LMFDB - Embedded newform 10.20.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,20,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, 20, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 20 $
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:	$22.8816696556$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 2925852 $ x^2 - x - 2925852
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1711.01$ 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)

$f(q)$	$=$	\(q+512.000 q^{2} -17348.2 q^{3} +262144. q^{4} +1.95312e6 q^{5} -8.88230e6 q^{6} +5.57963e7 q^{7} +1.34218e8 q^{8} -8.61300e8 q^{9} +1.00000e9 q^{10} -5.35830e9 q^{11} -4.54774e9 q^{12} +6.91495e10 q^{13} +2.85677e10 q^{14} -3.38833e10 q^{15} +6.87195e10 q^{16} +8.22149e11 q^{17} -4.40986e11 q^{18} -3.19849e11 q^{19} +5.12000e11 q^{20} -9.67968e11 q^{21} -2.74345e12 q^{22} +8.01595e12 q^{23} -2.32844e12 q^{24} +3.81470e12 q^{25} +3.54046e13 q^{26} +3.51052e13 q^{27} +1.46267e13 q^{28} +2.41111e13 q^{29} -1.73482e13 q^{30} +2.07759e14 q^{31} +3.51844e13 q^{32} +9.29571e13 q^{33} +4.20940e14 q^{34} +1.08977e14 q^{35} -2.25785e14 q^{36} -2.90774e14 q^{37} -1.63763e14 q^{38} -1.19962e15 q^{39} +2.62144e14 q^{40} +9.57878e14 q^{41} -4.95600e14 q^{42} -5.00622e15 q^{43} -1.40465e15 q^{44} -1.68223e15 q^{45} +4.10417e15 q^{46} -3.13847e14 q^{47} -1.19216e15 q^{48} -8.28567e15 q^{49} +1.95312e15 q^{50} -1.42628e16 q^{51} +1.81271e16 q^{52} -1.16717e16 q^{53} +1.79739e16 q^{54} -1.04654e16 q^{55} +7.48886e15 q^{56} +5.54882e15 q^{57} +1.23449e16 q^{58} -2.11995e16 q^{59} -8.88230e15 q^{60} +4.20425e16 q^{61} +1.06373e17 q^{62} -4.80574e16 q^{63} +1.80144e16 q^{64} +1.35058e17 q^{65} +4.75940e16 q^{66} +2.45879e17 q^{67} +2.15521e17 q^{68} -1.39063e17 q^{69} +5.57963e16 q^{70} -3.98392e17 q^{71} -1.15602e17 q^{72} -5.53484e17 q^{73} -1.48876e17 q^{74} -6.61783e16 q^{75} -8.38464e16 q^{76} -2.98973e17 q^{77} -6.14207e17 q^{78} -1.76148e18 q^{79} +1.34218e17 q^{80} +3.92041e17 q^{81} +4.90433e17 q^{82} +1.89559e18 q^{83} -2.53747e17 q^{84} +1.60576e18 q^{85} -2.56318e18 q^{86} -4.18286e17 q^{87} -7.19179e17 q^{88} +4.56180e18 q^{89} -8.61300e17 q^{90} +3.85829e18 q^{91} +2.10133e18 q^{92} -3.60426e18 q^{93} -1.60690e17 q^{94} -6.24705e17 q^{95} -6.10387e17 q^{96} +1.22283e19 q^{97} -4.24226e18 q^{98} +4.61510e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 1024 q^{2} + 33724 q^{3} + 524288 q^{4} + 3906250 q^{5} + 17266688 q^{6} + 83061292 q^{7} + 268435456 q^{8} + 584812954 q^{9} + 2000000000 q^{10} + 3549480144 q^{11} + 8840544256 q^{12} + 30250225564 q^{13}+ \cdots + 17\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 1024 * q^2 + 33724 * q^3 + 524288 * q^4 + 3906250 * q^5 + 17266688 * q^6 + 83061292 * q^7 + 268435456 * q^8 + 584812954 * q^9 + 2000000000 * q^10 + 3549480144 * q^11 + 8840544256 * q^12 + 30250225564 * q^13 + 42527381504 * q^14 + 65867187500 * q^15 + 137438953472 * q^16 + 329655779412 * q^17 + 299424232448 * q^18 + 383076809800 * q^19 + 1024000000000 * q^20 + 424515195104 * q^21 + 1817333833728 * q^22 + 2082856096884 * q^23 + 4526358659072 * q^24 + 7629394531250 * q^25 + 15488115488768 * q^26 + 49602163340440 * q^27 + 21774019330048 * q^28 + 166587684602220 * q^29 + 33724000000000 * q^30 + 418151119038664 * q^31 + 70368744177664 * q^32 + 547897533578928 * q^33 + 168783759058944 * q^34 + 162229085937500 * q^35 + 153305207013376 * q^36 - 1292219637694628 * q^37 + 196135326617600 * q^38 - 3186297306918232 * q^39 + 524288000000000 * q^40 - 3127192714527996 * q^41 + 217351779893248 * q^42 - 1795992338357636 * q^43 + 930474922868736 * q^44 + 1142212800781250 * q^45 + 1066422321604608 * q^46 - 6761653310165988 * q^47 + 2317495633444864 * q^48 - 18941182438871454 * q^49 + 3906250000000000 * q^50 - 39415550773661256 * q^51 + 7929915130249216 * q^52 - 9787568571066516 * q^53 + 25396307630305280 * q^54 + 6932578406250000 * q^55 + 11148297896984576 * q^56 + 41448804721422800 * q^57 + 85292894516336640 * q^58 - 25484316660294360 * q^59 + 17266688000000000 * q^60 - 77840503559636276 * q^61 + 214093372947795968 * q^62 - 8629133041886116 * q^63 + 36028797018963968 * q^64 + 59082471804687500 * q^65 + 280523537192411136 * q^66 + 439654835073204532 * q^67 + 86417284638179328 * q^68 - 442079200728708192 * q^69 + 83061292000000000 * q^70 - 29427662567526696 * q^71 + 78492265990848512 * q^72 - 1463308911724217756 * q^73 - 661616454499649536 * q^74 + 128646850585937500 * q^75 + 100421287228211200 * q^76 - 56103061801470576 * q^77 - 1631384221142134784 * q^78 - 1235969155825112720 * q^79 + 268435456000000000 * q^80 - 548329353045127838 * q^81 - 1601122669838333952 * q^82 - 877205635969635396 * q^83 + 111284111305342976 * q^84 + 643858944164062500 * q^85 - 919548077239109632 * q^86 + 6858312722579528040 * q^87 + 476403160508792832 * q^88 + 4172929077000032820 * q^89 + 584812954000000000 * q^90 + 2797700455846427144 * q^91 + 546008228661559296 * q^92 + 7140934358593491968 * q^93 - 3461966494804985856 * q^94 + 748196894140625000 * q^95 + 1186557764323770368 * q^96 + 11254578228347861332 * q^97 - 9697885408702184448 * q^98 + 17496761012343831888 * 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 $

$2$	512.000	0.707107
$2$	512.000	0.707107
$3$	−17348.2	−0.508866	−0.254433	−	0.967090i	$-0.581889\pi$
$3$	−17348.2	−0.508866	−0.254433	+	0.967090i	$0.581889\pi$
$4$	262144.	0.500000
$5$	1.95312e6	0.447214
$5$	1.95312e6	0.447214
$6$	−8.88230e6	−0.359823
$7$	5.57963e7	0.522606	0.261303	−	0.965257i	$-0.415848\pi$
$7$	5.57963e7	0.522606	0.261303	+	0.965257i	$0.415848\pi$
$8$	1.34218e8	0.353553
$9$	−8.61300e8	−0.741055
$10$	1.00000e9	0.316228
$11$	−5.35830e9	−0.685167	−0.342584	−	0.939487i	$-0.611302\pi$
$11$	−5.35830e9	−0.685167	−0.342584	+	0.939487i	$0.611302\pi$
$12$	−4.54774e9	−0.254433
$13$	6.91495e10	1.80854	0.904268	−	0.426965i	$-0.140417\pi$
$13$	6.91495e10	1.80854	0.904268	+	0.426965i	$0.140417\pi$
$14$	2.85677e10	0.369538
$15$	−3.38833e10	−0.227572
$16$	6.87195e10	0.250000
$17$	8.22149e11	1.68146	0.840728	−	0.541457i	$-0.182127\pi$
$17$	8.22149e11	1.68146	0.840728	+	0.541457i	$0.182127\pi$
$18$	−4.40986e11	−0.524005
$19$	−3.19849e11	−0.227397	−0.113699	−	0.993515i	$-0.536270\pi$
$19$	−3.19849e11	−0.227397	−0.113699	+	0.993515i	$0.536270\pi$
$20$	5.12000e11	0.223607
$21$	−9.67968e11	−0.265936
$22$	−2.74345e12	−0.484486
$23$	8.01595e12	0.927984	0.463992	−	0.885839i	$-0.346417\pi$
$23$	8.01595e12	0.927984	0.463992	+	0.885839i	$0.346417\pi$
$24$	−2.32844e12	−0.179911
$25$	3.81470e12	0.200000
$26$	3.54046e13	1.27883
$27$	3.51052e13	0.885964
$28$	1.46267e13	0.261303
$29$	2.41111e13	0.308629	0.154314	−	0.988022i	$-0.450683\pi$
$29$	2.41111e13	0.308629	0.154314	+	0.988022i	$0.450683\pi$
$30$	−1.73482e13	−0.160918
$31$	2.07759e14	1.41132	0.705658	−	0.708553i	$-0.250652\pi$
$31$	2.07759e14	1.41132	0.705658	+	0.708553i	$0.250652\pi$
$32$	3.51844e13	0.176777
$33$	9.29571e13	0.348659
$34$	4.20940e14	1.18897
$35$	1.08977e14	0.233716
$36$	−2.25785e14	−0.370528
$37$	−2.90774e14	−0.367823	−0.183912	−	0.982943i	$-0.558876\pi$
$37$	−2.90774e14	−0.367823	−0.183912	+	0.982943i	$0.558876\pi$
$38$	−1.63763e14	−0.160794
$39$	−1.19962e15	−0.920303
$40$	2.62144e14	0.158114
$41$	9.57878e14	0.456945	0.228472	−	0.973550i	$-0.426627\pi$
$41$	9.57878e14	0.456945	0.228472	+	0.973550i	$0.426627\pi$
$42$	−4.95600e14	−0.188045
$43$	−5.00622e15	−1.51901	−0.759503	−	0.650503i	$-0.774558\pi$
$43$	−5.00622e15	−1.51901	−0.759503	+	0.650503i	$0.774558\pi$
$44$	−1.40465e15	−0.342584
$45$	−1.68223e15	−0.331410
$46$	4.10417e15	0.656184
$47$	−3.13847e14	−0.0409062	−0.0204531	−	0.999791i	$-0.506511\pi$
$47$	−3.13847e14	−0.0409062	−0.0204531	+	0.999791i	$0.506511\pi$
$48$	−1.19216e15	−0.127217
$49$	−8.28567e15	−0.726883
$50$	1.95312e15	0.141421
$51$	−1.42628e16	−0.855636
$52$	1.81271e16	0.904268
$53$	−1.16717e16	−0.485861	−0.242930	−	0.970044i	$-0.578109\pi$
$53$	−1.16717e16	−0.485861	−0.242930	+	0.970044i	$0.578109\pi$
$54$	1.79739e16	0.626471
$55$	−1.04654e16	−0.306416
$56$	7.48886e15	0.184769
$57$	5.54882e15	0.115715
$58$	1.23449e16	0.218233
$59$	−2.11995e16	−0.318590	−0.159295	−	0.987231i	$-0.550922\pi$
$59$	−2.11995e16	−0.318590	−0.159295	+	0.987231i	$0.550922\pi$
$60$	−8.88230e15	−0.113786
$61$	4.20425e16	0.460314	0.230157	−	0.973153i	$-0.426076\pi$
$61$	4.20425e16	0.460314	0.230157	+	0.973153i	$0.426076\pi$
$62$	1.06373e17	0.997951
$63$	−4.80574e16	−0.387280
$64$	1.80144e16	0.125000
$65$	1.35058e17	0.808802
$66$	4.75940e16	0.246539
$67$	2.45879e17	1.10410	0.552052	−	0.833810i	$-0.313845\pi$
$67$	2.45879e17	1.10410	0.552052	+	0.833810i	$0.313845\pi$
$68$	2.15521e17	0.840728
$69$	−1.39063e17	−0.472220
$70$	5.57963e16	0.165262
$71$	−3.98392e17	−1.03123	−0.515616	−	0.856820i	$-0.672437\pi$
$71$	−3.98392e17	−1.03123	−0.515616	+	0.856820i	$0.672437\pi$
$72$	−1.15602e17	−0.262003
$73$	−5.53484e17	−1.10037	−0.550184	−	0.835044i	$-0.685442\pi$
$73$	−5.53484e17	−1.10037	−0.550184	+	0.835044i	$0.685442\pi$
$74$	−1.48876e17	−0.260090
$75$	−6.61783e16	−0.101773
$76$	−8.38464e16	−0.113699
$77$	−2.98973e17	−0.358072
$78$	−6.14207e17	−0.650753
$79$	−1.76148e18	−1.65356	−0.826780	−	0.562526i	$-0.809830\pi$
$79$	−1.76148e18	−1.65356	−0.826780	+	0.562526i	$0.809830\pi$
$80$	1.34218e17	0.111803
$81$	3.92041e17	0.290218
$82$	4.90433e17	0.323109
$83$	1.89559e18	1.11302	0.556511	−	0.830841i	$-0.312140\pi$
$83$	1.89559e18	1.11302	0.556511	+	0.830841i	$0.312140\pi$
$84$	−2.53747e17	−0.132968
$85$	1.60576e18	0.751970
$86$	−2.56318e18	−1.07410
$87$	−4.18286e17	−0.157051
$88$	−7.19179e17	−0.242243
$89$	4.56180e18	1.38016	0.690082	−	0.723731i	$-0.257574\pi$
$89$	4.56180e18	1.38016	0.690082	+	0.723731i	$0.257574\pi$
$90$	−8.61300e17	−0.234342
$91$	3.85829e18	0.945152
$92$	2.10133e18	0.463992
$93$	−3.60426e18	−0.718171
$94$	−1.60690e17	−0.0289250
$95$	−6.24705e17	−0.101695
$96$	−6.10387e17	−0.0899557
$97$	1.22283e19	1.63318	0.816592	−	0.577215i	$-0.195860\pi$
$97$	1.22283e19	1.63318	0.816592	+	0.577215i	$0.195860\pi$
$98$	−4.24226e18	−0.513984
$99$	4.61510e18	0.507747
$100$	1.00000e18	0.100000
$101$	−1.90414e18	−0.173239	−0.0866194	−	0.996241i	$-0.527606\pi$
$101$	−1.90414e18	−0.173239	−0.0866194	+	0.996241i	$0.527606\pi$
$102$	−7.30257e18	−0.605026
$103$	5.63296e17	0.0425386	0.0212693	−	0.999774i	$-0.493229\pi$
$103$	5.63296e17	0.0425386	0.0212693	+	0.999774i	$0.493229\pi$
$104$	9.28109e18	0.639414
$105$	−1.89056e18	−0.118930
$106$	−5.97589e18	−0.343556
$107$	−3.13426e19	−1.64812	−0.824062	−	0.566500i	$-0.808297\pi$
$107$	−3.13426e19	−1.64812	−0.824062	+	0.566500i	$0.808297\pi$
$108$	9.20263e18	0.442982
$109$	1.61520e19	0.712319	0.356160	−	0.934425i	$-0.384086\pi$
$109$	1.61520e19	0.712319	0.356160	+	0.934425i	$0.384086\pi$
$110$	−5.35830e18	−0.216669
$111$	5.04442e18	0.187173
$112$	3.83429e18	0.130651
$113$	−4.99152e19	−1.56310	−0.781551	−	0.623841i	$-0.785571\pi$
$113$	−4.99152e19	−1.56310	−0.781551	+	0.623841i	$0.785571\pi$
$114$	2.84099e18	0.0818228
$115$	1.56562e19	0.415007
$116$	6.32058e18	0.154314
$117$	−5.95585e19	−1.34023
$118$	−1.08542e19	−0.225277
$119$	4.58729e19	0.878739
$120$	−4.54774e18	−0.0804588
$121$	−3.24477e19	−0.530546
$122$	2.15257e19	0.325491
$123$	−1.66175e19	−0.232524
$124$	5.44628e19	0.705658
$125$	7.45058e18	0.0894427
$126$	−2.46054e19	−0.273848
$127$	−5.46401e19	−0.564126	−0.282063	−	0.959396i	$-0.591019\pi$
$127$	−5.46401e19	−0.564126	−0.282063	+	0.959396i	$0.591019\pi$
$128$	9.22337e18	0.0883883
$129$	8.68491e19	0.772971
$130$	6.91495e19	0.571910
$131$	−1.25613e20	−0.965958	−0.482979	−	0.875632i	$-0.660445\pi$
$131$	−1.25613e20	−0.965958	−0.482979	+	0.875632i	$0.660445\pi$
$132$	2.43682e19	0.174329
$133$	−1.78464e19	−0.118839
$134$	1.25890e20	0.780720
$135$	6.85649e19	0.396215
$136$	1.10347e20	0.594485
$137$	2.02938e20	1.01981	0.509904	−	0.860231i	$-0.329681\pi$
$137$	2.02938e20	1.01981	0.509904	+	0.860231i	$0.329681\pi$
$138$	−7.12001e19	−0.333910
$139$	3.97467e20	1.74045	0.870223	−	0.492657i	$-0.163974\pi$
$139$	3.97467e20	1.74045	0.870223	+	0.492657i	$0.163974\pi$
$140$	2.85677e19	0.116858
$141$	5.44470e18	0.0208158
$142$	−2.03977e20	−0.729191
$143$	−3.70524e20	−1.23915
$144$	−5.91881e19	−0.185264
$145$	4.70920e19	0.138023
$146$	−2.83384e20	−0.778077
$147$	1.43742e20	0.369886
$148$	−7.62246e19	−0.183912
$149$	7.30310e19	0.165287	0.0826433	−	0.996579i	$-0.473664\pi$
$149$	7.30310e19	0.165287	0.0826433	+	0.996579i	$0.473664\pi$
$150$	−3.38833e19	−0.0719646
$151$	−5.89188e20	−1.17482	−0.587412	−	0.809288i	$-0.699853\pi$
$151$	−5.89188e20	−1.17482	−0.587412	+	0.809288i	$0.699853\pi$
$152$	−4.29294e19	−0.0803971
$153$	−7.08116e20	−1.24605
$154$	−1.53074e20	−0.253195
$155$	4.05780e20	0.631159
$156$	−3.14474e20	−0.460152
$157$	4.26722e20	0.587623	0.293811	−	0.955863i	$-0.405076\pi$
$157$	4.26722e20	0.587623	0.293811	+	0.955863i	$0.405076\pi$
$158$	−9.01876e20	−1.16924
$159$	2.02483e20	0.247238
$160$	6.87195e19	0.0790569
$161$	4.47261e20	0.484970
$162$	2.00725e20	0.205215
$163$	−1.38073e21	−1.33146	−0.665729	−	0.746194i	$-0.731879\pi$
$163$	−1.38073e21	−1.33146	−0.665729	+	0.746194i	$0.731879\pi$
$164$	2.51102e20	0.228472
$165$	1.81557e20	0.155925
$166$	9.70544e20	0.787025
$167$	1.82808e19	0.0140020	0.00700099	−	0.999975i	$-0.497771\pi$
$167$	1.82808e19	0.0140020	0.00700099	+	0.999975i	$0.497771\pi$
$168$	−1.29918e20	−0.0940227
$169$	3.31974e21	2.27081
$170$	8.22149e20	0.531723
$171$	2.75486e20	0.168514
$172$	−1.31235e21	−0.759503
$173$	7.10579e20	0.389201	0.194601	−	0.980883i	$-0.437659\pi$
$173$	7.10579e20	0.389201	0.194601	+	0.980883i	$0.437659\pi$
$174$	−2.14162e20	−0.111052
$175$	2.12846e20	0.104521
$176$	−3.68220e20	−0.171292
$177$	3.67775e20	0.162120
$178$	2.33564e21	0.975923
$179$	−1.09003e21	−0.431851	−0.215926	−	0.976410i	$-0.569277\pi$
$179$	−1.09003e21	−0.431851	−0.215926	+	0.976410i	$0.569277\pi$
$180$	−4.40986e20	−0.165705
$181$	−2.79419e21	−0.996114	−0.498057	−	0.867144i	$-0.665953\pi$
$181$	−2.79419e21	−0.996114	−0.498057	+	0.867144i	$0.665953\pi$
$182$	1.97544e21	0.668323
$183$	−7.29363e20	−0.234239
$184$	1.07588e21	0.328092
$185$	−5.67918e20	−0.164495
$186$	−1.84538e21	−0.507823
$187$	−4.40532e21	−1.15208
$188$	−8.22732e19	−0.0204531
$189$	1.95874e21	0.463010
$190$	−3.19849e20	−0.0719094
$191$	4.63773e21	0.991947	0.495974	−	0.868338i	$-0.334811\pi$
$191$	4.63773e21	0.991947	0.495974	+	0.868338i	$0.334811\pi$
$192$	−3.12518e20	−0.0636083
$193$	−8.23942e20	−0.159625	−0.0798127	−	0.996810i	$-0.525432\pi$
$193$	−8.23942e20	−0.159625	−0.0798127	+	0.996810i	$0.525432\pi$
$194$	6.26090e21	1.15484
$195$	−2.34301e21	−0.411572
$196$	−2.17204e21	−0.363442
$197$	−8.41762e20	−0.134202	−0.0671012	−	0.997746i	$-0.521375\pi$
$197$	−8.41762e20	−0.134202	−0.0671012	+	0.997746i	$0.521375\pi$
$198$	2.36293e21	0.359031
$199$	−1.16067e22	−1.68114	−0.840571	−	0.541701i	$-0.817780\pi$
$199$	−1.16067e22	−1.68114	−0.840571	+	0.541701i	$0.817780\pi$
$200$	5.12000e20	0.0707107
$201$	−4.26556e21	−0.561841
$202$	−9.74918e20	−0.122498
$203$	1.34531e21	0.161291
$204$	−3.73892e21	−0.427818
$205$	1.87086e21	0.204352
$206$	2.88407e20	0.0300793
$207$	−6.90414e21	−0.687688
$208$	4.75192e21	0.452134
$209$	1.71385e21	0.155805
$210$	−9.67968e20	−0.0840965
$211$	7.16116e20	0.0594703	0.0297352	−	0.999558i	$-0.490534\pi$
$211$	7.16116e20	0.0594703	0.0297352	+	0.999558i	$0.490534\pi$
$212$	−3.05966e21	−0.242930
$213$	6.91140e21	0.524759
$214$	−1.60474e22	−1.16540
$215$	−9.77777e21	−0.679320
$216$	4.71175e21	0.313236
$217$	1.15922e22	0.737561
$218$	8.26983e21	0.503686
$219$	9.60197e21	0.559940
$220$	−2.74345e21	−0.153208
$221$	5.68512e22	3.04098
$222$	2.58274e21	0.132351
$223$	−1.19410e22	−0.586335	−0.293168	−	0.956061i	$-0.594709\pi$
$223$	−1.19410e22	−0.586335	−0.293168	+	0.956061i	$0.594709\pi$
$224$	1.96316e21	0.0923845
$225$	−3.28560e21	−0.148211
$226$	−2.55566e22	−1.10528
$227$	2.69537e22	1.11782	0.558911	−	0.829228i	$-0.311219\pi$
$227$	2.69537e22	1.11782	0.558911	+	0.829228i	$0.311219\pi$
$228$	1.45459e21	0.0578574
$229$	−4.02051e22	−1.53406	−0.767032	−	0.641609i	$-0.778267\pi$
$229$	−4.02051e22	−1.53406	−0.767032	+	0.641609i	$0.778267\pi$
$230$	8.01595e21	0.293454
$231$	5.18667e21	0.182211
$232$	3.23614e21	0.109117
$233$	5.19383e22	1.68115	0.840575	−	0.541696i	$-0.182217\pi$
$233$	5.19383e22	1.68115	0.840575	+	0.541696i	$0.182217\pi$
$234$	−3.04939e22	−0.947683
$235$	−6.12983e20	−0.0182938
$236$	−5.55733e21	−0.159295
$237$	3.05585e22	0.841440
$238$	2.34869e22	0.621362
$239$	−5.71264e22	−1.45230	−0.726151	−	0.687535i	$-0.758693\pi$
$239$	−5.71264e22	−1.45230	−0.726151	+	0.687535i	$0.758693\pi$
$240$	−2.32844e21	−0.0568930
$241$	2.38712e22	0.560675	0.280338	−	0.959901i	$-0.409554\pi$
$241$	2.38712e22	0.560675	0.280338	+	0.959901i	$0.409554\pi$
$242$	−1.66132e22	−0.375153
$243$	−4.76027e22	−1.03365
$244$	1.10212e22	0.230157
$245$	−1.61829e22	−0.325072
$246$	−8.50816e21	−0.164419
$247$	−2.21174e22	−0.411257
$248$	2.78850e22	0.498975
$249$	−3.28852e22	−0.566379
$250$	3.81470e21	0.0632456
$251$	−9.12101e22	−1.45594	−0.727968	−	0.685611i	$-0.759535\pi$
$251$	−9.12101e22	−1.45594	−0.727968	+	0.685611i	$0.759535\pi$
$252$	−1.25979e22	−0.193640
$253$	−4.29519e22	−0.635825
$254$	−2.79757e22	−0.398897
$255$	−2.78571e22	−0.382652
$256$	4.72237e21	0.0625000
$257$	9.15373e22	1.16744	0.583718	−	0.811956i	$-0.301597\pi$
$257$	9.15373e22	1.16744	0.583718	+	0.811956i	$0.301597\pi$
$258$	4.44668e22	0.546573
$259$	−1.62241e22	−0.192226
$260$	3.54046e22	0.404401
$261$	−2.07669e22	−0.228711
$262$	−6.43140e22	−0.683036
$263$	5.82421e22	0.596565	0.298282	−	0.954478i	$-0.403586\pi$
$263$	5.82421e22	0.596565	0.298282	+	0.954478i	$0.403586\pi$
$264$	1.24765e22	0.123269
$265$	−2.27962e22	−0.217284
$266$	−9.13735e21	−0.0840320
$267$	−7.91391e22	−0.702319
$268$	6.44556e22	0.552052
$269$	2.11389e23	1.74758	0.873788	−	0.486307i	$-0.161656\pi$
$269$	2.11389e23	1.74758	0.873788	+	0.486307i	$0.161656\pi$
$270$	3.51052e22	0.280166
$271$	1.73503e23	1.33690	0.668451	−	0.743757i	$-0.266958\pi$
$271$	1.73503e23	1.33690	0.668451	+	0.743757i	$0.266958\pi$
$272$	5.64976e22	0.420364
$273$	−6.69345e22	−0.480956
$274$	1.03904e23	0.721113
$275$	−2.04403e22	−0.137033
$276$	−3.64545e22	−0.236110
$277$	−8.04324e22	−0.503354	−0.251677	−	0.967811i	$-0.580982\pi$
$277$	−8.04324e22	−0.503354	−0.251677	+	0.967811i	$0.580982\pi$
$278$	2.03503e23	1.23068
$279$	−1.78943e23	−1.04586
$280$	1.46267e22	0.0826312
$281$	3.28300e23	1.79292	0.896459	−	0.443127i	$-0.146131\pi$
$281$	3.28300e23	1.79292	0.896459	+	0.443127i	$0.146131\pi$
$282$	2.78769e21	0.0147190
$283$	−3.19635e23	−1.63186	−0.815930	−	0.578151i	$-0.803775\pi$
$283$	−3.19635e23	−1.63186	−0.815930	+	0.578151i	$0.803775\pi$
$284$	−1.04436e23	−0.515616
$285$	1.08375e22	0.0517493
$286$	−1.89708e23	−0.876212
$287$	5.34461e22	0.238802
$288$	−3.03043e22	−0.131001
$289$	4.36856e23	1.82730
$290$	2.41111e22	0.0975970
$291$	−2.12140e23	−0.831073
$292$	−1.45092e23	−0.550184
$293$	−4.15387e23	−1.52479	−0.762396	−	0.647110i	$-0.775977\pi$
$293$	−4.15387e23	−1.52479	−0.762396	+	0.647110i	$0.775977\pi$
$294$	7.35958e22	0.261549
$295$	−4.14053e22	−0.142478
$296$	−3.90270e22	−0.130045
$297$	−1.88104e23	−0.607034
$298$	3.73919e22	0.116875
$299$	5.54299e23	1.67829
$300$	−1.73482e22	−0.0508866
$301$	−2.79329e23	−0.793842
$302$	−3.01664e23	−0.830726
$303$	3.30334e22	0.0881553
$304$	−2.19798e22	−0.0568494
$305$	8.21142e22	0.205859
$306$	−3.62556e23	−0.881092
$307$	4.98091e23	1.17353	0.586765	−	0.809757i	$-0.300401\pi$
$307$	4.98091e23	1.17353	0.586765	+	0.809757i	$0.300401\pi$
$308$	−7.83741e22	−0.179036
$309$	−9.77219e21	−0.0216464
$310$	2.07759e23	0.446297
$311$	4.96675e23	1.03478	0.517390	−	0.855750i	$-0.326904\pi$
$311$	4.96675e23	1.03478	0.517390	+	0.855750i	$0.326904\pi$
$312$	−1.61011e23	−0.325376
$313$	−8.89041e23	−1.74281	−0.871406	−	0.490562i	$-0.836792\pi$
$313$	−8.89041e23	−1.74281	−0.871406	+	0.490562i	$0.836792\pi$
$314$	2.18482e23	0.415512
$315$	−9.38620e22	−0.173197
$316$	−4.61761e23	−0.826780
$317$	2.61249e23	0.453934	0.226967	−	0.973902i	$-0.427119\pi$
$317$	2.61249e23	0.453934	0.226967	+	0.973902i	$0.427119\pi$
$318$	1.03671e23	0.174824
$319$	−1.29195e23	−0.211462
$320$	3.51844e22	0.0559017
$321$	5.43740e23	0.838674
$322$	2.28997e23	0.342926
$323$	−2.62963e23	−0.382359
$324$	1.02771e23	0.145109
$325$	2.63784e23	0.361707
$326$	−7.06935e23	−0.941483
$327$	−2.80209e23	−0.362475
$328$	1.28564e23	0.161554
$329$	−1.75115e22	−0.0213778
$330$	9.29571e22	0.110256
$331$	9.76825e22	0.112577	0.0562887	−	0.998415i	$-0.482073\pi$
$331$	9.76825e22	0.112577	0.0562887	+	0.998415i	$0.482073\pi$
$332$	4.96918e23	0.556511
$333$	2.50443e23	0.272577
$334$	9.35979e21	0.00990090
$335$	4.80232e23	0.493770
$336$	−6.65183e22	−0.0664841
$337$	3.88676e23	0.377662	0.188831	−	0.982010i	$-0.439530\pi$
$337$	3.88676e23	0.377662	0.188831	+	0.982010i	$0.439530\pi$
$338$	1.69970e24	1.60570
$339$	8.65941e23	0.795410
$340$	4.20940e23	0.375985
$341$	−1.11324e24	−0.966987
$342$	1.41049e23	0.119157
$343$	−1.09833e24	−0.902479
$344$	−6.71924e23	−0.537050
$345$	−2.71607e23	−0.211183
$346$	3.63816e23	0.275207
$347$	6.38185e23	0.469696	0.234848	−	0.972032i	$-0.424541\pi$
$347$	6.38185e23	0.469696	0.234848	+	0.972032i	$0.424541\pi$
$348$	−1.09651e23	−0.0785254
$349$	−7.25583e23	−0.505645	−0.252822	−	0.967513i	$-0.581359\pi$
$349$	−7.25583e23	−0.505645	−0.252822	+	0.967513i	$0.581359\pi$
$350$	1.08977e23	0.0739076
$351$	2.42751e24	1.60230
$352$	−1.88528e23	−0.121122
$353$	−8.60947e23	−0.538415	−0.269207	−	0.963082i	$-0.586762\pi$
$353$	−8.60947e23	−0.538415	−0.269207	+	0.963082i	$0.586762\pi$
$354$	1.88301e23	0.114636
$355$	−7.78109e23	−0.461181
$356$	1.19585e24	0.690082
$357$	−7.95814e23	−0.447160
$358$	−5.58095e23	−0.305365
$359$	−1.95940e24	−1.04406	−0.522030	−	0.852927i	$-0.674825\pi$
$359$	−1.95940e24	−1.04406	−0.522030	+	0.852927i	$0.674825\pi$
$360$	−2.25785e23	−0.117171
$361$	−1.87612e24	−0.948290
$362$	−1.43062e24	−0.704359
$363$	5.62911e23	0.269977
$364$	1.01143e24	0.472576
$365$	−1.08102e24	−0.492099
$366$	−3.73434e23	−0.165632
$367$	−1.70386e24	−0.736387	−0.368193	−	0.929749i	$-0.620024\pi$
$367$	−1.70386e24	−0.736387	−0.368193	+	0.929749i	$0.620024\pi$
$368$	5.50852e23	0.231996
$369$	−8.25020e23	−0.338621
$370$	−2.90774e23	−0.116316
$371$	−6.51236e23	−0.253914
$372$	−9.44834e23	−0.359085
$373$	−5.66530e22	−0.0209889	−0.0104944	−	0.999945i	$-0.503341\pi$
$373$	−5.66530e22	−0.0209889	−0.0104944	+	0.999945i	$0.503341\pi$
$374$	−2.25552e24	−0.814643
$375$	−1.29255e23	−0.0455144
$376$	−4.21239e22	−0.0144625
$377$	1.66727e24	0.558166
$378$	1.00288e24	0.327397
$379$	2.57014e23	0.0818247	0.0409123	−	0.999163i	$-0.486974\pi$
$379$	2.57014e23	0.0818247	0.0409123	+	0.999163i	$0.486974\pi$
$380$	−1.63763e23	−0.0508476
$381$	9.47909e23	0.287065
$382$	2.37452e24	0.701413
$383$	4.38632e24	1.26390	0.631949	−	0.775010i	$-0.282255\pi$
$383$	4.38632e24	1.26390	0.631949	+	0.775010i	$0.282255\pi$
$384$	−1.60009e23	−0.0449778
$385$	−5.83933e23	−0.160135
$386$	−4.21858e23	−0.112872
$387$	4.31186e24	1.12567
$388$	3.20558e24	0.816592
$389$	−1.37553e24	−0.341939	−0.170970	−	0.985276i	$-0.554690\pi$
$389$	−1.37553e24	−0.341939	−0.170970	+	0.985276i	$0.554690\pi$
$390$	−1.19962e24	−0.291025
$391$	6.59030e24	1.56037
$392$	−1.11208e24	−0.256992
$393$	2.17917e24	0.491544
$394$	−4.30982e23	−0.0948954
$395$	−3.44039e24	−0.739494
$396$	1.20982e24	0.253873
$397$	−4.17970e24	−0.856319	−0.428160	−	0.903703i	$-0.640838\pi$
$397$	−4.17970e24	−0.856319	−0.428160	+	0.903703i	$0.640838\pi$
$398$	−5.94263e24	−1.18875
$399$	3.09603e23	0.0604733
$400$	2.62144e23	0.0500000
$401$	3.45018e23	0.0642644	0.0321322	−	0.999484i	$-0.489770\pi$
$401$	3.45018e23	0.0642644	0.0321322	+	0.999484i	$0.489770\pi$
$402$	−2.18397e24	−0.397282
$403$	1.43664e25	2.55242
$404$	−4.99158e23	−0.0866194
$405$	7.65706e23	0.129789
$406$	6.88799e23	0.114050
$407$	1.55805e24	0.252020
$408$	−1.91433e24	−0.302513
$409$	1.82296e24	0.281452	0.140726	−	0.990049i	$-0.455056\pi$
$409$	1.82296e24	0.281452	0.140726	+	0.990049i	$0.455056\pi$
$410$	9.57878e23	0.144499
$411$	−3.52062e24	−0.518946
$412$	1.47665e23	0.0212693
$413$	−1.18286e24	−0.166497
$414$	−3.53492e24	−0.486269
$415$	3.70233e24	0.497758
$416$	2.43298e24	0.319707
$417$	−6.89536e24	−0.885655
$418$	8.77489e23	0.110171
$419$	−1.44355e25	−1.77174	−0.885869	−	0.463935i	$-0.846437\pi$
$419$	−1.44355e25	−1.77174	−0.885869	+	0.463935i	$0.846437\pi$
$420$	−4.95600e23	−0.0594652
$421$	−4.71956e24	−0.553632	−0.276816	−	0.960923i	$-0.589279\pi$
$421$	−4.71956e24	−0.553632	−0.276816	+	0.960923i	$0.589279\pi$
$422$	3.66652e23	0.0420519
$423$	2.70317e23	0.0303137
$424$	−1.56654e24	−0.171778
$425$	3.13625e24	0.336291
$426$	3.53864e24	0.371061
$427$	2.34581e24	0.240563
$428$	−8.21629e24	−0.824062
$429$	6.42794e24	0.630562
$430$	−5.00622e24	−0.480352
$431$	−1.44126e25	−1.35272	−0.676361	−	0.736570i	$-0.736444\pi$
$431$	−1.44126e25	−1.35272	−0.676361	+	0.736570i	$0.736444\pi$
$432$	2.41241e24	0.221491
$433$	−1.38601e25	−1.24489	−0.622447	−	0.782662i	$-0.713862\pi$
$433$	−1.38601e25	−1.24489	−0.622447	+	0.782662i	$0.713862\pi$
$434$	5.93520e24	0.521535
$435$	−8.16964e23	−0.0702352
$436$	4.23415e24	0.356160
$437$	−2.56389e24	−0.211021
$438$	4.91621e24	0.395937
$439$	−1.25797e25	−0.991418	−0.495709	−	0.868489i	$-0.665092\pi$
$439$	−1.25797e25	−0.991418	−0.495709	+	0.868489i	$0.665092\pi$
$440$	−1.40465e24	−0.108334
$441$	7.13644e24	0.538661
$442$	2.91078e25	2.15029
$443$	2.28568e24	0.165264	0.0826322	−	0.996580i	$-0.473667\pi$
$443$	2.28568e24	0.165264	0.0826322	+	0.996580i	$0.473667\pi$
$444$	1.32236e24	0.0935864
$445$	8.90976e24	0.617228
$446$	−6.11381e24	−0.414601
$447$	−1.26696e24	−0.0841088
$448$	1.00514e24	0.0653257
$449$	−4.27635e24	−0.272103	−0.136051	−	0.990702i	$-0.543441\pi$
$449$	−4.27635e24	−0.272103	−0.136051	+	0.990702i	$0.543441\pi$
$450$	−1.68223e24	−0.104801
$451$	−5.13260e24	−0.313083
$452$	−1.30850e25	−0.781551
$453$	1.02214e25	0.597828
$454$	1.38003e25	0.790420
$455$	7.53572e24	0.422685
$456$	7.44749e23	0.0409114
$457$	1.82618e25	0.982515	0.491257	−	0.871014i	$-0.336537\pi$
$457$	1.82618e25	0.982515	0.491257	+	0.871014i	$0.336537\pi$
$458$	−2.05850e25	−1.08475
$459$	2.88617e25	1.48971
$460$	4.10417e24	0.207504
$461$	−7.90654e24	−0.391587	−0.195793	−	0.980645i	$-0.562728\pi$
$461$	−7.90654e24	−0.391587	−0.195793	+	0.980645i	$0.562728\pi$
$462$	2.65557e24	0.128843
$463$	−2.91664e25	−1.38632	−0.693160	−	0.720784i	$-0.743782\pi$
$463$	−2.91664e25	−1.38632	−0.693160	+	0.720784i	$0.743782\pi$
$464$	1.65690e24	0.0771572
$465$	−7.03956e24	−0.321176
$466$	2.65924e25	1.18875
$467$	−2.90132e25	−1.27082	−0.635411	−	0.772174i	$-0.719169\pi$
$467$	−2.90132e25	−1.27082	−0.635411	+	0.772174i	$0.719169\pi$
$468$	−1.56129e25	−0.670113
$469$	1.37191e25	0.577011
$470$	−3.13847e23	−0.0129357
$471$	−7.40288e24	−0.299021
$472$	−2.84535e24	−0.112639
$473$	2.68248e25	1.04077
$474$	1.56460e25	0.594988
$475$	−1.22013e24	−0.0454795
$476$	1.20253e25	0.439369
$477$	1.00528e25	0.360050
$478$	−2.92487e25	−1.02693
$479$	4.33547e25	1.49228	0.746138	−	0.665792i	$-0.231906\pi$
$479$	4.33547e25	1.49228	0.746138	+	0.665792i	$0.231906\pi$
$480$	−1.19216e24	−0.0402294
$481$	−2.01069e25	−0.665222
$482$	1.22220e25	0.396457
$483$	−7.75919e24	−0.246785
$484$	−8.50597e24	−0.265273
$485$	2.38834e25	0.730382
$486$	−2.43726e25	−0.730898
$487$	−2.20894e25	−0.649619	−0.324809	−	0.945780i	$-0.605300\pi$
$487$	−2.20894e25	−0.649619	−0.324809	+	0.945780i	$0.605300\pi$
$488$	5.64284e24	0.162746
$489$	2.39533e25	0.677534
$490$	−8.28567e24	−0.229861
$491$	−1.76617e25	−0.480573	−0.240286	−	0.970702i	$-0.577241\pi$
$491$	−1.76617e25	−0.480573	−0.240286	+	0.970702i	$0.577241\pi$
$492$	−4.35618e24	−0.116262
$493$	1.98229e25	0.518946
$494$	−1.13241e25	−0.290802
$495$	9.01388e24	0.227071
$496$	1.42771e25	0.352829
$497$	−2.22288e25	−0.538928
$498$	−1.68372e25	−0.400490
$499$	−4.52317e25	−1.05557	−0.527786	−	0.849377i	$-0.676978\pi$
$499$	−4.52317e25	−1.05557	−0.527786	+	0.849377i	$0.676978\pi$
$500$	1.95313e24	0.0447214
$501$	−3.17140e23	−0.00712514
$502$	−4.66996e25	−1.02950
$503$	1.28554e25	0.278092	0.139046	−	0.990286i	$-0.455596\pi$
$503$	1.28554e25	0.278092	0.139046	+	0.990286i	$0.455596\pi$
$504$	−6.45015e24	−0.136924
$505$	−3.71902e24	−0.0774747
$506$	−2.19914e25	−0.449596
$507$	−5.75916e25	−1.15554
$508$	−1.43236e25	−0.282063
$509$	4.19437e25	0.810677	0.405338	−	0.914167i	$-0.367154\pi$
$509$	4.19437e25	0.810677	0.405338	+	0.914167i	$0.367154\pi$
$510$	−1.42628e25	−0.270576
$511$	−3.08824e25	−0.575058
$512$	2.41785e24	0.0441942
$513$	−1.12284e25	−0.201466
$514$	4.68671e25	0.825502
$515$	1.10019e24	0.0190238
$516$	2.27670e25	0.386486
$517$	1.68169e24	0.0280276
$518$	−8.30674e24	−0.135925
$519$	−1.23273e25	−0.198051
$520$	1.81271e25	0.285955
$521$	3.05094e25	0.472581	0.236290	−	0.971682i	$-0.424068\pi$
$521$	3.05094e25	0.472581	0.236290	+	0.971682i	$0.424068\pi$
$522$	−1.06327e25	−0.161723
$523$	6.76475e23	0.0101038	0.00505191	−	0.999987i	$-0.498392\pi$
$523$	6.76475e23	0.0101038	0.00505191	+	0.999987i	$0.498392\pi$
$524$	−3.29288e25	−0.482979
$525$	−3.69251e24	−0.0531873
$526$	2.98200e25	0.421835
$527$	1.70809e26	2.37306
$528$	6.38797e24	0.0871646
$529$	−1.03600e25	−0.138845
$530$	−1.16717e25	−0.153643
$531$	1.82592e25	0.236093
$532$	−4.67832e24	−0.0594196
$533$	6.62368e25	0.826401
$534$	−4.05192e25	−0.496614
$535$	−6.12161e25	−0.737063
$536$	3.30013e25	0.390360
$537$	1.89101e25	0.219755
$538$	1.08231e26	1.23572
$539$	4.43971e25	0.498037
$540$	1.79739e25	0.198108
$541$	−5.91055e25	−0.640109	−0.320055	−	0.947399i	$-0.603701\pi$
$541$	−5.91055e25	−0.640109	−0.320055	+	0.947399i	$0.603701\pi$
$542$	8.88336e25	0.945332
$543$	4.84742e25	0.506889
$544$	2.89268e25	0.297242
$545$	3.15469e25	0.318559
$546$	−3.42705e25	−0.340087
$547$	−8.46391e25	−0.825452	−0.412726	−	0.910855i	$-0.635423\pi$
$547$	−8.46391e25	−0.825452	−0.412726	+	0.910855i	$0.635423\pi$
$548$	5.31990e25	0.509904
$549$	−3.62112e25	−0.341118
$550$	−1.04654e25	−0.0968973
$551$	−7.71191e24	−0.0701814
$552$	−1.86647e25	−0.166955
$553$	−9.82840e25	−0.864159
$554$	−4.11814e25	−0.355925
$555$	9.85238e24	0.0837062
$556$	1.04194e26	0.870223
$557$	4.71567e25	0.387185	0.193593	−	0.981082i	$-0.437986\pi$
$557$	4.71567e25	0.387185	0.193593	+	0.981082i	$0.437986\pi$
$558$	−9.16188e25	−0.739536
$559$	−3.46178e26	−2.74718
$560$	7.48886e24	0.0584291
$561$	7.64246e25	0.586254
$562$	1.68089e26	1.26778
$563$	−5.00520e25	−0.371186	−0.185593	−	0.982627i	$-0.559421\pi$
$563$	−5.00520e25	−0.371186	−0.185593	+	0.982627i	$0.559421\pi$
$564$	1.42730e24	0.0104079
$565$	−9.74906e25	−0.699041
$566$	−1.63653e26	−1.15390
$567$	2.18745e25	0.151670
$568$	−5.34713e25	−0.364595
$569$	−2.44961e26	−1.64259	−0.821296	−	0.570502i	$-0.806749\pi$
$569$	−2.44961e26	−1.64259	−0.821296	+	0.570502i	$0.806749\pi$
$570$	5.54882e24	0.0365923
$571$	2.66645e26	1.72938	0.864690	−	0.502306i	$-0.167515\pi$
$571$	2.66645e26	1.72938	0.864690	+	0.502306i	$0.167515\pi$
$572$	−9.71306e25	−0.619575
$573$	−8.04565e25	−0.504768
$574$	2.73644e25	0.168858
$575$	3.05784e25	0.185597
$576$	−1.55158e25	−0.0926319
$577$	−1.31556e25	−0.0772576	−0.0386288	−	0.999254i	$-0.512299\pi$
$577$	−1.31556e25	−0.0772576	−0.0386288	+	0.999254i	$0.512299\pi$
$578$	2.23670e26	1.29209
$579$	1.42939e25	0.0812280
$580$	1.23449e25	0.0690115
$581$	1.05767e26	0.581671
$582$	−1.08616e26	−0.587657
$583$	6.25403e25	0.332896
$584$	−7.42873e25	−0.389039
$585$	−1.16325e26	−0.599367
$586$	−2.12678e26	−1.07819
$587$	−1.54368e26	−0.770009	−0.385005	−	0.922915i	$-0.625800\pi$
$587$	−1.54368e26	−0.770009	−0.385005	+	0.922915i	$0.625800\pi$
$588$	3.76810e25	0.184943
$589$	−6.64515e25	−0.320929
$590$	−2.11995e25	−0.100747
$591$	1.46031e25	0.0682911
$592$	−1.99818e25	−0.0919558
$593$	4.05526e26	1.83654	0.918268	−	0.395959i	$-0.129588\pi$
$593$	4.05526e26	1.83654	0.918268	+	0.395959i	$0.129588\pi$
$594$	−9.63095e25	−0.429238
$595$	8.95954e25	0.392984
$596$	1.91446e25	0.0826433
$597$	2.01356e26	0.855476
$598$	2.83801e26	1.18673
$599$	4.12101e26	1.69609	0.848045	−	0.529925i	$-0.177780\pi$
$599$	4.12101e26	1.69609	0.848045	+	0.529925i	$0.177780\pi$
$600$	−8.88230e24	−0.0359823
$601$	−2.12493e25	−0.0847300	−0.0423650	−	0.999102i	$-0.513489\pi$
$601$	−2.12493e25	−0.0847300	−0.0423650	+	0.999102i	$0.513489\pi$
$602$	−1.43016e26	−0.561331
$603$	−2.11775e26	−0.818202
$604$	−1.54452e26	−0.587412
$605$	−6.33744e25	−0.237267
$606$	1.69131e25	0.0623352
$607$	2.90231e26	1.05305	0.526527	−	0.850158i	$-0.323494\pi$
$607$	2.90231e26	1.05305	0.526527	+	0.850158i	$0.323494\pi$
$608$	−1.12537e25	−0.0401986
$609$	−2.33388e25	−0.0820756
$610$	4.20425e25	0.145564
$611$	−2.17024e25	−0.0739803
$612$	−1.85628e26	−0.623026
$613$	−4.17018e26	−1.37810	−0.689049	−	0.724715i	$-0.741972\pi$
$613$	−4.17018e26	−1.37810	−0.689049	+	0.724715i	$0.741972\pi$
$614$	2.55023e26	0.829811
$615$	−3.24561e25	−0.103988
$616$	−4.01275e25	−0.126598
$617$	−1.23091e26	−0.382400	−0.191200	−	0.981551i	$-0.561238\pi$
$617$	−1.23091e26	−0.382400	−0.191200	+	0.981551i	$0.561238\pi$
$618$	−5.00336e24	−0.0153063
$619$	5.61407e26	1.69128	0.845642	−	0.533750i	$-0.179218\pi$
$619$	5.61407e26	1.69128	0.845642	+	0.533750i	$0.179218\pi$
$620$	1.06373e26	0.315580
$621$	2.81402e26	0.822161
$622$	2.54297e26	0.731700
$623$	2.54531e26	0.721282
$624$	−8.24375e25	−0.230076
$625$	1.45519e25	0.0400000
$626$	−4.55189e26	−1.23235
$627$	−2.97322e25	−0.0792840
$628$	1.11863e26	0.293811
$629$	−2.39059e26	−0.618478
$630$	−4.80574e25	−0.122469
$631$	2.24570e25	0.0563732	0.0281866	−	0.999603i	$-0.491027\pi$
$631$	2.24570e25	0.0563732	0.0281866	+	0.999603i	$0.491027\pi$
$632$	−2.36421e26	−0.584621
$633$	−1.24234e25	−0.0302624
$634$	1.33760e26	0.320980
$635$	−1.06719e26	−0.252285
$636$	5.30797e25	0.123619
$637$	−5.72950e26	−1.31460
$638$	−6.61476e25	−0.149526
$639$	3.43135e26	0.764199
$640$	1.80144e25	0.0395285
$641$	3.71414e25	0.0802985	0.0401492	−	0.999194i	$-0.487217\pi$
$641$	3.71414e25	0.0802985	0.0401492	+	0.999194i	$0.487217\pi$
$642$	2.78395e26	0.593032
$643$	−3.15707e26	−0.662643	−0.331321	−	0.943518i	$-0.607494\pi$
$643$	−3.15707e26	−0.662643	−0.331321	+	0.943518i	$0.607494\pi$
$644$	1.17247e26	0.242485
$645$	1.69627e26	0.345683
$646$	−1.34637e26	−0.270368
$647$	−1.43071e25	−0.0283114	−0.0141557	−	0.999900i	$-0.504506\pi$
$647$	−1.43071e25	−0.0283114	−0.0141557	+	0.999900i	$0.504506\pi$
$648$	5.26189e25	0.102608
$649$	1.13593e26	0.218287
$650$	1.35058e26	0.255766
$651$	−2.01104e26	−0.375320
$652$	−3.61951e26	−0.665729
$653$	−8.73760e26	−1.58386	−0.791930	−	0.610612i	$-0.790924\pi$
$653$	−8.73760e26	−1.58386	−0.791930	+	0.610612i	$0.790924\pi$
$654$	−1.43467e26	−0.256309
$655$	−2.45339e26	−0.431990
$656$	6.58249e25	0.114236
$657$	4.76715e26	0.815433
$658$	−8.96591e24	−0.0151164
$659$	5.24673e25	0.0871922	0.0435961	−	0.999049i	$-0.486119\pi$
$659$	5.24673e25	0.0871922	0.0435961	+	0.999049i	$0.486119\pi$
$660$	4.75940e25	0.0779624
$661$	−2.51792e26	−0.406563	−0.203281	−	0.979120i	$-0.565161\pi$
$661$	−2.51792e26	−0.406563	−0.203281	+	0.979120i	$0.565161\pi$
$662$	5.00134e25	0.0796042
$663$	−9.86268e26	−1.54745
$664$	2.54422e26	0.393512
$665$	−3.48562e25	−0.0531465
$666$	1.28227e26	0.192741
$667$	1.93274e26	0.286403
$668$	4.79221e24	0.00700099
$669$	2.07156e26	0.298366
$670$	2.45879e26	0.349148
$671$	−2.25276e26	−0.315392
$672$	−3.40574e25	−0.0470114
$673$	−7.15963e26	−0.974423	−0.487212	−	0.873284i	$-0.661986\pi$
$673$	−7.15963e26	−0.974423	−0.487212	+	0.873284i	$0.661986\pi$
$674$	1.99002e26	0.267047
$675$	1.33916e26	0.177193
$676$	8.70249e26	1.13540
$677$	−4.37826e26	−0.563260	−0.281630	−	0.959523i	$-0.590875\pi$
$677$	−4.37826e26	−0.563260	−0.281630	+	0.959523i	$0.590875\pi$
$678$	4.43362e26	0.562440
$679$	6.82295e26	0.853512
$680$	2.15521e26	0.265862
$681$	−4.67599e26	−0.568822
$682$	−5.69977e26	−0.683763
$683$	4.02600e26	0.476296	0.238148	−	0.971229i	$-0.423460\pi$
$683$	4.02600e26	0.476296	0.238148	+	0.971229i	$0.423460\pi$
$684$	7.22169e25	0.0842570
$685$	3.96364e26	0.456072
$686$	−5.62343e26	−0.638149
$687$	6.97487e26	0.780633
$688$	−3.44025e26	−0.379752
$689$	−8.07090e26	−0.878697
$690$	−1.39063e26	−0.149329
$691$	5.80847e26	0.615206	0.307603	−	0.951515i	$-0.400473\pi$
$691$	5.80847e26	0.615206	0.307603	+	0.951515i	$0.400473\pi$
$692$	1.86274e26	0.194601
$693$	2.57506e26	0.265351
$694$	3.26751e26	0.332125
$695$	7.76303e26	0.778351
$696$	−5.61413e25	−0.0555258
$697$	7.87518e26	0.768332
$698$	−3.71498e26	−0.357545
$699$	−9.01038e26	−0.855480
$700$	5.57963e25	0.0522606
$701$	−6.65373e26	−0.614814	−0.307407	−	0.951578i	$-0.599461\pi$
$701$	−6.65373e26	−0.614814	−0.307407	+	0.951578i	$0.599461\pi$
$702$	1.24289e27	1.13300
$703$	9.30037e25	0.0836420
$704$	−9.65266e25	−0.0856459
$705$	1.06342e25	0.00930910
$706$	−4.40805e26	−0.380717
$707$	−1.06244e26	−0.0905356
$708$	9.64099e25	0.0810599
$709$	2.09393e27	1.73709	0.868546	−	0.495608i	$-0.165055\pi$
$709$	2.09393e27	1.73709	0.868546	+	0.495608i	$0.165055\pi$
$710$	−3.98392e26	−0.326104
$711$	1.51716e27	1.22538
$712$	6.12274e26	0.487962
$713$	1.66539e27	1.30968
$714$	−4.07457e26	−0.316190
$715$	−7.23680e26	−0.554165
$716$	−2.85744e26	−0.215926
$717$	9.91043e26	0.739028
$718$	−1.00321e27	−0.738262
$719$	9.61307e25	0.0698132	0.0349066	−	0.999391i	$-0.488887\pi$
$719$	9.61307e25	0.0698132	0.0349066	+	0.999391i	$0.488887\pi$
$720$	−1.15602e26	−0.0828525
$721$	3.14298e25	0.0222309
$722$	−9.60572e26	−0.670543
$723$	−4.14123e26	−0.285309
$724$	−7.32479e26	−0.498057
$725$	9.19766e25	0.0617257
$726$	2.88210e26	0.190902
$727$	−2.28716e27	−1.49527	−0.747637	−	0.664108i	$-0.768811\pi$
$727$	−2.28716e27	−1.49527	−0.747637	+	0.664108i	$0.768811\pi$
$728$	5.17851e26	0.334162
$729$	3.70169e26	0.235770
$730$	−5.53484e26	−0.347967
$731$	−4.11586e27	−2.55414
$732$	−1.91198e26	−0.117119
$733$	9.50008e26	0.574433	0.287217	−	0.957866i	$-0.407270\pi$
$733$	9.50008e26	0.574433	0.287217	+	0.957866i	$0.407270\pi$
$734$	−8.72376e26	−0.520704
$735$	2.80746e26	0.165418
$736$	2.82036e26	0.164046
$737$	−1.31749e27	−0.756496
$738$	−4.22410e26	−0.239441
$739$	−2.92022e27	−1.63415	−0.817077	−	0.576529i	$-0.804407\pi$
$739$	−2.92022e27	−1.63415	−0.817077	+	0.576529i	$0.804407\pi$
$740$	−1.48876e26	−0.0822477
$741$	3.83698e26	0.209275
$742$	−3.33433e26	−0.179544
$743$	2.06362e27	1.09707	0.548536	−	0.836127i	$-0.315185\pi$
$743$	2.06362e27	1.09707	0.548536	+	0.836127i	$0.315185\pi$
$744$	−4.83755e26	−0.253912
$745$	1.42639e26	0.0739185
$746$	−2.90063e25	−0.0148414
$747$	−1.63267e27	−0.824810
$748$	−1.15483e27	−0.576039
$749$	−1.74880e27	−0.861319
$750$	−6.61783e25	−0.0321835
$751$	2.97915e27	1.43058	0.715291	−	0.698827i	$-0.246294\pi$
$751$	2.97915e27	1.43058	0.715291	+	0.698827i	$0.246294\pi$
$752$	−2.15674e25	−0.0102265
$753$	1.58233e27	0.740877
$754$	8.53643e26	0.394683
$755$	−1.15076e27	−0.525397
$756$	5.13473e26	0.231505
$757$	2.29450e27	1.02159	0.510796	−	0.859702i	$-0.329351\pi$
$757$	2.29450e27	1.02159	0.510796	+	0.859702i	$0.329351\pi$
$758$	1.31591e26	0.0578588
$759$	7.45140e26	0.323550
$760$	−8.38464e25	−0.0359547
$761$	2.78541e27	1.17960	0.589801	−	0.807548i	$-0.299206\pi$
$761$	2.78541e27	1.17960	0.589801	+	0.807548i	$0.299206\pi$
$762$	4.85330e26	0.202985
$763$	9.01223e26	0.372262
$764$	1.21575e27	0.495974
$765$	−1.38304e27	−0.557251
$766$	2.24580e27	0.893710
$767$	−1.46594e27	−0.576182
$768$	−8.19248e25	−0.0318041
$769$	−2.23371e27	−0.856498	−0.428249	−	0.903661i	$-0.640869\pi$
$769$	−2.23371e27	−0.856498	−0.428249	+	0.903661i	$0.640869\pi$
$770$	−2.98973e26	−0.113232
$771$	−1.58801e27	−0.594069
$772$	−2.15991e26	−0.0798127
$773$	9.13265e26	0.333343	0.166672	−	0.986012i	$-0.446698\pi$
$773$	9.13265e26	0.333343	0.166672	+	0.986012i	$0.446698\pi$
$774$	2.20767e27	0.795967
$775$	7.92538e26	0.282263
$776$	1.64126e27	0.577418
$777$	2.81460e26	0.0978176
$778$	−7.04272e26	−0.241788
$779$	−3.06376e26	−0.103908
$780$	−6.14207e26	−0.205786
$781$	2.13470e27	0.706566
$782$	3.37424e27	1.10334
$783$	8.46426e26	0.273434
$784$	−5.69387e26	−0.181721
$785$	8.33442e26	0.262793
$786$	1.11574e27	0.347574
$787$	5.64471e26	0.173733	0.0868664	−	0.996220i	$-0.472315\pi$
$787$	5.64471e26	0.173733	0.0868664	+	0.996220i	$0.472315\pi$
$788$	−2.20663e26	−0.0671012
$789$	−1.01040e27	−0.303572
$790$	−1.76148e27	−0.522901
$791$	−2.78508e27	−0.816887
$792$	6.19429e26	0.179516
$793$	2.90722e27	0.832496
$794$	−2.14001e27	−0.605509
$795$	3.95474e26	0.110568
$796$	−3.04263e27	−0.840571
$797$	−1.25075e27	−0.341441	−0.170721	−	0.985319i	$-0.554610\pi$
$797$	−1.25075e27	−0.341441	−0.170721	+	0.985319i	$0.554610\pi$
$798$	1.58517e26	0.0427610
$799$	−2.58029e26	−0.0687820
$800$	1.34218e26	0.0353553
$801$	−3.92907e27	−1.02278
$802$	1.76649e26	0.0454418
$803$	2.96573e27	0.753936
$804$	−1.11819e27	−0.280921
$805$	8.73556e26	0.216885
$806$	7.35562e27	1.80483
$807$	−3.66723e27	−0.889283
$808$	−2.55569e26	−0.0612491
$809$	−2.25667e26	−0.0534510	−0.0267255	−	0.999643i	$-0.508508\pi$
$809$	−2.25667e26	−0.0534510	−0.0267255	+	0.999643i	$0.508508\pi$
$810$	3.92041e26	0.0917750
$811$	−1.12861e27	−0.261123	−0.130561	−	0.991440i	$-0.541678\pi$
$811$	−1.12861e27	−0.261123	−0.130561	+	0.991440i	$0.541678\pi$
$812$	3.52665e26	0.0806456
$813$	−3.00998e27	−0.680304
$814$	7.97724e26	0.178205
$815$	−2.69674e27	−0.595446
$816$	−9.80135e26	−0.213909
$817$	1.60123e27	0.345418
$818$	9.33354e26	0.199017
$819$	−3.32314e27	−0.700409
$820$	4.90433e26	0.102176
$821$	−4.62062e27	−0.951569	−0.475784	−	0.879562i	$-0.657836\pi$
$821$	−4.62062e27	−0.951569	−0.475784	+	0.879562i	$0.657836\pi$
$822$	−1.80256e27	−0.366950
$823$	5.30846e27	1.06824	0.534121	−	0.845408i	$-0.320643\pi$
$823$	5.30846e27	1.06824	0.534121	+	0.845408i	$0.320643\pi$
$824$	7.56043e25	0.0150397
$825$	3.54603e26	0.0697317
$826$	−6.05622e26	−0.117731
$827$	2.89805e27	0.556933	0.278467	−	0.960446i	$-0.410174\pi$
$827$	2.89805e27	0.556933	0.278467	+	0.960446i	$0.410174\pi$
$828$	−1.80988e27	−0.343844
$829$	−1.57547e27	−0.295898	−0.147949	−	0.988995i	$-0.547267\pi$
$829$	−1.57547e27	−0.295898	−0.147949	+	0.988995i	$0.547267\pi$
$830$	1.89559e27	0.351968
$831$	1.39536e27	0.256140
$832$	1.24569e27	0.226067
$833$	−6.81205e27	−1.22222
$834$	−3.53042e27	−0.626252
$835$	3.57048e25	0.00626188
$836$	4.49275e26	0.0779026
$837$	7.29343e27	1.25037
$838$	−7.39099e27	−1.25281
$839$	4.31895e27	0.723836	0.361918	−	0.932210i	$-0.382122\pi$
$839$	4.31895e27	0.723836	0.361918	+	0.932210i	$0.382122\pi$
$840$	−2.53747e26	−0.0420482
$841$	−5.52192e27	−0.904748
$842$	−2.41641e27	−0.391477
$843$	−5.69542e27	−0.912355
$844$	1.87726e26	0.0297352
$845$	6.48386e27	1.01553
$846$	1.38402e26	0.0214351
$847$	−1.81046e27	−0.277266
$848$	−8.02071e26	−0.121465
$849$	5.54510e27	0.830398
$850$	1.60576e27	0.237794
$851$	−2.33083e27	−0.341334
$852$	1.81178e27	0.262379
$853$	4.26621e26	0.0610979	0.0305490	−	0.999533i	$-0.490274\pi$
$853$	4.26621e26	0.0610979	0.0305490	+	0.999533i	$0.490274\pi$
$854$	1.20106e27	0.170104
$855$	5.38058e26	0.0753618
$856$	−4.20674e27	−0.582700
$857$	4.56728e27	0.625662	0.312831	−	0.949809i	$-0.398723\pi$
$857$	4.56728e27	0.625662	0.312831	+	0.949809i	$0.398723\pi$
$858$	3.29111e27	0.445874
$859$	1.40555e27	0.188326	0.0941631	−	0.995557i	$-0.469982\pi$
$859$	1.40555e27	0.188326	0.0941631	+	0.995557i	$0.469982\pi$
$860$	−2.56318e27	−0.339660
$861$	−9.27195e26	−0.121518
$862$	−7.37926e27	−0.956519
$863$	8.51803e27	1.09204	0.546018	−	0.837774i	$-0.316143\pi$
$863$	8.51803e27	1.09204	0.546018	+	0.837774i	$0.316143\pi$
$864$	1.23516e27	0.156618
$865$	1.38785e27	0.174056
$866$	−7.09639e27	−0.880274
$867$	−7.57868e27	−0.929849
$868$	3.03882e27	0.368781
$869$	9.43853e27	1.13296
$870$	−4.18286e26	−0.0496638
$871$	1.70024e28	1.99681
$872$	2.16789e27	0.251843
$873$	−1.05322e28	−1.21028
$874$	−1.31271e27	−0.149215
$875$	4.15715e26	0.0467433
$876$	2.51710e27	0.279970
$877$	−7.77367e27	−0.855322	−0.427661	−	0.903939i	$-0.640662\pi$
$877$	−7.77367e27	−0.855322	−0.427661	+	0.903939i	$0.640662\pi$
$878$	−6.44080e27	−0.701038
$879$	7.20624e27	0.775916
$880$	−7.19179e26	−0.0766040
$881$	9.90182e27	1.04338	0.521692	−	0.853134i	$-0.325301\pi$
$881$	9.90182e27	1.04338	0.521692	+	0.853134i	$0.325301\pi$
$882$	3.65386e27	0.380891
$883$	−1.01292e28	−1.04460	−0.522298	−	0.852763i	$-0.674925\pi$
$883$	−1.01292e28	−1.04460	−0.522298	+	0.852763i	$0.674925\pi$
$884$	1.49032e28	1.52049
$885$	7.18310e26	0.0725021
$886$	1.17027e27	0.116860
$887$	1.94019e28	1.91677	0.958384	−	0.285483i	$-0.0921539\pi$
$887$	1.94019e28	1.91677	0.958384	+	0.285483i	$0.0921539\pi$
$888$	6.77050e26	0.0661756
$889$	−3.04871e27	−0.294815
$890$	4.56180e27	0.436446
$891$	−2.10068e27	−0.198848
$892$	−3.13027e27	−0.293168
$893$	1.00384e26	0.00930196
$894$	−6.48684e26	−0.0594739
$895$	−2.12896e27	−0.193130
$896$	5.14630e26	0.0461923
$897$	−9.61612e27	−0.854027
$898$	−2.18949e27	−0.192406
$899$	5.00930e27	0.435572
$900$	−8.61300e26	−0.0741055
$901$	−9.59584e27	−0.816954
$902$	−2.62789e27	−0.221383
$903$	4.84586e27	0.403959
$904$	−6.69950e27	−0.552640
$905$	−5.45740e27	−0.445476
$906$	5.23334e27	0.422728
$907$	−1.39346e28	−1.11385	−0.556924	−	0.830563i	$-0.688019\pi$
$907$	−1.39346e28	−1.11385	−0.556924	+	0.830563i	$0.688019\pi$
$908$	7.06575e27	0.558911
$909$	1.64003e27	0.128379
$910$	3.85829e27	0.298883
$911$	−6.06821e27	−0.465196	−0.232598	−	0.972573i	$-0.574723\pi$
$911$	−6.06821e27	−0.465196	−0.232598	+	0.972573i	$0.574723\pi$
$912$	3.81312e26	0.0289287
$913$	−1.01572e28	−0.762606
$914$	9.35003e27	0.694743
$915$	−1.42454e27	−0.104755
$916$	−1.05395e28	−0.767032
$917$	−7.00876e27	−0.504815
$918$	1.47772e28	1.05338
$919$	2.20624e28	1.55652	0.778260	−	0.627942i	$-0.216102\pi$
$919$	2.20624e28	1.55652	0.778260	+	0.627942i	$0.216102\pi$
$920$	2.10133e27	0.146727
$921$	−8.64101e27	−0.597170
$922$	−4.04815e27	−0.276893
$923$	−2.75486e28	−1.86502
$924$	1.35965e27	0.0911055
$925$	−1.10921e27	−0.0735646
$926$	−1.49332e28	−0.980276
$927$	−4.85167e26	−0.0315234
$928$	8.48334e26	0.0545584
$929$	−2.55096e28	−1.62388	−0.811940	−	0.583740i	$-0.801589\pi$
$929$	−2.55096e28	−1.62388	−0.811940	+	0.583740i	$0.801589\pi$
$930$	−3.60426e27	−0.227106
$931$	2.65016e27	0.165291
$932$	1.36153e28	0.840575
$933$	−8.61643e27	−0.526565
$934$	−1.48547e28	−0.898607
$935$	−8.60414e27	−0.515225
$936$	−7.99380e27	−0.473841
$937$	1.82517e28	1.07097	0.535485	−	0.844545i	$-0.320129\pi$
$937$	1.82517e28	1.07097	0.535485	+	0.844545i	$0.320129\pi$
$938$	7.02419e27	0.408009
$939$	1.54233e28	0.886859
$940$	−1.60690e26	−0.00914690
$941$	2.32888e28	1.31234	0.656169	−	0.754614i	$-0.272176\pi$
$941$	2.32888e28	1.31234	0.656169	+	0.754614i	$0.272176\pi$
$942$	−3.79028e27	−0.211440
$943$	7.67830e27	0.424037
$944$	−1.45682e27	−0.0796475
$945$	3.82567e27	0.207064
$946$	1.37343e28	0.735938
$947$	−2.16819e28	−1.15020	−0.575098	−	0.818084i	$-0.695036\pi$
$947$	−2.16819e28	−1.15020	−0.575098	+	0.818084i	$0.695036\pi$
$948$	8.01074e27	0.420720
$949$	−3.82731e28	−1.99005
$950$	−6.24705e26	−0.0321589
$951$	−4.53222e27	−0.230992
$952$	6.15695e27	0.310681
$953$	−4.92023e27	−0.245812	−0.122906	−	0.992418i	$-0.539221\pi$
$953$	−4.92023e27	−0.245812	−0.122906	+	0.992418i	$0.539221\pi$
$954$	5.14703e27	0.254594
$955$	9.05807e27	0.443612
$956$	−1.49754e28	−0.726151
$957$	2.24130e27	0.107606
$958$	2.21976e28	1.05520
$959$	1.13232e28	0.532957
$960$	−6.10387e26	−0.0284465
$961$	2.14932e28	0.991811
$962$	−1.02947e28	−0.470383
$963$	2.69954e28	1.22135
$964$	6.25768e27	0.280338
$965$	−1.60926e27	−0.0713866
$966$	−3.97270e27	−0.174503
$967$	1.22764e28	0.533972	0.266986	−	0.963700i	$-0.413972\pi$
$967$	1.22764e28	0.533972	0.266986	+	0.963700i	$0.413972\pi$
$968$	−4.35506e27	−0.187576
$969$	4.56195e27	0.194569
$970$	1.22283e28	0.516458
$971$	2.18467e28	0.913698	0.456849	−	0.889544i	$-0.348978\pi$
$971$	2.18467e28	0.913698	0.456849	+	0.889544i	$0.348978\pi$
$972$	−1.24788e28	−0.516823
$973$	2.21772e28	0.909567
$974$	−1.13098e28	−0.459350
$975$	−4.57620e27	−0.184061
$976$	2.88914e27	0.115079
$977$	3.53418e28	1.39409	0.697043	−	0.717029i	$-0.254499\pi$
$977$	3.53418e28	1.39409	0.697043	+	0.717029i	$0.254499\pi$
$978$	1.22641e28	0.479089
$979$	−2.44435e28	−0.945643
$980$	−4.24226e27	−0.162536
$981$	−1.39117e28	−0.527868
$982$	−9.04281e27	−0.339816
$983$	2.24443e28	0.835309	0.417655	−	0.908606i	$-0.362852\pi$
$983$	2.24443e28	0.835309	0.417655	+	0.908606i	$0.362852\pi$
$984$	−2.23036e27	−0.0822095
$985$	−1.64407e27	−0.0600171
$986$	1.01493e28	0.366950
$987$	3.03794e26	0.0108784
$988$	−5.79794e27	−0.205628
$989$	−4.01296e28	−1.40961
$990$	4.61510e27	0.160564
$991$	3.80736e28	1.31197	0.655986	−	0.754773i	$-0.272253\pi$
$991$	3.80736e28	1.31197	0.655986	+	0.754773i	$0.272253\pi$
$992$	7.30987e27	0.249488
$993$	−1.69462e27	−0.0572868
$994$	−1.13811e28	−0.381079
$995$	−2.26693e28	−0.751830
$996$	−8.62066e27	−0.283189
$997$	4.84284e28	1.57578	0.787892	−	0.615814i	$-0.211173\pi$
$997$	4.84284e28	1.57578	0.787892	+	0.615814i	$0.211173\pi$
$998$	−2.31586e28	−0.746402
$999$	−1.02077e28	−0.325878

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.20.a.d.1.1	✓	2
3.2	odd	2		90.20.a.g.1.2		2
4.3	odd	2		80.20.a.d.1.2		2
5.2	odd	4		50.20.b.f.49.4		4
5.3	odd	4		50.20.b.f.49.1		4
5.4	even	2		50.20.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.20.a.d.1.1	✓	2	1.1	even	1	trivial
50.20.a.f.1.2		2	5.4	even	2
50.20.b.f.49.1		4	5.3	odd	4
50.20.b.f.49.4		4	5.2	odd	4
80.20.a.d.1.2		2	4.3	odd	2
90.20.a.g.1.2		2	3.2	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:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+512.000 q^{2} -17348.2 q^{3} +262144. q^{4} +1.95312e6 q^{5} -8.88230e6 q^{6} +5.57963e7 q^{7} +1.34218e8 q^{8} -8.61300e8 q^{9} +1.00000e9 q^{10} -5.35830e9 q^{11} -4.54774e9 q^{12} +6.91495e10 q^{13} +2.85677e10 q^{14} -3.38833e10 q^{15} +6.87195e10 q^{16} +8.22149e11 q^{17} -4.40986e11 q^{18} -3.19849e11 q^{19} +5.12000e11 q^{20} -9.67968e11 q^{21} -2.74345e12 q^{22} +8.01595e12 q^{23} -2.32844e12 q^{24} +3.81470e12 q^{25} +3.54046e13 q^{26} +3.51052e13 q^{27} +1.46267e13 q^{28} +2.41111e13 q^{29} -1.73482e13 q^{30} +2.07759e14 q^{31} +3.51844e13 q^{32} +9.29571e13 q^{33} +4.20940e14 q^{34} +1.08977e14 q^{35} -2.25785e14 q^{36} -2.90774e14 q^{37} -1.63763e14 q^{38} -1.19962e15 q^{39} +2.62144e14 q^{40} +9.57878e14 q^{41} -4.95600e14 q^{42} -5.00622e15 q^{43} -1.40465e15 q^{44} -1.68223e15 q^{45} +4.10417e15 q^{46} -3.13847e14 q^{47} -1.19216e15 q^{48} -8.28567e15 q^{49} +1.95312e15 q^{50} -1.42628e16 q^{51} +1.81271e16 q^{52} -1.16717e16 q^{53} +1.79739e16 q^{54} -1.04654e16 q^{55} +7.48886e15 q^{56} +5.54882e15 q^{57} +1.23449e16 q^{58} -2.11995e16 q^{59} -8.88230e15 q^{60} +4.20425e16 q^{61} +1.06373e17 q^{62} -4.80574e16 q^{63} +1.80144e16 q^{64} +1.35058e17 q^{65} +4.75940e16 q^{66} +2.45879e17 q^{67} +2.15521e17 q^{68} -1.39063e17 q^{69} +5.57963e16 q^{70} -3.98392e17 q^{71} -1.15602e17 q^{72} -5.53484e17 q^{73} -1.48876e17 q^{74} -6.61783e16 q^{75} -8.38464e16 q^{76} -2.98973e17 q^{77} -6.14207e17 q^{78} -1.76148e18 q^{79} +1.34218e17 q^{80} +3.92041e17 q^{81} +4.90433e17 q^{82} +1.89559e18 q^{83} -2.53747e17 q^{84} +1.60576e18 q^{85} -2.56318e18 q^{86} -4.18286e17 q^{87} -7.19179e17 q^{88} +4.56180e18 q^{89} -8.61300e17 q^{90} +3.85829e18 q^{91} +2.10133e18 q^{92} -3.60426e18 q^{93} -1.60690e17 q^{94} -6.24705e17 q^{95} -6.10387e17 q^{96} +1.22283e19 q^{97} -4.24226e18 q^{98} +4.61510e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 1024 q^{2} + 33724 q^{3} + 524288 q^{4} + 3906250 q^{5} + 17266688 q^{6} + 83061292 q^{7} + 268435456 q^{8} + 584812954 q^{9} + 2000000000 q^{10} + 3549480144 q^{11} + 8840544256 q^{12} + 30250225564 q^{13}+ \cdots + 17\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 1024 * q^2 + 33724 * q^3 + 524288 * q^4 + 3906250 * q^5 + 17266688 * q^6 + 83061292 * q^7 + 268435456 * q^8 + 584812954 * q^9 + 2000000000 * q^10 + 3549480144 * q^11 + 8840544256 * q^12 + 30250225564 * q^13 + 42527381504 * q^14 + 65867187500 * q^15 + 137438953472 * q^16 + 329655779412 * q^17 + 299424232448 * q^18 + 383076809800 * q^19 + 1024000000000 * q^20 + 424515195104 * q^21 + 1817333833728 * q^22 + 2082856096884 * q^23 + 4526358659072 * q^24 + 7629394531250 * q^25 + 15488115488768 * q^26 + 49602163340440 * q^27 + 21774019330048 * q^28 + 166587684602220 * q^29 + 33724000000000 * q^30 + 418151119038664 * q^31 + 70368744177664 * q^32 + 547897533578928 * q^33 + 168783759058944 * q^34 + 162229085937500 * q^35 + 153305207013376 * q^36 - 1292219637694628 * q^37 + 196135326617600 * q^38 - 3186297306918232 * q^39 + 524288000000000 * q^40 - 3127192714527996 * q^41 + 217351779893248 * q^42 - 1795992338357636 * q^43 + 930474922868736 * q^44 + 1142212800781250 * q^45 + 1066422321604608 * q^46 - 6761653310165988 * q^47 + 2317495633444864 * q^48 - 18941182438871454 * q^49 + 3906250000000000 * q^50 - 39415550773661256 * q^51 + 7929915130249216 * q^52 - 9787568571066516 * q^53 + 25396307630305280 * q^54 + 6932578406250000 * q^55 + 11148297896984576 * q^56 + 41448804721422800 * q^57 + 85292894516336640 * q^58 - 25484316660294360 * q^59 + 17266688000000000 * q^60 - 77840503559636276 * q^61 + 214093372947795968 * q^62 - 8629133041886116 * q^63 + 36028797018963968 * q^64 + 59082471804687500 * q^65 + 280523537192411136 * q^66 + 439654835073204532 * q^67 + 86417284638179328 * q^68 - 442079200728708192 * q^69 + 83061292000000000 * q^70 - 29427662567526696 * q^71 + 78492265990848512 * q^72 - 1463308911724217756 * q^73 - 661616454499649536 * q^74 + 128646850585937500 * q^75 + 100421287228211200 * q^76 - 56103061801470576 * q^77 - 1631384221142134784 * q^78 - 1235969155825112720 * q^79 + 268435456000000000 * q^80 - 548329353045127838 * q^81 - 1601122669838333952 * q^82 - 877205635969635396 * q^83 + 111284111305342976 * q^84 + 643858944164062500 * q^85 - 919548077239109632 * q^86 + 6858312722579528040 * q^87 + 476403160508792832 * q^88 + 4172929077000032820 * q^89 + 584812954000000000 * q^90 + 2797700455846427144 * q^91 + 546008228661559296 * q^92 + 7140934358593491968 * q^93 - 3461966494804985856 * q^94 + 748196894140625000 * q^95 + 1186557764323770368 * q^96 + 11254578228347861332 * q^97 - 9697885408702184448 * q^98 + 17496761012343831888 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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