LMFDB - Embedded newform 29.8.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,8,Mod(1,29)]

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([0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	29.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:	$9.05916573904$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 1101 x^{8} - 1540 x^{7} + 405148 x^{6} + 870160 x^{5} - 54569376 x^{4} - 87078400 x^{3} + \cdots - 9372051456 $ x^10 - 1101x^8 - 1540x^7 + 405148x^6 + 870160x^5 - 54569376x^4 - 87078400x^3 + 2140673280x^2 - 1918315520x - 9372051456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$21.4083$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21.4083 q^{2} -17.3673 q^{3} +330.317 q^{4} -555.983 q^{5} +371.805 q^{6} -1113.12 q^{7} -4331.27 q^{8} -1885.38 q^{9} +O(q^{10})$	\(q-21.4083 q^{2} -17.3673 q^{3} +330.317 q^{4} -555.983 q^{5} +371.805 q^{6} -1113.12 q^{7} -4331.27 q^{8} -1885.38 q^{9} +11902.7 q^{10} -560.510 q^{11} -5736.72 q^{12} -492.300 q^{13} +23830.1 q^{14} +9655.94 q^{15} +50444.7 q^{16} -519.277 q^{17} +40362.8 q^{18} -50.3572 q^{19} -183651. q^{20} +19332.0 q^{21} +11999.6 q^{22} -75226.9 q^{23} +75222.5 q^{24} +230993. q^{25} +10539.3 q^{26} +70726.2 q^{27} -367684. q^{28} -24389.0 q^{29} -206718. q^{30} +84266.1 q^{31} -525536. q^{32} +9734.56 q^{33} +11116.9 q^{34} +618878. q^{35} -622772. q^{36} -332692. q^{37} +1078.06 q^{38} +8549.94 q^{39} +2.40812e6 q^{40} +181791. q^{41} -413865. q^{42} -483121. q^{43} -185146. q^{44} +1.04824e6 q^{45} +1.61048e6 q^{46} -1.11740e6 q^{47} -876090. q^{48} +415501. q^{49} -4.94517e6 q^{50} +9018.45 q^{51} -162615. q^{52} +1.04466e6 q^{53} -1.51413e6 q^{54} +311634. q^{55} +4.82124e6 q^{56} +874.569 q^{57} +522128. q^{58} +12603.8 q^{59} +3.18952e6 q^{60} -1.61611e6 q^{61} -1.80400e6 q^{62} +2.09866e6 q^{63} +4.79392e6 q^{64} +273711. q^{65} -208401. q^{66} -1.72740e6 q^{67} -171526. q^{68} +1.30649e6 q^{69} -1.32492e7 q^{70} -1.88721e6 q^{71} +8.16608e6 q^{72} -4.05260e6 q^{73} +7.12238e6 q^{74} -4.01172e6 q^{75} -16633.8 q^{76} +623917. q^{77} -183040. q^{78} +5.94209e6 q^{79} -2.80464e7 q^{80} +2.89499e6 q^{81} -3.89185e6 q^{82} +3.87909e6 q^{83} +6.38568e6 q^{84} +288710. q^{85} +1.03428e7 q^{86} +423571. q^{87} +2.42772e6 q^{88} +3.84325e6 q^{89} -2.24410e7 q^{90} +547991. q^{91} -2.48487e7 q^{92} -1.46348e6 q^{93} +2.39216e7 q^{94} +27997.8 q^{95} +9.12714e6 q^{96} -5.95002e6 q^{97} -8.89520e6 q^{98} +1.05677e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) $ 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9} + 8496 q^{10} + 7384 q^{11} + 49720 q^{12} + 20820 q^{13} + 50976 q^{14} + 43516 q^{15} + 122082 q^{16} - 11620 q^{17} + 66060 q^{18} + 75068 q^{19} - 42914 q^{20} + 51480 q^{21} - 36950 q^{22} + 62040 q^{23} - 205942 q^{24} + 261022 q^{25} - 201528 q^{26} - 28060 q^{27} - 24980 q^{28} - 243890 q^{29} - 1284894 q^{30} + 200600 q^{31} - 1761460 q^{32} - 1068000 q^{33} - 503932 q^{34} + 107528 q^{35} - 26300 q^{36} - 367740 q^{37} + 766880 q^{38} + 392692 q^{39} - 865000 q^{40} + 932764 q^{41} - 2058060 q^{42} + 1443560 q^{43} - 1325912 q^{44} + 4245684 q^{45} + 1760460 q^{46} - 286960 q^{47} + 3187120 q^{48} + 4713194 q^{49} - 3682652 q^{50} + 1451016 q^{51} + 2560210 q^{52} + 3953220 q^{53} - 3147534 q^{54} + 3981316 q^{55} + 2082464 q^{56} + 2050640 q^{57} + 6712320 q^{59} + 7476756 q^{60} + 1905196 q^{61} - 8048490 q^{62} + 3643800 q^{63} + 8445458 q^{64} + 4667544 q^{65} - 12425580 q^{66} - 2718200 q^{67} - 17699740 q^{68} + 1109064 q^{69} - 30441624 q^{70} + 3447736 q^{71} - 22466840 q^{72} - 2554460 q^{73} - 4214584 q^{74} + 1088084 q^{75} - 8294848 q^{76} - 3967800 q^{77} - 24809970 q^{78} + 4187744 q^{79} - 17715290 q^{80} + 5161402 q^{81} + 7020500 q^{82} + 3498720 q^{83} + 22947224 q^{84} + 1817072 q^{85} - 361638 q^{86} - 1951120 q^{87} + 15118470 q^{88} - 303268 q^{89} - 28959160 q^{90} + 27215080 q^{91} - 10783380 q^{92} + 1097360 q^{93} + 55641726 q^{94} - 8810536 q^{95} - 53327238 q^{96} + 4908620 q^{97} + 40120080 q^{98} - 14408716 q^{99}+O(q^{100}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9 + 8496 * q^10 + 7384 * q^11 + 49720 * q^12 + 20820 * q^13 + 50976 * q^14 + 43516 * q^15 + 122082 * q^16 - 11620 * q^17 + 66060 * q^18 + 75068 * q^19 - 42914 * q^20 + 51480 * q^21 - 36950 * q^22 + 62040 * q^23 - 205942 * q^24 + 261022 * q^25 - 201528 * q^26 - 28060 * q^27 - 24980 * q^28 - 243890 * q^29 - 1284894 * q^30 + 200600 * q^31 - 1761460 * q^32 - 1068000 * q^33 - 503932 * q^34 + 107528 * q^35 - 26300 * q^36 - 367740 * q^37 + 766880 * q^38 + 392692 * q^39 - 865000 * q^40 + 932764 * q^41 - 2058060 * q^42 + 1443560 * q^43 - 1325912 * q^44 + 4245684 * q^45 + 1760460 * q^46 - 286960 * q^47 + 3187120 * q^48 + 4713194 * q^49 - 3682652 * q^50 + 1451016 * q^51 + 2560210 * q^52 + 3953220 * q^53 - 3147534 * q^54 + 3981316 * q^55 + 2082464 * q^56 + 2050640 * q^57 + 6712320 * q^59 + 7476756 * q^60 + 1905196 * q^61 - 8048490 * q^62 + 3643800 * q^63 + 8445458 * q^64 + 4667544 * q^65 - 12425580 * q^66 - 2718200 * q^67 - 17699740 * q^68 + 1109064 * q^69 - 30441624 * q^70 + 3447736 * q^71 - 22466840 * q^72 - 2554460 * q^73 - 4214584 * q^74 + 1088084 * q^75 - 8294848 * q^76 - 3967800 * q^77 - 24809970 * q^78 + 4187744 * q^79 - 17715290 * q^80 + 5161402 * q^81 + 7020500 * q^82 + 3498720 * q^83 + 22947224 * q^84 + 1817072 * q^85 - 361638 * q^86 - 1951120 * q^87 + 15118470 * q^88 - 303268 * q^89 - 28959160 * q^90 + 27215080 * q^91 - 10783380 * q^92 + 1097360 * q^93 + 55641726 * q^94 - 8810536 * q^95 - 53327238 * q^96 + 4908620 * q^97 + 40120080 * q^98 - 14408716 * 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 $

$2$	−21.4083	−1.89225	−0.946124	−	0.323805i	$-0.895038\pi$
$2$	−21.4083	−1.89225	−0.946124	+	0.323805i	$0.895038\pi$
$3$	−17.3673	−0.371371	−0.185686	−	0.982609i	$-0.559451\pi$
$3$	−17.3673	−0.371371	−0.185686	+	0.982609i	$0.559451\pi$
$4$	330.317	2.58060
$5$	−555.983	−1.98915	−0.994573	−	0.104037i	$-0.966824\pi$
$5$	−555.983	−1.98915	−0.994573	+	0.104037i	$0.966824\pi$
$6$	371.805	0.702726
$7$	−1113.12	−1.22659	−0.613296	−	0.789853i	$-0.710157\pi$
$7$	−1113.12	−1.22659	−0.613296	+	0.789853i	$0.710157\pi$
$8$	−4331.27	−2.99089
$9$	−1885.38	−0.862083
$10$	11902.7	3.76396
$11$	−560.510	−0.126972	−0.0634862	−	0.997983i	$-0.520222\pi$
$11$	−560.510	−0.126972	−0.0634862	+	0.997983i	$0.520222\pi$
$12$	−5736.72	−0.958361
$13$	−492.300	−0.0621482	−0.0310741	−	0.999517i	$-0.509893\pi$
$13$	−492.300	−0.0621482	−0.0310741	+	0.999517i	$0.509893\pi$
$14$	23830.1	2.32102
$15$	9655.94	0.738712
$16$	50444.7	3.07890
$17$	−519.277	−0.0256347	−0.0128173	−	0.999918i	$-0.504080\pi$
$17$	−519.277	−0.0256347	−0.0128173	+	0.999918i	$0.504080\pi$
$18$	40362.8	1.63128
$19$	−50.3572	−0.00168432	−0.000842158	−	1.00000i	$-0.500268\pi$
$19$	−50.3572	−0.00168432	−0.000842158		1.00000i	$0.500268\pi$
$20$	−183651.	−5.13320
$21$	19332.0	0.455521
$22$	11999.6	0.240263
$23$	−75226.9	−1.28922	−0.644608	−	0.764513i	$-0.722979\pi$
$23$	−75226.9	−1.28922	−0.644608	+	0.764513i	$0.722979\pi$
$24$	75222.5	1.11073
$25$	230993.	2.95671
$26$	10539.3	0.117600
$27$	70726.2	0.691524
$28$	−367684.	−3.16535
$29$	−24389.0	−0.185695
$29$	−24389.0	−0.185695
$30$	−206718.	−1.39783
$31$	84266.1	0.508027	0.254014	−	0.967201i	$-0.418249\pi$
$31$	84266.1	0.508027	0.254014	+	0.967201i	$0.418249\pi$
$32$	−525536.	−2.83516
$33$	9734.56	0.0471539
$34$	11116.9	0.0485072
$35$	618878.	2.43987
$36$	−622772.	−2.22469
$37$	−332692.	−1.07978	−0.539891	−	0.841735i	$-0.681535\pi$
$37$	−332692.	−1.07978	−0.539891	+	0.841735i	$0.681535\pi$
$38$	1078.06	0.00318715
$39$	8549.94	0.0230801
$40$	2.40812e6	5.94932
$41$	181791.	0.411936	0.205968	−	0.978559i	$-0.433966\pi$
$41$	181791.	0.411936	0.205968	+	0.978559i	$0.433966\pi$
$42$	−413865.	−0.861959
$43$	−483121.	−0.926651	−0.463326	−	0.886188i	$-0.653344\pi$
$43$	−483121.	−0.926651	−0.463326	+	0.886188i	$0.653344\pi$
$44$	−185146.	−0.327665
$45$	1.04824e6	1.71481
$46$	1.61048e6	2.43952
$47$	−1.11740e6	−1.56987	−0.784937	−	0.619575i	$-0.787305\pi$
$47$	−1.11740e6	−1.56987	−0.784937	+	0.619575i	$0.787305\pi$
$48$	−876090.	−1.14342
$49$	415501.	0.504529
$50$	−4.94517e6	−5.59482
$51$	9018.45	0.00951999
$52$	−162615.	−0.160380
$53$	1.04466e6	0.963851	0.481926	−	0.876212i	$-0.339938\pi$
$53$	1.04466e6	0.963851	0.481926	+	0.876212i	$0.339938\pi$
$54$	−1.51413e6	−1.30854
$55$	311634.	0.252567
$56$	4.82124e6	3.66860
$57$	874.569	0.000625507 0
$58$	522128.	0.351382
$59$	12603.8	0.00798948	0.00399474	−	0.999992i	$-0.498728\pi$
$59$	12603.8	0.00798948	0.00399474	+	0.999992i	$0.498728\pi$
$60$	3.18952e6	1.90632
$61$	−1.61611e6	−0.911627	−0.455813	−	0.890075i	$-0.650652\pi$
$61$	−1.61611e6	−0.911627	−0.455813	+	0.890075i	$0.650652\pi$
$62$	−1.80400e6	−0.961313
$63$	2.09866e6	1.05743
$64$	4.79392e6	2.28592
$65$	273711.	0.123622
$66$	−208401.	−0.0892268
$67$	−1.72740e6	−0.701667	−0.350834	−	0.936438i	$-0.614102\pi$
$67$	−1.72740e6	−0.701667	−0.350834	+	0.936438i	$0.614102\pi$
$68$	−171526.	−0.0661529
$69$	1.30649e6	0.478778
$70$	−1.32492e7	−4.61684
$71$	−1.88721e6	−0.625772	−0.312886	−	0.949791i	$-0.601296\pi$
$71$	−1.88721e6	−0.625772	−0.312886	+	0.949791i	$0.601296\pi$
$72$	8.16608e6	2.57840
$73$	−4.05260e6	−1.21928	−0.609640	−	0.792678i	$-0.708686\pi$
$73$	−4.05260e6	−1.21928	−0.609640	+	0.792678i	$0.708686\pi$
$74$	7.12238e6	2.04322
$75$	−4.01172e6	−1.09804
$76$	−16633.8	−0.00434655
$77$	623917.	0.155743
$78$	−183040.	−0.0436732
$79$	5.94209e6	1.35595	0.677977	−	0.735083i	$-0.262857\pi$
$79$	5.94209e6	1.35595	0.677977	+	0.735083i	$0.262857\pi$
$80$	−2.80464e7	−6.12439
$81$	2.89499e6	0.605271
$82$	−3.89185e6	−0.779485
$83$	3.87909e6	0.744658	0.372329	−	0.928101i	$-0.378559\pi$
$83$	3.87909e6	0.744658	0.372329	+	0.928101i	$0.378559\pi$
$84$	6.38568e6	1.17552
$85$	288710.	0.0509912
$86$	1.03428e7	1.75345
$87$	423571.	0.0689619
$88$	2.42772e6	0.379760
$89$	3.84325e6	0.577874	0.288937	−	0.957348i	$-0.406698\pi$
$89$	3.84325e6	0.577874	0.288937	+	0.957348i	$0.406698\pi$
$90$	−2.24410e7	−3.24485
$91$	547991.	0.0762305
$92$	−2.48487e7	−3.32695
$93$	−1.46348e6	−0.188667
$94$	2.39216e7	2.97059
$95$	27997.8	0.00335035
$96$	9.12714e6	1.05290
$97$	−5.95002e6	−0.661938	−0.330969	−	0.943642i	$-0.607376\pi$
$97$	−5.95002e6	−0.661938	−0.330969	+	0.943642i	$0.607376\pi$
$98$	−8.89520e6	−0.954694
$99$	1.05677e6	0.109461
$100$	7.63008e7	7.63008
$101$	−1.16123e7	−1.12149	−0.560743	−	0.827990i	$-0.689484\pi$
$101$	−1.16123e7	−1.12149	−0.560743	+	0.827990i	$0.689484\pi$
$102$	−193070.	−0.0180142
$103$	6.43931e6	0.580643	0.290322	−	0.956929i	$-0.406238\pi$
$103$	6.43931e6	0.580643	0.290322	+	0.956929i	$0.406238\pi$
$104$	2.13229e6	0.185878
$105$	−1.07483e7	−0.906098
$106$	−2.23645e7	−1.82385
$107$	1.10019e7	0.868212	0.434106	−	0.900862i	$-0.357064\pi$
$107$	1.10019e7	0.868212	0.434106	+	0.900862i	$0.357064\pi$
$108$	2.33621e7	1.78455
$109$	7.49755e6	0.554532	0.277266	−	0.960793i	$-0.410572\pi$
$109$	7.49755e6	0.554532	0.277266	+	0.960793i	$0.410572\pi$
$110$	−6.67157e6	−0.477919
$111$	5.77796e6	0.401000
$112$	−5.61512e7	−3.77656
$113$	2.34667e7	1.52995	0.764974	−	0.644061i	$-0.222752\pi$
$113$	2.34667e7	1.52995	0.764974	+	0.644061i	$0.222752\pi$
$114$	−18723.1	−0.00118361
$115$	4.18249e7	2.56444
$116$	−8.05610e6	−0.479206
$117$	928172.	0.0535769
$118$	−269826.	−0.0151181
$119$	578020.	0.0314433
$120$	−4.18225e7	−2.20941
$121$	−1.91730e7	−0.983878
$122$	3.45983e7	1.72502
$123$	−3.15723e6	−0.152981
$124$	2.78345e7	1.31102
$125$	−8.49918e7	−3.89217
$126$	−4.49288e7	−2.00091
$127$	−9.55729e6	−0.414020	−0.207010	−	0.978339i	$-0.566373\pi$
$127$	−9.55729e6	−0.414020	−0.207010	+	0.978339i	$0.566373\pi$
$128$	−3.53612e7	−1.49036
$129$	8.39051e6	0.344132
$130$	−5.85970e6	−0.233923
$131$	−5.91617e6	−0.229928	−0.114964	−	0.993370i	$-0.536675\pi$
$131$	−5.91617e6	−0.229928	−0.114964	+	0.993370i	$0.536675\pi$
$132$	3.21549e6	0.121685
$133$	56053.8	0.00206597
$134$	3.69808e7	1.32773
$135$	−3.93226e7	−1.37554
$136$	2.24913e6	0.0766705
$137$	−2.10228e7	−0.698502	−0.349251	−	0.937029i	$-0.613564\pi$
$137$	−2.10228e7	−0.698502	−0.349251	+	0.937029i	$0.613564\pi$
$138$	−2.79698e7	−0.905966
$139$	6.58008e6	0.207816	0.103908	−	0.994587i	$-0.466865\pi$
$139$	6.58008e6	0.207816	0.103908	+	0.994587i	$0.466865\pi$
$140$	2.04426e8	6.29634
$141$	1.94062e7	0.583006
$142$	4.04021e7	1.18412
$143$	275939.	0.00789110
$144$	−9.51073e7	−2.65427
$145$	1.35599e7	0.369375
$146$	8.67594e7	2.30718
$147$	−7.21614e6	−0.187368
$148$	−1.09894e8	−2.78649
$149$	−3.06008e7	−0.757845	−0.378922	−	0.925428i	$-0.623705\pi$
$149$	−3.06008e7	−0.757845	−0.378922	+	0.925428i	$0.623705\pi$
$150$	8.58843e7	2.07775
$151$	−2.89212e7	−0.683592	−0.341796	−	0.939774i	$-0.611035\pi$
$151$	−2.89212e7	−0.683592	−0.341796	+	0.939774i	$0.611035\pi$
$152$	218111.	0.00503761
$153$	979033.	0.0220992
$154$	−1.33570e7	−0.294705
$155$	−4.68506e7	−1.01054
$156$	2.82419e6	0.0595604
$157$	−3.36462e7	−0.693885	−0.346943	−	0.937886i	$-0.612780\pi$
$157$	−3.36462e7	−0.693885	−0.346943	+	0.937886i	$0.612780\pi$
$158$	−1.27210e8	−2.56580
$159$	−1.81430e7	−0.357947
$160$	2.92189e8	5.63954
$161$	8.37369e7	1.58134
$162$	−6.19770e7	−1.14532
$163$	7.01926e7	1.26951	0.634753	−	0.772715i	$-0.281102\pi$
$163$	7.01926e7	1.26951	0.634753	+	0.772715i	$0.281102\pi$
$164$	6.00487e7	1.06304
$165$	−5.41225e6	−0.0937960
$166$	−8.30450e7	−1.40908
$167$	7.32714e7	1.21738	0.608691	−	0.793407i	$-0.291695\pi$
$167$	7.32714e7	1.21738	0.608691	+	0.793407i	$0.291695\pi$
$168$	−8.37320e7	−1.36241
$169$	−6.25062e7	−0.996138
$170$	−6.18079e6	−0.0964879
$171$	94942.2	0.00145202
$172$	−1.59583e8	−2.39132
$173$	2.47496e7	0.363419	0.181709	−	0.983352i	$-0.441837\pi$
$173$	2.47496e7	0.363419	0.181709	+	0.983352i	$0.441837\pi$
$174$	−9.06796e6	−0.130493
$175$	−2.57123e8	−3.62667
$176$	−2.82748e7	−0.390935
$177$	−218894.	−0.00296706
$178$	−8.22775e7	−1.09348
$179$	9.63658e7	1.25585	0.627925	−	0.778274i	$-0.283905\pi$
$179$	9.63658e7	1.25585	0.627925	+	0.778274i	$0.283905\pi$
$180$	3.46251e8	4.42524
$181$	1.09672e8	1.37474	0.687369	−	0.726309i	$-0.258766\pi$
$181$	1.09672e8	1.37474	0.687369	+	0.726309i	$0.258766\pi$
$182$	−1.17316e7	−0.144247
$183$	2.80675e7	0.338552
$184$	3.25828e8	3.85590
$185$	1.84971e8	2.14785
$186$	3.13306e7	0.357004
$187$	291060.	0.00325490
$188$	−3.69095e8	−4.05122
$189$	−7.87271e7	−0.848218
$190$	−599386.	−0.00633970
$191$	−9.39972e7	−0.976108	−0.488054	−	0.872813i	$-0.662293\pi$
$191$	−9.39972e7	−0.976108	−0.488054	+	0.872813i	$0.662293\pi$
$192$	−8.32575e7	−0.848924
$193$	−5.83689e7	−0.584428	−0.292214	−	0.956353i	$-0.594392\pi$
$193$	−5.83689e7	−0.584428	−0.292214	+	0.956353i	$0.594392\pi$
$194$	1.27380e8	1.25255
$195$	−4.75362e6	−0.0459096
$196$	1.37247e8	1.30199
$197$	1.31972e8	1.22985	0.614923	−	0.788587i	$-0.289187\pi$
$197$	1.31972e8	1.22985	0.614923	+	0.788587i	$0.289187\pi$
$198$	−2.26237e7	−0.207127
$199$	7.64771e7	0.687933	0.343966	−	0.938982i	$-0.388229\pi$
$199$	7.64771e7	0.687933	0.343966	+	0.938982i	$0.388229\pi$
$200$	−1.00049e9	−8.84318
$201$	3.00003e7	0.260579
$202$	2.48600e8	2.12213
$203$	2.71480e7	0.227773
$204$	2.97895e6	0.0245673
$205$	−1.01073e8	−0.819401
$206$	−1.37855e8	−1.09872
$207$	1.41831e8	1.11141
$208$	−2.48340e7	−0.191348
$209$	28225.7	0.000213862 0
$210$	2.30102e8	1.71456
$211$	1.81634e8	1.33109	0.665546	−	0.746357i	$-0.268199\pi$
$211$	1.81634e8	1.33109	0.665546	+	0.746357i	$0.268199\pi$
$212$	3.45069e8	2.48732
$213$	3.27758e7	0.232394
$214$	−2.35533e8	−1.64287
$215$	2.68607e8	1.84325
$216$	−3.06335e8	−2.06827
$217$	−9.37986e7	−0.623142
$218$	−1.60510e8	−1.04931
$219$	7.03828e7	0.452806
$220$	1.02938e8	0.651774
$221$	255640.	0.00159315
$222$	−1.23697e8	−0.758791
$223$	−6.72466e7	−0.406072	−0.203036	−	0.979171i	$-0.565081\pi$
$223$	−6.72466e7	−0.406072	−0.203036	+	0.979171i	$0.565081\pi$
$224$	5.84986e8	3.47758
$225$	−4.35508e8	−2.54893
$226$	−5.02382e8	−2.89504
$227$	3.06945e8	1.74169	0.870844	−	0.491559i	$-0.163573\pi$
$227$	3.06945e8	1.74169	0.870844	+	0.491559i	$0.163573\pi$
$228$	288885.	0.00161418
$229$	−1.58085e7	−0.0869897	−0.0434948	−	0.999054i	$-0.513849\pi$
$229$	−1.58085e7	−0.0869897	−0.0434948	+	0.999054i	$0.513849\pi$
$230$	−8.95402e8	−4.85256
$231$	−1.08358e7	−0.0578386
$232$	1.05635e8	0.555394
$233$	−2.91731e7	−0.151090	−0.0755452	−	0.997142i	$-0.524070\pi$
$233$	−2.91731e7	−0.151090	−0.0755452	+	0.997142i	$0.524070\pi$
$234$	−1.98706e7	−0.101381
$235$	6.21254e8	3.12271
$236$	4.16324e6	0.0206177
$237$	−1.03198e8	−0.503562
$238$	−1.23744e7	−0.0594985
$239$	−8.32340e7	−0.394374	−0.197187	−	0.980366i	$-0.563181\pi$
$239$	−8.32340e7	−0.394374	−0.197187	+	0.980366i	$0.563181\pi$
$240$	4.87091e8	2.27442
$241$	−3.32442e8	−1.52988	−0.764939	−	0.644103i	$-0.777231\pi$
$241$	−3.32442e8	−1.52988	−0.764939	+	0.644103i	$0.777231\pi$
$242$	4.10462e8	1.86174
$243$	−2.04957e8	−0.916305
$244$	−5.33829e8	−2.35255
$245$	−2.31012e8	−1.00358
$246$	6.75910e7	0.289478
$247$	24790.9	0.000104677 0
$248$	−3.64979e8	−1.51945
$249$	−6.73695e7	−0.276545
$250$	1.81953e9	7.36496
$251$	2.29898e8	0.917651	0.458826	−	0.888526i	$-0.348270\pi$
$251$	2.29898e8	0.917651	0.458826	+	0.888526i	$0.348270\pi$
$252$	6.93222e8	2.72879
$253$	4.21654e7	0.163695
$254$	2.04606e8	0.783429
$255$	−5.01411e6	−0.0189366
$256$	1.43404e8	0.534222
$257$	1.27725e8	0.469364	0.234682	−	0.972072i	$-0.424595\pi$
$257$	1.27725e8	0.469364	0.234682	+	0.972072i	$0.424595\pi$
$258$	−1.79627e8	−0.651182
$259$	3.70327e8	1.32445
$260$	9.04114e7	0.319019
$261$	4.59824e7	0.160085
$262$	1.26655e8	0.435080
$263$	−5.02880e8	−1.70459	−0.852293	−	0.523064i	$-0.824789\pi$
$263$	−5.02880e8	−1.70459	−0.852293	+	0.523064i	$0.824789\pi$
$264$	−4.21630e7	−0.141032
$265$	−5.80814e8	−1.91724
$266$	−1.20002e6	−0.00390933
$267$	−6.67469e7	−0.214606
$268$	−5.70590e8	−1.81072
$269$	2.67038e8	0.836451	0.418226	−	0.908343i	$-0.362652\pi$
$269$	2.67038e8	0.836451	0.418226	+	0.908343i	$0.362652\pi$
$270$	8.41832e8	2.60287
$271$	−1.08335e8	−0.330657	−0.165329	−	0.986239i	$-0.552868\pi$
$271$	−1.08335e8	−0.330657	−0.165329	+	0.986239i	$0.552868\pi$
$272$	−2.61948e7	−0.0789267
$273$	−9.51714e6	−0.0283098
$274$	4.50062e8	1.32174
$275$	−1.29474e8	−0.375420
$276$	4.31556e8	1.23554
$277$	−4.99996e8	−1.41347	−0.706736	−	0.707478i	$-0.749833\pi$
$277$	−4.99996e8	−1.41347	−0.706736	+	0.707478i	$0.749833\pi$
$278$	−1.40869e8	−0.393240
$279$	−1.58873e8	−0.437962
$280$	−2.68053e9	−7.29739
$281$	−2.99882e8	−0.806267	−0.403133	−	0.915141i	$-0.632079\pi$
$281$	−2.99882e8	−0.806267	−0.403133	+	0.915141i	$0.632079\pi$
$282$	−4.15454e8	−1.10319
$283$	3.48859e8	0.914951	0.457475	−	0.889222i	$-0.348754\pi$
$283$	3.48859e8	0.914951	0.457475	+	0.889222i	$0.348754\pi$
$284$	−6.23378e8	−1.61487
$285$	−486246.	−0.00124423
$286$	−5.90740e6	−0.0149319
$287$	−2.02356e8	−0.505277
$288$	9.90832e8	2.44414
$289$	−4.10069e8	−0.999343
$290$	−2.90295e8	−0.698950
$291$	1.03336e8	0.245825
$292$	−1.33864e9	−3.14648
$293$	−3.80218e8	−0.883071	−0.441535	−	0.897244i	$-0.645566\pi$
$293$	−3.80218e8	−0.883071	−0.441535	+	0.897244i	$0.645566\pi$
$294$	1.54486e8	0.354546
$295$	−7.00749e6	−0.0158923
$296$	1.44098e9	3.22951
$297$	−3.96428e7	−0.0878044
$298$	6.55111e8	1.43403
$299$	3.70342e7	0.0801225
$300$	−1.32514e9	−2.83359
$301$	5.37773e8	1.13662
$302$	6.19155e8	1.29353
$303$	2.01675e8	0.416487
$304$	−2.54026e6	−0.00518585
$305$	8.98531e8	1.81336
$306$	−2.09595e7	−0.0418172
$307$	−4.43715e7	−0.0875225	−0.0437613	−	0.999042i	$-0.513934\pi$
$307$	−4.43715e7	−0.0875225	−0.0437613	+	0.999042i	$0.513934\pi$
$308$	2.06090e8	0.401911
$309$	−1.11834e8	−0.215634
$310$	1.00299e9	1.91219
$311$	5.54915e8	1.04608	0.523040	−	0.852308i	$-0.324798\pi$
$311$	5.54915e8	1.04608	0.523040	+	0.852308i	$0.324798\pi$
$312$	−3.70321e7	−0.0690299
$313$	4.37487e8	0.806418	0.403209	−	0.915108i	$-0.367895\pi$
$313$	4.37487e8	0.806418	0.403209	+	0.915108i	$0.367895\pi$
$314$	7.20310e8	1.31300
$315$	−1.16682e9	−2.10337
$316$	1.96277e9	3.49918
$317$	2.62334e8	0.462539	0.231269	−	0.972890i	$-0.425712\pi$
$317$	2.62334e8	0.462539	0.231269	+	0.972890i	$0.425712\pi$
$318$	3.88411e8	0.677324
$319$	1.36703e7	0.0235782
$320$	−2.66534e9	−4.54703
$321$	−1.91074e8	−0.322429
$322$	−1.79267e9	−2.99229
$323$	26149.3	4.31769e−5 0
$324$	9.56266e8	1.56196
$325$	−1.13718e8	−0.183754
$326$	−1.50271e9	−2.40222
$327$	−1.30212e8	−0.205937
$328$	−7.87387e8	−1.23205
$329$	1.24380e9	1.92560
$330$	1.15867e8	0.177485
$331$	−8.44477e8	−1.27994	−0.639970	−	0.768400i	$-0.721053\pi$
$331$	−8.44477e8	−1.27994	−0.639970	+	0.768400i	$0.721053\pi$
$332$	1.28133e9	1.92167
$333$	6.27249e8	0.930862
$334$	−1.56862e9	−2.30359
$335$	9.60406e8	1.39572
$336$	9.75196e8	1.40251
$337$	−7.04429e8	−1.00261	−0.501305	−	0.865270i	$-0.667147\pi$
$337$	−7.04429e8	−1.00261	−0.501305	+	0.865270i	$0.667147\pi$
$338$	1.33815e9	1.88494
$339$	−4.07553e8	−0.568179
$340$	9.53657e7	0.131588
$341$	−4.72320e7	−0.0645054
$342$	−2.03256e6	−0.00274758
$343$	4.54201e8	0.607741
$344$	2.09253e9	2.77151
$345$	−7.26387e8	−0.952360
$346$	−5.29848e8	−0.687678
$347$	−9.38969e8	−1.20642	−0.603209	−	0.797583i	$-0.706112\pi$
$347$	−9.38969e8	−1.20642	−0.603209	+	0.797583i	$0.706112\pi$
$348$	1.39913e8	0.177963
$349$	−3.13865e7	−0.0395233	−0.0197617	−	0.999805i	$-0.506291\pi$
$349$	−3.13865e7	−0.0395233	−0.0197617	+	0.999805i	$0.506291\pi$
$350$	5.50458e9	6.86256
$351$	−3.48186e7	−0.0429770
$352$	2.94568e8	0.359987
$353$	−9.22765e8	−1.11655	−0.558277	−	0.829655i	$-0.688537\pi$
$353$	−9.22765e8	−1.11655	−0.558277	+	0.829655i	$0.688537\pi$
$354$	4.68615e6	0.00561442
$355$	1.04926e9	1.24475
$356$	1.26949e9	1.49126
$357$	−1.00387e7	−0.0116771
$358$	−2.06303e9	−2.37638
$359$	−1.10168e9	−1.25669	−0.628343	−	0.777937i	$-0.716266\pi$
$359$	−1.10168e9	−1.25669	−0.628343	+	0.777937i	$0.716266\pi$
$360$	−4.54020e9	−5.12881
$361$	−8.93869e8	−0.999997
$362$	−2.34789e9	−2.60134
$363$	3.32984e8	0.365384
$364$	1.81011e8	0.196721
$365$	2.25318e9	2.42533
$366$	−6.00879e8	−0.640624
$367$	1.73563e9	1.83284	0.916421	−	0.400215i	$-0.131065\pi$
$367$	1.73563e9	1.83284	0.916421	+	0.400215i	$0.131065\pi$
$368$	−3.79480e9	−3.96937
$369$	−3.42745e8	−0.355123
$370$	−3.95993e9	−4.06426
$371$	−1.16284e9	−1.18225
$372$	−4.83411e8	−0.486874
$373$	−2.69964e8	−0.269355	−0.134677	−	0.990889i	$-0.543000\pi$
$373$	−2.69964e8	−0.269355	−0.134677	+	0.990889i	$0.543000\pi$
$374$	−6.23111e6	−0.00615907
$375$	1.47608e9	1.44544
$376$	4.83975e9	4.69532
$377$	1.20067e7	0.0115406
$378$	1.68542e9	1.60504
$379$	6.00121e8	0.566242	0.283121	−	0.959084i	$-0.408630\pi$
$379$	6.00121e8	0.566242	0.283121	+	0.959084i	$0.408630\pi$
$380$	9.24814e6	0.00864593
$381$	1.65984e8	0.153755
$382$	2.01232e9	1.84704
$383$	8.51456e8	0.774402	0.387201	−	0.921995i	$-0.373442\pi$
$383$	8.51456e8	0.774402	0.387201	+	0.921995i	$0.373442\pi$
$384$	6.14130e8	0.553479
$385$	−3.46888e8	−0.309796
$386$	1.24958e9	1.10588
$387$	9.10865e8	0.798851
$388$	−1.96539e9	−1.70820
$389$	−1.04415e9	−0.899370	−0.449685	−	0.893187i	$-0.648464\pi$
$389$	−1.04415e9	−0.899370	−0.449685	+	0.893187i	$0.648464\pi$
$390$	1.01767e8	0.0868724
$391$	3.90636e7	0.0330487
$392$	−1.79965e9	−1.50899
$393$	1.02748e8	0.0853885
$394$	−2.82531e9	−2.32717
$395$	−3.30371e9	−2.69719
$396$	3.49070e8	0.282475
$397$	1.61828e9	1.29804	0.649018	−	0.760773i	$-0.275180\pi$
$397$	1.61828e9	1.29804	0.649018	+	0.760773i	$0.275180\pi$
$398$	−1.63725e9	−1.30174
$399$	−973504.	−0.000767242 0
$400$	1.16524e10	9.10341
$401$	−1.05869e7	−0.00819902	−0.00409951	−	0.999992i	$-0.501305\pi$
$401$	−1.05869e7	−0.00819902	−0.00409951	+	0.999992i	$0.501305\pi$
$402$	−6.42257e8	−0.493080
$403$	−4.14842e7	−0.0315730
$404$	−3.83574e9	−2.89411
$405$	−1.60957e9	−1.20397
$406$	−5.81193e8	−0.431002
$407$	1.86477e8	0.137102
$408$	−3.90614e7	−0.0284732
$409$	8.75680e8	0.632869	0.316434	−	0.948614i	$-0.397514\pi$
$409$	8.75680e8	0.632869	0.316434	+	0.948614i	$0.397514\pi$
$410$	2.16380e9	1.55051
$411$	3.65109e8	0.259404
$412$	2.12702e9	1.49841
$413$	−1.40296e7	−0.00979984
$414$	−3.03637e9	−2.10307
$415$	−2.15671e9	−1.48123
$416$	2.58721e8	0.176200
$417$	−1.14278e8	−0.0771770
$418$	−604266.	−0.000404679 0
$419$	2.17459e9	1.44420	0.722100	−	0.691789i	$-0.243177\pi$
$419$	2.17459e9	1.44420	0.722100	+	0.691789i	$0.243177\pi$
$420$	−3.55033e9	−2.33828
$421$	−8.45208e8	−0.552047	−0.276024	−	0.961151i	$-0.589017\pi$
$421$	−8.45208e8	−0.552047	−0.276024	+	0.961151i	$0.589017\pi$
$422$	−3.88848e9	−2.51876
$423$	2.10671e9	1.35336
$424$	−4.52471e9	−2.88277
$425$	−1.19949e8	−0.0757942
$426$	−7.01675e8	−0.439747
$427$	1.79893e9	1.11819
$428$	3.63412e9	2.24051
$429$	−4.79233e6	−0.00293053
$430$	−5.75043e9	−3.48788
$431$	−2.57077e9	−1.54665	−0.773326	−	0.634009i	$-0.781408\pi$
$431$	−2.57077e9	−1.54665	−0.773326	+	0.634009i	$0.781408\pi$
$432$	3.56777e9	2.12914
$433$	1.81619e9	1.07511	0.537557	−	0.843227i	$-0.319347\pi$
$433$	1.81619e9	1.07511	0.537557	+	0.843227i	$0.319347\pi$
$434$	2.00807e9	1.17914
$435$	−2.35499e8	−0.137175
$436$	2.47657e9	1.43103
$437$	3.78822e6	0.00217145
$438$	−1.50678e9	−0.856821
$439$	−5.59916e8	−0.315862	−0.157931	−	0.987450i	$-0.550482\pi$
$439$	−5.59916e8	−0.315862	−0.157931	+	0.987450i	$0.550482\pi$
$440$	−1.34977e9	−0.755399
$441$	−7.83377e8	−0.434946
$442$	−5.47284e6	−0.00301463
$443$	−1.12567e9	−0.615176	−0.307588	−	0.951520i	$-0.599522\pi$
$443$	−1.12567e9	−0.615176	−0.307588	+	0.951520i	$0.599522\pi$
$444$	1.90856e9	1.03482
$445$	−2.13678e9	−1.14948
$446$	1.43964e9	0.768389
$447$	5.31453e8	0.281442
$448$	−5.33622e9	−2.80389
$449$	2.83306e9	1.47705	0.738523	−	0.674228i	$-0.235524\pi$
$449$	2.83306e9	1.47705	0.738523	+	0.674228i	$0.235524\pi$
$450$	9.32350e9	4.82320
$451$	−1.01896e8	−0.0523044
$452$	7.75144e9	3.94819
$453$	5.02283e8	0.253866
$454$	−6.57119e9	−3.29571
$455$	−3.04674e8	−0.151634
$456$	−3.78800e6	−0.00187082
$457$	1.21462e9	0.595299	0.297650	−	0.954675i	$-0.403797\pi$
$457$	1.21462e9	0.595299	0.297650	+	0.954675i	$0.403797\pi$
$458$	3.38435e8	0.164606
$459$	−3.67265e7	−0.0177270
$460$	1.38155e10	6.61780
$461$	−9.30568e8	−0.442379	−0.221190	−	0.975231i	$-0.570994\pi$
$461$	−9.30568e8	−0.442379	−0.221190	+	0.975231i	$0.570994\pi$
$462$	2.31976e8	0.109445
$463$	−3.09957e8	−0.145134	−0.0725668	−	0.997364i	$-0.523119\pi$
$463$	−3.09957e8	−0.145134	−0.0725668	+	0.997364i	$0.523119\pi$
$464$	−1.23030e9	−0.571738
$465$	8.13668e8	0.375286
$466$	6.24547e8	0.285900
$467$	−3.28841e9	−1.49409	−0.747045	−	0.664774i	$-0.768528\pi$
$467$	−3.28841e9	−1.49409	−0.747045	+	0.664774i	$0.768528\pi$
$468$	3.06591e8	0.138261
$469$	1.92281e9	0.860659
$470$	−1.33000e10	−5.90894
$471$	5.84345e8	0.257689
$472$	−5.45904e7	−0.0238957
$473$	2.70794e8	0.117659
$474$	2.20930e9	0.952864
$475$	−1.16321e7	−0.00498003
$476$	1.90930e8	0.0811427
$477$	−1.96958e9	−0.830920
$478$	1.78190e9	0.746253
$479$	−3.69945e9	−1.53802	−0.769011	−	0.639235i	$-0.779251\pi$
$479$	−3.69945e9	−1.53802	−0.769011	+	0.639235i	$0.779251\pi$
$480$	−5.07454e9	−2.09436
$481$	1.63784e8	0.0671065
$482$	7.11704e9	2.89491
$483$	−1.45428e9	−0.587265
$484$	−6.33317e9	−2.53900
$485$	3.30811e9	1.31669
$486$	4.38778e9	1.73388
$487$	2.65223e9	1.04054	0.520271	−	0.854001i	$-0.325831\pi$
$487$	2.65223e9	1.04054	0.520271	+	0.854001i	$0.325831\pi$
$488$	6.99982e9	2.72657
$489$	−1.21906e9	−0.471458
$490$	4.94558e9	1.89903
$491$	−4.26223e8	−0.162500	−0.0812498	−	0.996694i	$-0.525891\pi$
$491$	−4.26223e8	−0.162500	−0.0812498	+	0.996694i	$0.525891\pi$
$492$	−1.04289e9	−0.394783
$493$	1.26647e7	0.00476024
$494$	−530731.	−0.000198075 0
$495$	−5.87548e8	−0.217733
$496$	4.25078e9	1.56417
$497$	2.10070e9	0.767568
$498$	1.44227e9	0.523291
$499$	−3.33501e8	−0.120156	−0.0600779	−	0.998194i	$-0.519135\pi$
$499$	−3.33501e8	−0.120156	−0.0600779	+	0.998194i	$0.519135\pi$
$500$	−2.80743e10	−10.0441
$501$	−1.27253e9	−0.452101
$502$	−4.92174e9	−1.73642
$503$	9.70208e8	0.339920	0.169960	−	0.985451i	$-0.445636\pi$
$503$	9.70208e8	0.339920	0.169960	+	0.985451i	$0.445636\pi$
$504$	−9.08985e9	−3.16264
$505$	6.45625e9	2.23080
$506$	−9.02692e8	−0.309751
$507$	1.08556e9	0.369937
$508$	−3.15693e9	−1.06842
$509$	2.45615e9	0.825548	0.412774	−	0.910834i	$-0.364560\pi$
$509$	2.45615e9	0.825548	0.412774	+	0.910834i	$0.364560\pi$
$510$	1.07344e8	0.0358328
$511$	4.51104e9	1.49556
$512$	1.45620e9	0.479485
$513$	−3.56157e6	−0.00116475
$514$	−2.73438e9	−0.888153
$515$	−3.58015e9	−1.15498
$516$	2.77153e9	0.888066
$517$	6.26312e8	0.199331
$518$	−7.92809e9	−2.50619
$519$	−4.29834e8	−0.134963
$520$	−1.18552e9	−0.369739
$521$	−2.13155e9	−0.660333	−0.330167	−	0.943923i	$-0.607105\pi$
$521$	−2.13155e9	−0.660333	−0.330167	+	0.943923i	$0.607105\pi$
$522$	−9.84408e8	−0.302920
$523$	−2.27400e9	−0.695079	−0.347539	−	0.937665i	$-0.612983\pi$
$523$	−2.27400e9	−0.695079	−0.347539	+	0.937665i	$0.612983\pi$
$524$	−1.95421e9	−0.593352
$525$	4.46554e9	1.34684
$526$	1.07658e10	3.22550
$527$	−4.37575e7	−0.0130231
$528$	4.91057e8	0.145182
$529$	2.25426e9	0.662079
$530$	1.24343e10	3.62790
$531$	−2.37629e7	−0.00688760
$532$	1.85155e7	0.00533145
$533$	−8.94959e7	−0.0256011
$534$	1.42894e9	0.406087
$535$	−6.11689e9	−1.72700
$536$	7.48184e9	2.09861
$537$	−1.67362e9	−0.466386
$538$	−5.71685e9	−1.58277
$539$	−2.32893e8	−0.0640612
$540$	−1.29889e10	−3.54973
$541$	1.07263e9	0.291247	0.145623	−	0.989340i	$-0.453481\pi$
$541$	1.07263e9	0.291247	0.145623	+	0.989340i	$0.453481\pi$
$542$	2.31928e9	0.625685
$543$	−1.90470e9	−0.510538
$544$	2.72899e8	0.0726784
$545$	−4.16851e9	−1.10305
$546$	2.03746e8	0.0535692
$547$	5.97703e9	1.56146	0.780728	−	0.624871i	$-0.214848\pi$
$547$	5.97703e9	1.56146	0.780728	+	0.624871i	$0.214848\pi$
$548$	−6.94417e9	−1.80256
$549$	3.04698e9	0.785898
$550$	2.77182e9	0.710387
$551$	1.22816e6	0.000312770 0
$552$	−5.65876e9	−1.43197
$553$	−6.61429e9	−1.66320
$554$	1.07041e10	2.67464
$555$	−3.21245e9	−0.797648
$556$	2.17351e9	0.536291
$557$	−1.08950e9	−0.267138	−0.133569	−	0.991040i	$-0.542644\pi$
$557$	−1.08950e9	−0.267138	−0.133569	+	0.991040i	$0.542644\pi$
$558$	3.40121e9	0.828732
$559$	2.37841e8	0.0575897
$560$	3.12192e10	7.51213
$561$	−5.05493e6	−0.00120877
$562$	6.41998e9	1.52566
$563$	3.62998e9	0.857285	0.428642	−	0.903474i	$-0.358992\pi$
$563$	3.62998e9	0.857285	0.428642	+	0.903474i	$0.358992\pi$
$564$	6.41019e9	1.50451
$565$	−1.30471e10	−3.04329
$566$	−7.46850e9	−1.73131
$567$	−3.22249e9	−0.742421
$568$	8.17402e9	1.87162
$569$	3.79936e9	0.864606	0.432303	−	0.901729i	$-0.357701\pi$
$569$	3.79936e9	0.864606	0.432303	+	0.901729i	$0.357701\pi$
$570$	1.04097e7	0.00235438
$571$	−4.48098e9	−1.00727	−0.503636	−	0.863916i	$-0.668005\pi$
$571$	−4.48098e9	−1.00727	−0.503636	+	0.863916i	$0.668005\pi$
$572$	9.11475e7	0.0203638
$573$	1.63248e9	0.362499
$574$	4.33211e9	0.956110
$575$	−1.73769e10	−3.81183
$576$	−9.03834e9	−1.97065
$577$	3.53483e9	0.766042	0.383021	−	0.923740i	$-0.374884\pi$
$577$	3.53483e9	0.766042	0.383021	+	0.923740i	$0.374884\pi$
$578$	8.77890e9	1.89100
$579$	1.01371e9	0.217040
$580$	4.47906e9	0.953210
$581$	−4.31791e9	−0.913392
$582$	−2.21225e9	−0.465161
$583$	−5.85543e8	−0.122382
$584$	1.75529e10	3.64673
$585$	−5.16048e8	−0.106572
$586$	8.13983e9	1.67099
$587$	6.82623e9	1.39299	0.696494	−	0.717563i	$-0.254742\pi$
$587$	6.82623e9	1.39299	0.696494	+	0.717563i	$0.254742\pi$
$588$	−2.38361e9	−0.483521
$589$	−4.24340e6	−0.000855679 0
$590$	1.50019e8	0.0300721
$591$	−2.29200e9	−0.456730
$592$	−1.67826e10	−3.32454
$593$	5.72589e9	1.12759	0.563795	−	0.825915i	$-0.309341\pi$
$593$	5.72589e9	1.12759	0.563795	+	0.825915i	$0.309341\pi$
$594$	8.48686e8	0.166148
$595$	−3.21369e8	−0.0625454
$596$	−1.01079e10	−1.95570
$597$	−1.32820e9	−0.255478
$598$	−7.92842e8	−0.151612
$599$	8.45355e7	0.0160711	0.00803554	−	0.999968i	$-0.497442\pi$
$599$	8.45355e7	0.0160711	0.00803554	+	0.999968i	$0.497442\pi$
$600$	1.73759e10	3.28410
$601$	−7.17485e9	−1.34819	−0.674097	−	0.738643i	$-0.735467\pi$
$601$	−7.17485e9	−1.34819	−0.674097	+	0.738643i	$0.735467\pi$
$602$	−1.15128e10	−2.15077
$603$	3.25680e9	0.604895
$604$	−9.55316e9	−1.76408
$605$	1.06599e10	1.95708
$606$	−4.31752e9	−0.788097
$607$	−9.73302e9	−1.76639	−0.883197	−	0.469003i	$-0.844613\pi$
$607$	−9.73302e9	−1.76639	−0.883197	+	0.469003i	$0.844613\pi$
$608$	2.64645e7	0.00477530
$609$	−4.71487e8	−0.0845882
$610$	−1.92361e10	−3.43132
$611$	5.50095e8	0.0975649
$612$	3.23391e8	0.0570293
$613$	1.43582e9	0.251761	0.125881	−	0.992045i	$-0.459824\pi$
$613$	1.43582e9	0.251761	0.125881	+	0.992045i	$0.459824\pi$
$614$	9.49920e8	0.165614
$615$	1.75537e9	0.304302
$616$	−2.70235e9	−0.465811
$617$	−3.90430e9	−0.669184	−0.334592	−	0.942363i	$-0.608598\pi$
$617$	−3.90430e9	−0.669184	−0.334592	+	0.942363i	$0.608598\pi$
$618$	2.39417e9	0.408033
$619$	1.06024e10	1.79675	0.898377	−	0.439226i	$-0.144747\pi$
$619$	1.06024e10	1.79675	0.898377	+	0.439226i	$0.144747\pi$
$620$	−1.54755e10	−2.60780
$621$	−5.32052e9	−0.891524
$622$	−1.18798e10	−1.97944
$623$	−4.27801e9	−0.708816
$624$	4.31299e8	0.0710612
$625$	2.92078e10	4.78540
$626$	−9.36588e9	−1.52594
$627$	−490205.	−7.94221e−5 0
$628$	−1.11139e10	−1.79064
$629$	1.72759e8	0.0276799
$630$	2.49796e10	3.98010
$631$	−3.34188e9	−0.529527	−0.264763	−	0.964313i	$-0.585294\pi$
$631$	−3.34188e9	−0.529527	−0.264763	+	0.964313i	$0.585294\pi$
$632$	−2.57368e10	−4.05551
$633$	−3.15449e9	−0.494329
$634$	−5.61615e9	−0.875238
$635$	5.31369e9	0.823547
$636$	−5.99293e9	−0.923718
$637$	−2.04552e8	−0.0313556
$638$	−2.92658e8	−0.0446157
$639$	3.55810e9	0.539468
$640$	1.96603e10	2.96455
$641$	−9.88110e9	−1.48184	−0.740921	−	0.671592i	$-0.765611\pi$
$641$	−9.88110e9	−1.48184	−0.740921	+	0.671592i	$0.765611\pi$
$642$	4.09058e9	0.610115
$643$	1.17499e10	1.74299	0.871493	−	0.490408i	$-0.163152\pi$
$643$	1.17499e10	1.74299	0.871493	+	0.490408i	$0.163152\pi$
$644$	2.76597e10	4.08082
$645$	−4.66499e9	−0.684528
$646$	−559814.	−8.17015e−5 0
$647$	3.43909e8	0.0499205	0.0249603	−	0.999688i	$-0.492054\pi$
$647$	3.43909e8	0.0499205	0.0249603	+	0.999688i	$0.492054\pi$
$648$	−1.25390e10	−1.81030
$649$	−7.06454e6	−0.00101444
$650$	2.43451e9	0.347708
$651$	1.62903e9	0.231417
$652$	2.31858e10	3.27609
$653$	−1.92075e9	−0.269944	−0.134972	−	0.990849i	$-0.543094\pi$
$653$	−1.92075e9	−0.269944	−0.134972	+	0.990849i	$0.543094\pi$
$654$	2.78763e9	0.389684
$655$	3.28929e9	0.457360
$656$	9.17041e9	1.26831
$657$	7.64068e9	1.05112
$658$	−2.66277e10	−3.64371
$659$	−5.47057e9	−0.744618	−0.372309	−	0.928109i	$-0.621434\pi$
$659$	−5.47057e9	−0.744618	−0.372309	+	0.928109i	$0.621434\pi$
$660$	−1.78776e9	−0.242050
$661$	8.76326e9	1.18021	0.590107	−	0.807325i	$-0.299086\pi$
$661$	8.76326e9	1.18021	0.590107	+	0.807325i	$0.299086\pi$
$662$	1.80789e10	2.42197
$663$	−4.43979e6	−0.000591650 0
$664$	−1.68014e10	−2.22719
$665$	−3.11650e7	−0.00410952
$666$	−1.34284e10	−1.76142
$667$	1.83471e9	0.239401
$668$	2.42028e10	3.14158
$669$	1.16789e9	0.150804
$670$	−2.05607e10	−2.64105
$671$	9.05847e8	0.115751
$672$	−1.01596e10	−1.29147
$673$	−1.12854e10	−1.42713	−0.713564	−	0.700590i	$-0.752920\pi$
$673$	−1.12854e10	−1.42713	−0.713564	+	0.700590i	$0.752920\pi$
$674$	1.50806e10	1.89719
$675$	1.63372e10	2.04463
$676$	−2.06468e10	−2.57063
$677$	−9.59143e9	−1.18802	−0.594009	−	0.804458i	$-0.702456\pi$
$677$	−9.59143e9	−1.18802	−0.594009	+	0.804458i	$0.702456\pi$
$678$	8.72503e9	1.07514
$679$	6.62311e9	0.811928
$680$	−1.25048e9	−0.152509
$681$	−5.33082e9	−0.646813
$682$	1.01116e9	0.122060
$683$	−3.39785e9	−0.408067	−0.204033	−	0.978964i	$-0.565405\pi$
$683$	−3.39785e9	−0.408067	−0.204033	+	0.978964i	$0.565405\pi$
$684$	3.13610e7	0.00374709
$685$	1.16883e10	1.38942
$686$	−9.72368e9	−1.15000
$687$	2.74552e8	0.0323055
$688$	−2.43709e10	−2.85307
$689$	−5.14287e8	−0.0599016
$690$	1.55507e10	1.80210
$691$	4.24667e9	0.489639	0.244819	−	0.969569i	$-0.421271\pi$
$691$	4.24667e9	0.489639	0.244819	+	0.969569i	$0.421271\pi$
$692$	8.17522e9	0.937839
$693$	−1.17632e9	−0.134264
$694$	2.01018e10	2.28284
$695$	−3.65842e9	−0.413377
$696$	−1.83460e9	−0.206257
$697$	−9.44001e7	−0.0105598
$698$	6.71932e8	0.0747879
$699$	5.06658e8	0.0561106
$700$	−8.49322e10	−9.35900
$701$	9.84697e9	1.07967	0.539833	−	0.841772i	$-0.318487\pi$
$701$	9.84697e9	1.07967	0.539833	+	0.841772i	$0.318487\pi$
$702$	7.45408e8	0.0813231
$703$	1.67534e7	0.00181870
$704$	−2.68704e9	−0.290248
$705$	−1.07895e10	−1.15969
$706$	1.97549e10	2.11280
$707$	1.29259e10	1.37561
$708$	−7.23043e7	−0.00765681
$709$	1.66782e10	1.75747	0.878734	−	0.477312i	$-0.158389\pi$
$709$	1.66782e10	1.75747	0.878734	+	0.477312i	$0.158389\pi$
$710$	−2.24629e10	−2.35538
$711$	−1.12031e10	−1.16894
$712$	−1.66461e10	−1.72836
$713$	−6.33908e9	−0.654957
$714$	2.14911e8	0.0220960
$715$	−1.53418e8	−0.0156966
$716$	3.18313e10	3.24085
$717$	1.44555e9	0.146459
$718$	2.35852e10	2.37796
$719$	−1.39508e10	−1.39974	−0.699870	−	0.714271i	$-0.746759\pi$
$719$	−1.39508e10	−1.39974	−0.699870	+	0.714271i	$0.746759\pi$
$720$	5.28781e10	5.27974
$721$	−7.16775e9	−0.712213
$722$	1.91363e10	1.89224
$723$	5.77363e9	0.568153
$724$	3.62265e10	3.54765
$725$	−5.63368e9	−0.549046
$726$	−7.12862e9	−0.691397
$727$	−6.63843e9	−0.640760	−0.320380	−	0.947289i	$-0.603811\pi$
$727$	−6.63843e9	−0.640760	−0.320380	+	0.947289i	$0.603811\pi$
$728$	−2.37350e9	−0.227997
$729$	−2.77181e9	−0.264982
$730$	−4.82368e10	−4.58932
$731$	2.50874e8	0.0237544
$732$	9.27118e9	0.873668
$733$	1.50258e10	1.40920	0.704599	−	0.709605i	$-0.251127\pi$
$733$	1.50258e10	1.40920	0.704599	+	0.709605i	$0.251127\pi$
$734$	−3.71569e10	−3.46819
$735$	4.01206e9	0.372702
$736$	3.95344e10	3.65513
$737$	9.68225e8	0.0890923
$738$	7.33760e9	0.671981
$739$	−1.21753e10	−1.10975	−0.554874	−	0.831935i	$-0.687233\pi$
$739$	−1.21753e10	−1.10975	−0.554874	+	0.831935i	$0.687233\pi$
$740$	6.10991e10	5.54273
$741$	−430551.	−3.88741e−5 0
$742$	2.48944e10	2.23712
$743$	7.23748e9	0.647331	0.323666	−	0.946172i	$-0.395085\pi$
$743$	7.23748e9	0.647331	0.323666	+	0.946172i	$0.395085\pi$
$744$	6.33871e9	0.564281
$745$	1.70135e10	1.50746
$746$	5.77948e9	0.509686
$747$	−7.31355e9	−0.641958
$748$	9.61421e7	0.00839959
$749$	−1.22465e10	−1.06494
$750$	−3.16004e10	−2.73513
$751$	2.12281e9	0.182882	0.0914409	−	0.995811i	$-0.470853\pi$
$751$	2.12281e9	0.182882	0.0914409	+	0.995811i	$0.470853\pi$
$752$	−5.63668e10	−4.83349
$753$	−3.99272e9	−0.340789
$754$	−2.57044e8	−0.0218377
$755$	1.60797e10	1.35976
$756$	−2.60049e10	−2.18891
$757$	−1.11752e10	−0.936314	−0.468157	−	0.883645i	$-0.655082\pi$
$757$	−1.11752e10	−0.936314	−0.468157	+	0.883645i	$0.655082\pi$
$758$	−1.28476e10	−1.07147
$759$	−7.32301e8	−0.0607915
$760$	−1.21266e8	−0.0100205
$761$	−7.82620e9	−0.643731	−0.321866	−	0.946785i	$-0.604310\pi$
$761$	−7.82620e9	−0.643731	−0.321866	+	0.946785i	$0.604310\pi$
$762$	−3.55345e9	−0.290943
$763$	−8.34570e9	−0.680185
$764$	−3.10489e10	−2.51895
$765$	−5.44326e8	−0.0439586
$766$	−1.82283e10	−1.46536
$767$	−6.20484e6	−0.000496532 0
$768$	−2.49054e9	−0.198395
$769$	1.61981e10	1.28446	0.642232	−	0.766510i	$-0.278009\pi$
$769$	1.61981e10	1.28446	0.642232	+	0.766510i	$0.278009\pi$
$770$	7.42629e9	0.586211
$771$	−2.21824e9	−0.174308
$772$	−1.92803e10	−1.50818
$773$	−1.81273e10	−1.41157	−0.705787	−	0.708424i	$-0.749407\pi$
$773$	−1.81273e10	−1.41157	−0.705787	+	0.708424i	$0.749407\pi$
$774$	−1.95001e10	−1.51162
$775$	1.94648e10	1.50209
$776$	2.57711e10	1.97978
$777$	−6.43159e9	−0.491864
$778$	2.23535e10	1.70183
$779$	−9.15450e6	−0.000693830 0
$780$	−1.57020e9	−0.118474
$781$	1.05780e9	0.0794558
$782$	−8.36287e8	−0.0625363
$783$	−1.72494e9	−0.128413
$784$	2.09599e10	1.55340
$785$	1.87067e10	1.38024
$786$	−2.19966e9	−0.161576
$787$	1.16655e10	0.853081	0.426540	−	0.904469i	$-0.359732\pi$
$787$	1.16655e10	0.853081	0.426540	+	0.904469i	$0.359732\pi$
$788$	4.35927e10	3.17374
$789$	8.73367e9	0.633035
$790$	7.07269e10	5.10375
$791$	−2.61213e10	−1.87662
$792$	−4.57717e9	−0.327385
$793$	7.95613e8	0.0566559
$794$	−3.46447e10	−2.45621
$795$	1.00872e10	0.712008
$796$	2.52617e10	1.77528
$797$	−8.70154e9	−0.608824	−0.304412	−	0.952540i	$-0.598460\pi$
$797$	−8.70154e9	−0.608824	−0.304412	+	0.952540i	$0.598460\pi$
$798$	2.08411e7	0.00145181
$799$	5.80239e8	0.0402433
$800$	−1.21395e11	−8.38272
$801$	−7.24597e9	−0.498176
$802$	2.26647e8	0.0155146
$803$	2.27152e9	0.154815
$804$	9.90961e9	0.672450
$805$	−4.65563e10	−3.14552
$806$	8.88109e8	0.0597439
$807$	−4.63774e9	−0.310634
$808$	5.02960e10	3.35424
$809$	−2.59441e10	−1.72273	−0.861367	−	0.507983i	$-0.830391\pi$
$809$	−2.59441e10	−1.72273	−0.861367	+	0.507983i	$0.830391\pi$
$810$	3.44582e10	2.27822
$811$	−1.47007e10	−0.967753	−0.483876	−	0.875136i	$-0.660772\pi$
$811$	−1.47007e10	−0.967753	−0.483876	+	0.875136i	$0.660772\pi$
$812$	8.96744e9	0.587790
$813$	1.88149e9	0.122797
$814$	−3.99217e9	−0.259432
$815$	−3.90259e10	−2.52523
$816$	4.54933e8	0.0293111
$817$	2.43286e7	0.00156077
$818$	−1.87468e10	−1.19754
$819$	−1.03317e9	−0.0657171
$820$	−3.33861e10	−2.11455
$821$	−1.29014e10	−0.813645	−0.406822	−	0.913507i	$-0.633363\pi$
$821$	−1.29014e10	−0.813645	−0.406822	+	0.913507i	$0.633363\pi$
$822$	−7.81637e9	−0.490856
$823$	−1.69684e10	−1.06106	−0.530532	−	0.847665i	$-0.678008\pi$
$823$	−1.69684e10	−1.06106	−0.530532	+	0.847665i	$0.678008\pi$
$824$	−2.78904e10	−1.73664
$825$	2.24861e9	0.139420
$826$	3.00350e8	0.0185437
$827$	8.05883e9	0.495453	0.247727	−	0.968830i	$-0.420317\pi$
$827$	8.05883e9	0.495453	0.247727	+	0.968830i	$0.420317\pi$
$828$	4.68492e10	2.86811
$829$	1.62807e10	0.992504	0.496252	−	0.868179i	$-0.334709\pi$
$829$	1.62807e10	0.992504	0.496252	+	0.868179i	$0.334709\pi$
$830$	4.61716e10	2.80286
$831$	8.68358e9	0.524923
$832$	−2.36005e9	−0.142066
$833$	−2.15760e8	−0.0129334
$834$	2.44651e9	0.146038
$835$	−4.07377e10	−2.42155
$836$	9.32343e6	0.000551892 0
$837$	5.95983e9	0.351313
$838$	−4.65543e10	−2.73278
$839$	−1.08665e9	−0.0635220	−0.0317610	−	0.999495i	$-0.510112\pi$
$839$	−1.08665e9	−0.0635220	−0.0317610	+	0.999495i	$0.510112\pi$
$840$	4.65536e10	2.71004
$841$	5.94823e8	0.0344828
$842$	1.80945e10	1.04461
$843$	5.20815e9	0.299424
$844$	5.99967e10	3.43502
$845$	3.47524e10	1.98146
$846$	−4.51013e10	−2.56090
$847$	2.13419e10	1.20682
$848$	5.26977e10	2.96760
$849$	−6.05875e9	−0.339786
$850$	2.56791e9	0.143421
$851$	2.50274e10	1.39207
$852$	1.08264e10	0.599716
$853$	−2.73782e10	−1.51037	−0.755186	−	0.655511i	$-0.772453\pi$
$853$	−2.73782e10	−1.51037	−0.755186	+	0.655511i	$0.772453\pi$
$854$	−3.85122e10	−2.11590
$855$	−5.27863e7	−0.00288828
$856$	−4.76523e10	−2.59673
$857$	6.68113e9	0.362591	0.181295	−	0.983429i	$-0.441971\pi$
$857$	6.68113e9	0.362591	0.181295	+	0.983429i	$0.441971\pi$
$858$	1.02596e8	0.00554528
$859$	−1.64095e10	−0.883324	−0.441662	−	0.897181i	$-0.645611\pi$
$859$	−1.64095e10	−0.883324	−0.441662	+	0.897181i	$0.645611\pi$
$860$	8.87255e10	4.75668
$861$	3.51438e9	0.187645
$862$	5.50359e10	2.92665
$863$	1.98350e10	1.05049	0.525247	−	0.850950i	$-0.323973\pi$
$863$	1.98350e10	1.05049	0.525247	+	0.850950i	$0.323973\pi$
$864$	−3.71692e10	−1.96058
$865$	−1.37604e10	−0.722893
$866$	−3.88817e10	−2.03438
$867$	7.12180e9	0.371127
$868$	−3.09833e10	−1.60808
$869$	−3.33060e9	−0.172169
$870$	5.04164e9	0.259570
$871$	8.50400e8	0.0436073
$872$	−3.24739e10	−1.65854
$873$	1.12180e10	0.570646
$874$	−8.10994e7	−0.00410892
$875$	9.46064e10	4.77411
$876$	2.32486e10	1.16851
$877$	−1.12384e10	−0.562608	−0.281304	−	0.959619i	$-0.590767\pi$
$877$	−1.12384e10	−0.562608	−0.281304	+	0.959619i	$0.590767\pi$
$878$	1.19869e10	0.597689
$879$	6.60336e9	0.327947
$880$	1.57203e10	0.777628
$881$	1.80903e10	0.891311	0.445656	−	0.895204i	$-0.352971\pi$
$881$	1.80903e10	0.891311	0.445656	+	0.895204i	$0.352971\pi$
$882$	1.67708e10	0.823026
$883$	2.80221e10	1.36974	0.684870	−	0.728665i	$-0.259859\pi$
$883$	2.80221e10	1.36974	0.684870	+	0.728665i	$0.259859\pi$
$884$	8.44424e7	0.00411128
$885$	1.21701e8	0.00590193
$886$	2.40988e10	1.16407
$887$	3.91352e10	1.88293	0.941466	−	0.337109i	$-0.109449\pi$
$887$	3.91352e10	1.88293	0.941466	+	0.337109i	$0.109449\pi$
$888$	−2.50259e10	−1.19935
$889$	1.06384e10	0.507834
$890$	4.57449e10	2.17509
$891$	−1.62267e9	−0.0768527
$892$	−2.22127e10	−1.04791
$893$	5.62690e7	0.00264417
$894$	−1.13775e10	−0.532557
$895$	−5.35778e10	−2.49807
$896$	3.93614e10	1.82807
$897$	−6.43185e8	−0.0297552
$898$	−6.06512e10	−2.79494
$899$	−2.05517e9	−0.0943383
$900$	−1.43856e11	−6.57776
$901$	−5.42469e8	−0.0247080
$902$	2.18142e9	0.0989730
$903$	−9.33968e9	−0.422109
$904$	−1.01640e11	−4.57591
$905$	−6.09757e10	−2.73456
$906$	−1.07531e10	−0.480378
$907$	3.27554e10	1.45766	0.728832	−	0.684693i	$-0.240064\pi$
$907$	3.27554e10	1.45766	0.728832	+	0.684693i	$0.240064\pi$
$908$	1.01389e11	4.49460
$909$	2.18936e10	0.966814
$910$	6.52257e9	0.286928
$911$	7.89358e9	0.345907	0.172954	−	0.984930i	$-0.444669\pi$
$911$	7.89358e9	0.345907	0.172954	+	0.984930i	$0.444669\pi$
$912$	4.41174e7	0.00192588
$913$	−2.17427e9	−0.0945510
$914$	−2.60031e10	−1.12645
$915$	−1.56051e10	−0.673429
$916$	−5.22183e9	−0.224486
$917$	6.58543e9	0.282027
$918$	7.86254e8	0.0335439
$919$	3.35800e8	0.0142717	0.00713586	−	0.999975i	$-0.497729\pi$
$919$	3.35800e8	0.0142717	0.00713586	+	0.999975i	$0.497729\pi$
$920$	−1.81155e11	−7.66996
$921$	7.70614e8	0.0325033
$922$	1.99219e10	0.837091
$923$	9.29075e8	0.0388906
$924$	−3.57924e9	−0.149258
$925$	−7.68493e10	−3.19260
$926$	6.63566e9	0.274629
$927$	−1.21405e10	−0.500563
$928$	1.28173e10	0.526476
$929$	2.34093e10	0.957928	0.478964	−	0.877835i	$-0.341012\pi$
$929$	2.34093e10	0.957928	0.478964	+	0.877835i	$0.341012\pi$
$930$	−1.74193e10	−0.710134
$931$	−2.09235e7	−0.000849787 0
$932$	−9.63637e9	−0.389904
$933$	−9.63738e9	−0.388484
$934$	7.03993e10	2.82719
$935$	−1.61825e8	−0.00647447
$936$	−4.02016e9	−0.160243
$937$	1.44110e9	0.0572274	0.0286137	−	0.999591i	$-0.490891\pi$
$937$	1.44110e9	0.0572274	0.0286137	+	0.999591i	$0.490891\pi$
$938$	−4.11642e10	−1.62858
$939$	−7.59798e9	−0.299481
$940$	2.05211e11	8.05847
$941$	−2.06845e10	−0.809246	−0.404623	−	0.914484i	$-0.632597\pi$
$941$	−2.06845e10	−0.809246	−0.404623	+	0.914484i	$0.632597\pi$
$942$	−1.25099e10	−0.487612
$943$	−1.36756e10	−0.531074
$944$	6.35794e8	0.0245988
$945$	4.37709e10	1.68723
$946$	−5.79725e9	−0.222640
$947$	1.28193e10	0.490501	0.245250	−	0.969460i	$-0.421130\pi$
$947$	1.28193e10	0.490501	0.245250	+	0.969460i	$0.421130\pi$
$948$	−3.40881e10	−1.29949
$949$	1.99510e9	0.0757761
$950$	2.49025e8	0.00942345
$951$	−4.55605e9	−0.171774
$952$	−2.50356e9	−0.0940435
$953$	7.38574e9	0.276420	0.138210	−	0.990403i	$-0.455865\pi$
$953$	7.38574e9	0.276420	0.138210	+	0.990403i	$0.455865\pi$
$954$	4.21654e10	1.57231
$955$	5.22609e10	1.94162
$956$	−2.74936e10	−1.01772
$957$	−2.37416e8	−0.00875625
$958$	7.91990e10	2.91032
$959$	2.34009e10	0.856777
$960$	4.62898e10	1.68863
$961$	−2.04118e10	−0.741908
$962$	−3.50635e9	−0.126982
$963$	−2.07428e10	−0.748471
$964$	−1.09811e11	−3.94801
$965$	3.24522e10	1.16251
$966$	3.11338e10	1.11125
$967$	2.59694e10	0.923568	0.461784	−	0.886992i	$-0.347209\pi$
$967$	2.59694e10	0.923568	0.461784	+	0.886992i	$0.347209\pi$
$968$	8.30435e10	2.94267
$969$	−454144.	−1.60347e−5 0
$970$	−7.08212e10	−2.49151
$971$	−2.39705e10	−0.840251	−0.420125	−	0.907466i	$-0.638014\pi$
$971$	−2.39705e10	−0.840251	−0.420125	+	0.907466i	$0.638014\pi$
$972$	−6.77006e10	−2.36462
$973$	−7.32444e9	−0.254906
$974$	−5.67798e10	−1.96896
$975$	1.97497e9	0.0682409
$976$	−8.15244e10	−2.80681
$977$	3.88864e10	1.33403	0.667017	−	0.745043i	$-0.267571\pi$
$977$	3.88864e10	1.33403	0.667017	+	0.745043i	$0.267571\pi$
$978$	2.60980e10	0.892115
$979$	−2.15418e9	−0.0733740
$980$	−7.63072e10	−2.58985
$981$	−1.41357e10	−0.478053
$982$	9.12474e9	0.307489
$983$	4.15032e10	1.39362	0.696809	−	0.717256i	$-0.254602\pi$
$983$	4.15032e10	1.39362	0.696809	+	0.717256i	$0.254602\pi$
$984$	1.36748e10	0.457550
$985$	−7.33744e10	−2.44635
$986$	−2.71129e8	−0.00900756
$987$	−2.16015e10	−0.715111
$988$	8.18884e6	0.000270130 0
$989$	3.63437e10	1.19465
$990$	1.25784e10	0.412006
$991$	3.86787e10	1.26245	0.631224	−	0.775600i	$-0.282553\pi$
$991$	3.86787e10	1.26245	0.631224	+	0.775600i	$0.282553\pi$
$992$	−4.42848e10	−1.44034
$993$	1.46663e10	0.475333
$994$	−4.49725e10	−1.45243
$995$	−4.25200e10	−1.36840
$996$	−2.22533e10	−0.713652
$997$	2.65360e8	0.00848014	0.00424007	−	0.999991i	$-0.498650\pi$
$997$	2.65360e8	0.00848014	0.00424007	+	0.999991i	$0.498650\pi$
$998$	7.13969e9	0.227365
$999$	−2.35300e10	−0.746695

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.a.b.1.2	✓	10
3.2	odd	2		261.8.a.f.1.9		10
4.3	odd	2		464.8.a.g.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.a.b.1.2	✓	10	1.1	even	1	trivial
261.8.a.f.1.9		10	3.2	odd	2
464.8.a.g.1.7		10	4.3	odd	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-21.4083 q^{2} -17.3673 q^{3} +330.317 q^{4} -555.983 q^{5} +371.805 q^{6} -1113.12 q^{7} -4331.27 q^{8} -1885.38 q^{9} +O(q^{10})\)	\(q-21.4083 q^{2} -17.3673 q^{3} +330.317 q^{4} -555.983 q^{5} +371.805 q^{6} -1113.12 q^{7} -4331.27 q^{8} -1885.38 q^{9} +11902.7 q^{10} -560.510 q^{11} -5736.72 q^{12} -492.300 q^{13} +23830.1 q^{14} +9655.94 q^{15} +50444.7 q^{16} -519.277 q^{17} +40362.8 q^{18} -50.3572 q^{19} -183651. q^{20} +19332.0 q^{21} +11999.6 q^{22} -75226.9 q^{23} +75222.5 q^{24} +230993. q^{25} +10539.3 q^{26} +70726.2 q^{27} -367684. q^{28} -24389.0 q^{29} -206718. q^{30} +84266.1 q^{31} -525536. q^{32} +9734.56 q^{33} +11116.9 q^{34} +618878. q^{35} -622772. q^{36} -332692. q^{37} +1078.06 q^{38} +8549.94 q^{39} +2.40812e6 q^{40} +181791. q^{41} -413865. q^{42} -483121. q^{43} -185146. q^{44} +1.04824e6 q^{45} +1.61048e6 q^{46} -1.11740e6 q^{47} -876090. q^{48} +415501. q^{49} -4.94517e6 q^{50} +9018.45 q^{51} -162615. q^{52} +1.04466e6 q^{53} -1.51413e6 q^{54} +311634. q^{55} +4.82124e6 q^{56} +874.569 q^{57} +522128. q^{58} +12603.8 q^{59} +3.18952e6 q^{60} -1.61611e6 q^{61} -1.80400e6 q^{62} +2.09866e6 q^{63} +4.79392e6 q^{64} +273711. q^{65} -208401. q^{66} -1.72740e6 q^{67} -171526. q^{68} +1.30649e6 q^{69} -1.32492e7 q^{70} -1.88721e6 q^{71} +8.16608e6 q^{72} -4.05260e6 q^{73} +7.12238e6 q^{74} -4.01172e6 q^{75} -16633.8 q^{76} +623917. q^{77} -183040. q^{78} +5.94209e6 q^{79} -2.80464e7 q^{80} +2.89499e6 q^{81} -3.89185e6 q^{82} +3.87909e6 q^{83} +6.38568e6 q^{84} +288710. q^{85} +1.03428e7 q^{86} +423571. q^{87} +2.42772e6 q^{88} +3.84325e6 q^{89} -2.24410e7 q^{90} +547991. q^{91} -2.48487e7 q^{92} -1.46348e6 q^{93} +2.39216e7 q^{94} +27997.8 q^{95} +9.12714e6 q^{96} -5.95002e6 q^{97} -8.89520e6 q^{98} +1.05677e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9}+O(q^{10}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9	\( 10 q + 80 q^{3} + 922 q^{4} + 180 q^{5} + 358 q^{6} + 1040 q^{7} - 4620 q^{8} + 10986 q^{9} + 8496 q^{10} + 7384 q^{11} + 49720 q^{12} + 20820 q^{13} + 50976 q^{14} + 43516 q^{15} + 122082 q^{16} - 11620 q^{17} + 66060 q^{18} + 75068 q^{19} - 42914 q^{20} + 51480 q^{21} - 36950 q^{22} + 62040 q^{23} - 205942 q^{24} + 261022 q^{25} - 201528 q^{26} - 28060 q^{27} - 24980 q^{28} - 243890 q^{29} - 1284894 q^{30} + 200600 q^{31} - 1761460 q^{32} - 1068000 q^{33} - 503932 q^{34} + 107528 q^{35} - 26300 q^{36} - 367740 q^{37} + 766880 q^{38} + 392692 q^{39} - 865000 q^{40} + 932764 q^{41} - 2058060 q^{42} + 1443560 q^{43} - 1325912 q^{44} + 4245684 q^{45} + 1760460 q^{46} - 286960 q^{47} + 3187120 q^{48} + 4713194 q^{49} - 3682652 q^{50} + 1451016 q^{51} + 2560210 q^{52} + 3953220 q^{53} - 3147534 q^{54} + 3981316 q^{55} + 2082464 q^{56} + 2050640 q^{57} + 6712320 q^{59} + 7476756 q^{60} + 1905196 q^{61} - 8048490 q^{62} + 3643800 q^{63} + 8445458 q^{64} + 4667544 q^{65} - 12425580 q^{66} - 2718200 q^{67} - 17699740 q^{68} + 1109064 q^{69} - 30441624 q^{70} + 3447736 q^{71} - 22466840 q^{72} - 2554460 q^{73} - 4214584 q^{74} + 1088084 q^{75} - 8294848 q^{76} - 3967800 q^{77} - 24809970 q^{78} + 4187744 q^{79} - 17715290 q^{80} + 5161402 q^{81} + 7020500 q^{82} + 3498720 q^{83} + 22947224 q^{84} + 1817072 q^{85} - 361638 q^{86} - 1951120 q^{87} + 15118470 q^{88} - 303268 q^{89} - 28959160 q^{90} + 27215080 q^{91} - 10783380 q^{92} + 1097360 q^{93} + 55641726 q^{94} - 8810536 q^{95} - 53327238 q^{96} + 4908620 q^{97} + 40120080 q^{98} - 14408716 q^{99}+O(q^{100}) \) 10 * q + 80 * q^3 + 922 * q^4 + 180 * q^5 + 358 * q^6 + 1040 * q^7 - 4620 * q^8 + 10986 * q^9 + 8496 * q^10 + 7384 * q^11 + 49720 * q^12 + 20820 * q^13 + 50976 * q^14 + 43516 * q^15 + 122082 * q^16 - 11620 * q^17 + 66060 * q^18 + 75068 * q^19 - 42914 * q^20 + 51480 * q^21 - 36950 * q^22 + 62040 * q^23 - 205942 * q^24 + 261022 * q^25 - 201528 * q^26 - 28060 * q^27 - 24980 * q^28 - 243890 * q^29 - 1284894 * q^30 + 200600 * q^31 - 1761460 * q^32 - 1068000 * q^33 - 503932 * q^34 + 107528 * q^35 - 26300 * q^36 - 367740 * q^37 + 766880 * q^38 + 392692 * q^39 - 865000 * q^40 + 932764 * q^41 - 2058060 * q^42 + 1443560 * q^43 - 1325912 * q^44 + 4245684 * q^45 + 1760460 * q^46 - 286960 * q^47 + 3187120 * q^48 + 4713194 * q^49 - 3682652 * q^50 + 1451016 * q^51 + 2560210 * q^52 + 3953220 * q^53 - 3147534 * q^54 + 3981316 * q^55 + 2082464 * q^56 + 2050640 * q^57 + 6712320 * q^59 + 7476756 * q^60 + 1905196 * q^61 - 8048490 * q^62 + 3643800 * q^63 + 8445458 * q^64 + 4667544 * q^65 - 12425580 * q^66 - 2718200 * q^67 - 17699740 * q^68 + 1109064 * q^69 - 30441624 * q^70 + 3447736 * q^71 - 22466840 * q^72 - 2554460 * q^73 - 4214584 * q^74 + 1088084 * q^75 - 8294848 * q^76 - 3967800 * q^77 - 24809970 * q^78 + 4187744 * q^79 - 17715290 * q^80 + 5161402 * q^81 + 7020500 * q^82 + 3498720 * q^83 + 22947224 * q^84 + 1817072 * q^85 - 361638 * q^86 - 1951120 * q^87 + 15118470 * q^88 - 303268 * q^89 - 28959160 * q^90 + 27215080 * q^91 - 10783380 * q^92 + 1097360 * q^93 + 55641726 * q^94 - 8810536 * q^95 - 53327238 * q^96 + 4908620 * q^97 + 40120080 * q^98 - 14408716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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