LMFDB - Embedded newform 29.6.b.a.28.5

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			28.5
Root			$-3.61683i$ of defining polynomial
Character	$\chi$	$=$	29.28
Dual form			29.6.b.a.28.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.61683i q^{2} +5.13082i q^{3} +18.9185 q^{4} +15.9022 q^{5} +18.5573 q^{6} +69.7674 q^{7} -184.164i q^{8} +216.675 q^{9} +O(q^{10})$	\(q-3.61683i q^{2} +5.13082i q^{3} +18.9185 q^{4} +15.9022 q^{5} +18.5573 q^{6} +69.7674 q^{7} -184.164i q^{8} +216.675 q^{9} -57.5154i q^{10} -400.387i q^{11} +97.0675i q^{12} -178.686 q^{13} -252.337i q^{14} +81.5911i q^{15} -60.6968 q^{16} +1410.99i q^{17} -783.676i q^{18} +1727.73i q^{19} +300.845 q^{20} +357.964i q^{21} -1448.13 q^{22} -1109.14 q^{23} +944.911 q^{24} -2872.12 q^{25} +646.278i q^{26} +2358.51i q^{27} +1319.90 q^{28} +(-3442.35 - 2943.02i) q^{29} +295.101 q^{30} -2033.09i q^{31} -5673.71i q^{32} +2054.31 q^{33} +5103.31 q^{34} +1109.45 q^{35} +4099.17 q^{36} +7214.27i q^{37} +6248.90 q^{38} -916.806i q^{39} -2928.60i q^{40} -7337.02i q^{41} +1294.70 q^{42} +4978.67i q^{43} -7574.73i q^{44} +3445.60 q^{45} +4011.57i q^{46} +493.299i q^{47} -311.424i q^{48} -11939.5 q^{49} +10388.0i q^{50} -7239.53 q^{51} -3380.48 q^{52} -10825.6 q^{53} +8530.32 q^{54} -6367.02i q^{55} -12848.6i q^{56} -8864.65 q^{57} +(-10644.4 + 12450.4i) q^{58} -4332.32 q^{59} +1543.58i q^{60} +46481.5i q^{61} -7353.36 q^{62} +15116.8 q^{63} -22463.2 q^{64} -2841.50 q^{65} -7430.11i q^{66} -4487.33 q^{67} +26693.8i q^{68} -5690.79i q^{69} -4012.70i q^{70} +58697.7 q^{71} -39903.6i q^{72} -15317.2i q^{73} +26092.8 q^{74} -14736.3i q^{75} +32686.0i q^{76} -27934.0i q^{77} -3315.93 q^{78} -33868.5i q^{79} -965.210 q^{80} +40550.9 q^{81} -26536.8 q^{82} +45749.9 q^{83} +6772.15i q^{84} +22437.8i q^{85} +18007.0 q^{86} +(15100.1 - 17662.1i) q^{87} -73736.8 q^{88} -104566. i q^{89} -12462.1i q^{90} -12466.5 q^{91} -20983.3 q^{92} +10431.4 q^{93} +1784.18 q^{94} +27474.6i q^{95} +29110.8 q^{96} +151708. i q^{97} +43183.2i q^{98} -86753.8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.61683i		−	0.639372i	−0.947524	−	0.319686i	$-0.896423\pi$
$2$		−	3.61683i		−	0.639372i	0.947524	−	0.319686i	$-0.103577\pi$
$3$			5.13082i			0.329142i	0.986365	+	0.164571i	$0.0526240\pi$
$3$			5.13082i			0.329142i	−0.986365	+	0.164571i	$0.947376\pi$
$4$	18.9185			0.591204
$5$	15.9022			0.284466			0.142233	−	0.989833i	$-0.454572\pi$
$5$	15.9022			0.284466			0.142233	+	0.989833i	$0.454572\pi$
$6$	18.5573			0.210444
$7$	69.7674			0.538155			0.269078	−	0.963118i	$-0.413281\pi$
$7$	69.7674			0.538155			0.269078	+	0.963118i	$0.413281\pi$
$8$		−	184.164i		−	1.01737i
$9$	216.675			0.891666
$10$		−	57.5154i		−	0.181880i
$11$		−	400.387i		−	0.997697i	−0.866689	−	0.498848i	$-0.833756\pi$
$11$		−	400.387i		−	0.997697i	0.866689	−	0.498848i	$-0.166244\pi$
$12$			97.0675i			0.194590i
$13$	−178.686			−0.293246			−0.146623	−	0.989192i	$-0.546840\pi$
$13$	−178.686			−0.293246			−0.146623	+	0.989192i	$0.546840\pi$
$14$		−	252.337i		−	0.344081i
$15$			81.5911i			0.0936299i
$16$	−60.6968			−0.0592742
$17$			1410.99i			1.18414i	0.805888	+	0.592068i	$0.201688\pi$
$17$			1410.99i			1.18414i	−0.805888	+	0.592068i	$0.798312\pi$
$18$		−	783.676i		−	0.570106i
$19$			1727.73i			1.09797i	0.835832	+	0.548986i	$0.184986\pi$
$19$			1727.73i			1.09797i	−0.835832	+	0.548986i	$0.815014\pi$
$20$	300.845			0.168178
$21$			357.964i			0.177130i
$22$	−1448.13			−0.637899
$23$	−1109.14			−0.437186			−0.218593	−	0.975816i	$-0.570147\pi$
$23$	−1109.14			−0.437186			−0.218593	+	0.975816i	$0.570147\pi$
$24$	944.911			0.334859
$25$	−2872.12			−0.919079
$26$			646.278i			0.187493i
$27$			2358.51i			0.622627i
$28$	1319.90			0.318159
$29$	−3442.35	−	2943.02i	−0.760081	−	0.649828i
$29$	−3442.35	−	2943.02i	−0.760081	−	0.649828i
$30$	295.101			0.0598643
$31$		−	2033.09i		−	0.379973i	−0.981787	−	0.189987i	$-0.939156\pi$
$31$		−	2033.09i		−	0.379973i	0.981787	−	0.189987i	$-0.0608445\pi$
$32$		−	5673.71i		−	0.979472i
$33$	2054.31			0.328384
$34$	5103.31			0.757103
$35$	1109.45			0.153087
$36$	4099.17			0.527156
$37$			7214.27i			0.866339i	0.901312	+	0.433170i	$0.142605\pi$
$37$			7214.27i			0.866339i	−0.901312	+	0.433170i	$0.857395\pi$
$38$	6248.90			0.702012
$39$		−	916.806i		−	0.0965197i
$40$		−	2928.60i		−	0.289408i
$41$		−	7337.02i		−	0.681648i	−0.940127	−	0.340824i	$-0.889294\pi$
$41$		−	7337.02i		−	0.681648i	0.940127	−	0.340824i	$-0.110706\pi$
$42$	1294.70			0.113252
$43$			4978.67i			0.410622i	0.978697	+	0.205311i	$0.0658206\pi$
$43$			4978.67i			0.410622i	−0.978697	+	0.205311i	$0.934179\pi$
$44$		−	7574.73i		−	0.589842i
$45$	3445.60			0.253649
$46$			4011.57i			0.279525i
$47$			493.299i			0.0325736i	0.999867	+	0.0162868i	$0.00518447\pi$
$47$			493.299i			0.0325736i	−0.999867	+	0.0162868i	$0.994816\pi$
$48$		−	311.424i		−	0.0195096i
$49$	−11939.5			−0.710389
$50$			10388.0i			0.587633i
$51$	−7239.53			−0.389749
$52$	−3380.48			−0.173368
$53$	−10825.6			−0.529373			−0.264686	−	0.964335i	$-0.585268\pi$
$53$	−10825.6			−0.529373			−0.264686	+	0.964335i	$0.585268\pi$
$54$	8530.32			0.398090
$55$		−	6367.02i		−	0.283811i
$56$		−	12848.6i		−	0.547503i
$57$	−8864.65			−0.361389
$58$	−10644.4	+	12450.4i	−0.415482	+	0.485974i
$59$	−4332.32			−0.162028			−0.0810141	−	0.996713i	$-0.525816\pi$
$59$	−4332.32			−0.162028			−0.0810141	+	0.996713i	$0.525816\pi$
$60$			1543.58i			0.0553543i
$61$			46481.5i			1.59939i	0.600404	+	0.799697i	$0.295006\pi$
$61$			46481.5i			1.59939i	−0.600404	+	0.799697i	$0.704994\pi$
$62$	−7353.36			−0.242944
$63$	15116.8			0.479855
$64$	−22463.2			−0.685521
$65$	−2841.50			−0.0834187
$66$		−	7430.11i		−	0.209959i
$67$	−4487.33			−0.122124			−0.0610620	−	0.998134i	$-0.519449\pi$
$67$	−4487.33			−0.122124			−0.0610620	+	0.998134i	$0.519449\pi$
$68$			26693.8i			0.700065i
$69$		−	5690.79i		−	0.143896i
$70$		−	4012.70i		−	0.0978796i
$71$	58697.7			1.38189			0.690947	−	0.722905i	$-0.257194\pi$
$71$	58697.7			1.38189			0.690947	+	0.722905i	$0.257194\pi$
$72$		−	39903.6i		−	0.907154i
$73$		−	15317.2i		−	0.336414i	−0.985752	−	0.168207i	$-0.946202\pi$
$73$		−	15317.2i		−	0.336414i	0.985752	−	0.168207i	$-0.0537976\pi$
$74$	26092.8			0.553913
$75$		−	14736.3i		−	0.302507i
$76$			32686.0i			0.649125i
$77$		−	27934.0i		−	0.536916i
$78$	−3315.93			−0.0617120
$79$		−	33868.5i		−	0.610559i	−0.952263	−	0.305279i	$-0.901250\pi$
$79$		−	33868.5i		−	0.610559i	0.952263	−	0.305279i	$-0.0987499\pi$
$80$	−965.210			−0.0168615
$81$	40550.9			0.686733
$82$	−26536.8			−0.435826
$83$	45749.9			0.728945			0.364473	−	0.931214i	$-0.381249\pi$
$83$	45749.9			0.728945			0.364473	+	0.931214i	$0.381249\pi$
$84$			6772.15i			0.104720i
$85$			22437.8i			0.336847i
$86$	18007.0			0.262540
$87$	15100.1	−	17662.1i	0.213886	−	0.250175i
$88$	−73736.8			−1.01503
$89$		−	104566.i		−	1.39932i	−0.714478	−	0.699658i	$-0.753336\pi$
$89$		−	104566.i		−	1.39932i	0.714478	−	0.699658i	$-0.246664\pi$
$90$		−	12462.1i		−	0.162176i
$91$	−12466.5			−0.157812
$92$	−20983.3			−0.258466
$93$	10431.4			0.125065
$94$	1784.18			0.0208266
$95$			27474.6i			0.312336i
$96$	29110.8			0.322386
$97$			151708.i			1.63711i	0.574428	+	0.818555i	$0.305224\pi$
$97$			151708.i			1.63711i	−0.574428	+	0.818555i	$0.694776\pi$
$98$			43183.2i			0.454203i
$99$		−	86753.8i		−	0.889612i
$100$	−54336.3			−0.543363
$101$		−	24654.4i		−	0.240487i	−0.992744	−	0.120243i	$-0.961633\pi$
$101$		−	24654.4i		−	0.240487i	0.992744	−	0.120243i	$-0.0383675\pi$
$102$			26184.2i			0.249194i
$103$	−24585.9			−0.228346			−0.114173	−	0.993461i	$-0.536422\pi$
$103$	−24585.9			−0.228346			−0.114173	+	0.993461i	$0.536422\pi$
$104$			32907.5i			0.298340i
$105$			5692.40i			0.0503874i
$106$			39154.3i			0.338466i
$107$	100568.			0.849183			0.424591	−	0.905385i	$-0.360418\pi$
$107$	100568.			0.849183			0.424591	+	0.905385i	$0.360418\pi$
$108$			44619.5i			0.368099i
$109$	−147299.			−1.18750			−0.593748	−	0.804651i	$-0.702352\pi$
$109$	−147299.			−1.18750			−0.593748	+	0.804651i	$0.702352\pi$
$110$	−23028.4			−0.181461
$111$	−37015.1			−0.285149
$112$	−4234.66			−0.0318987
$113$			129508.i			0.954117i	0.878871	+	0.477059i	$0.158297\pi$
$113$			129508.i			0.954117i	−0.878871	+	0.477059i	$0.841703\pi$
$114$			32062.0i			0.231062i
$115$	−17637.7			−0.124365
$116$	−65124.2	−	55677.6i	−0.449363	−	0.384181i
$117$	−38716.8			−0.261478
$118$			15669.3i			0.103596i
$119$			98441.1i			0.637249i
$120$	15026.1			0.0952563
$121$	741.050			0.00460134
$122$	168116.			1.02261
$123$	37644.9			0.224359
$124$		−	38463.1i		−	0.224642i
$125$	−95367.2			−0.545914
$126$		−	54675.1i		−	0.306805i
$127$		−	327753.i		−	1.80317i	−0.432601	−	0.901586i	$-0.642404\pi$
$127$		−	327753.i		−	1.80317i	0.432601	−	0.901586i	$-0.357596\pi$
$128$		−	100313.i		−	0.541170i
$129$	−25544.7			−0.135153
$130$			10277.2i			0.0533356i
$131$		−	307291.i		−	1.56449i	−0.622972	−	0.782244i	$-0.714075\pi$
$131$		−	307291.i		−	1.56449i	0.622972	−	0.782244i	$-0.285925\pi$
$132$	38864.6			0.194142
$133$			120539.i			0.590879i
$134$			16229.9i			0.0780826i
$135$			37505.3i			0.177116i
$136$	259853.			1.20470
$137$			220879.i			1.00543i	0.864451	+	0.502717i	$0.167666\pi$
$137$			220879.i			1.00543i	−0.864451	+	0.502717i	$0.832334\pi$
$138$	−20582.6			−0.0920033
$139$	228651.			1.00378			0.501888	−	0.864932i	$-0.332639\pi$
$139$	228651.			1.00378			0.501888	+	0.864932i	$0.332639\pi$
$140$	20989.2			0.0905057
$141$	−2531.02			−0.0107213
$142$		−	212300.i		−	0.883544i
$143$			71543.7i			0.292571i
$144$	−13151.5			−0.0528528
$145$	−54740.8	−	46800.4i	−0.216218	−	0.184854i
$146$	−55399.9			−0.215093
$147$		−	61259.4i		−	0.233819i
$148$			136483.i			0.512183i
$149$	−276764.			−1.02128			−0.510640	−	0.859795i	$-0.670591\pi$
$149$	−276764.			−1.02128			−0.510640	+	0.859795i	$0.670591\pi$
$150$	−53298.8			−0.193415
$151$	401630.			1.43345			0.716727	−	0.697354i	$-0.245639\pi$
$151$	401630.			1.43345			0.716727	+	0.697354i	$0.245639\pi$
$152$	318185.			1.11704
$153$			305726.i			1.05585i
$154$	−101033.			−0.343289
$155$		−	32330.6i		−	0.108090i
$156$		−	17344.6i		−	0.0570628i
$157$		−	10880.1i		−	0.0352277i	−0.999845	−	0.0176138i	$-0.994393\pi$
$157$		−	10880.1i		−	0.0352277i	0.999845	−	0.0176138i	$-0.00560695\pi$
$158$	−122497.			−0.390374
$159$		−	55544.1i		−	0.174239i
$160$		−	90224.2i		−	0.278627i
$161$	−77381.8			−0.235274
$162$		−	146666.i		−	0.439078i
$163$			391732.i			1.15484i	0.816449	+	0.577418i	$0.195939\pi$
$163$			391732.i			1.15484i	−0.816449	+	0.577418i	$0.804061\pi$
$164$		−	138806.i		−	0.402993i
$165$	32668.0			0.0934142
$166$		−	165470.i		−	0.466067i
$167$	−220260.			−0.611144			−0.305572	−	0.952169i	$-0.598848\pi$
$167$	−220260.			−0.611144			−0.305572	+	0.952169i	$0.598848\pi$
$168$	65924.0			0.180206
$169$	−339364.			−0.914007
$170$	81153.7			0.215370
$171$			374355.i			0.979023i
$172$			94189.2i			0.242762i
$173$	−660949.			−1.67901			−0.839504	−	0.543353i	$-0.817154\pi$
$173$	−660949.			−1.67901			−0.839504	+	0.543353i	$0.817154\pi$
$174$	−63880.7	−	54614.6i	−0.159955	−	0.136753i
$175$	−200381.			−0.494607
$176$			24302.2i			0.0591377i
$177$		−	22228.3i		−	0.0533303i
$178$	−378198.			−0.894682
$179$	−230503.			−0.537706			−0.268853	−	0.963181i	$-0.586645\pi$
$179$	−230503.			−0.537706			−0.268853	+	0.963181i	$0.586645\pi$
$180$	65185.6			0.149958
$181$	576366.			1.30768			0.653841	−	0.756632i	$-0.273157\pi$
$181$	576366.			1.30768			0.653841	+	0.756632i	$0.273157\pi$
$182$			45089.2i			0.100901i
$183$	−238488.			−0.526428
$184$			204263.i			0.444781i
$185$			114722.i			0.246444i
$186$		−	37728.7i		−	0.0799632i
$187$	564942.			1.18141
$188$			9332.48i			0.0192576i
$189$			164547.i			0.335070i
$190$	99371.0			0.199699
$191$		−	254400.i		−	0.504584i	−0.967651	−	0.252292i	$-0.918816\pi$
$191$		−	254400.i		−	0.504584i	0.967651	−	0.252292i	$-0.0811844\pi$
$192$		−	115254.i		−	0.225634i
$193$		−	263088.i		−	0.508402i	−0.967151	−	0.254201i	$-0.918188\pi$
$193$		−	263088.i		−	0.508402i	0.967151	−	0.254201i	$-0.0818125\pi$
$194$	548701.			1.04672
$195$		−	14579.2i		−	0.0274566i
$196$	−225878.			−0.419985
$197$	515004.			0.945465			0.472732	−	0.881206i	$-0.343268\pi$
$197$	515004.			0.945465			0.472732	+	0.881206i	$0.343268\pi$
$198$	−313774.			−0.568793
$199$	733536.			1.31307			0.656536	−	0.754295i	$-0.272021\pi$
$199$	733536.			1.31307			0.656536	+	0.754295i	$0.272021\pi$
$200$			528941.i			0.935044i
$201$		−	23023.7i		−	0.0401961i
$202$	−89170.8			−0.153760
$203$	−240164.	−	205327.i	−0.409042	−	0.349708i
$204$	−136961.			−0.230421
$205$		−	116674.i		−	0.193906i
$206$			88923.0i			0.145998i
$207$	−240322.			−0.389824
$208$	10845.7			0.0173820
$209$	691760.			1.09544
$210$	20588.4			0.0322163
$211$		−	1.27615e6i		−	1.97331i	−0.162814	−	0.986657i	$-0.552057\pi$
$211$		−	1.27615e6i		−	1.97331i	0.162814	−	0.986657i	$-0.447943\pi$
$212$	−204804.			−0.312967
$213$			301167.i			0.454840i
$214$		−	363738.i		−	0.542943i
$215$			79171.7i			0.116808i
$216$	434351.			0.633442
$217$		−	141844.i		−	0.204485i
$218$			532754.i			0.759251i
$219$	78590.0			0.110728
$220$		−	120455.i		−	0.167790i
$221$		−	252124.i		−	0.347243i
$222$			133877.i			0.182316i
$223$	920981.			1.24019			0.620095	−	0.784526i	$-0.287094\pi$
$223$	920981.			1.24019			0.620095	+	0.784526i	$0.287094\pi$
$224$		−	395840.i		−	0.527108i
$225$	−622316.			−0.819511
$226$	468410.			0.610036
$227$	−829617.			−1.06859			−0.534297	−	0.845297i	$-0.679424\pi$
$227$	−829617.			−1.06859			−0.534297	+	0.845297i	$0.679424\pi$
$228$	−167706.			−0.213654
$229$		−	763360.i		−	0.961924i	−0.876741	−	0.480962i	$-0.840287\pi$
$229$		−	763360.i		−	0.961924i	0.876741	−	0.480962i	$-0.159713\pi$
$230$			63792.6i			0.0795154i
$231$	143324.			0.176722
$232$	−541998.	+	633956.i	−0.661116	+	0.773284i
$233$	−1.56800e6			−1.89216			−0.946078	−	0.323939i	$-0.894993\pi$
$233$	−1.56800e6			−1.89216			−0.946078	+	0.323939i	$0.894993\pi$
$234$			140032.i			0.167181i
$235$			7844.51i			0.00926608i
$236$	−81961.1			−0.0957916
$237$	173773.			0.200961
$238$	356045.			0.407439
$239$	1.00736e6			1.14075			0.570375	−	0.821384i	$-0.306798\pi$
$239$	1.00736e6			1.14075			0.570375	+	0.821384i	$0.306798\pi$
$240$		−	4952.32i		−	0.00554984i
$241$	264093.			0.292896			0.146448	−	0.989218i	$-0.453216\pi$
$241$	264093.			0.292896			0.146448	+	0.989218i	$0.453216\pi$
$242$		−	2680.25i		−	0.00294197i
$243$			781176.i			0.848659i
$244$			879361.i			0.945567i
$245$	−189864.			−0.202082
$246$		−	136155.i		−	0.143449i
$247$		−	308721.i		−	0.321976i
$248$	−374422.			−0.386574
$249$			234734.i			0.239927i
$250$			344927.i			0.349042i
$251$			359549.i			0.360225i	0.983646	+	0.180112i	$0.0576461\pi$
$251$			359549.i			0.360225i	−0.983646	+	0.180112i	$0.942354\pi$
$252$	285988.			0.283692
$253$			444085.i			0.436179i
$254$	−1.18543e6			−1.15290
$255$	−115124.			−0.110870
$256$	−1.08164e6			−1.03153
$257$	1.10353e6			1.04220			0.521101	−	0.853495i	$-0.325521\pi$
$257$	1.10353e6			1.04220			0.521101	+	0.853495i	$0.325521\pi$
$258$			92390.8i			0.0864131i
$259$			503321.i			0.466225i
$260$	−53756.9			−0.0493175
$261$	−745870.	−	637678.i	−0.677738	−	0.579429i
$262$	−1.11142e6			−1.00029
$263$			980576.i			0.874162i	0.899422	+	0.437081i	$0.143988\pi$
$263$			980576.i			0.874162i	−0.899422	+	0.437081i	$0.856012\pi$
$264$		−	378330.i		−	0.334088i
$265$	−172150.			−0.150589
$266$	435970.			0.377791
$267$	536509.			0.460573
$268$	−84893.6			−0.0722002
$269$			1.34518e6i			1.13344i	0.823910	+	0.566721i	$0.191788\pi$
$269$			1.34518e6i			1.13344i	−0.823910	+	0.566721i	$0.808212\pi$
$270$	135651.			0.113243
$271$		−	2.27613e6i		−	1.88267i	−0.337476	−	0.941334i	$-0.609573\pi$
$271$		−	2.27613e6i		−	1.88267i	0.337476	−	0.941334i	$-0.390427\pi$
$272$		−	85642.6i		−	0.0701887i
$273$		−	63963.2i		−	0.0519426i
$274$	798884.			0.642846
$275$			1.14996e6i			0.916962i
$276$		−	107661.i		−	0.0850721i
$277$	1.03963e6			0.814104			0.407052	−	0.913405i	$-0.366557\pi$
$277$	1.03963e6			0.814104			0.407052	+	0.913405i	$0.366557\pi$
$278$		−	826994.i		−	0.641786i
$279$		−	440520.i		−	0.338809i
$280$		−	204321.i		−	0.155746i
$281$	1.94505e6			1.46948			0.734741	−	0.678348i	$-0.237304\pi$
$281$	1.94505e6			1.46948			0.734741	+	0.678348i	$0.237304\pi$
$282$			9154.29i			0.00685491i
$283$	−2.37742e6			−1.76458			−0.882288	−	0.470710i	$-0.843998\pi$
$283$	−2.37742e6			−1.76458			−0.882288	+	0.470710i	$0.843998\pi$
$284$	1.11047e6			0.816981
$285$	−140967.			−0.102803
$286$	258761.			0.187062
$287$		−	511885.i		−	0.366832i
$288$		−	1.22935e6i		−	0.873362i
$289$	−571034.			−0.402177
$290$	−169269.	+	197988.i	−0.118191	+	0.138243i
$291$	−778383.			−0.538842
$292$		−	289780.i		−	0.198889i
$293$		−	1.68298e6i		−	1.14528i	−0.819808	−	0.572639i	$-0.805920\pi$
$293$		−	1.68298e6i		−	1.14528i	0.819808	−	0.572639i	$-0.194080\pi$
$294$	−221565.			−0.149497
$295$	−68893.2			−0.0460916
$296$	1.32861e6			0.881388
$297$	944316.			0.621193
$298$			1.00101e6i			0.652977i
$299$	198188.			0.128203
$300$		−	278790.i		−	0.178844i
$301$			347349.i			0.220979i
$302$		−	1.45263e6i		−	0.916510i
$303$	126497.			0.0791542
$304$		−	104868.i		−	0.0650814i
$305$			739156.i			0.454974i
$306$	1.10576e6			0.675082
$307$			2.20020e6i			1.33234i	0.745799	+	0.666171i	$0.232068\pi$
$307$			2.20020e6i			1.33234i	−0.745799	+	0.666171i	$0.767932\pi$
$308$		−	528470.i		−	0.317427i
$309$		−	126146.i		−	0.0751582i
$310$	−116934.			−0.0691095
$311$		−	258930.i		−	0.151803i	−0.997115	−	0.0759017i	$-0.975816\pi$
$311$		−	258930.i		−	0.151803i	0.997115	−	0.0759017i	$-0.0241835\pi$
$312$	−168842.			−0.0981963
$313$	1.48259e6			0.855384			0.427692	−	0.903924i	$-0.359327\pi$
$313$	1.48259e6			0.855384			0.427692	+	0.903924i	$0.359327\pi$
$314$	−39351.5			−0.0225236
$315$	240390.			0.136503
$316$		−	640741.i		−	0.360965i
$317$		−	1.94232e6i		−	1.08561i	−0.839859	−	0.542804i	$-0.817363\pi$
$317$		−	1.94232e6i		−	1.08561i	0.839859	−	0.542804i	$-0.182637\pi$
$318$	−200894.			−0.111403
$319$	−1.17835e6	+	1.37827e6i	−0.648331	+	0.758330i
$320$	−357213.			−0.195008
$321$			515997.i			0.279502i
$322$			279877.i			0.150428i
$323$	−2.43780e6			−1.30015
$324$	767163.			0.405999
$325$	513208.			0.269517
$326$	1.41683e6			0.738369
$327$		−	755762.i		−	0.390855i
$328$	−1.35121e6			−0.693488
$329$			34416.2i			0.0175296i
$330$		−	118155.i		−	0.0597264i
$331$			2.96478e6i			1.48738i	0.668523	+	0.743691i	$0.266927\pi$
$331$			2.96478e6i			1.48738i	−0.668523	+	0.743691i	$0.733073\pi$
$332$	865520.			0.430955
$333$			1.56315e6i			0.772485i
$334$			796642.i			0.390748i
$335$	−71358.2			−0.0347402
$336$		−	21727.3i		−	0.0104992i
$337$		−	2.71471e6i		−	1.30211i	−0.759029	−	0.651057i	$-0.774326\pi$
$337$		−	2.71471e6i		−	1.30211i	0.759029	−	0.651057i	$-0.225674\pi$
$338$			1.22742e6i			0.584390i
$339$	−664484.			−0.314040
$340$			424490.i			0.199145i
$341$	−814025.			−0.379098
$342$	1.35398e6			0.625960
$343$	−2.00557e6			−0.920455
$344$	916892.			0.417755
$345$		−	90495.8i		−	0.0409337i
$346$			2.39054e6i			1.07351i
$347$	−2.39738e6			−1.06884			−0.534420	−	0.845219i	$-0.679470\pi$
$347$	−2.39738e6			−1.06884			−0.534420	+	0.845219i	$0.679470\pi$
$348$	285672.	−	334140.i	0.126450	−	0.147904i
$349$	−1.29162e6			−0.567639			−0.283820	−	0.958878i	$-0.591602\pi$
$349$	−1.29162e6			−0.567639			−0.283820	+	0.958878i	$0.591602\pi$
$350$			724743.i			0.316238i
$351$		−	421433.i		−	0.182583i
$352$	−2.27168e6			−0.977216
$353$	−827351.			−0.353389			−0.176695	−	0.984266i	$-0.556540\pi$
$353$	−827351.			−0.353389			−0.176695	+	0.984266i	$0.556540\pi$
$354$	−80396.2			−0.0340979
$355$	933420.			0.393103
$356$		−	1.97823e6i		−	0.827280i
$357$	−505083.			−0.209745
$358$			833692.i			0.343794i
$359$			1.63510e6i			0.669590i	0.942291	+	0.334795i	$0.108667\pi$
$359$			1.63510e6i			0.669590i	−0.942291	+	0.334795i	$0.891333\pi$
$360$		−	634554.i		−	0.258055i
$361$	−508941.			−0.205542
$362$		−	2.08462e6i		−	0.836094i
$363$			3802.19i			0.00151449i
$364$	−235847.			−0.0932991
$365$		−	243577.i		−	0.0956984i
$366$			862571.i			0.336583i
$367$			1.76417e6i			0.683715i	0.939752	+	0.341858i	$0.111056\pi$
$367$			1.76417e6i			0.683715i	−0.939752	+	0.341858i	$0.888944\pi$
$368$	67321.2			0.0259139
$369$		−	1.58975e6i		−	0.607802i
$370$	414932.			0.157570
$371$	−755273.			−0.284885
$372$	197347.			0.0739390
$373$	1.23465e6			0.459487			0.229744	−	0.973251i	$-0.426211\pi$
$373$	1.23465e6			0.459487			0.229744	+	0.973251i	$0.426211\pi$
$374$		−	2.04330e6i		−	0.755359i
$375$		−	489311.i		−	0.179683i
$376$	90847.7			0.0331394
$377$	615100.	+	525877.i	0.222891	+	0.190560i
$378$	595139.			0.214234
$379$		−	3.06325e6i		−	1.09543i	−0.836665	−	0.547715i	$-0.815498\pi$
$379$		−	3.06325e6i		−	1.09543i	0.836665	−	0.547715i	$-0.184502\pi$
$380$			519779.i			0.184654i
$381$	1.68164e6			0.593499
$382$	−920122.			−0.322617
$383$	4.47059e6			1.55728			0.778642	−	0.627469i	$-0.215909\pi$
$383$	4.47059e6			1.55728			0.778642	+	0.627469i	$0.215909\pi$
$384$	514689.			0.178122
$385$		−	444211.i		−	0.152735i
$386$	−951544.			−0.325058
$387$			1.07875e6i			0.366138i
$388$			2.87008e6i			0.967865i
$389$			863569.i			0.289350i	0.989479	+	0.144675i	$0.0462136\pi$
$389$			863569.i			0.289350i	−0.989479	+	0.144675i	$0.953786\pi$
$390$	−52730.5			−0.0175550
$391$		−	1.56498e6i		−	0.517688i
$392$			2.19882e6i			0.722729i
$393$	1.57666e6			0.514939
$394$		−	1.86268e6i		−	0.604503i
$395$		−	538581.i		−	0.173684i
$396$		−	1.64125e6i		−	0.525942i
$397$	3.83756e6			1.22202			0.611011	−	0.791622i	$-0.290763\pi$
$397$	3.83756e6			1.22202			0.611011	+	0.791622i	$0.290763\pi$
$398$		−	2.65308e6i		−	0.839541i
$399$	−618464.			−0.194483
$400$	174329.			0.0544777
$401$	354668.			0.110144			0.0550721	−	0.998482i	$-0.482461\pi$
$401$	354668.			0.110144			0.0550721	+	0.998482i	$0.482461\pi$
$402$	−83272.7			−0.0257003
$403$			363286.i			0.111426i
$404$		−	466425.i		−	0.142177i
$405$	644847.			0.195352
$406$	−742634.	+	868633.i	−0.223594	+	0.261530i
$407$	2.88850e6			0.864344
$408$			1.33326e6i			0.396519i
$409$		−	511145.i		−	0.151090i	−0.997142	−	0.0755449i	$-0.975930\pi$
$409$		−	511145.i		−	0.151090i	0.997142	−	0.0755449i	$-0.0240696\pi$
$410$	−421992.			−0.123978
$411$	−1.13329e6			−0.330931
$412$	−465129.			−0.134999
$413$	−302255.			−0.0871963
$414$			869206.i			0.249242i
$415$	727522.			0.207360
$416$			1.01381e6i			0.287227i
$417$			1.17317e6i			0.330385i
$418$		−	2.50198e6i		−	0.700395i
$419$	335901.			0.0934708			0.0467354	−	0.998907i	$-0.485118\pi$
$419$	335901.			0.0934708			0.0467354	+	0.998907i	$0.485118\pi$
$420$			107692.i			0.0297892i
$421$		−	1.22224e6i		−	0.336085i	−0.985780	−	0.168043i	$-0.946255\pi$
$421$		−	1.22224e6i		−	0.336085i	0.985780	−	0.168043i	$-0.0537447\pi$
$422$	−4.61563e6			−1.26168
$423$			106885.i			0.0290447i
$424$			1.99368e6i			0.538568i
$425$		−	4.05253e6i		−	1.08831i
$426$	1.08927e6			0.290812
$427$			3.24289e6i			0.860722i
$428$	1.90260e6			0.502040
$429$	−367077.			−0.0962974
$430$	286351.			0.0746839
$431$	−3.09666e6			−0.802973			−0.401486	−	0.915865i	$-0.631506\pi$
$431$	−3.09666e6			−0.802973			−0.401486	+	0.915865i	$0.631506\pi$
$432$		−	143154.i		−	0.0369057i
$433$		−	3.64328e6i		−	0.933841i	−0.884299	−	0.466920i	$-0.845364\pi$
$433$		−	3.64328e6i		−	0.933841i	0.884299	−	0.466920i	$-0.154636\pi$
$434$	−513025.			−0.130742
$435$	240124.	−	280865.i	0.0608433	−	0.0711663i
$436$	−2.78667e6			−0.702052
$437$		−	1.91629e6i		−	0.480018i
$438$		−	284247.i		−	0.0707963i
$439$	2.94312e6			0.728865			0.364432	−	0.931230i	$-0.381263\pi$
$439$	2.94312e6			0.728865			0.364432	+	0.931230i	$0.381263\pi$
$440$	−1.17257e6			−0.288741
$441$	−2.58699e6			−0.633429
$442$	−911891.			−0.222018
$443$			2.50646e6i			0.606809i	0.952862	+	0.303405i	$0.0981234\pi$
$443$			2.50646e6i			0.606809i	−0.952862	+	0.303405i	$0.901877\pi$
$444$	−700271.			−0.168581
$445$		−	1.66283e6i		−	0.398058i
$446$		−	3.33103e6i		−	0.792943i
$447$		−	1.42003e6i		−	0.336146i
$448$	−1.56720e6			−0.368917
$449$			5.06356e6i			1.18533i	0.805448	+	0.592666i	$0.201925\pi$
$449$			5.06356e6i			1.18533i	−0.805448	+	0.592666i	$0.798075\pi$
$450$			2.25081e6i			0.523972i
$451$	−2.93765e6			−0.680078
$452$			2.45011e6i			0.564078i
$453$			2.06069e6i			0.471810i
$454$			3.00059e6i			0.683229i
$455$	−198244.			−0.0448922
$456$			1.63255e6i			0.367666i
$457$	1.05399e6			0.236073			0.118037	−	0.993009i	$-0.462340\pi$
$457$	1.05399e6			0.236073			0.118037	+	0.993009i	$0.462340\pi$
$458$	−2.76095e6			−0.615027
$459$	−3.32783e6			−0.737274
$460$	−333679.			−0.0735250
$461$			3.14678e6i			0.689627i	0.938671	+	0.344813i	$0.112058\pi$
$461$			3.14678e6i			0.689627i	−0.938671	+	0.344813i	$0.887942\pi$
$462$		−	518380.i		−	0.112991i
$463$	5.03811e6			1.09223			0.546116	−	0.837709i	$-0.316106\pi$
$463$	5.03811e6			1.09223			0.546116	+	0.837709i	$0.316106\pi$
$464$	208940.	+	178632.i	0.0450532	+	0.0385181i
$465$	165882.			0.0355769
$466$			5.67120e6i			1.20979i
$467$			4.52631e6i			0.960400i	0.877159	+	0.480200i	$0.159436\pi$
$467$			4.52631e6i			0.960400i	−0.877159	+	0.480200i	$0.840564\pi$
$468$	−732464.			−0.154587
$469$	−313069.			−0.0657217
$470$	28372.3			0.00592447
$471$	55823.8			0.0115949
$472$			797856.i			0.164843i
$473$	1.99340e6			0.409677
$474$		−	628507.i		−	0.128489i
$475$		−	4.96224e6i		−	1.00912i
$476$			1.86236e6i			0.376744i
$477$	−2.34563e6			−0.472023
$478$		−	3.64346e6i		−	0.729363i
$479$		−	6.73376e6i		−	1.34097i	−0.741924	−	0.670484i	$-0.766086\pi$
$479$		−	6.73376e6i		−	1.34097i	0.741924	−	0.670484i	$-0.233914\pi$
$480$	462924.			0.0917079
$481$		−	1.28909e6i		−	0.254051i
$482$		−	955179.i		−	0.187270i
$483$		−	397032.i		−	0.0774386i
$484$	14019.6			0.00272033
$485$			2.41248e6i			0.465703i
$486$	2.82538e6			0.542609
$487$	−1.18719e6			−0.226829			−0.113414	−	0.993548i	$-0.536179\pi$
$487$	−1.18719e6			−0.226829			−0.113414	+	0.993548i	$0.536179\pi$
$488$	8.56020e6			1.62718
$489$	−2.00990e6			−0.380105
$490$			686706.i			0.129205i
$491$			6.54103e6i			1.22445i	0.790682	+	0.612227i	$0.209726\pi$
$491$			6.54103e6i			1.22445i	−0.790682	+	0.612227i	$0.790274\pi$
$492$	712186.			0.132642
$493$	4.15257e6	−	4.85712e6i	0.769485	−	0.900039i
$494$	−1.11659e6			−0.205862
$495$		−	1.37957e6i		−	0.253065i
$496$			123402.i			0.0225226i
$497$	4.09519e6			0.743674
$498$	848995.			0.153402
$499$	−4.90073e6			−0.881067			−0.440534	−	0.897736i	$-0.645211\pi$
$499$	−4.90073e6			−0.881067			−0.440534	+	0.897736i	$0.645211\pi$
$500$	−1.80421e6			−0.322746
$501$		−	1.13011e6i		−	0.201153i
$502$	1.30043e6			0.230317
$503$		−	400862.i		−	0.0706439i	−0.999376	−	0.0353219i	$-0.988754\pi$
$503$		−	400862.i		−	0.0706439i	0.999376	−	0.0353219i	$-0.0112457\pi$
$504$		−	2.78397e6i		−	0.488190i
$505$		−	392058.i		−	0.0684104i
$506$	1.60618e6			0.278881
$507$		−	1.74122e6i		−	0.300838i
$508$		−	6.20060e6i		−	1.06604i
$509$	653951.			0.111880			0.0559398	−	0.998434i	$-0.482185\pi$
$509$	653951.			0.111880			0.0559398	+	0.998434i	$0.482185\pi$
$510$			416385.i			0.0708874i
$511$		−	1.06865e6i		−	0.181043i
$512$			702077.i			0.118361i
$513$	−4.07486e6			−0.683626
$514$		−	3.99129e6i		−	0.666355i
$515$	−390969.			−0.0649567
$516$	−483267.			−0.0799030
$517$	197510.			0.0324985
$518$	1.82043e6			0.298091
$519$		−	3.39121e6i		−	0.552632i
$520$			523301.i			0.0848678i
$521$	−7.46746e6			−1.20525			−0.602627	−	0.798023i	$-0.705879\pi$
$521$	−7.46746e6			−1.20525			−0.602627	+	0.798023i	$0.705879\pi$
$522$	−2.30638e6	+	2.69769e6i	−0.370471	+	0.433327i
$523$	1.19250e7			1.90636			0.953182	−	0.302398i	$-0.0977872\pi$
$523$	1.19250e7			1.90636			0.953182	+	0.302398i	$0.0977872\pi$
$524$		−	5.81350e6i		−	0.924931i
$525$		−	1.02812e6i		−	0.162796i
$526$	3.54658e6			0.558914
$527$	2.86867e6			0.449940
$528$	−124690.			−0.0194647
$529$	−5.20615e6			−0.808868
$530$			622638.i			0.0962822i
$531$	−938704.			−0.144475
$532$			2.28042e6i			0.349330i
$533$			1.31102e6i			0.199891i
$534$		−	1.94046e6i		−	0.294478i
$535$	1.59925e6			0.241564
$536$			826404.i			0.124245i
$537$		−	1.18267e6i		−	0.176982i
$538$	4.86529e6			0.724691
$539$			4.78043e6i			0.708753i
$540$			709546.i			0.104712i
$541$			3.10008e6i			0.455386i	0.973733	+	0.227693i	$0.0731182\pi$
$541$			3.10008e6i			0.455386i	−0.973733	+	0.227693i	$0.926882\pi$
$542$	−8.23238e6			−1.20373
$543$			2.95723e6i			0.430413i
$544$	8.00555e6			1.15983
$545$	−2.34236e6			−0.337803
$546$	−231344.			−0.0332106
$547$	−1.00371e6			−0.143430			−0.0717149	−	0.997425i	$-0.522847\pi$
$547$	−1.00371e6			−0.143430			−0.0717149	+	0.997425i	$0.522847\pi$
$548$			4.17871e6i			0.594417i
$549$			1.00714e7i			1.42612i
$550$	4.15922e6			0.586280
$551$	5.08474e6	−	5.94744e6i	0.713493	−	0.834548i
$552$	−1.04804e6			−0.146396
$553$		−	2.36291e6i		−	0.328576i
$554$		−	3.76017e6i		−	0.520515i
$555$	−588620.			−0.0811152
$556$	4.32575e6			0.593437
$557$	−1.19484e7			−1.63181			−0.815906	−	0.578184i	$-0.803762\pi$
$557$	−1.19484e7			−1.63181			−0.815906	+	0.578184i	$0.803762\pi$
$558$	−1.59329e6			−0.216625
$559$		−	889620.i		−	0.120414i
$560$	−67340.3			−0.00907412
$561$			2.89861e6i			0.388851i
$562$		−	7.03491e6i		−	0.939545i
$563$		−	1.50352e6i		−	0.199912i	−0.994992	−	0.0999558i	$-0.968130\pi$
$563$		−	1.50352e6i		−	0.199912i	0.994992	−	0.0999558i	$-0.0318701\pi$
$564$	−47883.2			−0.00633849
$565$			2.05946e6i			0.271414i
$566$			8.59874e6i			1.12822i
$567$	2.82913e6			0.369569
$568$		−	1.08100e7i		−	1.40590i
$569$			8.47841e6i			1.09783i	0.835879	+	0.548913i	$0.184958\pi$
$569$			8.47841e6i			1.09783i	−0.835879	+	0.548913i	$0.815042\pi$
$570$			509854.i			0.0657293i
$571$	−1.37549e7			−1.76549			−0.882747	−	0.469848i	$-0.844309\pi$
$571$	−1.37549e7			−1.76549			−0.882747	+	0.469848i	$0.844309\pi$
$572$			1.35350e6i			0.172969i
$573$	1.30528e6			0.166080
$574$	−1.85140e6			−0.234542
$575$	3.18558e6			0.401809
$576$	−4.86720e6			−0.611256
$577$			1.43166e7i			1.79019i	0.445875	+	0.895095i	$0.352893\pi$
$577$			1.43166e7i			1.79019i	−0.445875	+	0.895095i	$0.647107\pi$
$578$			2.06533e6i			0.257141i
$579$	1.34985e6			0.167336
$580$	−1.03561e6	−	885394.i	−0.127829	−	0.109287i
$581$	3.19185e6			0.392286
$582$			2.81528e6i			0.344520i
$583$			4.33442e6i			0.528153i
$584$	−2.82088e6			−0.342257
$585$	−615680.			−0.0743816
$586$	−6.08707e6			−0.732258
$587$	−7.54078e6			−0.903277			−0.451638	−	0.892201i	$-0.649160\pi$
$587$	−7.54078e6			−0.903277			−0.451638	+	0.892201i	$0.649160\pi$
$588$		−	1.15894e6i		−	0.138235i
$589$	3.51263e6			0.417200
$590$			249175.i			0.0294696i
$591$			2.64239e6i			0.311192i
$592$		−	437883.i		−	0.0513516i
$593$	−7.99284e6			−0.933392			−0.466696	−	0.884418i	$-0.654556\pi$
$593$	−7.99284e6			−0.933392			−0.466696	+	0.884418i	$0.654556\pi$
$594$		−	3.41543e6i		−	0.397173i
$595$			1.56543e6i			0.181276i
$596$	−5.23597e6			−0.603784
$597$			3.76364e6i			0.432187i
$598$		−	716812.i		−	0.0819695i
$599$		−	1.22235e7i		−	1.39196i	−0.718060	−	0.695981i	$-0.754970\pi$
$599$		−	1.22235e7i		−	1.39196i	0.718060	−	0.695981i	$-0.245030\pi$
$600$	−2.71390e6			−0.307762
$601$		−	1.34301e6i		−	0.151667i	−0.997120	−	0.0758337i	$-0.975838\pi$
$601$		−	1.34301e6i		−	0.151667i	0.997120	−	0.0758337i	$-0.0241618\pi$
$602$	1.25630e6			0.141287
$603$	−972291.			−0.108894
$604$	7.59825e6			0.847464
$605$	11784.3			0.00130893
$606$		−	457519.i		−	0.0506090i
$607$		−	1.50883e7i		−	1.66215i	−0.556163	−	0.831073i	$-0.687727\pi$
$607$		−	1.50883e7i		−	1.66215i	0.556163	−	0.831073i	$-0.312273\pi$
$608$	9.80262e6			1.07543
$609$	1.05350e6	−	1.23224e6i	0.115104	−	0.134633i
$610$	2.67340e6			0.290897
$611$		−	88145.6i		−	0.00955208i
$612$			5.78388e6i			0.624224i
$613$	4.95968e6			0.533092			0.266546	−	0.963822i	$-0.414118\pi$
$613$	4.95968e6			0.533092			0.266546	+	0.963822i	$0.414118\pi$
$614$	7.95774e6			0.851862
$615$	598635.			0.0638226
$616$	−5.14443e6			−0.546242
$617$		−	9.82407e6i		−	1.03891i	−0.854497	−	0.519456i	$-0.826135\pi$
$617$		−	9.82407e6i		−	1.03891i	0.854497	−	0.519456i	$-0.173865\pi$
$618$	−456248.			−0.0480540
$619$			1.35526e7i			1.42166i	0.703364	+	0.710830i	$0.251680\pi$
$619$			1.35526e7i			1.42166i	−0.703364	+	0.710830i	$0.748320\pi$
$620$		−	611647.i		−	0.0639030i
$621$		−	2.61591e6i		−	0.272204i
$622$	−936507.			−0.0970588
$623$		−	7.29530e6i		−	0.753049i
$624$			55647.2i			0.00572113i
$625$	7.45884e6			0.763785
$626$		−	5.36229e6i		−	0.546909i
$627$			3.54929e6i			0.360556i
$628$		−	205836.i		−	0.0208267i
$629$	−1.01793e7			−1.02586
$630$		−	869452.i		−	0.0872758i
$631$	7.34343e6			0.734219			0.367109	−	0.930178i	$-0.380347\pi$
$631$	7.34343e6			0.734219			0.367109	+	0.930178i	$0.380347\pi$
$632$	−6.23734e6			−0.621165
$633$	6.54770e6			0.649500
$634$	−7.02505e6			−0.694107
$635$		−	5.21197e6i		−	0.512942i
$636$		−	1.05081e6i		−	0.103011i
$637$	2.13342e6			0.208319
$638$	4.98498e6	+	4.26189e6i	0.484855	+	0.414525i
$639$	1.27183e7			1.23219
$640$		−	1.59520e6i		−	0.153945i
$641$			8.79727e6i			0.845674i	0.906206	+	0.422837i	$0.138966\pi$
$641$			8.79727e6i			0.845674i	−0.906206	+	0.422837i	$0.861034\pi$
$642$	1.86627e6			0.178705
$643$	−8.56541e6			−0.816998			−0.408499	−	0.912759i	$-0.633948\pi$
$643$	−8.56541e6			−0.816998			−0.408499	+	0.912759i	$0.633948\pi$
$644$	−1.46395e6			−0.139095
$645$	−406215.			−0.0384465
$646$			8.81713e6i			0.831277i
$647$	1.67135e7			1.56967			0.784833	−	0.619707i	$-0.212749\pi$
$647$	1.67135e7			1.56967			0.784833	+	0.619707i	$0.212749\pi$
$648$		−	7.46801e6i		−	0.698662i
$649$			1.73461e6i			0.161655i
$650$		−	1.85619e6i		−	0.172321i
$651$	727774.			0.0673045
$652$			7.41099e6i			0.682743i
$653$		−	1.18888e7i		−	1.09108i	−0.838085	−	0.545540i	$-0.816325\pi$
$653$		−	1.18888e7i		−	1.09108i	0.838085	−	0.545540i	$-0.183675\pi$
$654$	−2.73346e6			−0.249901
$655$		−	4.88660e6i		−	0.445044i
$656$			445334.i			0.0404042i
$657$		−	3.31886e6i		−	0.299968i
$658$	124478.			0.0112080
$659$		−	1.75331e6i		−	0.157269i	−0.996903	−	0.0786347i	$-0.974944\pi$
$659$		−	1.75331e6i		−	0.157269i	0.996903	−	0.0786347i	$-0.0250561\pi$
$660$	618031.			0.0552268
$661$	−1.32255e7			−1.17736			−0.588678	−	0.808367i	$-0.700352\pi$
$661$	−1.32255e7			−1.17736			−0.588678	+	0.808367i	$0.700352\pi$
$662$	1.07231e7			0.950990
$663$	1.29360e6			0.114292
$664$		−	8.42547e6i		−	0.741608i
$665$			1.91683e6i			0.168085i
$666$	5.65365e6			0.493905
$667$	3.81805e6	+	3.26422e6i	0.332297	+	0.284096i
$668$	−4.16698e6			−0.361311
$669$			4.72538e6i			0.408199i
$670$			258091.i			0.0222119i
$671$	1.86106e7			1.59571
$672$	2.03098e6			0.173493
$673$	−1.00137e7			−0.852229			−0.426114	−	0.904669i	$-0.640118\pi$
$673$	−1.00137e7			−0.852229			−0.426114	+	0.904669i	$0.640118\pi$
$674$	−9.81866e6			−0.832535
$675$		−	6.77392e6i		−	0.572243i
$676$	−6.42027e6			−0.540364
$677$		−	7.97980e6i		−	0.669145i	−0.942370	−	0.334573i	$-0.891408\pi$
$677$		−	7.97980e6i		−	0.669145i	0.942370	−	0.334573i	$-0.108592\pi$
$678$			2.40333e6i			0.200788i
$679$			1.05842e7i			0.881019i
$680$	4.13223e6			0.342698
$681$		−	4.25661e6i		−	0.351719i
$682$			2.94419e6i			0.242385i
$683$	754224.			0.0618655			0.0309328	−	0.999521i	$-0.490152\pi$
$683$	754224.			0.0618655			0.0309328	+	0.999521i	$0.490152\pi$
$684$			7.08224e6i			0.578802i
$685$			3.51246e6i			0.286012i
$686$			7.25381e6i			0.588513i
$687$	3.91666e6			0.316610
$688$		−	302190.i		−	0.0243393i
$689$	1.93438e6			0.155237
$690$	−327308.			−0.0261718
$691$	−5.62347e6			−0.448032			−0.224016	−	0.974585i	$-0.571917\pi$
$691$	−5.62347e6			−0.448032			−0.224016	+	0.974585i	$0.571917\pi$
$692$	−1.25042e7			−0.992636
$693$		−	6.05259e6i		−	0.478749i
$694$			8.67092e6i			0.683387i
$695$	3.63605e6			0.285541
$696$	−3.25271e6	−	2.78089e6i	−0.254520	−	0.217601i
$697$	1.03525e7			0.807163
$698$			4.67159e6i			0.362933i
$699$		−	8.04513e6i		−	0.622788i
$700$	−3.79090e6			−0.292414
$701$	−9.45506e6			−0.726723			−0.363362	−	0.931648i	$-0.618371\pi$
$701$	−9.45506e6			−0.726723			−0.363362	+	0.931648i	$0.618371\pi$
$702$	−1.52425e6			−0.116738
$703$	−1.24643e7			−0.951216
$704$			8.99396e6i			0.683942i
$705$	−40248.8			−0.00304986
$706$			2.99239e6i			0.225947i
$707$		−	1.72007e6i		−	0.129419i
$708$		−	420527.i		−	0.0315291i
$709$	−1.39260e7			−1.04043			−0.520213	−	0.854037i	$-0.674147\pi$
$709$	−1.39260e7			−1.04043			−0.520213	+	0.854037i	$0.674147\pi$
$710$		−	3.37602e6i		−	0.251339i
$711$		−	7.33844e6i		−	0.544414i
$712$	−1.92573e7			−1.42362
$713$			2.25498e6i			0.166119i
$714$			1.82680e6i			0.134105i
$715$			1.13770e6i			0.0832266i
$716$	−4.36078e6			−0.317894
$717$			5.16859e6i			0.375469i
$718$	5.91390e6			0.428117
$719$	−1.22839e7			−0.886167			−0.443083	−	0.896480i	$-0.646115\pi$
$719$	−1.22839e7			−0.886167			−0.443083	+	0.896480i	$0.646115\pi$
$720$	−209137.			−0.0150348
$721$	−1.71529e6			−0.122885
$722$			1.84076e6i			0.131417i
$723$			1.35501e6i			0.0964044i
$724$	1.09040e7			0.773106
$725$	9.88685e6	+	8.45272e6i	0.698575	+	0.597243i
$726$	13751.9			0.000968325
$727$		−	1.04182e7i		−	0.731068i	−0.930798	−	0.365534i	$-0.880886\pi$
$727$		−	1.04182e7i		−	0.731068i	0.930798	−	0.365534i	$-0.119114\pi$
$728$			2.29587e6i			0.160553i
$729$	5.84579e6			0.407403
$730$	−880978.			−0.0611868
$731$	−7.02486e6			−0.486233
$732$	−4.51184e6			−0.311226
$733$			9.07566e6i			0.623905i	0.950098	+	0.311952i	$0.100983\pi$
$733$			9.07566e6i			0.623905i	−0.950098	+	0.311952i	$0.899017\pi$
$734$	6.38071e6			0.437148
$735$		−	974157.i		−	0.0665136i
$736$			6.29294e6i			0.428212i
$737$			1.79667e6i			0.121843i
$738$	−5.74985e6			−0.388611
$739$			1.74982e7i			1.17864i	0.807899	+	0.589321i	$0.200604\pi$
$739$			1.74982e7i			1.17864i	−0.807899	+	0.589321i	$0.799396\pi$
$740$			2.17038e6i			0.145699i
$741$	1.58399e6			0.105976
$742$			2.73170e6i			0.182147i
$743$		−	2.26818e7i		−	1.50732i	−0.657266	−	0.753658i	$-0.728287\pi$
$743$		−	2.26818e7i		−	1.50732i	0.657266	−	0.753658i	$-0.271713\pi$
$744$		−	1.92109e6i		−	0.127238i
$745$	−4.40115e6			−0.290520
$746$		−	4.46554e6i		−	0.293783i
$747$	9.91285e6			0.649975
$748$	1.06879e7			0.698453
$749$	7.01638e6			0.456992
$750$	−1.76976e6			−0.114884
$751$			1.25596e7i			0.812598i	0.913740	+	0.406299i	$0.133181\pi$
$751$			1.25596e7i			0.812598i	−0.913740	+	0.406299i	$0.866819\pi$
$752$		−	29941.7i		−	0.00193077i
$753$	−1.84478e6			−0.118565
$754$	1.90201e6	−	2.22471e6i	0.121838	−	0.142510i
$755$	6.38679e6			0.407770
$756$			3.11298e6i			0.198095i
$757$		−	2.40929e7i		−	1.52809i	−0.645163	−	0.764045i	$-0.723211\pi$
$757$		−	2.40929e7i		−	1.52809i	0.645163	−	0.764045i	$-0.276789\pi$
$758$	−1.10793e7			−0.700387
$759$	−2.27852e6			−0.143565
$760$	5.05982e6			0.317762
$761$	1.54198e7			0.965198			0.482599	−	0.875841i	$-0.339693\pi$
$761$	1.54198e7			0.965198			0.482599	+	0.875841i	$0.339693\pi$
$762$		−	6.08221e6i		−	0.379467i
$763$	−1.02766e7			−0.639057
$764$		−	4.81287e6i		−	0.298312i
$765$			4.86170e6i			0.300355i
$766$		−	1.61694e7i		−	0.995683i
$767$	774125.			0.0475141
$768$		−	5.54968e6i		−	0.339520i
$769$			2.13698e7i			1.30312i	0.758597	+	0.651560i	$0.225885\pi$
$769$			2.13698e7i			1.30312i	−0.758597	+	0.651560i	$0.774115\pi$
$770$	−1.60664e6			−0.0976541
$771$			5.66202e6i			0.343033i
$772$		−	4.97723e6i		−	0.300569i
$773$			2.07154e7i			1.24694i	0.781849	+	0.623468i	$0.214277\pi$
$773$			2.07154e7i			1.24694i	−0.781849	+	0.623468i	$0.785723\pi$
$774$	3.90167e6			0.234098
$775$			5.83929e6i			0.349226i
$776$	2.79390e7			1.66555
$777$	−2.58245e6			−0.153454
$778$	3.12338e6			0.185002
$779$	1.26764e7			0.748430
$780$		−	275817.i		−	0.0162325i
$781$		−	2.35018e7i		−	1.37871i
$782$	−5.66028e6			−0.330995
$783$	6.94114e6	−	8.11880e6i	0.404600	−	0.473247i
$784$	724690.			0.0421078
$785$		−	173017.i		−	0.0100211i
$786$		−	5.70250e6i		−	0.329237i
$787$	1.34403e7			0.773523			0.386761	−	0.922180i	$-0.373594\pi$
$787$	1.34403e7			0.773523			0.386761	+	0.922180i	$0.373594\pi$
$788$	9.74312e6			0.558962
$789$	−5.03116e6			−0.287723
$790$	−1.94796e6			−0.111048
$791$			9.03547e6i			0.513463i
$792$	−1.59769e7			−0.905065
$793$		−	8.30560e6i		−	0.469016i
$794$		−	1.38798e7i		−	0.781326i
$795$		−	883270.i		−	0.0495651i
$796$	1.38774e7			0.776293
$797$			3.46238e6i			0.193076i	0.995329	+	0.0965381i	$0.0307770\pi$
$797$			3.46238e6i			0.193076i	−0.995329	+	0.0965381i	$0.969223\pi$
$798$			2.23688e6i			0.124347i
$799$	−696039.			−0.0385715
$800$			1.62956e7i			0.900212i
$801$		−	2.26568e7i		−	1.24772i
$802$		−	1.28278e6i		−	0.0704230i
$803$	−6.13283e6			−0.335639
$804$		−	435574.i		−	0.0237641i
$805$	−1.23054e6			−0.0669276
$806$	1.31394e6			0.0712425
$807$	−6.90187e6			−0.373063
$808$	−4.54045e6			−0.244664
$809$		−	2.78688e7i		−	1.49709i	−0.663086	−	0.748543i	$-0.730754\pi$
$809$		−	2.78688e7i		−	1.49709i	0.663086	−	0.748543i	$-0.269246\pi$
$810$		−	2.33230e6i		−	0.124903i
$811$	−2.87983e7			−1.53750			−0.768750	−	0.639549i	$-0.779121\pi$
$811$	−2.87983e7			−1.53750			−0.768750	+	0.639549i	$0.779121\pi$
$812$	−4.54355e6	−	3.88448e6i	−0.241827	−	0.206749i
$813$	1.16784e7			0.619665
$814$		−	1.04472e7i		−	0.552637i
$815$			6.22938e6i			0.328512i
$816$	439416.			0.0231021
$817$	−8.60179e6			−0.450852
$818$	−1.84872e6			−0.0966026
$819$	−2.70117e6			−0.140716
$820$		−	2.20731e6i		−	0.114638i
$821$	1.21782e7			0.630560			0.315280	−	0.948999i	$-0.397902\pi$
$821$	1.21782e7			0.630560			0.315280	+	0.948999i	$0.397902\pi$
$822$			4.09893e6i			0.211588i
$823$			1.29219e7i			0.665009i	0.943102	+	0.332504i	$0.107894\pi$
$823$			1.29219e7i			0.665009i	−0.943102	+	0.332504i	$0.892106\pi$
$824$			4.52783e6i			0.232312i
$825$	−5.90024e6			−0.301811
$826$			1.09320e6i			0.0557508i
$827$			1.94679e7i			0.989816i	0.868945	+	0.494908i	$0.164798\pi$
$827$			1.94679e7i			0.989816i	−0.868945	+	0.494908i	$0.835202\pi$
$828$	−4.54655e6			−0.230465
$829$		−	941471.i		−	0.0475796i	−0.999717	−	0.0237898i	$-0.992427\pi$
$829$		−	941471.i		−	0.0475796i	0.999717	−	0.0237898i	$-0.00757324\pi$
$830$		−	2.63133e6i		−	0.132580i
$831$			5.33416e6i			0.267956i
$832$	4.01386e6			0.201027
$833$		−	1.68465e7i		−	0.841197i
$834$	4.24316e6			0.211239
$835$	−3.50260e6			−0.173850
$836$	1.30871e7			0.647630
$837$	4.79507e6			0.236582
$838$		−	1.21490e6i		−	0.0597626i
$839$			8.91326e6i			0.437151i	0.975820	+	0.218576i	$0.0701410\pi$
$839$			8.91326e6i			0.437151i	−0.975820	+	0.218576i	$0.929859\pi$
$840$	1.04833e6			0.0512627
$841$	3.18839e6	+	2.02618e7i	0.155447	+	0.987844i
$842$	−4.42062e6			−0.214884
$843$			9.97967e6i			0.483668i
$844$		−	2.41429e7i		−	1.16663i
$845$	−5.39662e6			−0.260004
$846$	386586.			0.0185704
$847$	51701.2			0.00247623
$848$	657078.			0.0313782
$849$		−	1.21981e7i		−	0.580796i
$850$	−1.46573e7			−0.695837
$851$		−	8.00163e6i		−	0.378752i
$852$			5.69763e6i			0.268903i
$853$			3.30610e7i			1.55576i	0.628410	+	0.777882i	$0.283706\pi$
$853$			3.30610e7i			1.55576i	−0.628410	+	0.777882i	$0.716294\pi$
$854$	1.17290e7			0.550321
$855$			5.95305e6i			0.278499i
$856$		−	1.85210e7i		−	0.863934i
$857$	6.63537e6			0.308612			0.154306	−	0.988023i	$-0.450686\pi$
$857$	6.63537e6			0.308612			0.154306	+	0.988023i	$0.450686\pi$
$858$			1.32766e6i			0.0615698i
$859$			3.34962e7i			1.54886i	0.632659	+	0.774430i	$0.281963\pi$
$859$			3.34962e7i			1.54886i	−0.632659	+	0.774430i	$0.718037\pi$
$860$			1.49781e6i			0.0690575i
$861$	2.62639e6			0.120740
$862$			1.12001e7i			0.513398i
$863$	−4.22267e7			−1.93001			−0.965006	−	0.262226i	$-0.915543\pi$
$863$	−4.22267e7			−1.93001			−0.965006	+	0.262226i	$0.915543\pi$
$864$	1.33815e7			0.609846
$865$	−1.05105e7			−0.477622
$866$	−1.31771e7			−0.597071
$867$		−	2.92987e6i		−	0.132373i
$868$		−	2.68347e6i		−	0.120892i
$869$	−1.35605e7			−0.609153
$870$	−1.01584e6	−	868489.i	−0.0455017	−	0.0389015i
$871$	801824.			0.0358124
$872$			2.71270e7i			1.20812i
$873$			3.28712e7i			1.45975i
$874$	−6.93090e6			−0.306910
$875$	−6.65352e6			−0.293786
$876$	1.48681e6			0.0654627
$877$	1.96044e7			0.860707			0.430354	−	0.902660i	$-0.358389\pi$
$877$	1.96044e7			0.860707			0.430354	+	0.902660i	$0.358389\pi$
$878$		−	1.06448e7i		−	0.466016i
$879$	8.63508e6			0.376959
$880$			386458.i			0.0168227i
$881$			3.24692e7i			1.40939i	0.709509	+	0.704697i	$0.248917\pi$
$881$			3.24692e7i			1.40939i	−0.709509	+	0.704697i	$0.751083\pi$
$882$			9.35671e6i			0.404997i
$883$	−3.02499e7			−1.30564			−0.652819	−	0.757514i	$-0.726414\pi$
$883$	−3.02499e7			−1.30564			−0.652819	+	0.757514i	$0.726414\pi$
$884$		−	4.76982e6i		−	0.205292i
$885$		−	353478.i		−	0.0151707i
$886$	9.06546e6			0.387977
$887$		−	2.46024e7i		−	1.04995i	−0.851117	−	0.524976i	$-0.824074\pi$
$887$		−	2.46024e7i		−	1.04995i	0.851117	−	0.524976i	$-0.175926\pi$
$888$			6.81684e6i			0.290102i
$889$		−	2.28665e7i		−	0.970386i
$890$	−6.01416e6			−0.254507
$891$		−	1.62361e7i		−	0.685151i
$892$	1.74236e7			0.733205
$893$	−852285.			−0.0357648
$894$	−5.13600e6			−0.214922
$895$	−3.66550e6			−0.152959
$896$		−	6.99860e6i		−	0.291233i
$897$			1.01687e6i			0.0421971i
$898$	1.83140e7			0.757868
$899$	−5.98344e6	+	6.99862e6i	−0.246917	+	0.288811i
$900$	−1.17733e7			−0.484498
$901$		−	1.52748e7i		−	0.626849i
$902$			1.06250e7i			0.434822i
$903$	−1.78219e6			−0.0727333
$904$	2.38508e7			0.970691
$905$	9.16546e6			0.371991
$906$	7.45317e6			0.301662
$907$			7.64741e6i			0.308671i	0.988018	+	0.154336i	$0.0493237\pi$
$907$			7.64741e6i			0.308671i	−0.988018	+	0.154336i	$0.950676\pi$
$908$	−1.56951e7			−0.631757
$909$		−	5.34198e6i		−	0.214434i
$910$			717015.i			0.0287028i
$911$		−	1.93872e7i		−	0.773960i	−0.922088	−	0.386980i	$-0.873518\pi$
$911$		−	1.93872e7i		−	0.773960i	0.922088	−	0.386980i	$-0.126482\pi$
$912$	538056.			0.0214210
$913$		−	1.83177e7i		−	0.727266i
$914$		−	3.81211e6i		−	0.150939i
$915$	−3.79247e6			−0.149751
$916$		−	1.44417e7i		−	0.568693i
$917$		−	2.14389e7i		−	0.841937i
$918$			1.20362e7i			0.471392i
$919$	2.02240e7			0.789912			0.394956	−	0.918700i	$-0.370760\pi$
$919$	2.02240e7			0.789912			0.394956	+	0.918700i	$0.370760\pi$
$920$			3.24823e6i			0.126525i
$921$	−1.12888e7			−0.438530
$922$	1.13814e7			0.440928
$923$	−1.04885e7			−0.405236
$924$	2.71148e6			0.104478
$925$		−	2.07203e7i		−	0.796234i
$926$		−	1.82220e7i		−	0.698342i
$927$	−5.32714e6			−0.203608
$928$	−1.66979e7	+	1.95309e7i	−0.636489	+	0.744479i
$929$	−1.04574e7			−0.397544			−0.198772	−	0.980046i	$-0.563695\pi$
$929$	−1.04574e7			−0.397544			−0.198772	+	0.980046i	$0.563695\pi$
$930$		−	599968.i		−	0.0227468i
$931$		−	2.06282e7i		−	0.779987i
$932$	−2.96643e7			−1.11865
$933$	1.32852e6			0.0499649
$934$	1.63709e7			0.614052
$935$	8.98380e6			0.336071
$936$			7.13023e6i			0.266020i
$937$	3.57506e7			1.33025			0.665127	−	0.746730i	$-0.268377\pi$
$937$	3.57506e7			1.33025			0.665127	+	0.746730i	$0.268377\pi$
$938$			1.13232e6i			0.0420206i
$939$			7.60692e6i			0.281543i
$940$			148407.i			0.00547814i
$941$	2.85407e7			1.05073			0.525364	−	0.850878i	$-0.323929\pi$
$941$	2.85407e7			1.05073			0.525364	+	0.850878i	$0.323929\pi$
$942$		−	201905.i		−	0.00741346i
$943$			8.13778e6i			0.298007i
$944$	262958.			0.00960409
$945$			2.61665e6i			0.0953161i
$946$		−	7.20979e6i		−	0.261936i
$947$		−	2.87524e7i		−	1.04184i	−0.853606	−	0.520918i	$-0.825590\pi$
$947$		−	2.87524e7i		−	1.04184i	0.853606	−	0.520918i	$-0.174410\pi$
$948$	3.28752e6			0.118809
$949$			2.73698e6i			0.0986521i
$950$	−1.79476e7			−0.645204
$951$	9.96570e6			0.357319
$952$	1.81293e7			0.648318
$953$	8.91965e6			0.318138			0.159069	−	0.987267i	$-0.449151\pi$
$953$	8.91965e6			0.318138			0.159069	+	0.987267i	$0.449151\pi$
$954$			8.48375e6i			0.301798i
$955$		−	4.04551e6i		−	0.143537i
$956$	1.90578e7			0.674416
$957$	−7.07167e6	−	6.04589e6i	−0.249598	−	0.213393i
$958$	−2.43549e7			−0.857377
$959$			1.54102e7i			0.541080i
$960$		−	1.83279e6i		−	0.0641853i
$961$	2.44957e7			0.855620
$962$	−4.66242e6			−0.162433
$963$	2.17906e7			0.757187
$964$	4.99624e6			0.173161
$965$		−	4.18366e6i		−	0.144623i
$966$	−1.43600e6			−0.0495120
$967$		−	7.00946e6i		−	0.241056i	−0.992710	−	0.120528i	$-0.961541\pi$
$967$		−	7.00946e6i		−	0.241056i	0.992710	−	0.120528i	$-0.0384588\pi$
$968$		−	136475.i		−	0.00468127i
$969$		−	1.25079e7i		−	0.427933i
$970$	8.72552e6			0.297757
$971$			2.10516e7i			0.716535i	0.933619	+	0.358268i	$0.116632\pi$
$971$			2.10516e7i			0.716535i	−0.933619	+	0.358268i	$0.883368\pi$
$972$			1.47787e7i			0.501731i
$973$	1.59524e7			0.540188
$974$			4.29387e6i			0.145028i
$975$			2.63318e6i			0.0887092i
$976$		−	2.82128e6i		−	0.0948028i
$977$	3.48891e7			1.16937			0.584687	−	0.811259i	$-0.301217\pi$
$977$	3.48891e7			1.16937			0.584687	+	0.811259i	$0.301217\pi$
$978$			7.26949e6i			0.243028i
$979$	−4.18669e7			−1.39609
$980$	−3.59194e6			−0.119472
$981$	−3.19159e7			−1.05885
$982$	2.36578e7			0.782881
$983$			5.47844e7i			1.80831i	0.427204	+	0.904155i	$0.359499\pi$
$983$			5.47844e7i			1.80831i	−0.427204	+	0.904155i	$0.640501\pi$
$984$		−	6.93283e6i		−	0.228256i
$985$	8.18968e6			0.268953
$986$	−1.75674e7	−	1.50192e7i	−0.575460	−	0.491987i
$987$	−176583.			−0.00576974
$988$		−	5.84054e6i		−	0.190354i
$989$		−	5.52204e6i		−	0.179518i
$990$	−4.98968e6			−0.161802
$991$	8.43462e6			0.272823			0.136412	−	0.990652i	$-0.456443\pi$
$991$	8.43462e6			0.272823			0.136412	+	0.990652i	$0.456443\pi$
$992$	−1.15352e7			−0.372173
$993$	−1.52117e7			−0.489560
$994$		−	1.48116e7i		−	0.475484i
$995$	1.16648e7			0.373525
$996$			4.44083e6i			0.141845i
$997$		−	4.84695e7i		−	1.54430i	−0.635443	−	0.772148i	$-0.719183\pi$
$997$		−	4.84695e7i		−	1.54430i	0.635443	−	0.772148i	$-0.280817\pi$
$998$			1.77251e7i			0.563329i
$999$	−1.70149e7			−0.539406

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.b.a.28.5	✓	12
3.2	odd	2		261.6.c.b.28.8		12
4.3	odd	2		464.6.e.c.289.5		12
29.12	odd	4		841.6.a.d.1.8		12
29.17	odd	4		841.6.a.d.1.5		12
29.28	even	2	inner	29.6.b.a.28.8	yes	12
87.86	odd	2		261.6.c.b.28.5		12
116.115	odd	2		464.6.e.c.289.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.b.a.28.5	✓	12	1.1	even	1	trivial
29.6.b.a.28.8	yes	12	29.28	even	2	inner
261.6.c.b.28.5		12	87.86	odd	2
261.6.c.b.28.8		12	3.2	odd	2
464.6.e.c.289.5		12	4.3	odd	2
464.6.e.c.289.8		12	116.115	odd	2
841.6.a.d.1.5		12	29.17	odd	4
841.6.a.d.1.8		12	29.12	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)

\(f(q)\)	\(=\)	\(q-3.61683i q^{2} +5.13082i q^{3} +18.9185 q^{4} +15.9022 q^{5} +18.5573 q^{6} +69.7674 q^{7} -184.164i q^{8} +216.675 q^{9} +O(q^{10})\)	\(q-3.61683i q^{2} +5.13082i q^{3} +18.9185 q^{4} +15.9022 q^{5} +18.5573 q^{6} +69.7674 q^{7} -184.164i q^{8} +216.675 q^{9} -57.5154i q^{10} -400.387i q^{11} +97.0675i q^{12} -178.686 q^{13} -252.337i q^{14} +81.5911i q^{15} -60.6968 q^{16} +1410.99i q^{17} -783.676i q^{18} +1727.73i q^{19} +300.845 q^{20} +357.964i q^{21} -1448.13 q^{22} -1109.14 q^{23} +944.911 q^{24} -2872.12 q^{25} +646.278i q^{26} +2358.51i q^{27} +1319.90 q^{28} +(-3442.35 - 2943.02i) q^{29} +295.101 q^{30} -2033.09i q^{31} -5673.71i q^{32} +2054.31 q^{33} +5103.31 q^{34} +1109.45 q^{35} +4099.17 q^{36} +7214.27i q^{37} +6248.90 q^{38} -916.806i q^{39} -2928.60i q^{40} -7337.02i q^{41} +1294.70 q^{42} +4978.67i q^{43} -7574.73i q^{44} +3445.60 q^{45} +4011.57i q^{46} +493.299i q^{47} -311.424i q^{48} -11939.5 q^{49} +10388.0i q^{50} -7239.53 q^{51} -3380.48 q^{52} -10825.6 q^{53} +8530.32 q^{54} -6367.02i q^{55} -12848.6i q^{56} -8864.65 q^{57} +(-10644.4 + 12450.4i) q^{58} -4332.32 q^{59} +1543.58i q^{60} +46481.5i q^{61} -7353.36 q^{62} +15116.8 q^{63} -22463.2 q^{64} -2841.50 q^{65} -7430.11i q^{66} -4487.33 q^{67} +26693.8i q^{68} -5690.79i q^{69} -4012.70i q^{70} +58697.7 q^{71} -39903.6i q^{72} -15317.2i q^{73} +26092.8 q^{74} -14736.3i q^{75} +32686.0i q^{76} -27934.0i q^{77} -3315.93 q^{78} -33868.5i q^{79} -965.210 q^{80} +40550.9 q^{81} -26536.8 q^{82} +45749.9 q^{83} +6772.15i q^{84} +22437.8i q^{85} +18007.0 q^{86} +(15100.1 - 17662.1i) q^{87} -73736.8 q^{88} -104566. i q^{89} -12462.1i q^{90} -12466.5 q^{91} -20983.3 q^{92} +10431.4 q^{93} +1784.18 q^{94} +27474.6i q^{95} +29110.8 q^{96} +151708. i q^{97} +43183.2i q^{98} -86753.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 172 q^{4} + 46 q^{5} + 24 q^{6} + 20 q^{7} - 1574 q^{9}+O(q^{10}) \) 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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