LMFDB - Embedded newform 23.18.a.a.1.6

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			1.6
Root			$87.1216$ 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)

$f(q)$	$=$	$q-174.243 q^{2} -15437.5 q^{3} -100711. q^{4} -1.53801e6 q^{5} +2.68988e6 q^{6} -1.10011e7 q^{7} +4.03867e7 q^{8} +1.09177e8 q^{9} +O(q^{10})$	\(q-174.243 q^{2} -15437.5 q^{3} -100711. q^{4} -1.53801e6 q^{5} +2.68988e6 q^{6} -1.10011e7 q^{7} +4.03867e7 q^{8} +1.09177e8 q^{9} +2.67988e8 q^{10} +7.06915e8 q^{11} +1.55473e9 q^{12} -1.64078e9 q^{13} +1.91687e9 q^{14} +2.37430e10 q^{15} +6.16333e9 q^{16} -9.14220e9 q^{17} -1.90233e10 q^{18} -3.02576e10 q^{19} +1.54895e11 q^{20} +1.69830e11 q^{21} -1.23175e11 q^{22} -7.83110e10 q^{23} -6.23470e11 q^{24} +1.60253e12 q^{25} +2.85895e11 q^{26} +3.08185e11 q^{27} +1.10794e12 q^{28} -1.73523e12 q^{29} -4.13706e12 q^{30} +4.09336e11 q^{31} -6.36748e12 q^{32} -1.09130e13 q^{33} +1.59297e12 q^{34} +1.69199e13 q^{35} -1.09953e13 q^{36} +2.45894e13 q^{37} +5.27219e12 q^{38} +2.53295e13 q^{39} -6.21151e13 q^{40} +4.13739e13 q^{41} -2.95918e13 q^{42} +4.40233e13 q^{43} -7.11943e13 q^{44} -1.67915e14 q^{45} +1.36452e13 q^{46} -3.15126e14 q^{47} -9.51465e13 q^{48} -1.11605e14 q^{49} -2.79230e14 q^{50} +1.41133e14 q^{51} +1.65245e14 q^{52} +3.38774e14 q^{53} -5.36992e13 q^{54} -1.08724e15 q^{55} -4.44300e14 q^{56} +4.67103e14 q^{57} +3.02352e14 q^{58} -1.65877e15 q^{59} -2.39119e15 q^{60} +1.88072e15 q^{61} -7.13240e13 q^{62} -1.20107e15 q^{63} +3.01650e14 q^{64} +2.52353e15 q^{65} +1.90152e15 q^{66} -3.94774e15 q^{67} +9.20722e14 q^{68} +1.20893e15 q^{69} -2.94817e15 q^{70} +9.31048e15 q^{71} +4.40929e15 q^{72} +1.50546e15 q^{73} -4.28454e15 q^{74} -2.47391e16 q^{75} +3.04728e15 q^{76} -7.77687e15 q^{77} -4.41350e15 q^{78} +2.52180e16 q^{79} -9.47925e15 q^{80} -1.88567e16 q^{81} -7.20913e15 q^{82} +2.69711e16 q^{83} -1.71038e16 q^{84} +1.40608e16 q^{85} -7.67076e15 q^{86} +2.67876e16 q^{87} +2.85499e16 q^{88} +7.01485e16 q^{89} +2.92580e16 q^{90} +1.80504e16 q^{91} +7.88680e15 q^{92} -6.31913e15 q^{93} +5.49086e16 q^{94} +4.65365e16 q^{95} +9.82981e16 q^{96} -6.70443e16 q^{97} +1.94465e16 q^{98} +7.71787e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−174.243	−0.481283	−0.240642	−	0.970614i	$-0.577358\pi$
$2$	−174.243	−0.481283	−0.240642	+	0.970614i	$0.577358\pi$
$3$	−15437.5	−1.35846	−0.679230	−	0.733926i	$-0.737686\pi$
$3$	−15437.5	−1.35846	−0.679230	+	0.733926i	$0.737686\pi$
$4$	−100711.	−0.768366
$5$	−1.53801e6	−1.76082	−0.880408	−	0.474218i	$-0.842731\pi$
$5$	−1.53801e6	−1.76082	−0.880408	+	0.474218i	$0.842731\pi$
$6$	2.68988e6	0.653804
$7$	−1.10011e7	−0.721281	−0.360641	−	0.932705i	$-0.617442\pi$
$7$	−1.10011e7	−0.721281	−0.360641	+	0.932705i	$0.617442\pi$
$8$	4.03867e7	0.851085
$9$	1.09177e8	0.845413
$10$	2.67988e8	0.847451
$11$	7.06915e8	0.994327	0.497163	−	0.867657i	$-0.334375\pi$
$11$	7.06915e8	0.994327	0.497163	+	0.867657i	$0.334375\pi$
$12$	1.55473e9	1.04379
$13$	−1.64078e9	−0.557868	−0.278934	−	0.960310i	$-0.589981\pi$
$13$	−1.64078e9	−0.557868	−0.278934	+	0.960310i	$0.589981\pi$
$14$	1.91687e9	0.347141
$15$	2.37430e10	2.39200
$16$	6.16333e9	0.358753
$17$	−9.14220e9	−0.317859	−0.158930	−	0.987290i	$-0.550804\pi$
$17$	−9.14220e9	−0.317859	−0.158930	+	0.987290i	$0.550804\pi$
$18$	−1.90233e10	−0.406883
$19$	−3.02576e10	−0.408723	−0.204362	−	0.978895i	$-0.565512\pi$
$19$	−3.02576e10	−0.408723	−0.204362	+	0.978895i	$0.565512\pi$
$20$	1.54895e11	1.35295
$21$	1.69830e11	0.979831
$22$	−1.23175e11	−0.478553
$23$	−7.83110e10	−0.208514
$23$	−7.83110e10	−0.208514
$24$	−6.23470e11	−1.15617
$25$	1.60253e12	2.10047
$26$	2.85895e11	0.268493
$27$	3.08185e11	0.210000
$28$	1.10794e12	0.554208
$29$	−1.73523e12	−0.644130	−0.322065	−	0.946718i	$-0.604377\pi$
$29$	−1.73523e12	−0.644130	−0.322065	+	0.946718i	$0.604377\pi$
$30$	−4.13706e12	−1.15123
$31$	4.09336e11	0.0861997	0.0430998	−	0.999071i	$-0.486277\pi$
$31$	4.09336e11	0.0861997	0.0430998	+	0.999071i	$0.486277\pi$
$32$	−6.36748e12	−1.02375
$33$	−1.09130e13	−1.35075
$34$	1.59297e12	0.152980
$35$	1.69199e13	1.27004
$36$	−1.09953e13	−0.649587
$37$	2.45894e13	1.15089	0.575445	−	0.817840i	$-0.304829\pi$
$37$	2.45894e13	1.15089	0.575445	+	0.817840i	$0.304829\pi$
$38$	5.27219e12	0.196712
$39$	2.53295e13	0.757841
$40$	−6.21151e13	−1.49860
$41$	4.13739e13	0.809215	0.404607	−	0.914490i	$-0.367408\pi$
$41$	4.13739e13	0.809215	0.404607	+	0.914490i	$0.367408\pi$
$42$	−2.95918e13	−0.471577
$43$	4.40233e13	0.574382	0.287191	−	0.957873i	$-0.407279\pi$
$43$	4.40233e13	0.574382	0.287191	+	0.957873i	$0.407279\pi$
$44$	−7.11943e13	−0.764007
$45$	−1.67915e14	−1.48862
$46$	1.36452e13	0.100355
$47$	−3.15126e14	−1.93042	−0.965212	−	0.261468i	$-0.915793\pi$
$47$	−3.15126e14	−1.93042	−0.965212	+	0.261468i	$0.915793\pi$
$48$	−9.51465e13	−0.487351
$49$	−1.11605e14	−0.479754
$50$	−2.79230e14	−1.01092
$51$	1.41133e14	0.431799
$52$	1.65245e14	0.428647
$53$	3.38774e14	0.747421	0.373710	−	0.927545i	$-0.378085\pi$
$53$	3.38774e14	0.747421	0.373710	+	0.927545i	$0.378085\pi$
$54$	−5.36992e13	−0.101070
$55$	−1.08724e15	−1.75083
$56$	−4.44300e14	−0.613872
$57$	4.67103e14	0.555234
$58$	3.02352e14	0.310009
$59$	−1.65877e15	−1.47077	−0.735385	−	0.677649i	$-0.762999\pi$
$59$	−1.65877e15	−1.47077	−0.735385	+	0.677649i	$0.762999\pi$
$60$	−2.39119e15	−1.83793
$61$	1.88072e15	1.25609	0.628043	−	0.778179i	$-0.283856\pi$
$61$	1.88072e15	1.25609	0.628043	+	0.778179i	$0.283856\pi$
$62$	−7.13240e13	−0.0414865
$63$	−1.20107e15	−0.609780
$64$	3.01650e14	0.133960
$65$	2.52353e15	0.982302
$66$	1.90152e15	0.650095
$67$	−3.94774e15	−1.18772	−0.593858	−	0.804570i	$-0.702396\pi$
$67$	−3.94774e15	−1.18772	−0.593858	+	0.804570i	$0.702396\pi$
$68$	9.20722e14	0.244232
$69$	1.20893e15	0.283258
$70$	−2.94817e15	−0.611250
$71$	9.31048e15	1.71110	0.855552	−	0.517717i	$-0.173218\pi$
$71$	9.31048e15	1.71110	0.855552	+	0.517717i	$0.173218\pi$
$72$	4.40929e15	0.719519
$73$	1.50546e15	0.218486	0.109243	−	0.994015i	$-0.465157\pi$
$73$	1.50546e15	0.218486	0.109243	+	0.994015i	$0.465157\pi$
$74$	−4.28454e15	−0.553904
$75$	−2.47391e16	−2.85340
$76$	3.04728e15	0.314049
$77$	−7.77687e15	−0.717189
$78$	−4.41350e15	−0.364736
$79$	2.52180e16	1.87017	0.935084	−	0.354427i	$-0.115324\pi$
$79$	2.52180e16	1.87017	0.935084	+	0.354427i	$0.115324\pi$
$80$	−9.47925e15	−0.631698
$81$	−1.88567e16	−1.13069
$82$	−7.20913e15	−0.389462
$83$	2.69711e16	1.31442	0.657211	−	0.753707i	$-0.271736\pi$
$83$	2.69711e16	1.31442	0.657211	+	0.753707i	$0.271736\pi$
$84$	−1.71038e16	−0.752869
$85$	1.40608e16	0.559691
$86$	−7.67076e15	−0.276440
$87$	2.67876e16	0.875025
$88$	2.85499e16	0.846257
$89$	7.01485e16	1.88888	0.944438	−	0.328689i	$-0.106607\pi$
$89$	7.01485e16	1.88888	0.944438	+	0.328689i	$0.106607\pi$
$90$	2.92580e16	0.716446
$91$	1.80504e16	0.402380
$92$	7.88680e15	0.160215
$93$	−6.31913e15	−0.117099
$94$	5.49086e16	0.929081
$95$	4.65365e16	0.719686
$96$	9.82981e16	1.39072
$97$	−6.70443e16	−0.868564	−0.434282	−	0.900777i	$-0.642998\pi$
$97$	−6.70443e16	−0.868564	−0.434282	+	0.900777i	$0.642998\pi$
$98$	1.94465e16	0.230898
$99$	7.71787e16	0.840617
$100$	−1.61393e17	−1.61393
$101$	7.63711e16	0.701774	0.350887	−	0.936418i	$-0.385880\pi$
$101$	7.63711e16	0.701774	0.350887	+	0.936418i	$0.385880\pi$
$102$	−2.45914e16	−0.207818
$103$	−8.68652e16	−0.675662	−0.337831	−	0.941207i	$-0.609693\pi$
$103$	−8.68652e16	−0.675662	−0.337831	+	0.941207i	$0.609693\pi$
$104$	−6.62656e16	−0.474793
$105$	−2.61201e17	−1.72530
$106$	−5.90291e16	−0.359721
$107$	1.02925e17	0.579108	0.289554	−	0.957162i	$-0.406493\pi$
$107$	1.02925e17	0.579108	0.289554	+	0.957162i	$0.406493\pi$
$108$	−3.10377e16	−0.161357
$109$	−2.36351e17	−1.13614	−0.568071	−	0.822979i	$-0.692310\pi$
$109$	−2.36351e17	−1.13614	−0.568071	+	0.822979i	$0.692310\pi$
$110$	1.89444e17	0.842643
$111$	−3.79600e17	−1.56344
$112$	−6.78037e16	−0.258762
$113$	6.32322e16	0.223754	0.111877	−	0.993722i	$-0.464314\pi$
$113$	6.32322e16	0.223754	0.111877	+	0.993722i	$0.464314\pi$
$114$	−8.13895e16	−0.267225
$115$	1.20443e17	0.367155
$116$	1.74757e17	0.494928
$117$	−1.79135e17	−0.471629
$118$	2.89030e17	0.707858
$119$	1.00575e17	0.229266
$120$	9.58902e17	2.03579
$121$	−5.71872e15	−0.0113142
$122$	−3.27702e17	−0.604534
$123$	−6.38711e17	−1.09929
$124$	−4.12248e16	−0.0662329
$125$	−1.29130e18	−1.93772
$126$	2.09278e17	0.293477
$127$	−4.95908e17	−0.650234	−0.325117	−	0.945674i	$-0.605404\pi$
$127$	−4.95908e17	−0.650234	−0.325117	+	0.945674i	$0.605404\pi$
$128$	7.82038e17	0.959275
$129$	−6.79610e17	−0.780274
$130$	−4.39708e17	−0.472766
$131$	−1.92323e18	−1.93743	−0.968713	−	0.248184i	$-0.920166\pi$
$131$	−1.92323e18	−1.93743	−0.968713	+	0.248184i	$0.920166\pi$
$132$	1.09906e18	1.03787
$133$	3.32868e17	0.294804
$134$	6.87867e17	0.571628
$135$	−4.73992e17	−0.369772
$136$	−3.69223e17	−0.270525
$137$	−3.66683e17	−0.252444	−0.126222	−	0.992002i	$-0.540285\pi$
$137$	−3.66683e17	−0.252444	−0.126222	+	0.992002i	$0.540285\pi$
$138$	−2.10647e17	−0.136328
$139$	1.25532e18	0.764060	0.382030	−	0.924150i	$-0.375225\pi$
$139$	1.25532e18	0.764060	0.382030	+	0.924150i	$0.375225\pi$
$140$	−1.70402e18	−0.975858
$141$	4.86477e18	2.62240
$142$	−1.62229e18	−0.823526
$143$	−1.15989e18	−0.554703
$144$	6.72892e17	0.303294
$145$	2.66880e18	1.13419
$146$	−2.62316e17	−0.105154
$147$	1.72291e18	0.651726
$148$	−2.47643e18	−0.884305
$149$	−4.87316e17	−0.164334	−0.0821670	−	0.996619i	$-0.526184\pi$
$149$	−4.87316e17	−0.164334	−0.0821670	+	0.996619i	$0.526184\pi$
$150$	4.31062e18	1.37330
$151$	5.77915e18	1.74004	0.870021	−	0.493015i	$-0.164105\pi$
$151$	5.77915e18	1.74004	0.870021	+	0.493015i	$0.164105\pi$
$152$	−1.22200e18	−0.347858
$153$	−9.98115e17	−0.268722
$154$	1.35507e18	0.345171
$155$	−6.29562e17	−0.151782
$156$	−2.55097e18	−0.582300
$157$	6.23817e17	0.134868	0.0674342	−	0.997724i	$-0.478519\pi$
$157$	6.23817e17	0.134868	0.0674342	+	0.997724i	$0.478519\pi$
$158$	−4.39407e18	−0.900081
$159$	−5.22983e18	−1.01534
$160$	9.79324e18	1.80263
$161$	8.61510e17	0.150397
$162$	3.28566e18	0.544182
$163$	−1.76669e18	−0.277693	−0.138846	−	0.990314i	$-0.544339\pi$
$163$	−1.76669e18	−0.277693	−0.138846	+	0.990314i	$0.544339\pi$
$164$	−4.16682e18	−0.621773
$165$	1.67843e19	2.37843
$166$	−4.69953e18	−0.632610
$167$	3.18177e18	0.406986	0.203493	−	0.979076i	$-0.434771\pi$
$167$	3.18177e18	0.406986	0.203493	+	0.979076i	$0.434771\pi$
$168$	6.85888e18	0.833920
$169$	−5.95826e18	−0.688783
$170$	−2.45000e18	−0.269370
$171$	−3.30343e18	−0.345540
$172$	−4.43364e18	−0.441335
$173$	−1.27471e19	−1.20787	−0.603935	−	0.797033i	$-0.706402\pi$
$173$	−1.27471e19	−1.20787	−0.603935	+	0.797033i	$0.706402\pi$
$174$	−4.66756e18	−0.421135
$175$	−1.76297e19	−1.51503
$176$	4.35695e18	0.356718
$177$	2.56073e19	1.99798
$178$	−1.22229e19	−0.909085
$179$	1.87195e19	1.32753	0.663765	−	0.747941i	$-0.268958\pi$
$179$	1.87195e19	1.32753	0.663765	+	0.747941i	$0.268958\pi$
$180$	1.69109e19	1.14380
$181$	9.54928e18	0.616173	0.308086	−	0.951358i	$-0.400311\pi$
$181$	9.54928e18	0.616173	0.308086	+	0.951358i	$0.400311\pi$
$182$	−3.14517e18	−0.193659
$183$	−2.90336e19	−1.70634
$184$	−3.16272e18	−0.177464
$185$	−3.78188e19	−2.02650
$186$	1.10107e18	0.0563577
$187$	−6.46275e18	−0.316056
$188$	3.17368e19	1.48327
$189$	−3.39039e18	−0.151469
$190$	−8.10867e18	−0.346373
$191$	−3.33369e19	−1.36189	−0.680945	−	0.732335i	$-0.738431\pi$
$191$	−3.33369e19	−1.36189	−0.680945	+	0.732335i	$0.738431\pi$
$192$	−4.65673e18	−0.181979
$193$	−1.25082e19	−0.467688	−0.233844	−	0.972274i	$-0.575130\pi$
$193$	−1.25082e19	−0.467688	−0.233844	+	0.972274i	$0.575130\pi$
$194$	1.16820e19	0.418025
$195$	−3.89571e19	−1.33442
$196$	1.12399e19	0.368627
$197$	4.08608e19	1.28335	0.641673	−	0.766978i	$-0.278241\pi$
$197$	4.08608e19	1.28335	0.641673	+	0.766978i	$0.278241\pi$
$198$	−1.34479e19	−0.404575
$199$	−1.99036e19	−0.573696	−0.286848	−	0.957976i	$-0.592607\pi$
$199$	−1.99036e19	−0.573696	−0.286848	+	0.957976i	$0.592607\pi$
$200$	6.47209e19	1.78768
$201$	6.09433e19	1.61347
$202$	−1.33072e19	−0.337752
$203$	1.90895e19	0.464599
$204$	−1.42137e19	−0.331780
$205$	−6.36335e19	−1.42488
$206$	1.51357e19	0.325185
$207$	−8.54974e18	−0.176281
$208$	−1.01127e19	−0.200137
$209$	−2.13896e19	−0.406404
$210$	4.55124e19	0.830359
$211$	−3.15808e19	−0.553378	−0.276689	−	0.960960i	$-0.589237\pi$
$211$	−3.15808e19	−0.553378	−0.276689	+	0.960960i	$0.589237\pi$
$212$	−3.41184e19	−0.574293
$213$	−1.43731e20	−2.32447
$214$	−1.79340e19	−0.278715
$215$	−6.77082e19	−1.01138
$216$	1.24466e19	0.178728
$217$	−4.50316e18	−0.0621742
$218$	4.11826e19	0.546807
$219$	−2.32405e19	−0.296805
$220$	1.09497e20	1.34528
$221$	1.50003e19	0.177323
$222$	6.61427e19	0.752457
$223$	−4.86108e19	−0.532281	−0.266141	−	0.963934i	$-0.585749\pi$
$223$	−4.86108e19	−0.532281	−0.266141	+	0.963934i	$0.585749\pi$
$224$	7.00496e19	0.738409
$225$	1.74959e20	1.77576
$226$	−1.10178e19	−0.107689
$227$	3.57871e19	0.336905	0.168452	−	0.985710i	$-0.446123\pi$
$227$	3.57871e19	0.336905	0.168452	+	0.985710i	$0.446123\pi$
$228$	−4.70425e19	−0.426623
$229$	−4.02299e19	−0.351518	−0.175759	−	0.984433i	$-0.556238\pi$
$229$	−4.02299e19	−0.351518	−0.175759	+	0.984433i	$0.556238\pi$
$230$	−2.09864e19	−0.176706
$231$	1.20056e20	0.974272
$232$	−7.00801e19	−0.548210
$233$	1.84506e20	1.39150	0.695752	−	0.718282i	$-0.255071\pi$
$233$	1.84506e20	1.39150	0.695752	+	0.718282i	$0.255071\pi$
$234$	3.12130e19	0.226987
$235$	4.84667e20	3.39912
$236$	1.67057e20	1.13009
$237$	−3.89303e20	−2.54055
$238$	−1.75244e19	−0.110342
$239$	3.48386e19	0.211680	0.105840	−	0.994383i	$-0.466247\pi$
$239$	3.48386e19	0.211680	0.105840	+	0.994383i	$0.466247\pi$
$240$	1.46336e20	0.858136
$241$	−2.85515e20	−1.61616	−0.808080	−	0.589073i	$-0.799493\pi$
$241$	−2.85515e20	−1.61616	−0.808080	+	0.589073i	$0.799493\pi$
$242$	9.96449e17	0.00544533
$243$	2.51302e20	1.32600
$244$	−1.89409e20	−0.965134
$245$	1.71650e20	0.844758
$246$	1.11291e20	0.529068
$247$	4.96461e19	0.228014
$248$	1.65317e19	0.0733633
$249$	−4.16367e20	−1.78559
$250$	2.25000e20	0.932595
$251$	−1.28128e20	−0.513354	−0.256677	−	0.966497i	$-0.582628\pi$
$251$	−1.28128e20	−0.513354	−0.256677	+	0.966497i	$0.582628\pi$
$252$	1.20961e20	0.468535
$253$	−5.53592e19	−0.207331
$254$	8.64087e19	0.312947
$255$	−2.17064e20	−0.760318
$256$	−1.75803e20	−0.595643
$257$	−3.82858e20	−1.25489	−0.627445	−	0.778661i	$-0.715899\pi$
$257$	−3.82858e20	−1.25489	−0.627445	+	0.778661i	$0.715899\pi$
$258$	1.18417e20	0.375533
$259$	−2.70512e20	−0.830115
$260$	−2.54148e20	−0.754768
$261$	−1.89447e20	−0.544556
$262$	3.35110e20	0.932451
$263$	−7.87140e19	−0.212045	−0.106022	−	0.994364i	$-0.533812\pi$
$263$	−7.87140e19	−0.212045	−0.106022	+	0.994364i	$0.533812\pi$
$264$	−4.40740e20	−1.14961
$265$	−5.21037e20	−1.31607
$266$	−5.80001e19	−0.141884
$267$	−1.08292e21	−2.56596
$268$	3.97582e20	0.912601
$269$	7.51275e20	1.67072	0.835362	−	0.549700i	$-0.185258\pi$
$269$	7.51275e20	1.67072	0.835362	+	0.549700i	$0.185258\pi$
$270$	8.25898e19	0.177965
$271$	6.51396e20	1.36021	0.680106	−	0.733114i	$-0.261934\pi$
$271$	6.51396e20	1.36021	0.680106	+	0.733114i	$0.261934\pi$
$272$	−5.63464e19	−0.114033
$273$	−2.78654e20	−0.546616
$274$	6.38920e19	0.121497
$275$	1.13285e21	2.08855
$276$	−1.21753e20	−0.217646
$277$	−2.19587e20	−0.380653	−0.190326	−	0.981721i	$-0.560955\pi$
$277$	−2.19587e20	−0.380653	−0.190326	+	0.981721i	$0.560955\pi$
$278$	−2.18730e20	−0.367729
$279$	4.46900e19	0.0728743
$280$	6.83337e20	1.08091
$281$	−4.64666e20	−0.713078	−0.356539	−	0.934281i	$-0.616043\pi$
$281$	−4.64666e20	−0.713078	−0.356539	+	0.934281i	$0.616043\pi$
$282$	−8.47653e20	−1.26212
$283$	4.84568e20	0.700116	0.350058	−	0.936728i	$-0.386162\pi$
$283$	4.84568e20	0.700116	0.350058	+	0.936728i	$0.386162\pi$
$284$	−9.37671e20	−1.31475
$285$	−7.18408e20	−0.977664
$286$	2.02103e20	0.266969
$287$	−4.55160e20	−0.583671
$288$	−6.95181e20	−0.865489
$289$	−7.43661e20	−0.898966
$290$	−4.65020e20	−0.545869
$291$	1.03500e21	1.17991
$292$	−1.51617e20	−0.167878
$293$	1.69694e21	1.82512	0.912558	−	0.408946i	$-0.134104\pi$
$293$	1.69694e21	1.82512	0.912558	+	0.408946i	$0.134104\pi$
$294$	−3.00205e20	−0.313665
$295$	2.55121e21	2.58976
$296$	9.93085e20	0.979506
$297$	2.17861e20	0.208809
$298$	8.49115e19	0.0790912
$299$	1.28491e20	0.116324
$300$	2.49151e21	2.19246
$301$	−4.84306e20	−0.414291
$302$	−1.00698e21	−0.837453
$303$	−1.17898e21	−0.953332
$304$	−1.86488e20	−0.146631
$305$	−2.89256e21	−2.21174
$306$	1.73915e20	0.129332
$307$	−1.01852e20	−0.0736704	−0.0368352	−	0.999321i	$-0.511728\pi$
$307$	−1.01852e20	−0.0736704	−0.0368352	+	0.999321i	$0.511728\pi$
$308$	7.83219e20	0.551064
$309$	1.34098e21	0.917860
$310$	1.09697e20	0.0730500
$311$	7.45533e20	0.483063	0.241531	−	0.970393i	$-0.422350\pi$
$311$	7.45533e20	0.483063	0.241531	+	0.970393i	$0.422350\pi$
$312$	1.02298e21	0.644988
$313$	−2.61216e21	−1.60278	−0.801389	−	0.598143i	$-0.795905\pi$
$313$	−2.61216e21	−1.60278	−0.801389	+	0.598143i	$0.795905\pi$
$314$	−1.08696e20	−0.0649099
$315$	1.84726e21	1.07371
$316$	−2.53974e21	−1.43697
$317$	3.94333e20	0.217200	0.108600	−	0.994086i	$-0.465363\pi$
$317$	3.94333e20	0.217200	0.108600	+	0.994086i	$0.465363\pi$
$318$	9.11262e20	0.488667
$319$	−1.22666e21	−0.640476
$320$	−4.63941e20	−0.235878
$321$	−1.58891e21	−0.786695
$322$	−1.50112e20	−0.0723838
$323$	2.76621e20	0.129916
$324$	1.89908e21	0.868784
$325$	−2.62940e21	−1.17179
$326$	3.07833e20	0.133649
$327$	3.64868e21	1.54340
$328$	1.67095e21	0.688711
$329$	3.46675e21	1.39238
$330$	−2.92455e21	−1.14470
$331$	7.10781e20	0.271143	0.135571	−	0.990768i	$-0.456713\pi$
$331$	7.10781e20	0.271143	0.135571	+	0.990768i	$0.456713\pi$
$332$	−2.71629e21	−1.00996
$333$	2.68459e21	0.972977
$334$	−5.54402e20	−0.195875
$335$	6.07166e21	2.09135
$336$	1.04672e21	0.351517
$337$	2.49577e21	0.817243	0.408621	−	0.912704i	$-0.366010\pi$
$337$	2.49577e21	0.817243	0.408621	+	0.912704i	$0.366010\pi$
$338$	1.03819e21	0.331500
$339$	−9.76148e20	−0.303961
$340$	−1.41608e21	−0.430048
$341$	2.89366e20	0.0857106
$342$	5.75600e20	0.166303
$343$	3.78699e21	1.06732
$344$	1.77795e21	0.488848
$345$	−1.85934e21	−0.498766
$346$	2.22110e21	0.581328
$347$	−1.12059e21	−0.286185	−0.143092	−	0.989709i	$-0.545705\pi$
$347$	−1.12059e21	−0.286185	−0.143092	+	0.989709i	$0.545705\pi$
$348$	−2.69782e21	−0.672340
$349$	−3.44088e21	−0.836860	−0.418430	−	0.908249i	$-0.637420\pi$
$349$	−3.44088e21	−0.836860	−0.418430	+	0.908249i	$0.637420\pi$
$350$	3.07185e21	0.729159
$351$	−5.05664e20	−0.117152
$352$	−4.50126e21	−1.01794
$353$	8.41891e20	0.185854	0.0929268	−	0.995673i	$-0.470378\pi$
$353$	8.41891e20	0.185854	0.0929268	+	0.995673i	$0.470378\pi$
$354$	−4.46191e21	−0.961596
$355$	−1.43196e22	−3.01294
$356$	−7.06475e21	−1.45135
$357$	−1.55262e21	−0.311448
$358$	−3.26175e21	−0.638918
$359$	9.81186e21	1.87693	0.938466	−	0.345371i	$-0.112247\pi$
$359$	9.81186e21	1.87693	0.938466	+	0.345371i	$0.112247\pi$
$360$	−6.78152e21	−1.26694
$361$	−4.56486e21	−0.832945
$362$	−1.66390e21	−0.296554
$363$	8.82829e19	0.0153699
$364$	−1.81788e21	−0.309175
$365$	−2.31541e21	−0.384714
$366$	5.05890e21	0.821234
$367$	−6.27915e21	−0.995954	−0.497977	−	0.867190i	$-0.665924\pi$
$367$	−6.27915e21	−0.995954	−0.497977	+	0.867190i	$0.665924\pi$
$368$	−4.82656e20	−0.0748051
$369$	4.51707e21	0.684121
$370$	6.58966e21	0.975323
$371$	−3.72690e21	−0.539101
$372$	6.36408e20	0.0899747
$373$	1.35466e21	0.187200	0.0935998	−	0.995610i	$-0.470163\pi$
$373$	1.35466e21	0.187200	0.0935998	+	0.995610i	$0.470163\pi$
$374$	1.12609e21	0.152112
$375$	1.99345e22	2.63232
$376$	−1.27269e22	−1.64296
$377$	2.84713e21	0.359340
$378$	5.90753e20	0.0728996
$379$	3.65231e21	0.440691	0.220346	−	0.975422i	$-0.429281\pi$
$379$	3.65231e21	0.440691	0.220346	+	0.975422i	$0.429281\pi$
$380$	−4.68675e21	−0.552982
$381$	7.65559e21	0.883317
$382$	5.80873e21	0.655455
$383$	−1.39443e22	−1.53889	−0.769446	−	0.638711i	$-0.779468\pi$
$383$	−1.39443e22	−1.53889	−0.769446	+	0.638711i	$0.779468\pi$
$384$	−1.20727e22	−1.30314
$385$	1.19609e22	1.26284
$386$	2.17946e21	0.225090
$387$	4.80632e21	0.485590
$388$	6.75211e21	0.667375
$389$	5.05093e21	0.488427	0.244214	−	0.969721i	$-0.421470\pi$
$389$	5.05093e21	0.488427	0.244214	+	0.969721i	$0.421470\pi$
$390$	6.78800e21	0.642233
$391$	7.15934e20	0.0662782
$392$	−4.50737e21	−0.408311
$393$	2.96899e22	2.63192
$394$	−7.11971e21	−0.617653
$395$	−3.87855e22	−3.29302
$396$	−7.77276e21	−0.645902
$397$	−1.33632e22	−1.08690	−0.543451	−	0.839441i	$-0.682883\pi$
$397$	−1.33632e22	−1.08690	−0.543451	+	0.839441i	$0.682883\pi$
$398$	3.46808e21	0.276110
$399$	−5.13866e21	−0.400480
$400$	9.87693e21	0.753550
$401$	−1.22829e22	−0.917430	−0.458715	−	0.888583i	$-0.651690\pi$
$401$	−1.22829e22	−0.917430	−0.458715	+	0.888583i	$0.651690\pi$
$402$	−1.06190e22	−0.776534
$403$	−6.71630e20	−0.0480880
$404$	−7.69144e21	−0.539220
$405$	2.90018e22	1.99094
$406$	−3.32622e21	−0.223604
$407$	1.73826e22	1.14436
$408$	5.69988e21	0.367498
$409$	−1.59477e22	−1.00705	−0.503523	−	0.863982i	$-0.667963\pi$
$409$	−1.59477e22	−1.00705	−0.503523	+	0.863982i	$0.667963\pi$
$410$	1.10877e22	0.685770
$411$	5.66067e21	0.342935
$412$	8.74831e21	0.519156
$413$	1.82484e22	1.06084
$414$	1.48973e21	0.0848410
$415$	−4.14818e22	−2.31445
$416$	1.04476e22	0.571116
$417$	−1.93790e22	−1.03794
$418$	3.72699e21	0.195596
$419$	1.51804e22	0.780666	0.390333	−	0.920674i	$-0.372360\pi$
$419$	1.51804e22	0.780666	0.390333	+	0.920674i	$0.372360\pi$
$420$	2.63058e22	1.32566
$421$	3.50693e22	1.73193	0.865963	−	0.500107i	$-0.166706\pi$
$421$	3.50693e22	1.73193	0.865963	+	0.500107i	$0.166706\pi$
$422$	5.50274e21	0.266332
$423$	−3.44045e22	−1.63201
$424$	1.36820e22	0.636119
$425$	−1.46507e22	−0.667654
$426$	2.50441e22	1.11873
$427$	−2.06900e22	−0.905991
$428$	−1.03657e22	−0.444967
$429$	1.79058e22	0.753542
$430$	1.17977e22	0.486760
$431$	3.00469e22	1.21546	0.607732	−	0.794142i	$-0.292079\pi$
$431$	3.00469e22	1.21546	0.607732	+	0.794142i	$0.292079\pi$
$432$	1.89945e21	0.0753382
$433$	3.01629e22	1.17307	0.586537	−	0.809922i	$-0.300491\pi$
$433$	3.01629e22	1.17307	0.586537	+	0.809922i	$0.300491\pi$
$434$	7.84646e20	0.0299234
$435$	−4.11996e22	−1.54076
$436$	2.38033e22	0.872974
$437$	2.36950e21	0.0852247
$438$	4.04951e21	0.142847
$439$	5.19020e22	1.79571	0.897854	−	0.440293i	$-0.145126\pi$
$439$	5.19020e22	1.79571	0.897854	+	0.440293i	$0.145126\pi$
$440$	−4.39100e22	−1.49010
$441$	−1.21847e22	−0.405590
$442$	−2.61370e21	−0.0853428
$443$	5.62313e22	1.80114	0.900568	−	0.434715i	$-0.143151\pi$
$443$	5.62313e22	1.80114	0.900568	+	0.434715i	$0.143151\pi$
$444$	3.82300e22	1.20129
$445$	−1.07889e23	−3.32596
$446$	8.47010e21	0.256178
$447$	7.52295e21	0.223241
$448$	−3.31850e21	−0.0966226
$449$	−3.03232e22	−0.866327	−0.433163	−	0.901315i	$-0.642603\pi$
$449$	−3.03232e22	−0.866327	−0.433163	+	0.901315i	$0.642603\pi$
$450$	−3.04855e22	−0.854646
$451$	2.92478e22	0.804624
$452$	−6.36820e21	−0.171925
$453$	−8.92157e22	−2.36378
$454$	−6.23567e21	−0.162147
$455$	−2.77617e22	−0.708516
$456$	1.88647e22	0.472552
$457$	−4.43999e22	−1.09168	−0.545839	−	0.837890i	$-0.683789\pi$
$457$	−4.43999e22	−1.09168	−0.545839	+	0.837890i	$0.683789\pi$
$458$	7.00979e21	0.169180
$459$	−2.81749e21	−0.0667505
$460$	−1.21300e22	−0.282110
$461$	7.43454e22	1.69745	0.848724	−	0.528837i	$-0.177372\pi$
$461$	7.43454e22	1.69745	0.848724	+	0.528837i	$0.177372\pi$
$462$	−2.09189e22	−0.468901
$463$	−2.78913e21	−0.0613805	−0.0306902	−	0.999529i	$-0.509771\pi$
$463$	−2.78913e21	−0.0613805	−0.0306902	+	0.999529i	$0.509771\pi$
$464$	−1.06948e22	−0.231084
$465$	9.71888e21	0.206189
$466$	−3.21489e22	−0.669708
$467$	−4.54657e22	−0.930017	−0.465008	−	0.885306i	$-0.653949\pi$
$467$	−4.54657e22	−0.930017	−0.465008	+	0.885306i	$0.653949\pi$
$468$	1.80409e22	0.362384
$469$	4.34297e22	0.856678
$470$	−8.44499e22	−1.63594
$471$	−9.63018e21	−0.183213
$472$	−6.69923e22	−1.25175
$473$	3.11207e22	0.571123
$474$	6.78335e22	1.22272
$475$	−4.84888e22	−0.858511
$476$	−1.01290e22	−0.176160
$477$	3.69863e22	0.631879
$478$	−6.07040e21	−0.101878
$479$	3.64844e22	0.601527	0.300764	−	0.953699i	$-0.402758\pi$
$479$	3.64844e22	0.601527	0.300764	+	0.953699i	$0.402758\pi$
$480$	−1.51183e23	−2.44880
$481$	−4.03458e22	−0.642045
$482$	4.97491e22	0.777831
$483$	−1.32996e22	−0.204309
$484$	5.75940e20	0.00869344
$485$	1.03115e23	1.52938
$486$	−4.37876e22	−0.638180
$487$	−4.19488e22	−0.600791	−0.300396	−	0.953815i	$-0.597119\pi$
$487$	−4.19488e22	−0.600791	−0.300396	+	0.953815i	$0.597119\pi$
$488$	7.59558e22	1.06904
$489$	2.72732e22	0.377234
$490$	−2.99088e22	−0.406568
$491$	1.30606e23	1.74490	0.872449	−	0.488705i	$-0.162531\pi$
$491$	1.30606e23	1.74490	0.872449	+	0.488705i	$0.162531\pi$
$492$	6.43254e22	0.844654
$493$	1.58638e22	0.204743
$494$	−8.65049e21	−0.109739
$495$	−1.18701e23	−1.48017
$496$	2.52287e21	0.0309244
$497$	−1.02426e23	−1.23419
$498$	7.25491e22	0.859375
$499$	−1.24575e22	−0.145070	−0.0725348	−	0.997366i	$-0.523109\pi$
$499$	−1.24575e22	−0.145070	−0.0725348	+	0.997366i	$0.523109\pi$
$500$	1.30048e23	1.48888
$501$	−4.91187e22	−0.552874
$502$	2.23254e22	0.247069
$503$	−4.75976e22	−0.517913	−0.258957	−	0.965889i	$-0.583379\pi$
$503$	−4.75976e22	−0.517913	−0.258957	+	0.965889i	$0.583379\pi$
$504$	−4.85072e22	−0.518975
$505$	−1.17459e23	−1.23570
$506$	9.64596e21	0.0997852
$507$	9.19808e22	0.935684
$508$	4.99436e22	0.499618
$509$	1.19177e23	1.17244	0.586220	−	0.810152i	$-0.300615\pi$
$509$	1.19177e23	1.17244	0.586220	+	0.810152i	$0.300615\pi$
$510$	3.78218e22	0.365928
$511$	−1.65618e22	−0.157590
$512$	−7.18708e22	−0.672602
$513$	−9.32496e21	−0.0858320
$514$	6.67104e22	0.603958
$515$	1.33599e23	1.18972
$516$	6.84444e22	0.599536
$517$	−2.22767e23	−1.91947
$518$	4.71349e22	0.399521
$519$	1.96784e23	1.64084
$520$	1.01917e23	0.836023
$521$	7.80440e22	0.629823	0.314912	−	0.949121i	$-0.398025\pi$
$521$	7.80440e22	0.629823	0.314912	+	0.949121i	$0.398025\pi$
$522$	3.30098e22	0.262086
$523$	−1.86357e23	−1.45573	−0.727867	−	0.685718i	$-0.759488\pi$
$523$	−1.86357e23	−1.45573	−0.727867	+	0.685718i	$0.759488\pi$
$524$	1.93691e23	1.48865
$525$	2.72158e23	2.05811
$526$	1.37154e22	0.102054
$527$	−3.74223e21	−0.0273993
$528$	−6.72604e22	−0.484587
$529$	6.13261e21	0.0434783
$530$	9.07873e22	0.633403
$531$	−1.81100e23	−1.24341
$532$	−3.35236e22	−0.226518
$533$	−6.78854e22	−0.451435
$534$	1.88691e23	1.23496
$535$	−1.58300e23	−1.01970
$536$	−1.59436e23	−1.01085
$537$	−2.88983e23	−1.80340
$538$	−1.30905e23	−0.804092
$539$	−7.88955e22	−0.477032
$540$	4.77363e22	0.284120
$541$	−4.59874e22	−0.269440	−0.134720	−	0.990884i	$-0.543014\pi$
$541$	−4.59874e22	−0.269440	−0.134720	+	0.990884i	$0.543014\pi$
$542$	−1.13501e23	−0.654647
$543$	−1.47417e23	−0.837046
$544$	5.82128e22	0.325407
$545$	3.63510e23	2.00054
$546$	4.85536e22	0.263077
$547$	−1.36939e23	−0.730525	−0.365263	−	0.930904i	$-0.619021\pi$
$547$	−1.36939e23	−0.730525	−0.365263	+	0.930904i	$0.619021\pi$
$548$	3.69291e22	0.193970
$549$	2.05330e23	1.06191
$550$	−1.97392e23	−1.00519
$551$	5.25039e22	0.263271
$552$	4.88245e22	0.241077
$553$	−2.77427e23	−1.34892
$554$	3.82616e22	0.183202
$555$	5.83828e23	2.75293
$556$	−1.26425e23	−0.587078
$557$	−2.84876e23	−1.30283	−0.651414	−	0.758722i	$-0.725824\pi$
$557$	−2.84876e23	−1.30283	−0.651414	+	0.758722i	$0.725824\pi$
$558$	−7.78693e21	−0.0350732
$559$	−7.22324e22	−0.320429
$560$	1.04283e23	0.455631
$561$	9.97689e22	0.429349
$562$	8.09648e22	0.343192
$563$	−2.48809e23	−1.03883	−0.519415	−	0.854522i	$-0.673850\pi$
$563$	−2.48809e23	−1.03883	−0.519415	+	0.854522i	$0.673850\pi$
$564$	−4.89937e23	−2.01497
$565$	−9.72517e22	−0.393990
$566$	−8.44327e22	−0.336954
$567$	2.07446e23	0.815545
$568$	3.76019e23	1.45630
$569$	−2.59646e23	−0.990666	−0.495333	−	0.868703i	$-0.664954\pi$
$569$	−2.59646e23	−0.990666	−0.495333	+	0.868703i	$0.664954\pi$
$570$	1.25178e23	0.470534
$571$	2.92277e23	1.08240	0.541199	−	0.840894i	$-0.317970\pi$
$571$	2.92277e23	1.08240	0.541199	+	0.840894i	$0.317970\pi$
$572$	1.16814e23	0.426215
$573$	5.14639e23	1.85007
$574$	7.93086e22	0.280911
$575$	−1.25496e23	−0.437978
$576$	3.29332e22	0.113251
$577$	1.21422e21	0.00411438	0.00205719	−	0.999998i	$-0.499345\pi$
$577$	1.21422e21	0.00411438	0.00205719	+	0.999998i	$0.499345\pi$
$578$	1.29578e23	0.432657
$579$	1.93095e23	0.635335
$580$	−2.68778e23	−0.871477
$581$	−2.96713e23	−0.948068
$582$	−1.80341e23	−0.567871
$583$	2.39484e23	0.743181
$584$	6.08005e22	0.185951
$585$	2.75511e23	0.830451
$586$	−2.95680e23	−0.878399
$587$	5.70412e22	0.167019	0.0835093	−	0.996507i	$-0.473387\pi$
$587$	5.70412e22	0.167019	0.0835093	+	0.996507i	$0.473387\pi$
$588$	−1.73516e23	−0.500764
$589$	−1.23855e22	−0.0352318
$590$	−4.44531e23	−1.24641
$591$	−6.30789e23	−1.74337
$592$	1.51553e23	0.412885
$593$	−3.78493e23	−1.01647	−0.508234	−	0.861219i	$-0.669701\pi$
$593$	−3.78493e23	−1.01647	−0.508234	+	0.861219i	$0.669701\pi$
$594$	−3.79608e22	−0.100496
$595$	−1.54685e23	−0.403695
$596$	4.90782e22	0.126269
$597$	3.07263e23	0.779342
$598$	−2.23887e22	−0.0559846
$599$	1.88742e23	0.465309	0.232654	−	0.972559i	$-0.425259\pi$
$599$	1.88742e23	0.465309	0.232654	+	0.972559i	$0.425259\pi$
$600$	−9.99130e23	−2.42849
$601$	3.00479e23	0.720081	0.360040	−	0.932937i	$-0.382763\pi$
$601$	3.00479e23	0.720081	0.360040	+	0.932937i	$0.382763\pi$
$602$	8.43871e22	0.199391
$603$	−4.31002e23	−1.00411
$604$	−5.82025e23	−1.33699
$605$	8.79545e21	0.0199222
$606$	2.05429e23	0.458823
$607$	−2.37816e23	−0.523765	−0.261883	−	0.965100i	$-0.584343\pi$
$607$	−2.37816e23	−0.523765	−0.261883	+	0.965100i	$0.584343\pi$
$608$	1.92665e23	0.418429
$609$	−2.94694e23	−0.631139
$610$	5.04008e23	1.06447
$611$	5.17052e23	1.07692
$612$	1.00522e23	0.206477
$613$	−1.29000e23	−0.261323	−0.130661	−	0.991427i	$-0.541710\pi$
$613$	−1.29000e23	−0.261323	−0.130661	+	0.991427i	$0.541710\pi$
$614$	1.77470e22	0.0354563
$615$	9.82342e23	1.93564
$616$	−3.14082e23	−0.610389
$617$	−6.38091e23	−1.22309	−0.611545	−	0.791209i	$-0.709452\pi$
$617$	−6.38091e23	−1.22309	−0.611545	+	0.791209i	$0.709452\pi$
$618$	−2.33657e23	−0.441751
$619$	−3.16253e23	−0.589744	−0.294872	−	0.955537i	$-0.595277\pi$
$619$	−3.16253e23	−0.589744	−0.294872	+	0.955537i	$0.595277\pi$
$620$	6.34040e22	0.116624
$621$	−2.41343e22	−0.0437881
$622$	−1.29904e23	−0.232490
$623$	−7.71714e23	−1.36241
$624$	1.56114e23	0.271878
$625$	7.63396e23	1.31150
$626$	4.55152e23	0.771391
$627$	3.30202e23	0.552084
$628$	−6.28254e22	−0.103628
$629$	−2.24801e23	−0.365821
$630$	−3.21872e23	−0.516759
$631$	2.32336e23	0.368016	0.184008	−	0.982925i	$-0.441093\pi$
$631$	2.32336e23	0.368016	0.184008	+	0.982925i	$0.441093\pi$
$632$	1.01847e24	1.59167
$633$	4.87529e23	0.751742
$634$	−6.87098e22	−0.104535
$635$	7.62711e23	1.14494
$636$	5.26703e23	0.780154
$637$	1.83120e23	0.267639
$638$	2.13737e23	0.308251
$639$	1.01649e24	1.44659
$640$	−1.20278e24	−1.68911
$641$	−3.17880e23	−0.440524	−0.220262	−	0.975441i	$-0.570691\pi$
$641$	−3.17880e23	−0.440524	−0.220262	+	0.975441i	$0.570691\pi$
$642$	2.76857e23	0.378623
$643$	1.42533e23	0.192363	0.0961817	−	0.995364i	$-0.469337\pi$
$643$	1.42533e23	0.192363	0.0961817	+	0.995364i	$0.469337\pi$
$644$	−8.67638e22	−0.115560
$645$	1.04525e24	1.37392
$646$	−4.81994e22	−0.0625266
$647$	9.61300e23	1.23076	0.615379	−	0.788231i	$-0.289003\pi$
$647$	9.61300e23	1.23076	0.615379	+	0.788231i	$0.289003\pi$
$648$	−7.61560e23	−0.962314
$649$	−1.17261e24	−1.46243
$650$	4.58155e23	0.563961
$651$	6.95177e22	0.0844611
$652$	1.77925e23	0.213370
$653$	1.59824e23	0.189182	0.0945909	−	0.995516i	$-0.469846\pi$
$653$	1.59824e23	0.189182	0.0945909	+	0.995516i	$0.469846\pi$
$654$	−6.35757e23	−0.742815
$655$	2.95794e24	3.41145
$656$	2.55001e23	0.290308
$657$	1.64361e23	0.184711
$658$	−6.04058e23	−0.670129
$659$	−9.51466e22	−0.104200	−0.0520999	−	0.998642i	$-0.516591\pi$
$659$	−9.51466e22	−0.104200	−0.0520999	+	0.998642i	$0.516591\pi$
$660$	−1.69037e24	−1.82750
$661$	−7.21749e23	−0.770325	−0.385162	−	0.922849i	$-0.625855\pi$
$661$	−7.21749e23	−0.770325	−0.385162	+	0.922849i	$0.625855\pi$
$662$	−1.23849e23	−0.130496
$663$	−2.31568e23	−0.240887
$664$	1.08927e24	1.11869
$665$	−5.11955e23	−0.519096
$666$	−4.67772e23	−0.468278
$667$	1.35887e23	0.134310
$668$	−3.20440e23	−0.312714
$669$	7.50430e23	0.723083
$670$	−1.05795e24	−1.00653
$671$	1.32951e24	1.24896
$672$	−1.08139e24	−1.00310
$673$	−9.69497e23	−0.888011	−0.444006	−	0.896024i	$-0.646443\pi$
$673$	−9.69497e23	−0.888011	−0.444006	+	0.896024i	$0.646443\pi$
$674$	−4.34872e23	−0.393325
$675$	4.93877e23	0.441099
$676$	6.00064e23	0.529238
$677$	9.29078e20	0.000809186 0	0.000404593	−	1.00000i	$-0.499871\pi$
$677$	9.29078e20	0.000809186 0	0.000404593		1.00000i	$0.499871\pi$
$678$	1.70087e23	0.146292
$679$	7.37563e23	0.626479
$680$	5.67868e23	0.476345
$681$	−5.52464e23	−0.457671
$682$	−5.04200e22	−0.0412511
$683$	−1.71829e24	−1.38842	−0.694210	−	0.719773i	$-0.744246\pi$
$683$	−1.71829e24	−1.38842	−0.694210	+	0.719773i	$0.744246\pi$
$684$	3.32693e23	0.265501
$685$	5.63961e23	0.444508
$686$	−6.59857e23	−0.513683
$687$	6.21050e23	0.477523
$688$	2.71330e23	0.206061
$689$	−5.55853e23	−0.416962
$690$	3.23977e23	0.240048
$691$	−8.07063e23	−0.590669	−0.295335	−	0.955394i	$-0.595431\pi$
$691$	−8.07063e23	−0.590669	−0.295335	+	0.955394i	$0.595431\pi$
$692$	1.28378e24	0.928087
$693$	−8.49053e23	−0.606321
$694$	1.95255e23	0.137736
$695$	−1.93069e24	−1.34537
$696$	1.08186e24	0.744721
$697$	−3.78249e23	−0.257216
$698$	5.99549e23	0.402767
$699$	−2.84831e24	−1.89030
$700$	1.77551e24	1.16410
$701$	2.24001e24	1.45093	0.725466	−	0.688258i	$-0.241624\pi$
$701$	2.24001e24	1.45093	0.725466	+	0.688258i	$0.241624\pi$
$702$	8.81085e22	0.0563835
$703$	−7.44018e23	−0.470395
$704$	2.13241e23	0.133200
$705$	−7.48205e24	−4.61757
$706$	−1.46694e23	−0.0894483
$707$	−8.40170e23	−0.506177
$708$	−2.57895e24	−1.53518
$709$	2.39348e23	0.140778	0.0703892	−	0.997520i	$-0.477576\pi$
$709$	2.39348e23	0.140778	0.0703892	+	0.997520i	$0.477576\pi$
$710$	2.49509e24	1.45008
$711$	2.75322e24	1.58106
$712$	2.83307e24	1.60760
$713$	−3.20555e22	−0.0179739
$714$	2.70534e23	0.149895
$715$	1.78392e24	0.976730
$716$	−1.88527e24	−1.02003
$717$	−5.37822e23	−0.287558
$718$	−1.70965e24	−0.903337
$719$	−3.71831e24	−1.94156	−0.970778	−	0.239979i	$-0.922859\pi$
$719$	−3.71831e24	−1.94156	−0.970778	+	0.239979i	$0.922859\pi$
$720$	−1.03491e24	−0.534045
$721$	9.55617e23	0.487342
$722$	7.95396e23	0.400883
$723$	4.40764e24	2.19549
$724$	−9.61720e23	−0.473446
$725$	−2.78076e24	−1.35298
$726$	−1.53827e22	−0.00739726
$727$	7.34275e23	0.348992	0.174496	−	0.984658i	$-0.444170\pi$
$727$	7.34275e23	0.348992	0.174496	+	0.984658i	$0.444170\pi$
$728$	7.28997e23	0.342459
$729$	−1.44432e24	−0.670623
$730$	4.03444e23	0.185157
$731$	−4.02469e23	−0.182572
$732$	2.92401e24	1.31110
$733$	−8.04273e23	−0.356467	−0.178234	−	0.983988i	$-0.557038\pi$
$733$	−8.04273e23	−0.356467	−0.178234	+	0.983988i	$0.557038\pi$
$734$	1.09410e24	0.479336
$735$	−2.64985e24	−1.14757
$736$	4.98644e23	0.213466
$737$	−2.79072e24	−1.18098
$738$	−7.87069e23	−0.329256
$739$	3.67229e24	1.51866	0.759328	−	0.650709i	$-0.225528\pi$
$739$	3.67229e24	1.51866	0.759328	+	0.650709i	$0.225528\pi$
$740$	3.80878e24	1.55710
$741$	−7.66412e23	−0.309747
$742$	6.49387e23	0.259460
$743$	2.63864e24	1.04226	0.521128	−	0.853478i	$-0.325511\pi$
$743$	2.63864e24	1.04226	0.521128	+	0.853478i	$0.325511\pi$
$744$	−2.55209e23	−0.0996610
$745$	7.49496e23	0.289362
$746$	−2.36040e23	−0.0900961
$747$	2.94462e24	1.11123
$748$	6.50872e23	0.242847
$749$	−1.13230e24	−0.417700
$750$	−3.47345e24	−1.26689
$751$	−4.35827e24	−1.57172	−0.785859	−	0.618405i	$-0.787779\pi$
$751$	−4.35827e24	−1.57172	−0.785859	+	0.618405i	$0.787779\pi$
$752$	−1.94223e24	−0.692545
$753$	1.97798e24	0.697371
$754$	−4.96092e23	−0.172944
$755$	−8.88838e24	−3.06389
$756$	3.41451e23	0.116384
$757$	−1.47607e24	−0.497500	−0.248750	−	0.968568i	$-0.580020\pi$
$757$	−1.47607e24	−0.497500	−0.248750	+	0.968568i	$0.580020\pi$
$758$	−6.36390e23	−0.212097
$759$	8.54608e23	0.281651
$760$	1.87945e24	0.612514
$761$	9.84135e23	0.317165	0.158582	−	0.987346i	$-0.449308\pi$
$761$	9.84135e23	0.317165	0.158582	+	0.987346i	$0.449308\pi$
$762$	−1.33394e24	−0.425126
$763$	2.60014e24	0.819478
$764$	3.35740e24	1.04643
$765$	1.53511e24	0.473170
$766$	2.42971e24	0.740644
$767$	2.72168e24	0.820496
$768$	2.71396e24	0.809157
$769$	−5.64239e24	−1.66375	−0.831877	−	0.554960i	$-0.812734\pi$
$769$	−5.64239e24	−1.66375	−0.831877	+	0.554960i	$0.812734\pi$
$770$	−2.08410e24	−0.607783
$771$	5.91037e24	1.70472
$772$	1.25971e24	0.359356
$773$	1.67944e24	0.473848	0.236924	−	0.971528i	$-0.423861\pi$
$773$	1.67944e24	0.473848	0.236924	+	0.971528i	$0.423861\pi$
$774$	−8.37469e23	−0.233706
$775$	6.55974e23	0.181060
$776$	−2.70769e24	−0.739222
$777$	4.17603e24	1.12768
$778$	−8.80091e23	−0.235072
$779$	−1.25188e24	−0.330745
$780$	3.92342e24	1.02532
$781$	6.58172e24	1.70140
$782$	−1.24747e23	−0.0318986
$783$	−5.34772e23	−0.135268
$784$	−6.87860e23	−0.172113
$785$	−9.59435e23	−0.237478
$786$	−5.17326e24	−1.26670
$787$	6.14749e24	1.48906	0.744531	−	0.667588i	$-0.232673\pi$
$787$	6.14749e24	1.48906	0.744531	+	0.667588i	$0.232673\pi$
$788$	−4.11514e24	−0.986080
$789$	1.21515e24	0.288054
$790$	6.75811e24	1.58488
$791$	−6.95627e23	−0.161390
$792$	3.11699e24	0.715437
$793$	−3.08584e24	−0.700730
$794$	2.32844e24	0.523108
$795$	8.04352e24	1.78783
$796$	2.00452e24	0.440808
$797$	4.66965e24	1.01599	0.507994	−	0.861361i	$-0.330387\pi$
$797$	4.66965e24	1.01599	0.507994	+	0.861361i	$0.330387\pi$
$798$	8.95377e23	0.192744
$799$	2.88095e24	0.613603
$800$	−1.02041e25	−2.15035
$801$	7.65859e24	1.59688
$802$	2.14021e24	0.441544
$803$	1.06423e24	0.217247
$804$	−6.13768e24	−1.23973
$805$	−1.32501e24	−0.264822
$806$	1.17027e23	0.0231440
$807$	−1.15978e25	−2.26961
$808$	3.08438e24	0.597270
$809$	−4.06727e24	−0.779365	−0.389683	−	0.920949i	$-0.627415\pi$
$809$	−4.06727e24	−0.779365	−0.389683	+	0.920949i	$0.627415\pi$
$810$	−5.05337e24	−0.958205
$811$	2.00872e24	0.376914	0.188457	−	0.982081i	$-0.439651\pi$
$811$	2.00872e24	0.376914	0.188457	+	0.982081i	$0.439651\pi$
$812$	−1.92253e24	−0.356982
$813$	−1.00559e25	−1.84779
$814$	−3.02881e24	−0.550762
$815$	2.71718e24	0.488966
$816$	8.69848e23	0.154909
$817$	−1.33204e24	−0.234763
$818$	2.77877e24	0.484674
$819$	1.97069e24	0.340177
$820$	6.40861e24	1.09483
$821$	−3.38446e24	−0.572232	−0.286116	−	0.958195i	$-0.592364\pi$
$821$	−3.38446e24	−0.572232	−0.286116	+	0.958195i	$0.592364\pi$
$822$	−9.86333e23	−0.165049
$823$	−1.02755e25	−1.70179	−0.850893	−	0.525340i	$-0.823938\pi$
$823$	−1.02755e25	−1.70179	−0.850893	+	0.525340i	$0.823938\pi$
$824$	−3.50820e24	−0.575046
$825$	−1.74884e25	−2.83722
$826$	−3.17966e24	−0.510564
$827$	−1.16016e24	−0.184383	−0.0921915	−	0.995741i	$-0.529387\pi$
$827$	−1.16016e24	−0.184383	−0.0921915	+	0.995741i	$0.529387\pi$
$828$	8.61055e23	0.135448
$829$	−1.31128e24	−0.204165	−0.102082	−	0.994776i	$-0.532551\pi$
$829$	−1.31128e24	−0.204165	−0.102082	+	0.994776i	$0.532551\pi$
$830$	7.22792e24	1.11391
$831$	3.38988e24	0.517102
$832$	−4.94942e23	−0.0747318
$833$	1.02032e24	0.152494
$834$	3.37665e24	0.499546
$835$	−4.89359e24	−0.716626
$836$	2.15417e24	0.312267
$837$	1.26151e23	0.0181020
$838$	−2.64509e24	−0.375721
$839$	−7.40547e24	−1.04130	−0.520650	−	0.853770i	$-0.674310\pi$
$839$	−7.40547e24	−1.04130	−0.520650	+	0.853770i	$0.674310\pi$
$840$	−1.05490e25	−1.46838
$841$	−4.24613e24	−0.585096
$842$	−6.11059e24	−0.833548
$843$	7.17328e24	0.968687
$844$	3.18054e24	0.425197
$845$	9.16386e24	1.21282
$846$	5.99474e24	0.785457
$847$	6.29125e22	0.00816071
$848$	2.08798e24	0.268139
$849$	−7.48053e24	−0.951080
$850$	2.55278e24	0.321331
$851$	−1.92562e24	−0.239977
$852$	1.44753e25	1.78604
$853$	−2.23564e24	−0.273109	−0.136554	−	0.990633i	$-0.543603\pi$
$853$	−2.23564e24	−0.273109	−0.136554	+	0.990633i	$0.543603\pi$
$854$	3.60510e24	0.436039
$855$	5.08070e24	0.608432
$856$	4.15681e24	0.492871
$857$	−1.33072e25	−1.56224	−0.781121	−	0.624380i	$-0.785352\pi$
$857$	−1.33072e25	−1.56224	−0.781121	+	0.624380i	$0.785352\pi$
$858$	−3.11997e24	−0.362667
$859$	−1.28566e25	−1.47974	−0.739870	−	0.672750i	$-0.765113\pi$
$859$	−1.28566e25	−1.47974	−0.739870	+	0.672750i	$0.765113\pi$
$860$	6.81898e24	0.777110
$861$	7.02655e24	0.792894
$862$	−5.23546e24	−0.584983
$863$	7.00527e24	0.775056	0.387528	−	0.921858i	$-0.373329\pi$
$863$	7.00527e24	0.775056	0.387528	+	0.921858i	$0.373329\pi$
$864$	−1.96236e24	−0.214987
$865$	1.96052e25	2.12684
$866$	−5.25568e24	−0.564582
$867$	1.14803e25	1.22121
$868$	4.53519e23	0.0477725
$869$	1.78270e25	1.85956
$870$	7.17875e24	0.741541
$871$	6.47737e24	0.662589
$872$	−9.54544e24	−0.966954
$873$	−7.31967e24	−0.734295
$874$	−4.12870e23	−0.0410172
$875$	1.42058e25	1.39764
$876$	2.34058e24	0.228055
$877$	6.81593e24	0.657701	0.328851	−	0.944382i	$-0.393339\pi$
$877$	6.81593e24	0.657701	0.328851	+	0.944382i	$0.393339\pi$
$878$	−9.04357e24	−0.864245
$879$	−2.61965e25	−2.47935
$880$	−6.70102e24	−0.628114
$881$	1.68772e25	1.56677	0.783383	−	0.621539i	$-0.213492\pi$
$881$	1.68772e25	1.56677	0.783383	+	0.621539i	$0.213492\pi$
$882$	2.12310e24	0.195204
$883$	5.40418e24	0.492112	0.246056	−	0.969256i	$-0.420865\pi$
$883$	5.40418e24	0.492112	0.246056	+	0.969256i	$0.420865\pi$
$884$	−1.51070e24	−0.136249
$885$	−3.93843e25	−3.51808
$886$	−9.79793e24	−0.866857
$887$	−1.06075e25	−0.929531	−0.464765	−	0.885434i	$-0.653861\pi$
$887$	−1.06075e25	−0.929531	−0.464765	+	0.885434i	$0.653861\pi$
$888$	−1.53308e25	−1.33062
$889$	5.45556e24	0.469001
$890$	1.87989e25	1.60073
$891$	−1.33301e25	−1.12428
$892$	4.89566e24	0.408987
$893$	9.53497e24	0.789009
$894$	−1.31082e24	−0.107442
$895$	−2.87908e25	−2.33753
$896$	−8.60331e24	−0.691907
$897$	−1.98358e24	−0.158021
$898$	5.28362e24	0.416949
$899$	−7.10292e23	−0.0555238
$900$	−1.76204e25	−1.36444
$901$	−3.09714e24	−0.237575
$902$	−5.09624e24	−0.387252
$903$	7.47649e24	0.562797
$904$	2.55374e24	0.190434
$905$	−1.46869e25	−1.08497
$906$	1.55452e25	1.13765
$907$	1.13975e25	0.826322	0.413161	−	0.910658i	$-0.364425\pi$
$907$	1.13975e25	0.826322	0.413161	+	0.910658i	$0.364425\pi$
$908$	−3.60417e24	−0.258866
$909$	8.33795e24	0.593289
$910$	4.83729e24	0.340997
$911$	1.01971e25	0.712148	0.356074	−	0.934458i	$-0.384115\pi$
$911$	1.01971e25	0.712148	0.356074	+	0.934458i	$0.384115\pi$
$912$	2.87891e24	0.199192
$913$	1.90663e25	1.30696
$914$	7.73639e24	0.525407
$915$	4.46539e25	3.00455
$916$	4.05161e24	0.270095
$917$	2.11577e25	1.39743
$918$	4.90929e23	0.0321259
$919$	6.72424e24	0.435975	0.217987	−	0.975952i	$-0.430051\pi$
$919$	6.72424e24	0.435975	0.217987	+	0.975952i	$0.430051\pi$
$920$	4.86429e24	0.312481
$921$	1.57234e24	0.100078
$922$	−1.29542e25	−0.816953
$923$	−1.52764e25	−0.954570
$924$	−1.20910e25	−0.748598
$925$	3.94053e25	2.41741
$926$	4.85987e23	0.0295414
$927$	−9.48367e24	−0.571214
$928$	1.10490e25	0.659427
$929$	1.16354e25	0.688092	0.344046	−	0.938953i	$-0.388202\pi$
$929$	1.16354e25	0.688092	0.344046	+	0.938953i	$0.388202\pi$
$930$	−1.69345e24	−0.0992355
$931$	3.37691e24	0.196086
$932$	−1.85818e25	−1.06919
$933$	−1.15092e25	−0.656222
$934$	7.92210e24	0.447602
$935$	9.93977e24	0.556516
$936$	−7.23466e24	−0.401396
$937$	−1.69243e25	−0.930514	−0.465257	−	0.885176i	$-0.654038\pi$
$937$	−1.69243e25	−0.930514	−0.465257	+	0.885176i	$0.654038\pi$
$938$	−7.56733e24	−0.412305
$939$	4.03253e25	2.17731
$940$	−4.88114e25	−2.61177
$941$	−1.55280e25	−0.823388	−0.411694	−	0.911322i	$-0.635063\pi$
$941$	−1.55280e25	−0.823388	−0.411694	+	0.911322i	$0.635063\pi$
$942$	1.67799e24	0.0881775
$943$	−3.24003e24	−0.168733
$944$	−1.02236e25	−0.527643
$945$	5.21445e24	0.266709
$946$	−5.42257e24	−0.274872
$947$	−1.89019e25	−0.949580	−0.474790	−	0.880099i	$-0.657476\pi$
$947$	−1.89019e25	−0.949580	−0.474790	+	0.880099i	$0.657476\pi$
$948$	3.92072e25	1.95207
$949$	−2.47012e24	−0.121887
$950$	8.44884e24	0.413187
$951$	−6.08752e24	−0.295057
$952$	4.06187e24	0.195125
$953$	−3.44268e25	−1.63911	−0.819553	−	0.573004i	$-0.805778\pi$
$953$	−3.44268e25	−1.63911	−0.819553	+	0.573004i	$0.805778\pi$
$954$	−6.44460e24	−0.304113
$955$	5.12725e25	2.39804
$956$	−3.50864e24	−0.162647
$957$	1.89366e25	0.870061
$958$	−6.35716e24	−0.289505
$959$	4.03393e24	0.182083
$960$	7.16210e24	0.320431
$961$	−2.23826e25	−0.992570
$962$	7.02998e24	0.309006
$963$	1.12370e25	0.489586
$964$	2.87546e25	1.24180
$965$	1.92377e25	0.823512
$966$	2.31736e24	0.0983305
$967$	1.43791e25	0.604791	0.302396	−	0.953183i	$-0.402214\pi$
$967$	1.43791e25	0.604791	0.302396	+	0.953183i	$0.402214\pi$
$968$	−2.30960e23	−0.00962934
$969$	−4.27034e24	−0.176486
$970$	−1.79670e25	−0.736066
$971$	−3.00384e25	−1.21987	−0.609935	−	0.792451i	$-0.708805\pi$
$971$	−3.00384e25	−1.21987	−0.609935	+	0.792451i	$0.708805\pi$
$972$	−2.53089e25	−1.01885
$973$	−1.38099e25	−0.551102
$974$	7.30930e24	0.289151
$975$	4.05914e25	1.59182
$976$	1.15915e25	0.450625
$977$	−3.31531e25	−1.27768	−0.638838	−	0.769341i	$-0.720585\pi$
$977$	−3.31531e25	−1.27768	−0.638838	+	0.769341i	$0.720585\pi$
$978$	−4.75218e24	−0.181557
$979$	4.95890e25	1.87816
$980$	−1.72871e25	−0.649083
$981$	−2.58041e25	−0.960510
$982$	−2.27572e25	−0.839790
$983$	1.98936e25	0.727795	0.363897	−	0.931439i	$-0.381446\pi$
$983$	1.98936e25	0.727795	0.363897	+	0.931439i	$0.381446\pi$
$984$	−2.57954e25	−0.935586
$985$	−6.28442e25	−2.25973
$986$	−2.76416e24	−0.0985393
$987$	−5.35180e25	−1.89149
$988$	−4.99992e24	−0.175198
$989$	−3.44751e24	−0.119767
$990$	2.06829e25	0.712382
$991$	4.20713e25	1.43668	0.718341	−	0.695692i	$-0.244902\pi$
$991$	4.20713e25	1.43668	0.718341	+	0.695692i	$0.244902\pi$
$992$	−2.60644e24	−0.0882467
$993$	−1.09727e25	−0.368336
$994$	1.78470e25	0.593994
$995$	3.06120e25	1.01017
$996$	4.19328e25	1.37199
$997$	−5.19563e25	−1.68550	−0.842752	−	0.538302i	$-0.819066\pi$
$997$	−5.19563e25	−1.68550	−0.842752	+	0.538302i	$0.819066\pi$
$998$	2.17064e24	0.0698196
$999$	7.57810e24	0.241687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.18.a.a.1.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.18.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-174.243 q^{2} -15437.5 q^{3} -100711. q^{4} -1.53801e6 q^{5} +2.68988e6 q^{6} -1.10011e7 q^{7} +4.03867e7 q^{8} +1.09177e8 q^{9} +O(q^{10})\)	\(q-174.243 q^{2} -15437.5 q^{3} -100711. q^{4} -1.53801e6 q^{5} +2.68988e6 q^{6} -1.10011e7 q^{7} +4.03867e7 q^{8} +1.09177e8 q^{9} +2.67988e8 q^{10} +7.06915e8 q^{11} +1.55473e9 q^{12} -1.64078e9 q^{13} +1.91687e9 q^{14} +2.37430e10 q^{15} +6.16333e9 q^{16} -9.14220e9 q^{17} -1.90233e10 q^{18} -3.02576e10 q^{19} +1.54895e11 q^{20} +1.69830e11 q^{21} -1.23175e11 q^{22} -7.83110e10 q^{23} -6.23470e11 q^{24} +1.60253e12 q^{25} +2.85895e11 q^{26} +3.08185e11 q^{27} +1.10794e12 q^{28} -1.73523e12 q^{29} -4.13706e12 q^{30} +4.09336e11 q^{31} -6.36748e12 q^{32} -1.09130e13 q^{33} +1.59297e12 q^{34} +1.69199e13 q^{35} -1.09953e13 q^{36} +2.45894e13 q^{37} +5.27219e12 q^{38} +2.53295e13 q^{39} -6.21151e13 q^{40} +4.13739e13 q^{41} -2.95918e13 q^{42} +4.40233e13 q^{43} -7.11943e13 q^{44} -1.67915e14 q^{45} +1.36452e13 q^{46} -3.15126e14 q^{47} -9.51465e13 q^{48} -1.11605e14 q^{49} -2.79230e14 q^{50} +1.41133e14 q^{51} +1.65245e14 q^{52} +3.38774e14 q^{53} -5.36992e13 q^{54} -1.08724e15 q^{55} -4.44300e14 q^{56} +4.67103e14 q^{57} +3.02352e14 q^{58} -1.65877e15 q^{59} -2.39119e15 q^{60} +1.88072e15 q^{61} -7.13240e13 q^{62} -1.20107e15 q^{63} +3.01650e14 q^{64} +2.52353e15 q^{65} +1.90152e15 q^{66} -3.94774e15 q^{67} +9.20722e14 q^{68} +1.20893e15 q^{69} -2.94817e15 q^{70} +9.31048e15 q^{71} +4.40929e15 q^{72} +1.50546e15 q^{73} -4.28454e15 q^{74} -2.47391e16 q^{75} +3.04728e15 q^{76} -7.77687e15 q^{77} -4.41350e15 q^{78} +2.52180e16 q^{79} -9.47925e15 q^{80} -1.88567e16 q^{81} -7.20913e15 q^{82} +2.69711e16 q^{83} -1.71038e16 q^{84} +1.40608e16 q^{85} -7.67076e15 q^{86} +2.67876e16 q^{87} +2.85499e16 q^{88} +7.01485e16 q^{89} +2.92580e16 q^{90} +1.80504e16 q^{91} +7.88680e15 q^{92} -6.31913e15 q^{93} +5.49086e16 q^{94} +4.65365e16 q^{95} +9.82981e16 q^{96} -6.70443e16 q^{97} +1.94465e16 q^{98} +7.71787e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) \) 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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