LMFDB - Embedded newform 23.18.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,18,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, 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("23.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	23.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:	$42.1410800892$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 327680 x^{12} - 2885829 x^{11} + 40317445636 x^{10} + 536194434472 x^{9} + \cdots + 12\!\cdots\!92 $ x^14 - 327680x^12 - 2885829x^11 + 40317445636x^10 + 536194434472x^9 - 2300019484636976x^8 - 30461644509683376x^7 + 60510672631444445504x^6 + 637677963007481584640x^5 - 633979316201323448274944x^4 - 10096979557697212773105664x^3 + 2069146574976541180680732672x^2 + 62007390478567900843052367872x + 124088176545413917176959598592
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{33}\cdot 3^{12} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$259.571$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-519.142 q^{2} +13379.6 q^{3} +138436. q^{4} +329626. q^{5} -6.94591e6 q^{6} +1.47770e7 q^{7} -3.82310e6 q^{8} +4.98736e7 q^{9} +O(q^{10})$	\(q-519.142 q^{2} +13379.6 q^{3} +138436. q^{4} +329626. q^{5} -6.94591e6 q^{6} +1.47770e7 q^{7} -3.82310e6 q^{8} +4.98736e7 q^{9} -1.71123e8 q^{10} -3.09346e8 q^{11} +1.85222e9 q^{12} -5.57722e9 q^{13} -7.67136e9 q^{14} +4.41027e9 q^{15} -1.61604e10 q^{16} -4.02569e10 q^{17} -2.58915e10 q^{18} +1.16393e11 q^{19} +4.56322e10 q^{20} +1.97711e11 q^{21} +1.60594e11 q^{22} -7.83110e10 q^{23} -5.11516e10 q^{24} -6.54286e11 q^{25} +2.89537e12 q^{26} -1.06056e12 q^{27} +2.04567e12 q^{28} +2.70202e12 q^{29} -2.28956e12 q^{30} -4.10449e11 q^{31} +8.89063e12 q^{32} -4.13892e12 q^{33} +2.08990e13 q^{34} +4.87089e12 q^{35} +6.90431e12 q^{36} -2.24450e13 q^{37} -6.04244e13 q^{38} -7.46209e13 q^{39} -1.26020e12 q^{40} +1.25899e13 q^{41} -1.02640e14 q^{42} +5.34031e13 q^{43} -4.28247e13 q^{44} +1.64397e13 q^{45} +4.06545e13 q^{46} -3.17815e14 q^{47} -2.16220e14 q^{48} -1.42705e13 q^{49} +3.39667e14 q^{50} -5.38621e14 q^{51} -7.72089e14 q^{52} +4.36573e13 q^{53} +5.50579e14 q^{54} -1.01969e14 q^{55} -5.64940e13 q^{56} +1.55729e15 q^{57} -1.40273e15 q^{58} -2.43711e14 q^{59} +6.10541e14 q^{60} +1.52445e15 q^{61} +2.13081e14 q^{62} +7.36983e14 q^{63} -2.49733e15 q^{64} -1.83840e15 q^{65} +2.14869e15 q^{66} -5.39093e15 q^{67} -5.57301e15 q^{68} -1.04777e15 q^{69} -2.52868e15 q^{70} +5.08528e14 q^{71} -1.90672e14 q^{72} -5.69386e15 q^{73} +1.16521e16 q^{74} -8.75409e15 q^{75} +1.61130e16 q^{76} -4.57121e15 q^{77} +3.87389e16 q^{78} -8.08573e15 q^{79} -5.32689e15 q^{80} -2.06305e16 q^{81} -6.53594e15 q^{82} +9.04716e15 q^{83} +2.73703e16 q^{84} -1.32697e16 q^{85} -2.77238e16 q^{86} +3.61520e16 q^{87} +1.18266e15 q^{88} +3.54591e16 q^{89} -8.53451e15 q^{90} -8.24146e16 q^{91} -1.08411e16 q^{92} -5.49165e15 q^{93} +1.64991e17 q^{94} +3.83661e16 q^{95} +1.18953e17 q^{96} -5.46450e16 q^{97} +7.40840e15 q^{98} -1.54282e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) $ 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9} - 312719540 q^{10} - 45399620 q^{11} - 8621310628 q^{12} - 10510197306 q^{13} - 12286634640 q^{14} - 16443659490 q^{15} + 65383333632 q^{16} - 35705720330 q^{17} + 27658188862 q^{18} - 84895273414 q^{19} + 331348024336 q^{20} + 185190266362 q^{21} + 270540900120 q^{22} - 1096353793934 q^{23} + 1697198124384 q^{24} + 525715171346 q^{25} + 4272672484934 q^{26} - 3706093330604 q^{27} - 9883598189096 q^{28} - 4114009788386 q^{29} - 14194804268004 q^{30} + 3718266369468 q^{31} - 29197309605632 q^{32} - 16110579243626 q^{33} - 31423174598564 q^{34} + 13804822380504 q^{35} + 51950006703548 q^{36} - 58067881808868 q^{37} - 76590705469880 q^{38} + 69866971570764 q^{39} - 129282722434320 q^{40} - 74370388815170 q^{41} - 430581394397552 q^{42} - 127444248270174 q^{43} - 563872902913048 q^{44} - 602432292081270 q^{45} - 749727107945564 q^{47} - 17\!\cdots\!72 q^{48}+ \cdots + 35\!\cdots\!38 q^{99}+O(q^{100}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9 - 312719540 * q^10 - 45399620 * q^11 - 8621310628 * q^12 - 10510197306 * q^13 - 12286634640 * q^14 - 16443659490 * q^15 + 65383333632 * q^16 - 35705720330 * q^17 + 27658188862 * q^18 - 84895273414 * q^19 + 331348024336 * q^20 + 185190266362 * q^21 + 270540900120 * q^22 - 1096353793934 * q^23 + 1697198124384 * q^24 + 525715171346 * q^25 + 4272672484934 * q^26 - 3706093330604 * q^27 - 9883598189096 * q^28 - 4114009788386 * q^29 - 14194804268004 * q^30 + 3718266369468 * q^31 - 29197309605632 * q^32 - 16110579243626 * q^33 - 31423174598564 * q^34 + 13804822380504 * q^35 + 51950006703548 * q^36 - 58067881808868 * q^37 - 76590705469880 * q^38 + 69866971570764 * q^39 - 129282722434320 * q^40 - 74370388815170 * q^41 - 430581394397552 * q^42 - 127444248270174 * q^43 - 563872902913048 * q^44 - 602432292081270 * q^45 - 749727107945564 * q^47 - 1762369490938672 * q^48 - 560241909258462 * q^49 - 1212733967351616 * q^50 - 2013927378521294 * q^51 - 3438555393950964 * q^52 - 1954645162253818 * q^53 - 2748549190422938 * q^54 - 2426218557075404 * q^55 - 1321001371084560 * q^56 - 2335835167092904 * q^57 - 340295461037046 * q^58 - 1561709417167508 * q^59 - 7486616247365616 * q^60 - 679115861109266 * q^61 - 12552327168177062 * q^62 - 10591353756704576 * q^63 - 6775416249353536 * q^64 - 6252697705990982 * q^65 - 20881430274671372 * q^66 - 7577612038827396 * q^67 + 2901964856169680 * q^68 + 833228883389840 * q^69 - 10700966230255240 * q^70 + 25039332312392368 * q^71 - 7954969753997256 * q^72 - 18720848443128734 * q^73 - 6297551300657404 * q^74 + 22553223201966436 * q^75 + 34141945529937952 * q^76 + 35092380107507048 * q^77 + 27963841408286022 * q^78 + 965348846593408 * q^79 + 36943919850262880 * q^80 + 51275234750545798 * q^81 + 106728632435914846 * q^82 + 65089411455584544 * q^83 + 189770883431502392 * q^84 + 20919534362994588 * q^85 + 86205449672049764 * q^86 + 130649890213719716 * q^87 + 164304846335490592 * q^88 - 61322357257717500 * q^89 + 237420523836214152 * q^90 + 181977537844157150 * q^91 - 61586264776507392 * q^92 - 71304974484877430 * q^93 - 14005510384703054 * q^94 + 123323286964112684 * q^95 + 566787465801380768 * q^96 - 67350702995984898 * q^97 + 134333537201072600 * q^98 + 353912447692290838 * 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 $

$2$	−519.142	−1.43394	−0.716970	−	0.697104i	$-0.754472\pi$
$2$	−519.142	−1.43394	−0.716970	+	0.697104i	$0.754472\pi$
$3$	13379.6	1.17737	0.588684	−	0.808363i	$-0.299646\pi$
$3$	13379.6	1.17737	0.588684	+	0.808363i	$0.299646\pi$
$4$	138436.	1.05618
$5$	329626.	0.377378	0.188689	−	0.982037i	$-0.439576\pi$
$5$	329626.	0.377378	0.188689	+	0.982037i	$0.439576\pi$
$6$	−6.94591e6	−1.68828
$7$	1.47770e7	0.968843	0.484421	−	0.874835i	$-0.339030\pi$
$7$	1.47770e7	0.968843	0.484421	+	0.874835i	$0.339030\pi$
$8$	−3.82310e6	−0.0805659
$9$	4.98736e7	0.386197
$10$	−1.71123e8	−0.541138
$11$	−3.09346e8	−0.435117	−0.217559	−	0.976047i	$-0.569809\pi$
$11$	−3.09346e8	−0.435117	−0.217559	+	0.976047i	$0.569809\pi$
$12$	1.85222e9	1.24352
$13$	−5.57722e9	−1.89627	−0.948133	−	0.317875i	$-0.897031\pi$
$13$	−5.57722e9	−1.89627	−0.948133	+	0.317875i	$0.897031\pi$
$14$	−7.67136e9	−1.38926
$15$	4.41027e9	0.444313
$16$	−1.61604e10	−0.940658
$17$	−4.02569e10	−1.39967	−0.699833	−	0.714306i	$-0.746742\pi$
$17$	−4.02569e10	−1.39967	−0.699833	+	0.714306i	$0.746742\pi$
$18$	−2.58915e10	−0.553784
$19$	1.16393e11	1.57225	0.786123	−	0.618070i	$-0.212085\pi$
$19$	1.16393e11	1.57225	0.786123	+	0.618070i	$0.212085\pi$
$20$	4.56322e10	0.398581
$21$	1.97711e11	1.14069
$22$	1.60594e11	0.623932
$23$	−7.83110e10	−0.208514
$23$	−7.83110e10	−0.208514
$24$	−5.11516e10	−0.0948557
$25$	−6.54286e11	−0.857586
$26$	2.89537e12	2.71913
$27$	−1.06056e12	−0.722672
$28$	2.04567e12	1.02328
$29$	2.70202e12	1.00301	0.501505	−	0.865154i	$-0.332780\pi$
$29$	2.70202e12	1.00301	0.501505	+	0.865154i	$0.332780\pi$
$30$	−2.28956e12	−0.637119
$31$	−4.10449e11	−0.0864341	−0.0432171	−	0.999066i	$-0.513761\pi$
$31$	−4.10449e11	−0.0864341	−0.0432171	+	0.999066i	$0.513761\pi$
$32$	8.89063e12	1.42941
$33$	−4.13892e12	−0.512294
$34$	2.08990e13	2.00704
$35$	4.87089e12	0.365620
$36$	6.90431e12	0.407896
$37$	−2.24450e13	−1.05052	−0.525260	−	0.850941i	$-0.676032\pi$
$37$	−2.24450e13	−1.05052	−0.525260	+	0.850941i	$0.676032\pi$
$38$	−6.04244e13	−2.25451
$39$	−7.46209e13	−2.23260
$40$	−1.26020e12	−0.0304038
$41$	1.25899e13	0.246240	0.123120	−	0.992392i	$-0.460710\pi$
$41$	1.25899e13	0.246240	0.123120	+	0.992392i	$0.460710\pi$
$42$	−1.02640e14	−1.63567
$43$	5.34031e13	0.696762	0.348381	−	0.937353i	$-0.386732\pi$
$43$	5.34031e13	0.696762	0.348381	+	0.937353i	$0.386732\pi$
$44$	−4.28247e13	−0.459564
$45$	1.64397e13	0.145743
$46$	4.06545e13	0.298997
$47$	−3.17815e14	−1.94690	−0.973448	−	0.228907i	$-0.926485\pi$
$47$	−3.17815e14	−1.94690	−0.973448	+	0.228907i	$0.926485\pi$
$48$	−2.16220e14	−1.10750
$49$	−1.42705e13	−0.0613439
$50$	3.39667e14	1.22973
$51$	−5.38621e14	−1.64792
$52$	−7.72089e14	−2.00281
$53$	4.36573e13	0.0963191	0.0481595	−	0.998840i	$-0.484664\pi$
$53$	4.36573e13	0.0963191	0.0481595	+	0.998840i	$0.484664\pi$
$54$	5.50579e14	1.03627
$55$	−1.01969e14	−0.164204
$56$	−5.64940e13	−0.0780556
$57$	1.55729e15	1.85111
$58$	−1.40273e15	−1.43826
$59$	−2.43711e14	−0.216089	−0.108045	−	0.994146i	$-0.534459\pi$
$59$	−2.43711e14	−0.216089	−0.108045	+	0.994146i	$0.534459\pi$
$60$	6.10541e14	0.469277
$61$	1.52445e15	1.01814	0.509072	−	0.860724i	$-0.329989\pi$
$61$	1.52445e15	1.01814	0.509072	+	0.860724i	$0.329989\pi$
$62$	2.13081e14	0.123941
$63$	7.36983e14	0.374165
$64$	−2.49733e15	−1.10904
$65$	−1.83840e15	−0.715609
$66$	2.14869e15	0.734598
$67$	−5.39093e15	−1.62191	−0.810957	−	0.585106i	$-0.801053\pi$
$67$	−5.39093e15	−1.62191	−0.810957	+	0.585106i	$0.801053\pi$
$68$	−5.57301e15	−1.47831
$69$	−1.04777e15	−0.245498
$70$	−2.52868e15	−0.524278
$71$	5.08528e14	0.0934584	0.0467292	−	0.998908i	$-0.485120\pi$
$71$	5.08528e14	0.0934584	0.0467292	+	0.998908i	$0.485120\pi$
$72$	−1.90672e14	−0.0311143
$73$	−5.69386e15	−0.826348	−0.413174	−	0.910652i	$-0.635580\pi$
$73$	−5.69386e15	−0.826348	−0.413174	+	0.910652i	$0.635580\pi$
$74$	1.16521e16	1.50638
$75$	−8.75409e15	−1.00969
$76$	1.61130e16	1.66058
$77$	−4.57121e15	−0.421560
$78$	3.87389e16	3.20142
$79$	−8.08573e15	−0.599638	−0.299819	−	0.953996i	$-0.596926\pi$
$79$	−8.08573e15	−0.599638	−0.299819	+	0.953996i	$0.596926\pi$
$80$	−5.32689e15	−0.354984
$81$	−2.06305e16	−1.23705
$82$	−6.53594e15	−0.353094
$83$	9.04716e15	0.440909	0.220454	−	0.975397i	$-0.429246\pi$
$83$	9.04716e15	0.440909	0.220454	+	0.975397i	$0.429246\pi$
$84$	2.73703e16	1.20477
$85$	−1.32697e16	−0.528204
$86$	−2.77238e16	−0.999115
$87$	3.61520e16	1.18091
$88$	1.18266e15	0.0350556
$89$	3.54591e16	0.954801	0.477400	−	0.878686i	$-0.341579\pi$
$89$	3.54591e16	0.954801	0.477400	+	0.878686i	$0.341579\pi$
$90$	−8.53451e15	−0.208986
$91$	−8.24146e16	−1.83718
$92$	−1.08411e16	−0.220230
$93$	−5.49165e15	−0.101765
$94$	1.64991e17	2.79173
$95$	3.83661e16	0.593332
$96$	1.18953e17	1.68295
$97$	−5.46450e16	−0.707931	−0.353965	−	0.935259i	$-0.615167\pi$
$97$	−5.46450e16	−0.707931	−0.353965	+	0.935259i	$0.615167\pi$
$98$	7.40840e15	0.0879635
$99$	−1.54282e16	−0.168041
$100$	−9.05769e16	−0.905769
$101$	−4.05989e16	−0.373064	−0.186532	−	0.982449i	$-0.559725\pi$
$101$	−4.05989e16	−0.373064	−0.186532	+	0.982449i	$0.559725\pi$
$102$	2.79621e17	2.36302
$103$	2.53861e17	1.97460	0.987301	−	0.158862i	$-0.0507824\pi$
$103$	2.53861e17	1.97460	0.987301	+	0.158862i	$0.0507824\pi$
$104$	2.13223e16	0.152774
$105$	6.51706e16	0.430470
$106$	−2.26643e16	−0.138116
$107$	−1.29037e17	−0.726027	−0.363014	−	0.931784i	$-0.618252\pi$
$107$	−1.29037e17	−0.726027	−0.363014	+	0.931784i	$0.618252\pi$
$108$	−1.46819e17	−0.763275
$109$	−2.15820e17	−1.03745	−0.518723	−	0.854942i	$-0.673592\pi$
$109$	−2.15820e17	−1.03745	−0.518723	+	0.854942i	$0.673592\pi$
$110$	5.29361e16	0.235458
$111$	−3.00305e17	−1.23685
$112$	−2.38802e17	−0.911350
$113$	3.10764e17	1.09967	0.549837	−	0.835272i	$-0.314690\pi$
$113$	3.10764e17	1.09967	0.549837	+	0.835272i	$0.314690\pi$
$114$	−8.08454e17	−2.65439
$115$	−2.58134e16	−0.0786888
$116$	3.74058e17	1.05937
$117$	−2.78156e17	−0.732333
$118$	1.26521e17	0.309859
$119$	−5.94877e17	−1.35606
$120$	−1.68609e16	−0.0357965
$121$	−4.09752e17	−0.810673
$122$	−7.91406e17	−1.45996
$123$	1.68448e17	0.289916
$124$	−5.68211e16	−0.0912904
$125$	−4.67155e17	−0.701013
$126$	−3.82599e17	−0.536530
$127$	−1.08220e18	−1.41898	−0.709490	−	0.704716i	$-0.751075\pi$
$127$	−1.08220e18	−1.41898	−0.709490	+	0.704716i	$0.751075\pi$
$128$	1.31153e17	0.160877
$129$	7.14512e17	0.820345
$130$	9.54389e17	1.02614
$131$	−3.47774e16	−0.0350341	−0.0175171	−	0.999847i	$-0.505576\pi$
$131$	−3.47774e16	−0.0350341	−0.0175171	+	0.999847i	$0.505576\pi$
$132$	−5.72977e17	−0.541077
$133$	1.71994e18	1.52326
$134$	2.79866e18	2.32573
$135$	−3.49587e17	−0.272721
$136$	1.53906e17	0.112765
$137$	2.24048e18	1.54247	0.771235	−	0.636551i	$-0.219639\pi$
$137$	2.24048e18	1.54247	0.771235	+	0.636551i	$0.219639\pi$
$138$	5.43941e17	0.352030
$139$	5.05053e17	0.307405	0.153703	−	0.988117i	$-0.450880\pi$
$139$	5.05053e17	0.307405	0.153703	+	0.988117i	$0.450880\pi$
$140$	6.74308e17	0.386163
$141$	−4.25224e18	−2.29222
$142$	−2.63998e17	−0.134014
$143$	1.72529e18	0.825098
$144$	−8.05977e17	−0.363280
$145$	8.90657e17	0.378515
$146$	2.95592e18	1.18493
$147$	−1.90933e17	−0.0722244
$148$	−3.10720e18	−1.10954
$149$	2.51021e17	0.0846499	0.0423250	−	0.999104i	$-0.486524\pi$
$149$	2.51021e17	0.0846499	0.0423250	+	0.999104i	$0.486524\pi$
$150$	4.54461e18	1.44784
$151$	−2.21109e18	−0.665738	−0.332869	−	0.942973i	$-0.608017\pi$
$151$	−2.21109e18	−0.665738	−0.332869	+	0.942973i	$0.608017\pi$
$152$	−4.44982e17	−0.126669
$153$	−2.00776e18	−0.540547
$154$	2.37310e18	0.604492
$155$	−1.35295e17	−0.0326184
$156$	−1.03302e19	−2.35804
$157$	−1.66317e18	−0.359576	−0.179788	−	0.983705i	$-0.557541\pi$
$157$	−1.66317e18	−0.359576	−0.179788	+	0.983705i	$0.557541\pi$
$158$	4.19764e18	0.859845
$159$	5.84118e17	0.113403
$160$	2.93059e18	0.539430
$161$	−1.15720e18	−0.202018
$162$	1.07102e19	1.77385
$163$	−1.15483e19	−1.81519	−0.907594	−	0.419848i	$-0.862083\pi$
$163$	−1.15483e19	−1.81519	−0.907594	+	0.419848i	$0.862083\pi$
$164$	1.74290e18	0.260075
$165$	−1.36430e18	−0.193328
$166$	−4.69676e18	−0.632237
$167$	1.79528e18	0.229638	0.114819	−	0.993386i	$-0.463371\pi$
$167$	1.79528e18	0.229638	0.114819	+	0.993386i	$0.463371\pi$
$168$	−7.55868e17	−0.0919003
$169$	2.24549e19	2.59582
$170$	6.88887e18	0.757412
$171$	5.80493e18	0.607197
$172$	7.39292e18	0.735909
$173$	−3.43640e18	−0.325621	−0.162810	−	0.986657i	$-0.552056\pi$
$173$	−3.43640e18	−0.325621	−0.162810	+	0.986657i	$0.552056\pi$
$174$	−1.87680e19	−1.69336
$175$	−9.66839e18	−0.830866
$176$	4.99915e18	0.409297
$177$	−3.26076e18	−0.254417
$178$	−1.84083e19	−1.36913
$179$	−1.08006e19	−0.765944	−0.382972	−	0.923760i	$-0.625099\pi$
$179$	−1.08006e19	−0.765944	−0.382972	+	0.923760i	$0.625099\pi$
$180$	2.27584e18	0.153931
$181$	3.74963e18	0.241947	0.120974	−	0.992656i	$-0.461398\pi$
$181$	3.74963e18	0.241947	0.120974	+	0.992656i	$0.461398\pi$
$182$	4.27849e19	2.63441
$183$	2.03965e19	1.19873
$184$	2.99391e17	0.0167991
$185$	−7.39846e18	−0.396444
$186$	2.85095e18	0.145925
$187$	1.24533e19	0.609019
$188$	−4.39972e19	−2.05628
$189$	−1.56718e19	−0.700156
$190$	−1.99175e19	−0.850802
$191$	2.53342e19	1.03496	0.517480	−	0.855696i	$-0.326870\pi$
$191$	2.53342e19	1.03496	0.517480	+	0.855696i	$0.326870\pi$
$192$	−3.34132e19	−1.30574
$193$	2.61605e18	0.0978159	0.0489079	−	0.998803i	$-0.484426\pi$
$193$	2.61605e18	0.0978159	0.0489079	+	0.998803i	$0.484426\pi$
$194$	2.83685e19	1.01513
$195$	−2.45970e19	−0.842536
$196$	−1.97555e18	−0.0647905
$197$	−4.15983e19	−1.30651	−0.653256	−	0.757137i	$-0.726597\pi$
$197$	−4.15983e19	−1.30651	−0.653256	+	0.757137i	$0.726597\pi$
$198$	8.00942e18	0.240961
$199$	4.95448e19	1.42806	0.714031	−	0.700114i	$-0.246868\pi$
$199$	4.95448e19	1.42806	0.714031	+	0.700114i	$0.246868\pi$
$200$	2.50140e18	0.0690921
$201$	−7.21284e19	−1.90959
$202$	2.10766e19	0.534951
$203$	3.99278e19	0.971760
$204$	−7.45647e19	−1.74051
$205$	4.14996e18	0.0929257
$206$	−1.31790e20	−2.83146
$207$	−3.90565e18	−0.0805277
$208$	9.01300e19	1.78374
$209$	−3.60056e19	−0.684111
$210$	−3.38328e19	−0.617268
$211$	−9.00062e19	−1.57715	−0.788573	−	0.614942i	$-0.789180\pi$
$211$	−9.00062e19	−1.57715	−0.788573	+	0.614942i	$0.789180\pi$
$212$	6.04376e18	0.101731
$213$	6.80390e18	0.110035
$214$	6.69886e19	1.04108
$215$	1.76031e19	0.262943
$216$	4.05461e18	0.0582227
$217$	−6.06522e18	−0.0837411
$218$	1.12041e20	1.48764
$219$	−7.61816e19	−0.972916
$220$	−1.41161e19	−0.173430
$221$	2.24521e20	2.65414
$222$	1.55901e20	1.77357
$223$	−8.87500e19	−0.971800	−0.485900	−	0.874014i	$-0.661508\pi$
$223$	−8.87500e19	−0.971800	−0.485900	+	0.874014i	$0.661508\pi$
$224$	1.31377e20	1.38488
$225$	−3.26316e19	−0.331197
$226$	−1.61331e20	−1.57687
$227$	1.36159e20	1.28182	0.640910	−	0.767616i	$-0.278557\pi$
$227$	1.36159e20	1.28182	0.640910	+	0.767616i	$0.278557\pi$
$228$	2.15585e20	1.95512
$229$	−5.25532e19	−0.459196	−0.229598	−	0.973286i	$-0.573741\pi$
$229$	−5.25532e19	−0.459196	−0.229598	+	0.973286i	$0.573741\pi$
$230$	1.34008e19	0.112835
$231$	−6.11609e19	−0.496332
$232$	−1.03301e19	−0.0808084
$233$	9.42345e19	0.710697	0.355348	−	0.934734i	$-0.384362\pi$
$233$	9.42345e19	0.710697	0.355348	+	0.934734i	$0.384362\pi$
$234$	1.44402e20	1.05012
$235$	−1.04760e20	−0.734717
$236$	−3.37384e19	−0.228230
$237$	−1.08184e20	−0.705995
$238$	3.08825e20	1.94450
$239$	−8.25651e19	−0.501666	−0.250833	−	0.968030i	$-0.580704\pi$
$239$	−8.25651e19	−0.501666	−0.250833	+	0.968030i	$0.580704\pi$
$240$	−7.12717e19	−0.417947
$241$	−7.84282e19	−0.443943	−0.221972	−	0.975053i	$-0.571249\pi$
$241$	−7.84282e19	−0.443943	−0.221972	+	0.975053i	$0.571249\pi$
$242$	2.12720e20	1.16246
$243$	−1.39067e20	−0.733791
$244$	2.11039e20	1.07535
$245$	−4.70392e18	−0.0231499
$246$	−8.74482e19	−0.415722
$247$	−6.49148e20	−2.98140
$248$	1.56919e18	0.00696364
$249$	1.21047e20	0.519112
$250$	2.42520e20	1.00521
$251$	−4.94055e19	−0.197947	−0.0989734	−	0.995090i	$-0.531556\pi$
$251$	−4.94055e19	−0.197947	−0.0989734	+	0.995090i	$0.531556\pi$
$252$	1.02025e20	0.395187
$253$	2.42252e19	0.0907282
$254$	5.61816e20	2.03473
$255$	−1.77544e20	−0.621890
$256$	2.59242e20	0.878347
$257$	−1.56116e20	−0.511701	−0.255851	−	0.966716i	$-0.582355\pi$
$257$	−1.56116e20	−0.511701	−0.255851	+	0.966716i	$0.582355\pi$
$258$	−3.70933e20	−1.17633
$259$	−3.31670e20	−1.01779
$260$	−2.54501e20	−0.755816
$261$	1.34759e20	0.387360
$262$	1.80544e19	0.0502369
$263$	−1.65634e20	−0.446197	−0.223098	−	0.974796i	$-0.571617\pi$
$263$	−1.65634e20	−0.446197	−0.223098	+	0.974796i	$0.571617\pi$
$264$	1.58235e19	0.0412734
$265$	1.43906e19	0.0363487
$266$	−8.92892e20	−2.18426
$267$	4.74429e20	1.12415
$268$	−7.46300e20	−1.71304
$269$	8.82903e20	1.96344	0.981722	−	0.190320i	$-0.0609525\pi$
$269$	8.82903e20	1.96344	0.981722	+	0.190320i	$0.0609525\pi$
$270$	1.81485e20	0.391065
$271$	−4.96237e20	−1.03622	−0.518108	−	0.855315i	$-0.673363\pi$
$271$	−4.96237e20	−1.03622	−0.518108	+	0.855315i	$0.673363\pi$
$272$	6.50567e20	1.31661
$273$	−1.10267e21	−2.16304
$274$	−1.16313e21	−2.21181
$275$	2.02401e20	0.373150
$276$	−1.45049e20	−0.259292
$277$	−9.30642e20	−1.61326	−0.806631	−	0.591056i	$-0.798711\pi$
$277$	−9.30642e20	−1.61326	−0.806631	+	0.591056i	$0.798711\pi$
$278$	−2.62194e20	−0.440801
$279$	−2.04706e19	−0.0333806
$280$	−1.86219e19	−0.0294565
$281$	1.86727e20	0.286552	0.143276	−	0.989683i	$-0.454236\pi$
$281$	1.86727e20	0.286552	0.143276	+	0.989683i	$0.454236\pi$
$282$	2.20752e21	3.28690
$283$	1.74936e20	0.252752	0.126376	−	0.991982i	$-0.459665\pi$
$283$	1.74936e20	0.252752	0.126376	+	0.991982i	$0.459665\pi$
$284$	7.03987e19	0.0987094
$285$	5.13324e20	0.698570
$286$	−8.95669e20	−1.18314
$287$	1.86041e20	0.238568
$288$	4.43408e20	0.552036
$289$	7.93377e20	0.959065
$290$	−4.62377e20	−0.542767
$291$	−7.31129e20	−0.833496
$292$	−7.88237e20	−0.872776
$293$	9.01291e20	0.969371	0.484686	−	0.874688i	$-0.338934\pi$
$293$	9.01291e20	0.969371	0.484686	+	0.874688i	$0.338934\pi$
$294$	9.91214e19	0.103565
$295$	−8.03336e19	−0.0815474
$296$	8.58095e19	0.0846361
$297$	3.28078e20	0.314447
$298$	−1.30315e20	−0.121383
$299$	4.36757e20	0.395399
$300$	−1.21188e21	−1.06642
$301$	7.89138e20	0.675052
$302$	1.14787e21	0.954629
$303$	−5.43197e20	−0.439233
$304$	−1.88095e21	−1.47895
$305$	5.02499e20	0.384226
$306$	1.04231e21	0.775113
$307$	1.29894e21	0.939535	0.469768	−	0.882790i	$-0.344338\pi$
$307$	1.29894e21	0.939535	0.469768	+	0.882790i	$0.344338\pi$
$308$	−6.32821e20	−0.445245
$309$	3.39656e21	2.32483
$310$	7.02373e19	0.0467728
$311$	7.33184e20	0.475061	0.237531	−	0.971380i	$-0.423662\pi$
$311$	7.33184e20	0.475061	0.237531	+	0.971380i	$0.423662\pi$
$312$	2.85284e20	0.179872
$313$	8.66369e20	0.531589	0.265795	−	0.964030i	$-0.414366\pi$
$313$	8.66369e20	0.531589	0.265795	+	0.964030i	$0.414366\pi$
$314$	8.63423e20	0.515610
$315$	2.42929e20	0.141202
$316$	−1.11936e21	−0.633328
$317$	2.34453e21	1.29137	0.645687	−	0.763602i	$-0.276571\pi$
$317$	2.34453e21	1.29137	0.645687	+	0.763602i	$0.276571\pi$
$318$	−3.03240e20	−0.162613
$319$	−8.35859e20	−0.436427
$320$	−8.23185e20	−0.418526
$321$	−1.72647e21	−0.854802
$322$	6.00752e20	0.289681
$323$	−4.68561e21	−2.20062
$324$	−2.85601e21	−1.30655
$325$	3.64909e21	1.62621
$326$	5.99518e21	2.60287
$327$	−2.88758e21	−1.22146
$328$	−4.81324e19	−0.0198386
$329$	−4.69636e21	−1.88624
$330$	7.08264e20	0.277221
$331$	3.85490e21	1.47053	0.735267	−	0.677777i	$-0.237057\pi$
$331$	3.85490e21	1.47053	0.735267	+	0.677777i	$0.237057\pi$
$332$	1.25246e21	0.465681
$333$	−1.11941e21	−0.405708
$334$	−9.32007e20	−0.329287
$335$	−1.77699e21	−0.612075
$336$	−3.19508e21	−1.07299
$337$	1.12794e21	0.369345	0.184672	−	0.982800i	$-0.440878\pi$
$337$	1.12794e21	0.369345	0.184672	+	0.982800i	$0.440878\pi$
$338$	−1.16573e22	−3.72225
$339$	4.15790e21	1.29472
$340$	−1.83701e21	−0.557881
$341$	1.26971e20	0.0376090
$342$	−3.01358e21	−0.870685
$343$	−3.64846e21	−1.02828
$344$	−2.04165e20	−0.0561352
$345$	−3.45373e20	−0.0926458
$346$	1.78398e21	0.466921
$347$	4.46996e21	1.14157	0.570786	−	0.821099i	$-0.306639\pi$
$347$	4.46996e21	1.14157	0.570786	+	0.821099i	$0.306639\pi$
$348$	5.00474e21	1.24726
$349$	7.16631e21	1.74293	0.871464	−	0.490459i	$-0.163171\pi$
$349$	7.16631e21	1.74293	0.871464	+	0.490459i	$0.163171\pi$
$350$	5.01927e21	1.19141
$351$	5.91495e21	1.37038
$352$	−2.75028e21	−0.621963
$353$	2.26627e21	0.500295	0.250148	−	0.968208i	$-0.419521\pi$
$353$	2.26627e21	0.500295	0.250148	+	0.968208i	$0.419521\pi$
$354$	1.69279e21	0.364818
$355$	1.67624e20	0.0352692
$356$	4.90883e21	1.00845
$357$	−7.95921e21	−1.59658
$358$	5.60704e21	1.09832
$359$	1.01399e22	1.93968	0.969842	−	0.243735i	$-0.0783727\pi$
$359$	1.01399e22	1.93968	0.969842	+	0.243735i	$0.0783727\pi$
$360$	−6.28505e19	−0.0117419
$361$	8.06690e21	1.47196
$362$	−1.94659e21	−0.346938
$363$	−5.48232e21	−0.954461
$364$	−1.14092e22	−1.94040
$365$	−1.87685e21	−0.311846
$366$	−1.05887e22	−1.71891
$367$	−4.38015e21	−0.694748	−0.347374	−	0.937727i	$-0.612927\pi$
$367$	−4.38015e21	−0.694748	−0.347374	+	0.937727i	$0.612927\pi$
$368$	1.26554e21	0.196141
$369$	6.27903e20	0.0950973
$370$	3.84085e21	0.568477
$371$	6.45125e20	0.0933180
$372$	−7.60244e20	−0.107483
$373$	7.44005e20	0.102814	0.0514068	−	0.998678i	$-0.483629\pi$
$373$	7.44005e20	0.102814	0.0514068	+	0.998678i	$0.483629\pi$
$374$	−6.46503e21	−0.873297
$375$	−6.25035e21	−0.825350
$376$	1.21504e21	0.156853
$377$	−1.50698e22	−1.90197
$378$	8.13591e21	1.00398
$379$	−1.35935e22	−1.64021	−0.820103	−	0.572217i	$-0.806084\pi$
$379$	−1.35935e22	−1.64021	−0.820103	+	0.572217i	$0.806084\pi$
$380$	5.31127e21	0.626668
$381$	−1.44794e22	−1.67066
$382$	−1.31520e22	−1.48407
$383$	−7.78625e21	−0.859288	−0.429644	−	0.902998i	$-0.641361\pi$
$383$	−7.78625e21	−0.859288	−0.429644	+	0.902998i	$0.641361\pi$
$384$	1.75478e21	0.189412
$385$	−1.50679e21	−0.159088
$386$	−1.35810e21	−0.140262
$387$	2.66340e21	0.269088
$388$	−7.56485e21	−0.747706
$389$	2.91556e20	0.0281936	0.0140968	−	0.999901i	$-0.495513\pi$
$389$	2.91556e20	0.0281936	0.0140968	+	0.999901i	$0.495513\pi$
$390$	1.27693e22	1.20815
$391$	3.15256e21	0.291851
$392$	5.45575e19	0.00494223
$393$	−4.65308e20	−0.0412481
$394$	2.15954e22	1.87346
$395$	−2.66527e21	−0.226290
$396$	−2.13582e21	−0.177483
$397$	−8.66212e21	−0.704539	−0.352269	−	0.935899i	$-0.614590\pi$
$397$	−8.66212e21	−0.704539	−0.352269	+	0.935899i	$0.614590\pi$
$398$	−2.57208e22	−2.04776
$399$	2.30121e22	1.79344
$400$	1.05735e22	0.806695
$401$	2.05147e22	1.53228	0.766139	−	0.642675i	$-0.222175\pi$
$401$	2.05147e22	1.53228	0.766139	+	0.642675i	$0.222175\pi$
$402$	3.74449e22	2.73824
$403$	2.28917e21	0.163902
$404$	−5.62036e21	−0.394024
$405$	−6.80035e21	−0.466835
$406$	−2.07282e22	−1.39345
$407$	6.94326e21	0.457100
$408$	2.05920e21	0.132766
$409$	−1.81681e22	−1.14726	−0.573629	−	0.819115i	$-0.694465\pi$
$409$	−1.81681e22	−1.14726	−0.573629	+	0.819115i	$0.694465\pi$
$410$	−2.15442e21	−0.133250
$411$	2.99768e22	1.81606
$412$	3.51436e22	2.08554
$413$	−3.60132e21	−0.209356
$414$	2.02759e21	0.115472
$415$	2.98218e21	0.166389
$416$	−4.95850e22	−2.71055
$417$	6.75741e21	0.361929
$418$	1.86920e22	0.980975
$419$	−1.77720e22	−0.913941	−0.456970	−	0.889482i	$-0.651065\pi$
$419$	−1.77720e22	−0.913941	−0.456970	+	0.889482i	$0.651065\pi$
$420$	9.02198e21	0.454656
$421$	1.43747e22	0.709906	0.354953	−	0.934884i	$-0.384497\pi$
$421$	1.43747e22	0.709906	0.354953	+	0.934884i	$0.384497\pi$
$422$	4.67260e22	2.26153
$423$	−1.58506e22	−0.751886
$424$	−1.66906e20	−0.00776003
$425$	2.63395e22	1.20033
$426$	−3.53219e21	−0.157784
$427$	2.25268e22	0.986422
$428$	−1.78634e22	−0.766819
$429$	2.30837e22	0.971444
$430$	−9.13848e21	−0.377044
$431$	2.98425e22	1.20720	0.603599	−	0.797288i	$-0.293733\pi$
$431$	2.98425e22	1.20720	0.603599	+	0.797288i	$0.293733\pi$
$432$	1.71390e22	0.679787
$433$	1.65163e22	0.642340	0.321170	−	0.947021i	$-0.395924\pi$
$433$	1.65163e22	0.642340	0.321170	+	0.947021i	$0.395924\pi$
$434$	3.14871e21	0.120080
$435$	1.19166e22	0.445651
$436$	−2.98773e22	−1.09573
$437$	−9.11484e21	−0.327836
$438$	3.95491e22	1.39510
$439$	−4.86983e22	−1.68487	−0.842433	−	0.538801i	$-0.818878\pi$
$439$	−4.86983e22	−1.68487	−0.842433	+	0.538801i	$0.818878\pi$
$440$	3.89836e20	0.0132292
$441$	−7.11719e20	−0.0236909
$442$	−1.16558e23	−3.80588
$443$	−2.82979e22	−0.906407	−0.453203	−	0.891407i	$-0.649719\pi$
$443$	−2.82979e22	−0.906407	−0.453203	+	0.891407i	$0.649719\pi$
$444$	−4.15731e22	−1.30634
$445$	1.16883e22	0.360321
$446$	4.60738e22	1.39350
$447$	3.35856e21	0.0996642
$448$	−3.69030e22	−1.07448
$449$	3.13295e21	0.0895075	0.0447537	−	0.998998i	$-0.485750\pi$
$449$	3.13295e21	0.0895075	0.0447537	+	0.998998i	$0.485750\pi$
$450$	1.69404e22	0.474917
$451$	−3.89463e21	−0.107143
$452$	4.30210e22	1.16146
$453$	−2.95836e22	−0.783819
$454$	−7.06859e22	−1.83805
$455$	−2.71660e22	−0.693313
$456$	−5.95368e21	−0.149137
$457$	8.70379e19	0.00214003	0.00107002	−	0.999999i	$-0.499659\pi$
$457$	8.70379e19	0.00214003	0.00107002	+	0.999999i	$0.499659\pi$
$458$	2.72826e22	0.658459
$459$	4.26947e22	1.01150
$460$	−3.57351e21	−0.0831099
$461$	−5.76373e22	−1.31597	−0.657985	−	0.753031i	$-0.728591\pi$
$461$	−5.76373e22	−1.31597	−0.657985	+	0.753031i	$0.728591\pi$
$462$	3.17512e22	0.711710
$463$	1.95037e22	0.429218	0.214609	−	0.976700i	$-0.431152\pi$
$463$	1.95037e22	0.429218	0.214609	+	0.976700i	$0.431152\pi$
$464$	−4.36657e22	−0.943491
$465$	−1.81019e21	−0.0384038
$466$	−4.89211e22	−1.01910
$467$	6.70978e22	1.37251	0.686254	−	0.727362i	$-0.259254\pi$
$467$	6.70978e22	1.37251	0.686254	+	0.727362i	$0.259254\pi$
$468$	−3.85069e22	−0.773479
$469$	−7.96618e22	−1.57138
$470$	5.43854e22	1.05354
$471$	−2.22526e22	−0.423353
$472$	9.31732e20	0.0174094
$473$	−1.65200e22	−0.303173
$474$	5.61628e22	1.01235
$475$	−7.61542e22	−1.34834
$476$	−8.23525e22	−1.43225
$477$	2.17735e21	0.0371982
$478$	4.28630e22	0.719359
$479$	−7.93323e22	−1.30797	−0.653986	−	0.756507i	$-0.726904\pi$
$479$	−7.93323e22	−1.30797	−0.653986	+	0.756507i	$0.726904\pi$
$480$	3.92101e22	0.635108
$481$	1.25181e23	1.99207
$482$	4.07154e22	0.636588
$483$	−1.54829e22	−0.237849
$484$	−5.67246e22	−0.856221
$485$	−1.80124e22	−0.267158
$486$	7.21958e22	1.05221
$487$	9.39082e22	1.34495	0.672477	−	0.740118i	$-0.265230\pi$
$487$	9.39082e22	1.34495	0.672477	+	0.740118i	$0.265230\pi$
$488$	−5.82813e21	−0.0820277
$489$	−1.54511e23	−2.13715
$490$	2.44200e21	0.0331955
$491$	−5.93277e22	−0.792620	−0.396310	−	0.918117i	$-0.629709\pi$
$491$	−5.93277e22	−0.792620	−0.396310	+	0.918117i	$0.629709\pi$
$492$	2.33193e22	0.306204
$493$	−1.08775e23	−1.40388
$494$	3.37000e23	4.27514
$495$	−5.08554e21	−0.0634151
$496$	6.63302e21	0.0813050
$497$	7.51452e21	0.0905465
$498$	−6.28408e22	−0.744376
$499$	−7.67164e21	−0.0893375	−0.0446687	−	0.999002i	$-0.514223\pi$
$499$	−7.67164e21	−0.0893375	−0.0446687	+	0.999002i	$0.514223\pi$
$500$	−6.46712e22	−0.740399
$501$	2.40202e22	0.270368
$502$	2.56485e22	0.283844
$503$	3.14374e22	0.342073	0.171037	−	0.985265i	$-0.445288\pi$
$503$	3.14374e22	0.342073	0.171037	+	0.985265i	$0.445288\pi$
$504$	−2.81756e21	−0.0301449
$505$	−1.33825e22	−0.140786
$506$	−1.25763e22	−0.130099
$507$	3.00438e23	3.05624
$508$	−1.49816e23	−1.49870
$509$	9.34383e22	0.919229	0.459614	−	0.888119i	$-0.347988\pi$
$509$	9.34383e22	0.919229	0.459614	+	0.888119i	$0.347988\pi$
$510$	9.21704e22	0.891754
$511$	−8.41383e22	−0.800601
$512$	−1.51774e23	−1.42037
$513$	−1.23441e23	−1.13622
$514$	8.10464e22	0.733749
$515$	8.36793e22	0.745172
$516$	9.89143e22	0.866437
$517$	9.83148e22	0.847128
$518$	1.72184e23	1.45945
$519$	−4.59777e22	−0.383376
$520$	7.02838e21	0.0576537
$521$	−6.30712e22	−0.508991	−0.254496	−	0.967074i	$-0.581909\pi$
$521$	−6.30712e22	−0.508991	−0.254496	+	0.967074i	$0.581909\pi$
$522$	−6.99593e22	−0.555451
$523$	1.34972e23	1.05434	0.527168	−	0.849761i	$-0.323254\pi$
$523$	1.34972e23	1.05434	0.527168	+	0.849761i	$0.323254\pi$
$524$	−4.81446e21	−0.0370025
$525$	−1.29359e23	−0.978235
$526$	8.59877e22	0.639820
$527$	1.65234e22	0.120979
$528$	6.68866e22	0.481893
$529$	6.13261e21	0.0434783
$530$	−7.47077e21	−0.0521219
$531$	−1.21547e22	−0.0834531
$532$	2.38102e23	1.60884
$533$	−7.02165e22	−0.466937
$534$	−2.46296e23	−1.61197
$535$	−4.25341e22	−0.273987
$536$	2.06101e22	0.130671
$537$	−1.44508e23	−0.901799
$538$	−4.58352e23	−2.81546
$539$	4.41451e21	0.0266918
$540$	−4.83955e22	−0.288044
$541$	−1.97846e23	−1.15918	−0.579589	−	0.814909i	$-0.696787\pi$
$541$	−1.97846e23	−1.15918	−0.579589	+	0.814909i	$0.696787\pi$
$542$	2.57617e23	1.48587
$543$	5.01686e22	0.284861
$544$	−3.57909e23	−2.00070
$545$	−7.11398e22	−0.391510
$546$	5.72444e23	3.10167
$547$	−5.59847e22	−0.298660	−0.149330	−	0.988787i	$-0.547712\pi$
$547$	−5.59847e22	−0.298660	−0.149330	+	0.988787i	$0.547712\pi$
$548$	3.10164e23	1.62913
$549$	7.60298e22	0.393205
$550$	−1.05075e23	−0.535075
$551$	3.14496e23	1.57698
$552$	4.00573e21	0.0197788
$553$	−1.19483e23	−0.580955
$554$	4.83135e23	2.31332
$555$	−9.89885e22	−0.466761
$556$	6.99177e22	0.324677
$557$	−1.77921e23	−0.813689	−0.406844	−	0.913497i	$-0.633371\pi$
$557$	−1.77921e23	−0.813689	−0.406844	+	0.913497i	$0.633371\pi$
$558$	1.06271e22	0.0478658
$559$	−2.97840e23	−1.32124
$560$	−7.87155e22	−0.343924
$561$	1.66620e23	0.717040
$562$	−9.69379e22	−0.410899
$563$	−1.31161e23	−0.547625	−0.273812	−	0.961783i	$-0.588285\pi$
$563$	−1.31161e23	−0.547625	−0.273812	+	0.961783i	$0.588285\pi$
$564$	−5.88664e23	−2.42100
$565$	1.02436e23	0.414993
$566$	−9.08166e22	−0.362431
$567$	−3.04857e23	−1.19851
$568$	−1.94415e21	−0.00752956
$569$	3.58700e23	1.36860	0.684301	−	0.729199i	$-0.260107\pi$
$569$	3.58700e23	1.36860	0.684301	+	0.729199i	$0.260107\pi$
$570$	−2.66488e23	−1.00171
$571$	2.55897e23	0.947671	0.473835	−	0.880613i	$-0.342869\pi$
$571$	2.55897e23	0.947671	0.473835	+	0.880613i	$0.342869\pi$
$572$	2.38842e23	0.871456
$573$	3.38961e23	1.21853
$574$	−9.65816e22	−0.342092
$575$	5.12378e22	0.178819
$576$	−1.24551e23	−0.428307
$577$	8.52310e22	0.288804	0.144402	−	0.989519i	$-0.453874\pi$
$577$	8.52310e22	0.288804	0.144402	+	0.989519i	$0.453874\pi$
$578$	−4.11875e23	−1.37524
$579$	3.50017e22	0.115165
$580$	1.23299e23	0.399781
$581$	1.33690e23	0.427171
$582$	3.79559e23	1.19518
$583$	−1.35052e22	−0.0419101
$584$	2.17682e22	0.0665754
$585$	−9.16875e22	−0.276366
$586$	−4.67898e23	−1.39002
$587$	−9.75227e22	−0.285550	−0.142775	−	0.989755i	$-0.545603\pi$
$587$	−9.75227e22	−0.285550	−0.142775	+	0.989755i	$0.545603\pi$
$588$	−2.64321e22	−0.0762823
$589$	−4.77734e22	−0.135896
$590$	4.17045e22	0.116934
$591$	−5.56569e23	−1.53825
$592$	3.62720e23	0.988181
$593$	−6.27284e23	−1.68461	−0.842304	−	0.539002i	$-0.818801\pi$
$593$	−6.27284e23	−1.68461	−0.842304	+	0.539002i	$0.818801\pi$
$594$	−1.70319e23	−0.450898
$595$	−1.96087e23	−0.511746
$596$	3.47504e22	0.0894060
$597$	6.62890e23	1.68136
$598$	−2.26739e23	−0.566978
$599$	9.76858e22	0.240826	0.120413	−	0.992724i	$-0.461578\pi$
$599$	9.76858e22	0.240826	0.120413	+	0.992724i	$0.461578\pi$
$600$	3.34678e22	0.0813469
$601$	−6.07558e22	−0.145598	−0.0727989	−	0.997347i	$-0.523193\pi$
$601$	−6.07558e22	−0.145598	−0.0727989	+	0.997347i	$0.523193\pi$
$602$	−4.09674e23	−0.967985
$603$	−2.68865e23	−0.626379
$604$	−3.06096e23	−0.703142
$605$	−1.35065e23	−0.305930
$606$	2.81997e23	0.629834
$607$	5.95344e23	1.31119	0.655593	−	0.755115i	$-0.272419\pi$
$607$	5.95344e23	1.31119	0.655593	+	0.755115i	$0.272419\pi$
$608$	1.03481e24	2.24739
$609$	5.34218e23	1.14412
$610$	−2.60868e23	−0.550957
$611$	1.77252e24	3.69183
$612$	−2.77946e23	−0.570918
$613$	−4.16448e23	−0.843620	−0.421810	−	0.906684i	$-0.638605\pi$
$613$	−4.16448e23	−0.843620	−0.421810	+	0.906684i	$0.638605\pi$
$614$	−6.74334e23	−1.34724
$615$	5.55248e22	0.109408
$616$	1.74762e22	0.0339634
$617$	6.33626e23	1.21453	0.607266	−	0.794499i	$-0.292266\pi$
$617$	6.33626e23	1.21453	0.607266	+	0.794499i	$0.292266\pi$
$618$	−1.76330e24	−3.33367
$619$	−8.19049e23	−1.52735	−0.763677	−	0.645599i	$-0.776608\pi$
$619$	−8.19049e23	−1.52735	−0.763677	+	0.645599i	$0.776608\pi$
$620$	−1.87297e22	−0.0344510
$621$	8.30531e22	0.150688
$622$	−3.80626e23	−0.681209
$623$	5.23980e23	0.925052
$624$	1.20590e24	2.10012
$625$	3.45194e23	0.593039
$626$	−4.49768e23	−0.762267
$627$	−4.81741e23	−0.805451
$628$	−2.30244e23	−0.379779
$629$	9.03565e23	1.47038
$630$	−1.26115e23	−0.202475
$631$	−2.41624e23	−0.382728	−0.191364	−	0.981519i	$-0.561291\pi$
$631$	−2.41624e23	−0.382728	−0.191364	+	0.981519i	$0.561291\pi$
$632$	3.09126e22	0.0483103
$633$	−1.20425e24	−1.85688
$634$	−1.21714e24	−1.85175
$635$	−3.56722e23	−0.535492
$636$	8.08631e22	0.119775
$637$	7.95895e22	0.116324
$638$	4.33929e23	0.625811
$639$	2.53621e22	0.0360934
$640$	4.32316e22	0.0607116
$641$	−2.32152e23	−0.321721	−0.160860	−	0.986977i	$-0.551427\pi$
$641$	−2.32152e23	−0.321721	−0.160860	+	0.986977i	$0.551427\pi$
$642$	8.96281e23	1.22573
$643$	3.06092e23	0.413103	0.206552	−	0.978436i	$-0.433776\pi$
$643$	3.06092e23	0.413103	0.206552	+	0.978436i	$0.433776\pi$
$644$	−1.60199e23	−0.213368
$645$	2.35522e23	0.309581
$646$	2.43250e24	3.15556
$647$	7.88220e23	1.00916	0.504581	−	0.863364i	$-0.331647\pi$
$647$	7.88220e23	1.00916	0.504581	+	0.863364i	$0.331647\pi$
$648$	7.88725e22	0.0996639
$649$	7.53910e22	0.0940241
$650$	−1.89440e24	−2.33189
$651$	−8.11502e22	−0.0985941
$652$	−1.59870e24	−1.91717
$653$	−6.42016e23	−0.759947	−0.379974	−	0.924997i	$-0.624067\pi$
$653$	−6.42016e23	−0.759947	−0.379974	+	0.924997i	$0.624067\pi$
$654$	1.49906e24	1.75150
$655$	−1.14636e22	−0.0132211
$656$	−2.03457e23	−0.231628
$657$	−2.83974e23	−0.319133
$658$	2.43808e24	2.70475
$659$	−6.58499e22	−0.0721156	−0.0360578	−	0.999350i	$-0.511480\pi$
$659$	−6.58499e22	−0.0721156	−0.0360578	+	0.999350i	$0.511480\pi$
$660$	−1.88868e23	−0.204191
$661$	1.67054e24	1.78297	0.891486	−	0.453048i	$-0.149663\pi$
$661$	1.67054e24	1.78297	0.891486	+	0.453048i	$0.149663\pi$
$662$	−2.00124e24	−2.10866
$663$	3.00401e24	3.12490
$664$	−3.45882e22	−0.0355222
$665$	5.66937e23	0.574845
$666$	5.81134e23	0.581762
$667$	−2.11598e23	−0.209142
$668$	2.48532e23	0.242540
$669$	−1.18744e24	−1.14417
$670$	9.22511e23	0.877679
$671$	−4.71582e23	−0.443012
$672$	1.75777e24	1.63051
$673$	−2.16900e23	−0.198669	−0.0993347	−	0.995054i	$-0.531671\pi$
$673$	−2.16900e23	−0.198669	−0.0993347	+	0.995054i	$0.531671\pi$
$674$	−5.85561e23	−0.529618
$675$	6.93906e23	0.619753
$676$	3.10858e24	2.74167
$677$	−1.73878e24	−1.51441	−0.757203	−	0.653180i	$-0.773435\pi$
$677$	−1.73878e24	−1.51441	−0.757203	+	0.653180i	$0.773435\pi$
$678$	−2.15854e24	−1.85656
$679$	−8.07490e23	−0.685874
$680$	5.07316e22	0.0425552
$681$	1.82175e24	1.50917
$682$	−6.59158e22	−0.0539290
$683$	−1.53554e24	−1.24075	−0.620376	−	0.784305i	$-0.713020\pi$
$683$	−1.53554e24	−1.24075	−0.620376	+	0.784305i	$0.713020\pi$
$684$	8.03613e23	0.641313
$685$	7.38522e23	0.582095
$686$	1.89407e24	1.47449
$687$	−7.03141e23	−0.540643
$688$	−8.63014e23	−0.655415
$689$	−2.43486e23	−0.182646
$690$	1.79297e23	0.132848
$691$	1.50025e24	1.09799	0.548996	−	0.835825i	$-0.315010\pi$
$691$	1.50025e24	1.09799	0.548996	+	0.835825i	$0.315010\pi$
$692$	−4.75723e23	−0.343916
$693$	−2.27982e23	−0.162805
$694$	−2.32054e24	−1.63695
$695$	1.66479e23	0.116008
$696$	−1.38213e23	−0.0951413
$697$	−5.06830e23	−0.344654
$698$	−3.72033e24	−2.49926
$699$	1.26082e24	0.836753
$700$	−1.33846e24	−0.877548
$701$	−2.11219e24	−1.36814	−0.684068	−	0.729419i	$-0.739791\pi$
$701$	−2.11219e24	−1.36814	−0.684068	+	0.729419i	$0.739791\pi$
$702$	−3.07070e24	−1.96504
$703$	−2.61244e24	−1.65168
$704$	7.72537e23	0.482561
$705$	−1.40165e24	−0.865032
$706$	−1.17652e24	−0.717394
$707$	−5.99931e23	−0.361440
$708$	−4.51407e23	−0.268711
$709$	1.41755e24	0.833770	0.416885	−	0.908959i	$-0.363122\pi$
$709$	1.41755e24	0.833770	0.416885	+	0.908959i	$0.363122\pi$
$710$	−8.70207e22	−0.0505739
$711$	−4.03264e23	−0.231579
$712$	−1.35564e23	−0.0769244
$713$	3.21427e22	0.0180228
$714$	4.13196e24	2.28940
$715$	5.68701e23	0.311374
$716$	−1.49519e24	−0.808979
$717$	−1.10469e24	−0.590646
$718$	−5.26405e24	−2.78139
$719$	−4.81678e23	−0.251513	−0.125757	−	0.992061i	$-0.540136\pi$
$719$	−4.81678e23	−0.251513	−0.125757	+	0.992061i	$0.540136\pi$
$720$	−2.65671e23	−0.137094
$721$	3.75131e24	1.91308
$722$	−4.18786e24	−2.11070
$723$	−1.04934e24	−0.522685
$724$	5.19085e23	0.255541
$725$	−1.76789e24	−0.860168
$726$	2.84610e24	1.36864
$727$	1.10803e24	0.526634	0.263317	−	0.964709i	$-0.415184\pi$
$727$	1.10803e24	0.526634	0.263317	+	0.964709i	$0.415184\pi$
$728$	3.15079e23	0.148014
$729$	8.03557e23	0.373106
$730$	9.74350e23	0.447168
$731$	−2.14984e24	−0.975234
$732$	2.82362e24	1.26608
$733$	1.77744e24	0.787790	0.393895	−	0.919155i	$-0.371127\pi$
$733$	1.77744e24	0.787790	0.393895	+	0.919155i	$0.371127\pi$
$734$	2.27392e24	0.996227
$735$	−6.29366e22	−0.0272559
$736$	−6.96234e23	−0.298053
$737$	1.66766e24	0.705722
$738$	−3.25971e23	−0.136364
$739$	2.91360e24	1.20490	0.602452	−	0.798155i	$-0.294190\pi$
$739$	2.91360e24	1.20490	0.602452	+	0.798155i	$0.294190\pi$
$740$	−1.02422e24	−0.418718
$741$	−8.68534e24	−3.51020
$742$	−3.34911e23	−0.133812
$743$	1.43022e24	0.564935	0.282467	−	0.959277i	$-0.408847\pi$
$743$	1.43022e24	0.564935	0.282467	+	0.959277i	$0.408847\pi$
$744$	2.09951e22	0.00819877
$745$	8.27431e22	0.0319450
$746$	−3.86244e23	−0.147429
$747$	4.51215e23	0.170278
$748$	1.72399e24	0.643237
$749$	−1.90678e24	−0.703406
$750$	3.24482e24	1.18350
$751$	1.68756e24	0.608583	0.304291	−	0.952579i	$-0.401580\pi$
$751$	1.68756e24	0.608583	0.304291	+	0.952579i	$0.401580\pi$
$752$	5.13602e24	1.83136
$753$	−6.61026e23	−0.233057
$754$	7.82334e24	2.72732
$755$	−7.28835e23	−0.251235
$756$	−2.16955e24	−0.739494
$757$	−1.04121e24	−0.350932	−0.175466	−	0.984486i	$-0.556143\pi$
$757$	−1.04121e24	−0.350932	−0.175466	+	0.984486i	$0.556143\pi$
$758$	7.05696e24	2.35196
$759$	3.24123e23	0.106821
$760$	−1.46678e23	−0.0478023
$761$	−4.88953e24	−1.57579	−0.787893	−	0.615812i	$-0.788828\pi$
$761$	−4.88953e24	−1.57579	−0.787893	+	0.615812i	$0.788828\pi$
$762$	7.51687e24	2.39563
$763$	−3.18917e24	−1.00512
$764$	3.50717e24	1.09311
$765$	−6.61809e23	−0.203991
$766$	4.04217e24	1.23217
$767$	1.35923e24	0.409762
$768$	3.46856e24	1.03414
$769$	3.55271e24	1.04758	0.523789	−	0.851848i	$-0.324518\pi$
$769$	3.55271e24	1.04758	0.523789	+	0.851848i	$0.324518\pi$
$770$	7.82238e23	0.228122
$771$	−2.08877e24	−0.602461
$772$	3.62157e23	0.103312
$773$	−1.82819e24	−0.515817	−0.257908	−	0.966169i	$-0.583033\pi$
$773$	−1.82819e24	−0.515817	−0.257908	+	0.966169i	$0.583033\pi$
$774$	−1.38268e24	−0.385855
$775$	2.68551e23	0.0741247
$776$	2.08913e23	0.0570351
$777$	−4.43761e24	−1.19831
$778$	−1.51359e23	−0.0404279
$779$	1.46537e24	0.387150
$780$	−3.40512e24	−0.889874
$781$	−1.57311e23	−0.0406654
$782$	−1.63662e24	−0.418496
$783$	−2.86564e24	−0.724848
$784$	2.30616e23	0.0577037
$785$	−5.48226e23	−0.135696
$786$	2.41561e23	0.0591473
$787$	−2.07162e24	−0.501793	−0.250897	−	0.968014i	$-0.580725\pi$
$787$	−2.07162e24	−0.501793	−0.250897	+	0.968014i	$0.580725\pi$
$788$	−5.75872e24	−1.37992
$789$	−2.21612e24	−0.525338
$790$	1.38365e24	0.324487
$791$	4.59217e24	1.06541
$792$	5.89835e22	0.0135384
$793$	−8.50219e24	−1.93067
$794$	4.49687e24	1.01027
$795$	1.92541e23	0.0427959
$796$	6.85880e24	1.50830
$797$	−4.00415e24	−0.871194	−0.435597	−	0.900142i	$-0.643463\pi$
$797$	−4.00415e24	−0.871194	−0.435597	+	0.900142i	$0.643463\pi$
$798$	−1.19465e25	−2.57168
$799$	1.27943e25	2.72501
$800$	−5.81702e24	−1.22584
$801$	1.76847e24	0.368742
$802$	−1.06500e25	−2.19720
$803$	1.76137e24	0.359558
$804$	−9.98519e24	−2.01688
$805$	−3.81444e23	−0.0762371
$806$	−1.18840e24	−0.235026
$807$	1.18129e25	2.31170
$808$	1.55214e23	0.0300562
$809$	−4.91947e24	−0.942662	−0.471331	−	0.881956i	$-0.656226\pi$
$809$	−4.91947e24	−0.942662	−0.471331	+	0.881956i	$0.656226\pi$
$810$	3.53035e24	0.669414
$811$	2.38907e24	0.448283	0.224142	−	0.974557i	$-0.428042\pi$
$811$	2.38907e24	0.448283	0.224142	+	0.974557i	$0.428042\pi$
$812$	5.52745e24	1.02636
$813$	−6.63945e24	−1.22001
$814$	−3.60454e24	−0.655454
$815$	−3.80661e24	−0.685013
$816$	8.70433e24	1.55013
$817$	6.21573e24	1.09548
$818$	9.43182e24	1.64510
$819$	−4.11031e24	−0.709515
$820$	5.74505e23	0.0981467
$821$	6.74944e24	1.14117	0.570585	−	0.821238i	$-0.306716\pi$
$821$	6.74944e24	1.14117	0.570585	+	0.821238i	$0.306716\pi$
$822$	−1.55622e25	−2.60412
$823$	−3.28935e24	−0.544767	−0.272384	−	0.962189i	$-0.587812\pi$
$823$	−3.28935e24	−0.544767	−0.272384	+	0.962189i	$0.587812\pi$
$824$	−9.70537e23	−0.159085
$825$	2.70804e24	0.439336
$826$	1.86960e24	0.300205
$827$	1.14330e25	1.81703	0.908516	−	0.417849i	$-0.137216\pi$
$827$	1.14330e25	1.81703	0.908516	+	0.417849i	$0.137216\pi$
$828$	−5.40684e23	−0.0850522
$829$	3.49323e23	0.0543893	0.0271947	−	0.999630i	$-0.491343\pi$
$829$	3.49323e23	0.0543893	0.0271947	+	0.999630i	$0.491343\pi$
$830$	−1.54818e24	−0.238592
$831$	−1.24516e25	−1.89940
$832$	1.39281e25	2.10303
$833$	5.74485e23	0.0858610
$834$	−3.50805e24	−0.518985
$835$	5.91773e23	0.0866602
$836$	−4.98448e24	−0.722548
$837$	4.35304e23	0.0624635
$838$	9.22621e24	1.31054
$839$	9.49788e24	1.33552	0.667759	−	0.744377i	$-0.267254\pi$
$839$	9.49788e24	1.33552	0.667759	+	0.744377i	$0.267254\pi$
$840$	−2.49154e23	−0.0346812
$841$	4.37677e22	0.00603098
$842$	−7.46251e24	−1.01796
$843$	2.49833e24	0.337378
$844$	−1.24601e25	−1.66576
$845$	7.40174e24	0.979607
$846$	8.22870e24	1.07816
$847$	−6.05491e24	−0.785415
$848$	−7.05519e23	−0.0906033
$849$	2.34057e24	0.297582
$850$	−1.36739e25	−1.72121
$851$	1.75769e24	0.219049
$852$	9.41906e23	0.116217
$853$	−9.46706e24	−1.15651	−0.578254	−	0.815857i	$-0.696266\pi$
$853$	−9.46706e24	−1.15651	−0.578254	+	0.815857i	$0.696266\pi$
$854$	−1.16946e25	−1.41447
$855$	1.91346e24	0.229143
$856$	4.93323e23	0.0584930
$857$	−1.06232e25	−1.24715	−0.623575	−	0.781763i	$-0.714321\pi$
$857$	−1.06232e25	−1.24715	−0.623575	+	0.781763i	$0.714321\pi$
$858$	−1.19837e25	−1.39299
$859$	4.96784e24	0.571776	0.285888	−	0.958263i	$-0.407711\pi$
$859$	4.96784e24	0.571776	0.285888	+	0.958263i	$0.407711\pi$
$860$	2.43690e24	0.277716
$861$	2.48915e24	0.280883
$862$	−1.54925e25	−1.73105
$863$	−2.13298e24	−0.235990	−0.117995	−	0.993014i	$-0.537647\pi$
$863$	−2.13298e24	−0.235990	−0.117995	+	0.993014i	$0.537647\pi$
$864$	−9.42901e24	−1.03300
$865$	−1.13273e24	−0.122882
$866$	−8.57430e24	−0.921078
$867$	1.06151e25	1.12917
$868$	−8.39646e23	−0.0884461
$869$	2.50129e24	0.260913
$870$	−6.18643e24	−0.639037
$871$	3.00664e25	3.07558
$872$	8.25100e23	0.0835827
$873$	−2.72534e24	−0.273401
$874$	4.73189e24	0.470097
$875$	−6.90315e24	−0.679171
$876$	−1.05463e25	−1.02758
$877$	9.30749e24	0.898124	0.449062	−	0.893501i	$-0.351758\pi$
$877$	9.30749e24	0.898124	0.449062	+	0.893501i	$0.351758\pi$
$878$	2.52813e25	2.41600
$879$	1.20589e25	1.14131
$880$	1.64785e24	0.154460
$881$	−7.31924e24	−0.679471	−0.339735	−	0.940521i	$-0.610338\pi$
$881$	−7.31924e24	−0.679471	−0.339735	+	0.940521i	$0.610338\pi$
$882$	3.69483e23	0.0339713
$883$	−1.07748e25	−0.981168	−0.490584	−	0.871394i	$-0.663216\pi$
$883$	−1.07748e25	−0.981168	−0.490584	+	0.871394i	$0.663216\pi$
$884$	3.10819e25	2.80326
$885$	−1.07483e24	−0.0960113
$886$	1.46906e25	1.29973
$887$	1.86057e25	1.63041	0.815203	−	0.579176i	$-0.196625\pi$
$887$	1.86057e25	1.63041	0.815203	+	0.579176i	$0.196625\pi$
$888$	1.14810e24	0.0996479
$889$	−1.59917e25	−1.37477
$890$	−6.06787e24	−0.516679
$891$	6.38195e24	0.538261
$892$	−1.22862e25	−1.02640
$893$	−3.69914e25	−3.06100
$894$	−1.74357e24	−0.142913
$895$	−3.56016e24	−0.289051
$896$	1.93806e24	0.155865
$897$	5.84364e24	0.465530
$898$	−1.62644e24	−0.128348
$899$	−1.10904e24	−0.0866944
$900$	−4.51740e24	−0.349806
$901$	−1.75751e24	−0.134815
$902$	2.02186e24	0.153637
$903$	1.05583e25	0.794786
$904$	−1.18808e24	−0.0885963
$905$	1.23598e24	0.0913057
$906$	1.53581e25	1.12395
$907$	−1.29784e25	−0.940931	−0.470465	−	0.882418i	$-0.655914\pi$
$907$	−1.29784e25	−0.940931	−0.470465	+	0.882418i	$0.655914\pi$
$908$	1.88494e25	1.35384
$909$	−2.02481e24	−0.144076
$910$	1.41030e25	0.994169
$911$	−2.30174e25	−1.60750	−0.803749	−	0.594968i	$-0.797165\pi$
$911$	−2.30174e25	−1.60750	−0.803749	+	0.594968i	$0.797165\pi$
$912$	−2.51664e25	−1.74127
$913$	−2.79870e24	−0.191847
$914$	−4.51850e22	−0.00306868
$915$	6.72324e24	0.452375
$916$	−7.27527e24	−0.484995
$917$	−5.13906e23	−0.0339426
$918$	−2.21646e25	−1.45043
$919$	2.44384e24	0.158450	0.0792248	−	0.996857i	$-0.474756\pi$
$919$	2.44384e24	0.158450	0.0792248	+	0.996857i	$0.474756\pi$
$920$	9.86872e22	0.00633963
$921$	1.73793e25	1.10618
$922$	2.99219e25	1.88702
$923$	−2.83617e24	−0.177222
$924$	−8.46689e24	−0.524218
$925$	1.46854e25	0.900912
$926$	−1.01252e25	−0.615474
$927$	1.26610e25	0.762586
$928$	2.40227e25	1.43372
$929$	−2.89696e25	−1.71320	−0.856602	−	0.515977i	$-0.827429\pi$
$929$	−2.89696e25	−1.71320	−0.856602	+	0.515977i	$0.827429\pi$
$930$	9.39747e23	0.0550688
$931$	−1.66098e24	−0.0964477
$932$	1.30455e25	0.750627
$933$	9.80971e24	0.559322
$934$	−3.48333e25	−1.96810
$935$	4.10494e24	0.229830
$936$	1.06342e24	0.0590010
$937$	−2.02441e25	−1.11305	−0.556523	−	0.830832i	$-0.687865\pi$
$937$	−2.02441e25	−1.11305	−0.556523	+	0.830832i	$0.687865\pi$
$938$	4.13558e25	2.25326
$939$	1.15917e25	0.625876
$940$	−1.45026e25	−0.775997
$941$	1.75701e25	0.931668	0.465834	−	0.884872i	$-0.345754\pi$
$941$	1.75701e25	0.931668	0.465834	+	0.884872i	$0.345754\pi$
$942$	1.15523e25	0.607064
$943$	−9.85926e23	−0.0513446
$944$	3.93846e24	0.203266
$945$	−5.16585e24	−0.264224
$946$	8.57623e24	0.434732
$947$	−3.15487e25	−1.58492	−0.792458	−	0.609927i	$-0.791199\pi$
$947$	−3.15487e25	−1.58492	−0.792458	+	0.609927i	$0.791199\pi$
$948$	−1.49766e25	−0.745661
$949$	3.17559e25	1.56697
$950$	3.95348e25	1.93343
$951$	3.13689e25	1.52042
$952$	2.27427e24	0.109252
$953$	1.93333e25	0.920483	0.460242	−	0.887794i	$-0.347763\pi$
$953$	1.93333e25	0.920483	0.460242	+	0.887794i	$0.347763\pi$
$954$	−1.13035e24	−0.0533400
$955$	8.35081e24	0.390571
$956$	−1.14300e25	−0.529852
$957$	−1.11835e25	−0.513836
$958$	4.11847e25	1.87555
$959$	3.31076e25	1.49441
$960$	−1.10139e25	−0.492760
$961$	−2.23816e25	−0.992529
$962$	−6.49865e25	−2.85650
$963$	−6.43555e24	−0.280390
$964$	−1.08573e25	−0.468886
$965$	8.62320e23	0.0369136
$966$	8.03782e24	0.341062
$967$	2.08108e25	0.875315	0.437658	−	0.899142i	$-0.355808\pi$
$967$	2.08108e25	0.875315	0.437658	+	0.899142i	$0.355808\pi$
$968$	1.56652e24	0.0653126
$969$	−6.26916e25	−2.59094
$970$	9.35101e24	0.383088
$971$	−2.23459e25	−0.907476	−0.453738	−	0.891135i	$-0.649910\pi$
$971$	−2.23459e25	−0.907476	−0.453738	+	0.891135i	$0.649910\pi$
$972$	−1.92520e25	−0.775019
$973$	7.46317e24	0.297827
$974$	−4.87517e25	−1.92858
$975$	4.88234e25	1.91465
$976$	−2.46357e25	−0.957726
$977$	−2.11632e25	−0.815600	−0.407800	−	0.913071i	$-0.633704\pi$
$977$	−2.11632e25	−0.815600	−0.407800	+	0.913071i	$0.633704\pi$
$978$	8.02132e25	3.06454
$979$	−1.09691e25	−0.415450
$980$	−6.51193e23	−0.0244505
$981$	−1.07637e25	−0.400659
$982$	3.07995e25	1.13657
$983$	−2.86538e25	−1.04828	−0.524140	−	0.851632i	$-0.675613\pi$
$983$	−2.86538e25	−1.04828	−0.524140	+	0.851632i	$0.675613\pi$
$984$	−6.43993e23	−0.0233573
$985$	−1.37119e25	−0.493049
$986$	5.64696e25	2.01308
$987$	−6.28354e25	−2.22080
$988$	−8.98656e25	−3.14890
$989$	−4.18205e24	−0.145285
$990$	2.64011e24	0.0909334
$991$	−2.49524e25	−0.852091	−0.426045	−	0.904702i	$-0.640094\pi$
$991$	−2.49524e25	−0.852091	−0.426045	+	0.904702i	$0.640094\pi$
$992$	−3.64916e24	−0.123550
$993$	5.15770e25	1.73136
$994$	−3.90110e24	−0.129838
$995$	1.63313e25	0.538920
$996$	1.67574e25	0.548278
$997$	1.05625e25	0.342655	0.171328	−	0.985214i	$-0.445194\pi$
$997$	1.05625e25	0.342655	0.171328	+	0.985214i	$0.445194\pi$
$998$	3.98267e24	0.128105
$999$	2.38041e25	0.759182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.18.a.a.1.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.18.a.a.1.3	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q-519.142 q^{2} +13379.6 q^{3} +138436. q^{4} +329626. q^{5} -6.94591e6 q^{6} +1.47770e7 q^{7} -3.82310e6 q^{8} +4.98736e7 q^{9} +O(q^{10})\)	\(q-519.142 q^{2} +13379.6 q^{3} +138436. q^{4} +329626. q^{5} -6.94591e6 q^{6} +1.47770e7 q^{7} -3.82310e6 q^{8} +4.98736e7 q^{9} -1.71123e8 q^{10} -3.09346e8 q^{11} +1.85222e9 q^{12} -5.57722e9 q^{13} -7.67136e9 q^{14} +4.41027e9 q^{15} -1.61604e10 q^{16} -4.02569e10 q^{17} -2.58915e10 q^{18} +1.16393e11 q^{19} +4.56322e10 q^{20} +1.97711e11 q^{21} +1.60594e11 q^{22} -7.83110e10 q^{23} -5.11516e10 q^{24} -6.54286e11 q^{25} +2.89537e12 q^{26} -1.06056e12 q^{27} +2.04567e12 q^{28} +2.70202e12 q^{29} -2.28956e12 q^{30} -4.10449e11 q^{31} +8.89063e12 q^{32} -4.13892e12 q^{33} +2.08990e13 q^{34} +4.87089e12 q^{35} +6.90431e12 q^{36} -2.24450e13 q^{37} -6.04244e13 q^{38} -7.46209e13 q^{39} -1.26020e12 q^{40} +1.25899e13 q^{41} -1.02640e14 q^{42} +5.34031e13 q^{43} -4.28247e13 q^{44} +1.64397e13 q^{45} +4.06545e13 q^{46} -3.17815e14 q^{47} -2.16220e14 q^{48} -1.42705e13 q^{49} +3.39667e14 q^{50} -5.38621e14 q^{51} -7.72089e14 q^{52} +4.36573e13 q^{53} +5.50579e14 q^{54} -1.01969e14 q^{55} -5.64940e13 q^{56} +1.55729e15 q^{57} -1.40273e15 q^{58} -2.43711e14 q^{59} +6.10541e14 q^{60} +1.52445e15 q^{61} +2.13081e14 q^{62} +7.36983e14 q^{63} -2.49733e15 q^{64} -1.83840e15 q^{65} +2.14869e15 q^{66} -5.39093e15 q^{67} -5.57301e15 q^{68} -1.04777e15 q^{69} -2.52868e15 q^{70} +5.08528e14 q^{71} -1.90672e14 q^{72} -5.69386e15 q^{73} +1.16521e16 q^{74} -8.75409e15 q^{75} +1.61130e16 q^{76} -4.57121e15 q^{77} +3.87389e16 q^{78} -8.08573e15 q^{79} -5.32689e15 q^{80} -2.06305e16 q^{81} -6.53594e15 q^{82} +9.04716e15 q^{83} +2.73703e16 q^{84} -1.32697e16 q^{85} -2.77238e16 q^{86} +3.61520e16 q^{87} +1.18266e15 q^{88} +3.54591e16 q^{89} -8.53451e15 q^{90} -8.24146e16 q^{91} -1.08411e16 q^{92} -5.49165e15 q^{93} +1.64991e17 q^{94} +3.83661e16 q^{95} +1.18953e17 q^{96} -5.46450e16 q^{97} +7.40840e15 q^{98} -1.54282e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9} - 312719540 q^{10} - 45399620 q^{11} - 8621310628 q^{12} - 10510197306 q^{13} - 12286634640 q^{14} - 16443659490 q^{15} + 65383333632 q^{16} - 35705720330 q^{17} + 27658188862 q^{18} - 84895273414 q^{19} + 331348024336 q^{20} + 185190266362 q^{21} + 270540900120 q^{22} - 1096353793934 q^{23} + 1697198124384 q^{24} + 525715171346 q^{25} + 4272672484934 q^{26} - 3706093330604 q^{27} - 9883598189096 q^{28} - 4114009788386 q^{29} - 14194804268004 q^{30} + 3718266369468 q^{31} - 29197309605632 q^{32} - 16110579243626 q^{33} - 31423174598564 q^{34} + 13804822380504 q^{35} + 51950006703548 q^{36} - 58067881808868 q^{37} - 76590705469880 q^{38} + 69866971570764 q^{39} - 129282722434320 q^{40} - 74370388815170 q^{41} - 430581394397552 q^{42} - 127444248270174 q^{43} - 563872902913048 q^{44} - 602432292081270 q^{45} - 749727107945564 q^{47} - 17\!\cdots\!72 q^{48}+ \cdots + 35\!\cdots\!38 q^{99}+O(q^{100}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9 - 312719540 * q^10 - 45399620 * q^11 - 8621310628 * q^12 - 10510197306 * q^13 - 12286634640 * q^14 - 16443659490 * q^15 + 65383333632 * q^16 - 35705720330 * q^17 + 27658188862 * q^18 - 84895273414 * q^19 + 331348024336 * q^20 + 185190266362 * q^21 + 270540900120 * q^22 - 1096353793934 * q^23 + 1697198124384 * q^24 + 525715171346 * q^25 + 4272672484934 * q^26 - 3706093330604 * q^27 - 9883598189096 * q^28 - 4114009788386 * q^29 - 14194804268004 * q^30 + 3718266369468 * q^31 - 29197309605632 * q^32 - 16110579243626 * q^33 - 31423174598564 * q^34 + 13804822380504 * q^35 + 51950006703548 * q^36 - 58067881808868 * q^37 - 76590705469880 * q^38 + 69866971570764 * q^39 - 129282722434320 * q^40 - 74370388815170 * q^41 - 430581394397552 * q^42 - 127444248270174 * q^43 - 563872902913048 * q^44 - 602432292081270 * q^45 - 749727107945564 * q^47 - 1762369490938672 * q^48 - 560241909258462 * q^49 - 1212733967351616 * q^50 - 2013927378521294 * q^51 - 3438555393950964 * q^52 - 1954645162253818 * q^53 - 2748549190422938 * q^54 - 2426218557075404 * q^55 - 1321001371084560 * q^56 - 2335835167092904 * q^57 - 340295461037046 * q^58 - 1561709417167508 * q^59 - 7486616247365616 * q^60 - 679115861109266 * q^61 - 12552327168177062 * q^62 - 10591353756704576 * q^63 - 6775416249353536 * q^64 - 6252697705990982 * q^65 - 20881430274671372 * q^66 - 7577612038827396 * q^67 + 2901964856169680 * q^68 + 833228883389840 * q^69 - 10700966230255240 * q^70 + 25039332312392368 * q^71 - 7954969753997256 * q^72 - 18720848443128734 * q^73 - 6297551300657404 * q^74 + 22553223201966436 * q^75 + 34141945529937952 * q^76 + 35092380107507048 * q^77 + 27963841408286022 * q^78 + 965348846593408 * q^79 + 36943919850262880 * q^80 + 51275234750545798 * q^81 + 106728632435914846 * q^82 + 65089411455584544 * q^83 + 189770883431502392 * q^84 + 20919534362994588 * q^85 + 86205449672049764 * q^86 + 130649890213719716 * q^87 + 164304846335490592 * q^88 - 61322357257717500 * q^89 + 237420523836214152 * q^90 + 181977537844157150 * q^91 - 61586264776507392 * q^92 - 71304974484877430 * q^93 - 14005510384703054 * q^94 + 123323286964112684 * q^95 + 566787465801380768 * q^96 - 67350702995984898 * q^97 + 134333537201072600 * q^98 + 353912447692290838 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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