LMFDB - Embedded newform 17.10.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.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:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 $ x^7 - x^6 - 2986x^5 + 8252x^4 + 2252056x^3 - 10388768x^2 - 243559296*x - 675998208
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-5.44491$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.44491 q^{2} +106.475 q^{3} -482.353 q^{4} +1303.94 q^{5} +579.746 q^{6} +9199.27 q^{7} -5414.17 q^{8} -8346.12 q^{9} +O(q^{10})$	\(q+5.44491 q^{2} +106.475 q^{3} -482.353 q^{4} +1303.94 q^{5} +579.746 q^{6} +9199.27 q^{7} -5414.17 q^{8} -8346.12 q^{9} +7099.84 q^{10} +62238.4 q^{11} -51358.4 q^{12} +141901. q^{13} +50089.2 q^{14} +138837. q^{15} +217485. q^{16} +83521.0 q^{17} -45443.9 q^{18} -941163. q^{19} -628959. q^{20} +979491. q^{21} +338883. q^{22} +568165. q^{23} -576472. q^{24} -252865. q^{25} +772638. q^{26} -2.98439e6 q^{27} -4.43730e6 q^{28} -1.83597e6 q^{29} +755954. q^{30} -7.34903e6 q^{31} +3.95624e6 q^{32} +6.62682e6 q^{33} +454765. q^{34} +1.19953e7 q^{35} +4.02577e6 q^{36} -8.01674e6 q^{37} -5.12455e6 q^{38} +1.51089e7 q^{39} -7.05975e6 q^{40} +1.95674e7 q^{41} +5.33324e6 q^{42} +3.46966e7 q^{43} -3.00209e7 q^{44} -1.08828e7 q^{45} +3.09361e6 q^{46} -5.63645e7 q^{47} +2.31567e7 q^{48} +4.42730e7 q^{49} -1.37683e6 q^{50} +8.89288e6 q^{51} -6.84463e7 q^{52} -3.28783e7 q^{53} -1.62498e7 q^{54} +8.11551e7 q^{55} -4.98064e7 q^{56} -1.00210e8 q^{57} -9.99672e6 q^{58} +1.04852e8 q^{59} -6.69683e7 q^{60} +5.69264e7 q^{61} -4.00148e7 q^{62} -7.67782e7 q^{63} -8.98109e7 q^{64} +1.85030e8 q^{65} +3.60825e7 q^{66} -1.58325e7 q^{67} -4.02866e7 q^{68} +6.04952e7 q^{69} +6.53134e7 q^{70} -9.81097e7 q^{71} +4.51873e7 q^{72} -6.27365e7 q^{73} -4.36505e7 q^{74} -2.69238e7 q^{75} +4.53973e8 q^{76} +5.72548e8 q^{77} +8.22665e7 q^{78} -1.38282e8 q^{79} +2.83587e8 q^{80} -1.53486e8 q^{81} +1.06543e8 q^{82} -6.69421e8 q^{83} -4.72460e8 q^{84} +1.08906e8 q^{85} +1.88920e8 q^{86} -1.95485e8 q^{87} -3.36969e8 q^{88} -4.21417e7 q^{89} -5.92561e7 q^{90} +1.30538e9 q^{91} -2.74056e8 q^{92} -7.82486e8 q^{93} -3.06900e8 q^{94} -1.22722e9 q^{95} +4.21240e8 q^{96} -4.11288e8 q^{97} +2.41063e8 q^{98} -5.19449e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) $ 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * 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 $

$2$	5.44491	0.240633	0.120317	−	0.992736i	$-0.461609\pi$
$2$	5.44491	0.240633	0.120317	+	0.992736i	$0.461609\pi$
$3$	106.475	0.758929	0.379465	−	0.925206i	$-0.376108\pi$
$3$	106.475	0.758929	0.379465	+	0.925206i	$0.376108\pi$
$4$	−482.353	−0.942096
$5$	1303.94	0.933024	0.466512	−	0.884515i	$-0.345511\pi$
$5$	1303.94	0.933024	0.466512	+	0.884515i	$0.345511\pi$
$6$	579.746	0.182624
$7$	9199.27	1.44815	0.724073	−	0.689723i	$-0.242268\pi$
$7$	9199.27	1.44815	0.724073	+	0.689723i	$0.242268\pi$
$8$	−5414.17	−0.467333
$9$	−8346.12	−0.424027
$10$	7099.84	0.224517
$11$	62238.4	1.28171	0.640857	−	0.767660i	$-0.278579\pi$
$11$	62238.4	1.28171	0.640857	+	0.767660i	$0.278579\pi$
$12$	−51358.4	−0.714984
$13$	141901.	1.37797	0.688985	−	0.724775i	$-0.258056\pi$
$13$	141901.	1.37797	0.688985	+	0.724775i	$0.258056\pi$
$14$	50089.2	0.348472
$15$	138837.	0.708099
$16$	217485.	0.829640
$17$	83521.0	0.242536
$17$	83521.0	0.242536
$18$	−45443.9	−0.102035
$19$	−941163.	−1.65681	−0.828407	−	0.560127i	$-0.810753\pi$
$19$	−941163.	−1.65681	−0.828407	+	0.560127i	$0.810753\pi$
$20$	−628959.	−0.878997
$21$	979491.	1.09904
$22$	338883.	0.308423
$23$	568165.	0.423349	0.211675	−	0.977340i	$-0.432108\pi$
$23$	568165.	0.423349	0.211675	+	0.977340i	$0.432108\pi$
$24$	−576472.	−0.354673
$25$	−252865.	−0.129467
$26$	772638.	0.331586
$27$	−2.98439e6	−1.08074
$28$	−4.43730e6	−1.36429
$29$	−1.83597e6	−0.482032	−0.241016	−	0.970521i	$-0.577481\pi$
$29$	−1.83597e6	−0.482032	−0.241016	+	0.970521i	$0.577481\pi$
$30$	755954.	0.170392
$31$	−7.34903e6	−1.42923	−0.714615	−	0.699518i	$-0.753398\pi$
$31$	−7.34903e6	−1.42923	−0.714615	+	0.699518i	$0.753398\pi$
$32$	3.95624e6	0.666972
$33$	6.62682e6	0.972730
$34$	454765.	0.0583622
$35$	1.19953e7	1.35115
$36$	4.02577e6	0.399474
$37$	−8.01674e6	−0.703218	−0.351609	−	0.936147i	$-0.614365\pi$
$37$	−8.01674e6	−0.703218	−0.351609	+	0.936147i	$0.614365\pi$
$38$	−5.12455e6	−0.398685
$39$	1.51089e7	1.04578
$40$	−7.05975e6	−0.436033
$41$	1.95674e7	1.08145	0.540724	−	0.841200i	$-0.318150\pi$
$41$	1.95674e7	1.08145	0.540724	+	0.841200i	$0.318150\pi$
$42$	5.33324e6	0.264466
$43$	3.46966e7	1.54767	0.773835	−	0.633387i	$-0.218336\pi$
$43$	3.46966e7	1.54767	0.773835	+	0.633387i	$0.218336\pi$
$44$	−3.00209e7	−1.20750
$45$	−1.08828e7	−0.395627
$46$	3.09361e6	0.101872
$47$	−5.63645e7	−1.68486	−0.842432	−	0.538802i	$-0.818877\pi$
$47$	−5.63645e7	−1.68486	−0.842432	+	0.538802i	$0.818877\pi$
$48$	2.31567e7	0.629638
$49$	4.42730e7	1.09713
$50$	−1.37683e6	−0.0311541
$51$	8.89288e6	0.184067
$52$	−6.84463e7	−1.29818
$53$	−3.28783e7	−0.572359	−0.286179	−	0.958176i	$-0.592385\pi$
$53$	−3.28783e7	−0.572359	−0.286179	+	0.958176i	$0.592385\pi$
$54$	−1.62498e7	−0.260061
$55$	8.11551e7	1.19587
$56$	−4.98064e7	−0.676767
$57$	−1.00210e8	−1.25740
$58$	−9.99672e6	−0.115993
$59$	1.04852e8	1.12653	0.563267	−	0.826275i	$-0.309544\pi$
$59$	1.04852e8	1.12653	0.563267	+	0.826275i	$0.309544\pi$
$60$	−6.69683e7	−0.667097
$61$	5.69264e7	0.526416	0.263208	−	0.964739i	$-0.415219\pi$
$61$	5.69264e7	0.526416	0.263208	+	0.964739i	$0.415219\pi$
$62$	−4.00148e7	−0.343921
$63$	−7.67782e7	−0.614052
$64$	−8.98109e7	−0.669144
$65$	1.85030e8	1.28568
$66$	3.60825e7	0.234072
$67$	−1.58325e7	−0.0959872	−0.0479936	−	0.998848i	$-0.515283\pi$
$67$	−1.58325e7	−0.0959872	−0.0479936	+	0.998848i	$0.515283\pi$
$68$	−4.02866e7	−0.228492
$69$	6.04952e7	0.321292
$70$	6.53134e7	0.325133
$71$	−9.81097e7	−0.458194	−0.229097	−	0.973404i	$-0.573577\pi$
$71$	−9.81097e7	−0.458194	−0.229097	+	0.973404i	$0.573577\pi$
$72$	4.51873e7	0.198162
$73$	−6.27365e7	−0.258564	−0.129282	−	0.991608i	$-0.541267\pi$
$73$	−6.27365e7	−0.258564	−0.129282	+	0.991608i	$0.541267\pi$
$74$	−4.36505e7	−0.169218
$75$	−2.69238e7	−0.0982563
$76$	4.53973e8	1.56088
$77$	5.72548e8	1.85611
$78$	8.22665e7	0.251650
$79$	−1.38282e8	−0.399433	−0.199717	−	0.979854i	$-0.564002\pi$
$79$	−1.38282e8	−0.399433	−0.199717	+	0.979854i	$0.564002\pi$
$80$	2.83587e8	0.774073
$81$	−1.53486e8	−0.396175
$82$	1.06543e8	0.260233
$83$	−6.69421e8	−1.54827	−0.774137	−	0.633018i	$-0.781816\pi$
$83$	−6.69421e8	−1.54827	−0.774137	+	0.633018i	$0.781816\pi$
$84$	−4.72460e8	−1.03540
$85$	1.08906e8	0.226291
$86$	1.88920e8	0.372421
$87$	−1.95485e8	−0.365828
$88$	−3.36969e8	−0.598988
$89$	−4.21417e7	−0.0711963	−0.0355981	−	0.999366i	$-0.511334\pi$
$89$	−4.21417e7	−0.0711963	−0.0355981	+	0.999366i	$0.511334\pi$
$90$	−5.92561e7	−0.0952011
$91$	1.30538e9	1.99550
$92$	−2.74056e8	−0.398836
$93$	−7.82486e8	−1.08468
$94$	−3.06900e8	−0.405435
$95$	−1.22722e9	−1.54585
$96$	4.21240e8	0.506185
$97$	−4.11288e8	−0.471707	−0.235854	−	0.971789i	$-0.575789\pi$
$97$	−4.11288e8	−0.471707	−0.235854	+	0.971789i	$0.575789\pi$
$98$	2.41063e8	0.264005
$99$	−5.19449e8	−0.543481
$100$	1.21970e8	0.121970
$101$	1.81470e7	0.0173524	0.00867620	−	0.999962i	$-0.497238\pi$
$101$	1.81470e7	0.0173524	0.00867620	+	0.999962i	$0.497238\pi$
$102$	4.84210e7	0.0442928
$103$	7.17681e8	0.628296	0.314148	−	0.949374i	$-0.398281\pi$
$103$	7.17681e8	0.628296	0.314148	+	0.949374i	$0.398281\pi$
$104$	−7.68275e8	−0.643971
$105$	1.27720e9	1.02543
$106$	−1.79020e8	−0.137729
$107$	−7.18789e8	−0.530120	−0.265060	−	0.964232i	$-0.585392\pi$
$107$	−7.18789e8	−0.530120	−0.265060	+	0.964232i	$0.585392\pi$
$108$	1.43953e9	1.01816
$109$	3.41476e8	0.231708	0.115854	−	0.993266i	$-0.463040\pi$
$109$	3.41476e8	0.231708	0.115854	+	0.993266i	$0.463040\pi$
$110$	4.41883e8	0.287766
$111$	−8.53581e8	−0.533693
$112$	2.00070e9	1.20144
$113$	−1.70781e9	−0.985339	−0.492670	−	0.870216i	$-0.663979\pi$
$113$	−1.70781e9	−0.985339	−0.492670	+	0.870216i	$0.663979\pi$
$114$	−5.45636e8	−0.302574
$115$	7.40853e8	0.394995
$116$	8.85588e8	0.454120
$117$	−1.18432e9	−0.584296
$118$	5.70912e8	0.271082
$119$	7.68332e8	0.351227
$120$	−7.51685e8	−0.330918
$121$	1.51567e9	0.642792
$122$	3.09959e8	0.126673
$123$	2.08343e9	0.820743
$124$	3.54482e9	1.34647
$125$	−2.87648e9	−1.05382
$126$	−4.18051e8	−0.147762
$127$	1.94335e9	0.662880	0.331440	−	0.943476i	$-0.392466\pi$
$127$	1.94335e9	0.662880	0.331440	+	0.943476i	$0.392466\pi$
$128$	−2.51461e9	−0.827991
$129$	3.69431e9	1.17457
$130$	1.00747e9	0.309377
$131$	3.30692e9	0.981075	0.490538	−	0.871420i	$-0.336800\pi$
$131$	3.30692e9	0.981075	0.490538	+	0.871420i	$0.336800\pi$
$132$	−3.19647e9	−0.916405
$133$	−8.65802e9	−2.39931
$134$	−8.62067e7	−0.0230977
$135$	−3.89147e9	−1.00835
$136$	−4.52197e8	−0.113345
$137$	−4.83938e9	−1.17367	−0.586836	−	0.809706i	$-0.699627\pi$
$137$	−4.83938e9	−1.17367	−0.586836	+	0.809706i	$0.699627\pi$
$138$	3.29391e8	0.0773137
$139$	3.57524e9	0.812342	0.406171	−	0.913797i	$-0.366864\pi$
$139$	3.57524e9	0.812342	0.406171	+	0.913797i	$0.366864\pi$
$140$	−5.78597e9	−1.27292
$141$	−6.00139e9	−1.27869
$142$	−5.34199e8	−0.110257
$143$	8.83168e9	1.76616
$144$	−1.81516e9	−0.351789
$145$	−2.39400e9	−0.449747
$146$	−3.41595e8	−0.0622191
$147$	4.71396e9	0.832641
$148$	3.86690e9	0.662499
$149$	−2.20680e9	−0.366796	−0.183398	−	0.983039i	$-0.558710\pi$
$149$	−2.20680e9	−0.366796	−0.183398	+	0.983039i	$0.558710\pi$
$150$	−1.46598e8	−0.0236438
$151$	7.78978e9	1.21935	0.609676	−	0.792651i	$-0.291300\pi$
$151$	7.78978e9	1.21935	0.609676	+	0.792651i	$0.291300\pi$
$152$	5.09561e9	0.774284
$153$	−6.97076e8	−0.102842
$154$	3.11747e9	0.446642
$155$	−9.58269e9	−1.33351
$156$	−7.28780e9	−0.985226
$157$	5.99611e9	0.787627	0.393814	−	0.919190i	$-0.371155\pi$
$157$	5.99611e9	0.787627	0.393814	+	0.919190i	$0.371155\pi$
$158$	−7.52935e8	−0.0961171
$159$	−3.50071e9	−0.434380
$160$	5.15870e9	0.622301
$161$	5.22670e9	0.613072
$162$	−8.35719e8	−0.0953329
$163$	2.20096e9	0.244212	0.122106	−	0.992517i	$-0.461035\pi$
$163$	2.20096e9	0.244212	0.122106	+	0.992517i	$0.461035\pi$
$164$	−9.43839e9	−1.01883
$165$	8.64098e9	0.907580
$166$	−3.64494e9	−0.372567
$167$	−1.54378e9	−0.153589	−0.0767946	−	0.997047i	$-0.524469\pi$
$167$	−1.54378e9	−0.153589	−0.0767946	+	0.997047i	$0.524469\pi$
$168$	−5.30313e9	−0.513618
$169$	9.53135e9	0.898802
$170$	5.92986e8	0.0544533
$171$	7.85506e9	0.702533
$172$	−1.67360e10	−1.45805
$173$	1.36568e10	1.15916	0.579578	−	0.814917i	$-0.303217\pi$
$173$	1.36568e10	1.15916	0.579578	+	0.814917i	$0.303217\pi$
$174$	−1.06440e9	−0.0880304
$175$	−2.32618e9	−0.187487
$176$	1.35359e10	1.06336
$177$	1.11641e10	0.854959
$178$	−2.29458e8	−0.0171322
$179$	7.48481e9	0.544932	0.272466	−	0.962165i	$-0.412161\pi$
$179$	7.48481e9	0.544932	0.272466	+	0.962165i	$0.412161\pi$
$180$	5.24937e9	0.372718
$181$	−1.98188e10	−1.37254	−0.686269	−	0.727348i	$-0.740753\pi$
$181$	−1.98188e10	−1.37254	−0.686269	+	0.727348i	$0.740753\pi$
$182$	7.10771e9	0.480185
$183$	6.06123e9	0.399513
$184$	−3.07614e9	−0.197845
$185$	−1.04534e10	−0.656119
$186$	−4.26057e9	−0.261011
$187$	5.19821e9	0.310861
$188$	2.71876e10	1.58730
$189$	−2.74543e10	−1.56506
$190$	−6.68211e9	−0.371982
$191$	−3.54665e10	−1.92827	−0.964137	−	0.265405i	$-0.914494\pi$
$191$	−3.54665e10	−1.92827	−0.964137	+	0.265405i	$0.914494\pi$
$192$	−9.56260e9	−0.507833
$193$	−1.16540e10	−0.604599	−0.302299	−	0.953213i	$-0.597754\pi$
$193$	−1.16540e10	−0.604599	−0.302299	+	0.953213i	$0.597754\pi$
$194$	−2.23943e9	−0.113509
$195$	1.97011e10	0.975739
$196$	−2.13552e10	−1.03360
$197$	4.99943e9	0.236495	0.118248	−	0.992984i	$-0.462272\pi$
$197$	4.99943e9	0.236495	0.118248	+	0.992984i	$0.462272\pi$
$198$	−2.82835e9	−0.130780
$199$	−1.90482e9	−0.0861026	−0.0430513	−	0.999073i	$-0.513708\pi$
$199$	−1.90482e9	−0.0861026	−0.0430513	+	0.999073i	$0.513708\pi$
$200$	1.36906e9	0.0605043
$201$	−1.68576e9	−0.0728475
$202$	9.88091e7	0.00417557
$203$	−1.68896e10	−0.698052
$204$	−4.28951e9	−0.173409
$205$	2.55147e10	1.00902
$206$	3.90771e9	0.151189
$207$	−4.74197e9	−0.179511
$208$	3.08613e10	1.14322
$209$	−5.85765e10	−2.12356
$210$	6.95423e9	0.246753
$211$	4.45582e10	1.54759	0.773797	−	0.633434i	$-0.218355\pi$
$211$	4.45582e10	1.54759	0.773797	+	0.633434i	$0.218355\pi$
$212$	1.58590e10	0.539216
$213$	−1.04462e10	−0.347737
$214$	−3.91374e9	−0.127565
$215$	4.52422e10	1.44401
$216$	1.61580e10	0.505063
$217$	−6.76057e10	−2.06973
$218$	1.85931e9	0.0557567
$219$	−6.67986e9	−0.196232
$220$	−3.91454e10	−1.12662
$221$	1.18517e10	0.334207
$222$	−4.64768e9	−0.128424
$223$	−1.00748e10	−0.272812	−0.136406	−	0.990653i	$-0.543555\pi$
$223$	−1.00748e10	−0.272812	−0.136406	+	0.990653i	$0.543555\pi$
$224$	3.63945e10	0.965873
$225$	2.11044e9	0.0548975
$226$	−9.29886e9	−0.237106
$227$	7.51701e10	1.87901	0.939505	−	0.342536i	$-0.111286\pi$
$227$	7.51701e10	1.87901	0.939505	+	0.342536i	$0.111286\pi$
$228$	4.83367e10	1.18460
$229$	8.19379e10	1.96891	0.984453	−	0.175647i	$-0.0562016\pi$
$229$	8.19379e10	1.96891	0.984453	+	0.175647i	$0.0562016\pi$
$230$	4.03388e9	0.0950490
$231$	6.09619e10	1.40866
$232$	9.94027e9	0.225269
$233$	−4.97304e10	−1.10540	−0.552701	−	0.833380i	$-0.686403\pi$
$233$	−4.97304e10	−1.10540	−0.552701	+	0.833380i	$0.686403\pi$
$234$	−6.44853e9	−0.140601
$235$	−7.34959e10	−1.57202
$236$	−5.05759e10	−1.06130
$237$	−1.47236e10	−0.303142
$238$	4.18350e9	0.0845170
$239$	−4.06399e10	−0.805680	−0.402840	−	0.915270i	$-0.631977\pi$
$239$	−4.06399e10	−0.805680	−0.402840	+	0.915270i	$0.631977\pi$
$240$	3.01949e10	0.587467
$241$	−3.05939e10	−0.584196	−0.292098	−	0.956388i	$-0.594353\pi$
$241$	−3.05939e10	−0.584196	−0.292098	+	0.956388i	$0.594353\pi$
$242$	8.25269e9	0.154677
$243$	4.23994e10	0.780067
$244$	−2.74586e10	−0.495934
$245$	5.77293e10	1.02364
$246$	1.13441e10	0.197498
$247$	−1.33552e11	−2.28304
$248$	3.97889e10	0.667927
$249$	−7.12765e10	−1.17503
$250$	−1.56622e10	−0.253584
$251$	2.05450e10	0.326719	0.163359	−	0.986567i	$-0.447767\pi$
$251$	2.05450e10	0.326719	0.163359	+	0.986567i	$0.447767\pi$
$252$	3.70342e10	0.578496
$253$	3.53617e10	0.542613
$254$	1.05814e10	0.159511
$255$	1.15958e10	0.171739
$256$	3.22914e10	0.469901
$257$	−8.98169e10	−1.28428	−0.642139	−	0.766588i	$-0.721953\pi$
$257$	−8.98169e10	−1.28428	−0.642139	+	0.766588i	$0.721953\pi$
$258$	2.01152e10	0.282641
$259$	−7.37482e10	−1.01836
$260$	−8.92498e10	−1.21123
$261$	1.53233e10	0.204394
$262$	1.80059e10	0.236080
$263$	1.43373e11	1.84785	0.923923	−	0.382577i	$-0.124963\pi$
$263$	1.43373e11	1.84785	0.923923	+	0.382577i	$0.124963\pi$
$264$	−3.58787e10	−0.454589
$265$	−4.28714e10	−0.534024
$266$	−4.71422e10	−0.577354
$267$	−4.48703e9	−0.0540329
$268$	7.63686e9	0.0904291
$269$	−1.67468e11	−1.95005	−0.975025	−	0.222094i	$-0.928711\pi$
$269$	−1.67468e11	−1.95005	−0.975025	+	0.222094i	$0.928711\pi$
$270$	−2.11887e10	−0.242643
$271$	4.52996e10	0.510190	0.255095	−	0.966916i	$-0.417893\pi$
$271$	4.52996e10	0.510190	0.255095	+	0.966916i	$0.417893\pi$
$272$	1.81646e10	0.201217
$273$	1.38991e11	1.51444
$274$	−2.63500e10	−0.282425
$275$	−1.57379e10	−0.165940
$276$	−2.91800e10	−0.302688
$277$	1.93194e9	0.0197167	0.00985836	−	0.999951i	$-0.496862\pi$
$277$	1.93194e9	0.0197167	0.00985836	+	0.999951i	$0.496862\pi$
$278$	1.94669e10	0.195477
$279$	6.13358e10	0.606032
$280$	−6.49445e10	−0.631439
$281$	1.16694e11	1.11653	0.558265	−	0.829662i	$-0.311467\pi$
$281$	1.16694e11	1.11653	0.558265	+	0.829662i	$0.311467\pi$
$282$	−3.26771e10	−0.307696
$283$	−1.65132e8	−0.00153036	−0.000765180	−	1.00000i	$-0.500244\pi$
$283$	−1.65132e8	−0.00153036	−0.000765180		1.00000i	$0.500244\pi$
$284$	4.73235e10	0.431662
$285$	−1.30668e11	−1.17319
$286$	4.80877e10	0.424998
$287$	1.80006e11	1.56609
$288$	−3.30192e10	−0.282814
$289$	6.97576e9	0.0588235
$290$	−1.30351e10	−0.108224
$291$	−4.37918e10	−0.357993
$292$	3.02611e10	0.243592
$293$	6.45700e10	0.511831	0.255915	−	0.966699i	$-0.417623\pi$
$293$	6.45700e10	0.511831	0.255915	+	0.966699i	$0.417623\pi$
$294$	2.56671e10	0.200361
$295$	1.36721e11	1.05108
$296$	4.34040e10	0.328637
$297$	−1.85744e11	−1.38519
$298$	−1.20158e10	−0.0882633
$299$	8.06230e10	0.583363
$300$	1.29868e10	0.0925669
$301$	3.19183e11	2.24125
$302$	4.24147e10	0.293417
$303$	1.93220e9	0.0131692
$304$	−2.04689e11	−1.37456
$305$	7.42286e10	0.491159
$306$	−3.79552e9	−0.0247471
$307$	8.54538e10	0.549046	0.274523	−	0.961581i	$-0.411480\pi$
$307$	8.54538e10	0.549046	0.274523	+	0.961581i	$0.411480\pi$
$308$	−2.76170e11	−1.74863
$309$	7.64150e10	0.476832
$310$	−5.21769e10	−0.320886
$311$	−7.31980e10	−0.443688	−0.221844	−	0.975082i	$-0.571208\pi$
$311$	−7.31980e10	−0.443688	−0.221844	+	0.975082i	$0.571208\pi$
$312$	−8.18019e10	−0.488729
$313$	1.60425e10	0.0944764	0.0472382	−	0.998884i	$-0.484958\pi$
$313$	1.60425e10	0.0944764	0.0472382	+	0.998884i	$0.484958\pi$
$314$	3.26483e10	0.189530
$315$	−1.00114e11	−0.572925
$316$	6.67008e10	0.376304
$317$	8.53822e10	0.474899	0.237449	−	0.971400i	$-0.423689\pi$
$317$	8.53822e10	0.474899	0.237449	+	0.971400i	$0.423689\pi$
$318$	−1.90611e10	−0.104526
$319$	−1.14268e11	−0.617827
$320$	−1.17108e11	−0.624327
$321$	−7.65329e10	−0.402324
$322$	2.84589e10	0.147526
$323$	−7.86069e10	−0.401836
$324$	7.40345e10	0.373235
$325$	−3.58818e10	−0.178402
$326$	1.19840e10	0.0587656
$327$	3.63586e10	0.175850
$328$	−1.05941e11	−0.505397
$329$	−5.18512e11	−2.43993
$330$	4.70494e10	0.218394
$331$	5.68636e10	0.260380	0.130190	−	0.991489i	$-0.458441\pi$
$331$	5.68636e10	0.260380	0.130190	+	0.991489i	$0.458441\pi$
$332$	3.22897e11	1.45862
$333$	6.69087e10	0.298183
$334$	−8.40574e9	−0.0369587
$335$	−2.06447e10	−0.0895583
$336$	2.13025e11	0.911807
$337$	3.07106e11	1.29704	0.648521	−	0.761197i	$-0.275388\pi$
$337$	3.07106e11	1.29704	0.648521	+	0.761197i	$0.275388\pi$
$338$	5.18974e10	0.216282
$339$	−1.81838e11	−0.747803
$340$	−5.25313e10	−0.213188
$341$	−4.57392e11	−1.83187
$342$	4.27701e10	0.169053
$343$	3.60556e10	0.140653
$344$	−1.87853e11	−0.723278
$345$	7.88821e10	0.299773
$346$	7.43602e10	0.278932
$347$	3.34687e10	0.123924	0.0619621	−	0.998079i	$-0.480264\pi$
$347$	3.34687e10	0.123924	0.0619621	+	0.998079i	$0.480264\pi$
$348$	9.42928e10	0.344645
$349$	−3.80974e11	−1.37462	−0.687308	−	0.726366i	$-0.741208\pi$
$349$	−3.80974e11	−1.37462	−0.687308	+	0.726366i	$0.741208\pi$
$350$	−1.26658e10	−0.0451157
$351$	−4.23488e11	−1.48922
$352$	2.46230e11	0.854868
$353$	2.09902e11	0.719499	0.359750	−	0.933049i	$-0.382862\pi$
$353$	2.09902e11	0.719499	0.359750	+	0.933049i	$0.382862\pi$
$354$	6.07878e10	0.205732
$355$	−1.27929e11	−0.427506
$356$	2.03272e10	0.0670737
$357$	8.18080e10	0.266556
$358$	4.07542e10	0.131129
$359$	3.14148e11	0.998181	0.499091	−	0.866550i	$-0.333668\pi$
$359$	3.14148e11	0.998181	0.499091	+	0.866550i	$0.333668\pi$
$360$	5.89215e10	0.184890
$361$	5.63101e11	1.74503
$362$	−1.07912e11	−0.330279
$363$	1.61381e11	0.487834
$364$	−6.29656e11	−1.87995
$365$	−8.18047e10	−0.241246
$366$	3.30029e10	0.0961361
$367$	2.40379e11	0.691671	0.345835	−	0.938295i	$-0.387596\pi$
$367$	2.40379e11	0.691671	0.345835	+	0.938295i	$0.387596\pi$
$368$	1.23567e11	0.351227
$369$	−1.63312e11	−0.458563
$370$	−5.69176e10	−0.157884
$371$	−3.02457e11	−0.828859
$372$	3.77435e11	1.02188
$373$	2.93908e11	0.786179	0.393089	−	0.919500i	$-0.371406\pi$
$373$	2.93908e11	0.786179	0.393089	+	0.919500i	$0.371406\pi$
$374$	2.83038e10	0.0748037
$375$	−3.06273e11	−0.799774
$376$	3.05167e11	0.787393
$377$	−2.60526e11	−0.664225
$378$	−1.49486e11	−0.376606
$379$	3.76034e11	0.936161	0.468081	−	0.883686i	$-0.344946\pi$
$379$	3.76034e11	0.936161	0.468081	+	0.883686i	$0.344946\pi$
$380$	5.91953e11	1.45634
$381$	2.06918e11	0.503079
$382$	−1.93112e11	−0.464007
$383$	3.73836e11	0.887741	0.443870	−	0.896091i	$-0.353605\pi$
$383$	3.73836e11	0.887741	0.443870	+	0.896091i	$0.353605\pi$
$384$	−2.67742e11	−0.628386
$385$	7.46568e11	1.73179
$386$	−6.34550e10	−0.145487
$387$	−2.89582e11	−0.656253
$388$	1.98386e11	0.444394
$389$	−4.62613e10	−0.102434	−0.0512171	−	0.998688i	$-0.516310\pi$
$389$	−4.62613e10	−0.102434	−0.0512171	+	0.998688i	$0.516310\pi$
$390$	1.07271e11	0.234795
$391$	4.74537e10	0.102677
$392$	−2.39701e11	−0.512724
$393$	3.52103e11	0.744567
$394$	2.72215e10	0.0569087
$395$	−1.80312e11	−0.372681
$396$	2.50558e11	0.512011
$397$	−3.36827e11	−0.680534	−0.340267	−	0.940329i	$-0.610517\pi$
$397$	−3.36827e11	−0.680534	−0.340267	+	0.940329i	$0.610517\pi$
$398$	−1.03716e10	−0.0207192
$399$	−9.21861e11	−1.82091
$400$	−5.49944e10	−0.107411
$401$	−9.81350e11	−1.89528	−0.947642	−	0.319335i	$-0.896541\pi$
$401$	−9.81350e11	−1.89528	−0.947642	+	0.319335i	$0.896541\pi$
$402$	−9.17884e9	−0.0175295
$403$	−1.04283e12	−1.96944
$404$	−8.75328e9	−0.0163476
$405$	−2.00137e11	−0.369640
$406$	−9.19626e10	−0.167975
$407$	−4.98949e11	−0.901325
$408$	−4.81475e10	−0.0860208
$409$	8.17703e11	1.44491	0.722455	−	0.691418i	$-0.243014\pi$
$409$	8.17703e11	1.44491	0.722455	+	0.691418i	$0.243014\pi$
$410$	1.38925e11	0.242803
$411$	−5.15272e11	−0.890734
$412$	−3.46176e11	−0.591915
$413$	9.64566e11	1.63139
$414$	−2.58196e10	−0.0431965
$415$	−8.72885e11	−1.44458
$416$	5.61394e11	0.919068
$417$	3.80673e11	0.616510
$418$	−3.18944e11	−0.511000
$419$	−4.18196e11	−0.662852	−0.331426	−	0.943481i	$-0.607530\pi$
$419$	−4.18196e11	−0.662852	−0.331426	+	0.943481i	$0.607530\pi$
$420$	−6.16060e11	−0.966053
$421$	3.11784e11	0.483709	0.241855	−	0.970313i	$-0.422244\pi$
$421$	3.11784e11	0.483709	0.241855	+	0.970313i	$0.422244\pi$
$422$	2.42616e11	0.372403
$423$	4.70424e11	0.714427
$424$	1.78009e11	0.267482
$425$	−2.11196e10	−0.0314004
$426$	−5.68787e10	−0.0836771
$427$	5.23681e11	0.762328
$428$	3.46710e11	0.499424
$429$	9.40351e11	1.34039
$430$	2.46340e11	0.347478
$431$	8.66540e11	1.20960	0.604799	−	0.796378i	$-0.293253\pi$
$431$	8.66540e11	1.20960	0.604799	+	0.796378i	$0.293253\pi$
$432$	−6.49061e11	−0.896621
$433$	2.95119e11	0.403461	0.201730	−	0.979441i	$-0.435344\pi$
$433$	2.95119e11	0.403461	0.201730	+	0.979441i	$0.435344\pi$
$434$	−3.68107e11	−0.498047
$435$	−2.54901e11	−0.341326
$436$	−1.64712e11	−0.218291
$437$	−5.34736e11	−0.701411
$438$	−3.63713e10	−0.0472199
$439$	5.48786e11	0.705201	0.352600	−	0.935774i	$-0.385297\pi$
$439$	5.48786e11	0.705201	0.352600	+	0.935774i	$0.385297\pi$
$440$	−4.39387e11	−0.558870
$441$	−3.69508e11	−0.465211
$442$	6.45315e10	0.0804214
$443$	−1.03597e12	−1.27800	−0.638999	−	0.769207i	$-0.720651\pi$
$443$	−1.03597e12	−1.27800	−0.638999	+	0.769207i	$0.720651\pi$
$444$	4.11727e11	0.502790
$445$	−5.49503e10	−0.0664278
$446$	−5.48562e10	−0.0656476
$447$	−2.34968e11	−0.278372
$448$	−8.26195e11	−0.969018
$449$	−1.04924e12	−1.21833	−0.609167	−	0.793042i	$-0.708496\pi$
$449$	−1.04924e12	−1.21833	−0.609167	+	0.793042i	$0.708496\pi$
$450$	1.14912e10	0.0132102
$451$	1.21784e12	1.38611
$452$	8.23766e11	0.928284
$453$	8.29415e11	0.925401
$454$	4.09295e11	0.452153
$455$	1.70214e12	1.86185
$456$	5.42555e11	0.587627
$457$	1.13929e11	0.122183	0.0610917	−	0.998132i	$-0.480542\pi$
$457$	1.13929e11	0.122183	0.0610917	+	0.998132i	$0.480542\pi$
$458$	4.46145e11	0.473785
$459$	−2.49260e11	−0.262117
$460$	−3.57352e11	−0.372123
$461$	1.04783e12	1.08053	0.540264	−	0.841496i	$-0.318325\pi$
$461$	1.04783e12	1.08053	0.540264	+	0.841496i	$0.318325\pi$
$462$	3.31932e11	0.338970
$463$	1.26218e11	0.127646	0.0638231	−	0.997961i	$-0.479671\pi$
$463$	1.26218e11	0.127646	0.0638231	+	0.997961i	$0.479671\pi$
$464$	−3.99297e11	−0.399913
$465$	−1.02032e12	−1.01204
$466$	−2.70778e11	−0.265997
$467$	−1.20765e12	−1.17494	−0.587470	−	0.809246i	$-0.699876\pi$
$467$	−1.20765e12	−1.17494	−0.587470	+	0.809246i	$0.699876\pi$
$468$	5.71261e11	0.550463
$469$	−1.45648e11	−0.139003
$470$	−4.00179e11	−0.378280
$471$	6.38434e11	0.597753
$472$	−5.67688e11	−0.526467
$473$	2.15946e12	1.98367
$474$	−8.01686e10	−0.0729460
$475$	2.37988e11	0.214503
$476$	−3.70607e11	−0.330889
$477$	2.74406e11	0.242695
$478$	−2.21281e11	−0.193874
$479$	−1.58750e12	−1.37786	−0.688930	−	0.724828i	$-0.741919\pi$
$479$	−1.58750e12	−1.37786	−0.688930	+	0.724828i	$0.741919\pi$
$480$	5.49272e11	0.472282
$481$	−1.13758e12	−0.969014
$482$	−1.66581e11	−0.140577
$483$	5.56512e11	0.465278
$484$	−7.31088e11	−0.605572
$485$	−5.36294e11	−0.440114
$486$	2.30861e11	0.187710
$487$	9.39880e11	0.757167	0.378584	−	0.925567i	$-0.376411\pi$
$487$	9.39880e11	0.757167	0.378584	+	0.925567i	$0.376411\pi$
$488$	−3.08209e11	−0.246012
$489$	2.34347e11	0.185340
$490$	3.14331e11	0.246323
$491$	9.66438e11	0.750425	0.375213	−	0.926939i	$-0.377570\pi$
$491$	9.66438e11	0.750425	0.375213	+	0.926939i	$0.377570\pi$
$492$	−1.00495e12	−0.773218
$493$	−1.53342e11	−0.116910
$494$	−7.27178e11	−0.549376
$495$	−6.77330e11	−0.507081
$496$	−1.59830e12	−1.18575
$497$	−9.02538e11	−0.663532
$498$	−3.88094e11	−0.282752
$499$	−1.22995e12	−0.888045	−0.444022	−	0.896016i	$-0.646449\pi$
$499$	−1.22995e12	−0.888045	−0.444022	+	0.896016i	$0.646449\pi$
$500$	1.38748e12	0.992799
$501$	−1.64373e11	−0.116563
$502$	1.11866e11	0.0786195
$503$	−1.98521e12	−1.38277	−0.691386	−	0.722485i	$-0.743000\pi$
$503$	−1.98521e12	−1.38277	−0.691386	+	0.722485i	$0.743000\pi$
$504$	4.15690e11	0.286967
$505$	2.36626e10	0.0161902
$506$	1.92541e11	0.130571
$507$	1.01485e12	0.682127
$508$	−9.37382e11	−0.624496
$509$	2.25974e12	1.49221	0.746104	−	0.665830i	$-0.231922\pi$
$509$	2.25974e12	1.49221	0.746104	+	0.665830i	$0.231922\pi$
$510$	6.31381e10	0.0413262
$511$	−5.77130e11	−0.374438
$512$	1.46330e12	0.941065
$513$	2.80880e12	1.79058
$514$	−4.89045e11	−0.309040
$515$	9.35813e11	0.586215
$516$	−1.78196e12	−1.10656
$517$	−3.50803e12	−2.15952
$518$	−4.01553e11	−0.245052
$519$	1.45411e12	0.879717
$520$	−1.00178e12	−0.600840
$521$	4.78832e11	0.284717	0.142358	−	0.989815i	$-0.454531\pi$
$521$	4.78832e11	0.284717	0.142358	+	0.989815i	$0.454531\pi$
$522$	8.34338e10	0.0491841
$523$	−9.37326e11	−0.547814	−0.273907	−	0.961756i	$-0.588316\pi$
$523$	−9.37326e11	−0.547814	−0.273907	+	0.961756i	$0.588316\pi$
$524$	−1.59510e12	−0.924267
$525$	−2.47679e11	−0.142290
$526$	7.80653e11	0.444654
$527$	−6.13798e11	−0.346639
$528$	1.44123e12	0.807016
$529$	−1.47834e12	−0.820775
$530$	−2.33431e11	−0.128504
$531$	−8.75110e11	−0.477680
$532$	4.17622e12	2.26038
$533$	2.77663e12	1.49020
$534$	−2.44315e10	−0.0130021
$535$	−9.37257e11	−0.494614
$536$	8.57199e10	0.0448580
$537$	7.96944e11	0.413565
$538$	−9.11847e11	−0.469247
$539$	2.75548e12	1.40620
$540$	1.87706e12	0.949963
$541$	−3.44109e12	−1.72706	−0.863532	−	0.504293i	$-0.831753\pi$
$541$	−3.44109e12	−1.72706	−0.863532	+	0.504293i	$0.831753\pi$
$542$	2.46652e11	0.122769
$543$	−2.11021e12	−1.04166
$544$	3.30429e11	0.161765
$545$	4.45264e11	0.216189
$546$	7.56792e11	0.364426
$547$	8.05238e11	0.384575	0.192288	−	0.981339i	$-0.438409\pi$
$547$	8.05238e11	0.384575	0.192288	+	0.981339i	$0.438409\pi$
$548$	2.33429e12	1.10571
$549$	−4.75114e11	−0.223215
$550$	−8.56917e10	−0.0399307
$551$	1.72795e12	0.798637
$552$	−3.27531e11	−0.150151
$553$	−1.27210e12	−0.578438
$554$	1.05192e10	0.00474450
$555$	−1.11302e12	−0.497948
$556$	−1.72453e12	−0.765304
$557$	−2.13503e11	−0.0939842	−0.0469921	−	0.998895i	$-0.514964\pi$
$557$	−2.13503e11	−0.0939842	−0.0469921	+	0.998895i	$0.514964\pi$
$558$	3.33968e11	0.145832
$559$	4.92347e12	2.13264
$560$	2.60880e12	1.12097
$561$	5.53479e11	0.235922
$562$	6.35390e11	0.268675
$563$	−1.94290e12	−0.815010	−0.407505	−	0.913203i	$-0.633601\pi$
$563$	−1.94290e12	−0.815010	−0.407505	+	0.913203i	$0.633601\pi$
$564$	2.89479e12	1.20465
$565$	−2.22688e12	−0.919345
$566$	−8.99132e8	−0.000368256 0
$567$	−1.41196e12	−0.573719
$568$	5.31182e11	0.214129
$569$	−9.66618e11	−0.386589	−0.193295	−	0.981141i	$-0.561917\pi$
$569$	−9.66618e11	−0.386589	−0.193295	+	0.981141i	$0.561917\pi$
$570$	−7.11476e11	−0.282308
$571$	3.96159e12	1.55958	0.779788	−	0.626043i	$-0.215327\pi$
$571$	3.96159e12	1.55958	0.779788	+	0.626043i	$0.215327\pi$
$572$	−4.25999e12	−1.66390
$573$	−3.77629e12	−1.46342
$574$	9.80116e11	0.376855
$575$	−1.43669e11	−0.0548098
$576$	7.49573e11	0.283735
$577$	2.21488e12	0.831876	0.415938	−	0.909393i	$-0.363453\pi$
$577$	2.21488e12	0.831876	0.415938	+	0.909393i	$0.363453\pi$
$578$	3.79824e10	0.0141549
$579$	−1.24086e12	−0.458847
$580$	1.15475e12	0.423705
$581$	−6.15819e12	−2.24213
$582$	−2.38442e11	−0.0861450
$583$	−2.04629e12	−0.733600
$584$	3.39666e11	0.120835
$585$	−1.54428e12	−0.545162
$586$	3.51578e11	0.123164
$587$	−6.70503e11	−0.233093	−0.116546	−	0.993185i	$-0.537182\pi$
$587$	−6.70503e11	−0.233093	−0.116546	+	0.993185i	$0.537182\pi$
$588$	−2.27379e12	−0.784427
$589$	6.91664e12	2.36797
$590$	7.44435e11	0.252926
$591$	5.32314e11	0.179483
$592$	−1.74352e12	−0.583418
$593$	−4.14332e12	−1.37595	−0.687975	−	0.725735i	$-0.741500\pi$
$593$	−4.14332e12	−1.37595	−0.687975	+	0.725735i	$0.741500\pi$
$594$	−1.01136e12	−0.333324
$595$	1.00186e12	0.327703
$596$	1.06445e12	0.345556
$597$	−2.02816e11	−0.0653458
$598$	4.38986e11	0.140377
$599$	2.11940e12	0.672653	0.336327	−	0.941745i	$-0.390815\pi$
$599$	2.11940e12	0.672653	0.336327	+	0.941745i	$0.390815\pi$
$600$	1.45770e11	0.0459185
$601$	4.44856e12	1.39086	0.695431	−	0.718593i	$-0.255213\pi$
$601$	4.44856e12	1.39086	0.695431	+	0.718593i	$0.255213\pi$
$602$	1.73792e12	0.539320
$603$	1.32140e11	0.0407011
$604$	−3.75742e12	−1.14875
$605$	1.97634e12	0.599740
$606$	1.05207e10	0.00316896
$607$	8.59588e11	0.257005	0.128502	−	0.991709i	$-0.458983\pi$
$607$	8.59588e11	0.257005	0.128502	+	0.991709i	$0.458983\pi$
$608$	−3.72347e12	−1.10505
$609$	−1.79832e12	−0.529772
$610$	4.04168e11	0.118189
$611$	−7.99816e12	−2.32169
$612$	3.36237e11	0.0968866
$613$	−5.43289e12	−1.55403	−0.777013	−	0.629484i	$-0.783266\pi$
$613$	−5.43289e12	−1.55403	−0.777013	+	0.629484i	$0.783266\pi$
$614$	4.65289e11	0.132119
$615$	2.71667e12	0.765772
$616$	−3.09987e12	−0.867422
$617$	−1.22774e12	−0.341053	−0.170527	−	0.985353i	$-0.554547\pi$
$617$	−1.22774e12	−0.341053	−0.170527	+	0.985353i	$0.554547\pi$
$618$	4.16073e11	0.114742
$619$	4.33143e12	1.18583	0.592917	−	0.805264i	$-0.297976\pi$
$619$	4.33143e12	1.18583	0.592917	+	0.805264i	$0.297976\pi$
$620$	4.62224e12	1.25629
$621$	−1.69563e12	−0.457529
$622$	−3.98557e11	−0.106766
$623$	−3.87673e11	−0.103103
$624$	3.28595e12	0.867622
$625$	−3.25688e12	−0.853771
$626$	8.73502e10	0.0227342
$627$	−6.23692e12	−1.61163
$628$	−2.89224e12	−0.742020
$629$	−6.69566e11	−0.170555
$630$	−5.45113e11	−0.137865
$631$	1.79967e12	0.451919	0.225959	−	0.974137i	$-0.427448\pi$
$631$	1.79967e12	0.451919	0.225959	+	0.974137i	$0.427448\pi$
$632$	7.48683e11	0.186669
$633$	4.74433e12	1.17451
$634$	4.64899e11	0.114277
$635$	2.53402e12	0.618483
$636$	1.68858e12	0.409227
$637$	6.28238e12	1.51181
$638$	−6.22180e11	−0.148670
$639$	8.18835e11	0.194286
$640$	−3.27890e12	−0.772535
$641$	5.02365e12	1.17532	0.587662	−	0.809106i	$-0.300048\pi$
$641$	5.02365e12	1.17532	0.587662	+	0.809106i	$0.300048\pi$
$642$	−4.16715e11	−0.0968125
$643$	4.60458e12	1.06229	0.531143	−	0.847283i	$-0.321763\pi$
$643$	4.60458e12	1.06229	0.531143	+	0.847283i	$0.321763\pi$
$644$	−2.52111e12	−0.577572
$645$	4.81716e12	1.09590
$646$	−4.28008e11	−0.0966953
$647$	4.15507e12	0.932201	0.466100	−	0.884732i	$-0.345659\pi$
$647$	4.15507e12	0.932201	0.466100	+	0.884732i	$0.345659\pi$
$648$	8.31000e11	0.185146
$649$	6.52584e12	1.44390
$650$	−1.95373e11	−0.0429295
$651$	−7.19830e12	−1.57078
$652$	−1.06164e12	−0.230071
$653$	3.43743e11	0.0739817	0.0369909	−	0.999316i	$-0.488223\pi$
$653$	3.43743e11	0.0739817	0.0369909	+	0.999316i	$0.488223\pi$
$654$	1.97969e11	0.0423154
$655$	4.31202e12	0.915367
$656$	4.25562e12	0.897212
$657$	5.23606e11	0.109638
$658$	−2.82325e12	−0.587129
$659$	2.39727e12	0.495145	0.247572	−	0.968869i	$-0.420367\pi$
$659$	2.39727e12	0.495145	0.247572	+	0.968869i	$0.420367\pi$
$660$	−4.16800e12	−0.855027
$661$	−2.09899e12	−0.427665	−0.213833	−	0.976870i	$-0.568595\pi$
$661$	−2.09899e12	−0.427665	−0.213833	+	0.976870i	$0.568595\pi$
$662$	3.09617e11	0.0626563
$663$	1.26191e12	0.253639
$664$	3.62436e12	0.723560
$665$	−1.12895e13	−2.23861
$666$	3.64312e11	0.0717529
$667$	−1.04314e12	−0.204068
$668$	7.44646e11	0.144696
$669$	−1.07271e12	−0.207045
$670$	−1.12408e11	−0.0215507
$671$	3.54301e12	0.674715
$672$	3.87510e12	0.733029
$673$	−1.61276e12	−0.303042	−0.151521	−	0.988454i	$-0.548417\pi$
$673$	−1.61276e12	−0.303042	−0.151521	+	0.988454i	$0.548417\pi$
$674$	1.67217e12	0.312112
$675$	7.54650e11	0.139920
$676$	−4.59747e12	−0.846758
$677$	2.64830e12	0.484527	0.242264	−	0.970210i	$-0.422110\pi$
$677$	2.64830e12	0.484527	0.242264	+	0.970210i	$0.422110\pi$
$678$	−9.90094e11	−0.179946
$679$	−3.78355e12	−0.683101
$680$	−5.89637e11	−0.105754
$681$	8.00373e12	1.42604
$682$	−2.49046e12	−0.440808
$683$	−9.69821e12	−1.70529	−0.852645	−	0.522491i	$-0.825003\pi$
$683$	−9.69821e12	−1.70529	−0.852645	+	0.522491i	$0.825003\pi$
$684$	−3.78891e12	−0.661853
$685$	−6.31026e12	−1.09506
$686$	1.96320e11	0.0338458
$687$	8.72432e12	1.49426
$688$	7.54598e12	1.28401
$689$	−4.66546e12	−0.788693
$690$	4.29506e11	0.0721355
$691$	−7.85953e12	−1.31143	−0.655715	−	0.755008i	$-0.727633\pi$
$691$	−7.85953e12	−1.31143	−0.655715	+	0.755008i	$0.727633\pi$
$692$	−6.58740e12	−1.09204
$693$	−4.77855e12	−0.787040
$694$	1.82234e11	0.0298203
$695$	4.66190e12	0.757934
$696$	1.05839e12	0.170964
$697$	1.63429e12	0.262290
$698$	−2.07437e12	−0.330779
$699$	−5.29503e12	−0.838922
$700$	1.12204e12	0.176631
$701$	1.35808e12	0.212419	0.106210	−	0.994344i	$-0.466129\pi$
$701$	1.35808e12	0.212419	0.106210	+	0.994344i	$0.466129\pi$
$702$	−2.30586e12	−0.358356
$703$	7.54506e12	1.16510
$704$	−5.58969e12	−0.857651
$705$	−7.82546e12	−1.19305
$706$	1.14290e12	0.173136
$707$	1.66940e11	0.0251288
$708$	−5.38505e12	−0.805453
$709$	8.38924e12	1.24685	0.623426	−	0.781883i	$-0.285740\pi$
$709$	8.38924e12	1.24685	0.623426	+	0.781883i	$0.285740\pi$
$710$	−6.96563e11	−0.102872
$711$	1.15412e12	0.169370
$712$	2.28162e11	0.0332724
$713$	−4.17546e12	−0.605064
$714$	4.45438e11	0.0641424
$715$	1.15160e13	1.64787
$716$	−3.61032e12	−0.513378
$717$	−4.32713e12	−0.611454
$718$	1.71051e12	0.240196
$719$	1.05644e12	0.147423	0.0737117	−	0.997280i	$-0.476516\pi$
$719$	1.05644e12	0.147423	0.0737117	+	0.997280i	$0.476516\pi$
$720$	−2.36685e12	−0.328228
$721$	6.60214e12	0.909864
$722$	3.06604e12	0.419913
$723$	−3.25748e12	−0.443363
$724$	9.55967e12	1.29306
$725$	4.64254e11	0.0624072
$726$	8.78704e11	0.117389
$727$	1.20219e12	0.159614	0.0798068	−	0.996810i	$-0.474570\pi$
$727$	1.20219e12	0.159614	0.0798068	+	0.996810i	$0.474570\pi$
$728$	−7.06757e12	−0.932564
$729$	7.53554e12	0.988190
$730$	−4.45419e11	−0.0580519
$731$	2.89789e12	0.375365
$732$	−2.92365e12	−0.376379
$733$	−1.38044e13	−1.76624	−0.883121	−	0.469146i	$-0.844562\pi$
$733$	−1.38044e13	−1.76624	−0.883121	+	0.469146i	$0.844562\pi$
$734$	1.30884e12	0.166439
$735$	6.14672e12	0.776874
$736$	2.24780e12	0.282362
$737$	−9.85390e11	−0.123028
$738$	−8.89219e11	−0.110346
$739$	−1.03973e13	−1.28240	−0.641198	−	0.767375i	$-0.721562\pi$
$739$	−1.03973e13	−1.28240	−0.641198	+	0.767375i	$0.721562\pi$
$740$	5.04220e12	0.618127
$741$	−1.42199e13	−1.73267
$742$	−1.64685e12	−0.199451
$743$	7.06440e12	0.850405	0.425202	−	0.905098i	$-0.360203\pi$
$743$	7.06440e12	0.850405	0.425202	+	0.905098i	$0.360203\pi$
$744$	4.23651e12	0.506909
$745$	−2.87753e12	−0.342229
$746$	1.60030e12	0.189181
$747$	5.58707e12	0.656510
$748$	−2.50737e12	−0.292861
$749$	−6.61233e12	−0.767691
$750$	−1.66763e12	−0.192452
$751$	5.52292e12	0.633562	0.316781	−	0.948499i	$-0.397398\pi$
$751$	5.52292e12	0.633562	0.316781	+	0.948499i	$0.397398\pi$
$752$	−1.22584e13	−1.39783
$753$	2.18752e12	0.247956
$754$	−1.41854e12	−0.159835
$755$	1.01574e13	1.13768
$756$	1.32426e13	1.47444
$757$	−5.93646e12	−0.657046	−0.328523	−	0.944496i	$-0.606551\pi$
$757$	−5.93646e12	−0.657046	−0.328523	+	0.944496i	$0.606551\pi$
$758$	2.04747e12	0.225272
$759$	3.76513e12	0.411805
$760$	6.64438e12	0.722425
$761$	−1.16527e13	−1.25949	−0.629745	−	0.776802i	$-0.716840\pi$
$761$	−1.16527e13	−1.25949	−0.629745	+	0.776802i	$0.716840\pi$
$762$	1.12665e12	0.121058
$763$	3.14133e12	0.335547
$764$	1.71074e13	1.81662
$765$	−9.08945e11	−0.0959536
$766$	2.03550e12	0.213620
$767$	1.48786e13	1.55233
$768$	3.43822e12	0.356622
$769$	−3.13586e12	−0.323361	−0.161681	−	0.986843i	$-0.551691\pi$
$769$	−3.13586e12	−0.323361	−0.161681	+	0.986843i	$0.551691\pi$
$770$	4.06500e12	0.416728
$771$	−9.56324e12	−0.974676
$772$	5.62134e12	0.569590
$773$	1.41981e13	1.43029	0.715143	−	0.698979i	$-0.246362\pi$
$773$	1.41981e13	1.43029	0.715143	+	0.698979i	$0.246362\pi$
$774$	−1.57675e12	−0.157917
$775$	1.85831e12	0.185038
$776$	2.22678e12	0.220445
$777$	−7.85232e12	−0.772865
$778$	−2.51889e11	−0.0246491
$779$	−1.84161e13	−1.79176
$780$	−9.50286e12	−0.919239
$781$	−6.10619e12	−0.587274
$782$	2.58381e11	0.0247076
$783$	5.47927e12	0.520949
$784$	9.62871e12	0.910219
$785$	7.81856e12	0.734875
$786$	1.91717e12	0.179168
$787$	−7.60742e12	−0.706889	−0.353444	−	0.935456i	$-0.614990\pi$
$787$	−7.60742e12	−0.706889	−0.353444	+	0.935456i	$0.614990\pi$
$788$	−2.41149e12	−0.222801
$789$	1.52656e13	1.40238
$790$	−9.81782e11	−0.0896795
$791$	−1.57106e13	−1.42691
$792$	2.81238e12	0.253987
$793$	8.07790e12	0.725386
$794$	−1.83399e12	−0.163759
$795$	−4.56472e12	−0.405286
$796$	9.18798e11	0.0811169
$797$	8.82832e11	0.0775025	0.0387513	−	0.999249i	$-0.487662\pi$
$797$	8.82832e11	0.0775025	0.0387513	+	0.999249i	$0.487662\pi$
$798$	−5.01945e12	−0.438171
$799$	−4.70762e12	−0.408640
$800$	−1.00040e12	−0.0863510
$801$	3.51720e11	0.0301891
$802$	−5.34337e12	−0.456069
$803$	−3.90462e12	−0.331405
$804$	8.13133e11	0.0686293
$805$	6.81530e12	0.572010
$806$	−5.67814e12	−0.473913
$807$	−1.78311e13	−1.47995
$808$	−9.82511e10	−0.00810935
$809$	1.36683e13	1.12188	0.560940	−	0.827856i	$-0.310440\pi$
$809$	1.36683e13	1.12188	0.560940	+	0.827856i	$0.310440\pi$
$810$	−1.08973e12	−0.0889479
$811$	−1.63530e13	−1.32741	−0.663703	−	0.747996i	$-0.731016\pi$
$811$	−1.63530e13	−1.32741	−0.663703	+	0.747996i	$0.731016\pi$
$812$	8.14676e12	0.657632
$813$	4.82326e12	0.387198
$814$	−2.71674e12	−0.216889
$815$	2.86992e12	0.227856
$816$	1.93407e12	0.152710
$817$	−3.26551e13	−2.56420
$818$	4.45232e12	0.347694
$819$	−1.08949e13	−0.846146
$820$	−1.23071e13	−0.950590
$821$	−4.83235e12	−0.371206	−0.185603	−	0.982625i	$-0.559424\pi$
$821$	−4.83235e12	−0.371206	−0.185603	+	0.982625i	$0.559424\pi$
$822$	−2.80561e12	−0.214340
$823$	−1.61695e13	−1.22856	−0.614282	−	0.789087i	$-0.710554\pi$
$823$	−1.61695e13	−1.22856	−0.614282	+	0.789087i	$0.710554\pi$
$824$	−3.88565e12	−0.293623
$825$	−1.67569e12	−0.125937
$826$	5.25198e12	0.392566
$827$	1.37247e13	1.02030	0.510149	−	0.860086i	$-0.329590\pi$
$827$	1.37247e13	1.02030	0.510149	+	0.860086i	$0.329590\pi$
$828$	2.28730e12	0.169117
$829$	2.58304e13	1.89949	0.949743	−	0.313031i	$-0.101344\pi$
$829$	2.58304e13	1.89949	0.949743	+	0.313031i	$0.101344\pi$
$830$	−4.75278e12	−0.347613
$831$	2.05703e11	0.0149636
$832$	−1.27442e13	−0.922060
$833$	3.69773e12	0.266092
$834$	2.07273e12	0.148353
$835$	−2.01299e12	−0.143302
$836$	2.82545e13	2.00060
$837$	2.19324e13	1.54462
$838$	−2.27704e12	−0.159504
$839$	−5.42716e11	−0.0378132	−0.0189066	−	0.999821i	$-0.506019\pi$
$839$	−5.42716e11	−0.0378132	−0.0189066	+	0.999821i	$0.506019\pi$
$840$	−6.91496e12	−0.479218
$841$	−1.11363e13	−0.767645
$842$	1.69764e12	0.116397
$843$	1.24250e13	0.847368
$844$	−2.14928e13	−1.45798
$845$	1.24283e13	0.838604
$846$	2.56142e12	0.171915
$847$	1.39431e13	0.930857
$848$	−7.15054e12	−0.474851
$849$	−1.75824e10	−0.00116143
$850$	−1.14994e11	−0.00755598
$851$	−4.55483e12	−0.297707
$852$	5.03876e12	0.327601
$853$	−1.71048e13	−1.10623	−0.553116	−	0.833104i	$-0.686561\pi$
$853$	−1.71048e13	−1.10623	−0.553116	+	0.833104i	$0.686561\pi$
$854$	2.85140e12	0.183442
$855$	1.02425e13	0.655480
$856$	3.89164e12	0.247743
$857$	−6.06810e12	−0.384272	−0.192136	−	0.981368i	$-0.561542\pi$
$857$	−6.06810e12	−0.384272	−0.192136	+	0.981368i	$0.561542\pi$
$858$	5.12013e12	0.322544
$859$	−1.87986e13	−1.17803	−0.589016	−	0.808122i	$-0.700484\pi$
$859$	−1.87986e13	−1.17803	−0.589016	+	0.808122i	$0.700484\pi$
$860$	−2.18227e13	−1.36040
$861$	1.91661e13	1.18855
$862$	4.71824e12	0.291070
$863$	−6.53337e12	−0.400949	−0.200474	−	0.979699i	$-0.564248\pi$
$863$	−6.53337e12	−0.400949	−0.200474	+	0.979699i	$0.564248\pi$
$864$	−1.18070e13	−0.720820
$865$	1.78077e13	1.08152
$866$	1.60690e12	0.0970862
$867$	7.42742e11	0.0446429
$868$	3.26098e13	1.94989
$869$	−8.60646e12	−0.511960
$870$	−1.38791e12	−0.0821345
$871$	−2.24665e12	−0.132268
$872$	−1.84881e12	−0.108285
$873$	3.43265e12	0.200017
$874$	−2.91159e12	−0.168783
$875$	−2.64615e13	−1.52608
$876$	3.22205e12	0.184869
$877$	−1.60851e13	−0.918178	−0.459089	−	0.888390i	$-0.651824\pi$
$877$	−1.60851e13	−0.918178	−0.459089	+	0.888390i	$0.651824\pi$
$878$	2.98809e12	0.169695
$879$	6.87507e12	0.388443
$880$	1.76500e13	0.992141
$881$	3.30698e13	1.84944	0.924720	−	0.380647i	$-0.124299\pi$
$881$	3.30698e13	1.84944	0.924720	+	0.380647i	$0.124299\pi$
$882$	−2.01194e12	−0.111945
$883$	−7.25465e12	−0.401599	−0.200800	−	0.979632i	$-0.564354\pi$
$883$	−7.25465e12	−0.401599	−0.200800	+	0.979632i	$0.564354\pi$
$884$	−5.71670e12	−0.314855
$885$	1.45574e13	0.797697
$886$	−5.64077e12	−0.307529
$887$	−1.13226e13	−0.614170	−0.307085	−	0.951682i	$-0.599354\pi$
$887$	−1.13226e13	−0.614170	−0.307085	+	0.951682i	$0.599354\pi$
$888$	4.62143e12	0.249412
$889$	1.78774e13	0.959947
$890$	−2.99200e11	−0.0159848
$891$	−9.55274e12	−0.507783
$892$	4.85959e12	0.257015
$893$	5.30482e13	2.79151
$894$	−1.27938e12	−0.0669856
$895$	9.75974e12	0.508434
$896$	−2.31326e13	−1.19905
$897$	8.58432e12	0.442731
$898$	−5.71303e12	−0.293172
$899$	1.34926e13	0.688934
$900$	−1.01798e12	−0.0517187
$901$	−2.74603e12	−0.138817
$902$	6.63105e12	0.333544
$903$	3.39850e13	1.70095
$904$	9.24635e12	0.460482
$905$	−2.58426e13	−1.28061
$906$	4.51609e12	0.222683
$907$	3.43776e13	1.68672	0.843360	−	0.537348i	$-0.180574\pi$
$907$	3.43776e13	1.68672	0.843360	+	0.537348i	$0.180574\pi$
$908$	−3.62585e13	−1.77021
$909$	−1.51457e11	−0.00735788
$910$	9.26802e12	0.448024
$911$	−1.18306e13	−0.569082	−0.284541	−	0.958664i	$-0.591841\pi$
$911$	−1.18306e13	−0.569082	−0.284541	+	0.958664i	$0.591841\pi$
$912$	−2.17942e13	−1.04319
$913$	−4.16637e13	−1.98445
$914$	6.20334e11	0.0294014
$915$	7.90348e12	0.372755
$916$	−3.95230e13	−1.85490
$917$	3.04212e13	1.42074
$918$	−1.35720e12	−0.0630741
$919$	−2.68999e13	−1.24403	−0.622015	−	0.783005i	$-0.713686\pi$
$919$	−2.68999e13	−1.24403	−0.622015	+	0.783005i	$0.713686\pi$
$920$	−4.01110e12	−0.184594
$921$	9.09868e12	0.416687
$922$	5.70533e12	0.260011
$923$	−1.39218e13	−0.631378
$924$	−2.94052e13	−1.32709
$925$	2.02716e12	0.0910436
$926$	6.87248e11	0.0307160
$927$	−5.98985e12	−0.266414
$928$	−7.26356e12	−0.321502
$929$	−9.83481e12	−0.433207	−0.216603	−	0.976260i	$-0.569498\pi$
$929$	−9.83481e12	−0.433207	−0.216603	+	0.976260i	$0.569498\pi$
$930$	−5.55553e12	−0.243530
$931$	−4.16681e13	−1.81773
$932$	2.39876e13	1.04139
$933$	−7.79374e12	−0.336728
$934$	−6.57556e12	−0.282730
$935$	6.77816e12	0.290041
$936$	6.41211e12	0.273061
$937$	9.23144e12	0.391238	0.195619	−	0.980680i	$-0.437328\pi$
$937$	9.23144e12	0.391238	0.195619	+	0.980680i	$0.437328\pi$
$938$	−7.93039e11	−0.0334489
$939$	1.70812e12	0.0717009
$940$	3.54509e13	1.48099
$941$	−1.00553e13	−0.418062	−0.209031	−	0.977909i	$-0.567031\pi$
$941$	−1.00553e13	−0.418062	−0.209031	+	0.977909i	$0.567031\pi$
$942$	3.47622e12	0.143839
$943$	1.11175e13	0.457830
$944$	2.28038e13	0.934617
$945$	−3.57987e13	−1.46024
$946$	1.17581e13	0.477338
$947$	3.28956e13	1.32912	0.664558	−	0.747237i	$-0.268620\pi$
$947$	3.28956e13	1.32912	0.664558	+	0.747237i	$0.268620\pi$
$948$	7.10196e12	0.285588
$949$	−8.90236e12	−0.356293
$950$	1.29582e12	0.0516166
$951$	9.09106e12	0.360414
$952$	−4.15988e12	−0.164140
$953$	−2.79353e13	−1.09707	−0.548537	−	0.836126i	$-0.684815\pi$
$953$	−2.79353e13	−1.09707	−0.548537	+	0.836126i	$0.684815\pi$
$954$	1.49412e12	0.0584006
$955$	−4.62463e13	−1.79913
$956$	1.96028e13	0.759027
$957$	−1.21667e13	−0.468887
$958$	−8.64382e12	−0.331559
$959$	−4.45187e13	−1.69965
$960$	−1.24691e13	−0.473820
$961$	2.75686e13	1.04270
$962$	−6.19404e12	−0.233177
$963$	5.99909e12	0.224785
$964$	1.47571e13	0.550368
$965$	−1.51961e13	−0.564105
$966$	3.03016e12	0.111961
$967$	3.57620e13	1.31523	0.657617	−	0.753352i	$-0.271565\pi$
$967$	3.57620e13	1.31523	0.657617	+	0.753352i	$0.271565\pi$
$968$	−8.20609e12	−0.300398
$969$	−8.36965e12	−0.304965
$970$	−2.92008e12	−0.105906
$971$	−5.49737e12	−0.198458	−0.0992290	−	0.995065i	$-0.531638\pi$
$971$	−5.49737e12	−0.198458	−0.0992290	+	0.995065i	$0.531638\pi$
$972$	−2.04515e13	−0.734897
$973$	3.28896e13	1.17639
$974$	5.11756e12	0.182200
$975$	−3.82051e12	−0.135394
$976$	1.23806e13	0.436736
$977$	−1.41757e13	−0.497759	−0.248879	−	0.968534i	$-0.580062\pi$
$977$	−1.41757e13	−0.497759	−0.248879	+	0.968534i	$0.580062\pi$
$978$	1.27600e12	0.0445990
$979$	−2.62283e12	−0.0912533
$980$	−2.78459e13	−0.964371
$981$	−2.85000e12	−0.0982503
$982$	5.26217e12	0.180577
$983$	4.48632e13	1.53250	0.766248	−	0.642545i	$-0.222121\pi$
$983$	4.48632e13	1.53250	0.766248	+	0.642545i	$0.222121\pi$
$984$	−1.12801e13	−0.383560
$985$	6.51896e12	0.220656
$986$	−8.34936e11	−0.0281324
$987$	−5.52085e13	−1.85173
$988$	6.44191e13	2.15084
$989$	1.97134e13	0.655205
$990$	−3.68800e12	−0.122021
$991$	2.93025e13	0.965101	0.482550	−	0.875868i	$-0.339711\pi$
$991$	2.93025e13	0.965101	0.482550	+	0.875868i	$0.339711\pi$
$992$	−2.90745e13	−0.953257
$993$	6.05454e12	0.197610
$994$	−4.91424e12	−0.159668
$995$	−2.48378e12	−0.0803357
$996$	3.43804e13	1.10699
$997$	1.15625e13	0.370616	0.185308	−	0.982680i	$-0.440672\pi$
$997$	1.15625e13	0.370616	0.185308	+	0.982680i	$0.440672\pi$
$998$	−6.69697e12	−0.213693
$999$	2.39251e13	0.759993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.a.b.1.5	✓	7
3.2	odd	2		153.10.a.f.1.3		7
4.3	odd	2		272.10.a.g.1.4		7
17.16	even	2		289.10.a.b.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.b.1.5	✓	7	1.1	even	1	trivial
153.10.a.f.1.3		7	3.2	odd	2
272.10.a.g.1.4		7	4.3	odd	2
289.10.a.b.1.5		7	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q+5.44491 q^{2} +106.475 q^{3} -482.353 q^{4} +1303.94 q^{5} +579.746 q^{6} +9199.27 q^{7} -5414.17 q^{8} -8346.12 q^{9} +O(q^{10})\)	\(q+5.44491 q^{2} +106.475 q^{3} -482.353 q^{4} +1303.94 q^{5} +579.746 q^{6} +9199.27 q^{7} -5414.17 q^{8} -8346.12 q^{9} +7099.84 q^{10} +62238.4 q^{11} -51358.4 q^{12} +141901. q^{13} +50089.2 q^{14} +138837. q^{15} +217485. q^{16} +83521.0 q^{17} -45443.9 q^{18} -941163. q^{19} -628959. q^{20} +979491. q^{21} +338883. q^{22} +568165. q^{23} -576472. q^{24} -252865. q^{25} +772638. q^{26} -2.98439e6 q^{27} -4.43730e6 q^{28} -1.83597e6 q^{29} +755954. q^{30} -7.34903e6 q^{31} +3.95624e6 q^{32} +6.62682e6 q^{33} +454765. q^{34} +1.19953e7 q^{35} +4.02577e6 q^{36} -8.01674e6 q^{37} -5.12455e6 q^{38} +1.51089e7 q^{39} -7.05975e6 q^{40} +1.95674e7 q^{41} +5.33324e6 q^{42} +3.46966e7 q^{43} -3.00209e7 q^{44} -1.08828e7 q^{45} +3.09361e6 q^{46} -5.63645e7 q^{47} +2.31567e7 q^{48} +4.42730e7 q^{49} -1.37683e6 q^{50} +8.89288e6 q^{51} -6.84463e7 q^{52} -3.28783e7 q^{53} -1.62498e7 q^{54} +8.11551e7 q^{55} -4.98064e7 q^{56} -1.00210e8 q^{57} -9.99672e6 q^{58} +1.04852e8 q^{59} -6.69683e7 q^{60} +5.69264e7 q^{61} -4.00148e7 q^{62} -7.67782e7 q^{63} -8.98109e7 q^{64} +1.85030e8 q^{65} +3.60825e7 q^{66} -1.58325e7 q^{67} -4.02866e7 q^{68} +6.04952e7 q^{69} +6.53134e7 q^{70} -9.81097e7 q^{71} +4.51873e7 q^{72} -6.27365e7 q^{73} -4.36505e7 q^{74} -2.69238e7 q^{75} +4.53973e8 q^{76} +5.72548e8 q^{77} +8.22665e7 q^{78} -1.38282e8 q^{79} +2.83587e8 q^{80} -1.53486e8 q^{81} +1.06543e8 q^{82} -6.69421e8 q^{83} -4.72460e8 q^{84} +1.08906e8 q^{85} +1.88920e8 q^{86} -1.95485e8 q^{87} -3.36969e8 q^{88} -4.21417e7 q^{89} -5.92561e7 q^{90} +1.30538e9 q^{91} -2.74056e8 q^{92} -7.82486e8 q^{93} -3.06900e8 q^{94} -1.22722e9 q^{95} +4.21240e8 q^{96} -4.11288e8 q^{97} +2.41063e8 q^{98} -5.19449e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9}+O(q^{10}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9	\( 7 q - q^{2} + 88 q^{3} + 2389 q^{4} + 1362 q^{5} - 11720 q^{6} + 9388 q^{7} + 16821 q^{8} + 81419 q^{9} + 154226 q^{10} + 135536 q^{11} + 198160 q^{12} + 166122 q^{13} + 447252 q^{14} + 159048 q^{15} + 1463585 q^{16} + 584647 q^{17} + 149027 q^{18} + 777172 q^{19} - 917162 q^{20} - 3412104 q^{21} - 1222520 q^{22} + 1357764 q^{23} - 8487360 q^{24} + 1065785 q^{25} - 14379966 q^{26} - 4519064 q^{27} - 3328892 q^{28} + 967002 q^{29} - 12558992 q^{30} + 3546740 q^{31} + 4825461 q^{32} + 11928016 q^{33} - 83521 q^{34} - 530736 q^{35} + 4535009 q^{36} + 18296498 q^{37} - 49363020 q^{38} + 86306872 q^{39} + 127155062 q^{40} + 10285686 q^{41} + 14620416 q^{42} + 21913204 q^{43} + 96696624 q^{44} + 108916410 q^{45} - 151509484 q^{46} + 56639800 q^{47} - 201398496 q^{48} + 27010351 q^{49} - 261150303 q^{50} + 7349848 q^{51} - 156226378 q^{52} + 121813562 q^{53} - 93375344 q^{54} + 40793128 q^{55} - 196175436 q^{56} + 153612960 q^{57} - 236833910 q^{58} + 29222388 q^{59} - 628643488 q^{60} - 49915846 q^{61} - 73506556 q^{62} - 2185356 q^{63} + 317922057 q^{64} - 122633668 q^{65} - 624886144 q^{66} + 301863420 q^{67} + 199531669 q^{68} + 379683432 q^{69} + 966315960 q^{70} + 652473940 q^{71} + 655760385 q^{72} + 306656342 q^{73} + 249173874 q^{74} + 919071912 q^{75} + 128694700 q^{76} - 102442536 q^{77} + 323434416 q^{78} + 959147884 q^{79} - 692173602 q^{80} - 374486977 q^{81} + 1046441254 q^{82} - 1512945268 q^{83} - 481790592 q^{84} + 113755602 q^{85} - 164953236 q^{86} - 1612550856 q^{87} + 1132038848 q^{88} - 1971327114 q^{89} - 2284664662 q^{90} - 1061062864 q^{91} + 901186756 q^{92} - 798598936 q^{93} + 2534831232 q^{94} - 3249631512 q^{95} - 4442036640 q^{96} + 2006526254 q^{97} - 2170640009 q^{98} - 2579159272 q^{99}+O(q^{100}) \) 7 * q - q^2 + 88 * q^3 + 2389 * q^4 + 1362 * q^5 - 11720 * q^6 + 9388 * q^7 + 16821 * q^8 + 81419 * q^9 + 154226 * q^10 + 135536 * q^11 + 198160 * q^12 + 166122 * q^13 + 447252 * q^14 + 159048 * q^15 + 1463585 * q^16 + 584647 * q^17 + 149027 * q^18 + 777172 * q^19 - 917162 * q^20 - 3412104 * q^21 - 1222520 * q^22 + 1357764 * q^23 - 8487360 * q^24 + 1065785 * q^25 - 14379966 * q^26 - 4519064 * q^27 - 3328892 * q^28 + 967002 * q^29 - 12558992 * q^30 + 3546740 * q^31 + 4825461 * q^32 + 11928016 * q^33 - 83521 * q^34 - 530736 * q^35 + 4535009 * q^36 + 18296498 * q^37 - 49363020 * q^38 + 86306872 * q^39 + 127155062 * q^40 + 10285686 * q^41 + 14620416 * q^42 + 21913204 * q^43 + 96696624 * q^44 + 108916410 * q^45 - 151509484 * q^46 + 56639800 * q^47 - 201398496 * q^48 + 27010351 * q^49 - 261150303 * q^50 + 7349848 * q^51 - 156226378 * q^52 + 121813562 * q^53 - 93375344 * q^54 + 40793128 * q^55 - 196175436 * q^56 + 153612960 * q^57 - 236833910 * q^58 + 29222388 * q^59 - 628643488 * q^60 - 49915846 * q^61 - 73506556 * q^62 - 2185356 * q^63 + 317922057 * q^64 - 122633668 * q^65 - 624886144 * q^66 + 301863420 * q^67 + 199531669 * q^68 + 379683432 * q^69 + 966315960 * q^70 + 652473940 * q^71 + 655760385 * q^72 + 306656342 * q^73 + 249173874 * q^74 + 919071912 * q^75 + 128694700 * q^76 - 102442536 * q^77 + 323434416 * q^78 + 959147884 * q^79 - 692173602 * q^80 - 374486977 * q^81 + 1046441254 * q^82 - 1512945268 * q^83 - 481790592 * q^84 + 113755602 * q^85 - 164953236 * q^86 - 1612550856 * q^87 + 1132038848 * q^88 - 1971327114 * q^89 - 2284664662 * q^90 - 1061062864 * q^91 + 901186756 * q^92 - 798598936 * q^93 + 2534831232 * q^94 - 3249631512 * q^95 - 4442036640 * q^96 + 2006526254 * q^97 - 2170640009 * q^98 - 2579159272 * q^99

Introduction

L-functions

Modular forms

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