LMFDB - Embedded newform 29.6.b.a.28.11

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			28.11
Root			$9.02264i$ of defining polynomial
Character	$\chi$	$=$	29.28
Dual form			29.6.b.a.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.02264i q^{2} -26.5755i q^{3} -49.4080 q^{4} +71.1177 q^{5} +239.781 q^{6} +131.830 q^{7} -157.067i q^{8} -463.255 q^{9} +O(q^{10})$	\(q+9.02264i q^{2} -26.5755i q^{3} -49.4080 q^{4} +71.1177 q^{5} +239.781 q^{6} +131.830 q^{7} -157.067i q^{8} -463.255 q^{9} +641.670i q^{10} -522.530i q^{11} +1313.04i q^{12} +855.406 q^{13} +1189.45i q^{14} -1889.99i q^{15} -163.903 q^{16} +1260.08i q^{17} -4179.79i q^{18} -73.8977i q^{19} -3513.79 q^{20} -3503.44i q^{21} +4714.60 q^{22} -2405.40 q^{23} -4174.12 q^{24} +1932.73 q^{25} +7718.03i q^{26} +5853.39i q^{27} -6513.46 q^{28} +(-4132.55 + 1852.88i) q^{29} +17052.7 q^{30} -2051.01i q^{31} -6504.96i q^{32} -13886.5 q^{33} -11369.3 q^{34} +9375.44 q^{35} +22888.5 q^{36} +8662.06i q^{37} +666.753 q^{38} -22732.8i q^{39} -11170.2i q^{40} +5917.50i q^{41} +31610.3 q^{42} +2802.55i q^{43} +25817.2i q^{44} -32945.7 q^{45} -21703.0i q^{46} +21163.8i q^{47} +4355.79i q^{48} +572.118 q^{49} +17438.4i q^{50} +33487.2 q^{51} -42264.0 q^{52} -1449.06 q^{53} -52813.0 q^{54} -37161.1i q^{55} -20706.1i q^{56} -1963.87 q^{57} +(-16717.8 - 37286.5i) q^{58} +29959.8 q^{59} +93380.5i q^{60} +3684.78i q^{61} +18505.5 q^{62} -61070.9 q^{63} +53447.1 q^{64} +60834.6 q^{65} -125293. i q^{66} +978.846 q^{67} -62258.1i q^{68} +63924.5i q^{69} +84591.3i q^{70} -80092.5 q^{71} +72761.9i q^{72} -20955.2i q^{73} -78154.7 q^{74} -51363.3i q^{75} +3651.14i q^{76} -68885.0i q^{77} +205110. q^{78} -34238.3i q^{79} -11656.4 q^{80} +42985.4 q^{81} -53391.5 q^{82} +94218.4 q^{83} +173098. i q^{84} +89614.1i q^{85} -25286.4 q^{86} +(49241.1 + 109825. i) q^{87} -82071.9 q^{88} +72282.4i q^{89} -297257. i q^{90} +112768. q^{91} +118846. q^{92} -54506.6 q^{93} -190954. q^{94} -5255.44i q^{95} -172872. q^{96} -153195. i q^{97} +5162.02i q^{98} +242065. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			9.02264i			1.59499i	0.603324	+	0.797496i	$0.293843\pi$
$2$			9.02264i			1.59499i	−0.603324	+	0.797496i	$0.706157\pi$
$3$		−	26.5755i		−	1.70482i	−0.522877	−	0.852408i	$-0.675141\pi$
$3$		−	26.5755i		−	1.70482i	0.522877	−	0.852408i	$-0.324859\pi$
$4$	−49.4080			−1.54400
$5$	71.1177			1.27219			0.636096	−	0.771610i	$-0.280548\pi$
$5$	71.1177			1.27219			0.636096	+	0.771610i	$0.280548\pi$
$6$	239.781			2.71917
$7$	131.830			1.01688			0.508439	−	0.861098i	$-0.330223\pi$
$7$	131.830			1.01688			0.508439	+	0.861098i	$0.330223\pi$
$8$		−	157.067i		−	0.867678i
$9$	−463.255			−1.90640
$10$			641.670i			2.02914i
$11$		−	522.530i		−	1.30206i	−0.759054	−	0.651028i	$-0.774338\pi$
$11$		−	522.530i		−	1.30206i	0.759054	−	0.651028i	$-0.225662\pi$
$12$			1313.04i			2.63224i
$13$	855.406			1.40383			0.701914	−	0.712261i	$-0.252329\pi$
$13$	855.406			1.40383			0.701914	+	0.712261i	$0.252329\pi$
$14$			1189.45i			1.62191i
$15$		−	1889.99i		−	2.16886i
$16$	−163.903			−0.160061
$17$			1260.08i			1.05749i	0.848781	+	0.528745i	$0.177337\pi$
$17$			1260.08i			1.05749i	−0.848781	+	0.528745i	$0.822663\pi$
$18$		−	4179.79i		−	3.04069i
$19$		−	73.8977i		−	0.0469621i	−0.999724	−	0.0234810i	$-0.992525\pi$
$19$		−	73.8977i		−	0.0469621i	0.999724	−	0.0234810i	$-0.00747493\pi$
$20$	−3513.79			−1.96427
$21$		−	3503.44i		−	1.73359i
$22$	4714.60			2.07677
$23$	−2405.40			−0.948128			−0.474064	−	0.880490i	$-0.657213\pi$
$23$	−2405.40			−0.948128			−0.474064	+	0.880490i	$0.657213\pi$
$24$	−4174.12			−1.47923
$25$	1932.73			0.618474
$26$			7718.03i			2.23910i
$27$			5853.39i			1.54525i
$28$	−6513.46			−1.57006
$29$	−4132.55	+	1852.88i	−0.912480	+	0.409121i
$29$	−4132.55	+	1852.88i	−0.912480	+	0.409121i
$30$	17052.7			3.45931
$31$		−	2051.01i		−	0.383322i	−0.981461	−	0.191661i	$-0.938613\pi$
$31$		−	2051.01i		−	0.383322i	0.981461	−	0.191661i	$-0.0613874\pi$
$32$		−	6504.96i		−	1.12297i
$33$	−13886.5			−2.21977
$34$	−11369.3			−1.68669
$35$	9375.44			1.29366
$36$	22888.5			2.94348
$37$			8662.06i			1.04020i	0.854105	+	0.520100i	$0.174105\pi$
$37$			8662.06i			1.04020i	−0.854105	+	0.520100i	$0.825895\pi$
$38$	666.753			0.0749041
$39$		−	22732.8i		−	2.39327i
$40$		−	11170.2i		−	1.10385i
$41$			5917.50i			0.549767i	0.961478	+	0.274883i	$0.0886393\pi$
$41$			5917.50i			0.549767i	−0.961478	+	0.274883i	$0.911361\pi$
$42$	31610.3			2.76506
$43$			2802.55i			0.231144i	0.993299	+	0.115572i	$0.0368701\pi$
$43$			2802.55i			0.231144i	−0.993299	+	0.115572i	$0.963130\pi$
$44$			25817.2i			2.01037i
$45$	−32945.7			−2.42531
$46$		−	21703.0i		−	1.51226i
$47$			21163.8i			1.39749i	0.715369	+	0.698747i	$0.246259\pi$
$47$			21163.8i			1.39749i	−0.715369	+	0.698747i	$0.753741\pi$
$48$			4355.79i			0.272875i
$49$	572.118			0.0340405
$50$			17438.4i			0.986462i
$51$	33487.2			1.80283
$52$	−42264.0			−2.16751
$53$	−1449.06			−0.0708595			−0.0354298	−	0.999372i	$-0.511280\pi$
$53$	−1449.06			−0.0708595			−0.0354298	+	0.999372i	$0.511280\pi$
$54$	−52813.0			−2.46466
$55$		−	37161.1i		−	1.65647i
$56$		−	20706.1i		−	0.882323i
$57$	−1963.87			−0.0800617
$58$	−16717.8	−	37286.5i	−0.652545	−	1.45540i
$59$	29959.8			1.12049			0.560246	−	0.828326i	$-0.310707\pi$
$59$	29959.8			1.12049			0.560246	+	0.828326i	$0.310707\pi$
$60$			93380.5i			3.34872i
$61$			3684.78i			0.126790i	0.997989	+	0.0633952i	$0.0201929\pi$
$61$			3684.78i			0.126790i	−0.997989	+	0.0633952i	$0.979807\pi$
$62$	18505.5			0.611396
$63$	−61070.9			−1.93858
$64$	53447.1			1.63107
$65$	60834.6			1.78594
$66$		−	125293.i		−	3.54051i
$67$	978.846			0.0266396			0.0133198	−	0.999911i	$-0.495760\pi$
$67$	978.846			0.0266396			0.0133198	+	0.999911i	$0.495760\pi$
$68$		−	62258.1i		−	1.63277i
$69$			63924.5i			1.61638i
$70$			84591.3i			2.06339i
$71$	−80092.5			−1.88558			−0.942792	−	0.333382i	$-0.891810\pi$
$71$	−80092.5			−1.88558			−0.942792	+	0.333382i	$0.891810\pi$
$72$			72761.9i			1.65414i
$73$		−	20955.2i		−	0.460240i	−0.973162	−	0.230120i	$-0.926088\pi$
$73$		−	20955.2i		−	0.460240i	0.973162	−	0.230120i	$-0.0739118\pi$
$74$	−78154.7			−1.65911
$75$		−	51363.3i		−	1.05439i
$76$			3651.14i			0.0725095i
$77$		−	68885.0i		−	1.32403i
$78$	205110.			3.81725
$79$		−	34238.3i		−	0.617226i	−0.951188	−	0.308613i	$-0.900135\pi$
$79$		−	34238.3i		−	0.617226i	0.951188	−	0.308613i	$-0.0998648\pi$
$80$	−11656.4			−0.203629
$81$	42985.4			0.727962
$82$	−53391.5			−0.876874
$83$	94218.4			1.50121			0.750604	−	0.660753i	$-0.229763\pi$
$83$	94218.4			1.50121			0.750604	+	0.660753i	$0.229763\pi$
$84$			173098.i			2.67667i
$85$			89614.1i			1.34533i
$86$	−25286.4			−0.368673
$87$	49241.1	+	109825.i	0.697476	+	1.55561i
$88$	−82071.9			−1.12976
$89$			72282.4i			0.967291i	0.875264	+	0.483646i	$0.160688\pi$
$89$			72282.4i			0.967291i	−0.875264	+	0.483646i	$0.839312\pi$
$90$		−	297257.i		−	3.86835i
$91$	112768.			1.42752
$92$	118846.			1.46391
$93$	−54506.6			−0.653494
$94$	−190954.			−2.22899
$95$		−	5255.44i		−	0.0597448i
$96$	−172872.			−1.91447
$97$		−	153195.i		−	1.65316i	−0.562820	−	0.826579i	$-0.690284\pi$
$97$		−	153195.i		−	1.65316i	0.562820	−	0.826579i	$-0.309716\pi$
$98$			5162.02i			0.0542943i
$99$			242065.i			2.48224i
$100$	−95492.5			−0.954925
$101$		−	67161.3i		−	0.655112i	−0.944832	−	0.327556i	$-0.893775\pi$
$101$		−	67161.3i		−	0.655112i	0.944832	−	0.327556i	$-0.106225\pi$
$102$			302143.i			2.87549i
$103$	61938.1			0.575261			0.287630	−	0.957742i	$-0.407133\pi$
$103$	61938.1			0.575261			0.287630	+	0.957742i	$0.407133\pi$
$104$		−	134356.i		−	1.21807i
$105$		−	249157.i		−	2.20546i
$106$		−	13074.4i		−	0.113020i
$107$	−128633.			−1.08615			−0.543077	−	0.839683i	$-0.682741\pi$
$107$	−128633.			−1.08615			−0.543077	+	0.839683i	$0.682741\pi$
$108$		−	289204.i		−	2.38586i
$109$	−10663.4			−0.0859665			−0.0429832	−	0.999076i	$-0.513686\pi$
$109$	−10663.4			−0.0859665			−0.0429832	+	0.999076i	$0.513686\pi$
$110$	335292.			2.64205
$111$	230198.			1.77335
$112$	−21607.3			−0.162763
$113$		−	50042.1i		−	0.368671i	−0.982863	−	0.184336i	$-0.940987\pi$
$113$		−	50042.1i		−	0.368671i	0.982863	−	0.184336i	$-0.0590133\pi$
$114$		−	17719.3i		−	0.127698i
$115$	−171066.			−1.20620
$116$	204181.	−	91547.0i	1.40887	−	0.631683i
$117$	−396272.			−2.67626
$118$			270316.i			1.78718i
$119$			166116.i			1.07534i
$120$	−296854.			−1.88187
$121$	−111986.			−0.695348
$122$	−33246.4			−0.202230
$123$	157260.			0.937252
$124$			101336.i			0.591849i
$125$	−84791.4			−0.485374
$126$		−	551021.i		−	3.09201i
$127$		−	147208.i		−	0.809884i	−0.914342	−	0.404942i	$-0.867292\pi$
$127$		−	147208.i		−	0.809884i	0.914342	−	0.404942i	$-0.132708\pi$
$128$			274075.i			1.47858i
$129$	74479.2			0.394058
$130$			548888.i			2.84856i
$131$			286938.i			1.46086i	0.682986	+	0.730431i	$0.260681\pi$
$131$			286938.i			1.46086i	−0.682986	+	0.730431i	$0.739319\pi$
$132$	686103.			3.42732
$133$		−	9741.93i		−	0.0477547i
$134$			8831.77i			0.0424899i
$135$			416280.i			1.96585i
$136$	197916.			0.917560
$137$			155571.i			0.708155i	0.935216	+	0.354077i	$0.115205\pi$
$137$			155571.i			0.708155i	−0.935216	+	0.354077i	$0.884795\pi$
$138$	−576768.			−2.57812
$139$	191595.			0.841099			0.420549	−	0.907270i	$-0.361837\pi$
$139$	191595.			0.841099			0.420549	+	0.907270i	$0.361837\pi$
$140$	−463222.			−1.99742
$141$	562439.			2.38247
$142$		−	722646.i		−	3.00749i
$143$		−	446975.i		−	1.82786i
$144$	75928.8			0.305141
$145$	−293898.	+	131772.i	−1.16085	+	0.520480i
$146$	189071.			0.734079
$147$		−	15204.3i		−	0.0580328i
$148$		−	427976.i		−	1.60607i
$149$	−175887.			−0.649036			−0.324518	−	0.945880i	$-0.605202\pi$
$149$	−175887.			−0.649036			−0.324518	+	0.945880i	$0.605202\pi$
$150$	463432.			1.68174
$151$	−24080.9			−0.0859469			−0.0429734	−	0.999076i	$-0.513683\pi$
$151$	−24080.9			−0.0859469			−0.0429734	+	0.999076i	$0.513683\pi$
$152$	−11606.9			−0.0407479
$153$		−	583739.i		−	2.01600i
$154$	621525.			2.11182
$155$		−	145863.i		−	0.487659i
$156$			1.12318e6i			3.69521i
$157$		−	146295.i		−	0.473676i	−0.971549	−	0.236838i	$-0.923889\pi$
$157$		−	146295.i		−	0.473676i	0.971549	−	0.236838i	$-0.0761111\pi$
$158$	308920.			0.984471
$159$			38509.6i			0.120802i
$160$		−	462618.i		−	1.42864i
$161$	−317103.			−0.964130
$162$			387842.i			1.16109i
$163$		−	60401.7i		−	0.178066i	−0.996029	−	0.0890328i	$-0.971622\pi$
$163$		−	60401.7i		−	0.178066i	0.996029	−	0.0890328i	$-0.0283776\pi$
$164$		−	292372.i		−	0.848841i
$165$	−987575.			−2.82397
$166$			850099.i			2.39441i
$167$	−476570.			−1.32232			−0.661159	−	0.750246i	$-0.729935\pi$
$167$	−476570.			−1.32232			−0.661159	+	0.750246i	$0.729935\pi$
$168$	−550273.			−1.50420
$169$	360427.			0.970735
$170$	−808556.			−2.14579
$171$			34233.5i			0.0895285i
$172$		−	138469.i		−	0.356887i
$173$	454098.			1.15354			0.576772	−	0.816905i	$-0.304312\pi$
$173$	454098.			1.15354			0.576772	+	0.816905i	$0.304312\pi$
$174$	−990907.	+	444284.i	−2.48119	+	1.11247i
$175$	254792.			0.628913
$176$			85644.1i			0.208409i
$177$		−	796195.i		−	1.91023i
$178$	−652178.			−1.54282
$179$	−249435.			−0.581868			−0.290934	−	0.956743i	$-0.593966\pi$
$179$	−249435.			−0.581868			−0.290934	+	0.956743i	$0.593966\pi$
$180$	1.62778e6			3.74468
$181$	191810.			0.435185			0.217593	−	0.976040i	$-0.430180\pi$
$181$	191810.			0.435185			0.217593	+	0.976040i	$0.430180\pi$
$182$			1.01747e6i			2.27689i
$183$	97924.6			0.216154
$184$			377807.i			0.822670i
$185$			616026.i			1.32334i
$186$		−	491793.i		−	1.04232i
$187$	658430.			1.37691
$188$		−	1.04566e6i		−	2.15773i
$189$			771651.i			1.57133i
$190$	47417.9			0.0952925
$191$			175452.i			0.347996i	0.984746	+	0.173998i	$0.0556686\pi$
$191$			175452.i			0.347996i	−0.984746	+	0.173998i	$0.944331\pi$
$192$		−	1.42038e6i		−	2.78068i
$193$		−	270324.i		−	0.522385i	−0.965287	−	0.261193i	$-0.915884\pi$
$193$		−	270324.i		−	0.522385i	0.965287	−	0.261193i	$-0.0841158\pi$
$194$	1.38222e6			2.63678
$195$		−	1.61671e6i		−	3.04470i
$196$	−28267.2			−0.0525585
$197$	−421626.			−0.774037			−0.387019	−	0.922072i	$-0.626495\pi$
$197$	−421626.			−0.774037			−0.387019	+	0.922072i	$0.626495\pi$
$198$	−2.18406e6			−3.95915
$199$	960832.			1.71995			0.859973	−	0.510339i	$-0.170480\pi$
$199$	960832.			1.71995			0.859973	+	0.510339i	$0.170480\pi$
$200$		−	303568.i		−	0.536637i
$201$		−	26013.3i		−	0.0454156i
$202$	605972.			1.04490
$203$	−544794.	+	244265.i	−0.927881	+	0.416026i
$204$	−1.65454e6			−2.78357
$205$			420839.i			0.699409i
$206$			558845.i			0.917536i
$207$	1.11431e6			1.80751
$208$	−140203.			−0.224699
$209$	−38613.8			−0.0611472
$210$	2.24805e6			3.51769
$211$			29925.6i			0.0462740i	0.999732	+	0.0231370i	$0.00736539\pi$
$211$			29925.6i			0.0462740i	−0.999732	+	0.0231370i	$0.992635\pi$
$212$	71595.5			0.109407
$213$			2.12849e6i			3.21457i
$214$		−	1.16061e6i		−	1.73241i
$215$			199311.i			0.294060i
$216$	919371.			1.34078
$217$		−	270384.i		−	0.389792i
$218$		−	96212.0i		−	0.137116i
$219$	−556894.			−0.784625
$220$			1.83606e6i			2.55758i
$221$			1.07788e6i			1.48453i
$222$			2.07700e6i			2.82848i
$223$	292169.			0.393434			0.196717	−	0.980460i	$-0.436972\pi$
$223$	292169.			0.393434			0.196717	+	0.980460i	$0.436972\pi$
$224$		−	857549.i		−	1.14193i
$225$	−895349.			−1.17906
$226$	451512.			0.588028
$227$	542660.			0.698978			0.349489	−	0.936940i	$-0.386355\pi$
$227$	542660.			0.698978			0.349489	+	0.936940i	$0.386355\pi$
$228$	97030.8			0.123615
$229$		−	975835.i		−	1.22967i	−0.788657	−	0.614834i	$-0.789223\pi$
$229$		−	975835.i		−	1.22967i	0.788657	−	0.614834i	$-0.210777\pi$
$230$		−	1.54347e6i		−	1.92388i
$231$	−1.83065e6			−2.25723
$232$	291025.	+	649086.i	0.354985	+	0.791739i
$233$	1.33996e6			1.61698			0.808488	−	0.588513i	$-0.200286\pi$
$233$	1.33996e6			1.61698			0.808488	+	0.588513i	$0.200286\pi$
$234$		−	3.57542e6i		−	4.26861i
$235$			1.50512e6i			1.77788i
$236$	−1.48025e6			−1.73004
$237$	−909898.			−1.05226
$238$	−1.49881e6			−1.71516
$239$	−752478.			−0.852116			−0.426058	−	0.904696i	$-0.640098\pi$
$239$	−752478.			−0.852116			−0.426058	+	0.904696i	$0.640098\pi$
$240$			309774.i			0.347150i
$241$	−171384.			−0.190076			−0.0950381	−	0.995474i	$-0.530297\pi$
$241$	−171384.			−0.190076			−0.0950381	+	0.995474i	$0.530297\pi$
$242$		−	1.01041e6i		−	1.10907i
$243$			280016.i			0.304205i
$244$		−	182058.i		−	0.195765i
$245$	40687.8			0.0433060
$246$			1.41890e6i			1.49491i
$247$		−	63212.6i		−	0.0659267i
$248$	−322145.			−0.332600
$249$		−	2.50390e6i		−	2.55928i
$250$		−	765042.i		−	0.774168i
$251$		−	1.03888e6i		−	1.04084i	−0.853912	−	0.520418i	$-0.825776\pi$
$251$		−	1.03888e6i		−	1.04084i	0.853912	−	0.520418i	$-0.174224\pi$
$252$	3.01739e6			2.99316
$253$			1.25689e6i			1.23451i
$254$	1.32821e6			1.29176
$255$	2.38154e6			2.29354
$256$	−762572.			−0.727246
$257$	2228.93			0.00210506			0.00105253	−	0.999999i	$-0.499665\pi$
$257$	2228.93			0.00210506			0.00105253	+	0.999999i	$0.499665\pi$
$258$			671999.i			0.628520i
$259$			1.14192e6i			1.05776i
$260$	−3.00572e6			−2.75749
$261$	1.91443e6	−	858355.i	1.73955	−	0.779948i
$262$	−2.58893e6			−2.33006
$263$		−	575015.i		−	0.512614i	−0.966595	−	0.256307i	$-0.917494\pi$
$263$		−	575015.i		−	0.512614i	0.966595	−	0.256307i	$-0.0825057\pi$
$264$			2.18110e6i			1.92604i
$265$	−103054.			−0.0901470
$266$	87897.9			0.0761683
$267$	1.92094e6			1.64905
$268$	−48362.8			−0.0411315
$269$			1.56961e6i			1.32255i	0.750145	+	0.661274i	$0.229984\pi$
$269$			1.56961e6i			1.32255i	−0.750145	+	0.661274i	$0.770016\pi$
$270$	−3.75594e6			−3.13552
$271$		−	330306.i		−	0.273208i	−0.990626	−	0.136604i	$-0.956381\pi$
$271$		−	330306.i		−	0.273208i	0.990626	−	0.136604i	$-0.0436188\pi$
$272$		−	206531.i		−	0.169263i
$273$		−	2.99687e6i		−	2.43366i
$274$	−1.40366e6			−1.12950
$275$		−	1.00991e6i		−	0.805288i
$276$		−	3.15838e6i		−	2.49570i
$277$	−2.16066e6			−1.69195			−0.845974	−	0.533224i	$-0.820980\pi$
$277$	−2.16066e6			−1.69195			−0.845974	+	0.533224i	$0.820980\pi$
$278$			1.72869e6i			1.34155i
$279$			950141.i			0.730765i
$280$		−	1.47257e6i		−	1.12248i
$281$	1.71439e6			1.29522			0.647609	−	0.761973i	$-0.275769\pi$
$281$	1.71439e6			1.29522			0.647609	+	0.761973i	$0.275769\pi$
$282$			5.07468e6i			3.80002i
$283$	119310.			0.0885546			0.0442773	−	0.999019i	$-0.485901\pi$
$283$	119310.			0.0885546			0.0442773	+	0.999019i	$0.485901\pi$
$284$	3.95721e6			2.91134
$285$	−139666.			−0.101854
$286$	4.03290e6			2.91543
$287$			780103.i			0.559046i
$288$			3.01346e6i			2.14084i
$289$	−167946.			−0.118284
$290$	−1.18893e6	−	2.65173e6i	−0.830163	−	1.85155i
$291$	−4.07122e6			−2.81833
$292$			1.03535e6i			0.710611i
$293$		−	1.12423e6i		−	0.765040i	−0.923947	−	0.382520i	$-0.875056\pi$
$293$		−	1.12423e6i		−	0.765040i	0.923947	−	0.382520i	$-0.124944\pi$
$294$	137183.			0.0925618
$295$	2.13067e6			1.42548
$296$	1.36052e6			0.902559
$297$	3.05857e6			2.01200
$298$		−	1.58697e6i		−	1.03521i
$299$	−2.05759e6			−1.33101
$300$			2.53776e6i			1.62797i
$301$			369460.i			0.235045i
$302$		−	217273.i		−	0.137085i
$303$	−1.78484e6			−1.11685
$304$			12112.0i			0.00751681i
$305$			262053.i			0.161302i
$306$	5.26687e6			3.21550
$307$		−	1.39016e6i		−	0.841821i	−0.907102	−	0.420911i	$-0.861711\pi$
$307$		−	1.39016e6i		−	0.841821i	0.907102	−	0.420911i	$-0.138289\pi$
$308$			3.40348e6i			2.04431i
$309$		−	1.64603e6i		−	0.980714i
$310$	1.31607e6			0.777813
$311$		−	1.51817e6i		−	0.890060i	−0.895516	−	0.445030i	$-0.853193\pi$
$311$		−	1.51817e6i		−	0.890060i	0.895516	−	0.445030i	$-0.146807\pi$
$312$	−3.57057e6			−2.07659
$313$	−1.81550e6			−1.04746			−0.523729	−	0.851885i	$-0.675460\pi$
$313$	−1.81550e6			−1.04746			−0.523729	+	0.851885i	$0.675460\pi$
$314$	1.31997e6			0.755510
$315$	−4.34322e6			−2.46624
$316$			1.69165e6i			0.952998i
$317$		−	2.15136e6i		−	1.20245i	−0.799081	−	0.601223i	$-0.794680\pi$
$317$		−	2.15136e6i		−	1.20245i	0.799081	−	0.601223i	$-0.205320\pi$
$318$	−347458.			−0.192679
$319$	968183.	+	2.15938e6i	0.532698	+	1.18810i
$320$	3.80103e6			2.07504
$321$			3.41847e6i			1.85169i
$322$		−	2.86111e6i		−	1.53778i
$323$	93117.1			0.0496619
$324$	−2.12382e6			−1.12397
$325$	1.65327e6			0.868232
$326$	544982.			0.284013
$327$			283385.i			0.146557i
$328$	929441.			0.477021
$329$			2.79003e6i			1.42108i
$330$		−	8.91053e6i		−	4.50421i
$331$		−	1.20798e6i		−	0.606022i	−0.952987	−	0.303011i	$-0.902008\pi$
$331$		−	1.20798e6i		−	0.606022i	0.952987	−	0.303011i	$-0.0979919\pi$
$332$	−4.65515e6			−2.31787
$333$		−	4.01275e6i		−	1.98304i
$334$		−	4.29992e6i		−	2.10909i
$335$	69613.3			0.0338907
$336$			574224.i			0.277481i
$337$			3.60306e6i			1.72821i	0.503310	+	0.864106i	$0.332115\pi$
$337$			3.60306e6i			1.72821i	−0.503310	+	0.864106i	$0.667885\pi$
$338$			3.25201e6i			1.54832i
$339$	−1.32989e6			−0.628517
$340$		−	4.42766e6i		−	2.07719i
$341$	−1.07171e6			−0.499106
$342$	−308877.			−0.142797
$343$	−2.14024e6			−0.982263
$344$	440187.			0.200559
$345$			4.54617e6i			2.05635i
$346$			4.09716e6i			1.83989i
$347$	1.97939e6			0.882486			0.441243	−	0.897388i	$-0.354538\pi$
$347$	1.97939e6			0.882486			0.441243	+	0.897388i	$0.354538\pi$
$348$	−2.43290e6	−	5.42621e6i	−1.07690	−	2.40187i
$349$	2.79542e6			1.22852			0.614262	−	0.789102i	$-0.289454\pi$
$349$	2.79542e6			1.22852			0.614262	+	0.789102i	$0.289454\pi$
$350$			2.29890e6i			1.00311i
$351$			5.00702e6i			2.16926i
$352$	−3.39904e6			−1.46217
$353$	−752447.			−0.321395			−0.160697	−	0.987004i	$-0.551374\pi$
$353$	−752447.			−0.321395			−0.160697	+	0.987004i	$0.551374\pi$
$354$	7.18378e6			3.04681
$355$	−5.69600e6			−2.39883
$356$		−	3.57133e6i		−	1.49350i
$357$	4.41462e6			1.83325
$358$		−	2.25056e6i		−	0.928075i
$359$		−	3.08322e6i		−	1.26261i	−0.775536	−	0.631304i	$-0.782520\pi$
$359$		−	3.08322e6i		−	1.26261i	0.775536	−	0.631304i	$-0.217480\pi$
$360$			5.17466e6i			2.10439i
$361$	2.47064e6			0.997795
$362$			1.73063e6i			0.694117i
$363$			2.97609e6i			1.18544i
$364$	−5.57165e6			−2.20410
$365$		−	1.49028e6i		−	0.585514i
$366$			883539.i			0.344765i
$367$			458948.i			0.177868i	0.996038	+	0.0889340i	$0.0283460\pi$
$367$			458948.i			0.177868i	−0.996038	+	0.0889340i	$0.971654\pi$
$368$	394251.			0.151759
$369$		−	2.74131e6i		−	1.04808i
$370$	−5.55818e6			−2.11071
$371$	−191030.			−0.0720555
$372$	2.69306e6			1.00899
$373$	927542.			0.345193			0.172596	−	0.984993i	$-0.444784\pi$
$373$	927542.			0.345193			0.172596	+	0.984993i	$0.444784\pi$
$374$			5.94078e6i			2.19616i
$375$			2.25337e6i			0.827474i
$376$	3.32413e6			1.21257
$377$	−3.53501e6	+	1.58496e6i	−1.28097	+	0.574336i
$378$	−6.96233e6			−2.50625
$379$		−	4.87864e6i		−	1.74462i	−0.488955	−	0.872309i	$-0.662622\pi$
$379$		−	4.87864e6i		−	1.74462i	0.488955	−	0.872309i	$-0.337378\pi$
$380$			259661.i			0.0922460i
$381$	−3.91213e6			−1.38070
$382$	−1.58304e6			−0.555050
$383$	−2.84485e6			−0.990974			−0.495487	−	0.868615i	$-0.665010\pi$
$383$	−2.84485e6			−0.990974			−0.495487	+	0.868615i	$0.665010\pi$
$384$	7.28366e6			2.52070
$385$		−	4.89895e6i		−	1.68442i
$386$	2.43903e6			0.833201
$387$		−	1.29830e6i		−	0.440653i
$388$			7.56905e6i			2.55248i
$389$			362375.i			0.121418i	0.998155	+	0.0607091i	$0.0193362\pi$
$389$			362375.i			0.121418i	−0.998155	+	0.0607091i	$0.980664\pi$
$390$	1.45870e7			4.85628
$391$		−	3.03099e6i		−	1.00264i
$392$		−	89860.6i		−	0.0295362i
$393$	7.62550e6			2.49050
$394$		−	3.80418e6i		−	1.23458i
$395$		−	2.43495e6i		−	0.785230i
$396$		−	1.19599e7i		−	3.83258i
$397$	1.80408e6			0.574486			0.287243	−	0.957858i	$-0.407261\pi$
$397$	1.80408e6			0.574486			0.287243	+	0.957858i	$0.407261\pi$
$398$			8.66925e6i			2.74330i
$399$	−258896.			−0.0814130
$400$	−316780.			−0.0989938
$401$	−5.07861e6			−1.57719			−0.788595	−	0.614912i	$-0.789191\pi$
$401$	−5.07861e6			−1.57719			−0.788595	+	0.614912i	$0.789191\pi$
$402$	234708.			0.0724375
$403$		−	1.75445e6i		−	0.538118i
$404$			3.31831e6i			1.01149i
$405$	3.05702e6			0.926108
$406$	−2.20391e6	−	4.91548e6i	−0.663558	−	1.47996i
$407$	4.52619e6			1.35440
$408$		−	5.25972e6i		−	1.56427i
$409$			6.49035e6i			1.91849i	0.282574	+	0.959245i	$0.408812\pi$
$409$			6.49035e6i			1.91849i	−0.282574	+	0.959245i	$0.591188\pi$
$410$	−3.79708e6			−1.11555
$411$	4.13438e6			1.20727
$412$	−3.06024e6			−0.888203
$413$	3.94959e6			1.13940
$414$			1.00540e7i			2.88297i
$415$	6.70060e6			1.90983
$416$		−	5.56439e6i		−	1.57646i
$417$		−	5.09172e6i		−	1.43392i
$418$		−	348398.i		−	0.0975293i
$419$	−3.55010e6			−0.987882			−0.493941	−	0.869495i	$-0.664444\pi$
$419$	−3.55010e6			−0.987882			−0.493941	+	0.869495i	$0.664444\pi$
$420$			1.23103e7i			3.40523i
$421$			6.50906e6i			1.78983i	0.446233	+	0.894917i	$0.352765\pi$
$421$			6.50906e6i			1.78983i	−0.446233	+	0.894917i	$0.647235\pi$
$422$	−270008.			−0.0738067
$423$		−	9.80426e6i		−	2.66418i
$424$			227600.i			0.0614832i
$425$			2.43540e6i			0.654030i
$426$	−1.92046e7			−5.12722
$427$			485764.i			0.128930i
$428$	6.35548e6			1.67702
$429$	−1.18786e7			−3.11617
$430$	−1.79831e6			−0.469023
$431$	1.86190e6			0.482795			0.241397	−	0.970426i	$-0.422394\pi$
$431$	1.86190e6			0.482795			0.241397	+	0.970426i	$0.422394\pi$
$432$		−	959386.i		−	0.247334i
$433$			2.08659e6i			0.534831i	0.963581	+	0.267416i	$0.0861697\pi$
$433$			2.08659e6i			0.534831i	−0.963581	+	0.267416i	$0.913830\pi$
$434$	2.43958e6			0.621715
$435$	3.50191e6	+	7.81047e6i	0.887324	+	1.97904i
$436$	526857.			0.132732
$437$			177753.i			0.0445260i
$438$		−	5.02465e6i		−	1.25147i
$439$	3.90551e6			0.967200			0.483600	−	0.875289i	$-0.339329\pi$
$439$	3.90551e6			0.967200			0.483600	+	0.875289i	$0.339329\pi$
$440$	−5.83677e6			−1.43728
$441$	−265037.			−0.0648948
$442$	−9.72533e6			−2.36782
$443$		−	6.17523e6i		−	1.49501i	−0.664256	−	0.747505i	$-0.731252\pi$
$443$		−	6.17523e6i		−	1.49501i	0.664256	−	0.747505i	$-0.268748\pi$
$444$	−1.13736e7			−2.73806
$445$			5.14056e6i			1.23058i
$446$			2.63614e6i			0.627524i
$447$			4.67429e6i			1.10649i
$448$	7.04592e6			1.65860
$449$			2.11080e6i			0.494118i	0.969000	+	0.247059i	$0.0794641\pi$
$449$			2.11080e6i			0.494118i	−0.969000	+	0.247059i	$0.920536\pi$
$450$		−	8.07841e6i		−	1.88059i
$451$	3.09207e6			0.715827
$452$			2.47248e6i			0.569229i
$453$			639961.i			0.146524i
$454$			4.89623e6i			1.11486i
$455$	8.01981e6			1.81608
$456$			308458.i			0.0694678i
$457$	2.59488e6			0.581201			0.290601	−	0.956844i	$-0.406145\pi$
$457$	2.59488e6			0.581201			0.290601	+	0.956844i	$0.406145\pi$
$458$	8.80461e6			1.96131
$459$	−7.37574e6			−1.63408
$460$	8.45205e6			1.86238
$461$		−	7.88364e6i		−	1.72772i	−0.503729	−	0.863862i	$-0.668039\pi$
$461$		−	7.88364e6i		−	1.72772i	0.503729	−	0.863862i	$-0.331961\pi$
$462$		−	1.65173e7i		−	3.60027i
$463$	−8.34216e6			−1.80853			−0.904266	−	0.426971i	$-0.859581\pi$
$463$	−8.34216e6			−1.80853			−0.904266	+	0.426971i	$0.859581\pi$
$464$	677337.	−	303692.i	0.146053	−	0.0654844i
$465$	−3.87638e6			−0.831370
$466$			1.20900e7i			2.57907i
$467$		−	7.85805e6i		−	1.66733i	−0.552268	−	0.833667i	$-0.686238\pi$
$467$		−	7.85805e6i		−	1.66733i	0.552268	−	0.833667i	$-0.313762\pi$
$468$	1.95790e7			4.13215
$469$	129041.			0.0270892
$470$	−1.35802e7			−2.83571
$471$	−3.88787e6			−0.807531
$472$		−	4.70568e6i		−	0.972226i
$473$	1.46442e6			0.300962
$474$		−	8.20968e6i		−	1.67834i
$475$		−	142825.i		−	0.0290448i
$476$		−	8.20748e6i		−	1.66032i
$477$	671287.			0.135087
$478$		−	6.78934e6i		−	1.35912i
$479$		−	42383.8i		−	0.00844037i	−0.999991	−	0.00422019i	$-0.998657\pi$
$479$		−	42383.8i		−	0.00844037i	0.999991	−	0.00422019i	$-0.00134333\pi$
$480$	−1.22943e7			−2.43557
$481$			7.40959e6i			1.46026i
$482$		−	1.54634e6i		−	0.303170i
$483$			8.42716e6i			1.64367i
$484$	5.53303e6			1.07362
$485$		−	1.08949e7i		−	2.10314i
$486$	−2.52648e6			−0.485205
$487$	7.14412e6			1.36498			0.682490	−	0.730895i	$-0.260897\pi$
$487$	7.14412e6			1.36498			0.682490	+	0.730895i	$0.260897\pi$
$488$	578755.			0.110013
$489$	−1.60520e6			−0.303569
$490$			367111.i			0.0690728i
$491$			5.89873e6i			1.10422i	0.833772	+	0.552109i	$0.186177\pi$
$491$			5.89873e6i			1.10422i	−0.833772	+	0.552109i	$0.813823\pi$
$492$	−7.76992e6			−1.44712
$493$	−2.33477e6	−	5.20735e6i	−0.432641	−	0.964938i
$494$	570344.			0.105153
$495$			1.72151e7i			3.15789i
$496$			336166.i			0.0613550i
$497$	−1.05586e7			−1.91741
$498$	2.25918e7			4.08204
$499$	−2.78395e6			−0.500507			−0.250253	−	0.968180i	$-0.580514\pi$
$499$	−2.78395e6			−0.500507			−0.250253	+	0.968180i	$0.580514\pi$
$500$	4.18938e6			0.749418
$501$			1.26651e7i			2.25431i
$502$	9.37346e6			1.66012
$503$			6.87349e6i			1.21132i	0.795725	+	0.605658i	$0.207090\pi$
$503$			6.87349e6i			1.21132i	−0.795725	+	0.605658i	$0.792910\pi$
$504$			9.59219e6i			1.68206i
$505$		−	4.77636e6i		−	0.833429i
$506$	−1.13405e7			−1.96904
$507$		−	9.57852e6i		−	1.65493i
$508$			7.27327e6i			1.25046i
$509$	8.62539e6			1.47565			0.737827	−	0.674990i	$-0.235852\pi$
$509$	8.62539e6			1.47565			0.737827	+	0.674990i	$0.235852\pi$
$510$			2.14877e7i			3.65818i
$511$		−	2.76252e6i		−	0.468008i
$512$			1.88998e6i			0.318626i
$513$	432552.			0.0725679
$514$			20110.8i			0.00335755i
$515$	4.40490e6			0.731842
$516$	−3.67987e6			−0.608427
$517$	1.10587e7			1.81961
$518$	−1.03031e7			−1.68711
$519$		−	1.20679e7i		−	1.96658i
$520$		−	9.55507e6i		−	1.54962i
$521$	2.84126e6			0.458582			0.229291	−	0.973358i	$-0.426359\pi$
$521$	2.84126e6			0.458582			0.229291	+	0.973358i	$0.426359\pi$
$522$	7.74463e6	+	1.72732e7i	1.24401	+	2.77457i
$523$	−8.02412e6			−1.28275			−0.641376	−	0.767226i	$-0.721636\pi$
$523$	−8.02412e6			−1.28275			−0.641376	+	0.767226i	$0.721636\pi$
$524$		−	1.41770e7i		−	2.25557i
$525$		−	6.77121e6i		−	1.07218i
$526$	5.18816e6			0.817615
$527$	2.58444e6			0.405359
$528$	2.27603e6			0.355299
$529$	−650414.			−0.101053
$530$		−	929821.i		−	0.143784i
$531$	−1.38790e7			−2.13611
$532$			481330.i			0.0737333i
$533$			5.06187e6i			0.771779i
$534$			1.73319e7i			2.63023i
$535$	−9.14806e6			−1.38180
$536$		−	153744.i		−	0.0231146i
$537$			6.62884e6i			0.991978i
$538$	−1.41620e7			−2.10945
$539$		−	298949.i		−	0.0443226i
$540$		−	2.05676e7i		−	3.03528i
$541$		−	2.44431e6i		−	0.359057i	−0.983753	−	0.179529i	$-0.942543\pi$
$541$		−	2.44431e6i		−	0.359057i	0.983753	−	0.179529i	$-0.0574573\pi$
$542$	2.98024e6			0.435765
$543$		−	5.09743e6i		−	0.741911i
$544$	8.19678e6			1.18753
$545$	−758356.			−0.109366
$546$	2.70396e7			3.88168
$547$	−3.30094e6			−0.471703			−0.235852	−	0.971789i	$-0.575788\pi$
$547$	−3.30094e6			−0.471703			−0.235852	+	0.971789i	$0.575788\pi$
$548$		−	7.68648e6i		−	1.09339i
$549$		−	1.70699e6i		−	0.241713i
$550$	9.11206e6			1.28443
$551$	136923.	+	305386.i	0.0192132	+	0.0428519i
$552$	1.00404e7			1.40250
$553$		−	4.51363e6i		−	0.627643i
$554$		−	1.94949e7i		−	2.69865i
$555$	1.63712e7			2.25604
$556$	−9.46633e6			−1.29866
$557$	−1.38689e7			−1.89410			−0.947052	−	0.321079i	$-0.895954\pi$
$557$	−1.38689e7			−1.89410			−0.947052	+	0.321079i	$0.895954\pi$
$558$	−8.57278e6			−1.16556
$559$			2.39732e6i			0.324487i
$560$	−1.53666e6			−0.207066
$561$		−	1.74981e7i		−	2.34738i
$562$			1.54683e7i			2.06586i
$563$		−	779419.i		−	0.103633i	−0.998657	−	0.0518167i	$-0.983499\pi$
$563$		−	779419.i		−	0.103633i	0.998657	−	0.0518167i	$-0.0165012\pi$
$564$	−2.77890e7			−3.67854
$565$		−	3.55888e6i		−	0.469021i
$566$			1.07649e6i			0.141244i
$567$	5.66676e6			0.740248
$568$			1.25798e7i			1.63608i
$569$			2.31386e6i			0.299610i	0.988716	+	0.149805i	$0.0478645\pi$
$569$			2.31386e6i			0.299610i	−0.988716	+	0.149805i	$0.952135\pi$
$570$		−	1.26015e6i		−	0.162456i
$571$	5.42116e6			0.695827			0.347914	−	0.937527i	$-0.386890\pi$
$571$	5.42116e6			0.695827			0.347914	+	0.937527i	$0.386890\pi$
$572$			2.20842e7i			2.82222i
$573$	4.66271e6			0.593269
$574$	−7.03859e6			−0.891674
$575$	−4.64899e6			−0.586393
$576$	−2.47596e7			−3.10948
$577$			5.74406e6i			0.718256i	0.933288	+	0.359128i	$0.116926\pi$
$577$			5.74406e6i			0.718256i	−0.933288	+	0.359128i	$0.883074\pi$
$578$		−	1.51532e6i		−	0.188662i
$579$	−7.18398e6			−0.890571
$580$	1.45209e7	−	6.51062e6i	1.79236	−	0.803623i
$581$	1.24208e7			1.52654
$582$		−	3.67332e7i		−	4.49522i
$583$			757180.i			0.0922630i
$584$	−3.29136e6			−0.399340
$585$	−2.81819e7			−3.40472
$586$	1.01435e7			1.22023
$587$	7.20062e6			0.862530			0.431265	−	0.902225i	$-0.358067\pi$
$587$	7.20062e6			0.862530			0.431265	+	0.902225i	$0.358067\pi$
$588$			751215.i			0.0896027i
$589$	−151565.			−0.0180016
$590$			1.92243e7i			2.27363i
$591$			1.12049e7i			1.31959i
$592$		−	1.41974e6i		−	0.166496i
$593$	4.27993e6			0.499804			0.249902	−	0.968271i	$-0.419602\pi$
$593$	4.27993e6			0.499804			0.249902	+	0.968271i	$0.419602\pi$
$594$			2.75964e7i			3.20912i
$595$			1.18138e7i			1.36804i
$596$	8.69025e6			1.00211
$597$		−	2.55346e7i		−	2.93219i
$598$		−	1.85649e7i		−	2.12295i
$599$			7.57710e6i			0.862852i	0.902148	+	0.431426i	$0.141989\pi$
$599$			7.57710e6i			0.862852i	−0.902148	+	0.431426i	$0.858011\pi$
$600$	−8.06745e6			−0.914867
$601$		−	3.14913e6i		−	0.355635i	−0.984063	−	0.177818i	$-0.943096\pi$
$601$		−	3.14913e6i		−	0.355635i	0.984063	−	0.177818i	$-0.0569037\pi$
$602$	−3.33351e6			−0.374896
$603$	−453455.			−0.0507857
$604$	1.18979e6			0.132702
$605$	−7.96422e6			−0.884616
$606$		−	1.61040e7i		−	1.78136i
$607$		−	1.45413e7i		−	1.60189i	−0.598738	−	0.800945i	$-0.704331\pi$
$607$		−	1.45413e7i		−	1.60189i	0.598738	−	0.800945i	$-0.295669\pi$
$608$	−480702.			−0.0527372
$609$	6.49144e6	+	1.44782e7i	0.709248	+	1.58187i
$610$	−2.36441e6			−0.257275
$611$			1.81037e7i			1.96184i
$612$			2.88414e7i			3.11270i
$613$	−937793.			−0.100799			−0.0503995	−	0.998729i	$-0.516049\pi$
$613$	−937793.			−0.100799			−0.0503995	+	0.998729i	$0.516049\pi$
$614$	1.25429e7			1.34270
$615$	1.11840e7			1.19236
$616$	−1.08195e7			−1.14883
$617$		−	482209.i		−	0.0509944i	−0.999675	−	0.0254972i	$-0.991883\pi$
$617$		−	482209.i		−	0.0509944i	0.999675	−	0.0254972i	$-0.00811690\pi$
$618$	1.48516e7			1.56423
$619$		−	9.72668e6i		−	1.02032i	−0.860078	−	0.510162i	$-0.829585\pi$
$619$		−	9.72668e6i		−	1.02032i	0.860078	−	0.510162i	$-0.170415\pi$
$620$			7.20682e6i			0.752947i
$621$		−	1.40797e7i		−	1.46509i
$622$	1.36979e7			1.41964
$623$			9.52897e6i			0.983617i
$624$			3.72597e6i			0.383070i
$625$	−1.20700e7			−1.23596
$626$		−	1.63806e7i		−	1.67069i
$627$			1.02618e6i			0.104245i
$628$			7.22817e6i			0.731357i
$629$	−1.09149e7			−1.10000
$630$		−	3.91873e7i		−	3.93364i
$631$	−8.30023e6			−0.829883			−0.414941	−	0.909848i	$-0.636198\pi$
$631$	−8.30023e6			−0.829883			−0.414941	+	0.909848i	$0.636198\pi$
$632$	−5.37769e6			−0.535553
$633$	795287.			0.0788887
$634$	1.94110e7			1.91789
$635$		−	1.04691e7i		−	1.03033i
$636$		−	1.90268e6i		−	0.186519i
$637$	489394.			0.0477870
$638$	−1.94833e7	+	8.73557e6i	−1.89501	+	0.849649i
$639$	3.71033e7			3.59468
$640$			1.94916e7i			1.88104i
$641$			9.96008e6i			0.957453i	0.877964	+	0.478727i	$0.158902\pi$
$641$			9.96008e6i			0.957453i	−0.877964	+	0.478727i	$0.841098\pi$
$642$	−3.08436e7			−2.95344
$643$	3.42368e6			0.326562			0.163281	−	0.986580i	$-0.447792\pi$
$643$	3.42368e6			0.326562			0.163281	+	0.986580i	$0.447792\pi$
$644$	1.56674e7			1.48862
$645$	5.29679e6			0.501318
$646$			840162.i			0.0792103i
$647$	−1.10479e7			−1.03757			−0.518785	−	0.854905i	$-0.673615\pi$
$647$	−1.10479e7			−1.03757			−0.518785	+	0.854905i	$0.673615\pi$
$648$		−	6.75157e6i		−	0.631636i
$649$		−	1.56549e7i		−	1.45894i
$650$			1.49169e7i			1.38482i
$651$	−7.18559e6			−0.664523
$652$			2.98433e6i			0.274933i
$653$		−	5.49629e6i		−	0.504413i	−0.967673	−	0.252207i	$-0.918844\pi$
$653$		−	5.49629e6i		−	0.504413i	0.967673	−	0.252207i	$-0.0811562\pi$
$654$	−2.55688e6			−0.233757
$655$			2.04064e7i			1.85850i
$656$		−	969894.i		−	0.0879964i
$657$			9.70760e6i			0.877401i
$658$	−2.51734e7			−2.26661
$659$			1.46836e7i			1.31710i	0.752537	+	0.658550i	$0.228830\pi$
$659$			1.46836e7i			1.31710i	−0.752537	+	0.658550i	$0.771170\pi$
$660$	4.87941e7			4.36021
$661$	−2.36612e6			−0.210636			−0.105318	−	0.994439i	$-0.533586\pi$
$661$	−2.36612e6			−0.210636			−0.105318	+	0.994439i	$0.533586\pi$
$662$	1.08991e7			0.966601
$663$	2.86452e7			2.53086
$664$		−	1.47986e7i		−	1.30256i
$665$		−	692824.i		−	0.0607531i
$666$	3.62056e7			3.16293
$667$	9.94043e6	−	4.45690e6i	0.865148	−	0.387899i
$668$	2.35464e7			2.04166
$669$		−	7.76453e6i		−	0.670733i
$670$			628096.i			0.0540554i
$671$	1.92541e6			0.165088
$672$	−2.27898e7			−1.94678
$673$	3.07729e6			0.261897			0.130949	−	0.991389i	$-0.458198\pi$
$673$	3.07729e6			0.261897			0.130949	+	0.991389i	$0.458198\pi$
$674$	−3.25091e7			−2.75648
$675$			1.13130e7i			0.955695i
$676$	−1.78080e7			−1.49882
$677$			1.06504e7i			0.893087i	0.894762	+	0.446544i	$0.147345\pi$
$677$			1.06504e7i			0.893087i	−0.894762	+	0.446544i	$0.852655\pi$
$678$		−	1.19991e7i		−	1.00248i
$679$		−	2.01956e7i		−	1.68106i
$680$	1.40754e7			1.16731
$681$		−	1.44215e7i		−	1.19163i
$682$		−	9.66969e6i		−	0.796071i
$683$	−8.18064e6			−0.671020			−0.335510	−	0.942037i	$-0.608909\pi$
$683$	−8.18064e6			−0.671020			−0.335510	+	0.942037i	$0.608909\pi$
$684$		−	1.69141e6i		−	0.138232i
$685$			1.10639e7i			0.900909i
$686$		−	1.93106e7i		−	1.56670i
$687$	−2.59333e7			−2.09636
$688$		−	459346.i		−	0.0369972i
$689$	−1.23954e6			−0.0994746
$690$	−4.10184e7			−3.27987
$691$	−1.64985e7			−1.31447			−0.657234	−	0.753687i	$-0.728274\pi$
$691$	−1.64985e7			−1.31447			−0.657234	+	0.753687i	$0.728274\pi$
$692$	−2.24361e7			−1.78107
$693$			3.19114e7i			2.52413i
$694$			1.78593e7i			1.40756i
$695$	1.36258e7			1.07004
$696$	1.72498e7	−	7.73412e6i	1.34977	−	0.605185i
$697$	−7.45653e6			−0.581373
$698$			2.52221e7i			1.95949i
$699$		−	3.56102e7i		−	2.75665i
$700$	−1.25888e7			−0.971042
$701$	−2.38346e7			−1.83195			−0.915973	−	0.401240i	$-0.868579\pi$
$701$	−2.38346e7			−1.83195			−0.915973	+	0.401240i	$0.868579\pi$
$702$	−4.51766e7			−3.45996
$703$	640107.			0.0488499
$704$		−	2.79277e7i		−	2.12375i
$705$	3.99994e7			3.03096
$706$		−	6.78906e6i		−	0.512623i
$707$		−	8.85387e6i		−	0.666169i
$708$			3.93384e7i			2.94940i
$709$	5.07783e6			0.379369			0.189685	−	0.981845i	$-0.439253\pi$
$709$	5.07783e6			0.379369			0.189685	+	0.981845i	$0.439253\pi$
$710$		−	5.13929e7i		−	3.82611i
$711$			1.58611e7i			1.17668i
$712$	1.13531e7			0.839297
$713$			4.93349e6i			0.363438i
$714$			3.98315e7i			2.92403i
$715$		−	3.17879e7i		−	2.32539i
$716$	1.23241e7			0.898405
$717$			1.99974e7i			1.45270i
$718$	2.78188e7			2.01385
$719$	2.48136e7			1.79006			0.895031	−	0.446003i	$-0.147153\pi$
$719$	2.48136e7			1.79006			0.895031	+	0.446003i	$0.147153\pi$
$720$	5.39989e6			0.388198
$721$	8.16529e6			0.584970
$722$			2.22917e7i			1.59147i
$723$			4.55461e6i			0.324045i
$724$	−9.47694e6			−0.671926
$725$	−7.98712e6	+	3.58112e6i	−0.564346	+	0.253031i
$726$	−2.68522e7			−1.89077
$727$			2.04126e7i			1.43240i	0.697898	+	0.716198i	$0.254119\pi$
$727$			2.04126e7i			1.43240i	−0.697898	+	0.716198i	$0.745881\pi$
$728$		−	1.77121e7i		−	1.23863i
$729$	1.78870e7			1.24658
$730$	1.34463e7			0.933890
$731$	−3.53144e6			−0.244432
$732$	−4.83826e6			−0.333743
$733$			2.63500e7i			1.81143i	0.423889	+	0.905714i	$0.360665\pi$
$733$			2.63500e7i			1.81143i	−0.423889	+	0.905714i	$0.639335\pi$
$734$	−4.14092e6			−0.283698
$735$		−	1.08130e6i		−	0.0738289i
$736$			1.56470e7i			1.06472i
$737$		−	511476.i		−	0.0346862i
$738$	2.47339e7			1.67167
$739$			670865.i			0.0451881i	0.999745	+	0.0225940i	$0.00719252\pi$
$739$			670865.i			0.0451881i	−0.999745	+	0.0225940i	$0.992807\pi$
$740$		−	3.04367e7i		−	2.04323i
$741$	−1.67990e6			−0.112393
$742$		−	1.72360e6i		−	0.114928i
$743$		−	3.64550e6i		−	0.242262i	−0.992637	−	0.121131i	$-0.961348\pi$
$743$		−	3.64550e6i		−	0.242262i	0.992637	−	0.121131i	$-0.0386521\pi$
$744$			8.56115e6i			0.567022i
$745$	−1.25087e7			−0.825699
$746$			8.36888e6i			0.550580i
$747$	−4.36472e7			−2.86190
$748$	−3.25317e7			−2.12595
$749$	−1.69576e7			−1.10449
$750$	−2.03313e7			−1.31981
$751$			4.16150e6i			0.269246i	0.990897	+	0.134623i	$0.0429824\pi$
$751$			4.16150e6i			0.269246i	−0.990897	+	0.134623i	$0.957018\pi$
$752$		−	3.46881e6i		−	0.223685i
$753$	−2.76088e7			−1.77443
$754$	−1.43005e7	−	3.18952e7i	−0.916061	−	2.04313i
$755$	−1.71258e6			−0.109341
$756$		−	3.81258e7i		−	2.42613i
$757$		−	1.12780e7i		−	0.715305i	−0.933855	−	0.357652i	$-0.883577\pi$
$757$		−	1.12780e7i		−	0.715305i	0.933855	−	0.357652i	$-0.116423\pi$
$758$	4.40182e7			2.78265
$759$	3.34025e7			2.10462
$760$	−825453.			−0.0518392
$761$	1.25110e7			0.783125			0.391563	−	0.920151i	$-0.371935\pi$
$761$	1.25110e7			0.783125			0.391563	+	0.920151i	$0.371935\pi$
$762$		−	3.52977e7i		−	2.20221i
$763$	−1.40575e6			−0.0874174
$764$		−	8.66872e6i		−	0.537306i
$765$		−	4.15142e7i		−	2.56474i
$766$		−	2.56680e7i		−	1.58060i
$767$	2.56278e7			1.57298
$768$			2.02657e7i			1.23982i
$769$		−	1.84950e7i		−	1.12781i	−0.825838	−	0.563907i	$-0.809298\pi$
$769$		−	1.84950e7i		−	1.12781i	0.825838	−	0.563907i	$-0.190702\pi$
$770$	4.42015e7			2.68664
$771$		−	59234.9i		−	0.00358874i
$772$			1.33562e7i			0.806564i
$773$			2.00370e7i			1.20610i	0.797703	+	0.603050i	$0.206048\pi$
$773$			2.00370e7i			1.20610i	−0.797703	+	0.603050i	$0.793952\pi$
$774$	1.17141e7			0.702839
$775$		−	3.96405e6i		−	0.237075i
$776$	−2.40618e7			−1.43441
$777$	3.03470e7			1.80328
$778$	−3.26958e6			−0.193661
$779$	437290.			0.0258182
$780$			7.98783e7i			4.70102i
$781$			4.18507e7i			2.45513i
$782$	2.73476e7			1.59920
$783$	−1.08456e7	−	2.41894e7i	−0.632192	−	1.41001i
$784$	−93771.8			−0.00544856
$785$		−	1.04042e7i		−	0.602608i
$786$			6.88021e7i			3.97233i
$787$	2.03703e7			1.17236			0.586181	−	0.810180i	$-0.300631\pi$
$787$	2.03703e7			1.17236			0.586181	+	0.810180i	$0.300631\pi$
$788$	2.08317e7			1.19511
$789$	−1.52813e7			−0.873912
$790$	2.19697e7			1.25244
$791$		−	6.59704e6i		−	0.374894i
$792$	3.80203e7			2.15378
$793$			3.15198e6i			0.177992i
$794$			1.62776e7i			0.916301i
$795$			2.73871e6i			0.153684i
$796$	−4.74729e7			−2.65560
$797$			3.31007e7i			1.84583i	0.385008	+	0.922913i	$0.374199\pi$
$797$			3.31007e7i			1.84583i	−0.385008	+	0.922913i	$0.625801\pi$
$798$		−	2.33593e6i		−	0.129853i
$799$	−2.66681e7			−1.47783
$800$		−	1.25724e7i		−	0.694531i
$801$		−	3.34852e7i		−	1.84404i
$802$		−	4.58225e7i		−	2.51561i
$803$	−1.09497e7			−0.599258
$804$			1.28527e6i			0.0701217i
$805$	−2.25517e7			−1.22656
$806$	1.58297e7			0.858295
$807$	4.17131e7			2.25470
$808$	−1.05488e7			−0.568426
$809$		−	2.55067e7i		−	1.37020i	−0.728449	−	0.685100i	$-0.759759\pi$
$809$		−	2.55067e7i		−	1.37020i	0.728449	−	0.685100i	$-0.240241\pi$
$810$			2.75824e7i			1.47713i
$811$	1.57817e7			0.842562			0.421281	−	0.906930i	$-0.361581\pi$
$811$	1.57817e7			0.842562			0.421281	+	0.906930i	$0.361581\pi$
$812$	2.69172e7	−	1.20686e7i	1.43265	−	0.642344i
$813$	−8.77805e6			−0.465770
$814$			4.08382e7i			2.16026i
$815$		−	4.29563e6i		−	0.226534i
$816$	−5.48865e6			−0.288563
$817$	207102.			0.0108550
$818$	−5.85601e7			−3.05998
$819$	−5.22404e7			−2.72143
$820$		−	2.07928e7i		−	1.07989i
$821$	5.48950e6			0.284233			0.142117	−	0.989850i	$-0.454609\pi$
$821$	5.48950e6			0.284233			0.142117	+	0.989850i	$0.454609\pi$
$822$			3.73030e7i			1.92559i
$823$		−	1.04306e7i		−	0.536796i	−0.963308	−	0.268398i	$-0.913506\pi$
$823$		−	1.04306e7i		−	0.536796i	0.963308	−	0.268398i	$-0.0864942\pi$
$824$		−	9.72840e6i		−	0.499141i
$825$	−2.68388e7			−1.37287
$826$			3.56358e7i			1.81734i
$827$			8.52694e6i			0.433540i	0.976223	+	0.216770i	$0.0695522\pi$
$827$			8.52694e6i			0.433540i	−0.976223	+	0.216770i	$0.930448\pi$
$828$	−5.50560e7			−2.79080
$829$			186353.i			0.00941781i	0.999989	+	0.00470891i	$0.00149890\pi$
$829$			186353.i			0.00941781i	−0.999989	+	0.00470891i	$0.998501\pi$
$830$			6.04571e7i			3.04616i
$831$			5.74206e7i			2.88446i
$832$	4.57190e7			2.28975
$833$			720915.i			0.0359974i
$834$	4.59408e7			2.28709
$835$	−3.38926e7			−1.68224
$836$	1.90783e6			0.0944113
$837$	1.20054e7			0.592327
$838$		−	3.20312e7i		−	1.57566i
$839$		−	2.10511e7i		−	1.03245i	−0.856453	−	0.516226i	$-0.827337\pi$
$839$		−	2.10511e7i		−	1.03245i	0.856453	−	0.516226i	$-0.172663\pi$
$840$	−3.91342e7			−1.91363
$841$	1.36448e7	−	1.53142e7i	0.665240	−	0.746629i
$842$	−5.87289e7			−2.85477
$843$		−	4.55606e7i		−	2.20811i
$844$		−	1.47857e6i		−	0.0714471i
$845$	2.56328e7			1.23496
$846$	8.84603e7			4.24935
$847$	−1.47632e7			−0.707084
$848$	237506.			0.0113419
$849$		−	3.17072e6i		−	0.150969i
$850$	−2.19737e7			−1.04317
$851$		−	2.08357e7i		−	0.986243i
$852$		−	1.05165e8i		−	4.96331i
$853$		−	7.14772e6i		−	0.336353i	−0.985757	−	0.168176i	$-0.946212\pi$
$853$		−	7.14772e6i		−	0.336353i	0.985757	−	0.168176i	$-0.0537878\pi$
$854$	−4.38287e6			−0.205643
$855$			2.43461e6i			0.113897i
$856$			2.02039e7i			0.942432i
$857$	2.14008e7			0.995353			0.497677	−	0.867363i	$-0.334187\pi$
$857$	2.14008e7			0.995353			0.497677	+	0.867363i	$0.334187\pi$
$858$		−	1.07176e8i		−	4.97027i
$859$			1.95930e7i			0.905977i	0.891516	+	0.452988i	$0.149642\pi$
$859$			1.95930e7i			0.905977i	−0.891516	+	0.452988i	$0.850358\pi$
$860$		−	9.84758e6i		−	0.454029i
$861$	2.07316e7			0.953070
$862$			1.67992e7i			0.770054i
$863$	6.13010e6			0.280182			0.140091	−	0.990139i	$-0.455260\pi$
$863$	6.13010e6			0.280182			0.140091	+	0.990139i	$0.455260\pi$
$864$	3.80761e7			1.73527
$865$	3.22944e7			1.46753
$866$	−1.88265e7			−0.853052
$867$			4.46325e6i			0.201653i
$868$			1.33592e7i			0.601839i
$869$	−1.78905e7			−0.803662
$870$	−7.04711e7	+	3.15965e7i	−3.15655	+	1.41527i
$871$	837311.			0.0373974
$872$			1.67486e6i			0.0745912i
$873$			7.09683e7i			3.15158i
$874$	−1.60380e6			−0.0710187
$875$	−1.11780e7			−0.493566
$876$	2.75150e7			1.21146
$877$	3.58058e7			1.57201			0.786003	−	0.618223i	$-0.212147\pi$
$877$	3.58058e7			1.57201			0.786003	+	0.618223i	$0.212147\pi$
$878$			3.52380e7i			1.54268i
$879$	−2.98768e7			−1.30425
$880$			6.09081e6i			0.265136i
$881$		−	4.29609e7i		−	1.86481i	−0.361418	−	0.932404i	$-0.617707\pi$
$881$		−	4.29609e7i		−	1.86481i	0.361418	−	0.932404i	$-0.382293\pi$
$882$		−	2.39133e6i		−	0.103507i
$883$	−2.13639e7			−0.922102			−0.461051	−	0.887374i	$-0.652527\pi$
$883$	−2.13639e7			−0.922102			−0.461051	+	0.887374i	$0.652527\pi$
$884$		−	5.32560e7i		−	2.29212i
$885$		−	5.66236e7i		−	2.43018i
$886$	5.57169e7			2.38453
$887$		−	7.12705e6i		−	0.304159i	−0.988368	−	0.152079i	$-0.951403\pi$
$887$		−	7.12705e6i		−	0.304159i	0.988368	−	0.152079i	$-0.0485970\pi$
$888$		−	3.61564e7i		−	1.53870i
$889$		−	1.94064e7i		−	0.823553i
$890$	−4.63814e7			−1.96277
$891$		−	2.24612e7i		−	0.947846i
$892$	−1.44355e7			−0.607463
$893$	1.56396e6			0.0656292
$894$	−4.21744e7			−1.76484
$895$	−1.77392e7			−0.740248
$896$			3.61312e7i			1.50353i
$897$			5.46814e7i			2.26913i
$898$	−1.90449e7			−0.788114
$899$	3.80027e6	+	8.47591e6i	0.156825	+	0.349774i
$900$	4.42374e7			1.82047
$901$		−	1.82594e6i		−	0.0749332i
$902$			2.78986e7i			1.14174i
$903$	9.81858e6			0.400709
$904$	−7.85993e6			−0.319888
$905$	1.36411e7			0.553639
$906$	−5.77414e6			−0.233704
$907$			1.96553e7i			0.793344i	0.917960	+	0.396672i	$0.129835\pi$
$907$			1.96553e7i			0.793344i	−0.917960	+	0.396672i	$0.870165\pi$
$908$	−2.68118e7			−1.07922
$909$			3.11128e7i			1.24891i
$910$			7.23599e7i			2.89664i
$911$			4.67086e7i			1.86466i	0.361602	+	0.932332i	$0.382230\pi$
$911$			4.67086e7i			1.86466i	−0.361602	+	0.932332i	$0.617770\pi$
$912$	321883.			0.0128148
$913$		−	4.92319e7i		−	1.95465i
$914$			2.34126e7i			0.927011i
$915$	6.96418e6			0.274990
$916$			4.82141e7i			1.89861i
$917$			3.78270e7i			1.48552i
$918$		−	6.65486e7i		−	2.60635i
$919$	−2.45867e7			−0.960310			−0.480155	−	0.877184i	$-0.659420\pi$
$919$	−2.45867e7			−0.960310			−0.480155	+	0.877184i	$0.659420\pi$
$920$			2.68688e7i			1.04659i
$921$	−3.69442e7			−1.43515
$922$	7.11312e7			2.75571
$923$	−6.85116e7			−2.64704
$924$	9.04489e7			3.48517
$925$			1.67415e7i			0.643337i
$926$		−	7.52683e7i		−	2.88459i
$927$	−2.86931e7			−1.09668
$928$	1.20529e7	+	2.68821e7i	0.459432	+	1.02469i
$929$	−1.16775e7			−0.443925			−0.221963	−	0.975055i	$-0.571246\pi$
$929$	−1.16775e7			−0.443925			−0.221963	+	0.975055i	$0.571246\pi$
$930$		−	3.49752e7i		−	1.32603i
$931$		−	42278.2i		−	0.00159861i
$932$	−6.62050e7			−2.49661
$933$	−4.03461e7			−1.51739
$934$	7.09003e7			2.65938
$935$	4.68260e7			1.75169
$936$			6.22410e7i			2.32213i
$937$	2.58109e7			0.960404			0.480202	−	0.877158i	$-0.340563\pi$
$937$	2.58109e7			0.960404			0.480202	+	0.877158i	$0.340563\pi$
$938$			1.16429e6i			0.0432071i
$939$			4.82479e7i			1.78572i
$940$		−	7.43652e7i		−	2.74505i
$941$	1.87220e7			0.689253			0.344626	−	0.938740i	$-0.388006\pi$
$941$	1.87220e7			0.689253			0.344626	+	0.938740i	$0.388006\pi$
$942$		−	3.50789e7i		−	1.28801i
$943$		−	1.42339e7i		−	0.521249i
$944$	−4.91049e6			−0.179347
$945$			5.48781e7i			1.99903i
$946$			1.32129e7i			0.480033i
$947$			1.87594e7i			0.679741i	0.940472	+	0.339871i	$0.110383\pi$
$947$			1.87594e7i			0.679741i	−0.940472	+	0.339871i	$0.889617\pi$
$948$	4.49563e7			1.62469
$949$		−	1.79252e7i		−	0.646098i
$950$	1.28865e6			0.0463263
$951$	−5.71735e7			−2.04995
$952$	2.60913e7			0.933047
$953$	−1.99609e7			−0.711947			−0.355973	−	0.934496i	$-0.615851\pi$
$953$	−1.99609e7			−0.711947			−0.355973	+	0.934496i	$0.615851\pi$
$954$			6.05678e6i			0.215462i
$955$			1.24777e7i			0.442718i
$956$	3.71785e7			1.31567
$957$	5.73866e7	−	2.57299e7i	2.02549	−	0.908152i
$958$	382414.			0.0134623
$959$			2.05090e7i			0.720107i
$960$		−	1.01014e8i		−	3.53757i
$961$	2.44225e7			0.853064
$962$	−6.68540e7			−2.32911
$963$	5.95897e7			2.07064
$964$	8.46775e6			0.293478
$965$		−	1.92248e7i		−	0.664575i
$966$	−7.60352e7			−2.62163
$967$		−	4.72480e7i		−	1.62486i	−0.583055	−	0.812432i	$-0.698143\pi$
$967$		−	4.72480e7i		−	1.62486i	0.583055	−	0.812432i	$-0.301857\pi$
$968$			1.75893e7i			0.603338i
$969$		−	2.47463e6i		−	0.0846644i
$970$	9.83004e7			3.35449
$971$			8.02348e6i			0.273096i	0.990633	+	0.136548i	$0.0436007\pi$
$971$			8.02348e6i			0.273096i	−0.990633	+	0.136548i	$0.956399\pi$
$972$		−	1.38350e7i		−	0.469693i
$973$	2.52579e7			0.855295
$974$			6.44588e7i			2.17713i
$975$		−	4.39365e7i		−	1.48018i
$976$		−	603945.i		−	0.0202942i
$977$	4.37542e7			1.46650			0.733252	−	0.679957i	$-0.238002\pi$
$977$	4.37542e7			1.46650			0.733252	+	0.679957i	$0.238002\pi$
$978$		−	1.44832e7i		−	0.484190i
$979$	3.77697e7			1.25947
$980$	−2.01030e6			−0.0668646
$981$	4.93987e6			0.163887
$982$	−5.32221e7			−1.76122
$983$			4.10885e6i			0.135624i	0.997698	+	0.0678120i	$0.0216018\pi$
$983$			4.10885e6i			0.135624i	−0.997698	+	0.0678120i	$0.978398\pi$
$984$		−	2.47003e7i		−	0.813233i
$985$	−2.99851e7			−0.984725
$986$	4.69841e7	−	2.10658e7i	1.53907	−	0.690059i
$987$	7.41462e7			2.42268
$988$			3.12321e6i			0.101791i
$989$		−	6.74125e6i		−	0.219154i
$990$	−1.55326e8			−5.03680
$991$	−3.31591e7			−1.07255			−0.536277	−	0.844042i	$-0.680170\pi$
$991$	−3.31591e7			−1.07255			−0.536277	+	0.844042i	$0.680170\pi$
$992$	−1.33417e7			−0.430461
$993$	−3.21025e7			−1.03316
$994$		−	9.52663e7i		−	3.05825i
$995$	6.83322e7			2.18810
$996$			1.23713e8i			3.95154i
$997$			2.46810e7i			0.786365i	0.919461	+	0.393182i	$0.128626\pi$
$997$			2.46810e7i			0.786365i	−0.919461	+	0.393182i	$0.871374\pi$
$998$		−	2.51186e7i		−	0.798305i
$999$	−5.07024e7			−1.60737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.b.a.28.11	yes	12
3.2	odd	2		261.6.c.b.28.2		12
4.3	odd	2		464.6.e.c.289.12		12
29.12	odd	4		841.6.a.d.1.2		12
29.17	odd	4		841.6.a.d.1.11		12
29.28	even	2	inner	29.6.b.a.28.2	✓	12
87.86	odd	2		261.6.c.b.28.11		12
116.115	odd	2		464.6.e.c.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.b.a.28.2	✓	12	29.28	even	2	inner
29.6.b.a.28.11	yes	12	1.1	even	1	trivial
261.6.c.b.28.2		12	3.2	odd	2
261.6.c.b.28.11		12	87.86	odd	2
464.6.e.c.289.1		12	116.115	odd	2
464.6.e.c.289.12		12	4.3	odd	2
841.6.a.d.1.2		12	29.12	odd	4
841.6.a.d.1.11		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)

\(f(q)\)	\(=\)	\(q+9.02264i q^{2} -26.5755i q^{3} -49.4080 q^{4} +71.1177 q^{5} +239.781 q^{6} +131.830 q^{7} -157.067i q^{8} -463.255 q^{9} +O(q^{10})\)	\(q+9.02264i q^{2} -26.5755i q^{3} -49.4080 q^{4} +71.1177 q^{5} +239.781 q^{6} +131.830 q^{7} -157.067i q^{8} -463.255 q^{9} +641.670i q^{10} -522.530i q^{11} +1313.04i q^{12} +855.406 q^{13} +1189.45i q^{14} -1889.99i q^{15} -163.903 q^{16} +1260.08i q^{17} -4179.79i q^{18} -73.8977i q^{19} -3513.79 q^{20} -3503.44i q^{21} +4714.60 q^{22} -2405.40 q^{23} -4174.12 q^{24} +1932.73 q^{25} +7718.03i q^{26} +5853.39i q^{27} -6513.46 q^{28} +(-4132.55 + 1852.88i) q^{29} +17052.7 q^{30} -2051.01i q^{31} -6504.96i q^{32} -13886.5 q^{33} -11369.3 q^{34} +9375.44 q^{35} +22888.5 q^{36} +8662.06i q^{37} +666.753 q^{38} -22732.8i q^{39} -11170.2i q^{40} +5917.50i q^{41} +31610.3 q^{42} +2802.55i q^{43} +25817.2i q^{44} -32945.7 q^{45} -21703.0i q^{46} +21163.8i q^{47} +4355.79i q^{48} +572.118 q^{49} +17438.4i q^{50} +33487.2 q^{51} -42264.0 q^{52} -1449.06 q^{53} -52813.0 q^{54} -37161.1i q^{55} -20706.1i q^{56} -1963.87 q^{57} +(-16717.8 - 37286.5i) q^{58} +29959.8 q^{59} +93380.5i q^{60} +3684.78i q^{61} +18505.5 q^{62} -61070.9 q^{63} +53447.1 q^{64} +60834.6 q^{65} -125293. i q^{66} +978.846 q^{67} -62258.1i q^{68} +63924.5i q^{69} +84591.3i q^{70} -80092.5 q^{71} +72761.9i q^{72} -20955.2i q^{73} -78154.7 q^{74} -51363.3i q^{75} +3651.14i q^{76} -68885.0i q^{77} +205110. q^{78} -34238.3i q^{79} -11656.4 q^{80} +42985.4 q^{81} -53391.5 q^{82} +94218.4 q^{83} +173098. i q^{84} +89614.1i q^{85} -25286.4 q^{86} +(49241.1 + 109825. i) q^{87} -82071.9 q^{88} +72282.4i q^{89} -297257. i q^{90} +112768. q^{91} +118846. q^{92} -54506.6 q^{93} -190954. q^{94} -5255.44i q^{95} -172872. q^{96} -153195. i q^{97} +5162.02i q^{98} +242065. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 172 q^{4} + 46 q^{5} + 24 q^{6} + 20 q^{7} - 1574 q^{9}+O(q^{10}) \) 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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