LMFDB - Embedded newform 6.31.b.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,31,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, 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("6.5");

S:= CuspForms(chi, 31);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 31 $
Character orbit:	$[\chi]$	$=$	6.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:	$34.2085571416$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + \cdots + 17\!\cdots\!00 $ x^10 + 8552062877595970390x^8 + 25392807796994293834069533242559594025x^6 + 31363214047445929775687291161211122208644643150843750000x^4 + 14997479733093492468171154918719535444710088825890735887189931640625000000x^2 + 1779211874045772876005913493072356377360261727229346754892124420427761840820312500000000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{104}\cdot 3^{53}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.7
Root			$1.91213e9i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.31.b.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+23170.5i q^{2} +(-8.56717e6 + 1.15106e7i) q^{3} -5.36871e8 q^{4} +4.58912e10i q^{5} +(-2.66707e11 - 1.98505e11i) q^{6} -5.02434e12 q^{7} -1.24396e13i q^{8} +(-5.90983e13 - 1.97227e14i) q^{9} +O(q^{10})$	\(q+23170.5i q^{2} +(-8.56717e6 + 1.15106e7i) q^{3} -5.36871e8 q^{4} +4.58912e10i q^{5} +(-2.66707e11 - 1.98505e11i) q^{6} -5.02434e12 q^{7} -1.24396e13i q^{8} +(-5.90983e13 - 1.97227e14i) q^{9} -1.06332e15 q^{10} +5.42302e15i q^{11} +(4.59946e15 - 6.17973e15i) q^{12} -6.28201e16 q^{13} -1.16416e17i q^{14} +(-5.28237e17 - 3.93158e17i) q^{15} +2.88230e17 q^{16} +1.97340e18i q^{17} +(4.56985e18 - 1.36934e18i) q^{18} -1.24077e19 q^{19} -2.46377e19i q^{20} +(4.30444e19 - 5.78334e19i) q^{21} -1.25654e20 q^{22} +1.89781e19i q^{23} +(1.43187e20 + 1.06572e20i) q^{24} -1.17468e21 q^{25} -1.45557e21i q^{26} +(2.77652e21 + 1.00942e21i) q^{27} +2.69742e21 q^{28} +1.35101e22i q^{29} +(9.10965e21 - 1.22395e22i) q^{30} +3.24412e22 q^{31} +6.67843e21i q^{32} +(-6.24224e22 - 4.64599e22i) q^{33} -4.57247e22 q^{34} -2.30573e23i q^{35} +(3.17282e22 + 1.05886e23i) q^{36} +6.42669e23 q^{37} -2.87492e23i q^{38} +(5.38191e23 - 7.23100e23i) q^{39} +5.70866e23 q^{40} -5.25972e23i q^{41} +(1.34003e24 + 9.97359e23i) q^{42} +5.90491e23 q^{43} -2.91146e24i q^{44} +(9.05099e24 - 2.71209e24i) q^{45} -4.39732e23 q^{46} +3.38460e22i q^{47} +(-2.46932e24 + 3.31771e24i) q^{48} +2.70469e24 q^{49} -2.72179e25i q^{50} +(-2.27151e25 - 1.69065e25i) q^{51} +3.37263e25 q^{52} +7.47411e25i q^{53} +(-2.33887e25 + 6.43332e25i) q^{54} -2.48869e26 q^{55} +6.25006e25i q^{56} +(1.06299e26 - 1.42820e26i) q^{57} -3.13035e26 q^{58} +2.93423e26i q^{59} +(2.83595e26 + 2.11075e26i) q^{60} -3.02349e26 q^{61} +7.51678e26i q^{62} +(2.96930e26 + 9.90937e26i) q^{63} -1.54743e26 q^{64} -2.88289e27i q^{65} +(1.07650e27 - 1.44636e27i) q^{66} -3.18531e27 q^{67} -1.05946e27i q^{68} +(-2.18450e26 - 1.62589e26i) q^{69} +5.34249e27 q^{70} -2.30260e27i q^{71} +(-2.45342e27 + 7.35157e26i) q^{72} +1.38721e28 q^{73} +1.48909e28i q^{74} +(1.00637e28 - 1.35213e28i) q^{75} +6.66132e27 q^{76} -2.72471e28i q^{77} +(1.67546e28 + 1.24701e28i) q^{78} -3.59847e28 q^{79} +1.32272e28i q^{80} +(-3.54059e28 + 2.33116e28i) q^{81} +1.21870e28 q^{82} -2.29192e28i q^{83} +(-2.31093e28 + 3.10491e28i) q^{84} -9.05619e28 q^{85} +1.36820e28i q^{86} +(-1.55510e29 - 1.15743e29i) q^{87} +6.74599e28 q^{88} +1.44029e29i q^{89} +(6.28405e28 + 2.09716e29i) q^{90} +3.15630e29 q^{91} -1.01888e28i q^{92} +(-2.77929e29 + 3.73419e29i) q^{93} -7.84227e26 q^{94} -5.69403e29i q^{95} +(-7.68730e28 - 5.72153e28i) q^{96} -6.73435e29 q^{97} +6.26689e28i q^{98} +(1.06957e30 - 3.20491e29i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9}+O(q^{10}) $ 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9	$ 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9} - 11\!\cdots\!60 q^{10}+ \cdots + 27\!\cdots\!20 q^{99}+O(q^{100}) $ 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9 - 1111538175836160 * q^10 - 7591226920402944 * q^12 + 11241857908456580 * q^13 - 1208370750576105600 * q^15 + 2882303761517117440 * q^16 + 4378961453216956416 * q^18 - 406434941012438620 * q^19 + 189341373476724706020 * q^21 - 175966920878069907456 * q^22 + 78269746773932113920 * q^24 - 538750688835772733030 * q^25 - 509686212259700532126 * q^27 + 783474298257252810752 * q^28 + 3618734882327478927360 * q^30 - 3850790055930904811020 * q^31 + 13877514934601873876352 * q^33 - 21974427701517892976640 * q^34 - 22394560921038760181760 * q^36 + 691786417224189171658916 * q^37 + 264189297409049008449300 * q^39 + 596752514183975581777920 * q^40 + 2551733261187619598893056 * q^42 - 10594373354873893550389372 * q^43 + 21961398854703004532478720 * q^45 - 14905926072892021549301760 * q^46 + 4075508919955679952764928 * q^48 - 14303693611422252234715650 * q^49 + 100757981401326611204590080 * q^51 - 6035426507887496617000960 * q^52 + 186364360915292902942310400 * q^54 - 905529883473273884900970240 * q^55 + 1357830109447011748343825076 * q^57 - 1026862318649343581985177600 * q^58 + 648739106895918338880307200 * q^60 - 2949272535924647913201299260 * q^61 + 5088794127795653673352888692 * q^63 - 1547425049106725343623905280 * q^64 + 3787402697011447732654571520 * q^66 - 10556251754234326335356822044 * q^67 + 15764240424701154050198334720 * q^69 - 8691440888931957213379952640 * q^70 - 2350937029001432724922171392 * q^72 + 12106003505184711607130189300 * q^73 - 7500206691267464218185712830 * q^75 + 218203097450014125263421440 * q^76 - 23839067108381696719249735680 * q^78 + 68719005124237783442983312820 * q^79 - 111620808361643664456575921430 * q^81 + 18283730424263848186657898496 * q^82 - 101651875857781803693889290240 * q^84 + 403836274868708986530058828800 * q^85 - 512433611792960206983797969280 * q^87 + 94471521293641232015658319872 * q^88 - 426164288449255115819581440000 * q^90 + 1222541373056582384854822798600 * q^91 - 983623123086267594817934884284 * q^93 - 80746046881825464175401369600 * q^94 - 42020750332529991826318295040 * q^96 - 1391585232259866867438139103212 * q^97 + 2707446209006624257844338302720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$			23170.5i			0.707107i
$2$			23170.5i			0.707107i
$3$	−8.56717e6	+	1.15106e7i	−0.597061	+	0.802196i
$3$	−8.56717e6	+	1.15106e7i	−0.597061	+	0.802196i
$4$	−5.36871e8			−0.500000
$5$			4.58912e10i			1.50376i	0.659298	+	0.751881i	$0.270853\pi$
$5$			4.58912e10i			1.50376i	−0.659298	+	0.751881i	$0.729147\pi$
$6$	−2.66707e11	−	1.98505e11i	−0.567238	−	0.422186i
$7$	−5.02434e12			−1.05830			−0.529150	−	0.848528i	$-0.677489\pi$
$7$	−5.02434e12			−1.05830			−0.529150	+	0.848528i	$0.677489\pi$
$8$		−	1.24396e13i		−	0.353553i
$9$	−5.90983e13	−	1.97227e14i	−0.287037	−	0.957920i
$10$	−1.06332e15			−1.06332
$11$			5.42302e15i			1.29823i	0.760691	+	0.649114i	$0.224860\pi$
$11$			5.42302e15i			1.29823i	−0.760691	+	0.649114i	$0.775140\pi$
$12$	4.59946e15	−	6.17973e15i	0.298530	−	0.401098i
$13$	−6.28201e16			−1.22729			−0.613647	−	0.789581i	$-0.710298\pi$
$13$	−6.28201e16			−1.22729			−0.613647	+	0.789581i	$0.710298\pi$
$14$		−	1.16416e17i		−	0.748331i
$15$	−5.28237e17	−	3.93158e17i	−1.20631	−	0.897838i
$16$	2.88230e17			0.250000
$17$			1.97340e18i			0.689417i	0.938710	+	0.344709i	$0.112022\pi$
$17$			1.97340e18i			0.689417i	−0.938710	+	0.344709i	$0.887978\pi$
$18$	4.56985e18	−	1.36934e18i	0.677351	−	0.202966i
$19$	−1.24077e19			−0.817310			−0.408655	−	0.912689i	$-0.634002\pi$
$19$	−1.24077e19			−0.817310			−0.408655	+	0.912689i	$0.634002\pi$
$20$		−	2.46377e19i		−	0.751881i
$21$	4.30444e19	−	5.78334e19i	0.631869	−	0.848964i
$22$	−1.25654e20			−0.917986
$23$			1.89781e19i			0.0711764i	0.999367	+	0.0355882i	$0.0113305\pi$
$23$			1.89781e19i			0.0711764i	−0.999367	+	0.0355882i	$0.988670\pi$
$24$	1.43187e20	+	1.06572e20i	0.283619	+	0.211093i
$25$	−1.17468e21			−1.26130
$26$		−	1.45557e21i		−	0.867828i
$27$	2.77652e21	+	1.00942e21i	0.939818	+	0.341676i
$28$	2.69742e21			0.529150
$29$			1.35101e22i			1.56563i	0.622256	+	0.782814i	$0.286216\pi$
$29$			1.35101e22i			1.56563i	−0.622256	+	0.782814i	$0.713784\pi$
$30$	9.10965e21	−	1.22395e22i	0.634867	−	0.852992i
$31$	3.24412e22			1.38252			0.691260	−	0.722606i	$-0.257056\pi$
$31$	3.24412e22			1.38252			0.691260	+	0.722606i	$0.257056\pi$
$32$			6.67843e21i			0.176777i
$33$	−6.24224e22	−	4.64599e22i	−1.04143	−	0.775121i
$34$	−4.57247e22			−0.487492
$35$		−	2.30573e23i		−	1.59143i
$36$	3.17282e22	+	1.05886e23i	0.143518	+	0.478960i
$37$	6.42669e23			1.92735			0.963677	−	0.267070i	$-0.0860557\pi$
$37$	6.42669e23			1.92735			0.963677	+	0.267070i	$0.0860557\pi$
$38$		−	2.87492e23i		−	0.577925i
$39$	5.38191e23	−	7.23100e23i	0.732769	−	0.984530i
$40$	5.70866e23			0.531661
$41$		−	5.25972e23i		−	0.338224i	−0.985597	−	0.169112i	$-0.945910\pi$
$41$		−	5.25972e23i		−	0.338224i	0.985597	−	0.169112i	$-0.0540900\pi$
$42$	1.34003e24	+	9.97359e23i	0.600308	+	0.446799i
$43$	5.90491e23			0.185860			0.0929302	−	0.995673i	$-0.470377\pi$
$43$	5.90491e23			0.185860			0.0929302	+	0.995673i	$0.470377\pi$
$44$		−	2.91146e24i		−	0.649114i
$45$	9.05099e24	−	2.71209e24i	1.44048	−	0.431635i
$46$	−4.39732e23			−0.0503293
$47$			3.38460e22i			0.00280569i	0.999999	+	0.00140284i	$0.000446539\pi$
$47$			3.38460e22i			0.00280569i	−0.999999	+	0.00140284i	$0.999553\pi$
$48$	−2.46932e24	+	3.31771e24i	−0.149265	+	0.200549i
$49$	2.70469e24			0.119999
$50$		−	2.72179e25i		−	0.891876i
$51$	−2.27151e25	−	1.69065e25i	−0.553048	−	0.411624i
$52$	3.37263e25			0.613647
$53$			7.47411e25i			1.02193i	0.859601	+	0.510965i	$0.170712\pi$
$53$			7.47411e25i			1.02193i	−0.859601	+	0.510965i	$0.829288\pi$
$54$	−2.33887e25	+	6.43332e25i	−0.241602	+	0.664551i
$55$	−2.48869e26			−1.95223
$56$			6.25006e25i			0.374165i
$57$	1.06299e26	−	1.42820e26i	0.487984	−	0.655642i
$58$	−3.13035e26			−1.10707
$59$			2.93423e26i			0.802997i	0.915860	+	0.401498i	$0.131510\pi$
$59$			2.93423e26i			0.802997i	−0.915860	+	0.401498i	$0.868490\pi$
$60$	2.83595e26	+	2.11075e26i	0.603156	+	0.448919i
$61$	−3.02349e26			−0.501835			−0.250918	−	0.968008i	$-0.580732\pi$
$61$	−3.02349e26			−0.501835			−0.250918	+	0.968008i	$0.580732\pi$
$62$			7.51678e26i			0.977590i
$63$	2.96930e26	+	9.90937e26i	0.303771	+	1.01377i
$64$	−1.54743e26			−0.125000
$65$		−	2.88289e27i		−	1.84556i
$66$	1.07650e27	−	1.44636e27i	0.548093	−	0.736404i
$67$	−3.18531e27			−1.29428			−0.647142	−	0.762369i	$-0.724036\pi$
$67$	−3.18531e27			−1.29428			−0.647142	+	0.762369i	$0.724036\pi$
$68$		−	1.05946e27i		−	0.344709i
$69$	−2.18450e26	−	1.62589e26i	−0.0570974	−	0.0424966i
$70$	5.34249e27			1.12531
$71$		−	2.30260e27i		−	0.392051i	−0.980599	−	0.196026i	$-0.937196\pi$
$71$		−	2.30260e27i		−	0.392051i	0.980599	−	0.196026i	$-0.0628036\pi$
$72$	−2.45342e27	+	7.35157e26i	−0.338676	+	0.101483i
$73$	1.38721e28			1.55704			0.778521	−	0.627619i	$-0.215970\pi$
$73$	1.38721e28			1.55704			0.778521	+	0.627619i	$0.215970\pi$
$74$			1.48909e28i			1.36285i
$75$	1.00637e28	−	1.35213e28i	0.753075	−	1.01181i
$76$	6.66132e27			0.408655
$77$		−	2.72471e28i		−	1.37391i
$78$	1.67546e28	+	1.24701e28i	0.696168	+	0.518146i
$79$	−3.59847e28			−1.23513			−0.617563	−	0.786521i	$-0.711880\pi$
$79$	−3.59847e28			−1.23513			−0.617563	+	0.786521i	$0.711880\pi$
$80$			1.32272e28i			0.375941i
$81$	−3.54059e28	+	2.33116e28i	−0.835220	+	0.549916i
$82$	1.21870e28			0.239161
$83$		−	2.29192e28i		−	0.374997i	−0.982265	−	0.187498i	$-0.939962\pi$
$83$		−	2.29192e28i		−	0.374997i	0.982265	−	0.187498i	$-0.0600379\pi$
$84$	−2.31093e28	+	3.10491e28i	−0.315935	+	0.424482i
$85$	−9.05619e28			−1.03672
$86$			1.36820e28i			0.131423i
$87$	−1.55510e29	−	1.15743e29i	−1.25594	−	0.934775i
$88$	6.74599e28			0.458993
$89$			1.44029e29i			0.827178i	0.910464	+	0.413589i	$0.135725\pi$
$89$			1.44029e29i			0.827178i	−0.910464	+	0.413589i	$0.864275\pi$
$90$	6.28405e28	+	2.09716e29i	0.305212	+	1.01858i
$91$	3.15630e29			1.29884
$92$		−	1.01888e28i		−	0.0355882i
$93$	−2.77929e29	+	3.73419e29i	−0.825449	+	1.10905i
$94$	−7.84227e26			−0.00198392
$95$		−	5.69403e29i		−	1.22904i
$96$	−7.68730e28	−	5.72153e28i	−0.141810	−	0.105546i
$97$	−6.73435e29			−1.06346			−0.531728	−	0.846915i	$-0.678457\pi$
$97$	−6.73435e29			−1.06346			−0.531728	+	0.846915i	$0.678457\pi$
$98$			6.26689e28i			0.0848518i
$99$	1.06957e30	−	3.20491e29i	1.24360	−	0.372639i
$100$	6.30652e29			0.630652
$101$		−	1.51481e30i		−	1.30478i	−0.757882	−	0.652392i	$-0.773766\pi$
$101$		−	1.51481e30i		−	1.30478i	0.757882	−	0.652392i	$-0.226234\pi$
$102$	3.91731e29	−	5.26320e29i	0.291062	−	0.391064i
$103$	7.92307e29			0.508552			0.254276	−	0.967132i	$-0.418163\pi$
$103$	7.92307e29			0.508552			0.254276	+	0.967132i	$0.418163\pi$
$104$			7.81454e29i			0.433914i
$105$	2.65404e30	+	1.97536e30i	1.27664	+	0.950182i
$106$	−1.73179e30			−0.722614
$107$		−	3.11580e30i		−	1.12931i	−0.825327	−	0.564655i	$-0.809009\pi$
$107$		−	3.11580e30i		−	1.12931i	0.825327	−	0.564655i	$-0.190991\pi$
$108$	−1.49063e30	−	5.41928e29i	−0.469909	−	0.170838i
$109$	1.13374e30			0.311255			0.155628	−	0.987816i	$-0.450260\pi$
$109$	1.13374e30			0.311255			0.155628	+	0.987816i	$0.450260\pi$
$110$		−	5.76641e30i		−	1.38043i
$111$	−5.50585e30	+	7.39753e30i	−1.15075	+	1.54612i
$112$	−1.44817e30			−0.264575
$113$			8.71994e30i			1.39424i	0.716956	+	0.697119i	$0.245535\pi$
$113$			8.71994e30i			1.39424i	−0.716956	+	0.697119i	$0.754465\pi$
$114$	3.30921e30	+	2.46299e30i	0.463609	+	0.345056i
$115$	−8.70930e29			−0.107032
$116$		−	7.25318e30i		−	0.782814i
$117$	3.71256e30	+	1.23898e31i	0.352278	+	1.17565i
$118$	−6.79875e30			−0.567804
$119$		−	9.91506e30i		−	0.729610i
$120$	−4.89071e30	+	6.57103e30i	−0.317434	+	0.426496i
$121$	−1.19597e31			−0.685395
$122$		−	7.00557e30i		−	0.354851i
$123$	6.05427e30	+	4.50609e30i	0.271322	+	0.201940i
$124$	−1.74167e31			−0.691260
$125$		−	1.11680e31i		−	0.392938i
$126$	−2.29605e31	+	6.88002e30i	−0.716841	+	0.214799i
$127$	2.66968e31			0.740292			0.370146	−	0.928974i	$-0.379308\pi$
$127$	2.66968e31			0.740292			0.370146	+	0.928974i	$0.379308\pi$
$128$		−	3.58546e30i		−	0.0883883i
$129$	−5.05884e30	+	6.79693e30i	−0.110970	+	0.149096i
$130$	6.67980e31			1.30501
$131$		−	6.82028e31i		−	1.18777i	−0.804550	−	0.593885i	$-0.797593\pi$
$131$		−	6.82028e31i		−	1.18777i	0.804550	−	0.593885i	$-0.202407\pi$
$132$	3.35128e31	+	2.49430e31i	0.520716	+	0.387560i
$133$	6.23405e31			0.864959
$134$		−	7.38052e31i		−	0.915198i
$135$	−4.63235e31	+	1.27418e32i	−0.513800	+	1.41326i
$136$	2.45483e31			0.243746
$137$		−	8.83619e31i		−	0.786062i	−0.919525	−	0.393031i	$-0.871427\pi$
$137$		−	8.83619e31i		−	0.786062i	0.919525	−	0.393031i	$-0.128573\pi$
$138$	3.76726e30	−	5.06160e30i	0.0300497	−	0.0403740i
$139$	1.13527e32			0.812604			0.406302	−	0.913739i	$-0.366818\pi$
$139$	1.13527e32			0.812604			0.406302	+	0.913739i	$0.366818\pi$
$140$			1.23788e32i			0.795716i
$141$	−3.89589e29	−	2.89964e29i	−0.00225071	−	0.00167516i
$142$	5.33523e31			0.277222
$143$		−	3.40675e32i		−	1.59331i
$144$	−1.70339e31	−	5.68469e31i	−0.0717592	−	0.239480i
$145$	−6.19995e32			−2.35433
$146$			3.21424e32i			1.10099i
$147$	−2.31715e31	+	3.11327e31i	−0.0716464	+	0.0962623i
$148$	−3.45030e32			−0.963677
$149$		−	8.71714e31i		−	0.220080i	−0.993927	−	0.110040i	$-0.964902\pi$
$149$		−	8.71714e31i		−	0.220080i	0.993927	−	0.110040i	$-0.0350979\pi$
$150$	3.13295e32	+	2.33180e32i	0.715459	+	0.532504i
$151$	−4.38197e32			−0.905765			−0.452882	−	0.891570i	$-0.649604\pi$
$151$	−4.38197e32			−0.905765			−0.452882	+	0.891570i	$0.649604\pi$
$152$			1.54346e32i			0.288963i
$153$	3.89209e32	−	1.16625e32i	0.660406	−	0.197888i
$154$	6.31328e32			0.971504
$155$			1.48877e33i			2.07898i
$156$	−2.88939e32	+	3.88211e32i	−0.366385	+	0.492265i
$157$	6.14569e32			0.708069			0.354035	−	0.935232i	$-0.384810\pi$
$157$	6.14569e32			0.708069			0.354035	+	0.935232i	$0.384810\pi$
$158$		−	8.33782e32i		−	0.873366i
$159$	−8.60318e32	−	6.40320e32i	−0.819789	−	0.610155i
$160$	−3.06481e32			−0.265830
$161$		−	9.53527e31i		−	0.0753260i
$162$	−5.40141e32	−	8.20372e32i	−0.388850	−	0.590590i
$163$	−2.39138e32			−0.156976			−0.0784881	−	0.996915i	$-0.525009\pi$
$163$	−2.39138e32			−0.156976			−0.0784881	+	0.996915i	$0.525009\pi$
$164$			2.82379e32i			0.169112i
$165$	2.13210e33	−	2.86464e33i	1.16560	−	1.56607i
$166$	5.31048e32			0.265163
$167$			1.04514e33i			0.476898i	0.971155	+	0.238449i	$0.0766391\pi$
$167$			1.04514e33i			0.476898i	−0.971155	+	0.238449i	$0.923361\pi$
$168$	−7.19422e32	−	5.35453e32i	−0.300154	−	0.223400i
$169$	1.32637e33			0.506250
$170$		−	2.09836e33i		−	0.733072i
$171$	7.33273e32	+	2.44713e33i	0.234598	+	0.782917i
$172$	−3.17018e32			−0.0929302
$173$			2.94614e33i			0.791703i	0.918314	+	0.395852i	$0.129551\pi$
$173$			2.94614e33i			0.791703i	−0.918314	+	0.395852i	$0.870449\pi$
$174$	2.68183e33	−	3.60324e33i	0.660986	−	0.888084i
$175$	5.90200e33			1.33484
$176$			1.56308e33i			0.324557i
$177$	−3.37748e33	−	2.51380e33i	−0.644161	−	0.479438i
$178$	−3.33722e33			−0.584904
$179$		−	1.60902e33i		−	0.259278i	−0.991561	−	0.129639i	$-0.958618\pi$
$179$		−	1.60902e33i		−	0.259278i	0.991561	−	0.129639i	$-0.0413819\pi$
$180$	−4.85921e33	+	1.45604e33i	−0.720242	+	0.215818i
$181$	−3.05703e33			−0.416985			−0.208493	−	0.978024i	$-0.566856\pi$
$181$	−3.05703e33			−0.416985			−0.208493	+	0.978024i	$0.566856\pi$
$182$			7.31329e33i			0.918422i
$183$	2.59028e33	−	3.48023e33i	0.299626	−	0.402570i
$184$	2.36080e32			0.0251647
$185$			2.94929e34i			2.89828i
$186$	−8.65229e33	−	6.43975e33i	−0.784218	−	0.583680i
$187$	−1.07018e34			−0.895021
$188$		−	1.81709e31i		−	0.00140284i
$189$	−1.39502e34	−	5.07167e33i	−0.994609	−	0.361596i
$190$	1.31933e34			0.869062
$191$		−	3.17809e34i		−	1.93493i	−0.253006	−	0.967465i	$-0.581419\pi$
$191$		−	3.17809e34i		−	1.93493i	0.253006	−	0.967465i	$-0.418581\pi$
$192$	1.32571e33	−	1.78118e33i	0.0746326	−	0.100274i
$193$	−3.25034e33			−0.169266			−0.0846329	−	0.996412i	$-0.526972\pi$
$193$	−3.25034e33			−0.169266			−0.0846329	+	0.996412i	$0.526972\pi$
$194$		−	1.56038e34i		−	0.751977i
$195$	3.31839e34	+	2.46982e34i	1.48050	+	1.10191i
$196$	−1.45207e33			−0.0599993
$197$			1.91274e34i			0.732255i	0.930565	+	0.366128i	$0.119317\pi$
$197$			1.91274e34i			0.732255i	−0.930565	+	0.366128i	$0.880683\pi$
$198$	7.42594e33	+	2.47824e34i	0.263496	+	0.879356i
$199$	−5.71548e34			−1.88043			−0.940213	−	0.340587i	$-0.889374\pi$
$199$	−5.71548e34			−1.88043			−0.940213	+	0.340587i	$0.889374\pi$
$200$			1.46125e34i			0.445938i
$201$	2.72891e34	−	3.66650e34i	0.772767	−	1.03827i
$202$	3.50990e34			0.922622
$203$		−	6.78794e34i		−	1.65690i
$204$	1.21951e34	+	9.07660e33i	0.276524	+	0.205812i
$205$	2.41375e34			0.508609
$206$			1.83581e34i			0.359600i
$207$	3.74300e33	−	1.12158e33i	0.0681813	−	0.0204302i
$208$	−1.81067e34			−0.306823
$209$		−	6.72871e34i		−	1.06105i
$210$	−4.57700e34	+	6.14955e34i	−0.671880	+	0.902721i
$211$	1.00464e35			1.37332			0.686660	−	0.726979i	$-0.259076\pi$
$211$	1.00464e35			1.37332			0.686660	+	0.726979i	$0.259076\pi$
$212$		−	4.01263e34i		−	0.510965i
$213$	2.65044e34	+	1.97267e34i	0.314502	+	0.234078i
$214$	7.21946e34			0.798542
$215$			2.70984e34i			0.279490i
$216$	1.25567e34	−	3.45386e34i	0.120801	−	0.332276i
$217$	−1.62996e35			−1.46312
$218$			2.62693e34i			0.220091i
$219$	−1.18845e35	+	1.59677e35i	−0.929649	+	1.24905i
$220$	1.33610e35			0.976113
$221$		−	1.23969e35i		−	0.846118i
$222$	−1.71404e35	−	1.27573e35i	−1.09327	−	0.813701i
$223$	−3.10016e35			−1.84847			−0.924234	−	0.381828i	$-0.875295\pi$
$223$	−3.10016e35			−1.84847			−0.924234	+	0.381828i	$0.875295\pi$
$224$		−	3.35548e34i		−	0.187083i
$225$	6.94216e34	+	2.31679e35i	0.362040	+	1.20823i
$226$	−2.02045e35			−0.985875
$227$			1.65309e32i			0.000754935i	1.00000		0.000377467i	$0.000120152\pi$
$227$			1.65309e32i			0.000754935i	−1.00000		0.000377467i	$0.999880\pi$
$228$	−5.70687e34	+	7.66761e34i	−0.243992	+	0.327821i
$229$	3.38419e35			1.35495			0.677474	−	0.735547i	$-0.263075\pi$
$229$	3.38419e35			1.35495			0.677474	+	0.735547i	$0.263075\pi$
$230$		−	2.01799e34i		−	0.0756834i
$231$	3.13632e35	+	2.33431e35i	1.10215	+	0.820310i
$232$	1.68060e35			0.553533
$233$			3.40796e35i			1.05234i	0.850380	+	0.526169i	$0.176372\pi$
$233$			3.40796e35i			1.05234i	−0.850380	+	0.526169i	$0.823628\pi$
$234$	−2.87078e35	+	8.60219e34i	−0.831309	+	0.249098i
$235$	−1.55323e33			−0.00421909
$236$		−	1.57530e35i		−	0.401498i
$237$	3.08287e35	−	4.14206e35i	0.737445	−	0.990813i
$238$	2.29737e35			0.515912
$239$		−	2.12376e35i		−	0.447855i	−0.974606	−	0.223927i	$-0.928112\pi$
$239$		−	2.12376e35i		−	0.447855i	0.974606	−	0.223927i	$-0.0718878\pi$
$240$	−1.52254e35	−	1.13320e35i	−0.301578	−	0.224459i
$241$	−5.82708e35			−1.08441			−0.542207	−	0.840245i	$-0.682411\pi$
$241$	−5.82708e35			−1.08441			−0.542207	+	0.840245i	$0.682411\pi$
$242$		−	2.77113e35i		−	0.484647i
$243$	3.49975e34	−	6.07259e35i	0.0575364	−	0.998343i
$244$	1.62322e35			0.250918
$245$			1.24121e35i			0.180449i
$246$	−1.04408e35	+	1.40280e35i	−0.142793	+	0.191854i
$247$	7.79452e35			1.00308
$248$		−	4.03554e35i		−	0.488795i
$249$	2.63814e35	+	1.96352e35i	0.300821	+	0.223896i
$250$	2.58767e35			0.277849
$251$			2.38902e35i			0.241609i	0.992676	+	0.120805i	$0.0385475\pi$
$251$			2.38902e35i			0.241609i	−0.992676	+	0.120805i	$0.961453\pi$
$252$	−1.59413e35	−	5.32005e35i	−0.151885	−	0.506883i
$253$	−1.02919e35			−0.0924032
$254$			6.18577e35i			0.523466i
$255$	7.75859e35	−	1.04242e36i	0.618985	−	0.831653i
$256$	8.30767e34			0.0625000
$257$			1.50122e36i			1.06524i	0.846355	+	0.532619i	$0.178792\pi$
$257$			1.50122e36i			1.06524i	−0.846355	+	0.532619i	$0.821208\pi$
$258$	−1.57488e35	−	1.17216e35i	−0.105427	−	0.0784676i
$259$	−3.22899e36			−2.03972
$260$			1.54774e36i			0.922779i
$261$	2.66456e36	−	7.98424e35i	1.49975	−	0.449393i
$262$	1.58029e36			0.839881
$263$			1.89443e36i			0.950916i	0.879738	+	0.475458i	$0.157718\pi$
$263$			1.89443e36i			0.950916i	−0.879738	+	0.475458i	$0.842282\pi$
$264$	−5.77941e35	+	7.76507e35i	−0.274047	+	0.368202i
$265$	−3.42996e36			−1.53674
$266$			1.44446e36i			0.611618i
$267$	−1.65786e36	−	1.23392e36i	−0.663559	−	0.493876i
$268$	1.71010e36			0.647142
$269$		−	1.85051e36i		−	0.662227i	−0.943591	−	0.331113i	$-0.892576\pi$
$269$		−	1.85051e36i		−	0.662227i	0.943591	−	0.331113i	$-0.107424\pi$
$270$	−2.95233e36	−	1.07334e36i	−0.999328	−	0.363312i
$271$	−2.56451e36			−0.821230			−0.410615	−	0.911809i	$-0.634686\pi$
$271$	−2.56451e36			−0.821230			−0.410615	+	0.911809i	$0.634686\pi$
$272$			5.68795e35i			0.172354i
$273$	−2.70406e36	+	3.63310e36i	−0.775489	+	1.04193i
$274$	2.04739e36			0.555830
$275$		−	6.37031e36i		−	1.63746i
$276$	1.17280e35	+	8.72893e34i	0.0285487	+	0.0212483i
$277$	6.87983e36			1.58629			0.793143	−	0.609035i	$-0.208443\pi$
$277$	6.87983e36			1.58629			0.793143	+	0.609035i	$0.208443\pi$
$278$			2.63049e36i			0.574598i
$279$	−1.91722e36	−	6.39829e36i	−0.396834	−	1.32434i
$280$	−2.86823e36			−0.562656
$281$			4.60601e36i			0.856506i	0.903659	+	0.428253i	$0.140871\pi$
$281$			4.60601e36i			0.856506i	−0.903659	+	0.428253i	$0.859129\pi$
$282$	6.71861e33	−	9.02695e33i	0.00118452	−	0.00159149i
$283$	4.28898e36			0.717063			0.358531	−	0.933518i	$-0.383278\pi$
$283$	4.28898e36			0.717063			0.358531	+	0.933518i	$0.383278\pi$
$284$			1.23620e36i			0.196026i
$285$	6.55420e36	+	4.87818e36i	0.985931	+	0.733812i
$286$	7.89360e36			1.12664
$287$			2.64266e36i			0.357943i
$288$	1.31717e36	−	3.94684e35i	0.169338	−	0.0507414i
$289$	4.29914e36			0.524704
$290$		−	1.43656e37i		−	1.66476i
$291$	5.76943e36	−	7.75166e36i	0.634948	−	0.853100i
$292$	−7.44754e36			−0.778521
$293$			1.48473e36i			0.147446i	0.997279	+	0.0737229i	$0.0234880\pi$
$293$			1.48473e36i			0.147446i	−0.997279	+	0.0737229i	$0.976512\pi$
$294$	−7.21359e35	−	5.36895e35i	−0.0680678	−	0.0506617i
$295$	−1.34655e37			−1.20752
$296$		−	7.99452e36i		−	0.681423i
$297$	−5.47410e36	+	1.50571e37i	−0.443574	+	1.22010i
$298$	2.01980e36			0.155620
$299$		−	1.19221e36i		−	0.0873544i
$300$	−5.40290e36	+	7.25920e36i	−0.376537	+	0.505906i
$301$	−2.96683e36			−0.196696
$302$		−	1.01532e37i		−	0.640472i
$303$	1.74365e37	+	1.29777e37i	1.04669	+	0.779035i
$304$	−3.57627e36			−0.204327
$305$		−	1.38752e37i		−	0.754641i
$306$	2.70225e36	+	9.01815e36i	0.139928	+	0.466978i
$307$	6.09546e36			0.300560			0.150280	−	0.988644i	$-0.451983\pi$
$307$	6.09546e36			0.300560			0.150280	+	0.988644i	$0.451983\pi$
$308$			1.46282e37i			0.686957i
$309$	−6.78783e36	+	9.11996e36i	−0.303636	+	0.407958i
$310$	−3.44954e37			−1.47006
$311$		−	2.10426e37i		−	0.854464i	−0.904142	−	0.427232i	$-0.859489\pi$
$311$		−	2.10426e37i		−	0.854464i	0.904142	−	0.427232i	$-0.140511\pi$
$312$	−8.99504e36	−	6.69485e36i	−0.348084	−	0.259073i
$313$	2.30076e37			0.848608			0.424304	−	0.905520i	$-0.360519\pi$
$313$	2.30076e37			0.848608			0.424304	+	0.905520i	$0.360519\pi$
$314$			1.42398e37i			0.500680i
$315$	−4.54753e37	+	1.36265e37i	−1.52446	+	0.456800i
$316$	1.93191e37			0.617563
$317$			3.43253e37i			1.04647i	0.852189	+	0.523234i	$0.175274\pi$
$317$			3.43253e37i			1.04647i	−0.852189	+	0.523234i	$0.824726\pi$
$318$	1.48365e37	−	1.99340e37i	0.431445	−	0.579678i
$319$	−7.32655e37			−2.03254
$320$		−	7.10132e36i		−	0.187970i
$321$	3.58648e37	+	2.66936e37i	0.905927	+	0.674266i
$322$	2.20937e36			0.0532635
$323$		−	2.44854e37i		−	0.563467i
$324$	1.90084e37	−	1.25153e37i	0.417610	−	0.274958i
$325$	7.37935e37			1.54799
$326$		−	5.54093e36i		−	0.110999i
$327$	−9.71296e36	+	1.30501e37i	−0.185838	+	0.249688i
$328$	−6.54286e36			−0.119580
$329$		−	1.70054e35i		−	0.00296926i
$330$	6.63750e37	+	4.94018e37i	1.10738	+	0.824202i
$331$	1.16335e37			0.185477			0.0927385	−	0.995690i	$-0.470438\pi$
$331$	1.16335e37			0.185477			0.0927385	+	0.995690i	$0.470438\pi$
$332$			1.23046e37i			0.187498i
$333$	−3.79807e37	−	1.26752e38i	−0.553221	−	1.84625i
$334$	−2.42163e37			−0.337218
$335$		−	1.46178e38i		−	1.94630i
$336$	1.24067e37	−	1.66693e37i	0.157967	−	0.212241i
$337$	1.02043e38			1.24261			0.621304	−	0.783570i	$-0.286603\pi$
$337$	1.02043e38			1.24261			0.621304	+	0.783570i	$0.286603\pi$
$338$			3.07327e37i			0.357973i
$339$	−1.00372e38	−	7.47052e37i	−1.11845	−	0.832444i
$340$	4.86200e37			0.518360
$341$			1.75929e38i			1.79483i
$342$	−5.67012e37	+	1.69903e37i	−0.553606	+	0.165886i
$343$	9.96561e37			0.931305
$344$		−	7.34545e36i		−	0.0657116i
$345$	7.46140e36	−	1.00250e37i	0.0639049	−	0.0858610i
$346$	−6.82636e37			−0.559819
$347$		−	6.06469e37i		−	0.476285i	−0.971230	−	0.238142i	$-0.923462\pi$
$347$		−	6.06469e37i		−	0.476285i	0.971230	−	0.238142i	$-0.0765385\pi$
$348$	8.34887e37	+	6.21392e37i	0.627970	+	0.467387i
$349$	−1.91055e38			−1.37650			−0.688251	−	0.725473i	$-0.741621\pi$
$349$	−1.91055e38			−1.37650			−0.688251	+	0.725473i	$0.741621\pi$
$350$			1.36752e38i			0.943872i
$351$	−1.74421e38	−	6.34118e37i	−1.15343	−	0.419337i
$352$	−3.62173e37			−0.229496
$353$			2.71259e38i			1.64727i	0.567123	+	0.823633i	$0.308056\pi$
$353$			2.71259e38i			1.64727i	−0.567123	+	0.823633i	$0.691944\pi$
$354$	5.82460e37	−	7.82579e37i	0.339014	−	0.455490i
$355$	1.05669e38			0.589552
$356$		−	7.73249e37i		−	0.413589i
$357$	1.14129e38	+	8.49440e37i	0.585290	+	0.435622i
$358$	3.72818e37			0.183337
$359$			7.47561e36i			0.0352558i	0.999845	+	0.0176279i	$0.00561142\pi$
$359$			7.47561e36i			0.0352558i	−0.999845	+	0.0176279i	$0.994389\pi$
$360$	−3.37372e37	−	1.12590e38i	−0.152606	−	0.509288i
$361$	−7.65161e37			−0.332005
$362$		−	7.08328e37i		−	0.294853i
$363$	1.02461e38	−	1.37664e38i	0.409222	−	0.549821i
$364$	−1.69453e38			−0.649422
$365$			6.36609e38i			2.34142i
$366$	8.06386e37	+	6.00179e37i	0.284660	+	0.211868i
$367$	−2.66047e38			−0.901502			−0.450751	−	0.892650i	$-0.648844\pi$
$367$	−2.66047e38			−0.901502			−0.450751	+	0.892650i	$0.648844\pi$
$368$			5.47008e36i			0.0177941i
$369$	−1.03736e38	+	3.10841e37i	−0.323992	+	0.0970828i
$370$	−6.83363e38			−2.04940
$371$		−	3.75525e38i		−	1.08151i
$372$	1.49212e38	−	2.00478e38i	0.412724	−	0.554526i
$373$	5.05935e38			1.34419			0.672097	−	0.740463i	$-0.265394\pi$
$373$	5.05935e38			1.34419			0.672097	+	0.740463i	$0.265394\pi$
$374$		−	2.47966e38i		−	0.632875i
$375$	1.28550e38	+	9.56779e37i	0.315213	+	0.234608i
$376$	4.21029e35			0.000991960
$377$		−	8.48706e38i		−	1.92149i
$378$	1.17513e38	−	3.23232e38i	0.255687	−	0.703295i
$379$	7.33102e37			0.153312			0.0766561	−	0.997058i	$-0.475576\pi$
$379$	7.33102e37			0.153312			0.0766561	+	0.997058i	$0.475576\pi$
$380$			3.05696e38i			0.614520i
$381$	−2.28716e38	+	3.07297e38i	−0.441999	+	0.593859i
$382$	7.36378e38			1.36820
$383$			6.45982e38i			1.15409i	0.816713	+	0.577044i	$0.195794\pi$
$383$			6.45982e38i			1.15409i	−0.816713	+	0.577044i	$0.804206\pi$
$384$	4.12709e37	+	3.07172e37i	0.0709048	+	0.0527732i
$385$	1.25040e39			2.06604
$386$		−	7.53120e37i		−	0.119689i
$387$	−3.48971e37	−	1.16461e38i	−0.0533488	−	0.178039i
$388$	3.61548e38			0.531728
$389$		−	8.02555e37i		−	0.113561i	−0.998387	−	0.0567807i	$-0.981916\pi$
$389$		−	8.02555e37i		−	0.113561i	0.998387	−	0.0567807i	$-0.0180836\pi$
$390$	−5.72269e38	+	7.68887e38i	−0.779169	+	1.04687i
$391$	−3.74515e37			−0.0490702
$392$		−	3.36451e37i		−	0.0424259i
$393$	7.85057e38	+	5.84305e38i	0.952825	+	0.709171i
$394$	−4.43191e38			−0.517782
$395$		−	1.65138e39i		−	1.85734i
$396$	−5.74219e38	+	1.72062e38i	−0.621799	+	0.186320i
$397$	−1.16386e39			−1.21351			−0.606753	−	0.794890i	$-0.707528\pi$
$397$	−1.16386e39			−1.21351			−0.606753	+	0.794890i	$0.707528\pi$
$398$		−	1.32430e39i		−	1.32966i
$399$	−5.34081e38	+	7.17578e38i	−0.516433	+	0.693866i
$400$	−3.38578e38			−0.315326
$401$		−	8.84850e38i		−	0.793787i	−0.917865	−	0.396893i	$-0.870088\pi$
$401$		−	8.84850e38i		−	0.793787i	0.917865	−	0.396893i	$-0.129912\pi$
$402$	8.49545e38	+	6.32302e38i	0.734168	+	0.546429i
$403$	−2.03796e39			−1.69676
$404$			8.13259e38i			0.652392i
$405$	−1.06980e39	−	1.62482e39i	−0.826944	−	1.25597i
$406$	1.57280e39			1.17161
$407$			3.48521e39i			2.50214i
$408$	−2.10309e38	+	2.82566e38i	−0.145531	+	0.195532i
$409$	−7.14737e38			−0.476756			−0.238378	−	0.971172i	$-0.576616\pi$
$409$	−7.14737e38			−0.476756			−0.238378	+	0.971172i	$0.576616\pi$
$410$			5.59277e38i			0.359641i
$411$	1.01710e39	+	7.57012e38i	0.630576	+	0.469327i
$412$	−4.25367e38			−0.254276
$413$		−	1.47426e39i		−	0.849811i
$414$	2.59875e37	+	8.67272e37i	0.0144464	+	0.0482114i
$415$	1.05179e39			0.563906
$416$		−	4.19540e38i		−	0.216957i
$417$	−9.72609e38	+	1.30677e39i	−0.485174	+	0.651868i
$418$	1.55907e39			0.750278
$419$		−	1.55623e39i		−	0.722543i	−0.932461	−	0.361271i	$-0.882343\pi$
$419$		−	1.55623e39i		−	0.722543i	0.932461	−	0.361271i	$-0.117657\pi$
$420$	−1.42488e39	−	1.06051e39i	−0.638320	−	0.475091i
$421$	−8.25530e38			−0.356863			−0.178431	−	0.983952i	$-0.557102\pi$
$421$	−8.25530e38			−0.356863			−0.178431	+	0.983952i	$0.557102\pi$
$422$			2.32779e39i			0.971084i
$423$	6.67534e36	−	2.00024e36i	0.00268762	−	0.000805335i
$424$	9.29746e38			0.361307
$425$		−	2.31812e39i		−	0.869564i
$426$	−4.57078e38	+	6.14119e38i	−0.165518	+	0.222386i
$427$	1.51911e39			0.531092
$428$			1.67278e39i			0.564655i
$429$	3.92138e39	+	2.91862e39i	1.27814	+	0.951301i
$430$	−6.27882e38			−0.197629
$431$		−	2.08580e39i		−	0.634036i	−0.948420	−	0.317018i	$-0.897318\pi$
$431$		−	2.08580e39i		−	0.634036i	0.948420	−	0.317018i	$-0.102682\pi$
$432$	8.00276e38	+	2.90945e38i	0.234954	+	0.0854191i
$433$	−2.82587e39			−0.801372			−0.400686	−	0.916215i	$-0.631228\pi$
$433$	−2.82587e39			−0.801372			−0.400686	+	0.916215i	$0.631228\pi$
$434$		−	3.77669e39i		−	1.03458i
$435$	5.31160e39	−	7.13653e39i	1.40568	−	1.88864i
$436$	−6.08673e38			−0.155628
$437$		−	2.35475e38i		−	0.0581732i
$438$	−3.69979e39	−	2.75369e39i	−0.883214	−	0.657361i
$439$	1.46707e39			0.338441			0.169220	−	0.985578i	$-0.445875\pi$
$439$	1.46707e39			0.338441			0.169220	+	0.985578i	$0.445875\pi$
$440$			3.09582e39i			0.690216i
$441$	−1.59843e38	−	5.33438e38i	−0.0344440	−	0.114949i
$442$	2.87243e39			0.598295
$443$			8.86224e39i			1.78438i	0.451658	+	0.892191i	$0.350833\pi$
$443$			8.86224e39i			1.78438i	−0.451658	+	0.892191i	$0.649167\pi$
$444$	2.95593e39	−	3.97152e39i	0.575374	−	0.773058i
$445$	−6.60965e39			−1.24388
$446$		−	7.18323e39i		−	1.30706i
$447$	1.00340e39	+	7.46812e38i	0.176547	+	0.131401i
$448$	7.77480e38			0.132287
$449$			7.57100e39i			1.24583i	0.782290	+	0.622914i	$0.214051\pi$
$449$			7.57100e39i			1.24583i	−0.782290	+	0.622914i	$0.785949\pi$
$450$	−5.36811e39	+	1.60853e39i	−0.854345	+	0.256001i
$451$	2.85236e39			0.439092
$452$		−	4.68148e39i		−	0.697119i
$453$	3.75411e39	−	5.04393e39i	0.540797	−	0.726601i
$454$	−3.83029e36			−0.000533819
$455$			1.44846e40i			1.95315i
$456$	−1.77662e39	−	1.32231e39i	−0.231805	−	0.172528i
$457$	1.46258e39			0.184662			0.0923308	−	0.995728i	$-0.470568\pi$
$457$	1.46258e39			0.184662			0.0923308	+	0.995728i	$0.470568\pi$
$458$			7.84133e39i			0.958093i
$459$	−1.99199e39	+	5.47919e39i	−0.235558	+	0.647927i
$460$	4.67577e38			0.0535162
$461$		−	6.64681e39i		−	0.736375i	−0.929752	−	0.368188i	$-0.879978\pi$
$461$		−	6.64681e39i		−	0.736375i	0.929752	−	0.368188i	$-0.120022\pi$
$462$	−5.40870e39	+	7.26699e39i	−0.580047	+	0.779337i
$463$	−8.18362e39			−0.849631			−0.424816	−	0.905280i	$-0.639661\pi$
$463$	−8.18362e39			−0.849631			−0.424816	+	0.905280i	$0.639661\pi$
$464$			3.89402e39i			0.391407i
$465$	−1.71366e40	−	1.27545e40i	−1.66775	−	1.24128i
$466$	−7.89640e39			−0.744116
$467$		−	2.10165e39i		−	0.191781i	−0.995392	−	0.0958907i	$-0.969430\pi$
$467$		−	2.10165e39i		−	0.191781i	0.995392	−	0.0958907i	$-0.0305699\pi$
$468$	−1.99317e39	−	6.65174e39i	−0.176139	−	0.587824i
$469$	1.60041e40			1.36974
$470$		−	3.59891e37i		−	0.00298334i
$471$	−5.26511e39	+	7.07408e39i	−0.422760	+	0.568010i
$472$	3.65005e39			0.283902
$473$			3.20225e39i			0.241289i
$474$	9.59736e39	+	7.14315e39i	0.700611	+	0.521453i
$475$	1.45751e40			1.03088
$476$			5.32311e39i			0.364805i
$477$	1.47410e40	−	4.41707e39i	0.978927	−	0.293332i
$478$	4.92086e39			0.316681
$479$			1.89547e38i			0.0118218i	0.999983	+	0.00591092i	$0.00188152\pi$
$479$			1.89547e38i			0.0118218i	−0.999983	+	0.00591092i	$0.998118\pi$
$480$	2.62568e39	−	3.52780e39i	0.158717	−	0.213248i
$481$	−4.03725e40			−2.36543
$482$		−	1.35016e40i		−	0.766797i
$483$	1.09757e39	+	8.16903e38i	0.0604262	+	0.0449742i
$484$	6.42083e39			0.342697
$485$		−	3.09047e40i		−	1.59919i
$486$	1.40705e40	+	8.10908e38i	0.705935	+	0.0406844i
$487$	2.09019e40			1.01684			0.508419	−	0.861110i	$-0.330230\pi$
$487$	2.09019e40			1.01684			0.508419	+	0.861110i	$0.330230\pi$
$488$			3.76109e39i			0.177426i
$489$	2.04873e39	−	2.75263e39i	0.0937244	−	0.125926i
$490$	−2.87595e39			−0.127597
$491$		−	4.53699e40i		−	1.95230i	−0.217106	−	0.976148i	$-0.569662\pi$
$491$		−	4.53699e40i		−	1.95230i	0.217106	−	0.976148i	$-0.430338\pi$
$492$	−3.25036e39	−	2.41919e39i	−0.135661	−	0.100970i
$493$	−2.66609e40			−1.07937
$494$			1.80603e40i			0.709284i
$495$	1.47077e40	+	4.90837e40i	0.560361	+	1.87008i
$496$	9.35054e39			0.345630
$497$			1.15690e40i			0.414908i
$498$	−4.54958e39	+	6.11270e39i	−0.158318	+	0.212713i
$499$	1.93606e40			0.653748			0.326874	−	0.945068i	$-0.394005\pi$
$499$	1.93606e40			0.653748			0.326874	+	0.945068i	$0.394005\pi$
$500$			5.99576e39i			0.196469i
$501$	−1.20302e40	−	8.95386e39i	−0.382566	−	0.284737i
$502$	−5.53547e39			−0.170844
$503$		−	9.12513e39i		−	0.273350i	−0.990616	−	0.136675i	$-0.956358\pi$
$503$		−	9.12513e39i		−	0.273350i	0.990616	−	0.136675i	$-0.0436416\pi$
$504$	1.23268e40	−	3.69368e39i	0.358420	−	0.107399i
$505$	6.95166e40			1.96209
$506$		−	2.38468e39i		−	0.0653389i
$507$	−1.13633e40	+	1.52674e40i	−0.302262	+	0.406112i
$508$	−1.43327e40			−0.370146
$509$		−	3.20406e39i		−	0.0803405i	−0.999193	−	0.0401702i	$-0.987210\pi$
$509$		−	3.20406e39i		−	0.0803405i	0.999193	−	0.0401702i	$-0.0127900\pi$
$510$	2.41535e40	+	1.79770e40i	0.588067	+	0.437689i
$511$	−6.96984e40			−1.64782
$512$			1.92493e39i			0.0441942i
$513$	−3.44501e40	−	1.25246e40i	−0.768122	−	0.279255i
$514$	−3.47839e40			−0.753237
$515$			3.63599e40i			0.764741i
$516$	2.71594e39	−	3.64907e39i	0.0554850	−	0.0745482i
$517$	−1.83547e38			−0.00364242
$518$		−	7.48172e40i		−	1.44230i
$519$	−3.39120e40	−	2.52401e40i	−0.635101	−	0.472695i
$520$	−3.58619e40			−0.652504
$521$		−	2.94404e40i		−	0.520448i	−0.965548	−	0.260224i	$-0.916204\pi$
$521$		−	2.94404e40i		−	0.520448i	0.965548	−	0.260224i	$-0.0837964\pi$
$522$	1.84999e40	+	6.17391e40i	0.317769	+	1.06048i
$523$	−2.69994e40			−0.450639			−0.225320	−	0.974285i	$-0.572343\pi$
$523$	−2.69994e40			−0.450639			−0.225320	+	0.974285i	$0.572343\pi$
$524$			3.66161e40i			0.593885i
$525$	−5.05634e40	+	6.79357e40i	−0.796979	+	1.07080i
$526$	−4.38948e40			−0.672399
$527$			6.40196e40i			0.953134i
$528$	−1.79920e40	−	1.33912e40i	−0.260358	−	0.193780i
$529$	7.07342e40			0.994934
$530$		−	7.94738e40i		−	1.08664i
$531$	5.78709e40	−	1.73408e40i	0.769206	−	0.230490i
$532$	−3.34688e40			−0.432479
$533$			3.30416e40i			0.415101i
$534$	2.85905e40	−	3.84135e40i	0.349223	−	0.469207i
$535$	1.42988e41			1.69821
$536$			3.96239e40i			0.457599i
$537$	1.85208e40	+	1.37847e40i	0.207992	+	0.154805i
$538$	4.28771e40			0.468265
$539$			1.46676e40i			0.155785i
$540$	2.48697e40	−	6.84068e40i	0.256900	−	0.706631i
$541$	3.71909e40			0.373661			0.186830	−	0.982392i	$-0.440179\pi$
$541$	3.71909e40			0.373661			0.186830	+	0.982392i	$0.440179\pi$
$542$		−	5.94209e40i		−	0.580697i
$543$	2.61901e40	−	3.51883e40i	0.248966	−	0.334504i
$544$	−1.31792e40			−0.121873
$545$			5.20288e40i			0.468054i
$546$	−8.41807e40	−	6.26542e40i	−0.736754	−	0.548354i
$547$	−2.39025e40			−0.203532			−0.101766	−	0.994808i	$-0.532449\pi$
$547$	−2.39025e40			−0.203532			−0.101766	+	0.994808i	$0.532449\pi$
$548$			4.74389e40i			0.393031i
$549$	1.78683e40	+	5.96315e40i	0.144045	+	0.480718i
$550$	1.47603e41			1.15786
$551$		−	1.67629e41i		−	1.27960i
$552$	−2.02253e39	+	2.71743e39i	−0.0150248	+	0.0201870i
$553$	1.80799e41			1.30713
$554$			1.59409e41i			1.12167i
$555$	−3.39481e41	−	2.52670e41i	−2.32499	−	1.73045i
$556$	−6.09496e40			−0.406302
$557$			1.86305e41i			1.20892i	0.796636	+	0.604459i	$0.206611\pi$
$557$			1.86305e41i			1.20892i	−0.796636	+	0.604459i	$0.793389\pi$
$558$	1.48251e41	−	4.44229e40i	0.936452	−	0.280604i
$559$	−3.70947e40			−0.228105
$560$		−	6.64582e40i		−	0.397858i
$561$	9.16842e40	−	1.23185e41i	0.534382	−	0.717982i
$562$	−1.06723e41			−0.605641
$563$		−	2.91313e40i		−	0.160966i	−0.996756	−	0.0804828i	$-0.974354\pi$
$563$		−	2.91313e40i		−	0.160966i	0.996756	−	0.0804828i	$-0.0256462\pi$
$564$	2.09159e38	+	1.55673e38i	0.00112535	+	0.000837582i
$565$	−4.00168e41			−2.09660
$566$			9.93777e40i			0.507040i
$567$	1.77892e41	−	1.17125e41i	0.883913	−	0.581976i
$568$	−2.86433e40			−0.138611
$569$		−	2.47844e40i		−	0.116814i	−0.998293	−	0.0584069i	$-0.981398\pi$
$569$		−	2.47844e40i		−	0.116814i	0.998293	−	0.0584069i	$-0.0186021\pi$
$570$	−1.13030e41	+	1.51864e41i	−0.518883	+	0.697158i
$571$	−7.97205e40			−0.356474			−0.178237	−	0.983988i	$-0.557039\pi$
$571$	−7.97205e40			−0.356474			−0.178237	+	0.983988i	$0.557039\pi$
$572$			1.82898e41i			0.796653i
$573$	3.65818e41	+	2.72272e41i	1.55219	+	1.15527i
$574$	−6.12318e40			−0.253104
$575$		−	2.22932e40i		−	0.0897750i
$576$	9.14502e39	+	3.05194e40i	0.0358796	+	0.119740i
$577$	3.66947e40			0.140270			0.0701352	−	0.997537i	$-0.477657\pi$
$577$	3.66947e40			0.140270			0.0701352	+	0.997537i	$0.477657\pi$
$578$			9.96132e40i			0.371022i
$579$	2.78462e40	−	3.74135e40i	0.101062	−	0.135784i
$580$	3.32857e41			1.17717
$581$			1.15154e41i			0.396859i
$582$	1.79610e41	+	1.33680e41i	0.603233	+	0.448976i
$583$	−4.05322e41			−1.32670
$584$		−	1.72563e41i		−	0.550497i
$585$	−5.68584e41	+	1.70374e41i	−1.76790	+	0.529743i
$586$	−3.44018e40			−0.104260
$587$			3.42946e41i			1.01310i	0.862209	+	0.506552i	$0.169080\pi$
$587$			3.42946e41i			1.01310i	−0.862209	+	0.506552i	$0.830920\pi$
$588$	1.24401e40	−	1.67142e40i	0.0358232	−	0.0481312i
$589$	−4.02520e41			−1.12995
$590$		−	3.12003e41i		−	0.853843i
$591$	−2.20168e41	−	1.63868e41i	−0.587412	−	0.437201i
$592$	1.85237e41			0.481838
$593$			5.42621e40i			0.137618i	0.997630	+	0.0688091i	$0.0219199\pi$
$593$			5.42621e40i			0.137618i	−0.997630	+	0.0688091i	$0.978080\pi$
$594$	−3.48880e41	−	1.26837e41i	−0.862739	−	0.313654i
$595$	4.55014e41			1.09716
$596$			4.67998e40i			0.110040i
$597$	4.89655e41	−	6.57888e41i	1.12273	−	1.50847i
$598$	2.76240e40			0.0617689
$599$		−	6.98318e41i		−	1.52283i	−0.648266	−	0.761414i	$-0.724506\pi$
$599$		−	6.98318e41i		−	1.52283i	0.648266	−	0.761414i	$-0.275494\pi$
$600$	−1.68199e41	−	1.25188e41i	−0.357730	−	0.266252i
$601$	6.10922e41			1.26727			0.633635	−	0.773632i	$-0.281562\pi$
$601$	6.10922e41			1.26727			0.633635	+	0.773632i	$0.281562\pi$
$602$		−	6.87429e40i		−	0.139085i
$603$	1.88247e41	+	6.28230e41i	0.371507	+	1.23982i
$604$	2.35255e41			0.452882
$605$		−	5.48846e41i		−	1.03067i
$606$	−3.00699e41	+	4.04011e41i	−0.550861	+	0.740123i
$607$	−3.14568e41			−0.562191			−0.281095	−	0.959680i	$-0.590698\pi$
$607$	−3.14568e41			−0.562191			−0.281095	+	0.959680i	$0.590698\pi$
$608$		−	8.28639e40i		−	0.144481i
$609$	7.81335e41	+	5.81534e41i	1.32916	+	0.989272i
$610$	3.21494e41			0.533612
$611$		−	2.12621e39i		−	0.00344340i
$612$	−2.08955e41	+	6.26125e40i	−0.330203	+	0.0989441i
$613$	1.12831e42			1.73989			0.869947	−	0.493145i	$-0.164153\pi$
$613$	1.12831e42			1.73989			0.869947	+	0.493145i	$0.164153\pi$
$614$			1.41235e41i			0.212528i
$615$	−2.06790e41	+	2.77838e41i	−0.303671	+	0.408004i
$616$	−3.38942e41			−0.485752
$617$		−	3.28721e41i		−	0.459780i	−0.973217	−	0.229890i	$-0.926163\pi$
$617$		−	3.28721e41i		−	0.459780i	0.973217	−	0.229890i	$-0.0738366\pi$
$618$	−2.11314e41	−	1.57277e41i	−0.288470	−	0.214703i
$619$	−1.12587e42			−1.50013			−0.750066	−	0.661363i	$-0.769978\pi$
$619$	−1.12587e42			−1.50013			−0.750066	+	0.661363i	$0.769978\pi$
$620$		−	7.99275e41i		−	1.03949i
$621$	−1.91569e40	+	5.26931e40i	−0.0243193	+	0.0668928i
$622$	4.87567e41			0.604198
$623$		−	7.23650e41i		−	0.875403i
$624$	1.55123e41	−	2.08419e41i	0.183192	−	0.246133i
$625$	−5.81495e41			−0.670418
$626$			5.33098e41i			0.600057i
$627$	7.74517e41	+	5.76460e41i	0.851173	+	0.633514i
$628$	−3.29944e41			−0.354035
$629$			1.26825e42i			1.32875i
$630$	−3.15732e41	−	1.05368e42i	−0.323006	−	1.07796i
$631$	5.95453e41			0.594849			0.297425	−	0.954745i	$-0.403872\pi$
$631$	5.95453e41			0.594849			0.297425	+	0.954745i	$0.403872\pi$
$632$			4.47633e41i			0.436683i
$633$	−8.60688e41	+	1.15640e42i	−0.819955	+	1.10167i
$634$	−7.95334e41			−0.739964
$635$			1.22515e42i			1.11322i
$636$	4.61879e41	+	3.43769e41i	0.409894	+	0.305077i
$637$	−1.69909e41			−0.147273
$638$		−	1.69760e42i		−	1.43722i
$639$	−4.54135e41	+	1.36080e41i	−0.375553	+	0.112533i
$640$	1.64541e41			0.132915
$641$		−	6.38589e40i		−	0.0503907i	−0.999683	−	0.0251954i	$-0.991979\pi$
$641$		−	6.38589e40i		−	0.0503907i	0.999683	−	0.0251954i	$-0.00802078\pi$
$642$	−6.18503e41	+	8.31005e41i	−0.476778	+	0.640587i
$643$	−1.27866e42			−0.962922			−0.481461	−	0.876468i	$-0.659894\pi$
$643$	−1.27866e42			−0.962922			−0.481461	+	0.876468i	$0.659894\pi$
$644$			5.11921e40i			0.0376630i
$645$	−3.11919e41	−	2.32156e41i	−0.224206	−	0.166872i
$646$	5.67338e41			0.398432
$647$		−	2.16850e42i		−	1.48797i	−0.668196	−	0.743985i	$-0.732933\pi$
$647$		−	2.16850e42i		−	1.48797i	0.668196	−	0.743985i	$-0.267067\pi$
$648$	2.89986e41	+	4.40434e41i	0.194425	+	0.295295i
$649$	−1.59124e42			−1.04247
$650$			1.70983e42i			1.09459i
$651$	1.39641e42	−	1.87618e42i	0.873572	−	1.17371i
$652$	1.28386e41			0.0784881
$653$			8.56109e41i			0.511483i	0.966745	+	0.255742i	$0.0823196\pi$
$653$			8.56109e41i			0.511483i	−0.966745	+	0.255742i	$0.917680\pi$
$654$	−3.02377e41	−	2.25054e41i	−0.176556	−	0.131408i
$655$	3.12991e42			1.78613
$656$		−	1.51601e41i		−	0.0845561i
$657$	−8.19820e41	−	2.73596e42i	−0.446928	−	1.49152i
$658$	3.94023e39			0.00209958
$659$			1.24570e42i			0.648831i	0.945915	+	0.324415i	$0.105168\pi$
$659$			1.24570e42i			0.648831i	−0.945915	+	0.324415i	$0.894832\pi$
$660$	−1.14466e42	+	1.53794e42i	−0.582799	+	0.783034i
$661$	−2.57134e42			−1.27979			−0.639895	−	0.768463i	$-0.721022\pi$
$661$	−2.57134e42			−1.27979			−0.639895	+	0.768463i	$0.721022\pi$
$662$			2.69554e41i			0.131152i
$663$	1.42697e42	+	1.06207e42i	0.678752	+	0.505184i
$664$	−2.85104e41			−0.132581
$665$			2.86088e42i			1.30069i
$666$	2.93690e42	−	8.80030e41i	1.30550	−	0.391187i
$667$	−2.56396e41			−0.111436
$668$		−	5.61103e41i		−	0.238449i
$669$	2.65596e42	−	3.56849e42i	1.10365	−	1.48283i
$670$	3.38701e42			1.37624
$671$		−	1.63965e42i		−	0.651496i
$672$	3.86237e41	+	2.87469e41i	0.150077	+	0.111700i
$673$	−6.16059e41			−0.234097			−0.117049	−	0.993126i	$-0.537343\pi$
$673$	−6.16059e41			−0.234097			−0.117049	+	0.993126i	$0.537343\pi$
$674$			2.36438e42i			0.878656i
$675$	−3.26152e42	−	1.18574e42i	−1.18539	−	0.430958i
$676$	−7.12091e41			−0.253125
$677$		−	3.66987e42i		−	1.27591i	−0.770073	−	0.637956i	$-0.779780\pi$
$677$		−	3.66987e42i		−	1.27591i	0.770073	−	0.637956i	$-0.220220\pi$
$678$	1.73095e42	−	2.32567e42i	0.588627	−	0.790865i
$679$	3.38357e42			1.12546
$680$			1.12655e42i			0.366536i
$681$	−1.90281e39	−	1.41623e39i	−0.000605605	−	0.000450742i
$682$	−4.07636e42			−1.26913
$683$			2.91204e42i			0.886926i	0.896293	+	0.443463i	$0.146250\pi$
$683$			2.91204e42i			0.886926i	−0.896293	+	0.443463i	$0.853750\pi$
$684$	−3.93673e41	−	1.31379e42i	−0.117299	−	0.391458i
$685$	4.05504e42			1.18205
$686$			2.30908e42i			0.658532i
$687$	−2.89929e42	+	3.89542e42i	−0.808986	+	1.08693i
$688$	1.70198e41			0.0464651
$689$		−	4.69525e42i		−	1.25421i
$690$	2.32283e41	+	1.72884e41i	0.0607129	+	0.0451876i
$691$	2.87692e42			0.735797			0.367898	−	0.929866i	$-0.380077\pi$
$691$	2.87692e42			0.735797			0.367898	+	0.929866i	$0.380077\pi$
$692$		−	1.58170e42i		−	0.395852i
$693$	−5.37387e42	+	1.61026e42i	−1.31610	+	0.394364i
$694$	1.40522e42			0.336784
$695$			5.20991e42i			1.22196i
$696$	−1.43979e42	+	1.93447e42i	−0.330493	+	0.444042i
$697$	1.03796e42			0.233178
$698$		−	4.42683e42i		−	0.973334i
$699$	−3.92278e42	−	2.91966e42i	−0.844182	−	0.628310i
$700$	−3.16861e42			−0.667418
$701$		−	8.13040e40i		−	0.0167626i	−0.999965	−	0.00838130i	$-0.997332\pi$
$701$		−	8.13040e40i		−	0.0167626i	0.999965	−	0.00838130i	$-0.00266788\pi$
$702$	1.46928e42	−	4.04142e42i	0.296516	−	0.815600i
$703$	−7.97403e42			−1.57524
$704$		−	8.39172e41i		−	0.162278i
$705$	1.33068e40	−	1.78787e40i	0.00251905	−	0.00338453i
$706$	−6.28520e42			−1.16479
$707$			7.61095e42i			1.38085i
$708$	1.81327e42	+	1.34959e42i	0.322080	+	0.239719i
$709$	−3.12018e42			−0.542608			−0.271304	−	0.962494i	$-0.587455\pi$
$709$	−3.12018e42			−0.542608			−0.271304	+	0.962494i	$0.587455\pi$
$710$			2.44840e42i			0.416876i
$711$	2.12663e42	+	7.09715e42i	0.354527	+	1.18315i
$712$	1.79165e42			0.292452
$713$			6.15674e41i			0.0984028i
$714$	−1.96819e42	+	2.64441e42i	−0.308031	+	0.413863i
$715$	1.56340e43			2.39596
$716$			8.63836e41i			0.129639i
$717$	2.44458e42	+	1.81946e42i	0.359267	+	0.267397i
$718$	−1.73214e41			−0.0249296
$719$			4.77475e42i			0.673003i	0.941683	+	0.336502i	$0.109244\pi$
$719$			4.77475e42i			0.673003i	−0.941683	+	0.336502i	$0.890756\pi$
$720$	2.60877e42	−	7.81708e41i	0.360121	−	0.107909i
$721$	−3.98082e42			−0.538200
$722$		−	1.77291e42i		−	0.234763i
$723$	4.99216e42	−	6.70734e42i	0.647461	−	0.869913i
$724$	1.64123e42			0.208493
$725$		−	1.58700e43i		−	1.97473i
$726$	3.18974e42	+	2.37407e42i	0.388782	+	0.289364i
$727$	3.03925e42			0.362869			0.181435	−	0.983403i	$-0.441926\pi$
$727$	3.03925e42			0.362869			0.181435	+	0.983403i	$0.441926\pi$
$728$		−	3.92630e42i		−	0.459211i
$729$	6.69011e42	+	5.60534e42i	0.766514	+	0.642227i
$730$	−1.47505e43			−1.65564
$731$			1.16528e42i			0.128135i
$732$	−1.39064e42	+	1.86843e42i	−0.149813	+	0.201285i
$733$	−5.04733e42			−0.532724			−0.266362	−	0.963873i	$-0.585822\pi$
$733$	−5.04733e42			−0.532724			−0.266362	+	0.963873i	$0.585822\pi$
$734$		−	6.16443e42i		−	0.637458i
$735$	−1.42872e42	−	1.06337e42i	−0.144756	−	0.107739i
$736$	−1.26744e41			−0.0125823
$737$		−	1.72740e43i		−	1.68028i
$738$	−7.20233e41	−	2.40361e42i	−0.0686479	−	0.229097i
$739$	−1.68793e42			−0.157648			−0.0788239	−	0.996889i	$-0.525116\pi$
$739$	−1.68793e42			−0.157648			−0.0788239	+	0.996889i	$0.525116\pi$
$740$		−	1.58339e43i		−	1.44914i
$741$	−6.67770e42	+	8.97199e42i	−0.598899	+	0.804666i
$742$	8.70109e42			0.764742
$743$		−	1.91733e42i		−	0.165145i	−0.996585	−	0.0825725i	$-0.973686\pi$
$743$		−	1.91733e42i		−	0.165145i	0.996585	−	0.0825725i	$-0.0263136\pi$
$744$	4.64516e42	+	3.45732e42i	0.392109	+	0.291840i
$745$	4.00040e42			0.330948
$746$			1.17228e43i			0.950489i
$747$	−4.52028e42	+	1.35448e42i	−0.359217	+	0.107638i
$748$	5.74549e42			0.447510
$749$			1.56548e43i			1.19515i
$750$	−2.21690e42	+	2.97857e42i	−0.165893	+	0.222889i
$751$	1.52373e43			1.11766			0.558829	−	0.829283i	$-0.311251\pi$
$751$	1.52373e43			1.11766			0.558829	+	0.829283i	$0.311251\pi$
$752$			9.75543e39i			0.000701421i
$753$	−2.74991e42	−	2.04671e42i	−0.193818	−	0.144255i
$754$	1.96649e43			1.35870
$755$		−	2.01094e43i		−	1.36206i
$756$	7.48944e42	+	2.72283e42i	0.497304	+	0.180798i
$757$	−7.36973e42			−0.479748			−0.239874	−	0.970804i	$-0.577106\pi$
$757$	−7.36973e42			−0.479748			−0.239874	+	0.970804i	$0.577106\pi$
$758$			1.69863e42i			0.108408i
$759$	8.81723e41	−	1.18466e42i	0.0551703	−	0.0741255i
$760$	−7.08312e42			−0.434531
$761$			1.37774e43i			0.828699i	0.910118	+	0.414349i	$0.135991\pi$
$761$			1.37774e43i			0.828699i	−0.910118	+	0.414349i	$0.864009\pi$
$762$	−7.12022e42	−	5.29946e42i	−0.419922	−	0.312541i
$763$	−5.69631e42			−0.329401
$764$			1.70622e43i			0.967465i
$765$	5.35206e42	+	1.78613e43i	0.297577	+	0.993095i
$766$	−1.49677e43			−0.816063
$767$		−	1.84329e43i		−	0.985513i
$768$	−7.11733e41	+	9.56266e41i	−0.0373163	+	0.0501372i
$769$	−1.51703e43			−0.780008			−0.390004	−	0.920813i	$-0.627526\pi$
$769$	−1.51703e43			−0.780008			−0.390004	+	0.920813i	$0.627526\pi$
$770$			2.89724e43i			1.46091i
$771$	−1.72800e43	−	1.28612e43i	−0.854530	−	0.636012i
$772$	1.74501e42			0.0846329
$773$			4.56607e42i			0.217195i	0.994086	+	0.108597i	$0.0346360\pi$
$773$			4.56607e42i			0.217195i	−0.994086	+	0.108597i	$0.965364\pi$
$774$	2.69846e42	−	8.08581e41i	0.125893	−	0.0377233i
$775$	−3.81080e43			−1.74378
$776$			8.37723e42i			0.375988i
$777$	2.76633e43	−	3.71677e43i	1.21784	−	1.63625i
$778$	1.85956e42			0.0803001
$779$			6.52609e42i			0.276434i
$780$	−1.78155e43	−	1.32598e43i	−0.740250	−	0.550955i
$781$	1.24870e43			0.508972
$782$		−	8.67770e41i		−	0.0346979i
$783$	−1.36374e43	+	3.75110e43i	−0.534938	+	1.47140i
$784$	7.79573e41			0.0299996
$785$			2.82033e43i			1.06477i
$786$	−1.35386e43	+	1.81901e43i	−0.501460	+	0.673749i
$787$	−1.22810e43			−0.446284			−0.223142	−	0.974786i	$-0.571631\pi$
$787$	−1.22810e43			−0.446284			−0.223142	+	0.974786i	$0.571631\pi$
$788$		−	1.02689e43i		−	0.366128i
$789$	−2.18061e43	−	1.62299e43i	−0.762821	−	0.567755i
$790$	3.82633e43			1.31334
$791$		−	4.38120e43i		−	1.47552i
$792$	−3.98677e42	−	1.33049e43i	−0.131748	−	0.439678i
$793$	1.89936e43			0.615899
$794$		−	2.69671e43i		−	0.858079i
$795$	2.93850e43	−	3.94810e43i	0.917528	−	1.23277i
$796$	3.06847e43			0.940213
$797$			3.06083e43i			0.920374i	0.887822	+	0.460187i	$0.152218\pi$
$797$			3.06083e43i			0.920374i	−0.887822	+	0.460187i	$0.847782\pi$
$798$	−1.66266e43	−	1.23749e43i	−0.490638	−	0.365173i
$799$	−6.67918e40			−0.00193429
$800$		−	7.84502e42i		−	0.222969i
$801$	2.84064e43	−	8.51186e42i	0.792370	−	0.237431i
$802$	2.05024e43			0.561292
$803$			7.52288e43i			2.02139i
$804$	−1.46507e43	+	1.96844e43i	−0.386383	+	0.519135i
$805$	4.37585e42			0.113272
$806$		−	4.72205e43i		−	1.19979i
$807$	2.13005e43	+	1.58536e43i	0.531236	+	0.395390i
$808$	−1.88436e43			−0.461311
$809$			5.49719e43i			1.32103i	0.750812	+	0.660516i	$0.229662\pi$
$809$			5.49719e43i			1.32103i	−0.750812	+	0.660516i	$0.770338\pi$
$810$	3.76479e43	−	2.47877e43i	0.888107	−	0.584738i
$811$	5.45014e43			1.26210			0.631051	−	0.775741i	$-0.282624\pi$
$811$	5.45014e43			1.26210			0.631051	+	0.775741i	$0.282624\pi$
$812$			3.64425e43i			0.828452i
$813$	2.19706e43	−	2.95191e43i	0.490324	−	0.658788i
$814$	−8.07539e43			−1.76928
$815$		−	1.09743e43i		−	0.236055i
$816$	−6.54719e42	−	4.87296e42i	−0.138262	−	0.102906i
$817$	−7.32663e42			−0.151905
$818$		−	1.65608e43i		−	0.337118i
$819$	−1.86532e43	−	6.22508e43i	−0.372816	−	1.24419i
$820$	−1.29587e43			−0.254305
$821$		−	3.51603e43i		−	0.677494i	−0.940877	−	0.338747i	$-0.889997\pi$
$821$		−	3.51603e43i		−	0.677494i	0.940877	−	0.338747i	$-0.110003\pi$
$822$	−1.75403e43	+	2.35667e43i	−0.331864	+	0.445884i
$823$	−1.65600e43			−0.307653			−0.153827	−	0.988098i	$-0.549160\pi$
$823$	−1.65600e43			−0.307653			−0.153827	+	0.988098i	$0.549160\pi$
$824$		−	9.85595e42i		−	0.179800i
$825$	7.33263e43	+	5.45755e43i	1.31356	+	0.977662i
$826$	3.41592e43			0.600907
$827$		−	9.83930e43i		−	1.69974i	−0.526995	−	0.849868i	$-0.676681\pi$
$827$		−	9.83930e43i		−	1.69974i	0.526995	−	0.849868i	$-0.323319\pi$
$828$	−2.00951e42	+	6.02142e41i	−0.0340906	+	0.0102151i
$829$	−5.56602e43			−0.927314			−0.463657	−	0.886015i	$-0.653463\pi$
$829$	−5.56602e43			−0.927314			−0.463657	+	0.886015i	$0.653463\pi$
$830$			2.43704e43i			0.398742i
$831$	−5.89407e43	+	7.91913e43i	−0.947109	+	1.27251i
$832$	9.72094e42			0.153412
$833$			5.33744e42i			0.0827291i
$834$	−3.02786e43	−	2.25358e43i	−0.460940	−	0.343070i
$835$	−4.79626e43			−0.717142
$836$			3.61245e43i			0.530527i
$837$	9.00735e43	+	3.27468e43i	1.29932	+	0.472375i
$838$	3.60586e43			0.510915
$839$			4.20842e43i			0.585720i	0.956155	+	0.292860i	$0.0946070\pi$
$839$			4.20842e43i			0.585720i	−0.956155	+	0.292860i	$0.905393\pi$
$840$	2.45726e43	−	3.30151e43i	0.335940	−	0.451361i
$841$	−1.08060e44			−1.45119
$842$		−	1.91279e43i		−	0.252340i
$843$	−5.30181e43	−	3.94605e43i	−0.687086	−	0.511386i
$844$	−5.39359e43			−0.686660
$845$			6.08688e43i			0.761280i
$846$	4.63465e40	+	1.54671e41i	0.000569458	+	0.00190044i
$847$	6.00898e43			0.725353
$848$			2.15427e43i			0.255483i
$849$	−3.67444e43	+	4.93689e43i	−0.428130	+	0.575225i
$850$	5.37119e43			0.614875
$851$			1.21967e43i			0.137182i
$852$	−1.42294e43	−	1.05907e43i	−0.157251	−	0.117039i
$853$	7.51834e43			0.816369			0.408184	−	0.912900i	$-0.366162\pi$
$853$	7.51834e43			0.816369			0.408184	+	0.912900i	$0.366162\pi$
$854$			3.51984e43i			0.375539i
$855$	−1.12302e44	+	3.36508e43i	−1.17732	+	0.352780i
$856$	−3.87592e43			−0.399271
$857$		−	7.04573e43i		−	0.713204i	−0.934256	−	0.356602i	$-0.883935\pi$
$857$		−	7.04573e43i		−	0.713204i	0.934256	−	0.356602i	$-0.116065\pi$
$858$	−6.76258e43	+	9.08603e43i	−0.672671	+	0.903784i
$859$	4.38969e43			0.429078			0.214539	−	0.976715i	$-0.431175\pi$
$859$	4.38969e43			0.429078			0.214539	+	0.976715i	$0.431175\pi$
$860$		−	1.45483e43i		−	0.139745i
$861$	−3.04187e43	−	2.26402e43i	−0.287140	−	0.213714i
$862$	4.83290e43			0.448331
$863$		−	1.49093e44i		−	1.35924i	−0.733566	−	0.679618i	$-0.762146\pi$
$863$		−	1.49093e44i		−	1.35924i	0.733566	−	0.679618i	$-0.237854\pi$
$864$	−6.74134e42	+	1.85428e43i	−0.0604004	+	0.166138i
$865$	−1.35202e44			−1.19053
$866$		−	6.54768e43i		−	0.566655i
$867$	−3.68315e43	+	4.94859e43i	−0.313280	+	0.420915i
$868$	8.75077e43			0.731561
$869$		−	1.95146e44i		−	1.60347i
$870$	1.65357e44	+	1.23072e44i	1.33547	+	0.993966i
$871$	2.00102e44			1.58847
$872$		−	1.41032e43i		−	0.110045i
$873$	3.97989e43	+	1.32820e44i	0.305251	+	1.01871i
$874$	5.45606e42			0.0411346
$875$			5.61117e43i			0.415846i
$876$	6.38044e43	−	8.57260e43i	0.464824	−	0.624526i
$877$	2.39999e44			1.71876			0.859380	−	0.511337i	$-0.170850\pi$
$877$	2.39999e44			1.71876			0.859380	+	0.511337i	$0.170850\pi$
$878$			3.39927e43i			0.239314i
$879$	−1.70902e43	−	1.27199e43i	−0.118280	−	0.0880341i
$880$	−7.17316e43			−0.488057
$881$			1.61043e43i			0.107722i	0.998548	+	0.0538609i	$0.0171528\pi$
$881$			1.61043e43i			0.107722i	−0.998548	+	0.0538609i	$0.982847\pi$
$882$	1.23600e43	−	3.70363e42i	0.0812812	−	0.0243556i
$883$	−1.37945e44			−0.891858			−0.445929	−	0.895068i	$-0.647127\pi$
$883$	−1.37945e44			−0.891858			−0.445929	+	0.895068i	$0.647127\pi$
$884$			6.65556e43i			0.423059i
$885$	1.15361e44	−	1.54997e44i	0.720961	−	0.968665i
$886$	−2.05342e44			−1.26175
$887$		−	2.52186e44i		−	1.52359i	−0.647821	−	0.761793i	$-0.724320\pi$
$887$		−	2.52186e44i		−	1.52359i	0.647821	−	0.761793i	$-0.275680\pi$
$888$	9.20220e43	+	6.84904e43i	0.546634	+	0.406851i
$889$	−1.34134e44			−0.783451
$890$		−	1.53149e44i		−	0.879556i
$891$	−1.26419e44	−	1.92007e44i	−0.713916	−	1.08431i
$892$	1.66439e44			0.924234
$893$		−	4.19950e41i		−	0.00229311i
$894$	−1.73040e43	+	2.32492e43i	−0.0929145	+	0.124838i
$895$	7.38399e43			0.389893
$896$			1.80146e43i			0.0935414i
$897$	1.37231e43	+	1.02139e43i	0.0700753	+	0.0521559i
$898$	−1.75424e44			−0.880934
$899$			4.38284e44i			2.16451i
$900$	−3.72705e43	−	1.24382e44i	−0.181020	−	0.604113i
$901$	−1.47494e44			−0.704537
$902$			6.60904e43i			0.310485i
$903$	2.54174e43	−	3.41501e43i	0.117439	−	0.157789i
$904$	1.08472e44			0.492937
$905$		−	1.40291e44i		−	0.627047i
$906$	1.16870e44	+	8.69845e43i	0.513784	+	0.382401i
$907$	3.05359e44			1.32039			0.660195	−	0.751094i	$-0.270474\pi$
$907$	3.05359e44			1.32039			0.660195	+	0.751094i	$0.270474\pi$
$908$		−	8.87497e40i		−	0.000377467i
$909$	−2.98762e44	+	8.95230e43i	−1.24988	+	0.374521i
$910$	−3.35616e44			−1.38109
$911$			3.40953e44i			1.38013i	0.723748	+	0.690064i	$0.242418\pi$
$911$			3.40953e44i			1.38013i	−0.723748	+	0.690064i	$0.757582\pi$
$912$	3.06385e43	−	4.11651e43i	0.121996	−	0.163911i
$913$	1.24291e44			0.486831
$914$			3.38887e43i			0.130576i
$915$	1.59712e44	+	1.18871e44i	0.605370	+	0.450567i
$916$	−1.81687e44			−0.677474
$917$			3.42674e44i			1.25702i
$918$	−1.26955e44	−	4.61554e43i	−0.458153	−	0.166564i
$919$	2.44408e44			0.867728			0.433864	−	0.900978i	$-0.357150\pi$
$919$	2.44408e44			0.867728			0.433864	+	0.900978i	$0.357150\pi$
$920$			1.08340e43i			0.0378417i
$921$	−5.22208e43	+	7.01626e43i	−0.179452	+	0.241108i
$922$	1.54010e44			0.520696
$923$			1.44649e44i			0.481162i
$924$	−1.68380e44	−	1.25322e44i	−0.551074	−	0.410155i
$925$	−7.54930e44			−2.43098
$926$		−	1.89618e44i		−	0.600780i
$927$	−4.68240e43	−	1.56264e44i	−0.145973	−	0.487152i
$928$	−9.02263e43			−0.276766
$929$			3.10659e44i			0.937667i	0.883287	+	0.468834i	$0.155326\pi$
$929$			3.10659e44i			0.937667i	−0.883287	+	0.468834i	$0.844674\pi$
$930$	2.95528e44	−	3.97064e44i	0.877717	−	1.17928i
$931$	−3.35589e43			−0.0980760
$932$		−	1.82963e44i		−	0.526169i
$933$	2.42214e44	+	1.80276e44i	0.685448	+	0.510167i
$934$	4.86962e43			0.135610
$935$		−	4.91119e44i		−	1.34590i
$936$	1.54124e44	−	4.61826e43i	0.415655	−	0.124549i
$937$	4.55945e44			1.21009			0.605047	−	0.796190i	$-0.293155\pi$
$937$	4.55945e44			1.21009			0.605047	+	0.796190i	$0.293155\pi$
$938$			3.70823e44i			0.968554i
$939$	−1.97110e44	+	2.64833e44i	−0.506671	+	0.680750i
$940$	8.33885e41			0.00210954
$941$		−	5.14236e44i		−	1.28032i	−0.768242	−	0.640159i	$-0.778868\pi$
$941$		−	5.14236e44i		−	1.28032i	0.768242	−	0.640159i	$-0.221132\pi$
$942$	−1.63910e44	−	1.21995e44i	−0.401644	−	0.298937i
$943$	9.98197e42			0.0240736
$944$			8.45734e43i			0.200749i
$945$	2.32745e44	−	6.40190e44i	0.543755	−	1.49566i
$946$	−7.41976e43			−0.170617
$947$			7.79466e44i			1.76420i	0.471064	+	0.882099i	$0.343870\pi$
$947$			7.79466e44i			1.76420i	−0.471064	+	0.882099i	$0.656130\pi$
$948$	−1.65510e44	+	2.22375e44i	−0.368723	+	0.495406i
$949$	−8.71449e44			−1.91095
$950$			3.37711e44i			0.728939i
$951$	−3.95106e44	−	2.94071e44i	−0.839472	−	0.624805i
$952$	−1.23339e44			−0.257956
$953$		−	7.84581e44i		−	1.61527i	−0.589685	−	0.807633i	$-0.700748\pi$
$953$		−	7.84581e44i		−	1.61527i	0.589685	−	0.807633i	$-0.299252\pi$
$954$	1.02346e44	+	3.41555e44i	0.207417	+	0.692206i
$955$	1.45846e45			2.90968
$956$			1.14019e44i			0.223927i
$957$	6.27678e44	−	8.43333e44i	1.21355	−	1.63050i
$958$	−4.39190e42			−0.00835930
$959$			4.43961e44i			0.831889i
$960$	8.17407e43	+	6.08382e43i	0.150789	+	0.112230i
$961$	5.01813e44			0.911363
$962$		−	9.35451e44i		−	1.67261i
$963$	−6.14520e44	+	1.84139e44i	−1.08179	+	0.324153i
$964$	3.12839e44			0.542207
$965$		−	1.49162e44i		−	0.254536i
$966$	−1.89280e43	+	2.54312e43i	−0.0318016	+	0.0427278i
$967$	5.94743e44			0.983857			0.491928	−	0.870636i	$-0.336292\pi$
$967$	5.94743e44			0.983857			0.491928	+	0.870636i	$0.336292\pi$
$968$			1.48774e44i			0.242324i
$969$	2.81842e44	+	2.09770e44i	0.452011	+	0.336424i
$970$	7.16077e44			1.13080
$971$			4.33020e44i			0.673317i	0.941627	+	0.336658i	$0.109297\pi$
$971$			4.33020e44i			0.673317i	−0.941627	+	0.336658i	$0.890703\pi$
$972$	−1.87891e43	+	3.26020e44i	−0.0287682	+	0.499172i
$973$	−5.70401e44			−0.859979
$974$			4.84307e44i			0.719012i
$975$	−6.32202e44	+	8.49411e44i	−0.924244	+	1.24179i
$976$	−8.71462e43			−0.125459
$977$		−	2.85393e44i		−	0.404599i	−0.979324	−	0.202300i	$-0.935158\pi$
$977$		−	2.85393e44i		−	0.404599i	0.979324	−	0.202300i	$-0.0648415\pi$
$978$	6.37797e43	+	4.74701e43i	0.0890429	+	0.0662731i
$979$	−7.81071e44			−1.07387
$980$		−	6.66372e43i		−	0.0902247i
$981$	−6.70022e43	−	2.23605e44i	−0.0893417	−	0.298157i
$982$	1.05124e45			1.38048
$983$		−	1.62835e44i		−	0.210594i	−0.994441	−	0.105297i	$-0.966421\pi$
$983$		−	1.62835e44i		−	0.210594i	0.994441	−	0.105297i	$-0.0335793\pi$
$984$	5.60538e43	−	7.53124e43i	0.0713967	−	0.0959269i
$985$	−8.77779e44			−1.10114
$986$		−	6.17745e44i		−	0.763230i
$987$	1.95743e42	+	1.45688e42i	0.00238193	+	0.00177283i
$988$	−4.18465e44			−0.501539
$989$			1.12064e43i			0.0132289i
$990$	−1.13729e45	+	3.40785e44i	−1.32234	+	0.396235i
$991$	−1.33500e45			−1.52889			−0.764446	−	0.644688i	$-0.776987\pi$
$991$	−1.33500e45			−1.52889			−0.764446	+	0.644688i	$0.776987\pi$
$992$			2.16656e44i			0.244397i
$993$	−9.96661e43	+	1.33909e44i	−0.110741	+	0.148789i
$994$	−2.68060e44			−0.293384
$995$		−	2.62290e45i		−	2.82772i
$996$	−1.41634e44	−	1.05416e44i	−0.150410	−	0.111948i
$997$	−1.69353e45			−1.77160			−0.885802	−	0.464063i	$-0.846391\pi$
$997$	−1.69353e45			−1.77160			−0.885802	+	0.464063i	$0.846391\pi$
$998$			4.48594e44i			0.462270i
$999$	1.78438e45	+	6.48722e44i	1.81136	+	0.658532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.31.b.a.5.7	yes	10
3.2	odd	2	inner	6.31.b.a.5.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.31.b.a.5.2	✓	10	3.2	odd	2	inner
6.31.b.a.5.7	yes	10	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 31 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+23170.5i q^{2} +(-8.56717e6 + 1.15106e7i) q^{3} -5.36871e8 q^{4} +4.58912e10i q^{5} +(-2.66707e11 - 1.98505e11i) q^{6} -5.02434e12 q^{7} -1.24396e13i q^{8} +(-5.90983e13 - 1.97227e14i) q^{9} +O(q^{10})\)	\(q+23170.5i q^{2} +(-8.56717e6 + 1.15106e7i) q^{3} -5.36871e8 q^{4} +4.58912e10i q^{5} +(-2.66707e11 - 1.98505e11i) q^{6} -5.02434e12 q^{7} -1.24396e13i q^{8} +(-5.90983e13 - 1.97227e14i) q^{9} -1.06332e15 q^{10} +5.42302e15i q^{11} +(4.59946e15 - 6.17973e15i) q^{12} -6.28201e16 q^{13} -1.16416e17i q^{14} +(-5.28237e17 - 3.93158e17i) q^{15} +2.88230e17 q^{16} +1.97340e18i q^{17} +(4.56985e18 - 1.36934e18i) q^{18} -1.24077e19 q^{19} -2.46377e19i q^{20} +(4.30444e19 - 5.78334e19i) q^{21} -1.25654e20 q^{22} +1.89781e19i q^{23} +(1.43187e20 + 1.06572e20i) q^{24} -1.17468e21 q^{25} -1.45557e21i q^{26} +(2.77652e21 + 1.00942e21i) q^{27} +2.69742e21 q^{28} +1.35101e22i q^{29} +(9.10965e21 - 1.22395e22i) q^{30} +3.24412e22 q^{31} +6.67843e21i q^{32} +(-6.24224e22 - 4.64599e22i) q^{33} -4.57247e22 q^{34} -2.30573e23i q^{35} +(3.17282e22 + 1.05886e23i) q^{36} +6.42669e23 q^{37} -2.87492e23i q^{38} +(5.38191e23 - 7.23100e23i) q^{39} +5.70866e23 q^{40} -5.25972e23i q^{41} +(1.34003e24 + 9.97359e23i) q^{42} +5.90491e23 q^{43} -2.91146e24i q^{44} +(9.05099e24 - 2.71209e24i) q^{45} -4.39732e23 q^{46} +3.38460e22i q^{47} +(-2.46932e24 + 3.31771e24i) q^{48} +2.70469e24 q^{49} -2.72179e25i q^{50} +(-2.27151e25 - 1.69065e25i) q^{51} +3.37263e25 q^{52} +7.47411e25i q^{53} +(-2.33887e25 + 6.43332e25i) q^{54} -2.48869e26 q^{55} +6.25006e25i q^{56} +(1.06299e26 - 1.42820e26i) q^{57} -3.13035e26 q^{58} +2.93423e26i q^{59} +(2.83595e26 + 2.11075e26i) q^{60} -3.02349e26 q^{61} +7.51678e26i q^{62} +(2.96930e26 + 9.90937e26i) q^{63} -1.54743e26 q^{64} -2.88289e27i q^{65} +(1.07650e27 - 1.44636e27i) q^{66} -3.18531e27 q^{67} -1.05946e27i q^{68} +(-2.18450e26 - 1.62589e26i) q^{69} +5.34249e27 q^{70} -2.30260e27i q^{71} +(-2.45342e27 + 7.35157e26i) q^{72} +1.38721e28 q^{73} +1.48909e28i q^{74} +(1.00637e28 - 1.35213e28i) q^{75} +6.66132e27 q^{76} -2.72471e28i q^{77} +(1.67546e28 + 1.24701e28i) q^{78} -3.59847e28 q^{79} +1.32272e28i q^{80} +(-3.54059e28 + 2.33116e28i) q^{81} +1.21870e28 q^{82} -2.29192e28i q^{83} +(-2.31093e28 + 3.10491e28i) q^{84} -9.05619e28 q^{85} +1.36820e28i q^{86} +(-1.55510e29 - 1.15743e29i) q^{87} +6.74599e28 q^{88} +1.44029e29i q^{89} +(6.28405e28 + 2.09716e29i) q^{90} +3.15630e29 q^{91} -1.01888e28i q^{92} +(-2.77929e29 + 3.73419e29i) q^{93} -7.84227e26 q^{94} -5.69403e29i q^{95} +(-7.68730e28 - 5.72153e28i) q^{96} -6.73435e29 q^{97} +6.26689e28i q^{98} +(1.06957e30 - 3.20491e29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9}+O(q^{10}) \) 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9	\( 10 q + 14139762 q^{3} - 5368709120 q^{4} - 145788764160 q^{6} - 1459334601196 q^{7} + 41713120268730 q^{9} - 11\!\cdots\!60 q^{10}+ \cdots + 27\!\cdots\!20 q^{99}+O(q^{100}) \) 10 * q + 14139762 * q^3 - 5368709120 * q^4 - 145788764160 * q^6 - 1459334601196 * q^7 + 41713120268730 * q^9 - 1111538175836160 * q^10 - 7591226920402944 * q^12 + 11241857908456580 * q^13 - 1208370750576105600 * q^15 + 2882303761517117440 * q^16 + 4378961453216956416 * q^18 - 406434941012438620 * q^19 + 189341373476724706020 * q^21 - 175966920878069907456 * q^22 + 78269746773932113920 * q^24 - 538750688835772733030 * q^25 - 509686212259700532126 * q^27 + 783474298257252810752 * q^28 + 3618734882327478927360 * q^30 - 3850790055930904811020 * q^31 + 13877514934601873876352 * q^33 - 21974427701517892976640 * q^34 - 22394560921038760181760 * q^36 + 691786417224189171658916 * q^37 + 264189297409049008449300 * q^39 + 596752514183975581777920 * q^40 + 2551733261187619598893056 * q^42 - 10594373354873893550389372 * q^43 + 21961398854703004532478720 * q^45 - 14905926072892021549301760 * q^46 + 4075508919955679952764928 * q^48 - 14303693611422252234715650 * q^49 + 100757981401326611204590080 * q^51 - 6035426507887496617000960 * q^52 + 186364360915292902942310400 * q^54 - 905529883473273884900970240 * q^55 + 1357830109447011748343825076 * q^57 - 1026862318649343581985177600 * q^58 + 648739106895918338880307200 * q^60 - 2949272535924647913201299260 * q^61 + 5088794127795653673352888692 * q^63 - 1547425049106725343623905280 * q^64 + 3787402697011447732654571520 * q^66 - 10556251754234326335356822044 * q^67 + 15764240424701154050198334720 * q^69 - 8691440888931957213379952640 * q^70 - 2350937029001432724922171392 * q^72 + 12106003505184711607130189300 * q^73 - 7500206691267464218185712830 * q^75 + 218203097450014125263421440 * q^76 - 23839067108381696719249735680 * q^78 + 68719005124237783442983312820 * q^79 - 111620808361643664456575921430 * q^81 + 18283730424263848186657898496 * q^82 - 101651875857781803693889290240 * q^84 + 403836274868708986530058828800 * q^85 - 512433611792960206983797969280 * q^87 + 94471521293641232015658319872 * q^88 - 426164288449255115819581440000 * q^90 + 1222541373056582384854822798600 * q^91 - 983623123086267594817934884284 * q^93 - 80746046881825464175401369600 * q^94 - 42020750332529991826318295040 * q^96 - 1391585232259866867438139103212 * q^97 + 2707446209006624257844338302720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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