LMFDB - Embedded newform 29.6.b.a.28.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,6,Mod(28,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("29.28");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	29.b (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:	$4.65113077458$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 278x^{10} + 28285x^{8} + 1260472x^{6} + 22944832x^{4} + 140087936x^{2} + 966400 $ x^12 + 278x^10 + 28285x^8 + 1260472x^6 + 22944832x^4 + 140087936*x^2 + 966400
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{14}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			28.10
Root			$8.60273i$ of defining polynomial
Character	$\chi$	$=$	29.28
Dual form			29.6.b.a.28.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.60273i q^{2} -4.65015i q^{3} -42.0069 q^{4} -58.8511 q^{5} +40.0039 q^{6} -192.738 q^{7} -86.0865i q^{8} +221.376 q^{9} +O(q^{10})$	\(q+8.60273i q^{2} -4.65015i q^{3} -42.0069 q^{4} -58.8511 q^{5} +40.0039 q^{6} -192.738 q^{7} -86.0865i q^{8} +221.376 q^{9} -506.279i q^{10} +34.8202i q^{11} +195.338i q^{12} -149.346 q^{13} -1658.07i q^{14} +273.666i q^{15} -603.642 q^{16} +2028.79i q^{17} +1904.44i q^{18} +500.313i q^{19} +2472.15 q^{20} +896.259i q^{21} -299.548 q^{22} -1361.57 q^{23} -400.315 q^{24} +338.447 q^{25} -1284.78i q^{26} -2159.42i q^{27} +8096.32 q^{28} +(3317.42 - 3083.16i) q^{29} -2354.27 q^{30} +6704.78i q^{31} -7947.73i q^{32} +161.919 q^{33} -17453.1 q^{34} +11342.8 q^{35} -9299.32 q^{36} -2784.68i q^{37} -4304.06 q^{38} +694.482i q^{39} +5066.28i q^{40} -3741.93i q^{41} -7710.27 q^{42} +17974.1i q^{43} -1462.69i q^{44} -13028.2 q^{45} -11713.2i q^{46} -19035.2i q^{47} +2807.02i q^{48} +20340.9 q^{49} +2911.56i q^{50} +9434.17 q^{51} +6273.57 q^{52} +4075.70 q^{53} +18576.9 q^{54} -2049.20i q^{55} +16592.1i q^{56} +2326.53 q^{57} +(26523.6 + 28538.9i) q^{58} +30373.0 q^{59} -11495.9i q^{60} +8373.02i q^{61} -57679.4 q^{62} -42667.6 q^{63} +49055.6 q^{64} +8789.18 q^{65} +1392.94i q^{66} -49898.5 q^{67} -85223.2i q^{68} +6331.49i q^{69} +97579.3i q^{70} -40870.4 q^{71} -19057.5i q^{72} +83409.2i q^{73} +23955.9 q^{74} -1573.83i q^{75} -21016.6i q^{76} -6711.17i q^{77} -5974.44 q^{78} -99769.1i q^{79} +35525.0 q^{80} +43752.8 q^{81} +32190.8 q^{82} -91169.5 q^{83} -37649.1i q^{84} -119396. i q^{85} -154626. q^{86} +(-14337.1 - 15426.5i) q^{87} +2997.55 q^{88} +115905. i q^{89} -112078. i q^{90} +28784.7 q^{91} +57195.3 q^{92} +31178.2 q^{93} +163754. q^{94} -29444.0i q^{95} -36958.1 q^{96} -5605.95i q^{97} +174987. i q^{98} +7708.35i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 172 q^{4} + 46 q^{5} + 24 q^{6} + 20 q^{7} - 1574 q^{9}+O(q^{10}) $ 12 * q - 172 * q^4 + 46 * q^5 + 24 * q^6 + 20 * q^7 - 1574 * q^9	$ 12 q - 172 q^{4} + 46 q^{5} + 24 q^{6} + 20 q^{7} - 1574 q^{9} + 1362 q^{13} + 340 q^{16} - 4508 q^{20} + 11376 q^{22} + 5852 q^{23} - 6292 q^{24} + 12678 q^{25} - 25056 q^{28} + 11328 q^{29} + 14952 q^{30} - 22694 q^{33} - 22504 q^{34} + 4532 q^{35} + 22840 q^{36} - 43408 q^{38} + 8280 q^{42} - 52816 q^{45} + 102836 q^{49} + 58540 q^{51} + 15172 q^{52} + 25650 q^{53} - 89080 q^{54} - 32824 q^{57} + 4960 q^{58} - 3900 q^{59} + 37720 q^{62} - 146616 q^{63} + 252276 q^{64} + 169574 q^{65} - 28264 q^{67} - 286832 q^{71} - 263072 q^{74} + 519072 q^{78} - 230964 q^{80} - 24084 q^{81} - 178008 q^{82} + 85692 q^{83} - 126624 q^{86} - 137716 q^{87} - 83604 q^{88} - 182372 q^{91} - 5664 q^{92} + 377966 q^{93} + 192144 q^{94} - 415284 q^{96}+O(q^{100}) $ 12 * q - 172 * q^4 + 46 * q^5 + 24 * q^6 + 20 * q^7 - 1574 * q^9 + 1362 * q^13 + 340 * q^16 - 4508 * q^20 + 11376 * q^22 + 5852 * q^23 - 6292 * q^24 + 12678 * q^25 - 25056 * q^28 + 11328 * q^29 + 14952 * q^30 - 22694 * q^33 - 22504 * q^34 + 4532 * q^35 + 22840 * q^36 - 43408 * q^38 + 8280 * q^42 - 52816 * q^45 + 102836 * q^49 + 58540 * q^51 + 15172 * q^52 + 25650 * q^53 - 89080 * q^54 - 32824 * q^57 + 4960 * q^58 - 3900 * q^59 + 37720 * q^62 - 146616 * q^63 + 252276 * q^64 + 169574 * q^65 - 28264 * q^67 - 286832 * q^71 - 263072 * q^74 + 519072 * q^78 - 230964 * q^80 - 24084 * q^81 - 178008 * q^82 + 85692 * q^83 - 126624 * q^86 - 137716 * q^87 - 83604 * q^88 - 182372 * q^91 - 5664 * q^92 + 377966 * q^93 + 192144 * q^94 - 415284 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			8.60273i			1.52076i	0.649478	+	0.760381i	$0.274988\pi$
$2$			8.60273i			1.52076i	−0.649478	+	0.760381i	$0.725012\pi$
$3$		−	4.65015i		−	0.298307i	−0.988814	−	0.149153i	$-0.952345\pi$
$3$		−	4.65015i		−	0.298307i	0.988814	−	0.149153i	$-0.0476549\pi$
$4$	−42.0069			−1.31272
$5$	−58.8511			−1.05276			−0.526380	−	0.850250i	$-0.676451\pi$
$5$	−58.8511			−1.05276			−0.526380	+	0.850250i	$0.676451\pi$
$6$	40.0039			0.453654
$7$	−192.738			−1.48670			−0.743348	−	0.668905i	$-0.766763\pi$
$7$	−192.738			−1.48670			−0.743348	+	0.668905i	$0.766763\pi$
$8$		−	86.0865i		−	0.475565i
$9$	221.376			0.911013
$10$		−	506.279i		−	1.60100i
$11$			34.8202i			0.0867659i	0.999059	+	0.0433830i	$0.0138136\pi$
$11$			34.8202i			0.0867659i	−0.999059	+	0.0433830i	$0.986186\pi$
$12$			195.338i			0.391592i
$13$	−149.346			−0.245096			−0.122548	−	0.992463i	$-0.539107\pi$
$13$	−149.346			−0.245096			−0.122548	+	0.992463i	$0.539107\pi$
$14$		−	1658.07i		−	2.26091i
$15$			273.666i			0.314046i
$16$	−603.642			−0.589494
$17$			2028.79i			1.70261i	0.524672	+	0.851305i	$0.324188\pi$
$17$			2028.79i			1.70261i	−0.524672	+	0.851305i	$0.675812\pi$
$18$			1904.44i			1.38543i
$19$			500.313i			0.317950i	0.987283	+	0.158975i	$0.0508189\pi$
$19$			500.313i			0.317950i	−0.987283	+	0.158975i	$0.949181\pi$
$20$	2472.15			1.38197
$21$			896.259i			0.443492i
$22$	−299.548			−0.131950
$23$	−1361.57			−0.536686			−0.268343	−	0.963323i	$-0.586476\pi$
$23$	−1361.57			−0.536686			−0.268343	+	0.963323i	$0.586476\pi$
$24$	−400.315			−0.141864
$25$	338.447			0.108303
$26$		−	1284.78i		−	0.372732i
$27$		−	2159.42i		−	0.570068i
$28$	8096.32			1.95161
$29$	3317.42	−	3083.16i	0.732496	−	0.680771i
$29$	3317.42	−	3083.16i	0.732496	−	0.680771i
$30$	−2354.27			−0.477588
$31$			6704.78i			1.25308i	0.779387	+	0.626542i	$0.215531\pi$
$31$			6704.78i			1.25308i	−0.779387	+	0.626542i	$0.784469\pi$
$32$		−	7947.73i		−	1.37204i
$33$	161.919			0.0258829
$34$	−17453.1			−2.58926
$35$	11342.8			1.56513
$36$	−9299.32			−1.19590
$37$		−	2784.68i		−	0.334404i	−0.985923	−	0.167202i	$-0.946527\pi$
$37$		−	2784.68i		−	0.334404i	0.985923	−	0.167202i	$-0.0534732\pi$
$38$	−4304.06			−0.483525
$39$			694.482i			0.0731138i
$40$			5066.28i			0.500656i
$41$		−	3741.93i		−	0.347645i	−0.984777	−	0.173822i	$-0.944388\pi$
$41$		−	3741.93i		−	0.347645i	0.984777	−	0.173822i	$-0.0556118\pi$
$42$	−7710.27			−0.674445
$43$			17974.1i			1.48243i	0.671267	+	0.741216i	$0.265751\pi$
$43$			17974.1i			1.48243i	−0.671267	+	0.741216i	$0.734249\pi$
$44$		−	1462.69i		−	0.113899i
$45$	−13028.2			−0.959078
$46$		−	11713.2i		−	0.816171i
$47$		−	19035.2i		−	1.25693i	−0.777836	−	0.628467i	$-0.783683\pi$
$47$		−	19035.2i		−	1.25693i	0.777836	−	0.628467i	$-0.216317\pi$
$48$			2807.02i			0.175850i
$49$	20340.9			1.21026
$50$			2911.56i			0.164703i
$51$	9434.17			0.507900
$52$	6273.57			0.321741
$53$	4075.70			0.199302			0.0996512	−	0.995022i	$-0.468227\pi$
$53$	4075.70			0.199302			0.0996512	+	0.995022i	$0.468227\pi$
$54$	18576.9			0.866938
$55$		−	2049.20i		−	0.0913437i
$56$			16592.1i			0.707021i
$57$	2326.53			0.0948466
$58$	26523.6	+	28538.9i	1.03529	+	1.11395i
$59$	30373.0			1.13595			0.567973	−	0.823047i	$-0.307728\pi$
$59$	30373.0			1.13595			0.567973	+	0.823047i	$0.307728\pi$
$60$		−	11495.9i		−	0.412252i
$61$			8373.02i			0.288109i	0.989570	+	0.144055i	$0.0460141\pi$
$61$			8373.02i			0.288109i	−0.989570	+	0.144055i	$0.953986\pi$
$62$	−57679.4			−1.90564
$63$	−42667.6			−1.35440
$64$	49055.6			1.49706
$65$	8789.18			0.258027
$66$			1392.94i			0.0393617i
$67$	−49898.5			−1.35800			−0.679002	−	0.734137i	$-0.737587\pi$
$67$	−49898.5			−1.35800			−0.679002	+	0.734137i	$0.737587\pi$
$68$		−	85223.2i		−	2.23504i
$69$			6331.49i			0.160097i
$70$			97579.3i			2.38019i
$71$	−40870.4			−0.962195			−0.481098	−	0.876667i	$-0.659762\pi$
$71$	−40870.4			−0.962195			−0.481098	+	0.876667i	$0.659762\pi$
$72$		−	19057.5i		−	0.433246i
$73$			83409.2i			1.83192i	0.401268	+	0.915961i	$0.368570\pi$
$73$			83409.2i			1.83192i	−0.401268	+	0.915961i	$0.631430\pi$
$74$	23955.9			0.508549
$75$		−	1573.83i		−	0.0323075i
$76$		−	21016.6i		−	0.417377i
$77$		−	6711.17i		−	0.128995i
$78$	−5974.44			−0.111189
$79$		−	99769.1i		−	1.79857i	−0.437359	−	0.899287i	$-0.644086\pi$
$79$		−	99769.1i		−	1.79857i	0.437359	−	0.899287i	$-0.355914\pi$
$80$	35525.0			0.620596
$81$	43752.8			0.740958
$82$	32190.8			0.528685
$83$	−91169.5			−1.45263			−0.726314	−	0.687363i	$-0.758768\pi$
$83$	−91169.5			−1.45263			−0.726314	+	0.687363i	$0.758768\pi$
$84$		−	37649.1i		−	0.582178i
$85$		−	119396.i		−	1.79244i
$86$	−154626.			−2.25443
$87$	−14337.1	−	15426.5i	−0.203079	−	0.218509i
$88$	2997.55			0.0412628
$89$			115905.i			1.55105i	0.631314	+	0.775527i	$0.282516\pi$
$89$			115905.i			1.55105i	−0.631314	+	0.775527i	$0.717484\pi$
$90$		−	112078.i		−	1.45853i
$91$	28784.7			0.364383
$92$	57195.3			0.704515
$93$	31178.2			0.373804
$94$	163754.			1.91150
$95$		−	29444.0i		−	0.334724i
$96$	−36958.1			−0.409291
$97$		−	5605.95i		−	0.0604950i	−0.999542	−	0.0302475i	$-0.990370\pi$
$97$		−	5605.95i		−	0.0604950i	0.999542	−	0.0302475i	$-0.00962955\pi$
$98$			174987.i			1.84052i
$99$			7708.35i			0.0790449i
$100$	−14217.1			−0.142171
$101$			131196.i			1.27973i	0.768489	+	0.639864i	$0.221009\pi$
$101$			131196.i			1.27973i	−0.768489	+	0.639864i	$0.778991\pi$
$102$			81159.6i			0.772395i
$103$	−70765.0			−0.657243			−0.328621	−	0.944462i	$-0.606584\pi$
$103$	−70765.0			−0.657243			−0.328621	+	0.944462i	$0.606584\pi$
$104$			12856.7i			0.116559i
$105$		−	52745.8i		−	0.466890i
$106$			35062.1i			0.303091i
$107$	102088.			0.862015			0.431008	−	0.902348i	$-0.358158\pi$
$107$	102088.			0.862015			0.431008	+	0.902348i	$0.358158\pi$
$108$			90710.4i			0.748338i
$109$	−147399.			−1.18830			−0.594151	−	0.804353i	$-0.702512\pi$
$109$	−147399.			−1.18830			−0.594151	+	0.804353i	$0.702512\pi$
$110$	17628.7			0.138912
$111$	−12949.2			−0.0997551
$112$	116345.			0.876398
$113$		−	113291.i		−	0.834641i	−0.908759	−	0.417321i	$-0.862969\pi$
$113$		−	113291.i		−	0.834641i	0.908759	−	0.417321i	$-0.137031\pi$
$114$			20014.5i			0.144239i
$115$	80129.7			0.565001
$116$	−139354.	+	129514.i	−0.961559	+	0.893658i
$117$	−33061.7			−0.223285
$118$			261290.i			1.72750i
$119$		−	391025.i		−	2.53126i
$120$	23558.9			0.149349
$121$	159839.			0.992472
$122$	−72030.8			−0.438146
$123$	−17400.5			−0.103705
$124$		−	281647.i		−	1.64494i
$125$	163992.			0.938743
$126$		−	367057.i		−	2.05972i
$127$			261391.i			1.43808i	0.694970	+	0.719038i	$0.255417\pi$
$127$			261391.i			1.43808i	−0.694970	+	0.719038i	$0.744583\pi$
$128$			167685.i			0.904624i
$129$	83582.0			0.442220
$130$			75610.9i			0.392398i
$131$			118280.i			0.602188i	0.953594	+	0.301094i	$0.0973518\pi$
$131$			118280.i			0.602188i	−0.953594	+	0.301094i	$0.902648\pi$
$132$	−6801.71			−0.0339768
$133$		−	96429.4i		−	0.472694i
$134$		−	429263.i		−	2.06520i
$135$			127084.i			0.600145i
$136$	174651.			0.809702
$137$			61220.6i			0.278674i	0.990245	+	0.139337i	$0.0444971\pi$
$137$			61220.6i			0.278674i	−0.990245	+	0.139337i	$0.955503\pi$
$138$	−54468.1			−0.243469
$139$	−13334.2			−0.0585367			−0.0292684	−	0.999572i	$-0.509318\pi$
$139$	−13334.2			−0.0585367			−0.0292684	+	0.999572i	$0.509318\pi$
$140$	−476477.			−2.05457
$141$	−88516.4			−0.374952
$142$		−	351597.i		−	1.46327i
$143$		−	5200.26i		−	0.0212660i
$144$	−133632.			−0.537037
$145$	−195234.	+	181447.i	−0.771143	+	0.716688i
$146$	−717547.			−2.78592
$147$		−	94588.2i		−	0.361030i
$148$			116976.i			0.438977i
$149$	333145.			1.22933			0.614664	−	0.788789i	$-0.289292\pi$
$149$	333145.			1.22933			0.614664	+	0.788789i	$0.289292\pi$
$150$	13539.2			0.0491320
$151$	−136818.			−0.488314			−0.244157	−	0.969736i	$-0.578511\pi$
$151$	−136818.			−0.488314			−0.244157	+	0.969736i	$0.578511\pi$
$152$	43070.2			0.151206
$153$			449126.i			1.55110i
$154$	57734.3			0.196170
$155$		−	394584.i		−	1.31920i
$156$		−	29173.0i		−	0.0959776i
$157$			426395.i			1.38058i	0.723531	+	0.690292i	$0.242518\pi$
$157$			426395.i			1.38058i	−0.723531	+	0.690292i	$0.757482\pi$
$158$	858286.			2.73520
$159$		−	18952.6i		−	0.0594533i
$160$			467733.i			1.44443i
$161$	262426.			0.797888
$162$			376393.i			1.12682i
$163$		−	19636.8i		−	0.0578898i	−0.999581	−	0.0289449i	$-0.990785\pi$
$163$		−	19636.8i		−	0.0578898i	0.999581	−	0.0289449i	$-0.00921474\pi$
$164$			157187.i			0.456358i
$165$	−9529.09			−0.0272484
$166$		−	784306.i		−	2.20910i
$167$	−480640.			−1.33361			−0.666804	−	0.745233i	$-0.732338\pi$
$167$	−480640.			−1.33361			−0.666804	+	0.745233i	$0.732338\pi$
$168$	77155.8			0.210909
$169$	−348989.			−0.939928
$170$	1.02714e6			2.72587
$171$			110757.i			0.289656i
$172$		−	755034.i		−	1.94601i
$173$	721937.			1.83394			0.916968	−	0.398962i	$-0.130629\pi$
$173$	721937.			1.83394			0.916968	+	0.398962i	$0.130629\pi$
$174$	132710.	−	123338.i	0.332300	−	0.308834i
$175$	−65231.5			−0.161014
$176$		−	21018.9i		−	0.0511480i
$177$		−	141239.i		−	0.338860i
$178$	−997099.			−2.35878
$179$	−179122.			−0.417846			−0.208923	−	0.977932i	$-0.566996\pi$
$179$	−179122.			−0.417846			−0.208923	+	0.977932i	$0.566996\pi$
$180$	547275.			1.25900
$181$	28627.2			0.0649505			0.0324752	−	0.999473i	$-0.489661\pi$
$181$	28627.2			0.0649505			0.0324752	+	0.999473i	$0.489661\pi$
$182$			247627.i			0.554139i
$183$	38935.7			0.0859450
$184$			117213.i			0.255229i
$185$			163882.i			0.352047i
$186$			268218.i			0.568467i
$187$	−70642.8			−0.147728
$188$			799609.i			1.65000i
$189$			416202.i			0.847518i
$190$	253298.			0.509036
$191$		−	369627.i		−	0.733128i	−0.930393	−	0.366564i	$-0.880534\pi$
$191$		−	369627.i		−	0.733128i	0.930393	−	0.366564i	$-0.119466\pi$
$192$		−	228116.i		−	0.446583i
$193$		−	265892.i		−	0.513821i	−0.966435	−	0.256911i	$-0.917295\pi$
$193$		−	265892.i		−	0.513821i	0.966435	−	0.256911i	$-0.0827046\pi$
$194$	48226.4			0.0919985
$195$		−	40871.0i		−	0.0769713i
$196$	−854458.			−1.58873
$197$	703407.			1.29134			0.645671	−	0.763616i	$-0.276578\pi$
$197$	703407.			1.29134			0.645671	+	0.763616i	$0.276578\pi$
$198$	−66312.9			−0.120208
$199$	−46247.1			−0.0827851			−0.0413926	−	0.999143i	$-0.513179\pi$
$199$	−46247.1			−0.0827851			−0.0413926	+	0.999143i	$0.513179\pi$
$200$		−	29135.7i		−	0.0515051i
$201$			232035.i			0.405102i
$202$	−1.12864e6			−1.94616
$203$	−639393.	+	594242.i	−1.08900	+	1.01210i
$204$	−396300.			−0.666728
$205$			220216.i			0.365986i
$206$		−	608772.i		−	0.999509i
$207$	−301419.			−0.488927
$208$	90151.7			0.144483
$209$	−17421.0			−0.0275872
$210$	453758.			0.710029
$211$		−	857738.i		−	1.32632i	−0.748478	−	0.663160i	$-0.769215\pi$
$211$		−	857738.i		−	1.32632i	0.748478	−	0.663160i	$-0.230785\pi$
$212$	−171207.			−0.261627
$213$			190053.i			0.287030i
$214$			878234.i			1.31092i
$215$		−	1.05779e6i		−	1.56064i
$216$	−185897.			−0.271105
$217$		−	1.29227e6i		−	1.86296i
$218$		−	1.26803e6i		−	1.80712i
$219$	387865.			0.546475
$220$			86080.7i			0.119908i
$221$		−	302992.i		−	0.417302i
$222$		−	111398.i		−	0.151704i
$223$	382377.			0.514907			0.257454	−	0.966291i	$-0.417117\pi$
$223$	382377.			0.514907			0.257454	+	0.966291i	$0.417117\pi$
$224$			1.53183e6i			2.03981i
$225$	74924.0			0.0986654
$226$	974613.			1.26929
$227$	−134597.			−0.173369			−0.0866843	−	0.996236i	$-0.527627\pi$
$227$	−134597.			−0.173369			−0.0866843	+	0.996236i	$0.527627\pi$
$228$	−97730.3			−0.124507
$229$		−	671741.i		−	0.846473i	−0.906019	−	0.423237i	$-0.860894\pi$
$229$		−	671741.i		−	0.846473i	0.906019	−	0.423237i	$-0.139106\pi$
$230$			689334.i			0.859232i
$231$	−31207.9			−0.0384800
$232$	−265418.	−	285585.i	−0.323751	−	0.348350i
$233$	205463.			0.247938			0.123969	−	0.992286i	$-0.460438\pi$
$233$	205463.			0.247938			0.123969	+	0.992286i	$0.460438\pi$
$234$		−	284421.i		−	0.339564i
$235$			1.12024e6i			1.32325i
$236$	−1.27587e6			−1.49117
$237$	−463941.			−0.536527
$238$	3.36388e6			3.84945
$239$	948137.			1.07368			0.536842	−	0.843683i	$-0.319617\pi$
$239$	948137.			1.07368			0.536842	+	0.843683i	$0.319617\pi$
$240$		−	165196.i		−	0.185128i
$241$	−915203.			−1.01502			−0.507510	−	0.861646i	$-0.669434\pi$
$241$	−915203.			−1.01502			−0.507510	+	0.861646i	$0.669434\pi$
$242$			1.37505e6i			1.50931i
$243$		−	728195.i		−	0.791101i
$244$		−	351724.i		−	0.378206i
$245$	−1.19708e6			−1.27412
$246$		−	149692.i		−	0.157710i
$247$		−	74719.9i		−	0.0779281i
$248$	577191.			0.595923
$249$			423951.i			0.433329i
$250$			1.41077e6i			1.42760i
$251$			752104.i			0.753518i	0.926311	+	0.376759i	$0.122962\pi$
$251$			752104.i			0.753518i	−0.926311	+	0.376759i	$0.877038\pi$
$252$	1.79233e6			1.77794
$253$		−	47410.0i		−	0.0465660i
$254$	−2.24868e6			−2.18697
$255$	−555211.			−0.534697
$256$	127235.			0.121341
$257$	−522181.			−0.493160			−0.246580	−	0.969122i	$-0.579307\pi$
$257$	−522181.			−0.493160			−0.246580	+	0.969122i	$0.579307\pi$
$258$			719033.i			0.672511i
$259$			536714.i			0.497157i
$260$	−369206.			−0.338716
$261$	734398.	−	682538.i	0.667314	−	0.620191i
$262$	−1.01753e6			−0.915784
$263$			557834.i			0.497297i	0.968594	+	0.248648i	$0.0799864\pi$
$263$			557834.i			0.497297i	−0.968594	+	0.248648i	$0.920014\pi$
$264$		−	13939.0i		−	0.0123090i
$265$	−239859.			−0.209817
$266$	829556.			0.718855
$267$	538975.			0.462690
$268$	2.09608e6			1.78267
$269$			239387.i			0.201706i	0.994901	+	0.100853i	$0.0321572\pi$
$269$			239387.i			0.201706i	−0.994901	+	0.100853i	$0.967843\pi$
$270$	−1.09327e6			−0.912678
$271$		−	38347.5i		−	0.0317186i	−0.999874	−	0.0158593i	$-0.994952\pi$
$271$		−	38347.5i		−	0.0317186i	0.999874	−	0.0158593i	$-0.00504839\pi$
$272$		−	1.22466e6i		−	1.00368i
$273$		−	133853.i		−	0.108698i
$274$	−526664.			−0.423796
$275$			11784.8i			0.00939701i
$276$		−	265966.i		−	0.210162i
$277$	−941833.			−0.737521			−0.368761	−	0.929524i	$-0.620218\pi$
$277$	−941833.			−0.737521			−0.368761	+	0.929524i	$0.620218\pi$
$278$		−	114710.i		−	0.0890204i
$279$			1.48428e6i			1.14158i
$280$		−	976464.i		−	0.744323i
$281$	1.79001e6			1.35235			0.676174	−	0.736742i	$-0.263637\pi$
$281$	1.79001e6			1.35235			0.676174	+	0.736742i	$0.263637\pi$
$282$		−	761482.i		−	0.570213i
$283$	1.25941e6			0.934762			0.467381	−	0.884056i	$-0.345198\pi$
$283$	1.25941e6			0.934762			0.467381	+	0.884056i	$0.345198\pi$
$284$	1.71684e6			1.26309
$285$	−136919.			−0.0998506
$286$	44736.4			0.0323405
$287$			721211.i			0.516842i
$288$		−	1.75944e6i		−	1.24995i
$289$	−2.69614e6			−1.89888
$290$	−1.56094e6	−	1.67954e6i	−1.08991	−	1.17272i
$291$	−26068.5			−0.0180461
$292$		−	3.50376e6i		−	2.40479i
$293$			1.96914e6i			1.34001i	0.742358	+	0.670003i	$0.233707\pi$
$293$			1.96914e6i			1.34001i	−0.742358	+	0.670003i	$0.766293\pi$
$294$	813716.			0.549041
$295$	−1.78748e6			−1.19588
$296$	−239724.			−0.159031
$297$	75191.2			0.0494625
$298$			2.86596e6i			1.86952i
$299$	203345.			0.131539
$300$			66111.6i			0.0424106i
$301$		−	3.46428e6i		−	2.20393i
$302$		−	1.17700e6i		−	0.742610i
$303$	610081.			0.381752
$304$		−	302010.i		−	0.187429i
$305$		−	492761.i		−	0.303310i
$306$	−3.86371e6			−2.35885
$307$			371928.i			0.225223i	0.993639	+	0.112612i	$0.0359216\pi$
$307$			371928.i			0.225223i	−0.993639	+	0.112612i	$0.964078\pi$
$308$			281915.i			0.169333i
$309$			329068.i			0.196060i
$310$	3.39449e6			2.00618
$311$		−	1.37875e6i		−	0.808324i	−0.914688	−	0.404162i	$-0.867563\pi$
$311$		−	1.37875e6i		−	0.808324i	0.914688	−	0.404162i	$-0.132437\pi$
$312$	59785.5			0.0347704
$313$	1.49485e6			0.862458			0.431229	−	0.902242i	$-0.358080\pi$
$313$	1.49485e6			0.862458			0.431229	+	0.902242i	$0.358080\pi$
$314$	−3.66816e6			−2.09954
$315$	2.51103e6			1.42586
$316$			4.19099e6i			2.36102i
$317$			1.72816e6i			0.965910i	0.875645	+	0.482955i	$0.160437\pi$
$317$			1.72816e6i			0.965910i	−0.875645	+	0.482955i	$0.839563\pi$
$318$	163044.			0.0904143
$319$	107356.	+	115513.i	0.0590677	+	0.0635557i
$320$	−2.88698e6			−1.57604
$321$		−	474724.i		−	0.257145i
$322$			2.25758e6i			1.21340i
$323$	−1.01503e6			−0.541344
$324$	−1.83792e6			−0.972666
$325$	−50545.8			−0.0265446
$326$	168930.			0.0880366
$327$			685425.i			0.354479i
$328$	−322129.			−0.165328
$329$			3.66880e6i			1.86868i
$330$		−	81976.2i		−	0.0414384i
$331$		−	1.39927e6i		−	0.701993i	−0.936377	−	0.350997i	$-0.885843\pi$
$331$		−	1.39927e6i		−	0.701993i	0.936377	−	0.350997i	$-0.114157\pi$
$332$	3.82975e6			1.90689
$333$		−	616462.i		−	0.304646i
$334$		−	4.13481e6i		−	2.02810i
$335$	2.93658e6			1.42965
$336$		−	541020.i		−	0.261436i
$337$		−	182554.i		−	0.0875622i	−0.999041	−	0.0437811i	$-0.986060\pi$
$337$		−	182554.i		−	0.0875622i	0.999041	−	0.0437811i	$-0.0139404\pi$
$338$		−	3.00225e6i		−	1.42941i
$339$	−526820.			−0.248979
$340$			5.01547e6i			2.35296i
$341$	−233462.			−0.108725
$342$	−952816.			−0.440498
$343$	−681119.			−0.312599
$344$	1.54732e6			0.704993
$345$		−	372615.i		−	0.168544i
$346$			6.21063e6i			2.78898i
$347$	1.72393e6			0.768591			0.384295	−	0.923210i	$-0.374444\pi$
$347$	1.72393e6			0.768591			0.384295	+	0.923210i	$0.374444\pi$
$348$	602259.	+	648019.i	0.266585	+	0.286840i
$349$	351962.			0.154679			0.0773396	−	0.997005i	$-0.475357\pi$
$349$	351962.			0.154679			0.0773396	+	0.997005i	$0.475357\pi$
$350$		−	561169.i		−	0.244863i
$351$			322501.i			0.139721i
$352$	276741.			0.119047
$353$	1.24795e6			0.533040			0.266520	−	0.963829i	$-0.414126\pi$
$353$	1.24795e6			0.533040			0.266520	+	0.963829i	$0.414126\pi$
$354$	1.21504e6			0.515326
$355$	2.40527e6			1.01296
$356$		−	4.86881e6i		−	2.03609i
$357$	−1.81832e6			−0.755093
$358$		−	1.54094e6i		−	0.635444i
$359$		−	1.30667e6i		−	0.535094i	−0.963545	−	0.267547i	$-0.913787\pi$
$359$		−	1.30667e6i		−	0.535094i	0.963545	−	0.267547i	$-0.0862130\pi$
$360$			1.12155e6i			0.456104i
$361$	2.22579e6			0.898908
$362$			246272.i			0.0987741i
$363$		−	743273.i		−	0.296061i
$364$	−1.20915e6			−0.478331
$365$		−	4.90872e6i		−	1.92857i
$366$			334954.i			0.130702i
$367$			1.70382e6i			0.660325i	0.943924	+	0.330162i	$0.107103\pi$
$367$			1.70382e6i			0.660325i	−0.943924	+	0.330162i	$0.892897\pi$
$368$	821900.			0.316373
$369$		−	828373.i		−	0.316709i
$370$	−1.40983e6			−0.535380
$371$	−785542.			−0.296302
$372$	−1.30970e6			−0.490698
$373$	1.03735e6			0.386058			0.193029	−	0.981193i	$-0.438169\pi$
$373$	1.03735e6			0.386058			0.193029	+	0.981193i	$0.438169\pi$
$374$		−	607721.i		−	0.224660i
$375$		−	762585.i		−	0.280033i
$376$	−1.63867e6			−0.597754
$377$	−495444.	+	460458.i	−0.179532	+	0.166854i
$378$	−3.58047e6			−1.28887
$379$			3.48128e6i			1.24492i	0.782652	+	0.622460i	$0.213867\pi$
$379$			3.48128e6i			1.24492i	−0.782652	+	0.622460i	$0.786133\pi$
$380$			1.23685e6i			0.439398i
$381$	1.21551e6			0.428988
$382$	3.17980e6			1.11491
$383$	−3.95926e6			−1.37917			−0.689583	−	0.724206i	$-0.742206\pi$
$383$	−3.95926e6			−1.37917			−0.689583	+	0.724206i	$0.742206\pi$
$384$	779758.			0.269856
$385$			394959.i			0.135800i
$386$	2.28740e6			0.781400
$387$			3.97903e6i			1.35051i
$388$			235488.i			0.0794127i
$389$		−	2.93285e6i		−	0.982689i	−0.870965	−	0.491345i	$-0.836506\pi$
$389$		−	2.93285e6i		−	0.982689i	0.870965	−	0.491345i	$-0.163494\pi$
$390$	351602.			0.117055
$391$		−	2.76234e6i		−	0.913766i
$392$		−	1.75108e6i		−	0.575559i
$393$	550018.			0.179637
$394$			6.05122e6i			1.96382i
$395$			5.87152e6i			1.89347i
$396$		−	323804.i		−	0.103763i
$397$	−4.54389e6			−1.44694			−0.723471	−	0.690355i	$-0.757455\pi$
$397$	−4.54389e6			−1.44694			−0.723471	+	0.690355i	$0.757455\pi$
$398$		−	397852.i		−	0.125896i
$399$	−448411.			−0.141008
$400$	−204301.			−0.0638440
$401$	−4.94733e6			−1.53642			−0.768210	−	0.640198i	$-0.778852\pi$
$401$	−4.94733e6			−1.53642			−0.768210	+	0.640198i	$0.778852\pi$
$402$	−1.99614e6			−0.616063
$403$		−	1.00133e6i		−	0.307126i
$404$		−	5.51114e6i		−	1.67992i
$405$	−2.57490e6			−0.780050
$406$	−5.11210e6	−	5.50052e6i	−1.53916	−	1.65611i
$407$	96963.1			0.0290149
$408$		−	812155.i		−	0.241540i
$409$		−	3.64582e6i		−	1.07767i	−0.842410	−	0.538836i	$-0.818864\pi$
$409$		−	3.64582e6i		−	1.07767i	0.842410	−	0.538836i	$-0.181136\pi$
$410$	−1.89446e6			−0.556578
$411$	284685.			0.0831304
$412$	2.97262e6			0.862772
$413$	−5.85403e6			−1.68880
$414$		−	2.59302e6i		−	0.743542i
$415$	5.36542e6			1.52927
$416$			1.18696e6i			0.336282i
$417$			62005.8i			0.0174619i
$418$		−	149868.i		−	0.0419535i
$419$	1.34056e6			0.373036			0.186518	−	0.982452i	$-0.440280\pi$
$419$	1.34056e6			0.373036			0.186518	+	0.982452i	$0.440280\pi$
$420$			2.21569e6i			0.612894i
$421$			6.47105e6i			1.77938i	0.456562	+	0.889692i	$0.349081\pi$
$421$			6.47105e6i			1.77938i	−0.456562	+	0.889692i	$0.650919\pi$
$422$	7.37888e6			2.01702
$423$		−	4.21394e6i		−	1.14508i
$424$		−	350863.i		−	0.0947812i
$425$			686638.i			0.184398i
$426$	−1.63498e6			−0.436503
$427$		−	1.61380e6i		−	0.428331i
$428$	−4.28839e6			−1.13158
$429$	−24182.0			−0.00634378
$430$	9.09989e6			2.37337
$431$	350675.			0.0909308			0.0454654	−	0.998966i	$-0.485523\pi$
$431$	350675.			0.0909308			0.0454654	+	0.998966i	$0.485523\pi$
$432$			1.30351e6i			0.336052i
$433$		−	1.05881e6i		−	0.271392i	−0.990751	−	0.135696i	$-0.956673\pi$
$433$		−	1.05881e6i		−	0.271392i	0.990751	−	0.135696i	$-0.0433270\pi$
$434$	1.11170e7			2.83311
$435$	843756.	+	907865.i	0.213793	+	0.230037i
$436$	6.19175e6			1.55990
$437$		−	681211.i		−	0.170639i
$438$			3.33670e6i			0.831058i
$439$	−4.41822e6			−1.09417			−0.547087	−	0.837076i	$-0.684263\pi$
$439$	−4.41822e6			−1.09417			−0.547087	+	0.837076i	$0.684263\pi$
$440$	−176409.			−0.0434399
$441$	4.50299e6			1.10257
$442$	2.60656e6			0.634617
$443$			6.75286e6i			1.63485i	0.576034	+	0.817426i	$0.304600\pi$
$443$			6.75286e6i			1.63485i	−0.576034	+	0.817426i	$0.695400\pi$
$444$	543955.			0.130950
$445$		−	6.82113e6i		−	1.63289i
$446$			3.28948e6i			0.783051i
$447$		−	1.54917e6i		−	0.366717i
$448$	−9.45488e6			−2.22567
$449$		−	4.76417e6i		−	1.11525i	−0.830094	−	0.557624i	$-0.811713\pi$
$449$		−	4.76417e6i		−	1.11525i	0.830094	−	0.557624i	$-0.188287\pi$
$450$			644551.i			0.150047i
$451$	130294.			0.0301637
$452$			4.75901e6i			1.09565i
$453$			636222.i			0.145668i
$454$		−	1.15790e6i		−	0.263652i
$455$	−1.69401e6			−0.383608
$456$		−	200283.i		−	0.0451057i
$457$	−8.07906e6			−1.80955			−0.904774	−	0.425891i	$-0.859961\pi$
$457$	−8.07906e6			−1.80955			−0.904774	+	0.425891i	$0.859961\pi$
$458$	5.77880e6			1.28728
$459$	4.38100e6			0.970604
$460$	−3.36600e6			−0.741685
$461$			3.62540e6i			0.794518i	0.917707	+	0.397259i	$0.130039\pi$
$461$			3.62540e6i			0.794518i	−0.917707	+	0.397259i	$0.869961\pi$
$462$		−	268473.i		−	0.0585188i
$463$	−4.95618e6			−1.07447			−0.537235	−	0.843432i	$-0.680531\pi$
$463$	−4.95618e6			−1.07447			−0.537235	+	0.843432i	$0.680531\pi$
$464$	−2.00253e6	+	1.86112e6i	−0.431802	+	0.401310i
$465$	−1.83487e6			−0.393526
$466$			1.76754e6i			0.377054i
$467$		−	4.93194e6i		−	1.04647i	−0.852189	−	0.523233i	$-0.824726\pi$
$467$		−	4.93194e6i		−	1.04647i	0.852189	−	0.523233i	$-0.175274\pi$
$468$	1.38882e6			0.293110
$469$	9.61734e6			2.01894
$470$	−9.63712e6			−2.01235
$471$	1.98280e6			0.411838
$472$		−	2.61470e6i		−	0.540216i
$473$	−625859.			−0.128625
$474$		−	3.99116e6i		−	0.815930i
$475$			169329.i			0.0344349i
$476$			1.64257e7i			3.32283i
$477$	902263.			0.181567
$478$			8.15657e6i			1.63282i
$479$			7.82924e6i			1.55913i	0.626324	+	0.779563i	$0.284559\pi$
$479$			7.82924e6i			1.55913i	−0.626324	+	0.779563i	$0.715441\pi$
$480$	2.17502e6			0.430885
$481$			415882.i			0.0819610i
$482$		−	7.87324e6i		−	1.54360i
$483$		−	1.22032e6i		−	0.238016i
$484$	−6.71432e6			−1.30283
$485$			329916.i			0.0636867i
$486$	6.26446e6			1.20308
$487$	−7.75429e6			−1.48156			−0.740781	−	0.671747i	$-0.765544\pi$
$487$	−7.75429e6			−1.48156			−0.740781	+	0.671747i	$0.765544\pi$
$488$	720804.			0.137015
$489$	−91314.1			−0.0172689
$490$		−	1.02982e7i		−	1.93763i
$491$			2.92796e6i			0.548103i	0.961715	+	0.274051i	$0.0883638\pi$
$491$			2.92796e6i			0.548103i	−0.961715	+	0.274051i	$0.911636\pi$
$492$	730941.			0.136135
$493$	6.25509e6	+	6.73035e6i	1.15909	+	1.24716i
$494$	642795.			0.118510
$495$		−	453645.i		−	0.0832152i
$496$		−	4.04729e6i		−	0.738686i
$497$	7.87728e6			1.43049
$498$	−3.64714e6			−0.658990
$499$	4.22713e6			0.759966			0.379983	−	0.924994i	$-0.375930\pi$
$499$	4.22713e6			0.759966			0.379983	+	0.924994i	$0.375930\pi$
$500$	−6.88878e6			−1.23230
$501$			2.23504e6i			0.397825i
$502$	−6.47014e6			−1.14592
$503$		−	6.69146e6i		−	1.17924i	−0.807682	−	0.589619i	$-0.799278\pi$
$503$		−	6.69146e6i		−	1.17924i	0.807682	−	0.589619i	$-0.200722\pi$
$504$			3.67310e6i			0.644105i
$505$		−	7.72103e6i		−	1.34725i
$506$	407856.			0.0708158
$507$			1.62285e6i			0.280387i
$508$		−	1.09802e7i		−	1.88779i
$509$	−479870.			−0.0820974			−0.0410487	−	0.999157i	$-0.513070\pi$
$509$	−479870.			−0.0820974			−0.0410487	+	0.999157i	$0.513070\pi$
$510$		−	4.77633e6i		−	0.813146i
$511$		−	1.60761e7i		−	2.72351i
$512$			6.46048e6i			1.08916i
$513$	1.08039e6			0.181253
$514$		−	4.49218e6i		−	0.749979i
$515$	4.16460e6			0.691919
$516$	−3.51102e6			−0.580509
$517$	662808.			0.109059
$518$	−4.61720e6			−0.756057
$519$		−	3.35711e6i		−	0.547076i
$520$		−	756630.i		−	0.122709i
$521$	1.68786e6			0.272423			0.136211	−	0.990680i	$-0.456507\pi$
$521$	1.68786e6			0.272423			0.136211	+	0.990680i	$0.456507\pi$
$522$	5.87169e6	+	6.31782e6i	0.943163	+	1.01482i
$523$	1.26637e6			0.202444			0.101222	−	0.994864i	$-0.467725\pi$
$523$	1.26637e6			0.202444			0.101222	+	0.994864i	$0.467725\pi$
$524$		−	4.96856e6i		−	0.790501i
$525$			303336.i			0.0480315i
$526$	−4.79889e6			−0.756270
$527$	−1.36026e7			−2.13351
$528$	−97741.0			−0.0152578
$529$	−4.58247e6			−0.711969
$530$		−	2.06344e6i		−	0.319082i
$531$	6.72385e6			1.03486
$532$			4.05070e6i			0.620513i
$533$			558843.i			0.0852063i
$534$			4.63665e6i			0.703642i
$535$	−6.00798e6			−0.907495
$536$			4.29559e6i			0.645819i
$537$			832944.i			0.124646i
$538$	−2.05938e6			−0.306747
$539$			708274.i			0.105010i
$540$		−	5.33840e6i		−	0.787820i
$541$			4.10348e6i			0.602780i	0.953501	+	0.301390i	$0.0974506\pi$
$541$			4.10348e6i			0.602780i	−0.953501	+	0.301390i	$0.902549\pi$
$542$	329893.			0.0482365
$543$		−	133121.i		−	0.0193752i
$544$	1.61243e7			2.33606
$545$	8.67456e6			1.25100
$546$	1.15150e6			0.165304
$547$	1.95312e6			0.279101			0.139550	−	0.990215i	$-0.455434\pi$
$547$	1.95312e6			0.279101			0.139550	+	0.990215i	$0.455434\pi$
$548$		−	2.57169e6i		−	0.365819i
$549$			1.85359e6i			0.262471i
$550$	−101381.			−0.0142906
$551$	1.54255e6	+	1.65975e6i	0.216451	+	0.232897i
$552$	545056.			0.0761366
$553$			1.92293e7i			2.67393i
$554$		−	8.10233e6i		−	1.12159i
$555$	762073.			0.105018
$556$	560126.			0.0768420
$557$	−4.57733e6			−0.625135			−0.312567	−	0.949896i	$-0.601189\pi$
$557$	−4.57733e6			−0.625135			−0.312567	+	0.949896i	$0.601189\pi$
$558$	−1.27688e7			−1.73607
$559$		−	2.68436e6i		−	0.363338i
$560$	−6.84701e6			−0.922637
$561$			328499.i			0.0440684i
$562$			1.53989e7i			2.05660i
$563$			1.84422e6i			0.245212i	0.992455	+	0.122606i	$0.0391252\pi$
$563$			1.84422e6i			0.245212i	−0.992455	+	0.122606i	$0.960875\pi$
$564$	3.71830e6			0.492205
$565$			6.66731e6i			0.878677i
$566$			1.08344e7i			1.42155i
$567$	−8.43282e6			−1.10158
$568$			3.51839e6i			0.457587i
$569$			8.92744e6i			1.15597i	0.816048	+	0.577985i	$0.196161\pi$
$569$			8.92744e6i			1.15597i	−0.816048	+	0.577985i	$0.803839\pi$
$570$		−	1.17787e6i		−	0.151849i
$571$	6.11425e6			0.784789			0.392395	−	0.919797i	$-0.371647\pi$
$571$	6.11425e6			0.784789			0.392395	+	0.919797i	$0.371647\pi$
$572$			218447.i			0.0279162i
$573$	−1.71882e6			−0.218697
$574$	−6.20438e6			−0.785993
$575$	−460818.			−0.0581246
$576$	1.08597e7			1.36384
$577$		−	7.78000e6i		−	0.972837i	−0.873726	−	0.486418i	$-0.838303\pi$
$577$		−	7.78000e6i		−	0.972837i	0.873726	−	0.486418i	$-0.161697\pi$
$578$		−	2.31941e7i		−	2.88774i
$579$	−1.23644e6			−0.153277
$580$	8.20116e6	−	7.62203e6i	1.01229	−	0.940807i
$581$	1.75718e7			2.15961
$582$		−	224260.i		−	0.0274438i
$583$			141917.i			0.0172926i
$584$	7.18041e6			0.871198
$585$	1.94572e6			0.235066
$586$	−1.69400e7			−2.03783
$587$	1.00778e7			1.20718			0.603591	−	0.797294i	$-0.293736\pi$
$587$	1.00778e7			1.20718			0.603591	+	0.797294i	$0.293736\pi$
$588$			3.97336e6i			0.473930i
$589$	−3.35449e6			−0.398418
$590$		−	1.53772e7i		−	1.81864i
$591$		−	3.27095e6i		−	0.385216i
$592$			1.68095e6i			0.197129i
$593$	−6.70871e6			−0.783433			−0.391717	−	0.920086i	$-0.628119\pi$
$593$	−6.70871e6			−0.783433			−0.391717	+	0.920086i	$0.628119\pi$
$594$			646850.i			0.0752207i
$595$			2.30122e7i			2.66481i
$596$	−1.39944e7			−1.61376
$597$			215056.i			0.0246954i
$598$			1.74932e6i			0.200040i
$599$			4.51019e6i			0.513603i	0.966464	+	0.256802i	$0.0826687\pi$
$599$			4.51019e6i			0.513603i	−0.966464	+	0.256802i	$0.917331\pi$
$600$	−135485.			−0.0153643
$601$		−	1.52938e7i		−	1.72715i	−0.504224	−	0.863573i	$-0.668221\pi$
$601$		−	1.52938e7i		−	1.72715i	0.504224	−	0.863573i	$-0.331779\pi$
$602$	2.98023e7			3.35164
$603$	−1.10463e7			−1.23716
$604$	5.74728e6			0.641018
$605$	−9.40667e6			−1.04483
$606$			5.24836e6i			0.580553i
$607$		−	2.69488e6i		−	0.296871i	−0.988922	−	0.148435i	$-0.952576\pi$
$607$		−	2.69488e6i		−	0.296871i	0.988922	−	0.148435i	$-0.0474237\pi$
$608$	3.97636e6			0.436241
$609$	2.76331e6	+	2.97327e6i	0.301916	+	0.324856i
$610$	4.23909e6			0.461262
$611$			2.84283e6i			0.308069i
$612$		−	1.88664e7i		−	2.03615i
$613$	1.56344e7			1.68046			0.840232	−	0.542227i	$-0.182419\pi$
$613$	1.56344e7			1.68046			0.840232	+	0.542227i	$0.182419\pi$
$614$	−3.19959e6			−0.342511
$615$	1.02404e6			0.109176
$616$	−577741.			−0.0613453
$617$		−	1.27944e6i		−	0.135303i	−0.997709	−	0.0676515i	$-0.978449\pi$
$617$		−	1.27944e6i		−	0.135303i	0.997709	−	0.0676515i	$-0.0215506\pi$
$618$	−2.83088e6			−0.298161
$619$			2.99547e6i			0.314224i	0.987581	+	0.157112i	$0.0502183\pi$
$619$			2.99547e6i			0.314224i	−0.987581	+	0.157112i	$0.949782\pi$
$620$			1.65752e7i			1.73173i
$621$			2.94019e6i			0.305948i
$622$	1.18610e7			1.22927
$623$		−	2.23393e7i		−	2.30595i
$624$		−	419218.i		−	0.0431002i
$625$	−1.07087e7			−1.09657
$626$			1.28598e7i			1.31159i
$627$			81010.2i			0.00822945i
$628$		−	1.79115e7i		−	1.81231i
$629$	5.64954e6			0.569359
$630$			2.16017e7i			2.16839i
$631$	−2.10334e6			−0.210298			−0.105149	−	0.994456i	$-0.533532\pi$
$631$	−2.10334e6			−0.210298			−0.105149	+	0.994456i	$0.533532\pi$
$632$	−8.58877e6			−0.855339
$633$	−3.98861e6			−0.395651
$634$	−1.48669e7			−1.46892
$635$		−	1.53832e7i		−	1.51395i
$636$			796139.i			0.0780452i
$637$	−3.03784e6			−0.296631
$638$	−993728.	+	923555.i	−0.0966531	+	0.0898279i
$639$	−9.04774e6			−0.876572
$640$		−	9.86842e6i		−	0.952352i
$641$		−	1.68192e6i		−	0.161681i	−0.996727	−	0.0808407i	$-0.974239\pi$
$641$		−	1.68192e6i		−	0.161681i	0.996727	−	0.0808407i	$-0.0257605\pi$
$642$	4.08392e6			0.391056
$643$	−1.41971e7			−1.35416			−0.677082	−	0.735908i	$-0.736756\pi$
$643$	−1.41971e7			−1.35416			−0.677082	+	0.735908i	$0.736756\pi$
$644$	−1.10237e7			−1.04740
$645$	−4.91889e6			−0.465551
$646$		−	8.73204e6i		−	0.823255i
$647$	6.11744e6			0.574525			0.287263	−	0.957852i	$-0.407255\pi$
$647$	6.11744e6			0.574525			0.287263	+	0.957852i	$0.407255\pi$
$648$		−	3.76652e6i		−	0.352374i
$649$			1.05759e6i			0.0985613i
$650$		−	434831.i		−	0.0403680i
$651$	−6.00923e6			−0.555733
$652$			824882.i			0.0759929i
$653$		−	9.60351e6i		−	0.881347i	−0.897667	−	0.440674i	$-0.854740\pi$
$653$		−	9.60351e6i		−	0.881347i	0.897667	−	0.440674i	$-0.145260\pi$
$654$	−5.89652e6			−0.539078
$655$		−	6.96089e6i		−	0.633959i
$656$			2.25878e6i			0.204934i
$657$			1.84648e7i			1.66890i
$658$	−3.15617e7			−2.84181
$659$		−	759786.i		−	0.0681519i	−0.999419	−	0.0340759i	$-0.989151\pi$
$659$		−	759786.i		−	0.0681519i	0.999419	−	0.0340759i	$-0.0108488\pi$
$660$	400288.			0.0357695
$661$	−8.32182e6			−0.740824			−0.370412	−	0.928868i	$-0.620783\pi$
$661$	−8.32182e6			−0.740824			−0.370412	+	0.928868i	$0.620783\pi$
$662$	1.20376e7			1.06756
$663$	−1.40896e6			−0.124484
$664$			7.84846e6i			0.690819i
$665$			5.67497e6i			0.497633i
$666$	5.30326e6			0.463294
$667$	−4.51689e6	+	4.19793e6i	−0.393120	+	0.365360i
$668$	2.01902e7			1.75065
$669$		−	1.77811e6i		−	0.153600i
$670$			2.52626e7i			2.17416i
$671$	−291550.			−0.0249981
$672$	7.12323e6			0.608491
$673$	1.88077e7			1.60065			0.800326	−	0.599565i	$-0.204660\pi$
$673$	1.88077e7			1.60065			0.800326	+	0.599565i	$0.204660\pi$
$674$	1.57046e6			0.133161
$675$		−	730848.i		−	0.0617401i
$676$	1.46599e7			1.23386
$677$		−	18042.0i		−	0.00151291i	−1.00000		0.000756455i	$-0.999759\pi$
$677$		−	18042.0i		−	0.00151291i	1.00000		0.000756455i	$-0.000240787\pi$
$678$		−	4.53209e6i		−	0.378638i
$679$			1.08048e6i			0.0899377i
$680$	−1.02784e7			−0.852421
$681$			625895.i			0.0517171i
$682$		−	2.00841e6i		−	0.165345i
$683$	1.95502e7			1.60361			0.801805	−	0.597585i	$-0.203873\pi$
$683$	1.95502e7			1.60361			0.801805	+	0.597585i	$0.203873\pi$
$684$		−	4.65258e6i		−	0.380236i
$685$		−	3.60290e6i		−	0.293377i
$686$		−	5.85948e6i		−	0.475388i
$687$	−3.12369e6			−0.252509
$688$		−	1.08499e7i		−	0.873885i
$689$	−608690.			−0.0488482
$690$	3.20550e6			0.256315
$691$	1.36744e7			1.08946			0.544732	−	0.838610i	$-0.316632\pi$
$691$	1.36744e7			1.08946			0.544732	+	0.838610i	$0.316632\pi$
$692$	−3.03263e7			−2.40743
$693$		−	1.48569e6i		−	0.117516i
$694$			1.48305e7i			1.16884i
$695$	784729.			0.0616251
$696$	−1.32801e6	+	1.23423e6i	−0.103915	+	0.0965771i
$697$	7.59159e6			0.591903
$698$			3.02783e6i			0.235230i
$699$		−	955431.i		−	0.0739616i
$700$	2.74017e6			0.211365
$701$	8.74463e6			0.672119			0.336060	−	0.941841i	$-0.390906\pi$
$701$	8.74463e6			0.672119			0.336060	+	0.941841i	$0.390906\pi$
$702$	−2.77439e6			−0.212483
$703$	1.39321e6			0.106324
$704$			1.70812e6i			0.129894i
$705$	5.20928e6			0.394735
$706$			1.07357e7i			0.810626i
$707$		−	2.52865e7i		−	1.90256i
$708$			5.93300e6i			0.444827i
$709$	−6.19111e6			−0.462544			−0.231272	−	0.972889i	$-0.574289\pi$
$709$	−6.19111e6			−0.462544			−0.231272	+	0.972889i	$0.574289\pi$
$710$			2.06919e7i			1.54047i
$711$		−	2.20865e7i		−	1.63852i
$712$	9.97785e6			0.737627
$713$		−	9.12902e6i		−	0.672513i
$714$		−	1.56425e7i		−	1.14832i
$715$			306041.i			0.0223879i
$716$	7.52436e6			0.548513
$717$		−	4.40898e6i		−	0.320287i
$718$	1.12409e7			0.813750
$719$	−1.27516e7			−0.919907			−0.459953	−	0.887943i	$-0.652134\pi$
$719$	−1.27516e7			−0.919907			−0.459953	+	0.887943i	$0.652134\pi$
$720$	7.86438e6			0.565371
$721$	1.36391e7			0.977120
$722$			1.91478e7i			1.36702i
$723$			4.25583e6i			0.302788i
$724$	−1.20254e6			−0.0852614
$725$	1.12277e6	−	1.04349e6i	0.0793315	−	0.0737295i
$726$	6.39417e6			0.450238
$727$			1.43298e7i			1.00555i	0.864418	+	0.502775i	$0.167687\pi$
$727$			1.43298e7i			1.00555i	−0.864418	+	0.502775i	$0.832313\pi$
$728$		−	2.47797e6i		−	0.173288i
$729$	7.24572e6			0.504966
$730$	4.22284e7			2.93290
$731$	−3.64656e7			−2.52400
$732$	−1.63557e6			−0.112821
$733$			2.26727e6i			0.155863i	0.996959	+	0.0779316i	$0.0248316\pi$
$733$			2.26727e6i			0.155863i	−0.996959	+	0.0779316i	$0.975168\pi$
$734$	−1.46575e7			−1.00420
$735$			5.56662e6i			0.380078i
$736$			1.08214e7i			0.736357i
$737$		−	1.73748e6i		−	0.117828i
$738$	7.12627e6			0.481638
$739$			1.50384e7i			1.01296i	0.862252	+	0.506479i	$0.169053\pi$
$739$			1.50384e7i			1.01296i	−0.862252	+	0.506479i	$0.830947\pi$
$740$		−	6.88415e6i		−	0.462138i
$741$	−347459.			−0.0232465
$742$		−	6.75780e6i		−	0.450605i
$743$			2.29090e6i			0.152242i	0.997099	+	0.0761209i	$0.0242535\pi$
$743$			2.29090e6i			0.152242i	−0.997099	+	0.0761209i	$0.975746\pi$
$744$		−	2.68402e6i		−	0.177768i
$745$	−1.96059e7			−1.29419
$746$			8.92401e6i			0.587101i
$747$	−2.01827e7			−1.32336
$748$	2.96749e6			0.193925
$749$	−1.96762e7			−1.28155
$750$	6.56031e6			0.425864
$751$			7.61196e6i			0.492489i	0.969208	+	0.246245i	$0.0791967\pi$
$751$			7.61196e6i			0.492489i	−0.969208	+	0.246245i	$0.920803\pi$
$752$			1.14904e7i			0.740955i
$753$	3.49739e6			0.224780
$754$	−3.96120e6	−	4.26217e6i	−0.253745	−	0.273025i
$755$	8.05186e6			0.514078
$756$		−	1.74833e7i		−	1.11255i
$757$			1.30780e7i			0.829471i	0.909942	+	0.414735i	$0.136126\pi$
$757$			1.30780e7i			0.829471i	−0.909942	+	0.414735i	$0.863874\pi$
$758$	−2.99485e7			−1.89323
$759$	−220464.			−0.0138910
$760$	−2.53473e6			−0.159183
$761$	−5.31779e6			−0.332866			−0.166433	−	0.986053i	$-0.553225\pi$
$761$	−5.31779e6			−0.332866			−0.166433	+	0.986053i	$0.553225\pi$
$762$			1.04567e7i			0.652389i
$763$	2.84093e7			1.76664
$764$			1.55269e7i			0.962388i
$765$		−	2.64315e7i		−	1.63293i
$766$		−	3.40604e7i		−	2.09738i
$767$	−4.53609e6			−0.278415
$768$		−	591663.i		−	0.0361969i
$769$			7.20457e6i			0.439331i	0.975575	+	0.219666i	$0.0704966\pi$
$769$			7.20457e6i			0.439331i	−0.975575	+	0.219666i	$0.929503\pi$
$770$	−3.39773e6			−0.206520
$771$			2.42822e6i			0.147113i
$772$			1.11693e7i			0.674501i
$773$			8.81311e6i			0.530494i	0.964180	+	0.265247i	$0.0854535\pi$
$773$			8.81311e6i			0.530494i	−0.964180	+	0.265247i	$0.914546\pi$
$774$	−3.42305e7			−2.05381
$775$			2.26921e6i			0.135713i
$776$	−482596.			−0.0287693
$777$	2.49580e6			0.148305
$778$	2.52305e7			1.49444
$779$	1.87214e6			0.110533
$780$			1.71686e6i			0.101041i
$781$		−	1.42311e6i		−	0.0834858i
$782$	2.37636e7			1.38962
$783$	−6.65783e6	−	7.16369e6i	−0.388086	−	0.417573i
$784$	−1.22786e7			−0.713444
$785$		−	2.50938e7i		−	1.45342i
$786$			4.73165e6i			0.273185i
$787$	9.51059e6			0.547357			0.273679	−	0.961821i	$-0.411760\pi$
$787$	9.51059e6			0.547357			0.273679	+	0.961821i	$0.411760\pi$
$788$	−2.95479e7			−1.69516
$789$	2.59401e6			0.148347
$790$	−5.05111e7			−2.87951
$791$			2.18355e7i			1.24086i
$792$	663585.			0.0375910
$793$		−	1.25048e6i		−	0.0706144i
$794$		−	3.90898e7i		−	2.20045i
$795$			1.11538e6i			0.0625900i
$796$	1.94270e6			0.108673
$797$		−	2.22541e7i		−	1.24098i	−0.784216	−	0.620488i	$-0.786934\pi$
$797$		−	2.22541e7i		−	1.24098i	0.784216	−	0.620488i	$-0.213066\pi$
$798$		−	3.85755e6i		−	0.214440i
$799$	3.86184e7			2.14007
$800$		−	2.68988e6i		−	0.148597i
$801$			2.56586e7i			1.41303i
$802$		−	4.25605e7i		−	2.33653i
$803$	−2.90432e6			−0.158948
$804$		−	9.74709e6i		−	0.531783i
$805$	−1.54440e7			−0.839984
$806$	8.61420e6			0.467065
$807$	1.11318e6			0.0601704
$808$	1.12942e7			0.608594
$809$			2.03103e7i			1.09105i	0.838094	+	0.545525i	$0.183670\pi$
$809$			2.03103e7i			1.09105i	−0.838094	+	0.545525i	$0.816330\pi$
$810$		−	2.21511e7i		−	1.18627i
$811$	−3.99314e6			−0.213188			−0.106594	−	0.994303i	$-0.533994\pi$
$811$	−3.99314e6			−0.213188			−0.106594	+	0.994303i	$0.533994\pi$
$812$	2.68589e7	−	2.49622e7i	1.42955	−	1.32860i
$813$	−178322.			−0.00946189
$814$			834147.i			0.0441247i
$815$			1.15565e6i			0.0609441i
$816$	−5.69486e6			−0.299404
$817$	−8.99266e6			−0.471339
$818$	3.13640e7			1.63888
$819$	6.37224e6			0.331958
$820$		−	9.25060e6i		−	0.480436i
$821$	−1.77708e7			−0.920128			−0.460064	−	0.887886i	$-0.652174\pi$
$821$	−1.77708e7			−0.920128			−0.460064	+	0.887886i	$0.652174\pi$
$822$			2.44906e6i			0.126421i
$823$			2.36489e7i			1.21706i	0.793532	+	0.608528i	$0.208240\pi$
$823$			2.36489e7i			1.21706i	−0.793532	+	0.608528i	$0.791760\pi$
$824$			6.09191e6i			0.312562i
$825$	54800.9			0.00280319
$826$		−	5.03606e7i		−	2.56827i
$827$		−	1.25828e7i		−	0.639753i	−0.947459	−	0.319877i	$-0.896359\pi$
$827$		−	1.25828e7i		−	0.639753i	0.947459	−	0.319877i	$-0.103641\pi$
$828$	1.26617e7			0.641823
$829$			2.48827e7i			1.25751i	0.777604	+	0.628754i	$0.216435\pi$
$829$			2.48827e7i			1.25751i	−0.777604	+	0.628754i	$0.783565\pi$
$830$			4.61572e7i			2.32565i
$831$			4.37966e6i			0.220008i
$832$	−7.32627e6			−0.366923
$833$			4.12675e7i			2.06061i
$834$	−533418.			−0.0265554
$835$	2.82861e7			1.40397
$836$	731802.			0.0362141
$837$	1.44784e7			0.714344
$838$			1.15325e7i			0.567299i
$839$			1.12350e7i			0.551022i	0.961298	+	0.275511i	$0.0888470\pi$
$839$			1.12350e7i			0.551022i	−0.961298	+	0.275511i	$0.911153\pi$
$840$	−4.54070e6			−0.222037
$841$	1.49940e6	−	2.04563e7i	0.0731019	−	0.997324i
$842$	−5.56687e7			−2.70602
$843$		−	8.32379e6i		−	0.403415i
$844$			3.60309e7i			1.74108i
$845$	2.05384e7			0.989518
$846$	3.62513e7			1.74140
$847$	−3.08070e7			−1.47550
$848$	−2.46026e6			−0.117488
$849$		−	5.85644e6i		−	0.278846i
$850$	−5.90696e6			−0.280425
$851$			3.79154e6i			0.179470i
$852$		−	7.98355e6i		−	0.376788i
$853$		−	3.44587e7i		−	1.62153i	−0.585370	−	0.810767i	$-0.699051\pi$
$853$		−	3.44587e7i		−	1.62153i	0.585370	−	0.810767i	$-0.300949\pi$
$854$	1.38831e7			0.651389
$855$		−	6.51819e6i		−	0.304938i
$856$		−	8.78839e6i		−	0.409944i
$857$	1.43071e7			0.665427			0.332713	−	0.943028i	$-0.392036\pi$
$857$	1.43071e7			0.665427			0.332713	+	0.943028i	$0.392036\pi$
$858$		−	208031.i		−	0.00964738i
$859$			1.45763e7i			0.674006i	0.941504	+	0.337003i	$0.109413\pi$
$859$			1.45763e7i			0.674006i	−0.941504	+	0.337003i	$0.890587\pi$
$860$			4.44345e7i			2.04868i
$861$	3.35374e6			0.154178
$862$			3.01676e6i			0.138284i
$863$	1.24188e7			0.567612			0.283806	−	0.958882i	$-0.408403\pi$
$863$	1.24188e7			0.567612			0.283806	+	0.958882i	$0.408403\pi$
$864$	−1.71625e7			−0.782160
$865$	−4.24868e7			−1.93069
$866$	9.10863e6			0.412722
$867$			1.25374e7i			0.566449i
$868$			5.42841e7i			2.44553i
$869$	3.47398e6			0.156055
$870$	−7.81011e6	+	7.25860e6i	−0.349832	+	0.325128i
$871$	7.45216e6			0.332841
$872$			1.26890e7i			0.565115i
$873$		−	1.24102e6i		−	0.0551117i
$874$	5.86027e6			0.259501
$875$	−3.16074e7			−1.39562
$876$	−1.62930e7			−0.717366
$877$	1.26855e7			0.556941			0.278470	−	0.960445i	$-0.410173\pi$
$877$	1.26855e7			0.556941			0.278470	+	0.960445i	$0.410173\pi$
$878$		−	3.80088e7i		−	1.66398i
$879$	9.15678e6			0.399733
$880$			1.23699e6i			0.0538465i
$881$			3.87917e6i			0.168383i	0.996450	+	0.0841917i	$0.0268308\pi$
$881$			3.87917e6i			0.168383i	−0.996450	+	0.0841917i	$0.973169\pi$
$882$			3.87380e7i			1.67674i
$883$	1.43513e7			0.619427			0.309714	−	0.950830i	$-0.399767\pi$
$883$	1.43513e7			0.619427			0.309714	+	0.950830i	$0.399767\pi$
$884$			1.27278e7i			0.547799i
$885$			8.31205e6i			0.356739i
$886$	−5.80930e7			−2.48622
$887$		−	2.21879e7i		−	0.946906i	−0.880819	−	0.473453i	$-0.843007\pi$
$887$		−	2.21879e7i		−	0.946906i	0.880819	−	0.473453i	$-0.156993\pi$
$888$			1.11475e6i			0.0474400i
$889$		−	5.03800e7i		−	2.13798i
$890$	5.86803e7			2.48323
$891$			1.52348e6i			0.0642899i
$892$	−1.60625e7			−0.675927
$893$	9.52356e6			0.399642
$894$	1.33271e7			0.557689
$895$	1.05415e7			0.439892
$896$		−	3.23192e7i		−	1.34490i
$897$		−	945585.i		−	0.0392391i
$898$	4.09849e7			1.69603
$899$	2.06719e7	+	2.22426e7i	0.853064	+	0.917880i
$900$	−3.14733e6			−0.129520
$901$			8.26874e6i			0.339334i
$902$			1.12089e6i			0.0458718i
$903$	−1.61094e7			−0.657446
$904$	−9.75284e6			−0.396926
$905$	−1.68474e6			−0.0683772
$906$	−5.47324e6			−0.221526
$907$		−	7.47413e6i		−	0.301677i	−0.988558	−	0.150839i	$-0.951803\pi$
$907$		−	7.47413e6i		−	0.301677i	0.988558	−	0.150839i	$-0.0481974\pi$
$908$	5.65400e6			0.227584
$909$			2.90437e7i			1.16585i
$910$		−	1.45731e7i		−	0.583376i
$911$		−	2.95291e7i		−	1.17884i	−0.807828	−	0.589419i	$-0.799357\pi$
$911$		−	2.95291e7i		−	1.17884i	0.807828	−	0.589419i	$-0.200643\pi$
$912$	−1.40439e6			−0.0559115
$913$		−	3.17454e6i		−	0.126039i
$914$		−	6.95019e7i		−	2.75189i
$915$	−2.29141e6			−0.0904795
$916$			2.82177e7i			1.11118i
$917$		−	2.27970e7i		−	0.895271i
$918$			3.76886e7i			1.47606i
$919$	3.15741e7			1.23323			0.616613	−	0.787266i	$-0.288504\pi$
$919$	3.15741e7			1.23323			0.616613	+	0.787266i	$0.288504\pi$
$920$		−	6.89809e6i		−	0.268695i
$921$	1.72952e6			0.0671856
$922$	−3.11883e7			−1.20827
$923$	6.10384e6			0.235830
$924$	1.31095e6			0.0505132
$925$		−	942467.i		−	0.0362169i
$926$		−	4.26367e7i		−	1.63401i
$927$	−1.56657e7			−0.598757
$928$	−2.45041e7	−	2.63660e7i	−0.934048	−	1.00502i
$929$	4.81809e7			1.83162			0.915811	−	0.401610i	$-0.131549\pi$
$929$	4.81809e7			1.83162			0.915811	+	0.401610i	$0.131549\pi$
$930$		−	1.57849e7i		−	0.598459i
$931$			1.01768e7i			0.384803i
$932$	−8.63084e6			−0.325472
$933$	−6.41140e6			−0.241129
$934$	4.24281e7			1.59143
$935$	4.15741e6			0.155523
$936$			2.84616e6i			0.106187i
$937$	−2.09601e7			−0.779910			−0.389955	−	0.920834i	$-0.627509\pi$
$937$	−2.09601e7			−0.779910			−0.389955	+	0.920834i	$0.627509\pi$
$938$			8.27353e7i			3.07032i
$939$		−	6.95129e6i		−	0.257277i
$940$		−	4.70578e7i		−	1.73705i
$941$	−2.29762e7			−0.845872			−0.422936	−	0.906160i	$-0.639000\pi$
$941$	−2.29762e7			−0.845872			−0.422936	+	0.906160i	$0.639000\pi$
$942$			1.70575e7i			0.626307i
$943$			5.09489e6i			0.186576i
$944$	−1.83344e7			−0.669633
$945$		−	2.44939e7i		−	0.892233i
$946$		−	5.38410e6i		−	0.195607i
$947$		−	2.59268e7i		−	0.939452i	−0.882812	−	0.469726i	$-0.844353\pi$
$947$		−	2.59268e7i		−	0.939452i	0.882812	−	0.469726i	$-0.155647\pi$
$948$	1.94887e7			0.704307
$949$		−	1.24569e7i		−	0.448996i
$950$	−1.45670e6			−0.0523672
$951$	8.03621e6			0.288138
$952$	−3.36620e7			−1.20378
$953$	−2.36299e7			−0.842810			−0.421405	−	0.906873i	$-0.638463\pi$
$953$	−2.36299e7			−0.842810			−0.421405	+	0.906873i	$0.638463\pi$
$954$			7.76192e6i			0.276120i
$955$			2.17529e7i			0.771808i
$956$	−3.98283e7			−1.40944
$957$	537153.	−	499222.i	0.0189591	−	0.0176203i
$958$	−6.73528e7			−2.37106
$959$		−	1.17995e7i		−	0.414303i
$960$			1.34249e7i			0.470145i
$961$	−1.63250e7			−0.570222
$962$	−3.57772e6			−0.124643
$963$	2.25998e7			0.785307
$964$	3.84448e7			1.33243
$965$			1.56480e7i			0.540930i
$966$	1.04981e7			0.361965
$967$		−	3.54372e7i		−	1.21869i	−0.792905	−	0.609345i	$-0.791432\pi$
$967$		−	3.54372e7i		−	1.21869i	0.792905	−	0.609345i	$-0.208568\pi$
$968$		−	1.37599e7i		−	0.471985i
$969$			4.72004e6i			0.161487i
$970$	−2.83818e6			−0.0968523
$971$			3.65656e7i			1.24458i	0.782785	+	0.622292i	$0.213798\pi$
$971$			3.65656e7i			1.24458i	−0.782785	+	0.622292i	$0.786202\pi$
$972$			3.05892e7i			1.03849i
$973$	2.57000e6			0.0870263
$974$		−	6.67081e7i		−	2.25310i
$975$			235045.i			0.00791844i
$976$		−	5.05430e6i		−	0.169839i
$977$	−1.80970e7			−0.606554			−0.303277	−	0.952902i	$-0.598081\pi$
$977$	−1.80970e7			−0.606554			−0.303277	+	0.952902i	$0.598081\pi$
$978$		−	785550.i		−	0.0262619i
$979$	−4.03583e6			−0.134579
$980$	5.02858e7			1.67255
$981$	−3.26305e7			−1.08256
$982$	−2.51885e7			−0.833533
$983$			4.10427e7i			1.35473i	0.735648	+	0.677364i	$0.236878\pi$
$983$			4.10427e7i			1.35473i	−0.735648	+	0.677364i	$0.763122\pi$
$984$			1.49795e6i			0.0493184i
$985$	−4.13963e7			−1.35947
$986$	−5.78994e7	+	5.38108e7i	−1.89663	+	1.76269i
$987$	1.70605e7			0.557440
$988$			3.13875e6i			0.102297i
$989$		−	2.44729e7i		−	0.795600i
$990$	3.90258e6			0.126551
$991$	−3.85584e6			−0.124720			−0.0623598	−	0.998054i	$-0.519863\pi$
$991$	−3.85584e6			−0.124720			−0.0623598	+	0.998054i	$0.519863\pi$
$992$	5.32878e7			1.71929
$993$	−6.50683e6			−0.209409
$994$			6.77661e7i			2.17544i
$995$	2.72169e6			0.0871528
$996$		−	1.78089e7i		−	0.568837i
$997$			3.20654e6i			0.102164i	0.998694	+	0.0510821i	$0.0162670\pi$
$997$			3.20654e6i			0.102164i	−0.998694	+	0.0510821i	$0.983733\pi$
$998$			3.63648e7i			1.15573i
$999$	−6.01329e6			−0.190633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.b.a.28.10	yes	12
3.2	odd	2		261.6.c.b.28.3		12
4.3	odd	2		464.6.e.c.289.7		12
29.12	odd	4		841.6.a.d.1.3		12
29.17	odd	4		841.6.a.d.1.10		12
29.28	even	2	inner	29.6.b.a.28.3	✓	12
87.86	odd	2		261.6.c.b.28.10		12
116.115	odd	2		464.6.e.c.289.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.b.a.28.3	✓	12	29.28	even	2	inner
29.6.b.a.28.10	yes	12	1.1	even	1	trivial
261.6.c.b.28.3		12	3.2	odd	2
261.6.c.b.28.10		12	87.86	odd	2
464.6.e.c.289.6		12	116.115	odd	2
464.6.e.c.289.7		12	4.3	odd	2
841.6.a.d.1.3		12	29.12	odd	4
841.6.a.d.1.10		12	29.17	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	29.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+8.60273i q^{2} -4.65015i q^{3} -42.0069 q^{4} -58.8511 q^{5} +40.0039 q^{6} -192.738 q^{7} -86.0865i q^{8} +221.376 q^{9} +O(q^{10})\)	\(q+8.60273i q^{2} -4.65015i q^{3} -42.0069 q^{4} -58.8511 q^{5} +40.0039 q^{6} -192.738 q^{7} -86.0865i q^{8} +221.376 q^{9} -506.279i q^{10} +34.8202i q^{11} +195.338i q^{12} -149.346 q^{13} -1658.07i q^{14} +273.666i q^{15} -603.642 q^{16} +2028.79i q^{17} +1904.44i q^{18} +500.313i q^{19} +2472.15 q^{20} +896.259i q^{21} -299.548 q^{22} -1361.57 q^{23} -400.315 q^{24} +338.447 q^{25} -1284.78i q^{26} -2159.42i q^{27} +8096.32 q^{28} +(3317.42 - 3083.16i) q^{29} -2354.27 q^{30} +6704.78i q^{31} -7947.73i q^{32} +161.919 q^{33} -17453.1 q^{34} +11342.8 q^{35} -9299.32 q^{36} -2784.68i q^{37} -4304.06 q^{38} +694.482i q^{39} +5066.28i q^{40} -3741.93i q^{41} -7710.27 q^{42} +17974.1i q^{43} -1462.69i q^{44} -13028.2 q^{45} -11713.2i q^{46} -19035.2i q^{47} +2807.02i q^{48} +20340.9 q^{49} +2911.56i q^{50} +9434.17 q^{51} +6273.57 q^{52} +4075.70 q^{53} +18576.9 q^{54} -2049.20i q^{55} +16592.1i q^{56} +2326.53 q^{57} +(26523.6 + 28538.9i) q^{58} +30373.0 q^{59} -11495.9i q^{60} +8373.02i q^{61} -57679.4 q^{62} -42667.6 q^{63} +49055.6 q^{64} +8789.18 q^{65} +1392.94i q^{66} -49898.5 q^{67} -85223.2i q^{68} +6331.49i q^{69} +97579.3i q^{70} -40870.4 q^{71} -19057.5i q^{72} +83409.2i q^{73} +23955.9 q^{74} -1573.83i q^{75} -21016.6i q^{76} -6711.17i q^{77} -5974.44 q^{78} -99769.1i q^{79} +35525.0 q^{80} +43752.8 q^{81} +32190.8 q^{82} -91169.5 q^{83} -37649.1i q^{84} -119396. i q^{85} -154626. q^{86} +(-14337.1 - 15426.5i) q^{87} +2997.55 q^{88} +115905. i q^{89} -112078. i q^{90} +28784.7 q^{91} +57195.3 q^{92} +31178.2 q^{93} +163754. q^{94} -29444.0i q^{95} -36958.1 q^{96} -5605.95i q^{97} +174987. i q^{98} +7708.35i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 172 q^{4} + 46 q^{5} + 24 q^{6} + 20 q^{7} - 1574 q^{9}+O(q^{10}) \) 12 * q - 172 * q^4 + 46 * q^5 + 24 * q^6 + 20 * q^7 - 1574 * q^9	\( 12 q - 172 q^{4} + 46 q^{5} + 24 q^{6} + 20 q^{7} - 1574 q^{9} + 1362 q^{13} + 340 q^{16} - 4508 q^{20} + 11376 q^{22} + 5852 q^{23} - 6292 q^{24} + 12678 q^{25} - 25056 q^{28} + 11328 q^{29} + 14952 q^{30} - 22694 q^{33} - 22504 q^{34} + 4532 q^{35} + 22840 q^{36} - 43408 q^{38} + 8280 q^{42} - 52816 q^{45} + 102836 q^{49} + 58540 q^{51} + 15172 q^{52} + 25650 q^{53} - 89080 q^{54} - 32824 q^{57} + 4960 q^{58} - 3900 q^{59} + 37720 q^{62} - 146616 q^{63} + 252276 q^{64} + 169574 q^{65} - 28264 q^{67} - 286832 q^{71} - 263072 q^{74} + 519072 q^{78} - 230964 q^{80} - 24084 q^{81} - 178008 q^{82} + 85692 q^{83} - 126624 q^{86} - 137716 q^{87} - 83604 q^{88} - 182372 q^{91} - 5664 q^{92} + 377966 q^{93} + 192144 q^{94} - 415284 q^{96}+O(q^{100}) \) 12 * q - 172 * q^4 + 46 * q^5 + 24 * q^6 + 20 * q^7 - 1574 * q^9 + 1362 * q^13 + 340 * q^16 - 4508 * q^20 + 11376 * q^22 + 5852 * q^23 - 6292 * q^24 + 12678 * q^25 - 25056 * q^28 + 11328 * q^29 + 14952 * q^30 - 22694 * q^33 - 22504 * q^34 + 4532 * q^35 + 22840 * q^36 - 43408 * q^38 + 8280 * q^42 - 52816 * q^45 + 102836 * q^49 + 58540 * q^51 + 15172 * q^52 + 25650 * q^53 - 89080 * q^54 - 32824 * q^57 + 4960 * q^58 - 3900 * q^59 + 37720 * q^62 - 146616 * q^63 + 252276 * q^64 + 169574 * q^65 - 28264 * q^67 - 286832 * q^71 - 263072 * q^74 + 519072 * q^78 - 230964 * q^80 - 24084 * q^81 - 178008 * q^82 + 85692 * q^83 - 126624 * q^86 - 137716 * q^87 - 83604 * q^88 - 182372 * q^91 - 5664 * q^92 + 377966 * q^93 + 192144 * q^94 - 415284 * q^96

Introduction

L-functions

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