LMFDB - Embedded newform 27.16.c.a.10.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,16,Mod(10,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.10"); S:= CuspForms(chi, 16); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 16, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$38.5272463770$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.3
Character	$\chi$	$=$	27.10
Dual form			27.16.c.a.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-137.732 - 238.559i) q^{2} +(-21556.3 + 37336.6i) q^{4} +(-132801. + 230018. i) q^{5} +(1.52495e6 + 2.64129e6i) q^{7} +2.84956e6 q^{8} +7.31638e7 q^{10} +(3.23900e7 + 5.61011e7i) q^{11} +(-1.10951e8 + 1.92173e8i) q^{13} +(4.20069e8 - 7.27580e8i) q^{14} +(3.13880e8 + 5.43656e8i) q^{16} -3.44224e8 q^{17} -5.53098e9 q^{19} +(-5.72539e9 - 9.91667e9i) q^{20} +(8.92228e9 - 1.54538e10i) q^{22} +(2.61909e9 - 4.53640e9i) q^{23} +(-2.00134e10 - 3.46642e10i) q^{25} +6.11262e10 q^{26} -1.31489e11 q^{28} +(1.31524e10 + 2.27807e10i) q^{29} +(6.50356e10 - 1.12645e11i) q^{31} +(1.33150e11 - 2.30623e11i) q^{32} +(4.74107e10 + 8.21178e10i) q^{34} -8.10058e11 q^{35} -4.21643e11 q^{37} +(7.61794e11 + 1.31947e12i) q^{38} +(-3.78425e11 + 6.55451e11i) q^{40} +(-6.25093e11 + 1.08269e12i) q^{41} +(1.13660e12 + 1.96865e12i) q^{43} -2.79283e12 q^{44} -1.44293e12 q^{46} +(7.66415e11 + 1.32747e12i) q^{47} +(-2.27715e12 + 3.94414e12i) q^{49} +(-5.51298e12 + 9.54875e12i) q^{50} +(-4.78339e12 - 8.28507e12i) q^{52} +9.47435e12 q^{53} -1.72057e13 q^{55} +(4.34543e12 + 7.52651e12i) q^{56} +(3.62303e12 - 6.27527e12i) q^{58} +(1.97011e12 - 3.41233e12i) q^{59} +(-1.21384e13 - 2.10243e13i) q^{61} -3.58300e13 q^{62} -5.27857e13 q^{64} +(-2.94688e13 - 5.10415e13i) q^{65} +(1.82570e13 - 3.16221e13i) q^{67} +(7.42020e12 - 1.28522e13i) q^{68} +(1.11571e14 + 1.93247e14i) q^{70} +1.25963e14 q^{71} -1.07101e14 q^{73} +(5.80738e13 + 1.00587e14i) q^{74} +(1.19228e14 - 2.06508e14i) q^{76} +(-9.87860e13 + 1.71102e14i) q^{77} +(5.92284e13 + 1.02587e14i) q^{79} -1.66734e14 q^{80} +3.44382e14 q^{82} +(-5.33810e13 - 9.24586e13i) q^{83} +(4.57133e13 - 7.91777e13i) q^{85} +(3.13093e14 - 5.42293e14i) q^{86} +(9.22973e13 + 1.59864e14i) q^{88} -2.96622e14 q^{89} -6.76779e14 q^{91} +(1.12916e14 + 1.95576e14i) q^{92} +(2.11120e14 - 3.65670e14i) q^{94} +(7.34520e14 - 1.27223e15i) q^{95} +(1.66801e14 + 2.88908e14i) q^{97} +1.25455e15 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 129 q^{2} - 212993 q^{4} + 152655 q^{5} + 803705 q^{7} - 20162658 q^{8} + 65532 q^{10} + 60735990 q^{11} - 41509093 q^{13} - 215313024 q^{14} - 2952822785 q^{16} + 2121112242 q^{17} + 5670809246 q^{19}+ \cdots - 72\!\cdots\!90 q^{98}+O(q^{100}) $ 28 * q + 129 * q^2 - 212993 * q^4 + 152655 * q^5 + 803705 * q^7 - 20162658 * q^8 + 65532 * q^10 + 60735990 * q^11 - 41509093 * q^13 - 215313024 * q^14 - 2952822785 * q^16 + 2121112242 * q^17 + 5670809246 * q^19 + 1434155028 * q^20 + 7841223807 * q^22 + 49433203761 * q^23 - 59779497779 * q^25 - 28088907384 * q^26 - 103195803652 * q^28 + 152663830725 * q^29 - 13955906443 * q^31 + 779638216401 * q^32 - 15287791959 * q^34 - 2803990417206 * q^35 + 531598359836 * q^37 + 3598723579461 * q^38 - 1083028910664 * q^40 + 1656362316264 * q^41 + 2394872112236 * q^43 - 13185661781850 * q^44 + 1511321018232 * q^46 + 7686086213559 * q^47 - 7946464864203 * q^49 + 2177050903941 * q^50 + 1969798905818 * q^52 + 20778802614756 * q^53 - 21700105111626 * q^55 - 13789887516654 * q^56 + 15429496587216 * q^58 - 17132922121350 * q^59 - 17229834579991 * q^61 + 190512185539596 * q^62 + 11322374934466 * q^64 - 92170621979115 * q^65 - 19847122719016 * q^67 - 106742875854159 * q^68 - 85984052928798 * q^70 - 60954771085488 * q^71 + 206937948168362 * q^73 + 169102773629016 * q^74 - 274786877071699 * q^76 + 121510644149499 * q^77 + 137921083996235 * q^79 - 1189869535368192 * q^80 + 747645180639978 * q^82 + 243294491978445 * q^83 + 278537029457886 * q^85 + 1439527045654455 * q^86 + 8025917716587 * q^88 - 3513318445769832 * q^89 - 1924506955785338 * q^91 + 3448278918317022 * q^92 + 1100860396273032 * q^94 + 3375682767029028 * q^95 - 1883742033081100 * q^97 - 7254179697035790 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−137.732	−	238.559i	−0.760870	−	1.31787i	−0.942403	−	0.334480i	$-0.891439\pi$
$2$	−137.732	−	238.559i	−0.760870	−	1.31787i	0.181533	−	0.983385i	$-0.441894\pi$
$3$		0			0
$3$		0			0
$4$	−21556.3	+	37336.6i	−0.657846	+	1.13942i
$5$	−132801.	+	230018.i	−0.760197	+	1.31670i	0.182552	+	0.983196i	$0.441564\pi$
$5$	−132801.	+	230018.i	−0.760197	+	1.31670i	−0.942749	+	0.333504i	$0.891769\pi$
$6$		0			0
$7$	1.52495e6	+	2.64129e6i	0.699873	+	1.21222i	0.968510	+	0.248975i	$0.0800936\pi$
$7$	1.52495e6	+	2.64129e6i	0.699873	+	1.21222i	−0.268636	+	0.963242i	$0.586573\pi$
$8$	2.84956e6			0.480400
$9$		0			0
$10$	7.31638e7			2.31364
$11$	3.23900e7	+	5.61011e7i	0.501147	+	0.868013i	0.999999	+	0.00132545i	$0.000421903\pi$
$11$	3.23900e7	+	5.61011e7i	0.501147	+	0.868013i	−0.498852	+	0.866687i	$0.666245\pi$
$12$		0			0
$13$	−1.10951e8	+	1.92173e8i	−0.490407	+	0.849410i	−0.999939	−	0.0110419i	$-0.996485\pi$
$13$	−1.10951e8	+	1.92173e8i	−0.490407	+	0.849410i	0.509532	+	0.860452i	$0.329819\pi$
$14$	4.20069e8	−	7.27580e8i	1.06503	−	1.84468i
$15$		0			0
$16$	3.13880e8	+	5.43656e8i	0.292324	+	0.506319i
$17$	−3.44224e8			−0.203458			−0.101729	−	0.994812i	$-0.532437\pi$
$17$	−3.44224e8			−0.203458			−0.101729	+	0.994812i	$0.532437\pi$
$18$		0			0
$19$	−5.53098e9			−1.41955			−0.709775	−	0.704429i	$-0.751203\pi$
$19$	−5.53098e9			−1.41955			−0.709775	+	0.704429i	$0.751203\pi$
$20$	−5.72539e9	−	9.91667e9i	−1.00018	−	1.73237i
$21$		0			0
$22$	8.92228e9	−	1.54538e10i	0.762616	−	1.32089i
$23$	2.61909e9	−	4.53640e9i	0.160395	−	0.277813i	−0.774615	−	0.632433i	$-0.782056\pi$
$23$	2.61909e9	−	4.53640e9i	0.160395	−	0.277813i	0.935011	+	0.354620i	$0.115390\pi$
$24$		0			0
$25$	−2.00134e10	−	3.46642e10i	−0.655799	−	1.13588i
$26$	6.11262e10			1.49254
$27$		0			0
$28$	−1.31489e11			−1.84164
$29$	1.31524e10	+	2.27807e10i	0.141586	+	0.245235i	0.928094	−	0.372346i	$-0.121446\pi$
$29$	1.31524e10	+	2.27807e10i	0.141586	+	0.245235i	−0.786508	+	0.617580i	$0.788113\pi$
$30$		0			0
$31$	6.50356e10	−	1.12645e11i	0.424559	−	0.735358i	−0.571820	−	0.820379i	$-0.693762\pi$
$31$	6.50356e10	−	1.12645e11i	0.424559	−	0.735358i	0.996379	+	0.0850209i	$0.0270957\pi$
$32$	1.33150e11	−	2.30623e11i	0.685041	−	1.18653i
$33$		0			0
$34$	4.74107e10	+	8.21178e10i	0.154805	+	0.268130i
$35$	−8.10058e11			−2.12817
$36$		0			0
$37$	−4.21643e11			−0.730184			−0.365092	−	0.930971i	$-0.618962\pi$
$37$	−4.21643e11			−0.730184			−0.365092	+	0.930971i	$0.618962\pi$
$38$	7.61794e11	+	1.31947e12i	1.08009	+	1.87077i
$39$		0			0
$40$	−3.78425e11	+	6.55451e11i	−0.365199	+	0.632543i
$41$	−6.25093e11	+	1.08269e12i	−0.501263	+	0.868214i	0.498735	+	0.866754i	$0.333798\pi$
$41$	−6.25093e11	+	1.08269e12i	−0.501263	+	0.868214i	−0.999999	+	0.00145952i	$0.999535\pi$
$42$		0			0
$43$	1.13660e12	+	1.96865e12i	0.637668	+	1.10447i	0.985943	+	0.167081i	$0.0534343\pi$
$43$	1.13660e12	+	1.96865e12i	0.637668	+	1.10447i	−0.348275	+	0.937392i	$0.613232\pi$
$44$	−2.79283e12			−1.31871
$45$		0			0
$46$	−1.44293e12			−0.488160
$47$	7.66415e11	+	1.32747e12i	0.220663	+	0.382200i	0.955010	−	0.296575i	$-0.0958445\pi$
$47$	7.66415e11	+	1.32747e12i	0.220663	+	0.382200i	−0.734346	+	0.678775i	$0.762511\pi$
$48$		0			0
$49$	−2.27715e12	+	3.94414e12i	−0.479646	+	0.830771i
$50$	−5.51298e12	+	9.54875e12i	−0.997955	+	1.72851i
$51$		0			0
$52$	−4.78339e12	−	8.28507e12i	−0.645224	−	1.11756i
$53$	9.47435e12			1.10785			0.553925	−	0.832567i	$-0.313130\pi$
$53$	9.47435e12			1.10785			0.553925	+	0.832567i	$0.313130\pi$
$54$		0			0
$55$	−1.72057e13			−1.52388
$56$	4.34543e12	+	7.52651e12i	0.336220	+	0.582349i
$57$		0			0
$58$	3.62303e12	−	6.27527e12i	0.215458	−	0.373184i
$59$	1.97011e12	−	3.41233e12i	0.103062	−	0.178509i	−0.809883	−	0.586592i	$-0.800469\pi$
$59$	1.97011e12	−	3.41233e12i	0.103062	−	0.178509i	0.912945	+	0.408083i	$0.133803\pi$
$60$		0			0
$61$	−1.21384e13	−	2.10243e13i	−0.494525	−	0.856542i	0.505455	−	0.862853i	$-0.331325\pi$
$61$	−1.21384e13	−	2.10243e13i	−0.494525	−	0.856542i	−0.999980	+	0.00631073i	$0.997991\pi$
$62$	−3.58300e13			−1.29214
$63$		0			0
$64$	−5.27857e13			−1.50026
$65$	−2.94688e13	−	5.10415e13i	−0.745612	−	1.29144i
$66$		0			0
$67$	1.82570e13	−	3.16221e13i	0.368018	−	0.637426i	−0.621238	−	0.783622i	$-0.713370\pi$
$67$	1.82570e13	−	3.16221e13i	0.368018	−	0.637426i	0.989256	+	0.146197i	$0.0467032\pi$
$68$	7.42020e12	−	1.28522e13i	0.133844	−	0.231824i
$69$		0			0
$70$	1.11571e14	+	1.93247e14i	1.61926	+	2.80464i
$71$	1.25963e14			1.64363			0.821817	−	0.569751i	$-0.192960\pi$
$71$	1.25963e14			1.64363			0.821817	+	0.569751i	$0.192960\pi$
$72$		0			0
$73$	−1.07101e14			−1.13468			−0.567338	−	0.823485i	$-0.692027\pi$
$73$	−1.07101e14			−1.13468			−0.567338	+	0.823485i	$0.692027\pi$
$74$	5.80738e13	+	1.00587e14i	0.555575	+	0.962284i
$75$		0			0
$76$	1.19228e14	−	2.06508e14i	0.933844	−	1.61747i
$77$	−9.87860e13	+	1.71102e14i	−0.701480	+	1.21500i
$78$		0			0
$79$	5.92284e13	+	1.02587e14i	0.346998	+	0.601018i	0.985715	−	0.168424i	$-0.0538679\pi$
$79$	5.92284e13	+	1.02587e14i	0.346998	+	0.601018i	−0.638717	+	0.769442i	$0.720535\pi$
$80$	−1.66734e14			−0.888894
$81$		0			0
$82$	3.44382e14			1.52558
$83$	−5.33810e13	−	9.24586e13i	−0.215924	−	0.373991i	0.737634	−	0.675201i	$-0.235943\pi$
$83$	−5.33810e13	−	9.24586e13i	−0.215924	−	0.373991i	−0.953558	+	0.301209i	$0.902610\pi$
$84$		0			0
$85$	4.57133e13	−	7.91777e13i	0.154668	−	0.267893i
$86$	3.13093e14	−	5.42293e14i	0.970365	−	1.68072i
$87$		0			0
$88$	9.22973e13	+	1.59864e14i	0.240751	+	0.416994i
$89$	−2.96622e14			−0.710850			−0.355425	−	0.934705i	$-0.615664\pi$
$89$	−2.96622e14			−0.710850			−0.355425	+	0.934705i	$0.615664\pi$
$90$		0			0
$91$	−6.76779e14			−1.37289
$92$	1.12916e14	+	1.95576e14i	0.211031	+	0.365516i
$93$		0			0
$94$	2.11120e14	−	3.65670e14i	0.335792	−	0.581609i
$95$	7.34520e14	−	1.27223e15i	1.07914	−	1.86912i
$96$		0			0
$97$	1.66801e14	+	2.88908e14i	0.209610	+	0.363054i	0.951592	−	0.307365i	$-0.0994474\pi$
$97$	1.66801e14	+	2.88908e14i	0.209610	+	0.363054i	−0.741982	+	0.670420i	$0.766114\pi$
$98$	1.25455e15			1.45979
$99$		0			0
$100$	1.72566e15			1.72566
$101$	−6.51954e14	−	1.12922e15i	−0.605071	−	1.04801i	−0.992040	−	0.125921i	$-0.959811\pi$
$101$	−6.51954e14	−	1.12922e15i	−0.605071	−	1.04801i	0.386969	−	0.922093i	$-0.373522\pi$
$102$		0			0
$103$	4.31467e13	−	7.47322e13i	0.0345675	−	0.0598727i	−0.848224	−	0.529638i	$-0.822328\pi$
$103$	4.31467e13	−	7.47322e13i	0.0345675	−	0.0598727i	0.882792	+	0.469765i	$0.155661\pi$
$104$	−3.16162e14	+	5.47609e14i	−0.235592	+	0.408057i
$105$		0			0
$106$	−1.30492e15	−	2.26019e15i	−0.842929	−	1.46000i
$107$	−2.90781e15			−1.75060			−0.875302	−	0.483577i	$-0.839337\pi$
$107$	−2.90781e15			−1.75060			−0.875302	+	0.483577i	$0.839337\pi$
$108$		0			0
$109$	−3.46287e15			−1.81442			−0.907209	−	0.420680i	$-0.861791\pi$
$109$	−3.46287e15			−1.81442			−0.907209	+	0.420680i	$0.861791\pi$
$110$	2.36978e15	+	4.10457e15i	1.15948	+	2.00827i
$111$		0			0
$112$	−9.57301e14	+	1.65809e15i	−0.409179	+	0.708719i
$113$	−9.80119e14	+	1.69762e15i	−0.391914	+	0.678815i	−0.992702	−	0.120594i	$-0.961520\pi$
$113$	−9.80119e14	+	1.69762e15i	−0.391914	+	0.678815i	0.600788	+	0.799408i	$0.294854\pi$
$114$		0			0
$115$	6.95636e14	+	1.20488e15i	0.243864	+	0.422385i
$116$	−1.13407e15			−0.372568
$117$		0			0
$118$	−1.08539e15			−0.313668
$119$	−5.24924e14	−	9.09195e14i	−0.142395	−	0.246635i
$120$		0			0
$121$	−9.59721e12	+	1.66229e13i	−0.00229750	+	0.00397938i
$122$	−3.34370e15	+	5.79146e15i	−0.752538	+	1.30343i
$123$		0			0
$124$	2.80385e15	+	4.85641e15i	0.558589	+	0.967505i
$125$	2.52566e15			0.473751
$126$		0			0
$127$	9.85775e15			1.64153			0.820767	−	0.571263i	$-0.193546\pi$
$127$	9.85775e15			1.64153			0.820767	+	0.571263i	$0.193546\pi$
$128$	2.90723e15	+	5.03547e15i	0.456462	+	0.790615i
$129$		0			0
$130$	−8.11761e15	+	1.40601e16i	−1.13463	+	1.96523i
$131$	9.16339e14	−	1.58715e15i	0.120927	−	0.209451i	−0.799207	−	0.601056i	$-0.794747\pi$
$131$	9.16339e14	−	1.58715e15i	0.120927	−	0.209451i	0.920133	+	0.391605i	$0.128080\pi$
$132$		0			0
$133$	−8.43446e15	−	1.46089e16i	−0.993505	−	1.72080i
$134$	−1.00583e16			−1.12005
$135$		0			0
$136$	−9.80889e14			−0.0977412
$137$	−3.07239e15	−	5.32154e15i	−0.289783	−	0.501918i	0.683975	−	0.729505i	$-0.260250\pi$
$137$	−3.07239e15	−	5.32154e15i	−0.289783	−	0.501918i	−0.973758	+	0.227587i	$0.926916\pi$
$138$		0			0
$139$	5.56924e14	−	9.64621e14i	0.0471178	−	0.0816104i	−0.841505	−	0.540250i	$-0.818330\pi$
$139$	5.56924e14	−	9.64621e14i	0.0471178	−	0.0816104i	0.888622	+	0.458639i	$0.151663\pi$
$140$	1.74618e16	−	3.02448e16i	1.40001	−	2.42488i
$141$		0			0
$142$	−1.73492e16	−	3.00496e16i	−1.25059	−	2.16609i
$143$	−1.43748e16			−0.983065
$144$		0			0
$145$	−6.98663e15			−0.430534
$146$	1.47512e16	+	2.55499e16i	0.863341	+	1.49535i
$147$		0			0
$148$	9.08906e15	−	1.57427e16i	0.480348	−	0.831988i
$149$	1.39409e16	−	2.41463e16i	0.700476	−	1.21326i	−0.267824	−	0.963468i	$-0.586305\pi$
$149$	1.39409e16	−	2.41463e16i	0.700476	−	1.21326i	0.968300	−	0.249791i	$-0.0803621\pi$
$150$		0			0
$151$	1.39260e16	+	2.41205e16i	0.633137	+	1.09663i	0.986907	+	0.161293i	$0.0515665\pi$
$151$	1.39260e16	+	2.41205e16i	0.633137	+	1.09663i	−0.353769	+	0.935333i	$0.615100\pi$
$152$	−1.57609e16			−0.681952
$153$		0			0
$154$	5.44240e16			2.13494
$155$	1.72736e16	+	2.99187e16i	0.645497	+	1.11803i
$156$		0			0
$157$	4.68543e15	−	8.11541e15i	0.159039	−	0.275463i	−0.775484	−	0.631368i	$-0.782494\pi$
$157$	4.68543e15	−	8.11541e15i	0.159039	−	0.275463i	0.934522	+	0.355905i	$0.115827\pi$
$158$	1.63153e16	−	2.82589e16i	0.528040	−	0.914592i
$159$		0			0
$160$	3.53649e16	+	6.12538e16i	1.04153	+	1.80399i
$161$	1.59759e16			0.449026
$162$		0			0
$163$	−3.98660e14			−0.0102140			−0.00510700	−	0.999987i	$-0.501626\pi$
$163$	−3.98660e14			−0.0102140			−0.00510700	+	0.999987i	$0.501626\pi$
$164$	−2.69494e16	−	4.66777e16i	−0.659508	−	1.14230i
$165$		0			0
$166$	−1.47046e16	+	2.54690e16i	−0.328580	+	0.569118i
$167$	−2.16422e16	+	3.74854e16i	−0.462304	+	0.800735i	−0.999075	−	0.0429933i	$-0.986311\pi$
$167$	−2.16422e16	+	3.74854e16i	−0.462304	+	0.800735i	0.536771	+	0.843728i	$0.319644\pi$
$168$		0			0
$169$	9.72638e14	+	1.68466e15i	0.0190021	+	0.0329126i
$170$	−2.51848e16			−0.470729
$171$		0			0
$172$	−9.80037e16			−1.67795
$173$	−2.02476e16	−	3.50699e16i	−0.331916	−	0.574895i	0.650972	−	0.759102i	$-0.274362\pi$
$173$	−2.02476e16	−	3.50699e16i	−0.331916	−	0.574895i	−0.982887	+	0.184207i	$0.941028\pi$
$174$		0			0
$175$	6.10387e16	−	1.05722e17i	0.917952	−	1.58994i
$176$	−2.03331e16	+	3.52180e16i	−0.292994	+	0.507481i
$177$		0			0
$178$	4.08543e16	+	7.07618e16i	0.540864	+	0.936804i
$179$	−3.60083e16			−0.457093			−0.228546	−	0.973533i	$-0.573397\pi$
$179$	−3.60083e16			−0.457093			−0.228546	+	0.973533i	$0.573397\pi$
$180$		0			0
$181$	4.60359e16			0.537660			0.268830	−	0.963188i	$-0.413363\pi$
$181$	4.60359e16			0.537660			0.268830	+	0.963188i	$0.413363\pi$
$182$	9.32142e16	+	1.61452e17i	1.04459	+	1.80929i
$183$		0			0
$184$	7.46327e15	−	1.29268e16i	0.0770540	−	0.133461i
$185$	5.59946e16	−	9.69855e16i	0.555084	−	0.961433i
$186$		0			0
$187$	−1.11494e16	−	1.93113e16i	−0.101962	−	0.176604i
$188$	−6.60843e16			−0.580650
$189$		0			0
$190$	−4.04668e17			−3.28433
$191$	6.19011e16	+	1.07216e17i	0.483001	+	0.836583i	0.999809	−	0.0195185i	$-0.00621333\pi$
$191$	6.19011e16	+	1.07216e17i	0.483001	+	0.836583i	−0.516808	+	0.856101i	$0.672880\pi$
$192$		0			0
$193$	4.95967e16	−	8.59040e16i	0.357909	−	0.619917i	−0.629702	−	0.776837i	$-0.716823\pi$
$193$	4.95967e16	−	8.59040e16i	0.357909	−	0.619917i	0.987611	+	0.156920i	$0.0501564\pi$
$194$	4.59478e16	−	7.95839e16i	0.318971	−	0.552474i
$195$		0			0
$196$	−9.81737e16	−	1.70042e17i	−0.631066	−	1.09304i
$197$	5.95642e16			0.368543			0.184272	−	0.982875i	$-0.441007\pi$
$197$	5.95642e16			0.368543			0.184272	+	0.982875i	$0.441007\pi$
$198$		0			0
$199$	2.40730e17			1.38080			0.690401	−	0.723427i	$-0.257434\pi$
$199$	2.40730e17			1.38080			0.690401	+	0.723427i	$0.257434\pi$
$200$	−5.70294e16	−	9.87779e16i	−0.315046	−	0.545676i
$201$		0			0
$202$	−1.79590e17	+	3.11059e17i	−0.920761	+	1.59480i
$203$	−4.01136e16	+	6.94787e16i	−0.198185	+	0.343267i
$204$		0			0
$205$	−1.66026e17	−	2.87565e17i	−0.762118	−	1.32003i
$206$	−2.37707e16			−0.105206
$207$		0			0
$208$	−1.39301e17			−0.573430
$209$	−1.79148e17	−	3.10294e17i	−0.711403	−	1.23219i
$210$		0			0
$211$	−1.52601e17	+	2.64313e17i	−0.564209	+	0.977238i	0.432914	+	0.901435i	$0.357485\pi$
$211$	−1.52601e17	+	2.64313e17i	−0.564209	+	0.977238i	−0.997123	+	0.0758032i	$0.975848\pi$
$212$	−2.04232e17	+	3.53740e17i	−0.728794	+	1.26231i
$213$		0			0
$214$	4.00499e17	+	6.93685e17i	1.33198	+	2.30706i
$215$	−6.03767e17			−1.93901
$216$		0			0
$217$	3.96703e17			1.18855
$218$	4.76948e17	+	8.26099e17i	1.38054	+	2.39116i
$219$		0			0
$220$	3.70891e17	−	6.42401e17i	1.00248	−	1.73635i
$221$	3.81921e16	−	6.61506e16i	0.0997771	−	0.172819i
$222$		0			0
$223$	−1.53936e17	−	2.66626e17i	−0.375885	−	0.651051i	0.614574	−	0.788859i	$-0.289328\pi$
$223$	−1.53936e17	−	2.66626e17i	−0.375885	−	0.651051i	−0.990459	+	0.137808i	$0.955994\pi$
$224$	8.12187e17			1.91777
$225$		0			0
$226$	5.39976e17			1.19278
$227$	−3.78594e17	−	6.55744e17i	−0.809058	−	1.40133i	−0.913517	−	0.406800i	$-0.866645\pi$
$227$	−3.78594e17	−	6.55744e17i	−0.809058	−	1.40133i	0.104460	−	0.994529i	$-0.466689\pi$
$228$		0			0
$229$	−2.96019e17	+	5.12720e17i	−0.592316	+	1.02592i	0.401603	+	0.915814i	$0.368453\pi$
$229$	−2.96019e17	+	5.12720e17i	−0.592316	+	1.02592i	−0.993920	+	0.110108i	$0.964880\pi$
$230$	1.91623e17	−	3.31900e17i	0.371098	−	0.642760i
$231$		0			0
$232$	3.74787e16	+	6.49151e16i	0.0680182	+	0.117811i
$233$	2.89279e17			0.508332			0.254166	−	0.967161i	$-0.418199\pi$
$233$	2.89279e17			0.508332			0.254166	+	0.967161i	$0.418199\pi$
$234$		0			0
$235$	−4.07122e17			−0.670990
$236$	8.49365e16	+	1.47114e17i	0.135598	+	0.234863i
$237$		0			0
$238$	−1.44598e17	+	2.50451e17i	−0.216688	+	0.375314i
$239$	−3.55235e16	+	6.15285e16i	−0.0515859	+	0.0893495i	−0.890665	−	0.454660i	$-0.849761\pi$
$239$	−3.55235e16	+	6.15285e16i	−0.0515859	+	0.0893495i	0.839079	+	0.544009i	$0.183094\pi$
$240$		0			0
$241$	−2.20699e17	−	3.82263e17i	−0.301074	−	0.521476i	0.675305	−	0.737538i	$-0.264012\pi$
$241$	−2.20699e17	−	3.82263e17i	−0.301074	−	0.521476i	−0.976380	+	0.216063i	$0.930678\pi$
$242$	5.28738e15			0.00699238
$243$		0			0
$244$	1.04664e18			1.30128
$245$	−6.04815e17	−	1.04757e18i	−0.729251	−	1.26310i
$246$		0			0
$247$	6.13669e17	−	1.06291e18i	0.696157	−	1.20578i
$248$	1.85323e17	−	3.20989e17i	0.203958	−	0.353266i
$249$		0			0
$250$	−3.47865e17	−	6.02520e17i	−0.360463	−	0.624340i
$251$	8.74962e17			0.879906			0.439953	−	0.898021i	$-0.354995\pi$
$251$	8.74962e17			0.879906			0.439953	+	0.898021i	$0.354995\pi$
$252$		0			0
$253$	3.39329e17			0.321527
$254$	−1.35773e18	−	2.35166e18i	−1.24899	−	2.16332i
$255$		0			0
$256$	−6.40032e16	+	1.10857e17i	−0.0555139	+	0.0961529i
$257$	4.67476e16	−	8.09692e16i	0.0393787	−	0.0682058i	−0.845664	−	0.533715i	$-0.820795\pi$
$257$	4.67476e16	−	8.09692e16i	0.0393787	−	0.0682058i	0.885043	+	0.465509i	$0.154129\pi$
$258$		0			0
$259$	−6.42984e17	−	1.11368e18i	−0.511036	−	0.885141i
$260$	2.54095e18			1.96199
$261$		0			0
$262$	−5.04838e17			−0.368037
$263$	3.94870e17	+	6.83935e17i	0.279760	+	0.484559i	0.971325	−	0.237756i	$-0.0764117\pi$
$263$	3.94870e17	+	6.83935e17i	0.279760	+	0.484559i	−0.691565	+	0.722314i	$0.743078\pi$
$264$		0			0
$265$	−1.25820e18	+	2.17927e18i	−0.842184	+	1.45870i
$266$	−2.32339e18	+	4.02423e18i	−1.51186	+	2.61861i
$267$		0			0
$268$	7.87107e17	+	1.36331e18i	0.484198	+	0.838656i
$269$	−1.05884e18			−0.633417			−0.316708	−	0.948523i	$-0.602578\pi$
$269$	−1.05884e18			−0.633417			−0.316708	+	0.948523i	$0.602578\pi$
$270$		0			0
$271$	5.31177e17			0.300586			0.150293	−	0.988641i	$-0.451978\pi$
$271$	5.31177e17			0.300586			0.150293	+	0.988641i	$0.451978\pi$
$272$	−1.08045e17	−	1.87140e17i	−0.0594755	−	0.103015i
$273$		0			0
$274$	−8.46334e17	+	1.46589e18i	−0.440974	+	0.763789i
$275$	1.29647e18	−	2.24555e18i	0.657304	−	1.13848i
$276$		0			0
$277$	1.50118e16	+	2.60012e16i	0.00720834	+	0.0124852i	0.869607	−	0.493744i	$-0.164372\pi$
$277$	1.50118e16	+	2.60012e16i	0.00720834	+	0.0124852i	−0.862399	+	0.506230i	$0.831039\pi$
$278$	−3.06825e17			−0.143402
$279$		0			0
$280$	−2.30831e18			−1.02237
$281$	1.89478e18	+	3.28185e18i	0.817073	+	1.41521i	0.907830	+	0.419339i	$0.137738\pi$
$281$	1.89478e18	+	3.28185e18i	0.817073	+	1.41521i	−0.0907564	+	0.995873i	$0.528928\pi$
$282$		0			0
$283$	2.16296e18	−	3.74635e18i	0.884402	−	1.53183i	0.0380054	−	0.999278i	$-0.487900\pi$
$283$	2.16296e18	−	3.74635e18i	0.884402	−	1.53183i	0.846397	−	0.532552i	$-0.178767\pi$
$284$	−2.71530e18	+	4.70303e18i	−1.08126	+	1.87279i
$285$		0			0
$286$	1.97987e18	+	3.42924e18i	0.747984	+	1.29555i
$287$	−3.81294e18			−1.40328
$288$		0			0
$289$	−2.74393e18			−0.958605
$290$	9.62283e17	+	1.66672e18i	0.327581	+	0.567386i
$291$		0			0
$292$	2.30870e18	−	3.99879e18i	0.746442	−	1.29288i
$293$	−1.11203e18	+	1.92609e18i	−0.350436	+	0.606972i	−0.986326	−	0.164807i	$-0.947300\pi$
$293$	−1.11203e18	+	1.92609e18i	−0.350436	+	0.606972i	0.635890	+	0.771780i	$0.280633\pi$
$294$		0			0
$295$	5.23265e17	+	9.06321e17i	0.156695	+	0.271404i
$296$	−1.20150e18			−0.350781
$297$		0			0
$298$	−7.68043e18			−2.13188
$299$	5.81182e17	+	1.00664e18i	0.157318	+	0.272483i
$300$		0			0
$301$	−3.46651e18	+	6.00418e18i	−0.892574	+	1.54598i
$302$	3.83610e18	−	6.64433e18i	0.963470	−	1.66878i
$303$		0			0
$304$	−1.73607e18	−	3.00695e18i	−0.414968	−	0.718745i
$305$	6.44797e18			1.50374
$306$		0			0
$307$	5.41818e18			1.20314			0.601569	−	0.798821i	$-0.294543\pi$
$307$	5.41818e18			1.20314			0.601569	+	0.798821i	$0.294543\pi$
$308$	−4.25892e18	−	7.37667e18i	−0.922931	−	1.59856i
$309$		0			0
$310$	4.75825e18	−	8.24154e18i	0.982279	−	1.70136i
$311$	−1.16446e18	+	2.01691e18i	−0.234651	+	0.406428i	−0.959171	−	0.282826i	$-0.908728\pi$
$311$	−1.16446e18	+	2.01691e18i	−0.234651	+	0.406428i	0.724520	+	0.689254i	$0.242062\pi$
$312$		0			0
$313$	3.30724e18	+	5.72831e18i	0.635161	+	1.10013i	0.986481	+	0.163875i	$0.0523994\pi$
$313$	3.30724e18	+	5.72831e18i	0.635161	+	1.10013i	−0.351321	+	0.936255i	$0.614267\pi$
$314$	−2.58134e18			−0.484031
$315$		0			0
$316$	−5.10697e18			−0.913084
$317$	−2.12222e18	−	3.67579e18i	−0.370549	−	0.641809i	0.619101	−	0.785311i	$-0.287497\pi$
$317$	−2.12222e18	−	3.67579e18i	−0.370549	−	0.641809i	−0.989650	+	0.143502i	$0.954164\pi$
$318$		0			0
$319$	−8.52015e17	+	1.47573e18i	−0.141911	+	0.245798i
$320$	7.00999e18	−	1.21417e19i	1.14049	−	1.97539i
$321$		0			0
$322$	−2.20040e18	−	3.81120e18i	−0.341650	−	0.591756i
$323$	1.90390e18			0.288818
$324$		0			0
$325$	8.88204e18			1.28643
$326$	5.49083e16	+	9.51040e16i	0.00777152	+	0.0134607i
$327$		0			0
$328$	−1.78124e18	+	3.08520e18i	−0.240807	+	0.417090i
$329$	−2.33748e18	+	4.04864e18i	−0.308873	+	0.534983i
$330$		0			0
$331$	−3.04691e18	−	5.27739e18i	−0.384724	−	0.666361i	0.607007	−	0.794696i	$-0.292370\pi$
$331$	−3.04691e18	−	5.27739e18i	−0.384724	−	0.666361i	−0.991731	+	0.128335i	$0.959037\pi$
$332$	4.60279e18			0.568179
$333$		0			0
$334$	1.19233e19			1.40701
$335$	4.84910e18	+	8.39889e18i	0.559532	+	0.969138i
$336$		0			0
$337$	4.73297e18	−	8.19775e18i	0.522288	−	0.904629i	−0.477376	−	0.878699i	$-0.658412\pi$
$337$	4.73297e18	−	8.19775e18i	0.522288	−	0.904629i	0.999664	−	0.0259299i	$-0.00825467\pi$
$338$	2.67927e17	−	4.64063e17i	0.0289162	−	0.0500843i
$339$		0			0
$340$	1.97082e18	+	3.41356e18i	0.203495	+	0.352464i
$341$	8.42600e18			0.851067
$342$		0			0
$343$	5.89441e17			0.0569816
$344$	3.23882e18	+	5.60980e18i	0.306336	+	0.530590i
$345$		0			0
$346$	−5.57749e18	+	9.66050e18i	−0.505089	+	0.874841i
$347$	−6.75063e18	+	1.16924e19i	−0.598237	+	1.03618i	0.394845	+	0.918748i	$0.370798\pi$
$347$	−6.75063e18	+	1.16924e19i	−0.598237	+	1.03618i	−0.993081	+	0.117428i	$0.962535\pi$
$348$		0			0
$349$	−5.27022e18	−	9.12828e18i	−0.447340	−	0.774816i	0.550872	−	0.834590i	$-0.314295\pi$
$349$	−5.27022e18	−	9.12828e18i	−0.447340	−	0.774816i	−0.998212	+	0.0597741i	$0.980962\pi$
$350$	−3.36280e19			−2.79377
$351$		0			0
$352$	1.72509e19			1.37323
$353$	−1.15252e18	−	1.99623e18i	−0.0898131	−	0.155561i	0.817619	−	0.575760i	$-0.195294\pi$
$353$	−1.15252e18	−	1.99623e18i	−0.0898131	−	0.155561i	−0.907432	+	0.420199i	$0.861960\pi$
$354$		0			0
$355$	−1.67280e19	+	2.89738e19i	−1.24949	+	2.16417i
$356$	6.39406e18	−	1.10748e19i	0.467629	−	0.809958i
$357$		0			0
$358$	4.95949e18	+	8.59010e18i	0.347788	+	0.602387i
$359$	−4.68983e18			−0.322069			−0.161034	−	0.986949i	$-0.551483\pi$
$359$	−4.68983e18			−0.322069			−0.161034	+	0.986949i	$0.551483\pi$
$360$		0			0
$361$	1.54107e19			1.01512
$362$	−6.34062e18	−	1.09823e19i	−0.409089	−	0.708563i
$363$		0			0
$364$	1.45888e19	−	2.52686e19i	0.903151	−	1.56430i
$365$	1.42231e19	−	2.46352e19i	0.862578	−	1.49403i
$366$		0			0
$367$	3.97573e17	+	6.88617e17i	0.0231431	+	0.0400851i	0.877365	−	0.479824i	$-0.159299\pi$
$367$	3.97573e17	+	6.88617e17i	0.0231431	+	0.0400851i	−0.854222	+	0.519909i	$0.825966\pi$
$368$	3.28832e18			0.187549
$369$		0			0
$370$	−3.08490e19			−1.68939
$371$	1.44479e19	+	2.50245e19i	0.775354	+	1.34295i
$372$		0			0
$373$	−1.76537e19	+	3.05771e19i	−0.909953	+	1.57608i	−0.0958261	+	0.995398i	$0.530549\pi$
$373$	−1.76537e19	+	3.05771e19i	−0.909953	+	1.57608i	−0.814127	+	0.580687i	$0.802784\pi$
$374$	−3.07127e18	+	5.31959e18i	−0.155160	+	0.268745i
$375$		0			0
$376$	2.18395e18	+	3.78271e18i	0.106007	+	0.183609i
$377$	−5.83712e18			−0.277740
$378$		0			0
$379$	−2.08994e19			−0.955741			−0.477871	−	0.878430i	$-0.658591\pi$
$379$	−2.08994e19			−0.955741			−0.477871	+	0.878430i	$0.658591\pi$
$380$	3.16671e19	+	5.48489e19i	1.41981	+	2.45919i
$381$		0			0
$382$	1.70515e19	−	2.95341e19i	0.735002	−	1.27306i
$383$	1.28802e19	−	2.23092e19i	0.544419	−	0.942961i	−0.454224	−	0.890887i	$-0.650084\pi$
$383$	1.28802e19	−	2.23092e19i	0.544419	−	0.942961i	0.998643	−	0.0520738i	$-0.0165831\pi$
$384$		0			0
$385$	−2.62378e19	−	4.54451e19i	−1.06653	−	1.84728i
$386$	−2.73242e19			−1.08929
$387$		0			0
$388$	−1.43825e19			−0.551563
$389$	−2.76150e18	−	4.78306e18i	−0.103878	−	0.179922i	0.809401	−	0.587256i	$-0.199792\pi$
$389$	−2.76150e18	−	4.78306e18i	−0.103878	−	0.179922i	−0.913279	+	0.407334i	$0.866458\pi$
$390$		0			0
$391$	−9.01555e17	+	1.56154e18i	−0.0326337	+	0.0565232i
$392$	−6.48888e18	+	1.12391e19i	−0.230422	+	0.399103i
$393$		0			0
$394$	−8.20391e18	−	1.42096e19i	−0.280414	−	0.485691i
$395$	−3.14623e19			−1.05515
$396$		0			0
$397$	−3.81570e19			−1.23210			−0.616049	−	0.787708i	$-0.711268\pi$
$397$	−3.81570e19			−1.23210			−0.616049	+	0.787708i	$0.711268\pi$
$398$	−3.31562e19	−	5.74283e19i	−1.05061	−	1.81971i
$399$		0			0
$400$	1.25636e19	−	2.17608e19i	0.383411	−	0.664087i
$401$	−6.63101e18	+	1.14853e19i	−0.198608	+	0.343999i	−0.948077	−	0.318040i	$-0.896975\pi$
$401$	−6.63101e18	+	1.14853e19i	−0.198608	+	0.343999i	0.749469	+	0.662039i	$0.230309\pi$
$402$		0			0
$403$	1.44315e19	+	2.49962e19i	0.416414	+	0.721250i
$404$	5.62148e19			1.59217
$405$		0			0
$406$	2.20997e19			0.603172
$407$	−1.36570e19	−	2.36546e19i	−0.365930	−	0.633809i
$408$		0			0
$409$	−7.98802e18	+	1.38357e19i	−0.206307	+	0.357334i	−0.950548	−	0.310576i	$-0.899478\pi$
$409$	−7.98802e18	+	1.38357e19i	−0.206307	+	0.357334i	0.744241	+	0.667911i	$0.232811\pi$
$410$	−4.57342e19	+	7.92140e19i	−1.15975	+	2.00874i
$411$		0			0
$412$	1.86016e18	+	3.22190e18i	0.0454802	+	0.0787740i
$413$	1.20172e19			0.288522
$414$		0			0
$415$	2.83562e19			0.656579
$416$	2.95463e19	+	5.11757e19i	0.671897	+	1.16376i
$417$		0			0
$418$	−4.93490e19	+	8.54750e19i	−1.08257	+	1.87507i
$419$	−3.55495e18	+	6.15736e18i	−0.0766000	+	0.132675i	−0.901781	−	0.432193i	$-0.857740\pi$
$419$	−3.55495e18	+	6.15736e18i	−0.0766000	+	0.132675i	0.825181	+	0.564868i	$0.191073\pi$
$420$		0			0
$421$	2.81716e19	+	4.87946e19i	0.585728	+	1.01451i	0.994784	+	0.102001i	$0.0325245\pi$
$421$	2.81716e19	+	4.87946e19i	0.585728	+	1.01451i	−0.409057	+	0.912509i	$0.634142\pi$
$422$	8.40724e19			1.71716
$423$		0			0
$424$	2.69978e19			0.532211
$425$	6.88909e18	+	1.19323e19i	0.133427	+	0.231103i
$426$		0			0
$427$	3.70209e19	−	6.41220e19i	0.692210	−	1.19894i
$428$	6.26816e19	−	1.08568e20i	1.15163	−	1.99468i
$429$		0			0
$430$	8.31581e19	+	1.44034e20i	1.47534	+	2.55536i
$431$	−7.02079e19			−1.22407			−0.612036	−	0.790830i	$-0.709649\pi$
$431$	−7.02079e19			−1.22407			−0.612036	+	0.790830i	$0.709649\pi$
$432$		0			0
$433$	3.18856e19			0.536952			0.268476	−	0.963286i	$-0.413480\pi$
$433$	3.18856e19			0.536952			0.268476	+	0.963286i	$0.413480\pi$
$434$	−5.46388e19	−	9.46372e19i	−0.904333	−	1.56635i
$435$		0			0
$436$	7.46466e19	−	1.29292e20i	1.19361	−	2.06739i
$437$	−1.44862e19	+	2.50908e19i	−0.227689	+	0.394369i
$438$		0			0
$439$	2.80411e18	+	4.85686e18i	0.0425903	+	0.0737686i	0.886535	−	0.462662i	$-0.153106\pi$
$439$	2.80411e18	+	4.85686e18i	0.0425903	+	0.0737686i	−0.843944	+	0.536431i	$0.819772\pi$
$440$	−4.90287e19			−0.732074
$441$		0			0
$442$	−2.10411e19			−0.303670
$443$	2.39636e19	+	4.15062e19i	0.340036	+	0.588960i	0.984439	−	0.175726i	$-0.0562274\pi$
$443$	2.39636e19	+	4.15062e19i	0.340036	+	0.588960i	−0.644403	+	0.764686i	$0.722894\pi$
$444$		0			0
$445$	3.93916e19	−	6.82283e19i	0.540386	−	0.935975i
$446$	−4.24040e19	+	7.34458e19i	−0.571999	+	0.990731i
$447$		0			0
$448$	−8.04954e19	−	1.39422e20i	−1.04999	−	1.81864i
$449$	−7.81847e18			−0.100294			−0.0501469	−	0.998742i	$-0.515969\pi$
$449$	−7.81847e18			−0.100294			−0.0501469	+	0.998742i	$0.515969\pi$
$450$		0			0
$451$	−8.09871e19			−1.00483
$452$	−4.22555e19	−	7.31886e19i	−0.515638	−	0.893111i
$453$		0			0
$454$	−1.04289e20	+	1.80634e20i	−1.23118	+	2.13246i
$455$	8.98768e19	−	1.55671e20i	1.04367	−	1.80769i
$456$		0			0
$457$	−3.51740e19	−	6.09231e19i	−0.395230	−	0.684559i	0.597900	−	0.801570i	$-0.296002\pi$
$457$	−3.51740e19	−	6.09231e19i	−0.395230	−	0.684559i	−0.993131	+	0.117012i	$0.962668\pi$
$458$	1.63085e20			1.80270
$459$		0			0
$460$	−5.99813e19			−0.641700
$461$	−5.33612e19	−	9.24243e19i	−0.561653	−	0.972812i	−0.997352	−	0.0727199i	$-0.976832\pi$
$461$	−5.33612e19	−	9.24243e19i	−0.561653	−	0.972812i	0.435699	−	0.900092i	$-0.356501\pi$
$462$		0			0
$463$	7.14261e19	−	1.23714e20i	0.727779	−	1.26055i	−0.230041	−	0.973181i	$-0.573886\pi$
$463$	7.14261e19	−	1.23714e20i	0.727779	−	1.26055i	0.957820	−	0.287370i	$-0.0927808\pi$
$464$	−8.25658e18	+	1.43008e19i	−0.0827781	+	0.143376i
$465$		0			0
$466$	−3.98430e19	−	6.90101e19i	−0.386774	−	0.669913i
$467$	1.76373e20			1.68482			0.842412	−	0.538834i	$-0.181135\pi$
$467$	1.76373e20			1.68482			0.842412	+	0.538834i	$0.181135\pi$
$468$		0			0
$469$	1.11364e20			1.03026
$470$	5.60739e19	+	9.71228e19i	0.510536	+	0.884275i
$471$		0			0
$472$	5.61395e18	−	9.72364e18i	0.0495112	−	0.0857559i
$473$	−7.36290e19	+	1.27529e20i	−0.639132	+	1.10701i
$474$		0			0
$475$	1.10694e20	+	1.91727e20i	0.930939	+	1.61243i
$476$	4.52616e19			0.374695
$477$		0			0
$478$	1.95709e19			0.157001
$479$	−7.23554e19	−	1.25323e20i	−0.571419	−	0.989726i	−0.996421	−	0.0845340i	$-0.973060\pi$
$479$	−7.23554e19	−	1.25323e20i	−0.571419	−	0.989726i	0.425002	−	0.905193i	$-0.360273\pi$
$480$		0			0
$481$	4.67818e19	−	8.10284e19i	0.358087	−	0.620225i
$482$	−6.07948e19	+	1.05300e20i	−0.458156	+	0.793550i
$483$		0			0
$484$	−4.13760e17	−	7.16654e17i	−0.00302280	−	0.00523564i
$485$	−8.86054e19			−0.637378
$486$		0			0
$487$	−1.42606e20			−0.994653			−0.497326	−	0.867563i	$-0.665685\pi$
$487$	−1.42606e20			−0.994653			−0.497326	+	0.867563i	$0.665685\pi$
$488$	−3.45892e19	−	5.99102e19i	−0.237570	−	0.411483i
$489$		0			0
$490$	−1.66605e20	+	2.88568e20i	−1.10973	+	1.92211i
$491$	1.39466e19	−	2.41562e19i	0.0914865	−	0.158459i	−0.816650	−	0.577133i	$-0.804171\pi$
$491$	1.39466e19	−	2.41562e19i	0.0914865	−	0.158459i	0.908137	+	0.418674i	$0.137505\pi$
$492$		0			0
$493$	−4.52739e18	−	7.84167e18i	−0.0288069	−	0.0498950i
$494$	−3.38088e20			−2.11874
$495$		0			0
$496$	8.16535e19			0.496435
$497$	1.92087e20	+	3.32704e20i	1.15034	+	1.99244i
$498$		0			0
$499$	−8.04873e19	+	1.39408e20i	−0.467706	+	0.810091i	−0.999319	−	0.0368966i	$-0.988253\pi$
$499$	−8.04873e19	+	1.39408e20i	−0.467706	+	0.810091i	0.531613	+	0.846987i	$0.321586\pi$
$500$	−5.44440e19	+	9.42997e19i	−0.311655	+	0.539803i
$501$		0			0
$502$	−1.20510e20	−	2.08730e20i	−0.669494	−	1.15960i
$503$	−1.11533e20			−0.610441			−0.305220	−	0.952282i	$-0.598730\pi$
$503$	−1.11533e20			−0.610441			−0.305220	+	0.952282i	$0.598730\pi$
$504$		0			0
$505$	3.46320e20			1.83989
$506$	−4.67366e19	−	8.09501e19i	−0.244640	−	0.423729i
$507$		0			0
$508$	−2.12497e20	+	3.68055e20i	−1.07988	+	1.87040i
$509$	−6.32640e19	+	1.09576e20i	−0.316791	+	0.548699i	−0.979817	−	0.199898i	$-0.935939\pi$
$509$	−6.32640e19	+	1.09576e20i	−0.316791	+	0.548699i	0.663025	+	0.748597i	$0.269272\pi$
$510$		0			0
$511$	−1.63323e20	−	2.82884e20i	−0.794130	−	1.37547i
$512$	2.25789e20			1.08188
$513$		0			0
$514$	−2.57546e19			−0.119848
$515$	1.14598e19	+	1.98490e19i	0.0525562	+	0.0910301i
$516$		0			0
$517$	−4.96483e19	+	8.59934e19i	−0.221170	+	0.383077i
$518$	−1.77119e20	+	3.06779e20i	−0.777664	+	1.34695i
$519$		0			0
$520$	−8.39733e19	−	1.45446e20i	−0.358192	−	0.620407i
$521$	−7.06719e19			−0.297142			−0.148571	−	0.988902i	$-0.547467\pi$
$521$	−7.06719e19			−0.297142			−0.148571	+	0.988902i	$0.547467\pi$
$522$		0			0
$523$	−4.36571e20			−1.78358			−0.891789	−	0.452451i	$-0.850550\pi$
$523$	−4.36571e20			−1.78358			−0.891789	+	0.452451i	$0.850550\pi$
$524$	3.95058e19	+	6.84260e19i	0.159102	+	0.275573i
$525$		0			0
$526$	1.08773e20	−	1.88400e20i	0.425722	−	0.737372i
$527$	−2.23868e19	+	3.87751e19i	−0.0863799	+	0.149614i
$528$		0			0
$529$	1.19598e20	+	2.07150e20i	0.448547	+	0.776906i
$530$	6.93180e20			2.56317
$531$		0			0
$532$	7.27263e20			2.61429
$533$	−1.38710e20	−	2.40252e20i	−0.491646	−	0.851556i
$534$		0			0
$535$	3.86160e20	−	6.68849e20i	1.33080	−	2.30502i
$536$	5.20245e19	−	9.01091e19i	0.176796	−	0.306220i
$537$		0			0
$538$	1.45837e20	+	2.52597e20i	0.481948	+	0.834758i
$539$	−2.95027e20			−0.961493
$540$		0			0
$541$	−1.54088e20			−0.488416			−0.244208	−	0.969723i	$-0.578528\pi$
$541$	−1.54088e20			−0.488416			−0.244208	+	0.969723i	$0.578528\pi$
$542$	−7.31601e19	−	1.26717e20i	−0.228707	−	0.396132i
$543$		0			0
$544$	−4.58334e19	+	7.93859e19i	−0.139377	+	0.241408i
$545$	4.59872e20	−	7.96522e20i	1.37932	−	2.38904i
$546$		0			0
$547$	1.02165e20	+	1.76955e20i	0.298124	+	0.516366i	0.975707	−	0.219081i	$-0.0703057\pi$
$547$	1.02165e20	+	1.76955e20i	0.298124	+	0.516366i	−0.677583	+	0.735447i	$0.736972\pi$
$548$	2.64917e20			0.762529
$549$		0			0
$550$	−7.14261e20			−2.00049
$551$	−7.27460e19	−	1.26000e20i	−0.200989	−	0.348123i
$552$		0			0
$553$	−1.80640e20	+	3.12878e20i	−0.485709	+	0.841272i
$554$	4.13522e18	−	7.16241e18i	0.0109692	−	0.0189992i
$555$		0			0
$556$	2.40104e19	+	4.15873e19i	0.0619925	+	0.107374i
$557$	1.00161e20			0.255145			0.127572	−	0.991829i	$-0.459282\pi$
$557$	1.00161e20			0.255145			0.127572	+	0.991829i	$0.459282\pi$
$558$		0			0
$559$	−5.04429e20			−1.25087
$560$	−2.54261e20	−	4.40393e20i	−0.622113	−	1.07753i
$561$		0			0
$562$	5.21944e20	−	9.04033e20i	1.24337	−	2.15358i
$563$	1.78978e20	−	3.09998e20i	0.420713	−	0.728696i	−0.575296	−	0.817945i	$-0.695113\pi$
$563$	1.78978e20	−	3.09998e20i	0.420713	−	0.728696i	0.996009	+	0.0892488i	$0.0284466\pi$
$564$		0			0
$565$	−2.60322e20	−	4.50890e20i	−0.595864	−	1.03207i
$566$	−1.19164e21			−2.69166
$567$		0			0
$568$	3.58940e20			0.789603
$569$	3.49356e20	+	6.05102e20i	0.758448	+	1.31367i	0.943642	+	0.330969i	$0.107376\pi$
$569$	3.49356e20	+	6.05102e20i	0.758448	+	1.31367i	−0.185193	+	0.982702i	$0.559291\pi$
$570$		0			0
$571$	1.39464e19	−	2.41559e19i	0.0294912	−	0.0510802i	−0.850903	−	0.525323i	$-0.823945\pi$
$571$	1.39464e19	−	2.41559e19i	0.0294912	−	0.0510802i	0.880394	+	0.474242i	$0.157278\pi$
$572$	3.09868e20	−	5.36707e20i	0.646705	−	1.12013i
$573$		0			0
$574$	5.25164e20	+	9.09611e20i	1.06772	+	1.84934i
$575$	−2.09668e20			−0.420749
$576$		0			0
$577$	5.54993e20			1.08510			0.542549	−	0.840024i	$-0.317459\pi$
$577$	5.54993e20			1.08510			0.542549	+	0.840024i	$0.317459\pi$
$578$	3.77928e20	+	6.54590e20i	0.729374	+	1.26331i
$579$		0			0
$580$	1.50606e20	−	2.60857e20i	0.283225	−	0.490560i
$581$	1.62806e20	−	2.81989e20i	0.302239	−	0.523493i
$582$		0			0
$583$	3.06874e20	+	5.31522e20i	0.555196	+	0.961627i
$584$	−3.05191e20			−0.545099
$585$		0			0
$586$	6.12647e20			1.06654
$587$	2.93187e20	+	5.07815e20i	0.503917	+	0.872811i	0.999990	+	0.00452937i	$0.00144175\pi$
$587$	2.93187e20	+	5.07815e20i	0.503917	+	0.872811i	−0.496072	+	0.868281i	$0.665225\pi$
$588$		0			0
$589$	−3.59711e20	+	6.23037e20i	−0.602683	+	1.04388i
$590$	1.44141e20	−	2.49659e20i	0.238450	−	0.413007i
$591$		0			0
$592$	−1.32345e20	−	2.29229e20i	−0.213450	−	0.369706i
$593$	−8.57002e20			−1.36481			−0.682404	−	0.730975i	$-0.739066\pi$
$593$	−8.57002e20			−1.36481			−0.682404	+	0.730975i	$0.739066\pi$
$594$		0			0
$595$	2.78841e20			0.432992
$596$	6.01027e20	+	1.04101e21i	0.921610	+	1.59628i
$597$		0			0
$598$	1.60095e20	−	2.77293e20i	0.239397	−	0.414648i
$599$	−6.65191e20	+	1.15214e21i	−0.982302	+	1.70140i	−0.328940	+	0.944351i	$0.606691\pi$
$599$	−6.65191e20	+	1.15214e21i	−0.982302	+	1.70140i	−0.653362	+	0.757045i	$0.726642\pi$
$600$		0			0
$601$	5.36679e20	+	9.29555e20i	0.772958	+	1.33880i	0.935935	+	0.352172i	$0.114557\pi$
$601$	5.36679e20	+	9.29555e20i	0.772958	+	1.33880i	−0.162977	+	0.986630i	$0.552110\pi$
$602$	1.90980e21			2.71653
$603$		0			0
$604$	−1.20077e21			−1.66603
$605$	−2.54904e18	−	4.41506e18i	−0.00349310	−	0.00605022i
$606$		0			0
$607$	−2.45835e20	+	4.25799e20i	−0.328647	+	0.569233i	−0.982244	−	0.187610i	$-0.939926\pi$
$607$	−2.45835e20	+	4.25799e20i	−0.328647	+	0.569233i	0.653597	+	0.756843i	$0.273259\pi$
$608$	−7.36451e20	+	1.27557e21i	−0.972449	+	1.68433i
$609$		0			0
$610$	−8.88093e20	−	1.53822e21i	−1.14415	−	1.98173i
$611$	−3.40138e20			−0.432859
$612$		0			0
$613$	−1.38146e21			−1.71548			−0.857739	−	0.514086i	$-0.828131\pi$
$613$	−1.38146e21			−1.71548			−0.857739	+	0.514086i	$0.828131\pi$
$614$	−7.46257e20	−	1.29255e21i	−0.915431	−	1.58557i
$615$		0			0
$616$	−2.81497e20	+	4.87567e20i	−0.336991	+	0.583686i
$617$	6.74377e20	−	1.16805e21i	0.797561	−	1.38142i	−0.123639	−	0.992327i	$-0.539457\pi$
$617$	6.74377e20	−	1.16805e21i	0.797561	−	1.38142i	0.921200	−	0.389089i	$-0.127210\pi$
$618$		0			0
$619$	−4.41242e20	−	7.64253e20i	−0.509327	−	0.882180i	−0.999942	−	0.0108037i	$-0.996561\pi$
$619$	−4.41242e20	−	7.64253e20i	−0.509327	−	0.882180i	0.490615	−	0.871377i	$-0.336772\pi$
$620$	−1.48942e21			−1.69855
$621$		0			0
$622$	6.41537e20			0.714157
$623$	−4.52332e20	−	7.83462e20i	−0.497505	−	0.861703i
$624$		0			0
$625$	2.75350e20	−	4.76920e20i	0.295655	−	0.512089i
$626$	9.11027e20	−	1.57795e21i	0.966549	−	1.67411i
$627$		0			0
$628$	2.02001e20	+	3.49876e20i	0.209246	+	0.362424i
$629$	1.45140e20			0.148562
$630$		0			0
$631$	6.96183e20			0.695830			0.347915	−	0.937526i	$-0.386890\pi$
$631$	6.96183e20			0.695830			0.347915	+	0.937526i	$0.386890\pi$
$632$	1.68775e20	+	2.92327e20i	0.166698	+	0.288729i
$633$		0			0
$634$	−5.84595e20	+	1.01255e21i	−0.563879	+	0.976667i
$635$	−1.30912e21	+	2.26746e21i	−1.24789	+	2.16141i
$636$		0			0
$637$	−5.05304e20	−	8.75213e20i	−0.470443	−	0.814832i
$638$	4.69399e20			0.431904
$639$		0			0
$640$	−1.54433e21			−1.38800
$641$	8.83800e20	+	1.53079e21i	0.785089	+	1.35981i	0.928946	+	0.370215i	$0.120716\pi$
$641$	8.83800e20	+	1.53079e21i	0.785089	+	1.35981i	−0.143857	+	0.989598i	$0.545951\pi$
$642$		0			0
$643$	4.30187e20	−	7.45106e20i	0.373315	−	0.646600i	−0.616758	−	0.787152i	$-0.711554\pi$
$643$	4.30187e20	−	7.45106e20i	0.373315	−	0.646600i	0.990073	+	0.140552i	$0.0448878\pi$
$644$	−3.44381e20	+	5.96486e20i	−0.295390	+	0.511630i
$645$		0			0
$646$	−2.62228e20	−	4.54192e20i	−0.219753	−	0.380624i
$647$	4.99076e20			0.413414			0.206707	−	0.978403i	$-0.433725\pi$
$647$	4.99076e20			0.413414			0.206707	+	0.978403i	$0.433725\pi$
$648$		0			0
$649$	2.55247e20			0.206598
$650$	−1.22334e21	−	2.11889e21i	−0.978808	−	1.69535i
$651$		0			0
$652$	8.59363e18	−	1.48846e19i	0.00671924	−	0.0116381i
$653$	1.03787e21	−	1.79764e21i	0.802218	−	1.38948i	−0.115935	−	0.993257i	$-0.536986\pi$
$653$	1.03787e21	−	1.79764e21i	0.802218	−	1.38948i	0.918153	−	0.396226i	$-0.129680\pi$
$654$		0			0
$655$	2.43381e20	+	4.21549e20i	0.183856	+	0.318448i
$656$	−7.84818e20			−0.586125
$657$		0			0
$658$	1.28779e21			0.940048
$659$	8.40166e20	+	1.45521e21i	0.606351	+	1.05023i	0.991836	+	0.127517i	$0.0407008\pi$
$659$	8.40166e20	+	1.45521e21i	0.606351	+	1.05023i	−0.385485	+	0.922714i	$0.625966\pi$
$660$		0			0
$661$	−1.26525e21	+	2.19147e21i	−0.892616	+	1.54606i	−0.0558878	+	0.998437i	$0.517799\pi$
$661$	−1.26525e21	+	2.19147e21i	−0.892616	+	1.54606i	−0.836728	+	0.547619i	$0.815534\pi$
$662$	−8.39314e20	+	1.45373e21i	−0.585449	+	1.01403i
$663$		0			0
$664$	−1.52113e20	−	2.63467e20i	−0.103730	−	0.179666i
$665$	4.48042e21			3.02104
$666$		0			0
$667$	1.37790e20			0.0908392
$668$	−9.33051e20	−	1.61609e21i	−0.608250	−	1.05352i
$669$		0			0
$670$	1.33575e21	−	2.31359e21i	0.851462	−	1.47478i
$671$	7.86326e20	−	1.36196e21i	0.495660	−	0.858508i
$672$		0			0
$673$	9.57488e20	+	1.65842e21i	0.590229	+	1.02231i	0.994201	+	0.107535i	$0.0342958\pi$
$673$	9.57488e20	+	1.65842e21i	0.590229	+	1.02231i	−0.403972	+	0.914771i	$0.632371\pi$
$674$	−2.60753e21			−1.58957
$675$		0			0
$676$	−8.38659e19			−0.0500017
$677$	1.14475e21	+	1.98277e21i	0.674988	+	1.16911i	0.976472	+	0.215642i	$0.0691844\pi$
$677$	1.14475e21	+	1.98277e21i	0.674988	+	1.16911i	−0.301485	+	0.953471i	$0.597482\pi$
$678$		0			0
$679$	−5.08726e20	+	8.81139e20i	−0.293400	+	0.508184i
$680$	1.30263e20	−	2.25622e20i	0.0743026	−	0.128696i
$681$		0			0
$682$	−1.16053e21	−	2.01010e21i	−0.647551	−	1.12159i
$683$	−2.69703e21			−1.48844			−0.744220	−	0.667935i	$-0.767179\pi$
$683$	−2.69703e21			−1.48844			−0.744220	+	0.667935i	$0.767179\pi$
$684$		0			0
$685$	1.63207e21			0.881167
$686$	−8.11850e19	−	1.40617e20i	−0.0433556	−	0.0750941i
$687$		0			0
$688$	−7.13513e20	+	1.23584e21i	−0.372811	+	0.645728i
$689$	−1.05119e21	+	1.82072e21i	−0.543297	+	0.941018i
$690$		0			0
$691$	−7.18974e20	−	1.24530e21i	−0.363603	−	0.629779i	0.624948	−	0.780667i	$-0.285120\pi$
$691$	−7.18974e20	−	1.24530e21i	−0.363603	−	0.629779i	−0.988551	+	0.150887i	$0.951787\pi$
$692$	1.74585e21			0.873398
$693$		0			0
$694$	3.71911e21			1.82072
$695$	1.47920e20	+	2.56205e20i	0.0716376	+	0.124080i
$696$		0			0
$697$	2.15172e20	−	3.72689e20i	0.101986	−	0.176645i
$698$	−1.45176e21	+	2.51452e21i	−0.680735	+	1.17907i
$699$		0			0
$700$	2.63154e21	+	4.55796e21i	1.20774	+	2.09187i
$701$	−3.57059e21			−1.62127			−0.810634	−	0.585553i	$-0.800877\pi$
$701$	−3.57059e21			−1.62127			−0.810634	+	0.585553i	$0.800877\pi$
$702$		0			0
$703$	2.33210e21			1.03653
$704$	−1.70973e21	−	2.96134e21i	−0.751851	−	1.30224i
$705$		0			0
$706$	−3.17479e20	+	5.49890e20i	−0.136672	+	0.236723i
$707$	1.98839e21	−	3.44399e21i	0.846946	−	1.46695i
$708$		0			0
$709$	−3.06577e20	−	5.31006e20i	−0.127848	−	0.221438i	0.794995	−	0.606616i	$-0.207473\pi$
$709$	−3.06577e20	−	5.31006e20i	−0.127848	−	0.221438i	−0.922842	+	0.385178i	$0.874140\pi$
$710$	9.21594e21			3.80279
$711$		0			0
$712$	−8.45242e20			−0.341492
$713$	−3.40668e20	−	5.90055e20i	−0.136195	−	0.235896i
$714$		0			0
$715$	1.90899e21	−	3.30647e21i	0.747323	−	1.29440i
$716$	7.76204e20	−	1.34443e21i	0.300697	−	0.520822i
$717$		0			0
$718$	6.45940e20	+	1.11880e21i	0.245052	+	0.424443i
$719$	−1.13082e21			−0.424549			−0.212275	−	0.977210i	$-0.568087\pi$
$719$	−1.13082e21			−0.424549			−0.212275	+	0.977210i	$0.568087\pi$
$720$		0			0
$721$	2.63186e20			0.0967716
$722$	−2.12254e21	−	3.67635e21i	−0.772374	−	1.33779i
$723$		0			0
$724$	−9.92363e20	+	1.71882e21i	−0.353697	+	0.612621i
$725$	5.26450e20	−	9.11838e20i	0.185704	−	0.321649i
$726$		0			0
$727$	−2.57478e21	−	4.45964e21i	−0.889675	−	1.54096i	−0.840260	−	0.542183i	$-0.817598\pi$
$727$	−2.57478e21	−	4.45964e21i	−0.889675	−	1.54096i	−0.0494144	−	0.998778i	$-0.515735\pi$
$728$	−1.92852e21			−0.659538
$729$		0			0
$730$	−7.83592e21			−2.62524
$731$	−3.91246e20	−	6.77657e20i	−0.129739	−	0.224714i
$732$		0			0
$733$	−1.43966e20	+	2.49357e20i	−0.0467715	+	0.0810106i	−0.888463	−	0.458947i	$-0.848227\pi$
$733$	−1.43966e20	+	2.49357e20i	−0.0467715	+	0.0810106i	0.841692	+	0.539958i	$0.181560\pi$
$734$	1.09517e20	−	1.89689e20i	0.0352178	−	0.0609990i
$735$		0			0
$736$	−6.97464e20	−	1.20804e21i	−0.219755	−	0.380626i
$737$	2.36538e21			0.737725
$738$		0			0
$739$	−4.06686e21			−1.24287			−0.621435	−	0.783466i	$-0.713450\pi$
$739$	−4.06686e21			−1.24287			−0.621435	+	0.783466i	$0.713450\pi$
$740$	2.41407e21	+	4.18130e21i	0.730319	+	1.26495i
$741$		0			0
$742$	3.97988e21	−	6.89335e21i	1.17989	−	2.04362i
$743$	−2.32553e21	+	4.02794e21i	−0.682506	+	1.18213i	0.291708	+	0.956507i	$0.405776\pi$
$743$	−2.32553e21	+	4.02794e21i	−0.682506	+	1.18213i	−0.974214	+	0.225627i	$0.927557\pi$
$744$		0			0
$745$	3.70272e21	+	6.41330e21i	1.06500	+	1.84463i
$746$	9.72592e21			2.76942
$747$		0			0
$748$	9.61360e20			0.268302
$749$	−4.43426e21	−	7.68036e21i	−1.22520	−	2.12211i
$750$		0			0
$751$	−3.28330e21	+	5.68684e21i	−0.889224	+	1.54018i	−0.0484293	+	0.998827i	$0.515422\pi$
$751$	−3.28330e21	+	5.68684e21i	−0.889224	+	1.54018i	−0.840795	+	0.541354i	$0.817912\pi$
$752$	−4.81125e20	+	8.33332e20i	−0.129010	+	0.223452i
$753$		0			0
$754$	8.03958e20	+	1.39250e21i	0.211324	+	0.366024i
$755$	−7.39752e21			−1.92524
$756$		0			0
$757$	2.37137e21			0.605034			0.302517	−	0.953144i	$-0.402173\pi$
$757$	2.37137e21			0.605034			0.302517	+	0.953144i	$0.402173\pi$
$758$	2.87852e21	+	4.98575e21i	0.727195	+	1.25954i
$759$		0			0
$760$	2.09306e21	−	3.62529e21i	0.518418	−	0.897926i
$761$	−1.85117e21	+	3.20632e21i	−0.454005	+	0.786360i	−0.998630	−	0.0523193i	$-0.983339\pi$
$761$	−1.85117e21	+	3.20632e21i	−0.454005	+	0.786360i	0.544625	+	0.838680i	$0.316672\pi$
$762$		0			0
$763$	−5.28069e21	−	9.14643e21i	−1.26986	−	2.19947i
$764$	−5.33743e21			−1.27096
$765$		0			0
$766$	−7.09609e21			−1.65693
$767$	4.37172e20	+	7.57203e20i	0.101085	+	0.175084i
$768$		0			0
$769$	1.96260e21	−	3.39932e21i	0.445024	−	0.770804i	−0.553030	−	0.833161i	$-0.686528\pi$
$769$	1.96260e21	−	3.39932e21i	0.445024	−	0.770804i	0.998054	+	0.0623572i	$0.0198618\pi$
$770$	−7.22756e21	+	1.25185e22i	−1.62297	+	2.81107i
$771$		0			0
$772$	2.13824e21	+	3.70354e21i	0.470898	+	0.815619i
$773$	5.12588e21			1.11795			0.558975	−	0.829185i	$-0.311195\pi$
$773$	5.12588e21			1.11795			0.558975	+	0.829185i	$0.311195\pi$
$774$		0			0
$775$	−5.20633e21			−1.11370
$776$	4.75311e20	+	8.23262e20i	0.100697	+	0.174412i
$777$		0			0
$778$	−7.60695e20	+	1.31756e21i	−0.158075	+	0.273794i
$779$	3.45738e21	−	5.98836e21i	0.711568	−	1.23247i
$780$		0			0
$781$	4.07994e21	+	7.06666e21i	0.823703	+	1.42670i
$782$	4.96692e20			0.0993200
$783$		0			0
$784$	−2.85901e21			−0.560847
$785$	1.24446e21	+	2.15547e21i	0.241801	+	0.418812i
$786$		0			0
$787$	8.81628e20	−	1.52702e21i	0.168064	−	0.291095i	−0.769675	−	0.638436i	$-0.779582\pi$
$787$	8.81628e20	−	1.52702e21i	0.168064	−	0.291095i	0.937739	+	0.347340i	$0.112915\pi$
$788$	−1.28398e21	+	2.22392e21i	−0.242445	+	0.419927i
$789$		0			0
$790$	4.33337e21	+	7.50562e21i	0.802829	+	1.39054i
$791$	−5.97852e21			−1.09716
$792$		0			0
$793$	5.38708e21			0.970074
$794$	5.25544e21	+	9.10270e21i	0.937466	+	1.62374i
$795$		0			0
$796$	−5.18924e21	+	8.98803e21i	−0.908355	+	1.57332i
$797$	4.59047e21	−	7.95093e21i	0.796012	−	1.37873i	−0.126182	−	0.992007i	$-0.540272\pi$
$797$	4.59047e21	−	7.95093e21i	0.796012	−	1.37873i	0.922194	−	0.386726i	$-0.126394\pi$
$798$		0			0
$799$	−2.63819e20	−	4.56947e20i	−0.0448957	−	0.0777616i
$800$	−1.06591e22			−1.79700
$801$		0			0
$802$	3.65322e21			0.604460
$803$	−3.46900e21	−	6.00848e21i	−0.568640	−	0.984914i
$804$		0			0
$805$	−2.12162e21	+	3.67475e21i	−0.341348	+	0.591232i
$806$	3.97538e21	−	6.88555e21i	0.633673	−	1.09755i
$807$		0			0
$808$	−1.85778e21	−	3.21777e21i	−0.290676	−	0.503466i
$809$	−4.19147e20			−0.0649759			−0.0324879	−	0.999472i	$-0.510343\pi$
$809$	−4.19147e20			−0.0649759			−0.0324879	+	0.999472i	$0.510343\pi$
$810$		0			0
$811$	6.97363e21			1.06121			0.530606	−	0.847618i	$-0.321964\pi$
$811$	6.97363e21			1.06121			0.530606	+	0.847618i	$0.321964\pi$
$812$	−1.72940e21	−	2.99541e21i	−0.260751	−	0.451633i
$813$		0			0
$814$	−3.76202e21	+	6.51601e21i	−0.556850	+	0.964492i
$815$	5.29424e19	−	9.16990e19i	0.00776465	−	0.0134488i
$816$		0			0
$817$	−6.28653e21	−	1.08886e22i	−0.905201	−	1.56785i
$818$	4.40083e21			0.627891
$819$		0			0
$820$	1.43156e22			2.00542
$821$	5.91825e21	+	1.02507e22i	0.821523	+	1.42292i	0.904548	+	0.426373i	$0.140209\pi$
$821$	5.91825e21	+	1.02507e22i	0.821523	+	1.42292i	−0.0830241	+	0.996548i	$0.526458\pi$
$822$		0			0
$823$	3.41893e20	−	5.92177e20i	0.0466006	−	0.0807147i	−0.841784	−	0.539814i	$-0.818495\pi$
$823$	3.41893e20	−	5.92177e20i	0.0466006	−	0.0807147i	0.888385	+	0.459099i	$0.151828\pi$
$824$	1.22949e20	−	2.12954e20i	0.0166063	−	0.0287629i
$825$		0			0
$826$	−1.65516e21	−	2.86682e21i	−0.219528	−	0.380234i
$827$	1.03897e20			0.0136557			0.00682784	−	0.999977i	$-0.497827\pi$
$827$	1.03897e20			0.0136557			0.00682784	+	0.999977i	$0.497827\pi$
$828$		0			0
$829$	−3.32808e21			−0.429571			−0.214785	−	0.976661i	$-0.568905\pi$
$829$	−3.32808e21			−0.429571			−0.214785	+	0.976661i	$0.568905\pi$
$830$	−3.90556e21	−	6.76463e21i	−0.499571	−	0.865283i
$831$		0			0
$832$	5.85663e21	−	1.01440e22i	0.735738	−	1.27434i
$833$	7.83849e20	−	1.35767e21i	0.0975877	−	0.169027i
$834$		0			0
$835$	−5.74821e21	−	9.95619e21i	−0.702885	−	1.21743i
$836$	1.54471e22			1.87198
$837$		0			0
$838$	1.95853e21			0.233131
$839$	−3.56319e21	−	6.17162e21i	−0.420363	−	0.728090i	0.575612	−	0.817723i	$-0.304764\pi$
$839$	−3.56319e21	−	6.17162e21i	−0.420363	−	0.728090i	−0.995975	+	0.0896333i	$0.971430\pi$
$840$		0			0
$841$	3.96862e21	−	6.87385e21i	0.459907	−	0.796582i
$842$	7.76027e21	−	1.34412e22i	0.891325	−	1.54382i
$843$		0			0
$844$	−6.57904e21	−	1.13952e22i	−0.742325	−	1.28574i
$845$	−5.16669e20			−0.0577813
$846$		0			0
$847$	−5.85410e19			−0.00643182
$848$	2.97381e21	+	5.15079e21i	0.323850	+	0.560925i
$849$		0			0
$850$	1.89770e21	−	3.28691e21i	0.203042	−	0.351679i
$851$	−1.10432e21	+	1.91274e21i	−0.117118	+	0.202855i
$852$		0			0
$853$	−7.94231e19	−	1.37565e20i	−0.00827616	−	0.0143347i	0.861858	−	0.507150i	$-0.169301\pi$
$853$	−7.94231e19	−	1.37565e20i	−0.00827616	−	0.0143347i	−0.870134	+	0.492816i	$0.835968\pi$
$854$	−2.03959e22			−2.10673
$855$		0			0
$856$	−8.28599e21			−0.840991
$857$	4.63723e21	+	8.03191e21i	0.466554	+	0.808095i	0.999270	−	0.0381986i	$-0.0121619\pi$
$857$	4.63723e21	+	8.03191e21i	0.466554	+	0.808095i	−0.532716	+	0.846294i	$0.678829\pi$
$858$		0			0
$859$	−4.67905e21	+	8.10436e21i	−0.462604	+	0.801253i	−0.999090	−	0.0426560i	$-0.986418\pi$
$859$	−4.67905e21	+	8.10436e21i	−0.462604	+	0.801253i	0.536486	+	0.843909i	$0.319751\pi$
$860$	1.30150e22	−	2.25426e22i	1.27557	−	2.20936i
$861$		0			0
$862$	9.66989e21	+	1.67487e22i	0.931359	+	1.61316i
$863$	3.98396e20			0.0380394			0.0190197	−	0.999819i	$-0.493945\pi$
$863$	3.98396e20			0.0380394			0.0190197	+	0.999819i	$0.493945\pi$
$864$		0			0
$865$	1.07556e22			1.00929
$866$	−4.39167e21	−	7.60660e21i	−0.408550	−	0.707630i
$867$		0			0
$868$	−8.55145e21	+	1.48116e22i	−0.781883	+	1.35426i
$869$	−3.83681e21	+	6.64555e21i	−0.347794	+	0.602397i
$870$		0			0
$871$	4.05127e21	+	7.01701e21i	0.360957	+	0.625196i
$872$	−9.86766e21			−0.871647
$873$		0			0
$874$	7.98084e21			0.692967
$875$	3.85150e21	+	6.67100e21i	0.331566	+	0.574289i
$876$		0			0
$877$	−2.05723e21	+	3.56322e21i	−0.174094	+	0.301540i	−0.939848	−	0.341594i	$-0.889033\pi$
$877$	−2.05723e21	+	3.56322e21i	−0.174094	+	0.301540i	0.765753	+	0.643135i	$0.222366\pi$
$878$	7.72432e20	−	1.33789e21i	0.0648114	−	0.112257i
$879$		0			0
$880$	−5.40052e21	−	9.35397e21i	−0.445467	−	0.771571i
$881$	1.18310e22			0.967614			0.483807	−	0.875175i	$-0.339254\pi$
$881$	1.18310e22			0.967614			0.483807	+	0.875175i	$0.339254\pi$
$882$		0			0
$883$	5.86964e20			0.0471961			0.0235980	−	0.999722i	$-0.492488\pi$
$883$	5.86964e20			0.0471961			0.0235980	+	0.999722i	$0.492488\pi$
$884$	1.64656e21	+	2.85192e21i	0.131276	+	0.227377i
$885$		0			0
$886$	6.60113e21	−	1.14335e22i	0.517446	−	0.896243i
$887$	−1.39035e21	+	2.40816e21i	−0.108068	+	0.187179i	−0.914987	−	0.403482i	$-0.867800\pi$
$887$	−1.39035e21	+	2.40816e21i	−0.108068	+	0.187179i	0.806920	+	0.590661i	$0.201133\pi$
$888$		0			0
$889$	1.50326e22	+	2.60371e22i	1.14887	+	1.98990i
$890$	−2.17020e22			−1.64465
$891$		0			0
$892$	1.32732e22			0.989097
$893$	−4.23903e21	−	7.34221e21i	−0.313242	−	0.542552i
$894$		0			0
$895$	4.78193e21	−	8.28255e21i	0.347481	−	0.601854i
$896$	−8.86674e21	+	1.53576e22i	−0.638931	+	1.10666i
$897$		0			0
$898$	1.07685e21	+	1.86517e21i	0.0763106	+	0.132174i
$899$	3.42151e21			0.240447
$900$		0			0
$901$	−3.26130e21			−0.225401
$902$	1.11545e22	+	1.93202e22i	0.764543	+	1.32423i
$903$		0			0
$904$	−2.79291e21	+	4.83747e21i	−0.188276	+	0.326103i
$905$	−6.11361e21	+	1.05891e22i	−0.408727	+	0.707936i
$906$		0			0
$907$	5.35469e21	+	9.27459e21i	0.352111	+	0.609874i	0.986619	−	0.163042i	$-0.0521306\pi$
$907$	5.35469e21	+	9.27459e21i	0.352111	+	0.609874i	−0.634508	+	0.772916i	$0.718797\pi$
$908$	3.26443e22			2.12894
$909$		0			0
$910$	−4.95157e22			−3.17638
$911$	−1.44585e21	−	2.50428e21i	−0.0919888	−	0.159329i	0.816359	−	0.577545i	$-0.195989\pi$
$911$	−1.44585e21	−	2.50428e21i	−0.0919888	−	0.159329i	−0.908348	+	0.418215i	$0.862656\pi$
$912$		0			0
$913$	3.45802e21	−	5.98946e21i	0.216420	−	0.374850i
$914$	−9.68918e21	+	1.67821e22i	−0.601437	+	1.04172i
$915$		0			0
$916$	−1.27621e22	−	2.21047e22i	−0.779305	−	1.34980i
$917$	5.58948e21			0.338533
$918$		0			0
$919$	−1.58079e22			−0.941908			−0.470954	−	0.882158i	$-0.656090\pi$
$919$	−1.58079e22			−0.941908			−0.470954	+	0.882158i	$0.656090\pi$
$920$	1.98226e21	+	3.43337e21i	0.117152	+	0.202914i
$921$		0			0
$922$	−1.46991e22	+	2.54596e22i	−0.854690	+	1.48037i
$923$	−1.39757e22	+	2.42067e22i	−0.806050	+	1.39612i
$924$		0			0
$925$	8.43851e21	+	1.46159e22i	0.478854	+	0.829399i
$926$	−3.93507e22			−2.21498
$927$		0			0
$928$	7.00499e21			0.387970
$929$	−6.35595e21	−	1.10088e22i	−0.349191	−	0.604816i	0.636915	−	0.770934i	$-0.280210\pi$
$929$	−6.35595e21	−	1.10088e22i	−0.349191	−	0.604816i	−0.986106	+	0.166118i	$0.946877\pi$
$930$		0			0
$931$	1.25949e22	−	2.18150e22i	0.680881	−	1.17932i
$932$	−6.23578e21	+	1.08007e22i	−0.334404	+	0.579205i
$933$		0			0
$934$	−2.42922e22	−	4.20753e22i	−1.28193	−	2.22037i
$935$	5.92261e21			0.310046
$936$		0			0
$937$	−3.40311e22			−1.75319			−0.876595	−	0.481230i	$-0.840190\pi$
$937$	−3.40311e22			−1.75319			−0.876595	+	0.481230i	$0.840190\pi$
$938$	−1.53384e22	−	2.65669e22i	−0.783897	−	1.35775i
$939$		0			0
$940$	8.77605e21	−	1.52006e22i	0.441408	−	0.764541i
$941$	9.84071e21	−	1.70446e22i	0.491026	−	0.850482i	−0.508921	−	0.860813i	$-0.669955\pi$
$941$	9.84071e21	−	1.70446e22i	0.491026	−	0.850482i	0.999947	+	0.0103315i	$0.00328869\pi$
$942$		0			0
$943$	3.27435e21	+	5.67135e21i	0.160801	+	0.278515i
$944$	2.47351e21			0.120510
$945$		0			0
$946$	4.05643e22			1.94518
$947$	1.07304e22	+	1.85856e22i	0.510494	+	0.884202i	0.999926	+	0.0121603i	$0.00387085\pi$
$947$	1.07304e22	+	1.85856e22i	0.510494	+	0.884202i	−0.489432	+	0.872042i	$0.662796\pi$
$948$		0			0
$949$	1.18830e22	−	2.05819e22i	0.556453	−	0.963805i
$950$	3.04922e22	−	5.28140e22i	1.41665	−	2.45370i
$951$		0			0
$952$	−1.49580e21	−	2.59081e21i	−0.0684065	−	0.118484i
$953$	3.51332e22			1.59412			0.797060	−	0.603900i	$-0.206388\pi$
$953$	3.51332e22			1.59412			0.797060	+	0.603900i	$0.206388\pi$
$954$		0			0
$955$	−3.28821e22			−1.46870
$956$	−1.53151e21	−	2.65265e21i	−0.0678712	−	0.117556i
$957$		0			0
$958$	−1.99313e22	+	3.45221e22i	−0.869551	+	1.50611i
$959$	9.37047e21	−	1.62301e22i	0.405622	−	0.702558i
$960$		0			0
$961$	3.27338e21	+	5.66965e21i	0.139499	+	0.241619i
$962$	−2.57734e22			−1.08983
$963$		0			0
$964$	1.90298e22			0.792241
$965$	1.31730e22	+	2.28163e22i	0.544163	+	0.942518i
$966$		0			0
$967$	−1.23936e22	+	2.14663e22i	−0.504078	+	0.873089i	0.495911	+	0.868373i	$0.334834\pi$
$967$	−1.23936e22	+	2.14663e22i	−0.504078	+	0.873089i	−0.999989	+	0.00471519i	$0.998499\pi$
$968$	−2.73479e19	+	4.73679e19i	−0.00110372	+	0.00191170i
$969$		0			0
$970$	1.22038e22	+	2.11376e22i	0.484962	+	0.839979i
$971$	−4.50208e22			−1.77529			−0.887645	−	0.460528i	$-0.847660\pi$
$971$	−4.50208e22			−1.77529			−0.887645	+	0.460528i	$0.847660\pi$
$972$		0			0
$973$	3.39712e21			0.131906
$974$	1.96415e22	+	3.40200e22i	0.756801	+	1.31082i
$975$		0			0
$976$	7.62001e21	−	1.31982e22i	0.289123	−	0.500775i
$977$	2.66812e21	−	4.62132e21i	0.100461	−	0.174003i	−0.811414	−	0.584472i	$-0.801302\pi$
$977$	2.66812e21	−	4.62132e21i	0.100461	−	0.174003i	0.911875	+	0.410469i	$0.134635\pi$
$978$		0			0
$979$	−9.60757e21	−	1.66408e22i	−0.356240	−	0.617026i
$980$	5.21503e22			1.91894
$981$		0			0
$982$	−7.68358e21			−0.278437
$983$	−1.99181e22	−	3.44992e22i	−0.716303	−	1.24067i	−0.962455	−	0.271442i	$-0.912500\pi$
$983$	−1.99181e22	−	3.44992e22i	−0.716303	−	1.24067i	0.246152	−	0.969231i	$-0.420834\pi$
$984$		0			0
$985$	−7.91018e21	+	1.37008e22i	−0.280166	+	0.485261i
$986$	−1.24713e21	+	2.16010e21i	−0.0438365	+	0.0759271i
$987$		0			0
$988$	2.64569e22	+	4.58246e22i	0.915928	+	1.58643i
$989$	1.19075e22			0.409116
$990$		0			0
$991$	4.10420e22			1.38892			0.694459	−	0.719533i	$-0.255644\pi$
$991$	4.10420e22			1.38892			0.694459	+	0.719533i	$0.255644\pi$
$992$	−1.73190e22	−	2.99973e22i	−0.581681	−	1.00750i
$993$		0			0
$994$	5.29131e22	−	9.16482e22i	1.75051	−	3.03198i
$995$	−3.19691e22	+	5.53722e22i	−1.04968	+	1.81810i
$996$		0			0
$997$	7.82722e21	+	1.35571e22i	0.253159	+	0.438485i	0.964394	−	0.264470i	$-0.0851970\pi$
$997$	7.82722e21	+	1.35571e22i	0.253159	+	0.438485i	−0.711235	+	0.702955i	$0.751864\pi$
$998$	4.43427e22			1.42345
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.16.c.a.10.3		28
3.2	odd	2		9.16.c.a.4.12	✓	28
9.2	odd	6		9.16.c.a.7.12	yes	28
9.4	even	3		81.16.a.c.1.12		14
9.5	odd	6		81.16.a.e.1.3		14
9.7	even	3	inner	27.16.c.a.19.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.16.c.a.4.12	✓	28	3.2	odd	2
9.16.c.a.7.12	yes	28	9.2	odd	6
27.16.c.a.10.3		28	1.1	even	1	trivial
27.16.c.a.19.3		28	9.7	even	3	inner
81.16.a.c.1.12		14	9.4	even	3
81.16.a.e.1.3		14	9.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-137.732 - 238.559i) q^{2} +(-21556.3 + 37336.6i) q^{4} +(-132801. + 230018. i) q^{5} +(1.52495e6 + 2.64129e6i) q^{7} +2.84956e6 q^{8} +7.31638e7 q^{10} +(3.23900e7 + 5.61011e7i) q^{11} +(-1.10951e8 + 1.92173e8i) q^{13} +(4.20069e8 - 7.27580e8i) q^{14} +(3.13880e8 + 5.43656e8i) q^{16} -3.44224e8 q^{17} -5.53098e9 q^{19} +(-5.72539e9 - 9.91667e9i) q^{20} +(8.92228e9 - 1.54538e10i) q^{22} +(2.61909e9 - 4.53640e9i) q^{23} +(-2.00134e10 - 3.46642e10i) q^{25} +6.11262e10 q^{26} -1.31489e11 q^{28} +(1.31524e10 + 2.27807e10i) q^{29} +(6.50356e10 - 1.12645e11i) q^{31} +(1.33150e11 - 2.30623e11i) q^{32} +(4.74107e10 + 8.21178e10i) q^{34} -8.10058e11 q^{35} -4.21643e11 q^{37} +(7.61794e11 + 1.31947e12i) q^{38} +(-3.78425e11 + 6.55451e11i) q^{40} +(-6.25093e11 + 1.08269e12i) q^{41} +(1.13660e12 + 1.96865e12i) q^{43} -2.79283e12 q^{44} -1.44293e12 q^{46} +(7.66415e11 + 1.32747e12i) q^{47} +(-2.27715e12 + 3.94414e12i) q^{49} +(-5.51298e12 + 9.54875e12i) q^{50} +(-4.78339e12 - 8.28507e12i) q^{52} +9.47435e12 q^{53} -1.72057e13 q^{55} +(4.34543e12 + 7.52651e12i) q^{56} +(3.62303e12 - 6.27527e12i) q^{58} +(1.97011e12 - 3.41233e12i) q^{59} +(-1.21384e13 - 2.10243e13i) q^{61} -3.58300e13 q^{62} -5.27857e13 q^{64} +(-2.94688e13 - 5.10415e13i) q^{65} +(1.82570e13 - 3.16221e13i) q^{67} +(7.42020e12 - 1.28522e13i) q^{68} +(1.11571e14 + 1.93247e14i) q^{70} +1.25963e14 q^{71} -1.07101e14 q^{73} +(5.80738e13 + 1.00587e14i) q^{74} +(1.19228e14 - 2.06508e14i) q^{76} +(-9.87860e13 + 1.71102e14i) q^{77} +(5.92284e13 + 1.02587e14i) q^{79} -1.66734e14 q^{80} +3.44382e14 q^{82} +(-5.33810e13 - 9.24586e13i) q^{83} +(4.57133e13 - 7.91777e13i) q^{85} +(3.13093e14 - 5.42293e14i) q^{86} +(9.22973e13 + 1.59864e14i) q^{88} -2.96622e14 q^{89} -6.76779e14 q^{91} +(1.12916e14 + 1.95576e14i) q^{92} +(2.11120e14 - 3.65670e14i) q^{94} +(7.34520e14 - 1.27223e15i) q^{95} +(1.66801e14 + 2.88908e14i) q^{97} +1.25455e15 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 129 q^{2} - 212993 q^{4} + 152655 q^{5} + 803705 q^{7} - 20162658 q^{8} + 65532 q^{10} + 60735990 q^{11} - 41509093 q^{13} - 215313024 q^{14} - 2952822785 q^{16} + 2121112242 q^{17} + 5670809246 q^{19}+ \cdots - 72\!\cdots\!90 q^{98}+O(q^{100}) \) 28 * q + 129 * q^2 - 212993 * q^4 + 152655 * q^5 + 803705 * q^7 - 20162658 * q^8 + 65532 * q^10 + 60735990 * q^11 - 41509093 * q^13 - 215313024 * q^14 - 2952822785 * q^16 + 2121112242 * q^17 + 5670809246 * q^19 + 1434155028 * q^20 + 7841223807 * q^22 + 49433203761 * q^23 - 59779497779 * q^25 - 28088907384 * q^26 - 103195803652 * q^28 + 152663830725 * q^29 - 13955906443 * q^31 + 779638216401 * q^32 - 15287791959 * q^34 - 2803990417206 * q^35 + 531598359836 * q^37 + 3598723579461 * q^38 - 1083028910664 * q^40 + 1656362316264 * q^41 + 2394872112236 * q^43 - 13185661781850 * q^44 + 1511321018232 * q^46 + 7686086213559 * q^47 - 7946464864203 * q^49 + 2177050903941 * q^50 + 1969798905818 * q^52 + 20778802614756 * q^53 - 21700105111626 * q^55 - 13789887516654 * q^56 + 15429496587216 * q^58 - 17132922121350 * q^59 - 17229834579991 * q^61 + 190512185539596 * q^62 + 11322374934466 * q^64 - 92170621979115 * q^65 - 19847122719016 * q^67 - 106742875854159 * q^68 - 85984052928798 * q^70 - 60954771085488 * q^71 + 206937948168362 * q^73 + 169102773629016 * q^74 - 274786877071699 * q^76 + 121510644149499 * q^77 + 137921083996235 * q^79 - 1189869535368192 * q^80 + 747645180639978 * q^82 + 243294491978445 * q^83 + 278537029457886 * q^85 + 1439527045654455 * q^86 + 8025917716587 * q^88 - 3513318445769832 * q^89 - 1924506955785338 * q^91 + 3448278918317022 * q^92 + 1100860396273032 * q^94 + 3375682767029028 * q^95 - 1883742033081100 * q^97 - 7254179697035790 * q^98

Introduction

L-functions

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