LMFDB - Embedded newform 4.39.b.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,39,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 39, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 39);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 39 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$36.5853876134$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 $ x^18 - 9x^17 + 62197466427874200x^16 - 497579731422993396x^15 + 1533330651456954523834224606283158x^14 - 10733314560198672959194272341598390x^13 + 19481782443651984882412391050385129300654889992244x^12 - 116890694661911769761385063719584946156168645371260x^11 + 139136237606150959215813468176435276664250794192016778233210479201x^10 - 695681188030753724581032940024542714621854609744310005116371215353x^9 + 568497808401670574980605551637816112488442166027324531949553103951206327341764748x^8 - 2273991233606678125835294022030202761397409545881853066054780853036284586514186696x^7 + 1283345352716388020512119899733143277332875078305115652503919007522645061900921255799901780340080x^6 - 3850036058149156102567042075828911269459277293563124763645420508567574714938226584752670924974864x^5 + 1439289344267733945837233684997856126673028793147138744042225979486721504292452534506308895244176799020170408512x^4 - 2878578688535461474947703788071527631381805661197607189586491117390555337819668654857160404811027247469352955136x^3 + 595941113794922164474527754149079025845074143571524485346938332375224698791062016413718632611595715188157806349620071647759360x^2 - 595941113794920725185183486418983224669538300112471429188966406515013857315416680428086116138384986393156714104315884501606400*x + 9817075370481683892061162300824582856496888117704407266492938605020758056089024085664206842636148929977821744687833149264494609112760320000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.8
Root			$0.500000 + 5.46285e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.39.b.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-173179. + 494861. i) q^{2} -8.74057e8i q^{3} +(-2.14896e11 - 1.71399e11i) q^{4} +2.48589e13 q^{5} +(4.32536e14 + 1.51368e14i) q^{6} -8.29070e15i q^{7} +(1.22034e17 - 7.66608e16i) q^{8} +5.86877e17 q^{9} +O(q^{10})$	\(q+(-173179. + 494861. i) q^{2} -8.74057e8i q^{3} +(-2.14896e11 - 1.71399e11i) q^{4} +2.48589e13 q^{5} +(4.32536e14 + 1.51368e14i) q^{6} -8.29070e15i q^{7} +(1.22034e17 - 7.66608e16i) q^{8} +5.86877e17 q^{9} +(-4.30504e18 + 1.23017e19i) q^{10} +3.43238e19i q^{11} +(-1.49812e20 + 1.87831e20i) q^{12} +9.38699e20 q^{13} +(4.10274e21 + 1.43577e21i) q^{14} -2.17281e22i q^{15} +(1.68027e22 + 7.36659e22i) q^{16} -2.90046e23 q^{17} +(-1.01635e23 + 2.90422e23i) q^{18} -3.13139e24i q^{19} +(-5.34208e24 - 4.26079e24i) q^{20} -7.24654e24 q^{21} +(-1.69855e25 - 5.94416e24i) q^{22} +4.99393e25i q^{23} +(-6.70059e25 - 1.06665e26i) q^{24} +2.54167e26 q^{25} +(-1.62563e26 + 4.64525e26i) q^{26} -1.69368e27i q^{27} +(-1.42102e27 + 1.78164e27i) q^{28} +8.62415e27 q^{29} +(1.07524e28 + 3.76285e27i) q^{30} +1.05953e28i q^{31} +(-3.93642e28 - 4.44240e27i) q^{32} +3.00009e28 q^{33} +(5.02299e28 - 1.43532e29i) q^{34} -2.06098e29i q^{35} +(-1.26117e29 - 1.00590e29i) q^{36} -4.26856e29 q^{37} +(1.54960e30 + 5.42292e29i) q^{38} -8.20476e29i q^{39} +(3.03363e30 - 1.90570e30i) q^{40} +8.28192e30 q^{41} +(1.25495e30 - 3.58603e30i) q^{42} -3.48399e29i q^{43} +(5.88306e30 - 7.37605e30i) q^{44} +1.45891e31 q^{45} +(-2.47130e31 - 8.64844e30i) q^{46} -1.09265e32i q^{47} +(6.43881e31 - 1.46865e31i) q^{48} +6.11992e31 q^{49} +(-4.40164e31 + 1.25777e32i) q^{50} +2.53517e32i q^{51} +(-2.01723e32 - 1.60892e32i) q^{52} -3.01382e32 q^{53} +(8.38138e32 + 2.93311e32i) q^{54} +8.53252e32i q^{55} +(-6.35572e32 - 1.01175e33i) q^{56} -2.73702e33 q^{57} +(-1.49352e33 + 4.26775e33i) q^{58} -1.34443e33i q^{59} +(-3.72417e33 + 4.66928e33i) q^{60} -2.87786e33 q^{61} +(-5.24321e33 - 1.83489e33i) q^{62} -4.86562e33i q^{63} +(9.01542e33 - 1.87105e34i) q^{64} +2.33350e34 q^{65} +(-5.19553e33 + 1.48463e34i) q^{66} -9.77943e33i q^{67} +(6.23298e34 + 4.97136e34i) q^{68} +4.36498e34 q^{69} +(1.01990e35 + 3.56918e34i) q^{70} -2.88061e35i q^{71} +(7.16189e34 - 4.49905e34i) q^{72} -3.46504e35 q^{73} +(7.39226e34 - 2.11234e35i) q^{74} -2.22156e35i q^{75} +(-5.36717e35 + 6.72924e35i) q^{76} +2.84568e35 q^{77} +(4.06021e35 + 1.42089e35i) q^{78} -4.41569e35i q^{79} +(4.17696e35 + 1.83125e36i) q^{80} -6.87593e35 q^{81} +(-1.43425e36 + 4.09840e36i) q^{82} -3.81913e36i q^{83} +(1.55725e36 + 1.24205e36i) q^{84} -7.21023e36 q^{85} +(1.72409e35 + 6.03354e34i) q^{86} -7.53800e36i q^{87} +(2.63129e36 + 4.18867e36i) q^{88} -3.10884e36 q^{89} +(-2.52653e36 + 7.21957e36i) q^{90} -7.78247e36i q^{91} +(8.55954e36 - 1.07318e37i) q^{92} +9.26091e36 q^{93} +(5.40707e37 + 1.89223e37i) q^{94} -7.78430e37i q^{95} +(-3.88291e36 + 3.44065e37i) q^{96} +4.23861e37 q^{97} +(-1.05984e37 + 3.02851e37i) q^{98} +2.01438e37i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots - 75\!\cdots\!14 q^{9}+O(q^{10}) $ 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9	$ 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots + 79\!\cdots\!72 q^{98}+O(q^{100}) $ 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9 - 3330064307292995160 * q^10 + 214196660016355524480 * q^12 - 1351697142828804018156 * q^13 - 7517302305589491995328 * q^14 + 146524491404032531730688 * q^16 - 108377436655642595433244 * q^17 - 2269182475834354952235228 * q^18 + 14024643346150499263916960 * q^20 - 3613555902040956758482176 * q^21 - 48893102429006434191867360 * q^22 - 507867326842846671102786048 * q^24 + 441821122409714044642015590 * q^25 + 1408725703649472883667066984 * q^26 - 248593478439946838208756480 * q^28 + 12039386014829706600024980948 * q^29 - 36685926266894937628070825280 * q^30 + 40815302174771571873068643328 * q^32 - 25787267222238191864238656640 * q^33 + 36261374450642004292958003976 * q^34 - 580544496119856571348909156080 * q^36 - 1267140929573154455938088740044 * q^37 + 1030706182877614317326332452960 * q^38 + 3677775331309955303335927125120 * q^40 - 4228447688719256876424323554684 * q^41 - 14054054841750269128772739402240 * q^42 - 10408853597054255998042527960960 * q^44 + 5968962977750993515218889928340 * q^45 + 22407092921477343211835072559552 * q^46 - 235299721005018637688575231641600 * q^48 - 31615512188019323981649417734094 * q^49 + 24292124186551164152560477361580 * q^50 + 1002079305454954374889708255510176 * q^52 + 9170251390510729272958214802164 * q^53 - 787051683509089599494415837112896 * q^54 + 1152829073224199082248229376115712 * q^56 + 1668394969897754054685444684739200 * q^57 + 6129531800884682398669731348277224 * q^58 - 11636557112389656620532244922123520 * q^60 - 3962895304807674280127771339766444 * q^61 - 8994819235653434082008553861768960 * q^62 + 24667562443996411690757328278360064 * q^64 + 95108472178397576493345013351708360 * q^65 - 59643686483535838768039195759223040 * q^66 - 37428614071533769215405413189346016 * q^68 - 378107798255717180855219732084825856 * q^69 + 185830274294359588352082139216848000 * q^70 - 260290846480495236441760743958748352 * q^72 + 769773517671824524924524644742901764 * q^73 - 250034850108007402381953386687905624 * q^74 + 347277300516185248422743813412796800 * q^76 - 1122048032159971455828617866562814720 * q^77 - 1450998872578214468135780206011466560 * q^78 + 391473453760426152176293685484792320 * q^80 + 8894227269421968655762303906241837682 * q^81 + 344096947623408239895482884304277576 * q^82 - 6791395692770555756905407625225660416 * q^84 - 3198312652592605820819998423888978200 * q^85 + 8678996853442312035283130731028012832 * q^86 - 815671442380761053869289210355156480 * q^88 - 6268329434682461663886854261019826492 * q^89 - 23166185157487343623484458734705269400 * q^90 + 11421593562829281515681866911017506560 * q^92 + 41748150138354461655386813609302195200 * q^93 - 33742046901195882761657274622561154688 * q^94 - 31638035665740952392118263378397667328 * q^96 - 62817319233285161836922640968633412444 * q^97 + 79415378721147757612981391241727219972 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−173179.	+	494861.i	−0.330313	+	0.943872i
$2$	−173179.	+	494861.i	−0.330313	+	0.943872i
$3$		−	8.74057e8i		−	0.752031i	−0.926613	−	0.376015i	$-0.877294\pi$
$3$		−	8.74057e8i		−	0.752031i	0.926613	−	0.376015i	$-0.122706\pi$
$4$	−2.14896e11	−	1.71399e11i	−0.781787	−	0.623546i
$5$	2.48589e13			1.30332			0.651661	−	0.758510i	$-0.274072\pi$
$5$	2.48589e13			1.30332			0.651661	+	0.758510i	$0.274072\pi$
$6$	4.32536e14	+	1.51368e14i	0.709821	+	0.248405i
$7$		−	8.29070e15i		−	0.727324i	−0.931531	−	0.363662i	$-0.881526\pi$
$7$		−	8.29070e15i		−	0.727324i	0.931531	−	0.363662i	$-0.118474\pi$
$8$	1.22034e17	−	7.66608e16i	0.846781	−	0.531941i
$9$	5.86877e17			0.434449
$10$	−4.30504e18	+	1.23017e19i	−0.430504	+	1.23017i
$11$			3.43238e19i			0.561222i	0.959822	+	0.280611i	$0.0905370\pi$
$11$			3.43238e19i			0.561222i	−0.959822	+	0.280611i	$0.909463\pi$
$12$	−1.49812e20	+	1.87831e20i	−0.468926	+	0.587928i
$13$	9.38699e20			0.642100			0.321050	−	0.947062i	$-0.395964\pi$
$13$	9.38699e20			0.642100			0.321050	+	0.947062i	$0.395964\pi$
$14$	4.10274e21	+	1.43577e21i	0.686501	+	0.240245i
$15$		−	2.17281e22i		−	0.980139i
$16$	1.68027e22	+	7.36659e22i	0.222382	+	0.974960i
$17$	−2.90046e23			−1.21321			−0.606607	−	0.795002i	$-0.707470\pi$
$17$	−2.90046e23			−1.21321			−0.606607	+	0.795002i	$0.707470\pi$
$18$	−1.01635e23	+	2.90422e23i	−0.143504	+	0.410064i
$19$		−	3.13139e24i		−	1.58278i	−0.611315	−	0.791388i	$-0.709359\pi$
$19$		−	3.13139e24i		−	1.58278i	0.611315	−	0.791388i	$-0.290641\pi$
$20$	−5.34208e24	−	4.26079e24i	−1.01892	−	0.812681i
$21$	−7.24654e24			−0.546971
$22$	−1.69855e25	−	5.94416e24i	−0.529721	−	0.185379i
$23$			4.99393e25i			0.669289i	0.942345	+	0.334644i	$0.108616\pi$
$23$			4.99393e25i			0.669289i	−0.942345	+	0.334644i	$0.891384\pi$
$24$	−6.70059e25	−	1.06665e26i	−0.400036	−	0.636806i
$25$	2.54167e26			0.698649
$26$	−1.62563e26	+	4.64525e26i	−0.212094	+	0.606060i
$27$		−	1.69368e27i		−	1.07875i
$28$	−1.42102e27	+	1.78164e27i	−0.453520	+	0.568613i
$29$	8.62415e27			1.41304			0.706520	−	0.707693i	$-0.250264\pi$
$29$	8.62415e27			1.41304			0.706520	+	0.707693i	$0.250264\pi$
$30$	1.07524e28	+	3.76285e27i	0.925125	+	0.323752i
$31$			1.05953e28i			0.488925i	0.969659	+	0.244462i	$0.0786115\pi$
$31$			1.05953e28i			0.488925i	−0.969659	+	0.244462i	$0.921389\pi$
$32$	−3.93642e28	−	4.44240e27i	−0.993692	−	0.112142i
$33$	3.00009e28			0.422056
$34$	5.02299e28	−	1.43532e29i	0.400740	−	1.14512i
$35$		−	2.06098e29i		−	0.947938i
$36$	−1.26117e29	−	1.00590e29i	−0.339647	−	0.270899i
$37$	−4.26856e29			−0.683045			−0.341522	−	0.939874i	$-0.610943\pi$
$37$	−4.26856e29			−0.683045			−0.341522	+	0.939874i	$0.610943\pi$
$38$	1.54960e30	+	5.42292e29i	1.49394	+	0.522811i
$39$		−	8.20476e29i		−	0.482879i
$40$	3.03363e30	−	1.90570e30i	1.10363	−	0.693291i
$41$	8.28192e30			1.88468			0.942340	−	0.334656i	$-0.108620\pi$
$41$	8.28192e30			1.88468			0.942340	+	0.334656i	$0.108620\pi$
$42$	1.25495e30	−	3.58603e30i	0.180671	−	0.516270i
$43$		−	3.48399e29i		−	0.0320757i	−0.999871	−	0.0160378i	$-0.994895\pi$
$43$		−	3.48399e29i		−	0.0320757i	0.999871	−	0.0160378i	$-0.00510522\pi$
$44$	5.88306e30	−	7.37605e30i	0.349947	−	0.438756i
$45$	1.45891e31			0.566228
$46$	−2.47130e31	−	8.64844e30i	−0.631723	−	0.221075i
$47$		−	1.09265e32i		−	1.85618i	−0.372356	−	0.928090i	$-0.621450\pi$
$47$		−	1.09265e32i		−	1.85618i	0.372356	−	0.928090i	$-0.378550\pi$
$48$	6.43881e31	−	1.46865e31i	0.733200	−	0.167238i
$49$	6.11992e31			0.470999
$50$	−4.40164e31	+	1.25777e32i	−0.230773	+	0.659435i
$51$			2.53517e32i			0.912375i
$52$	−2.01723e32	−	1.60892e32i	−0.501986	−	0.400379i
$53$	−3.01382e32			−0.522247			−0.261123	−	0.965305i	$-0.584093\pi$
$53$	−3.01382e32			−0.522247			−0.261123	+	0.965305i	$0.584093\pi$
$54$	8.38138e32	+	2.93311e32i	1.01820	+	0.356325i
$55$			8.53252e32i			0.731453i
$56$	−6.35572e32	−	1.01175e33i	−0.386894	−	0.615885i
$57$	−2.73702e33			−1.19030
$58$	−1.49352e33	+	4.26775e33i	−0.466745	+	1.33373i
$59$		−	1.34443e33i		−	0.303634i	−0.988409	−	0.151817i	$-0.951487\pi$
$59$		−	1.34443e33i		−	0.303634i	0.988409	−	0.151817i	$-0.0485125\pi$
$60$	−3.72417e33	+	4.66928e33i	−0.611161	+	0.766260i
$61$	−2.87786e33			−0.344987			−0.172494	−	0.985011i	$-0.555182\pi$
$61$	−2.87786e33			−0.344987			−0.172494	+	0.985011i	$0.555182\pi$
$62$	−5.24321e33	−	1.83489e33i	−0.461482	−	0.161498i
$63$		−	4.86562e33i		−	0.315986i
$64$	9.01542e33	−	1.87105e34i	0.434077	−	0.900876i
$65$	2.33350e34			0.836864
$66$	−5.19553e33	+	1.48463e34i	−0.139411	+	0.398367i
$67$		−	9.77943e33i		−	0.197193i	−0.995127	−	0.0985966i	$-0.968565\pi$
$67$		−	9.77943e33i		−	0.197193i	0.995127	−	0.0985966i	$-0.0314354\pi$
$68$	6.23298e34	+	4.97136e34i	0.948475	+	0.756495i
$69$	4.36498e34			0.503326
$70$	1.01990e35	+	3.56918e34i	0.894732	+	0.313116i
$71$		−	2.88061e35i		−	1.93008i	−0.262097	−	0.965042i	$-0.584414\pi$
$71$		−	2.88061e35i		−	1.93008i	0.262097	−	0.965042i	$-0.415586\pi$
$72$	7.16189e34	−	4.49905e34i	0.367884	−	0.231102i
$73$	−3.46504e35			−1.36954			−0.684768	−	0.728761i	$-0.740096\pi$
$73$	−3.46504e35			−1.36954			−0.684768	+	0.728761i	$0.740096\pi$
$74$	7.39226e34	−	2.11234e35i	0.225618	−	0.644706i
$75$		−	2.22156e35i		−	0.525406i
$76$	−5.36717e35	+	6.72924e35i	−0.986933	+	1.23739i
$77$	2.84568e35			0.408190
$78$	4.06021e35	+	1.42089e35i	0.455776	+	0.159501i
$79$		−	4.41569e35i		−	0.389121i	−0.980891	−	0.194560i	$-0.937672\pi$
$79$		−	4.41569e35i		−	0.389121i	0.980891	−	0.194560i	$-0.0623280\pi$
$80$	4.17696e35	+	1.83125e36i	0.289835	+	1.27069i
$81$	−6.87593e35			−0.376804
$82$	−1.43425e36	+	4.09840e36i	−0.622534	+	1.77890i
$83$		−	3.81913e36i		−	1.31668i	−0.752721	−	0.658340i	$-0.771259\pi$
$83$		−	3.81913e36i		−	1.31668i	0.752721	−	0.658340i	$-0.228741\pi$
$84$	1.55725e36	+	1.24205e36i	0.427614	+	0.341061i
$85$	−7.21023e36			−1.58121
$86$	1.72409e35	+	6.03354e34i	0.0302753	+	0.0105950i
$87$		−	7.53800e36i		−	1.06265i
$88$	2.63129e36	+	4.18867e36i	0.298537	+	0.475232i
$89$	−3.10884e36			−0.284569			−0.142285	−	0.989826i	$-0.545445\pi$
$89$	−3.10884e36			−0.284569			−0.142285	+	0.989826i	$0.545445\pi$
$90$	−2.52653e36	+	7.21957e36i	−0.187032	+	0.534446i
$91$		−	7.78247e36i		−	0.467015i
$92$	8.55954e36	−	1.07318e37i	0.417332	−	0.523241i
$93$	9.26091e36			0.367687
$94$	5.40707e37	+	1.89223e37i	1.75200	+	0.613120i
$95$		−	7.78430e37i		−	2.06287i
$96$	−3.88291e36	+	3.44065e37i	−0.0843342	+	0.747287i
$97$	4.23861e37			0.756067			0.378034	−	0.925792i	$-0.376600\pi$
$97$	4.23861e37			0.756067			0.378034	+	0.925792i	$0.376600\pi$
$98$	−1.05984e37	+	3.02851e37i	−0.155577	+	0.444563i
$99$			2.01438e37i			0.243822i
$100$	−5.46195e37	−	4.35640e37i	−0.546195	−	0.435640i
$101$	−1.82770e37			−0.151286			−0.0756431	−	0.997135i	$-0.524101\pi$
$101$	−1.82770e37			−0.151286			−0.0756431	+	0.997135i	$0.524101\pi$
$102$	−1.25455e38	−	4.39038e37i	−0.861165	−	0.301369i
$103$			7.94465e37i			0.453072i	0.974003	+	0.226536i	$0.0727402\pi$
$103$			7.94465e37i			0.453072i	−0.974003	+	0.226536i	$0.927260\pi$
$104$	1.14553e38	−	7.19615e37i	0.543718	−	0.341560i
$105$	−1.80141e38			−0.712879
$106$	5.21930e37	−	1.49142e38i	0.172505	−	0.492934i
$107$			4.96685e38i			1.37338i	0.726952	+	0.686688i	$0.240936\pi$
$107$			4.96685e38i			1.37338i	−0.726952	+	0.686688i	$0.759064\pi$
$108$	−2.90296e38	+	3.63966e38i	−0.672650	+	0.843353i
$109$	−4.87318e38			−0.947783			−0.473892	−	0.880583i	$-0.657151\pi$
$109$	−4.87318e38			−0.947783			−0.473892	+	0.880583i	$0.657151\pi$
$110$	−4.22241e38	−	1.47765e38i	−0.690397	−	0.241608i
$111$			3.73097e38i			0.513671i
$112$	6.10741e38	−	1.39306e38i	0.709112	−	0.161744i
$113$	1.83355e39			1.79805			0.899027	−	0.437893i	$-0.144275\pi$
$113$	1.83355e39			1.79805			0.899027	+	0.437893i	$0.144275\pi$
$114$	4.73994e38	−	1.35444e39i	0.393170	−	1.12349i
$115$			1.24144e39i			0.872299i
$116$	−1.85329e39	−	1.47817e39i	−1.10470	−	0.881095i
$117$	5.50901e38			0.278960
$118$	6.65307e38	+	2.32828e38i	0.286592	+	0.100294i
$119$			2.40468e39i			0.882401i
$120$	−1.66569e39	−	2.65157e39i	−0.521376	−	0.829963i
$121$	2.56231e39			0.685030
$122$	4.98385e38	−	1.42414e39i	0.113954	−	0.325624i
$123$		−	7.23887e39i		−	1.41734i
$124$	1.81603e39	−	2.27689e39i	0.304867	−	0.382235i
$125$	−2.72530e39			−0.392757
$126$	2.40780e39	+	8.42623e38i	0.298250	+	0.104374i
$127$			5.95566e39i			0.634833i	0.948286	+	0.317416i	$0.102815\pi$
$127$			5.95566e39i			0.634833i	−0.948286	+	0.317416i	$0.897185\pi$
$128$	7.69779e39	+	7.70164e39i	0.706930	+	0.707283i
$129$	−3.04520e38			−0.0241219
$130$	−4.04114e39	+	1.15476e40i	−0.276427	+	0.789892i
$131$			1.99604e40i			1.18036i	0.807271	+	0.590181i	$0.200944\pi$
$131$			1.99604e40i			1.18036i	−0.807271	+	0.590181i	$0.799056\pi$
$132$	−6.44708e39	−	5.14213e39i	−0.329958	−	0.263171i
$133$	−2.59614e40			−1.15119
$134$	4.83945e39	+	1.69359e39i	0.186125	+	0.0651355i
$135$		−	4.21031e40i		−	1.40596i
$136$	−3.53955e40	+	2.22352e40i	−1.02733	+	0.645359i
$137$	1.58039e40			0.399093			0.199546	−	0.979888i	$-0.436053\pi$
$137$	1.58039e40			0.399093			0.199546	+	0.979888i	$0.436053\pi$
$138$	−7.55922e39	+	2.16005e40i	−0.166255	+	0.475075i
$139$		−	1.01319e41i		−	1.94272i	−0.237608	−	0.971361i	$-0.576363\pi$
$139$		−	1.01319e41i		−	1.94272i	0.237608	−	0.971361i	$-0.423637\pi$
$140$	−3.53249e40	+	4.42895e40i	−0.591083	+	0.741086i
$141$	−9.55034e40			−1.39590
$142$	1.42550e41	+	4.98861e40i	1.82175	+	0.637531i
$143$			3.22197e40i			0.360361i
$144$	9.86110e39	+	4.32328e40i	0.0966136	+	0.423571i
$145$	2.14387e41			1.84165
$146$	6.00072e40	−	1.71471e41i	0.452375	−	1.29267i
$147$		−	5.34916e40i		−	0.354206i
$148$	9.17297e40	+	7.31627e40i	0.533995	+	0.425910i
$149$	−6.34117e40			−0.324811			−0.162405	−	0.986724i	$-0.551925\pi$
$149$	−6.34117e40			−0.324811			−0.162405	+	0.986724i	$0.551925\pi$
$150$	1.09936e41	+	3.84728e40i	0.495916	+	0.173548i
$151$		−	1.44167e41i		−	0.573195i	−0.958051	−	0.286598i	$-0.907476\pi$
$151$		−	1.44167e41i		−	0.573195i	0.958051	−	0.286598i	$-0.0925243\pi$
$152$	−2.40055e41	−	3.82137e41i	−0.841944	−	1.34026i
$153$	−1.70221e41			−0.527080
$154$	−4.92812e40	+	1.40822e41i	−0.134830	+	0.385279i
$155$			2.63388e41i			0.637227i
$156$	−1.40629e41	+	1.76317e41i	−0.301097	+	0.377509i
$157$	−3.82249e40			−0.0724859			−0.0362429	−	0.999343i	$-0.511539\pi$
$157$	−3.82249e40			−0.0724859			−0.0362429	+	0.999343i	$0.511539\pi$
$158$	2.18515e41	+	7.64706e40i	0.367280	+	0.128532i
$159$			2.63425e41i			0.392746i
$160$	−9.78551e41	−	1.10433e41i	−1.29510	−	0.146157i
$161$	4.14031e41			0.486790
$162$	1.19077e41	−	3.40262e41i	0.124463	−	0.355655i
$163$			1.81527e42i			1.68801i	0.536333	+	0.844006i	$0.319809\pi$
$163$			1.81527e42i			1.68801i	−0.536333	+	0.844006i	$0.680191\pi$
$164$	−1.77975e42	−	1.41951e42i	−1.47342	−	1.17518i
$165$	7.45791e41			0.550075
$166$	1.88993e42	+	6.61393e41i	1.24278	+	0.434916i
$167$			1.97076e42i			1.15617i	0.815978	+	0.578083i	$0.196199\pi$
$167$			1.97076e42i			1.15617i	−0.815978	+	0.578083i	$0.803801\pi$
$168$	−8.84324e41	+	5.55526e41i	−0.463164	+	0.290956i
$169$	−1.25605e42			−0.587707
$170$	1.24866e42	−	3.56806e42i	0.522294	−	1.49246i
$171$		−	1.83774e42i		−	0.687636i
$172$	−5.97152e40	+	7.48695e40i	−0.0200007	+	0.0250764i
$173$	6.85037e41			0.205513			0.102756	−	0.994707i	$-0.467234\pi$
$173$	6.85037e41			0.205513			0.102756	+	0.994707i	$0.467234\pi$
$174$	3.73026e42	+	1.30542e42i	1.00300	+	0.351007i
$175$		−	2.10722e42i		−	0.508145i
$176$	−2.52849e42	+	5.76732e41i	−0.547168	+	0.124805i
$177$	−1.17511e42			−0.228342
$178$	5.38386e41	−	1.53844e42i	0.0939969	−	0.268597i
$179$		−	4.61389e42i		−	0.724202i	−0.932139	−	0.362101i	$-0.882060\pi$
$179$		−	4.61389e42i		−	0.724202i	0.932139	−	0.362101i	$-0.117940\pi$
$180$	−3.13514e42	−	2.50056e42i	−0.442669	−	0.353069i
$181$	1.22705e43			1.55945			0.779723	−	0.626124i	$-0.215360\pi$
$181$	1.22705e43			1.55945			0.779723	+	0.626124i	$0.215360\pi$
$182$	3.85124e42	+	1.34776e42i	0.440802	+	0.154261i
$183$			2.51541e42i			0.259441i
$184$	3.82839e42	+	6.09429e42i	0.356022	+	0.566741i
$185$	−1.06112e43			−0.890227
$186$	−1.60380e42	+	4.58286e42i	−0.121452	+	0.347049i
$187$		−	9.95549e42i		−	0.680882i
$188$	−1.87278e43	+	2.34805e43i	−1.15741	+	1.45114i
$189$	−1.40418e43			−0.784602
$190$	3.85214e43	+	1.34808e43i	1.94708	+	0.681391i
$191$		−	1.43427e43i		−	0.656142i	−0.944653	−	0.328071i	$-0.893601\pi$
$191$		−	1.43427e43i		−	0.656142i	0.944653	−	0.328071i	$-0.106399\pi$
$192$	−1.63540e43	−	7.87999e42i	−0.677487	−	0.326439i
$193$	−1.36311e43			−0.511614			−0.255807	−	0.966728i	$-0.582341\pi$
$193$	−1.36311e43			−0.511614			−0.255807	+	0.966728i	$0.582341\pi$
$194$	−7.34038e42	+	2.09752e43i	−0.249739	+	0.713630i
$195$		−	2.03961e43i		−	0.629347i
$196$	−1.31515e43	−	1.04895e43i	−0.368221	−	0.293689i
$197$	−3.49713e43			−0.888901			−0.444450	−	0.895804i	$-0.646601\pi$
$197$	−3.49713e43			−0.888901			−0.444450	+	0.895804i	$0.646601\pi$
$198$	−9.96839e42	−	3.48849e42i	−0.230137	−	0.0805376i
$199$			6.86906e43i			1.44108i	0.693412	+	0.720541i	$0.256107\pi$
$199$			6.86906e43i			1.44108i	−0.693412	+	0.720541i	$0.743893\pi$
$200$	3.10170e43	−	1.94847e43i	0.591603	−	0.371640i
$201$	−8.54777e42			−0.148295
$202$	3.16520e42	−	9.04458e42i	0.0499718	−	0.142795i
$203$		−	7.15002e43i		−	1.02774i
$204$	4.34525e43	−	5.44797e43i	0.568908	−	0.713283i
$205$	2.05879e44			2.45635
$206$	−3.93149e43	−	1.37585e43i	−0.427642	−	0.149656i
$207$			2.93082e43i			0.290772i
$208$	1.57727e43	+	6.91501e43i	0.142791	+	0.626022i
$209$	1.07481e44			0.888288
$210$	3.11966e43	−	8.91446e43i	0.235473	−	0.672866i
$211$			1.16874e44i			0.806032i	0.915193	+	0.403016i	$0.132038\pi$
$211$			1.16874e44i			0.806032i	−0.915193	+	0.403016i	$0.867962\pi$
$212$	6.47657e43	+	5.16565e43i	0.408286	+	0.325645i
$213$	−2.51782e44			−1.45148
$214$	−2.45790e44	−	8.60155e43i	−1.29629	−	0.453644i
$215$		−	8.66081e42i		−	0.0418050i
$216$	−1.29839e44	−	2.06687e44i	−0.573832	−	0.913466i
$217$	8.78426e43			0.355607
$218$	8.43933e43	−	2.41154e44i	0.313065	−	0.894586i
$219$			3.02864e44i			1.02993i
$220$	1.46246e44	−	1.83360e44i	0.456094	−	0.571840i
$221$	−2.72266e44			−0.779005
$222$	−1.84631e44	−	6.46125e43i	−0.484839	−	0.169672i
$223$			5.64827e44i			1.36183i	0.732362	+	0.680915i	$0.238418\pi$
$223$			5.64827e44i			1.36183i	−0.732362	+	0.680915i	$0.761582\pi$
$224$	−3.68306e43	+	3.26357e44i	−0.0815635	+	0.722737i
$225$	1.49165e44			0.303528
$226$	−3.17533e44	+	9.07352e44i	−0.593920	+	1.69713i
$227$		−	3.96498e44i		−	0.681946i	−0.940073	−	0.340973i	$-0.889244\pi$
$227$		−	3.96498e44i		−	0.681946i	0.940073	−	0.340973i	$-0.110756\pi$
$228$	5.88174e44	+	4.69121e44i	0.930558	+	0.742204i
$229$	−1.89874e44			−0.276435			−0.138217	−	0.990402i	$-0.544137\pi$
$229$	−1.89874e44			−0.276435			−0.138217	+	0.990402i	$0.544137\pi$
$230$	−6.14338e44	−	2.14991e44i	−0.823338	−	0.288131i
$231$		−	2.48729e44i		−	0.306972i
$232$	1.05244e45	−	6.61134e44i	1.19654	−	0.751654i
$233$	6.08866e44			0.637910			0.318955	−	0.947770i	$-0.396668\pi$
$233$	6.08866e44			0.637910			0.318955	+	0.947770i	$0.396668\pi$
$234$	−9.54045e43	+	2.72619e44i	−0.0921441	+	0.263302i
$235$		−	2.71620e45i		−	2.41920i
$236$	−2.30434e44	+	2.88913e44i	−0.189330	+	0.237377i
$237$	−3.85957e44			−0.292631
$238$	−1.18998e45	−	4.16441e44i	−0.832873	−	0.291468i
$239$			1.41312e45i			0.913308i	0.889644	+	0.456654i	$0.150952\pi$
$239$			1.41312e45i			0.913308i	−0.889644	+	0.456654i	$0.849048\pi$
$240$	1.60062e45	−	3.65090e44i	0.955596	−	0.217965i
$241$	−4.00978e44			−0.221206			−0.110603	−	0.993865i	$-0.535278\pi$
$241$	−4.00978e44			−0.221206			−0.110603	+	0.993865i	$0.535278\pi$
$242$	−4.43738e44	+	1.26799e45i	−0.226274	+	0.646581i
$243$		−	1.68692e45i		−	0.795382i
$244$	6.18441e44	+	4.93262e44i	0.269706	+	0.215115i
$245$	1.52134e45			0.613864
$246$	3.58223e45	+	1.25362e45i	1.33779	+	0.468165i
$247$		−	2.93944e45i		−	1.01630i
$248$	8.12246e44	+	1.29299e45i	0.260079	+	0.414012i
$249$	−3.33813e45			−0.990184
$250$	4.71965e44	−	1.34864e45i	0.129733	−	0.370712i
$251$			1.16135e45i			0.295911i	0.988994	+	0.147956i	$0.0472693\pi$
$251$			1.16135e45i			0.295911i	−0.988994	+	0.147956i	$0.952731\pi$
$252$	−8.33961e44	+	1.04560e45i	−0.197031	+	0.247033i
$253$	−1.71411e45			−0.375619
$254$	−2.94722e45	−	1.03140e45i	−0.599201	−	0.209693i
$255$			6.30215e45i			1.18912i
$256$	−5.14433e45	+	2.47557e45i	−0.901093	+	0.433626i
$257$	2.46040e45			0.400199			0.200099	−	0.979776i	$-0.435873\pi$
$257$	2.46040e45			0.400199			0.200099	+	0.979776i	$0.435873\pi$
$258$	5.27365e43	−	1.50695e44i	0.00796778	−	0.0227680i
$259$			3.53894e45i			0.496795i
$260$	−5.01460e45	−	3.99960e45i	−0.654249	−	0.521823i
$261$	5.06131e45			0.613894
$262$	−9.87762e45	−	3.45673e45i	−1.11411	−	0.389888i
$263$			6.11021e45i			0.641057i	0.947239	+	0.320529i	$0.103861\pi$
$263$			6.11021e45i			0.641057i	−0.947239	+	0.320529i	$0.896139\pi$
$264$	3.66114e45	−	2.29990e45i	0.357389	−	0.224509i
$265$	−7.49202e45			−0.680656
$266$	4.49597e45	−	1.28473e46i	0.380253	−	1.08658i
$267$			2.71730e45i			0.214005i
$268$	−1.67618e45	+	2.10156e45i	−0.122959	+	0.154163i
$269$	1.24324e46			0.849694			0.424847	−	0.905265i	$-0.360328\pi$
$269$	1.24324e46			0.849694			0.424847	+	0.905265i	$0.360328\pi$
$270$	2.08352e46	+	7.29138e45i	1.32705	+	0.464406i
$271$		−	5.17900e45i		−	0.307489i	−0.988111	−	0.153745i	$-0.950867\pi$
$271$		−	5.17900e45i		−	0.307489i	0.988111	−	0.153745i	$-0.0491333\pi$
$272$	−4.87356e45	−	2.13665e46i	−0.269797	−	1.18284i
$273$	−6.80232e45			−0.351210
$274$	−2.73691e45	+	7.82073e45i	−0.131825	+	0.376692i
$275$			8.72398e45i			0.392097i
$276$	−9.38016e45	−	7.48152e45i	−0.393494	−	0.313847i
$277$	3.30132e46			1.29292			0.646461	−	0.762947i	$-0.276248\pi$
$277$	3.30132e46			1.29292			0.646461	+	0.762947i	$0.276248\pi$
$278$	5.01389e46	+	1.75464e46i	1.83368	+	0.641706i
$279$			6.21815e45i			0.212413i
$280$	−1.57996e46	−	2.51509e46i	−0.504248	−	0.802696i
$281$	5.17847e45			0.154448			0.0772238	−	0.997014i	$-0.475394\pi$
$281$	5.17847e45			0.154448			0.0772238	+	0.997014i	$0.475394\pi$
$282$	1.65392e46	−	4.72609e46i	0.461085	−	1.31755i
$283$			8.63166e45i			0.224984i	0.993653	+	0.112492i	$0.0358833\pi$
$283$			8.63166e45i			0.224984i	−0.993653	+	0.112492i	$0.964117\pi$
$284$	−4.93734e46	+	6.19032e46i	−1.20349	+	1.50891i
$285$	−6.80392e46			−1.55134
$286$	−1.59443e46	−	5.57978e45i	−0.340134	−	0.119032i
$287$		−	6.86629e46i		−	1.37077i
$288$	−2.31019e46	−	2.60714e45i	−0.431709	−	0.0487200i
$289$	2.69712e46			0.471890
$290$	−3.71273e46	+	1.06092e47i	−0.608319	+	1.73828i
$291$		−	3.70478e46i		−	0.568586i
$292$	7.44622e46	+	5.93903e46i	1.07069	+	0.853968i
$293$	−9.90073e46			−1.33408			−0.667041	−	0.745021i	$-0.732439\pi$
$293$	−9.90073e46			−1.33408			−0.667041	+	0.745021i	$0.732439\pi$
$294$	2.64709e46	+	9.26361e45i	0.334325	+	0.116999i
$295$		−	3.34211e46i		−	0.395733i
$296$	−5.20910e46	+	3.27232e46i	−0.578389	+	0.363340i
$297$	5.81337e46			0.605418
$298$	1.09816e46	−	3.13799e46i	0.107289	−	0.306580i
$299$			4.68780e46i			0.429750i
$300$	−3.80774e46	+	4.77405e46i	−0.327615	+	0.410755i
$301$	−2.88847e45			−0.0233294
$302$	7.13423e46	+	2.49666e46i	0.541023	+	0.189334i
$303$			1.59752e46i			0.113772i
$304$	2.30677e47	−	5.26158e46i	1.54314	−	0.351980i
$305$	−7.15404e46			−0.449629
$306$	2.94788e46	−	8.42358e46i	0.174101	−	0.497496i
$307$			1.39496e46i			0.0774344i	0.999250	+	0.0387172i	$0.0123272\pi$
$307$			1.39496e46i			0.0774344i	−0.999250	+	0.0387172i	$0.987673\pi$
$308$	−6.11526e46	−	4.87747e46i	−0.319118	−	0.254525i
$309$	6.94408e46			0.340724
$310$	−1.30340e47	−	4.56133e46i	−0.601460	−	0.210484i
$311$		−	2.37380e47i		−	1.03038i	−0.857077	−	0.515189i	$-0.827722\pi$
$311$		−	2.37380e47i		−	1.03038i	0.857077	−	0.515189i	$-0.172278\pi$
$312$	−6.28984e46	−	1.00126e47i	−0.256863	−	0.408893i
$313$	1.06109e47			0.407764			0.203882	−	0.978995i	$-0.434644\pi$
$313$	1.06109e47			0.407764			0.203882	+	0.978995i	$0.434644\pi$
$314$	6.61976e45	−	1.89160e46i	0.0239430	−	0.0684174i
$315$		−	1.20954e47i		−	0.411831i
$316$	−7.56845e46	+	9.48915e46i	−0.242634	+	0.304209i
$317$	4.62385e46			0.139598			0.0697988	−	0.997561i	$-0.477764\pi$
$317$	4.62385e46			0.139598			0.0697988	+	0.997561i	$0.477764\pi$
$318$	−1.30359e47	−	4.56196e46i	−0.370701	−	0.129729i
$319$			2.96014e47i			0.793028i
$320$	2.24113e47	−	4.65121e47i	0.565742	−	1.17413i
$321$	4.34131e47			1.03282
$322$	−7.17016e46	+	2.04888e47i	−0.160793	+	0.459467i
$323$			9.08249e47i			1.92025i
$324$	1.47761e47	+	1.17853e47i	0.294581	+	0.234955i
$325$	2.38586e47			0.448603
$326$	−8.98303e47	−	3.14366e47i	−1.59327	−	0.557572i
$327$			4.25944e47i			0.712762i
$328$	1.01068e48	−	6.34899e47i	1.59591	−	1.00254i
$329$	−9.05879e47			−1.35004
$330$	−1.29155e47	+	3.69062e47i	−0.181697	+	0.519200i
$331$			4.13158e47i			0.548763i	0.961621	+	0.274381i	$0.0884730\pi$
$331$			4.13158e47i			0.548763i	−0.961621	+	0.274381i	$0.911527\pi$
$332$	−6.54594e47	+	8.20715e47i	−0.821010	+	1.02936i
$333$	−2.50512e47			−0.296748
$334$	−9.75251e47	−	3.41294e47i	−1.09127	−	0.381897i
$335$		−	2.43106e47i		−	0.257006i
$336$	−1.21761e47	−	5.33822e47i	−0.121636	−	0.533274i
$337$	−5.69409e47			−0.537596			−0.268798	−	0.963197i	$-0.586626\pi$
$337$	−5.69409e47			−0.537596			−0.268798	+	0.963197i	$0.586626\pi$
$338$	2.17522e47	−	6.21572e47i	0.194127	−	0.554720i
$339$		−	1.60263e48i		−	1.35219i
$340$	1.54945e48	+	1.23583e48i	1.23617	+	0.985957i
$341$	−3.63672e47			−0.274395
$342$	9.09426e47	+	3.18258e47i	0.649040	+	0.227135i
$343$		−	1.58463e48i		−	1.06989i
$344$	−2.67085e46	−	4.25165e46i	−0.0170624	−	0.0271611i
$345$	1.08509e48			0.655996
$346$	−1.18634e47	+	3.38998e47i	−0.0678834	+	0.193977i
$347$			2.72748e48i			1.47741i	0.674029	+	0.738705i	$0.264562\pi$
$347$			2.72748e48i			1.47741i	−0.674029	+	0.738705i	$0.735438\pi$
$348$	−1.29200e48	+	1.61988e48i	−0.662610	+	0.830766i
$349$	2.78256e48			1.35133			0.675665	−	0.737209i	$-0.263857\pi$
$349$	2.78256e48			1.35133			0.675665	+	0.737209i	$0.263857\pi$
$350$	1.04278e48	+	3.64927e47i	0.479623	+	0.167847i
$351$		−	1.58986e48i		−	0.692666i
$352$	1.52480e47	−	1.35113e48i	0.0629365	−	0.557682i
$353$	−8.40990e47			−0.328906			−0.164453	−	0.986385i	$-0.552586\pi$
$353$	−8.40990e47			−0.328906			−0.164453	+	0.986385i	$0.552586\pi$
$354$	2.03505e47	−	5.81516e47i	0.0754244	−	0.215526i
$355$		−	7.16088e48i		−	2.51552i
$356$	6.68077e47	+	5.32852e47i	0.222473	+	0.177442i
$357$	2.10183e48			0.663593
$358$	2.28323e48	+	7.99029e47i	0.683554	+	0.239213i
$359$			1.99311e48i			0.565896i	0.959135	+	0.282948i	$0.0913124\pi$
$359$			1.99311e48i			0.565896i	−0.959135	+	0.282948i	$0.908688\pi$
$360$	1.78037e48	−	1.11841e48i	0.479471	−	0.301200i
$361$	−5.89148e48			−1.50518
$362$	−2.12500e48	+	6.07220e48i	−0.515105	+	1.47192i
$363$		−	2.23960e48i		−	0.515164i
$364$	−1.33391e48	+	1.67242e48i	−0.291205	+	0.365106i
$365$	−8.61370e48			−1.78495
$366$	−1.24478e48	−	4.35617e47i	−0.244879	−	0.0856967i
$367$			8.38448e48i			1.56610i	0.621956	+	0.783052i	$0.286338\pi$
$367$			8.38448e48i			1.56610i	−0.621956	+	0.783052i	$0.713662\pi$
$368$	−3.67882e48	+	8.39114e47i	−0.652529	+	0.148838i
$369$	4.86047e48			0.818798
$370$	1.83763e48	−	5.25106e48i	0.294053	−	0.840260i
$371$			2.49867e48i			0.379843i
$372$	−1.99013e48	−	1.58731e48i	−0.287453	−	0.229269i
$373$	3.37603e47			0.0463382			0.0231691	−	0.999732i	$-0.492624\pi$
$373$	3.37603e47			0.0463382			0.0231691	+	0.999732i	$0.492624\pi$
$374$	4.92658e48	+	1.72408e48i	0.642665	+	0.224904i
$375$			2.38207e48i			0.295366i
$376$	−8.37631e48	−	1.33340e49i	−0.987379	−	1.57178i
$377$	8.09548e48			0.907313
$378$	2.43175e48	−	6.94874e48i	0.259164	−	0.740563i
$379$			4.59288e48i			0.465522i	0.972534	+	0.232761i	$0.0747760\pi$
$379$			4.59288e48i			0.465522i	−0.972534	+	0.232761i	$0.925224\pi$
$380$	−1.33422e49	+	1.67281e49i	−1.28629	+	1.61272i
$381$	5.20559e48			0.477414
$382$	7.09765e48	+	2.48386e48i	0.619314	+	0.216732i
$383$			8.86033e48i			0.735653i	0.929894	+	0.367826i	$0.119898\pi$
$383$			8.86033e48i			0.735653i	−0.929894	+	0.367826i	$0.880102\pi$
$384$	6.73167e48	−	6.72830e48i	0.531899	−	0.531633i
$385$	7.07405e48			0.532003
$386$	2.36062e48	−	6.74550e48i	0.168993	−	0.482898i
$387$		−	2.04467e47i		−	0.0139353i
$388$	−9.10860e48	−	7.26493e48i	−0.591083	−	0.471442i
$389$	−9.88367e48			−0.610768			−0.305384	−	0.952229i	$-0.598785\pi$
$389$	−9.88367e48			−0.610768			−0.305384	+	0.952229i	$0.598785\pi$
$390$	1.00932e49	+	3.53218e48i	0.594023	+	0.207881i
$391$		−	1.44847e49i		−	0.811991i
$392$	7.46838e48	−	4.69158e48i	0.398833	−	0.250544i
$393$	1.74465e49			0.887668
$394$	6.05629e48	−	1.73059e49i	0.293615	−	0.839008i
$395$		−	1.09769e49i		−	0.507150i
$396$	3.45263e48	−	4.32883e48i	0.152034	−	0.190617i
$397$	4.11516e48			0.172730			0.0863649	−	0.996264i	$-0.472475\pi$
$397$	4.11516e48			0.172730			0.0863649	+	0.996264i	$0.472475\pi$
$398$	−3.39923e49	−	1.18958e49i	−1.36020	−	0.476008i
$399$			2.26918e49i			0.865731i
$400$	4.27069e48	+	1.87234e49i	0.155367	+	0.681155i
$401$	−4.33161e49			−1.50282			−0.751409	−	0.659837i	$-0.770625\pi$
$401$	−4.33161e49			−1.50282			−0.751409	+	0.659837i	$0.770625\pi$
$402$	1.48029e48	−	4.22995e48i	0.0489839	−	0.139972i
$403$			9.94582e48i			0.313939i
$404$	3.92766e48	+	3.13266e48i	0.118274	+	0.0943339i
$405$	−1.70928e49			−0.491098
$406$	3.53826e49	+	1.23823e49i	0.970053	+	0.339475i
$407$		−	1.46513e49i		−	0.383339i
$408$	1.94348e49	+	3.09377e49i	0.485330	+	0.772582i
$409$	4.65038e49			1.10852			0.554262	−	0.832342i	$-0.313000\pi$
$409$	4.65038e49			1.10852			0.554262	+	0.832342i	$0.313000\pi$
$410$	−3.56540e49	+	1.01882e50i	−0.811363	+	2.31848i
$411$		−	1.38135e49i		−	0.300130i
$412$	1.36170e49	−	1.70727e49i	0.282511	−	0.354206i
$413$	−1.11463e49			−0.220841
$414$	−1.45035e49	−	5.07557e48i	−0.274451	−	0.0960457i
$415$		−	9.49393e49i		−	1.71606i
$416$	−3.69512e49	−	4.17008e48i	−0.638050	−	0.0720063i
$417$	−8.85588e49			−1.46099
$418$	−1.86135e49	+	5.31883e49i	−0.293413	+	0.838429i
$419$			3.58312e49i			0.539752i	0.962895	+	0.269876i	$0.0869827\pi$
$419$			3.58312e49i			0.539752i	−0.962895	+	0.269876i	$0.913017\pi$
$420$	3.87116e49	+	3.08760e49i	0.557319	+	0.444513i
$421$	7.60449e49			1.04643			0.523215	−	0.852201i	$-0.324732\pi$
$421$	7.60449e49			1.04643			0.523215	+	0.852201i	$0.324732\pi$
$422$	−5.78365e49	−	2.02402e49i	−0.760791	−	0.266243i
$423$		−	6.41248e49i		−	0.806416i
$424$	−3.67788e49	+	2.31042e49i	−0.442229	+	0.277805i
$425$	−7.37202e49			−0.847612
$426$	4.36033e49	−	1.24597e50i	0.479443	−	1.37001i
$427$			2.38595e49i			0.250918i
$428$	8.51314e49	−	1.06736e50i	0.856363	−	1.07369i
$429$	2.81619e49			0.271002
$430$	4.28590e48	+	1.49987e48i	0.0394585	+	0.0138087i
$431$			1.44601e50i			1.27381i	0.770944	+	0.636903i	$0.219785\pi$
$431$			1.44601e50i			1.27381i	−0.770944	+	0.636903i	$0.780215\pi$
$432$	1.24767e50	−	2.84584e49i	1.05174	−	0.239894i
$433$	4.40370e49			0.355261			0.177631	−	0.984097i	$-0.443157\pi$
$433$	4.40370e49			0.355261			0.177631	+	0.984097i	$0.443157\pi$
$434$	−1.52125e49	+	4.34698e49i	−0.117462	+	0.335647i
$435$		−	1.87386e50i		−	1.38497i
$436$	1.04723e50	+	8.35258e49i	0.740965	+	0.590986i
$437$	1.56380e50			1.05933
$438$	−1.49875e50	−	5.24496e49i	−0.972125	−	0.340200i
$439$			6.15859e49i			0.382521i	0.981539	+	0.191261i	$0.0612576\pi$
$439$			6.15859e49i			0.382521i	−0.981539	+	0.191261i	$0.938742\pi$
$440$	6.54110e49	+	1.04126e50i	0.389090	+	0.619380i
$441$	3.59164e49			0.204625
$442$	4.71508e49	−	1.34734e50i	0.257315	−	0.735281i
$443$			2.28103e50i			1.19250i	0.802797	+	0.596252i	$0.203344\pi$
$443$			2.28103e50i			1.19250i	−0.802797	+	0.596252i	$0.796656\pi$
$444$	6.39484e49	−	8.01770e49i	0.320297	−	0.401581i
$445$	−7.72823e49			−0.370886
$446$	−2.79511e50	−	9.78162e49i	−1.28539	−	0.449830i
$447$			5.54254e49i			0.244268i
$448$	−1.55123e50	−	7.47441e49i	−0.655229	−	0.315715i
$449$	2.44924e49			0.0991632			0.0495816	−	0.998770i	$-0.484211\pi$
$449$	2.44924e49			0.0991632			0.0495816	+	0.998770i	$0.484211\pi$
$450$	−2.58322e49	+	7.38157e49i	−0.100259	+	0.286491i
$451$			2.84267e50i			1.05772i
$452$	−3.94023e50	−	3.14269e50i	−1.40569	−	1.12117i
$453$	−1.26010e50			−0.431061
$454$	1.96211e50	+	6.86651e49i	0.643669	+	0.225255i
$455$		−	1.93464e50i		−	0.608671i
$456$	−3.34009e50	+	2.09822e50i	−1.00792	+	0.633168i
$457$	−1.46647e49			−0.0424489			−0.0212244	−	0.999775i	$-0.506756\pi$
$457$	−1.46647e49			−0.0424489			−0.0212244	+	0.999775i	$0.506756\pi$
$458$	3.28823e49	−	9.39614e49i	0.0913099	−	0.260919i
$459$			4.91247e50i			1.30876i
$460$	2.12781e50	−	2.66780e50i	0.543918	−	0.681952i
$461$	−1.75960e50			−0.431614			−0.215807	−	0.976436i	$-0.569238\pi$
$461$	−1.75960e50			−0.431614			−0.215807	+	0.976436i	$0.569238\pi$
$462$	1.23086e50	+	4.30746e49i	0.289742	+	0.101397i
$463$		−	1.98320e50i		−	0.448051i	−0.974583	−	0.224026i	$-0.928080\pi$
$463$		−	1.98320e50i		−	0.448051i	0.974583	−	0.224026i	$-0.0719200\pi$
$464$	1.44909e50	+	6.35305e50i	0.314234	+	1.37766i
$465$	2.30216e50			0.479214
$466$	−1.05443e50	+	3.01304e50i	−0.210710	+	0.602105i
$467$		−	4.93368e50i		−	0.946564i	−0.880911	−	0.473282i	$-0.843069\pi$
$467$		−	4.93368e50i		−	0.946564i	0.880911	−	0.473282i	$-0.156931\pi$
$468$	−1.18386e50	−	9.44238e49i	−0.218087	−	0.173944i
$469$	−8.10782e49			−0.143423
$470$	1.34414e51	+	4.70388e50i	2.28341	+	0.799093i
$471$			3.34108e49i			0.0545116i
$472$	−1.03065e50	−	1.64067e50i	−0.161516	−	0.257112i
$473$	1.19584e49			0.0180016
$474$	6.68396e49	−	1.90995e50i	0.0966597	−	0.276206i
$475$		−	7.95897e50i		−	1.10580i
$476$	4.12160e50	−	5.16757e50i	0.550217	−	0.689849i
$477$	−1.76874e50			−0.226890
$478$	−6.99295e50	−	2.44722e50i	−0.862046	−	0.301677i
$479$		−	7.53198e50i		−	0.892349i	−0.894946	−	0.446174i	$-0.852786\pi$
$479$		−	7.53198e50i		−	0.892349i	0.894946	−	0.446174i	$-0.147214\pi$
$480$	−9.65248e49	+	8.55309e50i	−0.109915	+	0.973956i
$481$	−4.00690e50			−0.438583
$482$	6.94410e49	−	1.98428e50i	0.0730672	−	0.208790i
$483$		−	3.61887e50i		−	0.366081i
$484$	−5.50630e50	−	4.39177e50i	−0.535548	−	0.427148i
$485$	1.05367e51			0.985399
$486$	8.34791e50	+	2.92139e50i	0.750738	+	0.262725i
$487$			5.87321e50i			0.507955i	0.967210	+	0.253978i	$0.0817390\pi$
$487$			5.87321e50i			0.507955i	−0.967210	+	0.253978i	$0.918261\pi$
$488$	−3.51197e50	+	2.20619e50i	−0.292129	+	0.183513i
$489$	1.58664e51			1.26944
$490$	−2.63465e50	+	7.52853e50i	−0.202767	+	0.579408i
$491$		−	1.41059e51i		−	1.04437i	−0.852833	−	0.522184i	$-0.825117\pi$
$491$		−	1.41059e51i		−	1.04437i	0.852833	−	0.522184i	$-0.174883\pi$
$492$	−1.24073e51	+	1.55560e51i	−0.883775	+	1.10806i
$493$	−2.50140e51			−1.71432
$494$	1.45461e51	+	5.09049e50i	0.959257	+	0.335697i
$495$			5.00754e50i			0.317779i
$496$	−7.80514e50	+	1.78030e50i	−0.476682	+	0.108728i
$497$	−2.38823e51			−1.40380
$498$	5.78095e50	−	1.65191e51i	0.327070	−	0.934607i
$499$			1.49434e51i			0.813840i	0.913464	+	0.406920i	$0.133397\pi$
$499$			1.49434e51i			0.813840i	−0.913464	+	0.406920i	$0.866603\pi$
$500$	5.85656e50	+	4.67114e50i	0.307052	+	0.244902i
$501$	1.72255e51			0.869473
$502$	−5.74705e50	−	2.01121e50i	−0.279302	−	0.0977433i
$503$			1.77067e51i			0.828603i	0.910140	+	0.414302i	$0.135974\pi$
$503$			1.77067e51i			0.828603i	−0.910140	+	0.414302i	$0.864026\pi$
$504$	−3.73002e50	−	5.93771e50i	−0.168086	−	0.267571i
$505$	−4.54347e50			−0.197175
$506$	2.96847e50	−	8.48244e50i	0.124072	−	0.354536i
$507$			1.09786e51i			0.441974i
$508$	1.02079e51	−	1.27985e51i	0.395847	−	0.496304i
$509$	3.68200e51			1.37545			0.687727	−	0.725970i	$-0.258609\pi$
$509$	3.68200e51			1.37545			0.687727	+	0.725970i	$0.258609\pi$
$510$	−3.11869e51	−	1.09140e51i	−1.12238	−	0.392781i
$511$			2.87276e51i			0.996097i
$512$	−3.34171e50	−	2.97444e51i	−0.111645	−	0.993748i
$513$	−5.30359e51			−1.70742
$514$	−4.26089e50	+	1.21755e51i	−0.132191	+	0.377736i
$515$			1.97495e51i			0.590499i
$516$	6.54402e49	+	5.21945e49i	0.0188582	+	0.0150411i
$517$	3.75038e51			1.04173
$518$	−1.75128e51	−	6.12870e50i	−0.468911	−	0.164098i
$519$		−	5.98762e50i		−	0.154552i
$520$	2.84767e51	−	1.78888e51i	0.708640	−	0.445162i
$521$	3.66204e51			0.878630			0.439315	−	0.898333i	$-0.355221\pi$
$521$	3.66204e51			0.878630			0.439315	+	0.898333i	$0.355221\pi$
$522$	−8.76513e50	+	2.50464e51i	−0.202777	+	0.579437i
$523$		−	6.86846e51i		−	1.53224i	−0.642696	−	0.766121i	$-0.722184\pi$
$523$		−	6.86846e51i		−	1.53224i	0.642696	−	0.766121i	$-0.277816\pi$
$524$	3.42119e51	−	4.28941e51i	0.736009	−	0.922791i
$525$	−1.84183e51			−0.382141
$526$	−3.02370e51	−	1.05816e51i	−0.605076	−	0.211749i
$527$		−	3.07313e51i		−	0.593171i
$528$	5.04096e50	+	2.21005e51i	0.0938575	+	0.411488i
$529$	3.07354e51			0.552053
$530$	1.29746e51	−	3.70751e51i	0.224829	−	0.642451i
$531$		−	7.89016e50i		−	0.131914i
$532$	5.57901e51	+	4.44976e51i	0.899986	+	0.717820i
$533$	7.77423e51			1.21015
$534$	−1.34468e51	−	4.70579e50i	−0.201993	−	0.0706886i
$535$			1.23471e52i			1.78995i
$536$	−7.49699e50	−	1.19342e51i	−0.104895	−	0.166980i
$537$	−4.03280e51			−0.544623
$538$	−2.15303e51	+	6.15232e51i	−0.280665	+	0.802002i
$539$			2.10059e51i			0.264335i
$540$	−7.21643e51	+	9.04779e51i	−0.876680	+	1.09916i
$541$	−1.11502e52			−1.30778			−0.653889	−	0.756591i	$-0.726864\pi$
$541$	−1.11502e52			−1.30778			−0.653889	+	0.756591i	$0.726864\pi$
$542$	2.56288e51	+	8.96895e50i	0.290230	+	0.101568i
$543$		−	1.07251e52i		−	1.17275i
$544$	1.14174e52	+	1.28850e51i	1.20556	+	0.136052i
$545$	−1.21142e52			−1.23527
$546$	1.17802e51	−	3.36620e51i	0.116009	−	0.331497i
$547$			6.56803e50i			0.0624706i	0.999512	+	0.0312353i	$0.00994412\pi$
$547$			6.56803e50i			0.0624706i	−0.999512	+	0.0312353i	$0.990056\pi$
$548$	−3.39620e51	−	2.70877e51i	−0.312005	−	0.248853i
$549$	−1.68895e51			−0.149879
$550$	−4.31715e51	−	1.51081e51i	−0.370089	−	0.129515i
$551$		−	2.70056e52i		−	2.23652i
$552$	5.32676e51	−	3.34623e51i	0.426207	−	0.267740i
$553$	−3.66092e51			−0.283017
$554$	−5.71720e51	+	1.63370e52i	−0.427069	+	1.22035i
$555$			9.27478e51i			0.669479i
$556$	−1.73660e52	+	2.17731e52i	−1.21138	+	1.51880i
$557$	−4.22504e51			−0.284828			−0.142414	−	0.989807i	$-0.545486\pi$
$557$	−4.22504e51			−0.284828			−0.142414	+	0.989807i	$0.545486\pi$
$558$	−3.07712e51	−	1.07685e51i	−0.200491	−	0.0701628i
$559$		−	3.27042e50i		−	0.0205958i
$560$	1.51824e52	−	3.46299e51i	0.924202	−	0.210804i
$561$	−8.70166e51			−0.512045
$562$	−8.96802e50	+	2.56262e51i	−0.0510160	+	0.145779i
$563$		−	9.30319e50i		−	0.0511650i	−0.999673	−	0.0255825i	$-0.991856\pi$
$563$		−	9.30319e50i		−	0.0511650i	0.999673	−	0.0255825i	$-0.00814404\pi$
$564$	2.05233e52	+	1.63692e52i	1.09130	+	0.870410i
$565$	4.55801e52			2.34344
$566$	−4.27147e51	−	1.49482e51i	−0.212356	−	0.0743152i
$567$			5.70062e51i			0.274059i
$568$	−2.20830e52	−	3.51533e52i	−1.02669	−	1.63436i
$569$	3.90477e52			1.75575			0.877875	−	0.478891i	$-0.158961\pi$
$569$	3.90477e52			1.75575			0.877875	+	0.478891i	$0.158961\pi$
$570$	1.17830e52	−	3.36699e52i	0.512427	−	1.46427i
$571$			2.40636e51i			0.101222i	0.998718	+	0.0506109i	$0.0161168\pi$
$571$			2.40636e51i			0.101222i	−0.998718	+	0.0506109i	$0.983883\pi$
$572$	5.52243e51	−	6.92389e51i	0.224701	−	0.281725i
$573$	−1.25364e52			−0.493439
$574$	3.39785e52	+	1.18910e52i	1.29383	+	0.452784i
$575$			1.26929e52i			0.467598i
$576$	5.29094e51	−	1.09807e52i	0.188584	−	0.391385i
$577$	−3.01356e52			−1.03930			−0.519649	−	0.854380i	$-0.673937\pi$
$577$	−3.01356e52			−1.03930			−0.519649	+	0.854380i	$0.673937\pi$
$578$	−4.67084e51	+	1.33470e52i	−0.155871	+	0.445404i
$579$			1.19144e52i			0.384749i
$580$	−4.60709e52	−	3.67457e52i	−1.43977	−	1.14835i
$581$	−3.16632e52			−0.957654
$582$	1.83335e52	+	6.41591e51i	0.536672	+	0.187811i
$583$		−	1.03446e52i		−	0.293096i
$584$	−4.22852e52	+	2.65633e52i	−1.15970	+	0.728513i
$585$	1.36948e52			0.363575
$586$	1.71460e52	−	4.89948e52i	0.440664	−	1.25920i
$587$		−	1.52217e51i		−	0.0378739i	−0.999821	−	0.0189369i	$-0.993972\pi$
$587$		−	1.52217e51i		−	0.0378739i	0.999821	−	0.0189369i	$-0.00602817\pi$
$588$	−9.16839e51	+	1.14951e52i	−0.220864	+	0.276914i
$589$	3.31781e52			0.773858
$590$	1.65388e52	+	5.78784e51i	0.373522	+	0.130716i
$591$			3.05669e52i			0.668481i
$592$	−7.17234e51	−	3.14448e52i	−0.151897	−	0.665941i
$593$	−5.13722e52			−1.05363			−0.526816	−	0.849979i	$-0.676614\pi$
$593$	−5.13722e52			−1.05363			−0.526816	+	0.849979i	$0.676614\pi$
$594$	−1.00675e52	+	2.87681e52i	−0.199977	+	0.571437i
$595$			5.97778e52i			1.15005i
$596$	1.36269e52	+	1.08687e52i	0.253933	+	0.202534i
$597$	6.00395e52			1.08374
$598$	−2.31981e52	−	8.11828e51i	−0.405629	−	0.141952i
$599$			5.89348e52i			0.998302i	0.866515	+	0.499151i	$0.166355\pi$
$599$			5.89348e52i			0.998302i	−0.866515	+	0.499151i	$0.833645\pi$
$600$	−1.70307e52	−	2.71106e52i	−0.279485	−	0.444904i
$601$	−4.61306e52			−0.733456			−0.366728	−	0.930328i	$-0.619522\pi$
$601$	−4.61306e52			−0.733456			−0.366728	+	0.930328i	$0.619522\pi$
$602$	5.00222e50	−	1.42939e51i	0.00770601	−	0.0220200i
$603$		−	5.73932e51i		−	0.0856705i
$604$	−2.47100e52	+	3.09808e52i	−0.357413	+	0.448117i
$605$	6.36962e52			0.892815
$606$	−7.90547e51	−	2.76656e51i	−0.107386	−	0.0375803i
$607$		−	2.29323e52i		−	0.301899i	−0.988541	−	0.150950i	$-0.951767\pi$
$607$		−	2.29323e52i		−	0.301899i	0.988541	−	0.150950i	$-0.0482332\pi$
$608$	−1.39109e52	+	1.23265e53i	−0.177495	+	1.57279i
$609$	−6.24952e52			−0.772891
$610$	1.23893e52	−	3.54025e52i	0.148518	−	0.424392i
$611$		−	1.02567e53i		−	1.19185i
$612$	3.65799e52	+	2.91758e52i	0.412065	+	0.328659i
$613$	9.31597e52			1.01737			0.508685	−	0.860953i	$-0.330132\pi$
$613$	9.31597e52			1.01737			0.508685	+	0.860953i	$0.330132\pi$
$614$	−6.90313e51	−	2.41579e51i	−0.0730882	−	0.0255776i
$615$		−	1.79950e53i		−	1.84725i
$616$	3.47270e52	−	2.18152e52i	0.345648	−	0.217133i
$617$	−1.79910e53			−1.73635			−0.868175	−	0.496258i	$-0.834707\pi$
$617$	−1.79910e53			−1.73635			−0.868175	+	0.496258i	$0.834707\pi$
$618$	−1.20257e52	+	3.43635e52i	−0.112546	+	0.321600i
$619$		−	5.33732e52i		−	0.484397i	−0.970227	−	0.242198i	$-0.922132\pi$
$619$		−	5.33732e52i		−	0.484397i	0.970227	−	0.242198i	$-0.0778685\pi$
$620$	4.51444e52	−	5.66010e52i	0.397340	−	0.498175i
$621$	8.45814e52			0.721995
$622$	1.17470e53	+	4.11092e52i	0.972544	+	0.340347i
$623$			2.57744e52i			0.206974i
$624$	6.04411e52	−	1.37862e52i	0.470788	−	0.107384i
$625$	−1.60213e53			−1.21054
$626$	−1.83758e52	+	5.25091e52i	−0.134690	+	0.384877i
$627$		−	9.39448e52i		−	0.668020i
$628$	8.21439e51	+	6.55171e51i	0.0566685	+	0.0451983i
$629$	1.23808e53			0.828680
$630$	5.98553e52	+	2.09467e52i	0.388716	+	0.136033i
$631$			8.87768e52i			0.559425i	0.960084	+	0.279712i	$0.0902391\pi$
$631$			8.87768e52i			0.559425i	−0.960084	+	0.279712i	$0.909761\pi$
$632$	−3.38511e52	−	5.38865e52i	−0.206989	−	0.329500i
$633$	1.02155e53			0.606161
$634$	−8.00754e51	+	2.28816e52i	−0.0461108	+	0.131762i
$635$			1.48051e53i			0.827392i
$636$	4.51507e52	−	5.66089e52i	0.244895	−	0.307043i
$637$	5.74476e52			0.302429
$638$	−1.46485e53	−	5.12633e52i	−0.748517	−	0.261947i
$639$		−	1.69056e53i		−	0.838523i
$640$	1.91359e53	+	1.91454e53i	0.921358	+	0.921818i
$641$	−1.08361e53			−0.506487			−0.253244	−	0.967403i	$-0.581497\pi$
$641$	−1.08361e53			−0.506487			−0.253244	+	0.967403i	$0.581497\pi$
$642$	−7.51824e52	+	2.14834e53i	−0.341154	+	0.974851i
$643$		−	4.88969e52i		−	0.215413i	−0.994183	−	0.107707i	$-0.965649\pi$
$643$		−	4.88969e52i		−	0.215413i	0.994183	−	0.107707i	$-0.0343507\pi$
$644$	−8.89737e52	−	7.09645e52i	−0.380566	−	0.303536i
$645$	−7.57004e51			−0.0314386
$646$	−4.49456e53	−	1.57290e53i	−1.81247	−	0.634282i
$647$			2.37610e53i			0.930430i	0.885198	+	0.465215i	$0.154023\pi$
$647$			2.37610e53i			0.930430i	−0.885198	+	0.465215i	$0.845977\pi$
$648$	−8.39097e52	+	5.27114e52i	−0.319071	+	0.200438i
$649$	4.61461e52			0.170406
$650$	−4.13182e52	+	1.18067e53i	−0.148179	+	0.423423i
$651$		−	7.67794e52i		−	0.267427i
$652$	3.11135e53	−	3.90093e53i	1.05255	−	1.31967i
$653$	−2.60826e53			−0.857039			−0.428519	−	0.903533i	$-0.640965\pi$
$653$	−2.60826e53			−0.857039			−0.428519	+	0.903533i	$0.640965\pi$
$654$	−2.10783e53	−	7.37645e52i	−0.672756	−	0.235435i
$655$			4.96194e53i			1.53839i
$656$	1.39159e53	+	6.10095e53i	0.419118	+	1.83749i
$657$	−2.03355e53			−0.594994
$658$	1.56879e53	−	4.48284e53i	0.445937	−	1.27427i
$659$		−	4.78396e51i		−	0.0132119i	−0.999978	−	0.00660593i	$-0.997897\pi$
$659$		−	4.78396e51i		−	0.0132119i	0.999978	−	0.00660593i	$-0.00210275\pi$
$660$	−1.60267e53	−	1.27828e53i	−0.430042	−	0.342997i
$661$	6.97248e53			1.81786			0.908928	−	0.416953i	$-0.136902\pi$
$661$	6.97248e53			1.81786			0.908928	+	0.416953i	$0.136902\pi$
$662$	−2.04456e53	−	7.15503e52i	−0.517961	−	0.181263i
$663$			2.37976e53i			0.585836i
$664$	−2.92777e53	−	4.66063e53i	−0.700397	−	1.11494i
$665$	−6.45373e53			−1.50037
$666$	4.33834e52	−	1.23969e53i	0.0980198	−	0.280092i
$667$			4.30684e53i			0.945731i
$668$	3.37786e53	−	4.23508e53i	0.720923	−	0.903876i
$669$	4.93691e53			1.02414
$670$	1.20303e53	+	4.21008e52i	0.242581	+	0.0848925i
$671$		−	9.87791e52i		−	0.193614i
$672$	2.85254e53	+	3.21920e52i	0.543520	+	0.0613383i
$673$	6.26013e53			1.15957			0.579785	−	0.814770i	$-0.303137\pi$
$673$	6.26013e53			1.15957			0.579785	+	0.814770i	$0.303137\pi$
$674$	9.86097e52	−	2.81778e53i	0.177575	−	0.507422i
$675$		−	4.30479e53i		−	0.753668i
$676$	2.69921e53	+	2.15286e53i	0.459462	+	0.366462i
$677$	−3.55253e52			−0.0587968			−0.0293984	−	0.999568i	$-0.509359\pi$
$677$	−3.55253e52			−0.0587968			−0.0293984	+	0.999568i	$0.509359\pi$
$678$	7.93077e53	+	2.77542e53i	1.27630	+	0.446646i
$679$		−	3.51410e53i		−	0.549906i
$680$	−8.79893e53	+	5.52742e53i	−1.33894	+	0.841111i
$681$	−3.46562e53			−0.512844
$682$	6.29803e52	−	1.79967e53i	0.0906362	−	0.258994i
$683$		−	8.24124e53i		−	1.15345i	−0.816938	−	0.576726i	$-0.804330\pi$
$683$		−	8.24124e53i		−	1.15345i	0.816938	−	0.576726i	$-0.195670\pi$
$684$	−3.14987e53	+	3.94923e53i	−0.428772	+	0.537585i
$685$	3.92868e53			0.520146
$686$	7.84173e53	+	2.74425e53i	1.00984	+	0.353400i
$687$			1.65961e53i			0.207887i
$688$	2.56651e52	−	5.85404e51i	0.0312725	−	0.00713305i
$689$	−2.82907e53			−0.335335
$690$	−1.87914e53	+	5.36966e53i	−0.216684	+	0.619176i
$691$			1.44384e54i			1.61970i	0.586635	+	0.809852i	$0.300452\pi$
$691$			1.44384e54i			1.61970i	−0.586635	+	0.809852i	$0.699548\pi$
$692$	−1.47212e53	−	1.17415e53i	−0.160667	−	0.128146i
$693$	1.67006e53			0.177338
$694$	−1.34972e54	−	4.72342e53i	−1.39449	−	0.488007i
$695$		−	2.51869e54i		−	2.53199i
$696$	−5.77869e53	−	9.19892e53i	−0.565267	−	0.899832i
$697$	−2.40214e54			−2.28652
$698$	−4.81881e53	+	1.37698e54i	−0.446361	+	1.27548i
$699$		−	5.32184e53i		−	0.479728i
$700$	−3.61176e53	+	4.52834e53i	−0.316851	+	0.397261i
$701$	2.24485e54			1.91666			0.958332	−	0.285657i	$-0.0922119\pi$
$701$	2.24485e54			1.91666			0.958332	+	0.285657i	$0.0922119\pi$
$702$	7.86759e53	+	2.75330e53i	0.653788	+	0.228796i
$703$			1.33666e54i			1.08111i
$704$	6.42214e53	+	3.09444e53i	0.505591	+	0.243613i
$705$	−2.37411e54			−1.81931
$706$	1.45642e53	−	4.16173e53i	0.108642	−	0.310445i
$707$			1.51529e53i			0.110034i
$708$	2.52527e53	+	2.01413e53i	0.178515	+	0.142382i
$709$	−2.25437e53			−0.155148			−0.0775740	−	0.996987i	$-0.524717\pi$
$709$	−2.25437e53			−0.155148			−0.0775740	+	0.996987i	$0.524717\pi$
$710$	3.54364e54	+	1.24011e54i	2.37433	+	0.830909i
$711$		−	2.59147e53i		−	0.169053i
$712$	−3.79384e53	+	2.38326e53i	−0.240968	+	0.151374i
$713$	−5.29123e53			−0.327232
$714$	−3.63993e53	+	1.04011e54i	−0.219193	+	0.626346i
$715$			8.00947e53i			0.469666i
$716$	−7.90816e53	+	9.91507e53i	−0.451573	+	0.566172i
$717$	1.23514e54			0.686836
$718$	−9.86311e53	−	3.45165e53i	−0.534133	−	0.186923i
$719$		−	1.91687e54i		−	1.01098i	−0.862832	−	0.505492i	$-0.831311\pi$
$719$		−	1.91687e54i		−	1.01098i	0.862832	−	0.505492i	$-0.168689\pi$
$720$	2.45136e53	+	1.07472e54i	0.125919	+	0.552049i
$721$	6.58667e53			0.329531
$722$	1.02028e54	−	2.91546e54i	0.497179	−	1.42069i
$723$			3.50478e53i			0.166354i
$724$	−2.63689e54	−	2.10316e54i	−1.21916	−	0.972386i
$725$	2.19198e54			0.987219
$726$	1.10829e54	+	3.87853e53i	0.486249	+	0.170165i
$727$			5.13707e53i			0.219564i	0.993956	+	0.109782i	$0.0350153\pi$
$727$			5.13707e53i			0.219564i	−0.993956	+	0.109782i	$0.964985\pi$
$728$	−5.96611e53	−	9.49726e53i	−0.248425	−	0.395460i
$729$	−2.40330e54			−0.974956
$730$	1.49171e54	−	4.26258e54i	0.589591	−	1.68476i
$731$			1.01052e53i			0.0389147i
$732$	4.31139e53	−	5.40552e53i	0.161773	−	0.202828i
$733$	5.27598e54			1.92898			0.964489	−	0.264121i	$-0.0850820\pi$
$733$	5.27598e54			1.92898			0.964489	+	0.264121i	$0.0850820\pi$
$734$	−4.14915e54	−	1.45202e54i	−1.47820	−	0.517304i
$735$		−	1.32974e54i		−	0.461645i
$736$	2.21850e53	−	1.96582e54i	0.0750553	−	0.665067i
$737$	3.35667e53			0.110669
$738$	−8.41731e53	+	2.40525e54i	−0.270460	+	0.772840i
$739$			4.03673e54i			1.26411i	0.774923	+	0.632056i	$0.217789\pi$
$739$			4.03673e54i			1.26411i	−0.774923	+	0.632056i	$0.782211\pi$
$740$	2.28030e54	+	1.81875e54i	0.695968	+	0.555097i
$741$	−2.56923e54			−0.764289
$742$	−1.23649e54	−	4.32716e53i	−0.358523	−	0.125467i
$743$			5.79693e54i			1.63837i	0.573533	+	0.819183i	$0.305572\pi$
$743$			5.79693e54i			1.63837i	−0.573533	+	0.819183i	$0.694428\pi$
$744$	1.13015e54	−	7.09949e53i	0.311350	−	0.195588i
$745$	−1.57635e54			−0.423333
$746$	−5.84658e52	+	1.67066e53i	−0.0153061	+	0.0437373i
$747$		−	2.24136e54i		−	0.572031i
$748$	−1.70636e54	+	2.13939e54i	−0.424561	+	0.532305i
$749$	4.11787e54			0.998890
$750$	−1.17879e54	−	4.12524e53i	−0.278787	−	0.0975630i
$751$			1.76746e54i			0.407559i	0.979017	+	0.203779i	$0.0653226\pi$
$751$			1.76746e54i			0.407559i	−0.979017	+	0.203779i	$0.934677\pi$
$752$	8.04907e54	−	1.83594e54i	1.80970	−	0.412780i
$753$	1.01508e54			0.222535
$754$	−1.40197e54	+	4.00614e54i	−0.299697	+	0.856387i
$755$		−	3.58382e54i		−	0.747058i
$756$	3.01753e54	+	2.40675e54i	0.613391	+	0.489235i
$757$	−4.76640e54			−0.944863			−0.472431	−	0.881367i	$-0.656624\pi$
$757$	−4.76640e54			−0.944863			−0.472431	+	0.881367i	$0.656624\pi$
$758$	−2.27283e54	−	7.95390e53i	−0.439393	−	0.153768i
$759$			1.49823e54i			0.282477i
$760$	−5.96751e54	−	9.49950e54i	−1.09732	−	1.74680i
$761$	−5.99263e54			−1.07475			−0.537377	−	0.843342i	$-0.680585\pi$
$761$	−5.99263e54			−1.07475			−0.537377	+	0.843342i	$0.680585\pi$
$762$	−9.01498e53	+	2.57604e54i	−0.157696	+	0.450617i
$763$			4.04021e54i			0.689346i
$764$	−2.45833e54	+	3.08219e54i	−0.409134	+	0.512963i
$765$	−4.23152e54			−0.686956
$766$	−4.38463e54	−	1.53442e54i	−0.694362	−	0.242996i
$767$		−	1.26202e54i		−	0.194964i
$768$	2.16379e54	+	4.49644e54i	0.326100	+	0.677650i
$769$	9.26319e53			0.136195			0.0680974	−	0.997679i	$-0.478307\pi$
$769$	9.26319e53			0.136195			0.0680974	+	0.997679i	$0.478307\pi$
$770$	−1.22508e54	+	3.50067e54i	−0.175728	+	0.502143i
$771$		−	2.15053e54i		−	0.300962i
$772$	2.92927e54	+	2.33636e54i	0.399973	+	0.319015i
$773$	2.05382e54			0.273623			0.136811	−	0.990597i	$-0.456315\pi$
$773$	2.05382e54			0.273623			0.136811	+	0.990597i	$0.456315\pi$
$774$	1.01183e53	+	3.54094e52i	0.0131531	+	0.00460300i
$775$			2.69298e54i			0.341587i
$776$	5.17254e54	−	3.24935e54i	0.640223	−	0.402183i
$777$	3.09323e54			0.373605
$778$	1.71164e54	−	4.89104e54i	0.201744	−	0.576486i
$779$		−	2.59340e55i		−	2.98303i
$780$	−3.49588e54	+	4.38305e54i	−0.392427	+	0.492016i
$781$	9.88735e54			1.08320
$782$	7.16791e54	+	2.50845e54i	0.766415	+	0.268211i
$783$		−	1.46066e55i		−	1.52432i
$784$	1.02831e54	+	4.50829e54i	0.104742	+	0.459205i
$785$	−9.50230e53			−0.0944725
$786$	−3.02137e54	+	8.63360e54i	−0.293208	+	0.837845i
$787$			1.53224e55i			1.45147i	0.687975	+	0.725734i	$0.258500\pi$
$787$			1.53224e55i			1.45147i	−0.687975	+	0.725734i	$0.741500\pi$
$788$	7.51519e54	+	5.99404e54i	0.694931	+	0.554270i
$789$	5.34067e54			0.482095
$790$	5.43205e54	+	1.90097e54i	0.478684	+	0.167518i
$791$		−	1.52014e55i		−	1.30777i
$792$	1.54424e54	+	2.45823e54i	0.129699	+	0.206464i
$793$	−2.70145e54			−0.221516
$794$	−7.12659e53	+	2.03643e54i	−0.0570548	+	0.163035i
$795$			6.54845e54i			0.511874i
$796$	1.17735e55	−	1.47613e55i	0.898581	−	1.12662i
$797$	−1.54598e55			−1.15211			−0.576057	−	0.817409i	$-0.695409\pi$
$797$	−1.54598e55			−1.15211			−0.576057	+	0.817409i	$0.695409\pi$
$798$	−1.12293e55	−	3.92974e54i	−0.817139	−	0.285962i
$799$			3.16918e55i			2.25194i
$800$	−1.00051e55	−	1.12911e54i	−0.694242	−	0.0783478i
$801$	−1.82450e54			−0.123631
$802$	7.50144e54	−	2.14354e55i	0.496400	−	1.41847i
$803$		−	1.18933e55i		−	0.768613i
$804$	1.83688e54	+	1.46508e54i	0.115935	+	0.0924690i
$805$	1.02924e55			0.634444
$806$	−4.92180e54	−	1.72241e54i	−0.296318	−	0.103698i
$807$		−	1.08666e55i		−	0.638996i
$808$	−2.23042e54	+	1.40113e54i	−0.128106	+	0.0804754i
$809$	−1.04749e55			−0.587664			−0.293832	−	0.955857i	$-0.594931\pi$
$809$	−1.04749e55			−0.587664			−0.293832	+	0.955857i	$0.594931\pi$
$810$	2.96011e54	−	8.45855e54i	0.162216	−	0.463533i
$811$			5.70326e54i			0.305300i	0.988280	+	0.152650i	$0.0487808\pi$
$811$			5.70326e54i			0.305300i	−0.988280	+	0.152650i	$0.951219\pi$
$812$	−1.22551e55	+	1.53651e55i	−0.640842	+	0.803472i
$813$	−4.52674e54			−0.231241
$814$	7.25037e54	+	2.53730e54i	0.361823	+	0.126622i
$815$			4.51255e55i			2.20002i
$816$	−1.86755e55	+	4.25976e54i	−0.889529	+	0.202896i
$817$	−1.09097e54			−0.0507686
$818$	−8.05348e54	+	2.30129e55i	−0.366160	+	1.04631i
$819$		−	4.56735e54i		−	0.202894i
$820$	−4.42427e55	−	3.52875e55i	−1.92034	−	1.53164i
$821$	−2.76428e54			−0.117236			−0.0586182	−	0.998280i	$-0.518669\pi$
$821$	−2.76428e54			−0.117236			−0.0586182	+	0.998280i	$0.518669\pi$
$822$	6.83576e54	+	2.39221e54i	0.283284	+	0.0991368i
$823$		−	2.17970e54i		−	0.0882675i	−0.999026	−	0.0441337i	$-0.985947\pi$
$823$		−	2.17970e54i		−	0.0882675i	0.999026	−	0.0441337i	$-0.0140528\pi$
$824$	6.09044e54	+	9.69518e54i	0.241008	+	0.383653i
$825$	7.62525e54			0.294869
$826$	1.93030e54	−	5.51586e54i	0.0729465	−	0.208445i
$827$			1.73081e55i			0.639213i	0.947550	+	0.319607i	$0.103551\pi$
$827$			1.73081e55i			0.639213i	−0.947550	+	0.319607i	$0.896449\pi$
$828$	5.02339e54	−	6.29821e54i	0.181310	−	0.227322i
$829$	4.08994e55			1.44272			0.721358	−	0.692562i	$-0.243518\pi$
$829$	4.08994e55			1.44272			0.721358	+	0.692562i	$0.243518\pi$
$830$	4.69817e55	+	1.64415e55i	1.61974	+	0.566836i
$831$		−	2.88554e55i		−	0.972318i
$832$	8.46277e54	−	1.75635e55i	0.278721	−	0.578453i
$833$	−1.77506e55			−0.571423
$834$	1.53365e55	−	4.38242e55i	0.482583	−	1.37898i
$835$			4.89909e55i			1.50686i
$836$	−2.30973e55	−	1.84222e55i	−0.694452	−	0.553888i
$837$	1.79451e55			0.527428
$838$	−1.77314e55	−	6.20520e54i	−0.509457	−	0.178287i
$839$		−	8.42036e54i		−	0.236512i	−0.992983	−	0.118256i	$-0.962270\pi$
$839$		−	8.42036e54i		−	0.236512i	0.992983	−	0.118256i	$-0.0377304\pi$
$840$	−2.19833e55	+	1.38098e55i	−0.603652	+	0.379210i
$841$	3.71262e55			0.996681
$842$	−1.31694e55	+	3.76316e55i	−0.345649	+	0.987696i
$843$		−	4.52627e54i		−	0.116149i
$844$	2.00321e55	−	2.51158e55i	0.502598	−	0.630146i
$845$	−3.12241e55			−0.765972
$846$	3.17328e55	+	1.11051e55i	0.761153	+	0.266370i
$847$		−	2.12433e55i		−	0.498239i
$848$	−5.06402e54	−	2.22016e55i	−0.116138	−	0.509169i
$849$	7.54456e54			0.169195
$850$	1.27668e55	−	3.64812e55i	0.279977	−	0.800036i
$851$		−	2.13169e55i		−	0.457154i
$852$	5.41069e55	+	4.31551e55i	1.13475	+	0.905065i
$853$	−7.89307e55			−1.61888			−0.809440	−	0.587203i	$-0.800229\pi$
$853$	−7.89307e55			−1.61888			−0.809440	+	0.587203i	$0.800229\pi$
$854$	−1.18071e55	−	4.13196e54i	−0.236834	−	0.0828813i
$855$		−	4.56842e55i		−	0.896211i
$856$	3.80763e55	+	6.06125e55i	0.730556	+	1.16295i
$857$	2.89450e55			0.543173			0.271587	−	0.962414i	$-0.412452\pi$
$857$	2.89450e55			0.543173			0.271587	+	0.962414i	$0.412452\pi$
$858$	−4.87705e54	+	1.39362e55i	−0.0895155	+	0.255791i
$859$		−	7.81007e55i		−	1.40212i	−0.713102	−	0.701060i	$-0.752711\pi$
$859$		−	7.81007e55i		−	1.40212i	0.713102	−	0.701060i	$-0.247289\pi$
$860$	−1.48445e54	+	1.86117e54i	−0.0260673	+	0.0326826i
$861$	−6.00152e55			−1.03086
$862$	−7.15573e55	−	2.50419e55i	−1.20231	−	0.420754i
$863$			3.27212e55i			0.537804i	0.963168	+	0.268902i	$0.0866608\pi$
$863$			3.27212e55i			0.537804i	−0.963168	+	0.268902i	$0.913339\pi$
$864$	−7.52402e54	+	6.66705e55i	−0.120973	+	1.07195i
$865$	1.70293e55			0.267849
$866$	−7.62629e54	+	2.17922e55i	−0.117347	+	0.335321i
$867$		−	2.35743e55i		−	0.354876i
$868$	−1.88770e55	−	1.50561e55i	−0.278009	−	0.221737i
$869$	1.51563e55			0.218383
$870$	9.27301e55	+	3.24514e55i	1.30724	+	0.457475i
$871$		−	9.17994e54i		−	0.126618i
$872$	−5.94694e55	+	3.73582e55i	−0.802565	+	0.504165i
$873$	2.48754e55			0.328473
$874$	−2.70817e55	+	7.73861e55i	−0.349911	+	0.999875i
$875$			2.25946e55i			0.285662i
$876$	5.19105e55	−	6.50842e55i	0.642210	−	0.805188i
$877$	−3.40864e55			−0.412657			−0.206328	−	0.978483i	$-0.566152\pi$
$877$	−3.40864e55			−0.412657			−0.206328	+	0.978483i	$0.566152\pi$
$878$	−3.04764e55	−	1.06654e55i	−0.361051	−	0.126352i
$879$			8.65380e55i			1.00327i
$880$	−6.28556e55	+	1.43369e55i	−0.713137	+	0.162662i
$881$	7.74971e55			0.860485			0.430243	−	0.902713i	$-0.358428\pi$
$881$	7.74971e55			0.860485			0.430243	+	0.902713i	$0.358428\pi$
$882$	−6.21996e54	+	1.77736e55i	−0.0675903	+	0.193140i
$883$			1.28708e56i			1.36884i	0.729088	+	0.684420i	$0.239945\pi$
$883$			1.28708e56i			1.36884i	−0.729088	+	0.684420i	$0.760055\pi$
$884$	5.85089e55	+	4.66661e55i	0.609016	+	0.485745i
$885$	−2.92120e55			−0.297604
$886$	−1.12879e56	−	3.95026e55i	−1.12557	−	0.393899i
$887$		−	1.67612e56i		−	1.63590i	−0.575287	−	0.817952i	$-0.695110\pi$
$887$		−	1.67612e56i		−	1.63590i	0.575287	−	0.817952i	$-0.304890\pi$
$888$	2.86019e55	+	4.55305e55i	0.273243	+	0.434967i
$889$	4.93766e55			0.461729
$890$	1.33837e55	−	3.82440e55i	0.122508	−	0.350068i
$891$		−	2.36008e55i		−	0.211471i
$892$	9.68108e55	−	1.21379e56i	0.849164	−	1.06466i
$893$	−3.42150e56			−2.93791
$894$	−2.74279e55	−	9.59852e54i	−0.230557	−	0.0806847i
$895$		−	1.14696e56i		−	0.943869i
$896$	6.38519e55	−	6.38200e55i	0.514425	−	0.514167i
$897$	4.09740e55			0.323186
$898$	−4.24156e54	+	1.21203e55i	−0.0327549	+	0.0935973i
$899$			9.13757e55i			0.690870i
$900$	−3.20549e55	−	2.55667e55i	−0.237294	−	0.189263i
$901$	8.74147e55			0.633597
$902$	−1.40673e56	−	4.92291e55i	−0.998355	−	0.349380i
$903$			2.52469e54i			0.0175445i
$904$	2.23756e56	−	1.40562e56i	1.52256	−	0.956459i
$905$	3.05032e56			2.03246
$906$	2.18222e55	−	6.23572e55i	0.142385	−	0.406866i
$907$			8.02498e55i			0.512750i	0.966577	+	0.256375i	$0.0825281\pi$
$907$			8.02498e55i			0.512750i	−0.966577	+	0.256375i	$0.917472\pi$
$908$	−6.79593e55	+	8.52058e55i	−0.425224	+	0.533136i
$909$	−1.07264e55			−0.0657262
$910$	9.57375e55	+	3.35038e55i	0.574508	+	0.201052i
$911$			2.48458e56i			1.46017i	0.683357	+	0.730084i	$0.260519\pi$
$911$			2.48458e56i			1.46017i	−0.683357	+	0.730084i	$0.739481\pi$
$912$	−4.59892e55	−	2.01625e56i	−0.264700	−	1.16049i
$913$	1.31087e56			0.738949
$914$	2.53962e54	−	7.25700e54i	0.0140214	−	0.0400663i
$915$			6.25304e55i			0.338135i
$916$	4.08032e55	+	3.25443e55i	0.216113	+	0.172370i
$917$	1.65486e56			0.858506
$918$	−2.43099e56	−	8.50736e55i	−1.23530	−	0.432299i
$919$			2.64953e56i			1.31879i	0.751799	+	0.659393i	$0.229186\pi$
$919$			2.64953e56i			1.31879i	−0.751799	+	0.659393i	$0.770814\pi$
$920$	9.51695e55	+	1.51497e56i	0.464012	+	0.738646i
$921$	1.21928e55			0.0582331
$922$	3.04725e55	−	8.70756e55i	0.142568	−	0.407389i
$923$		−	2.70403e56i		−	1.23931i
$924$	−4.26318e55	+	5.34508e55i	−0.191411	+	0.239986i
$925$	−1.08493e56			−0.477209
$926$	9.81408e55	+	3.43449e55i	0.422903	+	0.147997i
$927$			4.66253e55i			0.196837i
$928$	−3.39483e56	−	3.83119e55i	−1.40413	−	0.158461i
$929$	−3.18645e56			−1.29125			−0.645623	−	0.763657i	$-0.723402\pi$
$929$	−3.18645e56			−1.29125			−0.645623	+	0.763657i	$0.723402\pi$
$930$	−3.98686e55	+	1.13925e56i	−0.158291	+	0.452317i
$931$		−	1.91639e56i		−	0.745486i
$932$	−1.30843e56	−	1.04359e56i	−0.498710	−	0.397766i
$933$	−2.07483e56			−0.774876
$934$	2.44148e56	+	8.54409e55i	0.893435	+	0.312662i
$935$		−	2.47483e56i		−	0.887409i
$936$	6.72286e55	−	4.22325e55i	0.236218	−	0.148390i
$937$	4.73831e55			0.163144			0.0815721	−	0.996667i	$-0.474006\pi$
$937$	4.73831e55			0.163144			0.0815721	+	0.996667i	$0.474006\pi$
$938$	1.40410e55	−	4.01224e55i	0.0473746	−	0.135373i
$939$		−	9.27451e55i		−	0.306651i
$940$	−4.65553e56	+	5.83700e56i	−1.50848	+	1.89130i
$941$	7.71396e55			0.244948			0.122474	−	0.992472i	$-0.460917\pi$
$941$	7.71396e55			0.244948			0.122474	+	0.992472i	$0.460917\pi$
$942$	−1.65337e55	−	5.78604e54i	−0.0514520	−	0.0180059i
$943$			4.13593e56i			1.26140i
$944$	9.90388e55	−	2.25901e55i	0.296031	−	0.0675227i
$945$	−3.49064e56			−1.02259
$946$	−2.07094e54	+	5.91773e54i	−0.00594615	+	0.0169912i
$947$		−	6.04705e55i		−	0.170174i	−0.996374	−	0.0850872i	$-0.972883\pi$
$947$		−	6.04705e55i		−	0.170174i	0.996374	−	0.0850872i	$-0.0271169\pi$
$948$	8.29405e55	+	6.61526e55i	0.228775	+	0.182469i
$949$	−3.25263e56			−0.879379
$950$	3.93858e56	+	1.37833e56i	1.04374	+	0.365261i
$951$		−	4.04151e55i		−	0.104982i
$952$	1.84345e56	+	2.93453e56i	0.469385	+	0.747200i
$953$	2.68288e56			0.669633			0.334817	−	0.942283i	$-0.391326\pi$
$953$	2.68288e56			0.669633			0.334817	+	0.942283i	$0.391326\pi$
$954$	3.06309e55	−	8.75280e55i	0.0749446	−	0.214155i
$955$		−	3.56544e56i		−	0.855164i
$956$	2.42206e56	−	3.03673e56i	0.569489	−	0.714013i
$957$	2.58733e56			0.596382
$958$	3.72728e56	+	1.30438e56i	0.842263	+	0.294754i
$959$		−	1.31025e56i		−	0.290270i
$960$	−4.06543e56	−	1.95888e56i	−0.882983	−	0.425455i
$961$	3.57357e56			0.760953
$962$	6.93911e55	−	1.98286e56i	0.144870	−	0.413966i
$963$			2.91493e56i			0.596663i
$964$	8.61686e55	+	6.87272e55i	0.172936	+	0.137932i
$965$	−3.38854e56			−0.666798
$966$	1.79084e56	+	6.26712e55i	0.345534	+	0.120921i
$967$		−	8.89441e56i		−	1.68273i	−0.540469	−	0.841364i	$-0.681753\pi$
$967$		−	8.89441e56i		−	1.68273i	0.540469	−	0.841364i	$-0.318247\pi$
$968$	3.12689e56	−	1.96429e56i	0.580071	−	0.364396i
$969$	7.93861e56			1.44408
$970$	−1.82474e56	+	5.21420e56i	−0.325490	+	0.930090i
$971$		−	5.57103e56i		−	0.974473i	−0.873270	−	0.487236i	$-0.838005\pi$
$971$		−	5.57103e56i		−	0.974473i	0.873270	−	0.487236i	$-0.161995\pi$
$972$	−2.89137e56	+	3.62513e56i	−0.495957	+	0.621819i
$973$	−8.40007e56			−1.41299
$974$	−2.90642e56	−	1.01712e56i	−0.479444	−	0.167784i
$975$		−	2.08538e56i		−	0.337363i
$976$	−4.83558e55	−	2.12000e56i	−0.0767188	−	0.336349i
$977$	1.05425e57			1.64039			0.820193	−	0.572087i	$-0.193866\pi$
$977$	1.05425e57			1.64039			0.820193	+	0.572087i	$0.193866\pi$
$978$	−2.74774e56	+	7.85168e56i	−0.419311	+	1.19819i
$979$		−	1.06707e56i		−	0.159706i
$980$	−3.26931e56	−	2.60757e56i	−0.479911	−	0.382772i
$981$	−2.85996e56			−0.411764
$982$	6.98047e56	+	2.44285e56i	0.985749	+	0.344968i
$983$			1.19742e57i			1.65855i	0.558838	+	0.829277i	$0.311247\pi$
$983$			1.19742e57i			1.65855i	−0.558838	+	0.829277i	$0.688753\pi$
$984$	−5.54938e56	−	8.83388e56i	−0.753941	−	1.20018i
$985$	−8.69348e56			−1.15852
$986$	4.33190e56	−	1.23785e57i	0.566262	−	1.61810i
$987$			7.91790e56i			1.01528i
$988$	−5.03816e56	+	6.31673e56i	−0.633710	+	0.794530i
$989$	1.73988e55			0.0214679
$990$	−2.47803e56	−	8.67200e55i	−0.299943	−	0.104967i
$991$		−	6.67252e56i		−	0.792302i	−0.918185	−	0.396151i	$-0.870346\pi$
$991$		−	6.67252e56i		−	0.792302i	0.918185	−	0.396151i	$-0.129654\pi$
$992$	4.70686e55	−	4.17077e56i	0.0548289	−	0.485841i
$993$	3.61124e56			0.412686
$994$	4.13591e56	−	1.18184e57i	0.463692	−	1.32500i
$995$			1.70757e57i			1.87820i
$996$	7.17351e56	+	5.72152e56i	0.774113	+	0.617425i
$997$	5.88054e55			0.0622600			0.0311300	−	0.999515i	$-0.490089\pi$
$997$	5.88054e55			0.0622600			0.0311300	+	0.999515i	$0.490089\pi$
$998$	−7.39489e56	−	2.58788e56i	−0.768160	−	0.268822i
$999$			7.22960e56i			0.736835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.39.b.a.3.8	yes	18
4.3	odd	2	inner	4.39.b.a.3.7	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.39.b.a.3.7	✓	18	4.3	odd	2	inner
4.39.b.a.3.8	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 39 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-173179. + 494861. i) q^{2} -8.74057e8i q^{3} +(-2.14896e11 - 1.71399e11i) q^{4} +2.48589e13 q^{5} +(4.32536e14 + 1.51368e14i) q^{6} -8.29070e15i q^{7} +(1.22034e17 - 7.66608e16i) q^{8} +5.86877e17 q^{9} +O(q^{10})\)	\(q+(-173179. + 494861. i) q^{2} -8.74057e8i q^{3} +(-2.14896e11 - 1.71399e11i) q^{4} +2.48589e13 q^{5} +(4.32536e14 + 1.51368e14i) q^{6} -8.29070e15i q^{7} +(1.22034e17 - 7.66608e16i) q^{8} +5.86877e17 q^{9} +(-4.30504e18 + 1.23017e19i) q^{10} +3.43238e19i q^{11} +(-1.49812e20 + 1.87831e20i) q^{12} +9.38699e20 q^{13} +(4.10274e21 + 1.43577e21i) q^{14} -2.17281e22i q^{15} +(1.68027e22 + 7.36659e22i) q^{16} -2.90046e23 q^{17} +(-1.01635e23 + 2.90422e23i) q^{18} -3.13139e24i q^{19} +(-5.34208e24 - 4.26079e24i) q^{20} -7.24654e24 q^{21} +(-1.69855e25 - 5.94416e24i) q^{22} +4.99393e25i q^{23} +(-6.70059e25 - 1.06665e26i) q^{24} +2.54167e26 q^{25} +(-1.62563e26 + 4.64525e26i) q^{26} -1.69368e27i q^{27} +(-1.42102e27 + 1.78164e27i) q^{28} +8.62415e27 q^{29} +(1.07524e28 + 3.76285e27i) q^{30} +1.05953e28i q^{31} +(-3.93642e28 - 4.44240e27i) q^{32} +3.00009e28 q^{33} +(5.02299e28 - 1.43532e29i) q^{34} -2.06098e29i q^{35} +(-1.26117e29 - 1.00590e29i) q^{36} -4.26856e29 q^{37} +(1.54960e30 + 5.42292e29i) q^{38} -8.20476e29i q^{39} +(3.03363e30 - 1.90570e30i) q^{40} +8.28192e30 q^{41} +(1.25495e30 - 3.58603e30i) q^{42} -3.48399e29i q^{43} +(5.88306e30 - 7.37605e30i) q^{44} +1.45891e31 q^{45} +(-2.47130e31 - 8.64844e30i) q^{46} -1.09265e32i q^{47} +(6.43881e31 - 1.46865e31i) q^{48} +6.11992e31 q^{49} +(-4.40164e31 + 1.25777e32i) q^{50} +2.53517e32i q^{51} +(-2.01723e32 - 1.60892e32i) q^{52} -3.01382e32 q^{53} +(8.38138e32 + 2.93311e32i) q^{54} +8.53252e32i q^{55} +(-6.35572e32 - 1.01175e33i) q^{56} -2.73702e33 q^{57} +(-1.49352e33 + 4.26775e33i) q^{58} -1.34443e33i q^{59} +(-3.72417e33 + 4.66928e33i) q^{60} -2.87786e33 q^{61} +(-5.24321e33 - 1.83489e33i) q^{62} -4.86562e33i q^{63} +(9.01542e33 - 1.87105e34i) q^{64} +2.33350e34 q^{65} +(-5.19553e33 + 1.48463e34i) q^{66} -9.77943e33i q^{67} +(6.23298e34 + 4.97136e34i) q^{68} +4.36498e34 q^{69} +(1.01990e35 + 3.56918e34i) q^{70} -2.88061e35i q^{71} +(7.16189e34 - 4.49905e34i) q^{72} -3.46504e35 q^{73} +(7.39226e34 - 2.11234e35i) q^{74} -2.22156e35i q^{75} +(-5.36717e35 + 6.72924e35i) q^{76} +2.84568e35 q^{77} +(4.06021e35 + 1.42089e35i) q^{78} -4.41569e35i q^{79} +(4.17696e35 + 1.83125e36i) q^{80} -6.87593e35 q^{81} +(-1.43425e36 + 4.09840e36i) q^{82} -3.81913e36i q^{83} +(1.55725e36 + 1.24205e36i) q^{84} -7.21023e36 q^{85} +(1.72409e35 + 6.03354e34i) q^{86} -7.53800e36i q^{87} +(2.63129e36 + 4.18867e36i) q^{88} -3.10884e36 q^{89} +(-2.52653e36 + 7.21957e36i) q^{90} -7.78247e36i q^{91} +(8.55954e36 - 1.07318e37i) q^{92} +9.26091e36 q^{93} +(5.40707e37 + 1.89223e37i) q^{94} -7.78430e37i q^{95} +(-3.88291e36 + 3.44065e37i) q^{96} +4.23861e37 q^{97} +(-1.05984e37 + 3.02851e37i) q^{98} +2.01438e37i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots - 75\!\cdots\!14 q^{9}+O(q^{10}) \) 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9	\( 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots + 79\!\cdots\!72 q^{98}+O(q^{100}) \) 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9 - 3330064307292995160 * q^10 + 214196660016355524480 * q^12 - 1351697142828804018156 * q^13 - 7517302305589491995328 * q^14 + 146524491404032531730688 * q^16 - 108377436655642595433244 * q^17 - 2269182475834354952235228 * q^18 + 14024643346150499263916960 * q^20 - 3613555902040956758482176 * q^21 - 48893102429006434191867360 * q^22 - 507867326842846671102786048 * q^24 + 441821122409714044642015590 * q^25 + 1408725703649472883667066984 * q^26 - 248593478439946838208756480 * q^28 + 12039386014829706600024980948 * q^29 - 36685926266894937628070825280 * q^30 + 40815302174771571873068643328 * q^32 - 25787267222238191864238656640 * q^33 + 36261374450642004292958003976 * q^34 - 580544496119856571348909156080 * q^36 - 1267140929573154455938088740044 * q^37 + 1030706182877614317326332452960 * q^38 + 3677775331309955303335927125120 * q^40 - 4228447688719256876424323554684 * q^41 - 14054054841750269128772739402240 * q^42 - 10408853597054255998042527960960 * q^44 + 5968962977750993515218889928340 * q^45 + 22407092921477343211835072559552 * q^46 - 235299721005018637688575231641600 * q^48 - 31615512188019323981649417734094 * q^49 + 24292124186551164152560477361580 * q^50 + 1002079305454954374889708255510176 * q^52 + 9170251390510729272958214802164 * q^53 - 787051683509089599494415837112896 * q^54 + 1152829073224199082248229376115712 * q^56 + 1668394969897754054685444684739200 * q^57 + 6129531800884682398669731348277224 * q^58 - 11636557112389656620532244922123520 * q^60 - 3962895304807674280127771339766444 * q^61 - 8994819235653434082008553861768960 * q^62 + 24667562443996411690757328278360064 * q^64 + 95108472178397576493345013351708360 * q^65 - 59643686483535838768039195759223040 * q^66 - 37428614071533769215405413189346016 * q^68 - 378107798255717180855219732084825856 * q^69 + 185830274294359588352082139216848000 * q^70 - 260290846480495236441760743958748352 * q^72 + 769773517671824524924524644742901764 * q^73 - 250034850108007402381953386687905624 * q^74 + 347277300516185248422743813412796800 * q^76 - 1122048032159971455828617866562814720 * q^77 - 1450998872578214468135780206011466560 * q^78 + 391473453760426152176293685484792320 * q^80 + 8894227269421968655762303906241837682 * q^81 + 344096947623408239895482884304277576 * q^82 - 6791395692770555756905407625225660416 * q^84 - 3198312652592605820819998423888978200 * q^85 + 8678996853442312035283130731028012832 * q^86 - 815671442380761053869289210355156480 * q^88 - 6268329434682461663886854261019826492 * q^89 - 23166185157487343623484458734705269400 * q^90 + 11421593562829281515681866911017506560 * q^92 + 41748150138354461655386813609302195200 * q^93 - 33742046901195882761657274622561154688 * q^94 - 31638035665740952392118263378397667328 * q^96 - 62817319233285161836922640968633412444 * q^97 + 79415378721147757612981391241727219972 * q^98

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