LMFDB - Embedded newform 10.30.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,30,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	10.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:	$53.2780423830$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 2788867122 $ x^2 - x - 2788867122
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$52810.2$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+16384.0 q^{2} -1.13281e7 q^{3} +2.68435e8 q^{4} +6.10352e9 q^{5} -1.85600e11 q^{6} -1.13928e12 q^{7} +4.39805e12 q^{8} +5.96960e13 q^{9} +1.00000e14 q^{10} +8.82435e14 q^{11} -3.04087e15 q^{12} -4.32539e15 q^{13} -1.86659e16 q^{14} -6.91414e16 q^{15} +7.20576e16 q^{16} +3.39413e17 q^{17} +9.78060e17 q^{18} +2.08701e18 q^{19} +1.63840e18 q^{20} +1.29059e19 q^{21} +1.44578e19 q^{22} +3.66538e19 q^{23} -4.98216e19 q^{24} +3.72529e19 q^{25} -7.08672e19 q^{26} +1.01209e20 q^{27} -3.05822e20 q^{28} -2.44890e21 q^{29} -1.13281e21 q^{30} -6.72385e21 q^{31} +1.18059e21 q^{32} -9.99633e21 q^{33} +5.56094e21 q^{34} -6.95359e21 q^{35} +1.60245e22 q^{36} +2.27705e22 q^{37} +3.41935e22 q^{38} +4.89986e22 q^{39} +2.68435e22 q^{40} -2.16421e23 q^{41} +2.11450e23 q^{42} -7.28120e23 q^{43} +2.36877e23 q^{44} +3.64356e23 q^{45} +6.00537e23 q^{46} -1.17763e22 q^{47} -8.16277e23 q^{48} -1.92196e24 q^{49} +6.10352e23 q^{50} -3.84491e24 q^{51} -1.16109e24 q^{52} -4.78965e24 q^{53} +1.65821e24 q^{54} +5.38595e24 q^{55} -5.01059e24 q^{56} -2.36419e25 q^{57} -4.01228e25 q^{58} +1.10270e25 q^{59} -1.85600e25 q^{60} -1.50517e26 q^{61} -1.10164e26 q^{62} -6.80103e25 q^{63} +1.93428e25 q^{64} -2.64001e25 q^{65} -1.63780e26 q^{66} +1.06338e26 q^{67} +9.11104e25 q^{68} -4.15219e26 q^{69} -1.13928e26 q^{70} +9.12798e23 q^{71} +2.62546e26 q^{72} +3.38899e26 q^{73} +3.73071e26 q^{74} -4.22006e26 q^{75} +5.60227e26 q^{76} -1.00534e27 q^{77} +8.02793e26 q^{78} -5.65480e27 q^{79} +4.39805e26 q^{80} -5.24347e27 q^{81} -3.54585e27 q^{82} +5.57801e27 q^{83} +3.46439e27 q^{84} +2.07161e27 q^{85} -1.19295e28 q^{86} +2.77415e28 q^{87} +3.88099e27 q^{88} +3.24606e28 q^{89} +5.96960e27 q^{90} +4.92782e27 q^{91} +9.83919e27 q^{92} +7.61686e28 q^{93} -1.92944e26 q^{94} +1.27381e28 q^{95} -1.33739e28 q^{96} -8.84369e28 q^{97} -3.14893e28 q^{98} +5.26778e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 32768 q^{2} - 3644748 q^{3} + 536870912 q^{4} + 12207031250 q^{5} - 59715551232 q^{6} - 2619992530316 q^{7} + 8796093022208 q^{8} + 50099928783786 q^{9} + 200000000000000 q^{10} - 609601386608016 q^{11}+ \cdots + 66\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 32768 * q^2 - 3644748 * q^3 + 536870912 * q^4 + 12207031250 * q^5 - 59715551232 * q^6 - 2619992530316 * q^7 + 8796093022208 * q^8 + 50099928783786 * q^9 + 200000000000000 * q^10 - 609601386608016 * q^11 - 978379591385088 * q^12 - 23082045945895508 * q^13 - 42925957616697344 * q^14 - 22245776367187500 * q^15 + 144115188075855872 * q^16 - 212788505698107756 * q^17 + 820837233193549824 * q^18 - 1552916806248440360 * q^19 + 3276800000000000000 * q^20 + 1528960639160402784 * q^21 - 9987709118185734144 * q^22 + 48569213108206117932 * q^23 - 16029771225253281792 * q^24 + 74505805969238281250 * q^25 - 378176240777552003072 * q^26 - 499834094699922149880 * q^27 - 703298889591969284096 * q^28 - 956704614090527918340 * q^29 - 364474800000000000000 * q^30 - 6511575098724600253256 * q^31 + 2361183241434822606848 * q^32 - 21460205670988095790416 * q^33 - 3486326877357797474304 * q^34 - 15991165346166992187500 * q^35 + 13448597228643120316416 * q^36 + 66439751853531567521164 * q^37 - 25442988953574446858240 * q^38 - 95115872074782751314408 * q^39 + 53687091200000000000000 * q^40 - 91892384814903461498076 * q^41 + 25050491112004039213056 * q^42 - 238995461328392693017388 * q^43 - 163638626192355068215296 * q^44 + 305785698143225097656250 * q^45 + 795757987564849036197888 * q^46 + 3194171921256703883825124 * q^47 - 262631771754549768880128 * q^48 - 2949340368568478352337086 * q^49 + 1220703125000000000000000 * q^50 - 8087681914959142709504856 * q^51 - 6196039528899412018331648 * q^52 - 20940542608549012866299748 * q^53 - 8189281807563524503633920 * q^54 - 3720711588183691406250000 * q^55 - 11522849007074824750628864 * q^56 - 51608811383891390387075760 * q^57 - 15674648397259209414082560 * q^58 - 56386542314605437066955080 * q^59 - 5971555123200000000000000 * q^60 - 196473830091215280192586916 * q^61 - 106685646417503850549346304 * q^62 - 53801159179053017719352988 * q^63 + 38685626227668133590597632 * q^64 - 140881628087741137695312500 * q^65 - 351604009713468961430175744 * q^66 - 197664660356478435334723556 * q^67 - 57119979558630153818996736 * q^68 - 323669150960022130439724768 * q^69 - 261999253031600000000000000 * q^70 + 88675798275412809064073064 * q^71 + 220341816994088883264159744 * q^72 - 1207143104281105009657980668 * q^73 + 1088548894368261202266750976 * q^74 - 135777443647384643554687500 * q^75 - 416857931015363737325404160 * q^76 + 1203945463876494165080443728 * q^77 - 1558378448073240597535260672 * q^78 - 5568328716406737078915459440 * q^79 + 879609302220800000000000000 * q^80 - 9202933265485984731362760318 * q^81 - 1505564832807378313184477184 * q^82 + 14501131796523133613084409972 * q^83 + 410427246379074178466709504 * q^84 - 1298757969348802221679687500 * q^85 - 3915701638404385882396884992 * q^86 + 39206560880287419756561414360 * q^87 - 2681055251535545437639409664 * q^88 + 37316392549473006147343615380 * q^89 + 5009992878378600000000000000 * q^90 + 32701100919486363870999957464 * q^91 + 13037698868262486609066196992 * q^92 + 77799548305316321338678930944 * q^93 + 52333312757869836432590831616 * q^94 - 9478251991262453369140625000 * q^95 - 4302958948426543413332017152 * q^96 - 23376807728262299973955852076 * q^97 - 48321992598625949324690817024 * q^98 + 66995578378495912231289004912 * q^99

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 $

$2$	16384.0	0.707107
$2$	16384.0	0.707107
$3$	−1.13281e7	−1.36741	−0.683707	−	0.729757i	$-0.739633\pi$
$3$	−1.13281e7	−1.36741	−0.683707	+	0.729757i	$0.739633\pi$
$4$	2.68435e8	0.500000
$5$	6.10352e9	0.447214
$5$	6.10352e9	0.447214
$6$	−1.85600e11	−0.966907
$7$	−1.13928e12	−0.634903	−0.317452	−	0.948274i	$-0.602827\pi$
$7$	−1.13928e12	−0.634903	−0.317452	+	0.948274i	$0.602827\pi$
$8$	4.39805e12	0.353553
$9$	5.96960e13	0.869819
$10$	1.00000e14	0.316228
$11$	8.82435e14	0.700630	0.350315	−	0.936632i	$-0.386075\pi$
$11$	8.82435e14	0.700630	0.350315	+	0.936632i	$0.386075\pi$
$12$	−3.04087e15	−0.683707
$13$	−4.32539e15	−0.304682	−0.152341	−	0.988328i	$-0.548681\pi$
$13$	−4.32539e15	−0.304682	−0.152341	+	0.988328i	$0.548681\pi$
$14$	−1.86659e16	−0.448944
$15$	−6.91414e16	−0.611526
$16$	7.20576e16	0.250000
$17$	3.39413e17	0.488899	0.244449	−	0.969662i	$-0.421393\pi$
$17$	3.39413e17	0.488899	0.244449	+	0.969662i	$0.421393\pi$
$18$	9.78060e17	0.615055
$19$	2.08701e18	0.599235	0.299617	−	0.954059i	$-0.403141\pi$
$19$	2.08701e18	0.599235	0.299617	+	0.954059i	$0.403141\pi$
$20$	1.63840e18	0.223607
$21$	1.29059e19	0.868175
$22$	1.44578e19	0.495420
$23$	3.66538e19	0.659274	0.329637	−	0.944108i	$-0.393074\pi$
$23$	3.66538e19	0.659274	0.329637	+	0.944108i	$0.393074\pi$
$24$	−4.98216e19	−0.483454
$25$	3.72529e19	0.200000
$26$	−7.08672e19	−0.215443
$27$	1.01209e20	0.178011
$28$	−3.05822e20	−0.317452
$29$	−2.44890e21	−1.52827	−0.764135	−	0.645056i	$-0.776834\pi$
$29$	−2.44890e21	−1.52827	−0.764135	+	0.645056i	$0.776834\pi$
$30$	−1.13281e21	−0.432414
$31$	−6.72385e21	−1.59541	−0.797707	−	0.603046i	$-0.793954\pi$
$31$	−6.72385e21	−1.59541	−0.797707	+	0.603046i	$0.793954\pi$
$32$	1.18059e21	0.176777
$33$	−9.99633e21	−0.958051
$34$	5.56094e21	0.345704
$35$	−6.95359e21	−0.283937
$36$	1.60245e22	0.434910
$37$	2.27705e22	0.415381	0.207691	−	0.978195i	$-0.433405\pi$
$37$	2.27705e22	0.415381	0.207691	+	0.978195i	$0.433405\pi$
$38$	3.41935e22	0.423723
$39$	4.89986e22	0.416626
$40$	2.68435e22	0.158114
$41$	−2.16421e23	−0.891116	−0.445558	−	0.895253i	$-0.646995\pi$
$41$	−2.16421e23	−0.891116	−0.445558	+	0.895253i	$0.646995\pi$
$42$	2.11450e23	0.613892
$43$	−7.28120e23	−1.50283	−0.751416	−	0.659829i	$-0.770629\pi$
$43$	−7.28120e23	−1.50283	−0.751416	+	0.659829i	$0.770629\pi$
$44$	2.36877e23	0.350315
$45$	3.64356e23	0.388995
$46$	6.00537e23	0.466177
$47$	−1.17763e22	−0.00669255	−0.00334627	−	0.999994i	$-0.501065\pi$
$47$	−1.17763e22	−0.00669255	−0.00334627	+	0.999994i	$0.501065\pi$
$48$	−8.16277e23	−0.341853
$49$	−1.92196e24	−0.596898
$50$	6.10352e23	0.141421
$51$	−3.84491e24	−0.668527
$52$	−1.16109e24	−0.152341
$53$	−4.78965e24	−0.476765	−0.238382	−	0.971171i	$-0.576617\pi$
$53$	−4.78965e24	−0.476765	−0.238382	+	0.971171i	$0.576617\pi$
$54$	1.65821e24	0.125873
$55$	5.38595e24	0.313331
$56$	−5.01059e24	−0.224472
$57$	−2.36419e25	−0.819402
$58$	−4.01228e25	−1.08065
$59$	1.10270e25	0.231794	0.115897	−	0.993261i	$-0.463026\pi$
$59$	1.10270e25	0.231794	0.115897	+	0.993261i	$0.463026\pi$
$60$	−1.85600e25	−0.305763
$61$	−1.50517e26	−1.95121	−0.975603	−	0.219544i	$-0.929543\pi$
$61$	−1.50517e26	−1.95121	−0.975603	+	0.219544i	$0.929543\pi$
$62$	−1.10164e26	−1.12813
$63$	−6.80103e25	−0.552251
$64$	1.93428e25	0.125000
$65$	−2.64001e25	−0.136258
$66$	−1.63780e26	−0.677444
$67$	1.06338e26	0.353674	0.176837	−	0.984240i	$-0.443413\pi$
$67$	1.06338e26	0.353674	0.176837	+	0.984240i	$0.443413\pi$
$68$	9.11104e25	0.244449
$69$	−4.15219e26	−0.901500
$70$	−1.13928e26	−0.200774
$71$	9.12798e23	0.00130957	0.000654785	−	1.00000i	$-0.499792\pi$
$71$	9.12798e23	0.00130957	0.000654785		1.00000i	$0.499792\pi$
$72$	2.62546e26	0.307528
$73$	3.38899e26	0.325004	0.162502	−	0.986708i	$-0.448044\pi$
$73$	3.38899e26	0.325004	0.162502	+	0.986708i	$0.448044\pi$
$74$	3.73071e26	0.293719
$75$	−4.22006e26	−0.273483
$76$	5.60227e26	0.299617
$77$	−1.00534e27	−0.444832
$78$	8.02793e26	0.294599
$79$	−5.65480e27	−1.72514	−0.862570	−	0.505938i	$-0.831146\pi$
$79$	−5.65480e27	−1.72514	−0.862570	+	0.505938i	$0.831146\pi$
$80$	4.39805e26	0.111803
$81$	−5.24347e27	−1.11323
$82$	−3.54585e27	−0.630114
$83$	5.57801e27	0.831470	0.415735	−	0.909486i	$-0.363524\pi$
$83$	5.57801e27	0.831470	0.415735	+	0.909486i	$0.363524\pi$
$84$	3.46439e27	0.434087
$85$	2.07161e27	0.218642
$86$	−1.19295e28	−1.06266
$87$	2.77415e28	2.08978
$88$	3.88099e27	0.247710
$89$	3.24606e28	1.75874	0.879370	−	0.476139i	$-0.157964\pi$
$89$	3.24606e28	1.75874	0.879370	+	0.476139i	$0.157964\pi$
$90$	5.96960e27	0.275061
$91$	4.92782e27	0.193444
$92$	9.83919e27	0.329637
$93$	7.61686e28	2.18159
$94$	−1.92944e26	−0.00473235
$95$	1.27381e28	0.267986
$96$	−1.33739e28	−0.241727
$97$	−8.84369e28	−1.37544	−0.687722	−	0.725974i	$-0.741389\pi$
$97$	−8.84369e28	−1.37544	−0.687722	+	0.725974i	$0.741389\pi$
$98$	−3.14893e28	−0.422071
$99$	5.26778e28	0.609421
$100$	1.00000e28	0.100000
$101$	−1.11329e29	−0.963714	−0.481857	−	0.876250i	$-0.660038\pi$
$101$	−1.11329e29	−0.963714	−0.481857	+	0.876250i	$0.660038\pi$
$102$	−6.29950e28	−0.472720
$103$	2.11516e29	1.37786	0.688928	−	0.724830i	$-0.258082\pi$
$103$	2.11516e29	1.37786	0.688928	+	0.724830i	$0.258082\pi$
$104$	−1.90233e28	−0.107721
$105$	7.87711e28	0.388260
$106$	−7.84737e28	−0.337123
$107$	−3.06975e29	−1.15090	−0.575450	−	0.817837i	$-0.695173\pi$
$107$	−3.06975e29	−1.15090	−0.575450	+	0.817837i	$0.695173\pi$
$108$	2.71682e28	0.0890054
$109$	−3.95931e29	−1.13484	−0.567420	−	0.823428i	$-0.692059\pi$
$109$	−3.95931e29	−1.13484	−0.567420	+	0.823428i	$0.692059\pi$
$110$	8.82435e28	0.221559
$111$	−2.57947e29	−0.567998
$112$	−8.20935e28	−0.158726
$113$	6.07867e29	1.03317	0.516584	−	0.856237i	$-0.327203\pi$
$113$	6.07867e29	1.03317	0.516584	+	0.856237i	$0.327203\pi$
$114$	−3.87349e29	−0.579404
$115$	2.23717e29	0.294836
$116$	−6.57372e29	−0.764135
$117$	−2.58209e29	−0.265018
$118$	1.80666e29	0.163903
$119$	−3.86685e29	−0.310403
$120$	−3.04087e29	−0.216207
$121$	−8.07618e29	−0.509118
$122$	−2.46607e30	−1.37971
$123$	2.45165e30	1.21852
$124$	−1.80492e30	−0.797707
$125$	2.27374e29	0.0894427
$126$	−1.11428e30	−0.390500
$127$	1.94592e30	0.608094	0.304047	−	0.952657i	$-0.401662\pi$
$127$	1.94592e30	0.608094	0.304047	+	0.952657i	$0.401662\pi$
$128$	3.16913e29	0.0883883
$129$	8.24823e30	2.05499
$130$	−4.32539e29	−0.0963489
$131$	5.97259e30	1.19050	0.595249	−	0.803541i	$-0.297053\pi$
$131$	5.97259e30	1.19050	0.595249	+	0.803541i	$0.297053\pi$
$132$	−2.68337e30	−0.479025
$133$	−2.37768e30	−0.380456
$134$	1.74224e30	0.250085
$135$	6.17733e29	0.0796088
$136$	1.49275e30	0.172852
$137$	−2.32228e30	−0.241806	−0.120903	−	0.992664i	$-0.538579\pi$
$137$	−2.32228e30	−0.241806	−0.120903	+	0.992664i	$0.538579\pi$
$138$	−6.80295e30	−0.637457
$139$	1.58029e31	1.33359	0.666795	−	0.745241i	$-0.267666\pi$
$139$	1.58029e31	1.33359	0.666795	+	0.745241i	$0.267666\pi$
$140$	−1.86659e30	−0.141969
$141$	1.33404e29	0.00915148
$142$	1.49553e28	0.000926006 0
$143$	−3.81688e30	−0.213469
$144$	4.30155e30	0.217455
$145$	−1.49469e31	−0.683463
$146$	5.55252e30	0.229813
$147$	2.17722e31	0.816206
$148$	6.11240e30	0.207691
$149$	7.30661e30	0.225172	0.112586	−	0.993642i	$-0.464087\pi$
$149$	7.30661e30	0.225172	0.112586	+	0.993642i	$0.464087\pi$
$150$	−6.91414e30	−0.193381
$151$	4.13377e31	1.04998	0.524990	−	0.851109i	$-0.324069\pi$
$151$	4.13377e31	1.04998	0.524990	+	0.851109i	$0.324069\pi$
$152$	9.17876e30	0.211861
$153$	2.02616e31	0.425254
$154$	−1.64714e31	−0.314544
$155$	−4.10391e31	−0.713491
$156$	1.31530e31	0.208313
$157$	−4.72325e31	−0.681861	−0.340931	−	0.940088i	$-0.610742\pi$
$157$	−4.72325e31	−0.681861	−0.340931	+	0.940088i	$0.610742\pi$
$158$	−9.26482e31	−1.21986
$159$	5.42578e31	0.651934
$160$	7.20576e30	0.0790569
$161$	−4.17589e31	−0.418575
$162$	−8.59091e31	−0.787175
$163$	−7.30208e31	−0.611965	−0.305982	−	0.952037i	$-0.598985\pi$
$163$	−7.30208e31	−0.611965	−0.305982	+	0.952037i	$0.598985\pi$
$164$	−5.80952e31	−0.445558
$165$	−6.10128e31	−0.428453
$166$	9.13901e31	0.587938
$167$	−2.20886e32	−1.30251	−0.651253	−	0.758861i	$-0.725756\pi$
$167$	−2.20886e32	−1.30251	−0.651253	+	0.758861i	$0.725756\pi$
$168$	5.67606e31	0.306946
$169$	−1.82829e32	−0.907169
$170$	3.39413e31	0.154603
$171$	1.24586e32	0.521226
$172$	−1.95453e32	−0.751416
$173$	−3.35891e32	−1.18722	−0.593608	−	0.804754i	$-0.702297\pi$
$173$	−3.35891e32	−1.18722	−0.593608	+	0.804754i	$0.702297\pi$
$174$	4.54516e32	1.47770
$175$	−4.24413e31	−0.126981
$176$	6.35861e31	0.175157
$177$	−1.24915e32	−0.316959
$178$	5.31835e32	1.24362
$179$	6.57424e32	1.41735	0.708674	−	0.705536i	$-0.249294\pi$
$179$	6.57424e32	1.41735	0.708674	+	0.705536i	$0.249294\pi$
$180$	9.78060e31	0.194498
$181$	−9.44787e32	−1.73378	−0.866891	−	0.498497i	$-0.833885\pi$
$181$	−9.44787e32	−1.73378	−0.866891	+	0.498497i	$0.833885\pi$
$182$	8.07373e31	0.136785
$183$	1.70508e33	2.66810
$184$	1.61205e32	0.233089
$185$	1.38980e32	0.185764
$186$	1.24795e33	1.54262
$187$	2.99510e32	0.342537
$188$	−3.16119e30	−0.00334627
$189$	−1.15305e32	−0.113020
$190$	2.08701e32	0.189495
$191$	−1.69303e33	−1.42456	−0.712279	−	0.701896i	$-0.752337\pi$
$191$	−1.69303e33	−1.42456	−0.712279	+	0.701896i	$0.752337\pi$
$192$	−2.19118e32	−0.170927
$193$	−4.67493e32	−0.338216	−0.169108	−	0.985598i	$-0.554089\pi$
$193$	−4.67493e32	−0.338216	−0.169108	+	0.985598i	$0.554089\pi$
$194$	−1.44895e33	−0.972586
$195$	2.99064e32	0.186321
$196$	−5.15921e32	−0.298449
$197$	5.06239e32	0.272017	0.136008	−	0.990708i	$-0.456573\pi$
$197$	5.06239e32	0.272017	0.136008	+	0.990708i	$0.456573\pi$
$198$	8.63074e32	0.430926
$199$	−1.00457e33	−0.466241	−0.233120	−	0.972448i	$-0.574894\pi$
$199$	−1.00457e33	−0.466241	−0.233120	+	0.972448i	$0.574894\pi$
$200$	1.63840e32	0.0707107
$201$	−1.20461e33	−0.483619
$202$	−1.82401e33	−0.681449
$203$	2.78997e33	0.970304
$204$	−1.03211e33	−0.334263
$205$	−1.32093e33	−0.398519
$206$	3.46548e33	0.974291
$207$	2.18809e33	0.573449
$208$	−3.11677e32	−0.0761705
$209$	1.84165e33	0.419842
$210$	1.29059e33	0.274541
$211$	−4.62096e33	−0.917564	−0.458782	−	0.888549i	$-0.651714\pi$
$211$	−4.62096e33	−0.917564	−0.458782	+	0.888549i	$0.651714\pi$
$212$	−1.28571e33	−0.238382
$213$	−1.03403e31	−0.00179072
$214$	−5.02947e33	−0.813810
$215$	−4.44409e33	−0.672087
$216$	4.45124e32	0.0629363
$217$	7.66032e33	1.01293
$218$	−6.48693e33	−0.802454
$219$	−3.83909e33	−0.444415
$220$	1.44578e33	0.156666
$221$	−1.46809e33	−0.148959
$222$	−4.22620e33	−0.401635
$223$	−2.05052e34	−1.82576	−0.912880	−	0.408229i	$-0.866147\pi$
$223$	−2.05052e34	−1.82576	−0.912880	+	0.408229i	$0.866147\pi$
$224$	−1.34502e33	−0.112236
$225$	2.22385e33	0.173964
$226$	9.95929e33	0.730560
$227$	1.49366e34	1.02773	0.513863	−	0.857872i	$-0.328214\pi$
$227$	1.49366e34	1.02773	0.513863	+	0.857872i	$0.328214\pi$
$228$	−6.34632e33	−0.409701
$229$	−3.97878e33	−0.241066	−0.120533	−	0.992709i	$-0.538460\pi$
$229$	−3.97878e33	−0.241066	−0.120533	+	0.992709i	$0.538460\pi$
$230$	3.66538e33	0.208481
$231$	1.13886e34	0.608269
$232$	−1.07704e34	−0.540325
$233$	3.61387e33	0.170338	0.0851691	−	0.996367i	$-0.472857\pi$
$233$	3.61387e33	0.170338	0.0851691	+	0.996367i	$0.472857\pi$
$234$	−4.23049e33	−0.187396
$235$	−7.18771e31	−0.00299300
$236$	2.96003e33	0.115897
$237$	6.40582e34	2.35898
$238$	−6.33545e33	−0.219488
$239$	−2.66949e33	−0.0870281	−0.0435140	−	0.999053i	$-0.513855\pi$
$239$	−2.66949e33	−0.0870281	−0.0435140	+	0.999053i	$0.513855\pi$
$240$	−4.98216e33	−0.152881
$241$	6.10378e34	1.76340	0.881702	−	0.471808i	$-0.156398\pi$
$241$	6.10378e34	1.76340	0.881702	+	0.471808i	$0.156398\pi$
$242$	−1.32320e34	−0.360001
$243$	5.24527e34	1.34424
$244$	−4.04041e34	−0.975603
$245$	−1.17307e34	−0.266941
$246$	4.01678e34	0.861627
$247$	−9.02713e33	−0.182576
$248$	−2.95718e34	−0.564064
$249$	−6.31884e34	−1.13696
$250$	3.72529e33	0.0632456
$251$	−4.09524e34	−0.656160	−0.328080	−	0.944650i	$-0.606402\pi$
$251$	−4.09524e34	−0.656160	−0.328080	+	0.944650i	$0.606402\pi$
$252$	−1.82564e34	−0.276125
$253$	3.23446e34	0.461907
$254$	3.18819e34	0.429987
$255$	−2.34675e34	−0.298974
$256$	5.19230e33	0.0625000
$257$	5.85244e34	0.665743	0.332871	−	0.942972i	$-0.391982\pi$
$257$	5.85244e34	0.665743	0.332871	+	0.942972i	$0.391982\pi$
$258$	1.35139e35	1.45310
$259$	−2.59418e34	−0.263727
$260$	−7.08672e33	−0.0681290
$261$	−1.46190e35	−1.32932
$262$	9.78549e34	0.841809
$263$	1.14684e35	0.933565	0.466783	−	0.884372i	$-0.345413\pi$
$263$	1.14684e35	0.933565	0.466783	+	0.884372i	$0.345413\pi$
$264$	−4.39643e34	−0.338722
$265$	−2.92337e34	−0.213216
$266$	−3.89559e34	−0.269023
$267$	−3.67718e35	−2.40492
$268$	2.85448e34	0.176837
$269$	−2.06966e32	−0.00121476	−0.000607382	−	1.00000i	$-0.500193\pi$
$269$	−2.06966e32	−0.00121476	−0.000607382		1.00000i	$0.500193\pi$
$270$	1.01209e34	0.0562919
$271$	−2.04880e35	−1.08005	−0.540027	−	0.841648i	$-0.681586\pi$
$271$	−2.04880e35	−1.08005	−0.540027	+	0.841648i	$0.681586\pi$
$272$	2.44573e34	0.122225
$273$	−5.58229e34	−0.264517
$274$	−3.80483e34	−0.170983
$275$	3.28733e34	0.140126
$276$	−1.11460e35	−0.450750
$277$	−3.48284e35	−1.33652	−0.668262	−	0.743926i	$-0.732961\pi$
$277$	−3.48284e35	−1.33652	−0.668262	+	0.743926i	$0.732961\pi$
$278$	2.58915e35	0.942991
$279$	−4.01387e35	−1.38772
$280$	−3.05822e34	−0.100387
$281$	2.68138e35	0.835828	0.417914	−	0.908487i	$-0.362761\pi$
$281$	2.68138e35	0.835828	0.417914	+	0.908487i	$0.362761\pi$
$282$	2.18569e33	0.00647107
$283$	4.14392e35	1.16549	0.582744	−	0.812656i	$-0.301979\pi$
$283$	4.14392e35	1.16549	0.582744	+	0.812656i	$0.301979\pi$
$284$	2.45027e32	0.000654785 0
$285$	−1.44299e35	−0.366448
$286$	−6.25357e34	−0.150946
$287$	2.46564e35	0.565773
$288$	7.04766e34	0.153764
$289$	−3.66767e35	−0.760978
$290$	−2.44890e35	−0.483282
$291$	1.00182e36	1.88080
$292$	9.09725e34	0.162502
$293$	6.48883e35	1.10303	0.551513	−	0.834166i	$-0.314051\pi$
$293$	6.48883e35	1.10303	0.551513	+	0.834166i	$0.314051\pi$
$294$	3.56715e35	0.577145
$295$	6.73034e34	0.103662
$296$	1.00146e35	0.146859
$297$	8.93107e34	0.124720
$298$	1.19711e35	0.159221
$299$	−1.58542e35	−0.200869
$300$	−1.13281e35	−0.136741
$301$	8.29530e35	0.954152
$302$	6.77277e35	0.742447
$303$	1.26115e36	1.31780
$304$	1.50385e35	0.149809
$305$	−9.18683e35	−0.872606
$306$	3.31966e35	0.300700
$307$	−8.38296e35	−0.724254	−0.362127	−	0.932129i	$-0.617949\pi$
$307$	−8.38296e35	−0.724254	−0.362127	+	0.932129i	$0.617949\pi$
$308$	−2.69868e35	−0.222416
$309$	−2.39608e36	−1.88410
$310$	−6.72385e35	−0.504514
$311$	1.91308e36	1.36996	0.684978	−	0.728563i	$-0.259812\pi$
$311$	1.91308e36	1.36996	0.684978	+	0.728563i	$0.259812\pi$
$312$	2.15498e35	0.147300
$313$	−1.02248e36	−0.667206	−0.333603	−	0.942714i	$-0.608265\pi$
$313$	−1.02248e36	−0.667206	−0.333603	+	0.942714i	$0.608265\pi$
$314$	−7.73857e35	−0.482149
$315$	−4.15102e35	−0.246974
$316$	−1.51795e36	−0.862570
$317$	−1.04526e36	−0.567371	−0.283685	−	0.958917i	$-0.591557\pi$
$317$	−1.04526e36	−0.567371	−0.283685	+	0.958917i	$0.591557\pi$
$318$	8.88960e35	0.460987
$319$	−2.16100e36	−1.07075
$320$	1.18059e35	0.0559017
$321$	3.47745e36	1.57376
$322$	−6.84177e35	−0.295977
$323$	7.08358e35	0.292965
$324$	−1.40753e36	−0.556617
$325$	−1.61133e35	−0.0609364
$326$	−1.19637e36	−0.432725
$327$	4.48515e36	1.55180
$328$	−9.51832e35	−0.315057
$329$	1.34165e34	0.00424912
$330$	−9.99633e35	−0.302962
$331$	4.09787e35	0.118864	0.0594322	−	0.998232i	$-0.481071\pi$
$331$	4.09787e35	0.118864	0.0594322	+	0.998232i	$0.481071\pi$
$332$	1.49733e36	0.415735
$333$	1.35931e36	0.361306
$334$	−3.61900e36	−0.921011
$335$	6.49035e35	0.158168
$336$	9.29965e35	0.217044
$337$	3.32405e36	0.743076	0.371538	−	0.928418i	$-0.378830\pi$
$337$	3.32405e36	0.743076	0.371538	+	0.928418i	$0.378830\pi$
$338$	−2.99547e36	−0.641465
$339$	−6.88599e36	−1.41277
$340$	5.56094e35	0.109321
$341$	−5.93336e36	−1.11779
$342$	2.04122e36	0.368562
$343$	5.85800e36	1.01388
$344$	−3.20230e36	−0.531331
$345$	−2.53430e36	−0.403163
$346$	−5.50324e36	−0.839489
$347$	−3.68071e36	−0.538461	−0.269230	−	0.963076i	$-0.586769\pi$
$347$	−3.68071e36	−0.538461	−0.269230	+	0.963076i	$0.586769\pi$
$348$	7.44679e36	1.04489
$349$	−4.54962e36	−0.612359	−0.306180	−	0.951974i	$-0.599051\pi$
$349$	−4.54962e36	−0.612359	−0.306180	+	0.951974i	$0.599051\pi$
$350$	−6.95359e35	−0.0897889
$351$	−4.37770e35	−0.0542367
$352$	1.04180e36	0.123855
$353$	1.41923e37	1.61927	0.809637	−	0.586931i	$-0.199664\pi$
$353$	1.41923e37	1.61927	0.809637	+	0.586931i	$0.199664\pi$
$354$	−2.04661e36	−0.224124
$355$	5.57128e33	0.000585658 0
$356$	8.71358e36	0.879370
$357$	4.38042e36	0.424450
$358$	1.07712e37	1.00222
$359$	−1.36928e37	−1.22355	−0.611777	−	0.791030i	$-0.709545\pi$
$359$	−1.36928e37	−1.22355	−0.611777	+	0.791030i	$0.709545\pi$
$360$	1.60245e36	0.137531
$361$	−7.77422e36	−0.640918
$362$	−1.54794e37	−1.22597
$363$	9.14880e36	0.696174
$364$	1.32280e36	0.0967218
$365$	2.06848e36	0.145346
$366$	2.79360e37	1.88663
$367$	8.92349e36	0.579265	0.289632	−	0.957138i	$-0.406467\pi$
$367$	8.92349e36	0.579265	0.289632	+	0.957138i	$0.406467\pi$
$368$	2.64119e36	0.164819
$369$	−1.29195e37	−0.775110
$370$	2.27705e36	0.131355
$371$	5.45674e36	0.302699
$372$	2.04463e37	1.09079
$373$	2.37196e37	1.21711	0.608555	−	0.793512i	$-0.291749\pi$
$373$	2.37196e37	1.21711	0.608555	+	0.793512i	$0.291749\pi$
$374$	4.90717e36	0.242210
$375$	−2.57572e36	−0.122305
$376$	−5.17929e34	−0.00236617
$377$	1.05925e37	0.465637
$378$	−1.88916e36	−0.0799169
$379$	3.61331e35	0.0147108	0.00735540	−	0.999973i	$-0.497659\pi$
$379$	3.61331e35	0.0147108	0.00735540	+	0.999973i	$0.497659\pi$
$380$	3.41935e36	0.133993
$381$	−2.20436e37	−0.831515
$382$	−2.77386e37	−1.00731
$383$	−3.65114e37	−1.27657	−0.638287	−	0.769799i	$-0.720357\pi$
$383$	−3.65114e37	−1.27657	−0.638287	+	0.769799i	$0.720357\pi$
$384$	−3.59003e36	−0.120863
$385$	−6.13609e36	−0.198935
$386$	−7.65941e36	−0.239155
$387$	−4.34659e37	−1.30719
$388$	−2.37396e37	−0.687722
$389$	2.30956e37	0.644555	0.322277	−	0.946645i	$-0.395552\pi$
$389$	2.30956e37	0.644555	0.322277	+	0.946645i	$0.395552\pi$
$390$	4.89986e36	0.131749
$391$	1.24408e37	0.322318
$392$	−8.45285e36	−0.211035
$393$	−6.76582e37	−1.62790
$394$	8.29422e36	0.192345
$395$	−3.45141e37	−0.771506
$396$	1.41406e37	0.304711
$397$	3.69992e37	0.768652	0.384326	−	0.923197i	$-0.374434\pi$
$397$	3.69992e37	0.768652	0.384326	+	0.923197i	$0.374434\pi$
$398$	−1.64589e37	−0.329682
$399$	2.69346e37	0.520241
$400$	2.68435e36	0.0500000
$401$	−2.16794e37	−0.389451	−0.194726	−	0.980858i	$-0.562382\pi$
$401$	−2.16794e37	−0.389451	−0.194726	+	0.980858i	$0.562382\pi$
$402$	−1.97363e37	−0.341970
$403$	2.90833e37	0.486094
$404$	−2.98846e37	−0.481857
$405$	−3.20036e37	−0.497853
$406$	4.57109e37	0.686108
$407$	2.00934e37	0.291028
$408$	−1.69101e37	−0.236360
$409$	2.52481e37	0.340597	0.170299	−	0.985392i	$-0.445527\pi$
$409$	2.52481e37	0.340597	0.170299	+	0.985392i	$0.445527\pi$
$410$	−2.16421e37	−0.281796
$411$	2.63071e37	0.330649
$412$	5.67784e37	0.688928
$413$	−1.25628e37	−0.147167
$414$	3.58497e37	0.405490
$415$	3.40455e37	0.371845
$416$	−5.10652e36	−0.0538607
$417$	−1.79017e38	−1.82357
$418$	3.01736e37	0.296873
$419$	1.65354e38	1.57149	0.785745	−	0.618551i	$-0.212280\pi$
$419$	1.65354e38	1.57149	0.785745	+	0.618551i	$0.212280\pi$
$420$	2.11450e37	0.194130
$421$	−8.40843e37	−0.745803	−0.372902	−	0.927871i	$-0.621637\pi$
$421$	−8.40843e37	−0.745803	−0.372902	+	0.927871i	$0.621637\pi$
$422$	−7.57098e37	−0.648816
$423$	−7.03001e35	−0.00582131
$424$	−2.10651e37	−0.168562
$425$	1.26441e37	0.0977797
$426$	−1.69415e35	−0.00126623
$427$	1.71480e38	1.23883
$428$	−8.24029e37	−0.575450
$429$	4.32380e37	0.291901
$430$	−7.28120e37	−0.475237
$431$	1.80805e38	1.14101	0.570504	−	0.821295i	$-0.306748\pi$
$431$	1.80805e38	1.14101	0.570504	+	0.821295i	$0.306748\pi$
$432$	7.29291e36	0.0445027
$433$	1.16835e38	0.689441	0.344721	−	0.938705i	$-0.387974\pi$
$433$	1.16835e38	0.689441	0.344721	+	0.938705i	$0.387974\pi$
$434$	1.25507e38	0.716252
$435$	1.69320e38	0.934577
$436$	−1.06282e38	−0.567420
$437$	7.64969e37	0.395060
$438$	−6.28996e37	−0.314249
$439$	4.05073e38	1.95793	0.978965	−	0.204027i	$-0.0654032\pi$
$439$	4.05073e38	1.95793	0.978965	+	0.204027i	$0.0654032\pi$
$440$	2.36877e37	0.110779
$441$	−1.14733e38	−0.519194
$442$	−2.40532e37	−0.105330
$443$	−1.35343e37	−0.0573562	−0.0286781	−	0.999589i	$-0.509130\pi$
$443$	−1.35343e37	−0.0573562	−0.0286781	+	0.999589i	$0.509130\pi$
$444$	−6.92420e37	−0.283999
$445$	1.98124e38	0.786532
$446$	−3.35957e38	−1.29101
$447$	−8.27702e37	−0.307904
$448$	−2.20368e37	−0.0793629
$449$	−3.02080e38	−1.05329	−0.526647	−	0.850084i	$-0.676551\pi$
$449$	−3.02080e38	−1.05329	−0.526647	+	0.850084i	$0.676551\pi$
$450$	3.64356e37	0.123011
$451$	−1.90978e38	−0.624343
$452$	1.63173e38	0.516584
$453$	−4.68279e38	−1.43576
$454$	2.44722e38	0.726712
$455$	3.00770e37	0.0865106
$456$	−1.03978e38	−0.289702
$457$	−4.78002e38	−1.29016	−0.645082	−	0.764114i	$-0.723177\pi$
$457$	−4.78002e38	−1.29016	−0.645082	+	0.764114i	$0.723177\pi$
$458$	−6.51884e37	−0.170459
$459$	3.43518e37	0.0870292
$460$	6.00537e37	0.147418
$461$	−5.31155e38	−1.26345	−0.631725	−	0.775193i	$-0.717653\pi$
$461$	−5.31155e38	−1.26345	−0.631725	+	0.775193i	$0.717653\pi$
$462$	1.86591e38	0.430111
$463$	−7.96225e37	−0.177874	−0.0889368	−	0.996037i	$-0.528347\pi$
$463$	−7.96225e37	−0.177874	−0.0889368	+	0.996037i	$0.528347\pi$
$464$	−1.76462e38	−0.382068
$465$	4.64896e38	0.975637
$466$	5.92097e37	0.120447
$467$	−4.50964e38	−0.889297	−0.444649	−	0.895705i	$-0.646671\pi$
$467$	−4.50964e38	−0.889297	−0.444649	+	0.895705i	$0.646671\pi$
$468$	−6.93124e37	−0.132509
$469$	−1.21148e38	−0.224549
$470$	−1.17763e36	−0.00211637
$471$	5.35056e38	0.932386
$472$	4.84972e37	0.0819517
$473$	−6.42518e38	−1.05293
$474$	1.04953e39	1.66805
$475$	7.77471e37	0.119847
$476$	−1.03800e38	−0.155202
$477$	−2.85923e38	−0.414699
$478$	−4.37370e37	−0.0615381
$479$	−1.60452e38	−0.219018	−0.109509	−	0.993986i	$-0.534928\pi$
$479$	−1.60452e38	−0.219018	−0.109509	+	0.993986i	$0.534928\pi$
$480$	−8.16277e37	−0.108104
$481$	−9.84911e37	−0.126559
$482$	1.00004e39	1.24691
$483$	4.73050e38	0.572365
$484$	−2.16793e38	−0.254559
$485$	−5.39776e38	−0.615118
$486$	8.59385e38	0.950521
$487$	8.94545e38	0.960356	0.480178	−	0.877171i	$-0.340572\pi$
$487$	8.94545e38	0.960356	0.480178	+	0.877171i	$0.340572\pi$
$488$	−6.61981e38	−0.689855
$489$	8.27189e38	0.836809
$490$	−1.92196e38	−0.188756
$491$	−1.55946e39	−1.48693	−0.743466	−	0.668773i	$-0.766820\pi$
$491$	−1.55946e39	−1.48693	−0.743466	+	0.668773i	$0.766820\pi$
$492$	6.58110e38	0.609262
$493$	−8.31188e38	−0.747170
$494$	−1.47900e38	−0.129101
$495$	3.21520e38	0.272542
$496$	−4.84504e38	−0.398853
$497$	−1.03993e36	−0.000831450 0
$498$	−1.03528e39	−0.803955
$499$	−3.63205e38	−0.273964	−0.136982	−	0.990574i	$-0.543740\pi$
$499$	−3.63205e38	−0.273964	−0.136982	+	0.990574i	$0.543740\pi$
$500$	6.10352e37	0.0447214
$501$	2.50223e39	1.78106
$502$	−6.70964e38	−0.463975
$503$	−8.22824e38	−0.552804	−0.276402	−	0.961042i	$-0.589142\pi$
$503$	−8.22824e38	−0.552804	−0.276402	+	0.961042i	$0.589142\pi$
$504$	−2.99112e38	−0.195250
$505$	−6.79498e38	−0.430986
$506$	5.29934e38	0.326618
$507$	2.07111e39	1.24047
$508$	5.22353e38	0.304047
$509$	6.71381e38	0.379805	0.189903	−	0.981803i	$-0.439183\pi$
$509$	6.71381e38	0.379805	0.189903	+	0.981803i	$0.439183\pi$
$510$	−3.84491e38	−0.211407
$511$	−3.86100e38	−0.206346
$512$	8.50706e37	0.0441942
$513$	2.11225e38	0.106670
$514$	9.58863e38	0.470751
$515$	1.29099e39	0.616196
$516$	2.21412e39	1.02750
$517$	−1.03919e37	−0.00468900
$518$	−4.25031e38	−0.186483
$519$	3.80502e39	1.62342
$520$	−1.16109e38	−0.0481745
$521$	−2.56512e39	−1.03505	−0.517524	−	0.855669i	$-0.673146\pi$
$521$	−2.56512e39	−1.03505	−0.517524	+	0.855669i	$0.673146\pi$
$522$	−2.39517e39	−0.939971
$523$	2.72346e39	1.03955	0.519776	−	0.854302i	$-0.326015\pi$
$523$	2.72346e39	1.03955	0.519776	+	0.854302i	$0.326015\pi$
$524$	1.60325e39	0.595249
$525$	4.80781e38	0.173635
$526$	1.87898e39	0.660130
$527$	−2.28216e39	−0.779996
$528$	−7.20312e38	−0.239513
$529$	−1.74755e39	−0.565358
$530$	−4.78965e38	−0.150766
$531$	6.58267e38	0.201619
$532$	−6.38253e38	−0.190228
$533$	9.36108e38	0.271507
$534$	−6.02469e39	−1.70054
$535$	−1.87362e39	−0.514698
$536$	4.67679e38	0.125043
$537$	−7.44738e39	−1.93810
$538$	−3.39094e36	−0.000858967 0
$539$	−1.69600e39	−0.418205
$540$	1.65821e38	0.0398044
$541$	−5.03350e39	−1.17628	−0.588139	−	0.808760i	$-0.700139\pi$
$541$	−5.03350e39	−1.17628	−0.588139	+	0.808760i	$0.700139\pi$
$542$	−3.35676e39	−0.763714
$543$	1.07027e40	2.37080
$544$	4.00708e38	0.0864259
$545$	−2.41657e39	−0.507516
$546$	−9.14602e38	−0.187042
$547$	4.65567e39	0.927183	0.463592	−	0.886049i	$-0.346561\pi$
$547$	4.65567e39	0.927183	0.463592	+	0.886049i	$0.346561\pi$
$548$	−6.23383e38	−0.120903
$549$	−8.98527e39	−1.69720
$550$	5.38595e38	0.0990840
$551$	−5.11088e39	−0.915793
$552$	−1.82615e39	−0.318728
$553$	6.44238e39	1.09530
$554$	−5.70628e39	−0.945065
$555$	−1.57438e39	−0.254016
$556$	4.24206e39	0.666795
$557$	−5.36564e38	−0.0821715	−0.0410858	−	0.999156i	$-0.513082\pi$
$557$	−5.36564e38	−0.0821715	−0.0410858	+	0.999156i	$0.513082\pi$
$558$	−6.57632e39	−0.981267
$559$	3.14940e39	0.457886
$560$	−5.01059e38	−0.0709843
$561$	−3.39288e39	−0.468390
$562$	4.39318e39	0.591020
$563$	1.40550e40	1.84272	0.921358	−	0.388714i	$-0.127081\pi$
$563$	1.40550e40	1.84272	0.921358	+	0.388714i	$0.127081\pi$
$564$	3.58103e37	0.00457574
$565$	3.71012e39	0.462047
$566$	6.78940e39	0.824125
$567$	5.97376e39	0.706795
$568$	4.01453e36	0.000463003 0
$569$	−1.12025e40	−1.25947	−0.629733	−	0.776812i	$-0.716836\pi$
$569$	−1.12025e40	−1.25947	−0.629733	+	0.776812i	$0.716836\pi$
$570$	−2.36419e39	−0.259118
$571$	1.12874e40	1.20606	0.603032	−	0.797717i	$-0.293959\pi$
$571$	1.12874e40	1.20606	0.603032	+	0.797717i	$0.293959\pi$
$572$	−1.02458e39	−0.106735
$573$	1.91788e40	1.94796
$574$	4.03970e39	0.400062
$575$	1.36546e39	0.131855
$576$	1.15469e39	0.108727
$577$	2.40521e39	0.220853	0.110427	−	0.993884i	$-0.464778\pi$
$577$	2.40521e39	0.220853	0.110427	+	0.993884i	$0.464778\pi$
$578$	−6.00912e39	−0.538093
$579$	5.29582e39	0.462481
$580$	−4.01228e39	−0.341732
$581$	−6.35489e39	−0.527903
$582$	1.64139e40	1.32993
$583$	−4.22656e39	−0.334035
$584$	1.49049e39	0.114906
$585$	−1.57598e39	−0.118520
$586$	1.06313e40	0.779958
$587$	−7.82073e39	−0.559751	−0.279875	−	0.960036i	$-0.590293\pi$
$587$	−7.82073e39	−0.559751	−0.279875	+	0.960036i	$0.590293\pi$
$588$	5.84442e39	0.408103
$589$	−1.40327e40	−0.956027
$590$	1.10270e39	0.0732998
$591$	−5.73474e39	−0.371959
$592$	1.64078e39	0.103845
$593$	−3.08087e40	−1.90274	−0.951371	−	0.308047i	$-0.900324\pi$
$593$	−3.08087e40	−1.90274	−0.951371	+	0.308047i	$0.900324\pi$
$594$	1.46327e39	0.0881901
$595$	−2.36014e39	−0.138817
$596$	1.96135e39	0.112586
$597$	1.13799e40	0.637544
$598$	−2.59756e39	−0.142036
$599$	−2.16140e40	−1.15358	−0.576788	−	0.816894i	$-0.695694\pi$
$599$	−2.16140e40	−1.15358	−0.576788	+	0.816894i	$0.695694\pi$
$600$	−1.85600e39	−0.0966907
$601$	4.10064e39	0.208532	0.104266	−	0.994549i	$-0.466751\pi$
$601$	4.10064e39	0.208532	0.104266	+	0.994549i	$0.466751\pi$
$602$	1.35910e40	0.674687
$603$	6.34795e39	0.307633
$604$	1.10965e40	0.524990
$605$	−4.92931e39	−0.227684
$606$	2.06627e40	0.931822
$607$	1.19472e40	0.526052	0.263026	−	0.964789i	$-0.415279\pi$
$607$	1.19472e40	0.526052	0.263026	+	0.964789i	$0.415279\pi$
$608$	2.46390e39	0.105931
$609$	−3.16052e40	−1.32681
$610$	−1.50517e40	−0.617025
$611$	5.09373e37	0.00203910
$612$	5.43893e39	0.212627
$613$	2.77971e40	1.06126	0.530630	−	0.847603i	$-0.321955\pi$
$613$	2.77971e40	1.06126	0.530630	+	0.847603i	$0.321955\pi$
$614$	−1.37346e40	−0.512125
$615$	1.49637e40	0.544941
$616$	−4.42152e39	−0.157272
$617$	−3.99390e40	−1.38759	−0.693796	−	0.720171i	$-0.744063\pi$
$617$	−3.99390e40	−1.38759	−0.693796	+	0.720171i	$0.744063\pi$
$618$	−3.92574e40	−1.33226
$619$	−7.85149e39	−0.260278	−0.130139	−	0.991496i	$-0.541542\pi$
$619$	−7.85149e39	−0.260278	−0.130139	+	0.991496i	$0.541542\pi$
$620$	−1.10164e40	−0.356745
$621$	3.70971e39	0.117358
$622$	3.13439e40	0.968706
$623$	−3.69816e40	−1.11663
$624$	3.53072e39	0.104157
$625$	1.38778e39	0.0400000
$626$	−1.67522e40	−0.471786
$627$	−2.08624e40	−0.574097
$628$	−1.26789e40	−0.340931
$629$	7.72858e39	0.203079
$630$	−6.80103e39	−0.174637
$631$	4.84632e40	1.21615	0.608074	−	0.793880i	$-0.291942\pi$
$631$	4.84632e40	1.21615	0.608074	+	0.793880i	$0.291942\pi$
$632$	−2.48701e40	−0.609929
$633$	5.23468e40	1.25469
$634$	−1.71256e40	−0.401192
$635$	1.18769e40	0.271948
$636$	1.45647e40	0.325967
$637$	8.31321e39	0.181864
$638$	−3.54057e40	−0.757136
$639$	5.44904e37	0.00113909
$640$	1.93428e39	0.0395285
$641$	−6.50037e40	−1.29866	−0.649332	−	0.760505i	$-0.724951\pi$
$641$	−6.50037e40	−1.29866	−0.649332	+	0.760505i	$0.724951\pi$
$642$	5.69745e40	1.11281
$643$	3.24864e40	0.620358	0.310179	−	0.950678i	$-0.399611\pi$
$643$	3.24864e40	0.620358	0.310179	+	0.950678i	$0.399611\pi$
$644$	−1.12096e40	−0.209288
$645$	5.03432e40	0.919020
$646$	1.16057e40	0.207158
$647$	−8.73540e40	−1.52465	−0.762326	−	0.647193i	$-0.775943\pi$
$647$	−8.73540e40	−1.52465	−0.762326	+	0.647193i	$0.775943\pi$
$648$	−2.30610e40	−0.393588
$649$	9.73060e39	0.162402
$650$	−2.64001e39	−0.0430885
$651$	−8.67770e40	−1.38510
$652$	−1.96014e40	−0.305982
$653$	1.25208e41	1.91158	0.955790	−	0.294049i	$-0.0950030\pi$
$653$	1.25208e41	1.91158	0.955790	+	0.294049i	$0.0950030\pi$
$654$	7.34847e40	1.09729
$655$	3.64538e40	0.532407
$656$	−1.55948e40	−0.222779
$657$	2.02309e40	0.282695
$658$	2.19816e38	0.00300458
$659$	6.56917e40	0.878359	0.439180	−	0.898399i	$-0.355269\pi$
$659$	6.56917e40	0.878359	0.439180	+	0.898399i	$0.355269\pi$
$660$	−1.63780e40	−0.214227
$661$	4.78274e40	0.612006	0.306003	−	0.952031i	$-0.401008\pi$
$661$	4.78274e40	0.612006	0.306003	+	0.952031i	$0.401008\pi$
$662$	6.71394e39	0.0840498
$663$	1.66307e40	0.203688
$664$	2.45323e40	0.293969
$665$	−1.45122e40	−0.170145
$666$	2.22709e40	0.255482
$667$	−8.97616e40	−1.00755
$668$	−5.92937e40	−0.651253
$669$	2.32285e41	2.49657
$670$	1.06338e40	0.111842
$671$	−1.32821e41	−1.36707
$672$	1.52366e40	0.153473
$673$	6.08623e40	0.599971	0.299985	−	0.953944i	$-0.403018\pi$
$673$	6.08623e40	0.599971	0.299985	+	0.953944i	$0.403018\pi$
$674$	5.44612e40	0.525434
$675$	3.77034e39	0.0356022
$676$	−4.90778e40	−0.453584
$677$	3.90992e40	0.353697	0.176849	−	0.984238i	$-0.443410\pi$
$677$	3.90992e40	0.353697	0.176849	+	0.984238i	$0.443410\pi$
$678$	−1.12820e41	−0.998977
$679$	1.00754e41	0.873274
$680$	9.11104e39	0.0773017
$681$	−1.69204e41	−1.40533
$682$	−9.72121e40	−0.790400
$683$	−7.22111e40	−0.574783	−0.287391	−	0.957813i	$-0.592788\pi$
$683$	−7.22111e40	−0.574783	−0.287391	+	0.957813i	$0.592788\pi$
$684$	3.34433e40	0.260613
$685$	−1.41741e40	−0.108139
$686$	9.59775e40	0.716918
$687$	4.50722e40	0.329637
$688$	−5.24666e40	−0.375708
$689$	2.07171e40	0.145262
$690$	−4.15219e40	−0.285079
$691$	−6.18228e40	−0.415640	−0.207820	−	0.978167i	$-0.566637\pi$
$691$	−6.18228e40	−0.415640	−0.207820	+	0.978167i	$0.566637\pi$
$692$	−9.01651e40	−0.593608
$693$	−6.00146e40	−0.386924
$694$	−6.03047e40	−0.380749
$695$	9.64533e40	0.596400
$696$	1.22008e41	0.738848
$697$	−7.34562e40	−0.435666
$698$	−7.45410e40	−0.433003
$699$	−4.09384e40	−0.232923
$700$	−1.13928e40	−0.0634903
$701$	1.95882e41	1.06926	0.534631	−	0.845085i	$-0.320451\pi$
$701$	1.95882e41	1.06926	0.534631	+	0.845085i	$0.320451\pi$
$702$	−7.17243e39	−0.0383511
$703$	4.75221e40	0.248911
$704$	1.70688e40	0.0875787
$705$	8.14233e38	0.00409267
$706$	2.32527e41	1.14500
$707$	1.26834e41	0.611865
$708$	−3.35316e40	−0.158479
$709$	−1.54732e41	−0.716488	−0.358244	−	0.933628i	$-0.616624\pi$
$709$	−1.54732e41	−0.716488	−0.358244	+	0.933628i	$0.616624\pi$
$710$	9.12798e37	0.000414122 0
$711$	−3.37569e41	−1.50056
$712$	1.42763e41	0.621808
$713$	−2.46455e41	−1.05181
$714$	7.17687e40	0.300131
$715$	−2.32964e40	−0.0954664
$716$	1.76476e41	0.708674
$717$	3.02404e40	0.119003
$718$	−2.24343e41	−0.865184
$719$	2.87780e41	1.08766	0.543828	−	0.839197i	$-0.316974\pi$
$719$	2.87780e41	1.08766	0.543828	+	0.839197i	$0.316974\pi$
$720$	2.62546e40	0.0972488
$721$	−2.40975e41	−0.874804
$722$	−1.27373e41	−0.453197
$723$	−6.91444e41	−2.41130
$724$	−2.53614e41	−0.866891
$725$	−9.12287e40	−0.305654
$726$	1.49894e41	0.492270
$727$	−4.19375e41	−1.35006	−0.675031	−	0.737789i	$-0.735870\pi$
$727$	−4.19375e41	−1.35006	−0.675031	+	0.737789i	$0.735870\pi$
$728$	2.16728e40	0.0683926
$729$	−2.34329e41	−0.724898
$730$	3.38899e40	0.102775
$731$	−2.47133e41	−0.734732
$732$	4.57703e41	1.33405
$733$	3.83993e41	1.09727	0.548637	−	0.836061i	$-0.315147\pi$
$733$	3.83993e41	1.09727	0.548637	+	0.836061i	$0.315147\pi$
$734$	1.46203e41	0.409602
$735$	1.32887e41	0.365019
$736$	4.32732e40	0.116544
$737$	9.38362e40	0.247795
$738$	−2.11673e41	−0.548086
$739$	4.34726e41	1.10375	0.551876	−	0.833926i	$-0.313912\pi$
$739$	4.34726e41	1.10375	0.551876	+	0.833926i	$0.313912\pi$
$740$	3.73071e40	0.0928820
$741$	1.02260e41	0.249657
$742$	8.94032e40	0.214041
$743$	6.88261e40	0.161590	0.0807951	−	0.996731i	$-0.474254\pi$
$743$	6.88261e40	0.161590	0.0807951	+	0.996731i	$0.474254\pi$
$744$	3.34993e41	0.771308
$745$	4.45960e40	0.100700
$746$	3.88623e41	0.860627
$747$	3.32985e41	0.723229
$748$	8.03990e40	0.171269
$749$	3.49729e41	0.730710
$750$	−4.22006e40	−0.0864828
$751$	−6.97779e40	−0.140262	−0.0701308	−	0.997538i	$-0.522342\pi$
$751$	−6.97779e40	−0.140262	−0.0701308	+	0.997538i	$0.522342\pi$
$752$	−8.48575e38	−0.00167314
$753$	4.63913e41	0.897243
$754$	1.73547e41	0.329255
$755$	2.52305e41	0.469565
$756$	−3.09521e40	−0.0565098
$757$	6.69982e41	1.19998	0.599989	−	0.800008i	$-0.295172\pi$
$757$	6.69982e41	1.19998	0.599989	+	0.800008i	$0.295172\pi$
$758$	5.92005e39	0.0104021
$759$	−3.66404e41	−0.631618
$760$	5.60227e40	0.0947473
$761$	8.30046e41	1.37729	0.688644	−	0.725100i	$-0.258206\pi$
$761$	8.30046e41	1.37729	0.688644	+	0.725100i	$0.258206\pi$
$762$	−3.61162e41	−0.587970
$763$	4.51074e41	0.720514
$764$	−4.54469e41	−0.712279
$765$	1.23667e41	0.190179
$766$	−5.98202e41	−0.902674
$767$	−4.76960e40	−0.0706235
$768$	−5.88190e40	−0.0854633
$769$	−1.35470e42	−1.93157	−0.965787	−	0.259338i	$-0.916496\pi$
$769$	−1.35470e42	−1.93157	−0.965787	+	0.259338i	$0.916496\pi$
$770$	−1.00534e41	−0.140668
$771$	−6.62971e41	−0.910346
$772$	−1.25492e41	−0.169108
$773$	1.32622e42	1.75393	0.876963	−	0.480558i	$-0.159566\pi$
$773$	1.32622e42	1.75393	0.876963	+	0.480558i	$0.159566\pi$
$774$	−7.12145e41	−0.924324
$775$	−2.50483e41	−0.319083
$776$	−3.88949e41	−0.486293
$777$	2.93872e41	0.360623
$778$	3.78398e41	0.455769
$779$	−4.51673e41	−0.533988
$780$	8.02793e40	0.0931605
$781$	8.05485e38	0.000917524 0
$782$	2.03830e41	0.227913
$783$	−2.47852e41	−0.272049
$784$	−1.38491e41	−0.149225
$785$	−2.88284e41	−0.304938
$786$	−1.10851e42	−1.15110
$787$	−1.42306e42	−1.45074	−0.725372	−	0.688357i	$-0.758332\pi$
$787$	−1.42306e42	−1.45074	−0.725372	+	0.688357i	$0.758332\pi$
$788$	1.35893e41	0.136008
$789$	−1.29916e42	−1.27657
$790$	−5.65480e41	−0.545537
$791$	−6.92528e41	−0.655961
$792$	2.31680e41	0.215463
$793$	6.51045e41	0.594497
$794$	6.06195e41	0.543519
$795$	3.31163e41	0.291554
$796$	−2.69662e41	−0.233120
$797$	−7.08466e40	−0.0601414	−0.0300707	−	0.999548i	$-0.509573\pi$
$797$	−7.08466e40	−0.0601414	−0.0300707	+	0.999548i	$0.509573\pi$
$798$	4.41297e41	0.367866
$799$	−3.99704e39	−0.00327198
$800$	4.39805e40	0.0353553
$801$	1.93777e42	1.52979
$802$	−3.55195e41	−0.275384
$803$	2.99056e41	0.227708
$804$	−3.23360e41	−0.241809
$805$	−2.54876e41	−0.187192
$806$	4.76500e41	0.343720
$807$	2.34454e39	0.00166108
$808$	−4.89630e41	−0.340724
$809$	−2.64896e41	−0.181060	−0.0905299	−	0.995894i	$-0.528856\pi$
$809$	−2.64896e41	−0.181060	−0.0905299	+	0.995894i	$0.528856\pi$
$810$	−5.24347e41	−0.352035
$811$	5.45808e41	0.359946	0.179973	−	0.983672i	$-0.442399\pi$
$811$	5.45808e41	0.359946	0.179973	+	0.983672i	$0.442399\pi$
$812$	7.48928e41	0.485152
$813$	2.32091e42	1.47688
$814$	3.29211e41	0.205788
$815$	−4.45684e41	−0.273679
$816$	−2.77055e41	−0.167132
$817$	−1.51959e42	−0.900549
$818$	4.13665e41	0.240839
$819$	2.94171e41	0.168261
$820$	−3.54585e41	−0.199260
$821$	1.28422e42	0.709027	0.354514	−	0.935051i	$-0.384646\pi$
$821$	1.28422e42	0.709027	0.354514	+	0.935051i	$0.384646\pi$
$822$	4.31016e41	0.233804
$823$	−3.31448e42	−1.76652	−0.883259	−	0.468885i	$-0.844656\pi$
$823$	−3.31448e42	−1.76652	−0.883259	+	0.468885i	$0.844656\pi$
$824$	9.30257e41	0.487145
$825$	−3.72392e41	−0.191610
$826$	−2.05829e41	−0.104063
$827$	−1.88558e41	−0.0936730	−0.0468365	−	0.998903i	$-0.514914\pi$
$827$	−1.88558e41	−0.0936730	−0.0468365	+	0.998903i	$0.514914\pi$
$828$	5.87361e41	0.286725
$829$	−5.20112e41	−0.249492	−0.124746	−	0.992189i	$-0.539812\pi$
$829$	−5.20112e41	−0.249492	−0.124746	+	0.992189i	$0.539812\pi$
$830$	5.57801e41	0.262934
$831$	3.94540e42	1.82758
$832$	−8.36652e40	−0.0380852
$833$	−6.52336e41	−0.291823
$834$	−2.93302e42	−1.28946
$835$	−1.34818e42	−0.582499
$836$	4.94364e41	0.209921
$837$	−6.80517e41	−0.284001
$838$	2.70916e42	1.11121
$839$	3.93914e42	1.58801	0.794004	−	0.607913i	$-0.207993\pi$
$839$	3.93914e42	1.58801	0.794004	+	0.607913i	$0.207993\pi$
$840$	3.46439e41	0.137271
$841$	3.42943e42	1.33561
$842$	−1.37764e42	−0.527363
$843$	−3.03750e42	−1.14292
$844$	−1.24043e42	−0.458782
$845$	−1.11590e42	−0.405698
$846$	−1.15180e40	−0.00411629
$847$	9.20100e41	0.323240
$848$	−3.45131e41	−0.119191
$849$	−4.69428e42	−1.59370
$850$	2.07161e41	0.0691407
$851$	8.34625e41	0.273850
$852$	−2.77570e39	−0.000895362 0
$853$	2.68152e42	0.850392	0.425196	−	0.905101i	$-0.360205\pi$
$853$	2.68152e42	0.850392	0.425196	+	0.905101i	$0.360205\pi$
$854$	2.80954e42	0.875982
$855$	7.60413e41	0.233099
$856$	−1.35009e42	−0.406905
$857$	2.09539e42	0.620929	0.310465	−	0.950585i	$-0.399515\pi$
$857$	2.09539e42	0.620929	0.310465	+	0.950585i	$0.399515\pi$
$858$	7.08412e41	0.206405
$859$	4.56193e42	1.30691	0.653457	−	0.756963i	$-0.273318\pi$
$859$	4.56193e42	1.30691	0.653457	+	0.756963i	$0.273318\pi$
$860$	−1.19295e42	−0.336043
$861$	−2.79311e42	−0.773645
$862$	2.96230e42	0.806815
$863$	5.63111e41	0.150812	0.0754062	−	0.997153i	$-0.475975\pi$
$863$	5.63111e41	0.150812	0.0754062	+	0.997153i	$0.475975\pi$
$864$	1.19487e41	0.0314682
$865$	−2.05012e42	−0.530940
$866$	1.91422e42	0.487509
$867$	4.15479e42	1.04057
$868$	2.05630e42	0.506466
$869$	−4.98999e42	−1.20868
$870$	2.77415e42	0.660846
$871$	−4.59953e41	−0.107758
$872$	−1.74132e42	−0.401227
$873$	−5.27933e42	−1.19639
$874$	1.25333e42	0.279350
$875$	−2.59041e41	−0.0567875
$876$	−1.03055e42	−0.222207
$877$	−2.98436e42	−0.632933	−0.316466	−	0.948604i	$-0.602496\pi$
$877$	−2.98436e42	−0.632933	−0.316466	+	0.948604i	$0.602496\pi$
$878$	6.63671e42	1.38447
$879$	−7.35063e42	−1.50829
$880$	3.88099e41	0.0783328
$881$	−8.36857e42	−1.66150	−0.830750	−	0.556645i	$-0.812088\pi$
$881$	−8.36857e42	−1.66150	−0.830750	+	0.556645i	$0.812088\pi$
$882$	−1.87979e42	−0.367125
$883$	−1.29464e42	−0.248725	−0.124363	−	0.992237i	$-0.539689\pi$
$883$	−1.29464e42	−0.248725	−0.124363	+	0.992237i	$0.539689\pi$
$884$	−3.94088e41	−0.0744793
$885$	−7.62421e41	−0.141748
$886$	−2.21745e41	−0.0405570
$887$	5.57695e42	1.00347	0.501735	−	0.865022i	$-0.332695\pi$
$887$	5.57695e42	1.00347	0.501735	+	0.865022i	$0.332695\pi$
$888$	−1.13446e42	−0.200817
$889$	−2.21694e42	−0.386080
$890$	3.24606e42	0.556162
$891$	−4.62702e42	−0.779965
$892$	−5.50432e42	−0.912880
$893$	−2.45773e40	−0.00401041
$894$	−1.35611e42	−0.217721
$895$	4.01260e42	0.633857
$896$	−3.61051e41	−0.0561180
$897$	1.79599e42	0.274671
$898$	−4.94927e42	−0.744791
$899$	1.64660e43	2.43822
$900$	5.96960e41	0.0869819
$901$	−1.62567e42	−0.233090
$902$	−3.12898e42	−0.441477
$903$	−9.39701e42	−1.30472
$904$	2.67343e42	0.365280
$905$	−5.76652e42	−0.775371
$906$	−7.67228e42	−1.01523
$907$	6.70212e41	0.0872784	0.0436392	−	0.999047i	$-0.486105\pi$
$907$	6.70212e41	0.0872784	0.0436392	+	0.999047i	$0.486105\pi$
$908$	4.00952e42	0.513863
$909$	−6.64590e42	−0.838257
$910$	4.92782e41	0.0611722
$911$	−2.90514e41	−0.0354937	−0.0177468	−	0.999843i	$-0.505649\pi$
$911$	−2.90514e41	−0.0354937	−0.0177468	+	0.999843i	$0.505649\pi$
$912$	−1.70358e42	−0.204850
$913$	4.92223e42	0.582553
$914$	−7.83158e42	−0.912283
$915$	1.04070e43	1.19321
$916$	−1.06805e42	−0.120533
$917$	−6.80442e42	−0.755851
$918$	5.62819e41	0.0615390
$919$	1.45950e43	1.57083	0.785417	−	0.618967i	$-0.212448\pi$
$919$	1.45950e43	1.57083	0.785417	+	0.618967i	$0.212448\pi$
$920$	9.83919e41	0.104240
$921$	9.49632e42	0.990354
$922$	−8.70245e42	−0.893394
$923$	−3.94821e39	−0.000399002 0
$924$	3.05710e42	0.304135
$925$	8.48265e41	0.0830762
$926$	−1.30453e42	−0.125776
$927$	1.26267e43	1.19849
$928$	−2.89115e42	−0.270163
$929$	1.64002e43	1.50876	0.754380	−	0.656438i	$-0.227938\pi$
$929$	1.64002e43	1.50876	0.754380	+	0.656438i	$0.227938\pi$
$930$	7.61686e42	0.689879
$931$	−4.01114e42	−0.357682
$932$	9.70092e41	0.0851691
$933$	−2.16716e43	−1.87330
$934$	−7.38859e42	−0.628828
$935$	1.82806e42	0.153187
$936$	−1.13561e42	−0.0936981
$937$	2.23884e43	1.81886	0.909431	−	0.415855i	$-0.136517\pi$
$937$	2.23884e43	1.81886	0.909431	+	0.415855i	$0.136517\pi$
$938$	−1.98489e42	−0.158780
$939$	1.15827e43	0.912347
$940$	−1.92944e40	−0.00149650
$941$	−8.31227e41	−0.0634848	−0.0317424	−	0.999496i	$-0.510106\pi$
$941$	−8.31227e41	−0.0634848	−0.0317424	+	0.999496i	$0.510106\pi$
$942$	8.76635e42	0.659296
$943$	−7.93268e42	−0.587490
$944$	7.94578e41	0.0579486
$945$	−7.03769e41	−0.0505439
$946$	−1.05270e43	−0.744533
$947$	−2.07044e43	−1.44207	−0.721036	−	0.692897i	$-0.756334\pi$
$947$	−2.07044e43	−1.44207	−0.721036	+	0.692897i	$0.756334\pi$
$948$	1.71955e43	1.17949
$949$	−1.46587e42	−0.0990229
$950$	1.27381e42	0.0847446
$951$	1.18409e43	0.775831
$952$	−1.70066e42	−0.109744
$953$	1.20686e42	0.0767024	0.0383512	−	0.999264i	$-0.487789\pi$
$953$	1.20686e42	0.0767024	0.0383512	+	0.999264i	$0.487789\pi$
$954$	−4.68457e42	−0.293236
$955$	−1.03334e43	−0.637082
$956$	−7.16587e41	−0.0435140
$957$	2.44800e43	1.46416
$958$	−2.62884e42	−0.154869
$959$	2.64572e42	0.153523
$960$	−1.33739e42	−0.0764407
$961$	2.74482e43	1.54534
$962$	−1.61368e42	−0.0894908
$963$	−1.83252e43	−1.00108
$964$	1.63847e43	0.881702
$965$	−2.85335e42	−0.151255
$966$	7.75044e42	0.404723
$967$	−2.31073e43	−1.18868	−0.594342	−	0.804213i	$-0.702587\pi$
$967$	−2.31073e43	−1.18868	−0.594342	+	0.804213i	$0.702587\pi$
$968$	−3.55194e42	−0.180000
$969$	−8.02436e42	−0.400604
$970$	−8.84369e42	−0.434954
$971$	3.43616e43	1.66493	0.832463	−	0.554081i	$-0.186930\pi$
$971$	3.43616e43	1.66493	0.832463	+	0.554081i	$0.186930\pi$
$972$	1.40802e43	0.672120
$973$	−1.80039e43	−0.846701
$974$	1.46562e43	0.679074
$975$	1.82534e42	0.0833252
$976$	−1.08459e43	−0.487801
$977$	−2.51825e43	−1.11591	−0.557953	−	0.829873i	$-0.688413\pi$
$977$	−2.51825e43	−1.11591	−0.557953	+	0.829873i	$0.688413\pi$
$978$	1.35527e43	0.591713
$979$	2.86444e43	1.23223
$980$	−3.14893e42	−0.133470
$981$	−2.36355e43	−0.987107
$982$	−2.55501e43	−1.05142
$983$	−3.63495e43	−1.47392	−0.736958	−	0.675938i	$-0.763739\pi$
$983$	−3.63495e43	−1.47392	−0.736958	+	0.675938i	$0.763739\pi$
$984$	1.07825e43	0.430813
$985$	3.08984e42	0.121650
$986$	−1.36182e43	−0.528329
$987$	−1.51984e41	−0.00581030
$988$	−2.42320e42	−0.0912880
$989$	−2.66884e43	−0.990778
$990$	5.26778e42	0.192716
$991$	−1.99032e43	−0.717555	−0.358777	−	0.933423i	$-0.616806\pi$
$991$	−1.99032e43	−0.717555	−0.358777	+	0.933423i	$0.616806\pi$
$992$	−7.93812e42	−0.282032
$993$	−4.64211e42	−0.162537
$994$	−1.70382e40	−0.000587924 0
$995$	−6.13141e42	−0.208509
$996$	−1.69620e43	−0.568482
$997$	−4.87082e43	−1.60887	−0.804437	−	0.594038i	$-0.797533\pi$
$997$	−4.87082e43	−1.60887	−0.804437	+	0.594038i	$0.797533\pi$
$998$	−5.95074e42	−0.193722
$999$	2.30458e42	0.0739423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.30.a.a.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.30.a.a.1.1	✓	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+16384.0 q^{2} -1.13281e7 q^{3} +2.68435e8 q^{4} +6.10352e9 q^{5} -1.85600e11 q^{6} -1.13928e12 q^{7} +4.39805e12 q^{8} +5.96960e13 q^{9} +1.00000e14 q^{10} +8.82435e14 q^{11} -3.04087e15 q^{12} -4.32539e15 q^{13} -1.86659e16 q^{14} -6.91414e16 q^{15} +7.20576e16 q^{16} +3.39413e17 q^{17} +9.78060e17 q^{18} +2.08701e18 q^{19} +1.63840e18 q^{20} +1.29059e19 q^{21} +1.44578e19 q^{22} +3.66538e19 q^{23} -4.98216e19 q^{24} +3.72529e19 q^{25} -7.08672e19 q^{26} +1.01209e20 q^{27} -3.05822e20 q^{28} -2.44890e21 q^{29} -1.13281e21 q^{30} -6.72385e21 q^{31} +1.18059e21 q^{32} -9.99633e21 q^{33} +5.56094e21 q^{34} -6.95359e21 q^{35} +1.60245e22 q^{36} +2.27705e22 q^{37} +3.41935e22 q^{38} +4.89986e22 q^{39} +2.68435e22 q^{40} -2.16421e23 q^{41} +2.11450e23 q^{42} -7.28120e23 q^{43} +2.36877e23 q^{44} +3.64356e23 q^{45} +6.00537e23 q^{46} -1.17763e22 q^{47} -8.16277e23 q^{48} -1.92196e24 q^{49} +6.10352e23 q^{50} -3.84491e24 q^{51} -1.16109e24 q^{52} -4.78965e24 q^{53} +1.65821e24 q^{54} +5.38595e24 q^{55} -5.01059e24 q^{56} -2.36419e25 q^{57} -4.01228e25 q^{58} +1.10270e25 q^{59} -1.85600e25 q^{60} -1.50517e26 q^{61} -1.10164e26 q^{62} -6.80103e25 q^{63} +1.93428e25 q^{64} -2.64001e25 q^{65} -1.63780e26 q^{66} +1.06338e26 q^{67} +9.11104e25 q^{68} -4.15219e26 q^{69} -1.13928e26 q^{70} +9.12798e23 q^{71} +2.62546e26 q^{72} +3.38899e26 q^{73} +3.73071e26 q^{74} -4.22006e26 q^{75} +5.60227e26 q^{76} -1.00534e27 q^{77} +8.02793e26 q^{78} -5.65480e27 q^{79} +4.39805e26 q^{80} -5.24347e27 q^{81} -3.54585e27 q^{82} +5.57801e27 q^{83} +3.46439e27 q^{84} +2.07161e27 q^{85} -1.19295e28 q^{86} +2.77415e28 q^{87} +3.88099e27 q^{88} +3.24606e28 q^{89} +5.96960e27 q^{90} +4.92782e27 q^{91} +9.83919e27 q^{92} +7.61686e28 q^{93} -1.92944e26 q^{94} +1.27381e28 q^{95} -1.33739e28 q^{96} -8.84369e28 q^{97} -3.14893e28 q^{98} +5.26778e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32768 q^{2} - 3644748 q^{3} + 536870912 q^{4} + 12207031250 q^{5} - 59715551232 q^{6} - 2619992530316 q^{7} + 8796093022208 q^{8} + 50099928783786 q^{9} + 200000000000000 q^{10} - 609601386608016 q^{11}+ \cdots + 66\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 32768 * q^2 - 3644748 * q^3 + 536870912 * q^4 + 12207031250 * q^5 - 59715551232 * q^6 - 2619992530316 * q^7 + 8796093022208 * q^8 + 50099928783786 * q^9 + 200000000000000 * q^10 - 609601386608016 * q^11 - 978379591385088 * q^12 - 23082045945895508 * q^13 - 42925957616697344 * q^14 - 22245776367187500 * q^15 + 144115188075855872 * q^16 - 212788505698107756 * q^17 + 820837233193549824 * q^18 - 1552916806248440360 * q^19 + 3276800000000000000 * q^20 + 1528960639160402784 * q^21 - 9987709118185734144 * q^22 + 48569213108206117932 * q^23 - 16029771225253281792 * q^24 + 74505805969238281250 * q^25 - 378176240777552003072 * q^26 - 499834094699922149880 * q^27 - 703298889591969284096 * q^28 - 956704614090527918340 * q^29 - 364474800000000000000 * q^30 - 6511575098724600253256 * q^31 + 2361183241434822606848 * q^32 - 21460205670988095790416 * q^33 - 3486326877357797474304 * q^34 - 15991165346166992187500 * q^35 + 13448597228643120316416 * q^36 + 66439751853531567521164 * q^37 - 25442988953574446858240 * q^38 - 95115872074782751314408 * q^39 + 53687091200000000000000 * q^40 - 91892384814903461498076 * q^41 + 25050491112004039213056 * q^42 - 238995461328392693017388 * q^43 - 163638626192355068215296 * q^44 + 305785698143225097656250 * q^45 + 795757987564849036197888 * q^46 + 3194171921256703883825124 * q^47 - 262631771754549768880128 * q^48 - 2949340368568478352337086 * q^49 + 1220703125000000000000000 * q^50 - 8087681914959142709504856 * q^51 - 6196039528899412018331648 * q^52 - 20940542608549012866299748 * q^53 - 8189281807563524503633920 * q^54 - 3720711588183691406250000 * q^55 - 11522849007074824750628864 * q^56 - 51608811383891390387075760 * q^57 - 15674648397259209414082560 * q^58 - 56386542314605437066955080 * q^59 - 5971555123200000000000000 * q^60 - 196473830091215280192586916 * q^61 - 106685646417503850549346304 * q^62 - 53801159179053017719352988 * q^63 + 38685626227668133590597632 * q^64 - 140881628087741137695312500 * q^65 - 351604009713468961430175744 * q^66 - 197664660356478435334723556 * q^67 - 57119979558630153818996736 * q^68 - 323669150960022130439724768 * q^69 - 261999253031600000000000000 * q^70 + 88675798275412809064073064 * q^71 + 220341816994088883264159744 * q^72 - 1207143104281105009657980668 * q^73 + 1088548894368261202266750976 * q^74 - 135777443647384643554687500 * q^75 - 416857931015363737325404160 * q^76 + 1203945463876494165080443728 * q^77 - 1558378448073240597535260672 * q^78 - 5568328716406737078915459440 * q^79 + 879609302220800000000000000 * q^80 - 9202933265485984731362760318 * q^81 - 1505564832807378313184477184 * q^82 + 14501131796523133613084409972 * q^83 + 410427246379074178466709504 * q^84 - 1298757969348802221679687500 * q^85 - 3915701638404385882396884992 * q^86 + 39206560880287419756561414360 * q^87 - 2681055251535545437639409664 * q^88 + 37316392549473006147343615380 * q^89 + 5009992878378600000000000000 * q^90 + 32701100919486363870999957464 * q^91 + 13037698868262486609066196992 * q^92 + 77799548305316321338678930944 * q^93 + 52333312757869836432590831616 * q^94 - 9478251991262453369140625000 * q^95 - 4302958948426543413332017152 * q^96 - 23376807728262299973955852076 * q^97 - 48321992598625949324690817024 * q^98 + 66995578378495912231289004912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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