LMFDB - Embedded newform 285.10.a.h.1.15

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			1.15
Root			$-45.0746$ 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)

$f(q)$	$=$	$q+44.0746 q^{2} -81.0000 q^{3} +1430.57 q^{4} +625.000 q^{5} -3570.04 q^{6} -6480.81 q^{7} +40485.6 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+44.0746 q^{2} -81.0000 q^{3} +1430.57 q^{4} +625.000 q^{5} -3570.04 q^{6} -6480.81 q^{7} +40485.6 q^{8} +6561.00 q^{9} +27546.6 q^{10} -16845.3 q^{11} -115876. q^{12} -113957. q^{13} -285639. q^{14} -50625.0 q^{15} +1.05193e6 q^{16} +289208. q^{17} +289173. q^{18} -130321. q^{19} +894106. q^{20} +524945. q^{21} -742450. q^{22} +804006. q^{23} -3.27933e6 q^{24} +390625. q^{25} -5.02262e6 q^{26} -531441. q^{27} -9.27124e6 q^{28} +7.24242e6 q^{29} -2.23128e6 q^{30} +9.93122e6 q^{31} +2.56349e7 q^{32} +1.36447e6 q^{33} +1.27467e7 q^{34} -4.05051e6 q^{35} +9.38596e6 q^{36} +2.05418e7 q^{37} -5.74384e6 q^{38} +9.23053e6 q^{39} +2.53035e7 q^{40} -4.90838e6 q^{41} +2.31368e7 q^{42} -5.18880e6 q^{43} -2.40984e7 q^{44} +4.10062e6 q^{45} +3.54362e7 q^{46} -3.39717e7 q^{47} -8.52065e7 q^{48} +1.64727e6 q^{49} +1.72166e7 q^{50} -2.34258e7 q^{51} -1.63024e8 q^{52} +1.08619e7 q^{53} -2.34230e7 q^{54} -1.05283e7 q^{55} -2.62379e8 q^{56} +1.05560e7 q^{57} +3.19207e8 q^{58} +1.50863e8 q^{59} -7.24226e7 q^{60} -3.90769e7 q^{61} +4.37714e8 q^{62} -4.25206e7 q^{63} +5.91258e8 q^{64} -7.12233e7 q^{65} +6.01384e7 q^{66} -2.58318e8 q^{67} +4.13732e8 q^{68} -6.51245e7 q^{69} -1.78524e8 q^{70} +1.47177e8 q^{71} +2.65626e8 q^{72} -3.55554e8 q^{73} +9.05370e8 q^{74} -3.16406e7 q^{75} -1.86433e8 q^{76} +1.09171e8 q^{77} +4.06832e8 q^{78} +6.71093e8 q^{79} +6.57458e8 q^{80} +4.30467e7 q^{81} -2.16335e8 q^{82} +4.05588e8 q^{83} +7.50971e8 q^{84} +1.80755e8 q^{85} -2.28694e8 q^{86} -5.86636e8 q^{87} -6.81992e8 q^{88} +4.17963e8 q^{89} +1.80733e8 q^{90} +7.38535e8 q^{91} +1.15019e9 q^{92} -8.04429e8 q^{93} -1.49729e9 q^{94} -8.14506e7 q^{95} -2.07643e9 q^{96} -3.08832e8 q^{97} +7.26026e7 q^{98} -1.10522e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	44.0746	1.94784	0.973920	−	0.226892i	$-0.0728564\pi$
$2$	44.0746	1.94784	0.973920	+	0.226892i	$0.0728564\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	1430.57	2.79408
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−3570.04	−1.12459
$7$	−6480.81	−1.02021	−0.510103	−	0.860113i	$-0.670393\pi$
$7$	−6480.81	−1.02021	−0.510103	+	0.860113i	$0.670393\pi$
$8$	40485.6	3.49458
$9$	6561.00	0.333333
$10$	27546.6	0.871100
$11$	−16845.3	−0.346906	−0.173453	−	0.984842i	$-0.555492\pi$
$11$	−16845.3	−0.346906	−0.173453	+	0.984842i	$0.555492\pi$
$12$	−115876.	−1.61316
$13$	−113957.	−1.10662	−0.553308	−	0.832977i	$-0.686635\pi$
$13$	−113957.	−1.10662	−0.553308	+	0.832977i	$0.686635\pi$
$14$	−285639.	−1.98720
$15$	−50625.0	−0.258199
$16$	1.05193e6	4.01280
$17$	289208.	0.839827	0.419914	−	0.907564i	$-0.362060\pi$
$17$	289208.	0.839827	0.419914	+	0.907564i	$0.362060\pi$
$18$	289173.	0.649280
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	894106.	1.24955
$21$	524945.	0.589016
$22$	−742450.	−0.675717
$23$	804006.	0.599079	0.299539	−	0.954084i	$-0.403167\pi$
$23$	804006.	0.599079	0.299539	+	0.954084i	$0.403167\pi$
$24$	−3.27933e6	−2.01760
$25$	390625.	0.200000
$26$	−5.02262e6	−2.15551
$27$	−531441.	−0.192450
$28$	−9.27124e6	−2.85054
$29$	7.24242e6	1.90148	0.950742	−	0.309982i	$-0.100323\pi$
$29$	7.24242e6	1.90148	0.950742	+	0.309982i	$0.100323\pi$
$30$	−2.23128e6	−0.502930
$31$	9.93122e6	1.93141	0.965706	−	0.259637i	$-0.0836030\pi$
$31$	9.93122e6	1.93141	0.965706	+	0.259637i	$0.0836030\pi$
$32$	2.56349e7	4.32172
$33$	1.36447e6	0.200286
$34$	1.27467e7	1.63585
$35$	−4.05051e6	−0.456250
$36$	9.38596e6	0.931360
$37$	2.05418e7	1.80190	0.900949	−	0.433925i	$-0.142872\pi$
$37$	2.05418e7	1.80190	0.900949	+	0.433925i	$0.142872\pi$
$38$	−5.74384e6	−0.446865
$39$	9.23053e6	0.638905
$40$	2.53035e7	1.56282
$41$	−4.90838e6	−0.271276	−0.135638	−	0.990758i	$-0.543308\pi$
$41$	−4.90838e6	−0.271276	−0.135638	+	0.990758i	$0.543308\pi$
$42$	2.31368e7	1.14731
$43$	−5.18880e6	−0.231451	−0.115725	−	0.993281i	$-0.536919\pi$
$43$	−5.18880e6	−0.231451	−0.115725	+	0.993281i	$0.536919\pi$
$44$	−2.40984e7	−0.969283
$45$	4.10062e6	0.149071
$46$	3.54362e7	1.16691
$47$	−3.39717e7	−1.01549	−0.507747	−	0.861506i	$-0.669521\pi$
$47$	−3.39717e7	−1.01549	−0.507747	+	0.861506i	$0.669521\pi$
$48$	−8.52065e7	−2.31679
$49$	1.64727e6	0.0408208
$50$	1.72166e7	0.389568
$51$	−2.34258e7	−0.484874
$52$	−1.63024e8	−3.09197
$53$	1.08619e7	0.189088	0.0945439	−	0.995521i	$-0.469861\pi$
$53$	1.08619e7	0.189088	0.0945439	+	0.995521i	$0.469861\pi$
$54$	−2.34230e7	−0.374862
$55$	−1.05283e7	−0.155141
$56$	−2.62379e8	−3.56519
$57$	1.05560e7	0.132453
$58$	3.19207e8	3.70379
$59$	1.50863e8	1.62087	0.810436	−	0.585827i	$-0.199230\pi$
$59$	1.50863e8	1.62087	0.810436	+	0.585827i	$0.199230\pi$
$60$	−7.24226e7	−0.721428
$61$	−3.90769e7	−0.361356	−0.180678	−	0.983542i	$-0.557829\pi$
$61$	−3.90769e7	−0.361356	−0.180678	+	0.983542i	$0.557829\pi$
$62$	4.37714e8	3.76208
$63$	−4.25206e7	−0.340069
$64$	5.91258e8	4.40521
$65$	−7.12233e7	−0.494893
$66$	6.01384e7	0.390126
$67$	−2.58318e8	−1.56610	−0.783049	−	0.621960i	$-0.786336\pi$
$67$	−2.58318e8	−1.56610	−0.783049	+	0.621960i	$0.786336\pi$
$68$	4.13732e8	2.34654
$69$	−6.51245e7	−0.345878
$70$	−1.78524e8	−0.888702
$71$	1.47177e8	0.687349	0.343674	−	0.939089i	$-0.388328\pi$
$71$	1.47177e8	0.687349	0.343674	+	0.939089i	$0.388328\pi$
$72$	2.65626e8	1.16486
$73$	−3.55554e8	−1.46539	−0.732695	−	0.680557i	$-0.761738\pi$
$73$	−3.55554e8	−1.46539	−0.732695	+	0.680557i	$0.761738\pi$
$74$	9.05370e8	3.50981
$75$	−3.16406e7	−0.115470
$76$	−1.86433e8	−0.641006
$77$	1.09171e8	0.353916
$78$	4.06832e8	1.24448
$79$	6.71093e8	1.93848	0.969239	−	0.246122i	$-0.0791562\pi$
$79$	6.71093e8	1.93848	0.969239	+	0.246122i	$0.0791562\pi$
$80$	6.57458e8	1.79458
$81$	4.30467e7	0.111111
$82$	−2.16335e8	−0.528401
$83$	4.05588e8	0.938066	0.469033	−	0.883181i	$-0.344602\pi$
$83$	4.05588e8	0.938066	0.469033	+	0.883181i	$0.344602\pi$
$84$	7.50971e8	1.64576
$85$	1.80755e8	0.375582
$86$	−2.28694e8	−0.450829
$87$	−5.86636e8	−1.09782
$88$	−6.81992e8	−1.21229
$89$	4.17963e8	0.706128	0.353064	−	0.935599i	$-0.385140\pi$
$89$	4.17963e8	0.706128	0.353064	+	0.935599i	$0.385140\pi$
$90$	1.80733e8	0.290367
$91$	7.38535e8	1.12898
$92$	1.15019e9	1.67387
$93$	−8.04429e8	−1.11510
$94$	−1.49729e9	−1.97802
$95$	−8.14506e7	−0.102598
$96$	−2.07643e9	−2.49515
$97$	−3.08832e8	−0.354201	−0.177101	−	0.984193i	$-0.556672\pi$
$97$	−3.08832e8	−0.354201	−0.177101	+	0.984193i	$0.556672\pi$
$98$	7.26026e7	0.0795124
$99$	−1.10522e8	−0.115635
$100$	5.58816e8	0.558816
$101$	−8.05833e8	−0.770546	−0.385273	−	0.922803i	$-0.625893\pi$
$101$	−8.05833e8	−0.770546	−0.385273	+	0.922803i	$0.625893\pi$
$102$	−1.03248e9	−0.944458
$103$	5.85528e8	0.512601	0.256301	−	0.966597i	$-0.417496\pi$
$103$	5.85528e8	0.512601	0.256301	+	0.966597i	$0.417496\pi$
$104$	−4.61362e9	−3.86716
$105$	3.28091e8	0.263416
$106$	4.78733e8	0.368313
$107$	2.03970e9	1.50431	0.752157	−	0.658984i	$-0.229013\pi$
$107$	2.03970e9	1.50431	0.752157	+	0.658984i	$0.229013\pi$
$108$	−7.60263e8	−0.537721
$109$	−1.77914e9	−1.20723	−0.603615	−	0.797276i	$-0.706274\pi$
$109$	−1.77914e9	−1.20723	−0.603615	+	0.797276i	$0.706274\pi$
$110$	−4.64031e8	−0.302190
$111$	−1.66388e9	−1.04033
$112$	−6.81737e9	−4.09389
$113$	1.31492e9	0.758656	0.379328	−	0.925262i	$-0.376155\pi$
$113$	1.31492e9	0.758656	0.379328	+	0.925262i	$0.376155\pi$
$114$	4.65251e8	0.257998
$115$	5.02503e8	0.267916
$116$	1.03608e10	5.31290
$117$	−7.47673e8	−0.368872
$118$	6.64922e9	3.15720
$119$	−1.87430e9	−0.856797
$120$	−2.04958e9	−0.902297
$121$	−2.07418e9	−0.879656
$122$	−1.72230e9	−0.703864
$123$	3.97579e8	0.156621
$124$	1.42073e10	5.39652
$125$	2.44141e8	0.0894427
$126$	−1.87408e9	−0.662399
$127$	−2.78388e9	−0.949584	−0.474792	−	0.880098i	$-0.657477\pi$
$127$	−2.78388e9	−0.949584	−0.474792	+	0.880098i	$0.657477\pi$
$128$	1.29344e10	4.25893
$129$	4.20293e8	0.133628
$130$	−3.13914e9	−0.963973
$131$	−1.52925e9	−0.453689	−0.226844	−	0.973931i	$-0.572841\pi$
$131$	−1.52925e9	−0.453689	−0.226844	+	0.973931i	$0.572841\pi$
$132$	1.95197e9	0.559616
$133$	8.44585e8	0.234051
$134$	−1.13853e10	−3.05051
$135$	−3.32151e8	−0.0860663
$136$	1.17087e10	2.93484
$137$	9.14293e8	0.221739	0.110870	−	0.993835i	$-0.464636\pi$
$137$	9.14293e8	0.221739	0.110870	+	0.993835i	$0.464636\pi$
$138$	−2.87033e9	−0.673715
$139$	−2.61869e9	−0.595002	−0.297501	−	0.954722i	$-0.596153\pi$
$139$	−2.61869e9	−0.595002	−0.297501	+	0.954722i	$0.596153\pi$
$140$	−5.79453e9	−1.27480
$141$	2.75171e9	0.586295
$142$	6.48676e9	1.33885
$143$	1.91964e9	0.383892
$144$	6.90173e9	1.33760
$145$	4.52651e9	0.850370
$146$	−1.56709e10	−2.85434
$147$	−1.33429e8	−0.0235679
$148$	2.93864e10	5.03465
$149$	−4.38438e9	−0.728736	−0.364368	−	0.931255i	$-0.618715\pi$
$149$	−4.38438e9	−0.728736	−0.364368	+	0.931255i	$0.618715\pi$
$150$	−1.39455e9	−0.224917
$151$	7.10948e9	1.11286	0.556431	−	0.830894i	$-0.312170\pi$
$151$	7.10948e9	1.11286	0.556431	+	0.830894i	$0.312170\pi$
$152$	−5.27612e9	−0.801712
$153$	1.89749e9	0.279942
$154$	4.81168e9	0.689371
$155$	6.20701e9	0.863754
$156$	1.32049e10	1.78515
$157$	−1.37630e10	−1.80787	−0.903933	−	0.427675i	$-0.859333\pi$
$157$	−1.37630e10	−1.80787	−0.903933	+	0.427675i	$0.859333\pi$
$158$	2.95782e10	3.77584
$159$	−8.79812e8	−0.109170
$160$	1.60218e10	1.93273
$161$	−5.21061e9	−0.611184
$162$	1.89727e9	0.216427
$163$	2.86047e9	0.317390	0.158695	−	0.987328i	$-0.449271\pi$
$163$	2.86047e9	0.317390	0.158695	+	0.987328i	$0.449271\pi$
$164$	−7.02177e9	−0.757966
$165$	8.52794e8	0.0895708
$166$	1.78761e10	1.82720
$167$	9.52462e9	0.947596	0.473798	−	0.880633i	$-0.342883\pi$
$167$	9.52462e9	0.947596	0.473798	+	0.880633i	$0.342883\pi$
$168$	2.12527e10	2.05837
$169$	2.38175e9	0.224598
$170$	7.96670e9	0.731574
$171$	−8.55036e8	−0.0764719
$172$	−7.42293e9	−0.646692
$173$	8.87083e9	0.752934	0.376467	−	0.926430i	$-0.377139\pi$
$173$	8.87083e9	0.752934	0.376467	+	0.926430i	$0.377139\pi$
$174$	−2.58557e10	−2.13838
$175$	−2.53157e9	−0.204041
$176$	−1.77201e10	−1.39207
$177$	−1.22199e10	−0.935811
$178$	1.84216e10	1.37542
$179$	−4.18429e9	−0.304638	−0.152319	−	0.988331i	$-0.548674\pi$
$179$	−4.18429e9	−0.304638	−0.152319	+	0.988331i	$0.548674\pi$
$180$	5.86623e9	0.416517
$181$	1.84663e10	1.27887	0.639435	−	0.768845i	$-0.279168\pi$
$181$	1.84663e10	1.27887	0.639435	+	0.768845i	$0.279168\pi$
$182$	3.25506e10	2.19906
$183$	3.16523e9	0.208629
$184$	3.25506e10	2.09353
$185$	1.28386e10	0.805833
$186$	−3.54549e10	−2.17204
$187$	−4.87179e9	−0.291341
$188$	−4.85989e10	−2.83737
$189$	3.44417e9	0.196339
$190$	−3.58990e9	−0.199844
$191$	1.79582e10	0.976367	0.488183	−	0.872741i	$-0.337660\pi$
$191$	1.79582e10	0.976367	0.488183	+	0.872741i	$0.337660\pi$
$192$	−4.78919e10	−2.54335
$193$	7.83978e9	0.406721	0.203360	−	0.979104i	$-0.434814\pi$
$193$	7.83978e9	0.406721	0.203360	+	0.979104i	$0.434814\pi$
$194$	−1.36117e10	−0.689927
$195$	5.76908e9	0.285727
$196$	2.35653e9	0.114057
$197$	−6.77245e9	−0.320367	−0.160184	−	0.987087i	$-0.551209\pi$
$197$	−6.77245e9	−0.320367	−0.160184	+	0.987087i	$0.551209\pi$
$198$	−4.87121e9	−0.225239
$199$	−2.99734e10	−1.35487	−0.677435	−	0.735583i	$-0.736908\pi$
$199$	−2.99734e10	−1.35487	−0.677435	+	0.735583i	$0.736908\pi$
$200$	1.58147e10	0.698916
$201$	2.09238e10	0.904187
$202$	−3.55168e10	−1.50090
$203$	−4.69367e10	−1.93991
$204$	−3.35123e10	−1.35478
$205$	−3.06774e9	−0.121318
$206$	2.58069e10	0.998465
$207$	5.27508e9	0.199693
$208$	−1.19875e11	−4.44063
$209$	2.19530e9	0.0795857
$210$	1.44605e10	0.513092
$211$	1.54538e9	0.0536739	0.0268369	−	0.999640i	$-0.491457\pi$
$211$	1.54538e9	0.0536739	0.0268369	+	0.999640i	$0.491457\pi$
$212$	1.55387e10	0.528327
$213$	−1.19213e10	−0.396841
$214$	8.98988e10	2.93016
$215$	−3.24300e9	−0.103508
$216$	−2.15157e10	−0.672532
$217$	−6.43623e10	−1.97044
$218$	−7.84147e10	−2.35149
$219$	2.87999e10	0.846043
$220$	−1.50615e10	−0.433477
$221$	−3.29573e10	−0.929366
$222$	−7.33350e10	−2.02639
$223$	1.49507e10	0.404845	0.202423	−	0.979298i	$-0.435119\pi$
$223$	1.49507e10	0.404845	0.202423	+	0.979298i	$0.435119\pi$
$224$	−1.66135e11	−4.40905
$225$	2.56289e9	0.0666667
$226$	5.79543e10	1.47774
$227$	2.71727e10	0.679229	0.339615	−	0.940565i	$-0.389703\pi$
$227$	2.71727e10	0.679229	0.339615	+	0.940565i	$0.389703\pi$
$228$	1.51011e10	0.370085
$229$	4.04991e10	0.973163	0.486582	−	0.873635i	$-0.338244\pi$
$229$	4.04991e10	0.973163	0.486582	+	0.873635i	$0.338244\pi$
$230$	2.21476e10	0.521858
$231$	−8.84287e9	−0.204333
$232$	2.93213e11	6.64489
$233$	−3.95779e10	−0.879734	−0.439867	−	0.898063i	$-0.644974\pi$
$233$	−3.95779e10	−0.879734	−0.439867	+	0.898063i	$0.644974\pi$
$234$	−3.29534e10	−0.718503
$235$	−2.12323e10	−0.454142
$236$	2.15820e11	4.52885
$237$	−5.43585e10	−1.11918
$238$	−8.26090e10	−1.66890
$239$	7.30250e10	1.44771	0.723854	−	0.689953i	$-0.242369\pi$
$239$	7.30250e10	1.44771	0.723854	+	0.689953i	$0.242369\pi$
$240$	−5.32541e10	−1.03610
$241$	−7.35344e10	−1.40415	−0.702075	−	0.712103i	$-0.747743\pi$
$241$	−7.35344e10	−1.40415	−0.702075	+	0.712103i	$0.747743\pi$
$242$	−9.14188e10	−1.71343
$243$	−3.48678e9	−0.0641500
$244$	−5.59022e10	−1.00966
$245$	1.02954e9	0.0182556
$246$	1.75231e10	0.305073
$247$	1.48510e10	0.253875
$248$	4.02071e11	6.74948
$249$	−3.28526e10	−0.541593
$250$	1.07604e10	0.174220
$251$	−3.50482e10	−0.557358	−0.278679	−	0.960384i	$-0.589897\pi$
$251$	−3.50482e10	−0.557358	−0.278679	+	0.960384i	$0.589897\pi$
$252$	−6.08286e10	−0.950179
$253$	−1.35437e10	−0.207824
$254$	−1.22698e11	−1.84964
$255$	−1.46411e10	−0.216842
$256$	2.67353e11	3.89050
$257$	−6.00220e10	−0.858245	−0.429123	−	0.903246i	$-0.641177\pi$
$257$	−6.00220e10	−0.858245	−0.429123	+	0.903246i	$0.641177\pi$
$258$	1.85242e10	0.260286
$259$	−1.33127e11	−1.83831
$260$	−1.01890e11	−1.38277
$261$	4.75175e10	0.633828
$262$	−6.74011e10	−0.883713
$263$	−4.50367e10	−0.580451	−0.290225	−	0.956958i	$-0.593730\pi$
$263$	−4.50367e10	−0.580451	−0.290225	+	0.956958i	$0.593730\pi$
$264$	5.52413e10	0.699917
$265$	6.78867e9	0.0845626
$266$	3.72248e10	0.455895
$267$	−3.38550e10	−0.407683
$268$	−3.69542e11	−4.37580
$269$	1.46337e11	1.70400	0.851999	−	0.523543i	$-0.175390\pi$
$269$	1.46337e11	1.70400	0.851999	+	0.523543i	$0.175390\pi$
$270$	−1.46394e10	−0.167643
$271$	−4.20525e10	−0.473620	−0.236810	−	0.971556i	$-0.576102\pi$
$271$	−4.20525e10	−0.473620	−0.236810	+	0.971556i	$0.576102\pi$
$272$	3.04227e11	3.37006
$273$	−5.98213e10	−0.651815
$274$	4.02971e10	0.431913
$275$	−6.58020e9	−0.0693812
$276$	−9.31650e10	−0.966411
$277$	−1.25529e11	−1.28110	−0.640551	−	0.767915i	$-0.721294\pi$
$277$	−1.25529e11	−1.28110	−0.640551	+	0.767915i	$0.721294\pi$
$278$	−1.15418e11	−1.15897
$279$	6.51587e10	0.643804
$280$	−1.63987e11	−1.59440
$281$	7.64846e10	0.731805	0.365903	−	0.930653i	$-0.380760\pi$
$281$	7.64846e10	0.731805	0.365903	+	0.930653i	$0.380760\pi$
$282$	1.21280e11	1.14201
$283$	−1.23517e11	−1.14469	−0.572343	−	0.820014i	$-0.693965\pi$
$283$	−1.23517e11	−1.14469	−0.572343	+	0.820014i	$0.693965\pi$
$284$	2.10547e11	1.92051
$285$	6.59750e9	0.0592349
$286$	8.46075e10	0.747759
$287$	3.18103e10	0.276757
$288$	1.68191e11	1.44057
$289$	−3.49467e10	−0.294691
$290$	1.99504e11	1.65638
$291$	2.50154e10	0.204498
$292$	−5.08645e11	−4.09442
$293$	1.54221e11	1.22248	0.611238	−	0.791447i	$-0.290672\pi$
$293$	1.54221e11	1.22248	0.611238	+	0.791447i	$0.290672\pi$
$294$	−5.88081e9	−0.0459065
$295$	9.42894e10	0.724876
$296$	8.31645e11	6.29688
$297$	8.95229e9	0.0667621
$298$	−1.93240e11	−1.41946
$299$	−9.16222e10	−0.662950
$300$	−4.52641e10	−0.322633
$301$	3.36276e10	0.236128
$302$	3.13347e11	2.16768
$303$	6.52725e10	0.444875
$304$	−1.37089e11	−0.920601
$305$	−2.44231e10	−0.161603
$306$	8.36312e10	0.545283
$307$	9.77171e10	0.627839	0.313919	−	0.949450i	$-0.398358\pi$
$307$	9.77171e10	0.627839	0.313919	+	0.949450i	$0.398358\pi$
$308$	1.56177e11	0.988869
$309$	−4.74277e10	−0.295951
$310$	2.73572e11	1.68245
$311$	−1.54504e11	−0.936523	−0.468261	−	0.883590i	$-0.655119\pi$
$311$	−1.54504e11	−0.936523	−0.468261	+	0.883590i	$0.655119\pi$
$312$	3.73703e11	2.23270
$313$	−3.16612e11	−1.86456	−0.932282	−	0.361732i	$-0.882186\pi$
$313$	−3.16612e11	−1.86456	−0.932282	+	0.361732i	$0.882186\pi$
$314$	−6.06600e11	−3.52143
$315$	−2.65754e10	−0.152083
$316$	9.60045e11	5.41626
$317$	−1.83066e11	−1.01822	−0.509109	−	0.860702i	$-0.670025\pi$
$317$	−1.83066e11	−1.01822	−0.509109	+	0.860702i	$0.670025\pi$
$318$	−3.87774e10	−0.212645
$319$	−1.22001e11	−0.659637
$320$	3.69536e11	1.97007
$321$	−1.65215e11	−0.868516
$322$	−2.29655e11	−1.19049
$323$	−3.76899e10	−0.192670
$324$	6.15813e10	0.310453
$325$	−4.45145e10	−0.221323
$326$	1.26074e11	0.618226
$327$	1.44110e11	0.696995
$328$	−1.98718e11	−0.947995
$329$	2.20164e11	1.03601
$330$	3.75865e10	0.174469
$331$	−1.91317e11	−0.876050	−0.438025	−	0.898963i	$-0.644322\pi$
$331$	−1.91317e11	−0.876050	−0.438025	+	0.898963i	$0.644322\pi$
$332$	5.80221e11	2.62103
$333$	1.34775e11	0.600633
$334$	4.19793e11	1.84577
$335$	−1.61449e11	−0.700380
$336$	5.52207e11	2.36361
$337$	−3.93309e10	−0.166111	−0.0830556	−	0.996545i	$-0.526468\pi$
$337$	−3.93309e10	−0.166111	−0.0830556	+	0.996545i	$0.526468\pi$
$338$	1.04974e11	0.437480
$339$	−1.06508e11	−0.438010
$340$	2.58582e11	1.04941
$341$	−1.67294e11	−0.670019
$342$	−3.76854e10	−0.148955
$343$	2.50848e11	0.978561
$344$	−2.10071e11	−0.808824
$345$	−4.07028e10	−0.154681
$346$	3.90978e11	1.46659
$347$	−2.16441e11	−0.801412	−0.400706	−	0.916207i	$-0.631235\pi$
$347$	−2.16441e11	−0.801412	−0.400706	+	0.916207i	$0.631235\pi$
$348$	−8.39224e11	−3.06740
$349$	−2.02993e11	−0.732429	−0.366215	−	0.930530i	$-0.619346\pi$
$349$	−2.02993e11	−0.732429	−0.366215	+	0.930530i	$0.619346\pi$
$350$	−1.11578e11	−0.397440
$351$	6.05615e10	0.212968
$352$	−4.31828e11	−1.49923
$353$	2.08347e11	0.714169	0.357084	−	0.934072i	$-0.383771\pi$
$353$	2.08347e11	0.714169	0.357084	+	0.934072i	$0.383771\pi$
$354$	−5.38587e11	−1.82281
$355$	9.19856e10	0.307392
$356$	5.97925e11	1.97298
$357$	1.51818e11	0.494672
$358$	−1.84421e11	−0.593385
$359$	8.40964e10	0.267210	0.133605	−	0.991035i	$-0.457345\pi$
$359$	8.40964e10	0.267210	0.133605	+	0.991035i	$0.457345\pi$
$360$	1.66016e11	0.520941
$361$	1.69836e10	0.0526316
$362$	8.13895e11	2.49103
$363$	1.68009e11	0.507870
$364$	1.05653e12	3.15445
$365$	−2.22222e11	−0.655342
$366$	1.39506e11	0.406376
$367$	1.85725e11	0.534408	0.267204	−	0.963640i	$-0.413900\pi$
$367$	1.85725e11	0.534408	0.267204	+	0.963640i	$0.413900\pi$
$368$	8.45760e11	2.40399
$369$	−3.22039e10	−0.0904252
$370$	5.65857e11	1.56963
$371$	−7.03938e10	−0.192909
$372$	−1.15079e12	−3.11568
$373$	−1.06693e11	−0.285396	−0.142698	−	0.989766i	$-0.545578\pi$
$373$	−1.06693e11	−0.285396	−0.142698	+	0.989766i	$0.545578\pi$
$374$	−2.14722e11	−0.567486
$375$	−1.97754e10	−0.0516398
$376$	−1.37536e12	−3.54872
$377$	−8.25326e11	−2.10421
$378$	1.51800e11	0.382437
$379$	1.16373e11	0.289719	0.144859	−	0.989452i	$-0.453727\pi$
$379$	1.16373e11	0.289719	0.144859	+	0.989452i	$0.453727\pi$
$380$	−1.16521e11	−0.286667
$381$	2.25494e11	0.548243
$382$	7.91501e11	1.90181
$383$	−2.49862e11	−0.593342	−0.296671	−	0.954980i	$-0.595877\pi$
$383$	−2.49862e11	−0.593342	−0.296671	+	0.954980i	$0.595877\pi$
$384$	−1.04768e12	−2.45890
$385$	6.82320e10	0.158276
$386$	3.45535e11	0.792226
$387$	−3.40437e10	−0.0771503
$388$	−4.41806e11	−0.989667
$389$	8.71290e11	1.92925	0.964627	−	0.263618i	$-0.0849158\pi$
$389$	8.71290e11	1.92925	0.964627	+	0.263618i	$0.0849158\pi$
$390$	2.54270e11	0.556550
$391$	2.32525e11	0.503122
$392$	6.66905e10	0.142652
$393$	1.23869e11	0.261937
$394$	−2.98493e11	−0.624024
$395$	4.19433e11	0.866914
$396$	−1.58109e11	−0.323094
$397$	−3.39189e11	−0.685306	−0.342653	−	0.939462i	$-0.611325\pi$
$397$	−3.39189e11	−0.685306	−0.342653	+	0.939462i	$0.611325\pi$
$398$	−1.32107e12	−2.63907
$399$	−6.84114e10	−0.135130
$400$	4.10911e11	0.802561
$401$	2.63453e11	0.508808	0.254404	−	0.967098i	$-0.418121\pi$
$401$	2.63453e11	0.508808	0.254404	+	0.967098i	$0.418121\pi$
$402$	9.22207e11	1.76121
$403$	−1.13173e12	−2.13733
$404$	−1.15280e12	−2.15297
$405$	2.69042e10	0.0496904
$406$	−2.06872e12	−3.77863
$407$	−3.46033e11	−0.625089
$408$	−9.48408e11	−1.69443
$409$	2.46141e10	0.0434940	0.0217470	−	0.999764i	$-0.493077\pi$
$409$	2.46141e10	0.0434940	0.0217470	+	0.999764i	$0.493077\pi$
$410$	−1.35209e11	−0.236308
$411$	−7.40577e10	−0.128021
$412$	8.37638e11	1.43225
$413$	−9.77714e11	−1.65362
$414$	2.32497e11	0.388970
$415$	2.53492e11	0.419516
$416$	−2.92128e12	−4.78248
$417$	2.12114e11	0.343524
$418$	9.67568e10	0.155020
$419$	−4.37161e11	−0.692912	−0.346456	−	0.938066i	$-0.612615\pi$
$419$	−4.37161e11	−0.692912	−0.346456	+	0.938066i	$0.612615\pi$
$420$	4.69357e11	0.736006
$421$	−1.26591e12	−1.96397	−0.981983	−	0.188967i	$-0.939486\pi$
$421$	−1.26591e12	−1.96397	−0.981983	+	0.188967i	$0.939486\pi$
$422$	6.81118e10	0.104548
$423$	−2.22888e11	−0.338498
$424$	4.39749e11	0.660783
$425$	1.12972e11	0.167965
$426$	−5.25428e11	−0.772983
$427$	2.53250e11	0.368658
$428$	2.91793e12	4.20317
$429$	−1.55491e11	−0.221640
$430$	−1.42934e11	−0.201617
$431$	−1.24026e12	−1.73128	−0.865638	−	0.500670i	$-0.833087\pi$
$431$	−1.24026e12	−1.73128	−0.865638	+	0.500670i	$0.833087\pi$
$432$	−5.59040e11	−0.772265
$433$	−1.31908e12	−1.80333	−0.901663	−	0.432440i	$-0.857653\pi$
$433$	−1.31908e12	−1.80333	−0.901663	+	0.432440i	$0.857653\pi$
$434$	−2.83674e12	−3.83810
$435$	−3.66648e11	−0.490961
$436$	−2.54518e12	−3.37310
$437$	−1.04779e11	−0.137438
$438$	1.26934e12	1.64796
$439$	3.97666e11	0.511009	0.255504	−	0.966808i	$-0.417758\pi$
$439$	3.97666e11	0.511009	0.255504	+	0.966808i	$0.417758\pi$
$440$	−4.26245e11	−0.542153
$441$	1.08077e10	0.0136069
$442$	−1.45258e12	−1.81026
$443$	1.46310e12	1.80492	0.902459	−	0.430776i	$-0.141760\pi$
$443$	1.46310e12	1.80492	0.902459	+	0.430776i	$0.141760\pi$
$444$	−2.38030e12	−2.90676
$445$	2.61227e11	0.315790
$446$	6.58945e11	0.788574
$447$	3.55135e11	0.420736
$448$	−3.83183e12	−4.49423
$449$	−6.06007e11	−0.703670	−0.351835	−	0.936062i	$-0.614442\pi$
$449$	−6.06007e11	−0.703670	−0.351835	+	0.936062i	$0.614442\pi$
$450$	1.12958e11	0.129856
$451$	8.26831e10	0.0941071
$452$	1.88108e12	2.11975
$453$	−5.75867e11	−0.642511
$454$	1.19763e12	1.32303
$455$	4.61584e11	0.504893
$456$	4.27366e11	0.462869
$457$	−4.26247e10	−0.0457129	−0.0228565	−	0.999739i	$-0.507276\pi$
$457$	−4.26247e10	−0.0457129	−0.0228565	+	0.999739i	$0.507276\pi$
$458$	1.78498e12	1.89557
$459$	−1.53697e11	−0.161625
$460$	7.18866e11	0.748579
$461$	1.33600e12	1.37770	0.688848	−	0.724906i	$-0.258117\pi$
$461$	1.33600e12	1.37770	0.688848	+	0.724906i	$0.258117\pi$
$462$	−3.89746e11	−0.398009
$463$	6.09893e11	0.616792	0.308396	−	0.951258i	$-0.400208\pi$
$463$	6.09893e11	0.616792	0.308396	+	0.951258i	$0.400208\pi$
$464$	7.61854e12	7.63029
$465$	−5.02768e11	−0.498689
$466$	−1.74438e12	−1.71358
$467$	−1.43135e12	−1.39258	−0.696291	−	0.717760i	$-0.745168\pi$
$467$	−1.43135e12	−1.39258	−0.696291	+	0.717760i	$0.745168\pi$
$468$	−1.06960e12	−1.03066
$469$	1.67411e12	1.59774
$470$	−9.35806e11	−0.884597
$471$	1.11481e12	1.04377
$472$	6.10777e12	5.66427
$473$	8.74069e10	0.0802917
$474$	−2.39583e12	−2.17998
$475$	−5.09066e10	−0.0458831
$476$	−2.68132e12	−2.39396
$477$	7.12648e10	0.0630293
$478$	3.21855e12	2.81991
$479$	−7.23671e9	−0.00628103	−0.00314052	−	0.999995i	$-0.501000\pi$
$479$	−7.23671e9	−0.00628103	−0.00314052	+	0.999995i	$0.501000\pi$
$480$	−1.29777e12	−1.11586
$481$	−2.34088e12	−1.99401
$482$	−3.24100e12	−2.73506
$483$	4.22059e11	0.352867
$484$	−2.96726e12	−2.45783
$485$	−1.93020e11	−0.158404
$486$	−1.53679e11	−0.124954
$487$	7.23563e11	0.582903	0.291451	−	0.956586i	$-0.405862\pi$
$487$	7.23563e11	0.582903	0.291451	+	0.956586i	$0.405862\pi$
$488$	−1.58205e12	−1.26279
$489$	−2.31698e11	−0.183245
$490$	4.53766e10	0.0355590
$491$	1.80191e12	1.39916	0.699579	−	0.714555i	$-0.253371\pi$
$491$	1.80191e12	1.39916	0.699579	+	0.714555i	$0.253371\pi$
$492$	5.68764e11	0.437612
$493$	2.09456e12	1.59692
$494$	6.54552e11	0.494508
$495$	−6.90763e10	−0.0517137
$496$	1.04470e13	7.75038
$497$	−9.53825e11	−0.701237
$498$	−1.44797e12	−1.05494
$499$	−1.35285e12	−0.976778	−0.488389	−	0.872626i	$-0.662415\pi$
$499$	−1.35285e12	−0.976778	−0.488389	+	0.872626i	$0.662415\pi$
$500$	3.49260e11	0.249910
$501$	−7.71494e11	−0.547095
$502$	−1.54474e12	−1.08564
$503$	5.68061e10	0.0395675	0.0197838	−	0.999804i	$-0.493702\pi$
$503$	5.68061e10	0.0395675	0.0197838	+	0.999804i	$0.493702\pi$
$504$	−1.72147e12	−1.18840
$505$	−5.03646e11	−0.344599
$506$	−5.96934e11	−0.404808
$507$	−1.92921e11	−0.129672
$508$	−3.98253e12	−2.65321
$509$	−4.67991e11	−0.309035	−0.154518	−	0.987990i	$-0.549382\pi$
$509$	−4.67991e11	−0.309035	−0.154518	+	0.987990i	$0.549382\pi$
$510$	−6.45302e11	−0.422374
$511$	2.30428e12	1.49500
$512$	5.16109e12	3.31914
$513$	6.92579e10	0.0441511
$514$	−2.64544e12	−1.67172
$515$	3.65955e11	0.229242
$516$	6.01258e11	0.373368
$517$	5.72264e11	0.352281
$518$	−5.86753e12	−3.58073
$519$	−7.18537e11	−0.434707
$520$	−2.88351e12	−1.72945
$521$	1.37815e12	0.819456	0.409728	−	0.912208i	$-0.365624\pi$
$521$	1.37815e12	0.819456	0.409728	+	0.912208i	$0.365624\pi$
$522$	2.09432e12	1.23460
$523$	−1.08970e12	−0.636869	−0.318434	−	0.947945i	$-0.603157\pi$
$523$	−1.08970e12	−0.636869	−0.318434	+	0.947945i	$0.603157\pi$
$524$	−2.18770e12	−1.26764
$525$	2.05057e11	0.117803
$526$	−1.98497e12	−1.13063
$527$	2.87219e12	1.62205
$528$	1.43533e12	0.803710
$529$	−1.15473e12	−0.641105
$530$	2.99208e11	0.164714
$531$	9.89812e11	0.540291
$532$	1.20824e12	0.653958
$533$	5.59345e11	0.300198
$534$	−1.49215e12	−0.794101
$535$	1.27481e12	0.672750
$536$	−1.04582e13	−5.47285
$537$	3.38928e11	0.175883
$538$	6.44975e12	3.31912
$539$	−2.77487e10	−0.0141610
$540$	−4.75164e11	−0.240476
$541$	3.81155e11	0.191300	0.0956498	−	0.995415i	$-0.469507\pi$
$541$	3.81155e11	0.191300	0.0956498	+	0.995415i	$0.469507\pi$
$542$	−1.85345e12	−0.922536
$543$	−1.49577e12	−0.738356
$544$	7.41381e12	3.62950
$545$	−1.11196e12	−0.539890
$546$	−2.63660e12	−1.26963
$547$	−7.42468e11	−0.354597	−0.177298	−	0.984157i	$-0.556736\pi$
$547$	−7.42468e11	−0.354597	−0.177298	+	0.984157i	$0.556736\pi$
$548$	1.30796e12	0.619558
$549$	−2.56383e11	−0.120452
$550$	−2.90020e11	−0.135143
$551$	−9.43840e11	−0.436231
$552$	−2.63660e12	−1.20870
$553$	−4.34923e12	−1.97765
$554$	−5.53262e12	−2.49538
$555$	−1.03993e12	−0.465248
$556$	−3.74622e12	−1.66248
$557$	3.09585e12	1.36280	0.681399	−	0.731912i	$-0.261372\pi$
$557$	3.09585e12	1.36280	0.681399	+	0.731912i	$0.261372\pi$
$558$	2.87184e12	1.25403
$559$	5.91301e11	0.256127
$560$	−4.26086e12	−1.83084
$561$	3.94615e11	0.168206
$562$	3.37103e12	1.42544
$563$	2.39148e12	1.00318	0.501589	−	0.865106i	$-0.332749\pi$
$563$	2.39148e12	1.00318	0.501589	+	0.865106i	$0.332749\pi$
$564$	3.93651e12	1.63816
$565$	8.21822e11	0.339281
$566$	−5.44394e12	−2.22966
$567$	−2.78978e11	−0.113356
$568$	5.95854e12	2.40200
$569$	−1.16995e12	−0.467910	−0.233955	−	0.972247i	$-0.575167\pi$
$569$	−1.16995e12	−0.467910	−0.233955	+	0.972247i	$0.575167\pi$
$570$	2.90782e11	0.115380
$571$	1.70173e12	0.669927	0.334963	−	0.942231i	$-0.391276\pi$
$571$	1.70173e12	0.669927	0.334963	+	0.942231i	$0.391276\pi$
$572$	2.74618e12	1.07262
$573$	−1.45462e12	−0.563706
$574$	1.40202e12	0.539078
$575$	3.14065e11	0.119816
$576$	3.87924e12	1.46840
$577$	4.20521e11	0.157942	0.0789708	−	0.996877i	$-0.474837\pi$
$577$	4.20521e11	0.157942	0.0789708	+	0.996877i	$0.474837\pi$
$578$	−1.54026e12	−0.574010
$579$	−6.35022e11	−0.234820
$580$	6.47549e12	2.37600
$581$	−2.62854e12	−0.957021
$582$	1.10254e12	0.398330
$583$	−1.82972e11	−0.0655957
$584$	−1.43948e13	−5.12092
$585$	−4.67296e11	−0.164964
$586$	6.79724e12	2.38119
$587$	1.77537e12	0.617190	0.308595	−	0.951194i	$-0.400141\pi$
$587$	1.77537e12	0.617190	0.308595	+	0.951194i	$0.400141\pi$
$588$	−1.90879e11	−0.0658506
$589$	−1.29425e12	−0.443096
$590$	4.15576e12	1.41194
$591$	5.48569e11	0.184964
$592$	2.16086e13	7.23067
$593$	−4.24846e12	−1.41087	−0.705433	−	0.708777i	$-0.749247\pi$
$593$	−4.24846e12	−1.41087	−0.705433	+	0.708777i	$0.749247\pi$
$594$	3.94568e11	0.130042
$595$	−1.17144e12	−0.383171
$596$	−6.27216e12	−2.03615
$597$	2.42785e12	0.782234
$598$	−4.03821e12	−1.29132
$599$	−6.69285e10	−0.0212418	−0.0106209	−	0.999944i	$-0.503381\pi$
$599$	−6.69285e10	−0.0212418	−0.0106209	+	0.999944i	$0.503381\pi$
$600$	−1.28099e12	−0.403519
$601$	−2.76803e12	−0.865436	−0.432718	−	0.901529i	$-0.642445\pi$
$601$	−2.76803e12	−0.865436	−0.432718	+	0.901529i	$0.642445\pi$
$602$	1.48212e12	0.459939
$603$	−1.69483e12	−0.522032
$604$	1.01706e13	3.10943
$605$	−1.29636e12	−0.393394
$606$	2.87686e12	0.866546
$607$	−9.85957e11	−0.294787	−0.147394	−	0.989078i	$-0.547088\pi$
$607$	−9.85957e11	−0.294787	−0.147394	+	0.989078i	$0.547088\pi$
$608$	−3.34076e12	−0.991471
$609$	3.80188e12	1.12001
$610$	−1.07644e12	−0.314778
$611$	3.87132e12	1.12376
$612$	2.71449e12	0.782181
$613$	−1.08226e12	−0.309569	−0.154785	−	0.987948i	$-0.549468\pi$
$613$	−1.08226e12	−0.309569	−0.154785	+	0.987948i	$0.549468\pi$
$614$	4.30684e12	1.22293
$615$	2.48487e11	0.0700431
$616$	4.41986e12	1.23679
$617$	−1.91309e12	−0.531436	−0.265718	−	0.964051i	$-0.585609\pi$
$617$	−1.91309e12	−0.531436	−0.265718	+	0.964051i	$0.585609\pi$
$618$	−2.09036e12	−0.576464
$619$	−3.11172e12	−0.851909	−0.425955	−	0.904745i	$-0.640062\pi$
$619$	−3.11172e12	−0.851909	−0.425955	+	0.904745i	$0.640062\pi$
$620$	8.87956e12	2.41340
$621$	−4.27282e11	−0.115293
$622$	−6.80971e12	−1.82420
$623$	−2.70874e12	−0.720396
$624$	9.70990e12	2.56380
$625$	1.52588e11	0.0400000
$626$	−1.39545e13	−3.63187
$627$	−1.77819e11	−0.0459488
$628$	−1.96890e13	−5.05132
$629$	5.94084e12	1.51328
$630$	−1.17130e12	−0.296234
$631$	7.40098e12	1.85848	0.929238	−	0.369482i	$-0.120465\pi$
$631$	7.40098e12	1.85848	0.929238	+	0.369482i	$0.120465\pi$
$632$	2.71696e13	6.77417
$633$	−1.25175e11	−0.0309886
$634$	−8.06855e12	−1.98332
$635$	−1.73992e12	−0.424667
$636$	−1.25863e12	−0.305029
$637$	−1.87718e11	−0.0451729
$638$	−5.37714e12	−1.28487
$639$	9.65628e11	0.229116
$640$	8.08398e12	1.90465
$641$	−2.20386e12	−0.515611	−0.257805	−	0.966197i	$-0.582999\pi$
$641$	−2.20386e12	−0.515611	−0.257805	+	0.966197i	$0.582999\pi$
$642$	−7.28180e12	−1.69173
$643$	−1.58888e12	−0.366557	−0.183278	−	0.983061i	$-0.558671\pi$
$643$	−1.58888e12	−0.366557	−0.183278	+	0.983061i	$0.558671\pi$
$644$	−7.45413e12	−1.70770
$645$	2.62683e11	0.0597603
$646$	−1.66116e12	−0.375289
$647$	5.75384e12	1.29089	0.645444	−	0.763808i	$-0.276673\pi$
$647$	5.75384e12	1.29089	0.645444	+	0.763808i	$0.276673\pi$
$648$	1.74277e12	0.388287
$649$	−2.54133e12	−0.562290
$650$	−1.96196e12	−0.431102
$651$	5.21335e12	1.13763
$652$	4.09211e12	0.886814
$653$	4.53046e12	0.975064	0.487532	−	0.873105i	$-0.337897\pi$
$653$	4.53046e12	0.975064	0.487532	+	0.873105i	$0.337897\pi$
$654$	6.35159e12	1.35763
$655$	−9.55782e11	−0.202896
$656$	−5.16328e12	−1.08858
$657$	−2.33279e12	−0.488463
$658$	9.70364e12	2.01799
$659$	−6.30093e12	−1.30143	−0.650714	−	0.759323i	$-0.725530\pi$
$659$	−6.30093e12	−1.30143	−0.650714	+	0.759323i	$0.725530\pi$
$660$	1.21998e12	0.250268
$661$	9.57086e11	0.195004	0.0975022	−	0.995235i	$-0.468915\pi$
$661$	9.57086e11	0.195004	0.0975022	+	0.995235i	$0.468915\pi$
$662$	−8.43224e12	−1.70640
$663$	2.66954e12	0.536569
$664$	1.64204e13	3.27815
$665$	5.27866e11	0.104671
$666$	5.94014e12	1.16994
$667$	5.82295e12	1.13914
$668$	1.36256e13	2.64766
$669$	−1.21101e12	−0.233738
$670$	−7.11580e12	−1.36423
$671$	6.58262e11	0.125357
$672$	1.34569e13	2.54556
$673$	9.83184e11	0.184743	0.0923713	−	0.995725i	$-0.470555\pi$
$673$	9.83184e11	0.184743	0.0923713	+	0.995725i	$0.470555\pi$
$674$	−1.73349e12	−0.323558
$675$	−2.07594e11	−0.0384900
$676$	3.40725e12	0.627544
$677$	−9.04907e12	−1.65560	−0.827799	−	0.561025i	$-0.810407\pi$
$677$	−9.04907e12	−1.65560	−0.827799	+	0.561025i	$0.810407\pi$
$678$	−4.69430e12	−0.853174
$679$	2.00148e12	0.361358
$680$	7.31796e12	1.31250
$681$	−2.20099e12	−0.392153
$682$	−7.37343e12	−1.30509
$683$	1.79559e12	0.315729	0.157864	−	0.987461i	$-0.449539\pi$
$683$	1.79559e12	0.315729	0.157864	+	0.987461i	$0.449539\pi$
$684$	−1.22319e12	−0.213669
$685$	5.71433e11	0.0991649
$686$	1.10560e13	1.90608
$687$	−3.28043e12	−0.561856
$688$	−5.45827e12	−0.928767
$689$	−1.23779e12	−0.209247
$690$	−1.79396e12	−0.301295
$691$	4.59106e12	0.766058	0.383029	−	0.923736i	$-0.374881\pi$
$691$	4.59106e12	0.766058	0.383029	+	0.923736i	$0.374881\pi$
$692$	1.26903e13	2.10376
$693$	7.16272e11	0.117972
$694$	−9.53953e12	−1.56102
$695$	−1.63668e12	−0.266093
$696$	−2.37503e13	−3.83643
$697$	−1.41954e12	−0.227825
$698$	−8.94681e12	−1.42666
$699$	3.20581e12	0.507915
$700$	−3.62158e12	−0.570108
$701$	−5.07126e12	−0.793203	−0.396602	−	0.917991i	$-0.629811\pi$
$701$	−5.07126e12	−0.793203	−0.396602	+	0.917991i	$0.629811\pi$
$702$	2.66922e12	0.414828
$703$	−2.67703e12	−0.413384
$704$	−9.95992e12	−1.52820
$705$	1.71982e12	0.262199
$706$	9.18280e12	1.39109
$707$	5.22245e12	0.786116
$708$	−1.74814e13	−2.61473
$709$	−4.91552e12	−0.730569	−0.365284	−	0.930896i	$-0.619028\pi$
$709$	−4.91552e12	−0.730569	−0.365284	+	0.930896i	$0.619028\pi$
$710$	4.05423e12	0.598750
$711$	4.40304e12	0.646159
$712$	1.69215e13	2.46762
$713$	7.98476e12	1.15707
$714$	6.69133e12	0.963542
$715$	1.19978e12	0.171682
$716$	−5.98592e12	−0.851182
$717$	−5.91503e12	−0.835835
$718$	3.70651e12	0.520482
$719$	−6.89392e12	−0.962024	−0.481012	−	0.876714i	$-0.659731\pi$
$719$	−6.89392e12	−0.962024	−0.481012	+	0.876714i	$0.659731\pi$
$720$	4.31358e12	0.598194
$721$	−3.79469e12	−0.522959
$722$	7.48544e11	0.102518
$723$	5.95628e12	0.810687
$724$	2.64173e13	3.57327
$725$	2.82907e12	0.380297
$726$	7.40492e12	0.989249
$727$	1.69634e12	0.225221	0.112611	−	0.993639i	$-0.464079\pi$
$727$	1.69634e12	0.225221	0.112611	+	0.993639i	$0.464079\pi$
$728$	2.99000e13	3.94530
$729$	2.82430e11	0.0370370
$730$	−9.79432e12	−1.27650
$731$	−1.50064e12	−0.194379
$732$	4.52808e12	0.582927
$733$	1.39450e13	1.78423	0.892116	−	0.451807i	$-0.149220\pi$
$733$	1.39450e13	1.78423	0.892116	+	0.451807i	$0.149220\pi$
$734$	8.18575e12	1.04094
$735$	−8.33929e10	−0.0105399
$736$	2.06106e13	2.58905
$737$	4.35145e12	0.543289
$738$	−1.41937e12	−0.176134
$739$	−1.47101e13	−1.81433	−0.907164	−	0.420776i	$-0.861758\pi$
$739$	−1.47101e13	−1.81433	−0.907164	+	0.420776i	$0.861758\pi$
$740$	1.83665e13	2.25156
$741$	−1.20293e12	−0.146575
$742$	−3.10258e12	−0.375755
$743$	7.23918e11	0.0871445	0.0435722	−	0.999050i	$-0.486126\pi$
$743$	7.23918e11	0.0871445	0.0435722	+	0.999050i	$0.486126\pi$
$744$	−3.25678e13	−3.89681
$745$	−2.74024e12	−0.325901
$746$	−4.70247e12	−0.555906
$747$	2.66106e12	0.312689
$748$	−6.96944e12	−0.814030
$749$	−1.32189e13	−1.53471
$750$	−8.71592e11	−0.100586
$751$	−7.53196e12	−0.864028	−0.432014	−	0.901867i	$-0.642197\pi$
$751$	−7.53196e12	−0.864028	−0.432014	+	0.901867i	$0.642197\pi$
$752$	−3.57359e13	−4.07498
$753$	2.83891e12	0.321791
$754$	−3.63759e13	−4.09867
$755$	4.44342e12	0.497687
$756$	4.92712e12	0.548586
$757$	−4.62291e11	−0.0511663	−0.0255831	−	0.999673i	$-0.508144\pi$
$757$	−4.62291e11	−0.0511663	−0.0255831	+	0.999673i	$0.508144\pi$
$758$	5.12910e12	0.564325
$759$	1.09704e12	0.119987
$760$	−3.29757e12	−0.358536
$761$	7.87029e12	0.850667	0.425333	−	0.905037i	$-0.360157\pi$
$761$	7.87029e12	0.850667	0.425333	+	0.905037i	$0.360157\pi$
$762$	9.93856e12	1.06789
$763$	1.15302e13	1.23162
$764$	2.56905e13	2.72805
$765$	1.18593e12	0.125194
$766$	−1.10126e13	−1.15574
$767$	−1.71919e13	−1.79368
$768$	−2.16556e13	−2.24618
$769$	1.38588e13	1.42909	0.714543	−	0.699591i	$-0.246634\pi$
$769$	1.38588e13	1.42909	0.714543	+	0.699591i	$0.246634\pi$
$770$	3.00730e12	0.308296
$771$	4.86178e12	0.495508
$772$	1.12153e13	1.13641
$773$	−9.39099e10	−0.00946027	−0.00473014	−	0.999989i	$-0.501506\pi$
$773$	−9.39099e10	−0.00946027	−0.00473014	+	0.999989i	$0.501506\pi$
$774$	−1.50046e12	−0.150276
$775$	3.87938e12	0.386282
$776$	−1.25033e13	−1.23779
$777$	1.07833e13	1.06135
$778$	3.84017e13	3.75788
$779$	6.39665e11	0.0622349
$780$	8.25307e12	0.798344
$781$	−2.47924e12	−0.238445
$782$	1.02484e13	0.980002
$783$	−3.84892e12	−0.365941
$784$	1.73281e12	0.163806
$785$	−8.60190e12	−0.808502
$786$	5.45949e12	0.510212
$787$	1.83669e12	0.170667	0.0853337	−	0.996352i	$-0.472804\pi$
$787$	1.83669e12	0.170667	0.0853337	+	0.996352i	$0.472804\pi$
$788$	−9.68846e12	−0.895131
$789$	3.64797e12	0.335123
$790$	1.84863e13	1.68861
$791$	−8.52171e12	−0.773985
$792$	−4.47455e12	−0.404097
$793$	4.45309e12	0.399883
$794$	−1.49496e13	−1.33487
$795$	−5.49883e11	−0.0488223
$796$	−4.28791e13	−3.78561
$797$	6.43629e12	0.565033	0.282516	−	0.959263i	$-0.408831\pi$
$797$	6.43629e12	0.565033	0.282516	+	0.959263i	$0.408831\pi$
$798$	−3.01520e12	−0.263211
$799$	−9.82488e12	−0.852839
$800$	1.00136e13	0.864344
$801$	2.74226e12	0.235376
$802$	1.16116e13	0.991077
$803$	5.98942e12	0.508353
$804$	2.99329e13	2.52637
$805$	−3.25663e12	−0.273330
$806$	−4.98807e13	−4.16318
$807$	−1.18533e13	−0.983804
$808$	−3.26246e13	−2.69274
$809$	2.12306e13	1.74259	0.871293	−	0.490764i	$-0.163282\pi$
$809$	2.12306e13	1.74259	0.871293	+	0.490764i	$0.163282\pi$
$810$	1.18579e12	0.0967889
$811$	1.85699e13	1.50735	0.753676	−	0.657246i	$-0.228279\pi$
$811$	1.85699e13	1.50735	0.753676	+	0.657246i	$0.228279\pi$
$812$	−6.71463e13	−5.42025
$813$	3.40625e12	0.273445
$814$	−1.52512e13	−1.21757
$815$	1.78780e12	0.141941
$816$	−2.46424e13	−1.94571
$817$	6.76209e11	0.0530984
$818$	1.08486e12	0.0847194
$819$	4.84553e12	0.376325
$820$	−4.38861e12	−0.338973
$821$	2.59313e13	1.99196	0.995979	−	0.0895905i	$-0.0285558\pi$
$821$	2.59313e13	1.99196	0.995979	+	0.0895905i	$0.0285558\pi$
$822$	−3.26406e12	−0.249365
$823$	−6.50569e12	−0.494304	−0.247152	−	0.968977i	$-0.579495\pi$
$823$	−6.50569e12	−0.494304	−0.247152	+	0.968977i	$0.579495\pi$
$824$	2.37054e13	1.79133
$825$	5.32996e11	0.0400573
$826$	−4.30923e13	−3.22099
$827$	4.21977e12	0.313700	0.156850	−	0.987622i	$-0.449866\pi$
$827$	4.21977e12	0.313700	0.156850	+	0.987622i	$0.449866\pi$
$828$	7.54637e12	0.557958
$829$	−1.76300e13	−1.29645	−0.648226	−	0.761448i	$-0.724489\pi$
$829$	−1.76300e13	−1.29645	−0.648226	+	0.761448i	$0.724489\pi$
$830$	1.11726e13	0.817150
$831$	1.01678e13	0.739645
$832$	−6.73781e13	−4.87488
$833$	4.76402e11	0.0342824
$834$	9.34885e12	0.669130
$835$	5.95288e12	0.423778
$836$	3.14052e12	0.222369
$837$	−5.27786e12	−0.371700
$838$	−1.92677e13	−1.34968
$839$	6.41184e12	0.446739	0.223370	−	0.974734i	$-0.428294\pi$
$839$	6.41184e12	0.446739	0.223370	+	0.974734i	$0.428294\pi$
$840$	1.32829e13	0.920529
$841$	3.79455e13	2.61564
$842$	−5.57946e13	−3.82549
$843$	−6.19525e12	−0.422508
$844$	2.21077e12	0.149969
$845$	1.48859e12	0.100443
$846$	−9.82371e12	−0.659339
$847$	1.34424e13	0.897431
$848$	1.14260e13	0.758772
$849$	1.00048e13	0.660885
$850$	4.97919e12	0.327170
$851$	1.65157e13	1.07948
$852$	−1.70543e13	−1.10881
$853$	−1.41347e13	−0.914148	−0.457074	−	0.889429i	$-0.651103\pi$
$853$	−1.41347e13	−0.914148	−0.457074	+	0.889429i	$0.651103\pi$
$854$	1.11619e13	0.718087
$855$	−5.34398e11	−0.0341993
$856$	8.25782e13	5.25695
$857$	−1.39516e13	−0.883509	−0.441754	−	0.897136i	$-0.645644\pi$
$857$	−1.39516e13	−0.883509	−0.441754	+	0.897136i	$0.645644\pi$
$858$	−6.85321e12	−0.431719
$859$	1.30236e13	0.816137	0.408069	−	0.912951i	$-0.366202\pi$
$859$	1.30236e13	0.816137	0.408069	+	0.912951i	$0.366202\pi$
$860$	−4.63933e12	−0.289209
$861$	−2.57663e12	−0.159786
$862$	−5.46641e13	−3.37225
$863$	−2.48472e13	−1.52485	−0.762427	−	0.647075i	$-0.775992\pi$
$863$	−2.48472e13	−1.52485	−0.762427	+	0.647075i	$0.775992\pi$
$864$	−1.36234e13	−0.831715
$865$	5.54427e12	0.336722
$866$	−5.81377e13	−3.51259
$867$	2.83068e12	0.170140
$868$	−9.20748e13	−5.50557
$869$	−1.13048e13	−0.672470
$870$	−1.61598e13	−0.956314
$871$	2.94372e13	1.73307
$872$	−7.20294e13	−4.21877
$873$	−2.02625e12	−0.118067
$874$	−4.61808e12	−0.267707
$875$	−1.58223e12	−0.0912500
$876$	4.12003e13	2.36391
$877$	−2.65977e12	−0.151826	−0.0759130	−	0.997114i	$-0.524187\pi$
$877$	−2.65977e12	−0.151826	−0.0759130	+	0.997114i	$0.524187\pi$
$878$	1.75270e13	0.995363
$879$	−1.24919e13	−0.705797
$880$	−1.10751e13	−0.622551
$881$	−2.73738e13	−1.53089	−0.765444	−	0.643503i	$-0.777481\pi$
$881$	−2.73738e13	−1.53089	−0.765444	+	0.643503i	$0.777481\pi$
$882$	4.76346e11	0.0265041
$883$	−1.30273e13	−0.721157	−0.360579	−	0.932729i	$-0.617421\pi$
$883$	−1.30273e13	−0.721157	−0.360579	+	0.932729i	$0.617421\pi$
$884$	−4.71477e13	−2.59672
$885$	−7.63744e12	−0.418507
$886$	6.44856e13	3.51569
$887$	−1.66187e13	−0.901448	−0.450724	−	0.892663i	$-0.648834\pi$
$887$	−1.66187e13	−0.901448	−0.450724	+	0.892663i	$0.648834\pi$
$888$	−6.73633e13	−3.63551
$889$	1.80418e13	0.968772
$890$	1.15135e13	0.615108
$891$	−7.25135e11	−0.0385451
$892$	2.13880e13	1.13117
$893$	4.42723e12	0.232970
$894$	1.56524e13	0.819526
$895$	−2.61518e12	−0.136238
$896$	−8.38252e13	−4.34499
$897$	7.42140e12	0.382754
$898$	−2.67095e13	−1.37064
$899$	7.19261e13	3.67255
$900$	3.66639e12	0.186272
$901$	3.14134e12	0.158801
$902$	3.64423e12	0.183306
$903$	−2.72384e12	−0.136328
$904$	5.32351e13	2.65118
$905$	1.15414e13	0.571928
$906$	−2.53811e13	−1.25151
$907$	1.92284e13	0.943430	0.471715	−	0.881751i	$-0.343635\pi$
$907$	1.92284e13	0.943430	0.471715	+	0.881751i	$0.343635\pi$
$908$	3.88724e13	1.89782
$909$	−5.28707e12	−0.256849
$910$	2.03441e13	0.983452
$911$	−9.41594e12	−0.452930	−0.226465	−	0.974019i	$-0.572717\pi$
$911$	−9.41594e12	−0.452930	−0.226465	+	0.974019i	$0.572717\pi$
$912$	1.11042e13	0.531509
$913$	−6.83225e12	−0.325421
$914$	−1.87867e12	−0.0890414
$915$	1.97827e12	0.0933018
$916$	5.79368e13	2.71910
$917$	9.91078e12	0.462856
$918$	−6.77413e12	−0.314819
$919$	2.02616e13	0.937032	0.468516	−	0.883455i	$-0.344789\pi$
$919$	2.02616e13	0.937032	0.468516	+	0.883455i	$0.344789\pi$
$920$	2.03441e13	0.936255
$921$	−7.91509e12	−0.362483
$922$	5.88838e13	2.68353
$923$	−1.67719e13	−0.760631
$924$	−1.26503e13	−0.570924
$925$	8.02413e12	0.360380
$926$	2.68808e13	1.20141
$927$	3.84165e12	0.170867
$928$	1.85659e14	8.21768
$929$	−1.43793e13	−0.633382	−0.316691	−	0.948529i	$-0.602572\pi$
$929$	−1.43793e13	−0.633382	−0.316691	+	0.948529i	$0.602572\pi$
$930$	−2.21593e13	−0.971365
$931$	−2.14673e11	−0.00936493
$932$	−5.66189e13	−2.45805
$933$	1.25148e13	0.540702
$934$	−6.30863e13	−2.71253
$935$	−3.04487e12	−0.130292
$936$	−3.02700e13	−1.28905
$937$	2.74023e13	1.16134	0.580670	−	0.814139i	$-0.302791\pi$
$937$	2.74023e13	1.16134	0.580670	+	0.814139i	$0.302791\pi$
$938$	7.37858e13	3.11215
$939$	2.56455e13	1.07651
$940$	−3.03743e13	−1.26891
$941$	2.29331e13	0.953474	0.476737	−	0.879046i	$-0.341819\pi$
$941$	2.29331e13	0.953474	0.476737	+	0.879046i	$0.341819\pi$
$942$	4.91346e13	2.03310
$943$	−3.94636e12	−0.162515
$944$	1.58698e14	6.50424
$945$	2.15260e12	0.0878054
$946$	3.85242e12	0.156395
$947$	1.25586e13	0.507419	0.253710	−	0.967280i	$-0.418349\pi$
$947$	1.25586e13	0.507419	0.253710	+	0.967280i	$0.418349\pi$
$948$	−7.77637e13	−3.12708
$949$	4.05180e13	1.62162
$950$	−2.24369e12	−0.0893730
$951$	1.48283e13	0.587868
$952$	−7.58821e13	−2.99415
$953$	−3.50799e12	−0.137765	−0.0688826	−	0.997625i	$-0.521943\pi$
$953$	−3.50799e12	−0.137765	−0.0688826	+	0.997625i	$0.521943\pi$
$954$	3.14097e12	0.122771
$955$	1.12239e13	0.436644
$956$	1.04467e14	4.04501
$957$	9.88207e12	0.380841
$958$	−3.18955e11	−0.0122344
$959$	−5.92536e12	−0.226220
$960$	−2.99324e13	−1.13742
$961$	7.21895e13	2.73035
$962$	−1.03173e14	−3.88401
$963$	1.33824e13	0.501438
$964$	−1.05196e14	−3.92331
$965$	4.89986e12	0.181891
$966$	1.86021e13	0.687329
$967$	−1.77208e13	−0.651723	−0.325862	−	0.945417i	$-0.605654\pi$
$967$	−1.77208e13	−0.651723	−0.325862	+	0.945417i	$0.605654\pi$
$968$	−8.39745e13	−3.07403
$969$	3.05288e12	0.111238
$970$	−8.50729e12	−0.308545
$971$	−1.70176e12	−0.0614344	−0.0307172	−	0.999528i	$-0.509779\pi$
$971$	−1.70176e12	−0.0614344	−0.0307172	+	0.999528i	$0.509779\pi$
$972$	−4.98809e12	−0.179240
$973$	1.69713e13	0.607024
$974$	3.18907e13	1.13540
$975$	3.60568e12	0.127781
$976$	−4.11063e13	−1.45005
$977$	2.89765e13	1.01747	0.508733	−	0.860924i	$-0.330114\pi$
$977$	2.89765e13	1.01747	0.508733	+	0.860924i	$0.330114\pi$
$978$	−1.02120e13	−0.356933
$979$	−7.04072e12	−0.244960
$980$	1.47283e12	0.0510077
$981$	−1.16729e13	−0.402410
$982$	7.94185e13	2.72534
$983$	2.03910e13	0.696542	0.348271	−	0.937394i	$-0.386769\pi$
$983$	2.03910e13	0.696542	0.348271	+	0.937394i	$0.386769\pi$
$984$	1.60962e13	0.547325
$985$	−4.23278e12	−0.143273
$986$	9.23171e13	3.11054
$987$	−1.78333e13	−0.598142
$988$	2.12454e13	0.709347
$989$	−4.17182e12	−0.138657
$990$	−3.04451e12	−0.100730
$991$	3.71402e13	1.22324	0.611621	−	0.791151i	$-0.290518\pi$
$991$	3.71402e13	1.22324	0.611621	+	0.791151i	$0.290518\pi$
$992$	2.54586e14	8.34702
$993$	1.54967e13	0.505787
$994$	−4.20395e13	−1.36590
$995$	−1.87334e13	−0.605916
$996$	−4.69979e13	−1.51325
$997$	−1.45346e13	−0.465882	−0.232941	−	0.972491i	$-0.574835\pi$
$997$	−1.45346e13	−0.465882	−0.232941	+	0.972491i	$0.574835\pi$
$998$	−5.96261e13	−1.90261
$999$	−1.09167e13	−0.346776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.15	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+44.0746 q^{2} -81.0000 q^{3} +1430.57 q^{4} +625.000 q^{5} -3570.04 q^{6} -6480.81 q^{7} +40485.6 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+44.0746 q^{2} -81.0000 q^{3} +1430.57 q^{4} +625.000 q^{5} -3570.04 q^{6} -6480.81 q^{7} +40485.6 q^{8} +6561.00 q^{9} +27546.6 q^{10} -16845.3 q^{11} -115876. q^{12} -113957. q^{13} -285639. q^{14} -50625.0 q^{15} +1.05193e6 q^{16} +289208. q^{17} +289173. q^{18} -130321. q^{19} +894106. q^{20} +524945. q^{21} -742450. q^{22} +804006. q^{23} -3.27933e6 q^{24} +390625. q^{25} -5.02262e6 q^{26} -531441. q^{27} -9.27124e6 q^{28} +7.24242e6 q^{29} -2.23128e6 q^{30} +9.93122e6 q^{31} +2.56349e7 q^{32} +1.36447e6 q^{33} +1.27467e7 q^{34} -4.05051e6 q^{35} +9.38596e6 q^{36} +2.05418e7 q^{37} -5.74384e6 q^{38} +9.23053e6 q^{39} +2.53035e7 q^{40} -4.90838e6 q^{41} +2.31368e7 q^{42} -5.18880e6 q^{43} -2.40984e7 q^{44} +4.10062e6 q^{45} +3.54362e7 q^{46} -3.39717e7 q^{47} -8.52065e7 q^{48} +1.64727e6 q^{49} +1.72166e7 q^{50} -2.34258e7 q^{51} -1.63024e8 q^{52} +1.08619e7 q^{53} -2.34230e7 q^{54} -1.05283e7 q^{55} -2.62379e8 q^{56} +1.05560e7 q^{57} +3.19207e8 q^{58} +1.50863e8 q^{59} -7.24226e7 q^{60} -3.90769e7 q^{61} +4.37714e8 q^{62} -4.25206e7 q^{63} +5.91258e8 q^{64} -7.12233e7 q^{65} +6.01384e7 q^{66} -2.58318e8 q^{67} +4.13732e8 q^{68} -6.51245e7 q^{69} -1.78524e8 q^{70} +1.47177e8 q^{71} +2.65626e8 q^{72} -3.55554e8 q^{73} +9.05370e8 q^{74} -3.16406e7 q^{75} -1.86433e8 q^{76} +1.09171e8 q^{77} +4.06832e8 q^{78} +6.71093e8 q^{79} +6.57458e8 q^{80} +4.30467e7 q^{81} -2.16335e8 q^{82} +4.05588e8 q^{83} +7.50971e8 q^{84} +1.80755e8 q^{85} -2.28694e8 q^{86} -5.86636e8 q^{87} -6.81992e8 q^{88} +4.17963e8 q^{89} +1.80733e8 q^{90} +7.38535e8 q^{91} +1.15019e9 q^{92} -8.04429e8 q^{93} -1.49729e9 q^{94} -8.14506e7 q^{95} -2.07643e9 q^{96} -3.08832e8 q^{97} +7.26026e7 q^{98} -1.10522e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 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

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