50	+	4282.50i	0.146821	+	0.254301i
$658$		0			0
$659$	−2170.00	−	3758.55i	−0.128272	−	0.222173i	0.794735	−	0.606956i	$-0.207610\pi$
$659$	−2170.00	−	3758.55i	−0.128272	−	0.222173i	−0.923007	+	0.384783i	$0.874276\pi$
$660$		0			0
$661$	2089.50	−	3619.12i	0.122953	−	0.212961i	−0.797978	−	0.602687i	$-0.794097\pi$
$661$	2089.50	−	3619.12i	0.122953	−	0.212961i	0.920931	+	0.389726i	$0.127430\pi$
$662$		0			0
$663$	−1183.00	−	292.717i	−0.0692970	−	0.0171466i
$664$		0			0
$665$	−5100.00	+	8833.46i	−0.297398	+	0.515108i
$666$		0			0
$667$	7683.00	+	13307.3i	0.446007	+	0.772508i
$668$		0			0
$669$	5378.00	+	9314.97i	0.310800	+	0.538322i
$670$		0			0
$671$	4640.00			0.266953
$672$		0			0
$673$	−11433.5	+	19803.4i	−0.654872	+	1.13427i	0.327054	+	0.945006i	$0.393944\pi$
$673$	−11433.5	+	19803.4i	−0.654872	+	1.13427i	−0.981926	+	0.189266i	$0.939389\pi$
$674$		0			0
$675$	16400.0			0.935165
$676$		0			0
$677$	5410.00			0.307124			0.153562	−	0.988139i	$-0.450925\pi$
$677$	5410.00			0.307124			0.153562	+	0.988139i	$0.450925\pi$
$678$		0			0
$679$	2380.00	−	4122.28i	0.134515	−	0.232988i
$680$		0			0
$681$	−7948.00			−0.447236
$682$		0			0
$683$	−6789.00	−	11758.9i	−0.380342	−	0.658772i	0.610769	−	0.791809i	$-0.290861\pi$
$683$	−6789.00	−	11758.9i	−0.380342	−	0.658772i	−0.991111	+	0.133037i	$0.957527\pi$
$684$		0			0
$685$	−14203.5	−	24601.2i	−0.792245	−	1.37221i
$686$		0			0
$687$	−6298.00	+	10908.5i	−0.349758	+	0.605798i
$688$		0			0
$689$	−4231.50	−	1047.02i	−0.233973	−	0.0578933i
$690$		0			0
$691$	6372.00	−	11036.6i	0.350799	−	0.607602i	−0.635590	−	0.772026i	$-0.719243\pi$
$691$	6372.00	−	11036.6i	0.350799	−	0.607602i	0.986390	+	0.164424i	$0.0525766\pi$
$692$		0			0
$693$	−7360.00	−	12747.9i	−0.403439	−	0.698777i
$694$		0			0
$695$	7752.00	+	13426.9i	0.423094	+	0.732820i
$696$		0			0
$697$	2145.00			0.116568
$698$		0			0
$699$	4030.00	−	6980.16i	0.218067	−	0.377703i
$700$		0			0
$701$	16406.0			0.883946			0.441973	−	0.897028i	$-0.354279\pi$
$701$	16406.0			0.883946			0.441973	+	0.897028i	$0.354279\pi$
$702$		0			0
$703$	6810.00			0.365354
$704$		0			0
$705$	2754.00	−	4770.07i	0.147123	−	0.254824i
$706$		0			0
$707$	16380.0			0.871334
$708$		0			0
$709$	−354.500	−	614.012i	−0.0187779	−	0.0325243i	0.856484	−	0.516174i	$-0.172644\pi$
$709$	−354.500	−	614.012i	−0.0187779	−	0.0325243i	−0.875262	+	0.483650i	$0.839311\pi$
$710$		0			0
$711$	874.000	+	1513.81i	0.0461006	+	0.0798487i
$712$		0			0
$713$	2886.00	−	4998.70i	0.151587	−	0.262556i
$714$		0			0
$715$	17680.0	−	18373.6i	0.924748	−	0.961026i
$716$		0			0
$717$	984.000	−	1704.34i	0.0512527	−	0.0887722i
$718$		0			0
$719$	−3822.00	−	6619.90i	−0.198243	−	0.343367i	0.749716	−	0.661760i	$-0.230190\pi$
$719$	−3822.00	−	6619.90i	−0.198243	−	0.343367i	−0.947959	+	0.318393i	$0.896857\pi$
$720$		0			0
$721$	−16380.0	−	28371.0i	−0.846079	−	1.46545i
$722$		0			0
$723$	−1886.00			−0.0970140
$724$		0			0
$725$	−16154.0	+	27979.5i	−0.827510	+	1.43329i
$726$		0			0
$727$	15808.0			0.806446			0.403223	−	0.915102i	$-0.367890\pi$
$727$	15808.0			0.806446			0.403223	+	0.915102i	$0.367890\pi$
$728$		0			0
$729$	−4283.00			−0.217599
$730$		0			0
$731$	1014.00	−	1756.30i	0.0513053	−	0.0888633i
$732$		0			0
$733$	−2583.00			−0.130157			−0.0650786	−	0.997880i	$-0.520730\pi$
$733$	−2583.00			−0.130157			−0.0650786	+	0.997880i	$0.520730\pi$
$734$		0			0
$735$	969.000	+	1678.36i	0.0486287	+	0.0842274i
$736$		0			0
$737$	13792.0	+	23888.4i	0.689328	+	1.19395i
$738$		0			0
$739$	2038.00	−	3529.92i	0.101447	−	0.175711i	−0.810834	−	0.585276i	$-0.800986\pi$
$739$	2038.00	−	3529.92i	0.101447	−	0.175711i	0.912281	+	0.409565i	$0.134320\pi$
$740$		0			0
$741$	−2730.00	−	675.500i	−0.135343	−	0.0334887i
$742$		0			0
$743$	−17028.0	+	29493.4i	−0.840776	+	1.45627i	0.0484632	+	0.998825i	$0.484568\pi$
$743$	−17028.0	+	29493.4i	−0.840776	+	1.45627i	−0.889239	+	0.457442i	$0.848766\pi$
$744$		0			0
$745$	17977.5	+	31137.9i	0.884087	+	1.53128i
$746$		0			0
$747$	−7222.00	−	12508.9i	−0.353734	−	0.612685i
$748$		0			0
$749$	10440.0			0.509305
$750$		0			0
$751$	−182.000	+	315.233i	−0.00884324	+	0.0153169i	−0.870413	−	0.492322i	$-0.836148\pi$
$751$	−182.000	+	315.233i	−0.00884324	+	0.0153169i	0.861570	+	0.507639i	$0.169482\pi$
$752$		0			0
$753$	−5460.00			−0.264241
$754$		0			0
$755$	−8738.00			−0.421203
$756$		0			0
$757$	3457.00	−	5987.70i	0.165980	−	0.287486i	−0.771023	−	0.636807i	$-0.780255\pi$
$757$	3457.00	−	5987.70i	0.165980	−	0.287486i	0.937003	+	0.349322i	$0.113588\pi$
$758$		0			0
$759$	4992.00			0.238733
$760$		0			0
$761$	−6991.00	−	12108.8i	−0.333014	−	0.576797i	0.650087	−	0.759859i	$-0.274732\pi$
$761$	−6991.00	−	12108.8i	−0.333014	−	0.576797i	−0.983101	+	0.183062i	$0.941399\pi$
$762$		0			0
$763$	−16340.0	−	28301.7i	−0.775292	−	1.34284i
$764$		0			0
$765$	−2541.50	+	4402.01i	−0.120115	+	0.208046i
$766$		0			0
$767$	11232.0	+	38908.8i	0.528767	+	1.83170i
$768$		0			0
$769$	9033.00	−	15645.6i	0.423587	−	0.733674i	−0.572700	−	0.819765i	$-0.694104\pi$
$769$	9033.00	−	15645.6i	0.423587	−	0.733674i	0.996287	+	0.0860907i	$0.0274375\pi$
$770$		0			0
$771$	−1885.00	−	3264.92i	−0.0880501	−	0.152507i
$772$		0			0
$773$	−7217.00	−	12500.2i	−0.335805	−	0.581632i	0.647834	−	0.761782i	$-0.275675\pi$
$773$	−7217.00	−	12500.2i	−0.335805	−	0.581632i	−0.983639	+	0.180150i	$0.942342\pi$
$774$		0			0
$775$	12136.0			0.562501
$776$		0			0
$777$	4540.00	−	7863.51i	0.209616	−	0.363065i
$778$		0			0
$779$	4950.00			0.227666
$780$		0			0
$781$	−20928.0			−0.958851
$782$		0			0
$783$	−9850.00	+	17060.7i	−0.449566	+	0.778671i
$784$		0			0
$785$	49317.0			2.24229
$786$		0			0
$787$	−7699.00	−	13335.1i	−0.348716	−	0.603994i	0.637305	−	0.770611i	$-0.280049\pi$
$787$	−7699.00	−	13335.1i	−0.348716	−	0.603994i	−0.986022	+	0.166617i	$0.946716\pi$
$788$		0			0
$789$	−4032.00	−	6983.63i	−0.181930	−	0.315113i
$790$		0			0
$791$	3270.00	−	5663.81i	0.146988	−	0.254591i
$792$		0			0
$793$	1885.00	+	6529.83i	0.0844115	+	0.292410i
$794$		0			0
$795$	1581.00	−	2738.37i	0.0705312	−	0.122164i
$796$		0			0
$797$	18421.0	+	31906.1i	0.818702	+	1.41803i	0.906639	+	0.421907i	$0.138639\pi$
$797$	18421.0	+	31906.1i	0.818702	+	1.41803i	−0.0879373	+	0.996126i	$0.528028\pi$
$798$		0			0
$799$	1053.00	+	1823.85i	0.0466239	+	0.0807549i
$800$		0			0
$801$	6118.00			0.269874
$802$		0			0
$803$	−3440.00	+	5958.25i	−0.151177	+	0.261846i
$804$		0			0
$805$	26520.0			1.16113
$806$		0			0
$807$	−8012.00			−0.349487
$808$		0			0
$809$	−20755.5	+	35949.6i	−0.902008	+	1.56232i	−0.0771242	+	0.997021i	$0.524574\pi$
$809$	−20755.5	+	35949.6i	−0.902008	+	1.56232i	−0.824884	+	0.565302i	$0.808760\pi$
$810$		0			0
$811$	−23066.0			−0.998714			−0.499357	−	0.866396i	$-0.666430\pi$
$811$	−23066.0			−0.998714			−0.499357	+	0.866396i	$0.666430\pi$
$812$		0			0
$813$	4296.00	+	7440.89i	0.185323	+	0.320988i
$814$		0			0
$815$	20060.0	+	34744.9i	0.862173	+	1.49333i
$816$		0			0
$817$	2340.00	−	4053.00i	0.100203	−	0.173558i
$818$		0			0
$819$	14950.0	−	15536.5i	0.637845	−	0.662868i
$820$		0			0
$821$	−14419.0	+	24974.4i	−0.612943	+	1.06165i	0.377798	+	0.925888i	$0.376681\pi$
$821$	−14419.0	+	24974.4i	−0.612943	+	1.06165i	−0.990742	+	0.135761i	$0.956652\pi$
$822$		0			0
$823$	13728.0	+	23777.6i	0.581443	+	1.00709i	0.995309	+	0.0967514i	$0.0308452\pi$
$823$	13728.0	+	23777.6i	0.581443	+	1.00709i	−0.413865	+	0.910338i	$0.635821\pi$
$824$		0			0
$825$	5248.00	+	9089.80i	0.221469	+	0.383596i
$826$		0			0
$827$	33572.0			1.41162			0.705812	−	0.708399i	$-0.250582\pi$
$827$	33572.0			1.41162			0.705812	+	0.708399i	$0.250582\pi$
$828$		0			0
$829$	22899.5	−	39663.1i	0.959388	−	1.66171i	0.235396	−	0.971899i	$-0.424361\pi$
$829$	22899.5	−	39663.1i	0.959388	−	1.66171i	0.723991	−	0.689809i	$-0.242306\pi$
$830$		0			0
$831$	11102.0			0.463447
$832$		0			0
$833$	−741.000			−0.0308213
$834$		0			0
$835$	2380.00	−	4122.28i	0.0986387	−	0.170847i
$836$		0			0
$837$	7400.00			0.305593
$838$		0			0
$839$	16143.0	+	27960.5i	0.664265	+	1.15054i	0.979484	+	0.201522i	$0.0645886\pi$
$839$	16143.0	+	27960.5i	0.664265	+	1.15054i	−0.315219	+	0.949019i	$0.602078\pi$
$840$		0			0
$841$	−7210.00	−	12488.1i	−0.295625	−	0.512038i
$842$		0			0
$843$	−5557.00	+	9625.01i	−0.227038	+	0.393242i
$844$		0			0
$845$	33039.5	+	17416.6i	1.34508	+	0.709054i
$846$		0			0
$847$	−3070.00	+	5317.40i	−0.124541	+	0.215712i
$848$		0			0
$849$	−3120.00	−	5404.00i	−0.126123	−	0.218451i
$850$		0			0
$851$	−8853.00	−	15333.8i	−0.356612	−	0.617670i
$852$		0			0
$853$	20937.0			0.840409			0.420205	−	0.907429i	$-0.361958\pi$
$853$	20937.0			0.840409			0.420205	+	0.907429i	$0.361958\pi$
$854$		0			0
$855$	−5865.00	+	10158.5i	−0.234595	+	0.406331i
$856$		0			0
$857$	−7189.00			−0.286548			−0.143274	−	0.989683i	$-0.545763\pi$
$857$	−7189.00			−0.286548			−0.143274	+	0.989683i	$0.545763\pi$
$858$		0			0
$859$	32498.0			1.29082			0.645412	−	0.763835i	$-0.276686\pi$
$859$	32498.0			1.29082			0.645412	+	0.763835i	$0.276686\pi$
$860$		0			0
$861$	3300.00	−	5715.77i	0.130620	−	0.226240i
$862$		0			0
$863$	−8428.00			−0.332436			−0.166218	−	0.986089i	$-0.553156\pi$
$863$	−8428.00			−0.332436			−0.166218	+	0.986089i	$0.553156\pi$
$864$		0			0
$865$	−11271.0	−	19521.9i	−0.443035	−	0.767360i
$866$		0			0
$867$	−4744.00	−	8216.85i	−0.185830	−	0.321867i
$868$		0			0
$869$	−1216.00	+	2106.17i	−0.0474683	+	0.0822176i
$870$		0			0
$871$	−28015.0	+	29114.0i	−1.08984	+	1.13260i
$872$		0			0
$873$	2737.00	−	4740.62i	0.106109	−	0.183787i
$874$		0			0
$875$	6630.00	+	11483.5i	0.256154	+	0.443672i
$876$		0			0
$877$	3423.50	+	5929.68i	0.131817	+	0.228313i	0.924377	−	0.381480i	$-0.124586\pi$
$877$	3423.50	+	5929.68i	0.131817	+	0.228313i	−0.792560	+	0.609794i	$0.791252\pi$
$878$		0			0
$879$	−16602.0			−0.637055
$880$		0			0
$881$	−14865.5	+	25747.8i	−0.568481	+	0.984637i	0.428236	+	0.903667i	$0.359135\pi$
$881$	−14865.5	+	25747.8i	−0.568481	+	0.984637i	−0.996717	+	0.0809703i	$0.974198\pi$
$882$		0			0
$883$	23738.0			0.904697			0.452348	−	0.891841i	$-0.350586\pi$
$883$	23738.0			0.904697			0.452348	+	0.891841i	$0.350586\pi$
$884$		0			0
$885$	−29376.0			−1.11578
$886$		0			0
$887$	13794.0	−	23891.9i	0.522161	−	0.904410i	−0.477506	−	0.878628i	$-0.658459\pi$
$887$	13794.0	−	23891.9i	0.522161	−	0.904410i	0.999668	−	0.0257817i	$-0.00820749\pi$
$888$		0			0
$889$	−43160.0			−1.62828
$890$		0			0
$891$	−6736.00	−	11667.1i	−0.253271	−	0.438678i
$892$		0			0
$893$	2430.00	+	4208.88i	0.0910603	+	0.157721i
$894$		0			0
$895$	36244.0	−	62776.4i	1.35363	−	2.34456i
$896$		0			0
$897$	2028.00	+	7025.20i	0.0754882	+	0.261499i
$898$		0			0
$899$	−7289.00	+	12624.9i	−0.270414	+	0.468370i
$900$		0			0
$901$	604.500	+	1047.02i	0.0223516	+	0.0387142i
$902$		0			0
$903$	−3120.00	−	5404.00i	−0.114980	−	0.199152i
$904$		0			0
$905$	−6851.00			−0.251641
$906$		0			0
$907$	−18564.0	+	32153.8i	−0.679611	+	1.17712i	0.295487	+	0.955347i	$0.404518\pi$
$907$	−18564.0	+	32153.8i	−0.679611	+	1.17712i	−0.975098	+	0.221775i	$0.928815\pi$
$908$		0			0
$909$	18837.0			0.687331
$910$		0			0
$911$	−20516.0			−0.746131			−0.373066	−	0.927805i	$-0.621693\pi$
$911$	−20516.0			−0.746131			−0.373066	+	0.927805i	$0.621693\pi$
$912$		0			0
$913$	10048.0	−	17403.6i	0.364228	−	0.630862i
$914$		0			0
$915$	−4930.00			−0.178121
$916$		0			0
$917$	−7300.00	−	12644.0i	−0.262887	−	0.455333i
$918$		0			0
$919$	−10503.0	−	18191.7i	−0.376999	−	0.652981i	0.613625	−	0.789597i	$-0.289711\pi$
$919$	−10503.0	−	18191.7i	−0.376999	−	0.652981i	−0.990624	+	0.136616i	$0.956377\pi$
$920$		0			0
$921$	−8678.00	+	15030.7i	−0.310478	+	0.537763i
$922$		0			0
$923$	−8502.00	−	29451.8i	−0.303193	−	1.05029i
$924$		0			0
$925$	18614.0	−	32240.4i	0.661648	−	1.14601i
$926$		0			0
$927$	−18837.0	−	32626.6i	−0.667409	−	1.15599i
$928$		0			0
$929$	−10213.5	−	17690.3i	−0.360704	−	0.624758i	0.627373	−	0.778719i	$-0.284130\pi$
$929$	−10213.5	−	17690.3i	−0.360704	−	0.624758i	−0.988077	+	0.153961i	$0.950797\pi$
$930$		0			0
$931$	−1710.00			−0.0601965
$932$		0			0
$933$	−8658.00	+	14996.1i	−0.303805	+	0.526206i
$934$		0			0
$935$	−7072.00			−0.247357
$936$		0			0
$937$	33191.0			1.15721			0.578603	−	0.815609i	$-0.303598\pi$
$937$	33191.0			1.15721			0.578603	+	0.815609i	$0.303598\pi$
$938$		0			0
$939$	−5250.00	+	9093.27i	−0.182457	+	0.316025i
$940$		0			0
$941$	−36422.0			−1.26177			−0.630884	−	0.775877i	$-0.717308\pi$
$941$	−36422.0			−1.26177			−0.630884	+	0.775877i	$0.717308\pi$
$942$		0			0
$943$	−6435.00	−	11145.7i	−0.222219	−	0.384894i
$944$		0			0
$945$	17000.0	+	29444.9i	0.585196	+	1.01359i
$946$		0			0
$947$	−19815.0	+	34320.6i	−0.679938	+	1.17769i	0.295062	+	0.955478i	$0.404660\pi$
$947$	−19815.0	+	34320.6i	−0.679938	+	1.17769i	−0.974999	+	0.222208i	$0.928673\pi$
$948$		0			0
$949$	−9782.50	−	2420.54i	−0.334619	−	0.0827967i
$950$		0			0
$951$	6413.00	−	11107.6i	0.218671	−	0.378749i
$952$		0			0
$953$	−28821.0	−	49919.4i	−0.979647	−	1.69680i	−0.663658	−	0.748036i	$-0.730997\pi$
$953$	−28821.0	−	49919.4i	−0.979647	−	1.69680i	−0.315989	−	0.948763i	$-0.602336\pi$
$954$		0			0
$955$	−10591.0	−	18344.2i	−0.358866	−	0.621574i
$956$		0			0
$957$	−12608.0			−0.425871
$958$		0			0
$959$	16710.0	−	28942.6i	0.562663	−	0.974561i
$960$		0			0
$961$	−24315.0			−0.816186
$962$		0			0
$963$	12006.0			0.401753
$964$		0			0
$965$	−2269.50	+	3930.89i	−0.0757076	+	0.131129i
$966$		0			0
$967$	−2162.00			−0.0718979			−0.0359489	−	0.999354i	$-0.511445\pi$
$967$	−2162.00			−0.0718979			−0.0359489	+	0.999354i	$0.511445\pi$
$968$		0			0
$969$	390.000	+	675.500i	0.0129294	+	0.0223944i
$970$		0			0
$971$	−9879.00	−	17110.9i	−0.326501	−	0.565516i	0.655314	−	0.755356i	$-0.272536\pi$
$971$	−9879.00	−	17110.9i	−0.326501	−	0.565516i	−0.981815	+	0.189841i	$0.939203\pi$
$972$		0			0
$973$	−9120.00	+	15796.3i	−0.300487	+	0.520459i
$974$		0			0
$975$	−10660.0	+	11078.2i	−0.350147	+	0.363883i
$976$		0			0
$977$	6244.50	−	10815.8i	0.204482	−	0.354174i	−0.745485	−	0.666522i	$-0.767782\pi$
$977$	6244.50	−	10815.8i	0.204482	−	0.354174i	0.949968	+	0.312348i	$0.101116\pi$
$978$		0			0
$979$	4256.00	+	7371.61i	0.138940	+	0.240651i
$980$		0			0
$981$	−18791.0	−	32547.0i	−0.611570	−	1.05927i
$982$		0			0
$983$	28658.0			0.929856			0.464928	−	0.885349i	$-0.346080\pi$
$983$	28658.0			0.929856			0.464928	+	0.885349i	$0.346080\pi$
$984$		0			0
$985$	−10863.0	+	18815.3i	−0.351395	+	0.608634i
$986$		0			0
$987$	6480.00			0.208977
$988$		0			0
$989$	−12168.0			−0.391223
$990$		0			0
$991$	−21397.0	+	37060.7i	−0.685871	+	1.18796i	0.287291	+	0.957843i	$0.407245\pi$
$991$	−21397.0	+	37060.7i	−0.685871	+	1.18796i	−0.973162	+	0.230120i	$0.926088\pi$
$992$		0			0
$993$	6976.00			0.222937
$994$		0			0
$995$	36023.0	+	62393.7i	1.14774	+	1.98795i
$996$		0			0
$997$	26291.5	+	45538.2i	0.835166	+	1.44655i	0.893895	+	0.448275i	$0.147962\pi$
$997$	26291.5	+	45538.2i	0.835166	+	1.44655i	−0.0587298	+	0.998274i	$0.518705\pi$
$998$		0			0
$999$	11350.0	−	19658.8i	0.359458	−	0.622599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.i.b.113.1		2
4.3	odd	2		13.4.c.a.9.1	yes	2
12.11	even	2		117.4.g.c.100.1		2
13.3	even	3	inner	208.4.i.b.81.1		2
52.3	odd	6		13.4.c.a.3.1	✓	2
52.7	even	12		169.4.b.c.168.2		2
52.11	even	12		169.4.e.c.23.2		4
52.15	even	12		169.4.e.c.23.1		4
52.19	even	12		169.4.b.c.168.1		2
52.23	odd	6		169.4.c.d.146.1		2
52.31	even	4		169.4.e.c.147.2		4
52.35	odd	6		169.4.a.d.1.1		1
52.43	odd	6		169.4.a.a.1.1		1
52.47	even	4		169.4.e.c.147.1		4
52.51	odd	2		169.4.c.d.22.1		2
156.35	even	6		1521.4.a.b.1.1		1
156.95	even	6		1521.4.a.k.1.1		1
156.107	even	6		117.4.g.c.55.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.c.a.3.1	✓	2	52.3	odd	6
13.4.c.a.9.1	yes	2	4.3	odd	2
117.4.g.c.55.1		2	156.107	even	6
117.4.g.c.100.1		2	12.11	even	2
169.4.a.a.1.1		1	52.43	odd	6
169.4.a.d.1.1		1	52.35	odd	6
169.4.b.c.168.1		2	52.19	even	12
169.4.b.c.168.2		2	52.7	even	12
169.4.c.d.22.1		2	52.51	odd	2
169.4.c.d.146.1		2	52.23	odd	6
169.4.e.c.23.1		4	52.15	even	12
169.4.e.c.23.2		4	52.11	even	12
169.4.e.c.147.1		4	52.47	even	4
169.4.e.c.147.2		4	52.31	even	4
208.4.i.b.81.1		2	13.3	even	3	inner
208.4.i.b.113.1		2	1.1	even	1	trivial
1521.4.a.b.1.1		1	156.35	even	6
1521.4.a.k.1.1		1	156.95	even	6

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.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{3} +17.0000 q^{5} +(10.0000 + 17.3205i) q^{7} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{3} +17.0000 q^{5} +(10.0000 + 17.3205i) q^{7} +(11.5000 + 19.9186i) q^{9} +(-16.0000 + 27.7128i) q^{11} +(-45.5000 - 11.2583i) q^{13} +(17.0000 - 29.4449i) q^{15} +(6.50000 + 11.2583i) q^{17} +(15.0000 + 25.9808i) q^{19} +40.0000 q^{21} +(39.0000 - 67.5500i) q^{23} +164.000 q^{25} +100.000 q^{27} +(-98.5000 + 170.607i) q^{29} +74.0000 q^{31} +(32.0000 + 55.4256i) q^{33} +(170.000 + 294.449i) q^{35} +(113.500 - 196.588i) q^{37} +(-65.0000 + 67.5500i) q^{39} +(82.5000 - 142.894i) q^{41} +(-78.0000 - 135.100i) q^{43} +(195.500 + 338.616i) q^{45} +162.000 q^{47} +(-28.5000 + 49.3634i) q^{49} +26.0000 q^{51} +93.0000 q^{53} +(-272.000 + 471.118i) q^{55} +60.0000 q^{57} +(-432.000 - 748.246i) q^{59} +(-72.5000 - 125.574i) q^{61} +(-230.000 + 398.372i) q^{63} +(-773.500 - 191.392i) q^{65} +(431.000 - 746.514i) q^{67} +(-78.0000 - 135.100i) q^{69} +(327.000 + 566.381i) q^{71} +215.000 q^{73} +(164.000 - 284.056i) q^{75} -640.000 q^{77} +76.0000 q^{79} +(-210.500 + 364.597i) q^{81} -628.000 q^{83} +(110.500 + 191.392i) q^{85} +(197.000 + 341.214i) q^{87} +(133.000 - 230.363i) q^{89} +(-260.000 - 900.666i) q^{91} +(74.0000 - 128.172i) q^{93} +(255.000 + 441.673i) q^{95} +(-119.000 - 206.114i) q^{97} -736.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 34 q^{5} + 20 q^{7} + 23 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 34 * q^5 + 20 * q^7 + 23 * q^9	\( 2 q + 2 q^{3} + 34 q^{5} + 20 q^{7} + 23 q^{9} - 32 q^{11} - 91 q^{13} + 34 q^{15} + 13 q^{17} + 30 q^{19} + 80 q^{21} + 78 q^{23} + 328 q^{25} + 200 q^{27} - 197 q^{29} + 148 q^{31} + 64 q^{33} + 340 q^{35} + 227 q^{37} - 130 q^{39} + 165 q^{41} - 156 q^{43} + 391 q^{45} + 324 q^{47} - 57 q^{49} + 52 q^{51} + 186 q^{53} - 544 q^{55} + 120 q^{57} - 864 q^{59} - 145 q^{61} - 460 q^{63} - 1547 q^{65} + 862 q^{67} - 156 q^{69} + 654 q^{71} + 430 q^{73} + 328 q^{75} - 1280 q^{77} + 152 q^{79} - 421 q^{81} - 1256 q^{83} + 221 q^{85} + 394 q^{87} + 266 q^{89} - 520 q^{91} + 148 q^{93} + 510 q^{95} - 238 q^{97} - 1472 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 34 * q^5 + 20 * q^7 + 23 * q^9 - 32 * q^11 - 91 * q^13 + 34 * q^15 + 13 * q^17 + 30 * q^19 + 80 * q^21 + 78 * q^23 + 328 * q^25 + 200 * q^27 - 197 * q^29 + 148 * q^31 + 64 * q^33 + 340 * q^35 + 227 * q^37 - 130 * q^39 + 165 * q^41 - 156 * q^43 + 391 * q^45 + 324 * q^47 - 57 * q^49 + 52 * q^51 + 186 * q^53 - 544 * q^55 + 120 * q^57 - 864 * q^59 - 145 * q^61 - 460 * q^63 - 1547 * q^65 + 862 * q^67 - 156 * q^69 + 654 * q^71 + 430 * q^73 + 328 * q^75 - 1280 * q^77 + 152 * q^79 - 421 * q^81 - 1256 * q^83 + 221 * q^85 + 394 * q^87 + 266 * q^89 - 520 * q^91 + 148 * q^93 + 510 * q^95 - 238 * q^97 - 1472 * q^99

Introduction

L-functions

Modular forms

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