LMFDB - Embedded newform 10.22.a.c.1.1

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			1.1
Root			$344.930$ 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)

$f(q)$	$=$	\(q-1024.00 q^{2} -94506.7 q^{3} +1.04858e6 q^{4} +9.76562e6 q^{5} +9.67749e7 q^{6} +3.65434e8 q^{7} -1.07374e9 q^{8} -1.52883e9 q^{9} -1.00000e10 q^{10} -3.92190e10 q^{11} -9.90975e10 q^{12} -4.64598e11 q^{13} -3.74204e11 q^{14} -9.22917e11 q^{15} +1.09951e12 q^{16} +2.43124e11 q^{17} +1.56552e12 q^{18} -6.74889e12 q^{19} +1.02400e13 q^{20} -3.45360e13 q^{21} +4.01602e13 q^{22} -1.66102e14 q^{23} +1.01476e14 q^{24} +9.53674e13 q^{25} +4.75749e14 q^{26} +1.13306e15 q^{27} +3.83185e14 q^{28} +2.85150e15 q^{29} +9.45067e14 q^{30} +3.48202e15 q^{31} -1.12590e15 q^{32} +3.70646e15 q^{33} -2.48959e14 q^{34} +3.56869e15 q^{35} -1.60309e15 q^{36} +3.87028e15 q^{37} +6.91086e15 q^{38} +4.39077e16 q^{39} -1.04858e16 q^{40} +1.53913e17 q^{41} +3.53648e16 q^{42} -6.75910e15 q^{43} -4.11241e16 q^{44} -1.49300e16 q^{45} +1.70089e17 q^{46} -1.11128e17 q^{47} -1.03911e17 q^{48} -4.25004e17 q^{49} -9.76562e16 q^{50} -2.29769e16 q^{51} -4.87167e17 q^{52} -2.06153e18 q^{53} -1.16025e18 q^{54} -3.82998e17 q^{55} -3.92382e17 q^{56} +6.37815e17 q^{57} -2.91994e18 q^{58} +5.84178e18 q^{59} -9.67749e17 q^{60} +4.90762e18 q^{61} -3.56559e18 q^{62} -5.58686e17 q^{63} +1.15292e18 q^{64} -4.53709e18 q^{65} -3.79541e18 q^{66} +1.35893e19 q^{67} +2.54934e17 q^{68} +1.56978e19 q^{69} -3.65434e18 q^{70} +3.28855e19 q^{71} +1.64157e18 q^{72} +3.25004e19 q^{73} -3.96317e18 q^{74} -9.01286e18 q^{75} -7.07672e18 q^{76} -1.43319e19 q^{77} -4.49615e19 q^{78} +5.11527e19 q^{79} +1.07374e19 q^{80} -9.10896e19 q^{81} -1.57607e20 q^{82} +2.02190e20 q^{83} -3.62136e19 q^{84} +2.37426e18 q^{85} +6.92131e18 q^{86} -2.69486e20 q^{87} +4.21111e19 q^{88} +2.17189e20 q^{89} +1.52883e19 q^{90} -1.69780e20 q^{91} -1.74171e20 q^{92} -3.29075e20 q^{93} +1.13795e20 q^{94} -6.59071e19 q^{95} +1.06405e20 q^{96} -1.03286e21 q^{97} +4.35204e20 q^{98} +5.99592e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−94506.7	−0.924037	−0.462019	−	0.886870i	$-0.652875\pi$
$3$	−94506.7	−0.924037	−0.462019	+	0.886870i	$0.652875\pi$
$4$	1.04858e6	0.500000
$5$	9.76562e6	0.447214
$5$	9.76562e6	0.447214
$6$	9.67749e7	0.653393
$7$	3.65434e8	0.488967	0.244483	−	0.969653i	$-0.421382\pi$
$7$	3.65434e8	0.488967	0.244483	+	0.969653i	$0.421382\pi$
$8$	−1.07374e9	−0.353553
$9$	−1.52883e9	−0.146155
$10$	−1.00000e10	−0.316228
$11$	−3.92190e10	−0.455904	−0.227952	−	0.973672i	$-0.573203\pi$
$11$	−3.92190e10	−0.455904	−0.227952	+	0.973672i	$0.573203\pi$
$12$	−9.90975e10	−0.462019
$13$	−4.64598e11	−0.934701	−0.467350	−	0.884072i	$-0.654791\pi$
$13$	−4.64598e11	−0.934701	−0.467350	+	0.884072i	$0.654791\pi$
$14$	−3.74204e11	−0.345752
$15$	−9.22917e11	−0.413242
$16$	1.09951e12	0.250000
$17$	2.43124e11	0.0292492	0.0146246	−	0.999893i	$-0.495345\pi$
$17$	2.43124e11	0.0292492	0.0146246	+	0.999893i	$0.495345\pi$
$18$	1.56552e12	0.103347
$19$	−6.74889e12	−0.252534	−0.126267	−	0.991996i	$-0.540300\pi$
$19$	−6.74889e12	−0.252534	−0.126267	+	0.991996i	$0.540300\pi$
$20$	1.02400e13	0.223607
$21$	−3.45360e13	−0.451824
$22$	4.01602e13	0.322373
$23$	−1.66102e14	−0.836052	−0.418026	−	0.908435i	$-0.637278\pi$
$23$	−1.66102e14	−0.836052	−0.418026	+	0.908435i	$0.637278\pi$
$24$	1.01476e14	0.326697
$25$	9.53674e13	0.200000
$26$	4.75749e14	0.660933
$27$	1.13306e15	1.05909
$28$	3.83185e14	0.244483
$29$	2.85150e15	1.25862	0.629310	−	0.777155i	$-0.283338\pi$
$29$	2.85150e15	1.25862	0.629310	+	0.777155i	$0.283338\pi$
$30$	9.45067e14	0.292206
$31$	3.48202e15	0.763017	0.381508	−	0.924365i	$-0.375405\pi$
$31$	3.48202e15	0.763017	0.381508	+	0.924365i	$0.375405\pi$
$32$	−1.12590e15	−0.176777
$33$	3.70646e15	0.421272
$34$	−2.48959e14	−0.0206823
$35$	3.56869e15	0.218673
$36$	−1.60309e15	−0.0730774
$37$	3.87028e15	0.132320	0.0661598	−	0.997809i	$-0.478925\pi$
$37$	3.87028e15	0.132320	0.0661598	+	0.997809i	$0.478925\pi$
$38$	6.91086e15	0.178568
$39$	4.39077e16	0.863698
$40$	−1.04858e16	−0.158114
$41$	1.53913e17	1.79079	0.895396	−	0.445272i	$-0.146893\pi$
$41$	1.53913e17	1.79079	0.895396	+	0.445272i	$0.146893\pi$
$42$	3.53648e16	0.319488
$43$	−6.75910e15	−0.0476947	−0.0238473	−	0.999716i	$-0.507592\pi$
$43$	−6.75910e15	−0.0476947	−0.0238473	+	0.999716i	$0.507592\pi$
$44$	−4.11241e16	−0.227952
$45$	−1.49300e16	−0.0653624
$46$	1.70089e17	0.591178
$47$	−1.11128e17	−0.308174	−0.154087	−	0.988057i	$-0.549244\pi$
$47$	−1.11128e17	−0.308174	−0.154087	+	0.988057i	$0.549244\pi$
$48$	−1.03911e17	−0.231009
$49$	−4.25004e17	−0.760911
$50$	−9.76562e16	−0.141421
$51$	−2.29769e16	−0.0270274
$52$	−4.87167e17	−0.467350
$53$	−2.06153e18	−1.61917	−0.809584	−	0.587003i	$-0.800307\pi$
$53$	−2.06153e18	−1.61917	−0.809584	+	0.587003i	$0.800307\pi$
$54$	−1.16025e18	−0.748890
$55$	−3.82998e17	−0.203886
$56$	−3.92382e17	−0.172876
$57$	6.37815e17	0.233351
$58$	−2.91994e18	−0.889978
$59$	5.84178e18	1.48799	0.743993	−	0.668188i	$-0.232930\pi$
$59$	5.84178e18	1.48799	0.743993	+	0.668188i	$0.232930\pi$
$60$	−9.67749e17	−0.206621
$61$	4.90762e18	0.880861	0.440431	−	0.897787i	$-0.354826\pi$
$61$	4.90762e18	0.880861	0.440431	+	0.897787i	$0.354826\pi$
$62$	−3.56559e18	−0.539534
$63$	−5.58686e17	−0.0714648
$64$	1.15292e18	0.125000
$65$	−4.53709e18	−0.418011
$66$	−3.79541e18	−0.297884
$67$	1.35893e19	0.910776	0.455388	−	0.890293i	$-0.349500\pi$
$67$	1.35893e19	0.910776	0.455388	+	0.890293i	$0.349500\pi$
$68$	2.54934e17	0.0146246
$69$	1.56978e19	0.772543
$70$	−3.65434e18	−0.154625
$71$	3.28855e19	1.19893	0.599463	−	0.800403i	$-0.295381\pi$
$71$	3.28855e19	1.19893	0.599463	+	0.800403i	$0.295381\pi$
$72$	1.64157e18	0.0516735
$73$	3.25004e19	0.885112	0.442556	−	0.896741i	$-0.354072\pi$
$73$	3.25004e19	0.885112	0.442556	+	0.896741i	$0.354072\pi$
$74$	−3.96317e18	−0.0935641
$75$	−9.01286e18	−0.184807
$76$	−7.07672e18	−0.126267
$77$	−1.43319e19	−0.222922
$78$	−4.49615e19	−0.610727
$79$	5.11527e19	0.607832	0.303916	−	0.952699i	$-0.401706\pi$
$79$	5.11527e19	0.607832	0.303916	+	0.952699i	$0.401706\pi$
$80$	1.07374e19	0.111803
$81$	−9.10896e19	−0.832484
$82$	−1.57607e20	−1.26628
$83$	2.02190e20	1.43034	0.715171	−	0.698949i	$-0.246349\pi$
$83$	2.02190e20	1.43034	0.715171	+	0.698949i	$0.246349\pi$
$84$	−3.62136e19	−0.225912
$85$	2.37426e18	0.0130807
$86$	6.92131e18	0.0337252
$87$	−2.69486e20	−1.16301
$88$	4.21111e19	0.161186
$89$	2.17189e20	0.738316	0.369158	−	0.929367i	$-0.379646\pi$
$89$	2.17189e20	0.738316	0.369158	+	0.929367i	$0.379646\pi$
$90$	1.52883e19	0.0462182
$91$	−1.69780e20	−0.457038
$92$	−1.74171e20	−0.418026
$93$	−3.29075e20	−0.705056
$94$	1.13795e20	0.217912
$95$	−6.59071e19	−0.112937
$96$	1.06405e20	0.163348
$97$	−1.03286e21	−1.42213	−0.711063	−	0.703129i	$-0.751786\pi$
$97$	−1.03286e21	−1.42213	−0.711063	+	0.703129i	$0.751786\pi$
$98$	4.35204e20	0.538046
$99$	5.99592e19	0.0666325
$100$	1.00000e20	0.100000
$101$	−9.83683e20	−0.886096	−0.443048	−	0.896498i	$-0.646103\pi$
$101$	−9.83683e20	−0.886096	−0.443048	+	0.896498i	$0.646103\pi$
$102$	2.35283e19	0.0191113
$103$	1.00540e21	0.737140	0.368570	−	0.929600i	$-0.379848\pi$
$103$	1.00540e21	0.737140	0.368570	+	0.929600i	$0.379848\pi$
$104$	4.98859e20	0.330467
$105$	−3.37265e20	−0.202062
$106$	2.11100e21	1.14493
$107$	3.28755e21	1.61563	0.807817	−	0.589433i	$-0.200649\pi$
$107$	3.28755e21	1.61563	0.807817	+	0.589433i	$0.200649\pi$
$108$	1.18810e21	0.529545
$109$	2.52264e21	1.02065	0.510324	−	0.859982i	$-0.329525\pi$
$109$	2.52264e21	1.02065	0.510324	+	0.859982i	$0.329525\pi$
$110$	3.92190e20	0.144169
$111$	−3.65767e20	−0.122268
$112$	4.01799e20	0.122242
$113$	−2.85082e21	−0.790034	−0.395017	−	0.918674i	$-0.629261\pi$
$113$	−2.85082e21	−0.790034	−0.395017	+	0.918674i	$0.629261\pi$
$114$	−6.53123e20	−0.165004
$115$	−1.62209e21	−0.373894
$116$	2.99001e21	0.629310
$117$	7.10292e20	0.136611
$118$	−5.98198e21	−1.05216
$119$	8.88458e19	0.0143019
$120$	9.90975e20	0.146103
$121$	−5.86212e21	−0.792152
$122$	−5.02540e21	−0.622863
$123$	−1.45458e22	−1.65476
$124$	3.65117e21	0.381508
$125$	9.31323e20	0.0894427
$126$	5.72095e20	0.0505332
$127$	1.38451e21	0.112553	0.0562764	−	0.998415i	$-0.482077\pi$
$127$	1.38451e21	0.112553	0.0562764	+	0.998415i	$0.482077\pi$
$128$	−1.18059e21	−0.0883883
$129$	6.38780e20	0.0440717
$130$	4.64598e21	0.295578
$131$	−6.11455e21	−0.358935	−0.179468	−	0.983764i	$-0.557438\pi$
$131$	−6.11455e21	−0.358935	−0.179468	+	0.983764i	$0.557438\pi$
$132$	3.88650e21	0.210636
$133$	−2.46627e21	−0.123481
$134$	−1.39154e22	−0.644016
$135$	1.10650e22	0.473639
$136$	−2.61053e20	−0.0103412
$137$	3.06697e22	1.12498	0.562488	−	0.826806i	$-0.309844\pi$
$137$	3.06697e22	1.12498	0.562488	+	0.826806i	$0.309844\pi$
$138$	−1.60745e22	−0.546271
$139$	2.77909e21	0.0875483	0.0437742	−	0.999041i	$-0.486062\pi$
$139$	2.77909e21	0.0875483	0.0437742	+	0.999041i	$0.486062\pi$
$140$	3.74204e21	0.109336
$141$	1.05024e22	0.284765
$142$	−3.36748e22	−0.847768
$143$	1.82211e22	0.426134
$144$	−1.68097e21	−0.0365387
$145$	2.78467e22	0.562872
$146$	−3.32804e22	−0.625868
$147$	4.01657e22	0.703111
$148$	4.05828e21	0.0661598
$149$	1.15060e23	1.74771	0.873854	−	0.486188i	$-0.161613\pi$
$149$	1.15060e23	1.74771	0.873854	+	0.486188i	$0.161613\pi$
$150$	9.22917e21	0.130679
$151$	−9.22398e22	−1.21804	−0.609019	−	0.793156i	$-0.708437\pi$
$151$	−9.22398e22	−1.21804	−0.609019	+	0.793156i	$0.708437\pi$
$152$	7.24656e21	0.0892842
$153$	−3.71696e20	−0.00427491
$154$	1.46759e22	0.157630
$155$	3.40041e22	0.341231
$156$	4.60405e22	0.431849
$157$	−9.83630e22	−0.862751	−0.431375	−	0.902173i	$-0.641971\pi$
$157$	−9.83630e22	−0.862751	−0.431375	+	0.902173i	$0.641971\pi$
$158$	−5.23803e22	−0.429802
$159$	1.94828e23	1.49617
$160$	−1.09951e22	−0.0790569
$161$	−6.06994e22	−0.408802
$162$	9.32757e22	0.588655
$163$	−2.88242e23	−1.70525	−0.852623	−	0.522526i	$-0.824990\pi$
$163$	−2.88242e23	−1.70525	−0.852623	+	0.522526i	$0.824990\pi$
$164$	1.61390e23	0.895396
$165$	3.61959e22	0.188399
$166$	−2.07043e23	−1.01140
$167$	−1.80201e23	−0.826484	−0.413242	−	0.910621i	$-0.635604\pi$
$167$	−1.80201e23	−0.826484	−0.413242	+	0.910621i	$0.635604\pi$
$168$	3.70827e22	0.159744
$169$	−3.12128e22	−0.126335
$170$	−2.43124e21	−0.00924942
$171$	1.03179e22	0.0369090
$172$	−7.08743e21	−0.0238473
$173$	−4.53364e23	−1.43537	−0.717683	−	0.696370i	$-0.754797\pi$
$173$	−4.53364e23	−1.43537	−0.717683	+	0.696370i	$0.754797\pi$
$174$	2.75954e23	0.822373
$175$	3.48505e22	0.0977934
$176$	−4.31217e22	−0.113976
$177$	−5.52087e23	−1.37495
$178$	−2.22401e23	−0.522068
$179$	6.58352e23	1.45714	0.728570	−	0.684971i	$-0.240185\pi$
$179$	6.58352e23	1.45714	0.728570	+	0.684971i	$0.240185\pi$
$180$	−1.56552e22	−0.0326812
$181$	1.55219e23	0.305717	0.152858	−	0.988248i	$-0.451152\pi$
$181$	1.55219e23	0.305717	0.152858	+	0.988248i	$0.451152\pi$
$182$	1.73855e23	0.323174
$183$	−4.63803e23	−0.813949
$184$	1.78351e23	0.295589
$185$	3.77957e22	0.0591751
$186$	3.36973e23	0.498550
$187$	−9.53509e21	−0.0133348
$188$	−1.16526e23	−0.154087
$189$	4.14058e23	0.517860
$190$	6.74889e22	0.0798582
$191$	6.36717e23	0.713010	0.356505	−	0.934293i	$-0.383968\pi$
$191$	6.36717e23	0.713010	0.356505	+	0.934293i	$0.383968\pi$
$192$	−1.08959e23	−0.115505
$193$	−4.28896e23	−0.430527	−0.215263	−	0.976556i	$-0.569061\pi$
$193$	−4.28896e23	−0.430527	−0.215263	+	0.976556i	$0.569061\pi$
$194$	1.05765e24	1.00559
$195$	4.28786e23	0.386258
$196$	−4.45649e23	−0.380456
$197$	−2.72735e23	−0.220722	−0.110361	−	0.993892i	$-0.535201\pi$
$197$	−2.72735e23	−0.220722	−0.110361	+	0.993892i	$0.535201\pi$
$198$	−6.13982e22	−0.0471163
$199$	2.24441e24	1.63360	0.816799	−	0.576923i	$-0.195747\pi$
$199$	2.24441e24	1.63360	0.816799	+	0.576923i	$0.195747\pi$
$200$	−1.02400e23	−0.0707107
$201$	−1.28428e24	−0.841591
$202$	1.00729e24	0.626565
$203$	1.04203e24	0.615423
$204$	−2.40930e22	−0.0135137
$205$	1.50306e24	0.800866
$206$	−1.02953e24	−0.521236
$207$	2.53942e23	0.122193
$208$	−5.10831e23	−0.233675
$209$	2.64685e23	0.115131
$210$	3.45360e23	0.142879
$211$	−3.61254e24	−1.42183	−0.710913	−	0.703280i	$-0.751718\pi$
$211$	−3.61254e24	−1.42183	−0.710913	+	0.703280i	$0.751718\pi$
$212$	−2.16167e24	−0.809584
$213$	−3.10790e24	−1.10785
$214$	−3.36646e24	−1.14243
$215$	−6.60068e22	−0.0213297
$216$	−1.21661e24	−0.374445
$217$	1.27245e24	0.373090
$218$	−2.58318e24	−0.721708
$219$	−3.07150e24	−0.817876
$220$	−4.01602e23	−0.101943
$221$	−1.12955e23	−0.0273393
$222$	3.74546e23	0.0864567
$223$	4.19001e24	0.922600	0.461300	−	0.887244i	$-0.347383\pi$
$223$	4.19001e24	0.922600	0.461300	+	0.887244i	$0.347383\pi$
$224$	−4.11442e23	−0.0864379
$225$	−1.45801e23	−0.0292309
$226$	2.91924e24	0.558638
$227$	7.86051e24	1.43608	0.718041	−	0.696001i	$-0.245039\pi$
$227$	7.86051e24	1.43608	0.718041	+	0.696001i	$0.245039\pi$
$228$	6.68798e23	0.116675
$229$	3.29155e23	0.0548439	0.0274220	−	0.999624i	$-0.491270\pi$
$229$	3.29155e23	0.0548439	0.0274220	+	0.999624i	$0.491270\pi$
$230$	1.66102e24	0.264383
$231$	1.35447e24	0.205988
$232$	−3.06177e24	−0.444989
$233$	3.62417e24	0.503468	0.251734	−	0.967796i	$-0.418999\pi$
$233$	3.62417e24	0.503468	0.251734	+	0.967796i	$0.418999\pi$
$234$	−7.27339e23	−0.0965985
$235$	−1.08524e24	−0.137820
$236$	6.12555e24	0.743993
$237$	−4.83427e24	−0.561660
$238$	−9.09781e22	−0.0101130
$239$	−5.27026e23	−0.0560601	−0.0280301	−	0.999607i	$-0.508923\pi$
$239$	−5.27026e23	−0.0560601	−0.0280301	+	0.999607i	$0.508923\pi$
$240$	−1.01476e24	−0.103311
$241$	−3.17826e24	−0.309749	−0.154874	−	0.987934i	$-0.549497\pi$
$241$	−3.17826e24	−0.309749	−0.154874	+	0.987934i	$0.549497\pi$
$242$	6.00281e24	0.560136
$243$	−3.24361e24	−0.289843
$244$	5.14601e24	0.440431
$245$	−4.15043e24	−0.340290
$246$	1.48949e25	1.17009
$247$	3.13552e24	0.236043
$248$	−3.73880e24	−0.269767
$249$	−1.91083e25	−1.32169
$250$	−9.53674e23	−0.0632456
$251$	1.26683e25	0.805649	0.402824	−	0.915277i	$-0.368029\pi$
$251$	1.26683e25	0.805649	0.402824	+	0.915277i	$0.368029\pi$
$252$	−5.85825e23	−0.0357324
$253$	6.51436e24	0.381159
$254$	−1.41774e24	−0.0795868
$255$	−2.24384e23	−0.0120870
$256$	1.20893e24	0.0625000
$257$	−1.86982e24	−0.0927902	−0.0463951	−	0.998923i	$-0.514773\pi$
$257$	−1.86982e24	−0.0927902	−0.0463951	+	0.998923i	$0.514773\pi$
$258$	−6.54111e23	−0.0311634
$259$	1.41433e24	0.0646999
$260$	−4.75749e24	−0.209005
$261$	−4.35946e24	−0.183953
$262$	6.26130e24	0.253806
$263$	4.09180e25	1.59360	0.796800	−	0.604243i	$-0.206524\pi$
$263$	4.09180e25	1.59360	0.796800	+	0.604243i	$0.206524\pi$
$264$	−3.97978e24	−0.148942
$265$	−2.01321e25	−0.724114
$266$	2.52546e24	0.0873140
$267$	−2.05258e25	−0.682232
$268$	1.42494e25	0.455388
$269$	−3.93628e25	−1.20973	−0.604864	−	0.796329i	$-0.706772\pi$
$269$	−3.93628e25	−1.20973	−0.604864	+	0.796329i	$0.706772\pi$
$270$	−1.13306e25	−0.334914
$271$	−2.31984e25	−0.659600	−0.329800	−	0.944051i	$-0.606981\pi$
$271$	−2.31984e25	−0.659600	−0.329800	+	0.944051i	$0.606981\pi$
$272$	2.67318e23	0.00731231
$273$	1.60454e25	0.422320
$274$	−3.14057e25	−0.795478
$275$	−3.74021e24	−0.0911808
$276$	1.64603e25	0.386272
$277$	−6.39590e25	−1.44499	−0.722494	−	0.691378i	$-0.757004\pi$
$277$	−6.39590e25	−1.44499	−0.722494	+	0.691378i	$0.757004\pi$
$278$	−2.84579e24	−0.0619060
$279$	−5.32342e24	−0.111518
$280$	−3.83185e24	−0.0773124
$281$	−4.18321e25	−0.813005	−0.406503	−	0.913650i	$-0.633252\pi$
$281$	−4.18321e25	−0.813005	−0.406503	+	0.913650i	$0.633252\pi$
$282$	−1.07544e25	−0.201359
$283$	7.89427e25	1.42415	0.712073	−	0.702106i	$-0.247757\pi$
$283$	7.89427e25	1.42415	0.712073	+	0.702106i	$0.247757\pi$
$284$	3.44830e25	0.599463
$285$	6.22867e24	0.104358
$286$	−1.86584e25	−0.301322
$287$	5.62450e25	0.875638
$288$	1.72131e24	0.0258367
$289$	−6.90328e25	−0.999144
$290$	−2.85150e25	−0.398010
$291$	9.76121e25	1.31410
$292$	3.40791e25	0.442556
$293$	1.30571e26	1.63583	0.817913	−	0.575343i	$-0.195131\pi$
$293$	1.30571e26	1.63583	0.817913	+	0.575343i	$0.195131\pi$
$294$	−4.11297e25	−0.497174
$295$	5.70486e25	0.665447
$296$	−4.15568e24	−0.0467820
$297$	−4.44374e25	−0.482843
$298$	−1.17822e26	−1.23582
$299$	7.71709e25	0.781458
$300$	−9.45067e24	−0.0924037
$301$	−2.47000e24	−0.0233211
$302$	9.44536e25	0.861282
$303$	9.29647e25	0.818786
$304$	−7.42048e24	−0.0631334
$305$	4.79259e25	0.393933
$306$	3.80616e23	0.00302282
$307$	3.70803e25	0.284571	0.142285	−	0.989826i	$-0.454555\pi$
$307$	3.70803e25	0.284571	0.142285	+	0.989826i	$0.454555\pi$
$308$	−1.50281e25	−0.111461
$309$	−9.50175e25	−0.681145
$310$	−3.48202e25	−0.241287
$311$	1.83082e26	1.22648	0.613242	−	0.789895i	$-0.289865\pi$
$311$	1.83082e26	1.22648	0.613242	+	0.789895i	$0.289865\pi$
$312$	−4.71455e25	−0.305363
$313$	−2.37945e26	−1.49026	−0.745129	−	0.666921i	$-0.767612\pi$
$313$	−2.37945e26	−1.49026	−0.745129	+	0.666921i	$0.767612\pi$
$314$	1.00724e26	0.610057
$315$	−5.45592e24	−0.0319600
$316$	5.36375e25	0.303916
$317$	1.60193e26	0.878055	0.439027	−	0.898474i	$-0.355323\pi$
$317$	1.60193e26	0.878055	0.439027	+	0.898474i	$0.355323\pi$
$318$	−1.99504e26	−1.05795
$319$	−1.11833e26	−0.573809
$320$	1.12590e25	0.0559017
$321$	−3.10696e26	−1.49291
$322$	6.21562e25	0.289066
$323$	−1.64082e24	−0.00738642
$324$	−9.55143e25	−0.416242
$325$	−4.43076e25	−0.186940
$326$	2.95160e26	1.20579
$327$	−2.38406e26	−0.943118
$328$	−1.65263e26	−0.633140
$329$	−4.06100e25	−0.150687
$330$	−3.70646e25	−0.133218
$331$	−5.15992e26	−1.79659	−0.898295	−	0.439393i	$-0.855193\pi$
$331$	−5.15992e26	−1.79659	−0.898295	+	0.439393i	$0.855193\pi$
$332$	2.12012e26	0.715171
$333$	−5.91700e24	−0.0193391
$334$	1.84526e26	0.584413
$335$	1.32708e26	0.407312
$336$	−3.79727e25	−0.112956
$337$	−2.13485e26	−0.615535	−0.307768	−	0.951462i	$-0.599582\pi$
$337$	−2.13485e26	−0.615535	−0.307768	+	0.951462i	$0.599582\pi$
$338$	3.19620e25	0.0893322
$339$	2.69421e26	0.730021
$340$	2.48959e24	0.00654033
$341$	−1.36561e26	−0.347862
$342$	−1.05655e25	−0.0260986
$343$	−3.59422e26	−0.861027
$344$	7.25752e24	0.0168626
$345$	1.53299e26	0.345492
$346$	4.64244e26	1.01496
$347$	2.02825e26	0.430191	0.215095	−	0.976593i	$-0.430994\pi$
$347$	2.02825e26	0.430191	0.215095	+	0.976593i	$0.430994\pi$
$348$	−2.82577e26	−0.581506
$349$	7.65093e26	1.52773	0.763866	−	0.645375i	$-0.223299\pi$
$349$	7.65093e26	1.52773	0.763866	+	0.645375i	$0.223299\pi$
$350$	−3.56869e25	−0.0691504
$351$	−5.26417e26	−0.989932
$352$	4.41567e25	0.0805932
$353$	5.36101e26	0.949756	0.474878	−	0.880052i	$-0.342492\pi$
$353$	5.36101e26	0.949756	0.474878	+	0.880052i	$0.342492\pi$
$354$	5.65337e26	0.972240
$355$	3.21148e26	0.536176
$356$	2.27739e26	0.369158
$357$	−8.39653e24	−0.0132155
$358$	−6.74153e26	−1.03035
$359$	9.97471e26	1.48050	0.740250	−	0.672332i	$-0.234707\pi$
$359$	9.97471e26	1.48050	0.740250	+	0.672332i	$0.234707\pi$
$360$	1.60309e25	0.0231091
$361$	−6.68662e26	−0.936227
$362$	−1.58944e26	−0.216175
$363$	5.54010e26	0.731978
$364$	−1.78027e26	−0.228519
$365$	3.17386e26	0.395834
$366$	4.74934e26	0.575549
$367$	−7.27262e26	−0.856441	−0.428220	−	0.903674i	$-0.640859\pi$
$367$	−7.27262e26	−0.856441	−0.428220	+	0.903674i	$0.640859\pi$
$368$	−1.82631e26	−0.209013
$369$	−2.35307e26	−0.261733
$370$	−3.87028e25	−0.0418431
$371$	−7.53351e26	−0.791720
$372$	−3.45060e26	−0.352528
$373$	8.47344e26	0.841622	0.420811	−	0.907148i	$-0.361746\pi$
$373$	8.47344e26	0.841622	0.420811	+	0.907148i	$0.361746\pi$
$374$	9.76393e24	0.00942915
$375$	−8.80163e25	−0.0826484
$376$	1.19323e26	0.108956
$377$	−1.32480e27	−1.17643
$378$	−4.23995e26	−0.366182
$379$	9.08041e26	0.762771	0.381385	−	0.924416i	$-0.375447\pi$
$379$	9.08041e26	0.762771	0.381385	+	0.924416i	$0.375447\pi$
$380$	−6.91086e25	−0.0564683
$381$	−1.30845e26	−0.104003
$382$	−6.51998e26	−0.504175
$383$	−3.75246e25	−0.0282312	−0.0141156	−	0.999900i	$-0.504493\pi$
$383$	−3.75246e25	−0.0282312	−0.0141156	+	0.999900i	$0.504493\pi$
$384$	1.11574e26	0.0816741
$385$	−1.39960e26	−0.0996937
$386$	4.39189e26	0.304428
$387$	1.03335e25	0.00697080
$388$	−1.08303e27	−0.711063
$389$	−5.30842e26	−0.339230	−0.169615	−	0.985510i	$-0.554252\pi$
$389$	−5.30842e26	−0.339230	−0.169615	+	0.985510i	$0.554252\pi$
$390$	−4.39077e26	−0.273125
$391$	−4.03835e25	−0.0244539
$392$	4.56344e26	0.269023
$393$	5.77867e26	0.331670
$394$	2.79281e26	0.156074
$395$	4.99538e26	0.271831
$396$	6.28717e25	0.0333162
$397$	1.80269e27	0.930297	0.465149	−	0.885233i	$-0.346001\pi$
$397$	1.80269e27	0.930297	0.465149	+	0.885233i	$0.346001\pi$
$398$	−2.29828e27	−1.15513
$399$	2.33079e26	0.114101
$400$	1.04858e26	0.0500000
$401$	1.75068e27	0.813187	0.406594	−	0.913609i	$-0.366717\pi$
$401$	1.75068e27	0.813187	0.406594	+	0.913609i	$0.366717\pi$
$402$	1.31510e27	0.595095
$403$	−1.61774e27	−0.713192
$404$	−1.03147e27	−0.443048
$405$	−8.89547e26	−0.372298
$406$	−1.06704e27	−0.435170
$407$	−1.51788e26	−0.0603250
$408$	2.46712e25	0.00955563
$409$	−1.99836e27	−0.754362	−0.377181	−	0.926140i	$-0.623107\pi$
$409$	−1.99836e27	−0.754362	−0.377181	+	0.926140i	$0.623107\pi$
$410$	−1.53913e27	−0.566298
$411$	−2.89849e27	−1.03952
$412$	1.05424e27	0.368570
$413$	2.13478e27	0.727576
$414$	−2.60037e26	−0.0864035
$415$	1.97451e27	0.639669
$416$	5.23091e26	0.165233
$417$	−2.62643e26	−0.0808979
$418$	−2.71037e26	−0.0814100
$419$	−2.81050e27	−0.823259	−0.411630	−	0.911351i	$-0.635040\pi$
$419$	−2.81050e27	−0.823259	−0.411630	+	0.911351i	$0.635040\pi$
$420$	−3.53648e26	−0.101031
$421$	4.66949e27	1.30109	0.650546	−	0.759467i	$-0.274540\pi$
$421$	4.66949e27	1.30109	0.650546	+	0.759467i	$0.274540\pi$
$422$	3.69924e27	1.00538
$423$	1.69896e26	0.0450411
$424$	2.21355e27	0.572463
$425$	2.31861e25	0.00584985
$426$	3.18249e27	0.783370
$427$	1.79341e27	0.430712
$428$	3.44725e27	0.807817
$429$	−1.72201e27	−0.393763
$430$	6.75910e25	0.0150824
$431$	−6.66126e26	−0.145059	−0.0725296	−	0.997366i	$-0.523107\pi$
$431$	−6.66126e26	−0.145059	−0.0725296	+	0.997366i	$0.523107\pi$
$432$	1.24581e27	0.264772
$433$	8.02347e27	1.66433	0.832165	−	0.554528i	$-0.187101\pi$
$433$	8.02347e27	1.66433	0.832165	+	0.554528i	$0.187101\pi$
$434$	−1.30299e27	−0.263814
$435$	−2.63170e27	−0.520115
$436$	2.64518e27	0.510324
$437$	1.12101e27	0.211131
$438$	3.14522e27	0.578326
$439$	−6.00429e27	−1.07791	−0.538957	−	0.842333i	$-0.681182\pi$
$439$	−6.00429e27	−1.07791	−0.538957	+	0.842333i	$0.681182\pi$
$440$	4.11241e26	0.0720847
$441$	6.49759e26	0.111211
$442$	1.15666e26	0.0193318
$443$	−2.47404e27	−0.403802	−0.201901	−	0.979406i	$-0.564712\pi$
$443$	−2.47404e27	−0.403802	−0.201901	+	0.979406i	$0.564712\pi$
$444$	−3.83535e26	−0.0611341
$445$	2.12098e27	0.330185
$446$	−4.29057e27	−0.652377
$447$	−1.08740e28	−1.61495
$448$	4.21317e26	0.0611209
$449$	−1.39880e28	−1.98230	−0.991151	−	0.132738i	$-0.957623\pi$
$449$	−1.39880e28	−1.98230	−0.991151	+	0.132738i	$0.957623\pi$
$450$	1.49300e26	0.0206694
$451$	−6.03631e27	−0.816429
$452$	−2.98930e27	−0.395017
$453$	8.71729e27	1.12551
$454$	−8.04916e27	−1.01546
$455$	−1.65801e27	−0.204393
$456$	−6.84849e26	−0.0825019
$457$	5.38517e27	0.633985	0.316993	−	0.948428i	$-0.397327\pi$
$457$	5.38517e27	0.633985	0.316993	+	0.948428i	$0.397327\pi$
$458$	−3.37055e26	−0.0387805
$459$	2.75474e26	0.0309776
$460$	−1.70089e27	−0.186947
$461$	4.10176e27	0.440667	0.220334	−	0.975425i	$-0.429285\pi$
$461$	4.10176e27	0.440667	0.220334	+	0.975425i	$0.429285\pi$
$462$	−1.38697e27	−0.145656
$463$	−1.59610e27	−0.163855	−0.0819276	−	0.996638i	$-0.526108\pi$
$463$	−1.59610e27	−0.163855	−0.0819276	+	0.996638i	$0.526108\pi$
$464$	3.13526e27	0.314655
$465$	−3.21362e27	−0.315311
$466$	−3.71115e27	−0.356006
$467$	−5.00681e27	−0.469607	−0.234803	−	0.972043i	$-0.575445\pi$
$467$	−5.00681e27	−0.469607	−0.234803	+	0.972043i	$0.575445\pi$
$468$	7.44795e26	0.0683054
$469$	4.96599e27	0.445339
$470$	1.11128e27	0.0974532
$471$	9.29596e27	0.797214
$472$	−6.27256e27	−0.526082
$473$	2.65085e26	0.0217442
$474$	4.95029e27	0.397153
$475$	−6.43624e26	−0.0505067
$476$	9.31616e25	0.00715095
$477$	3.15172e27	0.236649
$478$	5.39674e26	0.0396405
$479$	4.44191e27	0.319188	0.159594	−	0.987183i	$-0.448981\pi$
$479$	4.44191e27	0.319188	0.159594	+	0.987183i	$0.448981\pi$
$480$	1.03911e27	0.0730516
$481$	−1.79813e27	−0.123679
$482$	3.25453e27	0.219026
$483$	5.73650e27	0.377748
$484$	−6.14688e27	−0.396076
$485$	−1.00865e28	−0.635994
$486$	3.32146e27	0.204950
$487$	1.46905e28	0.887119	0.443559	−	0.896245i	$-0.353716\pi$
$487$	1.46905e28	0.887119	0.443559	+	0.896245i	$0.353716\pi$
$488$	−5.26951e27	−0.311431
$489$	2.72408e28	1.57571
$490$	4.25004e27	0.240621
$491$	−2.20895e27	−0.122414	−0.0612069	−	0.998125i	$-0.519495\pi$
$491$	−2.20895e27	−0.122414	−0.0612069	+	0.998125i	$0.519495\pi$
$492$	−1.52524e28	−0.827379
$493$	6.93269e26	0.0368137
$494$	−3.21078e27	−0.166908
$495$	5.85539e26	0.0297990
$496$	3.82853e27	0.190754
$497$	1.20175e28	0.586235
$498$	1.95669e28	0.934576
$499$	3.64836e28	1.70625	0.853125	−	0.521707i	$-0.174705\pi$
$499$	3.64836e28	1.70625	0.853125	+	0.521707i	$0.174705\pi$
$500$	9.76563e26	0.0447214
$501$	1.70302e28	0.763702
$502$	−1.29724e28	−0.569680
$503$	−4.00705e28	−1.72330	−0.861651	−	0.507502i	$-0.830569\pi$
$503$	−4.00705e28	−1.72330	−0.861651	+	0.507502i	$0.830569\pi$
$504$	5.99885e26	0.0252666
$505$	−9.60628e27	−0.396274
$506$	−6.67071e27	−0.269520
$507$	2.94982e27	0.116738
$508$	1.45176e27	0.0562764
$509$	−4.63213e28	−1.75891	−0.879456	−	0.475979i	$-0.842094\pi$
$509$	−4.63213e28	−1.75891	−0.879456	+	0.475979i	$0.842094\pi$
$510$	2.29769e26	0.00854681
$511$	1.18767e28	0.432790
$512$	−1.23794e27	−0.0441942
$513$	−7.64689e27	−0.267456
$514$	1.91470e27	0.0656126
$515$	9.81840e27	0.329659
$516$	6.69810e26	0.0220358
$517$	4.35833e27	0.140498
$518$	−1.44828e27	−0.0457497
$519$	4.28459e28	1.32633
$520$	4.87167e27	0.147789
$521$	−1.41568e28	−0.420891	−0.210445	−	0.977606i	$-0.567491\pi$
$521$	−1.41568e28	−0.420891	−0.210445	+	0.977606i	$0.567491\pi$
$522$	4.46409e27	0.130075
$523$	−5.46471e28	−1.56063	−0.780314	−	0.625388i	$-0.784941\pi$
$523$	−5.46471e28	−1.56063	−0.780314	+	0.625388i	$0.784941\pi$
$524$	−6.41158e27	−0.179468
$525$	−3.29361e27	−0.0903647
$526$	−4.19001e28	−1.12685
$527$	8.46564e26	0.0223177
$528$	4.07529e27	0.105318
$529$	−1.18816e28	−0.301017
$530$	2.06153e28	0.512026
$531$	−8.93108e27	−0.217476
$532$	−2.58607e27	−0.0617403
$533$	−7.15078e28	−1.67385
$534$	2.10184e28	0.482411
$535$	3.21050e28	0.722534
$536$	−1.45914e28	−0.322008
$537$	−6.22187e28	−1.34645
$538$	4.03076e28	0.855406
$539$	1.66682e28	0.346902
$540$	1.16025e28	0.236820
$541$	−1.97332e28	−0.395026	−0.197513	−	0.980300i	$-0.563286\pi$
$541$	−1.97332e28	−0.395026	−0.197513	+	0.980300i	$0.563286\pi$
$542$	2.37552e28	0.466408
$543$	−1.46692e28	−0.282494
$544$	−2.73734e26	−0.00517058
$545$	2.46351e28	0.456448
$546$	−1.64304e28	−0.298625
$547$	4.31761e28	0.769797	0.384899	−	0.922959i	$-0.374236\pi$
$547$	4.31761e28	0.769797	0.384899	+	0.922959i	$0.374236\pi$
$548$	3.21595e28	0.562488
$549$	−7.50291e27	−0.128742
$550$	3.82998e27	0.0644745
$551$	−1.92445e28	−0.317844
$552$	−1.68554e28	−0.273135
$553$	1.86929e28	0.297210
$554$	6.54940e28	1.02176
$555$	−3.57195e27	−0.0546800
$556$	2.91409e27	0.0437742
$557$	3.91712e27	0.0577414	0.0288707	−	0.999583i	$-0.490809\pi$
$557$	3.91712e27	0.0577414	0.0288707	+	0.999583i	$0.490809\pi$
$558$	5.45119e27	0.0788555
$559$	3.14027e27	0.0445802
$560$	3.92382e27	0.0546682
$561$	9.01130e26	0.0123219
$562$	4.28361e28	0.574881
$563$	−2.70683e28	−0.356551	−0.178276	−	0.983981i	$-0.557052\pi$
$563$	−2.70683e28	−0.356551	−0.178276	+	0.983981i	$0.557052\pi$
$564$	1.10125e28	0.142382
$565$	−2.78400e28	−0.353314
$566$	−8.08373e28	−1.00702
$567$	−3.32872e28	−0.407057
$568$	−3.53106e28	−0.423884
$569$	4.56161e28	0.537575	0.268788	−	0.963199i	$-0.413377\pi$
$569$	4.56161e28	0.537575	0.268788	+	0.963199i	$0.413377\pi$
$570$	−6.37815e27	−0.0737920
$571$	1.31174e29	1.48994	0.744968	−	0.667100i	$-0.232465\pi$
$571$	1.31174e29	1.48994	0.744968	+	0.667100i	$0.232465\pi$
$572$	1.91062e28	0.213067
$573$	−6.01740e28	−0.658848
$574$	−5.75949e28	−0.619169
$575$	−1.58407e28	−0.167210
$576$	−1.76262e27	−0.0182693
$577$	1.42017e29	1.44542	0.722710	−	0.691151i	$-0.242896\pi$
$577$	1.42017e29	1.44542	0.722710	+	0.691151i	$0.242896\pi$
$578$	7.06896e28	0.706502
$579$	4.05336e28	0.397823
$580$	2.91994e28	0.281436
$581$	7.38871e28	0.699390
$582$	−9.99548e28	−0.929207
$583$	8.08510e28	0.738185
$584$	−3.48970e28	−0.312934
$585$	6.93644e27	0.0610942
$586$	−1.33705e29	−1.15670
$587$	9.99241e28	0.849122	0.424561	−	0.905399i	$-0.360428\pi$
$587$	9.99241e28	0.849122	0.424561	+	0.905399i	$0.360428\pi$
$588$	4.21168e28	0.351555
$589$	−2.34998e28	−0.192687
$590$	−5.84178e28	−0.470542
$591$	2.57753e28	0.203955
$592$	4.25542e27	0.0330799
$593$	−1.01433e29	−0.774647	−0.387323	−	0.921944i	$-0.626600\pi$
$593$	−1.01433e29	−0.774647	−0.387323	+	0.921944i	$0.626600\pi$
$594$	4.55039e28	0.341422
$595$	8.67635e26	0.00639601
$596$	1.20649e29	0.873854
$597$	−2.12112e29	−1.50950
$598$	−7.90230e28	−0.552574
$599$	5.05093e28	0.347048	0.173524	−	0.984830i	$-0.444485\pi$
$599$	5.05093e28	0.347048	0.173524	+	0.984830i	$0.444485\pi$
$600$	9.67749e27	0.0653393
$601$	1.29341e29	0.858130	0.429065	−	0.903274i	$-0.358843\pi$
$601$	1.29341e29	0.858130	0.429065	+	0.903274i	$0.358843\pi$
$602$	2.52928e27	0.0164905
$603$	−2.07757e28	−0.133114
$604$	−9.67205e28	−0.609019
$605$	−5.72473e28	−0.354261
$606$	−9.51958e28	−0.578969
$607$	−8.14047e28	−0.486596	−0.243298	−	0.969952i	$-0.578229\pi$
$607$	−8.14047e28	−0.486596	−0.243298	+	0.969952i	$0.578229\pi$
$608$	7.59857e27	0.0446421
$609$	−9.84793e28	−0.568674
$610$	−4.90762e28	−0.278553
$611$	5.16299e28	0.288051
$612$	−3.89751e26	−0.00213746
$613$	2.20870e28	0.119070	0.0595349	−	0.998226i	$-0.481038\pi$
$613$	2.20870e28	0.119070	0.0595349	+	0.998226i	$0.481038\pi$
$614$	−3.79702e28	−0.201222
$615$	−1.42049e29	−0.740030
$616$	1.53888e28	0.0788148
$617$	−1.09793e29	−0.552818	−0.276409	−	0.961040i	$-0.589144\pi$
$617$	−1.09793e29	−0.552818	−0.276409	+	0.961040i	$0.589144\pi$
$618$	9.72979e28	0.481642
$619$	−1.54602e29	−0.752424	−0.376212	−	0.926534i	$-0.622774\pi$
$619$	−1.54602e29	−0.752424	−0.376212	+	0.926534i	$0.622774\pi$
$620$	3.56559e28	0.170616
$621$	−1.88204e29	−0.885454
$622$	−1.87476e29	−0.867255
$623$	7.93682e28	0.361012
$624$	4.82770e28	0.215925
$625$	9.09495e27	0.0400000
$626$	2.43656e29	1.05377
$627$	−2.50145e28	−0.106385
$628$	−1.03141e29	−0.431375
$629$	9.40958e26	0.00387025
$630$	5.58686e27	0.0225992
$631$	−1.10811e29	−0.440832	−0.220416	−	0.975406i	$-0.570742\pi$
$631$	−1.10811e29	−0.440832	−0.220416	+	0.975406i	$0.570742\pi$
$632$	−5.49248e28	−0.214901
$633$	3.41409e29	1.31382
$634$	−1.64038e29	−0.620878
$635$	1.35206e28	0.0503351
$636$	2.04292e29	0.748086
$637$	1.97456e29	0.711224
$638$	1.14517e29	0.405744
$639$	−5.02764e28	−0.175229
$640$	−1.15292e28	−0.0395285
$641$	1.41424e29	0.476995	0.238497	−	0.971143i	$-0.423345\pi$
$641$	1.41424e29	0.476995	0.238497	+	0.971143i	$0.423345\pi$
$642$	3.18153e29	1.05564
$643$	5.97065e29	1.94897	0.974487	−	0.224442i	$-0.0720559\pi$
$643$	5.97065e29	1.94897	0.974487	+	0.224442i	$0.0720559\pi$
$644$	−6.36479e28	−0.204401
$645$	6.23809e27	0.0197094
$646$	1.68020e27	0.00522299
$647$	4.89100e29	1.49590	0.747951	−	0.663754i	$-0.231038\pi$
$647$	4.89100e29	1.49590	0.747951	+	0.663754i	$0.231038\pi$
$648$	9.78067e28	0.294328
$649$	−2.29109e29	−0.678378
$650$	4.53709e28	0.132187
$651$	−1.20255e29	−0.344749
$652$	−3.02244e29	−0.852623
$653$	2.34337e29	0.650508	0.325254	−	0.945627i	$-0.394550\pi$
$653$	2.34337e29	0.650508	0.325254	+	0.945627i	$0.394550\pi$
$654$	2.44128e29	0.666885
$655$	−5.97124e28	−0.160521
$656$	1.69229e29	0.447698
$657$	−4.96875e28	−0.129363
$658$	4.15846e28	0.106552
$659$	−4.06286e29	−1.02455	−0.512277	−	0.858820i	$-0.671198\pi$
$659$	−4.06286e29	−1.02455	−0.512277	+	0.858820i	$0.671198\pi$
$660$	3.79541e28	0.0941993
$661$	−3.10306e29	−0.758009	−0.379005	−	0.925395i	$-0.623734\pi$
$661$	−3.10306e29	−0.758009	−0.379005	+	0.925395i	$0.623734\pi$
$662$	5.28376e29	1.27038
$663$	1.06750e28	0.0252625
$664$	−2.17100e29	−0.505702
$665$	−2.40847e28	−0.0552222
$666$	6.05901e27	0.0136748
$667$	−4.73641e29	−1.05227
$668$	−1.88955e29	−0.413242
$669$	−3.95984e29	−0.852517
$670$	−1.35893e29	−0.288013
$671$	−1.92472e29	−0.401588
$672$	3.88840e28	0.0798719
$673$	−1.94077e29	−0.392478	−0.196239	−	0.980556i	$-0.562873\pi$
$673$	−1.94077e29	−0.392478	−0.196239	+	0.980556i	$0.562873\pi$
$674$	2.18608e29	0.435249
$675$	1.08057e29	0.211818
$676$	−3.27290e28	−0.0631674
$677$	2.34383e29	0.445395	0.222697	−	0.974888i	$-0.428514\pi$
$677$	2.34383e29	0.445395	0.222697	+	0.974888i	$0.428514\pi$
$678$	−2.75887e29	−0.516203
$679$	−3.77442e29	−0.695372
$680$	−2.54934e27	−0.00462471
$681$	−7.42871e29	−1.32699
$682$	1.39839e29	0.245976
$683$	−3.67410e29	−0.636405	−0.318202	−	0.948023i	$-0.603079\pi$
$683$	−3.67410e29	−0.636405	−0.318202	+	0.948023i	$0.603079\pi$
$684$	1.08191e28	0.0184545
$685$	2.99508e29	0.503104
$686$	3.68049e29	0.608838
$687$	−3.11074e28	−0.0506778
$688$	−7.43171e27	−0.0119237
$689$	9.57782e29	1.51344
$690$	−1.56978e29	−0.244300
$691$	9.60338e27	0.0147199	0.00735994	−	0.999973i	$-0.497657\pi$
$691$	9.60338e27	0.0147199	0.00735994	+	0.999973i	$0.497657\pi$
$692$	−4.75386e29	−0.717683
$693$	2.19111e28	0.0325811
$694$	−2.07692e29	−0.304191
$695$	2.71396e28	0.0391528
$696$	2.89358e29	0.411187
$697$	3.74200e28	0.0523793
$698$	−7.83455e29	−1.08027
$699$	−3.42509e29	−0.465223
$700$	3.65434e28	0.0488967
$701$	9.60216e29	1.26570	0.632849	−	0.774276i	$-0.281886\pi$
$701$	9.60216e29	1.26570	0.632849	+	0.774276i	$0.281886\pi$
$702$	5.39051e29	0.699988
$703$	−2.61201e28	−0.0334152
$704$	−4.52164e28	−0.0569880
$705$	1.02562e29	0.127351
$706$	−5.48967e29	−0.671579
$707$	−3.59471e29	−0.433272
$708$	−5.78905e29	−0.687477
$709$	1.47754e30	1.72884	0.864418	−	0.502775i	$-0.167687\pi$
$709$	1.47754e30	1.72884	0.864418	+	0.502775i	$0.167687\pi$
$710$	−3.28855e29	−0.379133
$711$	−7.82037e28	−0.0888376
$712$	−2.33205e29	−0.261034
$713$	−5.78372e29	−0.637922
$714$	8.59805e27	0.00934477
$715$	1.77940e29	0.190573
$716$	6.90332e29	0.728570
$717$	4.98075e28	0.0518016
$718$	−1.02141e30	−1.04687
$719$	−5.91742e29	−0.597695	−0.298847	−	0.954301i	$-0.596602\pi$
$719$	−5.91742e29	−0.597695	−0.298847	+	0.954301i	$0.596602\pi$
$720$	−1.64157e28	−0.0163406
$721$	3.67409e29	0.360437
$722$	6.84710e29	0.662012
$723$	3.00367e29	0.286220
$724$	1.62759e29	0.152858
$725$	2.71940e29	0.251724
$726$	−5.67306e29	−0.517587
$727$	−6.05957e29	−0.544917	−0.272459	−	0.962168i	$-0.587837\pi$
$727$	−6.05957e29	−0.544917	−0.272459	+	0.962168i	$0.587837\pi$
$728$	1.82300e29	0.161587
$729$	1.25937e30	1.10031
$730$	−3.25004e29	−0.279897
$731$	−1.64330e27	−0.00139503
$732$	−4.86333e29	−0.406974
$733$	2.10206e30	1.73402	0.867010	−	0.498291i	$-0.166039\pi$
$733$	2.10206e30	1.73402	0.867010	+	0.498291i	$0.166039\pi$
$734$	7.44717e29	0.605595
$735$	3.92243e29	0.314441
$736$	1.87015e29	0.147795
$737$	−5.32959e29	−0.415226
$738$	2.40954e29	0.185073
$739$	9.22542e29	0.698585	0.349293	−	0.937014i	$-0.386422\pi$
$739$	9.22542e29	0.698585	0.349293	+	0.937014i	$0.386422\pi$
$740$	3.96317e28	0.0295876
$741$	−2.96328e29	−0.218113
$742$	7.71432e29	0.559831
$743$	−6.11017e29	−0.437191	−0.218595	−	0.975816i	$-0.570147\pi$
$743$	−6.11017e29	−0.437191	−0.218595	+	0.975816i	$0.570147\pi$
$744$	3.53341e29	0.249275
$745$	1.12363e30	0.781599
$746$	−8.67680e29	−0.595116
$747$	−3.09114e29	−0.209051
$748$	−9.99826e27	−0.00666742
$749$	1.20138e30	0.789992
$750$	9.01286e28	0.0584413
$751$	−1.36857e30	−0.875078	−0.437539	−	0.899199i	$-0.644150\pi$
$751$	−1.36857e30	−0.875078	−0.437539	+	0.899199i	$0.644150\pi$
$752$	−1.22187e29	−0.0770436
$753$	−1.19724e30	−0.744450
$754$	1.35660e30	0.831863
$755$	−9.00780e29	−0.544723
$756$	4.34171e29	0.258930
$757$	−5.97591e29	−0.351477	−0.175739	−	0.984437i	$-0.556231\pi$
$757$	−5.97591e29	−0.351477	−0.175739	+	0.984437i	$0.556231\pi$
$758$	−9.29834e29	−0.539360
$759$	−6.15651e29	−0.352205
$760$	7.07672e28	0.0399291
$761$	−2.76098e30	−1.53647	−0.768236	−	0.640166i	$-0.778865\pi$
$761$	−2.76098e30	−1.53647	−0.768236	+	0.640166i	$0.778865\pi$
$762$	1.33986e29	0.0735412
$763$	9.21857e29	0.499064
$764$	6.67646e29	0.356505
$765$	−3.62984e27	−0.00191180
$766$	3.84252e28	0.0199625
$767$	−2.71408e30	−1.39082
$768$	−1.14252e29	−0.0577523
$769$	2.46811e30	1.23066	0.615330	−	0.788269i	$-0.289023\pi$
$769$	2.46811e30	1.23066	0.615330	+	0.788269i	$0.289023\pi$
$770$	1.43319e29	0.0704941
$771$	1.76711e29	0.0857416
$772$	−4.49730e29	−0.215263
$773$	−2.37027e30	−1.11921	−0.559606	−	0.828759i	$-0.689048\pi$
$773$	−2.37027e30	−1.11921	−0.559606	+	0.828759i	$0.689048\pi$
$774$	−1.05815e28	−0.00492910
$775$	3.32072e29	0.152603
$776$	1.10902e30	0.502797
$777$	−1.33664e29	−0.0597851
$778$	5.43582e29	0.239872
$779$	−1.03874e30	−0.452235
$780$	4.49615e29	0.193129
$781$	−1.28974e30	−0.546595
$782$	4.13527e28	0.0172915
$783$	3.23092e30	1.33299
$784$	−4.67297e29	−0.190228
$785$	−9.60576e29	−0.385834
$786$	−5.91735e29	−0.234526
$787$	2.43834e30	0.953585	0.476792	−	0.879016i	$-0.341799\pi$
$787$	2.43834e30	0.953585	0.476792	+	0.879016i	$0.341799\pi$
$788$	−2.85983e29	−0.110361
$789$	−3.86703e30	−1.47255
$790$	−5.11527e29	−0.192213
$791$	−1.04178e30	−0.386300
$792$	−6.43807e28	−0.0235581
$793$	−2.28007e30	−0.823341
$794$	−1.84596e30	−0.657820
$795$	1.90262e30	0.669109
$796$	2.35343e30	0.816799
$797$	−1.54506e29	−0.0529215	−0.0264608	−	0.999650i	$-0.508424\pi$
$797$	−1.54506e29	−0.0529215	−0.0264608	+	0.999650i	$0.508424\pi$
$798$	−2.38673e29	−0.0806814
$799$	−2.70179e28	−0.00901386
$800$	−1.07374e29	−0.0353553
$801$	−3.32045e29	−0.107908
$802$	−1.79269e30	−0.575010
$803$	−1.27463e30	−0.403526
$804$	−1.34667e30	−0.420796
$805$	−5.92768e29	−0.182822
$806$	1.65657e30	0.504303
$807$	3.72005e30	1.11783
$808$	1.05622e30	0.313282
$809$	−2.18140e30	−0.638668	−0.319334	−	0.947642i	$-0.603459\pi$
$809$	−2.18140e30	−0.638668	−0.319334	+	0.947642i	$0.603459\pi$
$810$	9.10896e29	0.263255
$811$	2.64431e30	0.754387	0.377193	−	0.926134i	$-0.376889\pi$
$811$	2.64431e30	0.754387	0.377193	+	0.926134i	$0.376889\pi$
$812$	1.09265e30	0.307712
$813$	2.19241e30	0.609495
$814$	1.55431e29	0.0426562
$815$	−2.81486e30	−0.762610
$816$	−2.52633e28	−0.00675685
$817$	4.56164e28	0.0120445
$818$	2.04632e30	0.533414
$819$	2.59565e29	0.0667982
$820$	1.57607e30	0.400433
$821$	4.66260e30	1.16957	0.584784	−	0.811189i	$-0.301179\pi$
$821$	4.66260e30	1.16957	0.584784	+	0.811189i	$0.301179\pi$
$822$	2.96805e30	0.735051
$823$	−2.92987e30	−0.716392	−0.358196	−	0.933646i	$-0.616608\pi$
$823$	−2.92987e30	−0.716392	−0.358196	+	0.933646i	$0.616608\pi$
$824$	−1.07954e30	−0.260618
$825$	3.53475e29	0.0842544
$826$	−2.18602e30	−0.514474
$827$	5.72515e30	1.33039	0.665195	−	0.746669i	$-0.268348\pi$
$827$	5.72515e30	1.33039	0.665195	+	0.746669i	$0.268348\pi$
$828$	2.66278e29	0.0610965
$829$	−7.48372e29	−0.169549	−0.0847745	−	0.996400i	$-0.527017\pi$
$829$	−7.48372e29	−0.169549	−0.0847745	+	0.996400i	$0.527017\pi$
$830$	−2.02190e30	−0.452314
$831$	6.04456e30	1.33522
$832$	−5.35645e29	−0.116838
$833$	−1.03329e29	−0.0222561
$834$	2.68947e29	0.0572035
$835$	−1.75978e30	−0.369615
$836$	2.77542e29	0.0575655
$837$	3.94534e30	0.808103
$838$	2.87795e30	0.582132
$839$	2.16889e30	0.433249	0.216625	−	0.976255i	$-0.430495\pi$
$839$	2.16889e30	0.433249	0.216625	+	0.976255i	$0.430495\pi$
$840$	3.62136e29	0.0714396
$841$	2.99821e30	0.584123
$842$	−4.78156e30	−0.920010
$843$	3.95342e30	0.751247
$844$	−3.78802e30	−0.710913
$845$	−3.04813e29	−0.0564986
$846$	−1.73973e29	−0.0318489
$847$	−2.14222e30	−0.387336
$848$	−2.26667e30	−0.404792
$849$	−7.46062e30	−1.31596
$850$	−2.37426e28	−0.00413647
$851$	−6.42862e29	−0.110626
$852$	−3.25887e30	−0.553926
$853$	4.43176e30	0.744065	0.372033	−	0.928220i	$-0.378661\pi$
$853$	4.43176e30	0.744065	0.372033	+	0.928220i	$0.378661\pi$
$854$	−1.83645e30	−0.304559
$855$	1.00761e29	0.0165062
$856$	−3.52998e30	−0.571213
$857$	−1.50790e30	−0.241031	−0.120515	−	0.992711i	$-0.538455\pi$
$857$	−1.50790e30	−0.241031	−0.120515	+	0.992711i	$0.538455\pi$
$858$	1.76334e30	0.278433
$859$	1.77910e30	0.277506	0.138753	−	0.990327i	$-0.455691\pi$
$859$	1.77910e30	0.277506	0.138753	+	0.990327i	$0.455691\pi$
$860$	−6.92131e28	−0.0106649
$861$	−5.31554e30	−0.809122
$862$	6.82113e29	0.102572
$863$	−5.78269e30	−0.859047	−0.429523	−	0.903056i	$-0.641318\pi$
$863$	−5.78269e30	−0.859047	−0.429523	+	0.903056i	$0.641318\pi$
$864$	−1.27571e30	−0.187222
$865$	−4.42738e30	−0.641915
$866$	−8.21604e30	−1.17686
$867$	6.52407e30	0.923247
$868$	1.33426e30	0.186545
$869$	−2.00616e30	−0.277113
$870$	2.69486e30	0.367777
$871$	−6.31357e30	−0.851303
$872$	−2.70866e30	−0.360854
$873$	1.57907e30	0.207850
$874$	−1.14791e30	−0.149292
$875$	3.40337e29	0.0437345
$876$	−3.22070e30	−0.408938
$877$	−1.01800e31	−1.27718	−0.638589	−	0.769548i	$-0.720482\pi$
$877$	−1.01800e31	−1.27718	−0.638589	+	0.769548i	$0.720482\pi$
$878$	6.14839e30	0.762201
$879$	−1.23398e31	−1.51156
$880$	−4.21111e29	−0.0509716
$881$	1.30842e31	1.56495	0.782473	−	0.622685i	$-0.213958\pi$
$881$	1.30842e31	1.56495	0.782473	+	0.622685i	$0.213958\pi$
$882$	−6.65353e29	−0.0786379
$883$	6.52955e30	0.762598	0.381299	−	0.924452i	$-0.375477\pi$
$883$	6.52955e30	0.762598	0.381299	+	0.924452i	$0.375477\pi$
$884$	−1.18442e29	−0.0136696
$885$	−5.39148e30	−0.614898
$886$	2.53342e30	0.285531
$887$	−1.68400e30	−0.187562	−0.0937810	−	0.995593i	$-0.529895\pi$
$887$	−1.68400e30	−0.187562	−0.0937810	+	0.995593i	$0.529895\pi$
$888$	3.92740e29	0.0432284
$889$	5.05946e29	0.0550346
$890$	−2.17189e30	−0.233476
$891$	3.57244e30	0.379533
$892$	4.39354e30	0.461300
$893$	7.49991e29	0.0778244
$894$	1.11349e31	1.14194
$895$	6.42922e30	0.651653
$896$	−4.31428e29	−0.0432190
$897$	−7.29317e30	−0.722097
$898$	1.43237e31	1.40170
$899$	9.92899e30	0.960348
$900$	−1.52883e29	−0.0146155
$901$	−5.01207e29	−0.0473594
$902$	6.18119e30	0.577302
$903$	2.33432e29	0.0215496
$904$	3.06104e30	0.279319
$905$	1.51581e30	0.136721
$906$	−8.92650e30	−0.795857
$907$	−6.67368e30	−0.588151	−0.294076	−	0.955782i	$-0.595012\pi$
$907$	−6.67368e30	−0.588151	−0.294076	+	0.955782i	$0.595012\pi$
$908$	8.24234e30	0.718041
$909$	1.50388e30	0.129507
$910$	1.69780e30	0.144528
$911$	1.76568e31	1.48583	0.742915	−	0.669385i	$-0.233442\pi$
$911$	1.76568e31	1.48583	0.742915	+	0.669385i	$0.233442\pi$
$912$	7.01285e29	0.0583377
$913$	−7.92969e30	−0.652098
$914$	−5.51441e30	−0.448295
$915$	−4.52932e30	−0.364009
$916$	3.45144e29	0.0274220
$917$	−2.23447e30	−0.175507
$918$	−2.82085e29	−0.0219044
$919$	−2.65243e30	−0.203625	−0.101812	−	0.994804i	$-0.532464\pi$
$919$	−2.65243e30	−0.203625	−0.101812	+	0.994804i	$0.532464\pi$
$920$	1.74171e30	0.132191
$921$	−3.50434e30	−0.262954
$922$	−4.20020e30	−0.311599
$923$	−1.52786e31	−1.12064
$924$	1.42026e30	0.102994
$925$	3.69099e29	0.0264639
$926$	1.63441e30	0.115863
$927$	−1.53709e30	−0.107736
$928$	−3.21050e30	−0.222495
$929$	1.93439e31	1.32550	0.662748	−	0.748842i	$-0.269390\pi$
$929$	1.93439e31	1.32550	0.662748	+	0.748842i	$0.269390\pi$
$930$	3.29075e30	0.222958
$931$	2.86830e30	0.192156
$932$	3.80022e30	0.251734
$933$	−1.73025e31	−1.13332
$934$	5.12698e30	0.332062
$935$	−9.31161e28	−0.00596352
$936$	−7.62670e29	−0.0482992
$937$	5.66629e30	0.354841	0.177420	−	0.984135i	$-0.443225\pi$
$937$	5.66629e30	0.354841	0.177420	+	0.984135i	$0.443225\pi$
$938$	−5.08518e30	−0.314903
$939$	2.24874e31	1.37705
$940$	−1.13795e30	−0.0689098
$941$	5.09478e30	0.305095	0.152547	−	0.988296i	$-0.451252\pi$
$941$	5.09478e30	0.305095	0.152547	+	0.988296i	$0.451252\pi$
$942$	−9.51907e30	−0.563715
$943$	−2.55653e31	−1.49719
$944$	6.42310e30	0.371996
$945$	4.04354e30	0.231594
$946$	−2.71447e29	−0.0153755
$947$	1.88265e31	1.05462	0.527310	−	0.849673i	$-0.323201\pi$
$947$	1.88265e31	1.05462	0.527310	+	0.849673i	$0.323201\pi$
$948$	−5.06910e30	−0.280830
$949$	−1.50996e31	−0.827314
$950$	6.59071e29	0.0357137
$951$	−1.51393e31	−0.811355
$952$	−9.53975e28	−0.00505649
$953$	−1.70882e29	−0.00895823	−0.00447911	−	0.999990i	$-0.501426\pi$
$953$	−1.70882e29	−0.00895823	−0.00447911	+	0.999990i	$0.501426\pi$
$954$	−3.22736e30	−0.167336
$955$	6.21794e30	0.318868
$956$	−5.52627e29	−0.0280301
$957$	1.05690e31	0.530221
$958$	−4.54852e30	−0.225700
$959$	1.12077e31	0.550076
$960$	−1.06405e30	−0.0516553
$961$	−8.70101e30	−0.417806
$962$	1.84128e30	0.0874544
$963$	−5.02611e30	−0.236133
$964$	−3.33264e30	−0.154874
$965$	−4.18844e30	−0.192537
$966$	−5.87418e30	−0.267108
$967$	−4.87103e30	−0.219100	−0.109550	−	0.993981i	$-0.534941\pi$
$967$	−4.87103e30	−0.219100	−0.109550	+	0.993981i	$0.534941\pi$
$968$	6.29440e30	0.280068
$969$	1.55068e29	0.00682533
$970$	1.03286e31	0.449715
$971$	−1.12704e31	−0.485443	−0.242722	−	0.970096i	$-0.578040\pi$
$971$	−1.12704e31	−0.485443	−0.242722	+	0.970096i	$0.578040\pi$
$972$	−3.40118e30	−0.144922
$973$	1.01558e30	0.0428082
$974$	−1.50430e31	−0.627288
$975$	4.18736e30	0.172740
$976$	5.39598e30	0.220215
$977$	1.66556e31	0.672462	0.336231	−	0.941780i	$-0.390848\pi$
$977$	1.66556e31	0.672462	0.336231	+	0.941780i	$0.390848\pi$
$978$	−2.78946e31	−1.11420
$979$	−8.51793e30	−0.336601
$980$	−4.35204e30	−0.170145
$981$	−3.85668e30	−0.149173
$982$	2.26196e30	0.0865596
$983$	−3.01316e31	−1.14080	−0.570402	−	0.821366i	$-0.693213\pi$
$983$	−3.01316e31	−1.14080	−0.570402	+	0.821366i	$0.693213\pi$
$984$	1.56185e31	0.585045
$985$	−2.66343e30	−0.0987098
$986$	−7.09907e29	−0.0260312
$987$	3.83792e30	0.139240
$988$	3.28783e30	0.118022
$989$	1.12270e30	0.0398752
$990$	−5.99592e29	−0.0210710
$991$	−3.83614e31	−1.33389	−0.666946	−	0.745106i	$-0.732399\pi$
$991$	−3.83614e31	−1.33389	−0.666946	+	0.745106i	$0.732399\pi$
$992$	−3.92041e30	−0.134884
$993$	4.87647e31	1.66012
$994$	−1.23059e31	−0.414531
$995$	2.19181e31	0.730567
$996$	−2.00365e31	−0.660845
$997$	−9.24504e30	−0.301724	−0.150862	−	0.988555i	$-0.548205\pi$
$997$	−9.24504e30	−0.301724	−0.150862	+	0.988555i	$0.548205\pi$
$998$	−3.73592e31	−1.20650
$999$	4.38525e30	0.140138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.22.a.c.1.1	✓	2
4.3	odd	2		80.22.a.b.1.2		2
5.2	odd	4		50.22.b.d.49.2		4
5.3	odd	4		50.22.b.d.49.3		4
5.4	even	2		50.22.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.22.a.c.1.1	✓	2	1.1	even	1	trivial
50.22.a.e.1.2		2	5.4	even	2
50.22.b.d.49.2		4	5.2	odd	4
50.22.b.d.49.3		4	5.3	odd	4
80.22.a.b.1.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1024.00 q^{2} -94506.7 q^{3} +1.04858e6 q^{4} +9.76562e6 q^{5} +9.67749e7 q^{6} +3.65434e8 q^{7} -1.07374e9 q^{8} -1.52883e9 q^{9} -1.00000e10 q^{10} -3.92190e10 q^{11} -9.90975e10 q^{12} -4.64598e11 q^{13} -3.74204e11 q^{14} -9.22917e11 q^{15} +1.09951e12 q^{16} +2.43124e11 q^{17} +1.56552e12 q^{18} -6.74889e12 q^{19} +1.02400e13 q^{20} -3.45360e13 q^{21} +4.01602e13 q^{22} -1.66102e14 q^{23} +1.01476e14 q^{24} +9.53674e13 q^{25} +4.75749e14 q^{26} +1.13306e15 q^{27} +3.83185e14 q^{28} +2.85150e15 q^{29} +9.45067e14 q^{30} +3.48202e15 q^{31} -1.12590e15 q^{32} +3.70646e15 q^{33} -2.48959e14 q^{34} +3.56869e15 q^{35} -1.60309e15 q^{36} +3.87028e15 q^{37} +6.91086e15 q^{38} +4.39077e16 q^{39} -1.04858e16 q^{40} +1.53913e17 q^{41} +3.53648e16 q^{42} -6.75910e15 q^{43} -4.11241e16 q^{44} -1.49300e16 q^{45} +1.70089e17 q^{46} -1.11128e17 q^{47} -1.03911e17 q^{48} -4.25004e17 q^{49} -9.76562e16 q^{50} -2.29769e16 q^{51} -4.87167e17 q^{52} -2.06153e18 q^{53} -1.16025e18 q^{54} -3.82998e17 q^{55} -3.92382e17 q^{56} +6.37815e17 q^{57} -2.91994e18 q^{58} +5.84178e18 q^{59} -9.67749e17 q^{60} +4.90762e18 q^{61} -3.56559e18 q^{62} -5.58686e17 q^{63} +1.15292e18 q^{64} -4.53709e18 q^{65} -3.79541e18 q^{66} +1.35893e19 q^{67} +2.54934e17 q^{68} +1.56978e19 q^{69} -3.65434e18 q^{70} +3.28855e19 q^{71} +1.64157e18 q^{72} +3.25004e19 q^{73} -3.96317e18 q^{74} -9.01286e18 q^{75} -7.07672e18 q^{76} -1.43319e19 q^{77} -4.49615e19 q^{78} +5.11527e19 q^{79} +1.07374e19 q^{80} -9.10896e19 q^{81} -1.57607e20 q^{82} +2.02190e20 q^{83} -3.62136e19 q^{84} +2.37426e18 q^{85} +6.92131e18 q^{86} -2.69486e20 q^{87} +4.21111e19 q^{88} +2.17189e20 q^{89} +1.52883e19 q^{90} -1.69780e20 q^{91} -1.74171e20 q^{92} -3.29075e20 q^{93} +1.13795e20 q^{94} -6.59071e19 q^{95} +1.06405e20 q^{96} -1.03286e21 q^{97} +4.35204e20 q^{98} +5.99592e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2048 q^{2} + 100308 q^{3} + 2097152 q^{4} + 19531250 q^{5} - 102715392 q^{6} + 1328895316 q^{7} - 2147483648 q^{8} + 25963598826 q^{9} - 20000000000 q^{10} + 21869194224 q^{11} + 105180561408 q^{12}+ \cdots + 17\!\cdots\!12 q^{99}+O(q^{100}) \) 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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