LMFDB - Embedded newform 29.6.b.a.28.7

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			28.7
Root			$0.0831044i$ of defining polynomial
Character	$\chi$	$=$	29.28
Dual form			29.6.b.a.28.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0831044i q^{2} +25.1364i q^{3} +31.9931 q^{4} -90.4149 q^{5} -2.08895 q^{6} -6.31225 q^{7} +5.31810i q^{8} -388.840 q^{9} +O(q^{10})$	\(q+0.0831044i q^{2} +25.1364i q^{3} +31.9931 q^{4} -90.4149 q^{5} -2.08895 q^{6} -6.31225 q^{7} +5.31810i q^{8} -388.840 q^{9} -7.51387i q^{10} +505.400i q^{11} +804.192i q^{12} +275.130 q^{13} -0.524575i q^{14} -2272.71i q^{15} +1023.34 q^{16} +1486.29i q^{17} -32.3143i q^{18} -2101.86i q^{19} -2892.65 q^{20} -158.667i q^{21} -42.0009 q^{22} +2690.82 q^{23} -133.678 q^{24} +5049.85 q^{25} +22.8645i q^{26} -3665.89i q^{27} -201.948 q^{28} +(3098.34 + 3303.24i) q^{29} +188.872 q^{30} +1909.79i q^{31} +255.223i q^{32} -12703.9 q^{33} -123.517 q^{34} +570.721 q^{35} -12440.2 q^{36} +9569.51i q^{37} +174.673 q^{38} +6915.79i q^{39} -480.836i q^{40} -18325.0i q^{41} +13.1859 q^{42} -6653.40i q^{43} +16169.3i q^{44} +35156.9 q^{45} +223.619i q^{46} -6494.11i q^{47} +25723.0i q^{48} -16767.2 q^{49} +419.665i q^{50} -37359.9 q^{51} +8802.27 q^{52} +13825.6 q^{53} +304.651 q^{54} -45695.7i q^{55} -33.5692i q^{56} +52833.1 q^{57} +(-274.514 + 257.486i) q^{58} -30295.3 q^{59} -72710.9i q^{60} +17014.3i q^{61} -158.712 q^{62} +2454.45 q^{63} +32725.6 q^{64} -24875.9 q^{65} -1055.75i q^{66} +42134.6 q^{67} +47550.9i q^{68} +67637.7i q^{69} +47.4294i q^{70} -45687.5 q^{71} -2067.89i q^{72} -56318.2i q^{73} -795.268 q^{74} +126935. i q^{75} -67244.9i q^{76} -3190.21i q^{77} -574.732 q^{78} +26403.0i q^{79} -92524.9 q^{80} -2340.79 q^{81} +1522.89 q^{82} +25549.1 q^{83} -5076.26i q^{84} -134382. i q^{85} +552.926 q^{86} +(-83031.7 + 77881.3i) q^{87} -2687.77 q^{88} -5785.59i q^{89} +2921.69i q^{90} -1736.69 q^{91} +86087.8 q^{92} -48005.3 q^{93} +539.689 q^{94} +190039. i q^{95} -6415.40 q^{96} +108843. i q^{97} -1393.42i q^{98} -196519. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.0831044i			0.0146909i	0.999973	+	0.00734546i	$0.00233815\pi$
$2$			0.0831044i			0.0146909i	−0.999973	+	0.00734546i	$0.997662\pi$
$3$			25.1364i			1.61250i	0.591574	+	0.806251i	$0.298507\pi$
$3$			25.1364i			1.61250i	−0.591574	+	0.806251i	$0.701493\pi$
$4$	31.9931			0.999784
$5$	−90.4149			−1.61739			−0.808695	−	0.588228i	$-0.799826\pi$
$5$	−90.4149			−1.61739			−0.808695	+	0.588228i	$0.799826\pi$
$6$	−2.08895			−0.0236891
$7$	−6.31225			−0.0486899			−0.0243450	−	0.999704i	$-0.507750\pi$
$7$	−6.31225			−0.0486899			−0.0243450	+	0.999704i	$0.507750\pi$
$8$			5.31810i			0.0293787i
$9$	−388.840			−1.60016
$10$		−	7.51387i		−	0.0237609i
$11$			505.400i			1.25937i	0.776851	+	0.629685i	$0.216816\pi$
$11$			505.400i			1.25937i	−0.776851	+	0.629685i	$0.783184\pi$
$12$			804.192i			1.61215i
$13$	275.130			0.451523			0.225762	−	0.974183i	$-0.427513\pi$
$13$	275.130			0.451523			0.225762	+	0.974183i	$0.427513\pi$
$14$		−	0.524575i		−	0.000715299i
$15$		−	2272.71i		−	2.60805i
$16$	1023.34			0.999353
$17$			1486.29i			1.24733i	0.781693	+	0.623663i	$0.214356\pi$
$17$			1486.29i			1.24733i	−0.781693	+	0.623663i	$0.785644\pi$
$18$		−	32.3143i		−	0.0235079i
$19$		−	2101.86i		−	1.33573i	−0.744282	−	0.667865i	$-0.767208\pi$
$19$		−	2101.86i		−	1.33573i	0.744282	−	0.667865i	$-0.232792\pi$
$20$	−2892.65			−1.61704
$21$		−	158.667i		−	0.0785126i
$22$	−42.0009			−0.0185013
$23$	2690.82			1.06063			0.530317	−	0.847799i	$-0.322073\pi$
$23$	2690.82			1.06063			0.530317	+	0.847799i	$0.322073\pi$
$24$	−133.678			−0.0473731
$25$	5049.85			1.61595
$26$			22.8645i			0.00663329i
$27$		−	3665.89i		−	0.967764i
$28$	−201.948			−0.0486794
$29$	3098.34	+	3303.24i	0.684124	+	0.729366i
$29$	3098.34	+	3303.24i	0.684124	+	0.729366i
$30$	188.872			0.0383146
$31$			1909.79i			0.356928i	0.983946	+	0.178464i	$0.0571129\pi$
$31$			1909.79i			0.356928i	−0.983946	+	0.178464i	$0.942887\pi$
$32$			255.223i			0.0440601i
$33$	−12703.9			−2.03074
$34$	−123.517			−0.0183244
$35$	570.721			0.0787506
$36$	−12440.2			−1.59982
$37$			9569.51i			1.14917i	0.818444	+	0.574586i	$0.194837\pi$
$37$			9569.51i			1.14917i	−0.818444	+	0.574586i	$0.805163\pi$
$38$	174.673			0.0196231
$39$			6915.79i			0.728082i
$40$		−	480.836i		−	0.0475168i
$41$		−	18325.0i		−	1.70249i	−0.524766	−	0.851247i	$-0.675847\pi$
$41$		−	18325.0i		−	1.70249i	0.524766	−	0.851247i	$-0.324153\pi$
$42$	13.1859			0.00115342
$43$		−	6653.40i		−	0.548747i	−0.961623	−	0.274374i	$-0.911529\pi$
$43$		−	6653.40i		−	0.548747i	0.961623	−	0.274374i	$-0.0884705\pi$
$44$			16169.3i			1.25910i
$45$	35156.9			2.58809
$46$			223.619i			0.0155817i
$47$		−	6494.11i		−	0.428820i	−0.976744	−	0.214410i	$-0.931217\pi$
$47$		−	6494.11i		−	0.428820i	0.976744	−	0.214410i	$-0.0687829\pi$
$48$			25723.0i			1.61146i
$49$	−16767.2			−0.997629
$50$			419.665i			0.0237398i
$51$	−37359.9			−2.01132
$52$	8802.27			0.451426
$53$	13825.6			0.676074			0.338037	−	0.941133i	$-0.390237\pi$
$53$	13825.6			0.676074			0.338037	+	0.941133i	$0.390237\pi$
$54$	304.651			0.0142173
$55$		−	45695.7i		−	2.03689i
$56$		−	33.5692i		−	0.00143044i
$57$	52833.1			2.15387
$58$	−274.514	+	257.486i	−0.0107151	+	0.0100504i
$59$	−30295.3			−1.13304			−0.566520	−	0.824048i	$-0.691711\pi$
$59$	−30295.3			−1.13304			−0.566520	+	0.824048i	$0.691711\pi$
$60$		−	72710.9i		−	2.60748i
$61$			17014.3i			0.585451i	0.956197	+	0.292725i	$0.0945622\pi$
$61$			17014.3i			0.585451i	−0.956197	+	0.292725i	$0.905438\pi$
$62$	−158.712			−0.00524360
$63$	2454.45			0.0779118
$64$	32725.6			0.998705
$65$	−24875.9			−0.730290
$66$		−	1055.75i		−	0.0298334i
$67$	42134.6			1.14671			0.573353	−	0.819308i	$-0.305642\pi$
$67$	42134.6			1.14671			0.573353	+	0.819308i	$0.305642\pi$
$68$			47550.9i			1.24706i
$69$			67637.7i			1.71027i
$70$			47.4294i			0.00115692i
$71$	−45687.5			−1.07560			−0.537801	−	0.843072i	$-0.680745\pi$
$71$	−45687.5			−1.07560			−0.537801	+	0.843072i	$0.680745\pi$
$72$		−	2067.89i		−	0.0470106i
$73$		−	56318.2i		−	1.23692i	−0.785816	−	0.618460i	$-0.787757\pi$
$73$		−	56318.2i		−	1.23692i	0.785816	−	0.618460i	$-0.212243\pi$
$74$	−795.268			−0.0168824
$75$			126935.i			2.60573i
$76$		−	67244.9i		−	1.33544i
$77$		−	3190.21i		−	0.0613186i
$78$	−574.732			−0.0106962
$79$			26403.0i			0.475977i	0.971268	+	0.237988i	$0.0764881\pi$
$79$			26403.0i			0.475977i	−0.971268	+	0.237988i	$0.923512\pi$
$80$	−92524.9			−1.61634
$81$	−2340.79			−0.0396415
$82$	1522.89			0.0250112
$83$	25549.1			0.407081			0.203540	−	0.979067i	$-0.434755\pi$
$83$	25549.1			0.407081			0.203540	+	0.979067i	$0.434755\pi$
$84$		−	5076.26i		−	0.0784957i
$85$		−	134382.i		−	2.01741i
$86$	552.926			0.00806160
$87$	−83031.7	+	77881.3i	−1.17610	+	1.10315i
$88$	−2687.77			−0.0369986
$89$		−	5785.59i		−	0.0774235i	−0.999250	−	0.0387117i	$-0.987675\pi$
$89$		−	5785.59i		−	0.0774235i	0.999250	−	0.0387117i	$-0.0123254\pi$
$90$			2921.69i			0.0380214i
$91$	−1736.69			−0.0219846
$92$	86087.8			1.06041
$93$	−48005.3			−0.575548
$94$	539.689			0.00629976
$95$			190039.i			2.16040i
$96$	−6415.40			−0.0710469
$97$			108843.i			1.17455i	0.809387	+	0.587276i	$0.199800\pi$
$97$			108843.i			1.17455i	−0.809387	+	0.587276i	$0.800200\pi$
$98$		−	1393.42i		−	0.0146561i
$99$		−	196519.i		−	2.01520i
$100$	161560.			1.61560
$101$		−	99152.1i		−	0.967160i	−0.875300	−	0.483580i	$-0.839336\pi$
$101$		−	99152.1i		−	0.967160i	0.875300	−	0.483580i	$-0.160664\pi$
$102$		−	3104.77i		−	0.0295481i
$103$	62251.1			0.578168			0.289084	−	0.957304i	$-0.406649\pi$
$103$	62251.1			0.578168			0.289084	+	0.957304i	$0.406649\pi$
$104$			1463.17i			0.0132651i
$105$			14345.9i			0.126986i
$106$			1148.97i			0.00993215i
$107$	98186.6			0.829073			0.414536	−	0.910033i	$-0.363944\pi$
$107$	98186.6			0.829073			0.414536	+	0.910033i	$0.363944\pi$
$108$		−	117283.i		−	0.967555i
$109$	192495.			1.55186			0.775932	−	0.630817i	$-0.217280\pi$
$109$	192495.			1.55186			0.775932	+	0.630817i	$0.217280\pi$
$110$	3797.51			0.0299238
$111$	−240543.			−1.85304
$112$	−6459.56			−0.0486584
$113$		−	246089.i		−	1.81299i	−0.422213	−	0.906497i	$-0.638747\pi$
$113$		−	246089.i		−	1.81299i	0.422213	−	0.906497i	$-0.361253\pi$
$114$			4390.66i			0.0316423i
$115$	−243290.			−1.71546
$116$	99125.6	+	105681.i	0.683976	+	0.729208i
$117$	−106982.			−0.722511
$118$		−	2517.67i		−	0.0166454i
$119$		−	9381.80i		−	0.0607322i
$120$	12086.5			0.0766209
$121$	−94377.8			−0.586012
$122$	−1413.97			−0.00860081
$123$	460626.			2.74527
$124$			61100.1i			0.356851i
$125$	−174035.			−0.996236
$126$			203.976i			0.00114460i
$127$			37572.3i			0.206709i	0.994645	+	0.103354i	$0.0329576\pi$
$127$			37572.3i			0.206709i	−0.994645	+	0.103354i	$0.967042\pi$
$128$			10886.8i			0.0587319i
$129$	167243.			0.884856
$130$		−	2067.29i		−	0.0107286i
$131$			95706.0i			0.487260i	0.969868	+	0.243630i	$0.0783382\pi$
$131$			95706.0i			0.487260i	−0.969868	+	0.243630i	$0.921662\pi$
$132$	−406438.			−2.03030
$133$			13267.4i			0.0650366i
$134$			3501.57i			0.0168462i
$135$			331451.i			1.56525i
$136$	−7904.22			−0.0366447
$137$			240974.i			1.09691i	0.836181	+	0.548453i	$0.184783\pi$
$137$			240974.i			1.09691i	−0.836181	+	0.548453i	$0.815217\pi$
$138$	−5620.98			−0.0251255
$139$	189225.			0.830693			0.415346	−	0.909663i	$-0.363660\pi$
$139$	189225.			0.830693			0.415346	+	0.909663i	$0.363660\pi$
$140$	18259.1			0.0787336
$141$	163239.			0.691473
$142$		−	3796.83i		−	0.0158016i
$143$			139051.i			0.568635i
$144$	−397914.			−1.59913
$145$	−280136.	−	298662.i	−1.10650	−	1.17967i
$146$	4680.29			0.0181715
$147$		−	421466.i		−	1.60868i
$148$			306158.i			1.14892i
$149$	−72324.7			−0.266883			−0.133442	−	0.991057i	$-0.542603\pi$
$149$	−72324.7			−0.266883			−0.133442	+	0.991057i	$0.542603\pi$
$150$	−10548.9			−0.0382805
$151$	32947.5			0.117593			0.0587963	−	0.998270i	$-0.481274\pi$
$151$	32947.5			0.117593			0.0587963	+	0.998270i	$0.481274\pi$
$152$	11177.9			0.0392420
$153$		−	577927.i		−	1.99592i
$154$	265.120			0.000900826
$155$		−	172673.i		−	0.577293i
$156$			221258.i			0.727925i
$157$			367855.i			1.19104i	0.803340	+	0.595521i	$0.203054\pi$
$157$			367855.i			1.19104i	−0.803340	+	0.595521i	$0.796946\pi$
$158$	−2194.21			−0.00699254
$159$			347526.i			1.09017i
$160$		−	23076.0i		−	0.0712623i
$161$	−16985.1			−0.0516422
$162$		−	194.530i		−	0.000582370i
$163$		−	272947.i		−	0.804653i	−0.915496	−	0.402326i	$-0.868202\pi$
$163$		−	272947.i		−	0.804653i	0.915496	−	0.402326i	$-0.131798\pi$
$164$		−	586275.i		−	1.70213i
$165$	1.14863e6			3.28449
$166$			2123.24i			0.00598039i
$167$	−242625.			−0.673200			−0.336600	−	0.941648i	$-0.609277\pi$
$167$	−242625.			−0.673200			−0.336600	+	0.941648i	$0.609277\pi$
$168$	843.810			0.00230659
$169$	−295596.			−0.796127
$170$	11167.8			0.0296376
$171$			817285.i			2.13739i
$172$		−	212863.i		−	0.548629i
$173$	372557.			0.946406			0.473203	−	0.880953i	$-0.343098\pi$
$173$	372557.			0.946406			0.473203	+	0.880953i	$0.343098\pi$
$174$	−6472.27	−	6900.29i	−0.0162063	−	0.0172780i
$175$	−31875.9			−0.0786806
$176$			517194.i			1.25855i
$177$		−	761516.i		−	1.82703i
$178$	480.808			0.00113742
$179$	−408428.			−0.952759			−0.476379	−	0.879240i	$-0.658051\pi$
$179$	−408428.			−0.952759			−0.476379	+	0.879240i	$0.658051\pi$
$180$	1.12478e6			2.58753
$181$	408180.			0.926095			0.463047	−	0.886334i	$-0.346756\pi$
$181$	408180.			0.926095			0.463047	+	0.886334i	$0.346756\pi$
$182$		−	144.327i		−	0.000322974i
$183$	−427679.			−0.944041
$184$			14310.1i			0.0311600i
$185$		−	865226.i		−	1.85866i
$186$		−	3989.45i		−	0.00845532i
$187$	−751168.			−1.57084
$188$		−	207767.i		−	0.428728i
$189$			23140.0i			0.0471204i
$190$	−15793.1			−0.0317382
$191$		−	417174.i		−	0.827435i	−0.910405	−	0.413717i	$-0.864230\pi$
$191$		−	417174.i		−	0.827435i	0.910405	−	0.413717i	$-0.135770\pi$
$192$			822604.i			1.61041i
$193$		−	87021.5i		−	0.168164i	−0.996459	−	0.0840821i	$-0.973204\pi$
$193$		−	87021.5i		−	0.168164i	0.996459	−	0.0840821i	$-0.0267958\pi$
$194$	−9045.35			−0.0172552
$195$		−	625291.i		−	1.17759i
$196$	−536433.			−0.997414
$197$	504758.			0.926654			0.463327	−	0.886187i	$-0.346656\pi$
$197$	504758.			0.926654			0.463327	+	0.886187i	$0.346656\pi$
$198$	16331.6			0.0296051
$199$	−494323.			−0.884866			−0.442433	−	0.896801i	$-0.645885\pi$
$199$	−494323.			−0.884866			−0.442433	+	0.896801i	$0.645885\pi$
$200$			26855.6i			0.0474745i
$201$			1.05911e6i			1.84907i
$202$	8239.97			0.0142085
$203$	−19557.5	−	20850.9i	−0.0333099	−	0.0355128i
$204$	−1.19526e6			−2.01088
$205$			1.65686e6i			2.75360i
$206$			5173.34i			0.00849382i
$207$	−1.04630e6			−1.69719
$208$	281551.			0.451231
$209$	1.06228e6			1.68218
$210$	−1192.21			−0.00186553
$211$			825111.i			1.27587i	0.770091	+	0.637934i	$0.220211\pi$
$211$			825111.i			1.27587i	−0.770091	+	0.637934i	$0.779789\pi$
$212$	442324.			0.675928
$213$		−	1.14842e6i		−	1.73441i
$214$			8159.73i			0.0121798i
$215$			601566.i			0.887539i
$216$	19495.6			0.0284316
$217$		−	12055.1i		−	0.0173788i
$218$			15997.2i			0.0227983i
$219$	1.41564e6			1.99454
$220$		−	1.46195e6i		−	2.03645i
$221$			408922.i			0.563197i
$222$		−	19990.2i		−	0.0272229i
$223$	312479.			0.420783			0.210392	−	0.977617i	$-0.432526\pi$
$223$	312479.			0.420783			0.210392	+	0.977617i	$0.432526\pi$
$224$		−	1611.03i		−	0.00214528i
$225$	−1.96358e6			−2.58579
$226$	20451.1			0.0266345
$227$	−632856.			−0.815155			−0.407577	−	0.913171i	$-0.633626\pi$
$227$	−632856.			−0.815155			−0.407577	+	0.913171i	$0.633626\pi$
$228$	1.69030e6			2.15340
$229$			519704.i			0.654889i	0.944870	+	0.327444i	$0.106187\pi$
$229$			519704.i			0.654889i	−0.944870	+	0.327444i	$0.893813\pi$
$230$		−	20218.5i		−	0.0252017i
$231$	80190.4			0.0988764
$232$	−17567.0	+	16477.3i	−0.0214278	+	0.0200986i
$233$	−250127.			−0.301836			−0.150918	−	0.988546i	$-0.548223\pi$
$233$	−250127.			−0.301836			−0.150918	+	0.988546i	$0.548223\pi$
$234$		−	8890.63i		−	0.0106143i
$235$			587164.i			0.693570i
$236$	−969241.			−1.13280
$237$	−663677.			−0.767514
$238$	779.669			0.000892211
$239$	−423081.			−0.479103			−0.239552	−	0.970884i	$-0.577000\pi$
$239$	−423081.			−0.479103			−0.239552	+	0.970884i	$0.577000\pi$
$240$		−	2.32574e6i		−	2.60636i
$241$	−747450.			−0.828971			−0.414486	−	0.910056i	$-0.636039\pi$
$241$	−747450.			−0.828971			−0.414486	+	0.910056i	$0.636039\pi$
$242$		−	7843.21i		−	0.00860905i
$243$		−	949649.i		−	1.03169i
$244$			544341.i			0.585324i
$245$	1.51600e6			1.61356
$246$			38280.0i			0.0403306i
$247$		−	578284.i		−	0.603113i
$248$	−10156.5			−0.0104861
$249$			642213.i			0.656419i
$250$		−	14463.1i		−	0.0146356i
$251$		−	518011.i		−	0.518985i	−0.965745	−	0.259492i	$-0.916445\pi$
$251$		−	518011.i		−	0.518985i	0.965745	−	0.259492i	$-0.0835552\pi$
$252$	78525.5			0.0778950
$253$			1.35994e6i			1.33573i
$254$	−3122.43			−0.00303674
$255$	3.37789e6			3.25308
$256$	1.04631e6			0.997842
$257$	1.37233e6			1.29606			0.648029	−	0.761616i	$-0.275594\pi$
$257$	1.37233e6			1.29606			0.648029	+	0.761616i	$0.275594\pi$
$258$			13898.6i			0.0129993i
$259$		−	60405.1i		−	0.0559531i
$260$	−795856.			−0.730132
$261$	−1.20476e6	−	1.28443e6i	−1.09471	−	1.16710i
$262$	−7953.58			−0.00715829
$263$		−	1.24673e6i		−	1.11143i	−0.831372	−	0.555717i	$-0.812444\pi$
$263$		−	1.24673e6i		−	1.11143i	0.831372	−	0.555717i	$-0.187556\pi$
$264$		−	67560.9i		−	0.0596603i
$265$	−1.25004e6			−1.09348
$266$	−1102.58			−0.000955447
$267$	145429.			0.124845
$268$	1.34802e6			1.14646
$269$			6871.12i			0.00578958i	0.999996	+	0.00289479i	$0.000921441\pi$
$269$			6871.12i			0.00578958i	−0.999996	+	0.00289479i	$0.999079\pi$
$270$	−27545.0			−0.0229950
$271$		−	1.52277e6i		−	1.25953i	−0.776784	−	0.629767i	$-0.783150\pi$
$271$		−	1.52277e6i		−	1.25953i	0.776784	−	0.629767i	$-0.216850\pi$
$272$			1.52097e6i			1.24652i
$273$		−	43654.2i		−	0.0354503i
$274$	−20026.0			−0.0161146
$275$			2.55219e6i			2.03508i
$276$			2.16394e6i			1.70991i
$277$	1.38347e6			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$277$	1.38347e6			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$278$			15725.4i			0.0122036i
$279$		−	742602.i		−	0.571144i
$280$			3035.16i			0.00231359i
$281$	−112124.			−0.0847097			−0.0423549	−	0.999103i	$-0.513486\pi$
$281$	−112124.			−0.0847097			−0.0423549	+	0.999103i	$0.513486\pi$
$282$			13565.8i			0.0101584i
$283$	−1.64456e6			−1.22063			−0.610316	−	0.792158i	$-0.708958\pi$
$283$	−1.64456e6			−1.22063			−0.610316	+	0.792158i	$0.708958\pi$
$284$	−1.46168e6			−1.07537
$285$	−4.77690e6			−3.48365
$286$	−11555.7			−0.00835376
$287$			115672.i			0.0828943i
$288$		−	99240.9i		−	0.0705033i
$289$	−789187.			−0.555821
$290$	24820.1	−	23280.6i	0.0173304	−	0.0162554i
$291$	−2.73593e6			−1.89397
$292$		−	1.80179e6i		−	1.23665i
$293$		−	606157.i		−	0.412492i	−0.978500	−	0.206246i	$-0.933875\pi$
$293$		−	606157.i		−	0.412492i	0.978500	−	0.206246i	$-0.0661248\pi$
$294$	35025.7			0.0236330
$295$	2.73915e6			1.83257
$296$	−50891.6			−0.0337611
$297$	1.85274e6			1.21877
$298$		−	6010.50i		−	0.00392076i
$299$	740327.			0.478901
$300$			4.06105e6i			2.60516i
$301$			41997.9i			0.0267185i
$302$			2738.08i			0.00172754i
$303$	2.49233e6			1.55955
$304$		−	2.15091e6i		−	1.33487i
$305$		−	1.53835e6i		−	0.946903i
$306$	48028.2			0.0293219
$307$			1.00187e6i			0.606689i	0.952881	+	0.303345i	$0.0981034\pi$
$307$			1.00187e6i			0.606689i	−0.952881	+	0.303345i	$0.901897\pi$
$308$		−	102065.i		−	0.0613054i
$309$			1.56477e6i			0.932298i
$310$	14349.9			0.00848096
$311$		−	1.15660e6i		−	0.678082i	−0.940772	−	0.339041i	$-0.889898\pi$
$311$		−	1.15660e6i		−	0.678082i	0.940772	−	0.339041i	$-0.110102\pi$
$312$	−36778.9			−0.0213901
$313$	−631083.			−0.364104			−0.182052	−	0.983289i	$-0.558274\pi$
$313$	−631083.			−0.364104			−0.182052	+	0.983289i	$0.558274\pi$
$314$	−30570.3			−0.0174975
$315$	−221919.			−0.126014
$316$			844714.i			0.475874i
$317$		−	354651.i		−	0.198223i	−0.995076	−	0.0991114i	$-0.968400\pi$
$317$		−	354651.i		−	0.198223i	0.995076	−	0.0991114i	$-0.0316000\pi$
$318$	−28880.9			−0.0160156
$319$	−1.66946e6	+	1.56590e6i	−0.918541	+	0.861565i
$320$	−2.95888e6			−1.61530
$321$			2.46806e6i			1.33688i
$322$		−	1411.54i		−	0.000758671i
$323$	3.12396e6			1.66609
$324$	−74889.2			−0.0396330
$325$	1.38937e6			0.729640
$326$	22683.0			0.0118211
$327$			4.83864e6i			2.50238i
$328$	97454.5			0.0500170
$329$			40992.5i			0.0208792i
$330$			95455.8i			0.0482522i
$331$		−	3.75107e6i		−	1.88185i	−0.338615	−	0.940925i	$-0.609959\pi$
$331$		−	3.75107e6i		−	1.88185i	0.338615	−	0.940925i	$-0.390041\pi$
$332$	817395.			0.406993
$333$		−	3.72100e6i		−	1.83886i
$334$		−	20163.2i		−	0.00988992i
$335$	−3.80960e6			−1.85467
$336$		−	162370.i		−	0.0784618i
$337$		−	788649.i		−	0.378276i	−0.981951	−	0.189138i	$-0.939431\pi$
$337$		−	788649.i		−	0.378276i	0.981951	−	0.189138i	$-0.0605693\pi$
$338$		−	24565.3i		−	0.0116958i
$339$	6.18580e6			2.92346
$340$		−	4.29931e6i		−	2.01698i
$341$	−965207.			−0.449505
$342$	−67919.9			−0.0314002
$343$	211928.			0.0972644
$344$	35383.5			0.0161215
$345$		−	6.11545e6i		−	2.76618i
$346$			30961.1i			0.0139036i
$347$	−1.86582e6			−0.831852			−0.415926	−	0.909399i	$-0.636542\pi$
$347$	−1.86582e6			−0.831852			−0.415926	+	0.909399i	$0.636542\pi$
$348$	−2.65644e6	+	2.49166e6i	−1.17585	+	1.10291i
$349$	3.35250e6			1.47335			0.736674	−	0.676248i	$-0.236395\pi$
$349$	3.35250e6			1.47335			0.736674	+	0.676248i	$0.236395\pi$
$350$		−	2649.03i		−	0.00115589i
$351$		−	1.00860e6i		−	0.436968i
$352$	−128990.			−0.0554879
$353$	−190138.			−0.0812143			−0.0406072	−	0.999175i	$-0.512929\pi$
$353$	−190138.			−0.0812143			−0.0406072	+	0.999175i	$0.512929\pi$
$354$	63285.3			0.0268407
$355$	4.13083e6			1.73967
$356$		−	185099.i		−	0.0774067i
$357$	235825.			0.0979308
$358$		−	33942.1i		−	0.0139969i
$359$		−	922926.i		−	0.377947i	−0.981982	−	0.188973i	$-0.939484\pi$
$359$		−	922926.i		−	0.377947i	0.981982	−	0.188973i	$-0.0605160\pi$
$360$			186968.i			0.0760346i
$361$	−1.94170e6			−0.784176
$362$			33921.5i			0.0136052i
$363$		−	2.37232e6i		−	0.944946i
$364$	−55562.1			−0.0219799
$365$			5.09201e6i			2.00058i
$366$		−	35542.0i		−	0.0138688i
$367$			2.35322e6i			0.912005i	0.889979	+	0.456002i	$0.150719\pi$
$367$			2.35322e6i			0.912005i	−0.889979	+	0.456002i	$0.849281\pi$
$368$	2.75362e6			1.05995
$369$			7.12550e6i			2.72427i
$370$	71904.0			0.0273054
$371$	−87270.6			−0.0329180
$372$	−1.53584e6			−0.575424
$373$	−1.80766e6			−0.672735			−0.336368	−	0.941731i	$-0.609198\pi$
$373$	−1.80766e6			−0.672735			−0.336368	+	0.941731i	$0.609198\pi$
$374$		−	62425.3i		−	0.0230771i
$375$		−	4.37462e6i		−	1.60643i
$376$	34536.4			0.0125982
$377$	852449.	+	908822.i	0.308898	+	0.329326i
$378$	−1923.03			−0.000692241
$379$		−	5.53962e6i		−	1.98099i	−0.137549	−	0.990495i	$-0.543923\pi$
$379$		−	5.53962e6i		−	1.98099i	0.137549	−	0.990495i	$-0.456077\pi$
$380$			6.07994e6i			2.15993i
$381$	−944434.			−0.333318
$382$	34669.0			0.0121558
$383$	−980444.			−0.341528			−0.170764	−	0.985312i	$-0.554624\pi$
$383$	−980444.			−0.341528			−0.170764	+	0.985312i	$0.554624\pi$
$384$	−273655.			−0.0947054
$385$			288442.i			0.0991762i
$386$	7231.87			0.00247048
$387$			2.58710e6i			0.878085i
$388$			3.48223e6i			1.17430i
$389$		−	1.30391e6i		−	0.436890i	−0.975849	−	0.218445i	$-0.929902\pi$
$389$		−	1.30391e6i		−	0.436890i	0.975849	−	0.218445i	$-0.0700985\pi$
$390$	51964.4			0.0172999
$391$			3.99933e6i			1.32296i
$392$		−	89169.5i		−	0.0293090i
$393$	−2.40570e6			−0.785708
$394$			41947.6i			0.0136134i
$395$		−	2.38723e6i		−	0.769841i
$396$		−	6.28726e6i		−	2.01476i
$397$	−4.15042e6			−1.32165			−0.660824	−	0.750541i	$-0.729793\pi$
$397$	−4.15042e6			−1.32165			−0.660824	+	0.750541i	$0.729793\pi$
$398$		−	41080.4i		−	0.0129995i
$399$	−333496.			−0.104872
$400$	5.16770e6			1.61491
$401$	1.14004e6			0.354044			0.177022	−	0.984207i	$-0.443354\pi$
$401$	1.14004e6			0.354044			0.177022	+	0.984207i	$0.443354\pi$
$402$	−88016.9			−0.0271645
$403$			525441.i			0.161162i
$404$		−	3.17218e6i		−	0.966951i
$405$	211642.			0.0641158
$406$	1732.80	−	1625.32i	0.000521715	−	0.000489353i
$407$	−4.83643e6			−1.44723
$408$		−	198684.i		−	0.0590897i
$409$		−	1.94471e6i		−	0.574841i	−0.957805	−	0.287420i	$-0.907202\pi$
$409$		−	1.94471e6i		−	0.574841i	0.957805	−	0.287420i	$-0.0927977\pi$
$410$	−137692.			−0.0404529
$411$	−6.05724e6			−1.76876
$412$	1.99161e6			0.578044
$413$	191232.			0.0551676
$414$		−	86952.0i		−	0.0249332i
$415$	−2.31002e6			−0.658409
$416$			70219.6i			0.0198941i
$417$			4.75643e6i			1.33949i
$418$			88279.9i			0.0247127i
$419$	−945905.			−0.263216			−0.131608	−	0.991302i	$-0.542014\pi$
$419$	−945905.			−0.263216			−0.131608	+	0.991302i	$0.542014\pi$
$420$			458969.i			0.126958i
$421$			2.19783e6i			0.604351i	0.953252	+	0.302176i	$0.0977129\pi$
$421$			2.19783e6i			0.604351i	−0.953252	+	0.302176i	$0.902287\pi$
$422$	−68570.3			−0.0187437
$423$			2.52517e6i			0.686182i
$424$			73526.0i			0.0198621i
$425$			7.50552e6i			2.01562i
$426$	95438.7			0.0254801
$427$		−	107399.i		−	0.0285056i
$428$	3.14129e6			0.828894
$429$	−3.49524e6			−0.916925
$430$	−49992.8			−0.0130388
$431$	6.43859e6			1.66954			0.834771	−	0.550597i	$-0.185600\pi$
$431$	6.43859e6			1.66954			0.834771	+	0.550597i	$0.185600\pi$
$432$		−	3.75144e6i		−	0.967137i
$433$			3.59239e6i			0.920797i	0.887712	+	0.460398i	$0.152293\pi$
$433$			3.59239e6i			0.920797i	−0.887712	+	0.460398i	$0.847707\pi$
$434$	1001.83			0.000255311
$435$	7.50730e6	−	7.04163e6i	1.90222	−	1.78423i
$436$	6.15852e6			1.55153
$437$		−	5.65572e6i		−	1.41672i
$438$			117646.i			0.0293016i
$439$	−5.57438e6			−1.38050			−0.690248	−	0.723573i	$-0.742499\pi$
$439$	−5.57438e6			−1.38050			−0.690248	+	0.723573i	$0.742499\pi$
$440$	243014.			0.0598412
$441$	6.51973e6			1.59637
$442$	−33983.2			−0.00827387
$443$			886666.i			0.214660i	0.994223	+	0.107330i	$0.0342301\pi$
$443$			886666.i			0.214660i	−0.994223	+	0.107330i	$0.965770\pi$
$444$	−7.69572e6			−1.85264
$445$			523103.i			0.125224i
$446$			25968.3i			0.00618169i
$447$		−	1.81798e6i		−	0.430350i
$448$	−206572.			−0.0486269
$449$		−	1.75268e6i		−	0.410287i	−0.978732	−	0.205143i	$-0.934234\pi$
$449$		−	1.75268e6i		−	0.410287i	0.978732	−	0.205143i	$-0.0657661\pi$
$450$		−	163182.i		−	0.0379876i
$451$	9.26147e6			2.14407
$452$		−	7.87315e6i		−	1.81260i
$453$			828182.i			0.189618i
$454$		−	52593.1i		−	0.0119754i
$455$	157023.			0.0355577
$456$			280972.i			0.0632778i
$457$	3.10638e6			0.695767			0.347883	−	0.937538i	$-0.386901\pi$
$457$	3.10638e6			0.695767			0.347883	+	0.937538i	$0.386901\pi$
$458$	−43189.7			−0.00962091
$459$	5.44855e6			1.20712
$460$	−7.78362e6			−1.71509
$461$			3.59330e6i			0.787482i	0.919221	+	0.393741i	$0.128819\pi$
$461$			3.59330e6i			0.787482i	−0.919221	+	0.393741i	$0.871181\pi$
$462$			6664.17i			0.00145258i
$463$	−8.60497e6			−1.86551			−0.932753	−	0.360516i	$-0.882601\pi$
$463$	−8.60497e6			−1.86551			−0.932753	+	0.360516i	$0.882601\pi$
$464$	3.17065e6	+	3.38033e6i	0.683681	+	0.728894i
$465$	4.34039e6			0.930886
$466$		−	20786.6i		−	0.00443424i
$467$		−	5.85487e6i		−	1.24230i	−0.783693	−	0.621148i	$-0.786666\pi$
$467$		−	5.85487e6i		−	1.24230i	0.783693	−	0.621148i	$-0.213334\pi$
$468$	−3.42267e6			−0.722355
$469$	−265964.			−0.0558330
$470$	−48795.9			−0.0101892
$471$	−9.24655e6			−1.92056
$472$		−	161114.i		−	0.0332872i
$473$	3.36263e6			0.691076
$474$		−	55154.5i		−	0.0112755i
$475$		−	1.06141e7i		−	2.15848i
$476$		−	300153.i		−	0.0607191i
$477$	−5.37594e6			−1.08183
$478$		−	35159.9i		−	0.00703846i
$479$			4.19876e6i			0.836146i	0.908413	+	0.418073i	$0.137294\pi$
$479$			4.19876e6i			0.836146i	−0.908413	+	0.418073i	$0.862706\pi$
$480$	580047.			0.114911
$481$			2.63286e6i			0.518878i
$482$		−	62116.3i		−	0.0121783i
$483$		−	426946.i		−	0.0832731i
$484$	−3.01944e6			−0.585886
$485$		−	9.84106e6i		−	1.89971i
$486$	78920.0			0.0151564
$487$	1.96429e6			0.375304			0.187652	−	0.982236i	$-0.439912\pi$
$487$	1.96429e6			0.375304			0.187652	+	0.982236i	$0.439912\pi$
$488$	−90484.0			−0.0171998
$489$	6.86090e6			1.29750
$490$			125986.i			0.0237046i
$491$			1.00724e7i			1.88551i	0.333491	+	0.942753i	$0.391773\pi$
$491$			1.00724e7i			1.88551i	−0.333491	+	0.942753i	$0.608227\pi$
$492$	1.47369e7			2.74468
$493$	−4.90956e6	+	4.60502e6i	−0.909757	+	0.853325i
$494$	48057.9			0.00886029
$495$			1.77683e7i			3.25936i
$496$			1.95436e6i			0.356697i
$497$	288391.			0.0523710
$498$	−53370.7			−0.00964339
$499$	−3.19475e6			−0.574361			−0.287181	−	0.957876i	$-0.592718\pi$
$499$	−3.19475e6			−0.574361			−0.287181	+	0.957876i	$0.592718\pi$
$500$	−5.56793e6			−0.996021
$501$		−	6.09872e6i		−	1.08554i
$502$	43049.0			0.00762436
$503$		−	3.71760e6i		−	0.655152i	−0.944825	−	0.327576i	$-0.893768\pi$
$503$		−	3.71760e6i		−	0.655152i	0.944825	−	0.327576i	$-0.106232\pi$
$504$			13053.0i			0.00228894i
$505$			8.96482e6i			1.56428i
$506$	−113017.			−0.0196231
$507$		−	7.43023e6i		−	1.28376i
$508$			1.20206e6i			0.206664i
$509$	−4.61593e6			−0.789706			−0.394853	−	0.918744i	$-0.629204\pi$
$509$	−4.61593e6			−0.789706			−0.394853	+	0.918744i	$0.629204\pi$
$510$			280717.i			0.0477907i
$511$			355495.i			0.0602256i
$512$			435330.i			0.0733912i
$513$	−7.70516e6			−1.29267
$514$			114046.i			0.0190403i
$515$	−5.62843e6			−0.935124
$516$	5.35061e6			0.884665
$517$	3.28212e6			0.540043
$518$	5019.93			0.000822002
$519$			9.36475e6i			1.52608i
$520$		−	132293.i		−	0.0214549i
$521$	6.37296e6			1.02860			0.514300	−	0.857610i	$-0.328052\pi$
$521$	6.37296e6			1.02860			0.514300	+	0.857610i	$0.328052\pi$
$522$	106742.	−	100121.i	0.0171458	−	0.0160823i
$523$	1.60365e6			0.256362			0.128181	−	0.991751i	$-0.459086\pi$
$523$	1.60365e6			0.256362			0.128181	+	0.991751i	$0.459086\pi$
$524$			3.06193e6i			0.487155i
$525$		−	801247.i		−	0.126873i
$526$	103609.			0.0163280
$527$	−2.83849e6			−0.445206
$528$	−1.30004e7			−2.02942
$529$	804188.			0.124945
$530$		−	103884.i		−	0.0160642i
$531$	1.17800e7			1.81305
$532$			424466.i			0.0650226i
$533$		−	5.04178e6i		−	0.768715i
$534$			12085.8i			0.00183409i
$535$	−8.87753e6			−1.34093
$536$			224076.i			0.0336887i
$537$		−	1.02664e7i		−	1.53633i
$538$	−571.020			−8.50542e−5
$539$		−	8.47412e6i		−	1.25638i
$540$			1.06041e7i			1.56491i
$541$		−	1.28252e7i		−	1.88396i	−0.335670	−	0.941980i	$-0.608963\pi$
$541$		−	1.28252e7i		−	1.88396i	0.335670	−	0.941980i	$-0.391037\pi$
$542$	126548.			0.0185037
$543$			1.02602e7i			1.49333i
$544$	−379334.			−0.0549572
$545$	−1.74044e7			−2.50997
$546$	3627.85			0.000520797
$547$	−1.06980e7			−1.52875			−0.764373	−	0.644774i	$-0.776952\pi$
$547$	−1.06980e7			−1.52875			−0.764373	+	0.644774i	$0.776952\pi$
$548$			7.70952e6i			1.09667i
$549$		−	6.61585e6i		−	0.936817i
$550$	−212098.			−0.0298972
$551$	6.94294e6	−	6.51227e6i	0.974236	−	0.913805i
$552$	−359704.			−0.0502456
$553$		−	166662.i		−	0.0231753i
$554$			114972.i			0.0159154i
$555$	2.17487e7			2.99709
$556$	6.05388e6			0.830514
$557$	6.24443e6			0.852815			0.426407	−	0.904531i	$-0.359779\pi$
$557$	6.24443e6			0.852815			0.426407	+	0.904531i	$0.359779\pi$
$558$	61713.4			0.00839062
$559$		−	1.83055e6i		−	0.247772i
$560$	584040.			0.0786996
$561$		−	1.88817e7i		−	2.53299i
$562$		−	9318.00i		−	0.00124446i
$563$			6.76916e6i			0.900043i	0.893018	+	0.450022i	$0.148584\pi$
$563$			6.76916e6i			0.900043i	−0.893018	+	0.450022i	$0.851416\pi$
$564$	5.22251e6			0.691324
$565$			2.22501e7i			2.93232i
$566$		−	136670.i		−	0.0179322i
$567$	14775.7			0.00193014
$568$		−	242971.i		−	0.0315997i
$569$		−	6.15143e6i		−	0.796517i	−0.917273	−	0.398259i	$-0.869615\pi$
$569$		−	6.15143e6i		−	0.796517i	0.917273	−	0.398259i	$-0.130385\pi$
$570$		−	396981.i		−	0.0511779i
$571$	−6.20471e6			−0.796399			−0.398200	−	0.917299i	$-0.630365\pi$
$571$	−6.20471e6			−0.796399			−0.398200	+	0.917299i	$0.630365\pi$
$572$			4.44867e6i			0.568512i
$573$	1.04863e7			1.33424
$574$	−9612.87			−0.00121779
$575$	1.35883e7			1.71393
$576$	−1.27250e7			−1.59809
$577$		−	1.63223e6i		−	0.204100i	−0.994779	−	0.102050i	$-0.967460\pi$
$577$		−	1.63223e6i		−	0.204100i	0.994779	−	0.102050i	$-0.0325401\pi$
$578$		−	65584.8i		−	0.00816552i
$579$	2.18741e6			0.271165
$580$	−8.96243e6	−	9.55513e6i	−1.10626	−	1.17941i
$581$	−161272.			−0.0198207
$582$		−	227368.i		−	0.0278241i
$583$			6.98745e6i			0.851427i
$584$	299506.			0.0363391
$585$	9.67273e6			1.16858
$586$	50374.3			0.00605989
$587$	−2.64142e6			−0.316404			−0.158202	−	0.987407i	$-0.550570\pi$
$587$	−2.64142e6			−0.316404			−0.158202	+	0.987407i	$0.550570\pi$
$588$		−	1.34840e7i		−	1.60833i
$589$	4.01410e6			0.476760
$590$			227635.i			0.0269221i
$591$			1.26878e7i			1.49423i
$592$			9.79283e6i			1.14843i
$593$	1.36143e7			1.58986			0.794930	−	0.606701i	$-0.207508\pi$
$593$	1.36143e7			1.58986			0.794930	+	0.606701i	$0.207508\pi$
$594$			153971.i			0.0179049i
$595$			848255.i			0.0982277i
$596$	−2.31389e6			−0.266826
$597$		−	1.24255e7i		−	1.42685i
$598$			61524.4i			0.00703549i
$599$		−	1.17939e7i		−	1.34305i	−0.740984	−	0.671523i	$-0.765640\pi$
$599$		−	1.17939e7i		−	1.34305i	0.740984	−	0.671523i	$-0.234360\pi$
$600$	−675055.			−0.0765528
$601$		−	8.77105e6i		−	0.990525i	−0.868743	−	0.495263i	$-0.835072\pi$
$601$		−	8.77105e6i		−	0.990525i	0.868743	−	0.495263i	$-0.164928\pi$
$602$	−3490.21			−0.000392519
$603$	−1.63836e7			−1.83492
$604$	1.05409e6			0.117567
$605$	8.53316e6			0.947811
$606$			207123.i			0.0229112i
$607$			7.15323e6i			0.788008i	0.919109	+	0.394004i	$0.128910\pi$
$607$			7.15323e6i			0.788008i	−0.919109	+	0.394004i	$0.871090\pi$
$608$	536442.			0.0588524
$609$	524117.	−	491606.i	0.0572644	−	0.0537123i
$610$	127844.			0.0139109
$611$		−	1.78673e6i		−	0.193622i
$612$		−	1.84897e7i		−	1.99549i
$613$	1.45936e7			1.56860			0.784301	−	0.620381i	$-0.213022\pi$
$613$	1.45936e7			1.56860			0.784301	+	0.620381i	$0.213022\pi$
$614$	−83260.0			−0.00891282
$615$	−4.16475e7			−4.44018
$616$	16965.9			0.00180146
$617$			1.14637e7i			1.21230i	0.795350	+	0.606151i	$0.207287\pi$
$617$			1.14637e7i			1.21230i	−0.795350	+	0.606151i	$0.792713\pi$
$618$	−130039.			−0.0136963
$619$			4.26349e6i			0.447238i	0.974677	+	0.223619i	$0.0717871\pi$
$619$			4.26349e6i			0.447238i	−0.974677	+	0.223619i	$0.928213\pi$
$620$		−	5.52436e6i		−	0.577168i
$621$		−	9.86425e6i		−	1.02644i
$622$	96118.5			0.00996164
$623$			36520.1i			0.00376974i
$624$			7.07719e6i			0.727611i
$625$	−45407.9			−0.00464977
$626$		−	52445.7i		−	0.00534902i
$627$			2.67018e7i			2.71252i
$628$			1.17688e7i			1.19078i
$629$	−1.42230e7			−1.43339
$630$		−	18442.4i		−	0.00185126i
$631$	1.82271e6			0.182240			0.0911199	−	0.995840i	$-0.470955\pi$
$631$	1.82271e6			0.182240			0.0911199	+	0.995840i	$0.470955\pi$
$632$	−140414.			−0.0139836
$633$	−2.07403e7			−2.05734
$634$	29473.1			0.00291207
$635$		−	3.39710e6i		−	0.334329i
$636$			1.11184e7i			1.08994i
$637$	−4.61315e6			−0.450453
$638$	−130133.	−	138739.i	−0.0126572	−	0.0134942i
$639$	1.77651e7			1.72114
$640$		−	984327.i		−	0.0949925i
$641$			1.44219e7i			1.38636i	0.720763	+	0.693181i	$0.243791\pi$
$641$			1.44219e7i			1.38636i	−0.720763	+	0.693181i	$0.756209\pi$
$642$	−205106.			−0.0196400
$643$	1.40022e7			1.33558			0.667791	−	0.744349i	$-0.267240\pi$
$643$	1.40022e7			1.33558			0.667791	+	0.744349i	$0.267240\pi$
$644$	−543407.			−0.0516310
$645$	−1.51212e7			−1.43116
$646$			259614.i			0.0244764i
$647$	1.50033e7			1.40905			0.704524	−	0.709680i	$-0.251161\pi$
$647$	1.50033e7			1.40905			0.704524	+	0.709680i	$0.251161\pi$
$648$		−	12448.6i		−	0.00116461i
$649$		−	1.53112e7i		−	1.42692i
$650$			115462.i			0.0107191i
$651$	303021.			0.0280234
$652$		−	8.73240e6i		−	0.804479i
$653$			1.52545e7i			1.39996i	0.714163	+	0.699979i	$0.246807\pi$
$653$			1.52545e7i			1.39996i	−0.714163	+	0.699979i	$0.753193\pi$
$654$	−402112.			−0.0367623
$655$		−	8.65324e6i		−	0.788090i
$656$		−	1.87527e7i		−	1.70139i
$657$			2.18988e7i			1.97928i
$658$	−3406.65			−0.000306735
$659$			5.92968e6i			0.531885i	0.963989	+	0.265942i	$0.0856831\pi$
$659$			5.92968e6i			0.531885i	−0.963989	+	0.265942i	$0.914317\pi$
$660$	3.67481e7			3.28379
$661$	1.03733e6			0.0923450			0.0461725	−	0.998933i	$-0.485298\pi$
$661$	1.03733e6			0.0923450			0.0461725	+	0.998933i	$0.485298\pi$
$662$	311730.			0.0276461
$663$	−1.02788e7			−0.908156
$664$			135873.i			0.0119595i
$665$		−	1.19957e6i		−	0.105190i
$666$	309232.			0.0270146
$667$	8.33710e6	+	8.88844e6i	0.725605	+	0.773590i
$668$	−7.76231e6			−0.673054
$669$			7.85460e6i			0.678514i
$670$		−	316594.i		−	0.0272468i
$671$	−8.59904e6			−0.737299
$672$	40495.6			0.00345927
$673$	−8.48418e6			−0.722058			−0.361029	−	0.932555i	$-0.617575\pi$
$673$	−8.48418e6			−0.722058			−0.361029	+	0.932555i	$0.617575\pi$
$674$	65540.1			0.00555722
$675$		−	1.85122e7i		−	1.56386i
$676$	−9.45704e6			−0.795955
$677$			2.74588e6i			0.230255i	0.993351	+	0.115128i	$0.0367277\pi$
$677$			2.74588e6i			0.230255i	−0.993351	+	0.115128i	$0.963272\pi$
$678$			514067.i			0.0429482i
$679$		−	687046.i		−	0.0571889i
$680$	714659.			0.0592689
$681$		−	1.59077e7i		−	1.31444i
$682$		−	80212.9i		−	0.00660364i
$683$	−1.63950e7			−1.34481			−0.672403	−	0.740185i	$-0.734738\pi$
$683$	−1.63950e7			−1.34481			−0.672403	+	0.740185i	$0.734738\pi$
$684$			2.61475e7i			2.13693i
$685$		−	2.17877e7i		−	1.77413i
$686$			17612.2i			0.00142890i
$687$	−1.30635e7			−1.05601
$688$		−	6.80867e6i		−	0.548392i
$689$	3.80384e6			0.305263
$690$	508221.			0.0406377
$691$	6.55046e6			0.521887			0.260943	−	0.965354i	$-0.415966\pi$
$691$	6.55046e6			0.521887			0.260943	+	0.965354i	$0.415966\pi$
$692$	1.19193e7			0.946202
$693$			1.24048e6i			0.0981198i
$694$		−	155058.i		−	0.0122207i
$695$	−1.71087e7			−1.34356
$696$	−414181.	−	441571.i	−0.0324091	−	0.0345524i
$697$	2.72362e7			2.12356
$698$			278607.i			0.0216448i
$699$		−	6.28730e6i		−	0.486711i
$700$	−1.01981e6			−0.0786636
$701$	−1.36218e7			−1.04698			−0.523492	−	0.852031i	$-0.675371\pi$
$701$	−1.36218e7			−1.04698			−0.523492	+	0.852031i	$0.675371\pi$
$702$	83818.7			0.00641946
$703$	2.01137e7			1.53498
$704$			1.65395e7i			1.25774i
$705$	−1.47592e7			−1.11838
$706$		−	15801.3i		−	0.00119311i
$707$			625873.i			0.0470910i
$708$		−	2.43632e7i		−	1.82664i
$709$	−7.75704e6			−0.579536			−0.289768	−	0.957097i	$-0.593578\pi$
$709$	−7.75704e6			−0.579536			−0.289768	+	0.957097i	$0.593578\pi$
$710$			343290.i			0.0255573i
$711$		−	1.02665e7i		−	0.761641i
$712$	30768.4			0.00227460
$713$			5.13891e6i			0.378571i
$714$			19598.1i			0.00143869i
$715$		−	1.25723e7i		−	0.919705i
$716$	−1.30669e7			−0.952553
$717$		−	1.06347e7i		−	0.772555i
$718$	76699.2			0.00555238
$719$	9.79097e6			0.706323			0.353162	−	0.935562i	$-0.385107\pi$
$719$	9.79097e6			0.706323			0.353162	+	0.935562i	$0.385107\pi$
$720$	3.59773e7			2.58641
$721$	−392945.			−0.0281510
$722$		−	161364.i		−	0.0115203i
$723$		−	1.87882e7i		−	1.33672i
$724$	1.30589e7			0.925895
$725$	1.56462e7	+	1.66809e7i	1.10551	+	1.17862i
$726$	197150.			0.0138821
$727$		−	1.79796e7i		−	1.26166i	−0.775920	−	0.630832i	$-0.782714\pi$
$727$		−	1.79796e7i		−	1.26166i	0.775920	−	0.630832i	$-0.217286\pi$
$728$		−	9235.91i		−	0.000645879i
$729$	2.33020e7			1.62395
$730$	−423168.			−0.0293904
$731$	9.88885e6			0.684467
$732$	−1.36828e7			−0.943837
$733$			1.87731e7i			1.29055i	0.763950	+	0.645275i	$0.223257\pi$
$733$			1.87731e7i			1.29055i	−0.763950	+	0.645275i	$0.776743\pi$
$734$	−195563.			−0.0133982
$735$			3.81068e7i			2.60186i
$736$			686760.i			0.0467316i
$737$			2.12948e7i			1.44413i
$738$	−592160.			−0.0400220
$739$		−	1.41904e7i		−	0.955833i	−0.878405	−	0.477917i	$-0.841392\pi$
$739$		−	1.41904e7i		−	0.955833i	0.878405	−	0.477917i	$-0.158608\pi$
$740$		−	2.76813e7i		−	1.85826i
$741$	1.45360e7			0.972522
$742$		−	7252.57i		−	0.000483595i
$743$			7.00495e6i			0.465514i	0.972535	+	0.232757i	$0.0747747\pi$
$743$			7.00495e6i			0.465514i	−0.972535	+	0.232757i	$0.925225\pi$
$744$		−	255297.i		−	0.0169088i
$745$	6.53923e6			0.431654
$746$		−	150224.i		−	0.00988310i
$747$	−9.93451e6			−0.651396
$748$	−2.40322e7			−1.57051
$749$	−619778.			−0.0403675
$750$	363550.			0.0236000
$751$		−	9.08104e6i		−	0.587538i	−0.955877	−	0.293769i	$-0.905090\pi$
$751$		−	9.08104e6i		−	0.587538i	0.955877	−	0.293769i	$-0.0949096\pi$
$752$		−	6.64566e6i		−	0.428542i
$753$	1.30209e7			0.836864
$754$	−75527.1	+	70842.2i	−0.00483809	+	0.00453799i
$755$	−2.97895e6			−0.190193
$756$			740320.i			0.0471102i
$757$			939201.i			0.0595688i	0.999556	+	0.0297844i	$0.00948207\pi$
$757$			939201.i			0.0595688i	−0.999556	+	0.0297844i	$0.990518\pi$
$758$	460367.			0.0291025
$759$	−3.41841e7			−2.15387
$760$	−1.01065e6			−0.0634696
$761$	−2.90461e7			−1.81813			−0.909067	−	0.416649i	$-0.863204\pi$
$761$	−2.90461e7			−1.81813			−0.909067	+	0.416649i	$0.863204\pi$
$762$		−	78486.6i		−	0.00489675i
$763$	−1.21508e6			−0.0755601
$764$		−	1.33467e7i		−	0.827256i
$765$			5.22532e7i			3.22819i
$766$		−	81479.2i		−	0.00501735i
$767$	−8.33516e6			−0.511594
$768$			2.63006e7i			1.60902i
$769$			3.95269e6i			0.241033i	0.992711	+	0.120517i	$0.0384551\pi$
$769$			3.95269e6i			0.241033i	−0.992711	+	0.120517i	$0.961545\pi$
$770$	−23970.8			−0.00145699
$771$			3.44954e7i			2.08990i
$772$		−	2.78409e6i		−	0.168128i
$773$		−	1.55320e7i		−	0.934927i	−0.884012	−	0.467464i	$-0.845168\pi$
$773$		−	1.55320e7i		−	0.934927i	0.884012	−	0.467464i	$-0.154832\pi$
$774$	−215000.			−0.0128999
$775$			9.64415e6i			0.576779i
$776$	−578840.			−0.0345068
$777$	1.51837e6			0.0902245
$778$	108360.			0.00641832
$779$	−3.85166e7			−2.27407
$780$		−	2.00050e7i		−	1.17734i
$781$		−	2.30905e7i		−	1.35458i
$782$	−332362.			−0.0194354
$783$	1.21093e7	−	1.13582e7i	0.705854	−	0.662070i
$784$	−1.71585e7			−0.996983
$785$		−	3.32595e7i		−	1.92638i
$786$		−	199925.i		−	0.0115428i
$787$	−2.17194e7			−1.25000			−0.625000	−	0.780624i	$-0.714901\pi$
$787$	−2.17194e7			−1.25000			−0.625000	+	0.780624i	$0.714901\pi$
$788$	1.61488e7			0.926454
$789$	3.13384e7			1.79219
$790$	198389.			0.0113097
$791$			1.55338e6i			0.0882745i
$792$	1.04511e6			0.0592038
$793$			4.68116e6i			0.264345i
$794$		−	344918.i		−	0.0194162i
$795$		−	3.14215e7i		−	1.76323i
$796$	−1.58149e7			−0.884675
$797$			2.27967e7i			1.27124i	0.772003	+	0.635619i	$0.219255\pi$
$797$			2.27967e7i			1.27124i	−0.772003	+	0.635619i	$0.780745\pi$
$798$		−	27715.0i		−	0.00154066i
$799$	9.65210e6			0.534878
$800$			1.28884e6i			0.0711990i
$801$			2.24967e6i			0.123890i
$802$			94741.9i			0.00520123i
$803$	2.84632e7			1.55774
$804$			3.38843e7i			1.84867i
$805$	1.53571e6			0.0835256
$806$	−43666.4			−0.00236761
$807$	−172715.			−0.00933571
$808$	527301.			0.0284139
$809$		−	2.01841e7i		−	1.08427i	−0.840291	−	0.542135i	$-0.817616\pi$
$809$		−	2.01841e7i		−	1.08427i	0.840291	−	0.542135i	$-0.182384\pi$
$810$			17588.4i			0.000941920i
$811$	3.03050e7			1.61794			0.808969	−	0.587851i	$-0.200026\pi$
$811$	3.03050e7			1.61794			0.808969	+	0.587851i	$0.200026\pi$
$812$	−625706.	−	667084.i	−0.0333027	−	0.0355051i
$813$	3.82769e7			2.03100
$814$		−	401928.i		−	0.0212612i
$815$			2.46784e7i			1.30144i
$816$	−3.82318e7			−2.01001
$817$	−1.39845e7			−0.732979
$818$	161614.			0.00844494
$819$	675294.			0.0351790
$820$			5.30080e7i			2.75300i
$821$	6.95618e6			0.360174			0.180087	−	0.983651i	$-0.442362\pi$
$821$	6.95618e6			0.360174			0.180087	+	0.983651i	$0.442362\pi$
$822$		−	503383.i		−	0.0259848i
$823$			6.77034e6i			0.348426i	0.984708	+	0.174213i	$0.0557382\pi$
$823$			6.77034e6i			0.348426i	−0.984708	+	0.174213i	$0.944262\pi$
$824$			331058.i			0.0169858i
$825$	−6.41530e7			−3.28157
$826$			15892.2i			0.000810463i
$827$		−	4.85171e6i		−	0.246678i	−0.992365	−	0.123339i	$-0.960640\pi$
$827$		−	4.85171e6i		−	0.246678i	0.992365	−	0.123339i	$-0.0393603\pi$
$828$	−3.34743e7			−1.69682
$829$		−	2.50053e7i		−	1.26370i	−0.775089	−	0.631852i	$-0.782295\pi$
$829$		−	2.50053e7i		−	1.26370i	0.775089	−	0.631852i	$-0.217705\pi$
$830$		−	191973.i		−	0.00967263i
$831$			3.47754e7i			1.74691i
$832$	9.00380e6			0.450939
$833$		−	2.49208e7i		−	1.24437i
$834$	−395280.			−0.0196784
$835$	2.19369e7			1.08883
$836$	3.39855e7			1.68182
$837$	7.00107e6			0.345422
$838$		−	78608.8i		−	0.00386688i
$839$			1.64107e6i			0.0804864i	0.999190	+	0.0402432i	$0.0128133\pi$
$839$			1.64107e6i			0.0804864i	−0.999190	+	0.0402432i	$0.987187\pi$
$840$	−76293.0			−0.00373066
$841$	−1.31167e6	+	2.04692e7i	−0.0639491	+	0.997953i
$842$	−182650.			−0.00887847
$843$		−	2.81840e6i		−	0.136595i
$844$			2.63978e7i			1.27559i
$845$	2.67263e7			1.28765
$846$	−209852.			−0.0100806
$847$	595736.			0.0285329
$848$	1.41482e7			0.675636
$849$		−	4.13385e7i		−	1.96827i
$850$	−623741.			−0.0296113
$851$			2.57499e7i			1.21885i
$852$		−	3.67415e7i		−	1.73404i
$853$		−	1.98157e7i		−	0.932472i	−0.884660	−	0.466236i	$-0.845610\pi$
$853$		−	1.98157e7i		−	0.932472i	0.884660	−	0.466236i	$-0.154390\pi$
$854$	8925.30			0.000418773
$855$		−	7.38947e7i		−	3.45699i
$856$			522167.i			0.0243570i
$857$	1.78659e7			0.830947			0.415474	−	0.909605i	$-0.363616\pi$
$857$	1.78659e7			0.830947			0.415474	+	0.909605i	$0.363616\pi$
$858$		−	290470.i		−	0.0134705i
$859$		−	1.75220e7i		−	0.810215i	−0.914269	−	0.405108i	$-0.867234\pi$
$859$		−	1.75220e7i		−	0.810215i	0.914269	−	0.405108i	$-0.132766\pi$
$860$			1.92460e7i			0.887347i
$861$	−2.90759e6			−0.133667
$862$			535075.i			0.0245271i
$863$	−1.67225e7			−0.764319			−0.382159	−	0.924096i	$-0.624819\pi$
$863$	−1.67225e7			−0.764319			−0.382159	+	0.924096i	$0.624819\pi$
$864$	935619.			0.0426397
$865$	−3.36847e7			−1.53071
$866$	−298543.			−0.0135273
$867$		−	1.98373e7i		−	0.896263i
$868$		−	385679.i		−	0.0173751i
$869$	−1.33441e7			−0.599431
$870$	585190.	+	623889.i	0.0262119	+	0.0279453i
$871$	1.15925e7			0.517764
$872$			1.02371e6i			0.0455917i
$873$		−	4.23226e7i		−	1.87948i
$874$	470015.			0.0208129
$875$	1.09855e6			0.0485067
$876$	4.52907e7			1.99411
$877$	−3.11380e7			−1.36708			−0.683538	−	0.729915i	$-0.739559\pi$
$877$	−3.11380e7			−1.36708			−0.683538	+	0.729915i	$0.739559\pi$
$878$		−	463255.i		−	0.0202808i
$879$	1.52366e7			0.665145
$880$		−	4.67621e7i		−	2.03557i
$881$		−	4.44250e6i		−	0.192836i	−0.995341	−	0.0964178i	$-0.969262\pi$
$881$		−	4.44250e6i		−	0.192836i	0.995341	−	0.0964178i	$-0.0307385\pi$
$882$			541818.i			0.0234521i
$883$	4.03827e7			1.74298			0.871492	−	0.490409i	$-0.163153\pi$
$883$	4.03827e7			1.74298			0.871492	+	0.490409i	$0.163153\pi$
$884$			1.30827e7i			0.563075i
$885$			6.88524e7i			2.95502i
$886$	−73685.8			−0.00315355
$887$			2.66294e6i			0.113646i	0.998384	+	0.0568228i	$0.0180970\pi$
$887$			2.66294e6i			0.113646i	−0.998384	+	0.0568228i	$0.981903\pi$
$888$		−	1.27923e6i		−	0.0544399i
$889$		−	237166.i		−	0.0100646i
$890$	−43472.2			−0.00183965
$891$		−	1.18304e6i		−	0.0499233i
$892$	9.99716e6			0.420692
$893$	−1.36497e7			−0.572788
$894$	151082.			0.00632223
$895$	3.69280e7			1.54098
$896$		−	68720.1i		−	0.00285965i
$897$			1.86092e7i			0.772229i
$898$	145656.			0.00602749
$899$	−6.30850e6	+	5.91718e6i	−0.260331	+	0.244183i
$900$	−6.28211e7			−2.58523
$901$			2.05488e7i			0.843285i
$902$			769669.i			0.0314983i
$903$	−1.05568e6			−0.0430836
$904$	1.30873e6			0.0532633
$905$	−3.69056e7			−1.49786
$906$	−68825.6			−0.00278567
$907$		−	2.03246e7i		−	0.820357i	−0.912005	−	0.410179i	$-0.865466\pi$
$907$		−	2.03246e7i		−	0.820357i	0.912005	−	0.410179i	$-0.134534\pi$
$908$	−2.02470e7			−0.814979
$909$			3.85543e7i			1.54761i
$910$			13049.3i			0.000522376i
$911$		−	1.02536e7i		−	0.409338i	−0.978831	−	0.204669i	$-0.934388\pi$
$911$		−	1.02536e7i		−	0.409338i	0.978831	−	0.204669i	$-0.0656118\pi$
$912$	5.40661e7			2.15247
$913$			1.29125e7i			0.512665i
$914$			258153.i			0.0102214i
$915$	3.86686e7			1.52688
$916$			1.66269e7i			0.654747i
$917$		−	604120.i		−	0.0237246i
$918$			452798.i			0.0177336i
$919$	−1.37447e7			−0.536841			−0.268421	−	0.963302i	$-0.586502\pi$
$919$	−1.37447e7			−0.536841			−0.268421	+	0.963302i	$0.586502\pi$
$920$		−	1.29384e6i		−	0.0503979i
$921$	−2.51835e7			−0.978288
$922$	−298618.			−0.0115688
$923$	−1.25700e7			−0.485659
$924$	2.56554e6			0.0988551
$925$			4.83246e7i			1.85701i
$926$		−	715110.i		−	0.0274060i
$927$	−2.42057e7			−0.925163
$928$	−843064.	+	790769.i	−0.0321359	+	0.0301425i
$929$	−5.62360e6			−0.213784			−0.106892	−	0.994271i	$-0.534090\pi$
$929$	−5.62360e6			−0.213784			−0.106892	+	0.994271i	$0.534090\pi$
$930$			360705.i			0.0136756i
$931$			3.52421e7i			1.33256i
$932$	−8.00234e6			−0.301771
$933$	2.90728e7			1.09341
$934$	486566.			0.0182505
$935$	6.79168e7			2.54067
$936$		−	568939.i		−	0.0212264i
$937$	−4.19175e7			−1.55972			−0.779860	−	0.625953i	$-0.784710\pi$
$937$	−4.19175e7			−1.55972			−0.779860	+	0.625953i	$0.784710\pi$
$938$		−	22102.8i		−	0.000820238i
$939$		−	1.58632e7i		−	0.587119i
$940$			1.87852e7i			0.693420i
$941$	9.27947e6			0.341625			0.170812	−	0.985304i	$-0.445361\pi$
$941$	9.27947e6			0.341625			0.170812	+	0.985304i	$0.445361\pi$
$942$		−	768428.i		−	0.0282147i
$943$		−	4.93095e7i		−	1.80572i
$944$	−3.10023e7			−1.13231
$945$		−	2.09220e6i		−	0.0762120i
$946$			279449.i			0.0101525i
$947$		−	3.00455e7i		−	1.08869i	−0.838861	−	0.544346i	$-0.816778\pi$
$947$		−	3.00455e7i		−	1.08869i	0.838861	−	0.544346i	$-0.183222\pi$
$948$	−2.12331e7			−0.767348
$949$		−	1.54949e7i		−	0.558499i
$950$	882075.			0.0317100
$951$	8.91467e6			0.319635
$952$	49893.4			0.00178423
$953$	1.26213e7			0.450164			0.225082	−	0.974340i	$-0.427735\pi$
$953$	1.26213e7			0.450164			0.225082	+	0.974340i	$0.427735\pi$
$954$		−	446764.i		−	0.0158931i
$955$			3.77187e7i			1.33829i
$956$	−1.35357e7			−0.479000
$957$	−3.93612e7	−	4.19642e7i	−1.38928	−	1.48115i
$958$	−348935.			−0.0122838
$959$		−	1.52109e6i		−	0.0534083i
$960$		−	7.43756e7i		−	2.60467i
$961$	2.49819e7			0.872602
$962$	−218802.			−0.00762279
$963$	−3.81788e7			−1.32665
$964$	−2.39132e7			−0.828792
$965$			7.86804e6i			0.271987i
$966$	35481.1			0.00122336
$967$		−	1.70612e7i		−	0.586737i	−0.955999	−	0.293368i	$-0.905224\pi$
$967$		−	1.70612e7i		−	0.586737i	0.955999	−	0.293368i	$-0.0947763\pi$
$968$		−	501911.i		−	0.0172162i
$969$			7.85251e7i			2.68658i
$970$	817835.			0.0279085
$971$			3.98552e7i			1.35655i	0.734807	+	0.678277i	$0.237273\pi$
$971$			3.98552e7i			1.35655i	−0.734807	+	0.678277i	$0.762727\pi$
$972$		−	3.03822e7i		−	1.03146i
$973$	−1.19443e6			−0.0404464
$974$			163241.i			0.00551355i
$975$			3.49237e7i			1.17655i
$976$			1.74114e7i			0.585072i
$977$	8.48397e6			0.284356			0.142178	−	0.989841i	$-0.454589\pi$
$977$	8.48397e6			0.284356			0.142178	+	0.989841i	$0.454589\pi$
$978$			570171.i			0.0190615i
$979$	2.92403e6			0.0975048
$980$	4.85015e7			1.61321
$981$	−7.48498e7			−2.48324
$982$	−837058.			−0.0276998
$983$			5.45705e7i			1.80125i	0.434595	+	0.900626i	$0.356892\pi$
$983$			5.45705e7i			1.80125i	−0.434595	+	0.900626i	$0.643108\pi$
$984$			2.44966e6i			0.0806525i
$985$	−4.56376e7			−1.49876
$986$	−382698.	−	408006.i	−0.0125361	−	0.0133652i
$987$	−1.03040e6			−0.0336678
$988$		−	1.85011e7i		−	0.602983i
$989$		−	1.79031e7i		−	0.582020i
$990$	−1.47662e6			−0.0478830
$991$	−5.48710e7			−1.77484			−0.887418	−	0.460965i	$-0.847503\pi$
$991$	−5.48710e7			−1.77484			−0.887418	+	0.460965i	$0.847503\pi$
$992$	−487422.			−0.0157263
$993$	9.42884e7			3.03449
$994$			23966.5i			0.000769378i
$995$	4.46941e7			1.43117
$996$			2.05464e7i			0.656277i
$997$			5.66984e7i			1.80648i	0.429136	+	0.903240i	$0.358818\pi$
$997$			5.66984e7i			1.80648i	−0.429136	+	0.903240i	$0.641182\pi$
$998$		−	265497.i		−	0.00843789i
$999$	3.50807e7			1.11213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.b.a.28.7	yes	12
3.2	odd	2		261.6.c.b.28.6		12
4.3	odd	2		464.6.e.c.289.2		12
29.12	odd	4		841.6.a.d.1.6		12
29.17	odd	4		841.6.a.d.1.7		12
29.28	even	2	inner	29.6.b.a.28.6	✓	12
87.86	odd	2		261.6.c.b.28.7		12
116.115	odd	2		464.6.e.c.289.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.b.a.28.6	✓	12	29.28	even	2	inner
29.6.b.a.28.7	yes	12	1.1	even	1	trivial
261.6.c.b.28.6		12	3.2	odd	2
261.6.c.b.28.7		12	87.86	odd	2
464.6.e.c.289.2		12	4.3	odd	2
464.6.e.c.289.11		12	116.115	odd	2
841.6.a.d.1.6		12	29.12	odd	4
841.6.a.d.1.7		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)

\(f(q)\)	\(=\)	\(q+0.0831044i q^{2} +25.1364i q^{3} +31.9931 q^{4} -90.4149 q^{5} -2.08895 q^{6} -6.31225 q^{7} +5.31810i q^{8} -388.840 q^{9} +O(q^{10})\)	\(q+0.0831044i q^{2} +25.1364i q^{3} +31.9931 q^{4} -90.4149 q^{5} -2.08895 q^{6} -6.31225 q^{7} +5.31810i q^{8} -388.840 q^{9} -7.51387i q^{10} +505.400i q^{11} +804.192i q^{12} +275.130 q^{13} -0.524575i q^{14} -2272.71i q^{15} +1023.34 q^{16} +1486.29i q^{17} -32.3143i q^{18} -2101.86i q^{19} -2892.65 q^{20} -158.667i q^{21} -42.0009 q^{22} +2690.82 q^{23} -133.678 q^{24} +5049.85 q^{25} +22.8645i q^{26} -3665.89i q^{27} -201.948 q^{28} +(3098.34 + 3303.24i) q^{29} +188.872 q^{30} +1909.79i q^{31} +255.223i q^{32} -12703.9 q^{33} -123.517 q^{34} +570.721 q^{35} -12440.2 q^{36} +9569.51i q^{37} +174.673 q^{38} +6915.79i q^{39} -480.836i q^{40} -18325.0i q^{41} +13.1859 q^{42} -6653.40i q^{43} +16169.3i q^{44} +35156.9 q^{45} +223.619i q^{46} -6494.11i q^{47} +25723.0i q^{48} -16767.2 q^{49} +419.665i q^{50} -37359.9 q^{51} +8802.27 q^{52} +13825.6 q^{53} +304.651 q^{54} -45695.7i q^{55} -33.5692i q^{56} +52833.1 q^{57} +(-274.514 + 257.486i) q^{58} -30295.3 q^{59} -72710.9i q^{60} +17014.3i q^{61} -158.712 q^{62} +2454.45 q^{63} +32725.6 q^{64} -24875.9 q^{65} -1055.75i q^{66} +42134.6 q^{67} +47550.9i q^{68} +67637.7i q^{69} +47.4294i q^{70} -45687.5 q^{71} -2067.89i q^{72} -56318.2i q^{73} -795.268 q^{74} +126935. i q^{75} -67244.9i q^{76} -3190.21i q^{77} -574.732 q^{78} +26403.0i q^{79} -92524.9 q^{80} -2340.79 q^{81} +1522.89 q^{82} +25549.1 q^{83} -5076.26i q^{84} -134382. i q^{85} +552.926 q^{86} +(-83031.7 + 77881.3i) q^{87} -2687.77 q^{88} -5785.59i q^{89} +2921.69i q^{90} -1736.69 q^{91} +86087.8 q^{92} -48005.3 q^{93} +539.689 q^{94} +190039. i q^{95} -6415.40 q^{96} +108843. i q^{97} -1393.42i q^{98} -196519. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 172 q^{4} + 46 q^{5} + 24 q^{6} + 20 q^{7} - 1574 q^{9}+O(q^{10}) \) 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

Modular forms

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