LMFDB - Embedded newform 3.41.b.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,41,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 41, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 41);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 41 $
Character orbit:	$[\chi]$	$=$	3.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:	$30.4026855589$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 249659905422 x^{10} + \cdots + 12\!\cdots\!00 $ x^12 + 249659905422x^10 + 21357900831219724160448x^8 + 757005714875983264074654770397184x^6 + 10196659004511185116272142565764285511761920x^4 + 42071301184141474816096210166597335428414342325862400*x^2 + 12606130133749306378798090199763505554693706712963960799232000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.8
Root			$81647.3i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.41.b.a.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+489884. i q^{2} +(-3.83248e8 - 3.46566e9i) q^{3} +8.59526e11 q^{4} +1.65087e14i q^{5} +(1.69777e15 - 1.87747e14i) q^{6} +1.22230e17 q^{7} +9.59700e17i q^{8} +(-1.18639e19 + 2.65641e18i) q^{9} +O(q^{10})$	\(q+489884. i q^{2} +(-3.83248e8 - 3.46566e9i) q^{3} +8.59526e11 q^{4} +1.65087e14i q^{5} +(1.69777e15 - 1.87747e14i) q^{6} +1.22230e17 q^{7} +9.59700e17i q^{8} +(-1.18639e19 + 2.65641e18i) q^{9} -8.08734e19 q^{10} -8.75756e19i q^{11} +(-3.29411e20 - 2.97882e21i) q^{12} -2.33097e22 q^{13} +5.98783e22i q^{14} +(5.72135e23 - 6.32692e22i) q^{15} +4.74917e23 q^{16} +8.49332e23i q^{17} +(-1.30133e24 - 5.81193e24i) q^{18} +1.15374e25 q^{19} +1.41896e26i q^{20} +(-4.68443e25 - 4.23606e26i) q^{21} +4.29018e25 q^{22} +1.67356e27i q^{23} +(3.32599e27 - 3.67803e26i) q^{24} -1.81587e28 q^{25} -1.14191e28i q^{26} +(1.37530e28 + 4.00982e28i) q^{27} +1.05060e29 q^{28} +9.66156e28i q^{29} +(3.09945e28 + 2.80279e29i) q^{30} -6.99390e29 q^{31} +1.28786e30i q^{32} +(-3.03507e29 + 3.35632e28i) q^{33} -4.16074e29 q^{34} +2.01785e31i q^{35} +(-1.01973e31 + 2.28326e30i) q^{36} +2.98539e31 q^{37} +5.65200e30i q^{38} +(8.93341e30 + 8.07836e31i) q^{39} -1.58434e32 q^{40} -1.54921e31i q^{41} +(2.07518e32 - 2.29482e31i) q^{42} +2.10270e32 q^{43} -7.52734e31i q^{44} +(-4.38539e32 - 1.95858e33i) q^{45} -8.19848e32 q^{46} -8.11564e32i q^{47} +(-1.82011e32 - 1.64590e33i) q^{48} +8.57329e33 q^{49} -8.89566e33i q^{50} +(2.94349e33 - 3.25505e32i) q^{51} -2.00353e34 q^{52} +2.65608e34i q^{53} +(-1.96434e34 + 6.73739e33i) q^{54} +1.44576e34 q^{55} +1.17304e35i q^{56} +(-4.42170e33 - 3.99848e34i) q^{57} -4.73304e34 q^{58} +3.47592e35i q^{59} +(4.91764e35 - 5.43815e34i) q^{60} -4.26412e34 q^{61} -3.42620e35i q^{62} +(-1.45012e36 + 3.24692e35i) q^{63} -1.08723e35 q^{64} -3.84813e36i q^{65} +(-1.64420e34 - 1.48683e35i) q^{66} +3.93010e36 q^{67} +7.30023e35i q^{68} +(5.79998e36 - 6.41387e35i) q^{69} -9.88512e36 q^{70} +1.43105e35i q^{71} +(-2.54936e36 - 1.13858e37i) q^{72} -1.95951e36 q^{73} +1.46250e37i q^{74} +(6.95929e36 + 6.29319e37i) q^{75} +9.91672e36 q^{76} -1.07043e37i q^{77} +(-3.95746e37 + 4.37633e36i) q^{78} -3.82460e37 q^{79} +7.84025e37i q^{80} +(1.33696e38 - 6.30309e37i) q^{81} +7.58933e36 q^{82} -6.29598e37i q^{83} +(-4.02639e37 - 3.64100e38i) q^{84} -1.40214e38 q^{85} +1.03008e38i q^{86} +(3.34837e38 - 3.70277e37i) q^{87} +8.40463e37 q^{88} -1.43005e39i q^{89} +(9.59474e38 - 2.14833e38i) q^{90} -2.84914e39 q^{91} +1.43847e39i q^{92} +(2.68040e38 + 2.42385e39i) q^{93} +3.97572e38 q^{94} +1.90468e39i q^{95} +(4.46327e39 - 4.93568e38i) q^{96} +2.20304e39 q^{97} +4.19991e39i q^{98} +(2.32637e38 + 1.03899e39i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) $ 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9	$ 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) $ 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9 - 129384136354706290080 * q^10 - 4708039830028985428272 * q^12 + 704368845864154901976 * q^13 + 320935800901459838631840 * q^15 + 6054431850962872672227456 * q^16 + 10227710367381761273509920 * q^18 + 37616619688417835612151720 * q^19 - 179163719456723608834234728 * q^21 + 846315150249292772829325920 * q^22 - 18213480358094369517645250944 * q^24 + 8842265325510151276196474700 * q^25 - 70717074113738779393083858252 * q^27 + 469404222007499612173589889696 * q^28 - 207809636542026559976510503200 * q^30 - 914600368399753689553849145016 * q^31 + 157344642221562801276041757600 * q^33 - 14575908480758621487300381842304 * q^34 + 41100171486790863962401658870544 * q^36 + 5673106137824212681873457220696 * q^37 - 9206461430638842876438079090008 * q^39 + 50495897877443363581635475618560 * q^40 - 939238658319640212873301303645920 * q^42 + 1012654832326802922602871229857576 * q^43 + 196109968512215856818385626472000 * q^45 - 3082500781506234684371181468390336 * q^46 + 6532128822166367998693520969705088 * q^48 + 8498166150175390075155260408801892 * q^49 + 27565453699222767413826960590504832 * q^51 - 57328509042562386918101767400001504 * q^52 - 102847607224782098537542351912875792 * q^54 - 9637639495259752880102706884884800 * q^55 - 40307213604482059940636368892395464 * q^57 + 772129436848561910287203884295052320 * q^58 - 114385571579949295944121547557720320 * q^60 - 494443282701607071691140418439862696 * q^61 + 1379291076525018665154441723571240776 * q^63 - 6231783699524672226208093043936541696 * q^64 + 2652084094607847915810184973553481440 * q^66 + 5401062423529881431761320436868275176 * q^67 + 7110274695178254111533494284632123328 * q^69 + 516103243900107216646679160954379200 * q^70 - 27544975046740790141119542770107057920 * q^72 + 30000154498324943042431295514883418136 * q^73 + 43820294796704764666539599709819928500 * q^75 - 215478934792040263381331019050660960352 * q^76 + 234946633516471169601955850003339878560 * q^78 - 128704557118405295534397879672035334840 * q^79 + 473157359902659920298963194247360443532 * q^81 - 639159997421964256448917103585883414720 * q^82 + 1283288903941350744781821238287455403552 * q^84 - 1077142486191382871466217243736209678080 * q^85 + 1076668306862385320797179121273520148960 * q^87 - 2918662713596496795370587920448329114880 * q^88 + 6571793457940570799819318674019816438880 * q^90 - 9859184204686878150356379414618151910256 * q^91 + 11506410044121210986218054652959643683416 * q^93 - 16857264118330945289191940748512432348544 * q^94 + 53068562519213731340201280418423192237056 * q^96 - 41841010071967618660163746722085070705064 * q^97 + 54341076855402233475300783474292013590080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			489884.i			0.467189i	0.972334	+	0.233595i	$0.0750489\pi$
$2$			489884.i			0.467189i	−0.972334	+	0.233595i	$0.924951\pi$
$3$	−3.83248e8	−	3.46566e9i	−0.109914	−	0.993941i
$3$	−3.83248e8	−	3.46566e9i	−0.109914	−	0.993941i
$4$	8.59526e11			0.781734
$5$			1.65087e14i			1.73106i	0.500856	+	0.865531i	$0.333019\pi$
$5$			1.65087e14i			1.73106i	−0.500856	+	0.865531i	$0.666981\pi$
$6$	1.69777e15	−	1.87747e14i	0.464359	−	0.0513509i
$7$	1.22230e17			1.53185			0.765924	−	0.642931i	$-0.222282\pi$
$7$	1.22230e17			1.53185			0.765924	+	0.642931i	$0.222282\pi$
$8$			9.59700e17i			0.832407i
$9$	−1.18639e19	+	2.65641e18i	−0.975838	+	0.218497i
$10$	−8.08734e19			−0.808734
$11$		−	8.75756e19i		−	0.130175i	−0.997880	−	0.0650877i	$-0.979267\pi$
$11$		−	8.75756e19i		−	0.130175i	0.997880	−	0.0650877i	$-0.0207327\pi$
$12$	−3.29411e20	−	2.97882e21i	−0.0859239	−	0.776998i
$13$	−2.33097e22			−1.22651			−0.613254	−	0.789886i	$-0.710140\pi$
$13$	−2.33097e22			−1.22651			−0.613254	+	0.789886i	$0.710140\pi$
$14$			5.98783e22i			0.715664i
$15$	5.72135e23	−	6.32692e22i	1.72057	−	0.190269i
$16$	4.74917e23			0.392842
$17$			8.49332e23i			0.208977i	0.994526	+	0.104489i	$0.0333206\pi$
$17$			8.49332e23i			0.208977i	−0.994526	+	0.104489i	$0.966679\pi$
$18$	−1.30133e24	−	5.81193e24i	−0.102079	−	0.455901i
$19$	1.15374e25			0.306929			0.153464	−	0.988154i	$-0.450957\pi$
$19$	1.15374e25			0.306929			0.153464	+	0.988154i	$0.450957\pi$
$20$			1.41896e26i			1.35323i
$21$	−4.68443e25	−	4.23606e26i	−0.168372	−	1.52257i
$22$	4.29018e25			0.0608166
$23$			1.67356e27i			0.975178i	0.873073	+	0.487589i	$0.162124\pi$
$23$			1.67356e27i			0.975178i	−0.873073	+	0.487589i	$0.837876\pi$
$24$	3.32599e27	−	3.67803e26i	0.827364	−	0.0914936i
$25$	−1.81587e28			−1.99657
$26$		−	1.14191e28i		−	0.573012i
$27$	1.37530e28	+	4.00982e28i	0.324432	+	0.945909i
$28$	1.05060e29			1.19750
$29$			9.66156e28i			0.545867i	0.962033	+	0.272934i	$0.0879940\pi$
$29$			9.66156e28i			0.545867i	−0.962033	+	0.272934i	$0.912006\pi$
$30$	3.09945e28	+	2.80279e29i	0.0888915	+	0.803833i
$31$	−6.99390e29			−1.04108			−0.520541	−	0.853836i	$-0.674270\pi$
$31$	−6.99390e29			−1.04108			−0.520541	+	0.853836i	$0.674270\pi$
$32$			1.28786e30i			1.01594i
$33$	−3.03507e29	+	3.35632e28i	−0.129387	+	0.0143082i
$34$	−4.16074e29			−0.0976320
$35$			2.01785e31i			2.65172i
$36$	−1.01973e31	+	2.28326e30i	−0.762845	+	0.170807i
$37$	2.98539e31			1.29112			0.645561	−	0.763709i	$-0.276624\pi$
$37$	2.98539e31			1.29112			0.645561	+	0.763709i	$0.276624\pi$
$38$			5.65200e30i			0.143394i
$39$	8.93341e30	+	8.07836e31i	0.134811	+	1.21908i
$40$	−1.58434e32			−1.44095
$41$		−	1.54921e31i		−	0.0859872i	−0.999075	−	0.0429936i	$-0.986310\pi$
$41$		−	1.54921e31i		−	0.0859872i	0.999075	−	0.0429936i	$-0.0136895\pi$
$42$	2.07518e32	−	2.29482e31i	0.711327	−	0.0786618i
$43$	2.10270e32			0.450203			0.225101	−	0.974335i	$-0.427729\pi$
$43$	2.10270e32			0.450203			0.225101	+	0.974335i	$0.427729\pi$
$44$		−	7.52734e31i		−	0.101763i
$45$	−4.38539e32	−	1.95858e33i	−0.378232	−	1.68923i
$46$	−8.19848e32			−0.455593
$47$		−	8.11564e32i		−	0.293336i	−0.989186	−	0.146668i	$-0.953145\pi$
$47$		−	8.11564e32i		−	0.293336i	0.989186	−	0.146668i	$-0.0468549\pi$
$48$	−1.82011e32	−	1.64590e33i	−0.0431790	−	0.390462i
$49$	8.57329e33			1.34656
$50$		−	8.89566e33i		−	0.932778i
$51$	2.94349e33	−	3.25505e32i	0.207711	−	0.0229696i
$52$	−2.00353e34			−0.958803
$53$			2.65608e34i			0.868408i	0.900814	+	0.434204i	$0.142970\pi$
$53$			2.65608e34i			0.868408i	−0.900814	+	0.434204i	$0.857030\pi$
$54$	−1.96434e34	+	6.73739e33i	−0.441919	+	0.151571i
$55$	1.44576e34			0.225342
$56$			1.17304e35i			1.27512i
$57$	−4.42170e33	−	3.99848e34i	−0.0337359	−	0.305069i
$58$	−4.73304e34			−0.255024
$59$			3.47592e35i			1.33055i	0.746600	+	0.665273i	$0.231685\pi$
$59$			3.47592e35i			1.33055i	−0.746600	+	0.665273i	$0.768315\pi$
$60$	4.91764e35	−	5.43815e34i	1.34503	−	0.148739i
$61$	−4.26412e34			−0.0837978			−0.0418989	−	0.999122i	$-0.513341\pi$
$61$	−4.26412e34			−0.0837978			−0.0418989	+	0.999122i	$0.513341\pi$
$62$		−	3.42620e35i		−	0.486383i
$63$	−1.45012e36	+	3.24692e35i	−1.49484	+	0.334704i
$64$	−1.08723e35			−0.0817939
$65$		−	3.84813e36i		−	2.12316i
$66$	−1.64420e34	−	1.48683e35i	−0.00668463	−	0.0604481i
$67$	3.93010e36			1.18279			0.591395	−	0.806382i	$-0.298577\pi$
$67$	3.93010e36			1.18279			0.591395	+	0.806382i	$0.298577\pi$
$68$			7.30023e35i			0.163365i
$69$	5.79998e36	−	6.41387e35i	0.969269	−	0.107186i
$70$	−9.88512e36			−1.23886
$71$			1.43105e35i			0.0135048i	0.999977	+	0.00675241i	$0.00214938\pi$
$71$			1.43105e35i			0.0135048i	−0.999977	+	0.00675241i	$0.997851\pi$
$72$	−2.54936e36	−	1.13858e37i	−0.181878	−	0.812294i
$73$	−1.95951e36			−0.106094			−0.0530469	−	0.998592i	$-0.516893\pi$
$73$	−1.95951e36			−0.106094			−0.0530469	+	0.998592i	$0.516893\pi$
$74$			1.46250e37i			0.603199i
$75$	6.95929e36	+	6.29319e37i	0.219452	+	1.98448i
$76$	9.91672e36			0.239936
$77$		−	1.07043e37i		−	0.199409i
$78$	−3.95746e37	+	4.37633e36i	−0.569540	+	0.0629822i
$79$	−3.82460e37			−0.426623			−0.213311	−	0.976984i	$-0.568425\pi$
$79$	−3.82460e37			−0.426623			−0.213311	+	0.976984i	$0.568425\pi$
$80$			7.84025e37i			0.680034i
$81$	1.33696e38	−	6.30309e37i	0.904518	−	0.426435i
$82$	7.58933e36			0.0401723
$83$		−	6.29598e37i		−	0.261518i	−0.991414	−	0.130759i	$-0.958259\pi$
$83$		−	6.29598e37i		−	0.261518i	0.991414	−	0.130759i	$-0.0417414\pi$
$84$	−4.02639e37	−	3.64100e38i	−0.131622	−	1.19024i
$85$	−1.40214e38			−0.361753
$86$			1.03008e38i			0.210330i
$87$	3.34837e38	−	3.70277e37i	0.542560	−	0.0599987i
$88$	8.40463e37			0.108359
$89$		−	1.43005e39i		−	1.47079i	−0.677637	−	0.735396i	$-0.736996\pi$
$89$		−	1.43005e39i		−	1.47079i	0.677637	−	0.735396i	$-0.263004\pi$
$90$	9.59474e38	−	2.14833e38i	0.789193	−	0.176706i
$91$	−2.84914e39			−1.87882
$92$			1.43847e39i			0.762330i
$93$	2.68040e38	+	2.42385e39i	0.114430	+	1.03478i
$94$	3.97572e38			0.137044
$95$			1.90468e39i			0.531312i
$96$	4.46327e39	−	4.93568e38i	1.00978	−	0.111666i
$97$	2.20304e39			0.405123			0.202562	−	0.979270i	$-0.435073\pi$
$97$	2.20304e39			0.405123			0.202562	+	0.979270i	$0.435073\pi$
$98$			4.19991e39i			0.629099i
$99$	2.32637e38	+	1.03899e39i	0.0284430	+	0.127030i
$100$	−1.56079e40			−1.56079
$101$		−	3.29786e37i		−	0.00270275i	−0.999999	−	0.00135137i	$-0.999570\pi$
$101$		−	3.29786e37i		−	0.00270275i	0.999999	−	0.00135137i	$-0.000430156\pi$
$102$	1.59459e38	+	1.44197e39i	0.0107312	+	0.0970404i
$103$	−1.96793e40			−1.08960			−0.544798	−	0.838568i	$-0.683394\pi$
$103$	−1.96793e40			−1.08960			−0.544798	+	0.838568i	$0.683394\pi$
$104$		−	2.23704e40i		−	1.02095i
$105$	6.99318e40	−	7.73337e39i	2.63566	−	0.291463i
$106$	−1.30117e40			−0.405711
$107$		−	5.02581e40i		−	1.29876i	−0.760462	−	0.649382i	$-0.775028\pi$
$107$		−	5.02581e40i		−	1.29876i	0.760462	−	0.649382i	$-0.224972\pi$
$108$	1.18211e40	+	3.44654e40i	0.253619	+	0.739449i
$109$	−4.37630e40			−0.780868			−0.390434	−	0.920631i	$-0.627675\pi$
$109$	−4.37630e40			−0.780868			−0.390434	+	0.920631i	$0.627675\pi$
$110$			7.08253e39i			0.105277i
$111$	−1.14415e40	−	1.03464e41i	−0.141913	−	1.28330i
$112$	5.80489e40			0.601775
$113$			1.85518e41i			1.60996i	0.593299	+	0.804982i	$0.297825\pi$
$113$			1.85518e41i			1.60996i	−0.593299	+	0.804982i	$0.702175\pi$
$114$	1.95879e40	−	2.16612e39i	0.142525	−	0.0157610i
$115$	−2.76282e41			−1.68809
$116$			8.30436e40i			0.426723i
$117$	2.76545e41	−	6.19203e40i	1.19687	−	0.267988i
$118$	−1.70280e41			−0.621617
$119$			1.03814e41i			0.320122i
$120$	6.07195e40	+	5.49078e41i	0.158381	+	1.43222i
$121$	4.44923e41			0.983054
$122$		−	2.08892e40i		−	0.0391495i
$123$	−5.36904e40	+	5.93732e39i	−0.0854662	+	0.00945123i
$124$	−6.01143e41			−0.813850
$125$		−	1.49631e42i		−	1.72513i
$126$	−1.59062e41	−	7.10391e41i	−0.156370	−	0.698371i
$127$	−7.52594e40			−0.0631664			−0.0315832	−	0.999501i	$-0.510055\pi$
$127$	−7.52594e40			−0.0631664			−0.0315832	+	0.999501i	$0.510055\pi$
$128$			1.36275e42i			0.977726i
$129$	−8.05856e40	−	7.28724e41i	−0.0494838	−	0.447475i
$130$	1.88514e42			0.991918
$131$		−	2.54195e42i		−	1.14747i	−0.819041	−	0.573735i	$-0.805494\pi$
$131$		−	2.54195e42i		−	1.14747i	0.819041	−	0.573735i	$-0.194506\pi$
$132$	−2.60872e41	+	2.88484e40i	−0.101146	+	0.0111852i
$133$	1.41022e42			0.470168
$134$			1.92529e42i			0.552587i
$135$	−6.61968e42	+	2.27045e42i	−1.63743	+	0.561611i
$136$	−8.15104e41			−0.173954
$137$		−	5.51045e42i		−	1.01572i	−0.861439	−	0.507862i	$-0.830436\pi$
$137$		−	5.51045e42i		−	1.01572i	0.861439	−	0.507862i	$-0.169564\pi$
$138$	3.14205e41	+	2.84131e42i	0.0500762	+	0.452832i
$139$	1.23600e43			1.70500			0.852499	−	0.522730i	$-0.175086\pi$
$139$	1.23600e43			1.70500			0.852499	+	0.522730i	$0.175086\pi$
$140$			1.73440e43i			2.07294i
$141$	−2.81260e42	+	3.11030e41i	−0.291559	+	0.0322419i
$142$	−7.01050e40			−0.00630931
$143$			2.04136e42i			0.159661i
$144$	−5.63437e42	+	1.26158e42i	−0.383350	+	0.0858348i
$145$	−1.59500e43			−0.944930
$146$		−	9.59931e41i		−	0.0495659i
$147$	−3.28570e42	−	2.97121e43i	−0.148006	−	1.33840i
$148$	2.56602e43			1.00931
$149$		−	1.41585e43i		−	0.486735i	−0.969934	−	0.243368i	$-0.921748\pi$
$149$		−	1.41585e43i		−	0.486735i	0.969934	−	0.243368i	$-0.0782521\pi$
$150$	−3.08293e43	+	3.40924e42i	−0.927126	+	0.102526i
$151$	4.05353e43			1.06732			0.533660	−	0.845699i	$-0.320816\pi$
$151$	4.05353e43			1.06732			0.533660	+	0.845699i	$0.320816\pi$
$152$			1.10725e43i			0.255490i
$153$	−2.25618e42	−	1.00764e43i	−0.0456609	−	0.203928i
$154$	5.24388e42			0.0931619
$155$		−	1.15460e44i		−	1.80218i
$156$	7.67849e42	+	6.94356e43i	0.105386	+	0.952994i
$157$	2.07145e43			0.250196			0.125098	−	0.992144i	$-0.460075\pi$
$157$	2.07145e43			0.250196			0.125098	+	0.992144i	$0.460075\pi$
$158$		−	1.87361e43i		−	0.199314i
$159$	9.20507e43	−	1.01794e43i	0.863147	−	0.0954506i
$160$	−2.12608e44			−1.75865
$161$			2.04558e44i			1.49383i
$162$	3.08778e43	+	6.54954e43i	0.199226	+	0.422581i
$163$	−1.46914e44			−0.838130			−0.419065	−	0.907956i	$-0.637642\pi$
$163$	−1.46914e44			−0.838130			−0.419065	+	0.907956i	$0.637642\pi$
$164$		−	1.33159e43i		−	0.0672191i
$165$	−5.54084e42	−	5.01050e43i	−0.0247683	−	0.223976i
$166$	3.08430e43			0.122178
$167$			3.73545e44i			1.31224i	0.754656	+	0.656120i	$0.227804\pi$
$167$			3.73545e44i			1.31224i	−0.754656	+	0.656120i	$0.772196\pi$
$168$	4.06535e44	−	4.49565e43i	1.26740	−	0.140154i
$169$	1.82155e44			0.504321
$170$		−	6.86883e43i		−	0.169007i
$171$	−1.36879e44	+	3.06482e43i	−0.299512	+	0.0670629i
$172$	1.80732e44			0.351939
$173$		−	1.11996e45i		−	1.94214i	−0.238798	−	0.971069i	$-0.576753\pi$
$173$		−	1.11996e45i		−	1.94214i	0.238798	−	0.971069i	$-0.423247\pi$
$174$	1.81393e43	+	1.64031e44i	0.0280308	+	0.253478i
$175$	−2.21954e45			−3.05845
$176$		−	4.15911e43i		−	0.0511384i
$177$	1.20464e45	−	1.33214e44i	1.32248	−	0.146246i
$178$	7.00559e44			0.687139
$179$			7.26520e44i			0.637070i	0.947911	+	0.318535i	$0.103191\pi$
$179$			7.26520e44i			0.637070i	−0.947911	+	0.318535i	$0.896809\pi$
$180$	−3.76935e44	−	1.68345e45i	−0.295677	−	1.32053i
$181$	1.80582e45			1.26796			0.633978	−	0.773351i	$-0.281421\pi$
$181$	1.80582e45			1.26796			0.633978	+	0.773351i	$0.281421\pi$
$182$		−	1.39575e45i		−	0.877767i
$183$	1.63422e43	+	1.47780e44i	0.00921059	+	0.0832901i
$184$	−1.60611e45			−0.811745
$185$			4.92849e45i			2.23501i
$186$	−1.18740e45	+	1.31308e44i	−0.483436	+	0.0534605i
$187$	7.43807e43			0.0272037
$188$		−	6.97560e44i		−	0.229311i
$189$	1.68103e45	+	4.90119e45i	0.496980	+	1.44899i
$190$	−9.33071e44			−0.248223
$191$		−	4.47455e45i		−	1.07172i	−0.844307	−	0.535860i	$-0.819987\pi$
$191$		−	4.47455e45i		−	1.07172i	0.844307	−	0.535860i	$-0.180013\pi$
$192$	4.16678e43	+	3.76796e44i	0.00899033	+	0.0812983i
$193$	3.71911e45			0.723257			0.361629	−	0.932322i	$-0.382221\pi$
$193$	3.71911e45			0.723257			0.361629	+	0.932322i	$0.382221\pi$
$194$			1.07923e45i			0.189269i
$195$	−1.33363e46	+	1.47479e45i	−2.11030	+	0.233366i
$196$	7.36896e45			1.05265
$197$			5.09172e45i			0.656961i	0.944511	+	0.328481i	$0.106537\pi$
$197$			5.09172e45i			0.656961i	−0.944511	+	0.328481i	$0.893463\pi$
$198$	−5.08983e44	+	1.13965e44i	−0.0593471	+	0.0132882i
$199$	5.93659e45			0.625857			0.312929	−	0.949777i	$-0.398690\pi$
$199$	5.93659e45			0.625857			0.312929	+	0.949777i	$0.398690\pi$
$200$		−	1.74269e46i		−	1.66196i
$201$	−1.50620e45	−	1.36204e46i	−0.130006	−	1.17562i
$202$	1.61557e43			0.00126269
$203$			1.18093e46i			0.836186i
$204$	2.53001e45	−	2.79780e44i	0.162375	−	0.0179561i
$205$	2.55754e45			0.148849
$206$		−	9.64057e45i		−	0.509047i
$207$	−4.44566e45	−	1.98549e46i	−0.213073	−	0.951615i
$208$	−1.10702e46			−0.481824
$209$		−	1.01040e45i		−	0.0399546i
$210$	3.78845e45	+	3.42585e46i	0.136168	+	1.23135i
$211$	2.06065e46			0.673526			0.336763	−	0.941589i	$-0.390668\pi$
$211$	2.06065e46			0.673526			0.336763	+	0.941589i	$0.390668\pi$
$212$			2.28297e46i			0.678864i
$213$	4.95954e44	−	5.48448e43i	0.0134230	−	0.00148438i
$214$	2.46206e46			0.606769
$215$			3.47128e46i			0.779329i
$216$	−3.84822e46	+	1.31988e46i	−0.787382	+	0.270059i
$217$	−8.54862e46			−1.59478
$218$		−	2.14388e46i		−	0.364813i
$219$	7.50977e44	+	6.79098e45i	0.0116612	+	0.105451i
$220$	1.24267e46			0.176157
$221$		−	1.97977e46i		−	0.256312i
$222$	5.06851e46	−	5.60499e45i	0.599544	−	0.0663002i
$223$	4.68104e46			0.506110			0.253055	−	0.967452i	$-0.418565\pi$
$223$	4.68104e46			0.506110			0.253055	+	0.967452i	$0.418565\pi$
$224$			1.57414e47i			1.55626i
$225$	2.15433e47	−	4.82371e46i	1.94833	−	0.436245i
$226$	−9.08821e46			−0.752159
$227$		−	1.69143e47i		−	1.28156i	−0.767726	−	0.640778i	$-0.778612\pi$
$227$		−	1.69143e47i		−	1.28156i	0.767726	−	0.640778i	$-0.221388\pi$
$228$	−3.80056e45	−	3.43680e46i	−0.0263725	−	0.238483i
$229$	−2.06867e47			−1.31517			−0.657584	−	0.753381i	$-0.728422\pi$
$229$	−2.06867e47			−1.31517			−0.657584	+	0.753381i	$0.728422\pi$
$230$		−	1.35346e47i		−	0.788659i
$231$	−3.70976e46	+	4.10241e45i	−0.198201	+	0.0219179i
$232$	−9.27220e46			−0.454384
$233$		−	4.18936e47i		−	1.88378i	−0.335927	−	0.941888i	$-0.609049\pi$
$233$		−	4.18936e47i		−	1.88378i	0.335927	−	0.941888i	$-0.390951\pi$
$234$	3.03337e46	+	1.35475e47i	0.125201	+	0.559166i
$235$	1.33979e47			0.507783
$236$			2.98764e47i			1.04013i
$237$	1.46577e46	+	1.32548e47i	0.0468920	+	0.424038i
$238$	−5.08566e46			−0.149557
$239$			1.58595e47i			0.428877i	0.976738	+	0.214438i	$0.0687921\pi$
$239$			1.58595e47i			0.428877i	−0.976738	+	0.214438i	$0.931208\pi$
$240$	2.71716e47	−	3.00476e46i	0.675913	−	0.0747455i
$241$	1.81409e47			0.415258			0.207629	−	0.978208i	$-0.433425\pi$
$241$	1.81409e47			0.415258			0.207629	+	0.978208i	$0.433425\pi$
$242$			2.17961e47i			0.459273i
$243$	−2.69682e47	−	4.39187e47i	−0.523271	−	0.852166i
$244$	−3.66512e46			−0.0655076
$245$			1.41534e48i			2.33098i
$246$	−2.90860e45	−	2.63020e46i	−0.00441552	−	0.0399289i
$247$	−2.68935e47			−0.376450
$248$		−	6.71205e47i		−	0.866605i
$249$	−2.18197e47	+	2.41292e46i	−0.259933	+	0.0287446i
$250$	7.33018e47			0.805962
$251$		−	1.83288e47i		−	0.186063i	−0.995663	−	0.0930315i	$-0.970344\pi$
$251$		−	1.83288e47i		−	0.186063i	0.995663	−	0.0930315i	$-0.0296557\pi$
$252$	−1.24642e48	+	2.79082e47i	−1.16856	+	0.261650i
$253$	1.46563e47			0.126944
$254$		−	3.68683e46i		−	0.0295107i
$255$	5.37366e46	+	4.85932e47i	0.0397618	+	0.359561i
$256$	−7.87131e47			−0.538577
$257$		−	2.16915e48i		−	1.37287i	−0.727193	−	0.686433i	$-0.759176\pi$
$257$		−	2.16915e48i		−	1.37287i	0.727193	−	0.686433i	$-0.240824\pi$
$258$	3.56990e47	−	3.94775e46i	0.209056	−	0.0231183i
$259$	3.64904e48			1.97780
$260$		−	3.30757e48i		−	1.65975i
$261$	−2.56651e47	−	1.14624e48i	−0.119270	−	0.532678i
$262$	1.24526e48			0.536085
$263$			4.12532e48i			1.64567i	0.568281	+	0.822835i	$0.307609\pi$
$263$			4.12532e48i			1.64567i	−0.568281	+	0.822835i	$0.692391\pi$
$264$	−3.22106e46	−	2.91276e47i	−0.0119102	−	0.107702i
$265$	−4.38484e48			−1.50327
$266$			6.90842e47i			0.219658i
$267$	−4.95607e48	+	5.48064e47i	−1.46188	+	0.161661i
$268$	3.37802e48			0.924627
$269$			2.46746e47i			0.0626908i	0.999509	+	0.0313454i	$0.00997918\pi$
$269$			2.46746e47i			0.0626908i	−0.999509	+	0.0313454i	$0.990021\pi$
$270$	−1.11225e48	−	3.24287e48i	−0.262379	−	0.764988i
$271$	2.93840e48			0.643761			0.321880	−	0.946780i	$-0.395685\pi$
$271$	2.93840e48			0.643761			0.321880	+	0.946780i	$0.395685\pi$
$272$			4.03362e47i			0.0820951i
$273$	1.09193e48	+	9.87415e48i	0.206510	+	1.86744i
$274$	2.69948e48			0.474535
$275$			1.59026e48i			0.259905i
$276$	4.98523e48	−	5.51289e47i	0.757711	−	0.0837911i
$277$	−8.81066e48			−1.24570			−0.622850	−	0.782342i	$-0.714025\pi$
$277$	−8.81066e48			−1.24570			−0.622850	+	0.782342i	$0.714025\pi$
$278$			6.05498e48i			0.796557i
$279$	8.29749e48	−	1.85787e48i	1.01593	−	0.227473i
$280$	−1.93653e49			−2.20731
$281$		−	6.58400e48i		−	0.698817i	−0.936970	−	0.349408i	$-0.886383\pi$
$281$		−	6.58400e48i		−	0.698817i	0.936970	−	0.349408i	$-0.113617\pi$
$282$	−1.52369e47	−	1.37785e48i	−0.0150631	−	0.136213i
$283$	9.35509e48			0.861627			0.430813	−	0.902441i	$-0.358227\pi$
$283$	9.35509e48			0.861627			0.430813	+	0.902441i	$0.358227\pi$
$284$			1.23003e47i			0.0105572i
$285$	6.60097e48	−	7.29964e47i	0.528093	−	0.0583989i
$286$	−1.00003e48			−0.0745921
$287$		−	1.89360e48i		−	0.131719i
$288$	−3.42108e48	−	1.52790e49i	−0.221980	−	0.991392i
$289$	1.57966e49			0.956328
$290$		−	7.81363e48i		−	0.441461i
$291$	−8.44309e47	−	7.63497e48i	−0.0445289	−	0.402668i
$292$	−1.68425e48			−0.0829371
$293$		−	5.87296e48i		−	0.270088i	−0.990840	−	0.135044i	$-0.956882\pi$
$293$		−	5.87296e48i		−	0.270088i	0.990840	−	0.135044i	$-0.0431175\pi$
$294$	1.45555e49	−	1.60961e48i	0.625287	−	0.0691470i
$295$	−5.73829e49			−2.30326
$296$			2.86508e49i			1.07474i
$297$	3.51162e48	−	1.20443e48i	0.123134	−	0.0422331i
$298$	6.93603e48			0.227398
$299$		−	3.90102e49i		−	1.19606i
$300$	5.98169e48	+	5.40916e49i	0.171553	+	1.55133i
$301$	2.57012e49			0.689643
$302$			1.98576e49i			0.498641i
$303$	−1.14293e47	+	1.26390e46i	−0.00268637	+	0.000297071i
$304$	5.47932e48			0.120574
$305$		−	7.03950e48i		−	0.145059i
$306$	4.93626e48	−	1.10526e48i	0.0952730	−	0.0213323i
$307$	−4.95061e49			−0.895141			−0.447570	−	0.894249i	$-0.647711\pi$
$307$	−4.95061e49			−0.895141			−0.447570	+	0.894249i	$0.647711\pi$
$308$		−	9.20065e48i		−	0.155885i
$309$	7.54205e48	+	6.82017e49i	0.119762	+	1.08299i
$310$	5.65620e49			0.841959
$311$			1.18792e50i			1.65799i	0.559259	+	0.828993i	$0.311086\pi$
$311$			1.18792e50i			1.65799i	−0.559259	+	0.828993i	$0.688914\pi$
$312$	−7.75280e49	+	8.57340e48i	−1.01477	+	0.112218i
$313$	1.00887e50			1.23865			0.619325	−	0.785135i	$-0.287406\pi$
$313$	1.00887e50			1.23865			0.619325	+	0.785135i	$0.287406\pi$
$314$			1.01477e49i			0.116889i
$315$	−5.36025e49	−	2.39396e50i	−0.579394	−	2.58765i
$316$	−3.28734e49			−0.333506
$317$		−	1.51367e50i		−	1.44160i	−0.693142	−	0.720801i	$-0.743774\pi$
$317$		−	1.51367e50i		−	1.44160i	0.693142	−	0.720801i	$-0.256226\pi$
$318$	4.98671e48	+	4.50941e49i	0.0445935	+	0.403253i
$319$	8.46116e48			0.0710586
$320$		−	1.79487e49i		−	0.141590i
$321$	−1.74177e50	+	1.92613e49i	−1.29090	+	0.142753i
$322$	−1.00210e50			−0.697899
$323$			9.79911e48i			0.0641411i
$324$	1.14915e50	−	5.41767e49i	0.707093	−	0.333359i
$325$	4.23275e50			2.44881
$326$		−	7.19708e49i		−	0.391566i
$327$	1.67721e49	+	1.51668e50i	0.0858286	+	0.776137i
$328$	1.48678e49			0.0715763
$329$		−	9.91972e49i		−	0.449347i
$330$	2.45456e49	−	2.71437e48i	0.104639	−	0.0115715i
$331$	4.63631e49			0.186043			0.0930214	−	0.995664i	$-0.470347\pi$
$331$	4.63631e49			0.186043			0.0930214	+	0.995664i	$0.470347\pi$
$332$		−	5.41155e49i		−	0.204437i
$333$	−3.54184e50	+	7.93044e49i	−1.25993	+	0.282106i
$334$	−1.82994e50			−0.613065
$335$			6.48808e50i			2.04748i
$336$	−2.22471e49	−	2.01178e50i	−0.0661437	−	0.598129i
$337$	−5.72886e50			−1.60498			−0.802491	−	0.596665i	$-0.796492\pi$
$337$	−5.72886e50			−1.60498			−0.802491	+	0.596665i	$0.796492\pi$
$338$			8.92348e49i			0.235614i
$339$	6.42941e50	−	7.10993e49i	1.60021	−	0.176958i
$340$	−1.20517e50			−0.282794
$341$			6.12494e49i			0.135523i
$342$	−1.50140e49	−	6.70548e49i	−0.0313311	−	0.139929i
$343$	2.69698e50			0.530878
$344$			2.01796e50i			0.374752i
$345$	1.05885e50	+	9.57500e50i	0.185546	+	1.67786i
$346$	5.48650e50			0.907347
$347$		−	4.60549e50i		−	0.718930i	−0.933159	−	0.359465i	$-0.882959\pi$
$347$		−	4.60549e50i		−	0.718930i	0.933159	−	0.359465i	$-0.117041\pi$
$348$	2.87801e50	−	3.18263e49i	0.424138	−	0.0469030i
$349$	−8.97154e50			−1.24841			−0.624206	−	0.781259i	$-0.714578\pi$
$349$	−8.97154e50			−1.24841			−0.624206	+	0.781259i	$0.714578\pi$
$350$		−	1.08731e51i		−	1.42887i
$351$	−3.20580e50	−	9.34678e50i	−0.397918	−	1.16016i
$352$	1.12785e50			0.132250
$353$		−	3.24713e50i		−	0.359753i	−0.983689	−	0.179877i	$-0.942430\pi$
$353$		−	3.24713e50i		−	0.359753i	0.983689	−	0.179877i	$-0.0575699\pi$
$354$	6.52594e49	+	5.90131e50i	0.0683247	+	0.617851i
$355$	−2.36248e49			−0.0233777
$356$		−	1.22917e51i		−	1.14977i
$357$	3.59782e50	−	3.97864e49i	0.318182	−	0.0351860i
$358$	−3.55910e50			−0.297632
$359$			1.73033e51i			1.36848i	0.729256	+	0.684241i	$0.239866\pi$
$359$			1.73033e51i			1.36848i	−0.729256	+	0.684241i	$0.760134\pi$
$360$	1.87965e51	−	4.20866e50i	1.40613	−	0.314843i
$361$	−1.27989e51			−0.905795
$362$			8.84644e50i			0.592375i
$363$	−1.70516e50	−	1.54195e51i	−0.108052	−	0.977098i
$364$	−2.44891e51			−1.46874
$365$		−	3.23489e50i		−	0.183655i
$366$	−7.23949e49	+	8.00575e48i	−0.0389122	+	0.00430309i
$367$	3.56240e51			1.81310			0.906548	−	0.422102i	$-0.138708\pi$
$367$	3.56240e51			1.81310			0.906548	+	0.422102i	$0.138708\pi$
$368$			7.94801e50i			0.383091i
$369$	4.11535e49	+	1.83797e50i	0.0187879	+	0.0839095i
$370$	−2.41439e51			−1.04417
$371$			3.24652e51i			1.33027i
$372$	2.30387e50	+	2.08336e51i	0.0894539	+	0.808919i
$373$	5.09239e51			1.87389			0.936947	−	0.349470i	$-0.113638\pi$
$373$	5.09239e51			1.87389			0.936947	+	0.349470i	$0.113638\pi$
$374$			3.64379e49i			0.0127093i
$375$	−5.18570e51	+	5.73458e50i	−1.71468	+	0.189617i
$376$	7.78858e50			0.244175
$377$		−	2.25208e51i		−	0.669511i
$378$	−2.40101e51	+	8.23509e50i	−0.676953	+	0.232184i
$379$	−1.59081e51			−0.425437			−0.212718	−	0.977114i	$-0.568232\pi$
$379$	−1.59081e51			−0.425437			−0.212718	+	0.977114i	$0.568232\pi$
$380$			1.63712e51i			0.415345i
$381$	2.88430e49	+	2.60823e50i	0.00694290	+	0.0627837i
$382$	2.19201e51			0.500697
$383$		−	6.61497e51i		−	1.43401i	−0.697067	−	0.717006i	$-0.745512\pi$
$383$		−	6.61497e51i		−	1.43401i	0.697067	−	0.717006i	$-0.254488\pi$
$384$	4.72283e51	−	5.22271e50i	0.971802	−	0.107466i
$385$	1.76714e51			0.345189
$386$			1.82193e51i			0.337898i
$387$	−2.49462e51	+	5.58564e50i	−0.439325	+	0.0983679i
$388$	1.89357e51			0.316698
$389$		−	8.76427e51i		−	1.39227i	−0.717911	−	0.696135i	$-0.754901\pi$
$389$		−	8.76427e51i		−	1.39227i	0.717911	−	0.696135i	$-0.245099\pi$
$390$	−7.22475e50	−	6.53324e51i	−0.109026	−	0.985908i
$391$	−1.42141e51			−0.203790
$392$			8.22779e51i			1.12089i
$393$	−8.80953e51	+	9.74197e50i	−1.14052	+	0.126123i
$394$	−2.49435e51			−0.306925
$395$		−	6.31391e51i		−	0.738510i
$396$	1.99957e50	+	8.93037e50i	0.0222348	+	0.0993038i
$397$	1.16131e52			1.22783			0.613913	−	0.789374i	$-0.289595\pi$
$397$	1.16131e52			1.22783			0.613913	+	0.789374i	$0.289595\pi$
$398$			2.90824e51i			0.292394i
$399$	−5.40463e50	−	4.88733e51i	−0.0516783	−	0.467319i
$400$	−8.62389e51			−0.784338
$401$			7.00683e51i			0.606226i	0.952955	+	0.303113i	$0.0980259\pi$
$401$			7.00683e51i			0.606226i	−0.952955	+	0.303113i	$0.901974\pi$
$402$	6.67241e51	−	7.37865e50i	0.549239	−	0.0607373i
$403$	1.63026e52			1.27690
$404$		−	2.83460e49i		−	0.00211283i
$405$	1.04056e52	+	2.20714e52i	0.738185	+	1.56578i
$406$	−5.78518e51			−0.390657
$407$		−	2.61448e51i		−	0.168072i
$408$	3.12387e50	+	2.82487e51i	0.0191201	+	0.172900i
$409$	−2.55948e52			−1.49172			−0.745858	−	0.666105i	$-0.767960\pi$
$409$	−2.55948e52			−1.49172			−0.745858	+	0.666105i	$0.767960\pi$
$410$			1.25290e51i			0.0695407i
$411$	−1.90973e52	+	2.11187e51i	−1.00957	+	0.111643i
$412$	−1.69149e52			−0.851774
$413$			4.24861e52i			2.03819i
$414$	9.72661e51	−	2.17786e51i	0.444585	−	0.0995457i
$415$	1.03938e52			0.452703
$416$		−	3.00196e52i		−	1.24606i
$417$	−4.73696e51	−	4.28357e52i	−0.187404	−	1.69467i
$418$	4.94977e50			0.0186664
$419$			3.81511e51i			0.137160i	0.997646	+	0.0685798i	$0.0218468\pi$
$419$			3.81511e51i			0.137160i	−0.997646	+	0.0685798i	$0.978153\pi$
$420$	6.01082e52	−	6.64703e51i	2.06038	−	0.227846i
$421$	3.63456e51			0.118798			0.0593991	−	0.998234i	$-0.481082\pi$
$421$	3.63456e51			0.118798			0.0593991	+	0.998234i	$0.481082\pi$
$422$			1.00948e52i			0.314664i
$423$	2.15585e51	+	9.62832e51i	0.0640931	+	0.286248i
$424$	−2.54904e52			−0.722870
$425$		−	1.54228e52i		−	0.417238i
$426$	2.68676e49	+	2.42960e50i	0.000693484	+	0.00627108i
$427$	−5.21202e51			−0.128366
$428$		−	4.31981e52i		−	1.01529i
$429$	7.07467e51	−	7.82348e50i	0.158694	−	0.0175491i
$430$	−1.70052e52			−0.364094
$431$		−	3.03326e52i		−	0.619960i	−0.950743	−	0.309980i	$-0.899678\pi$
$431$		−	3.03326e52i		−	0.619960i	0.950743	−	0.309980i	$-0.100322\pi$
$432$	6.53155e51	+	1.90433e52i	0.127450	+	0.371593i
$433$	1.72878e52			0.322094			0.161047	−	0.986947i	$-0.448513\pi$
$433$	1.72878e52			0.322094			0.161047	+	0.986947i	$0.448513\pi$
$434$		−	4.18783e52i		−	0.745065i
$435$	6.11279e51	+	5.52771e52i	0.103861	+	0.939205i
$436$	−3.76155e52			−0.610431
$437$			1.93086e52i			0.299310i
$438$	−3.32679e51	+	3.67892e50i	−0.0492656	+	0.00544801i
$439$	−2.11240e52			−0.298873			−0.149437	−	0.988771i	$-0.547746\pi$
$439$	−2.11240e52			−0.298873			−0.149437	+	0.988771i	$0.547746\pi$
$440$			1.38749e52i			0.187576i
$441$	−1.01713e53	+	2.27742e52i	−1.31402	+	0.294219i
$442$	9.69857e51			0.119746
$443$			1.09683e53i			1.29439i	0.762324	+	0.647195i	$0.224058\pi$
$443$			1.09683e53i			1.29439i	−0.762324	+	0.647195i	$0.775942\pi$
$444$	−9.83423e51	−	8.89296e52i	−0.110938	−	1.00320i
$445$	2.36083e53			2.54603
$446$			2.29316e52i			0.236449i
$447$	−4.90686e52	+	5.42623e51i	−0.483786	+	0.0534992i
$448$	−1.32891e52			−0.125296
$449$			1.74729e53i			1.57557i	0.615950	+	0.787785i	$0.288772\pi$
$449$			1.74729e53i			1.57557i	−0.615950	+	0.787785i	$0.711228\pi$
$450$	2.36306e52	+	1.05537e53i	0.203809	+	0.910240i
$451$	−1.35673e51			−0.0111934
$452$			1.59457e53i			1.25856i
$453$	−1.55351e52	−	1.40482e53i	−0.117314	−	1.06085i
$454$	8.28605e52			0.598729
$455$		−	4.70356e53i		−	3.25236i
$456$	3.83734e52	−	4.24351e51i	0.253942	−	0.0280820i
$457$	−2.19444e53			−1.38995			−0.694976	−	0.719033i	$-0.744585\pi$
$457$	−2.19444e53			−1.38995			−0.694976	+	0.719033i	$0.744585\pi$
$458$		−	1.01341e53i		−	0.614433i
$459$	−3.40567e52	+	1.16809e52i	−0.197674	+	0.0677989i
$460$	−2.37472e53			−1.31964
$461$			1.42669e53i			0.759120i	0.925167	+	0.379560i	$0.123925\pi$
$461$			1.42669e53i			0.759120i	−0.925167	+	0.379560i	$0.876075\pi$
$462$	−2.00971e51	−	1.81735e52i	−0.0102398	−	0.0925974i
$463$	3.67143e53			1.79149			0.895747	−	0.444563i	$-0.146641\pi$
$463$	3.67143e53			1.79149			0.895747	+	0.444563i	$0.146641\pi$
$464$			4.58844e52i			0.214440i
$465$	−4.00145e53	+	4.42498e52i	−1.79126	+	0.198085i
$466$	2.05230e53			0.880080
$467$		−	3.07801e53i		−	1.26454i	−0.774748	−	0.632270i	$-0.782124\pi$
$467$		−	3.07801e53i		−	1.26454i	0.774748	−	0.632270i	$-0.217876\pi$
$468$	2.37697e53	−	5.32221e52i	0.935636	−	0.209496i
$469$	4.80375e53			1.81186
$470$			6.56339e52i			0.237231i
$471$	−7.93878e51	−	7.17893e52i	−0.0275002	−	0.248681i
$472$	−3.33584e53			−1.10756
$473$		−	1.84145e52i		−	0.0586054i
$474$	−6.49329e52	+	7.18057e51i	−0.198106	+	0.0219075i
$475$	−2.09505e53			−0.612805
$476$			8.92304e52i			0.250250i
$477$	−7.05565e52	−	3.15115e53i	−0.189745	−	0.847426i
$478$	−7.76933e52			−0.200367
$479$			3.83358e53i			0.948187i	0.880475	+	0.474093i	$0.157224\pi$
$479$			3.83358e53i			0.948187i	−0.880475	+	0.474093i	$0.842776\pi$
$480$	8.14816e52	+	7.36827e53i	0.193301	+	1.74800i
$481$	−6.95888e53			−1.58357
$482$			8.88693e52i			0.194004i
$483$	7.08929e53	−	7.83966e52i	1.48477	−	0.164193i
$484$	3.82423e53			0.768487
$485$			3.63692e53i			0.701293i
$486$	2.15151e53	−	1.32113e53i	0.398123	−	0.244467i
$487$	−8.46444e51			−0.0150321			−0.00751603	−	0.999972i	$-0.502392\pi$
$487$	−8.46444e51			−0.0150321			−0.00751603	+	0.999972i	$0.502392\pi$
$488$		−	4.09228e52i		−	0.0697539i
$489$	5.63046e52	+	5.09154e53i	0.0921226	+	0.833052i
$490$	−6.93351e53			−1.08901
$491$		−	6.60349e53i		−	0.995735i	−0.867253	−	0.497868i	$-0.834117\pi$
$491$		−	6.60349e53i		−	0.995735i	0.867253	−	0.497868i	$-0.165883\pi$
$492$	−4.61483e52	+	5.10328e51i	−0.0668118	+	0.00738835i
$493$	−8.20587e52			−0.114074
$494$		−	1.31747e53i		−	0.175874i
$495$	−1.71523e53	+	3.84053e52i	−0.219897	+	0.0492365i
$496$	−3.32152e53			−0.408981
$497$			1.74917e52i			0.0206873i
$498$	−1.18205e52	−	1.06891e53i	−0.0134292	−	0.121438i
$499$	2.12829e53			0.232284			0.116142	−	0.993233i	$-0.462947\pi$
$499$	2.12829e53			0.232284			0.116142	+	0.993233i	$0.462947\pi$
$500$		−	1.28612e54i		−	1.34859i
$501$	1.29458e54	−	1.43160e53i	1.30429	−	0.144234i
$502$	8.97899e52			0.0869266
$503$			7.14659e53i			0.664874i	0.943125	+	0.332437i	$0.107871\pi$
$503$			7.14659e53i			0.664874i	−0.943125	+	0.332437i	$0.892129\pi$
$504$	−3.11607e53	−	1.39168e54i	−0.278610	−	1.24431i
$505$	5.44434e51			0.00467862
$506$			7.17987e52i			0.0593070i
$507$	−6.98106e52	−	6.31288e53i	−0.0554322	−	0.501266i
$508$	−6.46874e52			−0.0493793
$509$			1.00844e54i			0.740105i	0.929011	+	0.370053i	$0.120660\pi$
$509$			1.00844e54i			0.740105i	−0.929011	+	0.370053i	$0.879340\pi$
$510$	−2.38050e53	+	2.63247e52i	−0.167983	+	0.0185763i
$511$	−2.39510e53			−0.162520
$512$			1.11276e54i			0.726108i
$513$	1.58675e53	+	4.62630e53i	0.0995774	+	0.290326i
$514$	1.06263e54			0.641388
$515$		−	3.24879e54i		−	1.88616i
$516$	−6.92653e52	−	6.26357e53i	−0.0386832	−	0.349806i
$517$	−7.10732e52			−0.0381852
$518$			1.78760e54i			0.924009i
$519$	−3.88140e54	+	4.29222e53i	−1.93037	+	0.213469i
$520$	3.69305e54			1.76733
$521$			3.41798e54i			1.57404i	0.616928	+	0.787020i	$0.288377\pi$
$521$			3.41798e54i			1.57404i	−0.616928	+	0.787020i	$0.711623\pi$
$522$	5.61523e53	−	1.25729e53i	0.248862	−	0.0557219i
$523$	−2.89704e54			−1.23572			−0.617861	−	0.786287i	$-0.712001\pi$
$523$	−2.89704e54			−1.23572			−0.617861	+	0.786287i	$0.712001\pi$
$524$		−	2.18487e54i		−	0.897016i
$525$	8.50632e53	+	7.69215e54i	0.336168	+	3.03992i
$526$	−2.02093e54			−0.768840
$527$		−	5.94014e53i		−	0.217563i
$528$	−1.44141e53	+	1.59397e52i	−0.0508286	+	0.00562085i
$529$	1.44397e53			0.0490279
$530$		−	2.14806e54i		−	0.702311i
$531$	−9.23349e53	−	4.12380e54i	−0.290720	−	1.29840i
$532$	1.21212e54			0.367546
$533$			3.61117e53i			0.105464i
$534$	−2.68488e53	−	2.42790e54i	−0.0755265	−	0.682975i
$535$	8.29695e54			2.24824
$536$			3.77172e54i			0.984563i
$537$	2.51787e54	−	2.78437e53i	0.633210	−	0.0700232i
$538$	−1.20877e53			−0.0292885
$539$		−	7.50811e53i		−	0.175289i
$540$	−5.68979e54	+	1.95151e54i	−1.28003	+	0.439031i
$541$	1.12461e54			0.243813			0.121906	−	0.992542i	$-0.461099\pi$
$541$	1.12461e54			0.243813			0.121906	+	0.992542i	$0.461099\pi$
$542$			1.43947e54i			0.300758i
$543$	−6.92078e53	−	6.25837e54i	−0.139367	−	1.26027i
$544$	−1.09382e54			−0.212308
$545$		−	7.22470e54i		−	1.35173i
$546$	−4.83719e54	+	5.34918e53i	−0.872449	+	0.0964793i
$547$	−5.63336e54			−0.979538			−0.489769	−	0.871852i	$-0.662919\pi$
$547$	−5.63336e54			−0.979538			−0.489769	+	0.871852i	$0.662919\pi$
$548$		−	4.73637e54i		−	0.794026i
$549$	5.05891e53	−	1.13273e53i	0.0817731	−	0.0183096i
$550$	−7.79043e53			−0.121425
$551$			1.11470e54i			0.167542i
$552$	6.15540e53	+	5.56624e54i	0.0892225	+	0.806827i
$553$	−4.67480e54			−0.653522
$554$		−	4.31620e54i		−	0.581978i
$555$	1.70805e55	−	1.88884e54i	2.22147	−	0.245660i
$556$	1.06238e55			1.33285
$557$			5.53220e54i			0.669567i	0.942295	+	0.334783i	$0.108663\pi$
$557$			5.53220e54i			0.669567i	−0.942295	+	0.334783i	$0.891337\pi$
$558$	9.10139e53	+	4.06481e54i	0.106273	+	0.474631i
$559$	−4.90134e54			−0.552177
$560$			9.58312e54i			1.04171i
$561$	−2.85063e52	−	2.57778e53i	−0.00299008	−	0.0270389i
$562$	3.22539e54			0.326480
$563$			3.70989e54i			0.362404i	0.983446	+	0.181202i	$0.0579988\pi$
$563$			3.70989e54i			0.362404i	−0.983446	+	0.181202i	$0.942001\pi$
$564$	−2.41750e54	+	2.67338e53i	−0.227921	+	0.0252046i
$565$	−3.06265e55			−2.78695
$566$			4.58291e54i			0.402543i
$567$	1.63416e55	−	7.70424e54i	1.38558	−	0.653234i
$568$	−1.37338e53			−0.0112415
$569$			1.71662e55i			1.35653i	0.734819	+	0.678263i	$0.237267\pi$
$569$			1.71662e55i			1.35653i	−0.734819	+	0.678263i	$0.762733\pi$
$570$	3.57598e53	+	3.23371e54i	0.0272833	+	0.246719i
$571$	3.76870e54			0.277632			0.138816	−	0.990318i	$-0.455670\pi$
$571$	3.76870e54			0.277632			0.138816	+	0.990318i	$0.455670\pi$
$572$			1.75460e54i			0.124813i
$573$	−1.55072e55	+	1.71486e54i	−1.06523	+	0.117798i
$574$	9.27642e53			0.0615379
$575$		−	3.03897e55i		−	1.94701i
$576$	1.28988e54	−	2.88813e53i	0.0798176	−	0.0178717i
$577$	1.69152e55			1.01102			0.505511	−	0.862820i	$-0.331304\pi$
$577$	1.69152e55			1.01102			0.505511	+	0.862820i	$0.331304\pi$
$578$			7.73850e54i			0.446787i
$579$	−1.42534e54	−	1.28892e55i	−0.0794964	−	0.718875i
$580$	−1.37094e55			−0.738684
$581$		−	7.69555e54i		−	0.400606i
$582$	3.74025e54	−	4.13613e53i	0.188122	−	0.0208034i
$583$	2.32608e54			0.113045
$584$		−	1.88054e54i		−	0.0883132i
$585$	1.02222e55	+	4.56539e55i	0.463904	+	2.07186i
$586$	2.87707e54			0.126182
$587$		−	3.14150e55i		−	1.33160i	−0.746129	−	0.665802i	$-0.768090\pi$
$587$		−	3.14150e55i		−	1.33160i	0.746129	−	0.665802i	$-0.231910\pi$
$588$	−2.82414e54	−	2.55383e55i	−0.115702	−	1.04627i
$589$	−8.06916e54			−0.319538
$590$		−	2.81110e55i		−	1.07606i
$591$	1.76461e55	−	1.95139e54i	0.652981	−	0.0722095i
$592$	1.41781e55			0.507207
$593$			2.24450e55i			0.776293i	0.921598	+	0.388146i	$0.126885\pi$
$593$			2.24450e55i			0.776293i	−0.921598	+	0.388146i	$0.873115\pi$
$594$	5.90031e53	+	1.72029e54i	0.0197308	+	0.0575270i
$595$	−1.71383e55			−0.554150
$596$		−	1.21696e55i		−	0.380497i
$597$	−2.27518e54	−	2.05742e55i	−0.0687907	−	0.622065i
$598$	1.91104e55			0.558788
$599$			2.17706e55i			0.615650i	0.951443	+	0.307825i	$0.0996011\pi$
$599$			2.17706e55i			0.615650i	−0.951443	+	0.307825i	$0.900399\pi$
$600$	−6.03958e55	+	6.67884e54i	−1.65189	+	0.182674i
$601$	1.89308e55			0.500818			0.250409	−	0.968140i	$-0.419435\pi$
$601$	1.89308e55			0.500818			0.250409	+	0.968140i	$0.419435\pi$
$602$			1.25906e55i			0.322194i
$603$	−4.66264e55	+	1.04400e55i	−1.15421	+	0.258436i
$604$	3.48411e55			0.834360
$605$			7.34510e55i			1.70173i
$606$	−6.19164e51	−	5.59901e52i	−0.000138788	−	0.00125504i
$607$	−2.43549e55			−0.528216			−0.264108	−	0.964493i	$-0.585078\pi$
$607$	−2.43549e55			−0.528216			−0.264108	+	0.964493i	$0.585078\pi$
$608$			1.48586e55i			0.311821i
$609$	4.09270e55	−	4.52589e54i	0.831120	−	0.0919090i
$610$	3.44854e54			0.0677701
$611$			1.89173e55i			0.359779i
$612$	−1.93924e54	−	8.66092e54i	−0.0356947	−	0.159417i
$613$	5.49232e55			0.978467			0.489233	−	0.872153i	$-0.337277\pi$
$613$	5.49232e55			0.978467			0.489233	+	0.872153i	$0.337277\pi$
$614$		−	2.42522e55i		−	0.418200i
$615$	−9.80174e53	−	8.86358e54i	−0.0163607	−	0.147947i
$616$	1.02730e55			0.165990
$617$			8.81831e55i			1.37937i	0.724107	+	0.689687i	$0.242252\pi$
$617$			8.81831e55i			1.37937i	−0.724107	+	0.689687i	$0.757748\pi$
$618$	−3.34109e55	+	3.69473e54i	−0.505963	+	0.0559517i
$619$	−2.50972e55			−0.367970			−0.183985	−	0.982929i	$-0.558900\pi$
$619$	−2.50972e55			−0.367970			−0.183985	+	0.982929i	$0.558900\pi$
$620$		−	9.92409e55i		−	1.40882i
$621$	−6.71066e55	+	2.30165e55i	−0.922430	+	0.316379i
$622$	−5.81944e55			−0.774594
$623$		−	1.74795e56i		−	2.25303i
$624$	4.24263e54	+	3.83655e55i	0.0529594	+	0.478905i
$625$	8.18686e55			0.989731
$626$			4.94229e55i			0.578684i
$627$	−3.50169e54	+	3.87233e53i	−0.0397125	+	0.00439158i
$628$	1.78046e55			0.195587
$629$			2.53559e55i			0.269815i
$630$	1.17276e56	−	2.62590e55i	1.20892	−	0.270687i
$631$	2.84219e55			0.283835			0.141918	−	0.989878i	$-0.454673\pi$
$631$	2.84219e55			0.283835			0.141918	+	0.989878i	$0.454673\pi$
$632$		−	3.67047e55i		−	0.355124i
$633$	−7.89739e54	−	7.14150e55i	−0.0740302	−	0.669445i
$634$	7.41521e55			0.673501
$635$		−	1.24243e55i		−	0.109345i
$636$	7.91199e55	−	8.74944e54i	0.674751	−	0.0746170i
$637$	−1.99841e56			−1.65157
$638$			4.14499e54i			0.0331978i
$639$	−3.80147e53	−	1.69779e54i	−0.00295076	−	0.0131785i
$640$	−2.24972e56			−1.69250
$641$		−	7.15009e55i		−	0.521376i	−0.965423	−	0.260688i	$-0.916051\pi$
$641$		−	7.15009e55i		−	0.521376i	0.965423	−	0.260688i	$-0.0839493\pi$
$642$	−9.43580e54	−	8.53266e55i	−0.0666927	−	0.603093i
$643$	−5.16137e55			−0.353627			−0.176813	−	0.984244i	$-0.556579\pi$
$643$	−5.16137e55			−0.353627			−0.176813	+	0.984244i	$0.556579\pi$
$644$			1.75823e56i			1.16777i
$645$	1.20303e56	−	1.33036e55i	0.774607	−	0.0856595i
$646$	−4.80043e54			−0.0299660
$647$		−	9.19540e55i		−	0.556525i	−0.960505	−	0.278263i	$-0.910241\pi$
$647$		−	9.19540e55i		−	0.556525i	0.960505	−	0.278263i	$-0.0897586\pi$
$648$	6.04908e55	+	1.28308e56i	0.354968	+	0.752928i
$649$	3.04406e55			0.173204
$650$			2.07356e56i			1.14406i
$651$	3.27624e55	+	2.96266e56i	0.175290	+	1.58512i
$652$	−1.26276e56			−0.655195
$653$			9.49548e55i			0.477808i	0.971043	+	0.238904i	$0.0767881\pi$
$653$			9.49548e55i			0.477808i	−0.971043	+	0.238904i	$0.923212\pi$
$654$	−7.42995e55	+	8.21638e54i	−0.362603	+	0.0400982i
$655$	4.19642e56			1.98634
$656$		−	7.35747e54i		−	0.0337794i
$657$	2.32474e55	−	5.20526e54i	0.103530	−	0.0231812i
$658$	4.85951e55			0.209930
$659$		−	3.85689e56i		−	1.61633i	−0.588958	−	0.808164i	$-0.700461\pi$
$659$		−	3.85689e56i		−	1.61633i	0.588958	−	0.808164i	$-0.299539\pi$
$660$	−4.76249e54	−	4.30665e55i	−0.0193622	−	0.175090i
$661$	−2.91349e56			−1.14917			−0.574584	−	0.818445i	$-0.694836\pi$
$661$	−2.91349e56			−1.14917			−0.574584	+	0.818445i	$0.694836\pi$
$662$			2.27125e55i			0.0869173i
$663$	−6.86121e55	+	7.58743e54i	−0.254759	+	0.0281724i
$664$	6.04225e55			0.217689
$665$			2.32808e56i			0.813890i
$666$	−3.88499e55	−	1.73509e56i	−0.131797	−	0.588624i
$667$	−1.61692e56			−0.532318
$668$			3.21072e56i			1.02582i
$669$	−1.79400e55	−	1.62229e56i	−0.0556288	−	0.503043i
$670$	−3.17841e56			−0.956562
$671$			3.73433e54i			0.0109084i
$672$	5.45544e56	−	6.03287e55i	1.54684	−	0.171056i
$673$	3.82354e55			0.105236			0.0526180	−	0.998615i	$-0.483243\pi$
$673$	3.82354e55			0.105236			0.0526180	+	0.998615i	$0.483243\pi$
$674$		−	2.80647e56i		−	0.749830i
$675$	−2.49738e56	−	7.28132e56i	−0.647752	−	1.88858i
$676$	1.56567e56			0.394245
$677$		−	3.25766e56i		−	0.796403i	−0.917298	−	0.398201i	$-0.869634\pi$
$677$		−	3.25766e56i		−	0.796403i	0.917298	−	0.398201i	$-0.130366\pi$
$678$	3.48304e55	+	3.14966e56i	0.0826731	+	0.747601i
$679$	2.69276e56			0.620587
$680$		−	1.34563e56i		−	0.301125i
$681$	−5.86193e56	+	6.48238e55i	−1.27379	+	0.140861i
$682$	−3.00051e55			−0.0633151
$683$			1.66724e56i			0.341652i	0.985301	+	0.170826i	$0.0546435\pi$
$683$			1.66724e56i			0.341652i	−0.985301	+	0.170826i	$0.945356\pi$
$684$	−1.17651e56	+	2.63429e55i	−0.234139	+	0.0524254i
$685$	9.09703e56			1.75828
$686$			1.32120e56i			0.248021i
$687$	7.92813e55	+	7.16930e56i	0.144556	+	1.30720i
$688$	9.98608e55			0.176859
$689$		−	6.19126e56i		−	1.06511i
$690$	−4.69064e56	+	5.18712e55i	−0.783881	+	0.0866850i
$691$	4.88529e56			0.793103			0.396552	−	0.918012i	$-0.370207\pi$
$691$	4.88529e56			0.793103			0.396552	+	0.918012i	$0.370207\pi$
$692$		−	9.62634e56i		−	1.51824i
$693$	2.84351e55	+	1.26995e56i	0.0435703	+	0.194591i
$694$	2.25615e56			0.335876
$695$			2.04048e57i			2.95145i
$696$	3.55355e55	+	3.21343e56i	0.0499434	+	0.451631i
$697$	1.31580e55			0.0179694
$698$		−	4.39501e56i		−	0.583245i
$699$	−1.45189e57	+	1.60556e56i	−1.87236	+	0.207054i
$700$	−1.90775e57			−2.39089
$701$			8.50840e56i			1.03630i	0.855288	+	0.518152i	$0.173380\pi$
$701$			8.50840e56i			1.03630i	−0.855288	+	0.518152i	$0.826620\pi$
$702$	4.57884e56	−	1.57047e56i	0.542017	−	0.185903i
$703$	3.44438e56			0.396282
$704$			9.52146e54i			0.0106476i
$705$	−5.13470e55	−	4.64324e56i	−0.0558127	−	0.504706i
$706$	1.59071e56			0.168073
$707$		−	4.03097e54i		−	0.00414020i
$708$	1.03542e57	−	1.14501e56i	1.03383	−	0.114326i
$709$	5.06445e56			0.491595			0.245797	−	0.969321i	$-0.420950\pi$
$709$	5.06445e56			0.491595			0.245797	+	0.969321i	$0.420950\pi$
$710$		−	1.15734e55i		−	0.0109218i
$711$	4.53747e56	−	1.01597e56i	0.416315	−	0.0932158i
$712$	1.37242e57			1.22430
$713$		−	1.17047e57i		−	1.01524i
$714$	1.94907e55	+	1.76252e56i	0.0164385	+	0.148651i
$715$	−3.37002e56			−0.276383
$716$			6.24463e56i			0.498019i
$717$	5.49638e56	−	6.07814e55i	0.426278	−	0.0471398i
$718$	−8.47658e56			−0.639340
$719$			9.98659e56i			0.732554i	0.930506	+	0.366277i	$0.119368\pi$
$719$			9.98659e56i			0.732554i	−0.930506	+	0.366277i	$0.880632\pi$
$720$	−2.08270e56	−	9.30161e56i	−0.148585	−	0.663602i
$721$	−2.40539e57			−1.66910
$722$		−	6.26999e56i		−	0.423178i
$723$	−6.95247e55	−	6.28702e56i	−0.0456429	−	0.412742i
$724$	1.55215e57			0.991204
$725$		−	1.75442e57i		−	1.08986i
$726$	7.55377e56	−	8.35329e55i	0.456490	−	0.0504807i
$727$	−1.56708e57			−0.921301			−0.460651	−	0.887581i	$-0.652384\pi$
$727$	−1.56708e57			−0.921301			−0.460651	+	0.887581i	$0.652384\pi$
$728$		−	2.73432e57i		−	1.56395i
$729$	−1.41872e57	+	1.10294e57i	−0.789488	+	0.613766i
$730$	1.58472e56			0.0858016
$731$			1.78589e56i			0.0940822i
$732$	1.40465e55	+	1.27021e56i	0.00720023	+	0.0651107i
$733$	1.72275e57			0.859297			0.429648	−	0.902996i	$-0.358637\pi$
$733$	1.72275e57			0.859297			0.429648	+	0.902996i	$0.358637\pi$
$734$			1.74516e57i			0.847059i
$735$	4.90508e57	−	5.42425e56i	2.31686	−	0.256208i
$736$	−2.15530e57			−0.990721
$737$		−	3.44181e56i		−	0.153970i
$738$	−9.00392e55	+	2.01604e55i	−0.0392016	+	0.00877752i
$739$	−1.83154e57			−0.776116			−0.388058	−	0.921635i	$-0.626854\pi$
$739$	−1.83154e57			−0.776116			−0.388058	+	0.921635i	$0.626854\pi$
$740$			4.23617e57i			1.74718i
$741$	1.03069e56	+	9.32035e56i	0.0413773	+	0.374169i
$742$	−1.59042e57			−0.621488
$743$			2.03419e57i			0.773777i	0.922126	+	0.386889i	$0.126450\pi$
$743$			2.03419e57i			0.773777i	−0.922126	+	0.386889i	$0.873550\pi$
$744$	−2.32617e57	+	2.57238e56i	−0.861354	+	0.0952524i
$745$	2.33739e57			0.842568
$746$			2.49468e57i			0.875464i
$747$	1.67247e56	+	7.46949e56i	0.0571409	+	0.255199i
$748$	6.39322e55			0.0212661
$749$		−	6.14303e57i		−	1.98951i
$750$	−2.80928e56	−	2.54039e57i	−0.0885869	−	0.801079i
$751$	−8.10311e56			−0.248802			−0.124401	−	0.992232i	$-0.539701\pi$
$751$	−8.10311e56			−0.248802			−0.124401	+	0.992232i	$0.539701\pi$
$752$		−	3.85425e56i		−	0.115235i
$753$	−6.35214e56	+	7.02448e55i	−0.184936	+	0.0204510i
$754$	1.10326e57			0.312788
$755$			6.69185e57i			1.84760i
$756$	1.44489e57	+	4.21270e57i	0.388506	+	1.13272i
$757$	3.68855e57			0.965912			0.482956	−	0.875645i	$-0.339563\pi$
$757$	3.68855e57			0.965912			0.482956	+	0.875645i	$0.339563\pi$
$758$		−	7.79314e56i		−	0.198760i
$759$	−5.61699e55	−	5.07936e56i	−0.0139530	−	0.126175i
$760$	−1.82792e57			−0.442268
$761$		−	4.55169e57i		−	1.07270i	−0.843994	−	0.536352i	$-0.819802\pi$
$761$		−	4.55169e57i		−	1.07270i	0.843994	−	0.536352i	$-0.180198\pi$
$762$	−1.27773e56	+	1.41297e55i	−0.0293319	+	0.00324365i
$763$	−5.34914e57			−1.19617
$764$		−	3.84599e57i		−	0.837801i
$765$	1.66348e57	−	3.72465e56i	0.353012	−	0.0790418i
$766$	3.24057e57			0.669955
$767$		−	8.10228e57i		−	1.63192i
$768$	3.01666e56	+	2.72793e57i	0.0591974	+	0.535314i
$769$	−2.45509e57			−0.469398			−0.234699	−	0.972068i	$-0.575410\pi$
$769$	−2.45509e57			−0.469398			−0.234699	+	0.972068i	$0.575410\pi$
$770$			8.65695e56i			0.161269i
$771$	−7.51755e57	+	8.31324e56i	−1.36455	+	0.150898i
$772$	3.19667e57			0.565395
$773$			2.00590e57i			0.345716i	0.984947	+	0.172858i	$0.0553001\pi$
$773$			2.00590e57i			0.345716i	−0.984947	+	0.172858i	$0.944700\pi$
$774$	−2.73631e56	−	1.22208e57i	−0.0459565	−	0.205248i
$775$	1.27000e58			2.07860
$776$			2.11425e57i			0.337227i
$777$	−1.39849e57	−	1.26463e58i	−0.217389	−	1.96582i
$778$	4.29347e57			0.650454
$779$		−	1.78739e56i		−	0.0263919i
$780$	−1.14629e58	+	1.26762e57i	−1.64969	+	0.182430i
$781$	1.25325e55			0.00175800
$782$		−	6.96324e56i		−	0.0952086i
$783$	−3.87411e57	+	1.32876e57i	−0.516341	+	0.177097i
$784$	4.07160e57			0.528986
$785$			3.41969e57i			0.433105i
$786$	−4.77243e56	−	4.31564e57i	−0.0589235	−	0.532837i
$787$	−1.34052e58			−1.61354			−0.806769	−	0.590866i	$-0.798786\pi$
$787$	−1.34052e58			−1.61354			−0.806769	+	0.590866i	$0.798786\pi$
$788$			4.37646e57i			0.513569i
$789$	1.42969e58	−	1.58102e57i	1.63570	−	0.180883i
$790$	3.09308e57			0.345024
$791$			2.26758e58i			2.46622i
$792$	−9.97118e56	+	2.23262e56i	−0.105741	+	0.0236761i
$793$	9.93955e56			0.102779
$794$			5.68905e57i			0.573627i
$795$	1.68048e57	+	1.51964e58i	0.165231	+	1.49416i
$796$	5.10265e57			0.489254
$797$		−	1.28736e58i		−	1.20374i	−0.798594	−	0.601871i	$-0.794422\pi$
$797$		−	1.28736e58i		−	1.20374i	0.798594	−	0.601871i	$-0.205578\pi$
$798$	2.39422e57	−	2.64764e56i	0.218327	−	0.0241435i
$799$	6.89287e56			0.0613006
$800$		−	2.33858e58i		−	2.02840i
$801$	3.79881e57	+	1.69660e58i	0.321364	+	1.43525i
$802$	−3.43253e57			−0.283222
$803$			1.71605e56i			0.0138108i
$804$	−1.29462e57	−	1.17071e58i	−0.101630	−	0.919025i
$805$	−3.37699e58			−2.58590
$806$			7.98637e57i			0.596553i
$807$	8.55136e56	−	9.45647e55i	0.0623110	−	0.00689062i
$808$	3.16496e55			0.00224979
$809$			2.15311e57i			0.149313i	0.997209	+	0.0746563i	$0.0237860\pi$
$809$			2.15311e57i			0.149313i	−0.997209	+	0.0746563i	$0.976214\pi$
$810$	−1.08124e58	+	5.09752e57i	−0.731514	+	0.344872i
$811$	1.42110e58			0.938013			0.469007	−	0.883195i	$-0.344612\pi$
$811$	1.42110e58			0.938013			0.469007	+	0.883195i	$0.344612\pi$
$812$			1.01504e58i			0.653675i
$813$	−1.12613e57	−	1.01835e58i	−0.0707586	−	0.639860i
$814$	1.28079e57			0.0785217
$815$		−	2.42536e58i		−	1.45085i
$816$	1.39792e57	−	1.54588e56i	0.0815977	−	0.00902344i
$817$	2.42598e57			0.138180
$818$		−	1.25385e58i		−	0.696914i
$819$	3.38020e58	−	7.56850e57i	1.83343	−	0.410517i
$820$	2.19828e57			0.116360
$821$			3.12801e58i			1.61586i	0.589275	+	0.807932i	$0.299413\pi$
$821$			3.12801e58i			1.61586i	−0.589275	+	0.807932i	$0.700587\pi$
$822$	−1.03457e57	−	9.35547e57i	−0.0521583	−	0.471660i
$823$	2.91811e58			1.43583			0.717917	−	0.696128i	$-0.245096\pi$
$823$	2.91811e58			1.43583			0.717917	+	0.696128i	$0.245096\pi$
$824$		−	1.88862e58i		−	0.906987i
$825$	5.51130e57	−	6.09464e56i	0.258330	−	0.0285673i
$826$	−2.08132e58			−0.952223
$827$		−	2.06803e58i		−	0.923522i	−0.887004	−	0.461761i	$-0.847218\pi$
$827$		−	2.06803e58i		−	0.923522i	0.887004	−	0.461761i	$-0.152782\pi$
$828$	−3.82116e57	−	1.70658e58i	−0.166567	−	0.743910i
$829$	−3.04454e58			−1.29548			−0.647740	−	0.761862i	$-0.724286\pi$
$829$	−3.04454e58			−1.29548			−0.647740	+	0.761862i	$0.724286\pi$
$830$			5.09177e57i			0.211498i
$831$	3.37667e57	+	3.05347e58i	0.136920	+	1.23815i
$832$	2.53430e57			0.100321
$833$			7.28157e57i			0.281401i
$834$	2.09845e58	−	2.32056e57i	0.791730	−	0.0875531i
$835$	−6.16674e58			−2.27157
$836$		−	8.68462e56i		−	0.0312338i
$837$	−9.61873e57	−	2.80443e58i	−0.337760	−	0.984770i
$838$	−1.86896e57			−0.0640795
$839$			1.95312e57i			0.0653867i	0.999465	+	0.0326934i	$0.0104085\pi$
$839$			1.95312e57i			0.0653867i	−0.999465	+	0.0326934i	$0.989592\pi$
$840$	7.42172e57	+	6.71136e58i	0.242616	+	2.19394i
$841$	2.19925e58			0.702029
$842$			1.78051e57i			0.0555013i
$843$	−2.28179e58	+	2.52330e57i	−0.694583	+	0.0768101i
$844$	1.77118e58			0.526518
$845$			3.00714e58i			0.873011i
$846$	−4.71676e57	+	1.05612e57i	−0.133732	+	0.0299436i
$847$	5.43828e58			1.50589
$848$			1.26142e58i			0.341147i
$849$	−3.58532e57	−	3.24215e58i	−0.0947052	−	0.856406i
$850$	7.55537e57			0.194929
$851$			4.99623e58i			1.25907i
$852$	4.26285e56	−	4.71405e55i	0.0104932	−	0.00116039i
$853$	−5.58145e58			−1.34204			−0.671022	−	0.741438i	$-0.734144\pi$
$853$	−5.58145e58			−1.34204			−0.671022	+	0.741438i	$0.734144\pi$
$854$		−	2.55328e57i		−	0.0599710i
$855$	−5.05961e57	−	2.25969e58i	−0.116090	−	0.518474i
$856$	4.82327e58			1.08110
$857$		−	5.10087e58i		−	1.11694i	−0.829526	−	0.558468i	$-0.811389\pi$
$857$		−	5.10087e58i		−	1.11694i	0.829526	−	0.558468i	$-0.188611\pi$
$858$	3.83260e56	+	3.46576e57i	0.00819874	+	0.0741401i
$859$	−3.63005e58			−0.758663			−0.379332	−	0.925261i	$-0.623846\pi$
$859$	−3.63005e58			−0.758663			−0.379332	+	0.925261i	$0.623846\pi$
$860$			2.98366e58i			0.609228i
$861$	−6.56256e57	+	7.25717e56i	−0.130921	+	0.0144779i
$862$	1.48594e58			0.289639
$863$		−	8.80275e57i		−	0.167650i	−0.996481	−	0.0838248i	$-0.973286\pi$
$863$		−	8.80275e57i		−	0.167650i	0.996481	−	0.0838248i	$-0.0267136\pi$
$864$	−5.16407e58	+	1.77119e58i	−0.960986	+	0.329603i
$865$	1.84891e59			3.36196
$866$			8.46902e57i			0.150479i
$867$	−6.05402e57	−	5.47457e58i	−0.105114	−	0.950534i
$868$	−7.34776e58			−1.24670
$869$			3.34942e57i			0.0555359i
$870$	−2.70794e58	+	2.99456e57i	−0.438787	+	0.0485230i
$871$	−9.16096e58			−1.45070
$872$		−	4.19994e58i		−	0.650000i
$873$	−2.61366e58	+	5.85217e57i	−0.395334	+	0.0885182i
$874$	−9.45895e57			−0.139834
$875$		−	1.82894e59i		−	2.64264i
$876$	6.45484e56	+	5.83702e57i	0.00911598	+	0.0824346i
$877$	9.64955e58			1.33203			0.666017	−	0.745937i	$-0.267998\pi$
$877$	9.64955e58			1.33203			0.666017	+	0.745937i	$0.267998\pi$
$878$		−	1.03483e58i		−	0.139630i
$879$	−2.03537e58	+	2.25080e57i	−0.268451	+	0.0296865i
$880$	6.86615e57			0.0885237
$881$			9.28683e58i			1.17044i	0.810875	+	0.585220i	$0.198992\pi$
$881$			9.28683e58i			1.17044i	−0.810875	+	0.585220i	$0.801008\pi$
$882$	−1.11567e58	−	4.98274e58i	−0.137456	−	0.613898i
$883$	8.51996e58			1.02618			0.513090	−	0.858335i	$-0.328501\pi$
$883$	8.51996e58			1.02618			0.513090	+	0.858335i	$0.328501\pi$
$884$		−	1.70166e58i		−	0.200368i
$885$	2.19919e58	+	1.98870e59i	0.253161	+	2.28930i
$886$	−5.37320e58			−0.604725
$887$		−	6.63791e58i		−	0.730397i	−0.930930	−	0.365199i	$-0.881001\pi$
$887$		−	6.63791e58i		−	0.730397i	0.930930	−	0.365199i	$-0.118999\pi$
$888$	9.92940e58	−	1.09804e58i	1.06823	−	0.118129i
$889$	−9.19893e57			−0.0967614
$890$			1.15653e59i			1.18948i
$891$	−5.51996e57	−	1.17085e58i	−0.0555114	−	0.117746i
$892$	4.02347e58			0.395643
$893$		−	9.36337e57i		−	0.0900332i
$894$	−2.65822e57	−	2.40379e58i	−0.0249943	−	0.226020i
$895$	−1.19939e59			−1.10281
$896$			1.66569e59i			1.49773i
$897$	−1.35196e59	+	1.49506e58i	−1.18882	+	0.131465i
$898$	−8.55968e58			−0.736090
$899$		−	6.75719e58i		−	0.568293i
$900$	1.85171e59	−	4.14610e58i	1.52308	−	0.341028i
$901$	−2.25590e58			−0.181478
$902$		−	6.64640e56i		−	0.00522945i
$903$	−9.84995e57	−	8.90717e58i	−0.0758017	−	0.685464i
$904$	−1.78041e59			−1.34015
$905$			2.98118e59i			2.19491i
$906$	6.88196e58	−	7.61038e57i	0.495619	−	0.0548078i
$907$	7.84093e58			0.552360			0.276180	−	0.961106i	$-0.410931\pi$
$907$	7.84093e58			0.552360			0.276180	+	0.961106i	$0.410931\pi$
$908$		−	1.45383e59i		−	1.00184i
$909$	8.76049e55	+	3.91256e56i	0.000590542	+	0.00263744i
$910$	2.30420e59			1.51947
$911$			2.43595e59i			1.57145i	0.618574	+	0.785726i	$0.287711\pi$
$911$			2.43595e59i			1.57145i	−0.618574	+	0.785726i	$0.712289\pi$
$912$	−2.09994e57	−	1.89895e58i	−0.0132529	−	0.119844i
$913$	−5.51374e57			−0.0340432
$914$		−	1.07502e59i		−	0.649371i
$915$	−2.43965e58	+	2.69787e57i	−0.144180	+	0.0159441i
$916$	−1.77807e59			−1.02811
$917$		−	3.10702e59i		−	1.75775i
$918$	−5.72228e57	−	1.66838e58i	−0.0316749	−	0.0923510i
$919$	2.37132e59			1.28434			0.642171	−	0.766562i	$-0.278034\pi$
$919$	2.37132e59			1.28434			0.642171	+	0.766562i	$0.278034\pi$
$920$		−	2.65148e59i		−	1.40518i
$921$	1.89731e58	+	1.71571e59i	0.0983889	+	0.889717i
$922$	−6.98911e58			−0.354653
$923$		−	3.33575e57i		−	0.0165638i
$924$	−3.18863e58	+	3.52613e57i	−0.154940	+	0.0171340i
$925$	−5.42110e59			−2.57782
$926$			1.79857e59i			0.836967i
$927$	2.33473e59	−	5.22764e58i	1.06327	−	0.238073i
$928$	−1.24427e59			−0.554568
$929$		−	1.03651e59i		−	0.452124i	−0.974113	−	0.226062i	$-0.927415\pi$
$929$		−	1.03651e59i		−	0.452124i	0.974113	−	0.226062i	$-0.0725853\pi$
$930$	−2.16773e58	−	1.96025e59i	−0.0925434	−	0.836857i
$931$	9.89138e58			0.413298
$932$		−	3.60086e59i		−	1.47261i
$933$	4.11694e59	−	4.55269e58i	1.64794	−	0.182237i
$934$	1.50787e59			0.590779
$935$			1.22793e58i			0.0470913i
$936$	5.94249e58	+	2.65400e59i	0.223075	+	0.996285i
$937$	7.01760e58			0.257867			0.128934	−	0.991653i	$-0.458845\pi$
$937$	7.01760e58			0.257867			0.128934	+	0.991653i	$0.458845\pi$
$938$			2.35328e59i			0.846480i
$939$	−3.86647e58	−	3.49640e59i	−0.136145	−	1.23114i
$940$	1.15158e59			0.396951
$941$			3.10700e59i			1.04845i	0.851579	+	0.524227i	$0.175646\pi$
$941$			3.10700e59i			1.04845i	−0.851579	+	0.524227i	$0.824354\pi$
$942$	3.51684e58	−	3.88908e57i	0.116181	−	0.0128478i
$943$	2.59269e58			0.0838528
$944$			1.65077e59i			0.522694i
$945$	−8.09122e59	+	2.77516e59i	−2.50829	+	0.860303i
$946$	9.02097e57			0.0273798
$947$			4.24201e59i			1.26059i	0.776357	+	0.630293i	$0.217065\pi$
$947$			4.24201e59i			1.26059i	−0.776357	+	0.630293i	$0.782935\pi$
$948$	1.25987e58	+	1.13928e59i	0.0366571	+	0.331485i
$949$	4.56756e58			0.130125
$950$		−	1.02633e59i		−	0.286296i
$951$	−5.24586e59	+	5.80110e58i	−1.43287	+	0.158453i
$952$	−9.96299e58			−0.266472
$953$		−	2.02063e59i		−	0.529212i	−0.964357	−	0.264606i	$-0.914758\pi$
$953$		−	2.02063e59i		−	0.529212i	0.964357	−	0.264606i	$-0.0852419\pi$
$954$	1.54370e59	−	3.45645e58i	0.395908	−	0.0886467i
$955$	7.38689e59			1.85521
$956$			1.36317e59i			0.335268i
$957$	−3.24272e57	−	2.93235e58i	−0.00781036	−	0.0706280i
$958$	−1.87801e59			−0.442983
$959$		−	6.73540e59i		−	1.55593i
$960$	−6.22041e58	+	6.87880e57i	−0.140732	+	0.0155628i
$961$	3.78434e58			0.0838538
$962$		−	3.40904e59i		−	0.739828i
$963$	1.33506e59	+	5.96257e59i	0.283776	+	1.26738i
$964$	1.55926e59			0.324621
$965$			6.13976e59i			1.25200i
$966$	3.84052e58	+	3.47293e59i	0.0767092	+	0.693671i
$967$	−5.47274e59			−1.07072			−0.535359	−	0.844625i	$-0.679824\pi$
$967$	−5.47274e59			−1.07072			−0.535359	+	0.844625i	$0.679824\pi$
$968$			4.26993e59i			0.818302i
$969$	3.39604e58	−	3.75549e57i	0.0637525	−	0.00705003i
$970$	−1.78167e59			−0.327637
$971$		−	4.71828e59i		−	0.849962i	−0.905202	−	0.424981i	$-0.860281\pi$
$971$		−	4.71828e59i		−	0.849962i	0.905202	−	0.424981i	$-0.139719\pi$
$972$	−2.31799e59	−	3.77493e59i	−0.409059	−	0.666167i
$973$	1.51076e60			2.61180
$974$		−	4.14659e57i		−	0.00702282i
$975$	−1.62219e59	−	1.46693e60i	−0.269160	−	2.43398i
$976$	−2.02510e58			−0.0329193
$977$		−	7.94184e59i		−	1.26482i	−0.774633	−	0.632412i	$-0.782065\pi$
$977$		−	7.94184e59i		−	1.26482i	0.774633	−	0.632412i	$-0.217935\pi$
$978$	−2.49426e59	+	2.75827e58i	−0.389193	+	0.0430387i
$979$	−1.25238e59			−0.191461
$980$			1.21652e60i			1.82221i
$981$	5.19201e59	−	1.16253e59i	0.762000	−	0.170617i
$982$	3.23494e59			0.465197
$983$		−	7.28083e59i		−	1.02591i	−0.858415	−	0.512957i	$-0.828550\pi$
$983$		−	7.28083e59i		−	1.02591i	0.858415	−	0.512957i	$-0.171450\pi$
$984$	−5.69805e57	−	5.15267e58i	−0.00786727	−	0.0711427i
$985$	−8.40575e59			−1.13724
$986$		−	4.01992e58i		−	0.0532941i
$987$	−3.43784e59	+	3.80171e58i	−0.446624	+	0.0493897i
$988$	−2.31156e59			−0.294284
$989$			3.51899e59i			0.439028i
$990$	−1.88141e58	−	8.40265e58i	−0.0230028	−	0.102734i
$991$	−2.67471e59			−0.320482			−0.160241	−	0.987078i	$-0.551227\pi$
$991$	−2.67471e59			−0.320482			−0.160241	+	0.987078i	$0.551227\pi$
$992$		−	9.00713e59i		−	1.05768i
$993$	−1.77686e58	−	1.60679e59i	−0.0204488	−	0.184916i
$994$	−8.56891e57			−0.00966491
$995$			9.80052e59i			1.08340i
$996$	−1.87546e59	+	2.07397e58i	−0.203199	+	0.0224706i
$997$	−1.31877e60			−1.40044			−0.700220	−	0.713928i	$-0.746915\pi$
$997$	−1.31877e60			−1.40044			−0.700220	+	0.713928i	$0.746915\pi$
$998$			1.04261e59i			0.108521i
$999$	4.10582e59	+	1.19709e60i	0.418881	+	1.22128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.41.b.a.2.8	yes	12
3.2	odd	2	inner	3.41.b.a.2.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.41.b.a.2.5	✓	12	3.2	odd	2	inner
3.41.b.a.2.8	yes	12	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 41 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+489884. i q^{2} +(-3.83248e8 - 3.46566e9i) q^{3} +8.59526e11 q^{4} +1.65087e14i q^{5} +(1.69777e15 - 1.87747e14i) q^{6} +1.22230e17 q^{7} +9.59700e17i q^{8} +(-1.18639e19 + 2.65641e18i) q^{9} +O(q^{10})\)	\(q+489884. i q^{2} +(-3.83248e8 - 3.46566e9i) q^{3} +8.59526e11 q^{4} +1.65087e14i q^{5} +(1.69777e15 - 1.87747e14i) q^{6} +1.22230e17 q^{7} +9.59700e17i q^{8} +(-1.18639e19 + 2.65641e18i) q^{9} -8.08734e19 q^{10} -8.75756e19i q^{11} +(-3.29411e20 - 2.97882e21i) q^{12} -2.33097e22 q^{13} +5.98783e22i q^{14} +(5.72135e23 - 6.32692e22i) q^{15} +4.74917e23 q^{16} +8.49332e23i q^{17} +(-1.30133e24 - 5.81193e24i) q^{18} +1.15374e25 q^{19} +1.41896e26i q^{20} +(-4.68443e25 - 4.23606e26i) q^{21} +4.29018e25 q^{22} +1.67356e27i q^{23} +(3.32599e27 - 3.67803e26i) q^{24} -1.81587e28 q^{25} -1.14191e28i q^{26} +(1.37530e28 + 4.00982e28i) q^{27} +1.05060e29 q^{28} +9.66156e28i q^{29} +(3.09945e28 + 2.80279e29i) q^{30} -6.99390e29 q^{31} +1.28786e30i q^{32} +(-3.03507e29 + 3.35632e28i) q^{33} -4.16074e29 q^{34} +2.01785e31i q^{35} +(-1.01973e31 + 2.28326e30i) q^{36} +2.98539e31 q^{37} +5.65200e30i q^{38} +(8.93341e30 + 8.07836e31i) q^{39} -1.58434e32 q^{40} -1.54921e31i q^{41} +(2.07518e32 - 2.29482e31i) q^{42} +2.10270e32 q^{43} -7.52734e31i q^{44} +(-4.38539e32 - 1.95858e33i) q^{45} -8.19848e32 q^{46} -8.11564e32i q^{47} +(-1.82011e32 - 1.64590e33i) q^{48} +8.57329e33 q^{49} -8.89566e33i q^{50} +(2.94349e33 - 3.25505e32i) q^{51} -2.00353e34 q^{52} +2.65608e34i q^{53} +(-1.96434e34 + 6.73739e33i) q^{54} +1.44576e34 q^{55} +1.17304e35i q^{56} +(-4.42170e33 - 3.99848e34i) q^{57} -4.73304e34 q^{58} +3.47592e35i q^{59} +(4.91764e35 - 5.43815e34i) q^{60} -4.26412e34 q^{61} -3.42620e35i q^{62} +(-1.45012e36 + 3.24692e35i) q^{63} -1.08723e35 q^{64} -3.84813e36i q^{65} +(-1.64420e34 - 1.48683e35i) q^{66} +3.93010e36 q^{67} +7.30023e35i q^{68} +(5.79998e36 - 6.41387e35i) q^{69} -9.88512e36 q^{70} +1.43105e35i q^{71} +(-2.54936e36 - 1.13858e37i) q^{72} -1.95951e36 q^{73} +1.46250e37i q^{74} +(6.95929e36 + 6.29319e37i) q^{75} +9.91672e36 q^{76} -1.07043e37i q^{77} +(-3.95746e37 + 4.37633e36i) q^{78} -3.82460e37 q^{79} +7.84025e37i q^{80} +(1.33696e38 - 6.30309e37i) q^{81} +7.58933e36 q^{82} -6.29598e37i q^{83} +(-4.02639e37 - 3.64100e38i) q^{84} -1.40214e38 q^{85} +1.03008e38i q^{86} +(3.34837e38 - 3.70277e37i) q^{87} +8.40463e37 q^{88} -1.43005e39i q^{89} +(9.59474e38 - 2.14833e38i) q^{90} -2.84914e39 q^{91} +1.43847e39i q^{92} +(2.68040e38 + 2.42385e39i) q^{93} +3.97572e38 q^{94} +1.90468e39i q^{95} +(4.46327e39 - 4.93568e38i) q^{96} +2.20304e39 q^{97} +4.19991e39i q^{98} +(2.32637e38 + 1.03899e39i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) \) 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9	\( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) \) 12 * q - 372082572 * q^3 - 4781373657072 * q^4 + 8471862485327952 * q^6 - 94341749124766584 * q^7 - 23605502262041939220 * q^9 - 129384136354706290080 * q^10 - 4708039830028985428272 * q^12 + 704368845864154901976 * q^13 + 320935800901459838631840 * q^15 + 6054431850962872672227456 * q^16 + 10227710367381761273509920 * q^18 + 37616619688417835612151720 * q^19 - 179163719456723608834234728 * q^21 + 846315150249292772829325920 * q^22 - 18213480358094369517645250944 * q^24 + 8842265325510151276196474700 * q^25 - 70717074113738779393083858252 * q^27 + 469404222007499612173589889696 * q^28 - 207809636542026559976510503200 * q^30 - 914600368399753689553849145016 * q^31 + 157344642221562801276041757600 * q^33 - 14575908480758621487300381842304 * q^34 + 41100171486790863962401658870544 * q^36 + 5673106137824212681873457220696 * q^37 - 9206461430638842876438079090008 * q^39 + 50495897877443363581635475618560 * q^40 - 939238658319640212873301303645920 * q^42 + 1012654832326802922602871229857576 * q^43 + 196109968512215856818385626472000 * q^45 - 3082500781506234684371181468390336 * q^46 + 6532128822166367998693520969705088 * q^48 + 8498166150175390075155260408801892 * q^49 + 27565453699222767413826960590504832 * q^51 - 57328509042562386918101767400001504 * q^52 - 102847607224782098537542351912875792 * q^54 - 9637639495259752880102706884884800 * q^55 - 40307213604482059940636368892395464 * q^57 + 772129436848561910287203884295052320 * q^58 - 114385571579949295944121547557720320 * q^60 - 494443282701607071691140418439862696 * q^61 + 1379291076525018665154441723571240776 * q^63 - 6231783699524672226208093043936541696 * q^64 + 2652084094607847915810184973553481440 * q^66 + 5401062423529881431761320436868275176 * q^67 + 7110274695178254111533494284632123328 * q^69 + 516103243900107216646679160954379200 * q^70 - 27544975046740790141119542770107057920 * q^72 + 30000154498324943042431295514883418136 * q^73 + 43820294796704764666539599709819928500 * q^75 - 215478934792040263381331019050660960352 * q^76 + 234946633516471169601955850003339878560 * q^78 - 128704557118405295534397879672035334840 * q^79 + 473157359902659920298963194247360443532 * q^81 - 639159997421964256448917103585883414720 * q^82 + 1283288903941350744781821238287455403552 * q^84 - 1077142486191382871466217243736209678080 * q^85 + 1076668306862385320797179121273520148960 * q^87 - 2918662713596496795370587920448329114880 * q^88 + 6571793457940570799819318674019816438880 * q^90 - 9859184204686878150356379414618151910256 * q^91 + 11506410044121210986218054652959643683416 * q^93 - 16857264118330945289191940748512432348544 * q^94 + 53068562519213731340201280418423192237056 * q^96 - 41841010071967618660163746722085070705064 * q^97 + 54341076855402233475300783474292013590080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more