LMFDB - Embedded newform 7.20.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,20,Mod(1,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("7.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	7.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:	$16.0171687589$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 330513x^{2} - 30288715x + 14876898628 $ x^4 - x^3 - 330513x^2 - 30288715x + 14876898628
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-351.370$ of defining polynomial
Character	$\chi$	$=$	7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-788.739 q^{2} -48874.0 q^{3} +97821.5 q^{4} +1.27186e6 q^{5} +3.85488e7 q^{6} +4.03536e7 q^{7} +3.36371e8 q^{8} +1.22641e9 q^{9} +O(q^{10})$	\(q-788.739 q^{2} -48874.0 q^{3} +97821.5 q^{4} +1.27186e6 q^{5} +3.85488e7 q^{6} +4.03536e7 q^{7} +3.36371e8 q^{8} +1.22641e9 q^{9} -1.00316e9 q^{10} -1.85761e9 q^{11} -4.78092e9 q^{12} +4.46813e10 q^{13} -3.18285e10 q^{14} -6.21608e10 q^{15} -3.16595e11 q^{16} -4.46160e11 q^{17} -9.67314e11 q^{18} -9.17921e11 q^{19} +1.24415e11 q^{20} -1.97224e12 q^{21} +1.46517e12 q^{22} +1.30867e13 q^{23} -1.64398e13 q^{24} -1.74559e13 q^{25} -3.52419e13 q^{26} -3.13496e12 q^{27} +3.94745e12 q^{28} +4.64093e13 q^{29} +4.90287e13 q^{30} +2.15316e14 q^{31} +7.33561e13 q^{32} +9.07888e13 q^{33} +3.51904e14 q^{34} +5.13241e13 q^{35} +1.19969e14 q^{36} -1.10664e15 q^{37} +7.24000e14 q^{38} -2.18375e15 q^{39} +4.27816e14 q^{40} -1.88087e15 q^{41} +1.55558e15 q^{42} +2.11454e14 q^{43} -1.81714e14 q^{44} +1.55981e15 q^{45} -1.03220e16 q^{46} -1.24495e16 q^{47} +1.54733e16 q^{48} +1.62841e15 q^{49} +1.37681e16 q^{50} +2.18056e16 q^{51} +4.37079e15 q^{52} -3.30971e16 q^{53} +2.47267e15 q^{54} -2.36262e15 q^{55} +1.35738e16 q^{56} +4.48624e16 q^{57} -3.66048e16 q^{58} +1.30638e16 q^{59} -6.08066e15 q^{60} +9.68763e16 q^{61} -1.69828e17 q^{62} +4.94899e16 q^{63} +1.08128e17 q^{64} +5.68282e16 q^{65} -7.16087e16 q^{66} -1.33277e17 q^{67} -4.36441e16 q^{68} -6.39600e17 q^{69} -4.04813e16 q^{70} -5.00040e17 q^{71} +4.12527e17 q^{72} -6.02727e17 q^{73} +8.72846e17 q^{74} +8.53138e17 q^{75} -8.97923e16 q^{76} -7.49613e16 q^{77} +1.72241e18 q^{78} +2.00512e18 q^{79} -4.02665e17 q^{80} -1.27219e18 q^{81} +1.48351e18 q^{82} -2.33725e18 q^{83} -1.92928e17 q^{84} -5.67453e17 q^{85} -1.66782e17 q^{86} -2.26821e18 q^{87} -6.24846e17 q^{88} -1.48038e17 q^{89} -1.23029e18 q^{90} +1.80305e18 q^{91} +1.28016e18 q^{92} -1.05233e19 q^{93} +9.81943e18 q^{94} -1.16747e18 q^{95} -3.58520e18 q^{96} +9.98397e18 q^{97} -1.28439e18 q^{98} -2.27818e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 342 q^{2} - 29526 q^{3} + 576196 q^{4} - 2486610 q^{5} - 17324244 q^{6} + 161414428 q^{7} + 408794760 q^{8} - 335304432 q^{9}+O(q^{10}) $ 4 * q - 342 * q^2 - 29526 * q^3 + 576196 * q^4 - 2486610 * q^5 - 17324244 * q^6 + 161414428 * q^7 + 408794760 * q^8 - 335304432 * q^9	$ 4 q - 342 q^{2} - 29526 q^{3} + 576196 q^{4} - 2486610 q^{5} - 17324244 q^{6} + 161414428 q^{7} + 408794760 q^{8} - 335304432 q^{9} - 1397073720 q^{10} - 5232894012 q^{11} - 2652921096 q^{12} - 24071694934 q^{13} - 13800933594 q^{14} - 150674677560 q^{15} - 695063798768 q^{16} - 1122693554556 q^{17} - 2614443305094 q^{18} - 1689034371682 q^{19} - 6308977253040 q^{20} - 1191480600282 q^{21} - 16919940544224 q^{22} - 20343270469752 q^{23} - 9188544894480 q^{24} - 12146712350000 q^{25} - 5032107987984 q^{26} + 11404928663100 q^{27} + 23251586938972 q^{28} + 17794845083772 q^{29} + 274558228864560 q^{30} + 438619343652812 q^{31} + 172526736764448 q^{32} + 560272505144688 q^{33} + 582762872846028 q^{34} - 100343682702270 q^{35} + 218182607781732 q^{36} + 371101054682492 q^{37} + 269634109145940 q^{38} - 34\!\cdots\!08 q^{39}+ \cdots + 89\!\cdots\!76 q^{99}+O(q^{100}) $ 4 * q - 342 * q^2 - 29526 * q^3 + 576196 * q^4 - 2486610 * q^5 - 17324244 * q^6 + 161414428 * q^7 + 408794760 * q^8 - 335304432 * q^9 - 1397073720 * q^10 - 5232894012 * q^11 - 2652921096 * q^12 - 24071694934 * q^13 - 13800933594 * q^14 - 150674677560 * q^15 - 695063798768 * q^16 - 1122693554556 * q^17 - 2614443305094 * q^18 - 1689034371682 * q^19 - 6308977253040 * q^20 - 1191480600282 * q^21 - 16919940544224 * q^22 - 20343270469752 * q^23 - 9188544894480 * q^24 - 12146712350000 * q^25 - 5032107987984 * q^26 + 11404928663100 * q^27 + 23251586938972 * q^28 + 17794845083772 * q^29 + 274558228864560 * q^30 + 438619343652812 * q^31 + 172526736764448 * q^32 + 560272505144688 * q^33 + 582762872846028 * q^34 - 100343682702270 * q^35 + 218182607781732 * q^36 + 371101054682492 * q^37 + 269634109145940 * q^38 - 3445721278709808 * q^39 - 2289575448232800 * q^40 - 3519649536072516 * q^41 - 699095733948108 * q^42 - 4463367374178964 * q^43 - 6600729725725248 * q^44 - 1687781379790170 * q^45 - 6244953162457584 * q^46 - 12676380373106604 * q^47 + 4614181098145248 * q^48 + 6513654391641796 * q^49 + 23522915071245150 * q^50 + 8700163413214284 * q^51 + 35559530560574048 * q^52 + 15595612222940712 * q^53 + 68288349157759080 * q^54 + 37500795299828280 * q^55 + 16496343088699320 * q^56 + 66467738474740644 * q^57 + 37511423793126180 * q^58 - 128722843456786530 * q^59 + 10245923524095840 * q^60 - 99854565167649586 * q^61 + 49326848870064696 * q^62 - 13530743274286224 * q^63 - 127576935362475968 * q^64 - 222541932083245740 * q^65 - 95494018388787648 * q^66 - 559752529353715960 * q^67 - 6263410841045064 * q^68 - 1102648068919821312 * q^69 - 56376963846908040 * q^70 - 431823453358672584 * q^71 + 703582531856039880 * q^72 - 141778013178404848 * q^73 + 1377884102545752948 * q^74 + 593927230875286350 * q^75 + 1376586984318613256 * q^76 - 211166148432901284 * q^77 + 2441041974988075872 * q^78 - 278647331872313704 * q^79 + 2706945628302054720 * q^80 - 1240959746750205096 * q^81 + 5728992758934332076 * q^82 - 2246245523526488778 * q^83 - 107054935309993272 * q^84 - 738241927356169860 * q^85 + 1262160114799888656 * q^86 - 6303774078790689564 * q^87 - 1138532883653020800 * q^88 - 7106866925026829688 * q^89 + 3296867742504813960 * q^90 - 971379717190526938 * q^91 - 943516940294209248 * q^92 - 13447340691609448200 * q^93 - 8959883069564168952 * q^94 - 16322573541779844120 * q^95 + 8638732606243594176 * q^96 - 237692331127149724 * q^97 - 556917450485373558 * q^98 + 8957687784547224276 * 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 $

$2$	−788.739	−1.08930	−0.544651	−	0.838663i	$-0.683338\pi$
$2$	−788.739	−1.08930	−0.544651	+	0.838663i	$0.683338\pi$
$3$	−48874.0	−1.43359	−0.716796	−	0.697282i	$-0.754392\pi$
$3$	−48874.0	−1.43359	−0.716796	+	0.697282i	$0.754392\pi$
$4$	97821.5	0.186580
$5$	1.27186e6	0.291222	0.145611	−	0.989342i	$-0.453485\pi$
$5$	1.27186e6	0.291222	0.145611	+	0.989342i	$0.453485\pi$
$6$	3.85488e7	1.56162
$7$	4.03536e7	0.377964
$7$	4.03536e7	0.377964
$8$	3.36371e8	0.886061
$9$	1.22641e9	1.05519
$10$	−1.00316e9	−0.317229
$11$	−1.85761e9	−0.237533	−0.118767	−	0.992922i	$-0.537894\pi$
$11$	−1.85761e9	−0.237533	−0.118767	+	0.992922i	$0.537894\pi$
$12$	−4.78092e9	−0.267479
$13$	4.46813e10	1.16859	0.584297	−	0.811540i	$-0.301370\pi$
$13$	4.46813e10	1.16859	0.584297	+	0.811540i	$0.301370\pi$
$14$	−3.18285e10	−0.411718
$15$	−6.21608e10	−0.417493
$16$	−3.16595e11	−1.15177
$17$	−4.46160e11	−0.912486	−0.456243	−	0.889855i	$-0.650805\pi$
$17$	−4.46160e11	−0.912486	−0.456243	+	0.889855i	$0.650805\pi$
$18$	−9.67314e11	−1.14942
$19$	−9.17921e11	−0.652598	−0.326299	−	0.945267i	$-0.605802\pi$
$19$	−9.17921e11	−0.652598	−0.326299	+	0.945267i	$0.605802\pi$
$20$	1.24415e11	0.0543360
$21$	−1.97224e12	−0.541847
$22$	1.46517e12	0.258745
$23$	1.30867e13	1.51501	0.757506	−	0.652828i	$-0.226418\pi$
$23$	1.30867e13	1.51501	0.757506	+	0.652828i	$0.226418\pi$
$24$	−1.64398e13	−1.27025
$25$	−1.74559e13	−0.915190
$26$	−3.52419e13	−1.27295
$27$	−3.13496e12	−0.0791182
$28$	3.94745e12	0.0705205
$29$	4.64093e13	0.594051	0.297025	−	0.954870i	$-0.404005\pi$
$29$	4.64093e13	0.594051	0.297025	+	0.954870i	$0.404005\pi$
$30$	4.90287e13	0.454777
$31$	2.15316e14	1.46265	0.731324	−	0.682030i	$-0.238903\pi$
$31$	2.15316e14	1.46265	0.731324	+	0.682030i	$0.238903\pi$
$32$	7.33561e13	0.368563
$33$	9.07888e13	0.340526
$34$	3.51904e14	0.993973
$35$	5.13241e13	0.110071
$36$	1.19969e14	0.196877
$37$	−1.10664e15	−1.39987	−0.699936	−	0.714206i	$-0.746788\pi$
$37$	−1.10664e15	−1.39987	−0.699936	+	0.714206i	$0.746788\pi$
$38$	7.24000e14	0.710877
$39$	−2.18375e15	−1.67529
$40$	4.27816e14	0.258040
$41$	−1.88087e15	−0.897246	−0.448623	−	0.893721i	$-0.648085\pi$
$41$	−1.88087e15	−0.897246	−0.448623	+	0.893721i	$0.648085\pi$
$42$	1.55558e15	0.590235
$43$	2.11454e14	0.0641601	0.0320801	−	0.999485i	$-0.489787\pi$
$43$	2.11454e14	0.0641601	0.0320801	+	0.999485i	$0.489787\pi$
$44$	−1.81714e14	−0.0443188
$45$	1.55981e15	0.307294
$46$	−1.03220e16	−1.65031
$47$	−1.24495e16	−1.62264	−0.811322	−	0.584600i	$-0.801252\pi$
$47$	−1.24495e16	−1.62264	−0.811322	+	0.584600i	$0.801252\pi$
$48$	1.54733e16	1.65117
$49$	1.62841e15	0.142857
$50$	1.37681e16	0.996919
$51$	2.18056e16	1.30813
$52$	4.37079e15	0.218036
$53$	−3.30971e16	−1.37775	−0.688873	−	0.724882i	$-0.741894\pi$
$53$	−3.30971e16	−1.37775	−0.688873	+	0.724882i	$0.741894\pi$
$54$	2.47267e15	0.0861837
$55$	−2.36262e15	−0.0691748
$56$	1.35738e16	0.334899
$57$	4.48624e16	0.935560
$58$	−3.66048e16	−0.647101
$59$	1.30638e16	0.196324	0.0981622	−	0.995170i	$-0.468704\pi$
$59$	1.30638e16	0.196324	0.0981622	+	0.995170i	$0.468704\pi$
$60$	−6.08066e15	−0.0778958
$61$	9.68763e16	1.06068	0.530340	−	0.847785i	$-0.322064\pi$
$61$	9.68763e16	1.06068	0.530340	+	0.847785i	$0.322064\pi$
$62$	−1.69828e17	−1.59327
$63$	4.94899e16	0.398824
$64$	1.08128e17	0.750292
$65$	5.68282e16	0.340320
$66$	−7.16087e16	−0.370935
$67$	−1.33277e17	−0.598474	−0.299237	−	0.954179i	$-0.596732\pi$
$67$	−1.33277e17	−0.598474	−0.299237	+	0.954179i	$0.596732\pi$
$68$	−4.36441e16	−0.170251
$69$	−6.39600e17	−2.17191
$70$	−4.04813e16	−0.119901
$71$	−5.00040e17	−1.29435	−0.647173	−	0.762343i	$-0.724049\pi$
$71$	−5.00040e17	−1.29435	−0.647173	+	0.762343i	$0.724049\pi$
$72$	4.12527e17	0.934961
$73$	−6.02727e17	−1.19827	−0.599133	−	0.800650i	$-0.704488\pi$
$73$	−6.02727e17	−1.19827	−0.599133	+	0.800650i	$0.704488\pi$
$74$	8.72846e17	1.52488
$75$	8.53138e17	1.31201
$76$	−8.97923e16	−0.121762
$77$	−7.49613e16	−0.0897790
$78$	1.72241e18	1.82489
$79$	2.00512e18	1.88227	0.941135	−	0.338031i	$-0.109761\pi$
$79$	2.00512e18	1.88227	0.941135	+	0.338031i	$0.109761\pi$
$80$	−4.02665e17	−0.335420
$81$	−1.27219e18	−0.941765
$82$	1.48351e18	0.977372
$83$	−2.33725e18	−1.37235	−0.686173	−	0.727439i	$-0.740710\pi$
$83$	−2.33725e18	−1.37235	−0.686173	+	0.727439i	$0.740710\pi$
$84$	−1.92928e17	−0.101098
$85$	−5.67453e17	−0.265736
$86$	−1.66782e17	−0.0698898
$87$	−2.26821e18	−0.851627
$88$	−6.24846e17	−0.210469
$89$	−1.48038e17	−0.0447887	−0.0223943	−	0.999749i	$-0.507129\pi$
$89$	−1.48038e17	−0.0447887	−0.0223943	+	0.999749i	$0.507129\pi$
$90$	−1.23029e18	−0.334736
$91$	1.80305e18	0.441687
$92$	1.28016e18	0.282670
$93$	−1.05233e19	−2.09684
$94$	9.81943e18	1.76755
$95$	−1.16747e18	−0.190051
$96$	−3.58520e18	−0.528369
$97$	9.98397e18	1.33343	0.666717	−	0.745311i	$-0.267699\pi$
$97$	9.98397e18	1.33343	0.666717	+	0.745311i	$0.267699\pi$
$98$	−1.28439e18	−0.155615
$99$	−2.27818e18	−0.250642
$100$	−1.70756e18	−0.170756
$101$	−7.10200e18	−0.646141	−0.323071	−	0.946375i	$-0.604715\pi$
$101$	−7.10200e18	−0.646141	−0.323071	+	0.946375i	$0.604715\pi$
$102$	−1.71990e19	−1.42495
$103$	4.95141e18	0.373917	0.186958	−	0.982368i	$-0.440137\pi$
$103$	4.95141e18	0.373917	0.186958	+	0.982368i	$0.440137\pi$
$104$	1.50295e19	1.03544
$105$	−2.50841e18	−0.157798
$106$	2.61050e19	1.50078
$107$	6.00407e18	0.315718	0.157859	−	0.987462i	$-0.449541\pi$
$107$	6.00407e18	0.315718	0.157859	+	0.987462i	$0.449541\pi$
$108$	−3.06667e17	−0.0147619
$109$	−9.10349e18	−0.401473	−0.200736	−	0.979645i	$-0.564333\pi$
$109$	−9.10349e18	−0.401473	−0.200736	+	0.979645i	$0.564333\pi$
$110$	1.86349e18	0.0753523
$111$	5.40857e19	2.00685
$112$	−1.27758e19	−0.435327
$113$	−3.32614e19	−1.04159	−0.520793	−	0.853683i	$-0.674364\pi$
$113$	−3.32614e19	−1.04159	−0.520793	+	0.853683i	$0.674364\pi$
$114$	−3.53848e19	−1.01911
$115$	1.66444e19	0.441205
$116$	4.53982e18	0.110838
$117$	5.47973e19	1.23309
$118$	−1.03039e19	−0.213857
$119$	−1.80042e19	−0.344887
$120$	−2.09091e19	−0.369925
$121$	−5.77084e19	−0.943578
$122$	−7.64101e19	−1.15540
$123$	9.19255e19	1.28629
$124$	2.10625e19	0.272900
$125$	−4.64602e19	−0.557745
$126$	−3.90346e19	−0.434440
$127$	−1.36200e19	−0.140619	−0.0703093	−	0.997525i	$-0.522399\pi$
$127$	−1.36200e19	−0.140619	−0.0703093	+	0.997525i	$0.522399\pi$
$128$	−1.23745e20	−1.18586
$129$	−1.03346e19	−0.0919795
$130$	−4.48227e19	−0.370711
$131$	1.97489e20	1.51868	0.759340	−	0.650695i	$-0.225522\pi$
$131$	1.97489e20	1.51868	0.759340	+	0.650695i	$0.225522\pi$
$132$	8.88109e18	0.0635352
$133$	−3.70414e19	−0.246659
$134$	1.05121e20	0.651919
$135$	−3.98723e18	−0.0230410
$136$	−1.50075e20	−0.808518
$137$	−1.52513e20	−0.766410	−0.383205	−	0.923663i	$-0.625180\pi$
$137$	−1.52513e20	−0.766410	−0.383205	+	0.923663i	$0.625180\pi$
$138$	5.04477e20	2.36587
$139$	−1.24497e20	−0.545154	−0.272577	−	0.962134i	$-0.587876\pi$
$139$	−1.24497e20	−0.545154	−0.272577	+	0.962134i	$0.587876\pi$
$140$	5.02060e18	0.0205371
$141$	6.08458e20	2.32621
$142$	3.94401e20	1.40993
$143$	−8.30003e19	−0.277580
$144$	−3.88274e20	−1.21533
$145$	5.90260e19	0.173001
$146$	4.75394e20	1.30527
$147$	−7.95871e19	−0.204799
$148$	−1.08253e20	−0.261187
$149$	−4.86282e20	−1.10057	−0.550286	−	0.834976i	$-0.685481\pi$
$149$	−4.86282e20	−1.10057	−0.550286	+	0.834976i	$0.685481\pi$
$150$	−6.72903e20	−1.42918
$151$	−7.15114e20	−1.42592	−0.712959	−	0.701206i	$-0.752645\pi$
$151$	−7.15114e20	−1.42592	−0.712959	+	0.701206i	$0.752645\pi$
$152$	−3.08762e20	−0.578242
$153$	−5.47174e20	−0.962845
$154$	5.91249e19	0.0977965
$155$	2.73851e20	0.425955
$156$	−2.13618e20	−0.312575
$157$	1.10030e21	1.51518	0.757591	−	0.652730i	$-0.226376\pi$
$157$	1.10030e21	1.51518	0.757591	+	0.652730i	$0.226376\pi$
$158$	−1.58151e21	−2.05036
$159$	1.61759e21	1.97513
$160$	9.32985e19	0.107333
$161$	5.28096e20	0.572621
$162$	1.00342e21	1.02587
$163$	−1.29482e21	−1.24862	−0.624308	−	0.781179i	$-0.714619\pi$
$163$	−1.29482e21	−1.24862	−0.624308	+	0.781179i	$0.714619\pi$
$164$	−1.83989e20	−0.167408
$165$	1.15471e20	0.0991685
$166$	1.84348e21	1.49490
$167$	−9.17055e20	−0.702407	−0.351204	−	0.936299i	$-0.614228\pi$
$167$	−9.17055e20	−0.702407	−0.351204	+	0.936299i	$0.614228\pi$
$168$	−6.63405e20	−0.480110
$169$	5.34494e20	0.365611
$170$	4.47572e20	0.289467
$171$	−1.12574e21	−0.688614
$172$	2.06847e19	0.0119710
$173$	−1.03140e21	−0.564925	−0.282463	−	0.959278i	$-0.591151\pi$
$173$	−1.03140e21	−0.564925	−0.282463	+	0.959278i	$0.591151\pi$
$174$	1.78902e21	0.927680
$175$	−7.04407e20	−0.345909
$176$	5.88111e20	0.273583
$177$	−6.38478e20	−0.281449
$178$	1.16763e20	0.0487884
$179$	1.16901e21	0.463143	0.231571	−	0.972818i	$-0.425613\pi$
$179$	1.16901e21	0.463143	0.231571	+	0.972818i	$0.425613\pi$
$180$	1.52583e20	0.0573348
$181$	3.01695e21	1.07553	0.537764	−	0.843096i	$-0.319269\pi$
$181$	3.01695e21	1.07553	0.537764	+	0.843096i	$0.319269\pi$
$182$	−1.42214e21	−0.481131
$183$	−4.73473e21	−1.52058
$184$	4.40199e21	1.34239
$185$	−1.40748e21	−0.407673
$186$	8.30017e21	2.28410
$187$	8.28792e20	0.216746
$188$	−1.21783e21	−0.302752
$189$	−1.26507e20	−0.0299039
$190$	9.20826e20	0.207023
$191$	−7.85255e21	−1.67955	−0.839776	−	0.542933i	$-0.817314\pi$
$191$	−7.85255e21	−1.67955	−0.839776	+	0.542933i	$0.817314\pi$
$192$	−5.28467e21	−1.07561
$193$	−9.45636e20	−0.183202	−0.0916009	−	0.995796i	$-0.529198\pi$
$193$	−9.45636e20	−0.183202	−0.0916009	+	0.995796i	$0.529198\pi$
$194$	−7.87475e21	−1.45251
$195$	−2.77742e21	−0.487880
$196$	1.59294e20	0.0266542
$197$	−9.74790e21	−1.55411	−0.777055	−	0.629433i	$-0.783287\pi$
$197$	−9.74790e21	−1.55411	−0.777055	+	0.629433i	$0.783287\pi$
$198$	1.79689e21	0.273025
$199$	1.17693e22	1.70470	0.852348	−	0.522976i	$-0.175178\pi$
$199$	1.17693e22	1.70470	0.852348	+	0.522976i	$0.175178\pi$
$200$	−5.87164e21	−0.810914
$201$	6.51379e21	0.857968
$202$	5.60163e21	0.703843
$203$	1.87278e21	0.224530
$204$	2.13306e21	0.244071
$205$	−2.39220e21	−0.261298
$206$	−3.90537e21	−0.407308
$207$	1.60496e22	1.59862
$208$	−1.41459e22	−1.34595
$209$	1.70514e21	0.155014
$210$	1.97848e21	0.171889
$211$	4.30081e21	0.357163	0.178582	−	0.983925i	$-0.442849\pi$
$211$	4.30081e21	0.357163	0.178582	+	0.983925i	$0.442849\pi$
$212$	−3.23761e21	−0.257060
$213$	2.44389e22	1.85557
$214$	−4.73565e21	−0.343913
$215$	2.68939e20	0.0186848
$216$	−1.05451e21	−0.0701036
$217$	8.68877e21	0.552829
$218$	7.18028e21	0.437325
$219$	2.94577e22	1.71783
$220$	−2.31115e20	−0.0129066
$221$	−1.99350e22	−1.06633
$222$	−4.26595e22	−2.18606
$223$	−6.06376e20	−0.0297746	−0.0148873	−	0.999889i	$-0.504739\pi$
$223$	−6.06376e20	−0.0297746	−0.0148873	+	0.999889i	$0.504739\pi$
$224$	2.96018e21	0.139304
$225$	−2.14080e22	−0.965698
$226$	2.62346e22	1.13460
$227$	8.88416e21	0.368443	0.184222	−	0.982885i	$-0.441024\pi$
$227$	8.88416e21	0.368443	0.184222	+	0.982885i	$0.441024\pi$
$228$	4.38851e21	0.174557
$229$	−3.23682e22	−1.23504	−0.617520	−	0.786555i	$-0.711863\pi$
$229$	−3.23682e22	−1.23504	−0.617520	+	0.786555i	$0.711863\pi$
$230$	−1.31281e22	−0.480605
$231$	3.66366e21	0.128707
$232$	1.56107e22	0.526365
$233$	1.29936e22	0.420581	0.210290	−	0.977639i	$-0.432559\pi$
$233$	1.29936e22	0.420581	0.210290	+	0.977639i	$0.432559\pi$
$234$	−4.32208e22	−1.34320
$235$	−1.58340e22	−0.472549
$236$	1.27792e21	0.0366301
$237$	−9.79980e22	−2.69841
$238$	1.42006e22	0.375687
$239$	2.18589e22	0.555711	0.277855	−	0.960623i	$-0.410376\pi$
$239$	2.18589e22	0.555711	0.277855	+	0.960623i	$0.410376\pi$
$240$	1.96798e22	0.480855
$241$	−1.76662e22	−0.414935	−0.207468	−	0.978242i	$-0.566522\pi$
$241$	−1.76662e22	−0.414935	−0.207468	+	0.978242i	$0.566522\pi$
$242$	4.55169e22	1.02784
$243$	6.58204e22	1.42923
$244$	9.47658e21	0.197901
$245$	2.07111e21	0.0416031
$246$	−7.25052e22	−1.40115
$247$	−4.10138e22	−0.762622
$248$	7.24260e22	1.29600
$249$	1.14231e23	1.96738
$250$	3.66450e22	0.607553
$251$	1.77430e22	0.283222	0.141611	−	0.989922i	$-0.454772\pi$
$251$	1.77430e22	0.283222	0.141611	+	0.989922i	$0.454772\pi$
$252$	4.84117e21	0.0744124
$253$	−2.43100e22	−0.359865
$254$	1.07426e22	0.153176
$255$	2.77337e22	0.380957
$256$	4.09120e22	0.541465
$257$	−1.09500e23	−1.39653	−0.698267	−	0.715838i	$-0.746045\pi$
$257$	−1.09500e23	−1.39653	−0.698267	+	0.715838i	$0.746045\pi$
$258$	8.15130e21	0.100194
$259$	−4.46567e22	−0.529102
$260$	5.55902e21	0.0634968
$261$	5.69166e22	0.626836
$262$	−1.55767e23	−1.65430
$263$	−4.95899e22	−0.507941	−0.253971	−	0.967212i	$-0.581737\pi$
$263$	−4.95899e22	−0.507941	−0.253971	+	0.967212i	$0.581737\pi$
$264$	3.05387e22	0.301726
$265$	−4.20949e22	−0.401230
$266$	2.92160e22	0.268686
$267$	7.23521e21	0.0642087
$268$	−1.30374e22	−0.111663
$269$	1.06647e23	0.881660	0.440830	−	0.897591i	$-0.354684\pi$
$269$	1.06647e23	0.881660	0.440830	+	0.897591i	$0.354684\pi$
$270$	3.14488e21	0.0250986
$271$	−8.23978e22	−0.634903	−0.317452	−	0.948274i	$-0.602827\pi$
$271$	−8.23978e22	−0.634903	−0.317452	+	0.948274i	$0.602827\pi$
$272$	1.41252e23	1.05097
$273$	−8.81222e22	−0.633199
$274$	1.20293e23	0.834852
$275$	3.24262e22	0.217388
$276$	−6.25666e22	−0.405234
$277$	−2.15676e23	−1.34972	−0.674861	−	0.737945i	$-0.735796\pi$
$277$	−2.15676e23	−1.34972	−0.674861	+	0.737945i	$0.735796\pi$
$278$	9.81958e22	0.593837
$279$	2.64064e23	1.54337
$280$	1.72639e22	0.0975300
$281$	−1.66823e23	−0.911059	−0.455530	−	0.890221i	$-0.650550\pi$
$281$	−1.66823e23	−0.911059	−0.455530	+	0.890221i	$0.650550\pi$
$282$	−4.79915e23	−2.53395
$283$	1.31111e23	0.669373	0.334686	−	0.942330i	$-0.391370\pi$
$283$	1.31111e23	0.669373	0.334686	+	0.942330i	$0.391370\pi$
$284$	−4.89146e22	−0.241499
$285$	5.70587e22	0.272456
$286$	6.54656e22	0.302368
$287$	−7.58998e22	−0.339127
$288$	8.99642e22	0.388903
$289$	−4.00133e22	−0.167369
$290$	−4.65561e22	−0.188450
$291$	−4.87956e23	−1.91160
$292$	−5.89596e22	−0.223572
$293$	2.47934e23	0.910111	0.455056	−	0.890463i	$-0.349619\pi$
$293$	2.47934e23	0.910111	0.455056	+	0.890463i	$0.349619\pi$
$294$	6.27734e22	0.223088
$295$	1.66153e22	0.0571739
$296$	−3.72240e23	−1.24037
$297$	5.82354e21	0.0187932
$298$	3.83550e23	1.19886
$299$	5.84731e23	1.77043
$300$	8.34552e22	0.244794
$301$	8.53293e21	0.0242503
$302$	5.64039e23	1.55326
$303$	3.47103e23	0.926304
$304$	2.90610e23	0.751642
$305$	1.23213e23	0.308893
$306$	4.31577e23	1.04883
$307$	−8.09444e22	−0.190709	−0.0953547	−	0.995443i	$-0.530399\pi$
$307$	−8.09444e22	−0.190709	−0.0953547	+	0.995443i	$0.530399\pi$
$308$	−7.33282e21	−0.0167509
$309$	−2.41995e23	−0.536044
$310$	−2.15997e23	−0.463994
$311$	−2.12826e23	−0.443406	−0.221703	−	0.975114i	$-0.571162\pi$
$311$	−2.12826e23	−0.443406	−0.221703	+	0.975114i	$0.571162\pi$
$312$	−7.34550e23	−1.48441
$313$	8.23144e22	0.161363	0.0806816	−	0.996740i	$-0.474290\pi$
$313$	8.23144e22	0.161363	0.0806816	+	0.996740i	$0.474290\pi$
$314$	−8.67850e23	−1.65049
$315$	6.29441e22	0.116146
$316$	1.96143e23	0.351193
$317$	4.60369e23	0.799914	0.399957	−	0.916534i	$-0.369025\pi$
$317$	4.60369e23	0.799914	0.399957	+	0.916534i	$0.369025\pi$
$318$	−1.27586e24	−2.15151
$319$	−8.62103e22	−0.141107
$320$	1.37524e23	0.218501
$321$	−2.93443e23	−0.452612
$322$	−4.16530e23	−0.623757
$323$	4.09540e23	0.595487
$324$	−1.24447e23	−0.175714
$325$	−7.79950e23	−1.06948
$326$	1.02128e24	1.36012
$327$	4.44924e23	0.575548
$328$	−6.32669e23	−0.795014
$329$	−5.02383e23	−0.613302
$330$	−9.10761e22	−0.108024
$331$	1.23323e24	1.42128	0.710640	−	0.703556i	$-0.248406\pi$
$331$	1.23323e24	1.42128	0.710640	+	0.703556i	$0.248406\pi$
$332$	−2.28633e23	−0.256052
$333$	−1.35718e24	−1.47713
$334$	7.23317e23	0.765134
$335$	−1.69510e23	−0.174289
$336$	6.24403e23	0.624082
$337$	3.24852e22	0.0315647	0.0157824	−	0.999875i	$-0.494976\pi$
$337$	3.24852e22	0.0315647	0.0157824	+	0.999875i	$0.494976\pi$
$338$	−4.21576e23	−0.398261
$339$	1.62562e24	1.49321
$340$	−5.55091e22	−0.0495809
$341$	−3.99973e23	−0.347427
$342$	8.87917e23	0.750109
$343$	6.57124e22	0.0539949
$344$	7.11269e22	0.0568498
$345$	−8.13481e23	−0.632508
$346$	8.13509e23	0.615374
$347$	2.11941e24	1.55986	0.779929	−	0.625868i	$-0.215255\pi$
$347$	2.11941e24	1.55986	0.779929	+	0.625868i	$0.215255\pi$
$348$	−2.21879e23	−0.158896
$349$	−1.26184e24	−0.879354	−0.439677	−	0.898156i	$-0.644907\pi$
$349$	−1.26184e24	−0.879354	−0.439677	+	0.898156i	$0.644907\pi$
$350$	5.55593e23	0.376800
$351$	−1.40074e23	−0.0924571
$352$	−1.36267e23	−0.0875458
$353$	3.44721e23	0.215580	0.107790	−	0.994174i	$-0.465623\pi$
$353$	3.44721e23	0.215580	0.107790	+	0.994174i	$0.465623\pi$
$354$	5.03593e23	0.306583
$355$	−6.35980e23	−0.376942
$356$	−1.44813e22	−0.00835666
$357$	8.79936e23	0.494428
$358$	−9.22045e23	−0.504502
$359$	−3.48947e23	−0.185936	−0.0929678	−	0.995669i	$-0.529635\pi$
$359$	−3.48947e23	−0.185936	−0.0929678	+	0.995669i	$0.529635\pi$
$360$	5.24676e23	0.272281
$361$	−1.13584e24	−0.574115
$362$	−2.37959e24	−1.17157
$363$	2.82044e24	1.35271
$364$	1.76377e23	0.0824098
$365$	−7.66583e23	−0.348961
$366$	3.73447e24	1.65637
$367$	1.21565e24	0.525390	0.262695	−	0.964879i	$-0.415389\pi$
$367$	1.21565e24	0.525390	0.262695	+	0.964879i	$0.415389\pi$
$368$	−4.14319e24	−1.74494
$369$	−2.30671e24	−0.946764
$370$	1.11014e24	0.444079
$371$	−1.33559e24	−0.520739
$372$	−1.02941e24	−0.391228
$373$	−4.22552e24	−1.56547	−0.782737	−	0.622353i	$-0.786177\pi$
$373$	−4.22552e24	−1.56547	−0.782737	+	0.622353i	$0.786177\pi$
$374$	−6.53701e23	−0.236102
$375$	2.27069e24	0.799579
$376$	−4.18766e24	−1.43776
$377$	2.07362e24	0.694204
$378$	9.97811e22	0.0325744
$379$	−3.96713e23	−0.126300	−0.0631501	−	0.998004i	$-0.520115\pi$
$379$	−3.96713e23	−0.126300	−0.0631501	+	0.998004i	$0.520115\pi$
$380$	−1.14203e23	−0.0354596
$381$	6.65665e23	0.201590
$382$	6.19361e24	1.82954
$383$	−5.26292e24	−1.51649	−0.758243	−	0.651972i	$-0.773942\pi$
$383$	−5.26292e24	−1.51649	−0.758243	+	0.651972i	$0.773942\pi$
$384$	6.04790e24	1.70004
$385$	−9.53401e22	−0.0261456
$386$	7.45861e23	0.199562
$387$	2.59328e23	0.0677011
$388$	9.76646e23	0.248792
$389$	1.49013e24	0.370427	0.185213	−	0.982698i	$-0.440702\pi$
$389$	1.49013e24	0.370427	0.185213	+	0.982698i	$0.440702\pi$
$390$	2.19066e24	0.531449
$391$	−5.83877e24	−1.38243
$392$	5.47751e23	0.126580
$393$	−9.65208e24	−2.17717
$394$	7.68855e24	1.69290
$395$	2.55022e24	0.548158
$396$	−2.22855e23	−0.0467647
$397$	4.20886e23	0.0862294	0.0431147	−	0.999070i	$-0.486272\pi$
$397$	4.20886e23	0.0862294	0.0431147	+	0.999070i	$0.486272\pi$
$398$	−9.28292e24	−1.85693
$399$	1.81036e24	0.353609
$400$	5.52645e24	1.05409
$401$	−4.18246e24	−0.779041	−0.389521	−	0.921018i	$-0.627359\pi$
$401$	−4.18246e24	−0.779041	−0.389521	+	0.921018i	$0.627359\pi$
$402$	−5.13768e24	−0.934587
$403$	9.62058e24	1.70924
$404$	−6.94728e23	−0.120557
$405$	−1.61804e24	−0.274263
$406$	−1.47714e24	−0.244581
$407$	2.05570e24	0.332516
$408$	7.33478e24	1.15909
$409$	6.27308e24	0.968522	0.484261	−	0.874924i	$-0.339089\pi$
$409$	6.27308e24	0.968522	0.484261	+	0.874924i	$0.339089\pi$
$410$	1.88682e24	0.284632
$411$	7.45391e24	1.09872
$412$	4.84354e23	0.0697653
$413$	5.27170e23	0.0742036
$414$	−1.26590e25	−1.74138
$415$	−2.97265e24	−0.399657
$416$	3.27764e24	0.430700
$417$	6.08467e24	0.781528
$418$	−1.34491e24	−0.168857
$419$	2.20845e24	0.271053	0.135526	−	0.990774i	$-0.456727\pi$
$419$	2.20845e24	0.271053	0.135526	+	0.990774i	$0.456727\pi$
$420$	−2.45377e23	−0.0294418
$421$	1.24798e25	1.46395	0.731975	−	0.681332i	$-0.238599\pi$
$421$	1.24798e25	1.46395	0.731975	+	0.681332i	$0.238599\pi$
$422$	−3.39221e24	−0.389059
$423$	−1.52682e25	−1.71220
$424$	−1.11329e25	−1.22077
$425$	7.78812e24	0.835098
$426$	−1.92760e25	−2.02127
$427$	3.90931e24	0.400899
$428$	5.87327e23	0.0589066
$429$	4.05656e24	0.397936
$430$	−2.12123e23	−0.0203534
$431$	−1.42719e25	−1.33952	−0.669758	−	0.742579i	$-0.733602\pi$
$431$	−1.42719e25	−1.33952	−0.669758	+	0.742579i	$0.733602\pi$
$432$	9.92515e23	0.0911258
$433$	8.02637e24	0.720915	0.360458	−	0.932776i	$-0.382621\pi$
$433$	8.02637e24	0.720915	0.360458	+	0.932776i	$0.382621\pi$
$434$	−6.85317e24	−0.602198
$435$	−2.88484e24	−0.248012
$436$	−8.90516e23	−0.0749066
$437$	−1.20126e25	−0.988694
$438$	−2.32344e25	−1.87123
$439$	−1.38635e25	−1.09259	−0.546297	−	0.837591i	$-0.683963\pi$
$439$	−1.38635e25	−1.09259	−0.546297	+	0.837591i	$0.683963\pi$
$440$	−7.94716e23	−0.0612931
$441$	1.99709e24	0.150741
$442$	1.57235e25	1.16155
$443$	4.95486e24	0.358258	0.179129	−	0.983826i	$-0.442672\pi$
$443$	4.95486e24	0.358258	0.179129	+	0.983826i	$0.442672\pi$
$444$	5.29074e24	0.374436
$445$	−1.88283e23	−0.0130434
$446$	4.78273e23	0.0324336
$447$	2.37665e25	1.57777
$448$	4.36337e24	0.283584
$449$	2.29672e25	1.46140	0.730698	−	0.682701i	$-0.239195\pi$
$449$	2.29672e25	1.46140	0.730698	+	0.682701i	$0.239195\pi$
$450$	1.68853e25	1.05194
$451$	3.49392e24	0.213126
$452$	−3.25368e24	−0.194339
$453$	3.49505e25	2.04419
$454$	−7.00729e24	−0.401346
$455$	2.29322e24	0.128629
$456$	1.50904e25	0.828963
$457$	−2.58972e25	−1.39331	−0.696657	−	0.717405i	$-0.745330\pi$
$457$	−2.58972e25	−1.39331	−0.696657	+	0.717405i	$0.745330\pi$
$458$	2.55300e25	1.34533
$459$	1.39870e24	0.0721943
$460$	1.62818e24	0.0823198
$461$	−1.28888e23	−0.00638342	−0.00319171	−	0.999995i	$-0.501016\pi$
$461$	−1.28888e23	−0.00638342	−0.00319171	+	0.999995i	$0.501016\pi$
$462$	−2.88967e24	−0.140200
$463$	−2.29658e25	−1.09159	−0.545797	−	0.837917i	$-0.683773\pi$
$463$	−2.29658e25	−1.09159	−0.545797	+	0.837917i	$0.683773\pi$
$464$	−1.46930e25	−0.684209
$465$	−1.33842e25	−0.610646
$466$	−1.02486e25	−0.458139
$467$	−1.46437e25	−0.641415	−0.320708	−	0.947178i	$-0.603921\pi$
$467$	−1.46437e25	−0.641415	−0.320708	+	0.947178i	$0.603921\pi$
$468$	5.36035e24	0.230069
$469$	−5.37822e24	−0.226202
$470$	1.24889e25	0.514749
$471$	−5.37761e25	−2.17215
$472$	4.39427e24	0.173955
$473$	−3.92799e23	−0.0152402
$474$	7.72948e25	2.93938
$475$	1.60231e25	0.597251
$476$	−1.76120e24	−0.0643490
$477$	−4.05905e25	−1.45378
$478$	−1.72410e25	−0.605337
$479$	7.91146e24	0.272313	0.136157	−	0.990687i	$-0.456525\pi$
$479$	7.91146e24	0.272313	0.136157	+	0.990687i	$0.456525\pi$
$480$	−4.55987e24	−0.153872
$481$	−4.94458e25	−1.63588
$482$	1.39340e25	0.451990
$483$	−2.58102e25	−0.820905
$484$	−5.64512e24	−0.176052
$485$	1.26982e25	0.388325
$486$	−5.19151e25	−1.55686
$487$	5.75089e24	0.169126	0.0845629	−	0.996418i	$-0.473051\pi$
$487$	5.75089e24	0.169126	0.0845629	+	0.996418i	$0.473051\pi$
$488$	3.25864e25	0.939826
$489$	6.32832e25	1.79001
$490$	−1.63357e24	−0.0453184
$491$	5.50277e25	1.49729	0.748647	−	0.662969i	$-0.230704\pi$
$491$	5.50277e25	1.49729	0.748647	+	0.662969i	$0.230704\pi$
$492$	8.99228e24	0.239995
$493$	−2.07060e25	−0.542063
$494$	3.23492e25	0.830726
$495$	−2.89753e24	−0.0729925
$496$	−6.81680e25	−1.68463
$497$	−2.01784e25	−0.489217
$498$	−9.00983e25	−2.14308
$499$	4.15885e25	0.970549	0.485275	−	0.874362i	$-0.338720\pi$
$499$	4.15885e25	0.970549	0.485275	+	0.874362i	$0.338720\pi$
$500$	−4.54480e24	−0.104064
$501$	4.48201e25	1.00697
$502$	−1.39946e25	−0.308515
$503$	−5.77733e24	−0.124977	−0.0624886	−	0.998046i	$-0.519904\pi$
$503$	−5.77733e24	−0.124977	−0.0624886	+	0.998046i	$0.519904\pi$
$504$	1.66470e25	0.353382
$505$	−9.03274e24	−0.188170
$506$	1.91743e25	0.392002
$507$	−2.61228e25	−0.524137
$508$	−1.33233e24	−0.0262366
$509$	5.32578e24	0.102935	0.0514676	−	0.998675i	$-0.483610\pi$
$509$	5.32578e24	0.102935	0.0514676	+	0.998675i	$0.483610\pi$
$510$	−2.18747e25	−0.414977
$511$	−2.43222e25	−0.452902
$512$	3.26091e25	0.596038
$513$	2.87765e24	0.0516324
$514$	8.63673e25	1.52125
$515$	6.29749e24	0.108893
$516$	−1.01094e24	−0.0171615
$517$	2.31264e25	0.385432
$518$	3.52225e25	0.576352
$519$	5.04088e25	0.809873
$520$	1.91154e25	0.301544
$521$	1.85829e25	0.287842	0.143921	−	0.989589i	$-0.454029\pi$
$521$	1.85829e25	0.287842	0.143921	+	0.989589i	$0.454029\pi$
$522$	−4.48923e25	−0.682814
$523$	−6.34861e25	−0.948227	−0.474114	−	0.880464i	$-0.657231\pi$
$523$	−6.34861e25	−0.948227	−0.474114	+	0.880464i	$0.657231\pi$
$524$	1.93187e25	0.283355
$525$	3.44272e25	0.495893
$526$	3.91135e25	0.553301
$527$	−9.60654e25	−1.33465
$528$	−2.87433e25	−0.392206
$529$	9.66466e25	1.29526
$530$	3.32019e25	0.437061
$531$	1.60215e25	0.207159
$532$	−3.62345e24	−0.0460215
$533$	−8.40395e25	−1.04852
$534$	−5.70669e24	−0.0699427
$535$	7.63633e24	0.0919441
$536$	−4.48306e25	−0.530284
$537$	−5.71342e25	−0.663958
$538$	−8.41165e25	−0.960394
$539$	−3.02496e24	−0.0339333
$540$	−3.90037e23	−0.00429897
$541$	1.15314e26	1.24884	0.624420	−	0.781089i	$-0.285335\pi$
$541$	1.15314e26	1.24884	0.624420	+	0.781089i	$0.285335\pi$
$542$	6.49904e25	0.691601
$543$	−1.47450e26	−1.54187
$544$	−3.27286e25	−0.336308
$545$	−1.15783e25	−0.116918
$546$	6.95055e25	0.689745
$547$	−2.74651e25	−0.267856	−0.133928	−	0.990991i	$-0.542759\pi$
$547$	−2.74651e25	−0.267856	−0.133928	+	0.990991i	$0.542759\pi$
$548$	−1.49190e25	−0.142996
$549$	1.18810e26	1.11922
$550$	−2.55758e25	−0.236801
$551$	−4.26000e25	−0.387677
$552$	−2.15143e26	−1.92444
$553$	8.09136e25	0.711431
$554$	1.70112e26	1.47025
$555$	6.87893e25	0.584437
$556$	−1.21785e25	−0.101715
$557$	−7.62383e25	−0.625963	−0.312982	−	0.949759i	$-0.601328\pi$
$557$	−7.62383e25	−0.625963	−0.312982	+	0.949759i	$0.601328\pi$
$558$	−2.08278e26	−1.68120
$559$	9.44802e24	0.0749771
$560$	−1.62490e25	−0.126777
$561$	−4.05064e25	−0.310725
$562$	1.31580e26	0.992419
$563$	−1.93583e26	−1.43562	−0.717808	−	0.696241i	$-0.754854\pi$
$563$	−1.93583e26	−1.43562	−0.717808	+	0.696241i	$0.754854\pi$
$564$	5.95203e25	0.434024
$565$	−4.23038e25	−0.303333
$566$	−1.03412e26	−0.729149
$567$	−5.13373e25	−0.355954
$568$	−1.68199e26	−1.14687
$569$	1.22475e26	0.821263	0.410632	−	0.911801i	$-0.365308\pi$
$569$	1.22475e26	0.821263	0.410632	+	0.911801i	$0.365308\pi$
$570$	−4.50044e25	−0.296786
$571$	2.27202e26	1.47357	0.736783	−	0.676129i	$-0.236344\pi$
$571$	2.27202e26	1.47357	0.736783	+	0.676129i	$0.236344\pi$
$572$	−8.11921e24	−0.0517907
$573$	3.83785e26	2.40779
$574$	5.98651e25	0.369412
$575$	−2.28440e26	−1.38652
$576$	1.32609e26	0.791699
$577$	2.57522e26	1.51232	0.756161	−	0.654385i	$-0.227073\pi$
$577$	2.57522e26	1.51232	0.756161	+	0.654385i	$0.227073\pi$
$578$	3.15600e25	0.182315
$579$	4.62170e25	0.262637
$580$	5.77401e24	0.0322784
$581$	−9.43165e25	−0.518698
$582$	3.84870e26	2.08231
$583$	6.14815e25	0.327260
$584$	−2.02740e26	−1.06174
$585$	6.96944e25	0.359102
$586$	−1.95556e26	−0.991386
$587$	−1.77282e26	−0.884305	−0.442152	−	0.896940i	$-0.645785\pi$
$587$	−1.77282e26	−0.884305	−0.442152	+	0.896940i	$0.645785\pi$
$588$	−7.78532e24	−0.0382113
$589$	−1.97643e26	−0.954522
$590$	−1.31051e25	−0.0622797
$591$	4.76419e26	2.22796
$592$	3.50356e26	1.61233
$593$	3.25781e26	1.47539	0.737694	−	0.675135i	$-0.235915\pi$
$593$	3.25781e26	1.47539	0.737694	+	0.675135i	$0.235915\pi$
$594$	−4.59325e24	−0.0204715
$595$	−2.28988e25	−0.100439
$596$	−4.75688e25	−0.205344
$597$	−5.75213e26	−2.44384
$598$	−4.61200e26	−1.92854
$599$	2.34076e26	0.963392	0.481696	−	0.876338i	$-0.340021\pi$
$599$	2.34076e26	0.963392	0.481696	+	0.876338i	$0.340021\pi$
$600$	2.86971e26	1.16252
$601$	−6.43338e25	−0.256526	−0.128263	−	0.991740i	$-0.540940\pi$
$601$	−6.43338e25	−0.256526	−0.128263	+	0.991740i	$0.540940\pi$
$602$	−6.73025e24	−0.0264159
$603$	−1.63452e26	−0.631503
$604$	−6.99535e25	−0.266047
$605$	−7.33969e25	−0.274790
$606$	−2.73774e26	−1.00902
$607$	−3.35572e26	−1.21757	−0.608784	−	0.793336i	$-0.708343\pi$
$607$	−3.35572e26	−1.21757	−0.608784	+	0.793336i	$0.708343\pi$
$608$	−6.73350e25	−0.240523
$609$	−9.15303e25	−0.321885
$610$	−9.71829e25	−0.336478
$611$	−5.56260e26	−1.89621
$612$	−5.35253e25	−0.179647
$613$	1.80997e25	0.0598132	0.0299066	−	0.999553i	$-0.490479\pi$
$613$	1.80997e25	0.0598132	0.0299066	+	0.999553i	$0.490479\pi$
$614$	6.38440e25	0.207740
$615$	1.16916e26	0.374594
$616$	−2.52148e25	−0.0795497
$617$	−4.75421e26	−1.47696	−0.738480	−	0.674275i	$-0.764456\pi$
$617$	−4.75421e26	−1.47696	−0.738480	+	0.674275i	$0.764456\pi$
$618$	1.90871e26	0.583914
$619$	2.55104e26	0.768520	0.384260	−	0.923225i	$-0.374457\pi$
$619$	2.55104e26	0.768520	0.384260	+	0.923225i	$0.374457\pi$
$620$	2.67885e25	0.0794745
$621$	−4.10264e25	−0.119865
$622$	1.67864e26	0.483003
$623$	−5.97387e24	−0.0169285
$624$	6.91366e26	1.92954
$625$	2.73853e26	0.752762
$626$	−6.49246e25	−0.175773
$627$	−8.33369e25	−0.222226
$628$	1.07633e26	0.282702
$629$	4.93737e26	1.27736
$630$	−4.96465e25	−0.126518
$631$	3.60432e26	0.904783	0.452391	−	0.891819i	$-0.350571\pi$
$631$	3.60432e26	0.904783	0.452391	+	0.891819i	$0.350571\pi$
$632$	6.74462e26	1.66781
$633$	−2.10198e26	−0.512026
$634$	−3.63111e26	−0.871348
$635$	−1.73227e25	−0.0409512
$636$	1.58235e26	0.368519
$637$	7.27596e25	0.166942
$638$	6.79974e25	0.153708
$639$	−6.13252e26	−1.36578
$640$	−1.57386e26	−0.345347
$641$	−8.16548e26	−1.76535	−0.882674	−	0.469985i	$-0.844259\pi$
$641$	−8.16548e26	−1.76535	−0.882674	+	0.469985i	$0.844259\pi$
$642$	2.31450e26	0.493031
$643$	5.05701e26	1.06143	0.530713	−	0.847552i	$-0.321924\pi$
$643$	5.05701e26	1.06143	0.530713	+	0.847552i	$0.321924\pi$
$644$	5.16591e25	0.106839
$645$	−1.31441e25	−0.0267864
$646$	−3.23020e26	−0.648665
$647$	6.79494e26	1.34461	0.672303	−	0.740276i	$-0.265305\pi$
$647$	6.79494e26	1.34461	0.672303	+	0.740276i	$0.265305\pi$
$648$	−4.27926e26	−0.834461
$649$	−2.42674e25	−0.0466335
$650$	6.15177e26	1.16499
$651$	−4.24655e26	−0.792532
$652$	−1.26662e26	−0.232966
$653$	−4.54884e26	−0.824566	−0.412283	−	0.911056i	$-0.635269\pi$
$653$	−4.54884e26	−0.824566	−0.412283	+	0.911056i	$0.635269\pi$
$654$	−3.50929e26	−0.626946
$655$	2.51178e26	0.442272
$656$	5.95474e26	1.03342
$657$	−7.39187e26	−1.26440
$658$	3.96249e26	0.668071
$659$	7.87397e26	1.30853	0.654263	−	0.756267i	$-0.272979\pi$
$659$	7.87397e26	1.30853	0.654263	+	0.756267i	$0.272979\pi$
$660$	1.12955e25	0.0185028
$661$	−1.97539e26	−0.318962	−0.159481	−	0.987201i	$-0.550982\pi$
$661$	−1.97539e26	−0.318962	−0.159481	+	0.987201i	$0.550982\pi$
$662$	−9.72700e26	−1.54820
$663$	9.74303e26	1.52868
$664$	−7.86183e26	−1.21598
$665$	−4.71114e25	−0.0718325
$666$	1.07046e27	1.60904
$667$	6.07345e26	0.899994
$668$	−8.97077e25	−0.131055
$669$	2.96360e25	0.0426847
$670$	1.33699e26	0.189853
$671$	−1.79958e26	−0.251946
$672$	−1.44676e26	−0.199705
$673$	−9.72634e26	−1.32375	−0.661876	−	0.749613i	$-0.730239\pi$
$673$	−9.72634e26	−1.32375	−0.661876	+	0.749613i	$0.730239\pi$
$674$	−2.56224e25	−0.0343835
$675$	5.47235e25	0.0724082
$676$	5.22850e25	0.0682155
$677$	8.09882e26	1.04191	0.520954	−	0.853585i	$-0.325576\pi$
$677$	8.09882e26	1.04191	0.520954	+	0.853585i	$0.325576\pi$
$678$	−1.28219e27	−1.62656
$679$	4.02889e26	0.503991
$680$	−1.90875e26	−0.235458
$681$	−4.34204e26	−0.528198
$682$	3.15474e26	0.378453
$683$	−1.68743e26	−0.199632	−0.0998158	−	0.995006i	$-0.531825\pi$
$683$	−1.68743e26	−0.199632	−0.0998158	+	0.995006i	$0.531825\pi$
$684$	−1.10122e26	−0.128481
$685$	−1.93975e26	−0.223195
$686$	−5.18299e25	−0.0588168
$687$	1.58196e27	1.77054
$688$	−6.69453e25	−0.0738976
$689$	−1.47882e27	−1.61003
$690$	6.41624e26	0.688992
$691$	−1.76752e27	−1.87207	−0.936037	−	0.351902i	$-0.885535\pi$
$691$	−1.76752e27	−1.87207	−0.936037	+	0.351902i	$0.885535\pi$
$692$	−1.00893e26	−0.105404
$693$	−9.19329e25	−0.0947338
$694$	−1.67166e27	−1.69916
$695$	−1.58343e26	−0.158761
$696$	−7.62958e26	−0.754593
$697$	8.39169e26	0.818725
$698$	9.95264e26	0.957882
$699$	−6.35050e26	−0.602941
$700$	−6.89061e25	−0.0645396
$701$	−3.28129e26	−0.303196	−0.151598	−	0.988442i	$-0.548442\pi$
$701$	−3.28129e26	−0.303196	−0.151598	+	0.988442i	$0.548442\pi$
$702$	1.10482e26	0.100714
$703$	1.01580e27	0.913554
$704$	−2.00860e26	−0.178219
$705$	7.73873e26	0.677443
$706$	−2.71895e26	−0.234832
$707$	−2.86591e26	−0.244219
$708$	−6.24569e25	−0.0525127
$709$	1.87471e27	1.55523	0.777616	−	0.628740i	$-0.216429\pi$
$709$	1.87471e27	1.55523	0.777616	+	0.628740i	$0.216429\pi$
$710$	5.01622e26	0.410603
$711$	2.45908e27	1.98615
$712$	−4.97957e25	−0.0396855
$713$	2.81778e27	2.21593
$714$	−6.94040e26	−0.538582
$715$	−1.05565e26	−0.0808372
$716$	1.14354e26	0.0864130
$717$	−1.06833e27	−0.796663
$718$	2.75228e26	0.202540
$719$	−5.40653e26	−0.392640	−0.196320	−	0.980540i	$-0.562899\pi$
$719$	−5.40653e26	−0.392640	−0.196320	+	0.980540i	$0.562899\pi$
$720$	−4.93830e26	−0.353931
$721$	1.99807e26	0.141327
$722$	8.95882e26	0.625385
$723$	8.63416e26	0.594848
$724$	2.95122e26	0.200672
$725$	−8.10114e26	−0.543669
$726$	−2.22459e27	−1.47351
$727$	8.54249e26	0.558480	0.279240	−	0.960221i	$-0.409917\pi$
$727$	8.54249e26	0.558480	0.279240	+	0.960221i	$0.409917\pi$
$728$	6.06493e26	0.391361
$729$	−1.73829e27	−1.10716
$730$	6.04634e26	0.380124
$731$	−9.43424e25	−0.0585452
$732$	−4.63158e26	−0.283710
$733$	−2.25457e26	−0.136325	−0.0681626	−	0.997674i	$-0.521714\pi$
$733$	−2.25457e26	−0.136325	−0.0681626	+	0.997674i	$0.521714\pi$
$734$	−9.58833e26	−0.572309
$735$	−1.01224e26	−0.0596419
$736$	9.59990e26	0.558377
$737$	2.47577e26	0.142157
$738$	1.81939e27	1.03131
$739$	−1.35888e27	−0.760432	−0.380216	−	0.924898i	$-0.624150\pi$
$739$	−1.35888e27	−0.760432	−0.380216	+	0.924898i	$0.624150\pi$
$740$	−1.37682e26	−0.0760635
$741$	2.00451e27	1.09329
$742$	1.05343e27	0.567243
$743$	−1.24874e27	−0.663865	−0.331933	−	0.943303i	$-0.607701\pi$
$743$	−1.24874e27	−0.663865	−0.331933	+	0.943303i	$0.607701\pi$
$744$	−3.53975e27	−1.85793
$745$	−6.18482e26	−0.320511
$746$	3.33283e27	1.70527
$747$	−2.86642e27	−1.44808
$748$	8.10737e25	0.0404403
$749$	2.42286e26	0.119330
$750$	−1.79099e27	−0.870984
$751$	−2.08089e27	−0.999240	−0.499620	−	0.866245i	$-0.666527\pi$
$751$	−2.08089e27	−0.999240	−0.499620	+	0.866245i	$0.666527\pi$
$752$	3.94146e27	1.86891
$753$	−8.67173e26	−0.406026
$754$	−1.63555e27	−0.756198
$755$	−9.09524e26	−0.415258
$756$	−1.23751e25	−0.00557946
$757$	−3.56900e27	−1.58904	−0.794522	−	0.607235i	$-0.792279\pi$
$757$	−3.56900e27	−1.58904	−0.794522	+	0.607235i	$0.792279\pi$
$758$	3.12903e26	0.137579
$759$	1.18813e27	0.515901
$760$	−3.92701e26	−0.168397
$761$	−2.11298e27	−0.894833	−0.447416	−	0.894326i	$-0.647656\pi$
$761$	−2.11298e27	−0.894833	−0.447416	+	0.894326i	$0.647656\pi$
$762$	−5.25036e26	−0.219592
$763$	−3.67359e26	−0.151742
$764$	−7.68148e26	−0.313370
$765$	−6.95927e26	−0.280401
$766$	4.15107e27	1.65191
$767$	5.83705e26	0.229423
$768$	−1.99953e27	−0.776241
$769$	1.25590e27	0.481564	0.240782	−	0.970579i	$-0.422596\pi$
$769$	1.25590e27	0.481564	0.240782	+	0.970579i	$0.422596\pi$
$770$	7.51985e25	0.0284805
$771$	5.35172e27	2.00206
$772$	−9.25035e25	−0.0341817
$773$	−2.89524e27	−1.05677	−0.528384	−	0.849006i	$-0.677202\pi$
$773$	−2.89524e27	−1.05677	−0.528384	+	0.849006i	$0.677202\pi$
$774$	−2.04542e26	−0.0737469
$775$	−3.75852e27	−1.33860
$776$	3.35832e27	1.18150
$777$	2.18255e27	0.758516
$778$	−1.17532e27	−0.403507
$779$	1.72649e27	0.585541
$780$	−2.71692e26	−0.0910285
$781$	9.28879e26	0.307450
$782$	4.60527e27	1.50588
$783$	−1.45491e26	−0.0470003
$784$	−5.15548e26	−0.164538
$785$	1.39943e27	0.441254
$786$	7.61298e27	2.37159
$787$	−4.30676e27	−1.32553	−0.662766	−	0.748826i	$-0.730618\pi$
$787$	−4.30676e27	−1.32553	−0.662766	+	0.748826i	$0.730618\pi$
$788$	−9.53553e26	−0.289965
$789$	2.42365e27	0.728181
$790$	−2.01146e27	−0.597110
$791$	−1.34222e27	−0.393683
$792$	−7.66314e26	−0.222084
$793$	4.32855e27	1.23950
$794$	−3.31970e26	−0.0939298
$795$	2.05734e27	0.575200
$796$	1.15129e27	0.318061
$797$	−3.56455e27	−0.973085	−0.486542	−	0.873657i	$-0.661742\pi$
$797$	−3.56455e27	−0.973085	−0.486542	+	0.873657i	$0.661742\pi$
$798$	−1.42790e27	−0.385187
$799$	5.55449e27	1.48064
$800$	−1.28049e27	−0.337305
$801$	−1.81555e26	−0.0472605
$802$	3.29887e27	0.848611
$803$	1.11963e27	0.284628
$804$	6.37189e26	0.160079
$805$	6.71664e26	0.166760
$806$	−7.58813e27	−1.86188
$807$	−5.21225e27	−1.26394
$808$	−2.38891e27	−0.572521
$809$	−3.59382e27	−0.851227	−0.425614	−	0.904905i	$-0.639942\pi$
$809$	−3.59382e27	−0.851227	−0.425614	+	0.904905i	$0.639942\pi$
$810$	1.27621e27	0.298755
$811$	−7.30849e27	−1.69095	−0.845473	−	0.534018i	$-0.820681\pi$
$811$	−7.30849e27	−1.69095	−0.845473	+	0.534018i	$0.820681\pi$
$812$	1.83198e26	0.0418927
$813$	4.02711e27	0.910193
$814$	−1.62141e27	−0.362210
$815$	−1.64683e27	−0.363624
$816$	−6.90357e27	−1.50667
$817$	−1.94098e26	−0.0418708
$818$	−4.94782e27	−1.05501
$819$	2.21127e27	0.466063
$820$	−2.34008e26	−0.0487528
$821$	5.08388e27	1.04697	0.523486	−	0.852034i	$-0.324631\pi$
$821$	5.08388e27	1.04697	0.523486	+	0.852034i	$0.324631\pi$
$822$	−5.87919e27	−1.19684
$823$	7.67353e27	1.54418	0.772088	−	0.635516i	$-0.219213\pi$
$823$	7.67353e27	1.54418	0.772088	+	0.635516i	$0.219213\pi$
$824$	1.66551e27	0.331313
$825$	−1.58480e27	−0.311646
$826$	−4.15800e26	−0.0808302
$827$	2.99948e27	0.576426	0.288213	−	0.957566i	$-0.406939\pi$
$827$	2.99948e27	0.576426	0.288213	+	0.957566i	$0.406939\pi$
$828$	1.57000e27	0.298271
$829$	2.88077e27	0.541053	0.270527	−	0.962713i	$-0.412802\pi$
$829$	2.88077e27	0.541053	0.270527	+	0.962713i	$0.412802\pi$
$830$	2.34465e27	0.435347
$831$	1.05410e28	1.93495
$832$	4.83131e27	0.876786
$833$	−7.26534e26	−0.130355
$834$	−4.79922e27	−0.851321
$835$	−1.16636e27	−0.204556
$836$	1.66799e26	0.0289224
$837$	−6.75007e26	−0.115722
$838$	−1.74189e27	−0.295258
$839$	−9.34809e27	−1.56669	−0.783347	−	0.621584i	$-0.786489\pi$
$839$	−9.34809e27	−1.56669	−0.783347	+	0.621584i	$0.786489\pi$
$840$	−8.43757e26	−0.139818
$841$	−3.94944e27	−0.647104
$842$	−9.84327e27	−1.59468
$843$	8.15332e27	1.30609
$844$	4.20711e26	0.0666393
$845$	6.79801e26	0.106474
$846$	1.20426e28	1.86510
$847$	−2.32874e27	−0.356639
$848$	1.04784e28	1.58684
$849$	−6.40792e27	−0.959608
$850$	−6.14279e27	−0.909674
$851$	−1.44822e28	−2.12082
$852$	2.39065e27	0.346211
$853$	2.46935e27	0.353645	0.176822	−	0.984243i	$-0.443418\pi$
$853$	2.46935e27	0.353645	0.176822	+	0.984243i	$0.443418\pi$
$854$	−3.08342e27	−0.436700
$855$	−1.43179e27	−0.200540
$856$	2.01959e27	0.279746
$857$	9.53261e26	0.130585	0.0652926	−	0.997866i	$-0.479202\pi$
$857$	9.53261e26	0.130585	0.0652926	+	0.997866i	$0.479202\pi$
$858$	−3.19957e27	−0.433473
$859$	7.42066e27	0.994277	0.497138	−	0.867671i	$-0.334384\pi$
$859$	7.42066e27	0.994277	0.497138	+	0.867671i	$0.334384\pi$
$860$	2.63080e25	0.00348621
$861$	3.70952e27	0.486170
$862$	1.12568e28	1.45914
$863$	−4.59048e27	−0.588513	−0.294256	−	0.955727i	$-0.595072\pi$
$863$	−4.59048e27	−0.588513	−0.294256	+	0.955727i	$0.595072\pi$
$864$	−2.29968e26	−0.0291600
$865$	−1.31180e27	−0.164518
$866$	−6.33071e27	−0.785295
$867$	1.95561e27	0.239939
$868$	8.49948e26	0.103147
$869$	−3.72472e27	−0.447101
$870$	2.27538e27	0.270160
$871$	−5.95499e27	−0.699373
$872$	−3.06215e27	−0.355729
$873$	1.22444e28	1.40703
$874$	9.47478e27	1.07699
$875$	−1.87484e27	−0.210808
$876$	2.88159e27	0.320511
$877$	4.47463e27	0.492335	0.246168	−	0.969227i	$-0.420829\pi$
$877$	4.47463e27	0.492335	0.246168	+	0.969227i	$0.420829\pi$
$878$	1.09347e28	1.19017
$879$	−1.21175e28	−1.30473
$880$	7.47994e26	0.0796733
$881$	1.09776e28	1.15674	0.578370	−	0.815774i	$-0.303689\pi$
$881$	1.09776e28	1.15674	0.578370	+	0.815774i	$0.303689\pi$
$882$	−1.57519e27	−0.164203
$883$	1.79541e28	1.85156	0.925779	−	0.378065i	$-0.123410\pi$
$883$	1.79541e28	1.85156	0.925779	+	0.378065i	$0.123410\pi$
$884$	−1.95007e27	−0.198955
$885$	−8.12054e26	−0.0819642
$886$	−3.90809e27	−0.390251
$887$	−1.30974e28	−1.29393	−0.646966	−	0.762519i	$-0.723963\pi$
$887$	−1.30974e28	−1.29393	−0.646966	+	0.762519i	$0.723963\pi$
$888$	1.81928e28	1.77819
$889$	−5.49617e26	−0.0531488
$890$	1.48507e26	0.0142082
$891$	2.36322e27	0.223700
$892$	−5.93166e25	−0.00555534
$893$	1.14277e28	1.05893
$894$	−1.87456e28	−1.71867
$895$	1.48682e27	0.134877
$896$	−4.99355e27	−0.448212
$897$	−2.85781e28	−2.53808
$898$	−1.81151e28	−1.59190
$899$	9.99265e27	0.868887
$900$	−2.09416e27	−0.180180
$901$	1.47666e28	1.25718
$902$	−2.75579e27	−0.232158
$903$	−4.17038e26	−0.0347650
$904$	−1.11882e28	−0.922909
$905$	3.83713e27	0.313217
$906$	−2.75668e28	−2.22674
$907$	1.17918e27	0.0942566	0.0471283	−	0.998889i	$-0.484993\pi$
$907$	1.17918e27	0.0942566	0.0471283	+	0.998889i	$0.484993\pi$
$908$	8.69062e26	0.0687440
$909$	−8.70993e27	−0.681801
$910$	−1.80876e27	−0.140116
$911$	−1.14309e28	−0.876303	−0.438151	−	0.898901i	$-0.644367\pi$
$911$	−1.14309e28	−0.876303	−0.438151	+	0.898901i	$0.644367\pi$
$912$	−1.42032e28	−1.07755
$913$	4.34170e27	0.325977
$914$	2.04261e28	1.51774
$915$	−6.02191e27	−0.442827
$916$	−3.16630e27	−0.230433
$917$	7.96940e27	0.574007
$918$	−1.10321e27	−0.0786414
$919$	−1.86112e28	−1.31304	−0.656519	−	0.754309i	$-0.727972\pi$
$919$	−1.86112e28	−1.31304	−0.656519	+	0.754309i	$0.727972\pi$
$920$	5.59871e27	0.390934
$921$	3.95608e27	0.273400
$922$	1.01659e26	0.00695348
$923$	−2.23424e28	−1.51256
$924$	3.58384e26	0.0240140
$925$	1.93173e28	1.28115
$926$	1.81140e28	1.18908
$927$	6.07243e27	0.394553
$928$	3.40440e27	0.218945
$929$	2.16211e28	1.37635	0.688173	−	0.725547i	$-0.258413\pi$
$929$	2.16211e28	1.37635	0.688173	+	0.725547i	$0.258413\pi$
$930$	1.05566e28	0.665178
$931$	−1.49475e27	−0.0932283
$932$	1.27106e27	0.0784718
$933$	1.04017e28	0.635664
$934$	1.15500e28	0.698695
$935$	1.05411e27	0.0631210
$936$	1.84322e28	1.09259
$937$	−1.42929e28	−0.838677	−0.419338	−	0.907830i	$-0.637738\pi$
$937$	−1.42929e28	−0.838677	−0.419338	+	0.907830i	$0.637738\pi$
$938$	4.24201e27	0.246402
$939$	−4.02303e27	−0.231329
$940$	−1.54891e27	−0.0881681
$941$	−1.24192e28	−0.699831	−0.349915	−	0.936781i	$-0.613790\pi$
$941$	−1.24192e28	−0.699831	−0.349915	+	0.936781i	$0.613790\pi$
$942$	4.24153e28	2.36613
$943$	−2.46144e28	−1.35934
$944$	−4.13593e27	−0.226120
$945$	−1.60899e26	−0.00870866
$946$	3.09816e26	0.0166011
$947$	3.17025e28	1.68178	0.840888	−	0.541209i	$-0.182033\pi$
$947$	3.17025e28	1.68178	0.840888	+	0.541209i	$0.182033\pi$
$948$	−9.58631e27	−0.503468
$949$	−2.69306e28	−1.40029
$950$	−1.26380e28	−0.650587
$951$	−2.25001e28	−1.14675
$952$	−6.05608e27	−0.305591
$953$	1.17859e28	0.588818	0.294409	−	0.955680i	$-0.404877\pi$
$953$	1.17859e28	0.588818	0.294409	+	0.955680i	$0.404877\pi$
$954$	3.20153e28	1.58361
$955$	−9.98733e27	−0.489122
$956$	2.13827e27	0.103684
$957$	4.21344e27	0.202290
$958$	−6.24008e27	−0.296632
$959$	−6.15444e27	−0.289676
$960$	−6.72135e27	−0.313242
$961$	2.46902e28	1.13934
$962$	3.89999e28	1.78197
$963$	7.36342e27	0.333143
$964$	−1.72813e27	−0.0774185
$965$	−1.20272e27	−0.0533524
$966$	2.03575e28	0.894214
$967$	−2.75205e27	−0.119703	−0.0598515	−	0.998207i	$-0.519063\pi$
$967$	−2.75205e27	−0.119703	−0.0598515	+	0.998207i	$0.519063\pi$
$968$	−1.94114e28	−0.836067
$969$	−2.00159e28	−0.853686
$970$	−1.00156e28	−0.423004
$971$	−3.33947e28	−1.39667	−0.698337	−	0.715769i	$-0.746076\pi$
$971$	−3.33947e28	−1.39667	−0.698337	+	0.715769i	$0.746076\pi$
$972$	6.43865e27	0.266665
$973$	−5.02391e27	−0.206049
$974$	−4.53595e27	−0.184229
$975$	3.81193e28	1.53321
$976$	−3.06706e28	−1.22166
$977$	−1.79662e28	−0.708694	−0.354347	−	0.935114i	$-0.615297\pi$
$977$	−1.79662e28	−0.708694	−0.354347	+	0.935114i	$0.615297\pi$
$978$	−4.99140e28	−1.94986
$979$	2.74997e26	0.0106388
$980$	2.02599e26	0.00776229
$981$	−1.11646e28	−0.423630
$982$	−4.34025e28	−1.63101
$983$	3.29687e28	1.22700	0.613498	−	0.789696i	$-0.289762\pi$
$983$	3.29687e28	1.22700	0.613498	+	0.789696i	$0.289762\pi$
$984$	3.09211e28	1.13973
$985$	−1.23979e28	−0.452591
$986$	1.63316e28	0.590471
$987$	2.45535e28	0.879225
$988$	−4.01203e27	−0.142290
$989$	2.76724e27	0.0972034
$990$	2.28539e27	0.0795109
$991$	−2.53273e28	−0.872750	−0.436375	−	0.899765i	$-0.643738\pi$
$991$	−2.53273e28	−0.872750	−0.436375	+	0.899765i	$0.643738\pi$
$992$	1.57947e28	0.539077
$993$	−6.02730e28	−2.03754
$994$	1.59155e28	0.532905
$995$	1.49689e28	0.496444
$996$	1.11742e28	0.367074
$997$	4.02701e28	1.31032	0.655162	−	0.755488i	$-0.272600\pi$
$997$	4.02701e28	1.31032	0.655162	+	0.755488i	$0.272600\pi$
$998$	−3.28024e28	−1.05722
$999$	3.46926e27	0.110755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.20.a.a.1.2	✓	4
3.2	odd	2		63.20.a.b.1.3		4
7.6	odd	2		49.20.a.c.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.20.a.a.1.2	✓	4	1.1	even	1	trivial
49.20.a.c.1.2		4	7.6	odd	2
63.20.a.b.1.3		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	7.a (trivial)

\(f(q)\)	\(=\)	\(q-788.739 q^{2} -48874.0 q^{3} +97821.5 q^{4} +1.27186e6 q^{5} +3.85488e7 q^{6} +4.03536e7 q^{7} +3.36371e8 q^{8} +1.22641e9 q^{9} +O(q^{10})\)	\(q-788.739 q^{2} -48874.0 q^{3} +97821.5 q^{4} +1.27186e6 q^{5} +3.85488e7 q^{6} +4.03536e7 q^{7} +3.36371e8 q^{8} +1.22641e9 q^{9} -1.00316e9 q^{10} -1.85761e9 q^{11} -4.78092e9 q^{12} +4.46813e10 q^{13} -3.18285e10 q^{14} -6.21608e10 q^{15} -3.16595e11 q^{16} -4.46160e11 q^{17} -9.67314e11 q^{18} -9.17921e11 q^{19} +1.24415e11 q^{20} -1.97224e12 q^{21} +1.46517e12 q^{22} +1.30867e13 q^{23} -1.64398e13 q^{24} -1.74559e13 q^{25} -3.52419e13 q^{26} -3.13496e12 q^{27} +3.94745e12 q^{28} +4.64093e13 q^{29} +4.90287e13 q^{30} +2.15316e14 q^{31} +7.33561e13 q^{32} +9.07888e13 q^{33} +3.51904e14 q^{34} +5.13241e13 q^{35} +1.19969e14 q^{36} -1.10664e15 q^{37} +7.24000e14 q^{38} -2.18375e15 q^{39} +4.27816e14 q^{40} -1.88087e15 q^{41} +1.55558e15 q^{42} +2.11454e14 q^{43} -1.81714e14 q^{44} +1.55981e15 q^{45} -1.03220e16 q^{46} -1.24495e16 q^{47} +1.54733e16 q^{48} +1.62841e15 q^{49} +1.37681e16 q^{50} +2.18056e16 q^{51} +4.37079e15 q^{52} -3.30971e16 q^{53} +2.47267e15 q^{54} -2.36262e15 q^{55} +1.35738e16 q^{56} +4.48624e16 q^{57} -3.66048e16 q^{58} +1.30638e16 q^{59} -6.08066e15 q^{60} +9.68763e16 q^{61} -1.69828e17 q^{62} +4.94899e16 q^{63} +1.08128e17 q^{64} +5.68282e16 q^{65} -7.16087e16 q^{66} -1.33277e17 q^{67} -4.36441e16 q^{68} -6.39600e17 q^{69} -4.04813e16 q^{70} -5.00040e17 q^{71} +4.12527e17 q^{72} -6.02727e17 q^{73} +8.72846e17 q^{74} +8.53138e17 q^{75} -8.97923e16 q^{76} -7.49613e16 q^{77} +1.72241e18 q^{78} +2.00512e18 q^{79} -4.02665e17 q^{80} -1.27219e18 q^{81} +1.48351e18 q^{82} -2.33725e18 q^{83} -1.92928e17 q^{84} -5.67453e17 q^{85} -1.66782e17 q^{86} -2.26821e18 q^{87} -6.24846e17 q^{88} -1.48038e17 q^{89} -1.23029e18 q^{90} +1.80305e18 q^{91} +1.28016e18 q^{92} -1.05233e19 q^{93} +9.81943e18 q^{94} -1.16747e18 q^{95} -3.58520e18 q^{96} +9.98397e18 q^{97} -1.28439e18 q^{98} -2.27818e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 342 q^{2} - 29526 q^{3} + 576196 q^{4} - 2486610 q^{5} - 17324244 q^{6} + 161414428 q^{7} + 408794760 q^{8} - 335304432 q^{9}+O(q^{10}) \) 4 * q - 342 * q^2 - 29526 * q^3 + 576196 * q^4 - 2486610 * q^5 - 17324244 * q^6 + 161414428 * q^7 + 408794760 * q^8 - 335304432 * q^9	\( 4 q - 342 q^{2} - 29526 q^{3} + 576196 q^{4} - 2486610 q^{5} - 17324244 q^{6} + 161414428 q^{7} + 408794760 q^{8} - 335304432 q^{9} - 1397073720 q^{10} - 5232894012 q^{11} - 2652921096 q^{12} - 24071694934 q^{13} - 13800933594 q^{14} - 150674677560 q^{15} - 695063798768 q^{16} - 1122693554556 q^{17} - 2614443305094 q^{18} - 1689034371682 q^{19} - 6308977253040 q^{20} - 1191480600282 q^{21} - 16919940544224 q^{22} - 20343270469752 q^{23} - 9188544894480 q^{24} - 12146712350000 q^{25} - 5032107987984 q^{26} + 11404928663100 q^{27} + 23251586938972 q^{28} + 17794845083772 q^{29} + 274558228864560 q^{30} + 438619343652812 q^{31} + 172526736764448 q^{32} + 560272505144688 q^{33} + 582762872846028 q^{34} - 100343682702270 q^{35} + 218182607781732 q^{36} + 371101054682492 q^{37} + 269634109145940 q^{38} - 34\!\cdots\!08 q^{39}+ \cdots + 89\!\cdots\!76 q^{99}+O(q^{100}) \) 4 * q - 342 * q^2 - 29526 * q^3 + 576196 * q^4 - 2486610 * q^5 - 17324244 * q^6 + 161414428 * q^7 + 408794760 * q^8 - 335304432 * q^9 - 1397073720 * q^10 - 5232894012 * q^11 - 2652921096 * q^12 - 24071694934 * q^13 - 13800933594 * q^14 - 150674677560 * q^15 - 695063798768 * q^16 - 1122693554556 * q^17 - 2614443305094 * q^18 - 1689034371682 * q^19 - 6308977253040 * q^20 - 1191480600282 * q^21 - 16919940544224 * q^22 - 20343270469752 * q^23 - 9188544894480 * q^24 - 12146712350000 * q^25 - 5032107987984 * q^26 + 11404928663100 * q^27 + 23251586938972 * q^28 + 17794845083772 * q^29 + 274558228864560 * q^30 + 438619343652812 * q^31 + 172526736764448 * q^32 + 560272505144688 * q^33 + 582762872846028 * q^34 - 100343682702270 * q^35 + 218182607781732 * q^36 + 371101054682492 * q^37 + 269634109145940 * q^38 - 3445721278709808 * q^39 - 2289575448232800 * q^40 - 3519649536072516 * q^41 - 699095733948108 * q^42 - 4463367374178964 * q^43 - 6600729725725248 * q^44 - 1687781379790170 * q^45 - 6244953162457584 * q^46 - 12676380373106604 * q^47 + 4614181098145248 * q^48 + 6513654391641796 * q^49 + 23522915071245150 * q^50 + 8700163413214284 * q^51 + 35559530560574048 * q^52 + 15595612222940712 * q^53 + 68288349157759080 * q^54 + 37500795299828280 * q^55 + 16496343088699320 * q^56 + 66467738474740644 * q^57 + 37511423793126180 * q^58 - 128722843456786530 * q^59 + 10245923524095840 * q^60 - 99854565167649586 * q^61 + 49326848870064696 * q^62 - 13530743274286224 * q^63 - 127576935362475968 * q^64 - 222541932083245740 * q^65 - 95494018388787648 * q^66 - 559752529353715960 * q^67 - 6263410841045064 * q^68 - 1102648068919821312 * q^69 - 56376963846908040 * q^70 - 431823453358672584 * q^71 + 703582531856039880 * q^72 - 141778013178404848 * q^73 + 1377884102545752948 * q^74 + 593927230875286350 * q^75 + 1376586984318613256 * q^76 - 211166148432901284 * q^77 + 2441041974988075872 * q^78 - 278647331872313704 * q^79 + 2706945628302054720 * q^80 - 1240959746750205096 * q^81 + 5728992758934332076 * q^82 - 2246245523526488778 * q^83 - 107054935309993272 * q^84 - 738241927356169860 * q^85 + 1262160114799888656 * q^86 - 6303774078790689564 * q^87 - 1138532883653020800 * q^88 - 7106866925026829688 * q^89 + 3296867742504813960 * q^90 - 971379717190526938 * q^91 - 943516940294209248 * q^92 - 13447340691609448200 * q^93 - 8959883069564168952 * q^94 - 16322573541779844120 * q^95 + 8638732606243594176 * q^96 - 237692331127149724 * q^97 - 556917450485373558 * q^98 + 8957687784547224276 * q^99

Introduction

L-functions

Modular forms

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