LMFDB - Embedded newform 10.22.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,22,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, 22, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
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:	$27.9477344287$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{474529}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 118632 $ x^2 - x - 118632
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-343.930$ 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)

$f(q)$	$=$	\(q-1024.00 q^{2} +194815. q^{3} +1.04858e6 q^{4} +9.76562e6 q^{5} -1.99490e8 q^{6} +9.63461e8 q^{7} -1.07374e9 q^{8} +2.74924e10 q^{9} -1.00000e10 q^{10} +6.10882e10 q^{11} +2.04278e11 q^{12} +5.25383e10 q^{13} -9.86584e11 q^{14} +1.90249e12 q^{15} +1.09951e12 q^{16} -1.13179e13 q^{17} -2.81522e13 q^{18} -4.53240e13 q^{19} +1.02400e13 q^{20} +1.87696e14 q^{21} -6.25543e13 q^{22} +2.47091e14 q^{23} -2.09181e14 q^{24} +9.53674e13 q^{25} -5.37992e13 q^{26} +3.31810e15 q^{27} +1.01026e15 q^{28} -2.58718e15 q^{29} -1.94815e15 q^{30} -1.35601e15 q^{31} -1.12590e15 q^{32} +1.19009e16 q^{33} +1.15895e16 q^{34} +9.40880e15 q^{35} +2.88279e16 q^{36} -1.35920e16 q^{37} +4.64117e16 q^{38} +1.02352e16 q^{39} -1.04858e16 q^{40} +6.72480e16 q^{41} -1.92201e17 q^{42} -3.70641e16 q^{43} +6.40556e16 q^{44} +2.68481e17 q^{45} -2.53021e17 q^{46} +3.17182e17 q^{47} +2.14201e17 q^{48} +3.69712e17 q^{49} -9.76562e16 q^{50} -2.20489e18 q^{51} +5.50904e16 q^{52} +1.44909e18 q^{53} -3.39773e18 q^{54} +5.96564e17 q^{55} -1.03451e18 q^{56} -8.82978e18 q^{57} +2.64928e18 q^{58} -1.08957e18 q^{59} +1.99490e18 q^{60} -1.59498e17 q^{61} +1.38855e18 q^{62} +2.64879e19 q^{63} +1.15292e18 q^{64} +5.13069e17 q^{65} -1.21865e19 q^{66} +8.71262e18 q^{67} -1.18677e19 q^{68} +4.81370e19 q^{69} -9.63461e18 q^{70} -3.06845e19 q^{71} -2.95198e19 q^{72} +2.36491e19 q^{73} +1.39182e19 q^{74} +1.85790e19 q^{75} -4.75256e19 q^{76} +5.88561e19 q^{77} -1.04809e19 q^{78} -9.35354e19 q^{79} +1.07374e19 q^{80} +3.58834e20 q^{81} -6.88619e19 q^{82} -2.00855e20 q^{83} +1.96814e20 q^{84} -1.10526e20 q^{85} +3.79536e19 q^{86} -5.04022e20 q^{87} -6.55929e19 q^{88} +3.85510e19 q^{89} -2.74924e20 q^{90} +5.06186e19 q^{91} +2.59094e20 q^{92} -2.64170e20 q^{93} -3.24795e20 q^{94} -4.42617e20 q^{95} -2.19342e20 q^{96} -5.46564e20 q^{97} -3.78585e20 q^{98} +1.67946e21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2048 q^{2} + 100308 q^{3} + 2097152 q^{4} + 19531250 q^{5} - 102715392 q^{6} + 1328895316 q^{7} - 2147483648 q^{8} + 25963598826 q^{9} - 20000000000 q^{10} + 21869194224 q^{11} + 105180561408 q^{12}+ \cdots + 17\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 2048 * q^2 + 100308 * q^3 + 2097152 * q^4 + 19531250 * q^5 - 102715392 * q^6 + 1328895316 * q^7 - 2147483648 * q^8 + 25963598826 * q^9 - 20000000000 * q^10 + 21869194224 * q^11 + 105180561408 * q^12 - 412060138772 * q^13 - 1360788803584 * q^14 + 979570312500 * q^15 + 2199023255552 * q^16 - 11074763456364 * q^17 - 26586725197824 * q^18 - 52072861011560 * q^19 + 20480000000000 * q^20 + 153160512951264 * q^21 - 22394054885376 * q^22 + 80988875151948 * q^23 - 107704894881792 * q^24 + 190734863281250 * q^25 + 421949582102528 * q^26 + 4451157871435080 * q^27 + 1393447734870016 * q^28 + 264315081456060 * q^29 - 1003080000000000 * q^30 + 2126016880188664 * q^31 - 2251799813685248 * q^32 + 15607337679454896 * q^33 + 11340557779316736 * q^34 + 12977493320312500 * q^35 + 27224806602571776 * q^36 - 9721711577644724 * q^37 + 53322609675837440 * q^38 + 54142908513242712 * q^39 - 20971520000000000 * q^40 + 221161031209870884 * q^41 - 156836365262094336 * q^42 - 43823174002198412 * q^43 + 22931512202625024 * q^44 + 253550769785156250 * q^45 - 82932608155594752 * q^46 + 206054077207980996 * q^47 + 110289812358955008 * q^48 - 55291909660733886 * q^49 - 195312500000000000 * q^50 - 2227868183000485656 * q^51 - 432076372072988672 * q^52 - 612435371018710692 * q^53 - 4557985660349521920 * q^54 + 213566349843750000 * q^55 - 1426890480506896384 * q^56 - 8191962538091217840 * q^57 - 270658643411005440 * q^58 + 4752208294289856120 * q^59 + 1027153920000000000 * q^60 + 4748119038295687324 * q^61 - 2177041285313191936 * q^62 + 25929207578407210308 * q^63 + 2305843009213693952 * q^64 - 4024024792695312500 * q^65 - 15981913783761813504 * q^66 + 22301925713082765436 * q^67 - 11612731166020337664 * q^68 + 63834782007915333792 * q^69 - 13288953160000000000 * q^70 + 2201035283486261544 * q^71 - 27878201961033498624 * q^72 + 56149494460474652548 * q^73 + 9955032655508197376 * q^74 + 9566116333007812500 * q^75 - 54602352308057538560 * q^76 + 44524159286699802192 * q^77 - 55442338317560537088 * q^78 - 42382706176352134640 * q^79 + 21474836480000000000 * q^80 + 267744560981654170242 * q^81 - 226468895958907785216 * q^82 + 1335343926003173268 * q^83 + 160600438028384600064 * q^84 - 108151986878554687500 * q^85 + 44874930178251173888 * q^86 - 773507714954879145960 * q^87 - 23481868495488024576 * q^88 + 255739828586257500180 * q^89 - 259635988260000000000 * q^90 - 119161420763997884776 * q^91 + 84922990751329026048 * q^92 - 593245051996447282944 * q^93 - 210999375060972539904 * q^94 - 508524033316015625000 * q^95 - 112936767855569928192 * q^96 - 1579422980340785237804 * q^97 + 56618915492591499264 * q^98 + 1739421741088948265712 * 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 $

$2$	−1024.00	−0.707107
$2$	−1024.00	−0.707107
$3$	194815.	1.90480	0.952398	−	0.304856i	$-0.0986084\pi$
$3$	194815.	1.90480	0.952398	+	0.304856i	$0.0986084\pi$
$4$	1.04858e6	0.500000
$5$	9.76562e6	0.447214
$5$	9.76562e6	0.447214
$6$	−1.99490e8	−1.34689
$7$	9.63461e8	1.28915	0.644577	−	0.764539i	$-0.277033\pi$
$7$	9.63461e8	1.28915	0.644577	+	0.764539i	$0.277033\pi$
$8$	−1.07374e9	−0.353553
$9$	2.74924e10	2.62825
$10$	−1.00000e10	−0.316228
$11$	6.10882e10	0.710124	0.355062	−	0.934843i	$-0.384460\pi$
$11$	6.10882e10	0.710124	0.355062	+	0.934843i	$0.384460\pi$
$12$	2.04278e11	0.952398
$13$	5.25383e10	0.105699	0.0528495	−	0.998602i	$-0.483170\pi$
$13$	5.25383e10	0.105699	0.0528495	+	0.998602i	$0.483170\pi$
$14$	−9.86584e11	−0.911570
$15$	1.90249e12	0.851851
$16$	1.09951e12	0.250000
$17$	−1.13179e13	−1.36161	−0.680803	−	0.732466i	$-0.738369\pi$
$17$	−1.13179e13	−1.36161	−0.680803	+	0.732466i	$0.738369\pi$
$18$	−2.81522e13	−1.85845
$19$	−4.53240e13	−1.69596	−0.847979	−	0.530030i	$-0.822181\pi$
$19$	−4.53240e13	−1.69596	−0.847979	+	0.530030i	$0.822181\pi$
$20$	1.02400e13	0.223607
$21$	1.87696e14	2.45558
$22$	−6.25543e13	−0.502133
$23$	2.47091e14	1.24370	0.621849	−	0.783137i	$-0.286382\pi$
$23$	2.47091e14	1.24370	0.621849	+	0.783137i	$0.286382\pi$
$24$	−2.09181e14	−0.673447
$25$	9.53674e13	0.200000
$26$	−5.37992e13	−0.0747404
$27$	3.31810e15	3.10149
$28$	1.01026e15	0.644577
$29$	−2.58718e15	−1.14195	−0.570977	−	0.820966i	$-0.693435\pi$
$29$	−2.58718e15	−1.14195	−0.570977	+	0.820966i	$0.693435\pi$
$30$	−1.94815e15	−0.602350
$31$	−1.35601e15	−0.297142	−0.148571	−	0.988902i	$-0.547467\pi$
$31$	−1.35601e15	−0.297142	−0.148571	+	0.988902i	$0.547467\pi$
$32$	−1.12590e15	−0.176777
$33$	1.19009e16	1.35264
$34$	1.15895e16	0.962801
$35$	9.40880e15	0.576527
$36$	2.88279e16	1.31413
$37$	−1.35920e16	−0.464692	−0.232346	−	0.972633i	$-0.574640\pi$
$37$	−1.35920e16	−0.464692	−0.232346	+	0.972633i	$0.574640\pi$
$38$	4.64117e16	1.19922
$39$	1.02352e16	0.201335
$40$	−1.04858e16	−0.158114
$41$	6.72480e16	0.782436	0.391218	−	0.920298i	$-0.372054\pi$
$41$	6.72480e16	0.782436	0.391218	+	0.920298i	$0.372054\pi$
$42$	−1.92201e17	−1.73636
$43$	−3.70641e16	−0.261538	−0.130769	−	0.991413i	$-0.541745\pi$
$43$	−3.70641e16	−0.261538	−0.130769	+	0.991413i	$0.541745\pi$
$44$	6.40556e16	0.355062
$45$	2.68481e17	1.17539
$46$	−2.53021e17	−0.879427
$47$	3.17182e17	0.879592	0.439796	−	0.898098i	$-0.355051\pi$
$47$	3.17182e17	0.879592	0.439796	+	0.898098i	$0.355051\pi$
$48$	2.14201e17	0.476199
$49$	3.69712e17	0.661919
$50$	−9.76562e16	−0.141421
$51$	−2.20489e18	−2.59358
$52$	5.50904e16	0.0528495
$53$	1.44909e18	1.13815	0.569074	−	0.822286i	$-0.307302\pi$
$53$	1.44909e18	1.13815	0.569074	+	0.822286i	$0.307302\pi$
$54$	−3.39773e18	−2.19308
$55$	5.96564e17	0.317577
$56$	−1.03451e18	−0.455785
$57$	−8.82978e18	−3.23046
$58$	2.64928e18	0.807483
$59$	−1.08957e18	−0.277529	−0.138764	−	0.990325i	$-0.544313\pi$
$59$	−1.08957e18	−0.277529	−0.138764	+	0.990325i	$0.544313\pi$
$60$	1.99490e18	0.425925
$61$	−1.59498e17	−0.0286281	−0.0143140	−	0.999898i	$-0.504556\pi$
$61$	−1.59498e17	−0.0286281	−0.0143140	+	0.999898i	$0.504556\pi$
$62$	1.38855e18	0.210111
$63$	2.64879e19	3.38822
$64$	1.15292e18	0.125000
$65$	5.13069e17	0.0472700
$66$	−1.21865e19	−0.956462
$67$	8.71262e18	0.583934	0.291967	−	0.956428i	$-0.405690\pi$
$67$	8.71262e18	0.583934	0.291967	+	0.956428i	$0.405690\pi$
$68$	−1.18677e19	−0.680803
$69$	4.81370e19	2.36899
$70$	−9.63461e18	−0.407666
$71$	−3.06845e19	−1.11868	−0.559340	−	0.828938i	$-0.688946\pi$
$71$	−3.06845e19	−1.11868	−0.559340	+	0.828938i	$0.688946\pi$
$72$	−2.95198e19	−0.929227
$73$	2.36491e19	0.644059	0.322029	−	0.946730i	$-0.395635\pi$
$73$	2.36491e19	0.644059	0.322029	+	0.946730i	$0.395635\pi$
$74$	1.39182e19	0.328587
$75$	1.85790e19	0.380959
$76$	−4.75256e19	−0.847979
$77$	5.88561e19	0.915459
$78$	−1.04809e19	−0.142365
$79$	−9.35354e19	−1.11145	−0.555727	−	0.831365i	$-0.687560\pi$
$79$	−9.35354e19	−1.11145	−0.555727	+	0.831365i	$0.687560\pi$
$80$	1.07374e19	0.111803
$81$	3.58834e20	3.27945
$82$	−6.88619e19	−0.553266
$83$	−2.00855e20	−1.42090	−0.710448	−	0.703750i	$-0.751508\pi$
$83$	−2.00855e20	−1.42090	−0.710448	+	0.703750i	$0.751508\pi$
$84$	1.96814e20	1.22779
$85$	−1.10526e20	−0.608929
$86$	3.79536e19	0.184935
$87$	−5.04022e20	−2.17519
$88$	−6.55929e19	−0.251067
$89$	3.85510e19	0.131051	0.0655255	−	0.997851i	$-0.479128\pi$
$89$	3.85510e19	0.131051	0.0655255	+	0.997851i	$0.479128\pi$
$90$	−2.74924e20	−0.831126
$91$	5.06186e19	0.136262
$92$	2.59094e20	0.621849
$93$	−2.64170e20	−0.565996
$94$	−3.24795e20	−0.621965
$95$	−4.42617e20	−0.758456
$96$	−2.19342e20	−0.336724
$97$	−5.46564e20	−0.752554	−0.376277	−	0.926507i	$-0.622796\pi$
$97$	−5.46564e20	−0.752554	−0.376277	+	0.926507i	$0.622796\pi$
$98$	−3.78585e20	−0.468047
$99$	1.67946e21	1.86638
$100$	1.00000e20	0.100000
$101$	1.87063e21	1.68505	0.842524	−	0.538658i	$-0.181069\pi$
$101$	1.87063e21	1.68505	0.842524	+	0.538658i	$0.181069\pi$
$102$	2.25781e21	1.83394
$103$	−8.63482e20	−0.633086	−0.316543	−	0.948578i	$-0.602522\pi$
$103$	−8.63482e20	−0.633086	−0.316543	+	0.948578i	$0.602522\pi$
$104$	−5.64125e19	−0.0373702
$105$	1.83297e21	1.09817
$106$	−1.48387e21	−0.804792
$107$	−3.65685e21	−1.79712	−0.898561	−	0.438848i	$-0.855387\pi$
$107$	−3.65685e21	−1.79712	−0.898561	+	0.438848i	$0.855387\pi$
$108$	3.47928e21	1.55074
$109$	−6.39944e20	−0.258919	−0.129459	−	0.991585i	$-0.541324\pi$
$109$	−6.39944e20	−0.258919	−0.129459	+	0.991585i	$0.541324\pi$
$110$	−6.10882e20	−0.224561
$111$	−2.64792e21	−0.885143
$112$	1.05934e21	0.322289
$113$	6.17070e20	0.171006	0.0855029	−	0.996338i	$-0.472750\pi$
$113$	6.17070e20	0.171006	0.0855029	+	0.996338i	$0.472750\pi$
$114$	9.04169e21	2.28428
$115$	2.41300e21	0.556199
$116$	−2.71286e21	−0.570977
$117$	1.44440e21	0.277803
$118$	1.11572e21	0.196242
$119$	−1.09043e22	−1.75532
$120$	−2.04278e21	−0.301175
$121$	−3.66848e21	−0.495724
$122$	1.63326e20	0.0202431
$123$	1.31009e22	1.49038
$124$	−1.42188e21	−0.148571
$125$	9.31323e20	0.0894427
$126$	−2.71236e22	−2.39583
$127$	−1.40405e22	−1.14142	−0.570709	−	0.821152i	$-0.693332\pi$
$127$	−1.40405e22	−1.14142	−0.570709	+	0.821152i	$0.693332\pi$
$128$	−1.18059e21	−0.0883883
$129$	−7.22063e21	−0.498176
$130$	−5.25383e20	−0.0334249
$131$	2.03410e22	1.19405	0.597025	−	0.802222i	$-0.296349\pi$
$131$	2.03410e22	1.19405	0.597025	+	0.802222i	$0.296349\pi$
$132$	1.24790e22	0.676321
$133$	−4.36679e22	−2.18635
$134$	−8.92173e21	−0.412903
$135$	3.24033e22	1.38703
$136$	1.21525e22	0.481401
$137$	−1.10091e21	−0.0403819	−0.0201909	−	0.999796i	$-0.506427\pi$
$137$	−1.10091e21	−0.0403819	−0.0201909	+	0.999796i	$0.506427\pi$
$138$	−4.92923e22	−1.67513
$139$	4.14583e22	1.30604	0.653019	−	0.757342i	$-0.273502\pi$
$139$	4.14583e22	1.30604	0.653019	+	0.757342i	$0.273502\pi$
$140$	9.86584e21	0.288264
$141$	6.17918e22	1.67544
$142$	3.14209e22	0.791027
$143$	3.20947e21	0.0750593
$144$	3.02282e22	0.657063
$145$	−2.52655e22	−0.510697
$146$	−2.42167e22	−0.455418
$147$	7.20253e22	1.26082
$148$	−1.42522e22	−0.232346
$149$	9.61610e22	1.46064	0.730320	−	0.683106i	$-0.239371\pi$
$149$	9.61610e22	1.46064	0.730320	+	0.683106i	$0.239371\pi$
$150$	−1.90249e22	−0.269379
$151$	−1.13093e23	−1.49340	−0.746700	−	0.665161i	$-0.768363\pi$
$151$	−1.13093e23	−1.49340	−0.746700	+	0.665161i	$0.768363\pi$
$152$	4.86662e22	0.599612
$153$	−3.11156e23	−3.57864
$154$	−6.02687e22	−0.647327
$155$	−1.32423e22	−0.132886
$156$	1.07324e22	0.100667
$157$	3.75753e22	0.329576	0.164788	−	0.986329i	$-0.447306\pi$
$157$	3.75753e22	0.329576	0.164788	+	0.986329i	$0.447306\pi$
$158$	9.57802e22	0.785917
$159$	2.82304e23	2.16794
$160$	−1.09951e22	−0.0790569
$161$	2.38063e23	1.60332
$162$	−3.67446e23	−2.31892
$163$	2.53934e23	1.50228	0.751140	−	0.660143i	$-0.229504\pi$
$163$	2.53934e23	1.50228	0.751140	+	0.660143i	$0.229504\pi$
$164$	7.05146e22	0.391218
$165$	1.16220e23	0.604920
$166$	2.05675e23	1.00472
$167$	−7.88087e22	−0.361452	−0.180726	−	0.983533i	$-0.557845\pi$
$167$	−7.88087e22	−0.361452	−0.180726	+	0.983533i	$0.557845\pi$
$168$	−2.01538e23	−0.868178
$169$	−2.44304e23	−0.988828
$170$	1.13179e23	0.430578
$171$	−1.24607e24	−4.45740
$172$	−3.88645e22	−0.130769
$173$	−3.30387e23	−1.04602	−0.523009	−	0.852327i	$-0.675191\pi$
$173$	−3.30387e23	−1.04602	−0.523009	+	0.852327i	$0.675191\pi$
$174$	5.16118e23	1.53809
$175$	9.18828e22	0.257831
$176$	6.71672e22	0.177531
$177$	−2.12264e23	−0.528636
$178$	−3.94762e22	−0.0926671
$179$	4.40276e23	0.974470	0.487235	−	0.873271i	$-0.338005\pi$
$179$	4.40276e23	0.974470	0.487235	+	0.873271i	$0.338005\pi$
$180$	2.81522e23	0.587695
$181$	−8.24093e23	−1.62312	−0.811561	−	0.584268i	$-0.801382\pi$
$181$	−8.24093e23	−1.62312	−0.811561	+	0.584268i	$0.801382\pi$
$182$	−5.18334e22	−0.0963519
$183$	−3.10726e22	−0.0545306
$184$	−2.65312e23	−0.439714
$185$	−1.32734e23	−0.207816
$186$	2.70510e23	0.400219
$187$	−6.91389e23	−0.966909
$188$	3.32590e23	0.439796
$189$	3.19686e24	3.99829
$190$	4.53240e23	0.536309
$191$	2.97957e23	0.333659	0.166830	−	0.985986i	$-0.446647\pi$
$191$	2.97957e23	0.333659	0.166830	+	0.985986i	$0.446647\pi$
$192$	2.24606e23	0.238100
$193$	9.58444e23	0.962088	0.481044	−	0.876696i	$-0.340258\pi$
$193$	9.58444e23	0.962088	0.481044	+	0.876696i	$0.340258\pi$
$194$	5.59682e23	0.532136
$195$	9.99534e22	0.0900397
$196$	3.87671e23	0.330959
$197$	−7.67214e23	−0.620899	−0.310450	−	0.950590i	$-0.600480\pi$
$197$	−7.67214e23	−0.620899	−0.310450	+	0.950590i	$0.600480\pi$
$198$	−1.71977e24	−1.31973
$199$	−2.93227e23	−0.213426	−0.106713	−	0.994290i	$-0.534033\pi$
$199$	−2.93227e23	−0.213426	−0.106713	+	0.994290i	$0.534033\pi$
$200$	−1.02400e23	−0.0707107
$201$	1.69735e24	1.11227
$202$	−1.91552e24	−1.19151
$203$	−2.49265e24	−1.47215
$204$	−2.31200e24	−1.29679
$205$	6.56719e23	0.349916
$206$	8.84206e23	0.447659
$207$	6.79314e24	3.26875
$208$	5.77664e22	0.0264247
$209$	−2.76876e24	−1.20434
$210$	−1.87696e24	−0.776522
$211$	−2.05920e24	−0.810464	−0.405232	−	0.914214i	$-0.632809\pi$
$211$	−2.05920e24	−0.810464	−0.405232	+	0.914214i	$0.632809\pi$
$212$	1.51948e24	0.569074
$213$	−5.97779e24	−2.13086
$214$	3.74462e24	1.27076
$215$	−3.61954e23	−0.116963
$216$	−3.56278e24	−1.09654
$217$	−1.30646e24	−0.383062
$218$	6.55303e23	0.183083
$219$	4.60720e24	1.22680
$220$	6.25543e23	0.158788
$221$	−5.94622e23	−0.143920
$222$	2.71147e24	0.625891
$223$	−3.95841e24	−0.871605	−0.435803	−	0.900042i	$-0.643535\pi$
$223$	−3.95841e24	−0.871605	−0.435803	+	0.900042i	$0.643535\pi$
$224$	−1.08476e24	−0.227892
$225$	2.62188e24	0.525650
$226$	−6.31880e23	−0.120919
$227$	−6.66876e23	−0.121835	−0.0609177	−	0.998143i	$-0.519403\pi$
$227$	−6.66876e23	−0.121835	−0.0609177	+	0.998143i	$0.519403\pi$
$228$	−9.25869e24	−1.61523
$229$	−7.22731e24	−1.20421	−0.602107	−	0.798415i	$-0.705672\pi$
$229$	−7.22731e24	−1.20421	−0.602107	+	0.798415i	$0.705672\pi$
$230$	−2.47091e24	−0.393292
$231$	1.14660e25	1.74376
$232$	2.77797e24	0.403742
$233$	1.07597e25	1.49474	0.747368	−	0.664410i	$-0.231317\pi$
$233$	1.07597e25	1.49474	0.747368	+	0.664410i	$0.231317\pi$
$234$	−1.47907e24	−0.196437
$235$	3.09748e24	0.393365
$236$	−1.14249e24	−0.138764
$237$	−1.82221e25	−2.11709
$238$	1.11661e25	1.24120
$239$	3.16911e24	0.337101	0.168550	−	0.985693i	$-0.446091\pi$
$239$	3.16911e24	0.337101	0.168550	+	0.985693i	$0.446091\pi$
$240$	2.09181e24	0.212963
$241$	−1.75468e24	−0.171009	−0.0855043	−	0.996338i	$-0.527250\pi$
$241$	−1.75468e24	−0.171009	−0.0855043	+	0.996338i	$0.527250\pi$
$242$	3.75653e24	0.350530
$243$	3.51977e25	3.14520
$244$	−1.67246e23	−0.0143140
$245$	3.61047e24	0.296019
$246$	−1.34153e25	−1.05386
$247$	−2.38124e24	−0.179261
$248$	1.45600e24	0.105056
$249$	−3.91295e25	−2.70652
$250$	−9.53674e23	−0.0632456
$251$	1.75868e25	1.11844	0.559221	−	0.829019i	$-0.311100\pi$
$251$	1.75868e25	1.11844	0.559221	+	0.829019i	$0.311100\pi$
$252$	2.77746e25	1.69411
$253$	1.50944e25	0.883179
$254$	1.43775e25	0.807104
$255$	−2.15321e25	−1.15989
$256$	1.20893e24	0.0625000
$257$	−9.88264e24	−0.490428	−0.245214	−	0.969469i	$-0.578858\pi$
$257$	−9.88264e24	−0.490428	−0.245214	+	0.969469i	$0.578858\pi$
$258$	7.39392e24	0.352264
$259$	−1.30954e25	−0.599059
$260$	5.37992e23	0.0236350
$261$	−7.11280e25	−3.00134
$262$	−2.08291e25	−0.844321
$263$	−1.60390e25	−0.624656	−0.312328	−	0.949974i	$-0.601109\pi$
$263$	−1.60390e25	−0.624656	−0.312328	+	0.949974i	$0.601109\pi$
$264$	−1.27785e25	−0.478231
$265$	1.41513e25	0.508995
$266$	4.47159e25	1.54598
$267$	7.51030e24	0.249626
$268$	9.13585e24	0.291967
$269$	1.76073e25	0.541122	0.270561	−	0.962703i	$-0.412791\pi$
$269$	1.76073e25	0.541122	0.270561	+	0.962703i	$0.412791\pi$
$270$	−3.31810e25	−0.980776
$271$	3.45015e25	0.980981	0.490490	−	0.871447i	$-0.336818\pi$
$271$	3.45015e25	0.980981	0.490490	+	0.871447i	$0.336818\pi$
$272$	−1.24441e25	−0.340402
$273$	9.86125e24	0.259552
$274$	1.12733e24	0.0285543
$275$	5.82582e24	0.142025
$276$	5.04753e25	1.18450
$277$	−2.59482e25	−0.586231	−0.293116	−	0.956077i	$-0.594692\pi$
$277$	−2.59482e25	−0.586231	−0.293116	+	0.956077i	$0.594692\pi$
$278$	−4.24533e25	−0.923508
$279$	−3.72799e25	−0.780964
$280$	−1.01026e25	−0.203833
$281$	7.82254e25	1.52031	0.760154	−	0.649743i	$-0.225124\pi$
$281$	7.82254e25	1.52031	0.760154	+	0.649743i	$0.225124\pi$
$282$	−6.32748e25	−1.18472
$283$	8.38167e24	0.151207	0.0756037	−	0.997138i	$-0.475912\pi$
$283$	8.38167e24	0.151207	0.0756037	+	0.997138i	$0.475912\pi$
$284$	−3.21750e25	−0.559340
$285$	−8.62283e25	−1.44470
$286$	−3.28649e24	−0.0530749
$287$	6.47908e25	1.00868
$288$	−3.09537e25	−0.464613
$289$	5.90026e25	0.853973
$290$	2.58718e25	0.361117
$291$	−1.06479e26	−1.43346
$292$	2.47979e25	0.322029
$293$	4.97478e25	0.623252	0.311626	−	0.950205i	$-0.399126\pi$
$293$	4.97478e25	0.623252	0.311626	+	0.950205i	$0.399126\pi$
$294$	−7.37540e25	−0.891535
$295$	−1.06403e25	−0.124115
$296$	1.45943e25	0.164293
$297$	2.02697e26	2.20244
$298$	−9.84688e25	−1.03283
$299$	1.29817e25	0.131458
$300$	1.94815e25	0.190480
$301$	−3.57098e25	−0.337163
$302$	1.15807e26	1.05599
$303$	3.64425e26	3.20967
$304$	−4.98342e25	−0.423990
$305$	−1.55760e24	−0.0128029
$306$	3.18624e26	2.53048
$307$	−1.41280e26	−1.08425	−0.542123	−	0.840299i	$-0.682379\pi$
$307$	−1.41280e26	−1.08425	−0.542123	+	0.840299i	$0.682379\pi$
$308$	6.17151e25	0.457730
$309$	−1.68219e26	−1.20590
$310$	1.35601e25	0.0939646
$311$	1.39904e26	0.937232	0.468616	−	0.883402i	$-0.344753\pi$
$311$	1.39904e26	0.937232	0.468616	+	0.883402i	$0.344753\pi$
$312$	−1.09900e25	−0.0711827
$313$	−2.79550e26	−1.75083	−0.875414	−	0.483373i	$-0.839411\pi$
$313$	−2.79550e26	−1.75083	−0.875414	+	0.483373i	$0.839411\pi$
$314$	−3.84771e25	−0.233045
$315$	2.58671e26	1.51526
$316$	−9.80789e25	−0.555727
$317$	−1.16992e26	−0.641259	−0.320629	−	0.947205i	$-0.603894\pi$
$317$	−1.16992e26	−0.641259	−0.320629	+	0.947205i	$0.603894\pi$
$318$	−2.89079e26	−1.53297
$319$	−1.58046e26	−0.810928
$320$	1.12590e25	0.0559017
$321$	−7.12409e26	−3.42315
$322$	−2.43776e26	−1.13372
$323$	5.12972e26	2.30923
$324$	3.76265e26	1.63973
$325$	5.01044e24	0.0211398
$326$	−2.60028e26	−1.06227
$327$	−1.24671e26	−0.493188
$328$	−7.22070e25	−0.276633
$329$	3.05593e26	1.13393
$330$	−1.19009e26	−0.427743
$331$	−3.83627e26	−1.33572	−0.667859	−	0.744288i	$-0.732789\pi$
$331$	−3.83627e26	−1.33572	−0.667859	+	0.744288i	$0.732789\pi$
$332$	−2.10612e26	−0.710448
$333$	−3.73677e26	−1.22133
$334$	8.07001e25	0.255585
$335$	8.50842e25	0.261143
$336$	2.06374e26	0.613894
$337$	1.36118e26	0.392465	0.196233	−	0.980557i	$-0.437129\pi$
$337$	1.36118e26	0.392465	0.196233	+	0.980557i	$0.437129\pi$
$338$	2.50168e26	0.699207
$339$	1.20214e26	0.325731
$340$	−1.15895e26	−0.304465
$341$	−8.28360e25	−0.211008
$342$	1.27597e27	3.15186
$343$	−1.81934e26	−0.435839
$344$	3.97973e25	0.0924676
$345$	4.70088e26	1.05945
$346$	3.38316e26	0.739646
$347$	2.49928e26	0.530097	0.265048	−	0.964235i	$-0.414612\pi$
$347$	2.49928e26	0.530097	0.265048	+	0.964235i	$0.414612\pi$
$348$	−5.28505e26	−1.08759
$349$	1.05322e26	0.210307	0.105153	−	0.994456i	$-0.466467\pi$
$349$	1.05322e26	0.210307	0.105153	+	0.994456i	$0.466467\pi$
$350$	−9.40880e25	−0.182314
$351$	1.74327e26	0.327824
$352$	−6.87792e25	−0.125533
$353$	−1.44843e26	−0.256604	−0.128302	−	0.991735i	$-0.540953\pi$
$353$	−1.44843e26	−0.256604	−0.128302	+	0.991735i	$0.540953\pi$
$354$	2.17358e26	0.373802
$355$	−2.99653e26	−0.500289
$356$	4.04236e25	0.0655255
$357$	−2.12433e27	−3.34353
$358$	−4.50843e26	−0.689055
$359$	5.68219e25	0.0843382	0.0421691	−	0.999110i	$-0.486573\pi$
$359$	5.68219e25	0.0843382	0.0421691	+	0.999110i	$0.486573\pi$
$360$	−2.88279e26	−0.415563
$361$	1.34005e27	1.87627
$362$	8.43871e26	1.14772
$363$	−7.14675e26	−0.944254
$364$	5.30774e25	0.0681311
$365$	2.30949e26	0.288032
$366$	3.18183e25	0.0385590
$367$	3.29729e25	0.0388296	0.0194148	−	0.999812i	$-0.493820\pi$
$367$	3.29729e25	0.0388296	0.0194148	+	0.999812i	$0.493820\pi$
$368$	2.71680e26	0.310924
$369$	1.84881e27	2.05644
$370$	1.35920e26	0.146948
$371$	1.39614e27	1.46725
$372$	−2.77003e26	−0.282998
$373$	−6.24564e25	−0.0620346	−0.0310173	−	0.999519i	$-0.509875\pi$
$373$	−6.24564e25	−0.0620346	−0.0310173	+	0.999519i	$0.509875\pi$
$374$	7.07983e26	0.683708
$375$	1.81435e26	0.170370
$376$	−3.40572e26	−0.310983
$377$	−1.35926e26	−0.120703
$378$	−3.27359e27	−2.82722
$379$	1.65025e27	1.38624	0.693119	−	0.720823i	$-0.256236\pi$
$379$	1.65025e27	1.38624	0.693119	+	0.720823i	$0.256236\pi$
$380$	−4.64117e26	−0.379228
$381$	−2.73530e27	−2.17417
$382$	−3.05108e26	−0.235933
$383$	1.20420e27	0.905967	0.452983	−	0.891519i	$-0.350360\pi$
$383$	1.20420e27	0.905967	0.452983	+	0.891519i	$0.350360\pi$
$384$	−2.29997e26	−0.168362
$385$	5.74767e26	0.409406
$386$	−9.81446e26	−0.680299
$387$	−1.01898e27	−0.687387
$388$	−5.73114e26	−0.376277
$389$	1.68483e26	0.107667	0.0538337	−	0.998550i	$-0.482856\pi$
$389$	1.68483e26	0.107667	0.0538337	+	0.998550i	$0.482856\pi$
$390$	−1.02352e26	−0.0636677
$391$	−2.79655e27	−1.69343
$392$	−3.96975e26	−0.234024
$393$	3.96272e27	2.27442
$394$	7.85627e26	0.439042
$395$	−9.13431e26	−0.497057
$396$	1.76104e27	0.933192
$397$	1.48612e27	0.766925	0.383462	−	0.923557i	$-0.374732\pi$
$397$	1.48612e27	0.766925	0.383462	+	0.923557i	$0.374732\pi$
$398$	3.00264e26	0.150915
$399$	−8.50715e27	−4.16456
$400$	1.04858e26	0.0500000
$401$	−6.25371e26	−0.290484	−0.145242	−	0.989396i	$-0.546396\pi$
$401$	−6.25371e26	−0.290484	−0.145242	+	0.989396i	$0.546396\pi$
$402$	−1.73808e27	−0.786497
$403$	−7.12423e25	−0.0314076
$404$	1.96149e27	0.842524
$405$	3.50424e27	1.46661
$406$	2.55248e27	1.04097
$407$	−8.30310e26	−0.329989
$408$	2.36748e27	0.916970
$409$	3.35895e27	1.26797	0.633985	−	0.773345i	$-0.281418\pi$
$409$	3.35895e27	1.26797	0.633985	+	0.773345i	$0.281418\pi$
$410$	−6.72480e26	−0.247428
$411$	−2.14474e26	−0.0769192
$412$	−9.05427e26	−0.316543
$413$	−1.04976e27	−0.357777
$414$	−6.95617e27	−2.31136
$415$	−1.96147e27	−0.635444
$416$	−5.91528e25	−0.0186851
$417$	8.07668e27	2.48774
$418$	2.83521e27	0.851597
$419$	−1.39454e27	−0.408492	−0.204246	−	0.978920i	$-0.565474\pi$
$419$	−1.39454e27	−0.408492	−0.204246	+	0.978920i	$0.565474\pi$
$420$	1.92201e27	0.549084
$421$	−5.26111e27	−1.46594	−0.732968	−	0.680263i	$-0.761866\pi$
$421$	−5.26111e27	−1.46594	−0.732968	+	0.680263i	$0.761866\pi$
$422$	2.10862e27	0.573084
$423$	8.72011e27	2.31179
$424$	−1.55595e27	−0.402396
$425$	−1.07936e27	−0.272321
$426$	6.12126e27	1.50675
$427$	−1.53670e26	−0.0369060
$428$	−3.83449e27	−0.898561
$429$	6.25252e26	0.142973
$430$	3.70641e26	0.0827055
$431$	−3.99327e27	−0.869595	−0.434797	−	0.900528i	$-0.643180\pi$
$431$	−3.99327e27	−0.869595	−0.434797	+	0.900528i	$0.643180\pi$
$432$	3.64829e27	0.775372
$433$	1.71947e27	0.356674	0.178337	−	0.983969i	$-0.442928\pi$
$433$	1.71947e27	0.356674	0.178337	+	0.983969i	$0.442928\pi$
$434$	1.33782e27	0.270866
$435$	−4.92209e27	−0.972774
$436$	−6.71030e26	−0.129459
$437$	−1.11992e28	−2.10926
$438$	−4.71777e27	−0.867479
$439$	2.57641e27	0.462528	0.231264	−	0.972891i	$-0.425714\pi$
$439$	2.57641e27	0.462528	0.231264	+	0.972891i	$0.425714\pi$
$440$	−6.40556e26	−0.112280
$441$	1.01643e28	1.73969
$442$	6.08893e26	0.101767
$443$	−1.26523e27	−0.206504	−0.103252	−	0.994655i	$-0.532925\pi$
$443$	−1.26523e27	−0.206504	−0.103252	+	0.994655i	$0.532925\pi$
$444$	−2.77655e27	−0.442572
$445$	3.76475e26	0.0586078
$446$	4.05341e27	0.616318
$447$	1.87336e28	2.78222
$448$	1.11080e27	0.161144
$449$	3.20858e26	0.0454702	0.0227351	−	0.999742i	$-0.492763\pi$
$449$	3.20858e26	0.0454702	0.0227351	+	0.999742i	$0.492763\pi$
$450$	−2.68481e27	−0.371691
$451$	4.10806e27	0.555626
$452$	6.47045e26	0.0855029
$453$	−2.20321e28	−2.84462
$454$	6.82881e26	0.0861506
$455$	4.94322e26	0.0609383
$456$	9.48090e27	1.14214
$457$	−1.41432e28	−1.66506	−0.832528	−	0.553983i	$-0.813107\pi$
$457$	−1.41432e28	−1.66506	−0.832528	+	0.553983i	$0.813107\pi$
$458$	7.40076e27	0.851508
$459$	−3.75539e28	−4.22300
$460$	2.53021e27	0.278099
$461$	6.08545e27	0.653782	0.326891	−	0.945062i	$-0.393999\pi$
$461$	6.08545e27	0.653782	0.326891	+	0.945062i	$0.393999\pi$
$462$	−1.17412e28	−1.23303
$463$	6.53768e27	0.671155	0.335578	−	0.942013i	$-0.391069\pi$
$463$	6.53768e27	0.671155	0.335578	+	0.942013i	$0.391069\pi$
$464$	−2.84464e27	−0.285488
$465$	−2.57979e27	−0.253121
$466$	−1.10180e28	−1.05694
$467$	−9.77307e27	−0.916651	−0.458325	−	0.888784i	$-0.651551\pi$
$467$	−9.77307e27	−0.916651	−0.458325	+	0.888784i	$0.651551\pi$
$468$	1.51457e27	0.138902
$469$	8.39428e27	0.752781
$470$	−3.17182e27	−0.278151
$471$	7.32022e27	0.627775
$472$	1.16991e27	0.0981212
$473$	−2.26418e27	−0.185724
$474$	1.86594e28	1.49701
$475$	−4.32243e27	−0.339192
$476$	−1.14340e28	−0.877661
$477$	3.98390e28	2.99134
$478$	−3.24517e27	−0.238366
$479$	−1.53019e28	−1.09957	−0.549784	−	0.835307i	$-0.685290\pi$
$479$	−1.53019e28	−1.09957	−0.549784	+	0.835307i	$0.685290\pi$
$480$	−2.14201e27	−0.150587
$481$	−7.14100e26	−0.0491174
$482$	1.79679e27	0.120921
$483$	4.63781e28	3.05400
$484$	−3.84668e27	−0.247862
$485$	−5.33754e27	−0.336553
$486$	−3.60424e28	−2.22399
$487$	−2.24122e28	−1.35341	−0.676705	−	0.736254i	$-0.736593\pi$
$487$	−2.24122e28	−1.35341	−0.676705	+	0.736254i	$0.736593\pi$
$488$	1.71260e26	0.0101215
$489$	4.94701e28	2.86154
$490$	−3.69712e27	−0.209317
$491$	1.97103e28	1.09229	0.546145	−	0.837691i	$-0.316095\pi$
$491$	1.97103e28	1.09229	0.546145	+	0.837691i	$0.316095\pi$
$492$	1.37373e28	0.745191
$493$	2.92815e28	1.55489
$494$	2.43839e27	0.126757
$495$	1.64010e28	0.834672
$496$	−1.49095e27	−0.0742856
$497$	−2.95633e28	−1.44215
$498$	4.00686e28	1.91380
$499$	3.08705e28	1.44374	0.721869	−	0.692030i	$-0.243283\pi$
$499$	3.08705e28	1.44374	0.721869	+	0.692030i	$0.243283\pi$
$500$	9.76563e26	0.0447214
$501$	−1.53531e28	−0.688493
$502$	−1.80089e28	−0.790858
$503$	−2.52448e28	−1.08570	−0.542848	−	0.839831i	$-0.682654\pi$
$503$	−2.52448e28	−1.08570	−0.542848	+	0.839831i	$0.682654\pi$
$504$	−2.84412e28	−1.19792
$505$	1.82678e28	0.753577
$506$	−1.54566e28	−0.624502
$507$	−4.75941e28	−1.88352
$508$	−1.47226e28	−0.570709
$509$	2.42632e28	0.921323	0.460661	−	0.887576i	$-0.347612\pi$
$509$	2.42632e28	0.921323	0.460661	+	0.887576i	$0.347612\pi$
$510$	2.20489e28	0.820163
$511$	2.27850e28	0.830291
$512$	−1.23794e27	−0.0441942
$513$	−1.50389e29	−5.25999
$514$	1.01198e28	0.346785
$515$	−8.43244e27	−0.283125
$516$	−7.57138e27	−0.249088
$517$	1.93761e28	0.624619
$518$	1.34096e28	0.423599
$519$	−6.43643e28	−1.99245
$520$	−5.50904e26	−0.0167125
$521$	−1.28803e28	−0.382939	−0.191470	−	0.981499i	$-0.561325\pi$
$521$	−1.28803e28	−0.382939	−0.191470	+	0.981499i	$0.561325\pi$
$522$	7.28351e28	2.12227
$523$	4.72268e28	1.34872	0.674359	−	0.738404i	$-0.264420\pi$
$523$	4.72268e28	1.34872	0.674359	+	0.738404i	$0.264420\pi$
$524$	2.13290e28	0.597025
$525$	1.79001e28	0.491115
$526$	1.64239e28	0.441699
$527$	1.53471e28	0.404591
$528$	1.30852e28	0.338160
$529$	2.15825e28	0.546785
$530$	−1.44909e28	−0.359914
$531$	−2.99548e28	−0.729415
$532$	−4.57891e28	−1.09318
$533$	3.53309e27	0.0827026
$534$	−7.69055e27	−0.176512
$535$	−3.57114e28	−0.803698
$536$	−9.35511e27	−0.206452
$537$	8.57723e28	1.85617
$538$	−1.80299e28	−0.382631
$539$	2.25850e28	0.470044
$540$	3.39773e28	0.693513
$541$	1.70978e28	0.342270	0.171135	−	0.985248i	$-0.445257\pi$
$541$	1.70978e28	0.342270	0.171135	+	0.985248i	$0.445257\pi$
$542$	−3.53295e28	−0.693658
$543$	−1.60545e29	−3.09172
$544$	1.27428e28	0.240700
$545$	−6.24945e27	−0.115792
$546$	−1.00979e28	−0.183531
$547$	6.17365e28	1.10072	0.550358	−	0.834929i	$-0.314491\pi$
$547$	6.17365e28	1.10072	0.550358	+	0.834929i	$0.314491\pi$
$548$	−1.15439e27	−0.0201909
$549$	−4.38499e27	−0.0752417
$550$	−5.96564e27	−0.100427
$551$	1.17262e29	1.93671
$552$	−5.16867e28	−0.837565
$553$	−9.01177e28	−1.43284
$554$	2.65709e28	0.414528
$555$	−2.58586e28	−0.395848
$556$	4.34721e28	0.653019
$557$	−1.03162e29	−1.52069	−0.760346	−	0.649518i	$-0.774971\pi$
$557$	−1.03162e29	−1.52069	−0.760346	+	0.649518i	$0.774971\pi$
$558$	3.81747e28	0.552225
$559$	−1.94728e27	−0.0276443
$560$	1.03451e28	0.144132
$561$	−1.34693e29	−1.84177
$562$	−8.01028e28	−1.07502
$563$	−3.65428e28	−0.481353	−0.240677	−	0.970605i	$-0.577369\pi$
$563$	−3.65428e28	−0.481353	−0.240677	+	0.970605i	$0.577369\pi$
$564$	6.47934e28	0.837722
$565$	6.02608e27	0.0764761
$566$	−8.58283e27	−0.106920
$567$	3.45723e29	4.22772
$568$	3.29472e28	0.395513
$569$	4.54287e28	0.535367	0.267683	−	0.963507i	$-0.413742\pi$
$569$	4.54287e28	0.535367	0.267683	+	0.963507i	$0.413742\pi$
$570$	8.82978e28	1.02156
$571$	1.49843e29	1.70200	0.850998	−	0.525168i	$-0.175998\pi$
$571$	1.49843e29	1.70200	0.850998	+	0.525168i	$0.175998\pi$
$572$	3.36537e27	0.0375297
$573$	5.80464e28	0.635553
$574$	−6.63458e28	−0.713245
$575$	2.35644e28	0.248740
$576$	3.16966e28	0.328531
$577$	−1.44438e29	−1.47006	−0.735029	−	0.678035i	$-0.762832\pi$
$577$	−1.44438e29	−1.47006	−0.735029	+	0.678035i	$0.762832\pi$
$578$	−6.04187e28	−0.603850
$579$	1.86719e29	1.83258
$580$	−2.64928e28	−0.255349
$581$	−1.93516e29	−1.83175
$582$	1.09034e29	1.01361
$583$	8.85223e28	0.808226
$584$	−2.53931e28	−0.227709
$585$	1.41055e28	0.124237
$586$	−5.09417e28	−0.440706
$587$	−1.82681e29	−1.55237	−0.776183	−	0.630508i	$-0.782846\pi$
$587$	−1.82681e29	−1.55237	−0.776183	+	0.630508i	$0.782846\pi$
$588$	7.55241e28	0.630410
$589$	6.14597e28	0.503941
$590$	1.08957e28	0.0877623
$591$	−1.49465e29	−1.18269
$592$	−1.49446e28	−0.116173
$593$	1.28812e29	0.983742	0.491871	−	0.870668i	$-0.336313\pi$
$593$	1.28812e29	0.983742	0.491871	+	0.870668i	$0.336313\pi$
$594$	−2.07561e29	−1.55736
$595$	−1.06488e29	−0.785004
$596$	1.00832e29	0.730320
$597$	−5.71249e28	−0.406532
$598$	−1.32933e28	−0.0929545
$599$	−1.90622e28	−0.130976	−0.0654879	−	0.997853i	$-0.520860\pi$
$599$	−1.90622e28	−0.130976	−0.0654879	+	0.997853i	$0.520860\pi$
$600$	−1.99490e28	−0.134689
$601$	−4.02359e28	−0.266951	−0.133476	−	0.991052i	$-0.542614\pi$
$601$	−4.02359e28	−0.266951	−0.133476	+	0.991052i	$0.542614\pi$
$602$	3.65668e28	0.238410
$603$	2.39531e29	1.53472
$604$	−1.18586e29	−0.746700
$605$	−3.58250e28	−0.221695
$606$	−3.73172e29	−2.26958
$607$	1.34619e29	0.804681	0.402340	−	0.915490i	$-0.368197\pi$
$607$	1.34619e29	0.804681	0.402340	+	0.915490i	$0.368197\pi$
$608$	5.10303e28	0.299806
$609$	−4.85606e29	−2.80416
$610$	1.59498e27	0.00905299
$611$	1.66642e28	0.0929719
$612$	−3.26271e29	−1.78932
$613$	6.61541e28	0.356633	0.178316	−	0.983973i	$-0.442935\pi$
$613$	6.61541e28	0.356633	0.178316	+	0.983973i	$0.442935\pi$
$614$	1.44671e29	0.766677
$615$	1.27938e29	0.666519
$616$	−6.31963e28	−0.323664
$617$	−5.23241e28	−0.263456	−0.131728	−	0.991286i	$-0.542052\pi$
$617$	−5.23241e28	−0.263456	−0.131728	+	0.991286i	$0.542052\pi$
$618$	1.72256e29	0.852700
$619$	1.15227e29	0.560793	0.280397	−	0.959884i	$-0.409534\pi$
$619$	1.15227e29	0.560793	0.280397	+	0.959884i	$0.409534\pi$
$620$	−1.38855e28	−0.0664430
$621$	8.19873e29	3.85731
$622$	−1.43262e29	−0.662723
$623$	3.71424e28	0.168945
$624$	1.12538e28	0.0503337
$625$	9.09495e27	0.0400000
$626$	2.86259e29	1.23802
$627$	−5.39395e29	−2.29402
$628$	3.94005e28	0.164788
$629$	1.53833e29	0.632727
$630$	−2.64879e29	−1.07145
$631$	−1.82557e29	−0.726257	−0.363128	−	0.931739i	$-0.618291\pi$
$631$	−1.82557e29	−0.726257	−0.363128	+	0.931739i	$0.618291\pi$
$632$	1.00433e29	0.392958
$633$	−4.01163e29	−1.54377
$634$	1.19800e29	0.453438
$635$	−1.37115e29	−0.510458
$636$	2.96017e29	1.08397
$637$	1.94240e28	0.0699641
$638$	1.61840e29	0.573413
$639$	−8.43591e29	−2.94017
$640$	−1.15292e28	−0.0395285
$641$	4.06750e29	1.37189	0.685943	−	0.727655i	$-0.259390\pi$
$641$	4.06750e29	1.37189	0.685943	+	0.727655i	$0.259390\pi$
$642$	7.29506e29	2.42053
$643$	1.10344e29	0.360192	0.180096	−	0.983649i	$-0.442359\pi$
$643$	1.10344e29	0.360192	0.180096	+	0.983649i	$0.442359\pi$
$644$	2.49627e29	0.801659
$645$	−7.05140e28	−0.222791
$646$	−5.25283e29	−1.63287
$647$	5.65654e29	1.73004	0.865020	−	0.501737i	$-0.167306\pi$
$647$	5.65654e29	1.73004	0.865020	+	0.501737i	$0.167306\pi$
$648$	−3.85295e29	−1.15946
$649$	−6.65597e28	−0.197080
$650$	−5.13069e27	−0.0149481
$651$	−2.54518e29	−0.729656
$652$	2.66269e29	0.751140
$653$	9.98139e28	0.277078	0.138539	−	0.990357i	$-0.455759\pi$
$653$	9.98139e28	0.277078	0.138539	+	0.990357i	$0.455759\pi$
$654$	1.27663e29	0.348736
$655$	1.98642e29	0.533996
$656$	7.39399e28	0.195609
$657$	6.50172e29	1.69275
$658$	−3.12927e29	−0.801809
$659$	4.27384e29	1.07776	0.538880	−	0.842383i	$-0.318848\pi$
$659$	4.27384e29	1.07776	0.538880	+	0.842383i	$0.318848\pi$
$660$	1.21865e29	0.302460
$661$	1.06580e29	0.260352	0.130176	−	0.991491i	$-0.458446\pi$
$661$	1.06580e29	0.260352	0.130176	+	0.991491i	$0.458446\pi$
$662$	3.92834e29	0.944495
$663$	−1.15841e29	−0.274139
$664$	2.15666e29	0.502362
$665$	−4.26444e29	−0.977766
$666$	3.82645e29	0.863608
$667$	−6.39271e29	−1.42025
$668$	−8.26369e28	−0.180726
$669$	−7.71157e29	−1.66023
$670$	−8.71262e28	−0.184656
$671$	−9.74344e27	−0.0203295
$672$	−2.11327e29	−0.434089
$673$	9.20636e29	1.86179	0.930893	−	0.365292i	$-0.119031\pi$
$673$	9.20636e29	1.86179	0.930893	+	0.365292i	$0.119031\pi$
$674$	−1.39385e29	−0.277515
$675$	3.16439e29	0.620297
$676$	−2.56172e29	−0.494414
$677$	1.03701e29	0.197062	0.0985309	−	0.995134i	$-0.468586\pi$
$677$	1.03701e29	0.197062	0.0985309	+	0.995134i	$0.468586\pi$
$678$	−1.23100e29	−0.230327
$679$	−5.26593e29	−0.970159
$680$	1.18677e29	0.215289
$681$	−1.29917e29	−0.232072
$682$	8.48241e28	0.149205
$683$	−1.05066e30	−1.81988	−0.909942	−	0.414735i	$-0.863874\pi$
$683$	−1.05066e30	−1.81988	−0.909942	+	0.414735i	$0.863874\pi$
$684$	−1.30660e30	−2.22870
$685$	−1.07511e28	−0.0180593
$686$	1.86301e29	0.308185
$687$	−1.40799e30	−2.29378
$688$	−4.07524e28	−0.0653844
$689$	7.61327e28	0.120301
$690$	−4.81370e29	−0.749141
$691$	−2.09599e29	−0.321270	−0.160635	−	0.987014i	$-0.551354\pi$
$691$	−2.09599e29	−0.321270	−0.160635	+	0.987014i	$0.551354\pi$
$692$	−3.46436e29	−0.523009
$693$	1.61810e30	2.40606
$694$	−2.55926e29	−0.374835
$695$	4.04866e29	0.584078
$696$	5.41189e29	0.769046
$697$	−7.61105e29	−1.06537
$698$	−1.07850e29	−0.148709
$699$	2.09616e30	2.84717
$700$	9.63461e28	0.128915
$701$	−9.09765e29	−1.19920	−0.599598	−	0.800301i	$-0.704673\pi$
$701$	−9.09765e29	−1.19920	−0.599598	+	0.800301i	$0.704673\pi$
$702$	−1.78511e29	−0.231806
$703$	6.16043e29	0.788098
$704$	7.04299e28	0.0887655
$705$	6.03435e29	0.749281
$706$	1.48319e29	0.181446
$707$	1.80228e30	2.17229
$708$	−2.22575e29	−0.264318
$709$	−1.17415e30	−1.37385	−0.686925	−	0.726728i	$-0.741040\pi$
$709$	−1.17415e30	−1.37385	−0.686925	+	0.726728i	$0.741040\pi$
$710$	3.06845e29	0.353758
$711$	−2.57151e30	−2.92118
$712$	−4.13938e28	−0.0463335
$713$	−3.35057e29	−0.369555
$714$	2.17531e30	2.36423
$715$	3.13425e28	0.0335675
$716$	4.61663e29	0.487235
$717$	6.17390e29	0.642108
$718$	−5.81857e28	−0.0596361
$719$	2.38367e29	0.240765	0.120382	−	0.992728i	$-0.461588\pi$
$719$	2.38367e29	0.240765	0.120382	+	0.992728i	$0.461588\pi$
$720$	2.95198e29	0.293847
$721$	−8.31932e29	−0.816145
$722$	−1.37221e30	−1.32673
$723$	−3.41837e29	−0.325737
$724$	−8.64124e29	−0.811561
$725$	−2.46733e29	−0.228391
$726$	7.31827e29	0.667688
$727$	1.60120e30	1.43991	0.719954	−	0.694022i	$-0.244163\pi$
$727$	1.60120e30	1.43991	0.719954	+	0.694022i	$0.244163\pi$
$728$	−5.43513e28	−0.0481760
$729$	3.10350e30	2.71152
$730$	−2.36491e29	−0.203669
$731$	4.19487e29	0.356112
$732$	−3.25819e28	−0.0272653
$733$	−8.02614e28	−0.0662087	−0.0331043	−	0.999452i	$-0.510539\pi$
$733$	−8.02614e28	−0.0662087	−0.0331043	+	0.999452i	$0.510539\pi$
$734$	−3.37642e28	−0.0274567
$735$	7.03373e29	0.563856
$736$	−2.78200e29	−0.219857
$737$	5.32238e29	0.414665
$738$	−1.89318e30	−1.45412
$739$	2.07121e30	1.56840	0.784200	−	0.620508i	$-0.213073\pi$
$739$	2.07121e30	1.56840	0.784200	+	0.620508i	$0.213073\pi$
$740$	−1.39182e29	−0.103908
$741$	−4.63901e29	−0.341456
$742$	−1.42965e30	−1.03750
$743$	−2.00787e30	−1.43666	−0.718329	−	0.695704i	$-0.755093\pi$
$743$	−2.00787e30	−1.43666	−0.718329	+	0.695704i	$0.755093\pi$
$744$	2.83651e29	0.200110
$745$	9.39072e29	0.653218
$746$	6.39554e28	0.0438651
$747$	−5.52199e30	−3.73447
$748$	−7.24974e29	−0.483455
$749$	−3.52324e30	−2.31677
$750$	−1.85790e29	−0.120470
$751$	2.68196e30	1.71488	0.857440	−	0.514584i	$-0.172054\pi$
$751$	2.68196e30	1.71488	0.857440	+	0.514584i	$0.172054\pi$
$752$	3.48745e29	0.219898
$753$	3.42617e30	2.13040
$754$	1.39188e29	0.0853501
$755$	−1.10442e30	−0.667869
$756$	3.35215e30	1.99915
$757$	2.29494e30	1.34979	0.674894	−	0.737915i	$-0.264189\pi$
$757$	2.29494e30	1.34979	0.674894	+	0.737915i	$0.264189\pi$
$758$	−1.68986e30	−0.980219
$759$	2.94060e30	1.68228
$760$	4.75256e29	0.268155
$761$	3.17369e29	0.176614	0.0883072	−	0.996093i	$-0.471854\pi$
$761$	3.17369e29	0.176614	0.0883072	+	0.996093i	$0.471854\pi$
$762$	2.80095e30	1.53737
$763$	−6.16561e29	−0.333786
$764$	3.12430e29	0.166830
$765$	−3.03863e30	−1.60042
$766$	−1.23310e30	−0.640615
$767$	−5.72440e28	−0.0293345
$768$	2.35517e29	0.119050
$769$	3.31592e30	1.65340	0.826699	−	0.562644i	$-0.190216\pi$
$769$	3.31592e30	1.65340	0.826699	+	0.562644i	$0.190216\pi$
$770$	−5.88561e29	−0.289494
$771$	−1.92528e30	−0.934166
$772$	1.00500e30	0.481044
$773$	−2.86833e29	−0.135439	−0.0677196	−	0.997704i	$-0.521572\pi$
$773$	−2.86833e29	−0.135439	−0.0677196	+	0.997704i	$0.521572\pi$
$774$	1.04344e30	0.486056
$775$	−1.29319e29	−0.0594284
$776$	5.86869e29	0.266068
$777$	−2.55117e30	−1.14109
$778$	−1.72526e29	−0.0761323
$779$	−3.04795e30	−1.32698
$780$	1.04809e29	0.0450199
$781$	−1.87446e30	−0.794402
$782$	2.86367e30	1.19743
$783$	−8.58454e30	−3.54175
$784$	4.06503e29	0.165480
$785$	3.66946e29	0.147391
$786$	−4.05782e30	−1.60826
$787$	1.37451e30	0.537544	0.268772	−	0.963204i	$-0.413382\pi$
$787$	1.37451e30	0.537544	0.268772	+	0.963204i	$0.413382\pi$
$788$	−8.04482e29	−0.310450
$789$	−3.12463e30	−1.18984
$790$	9.35354e29	0.351473
$791$	5.94523e29	0.220453
$792$	−1.80331e30	−0.659866
$793$	−8.37975e27	−0.00302596
$794$	−1.52178e30	−0.542298
$795$	2.75688e30	0.969533
$796$	−3.07471e29	−0.106713
$797$	−4.30808e30	−1.47561	−0.737805	−	0.675014i	$-0.764138\pi$
$797$	−4.30808e30	−1.47561	−0.737805	+	0.675014i	$0.764138\pi$
$798$	8.71132e30	2.94479
$799$	−3.58983e30	−1.19766
$800$	−1.07374e29	−0.0353553
$801$	1.05986e30	0.344435
$802$	6.40380e29	0.205403
$803$	1.44468e30	0.457361
$804$	1.77980e30	0.556137
$805$	2.32483e30	0.717026
$806$	7.29521e28	0.0222085
$807$	3.43017e30	1.03073
$808$	−2.00857e30	−0.595755
$809$	−8.36783e29	−0.244993	−0.122496	−	0.992469i	$-0.539090\pi$
$809$	−8.36783e29	−0.244993	−0.122496	+	0.992469i	$0.539090\pi$
$810$	−3.58834e30	−1.03705
$811$	3.30696e30	0.943432	0.471716	−	0.881751i	$-0.343635\pi$
$811$	3.30696e30	0.943432	0.471716	+	0.881751i	$0.343635\pi$
$812$	−2.61374e30	−0.736077
$813$	6.72140e30	1.86857
$814$	8.50237e29	0.233337
$815$	2.47982e30	0.671840
$816$	−2.42430e30	−0.648396
$817$	1.67989e30	0.443557
$818$	−3.43957e30	−0.896591
$819$	1.39163e30	0.358131
$820$	6.88619e29	0.174958
$821$	7.58969e30	1.90380	0.951899	−	0.306413i	$-0.0991290\pi$
$821$	7.58969e30	1.90380	0.951899	+	0.306413i	$0.0991290\pi$
$822$	2.19621e29	0.0543901
$823$	5.61508e30	1.37296	0.686479	−	0.727149i	$-0.259155\pi$
$823$	5.61508e30	1.37296	0.686479	+	0.727149i	$0.259155\pi$
$824$	9.27157e29	0.223830
$825$	1.13496e30	0.270528
$826$	1.07495e30	0.252987
$827$	5.39629e30	1.25397	0.626985	−	0.779031i	$-0.284289\pi$
$827$	5.39629e30	1.25397	0.626985	+	0.779031i	$0.284289\pi$
$828$	7.12312e30	1.63437
$829$	−4.47440e30	−1.01371	−0.506853	−	0.862032i	$-0.669191\pi$
$829$	−4.47440e30	−1.01371	−0.506853	+	0.862032i	$0.669191\pi$
$830$	2.00855e30	0.449327
$831$	−5.05508e30	−1.11665
$832$	6.05725e28	0.0132124
$833$	−4.18436e30	−0.901273
$834$	−8.27052e30	−1.75910
$835$	−7.69616e29	−0.161646
$836$	−2.90325e30	−0.602170
$837$	−4.49937e30	−0.921582
$838$	1.42801e30	0.288847
$839$	−1.16605e30	−0.232925	−0.116462	−	0.993195i	$-0.537155\pi$
$839$	−1.16605e30	−0.232925	−0.116462	+	0.993195i	$0.537155\pi$
$840$	−1.96814e30	−0.388261
$841$	1.56068e30	0.304058
$842$	5.38738e30	1.03657
$843$	1.52395e31	2.89588
$844$	−2.15923e30	−0.405232
$845$	−2.38578e30	−0.442217
$846$	−8.92939e30	−1.63468
$847$	−3.53444e30	−0.639065
$848$	1.59329e30	0.284537
$849$	1.63287e30	0.288019
$850$	1.10526e30	0.192560
$851$	−3.35846e30	−0.577936
$852$	−6.26817e30	−1.06543
$853$	−1.08909e31	−1.82852	−0.914262	−	0.405123i	$-0.867229\pi$
$853$	−1.08909e31	−1.82852	−0.914262	+	0.405123i	$0.867229\pi$
$854$	1.57358e29	0.0260965
$855$	−1.21686e31	−1.99341
$856$	3.92651e30	0.635379
$857$	1.32603e30	0.211960	0.105980	−	0.994368i	$-0.466202\pi$
$857$	1.32603e30	0.211960	0.105980	+	0.994368i	$0.466202\pi$
$858$	−6.40258e29	−0.101097
$859$	−6.84458e30	−1.06762	−0.533812	−	0.845603i	$-0.679241\pi$
$859$	−6.84458e30	−1.06762	−0.533812	+	0.845603i	$0.679241\pi$
$860$	−3.79536e29	−0.0584816
$861$	1.26222e31	1.92133
$862$	4.08910e30	0.614896
$863$	3.45729e30	0.513597	0.256799	−	0.966465i	$-0.417332\pi$
$863$	3.45729e30	0.513597	0.256799	+	0.966465i	$0.417332\pi$
$864$	−3.73585e30	−0.548270
$865$	−3.22644e30	−0.467793
$866$	−1.76074e30	−0.252206
$867$	1.14946e31	1.62664
$868$	−1.36992e30	−0.191531
$869$	−5.71391e30	−0.789270
$870$	5.04022e30	0.687855
$871$	4.57746e29	0.0617212
$872$	6.87135e29	0.0915416
$873$	−1.50264e31	−1.97790
$874$	1.14679e31	1.49147
$875$	8.97293e29	0.115305
$876$	4.83100e30	0.613400
$877$	−1.37025e30	−0.171912	−0.0859558	−	0.996299i	$-0.527394\pi$
$877$	−1.37025e30	−0.171912	−0.0859558	+	0.996299i	$0.527394\pi$
$878$	−2.63825e30	−0.327057
$879$	9.69160e30	1.18717
$880$	6.55929e29	0.0793942
$881$	−3.75611e30	−0.449253	−0.224627	−	0.974445i	$-0.572116\pi$
$881$	−3.75611e30	−0.449253	−0.224627	+	0.974445i	$0.572116\pi$
$882$	−1.04082e31	−1.23015
$883$	6.64376e30	0.775937	0.387968	−	0.921673i	$-0.373177\pi$
$883$	6.64376e30	0.775937	0.387968	+	0.921673i	$0.373177\pi$
$884$	−6.23507e29	−0.0719602
$885$	−2.07289e30	−0.236413
$886$	1.29559e30	0.146021
$887$	−6.01786e30	−0.670261	−0.335131	−	0.942172i	$-0.608780\pi$
$887$	−6.01786e30	−0.670261	−0.335131	+	0.942172i	$0.608780\pi$
$888$	2.84318e30	0.312945
$889$	−1.35275e31	−1.47146
$890$	−3.85510e29	−0.0414420
$891$	2.19205e31	2.32882
$892$	−4.15070e30	−0.435803
$893$	−1.43760e31	−1.49175
$894$	−1.91832e31	−1.96733
$895$	4.29957e30	0.435796
$896$	−1.13745e30	−0.113946
$897$	2.52903e30	0.250400
$898$	−3.28559e29	−0.0321523
$899$	3.50824e30	0.339323
$900$	2.74924e30	0.262825
$901$	−1.64006e31	−1.54971
$902$	−4.20665e30	−0.392887
$903$	−6.95680e30	−0.642226
$904$	−6.62574e29	−0.0604597
$905$	−8.04778e30	−0.725882
$906$	2.25609e31	2.01145
$907$	1.42699e31	1.25761	0.628804	−	0.777564i	$-0.283545\pi$
$907$	1.42699e31	1.25761	0.628804	+	0.777564i	$0.283545\pi$
$908$	−6.99270e29	−0.0609177
$909$	5.14280e31	4.42873
$910$	−5.06186e29	−0.0430899
$911$	1.18912e31	1.00065	0.500326	−	0.865837i	$-0.333214\pi$
$911$	1.18912e31	1.00065	0.500326	+	0.865837i	$0.333214\pi$
$912$	−9.70844e30	−0.807614
$913$	−1.22699e31	−1.00901
$914$	1.44827e31	1.17737
$915$	−3.03443e29	−0.0243868
$916$	−7.57838e30	−0.602107
$917$	1.95977e31	1.53932
$918$	3.84552e31	2.98612
$919$	−3.13990e30	−0.241047	−0.120524	−	0.992710i	$-0.538457\pi$
$919$	−3.13990e30	−0.241047	−0.120524	+	0.992710i	$0.538457\pi$
$920$	−2.59094e30	−0.196646
$921$	−2.75234e31	−2.06527
$922$	−6.23150e30	−0.462294
$923$	−1.61211e30	−0.118243
$924$	1.20230e31	0.871882
$925$	−1.29623e30	−0.0929383
$926$	−6.69458e30	−0.474578
$927$	−2.37392e31	−1.66391
$928$	2.91291e30	0.201871
$929$	1.39588e30	0.0956498	0.0478249	−	0.998856i	$-0.484771\pi$
$929$	1.39588e30	0.0956498	0.0478249	+	0.998856i	$0.484771\pi$
$930$	2.64170e30	0.178983
$931$	−1.67568e31	−1.12259
$932$	1.12824e31	0.747368
$933$	2.72554e31	1.78524
$934$	1.00076e31	0.648170
$935$	−6.75185e30	−0.432415
$936$	−1.55092e30	−0.0982183
$937$	−2.22831e31	−1.39543	−0.697717	−	0.716374i	$-0.745801\pi$
$937$	−2.22831e31	−1.39543	−0.697717	+	0.716374i	$0.745801\pi$
$938$	−8.59574e30	−0.532296
$939$	−5.44604e31	−3.33497
$940$	3.24795e30	0.196683
$941$	2.09348e31	1.25366	0.626828	−	0.779157i	$-0.284353\pi$
$941$	2.09348e31	1.25366	0.626828	+	0.779157i	$0.284353\pi$
$942$	−7.49590e30	−0.443904
$943$	1.66164e31	0.973114
$944$	−1.19799e30	−0.0693822
$945$	3.12193e31	1.78809
$946$	2.31852e30	0.131327
$947$	2.96424e31	1.66050	0.830249	−	0.557393i	$-0.188198\pi$
$947$	2.96424e31	1.66050	0.830249	+	0.557393i	$0.188198\pi$
$948$	−1.91072e31	−1.05855
$949$	1.24248e30	0.0680763
$950$	4.42617e30	0.239845
$951$	−2.27917e31	−1.22147
$952$	1.17085e31	0.620600
$953$	3.78184e30	0.198257	0.0991283	−	0.995075i	$-0.468395\pi$
$953$	3.78184e30	0.198257	0.0991283	+	0.995075i	$0.468395\pi$
$954$	−4.07952e31	−2.11520
$955$	2.90973e30	0.149217
$956$	3.32305e30	0.168550
$957$	−3.07898e31	−1.54465
$958$	1.56691e31	0.777512
$959$	−1.06069e30	−0.0520584
$960$	2.19342e30	0.106481
$961$	−1.89867e31	−0.911707
$962$	7.31238e29	0.0347313
$963$	−1.00536e32	−4.72329
$964$	−1.83991e30	−0.0855043
$965$	9.35980e30	0.430259
$966$	−4.74912e31	−2.15950
$967$	−2.27343e31	−1.02259	−0.511297	−	0.859404i	$-0.670835\pi$
$967$	−2.27343e31	−1.02259	−0.511297	+	0.859404i	$0.670835\pi$
$968$	3.93900e30	0.175265
$969$	9.99344e31	4.39861
$970$	5.46564e30	0.237979
$971$	3.59388e31	1.54797	0.773983	−	0.633206i	$-0.218261\pi$
$971$	3.59388e31	1.54797	0.773983	+	0.633206i	$0.218261\pi$
$972$	3.69074e31	1.57260
$973$	3.99434e31	1.68368
$974$	2.29500e31	0.957006
$975$	9.76107e29	0.0402670
$976$	−1.75370e29	−0.00715702
$977$	8.76227e30	0.353772	0.176886	−	0.984231i	$-0.443398\pi$
$977$	8.76227e30	0.353772	0.176886	+	0.984231i	$0.443398\pi$
$978$	−5.06574e31	−2.02341
$979$	2.35501e30	0.0930625
$980$	3.78585e30	0.148010
$981$	−1.75936e31	−0.680504
$982$	−2.01834e31	−0.772365
$983$	3.99246e31	1.51157	0.755786	−	0.654819i	$-0.227255\pi$
$983$	3.99246e31	1.51157	0.755786	+	0.654819i	$0.227255\pi$
$984$	−1.40670e31	−0.526929
$985$	−7.49232e30	−0.277675
$986$	−2.99842e31	−1.09947
$987$	5.95340e31	2.15991
$988$	−2.49691e30	−0.0896305
$989$	−9.15821e30	−0.325274
$990$	−1.67946e31	−0.590202
$991$	4.03797e31	1.40407	0.702037	−	0.712141i	$-0.252274\pi$
$991$	4.03797e31	1.40407	0.702037	+	0.712141i	$0.252274\pi$
$992$	1.52673e30	0.0525278
$993$	−7.47361e31	−2.54427
$994$	3.02728e31	1.01976
$995$	−2.86354e30	−0.0954468
$996$	−4.10302e31	−1.35326
$997$	1.29884e31	0.423894	0.211947	−	0.977281i	$-0.432020\pi$
$997$	1.29884e31	0.423894	0.211947	+	0.977281i	$0.432020\pi$
$998$	−3.16114e31	−1.02088
$999$	−4.50996e31	−1.44124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.22.a.c.1.2	✓	2
4.3	odd	2		80.22.a.b.1.1		2
5.2	odd	4		50.22.b.d.49.1		4
5.3	odd	4		50.22.b.d.49.4		4
5.4	even	2		50.22.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.22.a.c.1.2	✓	2	1.1	even	1	trivial
50.22.a.e.1.1		2	5.4	even	2
50.22.b.d.49.1		4	5.2	odd	4
50.22.b.d.49.4		4	5.3	odd	4
80.22.a.b.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-1024.00 q^{2} +194815. q^{3} +1.04858e6 q^{4} +9.76562e6 q^{5} -1.99490e8 q^{6} +9.63461e8 q^{7} -1.07374e9 q^{8} +2.74924e10 q^{9} -1.00000e10 q^{10} +6.10882e10 q^{11} +2.04278e11 q^{12} +5.25383e10 q^{13} -9.86584e11 q^{14} +1.90249e12 q^{15} +1.09951e12 q^{16} -1.13179e13 q^{17} -2.81522e13 q^{18} -4.53240e13 q^{19} +1.02400e13 q^{20} +1.87696e14 q^{21} -6.25543e13 q^{22} +2.47091e14 q^{23} -2.09181e14 q^{24} +9.53674e13 q^{25} -5.37992e13 q^{26} +3.31810e15 q^{27} +1.01026e15 q^{28} -2.58718e15 q^{29} -1.94815e15 q^{30} -1.35601e15 q^{31} -1.12590e15 q^{32} +1.19009e16 q^{33} +1.15895e16 q^{34} +9.40880e15 q^{35} +2.88279e16 q^{36} -1.35920e16 q^{37} +4.64117e16 q^{38} +1.02352e16 q^{39} -1.04858e16 q^{40} +6.72480e16 q^{41} -1.92201e17 q^{42} -3.70641e16 q^{43} +6.40556e16 q^{44} +2.68481e17 q^{45} -2.53021e17 q^{46} +3.17182e17 q^{47} +2.14201e17 q^{48} +3.69712e17 q^{49} -9.76562e16 q^{50} -2.20489e18 q^{51} +5.50904e16 q^{52} +1.44909e18 q^{53} -3.39773e18 q^{54} +5.96564e17 q^{55} -1.03451e18 q^{56} -8.82978e18 q^{57} +2.64928e18 q^{58} -1.08957e18 q^{59} +1.99490e18 q^{60} -1.59498e17 q^{61} +1.38855e18 q^{62} +2.64879e19 q^{63} +1.15292e18 q^{64} +5.13069e17 q^{65} -1.21865e19 q^{66} +8.71262e18 q^{67} -1.18677e19 q^{68} +4.81370e19 q^{69} -9.63461e18 q^{70} -3.06845e19 q^{71} -2.95198e19 q^{72} +2.36491e19 q^{73} +1.39182e19 q^{74} +1.85790e19 q^{75} -4.75256e19 q^{76} +5.88561e19 q^{77} -1.04809e19 q^{78} -9.35354e19 q^{79} +1.07374e19 q^{80} +3.58834e20 q^{81} -6.88619e19 q^{82} -2.00855e20 q^{83} +1.96814e20 q^{84} -1.10526e20 q^{85} +3.79536e19 q^{86} -5.04022e20 q^{87} -6.55929e19 q^{88} +3.85510e19 q^{89} -2.74924e20 q^{90} +5.06186e19 q^{91} +2.59094e20 q^{92} -2.64170e20 q^{93} -3.24795e20 q^{94} -4.42617e20 q^{95} -2.19342e20 q^{96} -5.46564e20 q^{97} -3.78585e20 q^{98} +1.67946e21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2048 q^{2} + 100308 q^{3} + 2097152 q^{4} + 19531250 q^{5} - 102715392 q^{6} + 1328895316 q^{7} - 2147483648 q^{8} + 25963598826 q^{9} - 20000000000 q^{10} + 21869194224 q^{11} + 105180561408 q^{12}+ \cdots + 17\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 2048 * q^2 + 100308 * q^3 + 2097152 * q^4 + 19531250 * q^5 - 102715392 * q^6 + 1328895316 * q^7 - 2147483648 * q^8 + 25963598826 * q^9 - 20000000000 * q^10 + 21869194224 * q^11 + 105180561408 * q^12 - 412060138772 * q^13 - 1360788803584 * q^14 + 979570312500 * q^15 + 2199023255552 * q^16 - 11074763456364 * q^17 - 26586725197824 * q^18 - 52072861011560 * q^19 + 20480000000000 * q^20 + 153160512951264 * q^21 - 22394054885376 * q^22 + 80988875151948 * q^23 - 107704894881792 * q^24 + 190734863281250 * q^25 + 421949582102528 * q^26 + 4451157871435080 * q^27 + 1393447734870016 * q^28 + 264315081456060 * q^29 - 1003080000000000 * q^30 + 2126016880188664 * q^31 - 2251799813685248 * q^32 + 15607337679454896 * q^33 + 11340557779316736 * q^34 + 12977493320312500 * q^35 + 27224806602571776 * q^36 - 9721711577644724 * q^37 + 53322609675837440 * q^38 + 54142908513242712 * q^39 - 20971520000000000 * q^40 + 221161031209870884 * q^41 - 156836365262094336 * q^42 - 43823174002198412 * q^43 + 22931512202625024 * q^44 + 253550769785156250 * q^45 - 82932608155594752 * q^46 + 206054077207980996 * q^47 + 110289812358955008 * q^48 - 55291909660733886 * q^49 - 195312500000000000 * q^50 - 2227868183000485656 * q^51 - 432076372072988672 * q^52 - 612435371018710692 * q^53 - 4557985660349521920 * q^54 + 213566349843750000 * q^55 - 1426890480506896384 * q^56 - 8191962538091217840 * q^57 - 270658643411005440 * q^58 + 4752208294289856120 * q^59 + 1027153920000000000 * q^60 + 4748119038295687324 * q^61 - 2177041285313191936 * q^62 + 25929207578407210308 * q^63 + 2305843009213693952 * q^64 - 4024024792695312500 * q^65 - 15981913783761813504 * q^66 + 22301925713082765436 * q^67 - 11612731166020337664 * q^68 + 63834782007915333792 * q^69 - 13288953160000000000 * q^70 + 2201035283486261544 * q^71 - 27878201961033498624 * q^72 + 56149494460474652548 * q^73 + 9955032655508197376 * q^74 + 9566116333007812500 * q^75 - 54602352308057538560 * q^76 + 44524159286699802192 * q^77 - 55442338317560537088 * q^78 - 42382706176352134640 * q^79 + 21474836480000000000 * q^80 + 267744560981654170242 * q^81 - 226468895958907785216 * q^82 + 1335343926003173268 * q^83 + 160600438028384600064 * q^84 - 108151986878554687500 * q^85 + 44874930178251173888 * q^86 - 773507714954879145960 * q^87 - 23481868495488024576 * q^88 + 255739828586257500180 * q^89 - 259635988260000000000 * q^90 - 119161420763997884776 * q^91 + 84922990751329026048 * q^92 - 593245051996447282944 * q^93 - 210999375060972539904 * q^94 - 508524033316015625000 * q^95 - 112936767855569928192 * q^96 - 1579422980340785237804 * q^97 + 56618915492591499264 * q^98 + 1739421741088948265712 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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