LMFDB - Embedded newform 3.26.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,26,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	3.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:	$11.8799033986$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 783420x + 148321440 $ x^3 - x^2 - 783420*x + 148321440
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{6}\cdot 3^{5}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$768.963$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8744.24 q^{2} +531441. q^{3} +4.29073e7 q^{4} +4.98342e7 q^{5} +4.64705e9 q^{6} +5.50645e10 q^{7} +8.17835e10 q^{8} +2.82430e11 q^{9} +O(q^{10})$	\(q+8744.24 q^{2} +531441. q^{3} +4.29073e7 q^{4} +4.98342e7 q^{5} +4.64705e9 q^{6} +5.50645e10 q^{7} +8.17835e10 q^{8} +2.82430e11 q^{9} +4.35762e11 q^{10} -1.39744e13 q^{11} +2.28027e13 q^{12} +1.27551e14 q^{13} +4.81498e14 q^{14} +2.64840e13 q^{15} -7.24595e14 q^{16} +1.41846e15 q^{17} +2.46963e15 q^{18} -1.02899e16 q^{19} +2.13825e15 q^{20} +2.92636e16 q^{21} -1.22196e17 q^{22} -6.75984e16 q^{23} +4.34631e16 q^{24} -2.95540e17 q^{25} +1.11533e18 q^{26} +1.50095e17 q^{27} +2.36267e18 q^{28} -3.07242e18 q^{29} +2.31582e17 q^{30} +9.03157e17 q^{31} -9.08023e18 q^{32} -7.42657e18 q^{33} +1.24034e19 q^{34} +2.74410e18 q^{35} +1.21183e19 q^{36} -5.36810e18 q^{37} -8.99775e19 q^{38} +6.77857e19 q^{39} +4.07562e18 q^{40} +1.40813e20 q^{41} +2.55888e20 q^{42} +1.70911e20 q^{43} -5.99604e20 q^{44} +1.40747e19 q^{45} -5.91097e20 q^{46} -6.32772e20 q^{47} -3.85079e20 q^{48} +1.69104e21 q^{49} -2.58427e21 q^{50} +7.53830e20 q^{51} +5.47286e21 q^{52} +9.60635e20 q^{53} +1.31246e21 q^{54} -6.96404e20 q^{55} +4.50337e21 q^{56} -5.46848e21 q^{57} -2.68659e22 q^{58} +1.44777e22 q^{59} +1.13635e21 q^{60} +3.87814e21 q^{61} +7.89742e21 q^{62} +1.55519e22 q^{63} -5.50863e22 q^{64} +6.35639e21 q^{65} -6.49397e22 q^{66} +8.52923e22 q^{67} +6.08624e22 q^{68} -3.59246e22 q^{69} +2.39951e22 q^{70} +7.92209e22 q^{71} +2.30981e22 q^{72} +2.67527e23 q^{73} -4.69400e22 q^{74} -1.57062e23 q^{75} -4.41512e23 q^{76} -7.69494e23 q^{77} +5.92734e23 q^{78} -6.21605e23 q^{79} -3.61096e22 q^{80} +7.97664e22 q^{81} +1.23130e24 q^{82} +3.18211e23 q^{83} +1.25562e24 q^{84} +7.06881e22 q^{85} +1.49449e24 q^{86} -1.63281e24 q^{87} -1.14288e24 q^{88} -3.79033e24 q^{89} +1.23072e23 q^{90} +7.02353e24 q^{91} -2.90047e24 q^{92} +4.79975e23 q^{93} -5.53311e24 q^{94} -5.12790e23 q^{95} -4.82561e24 q^{96} +1.55884e24 q^{97} +1.47868e25 q^{98} -3.94678e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3678 q^{2} + 1594323 q^{3} + 90747588 q^{4} - 163152750 q^{5} - 1954639998 q^{6} - 9622572744 q^{7} - 268012830648 q^{8} + 847288609443 q^{9}+O(q^{10}) $ 3 * q - 3678 * q^2 + 1594323 * q^3 + 90747588 * q^4 - 163152750 * q^5 - 1954639998 * q^6 - 9622572744 * q^7 - 268012830648 * q^8 + 847288609443 * q^9	$ 3 q - 3678 q^{2} + 1594323 q^{3} + 90747588 q^{4} - 163152750 q^{5} - 1954639998 q^{6} - 9622572744 q^{7} - 268012830648 q^{8} + 847288609443 q^{9} + 8363188874700 q^{10} - 5946998130780 q^{11} + 48226988914308 q^{12} + 248137774407690 q^{13} + 754361641264848 q^{14} - 86706060612750 q^{15} + 23\!\cdots\!16 q^{16}+ \cdots - 16\!\cdots\!80 q^{99}+O(q^{100}) $ 3 * q - 3678 * q^2 + 1594323 * q^3 + 90747588 * q^4 - 163152750 * q^5 - 1954639998 * q^6 - 9622572744 * q^7 - 268012830648 * q^8 + 847288609443 * q^9 + 8363188874700 * q^10 - 5946998130780 * q^11 + 48226988914308 * q^12 + 248137774407690 * q^13 + 754361641264848 * q^14 - 86706060612750 * q^15 + 2394637852352016 * q^16 + 6640885201245174 * q^17 - 1038775835177118 * q^18 - 4282718959080516 * q^19 - 84999590549092200 * q^20 - 5113829681644104 * q^21 - 67279455312049512 * q^22 - 54558955951564152 * q^23 - 142433006732403768 * q^24 + 285270827389168125 * q^25 + 914405315527228956 * q^26 + 450283905890997363 * q^27 + 2416760102519597472 * q^28 - 506350856671782 * q^29 + 4444541458759442700 * q^30 - 120595458951353856 * q^31 - 23423805952813711584 * q^32 - 3160478633619853980 * q^33 - 30744163051965656604 * q^34 - 12895712434403329200 * q^35 + 25629799215608757828 * q^36 + 71124029266471833426 * q^37 - 151631523417421211736 * q^38 + 131870586968997181290 * q^39 + 487276555770533818800 * q^40 - 178237898435247428226 * q^41 + 400898704995432085968 * q^42 + 233732145791955002244 * q^43 - 1709130121883010683088 * q^44 - 46079155558100472750 * q^45 - 727064486838202905936 * q^46 - 578974907441950806192 * q^47 + 1272608734891807735056 * q^48 + 1540848623287695627627 * q^49 - 7598435156177129081250 * q^50 + 3529238672234936515734 * q^51 + 1549295968705274668344 * q^52 + 9056010625929165756258 * q^53 - 552048068622362767038 * q^54 + 16758715188531155952600 * q^55 + 7112451608305863332160 * q^56 - 2276012446332708503556 * q^57 - 43337630795958244629252 * q^58 + 23769324802557802948596 * q^59 - 45172267401000107860200 * q^60 - 11371716695373075009318 * q^61 - 21881713022451611321088 * q^62 - 2717698759842624273864 * q^63 - 55686925877484831566784 * q^64 + 89289247460368023248700 * q^65 - 35755061010490904706792 * q^66 + 52213761253321486240524 * q^67 + 318831609976592944413384 * q^68 - 28994866109855204503032 * q^69 - 78749858107500801357600 * q^70 + 262955361870665606618136 * q^71 - 75694739530875390869688 * q^72 - 11752720924176446629602 * q^73 - 498161580663483575957172 * q^74 + 151604613778526897518125 * q^75 + 4571105415149082363216 * q^76 - 1386525122949230445864288 * q^77 + 485952475289106083605596 * q^78 - 500543105756664483755760 * q^79 - 1540345885402641092176800 * q^80 + 239299329230617529590083 * q^81 + 4108759898128895060824212 * q^82 - 59055829437561671377284 * q^83 + 1284365405643117400117152 * q^84 - 2357173046017457952925500 * q^85 + 2057662432276923640084440 * q^86 - 269095605620508497862 * q^87 + 4527751242141959006666592 * q^88 - 3359875059386549548018866 * q^89 + 2362011557384576987930700 * q^90 + 1253870789177107094217744 * q^91 - 1905611545816878301689504 * q^92 - 64089371300566444586496 * q^93 - 18037990008720502135322400 * q^94 - 5406514800597015344021400 * q^95 - 12448370859369271697912544 * q^96 - 12029431225244267569541466 * q^97 + 24058796570011739277032850 * q^98 - 1679607925529568818985180 * 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 $

$2$	8744.24	1.50955	0.754774	−	0.655985i	$-0.227746\pi$
$2$	8744.24	1.50955	0.754774	+	0.655985i	$0.227746\pi$
$3$	531441.	0.577350
$3$	531441.	0.577350
$4$	4.29073e7	1.27874
$5$	4.98342e7	0.0912857	0.0456428	−	0.998958i	$-0.485466\pi$
$5$	4.98342e7	0.0912857	0.0456428	+	0.998958i	$0.485466\pi$
$6$	4.64705e9	0.871538
$7$	5.50645e10	1.50365	0.751825	−	0.659363i	$-0.229174\pi$
$7$	5.50645e10	1.50365	0.751825	+	0.659363i	$0.229174\pi$
$8$	8.17835e10	0.420766
$9$	2.82430e11	0.333333
$10$	4.35762e11	0.137800
$11$	−1.39744e13	−1.34253	−0.671266	−	0.741216i	$-0.734249\pi$
$11$	−1.39744e13	−1.34253	−0.671266	+	0.741216i	$0.734249\pi$
$12$	2.28027e13	0.738279
$13$	1.27551e14	1.51842	0.759209	−	0.650847i	$-0.225586\pi$
$13$	1.27551e14	1.51842	0.759209	+	0.650847i	$0.225586\pi$
$14$	4.81498e14	2.26983
$15$	2.64840e13	0.0527038
$16$	−7.24595e14	−0.643569
$17$	1.41846e15	0.590482	0.295241	−	0.955423i	$-0.404600\pi$
$17$	1.41846e15	0.590482	0.295241	+	0.955423i	$0.404600\pi$
$18$	2.46963e15	0.503183
$19$	−1.02899e16	−1.06658	−0.533288	−	0.845934i	$-0.679044\pi$
$19$	−1.02899e16	−1.06658	−0.533288	+	0.845934i	$0.679044\pi$
$20$	2.13825e15	0.116730
$21$	2.92636e16	0.868132
$22$	−1.22196e17	−2.02662
$23$	−6.75984e16	−0.643189	−0.321595	−	0.946877i	$-0.604219\pi$
$23$	−6.75984e16	−0.643189	−0.321595	+	0.946877i	$0.604219\pi$
$24$	4.34631e16	0.242930
$25$	−2.95540e17	−0.991667
$26$	1.11533e18	2.29212
$27$	1.50095e17	0.192450
$28$	2.36267e18	1.92277
$29$	−3.07242e18	−1.61252	−0.806260	−	0.591562i	$-0.798512\pi$
$29$	−3.07242e18	−1.61252	−0.806260	+	0.591562i	$0.798512\pi$
$30$	2.31582e17	0.0795590
$31$	9.03157e17	0.205941	0.102970	−	0.994684i	$-0.467165\pi$
$31$	9.03157e17	0.205941	0.102970	+	0.994684i	$0.467165\pi$
$32$	−9.08023e18	−1.39227
$33$	−7.42657e18	−0.775111
$34$	1.24034e19	0.891362
$35$	2.74410e18	0.137262
$36$	1.21183e19	0.426246
$37$	−5.36810e18	−0.134060	−0.0670300	−	0.997751i	$-0.521352\pi$
$37$	−5.36810e18	−0.134060	−0.0670300	+	0.997751i	$0.521352\pi$
$38$	−8.99775e19	−1.61005
$39$	6.77857e19	0.876659
$40$	4.07562e18	0.0384100
$41$	1.40813e20	0.974640	0.487320	−	0.873223i	$-0.337975\pi$
$41$	1.40813e20	0.974640	0.487320	+	0.873223i	$0.337975\pi$
$42$	2.55888e20	1.31049
$43$	1.70911e20	0.652250	0.326125	−	0.945327i	$-0.394257\pi$
$43$	1.70911e20	0.652250	0.326125	+	0.945327i	$0.394257\pi$
$44$	−5.99604e20	−1.71675
$45$	1.40747e19	0.0304286
$46$	−5.91097e20	−0.970925
$47$	−6.32772e20	−0.794372	−0.397186	−	0.917738i	$-0.630013\pi$
$47$	−6.32772e20	−0.794372	−0.397186	+	0.917738i	$0.630013\pi$
$48$	−3.85079e20	−0.371565
$49$	1.69104e21	1.26096
$50$	−2.58427e21	−1.49697
$51$	7.53830e20	0.340915
$52$	5.47286e21	1.94166
$53$	9.60635e20	0.268602	0.134301	−	0.990941i	$-0.457121\pi$
$53$	9.60635e20	0.268602	0.134301	+	0.990941i	$0.457121\pi$
$54$	1.31246e21	0.290513
$55$	−6.96404e20	−0.122554
$56$	4.50337e21	0.632685
$57$	−5.46848e21	−0.615788
$58$	−2.68659e22	−2.43418
$59$	1.44777e22	1.05937	0.529687	−	0.848193i	$-0.322309\pi$
$59$	1.44777e22	1.05937	0.529687	+	0.848193i	$0.322309\pi$
$60$	1.13635e21	0.0673943
$61$	3.87814e21	0.187069	0.0935343	−	0.995616i	$-0.470184\pi$
$61$	3.87814e21	0.187069	0.0935343	+	0.995616i	$0.470184\pi$
$62$	7.89742e21	0.310877
$63$	1.55519e22	0.501216
$64$	−5.50863e22	−1.45812
$65$	6.35639e21	0.138610
$66$	−6.49397e22	−1.17007
$67$	8.52923e22	1.27343	0.636715	−	0.771100i	$-0.280293\pi$
$67$	8.52923e22	1.27343	0.636715	+	0.771100i	$0.280293\pi$
$68$	6.08624e22	0.755071
$69$	−3.59246e22	−0.371345
$70$	2.39951e22	0.207203
$71$	7.92209e22	0.572941	0.286471	−	0.958089i	$-0.407518\pi$
$71$	7.92209e22	0.572941	0.286471	+	0.958089i	$0.407518\pi$
$72$	2.30981e22	0.140255
$73$	2.67527e23	1.36720	0.683599	−	0.729858i	$-0.260414\pi$
$73$	2.67527e23	1.36720	0.683599	+	0.729858i	$0.260414\pi$
$74$	−4.69400e22	−0.202370
$75$	−1.57062e23	−0.572539
$76$	−4.41512e23	−1.36387
$77$	−7.69494e23	−2.01870
$78$	5.92734e23	1.32336
$79$	−6.21605e23	−1.18352	−0.591760	−	0.806114i	$-0.701567\pi$
$79$	−6.21605e23	−1.18352	−0.591760	+	0.806114i	$0.701567\pi$
$80$	−3.61096e22	−0.0587487
$81$	7.97664e22	0.111111
$82$	1.23130e24	1.47127
$83$	3.18211e23	0.326767	0.163384	−	0.986563i	$-0.447759\pi$
$83$	3.18211e23	0.326767	0.163384	+	0.986563i	$0.447759\pi$
$84$	1.25562e24	1.11011
$85$	7.06881e22	0.0539026
$86$	1.49449e24	0.984603
$87$	−1.63281e24	−0.930989
$88$	−1.14288e24	−0.564893
$89$	−3.79033e24	−1.62668	−0.813339	−	0.581790i	$-0.802352\pi$
$89$	−3.79033e24	−1.62668	−0.813339	+	0.581790i	$0.802352\pi$
$90$	1.23072e23	0.0459334
$91$	7.02353e24	2.28317
$92$	−2.90047e24	−0.822470
$93$	4.79975e23	0.118900
$94$	−5.53311e24	−1.19914
$95$	−5.12790e23	−0.0973631
$96$	−4.82561e24	−0.803825
$97$	1.55884e24	0.228115	0.114058	−	0.993474i	$-0.463615\pi$
$97$	1.55884e24	0.228115	0.114058	+	0.993474i	$0.463615\pi$
$98$	1.47868e25	1.90348
$99$	−3.94678e24	−0.447511
$100$	−1.26808e25	−1.26808
$101$	9.09065e24	0.802745	0.401373	−	0.915915i	$-0.368533\pi$
$101$	9.09065e24	0.802745	0.401373	+	0.915915i	$0.368533\pi$
$102$	6.59167e24	0.514628
$103$	−1.47218e25	−1.01741	−0.508704	−	0.860941i	$-0.669875\pi$
$103$	−1.47218e25	−1.01741	−0.508704	+	0.860941i	$0.669875\pi$
$104$	1.04316e25	0.638899
$105$	1.45833e24	0.0792480
$106$	8.40002e24	0.405468
$107$	6.41645e24	0.275421	0.137711	−	0.990473i	$-0.456026\pi$
$107$	6.41645e24	0.275421	0.137711	+	0.990473i	$0.456026\pi$
$108$	6.44015e24	0.246093
$109$	3.04719e25	1.03769	0.518846	−	0.854868i	$-0.326362\pi$
$109$	3.04719e25	1.03769	0.518846	+	0.854868i	$0.326362\pi$
$110$	−6.08952e24	−0.185001
$111$	−2.85283e24	−0.0773996
$112$	−3.98995e25	−0.967702
$113$	−4.46482e25	−0.968999	−0.484500	−	0.874791i	$-0.660998\pi$
$113$	−4.46482e25	−0.968999	−0.484500	+	0.874791i	$0.660998\pi$
$114$	−4.78177e25	−0.929562
$115$	−3.36872e24	−0.0587140
$116$	−1.31829e26	−2.06199
$117$	3.60241e25	0.506139
$118$	1.26596e26	1.59918
$119$	7.81071e25	0.887878
$120$	2.16595e24	0.0221760
$121$	8.69369e25	0.802393
$122$	3.39114e25	0.282389
$123$	7.48338e25	0.562709
$124$	3.87520e25	0.263344
$125$	−2.95798e25	−0.181811
$126$	1.35989e26	0.756610
$127$	−3.17195e26	−1.59875	−0.799375	−	0.600833i	$-0.794836\pi$
$127$	−3.17195e26	−1.59875	−0.799375	+	0.600833i	$0.794836\pi$
$128$	−1.77006e26	−0.808842
$129$	9.08291e25	0.376577
$130$	5.55818e25	0.209238
$131$	−6.48276e25	−0.221753	−0.110876	−	0.993834i	$-0.535366\pi$
$131$	−6.48276e25	−0.221753	−0.110876	+	0.993834i	$0.535366\pi$
$132$	−3.18654e26	−0.991163
$133$	−5.66609e26	−1.60376
$134$	7.45816e26	1.92230
$135$	7.47985e24	0.0175679
$136$	1.16007e26	0.248455
$137$	1.29357e26	0.252804	0.126402	−	0.991979i	$-0.459657\pi$
$137$	1.29357e26	0.252804	0.126402	+	0.991979i	$0.459657\pi$
$138$	−3.14133e26	−0.560564
$139$	5.10639e26	0.832586	0.416293	−	0.909231i	$-0.363329\pi$
$139$	5.10639e26	0.832586	0.416293	+	0.909231i	$0.363329\pi$
$140$	1.17742e26	0.175521
$141$	−3.36281e26	−0.458631
$142$	6.92726e26	0.864883
$143$	−1.78245e27	−2.03852
$144$	−2.04647e26	−0.214523
$145$	−1.53111e26	−0.147200
$146$	2.33932e27	2.06385
$147$	8.98685e26	0.728016
$148$	−2.30331e26	−0.171427
$149$	1.21485e27	0.831175	0.415588	−	0.909553i	$-0.363576\pi$
$149$	1.21485e27	0.831175	0.415588	+	0.909553i	$0.363576\pi$
$150$	−1.37339e27	−0.864276
$151$	1.38229e27	0.800549	0.400274	−	0.916395i	$-0.368915\pi$
$151$	1.38229e27	0.800549	0.400274	+	0.916395i	$0.368915\pi$
$152$	−8.41546e26	−0.448779
$153$	4.00616e26	0.196827
$154$	−6.72864e27	−3.04732
$155$	4.50081e25	0.0187994
$156$	2.90850e27	1.12102
$157$	2.08082e27	0.740439	0.370219	−	0.928944i	$-0.379283\pi$
$157$	2.08082e27	0.740439	0.370219	+	0.928944i	$0.379283\pi$
$158$	−5.43546e27	−1.78658
$159$	5.10521e26	0.155078
$160$	−4.52506e26	−0.127094
$161$	−3.72228e27	−0.967131
$162$	6.97497e26	0.167728
$163$	5.55668e27	1.23729	0.618644	−	0.785672i	$-0.287682\pi$
$163$	5.55668e27	1.23729	0.618644	+	0.785672i	$0.287682\pi$
$164$	6.04190e27	1.24631
$165$	−3.70097e26	−0.0707566
$166$	2.78251e27	0.493271
$167$	−2.62982e27	−0.432484	−0.216242	−	0.976340i	$-0.569380\pi$
$167$	−2.62982e27	−0.432484	−0.216242	+	0.976340i	$0.569380\pi$
$168$	2.39328e27	0.365281
$169$	9.21279e27	1.30559
$170$	6.18113e26	0.0813686
$171$	−2.90618e27	−0.355525
$172$	7.33332e27	0.834056
$173$	−6.13848e27	−0.649358	−0.324679	−	0.945824i	$-0.605256\pi$
$173$	−6.13848e27	−0.649358	−0.324679	+	0.945824i	$0.605256\pi$
$174$	−1.42777e28	−1.40537
$175$	−1.62738e28	−1.49112
$176$	1.01258e28	0.864013
$177$	7.69404e27	0.611630
$178$	−3.31435e28	−2.45555
$179$	−2.77210e28	−1.91490	−0.957449	−	0.288604i	$-0.906809\pi$
$179$	−2.77210e28	−1.91490	−0.957449	+	0.288604i	$0.906809\pi$
$180$	6.03905e26	0.0389101
$181$	2.38876e28	1.43612	0.718058	−	0.695983i	$-0.245031\pi$
$181$	2.38876e28	1.43612	0.718058	+	0.695983i	$0.245031\pi$
$182$	6.14154e28	3.44655
$183$	2.06100e27	0.108004
$184$	−5.52844e27	−0.270632
$185$	−2.67515e26	−0.0122378
$186$	4.19701e27	0.179485
$187$	−1.98222e28	−0.792742
$188$	−2.71505e28	−1.01579
$189$	8.26489e27	0.289377
$190$	−4.48396e27	−0.146974
$191$	5.75666e28	1.76707	0.883534	−	0.468366i	$-0.155157\pi$
$191$	5.75666e28	1.76707	0.883534	+	0.468366i	$0.155157\pi$
$192$	−2.92751e28	−0.841848
$193$	−2.60098e28	−0.700925	−0.350462	−	0.936577i	$-0.613976\pi$
$193$	−2.60098e28	−0.700925	−0.350462	+	0.936577i	$0.613976\pi$
$194$	1.36309e28	0.344351
$195$	3.37805e27	0.0800264
$196$	7.25577e28	1.61244
$197$	−3.22821e28	−0.673184	−0.336592	−	0.941651i	$-0.609274\pi$
$197$	−3.22821e28	−0.673184	−0.336592	+	0.941651i	$0.609274\pi$
$198$	−3.45116e28	−0.675539
$199$	1.58916e28	0.292081	0.146040	−	0.989279i	$-0.453347\pi$
$199$	1.58916e28	0.292081	0.146040	+	0.989279i	$0.453347\pi$
$200$	−2.41703e28	−0.417260
$201$	4.53278e28	0.735215
$202$	7.94908e28	1.21178
$203$	−1.69181e29	−2.42466
$204$	3.23448e28	0.435941
$205$	7.01730e27	0.0889707
$206$	−1.28731e29	−1.53583
$207$	−1.90918e28	−0.214396
$208$	−9.24226e28	−0.977207
$209$	1.43795e29	1.43191
$210$	1.27520e28	0.119629
$211$	−6.39166e28	−0.565045	−0.282522	−	0.959261i	$-0.591171\pi$
$211$	−6.39166e28	−0.565045	−0.282522	+	0.959261i	$0.591171\pi$
$212$	4.12182e28	0.343472
$213$	4.21012e28	0.330788
$214$	5.61070e28	0.415762
$215$	8.51721e27	0.0595411
$216$	1.22753e28	0.0809765
$217$	4.97319e28	0.309662
$218$	2.66454e29	1.56645
$219$	1.42175e29	0.789352
$220$	−2.98808e28	−0.156714
$221$	1.80926e29	0.896599
$222$	−2.49458e28	−0.116838
$223$	−6.63030e28	−0.293577	−0.146789	−	0.989168i	$-0.546894\pi$
$223$	−6.63030e28	−0.293577	−0.146789	+	0.989168i	$0.546894\pi$
$224$	−4.99999e29	−2.09348
$225$	−8.34692e28	−0.330556
$226$	−3.90415e29	−1.46275
$227$	−3.51346e27	−0.0124570	−0.00622848	−	0.999981i	$-0.501983\pi$
$227$	−3.51346e27	−0.0124570	−0.00622848	+	0.999981i	$0.501983\pi$
$228$	−2.34638e29	−0.787430
$229$	4.86782e29	1.54665	0.773323	−	0.634012i	$-0.218593\pi$
$229$	4.86782e29	1.54665	0.773323	+	0.634012i	$0.218593\pi$
$230$	−2.94569e28	−0.0886316
$231$	−4.08941e29	−1.16550
$232$	−2.51273e29	−0.678494
$233$	1.99379e29	0.510189	0.255095	−	0.966916i	$-0.417893\pi$
$233$	1.99379e29	0.510189	0.255095	+	0.966916i	$0.417893\pi$
$234$	3.15003e29	0.764042
$235$	−3.15337e28	−0.0725148
$236$	6.21198e29	1.35466
$237$	−3.30346e29	−0.683306
$238$	6.82987e29	1.34030
$239$	−4.60678e29	−0.857875	−0.428937	−	0.903334i	$-0.641112\pi$
$239$	−4.60678e29	−0.857875	−0.428937	+	0.903334i	$0.641112\pi$
$240$	−1.91901e28	−0.0339186
$241$	−1.52298e29	−0.255553	−0.127776	−	0.991803i	$-0.540784\pi$
$241$	−1.52298e29	−0.255553	−0.127776	+	0.991803i	$0.540784\pi$
$242$	7.60197e29	1.21125
$243$	4.23912e28	0.0641500
$244$	1.66401e29	0.239211
$245$	8.42714e28	0.115108
$246$	6.54364e29	0.849436
$247$	−1.31249e30	−1.61951
$248$	7.38634e28	0.0866529
$249$	1.69110e29	0.188659
$250$	−2.58652e29	−0.274452
$251$	−1.25804e30	−1.26991	−0.634953	−	0.772551i	$-0.718981\pi$
$251$	−1.25804e30	−1.26991	−0.634953	+	0.772551i	$0.718981\pi$
$252$	6.67288e29	0.640924
$253$	9.44648e29	0.863502
$254$	−2.77363e30	−2.41339
$255$	3.75665e28	0.0311207
$256$	3.00607e29	0.237137
$257$	2.22083e30	1.66860	0.834298	−	0.551314i	$-0.185873\pi$
$257$	2.22083e30	1.66860	0.834298	+	0.551314i	$0.185873\pi$
$258$	7.94231e29	0.568461
$259$	−2.95592e29	−0.201579
$260$	2.72736e29	0.177245
$261$	−8.67741e29	−0.537506
$262$	−5.66868e29	−0.334746
$263$	2.91127e29	0.163921	0.0819607	−	0.996636i	$-0.473882\pi$
$263$	2.91127e29	0.163921	0.0819607	+	0.996636i	$0.473882\pi$
$264$	−6.07371e29	−0.326141
$265$	4.78725e28	0.0245196
$266$	−4.95457e30	−2.42095
$267$	−2.01433e30	−0.939163
$268$	3.65966e30	1.62838
$269$	2.44305e30	1.03760	0.518798	−	0.854897i	$-0.326380\pi$
$269$	2.44305e30	1.03760	0.518798	+	0.854897i	$0.326380\pi$
$270$	6.54056e28	0.0265197
$271$	1.17336e30	0.454271	0.227135	−	0.973863i	$-0.427064\pi$
$271$	1.17336e30	0.454271	0.227135	+	0.973863i	$0.427064\pi$
$272$	−1.02781e30	−0.380016
$273$	3.73259e30	1.31819
$274$	1.13113e30	0.381620
$275$	4.12999e30	1.33134
$276$	−1.54143e30	−0.474853
$277$	−6.07402e29	−0.178846	−0.0894230	−	0.995994i	$-0.528502\pi$
$277$	−6.07402e29	−0.178846	−0.0894230	+	0.995994i	$0.528502\pi$
$278$	4.46515e30	1.25683
$279$	2.55078e29	0.0686469
$280$	2.24422e29	0.0577551
$281$	−5.25609e30	−1.29370	−0.646851	−	0.762617i	$-0.723914\pi$
$281$	−5.25609e30	−1.29370	−0.646851	+	0.762617i	$0.723914\pi$
$282$	−2.94052e30	−0.692325
$283$	−6.78837e30	−1.52910	−0.764549	−	0.644566i	$-0.777038\pi$
$283$	−6.78837e30	−1.52910	−0.764549	+	0.644566i	$0.777038\pi$
$284$	3.39915e30	0.732641
$285$	−2.72518e29	−0.0562126
$286$	−1.55861e31	−3.07725
$287$	7.75380e30	1.46552
$288$	−2.56452e30	−0.464088
$289$	−3.75859e30	−0.651331
$290$	−1.33884e30	−0.222205
$291$	8.28431e29	0.131702
$292$	1.14788e31	1.74829
$293$	−2.23205e30	−0.325731	−0.162866	−	0.986648i	$-0.552074\pi$
$293$	−2.23205e30	−0.325731	−0.162866	+	0.986648i	$0.552074\pi$
$294$	7.85832e30	1.09898
$295$	7.21484e29	0.0967056
$296$	−4.39023e29	−0.0564080
$297$	−2.09748e30	−0.258370
$298$	1.06229e31	1.25470
$299$	−8.62223e30	−0.976630
$300$	−6.73910e30	−0.732127
$301$	9.41113e30	0.980755
$302$	1.20871e31	1.20847
$303$	4.83114e30	0.463465
$304$	7.45602e30	0.686415
$305$	1.93264e29	0.0170767
$306$	3.50308e30	0.297121
$307$	−5.25614e28	−0.00427993	−0.00213997	−	0.999998i	$-0.500681\pi$
$307$	−5.25614e28	−0.00427993	−0.00213997	+	0.999998i	$0.500681\pi$
$308$	−3.30169e31	−2.58138
$309$	−7.82376e30	−0.587401
$310$	3.93562e29	0.0283787
$311$	−1.61442e31	−1.11818	−0.559092	−	0.829106i	$-0.688850\pi$
$311$	−1.61442e31	−1.11818	−0.559092	+	0.829106i	$0.688850\pi$
$312$	5.54376e30	0.368869
$313$	−3.82407e30	−0.244468	−0.122234	−	0.992501i	$-0.539006\pi$
$313$	−3.82407e30	−0.244468	−0.122234	+	0.992501i	$0.539006\pi$
$314$	1.81952e31	1.11773
$315$	7.75015e29	0.0457539
$316$	−2.66714e31	−1.51341
$317$	5.56285e30	0.303429	0.151714	−	0.988424i	$-0.451521\pi$
$317$	5.56285e30	0.303429	0.151714	+	0.988424i	$0.451521\pi$
$318$	4.46411e30	0.234097
$319$	4.29352e31	2.16486
$320$	−2.74518e30	−0.133106
$321$	3.40996e30	0.159015
$322$	−3.25485e31	−1.45993
$323$	−1.45959e31	−0.629794
$324$	3.42256e30	0.142082
$325$	−3.76963e31	−1.50576
$326$	4.85890e31	1.86775
$327$	1.61940e31	0.599111
$328$	1.15162e31	0.410096
$329$	−3.48433e31	−1.19446
$330$	−3.23622e30	−0.106810
$331$	1.85124e31	0.588318	0.294159	−	0.955757i	$-0.404961\pi$
$331$	1.85124e31	0.588318	0.294159	+	0.955757i	$0.404961\pi$
$332$	1.36536e31	0.417849
$333$	−1.51611e30	−0.0446867
$334$	−2.29958e31	−0.652856
$335$	4.25048e30	0.116246
$336$	−2.12042e31	−0.558703
$337$	4.53401e31	1.15109	0.575544	−	0.817771i	$-0.304790\pi$
$337$	4.53401e31	1.15109	0.575544	+	0.817771i	$0.304790\pi$
$338$	8.05589e31	1.97085
$339$	−2.37279e31	−0.559452
$340$	3.03303e30	0.0689272
$341$	−1.26211e31	−0.276482
$342$	−2.54123e31	−0.536683
$343$	1.92707e31	0.392394
$344$	1.39777e31	0.274445
$345$	−1.79027e30	−0.0338985
$346$	−5.36763e31	−0.980238
$347$	6.42994e31	1.13263	0.566316	−	0.824189i	$-0.308368\pi$
$347$	6.42994e31	1.13263	0.566316	+	0.824189i	$0.308368\pi$
$348$	−7.00593e31	−1.19049
$349$	−4.38036e31	−0.718111	−0.359056	−	0.933316i	$-0.616901\pi$
$349$	−4.38036e31	−0.718111	−0.359056	+	0.933316i	$0.616901\pi$
$350$	−1.42302e32	−2.25092
$351$	1.91447e31	0.292220
$352$	1.26891e32	1.86916
$353$	−3.21175e31	−0.456624	−0.228312	−	0.973588i	$-0.573321\pi$
$353$	−3.21175e31	−0.456624	−0.228312	+	0.973588i	$0.573321\pi$
$354$	6.72785e31	0.923285
$355$	3.94791e30	0.0523013
$356$	−1.62633e32	−2.08009
$357$	4.15093e31	0.512617
$358$	−2.42399e32	−2.89063
$359$	6.74932e31	0.777283	0.388642	−	0.921389i	$-0.372944\pi$
$359$	6.74932e31	0.777283	0.388642	+	0.921389i	$0.372944\pi$
$360$	1.15108e30	0.0128033
$361$	1.28058e31	0.137584
$362$	2.08878e32	2.16789
$363$	4.62018e31	0.463262
$364$	3.01360e32	2.91957
$365$	1.33320e31	0.124806
$366$	1.80219e31	0.163037
$367$	−5.00736e31	−0.437807	−0.218903	−	0.975747i	$-0.570248\pi$
$367$	−5.00736e31	−0.437807	−0.218903	+	0.975747i	$0.570248\pi$
$368$	4.89815e31	0.413937
$369$	3.97697e31	0.324880
$370$	−2.33922e30	−0.0184735
$371$	5.28969e31	0.403884
$372$	2.05944e31	0.152042
$373$	−1.80823e32	−1.29091	−0.645453	−	0.763800i	$-0.723331\pi$
$373$	−1.80823e32	−1.29091	−0.645453	+	0.763800i	$0.723331\pi$
$374$	−1.73330e32	−1.19668
$375$	−1.57199e31	−0.104968
$376$	−5.17503e31	−0.334245
$377$	−3.91889e32	−2.44848
$378$	7.22702e31	0.436829
$379$	−5.00271e31	−0.292560	−0.146280	−	0.989243i	$-0.546730\pi$
$379$	−5.00271e31	−0.292560	−0.146280	+	0.989243i	$0.546730\pi$
$380$	−2.20024e31	−0.124502
$381$	−1.68571e32	−0.923038
$382$	5.03376e32	2.66748
$383$	2.19665e31	0.112662	0.0563308	−	0.998412i	$-0.482060\pi$
$383$	2.19665e31	0.112662	0.0563308	+	0.998412i	$0.482060\pi$
$384$	−9.40683e31	−0.466985
$385$	−3.83471e31	−0.184278
$386$	−2.27436e32	−1.05808
$387$	4.82703e31	0.217417
$388$	6.68855e31	0.291699
$389$	4.63443e32	1.95716	0.978580	−	0.205869i	$-0.0660020\pi$
$389$	4.63443e32	1.95716	0.978580	+	0.205869i	$0.0660020\pi$
$390$	2.95385e31	0.120804
$391$	−9.58860e31	−0.379792
$392$	1.38299e32	0.530570
$393$	−3.44521e31	−0.128029
$394$	−2.82282e32	−1.01620
$395$	−3.09772e31	−0.108038
$396$	−1.69346e32	−0.572248
$397$	5.84292e31	0.191315	0.0956574	−	0.995414i	$-0.469505\pi$
$397$	5.84292e31	0.191315	0.0956574	+	0.995414i	$0.469505\pi$
$398$	1.38960e32	0.440910
$399$	−3.01119e32	−0.925929
$400$	2.14147e32	0.638206
$401$	2.73092e32	0.788868	0.394434	−	0.918924i	$-0.370941\pi$
$401$	2.73092e32	0.788868	0.394434	+	0.918924i	$0.370941\pi$
$402$	3.96357e32	1.10984
$403$	1.15198e32	0.312704
$404$	3.90055e32	1.02650
$405$	3.97510e30	0.0101429
$406$	−1.47936e33	−3.66015
$407$	7.50161e31	0.179980
$408$	6.16509e31	0.143446
$409$	6.95562e32	1.56962	0.784810	−	0.619736i	$-0.212760\pi$
$409$	6.95562e32	1.56962	0.784810	+	0.619736i	$0.212760\pi$
$410$	6.13610e31	0.134306
$411$	6.87458e31	0.145956
$412$	−6.31672e32	−1.30100
$413$	7.97207e32	1.59293
$414$	−1.66943e32	−0.323642
$415$	1.58578e31	0.0298292
$416$	−1.15819e33	−2.11404
$417$	2.71374e32	0.480693
$418$	1.25738e33	2.16154
$419$	−7.74699e32	−1.29258	−0.646291	−	0.763091i	$-0.723681\pi$
$419$	−7.74699e32	−1.29258	−0.646291	+	0.763091i	$0.723681\pi$
$420$	6.25728e31	0.101337
$421$	−5.09337e32	−0.800716	−0.400358	−	0.916359i	$-0.631114\pi$
$421$	−5.09337e32	−0.800716	−0.400358	+	0.916359i	$0.631114\pi$
$422$	−5.58902e32	−0.852962
$423$	−1.78713e32	−0.264791
$424$	7.85641e31	0.113019
$425$	−4.19213e32	−0.585562
$426$	3.68143e32	0.499340
$427$	2.13548e32	0.281285
$428$	2.75312e32	0.352191
$429$	−9.47265e32	−1.17694
$430$	7.44765e31	0.0898802
$431$	−2.10895e32	−0.247229	−0.123615	−	0.992330i	$-0.539449\pi$
$431$	−2.10895e32	−0.247229	−0.123615	+	0.992330i	$0.539449\pi$
$432$	−1.08758e32	−0.123855
$433$	7.11239e32	0.786895	0.393448	−	0.919347i	$-0.371282\pi$
$433$	7.11239e32	0.786895	0.393448	+	0.919347i	$0.371282\pi$
$434$	4.34868e32	0.467451
$435$	−8.13697e31	−0.0849859
$436$	1.30747e33	1.32693
$437$	6.95582e32	0.686010
$438$	1.24321e33	1.19157
$439$	−2.02250e32	−0.188400	−0.0942002	−	0.995553i	$-0.530029\pi$
$439$	−2.02250e32	−0.188400	−0.0942002	+	0.995553i	$0.530029\pi$
$440$	−5.69544e31	−0.0515666
$441$	4.77598e32	0.420320
$442$	1.58206e33	1.35346
$443$	−1.09416e33	−0.909983	−0.454992	−	0.890496i	$-0.650358\pi$
$443$	−1.09416e33	−0.909983	−0.454992	+	0.890496i	$0.650358\pi$
$444$	−1.22407e32	−0.0989737
$445$	−1.88888e32	−0.148492
$446$	−5.79769e32	−0.443169
$447$	6.45619e32	0.479879
$448$	−3.03330e33	−2.19251
$449$	6.24011e32	0.438645	0.219322	−	0.975652i	$-0.429615\pi$
$449$	6.24011e32	0.438645	0.219322	+	0.975652i	$0.429615\pi$
$450$	−7.29874e32	−0.498990
$451$	−1.96778e33	−1.30849
$452$	−1.91573e33	−1.23910
$453$	7.34606e32	0.462197
$454$	−3.07225e31	−0.0188044
$455$	3.50012e32	0.208420
$456$	−4.47232e32	−0.259103
$457$	−1.82004e33	−1.02595	−0.512976	−	0.858403i	$-0.671457\pi$
$457$	−1.82004e33	−1.02595	−0.512976	+	0.858403i	$0.671457\pi$
$458$	4.25654e33	2.33474
$459$	2.12904e32	0.113638
$460$	−1.44542e32	−0.0750797
$461$	−9.08278e31	−0.0459153	−0.0229576	−	0.999736i	$-0.507308\pi$
$461$	−9.08278e31	−0.0459153	−0.0229576	+	0.999736i	$0.507308\pi$
$462$	−3.57588e33	−1.75937
$463$	−1.85633e33	−0.888982	−0.444491	−	0.895783i	$-0.646615\pi$
$463$	−1.85633e33	−0.888982	−0.444491	+	0.895783i	$0.646615\pi$
$464$	2.22626e33	1.03777
$465$	2.39192e31	0.0108539
$466$	1.74342e33	0.770155
$467$	1.45425e33	0.625430	0.312715	−	0.949847i	$-0.398762\pi$
$467$	1.45425e33	0.625430	0.312715	+	0.949847i	$0.398762\pi$
$468$	1.54570e33	0.647219
$469$	4.69658e33	1.91479
$470$	−2.75738e32	−0.109465
$471$	1.10583e33	0.427492
$472$	1.18404e33	0.445749
$473$	−2.38838e33	−0.875667
$474$	−2.88863e33	−1.03148
$475$	3.04108e33	1.05769
$476$	3.35136e33	1.13536
$477$	2.71312e32	0.0895341
$478$	−4.02828e33	−1.29500
$479$	−6.07905e33	−1.90389	−0.951944	−	0.306272i	$-0.900918\pi$
$479$	−6.07905e33	−1.90389	−0.951944	+	0.306272i	$0.900918\pi$
$480$	−2.40480e32	−0.0733777
$481$	−6.84706e32	−0.203559
$482$	−1.33173e33	−0.385769
$483$	−1.97817e33	−0.558373
$484$	3.73023e33	1.02605
$485$	7.76835e31	0.0208237
$486$	3.70678e32	0.0968376
$487$	−2.28204e33	−0.581046	−0.290523	−	0.956868i	$-0.593829\pi$
$487$	−2.28204e33	−0.581046	−0.290523	+	0.956868i	$0.593829\pi$
$488$	3.17168e32	0.0787122
$489$	2.95305e33	0.714348
$490$	7.36889e32	0.173761
$491$	7.33838e33	1.68687	0.843435	−	0.537231i	$-0.180530\pi$
$491$	7.33838e33	1.68687	0.843435	+	0.537231i	$0.180530\pi$
$492$	3.21091e33	0.719556
$493$	−4.35811e33	−0.952164
$494$	−1.14767e34	−2.44472
$495$	−1.96685e32	−0.0408513
$496$	−6.54423e32	−0.132537
$497$	4.36226e33	0.861503
$498$	1.47874e33	0.284790
$499$	5.95476e33	1.11843	0.559213	−	0.829024i	$-0.311103\pi$
$499$	5.95476e33	1.11843	0.559213	+	0.829024i	$0.311103\pi$
$500$	−1.26919e33	−0.232488
$501$	−1.39759e33	−0.249695
$502$	−1.10006e34	−1.91698
$503$	−7.60315e33	−1.29239	−0.646195	−	0.763173i	$-0.723641\pi$
$503$	−7.60315e33	−1.29239	−0.646195	+	0.763173i	$0.723641\pi$
$504$	1.27189e33	0.210895
$505$	4.53026e32	0.0732792
$506$	8.26023e33	1.30350
$507$	4.89606e33	0.753784
$508$	−1.36100e34	−2.04438
$509$	−9.71557e33	−1.42395	−0.711977	−	0.702202i	$-0.752200\pi$
$509$	−9.71557e33	−1.42395	−0.711977	+	0.702202i	$0.752200\pi$
$510$	3.28491e32	0.0469782
$511$	1.47312e34	2.05579
$512$	8.56792e33	1.16681
$513$	−1.54446e33	−0.205263
$514$	1.94195e34	2.51883
$515$	−7.33649e32	−0.0928748
$516$	3.89723e33	0.481542
$517$	8.84261e33	1.06647
$518$	−2.58473e33	−0.304294
$519$	−3.26224e33	−0.374907
$520$	5.19848e32	0.0583223
$521$	1.96923e33	0.215688	0.107844	−	0.994168i	$-0.465605\pi$
$521$	1.96923e33	0.215688	0.107844	+	0.994168i	$0.465605\pi$
$522$	−7.58773e33	−0.811392
$523$	−1.04065e34	−1.08651	−0.543256	−	0.839567i	$-0.682809\pi$
$523$	−1.04065e34	−1.08651	−0.543256	+	0.839567i	$0.682809\pi$
$524$	−2.78158e33	−0.283563
$525$	−8.64854e33	−0.860898
$526$	2.54568e33	0.247447
$527$	1.28110e33	0.121604
$528$	5.38125e33	0.498838
$529$	−6.47622e33	−0.586308
$530$	4.18608e32	0.0370135
$531$	4.08893e33	0.353125
$532$	−2.43117e34	−2.05078
$533$	1.79608e34	1.47991
$534$	−1.76138e34	−1.41771
$535$	3.19759e32	0.0251420
$536$	6.97551e33	0.535816
$537$	−1.47321e34	−1.10557
$538$	2.13626e34	1.56630
$539$	−2.36312e34	−1.69288
$540$	3.20940e32	0.0224648
$541$	−2.46584e34	−1.68655	−0.843276	−	0.537482i	$-0.819376\pi$
$541$	−2.46584e34	−1.68655	−0.843276	+	0.537482i	$0.819376\pi$
$542$	1.02601e34	0.685744
$543$	1.26948e34	0.829142
$544$	−1.28800e34	−0.822108
$545$	1.51854e33	0.0947264
$546$	3.26387e34	1.98987
$547$	5.24127e33	0.312316	0.156158	−	0.987732i	$-0.450089\pi$
$547$	5.24127e33	0.312316	0.156158	+	0.987732i	$0.450089\pi$
$548$	5.55037e33	0.323270
$549$	1.09530e33	0.0623562
$550$	3.61136e34	2.00973
$551$	3.16149e34	1.71987
$552$	−2.93804e33	−0.156250
$553$	−3.42284e34	−1.77960
$554$	−5.31127e33	−0.269977
$555$	−1.42169e32	−0.00706548
$556$	2.19101e34	1.06466
$557$	−1.39636e34	−0.663447	−0.331724	−	0.943377i	$-0.607630\pi$
$557$	−1.39636e34	−0.663447	−0.331724	+	0.943377i	$0.607630\pi$
$558$	2.23046e33	0.103626
$559$	2.17998e34	0.990388
$560$	−1.98836e33	−0.0883374
$561$	−1.05343e34	−0.457690
$562$	−4.59605e34	−1.95290
$563$	2.74629e34	1.14128	0.570639	−	0.821201i	$-0.306696\pi$
$563$	2.74629e34	1.14128	0.570639	+	0.821201i	$0.306696\pi$
$564$	−1.44289e34	−0.586468
$565$	−2.22501e33	−0.0884558
$566$	−5.93591e34	−2.30825
$567$	4.39230e33	0.167072
$568$	6.47896e33	0.241074
$569$	7.30928e33	0.266055	0.133027	−	0.991112i	$-0.457530\pi$
$569$	7.30928e33	0.266055	0.133027	+	0.991112i	$0.457530\pi$
$570$	−2.38296e33	−0.0848557
$571$	−4.69258e33	−0.163478	−0.0817391	−	0.996654i	$-0.526047\pi$
$571$	−4.69258e33	−0.163478	−0.0817391	+	0.996654i	$0.526047\pi$
$572$	−7.64799e34	−2.60674
$573$	3.05933e34	1.02022
$574$	6.78011e34	2.21227
$575$	1.99780e34	0.637829
$576$	−1.55580e34	−0.486041
$577$	4.41926e34	1.35099	0.675494	−	0.737365i	$-0.263930\pi$
$577$	4.41926e34	1.35099	0.675494	+	0.737365i	$0.263930\pi$
$578$	−3.28660e34	−0.983215
$579$	−1.38227e34	−0.404679
$580$	−6.56960e33	−0.188230
$581$	1.75221e34	0.491343
$582$	7.24400e33	0.198811
$583$	−1.34243e34	−0.360607
$584$	2.18793e34	0.575271
$585$	1.79523e33	0.0462033
$586$	−1.95176e34	−0.491707
$587$	−5.60784e34	−1.38299	−0.691495	−	0.722381i	$-0.743048\pi$
$587$	−5.60784e34	−1.38299	−0.691495	+	0.722381i	$0.743048\pi$
$588$	3.85601e34	0.930941
$589$	−9.29341e33	−0.219651
$590$	6.30883e33	0.145982
$591$	−1.71560e34	−0.388663
$592$	3.88970e33	0.0862769
$593$	6.18340e34	1.34290	0.671450	−	0.741049i	$-0.265672\pi$
$593$	6.18340e34	1.34290	0.671450	+	0.741049i	$0.265672\pi$
$594$	−1.83409e34	−0.390023
$595$	3.89241e33	0.0810506
$596$	5.21257e34	1.06285
$597$	8.44542e33	0.168633
$598$	−7.53949e34	−1.47427
$599$	1.94044e33	0.0371592	0.0185796	−	0.999827i	$-0.494086\pi$
$599$	1.94044e33	0.0371592	0.0185796	+	0.999827i	$0.494086\pi$
$600$	−1.28451e34	−0.240905
$601$	−6.00426e34	−1.10288	−0.551441	−	0.834214i	$-0.685922\pi$
$601$	−6.00426e34	−1.10288	−0.551441	+	0.834214i	$0.685922\pi$
$602$	8.22932e34	1.48050
$603$	2.40891e34	0.424476
$604$	5.93104e34	1.02369
$605$	4.33243e33	0.0732470
$606$	4.22447e34	0.699623
$607$	−3.34248e34	−0.542263	−0.271131	−	0.962542i	$-0.587398\pi$
$607$	−3.34248e34	−0.542263	−0.271131	+	0.962542i	$0.587398\pi$
$608$	9.34348e34	1.48496
$609$	−8.99098e34	−1.39988
$610$	1.68995e33	0.0257781
$611$	−8.07105e34	−1.20619
$612$	1.71894e34	0.251690
$613$	2.96622e33	0.0425547	0.0212773	−	0.999774i	$-0.493227\pi$
$613$	2.96622e33	0.0425547	0.0212773	+	0.999774i	$0.493227\pi$
$614$	−4.59609e32	−0.00646077
$615$	3.72928e33	0.0513672
$616$	−6.29320e34	−0.849400
$617$	2.57569e34	0.340666	0.170333	−	0.985387i	$-0.445516\pi$
$617$	2.57569e34	0.340666	0.170333	+	0.985387i	$0.445516\pi$
$618$	−6.84129e34	−0.886710
$619$	7.07255e34	0.898345	0.449172	−	0.893445i	$-0.351719\pi$
$619$	7.07255e34	0.898345	0.449172	+	0.893445i	$0.351719\pi$
$620$	1.93118e33	0.0240395
$621$	−1.01462e34	−0.123782
$622$	−1.41169e35	−1.68795
$623$	−2.08713e35	−2.44595
$624$	−4.91172e34	−0.564191
$625$	8.66036e34	0.975070
$626$	−3.34386e34	−0.369036
$627$	7.64188e34	0.826715
$628$	8.92824e34	0.946826
$629$	−7.61446e33	−0.0791601
$630$	6.77691e33	0.0690677
$631$	6.80195e34	0.679621	0.339810	−	0.940494i	$-0.389637\pi$
$631$	6.80195e34	0.679621	0.339810	+	0.940494i	$0.389637\pi$
$632$	−5.08371e34	−0.497986
$633$	−3.39679e34	−0.326229
$634$	4.86429e34	0.458040
$635$	−1.58072e34	−0.145943
$636$	2.19051e34	0.198303
$637$	2.15693e35	1.91467
$638$	3.75435e35	3.26796
$639$	2.23743e34	0.190980
$640$	−8.82096e33	−0.0738357
$641$	1.55817e35	1.27906	0.639529	−	0.768767i	$-0.279129\pi$
$641$	1.55817e35	1.27906	0.639529	+	0.768767i	$0.279129\pi$
$642$	2.98175e34	0.240040
$643$	−1.08662e35	−0.857909	−0.428954	−	0.903326i	$-0.641118\pi$
$643$	−1.08662e35	−0.857909	−0.428954	+	0.903326i	$0.641118\pi$
$644$	−1.59713e35	−1.23671
$645$	4.52640e33	0.0343761
$646$	−1.27630e35	−0.950705
$647$	−1.20185e35	−0.878104	−0.439052	−	0.898462i	$-0.644686\pi$
$647$	−1.20185e35	−0.878104	−0.439052	+	0.898462i	$0.644686\pi$
$648$	6.52358e33	0.0467518
$649$	−2.02317e35	−1.42224
$650$	−3.29626e35	−2.27302
$651$	2.64296e34	0.178784
$652$	2.38422e35	1.58216
$653$	9.66750e34	0.629360	0.314680	−	0.949198i	$-0.398103\pi$
$653$	9.66750e34	0.629360	0.314680	+	0.949198i	$0.398103\pi$
$654$	1.41604e35	0.904388
$655$	−3.23063e33	−0.0202428
$656$	−1.02032e35	−0.627248
$657$	7.55575e34	0.455733
$658$	−3.04678e35	−1.80309
$659$	−1.57161e35	−0.912594	−0.456297	−	0.889827i	$-0.650825\pi$
$659$	−1.57161e35	−0.912594	−0.456297	+	0.889827i	$0.650825\pi$
$660$	−1.58799e34	−0.0904790
$661$	−8.62130e34	−0.482008	−0.241004	−	0.970524i	$-0.577477\pi$
$661$	−8.62130e34	−0.482008	−0.241004	+	0.970524i	$0.577477\pi$
$662$	1.61877e35	0.888094
$663$	9.61516e34	0.517651
$664$	2.60244e34	0.137493
$665$	−2.82365e34	−0.146400
$666$	−1.32572e34	−0.0674567
$667$	2.07690e35	1.03716
$668$	−1.12838e35	−0.553033
$669$	−3.52361e34	−0.169497
$670$	3.71672e34	0.175479
$671$	−5.41947e34	−0.251146
$672$	−2.65720e35	−1.20867
$673$	−1.74150e35	−0.777561	−0.388780	−	0.921330i	$-0.627104\pi$
$673$	−1.74150e35	−0.777561	−0.388780	+	0.921330i	$0.627104\pi$
$674$	3.96465e35	1.73762
$675$	−4.43589e34	−0.190846
$676$	3.95296e35	1.66951
$677$	4.45135e35	1.84558	0.922791	−	0.385300i	$-0.125902\pi$
$677$	4.45135e35	1.84558	0.922791	+	0.385300i	$0.125902\pi$
$678$	−2.07482e35	−0.844520
$679$	8.58367e34	0.343005
$680$	5.78112e33	0.0226804
$681$	−1.86720e33	−0.00719202
$682$	−1.10362e35	−0.417363
$683$	−2.46415e35	−0.914972	−0.457486	−	0.889217i	$-0.651250\pi$
$683$	−2.46415e35	−0.914972	−0.457486	+	0.889217i	$0.651250\pi$
$684$	−1.24696e35	−0.454623
$685$	6.44642e33	0.0230774
$686$	1.68508e35	0.592337
$687$	2.58696e35	0.892956
$688$	−1.23841e35	−0.419768
$689$	1.22530e35	0.407851
$690$	−1.56546e34	−0.0511715
$691$	−1.63661e35	−0.525376	−0.262688	−	0.964881i	$-0.584609\pi$
$691$	−1.63661e35	−0.525376	−0.262688	+	0.964881i	$0.584609\pi$
$692$	−2.63385e35	−0.830358
$693$	−2.17328e35	−0.672899
$694$	5.62249e35	1.70976
$695$	2.54473e34	0.0760031
$696$	−1.33537e35	−0.391729
$697$	1.99738e35	0.575508
$698$	−3.83029e35	−1.08402
$699$	1.05958e35	0.294558
$700$	−6.98263e35	−1.90675
$701$	−4.73884e34	−0.127115	−0.0635576	−	0.997978i	$-0.520245\pi$
$701$	−4.73884e34	−0.127115	−0.0635576	+	0.997978i	$0.520245\pi$
$702$	1.67406e35	0.441120
$703$	5.52373e34	0.142985
$704$	7.69799e35	1.95758
$705$	−1.67583e34	−0.0418664
$706$	−2.80843e35	−0.689296
$707$	5.00573e35	1.20705
$708$	3.30130e35	0.782113
$709$	−5.14318e35	−1.19716	−0.598582	−	0.801061i	$-0.704269\pi$
$709$	−5.14318e35	−1.19716	−0.598582	+	0.801061i	$0.704269\pi$
$710$	3.45215e34	0.0789514
$711$	−1.75560e35	−0.394507
$712$	−3.09986e35	−0.684451
$713$	−6.10520e34	−0.132459
$714$	3.62967e35	0.773820
$715$	−8.88268e34	−0.186088
$716$	−1.18943e36	−2.44865
$717$	−2.44823e35	−0.495294
$718$	5.90176e35	1.17335
$719$	−9.28958e35	−1.81503	−0.907517	−	0.420015i	$-0.862025\pi$
$719$	−9.28958e35	−1.81503	−0.907517	+	0.420015i	$0.862025\pi$
$720$	−1.01984e34	−0.0195829
$721$	−8.10649e35	−1.52983
$722$	1.11977e35	0.207690
$723$	−8.09373e34	−0.147543
$724$	1.02495e36	1.83641
$725$	9.08021e35	1.59908
$726$	4.04000e35	0.699316
$727$	1.37796e35	0.234453	0.117227	−	0.993105i	$-0.462600\pi$
$727$	1.37796e35	0.234453	0.117227	+	0.993105i	$0.462600\pi$
$728$	5.74409e35	0.960680
$729$	2.25284e34	0.0370370
$730$	1.16578e35	0.188400
$731$	2.42431e35	0.385142
$732$	8.84321e34	0.138109
$733$	1.02698e36	1.57675	0.788377	−	0.615192i	$-0.210922\pi$
$733$	1.02698e36	1.57675	0.788377	+	0.615192i	$0.210922\pi$
$734$	−4.37855e35	−0.660891
$735$	4.47853e34	0.0664574
$736$	6.13809e35	0.895490
$737$	−1.19191e36	−1.70962
$738$	3.47756e35	0.490422
$739$	4.04128e35	0.560355	0.280177	−	0.959948i	$-0.409607\pi$
$739$	4.04128e35	0.560355	0.280177	+	0.959948i	$0.409607\pi$
$740$	−1.14784e34	−0.0156489
$741$	−6.97509e35	−0.935023
$742$	4.62543e35	0.609682
$743$	−1.04053e35	−0.134863	−0.0674317	−	0.997724i	$-0.521480\pi$
$743$	−1.04053e35	−0.134863	−0.0674317	+	0.997724i	$0.521480\pi$
$744$	3.92540e34	0.0500291
$745$	6.05409e34	0.0758744
$746$	−1.58116e36	−1.94868
$747$	8.98721e34	0.108922
$748$	−8.50516e35	−1.01371
$749$	3.53319e35	0.414137
$750$	−1.37458e35	−0.158455
$751$	9.79610e35	1.11059	0.555295	−	0.831653i	$-0.312605\pi$
$751$	9.79610e35	1.11059	0.555295	+	0.831653i	$0.312605\pi$
$752$	4.58503e35	0.511233
$753$	−6.68572e35	−0.733181
$754$	−3.42677e36	−3.69610
$755$	6.88854e34	0.0730786
$756$	3.54624e35	0.370038
$757$	−8.91698e35	−0.915207	−0.457603	−	0.889156i	$-0.651292\pi$
$757$	−8.91698e35	−0.915207	−0.457603	+	0.889156i	$0.651292\pi$
$758$	−4.37449e35	−0.441634
$759$	5.02025e35	0.498543
$760$	−4.19378e34	−0.0409671
$761$	5.48524e35	0.527093	0.263546	−	0.964647i	$-0.415108\pi$
$761$	5.48524e35	0.527093	0.263546	+	0.964647i	$0.415108\pi$
$762$	−1.47402e36	−1.39337
$763$	1.67792e36	1.56032
$764$	2.47003e36	2.25962
$765$	1.99644e34	0.0179675
$766$	1.92080e35	0.170068
$767$	1.84664e36	1.60857
$768$	1.59755e35	0.136911
$769$	−2.07696e36	−1.75125	−0.875626	−	0.482990i	$-0.839551\pi$
$769$	−2.07696e36	−1.75125	−0.875626	+	0.482990i	$0.839551\pi$
$770$	−3.35317e35	−0.278177
$771$	1.18024e36	0.963364
$772$	−1.11601e36	−0.896298
$773$	1.93835e36	1.53175	0.765875	−	0.642990i	$-0.222306\pi$
$773$	1.93835e36	1.53175	0.765875	+	0.642990i	$0.222306\pi$
$774$	4.22087e35	0.328201
$775$	−2.66919e35	−0.204225
$776$	1.27487e35	0.0959833
$777$	−1.57090e35	−0.116382
$778$	4.05245e36	2.95443
$779$	−1.44895e36	−1.03953
$780$	1.44943e35	0.102333
$781$	−1.10706e36	−0.769192
$782$	−8.38450e35	−0.573314
$783$	−4.61153e35	−0.310330
$784$	−1.22531e36	−0.811516
$785$	1.03696e35	0.0675914
$786$	−3.01257e35	−0.193266
$787$	8.30443e35	0.524355	0.262178	−	0.965020i	$-0.415559\pi$
$787$	8.30443e35	0.524355	0.262178	+	0.965020i	$0.415559\pi$
$788$	−1.38514e36	−0.860825
$789$	1.54717e35	0.0946400
$790$	−2.70872e35	−0.163089
$791$	−2.45853e36	−1.45704
$792$	−3.22782e35	−0.188298
$793$	4.94660e35	0.284048
$794$	5.10919e35	0.288799
$795$	2.54414e34	0.0141564
$796$	6.81863e35	0.373494
$797$	3.17577e36	1.71246	0.856228	−	0.516598i	$-0.172802\pi$
$797$	3.17577e36	1.71246	0.856228	+	0.516598i	$0.172802\pi$
$798$	−2.63306e36	−1.39773
$799$	−8.97564e35	−0.469062
$800$	2.68357e36	1.38066
$801$	−1.07050e36	−0.542226
$802$	2.38798e36	1.19083
$803$	−3.73853e36	−1.83551
$804$	1.94489e36	0.940146
$805$	−1.85497e35	−0.0882852
$806$	1.00732e36	0.472042
$807$	1.29834e36	0.599057
$808$	7.43466e35	0.337768
$809$	−3.80663e36	−1.70288	−0.851439	−	0.524453i	$-0.824270\pi$
$809$	−3.80663e36	−1.70288	−0.851439	+	0.524453i	$0.824270\pi$
$810$	3.47592e34	0.0153111
$811$	5.00187e35	0.216956	0.108478	−	0.994099i	$-0.465402\pi$
$811$	5.00187e35	0.216956	0.108478	+	0.994099i	$0.465402\pi$
$812$	−7.25910e36	−3.10051
$813$	6.23571e35	0.262273
$814$	6.55958e35	0.271688
$815$	2.76913e35	0.112947
$816$	−5.46221e35	−0.219402
$817$	−1.75866e36	−0.695674
$818$	6.08216e36	2.36942
$819$	1.98365e36	0.761056
$820$	3.01093e35	0.113770
$821$	−1.20094e36	−0.446922	−0.223461	−	0.974713i	$-0.571736\pi$
$821$	−1.20094e36	−0.446922	−0.223461	+	0.974713i	$0.571736\pi$
$822$	6.01130e35	0.220328
$823$	−4.67512e36	−1.68770	−0.843849	−	0.536581i	$-0.819716\pi$
$823$	−4.67512e36	−1.68770	−0.843849	+	0.536581i	$0.819716\pi$
$824$	−1.20400e36	−0.428091
$825$	2.19485e36	0.768652
$826$	6.97097e36	2.40460
$827$	−4.49466e34	−0.0152714	−0.00763569	−	0.999971i	$-0.502431\pi$
$827$	−4.49466e34	−0.0152714	−0.00763569	+	0.999971i	$0.502431\pi$
$828$	−8.19177e35	−0.274157
$829$	3.21659e36	1.06039	0.530194	−	0.847877i	$-0.322119\pi$
$829$	3.21659e36	1.06039	0.530194	+	0.847877i	$0.322119\pi$
$830$	1.38664e35	0.0450286
$831$	−3.22798e35	−0.103257
$832$	−7.02630e36	−2.21404
$833$	2.39867e36	0.744575
$834$	2.37296e36	0.725630
$835$	−1.31055e35	−0.0394796
$836$	6.16987e36	1.83104
$837$	1.35559e35	0.0396333
$838$	−6.77416e36	−1.95121
$839$	2.98709e36	0.847663	0.423832	−	0.905741i	$-0.360685\pi$
$839$	2.98709e36	0.847663	0.423832	+	0.905741i	$0.360685\pi$
$840$	1.19267e35	0.0333449
$841$	5.80937e36	1.60022
$842$	−4.45376e36	−1.20872
$843$	−2.79330e36	−0.746919
$844$	−2.74249e36	−0.722543
$845$	4.59112e35	0.119182
$846$	−1.56271e36	−0.399714
$847$	4.78714e36	1.20652
$848$	−6.96071e35	−0.172864
$849$	−3.60762e36	−0.882825
$850$	−3.66570e36	−0.883934
$851$	3.62875e35	0.0862260
$852$	1.80645e36	0.422991
$853$	2.95963e36	0.682928	0.341464	−	0.939895i	$-0.389077\pi$
$853$	2.95963e36	0.682928	0.341464	+	0.939895i	$0.389077\pi$
$854$	1.86732e36	0.424614
$855$	−1.44827e35	−0.0324544
$856$	5.24760e35	0.115888
$857$	−6.08561e36	−1.32448	−0.662238	−	0.749294i	$-0.730393\pi$
$857$	−6.08561e36	−1.32448	−0.662238	+	0.749294i	$0.730393\pi$
$858$	−8.28311e36	−1.77665
$859$	−8.19217e36	−1.73175	−0.865873	−	0.500263i	$-0.833237\pi$
$859$	−8.19217e36	−1.73175	−0.865873	+	0.500263i	$0.833237\pi$
$860$	3.65450e35	0.0761374
$861$	4.12069e36	0.846116
$862$	−1.84411e36	−0.373205
$863$	−7.15190e36	−1.42655	−0.713274	−	0.700885i	$-0.752789\pi$
$863$	−7.15190e36	−1.42655	−0.713274	+	0.700885i	$0.752789\pi$
$864$	−1.36289e36	−0.267942
$865$	−3.05906e35	−0.0592771
$866$	6.21924e36	1.18786
$867$	−1.99747e36	−0.376046
$868$	2.13386e36	0.395977
$869$	8.68656e36	1.58891
$870$	−7.11516e35	−0.128290
$871$	1.08791e37	1.93360
$872$	2.49210e36	0.436626
$873$	4.40262e35	0.0760384
$874$	6.08234e36	1.03557
$875$	−1.62880e36	−0.273379
$876$	6.10033e36	1.00937
$877$	9.67080e36	1.57749	0.788746	−	0.614719i	$-0.210730\pi$
$877$	9.67080e36	1.57749	0.788746	+	0.614719i	$0.210730\pi$
$878$	−1.76852e36	−0.284400
$879$	−1.18621e36	−0.188061
$880$	5.04610e35	0.0788720
$881$	−1.66656e36	−0.256816	−0.128408	−	0.991721i	$-0.540987\pi$
$881$	−1.66656e36	−0.256816	−0.128408	+	0.991721i	$0.540987\pi$
$882$	4.17623e36	0.634494
$883$	−8.07227e36	−1.20917	−0.604584	−	0.796541i	$-0.706661\pi$
$883$	−8.07227e36	−1.20917	−0.604584	+	0.796541i	$0.706661\pi$
$884$	7.76305e36	1.14651
$885$	3.83426e35	0.0558330
$886$	−9.56758e36	−1.37366
$887$	8.15872e35	0.115499	0.0577493	−	0.998331i	$-0.481608\pi$
$887$	8.15872e35	0.115499	0.0577493	+	0.998331i	$0.481608\pi$
$888$	−2.33315e35	−0.0325672
$889$	−1.74662e37	−2.40396
$890$	−1.65168e36	−0.224156
$891$	−1.11469e36	−0.149170
$892$	−2.84488e36	−0.375408
$893$	6.51117e36	0.847258
$894$	5.64544e36	0.724401
$895$	−1.38145e36	−0.174803
$896$	−9.74676e36	−1.21621
$897$	−4.58221e36	−0.563857
$898$	5.45650e36	0.662156
$899$	−2.77487e36	−0.332083
$900$	−3.58143e36	−0.422694
$901$	1.36263e36	0.158605
$902$	−1.72067e37	−1.97522
$903$	5.00146e36	0.566239
$904$	−3.65149e36	−0.407722
$905$	1.19042e36	0.131097
$906$	6.42357e36	0.697709
$907$	1.53866e37	1.64836	0.824180	−	0.566328i	$-0.191637\pi$
$907$	1.53866e37	1.64836	0.824180	+	0.566328i	$0.191637\pi$
$908$	−1.50753e35	−0.0159292
$909$	2.56747e36	0.267582
$910$	3.06059e36	0.314621
$911$	2.89781e36	0.293826	0.146913	−	0.989149i	$-0.453066\pi$
$911$	2.89781e36	0.293826	0.146913	+	0.989149i	$0.453066\pi$
$912$	3.96243e36	0.396302
$913$	−4.44680e36	−0.438696
$914$	−1.59148e37	−1.54873
$915$	1.02709e35	0.00985923
$916$	2.08865e37	1.97775
$917$	−3.56970e36	−0.333438
$918$	1.86168e36	0.171543
$919$	−9.25351e36	−0.841129	−0.420564	−	0.907263i	$-0.638168\pi$
$919$	−9.25351e36	−0.841129	−0.420564	+	0.907263i	$0.638168\pi$
$920$	−2.75506e35	−0.0247049
$921$	−2.79333e34	−0.00247102
$922$	−7.94220e35	−0.0693113
$923$	1.01047e37	0.869964
$924$	−1.75465e37	−1.49036
$925$	1.58649e36	0.132943
$926$	−1.62322e37	−1.34196
$927$	−4.15787e36	−0.339136
$928$	2.78982e37	2.24506
$929$	1.72533e37	1.36986	0.684930	−	0.728609i	$-0.259833\pi$
$929$	1.72533e37	1.36986	0.684930	+	0.728609i	$0.259833\pi$
$930$	2.09155e35	0.0163844
$931$	−1.74006e37	−1.34491
$932$	8.55483e36	0.652397
$933$	−8.57971e36	−0.645583
$934$	1.27163e37	0.944116
$935$	−9.87824e35	−0.0723660
$936$	2.94618e36	0.212966
$937$	−2.17221e37	−1.54938	−0.774689	−	0.632342i	$-0.782094\pi$
$937$	−2.17221e37	−1.54938	−0.774689	+	0.632342i	$0.782094\pi$
$938$	4.10680e37	2.89047
$939$	−2.03227e36	−0.141143
$940$	−1.35302e36	−0.0927273
$941$	−2.26758e37	−1.53353	−0.766765	−	0.641928i	$-0.778135\pi$
$941$	−2.26758e37	−1.53353	−0.766765	+	0.641928i	$0.778135\pi$
$942$	9.66967e36	0.645320
$943$	−9.51873e36	−0.626878
$944$	−1.04905e37	−0.681780
$945$	4.11875e35	0.0264160
$946$	−2.08845e37	−1.32186
$947$	1.96352e37	1.22648	0.613240	−	0.789896i	$-0.289866\pi$
$947$	1.96352e37	1.22648	0.613240	+	0.789896i	$0.289866\pi$
$948$	−1.41743e37	−0.873768
$949$	3.41232e37	2.07598
$950$	2.65919e37	1.59663
$951$	2.95633e36	0.175185
$952$	6.38787e36	0.373589
$953$	−1.65954e37	−0.957911	−0.478956	−	0.877839i	$-0.658984\pi$
$953$	−1.65954e37	−0.957911	−0.478956	+	0.877839i	$0.658984\pi$
$954$	2.37241e36	0.135156
$955$	2.86879e36	0.161308
$956$	−1.97664e37	−1.09700
$957$	2.28175e37	1.24988
$958$	−5.31566e37	−2.87401
$959$	7.12300e36	0.380129
$960$	−1.45890e36	−0.0768486
$961$	−1.84171e37	−0.957588
$962$	−5.98723e36	−0.307282
$963$	1.81219e36	0.0918071
$964$	−6.53468e36	−0.326785
$965$	−1.29618e36	−0.0639844
$966$	−1.72976e37	−0.842892
$967$	−3.52975e37	−1.69790	−0.848952	−	0.528470i	$-0.822766\pi$
$967$	−3.52975e37	−1.69790	−0.848952	+	0.528470i	$0.822766\pi$
$968$	7.11001e36	0.337620
$969$	−7.75685e36	−0.363612
$970$	6.79283e35	0.0314343
$971$	3.12463e37	1.42744	0.713721	−	0.700430i	$-0.247009\pi$
$971$	3.12463e37	1.42744	0.713721	+	0.700430i	$0.247009\pi$
$972$	1.81889e36	0.0820310
$973$	2.81181e37	1.25192
$974$	−1.99547e37	−0.877117
$975$	−2.00334e37	−0.869354
$976$	−2.81008e36	−0.120392
$977$	−8.81021e36	−0.372653	−0.186326	−	0.982488i	$-0.559658\pi$
$977$	−8.81021e36	−0.372653	−0.186326	+	0.982488i	$0.559658\pi$
$978$	2.58222e37	1.07834
$979$	5.29675e37	2.18387
$980$	3.61586e36	0.147192
$981$	8.60616e36	0.345897
$982$	6.41686e37	2.54641
$983$	3.55817e37	1.39414	0.697072	−	0.717001i	$-0.254486\pi$
$983$	3.55817e37	1.39414	0.697072	+	0.717001i	$0.254486\pi$
$984$	6.12017e36	0.236769
$985$	−1.60875e36	−0.0614520
$986$	−3.81084e37	−1.43734
$987$	−1.85171e37	−0.689620
$988$	−5.63152e37	−2.07092
$989$	−1.15533e37	−0.419520
$990$	−1.71986e36	−0.0616671
$991$	4.28314e37	1.51650	0.758248	−	0.651966i	$-0.226056\pi$
$991$	4.28314e37	1.51650	0.758248	+	0.651966i	$0.226056\pi$
$992$	−8.20087e36	−0.286724
$993$	9.83823e36	0.339665
$994$	3.81446e37	1.30048
$995$	7.91943e35	0.0266628
$996$	7.25606e36	0.241245
$997$	6.61852e35	0.0217306	0.0108653	−	0.999941i	$-0.496541\pi$
$997$	6.61852e35	0.0217306	0.0108653	+	0.999941i	$0.496541\pi$
$998$	5.20698e37	1.68832
$999$	−8.05724e35	−0.0257999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.26.a.b.1.3	✓	3
3.2	odd	2		9.26.a.c.1.1		3
4.3	odd	2		48.26.a.i.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.26.a.b.1.3	✓	3	1.1	even	1	trivial
9.26.a.c.1.1		3	3.2	odd	2
48.26.a.i.1.2		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+8744.24 q^{2} +531441. q^{3} +4.29073e7 q^{4} +4.98342e7 q^{5} +4.64705e9 q^{6} +5.50645e10 q^{7} +8.17835e10 q^{8} +2.82430e11 q^{9} +O(q^{10})\)	\(q+8744.24 q^{2} +531441. q^{3} +4.29073e7 q^{4} +4.98342e7 q^{5} +4.64705e9 q^{6} +5.50645e10 q^{7} +8.17835e10 q^{8} +2.82430e11 q^{9} +4.35762e11 q^{10} -1.39744e13 q^{11} +2.28027e13 q^{12} +1.27551e14 q^{13} +4.81498e14 q^{14} +2.64840e13 q^{15} -7.24595e14 q^{16} +1.41846e15 q^{17} +2.46963e15 q^{18} -1.02899e16 q^{19} +2.13825e15 q^{20} +2.92636e16 q^{21} -1.22196e17 q^{22} -6.75984e16 q^{23} +4.34631e16 q^{24} -2.95540e17 q^{25} +1.11533e18 q^{26} +1.50095e17 q^{27} +2.36267e18 q^{28} -3.07242e18 q^{29} +2.31582e17 q^{30} +9.03157e17 q^{31} -9.08023e18 q^{32} -7.42657e18 q^{33} +1.24034e19 q^{34} +2.74410e18 q^{35} +1.21183e19 q^{36} -5.36810e18 q^{37} -8.99775e19 q^{38} +6.77857e19 q^{39} +4.07562e18 q^{40} +1.40813e20 q^{41} +2.55888e20 q^{42} +1.70911e20 q^{43} -5.99604e20 q^{44} +1.40747e19 q^{45} -5.91097e20 q^{46} -6.32772e20 q^{47} -3.85079e20 q^{48} +1.69104e21 q^{49} -2.58427e21 q^{50} +7.53830e20 q^{51} +5.47286e21 q^{52} +9.60635e20 q^{53} +1.31246e21 q^{54} -6.96404e20 q^{55} +4.50337e21 q^{56} -5.46848e21 q^{57} -2.68659e22 q^{58} +1.44777e22 q^{59} +1.13635e21 q^{60} +3.87814e21 q^{61} +7.89742e21 q^{62} +1.55519e22 q^{63} -5.50863e22 q^{64} +6.35639e21 q^{65} -6.49397e22 q^{66} +8.52923e22 q^{67} +6.08624e22 q^{68} -3.59246e22 q^{69} +2.39951e22 q^{70} +7.92209e22 q^{71} +2.30981e22 q^{72} +2.67527e23 q^{73} -4.69400e22 q^{74} -1.57062e23 q^{75} -4.41512e23 q^{76} -7.69494e23 q^{77} +5.92734e23 q^{78} -6.21605e23 q^{79} -3.61096e22 q^{80} +7.97664e22 q^{81} +1.23130e24 q^{82} +3.18211e23 q^{83} +1.25562e24 q^{84} +7.06881e22 q^{85} +1.49449e24 q^{86} -1.63281e24 q^{87} -1.14288e24 q^{88} -3.79033e24 q^{89} +1.23072e23 q^{90} +7.02353e24 q^{91} -2.90047e24 q^{92} +4.79975e23 q^{93} -5.53311e24 q^{94} -5.12790e23 q^{95} -4.82561e24 q^{96} +1.55884e24 q^{97} +1.47868e25 q^{98} -3.94678e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3678 q^{2} + 1594323 q^{3} + 90747588 q^{4} - 163152750 q^{5} - 1954639998 q^{6} - 9622572744 q^{7} - 268012830648 q^{8} + 847288609443 q^{9}+O(q^{10}) \) 3 * q - 3678 * q^2 + 1594323 * q^3 + 90747588 * q^4 - 163152750 * q^5 - 1954639998 * q^6 - 9622572744 * q^7 - 268012830648 * q^8 + 847288609443 * q^9	\( 3 q - 3678 q^{2} + 1594323 q^{3} + 90747588 q^{4} - 163152750 q^{5} - 1954639998 q^{6} - 9622572744 q^{7} - 268012830648 q^{8} + 847288609443 q^{9} + 8363188874700 q^{10} - 5946998130780 q^{11} + 48226988914308 q^{12} + 248137774407690 q^{13} + 754361641264848 q^{14} - 86706060612750 q^{15} + 23\!\cdots\!16 q^{16}+ \cdots - 16\!\cdots\!80 q^{99}+O(q^{100}) \) 3 * q - 3678 * q^2 + 1594323 * q^3 + 90747588 * q^4 - 163152750 * q^5 - 1954639998 * q^6 - 9622572744 * q^7 - 268012830648 * q^8 + 847288609443 * q^9 + 8363188874700 * q^10 - 5946998130780 * q^11 + 48226988914308 * q^12 + 248137774407690 * q^13 + 754361641264848 * q^14 - 86706060612750 * q^15 + 2394637852352016 * q^16 + 6640885201245174 * q^17 - 1038775835177118 * q^18 - 4282718959080516 * q^19 - 84999590549092200 * q^20 - 5113829681644104 * q^21 - 67279455312049512 * q^22 - 54558955951564152 * q^23 - 142433006732403768 * q^24 + 285270827389168125 * q^25 + 914405315527228956 * q^26 + 450283905890997363 * q^27 + 2416760102519597472 * q^28 - 506350856671782 * q^29 + 4444541458759442700 * q^30 - 120595458951353856 * q^31 - 23423805952813711584 * q^32 - 3160478633619853980 * q^33 - 30744163051965656604 * q^34 - 12895712434403329200 * q^35 + 25629799215608757828 * q^36 + 71124029266471833426 * q^37 - 151631523417421211736 * q^38 + 131870586968997181290 * q^39 + 487276555770533818800 * q^40 - 178237898435247428226 * q^41 + 400898704995432085968 * q^42 + 233732145791955002244 * q^43 - 1709130121883010683088 * q^44 - 46079155558100472750 * q^45 - 727064486838202905936 * q^46 - 578974907441950806192 * q^47 + 1272608734891807735056 * q^48 + 1540848623287695627627 * q^49 - 7598435156177129081250 * q^50 + 3529238672234936515734 * q^51 + 1549295968705274668344 * q^52 + 9056010625929165756258 * q^53 - 552048068622362767038 * q^54 + 16758715188531155952600 * q^55 + 7112451608305863332160 * q^56 - 2276012446332708503556 * q^57 - 43337630795958244629252 * q^58 + 23769324802557802948596 * q^59 - 45172267401000107860200 * q^60 - 11371716695373075009318 * q^61 - 21881713022451611321088 * q^62 - 2717698759842624273864 * q^63 - 55686925877484831566784 * q^64 + 89289247460368023248700 * q^65 - 35755061010490904706792 * q^66 + 52213761253321486240524 * q^67 + 318831609976592944413384 * q^68 - 28994866109855204503032 * q^69 - 78749858107500801357600 * q^70 + 262955361870665606618136 * q^71 - 75694739530875390869688 * q^72 - 11752720924176446629602 * q^73 - 498161580663483575957172 * q^74 + 151604613778526897518125 * q^75 + 4571105415149082363216 * q^76 - 1386525122949230445864288 * q^77 + 485952475289106083605596 * q^78 - 500543105756664483755760 * q^79 - 1540345885402641092176800 * q^80 + 239299329230617529590083 * q^81 + 4108759898128895060824212 * q^82 - 59055829437561671377284 * q^83 + 1284365405643117400117152 * q^84 - 2357173046017457952925500 * q^85 + 2057662432276923640084440 * q^86 - 269095605620508497862 * q^87 + 4527751242141959006666592 * q^88 - 3359875059386549548018866 * q^89 + 2362011557384576987930700 * q^90 + 1253870789177107094217744 * q^91 - 1905611545816878301689504 * q^92 - 64089371300566444586496 * q^93 - 18037990008720502135322400 * q^94 - 5406514800597015344021400 * q^95 - 12448370859369271697912544 * q^96 - 12029431225244267569541466 * q^97 + 24058796570011739277032850 * q^98 - 1679607925529568818985180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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