LMFDB - Embedded newform 21.18.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,18,Mod(1,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	21.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:	$38.4766383424$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 401750x^{2} - 42202572x + 5013099432 $ x^4 - x^3 - 401750x^2 - 42202572x + 5013099432
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$673.806$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+579.806 q^{2} -6561.00 q^{3} +205104. q^{4} +3275.54 q^{5} -3.80411e6 q^{6} -5.76480e6 q^{7} +4.29240e7 q^{8} +4.30467e7 q^{9} +O(q^{10})$	\(q+579.806 q^{2} -6561.00 q^{3} +205104. q^{4} +3275.54 q^{5} -3.80411e6 q^{6} -5.76480e6 q^{7} +4.29240e7 q^{8} +4.30467e7 q^{9} +1.89918e6 q^{10} -5.18037e8 q^{11} -1.34568e9 q^{12} -2.75126e9 q^{13} -3.34247e9 q^{14} -2.14908e7 q^{15} -1.99573e9 q^{16} +1.79277e10 q^{17} +2.49588e10 q^{18} -9.37067e9 q^{19} +6.71824e8 q^{20} +3.78229e10 q^{21} -3.00361e11 q^{22} -2.27276e11 q^{23} -2.81624e11 q^{24} -7.62929e11 q^{25} -1.59520e12 q^{26} -2.82430e11 q^{27} -1.18238e12 q^{28} -4.34800e12 q^{29} -1.24605e10 q^{30} -3.53323e10 q^{31} -6.78327e12 q^{32} +3.39884e12 q^{33} +1.03946e13 q^{34} -1.88828e10 q^{35} +8.82904e12 q^{36} +1.79145e13 q^{37} -5.43317e12 q^{38} +1.80510e13 q^{39} +1.40599e11 q^{40} +5.22632e12 q^{41} +2.19299e13 q^{42} -6.97711e13 q^{43} -1.06251e14 q^{44} +1.41001e11 q^{45} -1.31776e14 q^{46} -1.91799e13 q^{47} +1.30940e13 q^{48} +3.32329e13 q^{49} -4.42351e14 q^{50} -1.17623e14 q^{51} -5.64294e14 q^{52} +2.13105e14 q^{53} -1.63754e14 q^{54} -1.69685e12 q^{55} -2.47448e14 q^{56} +6.14810e13 q^{57} -2.52100e15 q^{58} +1.09480e15 q^{59} -4.40784e12 q^{60} -1.01854e15 q^{61} -2.04859e13 q^{62} -2.48156e14 q^{63} -3.67140e15 q^{64} -9.01186e12 q^{65} +1.97067e15 q^{66} +5.44758e14 q^{67} +3.67703e15 q^{68} +1.49115e15 q^{69} -1.09484e13 q^{70} +7.36700e15 q^{71} +1.84774e15 q^{72} +7.63541e15 q^{73} +1.03870e16 q^{74} +5.00558e15 q^{75} -1.92196e15 q^{76} +2.98638e15 q^{77} +1.04661e16 q^{78} -1.89661e16 q^{79} -6.53709e12 q^{80} +1.85302e15 q^{81} +3.03025e15 q^{82} -1.88245e16 q^{83} +7.75760e15 q^{84} +5.87228e13 q^{85} -4.04538e16 q^{86} +2.85272e16 q^{87} -2.22362e16 q^{88} +6.24578e16 q^{89} +8.17534e13 q^{90} +1.58605e16 q^{91} -4.66150e16 q^{92} +2.31815e14 q^{93} -1.11206e16 q^{94} -3.06940e13 q^{95} +4.45050e16 q^{96} -1.04148e14 q^{97} +1.92687e16 q^{98} -2.22998e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 375 q^{2} - 26244 q^{3} + 314369 q^{4} - 154140 q^{5} + 2460375 q^{6} - 23059204 q^{7} - 3766143 q^{8} + 172186884 q^{9}+O(q^{10}) $ 4 * q - 375 * q^2 - 26244 * q^3 + 314369 * q^4 - 154140 * q^5 + 2460375 * q^6 - 23059204 * q^7 - 3766143 * q^8 + 172186884 * q^9	\( 4 q - 375 q^{2} - 26244 q^{3} + 314369 q^{4} - 154140 q^{5} + 2460375 q^{6} - 23059204 q^{7} - 3766143 q^{8} + 172186884 q^{9} + 23352830 q^{10} - 1452022884 q^{11} - 2062575009 q^{12} + 1793559040 q^{13} + 2161800375 q^{14} + 1011312540 q^{15} + 36719981057 q^{16} + 68581449948 q^{17} - 16142520375 q^{18} - 2578000592 q^{19} + 132998517630 q^{20} + 151291437444 q^{21} + 270530423852 q^{22} + 649239533556 q^{23} + 24709664223 q^{24} - 708242296300 q^{25} - 2508729280746 q^{26} - 1129718145924 q^{27} - 1812274725569 q^{28} - 3258162962760 q^{29} - 153217917630 q^{30} + 2414795507136 q^{31} - 18040133068671 q^{32} + 9526722141924 q^{33} + 8860338750210 q^{34} + 888586426140 q^{35} + 13532554634049 q^{36} + 23164217924208 q^{37} - 67011195804708 q^{38} - 11767540861440 q^{39} - 115859765446530 q^{40} - 117516076237164 q^{41} - 14183572260375 q^{42} - 175144919320720 q^{43} - 379640394802500 q^{44} - 6635221574940 q^{45} - 441875935197000 q^{46} - 392013343869480 q^{47} - 240919795714977 q^{48} + 132931722278404 q^{49} - 366102837059625 q^{50} - 449962893108828 q^{51} - 647834999852794 q^{52} - 86395731614976 q^{53} + 105911076180375 q^{54} - 987784569502880 q^{55} + 21711064932543 q^{56} + 16914261884112 q^{57} - 21\!\cdots\!66 q^{58}+ \cdots - 62\!\cdots\!64 q^{99}+O(q^{100}) \) 4 * q - 375 * q^2 - 26244 * q^3 + 314369 * q^4 - 154140 * q^5 + 2460375 * q^6 - 23059204 * q^7 - 3766143 * q^8 + 172186884 * q^9 + 23352830 * q^10 - 1452022884 * q^11 - 2062575009 * q^12 + 1793559040 * q^13 + 2161800375 * q^14 + 1011312540 * q^15 + 36719981057 * q^16 + 68581449948 * q^17 - 16142520375 * q^18 - 2578000592 * q^19 + 132998517630 * q^20 + 151291437444 * q^21 + 270530423852 * q^22 + 649239533556 * q^23 + 24709664223 * q^24 - 708242296300 * q^25 - 2508729280746 * q^26 - 1129718145924 * q^27 - 1812274725569 * q^28 - 3258162962760 * q^29 - 153217917630 * q^30 + 2414795507136 * q^31 - 18040133068671 * q^32 + 9526722141924 * q^33 + 8860338750210 * q^34 + 888586426140 * q^35 + 13532554634049 * q^36 + 23164217924208 * q^37 - 67011195804708 * q^38 - 11767540861440 * q^39 - 115859765446530 * q^40 - 117516076237164 * q^41 - 14183572260375 * q^42 - 175144919320720 * q^43 - 379640394802500 * q^44 - 6635221574940 * q^45 - 441875935197000 * q^46 - 392013343869480 * q^47 - 240919795714977 * q^48 + 132931722278404 * q^49 - 366102837059625 * q^50 - 449962893108828 * q^51 - 647834999852794 * q^52 - 86395731614976 * q^53 + 105911076180375 * q^54 - 987784569502880 * q^55 + 21711064932543 * q^56 + 16914261884112 * q^57 - 2149209668160466 * q^58 - 23145424510920 * q^59 - 872603274170430 * q^60 + 3424273979460952 * q^61 - 4542097297046784 * q^62 - 992623121070084 * q^63 - 3840648962754815 * q^64 + 2015724107462520 * q^65 - 1774950110892972 * q^66 + 2234127752098744 * q^67 - 1956571325658750 * q^68 - 4259660579660916 * q^69 - 134624417736830 * q^70 + 2815776345321804 * q^71 - 162120106967103 * q^72 + 11330038422344784 * q^73 + 2782049125778694 * q^74 + 4646777706024300 * q^75 + 33041781126411260 * q^76 + 8370622973706084 * q^77 + 16459772810974506 * q^78 - 12177038540666920 * q^79 + 35816456249313150 * q^80 + 7412080755407364 * q^81 + 79244490955525210 * q^82 - 4389820874951568 * q^83 + 11890334474458209 * q^84 + 46318093724780760 * q^85 - 79314655634282340 * q^86 + 21376807198668360 * q^87 + 93140307906096828 * q^88 + 100131520699583508 * q^89 + 1005262757570430 * q^90 - 10339510947351040 * q^91 - 14621524874654712 * q^92 - 15843473322319296 * q^93 + 120993183153224352 * q^94 - 115775864256900240 * q^95 + 118361313063550431 * q^96 - 44947325255962464 * q^97 - 12462348963600375 * q^98 - 62504823973163364 * 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 $

$2$	579.806	1.60150	0.800752	−	0.598996i	$-0.204433\pi$
$2$	579.806	1.60150	0.800752	+	0.598996i	$0.204433\pi$
$3$	−6561.00	−0.577350
$3$	−6561.00	−0.577350
$4$	205104.	1.56482
$5$	3275.54	0.00375005	0.00187503	−	0.999998i	$-0.499403\pi$
$5$	3275.54	0.00375005	0.00187503	+	0.999998i	$0.499403\pi$
$6$	−3.80411e6	−0.924629
$7$	−5.76480e6	−0.377964
$7$	−5.76480e6	−0.377964
$8$	4.29240e7	0.904555
$9$	4.30467e7	0.333333
$10$	1.89918e6	0.00600573
$11$	−5.18037e8	−0.728657	−0.364328	−	0.931271i	$-0.618701\pi$
$11$	−5.18037e8	−0.728657	−0.364328	+	0.931271i	$0.618701\pi$
$12$	−1.34568e9	−0.903447
$13$	−2.75126e9	−0.935435	−0.467717	−	0.883878i	$-0.654924\pi$
$13$	−2.75126e9	−0.935435	−0.467717	+	0.883878i	$0.654924\pi$
$14$	−3.34247e9	−0.605312
$15$	−2.14908e7	−0.00216509
$16$	−1.99573e9	−0.116167
$17$	1.79277e10	0.623316	0.311658	−	0.950194i	$-0.399116\pi$
$17$	1.79277e10	0.623316	0.311658	+	0.950194i	$0.399116\pi$
$18$	2.49588e10	0.533835
$19$	−9.37067e9	−0.126580	−0.0632900	−	0.997995i	$-0.520159\pi$
$19$	−9.37067e9	−0.126580	−0.0632900	+	0.997995i	$0.520159\pi$
$20$	6.71824e8	0.00586814
$21$	3.78229e10	0.218218
$22$	−3.00361e11	−1.16695
$23$	−2.27276e11	−0.605154	−0.302577	−	0.953125i	$-0.597847\pi$
$23$	−2.27276e11	−0.605154	−0.302577	+	0.953125i	$0.597847\pi$
$24$	−2.81624e11	−0.522245
$25$	−7.62929e11	−0.999986
$26$	−1.59520e12	−1.49810
$27$	−2.82430e11	−0.192450
$28$	−1.18238e12	−0.591445
$29$	−4.34800e12	−1.61401	−0.807006	−	0.590544i	$-0.798913\pi$
$29$	−4.34800e12	−1.61401	−0.807006	+	0.590544i	$0.798913\pi$
$30$	−1.24605e10	−0.00346741
$31$	−3.53323e10	−0.00744042	−0.00372021	−	0.999993i	$-0.501184\pi$
$31$	−3.53323e10	−0.00744042	−0.00372021	+	0.999993i	$0.501184\pi$
$32$	−6.78327e12	−1.09060
$33$	3.39884e12	0.420690
$34$	1.03946e13	0.998243
$35$	−1.88828e10	−0.00141739
$36$	8.82904e12	0.521605
$37$	1.79145e13	0.838475	0.419238	−	0.907877i	$-0.362297\pi$
$37$	1.79145e13	0.838475	0.419238	+	0.907877i	$0.362297\pi$
$38$	−5.43317e12	−0.202718
$39$	1.80510e13	0.540074
$40$	1.40599e11	0.00339213
$41$	5.22632e12	0.102219	0.0511097	−	0.998693i	$-0.483724\pi$
$41$	5.22632e12	0.102219	0.0511097	+	0.998693i	$0.483724\pi$
$42$	2.19299e13	0.349477
$43$	−6.97711e13	−0.910320	−0.455160	−	0.890410i	$-0.650418\pi$
$43$	−6.97711e13	−0.910320	−0.455160	+	0.890410i	$0.650418\pi$
$44$	−1.06251e14	−1.14021
$45$	1.41001e11	0.00125002
$46$	−1.31776e14	−0.969157
$47$	−1.91799e13	−0.117494	−0.0587469	−	0.998273i	$-0.518710\pi$
$47$	−1.91799e13	−0.117494	−0.0587469	+	0.998273i	$0.518710\pi$
$48$	1.30940e13	0.0670690
$49$	3.32329e13	0.142857
$50$	−4.42351e14	−1.60148
$51$	−1.17623e14	−0.359872
$52$	−5.64294e14	−1.46378
$53$	2.13105e14	0.470164	0.235082	−	0.971976i	$-0.424464\pi$
$53$	2.13105e14	0.470164	0.235082	+	0.971976i	$0.424464\pi$
$54$	−1.63754e14	−0.308210
$55$	−1.69685e12	−0.00273250
$56$	−2.47448e14	−0.341890
$57$	6.14810e13	0.0730810
$58$	−2.52100e15	−2.58485
$59$	1.09480e15	0.970721	0.485360	−	0.874314i	$-0.338688\pi$
$59$	1.09480e15	0.970721	0.485360	+	0.874314i	$0.338688\pi$
$60$	−4.40784e12	−0.00338797
$61$	−1.01854e15	−0.680261	−0.340130	−	0.940378i	$-0.610471\pi$
$61$	−1.01854e15	−0.680261	−0.340130	+	0.940378i	$0.610471\pi$
$62$	−2.04859e13	−0.0119159
$63$	−2.48156e14	−0.125988
$64$	−3.67140e15	−1.63043
$65$	−9.01186e12	−0.00350793
$66$	1.97067e15	0.673737
$67$	5.44758e14	0.163896	0.0819480	−	0.996637i	$-0.473886\pi$
$67$	5.44758e14	0.163896	0.0819480	+	0.996637i	$0.473886\pi$
$68$	3.67703e15	0.975374
$69$	1.49115e15	0.349386
$70$	−1.09484e13	−0.00226995
$71$	7.36700e15	1.35393	0.676963	−	0.736017i	$-0.263296\pi$
$71$	7.36700e15	1.35393	0.676963	+	0.736017i	$0.263296\pi$
$72$	1.84774e15	0.301518
$73$	7.63541e15	1.10812	0.554061	−	0.832476i	$-0.313077\pi$
$73$	7.63541e15	1.10812	0.554061	+	0.832476i	$0.313077\pi$
$74$	1.03870e16	1.34282
$75$	5.00558e15	0.577342
$76$	−1.92196e15	−0.198074
$77$	2.98638e15	0.275406
$78$	1.04661e16	0.864930
$79$	−1.89661e16	−1.40653	−0.703264	−	0.710929i	$-0.748275\pi$
$79$	−1.89661e16	−1.40653	−0.703264	+	0.710929i	$0.748275\pi$
$80$	−6.53709e12	−0.000435632 0
$81$	1.85302e15	0.111111
$82$	3.03025e15	0.163705
$83$	−1.88245e16	−0.917404	−0.458702	−	0.888590i	$-0.651685\pi$
$83$	−1.88245e16	−0.917404	−0.458702	+	0.888590i	$0.651685\pi$
$84$	7.75760e15	0.341471
$85$	5.87228e13	0.00233747
$86$	−4.04538e16	−1.45788
$87$	2.85272e16	0.931850
$88$	−2.22362e16	−0.659110
$89$	6.24578e16	1.68179	0.840894	−	0.541199i	$-0.182030\pi$
$89$	6.24578e16	1.68179	0.840894	+	0.541199i	$0.182030\pi$
$90$	8.17534e13	0.00200191
$91$	1.58605e16	0.353561
$92$	−4.66150e16	−0.946955
$93$	2.31815e14	0.00429573
$94$	−1.11206e16	−0.188167
$95$	−3.06940e13	−0.000474682 0
$96$	4.45050e16	0.629656
$97$	−1.04148e14	−0.00134925	−0.000674625	−	1.00000i	$-0.500215\pi$
$97$	−1.04148e14	−0.00134925	−0.000674625		1.00000i	$0.500215\pi$
$98$	1.92687e16	0.228786
$99$	−2.22998e16	−0.242886
$100$	−1.56479e17	−1.56479
$101$	1.12029e17	1.02943	0.514717	−	0.857360i	$-0.327897\pi$
$101$	1.12029e17	1.02943	0.514717	+	0.857360i	$0.327897\pi$
$102$	−6.81988e16	−0.576336
$103$	9.18797e16	0.714666	0.357333	−	0.933977i	$-0.383686\pi$
$103$	9.18797e16	0.714666	0.357333	+	0.933977i	$0.383686\pi$
$104$	−1.18095e17	−0.846153
$105$	1.23890e14	0.000818329 0
$106$	1.23560e17	0.752969
$107$	2.21720e16	0.124751	0.0623755	−	0.998053i	$-0.480132\pi$
$107$	2.21720e16	0.124751	0.0623755	+	0.998053i	$0.480132\pi$
$108$	−5.79273e16	−0.301149
$109$	1.27584e17	0.613295	0.306648	−	0.951823i	$-0.400793\pi$
$109$	1.27584e17	0.613295	0.306648	+	0.951823i	$0.400793\pi$
$110$	−9.83844e14	−0.00437611
$111$	−1.17537e17	−0.484094
$112$	1.15050e16	0.0439070
$113$	−1.26931e16	−0.0449159	−0.0224579	−	0.999748i	$-0.507149\pi$
$113$	−1.26931e16	−0.0449159	−0.0224579	+	0.999748i	$0.507149\pi$
$114$	3.56471e16	0.117039
$115$	−7.44449e14	−0.00226936
$116$	−8.91790e17	−2.52563
$117$	−1.18433e17	−0.311812
$118$	6.34775e17	1.55461
$119$	−1.03349e17	−0.235591
$120$	−9.22471e14	−0.00195845
$121$	−2.37085e17	−0.469059
$122$	−5.90558e17	−1.08944
$123$	−3.42899e16	−0.0590164
$124$	−7.24678e15	−0.0116429
$125$	−4.99804e15	−0.00750005
$126$	−1.43882e17	−0.201771
$127$	8.11706e17	1.06431	0.532154	−	0.846648i	$-0.321383\pi$
$127$	8.11706e17	1.06431	0.532154	+	0.846648i	$0.321383\pi$
$128$	−1.23960e18	−1.52054
$129$	4.57768e17	0.525573
$130$	−5.22514e15	−0.00561797
$131$	−1.72605e18	−1.73879	−0.869393	−	0.494120i	$-0.835490\pi$
$131$	−1.72605e18	−1.73879	−0.869393	+	0.494120i	$0.835490\pi$
$132$	6.97115e17	0.658303
$133$	5.40200e16	0.0478427
$134$	3.15854e17	0.262480
$135$	−9.25108e14	−0.000721698 0
$136$	7.69527e17	0.563824
$137$	−2.11323e18	−1.45486	−0.727432	−	0.686180i	$-0.759286\pi$
$137$	−2.11323e18	−1.45486	−0.727432	+	0.686180i	$0.759286\pi$
$138$	8.64581e17	0.559543
$139$	3.19308e18	1.94349	0.971747	−	0.236023i	$-0.0758441\pi$
$139$	3.19308e18	1.94349	0.971747	+	0.236023i	$0.0758441\pi$
$140$	−3.87293e15	−0.00221795
$141$	1.25839e17	0.0678351
$142$	4.27144e18	2.16832
$143$	1.42526e18	0.681611
$144$	−8.59097e16	−0.0387223
$145$	−1.42420e16	−0.00605263
$146$	4.42706e18	1.77466
$147$	−2.18041e17	−0.0824786
$148$	3.67433e18	1.31206
$149$	2.79688e18	0.943172	0.471586	−	0.881820i	$-0.343682\pi$
$149$	2.79688e18	0.943172	0.471586	+	0.881820i	$0.343682\pi$
$150$	2.90227e18	0.924616
$151$	−5.05909e18	−1.52324	−0.761619	−	0.648025i	$-0.775595\pi$
$151$	−5.05909e18	−1.52324	−0.761619	+	0.648025i	$0.775595\pi$
$152$	−4.02226e17	−0.114499
$153$	7.71728e17	0.207772
$154$	1.73152e18	0.441065
$155$	−1.15732e14	−2.79020e−5 0
$156$	3.70233e18	0.845116
$157$	−8.30018e18	−1.79449	−0.897244	−	0.441535i	$-0.854434\pi$
$157$	−8.30018e18	−1.79449	−0.897244	+	0.441535i	$0.854434\pi$
$158$	−1.09967e19	−2.25256
$159$	−1.39818e18	−0.271449
$160$	−2.22189e16	−0.00408980
$161$	1.31020e18	0.228727
$162$	1.07439e18	0.177945
$163$	−1.08404e19	−1.70393	−0.851965	−	0.523599i	$-0.824589\pi$
$163$	−1.08404e19	−1.70393	−0.851965	+	0.523599i	$0.824589\pi$
$164$	1.07194e18	0.159954
$165$	1.11330e16	0.00157761
$166$	−1.09146e19	−1.46923
$167$	−1.05243e19	−1.34618	−0.673090	−	0.739561i	$-0.735033\pi$
$167$	−1.05243e19	−1.34618	−0.673090	+	0.739561i	$0.735033\pi$
$168$	1.62351e18	0.197390
$169$	−1.08097e18	−0.124962
$170$	3.40478e16	0.00374346
$171$	−4.03377e17	−0.0421933
$172$	−1.43103e19	−1.42448
$173$	−1.08672e19	−1.02973	−0.514867	−	0.857270i	$-0.672159\pi$
$173$	−1.08672e19	−1.02973	−0.514867	+	0.857270i	$0.672159\pi$
$174$	1.65403e19	1.49236
$175$	4.39813e18	0.377959
$176$	1.03386e18	0.0846458
$177$	−7.18301e18	−0.560446
$178$	3.62134e19	2.69339
$179$	−8.72527e18	−0.618768	−0.309384	−	0.950937i	$-0.600123\pi$
$179$	−8.72527e18	−0.618768	−0.309384	+	0.950937i	$0.600123\pi$
$180$	2.89198e16	0.00195605
$181$	5.32474e18	0.343582	0.171791	−	0.985133i	$-0.445045\pi$
$181$	5.32474e18	0.343582	0.171791	+	0.985133i	$0.445045\pi$
$182$	9.19601e18	0.566230
$183$	6.68266e18	0.392749
$184$	−9.75557e18	−0.547395
$185$	5.86796e16	0.00314433
$186$	1.34408e17	0.00687963
$187$	−9.28720e18	−0.454183
$188$	−3.93387e18	−0.183856
$189$	1.62815e18	0.0727393
$190$	−1.77966e16	−0.000760205 0
$191$	−3.60001e19	−1.47069	−0.735343	−	0.677695i	$-0.762979\pi$
$191$	−3.60001e19	−1.47069	−0.735343	+	0.677695i	$0.762979\pi$
$192$	2.40881e19	0.941329
$193$	−8.73885e18	−0.326751	−0.163376	−	0.986564i	$-0.552238\pi$
$193$	−8.73885e18	−0.326751	−0.163376	+	0.986564i	$0.552238\pi$
$194$	−6.03858e16	−0.00216083
$195$	5.91268e16	0.00202530
$196$	6.81619e18	0.223545
$197$	5.93068e18	0.186270	0.0931348	−	0.995654i	$-0.470311\pi$
$197$	5.93068e18	0.186270	0.0931348	+	0.995654i	$0.470311\pi$
$198$	−1.29296e19	−0.388982
$199$	4.98122e19	1.43577	0.717884	−	0.696162i	$-0.245111\pi$
$199$	4.98122e19	1.43577	0.717884	+	0.696162i	$0.245111\pi$
$200$	−3.27479e19	−0.904543
$201$	−3.57416e18	−0.0946253
$202$	6.49551e19	1.64864
$203$	2.50654e19	0.610039
$204$	−2.41250e19	−0.563133
$205$	1.71190e16	0.000383328 0
$206$	5.32724e19	1.14454
$207$	−9.78347e18	−0.201718
$208$	5.49078e18	0.108667
$209$	4.85435e18	0.0922334
$210$	7.18323e16	0.00131056
$211$	−4.19793e19	−0.735587	−0.367793	−	0.929908i	$-0.619887\pi$
$211$	−4.19793e19	−0.735587	−0.367793	+	0.929908i	$0.619887\pi$
$212$	4.37086e19	0.735720
$213$	−4.83349e19	−0.781689
$214$	1.28555e19	0.199789
$215$	−2.28538e17	−0.00341375
$216$	−1.21230e19	−0.174082
$217$	2.03684e17	0.00281221
$218$	7.39738e19	0.982195
$219$	−5.00959e19	−0.639775
$220$	−3.48030e17	−0.00427586
$221$	−4.93237e19	−0.583071
$222$	−6.81488e19	−0.775279
$223$	1.40489e20	1.53833	0.769165	−	0.639050i	$-0.220672\pi$
$223$	1.40489e20	1.53833	0.769165	+	0.639050i	$0.220672\pi$
$224$	3.91042e19	0.412207
$225$	−3.28416e19	−0.333329
$226$	−7.35952e18	−0.0719329
$227$	−1.34756e20	−1.26861	−0.634306	−	0.773082i	$-0.718714\pi$
$227$	−1.34756e20	−1.26861	−0.634306	+	0.773082i	$0.718714\pi$
$228$	1.26100e19	0.114358
$229$	1.16495e19	0.101790	0.0508949	−	0.998704i	$-0.483793\pi$
$229$	1.16495e19	0.101790	0.0508949	+	0.998704i	$0.483793\pi$
$230$	−4.31637e17	−0.00363439
$231$	−1.95936e19	−0.159006
$232$	−1.86633e20	−1.45996
$233$	2.09012e20	1.57632	0.788162	−	0.615467i	$-0.211033\pi$
$233$	2.09012e20	1.57632	0.788162	+	0.615467i	$0.211033\pi$
$234$	−6.86681e19	−0.499368
$235$	−6.28246e16	−0.000440608 0
$236$	2.24548e20	1.51900
$237$	1.24437e20	0.812059
$238$	−5.99227e19	−0.377300
$239$	1.30388e20	0.792235	0.396117	−	0.918200i	$-0.370357\pi$
$239$	1.30388e20	0.792235	0.396117	+	0.918200i	$0.370357\pi$
$240$	4.28899e16	0.000251512 0
$241$	9.89039e18	0.0559846	0.0279923	−	0.999608i	$-0.491089\pi$
$241$	9.89039e18	0.0559846	0.0279923	+	0.999608i	$0.491089\pi$
$242$	−1.37463e20	−0.751200
$243$	−1.21577e19	−0.0641500
$244$	−2.08907e20	−1.06448
$245$	1.08856e17	0.000535722 0
$246$	−1.98815e19	−0.0945150
$247$	2.57812e19	0.118407
$248$	−1.51660e18	−0.00673027
$249$	1.23508e20	0.529663
$250$	−2.89789e18	−0.0120114
$251$	−4.45770e20	−1.78601	−0.893006	−	0.450044i	$-0.851408\pi$
$251$	−4.45770e20	−1.78601	−0.893006	+	0.450044i	$0.851408\pi$
$252$	−5.08976e19	−0.197148
$253$	1.17737e20	0.440950
$254$	4.70632e20	1.70449
$255$	−3.85280e17	−0.00134954
$256$	−2.37513e20	−0.804725
$257$	6.48375e19	0.212518	0.106259	−	0.994339i	$-0.466113\pi$
$257$	6.48375e19	0.212518	0.106259	+	0.994339i	$0.466113\pi$
$258$	2.65417e20	0.841708
$259$	−1.03274e20	−0.316914
$260$	−1.84837e18	−0.00548927
$261$	−1.87167e20	−0.538004
$262$	−1.00077e21	−2.78467
$263$	−8.96789e19	−0.241583	−0.120791	−	0.992678i	$-0.538543\pi$
$263$	−8.96789e19	−0.241583	−0.120791	+	0.992678i	$0.538543\pi$
$264$	1.45892e20	0.380538
$265$	6.98034e17	0.00176314
$266$	3.13212e19	0.0766203
$267$	−4.09785e20	−0.970981
$268$	1.11732e20	0.256467
$269$	−7.76453e20	−1.72672	−0.863358	−	0.504592i	$-0.831643\pi$
$269$	−7.76453e20	−1.72672	−0.863358	+	0.504592i	$0.831643\pi$
$270$	−5.36384e17	−0.00115580
$271$	−4.82686e20	−1.00792	−0.503960	−	0.863727i	$-0.668124\pi$
$271$	−4.82686e20	−1.00792	−0.503960	+	0.863727i	$0.668124\pi$
$272$	−3.57788e19	−0.0724087
$273$	−1.04061e20	−0.204129
$274$	−1.22527e21	−2.32997
$275$	3.95225e20	0.728647
$276$	3.05841e20	0.546725
$277$	9.59440e20	1.66318	0.831591	−	0.555388i	$-0.187430\pi$
$277$	9.59440e20	1.66318	0.831591	+	0.555388i	$0.187430\pi$
$278$	1.85137e21	3.11252
$279$	−1.52094e18	−0.00248014
$280$	−8.10526e17	−0.00128210
$281$	9.16949e19	0.140715	0.0703577	−	0.997522i	$-0.477586\pi$
$281$	9.16949e19	0.140715	0.0703577	+	0.997522i	$0.477586\pi$
$282$	7.29626e19	0.108638
$283$	8.26069e18	0.0119353	0.00596763	−	0.999982i	$-0.498100\pi$
$283$	8.26069e18	0.0119353	0.00596763	+	0.999982i	$0.498100\pi$
$284$	1.51100e21	2.11864
$285$	2.01383e17	0.000274058 0
$286$	8.26373e20	1.09160
$287$	−3.01287e19	−0.0386353
$288$	−2.91998e20	−0.363532
$289$	−5.05839e20	−0.611477
$290$	−8.25762e18	−0.00969331
$291$	6.83317e17	0.000778990 0
$292$	1.56605e21	1.73401
$293$	−4.22662e20	−0.454588	−0.227294	−	0.973826i	$-0.572988\pi$
$293$	−4.22662e20	−0.454588	−0.227294	+	0.973826i	$0.572988\pi$
$294$	−1.26422e20	−0.132090
$295$	3.58607e18	0.00364025
$296$	7.68962e20	0.758447
$297$	1.46309e20	0.140230
$298$	1.62165e21	1.51049
$299$	6.25295e20	0.566082
$300$	1.02666e21	0.903434
$301$	4.02217e20	0.344069
$302$	−2.93329e21	−2.43947
$303$	−7.35022e20	−0.594344
$304$	1.87013e19	0.0147044
$305$	−3.33627e18	−0.00255101
$306$	4.47453e20	0.332748
$307$	6.52210e20	0.471749	0.235874	−	0.971784i	$-0.424205\pi$
$307$	6.52210e20	0.471749	0.235874	+	0.971784i	$0.424205\pi$
$308$	6.12517e20	0.430960
$309$	−6.02822e20	−0.412612
$310$	−6.71023e16	−4.46851e−5 0
$311$	−8.44362e20	−0.547098	−0.273549	−	0.961858i	$-0.588198\pi$
$311$	−8.44362e20	−0.547098	−0.273549	+	0.961858i	$0.588198\pi$
$312$	7.74822e20	0.488526
$313$	2.89142e21	1.77413	0.887063	−	0.461648i	$-0.152742\pi$
$313$	2.89142e21	1.77413	0.887063	+	0.461648i	$0.152742\pi$
$314$	−4.81250e21	−2.87388
$315$	−8.12843e17	−0.000472462 0
$316$	−3.89002e21	−2.20096
$317$	−9.42786e20	−0.519290	−0.259645	−	0.965704i	$-0.583605\pi$
$317$	−9.42786e20	−0.519290	−0.259645	+	0.965704i	$0.583605\pi$
$318$	−8.10675e20	−0.434727
$319$	2.25243e21	1.17606
$320$	−1.20258e19	−0.00611420
$321$	−1.45471e20	−0.0720250
$322$	7.59661e20	0.366307
$323$	−1.67994e20	−0.0788993
$324$	3.80061e20	0.173868
$325$	2.09902e21	0.935422
$326$	−6.28535e21	−2.72885
$327$	−8.37076e20	−0.354086
$328$	2.24334e20	0.0924631
$329$	1.10568e20	0.0444085
$330$	6.45500e18	0.00252655
$331$	3.02132e21	1.15255	0.576273	−	0.817257i	$-0.304507\pi$
$331$	3.02132e21	1.15255	0.576273	+	0.817257i	$0.304507\pi$
$332$	−3.86098e21	−1.43557
$333$	7.71161e20	0.279492
$334$	−6.10206e21	−2.15591
$335$	1.78438e18	0.000614618 0
$336$	−7.54843e19	−0.0253497
$337$	2.52365e20	0.0826370	0.0413185	−	0.999146i	$-0.486844\pi$
$337$	2.52365e20	0.0826370	0.0413185	+	0.999146i	$0.486844\pi$
$338$	−6.26753e20	−0.200127
$339$	8.32792e19	0.0259322
$340$	1.20442e19	0.00365771
$341$	1.83034e19	0.00542151
$342$	−2.33880e20	−0.0675728
$343$	−1.91581e20	−0.0539949
$344$	−2.99486e21	−0.823435
$345$	4.88433e18	0.00131022
$346$	−6.30087e21	−1.64912
$347$	−1.00182e21	−0.255853	−0.127927	−	0.991784i	$-0.540832\pi$
$347$	−1.00182e21	−0.255853	−0.127927	+	0.991784i	$0.540832\pi$
$348$	5.85104e21	1.45817
$349$	5.01500e21	1.21971	0.609853	−	0.792515i	$-0.291228\pi$
$349$	5.01500e21	1.21971	0.609853	+	0.792515i	$0.291228\pi$
$350$	2.55007e21	0.605303
$351$	7.77038e20	0.180025
$352$	3.51399e21	0.794671
$353$	1.06436e21	0.234965	0.117482	−	0.993075i	$-0.462518\pi$
$353$	1.06436e21	0.234965	0.117482	+	0.993075i	$0.462518\pi$
$354$	−4.16476e21	−0.897557
$355$	2.41309e19	0.00507729
$356$	1.28103e22	2.63169
$357$	6.78076e20	0.136019
$358$	−5.05897e21	−0.990960
$359$	5.12127e21	0.979660	0.489830	−	0.871818i	$-0.337059\pi$
$359$	5.12127e21	0.979660	0.489830	+	0.871818i	$0.337059\pi$
$360$	6.05233e18	0.00113071
$361$	−5.39258e21	−0.983978
$362$	3.08732e21	0.550249
$363$	1.55551e21	0.270811
$364$	3.25304e21	0.553258
$365$	2.50101e19	0.00415552
$366$	3.87465e21	0.628989
$367$	9.39704e21	1.49049	0.745246	−	0.666789i	$-0.232332\pi$
$367$	9.39704e21	1.49049	0.745246	+	0.666789i	$0.232332\pi$
$368$	4.53581e20	0.0702989
$369$	2.24976e20	0.0340731
$370$	3.40228e19	0.00503565
$371$	−1.22851e21	−0.177705
$372$	4.75461e19	0.00672202
$373$	7.91816e21	1.09421	0.547103	−	0.837065i	$-0.315731\pi$
$373$	7.91816e21	1.09421	0.547103	+	0.837065i	$0.315731\pi$
$374$	−5.38478e21	−0.727377
$375$	3.27921e19	0.00433016
$376$	−8.23279e20	−0.106280
$377$	1.19625e22	1.50980
$378$	9.44012e20	0.116492
$379$	−1.41809e22	−1.71108	−0.855538	−	0.517739i	$-0.826774\pi$
$379$	−1.41809e22	−1.71108	−0.855538	+	0.517739i	$0.826774\pi$
$380$	−6.29544e18	−0.000742789 0
$381$	−5.32560e21	−0.614478
$382$	−2.08731e22	−2.35531
$383$	−4.11238e21	−0.453841	−0.226921	−	0.973913i	$-0.572866\pi$
$383$	−4.11238e21	−0.453841	−0.226921	+	0.973913i	$0.572866\pi$
$384$	8.13304e21	0.877885
$385$	9.78200e18	0.00103279
$386$	−5.06684e21	−0.523293
$387$	−3.00342e21	−0.303440
$388$	−2.13612e19	−0.00211133
$389$	−1.44560e22	−1.39790	−0.698949	−	0.715172i	$-0.746348\pi$
$389$	−1.44560e22	−1.39790	−0.698949	+	0.715172i	$0.746348\pi$
$390$	3.42821e19	0.00324353
$391$	−4.07452e21	−0.377202
$392$	1.42649e21	0.129222
$393$	1.13246e22	1.00389
$394$	3.43865e21	0.298311
$395$	−6.21242e19	−0.00527455
$396$	−4.57377e21	−0.380071
$397$	−9.68932e21	−0.788086	−0.394043	−	0.919092i	$-0.628924\pi$
$397$	−9.68932e21	−0.788086	−0.394043	+	0.919092i	$0.628924\pi$
$398$	2.88814e22	2.29939
$399$	−3.54425e20	−0.0276220
$400$	1.52260e21	0.116165
$401$	−1.34295e22	−1.00307	−0.501536	−	0.865137i	$-0.667232\pi$
$401$	−1.34295e22	−1.00307	−0.501536	+	0.865137i	$0.667232\pi$
$402$	−2.07232e21	−0.151543
$403$	9.72084e19	0.00696003
$404$	2.29775e22	1.61087
$405$	6.06964e18	0.000416673 0
$406$	1.45331e22	0.976980
$407$	−9.28038e21	−0.610961
$408$	−5.04887e21	−0.325524
$409$	−5.39990e19	−0.00340987	−0.00170493	−	0.999999i	$-0.500543\pi$
$409$	−5.39990e19	−0.00340987	−0.00170493	+	0.999999i	$0.500543\pi$
$410$	9.92571e18	0.000613902 0
$411$	1.38649e22	0.839966
$412$	1.88448e22	1.11832
$413$	−6.31133e21	−0.366898
$414$	−5.67252e21	−0.323052
$415$	−6.16605e19	−0.00344031
$416$	1.86626e22	1.02018
$417$	−2.09498e22	−1.12208
$418$	2.81459e21	0.147712
$419$	1.07690e22	0.553805	0.276902	−	0.960898i	$-0.410692\pi$
$419$	1.07690e22	0.553805	0.276902	+	0.960898i	$0.410692\pi$
$420$	2.54103e19	0.00128053
$421$	5.68170e21	0.280595	0.140298	−	0.990109i	$-0.455194\pi$
$421$	5.68170e21	0.280595	0.140298	+	0.990109i	$0.455194\pi$
$422$	−2.43398e22	−1.17805
$423$	−8.25633e20	−0.0391646
$424$	9.14732e21	0.425289
$425$	−1.36775e22	−0.623307
$426$	−2.80249e22	−1.25188
$427$	5.87169e21	0.257114
$428$	4.54757e21	0.195212
$429$	−9.35111e21	−0.393528
$430$	−1.32508e20	−0.00546713
$431$	9.84323e21	0.398181	0.199091	−	0.979981i	$-0.436201\pi$
$431$	9.84323e21	0.398181	0.199091	+	0.979981i	$0.436201\pi$
$432$	5.63654e20	0.0223563
$433$	−2.84959e22	−1.10824	−0.554121	−	0.832436i	$-0.686946\pi$
$433$	−2.84959e22	−1.10824	−0.554121	+	0.832436i	$0.686946\pi$
$434$	1.18097e20	0.00450377
$435$	9.34420e19	0.00349449
$436$	2.61679e22	0.959694
$437$	2.12972e21	0.0766004
$438$	−2.90459e22	−1.02460
$439$	−3.33148e22	−1.15263	−0.576314	−	0.817229i	$-0.695509\pi$
$439$	−3.33148e22	−1.15263	−0.576314	+	0.817229i	$0.695509\pi$
$440$	−7.28355e19	−0.00247170
$441$	1.43057e21	0.0476190
$442$	−2.85982e22	−0.933791
$443$	−3.01681e22	−0.966310	−0.483155	−	0.875535i	$-0.660509\pi$
$443$	−3.01681e22	−0.966310	−0.483155	+	0.875535i	$0.660509\pi$
$444$	−2.41073e22	−0.757518
$445$	2.04583e20	0.00630680
$446$	8.14562e22	2.46364
$447$	−1.83503e22	−0.544541
$448$	2.11649e22	0.616244
$449$	−3.27396e22	−0.935362	−0.467681	−	0.883897i	$-0.654910\pi$
$449$	−3.27396e22	−0.935362	−0.467681	+	0.883897i	$0.654910\pi$
$450$	−1.90418e22	−0.533827
$451$	−2.70743e21	−0.0744828
$452$	−2.60339e21	−0.0702851
$453$	3.31927e22	0.879442
$454$	−7.81325e22	−2.03169
$455$	5.19516e19	0.00132587
$456$	2.63901e21	0.0661058
$457$	5.71904e20	0.0140616	0.00703081	−	0.999975i	$-0.497762\pi$
$457$	5.71904e20	0.0140616	0.00703081	+	0.999975i	$0.497762\pi$
$458$	6.75443e21	0.163017
$459$	−5.06330e21	−0.119957
$460$	−1.52689e20	−0.00355113
$461$	4.91378e22	1.12191	0.560955	−	0.827846i	$-0.310434\pi$
$461$	4.91378e22	1.12191	0.560955	+	0.827846i	$0.310434\pi$
$462$	−1.13605e22	−0.254649
$463$	−2.34238e22	−0.515488	−0.257744	−	0.966213i	$-0.582979\pi$
$463$	−2.34238e22	−0.515488	−0.257744	+	0.966213i	$0.582979\pi$
$464$	8.67744e21	0.187495
$465$	7.59319e17	1.61092e−5 0
$466$	1.21186e23	2.52449
$467$	−8.59565e21	−0.175827	−0.0879134	−	0.996128i	$-0.528020\pi$
$467$	−8.59565e21	−0.175827	−0.0879134	+	0.996128i	$0.528020\pi$
$468$	−2.42910e22	−0.487928
$469$	−3.14042e21	−0.0619468
$470$	−3.64261e19	−0.000705636 0
$471$	5.44575e22	1.03605
$472$	4.69934e22	0.878071
$473$	3.61440e22	0.663311
$474$	7.21492e22	1.30052
$475$	7.14915e21	0.126578
$476$	−2.11973e22	−0.368657
$477$	9.17348e21	0.156721
$478$	7.55995e22	1.26877
$479$	−7.95581e22	−1.31169	−0.655847	−	0.754894i	$-0.727688\pi$
$479$	−7.95581e22	−1.31169	−0.655847	+	0.754894i	$0.727688\pi$
$480$	1.45778e20	0.00236125
$481$	−4.92875e22	−0.784339
$482$	5.73451e21	0.0896595
$483$	−8.59621e21	−0.132055
$484$	−4.86269e22	−0.733991
$485$	−3.41141e17	−5.05976e−6 0
$486$	−7.04909e21	−0.102737
$487$	1.05123e23	1.50558	0.752789	−	0.658262i	$-0.228708\pi$
$487$	1.05123e23	1.50558	0.752789	+	0.658262i	$0.228708\pi$
$488$	−4.37199e22	−0.615334
$489$	7.11240e22	0.983764
$490$	6.31152e19	0.000857961 0
$491$	6.66515e22	0.890466	0.445233	−	0.895415i	$-0.353121\pi$
$491$	6.66515e22	0.890466	0.445233	+	0.895415i	$0.353121\pi$
$492$	−7.03298e21	−0.0923498
$493$	−7.79495e22	−1.00604
$494$	1.49481e22	0.189630
$495$	−7.30438e19	−0.000910834 0
$496$	7.05138e19	0.000864331 0
$497$	−4.24693e22	−0.511736
$498$	7.16106e22	0.848258
$499$	6.75512e22	0.786644	0.393322	−	0.919401i	$-0.371326\pi$
$499$	6.75512e22	0.786644	0.393322	+	0.919401i	$0.371326\pi$
$500$	−1.02512e21	−0.0117362
$501$	6.90499e22	0.777217
$502$	−2.58461e23	−2.86031
$503$	−2.29329e22	−0.249535	−0.124767	−	0.992186i	$-0.539818\pi$
$503$	−2.29329e22	−0.249535	−0.124767	+	0.992186i	$0.539818\pi$
$504$	−1.06518e22	−0.113963
$505$	3.66955e20	0.00386043
$506$	6.82648e22	0.706183
$507$	7.09224e21	0.0721466
$508$	1.66484e23	1.66544
$509$	8.80078e22	0.865805	0.432903	−	0.901441i	$-0.357489\pi$
$509$	8.80078e22	0.865805	0.432903	+	0.901441i	$0.357489\pi$
$510$	−2.23388e20	−0.00216129
$511$	−4.40166e22	−0.418831
$512$	2.47658e22	0.231771
$513$	2.64655e21	0.0243603
$514$	3.75932e22	0.340348
$515$	3.00955e20	0.00268003
$516$	9.38899e22	0.822426
$517$	9.93591e21	0.0856127
$518$	−5.98787e22	−0.507539
$519$	7.12996e22	0.594518
$520$	−3.86825e20	−0.00317312
$521$	−1.23833e22	−0.0999342	−0.0499671	−	0.998751i	$-0.515912\pi$
$521$	−1.23833e22	−0.0999342	−0.0499671	+	0.998751i	$0.515912\pi$
$522$	−1.08521e23	−0.861615
$523$	−2.10907e23	−1.64751	−0.823754	−	0.566947i	$-0.808124\pi$
$523$	−2.10907e23	−1.64751	−0.823754	+	0.566947i	$0.808124\pi$
$524$	−3.54018e23	−2.72088
$525$	−2.88561e22	−0.218215
$526$	−5.19964e22	−0.386896
$527$	−6.33426e20	−0.00463773
$528$	−6.78318e21	−0.0488703
$529$	−8.93959e22	−0.633788
$530$	4.04724e20	0.00282367
$531$	4.71277e22	0.323574
$532$	1.10797e22	0.0748651
$533$	−1.43790e22	−0.0956195
$534$	−2.37596e23	−1.55503
$535$	7.26254e19	0.000467823 0
$536$	2.33832e22	0.148253
$537$	5.72465e22	0.357246
$538$	−4.50193e23	−2.76534
$539$	−1.72159e22	−0.104094
$540$	−1.89743e20	−0.00112932
$541$	2.98486e23	1.74883	0.874414	−	0.485181i	$-0.161246\pi$
$541$	2.98486e23	1.74883	0.874414	+	0.485181i	$0.161246\pi$
$542$	−2.79864e23	−1.61419
$543$	−3.49356e22	−0.198367
$544$	−1.21608e23	−0.679786
$545$	4.17905e20	0.00229989
$546$	−6.03350e22	−0.326913
$547$	−1.30331e23	−0.695272	−0.347636	−	0.937630i	$-0.613016\pi$
$547$	−1.30331e23	−0.695272	−0.347636	+	0.937630i	$0.613016\pi$
$548$	−4.33431e23	−2.27659
$549$	−4.38449e22	−0.226754
$550$	2.29154e23	1.16693
$551$	4.07437e22	0.204302
$552$	6.40063e22	0.316039
$553$	1.09336e23	0.531618
$554$	5.56290e23	2.66359
$555$	−3.84997e20	−0.00181538
$556$	6.54911e23	3.04121
$557$	−1.64680e23	−0.753135	−0.376567	−	0.926389i	$-0.622896\pi$
$557$	−1.64680e23	−0.753135	−0.376567	+	0.926389i	$0.622896\pi$
$558$	−8.81851e20	−0.00397195
$559$	1.91959e23	0.851545
$560$	3.76850e19	0.000164653 0
$561$	6.09333e22	0.262223
$562$	5.31653e22	0.225356
$563$	−1.92575e23	−0.804041	−0.402020	−	0.915631i	$-0.631692\pi$
$563$	−1.92575e23	−0.804041	−0.402020	+	0.915631i	$0.631692\pi$
$564$	2.58101e22	0.106149
$565$	−4.15766e19	−0.000168437 0
$566$	4.78960e21	0.0191144
$567$	−1.06823e22	−0.0419961
$568$	3.16221e23	1.22470
$569$	−5.49905e22	−0.209814	−0.104907	−	0.994482i	$-0.533454\pi$
$569$	−5.49905e22	−0.209814	−0.104907	+	0.994482i	$0.533454\pi$
$570$	1.16763e20	0.000438904 0
$571$	2.78347e23	1.03081	0.515407	−	0.856945i	$-0.327641\pi$
$571$	2.78347e23	1.03081	0.515407	+	0.856945i	$0.327641\pi$
$572$	2.92325e23	1.06660
$573$	2.36197e23	0.849101
$574$	−1.74688e22	−0.0618746
$575$	1.73395e23	0.605146
$576$	−1.58042e23	−0.543476
$577$	4.78014e23	1.61974	0.809872	−	0.586606i	$-0.199536\pi$
$577$	4.78014e23	1.61974	0.809872	+	0.586606i	$0.199536\pi$
$578$	−2.93289e23	−0.979284
$579$	5.73356e22	0.188650
$580$	−2.92109e21	−0.00947125
$581$	1.08520e23	0.346746
$582$	3.96191e20	0.00124756
$583$	−1.10396e23	−0.342588
$584$	3.27742e23	1.00236
$585$	−3.87931e20	−0.00116931
$586$	−2.45062e23	−0.728025
$587$	−4.85252e23	−1.42083	−0.710417	−	0.703781i	$-0.751494\pi$
$587$	−4.85252e23	−1.42083	−0.710417	+	0.703781i	$0.751494\pi$
$588$	−4.47210e22	−0.129064
$589$	3.31087e20	0.000941808 0
$590$	2.07923e21	0.00582988
$591$	−3.89112e22	−0.107543
$592$	−3.57526e22	−0.0974031
$593$	−1.11757e23	−0.300131	−0.150066	−	0.988676i	$-0.547948\pi$
$593$	−1.11757e23	−0.300131	−0.150066	+	0.988676i	$0.547948\pi$
$594$	8.48309e22	0.224579
$595$	−3.38525e20	−0.000883480 0
$596$	5.73651e23	1.47589
$597$	−3.26818e23	−0.828942
$598$	3.62550e23	0.906583
$599$	−6.39355e23	−1.57621	−0.788105	−	0.615541i	$-0.788938\pi$
$599$	−6.39355e23	−1.57621	−0.788105	+	0.615541i	$0.788938\pi$
$600$	2.14859e23	0.522238
$601$	4.25977e23	1.02083	0.510415	−	0.859928i	$-0.329492\pi$
$601$	4.25977e23	1.02083	0.510415	+	0.859928i	$0.329492\pi$
$602$	2.33208e23	0.551027
$603$	2.34501e22	0.0546320
$604$	−1.03764e24	−2.38359
$605$	−7.76579e20	−0.00175900
$606$	−4.26170e23	−0.951844
$607$	−8.59210e23	−1.89232	−0.946162	−	0.323692i	$-0.895076\pi$
$607$	−8.59210e23	−1.89232	−0.946162	+	0.323692i	$0.895076\pi$
$608$	6.35638e22	0.138048
$609$	−1.64454e23	−0.352206
$610$	−1.93439e21	−0.00408546
$611$	5.27690e22	0.109908
$612$	1.58284e23	0.325125
$613$	1.71142e23	0.346690	0.173345	−	0.984861i	$-0.444542\pi$
$613$	1.71142e23	0.346690	0.173345	+	0.984861i	$0.444542\pi$
$614$	3.78155e23	0.755508
$615$	−1.12318e20	−0.000221315 0
$616$	1.28187e23	0.249120
$617$	5.77283e23	1.10653	0.553267	−	0.833004i	$-0.313381\pi$
$617$	5.77283e23	1.10653	0.553267	+	0.833004i	$0.313381\pi$
$618$	−3.49520e23	−0.660801
$619$	−2.91521e23	−0.543625	−0.271813	−	0.962350i	$-0.587623\pi$
$619$	−2.91521e23	−0.543625	−0.271813	+	0.962350i	$0.587623\pi$
$620$	−2.37371e19	−4.36615e−5 0
$621$	6.41893e22	0.116462
$622$	−4.89567e23	−0.876180
$623$	−3.60057e23	−0.635656
$624$	−3.60250e22	−0.0627387
$625$	5.82052e23	0.999958
$626$	1.67646e24	2.84127
$627$	−3.18494e22	−0.0532510
$628$	−1.70240e24	−2.80804
$629$	3.21166e23	0.522635
$630$	−4.71292e20	−0.000756650 0
$631$	2.96332e23	0.469385	0.234693	−	0.972070i	$-0.424592\pi$
$631$	2.96332e23	0.469385	0.234693	+	0.972070i	$0.424592\pi$
$632$	−8.14102e23	−1.27228
$633$	2.75426e23	0.424691
$634$	−5.46634e23	−0.831644
$635$	2.65877e21	0.00399121
$636$	−2.86772e23	−0.424768
$637$	−9.14325e22	−0.133634
$638$	1.30597e24	1.88347
$639$	3.17125e23	0.451309
$640$	−4.06037e21	−0.00570211
$641$	−7.56808e23	−1.04880	−0.524400	−	0.851472i	$-0.675710\pi$
$641$	−7.56808e23	−1.04880	−0.524400	+	0.851472i	$0.675710\pi$
$642$	−8.43449e22	−0.115348
$643$	6.39882e23	0.863588	0.431794	−	0.901972i	$-0.357881\pi$
$643$	6.39882e23	0.863588	0.431794	+	0.901972i	$0.357881\pi$
$644$	2.68726e23	0.357915
$645$	1.49944e21	0.00197093
$646$	−9.74042e22	−0.126358
$647$	−6.61917e23	−0.847456	−0.423728	−	0.905789i	$-0.639279\pi$
$647$	−6.61917e23	−0.847456	−0.423728	+	0.905789i	$0.639279\pi$
$648$	7.95390e22	0.100506
$649$	−5.67149e23	−0.707322
$650$	1.21702e24	1.49808
$651$	−1.33637e21	−0.00162363
$652$	−2.22341e24	−2.66634
$653$	1.60600e24	1.90101	0.950505	−	0.310710i	$-0.100567\pi$
$653$	1.60600e24	1.90101	0.950505	+	0.310710i	$0.100567\pi$
$654$	−4.85342e23	−0.567071
$655$	−5.65373e21	−0.00652054
$656$	−1.04303e22	−0.0118745
$657$	3.28679e23	0.369374
$658$	6.41083e22	0.0711204
$659$	−7.03602e23	−0.770550	−0.385275	−	0.922802i	$-0.625893\pi$
$659$	−7.03602e23	−0.770550	−0.385275	+	0.922802i	$0.625893\pi$
$660$	2.28342e21	0.00246867
$661$	−4.71645e23	−0.503388	−0.251694	−	0.967807i	$-0.580988\pi$
$661$	−4.71645e23	−0.503388	−0.251694	+	0.967807i	$0.580988\pi$
$662$	1.75178e24	1.84581
$663$	3.23613e23	0.336636
$664$	−8.08024e23	−0.829842
$665$	1.76945e20	0.000179413 0
$666$	4.47124e23	0.447607
$667$	9.88194e23	0.976726
$668$	−2.15857e24	−2.10652
$669$	−9.21746e23	−0.888156
$670$	1.03459e21	0.000984314 0
$671$	5.27643e23	0.495677
$672$	−2.56563e23	−0.237988
$673$	1.68843e24	1.54652	0.773258	−	0.634092i	$-0.218626\pi$
$673$	1.68843e24	1.54652	0.773258	+	0.634092i	$0.218626\pi$
$674$	1.46323e23	0.132344
$675$	2.15474e23	0.192447
$676$	−2.21711e23	−0.195542
$677$	−2.17546e24	−1.89473	−0.947365	−	0.320155i	$-0.896265\pi$
$677$	−2.17546e24	−1.89473	−0.947365	+	0.320155i	$0.896265\pi$
$678$	4.82858e22	0.0415305
$679$	6.00394e20	0.000509968 0
$680$	2.52061e21	0.00211437
$681$	8.84135e23	0.732434
$682$	1.06125e22	0.00868258
$683$	−1.35699e24	−1.09648	−0.548239	−	0.836321i	$-0.684702\pi$
$683$	−1.35699e24	−1.09648	−0.548239	+	0.836321i	$0.684702\pi$
$684$	−8.27340e22	−0.0660248
$685$	−6.92197e21	−0.00545582
$686$	−1.11080e23	−0.0864731
$687$	−7.64321e22	−0.0587684
$688$	1.39245e23	0.105749
$689$	−5.86308e23	−0.439807
$690$	2.83197e21	0.00209832
$691$	7.81094e23	0.571663	0.285831	−	0.958280i	$-0.407730\pi$
$691$	7.81094e23	0.571663	0.285831	+	0.958280i	$0.407730\pi$
$692$	−2.22890e24	−1.61135
$693$	1.28554e23	0.0918021
$694$	−5.80865e23	−0.409750
$695$	1.04590e22	0.00728821
$696$	1.22450e24	0.842910
$697$	9.36957e22	0.0637149
$698$	2.90773e24	1.95336
$699$	−1.37133e24	−0.910092
$700$	9.02073e23	0.591437
$701$	−1.67887e24	−1.08746	−0.543731	−	0.839260i	$-0.682989\pi$
$701$	−1.67887e24	−1.08746	−0.543731	+	0.839260i	$0.682989\pi$
$702$	4.50532e23	0.288310
$703$	−1.67871e23	−0.106134
$704$	1.90192e24	1.18802
$705$	4.12192e20	0.000254385 0
$706$	6.17122e23	0.376297
$707$	−6.45824e23	−0.389089
$708$	−1.47326e24	−0.876995
$709$	2.86412e24	1.68460	0.842302	−	0.539005i	$-0.181200\pi$
$709$	2.86412e24	1.68460	0.842302	+	0.539005i	$0.181200\pi$
$710$	1.39912e22	0.00813131
$711$	−8.16429e23	−0.468843
$712$	2.68094e24	1.52127
$713$	8.03017e21	0.00450260
$714$	3.93153e23	0.217834
$715$	4.66848e21	0.00255608
$716$	−1.78958e24	−0.968259
$717$	−8.55472e23	−0.457397
$718$	2.96935e24	1.56893
$719$	−1.02551e24	−0.535481	−0.267741	−	0.963491i	$-0.586277\pi$
$719$	−1.02551e24	−0.535481	−0.267741	+	0.963491i	$0.586277\pi$
$720$	−2.81400e20	−0.000145211 0
$721$	−5.29668e23	−0.270118
$722$	−3.12665e24	−1.57584
$723$	−6.48908e22	−0.0323227
$724$	1.09212e24	0.537643
$725$	3.31721e24	1.61399
$726$	9.01896e23	0.433706
$727$	−2.14060e24	−1.01740	−0.508701	−	0.860943i	$-0.669874\pi$
$727$	−2.14060e24	−1.01740	−0.508701	+	0.860943i	$0.669874\pi$
$728$	6.80795e23	0.319816
$729$	7.97664e22	0.0370370
$730$	1.45010e22	0.00665508
$731$	−1.25083e24	−0.567417
$732$	1.37064e24	0.614580
$733$	3.01809e24	1.33767	0.668834	−	0.743412i	$-0.266794\pi$
$733$	3.01809e24	1.33767	0.668834	+	0.743412i	$0.266794\pi$
$734$	5.44847e24	2.38703
$735$	−7.14202e20	−0.000309299 0
$736$	1.54167e24	0.659979
$737$	−2.82205e23	−0.119424
$738$	1.30442e23	0.0545682
$739$	−1.27758e24	−0.528335	−0.264167	−	0.964477i	$-0.585097\pi$
$739$	−1.27758e24	−0.528335	−0.264167	+	0.964477i	$0.585097\pi$
$740$	1.20354e22	0.00492029
$741$	−1.69150e23	−0.0683625
$742$	−7.12297e23	−0.284596
$743$	−1.74393e23	−0.0688850	−0.0344425	−	0.999407i	$-0.510966\pi$
$743$	−1.74393e23	−0.0688850	−0.0344425	+	0.999407i	$0.510966\pi$
$744$	9.95043e21	0.00388572
$745$	9.16129e21	0.00353695
$746$	4.59100e24	1.75238
$747$	−8.10335e23	−0.305801
$748$	−1.90484e24	−0.710713
$749$	−1.27817e23	−0.0471514
$750$	1.90131e22	0.00693477
$751$	−8.19253e23	−0.295446	−0.147723	−	0.989029i	$-0.547194\pi$
$751$	−8.19253e23	−0.295446	−0.147723	+	0.989029i	$0.547194\pi$
$752$	3.82780e22	0.0136489
$753$	2.92470e24	1.03115
$754$	6.93593e24	2.41796
$755$	−1.65712e22	−0.00571223
$756$	3.33939e23	0.113824
$757$	−2.53750e24	−0.855245	−0.427623	−	0.903957i	$-0.640649\pi$
$757$	−2.53750e24	−0.855245	−0.427623	+	0.903957i	$0.640649\pi$
$758$	−8.22216e24	−2.74030
$759$	−7.72474e23	−0.254582
$760$	−1.31751e21	−0.000429376 0
$761$	−5.86180e22	−0.0188913	−0.00944563	−	0.999955i	$-0.503007\pi$
$761$	−5.86180e22	−0.0188913	−0.00944563	+	0.999955i	$0.503007\pi$
$762$	−3.08782e24	−0.984089
$763$	−7.35494e23	−0.231804
$764$	−7.38375e24	−2.30135
$765$	2.52782e21	0.000779156 0
$766$	−2.38439e24	−0.726829
$767$	−3.01209e24	−0.908046
$768$	1.55832e24	0.464608
$769$	−8.24496e23	−0.243117	−0.121558	−	0.992584i	$-0.538789\pi$
$769$	−8.24496e23	−0.243117	−0.121558	+	0.992584i	$0.538789\pi$
$770$	5.67167e21	0.00165402
$771$	−4.25399e23	−0.122697
$772$	−1.79237e24	−0.511305
$773$	−5.94460e24	−1.67725	−0.838623	−	0.544712i	$-0.816639\pi$
$773$	−5.94460e24	−1.67725	−0.838623	+	0.544712i	$0.816639\pi$
$774$	−1.74140e24	−0.485960
$775$	2.69560e22	0.00744032
$776$	−4.47046e21	−0.00122047
$777$	6.77578e23	0.182970
$778$	−8.38166e24	−2.23874
$779$	−4.89741e22	−0.0129389
$780$	1.21271e22	0.00316923
$781$	−3.81638e24	−0.986547
$782$	−2.36243e24	−0.604091
$783$	1.22800e24	0.310617
$784$	−6.63240e22	−0.0165953
$785$	−2.71875e22	−0.00672942
$786$	6.56607e24	1.60773
$787$	−4.77054e24	−1.15553	−0.577766	−	0.816202i	$-0.696075\pi$
$787$	−4.77054e24	−1.15553	−0.577766	+	0.816202i	$0.696075\pi$
$788$	1.21640e24	0.291478
$789$	5.88383e23	0.139478
$790$	−3.60200e22	−0.00844722
$791$	7.31730e22	0.0169766
$792$	−9.57196e23	−0.219703
$793$	2.80228e24	0.636340
$794$	−5.61793e24	−1.26212
$795$	−4.57980e21	−0.00101795
$796$	1.02167e25	2.24671
$797$	5.50255e24	1.19720	0.598602	−	0.801046i	$-0.295723\pi$
$797$	5.50255e24	1.19720	0.598602	+	0.801046i	$0.295723\pi$
$798$	−2.05498e23	−0.0442368
$799$	−3.43851e23	−0.0732358
$800$	5.17515e24	1.09058
$801$	2.68860e24	0.560596
$802$	−7.78651e24	−1.60642
$803$	−3.95542e24	−0.807441
$804$	−7.33073e23	−0.148071
$805$	4.29160e21	0.000857738 0
$806$	5.63621e22	0.0111465
$807$	5.09431e24	0.996920
$808$	4.80873e24	0.931180
$809$	4.06814e24	0.779531	0.389766	−	0.920914i	$-0.372556\pi$
$809$	4.06814e24	0.779531	0.389766	+	0.920914i	$0.372556\pi$
$810$	3.51921e21	0.000667303 0
$811$	3.33966e24	0.626650	0.313325	−	0.949646i	$-0.398557\pi$
$811$	3.33966e24	0.626650	0.313325	+	0.949646i	$0.398557\pi$
$812$	5.14099e24	0.954599
$813$	3.16690e24	0.581922
$814$	−5.38083e24	−0.978456
$815$	−3.55082e22	−0.00638983
$816$	2.34745e23	0.0418052
$817$	6.53802e23	0.115228
$818$	−3.13089e22	−0.00546091
$819$	6.82742e23	0.117854
$820$	3.51117e21	0.000599838 0
$821$	7.45518e24	1.26050	0.630248	−	0.776394i	$-0.282953\pi$
$821$	7.45518e24	1.26050	0.630248	+	0.776394i	$0.282953\pi$
$822$	8.03897e24	1.34521
$823$	−7.50658e24	−1.24321	−0.621603	−	0.783332i	$-0.713518\pi$
$823$	−7.50658e24	−1.24321	−0.621603	+	0.783332i	$0.713518\pi$
$824$	3.94384e24	0.646455
$825$	−2.59307e24	−0.420684
$826$	−3.65935e24	−0.587589
$827$	9.32722e24	1.48237	0.741183	−	0.671303i	$-0.234265\pi$
$827$	9.32722e24	1.48237	0.741183	+	0.671303i	$0.234265\pi$
$828$	−2.00662e24	−0.315652
$829$	−3.74578e24	−0.583215	−0.291607	−	0.956538i	$-0.594190\pi$
$829$	−3.74578e24	−0.583215	−0.291607	+	0.956538i	$0.594190\pi$
$830$	−3.57511e22	−0.00550968
$831$	−6.29489e24	−0.960239
$832$	1.01010e25	1.52516
$833$	5.95789e23	0.0890451
$834$	−1.21468e25	−1.79701
$835$	−3.44727e22	−0.00504825
$836$	9.95645e23	0.144328
$837$	9.97888e21	0.00143191
$838$	6.24394e24	0.886921
$839$	6.36275e24	0.894681	0.447341	−	0.894364i	$-0.352371\pi$
$839$	6.36275e24	0.894681	0.447341	+	0.894364i	$0.352371\pi$
$840$	5.31786e21	0.000740224 0
$841$	1.16480e25	1.60503
$842$	3.29429e24	0.449375
$843$	−6.01610e23	−0.0812421
$844$	−8.61010e24	−1.15106
$845$	−3.54076e21	−0.000468613 0
$846$	−4.78707e23	−0.0627223
$847$	1.36675e24	0.177288
$848$	−4.25301e23	−0.0546175
$849$	−5.41984e22	−0.00689082
$850$	−7.93032e24	−0.998229
$851$	−4.07153e24	−0.507407
$852$	−9.91366e24	−1.22320
$853$	8.71802e24	1.06500	0.532502	−	0.846429i	$-0.321252\pi$
$853$	8.71802e24	1.06500	0.532502	+	0.846429i	$0.321252\pi$
$854$	3.40445e24	0.411770
$855$	−1.32127e21	−0.000158227 0
$856$	9.51713e23	0.112844
$857$	1.18825e25	1.39499	0.697493	−	0.716592i	$-0.254299\pi$
$857$	1.18825e25	1.39499	0.697493	+	0.716592i	$0.254299\pi$
$858$	−5.42183e24	−0.630237
$859$	−6.84957e24	−0.788355	−0.394177	−	0.919034i	$-0.628970\pi$
$859$	−6.84957e24	−0.788355	−0.394177	+	0.919034i	$0.628970\pi$
$860$	−4.68739e22	−0.00534189
$861$	1.97674e23	0.0223061
$862$	5.70717e24	0.637689
$863$	1.02759e25	1.13691	0.568457	−	0.822713i	$-0.307541\pi$
$863$	1.02759e25	1.13691	0.568457	+	0.822713i	$0.307541\pi$
$864$	1.91580e24	0.209885
$865$	−3.55959e22	−0.00386156
$866$	−1.65221e25	−1.77486
$867$	3.31881e24	0.353037
$868$	4.17762e22	0.00440060
$869$	9.82516e24	1.02488
$870$	5.41783e22	0.00559644
$871$	−1.49877e24	−0.153314
$872$	5.47640e24	0.554760
$873$	−4.48324e21	−0.000449750 0
$874$	1.23483e24	0.122676
$875$	2.88127e22	0.00283475
$876$	−1.02748e25	−1.00113
$877$	2.38006e24	0.229663	0.114832	−	0.993385i	$-0.463367\pi$
$877$	2.38006e24	0.229663	0.114832	+	0.993385i	$0.463367\pi$
$878$	−1.93161e25	−1.84594
$879$	2.77308e24	0.262457
$880$	3.38646e21	0.000317426 0
$881$	−2.05906e24	−0.191150	−0.0955751	−	0.995422i	$-0.530469\pi$
$881$	−2.05906e24	−0.191150	−0.0955751	+	0.995422i	$0.530469\pi$
$882$	8.29453e23	0.0762621
$883$	3.03043e24	0.275955	0.137978	−	0.990435i	$-0.455940\pi$
$883$	3.03043e24	0.275955	0.137978	+	0.990435i	$0.455940\pi$
$884$	−1.01165e25	−0.912399
$885$	−2.35282e22	−0.00210170
$886$	−1.74917e25	−1.54755
$887$	−1.88219e24	−0.164935	−0.0824673	−	0.996594i	$-0.526280\pi$
$887$	−1.88219e24	−0.164935	−0.0824673	+	0.996594i	$0.526280\pi$
$888$	−5.04516e24	−0.437890
$889$	−4.67932e24	−0.402270
$890$	1.18618e23	0.0101004
$891$	−9.59933e23	−0.0809619
$892$	2.88147e25	2.40720
$893$	1.79729e23	0.0148724
$894$	−1.06397e25	−0.872084
$895$	−2.85799e22	−0.00232041
$896$	7.14607e24	0.574711
$897$	−4.10256e24	−0.326828
$898$	−1.89827e25	−1.49799
$899$	1.53625e23	0.0120089
$900$	−6.73593e24	−0.521598
$901$	3.82048e24	0.293060
$902$	−1.56978e24	−0.119285
$903$	−2.63894e24	−0.198648
$904$	−5.44837e23	−0.0406289
$905$	1.74414e22	0.00128845
$906$	1.92453e25	1.40843
$907$	−1.10566e25	−0.801606	−0.400803	−	0.916164i	$-0.631269\pi$
$907$	−1.10566e25	−0.801606	−0.400803	+	0.916164i	$0.631269\pi$
$908$	−2.76390e25	−1.98514
$909$	4.82248e24	0.343145
$910$	3.01219e22	0.00212339
$911$	−1.23349e25	−0.861447	−0.430723	−	0.902484i	$-0.641742\pi$
$911$	−1.23349e25	−0.861447	−0.430723	+	0.902484i	$0.641742\pi$
$912$	−1.22700e23	−0.00848959
$913$	9.75181e24	0.668473
$914$	3.31594e23	0.0225198
$915$	2.18893e22	0.00147283
$916$	2.38935e24	0.159282
$917$	9.95031e24	0.657200
$918$	−2.93574e24	−0.192112
$919$	−2.42568e25	−1.57272	−0.786362	−	0.617766i	$-0.788038\pi$
$919$	−2.42568e25	−1.57272	−0.786362	+	0.617766i	$0.788038\pi$
$920$	−3.19547e22	−0.00205276
$921$	−4.27915e24	−0.272364
$922$	2.84904e25	1.79674
$923$	−2.02686e25	−1.26651
$924$	−4.01873e24	−0.248815
$925$	−1.36675e25	−0.838464
$926$	−1.35813e25	−0.825556
$927$	3.95512e24	0.238222
$928$	2.94937e25	1.76024
$929$	2.00616e25	1.18640	0.593201	−	0.805054i	$-0.297864\pi$
$929$	2.00616e25	1.18640	0.593201	+	0.805054i	$0.297864\pi$
$930$	4.40258e20	2.57990e−5 0
$931$	−3.11415e23	−0.0180829
$932$	4.28691e25	2.46666
$933$	5.53986e24	0.315867
$934$	−4.98381e24	−0.281587
$935$	−3.04206e22	−0.00170321
$936$	−5.08361e24	−0.282051
$937$	1.93153e25	1.06198	0.530988	−	0.847379i	$-0.321821\pi$
$937$	1.93153e25	1.06198	0.530988	+	0.847379i	$0.321821\pi$
$938$	−1.82084e24	−0.0992081
$939$	−1.89706e25	−1.02429
$940$	−1.28855e22	−0.000689471 0
$941$	1.11009e24	0.0588636	0.0294318	−	0.999567i	$-0.490630\pi$
$941$	1.11009e24	0.0588636	0.0294318	+	0.999567i	$0.490630\pi$
$942$	3.15748e25	1.65924
$943$	−1.18781e24	−0.0618585
$944$	−2.18494e24	−0.112766
$945$	5.33307e21	0.000272776 0
$946$	2.09566e25	1.06230
$947$	−1.08567e25	−0.545408	−0.272704	−	0.962098i	$-0.587918\pi$
$947$	−1.08567e25	−0.545408	−0.272704	+	0.962098i	$0.587918\pi$
$948$	2.55224e25	1.27072
$949$	−2.10070e25	−1.03658
$950$	4.14512e24	0.202716
$951$	6.18562e24	0.299812
$952$	−4.43617e24	−0.213105
$953$	1.09499e25	0.521339	0.260670	−	0.965428i	$-0.416057\pi$
$953$	1.09499e25	0.521339	0.260670	+	0.965428i	$0.416057\pi$
$954$	5.31884e24	0.250990
$955$	−1.17920e23	−0.00551515
$956$	2.67429e25	1.23970
$957$	−1.47782e25	−0.678999
$958$	−4.61283e25	−2.10068
$959$	1.21824e25	0.549887
$960$	7.89013e22	0.00353003
$961$	−2.25489e25	−0.999945
$962$	−2.85772e25	−1.25612
$963$	9.54434e23	0.0415836
$964$	2.02855e24	0.0876056
$965$	−2.86244e22	−0.00122533
$966$	−4.98414e24	−0.211487
$967$	−1.73057e25	−0.727886	−0.363943	−	0.931421i	$-0.618570\pi$
$967$	−1.73057e25	−0.727886	−0.363943	+	0.931421i	$0.618570\pi$
$968$	−1.01766e25	−0.424290
$969$	1.10221e24	0.0455525
$970$	−1.97796e20	−8.10322e−6 0
$971$	−2.98981e25	−1.21417	−0.607086	−	0.794636i	$-0.707662\pi$
$971$	−2.98981e25	−1.21417	−0.607086	+	0.794636i	$0.707662\pi$
$972$	−2.49358e24	−0.100383
$973$	−1.84074e25	−0.734572
$974$	6.09512e25	2.41119
$975$	−1.37717e25	−0.540066
$976$	2.03274e24	0.0790238
$977$	3.29242e24	0.126885	0.0634426	−	0.997985i	$-0.479792\pi$
$977$	3.29242e24	0.126885	0.0634426	+	0.997985i	$0.479792\pi$
$978$	4.12382e25	1.57550
$979$	−3.23554e25	−1.22545
$980$	2.23267e22	0.000838306 0
$981$	5.49206e24	0.204432
$982$	3.86450e25	1.42608
$983$	−6.09693e23	−0.0223052	−0.0111526	−	0.999938i	$-0.503550\pi$
$983$	−6.09693e23	−0.0223052	−0.0111526	+	0.999938i	$0.503550\pi$
$984$	−1.47186e24	−0.0533836
$985$	1.94262e22	0.000698521 0
$986$	−4.51956e25	−1.61118
$987$	−7.25440e23	−0.0256393
$988$	5.28781e24	0.185286
$989$	1.58573e25	0.550884
$990$	−4.23513e22	−0.00145870
$991$	−1.07735e25	−0.367903	−0.183951	−	0.982935i	$-0.558889\pi$
$991$	−1.07735e25	−0.367903	−0.183951	+	0.982935i	$0.558889\pi$
$992$	2.39669e23	0.00811450
$993$	−1.98229e25	−0.665423
$994$	−2.46240e25	−0.819547
$995$	1.63162e23	0.00538421
$996$	2.53319e25	0.828826
$997$	1.79833e25	0.583392	0.291696	−	0.956511i	$-0.405780\pi$
$997$	1.79833e25	0.583392	0.291696	+	0.956511i	$0.405780\pi$
$998$	3.91666e25	1.25981
$999$	−5.05959e24	−0.161365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.18.a.b.1.4	✓	4
3.2	odd	2		63.18.a.d.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.18.a.b.1.4	✓	4	1.1	even	1	trivial
63.18.a.d.1.1		4	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q+579.806 q^{2} -6561.00 q^{3} +205104. q^{4} +3275.54 q^{5} -3.80411e6 q^{6} -5.76480e6 q^{7} +4.29240e7 q^{8} +4.30467e7 q^{9} +O(q^{10})\)	\(q+579.806 q^{2} -6561.00 q^{3} +205104. q^{4} +3275.54 q^{5} -3.80411e6 q^{6} -5.76480e6 q^{7} +4.29240e7 q^{8} +4.30467e7 q^{9} +1.89918e6 q^{10} -5.18037e8 q^{11} -1.34568e9 q^{12} -2.75126e9 q^{13} -3.34247e9 q^{14} -2.14908e7 q^{15} -1.99573e9 q^{16} +1.79277e10 q^{17} +2.49588e10 q^{18} -9.37067e9 q^{19} +6.71824e8 q^{20} +3.78229e10 q^{21} -3.00361e11 q^{22} -2.27276e11 q^{23} -2.81624e11 q^{24} -7.62929e11 q^{25} -1.59520e12 q^{26} -2.82430e11 q^{27} -1.18238e12 q^{28} -4.34800e12 q^{29} -1.24605e10 q^{30} -3.53323e10 q^{31} -6.78327e12 q^{32} +3.39884e12 q^{33} +1.03946e13 q^{34} -1.88828e10 q^{35} +8.82904e12 q^{36} +1.79145e13 q^{37} -5.43317e12 q^{38} +1.80510e13 q^{39} +1.40599e11 q^{40} +5.22632e12 q^{41} +2.19299e13 q^{42} -6.97711e13 q^{43} -1.06251e14 q^{44} +1.41001e11 q^{45} -1.31776e14 q^{46} -1.91799e13 q^{47} +1.30940e13 q^{48} +3.32329e13 q^{49} -4.42351e14 q^{50} -1.17623e14 q^{51} -5.64294e14 q^{52} +2.13105e14 q^{53} -1.63754e14 q^{54} -1.69685e12 q^{55} -2.47448e14 q^{56} +6.14810e13 q^{57} -2.52100e15 q^{58} +1.09480e15 q^{59} -4.40784e12 q^{60} -1.01854e15 q^{61} -2.04859e13 q^{62} -2.48156e14 q^{63} -3.67140e15 q^{64} -9.01186e12 q^{65} +1.97067e15 q^{66} +5.44758e14 q^{67} +3.67703e15 q^{68} +1.49115e15 q^{69} -1.09484e13 q^{70} +7.36700e15 q^{71} +1.84774e15 q^{72} +7.63541e15 q^{73} +1.03870e16 q^{74} +5.00558e15 q^{75} -1.92196e15 q^{76} +2.98638e15 q^{77} +1.04661e16 q^{78} -1.89661e16 q^{79} -6.53709e12 q^{80} +1.85302e15 q^{81} +3.03025e15 q^{82} -1.88245e16 q^{83} +7.75760e15 q^{84} +5.87228e13 q^{85} -4.04538e16 q^{86} +2.85272e16 q^{87} -2.22362e16 q^{88} +6.24578e16 q^{89} +8.17534e13 q^{90} +1.58605e16 q^{91} -4.66150e16 q^{92} +2.31815e14 q^{93} -1.11206e16 q^{94} -3.06940e13 q^{95} +4.45050e16 q^{96} -1.04148e14 q^{97} +1.92687e16 q^{98} -2.22998e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 375 q^{2} - 26244 q^{3} + 314369 q^{4} - 154140 q^{5} + 2460375 q^{6} - 23059204 q^{7} - 3766143 q^{8} + 172186884 q^{9}+O(q^{10}) \) 4 * q - 375 * q^2 - 26244 * q^3 + 314369 * q^4 - 154140 * q^5 + 2460375 * q^6 - 23059204 * q^7 - 3766143 * q^8 + 172186884 * q^9	\( 4 q - 375 q^{2} - 26244 q^{3} + 314369 q^{4} - 154140 q^{5} + 2460375 q^{6} - 23059204 q^{7} - 3766143 q^{8} + 172186884 q^{9} + 23352830 q^{10} - 1452022884 q^{11} - 2062575009 q^{12} + 1793559040 q^{13} + 2161800375 q^{14} + 1011312540 q^{15} + 36719981057 q^{16} + 68581449948 q^{17} - 16142520375 q^{18} - 2578000592 q^{19} + 132998517630 q^{20} + 151291437444 q^{21} + 270530423852 q^{22} + 649239533556 q^{23} + 24709664223 q^{24} - 708242296300 q^{25} - 2508729280746 q^{26} - 1129718145924 q^{27} - 1812274725569 q^{28} - 3258162962760 q^{29} - 153217917630 q^{30} + 2414795507136 q^{31} - 18040133068671 q^{32} + 9526722141924 q^{33} + 8860338750210 q^{34} + 888586426140 q^{35} + 13532554634049 q^{36} + 23164217924208 q^{37} - 67011195804708 q^{38} - 11767540861440 q^{39} - 115859765446530 q^{40} - 117516076237164 q^{41} - 14183572260375 q^{42} - 175144919320720 q^{43} - 379640394802500 q^{44} - 6635221574940 q^{45} - 441875935197000 q^{46} - 392013343869480 q^{47} - 240919795714977 q^{48} + 132931722278404 q^{49} - 366102837059625 q^{50} - 449962893108828 q^{51} - 647834999852794 q^{52} - 86395731614976 q^{53} + 105911076180375 q^{54} - 987784569502880 q^{55} + 21711064932543 q^{56} + 16914261884112 q^{57} - 21\!\cdots\!66 q^{58}+ \cdots - 62\!\cdots\!64 q^{99}+O(q^{100}) \) 4 * q - 375 * q^2 - 26244 * q^3 + 314369 * q^4 - 154140 * q^5 + 2460375 * q^6 - 23059204 * q^7 - 3766143 * q^8 + 172186884 * q^9 + 23352830 * q^10 - 1452022884 * q^11 - 2062575009 * q^12 + 1793559040 * q^13 + 2161800375 * q^14 + 1011312540 * q^15 + 36719981057 * q^16 + 68581449948 * q^17 - 16142520375 * q^18 - 2578000592 * q^19 + 132998517630 * q^20 + 151291437444 * q^21 + 270530423852 * q^22 + 649239533556 * q^23 + 24709664223 * q^24 - 708242296300 * q^25 - 2508729280746 * q^26 - 1129718145924 * q^27 - 1812274725569 * q^28 - 3258162962760 * q^29 - 153217917630 * q^30 + 2414795507136 * q^31 - 18040133068671 * q^32 + 9526722141924 * q^33 + 8860338750210 * q^34 + 888586426140 * q^35 + 13532554634049 * q^36 + 23164217924208 * q^37 - 67011195804708 * q^38 - 11767540861440 * q^39 - 115859765446530 * q^40 - 117516076237164 * q^41 - 14183572260375 * q^42 - 175144919320720 * q^43 - 379640394802500 * q^44 - 6635221574940 * q^45 - 441875935197000 * q^46 - 392013343869480 * q^47 - 240919795714977 * q^48 + 132931722278404 * q^49 - 366102837059625 * q^50 - 449962893108828 * q^51 - 647834999852794 * q^52 - 86395731614976 * q^53 + 105911076180375 * q^54 - 987784569502880 * q^55 + 21711064932543 * q^56 + 16914261884112 * q^57 - 2149209668160466 * q^58 - 23145424510920 * q^59 - 872603274170430 * q^60 + 3424273979460952 * q^61 - 4542097297046784 * q^62 - 992623121070084 * q^63 - 3840648962754815 * q^64 + 2015724107462520 * q^65 - 1774950110892972 * q^66 + 2234127752098744 * q^67 - 1956571325658750 * q^68 - 4259660579660916 * q^69 - 134624417736830 * q^70 + 2815776345321804 * q^71 - 162120106967103 * q^72 + 11330038422344784 * q^73 + 2782049125778694 * q^74 + 4646777706024300 * q^75 + 33041781126411260 * q^76 + 8370622973706084 * q^77 + 16459772810974506 * q^78 - 12177038540666920 * q^79 + 35816456249313150 * q^80 + 7412080755407364 * q^81 + 79244490955525210 * q^82 - 4389820874951568 * q^83 + 11890334474458209 * q^84 + 46318093724780760 * q^85 - 79314655634282340 * q^86 + 21376807198668360 * q^87 + 93140307906096828 * q^88 + 100131520699583508 * q^89 + 1005262757570430 * q^90 - 10339510947351040 * q^91 - 14621524874654712 * q^92 - 15843473322319296 * q^93 + 120993183153224352 * q^94 - 115775864256900240 * q^95 + 118361313063550431 * q^96 - 44947325255962464 * q^97 - 12462348963600375 * q^98 - 62504823973163364 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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