LMFDB - Embedded newform 100.11.b.e.51.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,11,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	100.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:	$63.5357252674$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 199481 x^{18} + 16413464051 x^{16} + 725560177607766 x^{14} + \cdots + 21\!\cdots\!25 $ x^20 + 199481x^18 + 16413464051x^16 + 725560177607766x^14 + 18834574233849489621x^12 + 294503164498899790078095x^10 + 2731275057520962661290869385x^8 + 14154171070179138865031966998950x^6 + 35770310815174676049504613026680775x^4 + 31929367165777304447910767061760715625*x^2 + 2155644618924695638814066662020965503125
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{97}\cdot 3^{4}\cdot 5^{29} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.4
Root			$160.986i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.11.b.e.51.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-30.5298 + 9.58811i) q^{2} +321.971i q^{3} +(840.136 - 585.446i) q^{4} +(-3087.10 - 9829.71i) q^{6} +9880.78i q^{7} +(-20035.9 + 25928.9i) q^{8} -44616.5 q^{9} +O(q^{10})$	\(q+(-30.5298 + 9.58811i) q^{2} +321.971i q^{3} +(840.136 - 585.446i) q^{4} +(-3087.10 - 9829.71i) q^{6} +9880.78i q^{7} +(-20035.9 + 25928.9i) q^{8} -44616.5 q^{9} +116297. i q^{11} +(188497. + 270500. i) q^{12} +522308. q^{13} +(-94738.1 - 301658. i) q^{14} +(363082. - 983709. i) q^{16} -1.21816e6 q^{17} +(1.36213e6 - 427788. i) q^{18} -1.43420e6i q^{19} -3.18133e6 q^{21} +(-1.11507e6 - 3.55052e6i) q^{22} +6.87353e6i q^{23} +(-8.34835e6 - 6.45097e6i) q^{24} +(-1.59460e7 + 5.00795e6i) q^{26} +4.64686e6i q^{27} +(5.78467e6 + 8.30120e6i) q^{28} +2.86090e7 q^{29} +3.98357e7i q^{31} +(-1.65289e6 + 3.35137e7i) q^{32} -3.74443e7 q^{33} +(3.71903e7 - 1.16799e7i) q^{34} +(-3.74839e7 + 2.61205e7i) q^{36} -1.09043e8 q^{37} +(1.37513e7 + 4.37858e7i) q^{38} +1.68168e8i q^{39} +3.34019e7 q^{41} +(9.71253e7 - 3.05029e7i) q^{42} -7.92659e7i q^{43} +(6.80856e7 + 9.77053e7i) q^{44} +(-6.59042e7 - 2.09847e8i) q^{46} +4.50036e8i q^{47} +(3.16726e8 + 1.16902e8i) q^{48} +1.84845e8 q^{49} -3.92213e8i q^{51} +(4.38810e8 - 3.05783e8i) q^{52} +2.29617e8 q^{53} +(-4.45546e7 - 1.41868e8i) q^{54} +(-2.56198e8 - 1.97970e8i) q^{56} +4.61771e8 q^{57} +(-8.73425e8 + 2.74306e8i) q^{58} +1.31191e9i q^{59} -8.17592e8 q^{61} +(-3.81949e8 - 1.21618e9i) q^{62} -4.40846e8i q^{63} +(-2.70871e8 - 1.03901e9i) q^{64} +(1.14317e9 - 3.59020e8i) q^{66} +5.25343e8i q^{67} +(-1.02342e9 + 7.13169e8i) q^{68} -2.21308e9 q^{69} -1.13070e9i q^{71} +(8.93929e8 - 1.15685e9i) q^{72} -1.23872e9 q^{73} +(3.32907e9 - 1.04552e9i) q^{74} +(-8.39647e8 - 1.20492e9i) q^{76} -1.14911e9 q^{77} +(-1.61242e9 - 5.13414e9i) q^{78} -1.72330e9i q^{79} -4.13071e9 q^{81} +(-1.01975e9 + 3.20261e8i) q^{82} -5.52854e9i q^{83} +(-2.67275e9 + 1.86250e9i) q^{84} +(7.60011e8 + 2.41997e9i) q^{86} +9.21126e9i q^{87} +(-3.01545e9 - 2.33011e9i) q^{88} -3.77598e8 q^{89} +5.16082e9i q^{91} +(4.02408e9 + 5.77470e9i) q^{92} -1.28260e10 q^{93} +(-4.31500e9 - 1.37395e10i) q^{94} +(-1.07904e10 - 5.32184e8i) q^{96} +3.29891e9 q^{97} +(-5.64329e9 + 1.77232e9i) q^{98} -5.18876e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) $ 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−30.5298	+	9.58811i	−0.954056	+	0.299629i
$2$	−30.5298	+	9.58811i	−0.954056	+	0.299629i
$3$			321.971i			1.32498i	0.749069	+	0.662492i	$0.230501\pi$
$3$			321.971i			1.32498i	−0.749069	+	0.662492i	$0.769499\pi$
$4$	840.136	−	585.446i	0.820445	−	0.571725i
$5$		0			0
$5$		0			0
$6$	−3087.10	−	9829.71i	−0.397003	−	1.26411i
$7$			9880.78i			0.587897i	0.955821	+	0.293948i	$0.0949694\pi$
$7$			9880.78i			0.587897i	−0.955821	+	0.293948i	$0.905031\pi$
$8$	−20035.9	+	25928.9i	−0.611446	+	0.791286i
$9$	−44616.5			−0.755584
$10$		0			0
$11$			116297.i			0.722113i	0.932544	+	0.361056i	$0.117584\pi$
$11$			116297.i			0.722113i	−0.932544	+	0.361056i	$0.882416\pi$
$12$	188497.	+	270500.i	0.757526	+	1.08708i
$13$	522308.			1.40673			0.703364	−	0.710830i	$-0.251680\pi$
$13$	522308.			1.40673			0.703364	+	0.710830i	$0.251680\pi$
$14$	−94738.1	−	301658.i	−0.176151	−	0.560886i
$15$		0			0
$16$	363082.	−	983709.i	0.346262	−	0.938138i
$17$	−1.21816e6			−0.857948			−0.428974	−	0.903317i	$-0.641125\pi$
$17$	−1.21816e6			−0.857948			−0.428974	+	0.903317i	$0.641125\pi$
$18$	1.36213e6	−	427788.i	0.720869	−	0.226394i
$19$		−	1.43420e6i		−	0.579217i	−0.957145	−	0.289609i	$-0.906475\pi$
$19$		−	1.43420e6i		−	0.579217i	0.957145	−	0.289609i	$-0.0935252\pi$
$20$		0			0
$21$	−3.18133e6			−0.778954
$22$	−1.11507e6	−	3.55052e6i	−0.216366	−	0.688936i
$23$			6.87353e6i			1.06792i	0.845508	+	0.533962i	$0.179298\pi$
$23$			6.87353e6i			1.06792i	−0.845508	+	0.533962i	$0.820702\pi$
$24$	−8.34835e6	−	6.45097e6i	−1.04844	−	0.810156i
$25$		0			0
$26$	−1.59460e7	+	5.00795e6i	−1.34210	+	0.421496i
$27$			4.64686e6i			0.323848i
$28$	5.78467e6	+	8.30120e6i	0.336115	+	0.482337i
$29$	2.86090e7			1.39480			0.697400	−	0.716682i	$-0.254340\pi$
$29$	2.86090e7			1.39480			0.697400	+	0.716682i	$0.254340\pi$
$30$		0			0
$31$			3.98357e7i			1.39144i	0.718313	+	0.695720i	$0.244914\pi$
$31$			3.98357e7i			1.39144i	−0.718313	+	0.695720i	$0.755086\pi$
$32$	−1.65289e6	+	3.35137e7i	−0.0492601	+	0.998786i
$33$	−3.74443e7			−0.956788
$34$	3.71903e7	−	1.16799e7i	0.818530	−	0.257066i
$35$		0			0
$36$	−3.74839e7	+	2.61205e7i	−0.619915	+	0.431986i
$37$	−1.09043e8			−1.57250			−0.786250	−	0.617909i	$-0.787980\pi$
$37$	−1.09043e8			−1.57250			−0.786250	+	0.617909i	$0.787980\pi$
$38$	1.37513e7	+	4.37858e7i	0.173550	+	0.552606i
$39$			1.68168e8i			1.86389i
$40$		0			0
$41$	3.34019e7			0.288305			0.144152	−	0.989555i	$-0.453954\pi$
$41$	3.34019e7			0.288305			0.144152	+	0.989555i	$0.453954\pi$
$42$	9.71253e7	−	3.05029e7i	0.743166	−	0.233397i
$43$		−	7.92659e7i		−	0.539193i	−0.962973	−	0.269597i	$-0.913110\pi$
$43$		−	7.92659e7i		−	0.539193i	0.962973	−	0.269597i	$-0.0868903\pi$
$44$	6.80856e7	+	9.77053e7i	0.412850	+	0.592454i
$45$		0			0
$46$	−6.59042e7	−	2.09847e8i	−0.319981	−	1.01886i
$47$			4.50036e8i			1.96227i	0.193331	+	0.981134i	$0.438071\pi$
$47$			4.50036e8i			1.96227i	−0.193331	+	0.981134i	$0.561929\pi$
$48$	3.16726e8	+	1.16902e8i	1.24302	+	0.458791i
$49$	1.84845e8			0.654377
$50$		0			0
$51$		−	3.92213e8i		−	1.13677i
$52$	4.38810e8	−	3.05783e8i	1.15414	−	0.804262i
$53$	2.29617e8			0.549065			0.274533	−	0.961578i	$-0.411477\pi$
$53$	2.29617e8			0.549065			0.274533	+	0.961578i	$0.411477\pi$
$54$	−4.45546e7	−	1.41868e8i	−0.0970340	−	0.308969i
$55$		0			0
$56$	−2.56198e8	−	1.97970e8i	−0.465195	−	0.359467i
$57$	4.61771e8			0.767454
$58$	−8.73425e8	+	2.74306e8i	−1.33072	+	0.417922i
$59$			1.31191e9i			1.83503i	0.397698	+	0.917516i	$0.369809\pi$
$59$			1.31191e9i			1.83503i	−0.397698	+	0.917516i	$0.630191\pi$
$60$		0			0
$61$	−8.17592e8			−0.968027			−0.484014	−	0.875060i	$-0.660822\pi$
$61$	−8.17592e8			−0.968027			−0.484014	+	0.875060i	$0.660822\pi$
$62$	−3.81949e8	−	1.21618e9i	−0.416915	−	1.32751i
$63$		−	4.40846e8i		−	0.444205i
$64$	−2.70871e8	−	1.03901e9i	−0.252268	−	0.967657i
$65$		0			0
$66$	1.14317e9	−	3.59020e8i	0.912830	−	0.286681i
$67$			5.25343e8i			0.389107i	0.980892	+	0.194554i	$0.0623258\pi$
$67$			5.25343e8i			0.389107i	−0.980892	+	0.194554i	$0.937674\pi$
$68$	−1.02342e9	+	7.13169e8i	−0.703899	+	0.490510i
$69$	−2.21308e9			−1.41498
$70$		0			0
$71$		−	1.13070e9i		−	0.626694i	−0.949639	−	0.313347i	$-0.898550\pi$
$71$		−	1.13070e9i		−	0.626694i	0.949639	−	0.313347i	$-0.101450\pi$
$72$	8.93929e8	−	1.15685e9i	0.461999	−	0.597883i
$73$	−1.23872e9			−0.597528			−0.298764	−	0.954327i	$-0.596574\pi$
$73$	−1.23872e9			−0.597528			−0.298764	+	0.954327i	$0.596574\pi$
$74$	3.32907e9	−	1.04552e9i	1.50025	−	0.471166i
$75$		0			0
$76$	−8.39647e8	−	1.20492e9i	−0.331153	−	0.475216i
$77$	−1.14911e9			−0.424528
$78$	−1.61242e9	−	5.13414e9i	−0.558476	−	1.77826i
$79$		−	1.72330e9i		−	0.560049i	−0.959993	−	0.280025i	$-0.909657\pi$
$79$		−	1.72330e9i		−	0.560049i	0.959993	−	0.280025i	$-0.0903426\pi$
$80$		0			0
$81$	−4.13071e9			−1.18468
$82$	−1.01975e9	+	3.20261e8i	−0.275059	+	0.0863844i
$83$		−	5.52854e9i		−	1.40352i	−0.712411	−	0.701762i	$-0.752397\pi$
$83$		−	5.52854e9i		−	1.40352i	0.712411	−	0.701762i	$-0.247603\pi$
$84$	−2.67275e9	+	1.86250e9i	−0.639089	+	0.445347i
$85$		0			0
$86$	7.60011e8	+	2.41997e9i	0.161558	+	0.514420i
$87$			9.21126e9i			1.84809i
$88$	−3.01545e9	−	2.33011e9i	−0.571398	−	0.441533i
$89$	−3.77598e8			−0.0676207			−0.0338104	−	0.999428i	$-0.510764\pi$
$89$	−3.77598e8			−0.0676207			−0.0338104	+	0.999428i	$0.510764\pi$
$90$		0			0
$91$			5.16082e9i			0.827011i
$92$	4.02408e9	+	5.77470e9i	0.610559	+	0.876174i
$93$	−1.28260e10			−1.84364
$94$	−4.31500e9	−	1.37395e10i	−0.587951	−	1.87211i
$95$		0			0
$96$	−1.07904e10	−	5.32184e8i	−1.32338	−	0.0652688i
$97$	3.29891e9			0.384160			0.192080	−	0.981379i	$-0.438477\pi$
$97$	3.29891e9			0.384160			0.192080	+	0.981379i	$0.438477\pi$
$98$	−5.64329e9	+	1.77232e9i	−0.624313	+	0.196070i
$99$		−	5.18876e9i		−	0.545617i
$100$		0			0
$101$	−1.36534e10			−1.29907			−0.649537	−	0.760330i	$-0.725037\pi$
$101$	−1.36534e10			−1.29907			−0.649537	+	0.760330i	$0.725037\pi$
$102$	3.76059e9	+	1.19742e10i	0.340608	+	1.08454i
$103$		−	7.59746e9i		−	0.655364i	−0.944788	−	0.327682i	$-0.893733\pi$
$103$		−	7.59746e9i		−	0.655364i	0.944788	−	0.327682i	$-0.106267\pi$
$104$	−1.04649e10	+	1.35429e10i	−0.860138	+	1.11313i
$105$		0			0
$106$	−7.01015e9	+	2.20159e9i	−0.523839	+	0.164516i
$107$		−	2.71478e10i		−	1.93560i	−0.251717	−	0.967801i	$-0.580995\pi$
$107$		−	2.71478e10i		−	1.93560i	0.251717	−	0.967801i	$-0.419005\pi$
$108$	2.72049e9	+	3.90399e9i	0.185152	+	0.265699i
$109$	1.34821e10			0.876245			0.438122	−	0.898915i	$-0.355644\pi$
$109$	1.34821e10			0.876245			0.438122	+	0.898915i	$0.355644\pi$
$110$		0			0
$111$		−	3.51088e10i		−	2.08354i
$112$	9.71981e9	+	3.58753e9i	0.551528	+	0.203566i
$113$	−1.51614e10			−0.822899			−0.411449	−	0.911433i	$-0.634977\pi$
$113$	−1.51614e10			−0.822899			−0.411449	+	0.911433i	$0.634977\pi$
$114$	−1.40978e10	+	4.42751e9i	−0.732194	+	0.229951i
$115$		0			0
$116$	2.40354e10	−	1.67490e10i	1.14436	−	0.797442i
$117$	−2.33036e10			−1.06290
$118$	−1.25787e10	−	4.00523e10i	−0.549828	−	1.75072i
$119$		−	1.20364e10i		−	0.504385i
$120$		0			0
$121$	1.24124e10			0.478553
$122$	2.49609e10	−	7.83917e9i	0.923552	−	0.290049i
$123$			1.07545e10i			0.382000i
$124$	2.33217e10	+	3.34674e10i	0.795520	+	1.14160i
$125$		0			0
$126$	4.22688e9	+	1.34589e10i	0.133097	+	0.423797i
$127$		−	4.87268e10i		−	1.47485i	−0.675427	−	0.737427i	$-0.736041\pi$
$127$		−	4.87268e10i		−	1.47485i	0.675427	−	0.737427i	$-0.263959\pi$
$128$	1.82318e10	+	2.91237e10i	0.530615	+	0.847613i
$129$	2.55214e10			0.714423
$130$		0			0
$131$		−	9.99247e8i		−	0.0259010i	−0.999916	−	0.0129505i	$-0.995878\pi$
$131$		−	9.99247e8i		−	0.0259010i	0.999916	−	0.0129505i	$-0.00412238\pi$
$132$	−3.14583e10	+	2.19216e10i	−0.784993	+	0.547020i
$133$	1.41710e10			0.340520
$134$	−5.03705e9	−	1.60386e10i	−0.116588	−	0.371230i
$135$		0			0
$136$	2.44069e10	−	3.15856e10i	0.524589	−	0.678882i
$137$	4.30128e10			0.891240			0.445620	−	0.895222i	$-0.352983\pi$
$137$	4.30128e10			0.891240			0.445620	+	0.895222i	$0.352983\pi$
$138$	6.75648e10	−	2.12192e10i	1.34997	−	0.423969i
$139$			1.98596e10i			0.382734i	0.981519	+	0.191367i	$0.0612921\pi$
$139$			1.98596e10i			0.382734i	−0.981519	+	0.191367i	$0.938708\pi$
$140$		0			0
$141$	−1.44899e11			−2.59997
$142$	1.08413e10	+	3.45200e10i	0.187776	+	0.597901i
$143$			6.07429e10i			1.01582i
$144$	−1.61994e10	+	4.38896e10i	−0.261630	+	0.708842i
$145$		0			0
$146$	3.78178e10	−	1.18770e10i	0.570075	−	0.179037i
$147$			5.95149e10i			0.867040i
$148$	−9.16112e10	+	6.38390e10i	−1.29015	+	0.899037i
$149$	−2.30686e10			−0.314116			−0.157058	−	0.987589i	$-0.550201\pi$
$149$	−2.30686e10			−0.314116			−0.157058	+	0.987589i	$0.550201\pi$
$150$		0			0
$151$		−	8.15340e9i		−	0.103861i	−0.998651	−	0.0519307i	$-0.983463\pi$
$151$		−	8.15340e9i		−	0.103861i	0.998651	−	0.0519307i	$-0.0165375\pi$
$152$	3.71872e10	+	2.87354e10i	0.458327	+	0.354160i
$153$	5.43501e10			0.648251
$154$	3.50819e10	−	1.10178e10i	0.405023	−	0.127201i
$155$		0			0
$156$	9.84535e10	+	1.41284e11i	1.06563	+	1.52922i
$157$	−1.66306e11			−1.74345			−0.871724	−	0.489997i	$-0.836998\pi$
$157$	−1.66306e11			−1.74345			−0.871724	+	0.489997i	$0.836998\pi$
$158$	1.65232e10	+	5.26121e10i	0.167807	+	0.534318i
$159$			7.39299e10i			0.727503i
$160$		0			0
$161$	−6.79159e10			−0.627830
$162$	1.26110e11	−	3.96057e10i	1.13025	−	0.354963i
$163$		−	7.41987e9i		−	0.0644849i	−0.999480	−	0.0322425i	$-0.989735\pi$
$163$		−	7.41987e9i		−	0.0644849i	0.999480	−	0.0322425i	$-0.0102649\pi$
$164$	2.80622e10	−	1.95550e10i	0.236538	−	0.164831i
$165$		0			0
$166$	5.30083e10	+	1.68785e11i	0.420536	+	1.33904i
$167$			8.08722e10i			0.622611i	0.950310	+	0.311306i	$0.100766\pi$
$167$			8.08722e10i			0.622611i	−0.950310	+	0.311306i	$0.899234\pi$
$168$	6.37406e10	−	8.24882e10i	0.476288	−	0.616376i
$169$	1.34948e11			0.978885
$170$		0			0
$171$			6.39889e10i			0.437647i
$172$	−4.64059e10	−	6.65942e10i	−0.308270	−	0.442379i
$173$	1.70411e11			1.09968			0.549841	−	0.835270i	$-0.314688\pi$
$173$	1.70411e11			1.09968			0.549841	+	0.835270i	$0.314688\pi$
$174$	−8.83186e10	−	2.81218e11i	−0.553740	−	1.76318i
$175$		0			0
$176$	1.14402e11	+	4.22253e10i	0.677442	+	0.250040i
$177$	−4.22397e11			−2.43139
$178$	1.15280e10	−	3.62045e9i	0.0645140	−	0.0202611i
$179$		−	4.09183e10i		−	0.222665i	−0.993783	−	0.111333i	$-0.964488\pi$
$179$		−	4.09183e10i		−	0.222665i	0.993783	−	0.111333i	$-0.0355119\pi$
$180$		0			0
$181$	7.20812e10			0.371047			0.185524	−	0.982640i	$-0.440602\pi$
$181$	7.20812e10			0.371047			0.185524	+	0.982640i	$0.440602\pi$
$182$	−4.94825e10	−	1.57559e11i	−0.247796	−	0.789015i
$183$		−	2.63241e11i		−	1.28262i
$184$	−1.78223e11	−	1.37717e11i	−0.845034	−	0.652978i
$185$		0			0
$186$	3.91574e11	−	1.22977e11i	1.75893	−	0.552406i
$187$		−	1.41669e11i		−	0.619535i
$188$	2.63472e11	+	3.78092e11i	1.12188	+	1.60993i
$189$	−4.59146e10			−0.190389
$190$		0			0
$191$			8.10586e10i			0.318884i	0.987207	+	0.159442i	$0.0509694\pi$
$191$			8.10586e10i			0.318884i	−0.987207	+	0.159442i	$0.949031\pi$
$192$	3.34533e11	−	8.72125e10i	1.28213	−	0.334251i
$193$	−4.12567e11			−1.54066			−0.770331	−	0.637644i	$-0.779909\pi$
$193$	−4.12567e11			−1.54066			−0.770331	+	0.637644i	$0.779909\pi$
$194$	−1.00715e11	+	3.16303e10i	−0.366510	+	0.115105i
$195$		0			0
$196$	1.55295e11	−	1.08217e11i	0.536881	−	0.374124i
$197$	−1.51409e11			−0.510295			−0.255148	−	0.966902i	$-0.582124\pi$
$197$	−1.51409e11			−0.510295			−0.255148	+	0.966902i	$0.582124\pi$
$198$	4.97504e10	+	1.58412e11i	0.163482	+	0.520549i
$199$			3.84001e11i			1.23046i	0.788348	+	0.615229i	$0.210936\pi$
$199$			3.84001e11i			1.23046i	−0.788348	+	0.615229i	$0.789064\pi$
$200$		0			0
$201$	−1.69145e11			−0.515561
$202$	4.16835e11	−	1.30910e11i	1.23939	−	0.389240i
$203$			2.82679e11i			0.819999i
$204$	−2.29620e11	−	3.29513e11i	−0.649918	−	0.932656i
$205$		0			0
$206$	7.28453e10	+	2.31949e11i	0.196366	+	0.625254i
$207$		−	3.06673e11i		−	0.806907i
$208$	1.89641e11	−	5.13800e11i	0.487096	−	1.31971i
$209$	1.66793e11			0.418260
$210$		0			0
$211$		−	3.93275e11i		−	0.940339i	−0.882576	−	0.470169i	$-0.844193\pi$
$211$		−	3.93275e11i		−	0.940339i	0.882576	−	0.470169i	$-0.155807\pi$
$212$	1.92909e11	−	1.34428e11i	0.450478	−	0.313914i
$213$	3.64053e11			0.830360
$214$	2.60296e11	+	8.28817e11i	0.579961	+	1.84667i
$215$		0			0
$216$	−1.20488e11	−	9.31038e10i	−0.256256	−	0.198015i
$217$	−3.93608e11			−0.818023
$218$	−4.11606e11	+	1.29268e11i	−0.835987	+	0.262548i
$219$		−	3.98832e11i		−	0.791716i
$220$		0			0
$221$	−6.36257e11			−1.20690
$222$	3.36627e11	+	1.07186e12i	0.624287	+	1.98781i
$223$			4.92177e11i			0.892476i	0.894914	+	0.446238i	$0.147237\pi$
$223$			4.92177e11i			0.892476i	−0.894914	+	0.446238i	$0.852763\pi$
$224$	−3.31142e11	−	1.63319e10i	−0.587183	−	0.0289598i
$225$		0			0
$226$	4.62874e11	−	1.45369e11i	0.785091	−	0.246564i
$227$			1.43066e11i			0.237359i	0.992933	+	0.118680i	$0.0378662\pi$
$227$			1.43066e11i			0.237359i	−0.992933	+	0.118680i	$0.962134\pi$
$228$	3.87950e11	−	2.70342e11i	0.629654	−	0.438772i
$229$	1.63175e11			0.259105			0.129553	−	0.991573i	$-0.458646\pi$
$229$	1.63175e11			0.259105			0.129553	+	0.991573i	$0.458646\pi$
$230$		0			0
$231$		−	3.69979e11i		−	0.562493i
$232$	−5.73205e11	+	7.41798e11i	−0.852845	+	1.10369i
$233$	2.54521e11			0.370633			0.185316	−	0.982679i	$-0.440669\pi$
$233$	2.54521e11			0.370633			0.185316	+	0.982679i	$0.440669\pi$
$234$	7.11453e11	−	2.23437e11i	1.01407	−	0.318476i
$235$		0			0
$236$	7.68052e11	+	1.10218e12i	1.04913	+	1.50554i
$237$	5.54854e11			0.742056
$238$	1.15406e11	+	3.67469e11i	0.151128	+	0.481211i
$239$			3.35494e11i			0.430224i	0.976589	+	0.215112i	$0.0690117\pi$
$239$			3.35494e11i			0.430224i	−0.976589	+	0.215112i	$0.930988\pi$
$240$		0			0
$241$	−1.29161e12			−1.58872			−0.794359	−	0.607449i	$-0.792193\pi$
$241$	−1.29161e12			−1.58872			−0.794359	+	0.607449i	$0.792193\pi$
$242$	−3.78949e11	+	1.19012e11i	−0.456566	+	0.143388i
$243$		−	1.05558e12i		−	1.24583i
$244$	−6.86889e11	+	4.78656e11i	−0.794214	+	0.553445i
$245$		0			0
$246$	−1.03115e11	−	3.28331e11i	−0.114458	−	0.364449i
$247$		−	7.49095e11i		−	0.814802i
$248$	−1.03290e12	−	7.98143e11i	−1.10103	−	0.850790i
$249$	1.78003e12			1.85965
$250$		0			0
$251$			3.91363e11i			0.392836i	0.980520	+	0.196418i	$0.0629309\pi$
$251$			3.91363e11i			0.392836i	−0.980520	+	0.196418i	$0.937069\pi$
$252$	−2.58091e11	−	3.70370e11i	−0.253963	−	0.364446i
$253$	−7.99371e11			−0.771162
$254$	4.67198e11	+	1.48762e12i	0.441908	+	1.40709i
$255$		0			0
$256$	−8.35855e11	−	7.14333e11i	−0.760206	−	0.649682i
$257$	−3.42869e11			−0.305818			−0.152909	−	0.988240i	$-0.548864\pi$
$257$	−3.42869e11			−0.305818			−0.152909	+	0.988240i	$0.548864\pi$
$258$	−7.79162e11	+	2.44702e11i	−0.681599	+	0.214061i
$259$		−	1.07743e12i		−	0.924467i
$260$		0			0
$261$	−1.27643e12			−1.05389
$262$	9.58089e9	+	3.05068e10i	0.00776067	+	0.0247110i
$263$			1.67441e12i			1.33071i	0.746526	+	0.665356i	$0.231720\pi$
$263$			1.67441e12i			1.33071i	−0.746526	+	0.665356i	$0.768280\pi$
$264$	7.50228e11	−	9.70888e11i	0.585024	−	0.757094i
$265$		0			0
$266$	−4.32638e11	+	1.35873e11i	−0.324875	+	0.102030i
$267$		−	1.21576e11i		−	0.0895964i
$268$	3.07560e11	+	4.41360e11i	0.222462	+	0.319241i
$269$	−2.68766e12			−1.90815			−0.954077	−	0.299561i	$-0.903160\pi$
$269$	−2.68766e12			−1.90815			−0.954077	+	0.299561i	$0.903160\pi$
$270$		0			0
$271$		−	1.92161e12i		−	1.31468i	−0.753595	−	0.657339i	$-0.771682\pi$
$271$		−	1.92161e12i		−	1.31468i	0.753595	−	0.657339i	$-0.228318\pi$
$272$	−4.42293e11	+	1.19832e12i	−0.297074	+	0.804873i
$273$	−1.66163e12			−1.09578
$274$	−1.31317e12	+	4.12411e11i	−0.850293	+	0.267041i
$275$		0			0
$276$	−1.85929e12	+	1.29564e12i	−1.16092	+	0.808981i
$277$	8.69557e11			0.533211			0.266605	−	0.963806i	$-0.414098\pi$
$277$	8.69557e11			0.533211			0.266605	+	0.963806i	$0.414098\pi$
$278$	−1.90416e11	−	6.06311e11i	−0.114678	−	0.365150i
$279$		−	1.77733e12i		−	1.05135i
$280$		0			0
$281$	1.80190e12			1.02849			0.514244	−	0.857644i	$-0.328072\pi$
$281$	1.80190e12			1.02849			0.514244	+	0.857644i	$0.328072\pi$
$282$	4.42373e12	−	1.38931e12i	2.48052	−	0.779026i
$283$		−	1.85966e12i		−	1.02448i	−0.858843	−	0.512238i	$-0.828816\pi$
$283$		−	1.85966e12i		−	1.02448i	0.858843	−	0.512238i	$-0.171184\pi$
$284$	−6.61964e11	−	9.49942e11i	−0.358297	−	0.514169i
$285$		0			0
$286$	−5.82410e11	−	1.85447e12i	−0.304368	−	0.969146i
$287$			3.30037e11i			0.169494i
$288$	7.37463e10	−	1.49526e12i	0.0372201	−	0.754667i
$289$	−5.32073e11			−0.263926
$290$		0			0
$291$			1.06215e12i			0.509006i
$292$	−1.04069e12	+	7.25203e11i	−0.490239	+	0.341622i
$293$	−8.47213e10			−0.0392333			−0.0196166	−	0.999808i	$-0.506245\pi$
$293$	−8.47213e10			−0.0392333			−0.0196166	+	0.999808i	$0.506245\pi$
$294$	−5.70636e11	−	1.81698e12i	−0.259790	−	0.827204i
$295$		0			0
$296$	2.18478e12	−	2.82737e12i	0.961498	−	1.24430i
$297$	−5.40416e11			−0.233855
$298$	7.04280e11	−	2.21184e11i	0.299684	−	0.0941181i
$299$			3.59010e12i			1.50228i
$300$		0			0
$301$	7.83210e11			0.316990
$302$	7.81758e10	+	2.48922e11i	0.0311198	+	0.0990896i
$303$		−	4.39600e12i		−	1.72125i
$304$	−1.41083e12	−	5.20731e11i	−0.543386	−	0.200561i
$305$		0			0
$306$	−1.65930e12	+	5.21115e11i	−0.618468	+	0.194235i
$307$			1.21008e12i			0.443734i	0.975077	+	0.221867i	$0.0712150\pi$
$307$			1.21008e12i			0.443734i	−0.975077	+	0.221867i	$0.928785\pi$
$308$	−9.65405e11	+	6.72739e11i	−0.348302	+	0.242713i
$309$	2.44616e12			0.868347
$310$		0			0
$311$			2.96100e10i			0.0101774i	0.999987	+	0.00508869i	$0.00161979\pi$
$311$			2.96100e10i			0.0101774i	−0.999987	+	0.00508869i	$0.998380\pi$
$312$	−4.36041e12	−	3.36940e12i	−1.47487	−	1.13967i
$313$	−2.37961e12			−0.792106			−0.396053	−	0.918228i	$-0.629620\pi$
$313$	−2.37961e12			−0.792106			−0.396053	+	0.918228i	$0.629620\pi$
$314$	5.07728e12	−	1.59456e12i	1.66335	−	0.522387i
$315$		0			0
$316$	−1.00890e12	−	1.44781e12i	−0.320194	−	0.459490i
$317$	4.50103e12			1.40610			0.703049	−	0.711141i	$-0.251821\pi$
$317$	4.50103e12			1.40610			0.703049	+	0.711141i	$0.251821\pi$
$318$	−7.08849e11	−	2.25707e12i	−0.217981	−	0.694078i
$319$			3.32714e12i			1.00720i
$320$		0			0
$321$	8.74081e12			2.56464
$322$	2.07346e12	−	6.51185e11i	0.598985	−	0.188116i
$323$			1.74709e12i			0.496938i
$324$	−3.47036e12	+	2.41831e12i	−0.971963	+	0.677309i
$325$		0			0
$326$	7.11425e10	+	2.26527e11i	0.0193215	+	0.0615222i
$327$			4.34085e12i			1.16101i
$328$	−6.69236e11	+	8.66074e11i	−0.176283	+	0.228132i
$329$	−4.44671e12			−1.15361
$330$		0			0
$331$			4.96316e12i			1.24916i	0.780960	+	0.624581i	$0.214730\pi$
$331$			4.96316e12i			1.24916i	−0.780960	+	0.624581i	$0.785270\pi$
$332$	−3.23666e12	−	4.64473e12i	−0.802430	−	1.15152i
$333$	4.86513e12			1.18815
$334$	−7.75412e11	−	2.46901e12i	−0.186552	−	0.594006i
$335$		0			0
$336$	−1.15508e12	+	3.12950e12i	−0.269722	+	0.730767i
$337$	−4.05843e12			−0.933702			−0.466851	−	0.884336i	$-0.654611\pi$
$337$	−4.05843e12			−0.933702			−0.466851	+	0.884336i	$0.654611\pi$
$338$	−4.11992e12	+	1.29389e12i	−0.933911	+	0.293302i
$339$		−	4.88153e12i		−	1.09033i
$340$		0			0
$341$	−4.63278e12			−1.00478
$342$	−6.13533e11	−	1.95357e12i	−0.131132	−	0.417540i
$343$			4.61749e12i			0.972603i
$344$	2.05528e12	+	1.58816e12i	0.426656	+	0.329687i
$345$		0			0
$346$	−5.20261e12	+	1.63392e12i	−1.04916	+	0.329496i
$347$			7.15107e12i			1.42142i	0.703483	+	0.710712i	$0.251627\pi$
$347$			7.15107e12i			1.42142i	−0.703483	+	0.710712i	$0.748373\pi$
$348$	5.39270e12	+	7.73871e12i	1.05660	+	1.51626i
$349$	−3.81727e12			−0.737268			−0.368634	−	0.929575i	$-0.620174\pi$
$349$	−3.81727e12			−0.737268			−0.368634	+	0.929575i	$0.620174\pi$
$350$		0			0
$351$			2.42709e12i			0.455566i
$352$	−3.89754e12	−	1.92227e11i	−0.721236	−	0.0355713i
$353$	5.12751e12			0.935477			0.467739	−	0.883867i	$-0.345069\pi$
$353$	5.12751e12			0.935477			0.467739	+	0.883867i	$0.345069\pi$
$354$	1.28957e13	−	4.04999e12i	2.31968	−	0.728514i
$355$		0			0
$356$	−3.17234e11	+	2.21063e11i	−0.0554791	+	0.0386604i
$357$	3.87538e12			0.668302
$358$	3.92329e11	+	1.24923e12i	0.0667169	+	0.212435i
$359$		−	2.06638e12i		−	0.346528i	−0.984875	−	0.173264i	$-0.944569\pi$
$359$		−	2.06638e12i		−	0.346528i	0.984875	−	0.173264i	$-0.0554315\pi$
$360$		0			0
$361$	4.07414e12			0.664507
$362$	−2.20062e12	+	6.91123e11i	−0.354000	+	0.111176i
$363$			3.99645e12i			0.634075i
$364$	3.02138e12	+	4.33579e12i	0.472823	+	0.678518i
$365$		0			0
$366$	2.52399e12	+	8.03670e12i	0.384310	+	1.22369i
$367$		−	1.18436e13i		−	1.77891i	−0.457024	−	0.889454i	$-0.651085\pi$
$367$		−	1.18436e13i		−	1.77891i	0.457024	−	0.889454i	$-0.348915\pi$
$368$	6.76155e12	+	2.49565e12i	1.00186	+	0.369781i
$369$	−1.49028e12			−0.217839
$370$		0			0
$371$			2.26879e12i			0.322794i
$372$	−1.07756e13	+	7.50891e12i	−1.51260	+	1.05405i
$373$	1.15627e13			1.60145			0.800726	−	0.599031i	$-0.204447\pi$
$373$	1.15627e13			1.60145			0.800726	+	0.599031i	$0.204447\pi$
$374$	1.35834e12	+	4.32512e12i	0.185630	+	0.591071i
$375$		0			0
$376$	−1.16689e13	−	9.01686e12i	−1.55271	−	1.19982i
$377$	1.49427e13			1.96211
$378$	1.40176e12	−	4.40234e11i	0.181642	−	0.0570460i
$379$			3.30334e12i			0.422432i	0.977439	+	0.211216i	$0.0677423\pi$
$379$			3.30334e12i			0.422432i	−0.977439	+	0.211216i	$0.932258\pi$
$380$		0			0
$381$	1.56886e13			1.95416
$382$	−7.77199e11	−	2.47470e12i	−0.0955467	−	0.304233i
$383$		−	5.18660e11i		−	0.0629345i	−0.999505	−	0.0314672i	$-0.989982\pi$
$383$		−	5.18660e11i		−	0.0629345i	0.999505	−	0.0314672i	$-0.0100180\pi$
$384$	−9.37701e12	+	5.87012e12i	−1.12307	+	0.703057i
$385$		0			0
$386$	1.25956e13	−	3.95574e12i	1.46988	−	0.461626i
$387$			3.53657e12i			0.407406i
$388$	2.77153e12	−	1.93133e12i	0.315182	−	0.219634i
$389$	3.58538e12			0.402520			0.201260	−	0.979538i	$-0.435496\pi$
$389$	3.58538e12			0.402520			0.201260	+	0.979538i	$0.435496\pi$
$390$		0			0
$391$		−	8.37308e12i		−	0.916224i
$392$	−3.70354e12	+	4.79283e12i	−0.400116	+	0.517800i
$393$	3.21729e11			0.0343184
$394$	4.62249e12	−	1.45173e12i	0.486850	−	0.152899i
$395$		0			0
$396$	−3.03774e12	−	4.35927e12i	−0.311943	−	0.447649i
$397$	−5.16380e11			−0.0523621			−0.0261811	−	0.999657i	$-0.508335\pi$
$397$	−5.16380e11			−0.0523621			−0.0261811	+	0.999657i	$0.508335\pi$
$398$	−3.68184e12	−	1.17235e13i	−0.368680	−	1.17393i
$399$			4.56266e12i			0.451184i
$400$		0			0
$401$	8.69234e12			0.838330			0.419165	−	0.907910i	$-0.362323\pi$
$401$	8.69234e12			0.838330			0.419165	+	0.907910i	$0.362323\pi$
$402$	5.16397e12	−	1.62179e12i	0.491874	−	0.154477i
$403$			2.08065e13i			1.95738i
$404$	−1.14707e13	+	7.99333e12i	−1.06582	+	0.742713i
$405$		0			0
$406$	−2.71036e12	−	8.63012e12i	−0.245695	−	0.782324i
$407$		−	1.26814e13i		−	1.13552i
$408$	1.01697e13	+	7.85833e12i	0.899508	+	0.695072i
$409$	1.87261e13			1.63618			0.818088	−	0.575093i	$-0.195034\pi$
$409$	1.87261e13			1.63618			0.818088	+	0.575093i	$0.195034\pi$
$410$		0			0
$411$			1.38489e13i			1.18088i
$412$	−4.44791e12	−	6.38290e12i	−0.374688	−	0.537690i
$413$	−1.29627e13			−1.07881
$414$	2.94041e12	+	9.36265e12i	0.241772	+	0.769834i
$415$		0			0
$416$	−8.63320e11	+	1.75045e13i	−0.0692955	+	1.40502i
$417$	−6.39423e12			−0.507117
$418$	−5.09216e12	+	1.59923e12i	−0.399044	+	0.125323i
$419$		−	1.83208e13i		−	1.41865i	−0.704883	−	0.709324i	$-0.749000\pi$
$419$		−	1.83208e13i		−	1.41865i	0.704883	−	0.709324i	$-0.251000\pi$
$420$		0			0
$421$	6.36675e12			0.481402			0.240701	−	0.970599i	$-0.422623\pi$
$421$	6.36675e12			0.481402			0.240701	+	0.970599i	$0.422623\pi$
$422$	3.77077e12	+	1.20066e13i	0.281752	+	0.897136i
$423$		−	2.00790e13i		−	1.48266i
$424$	−4.60057e12	+	5.95370e12i	−0.335724	+	0.434468i
$425$		0			0
$426$	−1.11145e13	+	3.49058e12i	−0.792210	+	0.248800i
$427$		−	8.07845e12i		−	0.569100i
$428$	−1.58936e13	−	2.28079e13i	−1.10663	−	1.58806i
$429$	−1.95575e13			−1.34594
$430$		0			0
$431$		−	2.18784e12i		−	0.147106i	−0.997291	−	0.0735528i	$-0.976566\pi$
$431$		−	2.18784e12i		−	0.147106i	0.997291	−	0.0735528i	$-0.0234337\pi$
$432$	4.57116e12	+	1.68719e12i	0.303814	+	0.112136i
$433$	−1.68547e13			−1.10734			−0.553672	−	0.832735i	$-0.686774\pi$
$433$	−1.68547e13			−1.10734			−0.553672	+	0.832735i	$0.686774\pi$
$434$	1.20168e13	−	3.77396e12i	0.780440	−	0.245103i
$435$		0			0
$436$	1.13268e13	−	7.89305e12i	0.718911	−	0.500971i
$437$	9.85801e12			0.618561
$438$	3.82404e12	+	1.21763e13i	0.237221	+	0.755341i
$439$		−	1.97691e12i		−	0.121245i	−0.998161	−	0.0606225i	$-0.980691\pi$
$439$		−	1.97691e12i		−	0.121245i	0.998161	−	0.0606225i	$-0.0193086\pi$
$440$		0			0
$441$	−8.24715e12			−0.494437
$442$	1.94248e13	−	6.10050e12i	1.15145	−	0.361622i
$443$		−	8.05360e12i		−	0.472032i	−0.971749	−	0.236016i	$-0.924158\pi$
$443$		−	8.05360e12i		−	0.472032i	0.971749	−	0.236016i	$-0.0758418\pi$
$444$	−2.05543e13	−	2.94962e13i	−1.19121	−	1.70943i
$445$		0			0
$446$	−4.71905e12	−	1.50261e13i	−0.267411	−	0.851473i
$447$		−	7.42743e12i		−	0.416199i
$448$	1.02663e13	−	2.67641e12i	0.568883	−	0.148308i
$449$	−8.91317e12			−0.488428			−0.244214	−	0.969721i	$-0.578530\pi$
$449$	−8.91317e12			−0.488428			−0.244214	+	0.969721i	$0.578530\pi$
$450$		0			0
$451$			3.88454e12i			0.208189i
$452$	−1.27376e13	+	8.87617e12i	−0.675144	+	0.470472i
$453$	2.62516e12			0.137615
$454$	−1.37173e12	−	4.36777e12i	−0.0711196	−	0.226454i
$455$		0			0
$456$	−9.25198e12	+	1.19732e13i	−0.469257	+	0.607276i
$457$	−1.48751e13			−0.746239			−0.373119	−	0.927783i	$-0.621712\pi$
$457$	−1.48751e13			−0.746239			−0.373119	+	0.927783i	$0.621712\pi$
$458$	−4.98170e12	+	1.56454e12i	−0.247201	+	0.0776354i
$459$		−	5.66063e12i		−	0.277844i
$460$		0			0
$461$	−1.35057e13			−0.648655			−0.324328	−	0.945945i	$-0.605138\pi$
$461$	−1.35057e13			−0.648655			−0.324328	+	0.945945i	$0.605138\pi$
$462$	3.54740e12	+	1.12954e13i	0.168539	+	0.536650i
$463$		−	1.57917e13i		−	0.742207i	−0.928591	−	0.371104i	$-0.878979\pi$
$463$		−	1.57917e13i		−	0.742207i	0.928591	−	0.371104i	$-0.121021\pi$
$464$	1.03874e13	−	2.81429e13i	0.482966	−	1.30851i
$465$		0			0
$466$	−7.77047e12	+	2.44038e12i	−0.353604	+	0.111052i
$467$			4.34882e13i			1.95789i	0.204133	+	0.978943i	$0.434562\pi$
$467$			4.34882e13i			1.95789i	−0.204133	+	0.978943i	$0.565438\pi$
$468$	−1.95782e13	+	1.36430e13i	−0.872053	+	0.607687i
$469$	−5.19080e12			−0.228755
$470$		0			0
$471$		−	5.35457e13i		−	2.31004i
$472$	−3.40163e13	−	2.62852e13i	−1.45204	−	1.12202i
$473$	9.21839e12			0.389358
$474$	−1.69396e13	+	5.32000e12i	−0.707963	+	0.222341i
$475$		0			0
$476$	−7.04667e12	−	1.01122e13i	−0.288369	−	0.413820i
$477$	−1.02447e13			−0.414865
$478$	−3.21675e12	−	1.02425e13i	−0.128907	−	0.410458i
$479$		−	4.52122e12i		−	0.179299i	−0.995973	−	0.0896496i	$-0.971425\pi$
$479$		−	4.52122e12i		−	0.179299i	0.995973	−	0.0896496i	$-0.0285747\pi$
$480$		0			0
$481$	−5.69543e13			−2.21208
$482$	3.94326e13	−	1.23841e13i	1.51573	−	0.476025i
$483$		−	2.18669e13i		−	0.831864i
$484$	1.04281e13	−	7.26681e12i	0.392627	−	0.273601i
$485$		0			0
$486$	1.01210e13	+	3.22266e13i	0.373286	+	1.18859i
$487$			1.43856e13i			0.525150i	0.964912	+	0.262575i	$0.0845717\pi$
$487$			1.43856e13i			0.525150i	−0.964912	+	0.262575i	$0.915428\pi$
$488$	1.63812e13	−	2.11992e13i	0.591896	−	0.765987i
$489$	2.38898e12			0.0854415
$490$		0			0
$491$			5.09640e13i			1.78589i	0.450161	+	0.892947i	$0.351367\pi$
$491$			5.09640e13i			1.78589i	−0.450161	+	0.892947i	$0.648633\pi$
$492$	6.29615e12	+	9.03521e12i	0.218399	+	0.313410i
$493$	−3.48504e13			−1.19667
$494$	7.18240e12	+	2.28697e13i	0.244138	+	0.777366i
$495$		0			0
$496$	3.91868e13	+	1.44636e13i	1.30536	+	0.481802i
$497$	1.11722e13			0.368432
$498$	−5.43440e13	+	1.70671e13i	−1.77421	+	0.557204i
$499$			4.39550e13i			1.42071i	0.703843	+	0.710356i	$0.251466\pi$
$499$			4.39550e13i			1.42071i	−0.703843	+	0.710356i	$0.748534\pi$
$500$		0			0
$501$	−2.60385e13			−0.824950
$502$	−3.75243e12	−	1.19482e13i	−0.117705	−	0.374787i
$503$			3.50091e13i			1.08728i	0.839319	+	0.543639i	$0.182954\pi$
$503$			3.50091e13i			1.08728i	−0.839319	+	0.543639i	$0.817046\pi$
$504$	1.14306e13	+	8.83272e12i	0.351494	+	0.271608i
$505$		0			0
$506$	2.44046e13	−	7.66446e12i	0.735732	−	0.231062i
$507$			4.34493e13i			1.29701i
$508$	−2.85269e13	−	4.09371e13i	−0.843210	−	1.21004i
$509$	3.35614e13			0.982315			0.491158	−	0.871071i	$-0.336574\pi$
$509$	3.35614e13			0.982315			0.491158	+	0.871071i	$0.336574\pi$
$510$		0			0
$511$		−	1.22395e13i		−	0.351285i
$512$	3.23676e13	+	1.37942e13i	0.919942	+	0.392054i
$513$	6.66452e12			0.187578
$514$	1.04677e13	−	3.28747e12i	0.291767	−	0.0916317i
$515$		0			0
$516$	2.14414e13	−	1.49414e13i	0.586145	−	0.408453i
$517$	−5.23379e13			−1.41698
$518$	1.03306e13	+	3.28938e13i	0.276997	+	0.881994i
$519$			5.48674e13i			1.45706i
$520$		0			0
$521$	−4.27804e13			−1.11444			−0.557219	−	0.830365i	$-0.688132\pi$
$521$	−4.27804e13			−1.11444			−0.557219	+	0.830365i	$0.688132\pi$
$522$	3.89692e13	−	1.22386e13i	1.00547	−	0.315775i
$523$		−	3.45386e13i		−	0.882665i	−0.897344	−	0.441332i	$-0.854506\pi$
$523$		−	3.45386e13i		−	0.882665i	0.897344	−	0.441332i	$-0.145494\pi$
$524$	−5.85005e11	−	8.39503e11i	−0.0148082	−	0.0212503i
$525$		0			0
$526$	−1.60545e13	−	5.11195e13i	−0.398719	−	1.26957i
$527$		−	4.85264e13i		−	1.19378i
$528$	−1.35953e13	+	3.68343e13i	−0.331299	+	0.897600i
$529$	−5.81890e12			−0.140463
$530$		0			0
$531$		−	5.85328e13i		−	1.38652i
$532$	1.19056e13	−	8.29637e12i	0.279378	−	0.194684i
$533$	1.74461e13			0.405567
$534$	1.16568e12	+	3.71168e12i	0.0268456	+	0.0854800i
$535$		0			0
$536$	−1.36216e13	−	1.05257e13i	−0.307895	−	0.237918i
$537$	1.31745e13			0.295028
$538$	8.20538e13	−	2.57696e13i	1.82049	−	0.571738i
$539$			2.14970e13i			0.472534i
$540$		0			0
$541$	−1.36577e13			−0.294707			−0.147353	−	0.989084i	$-0.547075\pi$
$541$	−1.36577e13			−0.294707			−0.147353	+	0.989084i	$0.547075\pi$
$542$	1.84246e13	+	5.86664e13i	0.393915	+	1.25428i
$543$			2.32081e13i			0.491632i
$544$	2.01349e12	−	4.08251e13i	0.0422625	−	0.856906i
$545$		0			0
$546$	5.07294e13	−	1.59319e13i	1.04543	−	0.328326i
$547$		−	6.18712e13i		−	1.26343i	−0.775200	−	0.631716i	$-0.782351\pi$
$547$		−	6.18712e13i		−	1.26343i	0.775200	−	0.631716i	$-0.217649\pi$
$548$	3.61366e13	−	2.51817e13i	0.731214	−	0.509544i
$549$	3.64781e13			0.731426
$550$		0			0
$551$		−	4.10309e13i		−	0.807892i
$552$	4.43409e13	−	5.73826e13i	0.865186	−	1.11966i
$553$	1.70276e13			0.329251
$554$	−2.65474e13	+	8.33741e12i	−0.508713	+	0.159765i
$555$		0			0
$556$	1.16268e13	+	1.66848e13i	0.218819	+	0.314013i
$557$	−5.87222e13			−1.09528			−0.547642	−	0.836713i	$-0.684474\pi$
$557$	−5.87222e13			−1.09528			−0.547642	+	0.836713i	$0.684474\pi$
$558$	1.70412e13	+	5.42615e13i	0.315014	+	1.00305i
$559$		−	4.14013e13i		−	0.758498i
$560$		0			0
$561$	4.56133e13			0.820874
$562$	−5.50117e13	+	1.72768e13i	−0.981236	+	0.308165i
$563$			2.89544e13i			0.511885i	0.966692	+	0.255942i	$0.0823858\pi$
$563$			2.89544e13i			0.511885i	−0.966692	+	0.255942i	$0.917614\pi$
$564$	−1.21735e14	+	8.48304e13i	−2.13314	+	1.48647i
$565$		0			0
$566$	1.78307e13	+	5.67751e13i	0.306962	+	0.977408i
$567$		−	4.08147e13i		−	0.696468i
$568$	2.93178e13	+	2.26546e13i	0.495895	+	0.383190i
$569$	1.61498e13			0.270774			0.135387	−	0.990793i	$-0.456772\pi$
$569$	1.61498e13			0.270774			0.135387	+	0.990793i	$0.456772\pi$
$570$		0			0
$571$			4.58480e13i			0.755335i	0.925941	+	0.377667i	$0.123274\pi$
$571$			4.58480e13i			0.755335i	−0.925941	+	0.377667i	$0.876726\pi$
$572$	3.55617e13	+	5.10323e13i	0.580768	+	0.833422i
$573$	−2.60985e13			−0.422516
$574$	−3.16443e12	−	1.00760e13i	−0.0507851	−	0.161706i
$575$		0			0
$576$	1.20853e13	+	4.63571e13i	0.190610	+	0.731146i
$577$	4.20889e12			0.0658095			0.0329048	−	0.999458i	$-0.489524\pi$
$577$	4.20889e12			0.0658095			0.0329048	+	0.999458i	$0.489524\pi$
$578$	1.62441e13	−	5.10157e12i	0.251800	−	0.0790797i
$579$		−	1.32835e14i		−	2.04135i
$580$		0			0
$581$	5.46263e13			0.825128
$582$	−1.01841e13	−	3.24273e13i	−0.152513	−	0.485620i
$583$			2.67037e13i			0.396487i
$584$	2.48188e13	−	3.21186e13i	0.365356	−	0.472816i
$585$		0			0
$586$	2.58652e12	−	8.12317e11i	0.0374307	−	0.0117554i
$587$			1.56343e13i			0.224331i	0.993690	+	0.112165i	$0.0357787\pi$
$587$			1.56343e13i			0.224331i	−0.993690	+	0.112165i	$0.964221\pi$
$588$	3.48428e13	+	5.00006e13i	0.495708	+	0.711359i
$589$	5.71324e13			0.805946
$590$		0			0
$591$		−	4.87494e13i		−	0.676133i
$592$	−3.95916e13	+	1.07267e14i	−0.544496	+	1.47522i
$593$	−5.47586e13			−0.746757			−0.373378	−	0.927679i	$-0.621801\pi$
$593$	−5.47586e13			−0.746757			−0.373378	+	0.927679i	$0.621801\pi$
$594$	1.64988e13	−	5.18157e12i	0.223110	−	0.0700695i
$595$		0			0
$596$	−1.93808e13	+	1.35054e13i	−0.257715	+	0.179588i
$597$	−1.23637e14			−1.63034
$598$	−3.44223e13	−	1.09605e14i	−0.450126	−	1.43326i
$599$			7.28349e13i			0.944507i	0.881463	+	0.472254i	$0.156559\pi$
$599$			7.28349e13i			0.944507i	−0.881463	+	0.472254i	$0.843441\pi$
$600$		0			0
$601$	−1.08097e14			−1.37861			−0.689303	−	0.724474i	$-0.742083\pi$
$601$	−1.08097e14			−1.37861			−0.689303	+	0.724474i	$0.742083\pi$
$602$	−2.39112e13	+	7.50950e12i	−0.302426	+	0.0949792i
$603$		−	2.34390e13i		−	0.294003i
$604$	−4.77338e12	−	6.84997e12i	−0.0593801	−	0.0852126i
$605$		0			0
$606$	4.21494e13	+	1.34209e14i	0.515737	+	1.64217i
$607$		−	1.24452e14i		−	1.51028i	−0.655561	−	0.755142i	$-0.727568\pi$
$607$		−	1.24452e14i		−	1.51028i	0.655561	−	0.755142i	$-0.272432\pi$
$608$	4.80653e13	+	2.37058e12i	0.578514	+	0.0285323i
$609$	−9.10144e13			−1.08649
$610$		0			0
$611$			2.35058e14i			2.76038i
$612$	4.56615e13	−	3.18191e13i	0.531855	−	0.370621i
$613$	1.02467e14			1.18381			0.591903	−	0.806009i	$-0.298377\pi$
$613$	1.02467e14			1.18381			0.591903	+	0.806009i	$0.298377\pi$
$614$	−1.16024e13	−	3.69435e13i	−0.132955	−	0.423347i
$615$		0			0
$616$	2.30233e13	−	2.97950e13i	0.259576	−	0.335923i
$617$	1.44047e13			0.161094			0.0805470	−	0.996751i	$-0.474333\pi$
$617$	1.44047e13			0.161094			0.0805470	+	0.996751i	$0.474333\pi$
$618$	−7.46809e13	+	2.34541e13i	−0.828452	+	0.260182i
$619$		−	1.46669e14i		−	1.61393i	−0.590596	−	0.806967i	$-0.701107\pi$
$619$		−	1.46669e14i		−	1.61393i	0.590596	−	0.806967i	$-0.298893\pi$
$620$		0			0
$621$	−3.19403e13			−0.345845
$622$	−2.83904e11	−	9.03986e11i	−0.00304943	−	0.00970979i
$623$		−	3.73097e12i		−	0.0397540i
$624$	1.65429e14	+	6.10588e13i	1.74859	+	0.645395i
$625$		0			0
$626$	7.26489e13	−	2.28159e13i	0.755713	−	0.237338i
$627$			5.37026e13i			0.554188i
$628$	−1.39720e14	+	9.73631e13i	−1.43040	+	0.996773i
$629$	1.32833e14			1.34912
$630$		0			0
$631$			1.47209e13i			0.147159i	0.997289	+	0.0735797i	$0.0234423\pi$
$631$			1.47209e13i			0.147159i	−0.997289	+	0.0735797i	$0.976558\pi$
$632$	4.46833e13	+	3.45278e13i	0.443159	+	0.342440i
$633$	1.26623e14			1.24593
$634$	−1.37416e14	+	4.31564e13i	−1.34150	+	0.421307i
$635$		0			0
$636$	4.32820e13	+	6.21112e13i	0.415931	+	0.596877i
$637$	9.65463e13			0.920531
$638$	−3.19009e13	−	1.01577e14i	−0.301787	−	0.960928i
$639$			5.04479e13i			0.473520i
$640$		0			0
$641$	1.33596e14			1.23454			0.617269	−	0.786752i	$-0.288239\pi$
$641$	1.33596e14			1.23454			0.617269	+	0.786752i	$0.288239\pi$
$642$	−2.66855e14	+	8.38079e13i	−2.44681	+	0.768440i
$643$			1.78623e14i			1.62511i	0.582885	+	0.812555i	$0.301924\pi$
$643$			1.78623e14i			1.62511i	−0.582885	+	0.812555i	$0.698076\pi$
$644$	−5.70586e13	+	3.97611e13i	−0.515100	+	0.358946i
$645$		0			0
$646$	−1.67513e13	−	5.33383e13i	−0.148897	−	0.474107i
$647$		−	7.75013e11i		−	0.00683578i	−0.999994	−	0.00341789i	$-0.998912\pi$
$647$		−	7.75013e11i		−	0.00683578i	0.999994	−	0.00341789i	$-0.00108795\pi$
$648$	8.27624e13	−	1.07105e14i	0.724366	−	0.937419i
$649$	−1.52571e14			−1.32510
$650$		0			0
$651$		−	1.26731e14i		−	1.08387i
$652$	−4.34393e12	−	6.23370e12i	−0.0368676	−	0.0529064i
$653$	−1.63485e14			−1.37693			−0.688463	−	0.725271i	$-0.741714\pi$
$653$	−1.63485e14			−1.37693			−0.688463	+	0.725271i	$0.741714\pi$
$654$	−4.16206e13	−	1.32525e14i	−0.347872	−	1.10767i
$655$		0			0
$656$	1.21276e13	−	3.28578e13i	0.0998289	−	0.270470i
$657$	5.52673e13			0.451483
$658$	1.35757e14	−	4.26356e13i	1.10061	−	0.345655i
$659$			8.74538e13i			0.703642i	0.936067	+	0.351821i	$0.114437\pi$
$659$			8.74538e13i			0.703642i	−0.936067	+	0.351821i	$0.885563\pi$
$660$		0			0
$661$	8.72541e13			0.691478			0.345739	−	0.938331i	$-0.387628\pi$
$661$	8.72541e13			0.691478			0.345739	+	0.938331i	$0.387628\pi$
$662$	−4.75874e13	−	1.51524e14i	−0.374284	−	1.19177i
$663$		−	2.04856e14i		−	1.59912i
$664$	1.43349e14	+	1.10769e14i	1.11059	+	0.858179i
$665$		0			0
$666$	−1.48531e14	+	4.66474e13i	−1.13357	+	0.356005i
$667$			1.96644e14i			1.48954i
$668$	4.73463e13	+	6.79437e13i	0.355962	+	0.510819i
$669$	−1.58467e14			−1.18252
$670$		0			0
$671$		−	9.50836e13i		−	0.699025i
$672$	5.25839e12	−	1.06618e14i	0.0383713	−	0.778009i
$673$	1.83493e14			1.32906			0.664531	−	0.747261i	$-0.268631\pi$
$673$	1.83493e14			1.32906			0.664531	+	0.747261i	$0.268631\pi$
$674$	1.23903e14	−	3.89126e13i	0.890803	−	0.279764i
$675$		0			0
$676$	1.13374e14	−	7.90046e13i	0.803122	−	0.559653i
$677$	2.25381e14			1.58480			0.792400	−	0.610002i	$-0.208831\pi$
$677$	2.25381e14			1.58480			0.792400	+	0.610002i	$0.208831\pi$
$678$	4.68046e13	+	1.49032e14i	0.326693	+	1.04023i
$679$			3.25958e13i			0.225846i
$680$		0			0
$681$	−4.60630e13			−0.314497
$682$	1.41438e14	−	4.44196e13i	0.958613	−	0.301060i
$683$			6.01818e13i			0.404913i	0.979291	+	0.202456i	$0.0648924\pi$
$683$			6.01818e13i			0.404913i	−0.979291	+	0.202456i	$0.935108\pi$
$684$	3.74621e13	+	5.37594e13i	0.250214	+	0.359066i
$685$		0			0
$686$	−4.42730e13	−	1.40971e14i	−0.291420	−	0.927918i
$687$			5.25377e13i			0.343311i
$688$	−7.79746e13	−	2.87800e13i	−0.505838	−	0.186702i
$689$	1.19931e14			0.772386
$690$		0			0
$691$		−	2.08918e13i		−	0.132613i	−0.997799	−	0.0663063i	$-0.978879\pi$
$691$		−	2.08918e13i		−	0.132613i	0.997799	−	0.0663063i	$-0.0211214\pi$
$692$	1.43168e14	−	9.97664e13i	0.902228	−	0.628715i
$693$	5.12690e13			0.320766
$694$	−6.85653e13	−	2.18321e14i	−0.425899	−	1.35612i
$695$		0			0
$696$	−2.38838e14	−	1.84555e14i	−1.46237	−	1.13001i
$697$	−4.06890e13			−0.247351
$698$	1.16540e14	−	3.66004e13i	0.703395	−	0.220906i
$699$			8.19484e13i			0.491083i
$700$		0			0
$701$	1.20064e14			0.709291			0.354645	−	0.935001i	$-0.384602\pi$
$701$	1.20064e14			0.709291			0.354645	+	0.935001i	$0.384602\pi$
$702$	−2.32713e13	−	7.40987e13i	−0.136500	−	0.434635i
$703$			1.56390e14i			0.910819i
$704$	1.20834e14	−	3.15014e13i	0.698758	−	0.182166i
$705$		0			0
$706$	−1.56542e14	+	4.91632e13i	−0.892498	+	0.280296i
$707$		−	1.34906e14i		−	0.763722i
$708$	−3.54871e14	+	2.47291e14i	−1.99482	+	1.39009i
$709$	−1.88963e14			−1.05474			−0.527371	−	0.849635i	$-0.676822\pi$
$709$	−1.88963e14			−1.05474			−0.527371	+	0.849635i	$0.676822\pi$
$710$		0			0
$711$			7.68877e13i			0.423164i
$712$	7.56550e12	−	9.79069e12i	0.0413464	−	0.0535074i
$713$	−2.73812e14			−1.48595
$714$	−1.18314e14	+	3.71575e13i	−0.637597	+	0.200242i
$715$		0			0
$716$	−2.39555e13	−	3.43770e13i	−0.127303	−	0.182685i
$717$	−1.08019e14			−0.570040
$718$	1.98127e13	+	6.30863e13i	0.103830	+	0.330608i
$719$			1.51449e14i			0.788174i	0.919073	+	0.394087i	$0.128939\pi$
$719$			1.51449e14i			0.788174i	−0.919073	+	0.394087i	$0.871061\pi$
$720$		0			0
$721$	7.50689e13			0.385286
$722$	−1.24383e14	+	3.90633e13i	−0.633977	+	0.199105i
$723$		−	4.15862e14i		−	2.10503i
$724$	6.05580e13	−	4.21997e13i	0.304424	−	0.212137i
$725$		0			0
$726$	−3.83184e13	−	1.22011e14i	−0.189987	−	0.604943i
$727$			1.11161e14i			0.547371i	0.961819	+	0.273686i	$0.0882428\pi$
$727$			1.11161e14i			0.547371i	−0.961819	+	0.273686i	$0.911757\pi$
$728$	−1.33814e14	−	1.03401e14i	−0.654403	−	0.505673i
$729$	9.59514e13			0.466030
$730$		0			0
$731$			9.65588e13i			0.462600i
$732$	−1.54114e14	−	2.21158e14i	−0.733306	−	1.05232i
$733$	−5.92775e13			−0.280137			−0.140068	−	0.990142i	$-0.544732\pi$
$733$	−5.92775e13			−0.280137			−0.140068	+	0.990142i	$0.544732\pi$
$734$	1.13558e14	+	3.61583e14i	0.533012	+	1.69718i
$735$		0			0
$736$	−2.30357e14	−	1.13612e13i	−1.06663	−	0.0526060i
$737$	−6.10959e13			−0.280979
$738$	4.54978e13	−	1.42889e13i	0.207830	−	0.0652706i
$739$			1.37698e14i			0.624748i	0.949959	+	0.312374i	$0.101124\pi$
$739$			1.37698e14i			0.624748i	−0.949959	+	0.312374i	$0.898876\pi$
$740$		0			0
$741$	2.41187e14			1.07960
$742$	−2.17534e13	−	6.92657e13i	−0.0967182	−	0.307963i
$743$		−	1.17414e14i		−	0.518533i	−0.965806	−	0.259266i	$-0.916519\pi$
$743$		−	1.17414e14i		−	0.518533i	0.965806	−	0.259266i	$-0.0834808\pi$
$744$	2.56979e14	−	3.32563e14i	1.12728	−	1.45884i
$745$		0			0
$746$	−3.53006e14	+	1.10864e14i	−1.52787	+	0.479841i
$747$			2.46664e14i			1.06048i
$748$	−8.29394e13	−	1.19021e14i	−0.354204	−	0.508295i
$749$	2.68242e14			1.13793
$750$		0			0
$751$			1.17502e14i			0.491864i	0.969287	+	0.245932i	$0.0790940\pi$
$751$			1.17502e14i			0.491864i	−0.969287	+	0.245932i	$0.920906\pi$
$752$	4.42705e14	+	1.63400e14i	1.84088	+	0.679458i
$753$	−1.26008e14			−0.520501
$754$	−4.56197e14	+	1.43272e14i	−1.87196	+	0.587903i
$755$		0			0
$756$	−3.85745e13	+	2.68805e13i	−0.156204	+	0.108850i
$757$	3.51706e14			1.41482			0.707409	−	0.706805i	$-0.249864\pi$
$757$	3.51706e14			1.41482			0.707409	+	0.706805i	$0.249864\pi$
$758$	−3.16728e13	−	1.00850e14i	−0.126573	−	0.403024i
$759$		−	2.57374e14i		−	1.02178i
$760$		0			0
$761$	−1.95381e14			−0.765525			−0.382763	−	0.923847i	$-0.625027\pi$
$761$	−1.95381e14			−0.765525			−0.382763	+	0.923847i	$0.625027\pi$
$762$	−4.78970e14	+	1.50424e14i	−1.86438	+	0.585521i
$763$			1.33214e14i			0.515142i
$764$	4.74555e13	+	6.81003e13i	0.182314	+	0.261627i
$765$		0			0
$766$	4.97297e12	+	1.58346e13i	0.0188570	+	0.0600430i
$767$			6.85221e14i			2.58139i
$768$	2.29995e14	−	2.69121e14i	0.860819	−	1.00726i
$769$	8.91848e13			0.331634			0.165817	−	0.986157i	$-0.446974\pi$
$769$	8.91848e13			0.331634			0.165817	+	0.986157i	$0.446974\pi$
$770$		0			0
$771$		−	1.10394e14i		−	0.405204i
$772$	−3.46612e14	+	2.41536e14i	−1.26403	+	0.880835i
$773$	9.96400e13			0.361024			0.180512	−	0.983573i	$-0.442225\pi$
$773$	9.96400e13			0.361024			0.180512	+	0.983573i	$0.442225\pi$
$774$	−3.39090e13	−	1.07971e14i	−0.122070	−	0.388688i
$775$		0			0
$776$	−6.60965e13	+	8.55370e13i	−0.234893	+	0.303980i
$777$	3.46903e14			1.22490
$778$	−1.09461e14	+	3.43770e13i	−0.384026	+	0.120606i
$779$		−	4.79050e13i		−	0.166991i
$780$		0			0
$781$	1.31497e14			0.452544
$782$	8.02820e13	+	2.55628e14i	0.274527	+	0.874129i
$783$			1.32942e14i			0.451703i
$784$	6.71140e13	−	1.81834e14i	0.226586	−	0.613896i
$785$		0			0
$786$	−9.82231e12	+	3.08477e12i	−0.0327417	+	0.0102828i
$787$		−	4.33579e14i		−	1.43613i	−0.695975	−	0.718066i	$-0.745027\pi$
$787$		−	4.33579e14i		−	1.43613i	0.695975	−	0.718066i	$-0.254973\pi$
$788$	−1.27204e14	+	8.86420e13i	−0.418669	+	0.291748i
$789$	−5.39113e14			−1.76317
$790$		0			0
$791$		−	1.49806e14i		−	0.483780i
$792$	1.34539e14	+	1.03961e14i	0.431739	+	0.333615i
$793$	−4.27035e14			−1.36175
$794$	1.57650e13	−	4.95111e12i	0.0499564	−	0.0156892i
$795$		0			0
$796$	2.24812e14	+	3.22613e14i	0.703483	+	1.00952i
$797$	2.10616e14			0.654939			0.327469	−	0.944862i	$-0.393804\pi$
$797$	2.10616e14			0.654939			0.327469	+	0.944862i	$0.393804\pi$
$798$	−4.37473e13	−	1.39297e14i	−0.135188	−	0.430455i
$799$		−	5.48217e14i		−	1.68352i
$800$		0			0
$801$	1.68471e13			0.0510931
$802$	−2.65375e14	+	8.33431e13i	−0.799813	+	0.251187i
$803$		−	1.44059e14i		−	0.431483i
$804$	−1.42105e14	+	9.90255e13i	−0.422990	+	0.294759i
$805$		0			0
$806$	−1.99495e14	−	6.35219e14i	−0.586486	−	1.86745i
$807$		−	8.65350e14i		−	2.52828i
$808$	2.73558e14	−	3.54017e14i	0.794313	−	1.02794i
$809$	−5.03919e14			−1.45418			−0.727090	−	0.686542i	$-0.759128\pi$
$809$	−5.03919e14			−1.45418			−0.727090	+	0.686542i	$0.759128\pi$
$810$		0			0
$811$			2.98074e14i			0.849610i	0.905285	+	0.424805i	$0.139657\pi$
$811$			2.98074e14i			0.849610i	−0.905285	+	0.424805i	$0.860343\pi$
$812$	1.65493e14	+	2.37489e14i	0.468813	+	0.672764i
$813$	6.18704e14			1.74193
$814$	1.21591e14	+	3.87161e14i	0.340235	+	1.08335i
$815$		0			0
$816$	−3.85824e14	−	1.42405e14i	−1.06644	−	0.393619i
$817$	−1.13683e14			−0.312310
$818$	−5.71703e14	+	1.79548e14i	−1.56100	+	0.490245i
$819$		−	2.30257e14i		−	0.624876i
$820$		0			0
$821$	−1.54116e14			−0.413174			−0.206587	−	0.978428i	$-0.566236\pi$
$821$	−1.54116e14			−0.413174			−0.206587	+	0.978428i	$0.566236\pi$
$822$	−1.32785e14	−	4.22803e14i	−0.353825	−	1.12662i
$823$		−	5.40009e13i		−	0.143022i	−0.997440	−	0.0715108i	$-0.977218\pi$
$823$		−	5.40009e13i		−	0.143022i	0.997440	−	0.0715108i	$-0.0227820\pi$
$824$	1.96994e14	+	1.52222e14i	0.518580	+	0.400720i
$825$		0			0
$826$	3.95748e14	−	1.24288e14i	1.02925	−	0.323242i
$827$		−	3.42473e14i		−	0.885316i	−0.896691	−	0.442658i	$-0.854036\pi$
$827$		−	3.42473e14i		−	0.885316i	0.896691	−	0.442658i	$-0.145964\pi$
$828$	−1.79540e14	−	2.57647e14i	−0.461328	−	0.662023i
$829$	−1.54734e14			−0.395195			−0.197598	−	0.980283i	$-0.563314\pi$
$829$	−1.54734e14			−0.395195			−0.197598	+	0.980283i	$0.563314\pi$
$830$		0			0
$831$			2.79972e14i			0.706496i
$832$	−1.41478e14	−	5.42686e14i	−0.354873	−	1.36123i
$833$	−2.25172e14			−0.561421
$834$	1.95215e14	−	6.13086e13i	0.483818	−	0.151947i
$835$		0			0
$836$	1.40129e14	−	9.76484e13i	0.343160	−	0.239130i
$837$	−1.85111e14			−0.450614
$838$	1.75662e14	+	5.59331e14i	0.425067	+	1.35347i
$839$		−	2.50962e14i		−	0.603668i	−0.953360	−	0.301834i	$-0.902401\pi$
$839$		−	2.50962e14i		−	0.603668i	0.953360	−	0.301834i	$-0.0975989\pi$
$840$		0			0
$841$	3.97765e14			0.945467
$842$	−1.94376e14	+	6.10452e13i	−0.459284	+	0.144242i
$843$			5.80161e14i			1.36273i
$844$	−2.30242e14	−	3.30405e14i	−0.537615	−	0.771497i
$845$		0			0
$846$	1.92520e14	+	6.13008e14i	0.444246	+	1.41454i
$847$			1.22645e14i			0.281340i
$848$	8.33696e13	−	2.25876e14i	0.190120	−	0.515099i
$849$	5.98758e14			1.35742
$850$		0			0
$851$		−	7.49512e14i		−	1.67931i
$852$	3.05854e14	−	2.13133e14i	0.681265	−	0.474738i
$853$	2.39173e14			0.529623			0.264812	−	0.964300i	$-0.414690\pi$
$853$	2.39173e14			0.529623			0.264812	+	0.964300i	$0.414690\pi$
$854$	7.74571e13	+	2.46633e14i	0.170519	+	0.542954i
$855$		0			0
$856$	7.03912e14	+	5.43930e14i	1.53161	+	1.18352i
$857$	6.21909e14			1.34531			0.672656	−	0.739956i	$-0.265154\pi$
$857$	6.21909e14			1.34531			0.672656	+	0.739956i	$0.265154\pi$
$858$	5.97085e14	−	1.87519e14i	1.28410	−	0.403283i
$859$			3.04870e14i			0.651853i	0.945395	+	0.325926i	$0.105676\pi$
$859$			3.04870e14i			0.651853i	−0.945395	+	0.325926i	$0.894324\pi$
$860$		0			0
$861$	−1.06262e14			−0.224576
$862$	2.09773e13	+	6.67943e13i	0.0440770	+	0.140347i
$863$			6.53448e13i			0.136508i	0.997668	+	0.0682538i	$0.0217428\pi$
$863$			6.53448e13i			0.136508i	−0.997668	+	0.0682538i	$0.978257\pi$
$864$	−1.55733e14	−	7.68076e12i	−0.323454	−	0.0159528i
$865$		0			0
$866$	5.14572e14	−	1.61605e14i	1.05647	−	0.331792i
$867$		−	1.71312e14i		−	0.349698i
$868$	−3.30684e14	+	2.30436e14i	−0.671143	+	0.467684i
$869$	2.00415e14			0.404419
$870$		0			0
$871$			2.74391e14i			0.547368i
$872$	−2.70126e14	+	3.49576e14i	−0.535776	+	0.693361i
$873$	−1.47186e14			−0.290265
$874$	−3.00963e14	+	9.45197e13i	−0.590141	+	0.185338i
$875$		0			0
$876$	−2.33495e14	−	3.35073e14i	−0.452643	−	0.649560i
$877$	−6.16479e14			−1.18829			−0.594143	−	0.804360i	$-0.702508\pi$
$877$	−6.16479e14			−1.18829			−0.594143	+	0.804360i	$0.702508\pi$
$878$	1.89548e13	+	6.03545e13i	0.0363284	+	0.115674i
$879$		−	2.72778e13i		−	0.0519835i
$880$		0			0
$881$	4.73843e14			0.892801			0.446401	−	0.894833i	$-0.352706\pi$
$881$	4.73843e14			0.892801			0.446401	+	0.894833i	$0.352706\pi$
$882$	2.51784e14	−	7.90746e13i	0.471720	−	0.148147i
$883$		−	1.26271e14i		−	0.235234i	−0.993059	−	0.117617i	$-0.962475\pi$
$883$		−	1.26271e14i		−	0.235234i	0.993059	−	0.117617i	$-0.0375255\pi$
$884$	−5.34542e14	+	3.72494e14i	−0.990195	+	0.690014i
$885$		0			0
$886$	7.72189e13	+	2.45875e14i	0.141434	+	0.450345i
$887$			4.38556e14i			0.798743i	0.916789	+	0.399372i	$0.130772\pi$
$887$			4.38556e14i			0.798743i	−0.916789	+	0.399372i	$0.869228\pi$
$888$	9.10332e14	+	7.03435e14i	1.64867	+	1.27397i
$889$	4.81458e14			0.867062
$890$		0			0
$891$		−	4.80390e14i		−	0.855470i
$892$	2.88143e14	+	4.13496e14i	0.510251	+	0.732228i
$893$	6.45442e14			1.13658
$894$	7.12150e13	+	2.26758e14i	0.124705	+	0.397077i
$895$		0			0
$896$	−2.87765e14	+	1.80145e14i	−0.498309	+	0.311947i
$897$	−1.15591e15			−1.99050
$898$	2.72117e14	−	8.54605e13i	0.465988	−	0.146347i
$899$			1.13966e15i			1.94078i
$900$		0			0
$901$	−2.79710e14			−0.471069
$902$	−3.72454e13	−	1.18594e14i	−0.0623793	−	0.198624i
$903$			2.52171e14i			0.420007i
$904$	3.03771e14	−	3.93117e14i	0.503158	−	0.651148i
$905$		0			0
$906$	−8.01456e13	+	2.51703e13i	−0.131292	+	0.0412333i
$907$		−	3.95261e13i		−	0.0643943i	−0.999482	−	0.0321972i	$-0.989750\pi$
$907$		−	3.95261e13i		−	0.0643943i	0.999482	−	0.0321972i	$-0.0102504\pi$
$908$	8.37573e13	+	1.20195e14i	0.135704	+	0.194740i
$909$	6.09166e14			0.981559
$910$		0			0
$911$			7.25957e14i			1.15696i	0.815696	+	0.578481i	$0.196354\pi$
$911$			7.25957e14i			1.15696i	−0.815696	+	0.578481i	$0.803646\pi$
$912$	1.67661e14	−	4.54248e14i	0.265740	−	0.719978i
$913$	6.42953e14			1.01350
$914$	4.54133e14	−	1.42624e14i	0.711954	−	0.223594i
$915$		0			0
$916$	1.37089e14	−	9.55302e13i	0.212582	−	0.148137i
$917$	9.87334e12			0.0152271
$918$	5.42748e13	+	1.72818e14i	0.0832501	+	0.265079i
$919$			1.05122e15i			1.60367i	0.597545	+	0.801836i	$0.296143\pi$
$919$			1.05122e15i			1.60367i	−0.597545	+	0.801836i	$0.703857\pi$
$920$		0			0
$921$	−3.89611e14			−0.587940
$922$	4.12327e14	−	1.29495e14i	0.618853	−	0.194356i
$923$		−	5.90574e14i		−	0.881589i
$924$	−2.16603e14	−	3.10833e14i	−0.321591	−	0.461495i
$925$		0			0
$926$	1.51413e14	+	4.82119e14i	0.222386	+	0.708107i
$927$			3.38972e14i			0.495182i
$928$	−4.72875e13	+	9.58792e14i	−0.0687079	+	1.39311i
$929$	2.69891e14			0.390040			0.195020	−	0.980799i	$-0.437523\pi$
$929$	2.69891e14			0.390040			0.195020	+	0.980799i	$0.437523\pi$
$930$		0			0
$931$		−	2.65105e14i		−	0.379027i
$932$	2.13832e14	−	1.49008e14i	0.304084	−	0.211900i
$933$	−9.53356e12			−0.0134849
$934$	−4.16970e14	−	1.32769e15i	−0.586639	−	1.86793i
$935$		0			0
$936$	4.66907e14	−	6.04235e14i	0.649907	−	0.841059i
$937$	−9.48225e14			−1.31284			−0.656422	−	0.754394i	$-0.727931\pi$
$937$	−9.48225e14			−1.31284			−0.656422	+	0.754394i	$0.727931\pi$
$938$	1.58474e14	−	4.97700e13i	0.218245	−	0.0685415i
$939$		−	7.66164e14i		−	1.04953i
$940$		0			0
$941$	−9.63938e14			−1.30648			−0.653238	−	0.757153i	$-0.726590\pi$
$941$	−9.63938e14			−1.30648			−0.653238	+	0.757153i	$0.726590\pi$
$942$	5.13402e14	+	1.63474e15i	0.692155	+	2.20391i
$943$			2.29589e14i			0.307888i
$944$	1.29054e15	+	4.76330e14i	1.72151	+	0.635401i
$945$		0			0
$946$	−2.81436e14	+	8.83870e13i	−0.371470	+	0.116663i
$947$			5.67490e14i			0.745089i	0.928014	+	0.372545i	$0.121515\pi$
$947$			5.67490e14i			0.745089i	−0.928014	+	0.372545i	$0.878485\pi$
$948$	4.66153e14	−	3.24837e14i	0.608817	−	0.424252i
$949$	−6.46993e14			−0.840560
$950$		0			0
$951$			1.44920e15i			1.86306i
$952$	3.12090e14	+	2.41160e14i	0.399113	+	0.308404i
$953$	−8.56825e14			−1.09000			−0.545002	−	0.838435i	$-0.683471\pi$
$953$	−8.56825e14			−1.09000			−0.545002	+	0.838435i	$0.683471\pi$
$954$	3.12768e14	−	9.82272e13i	0.395804	−	0.124305i
$955$		0			0
$956$	1.96413e14	+	2.81860e14i	0.245970	+	0.352975i
$957$	−1.07124e15			−1.33453
$958$	4.33500e13	+	1.38032e14i	0.0537232	+	0.171061i
$959$			4.25000e14i			0.523957i
$960$		0			0
$961$	−7.67257e14			−0.936103
$962$	1.73880e15	−	5.46084e14i	2.11045	−	0.662802i
$963$			1.21124e15i			1.46251i
$964$	−1.08513e15	+	7.56169e14i	−1.30346	+	0.908309i
$965$		0			0
$966$	2.09663e14	+	6.67593e14i	0.249250	+	0.793645i
$967$			1.02528e15i			1.21258i	0.795243	+	0.606290i	$0.207343\pi$
$967$			1.02528e15i			1.21258i	−0.795243	+	0.606290i	$0.792657\pi$
$968$	−2.48694e14	+	3.21840e14i	−0.292609	+	0.378672i
$969$	−5.62512e14			−0.658435
$970$		0			0
$971$		−	9.33882e14i		−	1.08192i	−0.841048	−	0.540961i	$-0.818061\pi$
$971$		−	9.33882e14i		−	1.08192i	0.841048	−	0.540961i	$-0.181939\pi$
$972$	−6.17984e14	−	8.86830e14i	−0.712272	−	1.02214i
$973$	−1.96229e14			−0.225008
$974$	−1.37931e14	−	4.39189e14i	−0.157350	−	0.501022i
$975$		0			0
$976$	−2.96853e14	+	8.04273e14i	−0.335191	+	0.908143i
$977$	7.61153e14			0.855065			0.427532	−	0.904000i	$-0.359383\pi$
$977$	7.61153e14			0.855065			0.427532	+	0.904000i	$0.359383\pi$
$978$	−7.29352e13	+	2.29058e13i	−0.0815160	+	0.0256007i
$979$		−	4.39135e13i		−	0.0488298i
$980$		0			0
$981$	−6.01524e14			−0.662077
$982$	−4.88648e14	−	1.55592e15i	−0.535105	−	1.70384i
$983$		−	1.84790e14i		−	0.201331i	−0.994920	−	0.100665i	$-0.967903\pi$
$983$		−	1.84790e14i		−	0.201331i	0.994920	−	0.100665i	$-0.0320971\pi$
$984$	−2.78851e14	−	2.15475e14i	−0.302271	−	0.233572i
$985$		0			0
$986$	1.06397e15	−	3.34149e14i	1.14169	−	0.358555i
$987$		−	1.43171e15i		−	1.52852i
$988$	−4.38555e14	−	6.29341e14i	−0.465842	−	0.668500i
$989$	5.44837e14			0.575818
$990$		0			0
$991$		−	2.82161e14i		−	0.295208i	−0.989047	−	0.147604i	$-0.952844\pi$
$991$		−	2.82161e14i		−	0.295208i	0.989047	−	0.147604i	$-0.0471562\pi$
$992$	−1.33504e15	−	6.58442e13i	−1.38975	−	0.0685424i
$993$	−1.59800e15			−1.65512
$994$	−3.41085e14	+	1.07120e14i	−0.351504	+	0.110393i
$995$		0			0
$996$	1.49547e15	−	1.04211e15i	1.52574	−	1.06321i
$997$	−6.39034e14			−0.648707			−0.324353	−	0.945936i	$-0.605147\pi$
$997$	−6.39034e14			−0.648707			−0.324353	+	0.945936i	$0.605147\pi$
$998$	−4.21446e14	−	1.34194e15i	−0.425686	−	1.35544i
$999$		−	5.06709e14i		−	0.509250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.e.51.4		20
4.3	odd	2	inner	100.11.b.e.51.3		20
5.2	odd	4		100.11.d.c.99.15		40
5.3	odd	4		100.11.d.c.99.26		40
5.4	even	2		20.11.b.a.11.17	✓	20
15.14	odd	2		180.11.c.a.91.4		20
20.3	even	4		100.11.d.c.99.16		40
20.7	even	4		100.11.d.c.99.25		40
20.19	odd	2		20.11.b.a.11.18	yes	20
40.19	odd	2		320.11.b.d.191.4		20
40.29	even	2		320.11.b.d.191.17		20
60.59	even	2		180.11.c.a.91.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.17	✓	20	5.4	even	2
20.11.b.a.11.18	yes	20	20.19	odd	2
100.11.b.e.51.3		20	4.3	odd	2	inner
100.11.b.e.51.4		20	1.1	even	1	trivial
100.11.d.c.99.15		40	5.2	odd	4
100.11.d.c.99.16		40	20.3	even	4
100.11.d.c.99.25		40	20.7	even	4
100.11.d.c.99.26		40	5.3	odd	4
180.11.c.a.91.3		20	60.59	even	2
180.11.c.a.91.4		20	15.14	odd	2
320.11.b.d.191.4		20	40.19	odd	2
320.11.b.d.191.17		20	40.29	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-30.5298 + 9.58811i) q^{2} +321.971i q^{3} +(840.136 - 585.446i) q^{4} +(-3087.10 - 9829.71i) q^{6} +9880.78i q^{7} +(-20035.9 + 25928.9i) q^{8} -44616.5 q^{9} +O(q^{10})\)	\(q+(-30.5298 + 9.58811i) q^{2} +321.971i q^{3} +(840.136 - 585.446i) q^{4} +(-3087.10 - 9829.71i) q^{6} +9880.78i q^{7} +(-20035.9 + 25928.9i) q^{8} -44616.5 q^{9} +116297. i q^{11} +(188497. + 270500. i) q^{12} +522308. q^{13} +(-94738.1 - 301658. i) q^{14} +(363082. - 983709. i) q^{16} -1.21816e6 q^{17} +(1.36213e6 - 427788. i) q^{18} -1.43420e6i q^{19} -3.18133e6 q^{21} +(-1.11507e6 - 3.55052e6i) q^{22} +6.87353e6i q^{23} +(-8.34835e6 - 6.45097e6i) q^{24} +(-1.59460e7 + 5.00795e6i) q^{26} +4.64686e6i q^{27} +(5.78467e6 + 8.30120e6i) q^{28} +2.86090e7 q^{29} +3.98357e7i q^{31} +(-1.65289e6 + 3.35137e7i) q^{32} -3.74443e7 q^{33} +(3.71903e7 - 1.16799e7i) q^{34} +(-3.74839e7 + 2.61205e7i) q^{36} -1.09043e8 q^{37} +(1.37513e7 + 4.37858e7i) q^{38} +1.68168e8i q^{39} +3.34019e7 q^{41} +(9.71253e7 - 3.05029e7i) q^{42} -7.92659e7i q^{43} +(6.80856e7 + 9.77053e7i) q^{44} +(-6.59042e7 - 2.09847e8i) q^{46} +4.50036e8i q^{47} +(3.16726e8 + 1.16902e8i) q^{48} +1.84845e8 q^{49} -3.92213e8i q^{51} +(4.38810e8 - 3.05783e8i) q^{52} +2.29617e8 q^{53} +(-4.45546e7 - 1.41868e8i) q^{54} +(-2.56198e8 - 1.97970e8i) q^{56} +4.61771e8 q^{57} +(-8.73425e8 + 2.74306e8i) q^{58} +1.31191e9i q^{59} -8.17592e8 q^{61} +(-3.81949e8 - 1.21618e9i) q^{62} -4.40846e8i q^{63} +(-2.70871e8 - 1.03901e9i) q^{64} +(1.14317e9 - 3.59020e8i) q^{66} +5.25343e8i q^{67} +(-1.02342e9 + 7.13169e8i) q^{68} -2.21308e9 q^{69} -1.13070e9i q^{71} +(8.93929e8 - 1.15685e9i) q^{72} -1.23872e9 q^{73} +(3.32907e9 - 1.04552e9i) q^{74} +(-8.39647e8 - 1.20492e9i) q^{76} -1.14911e9 q^{77} +(-1.61242e9 - 5.13414e9i) q^{78} -1.72330e9i q^{79} -4.13071e9 q^{81} +(-1.01975e9 + 3.20261e8i) q^{82} -5.52854e9i q^{83} +(-2.67275e9 + 1.86250e9i) q^{84} +(7.60011e8 + 2.41997e9i) q^{86} +9.21126e9i q^{87} +(-3.01545e9 - 2.33011e9i) q^{88} -3.77598e8 q^{89} +5.16082e9i q^{91} +(4.02408e9 + 5.77470e9i) q^{92} -1.28260e10 q^{93} +(-4.31500e9 - 1.37395e10i) q^{94} +(-1.07904e10 - 5.32184e8i) q^{96} +3.29891e9 q^{97} +(-5.64329e9 + 1.77232e9i) q^{98} -5.18876e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Introduction

L-functions

Modular forms

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