LMFDB - Embedded newform 3.28.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,28,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, 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("3.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	3.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:	$13.8556672451$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6469}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1617 $ x^2 - x - 1617
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$40.7150$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9997.93 q^{2} +1.59432e6 q^{3} -3.42591e7 q^{4} -1.80194e8 q^{5} -1.59399e10 q^{6} +1.89150e11 q^{7} +1.68442e12 q^{8} +2.54187e12 q^{9} +O(q^{10})$	\(q-9997.93 q^{2} +1.59432e6 q^{3} -3.42591e7 q^{4} -1.80194e8 q^{5} -1.59399e10 q^{6} +1.89150e11 q^{7} +1.68442e12 q^{8} +2.54187e12 q^{9} +1.80157e12 q^{10} -1.01311e14 q^{11} -5.46200e13 q^{12} -8.69880e14 q^{13} -1.89111e15 q^{14} -2.87287e14 q^{15} -1.22425e16 q^{16} -3.74265e16 q^{17} -2.54134e16 q^{18} -3.18562e17 q^{19} +6.17327e15 q^{20} +3.01566e17 q^{21} +1.01290e18 q^{22} +2.65629e18 q^{23} +2.68551e18 q^{24} -7.41811e18 q^{25} +8.69700e18 q^{26} +4.05256e18 q^{27} -6.48009e18 q^{28} -5.10440e18 q^{29} +2.87228e18 q^{30} -1.58256e20 q^{31} -1.03679e20 q^{32} -1.61522e20 q^{33} +3.74188e20 q^{34} -3.40836e19 q^{35} -8.70819e19 q^{36} +1.42786e21 q^{37} +3.18496e21 q^{38} -1.38687e21 q^{39} -3.03522e20 q^{40} -6.09020e20 q^{41} -3.01503e21 q^{42} -1.63843e22 q^{43} +3.47082e21 q^{44} -4.58029e20 q^{45} -2.65574e22 q^{46} +6.66286e22 q^{47} -1.95186e22 q^{48} -2.99348e22 q^{49} +7.41658e22 q^{50} -5.96700e22 q^{51} +2.98013e22 q^{52} +1.93048e23 q^{53} -4.05172e22 q^{54} +1.82556e22 q^{55} +3.18607e23 q^{56} -5.07890e23 q^{57} +5.10334e22 q^{58} -1.21400e24 q^{59} +9.84219e21 q^{60} -1.85637e24 q^{61} +1.58224e24 q^{62} +4.80793e23 q^{63} +2.67974e24 q^{64} +1.56747e23 q^{65} +1.61489e24 q^{66} +1.28917e23 q^{67} +1.28220e24 q^{68} +4.23498e24 q^{69} +3.40766e23 q^{70} -1.63319e25 q^{71} +4.28157e24 q^{72} +3.17629e24 q^{73} -1.42757e25 q^{74} -1.18269e25 q^{75} +1.09136e25 q^{76} -1.91629e25 q^{77} +1.38658e25 q^{78} +2.42286e25 q^{79} +2.20603e24 q^{80} +6.46108e24 q^{81} +6.08894e24 q^{82} +2.04985e24 q^{83} -1.03314e25 q^{84} +6.74403e24 q^{85} +1.63809e26 q^{86} -8.13806e24 q^{87} -1.70650e26 q^{88} +1.76821e26 q^{89} +4.57934e24 q^{90} -1.64537e26 q^{91} -9.10019e25 q^{92} -2.52312e26 q^{93} -6.66148e26 q^{94} +5.74029e25 q^{95} -1.65298e26 q^{96} +9.85376e26 q^{97} +2.99286e26 q^{98} -2.57519e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3168 q^{2} + 3188646 q^{3} + 4865024 q^{4} - 4906065060 q^{5} + 5050815264 q^{6} - 151657089584 q^{7} + 432422977536 q^{8} + 5083731656658 q^{9}+O(q^{10}) $ 2 * q + 3168 * q^2 + 3188646 * q^3 + 4865024 * q^4 - 4906065060 * q^5 + 5050815264 * q^6 - 151657089584 * q^7 + 432422977536 * q^8 + 5083731656658 * q^9	$ 2 q + 3168 q^{2} + 3188646 q^{3} + 4865024 q^{4} - 4906065060 q^{5} + 5050815264 q^{6} - 151657089584 q^{7} + 432422977536 q^{8} + 5083731656658 q^{9} - 60418938951360 q^{10} + 40854992127048 q^{11} + 7756419658752 q^{12} - 417397898638292 q^{13} - 63\!\cdots\!24 q^{14}+ \cdots + 10\!\cdots\!92 q^{99}+O(q^{100}) $ 2 * q + 3168 * q^2 + 3188646 * q^3 + 4865024 * q^4 - 4906065060 * q^5 + 5050815264 * q^6 - 151657089584 * q^7 + 432422977536 * q^8 + 5083731656658 * q^9 - 60418938951360 * q^10 + 40854992127048 * q^11 + 7756419658752 * q^12 - 417397898638292 * q^13 - 6378143375649024 * q^14 - 7821852364654380 * q^15 - 33977393317150720 * q^16 - 73795652103164508 * q^17 + 8052630944146272 * q^18 - 346903482355728584 * q^19 - 178722076778772480 * q^20 - 241790386036831632 * q^21 + 2884648366247624064 * q^22 + 2497625277930684432 * q^23 + 689421898814128128 * q^24 + 7465166899962582350 * q^25 + 14654342405239377984 * q^26 + 8105110306037952534 * q^27 - 19813833643227717632 * q^28 - 66866817822024885588 * q^29 - 96327304005749129280 * q^30 - 131371412087557498208 * q^31 - 221798282158915190784 * q^32 + 65136053612971548504 * q^33 - 104645686123668232512 * q^34 + 1576524909572257407840 * q^35 + 12366238259600464896 * q^36 - 247578887064220048004 * q^37 + 2811811879848292739712 * q^38 - 665467069950697616316 * q^39 + 5613252874049647411200 * q^40 + 5075362465608343410612 * q^41 - 10168820681094878890752 * q^42 - 35862665467692465632120 * q^43 + 9032931356628777725952 * q^44 - 12470559127572865084740 * q^45 - 28646330621234746514688 * q^46 + 48518144960084941517280 * q^47 - 54170939645579687362560 * q^48 + 20502047614180503101010 * q^49 + 270118022314323825021600 * q^50 - 117654105448073547888084 * q^51 + 47504180746517517248512 * q^52 + 350385928874194434085692 * q^53 + 12838494724764116813856 * q^54 - 653602484383437534351120 * q^55 + 745296153511182831452160 * q^56 - 553076200699832263228632 * q^57 - 762126478854004399790016 * q^58 - 1574701087781292940777176 * q^59 - 284940717616162876631040 * q^60 - 298583192683280602714100 * q^61 + 1936203801499437193354752 * q^62 - 385491973637399518025136 * q^63 + 4041790055686590773067776 * q^64 - 1981623229478787576516120 * q^65 + 4599061237221010740588672 * q^66 - 1451788236633679878778088 * q^67 - 140711495561838808713216 * q^68 + 3982021425986282595679536 * q^69 + 21545930212269822639383040 * q^70 - 18927618367388181178813776 * q^71 + 1099161189983037199417344 * q^72 - 18475598829856936295245388 * q^73 - 36334468497793316338471104 * q^74 + 11901887287449044179999050 * q^75 + 9804773679338363226198016 * q^76 - 67614050277859586781728448 * q^77 + 23363755146548460825584832 * q^78 - 29951640885798459169010240 * q^79 + 104922131781026456681840640 * q^80 + 12922163778453346597864482 * q^81 + 80929145969689652074441152 * q^82 + 68977464913739379133962936 * q^83 - 31589650695571744458203136 * q^84 + 178619857136873703182526840 * q^85 - 92642460447803684395923072 * q^86 - 106607305590464181665316924 * q^87 - 348641555423301021147070464 * q^88 + 525251854986446192504396436 * q^89 - 153576836304357969041077440 * q^90 - 318746170956550059362287648 * q^91 - 97209435326689254625910784 * q^92 - 209448463833670933215473184 * q^93 - 904589369407956626941257216 * q^94 + 191342642113513008280285200 * q^95 - 353618102606448143716319232 * q^96 + 792881154632193034514966212 * q^97 + 963334106172656502173965152 * q^98 + 103847908404393638125542792 * 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 $

$2$	−9997.93	−0.862989	−0.431495	−	0.902116i	$-0.642014\pi$
$2$	−9997.93	−0.862989	−0.431495	+	0.902116i	$0.642014\pi$
$3$	1.59432e6	0.577350
$3$	1.59432e6	0.577350
$4$	−3.42591e7	−0.255250
$5$	−1.80194e8	−0.0660154	−0.0330077	−	0.999455i	$-0.510509\pi$
$5$	−1.80194e8	−0.0660154	−0.0330077	+	0.999455i	$0.510509\pi$
$6$	−1.59399e10	−0.498247
$7$	1.89150e11	0.737873	0.368937	−	0.929455i	$-0.379722\pi$
$7$	1.89150e11	0.737873	0.368937	+	0.929455i	$0.379722\pi$
$8$	1.68442e12	1.08327
$9$	2.54187e12	0.333333
$10$	1.80157e12	0.0569705
$11$	−1.01311e14	−0.884821	−0.442410	−	0.896813i	$-0.645877\pi$
$11$	−1.01311e14	−0.884821	−0.442410	+	0.896813i	$0.645877\pi$
$12$	−5.46200e13	−0.147369
$13$	−8.69880e14	−0.796570	−0.398285	−	0.917262i	$-0.630394\pi$
$13$	−8.69880e14	−0.796570	−0.398285	+	0.917262i	$0.630394\pi$
$14$	−1.89111e15	−0.636777
$15$	−2.87287e14	−0.0381140
$16$	−1.22425e16	−0.679598
$17$	−3.74265e16	−0.916472	−0.458236	−	0.888831i	$-0.651518\pi$
$17$	−3.74265e16	−0.916472	−0.458236	+	0.888831i	$0.651518\pi$
$18$	−2.54134e16	−0.287663
$19$	−3.18562e17	−1.73788	−0.868940	−	0.494917i	$-0.835198\pi$
$19$	−3.18562e17	−1.73788	−0.868940	+	0.494917i	$0.835198\pi$
$20$	6.17327e15	0.0168504
$21$	3.01566e17	0.426011
$22$	1.01290e18	0.763591
$23$	2.65629e18	1.09888	0.549439	−	0.835534i	$-0.314842\pi$
$23$	2.65629e18	1.09888	0.549439	+	0.835534i	$0.314842\pi$
$24$	2.68551e18	0.625424
$25$	−7.41811e18	−0.995642
$26$	8.69700e18	0.687431
$27$	4.05256e18	0.192450
$28$	−6.48009e18	−0.188342
$29$	−5.10440e18	−0.0923786	−0.0461893	−	0.998933i	$-0.514708\pi$
$29$	−5.10440e18	−0.0923786	−0.0461893	+	0.998933i	$0.514708\pi$
$30$	2.87228e18	0.0328920
$31$	−1.58256e20	−1.16407	−0.582034	−	0.813164i	$-0.697743\pi$
$31$	−1.58256e20	−1.16407	−0.582034	+	0.813164i	$0.697743\pi$
$32$	−1.03679e20	−0.496782
$33$	−1.61522e20	−0.510852
$34$	3.74188e20	0.790905
$35$	−3.40836e19	−0.0487110
$36$	−8.70819e19	−0.0850833
$37$	1.42786e21	0.963748	0.481874	−	0.876240i	$-0.339956\pi$
$37$	1.42786e21	0.963748	0.481874	+	0.876240i	$0.339956\pi$
$38$	3.18496e21	1.49977
$39$	−1.38687e21	−0.459900
$40$	−3.03522e20	−0.0715123
$41$	−6.09020e20	−0.102813	−0.0514067	−	0.998678i	$-0.516370\pi$
$41$	−6.09020e20	−0.102813	−0.0514067	+	0.998678i	$0.516370\pi$
$42$	−3.01503e21	−0.367643
$43$	−1.63843e22	−1.45413	−0.727064	−	0.686569i	$-0.759116\pi$
$43$	−1.63843e22	−1.45413	−0.727064	+	0.686569i	$0.759116\pi$
$44$	3.47082e21	0.225850
$45$	−4.58029e20	−0.0220051
$46$	−2.65574e22	−0.948319
$47$	6.66286e22	1.77967	0.889835	−	0.456282i	$-0.150819\pi$
$47$	6.66286e22	1.77967	0.889835	+	0.456282i	$0.150819\pi$
$48$	−1.95186e22	−0.392366
$49$	−2.99348e22	−0.455543
$50$	7.41658e22	0.859228
$51$	−5.96700e22	−0.529125
$52$	2.98013e22	0.203324
$53$	1.93048e23	1.01845	0.509227	−	0.860632i	$-0.329931\pi$
$53$	1.93048e23	1.01845	0.509227	+	0.860632i	$0.329931\pi$
$54$	−4.05172e22	−0.166082
$55$	1.82556e22	0.0584118
$56$	3.18607e23	0.799314
$57$	−5.07890e23	−1.00337
$58$	5.10334e22	0.0797218
$59$	−1.21400e24	−1.50562	−0.752811	−	0.658237i	$-0.771302\pi$
$59$	−1.21400e24	−1.50562	−0.752811	+	0.658237i	$0.771302\pi$
$60$	9.84219e21	0.00972859
$61$	−1.85637e24	−1.46795	−0.733974	−	0.679177i	$-0.762337\pi$
$61$	−1.85637e24	−1.46795	−0.733974	+	0.679177i	$0.762337\pi$
$62$	1.58224e24	1.00458
$63$	4.80793e23	0.245958
$64$	2.67974e24	1.10831
$65$	1.56747e23	0.0525859
$66$	1.61489e24	0.440859
$67$	1.28917e23	0.0287276	0.0143638	−	0.999897i	$-0.495428\pi$
$67$	1.28917e23	0.0287276	0.0143638	+	0.999897i	$0.495428\pi$
$68$	1.28220e24	0.233929
$69$	4.23498e24	0.634437
$70$	3.40766e23	0.0420370
$71$	−1.63319e25	−1.66360	−0.831801	−	0.555074i	$-0.812690\pi$
$71$	−1.63319e25	−1.66360	−0.831801	+	0.555074i	$0.812690\pi$
$72$	4.28157e24	0.361089
$73$	3.17629e24	0.222363	0.111181	−	0.993800i	$-0.464537\pi$
$73$	3.17629e24	0.222363	0.111181	+	0.993800i	$0.464537\pi$
$74$	−1.42757e25	−0.831704
$75$	−1.18269e25	−0.574834
$76$	1.09136e25	0.443594
$77$	−1.91629e25	−0.652886
$78$	1.38658e25	0.396889
$79$	2.42286e25	0.583932	0.291966	−	0.956429i	$-0.405691\pi$
$79$	2.42286e25	0.583932	0.291966	+	0.956429i	$0.405691\pi$
$80$	2.20603e24	0.0448639
$81$	6.46108e24	0.111111
$82$	6.08894e24	0.0887268
$83$	2.04985e24	0.0253611	0.0126806	−	0.999920i	$-0.495964\pi$
$83$	2.04985e24	0.0253611	0.0126806	+	0.999920i	$0.495964\pi$
$84$	−1.03314e25	−0.108739
$85$	6.74403e24	0.0605012
$86$	1.63809e26	1.25490
$87$	−8.13806e24	−0.0533348
$88$	−1.70650e26	−0.958497
$89$	1.76821e26	0.852647	0.426323	−	0.904571i	$-0.359809\pi$
$89$	1.76821e26	0.852647	0.426323	+	0.904571i	$0.359809\pi$
$90$	4.57934e24	0.0189902
$91$	−1.64537e26	−0.587768
$92$	−9.10019e25	−0.280488
$93$	−2.52312e26	−0.672075
$94$	−6.66148e26	−1.53584
$95$	5.74029e25	0.114727
$96$	−1.65298e26	−0.286817
$97$	9.85376e26	1.48656	0.743282	−	0.668978i	$-0.233268\pi$
$97$	9.85376e26	1.48656	0.743282	+	0.668978i	$0.233268\pi$
$98$	2.99286e26	0.393128
$99$	−2.57519e26	−0.294940
$100$	2.54137e26	0.254137
$101$	1.13311e27	0.990680	0.495340	−	0.868699i	$-0.335043\pi$
$101$	1.13311e27	0.990680	0.495340	+	0.868699i	$0.335043\pi$
$102$	5.96576e26	0.456629
$103$	1.72781e27	1.15930	0.579648	−	0.814867i	$-0.303190\pi$
$103$	1.72781e27	1.15930	0.579648	+	0.814867i	$0.303190\pi$
$104$	−1.46524e27	−0.862898
$105$	−5.43403e25	−0.0281233
$106$	−1.93008e27	−0.878915
$107$	−2.19758e27	−0.881583	−0.440792	−	0.897610i	$-0.645302\pi$
$107$	−2.19758e27	−0.881583	−0.440792	+	0.897610i	$0.645302\pi$
$108$	−1.38837e26	−0.0491229
$109$	−1.49024e26	−0.0465584	−0.0232792	−	0.999729i	$-0.507411\pi$
$109$	−1.49024e26	−0.0465584	−0.0232792	+	0.999729i	$0.507411\pi$
$110$	−1.82518e26	−0.0504087
$111$	2.27648e27	0.556420
$112$	−2.31567e27	−0.501457
$113$	−4.97504e27	−0.955515	−0.477758	−	0.878492i	$-0.658550\pi$
$113$	−4.97504e27	−0.955515	−0.477758	+	0.878492i	$0.658550\pi$
$114$	5.07785e27	0.865894
$115$	−4.78647e26	−0.0725428
$116$	1.74872e26	0.0235796
$117$	−2.21112e27	−0.265523
$118$	1.21375e28	1.29933
$119$	−7.07921e27	−0.676240
$120$	−4.83912e26	−0.0412876
$121$	−2.84608e27	−0.217092
$122$	1.85598e28	1.26682
$123$	−9.70975e26	−0.0593593
$124$	5.42172e27	0.297128
$125$	2.67925e27	0.131743
$126$	−4.80694e27	−0.212259
$127$	2.65317e27	0.105297	0.0526483	−	0.998613i	$-0.483234\pi$
$127$	2.65317e27	0.105297	0.0526483	+	0.998613i	$0.483234\pi$
$128$	−1.28763e28	−0.459682
$129$	−2.61218e28	−0.839542
$130$	−1.56715e27	−0.0453810
$131$	1.85807e28	0.485177	0.242588	−	0.970129i	$-0.422004\pi$
$131$	1.85807e28	0.485177	0.242588	+	0.970129i	$0.422004\pi$
$132$	5.53361e27	0.130395
$133$	−6.02558e28	−1.28234
$134$	−1.28890e27	−0.0247916
$135$	−7.30246e26	−0.0127047
$136$	−6.30420e28	−0.992783
$137$	9.57623e28	1.36605	0.683025	−	0.730395i	$-0.260664\pi$
$137$	9.57623e28	1.36605	0.683025	+	0.730395i	$0.260664\pi$
$138$	−4.23411e28	−0.547512
$139$	−5.02115e27	−0.0588983	−0.0294492	−	0.999566i	$-0.509375\pi$
$139$	−5.02115e27	−0.0588983	−0.0294492	+	0.999566i	$0.509375\pi$
$140$	1.16767e27	0.0124335
$141$	1.06228e29	1.02749
$142$	1.63285e29	1.43567
$143$	8.81284e28	0.704822
$144$	−3.11189e28	−0.226533
$145$	9.19781e26	0.00609841
$146$	−3.17564e28	−0.191897
$147$	−4.77257e28	−0.263008
$148$	−4.89173e28	−0.245997
$149$	−2.46576e29	−1.13224	−0.566118	−	0.824324i	$-0.691555\pi$
$149$	−2.46576e29	−1.13224	−0.566118	+	0.824324i	$0.691555\pi$
$150$	1.18244e29	0.496076
$151$	−1.52175e28	−0.0583653	−0.0291827	−	0.999574i	$-0.509290\pi$
$151$	−1.52175e28	−0.0583653	−0.0291827	+	0.999574i	$0.509290\pi$
$152$	−5.36592e29	−1.88259
$153$	−9.51332e28	−0.305491
$154$	1.91590e29	0.563433
$155$	2.85168e28	0.0768464
$156$	4.75128e28	0.117389
$157$	3.60073e29	0.816105	0.408052	−	0.912959i	$-0.366208\pi$
$157$	3.60073e29	0.816105	0.408052	+	0.912959i	$0.366208\pi$
$158$	−2.42236e29	−0.503927
$159$	3.07781e29	0.588005
$160$	1.86823e28	0.0327952
$161$	5.02436e29	0.810833
$162$	−6.45975e28	−0.0958877
$163$	−5.00768e29	−0.684075	−0.342037	−	0.939686i	$-0.611117\pi$
$163$	−5.00768e29	−0.684075	−0.342037	+	0.939686i	$0.611117\pi$
$164$	2.08645e28	0.0262431
$165$	2.91054e28	0.0337240
$166$	−2.04943e28	−0.0218864
$167$	8.57872e29	0.844792	0.422396	−	0.906411i	$-0.361189\pi$
$167$	8.57872e29	0.844792	0.422396	+	0.906411i	$0.361189\pi$
$168$	5.07963e29	0.461484
$169$	−4.35843e29	−0.365476
$170$	−6.74264e28	−0.0522119
$171$	−8.09741e29	−0.579293
$172$	5.61310e29	0.371166
$173$	3.12943e29	0.191356	0.0956780	−	0.995412i	$-0.469498\pi$
$173$	3.12943e29	0.191356	0.0956780	+	0.995412i	$0.469498\pi$
$174$	8.13638e28	0.0460274
$175$	−1.40313e30	−0.734658
$176$	1.24030e30	0.601322
$177$	−1.93550e30	−0.869271
$178$	−1.76785e30	−0.735825
$179$	−1.13339e30	−0.437383	−0.218692	−	0.975794i	$-0.570179\pi$
$179$	−1.13339e30	−0.437383	−0.218692	+	0.975794i	$0.570179\pi$
$180$	1.56916e28	0.00561680
$181$	−7.27535e29	−0.241653	−0.120827	−	0.992674i	$-0.538555\pi$
$181$	−7.27535e29	−0.241653	−0.120827	+	0.992674i	$0.538555\pi$
$182$	1.64503e30	0.507237
$183$	−2.95965e30	−0.847520
$184$	4.47430e30	1.19038
$185$	−2.57292e29	−0.0636222
$186$	2.52260e30	0.579994
$187$	3.79172e30	0.810913
$188$	−2.28263e30	−0.454261
$189$	7.66539e29	0.142004
$190$	−5.73910e29	−0.0990080
$191$	1.15148e31	1.85058	0.925289	−	0.379263i	$-0.123822\pi$
$191$	1.15148e31	1.85058	0.925289	+	0.379263i	$0.123822\pi$
$192$	4.27237e30	0.639886
$193$	−5.09816e30	−0.711853	−0.355926	−	0.934514i	$-0.615835\pi$
$193$	−5.09816e30	−0.711853	−0.355926	+	0.934514i	$0.615835\pi$
$194$	−9.85173e30	−1.28289
$195$	2.49905e29	0.0303605
$196$	1.02554e30	0.116277
$197$	−6.50645e30	−0.688732	−0.344366	−	0.938835i	$-0.611906\pi$
$197$	−6.50645e30	−0.688732	−0.344366	+	0.938835i	$0.611906\pi$
$198$	2.57466e30	0.254530
$199$	1.71040e30	0.157972	0.0789862	−	0.996876i	$-0.474832\pi$
$199$	1.71040e30	0.157972	0.0789862	+	0.996876i	$0.474832\pi$
$200$	−1.24952e31	−1.07855
$201$	2.05535e29	0.0165859
$202$	−1.13288e31	−0.854946
$203$	−9.65495e29	−0.0681637
$204$	2.04424e30	0.135059
$205$	1.09742e29	0.00678726
$206$	−1.72746e31	−1.00046
$207$	6.75193e30	0.366293
$208$	1.06495e31	0.541347
$209$	3.22738e31	1.53771
$210$	5.43290e29	0.0242701
$211$	3.00548e31	1.25922	0.629609	−	0.776912i	$-0.283215\pi$
$211$	3.00548e31	1.25922	0.629609	+	0.776912i	$0.283215\pi$
$212$	−6.61365e30	−0.259960
$213$	−2.60384e31	−0.960481
$214$	2.19712e31	0.760797
$215$	2.95235e30	0.0959948
$216$	6.82620e30	0.208475
$217$	−2.99341e31	−0.858935
$218$	1.48993e30	0.0401794
$219$	5.06404e30	0.128381
$220$	−6.25420e29	−0.0149096
$221$	3.25566e31	0.730034
$222$	−2.27601e31	−0.480185
$223$	−7.77434e31	−1.54365	−0.771823	−	0.635838i	$-0.780655\pi$
$223$	−7.77434e31	−1.54365	−0.771823	+	0.635838i	$0.780655\pi$
$224$	−1.96108e31	−0.366562
$225$	−1.88558e31	−0.331881
$226$	4.97401e31	0.824599
$227$	1.21624e32	1.89963	0.949814	−	0.312816i	$-0.101272\pi$
$227$	1.21624e32	1.89963	0.949814	+	0.312816i	$0.101272\pi$
$228$	1.73998e31	0.256109
$229$	−1.17444e32	−1.62949	−0.814745	−	0.579819i	$-0.803123\pi$
$229$	−1.17444e32	−1.62949	−0.814745	+	0.579819i	$0.803123\pi$
$230$	4.78548e30	0.0626037
$231$	−3.05519e31	−0.376944
$232$	−8.59795e30	−0.100071
$233$	−1.32531e32	−1.45551	−0.727753	−	0.685839i	$-0.759435\pi$
$233$	−1.32531e32	−1.45551	−0.727753	+	0.685839i	$0.759435\pi$
$234$	2.21066e31	0.229144
$235$	−1.20061e31	−0.117486
$236$	4.15904e31	0.384310
$237$	3.86282e31	0.337133
$238$	7.07775e31	0.583588
$239$	3.53040e31	0.275076	0.137538	−	0.990496i	$-0.456081\pi$
$239$	3.53040e31	0.275076	0.137538	+	0.990496i	$0.456081\pi$
$240$	3.51713e30	0.0259022
$241$	1.21655e32	0.847031	0.423516	−	0.905889i	$-0.360796\pi$
$241$	1.21655e32	0.847031	0.423516	+	0.905889i	$0.360796\pi$
$242$	2.84549e31	0.187348
$243$	1.03011e31	0.0641500
$244$	6.35973e31	0.374694
$245$	5.39407e30	0.0300728
$246$	9.70774e30	0.0512264
$247$	2.77110e32	1.38434
$248$	−2.66570e32	−1.26100
$249$	3.26813e30	0.0146422
$250$	−2.67869e31	−0.113693
$251$	−2.16474e32	−0.870582	−0.435291	−	0.900290i	$-0.643355\pi$
$251$	−2.16474e32	−0.870582	−0.435291	+	0.900290i	$0.643355\pi$
$252$	−1.64715e31	−0.0627807
$253$	−2.69111e32	−0.972310
$254$	−2.65262e31	−0.0908698
$255$	1.07522e31	0.0349304
$256$	−2.30932e32	−0.711614
$257$	−4.50140e32	−1.31598	−0.657992	−	0.753025i	$-0.728594\pi$
$257$	−4.50140e32	−1.31598	−0.657992	+	0.753025i	$0.728594\pi$
$258$	2.61164e32	0.724515
$259$	2.70080e32	0.711124
$260$	−5.37000e30	−0.0134225
$261$	−1.29747e31	−0.0307929
$262$	−1.85769e32	−0.418702
$263$	7.08254e32	1.51630	0.758152	−	0.652078i	$-0.226102\pi$
$263$	7.08254e32	1.51630	0.758152	+	0.652078i	$0.226102\pi$
$264$	−2.72072e32	−0.553389
$265$	−3.47861e31	−0.0672337
$266$	6.02434e32	1.10664
$267$	2.81910e32	0.492276
$268$	−4.41657e30	−0.00733272
$269$	−2.10292e32	−0.332022	−0.166011	−	0.986124i	$-0.553089\pi$
$269$	−2.10292e32	−0.332022	−0.166011	+	0.986124i	$0.553089\pi$
$270$	7.30095e30	0.0109640
$271$	5.32486e32	0.760716	0.380358	−	0.924839i	$-0.375801\pi$
$271$	5.32486e32	0.760716	0.380358	+	0.924839i	$0.375801\pi$
$272$	4.58196e32	0.622832
$273$	−2.62326e32	−0.339348
$274$	−9.57425e32	−1.17889
$275$	7.51536e32	0.880965
$276$	−1.45086e32	−0.161940
$277$	−3.06573e32	−0.325880	−0.162940	−	0.986636i	$-0.552098\pi$
$277$	−3.06573e32	−0.325880	−0.162940	+	0.986636i	$0.552098\pi$
$278$	5.02011e31	0.0508286
$279$	−4.02267e32	−0.388023
$280$	−5.74111e31	−0.0527670
$281$	−1.35283e33	−1.18497	−0.592486	−	0.805581i	$-0.701853\pi$
$281$	−1.35283e33	−1.18497	−0.592486	+	0.805581i	$0.701853\pi$
$282$	−1.06206e33	−0.886715
$283$	1.39333e33	1.10902	0.554508	−	0.832179i	$-0.312907\pi$
$283$	1.39333e33	1.10902	0.554508	+	0.832179i	$0.312907\pi$
$284$	5.59516e32	0.424634
$285$	9.15187e31	0.0662376
$286$	−8.81102e32	−0.608253
$287$	−1.15196e32	−0.0758633
$288$	−2.63538e32	−0.165594
$289$	−2.66967e32	−0.160080
$290$	−9.19591e30	−0.00526286
$291$	1.57101e33	0.858268
$292$	−1.08817e32	−0.0567581
$293$	−1.48492e33	−0.739586	−0.369793	−	0.929114i	$-0.620571\pi$
$293$	−1.48492e33	−0.739586	−0.369793	+	0.929114i	$0.620571\pi$
$294$	4.77159e32	0.226973
$295$	2.18755e32	0.0993941
$296$	2.40512e33	1.04400
$297$	−4.10568e32	−0.170284
$298$	2.46526e33	0.977107
$299$	−2.31065e33	−0.875333
$300$	4.05177e32	0.146726
$301$	−3.09908e33	−1.07296
$302$	1.52144e32	0.0503686
$303$	1.80654e33	0.571969
$304$	3.90001e33	1.18106
$305$	3.34506e32	0.0969071
$306$	9.51135e32	0.263635
$307$	−1.59094e33	−0.421974	−0.210987	−	0.977489i	$-0.567668\pi$
$307$	−1.59094e33	−0.421974	−0.210987	+	0.977489i	$0.567668\pi$
$308$	6.56504e32	0.166649
$309$	2.75469e33	0.669320
$310$	−2.85110e32	−0.0663176
$311$	−3.61017e33	−0.804012	−0.402006	−	0.915637i	$-0.631687\pi$
$311$	−3.61017e33	−0.804012	−0.402006	+	0.915637i	$0.631687\pi$
$312$	−2.33607e33	−0.498194
$313$	9.38820e32	0.191749	0.0958746	−	0.995393i	$-0.469435\pi$
$313$	9.38820e32	0.191749	0.0958746	+	0.995393i	$0.469435\pi$
$314$	−3.59999e33	−0.704289
$315$	−8.66359e31	−0.0162370
$316$	−8.30048e32	−0.149049
$317$	−7.75720e33	−1.33477	−0.667383	−	0.744715i	$-0.732586\pi$
$317$	−7.75720e33	−1.33477	−0.667383	+	0.744715i	$0.732586\pi$
$318$	−3.07718e33	−0.507442
$319$	5.17132e32	0.0817385
$320$	−4.82873e32	−0.0731658
$321$	−3.50365e33	−0.508982
$322$	−5.02332e33	−0.699740
$323$	1.19227e34	1.59272
$324$	−2.21351e32	−0.0283611
$325$	6.45286e33	0.793098
$326$	5.00664e33	0.590349
$327$	−2.37592e32	−0.0268805
$328$	−1.02585e33	−0.111374
$329$	1.26028e34	1.31317
$330$	−2.90993e32	−0.0291035
$331$	1.33893e34	1.28552	0.642762	−	0.766066i	$-0.277788\pi$
$331$	1.33893e34	1.28552	0.642762	+	0.766066i	$0.277788\pi$
$332$	−7.02260e31	−0.00647342
$333$	3.62944e33	0.321249
$334$	−8.57695e33	−0.729047
$335$	−2.32300e31	−0.00189646
$336$	−3.69193e33	−0.289516
$337$	−1.62944e34	−1.22754	−0.613769	−	0.789485i	$-0.710348\pi$
$337$	−1.62944e34	−1.22754	−0.613769	+	0.789485i	$0.710348\pi$
$338$	4.35753e33	0.315402
$339$	−7.93182e33	−0.551667
$340$	−2.31044e32	−0.0154429
$341$	1.60331e34	1.02999
$342$	8.09574e33	0.499924
$343$	−1.80916e34	−1.07401
$344$	−2.75980e34	−1.57521
$345$	−7.63118e32	−0.0418826
$346$	−3.12878e33	−0.165138
$347$	4.20787e32	0.0213607	0.0106803	−	0.999943i	$-0.496600\pi$
$347$	4.20787e32	0.0213607	0.0106803	+	0.999943i	$0.496600\pi$
$348$	2.78802e32	0.0136137
$349$	3.07379e33	0.144388	0.0721939	−	0.997391i	$-0.477000\pi$
$349$	3.07379e33	0.144388	0.0721939	+	0.997391i	$0.477000\pi$
$350$	1.40284e34	0.634002
$351$	−3.52524e33	−0.153300
$352$	1.05038e34	0.439563
$353$	−2.31488e34	−0.932329	−0.466165	−	0.884698i	$-0.654365\pi$
$353$	−2.31488e34	−0.932329	−0.466165	+	0.884698i	$0.654365\pi$
$354$	1.93510e34	0.750171
$355$	2.94291e33	0.109823
$356$	−6.05773e33	−0.217638
$357$	−1.12865e34	−0.390427
$358$	1.13315e34	0.377457
$359$	−2.82833e34	−0.907307	−0.453654	−	0.891178i	$-0.649880\pi$
$359$	−2.82833e34	−0.907307	−0.453654	+	0.891178i	$0.649880\pi$
$360$	−7.71513e32	−0.0238374
$361$	6.78809e34	2.02023
$362$	7.27385e33	0.208544
$363$	−4.53757e33	−0.125338
$364$	5.63689e33	0.150028
$365$	−5.72349e32	−0.0146794
$366$	2.95903e34	0.731401
$367$	−1.61545e34	−0.384858	−0.192429	−	0.981311i	$-0.561637\pi$
$367$	−1.61545e34	−0.384858	−0.192429	+	0.981311i	$0.561637\pi$
$368$	−3.25197e34	−0.746795
$369$	−1.54805e33	−0.0342711
$370$	2.57239e33	0.0549053
$371$	3.65150e34	0.751491
$372$	8.64397e33	0.171547
$373$	−5.10881e34	−0.977801	−0.488901	−	0.872339i	$-0.662602\pi$
$373$	−5.10881e34	−0.977801	−0.488901	+	0.872339i	$0.662602\pi$
$374$	−3.79093e34	−0.699809
$375$	4.27159e33	0.0760619
$376$	1.12231e35	1.92786
$377$	4.44021e33	0.0735860
$378$	−7.66381e33	−0.122548
$379$	−8.57587e34	−1.32327	−0.661635	−	0.749826i	$-0.730137\pi$
$379$	−8.57587e34	−1.32327	−0.661635	+	0.749826i	$0.730137\pi$
$380$	−1.96657e33	−0.0292840
$381$	4.23000e33	0.0607930
$382$	−1.15125e35	−1.59703
$383$	−1.40733e34	−0.188457	−0.0942287	−	0.995551i	$-0.530038\pi$
$383$	−1.40733e34	−0.188457	−0.0942287	+	0.995551i	$0.530038\pi$
$384$	−2.05290e34	−0.265398
$385$	3.45304e33	0.0431005
$386$	5.09711e34	0.614321
$387$	−4.16466e34	−0.484710
$388$	−3.37581e34	−0.379445
$389$	1.65090e35	1.79226	0.896128	−	0.443795i	$-0.146368\pi$
$389$	1.65090e35	1.79226	0.896128	+	0.443795i	$0.146368\pi$
$390$	−2.49854e33	−0.0262007
$391$	−9.94156e34	−1.00709
$392$	−5.04227e34	−0.493474
$393$	2.96237e34	0.280117
$394$	6.50511e34	0.594368
$395$	−4.36584e33	−0.0385485
$396$	8.82236e33	0.0752835
$397$	1.28718e35	1.06162	0.530809	−	0.847492i	$-0.321888\pi$
$397$	1.28718e35	1.06162	0.530809	+	0.847492i	$0.321888\pi$
$398$	−1.71005e34	−0.136328
$399$	−9.60672e34	−0.740357
$400$	9.08165e34	0.676636
$401$	2.75647e35	1.98566	0.992828	−	0.119549i	$-0.0381448\pi$
$401$	2.75647e35	1.98566	0.992828	+	0.119549i	$0.0381448\pi$
$402$	−2.05493e33	−0.0143135
$403$	1.37664e35	0.927262
$404$	−3.88193e34	−0.252871
$405$	−1.16425e33	−0.00733504
$406$	9.65295e33	0.0588246
$407$	−1.44658e35	−0.852745
$408$	−1.00509e35	−0.573184
$409$	−2.55571e35	−1.41009	−0.705045	−	0.709163i	$-0.749073\pi$
$409$	−2.55571e35	−1.41009	−0.705045	+	0.709163i	$0.749073\pi$
$410$	−1.09719e33	−0.00585733
$411$	1.52676e35	0.788690
$412$	−5.91933e34	−0.295910
$413$	−2.29627e35	−1.11096
$414$	−6.75053e34	−0.316106
$415$	−3.69371e32	−0.00167422
$416$	9.01881e34	0.395721
$417$	−8.00533e33	−0.0340050
$418$	−3.22671e35	−1.32703
$419$	−2.92003e35	−1.16278	−0.581390	−	0.813625i	$-0.697491\pi$
$419$	−2.92003e35	−1.16278	−0.581390	+	0.813625i	$0.697491\pi$
$420$	1.86165e33	0.00717847
$421$	4.39412e35	1.64083	0.820415	−	0.571769i	$-0.193743\pi$
$421$	4.39412e35	1.64083	0.820415	+	0.571769i	$0.193743\pi$
$422$	−3.00486e35	−1.08669
$423$	1.69361e35	0.593224
$424$	3.25174e35	1.10326
$425$	2.77634e35	0.912478
$426$	2.60330e35	0.828885
$427$	−3.51131e35	−1.08316
$428$	7.52869e34	0.225024
$429$	1.40505e35	0.406929
$430$	−2.95174e34	−0.0828425
$431$	1.55323e35	0.422467	0.211233	−	0.977436i	$-0.432252\pi$
$431$	1.55323e35	0.422467	0.211233	+	0.977436i	$0.432252\pi$
$432$	−4.96136e34	−0.130789
$433$	6.74169e34	0.172259	0.0861296	−	0.996284i	$-0.472550\pi$
$433$	6.74169e34	0.172259	0.0861296	+	0.996284i	$0.472550\pi$
$434$	2.99280e35	0.741252
$435$	1.46643e33	0.00352092
$436$	5.10542e33	0.0118840
$437$	−8.46191e35	−1.90972
$438$	−5.06299e34	−0.110792
$439$	5.29596e35	1.12376	0.561880	−	0.827219i	$-0.310078\pi$
$439$	5.29596e35	1.12376	0.561880	+	0.827219i	$0.310078\pi$
$440$	3.07501e34	0.0632755
$441$	−7.60902e34	−0.151848
$442$	−3.25498e35	−0.630011
$443$	1.32392e35	0.248549	0.124275	−	0.992248i	$-0.460340\pi$
$443$	1.32392e35	0.248549	0.124275	+	0.992248i	$0.460340\pi$
$444$	−7.79899e34	−0.142026
$445$	−3.18621e34	−0.0562878
$446$	7.77273e35	1.33215
$447$	−3.93123e35	−0.653697
$448$	5.06872e35	0.817796
$449$	−8.27330e35	−1.29525	−0.647624	−	0.761960i	$-0.724237\pi$
$449$	−8.27330e35	−1.29525	−0.647624	+	0.761960i	$0.724237\pi$
$450$	1.88519e35	0.286409
$451$	6.17004e34	0.0909714
$452$	1.70440e35	0.243895
$453$	−2.42616e34	−0.0336972
$454$	−1.21598e36	−1.63936
$455$	2.96486e34	0.0388017
$456$	−8.55500e35	−1.08691
$457$	−1.68751e35	−0.208151	−0.104075	−	0.994569i	$-0.533188\pi$
$457$	−1.68751e35	−0.208151	−0.104075	+	0.994569i	$0.533188\pi$
$458$	1.17420e36	1.40623
$459$	−1.51673e35	−0.176375
$460$	1.63980e34	0.0185165
$461$	−5.84038e35	−0.640440	−0.320220	−	0.947343i	$-0.603757\pi$
$461$	−5.84038e35	−0.640440	−0.320220	+	0.947343i	$0.603757\pi$
$462$	3.05456e35	0.325298
$463$	−7.61199e35	−0.787326	−0.393663	−	0.919255i	$-0.628792\pi$
$463$	−7.61199e35	−0.787326	−0.393663	+	0.919255i	$0.628792\pi$
$464$	6.24908e34	0.0627803
$465$	4.54651e34	0.0443673
$466$	1.32504e36	1.25609
$467$	6.40031e35	0.589418	0.294709	−	0.955587i	$-0.404777\pi$
$467$	6.40031e35	0.589418	0.294709	+	0.955587i	$0.404777\pi$
$468$	7.57508e34	0.0677748
$469$	2.43846e34	0.0211974
$470$	1.20036e35	0.101389
$471$	5.74073e35	0.471178
$472$	−2.04488e36	−1.63099
$473$	1.65991e36	1.28664
$474$	−3.86202e35	−0.290942
$475$	2.36313e36	1.73031
$476$	2.42527e35	0.172610
$477$	4.90703e35	0.339485
$478$	−3.52967e35	−0.237387
$479$	−1.93651e34	−0.0126617	−0.00633083	−	0.999980i	$-0.502015\pi$
$479$	−1.93651e34	−0.0126617	−0.00633083	+	0.999980i	$0.502015\pi$
$480$	2.97856e34	0.0189343
$481$	−1.24207e36	−0.767693
$482$	−1.21630e36	−0.730979
$483$	8.01045e35	0.468134
$484$	9.75039e34	0.0554128
$485$	−1.77559e35	−0.0981361
$486$	−1.02989e35	−0.0553608
$487$	1.06929e36	0.559055	0.279527	−	0.960138i	$-0.409822\pi$
$487$	1.06929e36	0.559055	0.279527	+	0.960138i	$0.409822\pi$
$488$	−3.12690e36	−1.59018
$489$	−7.98385e35	−0.394951
$490$	−5.39295e34	−0.0259525
$491$	−6.72076e35	−0.314643	−0.157321	−	0.987547i	$-0.550286\pi$
$491$	−6.72076e35	−0.314643	−0.157321	+	0.987547i	$0.550286\pi$
$492$	3.32647e34	0.0151515
$493$	1.91040e35	0.0846624
$494$	−2.77053e36	−1.19467
$495$	4.64033e34	0.0194706
$496$	1.93746e36	0.791098
$497$	−3.08918e36	−1.22753
$498$	−3.26745e34	−0.0126361
$499$	−6.57326e35	−0.247414	−0.123707	−	0.992319i	$-0.539478\pi$
$499$	−6.57326e35	−0.247414	−0.123707	+	0.992319i	$0.539478\pi$
$500$	−9.17885e34	−0.0336274
$501$	1.36772e36	0.487741
$502$	2.16429e36	0.751303
$503$	3.47595e36	1.17464	0.587321	−	0.809354i	$-0.300183\pi$
$503$	3.47595e36	1.17464	0.587321	+	0.809354i	$0.300183\pi$
$504$	8.09857e35	0.266438
$505$	−2.04179e35	−0.0654001
$506$	2.69056e36	0.839093
$507$	−6.94874e35	−0.211008
$508$	−9.08949e34	−0.0268769
$509$	2.18254e35	0.0628452	0.0314226	−	0.999506i	$-0.489996\pi$
$509$	2.18254e35	0.0628452	0.0314226	+	0.999506i	$0.489996\pi$
$510$	−1.07499e35	−0.0301445
$511$	6.00795e35	0.164076
$512$	4.03707e36	1.07380
$513$	−1.29099e36	−0.334455
$514$	4.50047e36	1.13568
$515$	−3.11341e35	−0.0765314
$516$	8.94909e35	0.214293
$517$	−6.75021e36	−1.57469
$518$	−2.70024e36	−0.613693
$519$	4.98932e35	0.110479
$520$	2.64028e35	0.0569645
$521$	1.79986e36	0.378380	0.189190	−	0.981940i	$-0.439414\pi$
$521$	1.79986e36	0.378380	0.189190	+	0.981940i	$0.439414\pi$
$522$	1.29720e35	0.0265739
$523$	−6.45952e36	−1.28952	−0.644759	−	0.764386i	$-0.723042\pi$
$523$	−6.45952e36	−1.28952	−0.644759	+	0.764386i	$0.723042\pi$
$524$	−6.36558e35	−0.123841
$525$	−2.23705e36	−0.424155
$526$	−7.08108e36	−1.30855
$527$	5.92299e36	1.06684
$528$	1.97745e36	0.347173
$529$	1.21265e36	0.207532
$530$	3.47789e35	0.0580219
$531$	−3.08582e36	−0.501874
$532$	2.06431e36	0.327316
$533$	5.29774e35	0.0818980
$534$	−2.81852e36	−0.424829
$535$	3.95990e35	0.0581980
$536$	2.17150e35	0.0311197
$537$	−1.80698e36	−0.252523
$538$	2.10249e36	0.286531
$539$	3.03272e36	0.403074
$540$	2.50175e34	0.00324286
$541$	9.08831e35	0.114900	0.0574500	−	0.998348i	$-0.481703\pi$
$541$	9.08831e35	0.114900	0.0574500	+	0.998348i	$0.481703\pi$
$542$	−5.32376e36	−0.656490
$543$	−1.15993e36	−0.139519
$544$	3.88034e36	0.455286
$545$	2.68532e34	0.00307357
$546$	2.62272e36	0.292854
$547$	6.52899e36	0.711241	0.355621	−	0.934630i	$-0.384269\pi$
$547$	6.52899e36	0.711241	0.355621	+	0.934630i	$0.384269\pi$
$548$	−3.28072e36	−0.348684
$549$	−4.71863e36	−0.489316
$550$	−7.51381e36	−0.760263
$551$	1.62607e36	0.160543
$552$	7.13348e36	0.687265
$553$	4.58283e36	0.430868
$554$	3.06510e36	0.281231
$555$	−4.10207e35	−0.0367323
$556$	1.72020e35	0.0150338
$557$	−2.46550e36	−0.210310	−0.105155	−	0.994456i	$-0.533534\pi$
$557$	−2.46550e36	−0.210310	−0.105155	+	0.994456i	$0.533534\pi$
$558$	4.02184e36	0.334859
$559$	1.42523e37	1.15832
$560$	4.17270e35	0.0331039
$561$	6.04522e36	0.468181
$562$	1.35255e37	1.02262
$563$	−6.04964e36	−0.446546	−0.223273	−	0.974756i	$-0.571674\pi$
$563$	−6.04964e36	−0.446546	−0.223273	+	0.974756i	$0.571674\pi$
$564$	−3.63925e36	−0.262267
$565$	8.96472e35	0.0630787
$566$	−1.39304e37	−0.957068
$567$	1.22211e36	0.0819859
$568$	−2.75098e37	−1.80213
$569$	−3.18261e36	−0.203595	−0.101798	−	0.994805i	$-0.532459\pi$
$569$	−3.18261e36	−0.203595	−0.101798	+	0.994805i	$0.532459\pi$
$570$	−9.14998e35	−0.0571623
$571$	−2.69379e37	−1.64353	−0.821763	−	0.569830i	$-0.807009\pi$
$571$	−2.69379e37	−1.64353	−0.821763	+	0.569830i	$0.807009\pi$
$572$	−3.01919e36	−0.179906
$573$	1.83584e37	1.06843
$574$	1.15172e36	0.0654692
$575$	−1.97046e37	−1.09409
$576$	6.81154e36	0.369438
$577$	1.33919e37	0.709527	0.354764	−	0.934956i	$-0.384561\pi$
$577$	1.33919e37	0.709527	0.354764	+	0.934956i	$0.384561\pi$
$578$	2.66912e36	0.138147
$579$	−8.12812e36	−0.410988
$580$	−3.15108e34	−0.00155662
$581$	3.87729e35	0.0187133
$582$	−1.57068e37	−0.740676
$583$	−1.95579e37	−0.901150
$584$	5.35021e36	0.240878
$585$	3.98430e35	0.0175286
$586$	1.48461e37	0.638255
$587$	4.40381e37	1.85018	0.925090	−	0.379747i	$-0.123989\pi$
$587$	4.40381e37	1.85018	0.925090	+	0.379747i	$0.123989\pi$
$588$	1.63504e36	0.0671327
$589$	5.04144e37	2.02301
$590$	−2.18710e36	−0.0857760
$591$	−1.03734e37	−0.397640
$592$	−1.74807e37	−0.654961
$593$	1.51350e37	0.554298	0.277149	−	0.960827i	$-0.410610\pi$
$593$	1.51350e37	0.554298	0.277149	+	0.960827i	$0.410610\pi$
$594$	4.10484e36	0.146953
$595$	1.27563e36	0.0446422
$596$	8.44748e36	0.289003
$597$	2.72693e36	0.0912054
$598$	2.31017e37	0.755403
$599$	−3.29289e37	−1.05273	−0.526363	−	0.850260i	$-0.676445\pi$
$599$	−3.29289e37	−1.05273	−0.526363	+	0.850260i	$0.676445\pi$
$600$	−1.99214e37	−0.622699
$601$	−2.52800e37	−0.772630	−0.386315	−	0.922367i	$-0.626252\pi$
$601$	−2.52800e37	−0.772630	−0.386315	+	0.922367i	$0.626252\pi$
$602$	3.09844e37	0.925955
$603$	3.27689e35	0.00957587
$604$	5.21337e35	0.0148977
$605$	5.12846e35	0.0143314
$606$	−1.80617e37	−0.493603
$607$	−1.38731e37	−0.370788	−0.185394	−	0.982664i	$-0.559356\pi$
$607$	−1.38731e37	−0.370788	−0.185394	+	0.982664i	$0.559356\pi$
$608$	3.30281e37	0.863347
$609$	−1.53931e36	−0.0393544
$610$	−3.34437e36	−0.0836298
$611$	−5.79589e37	−1.41763
$612$	3.25917e36	0.0779764
$613$	−4.35129e37	−1.01836	−0.509181	−	0.860660i	$-0.670052\pi$
$613$	−4.35129e37	−1.01836	−0.509181	+	0.860660i	$0.670052\pi$
$614$	1.59061e37	0.364159
$615$	1.74964e35	0.00391863
$616$	−3.22784e37	−0.707250
$617$	1.11829e37	0.239720	0.119860	−	0.992791i	$-0.461755\pi$
$617$	1.11829e37	0.239720	0.119860	+	0.992791i	$0.461755\pi$
$618$	−2.75412e37	−0.577616
$619$	−2.98715e37	−0.612962	−0.306481	−	0.951877i	$-0.599152\pi$
$619$	−2.98715e37	−0.612962	−0.306481	+	0.951877i	$0.599152\pi$
$620$	−9.76960e35	−0.0196150
$621$	1.07648e37	0.211479
$622$	3.60942e37	0.693853
$623$	3.34457e37	0.629146
$624$	1.69788e37	0.312547
$625$	5.47864e37	0.986945
$626$	−9.38626e36	−0.165478
$627$	5.14549e37	0.887799
$628$	−1.23358e37	−0.208311
$629$	−5.34400e37	−0.883248
$630$	8.66180e35	0.0140123
$631$	−7.06907e37	−1.11935	−0.559675	−	0.828712i	$-0.689074\pi$
$631$	−7.06907e37	−1.11935	−0.559675	+	0.828712i	$0.689074\pi$
$632$	4.08111e37	0.632554
$633$	4.79171e37	0.727010
$634$	7.75560e37	1.15189
$635$	−4.78084e35	−0.00695119
$636$	−1.05443e37	−0.150088
$637$	2.60397e37	0.362872
$638$	−5.17025e36	−0.0705395
$639$	−4.15135e37	−0.554534
$640$	2.32024e36	0.0303461
$641$	−1.24047e38	−1.58855	−0.794277	−	0.607555i	$-0.792150\pi$
$641$	−1.24047e38	−1.58855	−0.794277	+	0.607555i	$0.792150\pi$
$642$	3.50292e37	0.439246
$643$	1.42543e38	1.75024	0.875119	−	0.483908i	$-0.160783\pi$
$643$	1.42543e38	1.75024	0.875119	+	0.483908i	$0.160783\pi$
$644$	−1.72130e37	−0.206965
$645$	4.70699e36	0.0554227
$646$	−1.19202e38	−1.37450
$647$	1.16719e37	0.131806	0.0659030	−	0.997826i	$-0.479007\pi$
$647$	1.16719e37	0.131806	0.0659030	+	0.997826i	$0.479007\pi$
$648$	1.08832e37	0.120363
$649$	1.22991e38	1.33220
$650$	−6.45153e37	−0.684435
$651$	−4.77247e37	−0.495906
$652$	1.71558e37	0.174610
$653$	5.21169e37	0.519578	0.259789	−	0.965665i	$-0.416347\pi$
$653$	5.21169e37	0.519578	0.259789	+	0.965665i	$0.416347\pi$
$654$	2.37543e36	0.0231976
$655$	−3.34813e36	−0.0320291
$656$	7.45596e36	0.0698717
$657$	8.07371e36	0.0741209
$658$	−1.26002e38	−1.13325
$659$	−3.26169e37	−0.287402	−0.143701	−	0.989621i	$-0.545900\pi$
$659$	−3.26169e37	−0.287402	−0.143701	+	0.989621i	$0.545900\pi$
$660$	−9.97122e35	−0.00860806
$661$	2.46979e36	0.0208901	0.0104451	−	0.999945i	$-0.496675\pi$
$661$	2.46979e36	0.0208901	0.0104451	+	0.999945i	$0.496675\pi$
$662$	−1.33865e38	−1.10939
$663$	5.19057e37	0.421485
$664$	3.45281e36	0.0274728
$665$	1.08577e37	0.0846539
$666$	−3.62869e37	−0.277235
$667$	−1.35588e37	−0.101513
$668$	−2.93899e37	−0.215633
$669$	−1.23948e38	−0.891224
$670$	2.32252e35	0.00163663
$671$	1.88070e38	1.29887
$672$	−3.12660e37	−0.211635
$673$	−2.34269e38	−1.55422	−0.777108	−	0.629367i	$-0.783314\pi$
$673$	−2.34269e38	−1.55422	−0.777108	+	0.629367i	$0.783314\pi$
$674$	1.62911e38	1.05935
$675$	−3.00623e37	−0.191611
$676$	1.49316e37	0.0932878
$677$	4.81490e37	0.294877	0.147438	−	0.989071i	$-0.452897\pi$
$677$	4.81490e37	0.294877	0.147438	+	0.989071i	$0.452897\pi$
$678$	7.93018e37	0.476083
$679$	1.86384e38	1.09690
$680$	1.13598e37	0.0655390
$681$	1.93907e38	1.09675
$682$	−1.60298e38	−0.888872
$683$	3.26245e38	1.77364	0.886818	−	0.462118i	$-0.152910\pi$
$683$	3.26245e38	1.77364	0.886818	+	0.462118i	$0.152910\pi$
$684$	2.77410e37	0.147865
$685$	−1.72558e37	−0.0901803
$686$	1.80879e38	0.926856
$687$	−1.87244e38	−0.940787
$688$	2.00585e38	0.988223
$689$	−1.67929e38	−0.811270
$690$	7.62960e36	0.0361442
$691$	−1.43882e38	−0.668424	−0.334212	−	0.942498i	$-0.608470\pi$
$691$	−1.43882e38	−0.668424	−0.334212	+	0.942498i	$0.608470\pi$
$692$	−1.07211e37	−0.0488436
$693$	−4.87096e37	−0.217629
$694$	−4.20701e36	−0.0184340
$695$	9.04780e35	0.00388820
$696$	−1.37079e37	−0.0577759
$697$	2.27935e37	0.0942255
$698$	−3.07315e37	−0.124605
$699$	−2.11298e38	−0.840337
$700$	4.80700e37	0.187521
$701$	−3.60290e38	−1.37867	−0.689333	−	0.724445i	$-0.742096\pi$
$701$	−3.60290e38	−1.37867	−0.689333	+	0.724445i	$0.742096\pi$
$702$	3.52451e37	0.132296
$703$	−4.54863e38	−1.67488
$704$	−2.71487e38	−0.980660
$705$	−1.91415e37	−0.0678303
$706$	2.31440e38	0.804590
$707$	2.14327e38	0.730997
$708$	6.63085e37	0.221881
$709$	7.37828e36	0.0242232	0.0121116	−	0.999927i	$-0.496145\pi$
$709$	7.37828e36	0.0242232	0.0121116	+	0.999927i	$0.496145\pi$
$710$	−2.94230e37	−0.0947763
$711$	6.15858e37	0.194644
$712$	2.97841e38	0.923644
$713$	−4.20375e38	−1.27917
$714$	1.12842e38	0.336935
$715$	−1.58802e37	−0.0465291
$716$	3.88287e37	0.111642
$717$	5.62860e37	0.158815
$718$	2.82774e38	0.782996
$719$	4.44047e38	1.20667	0.603335	−	0.797488i	$-0.293838\pi$
$719$	4.44047e38	1.20667	0.603335	+	0.797488i	$0.293838\pi$
$720$	5.60744e36	0.0149546
$721$	3.26815e38	0.855414
$722$	−6.78669e38	−1.74344
$723$	1.93957e38	0.489034
$724$	2.49247e37	0.0616820
$725$	3.78650e37	0.0919761
$726$	4.53663e37	0.108166
$727$	6.04633e37	0.141507	0.0707534	−	0.997494i	$-0.477460\pi$
$727$	6.04633e37	0.141507	0.0707534	+	0.997494i	$0.477460\pi$
$728$	−2.77150e38	−0.636709
$729$	1.64232e37	0.0370370
$730$	5.72231e36	0.0126681
$731$	6.13206e38	1.33267
$732$	1.01395e38	0.216329
$733$	−3.07433e38	−0.643942	−0.321971	−	0.946749i	$-0.604345\pi$
$733$	−3.07433e38	−0.643942	−0.321971	+	0.946749i	$0.604345\pi$
$734$	1.61511e38	0.332128
$735$	8.59988e36	0.0173626
$736$	−2.75401e38	−0.545902
$737$	−1.30607e37	−0.0254188
$738$	1.54773e37	0.0295756
$739$	−9.98454e37	−0.187339	−0.0936695	−	0.995603i	$-0.529860\pi$
$739$	−9.98454e37	−0.187339	−0.0936695	+	0.995603i	$0.529860\pi$
$740$	8.81460e36	0.0162396
$741$	4.41803e38	0.799251
$742$	−3.65075e38	−0.648528
$743$	−2.07471e38	−0.361917	−0.180959	−	0.983491i	$-0.557920\pi$
$743$	−2.07471e38	−0.361917	−0.180959	+	0.983491i	$0.557920\pi$
$744$	−4.24999e38	−0.728037
$745$	4.44316e37	0.0747450
$746$	5.10776e38	0.843832
$747$	5.21045e36	0.00845370
$748$	−1.29901e38	−0.206985
$749$	−4.15671e38	−0.650497
$750$	−4.27070e37	−0.0656406
$751$	4.49009e38	0.677822	0.338911	−	0.940818i	$-0.389941\pi$
$751$	4.49009e38	0.677822	0.338911	+	0.940818i	$0.389941\pi$
$752$	−8.15704e38	−1.20946
$753$	−3.45129e38	−0.502631
$754$	−4.43929e37	−0.0635040
$755$	2.74210e36	0.00385301
$756$	−2.62609e37	−0.0362465
$757$	−6.05696e38	−0.821222	−0.410611	−	0.911811i	$-0.634685\pi$
$757$	−6.05696e38	−0.821222	−0.410611	+	0.911811i	$0.634685\pi$
$758$	8.57409e38	1.14197
$759$	−4.29050e38	−0.561363
$760$	9.66905e37	0.124280
$761$	7.70983e38	0.973536	0.486768	−	0.873531i	$-0.338176\pi$
$761$	7.70983e38	0.973536	0.486768	+	0.873531i	$0.338176\pi$
$762$	−4.22913e37	−0.0524637
$763$	−2.81878e37	−0.0343542
$764$	−3.94487e38	−0.472360
$765$	1.71424e37	0.0201671
$766$	1.40704e38	0.162637
$767$	1.05603e39	1.19933
$768$	−3.68180e38	−0.410851
$769$	8.48230e36	0.00930054	0.00465027	−	0.999989i	$-0.498520\pi$
$769$	8.48230e36	0.00930054	0.00465027	+	0.999989i	$0.498520\pi$
$770$	−3.45233e37	−0.0371953
$771$	−7.17669e38	−0.759784
$772$	1.74658e38	0.181700
$773$	−1.55218e39	−1.58678	−0.793392	−	0.608711i	$-0.791687\pi$
$773$	−1.55218e39	−1.58678	−0.793392	+	0.608711i	$0.791687\pi$
$774$	4.16380e38	0.418299
$775$	1.17396e39	1.15900
$776$	1.65979e39	1.61035
$777$	4.30595e38	0.410568
$778$	−1.65056e39	−1.54670
$779$	1.94010e38	0.178677
$780$	−8.56152e36	−0.00774950
$781$	1.65460e39	1.47199
$782$	9.93951e38	0.869108
$783$	−2.06859e37	−0.0177783
$784$	3.66478e38	0.309586
$785$	−6.48830e37	−0.0538754
$786$	−2.96176e38	−0.241738
$787$	−1.80168e39	−1.44550	−0.722752	−	0.691107i	$-0.757123\pi$
$787$	−1.80168e39	−1.44550	−0.722752	+	0.691107i	$0.757123\pi$
$788$	2.22905e38	0.175799
$789$	1.12919e39	0.875439
$790$	4.36494e37	0.0332669
$791$	−9.41027e38	−0.705049
$792$	−4.33770e38	−0.319499
$793$	1.61481e39	1.16932
$794$	−1.28692e39	−0.916164
$795$	−5.54603e37	−0.0388174
$796$	−5.85967e37	−0.0403224
$797$	−1.09715e39	−0.742297	−0.371149	−	0.928573i	$-0.621036\pi$
$797$	−1.09715e39	−0.742297	−0.371149	+	0.928573i	$0.621036\pi$
$798$	9.60474e38	0.638920
$799$	−2.49368e39	−1.63102
$800$	7.69101e38	0.494617
$801$	4.49456e38	0.284216
$802$	−2.75590e39	−1.71360
$803$	−3.21794e38	−0.196751
$804$	−7.04144e36	−0.00423355
$805$	−9.05359e37	−0.0535274
$806$	−1.37636e39	−0.800217
$807$	−3.35273e38	−0.191693
$808$	1.90863e39	1.07317
$809$	−3.30686e39	−1.82857	−0.914284	−	0.405074i	$-0.867246\pi$
$809$	−3.30686e39	−1.82857	−0.914284	+	0.405074i	$0.867246\pi$
$810$	1.16401e37	0.00633006
$811$	2.37585e38	0.127068	0.0635342	−	0.997980i	$-0.479763\pi$
$811$	2.37585e38	0.127068	0.0635342	+	0.997980i	$0.479763\pi$
$812$	3.30769e37	0.0173988
$813$	8.48955e38	0.439200
$814$	1.44628e39	0.735909
$815$	9.02353e37	0.0451594
$816$	7.30512e38	0.359592
$817$	5.21940e39	2.52710
$818$	2.55518e39	1.21689
$819$	−4.18232e38	−0.195923
$820$	−3.75965e36	−0.00173245
$821$	−3.17719e38	−0.144016	−0.0720081	−	0.997404i	$-0.522941\pi$
$821$	−3.17719e38	−0.144016	−0.0720081	+	0.997404i	$0.522941\pi$
$822$	−1.52644e39	−0.680630
$823$	−1.63742e39	−0.718227	−0.359113	−	0.933294i	$-0.616921\pi$
$823$	−1.63742e39	−0.718227	−0.359113	+	0.933294i	$0.616921\pi$
$824$	2.91036e39	1.25583
$825$	1.19819e39	0.508625
$826$	2.29580e39	0.958744
$827$	−1.80121e39	−0.740015	−0.370007	−	0.929029i	$-0.620645\pi$
$827$	−1.80121e39	−0.740015	−0.370007	+	0.929029i	$0.620645\pi$
$828$	−2.31315e38	−0.0934961
$829$	−9.28904e38	−0.369390	−0.184695	−	0.982796i	$-0.559130\pi$
$829$	−9.28904e38	−0.369390	−0.184695	+	0.982796i	$0.559130\pi$
$830$	3.69294e36	0.00144484
$831$	−4.88777e38	−0.188147
$832$	−2.33105e39	−0.882850
$833$	1.12036e39	0.417492
$834$	8.00368e37	0.0293459
$835$	−1.54583e38	−0.0557693
$836$	−1.10567e39	−0.392501
$837$	−6.41343e38	−0.224025
$838$	2.91943e39	1.00347
$839$	3.33647e39	1.12850	0.564249	−	0.825604i	$-0.309166\pi$
$839$	3.33647e39	1.12850	0.564249	+	0.825604i	$0.309166\pi$
$840$	−9.15318e37	−0.0304650
$841$	−3.02708e39	−0.991466
$842$	−4.39321e39	−1.41602
$843$	−2.15685e39	−0.684144
$844$	−1.02965e39	−0.321415
$845$	7.85362e37	0.0241271
$846$	−1.69326e39	−0.511945
$847$	−5.38334e38	−0.160187
$848$	−2.36340e39	−0.692139
$849$	2.22142e39	0.640290
$850$	−2.77577e39	−0.787458
$851$	3.79282e39	1.05904
$852$	8.92049e38	0.245163
$853$	2.65708e39	0.718775	0.359387	−	0.933188i	$-0.382986\pi$
$853$	2.65708e39	0.718775	0.359387	+	0.933188i	$0.382986\pi$
$854$	3.51058e39	0.934755
$855$	1.45910e38	0.0382423
$856$	−3.70164e39	−0.954990
$857$	4.33429e39	1.10072	0.550360	−	0.834927i	$-0.314490\pi$
$857$	4.33429e39	1.10072	0.550360	+	0.834927i	$0.314490\pi$
$858$	−1.40476e39	−0.351175
$859$	−5.60377e39	−1.37903	−0.689513	−	0.724273i	$-0.742175\pi$
$859$	−5.60377e39	−1.37903	−0.689513	+	0.724273i	$0.742175\pi$
$860$	−1.01145e38	−0.0245027
$861$	−1.83659e38	−0.0437997
$862$	−1.55291e39	−0.364584
$863$	3.77071e39	0.871520	0.435760	−	0.900063i	$-0.356480\pi$
$863$	3.77071e39	0.871520	0.435760	+	0.900063i	$0.356480\pi$
$864$	−4.20164e38	−0.0956056
$865$	−5.63903e37	−0.0126324
$866$	−6.74030e38	−0.148658
$867$	−4.25631e38	−0.0924221
$868$	1.02552e39	0.219243
$869$	−2.45462e39	−0.516675
$870$	−1.46613e37	−0.00303851
$871$	−1.12142e38	−0.0228836
$872$	−2.51019e38	−0.0504352
$873$	2.50469e39	0.495521
$874$	8.46017e39	1.64807
$875$	5.06779e38	0.0972097
$876$	−1.73489e38	−0.0327693
$877$	3.78267e39	0.703564	0.351782	−	0.936082i	$-0.385576\pi$
$877$	3.78267e39	0.703564	0.351782	+	0.936082i	$0.385576\pi$
$878$	−5.29487e39	−0.969793
$879$	−2.36743e39	−0.427000
$880$	−2.23495e38	−0.0396965
$881$	8.42775e38	0.147413	0.0737067	−	0.997280i	$-0.476517\pi$
$881$	8.42775e38	0.147413	0.0737067	+	0.997280i	$0.476517\pi$
$882$	7.60745e38	0.131043
$883$	3.45702e39	0.586452	0.293226	−	0.956043i	$-0.405271\pi$
$883$	3.45702e39	0.586452	0.293226	+	0.956043i	$0.405271\pi$
$884$	−1.11536e39	−0.186341
$885$	3.48766e38	0.0573852
$886$	−1.32365e39	−0.214495
$887$	7.90347e39	1.26139	0.630695	−	0.776031i	$-0.282770\pi$
$887$	7.90347e39	1.26139	0.630695	+	0.776031i	$0.282770\pi$
$888$	3.83454e39	0.602752
$889$	5.01845e38	0.0776955
$890$	3.18555e38	0.0485758
$891$	−6.54579e38	−0.0983134
$892$	2.66341e39	0.394015
$893$	−2.12253e40	−3.09285
$894$	3.93041e39	0.564133
$895$	2.04229e38	0.0288740
$896$	−2.43555e39	−0.339187
$897$	−3.68392e39	−0.505374
$898$	8.27159e39	1.11778
$899$	8.07804e38	0.107535
$900$	6.45983e38	0.0847125
$901$	−7.22513e39	−0.933385
$902$	−6.16877e38	−0.0785073
$903$	−4.94093e39	−0.619476
$904$	−8.38006e39	−1.03508
$905$	1.31097e38	0.0159528
$906$	2.42566e38	0.0290803
$907$	1.86659e39	0.220470	0.110235	−	0.993906i	$-0.464840\pi$
$907$	1.86659e39	0.220470	0.110235	+	0.993906i	$0.464840\pi$
$908$	−4.16671e39	−0.484880
$909$	2.88021e39	0.330227
$910$	−2.96425e38	−0.0334854
$911$	−8.28523e39	−0.922161	−0.461080	−	0.887358i	$-0.652538\pi$
$911$	−8.28523e39	−0.922161	−0.461080	+	0.887358i	$0.652538\pi$
$912$	6.21787e39	0.681885
$913$	−2.07672e38	−0.0224400
$914$	1.68716e39	0.179632
$915$	5.33310e38	0.0559494
$916$	4.02352e39	0.415927
$917$	3.51454e39	0.357999
$918$	1.51642e39	0.152210
$919$	−8.87717e39	−0.878041	−0.439021	−	0.898477i	$-0.644674\pi$
$919$	−8.87717e39	−0.878041	−0.439021	+	0.898477i	$0.644674\pi$
$920$	−8.06242e38	−0.0785832
$921$	−2.53647e39	−0.243627
$922$	5.83917e39	0.552693
$923$	1.42068e40	1.32518
$924$	1.04668e39	0.0962148
$925$	−1.05921e40	−0.959548
$926$	7.61041e39	0.679454
$927$	4.39187e39	0.386432
$928$	5.29218e38	0.0458920
$929$	1.57531e40	1.34634	0.673168	−	0.739489i	$-0.264933\pi$
$929$	1.57531e40	1.34634	0.673168	+	0.739489i	$0.264933\pi$
$930$	−4.54557e38	−0.0382885
$931$	9.53608e39	0.791679
$932$	4.54040e39	0.371518
$933$	−5.75578e39	−0.464196
$934$	−6.39899e39	−0.508661
$935$	−6.83244e38	−0.0535327
$936$	−3.72445e39	−0.287633
$937$	1.50423e40	1.14506	0.572531	−	0.819883i	$-0.305962\pi$
$937$	1.50423e40	1.14506	0.572531	+	0.819883i	$0.305962\pi$
$938$	−2.43795e38	−0.0182931
$939$	1.49678e39	0.110706
$940$	4.11316e38	0.0299882
$941$	−1.39909e40	−1.00551	−0.502756	−	0.864429i	$-0.667680\pi$
$941$	−1.39909e40	−1.00551	−0.502756	+	0.864429i	$0.667680\pi$
$942$	−5.73955e39	−0.406622
$943$	−1.61773e39	−0.112979
$944$	1.48624e40	1.02322
$945$	−1.38126e38	−0.00937443
$946$	−1.65956e40	−1.11036
$947$	1.47903e40	0.975557	0.487779	−	0.872967i	$-0.337807\pi$
$947$	1.47903e40	0.975557	0.487779	+	0.872967i	$0.337807\pi$
$948$	−1.32337e39	−0.0860532
$949$	−2.76299e39	−0.177128
$950$	−2.36264e40	−1.49324
$951$	−1.23675e40	−0.770627
$952$	−1.19244e40	−0.732549
$953$	−2.14532e40	−1.29938	−0.649692	−	0.760198i	$-0.725102\pi$
$953$	−2.14532e40	−1.29938	−0.649692	+	0.760198i	$0.725102\pi$
$954$	−4.90601e39	−0.292972
$955$	−2.07490e39	−0.122167
$956$	−1.20948e39	−0.0702131
$957$	8.24475e38	0.0471918
$958$	1.93611e38	0.0109269
$959$	1.81134e40	1.00797
$960$	−7.69855e38	−0.0422423
$961$	6.56239e39	0.355055
$962$	1.24181e40	0.662511
$963$	−5.58595e39	−0.293861
$964$	−4.16778e39	−0.216205
$965$	9.18658e38	0.0469932
$966$	−8.00879e39	−0.403995
$967$	2.21400e40	1.10133	0.550667	−	0.834725i	$-0.314373\pi$
$967$	2.21400e40	1.10133	0.550667	+	0.834725i	$0.314373\pi$
$968$	−4.79399e39	−0.235169
$969$	1.90086e40	0.919556
$970$	1.77522e39	0.0846904
$971$	3.86122e39	0.181662	0.0908312	−	0.995866i	$-0.471048\pi$
$971$	3.86122e39	0.181662	0.0908312	+	0.995866i	$0.471048\pi$
$972$	−3.52904e38	−0.0163743
$973$	−9.49748e38	−0.0434595
$974$	−1.06907e40	−0.482458
$975$	1.02879e40	0.457896
$976$	2.27266e40	0.997614
$977$	1.76871e39	0.0765737	0.0382869	−	0.999267i	$-0.487810\pi$
$977$	1.76871e39	0.0765737	0.0382869	+	0.999267i	$0.487810\pi$
$978$	7.98220e39	0.340838
$979$	−1.79139e40	−0.754440
$980$	−1.84796e38	−0.00767608
$981$	−3.78799e38	−0.0155195
$982$	6.71937e39	0.271533
$983$	−2.54498e39	−0.101441	−0.0507204	−	0.998713i	$-0.516152\pi$
$983$	−2.54498e39	−0.101441	−0.0507204	+	0.998713i	$0.516152\pi$
$984$	−1.63553e39	−0.0643020
$985$	1.17242e39	0.0454669
$986$	−1.91000e39	−0.0730627
$987$	2.00929e40	0.758160
$988$	−9.49354e39	−0.353353
$989$	−4.35213e40	−1.59791
$990$	−4.63938e38	−0.0168029
$991$	−1.28339e40	−0.458527	−0.229264	−	0.973364i	$-0.573632\pi$
$991$	−1.28339e40	−0.458527	−0.229264	+	0.973364i	$0.573632\pi$
$992$	1.64078e40	0.578288
$993$	2.13469e40	0.742198
$994$	3.08854e40	1.05934
$995$	−3.08204e38	−0.0104286
$996$	−1.11963e38	−0.00373743
$997$	−4.45043e40	−1.46561	−0.732804	−	0.680440i	$-0.761789\pi$
$997$	−4.45043e40	−1.46561	−0.732804	+	0.680440i	$0.761789\pi$
$998$	6.57190e39	0.213515
$999$	5.78650e39	0.185473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.28.a.a.1.1	✓	2
3.2	odd	2		9.28.a.c.1.2		2
4.3	odd	2		48.28.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.28.a.a.1.1	✓	2	1.1	even	1	trivial
9.28.a.c.1.2		2	3.2	odd	2
48.28.a.d.1.2		2	4.3	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-9997.93 q^{2} +1.59432e6 q^{3} -3.42591e7 q^{4} -1.80194e8 q^{5} -1.59399e10 q^{6} +1.89150e11 q^{7} +1.68442e12 q^{8} +2.54187e12 q^{9} +O(q^{10})\)	\(q-9997.93 q^{2} +1.59432e6 q^{3} -3.42591e7 q^{4} -1.80194e8 q^{5} -1.59399e10 q^{6} +1.89150e11 q^{7} +1.68442e12 q^{8} +2.54187e12 q^{9} +1.80157e12 q^{10} -1.01311e14 q^{11} -5.46200e13 q^{12} -8.69880e14 q^{13} -1.89111e15 q^{14} -2.87287e14 q^{15} -1.22425e16 q^{16} -3.74265e16 q^{17} -2.54134e16 q^{18} -3.18562e17 q^{19} +6.17327e15 q^{20} +3.01566e17 q^{21} +1.01290e18 q^{22} +2.65629e18 q^{23} +2.68551e18 q^{24} -7.41811e18 q^{25} +8.69700e18 q^{26} +4.05256e18 q^{27} -6.48009e18 q^{28} -5.10440e18 q^{29} +2.87228e18 q^{30} -1.58256e20 q^{31} -1.03679e20 q^{32} -1.61522e20 q^{33} +3.74188e20 q^{34} -3.40836e19 q^{35} -8.70819e19 q^{36} +1.42786e21 q^{37} +3.18496e21 q^{38} -1.38687e21 q^{39} -3.03522e20 q^{40} -6.09020e20 q^{41} -3.01503e21 q^{42} -1.63843e22 q^{43} +3.47082e21 q^{44} -4.58029e20 q^{45} -2.65574e22 q^{46} +6.66286e22 q^{47} -1.95186e22 q^{48} -2.99348e22 q^{49} +7.41658e22 q^{50} -5.96700e22 q^{51} +2.98013e22 q^{52} +1.93048e23 q^{53} -4.05172e22 q^{54} +1.82556e22 q^{55} +3.18607e23 q^{56} -5.07890e23 q^{57} +5.10334e22 q^{58} -1.21400e24 q^{59} +9.84219e21 q^{60} -1.85637e24 q^{61} +1.58224e24 q^{62} +4.80793e23 q^{63} +2.67974e24 q^{64} +1.56747e23 q^{65} +1.61489e24 q^{66} +1.28917e23 q^{67} +1.28220e24 q^{68} +4.23498e24 q^{69} +3.40766e23 q^{70} -1.63319e25 q^{71} +4.28157e24 q^{72} +3.17629e24 q^{73} -1.42757e25 q^{74} -1.18269e25 q^{75} +1.09136e25 q^{76} -1.91629e25 q^{77} +1.38658e25 q^{78} +2.42286e25 q^{79} +2.20603e24 q^{80} +6.46108e24 q^{81} +6.08894e24 q^{82} +2.04985e24 q^{83} -1.03314e25 q^{84} +6.74403e24 q^{85} +1.63809e26 q^{86} -8.13806e24 q^{87} -1.70650e26 q^{88} +1.76821e26 q^{89} +4.57934e24 q^{90} -1.64537e26 q^{91} -9.10019e25 q^{92} -2.52312e26 q^{93} -6.66148e26 q^{94} +5.74029e25 q^{95} -1.65298e26 q^{96} +9.85376e26 q^{97} +2.99286e26 q^{98} -2.57519e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3168 q^{2} + 3188646 q^{3} + 4865024 q^{4} - 4906065060 q^{5} + 5050815264 q^{6} - 151657089584 q^{7} + 432422977536 q^{8} + 5083731656658 q^{9}+O(q^{10}) \) 2 * q + 3168 * q^2 + 3188646 * q^3 + 4865024 * q^4 - 4906065060 * q^5 + 5050815264 * q^6 - 151657089584 * q^7 + 432422977536 * q^8 + 5083731656658 * q^9	\( 2 q + 3168 q^{2} + 3188646 q^{3} + 4865024 q^{4} - 4906065060 q^{5} + 5050815264 q^{6} - 151657089584 q^{7} + 432422977536 q^{8} + 5083731656658 q^{9} - 60418938951360 q^{10} + 40854992127048 q^{11} + 7756419658752 q^{12} - 417397898638292 q^{13} - 63\!\cdots\!24 q^{14}+ \cdots + 10\!\cdots\!92 q^{99}+O(q^{100}) \) 2 * q + 3168 * q^2 + 3188646 * q^3 + 4865024 * q^4 - 4906065060 * q^5 + 5050815264 * q^6 - 151657089584 * q^7 + 432422977536 * q^8 + 5083731656658 * q^9 - 60418938951360 * q^10 + 40854992127048 * q^11 + 7756419658752 * q^12 - 417397898638292 * q^13 - 6378143375649024 * q^14 - 7821852364654380 * q^15 - 33977393317150720 * q^16 - 73795652103164508 * q^17 + 8052630944146272 * q^18 - 346903482355728584 * q^19 - 178722076778772480 * q^20 - 241790386036831632 * q^21 + 2884648366247624064 * q^22 + 2497625277930684432 * q^23 + 689421898814128128 * q^24 + 7465166899962582350 * q^25 + 14654342405239377984 * q^26 + 8105110306037952534 * q^27 - 19813833643227717632 * q^28 - 66866817822024885588 * q^29 - 96327304005749129280 * q^30 - 131371412087557498208 * q^31 - 221798282158915190784 * q^32 + 65136053612971548504 * q^33 - 104645686123668232512 * q^34 + 1576524909572257407840 * q^35 + 12366238259600464896 * q^36 - 247578887064220048004 * q^37 + 2811811879848292739712 * q^38 - 665467069950697616316 * q^39 + 5613252874049647411200 * q^40 + 5075362465608343410612 * q^41 - 10168820681094878890752 * q^42 - 35862665467692465632120 * q^43 + 9032931356628777725952 * q^44 - 12470559127572865084740 * q^45 - 28646330621234746514688 * q^46 + 48518144960084941517280 * q^47 - 54170939645579687362560 * q^48 + 20502047614180503101010 * q^49 + 270118022314323825021600 * q^50 - 117654105448073547888084 * q^51 + 47504180746517517248512 * q^52 + 350385928874194434085692 * q^53 + 12838494724764116813856 * q^54 - 653602484383437534351120 * q^55 + 745296153511182831452160 * q^56 - 553076200699832263228632 * q^57 - 762126478854004399790016 * q^58 - 1574701087781292940777176 * q^59 - 284940717616162876631040 * q^60 - 298583192683280602714100 * q^61 + 1936203801499437193354752 * q^62 - 385491973637399518025136 * q^63 + 4041790055686590773067776 * q^64 - 1981623229478787576516120 * q^65 + 4599061237221010740588672 * q^66 - 1451788236633679878778088 * q^67 - 140711495561838808713216 * q^68 + 3982021425986282595679536 * q^69 + 21545930212269822639383040 * q^70 - 18927618367388181178813776 * q^71 + 1099161189983037199417344 * q^72 - 18475598829856936295245388 * q^73 - 36334468497793316338471104 * q^74 + 11901887287449044179999050 * q^75 + 9804773679338363226198016 * q^76 - 67614050277859586781728448 * q^77 + 23363755146548460825584832 * q^78 - 29951640885798459169010240 * q^79 + 104922131781026456681840640 * q^80 + 12922163778453346597864482 * q^81 + 80929145969689652074441152 * q^82 + 68977464913739379133962936 * q^83 - 31589650695571744458203136 * q^84 + 178619857136873703182526840 * q^85 - 92642460447803684395923072 * q^86 - 106607305590464181665316924 * q^87 - 348641555423301021147070464 * q^88 + 525251854986446192504396436 * q^89 - 153576836304357969041077440 * q^90 - 318746170956550059362287648 * q^91 - 97209435326689254625910784 * q^92 - 209448463833670933215473184 * q^93 - 904589369407956626941257216 * q^94 + 191342642113513008280285200 * q^95 - 353618102606448143716319232 * q^96 + 792881154632193034514966212 * q^97 + 963334106172656502173965152 * q^98 + 103847908404393638125542792 * q^99

Introduction

L-functions

Modular forms

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