LMFDB - Embedded newform 19.12.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,12,Mod(1,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("19.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	19.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:	$14.5985204306$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3 x^{8} - 14682 x^{7} - 159158 x^{6} + 62351712 x^{5} + 1328163744 x^{4} - 57315079008 x^{3} + \cdots + 22065977221632 $ x^9 - 3x^8 - 14682x^7 - 159158x^6 + 62351712x^5 + 1328163744x^4 - 57315079008x^3 - 1216480603104x^2 - 215404261632x + 22065977221632
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-18.7044$ of defining polynomial
Character	$\chi$	$=$	19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+28.7044 q^{2} -650.711 q^{3} -1224.06 q^{4} -7939.47 q^{5} -18678.3 q^{6} +45630.6 q^{7} -93922.4 q^{8} +246277. q^{9} +O(q^{10})$	\(q+28.7044 q^{2} -650.711 q^{3} -1224.06 q^{4} -7939.47 q^{5} -18678.3 q^{6} +45630.6 q^{7} -93922.4 q^{8} +246277. q^{9} -227898. q^{10} +460302. q^{11} +796507. q^{12} +271614. q^{13} +1.30980e6 q^{14} +5.16630e6 q^{15} -189117. q^{16} -1.02833e7 q^{17} +7.06925e6 q^{18} -2.47610e6 q^{19} +9.71837e6 q^{20} -2.96923e7 q^{21} +1.32127e7 q^{22} +5.53882e7 q^{23} +6.11163e7 q^{24} +1.42070e7 q^{25} +7.79653e6 q^{26} -4.49839e7 q^{27} -5.58545e7 q^{28} +1.52134e8 q^{29} +1.48295e8 q^{30} -1.26421e8 q^{31} +1.86925e8 q^{32} -2.99524e8 q^{33} -2.95177e8 q^{34} -3.62283e8 q^{35} -3.01458e8 q^{36} -2.35220e8 q^{37} -7.10749e7 q^{38} -1.76742e8 q^{39} +7.45694e8 q^{40} +6.71114e8 q^{41} -8.52300e8 q^{42} +7.17145e8 q^{43} -5.63437e8 q^{44} -1.95531e9 q^{45} +1.58989e9 q^{46} -1.83199e9 q^{47} +1.23060e8 q^{48} +1.04824e8 q^{49} +4.07804e8 q^{50} +6.69148e9 q^{51} -3.32472e8 q^{52} +1.08618e9 q^{53} -1.29124e9 q^{54} -3.65456e9 q^{55} -4.28574e9 q^{56} +1.61122e9 q^{57} +4.36693e9 q^{58} +8.08476e9 q^{59} -6.32385e9 q^{60} +9.74498e9 q^{61} -3.62883e9 q^{62} +1.12378e10 q^{63} +5.75287e9 q^{64} -2.15647e9 q^{65} -8.59765e9 q^{66} +1.92927e9 q^{67} +1.25874e10 q^{68} -3.60417e10 q^{69} -1.03991e10 q^{70} +2.56789e9 q^{71} -2.31310e10 q^{72} +6.72739e9 q^{73} -6.75185e9 q^{74} -9.24466e9 q^{75} +3.03089e9 q^{76} +2.10039e10 q^{77} -5.07328e9 q^{78} -1.48304e9 q^{79} +1.50149e9 q^{80} -1.43558e10 q^{81} +1.92639e10 q^{82} +4.47182e8 q^{83} +3.63451e10 q^{84} +8.16442e10 q^{85} +2.05852e10 q^{86} -9.89955e10 q^{87} -4.32327e10 q^{88} -2.57353e10 q^{89} -5.61260e10 q^{90} +1.23939e10 q^{91} -6.77984e10 q^{92} +8.22633e10 q^{93} -5.25863e10 q^{94} +1.96589e10 q^{95} -1.21634e11 q^{96} +1.17705e11 q^{97} +3.00892e9 q^{98} +1.13362e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 87 q^{2} + 496 q^{3} + 11781 q^{4} + 2114 q^{5} + 84181 q^{6} - 19080 q^{7} - 76701 q^{8} + 632433 q^{9}+O(q^{10}) $ 9 * q + 87 * q^2 + 496 * q^3 + 11781 * q^4 + 2114 * q^5 + 84181 * q^6 - 19080 * q^7 - 76701 * q^8 + 632433 * q^9	\( 9 q + 87 q^{2} + 496 q^{3} + 11781 q^{4} + 2114 q^{5} + 84181 q^{6} - 19080 q^{7} - 76701 q^{8} + 632433 q^{9} - 268428 q^{10} + 175744 q^{11} + 3993305 q^{12} + 809154 q^{13} + 7041403 q^{14} + 4320440 q^{15} + 29590233 q^{16} + 13162874 q^{17} + 51670980 q^{18} - 22284891 q^{19} + 692380 q^{20} + 75424388 q^{21} + 63849138 q^{22} + 114786388 q^{23} + 310823511 q^{24} + 199152003 q^{25} + 97437497 q^{26} + 229481236 q^{27} - 224392209 q^{28} + 54612914 q^{29} - 327673696 q^{30} - 226600416 q^{31} + 346094139 q^{32} - 842576368 q^{33} - 790592985 q^{34} - 1068615828 q^{35} - 472860258 q^{36} - 371753970 q^{37} - 215420613 q^{38} - 1611645716 q^{39} - 4563855672 q^{40} + 504959690 q^{41} - 3956969929 q^{42} - 1620951792 q^{43} - 3829267498 q^{44} - 1391906830 q^{45} + 497259759 q^{46} - 1965882540 q^{47} + 3995891285 q^{48} + 7865370753 q^{49} + 13293164621 q^{50} + 8348428708 q^{51} - 7643204427 q^{52} + 14154895258 q^{53} + 3906695191 q^{54} + 8109135852 q^{55} + 24205597101 q^{56} - 1228145104 q^{57} + 14070688173 q^{58} + 22029386080 q^{59} - 20596280480 q^{60} - 1263984246 q^{61} - 11298124604 q^{62} + 10540367284 q^{63} + 24443845113 q^{64} + 14545843500 q^{65} - 34605988558 q^{66} + 14718513264 q^{67} - 73374346541 q^{68} + 18897730596 q^{69} - 75583659360 q^{70} + 34967811888 q^{71} + 27091585794 q^{72} + 18297073746 q^{73} - 85279476938 q^{74} + 95893305816 q^{75} - 29170922319 q^{76} + 2899255276 q^{77} - 205276367351 q^{78} - 15944238816 q^{79} - 286349413472 q^{80} - 41171883423 q^{81} - 201183193836 q^{82} - 2858023276 q^{83} - 15014021321 q^{84} + 234418807008 q^{85} - 66508042032 q^{86} + 81522171444 q^{87} - 171289266282 q^{88} + 207569871794 q^{89} - 127219826428 q^{90} + 285870230676 q^{91} + 184876887431 q^{92} + 122416682512 q^{93} + 234051593712 q^{94} - 5234473286 q^{95} + 498857169575 q^{96} + 58127902530 q^{97} - 279728403320 q^{98} + 188514162376 q^{99}+O(q^{100}) \) 9 * q + 87 * q^2 + 496 * q^3 + 11781 * q^4 + 2114 * q^5 + 84181 * q^6 - 19080 * q^7 - 76701 * q^8 + 632433 * q^9 - 268428 * q^10 + 175744 * q^11 + 3993305 * q^12 + 809154 * q^13 + 7041403 * q^14 + 4320440 * q^15 + 29590233 * q^16 + 13162874 * q^17 + 51670980 * q^18 - 22284891 * q^19 + 692380 * q^20 + 75424388 * q^21 + 63849138 * q^22 + 114786388 * q^23 + 310823511 * q^24 + 199152003 * q^25 + 97437497 * q^26 + 229481236 * q^27 - 224392209 * q^28 + 54612914 * q^29 - 327673696 * q^30 - 226600416 * q^31 + 346094139 * q^32 - 842576368 * q^33 - 790592985 * q^34 - 1068615828 * q^35 - 472860258 * q^36 - 371753970 * q^37 - 215420613 * q^38 - 1611645716 * q^39 - 4563855672 * q^40 + 504959690 * q^41 - 3956969929 * q^42 - 1620951792 * q^43 - 3829267498 * q^44 - 1391906830 * q^45 + 497259759 * q^46 - 1965882540 * q^47 + 3995891285 * q^48 + 7865370753 * q^49 + 13293164621 * q^50 + 8348428708 * q^51 - 7643204427 * q^52 + 14154895258 * q^53 + 3906695191 * q^54 + 8109135852 * q^55 + 24205597101 * q^56 - 1228145104 * q^57 + 14070688173 * q^58 + 22029386080 * q^59 - 20596280480 * q^60 - 1263984246 * q^61 - 11298124604 * q^62 + 10540367284 * q^63 + 24443845113 * q^64 + 14545843500 * q^65 - 34605988558 * q^66 + 14718513264 * q^67 - 73374346541 * q^68 + 18897730596 * q^69 - 75583659360 * q^70 + 34967811888 * q^71 + 27091585794 * q^72 + 18297073746 * q^73 - 85279476938 * q^74 + 95893305816 * q^75 - 29170922319 * q^76 + 2899255276 * q^77 - 205276367351 * q^78 - 15944238816 * q^79 - 286349413472 * q^80 - 41171883423 * q^81 - 201183193836 * q^82 - 2858023276 * q^83 - 15014021321 * q^84 + 234418807008 * q^85 - 66508042032 * q^86 + 81522171444 * q^87 - 171289266282 * q^88 + 207569871794 * q^89 - 127219826428 * q^90 + 285870230676 * q^91 + 184876887431 * q^92 + 122416682512 * q^93 + 234051593712 * q^94 - 5234473286 * q^95 + 498857169575 * q^96 + 58127902530 * q^97 - 279728403320 * q^98 + 188514162376 * 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 $

$2$	28.7044	0.634284	0.317142	−	0.948378i	$-0.397277\pi$
$2$	28.7044	0.634284	0.317142	+	0.948378i	$0.397277\pi$
$3$	−650.711	−1.54604	−0.773021	−	0.634381i	$-0.781255\pi$
$3$	−650.711	−1.54604	−0.773021	+	0.634381i	$0.781255\pi$
$4$	−1224.06	−0.597684
$5$	−7939.47	−1.13620	−0.568102	−	0.822958i	$-0.692322\pi$
$5$	−7939.47	−1.13620	−0.568102	+	0.822958i	$0.692322\pi$
$6$	−18678.3	−0.980629
$7$	45630.6	1.02616	0.513082	−	0.858340i	$-0.328504\pi$
$7$	45630.6	1.02616	0.513082	+	0.858340i	$0.328504\pi$
$8$	−93922.4	−1.01338
$9$	246277.	1.39024
$10$	−227898.	−0.720676
$11$	460302.	0.861754	0.430877	−	0.902411i	$-0.358204\pi$
$11$	460302.	0.861754	0.430877	+	0.902411i	$0.358204\pi$
$12$	796507.	0.924045
$13$	271614.	0.202892	0.101446	−	0.994841i	$-0.467653\pi$
$13$	271614.	0.202892	0.101446	+	0.994841i	$0.467653\pi$
$14$	1.30980e6	0.650879
$15$	5.16630e6	1.75662
$16$	−189117.	−0.0450890
$17$	−1.02833e7	−1.75657	−0.878284	−	0.478139i	$-0.841311\pi$
$17$	−1.02833e7	−1.75657	−0.878284	+	0.478139i	$0.841311\pi$
$18$	7.06925e6	0.881809
$19$	−2.47610e6	−0.229416
$19$	−2.47610e6	−0.229416
$20$	9.71837e6	0.679091
$21$	−2.96923e7	−1.58649
$22$	1.32127e7	0.546597
$23$	5.53882e7	1.79438	0.897190	−	0.441644i	$-0.145605\pi$
$23$	5.53882e7	1.79438	0.897190	+	0.441644i	$0.145605\pi$
$24$	6.11163e7	1.56673
$25$	1.42070e7	0.290960
$26$	7.79653e6	0.128691
$27$	−4.49839e7	−0.603332
$28$	−5.58545e7	−0.613322
$29$	1.52134e8	1.37733	0.688666	−	0.725079i	$-0.258197\pi$
$29$	1.52134e8	1.37733	0.688666	+	0.725079i	$0.258197\pi$
$30$	1.48295e8	1.11419
$31$	−1.26421e8	−0.793101	−0.396551	−	0.918013i	$-0.629793\pi$
$31$	−1.26421e8	−0.793101	−0.396551	+	0.918013i	$0.629793\pi$
$32$	1.86925e8	0.984786
$33$	−2.99524e8	−1.33231
$34$	−2.95177e8	−1.11416
$35$	−3.62283e8	−1.16593
$36$	−3.01458e8	−0.830927
$37$	−2.35220e8	−0.557654	−0.278827	−	0.960341i	$-0.589946\pi$
$37$	−2.35220e8	−0.557654	−0.278827	+	0.960341i	$0.589946\pi$
$38$	−7.10749e7	−0.145515
$39$	−1.76742e8	−0.313679
$40$	7.45694e8	1.15141
$41$	6.71114e8	0.904659	0.452330	−	0.891851i	$-0.350593\pi$
$41$	6.71114e8	0.904659	0.452330	+	0.891851i	$0.350593\pi$
$42$	−8.52300e8	−1.00629
$43$	7.17145e8	0.743927	0.371964	−	0.928247i	$-0.378685\pi$
$43$	7.17145e8	0.743927	0.371964	+	0.928247i	$0.378685\pi$
$44$	−5.63437e8	−0.515057
$45$	−1.95531e9	−1.57960
$46$	1.58989e9	1.13815
$47$	−1.83199e9	−1.16516	−0.582580	−	0.812773i	$-0.697957\pi$
$47$	−1.83199e9	−1.16516	−0.582580	+	0.812773i	$0.697957\pi$
$48$	1.23060e8	0.0697095
$49$	1.04824e8	0.0530131
$50$	4.07804e8	0.184551
$51$	6.69148e9	2.71573
$52$	−3.32472e8	−0.121265
$53$	1.08618e9	0.356767	0.178383	−	0.983961i	$-0.442913\pi$
$53$	1.08618e9	0.356767	0.178383	+	0.983961i	$0.442913\pi$
$54$	−1.29124e9	−0.382684
$55$	−3.65456e9	−0.979129
$56$	−4.28574e9	−1.03990
$57$	1.61122e9	0.354686
$58$	4.36693e9	0.873618
$59$	8.08476e9	1.47225	0.736124	−	0.676846i	$-0.236654\pi$
$59$	8.08476e9	1.47225	0.736124	+	0.676846i	$0.236654\pi$
$60$	−6.32385e9	−1.04990
$61$	9.74498e9	1.47729	0.738647	−	0.674092i	$-0.235465\pi$
$61$	9.74498e9	1.47729	0.738647	+	0.674092i	$0.235465\pi$
$62$	−3.62883e9	−0.503051
$63$	1.12378e10	1.42662
$64$	5.75287e9	0.669722
$65$	−2.15647e9	−0.230526
$66$	−8.59765e9	−0.845061
$67$	1.92927e9	0.174575	0.0872873	−	0.996183i	$-0.472180\pi$
$67$	1.92927e9	0.174575	0.0872873	+	0.996183i	$0.472180\pi$
$68$	1.25874e10	1.04987
$69$	−3.60417e10	−2.77419
$70$	−1.03991e10	−0.739532
$71$	2.56789e9	0.168910	0.0844550	−	0.996427i	$-0.473085\pi$
$71$	2.56789e9	0.168910	0.0844550	+	0.996427i	$0.473085\pi$
$72$	−2.31310e10	−1.40885
$73$	6.72739e9	0.379814	0.189907	−	0.981802i	$-0.439181\pi$
$73$	6.72739e9	0.379814	0.189907	+	0.981802i	$0.439181\pi$
$74$	−6.75185e9	−0.353711
$75$	−9.24466e9	−0.449836
$76$	3.03089e9	0.137118
$77$	2.10039e10	0.884301
$78$	−5.07328e9	−0.198961
$79$	−1.48304e9	−0.0542255	−0.0271128	−	0.999632i	$-0.508631\pi$
$79$	−1.48304e9	−0.0542255	−0.0271128	+	0.999632i	$0.508631\pi$
$80$	1.50149e9	0.0512303
$81$	−1.43558e10	−0.457467
$82$	1.92639e10	0.573810
$83$	4.47182e8	0.0124611	0.00623053	−	0.999981i	$-0.498017\pi$
$83$	4.47182e8	0.0124611	0.00623053	+	0.999981i	$0.498017\pi$
$84$	3.63451e10	0.948222
$85$	8.16442e10	1.99582
$86$	2.05852e10	0.471861
$87$	−9.89955e10	−2.12941
$88$	−4.32327e10	−0.873289
$89$	−2.57353e10	−0.488523	−0.244261	−	0.969709i	$-0.578545\pi$
$89$	−2.57353e10	−0.488523	−0.244261	+	0.969709i	$0.578545\pi$
$90$	−5.61260e10	−1.00191
$91$	1.23939e10	0.208200
$92$	−6.77984e10	−1.07247
$93$	8.22633e10	1.22617
$94$	−5.25863e10	−0.739042
$95$	1.96589e10	0.260663
$96$	−1.21634e11	−1.52252
$97$	1.17705e11	1.39171	0.695857	−	0.718181i	$-0.255025\pi$
$97$	1.17705e11	1.39171	0.695857	+	0.718181i	$0.255025\pi$
$98$	3.00892e9	0.0336253
$99$	1.13362e11	1.19805
$100$	−1.73902e10	−0.173902
$101$	1.07656e11	1.01923	0.509613	−	0.860404i	$-0.329789\pi$
$101$	1.07656e11	1.01923	0.509613	+	0.860404i	$0.329789\pi$
$102$	1.92075e11	1.72254
$103$	−1.32577e10	−0.112684	−0.0563422	−	0.998412i	$-0.517944\pi$
$103$	−1.32577e10	−0.112684	−0.0563422	+	0.998412i	$0.517944\pi$
$104$	−2.55107e10	−0.205607
$105$	2.35741e11	1.80258
$106$	3.11782e10	0.226291
$107$	−1.68238e10	−0.115961	−0.0579806	−	0.998318i	$-0.518466\pi$
$107$	−1.68238e10	−0.115961	−0.0579806	+	0.998318i	$0.518466\pi$
$108$	5.50629e10	0.360602
$109$	−3.08574e11	−1.92094	−0.960471	−	0.278381i	$-0.910202\pi$
$109$	−3.08574e11	−1.92094	−0.960471	+	0.278381i	$0.910202\pi$
$110$	−1.04902e11	−0.621045
$111$	1.53060e11	0.862156
$112$	−8.62952e9	−0.0462687
$113$	3.60156e11	1.83890	0.919452	−	0.393203i	$-0.128633\pi$
$113$	3.60156e11	1.83890	0.919452	+	0.393203i	$0.128633\pi$
$114$	4.62492e10	0.224972
$115$	−4.39753e11	−2.03878
$116$	−1.86221e11	−0.823209
$117$	6.68925e10	0.282069
$118$	2.32068e11	0.933823
$119$	−4.69235e11	−1.80253
$120$	−4.85231e11	−1.78013
$121$	−7.34334e10	−0.257380
$122$	2.79724e11	0.937023
$123$	−4.36701e11	−1.39864
$124$	1.54746e11	0.474024
$125$	2.74873e11	0.805614
$126$	3.22574e11	0.904880
$127$	−3.26977e11	−0.878206	−0.439103	−	0.898437i	$-0.644704\pi$
$127$	−3.26977e11	−0.878206	−0.439103	+	0.898437i	$0.644704\pi$
$128$	−2.17689e11	−0.559992
$129$	−4.66654e11	−1.15014
$130$	−6.19003e10	−0.146219
$131$	−6.76850e11	−1.53285	−0.766426	−	0.642333i	$-0.777967\pi$
$131$	−6.76850e11	−1.53285	−0.766426	+	0.642333i	$0.777967\pi$
$132$	3.66634e11	0.796299
$133$	−1.12986e11	−0.235418
$134$	5.53784e10	0.110730
$135$	3.57148e11	0.685509
$136$	9.65836e11	1.78008
$137$	−1.56106e11	−0.276347	−0.138174	−	0.990408i	$-0.544123\pi$
$137$	−1.56106e11	−0.276347	−0.138174	+	0.990408i	$0.544123\pi$
$138$	−1.03456e12	−1.75962
$139$	9.11667e11	1.49024	0.745118	−	0.666933i	$-0.232393\pi$
$139$	9.11667e11	1.49024	0.745118	+	0.666933i	$0.232393\pi$
$140$	4.43455e11	0.696859
$141$	1.19210e12	1.80139
$142$	7.37097e10	0.107137
$143$	1.25025e11	0.174843
$144$	−4.65753e10	−0.0626847
$145$	−1.20787e12	−1.56493
$146$	1.93106e11	0.240910
$147$	−6.82102e10	−0.0819604
$148$	2.87923e11	0.333301
$149$	1.67514e12	1.86864	0.934321	−	0.356432i	$-0.116007\pi$
$149$	1.67514e12	1.86864	0.934321	+	0.356432i	$0.116007\pi$
$150$	−2.65363e11	−0.285324
$151$	2.51272e11	0.260478	0.130239	−	0.991483i	$-0.458426\pi$
$151$	2.51272e11	0.260478	0.130239	+	0.991483i	$0.458426\pi$
$152$	2.32561e11	0.232486
$153$	−2.53255e12	−2.44206
$154$	6.02903e11	0.560898
$155$	1.00371e12	0.901125
$156$	2.16343e11	0.187481
$157$	−1.35978e12	−1.13768	−0.568840	−	0.822448i	$-0.692608\pi$
$157$	−1.35978e12	−1.13768	−0.568840	+	0.822448i	$0.692608\pi$
$158$	−4.25698e10	−0.0343944
$159$	−7.06789e11	−0.551576
$160$	−1.48408e12	−1.11892
$161$	2.52740e12	1.84133
$162$	−4.12074e11	−0.290164
$163$	4.54739e11	0.309549	0.154775	−	0.987950i	$-0.450535\pi$
$163$	4.54739e11	0.309549	0.154775	+	0.987950i	$0.450535\pi$
$164$	−8.21482e11	−0.540701
$165$	2.37806e12	1.51377
$166$	1.28361e10	0.00790384
$167$	−1.07795e12	−0.642182	−0.321091	−	0.947048i	$-0.604050\pi$
$167$	−1.07795e12	−0.642182	−0.321091	+	0.947048i	$0.604050\pi$
$168$	2.78877e12	1.60773
$169$	−1.71839e12	−0.958835
$170$	2.34355e12	1.26592
$171$	−6.09807e11	−0.318944
$172$	−8.77827e11	−0.444634
$173$	1.60774e12	0.788792	0.394396	−	0.918941i	$-0.370954\pi$
$173$	1.60774e12	0.788792	0.394396	+	0.918941i	$0.370954\pi$
$174$	−2.84161e12	−1.35065
$175$	6.48275e11	0.298573
$176$	−8.70510e10	−0.0388556
$177$	−5.26084e12	−2.27616
$178$	−7.38717e11	−0.309862
$179$	3.55865e11	0.144742	0.0723709	−	0.997378i	$-0.476943\pi$
$179$	3.55865e11	0.144742	0.0723709	+	0.997378i	$0.476943\pi$
$180$	2.39341e12	0.944102
$181$	2.27977e12	0.872288	0.436144	−	0.899877i	$-0.356344\pi$
$181$	2.27977e12	0.872288	0.436144	+	0.899877i	$0.356344\pi$
$182$	3.55760e11	0.132058
$183$	−6.34116e12	−2.28396
$184$	−5.20220e12	−1.81840
$185$	1.86752e12	0.633609
$186$	2.36132e12	0.777738
$187$	−4.73344e12	−1.51373
$188$	2.24247e12	0.696398
$189$	−2.05264e12	−0.619118
$190$	5.64297e11	0.165334
$191$	5.54734e12	1.57907	0.789535	−	0.613706i	$-0.210322\pi$
$191$	5.54734e12	1.57907	0.789535	+	0.613706i	$0.210322\pi$
$192$	−3.74346e12	−1.03542
$193$	6.67855e11	0.179522	0.0897609	−	0.995963i	$-0.471390\pi$
$193$	6.67855e11	0.179522	0.0897609	+	0.995963i	$0.471390\pi$
$194$	3.37865e12	0.882741
$195$	1.40324e12	0.356403
$196$	−1.28311e11	−0.0316851
$197$	−1.04820e11	−0.0251698	−0.0125849	−	0.999921i	$-0.504006\pi$
$197$	−1.04820e11	−0.0251698	−0.0125849	+	0.999921i	$0.504006\pi$
$198$	3.25399e12	0.759902
$199$	−5.61949e12	−1.27645	−0.638227	−	0.769848i	$-0.720332\pi$
$199$	−5.61949e12	−1.27645	−0.638227	+	0.769848i	$0.720332\pi$
$200$	−1.33436e12	−0.294854
$201$	−1.25539e12	−0.269899
$202$	3.09020e12	0.646478
$203$	6.94198e12	1.41337
$204$	−8.19075e12	−1.62315
$205$	−5.32829e12	−1.02788
$206$	−3.80555e11	−0.0714739
$207$	1.36409e13	2.49463
$208$	−5.13669e10	−0.00914819
$209$	−1.13975e12	−0.197700
$210$	6.76681e12	1.14335
$211$	1.18463e13	1.94997	0.974984	−	0.222273i	$-0.0713478\pi$
$211$	1.18463e13	1.94997	0.974984	+	0.222273i	$0.0713478\pi$
$212$	−1.32955e12	−0.213234
$213$	−1.67095e12	−0.261142
$214$	−4.82916e11	−0.0735522
$215$	−5.69375e12	−0.845253
$216$	4.22500e12	0.611408
$217$	−5.76865e12	−0.813852
$218$	−8.85744e12	−1.21842
$219$	−4.37759e12	−0.587208
$220$	4.47339e12	0.585210
$221$	−2.79310e12	−0.356393
$222$	4.39350e12	0.546851
$223$	7.33855e11	0.0891114	0.0445557	−	0.999007i	$-0.485813\pi$
$223$	7.33855e11	0.0891114	0.0445557	+	0.999007i	$0.485813\pi$
$224$	8.52948e12	1.01055
$225$	3.49887e12	0.404505
$226$	1.03381e13	1.16639
$227$	6.70230e12	0.738043	0.369022	−	0.929421i	$-0.379693\pi$
$227$	6.70230e12	0.738043	0.369022	+	0.929421i	$0.379693\pi$
$228$	−1.97223e12	−0.211990
$229$	−4.03423e12	−0.423317	−0.211658	−	0.977344i	$-0.567886\pi$
$229$	−4.03423e12	−0.423317	−0.211658	+	0.977344i	$0.567886\pi$
$230$	−1.26229e13	−1.29317
$231$	−1.36674e13	−1.36717
$232$	−1.42888e13	−1.39577
$233$	1.44144e13	1.37511	0.687557	−	0.726130i	$-0.258683\pi$
$233$	1.44144e13	1.37511	0.687557	+	0.726130i	$0.258683\pi$
$234$	1.92011e12	0.178912
$235$	1.45451e13	1.32386
$236$	−9.89621e12	−0.879940
$237$	9.65030e11	0.0838349
$238$	−1.34691e13	−1.14331
$239$	8.81297e12	0.731027	0.365514	−	0.930806i	$-0.380893\pi$
$239$	8.81297e12	0.731027	0.365514	+	0.930806i	$0.380893\pi$
$240$	−9.77035e11	−0.0792042
$241$	1.14369e13	0.906182	0.453091	−	0.891464i	$-0.350321\pi$
$241$	1.14369e13	0.906182	0.453091	+	0.891464i	$0.350321\pi$
$242$	−2.10786e12	−0.163252
$243$	1.73102e13	1.31059
$244$	−1.19284e13	−0.882956
$245$	−8.32248e11	−0.0602337
$246$	−1.25352e13	−0.887134
$247$	−6.72544e11	−0.0465466
$248$	1.18737e13	0.803717
$249$	−2.90986e11	−0.0192653
$250$	7.89007e12	0.510988
$251$	−2.17386e13	−1.37729	−0.688646	−	0.725098i	$-0.741795\pi$
$251$	−2.17386e13	−1.37729	−0.688646	+	0.725098i	$0.741795\pi$
$252$	−1.37557e13	−0.852667
$253$	2.54953e13	1.54632
$254$	−9.38567e12	−0.557031
$255$	−5.31268e13	−3.08562
$256$	−1.80305e13	−1.02492
$257$	−2.15069e12	−0.119659	−0.0598295	−	0.998209i	$-0.519056\pi$
$257$	−2.15069e12	−0.119659	−0.0598295	+	0.998209i	$0.519056\pi$
$258$	−1.33950e13	−0.729516
$259$	−1.07332e13	−0.572245
$260$	2.63965e12	0.137782
$261$	3.74673e13	1.91483
$262$	−1.94286e13	−0.972262
$263$	−2.28835e13	−1.12142	−0.560708	−	0.828014i	$-0.689471\pi$
$263$	−2.28835e13	−1.12142	−0.560708	+	0.828014i	$0.689471\pi$
$264$	2.81320e13	1.35014
$265$	−8.62369e12	−0.405360
$266$	−3.24319e12	−0.149322
$267$	1.67463e13	0.755276
$268$	−2.36153e12	−0.104340
$269$	3.52078e13	1.52406	0.762029	−	0.647543i	$-0.224203\pi$
$269$	3.52078e13	1.52406	0.762029	+	0.647543i	$0.224203\pi$
$270$	1.02517e13	0.434807
$271$	−6.79523e12	−0.282405	−0.141203	−	0.989981i	$-0.545097\pi$
$271$	−6.79523e12	−0.282405	−0.141203	+	0.989981i	$0.545097\pi$
$272$	1.94475e12	0.0792019
$273$	−8.06486e12	−0.321886
$274$	−4.48092e12	−0.175283
$275$	6.53953e12	0.250736
$276$	4.41172e13	1.65809
$277$	−5.29819e12	−0.195204	−0.0976020	−	0.995226i	$-0.531117\pi$
$277$	−5.29819e12	−0.195204	−0.0976020	+	0.995226i	$0.531117\pi$
$278$	2.61689e13	0.945232
$279$	−3.11346e13	−1.10260
$280$	3.40265e13	1.18154
$281$	2.18797e13	0.745000	0.372500	−	0.928032i	$-0.378501\pi$
$281$	2.18797e13	0.745000	0.372500	+	0.928032i	$0.378501\pi$
$282$	3.42184e13	1.14259
$283$	2.20518e12	0.0722135	0.0361067	−	0.999348i	$-0.488504\pi$
$283$	2.20518e12	0.0722135	0.0361067	+	0.999348i	$0.488504\pi$
$284$	−3.14325e12	−0.100955
$285$	−1.27923e13	−0.402996
$286$	3.58876e12	0.110900
$287$	3.06233e13	0.928329
$288$	4.60353e13	1.36909
$289$	7.14751e13	2.08553
$290$	−3.46711e13	−0.992609
$291$	−7.65918e13	−2.15165
$292$	−8.23471e12	−0.227009
$293$	−4.68014e12	−0.126615	−0.0633077	−	0.997994i	$-0.520165\pi$
$293$	−4.68014e12	−0.126615	−0.0633077	+	0.997994i	$0.520165\pi$
$294$	−1.95793e12	−0.0519861
$295$	−6.41887e13	−1.67278
$296$	2.20924e13	0.565118
$297$	−2.07062e13	−0.519924
$298$	4.80838e13	1.18525
$299$	1.50442e13	0.364065
$300$	1.13160e13	0.268860
$301$	3.27237e13	0.763391
$302$	7.21260e12	0.165217
$303$	−7.00528e13	−1.57576
$304$	4.68272e11	0.0103441
$305$	−7.73700e13	−1.67851
$306$	−7.26954e13	−1.54896
$307$	−3.73145e13	−0.780938	−0.390469	−	0.920616i	$-0.627687\pi$
$307$	−3.73145e13	−0.780938	−0.390469	+	0.920616i	$0.627687\pi$
$308$	−2.57099e13	−0.528533
$309$	8.62694e12	0.174215
$310$	2.88110e13	0.571569
$311$	−2.76421e13	−0.538753	−0.269376	−	0.963035i	$-0.586818\pi$
$311$	−2.76421e13	−0.538753	−0.269376	+	0.963035i	$0.586818\pi$
$312$	1.66001e13	0.317878
$313$	−9.38605e12	−0.176599	−0.0882997	−	0.996094i	$-0.528143\pi$
$313$	−9.38605e12	−0.176599	−0.0882997	+	0.996094i	$0.528143\pi$
$314$	−3.90316e13	−0.721612
$315$	−8.92220e13	−1.62093
$316$	1.81533e12	0.0324098
$317$	8.90245e13	1.56201	0.781005	−	0.624525i	$-0.214708\pi$
$317$	8.90245e13	1.56201	0.781005	+	0.624525i	$0.214708\pi$
$318$	−2.02880e13	−0.349856
$319$	7.00278e13	1.18692
$320$	−4.56747e13	−0.760941
$321$	1.09474e13	0.179281
$322$	7.25475e13	1.16792
$323$	2.54626e13	0.402984
$324$	1.75723e13	0.273421
$325$	3.85883e12	0.0590334
$326$	1.30530e13	0.196342
$327$	2.00793e14	2.96985
$328$	−6.30326e13	−0.916768
$329$	−8.35949e13	−1.19565
$330$	6.82607e13	0.960162
$331$	1.31792e14	1.82320	0.911599	−	0.411080i	$-0.134848\pi$
$331$	1.31792e14	1.82320	0.911599	+	0.411080i	$0.134848\pi$
$332$	−5.47377e11	−0.00744778
$333$	−5.79294e13	−0.775275
$334$	−3.09419e13	−0.407326
$335$	−1.53174e13	−0.198352
$336$	5.61532e12	0.0715334
$337$	−9.30934e13	−1.16669	−0.583343	−	0.812226i	$-0.698256\pi$
$337$	−9.30934e13	−1.16669	−0.583343	+	0.812226i	$0.698256\pi$
$338$	−4.93252e13	−0.608173
$339$	−2.34357e14	−2.84302
$340$	−9.99372e13	−1.19287
$341$	−5.81917e13	−0.683458
$342$	−1.75042e13	−0.202301
$343$	−8.54434e13	−0.971764
$344$	−6.73560e13	−0.753884
$345$	2.86152e14	3.15204
$346$	4.61492e13	0.500318
$347$	−1.24297e14	−1.32632	−0.663160	−	0.748477i	$-0.730785\pi$
$347$	−1.24297e14	−1.32632	−0.663160	+	0.748477i	$0.730785\pi$
$348$	1.21176e14	1.27272
$349$	3.14425e13	0.325070	0.162535	−	0.986703i	$-0.448033\pi$
$349$	3.14425e13	0.325070	0.162535	+	0.986703i	$0.448033\pi$
$350$	1.86083e13	0.189380
$351$	−1.22183e13	−0.122411
$352$	8.60419e13	0.848643
$353$	−1.95901e13	−0.190228	−0.0951142	−	0.995466i	$-0.530322\pi$
$353$	−1.95901e13	−0.190228	−0.0951142	+	0.995466i	$0.530322\pi$
$354$	−1.51009e14	−1.44373
$355$	−2.03877e13	−0.191916
$356$	3.15015e13	0.291982
$357$	3.05336e14	2.78678
$358$	1.02149e13	0.0918073
$359$	1.74741e13	0.154659	0.0773297	−	0.997006i	$-0.475361\pi$
$359$	1.74741e13	0.154659	0.0773297	+	0.997006i	$0.475361\pi$
$360$	1.83648e14	1.60074
$361$	6.13107e12	0.0526316
$362$	6.54395e13	0.553278
$363$	4.77839e13	0.397919
$364$	−1.51709e13	−0.124438
$365$	−5.34119e13	−0.431546
$366$	−1.82019e14	−1.44868
$367$	−7.81970e12	−0.0613094	−0.0306547	−	0.999530i	$-0.509759\pi$
$367$	−7.81970e12	−0.0613094	−0.0306547	+	0.999530i	$0.509759\pi$
$368$	−1.04749e13	−0.0809068
$369$	1.65280e14	1.25770
$370$	5.36061e13	0.401888
$371$	4.95631e13	0.366102
$372$	−1.00695e14	−0.732861
$373$	−2.10461e14	−1.50929	−0.754645	−	0.656134i	$-0.772191\pi$
$373$	−2.10461e14	−1.50929	−0.754645	+	0.656134i	$0.772191\pi$
$374$	−1.35871e14	−0.960134
$375$	−1.78863e14	−1.24551
$376$	1.72065e14	1.18076
$377$	4.13219e13	0.279449
$378$	−5.89199e13	−0.392696
$379$	2.07849e14	1.36531	0.682656	−	0.730739i	$-0.260825\pi$
$379$	2.07849e14	1.36531	0.682656	+	0.730739i	$0.260825\pi$
$380$	−2.40636e13	−0.155794
$381$	2.12767e14	1.35774
$382$	1.59233e14	1.00158
$383$	8.81413e13	0.546495	0.273247	−	0.961944i	$-0.411902\pi$
$383$	8.81413e13	0.546495	0.273247	+	0.961944i	$0.411902\pi$
$384$	1.41653e14	0.865770
$385$	−1.66760e14	−1.00475
$386$	1.91704e13	0.113868
$387$	1.76617e14	1.03424
$388$	−1.44078e14	−0.831805
$389$	6.07379e13	0.345730	0.172865	−	0.984946i	$-0.444698\pi$
$389$	6.07379e13	0.345730	0.172865	+	0.984946i	$0.444698\pi$
$390$	4.02792e13	0.226061
$391$	−5.69576e14	−3.15195
$392$	−9.84535e12	−0.0537227
$393$	4.40433e14	2.36985
$394$	−3.00879e12	−0.0159648
$395$	1.17745e13	0.0616113
$396$	−1.38762e14	−0.716055
$397$	−2.66607e14	−1.35682	−0.678411	−	0.734682i	$-0.737331\pi$
$397$	−2.66607e14	−1.35682	−0.678411	+	0.734682i	$0.737331\pi$
$398$	−1.61304e14	−0.809634
$399$	7.35211e13	0.363966
$400$	−2.68679e12	−0.0131191
$401$	−3.04667e14	−1.46734	−0.733671	−	0.679505i	$-0.762195\pi$
$401$	−3.04667e14	−1.46734	−0.733671	+	0.679505i	$0.762195\pi$
$402$	−3.60353e13	−0.171193
$403$	−3.43377e13	−0.160914
$404$	−1.31777e14	−0.609175
$405$	1.13977e14	0.519776
$406$	1.99265e14	0.896476
$407$	−1.08272e14	−0.480561
$408$	−6.28480e14	−2.75208
$409$	2.97508e14	1.28535	0.642673	−	0.766141i	$-0.277825\pi$
$409$	2.97508e14	1.28535	0.642673	+	0.766141i	$0.277825\pi$
$410$	−1.52945e14	−0.651966
$411$	1.01580e14	0.427244
$412$	1.62282e13	0.0673498
$413$	3.68912e14	1.51077
$414$	3.91553e14	1.58230
$415$	−3.55039e12	−0.0141583
$416$	5.07714e13	0.199805
$417$	−5.93232e14	−2.30397
$418$	−3.27160e13	−0.125398
$419$	−2.44419e14	−0.924610	−0.462305	−	0.886721i	$-0.652978\pi$
$419$	−2.44419e14	−0.924610	−0.462305	+	0.886721i	$0.652978\pi$
$420$	−2.88561e14	−1.07737
$421$	5.79487e13	0.213547	0.106773	−	0.994283i	$-0.465948\pi$
$421$	5.79487e13	0.213547	0.106773	+	0.994283i	$0.465948\pi$
$422$	3.40040e14	1.23683
$423$	−4.51179e14	−1.61986
$424$	−1.02017e14	−0.361542
$425$	−1.46096e14	−0.511091
$426$	−4.79637e13	−0.165638
$427$	4.44669e14	1.51595
$428$	2.05933e13	0.0693082
$429$	−8.13550e13	−0.270314
$430$	−1.63436e14	−0.536130
$431$	5.01207e14	1.62328	0.811638	−	0.584161i	$-0.198576\pi$
$431$	5.01207e14	1.62328	0.811638	+	0.584161i	$0.198576\pi$
$432$	8.50723e12	0.0272037
$433$	2.98562e13	0.0942651	0.0471325	−	0.998889i	$-0.484992\pi$
$433$	2.98562e13	0.0942651	0.0471325	+	0.998889i	$0.484992\pi$
$434$	−1.65586e14	−0.516213
$435$	7.85971e14	2.41945
$436$	3.77713e14	1.14812
$437$	−1.37147e14	−0.411659
$438$	−1.25656e14	−0.372456
$439$	3.77779e13	0.110582	0.0552909	−	0.998470i	$-0.482391\pi$
$439$	3.77779e13	0.110582	0.0552909	+	0.998470i	$0.482391\pi$
$440$	3.43245e14	0.992234
$441$	2.58158e13	0.0737011
$442$	−8.01743e13	−0.226054
$443$	2.33140e13	0.0649227	0.0324613	−	0.999473i	$-0.489665\pi$
$443$	2.33140e13	0.0649227	0.0324613	+	0.999473i	$0.489665\pi$
$444$	−1.87354e14	−0.515297
$445$	2.04325e14	0.555062
$446$	2.10649e13	0.0565219
$447$	−1.09003e15	−2.88900
$448$	2.62507e14	0.687245
$449$	2.53041e14	0.654389	0.327195	−	0.944957i	$-0.393897\pi$
$449$	2.53041e14	0.654389	0.327195	+	0.944957i	$0.393897\pi$
$450$	1.00433e14	0.256571
$451$	3.08915e14	0.779594
$452$	−4.40851e14	−1.09908
$453$	−1.63505e14	−0.402709
$454$	1.92386e14	0.468129
$455$	−9.84012e13	−0.236558
$456$	−1.51330e14	−0.359434
$457$	4.19566e14	0.984603	0.492301	−	0.870425i	$-0.336156\pi$
$457$	4.19566e14	0.984603	0.492301	+	0.870425i	$0.336156\pi$
$458$	−1.15800e14	−0.268503
$459$	4.62585e14	1.05979
$460$	5.38283e14	1.21855
$461$	7.65920e13	0.171328	0.0856640	−	0.996324i	$-0.472699\pi$
$461$	7.65920e13	0.171328	0.0856640	+	0.996324i	$0.472699\pi$
$462$	−3.92316e14	−0.867171
$463$	−5.01195e14	−1.09474	−0.547370	−	0.836891i	$-0.684371\pi$
$463$	−5.01195e14	−1.09474	−0.547370	+	0.836891i	$0.684371\pi$
$464$	−2.87712e13	−0.0621025
$465$	−6.53127e14	−1.39318
$466$	4.13757e14	0.872213
$467$	4.78699e14	0.997285	0.498643	−	0.866808i	$-0.333832\pi$
$467$	4.78699e14	0.997285	0.498643	+	0.866808i	$0.333832\pi$
$468$	−8.18803e13	−0.168588
$469$	8.80336e13	0.179142
$470$	4.17507e14	0.839702
$471$	8.84823e14	1.75890
$472$	−7.59341e14	−1.49195
$473$	3.30103e14	0.641082
$474$	2.77006e13	0.0531751
$475$	−3.51780e13	−0.0667508
$476$	5.74370e14	1.07734
$477$	2.67502e14	0.495993
$478$	2.52971e14	0.463679
$479$	1.07788e14	0.195310	0.0976549	−	0.995220i	$-0.468866\pi$
$479$	1.07788e14	0.195310	0.0976549	+	0.995220i	$0.468866\pi$
$480$	9.65708e14	1.72989
$481$	−6.38892e13	−0.113143
$482$	3.28290e14	0.574776
$483$	−1.64461e15	−2.84677
$484$	8.98867e13	0.153832
$485$	−9.34514e14	−1.58127
$486$	4.96880e14	0.831289
$487$	−5.70556e14	−0.943819	−0.471909	−	0.881647i	$-0.656435\pi$
$487$	−5.70556e14	−0.943819	−0.471909	+	0.881647i	$0.656435\pi$
$488$	−9.15272e14	−1.49707
$489$	−2.95903e14	−0.478576
$490$	−2.38892e13	−0.0382052
$491$	7.52817e14	1.19053	0.595266	−	0.803529i	$-0.297047\pi$
$491$	7.52817e14	1.19053	0.595266	+	0.803529i	$0.297047\pi$
$492$	5.34547e14	0.835945
$493$	−1.56445e15	−2.41938
$494$	−1.93050e13	−0.0295237
$495$	−9.00035e14	−1.36123
$496$	2.39083e13	0.0357602
$497$	1.17174e14	0.173329
$498$	−8.35258e12	−0.0122197
$499$	−1.37991e14	−0.199664	−0.0998318	−	0.995004i	$-0.531830\pi$
$499$	−1.37991e14	−0.199664	−0.0998318	+	0.995004i	$0.531830\pi$
$500$	−3.36461e14	−0.481503
$501$	7.01434e14	0.992840
$502$	−6.23993e14	−0.873594
$503$	−8.68696e14	−1.20294	−0.601470	−	0.798895i	$-0.705418\pi$
$503$	−8.68696e14	−1.20294	−0.601470	+	0.798895i	$0.705418\pi$
$504$	−1.05548e15	−1.44571
$505$	−8.54730e14	−1.15805
$506$	7.31828e14	0.980802
$507$	1.11817e15	1.48240
$508$	4.00238e14	0.524890
$509$	1.06617e15	1.38318	0.691592	−	0.722288i	$-0.256910\pi$
$509$	1.06617e15	1.38318	0.691592	+	0.722288i	$0.256910\pi$
$510$	−1.52497e15	−1.95716
$511$	3.06975e14	0.389752
$512$	−7.17279e13	−0.0900955
$513$	1.11385e14	0.138414
$514$	−6.17342e13	−0.0758977
$515$	1.05259e14	0.128033
$516$	5.71211e14	0.687422
$517$	−8.43271e14	−1.00408
$518$	−3.08091e14	−0.362965
$519$	−1.04617e15	−1.21951
$520$	2.02541e14	0.233612
$521$	−7.74569e14	−0.884001	−0.442001	−	0.897015i	$-0.645731\pi$
$521$	−7.74569e14	−0.884001	−0.442001	+	0.897015i	$0.645731\pi$
$522$	1.07548e15	1.21454
$523$	−2.54311e14	−0.284189	−0.142094	−	0.989853i	$-0.545384\pi$
$523$	−2.54311e14	−0.284189	−0.142094	+	0.989853i	$0.545384\pi$
$524$	8.28503e14	0.916161
$525$	−4.21840e14	−0.461606
$526$	−6.56858e14	−0.711296
$527$	1.30003e15	1.39314
$528$	5.66450e13	0.0600724
$529$	2.11505e15	2.21980
$530$	−2.47538e14	−0.257113
$531$	1.99109e15	2.04678
$532$	1.38301e14	0.140706
$533$	1.82284e14	0.183548
$534$	4.80691e14	0.479059
$535$	1.33572e14	0.131756
$536$	−1.81201e14	−0.176911
$537$	−2.31565e14	−0.223777
$538$	1.01062e15	0.966685
$539$	4.82508e13	0.0456843
$540$	−4.37170e14	−0.409718
$541$	−7.36974e14	−0.683702	−0.341851	−	0.939754i	$-0.611054\pi$
$541$	−7.36974e14	−0.683702	−0.341851	+	0.939754i	$0.611054\pi$
$542$	−1.95053e14	−0.179125
$543$	−1.48347e15	−1.34859
$544$	−1.92221e15	−1.72984
$545$	2.44992e15	2.18258
$546$	−2.31497e14	−0.204167
$547$	−1.48726e15	−1.29854	−0.649270	−	0.760558i	$-0.724926\pi$
$547$	−1.48726e15	−1.29854	−0.649270	+	0.760558i	$0.724926\pi$
$548$	1.91082e14	0.165169
$549$	2.39997e15	2.05380
$550$	1.87713e14	0.159038
$551$	−3.76700e14	−0.315981
$552$	3.38513e15	2.81132
$553$	−6.76720e13	−0.0556443
$554$	−1.52081e14	−0.123815
$555$	−1.21522e15	−0.979585
$556$	−1.11593e15	−0.890691
$557$	−1.18007e15	−0.932617	−0.466309	−	0.884622i	$-0.654416\pi$
$557$	−1.18007e15	−0.932617	−0.466309	+	0.884622i	$0.654416\pi$
$558$	−8.93699e14	−0.699364
$559$	1.94787e14	0.150937
$560$	6.85138e13	0.0525707
$561$	3.08010e15	2.34029
$562$	6.28043e14	0.472541
$563$	1.02472e15	0.763497	0.381748	−	0.924266i	$-0.375322\pi$
$563$	1.02472e15	0.763497	0.381748	+	0.924266i	$0.375322\pi$
$564$	−1.45920e15	−1.07666
$565$	−2.85945e15	−2.08937
$566$	6.32983e13	0.0458038
$567$	−6.55063e14	−0.469436
$568$	−2.41183e14	−0.171171
$569$	4.99396e14	0.351017	0.175508	−	0.984478i	$-0.443843\pi$
$569$	4.99396e14	0.351017	0.175508	+	0.984478i	$0.443843\pi$
$570$	−3.67194e14	−0.255614
$571$	−1.09796e14	−0.0756989	−0.0378494	−	0.999283i	$-0.512051\pi$
$571$	−1.09796e14	−0.0756989	−0.0378494	+	0.999283i	$0.512051\pi$
$572$	−1.53038e14	−0.104501
$573$	−3.60971e15	−2.44131
$574$	8.79024e14	0.588824
$575$	7.86902e14	0.522093
$576$	1.41680e15	0.931077
$577$	8.37671e14	0.545264	0.272632	−	0.962118i	$-0.412106\pi$
$577$	8.37671e14	0.545264	0.272632	+	0.962118i	$0.412106\pi$
$578$	2.05165e15	1.32282
$579$	−4.34580e14	−0.277548
$580$	1.47850e15	0.935334
$581$	2.04052e13	0.0127871
$582$	−2.19852e15	−1.36475
$583$	4.99971e14	0.307445
$584$	−6.31853e14	−0.384898
$585$	−5.31091e14	−0.320488
$586$	−1.34340e14	−0.0803101
$587$	−7.26009e14	−0.429965	−0.214982	−	0.976618i	$-0.568969\pi$
$587$	−7.26009e14	−0.429965	−0.214982	+	0.976618i	$0.568969\pi$
$588$	8.34933e13	0.0489865
$589$	3.13030e14	0.181950
$590$	−1.84250e15	−1.06101
$591$	6.82074e13	0.0389135
$592$	4.44841e13	0.0251441
$593$	−4.40009e14	−0.246411	−0.123206	−	0.992381i	$-0.539317\pi$
$593$	−4.40009e14	−0.246411	−0.123206	+	0.992381i	$0.539317\pi$
$594$	−5.94359e14	−0.329779
$595$	3.72547e15	2.04804
$596$	−2.05047e15	−1.11686
$597$	3.65666e15	1.97345
$598$	4.31836e14	0.230920
$599$	1.23468e15	0.654197	0.327098	−	0.944990i	$-0.393929\pi$
$599$	1.23468e15	0.654197	0.327098	+	0.944990i	$0.393929\pi$
$600$	8.68281e14	0.455857
$601$	1.71890e15	0.894212	0.447106	−	0.894481i	$-0.352455\pi$
$601$	1.71890e15	0.894212	0.447106	+	0.894481i	$0.352455\pi$
$602$	9.39315e14	0.484207
$603$	4.75135e14	0.242701
$604$	−3.07571e14	−0.155683
$605$	5.83022e14	0.292436
$606$	−2.01082e15	−0.999481
$607$	−4.07915e14	−0.200924	−0.100462	−	0.994941i	$-0.532032\pi$
$607$	−4.07915e14	−0.200924	−0.100462	+	0.994941i	$0.532032\pi$
$608$	−4.62844e14	−0.225925
$609$	−4.51722e15	−2.18513
$610$	−2.22086e15	−1.06465
$611$	−4.97596e14	−0.236401
$612$	3.09999e15	1.45958
$613$	−2.71422e15	−1.26652	−0.633261	−	0.773938i	$-0.718284\pi$
$613$	−2.71422e15	−1.26652	−0.633261	+	0.773938i	$0.718284\pi$
$614$	−1.07109e15	−0.495336
$615$	3.46717e15	1.58914
$616$	−1.97273e15	−0.896138
$617$	2.22060e14	0.0999776	0.0499888	−	0.998750i	$-0.484081\pi$
$617$	2.22060e14	0.0999776	0.0499888	+	0.998750i	$0.484081\pi$
$618$	2.47631e14	0.110502
$619$	−1.51025e15	−0.667960	−0.333980	−	0.942580i	$-0.608392\pi$
$619$	−1.51025e15	−0.667960	−0.333980	+	0.942580i	$0.608392\pi$
$620$	−1.22860e15	−0.538588
$621$	−2.49158e15	−1.08261
$622$	−7.93451e14	−0.341722
$623$	−1.17432e15	−0.501305
$624$	3.34250e13	0.0141435
$625$	−2.87605e15	−1.20630
$626$	−2.69421e14	−0.112014
$627$	7.41650e14	0.305652
$628$	1.66445e15	0.679974
$629$	2.41885e15	0.979557
$630$	−2.56106e15	−1.02813
$631$	−3.00603e15	−1.19628	−0.598139	−	0.801393i	$-0.704093\pi$
$631$	−3.00603e15	−1.19628	−0.598139	+	0.801393i	$0.704093\pi$
$632$	1.39291e14	0.0549513
$633$	−7.70849e15	−3.01473
$634$	2.55539e15	0.990757
$635$	2.59602e15	0.997821
$636$	8.65151e14	0.329669
$637$	2.84718e13	0.0107559
$638$	2.01011e15	0.752844
$639$	6.32414e14	0.234826
$640$	1.72833e15	0.636265
$641$	−2.89262e15	−1.05578	−0.527888	−	0.849314i	$-0.677016\pi$
$641$	−2.89262e15	−1.05578	−0.527888	+	0.849314i	$0.677016\pi$
$642$	3.14239e14	0.113715
$643$	3.03669e15	1.08953	0.544767	−	0.838588i	$-0.316618\pi$
$643$	3.03669e15	1.08953	0.544767	+	0.838588i	$0.316618\pi$
$644$	−3.09368e15	−1.10053
$645$	3.70498e15	1.30680
$646$	7.30887e14	0.255606
$647$	−2.48052e15	−0.860139	−0.430070	−	0.902796i	$-0.641511\pi$
$647$	−2.48052e15	−0.860139	−0.430070	+	0.902796i	$0.641511\pi$
$648$	1.34833e15	0.463590
$649$	3.72143e15	1.26872
$650$	1.10765e14	0.0374439
$651$	3.75372e15	1.25825
$652$	−5.56626e14	−0.185013
$653$	−2.13698e15	−0.704334	−0.352167	−	0.935937i	$-0.614555\pi$
$653$	−2.13698e15	−0.704334	−0.352167	+	0.935937i	$0.614555\pi$
$654$	5.76363e15	1.88373
$655$	5.37382e15	1.74163
$656$	−1.26919e14	−0.0407902
$657$	1.65680e15	0.528034
$658$	−2.39954e15	−0.758378
$659$	−2.42577e15	−0.760292	−0.380146	−	0.924927i	$-0.624126\pi$
$659$	−2.42577e15	−0.760292	−0.380146	+	0.924927i	$0.624126\pi$
$660$	−2.91088e15	−0.904759
$661$	3.01267e15	0.928630	0.464315	−	0.885670i	$-0.346300\pi$
$661$	3.01267e15	0.928630	0.464315	+	0.885670i	$0.346300\pi$
$662$	3.78300e15	1.15643
$663$	1.81750e15	0.550999
$664$	−4.20004e13	−0.0126278
$665$	8.97048e14	0.267483
$666$	−1.66283e15	−0.491744
$667$	8.42646e15	2.47146
$668$	1.31947e15	0.383822
$669$	−4.77527e14	−0.137770
$670$	−4.39675e14	−0.125812
$671$	4.48564e15	1.27306
$672$	−5.55023e15	−1.56235
$673$	−2.83220e15	−0.790753	−0.395377	−	0.918519i	$-0.629386\pi$
$673$	−2.83220e15	−0.790753	−0.395377	+	0.918519i	$0.629386\pi$
$674$	−2.67219e15	−0.740010
$675$	−6.39088e14	−0.175546
$676$	2.10340e15	0.573081
$677$	3.29326e15	0.889998	0.444999	−	0.895531i	$-0.353204\pi$
$677$	3.29326e15	0.889998	0.444999	+	0.895531i	$0.353204\pi$
$678$	−6.72708e15	−1.80328
$679$	5.37094e15	1.42813
$680$	−7.66822e15	−2.02253
$681$	−4.36126e15	−1.14105
$682$	−1.67036e15	−0.433506
$683$	1.33898e15	0.344715	0.172358	−	0.985034i	$-0.444862\pi$
$683$	1.33898e15	0.344715	0.172358	+	0.985034i	$0.444862\pi$
$684$	7.46439e14	0.190628
$685$	1.23940e15	0.313987
$686$	−2.45260e15	−0.616374
$687$	2.62512e15	0.654465
$688$	−1.35624e14	−0.0335429
$689$	2.95022e14	0.0723851
$690$	8.21382e15	1.99929
$691$	3.02626e13	0.00730763	0.00365381	−	0.999993i	$-0.498837\pi$
$691$	3.02626e13	0.00730763	0.00365381	+	0.999993i	$0.498837\pi$
$692$	−1.96797e15	−0.471449
$693$	5.17278e15	1.22939
$694$	−3.56787e15	−0.841263
$695$	−7.23815e15	−1.69321
$696$	9.29790e15	2.15791
$697$	−6.90129e15	−1.58910
$698$	9.02539e14	0.206187
$699$	−9.37960e15	−2.12598
$700$	−7.93526e14	−0.178452
$701$	−6.14079e15	−1.37017	−0.685086	−	0.728462i	$-0.740236\pi$
$701$	−6.14079e15	−1.37017	−0.685086	+	0.728462i	$0.740236\pi$
$702$	−3.50718e14	−0.0776434
$703$	5.82428e14	0.127935
$704$	2.64806e15	0.577136
$705$	−9.46462e15	−2.04674
$706$	−5.62322e14	−0.120659
$707$	4.91240e15	1.04589
$708$	6.43957e15	1.36042
$709$	−1.94033e15	−0.406745	−0.203372	−	0.979101i	$-0.565190\pi$
$709$	−1.94033e15	−0.406745	−0.203372	+	0.979101i	$0.565190\pi$
$710$	−5.85216e14	−0.121729
$711$	−3.65239e14	−0.0753867
$712$	2.41713e15	0.495062
$713$	−7.00222e15	−1.42313
$714$	8.76449e15	1.76761
$715$	−9.92630e14	−0.198657
$716$	−4.35599e14	−0.0865099
$717$	−5.73469e15	−1.13020
$718$	5.01584e14	0.0980979
$719$	6.33775e15	1.23006	0.615030	−	0.788504i	$-0.289144\pi$
$719$	6.33775e15	1.23006	0.615030	+	0.788504i	$0.289144\pi$
$720$	3.69783e14	0.0712226
$721$	−6.04958e14	−0.115633
$722$	1.75989e14	0.0333833
$723$	−7.44213e15	−1.40099
$724$	−2.79058e15	−0.521353
$725$	2.16138e15	0.400748
$726$	1.37161e15	0.252394
$727$	8.70565e15	1.58987	0.794936	−	0.606694i	$-0.207504\pi$
$727$	8.70565e15	1.58987	0.794936	+	0.606694i	$0.207504\pi$
$728$	−1.16407e15	−0.210987
$729$	−8.72087e15	−1.56877
$730$	−1.53316e15	−0.273723
$731$	−7.37464e15	−1.30676
$732$	7.76195e15	1.36509
$733$	9.38928e14	0.163893	0.0819465	−	0.996637i	$-0.473886\pi$
$733$	9.38928e14	0.163893	0.0819465	+	0.996637i	$0.473886\pi$
$734$	−2.24460e14	−0.0388875
$735$	5.41553e14	0.0931238
$736$	1.03534e16	1.76708
$737$	8.88046e14	0.150440
$738$	4.74427e15	0.797736
$739$	−7.75138e15	−1.29370	−0.646851	−	0.762616i	$-0.723915\pi$
$739$	−7.75138e15	−1.29370	−0.646851	+	0.762616i	$0.723915\pi$
$740$	−2.28595e15	−0.378698
$741$	4.37632e14	0.0719629
$742$	1.42268e15	0.232212
$743$	−2.71702e15	−0.440204	−0.220102	−	0.975477i	$-0.570639\pi$
$743$	−2.71702e15	−0.440204	−0.220102	+	0.975477i	$0.570639\pi$
$744$	−7.72637e15	−1.24258
$745$	−1.32997e16	−2.12316
$746$	−6.04115e15	−0.957317
$747$	1.10131e14	0.0173239
$748$	5.79401e15	0.904733
$749$	−7.67678e14	−0.118995
$750$	−5.13415e15	−0.790008
$751$	8.26381e15	1.26229	0.631147	−	0.775663i	$-0.282584\pi$
$751$	8.26381e15	1.26229	0.631147	+	0.775663i	$0.282584\pi$
$752$	3.46461e14	0.0525359
$753$	1.41455e16	2.12935
$754$	1.18612e15	0.177250
$755$	−1.99496e15	−0.295956
$756$	2.51255e15	0.370037
$757$	−5.15364e15	−0.753507	−0.376753	−	0.926314i	$-0.622960\pi$
$757$	−5.15364e15	−0.753507	−0.376753	+	0.926314i	$0.622960\pi$
$758$	5.96618e15	0.865996
$759$	−1.65901e16	−2.39067
$760$	−1.84641e15	−0.264152
$761$	2.70404e15	0.384058	0.192029	−	0.981389i	$-0.438493\pi$
$761$	2.70404e15	0.384058	0.192029	+	0.981389i	$0.438493\pi$
$762$	6.10735e15	0.861194
$763$	−1.40804e16	−1.97120
$764$	−6.79026e15	−0.943785
$765$	2.01071e16	2.77468
$766$	2.53004e15	0.346633
$767$	2.19594e15	0.298707
$768$	1.17326e16	1.58456
$769$	1.25018e16	1.67641	0.838203	−	0.545359i	$-0.183607\pi$
$769$	1.25018e16	1.67641	0.838203	+	0.545359i	$0.183607\pi$
$770$	−4.78673e15	−0.637294
$771$	1.39948e15	0.184998
$772$	−8.17493e14	−0.107297
$773$	1.37603e16	1.79325	0.896625	−	0.442790i	$-0.146011\pi$
$773$	1.37603e16	1.79325	0.896625	+	0.442790i	$0.146011\pi$
$774$	5.06967e15	0.656001
$775$	−1.79606e15	−0.230761
$776$	−1.10551e16	−1.41034
$777$	6.98423e15	0.884714
$778$	1.74344e15	0.219291
$779$	−1.66174e15	−0.207543
$780$	−1.71765e15	−0.213017
$781$	1.18201e15	0.145559
$782$	−1.63493e16	−1.99923
$783$	−6.84360e15	−0.830988
$784$	−1.98240e13	−0.00239031
$785$	1.07959e16	1.29264
$786$	1.26424e16	1.50316
$787$	−8.52763e15	−1.00686	−0.503428	−	0.864037i	$-0.667928\pi$
$787$	−8.52763e15	−1.00686	−0.503428	+	0.864037i	$0.667928\pi$
$788$	1.28305e14	0.0150436
$789$	1.48906e16	1.73376
$790$	3.37981e14	0.0390790
$791$	1.64341e16	1.88702
$792$	−1.06472e16	−1.21408
$793$	2.64688e15	0.299731
$794$	−7.65278e15	−0.860610
$795$	5.61153e15	0.626703
$796$	6.87858e15	0.762917
$797$	−7.19002e15	−0.791972	−0.395986	−	0.918257i	$-0.629597\pi$
$797$	−7.19002e15	−0.791972	−0.395986	+	0.918257i	$0.629597\pi$
$798$	2.11038e15	0.230858
$799$	1.88390e16	2.04668
$800$	2.65564e15	0.286533
$801$	−6.33803e15	−0.679165
$802$	−8.74528e15	−0.930711
$803$	3.09663e15	0.327306
$804$	1.53668e15	0.161315
$805$	−2.00662e16	−2.09213
$806$	−9.85642e14	−0.102065
$807$	−2.29101e16	−2.35626
$808$	−1.01113e16	−1.03287
$809$	1.20289e16	1.22042	0.610211	−	0.792239i	$-0.291084\pi$
$809$	1.20289e16	1.22042	0.610211	+	0.792239i	$0.291084\pi$
$810$	3.27165e15	0.329685
$811$	−1.77140e16	−1.77297	−0.886485	−	0.462758i	$-0.846860\pi$
$811$	−1.77140e16	−1.77297	−0.886485	+	0.462758i	$0.846860\pi$
$812$	−8.49739e15	−0.844748
$813$	4.42173e15	0.436610
$814$	−3.10789e15	−0.304812
$815$	−3.61038e15	−0.351711
$816$	−1.26547e15	−0.122449
$817$	−1.77572e15	−0.170669
$818$	8.53978e15	0.815274
$819$	3.05234e15	0.289449
$820$	6.52213e15	0.614346
$821$	9.23476e15	0.864048	0.432024	−	0.901862i	$-0.357800\pi$
$821$	9.23476e15	0.864048	0.432024	+	0.901862i	$0.357800\pi$
$822$	2.91578e15	0.270994
$823$	3.04281e15	0.280915	0.140458	−	0.990087i	$-0.455143\pi$
$823$	3.04281e15	0.280915	0.140458	+	0.990087i	$0.455143\pi$
$824$	1.24520e15	0.114193
$825$	−4.25534e15	−0.387648
$826$	1.05894e16	0.958256
$827$	8.79170e15	0.790301	0.395151	−	0.918616i	$-0.370692\pi$
$827$	8.79170e15	0.790301	0.395151	+	0.918616i	$0.370692\pi$
$828$	−1.66972e16	−1.49100
$829$	3.34447e15	0.296672	0.148336	−	0.988937i	$-0.452608\pi$
$829$	3.34447e15	0.296672	0.148336	+	0.988937i	$0.452608\pi$
$830$	−1.01912e14	−0.00898038
$831$	3.44759e15	0.301793
$832$	1.56256e15	0.135881
$833$	−1.07794e15	−0.0931211
$834$	−1.70284e16	−1.46137
$835$	8.55835e15	0.729650
$836$	1.39512e15	0.118162
$837$	5.68690e15	0.478504
$838$	−7.01591e15	−0.586465
$839$	1.49970e14	0.0124542	0.00622708	−	0.999981i	$-0.498018\pi$
$839$	1.49970e14	0.0124542	0.00622708	+	0.999981i	$0.498018\pi$
$840$	−2.21414e16	−1.82671
$841$	1.09444e16	0.897041
$842$	1.66338e15	0.135449
$843$	−1.42373e16	−1.15180
$844$	−1.45005e16	−1.16547
$845$	1.36431e16	1.08943
$846$	−1.29508e16	−1.02745
$847$	−3.35081e15	−0.264114
$848$	−2.05415e14	−0.0160863
$849$	−1.43493e15	−0.111645
$850$	−4.19359e15	−0.324177
$851$	−1.30284e16	−1.00064
$852$	2.04534e15	0.156080
$853$	−5.62808e15	−0.426717	−0.213359	−	0.976974i	$-0.568440\pi$
$853$	−5.62808e15	−0.426717	−0.213359	+	0.976974i	$0.568440\pi$
$854$	1.27640e16	0.961540
$855$	4.84155e15	0.362385
$856$	1.58013e15	0.117513
$857$	−9.57937e15	−0.707852	−0.353926	−	0.935273i	$-0.615154\pi$
$857$	−9.57937e15	−0.707852	−0.353926	+	0.935273i	$0.615154\pi$
$858$	−2.33525e15	−0.171456
$859$	1.13682e16	0.829333	0.414666	−	0.909974i	$-0.363898\pi$
$859$	1.13682e16	0.829333	0.414666	+	0.909974i	$0.363898\pi$
$860$	6.96948e15	0.505195
$861$	−1.99269e16	−1.43523
$862$	1.43868e16	1.02962
$863$	1.00999e16	0.718217	0.359108	−	0.933296i	$-0.383081\pi$
$863$	1.00999e16	0.718217	0.359108	+	0.933296i	$0.383081\pi$
$864$	−8.40860e15	−0.594153
$865$	−1.27646e16	−0.896229
$866$	8.57004e14	0.0597908
$867$	−4.65096e16	−3.22432
$868$	7.06116e15	0.486427
$869$	−6.82647e14	−0.0467291
$870$	2.25608e16	1.53461
$871$	5.24017e14	0.0354197
$872$	2.89821e16	1.94665
$873$	2.89881e16	1.93482
$874$	−3.93672e15	−0.261109
$875$	1.25426e16	0.826693
$876$	5.35842e15	0.350965
$877$	−4.55585e15	−0.296532	−0.148266	−	0.988948i	$-0.547369\pi$
$877$	−4.55585e15	−0.296532	−0.148266	+	0.988948i	$0.547369\pi$
$878$	1.08439e15	0.0701402
$879$	3.04541e15	0.195753
$880$	6.91139e14	0.0441480
$881$	1.21232e16	0.769570	0.384785	−	0.923006i	$-0.374276\pi$
$881$	1.21232e16	0.769570	0.384785	+	0.923006i	$0.374276\pi$
$882$	7.41028e14	0.0467474
$883$	3.68424e15	0.230974	0.115487	−	0.993309i	$-0.463157\pi$
$883$	3.68424e15	0.230974	0.115487	+	0.993309i	$0.463157\pi$
$884$	3.41892e15	0.213011
$885$	4.17683e16	2.58618
$886$	6.69214e14	0.0411794
$887$	1.12873e16	0.690255	0.345127	−	0.938556i	$-0.387836\pi$
$887$	1.12873e16	0.690255	0.345127	+	0.938556i	$0.387836\pi$
$888$	−1.43758e16	−0.873696
$889$	−1.49201e16	−0.901183
$890$	5.86502e15	0.352066
$891$	−6.60800e15	−0.394224
$892$	−8.98280e14	−0.0532605
$893$	4.53620e15	0.267306
$894$	−3.12887e16	−1.83244
$895$	−2.82538e15	−0.164456
$896$	−9.93328e15	−0.574644
$897$	−9.78945e15	−0.562860
$898$	7.26339e15	0.415068
$899$	−1.92329e16	−1.09236
$900$	−4.28282e15	−0.241766
$901$	−1.11696e16	−0.626685
$902$	8.86723e15	0.494484
$903$	−2.12937e16	−1.18023
$904$	−3.38267e16	−1.86352
$905$	−1.81002e16	−0.991097
$906$	−4.69332e15	−0.255432
$907$	1.03028e16	0.557333	0.278666	−	0.960388i	$-0.410108\pi$
$907$	1.03028e16	0.557333	0.278666	+	0.960388i	$0.410108\pi$
$908$	−8.20400e15	−0.441117
$909$	2.65132e16	1.41697
$910$	−2.82455e15	−0.150045
$911$	−1.49059e16	−0.787060	−0.393530	−	0.919312i	$-0.628746\pi$
$911$	−1.49059e16	−0.787060	−0.393530	+	0.919312i	$0.628746\pi$
$912$	−3.04710e14	−0.0159924
$913$	2.05839e14	0.0107384
$914$	1.20434e16	0.624517
$915$	5.03455e16	2.59504
$916$	4.93813e15	0.253010
$917$	−3.08850e16	−1.57296
$918$	1.32782e16	0.672210
$919$	3.89541e15	0.196028	0.0980139	−	0.995185i	$-0.468751\pi$
$919$	3.89541e15	0.196028	0.0980139	+	0.995185i	$0.468751\pi$
$920$	4.13027e16	2.06607
$921$	2.42809e16	1.20736
$922$	2.19853e15	0.108670
$923$	6.97476e14	0.0342705
$924$	1.67297e16	0.817134
$925$	−3.34178e15	−0.162255
$926$	−1.43865e16	−0.694376
$927$	−3.26508e15	−0.156659
$928$	2.84377e16	1.35638
$929$	−6.35600e15	−0.301368	−0.150684	−	0.988582i	$-0.548148\pi$
$929$	−6.35600e15	−0.301368	−0.150684	+	0.988582i	$0.548148\pi$
$930$	−1.87476e16	−0.883669
$931$	−2.59555e14	−0.0121620
$932$	−1.76441e16	−0.821884
$933$	1.79870e16	0.832934
$934$	1.37408e16	0.632562
$935$	3.75810e16	1.71991
$936$	−6.28271e15	−0.285844
$937$	−2.30279e16	−1.04156	−0.520782	−	0.853689i	$-0.674360\pi$
$937$	−2.30279e16	−1.04156	−0.520782	+	0.853689i	$0.674360\pi$
$938$	2.52695e15	0.113627
$939$	6.10760e15	0.273030
$940$	−1.78040e16	−0.791250
$941$	2.18026e16	0.963307	0.481654	−	0.876362i	$-0.340036\pi$
$941$	2.18026e16	0.963307	0.481654	+	0.876362i	$0.340036\pi$
$942$	2.53983e16	1.11564
$943$	3.71718e16	1.62330
$944$	−1.52897e15	−0.0663822
$945$	1.62969e16	0.703445
$946$	9.47542e15	0.406628
$947$	−1.53814e16	−0.656254	−0.328127	−	0.944634i	$-0.606417\pi$
$947$	−1.53814e16	−0.656254	−0.328127	+	0.944634i	$0.606417\pi$
$948$	−1.18125e15	−0.0501068
$949$	1.82726e15	0.0770611
$950$	−1.00976e15	−0.0423389
$951$	−5.79292e16	−2.41493
$952$	4.40717e16	1.82665
$953$	6.08100e15	0.250590	0.125295	−	0.992120i	$-0.460012\pi$
$953$	6.08100e15	0.250590	0.125295	+	0.992120i	$0.460012\pi$
$954$	7.67848e15	0.314600
$955$	−4.40429e16	−1.79415
$956$	−1.07876e16	−0.436924
$957$	−4.55678e16	−1.83503
$958$	3.09398e15	0.123882
$959$	−7.12319e15	−0.283578
$960$	2.97210e16	1.17645
$961$	−9.42630e15	−0.370990
$962$	−1.83390e15	−0.0717650
$963$	−4.14331e15	−0.161214
$964$	−1.39995e16	−0.541611
$965$	−5.30241e15	−0.203973
$966$	−4.72074e16	−1.80566
$967$	1.02164e16	0.388556	0.194278	−	0.980946i	$-0.437764\pi$
$967$	1.02164e16	0.388556	0.194278	+	0.980946i	$0.437764\pi$
$968$	6.89704e15	0.260825
$969$	−1.65688e16	−0.623030
$970$	−2.68247e16	−1.00297
$971$	−2.42570e16	−0.901844	−0.450922	−	0.892563i	$-0.648905\pi$
$971$	−2.42570e16	−0.901844	−0.450922	+	0.892563i	$0.648905\pi$
$972$	−2.11887e16	−0.783322
$973$	4.15999e16	1.52923
$974$	−1.63775e16	−0.598649
$975$	−2.51098e15	−0.0912680
$976$	−1.84294e15	−0.0666097
$977$	1.34774e16	0.484380	0.242190	−	0.970229i	$-0.422134\pi$
$977$	1.34774e16	0.484380	0.242190	+	0.970229i	$0.422134\pi$
$978$	−8.49372e15	−0.303553
$979$	−1.18460e16	−0.420987
$980$	1.01872e15	0.0360007
$981$	−7.59949e16	−2.67058
$982$	2.16092e16	0.755135
$983$	−1.55986e16	−0.542051	−0.271026	−	0.962572i	$-0.587363\pi$
$983$	−1.55986e16	−0.542051	−0.271026	+	0.962572i	$0.587363\pi$
$984$	4.10160e16	1.41736
$985$	8.32213e14	0.0285980
$986$	−4.49066e16	−1.53457
$987$	5.43961e16	1.84852
$988$	8.23233e14	0.0278202
$989$	3.97214e16	1.33489
$990$	−2.58350e16	−0.863404
$991$	7.17786e15	0.238556	0.119278	−	0.992861i	$-0.461942\pi$
$991$	7.17786e15	0.238556	0.119278	+	0.992861i	$0.461942\pi$
$992$	−2.36311e16	−0.781035
$993$	−8.57583e16	−2.81874
$994$	3.36342e15	0.109940
$995$	4.46158e16	1.45031
$996$	3.56184e14	0.0115146
$997$	1.51424e15	0.0486824	0.0243412	−	0.999704i	$-0.492251\pi$
$997$	1.51424e15	0.0486824	0.0243412	+	0.999704i	$0.492251\pi$
$998$	−3.96096e15	−0.126643
$999$	1.05811e16	0.336451

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.12.a.b.1.6	✓	9
3.2	odd	2		171.12.a.d.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.12.a.b.1.6	✓	9	1.1	even	1	trivial
171.12.a.d.1.4		9	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	19.a (trivial)

\(f(q)\)	\(=\)	\(q+28.7044 q^{2} -650.711 q^{3} -1224.06 q^{4} -7939.47 q^{5} -18678.3 q^{6} +45630.6 q^{7} -93922.4 q^{8} +246277. q^{9} +O(q^{10})\)	\(q+28.7044 q^{2} -650.711 q^{3} -1224.06 q^{4} -7939.47 q^{5} -18678.3 q^{6} +45630.6 q^{7} -93922.4 q^{8} +246277. q^{9} -227898. q^{10} +460302. q^{11} +796507. q^{12} +271614. q^{13} +1.30980e6 q^{14} +5.16630e6 q^{15} -189117. q^{16} -1.02833e7 q^{17} +7.06925e6 q^{18} -2.47610e6 q^{19} +9.71837e6 q^{20} -2.96923e7 q^{21} +1.32127e7 q^{22} +5.53882e7 q^{23} +6.11163e7 q^{24} +1.42070e7 q^{25} +7.79653e6 q^{26} -4.49839e7 q^{27} -5.58545e7 q^{28} +1.52134e8 q^{29} +1.48295e8 q^{30} -1.26421e8 q^{31} +1.86925e8 q^{32} -2.99524e8 q^{33} -2.95177e8 q^{34} -3.62283e8 q^{35} -3.01458e8 q^{36} -2.35220e8 q^{37} -7.10749e7 q^{38} -1.76742e8 q^{39} +7.45694e8 q^{40} +6.71114e8 q^{41} -8.52300e8 q^{42} +7.17145e8 q^{43} -5.63437e8 q^{44} -1.95531e9 q^{45} +1.58989e9 q^{46} -1.83199e9 q^{47} +1.23060e8 q^{48} +1.04824e8 q^{49} +4.07804e8 q^{50} +6.69148e9 q^{51} -3.32472e8 q^{52} +1.08618e9 q^{53} -1.29124e9 q^{54} -3.65456e9 q^{55} -4.28574e9 q^{56} +1.61122e9 q^{57} +4.36693e9 q^{58} +8.08476e9 q^{59} -6.32385e9 q^{60} +9.74498e9 q^{61} -3.62883e9 q^{62} +1.12378e10 q^{63} +5.75287e9 q^{64} -2.15647e9 q^{65} -8.59765e9 q^{66} +1.92927e9 q^{67} +1.25874e10 q^{68} -3.60417e10 q^{69} -1.03991e10 q^{70} +2.56789e9 q^{71} -2.31310e10 q^{72} +6.72739e9 q^{73} -6.75185e9 q^{74} -9.24466e9 q^{75} +3.03089e9 q^{76} +2.10039e10 q^{77} -5.07328e9 q^{78} -1.48304e9 q^{79} +1.50149e9 q^{80} -1.43558e10 q^{81} +1.92639e10 q^{82} +4.47182e8 q^{83} +3.63451e10 q^{84} +8.16442e10 q^{85} +2.05852e10 q^{86} -9.89955e10 q^{87} -4.32327e10 q^{88} -2.57353e10 q^{89} -5.61260e10 q^{90} +1.23939e10 q^{91} -6.77984e10 q^{92} +8.22633e10 q^{93} -5.25863e10 q^{94} +1.96589e10 q^{95} -1.21634e11 q^{96} +1.17705e11 q^{97} +3.00892e9 q^{98} +1.13362e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 87 q^{2} + 496 q^{3} + 11781 q^{4} + 2114 q^{5} + 84181 q^{6} - 19080 q^{7} - 76701 q^{8} + 632433 q^{9}+O(q^{10}) \) 9 * q + 87 * q^2 + 496 * q^3 + 11781 * q^4 + 2114 * q^5 + 84181 * q^6 - 19080 * q^7 - 76701 * q^8 + 632433 * q^9	\( 9 q + 87 q^{2} + 496 q^{3} + 11781 q^{4} + 2114 q^{5} + 84181 q^{6} - 19080 q^{7} - 76701 q^{8} + 632433 q^{9} - 268428 q^{10} + 175744 q^{11} + 3993305 q^{12} + 809154 q^{13} + 7041403 q^{14} + 4320440 q^{15} + 29590233 q^{16} + 13162874 q^{17} + 51670980 q^{18} - 22284891 q^{19} + 692380 q^{20} + 75424388 q^{21} + 63849138 q^{22} + 114786388 q^{23} + 310823511 q^{24} + 199152003 q^{25} + 97437497 q^{26} + 229481236 q^{27} - 224392209 q^{28} + 54612914 q^{29} - 327673696 q^{30} - 226600416 q^{31} + 346094139 q^{32} - 842576368 q^{33} - 790592985 q^{34} - 1068615828 q^{35} - 472860258 q^{36} - 371753970 q^{37} - 215420613 q^{38} - 1611645716 q^{39} - 4563855672 q^{40} + 504959690 q^{41} - 3956969929 q^{42} - 1620951792 q^{43} - 3829267498 q^{44} - 1391906830 q^{45} + 497259759 q^{46} - 1965882540 q^{47} + 3995891285 q^{48} + 7865370753 q^{49} + 13293164621 q^{50} + 8348428708 q^{51} - 7643204427 q^{52} + 14154895258 q^{53} + 3906695191 q^{54} + 8109135852 q^{55} + 24205597101 q^{56} - 1228145104 q^{57} + 14070688173 q^{58} + 22029386080 q^{59} - 20596280480 q^{60} - 1263984246 q^{61} - 11298124604 q^{62} + 10540367284 q^{63} + 24443845113 q^{64} + 14545843500 q^{65} - 34605988558 q^{66} + 14718513264 q^{67} - 73374346541 q^{68} + 18897730596 q^{69} - 75583659360 q^{70} + 34967811888 q^{71} + 27091585794 q^{72} + 18297073746 q^{73} - 85279476938 q^{74} + 95893305816 q^{75} - 29170922319 q^{76} + 2899255276 q^{77} - 205276367351 q^{78} - 15944238816 q^{79} - 286349413472 q^{80} - 41171883423 q^{81} - 201183193836 q^{82} - 2858023276 q^{83} - 15014021321 q^{84} + 234418807008 q^{85} - 66508042032 q^{86} + 81522171444 q^{87} - 171289266282 q^{88} + 207569871794 q^{89} - 127219826428 q^{90} + 285870230676 q^{91} + 184876887431 q^{92} + 122416682512 q^{93} + 234051593712 q^{94} - 5234473286 q^{95} + 498857169575 q^{96} + 58127902530 q^{97} - 279728403320 q^{98} + 188514162376 q^{99}+O(q^{100}) \) 9 * q + 87 * q^2 + 496 * q^3 + 11781 * q^4 + 2114 * q^5 + 84181 * q^6 - 19080 * q^7 - 76701 * q^8 + 632433 * q^9 - 268428 * q^10 + 175744 * q^11 + 3993305 * q^12 + 809154 * q^13 + 7041403 * q^14 + 4320440 * q^15 + 29590233 * q^16 + 13162874 * q^17 + 51670980 * q^18 - 22284891 * q^19 + 692380 * q^20 + 75424388 * q^21 + 63849138 * q^22 + 114786388 * q^23 + 310823511 * q^24 + 199152003 * q^25 + 97437497 * q^26 + 229481236 * q^27 - 224392209 * q^28 + 54612914 * q^29 - 327673696 * q^30 - 226600416 * q^31 + 346094139 * q^32 - 842576368 * q^33 - 790592985 * q^34 - 1068615828 * q^35 - 472860258 * q^36 - 371753970 * q^37 - 215420613 * q^38 - 1611645716 * q^39 - 4563855672 * q^40 + 504959690 * q^41 - 3956969929 * q^42 - 1620951792 * q^43 - 3829267498 * q^44 - 1391906830 * q^45 + 497259759 * q^46 - 1965882540 * q^47 + 3995891285 * q^48 + 7865370753 * q^49 + 13293164621 * q^50 + 8348428708 * q^51 - 7643204427 * q^52 + 14154895258 * q^53 + 3906695191 * q^54 + 8109135852 * q^55 + 24205597101 * q^56 - 1228145104 * q^57 + 14070688173 * q^58 + 22029386080 * q^59 - 20596280480 * q^60 - 1263984246 * q^61 - 11298124604 * q^62 + 10540367284 * q^63 + 24443845113 * q^64 + 14545843500 * q^65 - 34605988558 * q^66 + 14718513264 * q^67 - 73374346541 * q^68 + 18897730596 * q^69 - 75583659360 * q^70 + 34967811888 * q^71 + 27091585794 * q^72 + 18297073746 * q^73 - 85279476938 * q^74 + 95893305816 * q^75 - 29170922319 * q^76 + 2899255276 * q^77 - 205276367351 * q^78 - 15944238816 * q^79 - 286349413472 * q^80 - 41171883423 * q^81 - 201183193836 * q^82 - 2858023276 * q^83 - 15014021321 * q^84 + 234418807008 * q^85 - 66508042032 * q^86 + 81522171444 * q^87 - 171289266282 * q^88 + 207569871794 * q^89 - 127219826428 * q^90 + 285870230676 * q^91 + 184876887431 * q^92 + 122416682512 * q^93 + 234051593712 * q^94 - 5234473286 * q^95 + 498857169575 * q^96 + 58127902530 * q^97 - 279728403320 * q^98 + 188514162376 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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