LMFDB - Embedded newform 10.32.a.c.1.2

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			1.2
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)

$f(q)$	$=$	\(q+32768.0 q^{2} +3.52218e7 q^{3} +1.07374e9 q^{4} -3.05176e10 q^{5} +1.15415e12 q^{6} -2.37582e13 q^{7} +3.51844e13 q^{8} +6.22901e14 q^{9} -1.00000e15 q^{10} +5.09810e15 q^{11} +3.78191e16 q^{12} -5.15620e16 q^{13} -7.78507e17 q^{14} -1.07488e18 q^{15} +1.15292e18 q^{16} +8.28488e18 q^{17} +2.04112e19 q^{18} -9.12619e19 q^{19} -3.27680e19 q^{20} -8.36805e20 q^{21} +1.67054e20 q^{22} -1.66930e21 q^{23} +1.23926e21 q^{24} +9.31323e20 q^{25} -1.68959e21 q^{26} +1.84113e20 q^{27} -2.55101e22 q^{28} -4.80046e22 q^{29} -3.52218e22 q^{30} -1.93527e22 q^{31} +3.77789e22 q^{32} +1.79564e23 q^{33} +2.71479e23 q^{34} +7.25041e23 q^{35} +6.68834e23 q^{36} -3.21629e24 q^{37} -2.99047e24 q^{38} -1.81611e24 q^{39} -1.07374e24 q^{40} +4.47937e24 q^{41} -2.74204e25 q^{42} +1.68868e25 q^{43} +5.47404e24 q^{44} -1.90094e25 q^{45} -5.46995e25 q^{46} -6.67134e25 q^{47} +4.06080e25 q^{48} +4.06675e26 q^{49} +3.05176e25 q^{50} +2.91808e26 q^{51} -5.53643e25 q^{52} +1.30582e26 q^{53} +6.03301e24 q^{54} -1.55582e26 q^{55} -8.35916e26 q^{56} -3.21441e27 q^{57} -1.57301e27 q^{58} +4.20335e27 q^{59} -1.15415e27 q^{60} -9.20102e27 q^{61} -6.34148e26 q^{62} -1.47990e28 q^{63} +1.23794e27 q^{64} +1.57355e27 q^{65} +5.88395e27 q^{66} -7.54919e27 q^{67} +8.89582e27 q^{68} -5.87956e28 q^{69} +2.37582e28 q^{70} +2.25373e28 q^{71} +2.19164e28 q^{72} -1.27400e29 q^{73} -1.05391e29 q^{74} +3.28028e28 q^{75} -9.79917e28 q^{76} -1.21121e29 q^{77} -5.95102e28 q^{78} -6.18893e28 q^{79} -3.51844e28 q^{80} -3.78264e29 q^{81} +1.46780e29 q^{82} +9.49780e29 q^{83} -8.98512e29 q^{84} -2.52835e29 q^{85} +5.53348e29 q^{86} -1.69081e30 q^{87} +1.79373e29 q^{88} +2.46648e30 q^{89} -6.22901e29 q^{90} +1.22502e30 q^{91} -1.79239e30 q^{92} -6.81635e29 q^{93} -2.18606e30 q^{94} +2.78509e30 q^{95} +1.33064e30 q^{96} -5.11548e30 q^{97} +1.33259e31 q^{98} +3.17561e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.52218e7	1.41720	0.708601	−	0.705609i	$-0.249327\pi$
$3$	3.52218e7	1.41720	0.708601	+	0.705609i	$0.249327\pi$
$4$	1.07374e9	0.500000
$5$	−3.05176e10	−0.447214
$5$	−3.05176e10	−0.447214
$6$	1.15415e12	1.00211
$7$	−2.37582e13	−1.89144	−0.945721	−	0.324979i	$-0.894643\pi$
$7$	−2.37582e13	−1.89144	−0.945721	+	0.324979i	$0.894643\pi$
$8$	3.51844e13	0.353553
$9$	6.22901e14	1.00846
$10$	−1.00000e15	−0.316228
$11$	5.09810e15	0.367978	0.183989	−	0.982928i	$-0.441099\pi$
$11$	5.09810e15	0.367978	0.183989	+	0.982928i	$0.441099\pi$
$12$	3.78191e16	0.708601
$13$	−5.15620e16	−0.279388	−0.139694	−	0.990195i	$-0.544612\pi$
$13$	−5.15620e16	−0.279388	−0.139694	+	0.990195i	$0.544612\pi$
$14$	−7.78507e17	−1.33745
$15$	−1.07488e18	−0.633792
$16$	1.15292e18	0.250000
$17$	8.28488e18	0.701985	0.350993	−	0.936378i	$-0.385844\pi$
$17$	8.28488e18	0.701985	0.350993	+	0.936378i	$0.385844\pi$
$18$	2.04112e19	0.713091
$19$	−9.12619e19	−1.37914	−0.689570	−	0.724219i	$-0.742201\pi$
$19$	−9.12619e19	−1.37914	−0.689570	+	0.724219i	$0.742201\pi$
$20$	−3.27680e19	−0.223607
$21$	−8.36805e20	−2.68056
$22$	1.67054e20	0.260199
$23$	−1.66930e21	−1.30542	−0.652712	−	0.757606i	$-0.726369\pi$
$23$	−1.66930e21	−1.30542	−0.652712	+	0.757606i	$0.726369\pi$
$24$	1.23926e21	0.501057
$25$	9.31323e20	0.200000
$26$	−1.68959e21	−0.197557
$27$	1.84113e20	0.0119935
$28$	−2.55101e22	−0.945721
$29$	−4.80046e22	−1.03303	−0.516516	−	0.856277i	$-0.672771\pi$
$29$	−4.80046e22	−1.03303	−0.516516	+	0.856277i	$0.672771\pi$
$30$	−3.52218e22	−0.448159
$31$	−1.93527e22	−0.148127	−0.0740635	−	0.997254i	$-0.523597\pi$
$31$	−1.93527e22	−0.148127	−0.0740635	+	0.997254i	$0.523597\pi$
$32$	3.77789e22	0.176777
$33$	1.79564e23	0.521499
$34$	2.71479e23	0.496379
$35$	7.25041e23	0.845879
$36$	6.68834e23	0.504231
$37$	−3.21629e24	−1.58573	−0.792864	−	0.609399i	$-0.791411\pi$
$37$	−3.21629e24	−1.58573	−0.792864	+	0.609399i	$0.791411\pi$
$38$	−2.99047e24	−0.975200
$39$	−1.81611e24	−0.395950
$40$	−1.07374e24	−0.158114
$41$	4.47937e24	0.449849	0.224925	−	0.974376i	$-0.427786\pi$
$41$	4.47937e24	0.449849	0.224925	+	0.974376i	$0.427786\pi$
$42$	−2.74204e25	−1.89544
$43$	1.68868e25	0.810564	0.405282	−	0.914192i	$-0.367173\pi$
$43$	1.68868e25	0.810564	0.405282	+	0.914192i	$0.367173\pi$
$44$	5.47404e24	0.183989
$45$	−1.90094e25	−0.450998
$46$	−5.46995e25	−0.923074
$47$	−6.67134e25	−0.806671	−0.403335	−	0.915052i	$-0.632149\pi$
$47$	−6.67134e25	−0.806671	−0.403335	+	0.915052i	$0.632149\pi$
$48$	4.06080e25	0.354301
$49$	4.06675e26	2.57755
$50$	3.05176e25	0.141421
$51$	2.91808e26	0.994855
$52$	−5.53643e25	−0.139694
$53$	1.30582e26	0.245248	0.122624	−	0.992453i	$-0.460869\pi$
$53$	1.30582e26	0.245248	0.122624	+	0.992453i	$0.460869\pi$
$54$	6.03301e24	0.00848068
$55$	−1.55582e26	−0.164565
$56$	−8.35916e26	−0.668726
$57$	−3.21441e27	−1.95452
$58$	−1.57301e27	−0.730464
$59$	4.20335e27	1.49758	0.748789	−	0.662809i	$-0.230636\pi$
$59$	4.20335e27	1.49758	0.748789	+	0.662809i	$0.230636\pi$
$60$	−1.15415e27	−0.316896
$61$	−9.20102e27	−1.95534	−0.977672	−	0.210135i	$-0.932610\pi$
$61$	−9.20102e27	−1.95534	−0.977672	+	0.210135i	$0.932610\pi$
$62$	−6.34148e26	−0.104742
$63$	−1.47990e28	−1.90745
$64$	1.23794e27	0.125000
$65$	1.57355e27	0.124946
$66$	5.88395e27	0.368755
$67$	−7.54919e27	−0.374750	−0.187375	−	0.982288i	$-0.559998\pi$
$67$	−7.54919e27	−0.374750	−0.187375	+	0.982288i	$0.559998\pi$
$68$	8.89582e27	0.350993
$69$	−5.87956e28	−1.85005
$70$	2.37582e28	0.598127
$71$	2.25373e28	0.455406	0.227703	−	0.973731i	$-0.426879\pi$
$71$	2.25373e28	0.455406	0.227703	+	0.973731i	$0.426879\pi$
$72$	2.19164e28	0.356545
$73$	−1.27400e29	−1.67365	−0.836823	−	0.547474i	$-0.815590\pi$
$73$	−1.27400e29	−1.67365	−0.836823	+	0.547474i	$0.815590\pi$
$74$	−1.05391e29	−1.12128
$75$	3.28028e28	0.283440
$76$	−9.79917e28	−0.689570
$77$	−1.21121e29	−0.696008
$78$	−5.95102e28	−0.279979
$79$	−6.18893e28	−0.238999	−0.119499	−	0.992834i	$-0.538129\pi$
$79$	−6.18893e28	−0.238999	−0.119499	+	0.992834i	$0.538129\pi$
$80$	−3.51844e28	−0.111803
$81$	−3.78264e29	−0.991466
$82$	1.46780e29	0.318091
$83$	9.49780e29	1.70574	0.852870	−	0.522124i	$-0.174860\pi$
$83$	9.49780e29	1.70574	0.852870	+	0.522124i	$0.174860\pi$
$84$	−8.98512e29	−1.34028
$85$	−2.52835e29	−0.313937
$86$	5.53348e29	0.573155
$87$	−1.69081e30	−1.46402
$88$	1.79373e29	0.130100
$89$	2.46648e30	1.50153	0.750763	−	0.660572i	$-0.229686\pi$
$89$	2.46648e30	1.50153	0.750763	+	0.660572i	$0.229686\pi$
$90$	−6.22901e29	−0.318904
$91$	1.22502e30	0.528447
$92$	−1.79239e30	−0.652712
$93$	−6.81635e29	−0.209926
$94$	−2.18606e30	−0.570402
$95$	2.78509e30	0.616770
$96$	1.33064e30	0.250528
$97$	−5.11548e30	−0.820210	−0.410105	−	0.912038i	$-0.634508\pi$
$97$	−5.11548e30	−0.820210	−0.410105	+	0.912038i	$0.634508\pi$
$98$	1.33259e31	1.82261
$99$	3.17561e30	0.371092
$100$	1.00000e30	0.100000
$101$	2.57238e30	0.220473	0.110236	−	0.993905i	$-0.464839\pi$
$101$	2.57238e30	0.220473	0.110236	+	0.993905i	$0.464839\pi$
$102$	9.56197e30	0.703469
$103$	4.46866e30	0.282618	0.141309	−	0.989966i	$-0.454869\pi$
$103$	4.46866e30	0.282618	0.141309	+	0.989966i	$0.454869\pi$
$104$	−1.81418e30	−0.0987787
$105$	2.55372e31	1.19878
$106$	4.27890e30	0.173417
$107$	3.84053e31	1.34568	0.672842	−	0.739787i	$-0.265074\pi$
$107$	3.84053e31	1.34568	0.672842	+	0.739787i	$0.265074\pi$
$108$	1.97690e29	0.00599674
$109$	6.21983e31	1.63556	0.817782	−	0.575528i	$-0.195203\pi$
$109$	6.21983e31	1.63556	0.817782	+	0.575528i	$0.195203\pi$
$110$	−5.09810e30	−0.116365
$111$	−1.13284e32	−2.24730
$112$	−2.73913e31	−0.472861
$113$	6.41034e31	0.964195	0.482098	−	0.876118i	$-0.339875\pi$
$113$	6.41034e31	0.964195	0.482098	+	0.876118i	$0.339875\pi$
$114$	−1.05330e32	−1.38206
$115$	5.09429e31	0.583804
$116$	−5.15446e31	−0.516516
$117$	−3.21180e31	−0.281753
$118$	1.37735e32	1.05895
$119$	−1.96833e32	−1.32776
$120$	−3.78191e31	−0.224079
$121$	−1.65953e32	−0.864592
$122$	−3.01499e32	−1.38264
$123$	1.57771e32	0.637527
$124$	−2.07797e31	−0.0740635
$125$	−2.84217e31	−0.0894427
$126$	−4.84933e32	−1.34877
$127$	−5.60613e31	−0.137945	−0.0689724	−	0.997619i	$-0.521972\pi$
$127$	−5.60613e31	−0.137945	−0.0689724	+	0.997619i	$0.521972\pi$
$128$	4.05648e31	0.0883883
$129$	5.94785e32	1.14873
$130$	5.15620e31	0.0883503
$131$	−1.33520e32	−0.203161	−0.101580	−	0.994827i	$-0.532390\pi$
$131$	−1.33520e32	−0.203161	−0.101580	+	0.994827i	$0.532390\pi$
$132$	1.92805e32	0.260749
$133$	2.16821e33	2.60856
$134$	−2.47372e32	−0.264988
$135$	−5.61868e30	−0.00536365
$136$	2.91498e32	0.248189
$137$	−1.94615e33	−1.47913	−0.739566	−	0.673084i	$-0.764969\pi$
$137$	−1.94615e33	−1.47913	−0.739566	+	0.673084i	$0.764969\pi$
$138$	−1.92661e33	−1.30818
$139$	−2.95518e33	−1.79413	−0.897066	−	0.441896i	$-0.854306\pi$
$139$	−2.95518e33	−1.79413	−0.897066	+	0.441896i	$0.854306\pi$
$140$	7.78507e32	0.422939
$141$	−2.34976e33	−1.14322
$142$	7.38504e32	0.322020
$143$	−2.62868e32	−0.102809
$144$	7.18156e32	0.252116
$145$	1.46498e33	0.461986
$146$	−4.17463e33	−1.18345
$147$	1.43238e34	3.65292
$148$	−3.45347e33	−0.792864
$149$	3.80120e33	0.786200	0.393100	−	0.919496i	$-0.371403\pi$
$149$	3.80120e33	0.786200	0.393100	+	0.919496i	$0.371403\pi$
$150$	1.07488e33	0.200423
$151$	1.03876e34	1.74733	0.873664	−	0.486530i	$-0.161738\pi$
$151$	1.03876e34	1.74733	0.873664	+	0.486530i	$0.161738\pi$
$152$	−3.21099e33	−0.487600
$153$	5.16066e33	0.707926
$154$	−3.96891e33	−0.492152
$155$	5.90596e32	0.0662444
$156$	−1.95003e33	−0.197975
$157$	2.74241e33	0.252167	0.126083	−	0.992020i	$-0.459759\pi$
$157$	2.74241e33	0.252167	0.126083	+	0.992020i	$0.459759\pi$
$158$	−2.02799e33	−0.168998
$159$	4.59931e33	0.347566
$160$	−1.15292e33	−0.0790569
$161$	3.96594e34	2.46913
$162$	−1.23950e34	−0.701072
$163$	−2.69586e34	−1.38608	−0.693042	−	0.720897i	$-0.743730\pi$
$163$	−2.69586e34	−1.38608	−0.693042	+	0.720897i	$0.743730\pi$
$164$	4.80968e33	0.224925
$165$	−5.47986e33	−0.233221
$166$	3.11224e34	1.20614
$167$	−4.10368e33	−0.144900	−0.0724499	−	0.997372i	$-0.523082\pi$
$167$	−4.10368e33	−0.144900	−0.0724499	+	0.997372i	$0.523082\pi$
$168$	−2.94424e34	−0.947720
$169$	−3.14013e34	−0.921942
$170$	−8.28488e33	−0.221987
$171$	−5.68471e34	−1.39081
$172$	1.81321e34	0.405282
$173$	−2.91818e34	−0.596207	−0.298104	−	0.954534i	$-0.596354\pi$
$173$	−2.91818e34	−0.596207	−0.298104	+	0.954534i	$0.596354\pi$
$174$	−5.54044e34	−1.03522
$175$	−2.21265e34	−0.378288
$176$	5.87771e33	0.0919944
$177$	1.48049e35	2.12237
$178$	8.08216e34	1.06174
$179$	−5.46911e34	−0.658710	−0.329355	−	0.944206i	$-0.606831\pi$
$179$	−5.46911e34	−0.658710	−0.329355	+	0.944206i	$0.606831\pi$
$180$	−2.04112e34	−0.225499
$181$	−2.13974e34	−0.216942	−0.108471	−	0.994100i	$-0.534595\pi$
$181$	−2.13974e34	−0.216942	−0.108471	+	0.994100i	$0.534595\pi$
$182$	4.01414e34	0.373668
$183$	−3.24076e35	−2.77112
$184$	−5.87331e34	−0.461537
$185$	9.81534e34	0.709159
$186$	−2.23358e34	−0.148440
$187$	4.22371e34	0.258315
$188$	−7.16330e34	−0.403335
$189$	−4.37418e33	−0.0226850
$190$	9.12619e34	0.436123
$191$	−2.65145e35	−1.16806	−0.584032	−	0.811731i	$-0.698526\pi$
$191$	−2.65145e35	−1.16806	−0.584032	+	0.811731i	$0.698526\pi$
$192$	4.36025e34	0.177150
$193$	4.63721e34	0.173827	0.0869137	−	0.996216i	$-0.472300\pi$
$193$	4.63721e34	0.173827	0.0869137	+	0.996216i	$0.472300\pi$
$194$	−1.67624e35	−0.579976
$195$	5.54232e34	0.177074
$196$	4.36663e35	1.28878
$197$	4.99825e35	1.36330	0.681650	−	0.731679i	$-0.261263\pi$
$197$	4.99825e35	1.36330	0.681650	+	0.731679i	$0.261263\pi$
$198$	1.04058e35	0.262402
$199$	4.32129e35	1.00784	0.503918	−	0.863751i	$-0.331891\pi$
$199$	4.32129e35	1.00784	0.503918	+	0.863751i	$0.331891\pi$
$200$	3.27680e34	0.0707107
$201$	−2.65896e35	−0.531096
$202$	8.42919e34	0.155898
$203$	1.14050e36	1.95392
$204$	3.13327e35	0.497428
$205$	−1.36699e35	−0.201179
$206$	1.46429e35	0.199841
$207$	−1.03981e36	−1.31647
$208$	−5.94470e34	−0.0698471
$209$	−4.65262e35	−0.507493
$210$	8.36805e35	0.847666
$211$	−1.53179e36	−1.44152	−0.720762	−	0.693183i	$-0.756208\pi$
$211$	−1.53179e36	−1.44152	−0.720762	+	0.693183i	$0.756208\pi$
$212$	1.40211e35	0.122624
$213$	7.93806e35	0.645402
$214$	1.25847e36	0.951542
$215$	−5.15345e35	−0.362495
$216$	6.47789e33	0.00424034
$217$	4.59783e35	0.280174
$218$	2.03811e36	1.15652
$219$	−4.48724e36	−2.37189
$220$	−1.67054e35	−0.0822823
$221$	−4.27185e35	−0.196126
$222$	−3.71207e36	−1.58908
$223$	−3.72672e35	−0.148799	−0.0743996	−	0.997229i	$-0.523704\pi$
$223$	−3.72672e35	−0.148799	−0.0743996	+	0.997229i	$0.523704\pi$
$224$	−8.97558e35	−0.334363
$225$	5.80121e35	0.201693
$226$	2.10054e36	0.681789
$227$	4.30873e36	1.30602	0.653009	−	0.757350i	$-0.273507\pi$
$227$	4.30873e36	1.30602	0.653009	+	0.757350i	$0.273507\pi$
$228$	−3.45144e36	−0.977261
$229$	3.47204e36	0.918617	0.459308	−	0.888277i	$-0.348097\pi$
$229$	3.47204e36	0.918617	0.459308	+	0.888277i	$0.348097\pi$
$230$	1.66930e36	0.412811
$231$	−4.26611e36	−0.986385
$232$	−1.68901e36	−0.365232
$233$	2.19164e36	0.443357	0.221678	−	0.975120i	$-0.428847\pi$
$233$	2.19164e36	0.443357	0.221678	+	0.975120i	$0.428847\pi$
$234$	−1.05244e36	−0.199229
$235$	2.03593e36	0.360754
$236$	4.51331e36	0.748789
$237$	−2.17985e36	−0.338709
$238$	−6.44984e36	−0.938871
$239$	5.30459e36	0.723577	0.361788	−	0.932260i	$-0.382166\pi$
$239$	5.30459e36	0.723577	0.361788	+	0.932260i	$0.382166\pi$
$240$	−1.23926e36	−0.158448
$241$	−5.01813e36	−0.601559	−0.300779	−	0.953694i	$-0.597247\pi$
$241$	−5.01813e36	−0.601559	−0.300779	+	0.953694i	$0.597247\pi$
$242$	−5.43794e36	−0.611359
$243$	−1.34369e37	−1.41710
$244$	−9.87952e36	−0.977672
$245$	−1.24107e37	−1.15272
$246$	5.16985e36	0.450800
$247$	4.70565e36	0.385316
$248$	−6.80911e35	−0.0523708
$249$	3.34529e37	2.41738
$250$	−9.31323e35	−0.0632456
$251$	1.63154e37	1.04149	0.520746	−	0.853711i	$-0.325654\pi$
$251$	1.63154e37	1.04149	0.520746	+	0.853711i	$0.325654\pi$
$252$	−1.58903e37	−0.953725
$253$	−8.51023e36	−0.480367
$254$	−1.83702e36	−0.0975417
$255$	−8.90528e36	−0.444913
$256$	1.32923e36	0.0625000
$257$	−8.95801e36	−0.396505	−0.198252	−	0.980151i	$-0.563527\pi$
$257$	−8.95801e36	−0.396505	−0.198252	+	0.980151i	$0.563527\pi$
$258$	1.94899e37	0.812277
$259$	7.64131e37	2.99931
$260$	1.68959e36	0.0624731
$261$	−2.99021e37	−1.04177
$262$	−4.37517e36	−0.143656
$263$	7.96914e36	0.246659	0.123330	−	0.992366i	$-0.460643\pi$
$263$	7.96914e36	0.246659	0.123330	+	0.992366i	$0.460643\pi$
$264$	6.31785e36	0.184378
$265$	−3.98503e36	−0.109678
$266$	7.10480e37	1.84453
$267$	8.68738e37	2.12797
$268$	−8.10589e36	−0.187375
$269$	−4.48887e37	−0.979438	−0.489719	−	0.871880i	$-0.662901\pi$
$269$	−4.48887e37	−0.979438	−0.489719	+	0.871880i	$0.662901\pi$
$270$	−1.84113e35	−0.00379267
$271$	2.62953e37	0.511510	0.255755	−	0.966742i	$-0.417676\pi$
$271$	2.62953e37	0.511510	0.255755	+	0.966742i	$0.417676\pi$
$272$	9.55182e36	0.175496
$273$	4.31474e37	0.748916
$274$	−6.37713e37	−1.04590
$275$	4.74797e36	0.0735955
$276$	−6.31313e37	−0.925025
$277$	−5.64561e37	−0.782121	−0.391061	−	0.920365i	$-0.627892\pi$
$277$	−5.64561e37	−0.782121	−0.391061	+	0.920365i	$0.627892\pi$
$278$	−9.68353e37	−1.26864
$279$	−1.20548e37	−0.149381
$280$	2.55101e37	0.299063
$281$	−4.23820e37	−0.470147	−0.235073	−	0.971978i	$-0.575533\pi$
$281$	−4.23820e37	−0.470147	−0.235073	+	0.971978i	$0.575533\pi$
$282$	−7.69971e37	−0.808375
$283$	−9.68555e37	−0.962575	−0.481288	−	0.876563i	$-0.659831\pi$
$283$	−9.68555e37	−0.962575	−0.481288	+	0.876563i	$0.659831\pi$
$284$	2.41993e37	0.227703
$285$	9.80959e37	0.874089
$286$	−8.61367e36	−0.0726967
$287$	−1.06422e38	−0.850864
$288$	2.35325e37	0.178273
$289$	−7.06497e37	−0.507217
$290$	4.80046e37	0.326674
$291$	−1.80176e38	−1.16240
$292$	−1.36794e38	−0.836823
$293$	−1.59243e37	−0.0923875	−0.0461938	−	0.998932i	$-0.514709\pi$
$293$	−1.59243e37	−0.0923875	−0.0461938	+	0.998932i	$0.514709\pi$
$294$	4.69362e38	2.58300
$295$	−1.28276e38	−0.669737
$296$	−1.13163e38	−0.560639
$297$	9.38625e35	0.00441334
$298$	1.24558e38	0.555927
$299$	8.60723e37	0.364720
$300$	3.52218e37	0.141720
$301$	−4.01200e38	−1.53313
$302$	3.40382e38	1.23555
$303$	9.06040e37	0.312454
$304$	−1.05218e38	−0.344785
$305$	2.80793e38	0.874457
$306$	1.69104e38	0.500579
$307$	−2.31161e38	−0.650534	−0.325267	−	0.945622i	$-0.605454\pi$
$307$	−2.31161e38	−0.650534	−0.325267	+	0.945622i	$0.605454\pi$
$308$	−1.30053e38	−0.348004
$309$	1.57394e38	0.400527
$310$	1.93527e37	0.0468419
$311$	−1.66317e38	−0.382958	−0.191479	−	0.981497i	$-0.561328\pi$
$311$	−1.66317e38	−0.382958	−0.191479	+	0.981497i	$0.561328\pi$
$312$	−6.38986e37	−0.139989
$313$	−3.64676e38	−0.760273	−0.380137	−	0.924930i	$-0.624123\pi$
$313$	−3.64676e38	−0.760273	−0.380137	+	0.924930i	$0.624123\pi$
$314$	8.98633e37	0.178309
$315$	4.51629e38	0.853037
$316$	−6.64531e37	−0.119499
$317$	−4.36541e38	−0.747491	−0.373746	−	0.927531i	$-0.621927\pi$
$317$	−4.36541e38	−0.747491	−0.373746	+	0.927531i	$0.621927\pi$
$318$	1.50710e38	0.245767
$319$	−2.44732e38	−0.380133
$320$	−3.77789e37	−0.0559017
$321$	1.35270e39	1.90711
$322$	1.29956e39	1.74594
$323$	−7.56094e38	−0.968136
$324$	−4.06158e38	−0.495733
$325$	−4.80209e37	−0.0558777
$326$	−8.83379e38	−0.980109
$327$	2.19073e39	2.31793
$328$	1.57604e38	0.159046
$329$	1.58499e39	1.52577
$330$	−1.79564e38	−0.164912
$331$	6.98680e37	0.0612272	0.0306136	−	0.999531i	$-0.490254\pi$
$331$	6.98680e37	0.0612272	0.0306136	+	0.999531i	$0.490254\pi$
$332$	1.01982e39	0.852870
$333$	−2.00343e39	−1.59915
$334$	−1.34469e38	−0.102460
$335$	2.30383e38	0.167593
$336$	−9.64770e38	−0.670139
$337$	−1.85035e38	−0.122741	−0.0613706	−	0.998115i	$-0.519547\pi$
$337$	−1.85035e38	−0.122741	−0.0613706	+	0.998115i	$0.519547\pi$
$338$	−1.02896e39	−0.651912
$339$	2.25783e39	1.36646
$340$	−2.71479e38	−0.156969
$341$	−9.86617e37	−0.0545074
$342$	−1.86276e39	−0.983453
$343$	−5.91339e39	−2.98385
$344$	5.94153e38	0.286578
$345$	1.79430e39	0.827368
$346$	−9.56228e38	−0.421582
$347$	−1.68391e39	−0.709922	−0.354961	−	0.934881i	$-0.615506\pi$
$347$	−1.68391e39	−0.709922	−0.354961	+	0.934881i	$0.615506\pi$
$348$	−1.81549e39	−0.732008
$349$	1.83783e39	0.708778	0.354389	−	0.935098i	$-0.384689\pi$
$349$	1.83783e39	0.708778	0.354389	+	0.935098i	$0.384689\pi$
$350$	−7.25041e38	−0.267490
$351$	−9.49323e36	−0.00335084
$352$	1.92601e38	0.0650499
$353$	3.12661e39	1.01057	0.505283	−	0.862953i	$-0.331388\pi$
$353$	3.12661e39	1.01057	0.505283	+	0.862953i	$0.331388\pi$
$354$	4.85128e39	1.50074
$355$	−6.87785e38	−0.203664
$356$	2.64836e39	0.750763
$357$	−6.93283e39	−1.88171
$358$	−1.79212e39	−0.465778
$359$	3.96997e39	0.988151	0.494076	−	0.869419i	$-0.335507\pi$
$359$	3.96997e39	0.988151	0.494076	+	0.869419i	$0.335507\pi$
$360$	−6.68834e38	−0.159452
$361$	3.94986e39	0.902029
$362$	−7.01151e38	−0.153401
$363$	−5.84515e39	−1.22530
$364$	1.31535e39	0.264223
$365$	3.88793e39	0.748477
$366$	−1.06193e40	−1.95948
$367$	−2.60990e39	−0.461637	−0.230818	−	0.972997i	$-0.574140\pi$
$367$	−2.60990e39	−0.461637	−0.230818	+	0.972997i	$0.574140\pi$
$368$	−1.92457e39	−0.326356
$369$	2.79020e39	0.453656
$370$	3.21629e39	0.501451
$371$	−3.10238e39	−0.463873
$372$	−7.31900e38	−0.104963
$373$	−3.77343e38	−0.0519098	−0.0259549	−	0.999663i	$-0.508263\pi$
$373$	−3.77343e38	−0.0519098	−0.0259549	+	0.999663i	$0.508263\pi$
$374$	1.38403e39	0.182656
$375$	−1.00106e39	−0.126758
$376$	−2.34727e39	−0.285201
$377$	2.47522e39	0.288617
$378$	−1.43333e38	−0.0160407
$379$	9.19970e39	0.988248	0.494124	−	0.869391i	$-0.335489\pi$
$379$	9.19970e39	0.988248	0.494124	+	0.869391i	$0.335489\pi$
$380$	2.99047e39	0.308385
$381$	−1.97458e39	−0.195496
$382$	−8.68828e39	−0.825946
$383$	1.73092e40	1.58014	0.790070	−	0.613016i	$-0.210044\pi$
$383$	1.73092e40	1.58014	0.790070	+	0.613016i	$0.210044\pi$
$384$	1.42877e39	0.125264
$385$	3.69633e39	0.311264
$386$	1.51952e39	0.122915
$387$	1.05188e40	0.817424
$388$	−5.49271e39	−0.410105
$389$	−9.46483e39	−0.679038	−0.339519	−	0.940599i	$-0.610264\pi$
$389$	−9.46483e39	−0.679038	−0.339519	+	0.940599i	$0.610264\pi$
$390$	1.81611e39	0.125210
$391$	−1.38299e40	−0.916389
$392$	1.43086e40	0.911303
$393$	−4.70280e39	−0.287920
$394$	1.63783e40	0.963998
$395$	1.88871e39	0.106883
$396$	3.40978e39	0.185546
$397$	−1.45820e40	−0.763068	−0.381534	−	0.924355i	$-0.624604\pi$
$397$	−1.45820e40	−0.763068	−0.381534	+	0.924355i	$0.624604\pi$
$398$	1.41600e40	0.712648
$399$	7.63684e40	3.69686
$400$	1.07374e39	0.0500000
$401$	−2.92790e40	−1.31165	−0.655825	−	0.754913i	$-0.727679\pi$
$401$	−2.92790e40	−1.31165	−0.655825	+	0.754913i	$0.727679\pi$
$402$	−8.71288e39	−0.375542
$403$	9.97862e38	0.0413849
$404$	2.76208e39	0.110236
$405$	1.15437e40	0.443397
$406$	3.73719e40	1.38163
$407$	−1.63970e40	−0.583512
$408$	1.02671e40	0.351734
$409$	1.90045e40	0.626823	0.313411	−	0.949617i	$-0.398528\pi$
$409$	1.90045e40	0.626823	0.313411	+	0.949617i	$0.398528\pi$
$410$	−4.47937e39	−0.142255
$411$	−6.85468e40	−2.09623
$412$	4.79818e39	0.141309
$413$	−9.98638e40	−2.83258
$414$	−3.40723e40	−0.930886
$415$	−2.89850e40	−0.762830
$416$	−1.94796e39	−0.0493893
$417$	−1.04087e41	−2.54265
$418$	−1.52457e40	−0.358852
$419$	−1.26582e40	−0.287114	−0.143557	−	0.989642i	$-0.545854\pi$
$419$	−1.26582e40	−0.287114	−0.143557	+	0.989642i	$0.545854\pi$
$420$	2.74204e40	0.599391
$421$	4.33168e40	0.912608	0.456304	−	0.889824i	$-0.349173\pi$
$421$	4.33168e40	0.912608	0.456304	+	0.889824i	$0.349173\pi$
$422$	−5.01938e40	−1.01931
$423$	−4.15558e40	−0.813497
$424$	4.59443e39	0.0867083
$425$	7.71590e39	0.140397
$426$	2.60114e40	0.456368
$427$	2.18599e41	3.69842
$428$	4.12374e40	0.672842
$429$	−9.25869e39	−0.145701
$430$	−1.68868e40	−0.256323
$431$	−1.04557e41	−1.53093	−0.765466	−	0.643476i	$-0.777492\pi$
$431$	−1.04557e41	−1.53093	−0.765466	+	0.643476i	$0.777492\pi$
$432$	2.12268e38	0.00299837
$433$	−1.44324e41	−1.96687	−0.983434	−	0.181267i	$-0.941980\pi$
$433$	−1.44324e41	−1.96687	−0.983434	+	0.181267i	$0.941980\pi$
$434$	1.50662e40	0.198113
$435$	5.15994e40	0.654728
$436$	6.67849e40	0.817782
$437$	1.52343e41	1.80036
$438$	−1.47038e41	−1.67718
$439$	−7.72220e40	−0.850239	−0.425120	−	0.905137i	$-0.639768\pi$
$439$	−7.72220e40	−0.850239	−0.425120	+	0.905137i	$0.639768\pi$
$440$	−5.47404e39	−0.0581824
$441$	2.53318e41	2.59937
$442$	−1.39980e40	−0.138682
$443$	1.19317e41	1.14142	0.570710	−	0.821152i	$-0.306668\pi$
$443$	1.19317e41	1.14142	0.570710	+	0.821152i	$0.306668\pi$
$444$	−1.21637e41	−1.12365
$445$	−7.52710e40	−0.671502
$446$	−1.22117e40	−0.105217
$447$	1.33885e41	1.11420
$448$	−2.94112e40	−0.236430
$449$	−1.19683e41	−0.929425	−0.464713	−	0.885462i	$-0.653842\pi$
$449$	−1.19683e41	−0.929425	−0.464713	+	0.885462i	$0.653842\pi$
$450$	1.90094e40	0.142618
$451$	2.28362e40	0.165534
$452$	6.88305e40	0.482098
$453$	3.65871e41	2.47632
$454$	1.41189e41	0.923494
$455$	−3.73846e40	−0.236329
$456$	−1.13097e41	−0.691028
$457$	−1.81806e41	−1.07376	−0.536879	−	0.843659i	$-0.680397\pi$
$457$	−1.81806e41	−1.07376	−0.536879	+	0.843659i	$0.680397\pi$
$458$	1.13772e41	0.649560
$459$	1.52535e39	0.00841925
$460$	5.46995e40	0.291902
$461$	−1.75242e40	−0.0904218	−0.0452109	−	0.998977i	$-0.514396\pi$
$461$	−1.75242e40	−0.0904218	−0.0452109	+	0.998977i	$0.514396\pi$
$462$	−1.39792e41	−0.697479
$463$	−2.40699e41	−1.16137	−0.580683	−	0.814130i	$-0.697214\pi$
$463$	−2.40699e41	−1.16137	−0.580683	+	0.814130i	$0.697214\pi$
$464$	−5.53455e40	−0.258258
$465$	2.08018e40	0.0938817
$466$	7.18158e40	0.313500
$467$	−2.61745e41	−1.10527	−0.552633	−	0.833425i	$-0.686377\pi$
$467$	−2.61745e41	−1.10527	−0.552633	+	0.833425i	$0.686377\pi$
$468$	−3.44865e40	−0.140876
$469$	1.79355e41	0.708817
$470$	6.67134e40	0.255092
$471$	9.65926e40	0.357372
$472$	1.47892e41	0.529474
$473$	8.60907e40	0.298269
$474$	−7.14293e40	−0.239504
$475$	−8.49942e40	−0.275828
$476$	−2.11348e41	−0.663882
$477$	8.13393e40	0.247324
$478$	1.73821e41	0.511646
$479$	−4.66543e40	−0.132951	−0.0664755	−	0.997788i	$-0.521175\pi$
$479$	−4.66543e40	−0.132951	−0.0664755	+	0.997788i	$0.521175\pi$
$480$	−4.06080e40	−0.112040
$481$	1.65839e41	0.443034
$482$	−1.64434e41	−0.425366
$483$	1.39687e42	3.49926
$484$	−1.78191e41	−0.432296
$485$	1.56112e41	0.366809
$486$	−4.40299e41	−1.00204
$487$	3.74739e41	0.826095	0.413048	−	0.910709i	$-0.364464\pi$
$487$	3.74739e41	0.826095	0.413048	+	0.910709i	$0.364464\pi$
$488$	−3.23732e41	−0.691319
$489$	−9.49530e41	−1.96436
$490$	−4.06675e41	−0.815094
$491$	−8.31693e41	−1.61510	−0.807551	−	0.589798i	$-0.799207\pi$
$491$	−8.31693e41	−1.61510	−0.807551	+	0.589798i	$0.799207\pi$
$492$	1.69406e41	0.318764
$493$	−3.97712e41	−0.725174
$494$	1.54195e41	0.272459
$495$	−9.69119e40	−0.165957
$496$	−2.23121e40	−0.0370317
$497$	−5.35446e41	−0.861373
$498$	1.09619e42	1.70934
$499$	−1.58814e41	−0.240066	−0.120033	−	0.992770i	$-0.538300\pi$
$499$	−1.58814e41	−0.240066	−0.120033	+	0.992770i	$0.538300\pi$
$500$	−3.05176e40	−0.0447214
$501$	−1.44539e41	−0.205352
$502$	5.34624e41	0.736446
$503$	−3.58584e41	−0.478947	−0.239474	−	0.970903i	$-0.576975\pi$
$503$	−3.58584e41	−0.478947	−0.239474	+	0.970903i	$0.576975\pi$
$504$	−5.20692e41	−0.674385
$505$	−7.85030e40	−0.0985983
$506$	−2.78863e41	−0.339671
$507$	−1.10601e42	−1.30658
$508$	−6.01953e40	−0.0689724
$509$	−1.16627e42	−1.29621	−0.648105	−	0.761551i	$-0.724438\pi$
$509$	−1.16627e42	−1.29621	−0.648105	+	0.761551i	$0.724438\pi$
$510$	−2.91808e41	−0.314601
$511$	3.02678e42	3.16560
$512$	4.35561e40	0.0441942
$513$	−1.68025e40	−0.0165407
$514$	−2.93536e41	−0.280371
$515$	−1.36373e41	−0.126391
$516$	6.38645e41	0.574367
$517$	−3.40111e41	−0.296837
$518$	2.50391e42	2.12083
$519$	−1.02783e42	−0.844946
$520$	5.53643e40	0.0441752
$521$	3.39352e41	0.262824	0.131412	−	0.991328i	$-0.458049\pi$
$521$	3.39352e41	0.262824	0.131412	+	0.991328i	$0.458049\pi$
$522$	−9.79832e41	−0.736646
$523$	4.37668e41	0.319425	0.159712	−	0.987164i	$-0.448943\pi$
$523$	4.37668e41	0.319425	0.159712	+	0.987164i	$0.448943\pi$
$524$	−1.43366e41	−0.101580
$525$	−7.79335e41	−0.536111
$526$	2.61133e41	0.174414
$527$	−1.60334e41	−0.103983
$528$	2.07023e41	0.130375
$529$	1.15138e42	0.704133
$530$	−1.30582e41	−0.0775543
$531$	2.61827e42	1.51025
$532$	2.32810e42	1.30428
$533$	−2.30965e41	−0.125683
$534$	2.84668e42	1.50470
$535$	−1.17204e42	−0.601808
$536$	−2.65614e41	−0.132494
$537$	−1.92632e42	−0.933526
$538$	−1.47091e42	−0.692567
$539$	2.07327e42	0.948482
$540$	−6.03301e39	−0.00268183
$541$	−1.79457e42	−0.775178	−0.387589	−	0.921832i	$-0.626692\pi$
$541$	−1.79457e42	−0.775178	−0.387589	+	0.921832i	$0.626692\pi$
$542$	8.61645e41	0.361692
$543$	−7.53655e41	−0.307451
$544$	3.12994e41	0.124095
$545$	−1.89814e42	−0.731447
$546$	1.41385e42	0.529564
$547$	3.43685e42	1.25129	0.625644	−	0.780109i	$-0.284836\pi$
$547$	3.43685e42	1.25129	0.625644	+	0.780109i	$0.284836\pi$
$548$	−2.08966e42	−0.739566
$549$	−5.73132e42	−1.97189
$550$	1.55582e41	0.0520399
$551$	4.38099e42	1.42470
$552$	−2.06868e42	−0.654092
$553$	1.47037e42	0.452052
$554$	−1.84995e42	−0.553043
$555$	3.45714e42	1.00502
$556$	−3.17310e42	−0.897066
$557$	2.77020e42	0.761651	0.380826	−	0.924647i	$-0.375640\pi$
$557$	2.77020e42	0.761651	0.380826	+	0.924647i	$0.375640\pi$
$558$	−3.95011e41	−0.105628
$559$	−8.70720e41	−0.226462
$560$	8.35916e41	0.211470
$561$	1.48767e42	0.366085
$562$	−1.38877e42	−0.332444
$563$	2.56483e42	0.597280	0.298640	−	0.954366i	$-0.403467\pi$
$563$	2.56483e42	0.597280	0.298640	+	0.954366i	$0.403467\pi$
$564$	−2.52304e42	−0.571608
$565$	−1.95628e42	−0.431201
$566$	−3.17376e42	−0.680643
$567$	8.98686e42	1.87530
$568$	7.92962e41	0.161010
$569$	−2.92109e42	−0.577171	−0.288586	−	0.957454i	$-0.593185\pi$
$569$	−2.92109e42	−0.577171	−0.288586	+	0.957454i	$0.593185\pi$
$570$	3.21441e42	0.618074
$571$	−4.60895e42	−0.862467	−0.431234	−	0.902240i	$-0.641922\pi$
$571$	−4.60895e42	−0.862467	−0.431234	+	0.902240i	$0.641922\pi$
$572$	−2.82253e41	−0.0514043
$573$	−9.33889e42	−1.65538
$574$	−3.48722e42	−0.601652
$575$	−1.55465e42	−0.261085
$576$	7.71114e41	0.126058
$577$	−5.10320e41	−0.0812114	−0.0406057	−	0.999175i	$-0.512929\pi$
$577$	−5.10320e41	−0.0812114	−0.0406057	+	0.999175i	$0.512929\pi$
$578$	−2.31505e42	−0.358656
$579$	1.63331e42	0.246349
$580$	1.57301e42	0.230993
$581$	−2.25650e43	−3.22631
$582$	−5.90402e42	−0.821943
$583$	6.65717e41	0.0902459
$584$	−4.48247e42	−0.591723
$585$	9.80164e41	0.126004
$586$	−5.21809e41	−0.0653278
$587$	−1.10624e43	−1.34884	−0.674420	−	0.738348i	$-0.735606\pi$
$587$	−1.10624e43	−1.34884	−0.674420	+	0.738348i	$0.735606\pi$
$588$	1.53801e43	1.82646
$589$	1.76616e42	0.204288
$590$	−4.20335e42	−0.473576
$591$	1.76047e43	1.93207
$592$	−3.70813e42	−0.396432
$593$	1.06708e43	1.11134	0.555671	−	0.831402i	$-0.312461\pi$
$593$	1.06708e43	1.11134	0.555671	+	0.831402i	$0.312461\pi$
$594$	3.07569e40	0.00312070
$595$	6.00688e42	0.593794
$596$	4.08150e42	0.393100
$597$	1.52203e43	1.42831
$598$	2.82042e42	0.257896
$599$	8.59039e42	0.765415	0.382708	−	0.923869i	$-0.374992\pi$
$599$	8.59039e42	0.765415	0.382708	+	0.923869i	$0.374992\pi$
$600$	1.15415e42	0.100211
$601$	−1.50868e43	−1.27656	−0.638281	−	0.769804i	$-0.720354\pi$
$601$	−1.50868e43	−1.27656	−0.638281	+	0.769804i	$0.720354\pi$
$602$	−1.31465e43	−1.08409
$603$	−4.70240e42	−0.377921
$604$	1.11536e43	0.873664
$605$	5.06448e42	0.386657
$606$	2.96891e42	0.220939
$607$	5.07222e42	0.367937	0.183969	−	0.982932i	$-0.441106\pi$
$607$	5.07222e42	0.367937	0.183969	+	0.982932i	$0.441106\pi$
$608$	−3.44778e42	−0.243800
$609$	4.01705e43	2.76910
$610$	9.20102e42	0.618334
$611$	3.43988e42	0.225374
$612$	5.54121e42	0.353963
$613$	−1.13341e43	−0.705912	−0.352956	−	0.935640i	$-0.614823\pi$
$613$	−1.13341e43	−0.705912	−0.352956	+	0.935640i	$0.614823\pi$
$614$	−7.57469e42	−0.459997
$615$	−4.81480e42	−0.285111
$616$	−4.26158e42	−0.246076
$617$	1.98300e43	1.11661	0.558307	−	0.829634i	$-0.311451\pi$
$617$	1.98300e43	1.11661	0.558307	+	0.829634i	$0.311451\pi$
$618$	5.15749e42	0.283215
$619$	2.55689e43	1.36933	0.684664	−	0.728859i	$-0.259949\pi$
$619$	2.55689e43	1.36933	0.684664	+	0.728859i	$0.259949\pi$
$620$	6.34148e41	0.0331222
$621$	−3.07339e41	−0.0156566
$622$	−5.44988e42	−0.270792
$623$	−5.85990e43	−2.84005
$624$	−2.09383e42	−0.0989874
$625$	8.67362e41	0.0400000
$626$	−1.19497e43	−0.537594
$627$	−1.63874e43	−0.719220
$628$	2.94464e42	0.126083
$629$	−2.66466e43	−1.11316
$630$	1.47990e43	0.603188
$631$	2.34791e43	0.933740	0.466870	−	0.884326i	$-0.345382\pi$
$631$	2.34791e43	0.933740	0.466870	+	0.884326i	$0.345382\pi$
$632$	−2.17753e42	−0.0844988
$633$	−5.39524e43	−2.04293
$634$	−1.43046e43	−0.528556
$635$	1.71085e42	0.0616908
$636$	4.93848e42	0.173783
$637$	−2.09690e43	−0.720138
$638$	−8.01938e42	−0.268794
$639$	1.40385e43	0.459260
$640$	−1.23794e42	−0.0395285
$641$	1.33799e43	0.417018	0.208509	−	0.978020i	$-0.433139\pi$
$641$	1.33799e43	0.417018	0.208509	+	0.978020i	$0.433139\pi$
$642$	4.43254e43	1.34853
$643$	3.87420e43	1.15057	0.575283	−	0.817954i	$-0.304892\pi$
$643$	3.87420e43	1.15057	0.575283	+	0.817954i	$0.304892\pi$
$644$	4.25839e43	1.23457
$645$	−1.81514e43	−0.513729
$646$	−2.47757e43	−0.684576
$647$	−1.64899e43	−0.444837	−0.222418	−	0.974951i	$-0.571395\pi$
$647$	−1.64899e43	−0.444837	−0.222418	+	0.974951i	$0.571395\pi$
$648$	−1.33090e43	−0.350536
$649$	2.14291e43	0.551075
$650$	−1.57355e42	−0.0395115
$651$	1.61944e43	0.397063
$652$	−2.89466e43	−0.693042
$653$	−7.92927e43	−1.85387	−0.926935	−	0.375223i	$-0.877566\pi$
$653$	−7.92927e43	−1.85387	−0.926935	+	0.375223i	$0.877566\pi$
$654$	7.17860e43	1.63902
$655$	4.07470e42	0.0908563
$656$	5.16436e42	0.112462
$657$	−7.93573e43	−1.68781
$658$	5.19369e43	1.07888
$659$	−1.58692e43	−0.321981	−0.160990	−	0.986956i	$-0.551469\pi$
$659$	−1.58692e43	−0.321981	−0.160990	+	0.986956i	$0.551469\pi$
$660$	−5.88395e42	−0.116611
$661$	2.02729e43	0.392458	0.196229	−	0.980558i	$-0.437130\pi$
$661$	2.02729e43	0.392458	0.196229	+	0.980558i	$0.437130\pi$
$662$	2.28943e42	0.0432941
$663$	−1.50462e43	−0.277951
$664$	3.34174e43	0.603070
$665$	−6.61686e43	−1.16659
$666$	−6.56484e43	−1.13077
$667$	8.01339e43	1.34855
$668$	−4.40629e42	−0.0724499
$669$	−1.31262e43	−0.210879
$670$	7.54919e42	0.118506
$671$	−4.69077e43	−0.719523
$672$	−3.16136e43	−0.473860
$673$	1.34181e43	0.196543	0.0982715	−	0.995160i	$-0.468669\pi$
$673$	1.34181e43	0.196543	0.0982715	+	0.995160i	$0.468669\pi$
$674$	−6.06322e42	−0.0867911
$675$	1.71468e41	0.00239870
$676$	−3.37169e43	−0.460971
$677$	−8.12065e43	−1.08509	−0.542546	−	0.840026i	$-0.682539\pi$
$677$	−8.12065e43	−1.08509	−0.542546	+	0.840026i	$0.682539\pi$
$678$	7.39847e43	0.966233
$679$	1.21534e44	1.55138
$680$	−8.89582e42	−0.110994
$681$	1.51761e44	1.85089
$682$	−3.23295e42	−0.0385426
$683$	−1.40956e44	−1.64271	−0.821356	−	0.570417i	$-0.806782\pi$
$683$	−1.40956e44	−1.64271	−0.821356	+	0.570417i	$0.806782\pi$
$684$	−6.10391e43	−0.695406
$685$	5.93917e43	0.661488
$686$	−1.93770e44	−2.10990
$687$	1.22291e44	1.30187
$688$	1.94692e43	0.202641
$689$	−6.73305e42	−0.0685195
$690$	5.87956e43	0.585037
$691$	−3.41473e43	−0.332236	−0.166118	−	0.986106i	$-0.553123\pi$
$691$	−3.41473e43	−0.332236	−0.166118	+	0.986106i	$0.553123\pi$
$692$	−3.13337e43	−0.298104
$693$	−7.54466e43	−0.701899
$694$	−5.51782e43	−0.501991
$695$	9.01849e43	0.802361
$696$	−5.94900e43	−0.517608
$697$	3.71110e43	0.315788
$698$	6.02219e43	0.501182
$699$	7.71936e43	0.628326
$700$	−2.37582e43	−0.189144
$701$	2.42594e44	1.88908	0.944541	−	0.328392i	$-0.106507\pi$
$701$	2.42594e44	1.88908	0.944541	+	0.328392i	$0.106507\pi$
$702$	−3.11074e41	−0.00236940
$703$	2.93525e44	2.18694
$704$	6.31114e42	0.0459972
$705$	7.17091e43	0.511262
$706$	1.02453e44	0.714579
$707$	−6.11151e43	−0.417011
$708$	1.58967e44	1.06119
$709$	−1.05104e44	−0.686437	−0.343219	−	0.939256i	$-0.611517\pi$
$709$	−1.05104e44	−0.686437	−0.343219	+	0.939256i	$0.611517\pi$
$710$	−2.25373e43	−0.144012
$711$	−3.85509e43	−0.241021
$712$	8.67816e43	0.530869
$713$	3.23053e43	0.193369
$714$	−2.27175e44	−1.33057
$715$	8.02210e42	0.0459774
$716$	−5.87241e43	−0.329355
$717$	1.86837e44	1.02545
$718$	1.30088e44	0.698729
$719$	−1.64232e44	−0.863296	−0.431648	−	0.902042i	$-0.642068\pi$
$719$	−1.64232e44	−0.863296	−0.431648	+	0.902042i	$0.642068\pi$
$720$	−2.19164e43	−0.112750
$721$	−1.06167e44	−0.534556
$722$	1.29429e44	0.637831
$723$	−1.76748e44	−0.852530
$724$	−2.29753e43	−0.108471
$725$	−4.47078e43	−0.206606
$726$	−1.91534e44	−0.866420
$727$	−3.51233e43	−0.155529	−0.0777646	−	0.996972i	$-0.524778\pi$
$727$	−3.51233e43	−0.155529	−0.0777646	+	0.996972i	$0.524778\pi$
$728$	4.31015e43	0.186834
$729$	−2.39627e44	−1.01685
$730$	1.27400e44	0.529253
$731$	1.39905e44	0.569004
$732$	−3.47974e44	−1.38556
$733$	−2.34300e44	−0.913398	−0.456699	−	0.889621i	$-0.650968\pi$
$733$	−2.34300e44	−0.913398	−0.456699	+	0.889621i	$0.650968\pi$
$734$	−8.55213e43	−0.326426
$735$	−4.37128e44	−1.63363
$736$	−6.30642e43	−0.230769
$737$	−3.84865e43	−0.137899
$738$	9.14293e43	0.320783
$739$	2.51620e44	0.864483	0.432241	−	0.901758i	$-0.357723\pi$
$739$	2.51620e44	0.864483	0.432241	+	0.901758i	$0.357723\pi$
$740$	1.05391e44	0.354579
$741$	1.65741e44	0.546070
$742$	−1.01659e44	−0.328008
$743$	−9.07298e42	−0.0286697	−0.0143348	−	0.999897i	$-0.504563\pi$
$743$	−9.07298e42	−0.0286697	−0.0143348	+	0.999897i	$0.504563\pi$
$744$	−2.39829e43	−0.0742200
$745$	−1.16003e44	−0.351599
$746$	−1.23648e43	−0.0367058
$747$	5.91619e44	1.72017
$748$	4.53518e43	0.129157
$749$	−9.12440e44	−2.54528
$750$	−3.28028e43	−0.0896318
$751$	2.57663e44	0.689657	0.344829	−	0.938666i	$-0.387937\pi$
$751$	2.57663e44	0.689657	0.344829	+	0.938666i	$0.387937\pi$
$752$	−7.69153e43	−0.201668
$753$	5.74659e44	1.47601
$754$	8.11079e43	0.204083
$755$	−3.17006e44	−0.781429
$756$	−4.69674e42	−0.0113425
$757$	−3.81353e44	−0.902280	−0.451140	−	0.892453i	$-0.648982\pi$
$757$	−3.81353e44	−0.902280	−0.451140	+	0.892453i	$0.648982\pi$
$758$	3.01456e44	0.698797
$759$	−2.99745e44	−0.680777
$760$	9.79917e43	0.218061
$761$	8.14860e44	1.77673	0.888364	−	0.459140i	$-0.151842\pi$
$761$	8.14860e44	1.77673	0.888364	+	0.459140i	$0.151842\pi$
$762$	−6.47030e43	−0.138236
$763$	−1.47772e45	−3.09358
$764$	−2.84697e44	−0.584032
$765$	−1.57491e44	−0.316594
$766$	5.67188e44	1.11733
$767$	−2.16733e44	−0.418406
$768$	4.68178e43	0.0885752
$769$	3.27666e44	0.607538	0.303769	−	0.952746i	$-0.401755\pi$
$769$	3.27666e44	0.607538	0.303769	+	0.952746i	$0.401755\pi$
$770$	1.21121e44	0.220097
$771$	−3.15517e44	−0.561927
$772$	4.97917e43	0.0869137
$773$	4.92317e44	0.842291	0.421146	−	0.906993i	$-0.361628\pi$
$773$	4.92317e44	0.842291	0.421146	+	0.906993i	$0.361628\pi$
$774$	3.44681e44	0.578006
$775$	−1.80236e43	−0.0296254
$776$	−1.79985e44	−0.289988
$777$	2.69141e45	4.25063
$778$	−3.10144e44	−0.480152
$779$	−4.08795e44	−0.620405
$780$	5.95102e43	0.0885371
$781$	1.14898e44	0.167579
$782$	−4.53179e44	−0.647985
$783$	−8.83826e42	−0.0123897
$784$	4.68864e44	0.644388
$785$	−8.36918e43	−0.112772
$786$	−1.54101e44	−0.203590
$787$	4.15132e44	0.537747	0.268874	−	0.963175i	$-0.413349\pi$
$787$	4.15132e44	0.537747	0.268874	+	0.963175i	$0.413349\pi$
$788$	5.36683e44	0.681650
$789$	2.80687e44	0.349566
$790$	6.18893e43	0.0755780
$791$	−1.52298e45	−1.82372
$792$	1.11732e44	0.131201
$793$	4.74423e44	0.546300
$794$	−4.77822e44	−0.539570
$795$	−1.40360e44	−0.155436
$796$	4.63994e44	0.503918
$797$	−1.44562e45	−1.53975	−0.769875	−	0.638195i	$-0.779681\pi$
$797$	−1.44562e45	−1.53975	−0.769875	+	0.638195i	$0.779681\pi$
$798$	2.50244e45	2.61408
$799$	−5.52713e44	−0.566271
$800$	3.51844e43	0.0353553
$801$	1.53637e45	1.51423
$802$	−9.59413e44	−0.927477
$803$	−6.49495e44	−0.615864
$804$	−2.85504e44	−0.265548
$805$	−1.21031e45	−1.10423
$806$	3.26979e43	0.0292636
$807$	−1.58106e45	−1.38806
$808$	9.05077e43	0.0779488
$809$	1.84718e45	1.56066	0.780328	−	0.625370i	$-0.215052\pi$
$809$	1.84718e45	1.56066	0.780328	+	0.625370i	$0.215052\pi$
$810$	3.78264e44	0.313529
$811$	1.57093e45	1.27742	0.638710	−	0.769448i	$-0.279468\pi$
$811$	1.57093e45	1.27742	0.638710	+	0.769448i	$0.279468\pi$
$812$	1.22460e45	0.976961
$813$	9.26168e44	0.724913
$814$	−5.37296e44	−0.412606
$815$	8.22711e44	0.619875
$816$	3.36432e44	0.248714
$817$	−1.54112e45	−1.11788
$818$	6.22739e44	0.443231
$819$	7.63065e44	0.532919
$820$	−1.46780e44	−0.100589
$821$	−9.20960e44	−0.619329	−0.309665	−	0.950846i	$-0.600217\pi$
$821$	−9.20960e44	−0.619329	−0.309665	+	0.950846i	$0.600217\pi$
$822$	−2.24614e45	−1.48226
$823$	−7.13280e44	−0.461916	−0.230958	−	0.972964i	$-0.574186\pi$
$823$	−7.13280e44	−0.461916	−0.230958	+	0.972964i	$0.574186\pi$
$824$	1.57227e44	0.0999206
$825$	1.67232e44	0.104300
$826$	−3.27234e45	−2.00294
$827$	−2.24717e45	−1.34989	−0.674947	−	0.737866i	$-0.735834\pi$
$827$	−2.24717e45	−1.34989	−0.674947	+	0.737866i	$0.735834\pi$
$828$	−1.11648e45	−0.658236
$829$	−5.23977e44	−0.303191	−0.151596	−	0.988443i	$-0.548441\pi$
$829$	−5.23977e44	−0.303191	−0.151596	+	0.988443i	$0.548441\pi$
$830$	−9.49780e44	−0.539402
$831$	−1.98848e45	−1.10842
$832$	−6.38307e43	−0.0349235
$833$	3.36925e45	1.80940
$834$	−3.41071e45	−1.79792
$835$	1.25234e44	0.0648012
$836$	−4.99571e44	−0.253746
$837$	−3.56307e42	−0.00177656
$838$	−4.14783e44	−0.203020
$839$	2.09806e45	1.00811	0.504054	−	0.863672i	$-0.331841\pi$
$839$	2.09806e45	1.00811	0.504054	+	0.863672i	$0.331841\pi$
$840$	8.98512e44	0.423833
$841$	1.45018e44	0.0671559
$842$	1.41941e45	0.645311
$843$	−1.49277e45	−0.666293
$844$	−1.64475e45	−0.720762
$845$	9.58292e44	0.412305
$846$	−1.36170e45	−0.575229
$847$	3.94273e45	1.63533
$848$	1.50550e44	0.0613120
$849$	−3.41142e45	−1.36416
$850$	2.52835e44	0.0992757
$851$	5.36894e45	2.07005
$852$	8.52342e44	0.322701
$853$	−5.28030e45	−1.96313	−0.981563	−	0.191136i	$-0.938783\pi$
$853$	−5.28030e45	−1.96313	−0.981563	+	0.191136i	$0.938783\pi$
$854$	7.16306e45	2.61518
$855$	1.73484e45	0.621990
$856$	1.35127e45	0.475771
$857$	5.06528e45	1.75146	0.875731	−	0.482800i	$-0.160380\pi$
$857$	5.06528e45	1.75146	0.875731	+	0.482800i	$0.160380\pi$
$858$	−3.03389e44	−0.103026
$859$	3.71198e45	1.23797	0.618986	−	0.785402i	$-0.287544\pi$
$859$	3.71198e45	1.23797	0.618986	+	0.785402i	$0.287544\pi$
$860$	−5.53348e44	−0.181248
$861$	−3.74836e45	−1.20585
$862$	−3.42613e45	−1.08253
$863$	−3.40937e45	−1.05805	−0.529025	−	0.848606i	$-0.677442\pi$
$863$	−3.40937e45	−1.05805	−0.529025	+	0.848606i	$0.677442\pi$
$864$	6.95558e42	0.00212017
$865$	8.90557e44	0.266632
$866$	−4.72920e45	−1.39079
$867$	−2.48841e45	−0.718829
$868$	4.93689e44	0.140087
$869$	−3.15517e44	−0.0879461
$870$	1.69081e45	0.462963
$871$	3.89252e44	0.104701
$872$	2.18841e45	0.578259
$873$	−3.18644e45	−0.827151
$874$	4.99198e45	1.27305
$875$	6.75247e44	0.169176
$876$	−4.81814e45	−1.18595
$877$	4.36010e45	1.05439	0.527197	−	0.849743i	$-0.323243\pi$
$877$	4.36010e45	1.05439	0.527197	+	0.849743i	$0.323243\pi$
$878$	−2.53041e45	−0.601210
$879$	−5.60884e44	−0.130932
$880$	−1.79373e44	−0.0411412
$881$	6.44703e45	1.45289	0.726446	−	0.687223i	$-0.241171\pi$
$881$	6.44703e45	1.45289	0.726446	+	0.687223i	$0.241171\pi$
$882$	8.30072e45	1.83803
$883$	−1.83499e45	−0.399249	−0.199624	−	0.979873i	$-0.563972\pi$
$883$	−1.83499e45	−0.399249	−0.199624	+	0.979873i	$0.563972\pi$
$884$	−4.58687e44	−0.0980632
$885$	−4.51811e45	−0.949153
$886$	3.90979e45	0.807106
$887$	−8.08118e45	−1.63930	−0.819650	−	0.572864i	$-0.805832\pi$
$887$	−8.08118e45	−1.63930	−0.819650	+	0.572864i	$0.805832\pi$
$888$	−3.98581e45	−0.794540
$889$	1.33191e45	0.260915
$890$	−2.46648e45	−0.474824
$891$	−1.92843e45	−0.364837
$892$	−4.00153e44	−0.0743996
$893$	6.08839e45	1.11251
$894$	4.38714e45	0.787862
$895$	1.66904e45	0.294584
$896$	−9.63745e44	−0.167181
$897$	3.03162e45	0.516882
$898$	−3.92178e45	−0.657203
$899$	9.29016e44	0.153020
$900$	6.22901e44	0.100846
$901$	1.08185e45	0.172161
$902$	7.48298e44	0.117051
$903$	−1.41310e46	−2.17276
$904$	2.25544e45	0.340894
$905$	6.52997e44	0.0970194
$906$	1.19889e46	1.75102
$907$	−5.44637e45	−0.781978	−0.390989	−	0.920395i	$-0.627867\pi$
$907$	−5.44637e45	−0.781978	−0.390989	+	0.920395i	$0.627867\pi$
$908$	4.62647e45	0.653009
$909$	1.60234e45	0.222338
$910$	−1.22502e45	−0.167110
$911$	9.56226e45	1.28241	0.641203	−	0.767371i	$-0.278435\pi$
$911$	9.56226e45	1.28241	0.641203	+	0.767371i	$0.278435\pi$
$912$	−3.70596e45	−0.488630
$913$	4.84207e45	0.627674
$914$	−5.95741e45	−0.759262
$915$	9.89002e45	1.23928
$916$	3.72807e45	0.459308
$917$	3.17218e45	0.384267
$918$	4.99827e43	0.00595331
$919$	1.59837e46	1.87191	0.935957	−	0.352114i	$-0.114537\pi$
$919$	1.59837e46	1.87191	0.935957	+	0.352114i	$0.114537\pi$
$920$	1.79239e45	0.206406
$921$	−8.14191e45	−0.921939
$922$	−5.74232e44	−0.0639379
$923$	−1.16207e45	−0.127235
$924$	−4.58070e45	−0.493192
$925$	−2.99540e45	−0.317146
$926$	−7.88723e45	−0.821210
$927$	2.78353e45	0.285010
$928$	−1.81356e45	−0.182616
$929$	−1.13067e46	−1.11968	−0.559839	−	0.828602i	$-0.689137\pi$
$929$	−1.13067e46	−1.11968	−0.559839	+	0.828602i	$0.689137\pi$
$930$	6.81635e44	0.0663844
$931$	−3.71139e46	−3.55481
$932$	2.35326e45	0.221678
$933$	−5.85799e45	−0.542729
$934$	−8.57685e45	−0.781540
$935$	−1.28897e45	−0.115522
$936$	−1.13005e45	−0.0996146
$937$	−1.36916e46	−1.18711	−0.593553	−	0.804795i	$-0.702275\pi$
$937$	−1.36916e46	−1.18711	−0.593553	+	0.804795i	$0.702275\pi$
$938$	5.87710e45	0.501209
$939$	−1.28445e46	−1.07746
$940$	2.18606e45	0.180377
$941$	1.87173e45	0.151916	0.0759580	−	0.997111i	$-0.475799\pi$
$941$	1.87173e45	0.151916	0.0759580	+	0.997111i	$0.475799\pi$
$942$	3.16515e45	0.252700
$943$	−7.47739e45	−0.587244
$944$	4.84613e45	0.374394
$945$	1.33489e44	0.0101450
$946$	2.82102e45	0.210908
$947$	−6.24171e45	−0.459070	−0.229535	−	0.973300i	$-0.573721\pi$
$947$	−6.24171e45	−0.459070	−0.229535	+	0.973300i	$0.573721\pi$
$948$	−2.34060e45	−0.169355
$949$	6.56898e45	0.467597
$950$	−2.78509e45	−0.195040
$951$	−1.53757e46	−1.05935
$952$	−6.92546e45	−0.469436
$953$	9.73682e45	0.649348	0.324674	−	0.945826i	$-0.394745\pi$
$953$	9.73682e45	0.649348	0.324674	+	0.945826i	$0.394745\pi$
$954$	2.66533e45	0.174884
$955$	8.09159e45	0.522374
$956$	5.69576e45	0.361788
$957$	−8.61990e45	−0.538725
$958$	−1.52877e45	−0.0940105
$959$	4.62369e46	2.79769
$960$	−1.33064e45	−0.0792240
$961$	−1.66946e46	−0.978058
$962$	5.43420e45	0.313272
$963$	2.39227e46	1.35707
$964$	−5.38818e45	−0.300779
$965$	−1.41516e45	−0.0777380
$966$	4.57728e46	2.47435
$967$	4.32433e45	0.230043	0.115021	−	0.993363i	$-0.463306\pi$
$967$	4.32433e45	0.230043	0.115021	+	0.993363i	$0.463306\pi$
$968$	−5.83895e45	−0.305680
$969$	−2.66310e46	−1.37205
$970$	5.11548e45	0.259373
$971$	9.24316e44	0.0461235	0.0230618	−	0.999734i	$-0.492659\pi$
$971$	9.24316e44	0.0461235	0.0230618	+	0.999734i	$0.492659\pi$
$972$	−1.44277e46	−0.708550
$973$	7.02096e46	3.39350
$974$	1.22795e46	0.584138
$975$	−1.69138e45	−0.0791899
$976$	−1.06081e46	−0.488836
$977$	−1.36225e46	−0.617862	−0.308931	−	0.951084i	$-0.599971\pi$
$977$	−1.36225e46	−0.617862	−0.308931	+	0.951084i	$0.599971\pi$
$978$	−3.11142e46	−1.38901
$979$	1.25744e46	0.552528
$980$	−1.33259e46	−0.576359
$981$	3.87434e46	1.64941
$982$	−2.72529e46	−1.14205
$983$	2.98873e46	1.23284	0.616421	−	0.787417i	$-0.288582\pi$
$983$	2.98873e46	1.23284	0.616421	+	0.787417i	$0.288582\pi$
$984$	5.55108e45	0.225400
$985$	−1.52534e46	−0.609686
$986$	−1.30322e46	−0.512775
$987$	5.58261e46	2.16233
$988$	5.05265e45	0.192658
$989$	−2.81891e46	−1.05813
$990$	−3.17561e45	−0.117350
$991$	−1.29513e46	−0.471164	−0.235582	−	0.971854i	$-0.575700\pi$
$991$	−1.29513e46	−0.471164	−0.235582	+	0.971854i	$0.575700\pi$
$992$	−7.31122e44	−0.0261854
$993$	2.46087e45	0.0867713
$994$	−1.75455e46	−0.609083
$995$	−1.31875e46	−0.450718
$996$	3.59198e46	1.20869
$997$	3.73350e45	0.123692	0.0618460	−	0.998086i	$-0.480301\pi$
$997$	3.73350e45	0.123692	0.0618460	+	0.998086i	$0.480301\pi$
$998$	−5.20402e45	−0.169752
$999$	−5.92160e44	−0.0190184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.32.a.c.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.32.a.c.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+32768.0 q^{2} +3.52218e7 q^{3} +1.07374e9 q^{4} -3.05176e10 q^{5} +1.15415e12 q^{6} -2.37582e13 q^{7} +3.51844e13 q^{8} +6.22901e14 q^{9} -1.00000e15 q^{10} +5.09810e15 q^{11} +3.78191e16 q^{12} -5.15620e16 q^{13} -7.78507e17 q^{14} -1.07488e18 q^{15} +1.15292e18 q^{16} +8.28488e18 q^{17} +2.04112e19 q^{18} -9.12619e19 q^{19} -3.27680e19 q^{20} -8.36805e20 q^{21} +1.67054e20 q^{22} -1.66930e21 q^{23} +1.23926e21 q^{24} +9.31323e20 q^{25} -1.68959e21 q^{26} +1.84113e20 q^{27} -2.55101e22 q^{28} -4.80046e22 q^{29} -3.52218e22 q^{30} -1.93527e22 q^{31} +3.77789e22 q^{32} +1.79564e23 q^{33} +2.71479e23 q^{34} +7.25041e23 q^{35} +6.68834e23 q^{36} -3.21629e24 q^{37} -2.99047e24 q^{38} -1.81611e24 q^{39} -1.07374e24 q^{40} +4.47937e24 q^{41} -2.74204e25 q^{42} +1.68868e25 q^{43} +5.47404e24 q^{44} -1.90094e25 q^{45} -5.46995e25 q^{46} -6.67134e25 q^{47} +4.06080e25 q^{48} +4.06675e26 q^{49} +3.05176e25 q^{50} +2.91808e26 q^{51} -5.53643e25 q^{52} +1.30582e26 q^{53} +6.03301e24 q^{54} -1.55582e26 q^{55} -8.35916e26 q^{56} -3.21441e27 q^{57} -1.57301e27 q^{58} +4.20335e27 q^{59} -1.15415e27 q^{60} -9.20102e27 q^{61} -6.34148e26 q^{62} -1.47990e28 q^{63} +1.23794e27 q^{64} +1.57355e27 q^{65} +5.88395e27 q^{66} -7.54919e27 q^{67} +8.89582e27 q^{68} -5.87956e28 q^{69} +2.37582e28 q^{70} +2.25373e28 q^{71} +2.19164e28 q^{72} -1.27400e29 q^{73} -1.05391e29 q^{74} +3.28028e28 q^{75} -9.79917e28 q^{76} -1.21121e29 q^{77} -5.95102e28 q^{78} -6.18893e28 q^{79} -3.51844e28 q^{80} -3.78264e29 q^{81} +1.46780e29 q^{82} +9.49780e29 q^{83} -8.98512e29 q^{84} -2.52835e29 q^{85} +5.53348e29 q^{86} -1.69081e30 q^{87} +1.79373e29 q^{88} +2.46648e30 q^{89} -6.22901e29 q^{90} +1.22502e30 q^{91} -1.79239e30 q^{92} -6.81635e29 q^{93} -2.18606e30 q^{94} +2.78509e30 q^{95} +1.33064e30 q^{96} -5.11548e30 q^{97} +1.33259e31 q^{98} +3.17561e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 65536 q^{2} + 38938356 q^{3} + 2147483648 q^{4} - 61035156250 q^{5} + 1275932049408 q^{6} - 12036181345412 q^{7} + 70368744177664 q^{8} + 19040152114674 q^{9} - 20\!\cdots\!00 q^{10} - 39\!\cdots\!76 q^{11}+ \cdots + 86\!\cdots\!88 q^{99}+O(q^{100}) \) 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

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Groups

Database

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