LMFDB - Embedded newform 33.5.c.a.10.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,5,Mod(10,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("33.10");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	33.c (of order $2$, degree $1$, 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:	$3.41120878177$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 102x^{6} + 2913x^{4} + 23292x^{2} + 41364 $ x^8 + 102x^6 + 2913x^4 + 23292*x^2 + 41364
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.7
Root			$5.58567i$ of defining polynomial
Character	$\chi$	$=$	33.10
Dual form			33.5.c.a.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.58567i q^{2} -5.19615 q^{3} -15.1997 q^{4} -29.7487 q^{5} -29.0240i q^{6} -12.9420i q^{7} +4.47031i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+5.58567i q^{2} -5.19615 q^{3} -15.1997 q^{4} -29.7487 q^{5} -29.0240i q^{6} -12.9420i q^{7} +4.47031i q^{8} +27.0000 q^{9} -166.166i q^{10} +(-100.434 + 67.4829i) q^{11} +78.9799 q^{12} -36.6685i q^{13} +72.2898 q^{14} +154.579 q^{15} -268.165 q^{16} +464.257i q^{17} +150.813i q^{18} +327.633i q^{19} +452.171 q^{20} +67.2487i q^{21} +(-376.937 - 560.993i) q^{22} +396.812 q^{23} -23.2284i q^{24} +259.987 q^{25} +204.818 q^{26} -140.296 q^{27} +196.715i q^{28} -1152.21i q^{29} +863.426i q^{30} +437.378 q^{31} -1426.35i q^{32} +(521.872 - 350.651i) q^{33} -2593.18 q^{34} +385.009i q^{35} -410.391 q^{36} +276.604 q^{37} -1830.05 q^{38} +190.535i q^{39} -132.986i q^{40} +2782.30i q^{41} -375.629 q^{42} -1663.84i q^{43} +(1526.57 - 1025.72i) q^{44} -803.216 q^{45} +2216.46i q^{46} -1855.68 q^{47} +1393.42 q^{48} +2233.50 q^{49} +1452.20i q^{50} -2412.35i q^{51} +557.350i q^{52} +3745.57 q^{53} -783.647i q^{54} +(2987.79 - 2007.53i) q^{55} +57.8549 q^{56} -1702.43i q^{57} +6435.88 q^{58} -6573.17 q^{59} -2349.55 q^{60} +5140.56i q^{61} +2443.05i q^{62} -349.435i q^{63} +3676.50 q^{64} +1090.84i q^{65} +(1958.62 + 2915.00i) q^{66} -3464.58 q^{67} -7056.56i q^{68} -2061.90 q^{69} -2150.53 q^{70} -6031.86 q^{71} +120.698i q^{72} +3580.96i q^{73} +1545.02i q^{74} -1350.93 q^{75} -4979.92i q^{76} +(873.365 + 1299.82i) q^{77} -1064.27 q^{78} +9711.53i q^{79} +7977.55 q^{80} +729.000 q^{81} -15541.0 q^{82} -11837.3i q^{83} -1022.16i q^{84} -13811.1i q^{85} +9293.66 q^{86} +5987.07i q^{87} +(-301.670 - 448.973i) q^{88} +2584.72 q^{89} -4486.50i q^{90} -474.565 q^{91} -6031.42 q^{92} -2272.69 q^{93} -10365.2i q^{94} -9746.67i q^{95} +7411.55i q^{96} +1551.68 q^{97} +12475.6i q^{98} +(-2711.73 + 1822.04i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 76 q^{4} - 36 q^{5} + 216 q^{9}+O(q^{10}) $ 8 * q - 76 * q^4 - 36 * q^5 + 216 * q^9	$ 8 q - 76 q^{4} - 36 q^{5} + 216 q^{9} + 36 q^{11} - 360 q^{12} - 1140 q^{14} + 108 q^{15} + 1412 q^{16} + 2532 q^{20} - 780 q^{22} + 516 q^{23} - 2280 q^{25} - 1524 q^{26} + 2752 q^{31} + 1008 q^{33} - 4920 q^{34} - 2052 q^{36} + 5296 q^{37} + 696 q^{38} - 4356 q^{42} - 6540 q^{44} - 972 q^{45} + 420 q^{47} + 9936 q^{48} - 6832 q^{49} + 3540 q^{53} + 3784 q^{55} + 17964 q^{56} + 21624 q^{58} - 16632 q^{59} - 612 q^{60} - 27508 q^{64} + 360 q^{66} - 3656 q^{67} + 9036 q^{69} + 3312 q^{70} - 13212 q^{71} - 9288 q^{75} + 23268 q^{77} - 13140 q^{78} - 4476 q^{80} + 5832 q^{81} + 17088 q^{82} + 19896 q^{86} - 12516 q^{88} + 15528 q^{89} - 19752 q^{91} - 81180 q^{92} - 21384 q^{93} + 7624 q^{97} + 972 q^{99}+O(q^{100}) $ 8 * q - 76 * q^4 - 36 * q^5 + 216 * q^9 + 36 * q^11 - 360 * q^12 - 1140 * q^14 + 108 * q^15 + 1412 * q^16 + 2532 * q^20 - 780 * q^22 + 516 * q^23 - 2280 * q^25 - 1524 * q^26 + 2752 * q^31 + 1008 * q^33 - 4920 * q^34 - 2052 * q^36 + 5296 * q^37 + 696 * q^38 - 4356 * q^42 - 6540 * q^44 - 972 * q^45 + 420 * q^47 + 9936 * q^48 - 6832 * q^49 + 3540 * q^53 + 3784 * q^55 + 17964 * q^56 + 21624 * q^58 - 16632 * q^59 - 612 * q^60 - 27508 * q^64 + 360 * q^66 - 3656 * q^67 + 9036 * q^69 + 3312 * q^70 - 13212 * q^71 - 9288 * q^75 + 23268 * q^77 - 13140 * q^78 - 4476 * q^80 + 5832 * q^81 + 17088 * q^82 + 19896 * q^86 - 12516 * q^88 + 15528 * q^89 - 19752 * q^91 - 81180 * q^92 - 21384 * q^93 + 7624 * q^97 + 972 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$1$

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 $

$2$			5.58567i			1.39642i	0.715895	+	0.698208i	$0.246019\pi$
$2$			5.58567i			1.39642i	−0.715895	+	0.698208i	$0.753981\pi$
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	−15.1997			−0.949980
$5$	−29.7487			−1.18995			−0.594974	−	0.803745i	$-0.702838\pi$
$5$	−29.7487			−1.18995			−0.594974	+	0.803745i	$0.702838\pi$
$6$		−	29.0240i		−	0.806222i
$7$		−	12.9420i		−	0.264123i	−0.991242	−	0.132061i	$-0.957840\pi$
$7$		−	12.9420i		−	0.264123i	0.991242	−	0.132061i	$-0.0421596\pi$
$8$			4.47031i			0.0698486i
$9$	27.0000			0.333333
$10$		−	166.166i		−	1.66166i
$11$	−100.434	+	67.4829i	−0.830036	+	0.557710i
$11$	−100.434	+	67.4829i	−0.830036	+	0.557710i
$12$	78.9799			0.548471
$13$		−	36.6685i		−	0.216973i	−0.994098	−	0.108487i	$-0.965399\pi$
$13$		−	36.6685i		−	0.216973i	0.994098	−	0.108487i	$-0.0346005\pi$
$14$	72.2898			0.368826
$15$	154.579			0.687017
$16$	−268.165			−1.04752
$17$			464.257i			1.60643i	0.595692	+	0.803213i	$0.296878\pi$
$17$			464.257i			1.60643i	−0.595692	+	0.803213i	$0.703122\pi$
$18$			150.813i			0.465472i
$19$			327.633i			0.907571i	0.891111	+	0.453786i	$0.149927\pi$
$19$			327.633i			0.907571i	−0.891111	+	0.453786i	$0.850073\pi$
$20$	452.171			1.13043
$21$			67.2487i			0.152491i
$22$	−376.937	−	560.993i	−0.778796	−	1.15908i
$23$	396.812			0.750118			0.375059	−	0.927001i	$-0.377622\pi$
$23$	396.812			0.750118			0.375059	+	0.927001i	$0.377622\pi$
$24$		−	23.2284i		−	0.0403271i
$25$	259.987			0.415979
$26$	204.818			0.302985
$27$	−140.296			−0.192450
$28$			196.715i			0.250911i
$29$		−	1152.21i		−	1.37005i	−0.728519	−	0.685025i	$-0.759791\pi$
$29$		−	1152.21i		−	1.37005i	0.728519	−	0.685025i	$-0.240209\pi$
$30$			863.426i			0.959363i
$31$	437.378			0.455128			0.227564	−	0.973763i	$-0.426924\pi$
$31$	437.378			0.455128			0.227564	+	0.973763i	$0.426924\pi$
$32$		−	1426.35i		−	1.39292i
$33$	521.872	−	350.651i	0.479221	−	0.321994i
$34$	−2593.18			−2.24324
$35$			385.009i			0.314293i
$36$	−410.391			−0.316660
$37$	276.604			0.202049			0.101024	−	0.994884i	$-0.467788\pi$
$37$	276.604			0.202049			0.101024	+	0.994884i	$0.467788\pi$
$38$	−1830.05			−1.26735
$39$			190.535i			0.125270i
$40$		−	132.986i		−	0.0831163i
$41$			2782.30i			1.65515i	0.561358	+	0.827573i	$0.310279\pi$
$41$			2782.30i			1.65515i	−0.561358	+	0.827573i	$0.689721\pi$
$42$	−375.629			−0.212942
$43$		−	1663.84i		−	0.899860i	−0.893064	−	0.449930i	$-0.851449\pi$
$43$		−	1663.84i		−	0.899860i	0.893064	−	0.449930i	$-0.148551\pi$
$44$	1526.57	−	1025.72i	0.788518	−	0.529813i
$45$	−803.216			−0.396650
$46$			2216.46i			1.04748i
$47$	−1855.68			−0.840053			−0.420026	−	0.907512i	$-0.637979\pi$
$47$	−1855.68			−0.840053			−0.420026	+	0.907512i	$0.637979\pi$
$48$	1393.42			0.604785
$49$	2233.50			0.930239
$50$			1452.20i			0.580880i
$51$		−	2412.35i		−	0.927470i
$52$			557.350i			0.206120i
$53$	3745.57			1.33342			0.666709	−	0.745318i	$-0.267702\pi$
$53$	3745.57			1.33342			0.666709	+	0.745318i	$0.267702\pi$
$54$		−	783.647i		−	0.268741i
$55$	2987.79	−	2007.53i	0.987700	−	0.663646i
$56$	57.8549			0.0184486
$57$		−	1702.43i		−	0.523986i
$58$	6435.88			1.91316
$59$	−6573.17			−1.88830			−0.944150	−	0.329516i	$-0.893114\pi$
$59$	−6573.17			−1.88830			−0.944150	+	0.329516i	$0.893114\pi$
$60$	−2349.55			−0.652653
$61$			5140.56i			1.38150i	0.723094	+	0.690750i	$0.242719\pi$
$61$			5140.56i			1.38150i	−0.723094	+	0.690750i	$0.757281\pi$
$62$			2443.05i			0.635549i
$63$		−	349.435i		−	0.0880410i
$64$	3676.50			0.897583
$65$			1090.84i			0.258187i
$66$	1958.62	+	2915.00i	0.449638	+	0.669193i
$67$	−3464.58			−0.771793			−0.385897	−	0.922542i	$-0.626108\pi$
$67$	−3464.58			−0.771793			−0.385897	+	0.922542i	$0.626108\pi$
$68$		−	7056.56i		−	1.52607i
$69$	−2061.90			−0.433081
$70$	−2150.53			−0.438884
$71$	−6031.86			−1.19656			−0.598280	−	0.801287i	$-0.704149\pi$
$71$	−6031.86			−1.19656			−0.598280	+	0.801287i	$0.704149\pi$
$72$			120.698i			0.0232829i
$73$			3580.96i			0.671976i	0.941866	+	0.335988i	$0.109070\pi$
$73$			3580.96i			0.671976i	−0.941866	+	0.335988i	$0.890930\pi$
$74$			1545.02i			0.282144i
$75$	−1350.93			−0.240165
$76$		−	4979.92i		−	0.862174i
$77$	873.365	+	1299.82i	0.147304	+	0.219231i
$78$	−1064.27			−0.174929
$79$			9711.53i			1.55609i	0.628211	+	0.778043i	$0.283787\pi$
$79$			9711.53i			1.55609i	−0.628211	+	0.778043i	$0.716213\pi$
$80$	7977.55			1.24649
$81$	729.000			0.111111
$82$	−15541.0			−2.31127
$83$		−	11837.3i		−	1.71829i	−0.511729	−	0.859147i	$-0.670995\pi$
$83$		−	11837.3i		−	1.71829i	0.511729	−	0.859147i	$-0.329005\pi$
$84$		−	1022.16i		−	0.144864i
$85$		−	13811.1i		−	1.91156i
$86$	9293.66			1.25658
$87$			5987.07i			0.790999i
$88$	−301.670	−	448.973i	−0.0389553	−	0.0579769i
$89$	2584.72			0.326312			0.163156	−	0.986600i	$-0.447833\pi$
$89$	2584.72			0.326312			0.163156	+	0.986600i	$0.447833\pi$
$90$		−	4486.50i		−	0.553888i
$91$	−474.565			−0.0573077
$92$	−6031.42			−0.712597
$93$	−2272.69			−0.262769
$94$		−	10365.2i		−	1.17306i
$95$		−	9746.67i		−	1.07996i
$96$			7411.55i			0.804205i
$97$	1551.68			0.164915			0.0824574	−	0.996595i	$-0.473723\pi$
$97$	1551.68			0.164915			0.0824574	+	0.996595i	$0.473723\pi$
$98$			12475.6i			1.29900i
$99$	−2711.73	+	1822.04i	−0.276679	+	0.185903i
$100$	−3951.71			−0.395171
$101$			3939.16i			0.386154i	0.981184	+	0.193077i	$0.0618468\pi$
$101$			3939.16i			0.386154i	−0.981184	+	0.193077i	$0.938153\pi$
$102$	13474.6			1.29513
$103$	12210.1			1.15092			0.575459	−	0.817830i	$-0.304823\pi$
$103$	12210.1			1.15092			0.575459	+	0.817830i	$0.304823\pi$
$104$	163.920			0.0151553
$105$		−	2000.56i		−	0.181457i
$106$			20921.5i			1.86201i
$107$		−	3756.40i		−	0.328099i	−0.986452	−	0.164049i	$-0.947544\pi$
$107$		−	3756.40i		−	0.328099i	0.986452	−	0.164049i	$-0.0524556\pi$
$108$	2132.46			0.182824
$109$			15338.3i			1.29099i	0.763764	+	0.645495i	$0.223349\pi$
$109$			15338.3i			1.29099i	−0.763764	+	0.645495i	$0.776651\pi$
$110$	11213.4	+	16688.8i	0.926727	+	1.37924i
$111$	−1437.28			−0.116653
$112$			3470.59i			0.276673i
$113$	−7205.76			−0.564316			−0.282158	−	0.959368i	$-0.591050\pi$
$113$	−7205.76			−0.564316			−0.282158	+	0.959368i	$0.591050\pi$
$114$	9509.22			0.731703
$115$	−11804.7			−0.892602
$116$			17513.3i			1.30152i
$117$		−	990.050i		−	0.0723245i
$118$		−	36715.6i		−	2.63685i
$119$	6008.42			0.424294
$120$			691.016i			0.0479872i
$121$	5533.12	−	13555.2i	0.377919	−	0.925839i
$122$	−28713.5			−1.92915
$123$		−	14457.3i		−	0.955599i
$124$	−6648.01			−0.432363
$125$	10858.7			0.694956
$126$	1951.83			0.122942
$127$		−	10757.4i		−	0.666960i	−0.942757	−	0.333480i	$-0.891777\pi$
$127$		−	10757.4i		−	0.666960i	0.942757	−	0.333480i	$-0.108223\pi$
$128$		−	2285.94i		−	0.139523i
$129$			8645.57i			0.519534i
$130$	−6093.08			−0.360537
$131$			14623.4i			0.852131i	0.904692	+	0.426066i	$0.140101\pi$
$131$			14623.4i			0.852131i	−0.904692	+	0.426066i	$0.859899\pi$
$132$	−7932.29	+	5329.79i	−0.455251	+	0.305888i
$133$	4240.24			0.239710
$134$		−	19352.0i		−	1.07775i
$135$	4173.63			0.229006
$136$	−2075.37			−0.112207
$137$	25143.7			1.33964			0.669821	−	0.742523i	$-0.266371\pi$
$137$	25143.7			1.33964			0.669821	+	0.742523i	$0.266371\pi$
$138$		−	11517.1i		−	0.604761i
$139$			4454.38i			0.230546i	0.993334	+	0.115273i	$0.0367743\pi$
$139$			4454.38i			0.230546i	−0.993334	+	0.115273i	$0.963226\pi$
$140$		−	5852.01i		−	0.298572i
$141$	9642.38			0.485005
$142$		−	33692.0i		−	1.67090i
$143$	2474.50	+	3682.78i	0.121008	+	0.180096i
$144$	−7240.44			−0.349173
$145$			34276.9i			1.63029i
$146$	−20002.0			−0.938358
$147$	−11605.6			−0.537074
$148$	−4204.30			−0.191942
$149$		−	21755.9i		−	0.979950i	−0.871737	−	0.489975i	$-0.837006\pi$
$149$		−	21755.9i		−	0.979950i	0.871737	−	0.489975i	$-0.162994\pi$
$150$		−	7545.85i		−	0.335371i
$151$			20736.4i			0.909450i	0.890632	+	0.454725i	$0.150262\pi$
$151$			20736.4i			0.909450i	−0.890632	+	0.454725i	$0.849738\pi$
$152$	−1464.62			−0.0633926
$153$			12534.9i			0.535475i
$154$	−7260.38	+	4878.33i	−0.306139	+	0.205698i
$155$	−13011.5			−0.541580
$156$		−	2896.07i		−	0.119004i
$157$	−16991.5			−0.689340			−0.344670	−	0.938724i	$-0.612009\pi$
$157$	−16991.5			−0.689340			−0.344670	+	0.938724i	$0.612009\pi$
$158$	−54245.4			−2.17294
$159$	−19462.6			−0.769850
$160$			42432.2i			1.65751i
$161$		−	5135.55i		−	0.198123i
$162$			4071.95i			0.155157i
$163$	15654.2			0.589192			0.294596	−	0.955622i	$-0.404815\pi$
$163$	15654.2			0.589192			0.294596	+	0.955622i	$0.404815\pi$
$164$		−	42290.1i		−	1.57236i
$165$	−15525.0	+	10431.4i	−0.570249	+	0.383156i
$166$	66119.4			2.39945
$167$		−	13741.9i		−	0.492734i	−0.969177	−	0.246367i	$-0.920763\pi$
$167$		−	13741.9i		−	0.492734i	0.969177	−	0.246367i	$-0.0792369\pi$
$168$	−300.623			−0.0106513
$169$	27216.4			0.952923
$170$	77143.9			2.66934
$171$			8846.10i			0.302524i
$172$			25289.9i			0.854849i
$173$			41623.1i			1.39073i	0.718657	+	0.695365i	$0.244757\pi$
$173$			41623.1i			1.39073i	−0.718657	+	0.695365i	$0.755243\pi$
$174$	−33441.8			−1.10456
$175$		−	3364.75i		−	0.109869i
$176$	26932.9	−	18096.5i	0.869478	−	0.584211i
$177$	34155.2			1.09021
$178$			14437.4i			0.455668i
$179$	−17574.8			−0.548510			−0.274255	−	0.961657i	$-0.588431\pi$
$179$	−17574.8			−0.548510			−0.274255	+	0.961657i	$0.588431\pi$
$180$	12208.6			0.376809
$181$	10371.8			0.316588			0.158294	−	0.987392i	$-0.449401\pi$
$181$	10371.8			0.316588			0.158294	+	0.987392i	$0.449401\pi$
$182$		−	2650.76i		−	0.0800254i
$183$		−	26711.1i		−	0.797609i
$184$			1773.88i			0.0523947i
$185$	−8228.63			−0.240427
$186$		−	12694.5i		−	0.366934i
$187$	−31329.4	−	46627.3i	−0.895919	−	1.33339i
$188$	28205.7			0.798034
$189$			1815.72i			0.0508305i
$190$	54441.7			1.50808
$191$	−2219.45			−0.0608386			−0.0304193	−	0.999537i	$-0.509684\pi$
$191$	−2219.45			−0.0608386			−0.0304193	+	0.999537i	$0.509684\pi$
$192$	−19103.7			−0.518220
$193$			18368.1i			0.493117i	0.969128	+	0.246559i	$0.0792998\pi$
$193$			18368.1i			0.493117i	−0.969128	+	0.246559i	$0.920700\pi$
$194$			8667.19i			0.230290i
$195$		−	5668.18i		−	0.149065i
$196$	−33948.6			−0.883709
$197$			23671.0i			0.609936i	0.952363	+	0.304968i	$0.0986458\pi$
$197$			23671.0i			0.609936i	−0.952363	+	0.304968i	$0.901354\pi$
$198$	−10177.3	−	15146.8i	−0.259599	−	0.386359i
$199$	−27214.8			−0.687226			−0.343613	−	0.939111i	$-0.611651\pi$
$199$	−27214.8			−0.687226			−0.343613	+	0.939111i	$0.611651\pi$
$200$			1162.22i			0.0290555i
$201$	18002.5			0.445595
$202$	−22002.8			−0.539232
$203$	−14912.0			−0.361862
$204$			36666.9i			0.881078i
$205$		−	82769.9i		−	1.96954i
$206$			68201.5i			1.60716i
$207$	10713.9			0.250039
$208$			9833.20i			0.227284i
$209$	−22109.6	−	32905.6i	−0.506161	−	0.753317i
$210$	11174.5			0.253390
$211$			7465.71i			0.167690i	0.996479	+	0.0838449i	$0.0267200\pi$
$211$			7465.71i			0.167690i	−0.996479	+	0.0838449i	$0.973280\pi$
$212$	−56931.5			−1.26672
$213$	31342.5			0.690834
$214$	20982.0			0.458162
$215$			49497.1i			1.07079i
$216$		−	627.167i		−	0.0134424i
$217$		−	5660.56i		−	0.120210i
$218$	−85674.4			−1.80276
$219$		−	18607.2i		−	0.387965i
$220$	−45413.5	+	30513.8i	−0.938296	+	0.630451i
$221$	17023.6			0.348552
$222$		−	8028.16i		−	0.162896i
$223$	13654.6			0.274581			0.137291	−	0.990531i	$-0.456161\pi$
$223$	13654.6			0.274581			0.137291	+	0.990531i	$0.456161\pi$
$224$	−18459.9			−0.367903
$225$	7019.64			0.138660
$226$		−	40249.0i		−	0.788021i
$227$		−	15860.1i		−	0.307790i	−0.988087	−	0.153895i	$-0.950818\pi$
$227$		−	15860.1i		−	0.307790i	0.988087	−	0.153895i	$-0.0491817\pi$
$228$			25876.4i			0.497777i
$229$	−99238.3			−1.89238			−0.946190	−	0.323612i	$-0.895103\pi$
$229$	−99238.3			−1.89238			−0.946190	+	0.323612i	$0.895103\pi$
$230$		−	65936.9i		−	1.24644i
$231$	−4538.14	−	6754.08i	−0.0850460	−	0.126573i
$232$	5150.75			0.0956962
$233$			44066.2i			0.811697i	0.913940	+	0.405849i	$0.133024\pi$
$233$			44066.2i			0.811697i	−0.913940	+	0.405849i	$0.866976\pi$
$234$	5530.09			0.100995
$235$	55204.0			0.999620
$236$	99910.1			1.79385
$237$		−	50462.6i		−	0.898407i
$238$			33561.1i			0.592491i
$239$		−	57559.5i		−	1.00768i	−0.863798	−	0.503838i	$-0.831921\pi$
$239$		−	57559.5i		−	1.00768i	0.863798	−	0.503838i	$-0.168079\pi$
$240$	−41452.6			−0.719663
$241$		−	86315.0i		−	1.48611i	−0.669228	−	0.743057i	$-0.733375\pi$
$241$		−	86315.0i		−	1.48611i	0.669228	−	0.743057i	$-0.266625\pi$
$242$	75714.9	+	30906.2i	1.29286	+	0.527733i
$243$	−3788.00			−0.0641500
$244$		−	78134.9i		−	1.31240i
$245$	−66443.9			−1.10694
$246$	80753.4			1.33441
$247$	12013.8			0.196919
$248$			1955.22i			0.0317901i
$249$			61508.6i			0.992057i
$250$			60653.0i			0.970448i
$251$	93826.2			1.48928			0.744641	−	0.667465i	$-0.232621\pi$
$251$	93826.2			1.48928			0.744641	+	0.667465i	$0.232621\pi$
$252$			5311.29i			0.0836372i
$253$	−39853.6	+	26778.1i	−0.622625	+	0.418348i
$254$	60087.2			0.931354
$255$			71764.3i			1.10364i
$256$	71592.5			1.09241
$257$	−24489.3			−0.370775			−0.185387	−	0.982666i	$-0.559354\pi$
$257$	−24489.3			−0.370775			−0.185387	+	0.982666i	$0.559354\pi$
$258$	−48291.3			−0.725487
$259$		−	3579.82i		−	0.0533656i
$260$		−	16580.4i		−	0.245273i
$261$		−	31109.7i		−	0.456684i
$262$	−81681.6			−1.18993
$263$			74432.3i			1.07609i	0.842915	+	0.538047i	$0.180838\pi$
$263$			74432.3i			1.07609i	−0.842915	+	0.538047i	$0.819162\pi$
$264$	1567.52	+	2332.93i	0.0224908	+	0.0334730i
$265$	−111426.			−1.58670
$266$			23684.5i			0.334736i
$267$	−13430.6			−0.188397
$268$	52660.5			0.733188
$269$	114719.			1.58537			0.792684	−	0.609633i	$-0.208683\pi$
$269$	114719.			1.58537			0.792684	+	0.609633i	$0.208683\pi$
$270$			23312.5i			0.319788i
$271$			18016.5i			0.245319i	0.992449	+	0.122660i	$0.0391423\pi$
$271$			18016.5i			0.245319i	−0.992449	+	0.122660i	$0.960858\pi$
$272$		−	124497.i		−	1.68276i
$273$	2465.91			0.0330866
$274$			140445.i			1.87070i
$275$	−26111.6	+	17544.7i	−0.345277	+	0.231995i
$276$	31340.2			0.411418
$277$		−	82563.5i		−	1.07604i	−0.842932	−	0.538020i	$-0.819172\pi$
$277$		−	82563.5i		−	1.07604i	0.842932	−	0.538020i	$-0.180828\pi$
$278$	−24880.7			−0.321938
$279$	11809.2			0.151709
$280$	−1721.11			−0.0219529
$281$			7495.15i			0.0949222i	0.998873	+	0.0474611i	$0.0151130\pi$
$281$			7495.15i			0.0949222i	−0.998873	+	0.0474611i	$0.984887\pi$
$282$			53859.1i			0.677269i
$283$			104220.i			1.30130i	0.759376	+	0.650652i	$0.225505\pi$
$283$			104220.i			1.30130i	−0.759376	+	0.650652i	$0.774495\pi$
$284$	91682.3			1.13671
$285$			50645.2i			0.623517i
$286$	−20570.8	+	13821.7i	−0.251489	+	0.168978i
$287$	36008.6			0.437162
$288$		−	38511.5i		−	0.464308i
$289$	−132014.			−1.58060
$290$	−191459.			−2.27656
$291$	−8062.78			−0.0952136
$292$		−	54429.4i		−	0.638363i
$293$			54033.8i			0.629405i	0.949190	+	0.314703i	$0.101905\pi$
$293$			54033.8i			0.629405i	−0.949190	+	0.314703i	$0.898095\pi$
$294$		−	64825.2i		−	0.749979i
$295$	195543.			2.24698
$296$			1236.51i			0.0141128i
$297$	14090.5	−	9467.59i	0.159740	−	0.107331i
$298$	121521.			1.36842
$299$		−	14550.5i		−	0.162756i
$300$	20533.7			0.228152
$301$	−21533.5			−0.237674
$302$	−115826.			−1.26997
$303$		−	20468.5i		−	0.222946i
$304$		−	87859.6i		−	0.950697i
$305$		−	152925.i		−	1.64391i
$306$	−70016.0			−0.747747
$307$			69862.2i			0.741251i	0.928782	+	0.370625i	$0.120857\pi$
$307$			69862.2i			0.741251i	−0.928782	+	0.370625i	$0.879143\pi$
$308$	−13274.9	−	19756.9i	−0.139936	−	0.208266i
$309$	−63445.5			−0.664483
$310$		−	72677.6i		−	0.756271i
$311$	−34406.8			−0.355732			−0.177866	−	0.984055i	$-0.556919\pi$
$311$	−34406.8			−0.355732			−0.177866	+	0.984055i	$0.556919\pi$
$312$	−851.752			−0.00874992
$313$	34145.2			0.348531			0.174266	−	0.984699i	$-0.444245\pi$
$313$	34145.2			0.348531			0.174266	+	0.984699i	$0.444245\pi$
$314$		−	94909.0i		−	0.962605i
$315$			10395.2i			0.104764i
$316$		−	147612.i		−	1.47825i
$317$	67080.7			0.667543			0.333771	−	0.942654i	$-0.391679\pi$
$317$	67080.7			0.667543			0.333771	+	0.942654i	$0.391679\pi$
$318$		−	108711.i		−	1.07503i
$319$	77754.6	+	115722.i	0.764091	+	1.13719i
$320$	−109371.			−1.06808
$321$			19518.8i			0.189428i
$322$	28685.5			0.276663
$323$	−152106.			−1.45795
$324$	−11080.6			−0.105553
$325$		−	9533.32i		−	0.0902563i
$326$			87439.4i			0.822757i
$327$		−	79699.9i		−	0.745354i
$328$	−12437.8			−0.115610
$329$			24016.2i			0.221877i
$330$	−58266.5	−	86717.7i	−0.535046	−	0.796305i
$331$	−22562.2			−0.205933			−0.102967	−	0.994685i	$-0.532833\pi$
$331$	−22562.2			−0.205933			−0.102967	+	0.994685i	$0.532833\pi$
$332$			179924.i			1.63235i
$333$	7468.32			0.0673495
$334$	76757.5			0.688062
$335$	103067.			0.918395
$336$		−	18033.7i		−	0.159737i
$337$		−	54658.6i		−	0.481281i	−0.970614	−	0.240641i	$-0.922642\pi$
$337$		−	54658.6i		−	0.481281i	0.970614	−	0.240641i	$-0.0773575\pi$
$338$			152022.i			1.33068i
$339$	37442.2			0.325808
$340$			209924.i			1.81595i
$341$	−43927.8	+	29515.6i	−0.377773	+	0.253830i
$342$	−49411.3			−0.422449
$343$		−	59979.9i		−	0.509820i
$344$	7437.89			0.0628540
$345$	61338.8			0.515344
$346$	−232493.			−1.94204
$347$		−	116149.i		−	0.964618i	−0.876001	−	0.482309i	$-0.839798\pi$
$347$		−	116149.i		−	0.964618i	0.876001	−	0.482309i	$-0.160202\pi$
$348$		−	91001.6i		−	0.751433i
$349$			131862.i			1.08260i	0.840829	+	0.541301i	$0.182068\pi$
$349$			131862.i			1.08260i	−0.840829	+	0.541301i	$0.817932\pi$
$350$	18794.4			0.153424
$351$			5144.45i			0.0417566i
$352$	96254.4	+	143255.i	0.776847	+	1.15618i
$353$	27814.5			0.223215			0.111607	−	0.993752i	$-0.464400\pi$
$353$	27814.5			0.223215			0.111607	+	0.993752i	$0.464400\pi$
$354$			190780.i			1.52239i
$355$	179440.			1.42385
$356$	−39286.9			−0.309990
$357$	−31220.7			−0.244966
$358$		−	98167.0i		−	0.765948i
$359$			75277.7i			0.584087i	0.956405	+	0.292044i	$0.0943352\pi$
$359$			75277.7i			0.584087i	−0.956405	+	0.292044i	$0.905665\pi$
$360$		−	3590.62i		−	0.0277054i
$361$	22977.5			0.176315
$362$			57933.2i			0.442089i
$363$	−28750.9	+	70434.9i	−0.218192	+	0.534533i
$364$	7213.23			0.0544411
$365$		−	106529.i		−	0.799617i
$366$	149199.			1.11379
$367$	133254.			0.989346			0.494673	−	0.869079i	$-0.335288\pi$
$367$	133254.			0.989346			0.494673	+	0.869079i	$0.335288\pi$
$368$	−106411.			−0.785762
$369$			75122.1i			0.551715i
$370$		−	45962.4i		−	0.335737i
$371$		−	48475.3i		−	0.352186i
$372$	34544.1			0.249625
$373$		−	125160.i		−	0.899600i	−0.893129	−	0.449800i	$-0.851495\pi$
$373$		−	125160.i		−	0.899600i	0.893129	−	0.449800i	$-0.148505\pi$
$374$	260445.	−	174996.i	1.86197	−	1.25108i
$375$	−56423.4			−0.401233
$376$		−	8295.46i		−	0.0586766i
$377$	−42249.9			−0.297265
$378$	−10142.0			−0.0709805
$379$	−138734.			−0.965841			−0.482920	−	0.875664i	$-0.660424\pi$
$379$	−138734.			−0.965841			−0.482920	+	0.875664i	$0.660424\pi$
$380$			148146.i			1.02594i
$381$			55897.1i			0.385069i
$382$		−	12397.1i		−	0.0849561i
$383$	121841.			0.830611			0.415305	−	0.909682i	$-0.363675\pi$
$383$	121841.			0.830611			0.415305	+	0.909682i	$0.363675\pi$
$384$			11878.1i			0.0805534i
$385$	−25981.5	−	38668.1i	−0.175284	−	0.260874i
$386$	−102598.			−0.688597
$387$		−	44923.7i		−	0.299953i
$388$	−23585.1			−0.156666
$389$	275759.			1.82234			0.911172	−	0.412026i	$-0.135179\pi$
$389$	275759.			1.82234			0.911172	+	0.412026i	$0.135179\pi$
$390$	31660.6			0.208156
$391$			184223.i			1.20501i
$392$			9984.46i			0.0649759i
$393$		−	75985.6i		−	0.491978i
$394$	−132218.			−0.851725
$395$		−	288906.i		−	1.85166i
$396$	41217.4	−	27694.4i	0.262839	−	0.176604i
$397$	−1004.21			−0.00637151			−0.00318576	−	0.999995i	$-0.501014\pi$
$397$	−1004.21			−0.00637151			−0.00318576	+	0.999995i	$0.501014\pi$
$398$		−	152013.i		−	0.959654i
$399$	−22032.9			−0.138397
$400$	−69719.2			−0.435745
$401$	−127748.			−0.794447			−0.397224	−	0.917722i	$-0.630026\pi$
$401$	−127748.			−0.794447			−0.397224	+	0.917722i	$0.630026\pi$
$402$			100556.i			0.622237i
$403$		−	16038.0i		−	0.0987508i
$404$		−	59874.0i		−	0.366839i
$405$	−21686.8			−0.132217
$406$		−	83293.2i		−	0.505310i
$407$	−27780.6	+	18666.1i	−0.167708	+	0.112684i
$408$	10784.0			0.0647825
$409$		−	147696.i		−	0.882920i	−0.897281	−	0.441460i	$-0.854461\pi$
$409$		−	147696.i		−	0.882920i	0.897281	−	0.441460i	$-0.145539\pi$
$410$	462325.			2.75030
$411$	−130651.			−0.773443
$412$	−185590.			−1.09335
$413$			85070.1i			0.498743i
$414$			59844.5i			0.349159i
$415$			352145.i			2.04468i
$416$	−52302.3			−0.302227
$417$		−	23145.6i		−	0.133106i
$418$	183800.	−	123497.i	1.05194	−	0.706812i
$419$	−319997.			−1.82271			−0.911355	−	0.411621i	$-0.864963\pi$
$419$	−319997.			−1.82271			−0.911355	+	0.411621i	$0.864963\pi$
$420$			30407.9i			0.172381i
$421$	−244090.			−1.37716			−0.688582	−	0.725159i	$-0.741766\pi$
$421$	−244090.			−1.37716			−0.688582	+	0.725159i	$0.741766\pi$
$422$	−41701.0			−0.234165
$423$	−50103.3			−0.280018
$424$			16743.9i			0.0931375i
$425$			120701.i			0.668239i
$426$			175069.i			0.964693i
$427$	66529.2			0.364886
$428$			57096.1i			0.311687i
$429$	−12857.9	−	19136.3i	−0.0698642	−	0.103978i
$430$	−276475.			−1.49527
$431$			144764.i			0.779303i	0.920962	+	0.389651i	$0.127404\pi$
$431$			144764.i			0.779303i	−0.920962	+	0.389651i	$0.872596\pi$
$432$	37622.4			0.201595
$433$	−98589.6			−0.525842			−0.262921	−	0.964817i	$-0.584686\pi$
$433$	−98589.6			−0.525842			−0.262921	+	0.964817i	$0.584686\pi$
$434$	31618.0			0.167863
$435$		−	178108.i		−	0.941249i
$436$		−	233137.i		−	1.22642i
$437$			130009.i			0.680785i
$438$	103934.			0.541761
$439$		−	241475.i		−	1.25298i	−0.779430	−	0.626490i	$-0.784491\pi$
$439$		−	241475.i		−	1.25298i	0.779430	−	0.626490i	$-0.215509\pi$
$440$	8974.29	+	13356.4i	0.0463548	+	0.0689895i
$441$	60304.6			0.310080
$442$			95088.3i			0.486724i
$443$	−106301.			−0.541666			−0.270833	−	0.962626i	$-0.587299\pi$
$443$	−106301.			−0.541666			−0.270833	+	0.962626i	$0.587299\pi$
$444$	21846.2			0.110818
$445$	−76892.1			−0.388295
$446$			76270.3i			0.383430i
$447$			113047.i			0.565774i
$448$		−	47581.4i		−	0.237072i
$449$	−265627.			−1.31759			−0.658794	−	0.752323i	$-0.728933\pi$
$449$	−265627.			−1.31759			−0.658794	+	0.752323i	$0.728933\pi$
$450$			39209.4i			0.193627i
$451$	−187758.	−	279439.i	−0.923091	−	1.37383i
$452$	109525.			0.536089
$453$		−	107749.i		−	0.525071i
$454$	88589.2			0.429803
$455$	14117.7			0.0681932
$456$	7610.40			0.0365997
$457$			116157.i			0.556177i	0.960556	+	0.278088i	$0.0897008\pi$
$457$			116157.i			0.556177i	−0.960556	+	0.278088i	$0.910299\pi$
$458$		−	554312.i		−	2.64255i
$459$		−	65133.4i		−	0.309157i
$460$	179427.			0.847954
$461$		−	121516.i		−	0.571784i	−0.958262	−	0.285892i	$-0.907710\pi$
$461$		−	121516.i		−	0.571784i	0.958262	−	0.285892i	$-0.0922899\pi$
$462$	37726.1	−	25348.5i	0.176749	−	0.118760i
$463$	370675.			1.72914			0.864572	−	0.502509i	$-0.167590\pi$
$463$	370675.			1.72914			0.864572	+	0.502509i	$0.167590\pi$
$464$			308983.i			1.43515i
$465$	67609.5			0.312681
$466$	−246139.			−1.13347
$467$	17468.5			0.0800980			0.0400490	−	0.999198i	$-0.487249\pi$
$467$	17468.5			0.0800980			0.0400490	+	0.999198i	$0.487249\pi$
$468$			15048.4i			0.0687068i
$469$			44838.7i			0.203848i
$470$			308351.i			1.39589i
$471$	88290.6			0.397990
$472$		−	29384.1i		−	0.131895i
$473$	112281.	+	167107.i	0.501861	+	0.746916i
$474$	281867.			1.25455
$475$			85180.2i			0.377530i
$476$	−91326.1			−0.403071
$477$	101130.			0.444473
$478$	321508.			1.40714
$479$			37311.4i			0.162619i	0.996689	+	0.0813094i	$0.0259102\pi$
$479$			37311.4i			0.162619i	−0.996689	+	0.0813094i	$0.974090\pi$
$480$		−	220484.i		−	0.956962i
$481$		−	10142.7i		−	0.0438392i
$482$	482127.			2.07523
$483$			26685.1i			0.114387i
$484$	−84101.6	+	206035.i	−0.359016	+	0.879528i
$485$	−46160.6			−0.196240
$486$		−	21158.5i		−	0.0895802i
$487$	177099.			0.746721			0.373360	−	0.927686i	$-0.378205\pi$
$487$	177099.			0.746721			0.373360	+	0.927686i	$0.378205\pi$
$488$	−22979.9			−0.0964958
$489$	−81341.8			−0.340170
$490$		−	371134.i		−	1.54575i
$491$			127053.i			0.527013i	0.964658	+	0.263507i	$0.0848791\pi$
$491$			127053.i			0.527013i	−0.964658	+	0.263507i	$0.915121\pi$
$492$			219746.i			0.907800i
$493$	534923.			2.20088
$494$			67105.2i			0.274981i
$495$	80670.4	−	54203.3i	0.329233	−	0.221215i
$496$	−117289.			−0.476755
$497$			78064.5i			0.316039i
$498$	−343566.			−1.38533
$499$	−166524.			−0.668767			−0.334383	−	0.942437i	$-0.608528\pi$
$499$	−166524.			−0.668767			−0.334383	+	0.942437i	$0.608528\pi$
$500$	−165049.			−0.660194
$501$			71404.8i			0.284480i
$502$			524082.i			2.07966i
$503$		−	163251.i		−	0.645236i	−0.946529	−	0.322618i	$-0.895437\pi$
$503$		−	163251.i		−	0.645236i	0.946529	−	0.322618i	$-0.104563\pi$
$504$	1562.08			0.00614954
$505$		−	117185.i		−	0.459504i
$506$	−149573.	−	222609.i	−0.584189	−	0.869444i
$507$	−141421.			−0.550170
$508$			163509.i			0.633599i
$509$	−206271.			−0.796164			−0.398082	−	0.917350i	$-0.630324\pi$
$509$	−206271.			−0.796164			−0.398082	+	0.917350i	$0.630324\pi$
$510$	−400852.			−1.54114
$511$	46344.8			0.177484
$512$			363317.i			1.38594i
$513$		−	45965.7i		−	0.174662i
$514$		−	136789.i		−	0.517756i
$515$	−363235.			−1.36953
$516$		−	131410.i		−	0.493547i
$517$	186374.	−	125226.i	0.697274	−	0.468506i
$518$	19995.7			0.0745207
$519$		−	216280.i		−	0.802938i
$520$	−4876.40			−0.0180340
$521$	442001.			1.62835			0.814174	−	0.580620i	$-0.197190\pi$
$521$	442001.			1.62835			0.814174	+	0.580620i	$0.197190\pi$
$522$	173769.			0.637721
$523$			373577.i			1.36577i	0.730527	+	0.682884i	$0.239274\pi$
$523$			373577.i			1.36577i	−0.730527	+	0.682884i	$0.760726\pi$
$524$		−	222271.i		−	0.809508i
$525$			17483.8i			0.0634332i
$526$	−415754.			−1.50268
$527$			203056.i			0.731130i
$528$	−139948.	+	94032.3i	−0.501993	+	0.337294i
$529$	−122381.			−0.437323
$530$		−	622389.i		−	2.21569i
$531$	−177476.			−0.629433
$532$	−64450.2			−0.227720
$533$	102023.			0.359123
$534$		−	75018.9i		−	0.263080i
$535$			111748.i			0.390421i
$536$		−	15487.8i		−	0.0539087i
$537$	91321.4			0.316682
$538$			640781.i			2.21383i
$539$	−224321.	+	150723.i	−0.772132	+	0.518804i
$540$	−63437.9			−0.217551
$541$			339954.i			1.16152i	0.814075	+	0.580759i	$0.197244\pi$
$541$			339954.i			1.16152i	−0.814075	+	0.580759i	$0.802756\pi$
$542$	−100634.			−0.342568
$543$	−53893.2			−0.182782
$544$	662194.			2.23763
$545$		−	456294.i		−	1.53621i
$546$			13773.8i			0.0462027i
$547$		−	568245.i		−	1.89916i	−0.313531	−	0.949578i	$-0.601512\pi$
$547$		−	568245.i		−	1.89916i	0.313531	−	0.949578i	$-0.398488\pi$
$548$	−382177.			−1.27263
$549$			138795.i			0.460500i
$550$	−97998.6	−	145851.i	−0.323962	−	0.482151i
$551$	377503.			1.24342
$552$		−	9217.33i		−	0.0302501i
$553$	125687.			0.410998
$554$	461172.			1.50260
$555$	42757.2			0.138811
$556$		−	67705.2i		−	0.219014i
$557$		−	211216.i		−	0.680795i	−0.940282	−	0.340398i	$-0.889438\pi$
$557$		−	211216.i		−	0.680795i	0.940282	−	0.340398i	$-0.110562\pi$
$558$			65962.4i			0.211850i
$559$	−61010.6			−0.195246
$560$		−	103246.i		−	0.329227i
$561$	162792.	+	242283.i	0.517259	+	0.769834i
$562$	−41865.4			−0.132551
$563$		−	595910.i		−	1.88003i	−0.341140	−	0.940013i	$-0.610813\pi$
$563$		−	595910.i		−	1.88003i	0.341140	−	0.940013i	$-0.389187\pi$
$564$	−146561.			−0.460745
$565$	214362.			0.671508
$566$	−582139.			−1.81716
$567$		−	9434.73i		−	0.0293470i
$568$		−	26964.3i		−	0.0835781i
$569$			15875.4i			0.0490342i	0.999699	+	0.0245171i	$0.00780482\pi$
$569$			15875.4i			0.0490342i	−0.999699	+	0.0245171i	$0.992195\pi$
$570$	−282887.			−0.870690
$571$		−	413970.i		−	1.26969i	−0.772641	−	0.634843i	$-0.781065\pi$
$571$		−	413970.i		−	1.26969i	0.772641	−	0.634843i	$-0.218935\pi$
$572$	−37611.6	−	55977.1i	−0.114955	−	0.171087i
$573$	11532.6			0.0351252
$574$			201132.i			0.610460i
$575$	103166.			0.312033
$576$	99265.5			0.299194
$577$	−102654.			−0.308337			−0.154169	−	0.988045i	$-0.549270\pi$
$577$	−102654.			−0.308337			−0.154169	+	0.988045i	$0.549270\pi$
$578$		−	737384.i		−	2.20718i
$579$		−	95443.6i		−	0.284701i
$580$		−	520997.i		−	1.54874i
$581$	−153199.			−0.453841
$582$		−	45036.0i		−	0.132958i
$583$	−376184.	+	252762.i	−1.10679	+	0.743661i
$584$	−16008.0			−0.0469366
$585$			29452.7i			0.0860625i
$586$	−301815.			−0.878912
$587$	127414.			0.369779			0.184889	−	0.982759i	$-0.440807\pi$
$587$	127414.			0.369779			0.184889	+	0.982759i	$0.440807\pi$
$588$	176402.			0.510209
$589$			143300.i			0.413061i
$590$			1.09224e6i			3.13772i
$591$		−	122998.i		−	0.352147i
$592$	−74175.5			−0.211649
$593$			477628.i			1.35825i	0.734022	+	0.679126i	$0.237641\pi$
$593$			477628.i			1.35825i	−0.734022	+	0.679126i	$0.762359\pi$
$594$	52882.8	+	78705.1i	0.149879	+	0.223064i
$595$	−178743.			−0.504888
$596$			330682.i			0.930933i
$597$	141412.			0.396770
$598$	81274.4			0.227275
$599$	301738.			0.840961			0.420480	−	0.907302i	$-0.361862\pi$
$599$	301738.			0.840961			0.420480	+	0.907302i	$0.361862\pi$
$600$		−	6039.08i		−	0.0167752i
$601$			294665.i			0.815793i	0.913028	+	0.407896i	$0.133738\pi$
$601$			294665.i			0.815793i	−0.913028	+	0.407896i	$0.866262\pi$
$602$		−	120279.i		−	0.331891i
$603$	−93543.7			−0.257264
$604$		−	315186.i		−	0.863959i
$605$	−164603.	+	403250.i	−0.449705	+	1.10170i
$606$	114330.			0.311326
$607$			308433.i			0.837113i	0.908191	+	0.418556i	$0.137464\pi$
$607$			308433.i			0.837113i	−0.908191	+	0.418556i	$0.862536\pi$
$608$	467321.			1.26418
$609$	77484.8			0.208921
$610$	854189.			2.29559
$611$			68044.9i			0.182269i
$612$		−	190527.i		−	0.508691i
$613$			222563.i			0.592287i	0.955143	+	0.296144i	$0.0957007\pi$
$613$			222563.i			0.592287i	−0.955143	+	0.296144i	$0.904299\pi$
$614$	−390227.			−1.03510
$615$			430085.i			1.13711i
$616$	−5810.62	+	3904.22i	−0.0153130	+	0.0102890i
$617$	478612.			1.25723			0.628613	−	0.777718i	$-0.283623\pi$
$617$	478612.			1.25723			0.628613	+	0.777718i	$0.283623\pi$
$618$		−	354386.i		−	0.927896i
$619$	−110719.			−0.288963			−0.144482	−	0.989507i	$-0.546151\pi$
$619$	−110719.			−0.288963			−0.144482	+	0.989507i	$0.546151\pi$
$620$	197770.			0.514490
$621$	−55671.2			−0.144360
$622$		−	192185.i		−	0.496750i
$623$		−	33451.5i		−	0.0861866i
$624$		−	51094.8i		−	0.131222i
$625$	−485524.			−1.24294
$626$			190724.i			0.486695i
$627$	114885.	+	170983.i	0.292232	+	0.434928i
$628$	258266.			0.654859
$629$			128416.i			0.324576i
$630$	−58064.3			−0.146295
$631$	−77313.0			−0.194175			−0.0970876	−	0.995276i	$-0.530953\pi$
$631$	−77313.0			−0.194175			−0.0970876	+	0.995276i	$0.530953\pi$
$632$	−43413.6			−0.108690
$633$		−	38793.0i		−	0.0968157i
$634$			374690.i			0.932168i
$635$			320019.i			0.793648i
$636$	295825.			0.731342
$637$		−	81899.3i		−	0.201837i
$638$	−646383.	+	434312.i	−1.58799	+	1.06699i
$639$	−162860.			−0.398853
$640$			68003.7i			0.166025i
$641$	382285.			0.930404			0.465202	−	0.885205i	$-0.345982\pi$
$641$	382285.			0.930404			0.465202	+	0.885205i	$0.345982\pi$
$642$	−109026.			−0.264520
$643$	−216575.			−0.523825			−0.261912	−	0.965092i	$-0.584353\pi$
$643$	−216575.			−0.523825			−0.261912	+	0.965092i	$0.584353\pi$
$644$			78058.8i			0.188213i
$645$		−	257195.i		−	0.618219i
$646$		−	849613.i		−	2.03590i
$647$	−151109.			−0.360979			−0.180489	−	0.983577i	$-0.557768\pi$
$647$	−151109.			−0.360979			−0.180489	+	0.983577i	$0.557768\pi$
$648$			3258.86i			0.00776096i
$649$	660172.	−	443577.i	1.56736	−	1.05312i
$650$	53250.0			0.126035
$651$			29413.1i			0.0694032i
$652$	−237939.			−0.559721
$653$	−191077.			−0.448107			−0.224053	−	0.974577i	$-0.571929\pi$
$653$	−191077.			−0.448107			−0.224053	+	0.974577i	$0.571929\pi$
$654$	445177.			1.04082
$655$		−	435028.i		−	1.01399i
$656$		−	746114.i		−	1.73380i
$657$			96685.9i			0.223992i
$658$	−134147.			−0.309833
$659$			452930.i			1.04294i	0.853269	+	0.521471i	$0.174616\pi$
$659$			452930.i			1.04294i	−0.853269	+	0.521471i	$0.825384\pi$
$660$	235976.	−	158554.i	0.541725	−	0.363991i
$661$	307053.			0.702767			0.351383	−	0.936232i	$-0.385711\pi$
$661$	307053.			0.702767			0.351383	+	0.936232i	$0.385711\pi$
$662$		−	126025.i		−	0.287568i
$663$	−88457.3			−0.201236
$664$	52916.6			0.120020
$665$	−126142.			−0.285243
$666$			41715.6i			0.0940480i
$667$		−	457212.i		−	1.02770i
$668$			208872.i			0.468088i
$669$	−70951.6			−0.158529
$670$			575697.i			1.28246i
$671$	−346900.	−	516289.i	−0.770476	−	1.14669i
$672$	95920.4			0.212409
$673$		−	216281.i		−	0.477517i	−0.971079	−	0.238758i	$-0.923260\pi$
$673$		−	216281.i		−	0.477517i	0.971079	−	0.238758i	$-0.0767404\pi$
$674$	305305.			0.672069
$675$	−36475.1			−0.0800551
$676$	−413681.			−0.905257
$677$			23957.4i			0.0522712i	0.999658	+	0.0261356i	$0.00832017\pi$
$677$			23957.4i			0.0522712i	−0.999658	+	0.0261356i	$0.991680\pi$
$678$			209140.i			0.454964i
$679$		−	20081.9i		−	0.0435578i
$680$	61739.7			0.133520
$681$			82411.5i			0.177702i
$682$	−164864.	−	245366.i	−0.354452	−	0.527529i
$683$	547099.			1.17280			0.586401	−	0.810021i	$-0.300544\pi$
$683$	547099.			1.17280			0.586401	+	0.810021i	$0.300544\pi$
$684$		−	134458.i		−	0.287391i
$685$	−747994.			−1.59411
$686$	335028.			0.711922
$687$	515657.			1.09257
$688$			446183.i			0.942619i
$689$		−	137345.i		−	0.289316i
$690$			342618.i			0.719635i
$691$	−299138.			−0.626493			−0.313246	−	0.949672i	$-0.601417\pi$
$691$	−299138.			−0.626493			−0.313246	+	0.949672i	$0.601417\pi$
$692$		−	632658.i		−	1.32117i
$693$	23580.9	+	35095.2i	0.0491013	+	0.0730772i
$694$	648768.			1.34701
$695$		−	132512.i		−	0.274338i
$696$	−26764.1			−0.0552502
$697$	−1.29170e6			−2.65887
$698$	−736538.			−1.51176
$699$		−	228975.i		−	0.468633i
$700$			51143.2i			0.104374i
$701$		−	876409.i		−	1.78349i	−0.452538	−	0.891745i	$-0.649481\pi$
$701$		−	876409.i		−	1.78349i	0.452538	−	0.891745i	$-0.350519\pi$
$702$	−28735.2			−0.0583096
$703$			90624.8i			0.183373i
$704$	−369247.	+	248101.i	−0.745026	+	0.500591i
$705$	−286849.			−0.577131
$706$			155363.i			0.311701i
$707$	50980.7			0.101992
$708$	−519148.			−1.03568
$709$	266386.			0.529931			0.264965	−	0.964258i	$-0.414639\pi$
$709$	266386.			0.529931			0.264965	+	0.964258i	$0.414639\pi$
$710$			1.00229e6i			1.98828i
$711$			262211.i			0.518695i
$712$			11554.5i			0.0227925i
$713$	173557.			0.341400
$714$		−	174388.i		−	0.342075i
$715$	−73613.2	−	109558.i	−0.143994	−	0.214305i
$716$	267131.			0.521073
$717$			299088.i			0.581782i
$718$	−420476.			−0.815629
$719$	−747175.			−1.44532			−0.722661	−	0.691203i	$-0.757081\pi$
$719$	−747175.			−1.44532			−0.722661	+	0.691203i	$0.757081\pi$
$720$	215394.			0.415498
$721$		−	158023.i		−	0.303984i
$722$			128345.i			0.246209i
$723$			448506.i			0.858008i
$724$	−157647.			−0.300753
$725$		−	299560.i		−	0.569912i
$726$	−393426.	−	160593.i	−0.746431	−	0.304687i
$727$	−685597.			−1.29718			−0.648590	−	0.761138i	$-0.724641\pi$
$727$	−685597.			−1.29718			−0.648590	+	0.761138i	$0.724641\pi$
$728$		−	2121.45i		−	0.00400286i
$729$	19683.0			0.0370370
$730$	595035.			1.11660
$731$	772450.			1.44556
$732$			406001.i			0.757713i
$733$			64133.6i			0.119365i	0.998217	+	0.0596826i	$0.0190089\pi$
$733$			64133.6i			0.119365i	−0.998217	+	0.0596826i	$0.980991\pi$
$734$			744313.i			1.38154i
$735$	345253.			0.639090
$736$		−	565995.i		−	1.04486i
$737$	347963.	−	233800.i	0.640616	−	0.430437i
$738$	−419607.			−0.770425
$739$			350880.i			0.642495i	0.946995	+	0.321248i	$0.104102\pi$
$739$			350880.i			0.642495i	−0.946995	+	0.321248i	$0.895898\pi$
$740$	125073.			0.228401
$741$	−62425.7			−0.113691
$742$	270767.			0.491799
$743$		−	214737.i		−	0.388981i	−0.980904	−	0.194491i	$-0.937695\pi$
$743$		−	214737.i		−	0.388981i	0.980904	−	0.194491i	$-0.0623054\pi$
$744$		−	10159.6i		−	0.0183540i
$745$			647209.i			1.16609i
$746$	699105.			1.25622
$747$		−	319608.i		−	0.572765i
$748$	476197.	+	708721.i	0.851106	+	1.26669i
$749$	−48615.4			−0.0866583
$750$		−	315162.i		−	0.560288i
$751$	656340.			1.16372			0.581861	−	0.813288i	$-0.302325\pi$
$751$	656340.			1.16372			0.581861	+	0.813288i	$0.302325\pi$
$752$	497627.			0.879970
$753$	−487535.			−0.859837
$754$		−	235994.i		−	0.415105i
$755$		−	616880.i		−	1.08220i
$756$		−	27598.3i		−	0.0482879i
$757$	667153.			1.16422			0.582108	−	0.813111i	$-0.302228\pi$
$757$	667153.			1.16422			0.582108	+	0.813111i	$0.302228\pi$
$758$		−	774924.i		−	1.34872i
$759$	207085.	−	139143.i	0.359473	−	0.241533i
$760$	43570.7			0.0754340
$761$			125398.i			0.216532i	0.994122	+	0.108266i	$0.0345298\pi$
$761$			125398.i			0.216532i	−0.994122	+	0.108266i	$0.965470\pi$
$762$	−312222.			−0.537717
$763$	198508.			0.340980
$764$	33735.0			0.0577955
$765$		−	372898.i		−	0.637188i
$766$			680566.i			1.15988i
$767$			241028.i			0.409711i
$768$	−372006.			−0.630706
$769$		−	232947.i		−	0.393916i	−0.980412	−	0.196958i	$-0.936894\pi$
$769$		−	232947.i		−	0.393916i	0.980412	−	0.196958i	$-0.0631063\pi$
$770$	215987.	−	145124.i	0.364289	−	0.244770i
$771$	127250.			0.214067
$772$		−	279190.i		−	0.468452i
$773$	−283047.			−0.473697			−0.236848	−	0.971547i	$-0.576114\pi$
$773$	−283047.			−0.473697			−0.236848	+	0.971547i	$0.576114\pi$
$774$	250929.			0.418860
$775$	113713.			0.189324
$776$			6936.51i			0.0115191i
$777$			18601.3i			0.0308107i
$778$			1.54030e6i			2.54475i
$779$	−911574.			−1.50216
$780$			86154.5i			0.141608i
$781$	605806.	−	407047.i	0.993188	−	0.667333i
$782$	−1.02901e6			−1.68269
$783$			161651.i			0.263666i
$784$	−598947.			−0.974442
$785$	505476.			0.820279
$786$	424430.			0.687007
$787$			299296.i			0.483227i	0.970373	+	0.241613i	$0.0776766\pi$
$787$			299296.i			0.483227i	−0.970373	+	0.241613i	$0.922323\pi$
$788$		−	359792.i		−	0.579427i
$789$		−	386762.i		−	0.621283i
$790$	1.61373e6			2.58569
$791$			93257.0i			0.149049i
$792$	−8145.08	−	12122.3i	−0.0129851	−	0.0193256i
$793$	188497.			0.299749
$794$		−	5609.17i		−	0.00889729i
$795$	578986.			0.916082
$796$	413657.			0.652851
$797$	−768258.			−1.20946			−0.604729	−	0.796432i	$-0.706718\pi$
$797$	−768258.			−1.20946			−0.604729	+	0.796432i	$0.706718\pi$
$798$		−	123069.i		−	0.193260i
$799$		−	861511.i		−	1.34948i
$800$		−	370833.i		−	0.579426i
$801$	69787.5			0.108771
$802$		−	713557.i		−	1.10938i
$803$	−241653.	−	359651.i	−0.374767	−	0.557764i
$804$	−273632.			−0.423307
$805$			152776.i			0.235757i
$806$	89583.1			0.137897
$807$	−596096.			−0.915312
$808$	−17609.3			−0.0269723
$809$			982802.i			1.50165i	0.660500	+	0.750826i	$0.270344\pi$
$809$			982802.i			1.50165i	−0.660500	+	0.750826i	$0.729656\pi$
$810$		−	121135.i		−	0.184629i
$811$			322384.i			0.490153i	0.969504	+	0.245077i	$0.0788131\pi$
$811$			322384.i			0.490153i	−0.969504	+	0.245077i	$0.921187\pi$
$812$	226657.			0.343761
$813$		−	93616.4i		−	0.141635i
$814$	−104262.	−	155173.i	−0.157355	−	0.234190i
$815$	−465694.			−0.701108
$816$			646907.i			0.971542i
$817$	545129.			0.816687
$818$	824979.			1.23292
$819$	−12813.2			−0.0191026
$820$			1.25808e6i			1.87102i
$821$			862907.i			1.28020i	0.768292	+	0.640100i	$0.221107\pi$
$821$			862907.i			1.28020i	−0.768292	+	0.640100i	$0.778893\pi$
$822$		−	729771.i		−	1.08005i
$823$	−457793.			−0.675879			−0.337940	−	0.941168i	$-0.609730\pi$
$823$	−457793.			−0.675879			−0.337940	+	0.941168i	$0.609730\pi$
$824$			54583.0i			0.0803901i
$825$	135680.	−	91164.7i	0.199346	−	0.133943i
$826$	−475173.			−0.696453
$827$			1.26608e6i			1.85119i	0.378516	+	0.925595i	$0.376435\pi$
$827$			1.26608e6i			1.85119i	−0.378516	+	0.925595i	$0.623565\pi$
$828$	−162848.			−0.237532
$829$	336361.			0.489437			0.244718	−	0.969594i	$-0.421305\pi$
$829$	336361.			0.489437			0.244718	+	0.969594i	$0.421305\pi$
$830$	−1.96697e6			−2.85523
$831$			429013.i			0.621252i
$832$		−	134812.i		−	0.194752i
$833$			1.03692e6i			1.49436i
$834$	129284.			0.185871
$835$			408803.i			0.586329i
$836$	336059.	+	500155.i	0.480843	+	0.715636i
$837$	−61362.5			−0.0875895
$838$		−	1.78740e6i		−	2.54526i
$839$	673978.			0.957463			0.478732	−	0.877961i	$-0.341097\pi$
$839$	673978.			0.957463			0.478732	+	0.877961i	$0.341097\pi$
$840$	8943.14			0.0126745
$841$	−620313.			−0.877039
$842$		−	1.36341e6i		−	1.92309i
$843$		−	38946.0i		−	0.0548034i
$844$		−	113476.i		−	0.159302i
$845$	−809654.			−1.13393
$846$		−	279860.i		−	0.391021i
$847$	−175432.	−	71609.7i	−0.244535	−	0.0998171i
$848$	−1.00443e6			−1.39678
$849$		−	541544.i		−	0.751309i
$850$	−674193.			−0.933140
$851$	109760.			0.151560
$852$	−476395.			−0.656279
$853$			293271.i			0.403062i	0.979482	+	0.201531i	$0.0645916\pi$
$853$			293271.i			0.403062i	−0.979482	+	0.201531i	$0.935408\pi$
$854$			371610.i			0.509532i
$855$		−	263160.i		−	0.359988i
$856$	16792.3			0.0229172
$857$			404960.i			0.551379i	0.961247	+	0.275690i	$0.0889062\pi$
$857$			404960.i			0.551379i	−0.961247	+	0.275690i	$0.911094\pi$
$858$	106889.	−	71819.8i	0.145197	−	0.0975595i
$859$	−354890.			−0.480958			−0.240479	−	0.970654i	$-0.577305\pi$
$859$	−354890.			−0.480958			−0.240479	+	0.970654i	$0.577305\pi$
$860$		−	752341.i		−	1.01723i
$861$	−187106.			−0.252396
$862$	−808604.			−1.08823
$863$	1.17452e6			1.57703			0.788514	−	0.615017i	$-0.210851\pi$
$863$	1.17452e6			1.57703			0.788514	+	0.615017i	$0.210851\pi$
$864$			200112.i			0.268068i
$865$		−	1.23824e6i		−	1.65490i
$866$		−	550689.i		−	0.734294i
$867$	685962.			0.912561
$868$			86038.7i			0.114197i
$869$	−655362.	−	975371.i	−0.867845	−	1.29161i
$870$	994851.			1.31438
$871$			127041.i			0.167459i
$872$	−68566.8			−0.0901739
$873$	41895.4			0.0549716
$874$	−726187.			−0.950660
$875$		−	140533.i		−	0.183554i
$876$			282824.i			0.368559i
$877$		−	199151.i		−	0.258931i	−0.991584	−	0.129466i	$-0.958674\pi$
$877$		−	199151.i		−	0.258931i	0.991584	−	0.129466i	$-0.0413262\pi$
$878$	1.34880e6			1.74968
$879$		−	280768.i		−	0.363387i
$880$	−801220.	+	538348.i	−1.03463	+	0.695181i
$881$	538123.			0.693314			0.346657	−	0.937992i	$-0.387317\pi$
$881$	538123.			0.693314			0.346657	+	0.937992i	$0.387317\pi$
$882$			336842.i			0.433001i
$883$	1.41933e6			1.82038			0.910192	−	0.414187i	$-0.135934\pi$
$883$	1.41933e6			1.82038			0.910192	+	0.414187i	$0.135934\pi$
$884$	−258754.			−0.331117
$885$	−1.01607e6			−1.29729
$886$		−	593765.i		−	0.756392i
$887$			1.08483e6i			1.37884i	0.724360	+	0.689422i	$0.242135\pi$
$887$			1.08483e6i			1.37884i	−0.724360	+	0.689422i	$0.757865\pi$
$888$		−	6425.09i		−	0.00814804i
$889$	−139222.			−0.176159
$890$		−	429494.i		−	0.542222i
$891$	−73216.6	+	49195.0i	−0.0922262	+	0.0619678i
$892$	−207546.			−0.260847
$893$		−	607981.i		−	0.762408i
$894$	−631442.			−0.790057
$895$	522828.			0.652699
$896$	−29584.6			−0.0368511
$897$			75606.7i			0.0939671i
$898$		−	1.48371e6i		−	1.83990i
$899$		−	503953.i		−	0.623549i
$900$	−106696.			−0.131724
$901$			1.73891e6i			2.14204i
$902$	1.56085e6	−	1.04875e6i	1.91844	−	1.28902i
$903$	111891.			0.137221
$904$		−	32212.0i		−	0.0394167i
$905$	−308546.			−0.376724
$906$	601852.			0.733218
$907$	−396615.			−0.482119			−0.241060	−	0.970510i	$-0.577495\pi$
$907$	−396615.			−0.482119			−0.241060	+	0.970510i	$0.577495\pi$
$908$			241068.i			0.292394i
$909$			106357.i			0.128718i
$910$			78856.8i			0.0952261i
$911$	−5038.05			−0.00607052			−0.00303526	−	0.999995i	$-0.500966\pi$
$911$	−5038.05			−0.00607052			−0.00303526	+	0.999995i	$0.500966\pi$
$912$			456532.i			0.548885i
$913$	798817.	+	1.18887e6i	0.958310	+	1.42625i
$914$	−648814.			−0.776654
$915$			794622.i			0.949114i
$916$	1.50839e6			1.79772
$917$	189257.			0.225067
$918$	363814.			0.431712
$919$		−	1.61726e6i		−	1.91491i	−0.288574	−	0.957457i	$-0.593181\pi$
$919$		−	1.61726e6i		−	1.91491i	0.288574	−	0.957457i	$-0.406819\pi$
$920$		−	52770.5i		−	0.0623470i
$921$		−	363014.i		−	0.427961i
$922$	678749.			0.798449
$923$			221179.i			0.259622i
$924$	68978.3	+	102660.i	0.0807920	+	0.120242i
$925$	71913.5			0.0840479
$926$			2.07047e6i			2.41461i
$927$	329673.			0.383640
$928$	−1.64346e6			−1.90838
$929$	−433742.			−0.502575			−0.251287	−	0.967913i	$-0.580854\pi$
$929$	−433742.			−0.502575			−0.251287	+	0.967913i	$0.580854\pi$
$930$			377644.i			0.436633i
$931$			731770.i			0.844258i
$932$		−	669793.i		−	0.771096i
$933$	178783.			0.205382
$934$			97573.1i			0.111850i
$935$	932010.	+	1.38710e6i	1.06610	+	1.58667i
$936$	4425.83			0.00505177
$937$		−	428901.i		−	0.488515i	−0.969710	−	0.244257i	$-0.921456\pi$
$937$		−	428901.i		−	0.488515i	0.969710	−	0.244257i	$-0.0785442\pi$
$938$	−250454.			−0.284657
$939$	−177424.			−0.201224
$940$	−839084.			−0.949619
$941$		−	1.50772e6i		−	1.70272i	−0.524583	−	0.851359i	$-0.675779\pi$
$941$		−	1.50772e6i		−	1.70272i	0.524583	−	0.851359i	$-0.324221\pi$
$942$			493162.i			0.555760i
$943$			1.10405e6i			1.24155i
$944$	1.76269e6			1.97803
$945$		−	54015.2i		−	0.0604857i
$946$	−933403.	+	627163.i	−1.04301	+	0.700807i
$947$	130017.			0.144977			0.0724887	−	0.997369i	$-0.476906\pi$
$947$	130017.			0.144977			0.0724887	+	0.997369i	$0.476906\pi$
$948$			767015.i			0.853468i
$949$	131308.			0.145801
$950$	−475788.			−0.527189
$951$	−348561.			−0.385406
$952$			26859.5i			0.0296363i
$953$		−	1.78038e6i		−	1.96032i	−0.198209	−	0.980160i	$-0.563512\pi$
$953$		−	1.78038e6i		−	1.96032i	0.198209	−	0.980160i	$-0.436488\pi$
$954$			564881.i			0.620669i
$955$	66025.9			0.0723949
$956$			874886.i			0.957273i
$957$	−404025.	−	601308.i	−0.441148	−	0.656558i
$958$	−208409.			−0.227084
$959$		−	325411.i		−	0.353830i
$960$	568310.			0.616655
$961$	−732221.			−0.792858
$962$	56653.6			0.0612178
$963$		−	101423.i		−	0.109366i
$964$			1.31196e6i			1.41178i
$965$		−	546428.i		−	0.586785i
$966$	−149054.			−0.159731
$967$			445739.i			0.476680i	0.971182	+	0.238340i	$0.0766033\pi$
$967$			445739.i			0.476680i	−0.971182	+	0.238340i	$0.923397\pi$
$968$	60596.0	+	24734.8i	0.0646686	+	0.0263971i
$969$	790366.			0.841745
$970$		−	257838.i		−	0.274033i
$971$	1.44428e6			1.53183			0.765917	−	0.642939i	$-0.222285\pi$
$971$	1.44428e6			1.53183			0.765917	+	0.642939i	$0.222285\pi$
$972$	57576.3			0.0609413
$973$	57648.7			0.0608925
$974$			989216.i			1.04273i
$975$			49536.6i			0.0521095i
$976$		−	1.37852e6i		−	1.44715i
$977$	−1.79884e6			−1.88453			−0.942265	−	0.334868i	$-0.891308\pi$
$977$	−1.79884e6			−1.88453			−0.942265	+	0.334868i	$0.891308\pi$
$978$		−	454348.i		−	0.475019i
$979$	−259595.	+	174424.i	−0.270851	+	0.181988i
$980$	1.00993e6			1.05157
$981$			414133.i			0.430330i
$982$	−709675.			−0.735931
$983$	−562567.			−0.582194			−0.291097	−	0.956694i	$-0.594020\pi$
$983$	−562567.			−0.582194			−0.291097	+	0.956694i	$0.594020\pi$
$984$	64628.5			0.0667473
$985$		−	704182.i		−	0.725793i
$986$			2.98790e6i			3.07335i
$987$		−	124792.i		−	0.128101i
$988$	−182606.			−0.187069
$989$		−	660233.i		−	0.675001i
$990$	302762.	+	450598.i	0.308909	+	0.459747i
$991$	−679908.			−0.692313			−0.346157	−	0.938177i	$-0.612513\pi$
$991$	−679908.			−0.692313			−0.346157	+	0.938177i	$0.612513\pi$
$992$		−	623856.i		−	0.633959i
$993$	117237.			0.118895
$994$	−436042.			−0.441322
$995$	809607.			0.817764
$996$		−	934910.i		−	0.942435i
$997$			723578.i			0.727939i	0.931411	+	0.363970i	$0.118579\pi$
$997$			723578.i			0.727939i	−0.931411	+	0.363970i	$0.881421\pi$
$998$		−	930145.i		−	0.933877i
$999$	−38806.5			−0.0388843

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.5.c.a.10.7	yes	8
3.2	odd	2		99.5.c.c.10.2		8
4.3	odd	2		528.5.j.a.241.6		8
11.10	odd	2	inner	33.5.c.a.10.2	✓	8
33.32	even	2		99.5.c.c.10.7		8
44.43	even	2		528.5.j.a.241.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.5.c.a.10.2	✓	8	11.10	odd	2	inner
33.5.c.a.10.7	yes	8	1.1	even	1	trivial
99.5.c.c.10.2		8	3.2	odd	2
99.5.c.c.10.7		8	33.32	even	2
528.5.j.a.241.5		8	44.43	even	2
528.5.j.a.241.6		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	33.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.58567i q^{2} -5.19615 q^{3} -15.1997 q^{4} -29.7487 q^{5} -29.0240i q^{6} -12.9420i q^{7} +4.47031i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+5.58567i q^{2} -5.19615 q^{3} -15.1997 q^{4} -29.7487 q^{5} -29.0240i q^{6} -12.9420i q^{7} +4.47031i q^{8} +27.0000 q^{9} -166.166i q^{10} +(-100.434 + 67.4829i) q^{11} +78.9799 q^{12} -36.6685i q^{13} +72.2898 q^{14} +154.579 q^{15} -268.165 q^{16} +464.257i q^{17} +150.813i q^{18} +327.633i q^{19} +452.171 q^{20} +67.2487i q^{21} +(-376.937 - 560.993i) q^{22} +396.812 q^{23} -23.2284i q^{24} +259.987 q^{25} +204.818 q^{26} -140.296 q^{27} +196.715i q^{28} -1152.21i q^{29} +863.426i q^{30} +437.378 q^{31} -1426.35i q^{32} +(521.872 - 350.651i) q^{33} -2593.18 q^{34} +385.009i q^{35} -410.391 q^{36} +276.604 q^{37} -1830.05 q^{38} +190.535i q^{39} -132.986i q^{40} +2782.30i q^{41} -375.629 q^{42} -1663.84i q^{43} +(1526.57 - 1025.72i) q^{44} -803.216 q^{45} +2216.46i q^{46} -1855.68 q^{47} +1393.42 q^{48} +2233.50 q^{49} +1452.20i q^{50} -2412.35i q^{51} +557.350i q^{52} +3745.57 q^{53} -783.647i q^{54} +(2987.79 - 2007.53i) q^{55} +57.8549 q^{56} -1702.43i q^{57} +6435.88 q^{58} -6573.17 q^{59} -2349.55 q^{60} +5140.56i q^{61} +2443.05i q^{62} -349.435i q^{63} +3676.50 q^{64} +1090.84i q^{65} +(1958.62 + 2915.00i) q^{66} -3464.58 q^{67} -7056.56i q^{68} -2061.90 q^{69} -2150.53 q^{70} -6031.86 q^{71} +120.698i q^{72} +3580.96i q^{73} +1545.02i q^{74} -1350.93 q^{75} -4979.92i q^{76} +(873.365 + 1299.82i) q^{77} -1064.27 q^{78} +9711.53i q^{79} +7977.55 q^{80} +729.000 q^{81} -15541.0 q^{82} -11837.3i q^{83} -1022.16i q^{84} -13811.1i q^{85} +9293.66 q^{86} +5987.07i q^{87} +(-301.670 - 448.973i) q^{88} +2584.72 q^{89} -4486.50i q^{90} -474.565 q^{91} -6031.42 q^{92} -2272.69 q^{93} -10365.2i q^{94} -9746.67i q^{95} +7411.55i q^{96} +1551.68 q^{97} +12475.6i q^{98} +(-2711.73 + 1822.04i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 76 q^{4} - 36 q^{5} + 216 q^{9}+O(q^{10}) \) 8 * q - 76 * q^4 - 36 * q^5 + 216 * q^9	\( 8 q - 76 q^{4} - 36 q^{5} + 216 q^{9} + 36 q^{11} - 360 q^{12} - 1140 q^{14} + 108 q^{15} + 1412 q^{16} + 2532 q^{20} - 780 q^{22} + 516 q^{23} - 2280 q^{25} - 1524 q^{26} + 2752 q^{31} + 1008 q^{33} - 4920 q^{34} - 2052 q^{36} + 5296 q^{37} + 696 q^{38} - 4356 q^{42} - 6540 q^{44} - 972 q^{45} + 420 q^{47} + 9936 q^{48} - 6832 q^{49} + 3540 q^{53} + 3784 q^{55} + 17964 q^{56} + 21624 q^{58} - 16632 q^{59} - 612 q^{60} - 27508 q^{64} + 360 q^{66} - 3656 q^{67} + 9036 q^{69} + 3312 q^{70} - 13212 q^{71} - 9288 q^{75} + 23268 q^{77} - 13140 q^{78} - 4476 q^{80} + 5832 q^{81} + 17088 q^{82} + 19896 q^{86} - 12516 q^{88} + 15528 q^{89} - 19752 q^{91} - 81180 q^{92} - 21384 q^{93} + 7624 q^{97} + 972 q^{99}+O(q^{100}) \) 8 * q - 76 * q^4 - 36 * q^5 + 216 * q^9 + 36 * q^11 - 360 * q^12 - 1140 * q^14 + 108 * q^15 + 1412 * q^16 + 2532 * q^20 - 780 * q^22 + 516 * q^23 - 2280 * q^25 - 1524 * q^26 + 2752 * q^31 + 1008 * q^33 - 4920 * q^34 - 2052 * q^36 + 5296 * q^37 + 696 * q^38 - 4356 * q^42 - 6540 * q^44 - 972 * q^45 + 420 * q^47 + 9936 * q^48 - 6832 * q^49 + 3540 * q^53 + 3784 * q^55 + 17964 * q^56 + 21624 * q^58 - 16632 * q^59 - 612 * q^60 - 27508 * q^64 + 360 * q^66 - 3656 * q^67 + 9036 * q^69 + 3312 * q^70 - 13212 * q^71 - 9288 * q^75 + 23268 * q^77 - 13140 * q^78 - 4476 * q^80 + 5832 * q^81 + 17088 * q^82 + 19896 * q^86 - 12516 * q^88 + 15528 * q^89 - 19752 * q^91 - 81180 * q^92 - 21384 * q^93 + 7624 * q^97 + 972 * q^99

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