LMFDB - Embedded newform 289.10.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

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:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$1$
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} - 5 x^{11} - 4542 x^{10} + 30079 x^{9} + 7481825 x^{8} - 58373994 x^{7} - 5553197164 x^{6} + \cdots + 245077910606835 $ x^12 - 5x^11 - 4542x^10 + 30079x^9 + 7481825x^8 - 58373994x^7 - 5553197164x^6 + 45662797046x^5 + 1825619566875x^4 - 13493392282513x^3 - 214257360688838x^2 + 1064197876989579*x + 245077910606835
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$21.0274$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.0274 q^{2} -192.112 q^{3} -26.7930 q^{4} -2093.86 q^{5} -4231.72 q^{6} -11187.9 q^{7} -11868.2 q^{8} +17223.9 q^{9} +O(q^{10})$	\(q+22.0274 q^{2} -192.112 q^{3} -26.7930 q^{4} -2093.86 q^{5} -4231.72 q^{6} -11187.9 q^{7} -11868.2 q^{8} +17223.9 q^{9} -46122.3 q^{10} +32343.5 q^{11} +5147.26 q^{12} -53797.9 q^{13} -246440. q^{14} +402255. q^{15} -247708. q^{16} +379398. q^{18} +834504. q^{19} +56100.9 q^{20} +2.14933e6 q^{21} +712444. q^{22} +880984. q^{23} +2.28002e6 q^{24} +2.43112e6 q^{25} -1.18503e6 q^{26} +472424. q^{27} +299758. q^{28} -6.20562e6 q^{29} +8.86063e6 q^{30} +2.41097e6 q^{31} +620159. q^{32} -6.21357e6 q^{33} +2.34259e7 q^{35} -461480. q^{36} -1.92707e7 q^{37} +1.83820e7 q^{38} +1.03352e7 q^{39} +2.48504e7 q^{40} -1.42804e7 q^{41} +4.73441e7 q^{42} +3.24601e7 q^{43} -866581. q^{44} -3.60644e7 q^{45} +1.94058e7 q^{46} -2.93237e7 q^{47} +4.75876e7 q^{48} +8.48154e7 q^{49} +5.35513e7 q^{50} +1.44141e6 q^{52} -3.32529e7 q^{53} +1.04063e7 q^{54} -6.77228e7 q^{55} +1.32780e8 q^{56} -1.60318e8 q^{57} -1.36694e8 q^{58} -7.73279e6 q^{59} -1.07776e7 q^{60} +7.26723e6 q^{61} +5.31074e7 q^{62} -1.92699e8 q^{63} +1.40487e8 q^{64} +1.12645e8 q^{65} -1.36869e8 q^{66} +1.10825e7 q^{67} -1.69247e8 q^{69} +5.16012e8 q^{70} -1.06518e8 q^{71} -2.04417e8 q^{72} +2.10366e8 q^{73} -4.24483e8 q^{74} -4.67047e8 q^{75} -2.23589e7 q^{76} -3.61856e8 q^{77} +2.27658e8 q^{78} +2.66752e8 q^{79} +5.18666e8 q^{80} -4.29776e8 q^{81} -3.14559e8 q^{82} +3.11305e8 q^{83} -5.75870e7 q^{84} +7.15012e8 q^{86} +1.19217e9 q^{87} -3.83860e8 q^{88} -9.51149e8 q^{89} -7.94405e8 q^{90} +6.01886e8 q^{91} -2.36042e7 q^{92} -4.63175e8 q^{93} -6.45925e8 q^{94} -1.74733e9 q^{95} -1.19140e8 q^{96} +6.34102e8 q^{97} +1.86826e9 q^{98} +5.57081e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) $ 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9} + 2449 q^{10} - 152886 q^{11} - 41717 q^{12} + 23478 q^{13} - 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} + 2477218 q^{20} - 1395256 q^{21} - 2391095 q^{22} - 2012428 q^{23} - 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} - 3231638 q^{27} + 5978216 q^{28} - 12772842 q^{29} + 181633 q^{30} - 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} - 1352872 q^{37} + 3704404 q^{38} + 1380780 q^{39} - 44739331 q^{40} - 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} - 148233417 q^{44} + 79449336 q^{45} - 31855859 q^{46} + 133558002 q^{47} + 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} + 50215469 q^{54} - 91197532 q^{55} - 267350757 q^{56} - 49507694 q^{57} - 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} - 262041240 q^{61} + 314328847 q^{62} - 218532626 q^{63} + 595820098 q^{64} - 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} - 204290852 q^{71} - 208030791 q^{72} - 673538852 q^{73} - 1274510282 q^{74} - 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} - 165043245 q^{78} - 434002980 q^{79} - 599590757 q^{80} - 389011392 q^{81} + 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} + 262108460 q^{88} + 911678128 q^{89} + 2734590475 q^{90} + 560105446 q^{91} + 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} + 1116511966 q^{95} - 2204198979 q^{96} + 3589270998 q^{97} - 2677144485 q^{98} - 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9 + 2449 * q^10 - 152886 * q^11 - 41717 * q^12 + 23478 * q^13 - 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 + 2477218 * q^20 - 1395256 * q^21 - 2391095 * q^22 - 2012428 * q^23 - 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 - 3231638 * q^27 + 5978216 * q^28 - 12772842 * q^29 + 181633 * q^30 - 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 - 1352872 * q^37 + 3704404 * q^38 + 1380780 * q^39 - 44739331 * q^40 - 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 - 148233417 * q^44 + 79449336 * q^45 - 31855859 * q^46 + 133558002 * q^47 + 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 + 50215469 * q^54 - 91197532 * q^55 - 267350757 * q^56 - 49507694 * q^57 - 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 - 262041240 * q^61 + 314328847 * q^62 - 218532626 * q^63 + 595820098 * q^64 - 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 - 204290852 * q^71 - 208030791 * q^72 - 673538852 * q^73 - 1274510282 * q^74 - 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 - 165043245 * q^78 - 434002980 * q^79 - 599590757 * q^80 - 389011392 * q^81 + 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 + 262108460 * q^88 + 911678128 * q^89 + 2734590475 * q^90 + 560105446 * q^91 + 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 + 1116511966 * q^95 - 2204198979 * q^96 + 3589270998 * q^97 - 2677144485 * q^98 - 2056683494 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	22.0274	0.973483	0.486742	−	0.873546i	$-0.338185\pi$
$2$	22.0274	0.973483	0.486742	+	0.873546i	$0.338185\pi$
$3$	−192.112	−1.36933	−0.684665	−	0.728858i	$-0.740051\pi$
$3$	−192.112	−1.36933	−0.684665	+	0.728858i	$0.740051\pi$
$4$	−26.7930	−0.0523302
$5$	−2093.86	−1.49824	−0.749122	−	0.662432i	$-0.769524\pi$
$5$	−2093.86	−1.49824	−0.749122	+	0.662432i	$0.769524\pi$
$6$	−4231.72	−1.33302
$7$	−11187.9	−1.76119	−0.880597	−	0.473866i	$-0.842858\pi$
$7$	−11187.9	−1.76119	−0.880597	+	0.473866i	$0.842858\pi$
$8$	−11868.2	−1.02443
$9$	17223.9	0.875064
$10$	−46122.3	−1.45852
$11$	32343.5	0.666070	0.333035	−	0.942914i	$-0.391927\pi$
$11$	32343.5	0.666070	0.333035	+	0.942914i	$0.391927\pi$
$12$	5147.26	0.0716573
$13$	−53797.9	−0.522421	−0.261210	−	0.965282i	$-0.584122\pi$
$13$	−53797.9	−0.522421	−0.261210	+	0.965282i	$0.584122\pi$
$14$	−246440.	−1.71449
$15$	402255.	2.05159
$16$	−247708.	−0.944931
$17$	0	0
$17$	0	0
$18$	379398.	0.851860
$19$	834504.	1.46905	0.734526	−	0.678580i	$-0.237404\pi$
$19$	834504.	1.46905	0.734526	+	0.678580i	$0.237404\pi$
$20$	56100.9	0.0784033
$21$	2.14933e6	2.41166
$22$	712444.	0.648408
$23$	880984.	0.656437	0.328218	−	0.944602i	$-0.393552\pi$
$23$	880984.	0.656437	0.328218	+	0.944602i	$0.393552\pi$
$24$	2.28002e6	1.40278
$25$	2.43112e6	1.24473
$26$	−1.18503e6	−0.508568
$27$	472424.	0.171078
$28$	299758.	0.0921636
$29$	−6.20562e6	−1.62927	−0.814637	−	0.579972i	$-0.803064\pi$
$29$	−6.20562e6	−1.62927	−0.814637	+	0.579972i	$0.803064\pi$
$30$	8.86063e6	1.99719
$31$	2.41097e6	0.468882	0.234441	−	0.972130i	$-0.424674\pi$
$31$	2.41097e6	0.468882	0.234441	+	0.972130i	$0.424674\pi$
$32$	620159.	0.104551
$33$	−6.21357e6	−0.912070
$34$	0	0
$35$	2.34259e7	2.63870
$36$	−461480.	−0.0457922
$37$	−1.92707e7	−1.69040	−0.845200	−	0.534451i	$-0.820518\pi$
$37$	−1.92707e7	−1.69040	−0.845200	+	0.534451i	$0.820518\pi$
$38$	1.83820e7	1.43010
$39$	1.03352e7	0.715366
$40$	2.48504e7	1.53484
$41$	−1.42804e7	−0.789245	−0.394622	−	0.918843i	$-0.629125\pi$
$41$	−1.42804e7	−0.789245	−0.394622	+	0.918843i	$0.629125\pi$
$42$	4.73441e7	2.34771
$43$	3.24601e7	1.44791	0.723956	−	0.689847i	$-0.242322\pi$
$43$	3.24601e7	1.44791	0.723956	+	0.689847i	$0.242322\pi$
$44$	−866581.	−0.0348556
$45$	−3.60644e7	−1.31106
$46$	1.94058e7	0.639030
$47$	−2.93237e7	−0.876554	−0.438277	−	0.898840i	$-0.644411\pi$
$47$	−2.93237e7	−0.876554	−0.438277	+	0.898840i	$0.644411\pi$
$48$	4.75876e7	1.29392
$49$	8.48154e7	2.10181
$50$	5.35513e7	1.21173
$51$	0	0
$52$	1.44141e6	0.0273384
$53$	−3.32529e7	−0.578879	−0.289440	−	0.957196i	$-0.593469\pi$
$53$	−3.32529e7	−0.578879	−0.289440	+	0.957196i	$0.593469\pi$
$54$	1.04063e7	0.166542
$55$	−6.77228e7	−0.997936
$56$	1.32780e8	1.80421
$57$	−1.60318e8	−2.01162
$58$	−1.36694e8	−1.58607
$59$	−7.73279e6	−0.0830811	−0.0415405	−	0.999137i	$-0.513227\pi$
$59$	−7.73279e6	−0.0830811	−0.0415405	+	0.999137i	$0.513227\pi$
$60$	−1.07776e7	−0.107360
$61$	7.26723e6	0.0672024	0.0336012	−	0.999435i	$-0.489302\pi$
$61$	7.26723e6	0.0672024	0.0336012	+	0.999435i	$0.489302\pi$
$62$	5.31074e7	0.456449
$63$	−1.92699e8	−1.54116
$64$	1.40487e8	1.04671
$65$	1.12645e8	0.782714
$66$	−1.36869e8	−0.887885
$67$	1.10825e7	0.0671895	0.0335947	−	0.999436i	$-0.489304\pi$
$67$	1.10825e7	0.0671895	0.0335947	+	0.999436i	$0.489304\pi$
$68$	0	0
$69$	−1.69247e8	−0.898878
$70$	5.16012e8	2.56873
$71$	−1.06518e8	−0.497464	−0.248732	−	0.968572i	$-0.580014\pi$
$71$	−1.06518e8	−0.497464	−0.248732	+	0.968572i	$0.580014\pi$
$72$	−2.04417e8	−0.896438
$73$	2.10366e8	0.867009	0.433505	−	0.901151i	$-0.357277\pi$
$73$	2.10366e8	0.867009	0.433505	+	0.901151i	$0.357277\pi$
$74$	−4.24483e8	−1.64558
$75$	−4.67047e8	−1.70445
$76$	−2.23589e7	−0.0768758
$77$	−3.61856e8	−1.17308
$78$	2.27658e8	0.696397
$79$	2.66752e8	0.770523	0.385262	−	0.922807i	$-0.374111\pi$
$79$	2.66752e8	0.770523	0.385262	+	0.922807i	$0.374111\pi$
$80$	5.18666e8	1.41574
$81$	−4.29776e8	−1.10933
$82$	−3.14559e8	−0.768317
$83$	3.11305e8	0.720004	0.360002	−	0.932951i	$-0.382776\pi$
$83$	3.11305e8	0.720004	0.360002	+	0.932951i	$0.382776\pi$
$84$	−5.75870e7	−0.126202
$85$	0	0
$86$	7.15012e8	1.40952
$87$	1.19217e9	2.23101
$88$	−3.83860e8	−0.682340
$89$	−9.51149e8	−1.60692	−0.803459	−	0.595360i	$-0.797009\pi$
$89$	−9.51149e8	−1.60692	−0.803459	+	0.595360i	$0.797009\pi$
$90$	−7.94405e8	−1.27629
$91$	6.01886e8	0.920085
$92$	−2.36042e7	−0.0343514
$93$	−4.63175e8	−0.642054
$94$	−6.45925e8	−0.853310
$95$	−1.74733e9	−2.20100
$96$	−1.19140e8	−0.143165
$97$	6.34102e8	0.727255	0.363627	−	0.931544i	$-0.381538\pi$
$97$	6.34102e8	0.727255	0.363627	+	0.931544i	$0.381538\pi$
$98$	1.86826e9	2.04607
$99$	5.57081e8	0.582854
$100$	−6.51371e7	−0.0651371
$101$	−2.38911e8	−0.228450	−0.114225	−	0.993455i	$-0.536438\pi$
$101$	−2.38911e8	−0.228450	−0.114225	+	0.993455i	$0.536438\pi$
$102$	0	0
$103$	1.98732e9	1.73980	0.869900	−	0.493228i	$-0.164183\pi$
$103$	1.98732e9	1.73980	0.869900	+	0.493228i	$0.164183\pi$
$104$	6.38485e8	0.535181
$105$	−4.50038e9	−3.61325
$106$	−7.32475e8	−0.563529
$107$	2.01336e9	1.48489	0.742444	−	0.669908i	$-0.233666\pi$
$107$	2.01336e9	1.48489	0.742444	+	0.669908i	$0.233666\pi$
$108$	−1.26577e7	−0.00895256
$109$	1.10506e9	0.749839	0.374920	−	0.927057i	$-0.377670\pi$
$109$	1.10506e9	0.749839	0.374920	+	0.927057i	$0.377670\pi$
$110$	−1.49176e9	−0.971474
$111$	3.70212e9	2.31471
$112$	2.77133e9	1.66421
$113$	−7.75240e8	−0.447284	−0.223642	−	0.974671i	$-0.571795\pi$
$113$	−7.75240e8	−0.447284	−0.223642	+	0.974671i	$0.571795\pi$
$114$	−3.53139e9	−1.95828
$115$	−1.84466e9	−0.983502
$116$	1.66267e8	0.0852601
$117$	−9.26609e8	−0.457152
$118$	−1.70333e8	−0.0808780
$119$	0	0
$120$	−4.77405e9	−2.10170
$121$	−1.31184e9	−0.556350
$122$	1.60078e8	0.0654204
$123$	2.74342e9	1.08074
$124$	−6.45971e7	−0.0245367
$125$	−1.00086e9	−0.366671
$126$	−4.24466e9	−1.50029
$127$	2.09809e9	0.715661	0.357831	−	0.933787i	$-0.383517\pi$
$127$	2.09809e9	0.715661	0.357831	+	0.933787i	$0.383517\pi$
$128$	2.77704e9	0.914404
$129$	−6.23596e9	−1.98267
$130$	2.48128e9	0.761959
$131$	−2.53377e9	−0.751704	−0.375852	−	0.926680i	$-0.622650\pi$
$131$	−2.53377e9	−0.751704	−0.375852	+	0.926680i	$0.622650\pi$
$132$	1.66480e8	0.0477288
$133$	−9.33635e9	−2.58729
$134$	2.44119e8	0.0654078
$135$	−9.89190e8	−0.256317
$136$	0	0
$137$	4.62037e9	1.12056	0.560279	−	0.828304i	$-0.310694\pi$
$137$	4.62037e9	1.12056	0.560279	+	0.828304i	$0.310694\pi$
$138$	−3.72808e9	−0.875043
$139$	4.01724e9	0.912769	0.456385	−	0.889783i	$-0.349144\pi$
$139$	4.01724e9	0.912769	0.456385	+	0.889783i	$0.349144\pi$
$140$	−6.27651e8	−0.138084
$141$	5.63343e9	1.20029
$142$	−2.34632e9	−0.484273
$143$	−1.74001e9	−0.347969
$144$	−4.26650e9	−0.826876
$145$	1.29937e10	2.44105
$146$	4.63383e9	0.844019
$147$	−1.62940e10	−2.87807
$148$	5.16320e8	0.0884589
$149$	8.66524e8	0.144027	0.0720133	−	0.997404i	$-0.477058\pi$
$149$	8.66524e8	0.144027	0.0720133	+	0.997404i	$0.477058\pi$
$150$	−1.02878e10	−1.65925
$151$	−7.29819e9	−1.14240	−0.571201	−	0.820810i	$-0.693522\pi$
$151$	−7.29819e9	−1.14240	−0.571201	+	0.820810i	$0.693522\pi$
$152$	−9.90408e9	−1.50494
$153$	0	0
$154$	−7.97075e9	−1.14197
$155$	−5.04822e9	−0.702500
$156$	−2.76912e8	−0.0374352
$157$	−6.63285e9	−0.871268	−0.435634	−	0.900124i	$-0.643476\pi$
$157$	−6.63285e9	−0.871268	−0.435634	+	0.900124i	$0.643476\pi$
$158$	5.87586e9	0.750092
$159$	6.38827e9	0.792677
$160$	−1.29852e9	−0.156643
$161$	−9.85636e9	−1.15611
$162$	−9.46685e9	−1.07991
$163$	9.09277e9	1.00891	0.504454	−	0.863438i	$-0.331694\pi$
$163$	9.09277e9	1.00891	0.504454	+	0.863438i	$0.331694\pi$
$164$	3.82614e8	0.0413013
$165$	1.30103e10	1.36650
$166$	6.85725e9	0.700912
$167$	7.36183e9	0.732422	0.366211	−	0.930532i	$-0.380655\pi$
$167$	7.36183e9	0.732422	0.366211	+	0.930532i	$0.380655\pi$
$168$	−2.55087e10	−2.47056
$169$	−7.71028e9	−0.727077
$170$	0	0
$171$	1.43734e10	1.28552
$172$	−8.69705e8	−0.0757694
$173$	−6.55593e9	−0.556451	−0.278225	−	0.960516i	$-0.589746\pi$
$173$	−6.55593e9	−0.556451	−0.278225	+	0.960516i	$0.589746\pi$
$174$	2.62604e10	2.17185
$175$	−2.71991e10	−2.19222
$176$	−8.01175e9	−0.629391
$177$	1.48556e9	0.113765
$178$	−2.09514e10	−1.56431
$179$	−5.14265e9	−0.374410	−0.187205	−	0.982321i	$-0.559943\pi$
$179$	−5.14265e9	−0.374410	−0.187205	+	0.982321i	$0.559943\pi$
$180$	9.66275e8	0.0686079
$181$	2.46859e9	0.170960	0.0854801	−	0.996340i	$-0.472758\pi$
$181$	2.46859e9	0.170960	0.0854801	+	0.996340i	$0.472758\pi$
$182$	1.32580e10	0.895687
$183$	−1.39612e9	−0.0920222
$184$	−1.04557e10	−0.672471
$185$	4.03501e10	2.53263
$186$	−1.02025e10	−0.625029
$187$	0	0
$188$	7.85671e8	0.0458702
$189$	−5.28543e9	−0.301302
$190$	−3.84893e10	−2.14264
$191$	1.63189e10	0.887241	0.443621	−	0.896215i	$-0.353694\pi$
$191$	1.63189e10	0.887241	0.443621	+	0.896215i	$0.353694\pi$
$192$	−2.69892e10	−1.43329
$193$	−2.79846e9	−0.145182	−0.0725909	−	0.997362i	$-0.523127\pi$
$193$	−2.79846e9	−0.145182	−0.0725909	+	0.997362i	$0.523127\pi$
$194$	1.39676e10	0.707970
$195$	−2.16405e10	−1.07179
$196$	−2.27246e9	−0.109988
$197$	1.01263e10	0.479021	0.239511	−	0.970894i	$-0.423013\pi$
$197$	1.01263e10	0.479021	0.239511	+	0.970894i	$0.423013\pi$
$198$	1.22711e10	0.567399
$199$	−9.52805e9	−0.430690	−0.215345	−	0.976538i	$-0.569088\pi$
$199$	−9.52805e9	−0.430690	−0.215345	+	0.976538i	$0.569088\pi$
$200$	−2.88531e10	−1.27514
$201$	−2.12908e9	−0.0920046
$202$	−5.26260e9	−0.222392
$203$	6.94278e10	2.86947
$204$	0	0
$205$	2.99011e10	1.18248
$206$	4.37754e10	1.69367
$207$	1.51740e10	0.574424
$208$	1.33262e10	0.493652
$209$	2.69908e10	0.978492
$210$	−9.91318e10	−3.51744
$211$	−6.13785e9	−0.213179	−0.106590	−	0.994303i	$-0.533993\pi$
$211$	−6.13785e9	−0.213179	−0.106590	+	0.994303i	$0.533993\pi$
$212$	8.90946e8	0.0302929
$213$	2.04634e10	0.681192
$214$	4.43491e10	1.44551
$215$	−6.79669e10	−2.16932
$216$	−5.60683e9	−0.175257
$217$	−2.69736e10	−0.825792
$218$	2.43417e10	0.729956
$219$	−4.04139e10	−1.18722
$220$	1.81450e9	0.0522221
$221$	0	0
$222$	8.15482e10	2.25334
$223$	−3.31145e10	−0.896698	−0.448349	−	0.893859i	$-0.647988\pi$
$223$	−3.31145e10	−0.896698	−0.448349	+	0.893859i	$0.647988\pi$
$224$	−6.93827e9	−0.184134
$225$	4.18734e10	1.08922
$226$	−1.70765e10	−0.435423
$227$	−7.35128e10	−1.83758	−0.918790	−	0.394746i	$-0.870833\pi$
$227$	−7.35128e10	−1.83758	−0.918790	+	0.394746i	$0.870833\pi$
$228$	4.29541e9	0.105268
$229$	−9.70641e9	−0.233238	−0.116619	−	0.993177i	$-0.537206\pi$
$229$	−9.70641e9	−0.233238	−0.116619	+	0.993177i	$0.537206\pi$
$230$	−4.06330e10	−0.957423
$231$	6.95167e10	1.60633
$232$	7.36496e10	1.66907
$233$	5.50002e10	1.22254	0.611269	−	0.791423i	$-0.290659\pi$
$233$	5.50002e10	1.22254	0.611269	+	0.791423i	$0.290659\pi$
$234$	−2.04108e10	−0.445030
$235$	6.13997e10	1.31329
$236$	2.07185e8	0.00434765
$237$	−5.12462e10	−1.05510
$238$	0	0
$239$	6.66884e10	1.32209	0.661043	−	0.750348i	$-0.270114\pi$
$239$	6.66884e10	1.32209	0.661043	+	0.750348i	$0.270114\pi$
$240$	−9.96418e10	−1.93861
$241$	7.40099e10	1.41323	0.706616	−	0.707598i	$-0.250221\pi$
$241$	7.40099e10	1.41323	0.706616	+	0.707598i	$0.250221\pi$
$242$	−2.88965e10	−0.541598
$243$	7.32662e10	1.34796
$244$	−1.94711e8	−0.00351671
$245$	−1.77592e11	−3.14902
$246$	6.04305e10	1.05208
$247$	−4.48946e10	−0.767464
$248$	−2.86139e10	−0.480335
$249$	−5.98054e10	−0.985924
$250$	−2.20463e10	−0.356948
$251$	−6.27273e9	−0.0997527	−0.0498763	−	0.998755i	$-0.515883\pi$
$251$	−6.27273e9	−0.0997527	−0.0498763	+	0.998755i	$0.515883\pi$
$252$	5.16299e9	0.0806491
$253$	2.84941e10	0.437233
$254$	4.62155e10	0.696684
$255$	0	0
$256$	−1.07582e10	−0.156553
$257$	4.32445e10	0.618346	0.309173	−	0.951006i	$-0.399948\pi$
$257$	4.32445e10	0.618346	0.309173	+	0.951006i	$0.399948\pi$
$258$	−1.37362e11	−1.93009
$259$	2.15598e11	2.97712
$260$	−3.01811e9	−0.0409595
$261$	−1.06885e11	−1.42572
$262$	−5.58124e10	−0.731771
$263$	−3.37974e10	−0.435595	−0.217797	−	0.975994i	$-0.569887\pi$
$263$	−3.37974e10	−0.435595	−0.217797	+	0.975994i	$0.569887\pi$
$264$	7.37439e10	0.934348
$265$	6.96269e10	0.867302
$266$	−2.05656e11	−2.51868
$267$	1.82727e11	2.20040
$268$	−2.96934e8	−0.00351604
$269$	−1.41140e11	−1.64348	−0.821738	−	0.569865i	$-0.806995\pi$
$269$	−1.41140e11	−1.64348	−0.821738	+	0.569865i	$0.806995\pi$
$270$	−2.17893e10	−0.249520
$271$	−1.13865e11	−1.28242	−0.641209	−	0.767366i	$-0.721567\pi$
$271$	−1.13865e11	−1.28242	−0.641209	+	0.767366i	$0.721567\pi$
$272$	0	0
$273$	−1.15629e11	−1.25990
$274$	1.01775e11	1.09084
$275$	7.86310e10	0.829080
$276$	4.53465e9	0.0470384
$277$	9.38037e10	0.957329	0.478664	−	0.877998i	$-0.341121\pi$
$277$	9.38037e10	0.957329	0.478664	+	0.877998i	$0.341121\pi$
$278$	8.84894e10	0.888566
$279$	4.15262e10	0.410302
$280$	−2.78023e11	−2.70315
$281$	−1.31336e10	−0.125662	−0.0628311	−	0.998024i	$-0.520013\pi$
$281$	−1.31336e10	−0.125662	−0.0628311	+	0.998024i	$0.520013\pi$
$282$	1.24090e11	1.16846
$283$	6.46056e10	0.598730	0.299365	−	0.954139i	$-0.403225\pi$
$283$	6.46056e10	0.598730	0.299365	+	0.954139i	$0.403225\pi$
$284$	2.85395e9	0.0260324
$285$	3.35683e11	3.01389
$286$	−3.83280e10	−0.338742
$287$	1.59767e11	1.39001
$288$	1.06815e10	0.0914888
$289$	0	0
$290$	2.86217e11	2.37632
$291$	−1.21818e11	−0.995852
$292$	−5.63636e9	−0.0453707
$293$	3.15727e10	0.250269	0.125135	−	0.992140i	$-0.460064\pi$
$293$	3.15727e10	0.250269	0.125135	+	0.992140i	$0.460064\pi$
$294$	−3.58915e11	−2.80175
$295$	1.61914e10	0.124476
$296$	2.28709e11	1.73169
$297$	1.52799e10	0.113950
$298$	1.90873e10	0.140207
$299$	−4.73951e10	−0.342936
$300$	1.25136e10	0.0891942
$301$	−3.63160e11	−2.55005
$302$	−1.60760e11	−1.11211
$303$	4.58977e10	0.312823
$304$	−2.06713e11	−1.38815
$305$	−1.52166e10	−0.100686
$306$	0	0
$307$	−2.96457e11	−1.90476	−0.952378	−	0.304920i	$-0.901370\pi$
$307$	−2.96457e11	−1.90476	−0.952378	+	0.304920i	$0.901370\pi$
$308$	9.69522e9	0.0613874
$309$	−3.81786e11	−2.38236
$310$	−1.11199e11	−0.683872
$311$	−1.05806e11	−0.641339	−0.320669	−	0.947191i	$-0.603908\pi$
$311$	−1.05806e11	−0.641339	−0.320669	+	0.947191i	$0.603908\pi$
$312$	−1.22661e11	−0.732840
$313$	−1.05491e11	−0.621252	−0.310626	−	0.950532i	$-0.600539\pi$
$313$	−1.05491e11	−0.621252	−0.310626	+	0.950532i	$0.600539\pi$
$314$	−1.46105e11	−0.848165
$315$	4.03485e11	2.30903
$316$	−7.14710e9	−0.0403216
$317$	−3.62934e9	−0.0201865	−0.0100933	−	0.999949i	$-0.503213\pi$
$317$	−3.62934e9	−0.0201865	−0.0100933	+	0.999949i	$0.503213\pi$
$318$	1.40717e11	0.771658
$319$	−2.00711e11	−1.08521
$320$	−2.94160e11	−1.56823
$321$	−3.86789e11	−2.03330
$322$	−2.17110e11	−1.12546
$323$	0	0
$324$	1.15150e10	0.0580513
$325$	−1.30789e11	−0.650275
$326$	2.00290e11	0.982156
$327$	−2.12296e11	−1.02678
$328$	1.69482e11	0.808523
$329$	3.28071e11	1.54378
$330$	2.86584e11	1.33027
$331$	1.00989e11	0.462433	0.231216	−	0.972902i	$-0.425729\pi$
$331$	1.00989e11	0.462433	0.231216	+	0.972902i	$0.425729\pi$
$332$	−8.34082e9	−0.0376780
$333$	−3.31916e11	−1.47921
$334$	1.62162e11	0.713001
$335$	−2.32052e10	−0.100666
$336$	−5.32405e11	−2.27885
$337$	−3.68879e11	−1.55794	−0.778968	−	0.627064i	$-0.784257\pi$
$337$	−3.68879e11	−1.55794	−0.778968	+	0.627064i	$0.784257\pi$
$338$	−1.69838e11	−0.707797
$339$	1.48933e11	0.612479
$340$	0	0
$341$	7.79791e10	0.312308
$342$	3.16609e11	1.25143
$343$	−4.97434e11	−1.94049
$344$	−3.85244e11	−1.48328
$345$	3.54380e11	1.34674
$346$	−1.44410e11	−0.541695
$347$	−6.55187e10	−0.242596	−0.121298	−	0.992616i	$-0.538706\pi$
$347$	−6.55187e10	−0.242596	−0.121298	+	0.992616i	$0.538706\pi$
$348$	−3.19419e10	−0.116749
$349$	4.32432e9	0.0156028	0.00780142	−	0.999970i	$-0.497517\pi$
$349$	4.32432e9	0.0156028	0.00780142	+	0.999970i	$0.497517\pi$
$350$	−5.99127e11	−2.13409
$351$	−2.54154e10	−0.0893749
$352$	2.00581e10	0.0696383
$353$	6.69813e10	0.229598	0.114799	−	0.993389i	$-0.463378\pi$
$353$	6.69813e10	0.229598	0.114799	+	0.993389i	$0.463378\pi$
$354$	3.27230e10	0.110749
$355$	2.23034e11	0.745322
$356$	2.54842e10	0.0840903
$357$	0	0
$358$	−1.13279e11	−0.364482
$359$	−4.88297e11	−1.55153	−0.775764	−	0.631024i	$-0.782635\pi$
$359$	−4.88297e11	−1.55153	−0.775764	+	0.631024i	$0.782635\pi$
$360$	4.28020e11	1.34308
$361$	3.73709e11	1.15812
$362$	5.43766e10	0.166427
$363$	2.52021e11	0.761827
$364$	−1.61263e10	−0.0481482
$365$	−4.40478e11	−1.29899
$366$	−3.07529e10	−0.0895821
$367$	5.20006e11	1.49627	0.748137	−	0.663544i	$-0.230949\pi$
$367$	5.20006e11	1.49627	0.748137	+	0.663544i	$0.230949\pi$
$368$	−2.18227e11	−0.620288
$369$	−2.45963e11	−0.690640
$370$	8.88808e11	2.46547
$371$	3.72030e11	1.01952
$372$	1.24099e10	0.0335988
$373$	3.62135e11	0.968681	0.484341	−	0.874880i	$-0.339060\pi$
$373$	3.62135e11	0.968681	0.484341	+	0.874880i	$0.339060\pi$
$374$	0	0
$375$	1.92276e11	0.502094
$376$	3.48020e11	0.897964
$377$	3.33849e11	0.851166
$378$	−1.16424e11	−0.293313
$379$	4.48802e11	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$379$	4.48802e11	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$380$	4.68164e10	0.115179
$381$	−4.03068e11	−0.979976
$382$	3.59464e11	0.863715
$383$	4.03072e11	0.957167	0.478583	−	0.878042i	$-0.341150\pi$
$383$	4.03072e11	0.957167	0.478583	+	0.878042i	$0.341150\pi$
$384$	−5.33503e11	−1.25212
$385$	7.57675e11	1.75756
$386$	−6.16429e10	−0.141332
$387$	5.59089e11	1.26702
$388$	−1.69895e10	−0.0380574
$389$	2.94343e11	0.651749	0.325874	−	0.945413i	$-0.394341\pi$
$389$	2.94343e11	0.651749	0.325874	+	0.945413i	$0.394341\pi$
$390$	−4.76684e11	−1.04337
$391$	0	0
$392$	−1.00661e12	−2.15314
$393$	4.86767e11	1.02933
$394$	2.23057e11	0.466319
$395$	−5.58541e11	−1.15443
$396$	−1.49259e10	−0.0305009
$397$	4.25340e11	0.859368	0.429684	−	0.902979i	$-0.358625\pi$
$397$	4.25340e11	0.859368	0.429684	+	0.902979i	$0.358625\pi$
$398$	−2.09878e11	−0.419270
$399$	1.79362e12	3.54285
$400$	−6.02208e11	−1.17619
$401$	9.97575e11	1.92662	0.963310	−	0.268391i	$-0.0864920\pi$
$401$	9.97575e11	1.92662	0.963310	+	0.268391i	$0.0864920\pi$
$402$	−4.68981e10	−0.0895649
$403$	−1.29705e11	−0.244954
$404$	6.40116e9	0.0119548
$405$	8.99890e11	1.66204
$406$	1.52931e12	2.79338
$407$	−6.23281e11	−1.12592
$408$	0	0
$409$	−2.15490e11	−0.380778	−0.190389	−	0.981709i	$-0.560975\pi$
$409$	−2.15490e11	−0.380778	−0.190389	+	0.981709i	$0.560975\pi$
$410$	6.58643e11	1.15113
$411$	−8.87627e11	−1.53441
$412$	−5.32462e10	−0.0910440
$413$	8.65136e10	0.146322
$414$	3.34243e11	0.559192
$415$	−6.51830e11	−1.07874
$416$	−3.33632e10	−0.0546196
$417$	−7.71758e11	−1.24988
$418$	5.94537e11	0.952546
$419$	−9.55629e11	−1.51470	−0.757349	−	0.653010i	$-0.773506\pi$
$419$	−9.55629e11	−1.51470	−0.757349	+	0.653010i	$0.773506\pi$
$420$	1.20579e11	0.189082
$421$	5.62766e11	0.873089	0.436544	−	0.899683i	$-0.356202\pi$
$421$	5.62766e11	0.873089	0.436544	+	0.899683i	$0.356202\pi$
$422$	−1.35201e11	−0.207527
$423$	−5.05068e11	−0.767041
$424$	3.94653e11	0.593019
$425$	0	0
$426$	4.50756e11	0.663129
$427$	−8.13050e10	−0.118356
$428$	−5.39440e10	−0.0777045
$429$	3.34277e11	0.476484
$430$	−1.49713e12	−2.11180
$431$	3.14107e11	0.438460	0.219230	−	0.975673i	$-0.429646\pi$
$431$	3.14107e11	0.438460	0.219230	+	0.975673i	$0.429646\pi$
$432$	−1.17023e11	−0.161657
$433$	4.38260e11	0.599152	0.299576	−	0.954072i	$-0.403155\pi$
$433$	4.38260e11	0.599152	0.299576	+	0.954072i	$0.403155\pi$
$434$	−5.94160e11	−0.803895
$435$	−2.49624e12	−3.34260
$436$	−2.96080e10	−0.0392392
$437$	7.35185e11	0.964340
$438$	−8.90213e11	−1.15574
$439$	9.65559e11	1.24076	0.620381	−	0.784301i	$-0.286978\pi$
$439$	9.65559e11	1.24076	0.620381	+	0.784301i	$0.286978\pi$
$440$	8.03748e11	1.02231
$441$	1.46085e12	1.83921
$442$	0	0
$443$	4.24416e11	0.523570	0.261785	−	0.965126i	$-0.415689\pi$
$443$	4.24416e11	0.523570	0.261785	+	0.965126i	$0.415689\pi$
$444$	−9.91911e10	−0.121129
$445$	1.99157e12	2.40755
$446$	−7.29426e11	−0.872920
$447$	−1.66469e11	−0.197220
$448$	−1.57175e12	−1.84346
$449$	1.59292e12	1.84963	0.924816	−	0.380415i	$-0.124219\pi$
$449$	1.59292e12	1.84963	0.924816	+	0.380415i	$0.124219\pi$
$450$	9.22362e11	1.06034
$451$	−4.61877e11	−0.525693
$452$	2.07710e10	0.0234064
$453$	1.40207e12	1.56433
$454$	−1.61930e12	−1.78885
$455$	−1.26026e12	−1.37851
$456$	1.90269e12	2.06075
$457$	3.59424e11	0.385464	0.192732	−	0.981251i	$-0.438265\pi$
$457$	3.59424e11	0.385464	0.192732	+	0.981251i	$0.438265\pi$
$458$	−2.13807e11	−0.227053
$459$	0	0
$460$	4.94240e10	0.0514668
$461$	−9.94006e11	−1.02503	−0.512513	−	0.858679i	$-0.671285\pi$
$461$	−9.94006e11	−1.02503	−0.512513	+	0.858679i	$0.671285\pi$
$462$	1.53127e12	1.56374
$463$	−1.21022e12	−1.22391	−0.611957	−	0.790891i	$-0.709617\pi$
$463$	−1.21022e12	−1.22391	−0.611957	+	0.790891i	$0.709617\pi$
$464$	1.53718e12	1.53955
$465$	9.69823e11	0.961954
$466$	1.21151e12	1.19012
$467$	−3.83160e11	−0.372781	−0.186391	−	0.982476i	$-0.559679\pi$
$467$	−3.83160e11	−0.372781	−0.186391	+	0.982476i	$0.559679\pi$
$468$	2.48267e10	0.0239228
$469$	−1.23990e11	−0.118334
$470$	1.35248e12	1.27847
$471$	1.27425e12	1.19305
$472$	9.17744e10	0.0851104
$473$	1.04987e12	0.964411
$474$	−1.12882e12	−1.02712
$475$	2.02878e12	1.82858
$476$	0	0
$477$	−5.72744e11	−0.506557
$478$	1.46897e12	1.28703
$479$	−1.71629e11	−0.148964	−0.0744818	−	0.997222i	$-0.523730\pi$
$479$	−1.71629e11	−0.148964	−0.0744818	+	0.997222i	$0.523730\pi$
$480$	2.49462e11	0.214496
$481$	1.03672e12	0.883100
$482$	1.63025e12	1.37576
$483$	1.89352e12	1.58310
$484$	3.51483e10	0.0291139
$485$	−1.32772e12	−1.08960
$486$	1.61387e12	1.31221
$487$	1.54372e12	1.24362	0.621811	−	0.783167i	$-0.286397\pi$
$487$	1.54372e12	1.24362	0.621811	+	0.783167i	$0.286397\pi$
$488$	−8.62491e10	−0.0688439
$489$	−1.74683e12	−1.38153
$490$	−3.91188e12	−3.06552
$491$	−2.12970e12	−1.65368	−0.826841	−	0.562436i	$-0.809864\pi$
$491$	−2.12970e12	−1.65368	−0.826841	+	0.562436i	$0.809864\pi$
$492$	−7.35047e10	−0.0565551
$493$	0	0
$494$	−9.88912e11	−0.747113
$495$	−1.16645e12	−0.873258
$496$	−5.97216e11	−0.443061
$497$	1.19172e12	0.876131
$498$	−1.31736e12	−0.959780
$499$	8.43312e10	0.0608886	0.0304443	−	0.999536i	$-0.490308\pi$
$499$	8.43312e10	0.0608886	0.0304443	+	0.999536i	$0.490308\pi$
$500$	2.68160e10	0.0191880
$501$	−1.41429e12	−1.00293
$502$	−1.38172e11	−0.0971076
$503$	−1.00908e12	−0.702863	−0.351432	−	0.936214i	$-0.614305\pi$
$503$	−1.00908e12	−0.702863	−0.351432	+	0.936214i	$0.614305\pi$
$504$	2.28699e12	1.57880
$505$	5.00247e11	0.342273
$506$	6.27652e11	0.425639
$507$	1.48124e12	0.995608
$508$	−5.62142e10	−0.0374507
$509$	1.11028e11	0.0733163	0.0366582	−	0.999328i	$-0.488329\pi$
$509$	1.11028e11	0.0733163	0.0366582	+	0.999328i	$0.488329\pi$
$510$	0	0
$511$	−2.35356e12	−1.52697
$512$	−1.65882e12	−1.06681
$513$	3.94240e11	0.251323
$514$	9.52565e11	0.601950
$515$	−4.16116e12	−2.60664
$516$	1.67080e11	0.103753
$517$	−9.48432e11	−0.583846
$518$	4.74907e12	2.89818
$519$	1.25947e12	0.761965
$520$	−1.33690e12	−0.801832
$521$	−7.35215e11	−0.437164	−0.218582	−	0.975819i	$-0.570143\pi$
$521$	−7.35215e11	−0.437164	−0.218582	+	0.975819i	$0.570143\pi$
$522$	−2.35440e12	−1.38791
$523$	1.82881e12	1.06883	0.534417	−	0.845221i	$-0.320531\pi$
$523$	1.82881e12	1.06883	0.534417	+	0.845221i	$0.320531\pi$
$524$	6.78875e10	0.0393368
$525$	5.22527e12	3.00187
$526$	−7.44469e11	−0.424044
$527$	0	0
$528$	1.53915e12	0.861844
$529$	−1.02502e12	−0.569091
$530$	1.53370e12	0.844304
$531$	−1.33189e11	−0.0727013
$532$	2.50149e11	0.135393
$533$	7.68254e11	0.412318
$534$	4.02500e12	2.14205
$535$	−4.21569e12	−2.22472
$536$	−1.31530e11	−0.0688306
$537$	9.87962e11	0.512691
$538$	−3.10894e12	−1.59990
$539$	2.74323e12	1.39995
$540$	2.65034e10	0.0134131
$541$	−3.10113e12	−1.55644	−0.778219	−	0.627993i	$-0.783876\pi$
$541$	−3.10113e12	−1.55644	−0.778219	+	0.627993i	$0.783876\pi$
$542$	−2.50816e12	−1.24841
$543$	−4.74244e11	−0.234101
$544$	0	0
$545$	−2.31385e12	−1.12344
$546$	−2.54701e12	−1.22649
$547$	3.22486e12	1.54017	0.770084	−	0.637942i	$-0.220214\pi$
$547$	3.22486e12	1.54017	0.770084	+	0.637942i	$0.220214\pi$
$548$	−1.23794e11	−0.0586390
$549$	1.25170e11	0.0588064
$550$	1.73204e12	0.807096
$551$	−5.17861e12	−2.39349
$552$	2.00866e12	0.920834
$553$	−2.98439e12	−1.35704
$554$	2.06625e12	0.931944
$555$	−7.75172e12	−3.46801
$556$	−1.07634e11	−0.0477654
$557$	1.24940e12	0.549988	0.274994	−	0.961446i	$-0.411324\pi$
$557$	1.24940e12	0.549988	0.274994	+	0.961446i	$0.411324\pi$
$558$	9.14715e11	0.399422
$559$	−1.74629e12	−0.756419
$560$	−5.80278e12	−2.49339
$561$	0	0
$562$	−2.89299e11	−0.122330
$563$	3.77869e12	1.58509	0.792544	−	0.609815i	$-0.208756\pi$
$563$	3.77869e12	1.58509	0.792544	+	0.609815i	$0.208756\pi$
$564$	−1.50937e11	−0.0628114
$565$	1.62324e12	0.670140
$566$	1.42309e12	0.582854
$567$	4.80829e12	1.95374
$568$	1.26418e12	0.509615
$569$	−2.01532e12	−0.806007	−0.403003	−	0.915199i	$-0.632034\pi$
$569$	−2.01532e12	−0.806007	−0.403003	+	0.915199i	$0.632034\pi$
$570$	7.39423e12	2.93397
$571$	−2.72614e12	−1.07321	−0.536607	−	0.843833i	$-0.680294\pi$
$571$	−2.72614e12	−1.07321	−0.536607	+	0.843833i	$0.680294\pi$
$572$	4.66203e10	0.0182093
$573$	−3.13506e12	−1.21493
$574$	3.51926e12	1.35316
$575$	2.14178e12	0.817089
$576$	2.41973e12	0.915938
$577$	−1.09980e12	−0.413071	−0.206535	−	0.978439i	$-0.566219\pi$
$577$	−1.09980e12	−0.413071	−0.206535	+	0.978439i	$0.566219\pi$
$578$	0	0
$579$	5.37618e11	0.198802
$580$	−3.48140e11	−0.127740
$581$	−3.48285e12	−1.26807
$582$	−2.68335e12	−0.969445
$583$	−1.07552e12	−0.385574
$584$	−2.49668e12	−0.888187
$585$	1.94019e12	0.684925
$586$	6.95465e11	0.243633
$587$	9.43767e11	0.328090	0.164045	−	0.986453i	$-0.447546\pi$
$587$	9.43767e11	0.328090	0.164045	+	0.986453i	$0.447546\pi$
$588$	4.36567e11	0.150610
$589$	2.01196e12	0.688812
$590$	3.56654e11	0.121175
$591$	−1.94539e12	−0.655938
$592$	4.77350e12	1.59731
$593$	−9.91332e11	−0.329210	−0.164605	−	0.986360i	$-0.552635\pi$
$593$	−9.91332e11	−0.329210	−0.164605	+	0.986360i	$0.552635\pi$
$594$	3.36576e11	0.110929
$595$	0	0
$596$	−2.32168e10	−0.00753693
$597$	1.83045e12	0.589757
$598$	−1.04399e12	−0.333843
$599$	−1.94343e12	−0.616806	−0.308403	−	0.951256i	$-0.599794\pi$
$599$	−1.94343e12	−0.616806	−0.308403	+	0.951256i	$0.599794\pi$
$600$	5.54301e12	1.74608
$601$	−2.65148e12	−0.828998	−0.414499	−	0.910050i	$-0.636043\pi$
$601$	−2.65148e12	−0.828998	−0.414499	+	0.910050i	$0.636043\pi$
$602$	−7.99948e12	−2.48243
$603$	1.90884e11	0.0587951
$604$	1.95541e11	0.0597821
$605$	2.74682e12	0.833548
$606$	1.01101e12	0.304528
$607$	3.05667e12	0.913901	0.456950	−	0.889492i	$-0.348942\pi$
$607$	3.05667e12	0.913901	0.456950	+	0.889492i	$0.348942\pi$
$608$	5.17525e11	0.153591
$609$	−1.33379e13	−3.92925
$610$	−3.35181e11	−0.0980157
$611$	1.57755e12	0.457930
$612$	0	0
$613$	8.14159e11	0.232883	0.116441	−	0.993198i	$-0.462851\pi$
$613$	8.14159e11	0.232883	0.116441	+	0.993198i	$0.462851\pi$
$614$	−6.53019e12	−1.85425
$615$	−5.74434e12	−1.61921
$616$	4.29458e12	1.20173
$617$	3.14024e12	0.872328	0.436164	−	0.899867i	$-0.356337\pi$
$617$	3.14024e12	0.872328	0.436164	+	0.899867i	$0.356337\pi$
$618$	−8.40977e12	−2.31919
$619$	−1.91426e12	−0.524074	−0.262037	−	0.965058i	$-0.584394\pi$
$619$	−1.91426e12	−0.524074	−0.262037	+	0.965058i	$0.584394\pi$
$620$	1.35257e11	0.0367619
$621$	4.16198e11	0.112302
$622$	−2.33063e12	−0.624333
$623$	1.06414e13	2.83009
$624$	−2.56011e12	−0.675972
$625$	−2.65263e12	−0.695371
$626$	−2.32370e12	−0.604778
$627$	−5.18525e12	−1.33988
$628$	1.77714e11	0.0455936
$629$	0	0
$630$	8.88773e12	2.24780
$631$	1.88133e12	0.472424	0.236212	−	0.971702i	$-0.424094\pi$
$631$	1.88133e12	0.472424	0.236212	+	0.971702i	$0.424094\pi$
$632$	−3.16587e12	−0.789344
$633$	1.17915e12	0.291913
$634$	−7.99450e10	−0.0196512
$635$	−4.39311e12	−1.07223
$636$	−1.71161e11	−0.0414809
$637$	−4.56289e12	−1.09803
$638$	−4.42115e12	−1.05643
$639$	−1.83466e12	−0.435313
$640$	−5.81474e12	−1.37000
$641$	−4.79534e12	−1.12191	−0.560956	−	0.827846i	$-0.689566\pi$
$641$	−4.79534e12	−1.12191	−0.560956	+	0.827846i	$0.689566\pi$
$642$	−8.51997e12	−1.97939
$643$	3.80034e12	0.876745	0.438372	−	0.898793i	$-0.355555\pi$
$643$	3.80034e12	0.876745	0.438372	+	0.898793i	$0.355555\pi$
$644$	2.64082e11	0.0604996
$645$	1.30572e13	2.97052
$646$	0	0
$647$	1.97382e12	0.442831	0.221416	−	0.975180i	$-0.428932\pi$
$647$	1.97382e12	0.442831	0.221416	+	0.975180i	$0.428932\pi$
$648$	5.10067e12	1.13642
$649$	−2.50106e11	−0.0553378
$650$	−2.88095e12	−0.633032
$651$	5.18195e12	1.13078
$652$	−2.43623e11	−0.0527963
$653$	4.90558e10	0.0105580	0.00527900	−	0.999986i	$-0.498320\pi$
$653$	4.90558e10	0.0105580	0.00527900	+	0.999986i	$0.498320\pi$
$654$	−4.67633e12	−0.999551
$655$	5.30536e12	1.12624
$656$	3.53736e12	0.745782
$657$	3.62333e12	0.758689
$658$	7.22655e12	1.50285
$659$	6.53479e12	1.34973	0.674865	−	0.737941i	$-0.264202\pi$
$659$	6.53479e12	1.34973	0.674865	+	0.737941i	$0.264202\pi$
$660$	−3.48586e11	−0.0715093
$661$	1.65487e11	0.0337176	0.0168588	−	0.999858i	$-0.494633\pi$
$661$	1.65487e11	0.0337176	0.0168588	+	0.999858i	$0.494633\pi$
$662$	2.22453e12	0.450171
$663$	0	0
$664$	−3.69464e12	−0.737591
$665$	1.95490e13	3.87639
$666$	−7.31125e12	−1.43998
$667$	−5.46705e12	−1.06951
$668$	−1.97246e11	−0.0383278
$669$	6.36168e12	1.22787
$670$	−5.11151e11	−0.0979969
$671$	2.35048e11	0.0447615
$672$	1.33292e12	0.252141
$673$	−4.83260e12	−0.908057	−0.454029	−	0.890987i	$-0.650014\pi$
$673$	−4.83260e12	−0.908057	−0.454029	+	0.890987i	$0.650014\pi$
$674$	−8.12546e12	−1.51662
$675$	1.14852e12	0.212947
$676$	2.06582e11	0.0380480
$677$	6.35451e12	1.16261	0.581304	−	0.813687i	$-0.302543\pi$
$677$	6.35451e12	1.16261	0.581304	+	0.813687i	$0.302543\pi$
$678$	3.28060e12	0.596238
$679$	−7.09427e12	−1.28084
$680$	0	0
$681$	1.41227e13	2.51625
$682$	1.71768e12	0.304027
$683$	−5.98368e12	−1.05214	−0.526072	−	0.850440i	$-0.676336\pi$
$683$	−5.98368e12	−1.05214	−0.526072	+	0.850440i	$0.676336\pi$
$684$	−3.85107e11	−0.0672712
$685$	−9.67440e12	−1.67887
$686$	−1.09572e13	−1.88904
$687$	1.86471e12	0.319379
$688$	−8.04063e12	−1.36818
$689$	1.78894e12	0.302419
$690$	7.80608e12	1.31103
$691$	−3.11114e12	−0.519121	−0.259560	−	0.965727i	$-0.583578\pi$
$691$	−3.11114e12	−0.519121	−0.259560	+	0.965727i	$0.583578\pi$
$692$	1.75653e11	0.0291192
$693$	−6.23257e12	−1.02652
$694$	−1.44321e12	−0.236163
$695$	−8.41153e12	−1.36755
$696$	−1.41489e13	−2.28551
$697$	0	0
$698$	9.52536e10	0.0151891
$699$	−1.05662e13	−1.67406
$700$	7.28748e11	0.114719
$701$	2.52718e12	0.395280	0.197640	−	0.980275i	$-0.436672\pi$
$701$	2.52718e12	0.395280	0.197640	+	0.980275i	$0.436672\pi$
$702$	−5.59836e11	−0.0870050
$703$	−1.60815e13	−2.48328
$704$	4.54384e12	0.697182
$705$	−1.17956e13	−1.79833
$706$	1.47543e12	0.223510
$707$	2.67292e12	0.402344
$708$	−3.98026e10	−0.00595336
$709$	−6.25026e12	−0.928946	−0.464473	−	0.885587i	$-0.653756\pi$
$709$	−6.25026e12	−0.928946	−0.464473	+	0.885587i	$0.653756\pi$
$710$	4.91287e12	0.725559
$711$	4.59451e12	0.674257
$712$	1.12884e13	1.64617
$713$	2.12402e12	0.307791
$714$	0	0
$715$	3.64334e12	0.521342
$716$	1.37787e11	0.0195930
$717$	−1.28116e13	−1.81037
$718$	−1.07559e13	−1.51039
$719$	−1.03374e13	−1.44256	−0.721278	−	0.692646i	$-0.756445\pi$
$719$	−1.03374e13	−1.44256	−0.721278	+	0.692646i	$0.756445\pi$
$720$	8.93344e12	1.23886
$721$	−2.22339e13	−3.06413
$722$	8.23185e12	1.12741
$723$	−1.42182e13	−1.93518
$724$	−6.61410e10	−0.00894637
$725$	−1.50866e13	−2.02801
$726$	5.55136e12	0.741626
$727$	4.29476e12	0.570209	0.285105	−	0.958496i	$-0.407972\pi$
$727$	4.29476e12	0.570209	0.285105	+	0.958496i	$0.407972\pi$
$728$	−7.14331e12	−0.942558
$729$	−5.61602e12	−0.736469
$730$	−9.70259e12	−1.26455
$731$	0	0
$732$	3.74063e10	0.00481554
$733$	−1.23126e13	−1.57537	−0.787685	−	0.616078i	$-0.788721\pi$
$733$	−1.23126e13	−1.57537	−0.787685	+	0.616078i	$0.788721\pi$
$734$	1.14544e13	1.45660
$735$	3.41174e13	4.31204
$736$	5.46350e11	0.0686310
$737$	3.58447e11	0.0447529
$738$	−5.41794e12	−0.672327
$739$	1.29086e13	1.59214	0.796069	−	0.605206i	$-0.206909\pi$
$739$	1.29086e13	1.59214	0.796069	+	0.605206i	$0.206909\pi$
$740$	−1.08110e12	−0.132533
$741$	8.62477e12	1.05091
$742$	8.19486e12	0.992485
$743$	1.39397e13	1.67804	0.839022	−	0.544097i	$-0.183128\pi$
$743$	1.39397e13	1.67804	0.839022	+	0.544097i	$0.183128\pi$
$744$	5.49706e12	0.657737
$745$	−1.81438e12	−0.215787
$746$	7.97690e12	0.942995
$747$	5.36189e12	0.630050
$748$	0	0
$749$	−2.25252e13	−2.61518
$750$	4.23535e12	0.488780
$751$	6.01170e12	0.689632	0.344816	−	0.938670i	$-0.387941\pi$
$751$	6.01170e12	0.689632	0.344816	+	0.938670i	$0.387941\pi$
$752$	7.26372e12	0.828283
$753$	1.20506e12	0.136594
$754$	7.35384e12	0.828596
$755$	1.52814e13	1.71160
$756$	1.41613e11	0.0157672
$757$	5.29028e12	0.585527	0.292764	−	0.956185i	$-0.405425\pi$
$757$	5.29028e12	0.585527	0.292764	+	0.956185i	$0.405425\pi$
$758$	9.88594e12	1.08769
$759$	−5.47405e12	−0.598716
$760$	2.07377e13	2.25476
$761$	−2.96569e12	−0.320549	−0.160275	−	0.987072i	$-0.551238\pi$
$761$	−2.96569e12	−0.320549	−0.160275	+	0.987072i	$0.551238\pi$
$762$	−8.87854e12	−0.953991
$763$	−1.23633e13	−1.32061
$764$	−4.37234e11	−0.0464295
$765$	0	0
$766$	8.87862e12	0.931786
$767$	4.16008e11	0.0434033
$768$	2.06678e12	0.214373
$769$	−6.69576e12	−0.690449	−0.345225	−	0.938520i	$-0.612197\pi$
$769$	−6.69576e12	−0.690449	−0.345225	+	0.938520i	$0.612197\pi$
$770$	1.66896e13	1.71095
$771$	−8.30777e12	−0.846720
$772$	7.49794e10	0.00759738
$773$	−1.75155e13	−1.76448	−0.882239	−	0.470803i	$-0.843964\pi$
$773$	−1.75155e13	−1.76448	−0.882239	+	0.470803i	$0.843964\pi$
$774$	1.23153e13	1.23342
$775$	5.86135e12	0.583633
$776$	−7.52566e12	−0.745019
$777$	−4.14190e13	−4.07666
$778$	6.48361e12	0.634467
$779$	−1.19170e13	−1.15944
$780$	5.79814e11	0.0560871
$781$	−3.44518e12	−0.331346
$782$	0	0
$783$	−2.93168e12	−0.278733
$784$	−2.10095e13	−1.98606
$785$	1.38883e13	1.30537
$786$	1.07222e13	1.00204
$787$	−2.99054e11	−0.0277884	−0.0138942	−	0.999903i	$-0.504423\pi$
$787$	−2.99054e11	−0.0277884	−0.0138942	+	0.999903i	$0.504423\pi$
$788$	−2.71316e11	−0.0250672
$789$	6.49288e12	0.596473
$790$	−1.23032e13	−1.12382
$791$	8.67331e12	0.787754
$792$	−6.61156e12	−0.597091
$793$	−3.90962e11	−0.0351079
$794$	9.36915e12	0.836581
$795$	−1.33761e13	−1.18762
$796$	2.55285e11	0.0225381
$797$	2.69118e12	0.236254	0.118127	−	0.992998i	$-0.462311\pi$
$797$	2.69118e12	0.236254	0.118127	+	0.992998i	$0.462311\pi$
$798$	3.95088e13	3.44890
$799$	0	0
$800$	1.50768e12	0.130138
$801$	−1.63825e13	−1.40616
$802$	2.19740e13	1.87553
$803$	6.80399e12	0.577489
$804$	5.70445e10	0.00481461
$805$	2.06378e13	1.73214
$806$	−2.85707e12	−0.238458
$807$	2.71145e13	2.25046
$808$	2.83545e12	0.234030
$809$	−1.42567e13	−1.17018	−0.585088	−	0.810970i	$-0.698940\pi$
$809$	−1.42567e13	−1.17018	−0.585088	+	0.810970i	$0.698940\pi$
$810$	1.98223e13	1.61797
$811$	−7.85958e12	−0.637977	−0.318989	−	0.947759i	$-0.603343\pi$
$811$	−7.85958e12	−0.637977	−0.318989	+	0.947759i	$0.603343\pi$
$812$	−1.86018e12	−0.150160
$813$	2.18748e13	1.75605
$814$	−1.37293e13	−1.09607
$815$	−1.90390e13	−1.51159
$816$	0	0
$817$	2.70881e13	2.12706
$818$	−4.74669e12	−0.370681
$819$	1.03668e13	0.805133
$820$	−8.01140e11	−0.0618794
$821$	1.28791e13	0.989331	0.494665	−	0.869083i	$-0.335291\pi$
$821$	1.28791e13	0.989331	0.494665	+	0.869083i	$0.335291\pi$
$822$	−1.95521e13	−1.49373
$823$	−1.60307e13	−1.21802	−0.609008	−	0.793164i	$-0.708432\pi$
$823$	−1.60307e13	−1.21802	−0.609008	+	0.793164i	$0.708432\pi$
$824$	−2.35859e13	−1.78230
$825$	−1.51059e13	−1.13528
$826$	1.90567e12	0.142442
$827$	6.78477e12	0.504383	0.252191	−	0.967677i	$-0.418849\pi$
$827$	6.78477e12	0.504383	0.252191	+	0.967677i	$0.418849\pi$
$828$	−4.06557e11	−0.0300597
$829$	−1.53347e13	−1.12766	−0.563831	−	0.825890i	$-0.690673\pi$
$829$	−1.53347e13	−1.12766	−0.563831	+	0.825890i	$0.690673\pi$
$830$	−1.43581e13	−1.05014
$831$	−1.80208e13	−1.31090
$832$	−7.55791e12	−0.546823
$833$	0	0
$834$	−1.69998e13	−1.21674
$835$	−1.54146e13	−1.09735
$836$	−7.23166e11	−0.0512047
$837$	1.13900e12	0.0802156
$838$	−2.10500e13	−1.47453
$839$	1.33677e13	0.931384	0.465692	−	0.884947i	$-0.345806\pi$
$839$	1.33677e13	0.931384	0.465692	+	0.884947i	$0.345806\pi$
$840$	5.34115e13	3.70151
$841$	2.40025e13	1.65453
$842$	1.23963e13	0.849937
$843$	2.52311e12	0.172073
$844$	1.64452e11	0.0111557
$845$	1.61442e13	1.08934
$846$	−1.11253e13	−0.746701
$847$	1.46768e13	0.979841
$848$	8.23701e12	0.547001
$849$	−1.24115e13	−0.819859
$850$	0	0
$851$	−1.69772e13	−1.10964
$852$	−5.48277e11	−0.0356469
$853$	−7.55899e12	−0.488870	−0.244435	−	0.969666i	$-0.578602\pi$
$853$	−7.55899e12	−0.488870	−0.244435	+	0.969666i	$0.578602\pi$
$854$	−1.79094e12	−0.115218
$855$	−3.00959e13	−1.92601
$856$	−2.38950e13	−1.52116
$857$	8.84519e12	0.560136	0.280068	−	0.959980i	$-0.409643\pi$
$857$	8.84519e12	0.560136	0.280068	+	0.959980i	$0.409643\pi$
$858$	7.36326e12	0.463850
$859$	−2.32517e13	−1.45709	−0.728543	−	0.685000i	$-0.759802\pi$
$859$	−2.32517e13	−1.45709	−0.728543	+	0.685000i	$0.759802\pi$
$860$	1.82104e12	0.113521
$861$	−3.06931e13	−1.90339
$862$	6.91896e12	0.426833
$863$	−1.41089e13	−0.865854	−0.432927	−	0.901429i	$-0.642519\pi$
$863$	−1.41089e13	−0.865854	−0.432927	+	0.901429i	$0.642519\pi$
$864$	2.92978e11	0.0178864
$865$	1.37272e13	0.833699
$866$	9.65374e12	0.583264
$867$	0	0
$868$	7.22706e11	0.0432139
$869$	8.62770e12	0.513223
$870$	−5.49857e13	−3.25397
$871$	−5.96216e11	−0.0351012
$872$	−1.31151e13	−0.768155
$873$	1.09217e13	0.636395
$874$	1.61942e13	0.938769
$875$	1.11975e13	0.645779
$876$	1.08281e12	0.0621275
$877$	−5.37868e12	−0.307028	−0.153514	−	0.988146i	$-0.549059\pi$
$877$	−5.37868e12	−0.307028	−0.153514	+	0.988146i	$0.549059\pi$
$878$	2.12688e13	1.20786
$879$	−6.06548e12	−0.342701
$880$	1.67755e13	0.942981
$881$	−6.90006e12	−0.385888	−0.192944	−	0.981210i	$-0.561804\pi$
$881$	−6.90006e12	−0.385888	−0.192944	+	0.981210i	$0.561804\pi$
$882$	3.21788e13	1.79044
$883$	5.32421e12	0.294735	0.147368	−	0.989082i	$-0.452920\pi$
$883$	5.32421e12	0.294735	0.147368	+	0.989082i	$0.452920\pi$
$884$	0	0
$885$	−3.11055e12	−0.170448
$886$	9.34879e12	0.509687
$887$	9.76428e12	0.529644	0.264822	−	0.964297i	$-0.414687\pi$
$887$	9.76428e12	0.529644	0.264822	+	0.964297i	$0.414687\pi$
$888$	−4.39376e13	−2.37125
$889$	−2.34732e13	−1.26042
$890$	4.38692e13	2.34371
$891$	−1.39005e13	−0.738890
$892$	8.87238e11	0.0469243
$893$	−2.44708e13	−1.28770
$894$	−3.66689e12	−0.191990
$895$	1.07680e13	0.560958
$896$	−3.10693e13	−1.61044
$897$	9.10515e12	0.469593
$898$	3.50879e13	1.80059
$899$	−1.49615e13	−0.763937
$900$	−1.12191e12	−0.0569992
$901$	0	0
$902$	−1.01740e13	−0.511753
$903$	6.97673e13	3.49186
$904$	9.20072e12	0.458209
$905$	−5.16887e12	−0.256140
$906$	3.08839e13	1.52284
$907$	8.26585e12	0.405560	0.202780	−	0.979224i	$-0.435002\pi$
$907$	8.26585e12	0.405560	0.202780	+	0.979224i	$0.435002\pi$
$908$	1.96963e12	0.0961609
$909$	−4.11498e12	−0.199908
$910$	−2.77604e13	−1.34196
$911$	−2.87936e13	−1.38504	−0.692521	−	0.721398i	$-0.743500\pi$
$911$	−2.87936e13	−1.38504	−0.692521	+	0.721398i	$0.743500\pi$
$912$	3.97121e13	1.90084
$913$	1.00687e13	0.479574
$914$	7.91718e12	0.375243
$915$	2.92328e12	0.137872
$916$	2.60064e11	0.0122054
$917$	2.83476e13	1.32390
$918$	0	0
$919$	−2.43926e12	−0.112808	−0.0564038	−	0.998408i	$-0.517963\pi$
$919$	−2.43926e12	−0.112808	−0.0564038	+	0.998408i	$0.517963\pi$
$920$	2.18928e13	1.00752
$921$	5.69529e13	2.60824
$922$	−2.18954e13	−0.997846
$923$	5.73046e12	0.259886
$924$	−1.86256e12	−0.0840596
$925$	−4.68494e13	−2.10410
$926$	−2.66581e13	−1.19146
$927$	3.42293e13	1.52244
$928$	−3.84847e12	−0.170342
$929$	−3.64339e13	−1.60485	−0.802425	−	0.596753i	$-0.796457\pi$
$929$	−3.64339e13	−1.60485	−0.802425	+	0.596753i	$0.796457\pi$
$930$	2.13627e13	0.936446
$931$	7.07788e13	3.08766
$932$	−1.47362e12	−0.0639756
$933$	2.03265e13	0.878204
$934$	−8.44002e12	−0.362896
$935$	0	0
$936$	1.09972e13	0.468318
$937$	−6.77397e12	−0.287088	−0.143544	−	0.989644i	$-0.545850\pi$
$937$	−6.77397e12	−0.287088	−0.143544	+	0.989644i	$0.545850\pi$
$938$	−2.73118e12	−0.115196
$939$	2.02661e13	0.850698
$940$	−1.64508e12	−0.0687247
$941$	−4.94597e12	−0.205636	−0.102818	−	0.994700i	$-0.532786\pi$
$941$	−4.94597e12	−0.205636	−0.102818	+	0.994700i	$0.532786\pi$
$942$	2.80684e13	1.16142
$943$	−1.25808e13	−0.518089
$944$	1.91547e12	0.0785059
$945$	1.10670e13	0.451424
$946$	2.31260e13	0.938838
$947$	−6.76062e12	−0.273156	−0.136578	−	0.990629i	$-0.543611\pi$
$947$	−6.76062e12	−0.273156	−0.136578	+	0.990629i	$0.543611\pi$
$948$	1.37304e12	0.0552136
$949$	−1.13173e13	−0.452944
$950$	4.46888e13	1.78009
$951$	6.97239e11	0.0276420
$952$	0	0
$953$	5.35557e12	0.210323	0.105162	−	0.994455i	$-0.466464\pi$
$953$	5.35557e12	0.210323	0.105162	+	0.994455i	$0.466464\pi$
$954$	−1.26161e13	−0.493124
$955$	−3.41696e13	−1.32930
$956$	−1.78679e12	−0.0691850
$957$	3.85590e13	1.48601
$958$	−3.78054e12	−0.145014
$959$	−5.16922e13	−1.97352
$960$	5.65116e13	2.14742
$961$	−2.06269e13	−0.780150
$962$	2.28363e13	0.859683
$963$	3.46778e13	1.29937
$964$	−1.98295e12	−0.0739546
$965$	5.85959e12	0.217518
$966$	4.17094e13	1.54112
$967$	−1.71835e13	−0.631966	−0.315983	−	0.948765i	$-0.602334\pi$
$967$	−1.71835e13	−0.631966	−0.315983	+	0.948765i	$0.602334\pi$
$968$	1.55693e13	0.569940
$969$	0	0
$970$	−2.92463e13	−1.06071
$971$	3.68213e13	1.32927	0.664634	−	0.747169i	$-0.268588\pi$
$971$	3.68213e13	1.32927	0.664634	+	0.747169i	$0.268588\pi$
$972$	−1.96303e12	−0.0705388
$973$	−4.49445e13	−1.60756
$974$	3.40042e13	1.21065
$975$	2.51261e13	0.890441
$976$	−1.80015e12	−0.0635016
$977$	5.16075e13	1.81212	0.906060	−	0.423149i	$-0.139075\pi$
$977$	5.16075e13	1.81212	0.906060	+	0.423149i	$0.139075\pi$
$978$	−3.84781e13	−1.34490
$979$	−3.07635e13	−1.07032
$980$	4.75822e12	0.164789
$981$	1.90335e13	0.656158
$982$	−4.69118e13	−1.60983
$983$	−1.39095e13	−0.475138	−0.237569	−	0.971371i	$-0.576351\pi$
$983$	−1.39095e13	−0.475138	−0.237569	+	0.971371i	$0.576351\pi$
$984$	−3.25595e13	−1.10713
$985$	−2.12031e13	−0.717690
$986$	0	0
$987$	−6.30262e13	−2.11395
$988$	1.20286e12	0.0401615
$989$	2.85968e13	0.950462
$990$	−2.56939e13	−0.850102
$991$	4.91436e13	1.61859	0.809293	−	0.587405i	$-0.199850\pi$
$991$	4.91436e13	1.61859	0.809293	+	0.587405i	$0.199850\pi$
$992$	1.49518e12	0.0490220
$993$	−1.94012e13	−0.633223
$994$	2.62504e13	0.852899
$995$	1.99504e13	0.645279
$996$	1.60237e12	0.0515935
$997$	−4.79746e13	−1.53774	−0.768870	−	0.639405i	$-0.779181\pi$
$997$	−4.79746e13	−1.53774	−0.768870	+	0.639405i	$0.779181\pi$
$998$	1.85760e12	0.0592740
$999$	−9.10393e12	−0.289191

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.d.1.8	✓	12
17.16	even	2		289.10.a.e.1.8	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.8	✓	12	1.1	even	1	trivial
289.10.a.e.1.8	yes	12	17.16	even	2

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+22.0274 q^{2} -192.112 q^{3} -26.7930 q^{4} -2093.86 q^{5} -4231.72 q^{6} -11187.9 q^{7} -11868.2 q^{8} +17223.9 q^{9} +O(q^{10})\)	\(q+22.0274 q^{2} -192.112 q^{3} -26.7930 q^{4} -2093.86 q^{5} -4231.72 q^{6} -11187.9 q^{7} -11868.2 q^{8} +17223.9 q^{9} -46122.3 q^{10} +32343.5 q^{11} +5147.26 q^{12} -53797.9 q^{13} -246440. q^{14} +402255. q^{15} -247708. q^{16} +379398. q^{18} +834504. q^{19} +56100.9 q^{20} +2.14933e6 q^{21} +712444. q^{22} +880984. q^{23} +2.28002e6 q^{24} +2.43112e6 q^{25} -1.18503e6 q^{26} +472424. q^{27} +299758. q^{28} -6.20562e6 q^{29} +8.86063e6 q^{30} +2.41097e6 q^{31} +620159. q^{32} -6.21357e6 q^{33} +2.34259e7 q^{35} -461480. q^{36} -1.92707e7 q^{37} +1.83820e7 q^{38} +1.03352e7 q^{39} +2.48504e7 q^{40} -1.42804e7 q^{41} +4.73441e7 q^{42} +3.24601e7 q^{43} -866581. q^{44} -3.60644e7 q^{45} +1.94058e7 q^{46} -2.93237e7 q^{47} +4.75876e7 q^{48} +8.48154e7 q^{49} +5.35513e7 q^{50} +1.44141e6 q^{52} -3.32529e7 q^{53} +1.04063e7 q^{54} -6.77228e7 q^{55} +1.32780e8 q^{56} -1.60318e8 q^{57} -1.36694e8 q^{58} -7.73279e6 q^{59} -1.07776e7 q^{60} +7.26723e6 q^{61} +5.31074e7 q^{62} -1.92699e8 q^{63} +1.40487e8 q^{64} +1.12645e8 q^{65} -1.36869e8 q^{66} +1.10825e7 q^{67} -1.69247e8 q^{69} +5.16012e8 q^{70} -1.06518e8 q^{71} -2.04417e8 q^{72} +2.10366e8 q^{73} -4.24483e8 q^{74} -4.67047e8 q^{75} -2.23589e7 q^{76} -3.61856e8 q^{77} +2.27658e8 q^{78} +2.66752e8 q^{79} +5.18666e8 q^{80} -4.29776e8 q^{81} -3.14559e8 q^{82} +3.11305e8 q^{83} -5.75870e7 q^{84} +7.15012e8 q^{86} +1.19217e9 q^{87} -3.83860e8 q^{88} -9.51149e8 q^{89} -7.94405e8 q^{90} +6.01886e8 q^{91} -2.36042e7 q^{92} -4.63175e8 q^{93} -6.45925e8 q^{94} -1.74733e9 q^{95} -1.19140e8 q^{96} +6.34102e8 q^{97} +1.86826e9 q^{98} +5.57081e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9} + 2449 q^{10} - 152886 q^{11} - 41717 q^{12} + 23478 q^{13} - 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} + 2477218 q^{20} - 1395256 q^{21} - 2391095 q^{22} - 2012428 q^{23} - 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} - 3231638 q^{27} + 5978216 q^{28} - 12772842 q^{29} + 181633 q^{30} - 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} - 1352872 q^{37} + 3704404 q^{38} + 1380780 q^{39} - 44739331 q^{40} - 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} - 148233417 q^{44} + 79449336 q^{45} - 31855859 q^{46} + 133558002 q^{47} + 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} + 50215469 q^{54} - 91197532 q^{55} - 267350757 q^{56} - 49507694 q^{57} - 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} - 262041240 q^{61} + 314328847 q^{62} - 218532626 q^{63} + 595820098 q^{64} - 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} - 204290852 q^{71} - 208030791 q^{72} - 673538852 q^{73} - 1274510282 q^{74} - 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} - 165043245 q^{78} - 434002980 q^{79} - 599590757 q^{80} - 389011392 q^{81} + 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} + 262108460 q^{88} + 911678128 q^{89} + 2734590475 q^{90} + 560105446 q^{91} + 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} + 1116511966 q^{95} - 2204198979 q^{96} + 3589270998 q^{97} - 2677144485 q^{98} - 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9 + 2449 * q^10 - 152886 * q^11 - 41717 * q^12 + 23478 * q^13 - 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 + 2477218 * q^20 - 1395256 * q^21 - 2391095 * q^22 - 2012428 * q^23 - 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 - 3231638 * q^27 + 5978216 * q^28 - 12772842 * q^29 + 181633 * q^30 - 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 - 1352872 * q^37 + 3704404 * q^38 + 1380780 * q^39 - 44739331 * q^40 - 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 - 148233417 * q^44 + 79449336 * q^45 - 31855859 * q^46 + 133558002 * q^47 + 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 + 50215469 * q^54 - 91197532 * q^55 - 267350757 * q^56 - 49507694 * q^57 - 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 - 262041240 * q^61 + 314328847 * q^62 - 218532626 * q^63 + 595820098 * q^64 - 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 - 204290852 * q^71 - 208030791 * q^72 - 673538852 * q^73 - 1274510282 * q^74 - 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 - 165043245 * q^78 - 434002980 * q^79 - 599590757 * q^80 - 389011392 * q^81 + 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 + 262108460 * q^88 + 911678128 * q^89 + 2734590475 * q^90 + 560105446 * q^91 + 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 + 1116511966 * q^95 - 2204198979 * q^96 + 3589270998 * q^97 - 2677144485 * q^98 - 2056683494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more