LMFDB - Embedded newform 45.16.b.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,16,Mod(19,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("45.19");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	45.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:	$64.2120772950$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{4}\cdot 5^{6} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$-150.955i$ of defining polynomial
Character	$\chi$	$=$	45.19
Dual form			45.16.b.b.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-301.910i q^{2} -58381.4 q^{4} +(88431.8 - 150657. i) q^{5} -2.08791e6i q^{7} +7.73292e6i q^{8} +O(q^{10})$	\(q-301.910i q^{2} -58381.4 q^{4} +(88431.8 - 150657. i) q^{5} -2.08791e6i q^{7} +7.73292e6i q^{8} +(-4.54846e7 - 2.66984e7i) q^{10} +7.71305e7 q^{11} +1.32485e8i q^{13} -6.30361e8 q^{14} +4.21600e8 q^{16} -1.10174e9i q^{17} -6.23952e9 q^{19} +(-5.16277e9 + 8.79553e9i) q^{20} -2.32864e10i q^{22} -2.49754e10i q^{23} +(-1.48772e10 - 2.66457e10i) q^{25} +3.99986e10 q^{26} +1.21895e11i q^{28} -1.45836e11 q^{29} +4.01436e10 q^{31} +1.26107e11i q^{32} -3.32626e11 q^{34} +(-3.14558e11 - 1.84638e11i) q^{35} +5.28137e11i q^{37} +1.88377e12i q^{38} +(1.16501e12 + 6.83836e11i) q^{40} -6.88546e10 q^{41} +7.67330e11i q^{43} -4.50298e12 q^{44} -7.54032e12 q^{46} -8.92816e11i q^{47} +3.88180e11 q^{49} +(-8.04458e12 + 4.49157e12i) q^{50} -7.73468e12i q^{52} -5.86528e11i q^{53} +(6.82079e12 - 1.16202e13i) q^{55} +1.61457e13 q^{56} +4.40291e13i q^{58} -3.16543e10 q^{59} +5.85723e12 q^{61} -1.21197e13i q^{62} +5.18879e13 q^{64} +(1.99598e13 + 1.17159e13i) q^{65} +3.95005e13i q^{67} +6.43212e13i q^{68} +(-5.57440e13 + 9.49680e13i) q^{70} +7.83244e13 q^{71} -8.73027e13i q^{73} +1.59450e14 q^{74} +3.64272e14 q^{76} -1.61042e14i q^{77} -3.01801e13 q^{79} +(3.72829e13 - 6.35169e13i) q^{80} +2.07879e13i q^{82} -1.08491e14i q^{83} +(-1.65985e14 - 9.74290e13i) q^{85} +2.31664e14 q^{86} +5.96444e14i q^{88} -5.54023e14 q^{89} +2.76618e14 q^{91} +1.45810e15i q^{92} -2.69550e14 q^{94} +(-5.51772e14 + 9.40024e14i) q^{95} +1.50497e15i q^{97} -1.17195e14i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 38568 q^{4} + 238350 q^{5}+O(q^{10}) $ 6 * q - 38568 * q^4 + 238350 * q^5	$ 6 q - 38568 q^{4} + 238350 q^{5} - 48274200 q^{10} + 108590088 q^{11} - 663751704 q^{14} + 1155522336 q^{16} - 3630995640 q^{19} - 2533753800 q^{20} + 18250878750 q^{25} + 81970953168 q^{26} - 286168468740 q^{29} - 276236748288 q^{31} - 127784939136 q^{34} - 1171274911800 q^{35} + 4214283852000 q^{40} + 6153278882388 q^{41} - 8250173021664 q^{44} - 23334602656488 q^{46} + 11613390856242 q^{49} - 23694218070000 q^{50} + 33977390365800 q^{55} + 59280484297440 q^{56} - 14903258326680 q^{59} - 11352061428588 q^{61} + 73265851251072 q^{64} + 50675287275600 q^{65} - 156447825521400 q^{70} - 131693145807312 q^{71} + 353606797863216 q^{74} + 959127540575520 q^{76} - 26081853939360 q^{79} + 552945514077600 q^{80} - 548221025491200 q^{85} - 598387757484072 q^{86} - 59269690709820 q^{89} + 821206462566672 q^{91} - 308164835928456 q^{94} - 232287694599000 q^{95}+O(q^{100}) $ 6 * q - 38568 * q^4 + 238350 * q^5 - 48274200 * q^10 + 108590088 * q^11 - 663751704 * q^14 + 1155522336 * q^16 - 3630995640 * q^19 - 2533753800 * q^20 + 18250878750 * q^25 + 81970953168 * q^26 - 286168468740 * q^29 - 276236748288 * q^31 - 127784939136 * q^34 - 1171274911800 * q^35 + 4214283852000 * q^40 + 6153278882388 * q^41 - 8250173021664 * q^44 - 23334602656488 * q^46 + 11613390856242 * q^49 - 23694218070000 * q^50 + 33977390365800 * q^55 + 59280484297440 * q^56 - 14903258326680 * q^59 - 11352061428588 * q^61 + 73265851251072 * q^64 + 50675287275600 * q^65 - 156447825521400 * q^70 - 131693145807312 * q^71 + 353606797863216 * q^74 + 959127540575520 * q^76 - 26081853939360 * q^79 + 552945514077600 * q^80 - 548221025491200 * q^85 - 598387757484072 * q^86 - 59269690709820 * q^89 + 821206462566672 * q^91 - 308164835928456 * q^94 - 232287694599000 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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	$-0.313906\pi$
$3$		0			0
$3$		0			0
$4$	−58381.4			−1.78166
$5$	88431.8	−	150657.i	0.506213	−	0.862408i
$5$	88431.8	−	150657.i	0.506213	−	0.862408i
$6$		0			0
$7$		−	2.08791e6i		−	0.958246i	−0.877748	−	0.479123i	$-0.840955\pi$
$7$		−	2.08791e6i		−	0.958246i	0.877748	−	0.479123i	$-0.159045\pi$
$8$			7.73292e6i			1.30367i
$9$		0			0
$10$	−4.54846e7	−	2.66984e7i	−1.43835	−	0.844278i
$11$	7.71305e7			1.19339			0.596693	−	0.802469i	$-0.296481\pi$
$11$	7.71305e7			1.19339			0.596693	+	0.802469i	$0.296481\pi$
$12$		0			0
$13$			1.32485e8i			0.585589i	0.956175	+	0.292795i	$0.0945852\pi$
$13$			1.32485e8i			0.585589i	−0.956175	+	0.292795i	$0.905415\pi$
$14$	−6.30361e8			−1.59819
$15$		0			0
$16$	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	$-0.105566\pi$
$18$		0			0
$19$	−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
$21$		0			0
$22$		−	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	$-0.277142\pi$
$24$		0			0
$25$	−1.48772e10	−	2.66457e10i	−0.487496	−	0.873125i
$26$	3.99986e10			0.976663
$27$		0			0
$28$			1.21895e11i			1.70727i
$29$	−1.45836e11			−1.56992			−0.784962	−	0.619544i	$-0.787317\pi$
$29$	−1.45836e11			−1.56992			−0.784962	+	0.619544i	$0.787317\pi$
$30$		0			0
$31$	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
$33$		0			0
$34$	−3.32626e11			−1.08609
$35$	−3.14558e11	−	1.84638e11i	−0.826400	−	0.485077i
$36$		0			0
$37$			5.28137e11i			0.914605i	0.889311	+	0.457302i	$0.151184\pi$
$37$			5.28137e11i			0.914605i	−0.889311	+	0.457302i	$0.848816\pi$
$38$			1.88377e12i			2.67086i
$39$		0			0
$40$	1.16501e12	+	6.83836e11i	1.12430	+	0.659936i
$41$	−6.88546e10			−0.0552146			−0.0276073	−	0.999619i	$-0.508789\pi$
$41$	−6.88546e10			−0.0552146			−0.0276073	+	0.999619i	$0.508789\pi$
$42$		0			0
$43$			7.67330e11i			0.430495i	0.976559	+	0.215248i	$0.0690559\pi$
$43$			7.67330e11i			0.430495i	−0.976559	+	0.215248i	$0.930944\pi$
$44$	−4.50298e12			−2.12621
$45$		0			0
$46$	−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	$-0.0410253\pi$
$48$		0			0
$49$	3.88180e11			0.0817640
$50$	−8.04458e12	+	4.49157e12i	−1.45622	+	0.813061i
$51$		0			0
$52$		−	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	$-0.0109176\pi$
$54$		0			0
$55$	6.82079e12	−	1.16202e13i	0.604108	−	1.02919i
$56$	1.61457e13			1.24924
$57$		0			0
$58$			4.40291e13i			2.61837i
$59$	−3.16543e10			−0.00165593			−0.000827967	−	1.00000i	$-0.500264\pi$
$59$	−3.16543e10			−0.00165593			−0.000827967		1.00000i	$0.500264\pi$
$60$		0			0
$61$	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
$63$		0			0
$64$	5.18879e13			1.47474
$65$	1.99598e13	+	1.17159e13i	0.505017	+	0.296433i
$66$		0			0
$67$			3.95005e13i			0.796235i	0.917334	+	0.398118i	$0.130336\pi$
$67$			3.95005e13i			0.796235i	−0.917334	+	0.398118i	$0.869664\pi$
$68$			6.43212e13i			1.16021i
$69$		0			0
$70$	−5.57440e13	+	9.49680e13i	−0.809026	+	1.37829i
$71$	7.83244e13			1.02202			0.511010	−	0.859575i	$-0.329271\pi$
$71$	7.83244e13			1.02202			0.511010	+	0.859575i	$0.329271\pi$
$72$		0			0
$73$		−	8.73027e13i		−	0.924924i	−0.886639	−	0.462462i	$-0.846966\pi$
$73$		−	8.73027e13i		−	0.924924i	0.886639	−	0.462462i	$-0.153034\pi$
$74$	1.59450e14			1.52541
$75$		0			0
$76$	3.64272e14			2.85314
$77$		−	1.61042e14i		−	1.14356i
$78$		0			0
$79$	−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
$81$		0			0
$82$			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	$-0.0704167\pi$
$84$		0			0
$85$	−1.65985e14	−	9.74290e13i	−0.561598	−	0.329645i
$86$	2.31664e14			0.717993
$87$		0			0
$88$			5.96444e14i			1.55578i
$89$	−5.54023e14			−1.32771			−0.663854	−	0.747862i	$-0.731080\pi$
$89$	−5.54023e14			−1.32771			−0.663854	+	0.747862i	$0.731080\pi$
$90$		0			0
$91$	2.76618e14			0.561139
$92$			1.45810e15i			2.72508i
$93$		0			0
$94$	−2.69550e14			−0.428726
$95$	−5.51772e14	+	9.40024e14i	−0.810649	+	1.38106i
$96$		0			0
$97$			1.50497e15i			1.89121i	0.325313	+	0.945606i	$0.394530\pi$
$97$			1.50497e15i			1.89121i	−0.325313	+	0.945606i	$0.605470\pi$
$98$		−	1.17195e14i		−	0.136369i
$99$		0			0
$100$	8.68551e14	+	1.55561e15i	0.868551	+	1.55561i
$101$	1.04693e15			0.971649			0.485824	−	0.874056i	$-0.338519\pi$
$101$	1.04693e15			0.971649			0.485824	+	0.874056i	$0.338519\pi$
$102$		0			0
$103$		−	2.63263e14i		−	0.210916i	−0.994424	−	0.105458i	$-0.966369\pi$
$103$		−	2.63263e14i		−	0.210916i	0.994424	−	0.105458i	$-0.0336309\pi$
$104$	−1.02450e15			−0.763416
$105$		0			0
$106$	−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	$-0.0758698\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$		−	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	$0.747782\pi$
$114$		0			0
$115$	−3.76271e15	−	2.20862e15i	−1.31907	−	0.774262i
$116$	8.51408e15			2.79707
$117$		0			0
$118$			9.55674e12i			0.00276182i
$119$	−2.30034e15			−0.624008
$120$		0			0
$121$	1.77187e15			0.424171
$122$		−	1.76835e15i		−	0.397988i
$123$		0			0
$124$	−2.34364e15			−0.466905
$125$	−5.32996e15	−	1.14976e14i	−0.999767	−	0.0215666i
$126$		0			0
$127$		−	9.24721e15i		−	1.53987i	−0.638125	−	0.769933i	$-0.720290\pi$
$127$		−	9.24721e15i		−	1.53987i	0.638125	−	0.769933i	$-0.279710\pi$
$128$		−	1.15332e16i		−	1.81082i
$129$		0			0
$130$	3.53715e15	−	6.02605e15i	0.494400	−	0.842283i
$131$	3.50922e15			0.463101			0.231550	−	0.972823i	$-0.425620\pi$
$131$	3.50922e15			0.463101			0.231550	+	0.972823i	$0.425620\pi$
$132$		0			0
$133$			1.30276e16i			1.53453i
$134$	1.19256e16			1.32798
$135$		0			0
$136$	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	$-0.116745\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$		−	2.36469e16i		−	1.70456i
$143$			1.02187e16i			0.698834i
$144$		0			0
$145$	−1.28965e16	+	2.19711e16i	−0.794716	+	1.35392i
$146$	−2.63575e16			−1.54262
$147$		0			0
$148$		−	3.08333e16i		−	1.62951i
$149$	−2.20370e16			−1.10728			−0.553638	−	0.832758i	$-0.686761\pi$
$149$	−2.20370e16			−1.10728			−0.553638	+	0.832758i	$0.686761\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$	−4.86201e16			−1.90726
$155$	3.54997e15	−	6.04790e15i	0.132659	−	0.226004i
$156$		0			0
$157$		−	1.50192e16i		−	0.509799i	−0.966968	−	0.254899i	$-0.917958\pi$
$157$		−	1.50192e16i		−	0.509799i	0.966968	−	0.254899i	$-0.0820424\pi$
$158$			9.11165e15i			0.294896i
$159$		0			0
$160$	1.89988e16	+	1.11519e16i	0.559535	+	0.328434i
$161$	−5.21466e16			−1.46565
$162$		0			0
$163$		−	2.37456e16i		−	0.608382i	−0.952611	−	0.304191i	$-0.901614\pi$
$163$		−	2.37456e16i		−	0.608382i	0.952611	−	0.304191i	$-0.0983861\pi$
$164$	4.01982e15			0.0983735
$165$		0			0
$166$	−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	$0.619742\pi$
$168$		0			0
$169$	3.36335e16			0.657085
$170$	−2.94147e16	+	5.01123e16i	−0.549792	+	0.936651i
$171$		0			0
$172$		−	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	$-0.113214\pi$
$174$		0			0
$175$	−5.56338e16	+	3.10623e16i	−0.836669	+	0.467142i
$176$	3.25183e16			0.468578
$177$		0			0
$178$			1.67265e17i			2.21439i
$179$	−6.47281e16			−0.821666			−0.410833	−	0.911711i	$-0.634762\pi$
$179$	−6.47281e16			−0.821666			−0.410833	+	0.911711i	$0.634762\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	1.93133e17			1.99399
$185$	7.95673e16	+	4.67041e16i	0.788763	+	0.462985i
$186$		0			0
$187$		−	8.49779e16i		−	0.777131i
$188$			5.21238e16i			0.457986i
$189$		0			0
$190$	2.83802e17	+	1.66585e17i	2.30337	+	1.35202i
$191$	−4.71702e16			−0.368059			−0.184030	−	0.982921i	$-0.558914\pi$
$191$	−4.71702e16			−0.368059			−0.184030	+	0.982921i	$0.558914\pi$
$192$		0			0
$193$			9.79733e16i			0.707014i	0.935432	+	0.353507i	$0.115011\pi$
$193$			9.79733e16i			0.707014i	−0.935432	+	0.353507i	$0.884989\pi$
$194$	4.54365e17			3.15422
$195$		0			0
$196$	−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	$-0.191437\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$		−	3.16080e17i		−	1.62055i
$203$			3.04492e17i			1.50437i
$204$		0			0
$205$	−6.08894e15	+	1.03734e16i	−0.0279504	+	0.0476175i
$206$	−7.94815e16			−0.351772
$207$		0			0
$208$			5.58559e16i			0.229929i
$209$	−4.81257e17			−1.91109
$210$		0			0
$211$	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
$213$		0			0
$214$	−2.36801e17			−0.787554
$215$	1.15603e17	+	6.78563e16i	0.371263	+	0.217922i
$216$		0			0
$217$		−	8.38164e16i		−	0.251120i
$218$		−	2.49198e17i		−	0.721307i
$219$		0			0
$220$	−3.98207e17	+	6.78404e17i	−1.07631	+	1.83366i
$221$	1.45965e17			0.381334
$222$		0			0
$223$			5.08815e17i			1.24243i	0.783638	+	0.621217i	$0.213362\pi$
$223$			5.08815e17i			1.24243i	−0.783638	+	0.621217i	$0.786638\pi$
$224$	2.63300e17			0.621715
$225$		0			0
$226$	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	$-0.190690\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$		−	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	$0.853904\pi$
$234$		0			0
$235$	−1.34509e17	−	7.89534e16i	−0.221687	−	0.130125i
$236$	1.84802e15			0.00295031
$237$		0			0
$238$			6.94495e17i			1.04074i
$239$	−4.80698e17			−0.698052			−0.349026	−	0.937113i	$-0.613488\pi$
$239$	−4.80698e17			−0.698052			−0.349026	+	0.937113i	$0.613488\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−3.41953e17			−0.425151
$245$	3.43274e16	−	5.84818e16i	0.0413900	−	0.0705140i
$246$		0			0
$247$		−	8.26646e17i		−	0.937761i
$248$			3.10427e17i			0.341643i
$249$		0			0
$250$	−3.47123e16	+	1.60917e18i	−0.0359695	+	1.66744i
$251$	2.82502e17			0.284098			0.142049	−	0.989860i	$-0.454631\pi$
$251$	2.82502e17			0.284098			0.142049	+	0.989860i	$0.454631\pi$
$252$		0			0
$253$		−	1.92637e18i		−	1.82531i
$254$	−2.79182e18			−2.56823
$255$		0			0
$256$	−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	$-0.0940536\pi$
$258$		0			0
$259$	1.10270e18			0.876417
$260$	−1.16528e18	−	6.83992e17i	−0.899767	−	0.528142i
$261$		0			0
$262$		−	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	$-0.0502798\pi$
$264$		0			0
$265$	−8.83643e16	−	5.18678e16i	−0.0591470	−	0.0347179i
$266$	3.93315e18			2.55934
$267$		0			0
$268$		−	2.30609e18i		−	1.41862i
$269$	3.14482e18			1.88128			0.940641	−	0.339402i	$-0.110225\pi$
$269$	3.14482e18			1.88128			0.940641	+	0.339402i	$0.110225\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$	−2.29571e18			−1.19616
$275$	−1.14749e18	−	2.05519e18i	−0.581771	−	1.04198i
$276$		0			0
$277$		−	2.54882e18i		−	1.22388i	−0.790903	−	0.611942i	$-0.790389\pi$
$277$		−	2.54882e18i		−	1.22388i	0.790903	−	0.611942i	$-0.209611\pi$
$278$		−	1.00559e18i		−	0.469987i
$279$		0			0
$280$	1.42779e18	−	2.43245e18i	0.632381	−	1.07735i
$281$	2.10517e18			0.907799			0.453899	−	0.891053i	$-0.350033\pi$
$281$	2.10517e18			0.907799			0.453899	+	0.891053i	$0.350033\pi$
$282$		0			0
$283$			3.14365e18i			1.28539i	0.766121	+	0.642697i	$0.222185\pi$
$283$			3.14365e18i			1.28539i	−0.766121	+	0.642697i	$0.777815\pi$
$284$	−4.57268e18			−1.82089
$285$		0			0
$286$	3.08511e18			1.16554
$287$			1.43762e17i			0.0529092i
$288$		0			0
$289$	1.64859e18			0.575942
$290$	6.63328e18	+	3.89358e18i	2.25810	+	1.32545i
$291$		0			0
$292$			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	$-0.265845\pi$
$294$		0			0
$295$	−2.79925e15	+	4.76893e15i	−0.000838255	+	0.00142809i
$296$	−4.08404e18			−1.19234
$297$		0			0
$298$			6.65318e18i			1.84675i
$299$	3.30888e18			0.895669
$300$		0			0
$301$	1.60212e18			0.412521
$302$			3.53154e18i			0.886977i
$303$		0			0
$304$	−2.63058e18			−0.628782
$305$	5.17966e17	−	8.82430e17i	0.120796	−	0.205793i
$306$		0			0
$307$		−	4.22293e18i		−	0.937725i	−0.883271	−	0.468863i	$-0.844664\pi$
$307$		−	4.22293e18i		−	0.937725i	0.883271	−	0.468863i	$-0.155336\pi$
$308$			9.40184e18i			2.03743i
$309$		0			0
$310$	−1.82592e18	−	1.07177e18i	−0.376937	−	0.221253i
$311$	−9.72072e18			−1.95882			−0.979412	−	0.201872i	$-0.935298\pi$
$311$	−9.72072e18			−1.95882			−0.979412	+	0.201872i	$0.935298\pi$
$312$		0			0
$313$		−	6.04916e18i		−	1.16175i	−0.813993	−	0.580875i	$-0.802711\pi$
$313$		−	6.04916e18i		−	1.16175i	0.813993	−	0.580875i	$-0.197289\pi$
$314$	−4.53443e18			−0.850258
$315$		0			0
$316$	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	$0.974515\pi$
$318$		0			0
$319$	−1.12484e19			−1.87353
$320$	4.58854e18	−	7.81725e18i	0.746534	−	1.27183i
$321$		0			0
$322$			1.57435e19i			2.44446i
$323$			6.87434e18i			1.04283i
$324$		0			0
$325$	3.53016e18	−	1.97101e18i	0.511293	−	0.285473i
$326$	−7.16903e18			−1.01468
$327$		0			0
$328$		−	5.32447e17i		−	0.0719817i
$329$	−1.86412e18			−0.246323
$330$		0			0
$331$	−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
$333$		0			0
$334$	2.62905e19			3.10241
$335$	5.95100e18	+	3.49310e18i	0.686680	+	0.403065i
$336$		0			0
$337$			1.21070e19i			1.33601i	0.744156	+	0.668006i	$0.232852\pi$
$337$			1.21070e19i			1.33601i	−0.744156	+	0.668006i	$0.767148\pi$
$338$		−	1.01543e19i		−	1.09591i
$339$		0			0
$340$	9.69041e18	+	5.68804e18i	1.00058	+	0.587314i
$341$	3.09630e18			0.312741
$342$		0			0
$343$		−	1.07230e19i		−	1.03660i
$344$	−5.93369e18			−0.561225
$345$		0			0
$346$	−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	$-0.0498116\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$			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	$-0.194173\pi$
$354$		0			0
$355$	6.92637e18	−	1.18001e19i	0.517360	−	0.881399i
$356$	3.23446e19			2.36552
$357$		0			0
$358$			1.95420e19i			1.37040i
$359$	2.86436e18			0.196707			0.0983534	−	0.995152i	$-0.468642\pi$
$359$	2.86436e18			0.196707			0.0983534	+	0.995152i	$0.468642\pi$
$360$		0			0
$361$	2.37505e19			1.56447
$362$			2.66229e19i			1.71767i
$363$		0			0
$364$	−1.61493e19			−0.999757
$365$	−1.31527e19	−	7.72034e18i	−0.797662	−	0.468209i
$366$		0			0
$367$			2.57378e18i			0.149822i	0.997190	+	0.0749110i	$0.0238673\pi$
$367$			2.57378e18i			0.149822i	−0.997190	+	0.0749110i	$0.976133\pi$
$368$		−	1.05297e19i		−	0.600559i
$369$		0			0
$370$	1.41004e19	−	2.40221e19i	0.772181	−	1.31552i
$371$	−1.22462e18			−0.0657199
$372$		0			0
$373$		−	1.16191e19i		−	0.598904i	−0.954111	−	0.299452i	$-0.903196\pi$
$373$		−	1.16191e19i		−	0.598904i	0.954111	−	0.299452i	$-0.0968038\pi$
$374$	−2.56556e19			−1.29612
$375$		0			0
$376$	6.90407e18			0.335117
$377$		−	1.93211e19i		−	0.919330i
$378$		0			0
$379$	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
$381$		0			0
$382$			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	$0.948779\pi$
$384$		0			0
$385$	−2.42620e19	−	1.42412e19i	−0.986214	−	0.578884i
$386$	2.95791e19			1.17918
$387$		0			0
$388$		−	8.78623e19i		−	3.36949i
$389$	−3.55842e19			−1.33855			−0.669277	−	0.743013i	$-0.733396\pi$
$389$	−3.55842e19			−1.33855			−0.669277	+	0.743013i	$0.733396\pi$
$390$		0			0
$391$	−2.75165e19			−0.996018
$392$			3.00176e18i			0.106593i
$393$		0			0
$394$	−5.52172e19			−1.88735
$395$	−2.66888e18	+	4.54682e18i	−0.0895056	+	0.152486i
$396$		0			0
$397$			4.87189e18i			0.157314i	0.996902	+	0.0786572i	$0.0250633\pi$
$397$			4.87189e18i			0.157314i	−0.996902	+	0.0786572i	$0.974937\pi$
$398$			5.91648e18i			0.187474i
$399$		0			0
$400$	−6.27224e18	−	1.12338e19i	−0.191413	−	0.342829i
$401$	8.01043e18			0.239924			0.119962	−	0.992779i	$-0.461723\pi$
$401$	8.01043e18			0.239924			0.119962	+	0.992779i	$0.461723\pi$
$402$		0			0
$403$			5.31845e18i			0.153461i
$404$	−6.11215e19			−1.73115
$405$		0			0
$406$	9.19290e19			2.50904
$407$			4.07355e19i			1.09148i
$408$		0			0
$409$	−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
$411$		0			0
$412$			1.53696e19i			0.375780i
$413$			6.60915e16i			0.00158679i
$414$		0			0
$415$	−1.63449e19	−	9.59405e18i	−0.378461	−	0.222147i
$416$	−1.67073e19			−0.379933
$417$		0			0
$418$			1.45296e20i			3.18737i
$419$	−4.37426e19			−0.942539			−0.471269	−	0.881989i	$-0.656204\pi$
$419$	−4.37426e19			−0.942539			−0.471269	+	0.881989i	$0.656204\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	4.53557e18			0.0894105
$425$	−2.93566e19	+	1.63908e19i	−0.568577	+	0.317456i
$426$		0			0
$427$		−	1.22294e19i		−	0.228663i
$428$			4.57911e19i			0.841304i
$429$		0			0
$430$	2.04865e19	−	3.49017e19i	0.363458	−	0.619203i
$431$	−1.87054e19			−0.326127			−0.163064	−	0.986616i	$-0.552138\pi$
$431$	−1.87054e19			−0.326127			−0.163064	+	0.986616i	$0.552138\pi$
$432$		0			0
$433$		−	2.79482e19i		−	0.470647i	−0.971917	−	0.235323i	$-0.924385\pi$
$433$		−	2.79482e19i		−	0.470647i	0.971917	−	0.235323i	$-0.0756149\pi$
$434$	−2.53050e19			−0.418825
$435$		0			0
$436$	−4.81883e19			−0.770536
$437$			1.55835e20i			2.44937i
$438$		0			0
$439$	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
$441$		0			0
$442$		−	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	$-0.360216\pi$
$444$		0			0
$445$	−4.89932e19	+	8.34672e19i	−0.672103	+	1.14503i
$446$	1.53616e20			2.07217
$447$		0			0
$448$		−	1.08337e20i		−	1.41317i
$449$	−5.40721e19			−0.693627			−0.346814	−	0.937934i	$-0.612736\pi$
$449$	−5.40721e19			−0.693627			−0.346814	+	0.937934i	$0.612736\pi$
$450$		0			0
$451$	−5.31079e18			−0.0658924
$452$		−	2.07913e20i		−	2.53714i
$453$		0			0
$454$	−1.59325e20			−1.88090
$455$	2.44618e19	−	4.16743e19i	0.284056	−	0.483931i
$456$		0			0
$457$		−	3.69928e19i		−	0.415667i	−0.978164	−	0.207833i	$-0.933359\pi$
$457$		−	3.69928e19i		−	0.415667i	0.978164	−	0.207833i	$-0.0666412\pi$
$458$			9.82306e19i			1.08581i
$459$		0			0
$460$	2.19672e20	+	1.28942e20i	2.35013	+	1.37947i
$461$	4.38103e19			0.461126			0.230563	−	0.973057i	$-0.425943\pi$
$461$	4.38103e19			0.461126			0.230563	+	0.973057i	$0.425943\pi$
$462$		0			0
$463$		−	6.17232e19i		−	0.628913i	−0.949272	−	0.314457i	$-0.898178\pi$
$463$		−	6.17232e19i		−	0.628913i	0.949272	−	0.314457i	$-0.101822\pi$
$464$	−6.14843e19			−0.616424
$465$		0			0
$466$	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	$-0.387705\pi$
$468$		0			0
$469$	8.24736e19			0.762989
$470$	−2.38368e19	+	4.06094e19i	−0.217027	+	0.369737i
$471$		0			0
$472$		−	2.44780e17i		−	0.00215879i
$473$			5.91845e19i			0.513747i
$474$		0			0
$475$	9.28266e19	+	1.66256e20i	0.780675	+	1.39822i
$476$	1.34297e20			1.11177
$477$		0			0
$478$			1.45127e20i			1.16423i
$479$	7.54528e19			0.595881			0.297940	−	0.954585i	$-0.403700\pi$
$479$	7.54528e19			0.595881			0.297940	+	0.954585i	$0.403700\pi$
$480$		0			0
$481$	−6.99705e19			−0.535583
$482$			2.03648e20i			1.53471i
$483$		0			0
$484$	−1.03444e20			−0.755728
$485$	2.26734e20	+	1.33087e20i	1.63100	+	0.957357i
$486$		0			0
$487$		−	1.37432e20i		−	0.958560i	−0.877662	−	0.479280i	$-0.840898\pi$
$487$		−	1.37432e20i		−	0.958560i	0.877662	−	0.479280i	$-0.159102\pi$
$488$			4.52935e19i			0.311091i
$489$		0			0
$490$	−1.76562e19	−	1.03638e19i	−0.117605	−	0.0690316i
$491$	−1.58161e19			−0.103750			−0.0518750	−	0.998654i	$-0.516520\pi$
$491$	−1.58161e19			−0.103750			−0.0518750	+	0.998654i	$0.516520\pi$
$492$		0			0
$493$			1.60673e20i			1.02233i
$494$	−2.49572e20			−1.56403
$495$		0			0
$496$	1.69246e19			0.102898
$497$		−	1.63535e20i		−	0.979347i
$498$		0			0
$499$	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
$501$		0			0
$502$		−	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	$0.839920\pi$
$504$		0			0
$505$	9.25823e19	−	1.57728e20i	0.491861	−	0.837958i
$506$	−5.81589e20			−3.04430
$507$		0			0
$508$			5.39865e20i			2.74351i
$509$	1.78294e20			0.892796			0.446398	−	0.894834i	$-0.352707\pi$
$509$	1.78294e20			0.892796			0.446398	+	0.894834i	$0.352707\pi$
$510$		0			0
$511$	−1.82280e20			−0.886305
$512$			1.59997e20i			0.766632i
$513$		0			0
$514$	−2.08734e20			−0.971335
$515$	−3.96622e19	−	2.32808e19i	−0.181896	−	0.106769i
$516$		0			0
$517$		−	6.88634e19i		−	0.306768i
$518$		−	3.32917e20i		−	1.46171i
$519$		0			0
$520$	−9.05983e19	+	1.54347e20i	−0.386451	+	0.658377i
$521$	−2.55797e20			−1.07551			−0.537753	−	0.843102i	$-0.680727\pi$
$521$	−2.55797e20			−1.07551			−0.537753	+	0.843102i	$0.680727\pi$
$522$		0			0
$523$		−	3.28407e19i		−	0.134168i	−0.997747	−	0.0670842i	$-0.978630\pi$
$523$		−	3.28407e19i		−	0.134168i	0.997747	−	0.0670842i	$-0.0213696\pi$
$524$	−2.04873e20			−0.825087
$525$		0			0
$526$	−1.34064e20			−0.524708
$527$		−	4.42279e19i		−	0.170654i
$528$		0			0
$529$	−3.57138e20			−1.33942
$530$	−1.56594e19	+	2.66780e19i	−0.0579036	+	0.0986472i
$531$		0			0
$532$		−	7.60568e20i		−	2.73401i
$533$		−	9.12223e18i		−	0.0323331i
$534$		0			0
$535$	−1.18167e20	−	6.93610e19i	−0.407232	−	0.239035i
$536$	−3.05454e20			−1.03803
$537$		0			0
$538$		−	9.49452e20i		−	3.13766i
$539$	2.99405e19			0.0975761
$540$		0			0
$541$	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
$543$		0			0
$544$	1.38937e20			0.422500
$545$	7.29921e19	−	1.24353e20i	0.218928	−	0.372977i
$546$		0			0
$547$			4.60215e20i			1.34294i	0.741032	+	0.671469i	$0.234336\pi$
$547$			4.60215e20i			1.34294i	−0.741032	+	0.671469i	$0.765664\pi$
$548$			4.43930e20i			1.27779i
$549$		0			0
$550$	−6.20483e20	+	3.46437e20i	−1.73784	+	0.970296i
$551$	9.09944e20			2.51407
$552$		0			0
$553$			6.30133e19i			0.169431i
$554$	−7.69512e20			−2.04123
$555$		0			0
$556$	−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	$-0.0866154\pi$
$558$		0			0
$559$	−1.01660e20			−0.252093
$560$	−1.32618e20	−	7.78435e19i	−0.324483	−	0.190464i
$561$		0			0
$562$		−	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	$-0.00811740\pi$
$564$		0			0
$565$	5.36532e20	+	3.14932e20i	1.22810	+	0.720864i
$566$	9.49098e20			2.14382
$567$		0			0
$568$			6.05676e20i			1.33238i
$569$	2.23104e19			0.0484356			0.0242178	−	0.999707i	$-0.492290\pi$
$569$	2.23104e19			0.0484356			0.0242178	+	0.999707i	$0.492290\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	4.34032e19			0.0882435
$575$	−6.65487e20	+	3.71565e20i	−1.33546	+	0.745634i
$576$		0			0
$577$			5.07975e20i			0.993171i	0.867988	+	0.496585i	$0.165413\pi$
$577$			5.07975e20i			0.993171i	−0.867988	+	0.496585i	$0.834587\pi$
$578$		−	4.97724e20i		−	0.960573i
$579$		0			0
$580$	7.52915e20	−	1.28270e21i	1.41591	−	2.41221i
$581$	−2.26520e20			−0.420518
$582$		0			0
$583$		−	4.52392e19i		−	0.0818467i
$584$	6.75104e20			1.20580
$585$		0			0
$586$	−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	$0.709688\pi$
$588$		0			0
$589$	−2.50477e20			−0.419665
$590$	1.43979e18	+	8.45120e17i	0.00238181	+	0.00139807i
$591$		0			0
$592$			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	$-0.202165\pi$
$594$		0			0
$595$	−2.03423e20	+	3.46561e20i	−0.315881	+	0.538150i
$596$	1.28655e21			1.97278
$597$		0			0
$598$		−	9.98983e20i		−	1.49382i
$599$	3.78607e20			0.559098			0.279549	−	0.960131i	$-0.409815\pi$
$599$	3.78607e20			0.559098			0.279549	+	0.960131i	$0.409815\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	6.82907e20			0.947512
$605$	1.56690e20	−	2.66944e20i	0.214721	−	0.365809i
$606$		0			0
$607$		−	7.37841e20i		−	0.986388i	−0.869919	−	0.493194i	$-0.835829\pi$
$607$		−	7.37841e20i		−	0.986388i	0.869919	−	0.493194i	$-0.164171\pi$
$608$		−	7.86847e20i		−	1.03899i
$609$		0			0
$610$	−2.66414e20	−	1.56379e20i	−0.343229	−	0.201467i
$611$	1.18285e20			0.150529
$612$		0			0
$613$		−	6.78619e20i		−	0.842698i	−0.906898	−	0.421349i	$-0.861557\pi$
$613$		−	6.78619e20i		−	0.842698i	0.906898	−	0.421349i	$-0.138443\pi$
$614$	−1.27494e21			−1.56397
$615$		0			0
$616$	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	$0.885035\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$			2.93478e21i			3.26699i
$623$			1.15675e21i			1.27227i
$624$		0			0
$625$	−4.88660e20	+	7.92826e20i	−0.524695	+	0.851290i
$626$	−1.82630e21			−1.93760
$627$		0			0
$628$			8.76840e20i			0.908287i
$629$	5.81870e20			0.595589
$630$		0			0
$631$	−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
$633$		0			0
$634$	2.76578e20			0.266777
$635$	−1.39315e21	−	8.17748e20i	−1.32799	−	0.779500i
$636$		0			0
$637$			5.14282e19i			0.0478801i
$638$			3.39599e21i			3.12472i
$639$		0			0
$640$	−1.73755e21	−	1.01990e21i	−1.56166	−	0.916659i
$641$	−1.45703e21			−1.29430			−0.647150	−	0.762363i	$-0.724039\pi$
$641$	−1.45703e21			−1.29430			−0.647150	+	0.762363i	$0.724039\pi$
$642$		0			0
$643$			1.13525e21i			0.985166i	0.870266	+	0.492583i	$0.163947\pi$
$643$			1.13525e21i			0.985166i	−0.870266	+	0.492583i	$0.836053\pi$
$644$	3.04439e21			2.61129
$645$		0			0
$646$	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	$0.736250\pi$
$648$		0			0
$649$	−2.44151e18			−0.00197617
$650$	−5.95068e20	−	1.06579e21i	−0.476120	−	0.852749i
$651$		0			0
$652$			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	$0.937685\pi$
$654$		0			0
$655$	3.10327e20	−	5.28687e20i	0.234428	−	0.399382i
$656$	−2.90291e19			−0.0216798
$657$		0			0
$658$			5.62797e20i			0.410825i
$659$	−2.35681e21			−1.70092			−0.850461	−	0.526038i	$-0.823677\pi$
$659$	−2.35681e21			−1.70092			−0.850461	+	0.526038i	$0.823677\pi$
$660$		0			0
$661$	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
$663$		0			0
$664$	8.38951e20			0.572105
$665$	1.96269e21	+	1.15205e21i	1.32339	+	0.776801i
$666$		0			0
$667$			3.64231e21i			2.40123i
$668$		−	5.08388e21i		−	3.31415i
$669$		0			0
$670$	1.05460e21	−	1.79666e21i	0.672244	−	1.14527i
$671$	4.51771e20			0.284774
$672$		0			0
$673$		−	1.14413e21i		−	0.705281i	−0.935759	−	0.352641i	$-0.885284\pi$
$673$		−	1.14413e21i		−	0.705281i	0.935759	−	0.352641i	$-0.114716\pi$
$674$	3.65520e21			2.22824
$675$		0			0
$676$	−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	$-0.133580\pi$
$678$		0			0
$679$	3.14225e21			1.81225
$680$	7.53410e20	−	1.28354e21i	0.429749	−	0.732140i
$681$		0			0
$682$		−	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	$-0.243866\pi$
$684$		0			0
$685$	−1.14559e21	−	6.72433e20i	−0.618514	−	0.363053i
$686$	−3.23737e21			−1.72887
$687$		0			0
$688$			3.23507e20i			0.169032i
$689$	7.77065e19			0.0401618
$690$		0			0
$691$	−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
$693$		0			0
$694$	−1.06190e21			−0.519862
$695$	2.94546e20	−	5.01802e20i	0.142648	−	0.243023i
$696$		0			0
$697$			7.58600e19i			0.0359556i
$698$			3.62246e21i			1.69859i
$699$		0			0
$700$	3.24798e21	−	1.81346e21i	1.49066	−	0.832286i
$701$	−2.11598e21			−0.960787			−0.480393	−	0.877053i	$-0.659506\pi$
$701$	−2.11598e21			−0.960787			−0.480393	+	0.877053i	$0.659506\pi$
$702$		0			0
$703$		−	3.29532e21i		−	1.46465i
$704$	4.00214e21			1.75994
$705$		0			0
$706$	−4.43894e21			−1.91093
$707$		−	2.18591e21i		−	0.931079i
$708$		0			0
$709$	−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
$711$		0			0
$712$		−	4.28421e21i		−	1.73090i
$713$		−	1.00261e21i		−	0.400828i
$714$		0			0
$715$	1.53951e21	+	9.03656e20i	0.602681	+	0.353759i
$716$	3.77891e21			1.46393
$717$		0			0
$718$		−	8.64778e20i		−	0.328073i
$719$	1.17866e21			0.442510			0.221255	−	0.975216i	$-0.428985\pi$
$719$	1.17866e21			0.442510			0.221255	+	0.975216i	$0.428985\pi$
$720$		0			0
$721$	−5.49669e20			−0.202110
$722$		−	7.17050e21i		−	2.60928i
$723$		0			0
$724$	5.14817e21			1.83490
$725$	2.16963e21	+	3.88589e21i	0.765332	+	1.37074i
$726$		0			0
$727$			1.95489e21i			0.675484i	0.941239	+	0.337742i	$0.109663\pi$
$727$			1.95489e21i			0.675484i	−0.941239	+	0.337742i	$0.890337\pi$
$728$			2.13906e21i			0.731541i
$729$		0			0
$730$	−2.33084e21	+	3.97093e21i	−0.780893	+	1.33037i
$731$	8.45399e20			0.280338
$732$		0			0
$733$		−	5.70177e21i		−	1.85238i	−0.377059	−	0.926189i	$-0.623065\pi$
$733$		−	5.70177e21i		−	1.85238i	0.377059	−	0.926189i	$-0.376935\pi$
$734$	7.77048e20			0.249878
$735$		0			0
$736$	3.14958e21			0.992359
$737$			3.04669e21i			0.950216i
$738$		0			0
$739$	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
$741$		0			0
$742$			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	$-0.0294062\pi$
$744$		0			0
$745$	−1.94877e21	+	3.32002e21i	−0.560517	+	0.954923i
$746$	−3.50792e21			−0.998870
$747$		0			0
$748$			4.96113e21i			1.38458i
$749$	−1.63764e21			−0.452487
$750$		0			0
$751$	−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
$753$		0			0
$754$	−5.83322e21			−1.53329
$755$	−1.03442e21	+	1.76228e21i	−0.269212	+	0.458642i
$756$		0			0
$757$		−	2.60470e21i		−	0.664567i	−0.943180	−	0.332284i	$-0.892181\pi$
$757$		−	2.60470e21i		−	0.664567i	0.943180	−	0.332284i	$-0.107819\pi$
$758$		−	2.52268e21i		−	0.637298i
$759$		0			0
$760$	−7.26913e21	−	4.26681e21i	−1.80045	−	1.05682i
$761$	4.31540e20			0.105837			0.0529183	−	0.998599i	$-0.483148\pi$
$761$	4.31540e20			0.105837			0.0529183	+	0.998599i	$0.483148\pi$
$762$		0			0
$763$		−	1.72337e21i		−	0.414425i
$764$	2.75386e21			0.655756
$765$		0			0
$766$	2.28887e21			0.534449
$767$		−	4.19374e18i		−	0.000969697i
$768$		0			0
$769$	−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
$771$		0			0
$772$		−	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	$-0.154084\pi$
$774$		0			0
$775$	−5.97225e20	−	1.06965e21i	−0.127754	−	0.228813i
$776$	−1.16378e22			−2.46552
$777$		0			0
$778$			1.07432e22i			2.23248i
$779$	4.29620e20			0.0884205
$780$		0			0
$781$	6.04120e21			1.21967
$782$			8.30749e21i			1.66119i
$783$		0			0
$784$	1.63657e20			0.0321043
$785$	−2.26274e21	−	1.32817e21i	−0.439655	−	0.258067i
$786$		0			0
$787$		−	5.95930e21i		−	1.13602i	−0.823023	−	0.568008i	$-0.807714\pi$
$787$		−	5.95930e21i		−	1.13602i	0.823023	−	0.568008i	$-0.192286\pi$
$788$			1.06776e22i			2.01616i
$789$		0			0
$790$	1.37273e21	+	8.05759e20i	0.254321	+	0.149280i
$791$	7.43568e21			1.36457
$792$		0			0
$793$			7.75998e20i			0.139737i
$794$	1.47087e21			0.262374
$795$		0			0
$796$	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	$-0.257058\pi$
$798$		0			0
$799$	−9.83653e20			−0.167394
$800$	3.36020e21	−	1.87612e21i	0.566488	−	0.316290i
$801$		0			0
$802$		−	2.41842e21i		−	0.400152i
$803$		−	6.73370e21i		−	1.10379i
$804$		0			0
$805$	−4.61141e21	+	7.85622e21i	−0.741934	+	1.26399i
$806$	1.60569e21			0.255946
$807$		0			0
$808$			8.09586e21i			1.26671i
$809$	4.00498e20			0.0620850			0.0310425	−	0.999518i	$-0.490117\pi$
$809$	4.00498e20			0.0620850			0.0310425	+	0.999518i	$0.490117\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	1.22984e22			1.82040
$815$	−3.57743e21	−	2.09987e21i	−0.524674	−	0.307971i
$816$		0			0
$817$		−	4.78777e21i		−	0.689394i
$818$			1.56085e22i			2.22695i
$819$		0			0
$820$	3.55480e20	−	6.05613e20i	0.0497980	−	0.0848381i
$821$	−8.29377e20			−0.115127			−0.0575636	−	0.998342i	$-0.518333\pi$
$821$	−8.29377e20			−0.115127			−0.0575636	+	0.998342i	$0.518333\pi$
$822$		0			0
$823$		−	7.90016e21i		−	1.07681i	−0.842688	−	0.538403i	$-0.819028\pi$
$823$		−	7.90016e21i		−	1.07681i	0.842688	−	0.538403i	$-0.180972\pi$
$824$	2.03579e21			0.274966
$825$		0			0
$826$	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	$0.781976\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$			6.87439e21i			0.863594i
$833$		−	4.27674e20i		−	0.0532446i
$834$		0			0
$835$	1.31193e22	+	7.70070e21i	1.60421	+	0.941633i
$836$	2.80965e22			3.40490
$837$		0			0
$838$			1.32063e22i			1.57199i
$839$	5.99428e21			0.707168			0.353584	−	0.935403i	$-0.384963\pi$
$839$	5.99428e21			0.707168			0.353584	+	0.935403i	$0.384963\pi$
$840$		0			0
$841$	1.26388e22			1.46466
$842$			4.70866e21i			0.540825i
$843$		0			0
$844$	−1.00307e22			−1.13178
$845$	2.97427e21	−	5.06711e21i	0.332625	−	0.566676i
$846$		0			0
$847$		−	3.69951e21i		−	0.406461i
$848$		−	2.47281e20i		−	0.0269291i
$849$		0			0
$850$	4.94855e21	+	8.86305e21i	0.529463	+	0.948290i
$851$	1.31905e22			1.39890
$852$		0			0
$853$		−	5.27177e21i		−	0.549337i	−0.961539	−	0.274668i	$-0.911432\pi$
$853$		−	5.27177e21i		−	0.549337i	0.961539	−	0.274668i	$-0.0885681\pi$
$854$	−3.69217e21			−0.381371
$855$		0			0
$856$	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	$-0.0185129\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$			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	$-0.140932\pi$
$864$		0			0
$865$	−6.40055e21	−	3.75697e21i	−0.600615	−	0.352547i
$866$	−8.43784e21			−0.784959
$867$		0			0
$868$			4.89332e21i			0.447410i
$869$	−2.32780e21			−0.211008
$870$		0			0
$871$	−5.23324e21			−0.466267
$872$			6.38279e21i			0.563815i
$873$		0			0
$874$	4.70480e22			4.08513
$875$	−2.40060e20	+	1.11285e22i	−0.0206661	+	0.958023i
$876$		0			0
$877$		−	3.50814e21i		−	0.296879i	−0.988921	−	0.148440i	$-0.952575\pi$
$877$		−	3.50814e21i		−	0.296879i	0.988921	−	0.148440i	$-0.0474251\pi$
$878$		−	2.35830e22i		−	1.97874i
$879$		0			0
$880$	2.87565e21	−	4.89909e21i	0.237201	−	0.404106i
$881$	−1.73060e22			−1.41540			−0.707699	−	0.706514i	$-0.750267\pi$
$881$	−1.73060e22			−1.41540			−0.707699	+	0.706514i	$0.750267\pi$
$882$		0			0
$883$		−	1.95732e22i		−	1.57383i	−0.617062	−	0.786914i	$-0.711677\pi$
$883$		−	1.95732e22i		−	1.57383i	0.617062	−	0.786914i	$-0.288323\pi$
$884$	−8.52162e21			−0.679407
$885$		0			0
$886$	−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	$-0.0823780\pi$
$888$		0			0
$889$	−1.93074e22			−1.47557
$890$	2.51995e22	+	1.47915e22i	1.90971	+	1.12095i
$891$		0			0
$892$		−	2.97053e22i		−	2.21359i
$893$			5.57075e21i			0.411649i
$894$		0			0
$895$	−5.72402e21	+	9.75171e21i	−0.415938	+	0.708611i
$896$	−2.40803e22			−1.73521
$897$		0			0
$898$			1.63249e22i			1.15685i
$899$	−5.85437e21			−0.411417
$900$		0			0
$901$	−6.46203e20			−0.0446615
$902$			1.60338e21i			0.109897i
$903$		0			0
$904$	−2.75392e22			−1.85647
$905$	−7.79807e21	+	1.32851e22i	−0.521342	+	0.888182i
$906$		0			0
$907$			2.54107e22i			1.67095i	0.549531	+	0.835473i	$0.314806\pi$
$907$			2.54107e22i			1.67095i	−0.549531	+	0.835473i	$0.685194\pi$
$908$			3.08092e22i			2.00926i
$909$		0			0
$910$	−1.25819e22	−	7.38526e21i	−0.807114	−	0.473757i
$911$	−1.32653e22			−0.843975			−0.421987	−	0.906602i	$-0.638667\pi$
$911$	−1.32653e22			−0.843975			−0.421987	+	0.906602i	$0.638667\pi$
$912$		0			0
$913$		−	8.36796e21i		−	0.523707i
$914$	−1.11685e22			−0.693262
$915$		0			0
$916$	1.89952e22			1.15992
$917$		−	7.32694e21i		−	0.443765i
$918$		0			0
$919$	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
$921$		0			0
$922$		−	1.32268e22i		−	0.769080i
$923$			1.03768e22i			0.598484i
$924$		0			0
$925$	1.40726e22	−	7.85720e21i	0.798564	−	0.445866i
$926$	−1.86348e22			−1.04892
$927$		0			0
$928$		−	1.83909e22i		−	1.01857i
$929$	1.27699e22			0.701570			0.350785	−	0.936456i	$-0.385915\pi$
$929$	1.27699e22			0.701570			0.350785	+	0.936456i	$0.385915\pi$
$930$		0			0
$931$	−2.42206e21			−0.130937
$932$		−	2.94378e22i		−	1.57865i
$933$		0			0
$934$	−5.93168e22			−3.13023
$935$	−1.28025e22	−	7.51475e21i	−0.670204	−	0.393394i
$936$		0			0
$937$			3.23835e22i			1.66831i	0.551528	+	0.834156i	$0.314045\pi$
$937$			3.23835e22i			1.66831i	−0.551528	+	0.834156i	$0.685955\pi$
$938$		−	2.48996e22i		−	1.27254i
$939$		0			0
$940$	7.85280e21	+	4.60941e21i	0.394971	+	0.231839i
$941$	−1.02130e22			−0.509600			−0.254800	−	0.966994i	$-0.582010\pi$
$941$	−1.02130e22			−0.509600			−0.254800	+	0.966994i	$0.582010\pi$
$942$		0			0
$943$			1.71967e21i			0.0844517i
$944$	−1.33455e19			−0.000650196
$945$		0			0
$946$	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	$0.745857\pi$
$948$		0			0
$949$	1.15663e22			0.541626
$950$	5.01943e22	−	2.80252e22i	2.33199	−	1.30203i
$951$		0			0
$952$		−	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	$0.886312\pi$
$954$		0			0
$955$	−4.17135e21	+	7.10650e21i	−0.186316	+	0.317417i
$956$	2.80638e22			1.24369
$957$		0			0
$958$		−	2.27799e22i		−	0.993828i
$959$	−1.58764e22			−0.687248
$960$		0			0
$961$	−2.18538e22			−0.931324
$962$			2.11247e22i			0.893261i
$963$		0			0
$964$	3.93802e22			1.63946
$965$	1.47603e22	+	8.66395e21i	0.609734	+	0.357900i
$966$		0			0
$967$			4.24903e22i			1.72819i	0.503330	+	0.864094i	$0.332108\pi$
$967$			4.24903e22i			1.72819i	−0.503330	+	0.864094i	$0.667892\pi$
$968$			1.37017e22i			0.552980i
$969$		0			0
$970$	4.01804e22	−	6.84531e22i	1.59671	−	2.72023i
$971$	−1.25803e22			−0.496073			−0.248037	−	0.968751i	$-0.579785\pi$
$971$	−1.25803e22			−0.496073			−0.248037	+	0.968751i	$0.579785\pi$
$972$		0			0
$973$		−	6.95436e21i		−	0.270029i
$974$	−4.14919e22			−1.59872
$975$		0			0
$976$	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	$-0.0144456\pi$
$978$		0			0
$979$	−4.27321e22			−1.58447
$980$	−2.00408e21	+	3.41425e21i	−0.0737429	+	0.125632i
$981$		0			0
$982$			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	$-0.269434\pi$
$984$		0			0
$985$	−2.75541e22	−	1.61736e22i	−0.975919	−	0.572841i
$986$	4.85087e22			1.70507
$987$		0			0
$988$			4.82607e22i			1.67077i
$989$	1.91644e22			0.658450
$990$		0			0
$991$	−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
$993$		0			0
$994$	−4.93726e22			−1.63338
$995$	−1.73299e21	+	2.95240e21i	−0.0569013	+	0.0969396i
$996$		0			0
$997$		−	4.95508e22i		−	1.60264i	−0.598234	−	0.801321i	$-0.704131\pi$
$997$		−	4.95508e22i		−	1.60264i	0.598234	−	0.801321i	$-0.295869\pi$
$998$		−	7.16434e22i		−	2.29984i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.16.b.a.4.1	✓	6	15.14	odd	2
5.16.b.a.4.6	yes	6	3.2	odd	2
25.16.a.f.1.1		6	15.2	even	4
25.16.a.f.1.6		6	15.8	even	4
45.16.b.b.19.1		6	1.1	even	1	trivial
45.16.b.b.19.6		6	5.4	even	2	inner
80.16.c.a.49.3		6	12.11	even	2
80.16.c.a.49.4		6	60.59	even	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-301.910i q^{2} -58381.4 q^{4} +(88431.8 - 150657. i) q^{5} -2.08791e6i q^{7} +7.73292e6i q^{8} +O(q^{10})\)	\(q-301.910i q^{2} -58381.4 q^{4} +(88431.8 - 150657. i) q^{5} -2.08791e6i q^{7} +7.73292e6i q^{8} +(-4.54846e7 - 2.66984e7i) q^{10} +7.71305e7 q^{11} +1.32485e8i q^{13} -6.30361e8 q^{14} +4.21600e8 q^{16} -1.10174e9i q^{17} -6.23952e9 q^{19} +(-5.16277e9 + 8.79553e9i) q^{20} -2.32864e10i q^{22} -2.49754e10i q^{23} +(-1.48772e10 - 2.66457e10i) q^{25} +3.99986e10 q^{26} +1.21895e11i q^{28} -1.45836e11 q^{29} +4.01436e10 q^{31} +1.26107e11i q^{32} -3.32626e11 q^{34} +(-3.14558e11 - 1.84638e11i) q^{35} +5.28137e11i q^{37} +1.88377e12i q^{38} +(1.16501e12 + 6.83836e11i) q^{40} -6.88546e10 q^{41} +7.67330e11i q^{43} -4.50298e12 q^{44} -7.54032e12 q^{46} -8.92816e11i q^{47} +3.88180e11 q^{49} +(-8.04458e12 + 4.49157e12i) q^{50} -7.73468e12i q^{52} -5.86528e11i q^{53} +(6.82079e12 - 1.16202e13i) q^{55} +1.61457e13 q^{56} +4.40291e13i q^{58} -3.16543e10 q^{59} +5.85723e12 q^{61} -1.21197e13i q^{62} +5.18879e13 q^{64} +(1.99598e13 + 1.17159e13i) q^{65} +3.95005e13i q^{67} +6.43212e13i q^{68} +(-5.57440e13 + 9.49680e13i) q^{70} +7.83244e13 q^{71} -8.73027e13i q^{73} +1.59450e14 q^{74} +3.64272e14 q^{76} -1.61042e14i q^{77} -3.01801e13 q^{79} +(3.72829e13 - 6.35169e13i) q^{80} +2.07879e13i q^{82} -1.08491e14i q^{83} +(-1.65985e14 - 9.74290e13i) q^{85} +2.31664e14 q^{86} +5.96444e14i q^{88} -5.54023e14 q^{89} +2.76618e14 q^{91} +1.45810e15i q^{92} -2.69550e14 q^{94} +(-5.51772e14 + 9.40024e14i) q^{95} +1.50497e15i q^{97} -1.17195e14i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 38568 q^{4} + 238350 q^{5}+O(q^{10}) \) 6 * q - 38568 * q^4 + 238350 * q^5	\( 6 q - 38568 q^{4} + 238350 q^{5} - 48274200 q^{10} + 108590088 q^{11} - 663751704 q^{14} + 1155522336 q^{16} - 3630995640 q^{19} - 2533753800 q^{20} + 18250878750 q^{25} + 81970953168 q^{26} - 286168468740 q^{29} - 276236748288 q^{31} - 127784939136 q^{34} - 1171274911800 q^{35} + 4214283852000 q^{40} + 6153278882388 q^{41} - 8250173021664 q^{44} - 23334602656488 q^{46} + 11613390856242 q^{49} - 23694218070000 q^{50} + 33977390365800 q^{55} + 59280484297440 q^{56} - 14903258326680 q^{59} - 11352061428588 q^{61} + 73265851251072 q^{64} + 50675287275600 q^{65} - 156447825521400 q^{70} - 131693145807312 q^{71} + 353606797863216 q^{74} + 959127540575520 q^{76} - 26081853939360 q^{79} + 552945514077600 q^{80} - 548221025491200 q^{85} - 598387757484072 q^{86} - 59269690709820 q^{89} + 821206462566672 q^{91} - 308164835928456 q^{94} - 232287694599000 q^{95}+O(q^{100}) \) 6 * q - 38568 * q^4 + 238350 * q^5 - 48274200 * q^10 + 108590088 * q^11 - 663751704 * q^14 + 1155522336 * q^16 - 3630995640 * q^19 - 2533753800 * q^20 + 18250878750 * q^25 + 81970953168 * q^26 - 286168468740 * q^29 - 276236748288 * q^31 - 127784939136 * q^34 - 1171274911800 * q^35 + 4214283852000 * q^40 + 6153278882388 * q^41 - 8250173021664 * q^44 - 23334602656488 * q^46 + 11613390856242 * q^49 - 23694218070000 * q^50 + 33977390365800 * q^55 + 59280484297440 * q^56 - 14903258326680 * q^59 - 11352061428588 * q^61 + 73265851251072 * q^64 + 50675287275600 * q^65 - 156447825521400 * q^70 - 131693145807312 * q^71 + 353606797863216 * q^74 + 959127540575520 * q^76 - 26081853939360 * q^79 + 552945514077600 * q^80 - 548221025491200 * q^85 - 598387757484072 * q^86 - 59269690709820 * q^89 + 821206462566672 * q^91 - 308164835928456 * q^94 - 232287694599000 * q^95

Introduction

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