LMFDB - Embedded newform 5.28.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,28,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	5.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:	$23.0927787419$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 105406182x^{3} - 8285617904x^{2} + 1593173725628800x - 1939393055148057600 $ x^5 - 2x^4 - 105406182x^3 - 8285617904x^2 + 1593173725628800x - 1939393055148057600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{5}\cdot 5^{4}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1409.38$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1165.24 q^{2} -2.41575e6 q^{3} -1.32860e8 q^{4} -1.22070e9 q^{5} -2.81493e9 q^{6} -4.04373e11 q^{7} -3.11211e11 q^{8} -1.78977e12 q^{9} +O(q^{10})$	\(q+1165.24 q^{2} -2.41575e6 q^{3} -1.32860e8 q^{4} -1.22070e9 q^{5} -2.81493e9 q^{6} -4.04373e11 q^{7} -3.11211e11 q^{8} -1.78977e12 q^{9} -1.42242e12 q^{10} -7.68020e13 q^{11} +3.20956e14 q^{12} +4.89423e13 q^{13} -4.71193e14 q^{14} +2.94891e15 q^{15} +1.74695e16 q^{16} -5.14446e16 q^{17} -2.08552e15 q^{18} -2.66662e16 q^{19} +1.62183e17 q^{20} +9.76863e17 q^{21} -8.94931e16 q^{22} +1.01227e18 q^{23} +7.51805e17 q^{24} +1.49012e18 q^{25} +5.70297e16 q^{26} +2.27451e19 q^{27} +5.37250e19 q^{28} +7.39387e19 q^{29} +3.43620e18 q^{30} -1.35047e20 q^{31} +6.21262e19 q^{32} +1.85534e20 q^{33} -5.99455e19 q^{34} +4.93620e20 q^{35} +2.37789e20 q^{36} -2.44971e21 q^{37} -3.10726e19 q^{38} -1.18232e20 q^{39} +3.79896e20 q^{40} -1.08477e22 q^{41} +1.13828e21 q^{42} -1.14498e22 q^{43} +1.02039e22 q^{44} +2.18478e21 q^{45} +1.17955e21 q^{46} +2.01586e22 q^{47} -4.22019e22 q^{48} +9.78053e22 q^{49} +1.73635e21 q^{50} +1.24277e23 q^{51} -6.50247e21 q^{52} -8.85059e22 q^{53} +2.65036e22 q^{54} +9.37525e22 q^{55} +1.25845e23 q^{56} +6.44186e22 q^{57} +8.61566e22 q^{58} -8.13103e22 q^{59} -3.91792e23 q^{60} -2.23851e24 q^{61} -1.57363e23 q^{62} +7.23735e23 q^{63} -2.27233e24 q^{64} -5.97440e22 q^{65} +2.16193e23 q^{66} -1.42521e24 q^{67} +6.83493e24 q^{68} -2.44540e24 q^{69} +5.75187e23 q^{70} +1.09520e25 q^{71} +5.56996e23 q^{72} -4.29198e24 q^{73} -2.85451e24 q^{74} -3.59974e24 q^{75} +3.54286e24 q^{76} +3.10567e25 q^{77} -1.37769e23 q^{78} +7.60541e25 q^{79} -2.13251e25 q^{80} -4.12984e25 q^{81} -1.26402e25 q^{82} -1.10895e26 q^{83} -1.29786e26 q^{84} +6.27986e25 q^{85} -1.33418e25 q^{86} -1.78617e26 q^{87} +2.39016e25 q^{88} +2.32695e26 q^{89} +2.54580e24 q^{90} -1.97909e25 q^{91} -1.34491e26 q^{92} +3.26240e26 q^{93} +2.34896e25 q^{94} +3.25515e25 q^{95} -1.50081e26 q^{96} +3.39547e26 q^{97} +1.13967e26 q^{98} +1.37458e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 19916 q^{2} + 4870682 q^{3} + 251490240 q^{4} - 6103515625 q^{5} + 39384982360 q^{6} + 155646348206 q^{7} + 4844427693600 q^{8} + 9256436775085 q^{9}+O(q^{10}) $ 5 * q + 19916 * q^2 + 4870682 * q^3 + 251490240 * q^4 - 6103515625 * q^5 + 39384982360 * q^6 + 155646348206 * q^7 + 4844427693600 * q^8 + 9256436775085 * q^9	$ 5 q + 19916 q^{2} + 4870682 q^{3} + 251490240 q^{4} - 6103515625 q^{5} + 39384982360 q^{6} + 155646348206 q^{7} + 4844427693600 q^{8} + 9256436775085 q^{9} - 24311523437500 q^{10} - 34307841041440 q^{11} + 10\!\cdots\!96 q^{12}+ \cdots + 26\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q + 19916 * q^2 + 4870682 * q^3 + 251490240 * q^4 - 6103515625 * q^5 + 39384982360 * q^6 + 155646348206 * q^7 + 4844427693600 * q^8 + 9256436775085 * q^9 - 24311523437500 * q^10 - 34307841041440 * q^11 + 1067087945485696 * q^12 + 1264965428684322 * q^13 - 1494481038585720 * q^14 - 5945656738281250 * q^15 + 50480141682449280 * q^16 + 11381432659133186 * q^17 + 199164599348648492 * q^18 - 177889284152803500 * q^19 - 306994921875000000 * q^20 + 15690874972867260 * q^21 + 1661117755714509952 * q^22 + 5314231426153528362 * q^23 + 25461226121295412800 * q^24 + 7450580596923828125 * q^25 + 64194207115665583160 * q^26 + 69831879763488728300 * q^27 + 74243491650979261568 * q^28 + 142675767255557016550 * q^29 - 48077371044921875000 * q^30 + 490757140558660526660 * q^31 + 709255558573159910656 * q^32 + 262404778486784711104 * q^33 - 823451155892216853320 * q^34 - 189997983649902343750 * q^35 + 364604386623731602880 * q^36 - 1594690133202798011054 * q^37 - 8102840491936976962000 * q^38 - 3725217775868438909980 * q^39 - 5913608024414062500000 * q^40 - 14453824011731896105490 * q^41 - 18735431399125775369328 * q^42 - 6456338188721923591758 * q^43 - 61776067586935488773120 * q^44 - 11299361297711181640625 * q^45 + 41662242513049160161560 * q^46 + 19960747396802751518726 * q^47 + 306904049567056770080512 * q^48 + 64529931934369352760065 * q^49 + 29677152633666992187500 * q^50 + 45124322296416065252260 * q^51 + 694364047806293961951616 * q^52 + 203485571063020242199082 * q^53 + 430355877536329740706000 * q^54 + 41879688771289062500000 * q^55 - 514718506150627561339200 * q^56 - 1075206797979440282527000 * q^57 - 568257469475936639738200 * q^58 - 1753694580358227494398300 * q^59 - 1302597589704218750000000 * q^60 - 1715799924029775655491390 * q^61 + 856653132512718918087792 * q^62 - 3772385601985154457719778 * q^63 + 2825791291455308901232640 * q^64 - 1544147251811916503906250 * q^65 - 14020757899728664042151680 * q^66 - 52283413307813388053914 * q^67 - 18798756173665084661988992 * q^68 + 17423855056223403670703220 * q^69 + 1824317674054833984375000 * q^70 + 13737346388576400396156460 * q^71 + 48990987369760413733351200 * q^72 + 52785881484144679283287962 * q^73 + 44617246831379823508169080 * q^74 + 7257881760597229003906250 * q^75 - 50943444226830794465542400 * q^76 + 40527442829187717880256832 * q^77 + 96469318519881413261089264 * q^78 - 18659027886608771061377800 * q^79 - 61621266702208593750000000 * q^80 - 18780471510820240351050695 * q^81 - 233045910890443727506605688 * q^82 - 49391953045615520178004398 * q^83 - 276316883591574899554456320 * q^84 - 13893350413980939941406250 * q^85 - 246095687260751641221151240 * q^86 - 67750867272390013078210900 * q^87 - 662199546636275930413900800 * q^88 + 180573322691431536135373650 * q^89 - 243120848814268178710937500 * q^90 + 317295677016426969579588460 * q^91 - 379021343242797571985691264 * q^92 + 1482223660602013833974435784 * q^93 - 34623503302055809185576920 * q^94 + 217150005069340209960937500 * q^95 + 2545248606864865567495170560 * q^96 + 1118012018325586896775804426 * q^97 - 243326561625995319625007012 * q^98 + 2661033543665827983852919520 * 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 $

$2$	1165.24	0.100580	0.0502900	−	0.998735i	$-0.483985\pi$
$2$	1165.24	0.100580	0.0502900	+	0.998735i	$0.483985\pi$
$3$	−2.41575e6	−0.874811	−0.437406	−	0.899264i	$-0.644103\pi$
$3$	−2.41575e6	−0.874811	−0.437406	+	0.899264i	$0.644103\pi$
$4$	−1.32860e8	−0.989884
$5$	−1.22070e9	−0.447214
$5$	−1.22070e9	−0.447214
$6$	−2.81493e9	−0.0879885
$7$	−4.04373e11	−1.57746	−0.788731	−	0.614739i	$-0.789261\pi$
$7$	−4.04373e11	−1.57746	−0.788731	+	0.614739i	$0.789261\pi$
$8$	−3.11211e11	−0.200143
$9$	−1.78977e12	−0.234706
$10$	−1.42242e12	−0.0449808
$11$	−7.68020e13	−0.670767	−0.335383	−	0.942082i	$-0.608866\pi$
$11$	−7.68020e13	−0.670767	−0.335383	+	0.942082i	$0.608866\pi$
$12$	3.20956e14	0.865961
$13$	4.89423e13	0.0448176	0.0224088	−	0.999749i	$-0.492866\pi$
$13$	4.89423e13	0.0448176	0.0224088	+	0.999749i	$0.492866\pi$
$14$	−4.71193e14	−0.158661
$15$	2.94891e15	0.391227
$16$	1.74695e16	0.969753
$17$	−5.14446e16	−1.25974	−0.629868	−	0.776702i	$-0.716891\pi$
$17$	−5.14446e16	−1.25974	−0.629868	+	0.776702i	$0.716891\pi$
$18$	−2.08552e15	−0.0236067
$19$	−2.66662e16	−0.145474	−0.0727372	−	0.997351i	$-0.523173\pi$
$19$	−2.66662e16	−0.145474	−0.0727372	+	0.997351i	$0.523173\pi$
$20$	1.62183e17	0.442689
$21$	9.76863e17	1.37998
$22$	−8.94931e16	−0.0674657
$23$	1.01227e18	0.418767	0.209383	−	0.977834i	$-0.432854\pi$
$23$	1.01227e18	0.418767	0.209383	+	0.977834i	$0.432854\pi$
$24$	7.51805e17	0.175087
$25$	1.49012e18	0.200000
$26$	5.70297e16	0.00450776
$27$	2.27451e19	1.08013
$28$	5.37250e19	1.56150
$29$	7.39387e19	1.33813	0.669066	−	0.743203i	$-0.266694\pi$
$29$	7.39387e19	1.33813	0.669066	+	0.743203i	$0.266694\pi$
$30$	3.43620e18	0.0393497
$31$	−1.35047e20	−0.993352	−0.496676	−	0.867936i	$-0.665446\pi$
$31$	−1.35047e20	−0.993352	−0.496676	+	0.867936i	$0.665446\pi$
$32$	6.21262e19	0.297680
$33$	1.85534e20	0.586794
$34$	−5.99455e19	−0.126704
$35$	4.93620e20	0.705462
$36$	2.37789e20	0.232331
$37$	−2.44971e21	−1.65345	−0.826727	−	0.562604i	$-0.809800\pi$
$37$	−2.44971e21	−1.65345	−0.826727	+	0.562604i	$0.809800\pi$
$38$	−3.10726e19	−0.0146318
$39$	−1.18232e20	−0.0392070
$40$	3.79896e20	0.0895065
$41$	−1.08477e22	−1.83128	−0.915638	−	0.402003i	$-0.868314\pi$
$41$	−1.08477e22	−1.83128	−0.915638	+	0.402003i	$0.868314\pi$
$42$	1.13828e21	0.138799
$43$	−1.14498e22	−1.01619	−0.508095	−	0.861301i	$-0.669650\pi$
$43$	−1.14498e22	−1.01619	−0.508095	+	0.861301i	$0.669650\pi$
$44$	1.02039e22	0.663981
$45$	2.18478e21	0.104964
$46$	1.17955e21	0.0421196
$47$	2.01586e22	0.538442	0.269221	−	0.963078i	$-0.413234\pi$
$47$	2.01586e22	0.538442	0.269221	+	0.963078i	$0.413234\pi$
$48$	−4.22019e22	−0.848351
$49$	9.78053e22	1.48838
$50$	1.73635e21	0.0201160
$51$	1.24277e23	1.10203
$52$	−6.50247e21	−0.0443642
$53$	−8.85059e22	−0.466926	−0.233463	−	0.972366i	$-0.575006\pi$
$53$	−8.85059e22	−0.466926	−0.233463	+	0.972366i	$0.575006\pi$
$54$	2.65036e22	0.108640
$55$	9.37525e22	0.299976
$56$	1.25845e23	0.315717
$57$	6.44186e22	0.127263
$58$	8.61566e22	0.134589
$59$	−8.13103e22	−0.100842	−0.0504212	−	0.998728i	$-0.516056\pi$
$59$	−8.13103e22	−0.100842	−0.0504212	+	0.998728i	$0.516056\pi$
$60$	−3.91792e23	−0.387270
$61$	−2.23851e24	−1.77013	−0.885066	−	0.465465i	$-0.845887\pi$
$61$	−2.23851e24	−1.77013	−0.885066	+	0.465465i	$0.845887\pi$
$62$	−1.57363e23	−0.0999114
$63$	7.23735e23	0.370239
$64$	−2.27233e24	−0.939813
$65$	−5.97440e22	−0.0200431
$66$	2.16193e23	0.0590198
$67$	−1.42521e24	−0.317591	−0.158796	−	0.987311i	$-0.550761\pi$
$67$	−1.42521e24	−0.317591	−0.158796	+	0.987311i	$0.550761\pi$
$68$	6.83493e24	1.24699
$69$	−2.44540e24	−0.366342
$70$	5.75187e23	0.0709554
$71$	1.09520e25	1.11559	0.557795	−	0.829979i	$-0.311647\pi$
$71$	1.09520e25	1.11559	0.557795	+	0.829979i	$0.311647\pi$
$72$	5.56996e23	0.0469746
$73$	−4.29198e24	−0.300468	−0.150234	−	0.988650i	$-0.548003\pi$
$73$	−4.29198e24	−0.300468	−0.150234	+	0.988650i	$0.548003\pi$
$74$	−2.85451e24	−0.166304
$75$	−3.59974e24	−0.174962
$76$	3.54286e24	0.144003
$77$	3.10567e25	1.05811
$78$	−1.37769e23	−0.00394344
$79$	7.60541e25	1.83298	0.916488	−	0.400062i	$-0.131011\pi$
$79$	7.60541e25	1.83298	0.916488	+	0.400062i	$0.131011\pi$
$80$	−2.13251e25	−0.433687
$81$	−4.12984e25	−0.710208
$82$	−1.26402e25	−0.184190
$83$	−1.10895e26	−1.37201	−0.686005	−	0.727597i	$-0.740637\pi$
$83$	−1.10895e26	−1.37201	−0.686005	+	0.727597i	$0.740637\pi$
$84$	−1.29786e26	−1.36602
$85$	6.27986e25	0.563371
$86$	−1.33418e25	−0.102208
$87$	−1.78617e26	−1.17061
$88$	2.39016e25	0.134249
$89$	2.32695e26	1.12207	0.561037	−	0.827791i	$-0.310403\pi$
$89$	2.32695e26	1.12207	0.561037	+	0.827791i	$0.310403\pi$
$90$	2.54580e24	0.0105572
$91$	−1.97909e25	−0.0706981
$92$	−1.34491e26	−0.414530
$93$	3.26240e26	0.868995
$94$	2.34896e25	0.0541565
$95$	3.25515e25	0.0650582
$96$	−1.50081e26	−0.260414
$97$	3.39547e26	0.512250	0.256125	−	0.966644i	$-0.417554\pi$
$97$	3.39547e26	0.512250	0.256125	+	0.966644i	$0.417554\pi$
$98$	1.13967e26	0.149702
$99$	1.37458e26	0.157433
$100$	−1.97977e26	−0.197977
$101$	8.75541e26	0.765487	0.382744	−	0.923855i	$-0.374979\pi$
$101$	8.75541e26	0.765487	0.382744	+	0.923855i	$0.374979\pi$
$102$	1.44813e26	0.110842
$103$	1.52037e27	1.02011	0.510053	−	0.860143i	$-0.329626\pi$
$103$	1.52037e27	1.02011	0.510053	+	0.860143i	$0.329626\pi$
$104$	−1.52314e25	−0.00896992
$105$	−1.19246e27	−0.617146
$106$	−1.03131e26	−0.0469634
$107$	−1.85646e27	−0.744741	−0.372370	−	0.928084i	$-0.621455\pi$
$107$	−1.85646e27	−0.744741	−0.372370	+	0.928084i	$0.621455\pi$
$108$	−3.02192e27	−1.06921
$109$	−1.11017e27	−0.346843	−0.173421	−	0.984848i	$-0.555482\pi$
$109$	−1.11017e27	−0.346843	−0.173421	+	0.984848i	$0.555482\pi$
$110$	1.09244e26	0.0301716
$111$	5.91788e27	1.44646
$112$	−7.06421e27	−1.52975
$113$	9.59245e26	0.184234	0.0921171	−	0.995748i	$-0.470637\pi$
$113$	9.59245e26	0.184234	0.0921171	+	0.995748i	$0.470637\pi$
$114$	7.50634e25	0.0128001
$115$	−1.23569e27	−0.187278
$116$	−9.82349e27	−1.32459
$117$	−8.75955e25	−0.0105190
$118$	−9.47463e25	−0.0101427
$119$	2.08028e28	1.98718
$120$	−9.17731e26	−0.0783013
$121$	−7.21144e27	−0.550072
$122$	−2.60841e27	−0.178040
$123$	2.62052e28	1.60202
$124$	1.79424e28	0.983303
$125$	−1.81899e27	−0.0894427
$126$	8.43328e26	0.0372387
$127$	−3.42075e28	−1.35760	−0.678800	−	0.734324i	$-0.737499\pi$
$127$	−3.42075e28	−1.35760	−0.678800	+	0.734324i	$0.737499\pi$
$128$	−1.09863e28	−0.392207
$129$	2.76599e28	0.888974
$130$	−6.96163e25	−0.00201593
$131$	3.65282e28	0.953820	0.476910	−	0.878952i	$-0.341757\pi$
$131$	3.65282e28	0.953820	0.476910	+	0.878952i	$0.341757\pi$
$132$	−2.46501e28	−0.580858
$133$	1.07831e28	0.229480
$134$	−1.66071e27	−0.0319433
$135$	−2.77651e28	−0.483051
$136$	1.60101e28	0.252127
$137$	−1.15461e29	−1.64706	−0.823528	−	0.567276i	$-0.807997\pi$
$137$	−1.15461e29	−1.64706	−0.823528	+	0.567276i	$0.807997\pi$
$138$	−2.84948e27	−0.0368467
$139$	5.93019e28	0.695615	0.347808	−	0.937566i	$-0.386926\pi$
$139$	5.93019e28	0.695615	0.347808	+	0.937566i	$0.386926\pi$
$140$	−6.55823e28	−0.698326
$141$	−4.86980e28	−0.471035
$142$	1.27617e28	0.112206
$143$	−3.75887e27	−0.0300622
$144$	−3.12664e28	−0.227607
$145$	−9.02572e28	−0.598431
$146$	−5.00120e27	−0.0302211
$147$	−2.36273e29	−1.30206
$148$	3.25469e29	1.63673
$149$	3.26131e29	1.49754	0.748768	−	0.662833i	$-0.230646\pi$
$149$	3.26131e29	1.49754	0.748768	+	0.662833i	$0.230646\pi$
$150$	−4.19458e27	−0.0175977
$151$	2.73139e29	1.04760	0.523799	−	0.851842i	$-0.324514\pi$
$151$	2.73139e29	1.04760	0.523799	+	0.851842i	$0.324514\pi$
$152$	8.29879e27	0.0291156
$153$	9.20741e28	0.295667
$154$	3.61886e28	0.106425
$155$	1.64853e29	0.444241
$156$	1.57083e28	0.0388103
$157$	−7.27000e29	−1.64774	−0.823871	−	0.566777i	$-0.808190\pi$
$157$	−7.27000e29	−1.64774	−0.823871	+	0.566777i	$0.808190\pi$
$158$	8.86215e28	0.184361
$159$	2.13808e29	0.408472
$160$	−7.58377e28	−0.133127
$161$	−4.09336e29	−0.660589
$162$	−4.81227e28	−0.0714327
$163$	−1.20695e29	−0.164875	−0.0824376	−	0.996596i	$-0.526271\pi$
$163$	−1.20695e29	−0.164875	−0.0824376	+	0.996596i	$0.526271\pi$
$164$	1.44122e30	1.81275
$165$	−2.26482e29	−0.262422
$166$	−1.29220e29	−0.137997
$167$	−7.91777e29	−0.779705	−0.389853	−	0.920877i	$-0.627474\pi$
$167$	−7.91777e29	−0.779705	−0.389853	+	0.920877i	$0.627474\pi$
$168$	−3.04010e29	−0.276193
$169$	−1.19014e30	−0.997991
$170$	7.31757e28	0.0566639
$171$	4.77263e28	0.0341437
$172$	1.52122e30	1.00591
$173$	−2.07677e30	−1.26989	−0.634944	−	0.772558i	$-0.718977\pi$
$173$	−2.07677e30	−1.26989	−0.634944	+	0.772558i	$0.718977\pi$
$174$	−2.08132e29	−0.117740
$175$	−6.02563e29	−0.315492
$176$	−1.34170e30	−0.650478
$177$	1.96425e29	0.0882181
$178$	2.71146e29	0.112858
$179$	−4.78338e29	−0.184594	−0.0922972	−	0.995732i	$-0.529421\pi$
$179$	−4.78338e29	−0.184594	−0.0922972	+	0.995732i	$0.529421\pi$
$180$	−2.90270e29	−0.103902
$181$	5.46674e30	1.81580	0.907899	−	0.419189i	$-0.137685\pi$
$181$	5.46674e30	1.81580	0.907899	+	0.419189i	$0.137685\pi$
$182$	−2.30613e28	−0.00711082
$183$	5.40767e30	1.54853
$184$	−3.15030e29	−0.0838131
$185$	2.99037e30	0.739447
$186$	3.80149e29	0.0874036
$187$	3.95105e30	0.844989
$188$	−2.67827e30	−0.532995
$189$	−9.19752e30	−1.70387
$190$	3.79304e28	0.00654355
$191$	−5.02940e30	−0.808287	−0.404144	−	0.914695i	$-0.632430\pi$
$191$	−5.02940e30	−0.808287	−0.404144	+	0.914695i	$0.632430\pi$
$192$	5.48936e30	0.822158
$193$	3.44500e30	0.481023	0.240511	−	0.970646i	$-0.422685\pi$
$193$	3.44500e30	0.481023	0.240511	+	0.970646i	$0.422685\pi$
$194$	3.95655e29	0.0515221
$195$	1.44326e29	0.0175339
$196$	−1.29944e31	−1.47333
$197$	9.20973e30	0.974884	0.487442	−	0.873155i	$-0.337930\pi$
$197$	9.20973e30	0.974884	0.487442	+	0.873155i	$0.337930\pi$
$198$	1.60172e29	0.0158346
$199$	−1.47090e30	−0.135852	−0.0679261	−	0.997690i	$-0.521638\pi$
$199$	−1.47090e30	−0.135852	−0.0679261	+	0.997690i	$0.521638\pi$
$200$	−4.63740e29	−0.0400285
$201$	3.44294e30	0.277832
$202$	1.02022e30	0.0769927
$203$	−2.98988e31	−2.11085
$204$	−1.65114e31	−1.09088
$205$	1.32418e31	0.818972
$206$	1.77160e30	0.102602
$207$	−1.81174e30	−0.0982869
$208$	8.54998e29	0.0434620
$209$	2.04801e30	0.0975794
$210$	−1.38951e30	−0.0620726
$211$	2.48673e31	1.04187	0.520937	−	0.853595i	$-0.325583\pi$
$211$	2.48673e31	1.04187	0.520937	+	0.853595i	$0.325583\pi$
$212$	1.17589e31	0.462202
$213$	−2.64572e31	−0.975931
$214$	−2.16323e30	−0.0749060
$215$	1.39768e31	0.454454
$216$	−7.07853e30	−0.216181
$217$	5.46095e31	1.56697
$218$	−1.29362e30	−0.0348855
$219$	1.03683e31	0.262853
$220$	−1.24560e31	−0.296941
$221$	−2.51782e30	−0.0564584
$222$	6.89577e30	0.145485
$223$	7.04899e31	1.39962	0.699812	−	0.714327i	$-0.253267\pi$
$223$	7.04899e31	1.39962	0.699812	+	0.714327i	$0.253267\pi$
$224$	−2.51222e31	−0.469579
$225$	−2.66697e30	−0.0469411
$226$	1.11775e30	0.0185303
$227$	−1.63265e31	−0.255002	−0.127501	−	0.991838i	$-0.540696\pi$
$227$	−1.63265e31	−0.255002	−0.127501	+	0.991838i	$0.540696\pi$
$228$	−8.55866e30	−0.125975
$229$	−1.75183e31	−0.243060	−0.121530	−	0.992588i	$-0.538780\pi$
$229$	−1.75183e31	−0.243060	−0.121530	+	0.992588i	$0.538780\pi$
$230$	−1.43988e30	−0.0188364
$231$	−7.50250e31	−0.925645
$232$	−2.30105e31	−0.267817
$233$	5.16402e31	0.567130	0.283565	−	0.958953i	$-0.408483\pi$
$233$	5.16402e31	0.567130	0.283565	+	0.958953i	$0.408483\pi$
$234$	−1.02070e29	−0.00105800
$235$	−2.46076e31	−0.240798
$236$	1.08029e31	0.0998223
$237$	−1.83727e32	−1.60351
$238$	2.42403e31	0.199871
$239$	−1.74723e32	−1.36138	−0.680689	−	0.732573i	$-0.738319\pi$
$239$	−1.74723e32	−1.36138	−0.680689	+	0.732573i	$0.738319\pi$
$240$	5.15160e31	0.379394
$241$	1.06105e32	0.738766	0.369383	−	0.929277i	$-0.379569\pi$
$241$	1.06105e32	0.738766	0.369383	+	0.929277i	$0.379569\pi$
$242$	−8.40308e30	−0.0553263
$243$	−7.36789e31	−0.458837
$244$	2.97408e32	1.75223
$245$	−1.19391e32	−0.665626
$246$	3.05354e31	0.161131
$247$	−1.30510e30	−0.00651982
$248$	4.20282e31	0.198812
$249$	2.67894e32	1.20025
$250$	−2.11957e30	−0.00899615
$251$	−1.51426e32	−0.608985	−0.304492	−	0.952515i	$-0.598487\pi$
$251$	−1.51426e32	−0.608985	−0.304492	+	0.952515i	$0.598487\pi$
$252$	−9.61554e31	−0.366494
$253$	−7.77447e31	−0.280895
$254$	−3.98601e31	−0.136547
$255$	−1.51705e32	−0.492843
$256$	2.92185e32	0.900364
$257$	−1.37742e32	−0.402689	−0.201344	−	0.979521i	$-0.564531\pi$
$257$	−1.37742e32	−0.402689	−0.201344	+	0.979521i	$0.564531\pi$
$258$	3.22305e31	0.0894131
$259$	9.90598e32	2.60826
$260$	7.93758e30	0.0198403
$261$	−1.32333e32	−0.314067
$262$	4.25643e31	0.0959352
$263$	1.68128e32	0.359945	0.179973	−	0.983672i	$-0.442399\pi$
$263$	1.68128e32	0.359945	0.179973	+	0.983672i	$0.442399\pi$
$264$	−5.77402e31	−0.117442
$265$	1.08039e32	0.208816
$266$	1.25649e31	0.0230811
$267$	−5.62131e32	−0.981603
$268$	1.89353e32	0.314378
$269$	−6.76160e32	−1.06756	−0.533782	−	0.845622i	$-0.679230\pi$
$269$	−6.76160e32	−1.06756	−0.533782	+	0.845622i	$0.679230\pi$
$270$	−3.23531e31	−0.0485853
$271$	−2.99445e32	−0.427791	−0.213895	−	0.976857i	$-0.568615\pi$
$271$	−2.99445e32	−0.427791	−0.213895	+	0.976857i	$0.568615\pi$
$272$	−8.98713e32	−1.22163
$273$	4.78099e31	0.0618475
$274$	−1.34540e32	−0.165661
$275$	−1.14444e32	−0.134153
$276$	3.24895e32	0.362636
$277$	−8.22169e32	−0.873946	−0.436973	−	0.899475i	$-0.643949\pi$
$277$	−8.22169e32	−0.873946	−0.436973	+	0.899475i	$0.643949\pi$
$278$	6.91012e31	0.0699650
$279$	2.41704e32	0.233145
$280$	−1.53620e32	−0.141193
$281$	−3.89379e31	−0.0341065	−0.0170532	−	0.999855i	$-0.505428\pi$
$281$	−3.89379e31	−0.0341065	−0.0170532	+	0.999855i	$0.505428\pi$
$282$	−5.67450e31	−0.0473767
$283$	1.23075e33	0.979610	0.489805	−	0.871832i	$-0.337068\pi$
$283$	1.23075e33	0.979610	0.489805	+	0.871832i	$0.337068\pi$
$284$	−1.45508e33	−1.10430
$285$	−7.86360e31	−0.0569136
$286$	−4.38000e30	−0.00302365
$287$	4.38650e33	2.88877
$288$	−1.11192e32	−0.0698673
$289$	9.78836e32	0.586934
$290$	−1.05172e32	−0.0601902
$291$	−8.20260e32	−0.448122
$292$	5.70232e32	0.297429
$293$	−1.95646e33	−0.974447	−0.487223	−	0.873277i	$-0.661990\pi$
$293$	−1.95646e33	−0.974447	−0.487223	+	0.873277i	$0.661990\pi$
$294$	−2.75315e32	−0.130961
$295$	9.92557e31	0.0450981
$296$	7.62376e32	0.330926
$297$	−1.74687e33	−0.724518
$298$	3.80022e32	0.150622
$299$	4.95430e31	0.0187681
$300$	4.78261e32	0.173192
$301$	4.63000e33	1.60300
$302$	3.18273e32	0.105367
$303$	−2.11508e33	−0.669657
$304$	−4.65845e32	−0.141074
$305$	2.73255e33	0.791628
$306$	1.07289e32	0.0297382
$307$	4.66899e33	1.23838	0.619191	−	0.785240i	$-0.287461\pi$
$307$	4.66899e33	1.23838	0.619191	+	0.785240i	$0.287461\pi$
$308$	−4.12619e33	−1.04740
$309$	−3.67282e33	−0.892401
$310$	1.92094e32	0.0446817
$311$	−7.43499e33	−1.65583	−0.827914	−	0.560855i	$-0.810473\pi$
$311$	−7.43499e33	−1.65583	−0.827914	+	0.560855i	$0.810473\pi$
$312$	3.67951e31	0.00784698
$313$	4.38633e32	0.0895886	0.0447943	−	0.998996i	$-0.485737\pi$
$313$	4.38633e32	0.0895886	0.0447943	+	0.998996i	$0.485737\pi$
$314$	−8.47132e32	−0.165730
$315$	−8.83466e32	−0.165576
$316$	−1.01045e34	−1.81443
$317$	4.32726e33	0.744582	0.372291	−	0.928116i	$-0.378572\pi$
$317$	4.32726e33	0.744582	0.372291	+	0.928116i	$0.378572\pi$
$318$	2.49138e32	0.0410841
$319$	−5.67864e33	−0.897574
$320$	2.77384e33	0.420297
$321$	4.48474e33	0.651507
$322$	−4.76977e32	−0.0664420
$323$	1.37183e33	0.183259
$324$	5.48690e33	0.703023
$325$	7.29297e31	0.00896353
$326$	−1.40639e32	−0.0165831
$327$	2.68189e33	0.303422
$328$	3.37591e33	0.366516
$329$	−8.15158e33	−0.849371
$330$	−2.63907e32	−0.0263944
$331$	2.61158e33	0.250741	0.125370	−	0.992110i	$-0.459988\pi$
$331$	2.61158e33	0.250741	0.125370	+	0.992110i	$0.459988\pi$
$332$	1.47335e34	1.35813
$333$	4.38443e33	0.388075
$334$	−9.22613e32	−0.0784228
$335$	1.73976e33	0.142031
$336$	1.70653e34	1.33824
$337$	−1.67104e34	−1.25888	−0.629439	−	0.777050i	$-0.716715\pi$
$337$	−1.67104e34	−1.25888	−0.629439	+	0.777050i	$0.716715\pi$
$338$	−1.38680e33	−0.100378
$339$	−2.31729e33	−0.161170
$340$	−8.34342e33	−0.557672
$341$	1.03719e34	0.666308
$342$	5.56128e31	0.00343417
$343$	−1.29775e34	−0.770408
$344$	3.56331e33	0.203383
$345$	2.98510e33	0.163833
$346$	−2.41994e33	−0.127725
$347$	4.90415e33	0.248952	0.124476	−	0.992223i	$-0.460275\pi$
$347$	4.90415e33	0.248952	0.124476	+	0.992223i	$0.460275\pi$
$348$	2.37311e34	1.15877
$349$	−1.17877e33	−0.0553713	−0.0276856	−	0.999617i	$-0.508814\pi$
$349$	−1.17877e33	−0.0553713	−0.0276856	+	0.999617i	$0.508814\pi$
$350$	−7.02133e32	−0.0317322
$351$	1.11320e33	0.0484091
$352$	−4.77142e33	−0.199674
$353$	−2.62807e34	−1.05847	−0.529235	−	0.848475i	$-0.677521\pi$
$353$	−2.62807e34	−1.05847	−0.529235	+	0.848475i	$0.677521\pi$
$354$	2.28883e32	0.00887298
$355$	−1.33691e34	−0.498907
$356$	−3.09158e34	−1.11072
$357$	−5.02543e34	−1.73841
$358$	−5.57380e32	−0.0185665
$359$	5.86704e34	1.88211	0.941053	−	0.338259i	$-0.109838\pi$
$359$	5.86704e34	1.88211	0.941053	+	0.338259i	$0.109838\pi$
$360$	−6.79926e32	−0.0210077
$361$	−3.28895e34	−0.978837
$362$	6.37008e33	0.182633
$363$	1.74210e34	0.481209
$364$	2.62942e33	0.0699829
$365$	5.23923e33	0.134374
$366$	6.30125e33	0.155751
$367$	−3.78297e34	−0.901240	−0.450620	−	0.892716i	$-0.648797\pi$
$367$	−3.78297e34	−0.901240	−0.450620	+	0.892716i	$0.648797\pi$
$368$	1.76839e34	0.406100
$369$	1.94148e34	0.429811
$370$	3.48451e33	0.0743736
$371$	3.57894e34	0.736558
$372$	−4.33442e34	−0.860204
$373$	9.29388e33	0.177880	0.0889401	−	0.996037i	$-0.471652\pi$
$373$	9.29388e33	0.177880	0.0889401	+	0.996037i	$0.471652\pi$
$374$	4.60394e33	0.0849890
$375$	4.39422e33	0.0782455
$376$	−6.27356e33	−0.107765
$377$	3.61873e33	0.0599719
$378$	−1.07174e34	−0.171375
$379$	7.06413e34	1.09001	0.545004	−	0.838434i	$-0.316528\pi$
$379$	7.06413e34	1.09001	0.545004	+	0.838434i	$0.316528\pi$
$380$	−4.32478e33	−0.0644000
$381$	8.26367e34	1.18764
$382$	−5.86048e33	−0.0812976
$383$	1.21570e35	1.62796	0.813978	−	0.580895i	$-0.197297\pi$
$383$	1.21570e35	1.62796	0.813978	+	0.580895i	$0.197297\pi$
$384$	2.65400e34	0.343107
$385$	−3.79110e34	−0.473201
$386$	4.01427e33	0.0483813
$387$	2.04926e34	0.238506
$388$	−4.51122e34	−0.507068
$389$	−9.04714e34	−0.982181	−0.491091	−	0.871109i	$-0.663402\pi$
$389$	−9.04714e34	−0.982181	−0.491091	+	0.871109i	$0.663402\pi$
$390$	1.68175e32	0.00176356
$391$	−5.20760e34	−0.527535
$392$	−3.04380e34	−0.297889
$393$	−8.82429e34	−0.834412
$394$	1.07316e34	0.0980539
$395$	−9.28395e34	−0.819732
$396$	−1.82627e34	−0.155840
$397$	6.88420e34	0.567782	0.283891	−	0.958857i	$-0.408375\pi$
$397$	6.88420e34	0.567782	0.283891	+	0.958857i	$0.408375\pi$
$398$	−1.71396e33	−0.0136640
$399$	−2.60492e34	−0.200752
$400$	2.60316e34	0.193951
$401$	−6.94299e34	−0.500147	−0.250074	−	0.968227i	$-0.580455\pi$
$401$	−6.94299e34	−0.500147	−0.250074	+	0.968227i	$0.580455\pi$
$402$	4.01186e33	0.0279444
$403$	−6.60952e33	−0.0445197
$404$	−1.16324e35	−0.757743
$405$	5.04131e34	0.317614
$406$	−3.48394e34	−0.212309
$407$	1.88143e35	1.10908
$408$	−3.86763e34	−0.220563
$409$	−1.38926e35	−0.766513	−0.383257	−	0.923642i	$-0.625197\pi$
$409$	−1.38926e35	−0.766513	−0.383257	+	0.923642i	$0.625197\pi$
$410$	1.54299e34	0.0823722
$411$	2.78925e35	1.44086
$412$	−2.01996e35	−1.00979
$413$	3.28797e34	0.159075
$414$	−2.11112e33	−0.00988570
$415$	1.35370e35	0.613582
$416$	3.04060e33	0.0133413
$417$	−1.43258e35	−0.608532
$418$	2.38644e33	0.00981454
$419$	6.14955e34	0.244880	0.122440	−	0.992476i	$-0.460928\pi$
$419$	6.14955e34	0.244880	0.122440	+	0.992476i	$0.460928\pi$
$420$	1.58430e35	0.610903
$421$	−3.49328e35	−1.30444	−0.652222	−	0.758028i	$-0.726163\pi$
$421$	−3.49328e35	−1.30444	−0.652222	+	0.758028i	$0.726163\pi$
$422$	2.89764e34	0.104792
$423$	−3.60792e34	−0.126375
$424$	2.75440e34	0.0934518
$425$	−7.66584e34	−0.251947
$426$	−3.08291e34	−0.0981591
$427$	9.05193e35	2.79232
$428$	2.46649e35	0.737207
$429$	9.08047e33	0.0262987
$430$	1.62864e34	0.0457090
$431$	−7.72826e34	−0.210203	−0.105101	−	0.994462i	$-0.533517\pi$
$431$	−7.72826e34	−0.210203	−0.105101	+	0.994462i	$0.533517\pi$
$432$	3.97347e35	1.04746
$433$	−5.58593e35	−1.42728	−0.713640	−	0.700512i	$-0.752955\pi$
$433$	−5.58593e35	−1.42728	−0.713640	+	0.700512i	$0.752955\pi$
$434$	6.36334e34	0.157606
$435$	2.18038e35	0.523514
$436$	1.47497e35	0.343334
$437$	−2.69934e34	−0.0609199
$438$	1.20816e34	0.0264378
$439$	−1.65153e35	−0.350441	−0.175220	−	0.984529i	$-0.556064\pi$
$439$	−1.65153e35	−0.350441	−0.175220	+	0.984529i	$0.556064\pi$
$440$	−2.91768e34	−0.0600380
$441$	−1.75049e35	−0.349332
$442$	−2.93387e33	−0.00567858
$443$	−8.73849e35	−1.64054	−0.820268	−	0.571979i	$-0.806176\pi$
$443$	−8.73849e35	−1.64054	−0.820268	+	0.571979i	$0.806176\pi$
$444$	−7.86250e35	−1.43183
$445$	−2.84051e35	−0.501807
$446$	8.21379e34	0.140774
$447$	−7.87849e35	−1.31006
$448$	9.18868e35	1.48252
$449$	−5.29616e34	−0.0829154	−0.0414577	−	0.999140i	$-0.513200\pi$
$449$	−5.29616e34	−0.0829154	−0.0414577	+	0.999140i	$0.513200\pi$
$450$	−3.10767e33	−0.00472134
$451$	8.33123e35	1.22836
$452$	−1.27445e35	−0.182370
$453$	−6.59833e35	−0.916450
$454$	−1.90243e34	−0.0256481
$455$	2.41589e34	0.0316171
$456$	−2.00478e34	−0.0254707
$457$	1.22558e36	1.51172	0.755861	−	0.654732i	$-0.227219\pi$
$457$	1.22558e36	1.51172	0.755861	+	0.654732i	$0.227219\pi$
$458$	−2.04131e34	−0.0244469
$459$	−1.17011e36	−1.36068
$460$	1.64173e35	0.185384
$461$	−9.51355e35	−1.04323	−0.521615	−	0.853181i	$-0.674670\pi$
$461$	−9.51355e35	−1.04323	−0.521615	+	0.853181i	$0.674670\pi$
$462$	−8.74225e34	−0.0931014
$463$	1.48923e36	1.54034	0.770172	−	0.637836i	$-0.220170\pi$
$463$	1.48923e36	1.54034	0.770172	+	0.637836i	$0.220170\pi$
$464$	1.29167e36	1.29766
$465$	−3.98242e35	−0.388627
$466$	6.01734e34	0.0570420
$467$	−1.48826e36	−1.37057	−0.685284	−	0.728276i	$-0.740322\pi$
$467$	−1.48826e36	−1.37057	−0.685284	+	0.728276i	$0.740322\pi$
$468$	1.16379e34	0.0104125
$469$	5.76316e35	0.500988
$470$	−2.86739e34	−0.0242195
$471$	1.75625e36	1.44146
$472$	2.53046e34	0.0201829
$473$	8.79371e35	0.681627
$474$	−2.14087e35	−0.161281
$475$	−3.97357e34	−0.0290949
$476$	−2.76386e36	−1.96708
$477$	1.58405e35	0.109590
$478$	−2.03595e35	−0.136927
$479$	2.74014e36	1.79161	0.895806	−	0.444446i	$-0.146599\pi$
$479$	2.74014e36	1.79161	0.895806	+	0.444446i	$0.146599\pi$
$480$	1.83205e35	0.116461
$481$	−1.19895e35	−0.0741039
$482$	1.23639e35	0.0743051
$483$	9.88853e35	0.577890
$484$	9.58111e35	0.544507
$485$	−4.14487e35	−0.229085
$486$	−8.58538e34	−0.0461498
$487$	−5.62366e35	−0.294021	−0.147010	−	0.989135i	$-0.546965\pi$
$487$	−5.62366e35	−0.294021	−0.147010	+	0.989135i	$0.546965\pi$
$488$	6.96647e35	0.354279
$489$	2.91567e35	0.144235
$490$	−1.39120e35	−0.0669487
$491$	3.49830e36	1.63778	0.818891	−	0.573949i	$-0.194589\pi$
$491$	3.49830e36	1.63778	0.818891	+	0.573949i	$0.194589\pi$
$492$	−3.48162e36	−1.58581
$493$	−3.80375e36	−1.68569
$494$	−1.52076e33	−0.000655764 0
$495$	−1.67795e35	−0.0704061
$496$	−2.35921e36	−0.963306
$497$	−4.42868e36	−1.75980
$498$	3.12162e35	0.120721
$499$	3.42258e35	0.128824	0.0644119	−	0.997923i	$-0.479483\pi$
$499$	3.42258e35	0.128824	0.0644119	+	0.997923i	$0.479483\pi$
$500$	2.41671e35	0.0885379
$501$	1.91273e36	0.682095
$502$	−1.76449e35	−0.0612517
$503$	−3.95612e36	−1.33691	−0.668454	−	0.743754i	$-0.733044\pi$
$503$	−3.95612e36	−1.33691	−0.668454	+	0.743754i	$0.733044\pi$
$504$	−2.25234e35	−0.0741006
$505$	−1.06878e36	−0.342336
$506$	−9.05915e34	−0.0282524
$507$	2.87507e36	0.873054
$508$	4.54481e36	1.34387
$509$	6.89243e35	0.198464	0.0992321	−	0.995064i	$-0.468361\pi$
$509$	6.89243e35	0.198464	0.0992321	+	0.995064i	$0.468361\pi$
$510$	−1.76774e35	−0.0495702
$511$	1.73556e36	0.473977
$512$	1.81502e36	0.482765
$513$	−6.06525e35	−0.157132
$514$	−1.60503e35	−0.0405025
$515$	−1.85592e36	−0.456206
$516$	−3.67489e36	−0.879981
$517$	−1.54822e36	−0.361169
$518$	1.15429e36	0.262339
$519$	5.01694e36	1.11091
$520$	1.85930e34	0.00401147
$521$	9.78306e35	0.205667	0.102834	−	0.994699i	$-0.467209\pi$
$521$	9.78306e35	0.205667	0.102834	+	0.994699i	$0.467209\pi$
$522$	−1.54201e35	−0.0315889
$523$	6.48450e36	1.29451	0.647253	−	0.762275i	$-0.275918\pi$
$523$	6.48450e36	1.29451	0.647253	+	0.762275i	$0.275918\pi$
$524$	−4.85314e36	−0.944171
$525$	1.45564e36	0.275996
$526$	1.95910e35	0.0362033
$527$	6.94746e36	1.25136
$528$	3.24119e36	0.569046
$529$	−4.81851e36	−0.824634
$530$	1.25892e35	0.0210027
$531$	1.45527e35	0.0236683
$532$	−1.43264e36	−0.227159
$533$	−5.30909e35	−0.0820735
$534$	−6.55020e35	−0.0987296
$535$	2.26619e36	0.333058
$536$	4.43540e35	0.0635635
$537$	1.15554e36	0.161485
$538$	−7.87891e35	−0.107376
$539$	−7.51165e36	−0.998359
$540$	3.68886e36	0.478164
$541$	7.41266e35	0.0937154	0.0468577	−	0.998902i	$-0.485079\pi$
$541$	7.41266e35	0.0937154	0.0468577	+	0.998902i	$0.485079\pi$
$542$	−3.48926e35	−0.0430272
$543$	−1.32063e37	−1.58848
$544$	−3.19606e36	−0.374999
$545$	1.35519e36	0.155113
$546$	5.57102e34	0.00622062
$547$	−2.82772e35	−0.0308040	−0.0154020	−	0.999881i	$-0.504903\pi$
$547$	−2.82772e35	−0.0308040	−0.0154020	+	0.999881i	$0.504903\pi$
$548$	1.53402e37	1.63039
$549$	4.00642e36	0.415460
$550$	−1.33355e35	−0.0134931
$551$	−1.97166e36	−0.194664
$552$	7.61033e35	0.0733206
$553$	−3.07542e37	−2.89145
$554$	−9.58028e35	−0.0879015
$555$	−7.22398e36	−0.646876
$556$	−7.87885e36	−0.688578
$557$	2.08388e37	1.77758	0.888788	−	0.458318i	$-0.151548\pi$
$557$	2.08388e37	1.77758	0.888788	+	0.458318i	$0.151548\pi$
$558$	2.81644e35	0.0234498
$559$	−5.60381e35	−0.0455432
$560$	8.62330e36	0.684124
$561$	−9.54473e36	−0.739205
$562$	−4.53721e34	−0.00343043
$563$	−8.50023e36	−0.627433	−0.313716	−	0.949517i	$-0.601574\pi$
$563$	−8.50023e36	−0.627433	−0.313716	+	0.949517i	$0.601574\pi$
$564$	6.47001e36	0.466270
$565$	−1.17095e36	−0.0823921
$566$	1.43412e36	0.0985292
$567$	1.67000e37	1.12033
$568$	−3.40837e36	−0.223277
$569$	−1.56661e37	−1.00218	−0.501090	−	0.865395i	$-0.667067\pi$
$569$	−1.56661e37	−1.00218	−0.501090	+	0.865395i	$0.667067\pi$
$570$	−9.16301e34	−0.00572437
$571$	3.06021e36	0.186708	0.0933542	−	0.995633i	$-0.470241\pi$
$571$	3.06021e36	0.186708	0.0933542	+	0.995633i	$0.470241\pi$
$572$	4.99403e35	0.0297581
$573$	1.21498e37	0.707099
$574$	5.11134e36	0.290552
$575$	1.50841e36	0.0837534
$576$	4.06695e36	0.220579
$577$	−1.97202e36	−0.104481	−0.0522404	−	0.998635i	$-0.516636\pi$
$577$	−1.97202e36	−0.104481	−0.0522404	+	0.998635i	$0.516636\pi$
$578$	1.14058e36	0.0590338
$579$	−8.32225e36	−0.420804
$580$	1.19916e37	0.592377
$581$	4.48429e37	2.16429
$582$	−9.55803e35	−0.0450721
$583$	6.79743e36	0.313198
$584$	1.33571e36	0.0601365
$585$	1.06928e35	0.00470422
$586$	−2.27975e36	−0.0980099
$587$	1.94192e36	0.0815861	0.0407931	−	0.999168i	$-0.487012\pi$
$587$	1.94192e36	0.0815861	0.0407931	+	0.999168i	$0.487012\pi$
$588$	3.13912e37	1.28888
$589$	3.60119e36	0.144507
$590$	1.15657e35	0.00453597
$591$	−2.22484e37	−0.852839
$592$	−4.27953e37	−1.60344
$593$	−1.91214e36	−0.0700295	−0.0350147	−	0.999387i	$-0.511148\pi$
$593$	−1.91214e36	−0.0700295	−0.0350147	+	0.999387i	$0.511148\pi$
$594$	−2.03553e36	−0.0728721
$595$	−2.53941e37	−0.888696
$596$	−4.33297e37	−1.48239
$597$	3.55332e36	0.118845
$598$	5.77296e34	0.00188770
$599$	−1.51573e37	−0.484574	−0.242287	−	0.970205i	$-0.577898\pi$
$599$	−1.51573e37	−0.484574	−0.242287	+	0.970205i	$0.577898\pi$
$600$	1.12028e36	0.0350174
$601$	2.06264e37	0.630404	0.315202	−	0.949025i	$-0.397928\pi$
$601$	2.06264e37	0.630404	0.315202	+	0.949025i	$0.397928\pi$
$602$	5.39508e36	0.161230
$603$	2.55080e36	0.0745404
$604$	−3.62892e37	−1.03700
$605$	8.80303e36	0.246000
$606$	−2.46459e36	−0.0673541
$607$	−9.48486e36	−0.253503	−0.126752	−	0.991934i	$-0.540455\pi$
$607$	−9.48486e36	−0.253503	−0.126752	+	0.991934i	$0.540455\pi$
$608$	−1.65667e36	−0.0433049
$609$	7.22280e37	1.84660
$610$	3.18409e36	0.0796219
$611$	9.86606e35	0.0241317
$612$	−1.22330e37	−0.292676
$613$	1.58809e37	0.371671	0.185835	−	0.982581i	$-0.440501\pi$
$613$	1.58809e37	0.371671	0.185835	+	0.982581i	$0.440501\pi$
$614$	5.44051e36	0.124556
$615$	−3.19888e37	−0.716446
$616$	−9.66517e36	−0.211773
$617$	−5.23564e37	−1.12233	−0.561164	−	0.827704i	$-0.689646\pi$
$617$	−5.23564e37	−1.12233	−0.561164	+	0.827704i	$0.689646\pi$
$618$	−4.27973e36	−0.0897577
$619$	2.67111e37	0.548109	0.274055	−	0.961714i	$-0.411635\pi$
$619$	2.67111e37	0.548109	0.274055	+	0.961714i	$0.411635\pi$
$620$	−2.19023e37	−0.439746
$621$	2.30243e37	0.452324
$622$	−8.66358e36	−0.166543
$623$	−9.40955e37	−1.77003
$624$	−2.06546e36	−0.0380211
$625$	2.22045e36	0.0400000
$626$	5.11114e35	0.00901082
$627$	−4.94748e36	−0.0853636
$628$	9.65892e37	1.63107
$629$	1.26025e38	2.08291
$630$	−1.02945e36	−0.0166536
$631$	6.82519e37	1.08073	0.540367	−	0.841430i	$-0.318286\pi$
$631$	6.82519e37	1.08073	0.540367	+	0.841430i	$0.318286\pi$
$632$	−2.36688e37	−0.366857
$633$	−6.00730e37	−0.911442
$634$	5.04231e36	0.0748901
$635$	4.17572e37	0.607137
$636$	−2.84065e37	−0.404340
$637$	4.78681e36	0.0667059
$638$	−6.61700e36	−0.0902781
$639$	−1.96015e37	−0.261835
$640$	1.34110e37	0.175400
$641$	9.07891e37	1.16265	0.581326	−	0.813670i	$-0.302534\pi$
$641$	9.07891e37	1.16265	0.581326	+	0.813670i	$0.302534\pi$
$642$	5.22581e36	0.0655286
$643$	8.30887e37	1.02022	0.510110	−	0.860109i	$-0.329605\pi$
$643$	8.30887e37	1.02022	0.510110	+	0.860109i	$0.329605\pi$
$644$	5.43844e37	0.653906
$645$	−3.37645e37	−0.397561
$646$	1.59852e36	0.0184322
$647$	−6.31184e37	−0.712767	−0.356384	−	0.934340i	$-0.615990\pi$
$647$	−6.31184e37	−0.712767	−0.356384	+	0.934340i	$0.615990\pi$
$648$	1.28525e37	0.142143
$649$	6.24480e36	0.0676418
$650$	8.49808e34	0.000901552 0
$651$	−1.31923e38	−1.37081
$652$	1.60355e37	0.163207
$653$	2.29698e37	0.228996	0.114498	−	0.993423i	$-0.463474\pi$
$653$	2.29698e37	0.228996	0.114498	+	0.993423i	$0.463474\pi$
$654$	3.12506e36	0.0305182
$655$	−4.45901e37	−0.426561
$656$	−1.89503e38	−1.77589
$657$	7.68166e36	0.0705216
$658$	−9.49858e36	−0.0854298
$659$	−1.72605e38	−1.52090	−0.760450	−	0.649396i	$-0.775022\pi$
$659$	−1.72605e38	−1.52090	−0.760450	+	0.649396i	$0.775022\pi$
$660$	3.00904e37	0.259768
$661$	−3.20592e37	−0.271165	−0.135582	−	0.990766i	$-0.543291\pi$
$661$	−3.20592e37	−0.271165	−0.135582	+	0.990766i	$0.543291\pi$
$662$	3.04312e36	0.0252195
$663$	6.08240e36	0.0493904
$664$	3.45117e37	0.274598
$665$	−1.31629e37	−0.102627
$666$	5.10892e36	0.0390326
$667$	7.48462e37	0.560365
$668$	1.05195e38	0.771818
$669$	−1.70286e38	−1.22441
$670$	2.02724e36	0.0142855
$671$	1.71922e38	1.18735
$672$	6.06888e37	0.410793
$673$	−1.25410e38	−0.832013	−0.416006	−	0.909362i	$-0.636571\pi$
$673$	−1.25410e38	−0.832013	−0.416006	+	0.909362i	$0.636571\pi$
$674$	−1.94717e37	−0.126618
$675$	3.38929e37	0.216027
$676$	1.58122e38	0.987895
$677$	−6.48403e37	−0.397098	−0.198549	−	0.980091i	$-0.563623\pi$
$677$	−6.48403e37	−0.397098	−0.198549	+	0.980091i	$0.563623\pi$
$678$	−2.70021e36	−0.0162105
$679$	−1.37304e38	−0.808055
$680$	−1.95436e37	−0.112754
$681$	3.94407e37	0.223079
$682$	1.20858e37	0.0670172
$683$	−3.86748e37	−0.210256	−0.105128	−	0.994459i	$-0.533525\pi$
$683$	−3.86748e37	−0.210256	−0.105128	+	0.994459i	$0.533525\pi$
$684$	−6.34091e36	−0.0337983
$685$	1.40944e38	0.736586
$686$	−1.51220e37	−0.0774877
$687$	4.23197e37	0.212631
$688$	−2.00023e38	−0.985454
$689$	−4.33168e36	−0.0209265
$690$	3.47837e36	0.0164783
$691$	9.84865e37	0.457534	0.228767	−	0.973481i	$-0.426531\pi$
$691$	9.84865e37	0.457534	0.228767	+	0.973481i	$0.426531\pi$
$692$	2.75919e38	1.25704
$693$	−5.55844e37	−0.248344
$694$	5.71453e36	0.0250396
$695$	−7.23901e37	−0.311089
$696$	5.55875e37	0.234289
$697$	5.58054e38	2.30692
$698$	−1.37355e36	−0.00556925
$699$	−1.24749e38	−0.496132
$700$	8.00565e37	0.312301
$701$	−2.91000e38	−1.11353	−0.556763	−	0.830671i	$-0.687957\pi$
$701$	−2.91000e38	−1.11353	−0.556763	+	0.830671i	$0.687957\pi$
$702$	1.29715e36	0.00486898
$703$	6.53244e37	0.240535
$704$	1.74519e38	0.630395
$705$	5.94458e37	0.210653
$706$	−3.06234e37	−0.106461
$707$	−3.54045e38	−1.20753
$708$	−2.60970e37	−0.0873257
$709$	3.94832e38	1.29625	0.648124	−	0.761535i	$-0.275554\pi$
$709$	3.94832e38	1.29625	0.648124	+	0.761535i	$0.275554\pi$
$710$	−1.55783e37	−0.0501801
$711$	−1.36119e38	−0.430210
$712$	−7.24171e37	−0.224575
$713$	−1.36705e38	−0.415983
$714$	−5.85585e37	−0.174849
$715$	4.58846e36	0.0134442
$716$	6.35519e37	0.182727
$717$	4.22087e38	1.19095
$718$	6.83653e37	0.189302
$719$	−4.40958e38	−1.19828	−0.599138	−	0.800646i	$-0.704490\pi$
$719$	−4.40958e38	−1.19828	−0.599138	+	0.800646i	$0.704490\pi$
$720$	3.81670e37	0.101789
$721$	−6.14795e38	−1.60918
$722$	−3.83243e37	−0.0984515
$723$	−2.56323e38	−0.646281
$724$	−7.26311e38	−1.79743
$725$	1.10177e38	0.267626
$726$	2.02997e37	0.0484000
$727$	−3.39272e38	−0.794023	−0.397011	−	0.917814i	$-0.629953\pi$
$727$	−3.39272e38	−0.794023	−0.397011	+	0.917814i	$0.629953\pi$
$728$	6.15915e36	0.0141497
$729$	4.92914e38	1.11160
$730$	6.10498e36	0.0135153
$731$	5.89032e38	1.28013
$732$	−7.18462e38	−1.53287
$733$	2.06168e38	0.431835	0.215918	−	0.976412i	$-0.430726\pi$
$733$	2.06168e38	0.431835	0.215918	+	0.976412i	$0.430726\pi$
$734$	−4.40808e37	−0.0906468
$735$	2.88419e38	0.582297
$736$	6.28887e37	0.124659
$737$	1.09459e38	0.213030
$738$	2.26230e37	0.0432304
$739$	1.37342e38	0.257693	0.128847	−	0.991665i	$-0.458873\pi$
$739$	1.37342e38	0.257693	0.128847	+	0.991665i	$0.458873\pi$
$740$	−3.97301e38	−0.731966
$741$	3.15279e36	0.00570361
$742$	4.17034e37	0.0740830
$743$	9.98652e38	1.74207	0.871034	−	0.491223i	$-0.163450\pi$
$743$	9.98652e38	1.74207	0.871034	+	0.491223i	$0.163450\pi$
$744$	−1.01529e38	−0.173923
$745$	−3.98109e38	−0.669718
$746$	1.08296e37	0.0178912
$747$	1.98476e38	0.322019
$748$	−5.24936e38	−0.836441
$749$	7.50703e38	1.17480
$750$	5.12033e36	0.00786993
$751$	−3.18298e38	−0.480502	−0.240251	−	0.970711i	$-0.577230\pi$
$751$	−3.18298e38	−0.480502	−0.240251	+	0.970711i	$0.577230\pi$
$752$	3.52161e38	0.522156
$753$	3.65808e38	0.532747
$754$	4.21670e36	0.00603198
$755$	−3.33421e38	−0.468500
$756$	1.22198e39	1.68663
$757$	−4.05159e38	−0.549327	−0.274663	−	0.961540i	$-0.588566\pi$
$757$	−4.05159e38	−0.549327	−0.274663	+	0.961540i	$0.588566\pi$
$758$	8.23143e37	0.109633
$759$	1.87811e38	0.245730
$760$	−1.01304e37	−0.0130209
$761$	−3.56274e38	−0.449875	−0.224937	−	0.974373i	$-0.572218\pi$
$761$	−3.56274e38	−0.449875	−0.224937	+	0.974373i	$0.572218\pi$
$762$	9.62919e37	0.119453
$763$	4.48924e38	0.547131
$764$	6.68206e38	0.800111
$765$	−1.12395e38	−0.132226
$766$	1.41659e38	0.163740
$767$	−3.97951e36	−0.00451952
$768$	−7.05845e38	−0.787649
$769$	−2.67309e38	−0.293094	−0.146547	−	0.989204i	$-0.546816\pi$
$769$	−2.67309e38	−0.293094	−0.146547	+	0.989204i	$0.546816\pi$
$770$	−4.41755e37	−0.0475945
$771$	3.32750e38	0.352277
$772$	−4.57703e38	−0.476157
$773$	−4.52793e38	−0.462889	−0.231444	−	0.972848i	$-0.574345\pi$
$773$	−4.52793e38	−0.462889	−0.231444	+	0.972848i	$0.574345\pi$
$774$	2.38788e37	0.0239889
$775$	−2.01236e38	−0.198670
$776$	−1.05671e38	−0.102523
$777$	−2.39303e39	−2.28173
$778$	−1.05421e38	−0.0987878
$779$	2.89265e38	0.266404
$780$	−1.91752e37	−0.0173565
$781$	−8.41134e38	−0.748301
$782$	−6.06813e37	−0.0530595
$783$	1.68175e39	1.44536
$784$	1.70861e39	1.44337
$785$	8.87451e38	0.736893
$786$	−1.02825e38	−0.0839252
$787$	−3.46382e38	−0.277905	−0.138953	−	0.990299i	$-0.544374\pi$
$787$	−3.46382e38	−0.277905	−0.138953	+	0.990299i	$0.544374\pi$
$788$	−1.22360e39	−0.965022
$789$	−4.06154e38	−0.314884
$790$	−1.08181e38	−0.0824487
$791$	−3.87893e38	−0.290622
$792$	−4.27784e37	−0.0315090
$793$	−1.09558e38	−0.0793332
$794$	8.02176e37	0.0571075
$795$	−2.60996e38	−0.182674
$796$	1.95424e38	0.134478
$797$	−1.70780e39	−1.15545	−0.577724	−	0.816232i	$-0.696059\pi$
$797$	−1.70780e39	−1.15545	−0.577724	+	0.816232i	$0.696059\pi$
$798$	−3.03536e37	−0.0201916
$799$	−1.03705e39	−0.678294
$800$	9.25753e37	0.0595361
$801$	−4.16470e38	−0.263357
$802$	−8.09028e37	−0.0503048
$803$	3.29633e38	0.201544
$804$	−4.57429e38	−0.275022
$805$	4.99678e38	0.295424
$806$	−7.70171e36	−0.00447779
$807$	1.63343e39	0.933917
$808$	−2.72478e38	−0.153207
$809$	1.18552e39	0.655545	0.327772	−	0.944757i	$-0.393702\pi$
$809$	1.18552e39	0.655545	0.327772	+	0.944757i	$0.393702\pi$
$810$	5.87435e37	0.0319457
$811$	−1.56091e39	−0.834826	−0.417413	−	0.908717i	$-0.637063\pi$
$811$	−1.56091e39	−0.834826	−0.417413	+	0.908717i	$0.637063\pi$
$812$	3.97236e39	2.08950
$813$	7.23383e38	0.374236
$814$	2.19232e38	0.111551
$815$	1.47332e38	0.0737344
$816$	2.17106e39	1.06870
$817$	3.05323e38	0.147830
$818$	−1.61883e38	−0.0770959
$819$	3.54213e37	0.0165932
$820$	−1.75930e39	−0.810687
$821$	1.26350e38	0.0572718	0.0286359	−	0.999590i	$-0.490884\pi$
$821$	1.26350e38	0.0572718	0.0286359	+	0.999590i	$0.490884\pi$
$822$	3.25015e38	0.144922
$823$	1.86461e39	0.817882	0.408941	−	0.912561i	$-0.365898\pi$
$823$	1.86461e39	0.817882	0.408941	+	0.912561i	$0.365898\pi$
$824$	−4.73154e38	−0.204167
$825$	2.76467e38	0.117359
$826$	3.83129e37	0.0159998
$827$	2.77396e39	1.13966	0.569831	−	0.821762i	$-0.307009\pi$
$827$	2.77396e39	1.13966	0.569831	+	0.821762i	$0.307009\pi$
$828$	2.40707e38	0.0972926
$829$	−2.07020e39	−0.823241	−0.411621	−	0.911355i	$-0.635037\pi$
$829$	−2.07020e39	−0.823241	−0.411621	+	0.911355i	$0.635037\pi$
$830$	1.57739e38	0.0617141
$831$	1.98615e39	0.764537
$832$	−1.11213e38	−0.0421202
$833$	−5.03155e39	−1.87497
$834$	−1.66931e38	−0.0612062
$835$	9.66525e38	0.348695
$836$	−2.72099e38	−0.0965923
$837$	−3.07167e39	−1.07295
$838$	7.16572e37	0.0246301
$839$	−4.55507e39	−1.54067	−0.770333	−	0.637641i	$-0.779910\pi$
$839$	−4.55507e39	−1.54067	−0.770333	+	0.637641i	$0.779910\pi$
$840$	3.71106e38	0.123517
$841$	2.41380e39	0.790597
$842$	−4.07053e38	−0.131201
$843$	9.40640e37	0.0298367
$844$	−3.30386e39	−1.03133
$845$	1.45281e39	0.446315
$846$	−4.20411e37	−0.0127108
$847$	2.91611e39	0.867717
$848$	−1.54616e39	−0.452803
$849$	−2.97318e39	−0.856974
$850$	−8.93258e37	−0.0253408
$851$	−2.47978e39	−0.692411
$852$	3.51510e39	0.966058
$853$	6.38844e38	0.172816	0.0864079	−	0.996260i	$-0.472461\pi$
$853$	6.38844e38	0.172816	0.0864079	+	0.996260i	$0.472461\pi$
$854$	1.05477e39	0.280851
$855$	−5.82597e37	−0.0152695
$856$	5.77751e38	0.149054
$857$	2.03778e39	0.517508	0.258754	−	0.965943i	$-0.416688\pi$
$857$	2.03778e39	0.517508	0.258754	+	0.965943i	$0.416688\pi$
$858$	1.05810e37	0.00264513
$859$	5.64625e39	1.38948	0.694741	−	0.719260i	$-0.255519\pi$
$859$	5.64625e39	1.38948	0.694741	+	0.719260i	$0.255519\pi$
$860$	−1.85696e39	−0.449857
$861$	−1.05967e40	−2.52713
$862$	−9.00531e37	−0.0211422
$863$	4.71839e39	1.09056	0.545278	−	0.838255i	$-0.316424\pi$
$863$	4.71839e39	1.09056	0.545278	+	0.838255i	$0.316424\pi$
$864$	1.41307e39	0.321535
$865$	2.53512e39	0.567911
$866$	−6.50897e38	−0.143556
$867$	−2.36462e39	−0.513456
$868$	−7.25542e39	−1.55112
$869$	−5.84111e39	−1.22950
$870$	2.54068e38	0.0526550
$871$	−6.97529e37	−0.0142337
$872$	3.45497e38	0.0694180
$873$	−6.07712e38	−0.120228
$874$	−3.14539e37	−0.00612732
$875$	7.35550e38	0.141092
$876$	−1.37753e39	−0.260194
$877$	4.04383e39	0.752139	0.376069	−	0.926592i	$-0.377275\pi$
$877$	4.04383e39	0.752139	0.376069	+	0.926592i	$0.377275\pi$
$878$	−1.92443e38	−0.0352473
$879$	4.72631e39	0.852457
$880$	1.63781e39	0.290903
$881$	9.65118e39	1.68813	0.844065	−	0.536241i	$-0.180156\pi$
$881$	9.65118e39	1.68813	0.844065	+	0.536241i	$0.180156\pi$
$882$	−2.03975e38	−0.0351359
$883$	9.21433e39	1.56313	0.781564	−	0.623826i	$-0.214422\pi$
$883$	9.21433e39	1.56313	0.781564	+	0.623826i	$0.214422\pi$
$884$	3.34517e38	0.0558872
$885$	−2.39777e38	−0.0394523
$886$	−1.01825e39	−0.165005
$887$	−1.01937e39	−0.162691	−0.0813453	−	0.996686i	$-0.525922\pi$
$887$	−1.01937e39	−0.162691	−0.0813453	+	0.996686i	$0.525922\pi$
$888$	−1.84171e39	−0.289498
$889$	1.38326e40	2.14156
$890$	−3.30989e38	−0.0504717
$891$	3.17180e39	0.476384
$892$	−9.36528e39	−1.38546
$893$	−5.37551e38	−0.0783295
$894$	−9.18036e38	−0.131766
$895$	5.83908e38	0.0825531
$896$	4.44255e39	0.618691
$897$	−1.19683e38	−0.0164186
$898$	−6.17131e37	−0.00833964
$899$	−9.98523e39	−1.32924
$900$	3.54333e38	0.0464663
$901$	4.55315e39	0.588203
$902$	9.70791e38	0.123548
$903$	−1.11849e40	−1.40232
$904$	−2.98527e38	−0.0368731
$905$	−6.67327e39	−0.812050
$906$	−7.68867e38	−0.0921765
$907$	−1.04947e39	−0.123957	−0.0619787	−	0.998077i	$-0.519741\pi$
$907$	−1.04947e39	−0.123957	−0.0619787	+	0.998077i	$0.519741\pi$
$908$	2.16914e39	0.252422
$909$	−1.56702e39	−0.179664
$910$	2.81510e37	0.00318005
$911$	−3.63004e39	−0.404030	−0.202015	−	0.979382i	$-0.564749\pi$
$911$	−3.63004e39	−0.404030	−0.202015	+	0.979382i	$0.564749\pi$
$912$	1.12536e39	0.123413
$913$	8.51695e39	0.920299
$914$	1.42810e39	0.152049
$915$	−6.60115e39	−0.692524
$916$	2.32748e39	0.240601
$917$	−1.47710e40	−1.50461
$918$	−1.36347e39	−0.136858
$919$	−4.32204e39	−0.427493	−0.213747	−	0.976889i	$-0.568567\pi$
$919$	−4.32204e39	−0.427493	−0.213747	+	0.976889i	$0.568567\pi$
$920$	3.84558e38	0.0374823
$921$	−1.12791e40	−1.08335
$922$	−1.10856e39	−0.104928
$923$	5.36015e38	0.0499981
$924$	9.96782e39	0.916281
$925$	−3.65036e39	−0.330691
$926$	1.73531e39	0.154928
$927$	−2.72111e39	−0.239425
$928$	4.59353e39	0.398336
$929$	1.11143e40	0.949881	0.474940	−	0.880018i	$-0.342470\pi$
$929$	1.11143e40	0.949881	0.474940	+	0.880018i	$0.342470\pi$
$930$	−4.64049e38	−0.0390881
$931$	−2.60809e39	−0.216522
$932$	−6.86091e39	−0.561393
$933$	1.79610e40	1.44854
$934$	−1.73418e39	−0.137852
$935$	−4.82306e39	−0.377890
$936$	2.72606e37	0.00210529
$937$	3.94128e39	0.300022	0.150011	−	0.988684i	$-0.452069\pi$
$937$	3.94128e39	0.300022	0.150011	+	0.988684i	$0.452069\pi$
$938$	6.71548e38	0.0503894
$939$	−1.05963e39	−0.0783731
$940$	3.26937e39	0.238362
$941$	2.22229e39	0.159713	0.0798564	−	0.996806i	$-0.474554\pi$
$941$	2.22229e39	0.159713	0.0798564	+	0.996806i	$0.474554\pi$
$942$	2.04646e39	0.144982
$943$	−1.09808e40	−0.766878
$944$	−1.42045e39	−0.0977923
$945$	1.12274e40	0.761994
$946$	1.02468e39	0.0685580
$947$	−1.45465e40	−0.959473	−0.479737	−	0.877413i	$-0.659268\pi$
$947$	−1.45465e40	−0.959473	−0.479737	+	0.877413i	$0.659268\pi$
$948$	2.44100e40	1.58729
$949$	−2.10059e38	−0.0134663
$950$	−4.63017e37	−0.00292637
$951$	−1.04536e40	−0.651369
$952$	−6.47406e39	−0.397720
$953$	−2.13474e40	−1.29298	−0.646488	−	0.762924i	$-0.723763\pi$
$953$	−2.13474e40	−1.29298	−0.646488	+	0.762924i	$0.723763\pi$
$954$	1.84581e38	0.0110226
$955$	6.13941e39	0.361477
$956$	2.32137e40	1.34761
$957$	1.37182e40	0.785208
$958$	3.19293e39	0.180200
$959$	4.66894e40	2.59817
$960$	−6.70088e39	−0.367680
$961$	−2.44929e38	−0.0132518
$962$	−1.39706e38	−0.00745337
$963$	3.32264e39	0.174795
$964$	−1.40971e40	−0.731293
$965$	−4.20532e39	−0.215120
$966$	1.15225e39	0.0581242
$967$	−1.51981e40	−0.756019	−0.378010	−	0.925802i	$-0.623391\pi$
$967$	−1.51981e40	−0.756019	−0.378010	+	0.925802i	$0.623391\pi$
$968$	2.24428e39	0.110093
$969$	−3.31399e39	−0.160317
$970$	−4.82978e38	−0.0230414
$971$	9.81279e39	0.461671	0.230836	−	0.972993i	$-0.425854\pi$
$971$	9.81279e39	0.461671	0.230836	+	0.972993i	$0.425854\pi$
$972$	9.78897e39	0.454195
$973$	−2.39801e40	−1.09731
$974$	−6.55293e38	−0.0295726
$975$	−1.76180e38	−0.00784139
$976$	−3.91057e40	−1.71659
$977$	2.93243e40	1.26955	0.634777	−	0.772695i	$-0.281092\pi$
$977$	2.93243e40	1.26955	0.634777	+	0.772695i	$0.281092\pi$
$978$	3.39747e38	0.0145071
$979$	−1.78714e40	−0.752650
$980$	1.58623e40	0.658892
$981$	1.98696e39	0.0814060
$982$	4.07637e39	0.164728
$983$	−3.83159e40	−1.52724	−0.763619	−	0.645667i	$-0.776579\pi$
$983$	−3.83159e40	−1.52724	−0.763619	+	0.645667i	$0.776579\pi$
$984$	−8.15533e39	−0.320633
$985$	−1.12423e40	−0.435981
$986$	−4.43229e39	−0.169547
$987$	1.96922e40	0.743039
$988$	1.73396e38	0.00645386
$989$	−1.15904e40	−0.425547
$990$	−1.95523e38	−0.00708145
$991$	2.90396e40	1.03752	0.518760	−	0.854920i	$-0.326394\pi$
$991$	2.90396e40	1.03752	0.518760	+	0.854920i	$0.326394\pi$
$992$	−8.38998e39	−0.295701
$993$	−6.30891e39	−0.219351
$994$	−5.16050e39	−0.177001
$995$	1.79553e39	0.0607549
$996$	−3.55924e40	−1.18811
$997$	2.00603e40	0.660622	0.330311	−	0.943872i	$-0.392846\pi$
$997$	2.00603e40	0.660622	0.330311	+	0.943872i	$0.392846\pi$
$998$	3.98814e38	0.0129571
$999$	−5.57190e40	−1.78595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.28.a.b.1.3	✓	5
3.2	odd	2		45.28.a.d.1.3		5
5.2	odd	4		25.28.b.c.24.6		10
5.3	odd	4		25.28.b.c.24.5		10
5.4	even	2		25.28.a.c.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.28.a.b.1.3	✓	5	1.1	even	1	trivial
25.28.a.c.1.3		5	5.4	even	2
25.28.b.c.24.5		10	5.3	odd	4
25.28.b.c.24.6		10	5.2	odd	4
45.28.a.d.1.3		5	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+1165.24 q^{2} -2.41575e6 q^{3} -1.32860e8 q^{4} -1.22070e9 q^{5} -2.81493e9 q^{6} -4.04373e11 q^{7} -3.11211e11 q^{8} -1.78977e12 q^{9} +O(q^{10})\)	\(q+1165.24 q^{2} -2.41575e6 q^{3} -1.32860e8 q^{4} -1.22070e9 q^{5} -2.81493e9 q^{6} -4.04373e11 q^{7} -3.11211e11 q^{8} -1.78977e12 q^{9} -1.42242e12 q^{10} -7.68020e13 q^{11} +3.20956e14 q^{12} +4.89423e13 q^{13} -4.71193e14 q^{14} +2.94891e15 q^{15} +1.74695e16 q^{16} -5.14446e16 q^{17} -2.08552e15 q^{18} -2.66662e16 q^{19} +1.62183e17 q^{20} +9.76863e17 q^{21} -8.94931e16 q^{22} +1.01227e18 q^{23} +7.51805e17 q^{24} +1.49012e18 q^{25} +5.70297e16 q^{26} +2.27451e19 q^{27} +5.37250e19 q^{28} +7.39387e19 q^{29} +3.43620e18 q^{30} -1.35047e20 q^{31} +6.21262e19 q^{32} +1.85534e20 q^{33} -5.99455e19 q^{34} +4.93620e20 q^{35} +2.37789e20 q^{36} -2.44971e21 q^{37} -3.10726e19 q^{38} -1.18232e20 q^{39} +3.79896e20 q^{40} -1.08477e22 q^{41} +1.13828e21 q^{42} -1.14498e22 q^{43} +1.02039e22 q^{44} +2.18478e21 q^{45} +1.17955e21 q^{46} +2.01586e22 q^{47} -4.22019e22 q^{48} +9.78053e22 q^{49} +1.73635e21 q^{50} +1.24277e23 q^{51} -6.50247e21 q^{52} -8.85059e22 q^{53} +2.65036e22 q^{54} +9.37525e22 q^{55} +1.25845e23 q^{56} +6.44186e22 q^{57} +8.61566e22 q^{58} -8.13103e22 q^{59} -3.91792e23 q^{60} -2.23851e24 q^{61} -1.57363e23 q^{62} +7.23735e23 q^{63} -2.27233e24 q^{64} -5.97440e22 q^{65} +2.16193e23 q^{66} -1.42521e24 q^{67} +6.83493e24 q^{68} -2.44540e24 q^{69} +5.75187e23 q^{70} +1.09520e25 q^{71} +5.56996e23 q^{72} -4.29198e24 q^{73} -2.85451e24 q^{74} -3.59974e24 q^{75} +3.54286e24 q^{76} +3.10567e25 q^{77} -1.37769e23 q^{78} +7.60541e25 q^{79} -2.13251e25 q^{80} -4.12984e25 q^{81} -1.26402e25 q^{82} -1.10895e26 q^{83} -1.29786e26 q^{84} +6.27986e25 q^{85} -1.33418e25 q^{86} -1.78617e26 q^{87} +2.39016e25 q^{88} +2.32695e26 q^{89} +2.54580e24 q^{90} -1.97909e25 q^{91} -1.34491e26 q^{92} +3.26240e26 q^{93} +2.34896e25 q^{94} +3.25515e25 q^{95} -1.50081e26 q^{96} +3.39547e26 q^{97} +1.13967e26 q^{98} +1.37458e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 19916 q^{2} + 4870682 q^{3} + 251490240 q^{4} - 6103515625 q^{5} + 39384982360 q^{6} + 155646348206 q^{7} + 4844427693600 q^{8} + 9256436775085 q^{9}+O(q^{10}) \) 5 * q + 19916 * q^2 + 4870682 * q^3 + 251490240 * q^4 - 6103515625 * q^5 + 39384982360 * q^6 + 155646348206 * q^7 + 4844427693600 * q^8 + 9256436775085 * q^9	\( 5 q + 19916 q^{2} + 4870682 q^{3} + 251490240 q^{4} - 6103515625 q^{5} + 39384982360 q^{6} + 155646348206 q^{7} + 4844427693600 q^{8} + 9256436775085 q^{9} - 24311523437500 q^{10} - 34307841041440 q^{11} + 10\!\cdots\!96 q^{12}+ \cdots + 26\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q + 19916 * q^2 + 4870682 * q^3 + 251490240 * q^4 - 6103515625 * q^5 + 39384982360 * q^6 + 155646348206 * q^7 + 4844427693600 * q^8 + 9256436775085 * q^9 - 24311523437500 * q^10 - 34307841041440 * q^11 + 1067087945485696 * q^12 + 1264965428684322 * q^13 - 1494481038585720 * q^14 - 5945656738281250 * q^15 + 50480141682449280 * q^16 + 11381432659133186 * q^17 + 199164599348648492 * q^18 - 177889284152803500 * q^19 - 306994921875000000 * q^20 + 15690874972867260 * q^21 + 1661117755714509952 * q^22 + 5314231426153528362 * q^23 + 25461226121295412800 * q^24 + 7450580596923828125 * q^25 + 64194207115665583160 * q^26 + 69831879763488728300 * q^27 + 74243491650979261568 * q^28 + 142675767255557016550 * q^29 - 48077371044921875000 * q^30 + 490757140558660526660 * q^31 + 709255558573159910656 * q^32 + 262404778486784711104 * q^33 - 823451155892216853320 * q^34 - 189997983649902343750 * q^35 + 364604386623731602880 * q^36 - 1594690133202798011054 * q^37 - 8102840491936976962000 * q^38 - 3725217775868438909980 * q^39 - 5913608024414062500000 * q^40 - 14453824011731896105490 * q^41 - 18735431399125775369328 * q^42 - 6456338188721923591758 * q^43 - 61776067586935488773120 * q^44 - 11299361297711181640625 * q^45 + 41662242513049160161560 * q^46 + 19960747396802751518726 * q^47 + 306904049567056770080512 * q^48 + 64529931934369352760065 * q^49 + 29677152633666992187500 * q^50 + 45124322296416065252260 * q^51 + 694364047806293961951616 * q^52 + 203485571063020242199082 * q^53 + 430355877536329740706000 * q^54 + 41879688771289062500000 * q^55 - 514718506150627561339200 * q^56 - 1075206797979440282527000 * q^57 - 568257469475936639738200 * q^58 - 1753694580358227494398300 * q^59 - 1302597589704218750000000 * q^60 - 1715799924029775655491390 * q^61 + 856653132512718918087792 * q^62 - 3772385601985154457719778 * q^63 + 2825791291455308901232640 * q^64 - 1544147251811916503906250 * q^65 - 14020757899728664042151680 * q^66 - 52283413307813388053914 * q^67 - 18798756173665084661988992 * q^68 + 17423855056223403670703220 * q^69 + 1824317674054833984375000 * q^70 + 13737346388576400396156460 * q^71 + 48990987369760413733351200 * q^72 + 52785881484144679283287962 * q^73 + 44617246831379823508169080 * q^74 + 7257881760597229003906250 * q^75 - 50943444226830794465542400 * q^76 + 40527442829187717880256832 * q^77 + 96469318519881413261089264 * q^78 - 18659027886608771061377800 * q^79 - 61621266702208593750000000 * q^80 - 18780471510820240351050695 * q^81 - 233045910890443727506605688 * q^82 - 49391953045615520178004398 * q^83 - 276316883591574899554456320 * q^84 - 13893350413980939941406250 * q^85 - 246095687260751641221151240 * q^86 - 67750867272390013078210900 * q^87 - 662199546636275930413900800 * q^88 + 180573322691431536135373650 * q^89 - 243120848814268178710937500 * q^90 + 317295677016426969579588460 * q^91 - 379021343242797571985691264 * q^92 + 1482223660602013833974435784 * q^93 - 34623503302055809185576920 * q^94 + 217150005069340209960937500 * q^95 + 2545248606864865567495170560 * q^96 + 1118012018325586896775804426 * q^97 - 243326561625995319625007012 * q^98 + 2661033543665827983852919520 * q^99

Introduction

L-functions

Modular forms

Varieties

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