LMFDB - Embedded newform 285.10.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,10,Mod(1,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("285.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	285.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:	$146.785213307$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 6356 x^{13} + 18436 x^{12} + 15858707 x^{11} - 49616078 x^{10} + \cdots + 15\!\cdots\!00 $ x^15 - 2x^14 - 6356x^13 + 18436x^12 + 15858707x^11 - 49616078x^10 - 19804799606x^9 + 51117957936x^8 + 13077899446663x^7 - 17762605232062x^6 - 4369460380063800x^5 - 1105301955330540x^4 + 617735239298795077x^3 + 844341253042208334x^2 - 21881601450607548510x + 15712212684310961400
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{6}\cdot 5^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-14.0251$ of defining polynomial
Character	$\chi$	$=$	285.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+13.0251 q^{2} -81.0000 q^{3} -342.346 q^{4} +625.000 q^{5} -1055.03 q^{6} -10702.7 q^{7} -11128.0 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+13.0251 q^{2} -81.0000 q^{3} -342.346 q^{4} +625.000 q^{5} -1055.03 q^{6} -10702.7 q^{7} -11128.0 q^{8} +6561.00 q^{9} +8140.70 q^{10} +54651.2 q^{11} +27730.0 q^{12} -13720.8 q^{13} -139403. q^{14} -50625.0 q^{15} +30338.2 q^{16} -469454. q^{17} +85457.8 q^{18} -130321. q^{19} -213966. q^{20} +866916. q^{21} +711839. q^{22} -2.04664e6 q^{23} +901365. q^{24} +390625. q^{25} -178715. q^{26} -531441. q^{27} +3.66402e6 q^{28} -6.55370e6 q^{29} -659397. q^{30} -5.06147e6 q^{31} +6.09268e6 q^{32} -4.42675e6 q^{33} -6.11469e6 q^{34} -6.68916e6 q^{35} -2.24613e6 q^{36} +1.12068e7 q^{37} -1.69745e6 q^{38} +1.11138e6 q^{39} -6.95498e6 q^{40} -3.09118e7 q^{41} +1.12917e7 q^{42} -4.21335e7 q^{43} -1.87096e7 q^{44} +4.10062e6 q^{45} -2.66577e7 q^{46} -5.75921e7 q^{47} -2.45740e6 q^{48} +7.41934e7 q^{49} +5.08794e6 q^{50} +3.80258e7 q^{51} +4.69726e6 q^{52} +7.56828e7 q^{53} -6.92208e6 q^{54} +3.41570e7 q^{55} +1.19099e8 q^{56} +1.05560e7 q^{57} -8.53627e7 q^{58} +1.46811e8 q^{59} +1.73313e7 q^{60} -1.52549e8 q^{61} -6.59262e7 q^{62} -7.02202e7 q^{63} +6.38247e7 q^{64} -8.57550e6 q^{65} -5.76590e7 q^{66} +1.67895e8 q^{67} +1.60716e8 q^{68} +1.65778e8 q^{69} -8.71272e7 q^{70} +2.88477e8 q^{71} -7.30106e7 q^{72} -1.42189e8 q^{73} +1.45970e8 q^{74} -3.16406e7 q^{75} +4.46149e7 q^{76} -5.84914e8 q^{77} +1.44759e7 q^{78} +2.22508e8 q^{79} +1.89614e7 q^{80} +4.30467e7 q^{81} -4.02630e8 q^{82} -4.96541e8 q^{83} -2.96785e8 q^{84} -2.93409e8 q^{85} -5.48794e8 q^{86} +5.30850e8 q^{87} -6.08157e8 q^{88} -2.96115e7 q^{89} +5.34111e7 q^{90} +1.46849e8 q^{91} +7.00659e8 q^{92} +4.09979e8 q^{93} -7.50144e8 q^{94} -8.14506e7 q^{95} -4.93507e8 q^{96} -4.04851e8 q^{97} +9.66378e8 q^{98} +3.58567e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) $ 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9} - 10625 q^{10} + 138230 q^{11} - 409455 q^{12} - 176712 q^{13} - 555994 q^{14} - 759375 q^{15} + 1695731 q^{16} - 274992 q^{17} - 111537 q^{18} - 1954815 q^{19} + 3159375 q^{20} - 109512 q^{21} - 1031106 q^{22} + 1714212 q^{23} + 291357 q^{24} + 5859375 q^{25} + 9500004 q^{26} - 7971615 q^{27} + 14545598 q^{28} + 1754340 q^{29} + 860625 q^{30} + 8442914 q^{31} + 35638859 q^{32} - 11196630 q^{33} + 47218266 q^{34} + 845000 q^{35} + 33165855 q^{36} + 2956096 q^{37} + 2215457 q^{38} + 14313672 q^{39} - 2248125 q^{40} - 38550502 q^{41} + 45035514 q^{42} + 50753570 q^{43} + 212125630 q^{44} + 61509375 q^{45} - 117130008 q^{46} - 40252876 q^{47} - 137354211 q^{48} + 110123035 q^{49} - 6640625 q^{50} + 22274352 q^{51} - 87136648 q^{52} + 65532542 q^{53} + 9034497 q^{54} + 86393750 q^{55} - 377288898 q^{56} + 158340015 q^{57} + 211630876 q^{58} + 175407418 q^{59} - 255909375 q^{60} + 151231854 q^{61} - 30983940 q^{62} + 8870472 q^{63} + 836879575 q^{64} - 110445000 q^{65} + 83519586 q^{66} + 40009476 q^{67} - 124850430 q^{68} - 138851172 q^{69} - 347496250 q^{70} + 87578500 q^{71} - 23599917 q^{72} - 360657638 q^{73} + 1373397084 q^{74} - 474609375 q^{75} - 658772655 q^{76} - 304618172 q^{77} - 769500324 q^{78} + 205798286 q^{79} + 1059831875 q^{80} + 645700815 q^{81} - 2327138772 q^{82} - 63321462 q^{83} - 1178193438 q^{84} - 171870000 q^{85} - 848405762 q^{86} - 142101540 q^{87} - 3211126502 q^{88} - 381069174 q^{89} - 69710625 q^{90} + 1476892872 q^{91} - 2382818588 q^{92} - 683876034 q^{93} - 5137318040 q^{94} - 1221759375 q^{95} - 2886747579 q^{96} - 3915268828 q^{97} - 8273557437 q^{98} + 906927030 q^{99}+O(q^{100}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9 - 10625 * q^10 + 138230 * q^11 - 409455 * q^12 - 176712 * q^13 - 555994 * q^14 - 759375 * q^15 + 1695731 * q^16 - 274992 * q^17 - 111537 * q^18 - 1954815 * q^19 + 3159375 * q^20 - 109512 * q^21 - 1031106 * q^22 + 1714212 * q^23 + 291357 * q^24 + 5859375 * q^25 + 9500004 * q^26 - 7971615 * q^27 + 14545598 * q^28 + 1754340 * q^29 + 860625 * q^30 + 8442914 * q^31 + 35638859 * q^32 - 11196630 * q^33 + 47218266 * q^34 + 845000 * q^35 + 33165855 * q^36 + 2956096 * q^37 + 2215457 * q^38 + 14313672 * q^39 - 2248125 * q^40 - 38550502 * q^41 + 45035514 * q^42 + 50753570 * q^43 + 212125630 * q^44 + 61509375 * q^45 - 117130008 * q^46 - 40252876 * q^47 - 137354211 * q^48 + 110123035 * q^49 - 6640625 * q^50 + 22274352 * q^51 - 87136648 * q^52 + 65532542 * q^53 + 9034497 * q^54 + 86393750 * q^55 - 377288898 * q^56 + 158340015 * q^57 + 211630876 * q^58 + 175407418 * q^59 - 255909375 * q^60 + 151231854 * q^61 - 30983940 * q^62 + 8870472 * q^63 + 836879575 * q^64 - 110445000 * q^65 + 83519586 * q^66 + 40009476 * q^67 - 124850430 * q^68 - 138851172 * q^69 - 347496250 * q^70 + 87578500 * q^71 - 23599917 * q^72 - 360657638 * q^73 + 1373397084 * q^74 - 474609375 * q^75 - 658772655 * q^76 - 304618172 * q^77 - 769500324 * q^78 + 205798286 * q^79 + 1059831875 * q^80 + 645700815 * q^81 - 2327138772 * q^82 - 63321462 * q^83 - 1178193438 * q^84 - 171870000 * q^85 - 848405762 * q^86 - 142101540 * q^87 - 3211126502 * q^88 - 381069174 * q^89 - 69710625 * q^90 + 1476892872 * q^91 - 2382818588 * q^92 - 683876034 * q^93 - 5137318040 * q^94 - 1221759375 * q^95 - 2886747579 * q^96 - 3915268828 * q^97 - 8273557437 * q^98 + 906927030 * 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 $

$2$	13.0251	0.575634	0.287817	−	0.957685i	$-0.407070\pi$
$2$	13.0251	0.575634	0.287817	+	0.957685i	$0.407070\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−342.346	−0.668645
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−1055.03	−0.332343
$7$	−10702.7	−1.68481	−0.842405	−	0.538846i	$-0.818861\pi$
$7$	−10702.7	−1.68481	−0.842405	+	0.538846i	$0.818861\pi$
$8$	−11128.0	−0.960529
$9$	6561.00	0.333333
$10$	8140.70	0.257432
$11$	54651.2	1.12547	0.562734	−	0.826638i	$-0.309750\pi$
$11$	54651.2	1.12547	0.562734	+	0.826638i	$0.309750\pi$
$12$	27730.0	0.386042
$13$	−13720.8	−0.133240	−0.0666199	−	0.997778i	$-0.521222\pi$
$13$	−13720.8	−0.133240	−0.0666199	+	0.997778i	$0.521222\pi$
$14$	−139403.	−0.969834
$15$	−50625.0	−0.258199
$16$	30338.2	0.115731
$17$	−469454.	−1.36324	−0.681621	−	0.731706i	$-0.738725\pi$
$17$	−469454.	−1.36324	−0.681621	+	0.731706i	$0.738725\pi$
$18$	85457.8	0.191878
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−213966.	−0.299027
$21$	866916.	0.972725
$22$	711839.	0.647858
$23$	−2.04664e6	−1.52499	−0.762493	−	0.646996i	$-0.776025\pi$
$23$	−2.04664e6	−1.52499	−0.762493	+	0.646996i	$0.776025\pi$
$24$	901365.	0.554562
$25$	390625.	0.200000
$26$	−178715.	−0.0766975
$27$	−531441.	−0.192450
$28$	3.66402e6	1.12654
$29$	−6.55370e6	−1.72066	−0.860331	−	0.509736i	$-0.829743\pi$
$29$	−6.55370e6	−1.72066	−0.860331	+	0.509736i	$0.829743\pi$
$30$	−659397.	−0.148628
$31$	−5.06147e6	−0.984348	−0.492174	−	0.870497i	$-0.663798\pi$
$31$	−5.06147e6	−0.984348	−0.492174	+	0.870497i	$0.663798\pi$
$32$	6.09268e6	1.02715
$33$	−4.42675e6	−0.649789
$34$	−6.11469e6	−0.784729
$35$	−6.68916e6	−0.753470
$36$	−2.24613e6	−0.222882
$37$	1.12068e7	0.983047	0.491523	−	0.870864i	$-0.336440\pi$
$37$	1.12068e7	0.983047	0.491523	+	0.870864i	$0.336440\pi$
$38$	−1.69745e6	−0.132060
$39$	1.11138e6	0.0769261
$40$	−6.95498e6	−0.429562
$41$	−3.09118e7	−1.70843	−0.854215	−	0.519919i	$-0.825962\pi$
$41$	−3.09118e7	−1.70843	−0.854215	+	0.519919i	$0.825962\pi$
$42$	1.12917e7	0.559934
$43$	−4.21335e7	−1.87940	−0.939701	−	0.341998i	$-0.888896\pi$
$43$	−4.21335e7	−1.87940	−0.939701	+	0.341998i	$0.888896\pi$
$44$	−1.87096e7	−0.752538
$45$	4.10062e6	0.149071
$46$	−2.66577e7	−0.877835
$47$	−5.75921e7	−1.72156	−0.860781	−	0.508975i	$-0.830024\pi$
$47$	−5.75921e7	−1.72156	−0.860781	+	0.508975i	$0.830024\pi$
$48$	−2.45740e6	−0.0668174
$49$	7.41934e7	1.83858
$50$	5.08794e6	0.115127
$51$	3.80258e7	0.787068
$52$	4.69726e6	0.0890902
$53$	7.56828e7	1.31752	0.658758	−	0.752355i	$-0.271082\pi$
$53$	7.56828e7	1.31752	0.658758	+	0.752355i	$0.271082\pi$
$54$	−6.92208e6	−0.110781
$55$	3.41570e7	0.503324
$56$	1.19099e8	1.61831
$57$	1.05560e7	0.132453
$58$	−8.53627e7	−0.990472
$59$	1.46811e8	1.57734	0.788669	−	0.614818i	$-0.210771\pi$
$59$	1.46811e8	1.57734	0.788669	+	0.614818i	$0.210771\pi$
$60$	1.73313e7	0.172643
$61$	−1.52549e8	−1.41067	−0.705335	−	0.708874i	$-0.749203\pi$
$61$	−1.52549e8	−1.41067	−0.705335	+	0.708874i	$0.749203\pi$
$62$	−6.59262e7	−0.566625
$63$	−7.02202e7	−0.561603
$64$	6.38247e7	0.475531
$65$	−8.57550e6	−0.0595867
$66$	−5.76590e7	−0.374041
$67$	1.67895e8	1.01789	0.508945	−	0.860799i	$-0.330036\pi$
$67$	1.67895e8	1.01789	0.508945	+	0.860799i	$0.330036\pi$
$68$	1.60716e8	0.911525
$69$	1.65778e8	0.880451
$70$	−8.71272e7	−0.433723
$71$	2.88477e8	1.34725	0.673626	−	0.739072i	$-0.264736\pi$
$71$	2.88477e8	1.34725	0.673626	+	0.739072i	$0.264736\pi$
$72$	−7.30106e7	−0.320176
$73$	−1.42189e8	−0.586019	−0.293010	−	0.956109i	$-0.594657\pi$
$73$	−1.42189e8	−0.586019	−0.293010	+	0.956109i	$0.594657\pi$
$74$	1.45970e8	0.565876
$75$	−3.16406e7	−0.115470
$76$	4.46149e7	0.153398
$77$	−5.84914e8	−1.89620
$78$	1.44759e7	0.0442813
$79$	2.22508e8	0.642722	0.321361	−	0.946957i	$-0.395860\pi$
$79$	2.22508e8	0.642722	0.321361	+	0.946957i	$0.395860\pi$
$80$	1.89614e7	0.0517566
$81$	4.30467e7	0.111111
$82$	−4.02630e8	−0.983432
$83$	−4.96541e8	−1.14843	−0.574214	−	0.818705i	$-0.694692\pi$
$83$	−4.96541e8	−1.14843	−0.574214	+	0.818705i	$0.694692\pi$
$84$	−2.96785e8	−0.650408
$85$	−2.93409e8	−0.609660
$86$	−5.48794e8	−1.08185
$87$	5.30850e8	0.993425
$88$	−6.08157e8	−1.08104
$89$	−2.96115e7	−0.0500271	−0.0250135	−	0.999687i	$-0.507963\pi$
$89$	−2.96115e7	−0.0500271	−0.0250135	+	0.999687i	$0.507963\pi$
$90$	5.34111e7	0.0858105
$91$	1.46849e8	0.224484
$92$	7.00659e8	1.01967
$93$	4.09979e8	0.568314
$94$	−7.50144e8	−0.990990
$95$	−8.14506e7	−0.102598
$96$	−4.93507e8	−0.593024
$97$	−4.04851e8	−0.464326	−0.232163	−	0.972677i	$-0.574580\pi$
$97$	−4.04851e8	−0.464326	−0.232163	+	0.972677i	$0.574580\pi$
$98$	9.66378e8	1.05835
$99$	3.58567e8	0.375156
$100$	−1.33729e8	−0.133729
$101$	−7.95770e8	−0.760924	−0.380462	−	0.924796i	$-0.624235\pi$
$101$	−7.95770e8	−0.760924	−0.380462	+	0.924796i	$0.624235\pi$
$102$	4.95290e8	0.453063
$103$	−3.17275e8	−0.277759	−0.138879	−	0.990309i	$-0.544350\pi$
$103$	−3.17275e8	−0.277759	−0.138879	+	0.990309i	$0.544350\pi$
$104$	1.52684e8	0.127981
$105$	5.41822e8	0.435016
$106$	9.85777e8	0.758407
$107$	1.87027e9	1.37936	0.689681	−	0.724113i	$-0.257751\pi$
$107$	1.87027e9	1.37936	0.689681	+	0.724113i	$0.257751\pi$
$108$	1.81937e8	0.128681
$109$	3.40824e8	0.231266	0.115633	−	0.993292i	$-0.463110\pi$
$109$	3.40824e8	0.231266	0.115633	+	0.993292i	$0.463110\pi$
$110$	4.44899e8	0.289731
$111$	−9.07752e8	−0.567562
$112$	−3.24700e8	−0.194985
$113$	−9.98401e8	−0.576039	−0.288020	−	0.957624i	$-0.592997\pi$
$113$	−9.98401e8	−0.576039	−0.288020	+	0.957624i	$0.592997\pi$
$114$	1.37493e8	0.0762446
$115$	−1.27915e9	−0.681995
$116$	2.24363e9	1.15051
$117$	−9.00221e7	−0.0444133
$118$	1.91223e9	0.907970
$119$	5.02441e9	2.29680
$120$	5.63353e8	0.248008
$121$	6.28811e8	0.266677
$122$	−1.98697e9	−0.812030
$123$	2.50386e9	0.986363
$124$	1.73277e9	0.658180
$125$	2.44141e8	0.0894427
$126$	−9.14626e8	−0.323278
$127$	−4.93580e8	−0.168361	−0.0841804	−	0.996451i	$-0.526827\pi$
$127$	−4.93580e8	−0.168361	−0.0841804	+	0.996451i	$0.526827\pi$
$128$	−2.28813e9	−0.753416
$129$	3.41281e9	1.08507
$130$	−1.11697e8	−0.0343001
$131$	4.41011e9	1.30836	0.654181	−	0.756338i	$-0.273013\pi$
$131$	4.41011e9	1.30836	0.654181	+	0.756338i	$0.273013\pi$
$132$	1.51548e9	0.434478
$133$	1.39478e9	0.386522
$134$	2.18685e9	0.585933
$135$	−3.32151e8	−0.0860663
$136$	5.22407e9	1.30943
$137$	−7.47731e8	−0.181344	−0.0906719	−	0.995881i	$-0.528901\pi$
$137$	−7.47731e8	−0.181344	−0.0906719	+	0.995881i	$0.528901\pi$
$138$	2.15928e9	0.506818
$139$	−2.58949e9	−0.588366	−0.294183	−	0.955749i	$-0.595048\pi$
$139$	−2.58949e9	−0.588366	−0.294183	+	0.955749i	$0.595048\pi$
$140$	2.29001e9	0.503804
$141$	4.66496e9	0.993944
$142$	3.75745e9	0.775525
$143$	−7.49859e8	−0.149957
$144$	1.99049e8	0.0385771
$145$	−4.09606e9	−0.769503
$146$	−1.85202e9	−0.337333
$147$	−6.00967e9	−1.06151
$148$	−3.83661e9	−0.657309
$149$	5.48111e9	0.911026	0.455513	−	0.890229i	$-0.349456\pi$
$149$	5.48111e9	0.911026	0.455513	+	0.890229i	$0.349456\pi$
$150$	−4.12123e8	−0.0664685
$151$	6.79413e9	1.06350	0.531750	−	0.846901i	$-0.321534\pi$
$151$	6.79413e9	1.06350	0.531750	+	0.846901i	$0.321534\pi$
$152$	1.45021e9	0.220361
$153$	−3.08009e9	−0.454414
$154$	−7.61857e9	−1.09152
$155$	−3.16342e9	−0.440214
$156$	−3.80478e8	−0.0514362
$157$	5.97345e9	0.784652	0.392326	−	0.919826i	$-0.371671\pi$
$157$	5.97345e9	0.784652	0.392326	+	0.919826i	$0.371671\pi$
$158$	2.89819e9	0.369973
$159$	−6.13031e9	−0.760668
$160$	3.80792e9	0.459355
$161$	2.19045e10	2.56931
$162$	5.60689e8	0.0639594
$163$	1.46276e9	0.162304	0.0811520	−	0.996702i	$-0.474140\pi$
$163$	1.46276e9	0.162304	0.0811520	+	0.996702i	$0.474140\pi$
$164$	1.05825e10	1.14233
$165$	−2.76672e9	−0.290594
$166$	−6.46751e9	−0.661075
$167$	−1.54249e10	−1.53461	−0.767304	−	0.641283i	$-0.778402\pi$
$167$	−1.54249e10	−1.53461	−0.767304	+	0.641283i	$0.778402\pi$
$168$	−9.64701e9	−0.934331
$169$	−1.04162e10	−0.982247
$170$	−3.82168e9	−0.350941
$171$	−8.55036e8	−0.0764719
$172$	1.44242e10	1.25665
$173$	−1.08344e10	−0.919597	−0.459798	−	0.888023i	$-0.652078\pi$
$173$	−1.08344e10	−0.919597	−0.459798	+	0.888023i	$0.652078\pi$
$174$	6.91438e9	0.571849
$175$	−4.18073e9	−0.336962
$176$	1.65802e9	0.130252
$177$	−1.18917e10	−0.910677
$178$	−3.85693e8	−0.0287973
$179$	1.54813e10	1.12712	0.563558	−	0.826076i	$-0.309432\pi$
$179$	1.54813e10	1.12712	0.563558	+	0.826076i	$0.309432\pi$
$180$	−1.40383e9	−0.0996757
$181$	−2.71382e7	−0.00187944	−0.000939719	−	1.00000i	$-0.500299\pi$
$181$	−2.71382e7	−0.00187944	−0.000939719		1.00000i	$0.500299\pi$
$182$	1.91273e9	0.129221
$183$	1.23565e10	0.814451
$184$	2.27749e10	1.46479
$185$	7.00426e9	0.439632
$186$	5.34002e9	0.327141
$187$	−2.56562e10	−1.53428
$188$	1.97164e10	1.15111
$189$	5.68783e9	0.324242
$190$	−1.06090e9	−0.0590588
$191$	−1.20044e10	−0.652663	−0.326332	−	0.945255i	$-0.605813\pi$
$191$	−1.20044e10	−0.652663	−0.326332	+	0.945255i	$0.605813\pi$
$192$	−5.16980e9	−0.274548
$193$	1.73597e9	0.0900606	0.0450303	−	0.998986i	$-0.485662\pi$
$193$	1.73597e9	0.0900606	0.0450303	+	0.998986i	$0.485662\pi$
$194$	−5.27324e9	−0.267282
$195$	6.94615e8	0.0344024
$196$	−2.53998e10	−1.22936
$197$	1.41024e10	0.667105	0.333552	−	0.942732i	$-0.391753\pi$
$197$	1.41024e10	0.667105	0.333552	+	0.942732i	$0.391753\pi$
$198$	4.67038e9	0.215953
$199$	5.68299e9	0.256885	0.128442	−	0.991717i	$-0.459002\pi$
$199$	5.68299e9	0.256885	0.128442	+	0.991717i	$0.459002\pi$
$200$	−4.34686e9	−0.192106
$201$	−1.35995e10	−0.587679
$202$	−1.03650e10	−0.438014
$203$	7.01420e10	2.89899
$204$	−1.30180e10	−0.526269
$205$	−1.93199e10	−0.764033
$206$	−4.13254e9	−0.159888
$207$	−1.34280e10	−0.508329
$208$	−4.16265e8	−0.0154200
$209$	−7.12221e9	−0.258200
$210$	7.05730e9	0.250410
$211$	1.21056e10	0.420451	0.210225	−	0.977653i	$-0.432580\pi$
$211$	1.21056e10	0.420451	0.210225	+	0.977653i	$0.432580\pi$
$212$	−2.59097e10	−0.880950
$213$	−2.33667e10	−0.777836
$214$	2.43605e10	0.794008
$215$	−2.63334e10	−0.840494
$216$	5.91386e9	0.184854
$217$	5.41712e10	1.65844
$218$	4.43928e9	0.133124
$219$	1.15173e10	0.338339
$220$	−1.16935e10	−0.336545
$221$	6.44128e9	0.181638
$222$	−1.18236e10	−0.326708
$223$	6.70561e10	1.81579	0.907897	−	0.419194i	$-0.137687\pi$
$223$	6.70561e10	1.81579	0.907897	+	0.419194i	$0.137687\pi$
$224$	−6.52079e10	−1.73055
$225$	2.56289e9	0.0666667
$226$	−1.30043e10	−0.331588
$227$	5.15258e10	1.28798	0.643989	−	0.765035i	$-0.277278\pi$
$227$	5.15258e10	1.28798	0.643989	+	0.765035i	$0.277278\pi$
$228$	−3.61381e9	−0.0885642
$229$	1.72210e10	0.413807	0.206903	−	0.978361i	$-0.433661\pi$
$229$	1.72210e10	0.413807	0.206903	+	0.978361i	$0.433661\pi$
$230$	−1.66611e10	−0.392580
$231$	4.73780e10	1.09477
$232$	7.29293e10	1.65275
$233$	−9.95803e9	−0.221346	−0.110673	−	0.993857i	$-0.535301\pi$
$233$	−9.95803e9	−0.221346	−0.110673	+	0.993857i	$0.535301\pi$
$234$	−1.17255e9	−0.0255658
$235$	−3.59951e10	−0.769906
$236$	−5.02602e10	−1.05468
$237$	−1.80231e10	−0.371076
$238$	6.54435e10	1.32212
$239$	3.75987e10	0.745388	0.372694	−	0.927954i	$-0.378434\pi$
$239$	3.75987e10	0.745388	0.372694	+	0.927954i	$0.378434\pi$
$240$	−1.53587e9	−0.0298817
$241$	3.33208e10	0.636266	0.318133	−	0.948046i	$-0.396944\pi$
$241$	3.33208e10	0.636266	0.318133	+	0.948046i	$0.396944\pi$
$242$	8.19034e9	0.153509
$243$	−3.48678e9	−0.0641500
$244$	5.22246e10	0.943238
$245$	4.63709e10	0.822239
$246$	3.26131e10	0.567784
$247$	1.78811e9	0.0305673
$248$	5.63238e10	0.945496
$249$	4.02198e10	0.663045
$250$	3.17996e9	0.0514863
$251$	3.32217e10	0.528312	0.264156	−	0.964480i	$-0.414907\pi$
$251$	3.32217e10	0.528312	0.264156	+	0.964480i	$0.414907\pi$
$252$	2.40396e10	0.375513
$253$	−1.11851e11	−1.71632
$254$	−6.42894e9	−0.0969143
$255$	2.37661e10	0.351988
$256$	−6.24813e10	−0.909223
$257$	1.63588e9	0.0233912	0.0116956	−	0.999932i	$-0.496277\pi$
$257$	1.63588e9	0.0233912	0.0116956	+	0.999932i	$0.496277\pi$
$258$	4.44523e10	0.624605
$259$	−1.19943e11	−1.65625
$260$	2.93579e9	0.0398423
$261$	−4.29988e10	−0.573554
$262$	5.74422e10	0.753139
$263$	−8.99867e10	−1.15978	−0.579892	−	0.814693i	$-0.696905\pi$
$263$	−8.99867e10	−1.15978	−0.579892	+	0.814693i	$0.696905\pi$
$264$	4.92607e10	0.624142
$265$	4.73017e10	0.589211
$266$	1.81672e10	0.222495
$267$	2.39853e9	0.0288831
$268$	−5.74782e10	−0.680607
$269$	1.42241e10	0.165630	0.0828152	−	0.996565i	$-0.473609\pi$
$269$	1.42241e10	0.165630	0.0828152	+	0.996565i	$0.473609\pi$
$270$	−4.32630e9	−0.0495427
$271$	−1.09867e11	−1.23739	−0.618696	−	0.785631i	$-0.712339\pi$
$271$	−1.09867e11	−1.23739	−0.618696	+	0.785631i	$0.712339\pi$
$272$	−1.42424e10	−0.157770
$273$	−1.18948e10	−0.129606
$274$	−9.73929e9	−0.104388
$275$	2.13481e10	0.225094
$276$	−5.67534e10	−0.588709
$277$	1.26787e11	1.29395	0.646973	−	0.762513i	$-0.276035\pi$
$277$	1.26787e11	1.29395	0.646973	+	0.762513i	$0.276035\pi$
$278$	−3.37284e10	−0.338684
$279$	−3.32083e10	−0.328116
$280$	7.44368e10	0.723730
$281$	3.90046e10	0.373196	0.186598	−	0.982436i	$-0.440254\pi$
$281$	3.90046e10	0.373196	0.186598	+	0.982436i	$0.440254\pi$
$282$	6.07617e10	0.572149
$283$	−1.58751e11	−1.47122	−0.735611	−	0.677404i	$-0.763105\pi$
$283$	−1.58751e11	−1.47122	−0.735611	+	0.677404i	$0.763105\pi$
$284$	−9.87591e10	−0.900834
$285$	6.59750e9	0.0592349
$286$	−9.76700e9	−0.0863205
$287$	3.30839e11	2.87838
$288$	3.99740e10	0.342383
$289$	1.01799e11	0.858428
$290$	−5.33517e10	−0.442953
$291$	3.27930e10	0.268079
$292$	4.86778e10	0.391839
$293$	−1.89990e11	−1.50600	−0.753001	−	0.658019i	$-0.771394\pi$
$293$	−1.89990e11	−1.50600	−0.753001	+	0.658019i	$0.771394\pi$
$294$	−7.82766e10	−0.611039
$295$	9.17569e10	0.705407
$296$	−1.24709e11	−0.944246
$297$	−2.90439e10	−0.216596
$298$	7.13922e10	0.524418
$299$	2.80815e10	0.203189
$300$	1.08320e10	0.0772085
$301$	4.50941e11	3.16643
$302$	8.84944e10	0.612188
$303$	6.44574e10	0.439320
$304$	−3.95371e9	−0.0265506
$305$	−9.53432e10	−0.630871
$306$	−4.01185e10	−0.261576
$307$	−2.41121e11	−1.54922	−0.774610	−	0.632440i	$-0.782054\pi$
$307$	−2.41121e11	−1.54922	−0.774610	+	0.632440i	$0.782054\pi$
$308$	2.00243e11	1.26788
$309$	2.56992e10	0.160364
$310$	−4.12039e10	−0.253402
$311$	−3.69301e10	−0.223851	−0.111926	−	0.993717i	$-0.535702\pi$
$311$	−3.69301e10	−0.223851	−0.111926	+	0.993717i	$0.535702\pi$
$312$	−1.23674e10	−0.0738898
$313$	−2.96718e11	−1.74741	−0.873705	−	0.486457i	$-0.838289\pi$
$313$	−2.96718e11	−1.74741	−0.873705	+	0.486457i	$0.838289\pi$
$314$	7.78049e10	0.451672
$315$	−4.38876e10	−0.251157
$316$	−7.61746e10	−0.429753
$317$	7.42422e10	0.412937	0.206469	−	0.978453i	$-0.433803\pi$
$317$	7.42422e10	0.412937	0.206469	+	0.978453i	$0.433803\pi$
$318$	−7.98480e10	−0.437867
$319$	−3.58168e11	−1.93655
$320$	3.98904e10	0.212664
$321$	−1.51492e11	−0.796375
$322$	2.85309e11	1.47898
$323$	6.11797e10	0.312749
$324$	−1.47369e10	−0.0742939
$325$	−5.35969e9	−0.0266480
$326$	1.90526e10	0.0934277
$327$	−2.76068e10	−0.133521
$328$	3.43986e11	1.64100
$329$	6.16389e11	2.90050
$330$	−3.60369e10	−0.167276
$331$	−3.14188e10	−0.143868	−0.0719339	−	0.997409i	$-0.522917\pi$
$331$	−3.14188e10	−0.143868	−0.0719339	+	0.997409i	$0.522917\pi$
$332$	1.69989e11	0.767891
$333$	7.35279e10	0.327682
$334$	−2.00911e11	−0.883373
$335$	1.04934e11	0.455214
$336$	2.63007e10	0.112575
$337$	2.24854e11	0.949654	0.474827	−	0.880079i	$-0.342511\pi$
$337$	2.24854e11	0.949654	0.474827	+	0.880079i	$0.342511\pi$
$338$	−1.35673e11	−0.565415
$339$	8.08705e10	0.332576
$340$	1.00447e11	0.407646
$341$	−2.76615e11	−1.10785
$342$	−1.11369e10	−0.0440199
$343$	−3.62176e11	−1.41285
$344$	4.68860e11	1.80522
$345$	1.03611e11	0.393750
$346$	−1.41119e11	−0.529352
$347$	8.96350e10	0.331891	0.165945	−	0.986135i	$-0.446932\pi$
$347$	8.96350e10	0.331891	0.165945	+	0.986135i	$0.446932\pi$
$348$	−1.81734e11	−0.664248
$349$	−2.70486e11	−0.975955	−0.487977	−	0.872856i	$-0.662265\pi$
$349$	−2.70486e11	−0.975955	−0.487977	+	0.872856i	$0.662265\pi$
$350$	−5.44545e10	−0.193967
$351$	7.29179e9	0.0256420
$352$	3.32972e11	1.15602
$353$	1.89513e11	0.649610	0.324805	−	0.945781i	$-0.394701\pi$
$353$	1.89513e11	0.649610	0.324805	+	0.945781i	$0.394701\pi$
$354$	−1.54891e11	−0.524217
$355$	1.80298e11	0.602510
$356$	1.01374e10	0.0334504
$357$	−4.06977e11	−1.32606
$358$	2.01646e11	0.648807
$359$	−9.99305e10	−0.317522	−0.158761	−	0.987317i	$-0.550750\pi$
$359$	−9.99305e10	−0.317522	−0.158761	+	0.987317i	$0.550750\pi$
$360$	−4.56316e10	−0.143187
$361$	1.69836e10	0.0526316
$362$	−3.53479e8	−0.00108187
$363$	−5.09337e10	−0.153966
$364$	−5.02732e10	−0.150100
$365$	−8.88679e10	−0.262076
$366$	1.60945e11	0.468826
$367$	−4.32090e10	−0.124330	−0.0621652	−	0.998066i	$-0.519801\pi$
$367$	−4.32090e10	−0.124330	−0.0621652	+	0.998066i	$0.519801\pi$
$368$	−6.20914e10	−0.176489
$369$	−2.02813e11	−0.569477
$370$	9.12313e10	0.253067
$371$	−8.10007e11	−2.21976
$372$	−1.40355e11	−0.380000
$373$	−1.51936e11	−0.406415	−0.203208	−	0.979136i	$-0.565137\pi$
$373$	−1.51936e11	−0.406415	−0.203208	+	0.979136i	$0.565137\pi$
$374$	−3.34176e11	−0.883187
$375$	−1.97754e10	−0.0516398
$376$	6.40883e11	1.65361
$377$	8.99220e10	0.229261
$378$	7.40847e10	0.186645
$379$	−8.58143e10	−0.213640	−0.106820	−	0.994278i	$-0.534067\pi$
$379$	−8.58143e10	−0.213640	−0.106820	+	0.994278i	$0.534067\pi$
$380$	2.78843e10	0.0686015
$381$	3.99800e10	0.0972032
$382$	−1.56358e11	−0.375695
$383$	3.33456e11	0.791851	0.395926	−	0.918283i	$-0.370424\pi$
$383$	3.33456e11	0.791851	0.395926	+	0.918283i	$0.370424\pi$
$384$	1.85338e11	0.434985
$385$	−3.65571e11	−0.848006
$386$	2.26112e10	0.0518420
$387$	−2.76438e11	−0.626467
$388$	1.38599e11	0.310469
$389$	3.66903e11	0.812416	0.406208	−	0.913781i	$-0.366851\pi$
$389$	3.66903e11	0.812416	0.406208	+	0.913781i	$0.366851\pi$
$390$	9.04745e9	0.0198032
$391$	9.60803e11	2.07893
$392$	−8.25621e11	−1.76601
$393$	−3.57219e11	−0.755384
$394$	1.83685e11	0.384009
$395$	1.39067e11	0.287434
$396$	−1.22754e11	−0.250846
$397$	−7.25883e11	−1.46659	−0.733296	−	0.679910i	$-0.762019\pi$
$397$	−7.25883e11	−1.46659	−0.733296	+	0.679910i	$0.762019\pi$
$398$	7.40216e10	0.147872
$399$	−1.12977e11	−0.223158
$400$	1.18509e10	0.0231462
$401$	−2.95602e11	−0.570897	−0.285449	−	0.958394i	$-0.592143\pi$
$401$	−2.95602e11	−0.570897	−0.285449	+	0.958394i	$0.592143\pi$
$402$	−1.77135e11	−0.338288
$403$	6.94474e10	0.131154
$404$	2.72429e11	0.508788
$405$	2.69042e10	0.0496904
$406$	9.13609e11	1.66876
$407$	6.12466e11	1.10639
$408$	−4.23149e11	−0.756002
$409$	3.52400e11	0.622703	0.311351	−	0.950295i	$-0.399218\pi$
$409$	3.52400e11	0.622703	0.311351	+	0.950295i	$0.399218\pi$
$410$	−2.51644e11	−0.439804
$411$	6.05662e10	0.104699
$412$	1.08618e11	0.185722
$413$	−1.57127e12	−2.65751
$414$	−1.74901e11	−0.292612
$415$	−3.10338e11	−0.513593
$416$	−8.35964e10	−0.136857
$417$	2.09749e11	0.339693
$418$	−9.27676e10	−0.148629
$419$	−9.92291e11	−1.57281	−0.786405	−	0.617712i	$-0.788060\pi$
$419$	−9.92291e11	−1.57281	−0.786405	+	0.617712i	$0.788060\pi$
$420$	−1.85491e11	−0.290871
$421$	2.52840e11	0.392262	0.196131	−	0.980578i	$-0.437162\pi$
$421$	2.52840e11	0.392262	0.196131	+	0.980578i	$0.437162\pi$
$422$	1.57677e11	0.242026
$423$	−3.77862e11	−0.573854
$424$	−8.42195e11	−1.26551
$425$	−1.83380e11	−0.272648
$426$	−3.04353e11	−0.447749
$427$	1.63268e12	2.37671
$428$	−6.40281e11	−0.922303
$429$	6.07385e10	0.0865778
$430$	−3.42996e11	−0.483817
$431$	1.02662e12	1.43305	0.716525	−	0.697562i	$-0.245732\pi$
$431$	1.02662e12	1.43305	0.716525	+	0.697562i	$0.245732\pi$
$432$	−1.61230e10	−0.0222725
$433$	−1.02384e12	−1.39970	−0.699852	−	0.714288i	$-0.746751\pi$
$433$	−1.02384e12	−1.39970	−0.699852	+	0.714288i	$0.746751\pi$
$434$	7.05586e11	0.954655
$435$	3.31781e11	0.444273
$436$	−1.16680e11	−0.154635
$437$	2.66720e11	0.349856
$438$	1.50014e11	0.194759
$439$	−6.95374e11	−0.893568	−0.446784	−	0.894642i	$-0.647431\pi$
$439$	−6.95374e11	−0.893568	−0.446784	+	0.894642i	$0.647431\pi$
$440$	−3.80098e11	−0.483458
$441$	4.86783e11	0.612861
$442$	8.38985e10	0.104557
$443$	−6.40859e11	−0.790580	−0.395290	−	0.918556i	$-0.629356\pi$
$443$	−6.40859e11	−0.790580	−0.395290	+	0.918556i	$0.629356\pi$
$444$	3.10765e11	0.379498
$445$	−1.85072e10	−0.0223728
$446$	8.73414e11	1.04523
$447$	−4.43970e11	−0.525981
$448$	−6.83094e11	−0.801179
$449$	−1.02866e12	−1.19444	−0.597219	−	0.802078i	$-0.703728\pi$
$449$	−1.02866e12	−1.19444	−0.597219	+	0.802078i	$0.703728\pi$
$450$	3.33820e10	0.0383756
$451$	−1.68937e12	−1.92278
$452$	3.41799e11	0.385166
$453$	−5.50325e11	−0.614012
$454$	6.71130e11	0.741404
$455$	9.17807e10	0.100392
$456$	−1.17467e11	−0.127225
$457$	−1.04212e12	−1.11762	−0.558811	−	0.829295i	$-0.688742\pi$
$457$	−1.04212e12	−1.11762	−0.558811	+	0.829295i	$0.688742\pi$
$458$	2.24305e11	0.238202
$459$	2.49487e11	0.262356
$460$	4.37912e11	0.456012
$461$	−1.83118e12	−1.88832	−0.944162	−	0.329483i	$-0.893126\pi$
$461$	−1.83118e12	−1.88832	−0.944162	+	0.329483i	$0.893126\pi$
$462$	6.17104e11	0.630188
$463$	1.83564e12	1.85640	0.928202	−	0.372077i	$-0.121354\pi$
$463$	1.83564e12	1.85640	0.928202	+	0.372077i	$0.121354\pi$
$464$	−1.98828e11	−0.199134
$465$	2.56237e11	0.254158
$466$	−1.29705e11	−0.127414
$467$	1.87594e12	1.82513	0.912563	−	0.408935i	$-0.134100\pi$
$467$	1.87594e12	1.82513	0.912563	+	0.408935i	$0.134100\pi$
$468$	3.08187e10	0.0296967
$469$	−1.79692e12	−1.71495
$470$	−4.68840e11	−0.443184
$471$	−4.83849e11	−0.453019
$472$	−1.63371e12	−1.51508
$473$	−2.30265e12	−2.11521
$474$	−2.34753e11	−0.213604
$475$	−5.09066e10	−0.0458831
$476$	−1.72009e12	−1.53575
$477$	4.96555e11	0.439172
$478$	4.89727e11	0.429071
$479$	3.43451e11	0.298095	0.149048	−	0.988830i	$-0.452379\pi$
$479$	3.43451e11	0.298095	0.149048	+	0.988830i	$0.452379\pi$
$480$	−3.08442e11	−0.265209
$481$	−1.53766e11	−0.130981
$482$	4.34007e11	0.366257
$483$	−1.77426e12	−1.48339
$484$	−2.15271e11	−0.178312
$485$	−2.53032e11	−0.207653
$486$	−4.54158e10	−0.0369270
$487$	−1.08328e12	−0.872687	−0.436344	−	0.899780i	$-0.643727\pi$
$487$	−1.08328e12	−0.872687	−0.436344	+	0.899780i	$0.643727\pi$
$488$	1.69756e12	1.35499
$489$	−1.18484e11	−0.0937062
$490$	6.03986e11	0.473309
$491$	5.78633e11	0.449300	0.224650	−	0.974440i	$-0.427876\pi$
$491$	5.78633e11	0.449300	0.224650	+	0.974440i	$0.427876\pi$
$492$	−8.57187e11	−0.659527
$493$	3.07666e12	2.34568
$494$	2.32903e10	0.0175956
$495$	2.24104e11	0.167775
$496$	−1.53556e11	−0.113920
$497$	−3.08747e12	−2.26986
$498$	5.23868e11	0.381672
$499$	−3.32237e11	−0.239881	−0.119941	−	0.992781i	$-0.538270\pi$
$499$	−3.32237e11	−0.239881	−0.119941	+	0.992781i	$0.538270\pi$
$500$	−8.35806e10	−0.0598054
$501$	1.24941e12	0.886006
$502$	4.32717e11	0.304115
$503$	−2.09166e12	−1.45692	−0.728460	−	0.685088i	$-0.759764\pi$
$503$	−2.09166e12	−1.45692	−0.728460	+	0.685088i	$0.759764\pi$
$504$	7.81407e11	0.539436
$505$	−4.97356e11	−0.340296
$506$	−1.45688e12	−0.987975
$507$	8.43715e11	0.567101
$508$	1.68975e11	0.112574
$509$	1.16894e11	0.0771901	0.0385951	−	0.999255i	$-0.487712\pi$
$509$	1.16894e11	0.0771901	0.0385951	+	0.999255i	$0.487712\pi$
$510$	3.09556e11	0.202616
$511$	1.52180e12	0.987331
$512$	3.57694e11	0.230036
$513$	6.92579e10	0.0441511
$514$	2.13075e10	0.0134648
$515$	−1.98297e11	−0.124218
$516$	−1.16836e12	−0.725529
$517$	−3.14748e12	−1.93756
$518$	−1.56227e12	−0.953392
$519$	8.77586e11	0.530929
$520$	9.54278e10	0.0572348
$521$	2.75443e12	1.63780	0.818902	−	0.573933i	$-0.194583\pi$
$521$	2.75443e12	1.63780	0.818902	+	0.573933i	$0.194583\pi$
$522$	−5.60065e11	−0.330157
$523$	1.86141e12	1.08789	0.543945	−	0.839121i	$-0.316930\pi$
$523$	1.86141e12	1.08789	0.543945	+	0.839121i	$0.316930\pi$
$524$	−1.50978e12	−0.874830
$525$	3.38639e11	0.194545
$526$	−1.17209e12	−0.667612
$527$	2.37613e12	1.34190
$528$	−1.34300e11	−0.0752009
$529$	2.38758e12	1.32558
$530$	6.16111e11	0.339170
$531$	9.63228e11	0.525779
$532$	−4.77498e11	−0.258446
$533$	4.24135e11	0.227631
$534$	3.12411e10	0.0166261
$535$	1.16892e12	0.616869
$536$	−1.86833e12	−0.977714
$537$	−1.25398e12	−0.650741
$538$	1.85271e11	0.0953426
$539$	4.05476e12	2.06926
$540$	1.13711e11	0.0575478
$541$	−1.66506e12	−0.835683	−0.417842	−	0.908520i	$-0.637213\pi$
$541$	−1.66506e12	−0.835683	−0.417842	+	0.908520i	$0.637213\pi$
$542$	−1.43104e12	−0.712285
$543$	2.19820e9	0.00108509
$544$	−2.86023e12	−1.40025
$545$	2.13015e11	0.103425
$546$	−1.54931e11	−0.0746055
$547$	−3.77719e11	−0.180396	−0.0901979	−	0.995924i	$-0.528750\pi$
$547$	−3.77719e11	−0.180396	−0.0901979	+	0.995924i	$0.528750\pi$
$548$	2.55983e11	0.121255
$549$	−1.00087e12	−0.470223
$550$	2.78062e11	0.129572
$551$	8.54085e11	0.394747
$552$	−1.84477e12	−0.845700
$553$	−2.38142e12	−1.08286
$554$	1.65142e12	0.744839
$555$	−5.67345e11	−0.253822
$556$	8.86503e11	0.393408
$557$	2.62954e12	1.15753	0.578764	−	0.815495i	$-0.303535\pi$
$557$	2.62954e12	1.15753	0.578764	+	0.815495i	$0.303535\pi$
$558$	−4.32542e11	−0.188875
$559$	5.78105e11	0.250411
$560$	−2.02937e11	−0.0871999
$561$	2.07816e12	0.885820
$562$	5.08040e11	0.214825
$563$	−8.10555e11	−0.340012	−0.170006	−	0.985443i	$-0.554379\pi$
$563$	−8.10555e11	−0.340012	−0.170006	+	0.985443i	$0.554379\pi$
$564$	−1.59703e12	−0.664596
$565$	−6.24001e11	−0.257613
$566$	−2.06775e12	−0.846886
$567$	−4.60715e11	−0.187201
$568$	−3.21016e12	−1.29408
$569$	−3.41767e12	−1.36686	−0.683432	−	0.730014i	$-0.739514\pi$
$569$	−3.41767e12	−1.36686	−0.683432	+	0.730014i	$0.739514\pi$
$570$	8.59332e10	0.0340976
$571$	1.77233e12	0.697720	0.348860	−	0.937175i	$-0.386569\pi$
$571$	1.77233e12	0.697720	0.348860	+	0.937175i	$0.386569\pi$
$572$	2.56711e11	0.100268
$573$	9.72354e11	0.376815
$574$	4.30922e12	1.65689
$575$	−7.99468e11	−0.304997
$576$	4.18754e11	0.158510
$577$	3.79023e12	1.42356	0.711778	−	0.702404i	$-0.247890\pi$
$577$	3.79023e12	1.42356	0.711778	+	0.702404i	$0.247890\pi$
$578$	1.32595e12	0.494141
$579$	−1.40614e11	−0.0519965
$580$	1.40227e12	0.514525
$581$	5.31431e12	1.93488
$582$	4.27132e11	0.154315
$583$	4.13616e12	1.48282
$584$	1.58227e12	0.562889
$585$	−5.62638e10	−0.0198622
$586$	−2.47464e12	−0.866907
$587$	−2.61189e12	−0.907994	−0.453997	−	0.891003i	$-0.650002\pi$
$587$	−2.61189e12	−0.907994	−0.453997	+	0.891003i	$0.650002\pi$
$588$	2.05739e12	0.709770
$589$	6.59615e11	0.225825
$590$	1.19515e12	0.406057
$591$	−1.14229e12	−0.385153
$592$	3.39995e11	0.113769
$593$	1.98827e12	0.660282	0.330141	−	0.943932i	$-0.392904\pi$
$593$	1.98827e12	0.660282	0.330141	+	0.943932i	$0.392904\pi$
$594$	−3.78300e11	−0.124680
$595$	3.14026e12	1.02716
$596$	−1.87644e12	−0.609153
$597$	−4.60322e11	−0.148312
$598$	3.65765e11	0.116963
$599$	5.18573e12	1.64585	0.822923	−	0.568153i	$-0.192342\pi$
$599$	5.18573e12	1.64585	0.822923	+	0.568153i	$0.192342\pi$
$600$	3.52096e11	0.110912
$601$	4.67286e12	1.46099	0.730495	−	0.682918i	$-0.239289\pi$
$601$	4.67286e12	1.46099	0.730495	+	0.682918i	$0.239289\pi$
$602$	5.87356e12	1.82271
$603$	1.10156e12	0.339297
$604$	−2.32595e12	−0.711104
$605$	3.93007e11	0.119262
$606$	8.39565e11	0.252888
$607$	3.92598e12	1.17381	0.586907	−	0.809654i	$-0.300345\pi$
$607$	3.92598e12	1.17381	0.586907	+	0.809654i	$0.300345\pi$
$608$	−7.94004e11	−0.235644
$609$	−5.68151e12	−1.67373
$610$	−1.24186e12	−0.363151
$611$	7.90210e11	0.229381
$612$	1.05446e12	0.303842
$613$	−3.63666e12	−1.04023	−0.520117	−	0.854095i	$-0.674112\pi$
$613$	−3.63666e12	−1.04023	−0.520117	+	0.854095i	$0.674112\pi$
$614$	−3.14063e12	−0.891784
$615$	1.56491e12	0.441115
$616$	6.50890e12	1.82135
$617$	9.28779e10	0.0258006	0.0129003	−	0.999917i	$-0.495894\pi$
$617$	9.28779e10	0.0258006	0.0129003	+	0.999917i	$0.495894\pi$
$618$	3.34736e11	0.0923111
$619$	1.34091e12	0.367105	0.183553	−	0.983010i	$-0.441240\pi$
$619$	1.34091e12	0.367105	0.183553	+	0.983010i	$0.441240\pi$
$620$	1.08298e12	0.294347
$621$	1.08767e12	0.293484
$622$	−4.81020e11	−0.128856
$623$	3.16922e11	0.0842861
$624$	3.37174e10	0.00890275
$625$	1.52588e11	0.0400000
$626$	−3.86479e12	−1.00587
$627$	5.76899e11	0.149072
$628$	−2.04499e12	−0.524653
$629$	−5.26108e12	−1.34013
$630$	−5.71641e11	−0.144574
$631$	1.81580e12	0.455970	0.227985	−	0.973665i	$-0.426786\pi$
$631$	1.81580e12	0.455970	0.227985	+	0.973665i	$0.426786\pi$
$632$	−2.47606e12	−0.617353
$633$	−9.80554e11	−0.242747
$634$	9.67013e11	0.237701
$635$	−3.08488e11	−0.0752933
$636$	2.09869e12	0.508617
$637$	−1.01799e12	−0.244972
$638$	−4.66518e12	−1.11474
$639$	1.89270e12	0.449084
$640$	−1.43008e12	−0.336938
$641$	−5.43389e12	−1.27131	−0.635653	−	0.771975i	$-0.719269\pi$
$641$	−5.43389e12	−1.27131	−0.635653	+	0.771975i	$0.719269\pi$
$642$	−1.97320e12	−0.458421
$643$	9.87680e11	0.227859	0.113930	−	0.993489i	$-0.463656\pi$
$643$	9.87680e11	0.227859	0.113930	+	0.993489i	$0.463656\pi$
$644$	−7.49892e12	−1.71796
$645$	2.13301e12	0.485259
$646$	7.96873e11	0.180029
$647$	−4.48367e12	−1.00592	−0.502961	−	0.864309i	$-0.667756\pi$
$647$	−4.48367e12	−1.00592	−0.502961	+	0.864309i	$0.667756\pi$
$648$	−4.79022e11	−0.106725
$649$	8.02341e12	1.77524
$650$	−6.98105e10	−0.0153395
$651$	−4.38787e12	−0.957500
$652$	−5.00771e11	−0.108524
$653$	−5.75374e12	−1.23834	−0.619172	−	0.785256i	$-0.712532\pi$
$653$	−5.75374e12	−1.23834	−0.619172	+	0.785256i	$0.712532\pi$
$654$	−3.59581e11	−0.0768595
$655$	2.75632e12	0.585118
$656$	−9.37810e11	−0.197719
$657$	−9.32900e11	−0.195340
$658$	8.02854e12	1.66963
$659$	−1.50077e12	−0.309978	−0.154989	−	0.987916i	$-0.549534\pi$
$659$	−1.50077e12	−0.309978	−0.154989	+	0.987916i	$0.549534\pi$
$660$	9.47176e11	0.194305
$661$	−1.76135e11	−0.0358871	−0.0179436	−	0.999839i	$-0.505712\pi$
$661$	−1.76135e11	−0.0358871	−0.0179436	+	0.999839i	$0.505712\pi$
$662$	−4.09234e11	−0.0828153
$663$	−5.21744e11	−0.104869
$664$	5.52549e12	1.10310
$665$	8.71739e11	0.172858
$666$	9.57709e11	0.188625
$667$	1.34131e13	2.62399
$668$	5.28065e12	1.02611
$669$	−5.43154e12	−1.04835
$670$	1.36678e12	0.262037
$671$	−8.33700e12	−1.58766
$672$	5.28184e12	0.999133
$673$	5.47516e12	1.02880	0.514398	−	0.857552i	$-0.328015\pi$
$673$	5.47516e12	1.02880	0.514398	+	0.857552i	$0.328015\pi$
$674$	2.92874e12	0.546653
$675$	−2.07594e11	−0.0384900
$676$	3.56596e12	0.656775
$677$	4.80501e12	0.879115	0.439557	−	0.898215i	$-0.355135\pi$
$677$	4.80501e12	0.879115	0.439557	+	0.898215i	$0.355135\pi$
$678$	1.05335e12	0.191442
$679$	4.33299e12	0.782300
$680$	3.26504e12	0.585597
$681$	−4.17359e12	−0.743614
$682$	−3.60295e12	−0.637718
$683$	−3.52399e12	−0.619643	−0.309821	−	0.950795i	$-0.600269\pi$
$683$	−3.52399e12	−0.619643	−0.309821	+	0.950795i	$0.600269\pi$
$684$	2.92718e11	0.0511326
$685$	−4.67332e11	−0.0810994
$686$	−4.71739e12	−0.813285
$687$	−1.39490e12	−0.238912
$688$	−1.27826e12	−0.217505
$689$	−1.03843e12	−0.175546
$690$	1.34955e12	0.226656
$691$	−4.02229e12	−0.671155	−0.335577	−	0.942013i	$-0.608931\pi$
$691$	−4.02229e12	−0.671155	−0.335577	+	0.942013i	$0.608931\pi$
$692$	3.70912e12	0.614884
$693$	−3.83762e12	−0.632066
$694$	1.16751e12	0.191048
$695$	−1.61843e12	−0.263125
$696$	−5.90728e12	−0.954214
$697$	1.45117e13	2.32900
$698$	−3.52311e12	−0.561793
$699$	8.06601e11	0.127794
$700$	1.43126e12	0.225308
$701$	−7.62157e12	−1.19210	−0.596051	−	0.802947i	$-0.703264\pi$
$701$	−7.62157e12	−1.19210	−0.596051	+	0.802947i	$0.703264\pi$
$702$	9.49765e10	0.0147604
$703$	−1.46048e12	−0.225526
$704$	3.48810e12	0.535194
$705$	2.91560e12	0.444505
$706$	2.46843e12	0.373938
$707$	8.51686e12	1.28201
$708$	4.07108e12	0.608919
$709$	3.63365e12	0.540052	0.270026	−	0.962853i	$-0.412968\pi$
$709$	3.63365e12	0.540052	0.270026	+	0.962853i	$0.412968\pi$
$710$	2.34841e12	0.346825
$711$	1.45987e12	0.214241
$712$	3.29515e11	0.0480525
$713$	1.03590e13	1.50112
$714$	−5.30093e12	−0.763325
$715$	−4.68662e11	−0.0670629
$716$	−5.29996e12	−0.753641
$717$	−3.04549e12	−0.430350
$718$	−1.30161e12	−0.182776
$719$	1.05067e12	0.146618	0.0733088	−	0.997309i	$-0.476644\pi$
$719$	1.05067e12	0.146618	0.0733088	+	0.997309i	$0.476644\pi$
$720$	1.24406e11	0.0172522
$721$	3.39568e12	0.467971
$722$	2.21213e11	0.0302965
$723$	−2.69898e12	−0.367348
$724$	9.29067e9	0.00125668
$725$	−2.56004e12	−0.344132
$726$	−6.63417e11	−0.0886282
$727$	−1.22082e12	−0.162087	−0.0810435	−	0.996711i	$-0.525825\pi$
$727$	−1.22082e12	−0.162087	−0.0810435	+	0.996711i	$0.525825\pi$
$728$	−1.63413e12	−0.215623
$729$	2.82430e11	0.0370370
$730$	−1.15752e12	−0.150860
$731$	1.97797e13	2.56208
$732$	−4.23019e12	−0.544578
$733$	−4.05937e12	−0.519387	−0.259694	−	0.965691i	$-0.583622\pi$
$733$	−4.05937e12	−0.519387	−0.259694	+	0.965691i	$0.583622\pi$
$734$	−5.62803e11	−0.0715688
$735$	−3.75604e12	−0.474720
$736$	−1.24695e13	−1.56639
$737$	9.17567e12	1.14560
$738$	−2.64166e12	−0.327811
$739$	−6.87940e12	−0.848497	−0.424249	−	0.905546i	$-0.639462\pi$
$739$	−6.87940e12	−0.848497	−0.424249	+	0.905546i	$0.639462\pi$
$740$	−2.39788e12	−0.293958
$741$	−1.44837e11	−0.0176481
$742$	−1.05504e13	−1.27777
$743$	−1.05856e13	−1.27429	−0.637143	−	0.770745i	$-0.719884\pi$
$743$	−1.05856e13	−1.27429	−0.637143	+	0.770745i	$0.719884\pi$
$744$	−4.56223e12	−0.545882
$745$	3.42570e12	0.407423
$746$	−1.97898e12	−0.233946
$747$	−3.25781e12	−0.382809
$748$	8.78332e12	1.02589
$749$	−2.00169e13	−2.32396
$750$	−2.57577e11	−0.0297256
$751$	3.47000e12	0.398061	0.199031	−	0.979993i	$-0.436221\pi$
$751$	3.47000e12	0.398061	0.199031	+	0.979993i	$0.436221\pi$
$752$	−1.74724e12	−0.199238
$753$	−2.69096e12	−0.305021
$754$	1.17124e12	0.131970
$755$	4.24633e12	0.475612
$756$	−1.94721e12	−0.216803
$757$	9.52204e12	1.05390	0.526949	−	0.849897i	$-0.323336\pi$
$757$	9.52204e12	1.05390	0.526949	+	0.849897i	$0.323336\pi$
$758$	−1.11774e12	−0.122979
$759$	9.05996e12	0.990920
$760$	9.06379e11	0.0985482
$761$	6.84268e12	0.739597	0.369798	−	0.929112i	$-0.379427\pi$
$761$	6.84268e12	0.739597	0.369798	+	0.929112i	$0.379427\pi$
$762$	5.20744e11	0.0559535
$763$	−3.64773e12	−0.389639
$764$	4.10965e12	0.436400
$765$	−1.92505e12	−0.203220
$766$	4.34330e12	0.455817
$767$	−2.01436e12	−0.210164
$768$	5.06099e12	0.524940
$769$	1.40901e12	0.145294	0.0726468	−	0.997358i	$-0.476855\pi$
$769$	1.40901e12	0.145294	0.0726468	+	0.997358i	$0.476855\pi$
$770$	−4.76161e12	−0.488141
$771$	−1.32506e11	−0.0135049
$772$	−5.94303e11	−0.0602185
$773$	−6.28642e12	−0.633280	−0.316640	−	0.948546i	$-0.602555\pi$
$773$	−6.28642e12	−0.633280	−0.316640	+	0.948546i	$0.602555\pi$
$774$	−3.60064e12	−0.360616
$775$	−1.97714e12	−0.196870
$776$	4.50517e12	0.445999
$777$	9.71536e12	0.956234
$778$	4.77896e12	0.467655
$779$	4.02846e12	0.391941
$780$	−2.37799e11	−0.0230030
$781$	1.57656e13	1.51629
$782$	1.25146e13	1.19670
$783$	3.48290e12	0.331142
$784$	2.25090e12	0.212781
$785$	3.73341e12	0.350907
$786$	−4.65282e12	−0.434825
$787$	−2.29630e12	−0.213375	−0.106687	−	0.994293i	$-0.534024\pi$
$787$	−2.29630e12	−0.213375	−0.106687	+	0.994293i	$0.534024\pi$
$788$	−4.82789e12	−0.446056
$789$	7.28892e12	0.669602
$790$	1.81137e12	0.165457
$791$	1.06856e13	0.970516
$792$	−3.99012e12	−0.360348
$793$	2.09310e12	0.187958
$794$	−9.45471e12	−0.844220
$795$	−3.83144e12	−0.340181
$796$	−1.94555e12	−0.171765
$797$	−2.26453e13	−1.98799	−0.993997	−	0.109403i	$-0.965106\pi$
$797$	−2.26453e13	−1.98799	−0.993997	+	0.109403i	$0.965106\pi$
$798$	−1.47154e12	−0.128458
$799$	2.70369e13	2.34691
$800$	2.37995e12	0.205430
$801$	−1.94281e11	−0.0166757
$802$	−3.85025e12	−0.328628
$803$	−7.77079e12	−0.659546
$804$	4.65573e12	0.392949
$805$	1.36903e13	1.14903
$806$	9.04560e11	0.0754970
$807$	−1.15215e12	−0.0956268
$808$	8.85530e12	0.730890
$809$	8.32955e12	0.683681	0.341840	−	0.939758i	$-0.388950\pi$
$809$	8.32955e12	0.683681	0.341840	+	0.939758i	$0.388950\pi$
$810$	3.50430e11	0.0286035
$811$	−1.41864e13	−1.15154	−0.575768	−	0.817613i	$-0.695297\pi$
$811$	−1.41864e13	−1.15154	−0.575768	+	0.817613i	$0.695297\pi$
$812$	−2.40129e13	−1.93839
$813$	8.89926e12	0.714408
$814$	7.97744e12	0.636875
$815$	9.14225e11	0.0725845
$816$	1.15363e12	0.0910883
$817$	5.49088e12	0.431164
$818$	4.59005e12	0.358449
$819$	9.63477e11	0.0748279
$820$	6.61409e12	0.510867
$821$	1.72936e13	1.32844	0.664221	−	0.747537i	$-0.268764\pi$
$821$	1.72936e13	1.32844	0.664221	+	0.747537i	$0.268764\pi$
$822$	7.88882e11	0.0602683
$823$	−9.54184e12	−0.724991	−0.362496	−	0.931985i	$-0.618075\pi$
$823$	−9.54184e12	−0.724991	−0.362496	+	0.931985i	$0.618075\pi$
$824$	3.53062e12	0.266796
$825$	−1.72920e12	−0.129958
$826$	−2.04660e13	−1.52976
$827$	1.14789e13	0.853346	0.426673	−	0.904406i	$-0.359685\pi$
$827$	1.14789e13	0.853346	0.426673	+	0.904406i	$0.359685\pi$
$828$	4.59703e12	0.339892
$829$	−1.36358e13	−1.00274	−0.501368	−	0.865234i	$-0.667170\pi$
$829$	−1.36358e13	−1.00274	−0.501368	+	0.865234i	$0.667170\pi$
$830$	−4.04219e12	−0.295642
$831$	−1.02698e13	−0.747060
$832$	−8.75725e11	−0.0633597
$833$	−3.48304e13	−2.50643
$834$	2.73200e12	0.195539
$835$	−9.64055e12	−0.686298
$836$	2.43826e12	0.172644
$837$	2.68987e12	0.189438
$838$	−1.29247e13	−0.905363
$839$	1.95966e13	1.36537	0.682686	−	0.730712i	$-0.260812\pi$
$839$	1.95966e13	1.36537	0.682686	+	0.730712i	$0.260812\pi$
$840$	−6.02938e12	−0.417846
$841$	2.84438e13	1.96068
$842$	3.29327e12	0.225800
$843$	−3.15937e12	−0.215465
$844$	−4.14431e12	−0.281132
$845$	−6.51015e12	−0.439274
$846$	−4.92170e12	−0.330330
$847$	−6.72995e12	−0.449300
$848$	2.29608e12	0.152478
$849$	1.28589e13	0.849411
$850$	−2.38855e12	−0.156946
$851$	−2.29363e13	−1.49913
$852$	7.99949e12	0.520096
$853$	−2.57539e12	−0.166561	−0.0832804	−	0.996526i	$-0.526540\pi$
$853$	−2.57539e12	−0.166561	−0.0832804	+	0.996526i	$0.526540\pi$
$854$	2.12659e13	1.36812
$855$	−5.34398e11	−0.0341993
$856$	−2.08123e13	−1.32492
$857$	−5.83052e12	−0.369227	−0.184614	−	0.982811i	$-0.559103\pi$
$857$	−5.83052e12	−0.369227	−0.184614	+	0.982811i	$0.559103\pi$
$858$	7.91127e11	0.0498372
$859$	7.54040e12	0.472526	0.236263	−	0.971689i	$-0.424077\pi$
$859$	7.54040e12	0.472526	0.236263	+	0.971689i	$0.424077\pi$
$860$	9.01515e12	0.561992
$861$	−2.67980e13	−1.66183
$862$	1.33718e13	0.824913
$863$	2.75410e13	1.69017	0.845086	−	0.534631i	$-0.179549\pi$
$863$	2.75410e13	1.69017	0.845086	+	0.534631i	$0.179549\pi$
$864$	−3.23790e12	−0.197675
$865$	−6.77150e12	−0.411256
$866$	−1.33356e13	−0.805717
$867$	−8.24573e12	−0.495614
$868$	−1.85453e13	−1.10891
$869$	1.21603e13	0.723362
$870$	4.32149e12	0.255739
$871$	−2.30365e12	−0.135624
$872$	−3.79268e12	−0.222138
$873$	−2.65623e12	−0.154775
$874$	3.47406e12	0.201389
$875$	−2.61296e12	−0.150694
$876$	−3.94290e12	−0.226228
$877$	−1.48201e13	−0.845966	−0.422983	−	0.906138i	$-0.639017\pi$
$877$	−1.48201e13	−0.845966	−0.422983	+	0.906138i	$0.639017\pi$
$878$	−9.05732e12	−0.514369
$879$	1.53892e13	0.869491
$880$	1.03626e12	0.0582503
$881$	−3.36423e13	−1.88146	−0.940729	−	0.339159i	$-0.889857\pi$
$881$	−3.36423e13	−1.88146	−0.940729	+	0.339159i	$0.889857\pi$
$882$	6.34041e12	0.352784
$883$	1.14669e13	0.634778	0.317389	−	0.948295i	$-0.397194\pi$
$883$	1.14669e13	0.634778	0.317389	+	0.948295i	$0.397194\pi$
$884$	−2.20515e12	−0.121451
$885$	−7.43231e12	−0.407267
$886$	−8.34727e12	−0.455085
$887$	−1.44925e12	−0.0786114	−0.0393057	−	0.999227i	$-0.512515\pi$
$887$	−1.44925e12	−0.0786114	−0.0393057	+	0.999227i	$0.512515\pi$
$888$	1.01014e13	0.545160
$889$	5.28262e12	0.283656
$890$	−2.41058e11	−0.0128785
$891$	2.35256e12	0.125052
$892$	−2.29564e13	−1.21412
$893$	7.50546e12	0.394953
$894$	−5.78277e12	−0.302773
$895$	9.67581e12	0.504062
$896$	2.44890e13	1.26936
$897$	−2.27460e12	−0.117311
$898$	−1.33984e13	−0.687560
$899$	3.31713e13	1.69373
$900$	−8.77396e11	−0.0445763
$901$	−3.55296e13	−1.79609
$902$	−2.20042e13	−1.10682
$903$	−3.65262e13	−1.82814
$904$	1.11102e13	0.553303
$905$	−1.69614e10	−0.000840510 0
$906$	−7.16805e12	−0.353447
$907$	1.17411e13	0.576071	0.288035	−	0.957620i	$-0.406998\pi$
$907$	1.17411e13	0.576071	0.288035	+	0.957620i	$0.406998\pi$
$908$	−1.76397e13	−0.861200
$909$	−5.22105e12	−0.253641
$910$	1.19545e12	0.0577892
$911$	2.23131e12	0.107331	0.0536656	−	0.998559i	$-0.482909\pi$
$911$	2.23131e12	0.107331	0.0536656	+	0.998559i	$0.482909\pi$
$912$	3.20250e11	0.0153290
$913$	−2.71366e13	−1.29252
$914$	−1.35737e13	−0.643341
$915$	7.72280e12	0.364233
$916$	−5.89553e12	−0.276690
$917$	−4.71999e13	−2.20434
$918$	3.24960e12	0.151021
$919$	7.33394e12	0.339170	0.169585	−	0.985516i	$-0.445757\pi$
$919$	7.33394e12	0.339170	0.169585	+	0.985516i	$0.445757\pi$
$920$	1.42343e13	0.655076
$921$	1.95308e13	0.894442
$922$	−2.38513e13	−1.08698
$923$	−3.95814e12	−0.179508
$924$	−1.62197e13	−0.732013
$925$	4.37766e12	0.196609
$926$	2.39094e13	1.06861
$927$	−2.08164e12	−0.0925863
$928$	−3.99296e13	−1.76738
$929$	−1.92035e13	−0.845881	−0.422941	−	0.906157i	$-0.639002\pi$
$929$	−1.92035e13	−0.845881	−0.422941	+	0.906157i	$0.639002\pi$
$930$	3.33751e12	0.146302
$931$	−9.66896e12	−0.421800
$932$	3.40910e12	0.148002
$933$	2.99134e12	0.129240
$934$	2.44343e13	1.05061
$935$	−1.60352e13	−0.686153
$936$	1.00176e12	0.0426603
$937$	3.80847e13	1.61407	0.807035	−	0.590504i	$-0.201071\pi$
$937$	3.80847e13	1.61407	0.807035	+	0.590504i	$0.201071\pi$
$938$	−2.34051e13	−0.987185
$939$	2.40342e13	1.00887
$940$	1.23228e13	0.514794
$941$	−1.75227e13	−0.728530	−0.364265	−	0.931295i	$-0.618680\pi$
$941$	−1.75227e13	−0.728530	−0.364265	+	0.931295i	$0.618680\pi$
$942$	−6.30220e12	−0.260773
$943$	6.32654e13	2.60533
$944$	4.45399e12	0.182547
$945$	3.55490e12	0.145005
$946$	−2.99923e13	−1.21758
$947$	−1.13923e13	−0.460296	−0.230148	−	0.973156i	$-0.573921\pi$
$947$	−1.13923e13	−0.460296	−0.230148	+	0.973156i	$0.573921\pi$
$948$	6.17015e12	0.248118
$949$	1.95094e12	0.0780812
$950$	−6.63065e11	−0.0264119
$951$	−6.01361e12	−0.238409
$952$	−5.59114e13	−2.20615
$953$	−1.35556e13	−0.532354	−0.266177	−	0.963924i	$-0.585761\pi$
$953$	−1.35556e13	−0.532354	−0.266177	+	0.963924i	$0.585761\pi$
$954$	6.46769e12	0.252802
$955$	−7.50273e12	−0.291880
$956$	−1.28718e13	−0.498400
$957$	2.90116e13	1.11807
$958$	4.47349e12	0.171594
$959$	8.00271e12	0.305530
$960$	−3.23112e12	−0.122782
$961$	−8.21171e11	−0.0310583
$962$	−2.00283e12	−0.0753972
$963$	1.22709e13	0.459787
$964$	−1.14073e13	−0.425436
$965$	1.08498e12	0.0402763
$966$	−2.31100e13	−0.853892
$967$	−1.13041e12	−0.0415736	−0.0207868	−	0.999784i	$-0.506617\pi$
$967$	−1.13041e12	−0.0415736	−0.0207868	+	0.999784i	$0.506617\pi$
$968$	−6.99739e12	−0.256151
$969$	−4.95556e12	−0.180566
$970$	−3.29577e12	−0.119532
$971$	3.95571e13	1.42803	0.714016	−	0.700130i	$-0.246874\pi$
$971$	3.95571e13	1.42803	0.714016	+	0.700130i	$0.246874\pi$
$972$	1.19369e12	0.0428936
$973$	2.77145e13	0.991285
$974$	−1.41098e13	−0.502349
$975$	4.34135e11	0.0153852
$976$	−4.62807e12	−0.163259
$977$	1.59270e12	0.0559253	0.0279626	−	0.999609i	$-0.491098\pi$
$977$	1.59270e12	0.0559253	0.0279626	+	0.999609i	$0.491098\pi$
$978$	−1.54326e12	−0.0539405
$979$	−1.61830e12	−0.0563038
$980$	−1.58749e13	−0.549786
$981$	2.23615e12	0.0770886
$982$	7.53676e12	0.258632
$983$	3.35787e13	1.14702	0.573512	−	0.819197i	$-0.305581\pi$
$983$	3.35787e13	1.14702	0.573512	+	0.819197i	$0.305581\pi$
$984$	−2.78628e13	−0.947431
$985$	8.81398e12	0.298338
$986$	4.00739e13	1.35025
$987$	−4.99275e13	−1.67461
$988$	−6.12152e11	−0.0204387
$989$	8.62321e13	2.86606
$990$	2.91898e12	0.0965769
$991$	−1.83632e12	−0.0604809	−0.0302404	−	0.999543i	$-0.509627\pi$
$991$	−1.83632e12	−0.0604809	−0.0302404	+	0.999543i	$0.509627\pi$
$992$	−3.08379e13	−1.01107
$993$	2.54492e12	0.0830621
$994$	−4.02147e13	−1.30661
$995$	3.55187e12	0.114882
$996$	−1.37691e13	−0.443342
$997$	2.91194e13	0.933372	0.466686	−	0.884423i	$-0.345448\pi$
$997$	2.91194e13	0.933372	0.466686	+	0.884423i	$0.345448\pi$
$998$	−4.32743e12	−0.138084
$999$	−5.95576e12	−0.189187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.10	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.10	✓	15	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	285.a (trivial)

\(f(q)\)	\(=\)	\(q+13.0251 q^{2} -81.0000 q^{3} -342.346 q^{4} +625.000 q^{5} -1055.03 q^{6} -10702.7 q^{7} -11128.0 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+13.0251 q^{2} -81.0000 q^{3} -342.346 q^{4} +625.000 q^{5} -1055.03 q^{6} -10702.7 q^{7} -11128.0 q^{8} +6561.00 q^{9} +8140.70 q^{10} +54651.2 q^{11} +27730.0 q^{12} -13720.8 q^{13} -139403. q^{14} -50625.0 q^{15} +30338.2 q^{16} -469454. q^{17} +85457.8 q^{18} -130321. q^{19} -213966. q^{20} +866916. q^{21} +711839. q^{22} -2.04664e6 q^{23} +901365. q^{24} +390625. q^{25} -178715. q^{26} -531441. q^{27} +3.66402e6 q^{28} -6.55370e6 q^{29} -659397. q^{30} -5.06147e6 q^{31} +6.09268e6 q^{32} -4.42675e6 q^{33} -6.11469e6 q^{34} -6.68916e6 q^{35} -2.24613e6 q^{36} +1.12068e7 q^{37} -1.69745e6 q^{38} +1.11138e6 q^{39} -6.95498e6 q^{40} -3.09118e7 q^{41} +1.12917e7 q^{42} -4.21335e7 q^{43} -1.87096e7 q^{44} +4.10062e6 q^{45} -2.66577e7 q^{46} -5.75921e7 q^{47} -2.45740e6 q^{48} +7.41934e7 q^{49} +5.08794e6 q^{50} +3.80258e7 q^{51} +4.69726e6 q^{52} +7.56828e7 q^{53} -6.92208e6 q^{54} +3.41570e7 q^{55} +1.19099e8 q^{56} +1.05560e7 q^{57} -8.53627e7 q^{58} +1.46811e8 q^{59} +1.73313e7 q^{60} -1.52549e8 q^{61} -6.59262e7 q^{62} -7.02202e7 q^{63} +6.38247e7 q^{64} -8.57550e6 q^{65} -5.76590e7 q^{66} +1.67895e8 q^{67} +1.60716e8 q^{68} +1.65778e8 q^{69} -8.71272e7 q^{70} +2.88477e8 q^{71} -7.30106e7 q^{72} -1.42189e8 q^{73} +1.45970e8 q^{74} -3.16406e7 q^{75} +4.46149e7 q^{76} -5.84914e8 q^{77} +1.44759e7 q^{78} +2.22508e8 q^{79} +1.89614e7 q^{80} +4.30467e7 q^{81} -4.02630e8 q^{82} -4.96541e8 q^{83} -2.96785e8 q^{84} -2.93409e8 q^{85} -5.48794e8 q^{86} +5.30850e8 q^{87} -6.08157e8 q^{88} -2.96115e7 q^{89} +5.34111e7 q^{90} +1.46849e8 q^{91} +7.00659e8 q^{92} +4.09979e8 q^{93} -7.50144e8 q^{94} -8.14506e7 q^{95} -4.93507e8 q^{96} -4.04851e8 q^{97} +9.66378e8 q^{98} +3.58567e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9} - 10625 q^{10} + 138230 q^{11} - 409455 q^{12} - 176712 q^{13} - 555994 q^{14} - 759375 q^{15} + 1695731 q^{16} - 274992 q^{17} - 111537 q^{18} - 1954815 q^{19} + 3159375 q^{20} - 109512 q^{21} - 1031106 q^{22} + 1714212 q^{23} + 291357 q^{24} + 5859375 q^{25} + 9500004 q^{26} - 7971615 q^{27} + 14545598 q^{28} + 1754340 q^{29} + 860625 q^{30} + 8442914 q^{31} + 35638859 q^{32} - 11196630 q^{33} + 47218266 q^{34} + 845000 q^{35} + 33165855 q^{36} + 2956096 q^{37} + 2215457 q^{38} + 14313672 q^{39} - 2248125 q^{40} - 38550502 q^{41} + 45035514 q^{42} + 50753570 q^{43} + 212125630 q^{44} + 61509375 q^{45} - 117130008 q^{46} - 40252876 q^{47} - 137354211 q^{48} + 110123035 q^{49} - 6640625 q^{50} + 22274352 q^{51} - 87136648 q^{52} + 65532542 q^{53} + 9034497 q^{54} + 86393750 q^{55} - 377288898 q^{56} + 158340015 q^{57} + 211630876 q^{58} + 175407418 q^{59} - 255909375 q^{60} + 151231854 q^{61} - 30983940 q^{62} + 8870472 q^{63} + 836879575 q^{64} - 110445000 q^{65} + 83519586 q^{66} + 40009476 q^{67} - 124850430 q^{68} - 138851172 q^{69} - 347496250 q^{70} + 87578500 q^{71} - 23599917 q^{72} - 360657638 q^{73} + 1373397084 q^{74} - 474609375 q^{75} - 658772655 q^{76} - 304618172 q^{77} - 769500324 q^{78} + 205798286 q^{79} + 1059831875 q^{80} + 645700815 q^{81} - 2327138772 q^{82} - 63321462 q^{83} - 1178193438 q^{84} - 171870000 q^{85} - 848405762 q^{86} - 142101540 q^{87} - 3211126502 q^{88} - 381069174 q^{89} - 69710625 q^{90} + 1476892872 q^{91} - 2382818588 q^{92} - 683876034 q^{93} - 5137318040 q^{94} - 1221759375 q^{95} - 2886747579 q^{96} - 3915268828 q^{97} - 8273557437 q^{98} + 906927030 q^{99}+O(q^{100}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9 - 10625 * q^10 + 138230 * q^11 - 409455 * q^12 - 176712 * q^13 - 555994 * q^14 - 759375 * q^15 + 1695731 * q^16 - 274992 * q^17 - 111537 * q^18 - 1954815 * q^19 + 3159375 * q^20 - 109512 * q^21 - 1031106 * q^22 + 1714212 * q^23 + 291357 * q^24 + 5859375 * q^25 + 9500004 * q^26 - 7971615 * q^27 + 14545598 * q^28 + 1754340 * q^29 + 860625 * q^30 + 8442914 * q^31 + 35638859 * q^32 - 11196630 * q^33 + 47218266 * q^34 + 845000 * q^35 + 33165855 * q^36 + 2956096 * q^37 + 2215457 * q^38 + 14313672 * q^39 - 2248125 * q^40 - 38550502 * q^41 + 45035514 * q^42 + 50753570 * q^43 + 212125630 * q^44 + 61509375 * q^45 - 117130008 * q^46 - 40252876 * q^47 - 137354211 * q^48 + 110123035 * q^49 - 6640625 * q^50 + 22274352 * q^51 - 87136648 * q^52 + 65532542 * q^53 + 9034497 * q^54 + 86393750 * q^55 - 377288898 * q^56 + 158340015 * q^57 + 211630876 * q^58 + 175407418 * q^59 - 255909375 * q^60 + 151231854 * q^61 - 30983940 * q^62 + 8870472 * q^63 + 836879575 * q^64 - 110445000 * q^65 + 83519586 * q^66 + 40009476 * q^67 - 124850430 * q^68 - 138851172 * q^69 - 347496250 * q^70 + 87578500 * q^71 - 23599917 * q^72 - 360657638 * q^73 + 1373397084 * q^74 - 474609375 * q^75 - 658772655 * q^76 - 304618172 * q^77 - 769500324 * q^78 + 205798286 * q^79 + 1059831875 * q^80 + 645700815 * q^81 - 2327138772 * q^82 - 63321462 * q^83 - 1178193438 * q^84 - 171870000 * q^85 - 848405762 * q^86 - 142101540 * q^87 - 3211126502 * q^88 - 381069174 * q^89 - 69710625 * q^90 + 1476892872 * q^91 - 2382818588 * q^92 - 683876034 * q^93 - 5137318040 * q^94 - 1221759375 * q^95 - 2886747579 * q^96 - 3915268828 * q^97 - 8273557437 * q^98 + 906927030 * q^99

Introduction

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