LMFDB - Embedded newform 10.32.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,32,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, 32, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 32 $
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:	$60.8771328190$
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} - 478673959 $ x^2 - 478673959
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-21878.6$ 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)

$f(q)$	$=$	\(q+32768.0 q^{2} +3.71657e6 q^{3} +1.07374e9 q^{4} -3.05176e10 q^{5} +1.21785e11 q^{6} +1.17220e13 q^{7} +3.51844e13 q^{8} -6.03860e14 q^{9} -1.00000e15 q^{10} -9.08641e15 q^{11} +3.99064e15 q^{12} +5.73754e16 q^{13} +3.84106e17 q^{14} -1.13421e17 q^{15} +1.15292e18 q^{16} -8.37569e18 q^{17} -1.97873e19 q^{18} +1.80959e17 q^{19} -3.27680e19 q^{20} +4.35656e19 q^{21} -2.97743e20 q^{22} +2.07716e18 q^{23} +1.30765e20 q^{24} +9.31323e20 q^{25} +1.88008e21 q^{26} -4.53992e21 q^{27} +1.25864e22 q^{28} -4.65382e22 q^{29} -3.71657e21 q^{30} -1.09204e23 q^{31} +3.77789e22 q^{32} -3.37703e22 q^{33} -2.74455e23 q^{34} -3.57726e23 q^{35} -6.48390e23 q^{36} +1.04317e24 q^{37} +5.92966e21 q^{38} +2.13240e23 q^{39} -1.07374e24 q^{40} -1.45317e25 q^{41} +1.42756e24 q^{42} -6.31370e24 q^{43} -9.75646e24 q^{44} +1.84284e25 q^{45} +6.80644e22 q^{46} +7.71035e25 q^{47} +4.28492e24 q^{48} -2.03707e25 q^{49} +3.05176e25 q^{50} -3.11289e25 q^{51} +6.16064e25 q^{52} +2.22654e25 q^{53} -1.48764e26 q^{54} +2.77295e26 q^{55} +4.12430e26 q^{56} +6.72547e23 q^{57} -1.52496e27 q^{58} -4.61858e27 q^{59} -1.21785e26 q^{60} -1.68836e27 q^{61} -3.57841e27 q^{62} -7.07844e27 q^{63} +1.23794e27 q^{64} -1.75096e27 q^{65} -1.10658e27 q^{66} -2.09314e28 q^{67} -8.99333e27 q^{68} +7.71992e24 q^{69} -1.17220e28 q^{70} -7.31996e28 q^{71} -2.12465e28 q^{72} -1.79728e28 q^{73} +3.41826e28 q^{74} +3.46133e27 q^{75} +1.94303e26 q^{76} -1.06511e29 q^{77} +6.98744e27 q^{78} -3.55437e29 q^{79} -3.51844e28 q^{80} +3.56116e29 q^{81} -4.76175e29 q^{82} -1.38740e29 q^{83} +4.67782e28 q^{84} +2.55606e29 q^{85} -2.06887e29 q^{86} -1.72963e29 q^{87} -3.19700e29 q^{88} -2.03177e30 q^{89} +6.03860e29 q^{90} +6.72553e29 q^{91} +2.23033e27 q^{92} -4.05866e29 q^{93} +2.52653e30 q^{94} -5.52243e27 q^{95} +1.40408e29 q^{96} +8.65389e30 q^{97} -6.67507e29 q^{98} +5.48692e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 65536 q^{2} + 38938356 q^{3} + 2147483648 q^{4} - 61035156250 q^{5} + 1275932049408 q^{6} - 12036181345412 q^{7} + 70368744177664 q^{8} + 19040152114674 q^{9} - 20\!\cdots\!00 q^{10} - 39\!\cdots\!76 q^{11}+ \cdots + 86\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 65536 * q^2 + 38938356 * q^3 + 2147483648 * q^4 - 61035156250 * q^5 + 1275932049408 * q^6 - 12036181345412 * q^7 + 70368744177664 * q^8 + 19040152114674 * q^9 - 2000000000000000 * q^10 - 3988310318131776 * q^11 + 41809741395001344 * q^12 + 5813344460168596 * q^13 - 394401590326460416 * q^14 - 1188304321289062500 * q^15 + 2305843009213693952 * q^16 - 90808009705448652 * q^17 + 623907704493637632 * q^18 - 91080908739917057240 * q^19 - 65536000000000000000 * q^20 - 793239032282232341736 * q^21 - 130688952504542035968 * q^22 - 1667218224785847749964 * q^23 + 1370021606031404040192 * q^24 + 1862645149230957031250 * q^25 + 190491671270804553728 * q^26 - 4355806467630589185960 * q^27 - 12923751311817454911488 * q^28 - 94542828968363917878660 * q^29 - 38938356000000000000000 * q^30 - 128556968709873879790136 * q^31 + 75557863725914323419136 * q^32 + 145793762653453115916672 * q^33 - 2975596862028141428736 * q^34 + 367315104535278320312500 * q^35 + 20444207660847517925376 * q^36 - 2173120219461033185894732 * q^37 - 2984539217589602131640320 * q^38 - 1602867367214468925211512 * q^39 - 2147483648000000000000000 * q^40 - 10052341805841246213464916 * q^41 - 25992856609824189374005248 * q^42 + 10573141555224439188182116 * q^43 - 4282415595668833434599424 * q^44 - 581059329671447753906250 * q^45 - 54631406789782659070820352 * q^46 + 10390087245625542339131628 * q^47 + 44892867986437047589011456 * q^48 + 386303842774363980974316186 * q^49 + 61035156250000000000000000 * q^50 + 260679444017387780945734344 * q^51 + 6242031084201723616559104 * q^52 + 152846908077155422032107556 * q^53 - 142731066331319146445537280 * q^54 + 121713571720330078125000000 * q^55 - 423485482985634362539638784 * q^56 - 3213733198820989874995361520 * q^57 - 3097979419635348861047930880 * q^58 - 415231068507816075649147320 * q^59 - 1275932049408000000000000000 * q^60 - 10889372056215660723252719276 * q^61 - 4212554750685147292963176448 * q^62 - 21877406788274198968709510244 * q^63 + 2475880078570760549798248448 * q^64 - 177409193730731079101562500 * q^65 + 4777370014628351702357508096 * q^66 - 28480585995522502006916180852 * q^67 - 97504357974938138336821248 * q^68 - 58787840740996590120684814392 * q^69 + 12036181345412000000000000000 * q^70 - 50662232682174152543673482856 * q^71 + 669915796630651467378720768 * q^72 - 145372300926122387103956465564 * q^73 - 71208803351299135435398578176 * q^74 + 36264169961214065551757812500 * q^75 - 97797381081976082649590005760 * q^76 - 227631991648685526547205199744 * q^77 - 52522757888883717741330825216 * q^78 - 417326479480114326874443862160 * q^79 - 70368744177664000000000000000 * q^80 - 22148754802181045414258949558 * q^81 - 329395136293805955922818367488 * q^82 + 811040305513138169074221560676 * q^83 - 851733925390719037407403966464 * q^84 + 2771240530561787475585937500 * q^85 + 346460702481594423318351577088 * q^86 - 1863770506411185563582357839080 * q^87 - 140326194238876333984953925632 * q^88 + 434708332312346165366301452820 * q^89 - 19040152114674000000000000000 * q^90 + 1897571850361405527969264574424 * q^91 - 1790161937687598172432641294336 * q^92 - 1087500615621162675752907346608 * q^93 + 340462378864657771368665186304 * q^94 + 2779568748166414100341796875000 * q^95 + 1471049498179569175396727390208 * q^96 + 3538409289032585817785792346628 * q^97 + 12658404320030358928566392782848 * q^98 + 8662529629256392933545213540288 * 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 $

$2$	32768.0	0.707107
$2$	32768.0	0.707107
$3$	3.71657e6	0.149542	0.0747710	−	0.997201i	$-0.476177\pi$
$3$	3.71657e6	0.149542	0.0747710	+	0.997201i	$0.476177\pi$
$4$	1.07374e9	0.500000
$5$	−3.05176e10	−0.447214
$5$	−3.05176e10	−0.447214
$6$	1.21785e11	0.105742
$7$	1.17220e13	0.933214	0.466607	−	0.884465i	$-0.345476\pi$
$7$	1.17220e13	0.933214	0.466607	+	0.884465i	$0.345476\pi$
$8$	3.51844e13	0.353553
$9$	−6.03860e14	−0.977637
$10$	−1.00000e15	−0.316228
$11$	−9.08641e15	−0.655852	−0.327926	−	0.944703i	$-0.606350\pi$
$11$	−9.08641e15	−0.655852	−0.327926	+	0.944703i	$0.606350\pi$
$12$	3.99064e15	0.0747710
$13$	5.73754e16	0.310888	0.155444	−	0.987845i	$-0.450319\pi$
$13$	5.73754e16	0.310888	0.155444	+	0.987845i	$0.450319\pi$
$14$	3.84106e17	0.659882
$15$	−1.13421e17	−0.0668772
$16$	1.15292e18	0.250000
$17$	−8.37569e18	−0.709680	−0.354840	−	0.934927i	$-0.615465\pi$
$17$	−8.37569e18	−0.709680	−0.354840	+	0.934927i	$0.615465\pi$
$18$	−1.97873e19	−0.691294
$19$	1.80959e17	0.00273463	0.00136732	−	0.999999i	$-0.499565\pi$
$19$	1.80959e17	0.00273463	0.00136732	+	0.999999i	$0.499565\pi$
$20$	−3.27680e19	−0.223607
$21$	4.35656e19	0.139555
$22$	−2.97743e20	−0.463757
$23$	2.07716e18	0.00162438	0.000812192	−	1.00000i	$-0.499741\pi$
$23$	2.07716e18	0.00162438	0.000812192		1.00000i	$0.499741\pi$
$24$	1.30765e20	0.0528711
$25$	9.31323e20	0.200000
$26$	1.88008e21	0.219831
$27$	−4.53992e21	−0.295740
$28$	1.25864e22	0.466607
$29$	−4.65382e22	−1.00148	−0.500738	−	0.865599i	$-0.666938\pi$
$29$	−4.65382e22	−1.00148	−0.500738	+	0.865599i	$0.666938\pi$
$30$	−3.71657e21	−0.0472893
$31$	−1.09204e23	−0.835860	−0.417930	−	0.908479i	$-0.637244\pi$
$31$	−1.09204e23	−0.835860	−0.417930	+	0.908479i	$0.637244\pi$
$32$	3.77789e22	0.176777
$33$	−3.37703e22	−0.0980773
$34$	−2.74455e23	−0.501819
$35$	−3.57726e23	−0.417346
$36$	−6.48390e23	−0.488819
$37$	1.04317e24	0.514314	0.257157	−	0.966370i	$-0.417214\pi$
$37$	1.04317e24	0.514314	0.257157	+	0.966370i	$0.417214\pi$
$38$	5.92966e21	0.00193368
$39$	2.13240e23	0.0464908
$40$	−1.07374e24	−0.158114
$41$	−1.45317e25	−1.45938	−0.729688	−	0.683781i	$-0.760334\pi$
$41$	−1.45317e25	−1.45938	−0.729688	+	0.683781i	$0.760334\pi$
$42$	1.42756e24	0.0986800
$43$	−6.31370e24	−0.303056	−0.151528	−	0.988453i	$-0.548419\pi$
$43$	−6.31370e24	−0.303056	−0.151528	+	0.988453i	$0.548419\pi$
$44$	−9.75646e24	−0.327926
$45$	1.84284e25	0.437213
$46$	6.80644e22	0.00114861
$47$	7.71035e25	0.932303	0.466152	−	0.884705i	$-0.345640\pi$
$47$	7.71035e25	0.932303	0.466152	+	0.884705i	$0.345640\pi$
$48$	4.28492e24	0.0373855
$49$	−2.03707e25	−0.129112
$50$	3.05176e25	0.141421
$51$	−3.11289e25	−0.106127
$52$	6.16064e25	0.155444
$53$	2.22654e25	0.0418171	0.0209085	−	0.999781i	$-0.493344\pi$
$53$	2.22654e25	0.0418171	0.0209085	+	0.999781i	$0.493344\pi$
$54$	−1.48764e26	−0.209120
$55$	2.77295e26	0.293306
$56$	4.12430e26	0.329941
$57$	6.72547e23	0.000408943 0
$58$	−1.52496e27	−0.708151
$59$	−4.61858e27	−1.64552	−0.822758	−	0.568391i	$-0.807566\pi$
$59$	−4.61858e27	−1.64552	−0.822758	+	0.568391i	$0.807566\pi$
$60$	−1.21785e26	−0.0334386
$61$	−1.68836e27	−0.358799	−0.179400	−	0.983776i	$-0.557415\pi$
$61$	−1.68836e27	−0.358799	−0.179400	+	0.983776i	$0.557415\pi$
$62$	−3.57841e27	−0.591042
$63$	−7.07844e27	−0.912344
$64$	1.23794e27	0.125000
$65$	−1.75096e27	−0.139033
$66$	−1.10658e27	−0.0693512
$67$	−2.09314e28	−1.03906	−0.519528	−	0.854454i	$-0.673892\pi$
$67$	−2.09314e28	−1.03906	−0.519528	+	0.854454i	$0.673892\pi$
$68$	−8.99333e27	−0.354840
$69$	7.71992e24	0.000242914 0
$70$	−1.17220e28	−0.295108
$71$	−7.31996e28	−1.47912	−0.739561	−	0.673089i	$-0.764967\pi$
$71$	−7.31996e28	−1.47912	−0.739561	+	0.673089i	$0.764967\pi$
$72$	−2.12465e28	−0.345647
$73$	−1.79728e28	−0.236108	−0.118054	−	0.993007i	$-0.537666\pi$
$73$	−1.79728e28	−0.236108	−0.118054	+	0.993007i	$0.537666\pi$
$74$	3.41826e28	0.363675
$75$	3.46133e27	0.0299084
$76$	1.94303e26	0.00136732
$77$	−1.06511e29	−0.612050
$78$	6.98744e27	0.0328739
$79$	−3.55437e29	−1.37260	−0.686298	−	0.727320i	$-0.740766\pi$
$79$	−3.55437e29	−1.37260	−0.686298	+	0.727320i	$0.740766\pi$
$80$	−3.51844e28	−0.111803
$81$	3.56116e29	0.933412
$82$	−4.76175e29	−1.03193
$83$	−1.38740e29	−0.249167	−0.124584	−	0.992209i	$-0.539759\pi$
$83$	−1.38740e29	−0.249167	−0.124584	+	0.992209i	$0.539759\pi$
$84$	4.67782e28	0.0697773
$85$	2.55606e29	0.317378
$86$	−2.06887e29	−0.214293
$87$	−1.72963e29	−0.149763
$88$	−3.19700e29	−0.231879
$89$	−2.03177e30	−1.23689	−0.618443	−	0.785829i	$-0.712236\pi$
$89$	−2.03177e30	−1.23689	−0.618443	+	0.785829i	$0.712236\pi$
$90$	6.03860e29	0.309156
$91$	6.72553e29	0.290125
$92$	2.23033e27	0.000812192 0
$93$	−4.05866e29	−0.124996
$94$	2.52653e30	0.659238
$95$	−5.52243e27	−0.00122297
$96$	1.40408e29	0.0264355
$97$	8.65389e30	1.38755	0.693777	−	0.720190i	$-0.255946\pi$
$97$	8.65389e30	1.38755	0.693777	+	0.720190i	$0.255946\pi$
$98$	−6.67507e29	−0.0912960
$99$	5.48692e30	0.641185
$100$	1.00000e30	0.100000
$101$	1.49248e31	1.27916	0.639582	−	0.768723i	$-0.279107\pi$
$101$	1.49248e31	1.27916	0.639582	+	0.768723i	$0.279107\pi$
$102$	−1.02003e30	−0.0750430
$103$	2.46096e31	1.55643	0.778213	−	0.628001i	$-0.216127\pi$
$103$	2.46096e31	1.55643	0.778213	+	0.628001i	$0.216127\pi$
$104$	2.01872e30	0.109915
$105$	−1.32952e30	−0.0624107
$106$	7.29591e29	0.0295692
$107$	−2.46056e31	−0.862154	−0.431077	−	0.902315i	$-0.641866\pi$
$107$	−2.46056e31	−0.862154	−0.431077	+	0.902315i	$0.641866\pi$
$108$	−4.87470e30	−0.147870
$109$	1.88855e31	0.496614	0.248307	−	0.968681i	$-0.420126\pi$
$109$	1.88855e31	0.496614	0.248307	+	0.968681i	$0.420126\pi$
$110$	9.08641e30	0.207398
$111$	3.87702e30	0.0769116
$112$	1.35145e31	0.233303
$113$	4.97639e31	0.748511	0.374256	−	0.927326i	$-0.377898\pi$
$113$	4.97639e31	0.748511	0.374256	+	0.927326i	$0.377898\pi$
$114$	2.20380e28	0.000289166 0
$115$	−6.33899e28	−0.000726446 0
$116$	−4.99700e31	−0.500738
$117$	−3.46467e31	−0.303935
$118$	−1.51342e32	−1.16356
$119$	−9.81796e31	−0.662283
$120$	−3.99064e30	−0.0236447
$121$	−1.09381e32	−0.569859
$122$	−5.53240e31	−0.253709
$123$	−5.40082e31	−0.218238
$124$	−1.17257e32	−0.417930
$125$	−2.84217e31	−0.0894427
$126$	−2.31946e32	−0.645125
$127$	4.88140e32	1.20112	0.600560	−	0.799580i	$-0.294944\pi$
$127$	4.88140e32	1.20112	0.600560	+	0.799580i	$0.294944\pi$
$128$	4.05648e31	0.0883883
$129$	−2.34653e31	−0.0453196
$130$	−5.73754e31	−0.0983114
$131$	−2.85150e32	−0.433879	−0.216939	−	0.976185i	$-0.569607\pi$
$131$	−2.85150e32	−0.433879	−0.216939	+	0.976185i	$0.569607\pi$
$132$	−3.62606e31	−0.0490387
$133$	2.12120e30	0.00255200
$134$	−6.85880e32	−0.734723
$135$	1.38547e32	0.132259
$136$	−2.94693e32	−0.250910
$137$	1.07566e33	0.817533	0.408766	−	0.912639i	$-0.365959\pi$
$137$	1.07566e33	0.817533	0.408766	+	0.912639i	$0.365959\pi$
$138$	2.52966e29	0.000171766 0
$139$	6.52567e32	0.396183	0.198091	−	0.980184i	$-0.436526\pi$
$139$	6.52567e32	0.396183	0.198091	+	0.980184i	$0.436526\pi$
$140$	−3.84106e32	−0.208673
$141$	2.86561e32	0.139418
$142$	−2.39860e33	−1.04590
$143$	−5.21336e32	−0.203896
$144$	−6.96204e32	−0.244409
$145$	1.42023e33	0.447874
$146$	−5.88931e32	−0.166953
$147$	−7.57092e31	−0.0193077
$148$	1.12010e33	0.257157
$149$	3.57355e33	0.739116	0.369558	−	0.929208i	$-0.379509\pi$
$149$	3.57355e33	0.739116	0.369558	+	0.929208i	$0.379509\pi$
$150$	1.13421e32	0.0211484
$151$	8.68304e33	1.46059	0.730297	−	0.683130i	$-0.239382\pi$
$151$	8.68304e33	1.46059	0.730297	+	0.683130i	$0.239382\pi$
$152$	6.36693e30	0.000966839 0
$153$	5.05775e33	0.693809
$154$	−3.49014e33	−0.432784
$155$	3.33265e33	0.373808
$156$	2.28964e32	0.0232454
$157$	1.84314e34	1.69478	0.847390	−	0.530971i	$-0.178173\pi$
$157$	1.84314e34	1.69478	0.847390	+	0.530971i	$0.178173\pi$
$158$	−1.16470e34	−0.970573
$159$	8.27508e31	0.00625341
$160$	−1.15292e33	−0.0790569
$161$	2.43484e31	0.00151590
$162$	1.16692e34	0.660022
$163$	5.68871e33	0.292487	0.146243	−	0.989249i	$-0.453282\pi$
$163$	5.68871e33	0.292487	0.146243	+	0.989249i	$0.453282\pi$
$164$	−1.56033e34	−0.729688
$165$	1.03059e33	0.0438615
$166$	−4.54623e33	−0.176188
$167$	1.09643e34	0.387148	0.193574	−	0.981086i	$-0.437992\pi$
$167$	1.09643e34	0.387148	0.193574	+	0.981086i	$0.437992\pi$
$168$	1.53283e33	0.0493400
$169$	−3.07680e34	−0.903349
$170$	8.37569e33	0.224420
$171$	−1.09274e32	−0.00267348
$172$	−6.77928e33	−0.151528
$173$	−6.16674e34	−1.25991	−0.629957	−	0.776630i	$-0.716927\pi$
$173$	−6.16674e34	−1.25991	−0.629957	+	0.776630i	$0.716927\pi$
$174$	−5.66764e33	−0.105898
$175$	1.09169e34	0.186643
$176$	−1.04759e34	−0.163963
$177$	−1.71653e34	−0.246074
$178$	−6.65771e34	−0.874611
$179$	−9.62475e34	−1.15922	−0.579612	−	0.814892i	$-0.696796\pi$
$179$	−9.62475e34	−1.15922	−0.579612	+	0.814892i	$0.696796\pi$
$180$	1.97873e34	0.218606
$181$	−5.33071e34	−0.540465	−0.270232	−	0.962795i	$-0.587101\pi$
$181$	−5.33071e34	−0.540465	−0.270232	+	0.962795i	$0.587101\pi$
$182$	2.20382e34	0.205149
$183$	−6.27489e33	−0.0536555
$184$	7.30836e31	0.000574306 0
$185$	−3.18350e34	−0.230008
$186$	−1.32994e34	−0.0883856
$187$	7.61049e34	0.465444
$188$	8.27892e34	0.466152
$189$	−5.32168e34	−0.275988
$190$	−1.80959e32	−0.000864767 0
$191$	−9.73174e34	−0.428720	−0.214360	−	0.976755i	$-0.568766\pi$
$191$	−9.73174e34	−0.428720	−0.214360	+	0.976755i	$0.568766\pi$
$192$	4.60089e33	0.0186927
$193$	6.07031e34	0.227548	0.113774	−	0.993507i	$-0.463706\pi$
$193$	6.07031e34	0.227548	0.113774	+	0.993507i	$0.463706\pi$
$194$	2.83571e35	0.981148
$195$	−6.50756e33	−0.0207913
$196$	−2.18729e34	−0.0645561
$197$	6.58198e35	1.79527	0.897635	−	0.440740i	$-0.145284\pi$
$197$	6.58198e35	1.79527	0.897635	+	0.440740i	$0.145284\pi$
$198$	1.79795e35	0.453386
$199$	−2.79576e35	−0.652044	−0.326022	−	0.945362i	$-0.605708\pi$
$199$	−2.79576e35	−0.652044	−0.326022	+	0.945362i	$0.605708\pi$
$200$	3.27680e34	0.0707107
$201$	−7.77930e34	−0.155382
$202$	4.89055e35	0.904506
$203$	−5.45520e35	−0.934592
$204$	−3.34244e34	−0.0530634
$205$	4.43473e35	0.652652
$206$	8.06409e35	1.10056
$207$	−1.25431e33	−0.00158806
$208$	6.61493e34	0.0777220
$209$	−1.64427e33	−0.00179351
$210$	−4.35656e34	−0.0441311
$211$	−2.54302e35	−0.239316	−0.119658	−	0.992815i	$-0.538180\pi$
$211$	−2.54302e35	−0.239316	−0.119658	+	0.992815i	$0.538180\pi$
$212$	2.39073e34	0.0209085
$213$	−2.72052e35	−0.221191
$214$	−8.06276e35	−0.609635
$215$	1.92679e35	0.135531
$216$	−1.59734e35	−0.104560
$217$	−1.28009e36	−0.780036
$218$	6.18841e35	0.351159
$219$	−6.67971e34	−0.0353080
$220$	2.97743e35	0.146653
$221$	−4.80558e35	−0.220631
$222$	1.27042e35	0.0543847
$223$	1.46316e36	0.584205	0.292103	−	0.956387i	$-0.405645\pi$
$223$	1.46316e36	0.584205	0.292103	+	0.956387i	$0.405645\pi$
$224$	4.42844e35	0.164970
$225$	−5.62389e35	−0.195527
$226$	1.63066e36	0.529277
$227$	−2.78290e36	−0.843521	−0.421761	−	0.906707i	$-0.638588\pi$
$227$	−2.78290e36	−0.843521	−0.421761	+	0.906707i	$0.638588\pi$
$228$	7.22142e32	0.000204471 0
$229$	7.15525e35	0.189311	0.0946553	−	0.995510i	$-0.469825\pi$
$229$	7.15525e35	0.189311	0.0946553	+	0.995510i	$0.469825\pi$
$230$	−2.07716e33	−0.000513675 0
$231$	−3.95854e35	−0.0915271
$232$	−1.63742e36	−0.354075
$233$	−4.54393e36	−0.919210	−0.459605	−	0.888123i	$-0.652009\pi$
$233$	−4.54393e36	−0.919210	−0.459605	+	0.888123i	$0.652009\pi$
$234$	−1.13530e36	−0.214915
$235$	−2.35301e36	−0.416939
$236$	−4.95916e36	−0.822758
$237$	−1.32101e36	−0.205261
$238$	−3.21715e36	−0.468305
$239$	9.33307e36	1.27308	0.636542	−	0.771242i	$-0.280364\pi$
$239$	9.33307e36	1.27308	0.636542	+	0.771242i	$0.280364\pi$
$240$	−1.30765e35	−0.0167193
$241$	1.03054e36	0.123538	0.0617688	−	0.998090i	$-0.480326\pi$
$241$	1.03054e36	0.123538	0.0617688	+	0.998090i	$0.480326\pi$
$242$	−3.58418e36	−0.402951
$243$	4.12772e36	0.435324
$244$	−1.81286e36	−0.179400
$245$	6.21665e35	0.0577407
$246$	−1.76974e36	−0.154317
$247$	1.03826e34	0.000850164 0
$248$	−3.84229e36	−0.295521
$249$	−5.15636e35	−0.0372609
$250$	−9.31323e35	−0.0632456
$251$	−1.16237e36	−0.0741993	−0.0370997	−	0.999312i	$-0.511812\pi$
$251$	−1.16237e36	−0.0741993	−0.0370997	+	0.999312i	$0.511812\pi$
$252$	−7.60041e36	−0.456172
$253$	−1.88739e34	−0.00106535
$254$	1.59954e37	0.849320
$255$	9.49977e35	0.0474614
$256$	1.32923e36	0.0625000
$257$	2.28659e37	1.01210	0.506051	−	0.862503i	$-0.331105\pi$
$257$	2.28659e37	1.01210	0.506051	+	0.862503i	$0.331105\pi$
$258$	−7.68911e35	−0.0320458
$259$	1.22280e37	0.479965
$260$	−1.88008e36	−0.0695166
$261$	2.81026e37	0.979081
$262$	−9.34379e36	−0.306798
$263$	4.29199e37	1.32845	0.664223	−	0.747534i	$-0.268762\pi$
$263$	4.29199e37	1.32845	0.664223	+	0.747534i	$0.268762\pi$
$264$	−1.18819e36	−0.0346756
$265$	−6.79485e35	−0.0187012
$266$	6.95073e34	0.00180454
$267$	−7.55123e36	−0.184967
$268$	−2.24749e37	−0.519528
$269$	6.41753e37	1.40026	0.700128	−	0.714017i	$-0.253126\pi$
$269$	6.41753e37	1.40026	0.700128	+	0.714017i	$0.253126\pi$
$270$	4.53992e36	0.0935211
$271$	−2.22956e37	−0.433706	−0.216853	−	0.976204i	$-0.569579\pi$
$271$	−2.22956e37	−0.433706	−0.216853	+	0.976204i	$0.569579\pi$
$272$	−9.65651e36	−0.177420
$273$	2.49959e36	0.0433858
$274$	3.52471e37	0.578083
$275$	−8.46238e36	−0.131170
$276$	8.28920e33	0.000121457 0
$277$	−3.40565e37	−0.471806	−0.235903	−	0.971777i	$-0.575805\pi$
$277$	−3.40565e37	−0.471806	−0.235903	+	0.971777i	$0.575805\pi$
$278$	2.13833e37	0.280144
$279$	6.59442e37	0.817168
$280$	−1.25864e37	−0.147554
$281$	−8.61655e37	−0.955841	−0.477921	−	0.878403i	$-0.658609\pi$
$281$	−8.61655e37	−0.955841	−0.477921	+	0.878403i	$0.658609\pi$
$282$	9.39002e36	0.0985838
$283$	−1.43491e38	−1.42605	−0.713024	−	0.701140i	$-0.752675\pi$
$283$	−1.43491e38	−1.42605	−0.713024	+	0.701140i	$0.752675\pi$
$284$	−7.85975e37	−0.739561
$285$	−2.05245e34	−0.000182885 0
$286$	−1.70831e37	−0.144176
$287$	−1.70340e38	−1.36191
$288$	−2.28132e37	−0.172823
$289$	−6.91367e37	−0.496355
$290$	4.65382e37	0.316695
$291$	3.21628e37	0.207497
$292$	−1.92981e37	−0.118054
$293$	−2.93343e38	−1.70188	−0.850939	−	0.525265i	$-0.823966\pi$
$293$	−2.93343e38	−1.70188	−0.850939	+	0.525265i	$0.823966\pi$
$294$	−2.48084e36	−0.0136526
$295$	1.40948e38	0.735898
$296$	3.67033e37	0.181838
$297$	4.12516e37	0.193961
$298$	1.17098e38	0.522634
$299$	1.19178e35	0.000505001 0
$300$	3.71657e36	0.0149542
$301$	−7.40090e37	−0.282816
$302$	2.84526e38	1.03280
$303$	5.54690e37	0.191289
$304$	2.08631e35	0.000683658 0
$305$	5.15245e37	0.160460
$306$	1.65732e38	0.490597
$307$	−6.04330e37	−0.170071	−0.0850354	−	0.996378i	$-0.527100\pi$
$307$	−6.04330e37	−0.170071	−0.0850354	+	0.996378i	$0.527100\pi$
$308$	−1.14365e38	−0.306025
$309$	9.14635e37	0.232751
$310$	1.09204e38	0.264322
$311$	−4.60547e38	−1.06044	−0.530222	−	0.847859i	$-0.677891\pi$
$311$	−4.60547e38	−1.06044	−0.530222	+	0.847859i	$0.677891\pi$
$312$	7.50271e36	0.0164370
$313$	−5.36117e38	−1.11769	−0.558846	−	0.829271i	$-0.688756\pi$
$313$	−5.36117e38	−1.11769	−0.558846	+	0.829271i	$0.688756\pi$
$314$	6.03959e38	1.19839
$315$	2.16017e38	0.408013
$316$	−3.81648e38	−0.686298
$317$	1.12095e39	1.91941	0.959706	−	0.281006i	$-0.0906680\pi$
$317$	1.12095e39	1.91941	0.959706	+	0.281006i	$0.0906680\pi$
$318$	2.71158e36	0.00442183
$319$	4.22865e38	0.656820
$320$	−3.77789e37	−0.0559017
$321$	−9.14484e37	−0.128928
$322$	7.97849e35	0.00107190
$323$	−1.51566e36	−0.00194071
$324$	3.82376e38	0.466706
$325$	5.34350e37	0.0621776
$326$	1.86408e38	0.206819
$327$	7.01895e37	0.0742646
$328$	−5.11289e38	−0.515967
$329$	9.03805e38	0.870038
$330$	3.37703e37	0.0310148
$331$	−4.31573e38	−0.378199	−0.189100	−	0.981958i	$-0.560557\pi$
$331$	−4.31573e38	−0.378199	−0.189100	+	0.981958i	$0.560557\pi$
$332$	−1.48971e38	−0.124584
$333$	−6.29930e38	−0.502813
$334$	3.59279e38	0.273755
$335$	6.38775e38	0.464680
$336$	5.02277e37	0.0348887
$337$	−1.22680e39	−0.813783	−0.406891	−	0.913477i	$-0.633387\pi$
$337$	−1.22680e39	−0.813783	−0.406891	+	0.913477i	$0.633387\pi$
$338$	−1.00821e39	−0.638764
$339$	1.84951e38	0.111934
$340$	2.74455e38	0.158689
$341$	9.92275e38	0.548200
$342$	−3.58069e36	−0.00189044
$343$	−2.08822e39	−1.05370
$344$	−2.22143e38	−0.107146
$345$	−2.35593e35	−0.000108634 0
$346$	−2.02072e39	−0.890894
$347$	1.29889e39	0.547601	0.273800	−	0.961787i	$-0.411719\pi$
$347$	1.29889e39	0.547601	0.273800	+	0.961787i	$0.411719\pi$
$348$	−1.85717e38	−0.0748814
$349$	3.22255e39	1.24281	0.621407	−	0.783488i	$-0.286561\pi$
$349$	3.22255e39	1.24281	0.621407	+	0.783488i	$0.286561\pi$
$350$	3.57726e38	0.131976
$351$	−2.60480e38	−0.0919419
$352$	−3.43275e38	−0.115939
$353$	−3.92482e39	−1.26856	−0.634281	−	0.773103i	$-0.718704\pi$
$353$	−3.92482e39	−1.26856	−0.634281	+	0.773103i	$0.718704\pi$
$354$	−5.62472e38	−0.174001
$355$	2.23387e39	0.661484
$356$	−2.18160e39	−0.618443
$357$	−3.64892e38	−0.0990391
$358$	−3.15384e39	−0.819695
$359$	4.96900e39	1.23682	0.618408	−	0.785857i	$-0.287778\pi$
$359$	4.96900e39	1.23682	0.618408	+	0.785857i	$0.287778\pi$
$360$	6.48390e38	0.154578
$361$	−4.37883e39	−0.999993
$362$	−1.74677e39	−0.382166
$363$	−4.06521e38	−0.0852178
$364$	7.22148e38	0.145062
$365$	5.48485e38	0.105591
$366$	−2.05616e38	−0.0379402
$367$	−9.54762e39	−1.68877	−0.844387	−	0.535734i	$-0.820035\pi$
$367$	−9.54762e39	−1.68877	−0.844387	+	0.535734i	$0.820035\pi$
$368$	2.39480e36	0.000406096 0
$369$	8.77513e39	1.42674
$370$	−1.04317e39	−0.162640
$371$	2.60994e38	0.0390243
$372$	−4.35795e38	−0.0624981
$373$	−3.75612e39	−0.516716	−0.258358	−	0.966049i	$-0.583181\pi$
$373$	−3.75612e39	−0.516716	−0.258358	+	0.966049i	$0.583181\pi$
$374$	2.49381e39	0.329119
$375$	−1.05631e38	−0.0133754
$376$	2.71284e39	0.329619
$377$	−2.67015e39	−0.311347
$378$	−1.74381e39	−0.195153
$379$	1.24620e40	1.33869	0.669345	−	0.742951i	$-0.266575\pi$
$379$	1.24620e40	1.33869	0.669345	+	0.742951i	$0.266575\pi$
$380$	−5.92966e36	−0.000611483 0
$381$	1.81421e39	0.179618
$382$	−3.18890e39	−0.303150
$383$	−5.87670e39	−0.536479	−0.268240	−	0.963352i	$-0.586442\pi$
$383$	−5.87670e39	−0.536479	−0.268240	+	0.963352i	$0.586442\pi$
$384$	1.50762e38	0.0132178
$385$	3.25045e39	0.273717
$386$	1.98912e39	0.160901
$387$	3.81259e39	0.296279
$388$	9.29205e39	0.693777
$389$	2.52388e40	1.81072	0.905358	−	0.424650i	$-0.139603\pi$
$389$	2.52388e40	1.81072	0.905358	+	0.424650i	$0.139603\pi$
$390$	−2.13240e38	−0.0147017
$391$	−1.73976e37	−0.00115279
$392$	−7.16731e38	−0.0456480
$393$	−1.05978e39	−0.0648831
$394$	2.15678e40	1.26945
$395$	1.08471e40	0.613844
$396$	5.89154e39	0.320592
$397$	2.80809e39	0.146946	0.0734731	−	0.997297i	$-0.476592\pi$
$397$	2.80809e39	0.146946	0.0734731	+	0.997297i	$0.476592\pi$
$398$	−9.16114e39	−0.461065
$399$	7.88358e36	0.000381631 0
$400$	1.07374e39	0.0500000
$401$	−3.30620e40	−1.48113	−0.740563	−	0.671987i	$-0.765441\pi$
$401$	−3.30620e40	−1.48113	−0.740563	+	0.671987i	$0.765441\pi$
$402$	−2.54912e39	−0.109872
$403$	−6.26564e39	−0.259859
$404$	1.60253e40	0.639582
$405$	−1.08678e40	−0.417434
$406$	−1.78756e40	−0.660856
$407$	−9.47867e39	−0.337314
$408$	−1.09525e39	−0.0375215
$409$	−6.42045e39	−0.211765	−0.105883	−	0.994379i	$-0.533767\pi$
$409$	−6.42045e39	−0.211765	−0.105883	+	0.994379i	$0.533767\pi$
$410$	1.45317e40	0.461495
$411$	3.99776e39	0.122256
$412$	2.64244e40	0.778213
$413$	−5.41389e40	−1.53562
$414$	−4.11014e37	−0.00112293
$415$	4.23400e39	0.111431
$416$	2.16758e39	0.0549577
$417$	2.42531e39	0.0592460
$418$	−5.38793e37	−0.00126821
$419$	−3.15528e40	−0.715682	−0.357841	−	0.933783i	$-0.616487\pi$
$419$	−3.15528e40	−0.715682	−0.357841	+	0.933783i	$0.616487\pi$
$420$	−1.42756e39	−0.0312054
$421$	−7.71785e40	−1.62601	−0.813007	−	0.582255i	$-0.802171\pi$
$421$	−7.71785e40	−1.62601	−0.813007	+	0.582255i	$0.802171\pi$
$422$	−8.33298e39	−0.169222
$423$	−4.65597e40	−0.911454
$424$	7.83393e38	0.0147846
$425$	−7.80047e39	−0.141936
$426$	−8.91459e39	−0.156406
$427$	−1.97909e40	−0.334836
$428$	−2.64200e40	−0.431077
$429$	−1.93758e39	−0.0304911
$430$	6.31370e39	0.0958347
$431$	9.22561e40	1.35082	0.675410	−	0.737442i	$-0.263967\pi$
$431$	9.22561e40	1.35082	0.675410	+	0.737442i	$0.263967\pi$
$432$	−5.23417e39	−0.0739350
$433$	6.53246e40	0.890255	0.445128	−	0.895467i	$-0.353158\pi$
$433$	6.53246e40	0.890255	0.445128	+	0.895467i	$0.353158\pi$
$434$	−4.19460e40	−0.551569
$435$	5.27840e39	0.0669760
$436$	2.02782e40	0.248307
$437$	3.75881e35	4.44209e−6 0
$438$	−2.18881e39	−0.0249666
$439$	8.52177e40	0.938274	0.469137	−	0.883125i	$-0.344565\pi$
$439$	8.52177e40	0.938274	0.469137	+	0.883125i	$0.344565\pi$
$440$	9.75646e39	0.103699
$441$	1.23011e40	0.126225
$442$	−1.57469e40	−0.156009
$443$	−4.89158e40	−0.467942	−0.233971	−	0.972244i	$-0.575172\pi$
$443$	−4.89158e40	−0.467942	−0.233971	+	0.972244i	$0.575172\pi$
$444$	4.16292e39	0.0384558
$445$	6.20048e40	0.553153
$446$	4.79447e40	0.413096
$447$	1.32814e40	0.110529
$448$	1.45111e40	0.116652
$449$	−8.10411e40	−0.629343	−0.314671	−	0.949201i	$-0.601894\pi$
$449$	−8.10411e40	−0.629343	−0.314671	+	0.949201i	$0.601894\pi$
$450$	−1.84284e40	−0.138259
$451$	1.32041e41	0.957133
$452$	5.34336e40	0.374256
$453$	3.22712e40	0.218420
$454$	−9.11899e40	−0.596460
$455$	−2.05247e40	−0.129748
$456$	2.36631e37	0.000144583 0
$457$	2.68355e41	1.58492	0.792462	−	0.609921i	$-0.208799\pi$
$457$	2.68355e41	1.58492	0.792462	+	0.609921i	$0.208799\pi$
$458$	2.34463e40	0.133863
$459$	3.80250e40	0.209880
$460$	−6.80644e37	−0.000363223 0
$461$	−1.16938e41	−0.603381	−0.301690	−	0.953406i	$-0.597551\pi$
$461$	−1.16938e41	−0.603381	−0.301690	+	0.953406i	$0.597551\pi$
$462$	−1.29714e40	−0.0647195
$463$	2.03109e41	0.979993	0.489997	−	0.871724i	$-0.336998\pi$
$463$	2.03109e41	0.979993	0.489997	+	0.871724i	$0.336998\pi$
$464$	−5.36549e40	−0.250369
$465$	1.23860e40	0.0559000
$466$	−1.48895e41	−0.649980
$467$	2.49286e41	1.05265	0.526327	−	0.850282i	$-0.323569\pi$
$467$	2.49286e41	1.05265	0.526327	+	0.850282i	$0.323569\pi$
$468$	−3.72016e40	−0.151968
$469$	−2.45357e41	−0.969661
$470$	−7.71035e40	−0.294820
$471$	6.85015e40	0.253441
$472$	−1.62502e41	−0.581778
$473$	5.73688e40	0.198760
$474$	−4.32868e40	−0.145141
$475$	1.68531e38	0.000546927 0
$476$	−1.05420e41	−0.331141
$477$	−1.34452e40	−0.0408819
$478$	3.05826e41	0.900206
$479$	−2.95683e41	−0.842608	−0.421304	−	0.906920i	$-0.638427\pi$
$479$	−2.95683e41	−0.842608	−0.421304	+	0.906920i	$0.638427\pi$
$480$	−4.28492e39	−0.0118223
$481$	5.98523e40	0.159894
$482$	3.37686e40	0.0873543
$483$	9.04926e37	0.000226690 0
$484$	−1.17447e41	−0.284929
$485$	−2.64096e41	−0.620533
$486$	1.35257e41	0.307821
$487$	−2.29047e41	−0.504924	−0.252462	−	0.967607i	$-0.581240\pi$
$487$	−2.29047e41	−0.504924	−0.252462	+	0.967607i	$0.581240\pi$
$488$	−5.94037e40	−0.126855
$489$	2.11425e40	0.0437390
$490$	2.03707e40	0.0408288
$491$	4.43398e41	0.861055	0.430528	−	0.902577i	$-0.358328\pi$
$491$	4.43398e41	0.861055	0.430528	+	0.902577i	$0.358328\pi$
$492$	−5.79908e40	−0.109119
$493$	3.89790e41	0.710727
$494$	3.40217e38	0.000601157 0
$495$	−1.67448e41	−0.286747
$496$	−1.25904e41	−0.208965
$497$	−8.58044e41	−1.38034
$498$	−1.68964e40	−0.0263475
$499$	−9.05766e40	−0.136917	−0.0684585	−	0.997654i	$-0.521808\pi$
$499$	−9.05766e40	−0.136917	−0.0684585	+	0.997654i	$0.521808\pi$
$500$	−3.05176e40	−0.0447214
$501$	4.07497e40	0.0578949
$502$	−3.80884e40	−0.0524669
$503$	5.15192e41	0.688122	0.344061	−	0.938947i	$-0.388197\pi$
$503$	5.15192e41	0.688122	0.344061	+	0.938947i	$0.388197\pi$
$504$	−2.49050e41	−0.322562
$505$	−4.55468e41	−0.572060
$506$	−6.18461e38	−0.000753319 0
$507$	−1.14352e41	−0.135089
$508$	5.24136e41	0.600560
$509$	−1.43567e42	−1.59562	−0.797810	−	0.602909i	$-0.794008\pi$
$509$	−1.43567e42	−1.59562	−0.797810	+	0.602909i	$0.794008\pi$
$510$	3.11289e40	0.0335603
$511$	−2.10676e41	−0.220339
$512$	4.35561e40	0.0441942
$513$	−8.21539e38	−0.000808740 0
$514$	7.49269e41	0.715665
$515$	−7.51027e41	−0.696055
$516$	−2.51957e40	−0.0226598
$517$	−7.00594e41	−0.611453
$518$	4.00688e41	0.339387
$519$	−2.29191e41	−0.188410
$520$	−6.16064e40	−0.0491557
$521$	−1.70351e40	−0.0131935	−0.00659676	−	0.999978i	$-0.502100\pi$
$521$	−1.70351e40	−0.0131935	−0.00659676	+	0.999978i	$0.502100\pi$
$522$	9.20866e41	0.692315
$523$	2.39267e42	1.74625	0.873124	−	0.487497i	$-0.162090\pi$
$523$	2.39267e42	1.74625	0.873124	+	0.487497i	$0.162090\pi$
$524$	−3.06177e41	−0.216939
$525$	4.05736e40	0.0279109
$526$	1.40640e42	0.939354
$527$	9.14661e41	0.593193
$528$	−3.89345e40	−0.0245193
$529$	−1.63517e42	−0.999997
$530$	−2.22654e40	−0.0132237
$531$	2.78898e42	1.60872
$532$	2.27762e39	0.00127600
$533$	−8.33762e41	−0.453702
$534$	−2.47439e41	−0.130791
$535$	7.50903e41	0.385567
$536$	−7.36458e41	−0.367362
$537$	−3.57711e41	−0.173353
$538$	2.10290e42	0.990131
$539$	1.85097e41	0.0846784
$540$	1.48764e41	0.0661294
$541$	1.16929e42	0.505084	0.252542	−	0.967586i	$-0.418733\pi$
$541$	1.16929e42	0.505084	0.252542	+	0.967586i	$0.418733\pi$
$542$	−7.30583e41	−0.306677
$543$	−1.98120e41	−0.0808222
$544$	−3.16425e41	−0.125455
$545$	−5.76341e41	−0.222092
$546$	8.19066e40	0.0306784
$547$	2.63927e42	0.960903	0.480451	−	0.877021i	$-0.340473\pi$
$547$	2.63927e42	0.960903	0.480451	+	0.877021i	$0.340473\pi$
$548$	1.15498e42	0.408766
$549$	1.01953e42	0.350775
$550$	−2.77295e41	−0.0927514
$551$	−8.42151e39	−0.00273867
$552$	2.71620e38	8.58829e−5 0
$553$	−4.16643e42	−1.28093
$554$	−1.11596e42	−0.333617
$555$	−1.18317e41	−0.0343959
$556$	7.00688e41	0.198091
$557$	−1.64861e42	−0.453276	−0.226638	−	0.973979i	$-0.572773\pi$
$557$	−1.64861e42	−0.453276	−0.226638	+	0.973979i	$0.572773\pi$
$558$	2.16086e42	0.577825
$559$	−3.62251e41	−0.0942164
$560$	−4.12430e41	−0.104336
$561$	2.82849e41	0.0696035
$562$	−2.82347e42	−0.675882
$563$	1.07869e42	0.251199	0.125599	−	0.992081i	$-0.459915\pi$
$563$	1.07869e42	0.251199	0.125599	+	0.992081i	$0.459915\pi$
$564$	3.07692e41	0.0697092
$565$	−1.51867e42	−0.334744
$566$	−4.70190e42	−1.00837
$567$	4.17438e42	0.871073
$568$	−2.57548e42	−0.522949
$569$	−3.05975e42	−0.604569	−0.302285	−	0.953218i	$-0.597749\pi$
$569$	−3.05975e42	−0.604569	−0.302285	+	0.953218i	$0.597749\pi$
$570$	−6.72547e38	−0.000129319 0
$571$	−5.12850e42	−0.959689	−0.479845	−	0.877353i	$-0.659307\pi$
$571$	−5.12850e42	−0.959689	−0.479845	+	0.877353i	$0.659307\pi$
$572$	−5.59780e41	−0.101948
$573$	−3.61687e41	−0.0641116
$574$	−5.58171e42	−0.963015
$575$	1.93451e39	0.000324877 0
$576$	−7.47543e41	−0.122205
$577$	2.43929e42	0.388185	0.194092	−	0.980983i	$-0.437824\pi$
$577$	2.43929e42	0.388185	0.194092	+	0.980983i	$0.437824\pi$
$578$	−2.26547e42	−0.350976
$579$	2.25608e41	0.0340280
$580$	1.52496e42	0.223937
$581$	−1.62630e42	−0.232526
$582$	1.05391e42	0.146723
$583$	−2.02312e41	−0.0274258
$584$	−6.32360e41	−0.0834767
$585$	1.05733e42	0.135924
$586$	−9.61228e42	−1.20341
$587$	2.87287e42	0.350289	0.175144	−	0.984543i	$-0.443961\pi$
$587$	2.87287e42	0.350289	0.175144	+	0.984543i	$0.443961\pi$
$588$	−8.12922e40	−0.00965384
$589$	−1.97615e40	−0.00228577
$590$	4.61858e42	0.520358
$591$	2.44624e42	0.268468
$592$	1.20269e42	0.128579
$593$	−1.36765e43	−1.42438	−0.712191	−	0.701986i	$-0.752297\pi$
$593$	−1.36765e43	−1.42438	−0.712191	+	0.701986i	$0.752297\pi$
$594$	1.35173e42	0.137151
$595$	2.99620e42	0.296182
$596$	3.83707e42	0.369558
$597$	−1.03906e42	−0.0975079
$598$	3.90522e39	0.000357090 0
$599$	1.51714e43	1.35179	0.675896	−	0.736997i	$-0.263757\pi$
$599$	1.51714e43	1.35179	0.675896	+	0.736997i	$0.263757\pi$
$600$	1.21785e41	0.0105742
$601$	1.27660e43	1.08019	0.540097	−	0.841603i	$-0.318388\pi$
$601$	1.27660e43	1.08019	0.540097	+	0.841603i	$0.318388\pi$
$602$	−2.42513e42	−0.199981
$603$	1.26396e43	1.01582
$604$	9.32335e42	0.730297
$605$	3.33803e42	0.254849
$606$	1.81761e42	0.135262
$607$	2.34350e43	1.69997	0.849985	−	0.526807i	$-0.176611\pi$
$607$	2.34350e43	1.69997	0.849985	+	0.526807i	$0.176611\pi$
$608$	6.83644e39	0.000483420 0
$609$	−2.02746e42	−0.139761
$610$	1.68836e42	0.113462
$611$	4.42384e42	0.289842
$612$	5.43072e42	0.346905
$613$	−2.26166e43	−1.40861	−0.704304	−	0.709899i	$-0.748741\pi$
$613$	−2.26166e43	−1.40861	−0.704304	+	0.709899i	$0.748741\pi$
$614$	−1.98027e42	−0.120258
$615$	1.64820e42	0.0975989
$616$	−3.74751e42	−0.216392
$617$	−2.88548e43	−1.62479	−0.812396	−	0.583107i	$-0.801837\pi$
$617$	−2.88548e43	−1.62479	−0.812396	+	0.583107i	$0.801837\pi$
$618$	2.99708e42	0.164580
$619$	2.76080e43	1.47853	0.739265	−	0.673415i	$-0.235173\pi$
$619$	2.76080e43	1.47853	0.739265	+	0.673415i	$0.235173\pi$
$620$	3.57841e42	0.186904
$621$	−9.43014e39	−0.000480395 0
$622$	−1.50912e43	−0.749847
$623$	−2.38164e43	−1.15428
$624$	2.45849e41	0.0116227
$625$	8.67362e41	0.0400000
$626$	−1.75675e43	−0.790328
$627$	−6.11104e39	−0.000268206 0
$628$	1.97905e43	0.847390
$629$	−8.73727e42	−0.364998
$630$	7.07844e42	0.288509
$631$	1.61493e43	0.642241	0.321120	−	0.947038i	$-0.395941\pi$
$631$	1.61493e43	0.642241	0.321120	+	0.947038i	$0.395941\pi$
$632$	−1.25058e43	−0.485286
$633$	−9.45133e41	−0.0357878
$634$	3.67313e43	1.35723
$635$	−1.48968e43	−0.537157
$636$	8.88530e40	0.00312671
$637$	−1.16878e42	−0.0401394
$638$	1.38564e43	0.464442
$639$	4.42023e43	1.44605
$640$	−1.23794e42	−0.0395285
$641$	−5.20265e43	−1.62153	−0.810765	−	0.585371i	$-0.800949\pi$
$641$	−5.20265e43	−1.62153	−0.810765	+	0.585371i	$0.800949\pi$
$642$	−2.99658e42	−0.0911661
$643$	−6.52863e43	−1.93889	−0.969443	−	0.245318i	$-0.921108\pi$
$643$	−6.52863e43	−1.93889	−0.969443	+	0.245318i	$0.921108\pi$
$644$	2.61439e40	0.000757948 0
$645$	7.16104e41	0.0202675
$646$	−4.96650e40	−0.00137229
$647$	−3.65399e43	−0.985714	−0.492857	−	0.870110i	$-0.664047\pi$
$647$	−3.65399e43	−0.985714	−0.492857	+	0.870110i	$0.664047\pi$
$648$	1.25297e43	0.330011
$649$	4.19663e43	1.07921
$650$	1.75096e42	0.0439662
$651$	−4.75755e42	−0.116648
$652$	6.10821e42	0.146243
$653$	−6.96769e43	−1.62905	−0.814525	−	0.580128i	$-0.803003\pi$
$653$	−6.96769e43	−1.62905	−0.814525	+	0.580128i	$0.803003\pi$
$654$	2.29997e42	0.0525130
$655$	8.70209e42	0.194036
$656$	−1.67539e43	−0.364844
$657$	1.08530e43	0.230828
$658$	2.96159e43	0.615210
$659$	−2.01525e43	−0.408888	−0.204444	−	0.978878i	$-0.565539\pi$
$659$	−2.01525e43	−0.408888	−0.204444	+	0.978878i	$0.565539\pi$
$660$	1.10658e42	0.0219308
$661$	2.46780e43	0.477735	0.238868	−	0.971052i	$-0.423224\pi$
$661$	2.46780e43	0.477735	0.238868	+	0.971052i	$0.423224\pi$
$662$	−1.41418e43	−0.267427
$663$	−1.78603e42	−0.0329936
$664$	−4.88147e42	−0.0880939
$665$	−6.47338e40	−0.00114129
$666$	−2.06415e43	−0.355542
$667$	−9.66673e40	−0.00162678
$668$	1.17729e43	0.193574
$669$	5.43793e42	0.0873632
$670$	2.09314e43	0.328578
$671$	1.53411e43	0.235319
$672$	1.64586e42	0.0246700
$673$	−3.35922e43	−0.492046	−0.246023	−	0.969264i	$-0.579124\pi$
$673$	−3.35922e43	−0.492046	−0.246023	+	0.969264i	$0.579124\pi$
$674$	−4.01996e43	−0.575431
$675$	−4.22813e42	−0.0591480
$676$	−3.30369e43	−0.451674
$677$	−2.53983e43	−0.339375	−0.169687	−	0.985498i	$-0.554276\pi$
$677$	−2.53983e43	−0.339375	−0.169687	+	0.985498i	$0.554276\pi$
$678$	6.06048e42	0.0791492
$679$	1.01441e44	1.29488
$680$	8.99333e42	0.112210
$681$	−1.03428e43	−0.126142
$682$	3.25149e43	0.387636
$683$	−3.53141e43	−0.411554	−0.205777	−	0.978599i	$-0.565972\pi$
$683$	−3.53141e43	−0.411554	−0.205777	+	0.978599i	$0.565972\pi$
$684$	−1.17332e41	−0.00133674
$685$	−3.28265e43	−0.365612
$686$	−6.84269e43	−0.745080
$687$	2.65930e42	0.0283099
$688$	−7.27920e42	−0.0757639
$689$	1.27748e42	0.0130004
$690$	−7.71992e39	−7.68160e−5 0
$691$	1.98378e44	1.93011	0.965057	−	0.262039i	$-0.0843948\pi$
$691$	1.98378e44	1.93011	0.965057	+	0.262039i	$0.0843948\pi$
$692$	−6.62148e43	−0.629957
$693$	6.43176e43	0.598363
$694$	4.25619e43	0.387212
$695$	−1.99148e43	−0.177178
$696$	−6.08558e42	−0.0529492
$697$	1.21713e44	1.03569
$698$	1.05597e44	0.878802
$699$	−1.68878e43	−0.137460
$700$	1.17220e43	0.0933214
$701$	−8.09544e43	−0.630393	−0.315196	−	0.949026i	$-0.602070\pi$
$701$	−8.09544e43	−0.630393	−0.315196	+	0.949026i	$0.602070\pi$
$702$	−8.53540e42	−0.0650127
$703$	1.88771e41	0.00140646
$704$	−1.12484e43	−0.0819814
$705$	−8.74514e42	−0.0623498
$706$	−1.28608e44	−0.897009
$707$	1.74948e44	1.19373
$708$	−1.84311e43	−0.123037
$709$	4.65712e43	0.304159	0.152080	−	0.988368i	$-0.451403\pi$
$709$	4.65712e43	0.304159	0.152080	+	0.988368i	$0.451403\pi$
$710$	7.31996e43	0.467740
$711$	2.14634e44	1.34190
$712$	−7.14866e43	−0.437305
$713$	−2.26835e41	−0.00135776
$714$	−1.19568e43	−0.0700312
$715$	1.59099e43	0.0911852
$716$	−1.03345e44	−0.579612
$717$	3.46870e43	0.190380
$718$	1.62824e44	0.874561
$719$	−2.54329e44	−1.33690	−0.668448	−	0.743759i	$-0.733041\pi$
$719$	−2.54329e44	−1.33690	−0.668448	+	0.743759i	$0.733041\pi$
$720$	2.12465e43	0.109303
$721$	2.88474e44	1.45248
$722$	−1.43486e44	−0.707101
$723$	3.83006e42	0.0184741
$724$	−5.72381e43	−0.270232
$725$	−4.33421e43	−0.200295
$726$	−1.33209e43	−0.0602581
$727$	7.55040e42	0.0334338	0.0167169	−	0.999860i	$-0.494679\pi$
$727$	7.55040e42	0.0334338	0.0167169	+	0.999860i	$0.494679\pi$
$728$	2.36633e43	0.102575
$729$	−2.04622e44	−0.868312
$730$	1.79728e43	0.0746639
$731$	5.28816e43	0.215073
$732$	−6.73762e42	−0.0268278
$733$	−9.66566e43	−0.376808	−0.188404	−	0.982092i	$-0.560331\pi$
$733$	−9.66566e43	−0.376808	−0.188404	+	0.982092i	$0.560331\pi$
$734$	−3.12857e44	−1.19414
$735$	2.31046e42	0.00863466
$736$	7.84729e40	0.000287153 0
$737$	1.90191e44	0.681466
$738$	2.87543e44	1.00886
$739$	−4.93183e44	−1.69441	−0.847207	−	0.531263i	$-0.821718\pi$
$739$	−4.93183e44	−1.69441	−0.847207	+	0.531263i	$0.821718\pi$
$740$	−3.41826e43	−0.115004
$741$	3.85876e40	0.000127135 0
$742$	8.55225e42	0.0275943
$743$	−5.37148e44	−1.69734	−0.848668	−	0.528927i	$-0.822595\pi$
$743$	−5.37148e44	−1.69734	−0.848668	+	0.528927i	$0.822595\pi$
$744$	−1.42801e43	−0.0441928
$745$	−1.09056e44	−0.330543
$746$	−1.23080e44	−0.365373
$747$	8.37795e43	0.243595
$748$	8.17170e43	0.232722
$749$	−2.88426e44	−0.804574
$750$	−3.46133e42	−0.00945787
$751$	−2.98383e44	−0.798647	−0.399323	−	0.916810i	$-0.630755\pi$
$751$	−2.98383e44	−0.798647	−0.399323	+	0.916810i	$0.630755\pi$
$752$	8.88943e43	0.233076
$753$	−4.32002e42	−0.0110959
$754$	−8.74954e43	−0.220155
$755$	−2.64985e44	−0.653197
$756$	−5.71411e43	−0.137994
$757$	2.45658e44	0.581226	0.290613	−	0.956841i	$-0.406141\pi$
$757$	2.45658e44	0.581226	0.290613	+	0.956841i	$0.406141\pi$
$758$	4.08355e44	0.946597
$759$	−7.01463e40	−0.000159315 0
$760$	−1.94303e41	−0.000432384 0
$761$	2.66898e44	0.581947	0.290974	−	0.956731i	$-0.406021\pi$
$761$	2.66898e44	0.581947	0.290974	+	0.956731i	$0.406021\pi$
$762$	5.94479e43	0.127009
$763$	2.21376e44	0.463447
$764$	−1.04494e44	−0.214360
$765$	−1.54350e44	−0.310281
$766$	−1.92568e44	−0.379348
$767$	−2.64993e44	−0.511571
$768$	4.94017e42	0.00934637
$769$	5.03004e44	0.932638	0.466319	−	0.884617i	$-0.345580\pi$
$769$	5.03004e44	0.932638	0.466319	+	0.884617i	$0.345580\pi$
$770$	1.06511e44	0.193547
$771$	8.49827e43	0.151352
$772$	6.51795e43	0.113774
$773$	2.30815e44	0.394895	0.197448	−	0.980313i	$-0.436735\pi$
$773$	2.30815e44	0.394895	0.197448	+	0.980313i	$0.436735\pi$
$774$	1.24931e44	0.209501
$775$	−1.01704e44	−0.167172
$776$	3.04482e44	0.490574
$777$	4.54463e43	0.0717750
$778$	8.27026e44	1.28037
$779$	−2.62964e42	−0.00399086
$780$	−6.98744e42	−0.0103957
$781$	6.65121e44	0.970085
$782$	−5.70086e41	−0.000815147 0
$783$	2.11280e44	0.296177
$784$	−2.34858e43	−0.0322780
$785$	−5.62481e44	−0.757928
$786$	−3.47269e43	−0.0458793
$787$	−7.09018e44	−0.918436	−0.459218	−	0.888324i	$-0.651870\pi$
$787$	−7.09018e44	−0.918436	−0.459218	+	0.888324i	$0.651870\pi$
$788$	7.06734e44	0.897635
$789$	1.59515e44	0.198659
$790$	3.55437e44	0.434053
$791$	5.83331e44	0.698521
$792$	1.93054e44	0.226693
$793$	−9.68700e43	−0.111546
$794$	9.20155e43	0.103907
$795$	−2.52536e42	−0.00279661
$796$	−3.00192e44	−0.326022
$797$	5.10873e44	0.544138	0.272069	−	0.962278i	$-0.412292\pi$
$797$	5.10873e44	0.544138	0.272069	+	0.962278i	$0.412292\pi$
$798$	2.58329e41	0.000269854 0
$799$	−6.45795e44	−0.661637
$800$	3.51844e43	0.0353553
$801$	1.22691e45	1.20923
$802$	−1.08338e45	−1.04731
$803$	1.63308e44	0.154852
$804$	−8.35296e43	−0.0776912
$805$	−7.43055e41	−0.000677930 0
$806$	−2.05312e44	−0.183748
$807$	2.38512e44	0.209397
$808$	5.25119e44	0.452253
$809$	−4.75268e44	−0.401547	−0.200774	−	0.979638i	$-0.564346\pi$
$809$	−4.75268e44	−0.401547	−0.200774	+	0.979638i	$0.564346\pi$
$810$	−3.56116e44	−0.295171
$811$	−1.22424e45	−0.995507	−0.497753	−	0.867319i	$-0.665842\pi$
$811$	−1.22424e45	−0.995507	−0.497753	+	0.867319i	$0.665842\pi$
$812$	−5.85747e44	−0.467296
$813$	−8.28633e43	−0.0648573
$814$	−3.10597e44	−0.238517
$815$	−1.73606e44	−0.130804
$816$	−3.58891e43	−0.0265317
$817$	−1.14252e42	−0.000828747 0
$818$	−2.10385e44	−0.149741
$819$	−4.06128e44	−0.283637
$820$	4.76175e44	0.326326
$821$	1.17121e45	0.787621	0.393811	−	0.919192i	$-0.371157\pi$
$821$	1.17121e45	0.787621	0.393811	+	0.919192i	$0.371157\pi$
$822$	1.30999e44	0.0864477
$823$	−2.18225e45	−1.41321	−0.706606	−	0.707608i	$-0.749774\pi$
$823$	−2.18225e45	−1.41321	−0.706606	+	0.707608i	$0.749774\pi$
$824$	8.65875e44	0.550279
$825$	−3.14510e43	−0.0196155
$826$	−1.77402e45	−1.08585
$827$	−5.38658e44	−0.323577	−0.161788	−	0.986825i	$-0.551726\pi$
$827$	−5.38658e44	−0.323577	−0.161788	+	0.986825i	$0.551726\pi$
$828$	−1.34681e42	−0.000794029 0
$829$	9.22833e44	0.533983	0.266992	−	0.963699i	$-0.413970\pi$
$829$	9.22833e44	0.533983	0.266992	+	0.963699i	$0.413970\pi$
$830$	1.38740e44	0.0787935
$831$	−1.26573e44	−0.0705548
$832$	7.10273e43	0.0388610
$833$	1.70619e44	0.0916282
$834$	7.94726e43	0.0418932
$835$	−3.34605e44	−0.173138
$836$	−1.76552e42	−0.000896757 0
$837$	4.95779e44	0.247197
$838$	−1.03392e45	−0.506063
$839$	9.63372e44	0.462896	0.231448	−	0.972847i	$-0.425654\pi$
$839$	9.63372e44	0.462896	0.231448	+	0.972847i	$0.425654\pi$
$840$	−4.67782e43	−0.0220655
$841$	6.38218e42	0.00295550
$842$	−2.52899e45	−1.14976
$843$	−3.20241e44	−0.142938
$844$	−2.73055e44	−0.119658
$845$	9.38965e44	0.403990
$846$	−1.52567e45	−0.644496
$847$	−1.28216e45	−0.531800
$848$	2.56702e43	0.0104543
$849$	−5.33294e44	−0.213254
$850$	−2.55606e44	−0.100364
$851$	2.16683e42	0.000835444 0
$852$	−2.92113e44	−0.110595
$853$	1.08243e45	0.402431	0.201215	−	0.979547i	$-0.435511\pi$
$853$	1.08243e45	0.402431	0.201215	+	0.979547i	$0.435511\pi$
$854$	−6.48507e44	−0.236765
$855$	3.33478e42	0.00119562
$856$	−8.65732e44	−0.304818
$857$	2.89543e45	1.00118	0.500588	−	0.865686i	$-0.333117\pi$
$857$	2.89543e45	1.00118	0.500588	+	0.865686i	$0.333117\pi$
$858$	−6.34907e43	−0.0215604
$859$	4.47852e45	1.49362	0.746811	−	0.665037i	$-0.231584\pi$
$859$	4.47852e45	1.49362	0.746811	+	0.665037i	$0.231584\pi$
$860$	2.06887e44	0.0677653
$861$	−6.33082e44	−0.203663
$862$	3.02305e45	0.955174
$863$	−2.09655e44	−0.0650637	−0.0325318	−	0.999471i	$-0.510357\pi$
$863$	−2.09655e44	−0.0650637	−0.0325318	+	0.999471i	$0.510357\pi$
$864$	−1.71513e44	−0.0522799
$865$	1.88194e45	0.563451
$866$	2.14056e45	0.629506
$867$	−2.56952e44	−0.0742259
$868$	−1.37449e45	−0.390018
$869$	3.22965e45	0.900220
$870$	1.72963e44	0.0473592
$871$	−1.20095e45	−0.323030
$872$	6.64476e44	0.175579
$873$	−5.22574e45	−1.35652
$874$	1.23169e40	3.14103e−6 0
$875$	−3.33159e44	−0.0834692
$876$	−7.17228e43	−0.0176540
$877$	−2.72532e45	−0.659058	−0.329529	−	0.944145i	$-0.606890\pi$
$877$	−2.72532e45	−0.659058	−0.329529	+	0.944145i	$0.606890\pi$
$878$	2.79241e45	0.663460
$879$	−1.09023e45	−0.254502
$880$	3.19700e44	0.0733264
$881$	9.19216e44	0.207153	0.103576	−	0.994621i	$-0.466971\pi$
$881$	9.19216e44	0.207153	0.103576	+	0.994621i	$0.466971\pi$
$882$	4.03081e44	0.0892544
$883$	−7.82916e45	−1.70343	−0.851715	−	0.524006i	$-0.824437\pi$
$883$	−7.82916e45	−1.70343	−0.851715	+	0.524006i	$0.824437\pi$
$884$	−5.15996e44	−0.110315
$885$	5.23843e44	0.110048
$886$	−1.60287e45	−0.330885
$887$	6.91786e45	1.40332	0.701658	−	0.712514i	$-0.252443\pi$
$887$	6.91786e45	1.40332	0.701658	+	0.712514i	$0.252443\pi$
$888$	1.36411e44	0.0271924
$889$	5.72196e45	1.12090
$890$	2.03177e45	0.391138
$891$	−3.23581e45	−0.612180
$892$	1.57105e45	0.292103
$893$	1.39526e43	0.00254951
$894$	4.35204e44	0.0781558
$895$	2.93724e45	0.518421
$896$	4.75500e44	0.0824852
$897$	4.42933e41	7.55188e−5 0
$898$	−2.65555e45	−0.445012
$899$	5.08217e45	0.837094
$900$	−6.03860e44	−0.0977637
$901$	−1.86488e44	−0.0296767
$902$	4.32672e45	0.676796
$903$	−2.75060e44	−0.0422928
$904$	1.75091e45	0.264639
$905$	1.62680e45	0.241703
$906$	1.05746e45	0.154446
$907$	6.85626e45	0.984406	0.492203	−	0.870481i	$-0.336192\pi$
$907$	6.85626e45	0.984406	0.492203	+	0.870481i	$0.336192\pi$
$908$	−2.98811e45	−0.421761
$909$	−9.01248e45	−1.25056
$910$	−6.72553e44	−0.0917455
$911$	−5.37359e45	−0.720659	−0.360329	−	0.932825i	$-0.617336\pi$
$911$	−5.37359e45	−0.720659	−0.360329	+	0.932825i	$0.617336\pi$
$912$	7.75394e41	0.000102236 0
$913$	1.26065e45	0.163417
$914$	8.79346e45	1.12071
$915$	1.91495e44	0.0239955
$916$	7.68289e44	0.0946553
$917$	−3.34252e45	−0.404901
$918$	1.24600e45	0.148408
$919$	−6.16031e45	−0.721460	−0.360730	−	0.932670i	$-0.617472\pi$
$919$	−6.16031e45	−0.721460	−0.360730	+	0.932670i	$0.617472\pi$
$920$	−2.23033e42	−0.000256838 0
$921$	−2.24604e44	−0.0254327
$922$	−3.83182e45	−0.426654
$923$	−4.19985e45	−0.459841
$924$	−4.25045e44	−0.0457636
$925$	9.71528e44	0.102863
$926$	6.65547e45	0.692960
$927$	−1.48608e46	−1.52162
$928$	−1.75816e45	−0.177038
$929$	2.88812e45	0.286004	0.143002	−	0.989722i	$-0.454324\pi$
$929$	2.88812e45	0.286004	0.143002	+	0.989722i	$0.454324\pi$
$930$	4.05866e44	0.0395273
$931$	−3.68626e42	−0.000353074 0
$932$	−4.87901e45	−0.459605
$933$	−1.71166e45	−0.158581
$934$	8.16859e45	0.744339
$935$	−2.32254e45	−0.208153
$936$	−1.21902e45	−0.107457
$937$	−1.88038e46	−1.63035	−0.815176	−	0.579214i	$-0.803360\pi$
$937$	−1.88038e46	−1.63035	−0.815176	+	0.579214i	$0.803360\pi$
$938$	−8.03987e45	−0.685654
$939$	−1.99252e45	−0.167142
$940$	−2.52653e45	−0.208469
$941$	−1.34822e46	−1.09426	−0.547131	−	0.837047i	$-0.684280\pi$
$941$	−1.34822e46	−1.09426	−0.547131	+	0.837047i	$0.684280\pi$
$942$	2.24466e45	0.179210
$943$	−3.01847e43	−0.00237058
$944$	−5.32486e45	−0.411379
$945$	1.62405e45	0.123426
$946$	1.87986e45	0.140544
$947$	−6.95396e45	−0.511455	−0.255728	−	0.966749i	$-0.582315\pi$
$947$	−6.95396e45	−0.511455	−0.255728	+	0.966749i	$0.582315\pi$
$948$	−1.41842e45	−0.102630
$949$	−1.03119e45	−0.0734031
$950$	5.52243e42	0.000386736 0
$951$	4.16610e45	0.287033
$952$	−3.45439e45	−0.234152
$953$	2.10814e46	1.40592	0.702959	−	0.711231i	$-0.251862\pi$
$953$	2.10814e46	1.40592	0.702959	+	0.711231i	$0.251862\pi$
$954$	−4.40571e44	−0.0289079
$955$	2.96989e45	0.191729
$956$	1.00213e46	0.636542
$957$	1.57161e45	0.0982222
$958$	−9.68893e45	−0.595814
$959$	1.26088e46	0.762933
$960$	−1.40408e44	−0.00835965
$961$	−5.14359e45	−0.301338
$962$	1.96124e45	0.113062
$963$	1.48583e46	0.842874
$964$	1.10653e45	0.0617688
$965$	−1.85251e45	−0.101762
$966$	2.96526e42	0.000160294 0
$967$	1.29856e46	0.690798	0.345399	−	0.938456i	$-0.387744\pi$
$967$	1.29856e46	0.690798	0.345399	+	0.938456i	$0.387744\pi$
$968$	−3.84849e45	−0.201475
$969$	−5.63304e42	−0.000290218 0
$970$	−8.65389e45	−0.438783
$971$	−2.83985e45	−0.141709	−0.0708545	−	0.997487i	$-0.522573\pi$
$971$	−2.83985e45	−0.141709	−0.0708545	+	0.997487i	$0.522573\pi$
$972$	4.43210e45	0.217662
$973$	7.64937e45	0.369723
$974$	−7.50541e45	−0.357035
$975$	1.98595e44	0.00929816
$976$	−1.94654e45	−0.0896998
$977$	2.71188e46	1.23000	0.614999	−	0.788528i	$-0.289156\pi$
$977$	2.71188e46	1.23000	0.614999	+	0.788528i	$0.289156\pi$
$978$	6.92798e44	0.0309282
$979$	1.84615e46	0.811214
$980$	6.67507e44	0.0288703
$981$	−1.14042e46	−0.485508
$982$	1.45293e46	0.608858
$983$	3.99445e46	1.64770	0.823850	−	0.566808i	$-0.191822\pi$
$983$	3.99445e46	1.64770	0.823850	+	0.566808i	$0.191822\pi$
$984$	−1.90024e45	−0.0771587
$985$	−2.00866e46	−0.802869
$986$	1.27726e46	0.502560
$987$	3.35906e45	0.130107
$988$	1.11482e43	0.000425082 0
$989$	−1.31146e43	−0.000492279 0
$990$	−5.48692e45	−0.202760
$991$	4.15190e46	1.51045	0.755223	−	0.655468i	$-0.227528\pi$
$991$	4.15190e46	1.51045	0.755223	+	0.655468i	$0.227528\pi$
$992$	−4.12562e45	−0.147761
$993$	−1.60397e45	−0.0565566
$994$	−2.81164e46	−0.976046
$995$	8.53197e45	0.291603
$996$	−5.53660e44	−0.0186305
$997$	−2.30150e46	−0.762493	−0.381247	−	0.924473i	$-0.624505\pi$
$997$	−2.30150e46	−0.762493	−0.381247	+	0.924473i	$0.624505\pi$
$998$	−2.96801e45	−0.0968150
$999$	−4.73591e45	−0.152103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.32.a.c.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.32.a.c.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:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+32768.0 q^{2} +3.71657e6 q^{3} +1.07374e9 q^{4} -3.05176e10 q^{5} +1.21785e11 q^{6} +1.17220e13 q^{7} +3.51844e13 q^{8} -6.03860e14 q^{9} -1.00000e15 q^{10} -9.08641e15 q^{11} +3.99064e15 q^{12} +5.73754e16 q^{13} +3.84106e17 q^{14} -1.13421e17 q^{15} +1.15292e18 q^{16} -8.37569e18 q^{17} -1.97873e19 q^{18} +1.80959e17 q^{19} -3.27680e19 q^{20} +4.35656e19 q^{21} -2.97743e20 q^{22} +2.07716e18 q^{23} +1.30765e20 q^{24} +9.31323e20 q^{25} +1.88008e21 q^{26} -4.53992e21 q^{27} +1.25864e22 q^{28} -4.65382e22 q^{29} -3.71657e21 q^{30} -1.09204e23 q^{31} +3.77789e22 q^{32} -3.37703e22 q^{33} -2.74455e23 q^{34} -3.57726e23 q^{35} -6.48390e23 q^{36} +1.04317e24 q^{37} +5.92966e21 q^{38} +2.13240e23 q^{39} -1.07374e24 q^{40} -1.45317e25 q^{41} +1.42756e24 q^{42} -6.31370e24 q^{43} -9.75646e24 q^{44} +1.84284e25 q^{45} +6.80644e22 q^{46} +7.71035e25 q^{47} +4.28492e24 q^{48} -2.03707e25 q^{49} +3.05176e25 q^{50} -3.11289e25 q^{51} +6.16064e25 q^{52} +2.22654e25 q^{53} -1.48764e26 q^{54} +2.77295e26 q^{55} +4.12430e26 q^{56} +6.72547e23 q^{57} -1.52496e27 q^{58} -4.61858e27 q^{59} -1.21785e26 q^{60} -1.68836e27 q^{61} -3.57841e27 q^{62} -7.07844e27 q^{63} +1.23794e27 q^{64} -1.75096e27 q^{65} -1.10658e27 q^{66} -2.09314e28 q^{67} -8.99333e27 q^{68} +7.71992e24 q^{69} -1.17220e28 q^{70} -7.31996e28 q^{71} -2.12465e28 q^{72} -1.79728e28 q^{73} +3.41826e28 q^{74} +3.46133e27 q^{75} +1.94303e26 q^{76} -1.06511e29 q^{77} +6.98744e27 q^{78} -3.55437e29 q^{79} -3.51844e28 q^{80} +3.56116e29 q^{81} -4.76175e29 q^{82} -1.38740e29 q^{83} +4.67782e28 q^{84} +2.55606e29 q^{85} -2.06887e29 q^{86} -1.72963e29 q^{87} -3.19700e29 q^{88} -2.03177e30 q^{89} +6.03860e29 q^{90} +6.72553e29 q^{91} +2.23033e27 q^{92} -4.05866e29 q^{93} +2.52653e30 q^{94} -5.52243e27 q^{95} +1.40408e29 q^{96} +8.65389e30 q^{97} -6.67507e29 q^{98} +5.48692e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 65536 q^{2} + 38938356 q^{3} + 2147483648 q^{4} - 61035156250 q^{5} + 1275932049408 q^{6} - 12036181345412 q^{7} + 70368744177664 q^{8} + 19040152114674 q^{9} - 20\!\cdots\!00 q^{10} - 39\!\cdots\!76 q^{11}+ \cdots + 86\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 65536 * q^2 + 38938356 * q^3 + 2147483648 * q^4 - 61035156250 * q^5 + 1275932049408 * q^6 - 12036181345412 * q^7 + 70368744177664 * q^8 + 19040152114674 * q^9 - 2000000000000000 * q^10 - 3988310318131776 * q^11 + 41809741395001344 * q^12 + 5813344460168596 * q^13 - 394401590326460416 * q^14 - 1188304321289062500 * q^15 + 2305843009213693952 * q^16 - 90808009705448652 * q^17 + 623907704493637632 * q^18 - 91080908739917057240 * q^19 - 65536000000000000000 * q^20 - 793239032282232341736 * q^21 - 130688952504542035968 * q^22 - 1667218224785847749964 * q^23 + 1370021606031404040192 * q^24 + 1862645149230957031250 * q^25 + 190491671270804553728 * q^26 - 4355806467630589185960 * q^27 - 12923751311817454911488 * q^28 - 94542828968363917878660 * q^29 - 38938356000000000000000 * q^30 - 128556968709873879790136 * q^31 + 75557863725914323419136 * q^32 + 145793762653453115916672 * q^33 - 2975596862028141428736 * q^34 + 367315104535278320312500 * q^35 + 20444207660847517925376 * q^36 - 2173120219461033185894732 * q^37 - 2984539217589602131640320 * q^38 - 1602867367214468925211512 * q^39 - 2147483648000000000000000 * q^40 - 10052341805841246213464916 * q^41 - 25992856609824189374005248 * q^42 + 10573141555224439188182116 * q^43 - 4282415595668833434599424 * q^44 - 581059329671447753906250 * q^45 - 54631406789782659070820352 * q^46 + 10390087245625542339131628 * q^47 + 44892867986437047589011456 * q^48 + 386303842774363980974316186 * q^49 + 61035156250000000000000000 * q^50 + 260679444017387780945734344 * q^51 + 6242031084201723616559104 * q^52 + 152846908077155422032107556 * q^53 - 142731066331319146445537280 * q^54 + 121713571720330078125000000 * q^55 - 423485482985634362539638784 * q^56 - 3213733198820989874995361520 * q^57 - 3097979419635348861047930880 * q^58 - 415231068507816075649147320 * q^59 - 1275932049408000000000000000 * q^60 - 10889372056215660723252719276 * q^61 - 4212554750685147292963176448 * q^62 - 21877406788274198968709510244 * q^63 + 2475880078570760549798248448 * q^64 - 177409193730731079101562500 * q^65 + 4777370014628351702357508096 * q^66 - 28480585995522502006916180852 * q^67 - 97504357974938138336821248 * q^68 - 58787840740996590120684814392 * q^69 + 12036181345412000000000000000 * q^70 - 50662232682174152543673482856 * q^71 + 669915796630651467378720768 * q^72 - 145372300926122387103956465564 * q^73 - 71208803351299135435398578176 * q^74 + 36264169961214065551757812500 * q^75 - 97797381081976082649590005760 * q^76 - 227631991648685526547205199744 * q^77 - 52522757888883717741330825216 * q^78 - 417326479480114326874443862160 * q^79 - 70368744177664000000000000000 * q^80 - 22148754802181045414258949558 * q^81 - 329395136293805955922818367488 * q^82 + 811040305513138169074221560676 * q^83 - 851733925390719037407403966464 * q^84 + 2771240530561787475585937500 * q^85 + 346460702481594423318351577088 * q^86 - 1863770506411185563582357839080 * q^87 - 140326194238876333984953925632 * q^88 + 434708332312346165366301452820 * q^89 - 19040152114674000000000000000 * q^90 + 1897571850361405527969264574424 * q^91 - 1790161937687598172432641294336 * q^92 - 1087500615621162675752907346608 * q^93 + 340462378864657771368665186304 * q^94 + 2779568748166414100341796875000 * q^95 + 1471049498179569175396727390208 * q^96 + 3538409289032585817785792346628 * q^97 + 12658404320030358928566392782848 * q^98 + 8662529629256392933545213540288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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