LMFDB - Embedded newform 1.42.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,42,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 42, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 42 $
Character orbit:	$[\chi]$	$=$	1.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:	$10.6471670456$
Analytic rank:	$1$
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} - 2784108376x + 1945534874860 $ x^3 - x^2 - 2784108376*x + 1945534874860
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{3}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-53110.1$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66420e6 q^{2} -7.98359e9 q^{3} +4.89893e12 q^{4} +3.47255e13 q^{5} +2.12699e16 q^{6} +1.66807e17 q^{7} -7.19310e18 q^{8} +2.72647e19 q^{9} +O(q^{10})$	\(q-2.66420e6 q^{2} -7.98359e9 q^{3} +4.89893e12 q^{4} +3.47255e13 q^{5} +2.12699e16 q^{6} +1.66807e17 q^{7} -7.19310e18 q^{8} +2.72647e19 q^{9} -9.25156e19 q^{10} -1.73703e21 q^{11} -3.91111e22 q^{12} +9.18003e22 q^{13} -4.44406e23 q^{14} -2.77234e23 q^{15} +8.39097e24 q^{16} +2.02868e25 q^{17} -7.26386e25 q^{18} -1.01896e26 q^{19} +1.70118e26 q^{20} -1.33172e27 q^{21} +4.62780e27 q^{22} -1.07819e28 q^{23} +5.74267e28 q^{24} -4.42689e28 q^{25} -2.44574e29 q^{26} +7.35151e28 q^{27} +8.17174e29 q^{28} -8.13688e29 q^{29} +7.38607e29 q^{30} +2.07038e30 q^{31} -6.53743e30 q^{32} +1.38677e31 q^{33} -5.40481e31 q^{34} +5.79244e30 q^{35} +1.33568e32 q^{36} -3.24660e30 q^{37} +2.71472e32 q^{38} -7.32896e32 q^{39} -2.49784e32 q^{40} -1.06315e33 q^{41} +3.54796e33 q^{42} +1.71944e33 q^{43} -8.50960e33 q^{44} +9.46781e32 q^{45} +2.87252e34 q^{46} -9.87145e33 q^{47} -6.69901e34 q^{48} -1.67432e34 q^{49} +1.17941e35 q^{50} -1.61962e35 q^{51} +4.49723e35 q^{52} -1.57415e35 q^{53} -1.95859e35 q^{54} -6.03192e34 q^{55} -1.19986e36 q^{56} +8.13498e35 q^{57} +2.16783e36 q^{58} -1.93994e36 q^{59} -1.35815e36 q^{60} +6.18066e36 q^{61} -5.51589e36 q^{62} +4.54794e36 q^{63} -1.03493e36 q^{64} +3.18781e36 q^{65} -3.69464e37 q^{66} -4.06657e37 q^{67} +9.93837e37 q^{68} +8.60784e37 q^{69} -1.54322e37 q^{70} -6.45010e37 q^{71} -1.96118e38 q^{72} +3.02798e37 q^{73} +8.64959e36 q^{74} +3.53425e38 q^{75} -4.99183e38 q^{76} -2.89748e38 q^{77} +1.95258e39 q^{78} -1.38169e39 q^{79} +2.91380e38 q^{80} -1.58134e39 q^{81} +2.83245e39 q^{82} +1.09468e39 q^{83} -6.52399e39 q^{84} +7.04469e38 q^{85} -4.58093e39 q^{86} +6.49615e39 q^{87} +1.24946e40 q^{88} +6.39870e38 q^{89} -2.52241e39 q^{90} +1.53129e40 q^{91} -5.28199e40 q^{92} -1.65290e40 q^{93} +2.62995e40 q^{94} -3.53840e39 q^{95} +5.21922e40 q^{96} +3.04505e39 q^{97} +4.46072e40 q^{98} -4.73597e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 49\!\cdots\!76 q^{6}+ \cdots + 13\!\cdots\!19 q^{9}+O(q^{10}) $ 3 * q - 344688 * q^2 - 10820953044 * q^3 + 6271704903936 * q^4 - 212302350281550 * q^5 + 4970194114982976 * q^6 + 57878416258239192 * q^7 - 3555831711183237120 * q^8 + 13277004110931878919 * q^9	$ 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 49\!\cdots\!76 q^{6}+ \cdots + 45\!\cdots\!28 q^{99}+O(q^{100}) $ 3 * q - 344688 * q^2 - 10820953044 * q^3 + 6271704903936 * q^4 - 212302350281550 * q^5 + 4970194114982976 * q^6 + 57878416258239192 * q^7 - 3555831711183237120 * q^8 + 13277004110931878919 * q^9 - 911610678410074173600 * q^10 - 3064080929502798535164 * q^11 - 71233189317945674062848 * q^12 - 98515763053518962936694 * q^13 - 663773359066872932212608 * q^14 + 2322231962154213782968200 * q^15 + 13217913642093764057038848 * q^16 + 35582277130790298867301302 * q^17 - 51949630971262524069430704 * q^18 - 233456308095243376865478180 * q^19 - 1234817679506740618000857600 * q^20 - 784315067894306487816760224 * q^21 + 10093688647003206881596695744 * q^22 + 2812708670812770779627026056 * q^23 + 36949405163940557660187279360 * q^24 - 12630087813294771903109831875 * q^25 - 445502868787427067716672131104 * q^26 + 40981593702376529051426180280 * q^27 + 526606706694181610802628184064 * q^28 - 12736322664295346653179017670 * q^29 + 6115742110948196616210957398400 * q^30 - 55977552834365071134409017504 * q^31 - 14842037794660482009412112744448 * q^32 - 13829226714693448959900097020528 * q^33 - 42547131667082319398961759011808 * q^34 + 35330944415319146254058128592400 * q^35 + 209583308279267044115700704156928 * q^36 + 4945769903781582545269841455122 * q^37 + 384288369224763756133358504473920 * q^38 - 546470556552953849463965686898712 * q^39 - 1326138456985596139721995183104000 * q^40 - 3123151500646359746292805811918274 * q^41 + 5023322329604694017661024056308224 * q^42 + 1491980858362212236675453498061156 * q^43 + 6827579920847638909574240093432832 * q^44 - 3706804708974790460103758635956150 * q^45 + 34089155258950859800971794327519616 * q^46 - 63038106682044077762675687404413168 * q^47 - 48906179099557375982971001333612544 * q^48 - 97136113131667199274890334287198229 * q^49 + 286202165340727366859498513545830000 * q^50 - 157319866621422817701623275797858024 * q^51 + 364999309722184195149034320029732352 * q^52 + 79896749344137562310547533743021506 * q^53 + 279506543662409583024224141017979520 * q^54 - 1107430856215374719020572615529578600 * q^55 - 1507500925934438536531619079138017280 * q^56 - 120534128028213908789981458568129040 * q^57 + 1060511497310363735425511566792954080 * q^58 + 192512048683375799719343226678403860 * q^59 + 5905677886285900358494072637173094400 * q^60 + 8740556115036354715092732710435455386 * q^61 - 12005332293025961804297174175449366016 * q^62 + 4195060549596204507618981258341049336 * q^63 - 28669651485797320669854651690478731264 * q^64 + 23272939413910136331858458170260680700 * q^65 - 70374114793184440562716940658640274688 * q^66 + 11266872945514675454702655007279407852 * q^67 + 95413181576279049358373233907724317184 * q^68 + 110718129232411678126981084073658946848 * q^69 + 59324379124057015483688060122385068800 * q^70 - 140970915469820223119231433051520161384 * q^71 - 178095780793081630529589944776993320960 * q^72 + 45825493210252135256288871746499029406 * q^73 - 255935787825178849200244145003411599008 * q^74 - 247029389196459510298088488221820147500 * q^75 + 26100578647791289060370838422069130240 * q^76 - 429017620126390531124795910645506217696 * q^77 + 3378623821652934155171000156043557135232 * q^78 - 520184835554750143118446358634240850320 * q^79 + 715918562852781559130521454428746547200 * q^80 - 3191652631710460747876906046824191542997 * q^81 - 579816777788457983576303882284492608096 * q^82 - 619777491338381742927488037142663372644 * q^83 - 4198672691855986319203859063793898610688 * q^84 - 106299433069331216483654652405294143100 * q^85 - 4751113477095326918262488958359640807744 * q^86 + 13958176049210326842816445061163645008040 * q^87 + 18329036816788093472347699011602935234560 * q^88 - 142389067128374093799211866144944441010 * q^89 - 8753545150081132110036071066039970208800 * q^90 + 25080596935320871627133801126628392473296 * q^91 - 67617289414955565381239604024555789723648 * q^92 + 3477058704647981071307340824432458334592 * q^93 - 53008068396962431152763933809330449227008 * q^94 - 33170437179755379504247502944935502503000 * q^95 + 95174464657114272630879818889875681181696 * q^96 + 116011691364103339137369463947331771078182 * q^97 - 38494567059701712876195969460820421029616 * q^98 + 45849669342635847189814810549498192693428 * 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 $

$2$	−2.66420e6	−1.79660	−0.898301	−	0.439381i	$-0.855198\pi$
$2$	−2.66420e6	−1.79660	−0.898301	+	0.439381i	$0.855198\pi$
$3$	−7.98359e9	−1.32194	−0.660971	−	0.750411i	$-0.729855\pi$
$3$	−7.98359e9	−1.32194	−0.660971	+	0.750411i	$0.729855\pi$
$4$	4.89893e12	2.22778
$5$	3.47255e13	0.162841	0.0814204	−	0.996680i	$-0.474054\pi$
$5$	3.47255e13	0.162841	0.0814204	+	0.996680i	$0.474054\pi$
$6$	2.12699e16	2.37500
$7$	1.66807e17	0.790139	0.395069	−	0.918651i	$-0.370721\pi$
$7$	1.66807e17	0.790139	0.395069	+	0.918651i	$0.370721\pi$
$8$	−7.19310e18	−2.20583
$9$	2.72647e19	0.747532
$10$	−9.25156e19	−0.292560
$11$	−1.73703e21	−0.778498	−0.389249	−	0.921133i	$-0.627265\pi$
$11$	−1.73703e21	−0.778498	−0.389249	+	0.921133i	$0.627265\pi$
$12$	−3.91111e22	−2.94499
$13$	9.18003e22	1.33969	0.669846	−	0.742500i	$-0.266360\pi$
$13$	9.18003e22	1.33969	0.669846	+	0.742500i	$0.266360\pi$
$14$	−4.44406e23	−1.41956
$15$	−2.77234e23	−0.215266
$16$	8.39097e24	1.73521
$17$	2.02868e25	1.21063	0.605314	−	0.795987i	$-0.293047\pi$
$17$	2.02868e25	1.21063	0.605314	+	0.795987i	$0.293047\pi$
$18$	−7.26386e25	−1.34302
$19$	−1.01896e26	−0.621884	−0.310942	−	0.950429i	$-0.600644\pi$
$19$	−1.01896e26	−0.621884	−0.310942	+	0.950429i	$0.600644\pi$
$20$	1.70118e26	0.362773
$21$	−1.33172e27	−1.04452
$22$	4.62780e27	1.39865
$23$	−1.07819e28	−1.31001	−0.655006	−	0.755624i	$-0.727334\pi$
$23$	−1.07819e28	−1.31001	−0.655006	+	0.755624i	$0.727334\pi$
$24$	5.74267e28	2.91597
$25$	−4.42689e28	−0.973483
$26$	−2.44574e29	−2.40689
$27$	7.35151e28	0.333749
$28$	8.17174e29	1.76025
$29$	−8.13688e29	−0.853688	−0.426844	−	0.904325i	$-0.640375\pi$
$29$	−8.13688e29	−0.853688	−0.426844	+	0.904325i	$0.640375\pi$
$30$	7.38607e29	0.386747
$31$	2.07038e30	0.553522	0.276761	−	0.960939i	$-0.410739\pi$
$31$	2.07038e30	0.553522	0.276761	+	0.960939i	$0.410739\pi$
$32$	−6.53743e30	−0.911659
$33$	1.38677e31	1.02913
$34$	−5.40481e31	−2.17502
$35$	5.79244e30	0.128667
$36$	1.33568e32	1.66533
$37$	−3.24660e30	−0.0230831	−0.0115415	−	0.999933i	$-0.503674\pi$
$37$	−3.24660e30	−0.0230831	−0.0115415	+	0.999933i	$0.503674\pi$
$38$	2.71472e32	1.11728
$39$	−7.32896e32	−1.77100
$40$	−2.49784e32	−0.359198
$41$	−1.06315e33	−0.921566	−0.460783	−	0.887513i	$-0.652431\pi$
$41$	−1.06315e33	−0.921566	−0.460783	+	0.887513i	$0.652431\pi$
$42$	3.54796e33	1.87658
$43$	1.71944e33	0.561415	0.280707	−	0.959793i	$-0.409431\pi$
$43$	1.71944e33	0.561415	0.280707	+	0.959793i	$0.409431\pi$
$44$	−8.50960e33	−1.73432
$45$	9.46781e32	0.121729
$46$	2.87252e34	2.35357
$47$	−9.87145e33	−0.520445	−0.260223	−	0.965549i	$-0.583796\pi$
$47$	−9.87145e33	−0.520445	−0.260223	+	0.965549i	$0.583796\pi$
$48$	−6.69901e34	−2.29385
$49$	−1.67432e34	−0.375680
$50$	1.17941e35	1.74896
$51$	−1.61962e35	−1.60038
$52$	4.49723e35	2.98454
$53$	−1.57415e35	−0.706952	−0.353476	−	0.935444i	$-0.615000\pi$
$53$	−1.57415e35	−0.706952	−0.353476	+	0.935444i	$0.615000\pi$
$54$	−1.95859e35	−0.599613
$55$	−6.03192e34	−0.126771
$56$	−1.19986e36	−1.74291
$57$	8.13498e35	0.822095
$58$	2.16783e36	1.53374
$59$	−1.93994e36	−0.966768	−0.483384	−	0.875408i	$-0.660592\pi$
$59$	−1.93994e36	−0.966768	−0.483384	+	0.875408i	$0.660592\pi$
$60$	−1.35815e36	−0.479565
$61$	6.18066e36	1.55515	0.777576	−	0.628788i	$-0.216449\pi$
$61$	6.18066e36	1.55515	0.777576	+	0.628788i	$0.216449\pi$
$62$	−5.51589e36	−0.994458
$63$	4.54794e36	0.590654
$64$	−1.03493e36	−0.0973241
$65$	3.18781e36	0.218157
$66$	−3.69464e37	−1.84894
$67$	−4.06657e37	−1.49518	−0.747592	−	0.664158i	$-0.768790\pi$
$67$	−4.06657e37	−1.49518	−0.747592	+	0.664158i	$0.768790\pi$
$68$	9.93837e37	2.69701
$69$	8.60784e37	1.73176
$70$	−1.54322e37	−0.231163
$71$	−6.45010e37	−0.722388	−0.361194	−	0.932491i	$-0.617631\pi$
$71$	−6.45010e37	−0.722388	−0.361194	+	0.932491i	$0.617631\pi$
$72$	−1.96118e38	−1.64892
$73$	3.02798e37	0.191882	0.0959409	−	0.995387i	$-0.469414\pi$
$73$	3.02798e37	0.191882	0.0959409	+	0.995387i	$0.469414\pi$
$74$	8.64959e36	0.0414711
$75$	3.53425e38	1.28689
$76$	−4.99183e38	−1.38542
$77$	−2.89748e38	−0.615122
$78$	1.95258e39	3.18178
$79$	−1.38169e39	−1.73402	−0.867011	−	0.498289i	$-0.833962\pi$
$79$	−1.38169e39	−1.73402	−0.867011	+	0.498289i	$0.833962\pi$
$80$	2.91380e38	0.282563
$81$	−1.58134e39	−1.18873
$82$	2.83245e39	1.65569
$83$	1.09468e39	0.499100	0.249550	−	0.968362i	$-0.419717\pi$
$83$	1.09468e39	0.499100	0.249550	+	0.968362i	$0.419717\pi$
$84$	−6.52399e39	−2.32695
$85$	7.04469e38	0.197140
$86$	−4.58093e39	−1.00864
$87$	6.49615e39	1.12853
$88$	1.24946e40	1.71723
$89$	6.39870e38	0.0697585	0.0348792	−	0.999392i	$-0.488895\pi$
$89$	6.39870e38	0.0697585	0.0348792	+	0.999392i	$0.488895\pi$
$90$	−2.52241e39	−0.218698
$91$	1.53129e40	1.05854
$92$	−5.28199e40	−2.91841
$93$	−1.65290e40	−0.731724
$94$	2.62995e40	0.935032
$95$	−3.53840e39	−0.101268
$96$	5.21922e40	1.20516
$97$	3.04505e39	0.0568556	0.0284278	−	0.999596i	$-0.490950\pi$
$97$	3.04505e39	0.0568556	0.0284278	+	0.999596i	$0.490950\pi$
$98$	4.46072e40	0.674948
$99$	−4.73597e40	−0.581952
$100$	−2.16870e41	−2.16870
$101$	1.41851e41	1.15676	0.578380	−	0.815768i	$-0.303685\pi$
$101$	1.41851e41	1.15676	0.578380	+	0.815768i	$0.303685\pi$
$102$	4.31498e41	2.87525
$103$	−1.44731e41	−0.789582	−0.394791	−	0.918771i	$-0.629183\pi$
$103$	−1.44731e41	−0.789582	−0.394791	+	0.918771i	$0.629183\pi$
$104$	−6.60328e41	−2.95513
$105$	−4.62445e40	−0.170090
$106$	4.19384e41	1.27011
$107$	−2.29714e41	−0.573878	−0.286939	−	0.957949i	$-0.592638\pi$
$107$	−2.29714e41	−0.573878	−0.286939	+	0.957949i	$0.592638\pi$
$108$	3.60145e41	0.743517
$109$	1.95590e41	0.334274	0.167137	−	0.985934i	$-0.446548\pi$
$109$	1.95590e41	0.334274	0.167137	+	0.985934i	$0.446548\pi$
$110$	1.60702e41	0.227757
$111$	2.59195e40	0.0305145
$112$	1.39967e42	1.37106
$113$	−9.94546e41	−0.811926	−0.405963	−	0.913889i	$-0.633064\pi$
$113$	−9.94546e41	−0.811926	−0.405963	+	0.913889i	$0.633064\pi$
$114$	−2.16732e42	−1.47698
$115$	−3.74407e41	−0.213323
$116$	−3.98620e42	−1.90183
$117$	2.50291e42	1.00146
$118$	5.16839e42	1.73690
$119$	3.38398e42	0.956565
$120$	1.99417e42	0.474839
$121$	−1.96124e42	−0.393941
$122$	−1.64665e43	−2.79399
$123$	8.48777e42	1.21826
$124$	1.01426e43	1.23312
$125$	−3.11639e42	−0.321363
$126$	−1.21166e43	−1.06117
$127$	−8.67945e41	−0.0646422	−0.0323211	−	0.999478i	$-0.510290\pi$
$127$	−8.67945e41	−0.0646422	−0.0323211	+	0.999478i	$0.510290\pi$
$128$	1.71332e43	1.08651
$129$	−1.37273e43	−0.742158
$130$	−8.49296e42	−0.391941
$131$	−3.86168e43	−1.52305	−0.761526	−	0.648134i	$-0.775549\pi$
$131$	−3.86168e43	−1.52305	−0.761526	+	0.648134i	$0.775549\pi$
$132$	6.79371e43	2.29267
$133$	−1.69970e43	−0.491375
$134$	1.08341e44	2.68625
$135$	2.55285e42	0.0543479
$136$	−1.45925e44	−2.67044
$137$	1.03048e44	1.62282	0.811409	−	0.584478i	$-0.198701\pi$
$137$	1.03048e44	1.62282	0.811409	+	0.584478i	$0.198701\pi$
$138$	−2.29330e44	−3.11128
$139$	9.05865e42	0.105989	0.0529944	−	0.998595i	$-0.483123\pi$
$139$	9.05865e42	0.105989	0.0529944	+	0.998595i	$0.483123\pi$
$140$	2.83768e43	0.286641
$141$	7.88096e43	0.687998
$142$	1.71844e44	1.29784
$143$	−1.59460e44	−1.04295
$144$	2.28777e44	1.29713
$145$	−2.82557e43	−0.139015
$146$	−8.06713e43	−0.344735
$147$	1.33671e44	0.496628
$148$	−1.59049e43	−0.0514239
$149$	−7.42911e43	−0.209227	−0.104614	−	0.994513i	$-0.533361\pi$
$149$	−7.42911e43	−0.209227	−0.104614	+	0.994513i	$0.533361\pi$
$150$	−9.41593e44	−2.31203
$151$	−1.02392e44	−0.219402	−0.109701	−	0.993965i	$-0.534989\pi$
$151$	−1.02392e44	−0.219402	−0.109701	+	0.993965i	$0.534989\pi$
$152$	7.32949e44	1.37177
$153$	5.53114e44	0.904983
$154$	7.71947e44	1.10513
$155$	7.18948e43	0.0901359
$156$	−3.59041e45	−3.94539
$157$	−2.17395e44	−0.209559	−0.104780	−	0.994495i	$-0.533414\pi$
$157$	−2.17395e44	−0.209559	−0.104780	+	0.994495i	$0.533414\pi$
$158$	3.68109e45	3.11535
$159$	1.25673e45	0.934550
$160$	−2.27015e44	−0.148455
$161$	−1.79849e45	−1.03509
$162$	4.21301e45	2.13567
$163$	−4.01604e45	−1.79453	−0.897267	−	0.441488i	$-0.854451\pi$
$163$	−4.01604e45	−1.79453	−0.897267	+	0.441488i	$0.854451\pi$
$164$	−5.20831e45	−2.05304
$165$	4.81564e44	0.167584
$166$	−2.91645e45	−0.896684
$167$	2.44064e44	0.0663462	0.0331731	−	0.999450i	$-0.489439\pi$
$167$	2.44064e44	0.0663462	0.0331731	+	0.999450i	$0.489439\pi$
$168$	9.57916e45	2.30402
$169$	3.73184e45	0.794777
$170$	−1.87685e45	−0.354182
$171$	−2.77817e45	−0.464878
$172$	8.42342e45	1.25071
$173$	6.55042e45	0.863623	0.431811	−	0.901964i	$-0.357875\pi$
$173$	6.55042e45	0.863623	0.431811	+	0.901964i	$0.357875\pi$
$174$	−1.73070e46	−2.02751
$175$	−7.38434e45	−0.769187
$176$	−1.45754e46	−1.35086
$177$	1.54877e46	1.27801
$178$	−1.70474e45	−0.125328
$179$	6.15457e45	0.403376	0.201688	−	0.979450i	$-0.435357\pi$
$179$	6.15457e45	0.403376	0.201688	+	0.979450i	$0.435357\pi$
$180$	4.63821e45	0.271184
$181$	2.92877e46	1.52853	0.764265	−	0.644903i	$-0.223102\pi$
$181$	2.92877e46	1.52853	0.764265	+	0.644903i	$0.223102\pi$
$182$	−4.07966e46	−1.90178
$183$	−4.93438e46	−2.05582
$184$	7.75553e46	2.88966
$185$	−1.12740e44	−0.00375886
$186$	4.40366e46	1.31462
$187$	−3.52388e46	−0.942472
$188$	−4.83596e46	−1.15944
$189$	1.22628e46	0.263708
$190$	9.42699e45	0.181938
$191$	3.00845e46	0.521386	0.260693	−	0.965422i	$-0.416049\pi$
$191$	3.00845e46	0.521386	0.260693	+	0.965422i	$0.416049\pi$
$192$	8.26244e45	0.128657
$193$	−1.09658e47	−1.53503	−0.767515	−	0.641031i	$-0.778507\pi$
$193$	−1.09658e47	−1.53503	−0.767515	+	0.641031i	$0.778507\pi$
$194$	−8.11261e45	−0.102147
$195$	−2.54502e46	−0.288391
$196$	−8.20238e46	−0.836932
$197$	1.17853e47	1.08338	0.541691	−	0.840578i	$-0.317784\pi$
$197$	1.17853e47	1.08338	0.541691	+	0.840578i	$0.317784\pi$
$198$	1.26176e47	1.04554
$199$	−3.68209e46	−0.275173	−0.137587	−	0.990490i	$-0.543935\pi$
$199$	−3.68209e46	−0.275173	−0.137587	+	0.990490i	$0.543935\pi$
$200$	3.18430e47	2.14733
$201$	3.24658e47	1.97655
$202$	−3.77918e47	−2.07824
$203$	−1.35729e47	−0.674532
$204$	−7.93439e47	−3.56529
$205$	−3.69185e46	−0.150068
$206$	3.85591e47	1.41856
$207$	−2.93966e47	−0.979275
$208$	7.70293e47	2.32465
$209$	1.76997e47	0.484135
$210$	1.23204e47	0.305584
$211$	−2.90275e47	−0.653160	−0.326580	−	0.945170i	$-0.605896\pi$
$211$	−2.90275e47	−0.653160	−0.326580	+	0.945170i	$0.605896\pi$
$212$	−7.71164e47	−1.57493
$213$	5.14950e47	0.954955
$214$	6.12003e47	1.03103
$215$	5.97084e46	0.0914212
$216$	−5.28801e47	−0.736191
$217$	3.45352e47	0.437359
$218$	−5.21090e47	−0.600558
$219$	−2.41741e47	−0.253657
$220$	−2.95500e47	−0.282418
$221$	1.86234e48	1.62187
$222$	−6.90548e46	−0.0548223
$223$	−2.40281e48	−1.73968	−0.869841	−	0.493331i	$-0.835779\pi$
$223$	−2.40281e48	−1.73968	−0.869841	+	0.493331i	$0.835779\pi$
$224$	−1.09049e48	−0.720337
$225$	−1.20698e48	−0.727709
$226$	2.64967e48	1.45871
$227$	−7.19443e45	−0.00361798	−0.00180899	−	0.999998i	$-0.500576\pi$
$227$	−7.19443e45	−0.00361798	−0.00180899	+	0.999998i	$0.500576\pi$
$228$	3.98527e48	1.83144
$229$	−2.92838e48	−1.23027	−0.615135	−	0.788422i	$-0.710899\pi$
$229$	−2.92838e48	−1.23027	−0.615135	+	0.788422i	$0.710899\pi$
$230$	9.97495e47	0.383257
$231$	2.31323e48	0.813155
$232$	5.85294e48	1.88309
$233$	−4.34377e48	−1.27959	−0.639795	−	0.768546i	$-0.720981\pi$
$233$	−4.34377e48	−1.27959	−0.639795	+	0.768546i	$0.720981\pi$
$234$	−6.66825e48	−1.79923
$235$	−3.42791e47	−0.0847497
$236$	−9.50364e48	−2.15374
$237$	1.10308e49	2.29228
$238$	−9.01558e48	−1.71857
$239$	8.86442e48	1.55058	0.775289	−	0.631607i	$-0.217604\pi$
$239$	8.86442e48	1.55058	0.775289	+	0.631607i	$0.217604\pi$
$240$	−2.32626e48	−0.373532
$241$	−9.74066e48	−1.43628	−0.718140	−	0.695899i	$-0.755006\pi$
$241$	−9.74066e48	−1.43628	−0.718140	+	0.695899i	$0.755006\pi$
$242$	5.22514e48	0.707754
$243$	9.94346e48	1.23768
$244$	3.02786e49	3.46453
$245$	−5.81415e47	−0.0611761
$246$	−2.26131e49	−2.18872
$247$	−9.35410e48	−0.833133
$248$	−1.48924e49	−1.22097
$249$	−8.73950e48	−0.659782
$250$	8.30268e48	0.577362
$251$	−2.46125e48	−0.157705	−0.0788524	−	0.996886i	$-0.525126\pi$
$251$	−2.46125e48	−0.157705	−0.0788524	+	0.996886i	$0.525126\pi$
$252$	2.22800e49	1.31585
$253$	1.87285e49	1.01984
$254$	2.31238e48	0.116136
$255$	−5.62420e48	−0.260607
$256$	−4.33705e49	−1.85470
$257$	−3.77351e49	−1.48976	−0.744880	−	0.667199i	$-0.767493\pi$
$257$	−3.77351e49	−1.48976	−0.744880	+	0.667199i	$0.767493\pi$
$258$	3.65723e49	1.33336
$259$	−5.41554e47	−0.0182388
$260$	1.56169e49	0.486004
$261$	−2.21850e49	−0.638159
$262$	1.02883e50	2.73632
$263$	6.07205e49	1.49363	0.746814	−	0.665033i	$-0.231583\pi$
$263$	6.07205e49	1.49363	0.746814	+	0.665033i	$0.231583\pi$
$264$	−9.97520e49	−2.27008
$265$	−5.46630e48	−0.115121
$266$	4.52833e49	0.882804
$267$	−5.10846e48	−0.0922167
$268$	−1.99218e50	−3.33093
$269$	2.38634e49	0.369667	0.184833	−	0.982770i	$-0.440825\pi$
$269$	2.38634e49	0.369667	0.184833	+	0.982770i	$0.440825\pi$
$270$	−6.80129e48	−0.0976415
$271$	3.94573e49	0.525118	0.262559	−	0.964916i	$-0.415433\pi$
$271$	3.94573e49	0.525118	0.262559	+	0.964916i	$0.415433\pi$
$272$	1.70226e50	2.10070
$273$	−1.22252e50	−1.39933
$274$	−2.74542e50	−2.91556
$275$	7.68964e49	0.757855
$276$	4.21692e50	3.85797
$277$	7.70224e49	0.654307	0.327154	−	0.944971i	$-0.393911\pi$
$277$	7.70224e49	0.654307	0.327154	+	0.944971i	$0.393911\pi$
$278$	−2.41340e49	−0.190420
$279$	5.64482e49	0.413775
$280$	−4.16656e49	−0.283817
$281$	−2.59982e50	−1.64613	−0.823063	−	0.567950i	$-0.807737\pi$
$281$	−2.59982e50	−1.64613	−0.823063	+	0.567950i	$0.807737\pi$
$282$	−2.09964e50	−1.23606
$283$	1.82242e50	0.997760	0.498880	−	0.866671i	$-0.333745\pi$
$283$	1.82242e50	0.997760	0.498880	+	0.866671i	$0.333745\pi$
$284$	−3.15986e50	−1.60932
$285$	2.82491e49	0.133871
$286$	4.24833e50	1.87376
$287$	−1.77341e50	−0.728165
$288$	−1.78241e50	−0.681494
$289$	1.30749e50	0.465622
$290$	7.52788e49	0.249755
$291$	−2.43104e49	−0.0751598
$292$	1.48338e50	0.427470
$293$	3.62144e50	0.972960	0.486480	−	0.873692i	$-0.338281\pi$
$293$	3.62144e50	0.972960	0.486480	+	0.873692i	$0.338281\pi$
$294$	−3.56125e50	−0.892242
$295$	−6.73654e49	−0.157429
$296$	2.33531e49	0.0509172
$297$	−1.27698e50	−0.259823
$298$	1.97926e50	0.375898
$299$	−9.89783e50	−1.75501
$300$	1.73140e51	2.86690
$301$	2.86814e50	0.443596
$302$	2.72793e50	0.394177
$303$	−1.13248e51	−1.52917
$304$	−8.55008e50	−1.07910
$305$	2.14626e50	0.253242
$306$	−1.47361e51	−1.62589
$307$	3.93346e50	0.405917	0.202959	−	0.979187i	$-0.434944\pi$
$307$	3.93346e50	0.405917	0.202959	+	0.979187i	$0.434944\pi$
$308$	−1.41946e51	−1.37035
$309$	1.15547e51	1.04378
$310$	−1.91542e50	−0.161938
$311$	6.24856e50	0.494529	0.247264	−	0.968948i	$-0.420468\pi$
$311$	6.24856e50	0.494529	0.247264	+	0.968948i	$0.420468\pi$
$312$	5.27179e51	3.90651
$313$	8.35246e50	0.579636	0.289818	−	0.957082i	$-0.406405\pi$
$313$	8.35246e50	0.579636	0.289818	+	0.957082i	$0.406405\pi$
$314$	5.79183e50	0.376494
$315$	1.57929e50	0.0961825
$316$	−6.76880e51	−3.86301
$317$	2.55951e50	0.136912	0.0684560	−	0.997654i	$-0.478193\pi$
$317$	2.55951e50	0.136912	0.0684560	+	0.997654i	$0.478193\pi$
$318$	−3.34819e51	−1.67901
$319$	1.41340e51	0.664594
$320$	−3.59384e49	−0.0158483
$321$	1.83394e51	0.758634
$322$	4.79155e51	1.85965
$323$	−2.06715e51	−0.752871
$324$	−7.74688e51	−2.64822
$325$	−4.06389e51	−1.30417
$326$	1.06995e52	3.22406
$327$	−1.56151e51	−0.441891
$328$	7.64735e51	2.03281
$329$	−1.64662e51	−0.411224
$330$	−1.28298e51	−0.301082
$331$	−5.02554e51	−1.10843	−0.554215	−	0.832373i	$-0.686982\pi$
$331$	−5.02554e51	−1.10843	−0.554215	+	0.832373i	$0.686982\pi$
$332$	5.36278e51	1.11188
$333$	−8.85176e49	−0.0172553
$334$	−6.50235e50	−0.119198
$335$	−1.41214e51	−0.243477
$336$	−1.11744e52	−1.81246
$337$	1.26080e52	1.92413	0.962065	−	0.272821i	$-0.0879568\pi$
$337$	1.26080e52	1.92413	0.962065	+	0.272821i	$0.0879568\pi$
$338$	−9.94236e51	−1.42790
$339$	7.94005e51	1.07332
$340$	3.45115e51	0.439183
$341$	−3.59631e51	−0.430915
$342$	7.40160e51	0.835200
$343$	−1.02271e52	−1.08698
$344$	−1.23681e52	−1.23838
$345$	2.98911e51	0.282001
$346$	−1.74516e52	−1.55159
$347$	5.08739e51	0.426325	0.213162	−	0.977017i	$-0.431624\pi$
$347$	5.08739e51	0.426325	0.213162	+	0.977017i	$0.431624\pi$
$348$	3.18242e52	2.51410
$349$	−1.29582e52	−0.965213	−0.482606	−	0.875837i	$-0.660310\pi$
$349$	−1.29582e52	−0.965213	−0.482606	+	0.875837i	$0.660310\pi$
$350$	1.96734e52	1.38192
$351$	6.74871e51	0.447121
$352$	1.13557e52	0.709725
$353$	2.08258e52	1.22806	0.614031	−	0.789282i	$-0.289547\pi$
$353$	2.08258e52	1.22806	0.614031	+	0.789282i	$0.289547\pi$
$354$	−4.12623e52	−2.29608
$355$	−2.23983e51	−0.117634
$356$	3.13468e51	0.155406
$357$	−2.70163e52	−1.26452
$358$	−1.63970e52	−0.724706
$359$	1.91161e52	0.797926	0.398963	−	0.916967i	$-0.369370\pi$
$359$	1.91161e52	0.797926	0.398963	+	0.916967i	$0.369370\pi$
$360$	−6.81028e51	−0.268512
$361$	−1.64643e52	−0.613260
$362$	−7.80281e52	−2.74616
$363$	1.56577e52	0.520767
$364$	7.50168e52	2.35820
$365$	1.05148e51	0.0312462
$366$	1.31462e53	3.69349
$367$	4.90413e52	1.30289	0.651444	−	0.758697i	$-0.274163\pi$
$367$	4.90413e52	1.30289	0.651444	+	0.758697i	$0.274163\pi$
$368$	−9.04707e52	−2.27315
$369$	−2.89865e52	−0.688899
$370$	3.00361e50	0.00675318
$371$	−2.62578e52	−0.558590
$372$	−8.09746e52	−1.63012
$373$	−4.90037e52	−0.933679	−0.466840	−	0.884342i	$-0.654607\pi$
$373$	−4.90037e52	−0.933679	−0.466840	+	0.884342i	$0.654607\pi$
$374$	9.38833e52	1.69325
$375$	2.48800e52	0.424824
$376$	7.10063e52	1.14801
$377$	−7.46968e52	−1.14368
$378$	−3.26706e52	−0.473778
$379$	6.92124e52	0.950780	0.475390	−	0.879775i	$-0.342307\pi$
$379$	6.92124e52	0.950780	0.475390	+	0.879775i	$0.342307\pi$
$380$	−1.73344e52	−0.225603
$381$	6.92932e51	0.0854532
$382$	−8.01512e52	−0.936722
$383$	−3.57815e52	−0.396354	−0.198177	−	0.980166i	$-0.563502\pi$
$383$	−3.57815e52	−0.396354	−0.198177	+	0.980166i	$0.563502\pi$
$384$	−1.36785e53	−1.43631
$385$	−1.00616e52	−0.100167
$386$	2.92152e53	2.75784
$387$	4.68801e52	0.419675
$388$	1.49175e52	0.126662
$389$	−1.72457e52	−0.138904	−0.0694519	−	0.997585i	$-0.522125\pi$
$389$	−1.72457e52	−0.138904	−0.0694519	+	0.997585i	$0.522125\pi$
$390$	6.78043e52	0.518123
$391$	−2.18731e53	−1.58594
$392$	1.20435e53	0.828685
$393$	3.08301e53	2.01339
$394$	−3.13983e53	−1.94641
$395$	−4.79798e52	−0.282369
$396$	−2.32012e53	−1.29646
$397$	3.22268e53	1.71006	0.855030	−	0.518579i	$-0.173539\pi$
$397$	3.22268e53	1.71006	0.855030	+	0.518579i	$0.173539\pi$
$398$	9.80981e52	0.494376
$399$	1.35697e53	0.649569
$400$	−3.71459e53	−1.68920
$401$	−2.70239e53	−1.16759	−0.583793	−	0.811902i	$-0.698432\pi$
$401$	−2.70239e53	−1.16759	−0.583793	+	0.811902i	$0.698432\pi$
$402$	−8.64954e53	−3.55107
$403$	1.90061e53	0.741549
$404$	6.94916e53	2.57700
$405$	−5.49128e52	−0.193573
$406$	3.61608e53	1.21187
$407$	5.63944e51	0.0179701
$408$	1.16501e54	3.53016
$409$	2.13137e52	0.0614231	0.0307116	−	0.999528i	$-0.490223\pi$
$409$	2.13137e52	0.0614231	0.0307116	+	0.999528i	$0.490223\pi$
$410$	9.83581e52	0.269613
$411$	−8.22697e53	−2.14527
$412$	−7.09026e53	−1.75901
$413$	−3.23595e53	−0.763881
$414$	7.83184e53	1.75937
$415$	3.80134e52	0.0812738
$416$	−6.00138e53	−1.22134
$417$	−7.23205e52	−0.140111
$418$	−4.71555e53	−0.869798
$419$	−2.93657e53	−0.515767	−0.257883	−	0.966176i	$-0.583025\pi$
$419$	−2.93657e53	−0.515767	−0.257883	+	0.966176i	$0.583025\pi$
$420$	−2.26549e53	−0.378923
$421$	1.15034e54	1.83250	0.916249	−	0.400609i	$-0.131201\pi$
$421$	1.15034e54	1.83250	0.916249	+	0.400609i	$0.131201\pi$
$422$	7.73351e53	1.17347
$423$	−2.69142e53	−0.389049
$424$	1.13230e54	1.55941
$425$	−8.98074e53	−1.17853
$426$	−1.37193e54	−1.71567
$427$	1.03097e54	1.22879
$428$	−1.12535e54	−1.27847
$429$	1.27306e54	1.37872
$430$	−1.59075e53	−0.164247
$431$	−1.01552e53	−0.0999783	−0.0499892	−	0.998750i	$-0.515919\pi$
$431$	−1.01552e53	−0.0999783	−0.0499892	+	0.998750i	$0.515919\pi$
$432$	6.16863e53	0.579124
$433$	−8.64049e52	−0.0773636	−0.0386818	−	0.999252i	$-0.512316\pi$
$433$	−8.64049e52	−0.0773636	−0.0386818	+	0.999252i	$0.512316\pi$
$434$	−9.20088e53	−0.785760
$435$	2.25582e53	0.183770
$436$	9.58181e53	0.744689
$437$	1.09864e54	0.814675
$438$	6.44047e53	0.455720
$439$	−1.09372e54	−0.738553	−0.369277	−	0.929319i	$-0.620395\pi$
$439$	−1.09372e54	−0.738553	−0.369277	+	0.929319i	$0.620395\pi$
$440$	4.33882e53	0.279635
$441$	−4.56498e53	−0.280833
$442$	−4.96163e54	−2.91386
$443$	−3.38590e54	−1.89845	−0.949223	−	0.314604i	$-0.898128\pi$
$443$	−3.38590e54	−1.89845	−0.949223	+	0.314604i	$0.898128\pi$
$444$	1.26978e53	0.0679794
$445$	2.22198e52	0.0113595
$446$	6.40157e54	3.12552
$447$	5.93110e53	0.276586
$448$	−1.72633e53	−0.0768996
$449$	1.99320e54	0.848205	0.424103	−	0.905614i	$-0.360590\pi$
$449$	1.99320e54	0.848205	0.424103	+	0.905614i	$0.360590\pi$
$450$	3.21563e54	1.30740
$451$	1.84673e54	0.717437
$452$	−4.87221e54	−1.80879
$453$	8.17458e53	0.290036
$454$	1.91674e52	0.00650007
$455$	5.31748e53	0.172374
$456$	−5.85157e54	−1.81340
$457$	−1.51405e54	−0.448600	−0.224300	−	0.974520i	$-0.572010\pi$
$457$	−1.51405e54	−0.448600	−0.224300	+	0.974520i	$0.572010\pi$
$458$	7.80179e54	2.21031
$459$	1.49139e54	0.404046
$460$	−1.83420e54	−0.475237
$461$	−6.81127e54	−1.68795	−0.843974	−	0.536383i	$-0.819790\pi$
$461$	−6.81127e54	−1.68795	−0.843974	+	0.536383i	$0.819790\pi$
$462$	−6.16291e54	−1.46092
$463$	1.14829e54	0.260400	0.130200	−	0.991488i	$-0.458438\pi$
$463$	1.14829e54	0.260400	0.130200	+	0.991488i	$0.458438\pi$
$464$	−6.82763e54	−1.48133
$465$	−5.73979e53	−0.119154
$466$	1.15727e55	2.29891
$467$	2.77911e54	0.528335	0.264167	−	0.964477i	$-0.414903\pi$
$467$	2.77911e54	0.528335	0.264167	+	0.964477i	$0.414903\pi$
$468$	1.22616e55	2.23104
$469$	−6.78330e54	−1.18140
$470$	9.13263e53	0.152261
$471$	1.73559e54	0.277025
$472$	1.39542e55	2.13252
$473$	−2.98672e54	−0.437060
$474$	−2.93883e55	−4.11831
$475$	4.51083e54	0.605393
$476$	1.65779e55	2.13101
$477$	−4.29187e54	−0.528469
$478$	−2.36166e55	−2.78577
$479$	5.54208e54	0.626318	0.313159	−	0.949701i	$-0.398613\pi$
$479$	5.54208e54	0.626318	0.313159	+	0.949701i	$0.398613\pi$
$480$	1.81240e54	0.196249
$481$	−2.98039e53	−0.0309242
$482$	2.59511e55	2.58042
$483$	1.43584e55	1.36833
$484$	−9.60799e54	−0.877612
$485$	1.05741e53	0.00925841
$486$	−2.64914e55	−2.22362
$487$	−1.88066e54	−0.151345	−0.0756723	−	0.997133i	$-0.524110\pi$
$487$	−1.88066e54	−0.151345	−0.0756723	+	0.997133i	$0.524110\pi$
$488$	−4.44581e55	−3.43040
$489$	3.20624e55	2.37227
$490$	1.54901e54	0.109909
$491$	−1.63929e55	−1.11554	−0.557769	−	0.829996i	$-0.688342\pi$
$491$	−1.63929e55	−1.11554	−0.557769	+	0.829996i	$0.688342\pi$
$492$	4.15810e55	2.71400
$493$	−1.65071e55	−1.03350
$494$	2.49212e55	1.49681
$495$	−1.64459e54	−0.0947655
$496$	1.73725e55	0.960477
$497$	−1.07592e55	−0.570787
$498$	2.32838e55	1.18536
$499$	−3.46878e54	−0.169479	−0.0847395	−	0.996403i	$-0.527006\pi$
$499$	−3.46878e54	−0.169479	−0.0847395	+	0.996403i	$0.527006\pi$
$500$	−1.52670e55	−0.715926
$501$	−1.94851e54	−0.0877059
$502$	6.55727e54	0.283333
$503$	1.93714e53	0.00803557	0.00401778	−	0.999992i	$-0.498721\pi$
$503$	1.93714e53	0.00803557	0.00401778	+	0.999992i	$0.498721\pi$
$504$	−3.27137e55	−1.30288
$505$	4.92583e54	0.188368
$506$	−4.98965e55	−1.83225
$507$	−2.97935e55	−1.05065
$508$	−4.25200e54	−0.144008
$509$	−1.25363e54	−0.0407807	−0.0203904	−	0.999792i	$-0.506491\pi$
$509$	−1.25363e54	−0.0407807	−0.0203904	+	0.999792i	$0.506491\pi$
$510$	1.49840e55	0.468208
$511$	5.05086e54	0.151613
$512$	7.78712e55	2.24565
$513$	−7.49091e54	−0.207553
$514$	1.00534e56	2.67650
$515$	−5.02584e54	−0.128576
$516$	−6.72491e55	−1.65336
$517$	1.71470e55	0.405165
$518$	1.44281e54	0.0327679
$519$	−5.22959e55	−1.14166
$520$	−2.29302e55	−0.481215
$521$	2.35880e55	0.475902	0.237951	−	0.971277i	$-0.423524\pi$
$521$	2.35880e55	0.475902	0.237951	+	0.971277i	$0.423524\pi$
$522$	5.91052e55	1.14652
$523$	7.86347e55	1.46666	0.733330	−	0.679873i	$-0.237965\pi$
$523$	7.86347e55	1.46666	0.733330	+	0.679873i	$0.237965\pi$
$524$	−1.89181e56	−3.39302
$525$	5.89536e55	1.01682
$526$	−1.61771e56	−2.68345
$527$	4.20013e55	0.670109
$528$	1.16364e56	1.78576
$529$	4.85103e55	0.716131
$530$	1.45633e55	0.206826
$531$	−5.28919e55	−0.722690
$532$	−8.32670e55	−1.09467
$533$	−9.75976e55	−1.23461
$534$	1.36100e55	0.165677
$535$	−7.97692e54	−0.0934508
$536$	2.92512e56	3.29811
$537$	−4.91355e55	−0.533240
$538$	−6.35768e55	−0.664144
$539$	2.90834e55	0.292466
$540$	1.25062e55	0.121075
$541$	1.45744e56	1.35846	0.679232	−	0.733924i	$-0.262313\pi$
$541$	1.45744e56	1.35846	0.679232	+	0.733924i	$0.262313\pi$
$542$	−1.05122e56	−0.943428
$543$	−2.33821e56	−2.02063
$544$	−1.32624e56	−1.10368
$545$	6.79195e54	0.0544335
$546$	3.25703e56	2.51404
$547$	−1.05313e56	−0.782967	−0.391483	−	0.920185i	$-0.628038\pi$
$547$	−1.05313e56	−0.782967	−0.391483	+	0.920185i	$0.628038\pi$
$548$	5.04828e56	3.61528
$549$	1.68514e56	1.16253
$550$	−2.04867e56	−1.36156
$551$	8.29118e55	0.530895
$552$	−6.19170e56	−3.81996
$553$	−2.30475e56	−1.37012
$554$	−2.05203e56	−1.17553
$555$	9.00068e53	0.00496900
$556$	4.43777e55	0.236119
$557$	6.40305e55	0.328364	0.164182	−	0.986430i	$-0.447502\pi$
$557$	6.40305e55	0.328364	0.164182	+	0.986430i	$0.447502\pi$
$558$	−1.50389e56	−0.743389
$559$	1.57845e56	0.752123
$560$	4.86042e55	0.223264
$561$	2.81332e56	1.24589
$562$	6.92643e56	2.95743
$563$	−1.09202e56	−0.449581	−0.224791	−	0.974407i	$-0.572170\pi$
$563$	−1.09202e56	−0.449581	−0.224791	+	0.974407i	$0.572170\pi$
$564$	3.86083e56	1.53271
$565$	−3.45361e55	−0.132215
$566$	−4.85528e56	−1.79258
$567$	−2.63778e56	−0.939260
$568$	4.63962e56	1.59346
$569$	−2.43585e56	−0.806954	−0.403477	−	0.914990i	$-0.632198\pi$
$569$	−2.43585e56	−0.806954	−0.403477	+	0.914990i	$0.632198\pi$
$570$	−7.52612e55	−0.240512
$571$	−9.71845e55	−0.299610	−0.149805	−	0.988716i	$-0.547865\pi$
$571$	−9.71845e55	−0.299610	−0.149805	+	0.988716i	$0.547865\pi$
$572$	−7.81183e56	−2.32346
$573$	−2.40183e56	−0.689242
$574$	4.72471e56	1.30822
$575$	4.77303e56	1.27527
$576$	−2.82170e55	−0.0727529
$577$	−6.34210e56	−1.57808	−0.789040	−	0.614342i	$-0.789422\pi$
$577$	−6.34210e56	−1.57808	−0.789040	+	0.614342i	$0.789422\pi$
$578$	−3.48342e56	−0.836537
$579$	8.75467e56	2.02922
$580$	−1.38423e56	−0.309695
$581$	1.82600e56	0.394358
$582$	6.47677e55	0.135032
$583$	2.73434e56	0.550361
$584$	−2.17805e56	−0.423258
$585$	8.69147e55	0.163079
$586$	−9.64824e56	−1.74802
$587$	9.71961e56	1.70047	0.850233	−	0.526407i	$-0.176461\pi$
$587$	9.71961e56	1.70047	0.850233	+	0.526407i	$0.176461\pi$
$588$	6.54844e56	1.10638
$589$	−2.10964e56	−0.344226
$590$	1.79475e56	0.282838
$591$	−9.40888e56	−1.43217
$592$	−2.72421e55	−0.0400540
$593$	−3.07788e56	−0.437150	−0.218575	−	0.975820i	$-0.570141\pi$
$593$	−3.07788e56	−0.437150	−0.218575	+	0.975820i	$0.570141\pi$
$594$	3.40213e56	0.466798
$595$	1.17510e56	0.155768
$596$	−3.63947e56	−0.466112
$597$	2.93963e56	0.363763
$598$	2.63698e57	3.15306
$599$	9.26416e56	1.07043	0.535213	−	0.844717i	$-0.320231\pi$
$599$	9.26416e56	1.07043	0.535213	+	0.844717i	$0.320231\pi$
$600$	−2.54222e57	−2.83865
$601$	−1.47276e57	−1.58930	−0.794648	−	0.607071i	$-0.792345\pi$
$601$	−1.47276e57	−1.58930	−0.794648	+	0.607071i	$0.792345\pi$
$602$	−7.64130e56	−0.796964
$603$	−1.10874e57	−1.11770
$604$	−5.01613e56	−0.488778
$605$	−6.81050e55	−0.0641496
$606$	3.01714e57	2.74731
$607$	−1.51826e57	−1.33652	−0.668262	−	0.743926i	$-0.732962\pi$
$607$	−1.51826e57	−1.33652	−0.668262	+	0.743926i	$0.732962\pi$
$608$	6.66139e56	0.566946
$609$	1.08360e57	0.891692
$610$	−5.71807e56	−0.454976
$611$	−9.06202e56	−0.697237
$612$	2.70967e57	2.01610
$613$	−9.13614e56	−0.657390	−0.328695	−	0.944436i	$-0.606609\pi$
$613$	−9.13614e56	−0.657390	−0.328695	+	0.944436i	$0.606609\pi$
$614$	−1.04795e57	−0.729272
$615$	2.94742e56	0.198382
$616$	2.08419e57	1.35685
$617$	2.58224e57	1.62611	0.813057	−	0.582184i	$-0.197802\pi$
$617$	2.58224e57	1.62611	0.813057	+	0.582184i	$0.197802\pi$
$618$	−3.07840e57	−1.87526
$619$	2.63907e57	1.55522	0.777610	−	0.628747i	$-0.216432\pi$
$619$	2.63907e57	1.55522	0.777610	+	0.628747i	$0.216432\pi$
$620$	3.52208e56	0.200803
$621$	−7.92633e56	−0.437215
$622$	−1.66474e57	−0.888471
$623$	1.06735e56	0.0551189
$624$	−6.14971e57	−3.07305
$625$	1.90490e57	0.921152
$626$	−2.22526e57	−1.04137
$627$	−1.41307e57	−0.639999
$628$	−1.06500e57	−0.466851
$629$	−6.58632e55	−0.0279450
$630$	−4.20755e56	−0.172802
$631$	−5.93300e56	−0.235870	−0.117935	−	0.993021i	$-0.537627\pi$
$631$	−5.93300e56	−0.235870	−0.117935	+	0.993021i	$0.537627\pi$
$632$	9.93861e57	3.82495
$633$	2.31744e57	0.863440
$634$	−6.81904e56	−0.245976
$635$	−3.01398e55	−0.0105264
$636$	6.15666e57	2.08197
$637$	−1.53703e57	−0.503296
$638$	−3.76558e57	−1.19401
$639$	−1.75860e57	−0.540008
$640$	5.94959e56	0.176928
$641$	−3.05943e56	−0.0881152	−0.0440576	−	0.999029i	$-0.514029\pi$
$641$	−3.05943e56	−0.0881152	−0.0440576	+	0.999029i	$0.514029\pi$
$642$	−4.88598e57	−1.36296
$643$	8.49375e56	0.229496	0.114748	−	0.993395i	$-0.463394\pi$
$643$	8.49375e56	0.229496	0.114748	+	0.993395i	$0.463394\pi$
$644$	−8.81070e57	−2.30595
$645$	−4.76687e56	−0.120854
$646$	5.50730e57	1.35261
$647$	−1.01048e57	−0.240431	−0.120215	−	0.992748i	$-0.538359\pi$
$647$	−1.01048e57	−0.240431	−0.120215	+	0.992748i	$0.538359\pi$
$648$	1.13747e58	2.62213
$649$	3.36974e57	0.752627
$650$	1.08270e58	2.34307
$651$	−2.75715e57	−0.578163
$652$	−1.96743e58	−3.99782
$653$	−7.06012e57	−1.39025	−0.695123	−	0.718891i	$-0.744650\pi$
$653$	−7.06012e57	−1.39025	−0.695123	+	0.718891i	$0.744650\pi$
$654$	4.16017e57	0.793903
$655$	−1.34099e57	−0.248015
$656$	−8.92088e57	−1.59911
$657$	8.25569e56	0.143438
$658$	4.38693e57	0.738805
$659$	7.62589e57	1.24491	0.622457	−	0.782654i	$-0.286135\pi$
$659$	7.62589e57	1.24491	0.622457	+	0.782654i	$0.286135\pi$
$660$	2.35915e57	0.373340
$661$	4.22569e57	0.648288	0.324144	−	0.946008i	$-0.394924\pi$
$661$	4.22569e57	0.648288	0.324144	+	0.946008i	$0.394924\pi$
$662$	1.33890e58	1.99141
$663$	−1.48681e58	−2.14402
$664$	−7.87416e57	−1.10093
$665$	−5.90228e56	−0.0800158
$666$	2.35829e56	0.0310009
$667$	8.77312e57	1.11834
$668$	1.19565e57	0.147805
$669$	1.91831e58	2.29976
$670$	3.76221e57	0.437431
$671$	−1.07360e58	−1.21068
$672$	8.70600e57	0.952244
$673$	−3.42146e57	−0.362996	−0.181498	−	0.983391i	$-0.558095\pi$
$673$	−3.42146e57	−0.362996	−0.181498	+	0.983391i	$0.558095\pi$
$674$	−3.35903e58	−3.45689
$675$	−3.25443e57	−0.324898
$676$	1.82820e58	1.77059
$677$	−2.44766e57	−0.229976	−0.114988	−	0.993367i	$-0.536683\pi$
$677$	−2.44766e57	−0.229976	−0.114988	+	0.993367i	$0.536683\pi$
$678$	−2.11539e58	−1.92833
$679$	5.07934e56	0.0449238
$680$	−5.06732e57	−0.434856
$681$	5.74374e55	0.00478276
$682$	9.58128e57	0.774183
$683$	−4.22496e57	−0.331283	−0.165641	−	0.986186i	$-0.552969\pi$
$683$	−4.22496e57	−0.331283	−0.165641	+	0.986186i	$0.552969\pi$
$684$	−1.36101e58	−1.03564
$685$	3.57841e57	0.264261
$686$	2.72469e58	1.95287
$687$	2.33790e58	1.62635
$688$	1.44278e58	0.974173
$689$	−1.44507e58	−0.947099
$690$	−7.96359e57	−0.506644
$691$	6.48155e57	0.400294	0.200147	−	0.979766i	$-0.435858\pi$
$691$	6.48155e57	0.400294	0.200147	+	0.979766i	$0.435858\pi$
$692$	3.20901e58	1.92396
$693$	−7.89991e57	−0.459823
$694$	−1.35538e58	−0.765936
$695$	3.14566e56	0.0172593
$696$	−4.67274e58	−2.48933
$697$	−2.15680e58	−1.11567
$698$	3.45232e58	1.73410
$699$	3.46789e58	1.69154
$700$	−3.61754e58	−1.71358
$701$	−5.02893e57	−0.231343	−0.115671	−	0.993288i	$-0.536902\pi$
$701$	−5.02893e57	−0.231343	−0.115671	+	0.993288i	$0.536902\pi$
$702$	−1.79799e58	−0.803297
$703$	3.30816e56	0.0143550
$704$	1.79770e57	0.0757667
$705$	2.73670e57	0.112034
$706$	−5.54841e58	−2.20634
$707$	2.36616e58	0.914001
$708$	7.58732e58	2.84712
$709$	1.43455e58	0.522961	0.261481	−	0.965209i	$-0.415789\pi$
$709$	1.43455e58	0.522961	0.261481	+	0.965209i	$0.415789\pi$
$710$	5.96735e57	0.211342
$711$	−3.76713e58	−1.29624
$712$	−4.60265e57	−0.153875
$713$	−2.23226e58	−0.725120
$714$	7.19767e58	2.27185
$715$	−5.53732e57	−0.169835
$716$	3.01508e58	0.898632
$717$	−7.07699e58	−2.04977
$718$	−5.09290e58	−1.43355
$719$	−3.86957e58	−1.05857	−0.529286	−	0.848444i	$-0.677540\pi$
$719$	−3.86957e58	−1.05857	−0.529286	+	0.848444i	$0.677540\pi$
$720$	7.94441e57	0.211225
$721$	−2.41420e58	−0.623880
$722$	4.38641e58	1.10178
$723$	7.77654e58	1.89868
$724$	1.43478e59	3.40522
$725$	3.60211e58	0.831050
$726$	−4.17153e58	−0.935611
$727$	−2.07033e57	−0.0451423	−0.0225711	−	0.999745i	$-0.507185\pi$
$727$	−2.07033e57	−0.0451423	−0.0225711	+	0.999745i	$0.507185\pi$
$728$	−1.10147e59	−2.33496
$729$	−2.17083e58	−0.447416
$730$	−2.80135e57	−0.0561369
$731$	3.48820e58	0.679665
$732$	−2.41732e59	−4.57991
$733$	8.41125e58	1.54963	0.774817	−	0.632185i	$-0.217842\pi$
$733$	8.41125e58	1.54963	0.774817	+	0.632185i	$0.217842\pi$
$734$	−1.30656e59	−2.34077
$735$	4.64178e57	0.0808713
$736$	7.04860e58	1.19428
$737$	7.06375e58	1.16400
$738$	7.72259e58	1.23768
$739$	−4.41017e58	−0.687455	−0.343728	−	0.939069i	$-0.611690\pi$
$739$	−4.41017e58	−0.687455	−0.343728	+	0.939069i	$0.611690\pi$
$740$	−5.52304e56	−0.00837391
$741$	7.46793e58	1.10135
$742$	6.99561e58	1.00356
$743$	−7.66450e58	−1.06958	−0.534790	−	0.844985i	$-0.679609\pi$
$743$	−7.66450e58	−1.06958	−0.534790	+	0.844985i	$0.679609\pi$
$744$	1.18895e59	1.61405
$745$	−2.57979e57	−0.0340707
$746$	1.30556e59	1.67745
$747$	2.98462e58	0.373093
$748$	−1.72633e59	−2.09962
$749$	−3.83178e58	−0.453443
$750$	−6.62852e58	−0.763239
$751$	−4.55998e58	−0.510910	−0.255455	−	0.966821i	$-0.582225\pi$
$751$	−4.55998e58	−0.510910	−0.255455	+	0.966821i	$0.582225\pi$
$752$	−8.28310e58	−0.903082
$753$	1.96496e58	0.208477
$754$	1.99007e59	2.05474
$755$	−3.55562e57	−0.0357275
$756$	6.00747e58	0.587482
$757$	−1.30493e59	−1.24200	−0.621000	−	0.783811i	$-0.713273\pi$
$757$	−1.30493e59	−1.24200	−0.621000	+	0.783811i	$0.713273\pi$
$758$	−1.84396e59	−1.70817
$759$	−1.49521e59	−1.34817
$760$	2.54520e58	0.223380
$761$	4.11390e58	0.351454	0.175727	−	0.984439i	$-0.443772\pi$
$761$	4.11390e58	0.351454	0.175727	+	0.984439i	$0.443772\pi$
$762$	−1.84611e58	−0.153525
$763$	3.26257e58	0.264123
$764$	1.47382e59	1.16153
$765$	1.92072e58	0.147368
$766$	9.53290e58	0.712091
$767$	−1.78087e59	−1.29517
$768$	3.46252e59	2.45181
$769$	9.93012e58	0.684644	0.342322	−	0.939583i	$-0.388787\pi$
$769$	9.93012e58	0.684644	0.342322	+	0.939583i	$0.388787\pi$
$770$	2.68062e58	0.179960
$771$	3.01261e59	1.96938
$772$	−5.37209e59	−3.41970
$773$	−2.82910e58	−0.175375	−0.0876877	−	0.996148i	$-0.527948\pi$
$773$	−2.82910e58	−0.175375	−0.0876877	+	0.996148i	$0.527948\pi$
$774$	−1.24898e59	−0.753989
$775$	−9.16532e58	−0.538844
$776$	−2.19033e58	−0.125414
$777$	4.32355e57	0.0241107
$778$	4.59460e58	0.249555
$779$	1.08331e59	0.573107
$780$	−1.24679e59	−0.642470
$781$	1.12040e59	0.562377
$782$	5.82742e59	2.84930
$783$	−5.98184e58	−0.284917
$784$	−1.40492e59	−0.651885
$785$	−7.54914e57	−0.0341248
$786$	−8.21374e59	−3.61725
$787$	8.05210e57	0.0345484	0.0172742	−	0.999851i	$-0.494501\pi$
$787$	8.05210e57	0.0345484	0.0172742	+	0.999851i	$0.494501\pi$
$788$	5.77352e59	2.41353
$789$	−4.84768e59	−1.97449
$790$	1.27828e59	0.507305
$791$	−1.65897e59	−0.641535
$792$	3.40663e59	1.28368
$793$	5.67386e59	2.08343
$794$	−8.58585e59	−3.07230
$795$	4.36407e58	0.152183
$796$	−1.80383e59	−0.613024
$797$	3.46651e59	1.14814	0.574072	−	0.818805i	$-0.305363\pi$
$797$	3.46651e59	1.14814	0.574072	+	0.818805i	$0.305363\pi$
$798$	−3.61523e59	−1.16702
$799$	−2.00260e59	−0.630066
$800$	2.89405e59	0.887484
$801$	1.74459e58	0.0521467
$802$	7.19971e59	2.09769
$803$	−5.25969e58	−0.149380
$804$	1.59048e60	4.40330
$805$	−6.24536e58	−0.168555
$806$	−5.06361e59	−1.33227
$807$	−1.90516e59	−0.488678
$808$	−1.02034e60	−2.55161
$809$	−8.54307e57	−0.0208290	−0.0104145	−	0.999946i	$-0.503315\pi$
$809$	−8.54307e57	−0.0208290	−0.0104145	+	0.999946i	$0.503315\pi$
$810$	1.46299e59	0.347774
$811$	4.76651e59	1.10477	0.552387	−	0.833588i	$-0.313717\pi$
$811$	4.76651e59	1.10477	0.552387	+	0.833588i	$0.313717\pi$
$812$	−6.64925e59	−1.50271
$813$	−3.15011e59	−0.694176
$814$	−1.50246e58	−0.0322851
$815$	−1.39459e59	−0.292223
$816$	−1.35902e60	−2.77700
$817$	−1.75204e59	−0.349135
$818$	−5.67841e58	−0.110353
$819$	4.17502e59	0.791295
$820$	−1.80861e59	−0.334319
$821$	3.33204e59	0.600725	0.300362	−	0.953825i	$-0.402892\pi$
$821$	3.33204e59	0.600725	0.300362	+	0.953825i	$0.402892\pi$
$822$	2.19183e60	3.85420
$823$	−1.98842e59	−0.341045	−0.170522	−	0.985354i	$-0.554546\pi$
$823$	−1.98842e59	−0.341045	−0.170522	+	0.985354i	$0.554546\pi$
$824$	1.04106e60	1.74168
$825$	−6.13910e59	−1.00184
$826$	8.62121e59	1.37239
$827$	1.09198e60	1.69572	0.847858	−	0.530223i	$-0.177892\pi$
$827$	1.09198e60	1.69572	0.847858	+	0.530223i	$0.177892\pi$
$828$	−1.44012e60	−2.18161
$829$	−1.17320e60	−1.73382	−0.866908	−	0.498468i	$-0.833896\pi$
$829$	−1.17320e60	−1.73382	−0.866908	+	0.498468i	$0.833896\pi$
$830$	−1.01275e59	−0.146017
$831$	−6.14915e59	−0.864956
$832$	−9.50067e58	−0.130384
$833$	−3.39666e59	−0.454809
$834$	1.92676e59	0.251724
$835$	8.47524e57	0.0108039
$836$	8.67096e59	1.07855
$837$	1.52204e59	0.184737
$838$	7.82362e59	0.926628
$839$	−7.71620e57	−0.00891832	−0.00445916	−	0.999990i	$-0.501419\pi$
$839$	−7.71620e57	−0.00891832	−0.00445916	+	0.999990i	$0.501419\pi$
$840$	3.32641e59	0.375189
$841$	−2.46397e59	−0.271217
$842$	−3.06474e60	−3.29227
$843$	2.07559e60	2.17608
$844$	−1.42204e60	−1.45509
$845$	1.29590e59	0.129422
$846$	7.17049e59	0.698966
$847$	−3.27148e59	−0.311268
$848$	−1.32086e60	−1.22671
$849$	−1.45494e60	−1.31898
$850$	2.39265e60	2.11734
$851$	3.50046e58	0.0302391
$852$	2.52270e60	2.12743
$853$	1.20917e60	0.995476	0.497738	−	0.867327i	$-0.334164\pi$
$853$	1.20917e60	0.995476	0.497738	+	0.867327i	$0.334164\pi$
$854$	−2.74672e60	−2.20764
$855$	−9.64734e58	−0.0757011
$856$	1.65235e60	1.26587
$857$	−2.11243e59	−0.158007	−0.0790035	−	0.996874i	$-0.525174\pi$
$857$	−2.11243e59	−0.158007	−0.0790035	+	0.996874i	$0.525174\pi$
$858$	−3.39169e60	−2.47701
$859$	−2.05262e58	−0.0146369	−0.00731843	−	0.999973i	$-0.502330\pi$
$859$	−2.05262e58	−0.0146369	−0.00731843	+	0.999973i	$0.502330\pi$
$860$	2.92507e59	0.203666
$861$	1.41582e60	0.962592
$862$	2.70556e59	0.179621
$863$	2.59149e60	1.68008	0.840038	−	0.542527i	$-0.182532\pi$
$863$	2.59149e60	1.68008	0.840038	+	0.542527i	$0.182532\pi$
$864$	−4.80600e59	−0.304265
$865$	2.27467e59	0.140633
$866$	2.30200e59	0.138991
$867$	−1.04385e60	−0.615525
$868$	1.69186e60	0.974338
$869$	2.40003e60	1.34993
$870$	−6.00995e59	−0.330162
$871$	−3.73312e60	−2.00309
$872$	−1.40690e60	−0.737351
$873$	8.30223e58	0.0425014
$874$	−2.92699e60	−1.46365
$875$	−5.19835e59	−0.253922
$876$	−1.18427e60	−0.565090
$877$	−9.21584e59	−0.429579	−0.214790	−	0.976660i	$-0.568907\pi$
$877$	−9.21584e59	−0.429579	−0.214790	+	0.976660i	$0.568907\pi$
$878$	2.91388e60	1.32689
$879$	−2.89121e60	−1.28620
$880$	−5.06137e59	−0.219975
$881$	−2.25005e60	−0.955403	−0.477702	−	0.878522i	$-0.658530\pi$
$881$	−2.25005e60	−0.955403	−0.477702	+	0.878522i	$0.658530\pi$
$882$	1.21620e60	0.504545
$883$	−1.37181e59	−0.0556033	−0.0278017	−	0.999613i	$-0.508851\pi$
$883$	−1.37181e59	−0.0556033	−0.0278017	+	0.999613i	$0.508851\pi$
$884$	9.12345e60	3.61317
$885$	5.37818e59	0.208112
$886$	9.02072e60	3.41075
$887$	−3.21287e60	−1.18702	−0.593511	−	0.804826i	$-0.702259\pi$
$887$	−3.21287e60	−1.18702	−0.593511	+	0.804826i	$0.702259\pi$
$888$	−1.86442e59	−0.0673096
$889$	−1.44779e59	−0.0510763
$890$	−5.91980e58	−0.0204085
$891$	2.74684e60	0.925423
$892$	−1.17712e61	−3.87562
$893$	1.00586e60	0.323656
$894$	−1.58016e60	−0.496916
$895$	2.13720e59	0.0656861
$896$	2.85793e60	0.858495
$897$	7.90202e60	2.32003
$898$	−5.31028e60	−1.52389
$899$	−1.68464e60	−0.472535
$900$	−5.91291e60	−1.62117
$901$	−3.19344e60	−0.855857
$902$	−4.92005e60	−1.28895
$903$	−2.28981e60	−0.586408
$904$	7.15386e60	1.79097
$905$	1.01703e60	0.248907
$906$	−2.17787e60	−0.521079
$907$	7.56461e60	1.76945	0.884723	−	0.466118i	$-0.154348\pi$
$907$	7.56461e60	1.76945	0.884723	+	0.466118i	$0.154348\pi$
$908$	−3.52450e58	−0.00806005
$909$	3.86752e60	0.864714
$910$	−1.41668e60	−0.309687
$911$	1.56837e60	0.335214	0.167607	−	0.985854i	$-0.446396\pi$
$911$	1.56837e60	0.335214	0.167607	+	0.985854i	$0.446396\pi$
$912$	6.82604e60	1.42651
$913$	−1.90150e60	−0.388548
$914$	4.03374e60	0.805955
$915$	−1.71349e60	−0.334772
$916$	−1.43460e61	−2.74077
$917$	−6.44154e60	−1.20342
$918$	−3.97335e60	−0.725909
$919$	3.58150e60	0.639878	0.319939	−	0.947438i	$-0.396338\pi$
$919$	3.58150e60	0.639878	0.319939	+	0.947438i	$0.396338\pi$
$920$	2.69315e60	0.470554
$921$	−3.14031e60	−0.536599
$922$	1.81466e61	3.03257
$923$	−5.92121e60	−0.967778
$924$	1.13324e61	1.81153
$925$	1.43723e59	0.0224710
$926$	−3.05927e60	−0.467835
$927$	−3.94604e60	−0.590238
$928$	5.31943e60	0.778272
$929$	5.82803e60	0.834064	0.417032	−	0.908892i	$-0.363070\pi$
$929$	5.82803e60	0.834064	0.417032	+	0.908892i	$0.363070\pi$
$930$	1.52919e60	0.214073
$931$	1.70607e60	0.233630
$932$	−2.12798e61	−2.85064
$933$	−4.98859e60	−0.653739
$934$	−7.40409e60	−0.949207
$935$	−1.22369e60	−0.153473
$936$	−1.80037e61	−2.20905
$937$	1.44921e61	1.73968	0.869840	−	0.493334i	$-0.164222\pi$
$937$	1.44921e61	1.73968	0.869840	+	0.493334i	$0.164222\pi$
$938$	1.80721e61	2.12251
$939$	−6.66826e60	−0.766245
$940$	−1.67931e60	−0.188803
$941$	−1.35212e60	−0.148740	−0.0743700	−	0.997231i	$-0.523695\pi$
$941$	−1.35212e60	−0.148740	−0.0743700	+	0.997231i	$0.523695\pi$
$942$	−4.62396e60	−0.497704
$943$	1.14628e61	1.20726
$944$	−1.62780e61	−1.67755
$945$	4.25832e59	0.0429424
$946$	7.95722e60	0.785223
$947$	−4.89192e60	−0.472395	−0.236197	−	0.971705i	$-0.575901\pi$
$947$	−4.89192e60	−0.472395	−0.236197	+	0.971705i	$0.575901\pi$
$948$	5.40393e61	5.10668
$949$	2.77969e60	0.257063
$950$	−1.20178e61	−1.08765
$951$	−2.04341e60	−0.180990
$952$	−2.43413e61	−2.11001
$953$	−1.87046e61	−1.58688	−0.793440	−	0.608648i	$-0.791712\pi$
$953$	−1.87046e61	−1.58688	−0.793440	+	0.608648i	$0.791712\pi$
$954$	1.14344e61	0.949448
$955$	1.04470e60	0.0849029
$956$	4.34262e61	3.45434
$957$	−1.12840e61	−0.878555
$958$	−1.47652e61	−1.12524
$959$	1.71892e61	1.28225
$960$	2.86917e59	0.0209506
$961$	−9.70392e60	−0.693614
$962$	7.94034e59	0.0555585
$963$	−6.26308e60	−0.428992
$964$	−4.77188e61	−3.19971
$965$	−3.80794e60	−0.249965
$966$	−3.82538e61	−2.45835
$967$	−1.23904e61	−0.779546	−0.389773	−	0.920911i	$-0.627447\pi$
$967$	−1.23904e61	−0.779546	−0.389773	+	0.920911i	$0.627447\pi$
$968$	1.41074e61	0.868964
$969$	1.65033e61	0.995251
$970$	−2.81714e59	−0.0166337
$971$	2.22671e61	1.28727	0.643635	−	0.765332i	$-0.277425\pi$
$971$	2.22671e61	1.28727	0.643635	+	0.765332i	$0.277425\pi$
$972$	4.87123e61	2.75728
$973$	1.51104e60	0.0837459
$974$	5.01046e60	0.271906
$975$	3.24445e61	1.72404
$976$	5.18617e61	2.69852
$977$	−2.30397e61	−1.17392	−0.586960	−	0.809616i	$-0.699675\pi$
$977$	−2.30397e61	−1.17392	−0.586960	+	0.809616i	$0.699675\pi$
$978$	−8.54206e61	−4.26203
$979$	−1.11147e60	−0.0543068
$980$	−2.84831e60	−0.136287
$981$	5.33270e60	0.249881
$982$	4.36738e61	2.00418
$983$	−1.51641e61	−0.681505	−0.340753	−	0.940153i	$-0.610682\pi$
$983$	−1.51641e61	−0.681505	−0.340753	+	0.940153i	$0.610682\pi$
$984$	−6.10533e61	−2.68726
$985$	4.09249e60	0.176419
$986$	4.39783e61	1.85679
$987$	1.31460e61	0.543614
$988$	−4.58251e61	−1.85604
$989$	−1.85389e61	−0.735460
$990$	4.38151e60	0.170256
$991$	3.35177e61	1.27575	0.637873	−	0.770142i	$-0.279815\pi$
$991$	3.35177e61	1.27575	0.637873	+	0.770142i	$0.279815\pi$
$992$	−1.35349e61	−0.504623
$993$	4.01218e61	1.46528
$994$	2.86646e61	1.02548
$995$	−1.27862e60	−0.0448094
$996$	−4.28142e61	−1.46985
$997$	−3.35578e61	−1.12861	−0.564304	−	0.825567i	$-0.690856\pi$
$997$	−3.35578e61	−1.12861	−0.564304	+	0.825567i	$0.690856\pi$
$998$	9.24153e60	0.304486
$999$	−2.38674e59	−0.00770394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.42.a.a.1.1	✓	3
3.2	odd	2		9.42.a.b.1.3		3
4.3	odd	2		16.42.a.c.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.42.a.a.1.1	✓	3	1.1	even	1	trivial
9.42.a.b.1.3		3	3.2	odd	2
16.42.a.c.1.3		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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66420e6 q^{2} -7.98359e9 q^{3} +4.89893e12 q^{4} +3.47255e13 q^{5} +2.12699e16 q^{6} +1.66807e17 q^{7} -7.19310e18 q^{8} +2.72647e19 q^{9} +O(q^{10})\)	\(q-2.66420e6 q^{2} -7.98359e9 q^{3} +4.89893e12 q^{4} +3.47255e13 q^{5} +2.12699e16 q^{6} +1.66807e17 q^{7} -7.19310e18 q^{8} +2.72647e19 q^{9} -9.25156e19 q^{10} -1.73703e21 q^{11} -3.91111e22 q^{12} +9.18003e22 q^{13} -4.44406e23 q^{14} -2.77234e23 q^{15} +8.39097e24 q^{16} +2.02868e25 q^{17} -7.26386e25 q^{18} -1.01896e26 q^{19} +1.70118e26 q^{20} -1.33172e27 q^{21} +4.62780e27 q^{22} -1.07819e28 q^{23} +5.74267e28 q^{24} -4.42689e28 q^{25} -2.44574e29 q^{26} +7.35151e28 q^{27} +8.17174e29 q^{28} -8.13688e29 q^{29} +7.38607e29 q^{30} +2.07038e30 q^{31} -6.53743e30 q^{32} +1.38677e31 q^{33} -5.40481e31 q^{34} +5.79244e30 q^{35} +1.33568e32 q^{36} -3.24660e30 q^{37} +2.71472e32 q^{38} -7.32896e32 q^{39} -2.49784e32 q^{40} -1.06315e33 q^{41} +3.54796e33 q^{42} +1.71944e33 q^{43} -8.50960e33 q^{44} +9.46781e32 q^{45} +2.87252e34 q^{46} -9.87145e33 q^{47} -6.69901e34 q^{48} -1.67432e34 q^{49} +1.17941e35 q^{50} -1.61962e35 q^{51} +4.49723e35 q^{52} -1.57415e35 q^{53} -1.95859e35 q^{54} -6.03192e34 q^{55} -1.19986e36 q^{56} +8.13498e35 q^{57} +2.16783e36 q^{58} -1.93994e36 q^{59} -1.35815e36 q^{60} +6.18066e36 q^{61} -5.51589e36 q^{62} +4.54794e36 q^{63} -1.03493e36 q^{64} +3.18781e36 q^{65} -3.69464e37 q^{66} -4.06657e37 q^{67} +9.93837e37 q^{68} +8.60784e37 q^{69} -1.54322e37 q^{70} -6.45010e37 q^{71} -1.96118e38 q^{72} +3.02798e37 q^{73} +8.64959e36 q^{74} +3.53425e38 q^{75} -4.99183e38 q^{76} -2.89748e38 q^{77} +1.95258e39 q^{78} -1.38169e39 q^{79} +2.91380e38 q^{80} -1.58134e39 q^{81} +2.83245e39 q^{82} +1.09468e39 q^{83} -6.52399e39 q^{84} +7.04469e38 q^{85} -4.58093e39 q^{86} +6.49615e39 q^{87} +1.24946e40 q^{88} +6.39870e38 q^{89} -2.52241e39 q^{90} +1.53129e40 q^{91} -5.28199e40 q^{92} -1.65290e40 q^{93} +2.62995e40 q^{94} -3.53840e39 q^{95} +5.21922e40 q^{96} +3.04505e39 q^{97} +4.46072e40 q^{98} -4.73597e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 49\!\cdots\!76 q^{6}+ \cdots + 13\!\cdots\!19 q^{9}+O(q^{10}) \) 3 * q - 344688 * q^2 - 10820953044 * q^3 + 6271704903936 * q^4 - 212302350281550 * q^5 + 4970194114982976 * q^6 + 57878416258239192 * q^7 - 3555831711183237120 * q^8 + 13277004110931878919 * q^9	\( 3 q - 344688 q^{2} - 10820953044 q^{3} + 6271704903936 q^{4} - 212302350281550 q^{5} + 49\!\cdots\!76 q^{6}+ \cdots + 45\!\cdots\!28 q^{99}+O(q^{100}) \) 3 * q - 344688 * q^2 - 10820953044 * q^3 + 6271704903936 * q^4 - 212302350281550 * q^5 + 4970194114982976 * q^6 + 57878416258239192 * q^7 - 3555831711183237120 * q^8 + 13277004110931878919 * q^9 - 911610678410074173600 * q^10 - 3064080929502798535164 * q^11 - 71233189317945674062848 * q^12 - 98515763053518962936694 * q^13 - 663773359066872932212608 * q^14 + 2322231962154213782968200 * q^15 + 13217913642093764057038848 * q^16 + 35582277130790298867301302 * q^17 - 51949630971262524069430704 * q^18 - 233456308095243376865478180 * q^19 - 1234817679506740618000857600 * q^20 - 784315067894306487816760224 * q^21 + 10093688647003206881596695744 * q^22 + 2812708670812770779627026056 * q^23 + 36949405163940557660187279360 * q^24 - 12630087813294771903109831875 * q^25 - 445502868787427067716672131104 * q^26 + 40981593702376529051426180280 * q^27 + 526606706694181610802628184064 * q^28 - 12736322664295346653179017670 * q^29 + 6115742110948196616210957398400 * q^30 - 55977552834365071134409017504 * q^31 - 14842037794660482009412112744448 * q^32 - 13829226714693448959900097020528 * q^33 - 42547131667082319398961759011808 * q^34 + 35330944415319146254058128592400 * q^35 + 209583308279267044115700704156928 * q^36 + 4945769903781582545269841455122 * q^37 + 384288369224763756133358504473920 * q^38 - 546470556552953849463965686898712 * q^39 - 1326138456985596139721995183104000 * q^40 - 3123151500646359746292805811918274 * q^41 + 5023322329604694017661024056308224 * q^42 + 1491980858362212236675453498061156 * q^43 + 6827579920847638909574240093432832 * q^44 - 3706804708974790460103758635956150 * q^45 + 34089155258950859800971794327519616 * q^46 - 63038106682044077762675687404413168 * q^47 - 48906179099557375982971001333612544 * q^48 - 97136113131667199274890334287198229 * q^49 + 286202165340727366859498513545830000 * q^50 - 157319866621422817701623275797858024 * q^51 + 364999309722184195149034320029732352 * q^52 + 79896749344137562310547533743021506 * q^53 + 279506543662409583024224141017979520 * q^54 - 1107430856215374719020572615529578600 * q^55 - 1507500925934438536531619079138017280 * q^56 - 120534128028213908789981458568129040 * q^57 + 1060511497310363735425511566792954080 * q^58 + 192512048683375799719343226678403860 * q^59 + 5905677886285900358494072637173094400 * q^60 + 8740556115036354715092732710435455386 * q^61 - 12005332293025961804297174175449366016 * q^62 + 4195060549596204507618981258341049336 * q^63 - 28669651485797320669854651690478731264 * q^64 + 23272939413910136331858458170260680700 * q^65 - 70374114793184440562716940658640274688 * q^66 + 11266872945514675454702655007279407852 * q^67 + 95413181576279049358373233907724317184 * q^68 + 110718129232411678126981084073658946848 * q^69 + 59324379124057015483688060122385068800 * q^70 - 140970915469820223119231433051520161384 * q^71 - 178095780793081630529589944776993320960 * q^72 + 45825493210252135256288871746499029406 * q^73 - 255935787825178849200244145003411599008 * q^74 - 247029389196459510298088488221820147500 * q^75 + 26100578647791289060370838422069130240 * q^76 - 429017620126390531124795910645506217696 * q^77 + 3378623821652934155171000156043557135232 * q^78 - 520184835554750143118446358634240850320 * q^79 + 715918562852781559130521454428746547200 * q^80 - 3191652631710460747876906046824191542997 * q^81 - 579816777788457983576303882284492608096 * q^82 - 619777491338381742927488037142663372644 * q^83 - 4198672691855986319203859063793898610688 * q^84 - 106299433069331216483654652405294143100 * q^85 - 4751113477095326918262488958359640807744 * q^86 + 13958176049210326842816445061163645008040 * q^87 + 18329036816788093472347699011602935234560 * q^88 - 142389067128374093799211866144944441010 * q^89 - 8753545150081132110036071066039970208800 * q^90 + 25080596935320871627133801126628392473296 * q^91 - 67617289414955565381239604024555789723648 * q^92 + 3477058704647981071307340824432458334592 * q^93 - 53008068396962431152763933809330449227008 * q^94 - 33170437179755379504247502944935502503000 * q^95 + 95174464657114272630879818889875681181696 * q^96 + 116011691364103339137369463947331771078182 * q^97 - 38494567059701712876195969460820421029616 * q^98 + 45849669342635847189814810549498192693428 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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