LMFDB - Embedded newform 4.31.b.a.3.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,31,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, 31, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 31);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 31 $
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:	$22.8057047611$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 7 x^{13} + 7040347091761 x^{12} - 42242082550475 x^{11} + \cdots + 48\!\cdots\!00 $ x^14 - 7x^13 + 7040347091761x^12 - 42242082550475x^11 + 18008728830670915101223295x^10 - 90043644152967356416070621x^9 + 21189728137694531984698973691059207547x^8 - 84758912550237866073878555288648461401x^7 + 12092215554238283620631700081914283098967933222660x^6 - 36276646662418194667969645897789716351627569494760x^5 + 3068812077928688267104132515948151981977982628865973479570704x^4 - 6137624155796915456437666926180996318216113616424689721741328x^3 + 240224517591297395963498654659405852693819346574594371107838616625453504x^2 - 240224517588228583885606243038964074803354751677171360185114000107450880*x + 4800851985577239247844026939439062575281134066464418947338032535601205573916876800
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{182}\cdot 3^{19}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.14
Root			$0.500000 - 769735. i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.31.b.a.3.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(30824.3 + 11117.8i) q^{2} +1.23158e7i q^{3} +(8.26531e8 + 6.85396e8i) q^{4} +1.48412e9 q^{5} +(-1.36924e11 + 3.79624e11i) q^{6} +2.60240e12i q^{7} +(1.78571e13 + 3.03161e13i) q^{8} +5.42133e13 q^{9} +O(q^{10})$	\(q+(30824.3 + 11117.8i) q^{2} +1.23158e7i q^{3} +(8.26531e8 + 6.85396e8i) q^{4} +1.48412e9 q^{5} +(-1.36924e11 + 3.79624e11i) q^{6} +2.60240e12i q^{7} +(1.78571e13 + 3.03161e13i) q^{8} +5.42133e13 q^{9} +(4.57469e13 + 1.65001e13i) q^{10} +2.83042e15i q^{11} +(-8.44118e15 + 1.01794e16i) q^{12} -4.46946e16 q^{13} +(-2.89330e16 + 8.02171e16i) q^{14} +1.82780e16i q^{15} +(2.13385e17 + 1.13300e18i) q^{16} -8.36518e17 q^{17} +(1.67109e18 + 6.02733e17i) q^{18} -2.36927e19i q^{19} +(1.22667e18 + 1.01721e18i) q^{20} -3.20505e19 q^{21} +(-3.14680e19 + 8.72457e19i) q^{22} +4.21789e20i q^{23} +(-3.73365e20 + 2.19924e20i) q^{24} -9.29120e20 q^{25} +(-1.37768e21 - 4.96905e20i) q^{26} +3.20338e21i q^{27} +(-1.78368e21 + 2.15096e21i) q^{28} -3.89139e21 q^{29} +(-2.03212e20 + 5.63407e20i) q^{30} -8.50780e21i q^{31} +(-6.01907e21 + 3.72964e22i) q^{32} -3.48588e22 q^{33} +(-2.57851e22 - 9.30025e21i) q^{34} +3.86227e21i q^{35} +(4.48090e22 + 3.71576e22i) q^{36} +5.15665e23 q^{37} +(2.63411e23 - 7.30311e23i) q^{38} -5.50447e23i q^{39} +(2.65021e22 + 4.49926e22i) q^{40} +1.29344e24 q^{41} +(-9.87934e23 - 3.56331e23i) q^{42} -5.30732e23i q^{43} +(-1.93996e24 + 2.33943e24i) q^{44} +8.04589e22 q^{45} +(-4.68937e24 + 1.30014e25i) q^{46} -4.10844e23i q^{47} +(-1.39538e25 + 2.62800e24i) q^{48} +1.57669e25 q^{49} +(-2.86395e25 - 1.03298e25i) q^{50} -1.03024e25i q^{51} +(-3.69414e25 - 3.06335e25i) q^{52} +1.20519e26 q^{53} +(-3.56146e25 + 9.87420e25i) q^{54} +4.20068e24i q^{55} +(-7.88945e25 + 4.64714e25i) q^{56} +2.91794e26 q^{57} +(-1.19949e26 - 4.32637e25i) q^{58} -7.03393e26i q^{59} +(-1.25277e25 + 1.51074e25i) q^{60} +6.82535e26 q^{61} +(9.45881e25 - 2.62247e26i) q^{62} +1.41085e26i q^{63} +(-6.00187e26 + 1.08271e27i) q^{64} -6.63320e25 q^{65} +(-1.07450e27 - 3.87553e26i) q^{66} +3.12093e27i q^{67} +(-6.91408e26 - 5.73347e26i) q^{68} -5.19466e27 q^{69} +(-4.29399e25 + 1.19052e26i) q^{70} +1.56169e27i q^{71} +(9.68093e26 + 1.64353e27i) q^{72} -4.03265e27 q^{73} +(1.58950e28 + 5.73306e27i) q^{74} -1.14428e28i q^{75} +(1.62389e28 - 1.95828e28i) q^{76} -7.36588e27 q^{77} +(6.11976e27 - 1.69671e28i) q^{78} +6.28076e27i q^{79} +(3.16688e26 + 1.68151e27i) q^{80} -2.82900e28 q^{81} +(3.98693e28 + 1.43802e28i) q^{82} +6.96821e28i q^{83} +(-2.64907e28 - 2.19673e28i) q^{84} -1.24149e27 q^{85} +(5.90057e27 - 1.63594e28i) q^{86} -4.79254e28i q^{87} +(-8.58072e28 + 5.05431e28i) q^{88} -1.68366e28 q^{89} +(2.48009e27 + 8.94527e26i) q^{90} -1.16313e29i q^{91} +(-2.89093e29 + 3.48622e29i) q^{92} +1.04780e29 q^{93} +(4.56768e27 - 1.26640e28i) q^{94} -3.51628e28i q^{95} +(-4.59333e29 - 7.41293e28i) q^{96} +9.73339e29 q^{97} +(4.86002e29 + 1.75293e29i) q^{98} +1.53446e29i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 24476 q^{2} - 820787056 q^{4} + 14864798540 q^{5} - 454068012192 q^{6} - 31343321296064 q^{8} - 722181861644898 q^{9}+O(q^{10}) $ 14 * q - 24476 * q^2 - 820787056 * q^4 + 14864798540 * q^5 - 454068012192 * q^6 - 31343321296064 * q^8 - 722181861644898 * q^9	$ 14 q - 24476 q^{2} - 820787056 q^{4} + 14864798540 q^{5} - 454068012192 q^{6} - 31343321296064 q^{8} - 722181861644898 q^{9} - 12\!\cdots\!60 q^{10}+ \cdots + 47\!\cdots\!36 q^{98}+O(q^{100}) $ 14 * q - 24476 * q^2 - 820787056 * q^4 + 14864798540 * q^5 - 454068012192 * q^6 - 31343321296064 * q^8 - 722181861644898 * q^9 - 1287889809124760 * q^10 + 51879382052868480 * q^12 + 73473894124935532 * q^13 + 36761277666527808 * q^14 - 1064191557393108736 * q^16 - 4417201733411195812 * q^17 + 10773613739927673156 * q^18 + 31289641216539815840 * q^20 - 24107806000815293184 * q^21 - 63855041197225323360 * q^22 - 219200204962023547392 * q^24 + 2557307336405009852730 * q^25 + 2662172027973979655720 * q^26 + 2286217156307884458240 * q^28 - 5183126634353006173012 * q^29 - 19995309903793012445760 * q^30 + 42868919292290358744064 * q^32 + 45729663133049254147200 * q^33 + 189270161167001176158280 * q^34 - 265369932957818409094128 * q^36 - 627167100163080968189492 * q^37 - 1048227922470375880434720 * q^38 + 249748411367898391857280 * q^40 + 1494251155359817033760828 * q^41 + 2632732296455102155814400 * q^42 + 724029644533237152067200 * q^44 - 15629634719291168966183700 * q^45 + 6965410628317069602441408 * q^46 + 22826956997174454465976320 * q^48 + 36971394165784621527528302 * q^49 - 6257136580151365293802740 * q^50 - 3584406874106323077960032 * q^52 - 162298735436688848725454068 * q^53 + 103759862824624790541134016 * q^54 - 103480837826586244326484992 * q^56 - 178372120064399401723873920 * q^57 + 292818259345642447695165352 * q^58 + 673940775243590010378428160 * q^60 - 781363600109479145350441172 * q^61 - 700904834820308348700230400 * q^62 - 1886538399231001232282054656 * q^64 - 766208515593499839727344200 * q^65 + 4354147454872998865031212800 * q^66 - 1563708764577905097576648928 * q^68 + 12984546958279555654634831616 * q^69 + 5791600195068600540130627200 * q^70 - 12292930844134853078053553856 * q^72 - 13974688009272270633487568708 * q^73 - 1683916522088046880433965720 * q^74 - 43359191482193415443604585600 * q^76 - 13914563925551368590607269120 * q^77 + 103407672785786602276239960000 * q^78 - 142384583917045013024432289280 * q^80 + 142873441147816769491949878830 * q^81 + 100782649420724457106091722888 * q^82 - 274539668577865429004166211584 * q^84 - 166040172454330922908332123880 * q^85 + 409278053261716222570289186208 * q^86 - 745586494961630729936044285440 * q^88 + 98873747700972853801823899388 * q^89 + 1804754410453947165713321465640 * q^90 - 1825371837423533828188743456000 * q^92 - 123062607213511416597600107520 * q^93 + 2752292471954002780670205710208 * q^94 - 4054034025223909146350873812992 * q^96 - 1029388221334221132711894149732 * q^97 + 4774196460313129800493027312036 * 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 $

$2$	30824.3	+	11117.8i	0.940682	+	0.339288i
$2$	30824.3	+	11117.8i	0.940682	+	0.339288i
$3$			1.23158e7i			0.858306i	0.903232	+	0.429153i	$0.141188\pi$
$3$			1.23158e7i			0.858306i	−0.903232	+	0.429153i	$0.858812\pi$
$4$	8.26531e8	+	6.85396e8i	0.769767	+	0.638325i
$5$	1.48412e9			0.0486316			0.0243158	−	0.999704i	$-0.492259\pi$
$5$	1.48412e9			0.0486316			0.0243158	+	0.999704i	$0.492259\pi$
$6$	−1.36924e11	+	3.79624e11i	−0.291213	+	0.807394i
$7$			2.60240e12i			0.548155i	0.961708	+	0.274078i	$0.0883725\pi$
$7$			2.60240e12i			0.548155i	−0.961708	+	0.274078i	$0.911628\pi$
$8$	1.78571e13	+	3.03161e13i	0.507530	+	0.861634i
$9$	5.42133e13			0.263311
$10$	4.57469e13	+	1.65001e13i	0.0457469	+	0.0165001i
$11$			2.83042e15i			0.677580i	0.940862	+	0.338790i	$0.110018\pi$
$11$			2.83042e15i			0.677580i	−0.940862	+	0.338790i	$0.889982\pi$
$12$	−8.44118e15	+	1.01794e16i	−0.547878	+	0.660696i
$13$	−4.46946e16			−0.873181			−0.436591	−	0.899660i	$-0.643814\pi$
$13$	−4.46946e16			−0.873181			−0.436591	+	0.899660i	$0.643814\pi$
$14$	−2.89330e16	+	8.02171e16i	−0.185983	+	0.515640i
$15$			1.82780e16i			0.0417408i
$16$	2.13385e17	+	1.13300e18i	0.185082	+	0.982723i
$17$	−8.36518e17			−0.292241			−0.146121	−	0.989267i	$-0.546679\pi$
$17$	−8.36518e17			−0.292241			−0.146121	+	0.989267i	$0.546679\pi$
$18$	1.67109e18	+	6.02733e17i	0.247692	+	0.0893382i
$19$		−	2.36927e19i		−	1.56067i	−0.625363	−	0.780334i	$-0.715049\pi$
$19$		−	2.36927e19i		−	1.56067i	0.625363	−	0.780334i	$-0.284951\pi$
$20$	1.22667e18	+	1.01721e18i	0.0374350	+	0.0310428i
$21$	−3.20505e19			−0.470485
$22$	−3.14680e19	+	8.72457e19i	−0.229895	+	0.637388i
$23$			4.21789e20i			1.58190i	0.611883	+	0.790948i	$0.290412\pi$
$23$			4.21789e20i			1.58190i	−0.611883	+	0.790948i	$0.709588\pi$
$24$	−3.73365e20	+	2.19924e20i	−0.739546	+	0.435616i
$25$	−9.29120e20			−0.997635
$26$	−1.37768e21	−	4.96905e20i	−0.821386	−	0.296260i
$27$			3.20338e21i			1.08431i
$28$	−1.78368e21	+	2.15096e21i	−0.349901	+	0.421952i
$29$	−3.89139e21			−0.450957			−0.225478	−	0.974248i	$-0.572395\pi$
$29$	−3.89139e21			−0.450957			−0.225478	+	0.974248i	$0.572395\pi$
$30$	−2.03212e20	+	5.63407e20i	−0.0141622	+	0.0392648i
$31$		−	8.50780e21i		−	0.362570i	−0.983431	−	0.181285i	$-0.941974\pi$
$31$		−	8.50780e21i		−	0.362570i	0.983431	−	0.181285i	$-0.0580257\pi$
$32$	−6.01907e21	+	3.72964e22i	−0.159323	+	0.987226i
$33$	−3.48588e22			−0.581571
$34$	−2.57851e22	−	9.30025e21i	−0.274906	−	0.0991541i
$35$			3.86227e21i			0.0266577i
$36$	4.48090e22	+	3.71576e22i	0.202688	+	0.168078i
$37$	5.15665e23			1.54647			0.773235	−	0.634119i	$-0.218637\pi$
$37$	5.15665e23			1.54647			0.773235	+	0.634119i	$0.218637\pi$
$38$	2.63411e23	−	7.30311e23i	0.529517	−	1.46809i
$39$		−	5.50447e23i		−	0.749457i
$40$	2.65021e22	+	4.49926e22i	0.0246820	+	0.0419026i
$41$	1.29344e24			0.831740			0.415870	−	0.909424i	$-0.363477\pi$
$41$	1.29344e24			0.831740			0.415870	+	0.909424i	$0.363477\pi$
$42$	−9.87934e23	−	3.56331e23i	−0.442577	−	0.159630i
$43$		−	5.30732e23i		−	0.167051i	−0.996506	−	0.0835253i	$-0.973382\pi$
$43$		−	5.30732e23i		−	0.167051i	0.996506	−	0.0835253i	$-0.0266180\pi$
$44$	−1.93996e24	+	2.33943e24i	−0.432516	+	0.521579i
$45$	8.04589e22			0.0128052
$46$	−4.68937e24	+	1.30014e25i	−0.536719	+	1.48806i
$47$		−	4.10844e23i		−	0.0340572i	−0.999855	−	0.0170286i	$-0.994579\pi$
$47$		−	4.10844e23i		−	0.0340572i	0.999855	−	0.0170286i	$-0.00542063\pi$
$48$	−1.39538e25	+	2.62800e24i	−0.843477	+	0.158857i
$49$	1.57669e25			0.699526
$50$	−2.86395e25	−	1.03298e25i	−0.938458	−	0.338486i
$51$		−	1.03024e25i		−	0.250833i
$52$	−3.69414e25	−	3.06335e25i	−0.672146	−	0.557374i
$53$	1.20519e26			1.64785			0.823925	−	0.566700i	$-0.191780\pi$
$53$	1.20519e26			1.64785			0.823925	+	0.566700i	$0.191780\pi$
$54$	−3.56146e25	+	9.87420e25i	−0.367893	+	1.01999i
$55$			4.20068e24i			0.0329518i
$56$	−7.88945e25	+	4.64714e25i	−0.472309	+	0.278205i
$57$	2.91794e26			1.33953
$58$	−1.19949e26	−	4.32637e25i	−0.424207	−	0.153004i
$59$		−	7.03393e26i		−	1.92494i	−0.271382	−	0.962472i	$-0.587481\pi$
$59$		−	7.03393e26i		−	1.92494i	0.271382	−	0.962472i	$-0.412519\pi$
$60$	−1.25277e25	+	1.51074e25i	−0.0266442	+	0.0321307i
$61$	6.82535e26			1.13286			0.566432	−	0.824109i	$-0.308324\pi$
$61$	6.82535e26			1.13286			0.566432	+	0.824109i	$0.308324\pi$
$62$	9.45881e25	−	2.62247e26i	0.123016	−	0.341063i
$63$			1.41085e26i			0.144335i
$64$	−6.00187e26	+	1.08271e27i	−0.484827	+	0.874610i
$65$	−6.63320e25			−0.0424642
$66$	−1.07450e27	−	3.87553e26i	−0.547074	−	0.197320i
$67$			3.12093e27i			1.26812i	0.773282	+	0.634062i	$0.218614\pi$
$67$			3.12093e27i			1.26812i	−0.773282	+	0.634062i	$0.781386\pi$
$68$	−6.91408e26	−	5.73347e26i	−0.224958	−	0.186545i
$69$	−5.19466e27			−1.35775
$70$	−4.29399e25	+	1.19052e26i	−0.00904463	+	0.0250764i
$71$			1.56169e27i			0.265900i	0.991123	+	0.132950i	$0.0424450\pi$
$71$			1.56169e27i			0.265900i	−0.991123	+	0.132950i	$0.957555\pi$
$72$	9.68093e26	+	1.64353e27i	0.133638	+	0.226877i
$73$	−4.03265e27			−0.452634			−0.226317	−	0.974054i	$-0.572669\pi$
$73$	−4.03265e27			−0.452634			−0.226317	+	0.974054i	$0.572669\pi$
$74$	1.58950e28	+	5.73306e27i	1.45474	+	0.524699i
$75$		−	1.14428e28i		−	0.856276i
$76$	1.62389e28	−	1.95828e28i	0.996214	−	1.20135i
$77$	−7.36588e27			−0.371419
$78$	6.11976e27	−	1.69671e28i	0.254282	−	0.705001i
$79$			6.28076e27i			0.215579i	0.994174	+	0.107789i	$0.0343772\pi$
$79$			6.28076e27i			0.215579i	−0.994174	+	0.107789i	$0.965623\pi$
$80$	3.16688e26	+	1.68151e27i	0.00900082	+	0.0477914i
$81$	−2.82900e28			−0.667357
$82$	3.98693e28	+	1.43802e28i	0.782404	+	0.282200i
$83$			6.96821e28i			1.14012i	0.821604	+	0.570059i	$0.193080\pi$
$83$			6.96821e28i			1.14012i	−0.821604	+	0.570059i	$0.806920\pi$
$84$	−2.64907e28	−	2.19673e28i	−0.362164	−	0.300322i
$85$	−1.24149e27			−0.0142122
$86$	5.90057e27	−	1.63594e28i	0.0566784	−	0.157142i
$87$		−	4.79254e28i		−	0.387059i
$88$	−8.58072e28	+	5.05431e28i	−0.583826	+	0.343892i
$89$	−1.68366e28			−0.0966949			−0.0483474	−	0.998831i	$-0.515395\pi$
$89$	−1.68366e28			−0.0966949			−0.0483474	+	0.998831i	$0.515395\pi$
$90$	2.48009e27	+	8.94527e26i	0.0120456	+	0.00434466i
$91$		−	1.16313e29i		−	0.478639i
$92$	−2.89093e29	+	3.48622e29i	−1.00976	+	1.21769i
$93$	1.04780e29			0.311196
$94$	4.56768e27	−	1.26640e28i	0.0115552	−	0.0320370i
$95$		−	3.51628e28i		−	0.0758978i
$96$	−4.59333e29	−	7.41293e28i	−0.847343	−	0.136748i
$97$	9.73339e29			1.53705			0.768525	−	0.639820i	$-0.220991\pi$
$97$	9.73339e29			1.53705			0.768525	+	0.639820i	$0.220991\pi$
$98$	4.86002e29	+	1.75293e29i	0.658032	+	0.237341i
$99$			1.53446e29i			0.178414i
$100$	−7.67946e29	−	6.36816e29i	−0.767946	−	0.636816i
$101$	1.10122e30			0.948534			0.474267	−	0.880381i	$-0.342713\pi$
$101$	1.10122e30			0.948534			0.474267	+	0.880381i	$0.342713\pi$
$102$	1.14540e29	−	3.17563e29i	0.0851046	−	0.235954i
$103$		−	1.81135e30i		−	1.16263i	−0.813677	−	0.581317i	$-0.802538\pi$
$103$		−	1.81135e30i		−	1.16263i	0.813677	−	0.581317i	$-0.197462\pi$
$104$	−7.98116e29	−	1.35496e30i	−0.443165	−	0.752363i
$105$	−4.75668e28			−0.0228804
$106$	3.71491e30	+	1.33991e30i	1.55010	+	0.559096i
$107$			2.92961e29i			0.106183i	0.998590	+	0.0530913i	$0.0169074\pi$
$107$			2.92961e29i			0.106183i	−0.998590	+	0.0530913i	$0.983093\pi$
$108$	−2.19559e30	+	2.64769e30i	−0.692141	+	0.834664i
$109$	−3.71369e30			−1.01955			−0.509774	−	0.860308i	$-0.670271\pi$
$109$	−3.71369e30			−1.01955			−0.509774	+	0.860308i	$0.670271\pi$
$110$	−4.67023e28	+	1.29483e29i	−0.0111802	+	0.0309972i
$111$			6.35080e30i			1.32735i
$112$	−2.94853e30	+	5.55313e29i	−0.538685	+	0.101454i
$113$	−1.01435e31			−1.62185			−0.810926	−	0.585148i	$-0.801036\pi$
$113$	−1.01435e31			−1.62185			−0.810926	+	0.585148i	$0.801036\pi$
$114$	8.99433e30	+	3.24410e30i	1.26007	+	0.454487i
$115$			6.25985e29i			0.0769301i
$116$	−3.21636e30	−	2.66715e30i	−0.347132	−	0.287857i
$117$	−2.42304e30			−0.229918
$118$	7.82018e30	−	2.16816e31i	0.653111	−	1.81076i
$119$		−	2.17696e30i		−	0.160194i
$120$	−5.54118e29	+	3.26393e29i	−0.0359653	+	0.0211847i
$121$	9.43813e30			0.540885
$122$	2.10387e31	+	7.58829e30i	1.06566	+	0.384367i
$123$			1.59297e31i			0.713888i
$124$	5.83122e30	−	7.03196e30i	0.231438	−	0.279094i
$125$	−2.76112e30			−0.0971482
$126$	−1.56855e30	+	4.34883e30i	−0.0489712	+	0.135773i
$127$		−	6.67664e31i		−	1.85141i	−0.378250	−	0.925703i	$-0.623474\pi$
$127$		−	6.67664e31i		−	1.85141i	0.378250	−	0.925703i	$-0.376526\pi$
$128$	−3.05377e31	+	2.67011e31i	−0.752813	+	0.658234i
$129$	6.53636e30			0.143381
$130$	−2.04464e30	−	7.37466e29i	−0.0399453	−	0.0144076i
$131$			4.13459e31i			0.720050i	0.932943	+	0.360025i	$0.117232\pi$
$131$			4.13459e31i			0.720050i	−0.932943	+	0.360025i	$0.882768\pi$
$132$	−2.88118e31	−	2.38921e31i	−0.447674	−	0.371231i
$133$	6.16579e31			0.855488
$134$	−3.46979e31	+	9.62004e31i	−0.430260	+	1.19290i
$135$			4.75420e30i			0.0527316i
$136$	−1.49378e31	−	2.53599e31i	−0.148321	−	0.251805i
$137$	5.24365e31			0.466472			0.233236	−	0.972420i	$-0.425069\pi$
$137$	5.24365e31			0.466472			0.233236	+	0.972420i	$0.425069\pi$
$138$	−1.60122e32	−	5.77531e31i	−1.27721	−	0.460669i
$139$			4.02940e31i			0.288416i	0.989547	+	0.144208i	$0.0460634\pi$
$139$			4.02940e31i			0.288416i	−0.989547	+	0.144208i	$0.953937\pi$
$140$	−2.64719e30	+	3.19228e30i	−0.0170163	+	0.0205202i
$141$	5.05985e30			0.0292315
$142$	−1.73625e31	+	4.81379e31i	−0.0902168	+	0.250128i
$143$		−	1.26504e32i		−	0.591650i
$144$	1.15683e31	+	6.14238e31i	0.0487340	+	0.258761i
$145$	−5.77529e30			−0.0219308
$146$	−1.24304e32	−	4.48342e31i	−0.425785	−	0.153574i
$147$			1.94181e32i			0.600407i
$148$	4.26213e32	+	3.53435e32i	1.19042	+	0.987151i
$149$	3.21713e30			0.00812221			0.00406110	−	0.999992i	$-0.498707\pi$
$149$	3.21713e30			0.00812221			0.00406110	+	0.999992i	$0.498707\pi$
$150$	1.27219e32	−	3.52717e32i	0.290525	−	0.805484i
$151$		−	5.69412e32i		−	1.17699i	−0.808501	−	0.588494i	$-0.799721\pi$
$151$		−	5.69412e32i		−	1.17699i	0.808501	−	0.588494i	$-0.200279\pi$
$152$	7.18270e32	−	4.23083e32i	1.34473	−	0.792086i
$153$	−4.53504e31			−0.0769502
$154$	−2.27048e32	−	8.18924e31i	−0.349387	−	0.126018i
$155$		−	1.26266e31i		−	0.0176324i
$156$	3.77275e32	−	4.54962e32i	0.478397	−	0.576907i
$157$	−9.36107e32			−1.07853			−0.539263	−	0.842137i	$-0.681297\pi$
$157$	−9.36107e32			−1.07853			−0.539263	+	0.842137i	$0.681297\pi$
$158$	−6.98283e31	+	1.93600e32i	−0.0731434	+	0.202791i
$159$			1.48428e33i			1.41436i
$160$	−8.93300e30	+	5.53522e31i	−0.00774815	+	0.0480104i
$161$	−1.09766e33			−0.867125
$162$	−8.72020e32	−	3.14523e32i	−0.627771	−	0.226427i
$163$			2.09438e33i			1.37480i	0.726278	+	0.687402i	$0.241249\pi$
$163$			2.09438e33i			1.37480i	−0.726278	+	0.687402i	$0.758751\pi$
$164$	1.06907e33	+	8.86518e32i	0.640246	+	0.530921i
$165$	−5.17345e31			−0.0282827
$166$	−7.74712e32	+	2.14790e33i	−0.386829	+	1.07249i
$167$		−	3.15884e33i		−	1.44139i	−0.693254	−	0.720693i	$-0.743824\pi$
$167$		−	3.15884e33i		−	1.44139i	0.693254	−	0.720693i	$-0.256176\pi$
$168$	−5.72330e32	−	9.71646e32i	−0.238785	−	0.405386i
$169$	−6.22392e32			−0.237555
$170$	−3.82681e31	−	1.38027e31i	−0.0133691	−	0.00482202i
$171$		−	1.28446e33i		−	0.410940i
$172$	3.63762e32	−	4.38666e32i	0.106633	−	0.128590i
$173$	4.17334e33			1.12148			0.560741	−	0.827991i	$-0.310516\pi$
$173$	4.17334e33			1.12148			0.560741	+	0.827991i	$0.310516\pi$
$174$	5.32826e32	−	1.47727e33i	0.131325	−	0.364100i
$175$		−	2.41794e33i		−	0.546859i
$176$	−3.20687e33	+	6.03969e32i	−0.665873	+	0.125408i
$177$	8.66282e33			1.65219
$178$	−5.18975e32	−	1.87186e32i	−0.0909592	−	0.0328075i
$179$		−	1.87425e33i		−	0.302017i	−0.988532	−	0.151009i	$-0.951748\pi$
$179$		−	1.87425e33i		−	0.302017i	0.988532	−	0.151009i	$-0.0482521\pi$
$180$	6.65018e31	+	5.51463e31i	0.00985702	+	0.00817389i
$181$	1.15580e33			0.157653			0.0788266	−	0.996888i	$-0.474883\pi$
$181$	1.15580e33			0.157653			0.0788266	+	0.996888i	$0.474883\pi$
$182$	1.29315e33	−	3.58527e33i	0.162397	−	0.450247i
$183$			8.40593e33i			0.972343i
$184$	−1.27870e34	+	7.53194e33i	−1.36302	+	0.802860i
$185$	7.65307e32			0.0752073
$186$	3.22977e33	+	1.16492e33i	0.292737	+	0.105585i
$187$		−	2.36770e33i		−	0.198017i
$188$	2.81591e32	−	3.39575e32i	0.0217396	−	0.0262161i
$189$	−8.33648e33			−0.594369
$190$	3.90933e32	−	1.08387e33i	0.0257512	−	0.0713957i
$191$		−	6.72458e33i		−	0.409416i	−0.978823	−	0.204708i	$-0.934375\pi$
$191$		−	6.72458e33i		−	0.409416i	0.978823	−	0.204708i	$-0.0656245\pi$
$192$	−1.33345e34	−	7.39176e33i	−0.750683	−	0.416130i
$193$	−1.72119e34			−0.896331			−0.448166	−	0.893951i	$-0.647923\pi$
$193$	−1.72119e34			−0.896331			−0.448166	+	0.893951i	$0.647923\pi$
$194$	3.00025e34	+	1.08214e34i	1.44588	+	0.521503i
$195$		−	8.16929e32i		−	0.0364473i
$196$	1.30318e34	+	1.08065e34i	0.538472	+	0.446525i
$197$	−3.74886e33			−0.143518			−0.0717588	−	0.997422i	$-0.522861\pi$
$197$	−3.74886e33			−0.143518			−0.0717588	+	0.997422i	$0.522861\pi$
$198$	−1.70599e33	+	4.72987e33i	−0.0605338	+	0.167831i
$199$			3.68315e34i			1.21178i	0.795549	+	0.605890i	$0.207183\pi$
$199$			3.68315e34i			1.21178i	−0.795549	+	0.605890i	$0.792817\pi$
$200$	−1.65914e34	−	2.81673e34i	−0.506329	−	0.859596i
$201$	−3.84366e34			−1.08844
$202$	3.39443e34	+	1.22431e34i	0.892270	+	0.321827i
$203$		−	1.01270e34i		−	0.247194i
$204$	7.06120e33	−	8.51521e33i	0.160113	−	0.193083i
$205$	1.91961e33			0.0404489
$206$	2.01382e34	−	5.58335e34i	0.394468	−	1.09367i
$207$			2.28666e34i			0.416530i
$208$	−9.53714e33	−	5.06390e34i	−0.161610	−	0.858095i
$209$	6.70603e34			1.05748
$210$	−1.46621e33	−	5.28838e32i	−0.0215232	−	0.00776306i
$211$		−	7.41577e34i		−	1.01372i	−0.862028	−	0.506861i	$-0.830806\pi$
$211$		−	7.41577e34i		−	1.01372i	0.862028	−	0.506861i	$-0.169194\pi$
$212$	9.96127e34	+	8.26033e34i	1.26846	+	1.05186i
$213$	−1.92333e34			−0.228224
$214$	−3.25709e33	+	9.03032e33i	−0.0360265	+	0.0998842i
$215$		−	7.87669e32i		−	0.00812394i
$216$	−9.71139e34	+	5.72032e34i	−0.934276	+	0.550318i
$217$	2.21407e34			0.198745
$218$	−1.14472e35	−	4.12880e34i	−0.959071	−	0.345921i
$219$		−	4.96651e34i		−	0.388499i
$220$	−2.87913e33	+	3.47199e33i	−0.0210340	+	0.0253652i
$221$	3.73878e34			0.255180
$222$	−7.06069e34	+	1.95759e35i	−0.450353	+	1.24861i
$223$			7.88557e34i			0.470176i	0.971974	+	0.235088i	$0.0755378\pi$
$223$			7.88557e34i			0.470176i	−0.971974	+	0.235088i	$0.924462\pi$
$224$	−9.70600e34	−	1.56640e34i	−0.541153	−	0.0873339i
$225$	−5.03707e34			−0.262688
$226$	−3.12666e35	−	1.12773e35i	−1.52565	−	0.550276i
$227$			1.28465e35i			0.586675i	0.956009	+	0.293338i	$0.0947660\pi$
$227$			1.28465e35i			0.586675i	−0.956009	+	0.293338i	$0.905234\pi$
$228$	2.41176e35	+	1.99994e35i	1.03113	+	0.855057i
$229$	1.63336e35			0.653958			0.326979	−	0.945032i	$-0.393969\pi$
$229$	1.63336e35			0.653958			0.326979	+	0.945032i	$0.393969\pi$
$230$	−6.95958e33	+	1.92955e34i	−0.0261015	+	0.0723668i
$231$		−	9.07164e34i		−	0.318791i
$232$	−6.94891e34	−	1.17972e35i	−0.228874	−	0.388560i
$233$	3.93340e35			1.21459			0.607294	−	0.794477i	$-0.292255\pi$
$233$	3.93340e35			1.21459			0.607294	+	0.794477i	$0.292255\pi$
$234$	−7.46884e34	−	2.69389e34i	−0.216280	−	0.0780084i
$235$		−	6.09741e32i		−	0.00165626i
$236$	4.82103e35	−	5.81376e35i	1.22874	−	1.48176i
$237$	−7.73523e34			−0.185033
$238$	2.42030e34	−	6.71031e34i	0.0543518	−	0.150691i
$239$		−	7.72783e35i		−	1.62963i	−0.579720	−	0.814816i	$-0.696838\pi$
$239$		−	7.72783e35i		−	1.62963i	0.579720	−	0.814816i	$-0.303162\pi$
$240$	−2.07091e34	+	3.90026e33i	−0.0410196	+	0.00772546i
$241$	−6.39528e35			−1.19016			−0.595078	−	0.803668i	$-0.702879\pi$
$241$	−6.39528e35			−1.19016			−0.595078	+	0.803668i	$0.702879\pi$
$242$	2.90923e35	+	1.04931e35i	0.508801	+	0.183516i
$243$			3.11135e35i			0.511511i
$244$	5.64136e35	+	4.67807e35i	0.872040	+	0.723135i
$245$	2.33999e34			0.0340191
$246$	−1.77103e35	+	4.91021e35i	−0.242214	+	0.671542i
$247$			1.05894e36i			1.36275i
$248$	2.57923e35	−	1.51925e35i	0.312403	−	0.184015i
$249$	−8.58188e35			−0.978571
$250$	−8.51094e34	−	3.06975e34i	−0.0913856	−	0.0329612i
$251$		−	8.66435e33i		−	0.00876254i	−0.999990	−	0.00438127i	$-0.998605\pi$
$251$		−	8.66435e33i		−	0.00876254i	0.999990	−	0.00438127i	$-0.00139461\pi$
$252$	−9.66989e34	+	1.16611e35i	−0.0921327	+	0.111104i
$253$	−1.19384e36			−1.07186
$254$	7.42295e35	−	2.05802e36i	0.628161	−	1.74159i
$255$		−	1.52899e34i		−	0.0121984i
$256$	−1.23816e36	+	4.83531e35i	−0.931489	+	0.363768i
$257$	9.31173e35			0.660744			0.330372	−	0.943851i	$-0.392826\pi$
$257$	9.31173e35			0.660744			0.330372	+	0.943851i	$0.392826\pi$
$258$	2.01479e35	+	7.26700e34i	0.134876	+	0.0486474i
$259$			1.34197e36i			0.847706i
$260$	−5.48254e34	−	4.54637e34i	−0.0326875	−	0.0271060i
$261$	−2.10965e35			−0.118742
$262$	−4.59675e35	+	1.27446e36i	−0.244305	+	0.677338i
$263$		−	1.67601e36i		−	0.841278i	−0.907228	−	0.420639i	$-0.861806\pi$
$263$		−	1.67601e36i		−	0.841278i	0.907228	−	0.420639i	$-0.138194\pi$
$264$	−6.22477e35	−	1.05678e36i	−0.295165	−	0.501102i
$265$	1.78864e35			0.0801375
$266$	1.90056e36	+	6.85500e35i	0.804743	+	0.290257i
$267$		−	2.07355e35i		−	0.0829938i
$268$	−2.13907e36	+	2.57954e36i	−0.809476	+	0.976160i
$269$	4.20481e36			1.50474			0.752372	−	0.658739i	$-0.228910\pi$
$269$	4.20481e36			1.50474			0.752372	+	0.658739i	$0.228910\pi$
$270$	−5.28562e34	+	1.46545e35i	−0.0178912	+	0.0496037i
$271$		−	1.99698e36i		−	0.639490i	−0.947504	−	0.319745i	$-0.896403\pi$
$271$		−	1.99698e36i		−	0.639490i	0.947504	−	0.319745i	$-0.103597\pi$
$272$	−1.78500e35	−	9.47777e35i	−0.0540886	−	0.287192i
$273$	1.43248e36			0.410819
$274$	1.61632e36	+	5.82979e35i	0.438802	+	0.158268i
$275$		−	2.62980e36i		−	0.675977i
$276$	−4.29354e36	−	3.56040e36i	−1.04515	−	0.866687i
$277$	1.56415e36			0.360646			0.180323	−	0.983607i	$-0.442286\pi$
$277$	1.56415e36			0.360646			0.180323	+	0.983607i	$0.442286\pi$
$278$	−4.47981e35	+	1.24204e36i	−0.0978561	+	0.271308i
$279$		−	4.61236e35i		−	0.0954685i
$280$	−1.17089e35	+	6.89690e34i	−0.0229691	+	0.0135296i
$281$	2.24269e36			0.417037			0.208518	−	0.978018i	$-0.433136\pi$
$281$	2.24269e36			0.417037			0.208518	+	0.978018i	$0.433136\pi$
$282$	1.55966e35	+	5.62544e34i	0.0274976	+	0.00991791i
$283$			2.21012e36i			0.369504i	0.982785	+	0.184752i	$0.0591482\pi$
$283$			2.21012e36i			0.369504i	−0.982785	+	0.184752i	$0.940852\pi$
$284$	−1.07037e36	+	1.29078e36i	−0.169731	+	0.204681i
$285$	4.33056e35			0.0651435
$286$	1.40645e36	−	3.89941e36i	0.200740	−	0.556555i
$287$			3.36604e36i			0.455923i
$288$	−3.26313e35	+	2.02196e36i	−0.0419515	+	0.259947i
$289$	−7.49370e36			−0.914595
$290$	−1.78019e35	−	6.42085e34i	−0.0206299	−	0.00744085i
$291$			1.19874e37i			1.31926i
$292$	−3.33311e36	−	2.76396e36i	−0.348423	−	0.288928i
$293$	−1.28230e37			−1.27343			−0.636713	−	0.771101i	$-0.719707\pi$
$293$	−1.28230e37			−1.27343			−0.636713	+	0.771101i	$0.719707\pi$
$294$	−2.15886e36	+	5.98548e36i	−0.203711	+	0.564793i
$295$		−	1.04392e36i		−	0.0936130i
$296$	9.20828e36	+	1.56329e37i	0.784880	+	1.33249i
$297$	−9.06692e36			−0.734705
$298$	9.91656e34	+	3.57674e34i	0.00764042	+	0.00275577i
$299$		−	1.88517e37i		−	1.38128i
$300$	7.84286e36	−	9.45784e36i	0.546583	−	0.659133i
$301$	1.38118e36			0.0915697
$302$	6.33061e36	−	1.75517e37i	0.399339	−	1.10717i
$303$			1.35623e37i			0.814133i
$304$	2.68439e37	−	5.05566e36i	1.53371	−	0.288851i
$305$	1.01296e36			0.0550929
$306$	−1.39789e36	−	5.04197e35i	−0.0723857	−	0.0261083i
$307$		−	2.34281e37i		−	1.15521i	−0.816315	−	0.577607i	$-0.803987\pi$
$307$		−	2.34281e37i		−	1.15521i	0.816315	−	0.577607i	$-0.196013\pi$
$308$	−6.08813e36	−	5.04855e36i	−0.285906	−	0.237086i
$309$	2.23081e37			0.997896
$310$	1.40380e35	−	3.89205e35i	0.00598246	−	0.0165865i
$311$			2.78217e37i			1.12974i	0.825180	+	0.564870i	$0.191074\pi$
$311$			2.78217e37i			1.12974i	−0.825180	+	0.564870i	$0.808926\pi$
$312$	1.66874e37	−	9.82940e36i	0.645758	−	0.380372i
$313$	−1.07520e36			−0.0396574			−0.0198287	−	0.999803i	$-0.506312\pi$
$313$	−1.07520e36			−0.0396574			−0.0198287	+	0.999803i	$0.506312\pi$
$314$	−2.88548e37	−	1.04074e37i	−1.01455	−	0.365931i
$315$			2.09386e35i			0.00701924i
$316$	−4.30481e36	+	5.19124e36i	−0.137609	+	0.165945i
$317$	−7.65364e36			−0.233335			−0.116667	−	0.993171i	$-0.537221\pi$
$317$	−7.65364e36			−0.233335			−0.116667	+	0.993171i	$0.537221\pi$
$318$	−1.65020e37	+	4.57519e37i	−0.479876	+	1.33046i
$319$		−	1.10143e37i		−	0.305559i
$320$	−8.90748e35	+	1.60688e36i	−0.0235779	+	0.0425337i
$321$	−3.60804e36			−0.0911372
$322$	−3.38347e37	−	1.22036e37i	−0.815689	−	0.294205i
$323$			1.98194e37i			0.456092i
$324$	−2.33826e37	−	1.93899e37i	−0.513709	−	0.425991i
$325$	4.15266e37			0.871116
$326$	−2.32849e37	+	6.45576e37i	−0.466455	+	1.29325i
$327$		−	4.57368e37i		−	0.875084i
$328$	2.30971e37	+	3.92119e37i	0.422133	+	0.716656i
$329$	1.06918e36			0.0186686
$330$	−1.59468e36	−	5.75174e35i	−0.0266051	−	0.00959600i
$331$			1.22768e37i			0.195734i	0.995200	+	0.0978668i	$0.0312019\pi$
$331$			1.22768e37i			0.195734i	−0.995200	+	0.0978668i	$0.968798\pi$
$332$	−4.77599e37	+	5.75944e37i	−0.727767	+	0.877626i
$333$	2.79559e37			0.407202
$334$	3.51193e37	−	9.73689e37i	0.489046	−	1.35589i
$335$			4.63183e36i			0.0616709i
$336$	−6.83909e36	−	3.63133e37i	−0.0870782	−	0.462356i
$337$	−6.79060e36			−0.0826912			−0.0413456	−	0.999145i	$-0.513164\pi$
$337$	−6.79060e36			−0.0826912			−0.0413456	+	0.999145i	$0.513164\pi$
$338$	−1.91848e37	−	6.91963e36i	−0.223464	−	0.0805995i
$339$		−	1.24925e38i		−	1.39205i
$340$	−1.02613e36	−	8.50914e35i	−0.0109400	−	0.00907198i
$341$	2.40807e37			0.245670
$342$	1.42804e37	−	3.95926e37i	0.139427	−	0.386564i
$343$			9.96880e37i			0.931604i
$344$	1.60897e37	−	9.47734e36i	0.143937	−	0.0847832i
$345$	−7.70948e36			−0.0660296
$346$	1.28640e38	+	4.63984e37i	1.05496	+	0.380506i
$347$			2.16072e38i			1.69690i	0.529277	+	0.848449i	$0.322463\pi$
$347$			2.16072e38i			1.69690i	−0.529277	+	0.848449i	$0.677537\pi$
$348$	3.28479e37	−	3.96119e37i	0.247070	−	0.297945i
$349$	1.66055e37			0.119639			0.0598193	−	0.998209i	$-0.480948\pi$
$349$	1.66055e37			0.119639			0.0598193	+	0.998209i	$0.480948\pi$
$350$	2.68822e37	−	7.45313e37i	0.185543	−	0.514420i
$351$		−	1.43174e38i		−	0.946797i
$352$	−1.05564e38	−	1.70365e37i	−0.668925	−	0.107954i
$353$	−2.28076e38			−1.38503			−0.692514	−	0.721404i	$-0.743497\pi$
$353$	−2.28076e38			−1.38503			−0.692514	+	0.721404i	$0.743497\pi$
$354$	2.67025e38	+	9.63115e37i	1.55419	+	0.560569i
$355$			2.31773e36i			0.0129311i
$356$	−1.39159e37	−	1.15397e37i	−0.0744325	−	0.0617228i
$357$	2.68109e37			0.137495
$358$	2.08375e37	−	5.77723e37i	0.102471	−	0.284102i
$359$		−	2.56003e38i		−	1.20734i	−0.797235	−	0.603669i	$-0.793705\pi$
$359$		−	2.56003e38i		−	1.20734i	0.797235	−	0.603669i	$-0.206295\pi$
$360$	1.43676e36	+	2.43920e36i	0.00649902	+	0.0110334i
$361$	−3.30878e38			−1.43569
$362$	3.56266e37	+	1.28499e37i	0.148302	+	0.0534899i
$363$			1.16238e38i			0.464245i
$364$	7.97206e37	−	9.61364e37i	0.305527	−	0.368440i
$365$	−5.98493e36			−0.0220123
$366$	−9.34555e37	+	2.59107e38i	−0.329905	+	0.914666i
$367$			3.55222e38i			1.20367i	0.798619	+	0.601837i	$0.205564\pi$
$367$			3.55222e38i			1.20367i	−0.798619	+	0.601837i	$0.794436\pi$
$368$	−4.77888e38	+	9.00034e37i	−1.55457	+	0.292780i
$369$	7.01215e37			0.219006
$370$	2.35901e37	+	8.50854e36i	0.0707462	+	0.0255170i
$371$			3.13639e38i			0.903277i
$372$	8.66039e37	+	7.18159e37i	0.239549	+	0.198644i
$373$	1.34477e38			0.357286			0.178643	−	0.983914i	$-0.442829\pi$
$373$	1.34477e38			0.357286			0.178643	+	0.983914i	$0.442829\pi$
$374$	2.63236e37	−	7.29826e37i	0.0671848	−	0.186271i
$375$		−	3.40052e37i		−	0.0833829i
$376$	1.24552e37	−	7.33649e36i	0.0293448	−	0.0172850i
$377$	1.73924e38			0.393767
$378$	−2.56966e38	−	9.26834e37i	−0.559112	−	0.201662i
$379$		−	6.57015e38i		−	1.37400i	−0.726656	−	0.687001i	$-0.758927\pi$
$379$		−	6.57015e38i		−	1.37400i	0.726656	−	0.687001i	$-0.241073\pi$
$380$	2.41004e37	−	2.90631e37i	0.0484475	−	0.0584236i
$381$	8.22278e38			1.58907
$382$	7.47626e37	−	2.07280e38i	0.138910	−	0.385131i
$383$		−	4.93610e38i		−	0.881866i	−0.897540	−	0.440933i	$-0.854648\pi$
$383$		−	4.93610e38i		−	0.881866i	0.897540	−	0.440933i	$-0.145352\pi$
$384$	−3.28845e38	−	3.76095e38i	−0.564966	−	0.646144i
$385$	−1.09318e37			−0.0180627
$386$	−5.30544e38	−	1.91358e38i	−0.843163	−	0.304115i
$387$		−	2.87727e37i		−	0.0439862i
$388$	8.04495e38	+	6.67123e38i	1.18317	+	0.981138i
$389$	9.24763e38			1.30854			0.654269	−	0.756262i	$-0.272976\pi$
$389$	9.24763e38			1.30854			0.654269	+	0.756262i	$0.272976\pi$
$390$	9.08245e36	−	2.51812e37i	0.0123661	−	0.0342853i
$391$		−	3.52835e38i		−	0.462296i
$392$	2.81551e38	+	4.77989e38i	0.355030	+	0.602736i
$393$	−5.09205e38			−0.618023
$394$	−1.15556e38	−	4.16790e37i	−0.135005	−	0.0486939i
$395$			9.32139e36i			0.0104839i
$396$	−1.05172e38	+	1.26828e38i	−0.113886	+	0.137337i
$397$	1.07073e38			0.111641			0.0558205	−	0.998441i	$-0.482223\pi$
$397$	1.07073e38			0.111641			0.0558205	+	0.998441i	$0.482223\pi$
$398$	−4.09485e38	+	1.13530e39i	−0.411143	+	1.13990i
$399$			7.59364e38i			0.734271i
$400$	−1.98260e38	−	1.05270e39i	−0.184644	−	0.980399i
$401$	−1.55709e39			−1.39685			−0.698423	−	0.715685i	$-0.746115\pi$
$401$	−1.55709e39			−1.39685			−0.698423	+	0.715685i	$0.746115\pi$
$402$	−1.18478e39	−	4.27331e38i	−1.02388	−	0.369295i
$403$			3.80253e38i			0.316589i
$404$	9.10191e38	+	7.54772e38i	0.730150	+	0.605473i
$405$	−4.19858e37			−0.0324546
$406$	1.12590e38	−	3.12156e38i	0.0838702	−	0.232531i
$407$			1.45955e39i			1.04786i
$408$	3.12327e38	−	1.83970e38i	0.216126	−	0.127305i
$409$	−2.63744e39			−1.75927			−0.879637	−	0.475646i	$-0.842214\pi$
$409$	−2.63744e39			−1.75927			−0.879637	+	0.475646i	$0.842214\pi$
$410$	5.91708e37	+	2.13419e37i	0.0380495	+	0.0137238i
$411$			6.45795e38i			0.400375i
$412$	1.24149e39	−	1.49713e39i	0.742139	−	0.894957i
$413$	1.83051e39			1.05517
$414$	−2.54226e38	+	7.04846e38i	−0.141324	+	0.391822i
$415$			1.03417e38i			0.0554458i
$416$	2.69019e38	−	1.66694e39i	0.139118	−	0.862028i
$417$	−4.96252e38			−0.247549
$418$	2.06709e39	+	7.45563e38i	0.994751	+	0.358790i
$419$		−	3.43579e39i		−	1.59521i	−0.603183	−	0.797603i	$-0.706101\pi$
$419$		−	3.43579e39i		−	1.59521i	0.603183	−	0.797603i	$-0.293899\pi$
$420$	−3.93154e37	−	3.26021e37i	−0.0176126	−	0.0146052i
$421$	−1.12881e39			−0.487968			−0.243984	−	0.969779i	$-0.578454\pi$
$421$	−1.12881e39			−0.487968			−0.243984	+	0.969779i	$0.578454\pi$
$422$	8.24470e38	−	2.28586e39i	0.343944	−	0.953591i
$423$		−	2.22732e37i		−	0.00896762i
$424$	2.15212e39	+	3.65366e39i	0.836332	+	1.41984i
$425$	7.77226e38			0.291550
$426$	−5.92854e38	−	2.13833e38i	−0.214686	−	0.0774337i
$427$			1.77623e39i			0.620985i
$428$	−2.00795e38	+	2.42142e38i	−0.0677791	+	0.0817359i
$429$	1.55800e39			0.507817
$430$	8.75714e36	−	2.42793e37i	0.00275636	−	0.00764205i
$431$		−	2.68905e39i		−	0.817409i	−0.912667	−	0.408704i	$-0.865981\pi$
$431$		−	2.68905e39i		−	0.817409i	0.912667	−	0.408704i	$-0.134019\pi$
$432$	−3.62944e39	+	6.83553e38i	−1.06557	+	0.200686i
$433$	−4.92725e39			−1.39729			−0.698645	−	0.715469i	$-0.746213\pi$
$433$	−4.92725e39			−1.39729			−0.698645	+	0.715469i	$0.746213\pi$
$434$	6.82471e38	+	2.46156e38i	0.186956	+	0.0674318i
$435$		−	7.11270e37i		−	0.0188233i
$436$	−3.06948e39	−	2.54535e39i	−0.784814	−	0.650803i
$437$	9.99333e39			2.46882
$438$	5.52167e38	−	1.53089e39i	0.131813	−	0.365454i
$439$			5.52011e39i			1.27344i	0.771093	+	0.636722i	$0.219710\pi$
$439$			5.52011e39i			1.27344i	−0.771093	+	0.636722i	$0.780290\pi$
$440$	−1.27348e38	+	7.50120e37i	−0.0283924	+	0.0167240i
$441$	8.54773e38			0.184193
$442$	1.15245e39	+	4.15670e38i	0.240043	+	0.0865795i
$443$		−	5.23056e39i		−	1.05316i	−0.850127	−	0.526578i	$-0.823475\pi$
$443$		−	5.23056e39i		−	1.05316i	0.850127	−	0.526578i	$-0.176525\pi$
$444$	−4.35282e39	+	5.24913e39i	−0.847278	+	1.02175i
$445$	−2.49875e37			−0.00470243
$446$	−8.76702e38	+	2.43067e39i	−0.159525	+	0.442286i
$447$			3.96213e37i			0.00697134i
$448$	−2.81766e39	−	1.56193e39i	−0.479422	−	0.265760i
$449$	−2.16756e39			−0.356677			−0.178339	−	0.983969i	$-0.557072\pi$
$449$	−2.16756e39			−0.356677			−0.178339	+	0.983969i	$0.557072\pi$
$450$	−1.55264e39	−	5.60011e38i	−0.247106	−	0.0891269i
$451$			3.66097e39i			0.563571i
$452$	−8.38392e39	−	6.95232e39i	−1.24845	−	1.03527i
$453$	7.01274e39			1.01022
$454$	−1.42825e39	+	3.95985e39i	−0.199052	+	0.551875i
$455$		−	1.72622e38i		−	0.0232770i
$456$	5.21059e39	+	8.84603e39i	0.679852	+	1.15419i
$457$	−1.46065e40			−1.84417			−0.922087	−	0.386984i	$-0.873517\pi$
$457$	−1.46065e40			−1.84417			−0.922087	+	0.386984i	$0.873517\pi$
$458$	5.03472e39	+	1.81594e39i	0.615167	+	0.221880i
$459$		−	2.67969e39i		−	0.316879i
$460$	−4.29048e38	+	5.17396e38i	−0.0491065	+	0.0592183i
$461$	1.02830e40			1.13921			0.569605	−	0.821918i	$-0.307096\pi$
$461$	1.02830e40			1.13921			0.569605	+	0.821918i	$0.307096\pi$
$462$	1.00857e39	−	2.79627e39i	0.108162	−	0.299881i
$463$		−	8.34159e39i		−	0.866032i	−0.901386	−	0.433016i	$-0.857449\pi$
$463$		−	8.34159e39i		−	0.866032i	0.901386	−	0.433016i	$-0.142551\pi$
$464$	−8.30364e38	−	4.40896e39i	−0.0834639	−	0.443166i
$465$	1.55506e38			0.0151340
$466$	1.21244e40	+	4.37307e39i	1.14254	+	0.412095i
$467$			9.03610e39i			0.824570i	0.911055	+	0.412285i	$0.135269\pi$
$467$			9.03610e39i			0.824570i	−0.911055	+	0.412285i	$0.864731\pi$
$468$	−2.00272e39	−	1.66074e39i	−0.176983	−	0.146762i
$469$	−8.12191e39			−0.695129
$470$	6.77898e36	−	1.87948e37i	0.000561948	−	0.00155801i
$471$		−	1.15289e40i		−	0.925705i
$472$	2.13241e40	−	1.25606e40i	1.65860	−	0.976966i
$473$	1.50219e39			0.113190
$474$	−2.38433e39	−	8.59988e38i	−0.174057	−	0.0627794i
$475$			2.20134e40i			1.55698i
$476$	1.49208e39	−	1.79932e39i	0.102256	−	0.123312i
$477$	6.53373e39			0.433896
$478$	8.59165e39	−	2.38205e40i	0.552915	−	1.53297i
$479$		−	7.97628e39i		−	0.497471i	−0.968571	−	0.248735i	$-0.919985\pi$
$479$		−	7.97628e39i		−	0.497471i	0.968571	−	0.248735i	$-0.0800150\pi$
$480$	−6.81704e38	−	1.10017e38i	−0.0412076	−	0.00665028i
$481$	−2.30474e40			−1.35035
$482$	−1.97130e40	−	7.11014e39i	−1.11956	−	0.403806i
$483$		−	1.35186e40i		−	0.744258i
$484$	7.80090e39	+	6.46886e39i	0.416356	+	0.345261i
$485$	1.44455e39			0.0747492
$486$	−3.45914e39	+	9.59051e39i	−0.173550	+	0.481169i
$487$			2.63291e40i			1.28086i	0.768016	+	0.640431i	$0.221244\pi$
$487$			2.63291e40i			1.28086i	−0.768016	+	0.640431i	$0.778756\pi$
$488$	1.21881e40	+	2.06918e40i	0.574962	+	0.976114i
$489$	−2.57938e40			−1.18000
$490$	7.21284e38	+	2.60155e38i	0.0320011	+	0.0115423i
$491$			2.35038e40i			1.01138i	0.862714	+	0.505692i	$0.168763\pi$
$491$			2.35038e40i			1.01138i	−0.862714	+	0.505692i	$0.831237\pi$
$492$	−1.09181e40	+	1.31664e40i	−0.455693	+	0.549527i
$493$	3.25522e39			0.131788
$494$	−1.17730e40	+	3.26409e40i	−0.462364	+	1.28191i
$495$			2.27733e38i			0.00867655i
$496$	9.63936e39	−	1.81544e39i	0.356306	−	0.0671051i
$497$	−4.06413e39			−0.145755
$498$	−2.64530e40	−	9.54117e39i	−0.920524	−	0.332018i
$499$		−	3.86480e40i		−	1.30503i	−0.757778	−	0.652513i	$-0.773715\pi$
$499$		−	3.86480e40i		−	1.30503i	0.757778	−	0.652513i	$-0.226285\pi$
$500$	−2.28215e39	−	1.89246e39i	−0.0747814	−	0.0620121i
$501$	3.89035e40			1.23715
$502$	9.63285e37	−	2.67072e38i	0.00297303	−	0.00824277i
$503$		−	2.12328e40i		−	0.636045i	−0.948083	−	0.318023i	$-0.896981\pi$
$503$		−	2.12328e40i		−	0.636045i	0.948083	−	0.318023i	$-0.103019\pi$
$504$	−4.27713e39	+	2.51937e39i	−0.124364	+	0.0732543i
$505$	1.63434e39			0.0461287
$506$	−3.67993e40	−	1.32729e40i	−1.00828	−	0.363670i
$507$		−	7.66523e39i		−	0.203895i
$508$	4.57614e40	−	5.51845e40i	1.18180	−	1.42515i
$509$	3.12051e40			0.782454			0.391227	−	0.920294i	$-0.372051\pi$
$509$	3.12051e40			0.782454			0.391227	+	0.920294i	$0.372051\pi$
$510$	1.69990e38	−	4.71301e38i	0.00413877	−	0.0114748i
$511$		−	1.04946e40i		−	0.248114i
$512$	−4.35413e40	+	1.13886e39i	−0.999658	+	0.0261469i
$513$	7.58968e40			1.69224
$514$	2.87027e40	+	1.03526e40i	0.621550	+	0.224183i
$515$		−	2.68825e39i		−	0.0565408i
$516$	5.40251e39	+	4.48000e39i	0.110370	+	0.0915235i
$517$	1.16286e39			0.0230765
$518$	−1.49197e40	+	4.13651e40i	−0.287617	+	0.797422i
$519$			5.13978e40i			0.962575i
$520$	−1.18450e39	−	2.01093e39i	−0.0215518	−	0.0365886i
$521$	−1.28074e40			−0.226409			−0.113205	−	0.993572i	$-0.536112\pi$
$521$	−1.28074e40			−0.226409			−0.113205	+	0.993572i	$0.536112\pi$
$522$	−6.50285e39	−	2.34547e39i	−0.111698	−	0.0402877i
$523$		−	1.90900e40i		−	0.318626i	−0.987228	−	0.159313i	$-0.949072\pi$
$523$		−	1.90900e40i		−	0.318626i	0.987228	−	0.159313i	$-0.0509279\pi$
$524$	−2.83383e40	+	3.41736e40i	−0.459626	+	0.554270i
$525$	2.97788e40			0.469372
$526$	1.86335e40	−	5.16617e40i	0.285436	−	0.791376i
$527$			7.11693e39i			0.105958i
$528$	−7.43833e39	−	3.94951e40i	−0.107638	−	0.571523i
$529$	−1.06812e41			−1.50240
$530$	5.51337e39	+	1.98858e39i	0.0753839	+	0.0271897i
$531$		−	3.81333e40i		−	0.506858i
$532$	5.09622e40	+	4.22601e40i	0.658527	+	0.546080i
$533$	−5.78096e40			−0.726260
$534$	2.30533e39	−	6.39157e39i	0.0281588	−	0.0780708i
$535$			4.34789e38i			0.00516383i
$536$	−9.46143e40	+	5.57308e40i	−1.09266	+	0.643611i
$537$	2.30828e40			0.259223
$538$	1.29610e41	+	4.67483e40i	1.41549	+	0.510542i
$539$			4.46268e40i			0.473985i
$540$	−3.25851e39	+	3.92949e39i	−0.0336599	+	0.0405910i
$541$	−1.61682e41			−1.62444			−0.812220	−	0.583351i	$-0.801741\pi$
$541$	−1.61682e41			−1.62444			−0.812220	+	0.583351i	$0.801741\pi$
$542$	2.22020e40	−	6.15554e40i	0.216971	−	0.601557i
$543$			1.42345e40i			0.135315i
$544$	5.03506e39	−	3.11991e40i	0.0465609	−	0.288508i
$545$	−5.51155e39			−0.0495822
$546$	4.41553e40	+	1.59261e40i	0.386450	+	0.139386i
$547$			5.59578e40i			0.476487i	0.971205	+	0.238244i	$0.0765716\pi$
$547$			5.59578e40i			0.476487i	−0.971205	+	0.238244i	$0.923428\pi$
$548$	4.33404e40	+	3.59398e40i	0.359074	+	0.297761i
$549$	3.70025e40			0.298295
$550$	2.92376e40	−	8.10617e40i	0.229351	−	0.635880i
$551$			9.21976e40i			0.703794i
$552$	−9.27616e40	−	1.57481e41i	−0.689099	−	1.16989i
$553$	−1.63451e40			−0.118171
$554$	4.82137e40	+	1.73899e40i	0.339253	+	0.122363i
$555$			9.42534e39i			0.0645509i
$556$	−2.76174e40	+	3.33043e40i	−0.184103	+	0.222013i
$557$	−2.68050e39			−0.0173935			−0.00869677	−	0.999962i	$-0.502768\pi$
$557$	−2.68050e39			−0.0173935			−0.00869677	+	0.999962i	$0.502768\pi$
$558$	5.12793e39	−	1.42173e40i	0.0323914	−	0.0898056i
$559$			2.37208e40i			0.145866i
$560$	−4.37596e39	+	8.24150e38i	−0.0261971	+	0.00493385i
$561$	2.91600e40			0.169959
$562$	6.91293e40	+	2.49338e40i	0.392299	+	0.141496i
$563$		−	2.71651e41i		−	1.50102i	−0.660860	−	0.750509i	$-0.729808\pi$
$563$		−	2.71651e41i		−	1.50102i	0.660860	−	0.750509i	$-0.270192\pi$
$564$	4.18212e39	+	3.46801e39i	0.0225014	+	0.0186592i
$565$	−1.50542e40			−0.0788733
$566$	−2.45717e40	+	6.81254e40i	−0.125369	+	0.347586i
$567$		−	7.36220e40i		−	0.365815i
$568$	−4.73442e40	+	2.78872e40i	−0.229109	+	0.134952i
$569$	3.86044e41			1.81951			0.909753	−	0.415151i	$-0.136271\pi$
$569$	3.86044e41			1.81951			0.909753	+	0.415151i	$0.136271\pi$
$570$	1.33486e40	+	4.81463e39i	0.0612794	+	0.0221024i
$571$			1.88696e41i			0.843763i	0.906651	+	0.421882i	$0.138630\pi$
$571$			1.88696e41i			0.843763i	−0.906651	+	0.421882i	$0.861370\pi$
$572$	8.67056e40	−	1.04560e41i	0.377665	−	0.455433i
$573$	8.28183e40			0.351404
$574$	−3.74230e40	+	1.03756e41i	−0.154689	+	0.428878i
$575$		−	3.91893e41i		−	1.57816i
$576$	−3.25381e40	+	5.86975e40i	−0.127660	+	0.230294i
$577$	8.34400e40			0.318961			0.159480	−	0.987201i	$-0.449018\pi$
$577$	8.34400e40			0.318961			0.159480	+	0.987201i	$0.449018\pi$
$578$	−2.30988e41	−	8.33135e40i	−0.860343	−	0.310311i
$579$		−	2.11977e41i		−	0.769327i
$580$	−4.77345e39	−	3.95836e39i	−0.0168816	−	0.0139990i
$581$	−1.81341e41			−0.624962
$582$	−1.33274e41	+	3.69503e41i	−0.447609	+	1.24100i
$583$			3.41119e41i			1.11655i
$584$	−7.20115e40	−	1.22254e41i	−0.229725	−	0.390005i
$585$	−3.59608e39			−0.0111813
$586$	−3.95259e41	−	1.42563e41i	−1.19789	−	0.432059i
$587$			4.78089e41i			1.41233i	0.708046	+	0.706166i	$0.249577\pi$
$587$			4.78089e41i			1.41233i	−0.708046	+	0.706166i	$0.750423\pi$
$588$	−1.33091e41	+	1.60496e41i	−0.383255	+	0.462174i
$589$	−2.01573e41			−0.565852
$590$	1.16061e40	−	3.21780e40i	0.0317618	−	0.0880601i
$591$		−	4.61700e40i		−	0.123182i
$592$	1.10035e41	+	5.84250e41i	0.286224	+	1.51975i
$593$	4.88785e41			1.23965			0.619823	−	0.784742i	$-0.287204\pi$
$593$	4.88785e41			1.23965			0.619823	+	0.784742i	$0.287204\pi$
$594$	−2.79481e41	−	1.00804e41i	−0.691124	−	0.249277i
$595$		−	3.23086e39i		−	0.00779047i
$596$	2.65905e39	+	2.20501e39i	0.00625221	+	0.00518461i
$597$	−4.53608e41			−1.04008
$598$	2.09589e41	−	5.81090e41i	0.468653	−	1.29935i
$599$			1.46289e41i			0.319015i	0.987197	+	0.159507i	$0.0509906\pi$
$599$			1.46289e41i			0.319015i	−0.987197	+	0.159507i	$0.949009\pi$
$600$	3.46901e41	−	2.04336e41i	0.737797	−	0.434586i
$601$	1.23844e40			0.0256896			0.0128448	−	0.999918i	$-0.495911\pi$
$601$	1.23844e40			0.0256896			0.0128448	+	0.999918i	$0.495911\pi$
$602$	4.25738e40	+	1.53556e40i	0.0861380	+	0.0310685i
$603$			1.69196e41i			0.333911i
$604$	3.90273e41	−	4.70637e41i	0.751302	−	0.906007i
$605$	1.40073e40			0.0263041
$606$	−1.50783e41	+	4.18049e41i	−0.276226	+	0.765840i
$607$		−	9.74355e41i		−	1.74135i	−0.491856	−	0.870677i	$-0.663681\pi$
$607$		−	9.74355e41i		−	1.74135i	0.491856	−	0.870677i	$-0.336319\pi$
$608$	8.83652e41	+	1.42608e41i	1.54073	+	0.248651i
$609$	1.24721e41			0.212168
$610$	3.12238e40	+	1.12619e40i	0.0518249	+	0.0186924i
$611$			1.83625e40i			0.0297381i
$612$	−3.74835e40	−	3.10830e40i	−0.0592337	−	0.0491193i
$613$	−1.96840e41			−0.303534			−0.151767	−	0.988416i	$-0.548496\pi$
$613$	−1.96840e41			−0.303534			−0.151767	+	0.988416i	$0.548496\pi$
$614$	2.60469e41	−	7.22156e41i	0.391951	−	1.08669i
$615$			2.36415e40i			0.0347175i
$616$	−1.31533e41	−	2.23305e41i	−0.188506	−	0.320027i
$617$	−2.99374e41			−0.418733			−0.209366	−	0.977837i	$-0.567140\pi$
$617$	−2.99374e41			−0.418733			−0.209366	+	0.977837i	$0.567140\pi$
$618$	6.87631e41	+	2.48017e41i	0.938704	+	0.338575i
$619$		−	2.15729e41i		−	0.287442i	−0.989618	−	0.143721i	$-0.954093\pi$
$619$		−	2.15729e41i		−	0.287442i	0.989618	−	0.143721i	$-0.0459067\pi$
$620$	8.65422e39	−	1.04363e40i	0.0112552	−	0.0135728i
$621$	−1.35115e42			−1.71526
$622$	−3.09317e41	+	8.57585e41i	−0.383308	+	1.06273i
$623$		−	4.38155e40i		−	0.0530038i
$624$	6.23658e41	−	1.17457e41i	0.736508	−	0.138711i
$625$	8.61213e41			0.992911
$626$	−3.31423e40	−	1.19539e40i	−0.0373050	−	0.0134553i
$627$			8.25898e41i			0.907640i
$628$	−7.73721e41	−	6.41604e41i	−0.830213	−	0.688450i
$629$	−4.31363e41			−0.451943
$630$	−2.32792e39	+	6.45418e39i	−0.00238155	+	0.00660288i
$631$			1.79266e42i			1.79084i	0.445218	+	0.895422i	$0.353126\pi$
$631$			1.79266e42i			1.79084i	−0.445218	+	0.895422i	$0.646874\pi$
$632$	−1.90408e41	+	1.12156e41i	−0.185750	+	0.109413i
$633$	9.13308e41			0.870084
$634$	−2.35918e41	−	8.50917e40i	−0.219494	−	0.0791677i
$635$		−	9.90892e40i		−	0.0900369i
$636$	−1.01732e42	+	1.22681e42i	−0.902821	+	1.08873i
$637$	−7.04693e41			−0.610813
$638$	1.22455e41	−	3.39507e41i	0.103673	−	0.287434i
$639$			8.46642e40i			0.0700143i
$640$	−4.53216e40	+	3.96277e40i	−0.0366105	+	0.0320110i
$641$	−8.85152e40			−0.0698469			−0.0349235	−	0.999390i	$-0.511119\pi$
$641$	−8.85152e40			−0.0698469			−0.0349235	+	0.999390i	$0.511119\pi$
$642$	−1.11215e41	−	4.01135e40i	−0.0857312	−	0.0309218i
$643$		−	1.65792e42i		−	1.24853i	−0.781214	−	0.624263i	$-0.785399\pi$
$643$		−	1.65792e42i		−	1.24853i	0.781214	−	0.624263i	$-0.214601\pi$
$644$	−9.07254e41	−	7.52336e41i	−0.667484	−	0.553508i
$645$	9.70074e39			0.00697283
$646$	−2.20348e41	+	6.10918e41i	−0.154747	+	0.429038i
$647$		−	1.82523e42i		−	1.25243i	−0.779649	−	0.626216i	$-0.784603\pi$
$647$		−	1.82523e42i		−	1.25243i	0.779649	−	0.626216i	$-0.215397\pi$
$648$	−5.05178e41	−	8.57643e41i	−0.338704	−	0.575018i
$649$	1.99090e42			1.30430
$650$	1.28003e42	+	4.61685e41i	0.819444	+	0.295560i
$651$			2.72680e41i			0.170584i
$652$	−1.43548e42	+	1.73107e42i	−0.877572	+	1.05828i
$653$	1.52891e42			0.913450			0.456725	−	0.889608i	$-0.349022\pi$
$653$	1.52891e42			0.913450			0.456725	+	0.889608i	$0.349022\pi$
$654$	5.08493e41	−	1.40981e42i	0.296906	−	0.823176i
$655$			6.13621e40i			0.0350172i
$656$	2.76000e41	+	1.46547e42i	0.153940	+	0.817370i
$657$	−2.18623e41			−0.119183
$658$	3.29567e40	+	1.18869e40i	0.0175612	+	0.00633405i
$659$			9.99440e40i			0.0520566i	0.999661	+	0.0260283i	$0.00828600\pi$
$659$			9.99440e40i			0.0520566i	−0.999661	+	0.0260283i	$0.991714\pi$
$660$	−4.27602e40	−	3.54587e40i	−0.0217711	−	0.0180536i
$661$	9.63022e41			0.479308			0.239654	−	0.970858i	$-0.422966\pi$
$661$	9.63022e41			0.479308			0.239654	+	0.970858i	$0.422966\pi$
$662$	−1.36491e41	+	3.78424e41i	−0.0664102	+	0.184123i
$663$			4.60459e41i			0.219022i
$664$	−2.11249e42	+	1.24432e42i	−0.982365	+	0.578644i
$665$	9.15076e40			0.0416038
$666$	8.61720e41	+	3.10808e41i	0.383048	+	0.138159i
$667$		−	1.64135e42i		−	0.713367i
$668$	2.16506e42	−	2.61088e42i	0.920073	−	1.10953i
$669$	−9.71167e41			−0.403555
$670$	−5.14958e40	+	1.42773e41i	−0.0209242	+	0.0580127i
$671$			1.93186e42i			0.767605i
$672$	1.92914e41	−	1.19537e42i	0.0749592	−	0.464475i
$673$	2.95026e42			1.12107			0.560537	−	0.828129i	$-0.310595\pi$
$673$	2.95026e42			1.12107			0.560537	+	0.828129i	$0.310595\pi$
$674$	−2.09315e41	−	7.54965e40i	−0.0777862	−	0.0280562i
$675$		−	2.97633e42i		−	1.08174i
$676$	−5.14426e41	−	4.26585e41i	−0.182862	−	0.151637i
$677$	−3.76886e42			−1.31033			−0.655163	−	0.755487i	$-0.727400\pi$
$677$	−3.76886e42			−1.31033			−0.655163	+	0.755487i	$0.727400\pi$
$678$	1.38889e42	−	3.85072e42i	0.472305	−	1.30947i
$679$			2.53302e42i			0.842542i
$680$	−2.21695e40	−	3.76371e40i	−0.00721309	−	0.0122457i
$681$	−1.58215e42			−0.503547
$682$	7.42269e41	+	2.67724e41i	0.231098	+	0.0833531i
$683$			1.70063e42i			0.517963i	0.965882	+	0.258981i	$0.0833868\pi$
$683$			1.70063e42i			0.517963i	−0.965882	+	0.258981i	$0.916613\pi$
$684$	8.80364e41	−	1.06165e42i	0.262314	−	0.316328i
$685$	7.78220e40			0.0226853
$686$	−1.10831e42	+	3.07281e42i	−0.316082	+	0.876343i
$687$			2.01161e42i			0.561296i
$688$	6.01321e41	−	1.13250e41i	0.164165	−	0.0309180i
$689$	−5.38654e42			−1.43887
$690$	−2.37639e41	−	8.57125e40i	−0.0621129	−	0.0224031i
$691$			1.13167e42i			0.289434i	0.989473	+	0.144717i	$0.0462272\pi$
$691$			1.13167e42i			0.289434i	−0.989473	+	0.144717i	$0.953773\pi$
$692$	3.44939e42	+	2.86039e42i	0.863279	+	0.715870i
$693$	−3.99329e41			−0.0977985
$694$	−2.40224e42	+	6.66025e42i	−0.575738	+	1.59624i
$695$			5.98011e40i			0.0140261i
$696$	1.45291e42	−	8.55810e41i	0.333503	−	0.196444i
$697$	−1.08198e42			−0.243069
$698$	5.11853e41	+	1.84617e41i	0.112542	+	0.0405920i
$699$			4.84427e42i			1.04249i
$700$	1.65725e42	−	1.99850e42i	0.349074	−	0.420954i
$701$	−7.45311e42			−1.53662			−0.768312	−	0.640076i	$-0.778903\pi$
$701$	−7.45311e42			−1.53662			−0.768312	+	0.640076i	$0.778903\pi$
$702$	1.59178e42	−	4.41323e42i	0.321237	−	0.890635i
$703$		−	1.22175e43i		−	2.41353i
$704$	−3.06454e42	−	1.69878e42i	−0.592618	−	0.328509i
$705$	7.50942e39			0.00142157
$706$	−7.03027e42	−	2.53570e42i	−1.30287	−	0.469924i
$707$			2.86581e42i			0.519944i
$708$	7.16009e42	+	5.93746e42i	1.27180	+	1.05463i
$709$	8.47413e42			1.47367			0.736837	−	0.676070i	$-0.236318\pi$
$709$	8.47413e42			1.47367			0.736837	+	0.676070i	$0.236318\pi$
$710$	−2.57680e40	+	7.14423e40i	−0.00438739	+	0.0121641i
$711$			3.40501e41i			0.0567641i
$712$	−3.00653e41	−	5.10418e41i	−0.0490755	−	0.0833156i
$713$	3.58850e42			0.573549
$714$	8.26425e41	+	2.98078e41i	0.129339	+	0.0466505i
$715$		−	1.87747e41i		−	0.0287729i
$716$	1.28460e42	−	1.54912e42i	0.192785	−	0.232483i
$717$	9.51741e42			1.39872
$718$	2.84619e42	−	7.89112e42i	0.409636	−	1.13572i
$719$			5.12378e42i			0.722199i	0.932527	+	0.361100i	$0.117599\pi$
$719$			5.12378e42i			0.722199i	−0.932527	+	0.361100i	$0.882401\pi$
$720$	1.71687e40	+	9.11602e40i	0.00237001	+	0.0125840i
$721$	4.71385e42			0.637304
$722$	−1.01991e43	−	3.67863e42i	−1.35052	−	0.487112i
$723$		−	7.87627e42i		−	1.02152i
$724$	9.55301e41	+	7.92179e41i	0.121356	+	0.100634i
$725$	3.61557e42			0.449890
$726$	−1.29231e42	+	3.58294e42i	−0.157513	+	0.436707i
$727$		−	6.23530e42i		−	0.744459i	−0.928141	−	0.372230i	$-0.878593\pi$
$727$		−	6.23530e42i		−	0.744459i	0.928141	−	0.372230i	$-0.121407\pi$
$728$	3.52616e42	−	2.07702e42i	0.412411	−	0.242923i
$729$	−9.65653e42			−1.10639
$730$	−1.84481e41	−	6.65392e40i	−0.0207066	−	0.00746853i
$731$			4.43967e41i			0.0488191i
$732$	−5.76140e42	+	6.94776e42i	−0.620671	+	0.748478i
$733$	1.67047e43			1.76311			0.881555	−	0.472080i	$-0.156497\pi$
$733$	1.67047e43			1.76311			0.881555	+	0.472080i	$0.156497\pi$
$734$	−3.94929e42	+	1.09495e43i	−0.408393	+	1.13228i
$735$			2.88187e41i			0.0291988i
$736$	−1.57312e43	−	2.53878e42i	−1.56169	−	0.252033i
$737$	−8.83354e42			−0.859256
$738$	2.16145e42	+	7.79597e41i	0.206015	+	0.0743062i
$739$			8.93132e42i			0.834160i	0.908870	+	0.417080i	$0.136946\pi$
$739$			8.93132e42i			0.834160i	−0.908870	+	0.417080i	$0.863054\pi$
$740$	6.32550e41	+	5.24539e41i	0.0578921	+	0.0480067i
$741$	−1.30416e43			−1.16965
$742$	−3.48697e42	+	9.66768e42i	−0.306471	+	0.849697i
$743$		−	2.11894e42i		−	0.182510i	−0.995828	−	0.0912548i	$-0.970912\pi$
$743$		−	2.11894e42i		−	0.182510i	0.995828	−	0.0912548i	$-0.0290878\pi$
$744$	1.87107e42	+	3.17652e42i	0.157941	+	0.268137i
$745$	4.77460e39			0.000394996
$746$	4.14516e42	+	1.49509e42i	0.336092	+	0.121223i
$747$			3.77770e42i			0.300205i
$748$	1.62281e42	−	1.95698e42i	0.126399	−	0.152427i
$749$	−7.62402e41			−0.0582046
$750$	3.78063e41	−	1.04819e42i	0.0282908	−	0.0784368i
$751$			3.95729e42i			0.290268i	0.989412	+	0.145134i	$0.0463613\pi$
$751$			3.95729e42i			0.290268i	−0.989412	+	0.145134i	$0.953639\pi$
$752$	4.65487e41	−	8.76678e40i	0.0334688	−	0.00630337i
$753$	1.06708e41			0.00752095
$754$	5.36108e42	+	1.93365e42i	0.370410	+	0.133601i
$755$		−	8.45075e41i		−	0.0572388i
$756$	−6.89036e42	−	5.71380e42i	−0.457525	−	0.379400i
$757$	6.69755e42			0.435991			0.217995	−	0.975950i	$-0.430048\pi$
$757$	6.69755e42			0.435991			0.217995	+	0.975950i	$0.430048\pi$
$758$	7.30457e42	−	2.02520e43i	0.466183	−	1.29250i
$759$		−	1.47031e43i		−	0.919985i
$760$	1.06600e42	−	6.27906e41i	0.0653961	−	0.0385204i
$761$	−1.07020e43			−0.643714			−0.321857	−	0.946788i	$-0.604307\pi$
$761$	−1.07020e43			−0.643714			−0.321857	+	0.946788i	$0.604307\pi$
$762$	2.53461e43	+	9.14193e42i	1.49481	+	0.539154i
$763$		−	9.66449e42i		−	0.558870i
$764$	4.60901e42	−	5.55808e42i	0.261341	−	0.315155i
$765$	−6.73054e40			−0.00374221
$766$	5.48786e42	−	1.52152e43i	0.299207	−	0.829556i
$767$			3.14378e43i			1.68082i
$768$	−5.95505e42	−	1.52489e43i	−0.312225	−	0.799503i
$769$	−2.37576e43			−1.22154			−0.610769	−	0.791809i	$-0.709140\pi$
$769$	−2.37576e43			−1.22154			−0.610769	+	0.791809i	$0.709140\pi$
$770$	−3.36966e41	−	1.21538e41i	−0.0169913	−	0.00612846i
$771$			1.14681e43i			0.567121i
$772$	−1.42261e43	−	1.17970e43i	−0.689966	−	0.572151i
$773$	2.33315e43			1.10981			0.554907	−	0.831912i	$-0.312754\pi$
$773$	2.33315e43			1.10981			0.554907	+	0.831912i	$0.312754\pi$
$774$	3.19889e41	−	8.86898e41i	0.0149240	−	0.0413770i
$775$			7.90477e42i			0.361713i
$776$	1.73810e43	+	2.95078e43i	0.780099	+	1.32438i
$777$	−1.65273e43			−0.727591
$778$	2.85052e43	+	1.02813e43i	1.23092	+	0.443972i
$779$		−	3.06450e43i		−	1.29807i
$780$	5.59920e41	−	6.75217e41i	0.0232652	−	0.0280559i
$781$	−4.42023e42			−0.180169
$782$	3.92274e42	−	1.08759e43i	0.156852	−	0.434873i
$783$		−	1.24656e43i		−	0.488976i
$784$	3.36441e42	+	1.78639e43i	0.129470	+	0.687440i
$785$	−1.38929e42			−0.0524504
$786$	−1.56959e43	−	5.66124e42i	−0.581363	−	0.209688i
$787$			2.37587e43i			0.863379i	0.902022	+	0.431690i	$0.142082\pi$
$787$			2.37587e43i			0.863379i	−0.902022	+	0.431690i	$0.857918\pi$
$788$	−3.09855e42	−	2.56945e42i	−0.110475	−	0.0916110i
$789$	2.06413e43			0.722074
$790$	−1.03633e41	+	2.87325e41i	−0.00355708	+	0.00986205i
$791$		−	2.63975e43i		−	0.889027i
$792$	−4.65189e42	+	2.74011e42i	−0.153728	+	0.0905504i
$793$	−3.05056e43			−0.989195
$794$	3.30046e42	+	1.19042e42i	0.105019	+	0.0378785i
$795$			2.20285e42i			0.0687825i
$796$	−2.52442e43	+	3.04424e43i	−0.773509	+	0.932787i
$797$	2.54490e43			0.765237			0.382618	−	0.923907i	$-0.375022\pi$
$797$	2.54490e43			0.765237			0.382618	+	0.923907i	$0.375022\pi$
$798$	−8.44245e42	+	2.34068e43i	−0.249130	+	0.690716i
$799$			3.43678e41i			0.00995292i
$800$	5.59243e42	−	3.46528e43i	0.158947	−	0.984892i
$801$	−9.12766e41			−0.0254608
$802$	−4.79962e43	−	1.73114e43i	−1.31399	−	0.473934i
$803$		−	1.14141e43i		−	0.306696i
$804$	−3.17690e43	−	2.63443e43i	−0.837844	−	0.694778i
$805$	−1.62906e42			−0.0421696
$806$	−4.22757e42	+	1.17210e43i	−0.107415	+	0.297810i
$807$			5.17854e43i			1.29153i
$808$	1.96646e43	+	3.33846e43i	0.481409	+	0.817290i
$809$	4.11693e43			0.989340			0.494670	−	0.869081i	$-0.335289\pi$
$809$	4.11693e43			0.989340			0.494670	+	0.869081i	$0.335289\pi$
$810$	−1.29418e42	−	4.66789e41i	−0.0305295	−	0.0110115i
$811$		−	8.60370e42i		−	0.199238i	−0.995026	−	0.0996190i	$-0.968238\pi$
$811$		−	8.60370e42i		−	0.199238i	0.995026	−	0.0996190i	$-0.0317624\pi$
$812$	6.94098e42	−	8.37025e42i	0.157790	−	0.190282i
$813$	2.45943e43			0.548878
$814$	−1.62270e43	+	4.49895e43i	−0.355526	+	0.985701i
$815$			3.10830e42i			0.0668589i
$816$	1.16726e43	−	2.19837e42i	0.246499	−	0.0464245i
$817$	−1.25745e43			−0.260711
$818$	−8.12972e43	−	2.93226e43i	−1.65492	−	0.596901i
$819$		−	6.30572e42i		−	0.126031i
$820$	1.58662e42	+	1.31570e42i	0.0311362	+	0.0258195i
$821$	3.34458e43			0.644458			0.322229	−	0.946662i	$-0.395568\pi$
$821$	3.34458e43			0.644458			0.322229	+	0.946662i	$0.395568\pi$
$822$	−7.17982e42	+	1.99062e43i	−0.135843	+	0.376626i
$823$			2.35300e43i			0.437144i	0.975821	+	0.218572i	$0.0701398\pi$
$823$			2.35300e43i			0.437144i	−0.975821	+	0.218572i	$0.929860\pi$
$824$	5.49129e43	−	3.23454e43i	1.00177	−	0.590072i
$825$	3.23880e43			0.580196
$826$	5.64242e43	+	2.03512e43i	0.992577	+	0.358006i
$827$		−	9.91861e43i		−	1.71344i	−0.515784	−	0.856718i	$-0.672499\pi$
$827$		−	9.91861e43i		−	1.71344i	0.515784	−	0.856718i	$-0.327501\pi$
$828$	−1.56727e43	+	1.88999e43i	−0.265882	+	0.320631i
$829$	−3.32563e43			−0.554059			−0.277030	−	0.960861i	$-0.589350\pi$
$829$	−3.32563e43			−0.554059			−0.277030	+	0.960861i	$0.589350\pi$
$830$	−1.14976e42	+	3.18774e42i	−0.0188121	+	0.0521569i
$831$			1.92637e43i			0.309545i
$832$	2.68251e43	−	4.83915e43i	0.423342	−	0.763693i
$833$	−1.31893e43			−0.204430
$834$	−1.52966e43	−	5.51723e42i	−0.232865	−	0.0839905i
$835$		−	4.68809e42i		−	0.0700969i
$836$	5.54274e43	+	4.59629e43i	0.814011	+	0.675015i
$837$	2.72538e43			0.393137
$838$	3.81985e43	−	1.05906e44i	0.541235	−	1.50058i
$839$		−	1.18245e44i		−	1.64572i	−0.568247	−	0.822858i	$-0.692378\pi$
$839$		−	1.18245e44i		−	1.64572i	0.568247	−	0.822858i	$-0.307622\pi$
$840$	−8.49405e41	−	1.44204e42i	−0.0116125	−	0.0197146i
$841$	−5.93200e43			−0.796638
$842$	−3.47949e43	−	1.25499e43i	−0.459023	−	0.165562i
$843$			2.76204e43i			0.357945i
$844$	5.08274e43	−	6.12936e43i	0.647085	−	0.780330i
$845$	−9.23704e41			−0.0115527
$846$	2.47629e41	−	6.86555e41i	0.00304261	−	0.00843568i
$847$			2.45618e43i			0.296489i
$848$	2.57169e43	+	1.36548e44i	0.304987	+	1.61938i
$849$	−2.72193e43			−0.317148
$850$	2.39574e43	+	8.64104e42i	0.274256	+	0.0989196i
$851$			2.17502e44i			2.44636i
$852$	−1.58970e43	−	1.31825e43i	−0.175679	−	0.145681i
$853$	−1.36375e44			−1.48081			−0.740407	−	0.672159i	$-0.765367\pi$
$853$	−1.36375e44			−1.48081			−0.740407	+	0.672159i	$0.765367\pi$
$854$	−1.97478e43	+	5.47510e43i	−0.210693	+	0.584149i
$855$		−	1.90629e42i		−	0.0199847i
$856$	−8.88143e42	+	5.23144e42i	−0.0914906	+	0.0538909i
$857$	−5.45027e43			−0.551704			−0.275852	−	0.961200i	$-0.588960\pi$
$857$	−5.45027e43			−0.551704			−0.275852	+	0.961200i	$0.588960\pi$
$858$	4.80241e43	+	1.73215e43i	0.477694	+	0.172296i
$859$			7.22934e43i			0.706645i	0.935502	+	0.353322i	$0.114948\pi$
$859$			7.22934e43i			0.706645i	−0.935502	+	0.353322i	$0.885052\pi$
$860$	5.39865e41	−	6.51032e41i	0.00518572	−	0.00625354i
$861$	−4.14554e43			−0.391321
$862$	2.98963e43	−	8.28880e43i	0.277337	−	0.768922i
$863$			1.26701e44i			1.15509i	0.816358	+	0.577547i	$0.195990\pi$
$863$			1.26701e44i			1.15509i	−0.816358	+	0.577547i	$0.804010\pi$
$864$	−1.19475e44	−	1.92814e43i	−1.07046	−	0.172755i
$865$	6.19373e42			0.0545394
$866$	−1.51879e44	−	5.47802e43i	−1.31441	−	0.474084i
$867$		−	9.22906e43i		−	0.785003i
$868$	1.83000e43	+	1.51752e43i	0.152987	+	0.126864i
$869$	−1.77772e43			−0.146072
$870$	7.90776e41	−	2.19244e42i	0.00638653	−	0.0177067i
$871$		−	1.39489e44i		−	1.10730i
$872$	−6.63157e43	−	1.12584e44i	−0.517451	−	0.878477i
$873$	5.27679e43			0.404721
$874$	3.08037e44	+	1.11104e44i	2.32237	+	0.837641i
$875$		−	7.18553e42i		−	0.0532523i
$876$	3.40403e43	−	4.10498e43i	0.247989	−	0.299054i
$877$	4.09599e43			0.293336			0.146668	−	0.989186i	$-0.453145\pi$
$877$	4.09599e43			0.293336			0.146668	+	0.989186i	$0.453145\pi$
$878$	−6.13715e43	+	1.70153e44i	−0.432065	+	1.19791i
$879$		−	1.57924e44i		−	1.09299i
$880$	−4.75938e42	+	8.96361e41i	−0.0323825	+	0.00609878i
$881$	1.83234e44			1.22565			0.612827	−	0.790217i	$-0.290032\pi$
$881$	1.83234e44			1.22565			0.612827	+	0.790217i	$0.290032\pi$
$882$	2.63478e43	+	9.50320e42i	0.173267	+	0.0624944i
$883$		−	3.02491e43i		−	0.195570i	−0.995208	−	0.0977851i	$-0.968824\pi$
$883$		−	3.02491e43i		−	0.195570i	0.995208	−	0.0977851i	$-0.0311758\pi$
$884$	3.09022e43	+	2.56255e43i	0.196429	+	0.162888i
$885$	1.28566e43			0.0803487
$886$	5.81524e43	−	1.61228e44i	0.357323	−	0.990685i
$887$		−	1.06185e43i		−	0.0641516i	−0.999485	−	0.0320758i	$-0.989788\pi$
$887$		−	1.06185e43i		−	0.0641516i	0.999485	−	0.0320758i	$-0.0102118\pi$
$888$	−1.92531e44	+	1.13407e44i	−1.14369	+	0.673667i
$889$	1.73753e44			1.01486
$890$	−7.70221e41	−	2.77806e41i	−0.00442349	−	0.00159548i
$891$		−	8.00727e43i		−	0.452188i
$892$	−5.40474e43	+	6.51766e43i	−0.300125	+	0.361925i
$893$	−9.73400e42			−0.0531520
$894$	−4.40502e41	+	1.22130e42i	−0.00236530	+	0.00655782i
$895$		−	2.78160e42i		−	0.0146876i
$896$	−6.94871e43	−	7.94714e43i	−0.360814	−	0.412658i
$897$	2.32173e44			1.18556
$898$	−6.68134e43	−	2.40985e43i	−0.335520	−	0.121016i
$899$			3.31072e43i			0.163504i
$900$	−4.16329e43	−	3.45239e43i	−0.202208	−	0.167680i
$901$	−1.00816e44			−0.481570
$902$	−4.07020e43	+	1.12847e44i	−0.191213	+	0.530141i
$903$			1.70102e43i			0.0785948i
$904$	−1.81134e44	−	3.07511e44i	−0.823138	−	1.39744i
$905$	1.71534e42			0.00766692
$906$	2.16163e44	+	7.79662e43i	0.950293	+	0.342755i
$907$			1.59505e44i			0.689706i	0.938657	+	0.344853i	$0.112071\pi$
$907$			1.59505e44i			0.689706i	−0.938657	+	0.344853i	$0.887929\pi$
$908$	−8.80497e43	+	1.06181e44i	−0.374490	+	0.451603i
$909$	5.97007e43			0.249759
$910$	1.91918e42	−	5.32096e42i	0.00789760	−	0.0218962i
$911$		−	3.58460e43i		−	0.145099i	−0.997365	−	0.0725497i	$-0.976886\pi$
$911$		−	3.58460e43i		−	0.145099i	0.997365	−	0.0725497i	$-0.0231136\pi$
$912$	6.22643e43	+	3.30603e44i	0.247923	+	1.31639i
$913$	−1.97230e44			−0.772522
$914$	−4.50233e44	−	1.62392e44i	−1.73478	−	0.625707i
$915$			1.24754e43i			0.0472866i
$916$	1.35002e44	+	1.11950e44i	0.503395	+	0.417438i
$917$	−1.07598e44			−0.394699
$918$	2.97922e43	−	8.25995e43i	0.107513	−	0.298083i
$919$			3.59822e44i			1.27748i	0.769421	+	0.638742i	$0.220545\pi$
$919$			3.59822e44i			1.27748i	−0.769421	+	0.638742i	$0.779455\pi$
$920$	−1.89774e43	+	1.11783e43i	−0.0662856	+	0.0390443i
$921$	2.88535e44			0.991527
$922$	3.16965e44	+	1.14324e44i	1.07164	+	0.386521i
$923$		−	6.97989e43i		−	0.232179i
$924$	6.21767e43	−	7.49799e43i	0.203492	−	0.245395i
$925$	−4.79114e44			−1.54281
$926$	9.27401e43	−	2.57123e44i	0.293835	−	0.814661i
$927$		−	9.81991e43i		−	0.306134i
$928$	2.34225e43	−	1.45135e44i	0.0718480	−	0.445197i
$929$	−3.98578e43			−0.120303			−0.0601516	−	0.998189i	$-0.519158\pi$
$929$	−3.98578e43			−0.120303			−0.0601516	+	0.998189i	$0.519158\pi$
$930$	4.79336e42	+	1.72888e42i	0.0142363	+	0.00513478i
$931$		−	3.73559e44i		−	1.09173i
$932$	3.25107e44	+	2.69594e44i	0.934949	+	0.775302i
$933$	−3.42646e44			−0.969662
$934$	−1.00462e44	+	2.78531e44i	−0.279767	+	0.775659i
$935$		−	3.51394e42i		−	0.00962987i
$936$	−4.32685e43	−	7.34570e43i	−0.116690	−	0.198105i
$937$	5.84868e43			0.155226			0.0776130	−	0.996984i	$-0.475270\pi$
$937$	5.84868e43			0.155226			0.0776130	+	0.996984i	$0.475270\pi$
$938$	−2.50352e44	−	9.02978e43i	−0.653896	−	0.235849i
$939$		−	1.32419e43i		−	0.0340382i
$940$	4.17914e41	−	5.03970e41i	0.00105723	−	0.00127493i
$941$	−4.09952e44			−1.02068			−0.510339	−	0.859973i	$-0.670480\pi$
$941$	−4.09952e44			−1.02068			−0.510339	+	0.859973i	$0.670480\pi$
$942$	1.28176e44	−	3.55369e44i	0.314081	−	0.870795i
$943$			5.45558e44i			1.31573i
$944$	7.96946e44	−	1.50093e44i	1.89169	−	0.356272i
$945$	−1.23723e43			−0.0289051
$946$	4.63040e43	+	1.67011e43i	0.106476	+	0.0384041i
$947$			1.36620e43i			0.0309218i	0.999880	+	0.0154609i	$0.00492155\pi$
$947$			1.36620e43i			0.0309218i	−0.999880	+	0.0154609i	$0.995078\pi$
$948$	−6.39341e43	−	5.30170e43i	−0.142432	−	0.118111i
$949$	1.80237e44			0.395232
$950$	−2.44740e44	+	6.78546e44i	−0.528264	+	1.46462i
$951$		−	9.42604e43i		−	0.200273i
$952$	6.59967e43	−	3.88741e43i	0.138028	−	0.0813030i
$953$	3.20327e44			0.659478			0.329739	−	0.944072i	$-0.393039\pi$
$953$	3.20327e44			0.659478			0.329739	+	0.944072i	$0.393039\pi$
$954$	2.01398e44	+	7.26407e43i	0.408158	+	0.147216i
$955$		−	9.98008e42i		−	0.0199106i
$956$	5.29663e44	−	6.38729e44i	1.04023	−	1.25444i
$957$	1.35649e44			0.262264
$958$	8.86787e43	−	2.45863e44i	0.168786	−	0.467962i
$959$			1.36461e44i			0.255699i
$960$	−1.97899e43	−	1.09702e43i	−0.0365069	−	0.0202371i
$961$	4.78236e44			0.868543
$962$	−7.10420e44	−	2.56237e44i	−1.27025	−	0.458158i
$963$			1.58824e43i			0.0279590i
$964$	−5.28590e44	−	4.38330e44i	−0.916143	−	0.759707i
$965$	−2.55445e43			−0.0435900
$966$	1.50297e44	−	4.16700e44i	0.252518	−	0.700111i
$967$		−	8.03089e44i		−	1.32851i	−0.747504	−	0.664257i	$-0.768748\pi$
$967$		−	8.03089e44i		−	1.32851i	0.747504	−	0.664257i	$-0.231252\pi$
$968$	1.68538e44	+	2.86127e44i	0.274515	+	0.466045i
$969$	−2.44091e44			−0.391466
$970$	4.45272e43	+	1.60602e43i	0.0703152	+	0.0253615i
$971$		−	1.43309e44i		−	0.222836i	−0.993774	−	0.111418i	$-0.964461\pi$
$971$		−	1.43309e44i		−	0.222836i	0.993774	−	0.111418i	$-0.0355392\pi$
$972$	−2.13251e44	+	2.57163e44i	−0.326510	+	0.393744i
$973$	−1.04861e44			−0.158097
$974$	−2.92722e44	+	8.11577e44i	−0.434581	+	1.20488i
$975$			5.11432e44i			0.747684i
$976$	1.45643e44	+	7.73314e44i	0.209672	+	1.11329i
$977$	4.52862e44			0.642018			0.321009	−	0.947076i	$-0.395978\pi$
$977$	4.52862e44			0.642018			0.321009	+	0.947076i	$0.395978\pi$
$978$	−7.95076e44	−	2.86771e44i	−1.11001	−	0.400361i
$979$		−	4.76546e43i		−	0.0655185i
$980$	1.93407e43	+	1.60382e43i	0.0261867	+	0.0217152i
$981$	−2.01331e44			−0.268458
$982$	−2.61311e44	+	7.24489e44i	−0.343151	+	0.951392i
$983$			2.14694e44i			0.277663i	0.990316	+	0.138831i	$0.0443346\pi$
$983$			2.14694e44i			0.277663i	−0.990316	+	0.138831i	$0.955665\pi$
$984$	−4.82925e44	+	2.84458e44i	−0.615110	+	0.362319i
$985$	−5.56375e42			−0.00697949
$986$	1.00340e44	+	3.61909e43i	0.123971	+	0.0447142i
$987$			1.31678e43i			0.0160234i
$988$	−7.25790e44	+	8.75242e44i	−0.869875	+	1.04900i
$989$	2.23857e44			0.264257
$990$	−2.53189e42	+	7.01969e42i	−0.00294385	+	0.00816188i
$991$		−	8.79235e44i		−	1.00693i	−0.864015	−	0.503466i	$-0.832058\pi$
$991$		−	8.79235e44i		−	1.00693i	0.864015	−	0.503466i	$-0.167942\pi$
$992$	3.17310e44	+	5.12090e43i	0.357939	+	0.0577659i
$993$	−1.51198e44			−0.167999
$994$	−1.25274e44	−	4.51842e43i	−0.137109	−	0.0494528i
$995$			5.46623e43i			0.0589307i
$996$	−7.09319e44	−	5.88199e44i	−0.753271	−	0.624647i
$997$	6.41809e44			0.671396			0.335698	−	0.941970i	$-0.391028\pi$
$997$	6.41809e44			0.671396			0.335698	+	0.941970i	$0.391028\pi$
$998$	4.29681e44	−	1.19130e45i	0.442780	−	1.22761i
$999$			1.65187e45i			1.67685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.31.b.a.3.14	yes	14
3.2	odd	2		36.31.d.c.19.1		14
4.3	odd	2	inner	4.31.b.a.3.13	✓	14
12.11	even	2		36.31.d.c.19.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.31.b.a.3.13	✓	14	4.3	odd	2	inner
4.31.b.a.3.14	yes	14	1.1	even	1	trivial
36.31.d.c.19.1		14	3.2	odd	2
36.31.d.c.19.2		14	12.11	even	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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 31 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(30824.3 + 11117.8i) q^{2} +1.23158e7i q^{3} +(8.26531e8 + 6.85396e8i) q^{4} +1.48412e9 q^{5} +(-1.36924e11 + 3.79624e11i) q^{6} +2.60240e12i q^{7} +(1.78571e13 + 3.03161e13i) q^{8} +5.42133e13 q^{9} +O(q^{10})\)	\(q+(30824.3 + 11117.8i) q^{2} +1.23158e7i q^{3} +(8.26531e8 + 6.85396e8i) q^{4} +1.48412e9 q^{5} +(-1.36924e11 + 3.79624e11i) q^{6} +2.60240e12i q^{7} +(1.78571e13 + 3.03161e13i) q^{8} +5.42133e13 q^{9} +(4.57469e13 + 1.65001e13i) q^{10} +2.83042e15i q^{11} +(-8.44118e15 + 1.01794e16i) q^{12} -4.46946e16 q^{13} +(-2.89330e16 + 8.02171e16i) q^{14} +1.82780e16i q^{15} +(2.13385e17 + 1.13300e18i) q^{16} -8.36518e17 q^{17} +(1.67109e18 + 6.02733e17i) q^{18} -2.36927e19i q^{19} +(1.22667e18 + 1.01721e18i) q^{20} -3.20505e19 q^{21} +(-3.14680e19 + 8.72457e19i) q^{22} +4.21789e20i q^{23} +(-3.73365e20 + 2.19924e20i) q^{24} -9.29120e20 q^{25} +(-1.37768e21 - 4.96905e20i) q^{26} +3.20338e21i q^{27} +(-1.78368e21 + 2.15096e21i) q^{28} -3.89139e21 q^{29} +(-2.03212e20 + 5.63407e20i) q^{30} -8.50780e21i q^{31} +(-6.01907e21 + 3.72964e22i) q^{32} -3.48588e22 q^{33} +(-2.57851e22 - 9.30025e21i) q^{34} +3.86227e21i q^{35} +(4.48090e22 + 3.71576e22i) q^{36} +5.15665e23 q^{37} +(2.63411e23 - 7.30311e23i) q^{38} -5.50447e23i q^{39} +(2.65021e22 + 4.49926e22i) q^{40} +1.29344e24 q^{41} +(-9.87934e23 - 3.56331e23i) q^{42} -5.30732e23i q^{43} +(-1.93996e24 + 2.33943e24i) q^{44} +8.04589e22 q^{45} +(-4.68937e24 + 1.30014e25i) q^{46} -4.10844e23i q^{47} +(-1.39538e25 + 2.62800e24i) q^{48} +1.57669e25 q^{49} +(-2.86395e25 - 1.03298e25i) q^{50} -1.03024e25i q^{51} +(-3.69414e25 - 3.06335e25i) q^{52} +1.20519e26 q^{53} +(-3.56146e25 + 9.87420e25i) q^{54} +4.20068e24i q^{55} +(-7.88945e25 + 4.64714e25i) q^{56} +2.91794e26 q^{57} +(-1.19949e26 - 4.32637e25i) q^{58} -7.03393e26i q^{59} +(-1.25277e25 + 1.51074e25i) q^{60} +6.82535e26 q^{61} +(9.45881e25 - 2.62247e26i) q^{62} +1.41085e26i q^{63} +(-6.00187e26 + 1.08271e27i) q^{64} -6.63320e25 q^{65} +(-1.07450e27 - 3.87553e26i) q^{66} +3.12093e27i q^{67} +(-6.91408e26 - 5.73347e26i) q^{68} -5.19466e27 q^{69} +(-4.29399e25 + 1.19052e26i) q^{70} +1.56169e27i q^{71} +(9.68093e26 + 1.64353e27i) q^{72} -4.03265e27 q^{73} +(1.58950e28 + 5.73306e27i) q^{74} -1.14428e28i q^{75} +(1.62389e28 - 1.95828e28i) q^{76} -7.36588e27 q^{77} +(6.11976e27 - 1.69671e28i) q^{78} +6.28076e27i q^{79} +(3.16688e26 + 1.68151e27i) q^{80} -2.82900e28 q^{81} +(3.98693e28 + 1.43802e28i) q^{82} +6.96821e28i q^{83} +(-2.64907e28 - 2.19673e28i) q^{84} -1.24149e27 q^{85} +(5.90057e27 - 1.63594e28i) q^{86} -4.79254e28i q^{87} +(-8.58072e28 + 5.05431e28i) q^{88} -1.68366e28 q^{89} +(2.48009e27 + 8.94527e26i) q^{90} -1.16313e29i q^{91} +(-2.89093e29 + 3.48622e29i) q^{92} +1.04780e29 q^{93} +(4.56768e27 - 1.26640e28i) q^{94} -3.51628e28i q^{95} +(-4.59333e29 - 7.41293e28i) q^{96} +9.73339e29 q^{97} +(4.86002e29 + 1.75293e29i) q^{98} +1.53446e29i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 24476 q^{2} - 820787056 q^{4} + 14864798540 q^{5} - 454068012192 q^{6} - 31343321296064 q^{8} - 722181861644898 q^{9}+O(q^{10}) \) 14 * q - 24476 * q^2 - 820787056 * q^4 + 14864798540 * q^5 - 454068012192 * q^6 - 31343321296064 * q^8 - 722181861644898 * q^9	\( 14 q - 24476 q^{2} - 820787056 q^{4} + 14864798540 q^{5} - 454068012192 q^{6} - 31343321296064 q^{8} - 722181861644898 q^{9} - 12\!\cdots\!60 q^{10}+ \cdots + 47\!\cdots\!36 q^{98}+O(q^{100}) \) 14 * q - 24476 * q^2 - 820787056 * q^4 + 14864798540 * q^5 - 454068012192 * q^6 - 31343321296064 * q^8 - 722181861644898 * q^9 - 1287889809124760 * q^10 + 51879382052868480 * q^12 + 73473894124935532 * q^13 + 36761277666527808 * q^14 - 1064191557393108736 * q^16 - 4417201733411195812 * q^17 + 10773613739927673156 * q^18 + 31289641216539815840 * q^20 - 24107806000815293184 * q^21 - 63855041197225323360 * q^22 - 219200204962023547392 * q^24 + 2557307336405009852730 * q^25 + 2662172027973979655720 * q^26 + 2286217156307884458240 * q^28 - 5183126634353006173012 * q^29 - 19995309903793012445760 * q^30 + 42868919292290358744064 * q^32 + 45729663133049254147200 * q^33 + 189270161167001176158280 * q^34 - 265369932957818409094128 * q^36 - 627167100163080968189492 * q^37 - 1048227922470375880434720 * q^38 + 249748411367898391857280 * q^40 + 1494251155359817033760828 * q^41 + 2632732296455102155814400 * q^42 + 724029644533237152067200 * q^44 - 15629634719291168966183700 * q^45 + 6965410628317069602441408 * q^46 + 22826956997174454465976320 * q^48 + 36971394165784621527528302 * q^49 - 6257136580151365293802740 * q^50 - 3584406874106323077960032 * q^52 - 162298735436688848725454068 * q^53 + 103759862824624790541134016 * q^54 - 103480837826586244326484992 * q^56 - 178372120064399401723873920 * q^57 + 292818259345642447695165352 * q^58 + 673940775243590010378428160 * q^60 - 781363600109479145350441172 * q^61 - 700904834820308348700230400 * q^62 - 1886538399231001232282054656 * q^64 - 766208515593499839727344200 * q^65 + 4354147454872998865031212800 * q^66 - 1563708764577905097576648928 * q^68 + 12984546958279555654634831616 * q^69 + 5791600195068600540130627200 * q^70 - 12292930844134853078053553856 * q^72 - 13974688009272270633487568708 * q^73 - 1683916522088046880433965720 * q^74 - 43359191482193415443604585600 * q^76 - 13914563925551368590607269120 * q^77 + 103407672785786602276239960000 * q^78 - 142384583917045013024432289280 * q^80 + 142873441147816769491949878830 * q^81 + 100782649420724457106091722888 * q^82 - 274539668577865429004166211584 * q^84 - 166040172454330922908332123880 * q^85 + 409278053261716222570289186208 * q^86 - 745586494961630729936044285440 * q^88 + 98873747700972853801823899388 * q^89 + 1804754410453947165713321465640 * q^90 - 1825371837423533828188743456000 * q^92 - 123062607213511416597600107520 * q^93 + 2752292471954002780670205710208 * q^94 - 4054034025223909146350873812992 * q^96 - 1029388221334221132711894149732 * q^97 + 4774196460313129800493027312036 * q^98

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