LMFDB - Embedded newform 5.18.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,18,Mod(1,5)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	5.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:	$9.16110436723$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{39}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 39 $ x^2 - 39
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$6.24500$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+564.820 q^{2} -17180.6 q^{3} +187950. q^{4} -390625. q^{5} -9.70397e6 q^{6} -2.21307e7 q^{7} +3.21256e7 q^{8} +1.66034e8 q^{9} +O(q^{10})$	\(q+564.820 q^{2} -17180.6 q^{3} +187950. q^{4} -390625. q^{5} -9.70397e6 q^{6} -2.21307e7 q^{7} +3.21256e7 q^{8} +1.66034e8 q^{9} -2.20633e8 q^{10} -7.27892e8 q^{11} -3.22909e9 q^{12} +3.52539e9 q^{13} -1.24998e10 q^{14} +6.71119e9 q^{15} -6.48976e9 q^{16} +3.37530e10 q^{17} +9.37794e10 q^{18} -7.67459e10 q^{19} -7.34178e10 q^{20} +3.80219e11 q^{21} -4.11128e11 q^{22} +5.48049e10 q^{23} -5.51938e11 q^{24} +1.52588e11 q^{25} +1.99121e12 q^{26} -6.33861e11 q^{27} -4.15945e12 q^{28} -2.43412e12 q^{29} +3.79061e12 q^{30} -8.21245e11 q^{31} -7.87631e12 q^{32} +1.25056e13 q^{33} +1.90644e13 q^{34} +8.64479e12 q^{35} +3.12060e13 q^{36} -2.72120e13 q^{37} -4.33476e13 q^{38} -6.05685e13 q^{39} -1.25491e13 q^{40} -7.17143e13 q^{41} +2.14755e14 q^{42} +2.55305e13 q^{43} -1.36807e14 q^{44} -6.48571e13 q^{45} +3.09549e13 q^{46} +3.00475e12 q^{47} +1.11498e14 q^{48} +2.57136e14 q^{49} +8.61847e13 q^{50} -5.79898e14 q^{51} +6.62596e14 q^{52} -6.88051e13 q^{53} -3.58017e14 q^{54} +2.84333e14 q^{55} -7.10960e14 q^{56} +1.31854e15 q^{57} -1.37484e15 q^{58} -8.49663e14 q^{59} +1.26136e15 q^{60} +1.42806e15 q^{61} -4.63855e14 q^{62} -3.67444e15 q^{63} -3.59807e15 q^{64} -1.37711e15 q^{65} +7.06343e15 q^{66} -1.19425e15 q^{67} +6.34386e15 q^{68} -9.41583e14 q^{69} +4.88275e15 q^{70} -1.19599e15 q^{71} +5.33394e15 q^{72} +9.91346e15 q^{73} -1.53699e16 q^{74} -2.62156e15 q^{75} -1.44244e16 q^{76} +1.61087e16 q^{77} -3.42103e16 q^{78} +7.23279e15 q^{79} +2.53506e15 q^{80} -1.05515e16 q^{81} -4.05057e16 q^{82} +2.82999e16 q^{83} +7.14620e16 q^{84} -1.31848e16 q^{85} +1.44201e16 q^{86} +4.18197e16 q^{87} -2.33839e16 q^{88} +5.95425e15 q^{89} -3.66326e16 q^{90} -7.80193e16 q^{91} +1.03006e16 q^{92} +1.41095e16 q^{93} +1.69714e15 q^{94} +2.99789e16 q^{95} +1.35320e17 q^{96} -1.10249e17 q^{97} +1.45235e17 q^{98} -1.20855e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 680 q^{2} - 10980 q^{3} + 70144 q^{4} - 781250 q^{5} - 8989776 q^{6} - 22820700 q^{7} + 3459840 q^{8} + 75341826 q^{9}+O(q^{10}) $ 2 * q + 680 * q^2 - 10980 * q^3 + 70144 * q^4 - 781250 * q^5 - 8989776 * q^6 - 22820700 * q^7 + 3459840 * q^8 + 75341826 * q^9	\( 2 q + 680 q^{2} - 10980 q^{3} + 70144 q^{4} - 781250 q^{5} - 8989776 q^{6} - 22820700 q^{7} + 3459840 q^{8} + 75341826 q^{9} - 265625000 q^{10} - 1053355456 q^{11} - 3959562240 q^{12} - 1637425660 q^{13} - 12579318192 q^{14} + 4289062500 q^{15} + 5649528832 q^{16} + 45284557940 q^{17} + 83333425320 q^{18} + 6966491000 q^{19} - 27400000000 q^{20} + 375940212984 q^{21} - 448614615040 q^{22} + 72199566060 q^{23} - 729683596800 q^{24} + 305175781250 q^{25} + 1396559073104 q^{26} - 1996962267960 q^{27} - 4078158120960 q^{28} - 4189598736500 q^{29} + 3511631250000 q^{30} + 4612322416824 q^{31} - 2720829317120 q^{32} + 10487556973440 q^{33} + 20392568799248 q^{34} + 8914335937500 q^{35} + 41890087567872 q^{36} - 24562012109180 q^{37} - 33705624391840 q^{38} - 92581290596808 q^{39} - 1351500000000 q^{40} - 145472731192436 q^{41} + 214262382630240 q^{42} - 50209039981300 q^{43} - 98465439352832 q^{44} - 29430400781250 q^{45} + 32958421369584 q^{46} + 212531927495060 q^{47} + 186769497231360 q^{48} + 24981386945914 q^{49} + 103759765625000 q^{50} - 508394816272296 q^{51} + 12\!\cdots\!00 q^{52}+ \cdots - 91\!\cdots\!28 q^{99}+O(q^{100}) \) 2 * q + 680 * q^2 - 10980 * q^3 + 70144 * q^4 - 781250 * q^5 - 8989776 * q^6 - 22820700 * q^7 + 3459840 * q^8 + 75341826 * q^9 - 265625000 * q^10 - 1053355456 * q^11 - 3959562240 * q^12 - 1637425660 * q^13 - 12579318192 * q^14 + 4289062500 * q^15 + 5649528832 * q^16 + 45284557940 * q^17 + 83333425320 * q^18 + 6966491000 * q^19 - 27400000000 * q^20 + 375940212984 * q^21 - 448614615040 * q^22 + 72199566060 * q^23 - 729683596800 * q^24 + 305175781250 * q^25 + 1396559073104 * q^26 - 1996962267960 * q^27 - 4078158120960 * q^28 - 4189598736500 * q^29 + 3511631250000 * q^30 + 4612322416824 * q^31 - 2720829317120 * q^32 + 10487556973440 * q^33 + 20392568799248 * q^34 + 8914335937500 * q^35 + 41890087567872 * q^36 - 24562012109180 * q^37 - 33705624391840 * q^38 - 92581290596808 * q^39 - 1351500000000 * q^40 - 145472731192436 * q^41 + 214262382630240 * q^42 - 50209039981300 * q^43 - 98465439352832 * q^44 - 29430400781250 * q^45 + 32958421369584 * q^46 + 212531927495060 * q^47 + 186769497231360 * q^48 + 24981386945914 * q^49 + 103759765625000 * q^50 - 508394816272296 * q^51 + 1270805189555200 * q^52 - 479521291130380 * q^53 - 515019559413600 * q^54 + 411466975000000 * q^55 - 691179867302400 * q^56 + 1837613993665680 * q^57 - 1577035882898960 * q^58 - 3102413298049000 * q^59 + 1546704000000000 * q^60 + 463551587866244 * q^61 + 161983263800160 * q^62 - 3611863782723420 * q^63 - 4595382572548096 * q^64 + 639619398437500 * q^65 + 6830991818108928 * q^66 + 2917128685399140 * q^67 + 4985377003832320 * q^68 - 833725200946968 * q^69 + 4913796168750000 * q^70 + 5121177395190184 * q^71 + 7933701377329920 * q^72 + 4758930266870660 * q^73 - 15064668041604272 * q^74 - 1675415039062500 * q^75 - 24286148533299200 * q^76 + 16333305199209600 * q^77 - 37897540638141600 * q^78 - 2609334097158000 * q^79 - 2206847200000000 * q^80 - 7291608647282838 * q^81 - 49001159307188240 * q^82 + 50638331521860780 * q^83 + 71966018096437248 * q^84 - 17689280445312500 * q^85 + 5696451371679344 * q^86 + 30934657312810920 * q^87 - 14054273022443520 * q^88 + 61192864176640500 * q^89 - 32552119265625000 * q^90 - 74456784720599736 * q^91 + 8251370039101440 * q^92 + 47801080543476240 * q^93 + 25830496599914768 * q^94 - 2721285546875000 * q^95 + 167287242157277184 * q^96 - 257524797515055740 * q^97 + 118495839739185160 * q^98 - 91337759750651328 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	564.820	1.56011	0.780055	−	0.625711i	$-0.215191\pi$
$2$	564.820	1.56011	0.780055	+	0.625711i	$0.215191\pi$
$3$	−17180.6	−1.51185	−0.755925	−	0.654658i	$-0.772812\pi$
$3$	−17180.6	−1.51185	−0.755925	+	0.654658i	$0.772812\pi$
$4$	187950.	1.43394
$5$	−390625.	−0.447214
$5$	−390625.	−0.447214
$6$	−9.70397e6	−2.35865
$7$	−2.21307e7	−1.45098	−0.725489	−	0.688233i	$-0.758387\pi$
$7$	−2.21307e7	−1.45098	−0.725489	+	0.688233i	$0.758387\pi$
$8$	3.21256e7	0.676996
$9$	1.66034e8	1.28569
$10$	−2.20633e8	−0.697702
$11$	−7.27892e8	−1.02383	−0.511916	−	0.859035i	$-0.671064\pi$
$11$	−7.27892e8	−1.02383	−0.511916	+	0.859035i	$0.671064\pi$
$12$	−3.22909e9	−2.16790
$13$	3.52539e9	1.19864	0.599321	−	0.800509i	$-0.295437\pi$
$13$	3.52539e9	1.19864	0.599321	+	0.800509i	$0.295437\pi$
$14$	−1.24998e10	−2.26369
$15$	6.71119e9	0.676120
$16$	−6.48976e9	−0.377754
$17$	3.37530e10	1.17354	0.586768	−	0.809755i	$-0.300400\pi$
$17$	3.37530e10	1.17354	0.586768	+	0.809755i	$0.300400\pi$
$18$	9.37794e10	2.00582
$19$	−7.67459e10	−1.03669	−0.518346	−	0.855171i	$-0.673452\pi$
$19$	−7.67459e10	−1.03669	−0.518346	+	0.855171i	$0.673452\pi$
$20$	−7.34178e10	−0.641278
$21$	3.80219e11	2.19366
$22$	−4.11128e11	−1.59729
$23$	5.48049e10	0.145926	0.0729630	−	0.997335i	$-0.476754\pi$
$23$	5.48049e10	0.145926	0.0729630	+	0.997335i	$0.476754\pi$
$24$	−5.51938e11	−1.02352
$25$	1.52588e11	0.200000
$26$	1.99121e12	1.87001
$27$	−6.33861e11	−0.431919
$28$	−4.15945e12	−2.08062
$29$	−2.43412e12	−0.903564	−0.451782	−	0.892128i	$-0.649212\pi$
$29$	−2.43412e12	−0.903564	−0.451782	+	0.892128i	$0.649212\pi$
$30$	3.79061e12	1.05482
$31$	−8.21245e11	−0.172941	−0.0864705	−	0.996254i	$-0.527559\pi$
$31$	−8.21245e11	−0.172941	−0.0864705	+	0.996254i	$0.527559\pi$
$32$	−7.87631e12	−1.26633
$33$	1.25056e13	1.54788
$34$	1.90644e13	1.83084
$35$	8.64479e12	0.648897
$36$	3.12060e13	1.84360
$37$	−2.72120e13	−1.27364	−0.636819	−	0.771013i	$-0.719750\pi$
$37$	−2.72120e13	−1.27364	−0.636819	+	0.771013i	$0.719750\pi$
$38$	−4.33476e13	−1.61735
$39$	−6.05685e13	−1.81217
$40$	−1.25491e13	−0.302762
$41$	−7.17143e13	−1.40263	−0.701315	−	0.712852i	$-0.747403\pi$
$41$	−7.17143e13	−1.40263	−0.701315	+	0.712852i	$0.747403\pi$
$42$	2.14755e14	3.42235
$43$	2.55305e13	0.333102	0.166551	−	0.986033i	$-0.446737\pi$
$43$	2.55305e13	0.333102	0.166551	+	0.986033i	$0.446737\pi$
$44$	−1.36807e14	−1.46812
$45$	−6.48571e13	−0.574978
$46$	3.09549e13	0.227661
$47$	3.00475e12	0.0184067	0.00920335	−	0.999958i	$-0.497070\pi$
$47$	3.00475e12	0.0184067	0.00920335	+	0.999958i	$0.497070\pi$
$48$	1.11498e14	0.571107
$49$	2.57136e14	1.10534
$50$	8.61847e13	0.312022
$51$	−5.79898e14	−1.77421
$52$	6.62596e14	1.71878
$53$	−6.88051e13	−0.151801	−0.0759006	−	0.997115i	$-0.524183\pi$
$53$	−6.88051e13	−0.151801	−0.0759006	+	0.997115i	$0.524183\pi$
$54$	−3.58017e14	−0.673841
$55$	2.84333e14	0.457872
$56$	−7.10960e14	−0.982307
$57$	1.31854e15	1.56732
$58$	−1.37484e15	−1.40966
$59$	−8.49663e14	−0.753364	−0.376682	−	0.926343i	$-0.622935\pi$
$59$	−8.49663e14	−0.753364	−0.376682	+	0.926343i	$0.622935\pi$
$60$	1.26136e15	0.969516
$61$	1.42806e15	0.953770	0.476885	−	0.878966i	$-0.341766\pi$
$61$	1.42806e15	0.953770	0.476885	+	0.878966i	$0.341766\pi$
$62$	−4.63855e14	−0.269807
$63$	−3.67444e15	−1.86551
$64$	−3.59807e15	−1.59786
$65$	−1.37711e15	−0.536049
$66$	7.06343e15	2.41486
$67$	−1.19425e15	−0.359303	−0.179651	−	0.983730i	$-0.557497\pi$
$67$	−1.19425e15	−0.359303	−0.179651	+	0.983730i	$0.557497\pi$
$68$	6.34386e15	1.68278
$69$	−9.41583e14	−0.220618
$70$	4.88275e15	1.01235
$71$	−1.19599e15	−0.219802	−0.109901	−	0.993943i	$-0.535053\pi$
$71$	−1.19599e15	−0.219802	−0.109901	+	0.993943i	$0.535053\pi$
$72$	5.33394e15	0.870406
$73$	9.91346e15	1.43873	0.719367	−	0.694630i	$-0.244432\pi$
$73$	9.91346e15	1.43873	0.719367	+	0.694630i	$0.244432\pi$
$74$	−1.53699e16	−1.98702
$75$	−2.62156e15	−0.302370
$76$	−1.44244e16	−1.48656
$77$	1.61087e16	1.48556
$78$	−3.42103e16	−2.82718
$79$	7.23279e15	0.536384	0.268192	−	0.963366i	$-0.413574\pi$
$79$	7.23279e15	0.536384	0.268192	+	0.963366i	$0.413574\pi$
$80$	2.53506e15	0.168937
$81$	−1.05515e16	−0.632693
$82$	−4.05057e16	−2.18825
$83$	2.82999e16	1.37918	0.689590	−	0.724200i	$-0.257791\pi$
$83$	2.82999e16	1.37918	0.689590	+	0.724200i	$0.257791\pi$
$84$	7.14620e16	3.14558
$85$	−1.31848e16	−0.524821
$86$	1.44201e16	0.519676
$87$	4.18197e16	1.36605
$88$	−2.33839e16	−0.693130
$89$	5.95425e15	0.160329	0.0801645	−	0.996782i	$-0.474455\pi$
$89$	5.95425e15	0.160329	0.0801645	+	0.996782i	$0.474455\pi$
$90$	−3.66326e16	−0.897028
$91$	−7.80193e16	−1.73920
$92$	1.03006e16	0.209249
$93$	1.41095e16	0.261461
$94$	1.69714e15	0.0287165
$95$	2.99789e16	0.463623
$96$	1.35320e17	1.91450
$97$	−1.10249e17	−1.42829	−0.714143	−	0.700000i	$-0.753183\pi$
$97$	−1.10249e17	−1.42829	−0.714143	+	0.700000i	$0.753183\pi$
$98$	1.45235e17	1.72445
$99$	−1.20855e17	−1.31633
$100$	2.86788e16	0.286788
$101$	5.19625e16	0.477483	0.238742	−	0.971083i	$-0.423265\pi$
$101$	5.19625e16	0.477483	0.238742	+	0.971083i	$0.423265\pi$
$102$	−3.27538e17	−2.76796
$103$	7.41468e16	0.576734	0.288367	−	0.957520i	$-0.406888\pi$
$103$	7.41468e16	0.576734	0.288367	+	0.957520i	$0.406888\pi$
$104$	1.13255e17	0.811475
$105$	−1.48523e17	−0.981035
$106$	−3.88625e16	−0.236827
$107$	−9.50480e16	−0.534787	−0.267393	−	0.963587i	$-0.586162\pi$
$107$	−9.50480e16	−0.534787	−0.267393	+	0.963587i	$0.586162\pi$
$108$	−1.19134e17	−0.619346
$109$	−5.57380e16	−0.267933	−0.133967	−	0.990986i	$-0.542771\pi$
$109$	−5.57380e16	−0.267933	−0.133967	+	0.990986i	$0.542771\pi$
$110$	1.60597e17	0.714330
$111$	4.67520e17	1.92555
$112$	1.43623e17	0.548113
$113$	−3.30512e17	−1.16956	−0.584778	−	0.811194i	$-0.698818\pi$
$113$	−3.30512e17	−1.16956	−0.584778	+	0.811194i	$0.698818\pi$
$114$	7.44740e17	2.44519
$115$	−2.14082e16	−0.0652601
$116$	−4.57492e17	−1.29566
$117$	5.85336e17	1.54108
$118$	−4.79907e17	−1.17533
$119$	−7.46976e17	−1.70278
$120$	2.15601e17	0.457730
$121$	2.43791e16	0.0482327
$122$	8.06598e17	1.48799
$123$	1.23210e18	2.12056
$124$	−1.54353e17	−0.247987
$125$	−5.96046e16	−0.0894427
$126$	−2.07540e18	−2.91040
$127$	−1.41324e18	−1.85304	−0.926522	−	0.376241i	$-0.877216\pi$
$127$	−1.41324e18	−1.85304	−0.926522	+	0.376241i	$0.877216\pi$
$128$	−9.99898e17	−1.22651
$129$	−4.38630e17	−0.503600
$130$	−7.77818e17	−0.836295
$131$	4.77855e17	0.481382	0.240691	−	0.970602i	$-0.422626\pi$
$131$	4.77855e17	0.481382	0.240691	+	0.970602i	$0.422626\pi$
$132$	2.35043e18	2.21957
$133$	1.69844e18	1.50422
$134$	−6.74538e17	−0.560552
$135$	2.47602e17	0.193160
$136$	1.08433e18	0.794479
$137$	2.70610e18	1.86303	0.931514	−	0.363707i	$-0.118489\pi$
$137$	2.70610e18	1.86303	0.931514	+	0.363707i	$0.118489\pi$
$138$	−5.31825e17	−0.344189
$139$	−1.60721e18	−0.978241	−0.489121	−	0.872216i	$-0.662682\pi$
$139$	−1.60721e18	−0.978241	−0.489121	+	0.872216i	$0.662682\pi$
$140$	1.62478e18	0.930481
$141$	−5.16235e16	−0.0278282
$142$	−6.75518e17	−0.342914
$143$	−2.56610e18	−1.22721
$144$	−1.07752e18	−0.485674
$145$	9.50828e17	0.404086
$146$	5.59932e18	2.24458
$147$	−4.41776e18	−1.67111
$148$	−5.11449e18	−1.82632
$149$	5.89349e17	0.198742	0.0993710	−	0.995050i	$-0.468317\pi$
$149$	5.89349e17	0.198742	0.0993710	+	0.995050i	$0.468317\pi$
$150$	−1.48071e18	−0.471730
$151$	1.52832e18	0.460160	0.230080	−	0.973172i	$-0.426101\pi$
$151$	1.52832e18	0.460160	0.230080	+	0.973172i	$0.426101\pi$
$152$	−2.46551e18	−0.701836
$153$	5.60415e18	1.50880
$154$	9.09853e18	2.31763
$155$	3.20799e17	0.0773416
$156$	−1.13838e19	−2.59854
$157$	−3.25942e18	−0.704681	−0.352341	−	0.935872i	$-0.614614\pi$
$157$	−3.25942e18	−0.704681	−0.352341	+	0.935872i	$0.614614\pi$
$158$	4.08522e18	0.836817
$159$	1.18211e18	0.229501
$160$	3.07668e18	0.566321
$161$	−1.21287e18	−0.211736
$162$	−5.95971e18	−0.987070
$163$	−3.44735e18	−0.541865	−0.270933	−	0.962598i	$-0.587332\pi$
$163$	−3.44735e18	−0.541865	−0.270933	+	0.962598i	$0.587332\pi$
$164$	−1.34787e19	−2.01129
$165$	−4.88502e18	−0.692233
$166$	1.59843e19	2.15167
$167$	9.63268e18	1.23213	0.616066	−	0.787695i	$-0.288726\pi$
$167$	9.63268e18	1.23213	0.616066	+	0.787695i	$0.288726\pi$
$168$	1.22147e19	1.48510
$169$	3.77799e18	0.436741
$170$	−7.44702e18	−0.818779
$171$	−1.27424e19	−1.33286
$172$	4.79845e18	0.477649
$173$	1.48938e18	0.141128	0.0705638	−	0.997507i	$-0.477520\pi$
$173$	1.48938e18	0.141128	0.0705638	+	0.997507i	$0.477520\pi$
$174$	2.36206e19	2.13119
$175$	−3.37687e18	−0.290196
$176$	4.72384e18	0.386756
$177$	1.45978e19	1.13897
$178$	3.36308e18	0.250131
$179$	1.51604e18	0.107513	0.0537565	−	0.998554i	$-0.482881\pi$
$179$	1.51604e18	0.107513	0.0537565	+	0.998554i	$0.482881\pi$
$180$	−1.21899e19	−0.824484
$181$	−2.24522e19	−1.44874	−0.724370	−	0.689411i	$-0.757869\pi$
$181$	−2.24522e19	−1.44874	−0.724370	+	0.689411i	$0.757869\pi$
$182$	−4.40669e19	−2.71335
$183$	−2.45350e19	−1.44196
$184$	1.76064e18	0.0987913
$185$	1.06297e19	0.569589
$186$	7.96933e18	0.407908
$187$	−2.45685e19	−1.20150
$188$	5.64741e17	0.0263941
$189$	1.40278e19	0.626705
$190$	1.69327e19	0.723302
$191$	−1.34669e19	−0.550156	−0.275078	−	0.961422i	$-0.588704\pi$
$191$	−1.34669e19	−0.550156	−0.275078	+	0.961422i	$0.588704\pi$
$192$	6.18171e19	2.41573
$193$	2.95630e19	1.10538	0.552690	−	0.833387i	$-0.313601\pi$
$193$	2.95630e19	1.10538	0.552690	+	0.833387i	$0.313601\pi$
$194$	−6.22709e19	−2.22828
$195$	2.36596e19	0.810425
$196$	4.83285e19	1.58499
$197$	−2.82885e19	−0.888478	−0.444239	−	0.895908i	$-0.646526\pi$
$197$	−2.82885e19	−0.888478	−0.444239	+	0.895908i	$0.646526\pi$
$198$	−6.82612e19	−2.05362
$199$	4.75300e19	1.36999	0.684993	−	0.728549i	$-0.259805\pi$
$199$	4.75300e19	1.36999	0.684993	+	0.728549i	$0.259805\pi$
$200$	4.90197e18	0.135399
$201$	2.05180e19	0.543212
$202$	2.93494e19	0.744926
$203$	5.38687e19	1.31105
$204$	−1.08992e20	−2.54411
$205$	2.80134e19	0.627275
$206$	4.18796e19	0.899769
$207$	9.09948e18	0.187616
$208$	−2.28790e19	−0.452791
$209$	5.58627e19	1.06140
$210$	−8.38887e19	−1.53052
$211$	−7.04136e19	−1.23383	−0.616916	−	0.787029i	$-0.711618\pi$
$211$	−7.04136e19	−1.23383	−0.616916	+	0.787029i	$0.711618\pi$
$212$	−1.29319e19	−0.217674
$213$	2.05478e19	0.332307
$214$	−5.36850e19	−0.834326
$215$	−9.97285e18	−0.148968
$216$	−2.03632e19	−0.292407
$217$	1.81747e19	0.250934
$218$	−3.14819e19	−0.418005
$219$	−1.70319e20	−2.17515
$220$	5.34402e19	0.656561
$221$	1.18993e20	1.40665
$222$	2.64065e20	3.00407
$223$	−1.73587e20	−1.90075	−0.950375	−	0.311107i	$-0.899300\pi$
$223$	−1.73587e20	−1.90075	−0.950375	+	0.311107i	$0.899300\pi$
$224$	1.74308e20	1.83742
$225$	2.53348e19	0.257138
$226$	−1.86680e20	−1.82463
$227$	−2.97928e19	−0.280474	−0.140237	−	0.990118i	$-0.544786\pi$
$227$	−2.97928e19	−0.280474	−0.140237	+	0.990118i	$0.544786\pi$
$228$	2.47820e20	2.24745
$229$	−7.83039e19	−0.684198	−0.342099	−	0.939664i	$-0.611138\pi$
$229$	−7.83039e19	−0.684198	−0.342099	+	0.939664i	$0.611138\pi$
$230$	−1.20918e19	−0.101813
$231$	−2.76758e20	−2.24594
$232$	−7.81975e19	−0.611709
$233$	1.73319e20	1.30714	0.653568	−	0.756868i	$-0.273271\pi$
$233$	1.73319e20	1.30714	0.653568	+	0.756868i	$0.273271\pi$
$234$	3.30609e20	2.40425
$235$	−1.17373e18	−0.00823173
$236$	−1.59694e20	−1.08028
$237$	−1.24264e20	−0.810932
$238$	−4.21907e20	−2.65652
$239$	1.81871e20	1.10505	0.552524	−	0.833497i	$-0.313665\pi$
$239$	1.81871e20	1.10505	0.552524	+	0.833497i	$0.313665\pi$
$240$	−4.35540e19	−0.255407
$241$	2.82549e20	1.59937	0.799685	−	0.600420i	$-0.205000\pi$
$241$	2.82549e20	1.59937	0.799685	+	0.600420i	$0.205000\pi$
$242$	1.37698e19	0.0752484
$243$	2.63139e20	1.38846
$244$	2.68404e20	1.36765
$245$	−1.00444e20	−0.494323
$246$	6.95913e20	3.30831
$247$	−2.70560e20	−1.24262
$248$	−2.63830e19	−0.117080
$249$	−4.86210e20	−2.08511
$250$	−3.36659e19	−0.139540
$251$	2.26036e19	0.0905629	0.0452814	−	0.998974i	$-0.485582\pi$
$251$	2.26036e19	0.0905629	0.0452814	+	0.998974i	$0.485582\pi$
$252$	−6.90610e20	−2.67503
$253$	−3.98920e19	−0.149404
$254$	−7.98228e20	−2.89095
$255$	2.26523e20	0.793451
$256$	−9.31562e19	−0.315626
$257$	1.93339e20	0.633706	0.316853	−	0.948475i	$-0.397374\pi$
$257$	1.93339e20	0.633706	0.316853	+	0.948475i	$0.397374\pi$
$258$	−2.47747e20	−0.785672
$259$	6.02220e20	1.84802
$260$	−2.58827e20	−0.768662
$261$	−4.04147e20	−1.16170
$262$	2.69902e20	0.751009
$263$	6.89343e20	1.85700	0.928499	−	0.371335i	$-0.121100\pi$
$263$	6.89343e20	1.85700	0.928499	+	0.371335i	$0.121100\pi$
$264$	4.01751e20	1.04791
$265$	2.68770e19	0.0678876
$266$	9.59312e20	2.34674
$267$	−1.02298e20	−0.242393
$268$	−2.24459e20	−0.515219
$269$	−8.00029e20	−1.77915	−0.889573	−	0.456794i	$-0.848998\pi$
$269$	−8.00029e20	−1.77915	−0.889573	+	0.456794i	$0.848998\pi$
$270$	1.39851e20	0.301351
$271$	−4.68195e20	−0.977660	−0.488830	−	0.872379i	$-0.662576\pi$
$271$	−4.68195e20	−0.977660	−0.488830	+	0.872379i	$0.662576\pi$
$272$	−2.19049e20	−0.443308
$273$	1.34042e21	2.62941
$274$	1.52846e21	2.90653
$275$	−1.11067e20	−0.204766
$276$	−1.76970e20	−0.316354
$277$	−1.67513e19	−0.0290383	−0.0145192	−	0.999895i	$-0.504622\pi$
$277$	−1.67513e19	−0.0290383	−0.0145192	+	0.999895i	$0.504622\pi$
$278$	−9.07782e20	−1.52616
$279$	−1.36355e20	−0.222348
$280$	2.77719e20	0.439301
$281$	−1.16305e21	−1.78482	−0.892409	−	0.451227i	$-0.850987\pi$
$281$	−1.16305e21	−1.78482	−0.892409	+	0.451227i	$0.850987\pi$
$282$	−2.91580e19	−0.0434150
$283$	−1.10305e21	−1.59371	−0.796854	−	0.604172i	$-0.793504\pi$
$283$	−1.10305e21	−1.59371	−0.796854	+	0.604172i	$0.793504\pi$
$284$	−2.24785e20	−0.315183
$285$	−5.15056e20	−0.700928
$286$	−1.44939e21	−1.91458
$287$	1.58708e21	2.03519
$288$	−1.30774e21	−1.62811
$289$	3.12024e20	0.377187
$290$	5.37047e20	0.630419
$291$	1.89415e21	2.15935
$292$	1.86323e21	2.06306
$293$	3.88758e20	0.418124	0.209062	−	0.977902i	$-0.432959\pi$
$293$	3.88758e20	0.418124	0.209062	+	0.977902i	$0.432959\pi$
$294$	−2.49524e21	−2.60711
$295$	3.31900e20	0.336914
$296$	−8.74202e20	−0.862248
$297$	4.61382e20	0.442213
$298$	3.32876e20	0.310059
$299$	1.93209e20	0.174913
$300$	−4.92720e20	−0.433581
$301$	−5.65007e20	−0.483324
$302$	8.63223e20	0.717900
$303$	−8.92749e20	−0.721883
$304$	4.98063e20	0.391614
$305$	−5.57837e20	−0.426539
$306$	3.16533e21	2.35390
$307$	−1.80153e21	−1.30306	−0.651532	−	0.758621i	$-0.725873\pi$
$307$	−1.80153e21	−1.30306	−0.651532	+	0.758621i	$0.725873\pi$
$308$	3.02763e21	2.13020
$309$	−1.27389e21	−0.871935
$310$	1.81194e20	0.120661
$311$	−8.62093e20	−0.558587	−0.279293	−	0.960206i	$-0.590100\pi$
$311$	−8.62093e20	−0.558587	−0.279293	+	0.960206i	$0.590100\pi$
$312$	−1.94580e21	−1.22683
$313$	1.32283e21	0.811668	0.405834	−	0.913947i	$-0.366981\pi$
$313$	1.32283e21	0.811668	0.405834	+	0.913947i	$0.366981\pi$
$314$	−1.84098e21	−1.09938
$315$	1.43533e21	0.834280
$316$	1.35940e21	0.769143
$317$	−1.89123e21	−1.04169	−0.520847	−	0.853650i	$-0.674384\pi$
$317$	−1.89123e21	−1.04169	−0.520847	+	0.853650i	$0.674384\pi$
$318$	6.67682e20	0.358046
$319$	1.77178e21	0.925098
$320$	1.40550e21	0.714587
$321$	1.63298e21	0.808517
$322$	−6.85053e20	−0.330331
$323$	−2.59040e21	−1.21660
$324$	−1.98316e21	−0.907244
$325$	5.37933e20	0.239728
$326$	−1.94713e21	−0.845369
$327$	9.57615e20	0.405075
$328$	−2.30386e21	−0.949574
$329$	−6.64970e19	−0.0267077
$330$	−2.75915e21	−1.07996
$331$	9.83194e18	0.00375060	0.00187530	−	0.999998i	$-0.499403\pi$
$331$	9.83194e18	0.00375060	0.00187530	+	0.999998i	$0.499403\pi$
$332$	5.31895e21	1.97766
$333$	−4.51813e21	−1.63750
$334$	5.44073e21	1.92226
$335$	4.66505e20	0.160685
$336$	−2.46753e21	−0.828664
$337$	−3.22406e21	−1.05572	−0.527861	−	0.849331i	$-0.677006\pi$
$337$	−3.22406e21	−1.05572	−0.527861	+	0.849331i	$0.677006\pi$
$338$	2.13388e21	0.681364
$339$	5.67841e21	1.76819
$340$	−2.47807e21	−0.752563
$341$	5.97777e20	0.177063
$342$	−7.19718e21	−2.07941
$343$	−5.42317e20	−0.152846
$344$	8.20182e20	0.225509
$345$	3.67806e20	0.0986635
$346$	8.41229e20	0.220175
$347$	−4.53030e21	−1.15698	−0.578490	−	0.815689i	$-0.696358\pi$
$347$	−4.53030e21	−1.15698	−0.578490	+	0.815689i	$0.696358\pi$
$348$	7.86000e21	1.95884
$349$	−4.45189e21	−1.08275	−0.541375	−	0.840781i	$-0.682096\pi$
$349$	−4.45189e21	−1.08275	−0.541375	+	0.840781i	$0.682096\pi$
$350$	−1.90732e21	−0.452737
$351$	−2.23461e21	−0.517716
$352$	5.73310e21	1.29651
$353$	5.07798e21	1.12100	0.560501	−	0.828154i	$-0.310609\pi$
$353$	5.07798e21	1.12100	0.560501	+	0.828154i	$0.310609\pi$
$354$	8.24510e21	1.77692
$355$	4.67183e20	0.0982982
$356$	1.11910e21	0.229902
$357$	1.28335e22	2.57434
$358$	8.56292e20	0.167732
$359$	7.66889e21	1.46700	0.733500	−	0.679690i	$-0.237886\pi$
$359$	7.66889e21	1.46700	0.733500	+	0.679690i	$0.237886\pi$
$360$	−2.08357e21	−0.389257
$361$	4.09550e20	0.0747301
$362$	−1.26814e22	−2.26019
$363$	−4.18848e20	−0.0729207
$364$	−1.46637e22	−2.49392
$365$	−3.87244e21	−0.643422
$366$	−1.38579e22	−2.24961
$367$	4.94937e21	0.785033	0.392517	−	0.919745i	$-0.371605\pi$
$367$	4.94937e21	0.785033	0.392517	+	0.919745i	$0.371605\pi$
$368$	−3.55671e20	−0.0551241
$369$	−1.19070e22	−1.80335
$370$	6.00387e21	0.888621
$371$	1.52270e21	0.220260
$372$	2.65188e21	0.374920
$373$	−3.93321e21	−0.543528	−0.271764	−	0.962364i	$-0.587607\pi$
$373$	−3.93321e21	−0.543528	−0.271764	+	0.962364i	$0.587607\pi$
$374$	−1.38768e22	−1.87448
$375$	1.02405e21	0.135224
$376$	9.65292e19	0.0124613
$377$	−8.58124e21	−1.08305
$378$	7.92316e21	0.977729
$379$	1.21415e22	1.46501	0.732504	−	0.680763i	$-0.238352\pi$
$379$	1.21415e22	1.46501	0.732504	+	0.680763i	$0.238352\pi$
$380$	5.63452e21	0.664808
$381$	2.42804e22	2.80152
$382$	−7.60640e21	−0.858303
$383$	−1.46593e22	−1.61779	−0.808896	−	0.587952i	$-0.799934\pi$
$383$	−1.46593e22	−1.61779	−0.808896	+	0.587952i	$0.799934\pi$
$384$	1.71789e22	1.85430
$385$	−6.29247e21	−0.664362
$386$	1.66978e22	1.72451
$387$	4.23893e21	0.428266
$388$	−2.07213e22	−2.04808
$389$	1.63955e22	1.58545	0.792725	−	0.609579i	$-0.208662\pi$
$389$	1.63955e22	1.58545	0.792725	+	0.609579i	$0.208662\pi$
$390$	1.33634e22	1.26435
$391$	1.84983e21	0.171249
$392$	8.26063e21	0.748310
$393$	−8.20986e21	−0.727778
$394$	−1.59779e22	−1.38612
$395$	−2.82531e21	−0.239878
$396$	−2.27146e22	−1.88754
$397$	−3.76489e21	−0.306219	−0.153110	−	0.988209i	$-0.548929\pi$
$397$	−3.76489e21	−0.306219	−0.153110	+	0.988209i	$0.548929\pi$
$398$	2.68459e22	2.13733
$399$	−2.91802e22	−2.27415
$400$	−9.90259e20	−0.0755507
$401$	−8.98376e21	−0.671013	−0.335506	−	0.942038i	$-0.608907\pi$
$401$	−8.98376e21	−0.671013	−0.335506	+	0.942038i	$0.608907\pi$
$402$	1.15890e22	0.847470
$403$	−2.89521e21	−0.207294
$404$	9.76633e21	0.684683
$405$	4.12169e21	0.282949
$406$	3.04261e22	2.04539
$407$	1.98074e22	1.30399
$408$	−1.86296e22	−1.20113
$409$	−2.74380e22	−1.73262	−0.866311	−	0.499505i	$-0.833515\pi$
$409$	−2.74380e22	−1.73262	−0.866311	+	0.499505i	$0.833515\pi$
$410$	1.58225e22	0.978617
$411$	−4.64925e22	−2.81662
$412$	1.39359e22	0.827003
$413$	1.88036e22	1.09311
$414$	5.13957e21	0.292701
$415$	−1.10546e22	−0.616788
$416$	−2.77671e22	−1.51788
$417$	2.76128e22	1.47895
$418$	3.15524e22	1.65590
$419$	−5.84603e21	−0.300636	−0.150318	−	0.988638i	$-0.548030\pi$
$419$	−5.84603e21	−0.300636	−0.150318	+	0.988638i	$0.548030\pi$
$420$	−2.79148e22	−1.40675
$421$	5.49695e21	0.271471	0.135736	−	0.990745i	$-0.456660\pi$
$421$	5.49695e21	0.271471	0.135736	+	0.990745i	$0.456660\pi$
$422$	−3.97710e22	−1.92491
$423$	4.98890e20	0.0236653
$424$	−2.21040e21	−0.102769
$425$	5.15030e21	0.234707
$426$	1.16058e22	0.518435
$427$	−3.16040e22	−1.38390
$428$	−1.78642e22	−0.766853
$429$	4.40873e22	1.85535
$430$	−5.63287e21	−0.232406
$431$	3.05715e22	1.23669	0.618343	−	0.785908i	$-0.287804\pi$
$431$	3.05715e22	1.23669	0.618343	+	0.785908i	$0.287804\pi$
$432$	4.11361e21	0.163159
$433$	3.52788e22	1.37204	0.686019	−	0.727584i	$-0.259357\pi$
$433$	3.52788e22	1.37204	0.686019	+	0.727584i	$0.259357\pi$
$434$	1.02654e22	0.391484
$435$	−1.63358e22	−0.610918
$436$	−1.04759e22	−0.384200
$437$	−4.20605e21	−0.151280
$438$	−9.61998e22	−3.39347
$439$	−2.82873e22	−0.978686	−0.489343	−	0.872091i	$-0.662763\pi$
$439$	−2.82873e22	−0.978686	−0.489343	+	0.872091i	$0.662763\pi$
$440$	9.13435e21	0.309977
$441$	4.26933e22	1.42112
$442$	6.72094e22	2.19453
$443$	2.21793e22	0.710421	0.355211	−	0.934786i	$-0.384409\pi$
$443$	2.21793e22	0.710421	0.355211	+	0.934786i	$0.384409\pi$
$444$	8.78702e22	2.76113
$445$	−2.32588e21	−0.0717013
$446$	−9.80452e22	−2.96538
$447$	−1.01254e22	−0.300468
$448$	7.96277e22	2.31847
$449$	2.11655e20	0.00604692	0.00302346	−	0.999995i	$-0.499038\pi$
$449$	2.11655e20	0.00604692	0.00302346	+	0.999995i	$0.499038\pi$
$450$	1.43096e22	0.401163
$451$	5.22002e22	1.43606
$452$	−6.21196e22	−1.67707
$453$	−2.62574e22	−0.695693
$454$	−1.68276e22	−0.437570
$455$	3.04763e22	0.777795
$456$	4.23590e22	1.06107
$457$	−2.66616e22	−0.655539	−0.327770	−	0.944758i	$-0.606297\pi$
$457$	−2.66616e22	−0.655539	−0.327770	+	0.944758i	$0.606297\pi$
$458$	−4.42276e22	−1.06742
$459$	−2.13947e22	−0.506872
$460$	−4.02366e21	−0.0935792
$461$	−3.51680e22	−0.802952	−0.401476	−	0.915869i	$-0.631503\pi$
$461$	−3.51680e22	−0.802952	−0.401476	+	0.915869i	$0.631503\pi$
$462$	−1.56318e23	−3.50392
$463$	−6.26683e22	−1.37914	−0.689572	−	0.724217i	$-0.742201\pi$
$463$	−6.26683e22	−1.37914	−0.689572	+	0.724217i	$0.742201\pi$
$464$	1.57969e22	0.341325
$465$	−5.51153e21	−0.116929
$466$	9.78940e22	2.03927
$467$	−8.75525e21	−0.179092	−0.0895458	−	0.995983i	$-0.528542\pi$
$467$	−8.75525e21	−0.179092	−0.0895458	+	0.995983i	$0.528542\pi$
$468$	1.10014e23	2.20982
$469$	2.64296e22	0.521341
$470$	−6.62946e20	−0.0128424
$471$	5.59988e22	1.06537
$472$	−2.72959e22	−0.510024
$473$	−1.85834e22	−0.341041
$474$	−7.01868e22	−1.26514
$475$	−1.17105e22	−0.207338
$476$	−1.40394e23	−2.44168
$477$	−1.14240e22	−0.195169
$478$	1.02724e23	1.72400
$479$	−1.08139e22	−0.178291	−0.0891456	−	0.996019i	$-0.528414\pi$
$479$	−1.08139e22	−0.178291	−0.0891456	+	0.996019i	$0.528414\pi$
$480$	−5.28594e22	−0.856193
$481$	−9.59331e22	−1.52664
$482$	1.59589e23	2.49519
$483$	2.08379e22	0.320112
$484$	4.58204e21	0.0691629
$485$	4.30660e22	0.638749
$486$	1.48626e23	2.16614
$487$	3.96471e22	0.567826	0.283913	−	0.958850i	$-0.408367\pi$
$487$	3.96471e22	0.567826	0.283913	+	0.958850i	$0.408367\pi$
$488$	4.58773e22	0.645698
$489$	5.92277e22	0.819219
$490$	−5.67326e22	−0.771198
$491$	6.00195e22	0.801861	0.400931	−	0.916108i	$-0.368687\pi$
$491$	6.00195e22	0.801861	0.400931	+	0.916108i	$0.368687\pi$
$492$	2.31572e23	3.04076
$493$	−8.21588e22	−1.06037
$494$	−1.52817e23	−1.93863
$495$	4.72089e22	0.588681
$496$	5.32968e21	0.0653291
$497$	2.64680e22	0.318927
$498$	−2.74621e23	−3.25300
$499$	4.84975e22	0.564761	0.282381	−	0.959302i	$-0.408876\pi$
$499$	4.84975e22	0.564761	0.282381	+	0.959302i	$0.408876\pi$
$500$	−1.12027e22	−0.128256
$501$	−1.65495e23	−1.86280
$502$	1.27669e22	0.141288
$503$	1.48522e23	1.61608	0.808041	−	0.589126i	$-0.200528\pi$
$503$	1.48522e23	1.61608	0.808041	+	0.589126i	$0.200528\pi$
$504$	−1.18044e23	−1.26294
$505$	−2.02978e22	−0.213537
$506$	−2.25318e22	−0.233086
$507$	−6.49083e22	−0.660287
$508$	−2.65619e23	−2.65716
$509$	1.06498e23	1.04771	0.523855	−	0.851807i	$-0.324493\pi$
$509$	1.06498e23	1.04771	0.523855	+	0.851807i	$0.324493\pi$
$510$	1.27944e23	1.23787
$511$	−2.19391e23	−2.08757
$512$	7.84422e22	0.734100
$513$	4.86463e22	0.447767
$514$	1.09202e23	0.988650
$515$	−2.89636e22	−0.257923
$516$	−8.24404e22	−0.722133
$517$	−2.18713e21	−0.0188454
$518$	3.40146e23	2.88312
$519$	−2.55884e22	−0.213364
$520$	−4.42404e22	−0.362903
$521$	2.90787e21	0.0234668	0.0117334	−	0.999931i	$-0.496265\pi$
$521$	2.90787e21	0.0234668	0.0117334	+	0.999931i	$0.496265\pi$
$522$	−2.28270e23	−1.81238
$523$	1.05919e23	0.827390	0.413695	−	0.910416i	$-0.364238\pi$
$523$	1.05919e23	0.827390	0.413695	+	0.910416i	$0.364238\pi$
$524$	8.98127e22	0.690274
$525$	5.80168e22	0.438732
$526$	3.89355e23	2.89712
$527$	−2.77195e22	−0.202953
$528$	−8.11586e22	−0.584718
$529$	−1.38046e23	−0.978706
$530$	1.51807e22	0.105912
$531$	−1.41073e23	−0.968591
$532$	3.19221e23	2.15696
$533$	−2.52821e23	−1.68125
$534$	−5.77798e22	−0.378160
$535$	3.71281e22	0.239164
$536$	−3.83661e22	−0.243246
$537$	−2.60466e22	−0.162544
$538$	−4.51872e23	−2.77566
$539$	−1.87167e23	−1.13168
$540$	4.65367e22	0.276980
$541$	−2.58434e22	−0.151416	−0.0757081	−	0.997130i	$-0.524122\pi$
$541$	−2.58434e22	−0.151416	−0.0757081	+	0.997130i	$0.524122\pi$
$542$	−2.64446e23	−1.52526
$543$	3.85743e23	2.19028
$544$	−2.65849e23	−1.48609
$545$	2.17727e22	0.119823
$546$	7.57097e23	4.10217
$547$	1.74286e23	0.929759	0.464879	−	0.885374i	$-0.346098\pi$
$547$	1.74286e23	0.929759	0.464879	+	0.885374i	$0.346098\pi$
$548$	5.08610e23	2.67147
$549$	2.37107e23	1.22625
$550$	−6.27331e22	−0.319458
$551$	1.86809e23	0.936718
$552$	−3.02489e22	−0.149358
$553$	−1.60066e23	−0.778282
$554$	−9.46148e21	−0.0453029
$555$	−1.82625e23	−0.861132
$556$	−3.02074e23	−1.40274
$557$	−2.23690e23	−1.02300	−0.511502	−	0.859282i	$-0.670911\pi$
$557$	−2.23690e23	−1.02300	−0.511502	+	0.859282i	$0.670911\pi$
$558$	−7.70158e22	−0.346888
$559$	9.00051e22	0.399270
$560$	−5.61026e22	−0.245123
$561$	4.22103e23	1.81649
$562$	−6.56913e23	−2.78451
$563$	−5.68895e22	−0.237526	−0.118763	−	0.992923i	$-0.537893\pi$
$563$	−5.68895e22	−0.237526	−0.118763	+	0.992923i	$0.537893\pi$
$564$	−9.70261e21	−0.0399040
$565$	1.29106e23	0.523041
$566$	−6.23022e23	−2.48636
$567$	2.33512e23	0.918024
$568$	−3.84218e22	−0.148805
$569$	2.49161e23	0.950662	0.475331	−	0.879807i	$-0.342328\pi$
$569$	2.49161e23	0.950662	0.475331	+	0.879807i	$0.342328\pi$
$570$	−2.90914e23	−1.09352
$571$	−1.59046e23	−0.589001	−0.294500	−	0.955651i	$-0.595153\pi$
$571$	−1.59046e23	−0.589001	−0.294500	+	0.955651i	$0.595153\pi$
$572$	−4.82298e23	−1.75974
$573$	2.31371e23	0.831752
$574$	8.96417e23	3.17511
$575$	8.36257e21	0.0291852
$576$	−5.97402e23	−2.05436
$577$	−5.53720e22	−0.187627	−0.0938137	−	0.995590i	$-0.529906\pi$
$577$	−5.53720e22	−0.187627	−0.0938137	+	0.995590i	$0.529906\pi$
$578$	1.76237e23	0.588453
$579$	−5.07912e23	−1.67117
$580$	1.78708e23	0.579436
$581$	−6.26296e23	−2.00116
$582$	1.06985e24	3.36883
$583$	5.00826e22	0.155419
$584$	3.18475e23	0.974018
$585$	−2.28647e23	−0.689192
$586$	2.19578e23	0.652318
$587$	2.87790e23	0.842660	0.421330	−	0.906907i	$-0.361563\pi$
$587$	2.87790e23	0.842660	0.421330	+	0.906907i	$0.361563\pi$
$588$	−8.30315e23	−2.39627
$589$	6.30272e22	0.179287
$590$	1.87464e23	0.525623
$591$	4.86014e23	1.34325
$592$	1.76600e23	0.481122
$593$	5.72587e23	1.53772	0.768859	−	0.639419i	$-0.220825\pi$
$593$	5.72587e23	1.53772	0.768859	+	0.639419i	$0.220825\pi$
$594$	2.60598e23	0.689900
$595$	2.91788e23	0.761505
$596$	1.10768e23	0.284984
$597$	−8.16595e23	−2.07121
$598$	1.09128e23	0.272883
$599$	−9.84730e22	−0.242767	−0.121383	−	0.992606i	$-0.538733\pi$
$599$	−9.84730e22	−0.242767	−0.121383	+	0.992606i	$0.538733\pi$
$600$	−8.42190e22	−0.204703
$601$	4.14229e23	0.992675	0.496337	−	0.868130i	$-0.334678\pi$
$601$	4.14229e23	0.992675	0.496337	+	0.868130i	$0.334678\pi$
$602$	−3.19127e23	−0.754039
$603$	−1.98287e23	−0.461952
$604$	2.87246e23	0.659843
$605$	−9.52309e21	−0.0215703
$606$	−5.04242e23	−1.12622
$607$	3.86832e23	0.851958	0.425979	−	0.904733i	$-0.359930\pi$
$607$	3.86832e23	0.851958	0.425979	+	0.904733i	$0.359930\pi$
$608$	6.04475e23	1.31280
$609$	−9.25499e23	−1.98211
$610$	−3.15077e23	−0.665447
$611$	1.05929e22	0.0220630
$612$	1.05330e24	2.16353
$613$	−4.00012e23	−0.810324	−0.405162	−	0.914245i	$-0.632785\pi$
$613$	−4.00012e23	−0.810324	−0.405162	+	0.914245i	$0.632785\pi$
$614$	−1.01754e24	−2.03292
$615$	−4.81288e23	−0.948345
$616$	5.17502e23	1.00572
$617$	−3.66504e23	−0.702513	−0.351256	−	0.936279i	$-0.614245\pi$
$617$	−3.66504e23	−0.702513	−0.351256	+	0.936279i	$0.614245\pi$
$618$	−7.19518e23	−1.36031
$619$	3.54711e23	0.661460	0.330730	−	0.943725i	$-0.392705\pi$
$619$	3.54711e23	0.661460	0.330730	+	0.943725i	$0.392705\pi$
$620$	6.02940e22	0.110903
$621$	−3.47387e22	−0.0630282
$622$	−4.86927e23	−0.871456
$623$	−1.31772e23	−0.232634
$624$	3.93075e23	0.684552
$625$	2.32831e22	0.0400000
$626$	7.47163e23	1.26629
$627$	−9.59757e23	−1.60468
$628$	−6.12606e23	−1.01047
$629$	−9.18487e23	−1.49466
$630$	8.10703e23	1.30157
$631$	2.16428e23	0.342817	0.171409	−	0.985200i	$-0.445168\pi$
$631$	2.16428e23	0.342817	0.171409	+	0.985200i	$0.445168\pi$
$632$	2.32358e23	0.363130
$633$	1.20975e24	1.86537
$634$	−1.06820e24	−1.62516
$635$	5.52048e23	0.828706
$636$	2.22178e23	0.329091
$637$	9.06505e23	1.32491
$638$	1.00073e24	1.44325
$639$	−1.98575e23	−0.282596
$640$	3.90585e23	0.548512
$641$	1.31951e23	0.182860	0.0914300	−	0.995812i	$-0.470856\pi$
$641$	1.31951e23	0.182860	0.0914300	+	0.995812i	$0.470856\pi$
$642$	9.22342e23	1.26138
$643$	−5.55370e23	−0.749531	−0.374765	−	0.927120i	$-0.622277\pi$
$643$	−5.55370e23	−0.749531	−0.374765	+	0.927120i	$0.622277\pi$
$644$	−2.27958e23	−0.303616
$645$	1.71340e23	0.225217
$646$	−1.46311e24	−1.89802
$647$	−8.90545e22	−0.114017	−0.0570085	−	0.998374i	$-0.518156\pi$
$647$	−8.90545e22	−0.114017	−0.0570085	+	0.998374i	$0.518156\pi$
$648$	−3.38974e23	−0.428330
$649$	6.18463e23	0.771318
$650$	3.03835e23	0.374002
$651$	−3.12253e23	−0.379374
$652$	−6.47929e23	−0.777003
$653$	−6.88691e23	−0.815197	−0.407598	−	0.913161i	$-0.633634\pi$
$653$	−6.88691e23	−0.815197	−0.407598	+	0.913161i	$0.633634\pi$
$654$	5.40880e23	0.631961
$655$	−1.86662e23	−0.215281
$656$	4.65408e23	0.529848
$657$	1.64597e24	1.84977
$658$	−3.75589e22	−0.0416670
$659$	8.62900e22	0.0945005	0.0472503	−	0.998883i	$-0.484954\pi$
$659$	8.62900e22	0.0945005	0.0472503	+	0.998883i	$0.484954\pi$
$660$	−9.18137e23	−0.992622
$661$	1.26260e24	1.34757	0.673786	−	0.738927i	$-0.264667\pi$
$661$	1.26260e24	1.34757	0.673786	+	0.738927i	$0.264667\pi$
$662$	5.55328e21	0.00585135
$663$	−2.04437e24	−2.12664
$664$	9.09150e23	0.933699
$665$	−6.63452e23	−0.672707
$666$	−2.55193e24	−2.55468
$667$	−1.33402e23	−0.131854
$668$	1.81046e24	1.76680
$669$	2.98233e24	2.87365
$670$	2.63491e23	0.250686
$671$	−1.03947e24	−0.976500
$672$	−2.99472e24	−2.77791
$673$	−1.39756e24	−1.28009	−0.640046	−	0.768336i	$-0.721085\pi$
$673$	−1.39756e24	−1.28009	−0.640046	+	0.768336i	$0.721085\pi$
$674$	−1.82102e24	−1.64704
$675$	−9.67196e22	−0.0863838
$676$	7.10072e23	0.626261
$677$	1.98205e24	1.72628	0.863140	−	0.504965i	$-0.168495\pi$
$677$	1.98205e24	1.72628	0.863140	+	0.504965i	$0.168495\pi$
$678$	3.20728e24	2.75857
$679$	2.43989e24	2.07241
$680$	−4.23568e23	−0.355302
$681$	5.11860e23	0.424034
$682$	3.37636e23	0.276237
$683$	−1.91565e24	−1.54789	−0.773946	−	0.633252i	$-0.781720\pi$
$683$	−1.91565e24	−1.54789	−0.773946	+	0.633252i	$0.781720\pi$
$684$	−2.39494e24	−1.91125
$685$	−1.05707e24	−0.833171
$686$	−3.06312e23	−0.238456
$687$	1.34531e24	1.03440
$688$	−1.65687e23	−0.125831
$689$	−2.42565e23	−0.181955
$690$	2.07744e23	0.153926
$691$	−9.32183e23	−0.682241	−0.341121	−	0.940020i	$-0.610806\pi$
$691$	−9.32183e23	−0.682241	−0.341121	+	0.940020i	$0.610806\pi$
$692$	2.79927e23	0.202369
$693$	2.67460e24	1.90997
$694$	−2.55880e24	−1.80502
$695$	6.27815e23	0.437483
$696$	1.34348e24	0.924812
$697$	−2.42057e24	−1.64604
$698$	−2.51452e24	−1.68921
$699$	−2.97773e24	−1.97619
$700$	−6.34681e23	−0.416124
$701$	−9.43006e23	−0.610817	−0.305408	−	0.952221i	$-0.598793\pi$
$701$	−9.43006e23	−0.610817	−0.305408	+	0.952221i	$0.598793\pi$
$702$	−1.26215e24	−0.807693
$703$	2.08841e24	1.32037
$704$	2.61901e24	1.63595
$705$	2.01654e22	0.0124451
$706$	2.86815e24	1.74888
$707$	−1.14996e24	−0.692818
$708$	2.74364e24	1.63322
$709$	8.30727e23	0.488614	0.244307	−	0.969698i	$-0.421440\pi$
$709$	8.30727e23	0.488614	0.244307	+	0.969698i	$0.421440\pi$
$710$	2.63874e23	0.153356
$711$	1.20089e24	0.689623
$712$	1.91284e23	0.108542
$713$	−4.50082e22	−0.0252366
$714$	7.24863e24	4.01625
$715$	1.00238e24	0.548824
$716$	2.84940e23	0.154167
$717$	−3.12466e24	−1.67067
$718$	4.33154e24	2.28868
$719$	2.57313e24	1.34359	0.671794	−	0.740738i	$-0.265524\pi$
$719$	2.57313e24	1.34359	0.671794	+	0.740738i	$0.265524\pi$
$720$	4.20907e23	0.217200
$721$	−1.64092e24	−0.836829
$722$	2.31322e23	0.116587
$723$	−4.85437e24	−2.41801
$724$	−4.21988e24	−2.07741
$725$	−3.71417e23	−0.180713
$726$	−2.36574e23	−0.113764
$727$	−1.02839e23	−0.0488783	−0.0244391	−	0.999701i	$-0.507780\pi$
$727$	−1.02839e23	−0.0488783	−0.0244391	+	0.999701i	$0.507780\pi$
$728$	−2.50642e24	−1.17743
$729$	−3.15827e24	−1.46644
$730$	−2.18723e24	−1.00381
$731$	8.61731e23	0.390907
$732$	−4.61135e24	−2.06768
$733$	2.97764e23	0.131974	0.0659870	−	0.997820i	$-0.478980\pi$
$733$	2.97764e23	0.131974	0.0659870	+	0.997820i	$0.478980\pi$
$734$	2.79550e24	1.22474
$735$	1.72569e24	0.747342
$736$	−4.31660e23	−0.184791
$737$	8.69287e23	0.367866
$738$	−6.72532e24	−2.81342
$739$	−3.64205e24	−1.50615	−0.753074	−	0.657936i	$-0.771430\pi$
$739$	−3.64205e24	−1.50615	−0.753074	+	0.657936i	$0.771430\pi$
$740$	1.99785e24	0.816757
$741$	4.64839e24	1.87866
$742$	8.60052e23	0.343630
$743$	2.08027e24	0.821701	0.410851	−	0.911703i	$-0.365232\pi$
$743$	2.08027e24	0.821701	0.410851	+	0.911703i	$0.365232\pi$
$744$	4.53276e23	0.177008
$745$	−2.30215e23	−0.0888801
$746$	−2.22155e24	−0.847962
$747$	4.69875e24	1.77320
$748$	−4.61764e24	−1.72289
$749$	2.10348e24	0.775965
$750$	5.78401e23	0.210964
$751$	−1.01283e24	−0.365256	−0.182628	−	0.983182i	$-0.558460\pi$
$751$	−1.01283e24	−0.365256	−0.182628	+	0.983182i	$0.558460\pi$
$752$	−1.95001e22	−0.00695320
$753$	−3.88343e23	−0.136917
$754$	−4.84685e24	−1.68968
$755$	−5.96998e23	−0.205790
$756$	2.63651e24	0.898659
$757$	1.79501e24	0.604996	0.302498	−	0.953150i	$-0.402179\pi$
$757$	1.79501e24	0.604996	0.302498	+	0.953150i	$0.402179\pi$
$758$	6.85777e24	2.28557
$759$	6.85370e23	0.225876
$760$	9.63089e23	0.313871
$761$	−1.05630e23	−0.0340423	−0.0170212	−	0.999855i	$-0.505418\pi$
$761$	−1.05630e23	−0.0340423	−0.0170212	+	0.999855i	$0.505418\pi$
$762$	1.37141e25	4.37068
$763$	1.23352e24	0.388765
$764$	−2.53111e24	−0.788891
$765$	−2.18912e24	−0.674757
$766$	−8.27984e24	−2.52393
$767$	−2.99540e24	−0.903013
$768$	1.60048e24	0.477178
$769$	−9.59386e23	−0.282891	−0.141446	−	0.989946i	$-0.545175\pi$
$769$	−9.59386e23	−0.282891	−0.141446	+	0.989946i	$0.545175\pi$
$770$	−3.55411e24	−1.03648
$771$	−3.32169e24	−0.958068
$772$	5.55636e24	1.58505
$773$	−8.69614e23	−0.245358	−0.122679	−	0.992446i	$-0.539149\pi$
$773$	−8.69614e23	−0.245358	−0.122679	+	0.992446i	$0.539149\pi$
$774$	2.39423e24	0.668142
$775$	−1.25312e23	−0.0345882
$776$	−3.54182e24	−0.966944
$777$	−1.03465e25	−2.79393
$778$	9.26050e24	2.47348
$779$	5.50378e24	1.45409
$780$	4.44681e24	1.16210
$781$	8.70549e23	0.225040
$782$	1.04482e24	0.267168
$783$	1.54289e24	0.390267
$784$	−1.66875e24	−0.417546
$785$	1.27321e24	0.315143
$786$	−4.63709e24	−1.13541
$787$	6.67023e24	1.61568	0.807840	−	0.589401i	$-0.200636\pi$
$787$	6.67023e24	1.61568	0.807840	+	0.589401i	$0.200636\pi$
$788$	−5.31681e24	−1.27403
$789$	−1.18433e25	−2.80750
$790$	−1.59579e24	−0.374236
$791$	7.31446e24	1.69700
$792$	−3.88253e24	−0.891150
$793$	5.03448e24	1.14323
$794$	−2.12648e24	−0.477736
$795$	−4.61764e23	−0.102636
$796$	8.93324e24	1.96448
$797$	−4.58059e24	−0.996612	−0.498306	−	0.867001i	$-0.666044\pi$
$797$	−4.58059e24	−0.996612	−0.498306	+	0.867001i	$0.666044\pi$
$798$	−1.64816e25	−3.54792
$799$	1.01419e23	0.0216009
$800$	−1.20183e24	−0.253267
$801$	9.88609e23	0.206133
$802$	−5.07421e24	−1.04685
$803$	−7.21592e24	−1.47302
$804$	3.85635e24	0.778934
$805$	4.73777e23	0.0946910
$806$	−1.63527e24	−0.323402
$807$	1.37450e25	2.68980
$808$	1.66932e24	0.323254
$809$	3.33659e24	0.639352	0.319676	−	0.947527i	$-0.396426\pi$
$809$	3.33659e24	0.639352	0.319676	+	0.947527i	$0.396426\pi$
$810$	2.32801e24	0.441431
$811$	−7.47175e24	−1.40199	−0.700995	−	0.713166i	$-0.747261\pi$
$811$	−7.47175e24	−1.40199	−0.700995	+	0.713166i	$0.747261\pi$
$812$	1.01246e25	1.87997
$813$	8.04389e24	1.47808
$814$	1.11876e25	2.03437
$815$	1.34662e24	0.242329
$816$	3.76340e24	0.670214
$817$	−1.95936e24	−0.345324
$818$	−1.54975e25	−2.70308
$819$	−1.29539e25	−2.23607
$820$	5.26510e24	0.899475
$821$	−1.52582e24	−0.257981	−0.128990	−	0.991646i	$-0.541174\pi$
$821$	−1.52582e24	−0.257981	−0.128990	+	0.991646i	$0.541174\pi$
$822$	−2.62599e25	−4.39423
$823$	6.12175e24	1.01386	0.506929	−	0.861988i	$-0.330781\pi$
$823$	6.12175e24	1.01386	0.506929	+	0.861988i	$0.330781\pi$
$824$	2.38201e24	0.390447
$825$	1.90821e24	0.309576
$826$	1.06207e25	1.70538
$827$	−4.78747e24	−0.760868	−0.380434	−	0.924808i	$-0.624225\pi$
$827$	−4.78747e24	−0.760868	−0.380434	+	0.924808i	$0.624225\pi$
$828$	1.71024e24	0.269030
$829$	8.83452e24	1.37553	0.687764	−	0.725934i	$-0.258592\pi$
$829$	8.83452e24	1.37553	0.687764	+	0.725934i	$0.258592\pi$
$830$	−6.24389e24	−0.962257
$831$	2.87798e23	0.0439015
$832$	−1.26846e25	−1.91527
$833$	8.67910e24	1.29716
$834$	1.55963e25	2.30733
$835$	−3.76276e24	−0.551026
$836$	1.04994e25	1.52198
$837$	5.20555e23	0.0746965
$838$	−3.30195e24	−0.469026
$839$	−5.00324e24	−0.703517	−0.351759	−	0.936091i	$-0.614416\pi$
$839$	−5.00324e24	−0.703517	−0.351759	+	0.936091i	$0.614416\pi$
$840$	−4.77139e24	−0.664157
$841$	−1.33221e24	−0.183571
$842$	3.10478e24	0.423525
$843$	1.99819e25	2.69838
$844$	−1.32342e25	−1.76924
$845$	−1.47578e24	−0.195316
$846$	2.81783e23	0.0369205
$847$	−5.39526e23	−0.0699847
$848$	4.46528e23	0.0573435
$849$	1.89510e25	2.40945
$850$	2.90899e24	0.366169
$851$	−1.49135e24	−0.185857
$852$	3.86196e24	0.476509
$853$	−8.76800e24	−1.07111	−0.535554	−	0.844501i	$-0.679897\pi$
$853$	−8.76800e24	−1.07111	−0.535554	+	0.844501i	$0.679897\pi$
$854$	−1.78506e25	−2.15904
$855$	4.97752e24	0.596075
$856$	−3.05347e24	−0.362049
$857$	−9.35381e24	−1.09812	−0.549062	−	0.835782i	$-0.685015\pi$
$857$	−9.35381e24	−1.09812	−0.549062	+	0.835782i	$0.685015\pi$
$858$	2.49014e25	2.89455
$859$	−7.35462e24	−0.846483	−0.423241	−	0.906017i	$-0.639108\pi$
$859$	−7.35462e24	−0.846483	−0.423241	+	0.906017i	$0.639108\pi$
$860$	−1.87439e24	−0.213611
$861$	−2.72671e25	−3.07689
$862$	1.72674e25	1.92937
$863$	−8.81310e24	−0.975072	−0.487536	−	0.873103i	$-0.662104\pi$
$863$	−8.81310e24	−0.975072	−0.487536	+	0.873103i	$0.662104\pi$
$864$	4.99249e24	0.546953
$865$	−5.81787e23	−0.0631142
$866$	1.99261e25	2.14053
$867$	−5.36077e24	−0.570250
$868$	3.41592e24	0.359824
$869$	−5.26469e24	−0.549167
$870$	−9.22681e24	−0.953098
$871$	−4.21021e24	−0.430675
$872$	−1.79062e24	−0.181390
$873$	−1.83051e25	−1.83633
$874$	−2.37566e24	−0.236014
$875$	1.31909e24	0.129779
$876$	−3.20115e25	−3.11904
$877$	3.60902e24	0.348252	0.174126	−	0.984723i	$-0.444290\pi$
$877$	3.60902e24	0.348252	0.174126	+	0.984723i	$0.444290\pi$
$878$	−1.59772e25	−1.52686
$879$	−6.67911e24	−0.632140
$880$	−1.84525e24	−0.172963
$881$	−1.96188e24	−0.182128	−0.0910639	−	0.995845i	$-0.529027\pi$
$881$	−1.96188e24	−0.182128	−0.0910639	+	0.995845i	$0.529027\pi$
$882$	2.41140e25	2.21711
$883$	−7.10082e24	−0.646610	−0.323305	−	0.946295i	$-0.604794\pi$
$883$	−7.10082e24	−0.646610	−0.323305	+	0.946295i	$0.604794\pi$
$884$	2.23646e25	2.01705
$885$	−5.70225e24	−0.509364
$886$	1.25273e25	1.10833
$887$	1.89470e25	1.66031	0.830156	−	0.557532i	$-0.188252\pi$
$887$	1.89470e25	1.66031	0.830156	+	0.557532i	$0.188252\pi$
$888$	1.50193e25	1.30359
$889$	3.12760e25	2.68873
$890$	−1.31370e24	−0.111862
$891$	7.68037e24	0.647771
$892$	−3.26255e25	−2.72556
$893$	−2.30602e23	−0.0190821
$894$	−5.71903e24	−0.468763
$895$	−5.92205e23	−0.0480813
$896$	2.21284e25	1.77964
$897$	−3.31945e24	−0.264442
$898$	1.19547e23	0.00943386
$899$	1.99901e24	0.156263
$900$	4.76166e24	0.368721
$901$	−2.32238e24	−0.178144
$902$	2.94837e25	2.24041
$903$	9.70718e24	0.730714
$904$	−1.06179e25	−0.791784
$905$	8.77039e24	0.647897
$906$	−1.48307e25	−1.08536
$907$	−7.47138e24	−0.541675	−0.270837	−	0.962625i	$-0.587301\pi$
$907$	−7.47138e24	−0.541675	−0.270837	+	0.962625i	$0.587301\pi$
$908$	−5.59955e24	−0.402183
$909$	8.62754e24	0.613895
$910$	1.72136e25	1.21345
$911$	1.50719e25	1.05260	0.526300	−	0.850299i	$-0.323579\pi$
$911$	1.50719e25	1.05260	0.526300	+	0.850299i	$0.323579\pi$
$912$	−8.55703e24	−0.592062
$913$	−2.05993e25	−1.41205
$914$	−1.50590e25	−1.02271
$915$	9.58399e24	0.644863
$916$	−1.47172e25	−0.981100
$917$	−1.05753e25	−0.698476
$918$	−1.20842e25	−0.790776
$919$	−1.28199e25	−0.831197	−0.415599	−	0.909548i	$-0.636428\pi$
$919$	−1.28199e25	−0.831197	−0.415599	+	0.909548i	$0.636428\pi$
$920$	−6.87750e23	−0.0441808
$921$	3.09515e25	1.97004
$922$	−1.98636e25	−1.25269
$923$	−4.21633e24	−0.263463
$924$	−5.20166e25	−3.22055
$925$	−4.15223e24	−0.254728
$926$	−3.53963e25	−2.15161
$927$	1.23109e25	0.741501
$928$	1.91719e25	1.14421
$929$	−1.41590e24	−0.0837335	−0.0418667	−	0.999123i	$-0.513330\pi$
$929$	−1.41590e24	−0.0837335	−0.0418667	+	0.999123i	$0.513330\pi$
$930$	−3.11302e24	−0.182422
$931$	−1.97341e25	−1.14590
$932$	3.25752e25	1.87436
$933$	1.48113e25	0.844499
$934$	−4.94514e24	−0.279402
$935$	9.59708e24	0.537329
$936$	1.88042e25	1.04330
$937$	−2.47144e24	−0.135883	−0.0679414	−	0.997689i	$-0.521643\pi$
$937$	−2.47144e24	−0.135883	−0.0679414	+	0.997689i	$0.521643\pi$
$938$	1.49280e25	0.813348
$939$	−2.27271e25	−1.22712
$940$	−2.20602e23	−0.0118038
$941$	2.72156e25	1.44313	0.721567	−	0.692345i	$-0.243422\pi$
$941$	2.72156e25	1.44313	0.721567	+	0.692345i	$0.243422\pi$
$942$	3.16293e25	1.66210
$943$	−3.93029e24	−0.204680
$944$	5.51411e24	0.284586
$945$	−5.47960e24	−0.280271
$946$	−1.04963e25	−0.532061
$947$	−4.52899e23	−0.0227524	−0.0113762	−	0.999935i	$-0.503621\pi$
$947$	−4.52899e23	−0.0227524	−0.0113762	+	0.999935i	$0.503621\pi$
$948$	−2.33554e25	−1.16283
$949$	3.49488e25	1.72453
$950$	−6.61432e24	−0.323471
$951$	3.24925e25	1.57489
$952$	−2.39970e25	−1.15277
$953$	9.70376e24	0.462009	0.231004	−	0.972953i	$-0.425799\pi$
$953$	9.70376e24	0.462009	0.231004	+	0.972953i	$0.425799\pi$
$954$	−6.45249e24	−0.304485
$955$	5.26053e24	0.246037
$956$	3.41826e25	1.58457
$957$	−3.04402e25	−1.39861
$958$	−6.10790e24	−0.278154
$959$	−5.98878e25	−2.70321
$960$	−2.41473e25	−1.08035
$961$	−2.18757e25	−0.970091
$962$	−5.41850e25	−2.38172
$963$	−1.57812e25	−0.687570
$964$	5.31049e25	2.29340
$965$	−1.15481e25	−0.494341
$966$	1.17696e25	0.499410
$967$	3.03622e25	1.27705	0.638525	−	0.769601i	$-0.279545\pi$
$967$	3.03622e25	1.27705	0.638525	+	0.769601i	$0.279545\pi$
$968$	7.83193e23	0.0326534
$969$	4.45048e25	1.83931
$970$	2.43246e25	0.996518
$971$	−3.15755e25	−1.28229	−0.641145	−	0.767420i	$-0.721540\pi$
$971$	−3.15755e25	−1.28229	−0.641145	+	0.767420i	$0.721540\pi$
$972$	4.94568e25	1.99096
$973$	3.55686e25	1.41941
$974$	2.23935e25	0.885871
$975$	−9.24202e24	−0.362433
$976$	−9.26778e24	−0.360290
$977$	−1.27985e25	−0.493238	−0.246619	−	0.969113i	$-0.579320\pi$
$977$	−1.27985e25	−0.493238	−0.246619	+	0.969113i	$0.579320\pi$
$978$	3.34530e25	1.27807
$979$	−4.33405e24	−0.164150
$980$	−1.88783e25	−0.708830
$981$	−9.25441e24	−0.344479
$982$	3.39002e25	1.25099
$983$	−3.20093e25	−1.17104	−0.585519	−	0.810659i	$-0.699109\pi$
$983$	−3.20093e25	−1.17104	−0.585519	+	0.810659i	$0.699109\pi$
$984$	3.95818e25	1.43561
$985$	1.10502e25	0.397340
$986$	−4.64050e25	−1.65429
$987$	1.14246e24	0.0403781
$988$	−5.08516e25	−1.78185
$989$	1.39920e24	0.0486083
$990$	2.66645e25	0.918406
$991$	−4.78103e25	−1.63266	−0.816330	−	0.577586i	$-0.803995\pi$
$991$	−4.78103e25	−1.63266	−0.816330	+	0.577586i	$0.803995\pi$
$992$	6.46838e24	0.219001
$993$	−1.68919e23	−0.00567035
$994$	1.49497e25	0.497562
$995$	−1.85664e25	−0.612677
$996$	−9.13830e25	−2.98993
$997$	3.63445e25	1.17904	0.589521	−	0.807753i	$-0.299316\pi$
$997$	3.63445e25	1.17904	0.589521	+	0.807753i	$0.299316\pi$
$998$	2.73924e25	0.881089
$999$	1.72487e25	0.550109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.18.a.a.1.2	✓	2
3.2	odd	2		45.18.a.a.1.1		2
4.3	odd	2		80.18.a.f.1.2		2
5.2	odd	4		25.18.b.b.24.4		4
5.3	odd	4		25.18.b.b.24.1		4
5.4	even	2		25.18.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.18.a.a.1.2	✓	2	1.1	even	1	trivial
25.18.a.b.1.1		2	5.4	even	2
25.18.b.b.24.1		4	5.3	odd	4
25.18.b.b.24.4		4	5.2	odd	4
45.18.a.a.1.1		2	3.2	odd	2
80.18.a.f.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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+564.820 q^{2} -17180.6 q^{3} +187950. q^{4} -390625. q^{5} -9.70397e6 q^{6} -2.21307e7 q^{7} +3.21256e7 q^{8} +1.66034e8 q^{9} +O(q^{10})\)	\(q+564.820 q^{2} -17180.6 q^{3} +187950. q^{4} -390625. q^{5} -9.70397e6 q^{6} -2.21307e7 q^{7} +3.21256e7 q^{8} +1.66034e8 q^{9} -2.20633e8 q^{10} -7.27892e8 q^{11} -3.22909e9 q^{12} +3.52539e9 q^{13} -1.24998e10 q^{14} +6.71119e9 q^{15} -6.48976e9 q^{16} +3.37530e10 q^{17} +9.37794e10 q^{18} -7.67459e10 q^{19} -7.34178e10 q^{20} +3.80219e11 q^{21} -4.11128e11 q^{22} +5.48049e10 q^{23} -5.51938e11 q^{24} +1.52588e11 q^{25} +1.99121e12 q^{26} -6.33861e11 q^{27} -4.15945e12 q^{28} -2.43412e12 q^{29} +3.79061e12 q^{30} -8.21245e11 q^{31} -7.87631e12 q^{32} +1.25056e13 q^{33} +1.90644e13 q^{34} +8.64479e12 q^{35} +3.12060e13 q^{36} -2.72120e13 q^{37} -4.33476e13 q^{38} -6.05685e13 q^{39} -1.25491e13 q^{40} -7.17143e13 q^{41} +2.14755e14 q^{42} +2.55305e13 q^{43} -1.36807e14 q^{44} -6.48571e13 q^{45} +3.09549e13 q^{46} +3.00475e12 q^{47} +1.11498e14 q^{48} +2.57136e14 q^{49} +8.61847e13 q^{50} -5.79898e14 q^{51} +6.62596e14 q^{52} -6.88051e13 q^{53} -3.58017e14 q^{54} +2.84333e14 q^{55} -7.10960e14 q^{56} +1.31854e15 q^{57} -1.37484e15 q^{58} -8.49663e14 q^{59} +1.26136e15 q^{60} +1.42806e15 q^{61} -4.63855e14 q^{62} -3.67444e15 q^{63} -3.59807e15 q^{64} -1.37711e15 q^{65} +7.06343e15 q^{66} -1.19425e15 q^{67} +6.34386e15 q^{68} -9.41583e14 q^{69} +4.88275e15 q^{70} -1.19599e15 q^{71} +5.33394e15 q^{72} +9.91346e15 q^{73} -1.53699e16 q^{74} -2.62156e15 q^{75} -1.44244e16 q^{76} +1.61087e16 q^{77} -3.42103e16 q^{78} +7.23279e15 q^{79} +2.53506e15 q^{80} -1.05515e16 q^{81} -4.05057e16 q^{82} +2.82999e16 q^{83} +7.14620e16 q^{84} -1.31848e16 q^{85} +1.44201e16 q^{86} +4.18197e16 q^{87} -2.33839e16 q^{88} +5.95425e15 q^{89} -3.66326e16 q^{90} -7.80193e16 q^{91} +1.03006e16 q^{92} +1.41095e16 q^{93} +1.69714e15 q^{94} +2.99789e16 q^{95} +1.35320e17 q^{96} -1.10249e17 q^{97} +1.45235e17 q^{98} -1.20855e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 680 q^{2} - 10980 q^{3} + 70144 q^{4} - 781250 q^{5} - 8989776 q^{6} - 22820700 q^{7} + 3459840 q^{8} + 75341826 q^{9}+O(q^{10}) \) 2 * q + 680 * q^2 - 10980 * q^3 + 70144 * q^4 - 781250 * q^5 - 8989776 * q^6 - 22820700 * q^7 + 3459840 * q^8 + 75341826 * q^9	\( 2 q + 680 q^{2} - 10980 q^{3} + 70144 q^{4} - 781250 q^{5} - 8989776 q^{6} - 22820700 q^{7} + 3459840 q^{8} + 75341826 q^{9} - 265625000 q^{10} - 1053355456 q^{11} - 3959562240 q^{12} - 1637425660 q^{13} - 12579318192 q^{14} + 4289062500 q^{15} + 5649528832 q^{16} + 45284557940 q^{17} + 83333425320 q^{18} + 6966491000 q^{19} - 27400000000 q^{20} + 375940212984 q^{21} - 448614615040 q^{22} + 72199566060 q^{23} - 729683596800 q^{24} + 305175781250 q^{25} + 1396559073104 q^{26} - 1996962267960 q^{27} - 4078158120960 q^{28} - 4189598736500 q^{29} + 3511631250000 q^{30} + 4612322416824 q^{31} - 2720829317120 q^{32} + 10487556973440 q^{33} + 20392568799248 q^{34} + 8914335937500 q^{35} + 41890087567872 q^{36} - 24562012109180 q^{37} - 33705624391840 q^{38} - 92581290596808 q^{39} - 1351500000000 q^{40} - 145472731192436 q^{41} + 214262382630240 q^{42} - 50209039981300 q^{43} - 98465439352832 q^{44} - 29430400781250 q^{45} + 32958421369584 q^{46} + 212531927495060 q^{47} + 186769497231360 q^{48} + 24981386945914 q^{49} + 103759765625000 q^{50} - 508394816272296 q^{51} + 12\!\cdots\!00 q^{52}+ \cdots - 91\!\cdots\!28 q^{99}+O(q^{100}) \) 2 * q + 680 * q^2 - 10980 * q^3 + 70144 * q^4 - 781250 * q^5 - 8989776 * q^6 - 22820700 * q^7 + 3459840 * q^8 + 75341826 * q^9 - 265625000 * q^10 - 1053355456 * q^11 - 3959562240 * q^12 - 1637425660 * q^13 - 12579318192 * q^14 + 4289062500 * q^15 + 5649528832 * q^16 + 45284557940 * q^17 + 83333425320 * q^18 + 6966491000 * q^19 - 27400000000 * q^20 + 375940212984 * q^21 - 448614615040 * q^22 + 72199566060 * q^23 - 729683596800 * q^24 + 305175781250 * q^25 + 1396559073104 * q^26 - 1996962267960 * q^27 - 4078158120960 * q^28 - 4189598736500 * q^29 + 3511631250000 * q^30 + 4612322416824 * q^31 - 2720829317120 * q^32 + 10487556973440 * q^33 + 20392568799248 * q^34 + 8914335937500 * q^35 + 41890087567872 * q^36 - 24562012109180 * q^37 - 33705624391840 * q^38 - 92581290596808 * q^39 - 1351500000000 * q^40 - 145472731192436 * q^41 + 214262382630240 * q^42 - 50209039981300 * q^43 - 98465439352832 * q^44 - 29430400781250 * q^45 + 32958421369584 * q^46 + 212531927495060 * q^47 + 186769497231360 * q^48 + 24981386945914 * q^49 + 103759765625000 * q^50 - 508394816272296 * q^51 + 1270805189555200 * q^52 - 479521291130380 * q^53 - 515019559413600 * q^54 + 411466975000000 * q^55 - 691179867302400 * q^56 + 1837613993665680 * q^57 - 1577035882898960 * q^58 - 3102413298049000 * q^59 + 1546704000000000 * q^60 + 463551587866244 * q^61 + 161983263800160 * q^62 - 3611863782723420 * q^63 - 4595382572548096 * q^64 + 639619398437500 * q^65 + 6830991818108928 * q^66 + 2917128685399140 * q^67 + 4985377003832320 * q^68 - 833725200946968 * q^69 + 4913796168750000 * q^70 + 5121177395190184 * q^71 + 7933701377329920 * q^72 + 4758930266870660 * q^73 - 15064668041604272 * q^74 - 1675415039062500 * q^75 - 24286148533299200 * q^76 + 16333305199209600 * q^77 - 37897540638141600 * q^78 - 2609334097158000 * q^79 - 2206847200000000 * q^80 - 7291608647282838 * q^81 - 49001159307188240 * q^82 + 50638331521860780 * q^83 + 71966018096437248 * q^84 - 17689280445312500 * q^85 + 5696451371679344 * q^86 + 30934657312810920 * q^87 - 14054273022443520 * q^88 + 61192864176640500 * q^89 - 32552119265625000 * q^90 - 74456784720599736 * q^91 + 8251370039101440 * q^92 + 47801080543476240 * q^93 + 25830496599914768 * q^94 - 2721285546875000 * q^95 + 167287242157277184 * q^96 - 257524797515055740 * q^97 + 118495839739185160 * q^98 - 91337759750651328 * q^99

Introduction

L-functions

Modular forms

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