LMFDB - Embedded newform 75.9.f.e.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(7,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("75.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.f (of order $4$, degree $2$, 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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4140 x^{13} + 1109893 x^{12} - 3063780 x^{11} + 8569800 x^{10} - 2336277960 x^{9} + \cdots + 66\!\cdots\!00 $ x^16 - 4140x^13 + 1109893x^12 - 3063780x^11 + 8569800x^10 - 2336277960x^9 + 311176823556x^8 - 1727244961920x^7 + 4854003667200x^6 - 30001722912000x^5 + 6803138028400000x^4 - 35113381084800000x^3 + 91055220768000000x^2 - 110364533280000000*x + 66884304400000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{20}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$16.9634 + 16.9634i$ of defining polynomial
Character	$\chi$	$=$	75.7
Dual form			75.9.f.e.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-19.4129 - 19.4129i) q^{2} +(33.0681 - 33.0681i) q^{3} +497.724i q^{4} -1283.90 q^{6} +(-1858.12 - 1858.12i) q^{7} +(4692.57 - 4692.57i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(-19.4129 - 19.4129i) q^{2} +(33.0681 - 33.0681i) q^{3} +497.724i q^{4} -1283.90 q^{6} +(-1858.12 - 1858.12i) q^{7} +(4692.57 - 4692.57i) q^{8} -2187.00i q^{9} +15590.3 q^{11} +(16458.8 + 16458.8i) q^{12} +(23917.0 - 23917.0i) q^{13} +72143.3i q^{14} -54775.7 q^{16} +(-83617.2 - 83617.2i) q^{17} +(-42456.1 + 42456.1i) q^{18} -133473. i q^{19} -122889. q^{21} +(-302653. - 302653. i) q^{22} +(-205057. + 205057. i) q^{23} -310349. i q^{24} -928597. q^{26} +(-72320.0 - 72320.0i) q^{27} +(924833. - 924833. i) q^{28} -404590. i q^{29} -650847. q^{31} +(-137940. - 137940. i) q^{32} +(515541. - 515541. i) q^{33} +3.24651e6i q^{34} +1.08852e6 q^{36} +(2.14811e6 + 2.14811e6i) q^{37} +(-2.59111e6 + 2.59111e6i) q^{38} -1.58178e6i q^{39} -896737. q^{41} +(2.38564e6 + 2.38564e6i) q^{42} +(856967. - 856967. i) q^{43} +7.75965e6i q^{44} +7.96152e6 q^{46} +(-1.34921e6 - 1.34921e6i) q^{47} +(-1.81133e6 + 1.81133e6i) q^{48} +1.14045e6i q^{49} -5.53012e6 q^{51} +(1.19040e7 + 1.19040e7i) q^{52} +(-1.06166e7 + 1.06166e7i) q^{53} +2.80788e6i q^{54} -1.74388e7 q^{56} +(-4.41371e6 - 4.41371e6i) q^{57} +(-7.85428e6 + 7.85428e6i) q^{58} +6.21053e6i q^{59} +4.93632e6 q^{61} +(1.26348e7 + 1.26348e7i) q^{62} +(-4.06372e6 + 4.06372e6i) q^{63} +1.93782e7i q^{64} -2.00163e7 q^{66} +(-9.20397e6 - 9.20397e6i) q^{67} +(4.16183e7 - 4.16183e7i) q^{68} +1.35617e7i q^{69} +5.87863e6 q^{71} +(-1.02626e7 - 1.02626e7i) q^{72} +(1.98532e7 - 1.98532e7i) q^{73} -8.34021e7i q^{74} +6.64329e7 q^{76} +(-2.89687e7 - 2.89687e7i) q^{77} +(-3.07069e7 + 3.07069e7i) q^{78} +2.35429e7i q^{79} -4.78297e6 q^{81} +(1.74083e7 + 1.74083e7i) q^{82} +(-1.52261e7 + 1.52261e7i) q^{83} -6.11650e7i q^{84} -3.32725e7 q^{86} +(-1.33790e7 - 1.33790e7i) q^{87} +(7.31584e7 - 7.31584e7i) q^{88} +5.52935e6i q^{89} -8.88814e7 q^{91} +(-1.02062e8 - 1.02062e8i) q^{92} +(-2.15223e7 + 2.15223e7i) q^{93} +5.23844e7i q^{94} -9.12283e6 q^{96} +(-2.95502e7 - 2.95502e7i) q^{97} +(2.21395e7 - 2.21395e7i) q^{98} -3.40959e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) $ 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8	$ 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8} - 23616 q^{11} - 22680 q^{12} - 133420 q^{13} - 471380 q^{16} - 573300 q^{17} + 163944 q^{21} + 234700 q^{22} - 651480 q^{23} - 448848 q^{26} + 3567940 q^{28} + 1311776 q^{31} - 641460 q^{32} + 3815100 q^{33} + 5519988 q^{36} + 3607340 q^{37} - 8139840 q^{38} - 14740104 q^{41} + 9643860 q^{42} + 4805480 q^{43} + 14024216 q^{46} - 26529600 q^{47} - 3661200 q^{48} - 6168312 q^{51} + 15861080 q^{52} - 16612140 q^{53} + 10752000 q^{56} - 4714200 q^{57} - 63562980 q^{58} - 12550600 q^{61} + 35190840 q^{62} - 9928980 q^{63} + 46958616 q^{66} - 46836760 q^{67} + 197811840 q^{68} - 85681968 q^{71} + 38185020 q^{72} + 50835800 q^{73} + 101166648 q^{76} - 97175880 q^{77} - 131709240 q^{78} - 76527504 q^{81} + 181542400 q^{82} + 208234800 q^{83} - 187512576 q^{86} + 74298060 q^{87} - 138207420 q^{88} + 38623856 q^{91} - 652331400 q^{92} - 159787080 q^{93} + 531512604 q^{96} + 138370520 q^{97} + 50186520 q^{98}+O(q^{100}) $ 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8 - 23616 * q^11 - 22680 * q^12 - 133420 * q^13 - 471380 * q^16 - 573300 * q^17 + 163944 * q^21 + 234700 * q^22 - 651480 * q^23 - 448848 * q^26 + 3567940 * q^28 + 1311776 * q^31 - 641460 * q^32 + 3815100 * q^33 + 5519988 * q^36 + 3607340 * q^37 - 8139840 * q^38 - 14740104 * q^41 + 9643860 * q^42 + 4805480 * q^43 + 14024216 * q^46 - 26529600 * q^47 - 3661200 * q^48 - 6168312 * q^51 + 15861080 * q^52 - 16612140 * q^53 + 10752000 * q^56 - 4714200 * q^57 - 63562980 * q^58 - 12550600 * q^61 + 35190840 * q^62 - 9928980 * q^63 + 46958616 * q^66 - 46836760 * q^67 + 197811840 * q^68 - 85681968 * q^71 + 38185020 * q^72 + 50835800 * q^73 + 101166648 * q^76 - 97175880 * q^77 - 131709240 * q^78 - 76527504 * q^81 + 181542400 * q^82 + 208234800 * q^83 - 187512576 * q^86 + 74298060 * q^87 - 138207420 * q^88 + 38623856 * q^91 - 652331400 * q^92 - 159787080 * q^93 + 531512604 * q^96 + 138370520 * q^97 + 50186520 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−19.4129	−	19.4129i	−1.21331	−	1.21331i	−0.969932	−	0.243376i	$-0.921745\pi$
$2$	−19.4129	−	19.4129i	−1.21331	−	1.21331i	−0.243376	−	0.969932i	$-0.578255\pi$
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$4$			497.724i			1.94423i
$5$		0			0
$5$		0			0
$6$	−1283.90			−0.990662
$7$	−1858.12	−	1858.12i	−0.773896	−	0.773896i	0.204889	−	0.978785i	$-0.434317\pi$
$7$	−1858.12	−	1858.12i	−0.773896	−	0.773896i	−0.978785	+	0.204889i	$0.934317\pi$
$8$	4692.57	−	4692.57i	1.14565	−	1.14565i
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	15590.3			1.06484			0.532418	−	0.846481i	$-0.321283\pi$
$11$	15590.3			1.06484			0.532418	+	0.846481i	$0.321283\pi$
$12$	16458.8	+	16458.8i	0.793730	+	0.793730i
$13$	23917.0	−	23917.0i	0.837400	−	0.837400i	−0.151116	−	0.988516i	$-0.548287\pi$
$13$	23917.0	−	23917.0i	0.837400	−	0.837400i	0.988516	+	0.151116i	$0.0482868\pi$
$14$			72143.3i			1.87795i
$15$		0			0
$16$	−54775.7			−0.835811
$17$	−83617.2	−	83617.2i	−1.00115	−	1.00115i	−0.999999	−	0.00115191i	$-0.999633\pi$
$17$	−83617.2	−	83617.2i	−1.00115	−	1.00115i	−0.00115191	−	0.999999i	$-0.500367\pi$
$18$	−42456.1	+	42456.1i	−0.404436	+	0.404436i
$19$		−	133473.i		−	1.02419i	−0.858929	−	0.512095i	$-0.828870\pi$
$19$		−	133473.i		−	1.02419i	0.858929	−	0.512095i	$-0.171130\pi$
$20$		0			0
$21$	−122889.			−0.631884
$22$	−302653.	−	302653.i	−1.29198	−	1.29198i
$23$	−205057.	+	205057.i	−0.732763	+	0.732763i	−0.971166	−	0.238403i	$-0.923376\pi$
$23$	−205057.	+	205057.i	−0.732763	+	0.732763i	0.238403	+	0.971166i	$0.423376\pi$
$24$		−	310349.i		−	0.935417i
$25$		0			0
$26$	−928597.			−2.03205
$27$	−72320.0	−	72320.0i	−0.136083	−	0.136083i
$28$	924833.	−	924833.i	1.50464	−	1.50464i
$29$		−	404590.i		−	0.572036i	−0.958224	−	0.286018i	$-0.907668\pi$
$29$		−	404590.i		−	0.572036i	0.958224	−	0.286018i	$-0.0923317\pi$
$30$		0			0
$31$	−650847.			−0.704745			−0.352372	−	0.935860i	$-0.614625\pi$
$31$	−650847.			−0.704745			−0.352372	+	0.935860i	$0.614625\pi$
$32$	−137940.	−	137940.i	−0.131550	−	0.131550i
$33$	515541.	−	515541.i	0.434718	−	0.434718i
$34$			3.24651e6i			2.42941i
$35$		0			0
$36$	1.08852e6			0.648078
$37$	2.14811e6	+	2.14811e6i	1.14617	+	1.14617i	0.987300	+	0.158870i	$0.0507849\pi$
$37$	2.14811e6	+	2.14811e6i	1.14617	+	1.14617i	0.158870	+	0.987300i	$0.449215\pi$
$38$	−2.59111e6	+	2.59111e6i	−1.24266	+	1.24266i
$39$		−	1.58178e6i		−	0.683734i
$40$		0			0
$41$	−896737.			−0.317343			−0.158672	−	0.987331i	$-0.550721\pi$
$41$	−896737.			−0.317343			−0.158672	+	0.987331i	$0.550721\pi$
$42$	2.38564e6	+	2.38564e6i	0.766670	+	0.766670i
$43$	856967.	−	856967.i	0.250663	−	0.250663i	−0.570579	−	0.821242i	$-0.693281\pi$
$43$	856967.	−	856967.i	0.250663	−	0.250663i	0.821242	+	0.570579i	$0.193281\pi$
$44$			7.75965e6i			2.07029i
$45$		0			0
$46$	7.96152e6			1.77814
$47$	−1.34921e6	−	1.34921e6i	−0.276496	−	0.276496i	0.555212	−	0.831709i	$-0.312637\pi$
$47$	−1.34921e6	−	1.34921e6i	−0.276496	−	0.276496i	−0.831709	+	0.555212i	$0.812637\pi$
$48$	−1.81133e6	+	1.81133e6i	−0.341219	+	0.341219i
$49$			1.14045e6i			0.197830i
$50$		0			0
$51$	−5.53012e6			−0.817437
$52$	1.19040e7	+	1.19040e7i	1.62810	+	1.62810i
$53$	−1.06166e7	+	1.06166e7i	−1.34550	+	1.34550i	−0.455014	+	0.890484i	$0.650366\pi$
$53$	−1.06166e7	+	1.06166e7i	−1.34550	+	1.34550i	−0.890484	+	0.455014i	$0.849634\pi$
$54$			2.80788e6i			0.330221i
$55$		0			0
$56$	−1.74388e7			−1.77322
$57$	−4.41371e6	−	4.41371e6i	−0.418124	−	0.418124i
$58$	−7.85428e6	+	7.85428e6i	−0.694056	+	0.694056i
$59$			6.21053e6i			0.512532i	0.966606	+	0.256266i	$0.0824923\pi$
$59$			6.21053e6i			0.512532i	−0.966606	+	0.256266i	$0.917508\pi$
$60$		0			0
$61$	4.93632e6			0.356520			0.178260	−	0.983983i	$-0.442953\pi$
$61$	4.93632e6			0.356520			0.178260	+	0.983983i	$0.442953\pi$
$62$	1.26348e7	+	1.26348e7i	0.855073	+	0.855073i
$63$	−4.06372e6	+	4.06372e6i	−0.257965	+	0.257965i
$64$			1.93782e7i			1.15503i
$65$		0			0
$66$	−2.00163e7			−1.05489
$67$	−9.20397e6	−	9.20397e6i	−0.456747	−	0.456747i	0.440839	−	0.897586i	$-0.354681\pi$
$67$	−9.20397e6	−	9.20397e6i	−0.456747	−	0.456747i	−0.897586	+	0.440839i	$0.854681\pi$
$68$	4.16183e7	−	4.16183e7i	1.94647	−	1.94647i
$69$			1.35617e7i			0.598299i
$70$		0			0
$71$	5.87863e6			0.231336			0.115668	−	0.993288i	$-0.463099\pi$
$71$	5.87863e6			0.231336			0.115668	+	0.993288i	$0.463099\pi$
$72$	−1.02626e7	−	1.02626e7i	−0.381882	−	0.381882i
$73$	1.98532e7	−	1.98532e7i	0.699101	−	0.699101i	−0.265115	−	0.964217i	$-0.585410\pi$
$73$	1.98532e7	−	1.98532e7i	0.699101	−	0.699101i	0.964217	+	0.265115i	$0.0854101\pi$
$74$		−	8.34021e7i		−	2.78131i
$75$		0			0
$76$	6.64329e7			1.99126
$77$	−2.89687e7	−	2.89687e7i	−0.824073	−	0.824073i
$78$	−3.07069e7	+	3.07069e7i	−0.829580	+	0.829580i
$79$			2.35429e7i			0.604438i	0.953239	+	0.302219i	$0.0977274\pi$
$79$			2.35429e7i			0.604438i	−0.953239	+	0.302219i	$0.902273\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	1.74083e7	+	1.74083e7i	0.385035	+	0.385035i
$83$	−1.52261e7	+	1.52261e7i	−0.320831	+	0.320831i	−0.849086	−	0.528255i	$-0.822846\pi$
$83$	−1.52261e7	+	1.52261e7i	−0.320831	+	0.320831i	0.528255	+	0.849086i	$0.322846\pi$
$84$		−	6.11650e7i		−	1.22853i
$85$		0			0
$86$	−3.32725e7			−0.608263
$87$	−1.33790e7	−	1.33790e7i	−0.233533	−	0.233533i
$88$	7.31584e7	−	7.31584e7i	1.21993	−	1.21993i
$89$			5.52935e6i			0.0881280i	0.999029	+	0.0440640i	$0.0140306\pi$
$89$			5.52935e6i			0.0881280i	−0.999029	+	0.0440640i	$0.985969\pi$
$90$		0			0
$91$	−8.88814e7			−1.29612
$92$	−1.02062e8	−	1.02062e8i	−1.42466	−	1.42466i
$93$	−2.15223e7	+	2.15223e7i	−0.287711	+	0.287711i
$94$			5.23844e7i			0.670950i
$95$		0			0
$96$	−9.12283e6			−0.107410
$97$	−2.95502e7	−	2.95502e7i	−0.333790	−	0.333790i	0.520234	−	0.854024i	$-0.325845\pi$
$97$	−2.95502e7	−	2.95502e7i	−0.333790	−	0.333790i	−0.854024	+	0.520234i	$0.825845\pi$
$98$	2.21395e7	−	2.21395e7i	0.240029	−	0.240029i
$99$		−	3.40959e7i		−	0.354946i
$100$		0			0
$101$	−1.28628e8			−1.23609			−0.618046	−	0.786142i	$-0.712076\pi$
$101$	−1.28628e8			−1.23609			−0.618046	+	0.786142i	$0.712076\pi$
$102$	1.07356e8	+	1.07356e8i	0.991803	+	0.991803i
$103$	−8.23215e7	+	8.23215e7i	−0.731415	+	0.731415i	−0.970900	−	0.239485i	$-0.923022\pi$
$103$	−8.23215e7	+	8.23215e7i	−0.731415	+	0.731415i	0.239485	+	0.970900i	$0.423022\pi$
$104$		−	2.24464e8i		−	1.91873i
$105$		0			0
$106$	4.12200e8			3.26501
$107$	3.38936e7	+	3.38936e7i	0.258573	+	0.258573i	0.824473	−	0.565901i	$-0.191471\pi$
$107$	3.38936e7	+	3.38936e7i	0.258573	+	0.258573i	−0.565901	+	0.824473i	$0.691471\pi$
$108$	3.59954e7	−	3.59954e7i	0.264577	−	0.264577i
$109$		−	1.86006e7i		−	0.131772i	−0.997827	−	0.0658858i	$-0.979013\pi$
$109$		−	1.86006e7i		−	0.131772i	0.997827	−	0.0658858i	$-0.0209873\pi$
$110$		0			0
$111$	1.42068e8			0.935843
$112$	1.01780e8	+	1.01780e8i	0.646831	+	0.646831i
$113$	−1.89831e8	+	1.89831e8i	−1.16427	+	1.16427i	−0.180737	+	0.983531i	$0.557848\pi$
$113$	−1.89831e8	+	1.89831e8i	−1.16427	+	1.16427i	−0.983531	+	0.180737i	$0.942152\pi$
$114$			1.71366e8i			1.01463i
$115$		0			0
$116$	2.01374e8			1.11217
$117$	−5.23064e7	−	5.23064e7i	−0.279133	−	0.279133i
$118$	1.20565e8	−	1.20565e8i	0.621859	−	0.621859i
$119$			3.10742e8i			1.54957i
$120$		0			0
$121$	2.86978e7			0.133877
$122$	−9.58284e7	−	9.58284e7i	−0.432568	−	0.432568i
$123$	−2.96534e7	+	2.96534e7i	−0.129555	+	0.129555i
$124$		−	3.23942e8i		−	1.37019i
$125$		0			0
$126$	1.57777e8			0.625983
$127$	1.46480e8	+	1.46480e8i	0.563070	+	0.563070i	0.930178	−	0.367108i	$-0.119652\pi$
$127$	1.46480e8	+	1.46480e8i	0.563070	+	0.563070i	−0.367108	+	0.930178i	$0.619652\pi$
$128$	3.40876e8	−	3.40876e8i	1.26986	−	1.26986i
$129$		−	5.66765e7i		−	0.204665i
$130$		0			0
$131$	−1.80306e8			−0.612245			−0.306123	−	0.951992i	$-0.599032\pi$
$131$	−1.80306e8			−0.612245			−0.306123	+	0.951992i	$0.599032\pi$
$132$	2.56597e8	+	2.56597e8i	0.845193	+	0.845193i
$133$	−2.48010e8	+	2.48010e8i	−0.792616	+	0.792616i
$134$			3.57352e8i			1.10835i
$135$		0			0
$136$	−7.84759e8			−2.29393
$137$	−2.80423e8	−	2.80423e8i	−0.796033	−	0.796033i	0.186435	−	0.982467i	$-0.440307\pi$
$137$	−2.80423e8	−	2.80423e8i	−0.796033	−	0.796033i	−0.982467	+	0.186435i	$0.940307\pi$
$138$	2.63273e8	−	2.63273e8i	0.725921	−	0.725921i
$139$		−	4.03054e8i		−	1.07970i	−0.841761	−	0.539851i	$-0.818481\pi$
$139$		−	4.03054e8i		−	1.07970i	0.841761	−	0.539851i	$-0.181519\pi$
$140$		0			0
$141$	−8.92318e7			−0.225758
$142$	−1.14122e8	−	1.14122e8i	−0.280682	−	0.280682i
$143$	3.72872e8	−	3.72872e8i	0.891694	−	0.891694i
$144$			1.19795e8i			0.278604i
$145$		0			0
$146$	−7.70819e8			−1.69645
$147$	3.77126e7	+	3.77126e7i	0.0807639	+	0.0807639i
$148$	−1.06916e9	+	1.06916e9i	−2.22842	+	2.22842i
$149$		−	5.39860e8i		−	1.09531i	−0.836705	−	0.547654i	$-0.815521\pi$
$149$		−	5.39860e8i		−	1.09531i	0.836705	−	0.547654i	$-0.184479\pi$
$150$		0			0
$151$	−9.58022e8			−1.84276			−0.921378	−	0.388668i	$-0.872935\pi$
$151$	−9.58022e8			−1.84276			−0.921378	+	0.388668i	$0.872935\pi$
$152$	−6.26333e8	−	6.26333e8i	−1.17336	−	1.17336i
$153$	−1.82871e8	+	1.82871e8i	−0.333717	+	0.333717i
$154$			1.12473e9i			1.99971i
$155$		0			0
$156$	7.87289e8			1.32934
$157$	−8.67448e7	−	8.67448e7i	−0.142773	−	0.142773i	0.632108	−	0.774880i	$-0.282190\pi$
$157$	−8.67448e7	−	8.67448e7i	−0.142773	−	0.142773i	−0.774880	+	0.632108i	$0.782190\pi$
$158$	4.57037e8	−	4.57037e8i	0.733370	−	0.733370i
$159$			7.02144e8i			1.09859i
$160$		0			0
$161$	7.62044e8			1.13417
$162$	9.28515e7	+	9.28515e7i	0.134812	+	0.134812i
$163$	4.62279e8	−	4.62279e8i	0.654868	−	0.654868i	−0.299293	−	0.954161i	$-0.596751\pi$
$163$	4.62279e8	−	4.62279e8i	0.654868	−	0.654868i	0.954161	+	0.299293i	$0.0967508\pi$
$164$		−	4.46327e8i		−	0.616990i
$165$		0			0
$166$	5.91166e8			0.778533
$167$	6.53879e8	+	6.53879e8i	0.840681	+	0.840681i	0.988947	−	0.148266i	$-0.0473693\pi$
$167$	6.53879e8	+	6.53879e8i	0.840681	+	0.840681i	−0.148266	+	0.988947i	$0.547369\pi$
$168$	−5.76667e8	+	5.76667e8i	−0.723915	+	0.723915i
$169$		−	3.28312e8i		−	0.402476i
$170$		0			0
$171$	−2.91906e8			−0.341396
$172$	4.26533e8	+	4.26533e8i	0.487347	+	0.487347i
$173$	−2.97784e8	+	2.97784e8i	−0.332443	+	0.332443i	−0.853513	−	0.521071i	$-0.825533\pi$
$173$	−2.97784e8	+	2.97784e8i	−0.332443	+	0.332443i	0.521071	+	0.853513i	$0.325533\pi$
$174$			5.19453e8i			0.566695i
$175$		0			0
$176$	−8.53969e8			−0.890003
$177$	2.05371e8	+	2.05371e8i	0.209240	+	0.209240i
$178$	1.07341e8	−	1.07341e8i	0.106926	−	0.106926i
$179$		−	1.90030e8i		−	0.185101i	−0.995708	−	0.0925506i	$-0.970498\pi$
$179$		−	1.90030e8i		−	0.185101i	0.995708	−	0.0925506i	$-0.0295020\pi$
$180$		0			0
$181$	7.38196e8			0.687792			0.343896	−	0.939008i	$-0.388253\pi$
$181$	7.38196e8			0.687792			0.343896	+	0.939008i	$0.388253\pi$
$182$	1.72545e9	+	1.72545e9i	1.57259	+	1.57259i
$183$	1.63235e8	−	1.63235e8i	0.145549	−	0.145549i
$184$			1.92449e9i			1.67898i
$185$		0			0
$186$	8.35621e8			0.698164
$187$	−1.30361e9	−	1.30361e9i	−1.06606	−	1.06606i
$188$	6.71535e8	−	6.71535e8i	0.537573	−	0.537573i
$189$			2.68759e8i			0.210628i
$190$		0			0
$191$	−1.77932e8			−0.133697			−0.0668483	−	0.997763i	$-0.521294\pi$
$191$	−1.77932e8			−0.133697			−0.0668483	+	0.997763i	$0.521294\pi$
$192$	6.40801e8	+	6.40801e8i	0.471540	+	0.471540i
$193$	3.18351e7	−	3.18351e7i	0.0229444	−	0.0229444i	−0.695542	−	0.718486i	$-0.744835\pi$
$193$	3.18351e7	−	3.18351e7i	0.0229444	−	0.0229444i	0.718486	+	0.695542i	$0.244835\pi$
$194$			1.14731e9i			0.809980i
$195$		0			0
$196$	−5.67631e8			−0.384629
$197$	−1.05878e9	−	1.05878e9i	−0.702975	−	0.702975i	0.262073	−	0.965048i	$-0.415594\pi$
$197$	−1.05878e9	−	1.05878e9i	−0.702975	−	0.702975i	−0.965048	+	0.262073i	$0.915594\pi$
$198$	−6.61902e8	+	6.61902e8i	−0.430658	+	0.430658i
$199$		−	1.90302e9i		−	1.21347i	−0.794903	−	0.606737i	$-0.792478\pi$
$199$		−	1.90302e9i		−	1.21347i	0.794903	−	0.606737i	$-0.207522\pi$
$200$		0			0
$201$	−6.08716e8			−0.372933
$202$	2.49705e9	+	2.49705e9i	1.49976	+	1.49976i
$203$	−7.51779e8	+	7.51779e8i	−0.442697	+	0.442697i
$204$		−	2.75247e9i		−	1.58929i
$205$		0			0
$206$	3.19620e9			1.77486
$207$	4.48460e8	+	4.48460e8i	0.244254	+	0.244254i
$208$	−1.31007e9	+	1.31007e9i	−0.699908	+	0.699908i
$209$		−	2.08089e9i		−	1.09059i
$210$		0			0
$211$	3.35687e8			0.169357			0.0846787	−	0.996408i	$-0.473014\pi$
$211$	3.35687e8			0.169357			0.0846787	+	0.996408i	$0.473014\pi$
$212$	−5.28415e9	−	5.28415e9i	−2.61596	−	2.61596i
$213$	1.94395e8	−	1.94395e8i	0.0944425	−	0.0944425i
$214$		−	1.31595e9i		−	0.627457i
$215$		0			0
$216$	−6.78733e8			−0.311806
$217$	1.20935e9	+	1.20935e9i	0.545399	+	0.545399i
$218$	−3.61093e8	+	3.61093e8i	−0.159880	+	0.159880i
$219$		−	1.31302e9i		−	0.570814i
$220$		0			0
$221$	−3.99974e9			−1.67673
$222$	−2.75795e9	−	2.75795e9i	−1.13547	−	1.13547i
$223$	2.23298e9	−	2.23298e9i	0.902955	−	0.902955i	−0.0927362	−	0.995691i	$-0.529561\pi$
$223$	2.23298e9	−	2.23298e9i	0.902955	−	0.902955i	0.995691	+	0.0927362i	$0.0295613\pi$
$224$			5.12620e8i			0.203612i
$225$		0			0
$226$	7.37035e9			2.82523
$227$	1.11337e9	+	1.11337e9i	0.419312	+	0.419312i	0.884967	−	0.465654i	$-0.154181\pi$
$227$	1.11337e9	+	1.11337e9i	0.419312	+	0.419312i	−0.465654	+	0.884967i	$0.654181\pi$
$228$	2.19681e9	−	2.19681e9i	0.812930	−	0.812930i
$229$			6.33884e7i			0.0230498i	0.999934	+	0.0115249i	$0.00366858\pi$
$229$			6.33884e7i			0.0230498i	−0.999934	+	0.0115249i	$0.996331\pi$
$230$		0			0
$231$	−1.91588e9			−0.672853
$232$	−1.89857e9	−	1.89857e9i	−0.655351	−	0.655351i
$233$	−5.52434e8	+	5.52434e8i	−0.187438	+	0.187438i	−0.794587	−	0.607150i	$-0.792313\pi$
$233$	−5.52434e8	+	5.52434e8i	−0.187438	+	0.187438i	0.607150	+	0.794587i	$0.292313\pi$
$234$			2.03084e9i			0.677349i
$235$		0			0
$236$	−3.09113e9			−0.996482
$237$	7.78519e8	+	7.78519e8i	0.246761	+	0.246761i
$238$	6.03242e9	−	6.03242e9i	1.88011	−	1.88011i
$239$			1.09564e9i			0.335796i	0.985804	+	0.167898i	$0.0536979\pi$
$239$			1.09564e9i			0.335796i	−0.985804	+	0.167898i	$0.946302\pi$
$240$		0			0
$241$	2.11459e9			0.626842			0.313421	−	0.949614i	$-0.398525\pi$
$241$	2.11459e9			0.626842			0.313421	+	0.949614i	$0.398525\pi$
$242$	−5.57108e8	−	5.57108e8i	−0.162434	−	0.162434i
$243$	−1.58164e8	+	1.58164e8i	−0.0453609	+	0.0453609i
$244$			2.45692e9i			0.693158i
$245$		0			0
$246$	1.15132e9			0.314380
$247$	−3.19228e9	−	3.19228e9i	−0.857656	−	0.857656i
$248$	−3.05414e9	+	3.05414e9i	−0.807389	+	0.807389i
$249$			1.00700e9i			0.261957i
$250$		0			0
$251$	−3.62394e9			−0.913033			−0.456516	−	0.889715i	$-0.650903\pi$
$251$	−3.62394e9			−0.913033			−0.456516	+	0.889715i	$0.650903\pi$
$252$	−2.02261e9	−	2.02261e9i	−0.501545	−	0.501545i
$253$	−3.19690e9	+	3.19690e9i	−0.780273	+	0.780273i
$254$		−	5.68720e9i		−	1.36635i
$255$		0			0
$256$	−8.27396e9			−1.92643
$257$	3.24505e9	+	3.24505e9i	0.743857	+	0.743857i	0.973318	−	0.229461i	$-0.0736964\pi$
$257$	3.24505e9	+	3.24505e9i	0.743857	+	0.743857i	−0.229461	+	0.973318i	$0.573696\pi$
$258$	−1.10026e9	+	1.10026e9i	−0.248322	+	0.248322i
$259$		−	7.98290e9i		−	1.77403i
$260$		0			0
$261$	−8.84839e8			−0.190679
$262$	3.50027e9	+	3.50027e9i	0.742842	+	0.742842i
$263$	4.51031e9	−	4.51031e9i	0.942722	−	0.942722i	−0.0557241	−	0.998446i	$-0.517747\pi$
$263$	4.51031e9	−	4.51031e9i	0.942722	−	0.942722i	0.998446	+	0.0557241i	$0.0177467\pi$
$264$		−	4.83842e9i		−	0.996066i
$265$		0			0
$266$	9.62921e9			1.92338
$267$	1.82845e8	+	1.82845e8i	0.0359781	+	0.0359781i
$268$	4.58103e9	−	4.58103e9i	0.888023	−	0.888023i
$269$			2.77553e9i			0.530075i	0.964238	+	0.265037i	$0.0853843\pi$
$269$			2.77553e9i			0.530075i	−0.964238	+	0.265037i	$0.914616\pi$
$270$		0			0
$271$	1.01964e10			1.89048			0.945238	−	0.326382i	$-0.105829\pi$
$271$	1.01964e10			1.89048			0.945238	+	0.326382i	$0.105829\pi$
$272$	4.58019e9	+	4.58019e9i	0.836774	+	0.836774i
$273$	−2.93914e9	+	2.93914e9i	−0.529139	+	0.529139i
$274$			1.08877e10i			1.93167i
$275$		0			0
$276$	−6.74999e9			−1.16323
$277$	−6.87648e9	−	6.87648e9i	−1.16801	−	1.16801i	−0.982675	−	0.185335i	$-0.940663\pi$
$277$	−6.87648e9	−	6.87648e9i	−1.16801	−	1.16801i	−0.185335	−	0.982675i	$-0.559337\pi$
$278$	−7.82445e9	+	7.82445e9i	−1.31001	+	1.31001i
$279$			1.42340e9i			0.234915i
$280$		0			0
$281$	−1.35670e9			−0.217600			−0.108800	−	0.994064i	$-0.534701\pi$
$281$	−1.35670e9			−0.217600			−0.108800	+	0.994064i	$0.534701\pi$
$282$	1.73225e9	+	1.73225e9i	0.273914	+	0.273914i
$283$	−5.98075e9	+	5.98075e9i	−0.932416	+	0.932416i	−0.997856	−	0.0654404i	$-0.979155\pi$
$283$	−5.98075e9	+	5.98075e9i	−0.932416	+	0.932416i	0.0654404	+	0.997856i	$0.479155\pi$
$284$			2.92594e9i			0.449771i
$285$		0			0
$286$	−1.44771e10			−2.16380
$287$	1.66625e9	+	1.66625e9i	0.245591	+	0.245591i
$288$	−3.01675e8	+	3.01675e8i	−0.0438500	+	0.0438500i
$289$			7.00790e9i			1.00461i
$290$		0			0
$291$	−1.95434e9			−0.272538
$292$	9.88143e9	+	9.88143e9i	1.35922	+	1.35922i
$293$	−9.86843e8	+	9.86843e8i	−0.133899	+	0.133899i	−0.770880	−	0.636981i	$-0.780183\pi$
$293$	−9.86843e8	+	9.86843e8i	−0.133899	+	0.133899i	0.636981	+	0.770880i	$0.280183\pi$
$294$		−	1.46423e9i		−	0.195983i
$295$		0			0
$296$	2.01603e10			2.62621
$297$	−1.12749e9	−	1.12749e9i	−0.144906	−	0.144906i
$298$	−1.04803e10	+	1.04803e10i	−1.32895	+	1.32895i
$299$			9.80869e9i			1.22723i
$300$		0			0
$301$	−3.18470e9			−0.387974
$302$	1.85980e10	+	1.85980e10i	2.23583	+	2.23583i
$303$	−4.25349e9	+	4.25349e9i	−0.504633	+	0.504633i
$304$			7.31110e9i			0.856029i
$305$		0			0
$306$	7.10011e9			0.809803
$307$	3.24275e9	+	3.24275e9i	0.365056	+	0.365056i	0.865670	−	0.500614i	$-0.166893\pi$
$307$	3.24275e9	+	3.24275e9i	0.365056	+	0.365056i	−0.500614	+	0.865670i	$0.666893\pi$
$308$	1.44184e10	−	1.44184e10i	1.60219	−	1.60219i
$309$			5.44443e9i			0.597198i
$310$		0			0
$311$	7.77719e9			0.831345			0.415672	−	0.909514i	$-0.363546\pi$
$311$	7.77719e9			0.831345			0.415672	+	0.909514i	$0.363546\pi$
$312$	−7.42260e9	−	7.42260e9i	−0.783317	−	0.783317i
$313$	1.12217e10	−	1.12217e10i	1.16918	−	1.16918i	0.186776	−	0.982403i	$-0.440196\pi$
$313$	1.12217e10	−	1.12217e10i	1.16918	−	1.16918i	0.982403	−	0.186776i	$-0.0598038\pi$
$314$			3.36794e9i			0.346454i
$315$		0			0
$316$	−1.17179e10			−1.17517
$317$	2.13202e9	+	2.13202e9i	0.211132	+	0.211132i	0.804748	−	0.593616i	$-0.202300\pi$
$317$	2.13202e9	+	2.13202e9i	0.211132	+	0.211132i	−0.593616	+	0.804748i	$0.702300\pi$
$318$	1.36307e10	−	1.36307e10i	1.33293	−	1.33293i
$319$		−	6.30767e9i		−	0.609125i
$320$		0			0
$321$	2.24159e9			0.211124
$322$	−1.47935e10	−	1.47935e10i	−1.37609	−	1.37609i
$323$	−1.11607e10	+	1.11607e10i	−1.02537	+	1.02537i
$324$		−	2.38060e9i		−	0.216026i
$325$		0			0
$326$	−1.79484e10			−1.58911
$327$	−6.15088e8	−	6.15088e8i	−0.0537955	−	0.0537955i
$328$	−4.20800e9	+	4.20800e9i	−0.363563	+	0.363563i
$329$			5.01401e9i			0.427959i
$330$		0			0
$331$	−1.73132e10			−1.44233			−0.721166	−	0.692762i	$-0.756394\pi$
$331$	−1.73132e10			−1.44233			−0.721166	+	0.692762i	$0.756394\pi$
$332$	−7.57839e9	−	7.57839e9i	−0.623770	−	0.623770i
$333$	4.69791e9	−	4.69791e9i	0.382056	−	0.382056i
$334$		−	2.53874e10i		−	2.04001i
$335$		0			0
$336$	6.73135e9			0.528135
$337$	−1.65976e10	−	1.65976e10i	−1.28685	−	1.28685i	−0.936692	−	0.350154i	$-0.886129\pi$
$337$	−1.65976e10	−	1.65976e10i	−1.28685	−	1.28685i	−0.350154	−	0.936692i	$-0.613871\pi$
$338$	−6.37350e9	+	6.37350e9i	−0.488328	+	0.488328i
$339$			1.25547e10i			0.950621i
$340$		0			0
$341$	−1.01469e10			−0.750438
$342$	5.66676e9	+	5.66676e9i	0.414219	+	0.414219i
$343$	−8.59261e9	+	8.59261e9i	−0.620796	+	0.620796i
$344$		−	8.04275e9i		−	0.574342i
$345$		0			0
$346$	1.15617e10			0.806711
$347$	−6.76658e9	−	6.76658e9i	−0.466715	−	0.466715i	0.434134	−	0.900848i	$-0.357055\pi$
$347$	−6.76658e9	−	6.76658e9i	−0.466715	−	0.466715i	−0.900848	+	0.434134i	$0.857055\pi$
$348$	6.65907e9	−	6.65907e9i	0.454042	−	0.454042i
$349$		−	1.80659e10i		−	1.21775i	−0.793266	−	0.608875i	$-0.791621\pi$
$349$		−	1.80659e10i		−	1.21775i	0.793266	−	0.608875i	$-0.208379\pi$
$350$		0			0
$351$	−3.45935e9			−0.227911
$352$	−2.15052e9	−	2.15052e9i	−0.140079	−	0.140079i
$353$	−8.85924e9	+	8.85924e9i	−0.570555	+	0.570555i	−0.932284	−	0.361728i	$-0.882187\pi$
$353$	−8.85924e9	+	8.85924e9i	−0.570555	+	0.570555i	0.361728	+	0.932284i	$0.382187\pi$
$354$		−	7.97369e9i		−	0.507746i
$355$		0			0
$356$	−2.75209e9			−0.171341
$357$	1.02757e10	+	1.02757e10i	0.632611	+	0.632611i
$358$	−3.68903e9	+	3.68903e9i	−0.224585	+	0.224585i
$359$		−	1.28150e9i		−	0.0771507i	−0.999256	−	0.0385753i	$-0.987718\pi$
$359$		−	1.28150e9i		−	0.0771507i	0.999256	−	0.0385753i	$-0.0122820\pi$
$360$		0			0
$361$	−8.31578e8			−0.0489637
$362$	−1.43305e10	−	1.43305e10i	−0.834504	−	0.834504i
$363$	9.48981e8	−	9.48981e8i	0.0546551	−	0.0546551i
$364$		−	4.42384e10i		−	2.51996i
$365$		0			0
$366$	−6.33773e9			−0.353191
$367$	1.55637e10	+	1.55637e10i	0.857924	+	0.857924i	0.991093	−	0.133169i	$-0.0425154\pi$
$367$	1.55637e10	+	1.55637e10i	0.857924	+	0.857924i	−0.133169	+	0.991093i	$0.542515\pi$
$368$	1.12322e10	−	1.12322e10i	0.612452	−	0.612452i
$369$			1.96116e9i			0.105781i
$370$		0			0
$371$	3.94540e10			2.08255
$372$	−1.07121e10	−	1.07121e10i	−0.559377	−	0.559377i
$373$	2.20163e10	−	2.20163e10i	1.13739	−	1.13739i	0.148471	−	0.988917i	$-0.452565\pi$
$373$	2.20163e10	−	2.20163e10i	1.13739	−	1.13739i	0.988917	−	0.148471i	$-0.0474350\pi$
$374$			5.06140e10i			2.58693i
$375$		0			0
$376$	−1.26625e10			−0.633534
$377$	−9.67657e9	−	9.67657e9i	−0.479023	−	0.479023i
$378$	5.21740e9	−	5.21740e9i	0.255557	−	0.255557i
$379$			1.22143e10i			0.591984i	0.955190	+	0.295992i	$0.0956502\pi$
$379$			1.22143e10i			0.591984i	−0.955190	+	0.295992i	$0.904350\pi$
$380$		0			0
$381$	9.68761e9			0.459745
$382$	3.45418e9	+	3.45418e9i	0.162215	+	0.162215i
$383$	3.02578e10	−	3.02578e10i	1.40619	−	1.40619i	0.627860	−	0.778326i	$-0.283931\pi$
$383$	3.02578e10	−	3.02578e10i	1.40619	−	1.40619i	0.778326	−	0.627860i	$-0.216069\pi$
$384$		−	2.25442e10i		−	1.03684i
$385$		0			0
$386$	−1.23602e9			−0.0556773
$387$	−1.87419e9	−	1.87419e9i	−0.0835543	−	0.0835543i
$388$	1.47078e10	−	1.47078e10i	0.648966	−	0.648966i
$389$		−	2.63446e10i		−	1.15052i	−0.817971	−	0.575260i	$-0.804901\pi$
$389$		−	2.63446e10i		−	1.15052i	0.817971	−	0.575260i	$-0.195099\pi$
$390$		0			0
$391$	3.42926e10			1.46721
$392$	5.35165e9	+	5.35165e9i	0.226644	+	0.226644i
$393$	−5.96238e9	+	5.96238e9i	−0.249948	+	0.249948i
$394$			4.11080e10i			1.70585i
$395$		0			0
$396$	1.69704e10			0.690097
$397$	2.24429e10	+	2.24429e10i	0.903477	+	0.903477i	0.995735	−	0.0922585i	$-0.0294086\pi$
$397$	2.24429e10	+	2.24429e10i	0.903477	+	0.903477i	−0.0922585	+	0.995735i	$0.529409\pi$
$398$	−3.69431e10	+	3.69431e10i	−1.47232	+	1.47232i
$399$			1.64025e10i			0.647168i
$400$		0			0
$401$	2.74904e9			0.106317			0.0531585	−	0.998586i	$-0.483071\pi$
$401$	2.74904e9			0.106317			0.0531585	+	0.998586i	$0.483071\pi$
$402$	1.18170e10	+	1.18170e10i	0.452482	+	0.452482i
$403$	−1.55663e10	+	1.55663e10i	−0.590153	+	0.590153i
$404$		−	6.40214e10i		−	2.40325i
$405$		0			0
$406$	2.91885e10			1.07425
$407$	3.34896e10	+	3.34896e10i	1.22048	+	1.22048i
$408$	−2.59505e10	+	2.59505e10i	−0.936494	+	0.936494i
$409$			3.11392e10i			1.11279i	0.830917	+	0.556397i	$0.187816\pi$
$409$			3.11392e10i			1.11279i	−0.830917	+	0.556397i	$0.812184\pi$
$410$		0			0
$411$	−1.85461e10			−0.649958
$412$	−4.09734e10	−	4.09734e10i	−1.42204	−	1.42204i
$413$	1.15399e10	−	1.15399e10i	0.396647	−	0.396647i
$414$		−	1.74119e10i		−	0.592712i
$415$		0			0
$416$	−6.59822e9			−0.220320
$417$	−1.33282e10	−	1.33282e10i	−0.440786	−	0.440786i
$418$	−4.03961e10	+	4.03961e10i	−1.32323	+	1.32323i
$419$		−	1.63963e9i		−	0.0531972i	−0.999646	−	0.0265986i	$-0.991532\pi$
$419$		−	1.63963e9i		−	0.0531972i	0.999646	−	0.0265986i	$-0.00846760\pi$
$420$		0			0
$421$	−2.53846e9			−0.0808056			−0.0404028	−	0.999183i	$-0.512864\pi$
$421$	−2.53846e9			−0.0808056			−0.0404028	+	0.999183i	$0.512864\pi$
$422$	−6.51666e9	−	6.51666e9i	−0.205483	−	0.205483i
$423$	−2.95073e9	+	2.95073e9i	−0.0921654	+	0.0921654i
$424$			9.96385e10i			3.08293i
$425$		0			0
$426$	−7.54757e9			−0.229176
$427$	−9.17229e9	−	9.17229e9i	−0.275909	−	0.275909i
$428$	−1.68697e10	+	1.68697e10i	−0.502726	+	0.502726i
$429$		−	2.46604e10i		−	0.728065i
$430$		0			0
$431$	−4.71105e9			−0.136524			−0.0682619	−	0.997667i	$-0.521745\pi$
$431$	−4.71105e9			−0.136524			−0.0682619	+	0.997667i	$0.521745\pi$
$432$	3.96138e9	+	3.96138e9i	0.113740	+	0.113740i
$433$	2.90761e10	−	2.90761e10i	0.827149	−	0.827149i	−0.159972	−	0.987122i	$-0.551140\pi$
$433$	2.90761e10	−	2.90761e10i	0.827149	−	0.827149i	0.987122	+	0.159972i	$0.0511404\pi$
$434$		−	4.69542e10i		−	1.32348i
$435$		0			0
$436$	9.25798e9			0.256195
$437$	2.73697e10	+	2.73697e10i	0.750488	+	0.750488i
$438$	−2.54895e10	+	2.54895e10i	−0.692573	+	0.692573i
$439$		−	5.56684e10i		−	1.49882i	−0.662105	−	0.749411i	$-0.730337\pi$
$439$		−	5.56684e10i		−	1.49882i	0.662105	−	0.749411i	$-0.269663\pi$
$440$		0			0
$441$	2.49417e9			0.0659435
$442$	7.76466e10	+	7.76466e10i	2.03439	+	2.03439i
$443$	4.65618e10	−	4.65618e10i	1.20897	−	1.20897i	0.237608	−	0.971361i	$-0.423637\pi$
$443$	4.65618e10	−	4.65618e10i	1.20897	−	1.20897i	0.971361	−	0.237608i	$-0.0763633\pi$
$444$			7.07104e10i			1.81950i
$445$		0			0
$446$	−8.66975e10			−2.19112
$447$	−1.78521e10	−	1.78521e10i	−0.447157	−	0.447157i
$448$	3.60072e10	−	3.60072e10i	0.893875	−	0.893875i
$449$		−	7.28657e9i		−	0.179282i	−0.995974	−	0.0896412i	$-0.971428\pi$
$449$		−	7.28657e9i		−	0.179282i	0.995974	−	0.0896412i	$-0.0285720\pi$
$450$		0			0
$451$	−1.39804e10			−0.337919
$452$	−9.44834e10	−	9.44834e10i	−2.26361	−	2.26361i
$453$	−3.16800e10	+	3.16800e10i	−0.752302	+	0.752302i
$454$		−	4.32277e10i		−	1.01751i
$455$		0			0
$456$	−4.14233e10			−0.958044
$457$	−2.72853e10	−	2.72853e10i	−0.625552	−	0.625552i	0.321394	−	0.946946i	$-0.395849\pi$
$457$	−2.72853e10	−	2.72853e10i	−0.625552	−	0.625552i	−0.946946	+	0.321394i	$0.895849\pi$
$458$	1.23055e9	−	1.23055e9i	0.0279666	−	0.0279666i
$459$			1.20944e10i			0.272479i
$460$		0			0
$461$	4.02398e10			0.890947			0.445473	−	0.895295i	$-0.353035\pi$
$461$	4.02398e10			0.890947			0.445473	+	0.895295i	$0.353035\pi$
$462$	3.71928e10	+	3.71928e10i	0.816378	+	0.816378i
$463$	−1.21358e9	+	1.21358e9i	−0.0264085	+	0.0264085i	−0.720188	−	0.693779i	$-0.755944\pi$
$463$	−1.21358e9	+	1.21358e9i	−0.0264085	+	0.0264085i	0.693779	+	0.720188i	$0.255944\pi$
$464$			2.21617e10i			0.478114i
$465$		0			0
$466$	2.14487e10			0.454839
$467$	−1.98706e10	−	1.98706e10i	−0.417775	−	0.417775i	0.466661	−	0.884436i	$-0.345457\pi$
$467$	−1.98706e10	−	1.98706e10i	−0.417775	−	0.417775i	−0.884436	+	0.466661i	$0.845457\pi$
$468$	2.60341e10	−	2.60341e10i	0.542700	−	0.542700i
$469$			3.42042e10i			0.706950i
$470$		0			0
$471$	−5.73697e9			−0.116573
$472$	2.91434e10	+	2.91434e10i	0.587181	+	0.587181i
$473$	1.33603e10	−	1.33603e10i	0.266915	−	0.266915i
$474$		−	3.02267e10i		−	0.598794i
$475$		0			0
$476$	−1.54664e11			−3.01273
$477$	2.32186e10	+	2.32186e10i	0.448499	+	0.448499i
$478$	2.12696e10	−	2.12696e10i	0.407424	−	0.407424i
$479$			4.55401e10i			0.865072i	0.901617	+	0.432536i	$0.142381\pi$
$479$			4.55401e10i			0.865072i	−0.901617	+	0.432536i	$0.857619\pi$
$480$		0			0
$481$	1.02752e11			1.91960
$482$	−4.10504e10	−	4.10504e10i	−0.760552	−	0.760552i
$483$	2.51993e10	−	2.51993e10i	0.463021	−	0.463021i
$484$			1.42836e10i			0.260289i
$485$		0			0
$486$	6.14084e9			0.110074
$487$	1.61314e10	+	1.61314e10i	0.286785	+	0.286785i	0.835808	−	0.549023i	$-0.185000\pi$
$487$	1.61314e10	+	1.61314e10i	0.286785	+	0.286785i	−0.549023	+	0.835808i	$0.685000\pi$
$488$	2.31640e10	−	2.31640e10i	0.408446	−	0.408446i
$489$		−	3.05734e10i		−	0.534698i
$490$		0			0
$491$	−8.80720e10			−1.51535			−0.757673	−	0.652635i	$-0.773664\pi$
$491$	−8.80720e10			−1.51535			−0.757673	+	0.652635i	$0.773664\pi$
$492$	−1.47592e10	−	1.47592e10i	−0.251885	−	0.251885i
$493$	−3.38307e10	+	3.38307e10i	−0.572695	+	0.572695i
$494$			1.23943e11i			2.08120i
$495$		0			0
$496$	3.56506e10			0.589034
$497$	−1.09232e10	−	1.09232e10i	−0.179030	−	0.179030i
$498$	1.95487e10	−	1.95487e10i	0.317835	−	0.317835i
$499$			9.21946e10i			1.48697i	0.668751	+	0.743487i	$0.266829\pi$
$499$			9.21946e10i			1.48697i	−0.668751	+	0.743487i	$0.733171\pi$
$500$		0			0
$501$	4.32451e10			0.686413
$502$	7.03513e10	+	7.03513e10i	1.10779	+	1.10779i
$503$	1.22634e10	−	1.22634e10i	0.191575	−	0.191575i	−0.604801	−	0.796376i	$-0.706747\pi$
$503$	1.22634e10	−	1.22634e10i	0.191575	−	0.191575i	0.796376	+	0.604801i	$0.206747\pi$
$504$			3.81386e10i			0.591074i
$505$		0			0
$506$	1.24122e11			1.89342
$507$	−1.08567e10	−	1.08567e10i	−0.164310	−	0.164310i
$508$	−7.29064e10	+	7.29064e10i	−1.09474	+	1.09474i
$509$		−	1.02648e11i		−	1.52925i	−0.644474	−	0.764626i	$-0.722924\pi$
$509$		−	1.02648e11i		−	1.52925i	0.644474	−	0.764626i	$-0.277076\pi$
$510$		0			0
$511$	−7.37796e10			−1.08206
$512$	7.33577e10	+	7.33577e10i	1.06750	+	1.06750i
$513$	−9.65279e9	+	9.65279e9i	−0.139375	+	0.139375i
$514$		−	1.25992e11i		−	1.80505i
$515$		0			0
$516$	2.82093e10			0.397917
$517$	−2.10346e10	−	2.10346e10i	−0.294423	−	0.294423i
$518$	−1.54971e11	+	1.54971e11i	−2.15245	+	2.15245i
$519$			1.96943e10i			0.271438i
$520$		0			0
$521$	1.05147e11			1.42708			0.713539	−	0.700616i	$-0.247091\pi$
$521$	1.05147e11			1.42708			0.713539	+	0.700616i	$0.247091\pi$
$522$	1.71773e10	+	1.71773e10i	0.231352	+	0.231352i
$523$	−4.14732e10	+	4.14732e10i	−0.554320	+	0.554320i	−0.927685	−	0.373365i	$-0.878204\pi$
$523$	−4.14732e10	+	4.14732e10i	−0.554320	+	0.554320i	0.373365	+	0.927685i	$0.378204\pi$
$524$		−	8.97427e10i		−	1.19035i
$525$		0			0
$526$	−1.75117e11			−2.28763
$527$	5.44219e10	+	5.44219e10i	0.705556	+	0.705556i
$528$	−2.82391e10	+	2.82391e10i	−0.363342	+	0.363342i
$529$		−	5.78593e9i		−	0.0738840i
$530$		0			0
$531$	1.35824e10			0.170844
$532$	−1.23441e11	−	1.23441e11i	−1.54103	−	1.54103i
$533$	−2.14472e10	+	2.14472e10i	−0.265743	+	0.265743i
$534$		−	7.09912e9i		−	0.0873051i
$535$		0			0
$536$	−8.63805e10			−1.04654
$537$	−6.28392e9	−	6.28392e9i	−0.0755673	−	0.0755673i
$538$	5.38812e10	−	5.38812e10i	0.643144	−	0.643144i
$539$			1.77800e10i			0.210657i
$540$		0			0
$541$	−4.47918e10			−0.522889			−0.261445	−	0.965219i	$-0.584199\pi$
$541$	−4.47918e10			−0.522889			−0.261445	+	0.965219i	$0.584199\pi$
$542$	−1.97943e11	−	1.97943e11i	−2.29373	−	2.29373i
$543$	2.44107e10	−	2.44107e10i	0.280790	−	0.280790i
$544$			2.30683e10i			0.263403i
$545$		0			0
$546$	1.14115e11			1.28402
$547$	1.02456e11	+	1.02456e11i	1.14443	+	1.14443i	0.987631	+	0.156797i	$0.0501170\pi$
$547$	1.02456e11	+	1.02456e11i	1.14443	+	1.14443i	0.156797	+	0.987631i	$0.449883\pi$
$548$	1.39573e11	−	1.39573e11i	1.54767	−	1.54767i
$549$		−	1.07957e10i		−	0.118840i
$550$		0			0
$551$	−5.40020e10			−0.585873
$552$	6.36393e10	+	6.36393e10i	0.685439	+	0.685439i
$553$	4.37457e10	−	4.37457e10i	0.467772	−	0.467772i
$554$			2.66985e11i			2.83431i
$555$		0			0
$556$	2.00609e11			2.09919
$557$	6.26840e10	+	6.26840e10i	0.651232	+	0.651232i	0.953290	−	0.302058i	$-0.0976735\pi$
$557$	6.26840e10	+	6.26840e10i	0.651232	+	0.651232i	−0.302058	+	0.953290i	$0.597674\pi$
$558$	2.76324e10	−	2.76324e10i	0.285024	−	0.285024i
$559$		−	4.09921e10i		−	0.419810i
$560$		0			0
$561$	−8.62161e10			−0.870436
$562$	2.63376e10	+	2.63376e10i	0.264016	+	0.264016i
$563$	−6.34578e10	+	6.34578e10i	−0.631614	+	0.631614i	−0.948473	−	0.316859i	$-0.897372\pi$
$563$	−6.34578e10	+	6.34578e10i	−0.631614	+	0.631614i	0.316859	+	0.948473i	$0.397372\pi$
$564$		−	4.44128e10i		−	0.438927i
$565$		0			0
$566$	2.32208e11			2.26262
$567$	8.88735e9	+	8.88735e9i	0.0859885	+	0.0859885i
$568$	2.75859e10	−	2.75859e10i	0.265029	−	0.265029i
$569$		−	1.89060e11i		−	1.80364i	−0.432108	−	0.901822i	$-0.642230\pi$
$569$		−	1.89060e11i		−	1.80364i	0.432108	−	0.901822i	$-0.357770\pi$
$570$		0			0
$571$	−4.33399e10			−0.407703			−0.203851	−	0.979002i	$-0.565346\pi$
$571$	−4.33399e10			−0.407703			−0.203851	+	0.979002i	$0.565346\pi$
$572$	1.85587e11	+	1.85587e11i	1.73366	+	1.73366i
$573$	−5.88387e9	+	5.88387e9i	−0.0545814	+	0.0545814i
$574$		−	6.46935e10i		−	0.595955i
$575$		0			0
$576$	4.23802e10			0.385011
$577$	−9.74163e10	−	9.74163e10i	−0.878878	−	0.878878i	0.114541	−	0.993419i	$-0.463460\pi$
$577$	−9.74163e10	−	9.74163e10i	−0.878878	−	0.878878i	−0.993419	+	0.114541i	$0.963460\pi$
$578$	1.36044e11	−	1.36044e11i	1.21890	−	1.21890i
$579$		−	2.10545e9i		−	0.0187340i
$580$		0			0
$581$	5.65839e10			0.496579
$582$	3.79394e10	+	3.79394e10i	0.330673	+	0.330673i
$583$	−1.65516e11	+	1.65516e11i	−1.43274	+	1.43274i
$584$		−	1.86325e11i		−	1.60185i
$585$		0			0
$586$	3.83150e10			0.324922
$587$	−9.73139e10	−	9.73139e10i	−0.819639	−	0.819639i	0.166417	−	0.986056i	$-0.446780\pi$
$587$	−9.73139e10	−	9.73139e10i	−0.819639	−	0.819639i	−0.986056	+	0.166417i	$0.946780\pi$
$588$	−1.87705e10	+	1.87705e10i	−0.157024	+	0.157024i
$589$			8.68707e10i			0.721792i
$590$		0			0
$591$	−7.00236e10			−0.573977
$592$	−1.17664e11	−	1.17664e11i	−0.957981	−	0.957981i
$593$	6.25106e10	−	6.25106e10i	0.505516	−	0.505516i	−0.407631	−	0.913147i	$-0.633645\pi$
$593$	6.25106e10	−	6.25106e10i	0.505516	−	0.505516i	0.913147	+	0.407631i	$0.133645\pi$
$594$			4.37757e10i			0.351631i
$595$		0			0
$596$	2.68701e11			2.12953
$597$	−6.29292e10	−	6.29292e10i	−0.495398	−	0.495398i
$598$	1.90416e11	−	1.90416e11i	1.48901	−	1.48901i
$599$			2.17762e11i			1.69151i	0.533570	+	0.845756i	$0.320850\pi$
$599$			2.17762e11i			1.69151i	−0.533570	+	0.845756i	$0.679150\pi$
$600$		0			0
$601$	−1.88847e11			−1.44748			−0.723738	−	0.690075i	$-0.757578\pi$
$601$	−1.88847e11			−1.44748			−0.723738	+	0.690075i	$0.757578\pi$
$602$	6.18244e10	+	6.18244e10i	0.470732	+	0.470732i
$603$	−2.01291e10	+	2.01291e10i	−0.152249	+	0.152249i
$604$		−	4.76830e11i		−	3.58275i
$605$		0			0
$606$	1.65146e11			1.22455
$607$	−1.27801e11	−	1.27801e11i	−0.941413	−	0.941413i	0.0569634	−	0.998376i	$-0.481858\pi$
$607$	−1.27801e11	−	1.27801e11i	−0.941413	−	0.941413i	−0.998376	+	0.0569634i	$0.981858\pi$
$608$	−1.84113e10	+	1.84113e10i	−0.134732	+	0.134732i
$609$			4.97198e10i			0.361460i
$610$		0			0
$611$	−6.45382e10			−0.463075
$612$	−9.10191e10	−	9.10191e10i	−0.648824	−	0.648824i
$613$	−1.44086e11	+	1.44086e11i	−1.02042	+	1.02042i	−0.0206369	+	0.999787i	$0.506569\pi$
$613$	−1.44086e11	+	1.44086e11i	−1.02042	+	1.02042i	−0.999787	+	0.0206369i	$0.993431\pi$
$614$		−	1.25902e11i		−	0.885851i
$615$		0			0
$616$	−2.71875e11			−1.88819
$617$	−1.11558e11	−	1.11558e11i	−0.769771	−	0.769771i	0.208295	−	0.978066i	$-0.433209\pi$
$617$	−1.11558e11	−	1.11558e11i	−0.769771	−	0.769771i	−0.978066	+	0.208295i	$0.933209\pi$
$618$	1.05692e11	−	1.05692e11i	0.724586	−	0.724586i
$619$			2.54678e11i			1.73472i	0.497685	+	0.867358i	$0.334184\pi$
$619$			2.54678e11i			1.73472i	−0.497685	+	0.867358i	$0.665816\pi$
$620$		0			0
$621$	2.96595e10			0.199433
$622$	−1.50978e11	−	1.50978e11i	−1.00868	−	1.00868i
$623$	1.02742e10	−	1.02742e10i	0.0682019	−	0.0682019i
$624$			8.66431e10i			0.571473i
$625$		0			0
$626$	−4.35692e11			−2.83715
$627$	−6.88110e10	−	6.88110e10i	−0.445233	−	0.445233i
$628$	4.31749e10	−	4.31749e10i	0.277583	−	0.277583i
$629$		−	3.59237e11i		−	2.29498i
$630$		0			0
$631$	−1.40092e11			−0.883684			−0.441842	−	0.897093i	$-0.645675\pi$
$631$	−1.40092e11			−0.883684			−0.441842	+	0.897093i	$0.645675\pi$
$632$	1.10477e11	+	1.10477e11i	0.692472	+	0.692472i
$633$	1.11005e10	−	1.11005e10i	0.0691399	−	0.0691399i
$634$		−	8.27776e10i		−	0.512337i
$635$		0			0
$636$	−3.49474e11			−2.13592
$637$	2.72762e10	+	2.72762e10i	0.165663	+	0.165663i
$638$	−1.22450e11	+	1.22450e11i	−0.739057	+	0.739057i
$639$		−	1.28566e10i		−	0.0771120i
$640$		0			0
$641$	1.53604e11			0.909849			0.454924	−	0.890530i	$-0.349666\pi$
$641$	1.53604e11			0.909849			0.454924	+	0.890530i	$0.349666\pi$
$642$	−4.35159e10	−	4.35159e10i	−0.256158	−	0.256158i
$643$	−1.24980e11	+	1.24980e11i	−0.731132	+	0.731132i	−0.970844	−	0.239712i	$-0.922947\pi$
$643$	−1.24980e11	+	1.24980e11i	−0.731132	+	0.731132i	0.239712	+	0.970844i	$0.422947\pi$
$644$			3.79287e11i			2.20508i
$645$		0			0
$646$	4.33322e11			2.48818
$647$	2.71251e10	+	2.71251e10i	0.154794	+	0.154794i	0.780255	−	0.625461i	$-0.215089\pi$
$647$	2.71251e10	+	2.71251e10i	0.154794	+	0.154794i	−0.625461	+	0.780255i	$0.715089\pi$
$648$	−2.24444e10	+	2.24444e10i	−0.127294	+	0.127294i
$649$			9.68239e10i			0.545763i
$650$		0			0
$651$	7.99821e10			0.445317
$652$	2.30087e11	+	2.30087e11i	1.27322	+	1.27322i
$653$	2.28093e11	−	2.28093e11i	1.25447	−	1.25447i	0.300774	−	0.953695i	$-0.402755\pi$
$653$	2.28093e11	−	2.28093e11i	1.25447	−	1.25447i	0.953695	−	0.300774i	$-0.0972451\pi$
$654$			2.38813e10i			0.130541i
$655$		0			0
$656$	4.91194e10			0.265239
$657$	−4.34191e10	−	4.34191e10i	−0.233034	−	0.233034i
$658$	9.73367e10	−	9.73367e10i	0.519246	−	0.519246i
$659$		−	2.82926e11i		−	1.50014i	−0.661359	−	0.750069i	$-0.730020\pi$
$659$		−	2.82926e11i		−	1.50014i	0.661359	−	0.750069i	$-0.269980\pi$
$660$		0			0
$661$	−2.72919e11			−1.42964			−0.714821	−	0.699308i	$-0.753492\pi$
$661$	−2.72919e11			−1.42964			−0.714821	+	0.699308i	$0.753492\pi$
$662$	3.36100e11	+	3.36100e11i	1.74999	+	1.74999i
$663$	−1.32264e11	+	1.32264e11i	−0.684521	+	0.684521i
$664$			1.42899e11i			0.735117i
$665$		0			0
$666$	−1.82400e11			−0.927104
$667$	8.29642e10	+	8.29642e10i	0.419167	+	0.419167i
$668$	−3.25451e11	+	3.25451e11i	−1.63448	+	1.63448i
$669$		−	1.47681e11i		−	0.737259i
$670$		0			0
$671$	7.69585e10			0.379635
$672$	1.69514e10	+	1.69514e10i	0.0831242	+	0.0831242i
$673$	−3.97815e9	+	3.97815e9i	−0.0193919	+	0.0193919i	−0.716736	−	0.697344i	$-0.754365\pi$
$673$	−3.97815e9	+	3.97815e9i	−0.0193919	+	0.0193919i	0.697344	+	0.716736i	$0.254365\pi$
$674$			6.44418e11i			3.12268i
$675$		0			0
$676$	1.63409e11			0.782508
$677$	−7.72261e10	−	7.72261e10i	−0.367629	−	0.367629i	0.498983	−	0.866612i	$-0.333707\pi$
$677$	−7.72261e10	−	7.72261e10i	−0.367629	−	0.367629i	−0.866612	+	0.498983i	$0.833707\pi$
$678$	2.43724e11	−	2.43724e11i	1.15340	−	1.15340i
$679$			1.09816e11i			0.516638i
$680$		0			0
$681$	7.36343e10			0.342367
$682$	1.96981e11	+	1.96981e11i	0.910513	+	0.910513i
$683$	−7.08930e10	+	7.08930e10i	−0.325777	+	0.325777i	−0.850978	−	0.525201i	$-0.823990\pi$
$683$	−7.08930e10	+	7.08930e10i	−0.325777	+	0.325777i	0.525201	+	0.850978i	$0.323990\pi$
$684$		−	1.45289e11i		−	0.663754i
$685$		0			0
$686$	3.33616e11			1.50643
$687$	2.09613e9	+	2.09613e9i	0.00941006	+	0.00941006i
$688$	−4.69410e10	+	4.69410e10i	−0.209507	+	0.209507i
$689$			5.07835e11i			2.25344i
$690$		0			0
$691$	1.37022e11			0.601005			0.300502	−	0.953781i	$-0.402846\pi$
$691$	1.37022e11			0.601005			0.300502	+	0.953781i	$0.402846\pi$
$692$	−1.48214e11	−	1.48214e11i	−0.646346	−	0.646346i
$693$	−6.33545e10	+	6.33545e10i	−0.274691	+	0.274691i
$694$			2.62718e11i			1.13254i
$695$		0			0
$696$	−1.25564e11			−0.535092
$697$	7.49826e10	+	7.49826e10i	0.317709	+	0.317709i
$698$	−3.50713e11	+	3.50713e11i	−1.47751	+	1.47751i
$699$			3.65359e10i			0.153042i
$700$		0			0
$701$	−2.41861e11			−1.00160			−0.500800	−	0.865563i	$-0.666961\pi$
$701$	−2.41861e11			−1.00160			−0.500800	+	0.865563i	$0.666961\pi$
$702$	6.71561e10	+	6.71561e10i	0.276527	+	0.276527i
$703$	2.86715e11	−	2.86715e11i	1.17389	−	1.17389i
$704$			3.02112e11i			1.22992i
$705$		0			0
$706$	3.43968e11			1.38452
$707$	2.39007e11	+	2.39007e11i	0.956607	+	0.956607i
$708$	−1.02218e11	+	1.02218e11i	−0.406812	+	0.406812i
$709$		−	4.24635e11i		−	1.68047i	−0.542222	−	0.840235i	$-0.682417\pi$
$709$		−	4.24635e11i		−	1.68047i	0.542222	−	0.840235i	$-0.317583\pi$
$710$		0			0
$711$	5.14883e10			0.201479
$712$	2.59468e10	+	2.59468e10i	0.100964	+	0.100964i
$713$	1.33461e11	−	1.33461e11i	0.516411	−	0.516411i
$714$		−	3.98961e11i		−	1.53510i
$715$		0			0
$716$	9.45823e10			0.359880
$717$	3.62307e10	+	3.62307e10i	0.137088	+	0.137088i
$718$	−2.48776e10	+	2.48776e10i	−0.0936076	+	0.0936076i
$719$		−	3.42762e11i		−	1.28256i	−0.767307	−	0.641280i	$-0.778404\pi$
$719$		−	3.42762e11i		−	1.28256i	0.767307	−	0.641280i	$-0.221596\pi$
$720$		0			0
$721$	3.05927e11			1.13208
$722$	1.61434e10	+	1.61434e10i	0.0594081	+	0.0594081i
$723$	6.99255e10	−	6.99255e10i	0.255907	−	0.255907i
$724$			3.67418e11i			1.33723i
$725$		0			0
$726$	−3.68450e10			−0.132627
$727$	3.21958e11	+	3.21958e11i	1.15256	+	1.15256i	0.986039	+	0.166517i	$0.0532521\pi$
$727$	3.21958e11	+	3.21958e11i	1.15256	+	1.15256i	0.166517	+	0.986039i	$0.446748\pi$
$728$	−4.17082e11	+	4.17082e11i	−1.48490	+	1.48490i
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	−1.43314e11			−0.501903
$732$	8.12458e10	+	8.12458e10i	0.282981	+	0.282981i
$733$	1.89946e11	−	1.89946e11i	0.657984	−	0.657984i	−0.296919	−	0.954903i	$-0.595959\pi$
$733$	1.89946e11	−	1.89946e11i	0.657984	−	0.657984i	0.954903	+	0.296919i	$0.0959591\pi$
$734$		−	6.04274e11i		−	2.08185i
$735$		0			0
$736$	5.65712e10			0.192790
$737$	−1.43492e11	−	1.43492e11i	−0.486361	−	0.486361i
$738$	3.80719e10	−	3.80719e10i	0.128345	−	0.128345i
$739$		−	7.07724e10i		−	0.237294i	−0.992937	−	0.118647i	$-0.962144\pi$
$739$		−	7.07724e10i		−	0.237294i	0.992937	−	0.118647i	$-0.0378556\pi$
$740$		0			0
$741$	−2.11125e11			−0.700273
$742$	−7.65918e11	−	7.65918e11i	−2.52678	−	2.52678i
$743$	−2.21433e11	+	2.21433e11i	−0.726585	+	0.726585i	−0.969938	−	0.243353i	$-0.921753\pi$
$743$	−2.21433e11	+	2.21433e11i	−0.726585	+	0.726585i	0.243353	+	0.969938i	$0.421753\pi$
$744$			2.01989e11i			0.659230i
$745$		0			0
$746$	−8.54801e11			−2.76000
$747$	3.32994e10	+	3.32994e10i	0.106944	+	0.106944i
$748$	6.48840e11	−	6.48840e11i	2.07267	−	2.07267i
$749$		−	1.25957e11i		−	0.400217i
$750$		0			0
$751$	1.25419e10			0.0394278			0.0197139	−	0.999806i	$-0.493724\pi$
$751$	1.25419e10			0.0394278			0.0197139	+	0.999806i	$0.493724\pi$
$752$	7.39041e10	+	7.39041e10i	0.231099	+	0.231099i
$753$	−1.19837e11	+	1.19837e11i	−0.372744	+	0.372744i
$754$			3.75701e11i			1.16240i
$755$		0			0
$756$	−1.33768e11			−0.409510
$757$	−1.00768e10	−	1.00768e10i	−0.0306859	−	0.0306859i	0.691597	−	0.722283i	$-0.256907\pi$
$757$	−1.00768e10	−	1.00768e10i	−0.0306859	−	0.0306859i	−0.722283	+	0.691597i	$0.756907\pi$
$758$	2.37115e11	−	2.37115e11i	0.718260	−	0.718260i
$759$			2.11431e11i			0.637090i
$760$		0			0
$761$	8.03716e10			0.239643			0.119821	−	0.992795i	$-0.461768\pi$
$761$	8.03716e10			0.239643			0.119821	+	0.992795i	$0.461768\pi$
$762$	−1.88065e11	−	1.88065e11i	−0.557812	−	0.557812i
$763$	−3.45623e10	+	3.45623e10i	−0.101978	+	0.101978i
$764$		−	8.85610e10i		−	0.259938i
$765$		0			0
$766$	−1.17479e12			−3.41228
$767$	1.48537e11	+	1.48537e11i	0.429194	+	0.429194i
$768$	−2.73604e11	+	2.73604e11i	−0.786463	+	0.786463i
$769$		−	3.00714e9i		−	0.00859900i	−0.999991	−	0.00429950i	$-0.998631\pi$
$769$		−	3.00714e9i		−	0.00859900i	0.999991	−	0.00429950i	$-0.00136858\pi$
$770$		0			0
$771$	2.14616e11			0.607356
$772$	1.58451e10	+	1.58451e10i	0.0446093	+	0.0446093i
$773$	6.41083e10	−	6.41083e10i	0.179554	−	0.179554i	−0.611607	−	0.791162i	$-0.709477\pi$
$773$	6.41083e10	−	6.41083e10i	0.179554	−	0.179554i	0.791162	+	0.611607i	$0.209477\pi$
$774$			7.27669e10i			0.202754i
$775$		0			0
$776$	−2.77333e11			−0.764811
$777$	−2.63979e11	−	2.63979e11i	−0.724245	−	0.724245i
$778$	−5.11427e11	+	5.11427e11i	−1.39593	+	1.39593i
$779$			1.19690e11i			0.325020i
$780$		0			0
$781$	9.16495e10			0.246335
$782$	−6.65720e11	−	6.65720e11i	−1.78018	−	1.78018i
$783$	−2.92600e10	+	2.92600e10i	−0.0778443	+	0.0778443i
$784$		−	6.24691e10i		−	0.165349i
$785$		0			0
$786$	2.31495e11			0.606528
$787$	−1.47340e11	−	1.47340e11i	−0.384081	−	0.384081i	0.488489	−	0.872570i	$-0.337548\pi$
$787$	−1.47340e11	−	1.47340e11i	−0.384081	−	0.384081i	−0.872570	+	0.488489i	$0.837548\pi$
$788$	5.26979e11	−	5.26979e11i	1.36675	−	1.36675i
$789$		−	2.98295e11i		−	0.769729i
$790$		0			0
$791$	7.05459e11			1.80205
$792$	−1.59997e11	−	1.59997e11i	−0.406642	−	0.406642i
$793$	1.18062e11	−	1.18062e11i	0.298550	−	0.298550i
$794$		−	8.71365e11i		−	2.19239i
$795$		0			0
$796$	9.47177e11			2.35928
$797$	1.91789e11	+	1.91789e11i	0.475324	+	0.475324i	0.903632	−	0.428309i	$-0.140890\pi$
$797$	1.91789e11	+	1.91789e11i	0.475324	+	0.475324i	−0.428309	+	0.903632i	$0.640890\pi$
$798$	3.18420e11	−	3.18420e11i	0.785215	−	0.785215i
$799$			2.25635e11i			0.553629i
$800$		0			0
$801$	1.20927e10			0.0293760
$802$	−5.33668e10	−	5.33668e10i	−0.128995	−	0.128995i
$803$	3.09518e11	−	3.09518e11i	0.744429	−	0.744429i
$804$		−	3.02972e11i		−	0.725068i
$805$		0			0
$806$	6.04374e11			1.43208
$807$	9.17816e10	+	9.17816e10i	0.216402	+	0.216402i
$808$	−6.03597e11	+	6.03597e11i	−1.41613	+	1.41613i
$809$		−	5.13179e11i		−	1.19805i	−0.800731	−	0.599024i	$-0.795555\pi$
$809$		−	5.13179e11i		−	1.19805i	0.800731	−	0.599024i	$-0.204445\pi$
$810$		0			0
$811$	−3.20859e11			−0.741705			−0.370853	−	0.928692i	$-0.620935\pi$
$811$	−3.20859e11			−0.741705			−0.370853	+	0.928692i	$0.620935\pi$
$812$	−3.74178e11	−	3.74178e11i	−0.860706	−	0.860706i
$813$	3.37177e11	−	3.37177e11i	0.771784	−	0.771784i
$814$		−	1.30026e12i		−	2.96164i
$815$		0			0
$816$	3.02917e11			0.683223
$817$	−1.14382e11	−	1.14382e11i	−0.256726	−	0.256726i
$818$	6.04504e11	−	6.04504e11i	1.35016	−	1.35016i
$819$			1.94384e11i			0.432040i
$820$		0			0
$821$	3.45545e11			0.760557			0.380278	−	0.924872i	$-0.375828\pi$
$821$	3.45545e11			0.760557			0.380278	+	0.924872i	$0.375828\pi$
$822$	3.60034e11	+	3.60034e11i	0.788599	+	0.788599i
$823$	−3.43395e11	+	3.43395e11i	−0.748504	+	0.748504i	−0.974198	−	0.225694i	$-0.927535\pi$
$823$	−3.43395e11	+	3.43395e11i	−0.748504	+	0.748504i	0.225694	+	0.974198i	$0.427535\pi$
$824$			7.72598e11i			1.67589i
$825$		0			0
$826$	−4.48048e11			−0.962509
$827$	3.01083e11	+	3.01083e11i	0.643671	+	0.643671i	0.951456	−	0.307785i	$-0.0995876\pi$
$827$	3.01083e11	+	3.01083e11i	0.643671	+	0.643671i	−0.307785	+	0.951456i	$0.599588\pi$
$828$	−2.23209e11	+	2.23209e11i	−0.474888	+	0.474888i
$829$		−	2.61321e11i		−	0.553293i	−0.960972	−	0.276647i	$-0.910777\pi$
$829$		−	2.61321e11i		−	0.553293i	0.960972	−	0.276647i	$-0.0892232\pi$
$830$		0			0
$831$	−4.54784e11			−0.953677
$832$	4.63469e11	+	4.63469e11i	0.967224	+	0.967224i
$833$	9.53614e10	−	9.53614e10i	0.198058	−	0.198058i
$834$			5.17480e11i			1.06962i
$835$		0			0
$836$	1.03571e12			2.12037
$837$	4.70692e10	+	4.70692e10i	0.0959036	+	0.0959036i
$838$	−3.18300e10	+	3.18300e10i	−0.0645446	+	0.0645446i
$839$			6.06418e11i			1.22384i	0.790920	+	0.611920i	$0.209603\pi$
$839$			6.06418e11i			1.22384i	−0.790920	+	0.611920i	$0.790397\pi$
$840$		0			0
$841$	3.36553e11			0.672775
$842$	4.92789e10	+	4.92789e10i	0.0980421	+	0.0980421i
$843$	−4.48636e10	+	4.48636e10i	−0.0888349	+	0.0888349i
$844$			1.67079e11i			0.329270i
$845$		0			0
$846$	1.14565e11			0.223650
$847$	−5.33240e10	−	5.33240e10i	−0.103607	−	0.103607i
$848$	5.81534e11	−	5.81534e11i	1.12458	−	1.12458i
$849$			3.95544e11i			0.761315i
$850$		0			0
$851$	−8.80969e11			−1.67974
$852$	9.67552e10	+	9.67552e10i	0.183618	+	0.183618i
$853$	−1.46578e11	+	1.46578e11i	−0.276867	+	0.276867i	−0.831857	−	0.554990i	$-0.812722\pi$
$853$	−1.46578e11	+	1.46578e11i	−0.276867	+	0.276867i	0.554990	+	0.831857i	$0.312722\pi$
$854$			3.56122e11i			0.669526i
$855$		0			0
$856$	3.18096e11			0.592466
$857$	−1.16498e11	−	1.16498e11i	−0.215971	−	0.215971i	0.590827	−	0.806798i	$-0.298801\pi$
$857$	−1.16498e11	−	1.16498e11i	−0.215971	−	0.215971i	−0.806798	+	0.590827i	$0.798801\pi$
$858$	−4.78730e11	+	4.78730e11i	−0.883367	+	0.883367i
$859$			7.72382e10i			0.141860i	0.997481	+	0.0709299i	$0.0225967\pi$
$859$			7.72382e10i			0.141860i	−0.997481	+	0.0709299i	$0.977403\pi$
$860$		0			0
$861$	1.10199e11			0.200524
$862$	9.14553e10	+	9.14553e10i	0.165646	+	0.165646i
$863$	−3.72535e10	+	3.72535e10i	−0.0671620	+	0.0671620i	−0.739890	−	0.672728i	$-0.765122\pi$
$863$	−3.72535e10	+	3.72535e10i	−0.0671620	+	0.0671620i	0.672728	+	0.739890i	$0.265122\pi$
$864$			1.99516e10i			0.0358033i
$865$		0			0
$866$	−1.12890e12			−2.00717
$867$	2.31738e11	+	2.31738e11i	0.410129	+	0.410129i
$868$	−6.01924e11	+	6.01924e11i	−1.06038	+	1.06038i
$869$			3.67040e11i			0.643628i
$870$		0			0
$871$	−4.40262e11			−0.764960
$872$	−8.72848e10	−	8.72848e10i	−0.150964	−	0.150964i
$873$	−6.46263e10	+	6.46263e10i	−0.111263	+	0.111263i
$874$		−	1.06265e12i		−	1.82115i
$875$		0			0
$876$	6.53521e11			1.10980
$877$	−8.93631e10	−	8.93631e10i	−0.151064	−	0.151064i	0.627529	−	0.778593i	$-0.284066\pi$
$877$	−8.93631e10	−	8.93631e10i	−0.151064	−	0.151064i	−0.778593	+	0.627529i	$0.784066\pi$
$878$	−1.08069e12	+	1.08069e12i	−1.81853	+	1.81853i
$879$			6.52661e10i			0.109328i
$880$		0			0
$881$	5.86329e11			0.973280			0.486640	−	0.873603i	$-0.338222\pi$
$881$	5.86329e11			0.973280			0.486640	+	0.873603i	$0.338222\pi$
$882$	−4.84192e10	−	4.84192e10i	−0.0800098	−	0.0800098i
$883$	6.96886e11	−	6.96886e11i	1.14635	−	1.14635i	0.159090	−	0.987264i	$-0.449144\pi$
$883$	6.96886e11	−	6.96886e11i	1.14635	−	1.14635i	0.987264	−	0.159090i	$-0.0508562\pi$
$884$		−	1.99076e12i		−	3.25995i
$885$		0			0
$886$	−1.80780e12			−2.93370
$887$	−2.84383e11	−	2.84383e11i	−0.459419	−	0.459419i	0.439046	−	0.898465i	$-0.355317\pi$
$887$	−2.84383e11	−	2.84383e11i	−0.459419	−	0.459419i	−0.898465	+	0.439046i	$0.855317\pi$
$888$	6.66662e11	−	6.66662e11i	1.07215	−	1.07215i
$889$		−	5.44355e11i		−	0.871515i
$890$		0			0
$891$	−7.45678e10			−0.118315
$892$	1.11141e12	+	1.11141e12i	1.75555	+	1.75555i
$893$	−1.80084e11	+	1.80084e11i	−0.283184	+	0.283184i
$894$			6.93125e11i			1.08508i
$895$		0			0
$896$	−1.26678e12			−1.96548
$897$	3.24355e11	+	3.24355e11i	0.501015	+	0.501015i
$898$	−1.41454e11	+	1.41454e11i	−0.217525	+	0.217525i
$899$			2.63326e11i			0.403140i
$900$		0			0
$901$	1.77546e12			2.69409
$902$	2.71400e11	+	2.71400e11i	0.410000	+	0.410000i
$903$	−1.05312e11	+	1.05312e11i	−0.158390	+	0.158390i
$904$			1.78159e12i			2.66768i
$905$		0			0
$906$	1.23000e12			1.82555
$907$	−8.58443e11	−	8.58443e11i	−1.26848	−	1.26848i	−0.946876	−	0.321600i	$-0.895779\pi$
$907$	−8.58443e11	−	8.58443e11i	−1.26848	−	1.26848i	−0.321600	−	0.946876i	$-0.604221\pi$
$908$	−5.54153e11	+	5.54153e11i	−0.815241	+	0.815241i
$909$			2.81310e11i			0.412031i
$910$		0			0
$911$	4.32381e11			0.627759			0.313879	−	0.949463i	$-0.398371\pi$
$911$	4.32381e11			0.627759			0.313879	+	0.949463i	$0.398371\pi$
$912$	2.41764e11	+	2.41764e11i	0.349472	+	0.349472i
$913$	−2.37379e11	+	2.37379e11i	−0.341632	+	0.341632i
$914$			1.05937e12i			1.51797i
$915$		0			0
$916$	−3.15499e10			−0.0448143
$917$	3.35031e11	+	3.35031e11i	0.473814	+	0.473814i
$918$	2.34787e11	−	2.34787e11i	0.330601	−	0.330601i
$919$			9.19895e11i			1.28966i	0.764325	+	0.644831i	$0.223072\pi$
$919$			9.19895e11i			1.28966i	−0.764325	+	0.644831i	$0.776928\pi$
$920$		0			0
$921$	2.14463e11			0.298067
$922$	−7.81172e11	−	7.81172e11i	−1.08099	−	1.08099i
$923$	1.40599e11	−	1.40599e11i	0.193721	−	0.193721i
$924$		−	9.53578e11i		−	1.30818i
$925$		0			0
$926$	4.71182e10			0.0640832
$927$	1.80037e11	+	1.80037e11i	0.243805	+	0.243805i
$928$	−5.58092e10	+	5.58092e10i	−0.0752513	+	0.0752513i
$929$			4.57755e11i			0.614569i	0.951618	+	0.307284i	$0.0994203\pi$
$929$			4.57755e11i			0.614569i	−0.951618	+	0.307284i	$0.900580\pi$
$930$		0			0
$931$	1.52220e11			0.202616
$932$	−2.74960e11	−	2.74960e11i	−0.364423	−	0.364423i
$933$	2.57177e11	−	2.57177e11i	0.339395	−	0.339395i
$934$			7.71491e11i			1.01378i
$935$		0			0
$936$	−4.90903e11			−0.639576
$937$	−4.63343e11	−	4.63343e11i	−0.601096	−	0.601096i	0.339507	−	0.940603i	$-0.389740\pi$
$937$	−4.63343e11	−	4.63343e11i	−0.601096	−	0.601096i	−0.940603	+	0.339507i	$0.889740\pi$
$938$	6.64005e11	−	6.64005e11i	0.857748	−	0.857748i
$939$		−	7.42160e11i		−	0.954630i
$940$		0			0
$941$	−5.73573e11			−0.731527			−0.365764	−	0.930708i	$-0.619192\pi$
$941$	−5.73573e11			−0.731527			−0.365764	+	0.930708i	$0.619192\pi$
$942$	1.11371e11	+	1.11371e11i	0.141439	+	0.141439i
$943$	1.83882e11	−	1.83882e11i	0.232538	−	0.232538i
$944$		−	3.40187e11i		−	0.428380i
$945$		0			0
$946$	−5.18727e11			−0.647700
$947$	3.66272e10	+	3.66272e10i	0.0455411	+	0.0455411i	0.729511	−	0.683970i	$-0.239748\pi$
$947$	3.66272e10	+	3.66272e10i	0.0455411	+	0.0455411i	−0.683970	+	0.729511i	$0.739748\pi$
$948$	−3.87488e11	+	3.87488e11i	−0.479761	+	0.479761i
$949$		−	9.49659e11i		−	1.17085i
$950$		0			0
$951$	1.41004e11			0.172389
$952$	1.45818e12	+	1.45818e12i	1.77526	+	1.77526i
$953$	−5.81775e11	+	5.81775e11i	−0.705315	+	0.705315i	−0.965546	−	0.260231i	$-0.916201\pi$
$953$	−5.81775e11	+	5.81775e11i	−0.705315	+	0.705315i	0.260231	+	0.965546i	$0.416201\pi$
$954$		−	9.01481e11i		−	1.08834i
$955$		0			0
$956$	−5.45325e11			−0.652866
$957$	−2.08583e11	−	2.08583e11i	−0.248674	−	0.248674i
$958$	8.84067e11	−	8.84067e11i	1.04960	−	1.04960i
$959$			1.04212e12i			1.23209i
$960$		0			0
$961$	−4.29290e11			−0.503335
$962$	−1.99472e12	−	1.99472e12i	−2.32907	−	2.32907i
$963$	7.41253e10	−	7.41253e10i	0.0861909	−	0.0861909i
$964$			1.05248e12i			1.21873i
$965$		0			0
$966$	−9.78386e11			−1.12357
$967$	7.69761e11	+	7.69761e11i	0.880339	+	0.880339i	0.993569	−	0.113230i	$-0.0361198\pi$
$967$	7.69761e11	+	7.69761e11i	0.880339	+	0.880339i	−0.113230	+	0.993569i	$0.536120\pi$
$968$	1.34666e11	−	1.34666e11i	0.153376	−	0.153376i
$969$			7.38124e11i			0.837210i
$970$		0			0
$971$	−1.16975e12			−1.31588			−0.657941	−	0.753069i	$-0.728573\pi$
$971$	−1.16975e12			−1.31588			−0.657941	+	0.753069i	$0.728573\pi$
$972$	−7.87219e10	−	7.87219e10i	−0.0881922	−	0.0881922i
$973$	−7.48924e11	+	7.48924e11i	−0.835577	+	0.835577i
$974$		−	6.26316e11i		−	0.695917i
$975$		0			0
$976$	−2.70390e11			−0.297983
$977$	−8.48622e11	−	8.48622e11i	−0.931400	−	0.931400i	0.0663937	−	0.997794i	$-0.478851\pi$
$977$	−8.48622e11	−	8.48622e11i	−0.931400	−	0.931400i	−0.997794	+	0.0663937i	$0.978851\pi$
$978$	−5.93519e11	+	5.93519e11i	−0.648753	+	0.648753i
$979$			8.62041e10i			0.0938419i
$980$		0			0
$981$	−4.06796e10			−0.0439239
$982$	1.70974e12	+	1.70974e12i	1.83858	+	1.83858i
$983$	−2.24999e10	+	2.24999e10i	−0.0240972	+	0.0240972i	−0.719053	−	0.694956i	$-0.755424\pi$
$983$	−2.24999e10	+	2.24999e10i	−0.0240972	+	0.0240972i	0.694956	+	0.719053i	$0.255424\pi$
$984$			2.78301e11i			0.296848i
$985$		0			0
$986$	1.31351e12			1.38971
$987$	1.65804e11	+	1.65804e11i	0.174713	+	0.174713i
$988$	1.58887e12	−	1.58887e12i	1.66748	−	1.66748i
$989$			3.51454e11i			0.367353i
$990$		0			0
$991$	1.33051e11			0.137951			0.0689754	−	0.997618i	$-0.478027\pi$
$991$	1.33051e11			0.137951			0.0689754	+	0.997618i	$0.478027\pi$
$992$	8.97778e10	+	8.97778e10i	0.0927091	+	0.0927091i
$993$	−5.72515e11	+	5.72515e11i	−0.588830	+	0.588830i
$994$			4.24104e11i			0.434437i
$995$		0			0
$996$	−5.01206e11			−0.509306
$997$	−1.33967e12	−	1.33967e12i	−1.35587	−	1.35587i	−0.878942	−	0.476928i	$-0.841750\pi$
$997$	−1.33967e12	−	1.33967e12i	−1.35587	−	1.35587i	−0.476928	−	0.878942i	$-0.658250\pi$
$998$	1.78977e12	−	1.78977e12i	1.80416	−	1.80416i
$999$		−	3.10702e11i		−	0.311948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.e.7.1		16
5.2	odd	4		15.9.f.a.13.8	yes	16
5.3	odd	4	inner	75.9.f.e.43.1		16
5.4	even	2		15.9.f.a.7.8	✓	16
15.2	even	4		45.9.g.c.28.1		16
15.14	odd	2		45.9.g.c.37.1		16
20.7	even	4		240.9.bg.d.193.5		16
20.19	odd	2		240.9.bg.d.97.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.f.a.7.8	✓	16	5.4	even	2
15.9.f.a.13.8	yes	16	5.2	odd	4
45.9.g.c.28.1		16	15.2	even	4
45.9.g.c.37.1		16	15.14	odd	2
75.9.f.e.7.1		16	1.1	even	1	trivial
75.9.f.e.43.1		16	5.3	odd	4	inner
240.9.bg.d.97.5		16	20.19	odd	2
240.9.bg.d.193.5		16	20.7	even	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-19.4129 - 19.4129i) q^{2} +(33.0681 - 33.0681i) q^{3} +497.724i q^{4} -1283.90 q^{6} +(-1858.12 - 1858.12i) q^{7} +(4692.57 - 4692.57i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(-19.4129 - 19.4129i) q^{2} +(33.0681 - 33.0681i) q^{3} +497.724i q^{4} -1283.90 q^{6} +(-1858.12 - 1858.12i) q^{7} +(4692.57 - 4692.57i) q^{8} -2187.00i q^{9} +15590.3 q^{11} +(16458.8 + 16458.8i) q^{12} +(23917.0 - 23917.0i) q^{13} +72143.3i q^{14} -54775.7 q^{16} +(-83617.2 - 83617.2i) q^{17} +(-42456.1 + 42456.1i) q^{18} -133473. i q^{19} -122889. q^{21} +(-302653. - 302653. i) q^{22} +(-205057. + 205057. i) q^{23} -310349. i q^{24} -928597. q^{26} +(-72320.0 - 72320.0i) q^{27} +(924833. - 924833. i) q^{28} -404590. i q^{29} -650847. q^{31} +(-137940. - 137940. i) q^{32} +(515541. - 515541. i) q^{33} +3.24651e6i q^{34} +1.08852e6 q^{36} +(2.14811e6 + 2.14811e6i) q^{37} +(-2.59111e6 + 2.59111e6i) q^{38} -1.58178e6i q^{39} -896737. q^{41} +(2.38564e6 + 2.38564e6i) q^{42} +(856967. - 856967. i) q^{43} +7.75965e6i q^{44} +7.96152e6 q^{46} +(-1.34921e6 - 1.34921e6i) q^{47} +(-1.81133e6 + 1.81133e6i) q^{48} +1.14045e6i q^{49} -5.53012e6 q^{51} +(1.19040e7 + 1.19040e7i) q^{52} +(-1.06166e7 + 1.06166e7i) q^{53} +2.80788e6i q^{54} -1.74388e7 q^{56} +(-4.41371e6 - 4.41371e6i) q^{57} +(-7.85428e6 + 7.85428e6i) q^{58} +6.21053e6i q^{59} +4.93632e6 q^{61} +(1.26348e7 + 1.26348e7i) q^{62} +(-4.06372e6 + 4.06372e6i) q^{63} +1.93782e7i q^{64} -2.00163e7 q^{66} +(-9.20397e6 - 9.20397e6i) q^{67} +(4.16183e7 - 4.16183e7i) q^{68} +1.35617e7i q^{69} +5.87863e6 q^{71} +(-1.02626e7 - 1.02626e7i) q^{72} +(1.98532e7 - 1.98532e7i) q^{73} -8.34021e7i q^{74} +6.64329e7 q^{76} +(-2.89687e7 - 2.89687e7i) q^{77} +(-3.07069e7 + 3.07069e7i) q^{78} +2.35429e7i q^{79} -4.78297e6 q^{81} +(1.74083e7 + 1.74083e7i) q^{82} +(-1.52261e7 + 1.52261e7i) q^{83} -6.11650e7i q^{84} -3.32725e7 q^{86} +(-1.33790e7 - 1.33790e7i) q^{87} +(7.31584e7 - 7.31584e7i) q^{88} +5.52935e6i q^{89} -8.88814e7 q^{91} +(-1.02062e8 - 1.02062e8i) q^{92} +(-2.15223e7 + 2.15223e7i) q^{93} +5.23844e7i q^{94} -9.12283e6 q^{96} +(-2.95502e7 - 2.95502e7i) q^{97} +(2.21395e7 - 2.21395e7i) q^{98} -3.40959e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8	\( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8} - 23616 q^{11} - 22680 q^{12} - 133420 q^{13} - 471380 q^{16} - 573300 q^{17} + 163944 q^{21} + 234700 q^{22} - 651480 q^{23} - 448848 q^{26} + 3567940 q^{28} + 1311776 q^{31} - 641460 q^{32} + 3815100 q^{33} + 5519988 q^{36} + 3607340 q^{37} - 8139840 q^{38} - 14740104 q^{41} + 9643860 q^{42} + 4805480 q^{43} + 14024216 q^{46} - 26529600 q^{47} - 3661200 q^{48} - 6168312 q^{51} + 15861080 q^{52} - 16612140 q^{53} + 10752000 q^{56} - 4714200 q^{57} - 63562980 q^{58} - 12550600 q^{61} + 35190840 q^{62} - 9928980 q^{63} + 46958616 q^{66} - 46836760 q^{67} + 197811840 q^{68} - 85681968 q^{71} + 38185020 q^{72} + 50835800 q^{73} + 101166648 q^{76} - 97175880 q^{77} - 131709240 q^{78} - 76527504 q^{81} + 181542400 q^{82} + 208234800 q^{83} - 187512576 q^{86} + 74298060 q^{87} - 138207420 q^{88} + 38623856 q^{91} - 652331400 q^{92} - 159787080 q^{93} + 531512604 q^{96} + 138370520 q^{97} + 50186520 q^{98}+O(q^{100}) \) 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8 - 23616 * q^11 - 22680 * q^12 - 133420 * q^13 - 471380 * q^16 - 573300 * q^17 + 163944 * q^21 + 234700 * q^22 - 651480 * q^23 - 448848 * q^26 + 3567940 * q^28 + 1311776 * q^31 - 641460 * q^32 + 3815100 * q^33 + 5519988 * q^36 + 3607340 * q^37 - 8139840 * q^38 - 14740104 * q^41 + 9643860 * q^42 + 4805480 * q^43 + 14024216 * q^46 - 26529600 * q^47 - 3661200 * q^48 - 6168312 * q^51 + 15861080 * q^52 - 16612140 * q^53 + 10752000 * q^56 - 4714200 * q^57 - 63562980 * q^58 - 12550600 * q^61 + 35190840 * q^62 - 9928980 * q^63 + 46958616 * q^66 - 46836760 * q^67 + 197811840 * q^68 - 85681968 * q^71 + 38185020 * q^72 + 50835800 * q^73 + 101166648 * q^76 - 97175880 * q^77 - 131709240 * q^78 - 76527504 * q^81 + 181542400 * q^82 + 208234800 * q^83 - 187512576 * q^86 + 74298060 * q^87 - 138207420 * q^88 + 38623856 * q^91 - 652331400 * q^92 - 159787080 * q^93 + 531512604 * q^96 + 138370520 * q^97 + 50186520 * q^98

Introduction

L-functions

Modular forms

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