LMFDB - Embedded newform 23.25.b.c.22.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,25,Mod(22,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 25, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("23.22"); S:= CuspForms(chi, 25); N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	23.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$83.9424450193$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.27
Character	$\chi$	$=$	23.22
Dual form			23.25.b.c.22.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2541.92 q^{2} +699314. q^{3} -1.03159e7 q^{4} +3.93724e8i q^{5} +1.77760e9 q^{6} -1.74256e10i q^{7} -6.88684e10 q^{8} +2.06610e11 q^{9} +1.00081e12i q^{10} -1.74676e12i q^{11} -7.21402e12 q^{12} +1.93975e13 q^{13} -4.42946e13i q^{14} +2.75336e14i q^{15} -1.98670e12 q^{16} -4.91787e14i q^{17} +5.25187e14 q^{18} -1.35367e15i q^{19} -4.06160e15i q^{20} -1.21860e16i q^{21} -4.44012e15i q^{22} +(2.15931e16 + 3.74024e15i) q^{23} -4.81607e16 q^{24} -9.54137e16 q^{25} +4.93068e16 q^{26} -5.30213e16 q^{27} +1.79760e17i q^{28} +5.62494e17 q^{29} +6.99883e17i q^{30} +6.23769e17 q^{31} +1.15037e18 q^{32} -1.22153e18i q^{33} -1.25008e18i q^{34} +6.86088e18 q^{35} -2.13136e18 q^{36} +2.82001e18i q^{37} -3.44093e18i q^{38} +1.35649e19 q^{39} -2.71151e19i q^{40} +1.28323e19 q^{41} -3.09758e19i q^{42} +3.38446e19i q^{43} +1.80193e19i q^{44} +8.13474e19i q^{45} +(5.48879e19 + 9.50739e18i) q^{46} +4.15911e19 q^{47} -1.38933e18 q^{48} -1.12071e20 q^{49} -2.42534e20 q^{50} -3.43914e20i q^{51} -2.00101e20 q^{52} +4.49064e20i q^{53} -1.34776e20 q^{54} +6.87741e20 q^{55} +1.20008e21i q^{56} -9.46643e20i q^{57} +1.42981e21 q^{58} +1.91911e20 q^{59} -2.84033e21i q^{60} -1.43280e21i q^{61} +1.58557e21 q^{62} -3.60032e21i q^{63} +2.95748e21 q^{64} +7.63724e21i q^{65} -3.10504e21i q^{66} +3.75498e21i q^{67} +5.07321e21i q^{68} +(1.51003e22 + 2.61560e21i) q^{69} +1.74398e22 q^{70} +1.87365e22 q^{71} -1.42289e22 q^{72} -2.86950e22 q^{73} +7.16823e21i q^{74} -6.67241e22 q^{75} +1.39643e22i q^{76} -3.04384e22 q^{77} +3.44809e22 q^{78} -1.13068e23i q^{79} -7.82211e20i q^{80} -9.54315e22 q^{81} +3.26187e22 q^{82} -1.35941e23i q^{83} +1.25709e23i q^{84} +1.93628e23 q^{85} +8.60302e22i q^{86} +3.93360e23 q^{87} +1.20297e23i q^{88} +1.69175e23i q^{89} +2.06779e23i q^{90} -3.38013e23i q^{91} +(-2.22751e23 - 3.85838e22i) q^{92} +4.36211e23 q^{93} +1.05721e23 q^{94} +5.32974e23 q^{95} +8.04470e23 q^{96} -5.75406e23i q^{97} -2.84876e23 q^{98} -3.60899e23i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) $ 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2541.92			0.620586			0.310293	−	0.950641i	$-0.399573\pi$
$2$	2541.92			0.620586			0.310293	+	0.950641i	$0.399573\pi$
$3$	699314.			1.31588			0.657941	−	0.753069i	$-0.271427\pi$
$3$	699314.			1.31588			0.657941	+	0.753069i	$0.271427\pi$
$4$	−1.03159e7			−0.614873
$5$			3.93724e8i			1.61269i	0.591444	+	0.806346i	$0.298558\pi$
$5$			3.93724e8i			1.61269i	−0.591444	+	0.806346i	$0.701442\pi$
$6$	1.77760e9			0.816618
$7$		−	1.74256e10i		−	1.25896i	−0.777017	−	0.629480i	$-0.783268\pi$
$7$		−	1.74256e10i		−	1.25896i	0.777017	−	0.629480i	$-0.216732\pi$
$8$	−6.88684e10			−1.00217
$9$	2.06610e11			0.731547
$10$			1.00081e12i			1.00081i
$11$		−	1.74676e12i		−	0.556571i	−0.960498	−	0.278286i	$-0.910234\pi$
$11$		−	1.74676e12i		−	0.556571i	0.960498	−	0.278286i	$-0.0897662\pi$
$12$	−7.21402e12			−0.809101
$13$	1.93975e13			0.832577			0.416289	−	0.909233i	$-0.363331\pi$
$13$	1.93975e13			0.832577			0.416289	+	0.909233i	$0.363331\pi$
$14$		−	4.42946e13i		−	0.781293i
$15$			2.75336e14i			2.12211i
$16$	−1.98670e12			−0.00705818
$17$		−	4.91787e14i		−	0.844092i	−0.906574	−	0.422046i	$-0.861312\pi$
$17$		−	4.91787e14i		−	0.844092i	0.906574	−	0.422046i	$-0.138688\pi$
$18$	5.25187e14			0.453988
$19$		−	1.35367e15i		−	0.611605i	−0.952095	−	0.305802i	$-0.901075\pi$
$19$		−	1.35367e15i		−	0.611605i	0.952095	−	0.305802i	$-0.0989247\pi$
$20$		−	4.06160e15i		−	0.991601i
$21$		−	1.21860e16i		−	1.65664i
$22$		−	4.44012e15i		−	0.345400i
$23$	2.15931e16	+	3.74024e15i	0.985328	+	0.170673i
$23$	2.15931e16	+	3.74024e15i	0.985328	+	0.170673i
$24$	−4.81607e16			−1.31873
$25$	−9.54137e16			−1.60078
$26$	4.93068e16			0.516686
$27$	−5.30213e16			−0.353253
$28$			1.79760e17i			0.774101i
$29$	5.62494e17			1.58980			0.794899	−	0.606742i	$-0.207524\pi$
$29$	5.62494e17			1.58980			0.794899	+	0.606742i	$0.207524\pi$
$30$			6.99883e17i			1.31695i
$31$	6.23769e17			0.791924			0.395962	−	0.918267i	$-0.370411\pi$
$31$	6.23769e17			0.791924			0.395962	+	0.918267i	$0.370411\pi$
$32$	1.15037e18			0.997787
$33$		−	1.22153e18i		−	0.732383i
$34$		−	1.25008e18i		−	0.523832i
$35$	6.86088e18			2.03032
$36$	−2.13136e18			−0.449809
$37$			2.82001e18i			0.428380i	0.976792	+	0.214190i	$0.0687112\pi$
$37$			2.82001e18i			0.428380i	−0.976792	+	0.214190i	$0.931289\pi$
$38$		−	3.44093e18i		−	0.379553i
$39$	1.35649e19			1.09557
$40$		−	2.71151e19i		−	1.61619i
$41$	1.28323e19			0.568721			0.284360	−	0.958717i	$-0.408219\pi$
$41$	1.28323e19			0.568721			0.284360	+	0.958717i	$0.408219\pi$
$42$		−	3.09758e19i		−	1.02809i
$43$			3.38446e19i			0.846969i	0.905903	+	0.423484i	$0.139193\pi$
$43$			3.38446e19i			0.846969i	−0.905903	+	0.423484i	$0.860807\pi$
$44$			1.80193e19i			0.342221i
$45$			8.13474e19i			1.17976i
$46$	5.48879e19	+	9.50739e18i	0.611481	+	0.105917i
$47$	4.15911e19			0.357953			0.178977	−	0.983853i	$-0.442721\pi$
$47$	4.15911e19			0.357953			0.178977	+	0.983853i	$0.442721\pi$
$48$	−1.38933e18			−0.00928774
$49$	−1.12071e20			−0.584981
$50$	−2.42534e20			−0.993419
$51$		−	3.43914e20i		−	1.11073i
$52$	−2.00101e20			−0.511929
$53$			4.49064e20i			0.914109i	0.889439	+	0.457055i	$0.151096\pi$
$53$			4.49064e20i			0.914109i	−0.889439	+	0.457055i	$0.848904\pi$
$54$	−1.34776e20			−0.219224
$55$	6.87741e20			0.897578
$56$			1.20008e21i			1.26169i
$57$		−	9.46643e20i		−	0.804800i
$58$	1.42981e21			0.986606
$59$	1.91911e20			0.107864			0.0539318	−	0.998545i	$-0.482825\pi$
$59$	1.91911e20			0.107864			0.0539318	+	0.998545i	$0.482825\pi$
$60$		−	2.84033e21i		−	1.30483i
$61$		−	1.43280e21i		−	0.539793i	−0.962889	−	0.269896i	$-0.913011\pi$
$61$		−	1.43280e21i		−	0.539793i	0.962889	−	0.269896i	$-0.0869894\pi$
$62$	1.58557e21			0.491457
$63$		−	3.60032e21i		−	0.920989i
$64$	2.95748e21			0.626271
$65$			7.63724e21i			1.34269i
$66$		−	3.10504e21i		−	0.454506i
$67$			3.75498e21i			0.458891i	0.973322	+	0.229446i	$0.0736913\pi$
$67$			3.75498e21i			0.458891i	−0.973322	+	0.229446i	$0.926309\pi$
$68$			5.07321e21i			0.519010i
$69$	1.51003e22	+	2.61560e21i	1.29658	+	0.224586i
$70$	1.74398e22			1.25999
$71$	1.87365e22			1.14180			0.570899	−	0.821020i	$-0.306595\pi$
$71$	1.87365e22			1.14180			0.570899	+	0.821020i	$0.306595\pi$
$72$	−1.42289e22			−0.733133
$73$	−2.86950e22			−1.25294			−0.626472	−	0.779444i	$-0.715502\pi$
$73$	−2.86950e22			−1.25294			−0.626472	+	0.779444i	$0.715502\pi$
$74$			7.16823e21i			0.265847i
$75$	−6.67241e22			−2.10643
$76$			1.39643e22i			0.376059i
$77$	−3.04384e22			−0.700701
$78$	3.44809e22			0.679898
$79$		−	1.13068e23i		−	1.91343i	−0.291019	−	0.956717i	$-0.593994\pi$
$79$		−	1.13068e23i		−	1.91343i	0.291019	−	0.956717i	$-0.406006\pi$
$80$		−	7.82211e20i		−	0.0113827i
$81$	−9.54315e22			−1.19639
$82$	3.26187e22			0.352940
$83$		−	1.35941e23i		−	1.27178i	−0.771778	−	0.635892i	$-0.780632\pi$
$83$		−	1.35941e23i		−	1.27178i	0.771778	−	0.635892i	$-0.219368\pi$
$84$			1.25709e23i			1.01863i
$85$	1.93628e23			1.36126
$86$			8.60302e22i			0.525617i
$87$	3.93360e23			2.09199
$88$			1.20297e23i			0.557778i
$89$			1.69175e23i			0.684947i	0.939527	+	0.342474i	$0.111265\pi$
$89$			1.69175e23i			0.684947i	−0.939527	+	0.342474i	$0.888735\pi$
$90$			2.06779e23i			0.732143i
$91$		−	3.38013e23i		−	1.04818i
$92$	−2.22751e23	−	3.85838e22i	−0.605851	−	0.104942i
$93$	4.36211e23			1.04208
$94$	1.05721e23			0.222141
$95$	5.32974e23			0.986330
$96$	8.04470e23			1.31297
$97$		−	5.75406e23i		−	0.829304i	−0.909980	−	0.414652i	$-0.863903\pi$
$97$		−	5.75406e23i		−	0.829304i	0.909980	−	0.414652i	$-0.136097\pi$
$98$	−2.84876e23			−0.363031
$99$		−	3.60899e23i		−	0.407158i
$100$	9.84274e23			0.984274
$101$	1.98837e24			1.76458			0.882288	−	0.470710i	$-0.156002\pi$
$101$	1.98837e24			1.76458			0.882288	+	0.470710i	$0.156002\pi$
$102$		−	8.74201e23i		−	0.689301i
$103$		−	8.38180e23i		−	0.587883i	−0.955823	−	0.293941i	$-0.905033\pi$
$103$		−	8.38180e23i		−	0.587883i	0.955823	−	0.293941i	$-0.0949670\pi$
$104$	−1.33587e24			−0.834382
$105$	4.79791e24			2.67166
$106$			1.14149e24i			0.567283i
$107$		−	3.56813e24i		−	1.58429i	−0.610332	−	0.792145i	$-0.708964\pi$
$107$		−	3.56813e24i		−	1.58429i	0.610332	−	0.792145i	$-0.291036\pi$
$108$	5.46960e23			0.217205
$109$			1.77201e24i			0.630010i	0.949090	+	0.315005i	$0.102006\pi$
$109$			1.77201e24i			0.630010i	−0.949090	+	0.315005i	$0.897994\pi$
$110$	1.74818e24			0.557025
$111$			1.97207e24i			0.563698i
$112$			3.46195e22i			0.00888597i
$113$			6.13562e24i			1.41552i	0.706451	+	0.707762i	$0.250295\pi$
$113$			6.13562e24i			1.41552i	−0.706451	+	0.707762i	$0.749705\pi$
$114$		−	2.40629e24i		−	0.499448i
$115$	−1.47262e24	+	8.50171e24i	−0.275243	+	1.58903i
$116$	−5.80261e24			−0.977523
$117$	4.00772e24			0.609069
$118$	4.87821e23			0.0669386
$119$	−8.56970e24			−1.06268
$120$		−	1.89620e25i		−	2.12671i
$121$	6.79856e24			0.690228
$122$		−	3.64206e24i		−	0.334988i
$123$	8.97382e24			0.748369
$124$	−6.43472e24			−0.486933
$125$		−	1.40989e25i		−	0.968867i
$126$		−	9.15172e24i		−	0.571553i
$127$	2.67390e25			1.51880			0.759400	−	0.650624i	$-0.225493\pi$
$127$	2.67390e25			1.51880			0.759400	+	0.650624i	$0.225493\pi$
$128$	−1.17823e25			−0.609132
$129$			2.36680e25i			1.11451i
$130$			1.94132e25i			0.833255i
$131$	1.04312e25			0.408393			0.204196	−	0.978930i	$-0.434542\pi$
$131$	1.04312e25			0.408393			0.204196	+	0.978930i	$0.434542\pi$
$132$			1.26012e25i			0.450322i
$133$	−2.35886e25			−0.769986
$134$			9.54485e24i			0.284781i
$135$		−	2.08757e25i		−	0.569688i
$136$			3.38686e25i			0.845922i
$137$		−	6.65473e25i		−	1.52224i	−0.648610	−	0.761121i	$-0.724649\pi$
$137$		−	6.65473e25i		−	1.52224i	0.648610	−	0.761121i	$-0.275351\pi$
$138$	3.83839e25	+	6.64865e24i	0.804637	+	0.139375i
$139$	7.88600e23			0.0151593			0.00757965	−	0.999971i	$-0.497587\pi$
$139$	7.88600e23			0.0151593			0.00757965	+	0.999971i	$0.497587\pi$
$140$	−7.07759e25			−1.24839
$141$	2.90853e25			0.471025
$142$	4.76268e25			0.708584
$143$		−	3.38827e25i		−	0.463389i
$144$	−4.10473e23			−0.00516339
$145$			2.21467e26i			2.56385i
$146$	−7.29404e25			−0.777560
$147$	−7.83730e25			−0.769766
$148$		−	2.90908e25i		−	0.263399i
$149$		−	2.09985e26i		−	1.75369i	−0.480772	−	0.876846i	$-0.659644\pi$
$149$		−	2.09985e26i		−	1.75369i	0.480772	−	0.876846i	$-0.340356\pi$
$150$	−1.69607e26			−1.30722
$151$	−1.21831e26			−0.867028			−0.433514	−	0.901147i	$-0.642727\pi$
$151$	−1.21831e26			−0.867028			−0.433514	+	0.901147i	$0.642727\pi$
$152$			9.32254e25i			0.612930i
$153$		−	1.01608e26i		−	0.617493i
$154$	−7.73719e25			−0.434845
$155$			2.45593e26i			1.27713i
$156$	−1.39934e26			−0.673639
$157$		−	1.95137e26i		−	0.870049i	−0.900419	−	0.435025i	$-0.856740\pi$
$157$		−	1.95137e26i		−	0.870049i	0.900419	−	0.435025i	$-0.143260\pi$
$158$		−	2.87409e26i		−	1.18745i
$159$			3.14037e26i			1.20286i
$160$			4.52928e26i			1.60912i
$161$	6.51760e25	−	3.76273e26i	0.214871	−	1.24049i
$162$	−2.42579e26			−0.742460
$163$	−5.22411e26			−1.48512			−0.742559	−	0.669781i	$-0.766388\pi$
$163$	−5.22411e26			−1.48512			−0.742559	+	0.669781i	$0.766388\pi$
$164$	−1.32376e26			−0.349691
$165$	4.80947e26			1.18111
$166$		−	3.45551e26i		−	0.789252i
$167$	−2.39657e25			−0.0509322			−0.0254661	−	0.999676i	$-0.508107\pi$
$167$	−2.39657e25			−0.0509322			−0.0254661	+	0.999676i	$0.508107\pi$
$168$			8.39230e26i			1.66023i
$169$	−1.66540e26			−0.306815
$170$	4.92187e26			0.844780
$171$		−	2.79683e26i		−	0.447418i
$172$		−	3.49136e26i		−	0.520778i
$173$	−8.49695e26			−1.18225			−0.591125	−	0.806580i	$-0.701316\pi$
$173$	−8.49695e26			−1.18225			−0.591125	+	0.806580i	$0.701316\pi$
$174$	9.99889e26			1.29826
$175$			1.66264e27i			2.01531i
$176$			3.47029e24i			0.00392838i
$177$	1.34206e26			0.141936
$178$			4.30030e26i			0.425069i
$179$	1.30857e27			1.20937			0.604685	−	0.796465i	$-0.293299\pi$
$179$	1.30857e27			1.20937			0.604685	+	0.796465i	$0.293299\pi$
$180$		−	8.39169e26i		−	0.725403i
$181$		−	1.62056e27i		−	1.31076i	−0.755299	−	0.655380i	$-0.772508\pi$
$181$		−	1.62056e27i		−	1.31076i	0.755299	−	0.655380i	$-0.227492\pi$
$182$		−	8.59202e26i		−	0.650487i
$183$		−	1.00198e27i		−	0.710304i
$184$	−1.48708e27	−	2.57584e26i	−0.987463	−	0.171043i
$185$	−1.11030e27			−0.690845
$186$	1.10881e27			0.646700
$187$	−8.59034e26			−0.469798
$188$	−4.29048e26			−0.220096
$189$			9.23930e26i			0.444731i
$190$	1.35478e27			0.612103
$191$			5.36497e26i			0.227597i	0.993504	+	0.113799i	$0.0363019\pi$
$191$			5.36497e26i			0.227597i	−0.993504	+	0.113799i	$0.963698\pi$
$192$	2.06821e27			0.824099
$193$	−1.79936e27			−0.673644			−0.336822	−	0.941568i	$-0.609352\pi$
$193$	−1.79936e27			−0.673644			−0.336822	+	0.941568i	$0.609352\pi$
$194$		−	1.46264e27i		−	0.514654i
$195$			5.34083e27i			1.76682i
$196$	1.15611e27			0.359689
$197$	1.87528e27			0.548873			0.274436	−	0.961605i	$-0.411509\pi$
$197$	1.87528e27			0.548873			0.274436	+	0.961605i	$0.411509\pi$
$198$		−	9.17376e26i		−	0.252677i
$199$		−	5.46782e26i		−	0.141768i	−0.997485	−	0.0708838i	$-0.977418\pi$
$199$		−	5.46782e26i		−	0.141768i	0.997485	−	0.0708838i	$-0.0225820\pi$
$200$	6.57099e27			1.60425
$201$			2.62591e27i			0.603847i
$202$	5.05427e27			1.09507
$203$		−	9.80181e27i		−	2.00149i
$204$			3.54776e27i			0.682956i
$205$			5.05239e27i			0.917171i
$206$		−	2.13059e27i		−	0.364832i
$207$	4.46136e27	+	7.72773e26i	0.720814	+	0.124855i
$208$	−3.85369e25			−0.00587648
$209$	−2.36454e27			−0.340402
$210$	1.21959e28			1.65799
$211$	8.17419e27			1.04968			0.524838	−	0.851202i	$-0.324126\pi$
$211$	8.17419e27			1.04968			0.524838	+	0.851202i	$0.324126\pi$
$212$		−	4.63248e27i		−	0.562061i
$213$	1.31027e28			1.50247
$214$		−	9.06989e27i		−	0.983189i
$215$	−1.33254e28			−1.36590
$216$	3.65150e27			0.354018
$217$		−	1.08696e28i		−	0.997001i
$218$			4.50430e27i			0.390976i
$219$	−2.00668e28			−1.64873
$220$	−7.09463e27			−0.551897
$221$		−	9.53942e27i		−	0.702772i
$222$			5.01284e27i			0.349823i
$223$	−7.61982e27			−0.503833			−0.251916	−	0.967749i	$-0.581061\pi$
$223$	−7.61982e27			−0.503833			−0.251916	+	0.967749i	$0.581061\pi$
$224$		−	2.00459e28i		−	1.25617i
$225$	−1.97135e28			−1.17104
$226$			1.55963e28i			0.878455i
$227$			2.76857e28i			1.47892i	0.673199	+	0.739461i	$0.264920\pi$
$227$			2.76857e28i			1.47892i	−0.673199	+	0.739461i	$0.735080\pi$
$228$			9.76544e27i			0.494850i
$229$			3.30372e28i			1.58846i	0.607614	+	0.794232i	$0.292127\pi$
$229$			3.30372e28i			1.58846i	−0.607614	+	0.794232i	$0.707873\pi$
$230$	−3.74329e27	+	2.16107e28i	−0.170812	+	0.986130i
$231$	−2.12860e28			−0.922041
$232$	−3.87381e28			−1.59324
$233$	−1.69123e28			−0.660588			−0.330294	−	0.943878i	$-0.607148\pi$
$233$	−1.69123e28			−0.660588			−0.330294	+	0.943878i	$0.607148\pi$
$234$	1.01873e28			0.377980
$235$			1.63754e28i			0.577269i
$236$	−1.97972e27			−0.0663224
$237$		−	7.90698e28i		−	2.51786i
$238$	−2.17835e28			−0.659484
$239$	3.66645e28			1.05553			0.527766	−	0.849390i	$-0.323030\pi$
$239$	3.66645e28			1.05553			0.527766	+	0.849390i	$0.323030\pi$
$240$		−	5.47011e26i		−	0.0149783i
$241$			3.77303e28i			0.982846i	0.870921	+	0.491423i	$0.163523\pi$
$241$			3.77303e28i			0.982846i	−0.870921	+	0.491423i	$0.836477\pi$
$242$	1.72814e28			0.428346
$243$	−5.17618e28			−1.22105
$244$			1.47805e28i			0.331904i
$245$		−	4.41251e28i		−	0.943394i
$246$	2.28107e28			0.464428
$247$		−	2.62578e28i		−	0.509208i
$248$	−4.29580e28			−0.793641
$249$		−	9.50655e28i		−	1.67352i
$250$		−	3.58382e28i		−	0.601266i
$251$			8.27468e28i			1.32332i	0.749802	+	0.661662i	$0.230149\pi$
$251$			8.27468e28i			1.32332i	−0.749802	+	0.661662i	$0.769851\pi$
$252$			3.71404e28i			0.566291i
$253$	6.53330e27	−	3.77179e28i	0.0949918	−	0.548405i
$254$	6.79684e28			0.942546
$255$	1.35407e29			1.79126
$256$	−7.95681e28			−1.00429
$257$	−1.30943e29			−1.57719			−0.788596	−	0.614911i	$-0.789192\pi$
$257$	−1.30943e29			−1.57719			−0.788596	+	0.614911i	$0.789192\pi$
$258$			6.01621e28i			0.691650i
$259$	4.91404e28			0.539313
$260$		−	7.87846e28i		−	0.825584i
$261$	1.16217e29			1.16301
$262$	2.65152e28			0.253443
$263$			2.04693e29i			1.86910i	0.355828	+	0.934552i	$0.384199\pi$
$263$			2.04693e29i			1.86910i	−0.355828	+	0.934552i	$0.615801\pi$
$264$			8.41251e28i			0.733970i
$265$	−1.76807e29			−1.47418
$266$	−5.99604e28			−0.477843
$267$			1.18307e29i			0.901310i
$268$		−	3.87358e28i		−	0.282160i
$269$	2.27355e29			1.58371			0.791856	−	0.610708i	$-0.209115\pi$
$269$	2.27355e29			1.58371			0.791856	+	0.610708i	$0.209115\pi$
$270$		−	5.30645e28i		−	0.353540i
$271$	1.31621e29			0.838871			0.419435	−	0.907785i	$-0.362228\pi$
$271$	1.31621e29			0.838871			0.419435	+	0.907785i	$0.362228\pi$
$272$			9.77034e26i			0.00595776i
$273$		−	2.36377e29i		−	1.37928i
$274$		−	1.69158e29i		−	0.944682i
$275$			1.66665e29i			0.890946i
$276$	−1.55773e29	−	2.69822e28i	−0.797229	−	0.138092i
$277$	−2.41347e29			−1.18273			−0.591363	−	0.806405i	$-0.701410\pi$
$277$	−2.41347e29			−1.18273			−0.591363	+	0.806405i	$0.701410\pi$
$278$	2.00456e27			0.00940765
$279$	1.28877e29			0.579330
$280$	−4.72498e29			−2.03472
$281$		−	3.28290e29i		−	1.35451i	−0.735750	−	0.677254i	$-0.763170\pi$
$281$		−	3.28290e29i		−	1.35451i	0.735750	−	0.677254i	$-0.236830\pi$
$282$	7.39324e28			0.292311
$283$			2.54573e29i			0.964662i	0.875989	+	0.482331i	$0.160210\pi$
$283$			2.54573e29i			0.964662i	−0.875989	+	0.482331i	$0.839790\pi$
$284$	−1.93284e29			−0.702061
$285$	3.72716e29			1.29789
$286$		−	8.61271e28i		−	0.287572i
$287$		−	2.23611e29i		−	0.715996i
$288$	2.37679e29			0.729928
$289$	9.75942e28			0.287508
$290$			5.62952e29i			1.59109i
$291$		−	4.02390e29i		−	1.09127i
$292$	2.96013e29			0.770402
$293$			5.95188e29i			1.48677i	0.668866	+	0.743383i	$0.266780\pi$
$293$			5.95188e29i			1.48677i	−0.668866	+	0.743383i	$0.733220\pi$
$294$	−1.99218e29			−0.477706
$295$			7.55597e28i			0.173951i
$296$		−	1.94209e29i		−	0.429309i
$297$			9.26155e28i			0.196610i
$298$		−	5.33765e29i		−	1.08832i
$299$	4.18851e29	+	7.25511e28i	0.820361	+	0.142099i
$300$	6.88317e29			1.29519
$301$	5.89763e29			1.06630
$302$	−3.09684e29			−0.538065
$303$	1.39049e30			2.32198
$304$			2.68935e27i			0.00431682i
$305$	5.64127e29			0.870520
$306$		−	2.58280e29i		−	0.383208i
$307$	−7.02080e29			−1.00167			−0.500837	−	0.865542i	$-0.666974\pi$
$307$	−7.02080e29			−1.00167			−0.500837	+	0.865542i	$0.666974\pi$
$308$	3.13998e29			0.430842
$309$		−	5.86151e29i		−	0.773584i
$310$			6.24277e29i			0.792569i
$311$	−5.34746e29			−0.653164			−0.326582	−	0.945169i	$-0.605897\pi$
$311$	−5.34746e29			−0.653164			−0.326582	+	0.945169i	$0.605897\pi$
$312$	−9.34194e29			−1.09795
$313$			4.04750e29i			0.457778i	0.973453	+	0.228889i	$0.0735093\pi$
$313$			4.04750e29i			0.457778i	−0.973453	+	0.228889i	$0.926491\pi$
$314$		−	4.96023e29i		−	0.539940i
$315$	1.41753e30			1.48527
$316$			1.16639e30i			1.17652i
$317$	−1.39151e30			−1.35137			−0.675686	−	0.737189i	$-0.736153\pi$
$317$	−1.39151e30			−1.35137			−0.675686	+	0.737189i	$0.736153\pi$
$318$			7.98257e29i			0.746478i
$319$		−	9.82541e29i		−	0.884836i
$320$			1.16443e30i			1.00998i
$321$		−	2.49524e30i		−	2.08474i
$322$	1.65672e29	−	9.56456e29i	0.133346	−	0.769830i
$323$	−6.65719e29			−0.516251
$324$	9.84457e29			0.735625
$325$	−1.85078e30			−1.33277
$326$	−1.32793e30			−0.921643
$327$			1.23919e30i			0.829020i
$328$	−8.83742e29			−0.569953
$329$		−	7.24752e29i		−	0.450649i
$330$	1.22253e30			0.732979
$331$	−1.11503e29			−0.0644691			−0.0322345	−	0.999480i	$-0.510262\pi$
$331$	−1.11503e29			−0.0644691			−0.0322345	+	0.999480i	$0.510262\pi$
$332$			1.40235e30i			0.781986i
$333$			5.82643e29i			0.313380i
$334$	−6.09189e28			−0.0316078
$335$	−1.47842e30			−0.740050
$336$			2.42099e28i			0.0116929i
$337$		−	2.89378e30i		−	1.34867i	−0.738424	−	0.674337i	$-0.764430\pi$
$337$		−	2.89378e30i		−	1.34867i	0.738424	−	0.674337i	$-0.235570\pi$
$338$	−4.23330e29			−0.190405
$339$			4.29073e30i			1.86266i
$340$	−1.99744e30			−0.837003
$341$		−	1.08958e30i		−	0.440763i
$342$		−	7.10933e29i		−	0.277661i
$343$		−	1.38551e30i		−	0.522493i
$344$		−	2.33082e30i		−	0.848805i
$345$	−1.02982e30	+	5.94536e30i	−0.362188	+	2.09098i
$346$	−2.15986e30			−0.733688
$347$	−3.21652e30			−1.05544			−0.527719	−	0.849419i	$-0.676953\pi$
$347$	−3.21652e30			−1.05544			−0.527719	+	0.849419i	$0.676953\pi$
$348$	−4.05784e30			−1.28631
$349$	5.34785e30			1.63785			0.818925	−	0.573901i	$-0.194570\pi$
$349$	5.34785e30			1.63785			0.818925	+	0.573901i	$0.194570\pi$
$350$			4.22631e30i			1.25068i
$351$	−1.02848e30			−0.294110
$352$		−	2.00942e30i		−	0.555340i
$353$	−6.63138e29			−0.177136			−0.0885681	−	0.996070i	$-0.528229\pi$
$353$	−6.63138e29			−0.177136			−0.0885681	+	0.996070i	$0.528229\pi$
$354$	3.41140e29			0.0880833
$355$			7.37702e30i			1.84137i
$356$		−	1.74519e30i		−	0.421156i
$357$	−5.99291e30			−1.39836
$358$	3.32627e30			0.750518
$359$		−	3.45859e30i		−	0.754686i	−0.926074	−	0.377343i	$-0.876838\pi$
$359$		−	3.45859e30i		−	0.754686i	0.926074	−	0.377343i	$-0.123162\pi$
$360$		−	5.60227e30i		−	1.18232i
$361$	3.06633e30			0.625940
$362$		−	4.11934e30i		−	0.813439i
$363$	4.75433e30			0.908259
$364$			3.48689e30i			0.644498i
$365$		−	1.12979e31i		−	2.02061i
$366$		−	2.54694e30i		−	0.440805i
$367$			4.45532e30i			0.746253i	0.927780	+	0.373127i	$0.121714\pi$
$367$			4.45532e30i			0.746253i	−0.927780	+	0.373127i	$0.878286\pi$
$368$	−4.28990e28	−	7.43074e27i	−0.00695462	−	0.00120464i
$369$	2.65129e30			0.416046
$370$	−2.82230e30			−0.428729
$371$	7.82523e30			1.15083
$372$	−4.49989e30			−0.640747
$373$			1.27650e31i			1.76000i	0.474969	+	0.880002i	$0.342459\pi$
$373$			1.27650e31i			1.76000i	−0.474969	+	0.880002i	$0.657541\pi$
$374$	−2.18360e30			−0.291550
$375$		−	9.85954e30i		−	1.27492i
$376$	−2.86432e30			−0.358729
$377$	1.09109e31			1.32363
$378$			2.34856e30i			0.275994i
$379$			8.82933e30i			1.00521i	0.864516	+	0.502606i	$0.167625\pi$
$379$			8.82933e30i			1.00521i	−0.864516	+	0.502606i	$0.832375\pi$
$380$	−5.49808e30			−0.606468
$381$	1.86990e31			1.99856
$382$			1.36373e30i			0.141244i
$383$		−	8.17359e30i		−	0.820404i	−0.911995	−	0.410202i	$-0.865458\pi$
$383$		−	8.17359e30i		−	0.820404i	0.911995	−	0.410202i	$-0.134542\pi$
$384$	−8.23955e30			−0.801547
$385$		−	1.19843e31i		−	1.13002i
$386$	−4.57383e30			−0.418054
$387$			6.99264e30i			0.619598i
$388$			5.93581e30i			0.509917i
$389$			6.50131e30i			0.541509i	0.962648	+	0.270754i	$0.0872731\pi$
$389$			6.50131e30i			0.541509i	−0.962648	+	0.270754i	$0.912727\pi$
$390$			1.35760e31i			1.09647i
$391$	1.83940e30	−	1.06192e31i	0.144064	−	0.831708i
$392$	7.71817e30			0.586249
$393$	7.29467e30			0.537397
$394$	4.76681e30			0.340623
$395$	4.45174e31			3.08578
$396$			3.72298e30i			0.250351i
$397$	−1.55425e31			−1.01399			−0.506996	−	0.861948i	$-0.669244\pi$
$397$	−1.55425e31			−1.01399			−0.506996	+	0.861948i	$0.669244\pi$
$398$		−	1.38988e30i		−	0.0879790i
$399$	−1.64959e31			−1.01321
$400$	1.89559e29			0.0112986
$401$			1.53590e30i			0.0888445i	0.999013	+	0.0444223i	$0.0141447\pi$
$401$			1.53590e30i			0.0888445i	−0.999013	+	0.0444223i	$0.985855\pi$
$402$			6.67485e30i			0.374739i
$403$	1.20995e31			0.659338
$404$	−2.05117e31			−1.08499
$405$		−	3.75736e31i		−	1.92940i
$406$		−	2.49154e31i		−	1.24210i
$407$	4.92587e30			0.238424
$408$			2.36848e31i			1.11313i
$409$	−2.47264e31			−1.12845			−0.564223	−	0.825623i	$-0.690824\pi$
$409$	−2.47264e31			−1.12845			−0.564223	+	0.825623i	$0.690824\pi$
$410$			1.28428e31i			0.569184i
$411$		−	4.65375e31i		−	2.00309i
$412$			8.64654e30i			0.361473i
$413$		−	3.34416e30i		−	0.135796i
$414$	1.13404e31	+	1.96433e30i	0.447327	+	0.0774836i
$415$	5.35232e31			2.05100
$416$	2.23143e31			0.830735
$417$	5.51479e29			0.0199479
$418$	−6.01048e30			−0.211249
$419$			2.49482e30i			0.0852061i	0.999092	+	0.0426031i	$0.0135651\pi$
$419$			2.49482e30i			0.0852061i	−0.999092	+	0.0426031i	$0.986435\pi$
$420$	−4.94946e31			−1.64273
$421$			2.74504e30i			0.0885449i	0.999019	+	0.0442725i	$0.0140970\pi$
$421$			2.74504e30i			0.0885449i	−0.999019	+	0.0442725i	$0.985903\pi$
$422$	2.07781e31			0.651414
$423$	8.59317e30			0.261860
$424$		−	3.09263e31i		−	0.916090i
$425$			4.69232e31i			1.35120i
$426$	3.33061e31			0.932413
$427$	−2.49674e31			−0.679578
$428$			3.68083e31i			0.974138i
$429$		−	2.36946e31i		−	0.609765i
$430$	−3.38721e31			−0.847659
$431$			4.06630e31i			0.989627i	0.868999	+	0.494814i	$0.164764\pi$
$431$			4.06630e31i			0.989627i	−0.868999	+	0.494814i	$0.835236\pi$
$432$	1.05338e29			0.00249332
$433$			3.01559e31i			0.694253i	0.937818	+	0.347126i	$0.112843\pi$
$433$			3.01559e31i			0.694253i	−0.937818	+	0.347126i	$0.887157\pi$
$434$		−	2.76296e31i		−	0.618725i
$435$			1.54875e32i			3.37373i
$436$		−	1.82798e31i		−	0.387376i
$437$	5.06307e30	−	2.92300e31i	0.104385	−	0.602631i
$438$	−5.10082e31			−1.02318
$439$	−5.10820e31			−0.996997			−0.498499	−	0.866891i	$-0.666115\pi$
$439$	−5.10820e31			−0.996997			−0.498499	+	0.866891i	$0.666115\pi$
$440$	−4.73636e31			−0.899524
$441$	−2.31551e31			−0.427941
$442$		−	2.42484e31i		−	0.436131i
$443$	−4.41029e30			−0.0772010			−0.0386005	−	0.999255i	$-0.512290\pi$
$443$	−4.41029e30			−0.0772010			−0.0386005	+	0.999255i	$0.512290\pi$
$444$		−	2.03436e31i		−	0.346603i
$445$	−6.66084e31			−1.10461
$446$	−1.93690e31			−0.312671
$447$		−	1.46845e32i		−	2.30765i
$448$		−	5.15360e31i		−	0.788450i
$449$	−5.99267e31			−0.892616			−0.446308	−	0.894879i	$-0.647261\pi$
$449$	−5.99267e31			−0.892616			−0.446308	+	0.894879i	$0.647261\pi$
$450$	−5.01101e31			−0.726733
$451$		−	2.24150e31i		−	0.316534i
$452$		−	6.32942e31i		−	0.870368i
$453$	−8.51979e31			−1.14091
$454$			7.03748e31i			0.917798i
$455$	1.33084e32			1.69039
$456$			6.51938e31i			0.806545i
$457$		−	5.88611e31i		−	0.709307i	−0.934998	−	0.354653i	$-0.884599\pi$
$457$		−	5.88611e31i		−	0.709307i	0.934998	−	0.354653i	$-0.115401\pi$
$458$			8.39779e31i			0.985779i
$459$			2.60752e31i			0.298178i
$460$	1.51913e31	−	8.77024e31i	0.169240	−	0.977052i
$461$	1.33008e32			1.44367			0.721833	−	0.692068i	$-0.243300\pi$
$461$	1.33008e32			1.44367			0.721833	+	0.692068i	$0.243300\pi$
$462$	−5.41073e31			−0.572205
$463$	1.03421e32			1.06570			0.532852	−	0.846208i	$-0.321120\pi$
$463$	1.03421e32			1.06570			0.532852	+	0.846208i	$0.321120\pi$
$464$	−1.11751e30			−0.0112211
$465$			1.71746e32i			1.68055i
$466$	−4.29896e31			−0.409952
$467$			9.99569e31i			0.928988i	0.885576	+	0.464494i	$0.153764\pi$
$467$			9.99569e31i			0.928988i	−0.885576	+	0.464494i	$0.846236\pi$
$468$	−4.13430e31			−0.374500
$469$	6.54328e31			0.577726
$470$			4.16250e31i			0.358245i
$471$		−	1.36462e32i		−	1.14488i
$472$	−1.32166e31			−0.108097
$473$	5.91183e31			0.471399
$474$		−	2.00989e32i		−	1.56255i
$475$			1.29159e32i			0.979042i
$476$	8.84038e31			0.653412
$477$			9.27814e31i			0.668714i
$478$	9.31983e31			0.655048
$479$		−	1.49113e32i		−	1.02209i	−0.859553	−	0.511046i	$-0.829258\pi$
$479$		−	1.49113e32i		−	1.02209i	0.859553	−	0.511046i	$-0.170742\pi$
$480$			3.16739e32i			2.11742i
$481$			5.47009e31i			0.356659i
$482$			9.59074e31i			0.609941i
$483$	4.55785e31	−	2.63133e32i	0.282745	−	1.63234i
$484$	−7.01330e31			−0.424403
$485$	2.26551e32			1.33741
$486$	−1.31574e32			−0.757767
$487$	−1.37978e32			−0.775285			−0.387643	−	0.921810i	$-0.626711\pi$
$487$	−1.37978e32			−0.775285			−0.387643	+	0.921810i	$0.626711\pi$
$488$			9.86746e31i			0.540963i
$489$	−3.65329e32			−1.95424
$490$		−	1.12163e32i		−	0.585457i
$491$	1.81487e32			0.924419			0.462209	−	0.886771i	$-0.347057\pi$
$491$	1.81487e32			0.924419			0.462209	+	0.886771i	$0.347057\pi$
$492$	−9.25727e31			−0.460152
$493$		−	2.76627e32i		−	1.34194i
$494$		−	6.67453e31i		−	0.316007i
$495$	1.42094e32			0.656621
$496$	−1.23924e30			−0.00558955
$497$		−	3.26496e32i		−	1.43748i
$498$		−	2.41649e32i		−	1.03856i
$499$	3.45332e32			1.44887			0.724437	−	0.689341i	$-0.242100\pi$
$499$	3.45332e32			1.44887			0.724437	+	0.689341i	$0.242100\pi$
$500$			1.45442e32i			0.595730i
$501$	−1.67596e31			−0.0670208
$502$			2.10336e32i			0.821237i
$503$		−	5.08675e32i		−	1.93921i	−0.244676	−	0.969605i	$-0.578682\pi$
$503$		−	5.08675e32i		−	1.93921i	0.244676	−	0.969605i	$-0.421318\pi$
$504$			2.47948e32i			0.922985i
$505$			7.82868e32i			2.84572i
$506$	1.66071e31	−	9.58760e31i	0.0589506	−	0.340333i
$507$	−1.16463e32			−0.403733
$508$	−2.75836e32			−0.933869
$509$	8.52710e31			0.281960			0.140980	−	0.990012i	$-0.454975\pi$
$509$	8.52710e31			0.281960			0.140980	+	0.990012i	$0.454975\pi$
$510$	3.44194e32			1.11163
$511$			5.00028e32i			1.57741i
$512$	−4.58092e30			−0.0141160
$513$			7.17736e31i			0.216051i
$514$	−3.32847e32			−0.978784
$515$	3.30011e32			0.948074
$516$		−	2.44155e32i		−	0.685283i
$517$		−	7.26497e31i		−	0.199227i
$518$	1.24911e32			0.334690
$519$	−5.94203e32			−1.55570
$520$		−	5.25965e32i		−	1.34560i
$521$		−	6.19733e32i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$521$		−	6.19733e32i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$522$	2.95415e32			0.721749
$523$		−	3.84882e32i		−	0.918983i	−0.888182	−	0.459491i	$-0.848032\pi$
$523$		−	3.84882e32i		−	0.918983i	0.888182	−	0.459491i	$-0.151968\pi$
$524$	−1.07607e32			−0.251110
$525$			1.16271e33i			2.65192i
$526$			5.20312e32i			1.15994i
$527$		−	3.06762e32i		−	0.668457i
$528$			2.42682e30i			0.00516929i
$529$	4.52272e32	+	1.61527e32i	0.941741	+	0.336338i
$530$	−4.49430e32			−0.914853
$531$	3.96507e31			0.0789072
$532$	2.43337e32			0.473444
$533$	2.48914e32			0.473504
$534$			3.00726e32i			0.559340i
$535$	1.40486e33			2.55497
$536$		−	2.58599e32i		−	0.459886i
$537$	9.15098e32			1.59139
$538$	5.77917e32			0.982830
$539$			1.95762e32i			0.325583i
$540$			2.15351e32i			0.350286i
$541$	−3.09149e32			−0.491813			−0.245907	−	0.969294i	$-0.579086\pi$
$541$	−3.09149e32			−0.491813			−0.245907	+	0.969294i	$0.579086\pi$
$542$	3.34571e32			0.520592
$543$		−	1.13328e33i		−	1.72481i
$544$		−	5.65737e32i		−	0.842225i
$545$	−6.97682e32			−1.01601
$546$		−	6.00852e32i		−	0.855964i
$547$	1.06440e33			1.48339			0.741697	−	0.670735i	$-0.234021\pi$
$547$	1.06440e33			1.48339			0.741697	+	0.670735i	$0.234021\pi$
$548$			6.86493e32i			0.935985i
$549$		−	2.96031e32i		−	0.394884i
$550$			4.23649e32i			0.552909i
$551$		−	7.61433e32i		−	0.972328i
$552$	−1.03994e33	−	1.80132e32i	−1.29939	−	0.225073i
$553$	−1.97028e33			−2.40894
$554$	−6.13484e32			−0.733983
$555$	−7.76450e32			−0.909071
$556$	−8.13508e30			−0.00932104
$557$			7.14655e32i			0.801371i	0.916216	+	0.400686i	$0.131228\pi$
$557$			7.14655e32i			0.801371i	−0.916216	+	0.400686i	$0.868772\pi$
$558$	3.27596e32			0.359524
$559$			6.56498e32i			0.705167i
$560$	−1.36305e31			−0.0143303
$561$	−6.00734e32			−0.618199
$562$		−	8.34486e32i		−	0.840588i
$563$			5.05716e31i			0.0498662i	0.999689	+	0.0249331i	$0.00793727\pi$
$563$			5.05716e31i			0.0498662i	−0.999689	+	0.0249331i	$0.992063\pi$
$564$	−3.00039e32			−0.289620
$565$	−2.41574e33			−2.28281
$566$			6.47104e32i			0.598656i
$567$			1.66295e33i			1.50620i
$568$	−1.29036e33			−1.14427
$569$			1.29822e33i			1.12720i	0.826046	+	0.563602i	$0.190585\pi$
$569$			1.29822e33i			1.12720i	−0.826046	+	0.563602i	$0.809415\pi$
$570$	9.47414e32			0.805455
$571$			3.51345e32i			0.292483i	0.989249	+	0.146241i	$0.0467176\pi$
$571$			3.51345e32i			0.292483i	−0.989249	+	0.146241i	$0.953282\pi$
$572$			3.49529e32i			0.284925i
$573$			3.75180e32i			0.299491i
$574$		−	5.68402e32i		−	0.444337i
$575$	−2.06028e33	−	3.56870e32i	−1.57729	−	0.273210i
$576$	6.11047e32			0.458147
$577$	−6.61462e32			−0.485730			−0.242865	−	0.970060i	$-0.578087\pi$
$577$	−6.61462e32			−0.485730			−0.242865	+	0.970060i	$0.578087\pi$
$578$	2.48077e32			0.178423
$579$	−1.25832e33			−0.886437
$580$		−	2.28462e33i		−	1.57644i
$581$	−2.36886e33			−1.60113
$582$		−	1.02284e33i		−	0.677225i
$583$	7.84407e32			0.508767
$584$	1.97618e33			1.25566
$585$			1.57793e33i			0.982241i
$586$			1.51292e33i			0.922666i
$587$	−4.14432e32			−0.247626			−0.123813	−	0.992306i	$-0.539512\pi$
$587$	−4.14432e32			−0.247626			−0.123813	+	0.992306i	$0.539512\pi$
$588$	8.08485e32			0.473308
$589$		−	8.44380e32i		−	0.484345i
$590$			1.92067e32i			0.107951i
$591$	1.31141e33			0.722252
$592$		−	5.60251e30i		−	0.00302358i
$593$	−2.03259e33			−1.07496			−0.537480	−	0.843276i	$-0.680624\pi$
$593$	−2.03259e33			−1.07496			−0.537480	+	0.843276i	$0.680624\pi$
$594$			2.35421e32i			0.122014i
$595$		−	3.37409e33i		−	1.71377i
$596$			2.16618e33i			1.07830i
$597$		−	3.82372e32i		−	0.186550i
$598$	1.06469e33	+	1.84419e32i	0.509105	+	0.0881844i
$599$	−1.34782e33			−0.631701			−0.315851	−	0.948809i	$-0.602290\pi$
$599$	−1.34782e33			−0.631701			−0.315851	+	0.948809i	$0.602290\pi$
$600$	4.59519e33			2.11100
$601$	−1.60546e33			−0.722947			−0.361474	−	0.932382i	$-0.617726\pi$
$601$	−1.60546e33			−0.722947			−0.361474	+	0.932382i	$0.617726\pi$
$602$	1.49913e33			0.661731
$603$			7.75818e32i			0.335700i
$604$	1.25679e33			0.533112
$605$			2.67676e33i			1.11313i
$606$	3.53452e33			1.44099
$607$	1.42779e33			0.570689			0.285344	−	0.958425i	$-0.407892\pi$
$607$	1.42779e33			0.570689			0.285344	+	0.958425i	$0.407892\pi$
$608$		−	1.55723e33i		−	0.610252i
$609$		−	6.85454e33i		−	2.63373i
$610$	1.43396e33			0.540232
$611$	8.06762e32			0.298024
$612$			1.04818e33i			0.379680i
$613$			5.89613e32i			0.209431i	0.994502	+	0.104716i	$0.0333932\pi$
$613$			5.89613e32i			0.209431i	−0.994502	+	0.104716i	$0.966607\pi$
$614$	−1.78463e33			−0.621625
$615$			3.53321e33i			1.20689i
$616$	2.09624e33			0.702220
$617$		−	5.32793e33i		−	1.75040i	−0.483764	−	0.875198i	$-0.660731\pi$
$617$		−	5.32793e33i		−	1.75040i	0.483764	−	0.875198i	$-0.339269\pi$
$618$		−	1.48995e33i		−	0.480076i
$619$			2.25769e32i			0.0713472i	0.999363	+	0.0356736i	$0.0113577\pi$
$619$			2.25769e32i			0.0713472i	−0.999363	+	0.0356736i	$0.988642\pi$
$620$		−	2.53350e33i		−	0.785273i
$621$	−1.14489e33	−	1.98312e32i	−0.348070	−	0.0602908i
$622$	−1.35928e33			−0.405345
$623$	2.94799e33			0.862321
$624$	−2.69494e31			−0.00773276
$625$	−1.36039e32			−0.0382914
$626$			1.02884e33i			0.284091i
$627$	−1.65356e33			−0.447929
$628$			2.01301e33i			0.534970i
$629$	1.38684e33			0.361592
$630$	3.60325e33			0.921738
$631$			5.19609e33i			1.30414i	0.758159	+	0.652070i	$0.226099\pi$
$631$			5.19609e33i			1.30414i	−0.758159	+	0.652070i	$0.773901\pi$
$632$			7.78680e33i			1.91758i
$633$	5.71633e33			1.38125
$634$	−3.53711e33			−0.838643
$635$			1.05278e34i			2.44936i
$636$		−	3.23956e33i		−	0.739606i
$637$	−2.17390e33			−0.487041
$638$		−	2.49754e33i		−	0.549117i
$639$	3.87117e33			0.835279
$640$		−	4.63898e33i		−	0.982343i
$641$		−	4.86886e33i		−	1.01188i	−0.862567	−	0.505942i	$-0.831145\pi$
$641$		−	4.86886e33i		−	1.01188i	0.862567	−	0.505942i	$-0.168855\pi$
$642$		−	6.34270e33i		−	1.29376i
$643$			7.79323e32i			0.156022i	0.996952	+	0.0780110i	$0.0248569\pi$
$643$			7.79323e32i			0.156022i	−0.996952	+	0.0780110i	$0.975143\pi$
$644$	−6.72347e32	+	3.88158e33i	−0.132118	+	0.762743i
$645$	−9.31864e33			−1.79736
$646$	−1.69221e33			−0.320378
$647$	5.61019e33			1.04262			0.521310	−	0.853367i	$-0.325443\pi$
$647$	5.61019e33			1.04262			0.521310	+	0.853367i	$0.325443\pi$
$648$	6.57221e33			1.19898
$649$		−	3.35222e32i		−	0.0600338i
$650$	−4.70454e33			−0.827098
$651$		−	7.60124e33i		−	1.31194i
$652$	5.38911e33			0.913159
$653$	−1.33164e33			−0.221528			−0.110764	−	0.993847i	$-0.535330\pi$
$653$	−1.33164e33			−0.221528			−0.110764	+	0.993847i	$0.535330\pi$
$654$			3.14992e33i			0.514478i
$655$			4.10700e33i			0.658612i
$656$	−2.54940e31			−0.00401413
$657$	−5.92869e33			−0.916588
$658$		−	1.84226e33i		−	0.279667i
$659$		−	1.91061e33i		−	0.284805i	−0.989809	−	0.142402i	$-0.954517\pi$
$659$		−	1.91061e33i		−	0.284805i	0.989809	−	0.142402i	$-0.0454827\pi$
$660$	−4.96138e33			−0.726231
$661$		−	1.95955e33i		−	0.281669i	−0.990033	−	0.140835i	$-0.955021\pi$
$661$		−	1.95955e33i		−	0.281669i	0.990033	−	0.140835i	$-0.0449786\pi$
$662$	−2.83432e32			−0.0400086
$663$		−	6.67105e33i		−	0.924766i
$664$			9.36205e33i			1.27454i
$665$		−	9.28740e33i		−	1.24175i
$666$			1.48103e33i			0.194479i
$667$	1.21460e34	+	2.10386e33i	1.56647	+	0.271336i
$668$	2.47227e32			0.0313168
$669$	−5.32865e33			−0.662985
$670$	−3.75803e33			−0.459265
$671$	−2.50275e33			−0.300433
$672$		−	1.40184e34i		−	1.65298i
$673$	3.67103e33			0.425213			0.212607	−	0.977138i	$-0.431805\pi$
$673$	3.67103e33			0.425213			0.212607	+	0.977138i	$0.431805\pi$
$674$		−	7.35576e33i		−	0.836968i
$675$	5.05896e33			0.565478
$676$	1.71800e33			0.188653
$677$			3.61652e33i			0.390146i	0.980789	+	0.195073i	$0.0624943\pi$
$677$			3.61652e33i			0.390146i	−0.980789	+	0.195073i	$0.937506\pi$
$678$			1.09067e34i			1.15594i
$679$	−1.00268e34			−1.04406
$680$	−1.33349e34			−1.36421
$681$			1.93610e34i			1.94609i
$682$		−	2.76961e33i		−	0.273531i
$683$	−1.41895e34			−1.37695			−0.688477	−	0.725259i	$-0.741720\pi$
$683$	−1.41895e34			−1.37695			−0.688477	+	0.725259i	$0.741720\pi$
$684$			2.88517e33i			0.275105i
$685$	2.62013e34			2.45491
$686$		−	3.52186e33i		−	0.324252i
$687$			2.31034e34i			2.09023i
$688$		−	6.72390e31i		−	0.00597806i
$689$			8.71070e33i			0.761066i
$690$	−2.61773e33	+	1.51126e34i	−0.224769	+	1.29763i
$691$	1.53752e33			0.129743			0.0648716	−	0.997894i	$-0.479336\pi$
$691$	1.53752e33			0.129743			0.0648716	+	0.997894i	$0.479336\pi$
$692$	8.76533e33			0.726934
$693$	−6.28889e33			−0.512596
$694$	−8.17615e33			−0.654991
$695$			3.10490e32i			0.0244473i
$696$	−2.70901e34			−2.09652
$697$		−	6.31077e33i		−	0.480053i
$698$	1.35938e34			1.01643
$699$	−1.18270e34			−0.869256
$700$		−	1.71516e34i		−	1.23916i
$701$		−	2.01123e34i		−	1.42839i	−0.699947	−	0.714195i	$-0.746793\pi$
$701$		−	2.01123e34i		−	1.42839i	0.699947	−	0.714195i	$-0.253207\pi$
$702$	−2.61431e33			−0.182521
$703$	3.81737e33			0.261999
$704$		−	5.16601e33i		−	0.348565i
$705$			1.14516e34i			0.759618i
$706$	−1.68564e33			−0.109928
$707$		−	3.46486e34i		−	2.22153i
$708$	−1.38445e33			−0.0872725
$709$			1.17767e33i			0.0729908i	0.999334	+	0.0364954i	$0.0116194\pi$
$709$			1.17767e33i			0.0729908i	−0.999334	+	0.0364954i	$0.988381\pi$
$710$			1.87518e34i			1.14273i
$711$		−	2.33610e34i		−	1.39977i
$712$		−	1.16508e34i		−	0.686432i
$713$	1.34691e34	+	2.33305e33i	0.780305	+	0.135160i
$714$	−1.52335e34			−0.867803
$715$	1.33404e34			0.747303
$716$	−1.34990e34			−0.743609
$717$	2.56400e34			1.38896
$718$		−	8.79147e33i		−	0.468347i
$719$	−3.45260e34			−1.80884			−0.904419	−	0.426645i	$-0.859696\pi$
$719$	−3.45260e34			−1.80884			−0.904419	+	0.426645i	$0.859696\pi$
$720$		−	1.61613e32i		−	0.00832696i
$721$	−1.46058e34			−0.740121
$722$	7.79437e33			0.388449
$723$			2.63853e34i			1.29331i
$724$			1.67175e34i			0.805951i
$725$	−5.36696e34			−2.54491
$726$	1.20851e34			0.563653
$727$			4.15565e34i			1.90645i	0.302261	+	0.953225i	$0.402259\pi$
$727$			4.15565e34i			1.90645i	−0.302261	+	0.953225i	$0.597741\pi$
$728$			2.32784e34i			1.05045i
$729$	−9.24506e33			−0.410374
$730$		−	2.87184e34i		−	1.25396i
$731$	1.66443e34			0.714920
$732$			1.03362e34i			0.436747i
$733$		−	1.68928e34i		−	0.702189i	−0.936340	−	0.351095i	$-0.885810\pi$
$733$		−	1.68928e34i		−	0.702189i	0.936340	−	0.351095i	$-0.114190\pi$
$734$			1.13251e34i			0.463114i
$735$		−	3.08573e34i		−	1.24140i
$736$	2.48401e34	+	4.30266e33i	0.983148	+	0.170296i
$737$	6.55904e33			0.255406
$738$	6.73937e33			0.258192
$739$	2.35594e34			0.888037			0.444019	−	0.896018i	$-0.353552\pi$
$739$	2.35594e34			0.888037			0.444019	+	0.896018i	$0.353552\pi$
$740$	1.14537e34			0.424782
$741$		−	1.83625e34i		−	0.670058i
$742$	1.98911e34			0.714187
$743$			1.80673e34i			0.638303i	0.947704	+	0.319152i	$0.103398\pi$
$743$			1.80673e34i			0.638303i	−0.947704	+	0.319152i	$0.896602\pi$
$744$	−3.00411e34			−1.04434
$745$	8.26761e34			2.82816
$746$			3.24475e34i			1.09223i
$747$		−	2.80868e34i		−	0.930370i
$748$	8.86167e33			0.288866
$749$	−6.21768e34			−1.99456
$750$		−	2.50622e34i		−	0.791195i
$751$			4.06101e34i			1.26170i	0.775906	+	0.630848i	$0.217293\pi$
$751$			4.06101e34i			1.26170i	−0.775906	+	0.630848i	$0.782707\pi$
$752$	−8.26292e31			−0.00252650
$753$			5.78660e34i			1.74134i
$754$	2.77348e34			0.821426
$755$		−	4.79676e34i		−	1.39825i
$756$		−	9.53113e33i		−	0.273453i
$757$		−	2.01142e34i		−	0.568005i	−0.958824	−	0.284003i	$-0.908338\pi$
$757$		−	2.01142e34i		−	0.568005i	0.958824	−	0.284003i	$-0.0916624\pi$
$758$			2.24435e34i			0.623820i
$759$	4.56883e33	−	2.63767e34i	0.124998	−	0.721637i
$760$	−3.67051e34			−0.988468
$761$	5.35041e34			1.41831			0.709155	−	0.705052i	$-0.249077\pi$
$761$	5.35041e34			1.41831			0.709155	+	0.705052i	$0.249077\pi$
$762$	4.75313e34			1.24028
$763$	3.08784e34			0.793158
$764$		−	5.53443e33i		−	0.139943i
$765$	4.00056e34			0.995827
$766$		−	2.07766e34i		−	0.509131i
$767$	3.72257e33			0.0898047
$768$	−5.56431e34			−1.32153
$769$		−	4.62225e33i		−	0.108078i	−0.998539	−	0.0540390i	$-0.982790\pi$
$769$		−	4.62225e33i		−	0.108078i	0.998539	−	0.0540390i	$-0.0172095\pi$
$770$		−	3.04632e34i		−	0.701272i
$771$	−9.15703e34			−2.07540
$772$	1.85620e34			0.414206
$773$		−	4.14954e34i		−	0.911688i	−0.890060	−	0.455844i	$-0.849338\pi$
$773$		−	4.14954e34i		−	0.911688i	0.890060	−	0.455844i	$-0.150662\pi$
$774$			1.77747e34i			0.384514i
$775$	−5.95162e34			−1.26769
$776$			3.96273e34i			0.831102i
$777$	3.43645e34			0.709673
$778$			1.65258e34i			0.336053i
$779$		−	1.73708e34i		−	0.347832i
$780$		−	5.50952e34i		−	1.08637i
$781$		−	3.27282e34i		−	0.635492i
$782$	4.67561e33	−	2.69932e34i	0.0894041	−	0.516146i
$783$	−2.98242e34			−0.561600
$784$	2.22652e32			0.00412890
$785$	7.68301e34			1.40312
$786$	1.85425e34			0.333501
$787$		−	1.61464e34i		−	0.286008i	−0.989722	−	0.143004i	$-0.954324\pi$
$787$		−	1.61464e34i		−	0.286008i	0.989722	−	0.143004i	$-0.0456762\pi$
$788$	−1.93451e34			−0.337487
$789$			1.43144e35i			2.45952i
$790$	1.13160e35			1.91499
$791$	1.06917e35			1.78209
$792$			2.48545e34i			0.408041i
$793$		−	2.77926e34i		−	0.449419i
$794$	−3.95078e34			−0.629269
$795$	−1.23644e35			−1.93984
$796$			5.64052e33i			0.0871691i
$797$			1.17547e35i			1.78941i	0.446655	+	0.894706i	$0.352615\pi$
$797$			1.17547e35i			1.78941i	−0.446655	+	0.894706i	$0.647385\pi$
$798$	−4.19311e34			−0.628785
$799$		−	2.04540e34i		−	0.302146i
$800$	−1.09761e35			−1.59723
$801$			3.49534e34i			0.501071i
$802$			3.90414e33i			0.0551357i
$803$			5.01233e34i			0.697353i
$804$		−	2.70885e34i		−	0.371289i
$805$	1.48148e35	+	2.56613e34i	2.00053	+	0.346520i
$806$	3.07561e34			0.409176
$807$	1.58992e35			2.08398
$808$	−1.36936e35			−1.76840
$809$	−1.03496e35			−1.31686			−0.658431	−	0.752641i	$-0.728780\pi$
$809$	−1.03496e35			−1.31686			−0.658431	+	0.752641i	$0.728780\pi$
$810$		−	9.55092e34i		−	1.19736i
$811$	−4.75680e34			−0.587576			−0.293788	−	0.955871i	$-0.594916\pi$
$811$	−4.75680e34			−0.587576			−0.293788	+	0.955871i	$0.594916\pi$
$812$			1.01114e35i			1.23066i
$813$	9.20447e34			1.10386
$814$	1.25212e34			0.147963
$815$		−	2.05685e35i		−	2.39504i
$816$			6.83254e32i			0.00783971i
$817$	4.58145e34			0.518010
$818$	−6.28524e34			−0.700297
$819$		−	6.98370e34i		−	0.766794i
$820$		−	5.21197e34i		−	0.563944i
$821$	−8.46205e34			−0.902314			−0.451157	−	0.892445i	$-0.648988\pi$
$821$	−8.46205e34			−0.902314			−0.451157	+	0.892445i	$0.648988\pi$
$822$		−	1.18295e35i		−	1.24309i
$823$	1.61285e34			0.167031			0.0835154	−	0.996506i	$-0.473385\pi$
$823$	1.61285e34			0.167031			0.0835154	+	0.996506i	$0.473385\pi$
$824$			5.77241e34i			0.589157i
$825$			1.16551e35i			1.17238i
$826$		−	8.50059e33i		−	0.0842730i
$827$			1.06505e35i			1.04064i	0.853970	+	0.520322i	$0.174188\pi$
$827$			1.06505e35i			1.04064i	−0.853970	+	0.520322i	$0.825812\pi$
$828$	−4.60227e34	−	7.97181e33i	−0.443209	−	0.0767703i
$829$	−9.14234e34			−0.867766			−0.433883	−	0.900969i	$-0.642857\pi$
$829$	−9.14234e34			−0.867766			−0.433883	+	0.900969i	$0.642857\pi$
$830$	1.36052e35			1.27282
$831$	−1.68777e35			−1.55633
$832$	5.73676e34			0.521419
$833$			5.51152e34i			0.493778i
$834$	1.40182e33			0.0123794
$835$		−	9.43587e33i		−	0.0821380i
$836$	2.43923e34			0.209304
$837$	−3.30731e34			−0.279749
$838$			6.34163e33i			0.0528777i
$839$			4.49497e34i			0.369473i	0.982788	+	0.184737i	$0.0591432\pi$
$839$			4.49497e34i			0.369473i	−0.982788	+	0.184737i	$0.940857\pi$
$840$	−3.30425e35			−2.67745
$841$	1.91214e35			1.52746
$842$			6.97768e33i			0.0549497i
$843$		−	2.29577e35i		−	1.78237i
$844$	−8.43238e34			−0.645418
$845$		−	6.55706e34i		−	0.494799i
$846$	2.18431e34			0.162507
$847$		−	1.18469e35i		−	0.868970i
$848$		−	8.92156e32i		−	0.00645195i
$849$			1.78026e35i			1.26938i
$850$			1.19275e35i			0.838538i
$851$	−1.05475e34	+	6.08926e34i	−0.0731130	+	0.422095i
$852$	−1.35166e35			−0.923830
$853$	8.90497e34			0.600128			0.300064	−	0.953919i	$-0.402992\pi$
$853$	8.90497e34			0.600128			0.300064	+	0.953919i	$0.402992\pi$
$854$	−6.34652e34			−0.421736
$855$	1.10118e35			0.721547
$856$			2.45731e35i			1.58772i
$857$	−5.24238e34			−0.334009			−0.167005	−	0.985956i	$-0.553409\pi$
$857$	−5.24238e34			−0.334009			−0.167005	+	0.985956i	$0.553409\pi$
$858$		−	6.02299e34i		−	0.378412i
$859$	5.73350e34			0.355224			0.177612	−	0.984101i	$-0.443163\pi$
$859$	5.73350e34			0.355224			0.177612	+	0.984101i	$0.443163\pi$
$860$	1.37463e35			0.839855
$861$		−	1.56374e35i		−	0.942167i
$862$			1.03362e35i			0.614149i
$863$	−1.78496e35			−1.04592			−0.522961	−	0.852357i	$-0.675173\pi$
$863$	−1.78496e35			−1.04592			−0.522961	+	0.852357i	$0.675173\pi$
$864$	−6.09942e34			−0.352471
$865$		−	3.34545e35i		−	1.90661i
$866$			7.66539e34i			0.430844i
$867$	6.82490e34			0.378327
$868$			1.12129e35i			0.613029i
$869$	−1.97502e35			−1.06496
$870$			3.93680e35i			2.09369i
$871$			7.28370e34i			0.382062i
$872$		−	1.22035e35i		−	0.631376i
$873$		−	1.18885e35i		−	0.606675i
$874$	1.28699e34	−	7.43003e34i	0.0647796	−	0.373984i
$875$	−2.45682e35			−1.21977
$876$	2.07006e35			1.01376
$877$	1.39024e35			0.671575			0.335788	−	0.941938i	$-0.390998\pi$
$877$	1.39024e35			0.671575			0.335788	+	0.941938i	$0.390998\pi$
$878$	−1.29846e35			−0.618722
$879$			4.16223e35i			1.95641i
$880$	−1.36634e33			−0.00633527
$881$		−	3.77161e35i		−	1.72511i	−0.505964	−	0.862554i	$-0.668863\pi$
$881$		−	3.77161e35i		−	1.72511i	0.505964	−	0.862554i	$-0.331137\pi$
$882$	−5.88584e34			−0.265574
$883$	−2.90854e35			−1.29463			−0.647317	−	0.762221i	$-0.724109\pi$
$883$	−2.90854e35			−1.29463			−0.647317	+	0.762221i	$0.724109\pi$
$884$			9.84073e34i			0.432116i
$885$			5.28400e34i			0.228899i
$886$	−1.12106e34			−0.0479098
$887$	−1.71434e35			−0.722791			−0.361396	−	0.932413i	$-0.617700\pi$
$887$	−1.71434e35			−0.722791			−0.361396	+	0.932413i	$0.617700\pi$
$888$		−	1.35813e35i		−	0.564920i
$889$		−	4.65944e35i		−	1.91211i
$890$	−1.69313e35			−0.685505
$891$			1.66696e35i			0.665874i
$892$	7.86050e34			0.309793
$893$		−	5.63008e34i		−	0.218926i
$894$		−	3.73269e35i		−	1.43210i
$895$			5.15213e35i			1.95034i
$896$			2.05315e35i			0.766873i
$897$	2.92908e35	+	5.07360e34i	1.07950	+	0.186985i
$898$	−1.52329e35			−0.553945
$899$	3.50866e35			1.25900
$900$	2.03361e35			0.720043
$901$	2.20844e35			0.771593
$902$		−	5.69771e34i		−	0.196436i
$903$	4.12429e35			1.40313
$904$		−	4.22551e35i		−	1.41859i
$905$	6.38054e35			2.11385
$906$	−2.16566e35			−0.708031
$907$		−	2.82539e34i		−	0.0911571i	−0.998961	−	0.0455785i	$-0.985487\pi$
$907$		−	2.82539e34i		−	0.0911571i	0.998961	−	0.0455785i	$-0.0145131\pi$
$908$		−	2.85602e35i		−	0.909349i
$909$	4.10818e35			1.29087
$910$	3.38288e35			1.04903
$911$			5.14033e35i			1.57315i	0.617494	+	0.786576i	$0.288148\pi$
$911$			5.14033e35i			1.57315i	−0.617494	+	0.786576i	$0.711852\pi$
$912$			1.88070e33i			0.00568042i
$913$	−2.37456e35			−0.707839
$914$		−	1.49620e35i		−	0.440186i
$915$	3.94502e35			1.14550
$916$		−	3.40807e35i		−	0.976704i
$917$		−	1.81770e35i		−	0.514150i
$918$			6.62811e34i			0.185045i
$919$			5.17091e35i			1.42489i	0.701729	+	0.712444i	$0.252412\pi$
$919$			5.17091e35i			1.42489i	−0.701729	+	0.712444i	$0.747588\pi$
$920$	1.01417e35	−	5.85499e35i	0.275840	−	1.59247i
$921$	−4.90975e35			−1.31808
$922$	3.38096e35			0.895918
$923$	3.63441e35			0.950635
$924$	2.19583e35			0.566938
$925$		−	2.69067e35i		−	0.685741i
$926$	2.62888e35			0.661361
$927$		−	1.73177e35i		−	0.430064i
$928$	6.47076e35			1.58628
$929$	−2.85109e35			−0.689957			−0.344978	−	0.938611i	$-0.612114\pi$
$929$	−2.85109e35			−0.689957			−0.344978	+	0.938611i	$0.612114\pi$
$930$			4.36566e35i			1.04293i
$931$			1.51708e35i			0.357777i
$932$	1.74464e35			0.406178
$933$	−3.73955e35			−0.859488
$934$			2.54082e35i			0.576517i
$935$		−	3.38222e35i		−	0.757639i
$936$	−2.76005e35			−0.610390
$937$			4.82264e35i			1.05296i	0.850189	+	0.526478i	$0.176488\pi$
$937$			4.82264e35i			1.05296i	−0.850189	+	0.526478i	$0.823512\pi$
$938$	1.66325e35			0.358528
$939$			2.83048e35i			0.602382i
$940$		−	1.68926e35i		−	0.354947i
$941$			5.39815e35i			1.11988i	0.828535	+	0.559938i	$0.189175\pi$
$941$			5.39815e35i			1.11988i	−0.828535	+	0.559938i	$0.810825\pi$
$942$		−	3.46876e35i		−	0.710498i
$943$	2.77089e35	+	4.79960e34i	0.560376	+	0.0970654i
$944$	−3.81269e32			−0.000761320
$945$	−3.63773e35			−0.717214
$946$	1.50274e35			0.292543
$947$	−6.96308e35			−1.33845			−0.669224	−	0.743061i	$-0.733373\pi$
$947$	−6.96308e35			−1.33845			−0.669224	+	0.743061i	$0.733373\pi$
$948$			8.15673e35i			1.54816i
$949$	−5.56610e35			−1.04317
$950$			3.28312e35i			0.607580i
$951$	−9.73102e35			−1.77825
$952$	5.90182e35			1.06498
$953$		−	2.53890e35i		−	0.452408i	−0.974080	−	0.226204i	$-0.927368\pi$
$953$		−	2.53890e35i		−	0.452408i	0.974080	−	0.226204i	$-0.0726317\pi$
$954$			2.35843e35i			0.414994i
$955$	−2.11232e35			−0.367044
$956$	−3.78226e35			−0.649018
$957$		−	6.87105e35i		−	1.16434i
$958$		−	3.79034e35i		−	0.634296i
$959$	−1.15963e36			−1.91644
$960$			8.14303e35i			1.32902i
$961$	−2.31324e35			−0.372856
$962$			1.39045e35i			0.221338i
$963$		−	7.37212e35i		−	1.15898i
$964$		−	3.89220e35i		−	0.604326i
$965$		−	7.08451e35i		−	1.08638i
$966$	1.15857e35	−	6.68863e35i	0.175467	−	1.01301i
$967$	1.39622e34			0.0208851			0.0104425	−	0.999945i	$-0.496676\pi$
$967$	1.39622e34			0.0208851			0.0104425	+	0.999945i	$0.496676\pi$
$968$	−4.68206e35			−0.691724
$969$	−4.65547e35			−0.679326
$970$	5.75875e35			0.829979
$971$		−	7.68732e35i		−	1.09432i	−0.837028	−	0.547160i	$-0.815709\pi$
$971$		−	7.68732e35i		−	1.09432i	0.837028	−	0.547160i	$-0.184291\pi$
$972$	5.33967e35			0.750791
$973$		−	1.37418e34i		−	0.0190850i
$974$	−3.50728e35			−0.481131
$975$	−1.29428e36			−1.75377
$976$			2.84654e33i			0.00380995i
$977$			2.95612e35i			0.390829i	0.980721	+	0.195415i	$0.0626053\pi$
$977$			2.95612e35i			0.390829i	−0.980721	+	0.195415i	$0.937395\pi$
$978$	−9.28637e35			−1.21277
$979$	2.95509e35			0.381222
$980$			4.55188e35i			0.580067i
$981$			3.66115e35i			0.460882i
$982$	4.61327e35			0.573681
$983$			1.58130e36i			1.94255i	0.237965	+	0.971274i	$0.423520\pi$
$983$			1.58130e36i			1.94255i	−0.237965	+	0.971274i	$0.576480\pi$
$984$	−6.18013e35			−0.749992
$985$			7.38343e35i			0.885163i
$986$		−	7.03164e35i		−	0.832787i
$987$		−	5.06829e35i		−	0.593001i
$988$			2.70872e35i			0.313098i
$989$	−1.26587e35	+	7.30809e35i	−0.144555	+	0.834542i
$990$	3.61193e35			0.407490
$991$	1.35345e35			0.150854			0.0754271	−	0.997151i	$-0.475968\pi$
$991$	1.35345e35			0.150854			0.0754271	+	0.997151i	$0.475968\pi$
$992$	7.17566e35			0.790172
$993$	−7.79757e34			−0.0848337
$994$		−	8.29927e35i		−	0.892079i
$995$	2.15281e35			0.228628
$996$			9.80682e35i			1.02900i
$997$	8.11789e35			0.841592			0.420796	−	0.907155i	$-0.361751\pi$
$997$	8.11789e35			0.841592			0.420796	+	0.907155i	$0.361751\pi$
$998$	8.77807e35			0.899151
$999$		−	1.49520e35i		−	0.151326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.25.b.c.22.27	✓	44
23.22	odd	2	inner	23.25.b.c.22.28	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.25.b.c.22.27	✓	44	1.1	even	1	trivial
23.25.b.c.22.28	yes	44	23.22	odd	2	inner

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	23.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2541.92 q^{2} +699314. q^{3} -1.03159e7 q^{4} +3.93724e8i q^{5} +1.77760e9 q^{6} -1.74256e10i q^{7} -6.88684e10 q^{8} +2.06610e11 q^{9} +1.00081e12i q^{10} -1.74676e12i q^{11} -7.21402e12 q^{12} +1.93975e13 q^{13} -4.42946e13i q^{14} +2.75336e14i q^{15} -1.98670e12 q^{16} -4.91787e14i q^{17} +5.25187e14 q^{18} -1.35367e15i q^{19} -4.06160e15i q^{20} -1.21860e16i q^{21} -4.44012e15i q^{22} +(2.15931e16 + 3.74024e15i) q^{23} -4.81607e16 q^{24} -9.54137e16 q^{25} +4.93068e16 q^{26} -5.30213e16 q^{27} +1.79760e17i q^{28} +5.62494e17 q^{29} +6.99883e17i q^{30} +6.23769e17 q^{31} +1.15037e18 q^{32} -1.22153e18i q^{33} -1.25008e18i q^{34} +6.86088e18 q^{35} -2.13136e18 q^{36} +2.82001e18i q^{37} -3.44093e18i q^{38} +1.35649e19 q^{39} -2.71151e19i q^{40} +1.28323e19 q^{41} -3.09758e19i q^{42} +3.38446e19i q^{43} +1.80193e19i q^{44} +8.13474e19i q^{45} +(5.48879e19 + 9.50739e18i) q^{46} +4.15911e19 q^{47} -1.38933e18 q^{48} -1.12071e20 q^{49} -2.42534e20 q^{50} -3.43914e20i q^{51} -2.00101e20 q^{52} +4.49064e20i q^{53} -1.34776e20 q^{54} +6.87741e20 q^{55} +1.20008e21i q^{56} -9.46643e20i q^{57} +1.42981e21 q^{58} +1.91911e20 q^{59} -2.84033e21i q^{60} -1.43280e21i q^{61} +1.58557e21 q^{62} -3.60032e21i q^{63} +2.95748e21 q^{64} +7.63724e21i q^{65} -3.10504e21i q^{66} +3.75498e21i q^{67} +5.07321e21i q^{68} +(1.51003e22 + 2.61560e21i) q^{69} +1.74398e22 q^{70} +1.87365e22 q^{71} -1.42289e22 q^{72} -2.86950e22 q^{73} +7.16823e21i q^{74} -6.67241e22 q^{75} +1.39643e22i q^{76} -3.04384e22 q^{77} +3.44809e22 q^{78} -1.13068e23i q^{79} -7.82211e20i q^{80} -9.54315e22 q^{81} +3.26187e22 q^{82} -1.35941e23i q^{83} +1.25709e23i q^{84} +1.93628e23 q^{85} +8.60302e22i q^{86} +3.93360e23 q^{87} +1.20297e23i q^{88} +1.69175e23i q^{89} +2.06779e23i q^{90} -3.38013e23i q^{91} +(-2.22751e23 - 3.85838e22i) q^{92} +4.36211e23 q^{93} +1.05721e23 q^{94} +5.32974e23 q^{95} +8.04470e23 q^{96} -5.75406e23i q^{97} -2.84876e23 q^{98} -3.60899e23i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) \) 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more