LMFDB - Embedded newform 29.6.b.a.28.1

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			28.1
Root			$-9.47123i$ of defining polynomial
Character	$\chi$	$=$	29.28
Dual form			29.6.b.a.28.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.47123i q^{2} -19.9099i q^{3} -57.7042 q^{4} -4.84615 q^{5} -188.571 q^{6} +219.131 q^{7} +243.450i q^{8} -153.403 q^{9} +O(q^{10})$	\(q-9.47123i q^{2} -19.9099i q^{3} -57.7042 q^{4} -4.84615 q^{5} -188.571 q^{6} +219.131 q^{7} +243.450i q^{8} -153.403 q^{9} +45.8990i q^{10} +12.7646i q^{11} +1148.88i q^{12} -566.970 q^{13} -2075.44i q^{14} +96.4863i q^{15} +459.241 q^{16} +1156.19i q^{17} +1452.92i q^{18} -2227.86i q^{19} +279.643 q^{20} -4362.86i q^{21} +120.897 q^{22} +4382.29 q^{23} +4847.07 q^{24} -3101.51 q^{25} +5369.91i q^{26} -1783.86i q^{27} -12644.8 q^{28} +(4035.37 + 2055.94i) q^{29} +913.844 q^{30} +2588.50i q^{31} +3440.84i q^{32} +254.142 q^{33} +10950.5 q^{34} -1061.94 q^{35} +8852.00 q^{36} -12430.1i q^{37} -21100.6 q^{38} +11288.3i q^{39} -1179.80i q^{40} -3689.31i q^{41} -41321.7 q^{42} +12839.1i q^{43} -736.572i q^{44} +743.415 q^{45} -41505.7i q^{46} +6917.34i q^{47} -9143.42i q^{48} +31211.2 q^{49} +29375.2i q^{50} +23019.6 q^{51} +32716.6 q^{52} +21951.5 q^{53} -16895.4 q^{54} -61.8593i q^{55} +53347.4i q^{56} -44356.4 q^{57} +(19472.3 - 38220.0i) q^{58} +6943.35 q^{59} -5567.67i q^{60} +24856.9i q^{61} +24516.2 q^{62} -33615.3 q^{63} +47284.7 q^{64} +2747.62 q^{65} -2407.04i q^{66} -43952.6 q^{67} -66717.1i q^{68} -87250.9i q^{69} +10057.9i q^{70} -12059.2 q^{71} -37346.0i q^{72} -39425.0i q^{73} -117728. q^{74} +61750.8i q^{75} +128557. i q^{76} +2797.12i q^{77} +106914. q^{78} -34619.6i q^{79} -2225.55 q^{80} -72793.4 q^{81} -34942.3 q^{82} +21990.2 q^{83} +251755. i q^{84} -5603.08i q^{85} +121602. q^{86} +(40933.6 - 80343.8i) q^{87} -3107.55 q^{88} +64375.4i q^{89} -7041.05i q^{90} -124240. q^{91} -252877. q^{92} +51536.6 q^{93} +65515.7 q^{94} +10796.5i q^{95} +68506.7 q^{96} +143461. i q^{97} -295608. i q^{98} -1958.13i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	9.47123i		−	1.67429i	−0.546979	−	0.837146i	$-0.684222\pi$
$2$		−	9.47123i		−	1.67429i	0.546979	−	0.837146i	$-0.315778\pi$
$3$		−	19.9099i		−	1.27722i	−0.769531	−	0.638609i	$-0.779510\pi$
$3$		−	19.9099i		−	1.27722i	0.769531	−	0.638609i	$-0.220490\pi$
$4$	−57.7042			−1.80326
$5$	−4.84615			−0.0866906			−0.0433453	−	0.999060i	$-0.513802\pi$
$5$	−4.84615			−0.0866906			−0.0433453	+	0.999060i	$0.513802\pi$
$6$	−188.571			−2.13844
$7$	219.131			1.69028			0.845138	−	0.534548i	$-0.179518\pi$
$7$	219.131			1.69028			0.845138	+	0.534548i	$0.179518\pi$
$8$			243.450i			1.34489i
$9$	−153.403			−0.631288
$10$			45.8990i			0.145145i
$11$			12.7646i			0.0318072i	0.999874	+	0.0159036i	$0.00506249\pi$
$11$			12.7646i			0.0318072i	−0.999874	+	0.0159036i	$0.994938\pi$
$12$			1148.88i			2.30315i
$13$	−566.970			−0.930469			−0.465234	−	0.885187i	$-0.654030\pi$
$13$	−566.970			−0.930469			−0.465234	+	0.885187i	$0.654030\pi$
$14$		−	2075.44i		−	2.83002i
$15$			96.4863i			0.110723i
$16$	459.241			0.448477
$17$			1156.19i			0.970302i	0.874430	+	0.485151i	$0.161235\pi$
$17$			1156.19i			0.970302i	−0.874430	+	0.485151i	$0.838765\pi$
$18$			1452.92i			1.05696i
$19$		−	2227.86i		−	1.41580i	−0.706310	−	0.707902i	$-0.749642\pi$
$19$		−	2227.86i		−	1.41580i	0.706310	−	0.707902i	$-0.250358\pi$
$20$	279.643			0.156325
$21$		−	4362.86i		−	2.15885i
$22$	120.897			0.0532546
$23$	4382.29			1.72736			0.863678	−	0.504044i	$-0.168155\pi$
$23$	4382.29			1.72736			0.863678	+	0.504044i	$0.168155\pi$
$24$	4847.07			1.71771
$25$	−3101.51			−0.992485
$26$			5369.91i			1.55788i
$27$		−	1783.86i		−	0.470926i
$28$	−12644.8			−3.04800
$29$	4035.37	+	2055.94i	0.891023	+	0.453959i
$29$	4035.37	+	2055.94i	0.891023	+	0.453959i
$30$	913.844			0.185383
$31$			2588.50i			0.483775i	0.970304	+	0.241887i	$0.0777665\pi$
$31$			2588.50i			0.483775i	−0.970304	+	0.241887i	$0.922234\pi$
$32$			3440.84i			0.594004i
$33$	254.142			0.0406248
$34$	10950.5			1.62457
$35$	−1061.94			−0.146531
$36$	8852.00			1.13837
$37$		−	12430.1i		−	1.49269i	−0.665558	−	0.746346i	$-0.731806\pi$
$37$		−	12430.1i		−	1.49269i	0.665558	−	0.746346i	$-0.268194\pi$
$38$	−21100.6			−2.37047
$39$			11288.3i			1.18841i
$40$		−	1179.80i		−	0.116589i
$41$		−	3689.31i		−	0.342756i	−0.985205	−	0.171378i	$-0.945178\pi$
$41$		−	3689.31i		−	0.342756i	0.985205	−	0.171378i	$-0.0548220\pi$
$42$	−41321.7			−3.61455
$43$			12839.1i			1.05892i	0.848336	+	0.529459i	$0.177605\pi$
$43$			12839.1i			1.05892i	−0.848336	+	0.529459i	$0.822395\pi$
$44$		−	736.572i		−	0.0573566i
$45$	743.415			0.0547268
$46$		−	41505.7i		−	2.89210i
$47$			6917.34i			0.456767i	0.973571	+	0.228383i	$0.0733439\pi$
$47$			6917.34i			0.456767i	−0.973571	+	0.228383i	$0.926656\pi$
$48$		−	9143.42i		−	0.572804i
$49$	31211.2			1.85704
$50$			29375.2i			1.66171i
$51$	23019.6			1.23929
$52$	32716.6			1.67787
$53$	21951.5			1.07343			0.536716	−	0.843763i	$-0.319665\pi$
$53$	21951.5			1.07343			0.536716	+	0.843763i	$0.319665\pi$
$54$	−16895.4			−0.788468
$55$		−	61.8593i		−	0.00275739i
$56$			53347.4i			2.27323i
$57$	−44356.4			−1.80829
$58$	19472.3	−	38220.0i	0.760060	−	1.49183i
$59$	6943.35			0.259680			0.129840	−	0.991535i	$-0.458554\pi$
$59$	6943.35			0.259680			0.129840	+	0.991535i	$0.458554\pi$
$60$		−	5567.67i		−	0.199662i
$61$			24856.9i			0.855306i	0.903943	+	0.427653i	$0.140660\pi$
$61$			24856.9i			0.855306i	−0.903943	+	0.427653i	$0.859340\pi$
$62$	24516.2			0.809981
$63$	−33615.3			−1.06705
$64$	47284.7			1.44301
$65$	2747.62			0.0806629
$66$		−	2407.04i		−	0.0680178i
$67$	−43952.6			−1.19618			−0.598091	−	0.801428i	$-0.704074\pi$
$67$	−43952.6			−1.19618			−0.598091	+	0.801428i	$0.704074\pi$
$68$		−	66717.1i		−	1.74970i
$69$		−	87250.9i		−	2.20621i
$70$			10057.9i			0.245336i
$71$	−12059.2			−0.283905			−0.141952	−	0.989874i	$-0.545338\pi$
$71$	−12059.2			−0.283905			−0.141952	+	0.989874i	$0.545338\pi$
$72$		−	37346.0i		−	0.849011i
$73$		−	39425.0i		−	0.865893i	−0.901420	−	0.432947i	$-0.857474\pi$
$73$		−	39425.0i		−	0.865893i	0.901420	−	0.432947i	$-0.142526\pi$
$74$	−117728.			−2.49921
$75$			61750.8i			1.26762i
$76$			128557.i			2.55306i
$77$			2797.12i			0.0537630i
$78$	106914.			1.98975
$79$		−	34619.6i		−	0.624101i	−0.950066	−	0.312050i	$-0.898984\pi$
$79$		−	34619.6i		−	0.624101i	0.950066	−	0.312050i	$-0.101016\pi$
$80$	−2225.55			−0.0388788
$81$	−72793.4			−1.23276
$82$	−34942.3			−0.573875
$83$	21990.2			0.350376			0.175188	−	0.984535i	$-0.443947\pi$
$83$	21990.2			0.350376			0.175188	+	0.984535i	$0.443947\pi$
$84$			251755.i			3.89297i
$85$		−	5603.08i		−	0.0841161i
$86$	121602.			1.77294
$87$	40933.6	−	80343.8i	0.579805	−	1.13803i
$88$	−3107.55			−0.0427771
$89$			64375.4i			0.861480i	0.902476	+	0.430740i	$0.141747\pi$
$89$			64375.4i			0.861480i	−0.902476	+	0.430740i	$0.858253\pi$
$90$		−	7041.05i		−	0.0916286i
$91$	−124240.			−1.57275
$92$	−252877.			−3.11487
$93$	51536.6			0.617887
$94$	65515.7			0.764761
$95$			10796.5i			0.122737i
$96$	68506.7			0.758673
$97$			143461.i			1.54812i	0.633110	+	0.774062i	$0.281778\pi$
$97$			143461.i			1.54812i	−0.633110	+	0.774062i	$0.718222\pi$
$98$		−	295608.i		−	3.10922i
$99$		−	1958.13i		−	0.0200795i
$100$	178970.			1.78970
$101$		−	4588.83i		−	0.0447609i	−0.999750	−	0.0223804i	$-0.992875\pi$
$101$		−	4588.83i		−	0.0447609i	0.999750	−	0.0223804i	$-0.00712451\pi$
$102$		−	218024.i		−	2.07493i
$103$	63906.9			0.593546			0.296773	−	0.954948i	$-0.404090\pi$
$103$	63906.9			0.593546			0.296773	+	0.954948i	$0.404090\pi$
$104$		−	138029.i		−	1.25137i
$105$			21143.1i			0.187152i
$106$		−	207908.i		−	1.79724i
$107$	−38764.2			−0.327319			−0.163660	−	0.986517i	$-0.552330\pi$
$107$	−38764.2			−0.327319			−0.163660	+	0.986517i	$0.552330\pi$
$108$			102936.i			0.849200i
$109$	159706.			1.28752			0.643761	−	0.765227i	$-0.277373\pi$
$109$	159706.			1.28752			0.643761	+	0.765227i	$0.277373\pi$
$110$	−585.883			−0.00461668
$111$	−247482.			−1.90650
$112$	100634.			0.758051
$113$			56711.6i			0.417807i	0.977936	+	0.208904i	$0.0669895\pi$
$113$			56711.6i			0.417807i	−0.977936	+	0.208904i	$0.933011\pi$
$114$			420109.i			3.02761i
$115$	−21237.3			−0.149746
$116$	−232858.	−	118637.i	−1.60674	−	0.818604i
$117$	86974.9			0.587394
$118$		−	65762.1i		−	0.434781i
$119$			253357.i			1.64008i
$120$	−23489.6			−0.148910
$121$	160888.			0.998988
$122$	235425.			1.43203
$123$	−73453.7			−0.437775
$124$		−	149367.i		−	0.872370i
$125$	30174.6			0.172730
$126$			318378.i			1.78656i
$127$			158805.i			0.873682i	0.899539	+	0.436841i	$0.143903\pi$
$127$			158805.i			0.873682i	−0.899539	+	0.436841i	$0.856097\pi$
$128$		−	337737.i		−	1.82202i
$129$	255624.			1.35247
$130$		−	26023.4i		−	0.135053i
$131$		−	90328.1i		−	0.459880i	−0.973205	−	0.229940i	$-0.926147\pi$
$131$		−	90328.1i		−	0.459880i	0.973205	−	0.229940i	$-0.0738530\pi$
$132$	−14665.0			−0.0732569
$133$		−	488192.i		−	2.39310i
$134$			416285.i			2.00276i
$135$			8644.88i			0.0408248i
$136$	−281475.			−1.30495
$137$			221885.i			1.01001i	0.863116	+	0.505006i	$0.168510\pi$
$137$			221885.i			1.01001i	−0.863116	+	0.505006i	$0.831490\pi$
$138$	−826373.			−3.69384
$139$	−72649.2			−0.318929			−0.159465	−	0.987204i	$-0.550977\pi$
$139$	−72649.2			−0.318929			−0.159465	+	0.987204i	$0.550977\pi$
$140$	61278.4			0.264233
$141$	137723.			0.583391
$142$			114215.i			0.475339i
$143$		−	7237.15i		−	0.0295956i
$144$	−70448.9			−0.283118
$145$	−19556.0	−	9963.42i	−0.0772433	−	0.0393540i
$146$	−373403.			−1.44976
$147$		−	621411.i		−	2.37184i
$148$			717269.i			2.69171i
$149$	−284587.			−1.05014			−0.525072	−	0.851058i	$-0.675962\pi$
$149$	−284587.			−1.05014			−0.525072	+	0.851058i	$0.675962\pi$
$150$	584856.			2.12237
$151$	−345064.			−1.23157			−0.615783	−	0.787916i	$-0.711160\pi$
$151$	−345064.			−1.23157			−0.615783	+	0.787916i	$0.711160\pi$
$152$	542373.			1.90410
$153$		−	177363.i		−	0.612540i
$154$	26492.1			0.0900150
$155$		−	12544.3i		−	0.0419388i
$156$		−	651383.i		−	2.14301i
$157$		−	111826.i		−	0.362071i	−0.983477	−	0.181035i	$-0.942055\pi$
$157$		−	111826.i		−	0.362071i	0.983477	−	0.181035i	$-0.0579449\pi$
$158$	−327891.			−1.04493
$159$		−	437052.i		−	1.37101i
$160$		−	16674.8i		−	0.0514946i
$161$	960294.			2.91971
$162$			689444.i			2.06401i
$163$			563756.i			1.66197i	0.556297	+	0.830984i	$0.312222\pi$
$163$			563756.i			1.66197i	−0.556297	+	0.830984i	$0.687778\pi$
$164$			212889.i			0.618078i
$165$	−1231.61			−0.00352179
$166$		−	208275.i		−	0.586632i
$167$	100531.			0.278938			0.139469	−	0.990226i	$-0.455460\pi$
$167$	100531.			0.278938			0.139469	+	0.990226i	$0.455460\pi$
$168$	1.06214e6			2.90341
$169$	−49837.8			−0.134228
$170$	−53068.0			−0.140835
$171$			341760.i			0.893781i
$172$		−	740868.i		−	1.90950i
$173$	−522238.			−1.32664			−0.663321	−	0.748335i	$-0.730853\pi$
$173$	−522238.			−1.32664			−0.663321	+	0.748335i	$0.730853\pi$
$174$	−760954.	−	387692.i	−1.90540	−	0.970763i
$175$	−679637.			−1.67757
$176$			5862.03i			0.0142648i
$177$		−	138241.i		−	0.331669i
$178$	609715.			1.44237
$179$	700959.			1.63516			0.817579	−	0.575816i	$-0.195316\pi$
$179$	700959.			1.63516			0.817579	+	0.575816i	$0.195316\pi$
$180$	−42898.1			−0.0986864
$181$	−228696.			−0.518873			−0.259437	−	0.965760i	$-0.583537\pi$
$181$	−228696.			−0.518873			−0.259437	+	0.965760i	$0.583537\pi$
$182$			1.17671e6i			2.63324i
$183$	494897.			1.09241
$184$			1.06687e6i			2.32310i
$185$			60238.2i			0.129402i
$186$		−	488115.i		−	1.03452i
$187$	−14758.3			−0.0308626
$188$		−	399160.i		−	0.823667i
$189$		−	390899.i		−	0.795995i
$190$	102257.			0.205498
$191$			824840.i			1.63601i	0.575211	+	0.818005i	$0.304920\pi$
$191$			824840.i			1.63601i	−0.575211	+	0.818005i	$0.695080\pi$
$192$		−	941432.i		−	1.84305i
$193$		−	937075.i		−	1.81084i	−0.424512	−	0.905422i	$-0.639554\pi$
$193$		−	937075.i		−	1.81084i	0.424512	−	0.905422i	$-0.360446\pi$
$194$	1.35876e6			2.59201
$195$		−	54704.9i		−	0.103024i
$196$	−1.80102e6			−3.34871
$197$	44740.0			0.0821354			0.0410677	−	0.999156i	$-0.486924\pi$
$197$	44740.0			0.0821354			0.0410677	+	0.999156i	$0.486924\pi$
$198$	−18545.9			−0.0336190
$199$	−237978.			−0.425996			−0.212998	−	0.977053i	$-0.568323\pi$
$199$	−237978.			−0.425996			−0.212998	+	0.977053i	$0.568323\pi$
$200$		−	755065.i		−	1.33478i
$201$			875091.i			1.52779i
$202$	−43461.9			−0.0749428
$203$	884274.	+	450520.i	1.50607	+	0.767316i
$204$	−1.32833e6			−2.23475
$205$			17879.0i			0.0297138i
$206$		−	605277.i		−	0.993770i
$207$	−672257.			−1.09046
$208$	−260376.			−0.417294
$209$	28437.7			0.0450328
$210$	200251.			0.313348
$211$			194564.i			0.300855i	0.988621	+	0.150427i	$0.0480649\pi$
$211$			194564.i			0.300855i	−0.988621	+	0.150427i	$0.951935\pi$
$212$	−1.26669e6			−1.93567
$213$			240097.i			0.362608i
$214$			367145.i			0.548029i
$215$		−	62220.1i		−	0.0917982i
$216$	434283.			0.633342
$217$			567219.i			0.817714i
$218$		−	1.51261e6i		−	2.15569i
$219$	−784947.			−1.10594
$220$			3569.54i			0.00497228i
$221$		−	655526.i		−	0.902836i
$222$			2.34396e6i			3.19203i
$223$	242137.			0.326061			0.163031	−	0.986621i	$-0.447873\pi$
$223$	242137.			0.326061			0.163031	+	0.986621i	$0.447873\pi$
$224$			753993.i			1.00403i
$225$	475782.			0.626544
$226$	537129.			0.699532
$227$	−1.27196e6			−1.63835			−0.819177	−	0.573540i	$-0.805570\pi$
$227$	−1.27196e6			−1.63835			−0.819177	+	0.573540i	$0.805570\pi$
$228$	2.55955e6			3.26082
$229$			48917.8i			0.0616422i	0.999525	+	0.0308211i	$0.00981222\pi$
$229$			48917.8i			0.0616422i	−0.999525	+	0.0308211i	$0.990188\pi$
$230$			201143.i			0.250718i
$231$	55690.2			0.0686672
$232$	−500521.	+	982413.i	−0.610523	+	1.19832i
$233$	467458.			0.564095			0.282048	−	0.959400i	$-0.408986\pi$
$233$	467458.			0.564095			0.282048	+	0.959400i	$0.408986\pi$
$234$		−	823760.i		−	0.983470i
$235$		−	33522.5i		−	0.0395974i
$236$	−400660.			−0.468270
$237$	−689273.			−0.797113
$238$	2.39960e6			2.74597
$239$	297093.			0.336432			0.168216	−	0.985750i	$-0.446199\pi$
$239$	297093.			0.336432			0.168216	+	0.985750i	$0.446199\pi$
$240$			44310.4i			0.0496567i
$241$	−212345.			−0.235504			−0.117752	−	0.993043i	$-0.537569\pi$
$241$	−212345.			−0.235504			−0.117752	+	0.993043i	$0.537569\pi$
$242$		−	1.52381e6i		−	1.67260i
$243$			1.01583e6i			1.10358i
$244$		−	1.43435e6i		−	1.54234i
$245$	−151254.			−0.160988
$246$			695697.i			0.732963i
$247$			1.26313e6i			1.31736i
$248$	−630171.			−0.650622
$249$		−	437823.i		−	0.447507i
$250$		−	285791.i		−	0.289200i
$251$		−	531502.i		−	0.532502i	−0.963904	−	0.266251i	$-0.914215\pi$
$251$		−	531502.i		−	0.532502i	0.963904	−	0.266251i	$-0.0857849\pi$
$252$	1.93974e6			1.92417
$253$			55938.3i			0.0549424i
$254$	1.50407e6			1.46280
$255$	−111557.			−0.107435
$256$	−1.68568e6			−1.60759
$257$	−796939.			−0.752649			−0.376324	−	0.926488i	$-0.622812\pi$
$257$	−796939.			−0.752649			−0.376324	+	0.926488i	$0.622812\pi$
$258$		−	2.42107e6i		−	2.26443i
$259$		−	2.72382e6i		−	2.52306i
$260$	−158549.			−0.145456
$261$	−619039.	−	315388.i	−0.562492	−	0.286579i
$262$	−855518.			−0.769974
$263$		−	96852.0i		−	0.0863414i	−0.999068	−	0.0431707i	$-0.986254\pi$
$263$		−	96852.0i		−	0.0863414i	0.999068	−	0.0431707i	$-0.0137459\pi$
$264$			61870.9i			0.0546357i
$265$	−106380.			−0.0930565
$266$	−4.62378e6			−4.00675
$267$	1.28171e6			1.10030
$268$	2.53625e6			2.15702
$269$		−	1.97762e6i		−	1.66634i	−0.553020	−	0.833168i	$-0.686525\pi$
$269$		−	1.97762e6i		−	1.66634i	0.553020	−	0.833168i	$-0.313475\pi$
$270$	81877.7			0.0683527
$271$			441551.i			0.365223i	0.983185	+	0.182611i	$0.0584550\pi$
$271$			441551.i			0.365223i	−0.983185	+	0.182611i	$0.941545\pi$
$272$			530970.i			0.435158i
$273$			2.47361e6i			2.00875i
$274$	2.10152e6			1.69106
$275$		−	39589.6i		−	0.0315682i
$276$			5.03474e6i			3.97837i
$277$	−443173.			−0.347035			−0.173518	−	0.984831i	$-0.555513\pi$
$277$	−443173.			−0.347035			−0.173518	+	0.984831i	$0.555513\pi$
$278$			688078.i			0.533981i
$279$		−	397083.i		−	0.305401i
$280$		−	258530.i		−	0.197068i
$281$	1.37176e6			1.03637			0.518183	−	0.855270i	$-0.326609\pi$
$281$	1.37176e6			1.03637			0.518183	+	0.855270i	$0.326609\pi$
$282$		−	1.30441e6i		−	0.976767i
$283$	−736175.			−0.546405			−0.273203	−	0.961956i	$-0.588083\pi$
$283$	−736175.			−0.546405			−0.273203	+	0.961956i	$0.588083\pi$
$284$	695866.			0.511953
$285$	214958.			0.156762
$286$	−68544.8			−0.0495518
$287$		−	808441.i		−	0.579353i
$288$		−	527835.i		−	0.374988i
$289$	83080.5			0.0585133
$290$	−94365.9	+	185220.i	−0.0658901	+	0.129328i
$291$	2.85630e6			1.97729
$292$			2.27499e6i			1.56143i
$293$			1.61860e6i			1.10147i	0.834681	+	0.550734i	$0.185652\pi$
$293$			1.61860e6i			1.10147i	−0.834681	+	0.550734i	$0.814348\pi$
$294$	−5.88553e6			−3.97116
$295$	−33648.5			−0.0225118
$296$	3.02611e6			2.00750
$297$	22770.3			0.0149788
$298$			2.69539e6i			1.75825i
$299$	−2.48463e6			−1.60725
$300$		−	3.56328e6i		−	2.28584i
$301$			2.81343e6i			1.78986i
$302$			3.26818e6i			2.06200i
$303$	−91363.0			−0.0571694
$304$		−	1.02312e6i		−	0.634956i
$305$		−	120460.i		−	0.0741471i
$306$	−1.67985e6			−1.02557
$307$		−	909944.i		−	0.551022i	−0.961298	−	0.275511i	$-0.911153\pi$
$307$		−	909944.i		−	0.551022i	0.961298	−	0.275511i	$-0.0888470\pi$
$308$		−	161405.i		−	0.0969485i
$309$		−	1.27238e6i		−	0.758088i
$310$	−118810.			−0.0702178
$311$		−	2.84768e6i		−	1.66952i	−0.550616	−	0.834758i	$-0.685607\pi$
$311$		−	2.84768e6i		−	1.66952i	0.550616	−	0.834758i	$-0.314393\pi$
$312$	−2.74814e6			−1.59828
$313$	−2.05227e6			−1.18406			−0.592029	−	0.805917i	$-0.701673\pi$
$313$	−2.05227e6			−1.18406			−0.592029	+	0.805917i	$0.701673\pi$
$314$	−1.05913e6			−0.606213
$315$	162905.			0.0925034
$316$			1.99770e6i			1.12541i
$317$		−	1.41233e6i		−	0.789382i	−0.918814	−	0.394691i	$-0.870852\pi$
$317$		−	1.41233e6i		−	0.789382i	0.918814	−	0.394691i	$-0.129148\pi$
$318$	−4.13942e6			−2.29547
$319$	−26243.3	+	51510.0i	−0.0144392	+	0.0283410i
$320$	−229149.			−0.125096
$321$			771791.i			0.418059i
$322$		−	9.09517e6i		−	4.88845i
$323$	2.57583e6			1.37376
$324$	4.20049e6			2.22299
$325$	1.75847e6			0.923476
$326$	5.33947e6			2.78262
$327$		−	3.17972e6i		−	1.64445i
$328$	898164.			0.460968
$329$			1.51580e6i			0.772062i
$330$			11664.9i			0.00589651i
$331$			1.52835e6i			0.766746i	0.923594	+	0.383373i	$0.125238\pi$
$331$			1.52835e6i			0.766746i	−0.923594	+	0.383373i	$0.874762\pi$
$332$	−1.26893e6			−0.631818
$333$			1.90682e6i			0.942319i
$334$		−	952151.i		−	0.467024i
$335$	213001.			0.103698
$336$		−	2.00360e6i		−	0.968197i
$337$		−	935271.i		−	0.448604i	−0.974520	−	0.224302i	$-0.927990\pi$
$337$		−	935271.i		−	0.448604i	0.974520	−	0.224302i	$-0.0720101\pi$
$338$			472025.i			0.224736i
$339$	1.12912e6			0.533631
$340$			323321.i			0.151683i
$341$	−33041.2			−0.0153875
$342$	3.23689e6			1.49645
$343$	3.15640e6			1.44863
$344$	−3.12568e6			−1.42412
$345$			422831.i			0.191258i
$346$			4.94624e6i			2.22119i
$347$	1.16833e6			0.520886			0.260443	−	0.965489i	$-0.416131\pi$
$347$	1.16833e6			0.520886			0.260443	+	0.965489i	$0.416131\pi$
$348$	−2.36204e6	+	4.63617e6i	−1.04554	+	2.05216i
$349$	−3.70492e6			−1.62823			−0.814114	−	0.580706i	$-0.802777\pi$
$349$	−3.70492e6			−1.62823			−0.814114	+	0.580706i	$0.802777\pi$
$350$			6.43700e6i			2.80875i
$351$			1.01140e6i			0.438182i
$352$	−43921.0			−0.0188936
$353$	−2.64790e6			−1.13100			−0.565502	−	0.824747i	$-0.691318\pi$
$353$	−2.64790e6			−1.13100			−0.565502	+	0.824747i	$0.691318\pi$
$354$	−1.30931e6			−0.555310
$355$	58440.7			0.0246119
$356$		−	3.71473e6i		−	1.55347i
$357$	5.04430e6			2.09474
$358$		−	6.63894e6i		−	2.73773i
$359$			3.45478e6i			1.41476i	0.706831	+	0.707382i	$0.250124\pi$
$359$			3.45478e6i			1.41476i	−0.706831	+	0.707382i	$0.749876\pi$
$360$			180985.i			0.0736013i
$361$	−2.48725e6			−1.00450
$362$			2.16603e6i			0.868746i
$363$		−	3.20326e6i		−	1.27593i
$364$	7.16920e6			2.83607
$365$			191060.i			0.0750649i
$366$		−	4.68728e6i		−	1.82902i
$367$			1.44664e6i			0.560654i	0.959905	+	0.280327i	$0.0904429\pi$
$367$			1.44664e6i			0.560654i	−0.959905	+	0.280327i	$0.909557\pi$
$368$	2.01253e6			0.774680
$369$			565951.i			0.216378i
$370$	570530.			0.216658
$371$	4.81025e6			1.81440
$372$	−2.97388e6			−1.11421
$373$	1.80613e6			0.672168			0.336084	−	0.941832i	$-0.390897\pi$
$373$	1.80613e6			0.672168			0.336084	+	0.941832i	$0.390897\pi$
$374$			139779.i			0.0516731i
$375$		−	600773.i		−	0.220614i
$376$	−1.68403e6			−0.614299
$377$	−2.28794e6	−	1.16566e6i	−0.829069	−	0.422395i
$378$	−3.70230e6			−1.33273
$379$		−	1.53246e6i		−	0.548015i	−0.961728	−	0.274007i	$-0.911651\pi$
$379$		−	1.53246e6i		−	0.548015i	0.961728	−	0.274007i	$-0.0883492\pi$
$380$		−	623006.i		−	0.221326i
$381$	3.16178e6			1.11588
$382$	7.81225e6			2.73916
$383$	−3.49639e6			−1.21793			−0.608966	−	0.793197i	$-0.708415\pi$
$383$	−3.49639e6			−1.21793			−0.608966	+	0.793197i	$0.708415\pi$
$384$	−6.72431e6			−2.32712
$385$		−	13555.3i		−	0.00466075i
$386$	−8.87526e6			−3.03188
$387$		−	1.96955e6i		−	0.668482i
$388$		−	8.27833e6i		−	2.79167i
$389$			2.08406e6i			0.698290i	0.937069	+	0.349145i	$0.113528\pi$
$389$			2.08406e6i			0.698290i	−0.937069	+	0.349145i	$0.886472\pi$
$390$	−518122.			−0.172493
$391$			5.06677e6i			1.67606i
$392$			7.59838e6i			2.49750i
$393$	−1.79842e6			−0.587367
$394$		−	423743.i		−	0.137519i
$395$			167772.i			0.0541037i
$396$			112992.i			0.0362085i
$397$	−4.95385e6			−1.57749			−0.788745	−	0.614721i	$-0.789269\pi$
$397$	−4.95385e6			−1.57749			−0.788745	+	0.614721i	$0.789269\pi$
$398$			2.25395e6i			0.713241i
$399$	−9.71983e6			−3.05652
$400$	−1.42434e6			−0.445107
$401$	−967567.			−0.300483			−0.150242	−	0.988649i	$-0.548005\pi$
$401$	−967567.			−0.300483			−0.150242	+	0.988649i	$0.548005\pi$
$402$	8.28819e6			2.55796
$403$		−	1.46760e6i		−	0.450138i
$404$			264795.i			0.0807153i
$405$	352768.			0.106869
$406$	4.26698e6	−	8.37516e6i	1.28471	−	2.52161i
$407$	158665.			0.0474784
$408$			5.60413e6i			1.66670i
$409$		−	1.99514e6i		−	0.589745i	−0.955537	−	0.294872i	$-0.904723\pi$
$409$		−	1.99514e6i		−	0.589745i	0.955537	−	0.294872i	$-0.0952771\pi$
$410$	169336.			0.0497495
$411$	4.41770e6			1.29001
$412$	−3.68770e6			−1.07032
$413$	1.52150e6			0.438932
$414$			6.36710e6i			1.82575i
$415$	−106568.			−0.0303743
$416$		−	1.95085e6i		−	0.552702i
$417$			1.44644e6i			0.407342i
$418$		−	269340.i		−	0.0753981i
$419$	2.26440e6			0.630113			0.315056	−	0.949073i	$-0.397977\pi$
$419$	2.26440e6			0.630113			0.315056	+	0.949073i	$0.397977\pi$
$420$		−	1.22005e6i		−	0.337484i
$421$			3.11193e6i			0.855706i	0.903848	+	0.427853i	$0.140730\pi$
$421$			3.11193e6i			0.855706i	−0.903848	+	0.427853i	$0.859270\pi$
$422$	1.84276e6			0.503719
$423$		−	1.06114e6i		−	0.288351i
$424$			5.34410e6i			1.44364i
$425$		−	3.58594e6i		−	0.963010i
$426$	2.27401e6			0.607112
$427$			5.44690e6i			1.44570i
$428$	2.23686e6			0.590241
$429$	−144091.			−0.0378001
$430$	−589301.			−0.153697
$431$	−3.79285e6			−0.983495			−0.491747	−	0.870738i	$-0.663642\pi$
$431$	−3.79285e6			−0.983495			−0.491747	+	0.870738i	$0.663642\pi$
$432$		−	819223.i		−	0.211199i
$433$		−	3.89522e6i		−	0.998418i	−0.866482	−	0.499209i	$-0.833624\pi$
$433$		−	3.89522e6i		−	0.998418i	0.866482	−	0.499209i	$-0.166376\pi$
$434$	5.37226e6			1.36909
$435$	−198371.	+	389358.i	−0.0502636	+	0.0986566i
$436$	−9.21570e6			−2.32173
$437$		−	9.76313e6i		−	2.44560i
$438$			7.43441e6i			1.85166i
$439$	4.74191e6			1.17434			0.587168	−	0.809465i	$-0.300243\pi$
$439$	4.74191e6			1.17434			0.587168	+	0.809465i	$0.300243\pi$
$440$	15059.7			0.00370837
$441$	−4.78789e6			−1.17232
$442$	−6.20863e6			−1.51161
$443$		−	3.59596e6i		−	0.870573i	−0.900292	−	0.435286i	$-0.856647\pi$
$443$		−	3.59596e6i		−	0.870573i	0.900292	−	0.435286i	$-0.143353\pi$
$444$	1.42807e7			3.43790
$445$		−	311973.i		−	0.0746822i
$446$		−	2.29334e6i		−	0.545922i
$447$			5.66609e6i			1.34126i
$448$	1.03615e7			2.43909
$449$		−	6.68678e6i		−	1.56531i	−0.622454	−	0.782656i	$-0.713864\pi$
$449$		−	6.68678e6i		−	1.56531i	0.622454	−	0.782656i	$-0.286136\pi$
$450$		−	4.50624e6i		−	1.04902i
$451$	47092.6			0.0109021
$452$		−	3.27250e6i		−	0.753413i
$453$			6.87019e6i			1.57298i
$454$			1.20470e7i			2.74309i
$455$	602089.			0.136343
$456$		−	1.07986e7i		−	2.43195i
$457$	744507.			0.166755			0.0833774	−	0.996518i	$-0.473429\pi$
$457$	744507.			0.166755			0.0833774	+	0.996518i	$0.473429\pi$
$458$	463312.			0.103207
$459$	2.06249e6			0.456940
$460$	1.22548e6			0.270030
$461$			4.37930e6i			0.959738i	0.877340	+	0.479869i	$0.159316\pi$
$461$			4.37930e6i			0.959738i	−0.877340	+	0.479869i	$0.840684\pi$
$462$		−	527455.i		−	0.114969i
$463$	201229.			0.0436253			0.0218126	−	0.999762i	$-0.493056\pi$
$463$	201229.			0.0436253			0.0218126	+	0.999762i	$0.493056\pi$
$464$	1.85321e6	+	944173.i	0.399603	+	0.203590i
$465$	−249754.			−0.0535650
$466$		−	4.42740e6i		−	0.944461i
$467$		−	1.00691e6i		−	0.213647i	−0.994278	−	0.106824i	$-0.965932\pi$
$467$		−	1.00691e6i		−	0.213647i	0.994278	−	0.106824i	$-0.0340680\pi$
$468$	−5.01882e6			−1.05922
$469$	−9.63136e6			−2.02188
$470$	−317499.			−0.0662976
$471$	−2.22644e6			−0.462444
$472$			1.69036e6i			0.349241i
$473$	−163886.			−0.0336812
$474$			6.52826e6i			1.33460i
$475$			6.90973e6i			1.40516i
$476$		−	1.46197e7i		−	2.95748i
$477$	−3.36743e6			−0.677645
$478$		−	2.81383e6i		−	0.563285i
$479$		−	4.24063e6i		−	0.844485i	−0.906483	−	0.422242i	$-0.861243\pi$
$479$		−	4.24063e6i		−	0.844485i	0.906483	−	0.422242i	$-0.138757\pi$
$480$	−331994.			−0.0657699
$481$			7.04750e6i			1.38890i
$482$			2.01117e6i			0.394303i
$483$		−	1.91193e7i		−	3.72911i
$484$	−9.28392e6			−1.80143
$485$		−	695236.i		−	0.134208i
$486$	9.62115e6			1.84772
$487$	−2.67952e6			−0.511959			−0.255979	−	0.966682i	$-0.582398\pi$
$487$	−2.67952e6			−0.511959			−0.255979	+	0.966682i	$0.582398\pi$
$488$	−6.05141e6			−1.15029
$489$	1.12243e7			2.12270
$490$			1.43256e6i			0.269540i
$491$			9.91828e6i			1.85666i	0.371756	+	0.928330i	$0.378756\pi$
$491$			9.91828e6i			1.85666i	−0.371756	+	0.928330i	$0.621244\pi$
$492$	4.23859e6			0.789420
$493$	−2.37706e6	+	4.66566e6i	−0.440477	+	0.864561i
$494$	1.19634e7			2.20565
$495$			9489.40i			0.00174071i
$496$			1.18874e6i			0.216962i
$497$	−2.64254e6			−0.479877
$498$	−4.14672e6			−0.749258
$499$	4.06076e6			0.730055			0.365028	−	0.930997i	$-0.381060\pi$
$499$	4.06076e6			0.730055			0.365028	+	0.930997i	$0.381060\pi$
$500$	−1.74120e6			−0.311476
$501$		−	2.00156e6i		−	0.356265i
$502$	−5.03398e6			−0.891564
$503$			9.67589e6i			1.70518i	0.522578	+	0.852592i	$0.324970\pi$
$503$			9.67589e6i			1.70518i	−0.522578	+	0.852592i	$0.675030\pi$
$504$		−	8.18366e6i		−	1.43506i
$505$			22238.2i			0.00388035i
$506$	529804.			0.0919897
$507$			992264.i			0.171438i
$508$		−	9.16369e6i		−	1.57547i
$509$	7.29038e6			1.24726			0.623628	−	0.781721i	$-0.285658\pi$
$509$	7.29038e6			1.24726			0.623628	+	0.781721i	$0.285658\pi$
$510$			1.05658e6i			0.179877i
$511$		−	8.63922e6i		−	1.46360i
$512$			5.15785e6i			0.869548i
$513$	−3.97420e6			−0.666739
$514$			7.54799e6i			1.26015i
$515$	−309703.			−0.0514549
$516$	−1.47506e7			−2.43885
$517$	−88297.1			−0.0145285
$518$	−2.57979e7			−4.22435
$519$			1.03977e7i			1.69441i
$520$			668910.i			0.108482i
$521$	7.34925e6			1.18618			0.593088	−	0.805138i	$-0.297909\pi$
$521$	7.34925e6			1.18618			0.593088	+	0.805138i	$0.297909\pi$
$522$	−2.98711e6	+	5.86306e6i	−0.479817	+	0.941776i
$523$	7.99648e6			1.27834			0.639168	−	0.769067i	$-0.279279\pi$
$523$	7.99648e6			1.27834			0.639168	+	0.769067i	$0.279279\pi$
$524$			5.21231e6i			0.829282i
$525$			1.35315e7i			2.14263i
$526$	−917307.			−0.144561
$527$	−2.99280e6			−0.469408
$528$	116712.			0.0182193
$529$	1.27682e7			1.98376
$530$			1.00755e6i			0.155804i
$531$	−1.06513e6			−0.163933
$532$			2.81707e7i			4.31538i
$533$			2.09173e6i			0.318924i
$534$		−	1.21393e7i		−	1.84222i
$535$	187857.			0.0283755
$536$		−	1.07003e7i		−	1.60873i
$537$		−	1.39560e7i		−	2.08845i
$538$	−1.87305e7			−2.78993
$539$			398399.i			0.0590672i
$540$		−	498846.i		−	0.0736177i
$541$		−	1.20377e6i		−	0.176828i	−0.996084	−	0.0884142i	$-0.971820\pi$
$541$		−	1.20377e6i		−	0.176828i	0.996084	−	0.0884142i	$-0.0281799\pi$
$542$	4.18203e6			0.611490
$543$			4.55330e6i			0.662715i
$544$	−3.97827e6			−0.576364
$545$	−773959.			−0.111616
$546$	2.34282e7			3.36323
$547$	2.80819e6			0.401290			0.200645	−	0.979664i	$-0.435696\pi$
$547$	2.80819e6			0.401290			0.200645	+	0.979664i	$0.435696\pi$
$548$		−	1.28037e7i		−	1.82131i
$549$		−	3.81312e6i		−	0.539945i
$550$	−374963.			−0.0528544
$551$	4.58035e6	−	8.99024e6i	0.642717	−	1.26151i
$552$	2.12413e7			2.96710
$553$		−	7.58622e6i		−	1.05490i
$554$			4.19739e6i			0.581039i
$555$	1.19933e6			0.165275
$556$	4.19217e6			0.575111
$557$	4.86294e6			0.664142			0.332071	−	0.943254i	$-0.392253\pi$
$557$	4.86294e6			0.664142			0.332071	+	0.943254i	$0.392253\pi$
$558$	−3.76087e6			−0.511331
$559$		−	7.27937e6i		−	0.985290i
$560$	−487686.			−0.0657159
$561$			293836.i			0.0394183i
$562$		−	1.29923e7i		−	1.73518i
$563$		−	2.75688e6i		−	0.366562i	−0.983061	−	0.183281i	$-0.941328\pi$
$563$		−	2.75688e6i		−	0.366562i	0.983061	−	0.183281i	$-0.0586718\pi$
$564$	−7.94722e6			−1.05200
$565$		−	274833.i		−	0.0362200i
$566$			6.97248e6i			0.914843i
$567$	−1.59513e7			−2.08371
$568$		−	2.93582e6i		−	0.381819i
$569$			2.41402e6i			0.312579i	0.987711	+	0.156289i	$0.0499533\pi$
$569$			2.41402e6i			0.312579i	−0.987711	+	0.156289i	$0.950047\pi$
$570$		−	2.03591e6i		−	0.262466i
$571$	−5.43385e6			−0.697457			−0.348729	−	0.937224i	$-0.613386\pi$
$571$	−5.43385e6			−0.697457			−0.348729	+	0.937224i	$0.613386\pi$
$572$			417614.i			0.0533685i
$573$	1.64225e7			2.08954
$574$	−7.65693e6			−0.970007
$575$	−1.35917e7			−1.71437
$576$	−7.25361e6			−0.910958
$577$		−	407216.i		−	0.0509197i	−0.999676	−	0.0254598i	$-0.991895\pi$
$577$		−	407216.i		−	0.0509197i	0.999676	−	0.0254598i	$-0.00810500\pi$
$578$		−	786875.i		−	0.0979684i
$579$	−1.86571e7			−2.31285
$580$	1.12847e6	+	574931.i	0.139290	+	0.0709653i
$581$	4.81873e6			0.592233
$582$		−	2.70527e7i		−	3.31057i
$583$			280202.i			0.0341429i
$584$	9.59803e6			1.16453
$585$	−421494.			−0.0509216
$586$	1.53302e7			1.84418
$587$	−3.72960e6			−0.446752			−0.223376	−	0.974732i	$-0.571708\pi$
$587$	−3.72960e6			−0.446752			−0.223376	+	0.974732i	$0.571708\pi$
$588$			3.58580e7i			4.27704i
$589$	5.76680e6			0.684931
$590$			318693.i			0.0376914i
$591$		−	890768.i		−	0.104905i
$592$		−	5.70841e6i		−	0.669439i
$593$	−1.06458e7			−1.24321			−0.621603	−	0.783333i	$-0.713518\pi$
$593$	−1.06458e7			−1.24321			−0.621603	+	0.783333i	$0.713518\pi$
$594$		−	215663.i		−	0.0250790i
$595$		−	1.22781e6i		−	0.142180i
$596$	1.64219e7			1.89368
$597$			4.73812e6i			0.544090i
$598$			2.35325e7i			2.69101i
$599$			1.25592e7i			1.43019i	0.699027	+	0.715096i	$0.253617\pi$
$599$			1.25592e7i			1.43019i	−0.699027	+	0.715096i	$0.746383\pi$
$600$	−1.50333e7			−1.70481
$601$			3.82602e6i			0.432077i	0.976385	+	0.216038i	$0.0693136\pi$
$601$			3.82602e6i			0.432077i	−0.976385	+	0.216038i	$0.930686\pi$
$602$	2.66467e7			2.99676
$603$	6.74246e6			0.755136
$604$	1.99117e7			2.22083
$605$	−779688.			−0.0866029
$606$			865320.i			0.0957183i
$607$		−	1.49470e7i		−	1.64658i	−0.567620	−	0.823291i	$-0.692136\pi$
$607$		−	1.49470e7i		−	1.64658i	0.567620	−	0.823291i	$-0.307864\pi$
$608$	7.66570e6			0.840994
$609$	8.96980e6	−	1.76058e7i	0.980031	−	1.92359i
$610$	−1.14091e6			−0.124144
$611$		−	3.92193e6i		−	0.425007i
$612$			1.02346e7i			1.10457i
$613$	−3.48547e6			−0.374636			−0.187318	−	0.982299i	$-0.559980\pi$
$613$	−3.48547e6			−0.374636			−0.187318	+	0.982299i	$0.559980\pi$
$614$	−8.61829e6			−0.922572
$615$	355968.			0.0379510
$616$	−680959.			−0.0723052
$617$			5.45591e6i			0.576971i	0.957484	+	0.288486i	$0.0931518\pi$
$617$			5.45591e6i			0.576971i	−0.957484	+	0.288486i	$0.906848\pi$
$618$	−1.20510e7			−1.26926
$619$		−	1.36253e7i		−	1.42929i	−0.699489	−	0.714644i	$-0.746589\pi$
$619$		−	1.36253e7i		−	1.42929i	0.699489	−	0.714644i	$-0.253411\pi$
$620$			723856.i			0.0756263i
$621$		−	7.81742e6i		−	0.813456i
$622$	−2.69711e7			−2.79526
$623$			1.41066e7i			1.45614i
$624$			5.18405e6i			0.532976i
$625$	9.54600e6			0.977511
$626$			1.94375e7i			1.98246i
$627$		−	566192.i		−	0.0575168i
$628$			6.45283e6i			0.652906i
$629$	1.43716e7			1.44836
$630$		−	1.54291e6i		−	0.154878i
$631$	−4.70379e6			−0.470299			−0.235150	−	0.971959i	$-0.575558\pi$
$631$	−4.70379e6			−0.470299			−0.235150	+	0.971959i	$0.575558\pi$
$632$	8.42817e6			0.839345
$633$	3.87375e6			0.384257
$634$	−1.33765e7			−1.32166
$635$		−	769591.i		−	0.0757401i
$636$			2.52197e7i			2.47228i
$637$	−1.76958e7			−1.72791
$638$	487863.	+	248557.i	0.0474511	+	0.0241754i
$639$	1.84992e6			0.179226
$640$			1.63673e6i			0.157952i
$641$			3.61550e6i			0.347555i	0.984785	+	0.173777i	$0.0555973\pi$
$641$			3.61550e6i			0.347555i	−0.984785	+	0.173777i	$0.944403\pi$
$642$	7.30981e6			0.699953
$643$	1.80915e6			0.172563			0.0862816	−	0.996271i	$-0.472502\pi$
$643$	1.80915e6			0.172563			0.0862816	+	0.996271i	$0.472502\pi$
$644$	−5.54130e7			−5.26499
$645$	−1.23879e6			−0.117246
$646$		−	2.43963e7i		−	2.30007i
$647$	−1.01979e7			−0.957749			−0.478874	−	0.877883i	$-0.658955\pi$
$647$	−1.01979e7			−0.957749			−0.478874	+	0.877883i	$0.658955\pi$
$648$		−	1.77216e7i		−	1.65793i
$649$			88629.2i			0.00825971i
$650$		−	1.66548e7i		−	1.54617i
$651$	1.12933e7			1.04440
$652$		−	3.25311e7i		−	2.99695i
$653$		−	1.40580e7i		−	1.29015i	−0.764119	−	0.645076i	$-0.776826\pi$
$653$		−	1.40580e7i		−	1.29015i	0.764119	−	0.645076i	$-0.223174\pi$
$654$	−3.01159e7			−2.75329
$655$			437744.i			0.0398673i
$656$		−	1.69428e6i		−	0.153718i
$657$			6.04791e6i			0.546628i
$658$	1.43565e7			1.29266
$659$			4.98482e6i			0.447132i	0.974689	+	0.223566i	$0.0717698\pi$
$659$			4.98482e6i			0.447132i	−0.974689	+	0.223566i	$0.928230\pi$
$660$	71069.1			0.00635069
$661$	−1.50599e7			−1.34066			−0.670331	−	0.742062i	$-0.733848\pi$
$661$	−1.50599e7			−1.34066			−0.670331	+	0.742062i	$0.733848\pi$
$662$	1.44753e7			1.28376
$663$	−1.30514e7			−1.15312
$664$			5.35353e6i			0.471216i
$665$			2.36585e6i			0.207460i
$666$	1.80599e7			1.57772
$667$	1.76842e7	+	9.00975e6i	1.53911	+	0.784149i
$668$	−5.80105e6			−0.502997
$669$		−	4.82092e6i		−	0.416452i
$670$		−	2.01738e6i		−	0.173621i
$671$	−317288.			−0.0272049
$672$	1.50119e7			1.28237
$673$	−1.05492e7			−0.897806			−0.448903	−	0.893580i	$-0.648185\pi$
$673$	−1.05492e7			−0.897806			−0.448903	+	0.893580i	$0.648185\pi$
$674$	−8.85817e6			−0.751094
$675$			5.53268e6i			0.467387i
$676$	2.87585e6			0.242047
$677$			1.35259e7i			1.13421i	0.823644	+	0.567107i	$0.191937\pi$
$677$			1.35259e7i			1.13421i	−0.823644	+	0.567107i	$0.808063\pi$
$678$		−	1.06942e7i		−	0.893455i
$679$			3.14368e7i			2.61676i
$680$	1.36407e6			0.113127
$681$			2.53245e7i			2.09254i
$682$			312940.i			0.0257633i
$683$	2.06766e7			1.69600			0.848002	−	0.529993i	$-0.177805\pi$
$683$	2.06766e7			1.69600			0.848002	+	0.529993i	$0.177805\pi$
$684$		−	1.97210e7i		−	1.61172i
$685$		−	1.07529e6i		−	0.0875586i
$686$		−	2.98950e7i		−	2.42543i
$687$	973947.			0.0787306
$688$			5.89622e6i			0.474900i
$689$	−1.24459e7			−0.998795
$690$	4.00473e6			0.320222
$691$	−9.29798e6			−0.740787			−0.370394	−	0.928875i	$-0.620777\pi$
$691$	−9.29798e6			−0.740787			−0.370394	+	0.928875i	$0.620777\pi$
$692$	3.01354e7			2.39227
$693$		−	429086.i		−	0.0339400i
$694$		−	1.10655e7i		−	0.872116i
$695$	352069.			0.0276482
$696$	1.95597e7	+	9.96530e6i	1.53052	+	0.779772i
$697$	4.26555e6			0.332577
$698$			3.50901e7i			2.72613i
$699$		−	9.30702e6i		−	0.720473i
$700$	3.92179e7			3.02510
$701$	−593091.			−0.0455855			−0.0227927	−	0.999740i	$-0.507256\pi$
$701$	−593091.			−0.0455855			−0.0227927	+	0.999740i	$0.507256\pi$
$702$	9.57918e6			0.733645
$703$	−2.76925e7			−2.11336
$704$			603571.i			0.0458983i
$705$	−667428.			−0.0505745
$706$			2.50788e7i			1.89363i
$707$		−	1.00555e6i		−	0.0756582i
$708$			7.97710e6i			0.598084i
$709$	8.81645e6			0.658685			0.329343	−	0.944210i	$-0.393173\pi$
$709$	8.81645e6			0.658685			0.329343	+	0.944210i	$0.393173\pi$
$710$		−	553505.i		−	0.0412075i
$711$			5.31076e6i			0.393988i
$712$	−1.56722e7			−1.15859
$713$			1.13436e7i			0.835652i
$714$		−	4.77757e7i		−	3.50721i
$715$			35072.4i			0.00256566i
$716$	−4.04483e7			−2.94861
$717$		−	5.91508e6i		−	0.429697i
$718$	3.27210e7			2.36873
$719$	2.04104e7			1.47241			0.736206	−	0.676758i	$-0.236616\pi$
$719$	2.04104e7			1.47241			0.736206	+	0.676758i	$0.236616\pi$
$720$	341406.			0.0245437
$721$	1.40039e7			1.00326
$722$			2.35573e7i			1.68183i
$723$			4.22776e6i			0.300791i
$724$	1.31967e7			0.935661
$725$	−1.25158e7	−	6.37654e6i	−0.884326	−	0.450547i
$726$	−3.03388e7			−2.13627
$727$			1.37388e7i			0.964077i	0.876150	+	0.482038i	$0.160103\pi$
$727$			1.37388e7i			0.964077i	−0.876150	+	0.482038i	$0.839897\pi$
$728$		−	3.02464e7i		−	2.11517i
$729$	2.53622e6			0.176754
$730$	1.80957e6			0.125681
$731$	−1.48444e7			−1.02747
$732$	−2.85576e7			−1.96990
$733$		−	2.01671e7i		−	1.38639i	−0.720752	−	0.693193i	$-0.756203\pi$
$733$		−	2.01671e7i		−	1.38639i	0.720752	−	0.693193i	$-0.243797\pi$
$734$	1.37015e7			0.938699
$735$			3.01145e6i			0.205616i
$736$			1.50788e7i			1.02606i
$737$		−	561038.i		−	0.0380473i
$738$	5.36026e6			0.362280
$739$		−	8.07578e6i		−	0.543968i	−0.962302	−	0.271984i	$-0.912320\pi$
$739$		−	8.07578e6i		−	0.543968i	0.962302	−	0.271984i	$-0.0876798\pi$
$740$		−	3.47600e6i		−	0.233346i
$741$	2.51487e7			1.68256
$742$		−	4.55589e7i		−	3.03783i
$743$		−	189310.i		−	0.0125806i	−0.999980	−	0.00629032i	$-0.997998\pi$
$743$		−	189310.i		−	0.0125806i	0.999980	−	0.00629032i	$-0.00200228\pi$
$744$			1.25466e7i			0.830987i
$745$	1.37915e6			0.0910377
$746$		−	1.71063e7i		−	1.12541i
$747$	−3.37337e6			−0.221188
$748$	851617.			0.0556532
$749$	−8.49443e6			−0.553260
$750$	−5.69006e6			−0.369372
$751$		−	2.39016e7i		−	1.54642i	−0.634153	−	0.773208i	$-0.718651\pi$
$751$		−	2.39016e7i		−	1.54642i	0.634153	−	0.773208i	$-0.281349\pi$
$752$			3.17672e6i			0.204849i
$753$	−1.05821e7			−0.680121
$754$	−1.10402e7	+	2.16696e7i	−0.707212	+	1.38810i
$755$	1.67223e6			0.106765
$756$			2.25565e7i			1.43538i
$757$		−	1.42248e7i		−	0.902208i	−0.892471	−	0.451104i	$-0.851030\pi$
$757$		−	1.42248e7i		−	0.902208i	0.892471	−	0.451104i	$-0.148970\pi$
$758$	−1.45143e7			−0.917537
$759$	1.11372e6			0.0701735
$760$	−2.62842e6			−0.165067
$761$	8.90653e6			0.557502			0.278751	−	0.960363i	$-0.410080\pi$
$761$	8.90653e6			0.557502			0.278751	+	0.960363i	$0.410080\pi$
$762$		−	2.99459e7i		−	1.86832i
$763$	3.49964e7			2.17627
$764$		−	4.75967e7i		−	2.95015i
$765$			859529.i			0.0531015i
$766$			3.31151e7i			2.03917i
$767$	−3.93667e6			−0.241624
$768$			3.35616e7i			2.05324i
$769$		−	1.35750e7i		−	0.827795i	−0.910324	−	0.413897i	$-0.864167\pi$
$769$		−	1.35750e7i		−	0.827795i	0.910324	−	0.413897i	$-0.135833\pi$
$770$	−128385.			−0.00780346
$771$			1.58670e7i			0.961297i
$772$			5.40732e7i			3.26542i
$773$		−	2.44300e7i		−	1.47054i	−0.677777	−	0.735268i	$-0.737057\pi$
$773$		−	2.44300e7i		−	1.47054i	0.677777	−	0.735268i	$-0.262943\pi$
$774$	−1.86541e7			−1.11923
$775$		−	8.02826e6i		−	0.480139i
$776$	−3.49257e7			−2.08205
$777$	−5.42308e7			−3.22251
$778$	1.97386e7			1.16914
$779$	−8.21926e6			−0.485276
$780$			3.15670e6i			0.185779i
$781$		−	153931.i		−	0.00903022i
$782$	4.79885e7			2.80621
$783$	3.66753e6	−	7.19856e6i	0.213781	−	0.419605i
$784$	1.43334e7			0.832838
$785$			541926.i			0.0313881i
$786$			1.70333e7i			0.983425i
$787$	−9.09886e6			−0.523661			−0.261830	−	0.965114i	$-0.584326\pi$
$787$	−9.09886e6			−0.523661			−0.261830	+	0.965114i	$0.584326\pi$
$788$	−2.58169e6			−0.148111
$789$	−1.92831e6			−0.110277
$790$	1.58901e6			0.0905854
$791$			1.24272e7i			0.706210i
$792$	476708.			0.0270047
$793$		−	1.40931e7i		−	0.795836i
$794$			4.69190e7i			2.64118i
$795$			2.11802e6i			0.118854i
$796$	1.37324e7			0.768179
$797$			3.33609e6i			0.186034i	0.995665	+	0.0930170i	$0.0296511\pi$
$797$			3.33609e6i			0.186034i	−0.995665	+	0.0930170i	$0.970349\pi$
$798$			9.20588e7i			5.11750i
$799$	−7.99776e6			−0.443202
$800$		−	1.06718e7i		−	0.589540i
$801$		−	9.87539e6i		−	0.543842i
$802$			9.16405e6i			0.503097i
$803$	503245.			0.0275417
$804$		−	5.04964e7i		−	2.75499i
$805$	−4.65373e6			−0.253111
$806$	−1.39000e7			−0.753662
$807$	−3.93742e7			−2.12828
$808$	1.11715e6			0.0601983
$809$			1.22656e7i			0.658895i	0.944174	+	0.329448i	$0.106863\pi$
$809$			1.22656e7i			0.658895i	−0.944174	+	0.329448i	$0.893137\pi$
$810$		−	3.34115e6i		−	0.178930i
$811$	1.58437e7			0.845873			0.422936	−	0.906159i	$-0.360999\pi$
$811$	1.58437e7			0.845873			0.422936	+	0.906159i	$0.360999\pi$
$812$	−5.10263e7	−	2.59969e7i	−2.71584	−	1.38367i
$813$	8.79123e6			0.466469
$814$		−	1.50276e6i		−	0.0794928i
$815$		−	2.73205e6i		−	0.144077i
$816$	1.05715e7			0.555793
$817$	2.86036e7			1.49922
$818$	−1.88964e7			−0.987405
$819$	1.90589e7			0.992858
$820$		−	1.03169e6i		−	0.0535815i
$821$	9.00970e6			0.466501			0.233251	−	0.972417i	$-0.425064\pi$
$821$	9.00970e6			0.466501			0.233251	+	0.972417i	$0.425064\pi$
$822$		−	4.18411e7i		−	2.15985i
$823$			7.29604e6i			0.375481i	0.982219	+	0.187740i	$0.0601163\pi$
$823$			7.29604e6i			0.375481i	−0.982219	+	0.187740i	$0.939884\pi$
$824$			1.55582e7i			0.798252i
$825$	−788224.			−0.0403195
$826$		−	1.44105e7i		−	0.734900i
$827$			2.34866e7i			1.19414i	0.802188	+	0.597072i	$0.203669\pi$
$827$			2.34866e7i			1.19414i	−0.802188	+	0.597072i	$0.796331\pi$
$828$	3.87921e7			1.96638
$829$		−	1.67228e7i		−	0.845127i	−0.906333	−	0.422564i	$-0.861130\pi$
$829$		−	1.67228e7i		−	0.845127i	0.906333	−	0.422564i	$-0.138870\pi$
$830$			1.00933e6i			0.0508555i
$831$			8.82351e6i			0.443240i
$832$	−2.68090e7			−1.34268
$833$			3.60861e7i			1.80189i
$834$	1.36995e7			0.682010
$835$	−487188.			−0.0241813
$836$	−1.64098e6			−0.0812057
$837$	4.61753e6			0.227822
$838$		−	2.14467e7i		−	1.05499i
$839$		−	2.63609e7i		−	1.29287i	−0.762968	−	0.646436i	$-0.776259\pi$
$839$		−	2.63609e7i		−	1.29287i	0.762968	−	0.646436i	$-0.223741\pi$
$840$	−5.14730e6			−0.251699
$841$	1.20573e7	+	1.65930e7i	0.587843	+	0.808975i
$842$	2.94738e7			1.43270
$843$		−	2.73116e7i		−	1.32367i
$844$		−	1.12272e7i		−	0.542518i
$845$	241522.			0.0116363
$846$	−1.00503e7			−0.482785
$847$	3.52555e7			1.68857
$848$	1.00810e7			0.481410
$849$			1.46571e7i			0.697879i
$850$	−3.39633e7			−1.61236
$851$		−	5.44724e7i		−	2.57841i
$852$		−	1.38546e7i		−	0.653876i
$853$			1.49192e7i			0.702060i	0.936364	+	0.351030i	$0.114169\pi$
$853$			1.49192e7i			0.702060i	−0.936364	+	0.351030i	$0.885831\pi$
$854$	5.15888e7			2.42053
$855$		−	1.65622e6i		−	0.0774824i
$856$		−	9.43717e6i		−	0.440208i
$857$	8.16583e6			0.379794			0.189897	−	0.981804i	$-0.439185\pi$
$857$	8.16583e6			0.379794			0.189897	+	0.981804i	$0.439185\pi$
$858$			1.36472e6i			0.0632885i
$859$		−	1.28694e7i		−	0.595082i	−0.954709	−	0.297541i	$-0.903833\pi$
$859$		−	1.28694e7i		−	0.595082i	0.954709	−	0.297541i	$-0.0961665\pi$
$860$			3.59036e6i			0.165536i
$861$	−1.60959e7			−0.739961
$862$			3.59229e7i			1.64666i
$863$	−1.98390e7			−0.906761			−0.453381	−	0.891317i	$-0.649782\pi$
$863$	−1.98390e7			−0.906761			−0.453381	+	0.891317i	$0.649782\pi$
$864$	6.13799e6			0.279732
$865$	2.53085e6			0.115007
$866$	−3.68925e7			−1.67164
$867$		−	1.65412e6i		−	0.0747343i
$868$		−	3.27309e7i		−	1.47455i
$869$	441906.			0.0198509
$870$	3.68770e6	+	1.87881e6i	0.165180	+	0.0841561i
$871$	2.49198e7			1.11301
$872$			3.88805e7i			1.73157i
$873$		−	2.20074e7i		−	0.977313i
$874$	−9.24688e7			−4.09465
$875$	6.61219e6			0.291961
$876$	4.52947e7			1.99429
$877$	−1.76108e7			−0.773180			−0.386590	−	0.922252i	$-0.626347\pi$
$877$	−1.76108e7			−0.773180			−0.386590	+	0.922252i	$0.626347\pi$
$878$		−	4.49118e7i		−	1.96618i
$879$	3.22262e7			1.40681
$880$		−	28408.3i		−	0.00123663i
$881$		−	2.13701e7i		−	0.927611i	−0.885937	−	0.463805i	$-0.846484\pi$
$881$		−	2.13701e7i		−	0.927611i	0.885937	−	0.463805i	$-0.153516\pi$
$882$			4.53472e7i			1.96281i
$883$	−4.74540e6			−0.204819			−0.102410	−	0.994742i	$-0.532655\pi$
$883$	−4.74540e6			−0.204819			−0.102410	+	0.994742i	$0.532655\pi$
$884$			3.78266e7i			1.62805i
$885$			669938.i			0.0287526i
$886$	−3.40581e7			−1.45759
$887$			3.34157e7i			1.42607i	0.701128	+	0.713035i	$0.252680\pi$
$887$			3.34157e7i			1.42607i	−0.701128	+	0.713035i	$0.747320\pi$
$888$		−	6.02496e7i		−	2.56402i
$889$			3.47989e7i			1.47676i
$890$	−2.95477e6			−0.125040
$891$		−	929180.i		−	0.0392108i
$892$	−1.39723e7			−0.587972
$893$	1.54108e7			0.646692
$894$	5.36648e7			2.24567
$895$	−3.39695e6			−0.141753
$896$		−	7.40086e7i		−	3.07972i
$897$			4.94687e7i			2.05281i
$898$	−6.33320e7			−2.62079
$899$	−5.32181e6	+	1.04456e7i	−0.219614	+	0.431054i
$900$	−2.74546e7			−1.12982
$901$			2.53801e7i			1.04155i
$902$		−	446025.i		−	0.0182534i
$903$	5.60150e7			2.28605
$904$	−1.38065e7			−0.561903
$905$	1.10829e6			0.0449814
$906$	6.50691e7			2.63363
$907$			2.39221e7i			0.965563i	0.875741	+	0.482782i	$0.160373\pi$
$907$			2.39221e7i			0.965563i	−0.875741	+	0.482782i	$0.839627\pi$
$908$	7.33973e7			2.95437
$909$			703940.i			0.0282570i
$910$		−	5.70252e6i		−	0.228278i
$911$		−	2.80696e7i		−	1.12057i	−0.828299	−	0.560286i	$-0.810691\pi$
$911$		−	2.80696e7i		−	1.12057i	0.828299	−	0.560286i	$-0.189309\pi$
$912$	−2.03702e7			−0.810978
$913$			280697.i			0.0111445i
$914$		−	7.05140e6i		−	0.279196i
$915$	−2.39835e6			−0.0947020
$916$		−	2.82276e6i		−	0.111157i
$917$		−	1.97936e7i		−	0.777325i
$918$		−	1.95343e7i		−	0.765052i
$919$	1.78543e7			0.697356			0.348678	−	0.937243i	$-0.386631\pi$
$919$	1.78543e7			0.697356			0.348678	+	0.937243i	$0.386631\pi$
$920$		−	5.17022e6i		−	0.201391i
$921$	−1.81169e7			−0.703776
$922$	4.14774e7			1.60688
$923$	6.83720e6			0.264164
$924$	−3.21356e6			−0.123824
$925$			3.85522e7i			1.48147i
$926$		−	1.90589e6i		−	0.0730415i
$927$	−9.80351e6			−0.374699
$928$	−7.07418e6	+	1.38851e7i	−0.269653	+	0.529271i
$929$	−1.34684e7			−0.512007			−0.256004	−	0.966676i	$-0.582406\pi$
$929$	−1.34684e7			−0.512007			−0.256004	+	0.966676i	$0.582406\pi$
$930$			2.36548e6i			0.0896835i
$931$		−	6.95341e7i		−	2.62920i
$932$	−2.69743e7			−1.01721
$933$	−5.66970e7			−2.13234
$934$	−9.53665e6			−0.357708
$935$	71521.1			0.00267550
$936$			2.11741e7i			0.789978i
$937$	−3.40806e7			−1.26811			−0.634056	−	0.773287i	$-0.718611\pi$
$937$	−3.40806e7			−1.26811			−0.634056	+	0.773287i	$0.718611\pi$
$938$			9.12208e7i			3.38522i
$939$			4.08604e7i			1.51230i
$940$			1.93439e6i			0.0714042i
$941$	−4.59724e7			−1.69248			−0.846239	−	0.532803i	$-0.821139\pi$
$941$	−4.59724e7			−1.69248			−0.846239	+	0.532803i	$0.821139\pi$
$942$			2.10871e7i			0.774266i
$943$		−	1.61676e7i		−	0.592062i
$944$	3.18867e6			0.116461
$945$			1.89436e6i			0.0690053i
$946$			1.55220e6i			0.0563923i
$947$			1.76546e6i			0.0639711i	0.999488	+	0.0319856i	$0.0101831\pi$
$947$			1.76546e6i			0.0639711i	−0.999488	+	0.0319856i	$0.989817\pi$
$948$	3.97739e7			1.43740
$949$			2.23528e7i			0.805687i
$950$	6.54437e7			2.35266
$951$	−2.81193e7			−1.00821
$952$	−6.16798e7			−2.20572
$953$	7.46519e6			0.266262			0.133131	−	0.991098i	$-0.457497\pi$
$953$	7.46519e6			0.266262			0.133131	+	0.991098i	$0.457497\pi$
$954$			3.18937e7i			1.13458i
$955$		−	3.99730e6i		−	0.141827i
$956$	−1.71435e7			−0.606673
$957$	1.02556e6	+	522501.i	0.0361976	+	0.0184420i
$958$	−4.01640e7			−1.41391
$959$			4.86218e7i			1.70720i
$960$			4.56232e6i			0.159775i
$961$	2.19288e7			0.765962
$962$	6.67485e7			2.32543
$963$	5.94655e6			0.206633
$964$	1.22532e7			0.424675
$965$			4.54121e6i			0.156983i
$966$	−1.81084e8			−6.24362
$967$		−	4.13396e7i		−	1.42167i	−0.703356	−	0.710837i	$-0.748316\pi$
$967$		−	4.13396e7i		−	1.42167i	0.703356	−	0.710837i	$-0.251684\pi$
$968$			3.91683e7i			1.34353i
$969$		−	5.12844e7i		−	1.75459i
$970$	−6.58474e6			−0.224703
$971$		−	1.41844e6i		−	0.0482796i	−0.999709	−	0.0241398i	$-0.992315\pi$
$971$		−	1.41844e6i		−	0.0482796i	0.999709	−	0.0241398i	$-0.00768469\pi$
$972$		−	5.86176e7i		−	1.99004i
$973$	−1.59197e7			−0.539078
$974$			2.53784e7i			0.857169i
$975$		−	3.50108e7i		−	1.17948i
$976$			1.14153e7i			0.383585i
$977$	4.93091e7			1.65269			0.826344	−	0.563165i	$-0.190417\pi$
$977$	4.93091e7			1.65269			0.826344	+	0.563165i	$0.190417\pi$
$978$		−	1.06308e8i		−	3.55401i
$979$	−821727.			−0.0274013
$980$	8.72801e6			0.290302
$981$	−2.44994e7			−0.812797
$982$	9.39383e7			3.10859
$983$		−	2.20571e7i		−	0.728056i	−0.931388	−	0.364028i	$-0.881401\pi$
$983$		−	2.20571e7i		−	0.728056i	0.931388	−	0.364028i	$-0.118599\pi$
$984$		−	1.78823e7i		−	0.588758i
$985$	−216817.			−0.00712037
$986$	4.41895e7	+	2.25137e7i	1.44753	+	0.737488i
$987$	3.01794e7			0.986092
$988$		−	7.28878e7i		−	2.37554i
$989$			5.62645e7i			1.82913i
$990$	89876.3			0.00291445
$991$	−4.19924e7			−1.35827			−0.679135	−	0.734013i	$-0.737645\pi$
$991$	−4.19924e7			−1.35827			−0.679135	+	0.734013i	$0.737645\pi$
$992$	−8.90660e6			−0.287364
$993$	3.04292e7			0.979302
$994$			2.50281e7i			0.803455i
$995$	1.15328e6			0.0369298
$996$			2.52642e7i			0.806970i
$997$		−	3.76102e7i		−	1.19831i	−0.800635	−	0.599153i	$-0.795504\pi$
$997$		−	3.76102e7i		−	1.19831i	0.800635	−	0.599153i	$-0.204496\pi$
$998$		−	3.84604e7i		−	1.22233i
$999$	−2.21736e7			−0.702948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.b.a.28.1	✓	12
3.2	odd	2		261.6.c.b.28.12		12
4.3	odd	2		464.6.e.c.289.9		12
29.12	odd	4		841.6.a.d.1.12		12
29.17	odd	4		841.6.a.d.1.1		12
29.28	even	2	inner	29.6.b.a.28.12	yes	12
87.86	odd	2		261.6.c.b.28.1		12
116.115	odd	2		464.6.e.c.289.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.b.a.28.1	✓	12	1.1	even	1	trivial
29.6.b.a.28.12	yes	12	29.28	even	2	inner
261.6.c.b.28.1		12	87.86	odd	2
261.6.c.b.28.12		12	3.2	odd	2
464.6.e.c.289.4		12	116.115	odd	2
464.6.e.c.289.9		12	4.3	odd	2
841.6.a.d.1.1		12	29.17	odd	4
841.6.a.d.1.12		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)

\(f(q)\)	\(=\)	\(q-9.47123i q^{2} -19.9099i q^{3} -57.7042 q^{4} -4.84615 q^{5} -188.571 q^{6} +219.131 q^{7} +243.450i q^{8} -153.403 q^{9} +O(q^{10})\)	\(q-9.47123i q^{2} -19.9099i q^{3} -57.7042 q^{4} -4.84615 q^{5} -188.571 q^{6} +219.131 q^{7} +243.450i q^{8} -153.403 q^{9} +45.8990i q^{10} +12.7646i q^{11} +1148.88i q^{12} -566.970 q^{13} -2075.44i q^{14} +96.4863i q^{15} +459.241 q^{16} +1156.19i q^{17} +1452.92i q^{18} -2227.86i q^{19} +279.643 q^{20} -4362.86i q^{21} +120.897 q^{22} +4382.29 q^{23} +4847.07 q^{24} -3101.51 q^{25} +5369.91i q^{26} -1783.86i q^{27} -12644.8 q^{28} +(4035.37 + 2055.94i) q^{29} +913.844 q^{30} +2588.50i q^{31} +3440.84i q^{32} +254.142 q^{33} +10950.5 q^{34} -1061.94 q^{35} +8852.00 q^{36} -12430.1i q^{37} -21100.6 q^{38} +11288.3i q^{39} -1179.80i q^{40} -3689.31i q^{41} -41321.7 q^{42} +12839.1i q^{43} -736.572i q^{44} +743.415 q^{45} -41505.7i q^{46} +6917.34i q^{47} -9143.42i q^{48} +31211.2 q^{49} +29375.2i q^{50} +23019.6 q^{51} +32716.6 q^{52} +21951.5 q^{53} -16895.4 q^{54} -61.8593i q^{55} +53347.4i q^{56} -44356.4 q^{57} +(19472.3 - 38220.0i) q^{58} +6943.35 q^{59} -5567.67i q^{60} +24856.9i q^{61} +24516.2 q^{62} -33615.3 q^{63} +47284.7 q^{64} +2747.62 q^{65} -2407.04i q^{66} -43952.6 q^{67} -66717.1i q^{68} -87250.9i q^{69} +10057.9i q^{70} -12059.2 q^{71} -37346.0i q^{72} -39425.0i q^{73} -117728. q^{74} +61750.8i q^{75} +128557. i q^{76} +2797.12i q^{77} +106914. q^{78} -34619.6i q^{79} -2225.55 q^{80} -72793.4 q^{81} -34942.3 q^{82} +21990.2 q^{83} +251755. i q^{84} -5603.08i q^{85} +121602. q^{86} +(40933.6 - 80343.8i) q^{87} -3107.55 q^{88} +64375.4i q^{89} -7041.05i q^{90} -124240. q^{91} -252877. q^{92} +51536.6 q^{93} +65515.7 q^{94} +10796.5i q^{95} +68506.7 q^{96} +143461. i q^{97} -295608. i q^{98} -1958.13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 172 q^{4} + 46 q^{5} + 24 q^{6} + 20 q^{7} - 1574 q^{9}+O(q^{10}) \) 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

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