LMFDB - Embedded newform 5.16.b.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,16,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.13467525500$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 29397x^{4} + 153469728x^{2} + 65015354624 $ x^6 + 29397x^4 + 153469728x^2 + 65015354624
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{4}\cdot 5^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.1
Root			$-150.955i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.16.b.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-301.910i q^{2} -779.290i q^{3} -58381.4 q^{4} +(-88431.8 - 150657. i) q^{5} -235275. q^{6} +2.08791e6i q^{7} +7.73292e6i q^{8} +1.37416e7 q^{9} +O(q^{10})$	\(q-301.910i q^{2} -779.290i q^{3} -58381.4 q^{4} +(-88431.8 - 150657. i) q^{5} -235275. q^{6} +2.08791e6i q^{7} +7.73292e6i q^{8} +1.37416e7 q^{9} +(-4.54846e7 + 2.66984e7i) q^{10} -7.71305e7 q^{11} +4.54960e7i q^{12} -1.32485e8i q^{13} +6.30361e8 q^{14} +(-1.17405e8 + 6.89140e7i) q^{15} +4.21600e8 q^{16} -1.10174e9i q^{17} -4.14872e9i q^{18} -6.23952e9 q^{19} +(5.16277e9 + 8.79553e9i) q^{20} +1.62709e9 q^{21} +2.32864e10i q^{22} -2.49754e10i q^{23} +6.02618e9 q^{24} +(-1.48772e10 + 2.66457e10i) q^{25} -3.99986e10 q^{26} -2.18907e10i q^{27} -1.21895e11i q^{28} +1.45836e11 q^{29} +(2.08058e10 + 3.54457e10i) q^{30} +4.01436e10 q^{31} +1.26107e11i q^{32} +6.01070e10i q^{33} -3.32626e11 q^{34} +(3.14558e11 - 1.84638e11i) q^{35} -8.02254e11 q^{36} -5.28137e11i q^{37} +1.88377e12i q^{38} -1.03245e11 q^{39} +(1.16501e12 - 6.83836e11i) q^{40} +6.88546e10 q^{41} -4.91234e11i q^{42} -7.67330e11i q^{43} +4.50298e12 q^{44} +(-1.21520e12 - 2.07026e12i) q^{45} -7.54032e12 q^{46} -8.92816e11i q^{47} -3.28549e11i q^{48} +3.88180e11 q^{49} +(8.04458e12 + 4.49157e12i) q^{50} -8.58576e11 q^{51} +7.73468e12i q^{52} -5.86528e11i q^{53} -6.60900e12 q^{54} +(6.82079e12 + 1.16202e13i) q^{55} -1.61457e13 q^{56} +4.86239e12i q^{57} -4.40291e13i q^{58} +3.16543e10 q^{59} +(6.85427e12 - 4.02329e12i) q^{60} +5.85723e12 q^{61} -1.21197e13i q^{62} +2.86913e13i q^{63} +5.18879e13 q^{64} +(-1.99598e13 + 1.17159e13i) q^{65} +1.81469e13 q^{66} -3.95005e13i q^{67} +6.43212e13i q^{68} -1.94631e13 q^{69} +(-5.57440e13 - 9.49680e13i) q^{70} -7.83244e13 q^{71} +1.06263e14i q^{72} +8.73027e13i q^{73} -1.59450e14 q^{74} +(2.07647e13 + 1.15937e13i) q^{75} +3.64272e14 q^{76} -1.61042e14i q^{77} +3.11705e13i q^{78} -3.01801e13 q^{79} +(-3.72829e13 - 6.35169e13i) q^{80} +1.80118e14 q^{81} -2.07879e13i q^{82} -1.08491e14i q^{83} -9.49917e13 q^{84} +(-1.65985e14 + 9.74290e13i) q^{85} -2.31664e14 q^{86} -1.13648e14i q^{87} -5.96444e14i q^{88} +5.54023e14 q^{89} +(-6.25032e14 + 3.66879e14i) q^{90} +2.76618e14 q^{91} +1.45810e15i q^{92} -3.12835e13i q^{93} -2.69550e14 q^{94} +(5.51772e14 + 9.40024e14i) q^{95} +9.82739e13 q^{96} -1.50497e15i q^{97} -1.17195e14i q^{98} -1.05990e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 38568 q^{4} - 238350 q^{5} - 515448 q^{6} - 11416662 q^{9}+O(q^{10}) $ 6 * q - 38568 * q^4 - 238350 * q^5 - 515448 * q^6 - 11416662 * q^9	\( 6 q - 38568 q^{4} - 238350 q^{5} - 515448 q^{6} - 11416662 q^{9} - 48274200 q^{10} - 108590088 q^{11} + 663751704 q^{14} + 297743400 q^{15} + 1155522336 q^{16} - 3630995640 q^{19} + 2533753800 q^{20} - 8917537608 q^{21} - 2959765920 q^{24} + 18250878750 q^{25} - 81970953168 q^{26} + 286168468740 q^{29} + 203897251800 q^{30} - 276236748288 q^{31} - 127784939136 q^{34} + 1171274911800 q^{35} - 3326879331864 q^{36} + 2186980965936 q^{39} + 4214283852000 q^{40} - 6153278882388 q^{41} + 8250173021664 q^{44} + 10442765857950 q^{45} - 23334602656488 q^{46} + 11613390856242 q^{49} + 23694218070000 q^{50} - 43487373385728 q^{51} + 10162879468560 q^{54} + 33977390365800 q^{55} - 59280484297440 q^{56} + 14903258326680 q^{59} + 39248254864800 q^{60} - 11352061428588 q^{61} + 73265851251072 q^{64} - 50675287275600 q^{65} + 76208211455904 q^{66} - 150489671962824 q^{69} - 156447825521400 q^{70} + 131693145807312 q^{71} - 353606797863216 q^{74} - 360965926890000 q^{75} + 959127540575520 q^{76} - 26081853939360 q^{79} - 552945514077600 q^{80} + 11\!\cdots\!46 q^{81}+ \cdots + 506999099666376 q^{99}+O(q^{100}) \) 6 * q - 38568 * q^4 - 238350 * q^5 - 515448 * q^6 - 11416662 * q^9 - 48274200 * q^10 - 108590088 * q^11 + 663751704 * q^14 + 297743400 * q^15 + 1155522336 * q^16 - 3630995640 * q^19 + 2533753800 * q^20 - 8917537608 * q^21 - 2959765920 * q^24 + 18250878750 * q^25 - 81970953168 * q^26 + 286168468740 * q^29 + 203897251800 * q^30 - 276236748288 * q^31 - 127784939136 * q^34 + 1171274911800 * q^35 - 3326879331864 * q^36 + 2186980965936 * q^39 + 4214283852000 * q^40 - 6153278882388 * q^41 + 8250173021664 * q^44 + 10442765857950 * q^45 - 23334602656488 * q^46 + 11613390856242 * q^49 + 23694218070000 * q^50 - 43487373385728 * q^51 + 10162879468560 * q^54 + 33977390365800 * q^55 - 59280484297440 * q^56 + 14903258326680 * q^59 + 39248254864800 * q^60 - 11352061428588 * q^61 + 73265851251072 * q^64 - 50675287275600 * q^65 + 76208211455904 * q^66 - 150489671962824 * q^69 - 156447825521400 * q^70 + 131693145807312 * q^71 - 353606797863216 * q^74 - 360965926890000 * q^75 + 959127540575520 * q^76 - 26081853939360 * q^79 - 552945514077600 * q^80 + 1148641568615646 * q^81 - 686155736066976 * q^84 - 548221025491200 * q^85 + 598387757484072 * q^86 + 59269690709820 * q^89 - 1014408610626600 * q^90 + 821206462566672 * q^91 - 308164835928456 * q^94 + 232287694599000 * q^95 - 1208921682814848 * q^96 + 506999099666376 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		−	301.910i		−	1.66783i	−0.551893	−	0.833915i	$-0.686094\pi$
$2$		−	301.910i		−	1.66783i	0.551893	−	0.833915i	$-0.313906\pi$
$3$		−	779.290i		−	0.205726i	−0.994696	−	0.102863i	$-0.967200\pi$
$3$		−	779.290i		−	0.205726i	0.994696	−	0.102863i	$-0.0328004\pi$
$4$	−58381.4			−1.78166
$5$	−88431.8	−	150657.i	−0.506213	−	0.862408i
$5$	−88431.8	−	150657.i	−0.506213	−	0.862408i
$6$	−235275.			−0.343116
$7$			2.08791e6i			0.958246i	0.877748	+	0.479123i	$0.159045\pi$
$7$			2.08791e6i			0.958246i	−0.877748	+	0.479123i	$0.840955\pi$
$8$			7.73292e6i			1.30367i
$9$	1.37416e7			0.957677
$10$	−4.54846e7	+	2.66984e7i	−1.43835	+	0.844278i
$11$	−7.71305e7			−1.19339			−0.596693	−	0.802469i	$-0.703519\pi$
$11$	−7.71305e7			−1.19339			−0.596693	+	0.802469i	$0.703519\pi$
$12$			4.54960e7i			0.366534i
$13$		−	1.32485e8i		−	0.585589i	−0.956175	−	0.292795i	$-0.905415\pi$
$13$		−	1.32485e8i		−	0.585589i	0.956175	−	0.292795i	$-0.0945852\pi$
$14$	6.30361e8			1.59819
$15$	−1.17405e8	+	6.89140e7i	−0.177420	+	0.104141i
$16$	4.21600e8			0.392646
$17$		−	1.10174e9i		−	0.651198i	−0.945508	−	0.325599i	$-0.894434\pi$
$17$		−	1.10174e9i		−	0.651198i	0.945508	−	0.325599i	$-0.105566\pi$
$18$		−	4.14872e9i		−	1.59724i
$19$	−6.23952e9			−1.60140			−0.800699	−	0.599067i	$-0.795538\pi$
$19$	−6.23952e9			−1.60140			−0.800699	+	0.599067i	$0.795538\pi$
$20$	5.16277e9	+	8.79553e9i	0.901899	+	1.53652i
$21$	1.62709e9			0.197136
$22$			2.32864e10i			1.99037i
$23$		−	2.49754e10i		−	1.52952i	−0.644317	−	0.764759i	$-0.722858\pi$
$23$		−	2.49754e10i		−	1.52952i	0.644317	−	0.764759i	$-0.277142\pi$
$24$	6.02618e9			0.268199
$25$	−1.48772e10	+	2.66457e10i	−0.487496	+	0.873125i
$26$	−3.99986e10			−0.976663
$27$		−	2.18907e10i		−	0.402745i
$28$		−	1.21895e11i		−	1.70727i
$29$	1.45836e11			1.56992			0.784962	−	0.619544i	$-0.212683\pi$
$29$	1.45836e11			1.56992			0.784962	+	0.619544i	$0.212683\pi$
$30$	2.08058e10	+	3.54457e10i	0.173690	+	0.295906i
$31$	4.01436e10			0.262062			0.131031	−	0.991378i	$-0.458171\pi$
$31$	4.01436e10			0.262062			0.131031	+	0.991378i	$0.458171\pi$
$32$			1.26107e11i			0.648805i
$33$			6.01070e10i			0.245511i
$34$	−3.32626e11			−1.08609
$35$	3.14558e11	−	1.84638e11i	0.826400	−	0.485077i
$36$	−8.02254e11			−1.70625
$37$		−	5.28137e11i		−	0.914605i	−0.889311	−	0.457302i	$-0.848816\pi$
$37$		−	5.28137e11i		−	0.914605i	0.889311	−	0.457302i	$-0.151184\pi$
$38$			1.88377e12i			2.67086i
$39$	−1.03245e11			−0.120471
$40$	1.16501e12	−	6.83836e11i	1.12430	−	0.659936i
$41$	6.88546e10			0.0552146			0.0276073	−	0.999619i	$-0.491211\pi$
$41$	6.88546e10			0.0552146			0.0276073	+	0.999619i	$0.491211\pi$
$42$		−	4.91234e11i		−	0.328790i
$43$		−	7.67330e11i		−	0.430495i	−0.976559	−	0.215248i	$-0.930944\pi$
$43$		−	7.67330e11i		−	0.430495i	0.976559	−	0.215248i	$-0.0690559\pi$
$44$	4.50298e12			2.12621
$45$	−1.21520e12	−	2.07026e12i	−0.484789	−	0.825908i
$46$	−7.54032e12			−2.55098
$47$		−	8.92816e11i		−	0.257056i	−0.991706	−	0.128528i	$-0.958975\pi$
$47$		−	8.92816e11i		−	0.257056i	0.991706	−	0.128528i	$-0.0410253\pi$
$48$		−	3.28549e11i		−	0.0807776i
$49$	3.88180e11			0.0817640
$50$	8.04458e12	+	4.49157e12i	1.45622	+	0.813061i
$51$	−8.58576e11			−0.133968
$52$			7.73468e12i			1.04332i
$53$		−	5.86528e11i		−	0.0685836i	−0.999412	−	0.0342918i	$-0.989082\pi$
$53$		−	5.86528e11i		−	0.0685836i	0.999412	−	0.0342918i	$-0.0109176\pi$
$54$	−6.60900e12			−0.671711
$55$	6.82079e12	+	1.16202e13i	0.604108	+	1.02919i
$56$	−1.61457e13			−1.24924
$57$			4.86239e12i			0.329449i
$58$		−	4.40291e13i		−	2.61837i
$59$	3.16543e10			0.00165593			0.000827967	−	1.00000i	$-0.499736\pi$
$59$	3.16543e10			0.00165593			0.000827967		1.00000i	$0.499736\pi$
$60$	6.85427e12	−	4.02329e12i	0.316102	−	0.185544i
$61$	5.85723e12			0.238627			0.119313	−	0.992857i	$-0.461931\pi$
$61$	5.85723e12			0.238627			0.119313	+	0.992857i	$0.461931\pi$
$62$		−	1.21197e13i		−	0.437075i
$63$			2.86913e13i			0.917690i
$64$	5.18879e13			1.47474
$65$	−1.99598e13	+	1.17159e13i	−0.505017	+	0.296433i
$66$	1.81469e13			0.409470
$67$		−	3.95005e13i		−	0.796235i	−0.917334	−	0.398118i	$-0.869664\pi$
$67$		−	3.95005e13i		−	0.796235i	0.917334	−	0.398118i	$-0.130336\pi$
$68$			6.43212e13i			1.16021i
$69$	−1.94631e13			−0.314662
$70$	−5.57440e13	−	9.49680e13i	−0.809026	−	1.37829i
$71$	−7.83244e13			−1.02202			−0.511010	−	0.859575i	$-0.670729\pi$
$71$	−7.83244e13			−1.02202			−0.511010	+	0.859575i	$0.670729\pi$
$72$			1.06263e14i			1.24850i
$73$			8.73027e13i			0.924924i	0.886639	+	0.462462i	$0.153034\pi$
$73$			8.73027e13i			0.924924i	−0.886639	+	0.462462i	$0.846966\pi$
$74$	−1.59450e14			−1.52541
$75$	2.07647e13	+	1.15937e13i	0.179625	+	0.100291i
$76$	3.64272e14			2.85314
$77$		−	1.61042e14i		−	1.14356i
$78$			3.11705e13i			0.200925i
$79$	−3.01801e13			−0.176814			−0.0884070	−	0.996084i	$-0.528178\pi$
$79$	−3.01801e13			−0.176814			−0.0884070	+	0.996084i	$0.528178\pi$
$80$	−3.72829e13	−	6.35169e13i	−0.198763	−	0.338621i
$81$	1.80118e14			0.874821
$82$		−	2.07879e13i		−	0.0920886i
$83$		−	1.08491e14i		−	0.438841i	−0.975630	−	0.219421i	$-0.929583\pi$
$83$		−	1.08491e14i		−	0.438841i	0.975630	−	0.219421i	$-0.0704167\pi$
$84$	−9.49917e13			−0.351229
$85$	−1.65985e14	+	9.74290e13i	−0.561598	+	0.329645i
$86$	−2.31664e14			−0.717993
$87$		−	1.13648e14i		−	0.322974i
$88$		−	5.96444e14i		−	1.55578i
$89$	5.54023e14			1.32771			0.663854	−	0.747862i	$-0.268920\pi$
$89$	5.54023e14			1.32771			0.663854	+	0.747862i	$0.268920\pi$
$90$	−6.25032e14	+	3.66879e14i	−1.37747	+	0.808545i
$91$	2.76618e14			0.561139
$92$			1.45810e15i			2.72508i
$93$		−	3.12835e13i		−	0.0539130i
$94$	−2.69550e14			−0.428726
$95$	5.51772e14	+	9.40024e14i	0.810649	+	1.38106i
$96$	9.82739e13			0.133476
$97$		−	1.50497e15i		−	1.89121i	−0.325313	−	0.945606i	$-0.605470\pi$
$97$		−	1.50497e15i		−	1.89121i	0.325313	−	0.945606i	$-0.394530\pi$
$98$		−	1.17195e14i		−	0.136369i
$99$	−1.05990e15			−1.14288
$100$	8.68551e14	−	1.55561e15i	0.868551	−	1.55561i
$101$	−1.04693e15			−0.971649			−0.485824	−	0.874056i	$-0.661481\pi$
$101$	−1.04693e15			−0.971649			−0.485824	+	0.874056i	$0.661481\pi$
$102$			2.59212e14i			0.223437i
$103$			2.63263e14i			0.210916i	0.994424	+	0.105458i	$0.0336309\pi$
$103$			2.63263e14i			0.210916i	−0.994424	+	0.105458i	$0.966369\pi$
$104$	1.02450e15			0.763416
$105$	−1.43886e14	−	2.45132e14i	−0.0997930	−	0.170012i
$106$	−1.77078e14			−0.114386
$107$		−	7.84345e14i		−	0.472203i	−0.971728	−	0.236101i	$-0.924130\pi$
$107$		−	7.84345e14i		−	0.472203i	0.971728	−	0.236101i	$-0.0758698\pi$
$108$			1.27801e15i			0.717554i
$109$	8.25405e14			0.432483			0.216241	−	0.976340i	$-0.430620\pi$
$109$	8.25405e14			0.432483			0.216241	+	0.976340i	$0.430620\pi$
$110$	3.50825e15	−	2.05926e15i	1.71651	−	1.00755i
$111$	−4.11572e14			−0.188158
$112$			8.80265e14i			0.376252i
$113$			3.56130e15i			1.42403i	0.702163	+	0.712016i	$0.252218\pi$
$113$			3.56130e15i			1.42403i	−0.702163	+	0.712016i	$0.747782\pi$
$114$	1.46800e15			0.549466
$115$	−3.76271e15	+	2.20862e15i	−1.31907	+	0.774262i
$116$	−8.51408e15			−2.79707
$117$		−	1.82056e15i		−	0.560805i
$118$		−	9.55674e12i		−	0.00276182i
$119$	2.30034e15			0.624008
$120$	−5.32906e14	−	9.07884e14i	−0.135766	−	0.231297i
$121$	1.77187e15			0.424171
$122$		−	1.76835e15i		−	0.397988i
$123$		−	5.36577e13i		−	0.0113591i
$124$	−2.34364e15			−0.466905
$125$	5.32996e15	−	1.14976e14i	0.999767	−	0.0215666i
$126$	8.66218e15			1.53055
$127$			9.24721e15i			1.53987i	0.638125	+	0.769933i	$0.279710\pi$
$127$			9.24721e15i			1.53987i	−0.638125	+	0.769933i	$0.720290\pi$
$128$		−	1.15332e16i		−	1.81082i
$129$	−5.97972e14			−0.0885642
$130$	3.53715e15	+	6.02605e15i	0.494400	+	0.842283i
$131$	−3.50922e15			−0.463101			−0.231550	−	0.972823i	$-0.574380\pi$
$131$	−3.50922e15			−0.463101			−0.231550	+	0.972823i	$0.574380\pi$
$132$		−	3.50913e15i		−	0.437416i
$133$		−	1.30276e16i		−	1.53453i
$134$	−1.19256e16			−1.32798
$135$	−3.29797e15	+	1.93583e15i	−0.347331	+	0.203875i
$136$	8.51968e15			0.848948
$137$		−	7.60397e15i		−	0.717194i	−0.933493	−	0.358597i	$-0.883255\pi$
$137$		−	7.60397e15i		−	0.717194i	0.933493	−	0.358597i	$-0.116745\pi$
$138$			5.87610e15i			0.524802i
$139$	3.33077e15			0.281795			0.140898	−	0.990024i	$-0.455001\pi$
$139$	3.33077e15			0.281795			0.140898	+	0.990024i	$0.455001\pi$
$140$	−1.83643e16	+	1.07794e16i	−1.47236	+	0.864241i
$141$	−6.95763e14			−0.0528832
$142$			2.36469e16i			1.70456i
$143$			1.02187e16i			0.698834i
$144$	5.79347e15			0.376028
$145$	−1.28965e16	−	2.19711e16i	−0.794716	−	1.35392i
$146$	2.63575e16			1.54262
$147$		−	3.02505e14i		−	0.0168210i
$148$			3.08333e16i			1.62951i
$149$	2.20370e16			1.10728			0.553638	−	0.832758i	$-0.313239\pi$
$149$	2.20370e16			1.10728			0.553638	+	0.832758i	$0.313239\pi$
$150$	3.50023e15	−	6.26906e15i	0.167268	−	0.299583i
$151$	−1.16974e16			−0.531815			−0.265907	−	0.963999i	$-0.585672\pi$
$151$	−1.16974e16			−0.531815			−0.265907	+	0.963999i	$0.585672\pi$
$152$		−	4.82497e16i		−	2.08770i
$153$		−	1.51397e16i		−	0.623637i
$154$	−4.86201e16			−1.90726
$155$	−3.54997e15	−	6.04790e15i	−0.132659	−	0.226004i
$156$	6.02756e15			0.214638
$157$			1.50192e16i			0.509799i	0.966968	+	0.254899i	$0.0820424\pi$
$157$			1.50192e16i			0.509799i	−0.966968	+	0.254899i	$0.917958\pi$
$158$			9.11165e15i			0.294896i
$159$	−4.57076e14			−0.0141094
$160$	1.89988e16	−	1.11519e16i	0.559535	−	0.328434i
$161$	5.21466e16			1.46565
$162$		−	5.43793e16i		−	1.45905i
$163$			2.37456e16i			0.608382i	0.952611	+	0.304191i	$0.0983861\pi$
$163$			2.37456e16i			0.608382i	−0.952611	+	0.304191i	$0.901614\pi$
$164$	−4.01982e15			−0.0983735
$165$	9.05552e15	−	5.31537e15i	0.211731	−	0.124281i
$166$	−3.27544e16			−0.731913
$167$			8.70806e16i			1.86015i	0.367370	+	0.930075i	$0.380258\pi$
$167$			8.70806e16i			1.86015i	−0.367370	+	0.930075i	$0.619742\pi$
$168$			1.25821e16i			0.257001i
$169$	3.36335e16			0.657085
$170$	2.94147e16	+	5.01123e16i	0.549792	+	0.936651i
$171$	−8.57411e16			−1.53362
$172$			4.47977e16i			0.766995i
$173$		−	4.24844e16i		−	0.696440i	−0.937413	−	0.348220i	$-0.886786\pi$
$173$		−	4.24844e16i		−	0.696440i	0.937413	−	0.348220i	$-0.113214\pi$
$174$	−3.43115e16			−0.538666
$175$	−5.56338e16	−	3.10623e16i	−0.836669	−	0.467142i
$176$	−3.25183e16			−0.468578
$177$		−	2.46679e13i		−	0.000340669i
$178$		−	1.67265e17i		−	2.21439i
$179$	6.47281e16			0.821666			0.410833	−	0.911711i	$-0.365238\pi$
$179$	6.47281e16			0.821666			0.410833	+	0.911711i	$0.365238\pi$
$180$	7.09448e16	+	1.20865e17i	0.863727	+	1.47149i
$181$	−8.81817e16			−1.02989			−0.514943	−	0.857225i	$-0.672187\pi$
$181$	−8.81817e16			−1.02989			−0.514943	+	0.857225i	$0.672187\pi$
$182$		−	8.35137e16i		−	0.935884i
$183$		−	4.56448e15i		−	0.0490917i
$184$	1.93133e17			1.99399
$185$	−7.95673e16	+	4.67041e16i	−0.788763	+	0.462985i
$186$	−9.44479e15			−0.0899177
$187$			8.49779e16i			0.777131i
$188$			5.21238e16i			0.457986i
$189$	4.57058e16			0.385929
$190$	2.83802e17	−	1.66585e17i	2.30337	−	1.35202i
$191$	4.71702e16			0.368059			0.184030	−	0.982921i	$-0.441086\pi$
$191$	4.71702e16			0.368059			0.184030	+	0.982921i	$0.441086\pi$
$192$		−	4.04357e16i		−	0.303393i
$193$		−	9.79733e16i		−	0.707014i	−0.935432	−	0.353507i	$-0.884989\pi$
$193$		−	9.79733e16i		−	0.707014i	0.935432	−	0.353507i	$-0.115011\pi$
$194$	−4.54365e17			−3.15422
$195$	9.13010e15	+	1.55545e16i	0.0609840	+	0.103895i
$196$	−2.26625e16			−0.145676
$197$		−	1.82893e17i		−	1.13162i	−0.824536	−	0.565810i	$-0.808563\pi$
$197$		−	1.82893e17i		−	1.13162i	0.824536	−	0.565810i	$-0.191437\pi$
$198$			3.19993e17i			1.90613i
$199$	−1.95969e16			−0.112406			−0.0562029	−	0.998419i	$-0.517899\pi$
$199$	−1.95969e16			−0.112406			−0.0562029	+	0.998419i	$0.517899\pi$
$200$	−2.06049e17	−	1.15044e17i	−1.13827	−	0.635535i
$201$	−3.07823e16			−0.163806
$202$			3.16080e17i			1.62055i
$203$			3.04492e17i			1.50437i
$204$	5.01248e16			0.238686
$205$	−6.08894e15	−	1.03734e16i	−0.0279504	−	0.0476175i
$206$	7.94815e16			0.351772
$207$		−	3.43203e17i		−	1.46478i
$208$		−	5.58559e16i		−	0.229929i
$209$	4.81257e17			1.91109
$210$	−7.40076e16	+	4.34407e16i	−0.283551	+	0.166438i
$211$	1.71813e17			0.635241			0.317620	−	0.948218i	$-0.397116\pi$
$211$	1.71813e17			0.635241			0.317620	+	0.948218i	$0.397116\pi$
$212$			3.42423e16i			0.122192i
$213$			6.10374e16i			0.210256i
$214$	−2.36801e17			−0.787554
$215$	−1.15603e17	+	6.78563e16i	−0.371263	+	0.217922i
$216$	1.69279e17			0.525048
$217$			8.38164e16i			0.251120i
$218$		−	2.49198e17i		−	0.721307i
$219$	6.80341e16			0.190281
$220$	−3.98207e17	−	6.78404e17i	−1.07631	−	1.83366i
$221$	−1.45965e17			−0.381334
$222$			1.24257e17i			0.313816i
$223$		−	5.08815e17i		−	1.24243i	−0.783638	−	0.621217i	$-0.786638\pi$
$223$		−	5.08815e17i		−	1.24243i	0.783638	−	0.621217i	$-0.213362\pi$
$224$	−2.63300e17			−0.621715
$225$	−2.04437e17	+	3.66154e17i	−0.466864	+	0.836172i
$226$	1.07519e18			2.37504
$227$		−	5.27724e17i		−	1.12775i	−0.825860	−	0.563875i	$-0.809310\pi$
$227$		−	5.27724e17i		−	1.12775i	0.825860	−	0.563875i	$-0.190690\pi$
$228$		−	2.83873e17i		−	0.586966i
$229$	−3.25364e17			−0.651034			−0.325517	−	0.945536i	$-0.605538\pi$
$229$	−3.25364e17			−0.651034			−0.325517	+	0.945536i	$0.605538\pi$
$230$	6.66805e17	+	1.13600e18i	1.29134	+	2.19998i
$231$	−1.25498e17			−0.235260
$232$			1.12773e18i			2.04667i
$233$			5.04233e17i			0.886057i	0.896507	+	0.443029i	$0.146096\pi$
$233$			5.04233e17i			0.886057i	−0.896507	+	0.443029i	$0.853904\pi$
$234$	−5.49646e17			−0.935328
$235$	−1.34509e17	+	7.89534e16i	−0.221687	+	0.130125i
$236$	−1.84802e15			−0.00295031
$237$			2.35190e16i			0.0363753i
$238$		−	6.94495e17i		−	1.04074i
$239$	4.80698e17			0.698052			0.349026	−	0.937113i	$-0.386512\pi$
$239$	4.80698e17			0.698052			0.349026	+	0.937113i	$0.386512\pi$
$240$	−4.94980e16	+	2.90542e16i	−0.0696632	+	0.0408907i
$241$	−6.74534e17			−0.920186			−0.460093	−	0.887871i	$-0.652184\pi$
$241$	−6.74534e17			−0.920186			−0.460093	+	0.887871i	$0.652184\pi$
$242$		−	5.34944e17i		−	0.707446i
$243$		−	4.54471e17i		−	0.582719i
$244$	−3.41953e17			−0.425151
$245$	−3.43274e16	−	5.84818e16i	−0.0413900	−	0.0705140i
$246$	−1.61998e16			−0.0189450
$247$			8.26646e17i			0.937761i
$248$			3.10427e17i			0.341643i
$249$	−8.45459e16			−0.0902812
$250$	−3.47123e16	−	1.60917e18i	−0.0359695	−	1.66744i
$251$	−2.82502e17			−0.284098			−0.142049	−	0.989860i	$-0.545369\pi$
$251$	−2.82502e17			−0.284098			−0.142049	+	0.989860i	$0.545369\pi$
$252$		−	1.67504e18i		−	1.63501i
$253$			1.92637e18i			1.82531i
$254$	2.79182e18			2.56823
$255$	7.59254e16	+	1.29350e17i	0.0678166	+	0.115535i
$256$	−1.78171e18			−1.54539
$257$		−	6.91378e17i		−	0.582394i	−0.956663	−	0.291197i	$-0.905946\pi$
$257$		−	6.91378e17i		−	0.582394i	0.956663	−	0.291197i	$-0.0940536\pi$
$258$			1.80533e17i			0.147710i
$259$	1.10270e18			0.876417
$260$	1.16528e18	−	6.83992e17i	0.899767	−	0.528142i
$261$	2.00402e18			1.50348
$262$			1.05947e18i			0.772374i
$263$		−	4.44052e17i		−	0.314605i	−0.987550	−	0.157303i	$-0.949720\pi$
$263$		−	4.44052e17i		−	0.314605i	0.987550	−	0.157303i	$-0.0502798\pi$
$264$	−4.64803e17			−0.320066
$265$	−8.83643e16	+	5.18678e16i	−0.0591470	+	0.0347179i
$266$	−3.93315e18			−2.55934
$267$		−	4.31744e17i		−	0.273144i
$268$			2.30609e18i			1.41862i
$269$	−3.14482e18			−1.88128			−0.940641	−	0.339402i	$-0.889775\pi$
$269$	−3.14482e18			−1.88128			−0.940641	+	0.339402i	$0.889775\pi$
$270$	5.84446e17	+	9.95689e17i	0.340029	+	0.579289i
$271$	4.09117e17			0.231514			0.115757	−	0.993278i	$-0.463071\pi$
$271$	4.09117e17			0.231514			0.115757	+	0.993278i	$0.463071\pi$
$272$		−	4.64495e17i		−	0.255690i
$273$		−	2.15566e17i		−	0.115441i
$274$	−2.29571e18			−1.19616
$275$	1.14749e18	−	2.05519e18i	0.581771	−	1.04198i
$276$	1.13628e18			0.560620
$277$			2.54882e18i			1.22388i	0.790903	+	0.611942i	$0.209611\pi$
$277$			2.54882e18i			1.22388i	−0.790903	+	0.611942i	$0.790389\pi$
$278$		−	1.00559e18i		−	0.469987i
$279$	5.51638e17			0.250971
$280$	1.42779e18	+	2.43245e18i	0.632381	+	1.07735i
$281$	−2.10517e18			−0.907799			−0.453899	−	0.891053i	$-0.649967\pi$
$281$	−2.10517e18			−0.907799			−0.453899	+	0.891053i	$0.649967\pi$
$282$			2.10057e17i			0.0882002i
$283$		−	3.14365e18i		−	1.28539i	−0.766121	−	0.642697i	$-0.777815\pi$
$283$		−	3.14365e18i		−	1.28539i	0.766121	−	0.642697i	$-0.222185\pi$
$284$	4.57268e18			1.82089
$285$	7.32551e17	−	4.29990e17i	0.284120	−	0.166772i
$286$	3.08511e18			1.16554
$287$			1.43762e17i			0.0529092i
$288$			1.73291e18i			0.621346i
$289$	1.64859e18			0.575942
$290$	−6.63328e18	+	3.89358e18i	−2.25810	+	1.32545i
$291$	−1.17281e18			−0.389072
$292$		−	5.09685e18i		−	1.64790i
$293$		−	4.70542e18i		−	1.48283i	−0.671047	−	0.741415i	$-0.734155\pi$
$293$		−	4.70542e18i		−	1.48283i	0.671047	−	0.741415i	$-0.265845\pi$
$294$	−9.13290e16			−0.0280546
$295$	−2.79925e15	−	4.76893e15i	−0.000838255	−	0.00142809i
$296$	4.08404e18			1.19234
$297$			1.68844e18i			0.480631i
$298$		−	6.65318e18i		−	1.84675i
$299$	−3.30888e18			−0.895669
$300$	−1.21227e18	−	6.76853e17i	−0.320030	−	0.178684i
$301$	1.60212e18			0.412521
$302$			3.53154e18i			0.886977i
$303$			8.15865e17i			0.199894i
$304$	−2.63058e18			−0.628782
$305$	−5.17966e17	−	8.82430e17i	−0.120796	−	0.205793i
$306$	−4.57082e18			−1.04012
$307$			4.22293e18i			0.937725i	0.883271	+	0.468863i	$0.155336\pi$
$307$			4.22293e18i			0.937725i	−0.883271	+	0.468863i	$0.844664\pi$
$308$			9.40184e18i			2.03743i
$309$	2.05158e17			0.0433910
$310$	−1.82592e18	+	1.07177e18i	−0.376937	+	0.221253i
$311$	9.72072e18			1.95882			0.979412	−	0.201872i	$-0.0647024\pi$
$311$	9.72072e18			1.95882			0.979412	+	0.201872i	$0.0647024\pi$
$312$		−	7.98382e17i		−	0.157055i
$313$			6.04916e18i			1.16175i	0.813993	+	0.580875i	$0.197289\pi$
$313$			6.04916e18i			1.16175i	−0.813993	+	0.580875i	$0.802711\pi$
$314$	4.53443e18			0.850258
$315$	4.32253e18	−	2.53722e18i	0.791424	−	0.464547i
$316$	1.76195e18			0.315022
$317$			9.16096e17i			0.159955i	0.996797	+	0.0799773i	$0.0254848\pi$
$317$			9.16096e17i			0.159955i	−0.996797	+	0.0799773i	$0.974515\pi$
$318$			1.37995e17i			0.0235321i
$319$	−1.12484e19			−1.87353
$320$	−4.58854e18	−	7.81725e18i	−0.746534	−	1.27183i
$321$	−6.11232e17			−0.0971445
$322$		−	1.57435e19i		−	2.44446i
$323$			6.87434e18i			1.04283i
$324$	−1.05155e19			−1.55863
$325$	3.53016e18	+	1.97101e18i	0.511293	+	0.285473i
$326$	7.16903e18			1.01468
$327$		−	6.43230e17i		−	0.0889730i
$328$			5.32447e17i			0.0719817i
$329$	1.86412e18			0.246323
$330$	−1.60476e18	−	2.73395e18i	−0.207279	−	0.353131i
$331$	−9.14544e18			−1.15477			−0.577384	−	0.816473i	$-0.695926\pi$
$331$	−9.14544e18			−1.15477			−0.577384	+	0.816473i	$0.695926\pi$
$332$			6.33385e18i			0.781865i
$333$		−	7.25745e18i		−	0.875896i
$334$	2.62905e19			3.10241
$335$	−5.95100e18	+	3.49310e18i	−0.686680	+	0.403065i
$336$	6.85982e17			0.0774048
$337$		−	1.21070e19i		−	1.33601i	−0.744156	−	0.668006i	$-0.767148\pi$
$337$		−	1.21070e19i		−	1.33601i	0.744156	−	0.668006i	$-0.232852\pi$
$338$		−	1.01543e19i		−	1.09591i
$339$	2.77528e18			0.292961
$340$	9.69041e18	−	5.68804e18i	1.00058	−	0.587314i
$341$	−3.09630e18			−0.312741
$342$			2.58860e19i			2.55782i
$343$			1.07230e19i			1.03660i
$344$	5.93369e18			0.561225
$345$	1.72116e18	+	2.93224e18i	0.159286	+	0.271367i
$346$	−1.28264e19			−1.16154
$347$		−	3.51728e18i		−	0.311700i	−0.987781	−	0.155850i	$-0.950188\pi$
$347$		−	3.51728e18i		−	0.311700i	0.987781	−	0.155850i	$-0.0498116\pi$
$348$			6.63493e18i			0.575430i
$349$	−1.19985e19			−1.01844			−0.509221	−	0.860636i	$-0.670066\pi$
$349$	−1.19985e19			−1.01844			−0.509221	+	0.860636i	$0.670066\pi$
$350$	−9.37801e18	+	1.67964e19i	−0.779113	+	1.39542i
$351$	−2.90019e18			−0.235843
$352$		−	9.72670e18i		−	0.774275i
$353$		−	1.47029e19i		−	1.14576i	−0.819641	−	0.572878i	$-0.805827\pi$
$353$		−	1.47029e19i		−	1.14576i	0.819641	−	0.572878i	$-0.194173\pi$
$354$	−7.44747e15			−0.000568178
$355$	6.92637e18	+	1.18001e19i	0.517360	+	0.881399i
$356$	−3.23446e19			−2.36552
$357$		−	1.79263e18i		−	0.128375i
$358$		−	1.95420e19i		−	1.37040i
$359$	−2.86436e18			−0.196707			−0.0983534	−	0.995152i	$-0.531358\pi$
$359$	−2.86436e18			−0.196707			−0.0983534	+	0.995152i	$0.531358\pi$
$360$	1.60092e19	−	9.39701e18i	1.07671	−	0.632005i
$361$	2.37505e19			1.56447
$362$			2.66229e19i			1.71767i
$363$		−	1.38080e18i		−	0.0872631i
$364$	−1.61493e19			−0.999757
$365$	1.31527e19	−	7.72034e18i	0.797662	−	0.468209i
$366$	−1.37806e18			−0.0818766
$367$		−	2.57378e18i		−	0.149822i	−0.997190	−	0.0749110i	$-0.976133\pi$
$367$		−	2.57378e18i		−	0.149822i	0.997190	−	0.0749110i	$-0.0238673\pi$
$368$		−	1.05297e19i		−	0.600559i
$369$	9.46173e17			0.0528777
$370$	1.41004e19	+	2.40221e19i	0.772181	+	1.31552i
$371$	1.22462e18			0.0657199
$372$			1.82637e18i			0.0960545i
$373$			1.16191e19i			0.598904i	0.954111	+	0.299452i	$0.0968038\pi$
$373$			1.16191e19i			0.598904i	−0.954111	+	0.299452i	$0.903196\pi$
$374$	2.56556e19			1.29612
$375$	−8.95996e16	−	4.15358e18i	−0.00443682	−	0.205678i
$376$	6.90407e18			0.335117
$377$		−	1.93211e19i		−	0.919330i
$378$		−	1.37990e19i		−	0.643664i
$379$	8.35574e18			0.382112			0.191056	−	0.981579i	$-0.438809\pi$
$379$	8.35574e18			0.382112			0.191056	+	0.981579i	$0.438809\pi$
$380$	−3.22132e19	−	5.48799e19i	−1.44430	−	2.46057i
$381$	7.20626e18			0.316791
$382$		−	1.42411e19i		−	0.613860i
$383$			7.58133e18i			0.320446i	0.987081	+	0.160223i	$0.0512213\pi$
$383$			7.58133e18i			0.320446i	−0.987081	+	0.160223i	$0.948779\pi$
$384$	−8.98769e18			−0.372532
$385$	−2.42620e19	+	1.42412e19i	−0.986214	+	0.578884i
$386$	−2.95791e19			−1.17918
$387$		−	1.05443e19i		−	0.412275i
$388$			8.78623e19i			3.36949i
$389$	3.55842e19			1.33855			0.669277	−	0.743013i	$-0.266604\pi$
$389$	3.55842e19			1.33855			0.669277	+	0.743013i	$0.266604\pi$
$390$	4.69604e18	−	2.75647e18i	0.173280	−	0.101711i
$391$	−2.75165e19			−0.996018
$392$			3.00176e18i			0.106593i
$393$			2.73470e18i			0.0952720i
$394$	−5.52172e19			−1.88735
$395$	2.66888e18	+	4.54682e18i	0.0895056	+	0.152486i
$396$	6.18783e19			2.03622
$397$		−	4.87189e18i		−	0.157314i	−0.996902	−	0.0786572i	$-0.974937\pi$
$397$		−	4.87189e18i		−	0.157314i	0.996902	−	0.0786572i	$-0.0250633\pi$
$398$			5.91648e18i			0.187474i
$399$	−1.01523e19			−0.315694
$400$	−6.27224e18	+	1.12338e19i	−0.191413	+	0.342829i
$401$	−8.01043e18			−0.239924			−0.119962	−	0.992779i	$-0.538277\pi$
$401$	−8.01043e18			−0.239924			−0.119962	+	0.992779i	$0.538277\pi$
$402$			9.29347e18i			0.273201i
$403$		−	5.31845e18i		−	0.153461i
$404$	6.11215e19			1.73115
$405$	−1.59282e19	−	2.71360e19i	−0.442846	−	0.754453i
$406$	9.19290e19			2.50904
$407$			4.07355e19i			1.09148i
$408$		−	6.63930e18i		−	0.174651i
$409$	−5.16991e19			−1.33524			−0.667619	−	0.744503i	$-0.732686\pi$
$409$	−5.16991e19			−1.33524			−0.667619	+	0.744503i	$0.732686\pi$
$410$	−3.13183e18	+	1.83831e18i	−0.0794180	+	0.0466165i
$411$	−5.92570e18			−0.147545
$412$		−	1.53696e19i		−	0.375780i
$413$			6.60915e16i			0.00158679i
$414$	−1.03616e20			−2.44301
$415$	−1.63449e19	+	9.59405e18i	−0.378461	+	0.222147i
$416$	1.67073e19			0.379933
$417$		−	2.59563e18i		−	0.0579727i
$418$		−	1.45296e20i		−	3.18737i
$419$	4.37426e19			0.942539			0.471269	−	0.881989i	$-0.343796\pi$
$419$	4.37426e19			0.942539			0.471269	+	0.881989i	$0.343796\pi$
$420$	8.40029e18	+	1.43111e19i	0.177797	+	0.302903i
$421$	−1.55963e19			−0.324268			−0.162134	−	0.986769i	$-0.551838\pi$
$421$	−1.55963e19			−0.324268			−0.162134	+	0.986769i	$0.551838\pi$
$422$		−	5.18721e19i		−	1.05947i
$423$		−	1.22687e19i		−	0.246177i
$424$	4.53557e18			0.0894105
$425$	2.93566e19	+	1.63908e19i	0.568577	+	0.317456i
$426$	1.84278e19			0.350672
$427$			1.22294e19i			0.228663i
$428$			4.57911e19i			0.841304i
$429$	7.96331e18			0.143769
$430$	2.04865e19	+	3.49017e19i	0.363458	+	0.619203i
$431$	1.87054e19			0.326127			0.163064	−	0.986616i	$-0.447862\pi$
$431$	1.87054e19			0.326127			0.163064	+	0.986616i	$0.447862\pi$
$432$		−	9.22911e18i		−	0.158136i
$433$			2.79482e19i			0.470647i	0.971917	+	0.235323i	$0.0756149\pi$
$433$			2.79482e19i			0.470647i	−0.971917	+	0.235323i	$0.924385\pi$
$434$	2.53050e19			0.418825
$435$	−1.71218e19	+	1.00501e19i	−0.278536	+	0.163494i
$436$	−4.81883e19			−0.770536
$437$			1.55835e20i			2.44937i
$438$		−	2.05401e19i		−	0.317357i
$439$	7.81127e19			1.18642			0.593209	−	0.805049i	$-0.297861\pi$
$439$	7.81127e19			1.18642			0.593209	+	0.805049i	$0.297861\pi$
$440$	−8.98582e19	+	5.27446e19i	−1.34172	+	0.787559i
$441$	5.33422e18			0.0783035
$442$			4.40682e19i			0.636001i
$443$		−	1.27574e20i		−	1.81023i	−0.425167	−	0.905115i	$-0.639784\pi$
$443$		−	1.27574e20i		−	1.81023i	0.425167	−	0.905115i	$-0.360216\pi$
$444$	2.40281e19			0.335233
$445$	−4.89932e19	−	8.34672e19i	−0.672103	−	1.14503i
$446$	−1.53616e20			−2.07217
$447$		−	1.71732e19i		−	0.227795i
$448$			1.08337e20i			1.41317i
$449$	5.40721e19			0.693627			0.346814	−	0.937934i	$-0.387264\pi$
$449$	5.40721e19			0.693627			0.346814	+	0.937934i	$0.387264\pi$
$450$	1.10546e20	+	6.17214e19i	1.39459	+	0.778650i
$451$	−5.31079e18			−0.0658924
$452$		−	2.07913e20i		−	2.53714i
$453$			9.11563e18i			0.109408i
$454$	−1.59325e20			−1.88090
$455$	−2.44618e19	−	4.16743e19i	−0.284056	−	0.483931i
$456$	−3.76005e19			−0.429494
$457$			3.69928e19i			0.415667i	0.978164	+	0.207833i	$0.0666412\pi$
$457$			3.69928e19i			0.415667i	−0.978164	+	0.207833i	$0.933359\pi$
$458$			9.82306e19i			1.08581i
$459$	−2.41178e19			−0.262267
$460$	2.19672e20	−	1.28942e20i	2.35013	−	1.37947i
$461$	−4.38103e19			−0.461126			−0.230563	−	0.973057i	$-0.574057\pi$
$461$	−4.38103e19			−0.461126			−0.230563	+	0.973057i	$0.574057\pi$
$462$			3.78891e19i			0.392373i
$463$			6.17232e19i			0.628913i	0.949272	+	0.314457i	$0.101822\pi$
$463$			6.17232e19i			0.628913i	−0.949272	+	0.314457i	$0.898178\pi$
$464$	6.14843e19			0.616424
$465$	−4.71307e18	+	2.76646e18i	−0.0464950	+	0.0272915i
$466$	1.52233e20			1.47779
$467$		−	1.96472e20i		−	1.87683i	−0.345513	−	0.938414i	$-0.612295\pi$
$467$		−	1.96472e20i		−	1.87683i	0.345513	−	0.938414i	$-0.387705\pi$
$468$			1.06287e20i			0.999163i
$469$	8.24736e19			0.762989
$470$	2.38368e19	+	4.06094e19i	0.217027	+	0.369737i
$471$	1.17043e19			0.104879
$472$			2.44780e17i			0.00215879i
$473$			5.91845e19i			0.513747i
$474$	7.10061e18			0.0606678
$475$	9.28266e19	−	1.66256e20i	0.780675	−	1.39822i
$476$	−1.34297e20			−1.11177
$477$		−	8.05985e18i		−	0.0656809i
$478$		−	1.45127e20i		−	1.16423i
$479$	−7.54528e19			−0.595881			−0.297940	−	0.954585i	$-0.596300\pi$
$479$	−7.54528e19			−0.595881			−0.297940	+	0.954585i	$0.596300\pi$
$480$	−8.69054e18	−	1.48056e19i	−0.0675674	−	0.115111i
$481$	−6.99705e19			−0.535583
$482$			2.03648e20i			1.53471i
$483$		−	4.06373e19i		−	0.301523i
$484$	−1.03444e20			−0.755728
$485$	−2.26734e20	+	1.33087e20i	−1.63100	+	0.957357i
$486$	−1.37209e20			−0.971876
$487$			1.37432e20i			0.958560i	0.877662	+	0.479280i	$0.159102\pi$
$487$			1.37432e20i			0.958560i	−0.877662	+	0.479280i	$0.840898\pi$
$488$			4.52935e19i			0.311091i
$489$	1.85047e19			0.125160
$490$	−1.76562e19	+	1.03638e19i	−0.117605	+	0.0690316i
$491$	1.58161e19			0.103750			0.0518750	−	0.998654i	$-0.483480\pi$
$491$	1.58161e19			0.103750			0.0518750	+	0.998654i	$0.483480\pi$
$492$			3.13261e18i			0.0202380i
$493$		−	1.60673e20i		−	1.02233i
$494$	2.49572e20			1.56403
$495$	9.37287e19	+	1.59681e20i	0.578540	+	0.985628i
$496$	1.69246e19			0.102898
$497$		−	1.63535e20i		−	0.979347i
$498$			2.55252e19i			0.150574i
$499$	2.37301e20			1.37894			0.689470	−	0.724314i	$-0.257843\pi$
$499$	2.37301e20			1.37894			0.689470	+	0.724314i	$0.257843\pi$
$500$	−3.11170e20	+	6.71245e18i	−1.78124	+	0.0384243i
$501$	6.78610e19			0.382682
$502$			8.52900e19i			0.473828i
$503$			1.76122e20i			0.963948i	0.876185	+	0.481974i	$0.160080\pi$
$503$			1.76122e20i			0.963948i	−0.876185	+	0.481974i	$0.839920\pi$
$504$	−2.21867e20			−1.19637
$505$	9.25823e19	+	1.57728e20i	0.491861	+	0.837958i
$506$	5.81589e20			3.04430
$507$		−	2.62102e19i		−	0.135180i
$508$		−	5.39865e20i		−	2.74351i
$509$	−1.78294e20			−0.892796			−0.446398	−	0.894834i	$-0.647293\pi$
$509$	−1.78294e20			−0.892796			−0.446398	+	0.894834i	$0.647293\pi$
$510$	3.90520e19	−	2.29226e19i	0.192694	−	0.113107i
$511$	−1.82280e20			−0.886305
$512$			1.59997e20i			0.766632i
$513$			1.36587e20i			0.644955i
$514$	−2.08734e20			−0.971335
$515$	3.96622e19	−	2.32808e19i	0.181896	−	0.106769i
$516$	3.49104e19			0.157791
$517$			6.88634e19i			0.306768i
$518$		−	3.32917e20i		−	1.46171i
$519$	−3.31076e19			−0.143276
$520$	−9.05983e19	−	1.54347e20i	−0.386451	−	0.658377i
$521$	2.55797e20			1.07551			0.537753	−	0.843102i	$-0.319273\pi$
$521$	2.55797e20			1.07551			0.537753	+	0.843102i	$0.319273\pi$
$522$		−	6.05032e20i		−	2.50755i
$523$			3.28407e19i			0.134168i	0.997747	+	0.0670842i	$0.0213696\pi$
$523$			3.28407e19i			0.134168i	−0.997747	+	0.0670842i	$0.978630\pi$
$524$	2.04873e20			0.825087
$525$	−2.42065e19	+	4.33549e19i	−0.0961032	+	0.172125i
$526$	−1.34064e20			−0.524708
$527$		−	4.42279e19i		−	0.170654i
$528$			2.53411e19i			0.0963989i
$529$	−3.57138e20			−1.33942
$530$	1.56594e19	+	2.66780e19i	0.0579036	+	0.0986472i
$531$	4.34981e17			0.00158585
$532$			7.60568e20i			2.73401i
$533$		−	9.12223e18i		−	0.0323331i
$534$	−1.30348e20			−0.455558
$535$	−1.18167e20	+	6.93610e19i	−0.407232	+	0.239035i
$536$	3.05454e20			1.03803
$537$		−	5.04419e19i		−	0.169038i
$538$			9.49452e20i			3.13766i
$539$	−2.99405e19			−0.0975761
$540$	1.92540e20	−	1.13016e20i	0.618825	−	0.363235i
$541$	4.27990e20			1.35661			0.678303	−	0.734782i	$-0.262716\pi$
$541$	4.27990e20			1.35661			0.678303	+	0.734782i	$0.262716\pi$
$542$		−	1.23516e20i		−	0.386127i
$543$			6.87191e19i			0.211874i
$544$	1.38937e20			0.422500
$545$	−7.29921e19	−	1.24353e20i	−0.218928	−	0.372977i
$546$	−6.50813e19			−0.192536
$547$		−	4.60215e20i		−	1.34294i	−0.741032	−	0.671469i	$-0.765664\pi$
$547$		−	4.60215e20i		−	1.34294i	0.741032	−	0.671469i	$-0.234336\pi$
$548$			4.43930e20i			1.27779i
$549$	8.04878e19			0.228527
$550$	−6.20483e20	−	3.46437e20i	−1.73784	−	0.970296i
$551$	−9.09944e20			−2.51407
$552$		−	1.50507e20i		−	0.410216i
$553$		−	6.30133e19i		−	0.169431i
$554$	7.69512e20			2.04123
$555$	3.63960e19	+	6.20060e19i	0.0952482	+	0.162269i
$556$	−1.94455e20			−0.502063
$557$		−	2.11016e20i		−	0.537529i	−0.963206	−	0.268765i	$-0.913385\pi$
$557$		−	2.11016e20i		−	0.537529i	0.963206	−	0.268765i	$-0.0866154\pi$
$558$		−	1.66545e20i		−	0.418576i
$559$	−1.01660e20			−0.252093
$560$	1.32618e20	−	7.78435e19i	0.324483	−	0.190464i
$561$	6.62224e19			0.159876
$562$			6.35571e20i			1.51405i
$563$		−	2.16952e19i		−	0.0509976i	−0.999675	−	0.0254988i	$-0.991883\pi$
$563$		−	2.16952e19i		−	0.0509976i	0.999675	−	0.0254988i	$-0.00811740\pi$
$564$	4.06196e19			0.0942198
$565$	5.36532e20	−	3.14932e20i	1.22810	−	0.720864i
$566$	−9.49098e20			−2.14382
$567$			3.76071e20i			0.838294i
$568$		−	6.05676e20i		−	1.33238i
$569$	−2.23104e19			−0.0484356			−0.0242178	−	0.999707i	$-0.507710\pi$
$569$	−2.23104e19			−0.0484356			−0.0242178	+	0.999707i	$0.507710\pi$
$570$	−1.29818e20	−	2.21164e20i	−0.278147	−	0.473864i
$571$	6.99283e20			1.47871			0.739353	−	0.673317i	$-0.235131\pi$
$571$	6.99283e20			1.47871			0.739353	+	0.673317i	$0.235131\pi$
$572$		−	5.96580e20i		−	1.24508i
$573$		−	3.67593e19i		−	0.0757194i
$574$	4.34032e19			0.0882435
$575$	6.65487e20	+	3.71565e20i	1.33546	+	0.745634i
$576$	7.13024e20			1.41233
$577$		−	5.07975e20i		−	0.993171i	−0.867988	−	0.496585i	$-0.834587\pi$
$577$		−	5.07975e20i		−	0.993171i	0.867988	−	0.496585i	$-0.165413\pi$
$578$		−	4.97724e20i		−	0.960573i
$579$	−7.63496e19			−0.145451
$580$	7.52915e20	+	1.28270e21i	1.41591	+	2.41221i
$581$	2.26520e20			0.420518
$582$			3.54082e20i			0.648906i
$583$			4.52392e19i			0.0818467i
$584$	−6.75104e20			−1.20580
$585$	−2.74280e20	+	1.60996e20i	−0.483643	+	0.283887i
$586$	−1.42061e21			−2.47311
$587$			9.20148e20i			1.58151i	0.612133	+	0.790755i	$0.290312\pi$
$587$			9.20148e20i			1.58151i	−0.612133	+	0.790755i	$0.709688\pi$
$588$			1.76606e19i			0.0299693i
$589$	−2.50477e20			−0.419665
$590$	−1.43979e18	+	8.45120e17i	−0.00238181	+	0.00139807i
$591$	−1.42527e20			−0.232804
$592$		−	2.22663e20i		−	0.359116i
$593$		−	7.45068e20i		−	1.18655i	−0.805000	−	0.593275i	$-0.797835\pi$
$593$		−	7.45068e20i		−	1.18655i	0.805000	−	0.593275i	$-0.202165\pi$
$594$	5.09755e20			0.801611
$595$	−2.03423e20	−	3.46561e20i	−0.315881	−	0.538150i
$596$	−1.28655e21			−1.97278
$597$			1.52716e19i			0.0231248i
$598$			9.98983e20i			1.49382i
$599$	−3.78607e20			−0.559098			−0.279549	−	0.960131i	$-0.590185\pi$
$599$	−3.78607e20			−0.559098			−0.279549	+	0.960131i	$0.590185\pi$
$600$	−8.96527e19	+	1.60572e20i	−0.130746	+	0.234172i
$601$	5.38635e20			0.775775			0.387887	−	0.921707i	$-0.373205\pi$
$601$	5.38635e20			0.775775			0.387887	+	0.921707i	$0.373205\pi$
$602$		−	4.83695e20i		−	0.688014i
$603$		−	5.42800e20i		−	0.762536i
$604$	6.82907e20			0.947512
$605$	−1.56690e20	−	2.66944e20i	−0.214721	−	0.365809i
$606$	2.46318e20			0.333389
$607$			7.37841e20i			0.986388i	0.869919	+	0.493194i	$0.164171\pi$
$607$			7.37841e20i			0.986388i	−0.869919	+	0.493194i	$0.835829\pi$
$608$		−	7.86847e20i		−	1.03899i
$609$	2.37288e20			0.309489
$610$	−2.66414e20	+	1.56379e20i	−0.343229	+	0.201467i
$611$	−1.18285e20			−0.150529
$612$			8.83877e20i			1.11111i
$613$			6.78619e20i			0.842698i	0.906898	+	0.421349i	$0.138443\pi$
$613$			6.78619e20i			0.842698i	−0.906898	+	0.421349i	$0.861557\pi$
$614$	1.27494e21			1.56397
$615$	−8.08388e18	+	4.74505e18i	−0.00979617	+	0.00575012i
$616$	1.24532e21			1.49082
$617$			5.97586e20i			0.706743i	0.935483	+	0.353372i	$0.114965\pi$
$617$			5.97586e20i			0.706743i	−0.935483	+	0.353372i	$0.885035\pi$
$618$		−	6.19391e19i		−	0.0723688i
$619$	−3.49530e20			−0.403463			−0.201732	−	0.979441i	$-0.564657\pi$
$619$	−3.49530e20			−0.403463			−0.201732	+	0.979441i	$0.564657\pi$
$620$	2.07252e20	+	3.53085e20i	0.236353	+	0.402662i
$621$	−5.46729e20			−0.616006
$622$		−	2.93478e21i		−	3.26699i
$623$			1.15675e21i			1.27227i
$624$	−4.35280e19			−0.0473025
$625$	−4.88660e20	−	7.92826e20i	−0.524695	−	0.851290i
$626$	1.82630e21			1.93760
$627$		−	3.75039e20i		−	0.393160i
$628$		−	8.76840e20i		−	0.908287i
$629$	−5.81870e20			−0.595589
$630$	−7.66012e20	−	1.30501e21i	−0.774785	−	1.31996i
$631$	−1.66495e21			−1.66410			−0.832052	−	0.554697i	$-0.812834\pi$
$631$	−1.66495e21			−1.66410			−0.832052	+	0.554697i	$0.812834\pi$
$632$		−	2.33380e20i		−	0.230508i
$633$		−	1.33892e20i		−	0.130686i
$634$	2.76578e20			0.266777
$635$	1.39315e21	−	8.17748e20i	1.32799	−	0.779500i
$636$	2.66847e19			0.0251382
$637$		−	5.14282e19i		−	0.0478801i
$638$			3.39599e21i			3.12472i
$639$	−1.07630e21			−0.978765
$640$	−1.73755e21	+	1.01990e21i	−1.56166	+	0.916659i
$641$	1.45703e21			1.29430			0.647150	−	0.762363i	$-0.275961\pi$
$641$	1.45703e21			1.29430			0.647150	+	0.762363i	$0.275961\pi$
$642$			1.84537e20i			0.162021i
$643$		−	1.13525e21i		−	0.985166i	−0.870266	−	0.492583i	$-0.836053\pi$
$643$		−	1.13525e21i		−	0.985166i	0.870266	−	0.492583i	$-0.163947\pi$
$644$	−3.04439e21			−2.61129
$645$	5.28798e19	+	9.00884e19i	0.0448324	+	0.0763785i
$646$	2.07543e21			1.73926
$647$			1.77938e21i			1.47397i	0.675912	+	0.736983i	$0.263750\pi$
$647$			1.77938e21i			1.47397i	−0.675912	+	0.736983i	$0.736250\pi$
$648$			1.39284e21i			1.14048i
$649$	−2.44151e18			−0.00197617
$650$	5.95068e20	−	1.06579e21i	0.476120	−	0.852749i
$651$	6.53173e19			0.0516619
$652$		−	1.38630e21i		−	1.08393i
$653$			5.03322e20i			0.389043i	0.980898	+	0.194521i	$0.0623153\pi$
$653$			5.03322e20i			0.389043i	−0.980898	+	0.194521i	$0.937685\pi$
$654$	−1.94197e20			−0.148392
$655$	3.10327e20	+	5.28687e20i	0.234428	+	0.399382i
$656$	2.90291e19			0.0216798
$657$			1.19968e21i			0.885779i
$658$		−	5.62797e20i		−	0.410825i
$659$	2.35681e21			1.70092			0.850461	−	0.526038i	$-0.176323\pi$
$659$	2.35681e21			1.70092			0.850461	+	0.526038i	$0.176323\pi$
$660$	−5.28673e20	+	3.10319e20i	−0.377231	+	0.221426i
$661$	1.75909e21			1.24102			0.620508	−	0.784200i	$-0.286926\pi$
$661$	1.75909e21			1.24102			0.620508	+	0.784200i	$0.286926\pi$
$662$			2.76110e21i			1.92596i
$663$			1.13749e20i			0.0784505i
$664$	8.38951e20			0.572105
$665$	−1.96269e21	+	1.15205e21i	−1.32339	+	0.776801i
$666$	−2.19109e21			−1.46085
$667$		−	3.64231e21i		−	2.40123i
$668$		−	5.08388e21i		−	3.31415i
$669$	−3.96514e20			−0.255601
$670$	1.05460e21	+	1.79666e21i	0.672244	+	1.14527i
$671$	−4.51771e20			−0.284774
$672$			2.05187e20i			0.127903i
$673$			1.14413e21i			0.705281i	0.935759	+	0.352641i	$0.114716\pi$
$673$			1.14413e21i			0.705281i	−0.935759	+	0.352641i	$0.885284\pi$
$674$	−3.65520e21			−2.22824
$675$	5.83291e20	+	3.25672e20i	0.351647	+	0.196337i
$676$	−1.96357e21			−1.17070
$677$		−	1.38202e21i		−	0.814889i	−0.913230	−	0.407444i	$-0.866420\pi$
$677$		−	1.38202e21i		−	0.814889i	0.913230	−	0.407444i	$-0.133580\pi$
$678$		−	8.37884e20i		−	0.488608i
$679$	3.14225e21			1.81225
$680$	−7.53410e20	−	1.28354e21i	−0.429749	−	0.732140i
$681$	−4.11250e20			−0.232008
$682$			9.34802e20i			0.521599i
$683$		−	2.51269e21i		−	1.38670i	−0.720600	−	0.693351i	$-0.756134\pi$
$683$		−	2.51269e21i		−	1.38670i	0.720600	−	0.693351i	$-0.243866\pi$
$684$	5.00568e21			2.73239
$685$	−1.14559e21	+	6.72433e20i	−0.618514	+	0.363053i
$686$	3.23737e21			1.72887
$687$			2.53553e20i			0.133935i
$688$		−	3.23507e20i		−	0.169032i
$689$	−7.77065e19			−0.0401618
$690$	8.85272e20	−	5.19634e20i	0.452594	−	0.265662i
$691$	−3.22434e21			−1.63063			−0.815314	−	0.579019i	$-0.803436\pi$
$691$	−3.22434e21			−1.63063			−0.815314	+	0.579019i	$0.803436\pi$
$692$			2.48030e21i			1.24082i
$693$		−	2.21297e21i		−	1.09516i
$694$	−1.06190e21			−0.519862
$695$	−2.94546e20	−	5.01802e20i	−0.142648	−	0.243023i
$696$	8.78832e20			0.421053
$697$		−	7.58600e19i		−	0.0359556i
$698$			3.62246e21i			1.69859i
$699$	3.92944e20			0.182285
$700$	3.24798e21	+	1.81346e21i	1.49066	+	0.832286i
$701$	2.11598e21			0.960787			0.480393	−	0.877053i	$-0.340494\pi$
$701$	2.11598e21			0.960787			0.480393	+	0.877053i	$0.340494\pi$
$702$			8.75596e20i			0.393347i
$703$			3.29532e21i			1.46465i
$704$	−4.00214e21			−1.75994
$705$	6.15276e19	+	1.04821e20i	0.0267702	+	0.0456069i
$706$	−4.43894e21			−1.91093
$707$		−	2.18591e21i		−	0.931079i
$708$			1.44014e18i			0.000606955i
$709$	−2.68880e21			−1.12127			−0.560637	−	0.828062i	$-0.689444\pi$
$709$	−2.68880e21			−1.12127			−0.560637	+	0.828062i	$0.689444\pi$
$710$	3.56256e21	−	2.09114e21i	1.47002	−	0.862869i
$711$	−4.14723e20			−0.169331
$712$			4.28421e21i			1.73090i
$713$		−	1.00261e21i		−	0.400828i
$714$	−5.41213e20			−0.214107
$715$	1.53951e21	−	9.03656e20i	0.602681	−	0.353759i
$716$	−3.77891e21			−1.46393
$717$		−	3.74603e20i		−	0.143608i
$718$			8.64778e20i			0.328073i
$719$	−1.17866e21			−0.442510			−0.221255	−	0.975216i	$-0.571015\pi$
$719$	−1.17866e21			−0.442510			−0.221255	+	0.975216i	$0.571015\pi$
$720$	−5.12327e20	−	8.72824e20i	−0.190350	−	0.324290i
$721$	−5.49669e20			−0.202110
$722$		−	7.17050e21i		−	2.60928i
$723$			5.25657e20i			0.189306i
$724$	5.14817e21			1.83490
$725$	−2.16963e21	+	3.88589e21i	−0.765332	+	1.37074i
$726$	−4.16876e20			−0.145540
$727$		−	1.95489e21i		−	0.675484i	−0.941239	−	0.337742i	$-0.890337\pi$
$727$		−	1.95489e21i		−	0.675484i	0.941239	−	0.337742i	$-0.109663\pi$
$728$			2.13906e21i			0.731541i
$729$	2.23033e21			0.754941
$730$	−2.33084e21	−	3.97093e21i	−0.780893	−	1.33037i
$731$	−8.45399e20			−0.280338
$732$			2.66481e20i			0.0874646i
$733$			5.70177e21i			1.85238i	0.377059	+	0.926189i	$0.376935\pi$
$733$			5.70177e21i			1.85238i	−0.377059	+	0.926189i	$0.623065\pi$
$734$	−7.77048e20			−0.249878
$735$	−4.55743e19	+	2.67510e19i	−0.0145066	+	0.00851501i
$736$	3.14958e21			0.992359
$737$			3.04669e21i			0.950216i
$738$		−	2.85659e20i		−	0.0881911i
$739$	5.49336e21			1.67882			0.839411	−	0.543497i	$-0.182900\pi$
$739$	5.49336e21			1.67882			0.839411	+	0.543497i	$0.182900\pi$
$740$	4.64524e21	−	2.72665e21i	1.40531	−	0.824881i
$741$	6.44197e20			0.192922
$742$		−	3.69725e20i		−	0.109610i
$743$		−	6.28661e20i		−	0.184502i	−0.995736	−	0.0922509i	$-0.970594\pi$
$743$		−	6.28661e20i		−	0.184502i	0.995736	−	0.0922509i	$-0.0294062\pi$
$744$	2.41913e20			0.0702849
$745$	−1.94877e21	−	3.32002e21i	−0.560517	−	0.954923i
$746$	3.50792e21			0.998870
$747$		−	1.49084e21i		−	0.420268i
$748$		−	4.96113e21i		−	1.38458i
$749$	1.63764e21			0.452487
$750$	−1.25401e21	+	2.70510e19i	−0.343037	+	0.00739986i
$751$	−2.29542e21			−0.621673			−0.310837	−	0.950463i	$-0.600609\pi$
$751$	−2.29542e21			−0.621673			−0.310837	+	0.950463i	$0.600609\pi$
$752$		−	3.76412e20i		−	0.100932i
$753$			2.20151e20i			0.0584465i
$754$	−5.83322e21			−1.53329
$755$	1.03442e21	+	1.76228e21i	0.269212	+	0.458642i
$756$	−2.66837e21			−0.687594
$757$			2.60470e21i			0.664567i	0.943180	+	0.332284i	$0.107819\pi$
$757$			2.60470e21i			0.664567i	−0.943180	+	0.332284i	$0.892181\pi$
$758$		−	2.52268e21i		−	0.637298i
$759$	1.50120e21			0.375513
$760$	−7.26913e21	+	4.26681e21i	−1.80045	+	1.05682i
$761$	−4.31540e20			−0.105837			−0.0529183	−	0.998599i	$-0.516852\pi$
$761$	−4.31540e20			−0.105837			−0.0529183	+	0.998599i	$0.516852\pi$
$762$		−	2.17564e21i		−	0.528353i
$763$			1.72337e21i			0.414425i
$764$	−2.75386e21			−0.655756
$765$	−2.28090e21	+	1.33883e21i	−0.537830	+	0.315693i
$766$	2.28887e21			0.534449
$767$		−	4.19374e18i		−	0.000969697i
$768$			1.38847e21i			0.317927i
$769$	−4.79403e21			−1.08706			−0.543530	−	0.839390i	$-0.682912\pi$
$769$	−4.79403e21			−1.08706			−0.543530	+	0.839390i	$0.682912\pi$
$770$	4.29956e21	+	7.32493e21i	0.965481	+	1.64484i
$771$	−5.38784e20			−0.119814
$772$			5.71981e21i			1.25966i
$773$		−	4.26764e21i		−	0.930767i	−0.885109	−	0.465384i	$-0.845916\pi$
$773$		−	4.26764e21i		−	0.930767i	0.885109	−	0.465384i	$-0.154084\pi$
$774$	−3.18344e21			−0.687605
$775$	−5.97225e20	+	1.06965e21i	−0.127754	+	0.228813i
$776$	1.16378e22			2.46552
$777$		−	8.59326e20i		−	0.180302i
$778$		−	1.07432e22i		−	2.23248i
$779$	−4.29620e20			−0.0884205
$780$	−5.33028e20	−	9.08091e20i	−0.108653	−	0.185106i
$781$	6.04120e21			1.21967
$782$			8.30749e21i			1.66119i
$783$		−	3.19244e21i		−	0.632279i
$784$	1.63657e20			0.0321043
$785$	2.26274e21	−	1.32817e21i	0.439655	−	0.258067i
$786$	8.25631e20			0.158897
$787$			5.95930e21i			1.13602i	0.823023	+	0.568008i	$0.192286\pi$
$787$			5.95930e21i			1.13602i	−0.823023	+	0.568008i	$0.807714\pi$
$788$			1.06776e22i			2.01616i
$789$	−3.46045e20			−0.0647225
$790$	1.37273e21	−	8.05759e20i	0.254321	−	0.149280i
$791$	−7.43568e21			−1.36457
$792$		−	8.19610e21i		−	1.48994i
$793$		−	7.75998e20i		−	0.139737i
$794$	−1.47087e21			−0.262374
$795$	4.04200e19	+	6.88614e19i	0.00714238	+	0.0121681i
$796$	1.14409e21			0.200269
$797$		−	8.33436e21i		−	1.44522i	−0.691255	−	0.722611i	$-0.742942\pi$
$797$		−	8.33436e21i		−	1.44522i	0.691255	−	0.722611i	$-0.257058\pi$
$798$			3.06506e21i			0.526523i
$799$	−9.83653e20			−0.167394
$800$	−3.36020e21	−	1.87612e21i	−0.566488	−	0.316290i
$801$	7.61317e21			1.27152
$802$			2.41842e21i			0.400152i
$803$		−	6.73370e21i		−	1.10379i
$804$	1.79711e21			0.291847
$805$	−4.61141e21	−	7.85622e21i	−0.741934	−	1.26399i
$806$	−1.60569e21			−0.255946
$807$			2.45073e21i			0.387029i
$808$		−	8.09586e21i		−	1.26671i
$809$	−4.00498e20			−0.0620850			−0.0310425	−	0.999518i	$-0.509883\pi$
$809$	−4.00498e20			−0.0620850			−0.0310425	+	0.999518i	$0.509883\pi$
$810$	−8.19260e21	+	4.80886e21i	−1.25830	+	0.738592i
$811$	−4.61659e21			−0.702529			−0.351265	−	0.936276i	$-0.614248\pi$
$811$	−4.61659e21			−0.702529			−0.351265	+	0.936276i	$0.614248\pi$
$812$		−	1.77767e22i		−	2.68028i
$813$		−	3.18821e20i		−	0.0476286i
$814$	1.22984e22			1.82040
$815$	3.57743e21	−	2.09987e21i	0.524674	−	0.307971i
$816$	−3.61976e20			−0.0526022
$817$			4.78777e21i			0.689394i
$818$			1.56085e22i			2.22695i
$819$	3.80118e21			0.537390
$820$	3.55480e20	+	6.05613e20i	0.0497980	+	0.0848381i
$821$	8.29377e20			0.115127			0.0575636	−	0.998342i	$-0.481667\pi$
$821$	8.29377e20			0.115127			0.0575636	+	0.998342i	$0.481667\pi$
$822$			1.78902e21i			0.246081i
$823$			7.90016e21i			1.07681i	0.842688	+	0.538403i	$0.180972\pi$
$823$			7.90016e21i			1.07681i	−0.842688	+	0.538403i	$0.819028\pi$
$824$	−2.03579e21			−0.274966
$825$	−1.60159e21	−	8.94225e20i	−0.214362	−	0.119686i
$826$	1.99536e19			0.00264650
$827$			9.62655e21i			1.26526i	0.774455	+	0.632629i	$0.218024\pi$
$827$			9.62655e21i			1.26526i	−0.774455	+	0.632629i	$0.781976\pi$
$828$			2.00367e22i			2.60974i
$829$	3.97587e21			0.513185			0.256592	−	0.966520i	$-0.417400\pi$
$829$	3.97587e21			0.513185			0.256592	+	0.966520i	$0.417400\pi$
$830$	2.89653e21	+	4.93467e21i	0.370504	+	0.631208i
$831$	1.98627e21			0.251785
$832$		−	6.87439e21i		−	0.863594i
$833$		−	4.27674e20i		−	0.0532446i
$834$	−7.83647e20			−0.0966885
$835$	1.31193e22	−	7.70070e21i	1.60421	−	0.941633i
$836$	−2.80965e22			−3.40490
$837$		−	8.78770e20i		−	0.105544i
$838$		−	1.32063e22i		−	1.57199i
$839$	−5.99428e21			−0.707168			−0.353584	−	0.935403i	$-0.615037\pi$
$839$	−5.99428e21			−0.707168			−0.353584	+	0.935403i	$0.615037\pi$
$840$	1.89558e21	−	1.11266e21i	0.221640	−	0.130097i
$841$	1.26388e22			1.46466
$842$			4.70866e21i			0.540825i
$843$			1.64054e21i			0.186758i
$844$	−1.00307e22			−1.13178
$845$	−2.97427e21	−	5.06711e21i	−0.332625	−	0.566676i
$846$	−3.70405e21			−0.410581
$847$			3.69951e21i			0.406461i
$848$		−	2.47281e20i		−	0.0269291i
$849$	−2.44982e21			−0.264439
$850$	4.94855e21	−	8.86305e21i	0.529463	−	0.948290i
$851$	−1.31905e22			−1.39890
$852$		−	3.56345e21i		−	0.374605i
$853$			5.27177e21i			0.549337i	0.961539	+	0.274668i	$0.0885681\pi$
$853$			5.27177e21i			0.549337i	−0.961539	+	0.274668i	$0.911432\pi$
$854$	3.69217e21			0.381371
$855$	7.58224e21	+	1.29175e22i	0.776339	+	1.32261i
$856$	6.06527e21			0.615598
$857$		−	1.15549e21i		−	0.116254i	−0.998309	−	0.0581271i	$-0.981487\pi$
$857$		−	1.15549e21i		−	0.116254i	0.998309	−	0.0581271i	$-0.0185129\pi$
$858$		−	2.40420e21i		−	0.239781i
$859$	−1.29668e22			−1.28199			−0.640995	−	0.767545i	$-0.721478\pi$
$859$	−1.29668e22			−1.28199			−0.640995	+	0.767545i	$0.721478\pi$
$860$	6.74907e21	−	3.96155e21i	0.661463	−	0.388263i
$861$	1.12033e20			0.0108848
$862$		−	5.64734e21i		−	0.543925i
$863$		−	8.97402e21i		−	0.856852i	−0.903577	−	0.428426i	$-0.859068\pi$
$863$		−	8.97402e21i		−	0.856852i	0.903577	−	0.428426i	$-0.140932\pi$
$864$	2.76056e21			0.261303
$865$	−6.40055e21	+	3.75697e21i	−0.600615	+	0.352547i
$866$	8.43784e21			0.784959
$867$		−	1.28473e21i		−	0.118486i
$868$		−	4.89332e21i		−	0.447410i
$869$	2.32780e21			0.211008
$870$	3.03422e21	+	5.16925e21i	0.272680	+	0.464550i
$871$	−5.23324e21			−0.466267
$872$			6.38279e21i			0.563815i
$873$		−	2.06807e22i		−	1.81117i
$874$	4.70480e22			4.08513
$875$	2.40060e20	+	1.11285e22i	0.0206661	+	0.958023i
$876$	−3.97192e21			−0.339016
$877$			3.50814e21i			0.296879i	0.988921	+	0.148440i	$0.0474251\pi$
$877$			3.50814e21i			0.296879i	−0.988921	+	0.148440i	$0.952575\pi$
$878$		−	2.35830e22i		−	1.97874i
$879$	−3.66689e21			−0.305057
$880$	2.87565e21	+	4.89909e21i	0.237201	+	0.404106i
$881$	1.73060e22			1.41540			0.707699	−	0.706514i	$-0.249733\pi$
$881$	1.73060e22			1.41540			0.707699	+	0.706514i	$0.249733\pi$
$882$		−	1.61045e21i		−	0.130597i
$883$			1.95732e22i			1.57383i	0.617062	+	0.786914i	$0.288323\pi$
$883$			1.95732e22i			1.57383i	−0.617062	+	0.786914i	$0.711677\pi$
$884$	8.52162e21			0.679407
$885$	−3.71638e18	+	2.18143e18i	−0.000293796	+	0.000172451i
$886$	−3.85158e22			−3.01916
$887$		−	6.58506e21i		−	0.511838i	−0.966698	−	0.255919i	$-0.917622\pi$
$887$		−	6.58506e21i		−	0.511838i	0.966698	−	0.255919i	$-0.0823780\pi$
$888$		−	3.18265e21i		−	0.245297i
$889$	−1.93074e22			−1.47557
$890$	−2.51995e22	+	1.47915e22i	−1.90971	+	1.12095i
$891$	−1.38926e22			−1.04400
$892$			2.97053e22i			2.21359i
$893$			5.57075e21i			0.411649i
$894$	−5.18476e21			−0.379924
$895$	−5.72402e21	−	9.75171e21i	−0.415938	−	0.708611i
$896$	2.40803e22			1.73521
$897$			2.57858e21i			0.184263i
$898$		−	1.63249e22i		−	1.15685i
$899$	5.85437e21			0.411417
$900$	1.19353e22	−	2.13766e22i	0.831792	−	1.48977i
$901$	−6.46203e20			−0.0446615
$902$			1.60338e21i			0.109897i
$903$		−	1.24851e21i		−	0.0848663i
$904$	−2.75392e22			−1.85647
$905$	7.79807e21	+	1.32851e22i	0.521342	+	0.888182i
$906$	2.75209e21			0.182474
$907$		−	2.54107e22i		−	1.67095i	−0.549531	−	0.835473i	$-0.685194\pi$
$907$		−	2.54107e22i		−	1.67095i	0.549531	−	0.835473i	$-0.314806\pi$
$908$			3.08092e22i			2.00926i
$909$	−1.43866e22			−0.930525
$910$	−1.25819e22	+	7.38526e21i	−0.807114	+	0.473757i
$911$	1.32653e22			0.843975			0.421987	−	0.906602i	$-0.361333\pi$
$911$	1.32653e22			0.843975			0.421987	+	0.906602i	$0.361333\pi$
$912$			2.04999e21i			0.129357i
$913$			8.36796e21i			0.523707i
$914$	1.11685e22			0.693262
$915$	−6.87669e20	+	4.03645e20i	−0.0423371	+	0.0248509i
$916$	1.89952e22			1.15992
$917$		−	7.32694e21i		−	0.443765i
$918$			7.28141e21i			0.437417i
$919$	2.44915e22			1.45932			0.729659	−	0.683812i	$-0.239679\pi$
$919$	2.44915e22			1.45932			0.729659	+	0.683812i	$0.239679\pi$
$920$	−1.70791e22	−	2.90967e22i	−1.00938	−	1.71963i
$921$	3.29088e21			0.192915
$922$			1.32268e22i			0.769080i
$923$			1.03768e22i			0.598484i
$924$	7.32676e21			0.419152
$925$	1.40726e22	+	7.85720e21i	0.798564	+	0.445866i
$926$	1.86348e22			1.04892
$927$			3.61765e21i			0.201990i
$928$			1.83909e22i			1.01857i
$929$	−1.27699e22			−0.701570			−0.350785	−	0.936456i	$-0.614085\pi$
$929$	−1.27699e22			−0.701570			−0.350785	+	0.936456i	$0.614085\pi$
$930$	8.35220e20	+	1.42292e21i	0.0455176	+	0.0775458i
$931$	−2.42206e21			−0.130937
$932$		−	2.94378e22i		−	1.57865i
$933$		−	7.57526e21i		−	0.402981i
$934$	−5.93168e22			−3.13023
$935$	1.28025e22	−	7.51475e21i	0.670204	−	0.393394i
$936$	1.40783e22			0.731106
$937$		−	3.23835e22i		−	1.66831i	−0.551528	−	0.834156i	$-0.685955\pi$
$937$		−	3.23835e22i		−	1.66831i	0.551528	−	0.834156i	$-0.314045\pi$
$938$		−	2.48996e22i		−	1.27254i
$939$	4.71405e21			0.239002
$940$	7.85280e21	−	4.60941e21i	0.394971	−	0.231839i
$941$	1.02130e22			0.509600			0.254800	−	0.966994i	$-0.417990\pi$
$941$	1.02130e22			0.509600			0.254800	+	0.966994i	$0.417990\pi$
$942$		−	3.53364e21i		−	0.174920i
$943$		−	1.71967e21i		−	0.0844517i
$944$	1.33455e19			0.000650196
$945$	−4.04185e21	−	6.88588e21i	−0.195362	−	0.332829i
$946$	1.78684e22			0.856843
$947$			3.01106e22i			1.43250i	0.697844	+	0.716249i	$0.254143\pi$
$947$			3.01106e22i			1.43250i	−0.697844	+	0.716249i	$0.745857\pi$
$948$		−	1.37307e21i		−	0.0648083i
$949$	1.15663e22			0.541626
$950$	−5.01943e22	−	2.80252e22i	−2.33199	−	1.30203i
$951$	7.13904e20			0.0329068
$952$			1.77883e22i			0.813502i
$953$			1.54106e22i			0.699233i	0.936893	+	0.349616i	$0.113688\pi$
$953$			1.54106e22i			0.699233i	−0.936893	+	0.349616i	$0.886312\pi$
$954$	−2.43334e21			−0.109545
$955$	−4.17135e21	−	7.10650e21i	−0.186316	−	0.317417i
$956$	−2.80638e22			−1.24369
$957$			8.76574e21i			0.385433i
$958$			2.27799e22i			0.993828i
$959$	1.58764e22			0.687248
$960$	−6.09190e21	+	3.57580e21i	−0.261649	+	0.153582i
$961$	−2.18538e22			−0.931324
$962$			2.11247e22i			0.893261i
$963$		−	1.07782e22i		−	0.452218i
$964$	3.93802e22			1.63946
$965$	−1.47603e22	+	8.66395e21i	−0.609734	+	0.357900i
$966$	−1.22688e22			−0.502890
$967$		−	4.24903e22i		−	1.72819i	−0.503330	−	0.864094i	$-0.667892\pi$
$967$		−	4.24903e22i		−	1.72819i	0.503330	−	0.864094i	$-0.332108\pi$
$968$			1.37017e22i			0.552980i
$969$	5.35710e21			0.214537
$970$	4.01804e22	+	6.84531e22i	1.59671	+	2.72023i
$971$	1.25803e22			0.496073			0.248037	−	0.968751i	$-0.420215\pi$
$971$	1.25803e22			0.496073			0.248037	+	0.968751i	$0.420215\pi$
$972$			2.65326e22i			1.03821i
$973$			6.95436e21i			0.270029i
$974$	4.14919e22			1.59872
$975$	1.53599e21	−	2.75102e21i	0.0587292	−	0.105186i
$976$	2.46941e21			0.0936958
$977$		−	2.40977e21i		−	0.0907331i	−0.998970	−	0.0453665i	$-0.985554\pi$
$977$		−	2.40977e21i		−	0.0907331i	0.998970	−	0.0453665i	$-0.0144456\pi$
$978$		−	5.58675e21i		−	0.208746i
$979$	−4.27321e22			−1.58447
$980$	2.00408e21	+	3.41425e21i	0.0737429	+	0.125632i
$981$	1.13424e22			0.414178
$982$		−	4.77503e21i		−	0.173037i
$983$		−	4.16509e22i		−	1.49787i	−0.662645	−	0.748934i	$-0.730566\pi$
$983$		−	4.16509e22i		−	1.49787i	0.662645	−	0.748934i	$-0.269434\pi$
$984$	4.14930e20			0.0148085
$985$	−2.75541e22	+	1.61736e22i	−0.975919	+	0.572841i
$986$	−4.85087e22			−1.70507
$987$		−	1.45269e21i		−	0.0506751i
$988$		−	4.82607e22i		−	1.67077i
$989$	−1.91644e22			−0.658450
$990$	4.82091e22	−	2.82976e22i	1.64386	−	0.964907i
$991$	−2.71460e21			−0.0918656			−0.0459328	−	0.998945i	$-0.514626\pi$
$991$	−2.71460e21			−0.0918656			−0.0459328	+	0.998945i	$0.514626\pi$
$992$			5.06239e21i			0.170027i
$993$			7.12695e21i			0.237566i
$994$	−4.93726e22			−1.63338
$995$	1.73299e21	+	2.95240e21i	0.0569013	+	0.0969396i
$996$	4.93590e21			0.160850
$997$			4.95508e22i			1.60264i	0.598234	+	0.801321i	$0.295869\pi$
$997$			4.95508e22i			1.60264i	−0.598234	+	0.801321i	$0.704131\pi$
$998$		−	7.16434e22i		−	2.29984i
$999$	−1.15613e22			−0.368353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.16.b.a.4.1	✓	6
3.2	odd	2		45.16.b.b.19.6		6
4.3	odd	2		80.16.c.a.49.4		6
5.2	odd	4		25.16.a.f.1.6		6
5.3	odd	4		25.16.a.f.1.1		6
5.4	even	2	inner	5.16.b.a.4.6	yes	6
15.14	odd	2		45.16.b.b.19.1		6
20.19	odd	2		80.16.c.a.49.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.16.b.a.4.1	✓	6	1.1	even	1	trivial
5.16.b.a.4.6	yes	6	5.4	even	2	inner
25.16.a.f.1.1		6	5.3	odd	4
25.16.a.f.1.6		6	5.2	odd	4
45.16.b.b.19.1		6	15.14	odd	2
45.16.b.b.19.6		6	3.2	odd	2
80.16.c.a.49.3		6	20.19	odd	2
80.16.c.a.49.4		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-301.910i q^{2} -779.290i q^{3} -58381.4 q^{4} +(-88431.8 - 150657. i) q^{5} -235275. q^{6} +2.08791e6i q^{7} +7.73292e6i q^{8} +1.37416e7 q^{9} +O(q^{10})\)	\(q-301.910i q^{2} -779.290i q^{3} -58381.4 q^{4} +(-88431.8 - 150657. i) q^{5} -235275. q^{6} +2.08791e6i q^{7} +7.73292e6i q^{8} +1.37416e7 q^{9} +(-4.54846e7 + 2.66984e7i) q^{10} -7.71305e7 q^{11} +4.54960e7i q^{12} -1.32485e8i q^{13} +6.30361e8 q^{14} +(-1.17405e8 + 6.89140e7i) q^{15} +4.21600e8 q^{16} -1.10174e9i q^{17} -4.14872e9i q^{18} -6.23952e9 q^{19} +(5.16277e9 + 8.79553e9i) q^{20} +1.62709e9 q^{21} +2.32864e10i q^{22} -2.49754e10i q^{23} +6.02618e9 q^{24} +(-1.48772e10 + 2.66457e10i) q^{25} -3.99986e10 q^{26} -2.18907e10i q^{27} -1.21895e11i q^{28} +1.45836e11 q^{29} +(2.08058e10 + 3.54457e10i) q^{30} +4.01436e10 q^{31} +1.26107e11i q^{32} +6.01070e10i q^{33} -3.32626e11 q^{34} +(3.14558e11 - 1.84638e11i) q^{35} -8.02254e11 q^{36} -5.28137e11i q^{37} +1.88377e12i q^{38} -1.03245e11 q^{39} +(1.16501e12 - 6.83836e11i) q^{40} +6.88546e10 q^{41} -4.91234e11i q^{42} -7.67330e11i q^{43} +4.50298e12 q^{44} +(-1.21520e12 - 2.07026e12i) q^{45} -7.54032e12 q^{46} -8.92816e11i q^{47} -3.28549e11i q^{48} +3.88180e11 q^{49} +(8.04458e12 + 4.49157e12i) q^{50} -8.58576e11 q^{51} +7.73468e12i q^{52} -5.86528e11i q^{53} -6.60900e12 q^{54} +(6.82079e12 + 1.16202e13i) q^{55} -1.61457e13 q^{56} +4.86239e12i q^{57} -4.40291e13i q^{58} +3.16543e10 q^{59} +(6.85427e12 - 4.02329e12i) q^{60} +5.85723e12 q^{61} -1.21197e13i q^{62} +2.86913e13i q^{63} +5.18879e13 q^{64} +(-1.99598e13 + 1.17159e13i) q^{65} +1.81469e13 q^{66} -3.95005e13i q^{67} +6.43212e13i q^{68} -1.94631e13 q^{69} +(-5.57440e13 - 9.49680e13i) q^{70} -7.83244e13 q^{71} +1.06263e14i q^{72} +8.73027e13i q^{73} -1.59450e14 q^{74} +(2.07647e13 + 1.15937e13i) q^{75} +3.64272e14 q^{76} -1.61042e14i q^{77} +3.11705e13i q^{78} -3.01801e13 q^{79} +(-3.72829e13 - 6.35169e13i) q^{80} +1.80118e14 q^{81} -2.07879e13i q^{82} -1.08491e14i q^{83} -9.49917e13 q^{84} +(-1.65985e14 + 9.74290e13i) q^{85} -2.31664e14 q^{86} -1.13648e14i q^{87} -5.96444e14i q^{88} +5.54023e14 q^{89} +(-6.25032e14 + 3.66879e14i) q^{90} +2.76618e14 q^{91} +1.45810e15i q^{92} -3.12835e13i q^{93} -2.69550e14 q^{94} +(5.51772e14 + 9.40024e14i) q^{95} +9.82739e13 q^{96} -1.50497e15i q^{97} -1.17195e14i q^{98} -1.05990e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 38568 q^{4} - 238350 q^{5} - 515448 q^{6} - 11416662 q^{9}+O(q^{10}) \) 6 * q - 38568 * q^4 - 238350 * q^5 - 515448 * q^6 - 11416662 * q^9	\( 6 q - 38568 q^{4} - 238350 q^{5} - 515448 q^{6} - 11416662 q^{9} - 48274200 q^{10} - 108590088 q^{11} + 663751704 q^{14} + 297743400 q^{15} + 1155522336 q^{16} - 3630995640 q^{19} + 2533753800 q^{20} - 8917537608 q^{21} - 2959765920 q^{24} + 18250878750 q^{25} - 81970953168 q^{26} + 286168468740 q^{29} + 203897251800 q^{30} - 276236748288 q^{31} - 127784939136 q^{34} + 1171274911800 q^{35} - 3326879331864 q^{36} + 2186980965936 q^{39} + 4214283852000 q^{40} - 6153278882388 q^{41} + 8250173021664 q^{44} + 10442765857950 q^{45} - 23334602656488 q^{46} + 11613390856242 q^{49} + 23694218070000 q^{50} - 43487373385728 q^{51} + 10162879468560 q^{54} + 33977390365800 q^{55} - 59280484297440 q^{56} + 14903258326680 q^{59} + 39248254864800 q^{60} - 11352061428588 q^{61} + 73265851251072 q^{64} - 50675287275600 q^{65} + 76208211455904 q^{66} - 150489671962824 q^{69} - 156447825521400 q^{70} + 131693145807312 q^{71} - 353606797863216 q^{74} - 360965926890000 q^{75} + 959127540575520 q^{76} - 26081853939360 q^{79} - 552945514077600 q^{80} + 11\!\cdots\!46 q^{81}+ \cdots + 506999099666376 q^{99}+O(q^{100}) \) 6 * q - 38568 * q^4 - 238350 * q^5 - 515448 * q^6 - 11416662 * q^9 - 48274200 * q^10 - 108590088 * q^11 + 663751704 * q^14 + 297743400 * q^15 + 1155522336 * q^16 - 3630995640 * q^19 + 2533753800 * q^20 - 8917537608 * q^21 - 2959765920 * q^24 + 18250878750 * q^25 - 81970953168 * q^26 + 286168468740 * q^29 + 203897251800 * q^30 - 276236748288 * q^31 - 127784939136 * q^34 + 1171274911800 * q^35 - 3326879331864 * q^36 + 2186980965936 * q^39 + 4214283852000 * q^40 - 6153278882388 * q^41 + 8250173021664 * q^44 + 10442765857950 * q^45 - 23334602656488 * q^46 + 11613390856242 * q^49 + 23694218070000 * q^50 - 43487373385728 * q^51 + 10162879468560 * q^54 + 33977390365800 * q^55 - 59280484297440 * q^56 + 14903258326680 * q^59 + 39248254864800 * q^60 - 11352061428588 * q^61 + 73265851251072 * q^64 - 50675287275600 * q^65 + 76208211455904 * q^66 - 150489671962824 * q^69 - 156447825521400 * q^70 + 131693145807312 * q^71 - 353606797863216 * q^74 - 360965926890000 * q^75 + 959127540575520 * q^76 - 26081853939360 * q^79 - 552945514077600 * q^80 + 1148641568615646 * q^81 - 686155736066976 * q^84 - 548221025491200 * q^85 + 598387757484072 * q^86 + 59269690709820 * q^89 - 1014408610626600 * q^90 + 821206462566672 * q^91 - 308164835928456 * q^94 + 232287694599000 * q^95 - 1208921682814848 * q^96 + 506999099666376 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more