LMFDB - Embedded newform 75.9.f.e.7.8

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			7.8
Root			$-18.7966 - 18.7966i$ of defining polynomial
Character	$\chi$	$=$	75.7
Dual form			75.9.f.e.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(21.2461 + 21.2461i) q^{2} +(-33.0681 + 33.0681i) q^{3} +646.792i q^{4} -1405.14 q^{6} +(-1862.28 - 1862.28i) q^{7} +(-8302.80 + 8302.80i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(21.2461 + 21.2461i) q^{2} +(-33.0681 + 33.0681i) q^{3} +646.792i q^{4} -1405.14 q^{6} +(-1862.28 - 1862.28i) q^{7} +(-8302.80 + 8302.80i) q^{8} -2187.00i q^{9} -3926.69 q^{11} +(-21388.2 - 21388.2i) q^{12} +(3479.04 - 3479.04i) q^{13} -79132.5i q^{14} -187225. q^{16} +(-100058. - 100058. i) q^{17} +(46465.2 - 46465.2i) q^{18} +152908. i q^{19} +123164. q^{21} +(-83426.7 - 83426.7i) q^{22} +(76182.9 - 76182.9i) q^{23} -549116. i q^{24} +147832. q^{26} +(72320.0 + 72320.0i) q^{27} +(1.20451e6 - 1.20451e6i) q^{28} +935605. i q^{29} -273508. q^{31} +(-1.85228e6 - 1.85228e6i) q^{32} +(129848. - 129848. i) q^{33} -4.25168e6i q^{34} +1.41453e6 q^{36} +(-1.05800e6 - 1.05800e6i) q^{37} +(-3.24869e6 + 3.24869e6i) q^{38} +230091. i q^{39} -2.83041e6 q^{41} +(2.61676e6 + 2.61676e6i) q^{42} +(382541. - 382541. i) q^{43} -2.53975e6i q^{44} +3.23718e6 q^{46} +(2.79713e6 + 2.79713e6i) q^{47} +(6.19118e6 - 6.19118e6i) q^{48} +1.17140e6i q^{49} +6.61745e6 q^{51} +(2.25021e6 + 2.25021e6i) q^{52} +(1.27793e6 - 1.27793e6i) q^{53} +3.07303e6i q^{54} +3.09243e7 q^{56} +(-5.05637e6 - 5.05637e6i) q^{57} +(-1.98779e7 + 1.98779e7i) q^{58} +9.64312e6i q^{59} -8.78687e6 q^{61} +(-5.81097e6 - 5.81097e6i) q^{62} +(-4.07282e6 + 4.07282e6i) q^{63} -3.07779e7i q^{64} +5.51753e6 q^{66} +(-1.74595e7 - 1.74595e7i) q^{67} +(6.47166e7 - 6.47166e7i) q^{68} +5.03845e6i q^{69} -2.53806e7 q^{71} +(1.81582e7 + 1.81582e7i) q^{72} +(-3.10129e7 + 3.10129e7i) q^{73} -4.49568e7i q^{74} -9.88995e7 q^{76} +(7.31261e6 + 7.31261e6i) q^{77} +(-4.88852e6 + 4.88852e6i) q^{78} -3.27530e7i q^{79} -4.78297e6 q^{81} +(-6.01351e7 - 6.01351e7i) q^{82} +(-1.57518e7 + 1.57518e7i) q^{83} +7.96618e7i q^{84} +1.62550e7 q^{86} +(-3.09387e7 - 3.09387e7i) q^{87} +(3.26025e7 - 3.26025e7i) q^{88} +2.96432e7i q^{89} -1.29579e7 q^{91} +(4.92745e7 + 4.92745e7i) q^{92} +(9.04439e6 - 9.04439e6i) q^{93} +1.18856e8i q^{94} +1.22503e8 q^{96} +(7.80155e7 + 7.80155e7i) q^{97} +(-2.48877e7 + 2.48877e7i) q^{98} +8.58766e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	21.2461	+	21.2461i	1.32788	+	1.32788i	0.907217	+	0.420663i	$0.138203\pi$
$2$	21.2461	+	21.2461i	1.32788	+	1.32788i	0.420663	+	0.907217i	$0.361797\pi$
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$4$			646.792i			2.52653i
$5$		0			0
$5$		0			0
$6$	−1405.14			−1.08421
$7$	−1862.28	−	1862.28i	−0.775629	−	0.775629i	0.203456	−	0.979084i	$-0.434783\pi$
$7$	−1862.28	−	1862.28i	−0.775629	−	0.775629i	−0.979084	+	0.203456i	$0.934783\pi$
$8$	−8302.80	+	8302.80i	−2.02705	+	2.02705i
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	−3926.69			−0.268198			−0.134099	−	0.990968i	$-0.542814\pi$
$11$	−3926.69			−0.268198			−0.134099	+	0.990968i	$0.542814\pi$
$12$	−21388.2	−	21388.2i	−1.03145	−	1.03145i
$13$	3479.04	−	3479.04i	0.121811	−	0.121811i	−0.643573	−	0.765384i	$-0.722549\pi$
$13$	3479.04	−	3479.04i	0.121811	−	0.121811i	0.765384	+	0.643573i	$0.222549\pi$
$14$		−	79132.5i		−	2.05988i
$15$		0			0
$16$	−187225.			−2.85683
$17$	−100058.	−	100058.i	−1.19800	−	1.19800i	−0.974766	−	0.223231i	$-0.928340\pi$
$17$	−100058.	−	100058.i	−1.19800	−	1.19800i	−0.223231	−	0.974766i	$-0.571660\pi$
$18$	46465.2	−	46465.2i	0.442627	−	0.442627i
$19$			152908.i			1.17332i	0.809835	+	0.586658i	$0.199557\pi$
$19$			152908.i			1.17332i	−0.809835	+	0.586658i	$0.800443\pi$
$20$		0			0
$21$	123164.			0.633298
$22$	−83426.7	−	83426.7i	−0.356135	−	0.356135i
$23$	76182.9	−	76182.9i	0.272236	−	0.272236i	−0.557763	−	0.830000i	$-0.688340\pi$
$23$	76182.9	−	76182.9i	0.272236	−	0.272236i	0.830000	+	0.557763i	$0.188340\pi$
$24$		−	549116.i		−	1.65508i
$25$		0			0
$26$	147832.			0.323500
$27$	72320.0	+	72320.0i	0.136083	+	0.136083i
$28$	1.20451e6	−	1.20451e6i	1.95965	−	1.95965i
$29$			935605.i			1.32282i	0.750025	+	0.661410i	$0.230042\pi$
$29$			935605.i			1.32282i	−0.750025	+	0.661410i	$0.769958\pi$
$30$		0			0
$31$	−273508.			−0.296158			−0.148079	−	0.988976i	$-0.547309\pi$
$31$	−273508.			−0.296158			−0.148079	+	0.988976i	$0.547309\pi$
$32$	−1.85228e6	−	1.85228e6i	−1.76647	−	1.76647i
$33$	129848.	−	129848.i	0.109491	−	0.109491i
$34$		−	4.25168e6i		−	3.18159i
$35$		0			0
$36$	1.41453e6			0.842177
$37$	−1.05800e6	−	1.05800e6i	−0.564521	−	0.564521i	0.366067	−	0.930588i	$-0.380704\pi$
$37$	−1.05800e6	−	1.05800e6i	−0.564521	−	0.564521i	−0.930588	+	0.366067i	$0.880704\pi$
$38$	−3.24869e6	+	3.24869e6i	−1.55802	+	1.55802i
$39$			230091.i			0.0994581i
$40$		0			0
$41$	−2.83041e6			−1.00165			−0.500823	−	0.865550i	$-0.666969\pi$
$41$	−2.83041e6			−1.00165			−0.500823	+	0.865550i	$0.666969\pi$
$42$	2.61676e6	+	2.61676e6i	0.840944	+	0.840944i
$43$	382541.	−	382541.i	0.111893	−	0.111893i	−0.648943	−	0.760837i	$-0.724789\pi$
$43$	382541.	−	382541.i	0.111893	−	0.111893i	0.760837	+	0.648943i	$0.224789\pi$
$44$		−	2.53975e6i		−	0.677610i
$45$		0			0
$46$	3.23718e6			0.722995
$47$	2.79713e6	+	2.79713e6i	0.573219	+	0.573219i	0.933027	−	0.359807i	$-0.117158\pi$
$47$	2.79713e6	+	2.79713e6i	0.573219	+	0.573219i	−0.359807	+	0.933027i	$0.617158\pi$
$48$	6.19118e6	−	6.19118e6i	1.16629	−	1.16629i
$49$			1.17140e6i			0.203199i
$50$		0			0
$51$	6.61745e6			0.978160
$52$	2.25021e6	+	2.25021e6i	0.307759	+	0.307759i
$53$	1.27793e6	−	1.27793e6i	0.161959	−	0.161959i	−0.621475	−	0.783434i	$-0.713466\pi$
$53$	1.27793e6	−	1.27793e6i	0.161959	−	0.161959i	0.783434	+	0.621475i	$0.213466\pi$
$54$			3.07303e6i			0.361403i
$55$		0			0
$56$	3.09243e7			3.14448
$57$	−5.05637e6	−	5.05637e6i	−0.479004	−	0.479004i
$58$	−1.98779e7	+	1.98779e7i	−1.75655	+	1.75655i
$59$			9.64312e6i			0.795811i	0.917426	+	0.397905i	$0.130263\pi$
$59$			9.64312e6i			0.795811i	−0.917426	+	0.397905i	$0.869737\pi$
$60$		0			0
$61$	−8.78687e6			−0.634622			−0.317311	−	0.948322i	$-0.602780\pi$
$61$	−8.78687e6			−0.634622			−0.317311	+	0.948322i	$0.602780\pi$
$62$	−5.81097e6	−	5.81097e6i	−0.393262	−	0.393262i
$63$	−4.07282e6	+	4.07282e6i	−0.258543	+	0.258543i
$64$		−	3.07779e7i		−	1.83450i
$65$		0			0
$66$	5.51753e6			0.290783
$67$	−1.74595e7	−	1.74595e7i	−0.866430	−	0.866430i	0.125645	−	0.992075i	$-0.459900\pi$
$67$	−1.74595e7	−	1.74595e7i	−0.866430	−	0.866430i	−0.992075	+	0.125645i	$0.959900\pi$
$68$	6.47166e7	−	6.47166e7i	3.02678	−	3.02678i
$69$			5.03845e6i			0.222280i
$70$		0			0
$71$	−2.53806e7			−0.998778			−0.499389	−	0.866378i	$-0.666442\pi$
$71$	−2.53806e7			−0.998778			−0.499389	+	0.866378i	$0.666442\pi$
$72$	1.81582e7	+	1.81582e7i	0.675683	+	0.675683i
$73$	−3.10129e7	+	3.10129e7i	−1.09207	+	1.09207i	−0.0967652	+	0.995307i	$0.530850\pi$
$73$	−3.10129e7	+	3.10129e7i	−1.09207	+	1.09207i	−0.995307	+	0.0967652i	$0.969150\pi$
$74$		−	4.49568e7i		−	1.49923i
$75$		0			0
$76$	−9.88995e7			−2.96442
$77$	7.31261e6	+	7.31261e6i	0.208022	+	0.208022i
$78$	−4.88852e6	+	4.88852e6i	−0.132068	+	0.132068i
$79$		−	3.27530e7i		−	0.840898i	−0.907316	−	0.420449i	$-0.861873\pi$
$79$		−	3.27530e7i		−	0.840898i	0.907316	−	0.420449i	$-0.138127\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	−6.01351e7	−	6.01351e7i	−1.33006	−	1.33006i
$83$	−1.57518e7	+	1.57518e7i	−0.331908	+	0.331908i	−0.853311	−	0.521403i	$-0.825409\pi$
$83$	−1.57518e7	+	1.57518e7i	−0.331908	+	0.331908i	0.521403	+	0.853311i	$0.325409\pi$
$84$			7.96618e7i			1.60005i
$85$		0			0
$86$	1.62550e7			0.297162
$87$	−3.09387e7	−	3.09387e7i	−0.540039	−	0.540039i
$88$	3.26025e7	−	3.26025e7i	0.543651	−	0.543651i
$89$			2.96432e7i			0.472460i	0.971697	+	0.236230i	$0.0759119\pi$
$89$			2.96432e7i			0.472460i	−0.971697	+	0.236230i	$0.924088\pi$
$90$		0			0
$91$	−1.29579e7			−0.188960
$92$	4.92745e7	+	4.92745e7i	0.687814	+	0.687814i
$93$	9.04439e6	−	9.04439e6i	0.120906	−	0.120906i
$94$			1.18856e8i			1.52233i
$95$		0			0
$96$	1.22503e8			1.44232
$97$	7.80155e7	+	7.80155e7i	0.881240	+	0.881240i	0.993661	−	0.112421i	$-0.0358606\pi$
$97$	7.80155e7	+	7.80155e7i	0.881240	+	0.881240i	−0.112421	+	0.993661i	$0.535861\pi$
$98$	−2.48877e7	+	2.48877e7i	−0.269824	+	0.269824i
$99$			8.58766e6i			0.0893993i
$100$		0			0
$101$	6.32519e7			0.607838			0.303919	−	0.952698i	$-0.401705\pi$
$101$	6.32519e7			0.607838			0.303919	+	0.952698i	$0.401705\pi$
$102$	1.40595e8	+	1.40595e8i	1.29888	+	1.29888i
$103$	−4.02275e7	+	4.02275e7i	−0.357416	+	0.357416i	−0.862860	−	0.505444i	$-0.831329\pi$
$103$	−4.02275e7	+	4.02275e7i	−0.357416	+	0.357416i	0.505444	+	0.862860i	$0.331329\pi$
$104$			5.77715e7i			0.493833i
$105$		0			0
$106$	5.43022e7			0.430124
$107$	−1.53914e8	−	1.53914e8i	−1.17421	−	1.17421i	−0.981197	−	0.193009i	$-0.938175\pi$
$107$	−1.53914e8	−	1.53914e8i	−1.17421	−	1.17421i	−0.193009	−	0.981197i	$-0.561825\pi$
$108$	−4.67760e7	+	4.67760e7i	−0.343817	+	0.343817i
$109$			1.47803e8i			1.04707i	0.852003	+	0.523537i	$0.175388\pi$
$109$			1.47803e8i			1.04707i	−0.852003	+	0.523537i	$0.824612\pi$
$110$		0			0
$111$	6.99723e7			0.460929
$112$	3.48666e8	+	3.48666e8i	2.21584	+	2.21584i
$113$	−1.32920e8	+	1.32920e8i	−0.815222	+	0.815222i	−0.985411	−	0.170189i	$-0.945562\pi$
$113$	−1.32920e8	+	1.32920e8i	−0.815222	+	0.815222i	0.170189	+	0.985411i	$0.445562\pi$
$114$		−	2.14856e8i		−	1.27212i
$115$		0			0
$116$	−6.05142e8			−3.34215
$117$	−7.60866e6	−	7.60866e6i	−0.0406036	−	0.0406036i
$118$	−2.04879e8	+	2.04879e8i	−1.05674	+	1.05674i
$119$			3.72672e8i			1.85840i
$120$		0			0
$121$	−1.98940e8			−0.928070
$122$	−1.86687e8	−	1.86687e8i	−0.842702	−	0.842702i
$123$	9.35963e7	−	9.35963e7i	0.408920	−	0.408920i
$124$		−	1.76903e8i		−	0.748252i
$125$		0			0
$126$	−1.73063e8			−0.686628
$127$	−1.62570e7	−	1.62570e7i	−0.0624923	−	0.0624923i	0.675170	−	0.737662i	$-0.264070\pi$
$127$	−1.62570e7	−	1.62570e7i	−0.0624923	−	0.0624923i	−0.737662	+	0.675170i	$0.764070\pi$
$128$	1.79725e8	−	1.79725e8i	0.669527	−	0.669527i
$129$			2.52998e7i			0.0913606i
$130$		0			0
$131$	5.14855e8			1.74824			0.874118	−	0.485714i	$-0.161441\pi$
$131$	5.14855e8			1.74824			0.874118	+	0.485714i	$0.161441\pi$
$132$	8.39847e7	+	8.39847e7i	0.276633	+	0.276633i
$133$	2.84758e8	−	2.84758e8i	0.910058	−	0.910058i
$134$		−	7.41894e8i		−	2.30103i
$135$		0			0
$136$	1.66152e9			4.85680
$137$	9.80051e7	+	9.80051e7i	0.278206	+	0.278206i	0.832392	−	0.554187i	$-0.186971\pi$
$137$	9.80051e7	+	9.80051e7i	0.278206	+	0.278206i	−0.554187	+	0.832392i	$0.686971\pi$
$138$	−1.07047e8	+	1.07047e8i	−0.295161	+	0.295161i
$139$		−	1.41620e8i		−	0.379372i	−0.981845	−	0.189686i	$-0.939253\pi$
$139$		−	1.41620e8i		−	0.379372i	0.981845	−	0.189686i	$-0.0607470\pi$
$140$		0			0
$141$	−1.84991e8			−0.468032
$142$	−5.39239e8	−	5.39239e8i	−1.32626	−	1.32626i
$143$	−1.36611e7	+	1.36611e7i	−0.0326694	+	0.0326694i
$144$			4.09461e8i			0.952276i
$145$		0			0
$146$	−1.31781e9			−2.90028
$147$	−3.87361e7	−	3.87361e7i	−0.0829557	−	0.0829557i
$148$	6.84308e8	−	6.84308e8i	1.42628	−	1.42628i
$149$		−	2.13302e8i		−	0.432763i	−0.976309	−	0.216381i	$-0.930575\pi$
$149$		−	2.13302e8i		−	0.432763i	0.976309	−	0.216381i	$-0.0694255\pi$
$150$		0			0
$151$	−7.00987e6			−0.0134835			−0.00674175	−	0.999977i	$-0.502146\pi$
$151$	−7.00987e6			−0.0134835			−0.00674175	+	0.999977i	$0.502146\pi$
$152$	−1.26956e9	−	1.26956e9i	−2.37837	−	2.37837i
$153$	−2.18827e8	+	2.18827e8i	−0.399332	+	0.399332i
$154$			3.10728e8i			0.552457i
$155$		0			0
$156$	−1.48821e8			−0.251284
$157$	5.27766e8	+	5.27766e8i	0.868647	+	0.868647i	0.992323	−	0.123676i	$-0.0394683\pi$
$157$	5.27766e8	+	5.27766e8i	0.868647	+	0.868647i	−0.123676	+	0.992323i	$0.539468\pi$
$158$	6.95874e8	−	6.95874e8i	1.11661	−	1.11661i
$159$			8.45178e7i			0.132239i
$160$		0			0
$161$	−2.83748e8			−0.422309
$162$	−1.01619e8	−	1.01619e8i	−0.147542	−	0.147542i
$163$	−4.72984e8	+	4.72984e8i	−0.670033	+	0.670033i	−0.957723	−	0.287691i	$-0.907113\pi$
$163$	−4.72984e8	+	4.72984e8i	−0.670033	+	0.670033i	0.287691	+	0.957723i	$0.407113\pi$
$164$		−	1.83069e9i		−	2.53069i
$165$		0			0
$166$	−6.69327e8			−0.881467
$167$	2.94721e8	+	2.94721e8i	0.378918	+	0.378918i	0.870712	−	0.491794i	$-0.163659\pi$
$167$	2.94721e8	+	2.94721e8i	0.378918	+	0.378918i	−0.491794	+	0.870712i	$0.663659\pi$
$168$	−1.02261e9	+	1.02261e9i	−1.28373	+	1.28373i
$169$			7.91523e8i			0.970324i
$170$		0			0
$171$	3.34409e8			0.391105
$172$	2.47425e8	+	2.47425e8i	0.282702	+	0.282702i
$173$	1.00256e9	−	1.00256e9i	1.11925	−	1.11925i	0.127394	−	0.991852i	$-0.459339\pi$
$173$	1.00256e9	−	1.00256e9i	1.11925	−	1.11925i	0.991852	−	0.127394i	$-0.0406611\pi$
$174$		−	1.31465e9i		−	1.43421i
$175$		0			0
$176$	7.35174e8			0.766195
$177$	−3.18880e8	−	3.18880e8i	−0.324888	−	0.324888i
$178$	−6.29802e8	+	6.29802e8i	−0.627370	+	0.627370i
$179$		−	1.24430e9i		−	1.21203i	−0.795454	−	0.606013i	$-0.792768\pi$
$179$		−	1.24430e9i		−	1.21203i	0.795454	−	0.606013i	$-0.207232\pi$
$180$		0			0
$181$	1.03404e9			0.963434			0.481717	−	0.876327i	$-0.340013\pi$
$181$	1.03404e9			0.963434			0.481717	+	0.876327i	$0.340013\pi$
$182$	−2.75305e8	−	2.75305e8i	−0.250916	−	0.250916i
$183$	2.90565e8	−	2.90565e8i	0.259083	−	0.259083i
$184$			1.26506e9i			1.10367i
$185$		0			0
$186$	3.84316e8			0.321097
$187$	3.92896e8	+	3.92896e8i	0.321300	+	0.321300i
$188$	−1.80916e9	+	1.80916e9i	−1.44826	+	1.44826i
$189$		−	2.69361e8i		−	0.211099i
$190$		0			0
$191$	1.72766e9			1.29815			0.649074	−	0.760725i	$-0.275157\pi$
$191$	1.72766e9			1.29815			0.649074	+	0.760725i	$0.275157\pi$
$192$	1.01777e9	+	1.01777e9i	0.748933	+	0.748933i
$193$	5.36850e8	−	5.36850e8i	0.386922	−	0.386922i	−0.486666	−	0.873588i	$-0.661787\pi$
$193$	5.36850e8	−	5.36850e8i	0.386922	−	0.386922i	0.873588	+	0.486666i	$0.161787\pi$
$194$			3.31505e9i			2.34036i
$195$		0			0
$196$	−7.57654e8			−0.513389
$197$	7.46607e8	+	7.46607e8i	0.495709	+	0.495709i	0.910099	−	0.414390i	$-0.136005\pi$
$197$	7.46607e8	+	7.46607e8i	0.495709	+	0.495709i	−0.414390	+	0.910099i	$0.636005\pi$
$198$	−1.82454e8	+	1.82454e8i	−0.118712	+	0.118712i
$199$			1.24907e9i			0.796480i	0.917281	+	0.398240i	$0.130379\pi$
$199$			1.24907e9i			0.796480i	−0.917281	+	0.398240i	$0.869621\pi$
$200$		0			0
$201$	1.15471e9			0.707437
$202$	1.34386e9	+	1.34386e9i	0.807137	+	0.807137i
$203$	1.74236e9	−	1.74236e9i	1.02602	−	1.02602i
$204$			4.28011e9i			2.47135i
$205$		0			0
$206$	−1.70935e9			−0.949211
$207$	−1.66612e8	−	1.66612e8i	−0.0907455	−	0.0907455i
$208$	−6.51363e8	+	6.51363e8i	−0.347993	+	0.347993i
$209$		−	6.00421e8i		−	0.314681i
$210$		0			0
$211$	1.93374e9			0.975593			0.487796	−	0.872958i	$-0.337801\pi$
$211$	1.93374e9			0.975593			0.487796	+	0.872958i	$0.337801\pi$
$212$	8.26558e8	+	8.26558e8i	0.409195	+	0.409195i
$213$	8.39290e8	−	8.39290e8i	0.407750	−	0.407750i
$214$		−	6.54016e9i		−	3.11841i
$215$		0			0
$216$	−1.20092e9			−0.551693
$217$	5.09350e8	+	5.09350e8i	0.229708	+	0.229708i
$218$	−3.14024e9	+	3.14024e9i	−1.39039	+	1.39039i
$219$		−	2.05108e9i		−	0.891673i
$220$		0			0
$221$	−6.96211e8			−0.291858
$222$	1.48664e9	+	1.48664e9i	0.612059	+	0.612059i
$223$	1.77904e9	−	1.77904e9i	0.719394	−	0.719394i	−0.249087	−	0.968481i	$-0.580131\pi$
$223$	1.77904e9	−	1.77904e9i	0.719394	−	0.719394i	0.968481	+	0.249087i	$0.0801306\pi$
$224$			6.89895e9i			2.74026i
$225$		0			0
$226$	−5.64805e9			−2.16503
$227$	3.36879e8	+	3.36879e8i	0.126873	+	0.126873i	0.767692	−	0.640819i	$-0.221405\pi$
$227$	3.36879e8	+	3.36879e8i	0.126873	+	0.126873i	−0.640819	+	0.767692i	$0.721405\pi$
$228$	3.27042e9	−	3.27042e9i	1.21022	−	1.21022i
$229$			1.26928e9i			0.461547i	0.973008	+	0.230773i	$0.0741256\pi$
$229$			1.26928e9i			0.461547i	−0.973008	+	0.230773i	$0.925874\pi$
$230$		0			0
$231$	−4.83628e8			−0.169849
$232$	−7.76814e9	−	7.76814e9i	−2.68142	−	2.68142i
$233$	−1.42630e8	+	1.42630e8i	−0.0483934	+	0.0483934i	−0.730889	−	0.682496i	$-0.760894\pi$
$233$	−1.42630e8	+	1.42630e8i	−0.0483934	+	0.0483934i	0.682496	+	0.730889i	$0.260894\pi$
$234$		−	3.23308e8i		−	0.107833i
$235$		0			0
$236$	−6.23709e9			−2.01064
$237$	1.08308e9	+	1.08308e9i	0.343295	+	0.343295i
$238$	−7.91783e9	+	7.91783e9i	−2.46773	+	2.46773i
$239$			1.04541e8i			0.0320402i	0.999872	+	0.0160201i	$0.00509957\pi$
$239$			1.04541e8i			0.0320402i	−0.999872	+	0.0160201i	$0.994900\pi$
$240$		0			0
$241$	−5.66112e9			−1.67816			−0.839082	−	0.544005i	$-0.816907\pi$
$241$	−5.66112e9			−1.67816			−0.839082	+	0.544005i	$0.816907\pi$
$242$	−4.22670e9	−	4.22670e9i	−1.23237	−	1.23237i
$243$	1.58164e8	−	1.58164e8i	0.0453609	−	0.0453609i
$244$		−	5.68328e9i		−	1.60339i
$245$		0			0
$246$	3.97711e9			1.08599
$247$	5.31972e8	+	5.31972e8i	0.142923	+	0.142923i
$248$	2.27088e9	−	2.27088e9i	0.600327	−	0.600327i
$249$		−	1.04176e9i		−	0.271001i
$250$		0			0
$251$	4.40303e9			1.10932			0.554659	−	0.832078i	$-0.312849\pi$
$251$	4.40303e9			1.10932			0.554659	+	0.832078i	$0.312849\pi$
$252$	−2.63426e9	−	2.63426e9i	−0.653216	−	0.653216i
$253$	−2.99146e8	+	2.99146e8i	−0.0730133	+	0.0730133i
$254$		−	6.90797e8i		−	0.165965i
$255$		0			0
$256$	−2.42237e8			−0.0564002
$257$	−3.71277e9	−	3.71277e9i	−0.851071	−	0.851071i	0.139195	−	0.990265i	$-0.455549\pi$
$257$	−3.71277e9	−	3.71277e9i	−0.851071	−	0.851071i	−0.990265	+	0.139195i	$0.955549\pi$
$258$	−5.37522e8	+	5.37522e8i	−0.121316	+	0.121316i
$259$			3.94060e9i			0.875717i
$260$		0			0
$261$	2.04617e9			0.440940
$262$	1.09387e10	+	1.09387e10i	2.32145	+	2.32145i
$263$	1.60364e9	−	1.60364e9i	0.335185	−	0.335185i	−0.519366	−	0.854552i	$-0.673832\pi$
$263$	1.60364e9	−	1.60364e9i	0.335185	−	0.335185i	0.854552	+	0.519366i	$0.173832\pi$
$264$			2.15620e9i			0.443889i
$265$		0			0
$266$	1.21000e10			2.41689
$267$	−9.80245e8	−	9.80245e8i	−0.192881	−	0.192881i
$268$	1.12927e10	−	1.12927e10i	2.18906	−	2.18906i
$269$		−	4.14004e8i		−	0.0790671i	−0.999218	−	0.0395336i	$-0.987413\pi$
$269$		−	4.14004e8i		−	0.0790671i	0.999218	−	0.0395336i	$-0.0125872\pi$
$270$		0			0
$271$	1.32482e9			0.245630			0.122815	−	0.992430i	$-0.460808\pi$
$271$	1.32482e9			0.245630			0.122815	+	0.992430i	$0.460808\pi$
$272$	1.87333e10	+	1.87333e10i	3.42247	+	3.42247i
$273$	4.28494e8	−	4.28494e8i	0.0771426	−	0.0771426i
$274$			4.16445e9i			0.738848i
$275$		0			0
$276$	−3.25883e9			−0.561598
$277$	−4.79795e9	−	4.79795e9i	−0.814961	−	0.814961i	0.170412	−	0.985373i	$-0.445490\pi$
$277$	−4.79795e9	−	4.79795e9i	−0.814961	−	0.814961i	−0.985373	+	0.170412i	$0.945490\pi$
$278$	3.00887e9	−	3.00887e9i	0.503760	−	0.503760i
$279$			5.98162e8i			0.0987193i
$280$		0			0
$281$	4.64725e9			0.745368			0.372684	−	0.927958i	$-0.378437\pi$
$281$	4.64725e9			0.745368			0.372684	+	0.927958i	$0.378437\pi$
$282$	−3.93034e9	−	3.93034e9i	−0.621490	−	0.621490i
$283$	−6.31397e9	+	6.31397e9i	−0.984367	+	0.984367i	−0.999880	−	0.0155126i	$-0.995062\pi$
$283$	−6.31397e9	+	6.31397e9i	−0.984367	+	0.984367i	0.0155126	+	0.999880i	$0.495062\pi$
$284$		−	1.64160e10i		−	2.52344i
$285$		0			0
$286$	−5.80490e8			−0.0867621
$287$	5.27103e9	+	5.27103e9i	0.776904	+	0.776904i
$288$	−4.05094e9	+	4.05094e9i	−0.588825	+	0.588825i
$289$			1.30474e10i			1.87039i
$290$		0			0
$291$	−5.15965e9			−0.719529
$292$	−2.00589e10	−	2.00589e10i	−2.75915	−	2.75915i
$293$	−9.75293e9	+	9.75293e9i	−1.32332	+	1.32332i	−0.412247	+	0.911072i	$0.635256\pi$
$293$	−9.75293e9	+	9.75293e9i	−1.32332	+	1.32332i	−0.911072	+	0.412247i	$0.864744\pi$
$294$		−	1.64598e9i		−	0.220310i
$295$		0			0
$296$	1.75688e10			2.28862
$297$	−2.83978e8	−	2.83978e8i	−0.0364971	−	0.0364971i
$298$	4.53183e9	−	4.53183e9i	0.574657	−	0.574657i
$299$		−	5.30087e8i		−	0.0663227i
$300$		0			0
$301$	−1.42480e9			−0.173575
$302$	−1.48932e8	−	1.48932e8i	−0.0179045	−	0.0179045i
$303$	−2.09162e9	+	2.09162e9i	−0.248149	+	0.248149i
$304$		−	2.86282e10i		−	3.35196i
$305$		0			0
$306$	−9.29841e9			−1.06053
$307$	1.20878e10	+	1.20878e10i	1.36080	+	1.36080i	0.872902	+	0.487895i	$0.162235\pi$
$307$	1.20878e10	+	1.20878e10i	1.36080	+	1.36080i	0.487895	+	0.872902i	$0.337765\pi$
$308$	−4.72973e9	+	4.72973e9i	−0.525574	+	0.525574i
$309$		−	2.66049e9i		−	0.291829i
$310$		0			0
$311$	−1.17392e10			−1.25486			−0.627432	−	0.778671i	$-0.715894\pi$
$311$	−1.17392e10			−1.25486			−0.627432	+	0.778671i	$0.715894\pi$
$312$	−1.91039e9	−	1.91039e9i	−0.201607	−	0.201607i
$313$	−7.24148e9	+	7.24148e9i	−0.754484	+	0.754484i	−0.975313	−	0.220829i	$-0.929124\pi$
$313$	−7.24148e9	+	7.24148e9i	−0.754484	+	0.754484i	0.220829	+	0.975313i	$0.429124\pi$
$314$			2.24259e10i			2.30692i
$315$		0			0
$316$	2.11844e10			2.12455
$317$	−6.58929e9	−	6.58929e9i	−0.652531	−	0.652531i	0.301071	−	0.953602i	$-0.402656\pi$
$317$	−6.58929e9	−	6.58929e9i	−0.652531	−	0.652531i	−0.953602	+	0.301071i	$0.902656\pi$
$318$	−1.79567e9	+	1.79567e9i	−0.175598	+	0.175598i
$319$		−	3.67383e9i		−	0.354778i
$320$		0			0
$321$	1.01793e10			0.958735
$322$	−6.02854e9	−	6.02854e9i	−0.560775	−	0.560775i
$323$	1.52996e10	−	1.52996e10i	1.40563	−	1.40563i
$324$		−	3.09359e9i		−	0.280726i
$325$		0			0
$326$	−2.00981e10			−1.77945
$327$	−4.88757e9	−	4.88757e9i	−0.427467	−	0.427467i
$328$	2.35003e10	−	2.35003e10i	2.03038	−	2.03038i
$329$		−	1.04181e10i		−	0.889210i
$330$		0			0
$331$	−1.21922e10			−1.01571			−0.507857	−	0.861442i	$-0.669562\pi$
$331$	−1.21922e10			−1.01571			−0.507857	+	0.861442i	$0.669562\pi$
$332$	−1.01881e10	−	1.01881e10i	−0.838575	−	0.838575i
$333$	−2.31385e9	+	2.31385e9i	−0.188174	+	0.188174i
$334$			1.25233e10i			1.00632i
$335$		0			0
$336$	−2.30595e10			−1.80922
$337$	1.41931e10	+	1.41931e10i	1.10042	+	1.10042i	0.994360	+	0.106056i	$0.0338223\pi$
$337$	1.41931e10	+	1.41931e10i	1.10042	+	1.10042i	0.106056	+	0.994360i	$0.466178\pi$
$338$	−1.68168e10	+	1.68168e10i	−1.28847	+	1.28847i
$339$		−	8.79081e9i		−	0.665626i
$340$		0			0
$341$	1.07398e9			0.0794289
$342$	7.10489e9	+	7.10489e9i	0.519341	+	0.519341i
$343$	−8.55421e9	+	8.55421e9i	−0.618021	+	0.618021i
$344$			6.35233e9i			0.453627i
$345$		0			0
$346$	4.26009e10			2.97245
$347$	−1.20895e10	−	1.20895e10i	−0.833856	−	0.833856i	0.154186	−	0.988042i	$-0.450724\pi$
$347$	−1.20895e10	−	1.20895e10i	−0.833856	−	0.833856i	−0.988042	+	0.154186i	$0.950724\pi$
$348$	2.00109e10	−	2.00109e10i	1.36443	−	1.36443i
$349$			2.69800e10i			1.81861i	0.416128	+	0.909306i	$0.363387\pi$
$349$			2.69800e10i			1.81861i	−0.416128	+	0.909306i	$0.636613\pi$
$350$		0			0
$351$	5.03208e8			0.0331527
$352$	7.27333e9	+	7.27333e9i	0.473765	+	0.473765i
$353$	−5.78837e9	+	5.78837e9i	−0.372784	+	0.372784i	−0.868490	−	0.495706i	$-0.834909\pi$
$353$	−5.78837e9	+	5.78837e9i	−0.372784	+	0.372784i	0.495706	+	0.868490i	$0.334909\pi$
$354$		−	1.35499e10i		−	0.862825i
$355$		0			0
$356$	−1.91730e10			−1.19369
$357$	−1.23236e10	−	1.23236e10i	−0.758689	−	0.758689i
$358$	2.64364e10	−	2.64364e10i	1.60943	−	1.60943i
$359$		−	9.89509e9i		−	0.595720i	−0.954610	−	0.297860i	$-0.903727\pi$
$359$		−	9.89509e9i		−	0.595720i	0.954610	−	0.297860i	$-0.0962728\pi$
$360$		0			0
$361$	−6.39722e9			−0.376671
$362$	2.19692e10	+	2.19692e10i	1.27932	+	1.27932i
$363$	6.57857e9	−	6.57857e9i	0.378883	−	0.378883i
$364$		−	8.38108e9i		−	0.477413i
$365$		0			0
$366$	1.23467e10			0.688063
$367$	−2.51592e10	−	2.51592e10i	−1.38686	−	1.38686i	−0.831832	−	0.555028i	$-0.812708\pi$
$367$	−2.51592e10	−	2.51592e10i	−1.38686	−	1.38686i	−0.555028	−	0.831832i	$-0.687292\pi$
$368$	−1.42633e10	+	1.42633e10i	−0.777733	+	0.777733i
$369$			6.19011e9i			0.333882i
$370$		0			0
$371$	−4.75976e9			−0.251240
$372$	5.84984e9	+	5.84984e9i	0.305473	+	0.305473i
$373$	9.35036e8	−	9.35036e8i	0.0483051	−	0.0483051i	−0.682542	−	0.730847i	$-0.739125\pi$
$373$	9.35036e8	−	9.35036e8i	0.0483051	−	0.0483051i	0.730847	+	0.682542i	$0.239125\pi$
$374$			1.66950e10i			0.853296i
$375$		0			0
$376$	−4.64480e10			−2.32389
$377$	3.25501e9	+	3.25501e9i	0.161134	+	0.161134i
$378$	5.72286e9	−	5.72286e9i	0.280315	−	0.280315i
$379$		−	1.05801e10i		−	0.512780i	−0.966573	−	0.256390i	$-0.917467\pi$
$379$		−	1.05801e10i		−	0.512780i	0.966573	−	0.256390i	$-0.0825332\pi$
$380$		0			0
$381$	1.07518e9			0.0510248
$382$	3.67060e10	+	3.67060e10i	1.72379	+	1.72379i
$383$	1.66202e9	−	1.66202e9i	0.0772400	−	0.0772400i	−0.667431	−	0.744671i	$-0.732606\pi$
$383$	1.66202e9	−	1.66202e9i	0.0772400	−	0.0772400i	0.744671	+	0.667431i	$0.232606\pi$
$384$			1.18863e10i			0.546667i
$385$		0			0
$386$	2.28119e10			1.02757
$387$	−8.36618e8	−	8.36618e8i	−0.0372978	−	0.0372978i
$388$	−5.04598e10	+	5.04598e10i	−2.22648	+	2.22648i
$389$		−	2.70771e8i		−	0.0118251i	−0.999983	−	0.00591253i	$-0.998118\pi$
$389$		−	2.70771e8i		−	0.0118251i	0.999983	−	0.00591253i	$-0.00188203\pi$
$390$		0			0
$391$	−1.52454e10			−0.652277
$392$	−9.72592e9	−	9.72592e9i	−0.411895	−	0.411895i
$393$	−1.70253e10	+	1.70253e10i	−0.713714	+	0.713714i
$394$			3.17249e10i			1.31649i
$395$		0			0
$396$	−5.55443e9			−0.225870
$397$	2.23747e9	+	2.23747e9i	0.0900732	+	0.0900732i	0.750708	−	0.660634i	$-0.229713\pi$
$397$	2.23747e9	+	2.23747e9i	0.0900732	+	0.0900732i	−0.660634	+	0.750708i	$0.729713\pi$
$398$	−2.65379e10	+	2.65379e10i	−1.05763	+	1.05763i
$399$			1.88328e10i			0.743059i
$400$		0			0
$401$	−1.04550e10			−0.404339			−0.202170	−	0.979351i	$-0.564799\pi$
$401$	−1.04550e10			−0.404339			−0.202170	+	0.979351i	$0.564799\pi$
$402$	2.45330e10	+	2.45330e10i	0.939392	+	0.939392i
$403$	−9.51545e8	+	9.51545e8i	−0.0360752	+	0.0360752i
$404$			4.09108e10i			1.53572i
$405$		0			0
$406$	7.40368e10			2.72485
$407$	4.15445e9	+	4.15445e9i	0.151403	+	0.151403i
$408$	−5.49433e10	+	5.49433e10i	−1.98278	+	1.98278i
$409$		−	3.04679e10i		−	1.08880i	−0.838825	−	0.544402i	$-0.816757\pi$
$409$		−	3.04679e10i		−	1.08880i	0.838825	−	0.544402i	$-0.183243\pi$
$410$		0			0
$411$	−6.48168e9			−0.227154
$412$	−2.60188e10	−	2.60188e10i	−0.903023	−	0.903023i
$413$	1.79582e10	−	1.79582e10i	0.617253	−	0.617253i
$414$		−	7.07971e9i		−	0.240998i
$415$		0			0
$416$	−1.28883e10			−0.430351
$417$	4.68310e9	+	4.68310e9i	0.154878	+	0.154878i
$418$	1.27566e10	−	1.27566e10i	0.417859	−	0.417859i
$419$		−	1.70759e10i		−	0.554021i	−0.960867	−	0.277011i	$-0.910656\pi$
$419$		−	1.70759e10i		−	0.554021i	0.960867	−	0.277011i	$-0.0893437\pi$
$420$		0			0
$421$	−3.92537e10			−1.24955			−0.624773	−	0.780807i	$-0.714808\pi$
$421$	−3.92537e10			−1.24955			−0.624773	+	0.780807i	$0.714808\pi$
$422$	4.10844e10	+	4.10844e10i	1.29547	+	1.29547i
$423$	6.11732e9	−	6.11732e9i	0.191073	−	0.191073i
$424$			2.12209e10i			0.656598i
$425$		0			0
$426$	3.56632e10			1.08288
$427$	1.63637e10	+	1.63637e10i	0.492231	+	0.492231i
$428$	9.95506e10	−	9.95506e10i	2.96667	−	2.96667i
$429$		−	9.03493e8i		−	0.0266745i
$430$		0			0
$431$	6.03146e10			1.74789			0.873944	−	0.486027i	$-0.161554\pi$
$431$	6.03146e10			1.74789			0.873944	+	0.486027i	$0.161554\pi$
$432$	−1.35401e10	−	1.35401e10i	−0.388765	−	0.388765i
$433$	1.37835e10	−	1.37835e10i	0.392110	−	0.392110i	−0.483329	−	0.875439i	$-0.660572\pi$
$433$	1.37835e10	−	1.37835e10i	0.392110	−	0.392110i	0.875439	+	0.483329i	$0.160572\pi$
$434$			2.16434e10i			0.610051i
$435$		0			0
$436$	−9.55979e10			−2.64547
$437$	1.16490e10	+	1.16490e10i	0.319419	+	0.319419i
$438$	4.35774e10	−	4.35774e10i	1.18404	−	1.18404i
$439$		−	4.22605e10i		−	1.13783i	−0.822397	−	0.568914i	$-0.807364\pi$
$439$		−	4.22605e10i		−	1.13783i	0.822397	−	0.568914i	$-0.192636\pi$
$440$		0			0
$441$	2.56186e9			0.0677331
$442$	−1.47917e10	−	1.47917e10i	−0.387552	−	0.387552i
$443$	2.37697e10	−	2.37697e10i	0.617176	−	0.617176i	−0.327630	−	0.944806i	$-0.606250\pi$
$443$	2.37697e10	−	2.37697e10i	0.617176	−	0.617176i	0.944806	+	0.327630i	$0.106250\pi$
$444$			4.52575e10i			1.16455i
$445$		0			0
$446$	7.55953e10			1.91054
$447$	7.05350e9	+	7.05350e9i	0.176675	+	0.176675i
$448$	−5.73171e10	+	5.73171e10i	−1.42289	+	1.42289i
$449$		−	6.99774e10i		−	1.72176i	−0.508808	−	0.860880i	$-0.669914\pi$
$449$		−	6.99774e10i		−	1.72176i	0.508808	−	0.860880i	$-0.330086\pi$
$450$		0			0
$451$	1.11141e10			0.268639
$452$	−8.59714e10	−	8.59714e10i	−2.05968	−	2.05968i
$453$	2.31803e8	−	2.31803e8i	0.00550461	−	0.00550461i
$454$			1.43147e10i			0.336945i
$455$		0			0
$456$	8.39640e10			1.94193
$457$	1.92130e10	+	1.92130e10i	0.440483	+	0.440483i	0.892174	−	0.451691i	$-0.149179\pi$
$457$	1.92130e10	+	1.92130e10i	0.440483	+	0.440483i	−0.451691	+	0.892174i	$0.649179\pi$
$458$	−2.69672e10	+	2.69672e10i	−0.612878	+	0.612878i
$459$		−	1.44724e10i		−	0.326053i
$460$		0			0
$461$	−3.94852e8			−0.00874240			−0.00437120	−	0.999990i	$-0.501391\pi$
$461$	−3.94852e8			−0.00874240			−0.00437120	+	0.999990i	$0.501391\pi$
$462$	−1.02752e10	−	1.02752e10i	−0.225539	−	0.225539i
$463$	−5.68672e10	+	5.68672e10i	−1.23748	+	1.23748i	−0.276450	+	0.961028i	$0.589158\pi$
$463$	−5.68672e10	+	5.68672e10i	−1.23748	+	1.23748i	−0.961028	+	0.276450i	$0.910842\pi$
$464$		−	1.75169e11i		−	3.77907i
$465$		0			0
$466$	−6.06064e9			−0.128521
$467$	5.16079e9	+	5.16079e9i	0.108505	+	0.108505i	0.759275	−	0.650770i	$-0.225554\pi$
$467$	5.16079e9	+	5.16079e9i	0.108505	+	0.108505i	−0.650770	+	0.759275i	$0.725554\pi$
$468$	4.92122e9	−	4.92122e9i	0.102586	−	0.102586i
$469$			6.50292e10i			1.34406i
$470$		0			0
$471$	−3.49045e10			−0.709247
$472$	−8.00649e10	−	8.00649e10i	−1.61315	−	1.61315i
$473$	−1.50212e9	+	1.50212e9i	−0.0300096	+	0.0300096i
$474$			4.60225e10i			0.911710i
$475$		0			0
$476$	−2.41041e11			−4.69531
$477$	−2.79484e9	−	2.79484e9i	−0.0539863	−	0.0539863i
$478$	−2.22109e9	+	2.22109e9i	−0.0425455	+	0.0425455i
$479$			3.02182e10i			0.574020i	0.957928	+	0.287010i	$0.0926613\pi$
$479$			3.02182e10i			0.574020i	−0.957928	+	0.287010i	$0.907339\pi$
$480$		0			0
$481$	−7.36167e9			−0.137530
$482$	−1.20277e11	−	1.20277e11i	−2.22840	−	2.22840i
$483$	9.38303e9	−	9.38303e9i	0.172407	−	0.172407i
$484$		−	1.28673e11i		−	2.34480i
$485$		0			0
$486$	6.72072e9			0.120468
$487$	−3.90286e10	−	3.90286e10i	−0.693853	−	0.693853i	0.269224	−	0.963078i	$-0.413233\pi$
$487$	−3.90286e10	−	3.90286e10i	−0.693853	−	0.693853i	−0.963078	+	0.269224i	$0.913233\pi$
$488$	7.29556e10	−	7.29556e10i	1.28641	−	1.28641i
$489$		−	3.12814e10i		−	0.547079i
$490$		0			0
$491$	5.06400e10			0.871299			0.435650	−	0.900116i	$-0.356519\pi$
$491$	5.06400e10			0.871299			0.435650	+	0.900116i	$0.356519\pi$
$492$	6.05373e10	+	6.05373e10i	1.03315	+	1.03315i
$493$	9.36147e10	−	9.36147e10i	1.58473	−	1.58473i
$494$			2.26046e10i			0.379568i
$495$		0			0
$496$	5.12075e10			0.846072
$497$	4.72660e10	+	4.72660e10i	0.774681	+	0.774681i
$498$	2.21334e10	−	2.21334e10i	0.359857	−	0.359857i
$499$		−	6.09714e10i		−	0.983386i	−0.870769	−	0.491693i	$-0.836378\pi$
$499$		−	6.09714e10i		−	0.983386i	0.870769	−	0.491693i	$-0.163622\pi$
$500$		0			0
$501$	−1.94917e10			−0.309385
$502$	9.35470e10	+	9.35470e10i	1.47304	+	1.47304i
$503$	−3.29281e10	+	3.29281e10i	−0.514393	+	0.514393i	−0.915869	−	0.401477i	$-0.868497\pi$
$503$	−3.29281e10	+	3.29281e10i	−0.514393	+	0.514393i	0.401477	+	0.915869i	$0.368497\pi$
$504$		−	6.76315e10i		−	1.04816i
$505$		0			0
$506$	−1.27114e10			−0.193906
$507$	−2.61742e10	−	2.61742e10i	−0.396133	−	0.396133i
$508$	1.05149e10	−	1.05149e10i	0.157889	−	0.157889i
$509$			5.49081e10i			0.818023i	0.912529	+	0.409011i	$0.134126\pi$
$509$			5.49081e10i			0.818023i	−0.912529	+	0.409011i	$0.865874\pi$
$510$		0			0
$511$	1.15510e11			1.69409
$512$	−5.11562e10	−	5.11562e10i	−0.744420	−	0.744420i
$513$	−1.10583e10	+	1.10583e10i	−0.159668	+	0.159668i
$514$		−	1.57764e11i		−	2.26024i
$515$		0			0
$516$	−1.63637e10			−0.230825
$517$	−1.09834e10	−	1.09834e10i	−0.153736	−	0.153736i
$518$	−8.37224e10	+	8.37224e10i	−1.16285	+	1.16285i
$519$			6.63055e10i			0.913860i
$520$		0			0
$521$	−6.84754e10			−0.929359			−0.464679	−	0.885479i	$-0.653830\pi$
$521$	−6.84754e10			−0.929359			−0.464679	+	0.885479i	$0.653830\pi$
$522$	4.34731e10	+	4.34731e10i	0.585515	+	0.585515i
$523$	−3.05582e10	+	3.05582e10i	−0.408434	+	0.408434i	−0.881192	−	0.472758i	$-0.843258\pi$
$523$	−3.05582e10	+	3.05582e10i	−0.408434	+	0.408434i	0.472758	+	0.881192i	$0.343258\pi$
$524$			3.33004e11i			4.41697i
$525$		0			0
$526$	6.81423e10			0.890172
$527$	2.73666e10	+	2.73666e10i	0.354796	+	0.354796i
$528$	−2.43108e10	+	2.43108e10i	−0.312798	+	0.312798i
$529$			6.67033e10i			0.851775i
$530$		0			0
$531$	2.10895e10			0.265270
$532$	1.84179e11	+	1.84179e11i	2.29929	+	2.29929i
$533$	−9.84711e9	+	9.84711e9i	−0.122011	+	0.122011i
$534$		−	4.16527e10i		−	0.512246i
$535$		0			0
$536$	2.89926e11			3.51259
$537$	4.11466e10	+	4.11466e10i	0.494808	+	0.494808i
$538$	8.79597e9	−	8.79597e9i	0.104992	−	0.104992i
$539$		−	4.59973e9i		−	0.0544976i
$540$		0			0
$541$	−4.72291e10			−0.551341			−0.275671	−	0.961252i	$-0.588900\pi$
$541$	−4.72291e10			−0.551341			−0.275671	+	0.961252i	$0.588900\pi$
$542$	2.81473e10	+	2.81473e10i	0.326167	+	0.326167i
$543$	−3.41937e10	+	3.41937e10i	−0.393320	+	0.393320i
$544$			3.70671e11i			4.23246i
$545$		0			0
$546$	1.82076e10			0.204872
$547$	−1.19479e11	−	1.19479e11i	−1.33457	−	1.33457i	−0.901230	−	0.433340i	$-0.857335\pi$
$547$	−1.19479e11	−	1.19479e11i	−1.33457	−	1.33457i	−0.433340	−	0.901230i	$-0.642665\pi$
$548$	−6.33889e10	+	6.33889e10i	−0.702896	+	0.702896i
$549$			1.92169e10i			0.211541i
$550$		0			0
$551$	−1.43061e11			−1.55209
$552$	−4.18332e10	−	4.18332e10i	−0.450573	−	0.450573i
$553$	−6.09955e10	+	6.09955e10i	−0.652224	+	0.652224i
$554$		−	2.03875e11i		−	2.16434i
$555$		0			0
$556$	9.15986e10			0.958494
$557$	5.46408e10	+	5.46408e10i	0.567670	+	0.567670i	0.931475	−	0.363805i	$-0.118522\pi$
$557$	5.46408e10	+	5.46408e10i	0.567670	+	0.567670i	−0.363805	+	0.931475i	$0.618522\pi$
$558$	−1.27086e10	+	1.27086e10i	−0.131087	+	0.131087i
$559$		−	2.66175e9i		−	0.0272597i
$560$		0			0
$561$	−2.59847e10			−0.262341
$562$	9.87359e10	+	9.87359e10i	0.989760	+	0.989760i
$563$	1.11440e11	−	1.11440e11i	1.10919	−	1.10919i	0.115937	−	0.993257i	$-0.463013\pi$
$563$	1.11440e11	−	1.11440e11i	1.10919	−	1.10919i	0.993257	−	0.115937i	$-0.0369870\pi$
$564$		−	1.19651e11i		−	1.18250i
$565$		0			0
$566$	−2.68294e11			−2.61424
$567$	8.90725e9	+	8.90725e9i	0.0861809	+	0.0861809i
$568$	2.10730e11	−	2.10730e11i	2.02457	−	2.02457i
$569$		−	4.28086e8i		−	0.00408396i	−0.999998	−	0.00204198i	$-0.999350\pi$
$569$		−	4.28086e8i		−	0.00408396i	0.999998	−	0.00204198i	$-0.000649983\pi$
$570$		0			0
$571$	1.84599e11			1.73654			0.868269	−	0.496093i	$-0.165232\pi$
$571$	1.84599e11			1.73654			0.868269	+	0.496093i	$0.165232\pi$
$572$	−8.83589e9	−	8.83589e9i	−0.0825403	−	0.0825403i
$573$	−5.71304e10	+	5.71304e10i	−0.529967	+	0.529967i
$574$			2.23977e11i			2.06327i
$575$		0			0
$576$	−6.73112e10			−0.611501
$577$	−6.20051e10	−	6.20051e10i	−0.559402	−	0.559402i	0.369735	−	0.929137i	$-0.379448\pi$
$577$	−6.20051e10	−	6.20051e10i	−0.559402	−	0.559402i	−0.929137	+	0.369735i	$0.879448\pi$
$578$	−2.77206e11	+	2.77206e11i	−2.48366	+	2.48366i
$579$			3.55052e10i			0.315921i
$580$		0			0
$581$	5.86686e10			0.514874
$582$	−1.09622e11	−	1.09622e11i	−0.955448	−	0.955448i
$583$	−5.01805e9	+	5.01805e9i	−0.0434371	+	0.0434371i
$584$		−	5.14988e11i		−	4.42737i
$585$		0			0
$586$	−4.14423e11			−3.51442
$587$	1.94324e10	+	1.94324e10i	0.163672	+	0.163672i	0.784191	−	0.620519i	$-0.213078\pi$
$587$	1.94324e10	+	1.94324e10i	0.163672	+	0.163672i	−0.620519	+	0.784191i	$0.713078\pi$
$588$	2.50542e10	−	2.50542e10i	0.209590	−	0.209590i
$589$		−	4.18215e10i		−	0.347487i
$590$		0			0
$591$	−4.93778e10			−0.404745
$592$	1.98085e11	+	1.98085e11i	1.61274	+	1.61274i
$593$	−8.34787e9	+	8.34787e9i	−0.0675082	+	0.0675082i	−0.740055	−	0.672547i	$-0.765200\pi$
$593$	−8.34787e9	+	8.34787e9i	−0.0675082	+	0.0675082i	0.672547	+	0.740055i	$0.265200\pi$
$594$		−	1.20668e10i		−	0.0969276i
$595$		0			0
$596$	1.37962e11			1.09339
$597$	−4.13044e10	−	4.13044e10i	−0.325162	−	0.325162i
$598$	1.12623e10	−	1.12623e10i	0.0880686	−	0.0880686i
$599$		−	1.65282e10i		−	0.128386i	−0.997937	−	0.0641931i	$-0.979553\pi$
$599$		−	1.65282e10i		−	0.128386i	0.997937	−	0.0641931i	$-0.0204474\pi$
$600$		0			0
$601$	−6.14781e10			−0.471219			−0.235610	−	0.971848i	$-0.575709\pi$
$601$	−6.14781e10			−0.471219			−0.235610	+	0.971848i	$0.575709\pi$
$602$	−3.02714e10	−	3.02714e10i	−0.230487	−	0.230487i
$603$	−3.81840e10	+	3.81840e10i	−0.288810	+	0.288810i
$604$		−	4.53393e9i		−	0.0340665i
$605$		0			0
$606$	−8.88775e10			−0.659024
$607$	−7.33357e10	−	7.33357e10i	−0.540208	−	0.540208i	0.383382	−	0.923590i	$-0.374759\pi$
$607$	−7.33357e10	−	7.33357e10i	−0.540208	−	0.540208i	−0.923590	+	0.383382i	$0.874759\pi$
$608$	2.83228e11	−	2.83228e11i	2.07263	−	2.07263i
$609$			1.15233e11i			0.837739i
$610$		0			0
$611$	1.94626e10			0.139649
$612$	−1.41535e11	−	1.41535e11i	−1.00893	−	1.00893i
$613$	9.78422e10	−	9.78422e10i	0.692922	−	0.692922i	−0.269952	−	0.962874i	$-0.587008\pi$
$613$	9.78422e10	−	9.78422e10i	0.692922	−	0.692922i	0.962874	+	0.269952i	$0.0870077\pi$
$614$			5.13636e11i			3.61395i
$615$		0			0
$616$	−1.21430e11			−0.843342
$617$	4.40834e10	+	4.40834e10i	0.304182	+	0.304182i	0.842648	−	0.538465i	$-0.180996\pi$
$617$	4.40834e10	+	4.40834e10i	0.304182	+	0.304182i	−0.538465	+	0.842648i	$0.680996\pi$
$618$	5.65251e10	−	5.65251e10i	0.387514	−	0.387514i
$619$			8.91413e10i			0.607178i	0.952803	+	0.303589i	$0.0981850\pi$
$619$			8.91413e10i			0.607178i	−0.952803	+	0.303589i	$0.901815\pi$
$620$		0			0
$621$	1.10191e10			0.0740934
$622$	−2.49412e11	−	2.49412e11i	−1.66631	−	1.66631i
$623$	5.52041e10	−	5.52041e10i	0.366454	−	0.366454i
$624$		−	4.30787e10i		−	0.284135i
$625$		0			0
$626$	−3.07706e11			−2.00373
$627$	1.98548e10	+	1.98548e10i	0.128468	+	0.128468i
$628$	−3.41355e11	+	3.41355e11i	−2.19466	+	2.19466i
$629$			2.11723e11i			1.35259i
$630$		0			0
$631$	1.59661e11			1.00712			0.503560	−	0.863960i	$-0.332023\pi$
$631$	1.59661e11			1.00712			0.503560	+	0.863960i	$0.332023\pi$
$632$	2.71942e11	+	2.71942e11i	1.70454	+	1.70454i
$633$	−6.39452e10	+	6.39452e10i	−0.398284	+	0.398284i
$634$		−	2.79993e11i		−	1.73297i
$635$		0			0
$636$	−5.46654e10			−0.334106
$637$	4.07536e9	+	4.07536e9i	0.0247519	+	0.0247519i
$638$	7.80545e10	−	7.80545e10i	0.471102	−	0.471102i
$639$			5.55075e10i			0.332926i
$640$		0			0
$641$	2.16126e11			1.28019			0.640095	−	0.768295i	$-0.278895\pi$
$641$	2.16126e11			1.28019			0.640095	+	0.768295i	$0.278895\pi$
$642$	2.16271e11	+	2.16271e11i	1.27309	+	1.27309i
$643$	4.17519e10	−	4.17519e10i	0.244249	−	0.244249i	−0.574356	−	0.818605i	$-0.694748\pi$
$643$	4.17519e10	−	4.17519e10i	0.244249	−	0.244249i	0.818605	+	0.574356i	$0.194748\pi$
$644$		−	1.83526e11i		−	1.06698i
$645$		0			0
$646$	6.50114e11			3.73301
$647$	−8.12795e10	−	8.12795e10i	−0.463835	−	0.463835i	0.436075	−	0.899910i	$-0.356368\pi$
$647$	−8.12795e10	−	8.12795e10i	−0.463835	−	0.463835i	−0.899910	+	0.436075i	$0.856368\pi$
$648$	3.97120e10	−	3.97120e10i	0.225228	−	0.225228i
$649$		−	3.78655e10i		−	0.213435i
$650$		0			0
$651$	−3.36865e10			−0.187556
$652$	−3.05922e11	−	3.05922e11i	−1.69286	−	1.69286i
$653$	1.08262e11	−	1.08262e11i	0.595422	−	0.595422i	−0.343669	−	0.939091i	$-0.611670\pi$
$653$	1.08262e11	−	1.08262e11i	0.595422	−	0.595422i	0.939091	+	0.343669i	$0.111670\pi$
$654$		−	2.07683e11i		−	1.13525i
$655$		0			0
$656$	5.29924e11			2.86153
$657$	6.78253e10	+	6.78253e10i	0.364024	+	0.364024i
$658$	2.21344e11	−	2.21344e11i	1.18076	−	1.18076i
$659$		−	3.33068e11i		−	1.76600i	−0.469372	−	0.883001i	$-0.655520\pi$
$659$		−	3.33068e11i		−	1.76600i	0.469372	−	0.883001i	$-0.344480\pi$
$660$		0			0
$661$	−8.49280e10			−0.444882			−0.222441	−	0.974946i	$-0.571403\pi$
$661$	−8.49280e10			−0.444882			−0.222441	+	0.974946i	$0.571403\pi$
$662$	−2.59037e11	−	2.59037e11i	−1.34875	−	1.34875i
$663$	2.30224e10	−	2.30224e10i	0.119151	−	0.119151i
$664$		−	2.61568e11i		−	1.34559i
$665$		0			0
$666$	−9.83206e10			−0.499744
$667$	7.12772e10	+	7.12772e10i	0.360120	+	0.360120i
$668$	−1.90623e11	+	1.90623e11i	−0.957348	+	0.957348i
$669$			1.17659e11i			0.587382i
$670$		0			0
$671$	3.45033e10			0.170204
$672$	−2.28135e11	−	2.28135e11i	−1.11870	−	1.11870i
$673$	−2.37471e11	+	2.37471e11i	−1.15758	+	1.15758i	−0.172582	+	0.984995i	$0.555211\pi$
$673$	−2.37471e11	+	2.37471e11i	−1.15758	+	1.15758i	−0.984995	+	0.172582i	$0.944789\pi$
$674$			6.03095e11i			2.92244i
$675$		0			0
$676$	−5.11951e11			−2.45155
$677$	3.94744e10	+	3.94744e10i	0.187915	+	0.187915i	0.794794	−	0.606879i	$-0.207579\pi$
$677$	3.94744e10	+	3.94744e10i	0.187915	+	0.187915i	−0.606879	+	0.794794i	$0.707579\pi$
$678$	1.86770e11	−	1.86770e11i	0.883871	−	0.883871i
$679$		−	2.90574e11i		−	1.36703i
$680$		0			0
$681$	−2.22799e10			−0.103592
$682$	2.28179e10	+	2.28179e10i	0.105472	+	0.105472i
$683$	−1.48061e11	+	1.48061e11i	−0.680388	+	0.680388i	−0.960088	−	0.279700i	$-0.909765\pi$
$683$	−1.48061e11	+	1.48061e11i	−0.680388	+	0.680388i	0.279700	+	0.960088i	$0.409765\pi$
$684$			2.16293e11i			0.988140i
$685$		0			0
$686$	−3.63487e11			−1.64132
$687$	−4.19727e10	−	4.19727e10i	−0.188426	−	0.188426i
$688$	−7.16213e10	+	7.16213e10i	−0.319660	+	0.319660i
$689$		−	8.89197e9i		−	0.0394567i
$690$		0			0
$691$	−2.76640e11			−1.21340			−0.606699	−	0.794931i	$-0.707507\pi$
$691$	−2.76640e11			−1.21340			−0.606699	+	0.794931i	$0.707507\pi$
$692$	6.48447e11	+	6.48447e11i	2.82781	+	2.82781i
$693$	1.59927e10	−	1.59927e10i	0.0693407	−	0.0693407i
$694$		−	5.13710e11i		−	2.21452i
$695$		0			0
$696$	5.13756e11			2.18937
$697$	2.83205e11	+	2.83205e11i	1.19997	+	1.19997i
$698$	−5.73219e11	+	5.73219e11i	−2.41490	+	2.41490i
$699$		−	9.43299e9i		−	0.0395130i
$700$		0			0
$701$	1.47253e11			0.609805			0.304902	−	0.952384i	$-0.401376\pi$
$701$	1.47253e11			0.609805			0.304902	+	0.952384i	$0.401376\pi$
$702$	1.06912e10	+	1.06912e10i	0.0440228	+	0.0440228i
$703$	1.61777e11	−	1.61777e11i	0.662362	−	0.662362i
$704$			1.20855e11i			0.492010i
$705$		0			0
$706$	−2.45960e11			−0.990025
$707$	−1.17793e11	−	1.17793e11i	−0.471457	−	0.471457i
$708$	2.06249e11	−	2.06249e11i	0.820840	−	0.820840i
$709$			2.59381e11i			1.02648i	0.858244	+	0.513242i	$0.171556\pi$
$709$			2.59381e11i			1.02648i	−0.858244	+	0.513242i	$0.828444\pi$
$710$		0			0
$711$	−7.16309e10			−0.280299
$712$	−2.46122e11	−	2.46122e11i	−0.957700	−	0.957700i
$713$	−2.08366e10	+	2.08366e10i	−0.0806250	+	0.0806250i
$714$		−	5.23655e11i		−	2.01490i
$715$		0			0
$716$	8.04802e11			3.06222
$717$	−3.45697e9	−	3.45697e9i	−0.0130803	−	0.0130803i
$718$	2.10232e11	−	2.10232e11i	0.791044	−	0.791044i
$719$			5.41235e10i			0.202521i	0.994860	+	0.101261i	$0.0322876\pi$
$719$			5.41235e10i			0.202521i	−0.994860	+	0.101261i	$0.967712\pi$
$720$		0			0
$721$	1.49830e11			0.554444
$722$	−1.35916e11	−	1.35916e11i	−0.500174	−	0.500174i
$723$	1.87203e11	−	1.87203e11i	0.685107	−	0.685107i
$724$			6.68807e11i			2.43415i
$725$		0			0
$726$	2.79538e11			1.00622
$727$	1.66823e11	+	1.66823e11i	0.597199	+	0.597199i	0.939566	−	0.342367i	$-0.111229\pi$
$727$	1.66823e11	+	1.66823e11i	0.597199	+	0.597199i	−0.342367	+	0.939566i	$0.611229\pi$
$728$	1.07587e11	−	1.07587e11i	0.383031	−	0.383031i
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	−7.65525e10			−0.268096
$732$	1.87935e11	+	1.87935e11i	0.654582	+	0.654582i
$733$	−1.05003e11	+	1.05003e11i	−0.363734	+	0.363734i	−0.865186	−	0.501451i	$-0.832800\pi$
$733$	−1.05003e11	+	1.05003e11i	−0.363734	+	0.363734i	0.501451	+	0.865186i	$0.332800\pi$
$734$		−	1.06907e12i		−	3.68317i
$735$		0			0
$736$	−2.82225e11			−0.961797
$737$	6.85581e10	+	6.85581e10i	0.232375	+	0.232375i
$738$	−1.31515e11	+	1.31515e11i	−0.443355	+	0.443355i
$739$		−	2.16244e11i		−	0.725047i	−0.931975	−	0.362524i	$-0.881915\pi$
$739$		−	2.16244e11i		−	0.725047i	0.931975	−	0.362524i	$-0.118085\pi$
$740$		0			0
$741$	−3.51826e10			−0.116696
$742$	−1.01126e11	−	1.01126e11i	−0.333617	−	0.333617i
$743$	3.82191e11	−	3.82191e11i	1.25408	−	1.25408i	0.300205	−	0.953875i	$-0.402945\pi$
$743$	3.82191e11	−	3.82191e11i	1.25408	−	1.25408i	0.953875	−	0.300205i	$-0.0970551\pi$
$744$			1.50187e11i			0.490165i
$745$		0			0
$746$	3.97317e10			0.128287
$747$	3.44491e10	+	3.44491e10i	0.110636	+	0.110636i
$748$	−2.54122e11	+	2.54122e11i	−0.811775	+	0.811775i
$749$			5.73265e11i			1.82150i
$750$		0			0
$751$	5.51392e10			0.173341			0.0866704	−	0.996237i	$-0.472377\pi$
$751$	5.51392e10			0.173341			0.0866704	+	0.996237i	$0.472377\pi$
$752$	−5.23692e11	−	5.23692e11i	−1.63759	−	1.63759i
$753$	−1.45600e11	+	1.45600e11i	−0.452877	+	0.452877i
$754$			1.38312e11i			0.427933i
$755$		0			0
$756$	1.74220e11			0.533349
$757$	−3.23968e11	−	3.23968e11i	−0.986550	−	0.986550i	0.0133606	−	0.999911i	$-0.495747\pi$
$757$	−3.23968e11	−	3.23968e11i	−0.986550	−	0.986550i	−0.999911	+	0.0133606i	$0.995747\pi$
$758$	2.24785e11	−	2.24785e11i	0.680911	−	0.680911i
$759$		−	1.97844e10i		−	0.0596151i
$760$		0			0
$761$	6.14791e10			0.183311			0.0916556	−	0.995791i	$-0.470784\pi$
$761$	6.14791e10			0.183311			0.0916556	+	0.995791i	$0.470784\pi$
$762$	2.28433e10	+	2.28433e10i	0.0677548	+	0.0677548i
$763$	2.75251e11	−	2.75251e11i	0.812141	−	0.812141i
$764$			1.11744e12i			3.27981i
$765$		0			0
$766$	7.06230e10			0.205131
$767$	3.35488e10	+	3.35488e10i	0.0969384	+	0.0969384i
$768$	8.01032e9	−	8.01032e9i	0.0230253	−	0.0230253i
$769$		−	8.75464e10i		−	0.250342i	−0.992135	−	0.125171i	$-0.960052\pi$
$769$		−	8.75464e10i		−	0.250342i	0.992135	−	0.125171i	$-0.0399479\pi$
$770$		0			0
$771$	2.45549e11			0.694896
$772$	3.47230e11	+	3.47230e11i	0.977570	+	0.977570i
$773$	1.37937e11	−	1.37937e11i	0.386334	−	0.386334i	−0.487044	−	0.873378i	$-0.661925\pi$
$773$	1.37937e11	−	1.37937e11i	0.386334	−	0.386334i	0.873378	+	0.487044i	$0.161925\pi$
$774$		−	3.55497e10i		−	0.0990540i
$775$		0			0
$776$	−1.29549e12			−3.57263
$777$	−1.30308e11	−	1.30308e11i	−0.357510	−	0.357510i
$778$	5.75281e9	−	5.75281e9i	0.0157023	−	0.0157023i
$779$		−	4.32792e11i		−	1.17525i
$780$		0			0
$781$	9.96618e10			0.267870
$782$	−3.23905e11	−	3.23905e11i	−0.866145	−	0.866145i
$783$	−6.76629e10	+	6.76629e10i	−0.180013	+	0.180013i
$784$		−	2.19316e11i		−	0.580505i
$785$		0			0
$786$	−7.23441e11			−1.89545
$787$	−2.49953e11	−	2.49953e11i	−0.651568	−	0.651568i	0.301802	−	0.953371i	$-0.402412\pi$
$787$	−2.49953e11	−	2.49953e11i	−0.651568	−	0.651568i	−0.953371	+	0.301802i	$0.902412\pi$
$788$	−4.82899e11	+	4.82899e11i	−1.25242	+	1.25242i
$789$			1.06059e11i			0.273678i
$790$		0			0
$791$	4.95069e11			1.26462
$792$	−7.13016e10	−	7.13016e10i	−0.181217	−	0.181217i
$793$	−3.05699e10	+	3.05699e10i	−0.0773038	+	0.0773038i
$794$			9.50751e10i			0.239213i
$795$		0			0
$796$	−8.07889e11			−2.01233
$797$	2.79158e11	+	2.79158e11i	0.691859	+	0.691859i	0.962641	−	0.270782i	$-0.0872822\pi$
$797$	2.79158e11	+	2.79158e11i	0.691859	+	0.691859i	−0.270782	+	0.962641i	$0.587282\pi$
$798$	−4.00123e11	+	4.00123e11i	−0.986693	+	0.986693i
$799$		−	5.59749e11i		−	1.37343i
$800$		0			0
$801$	6.48297e10			0.157487
$802$	−2.22127e11	−	2.22127e11i	−0.536914	−	0.536914i
$803$	1.21778e11	−	1.21778e11i	0.292892	−	0.292892i
$804$			7.46856e11i			1.78736i
$805$		0			0
$806$	−4.04332e10			−0.0958072
$807$	1.36903e10	+	1.36903e10i	0.0322790	+	0.0322790i
$808$	−5.25168e11	+	5.25168e11i	−1.23212	+	1.23212i
$809$		−	6.81097e11i		−	1.59006i	−0.606567	−	0.795032i	$-0.707454\pi$
$809$		−	6.81097e11i		−	1.59006i	0.606567	−	0.795032i	$-0.292546\pi$
$810$		0			0
$811$	1.26207e10			0.0291743			0.0145872	−	0.999894i	$-0.495357\pi$
$811$	1.26207e10			0.0291743			0.0145872	+	0.999894i	$0.495357\pi$
$812$	1.12695e12	+	1.12695e12i	2.59226	+	2.59226i
$813$	−4.38094e10	+	4.38094e10i	−0.100278	+	0.100278i
$814$			1.76531e11i			0.402091i
$815$		0			0
$816$	−1.23895e12			−2.79443
$817$	5.84935e10	+	5.84935e10i	0.131286	+	0.131286i
$818$	6.47324e11	−	6.47324e11i	1.44580	−	1.44580i
$819$			2.83390e10i			0.0629866i
$820$		0			0
$821$	−8.73981e11			−1.92366			−0.961832	−	0.273641i	$-0.911772\pi$
$821$	−8.73981e11			−1.92366			−0.961832	+	0.273641i	$0.911772\pi$
$822$	−1.37710e11	−	1.37710e11i	−0.301633	−	0.301633i
$823$	1.64901e11	−	1.64901e11i	0.359439	−	0.359439i	−0.504167	−	0.863606i	$-0.668201\pi$
$823$	1.64901e11	−	1.64901e11i	0.359439	−	0.359439i	0.863606	+	0.504167i	$0.168201\pi$
$824$		−	6.68001e11i		−	1.44900i
$825$		0			0
$826$	7.63084e11			1.63928
$827$	2.82881e11	+	2.82881e11i	0.604758	+	0.604758i	0.941571	−	0.336814i	$-0.109349\pi$
$827$	2.82881e11	+	2.82881e11i	0.604758	+	0.604758i	−0.336814	+	0.941571i	$0.609349\pi$
$828$	1.07763e11	−	1.07763e11i	0.229271	−	0.229271i
$829$			5.69534e11i			1.20587i	0.797789	+	0.602936i	$0.206003\pi$
$829$			5.69534e11i			1.20587i	−0.797789	+	0.602936i	$0.793997\pi$
$830$		0			0
$831$	3.17318e11			0.665413
$832$	−1.07077e11	−	1.07077e11i	−0.223462	−	0.223462i
$833$	1.17208e11	−	1.17208e11i	0.243432	−	0.243432i
$834$			1.98995e11i			0.411318i
$835$		0			0
$836$	3.88347e11			0.795051
$837$	−1.97801e10	−	1.97801e10i	−0.0403020	−	0.0403020i
$838$	3.62795e11	−	3.62795e11i	0.735674	−	0.735674i
$839$		−	3.14449e11i		−	0.634603i	−0.948325	−	0.317301i	$-0.897223\pi$
$839$		−	3.14449e11i		−	0.634603i	0.948325	−	0.317301i	$-0.102777\pi$
$840$		0			0
$841$	−3.75111e11			−0.749853
$842$	−8.33987e11	−	8.33987e11i	−1.65925	−	1.65925i
$843$	−1.53676e11	+	1.53676e11i	−0.304295	+	0.304295i
$844$			1.25073e12i			2.46486i
$845$		0			0
$846$	2.59938e11			0.507444
$847$	3.70483e11	+	3.70483e11i	0.719837	+	0.719837i
$848$	−2.39261e11	+	2.39261e11i	−0.462689	+	0.462689i
$849$		−	4.17582e11i		−	0.803732i
$850$		0			0
$851$	−1.61204e11			−0.307366
$852$	5.42846e11	+	5.42846e11i	1.03019	+	1.03019i
$853$	−5.48548e11	+	5.48548e11i	−1.03614	+	1.03614i	−0.0368179	+	0.999322i	$0.511722\pi$
$853$	−5.48548e11	+	5.48548e11i	−1.03614	+	1.03614i	−0.999322	+	0.0368179i	$0.988278\pi$
$854$			6.95327e11i			1.30725i
$855$		0			0
$856$	2.55584e12			4.76035
$857$	1.73941e11	+	1.73941e11i	0.322463	+	0.322463i	0.849711	−	0.527248i	$-0.176776\pi$
$857$	1.73941e11	+	1.73941e11i	0.322463	+	0.322463i	−0.527248	+	0.849711i	$0.676776\pi$
$858$	1.91957e10	−	1.91957e10i	0.0354205	−	0.0354205i
$859$			8.49325e11i			1.55992i	0.625832	+	0.779958i	$0.284760\pi$
$859$			8.49325e11i			1.55992i	−0.625832	+	0.779958i	$0.715240\pi$
$860$		0			0
$861$	−3.48606e11			−0.634340
$862$	1.28145e12	+	1.28145e12i	2.32099	+	2.32099i
$863$	−5.24438e11	+	5.24438e11i	−0.945477	+	0.945477i	−0.998589	−	0.0531114i	$-0.983086\pi$
$863$	−5.24438e11	+	5.24438e11i	−0.945477	+	0.945477i	0.0531114	+	0.998589i	$0.483086\pi$
$864$		−	2.67914e11i		−	0.480773i
$865$		0			0
$866$	5.85691e11			1.04135
$867$	−4.31453e11	−	4.31453e11i	−0.763584	−	0.763584i
$868$	−3.29443e11	+	3.29443e11i	−0.580365	+	0.580365i
$869$			1.28611e11i			0.225527i
$870$		0			0
$871$	−1.21485e11			−0.211081
$872$	−1.22718e12	−	1.22718e12i	−2.12247	−	2.12247i
$873$	1.70620e11	−	1.70620e11i	0.293747	−	0.293747i
$874$			4.94989e11i			0.848302i
$875$		0			0
$876$	1.32662e12			2.25284
$877$	2.47056e11	+	2.47056e11i	0.417635	+	0.417635i	0.884388	−	0.466753i	$-0.154576\pi$
$877$	2.47056e11	+	2.47056e11i	0.417635	+	0.417635i	−0.466753	+	0.884388i	$0.654576\pi$
$878$	8.97871e11	−	8.97871e11i	1.51090	−	1.51090i
$879$		−	6.45022e11i		−	1.08049i
$880$		0			0
$881$	−3.39509e11			−0.563570			−0.281785	−	0.959478i	$-0.590927\pi$
$881$	−3.39509e11			−0.563570			−0.281785	+	0.959478i	$0.590927\pi$
$882$	5.44294e10	+	5.44294e10i	0.0899414	+	0.0899414i
$883$	−4.96666e11	+	4.96666e11i	−0.816999	+	0.816999i	−0.985672	−	0.168673i	$-0.946052\pi$
$883$	−4.96666e11	+	4.96666e11i	−0.816999	+	0.816999i	0.168673	+	0.985672i	$0.446052\pi$
$884$		−	4.50303e11i		−	0.737388i
$885$		0			0
$886$	1.01003e12			1.63907
$887$	−9.60619e10	−	9.60619e10i	−0.155188	−	0.155188i	0.625243	−	0.780430i	$-0.285000\pi$
$887$	−9.60619e10	−	9.60619e10i	−0.155188	−	0.155188i	−0.780430	+	0.625243i	$0.785000\pi$
$888$	−5.80966e11	+	5.80966e11i	−0.934327	+	0.934327i
$889$			6.05505e10i			0.0969417i
$890$		0			0
$891$	1.87812e10			0.0297998
$892$	1.15067e12	+	1.15067e12i	1.81757	+	1.81757i
$893$	−4.27702e11	+	4.27702e11i	−0.672568	+	0.672568i
$894$			2.99718e11i			0.469206i
$895$		0			0
$896$	−6.69397e11			−1.03861
$897$	1.75290e10	+	1.75290e10i	0.0270761	+	0.0270761i
$898$	1.48675e12	−	1.48675e12i	2.28629	−	2.28629i
$899$		−	2.55896e11i		−	0.391763i
$900$		0			0
$901$	−2.55735e11			−0.388053
$902$	2.36132e11	+	2.36132e11i	0.356721	+	0.356721i
$903$	4.71155e10	−	4.71155e10i	0.0708619	−	0.0708619i
$904$		−	2.20721e12i		−	3.30499i
$905$		0			0
$906$	9.84982e9			0.0146189
$907$	−9.12273e11	−	9.12273e11i	−1.34802	−	1.34802i	−0.887812	−	0.460205i	$-0.847776\pi$
$907$	−9.12273e11	−	9.12273e11i	−1.34802	−	1.34802i	−0.460205	−	0.887812i	$-0.652224\pi$
$908$	−2.17890e11	+	2.17890e11i	−0.320549	+	0.320549i
$909$		−	1.38332e11i		−	0.202613i
$910$		0			0
$911$	9.27012e11			1.34590			0.672949	−	0.739689i	$-0.265027\pi$
$911$	9.27012e11			1.34590			0.672949	+	0.739689i	$0.265027\pi$
$912$	9.46679e11	+	9.46679e11i	1.36843	+	1.36843i
$913$	6.18523e10	−	6.18523e10i	0.0890169	−	0.0890169i
$914$			8.16400e11i			1.16982i
$915$		0			0
$916$	−8.20960e11			−1.16611
$917$	−9.58806e11	−	9.58806e11i	−1.35598	−	1.35598i
$918$	3.07481e11	−	3.07481e11i	0.432960	−	0.432960i
$919$			4.43433e11i			0.621679i	0.950462	+	0.310840i	$0.100610\pi$
$919$			4.43433e11i			0.621679i	−0.950462	+	0.310840i	$0.899390\pi$
$920$		0			0
$921$	−7.99441e11			−1.11109
$922$	−8.38906e9	−	8.38906e9i	−0.0116089	−	0.0116089i
$923$	−8.83002e10	+	8.83002e10i	−0.121662	+	0.121662i
$924$		−	3.12807e11i		−	0.429129i
$925$		0			0
$926$	−2.41641e12			−3.28645
$927$	8.79775e10	+	8.79775e10i	0.119139	+	0.119139i
$928$	1.73301e12	−	1.73301e12i	2.33673	−	2.33673i
$929$			8.51334e11i			1.14298i	0.820610	+	0.571488i	$0.193634\pi$
$929$			8.51334e11i			1.14298i	−0.820610	+	0.571488i	$0.806366\pi$
$930$		0			0
$931$	−1.79117e11			−0.238417
$932$	−9.22517e10	−	9.22517e10i	−0.122267	−	0.122267i
$933$	3.88193e11	−	3.88193e11i	0.512296	−	0.512296i
$934$			2.19293e11i			0.288162i
$935$		0			0
$936$	1.26346e11			0.164611
$937$	2.39323e11	+	2.39323e11i	0.310475	+	0.310475i	0.845094	−	0.534618i	$-0.179545\pi$
$937$	2.39323e11	+	2.39323e11i	0.310475	+	0.310475i	−0.534618	+	0.845094i	$0.679545\pi$
$938$	−1.38162e12	+	1.38162e12i	−1.78475	+	1.78475i
$939$		−	4.78924e11i		−	0.616033i
$940$		0			0
$941$	−1.23183e12			−1.57105			−0.785527	−	0.618827i	$-0.787608\pi$
$941$	−1.23183e12			−1.57105			−0.785527	+	0.618827i	$0.787608\pi$
$942$	−7.41583e11	−	7.41583e11i	−0.941795	−	0.941795i
$943$	−2.15629e11	+	2.15629e11i	−0.272684	+	0.272684i
$944$		−	1.80543e12i		−	2.27349i
$945$		0			0
$946$	−6.38283e10			−0.0796983
$947$	−9.71841e11	−	9.71841e11i	−1.20836	−	1.20836i	−0.971559	−	0.236798i	$-0.923902\pi$
$947$	−9.71841e11	−	9.71841e11i	−1.20836	−	1.20836i	−0.236798	−	0.971559i	$-0.576098\pi$
$948$	−7.00528e11	+	7.00528e11i	−0.867346	+	0.867346i
$949$			2.15790e11i			0.266053i
$950$		0			0
$951$	4.35791e11			0.532790
$952$	−3.09422e12	−	3.09422e12i	−3.76707	−	3.76707i
$953$	−5.72718e11	+	5.72718e11i	−0.694335	+	0.694335i	−0.963183	−	0.268848i	$-0.913357\pi$
$953$	−5.72718e11	+	5.72718e11i	−0.694335	+	0.694335i	0.268848	+	0.963183i	$0.413357\pi$
$954$		−	1.18759e11i		−	0.143375i
$955$		0			0
$956$	−6.76162e10			−0.0809505
$957$	1.21487e11	+	1.21487e11i	0.144837	+	0.144837i
$958$	−6.42019e11	+	6.42019e11i	−0.762230	+	0.762230i
$959$		−	3.65027e11i		−	0.431569i
$960$		0			0
$961$	−7.78084e11			−0.912291
$962$	−1.56407e11	−	1.56407e11i	−0.182623	−	0.182623i
$963$	−3.36611e11	+	3.36611e11i	−0.391402	+	0.391402i
$964$		−	3.66157e12i		−	4.23993i
$965$		0			0
$966$	3.98705e11			0.457871
$967$	−2.00243e11	−	2.00243e11i	−0.229009	−	0.229009i	0.583270	−	0.812279i	$-0.301773\pi$
$967$	−2.00243e11	−	2.00243e11i	−0.229009	−	0.229009i	−0.812279	+	0.583270i	$0.801773\pi$
$968$	1.65176e12	−	1.65176e12i	1.88124	−	1.88124i
$969$			1.01186e12i			1.14769i
$970$		0			0
$971$	3.20180e11			0.360178			0.180089	−	0.983650i	$-0.442361\pi$
$971$	3.20180e11			0.360178			0.180089	+	0.983650i	$0.442361\pi$
$972$	1.02299e11	+	1.02299e11i	0.114606	+	0.114606i
$973$	−2.63736e11	+	2.63736e11i	−0.294252	+	0.294252i
$974$		−	1.65841e12i		−	1.84271i
$975$		0			0
$976$	1.64512e12			1.81300
$977$	−2.66011e11	−	2.66011e11i	−0.291959	−	0.291959i	0.545895	−	0.837854i	$-0.316190\pi$
$977$	−2.66011e11	−	2.66011e11i	−0.291959	−	0.291959i	−0.837854	+	0.545895i	$0.816190\pi$
$978$	6.64607e11	−	6.64607e11i	0.726456	−	0.726456i
$979$		−	1.16400e11i		−	0.126713i
$980$		0			0
$981$	3.23246e11			0.349025
$982$	1.07590e12	+	1.07590e12i	1.15698	+	1.15698i
$983$	2.09747e11	−	2.09747e11i	0.224637	−	0.224637i	−0.585811	−	0.810448i	$-0.699224\pi$
$983$	2.09747e11	−	2.09747e11i	0.224637	−	0.224637i	0.810448	+	0.585811i	$0.199224\pi$
$984$			1.55422e12i			1.65780i
$985$		0			0
$986$	3.97789e12			4.20867
$987$	3.44507e11	+	3.44507e11i	0.363019	+	0.363019i
$988$	−3.44075e11	+	3.44075e11i	−0.361098	+	0.361098i
$989$		−	5.82862e10i		−	0.0609229i
$990$		0			0
$991$	−9.20700e11			−0.954604			−0.477302	−	0.878739i	$-0.658385\pi$
$991$	−9.20700e11			−0.954604			−0.477302	+	0.878739i	$0.658385\pi$
$992$	5.06614e11	+	5.06614e11i	0.523155	+	0.523155i
$993$	4.03174e11	−	4.03174e11i	0.414663	−	0.414663i
$994$			2.00843e12i			2.05737i
$995$		0			0
$996$	6.73804e11			0.684693
$997$	9.42579e11	+	9.42579e11i	0.953976	+	0.953976i	0.998986	−	0.0450109i	$-0.0143323\pi$
$997$	9.42579e11	+	9.42579e11i	0.953976	+	0.953976i	−0.0450109	+	0.998986i	$0.514332\pi$
$998$	1.29540e12	−	1.29540e12i	1.30582	−	1.30582i
$999$		−	1.53029e11i		−	0.153643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.e.7.8		16
5.2	odd	4		15.9.f.a.13.1	yes	16
5.3	odd	4	inner	75.9.f.e.43.8		16
5.4	even	2		15.9.f.a.7.1	✓	16
15.2	even	4		45.9.g.c.28.8		16
15.14	odd	2		45.9.g.c.37.8		16
20.7	even	4		240.9.bg.d.193.1		16
20.19	odd	2		240.9.bg.d.97.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.f.a.7.1	✓	16	5.4	even	2
15.9.f.a.13.1	yes	16	5.2	odd	4
45.9.g.c.28.8		16	15.2	even	4
45.9.g.c.37.8		16	15.14	odd	2
75.9.f.e.7.8		16	1.1	even	1	trivial
75.9.f.e.43.8		16	5.3	odd	4	inner
240.9.bg.d.97.1		16	20.19	odd	2
240.9.bg.d.193.1		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)

\(f(q)\)	\(=\)	\(q+(21.2461 + 21.2461i) q^{2} +(-33.0681 + 33.0681i) q^{3} +646.792i q^{4} -1405.14 q^{6} +(-1862.28 - 1862.28i) q^{7} +(-8302.80 + 8302.80i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(21.2461 + 21.2461i) q^{2} +(-33.0681 + 33.0681i) q^{3} +646.792i q^{4} -1405.14 q^{6} +(-1862.28 - 1862.28i) q^{7} +(-8302.80 + 8302.80i) q^{8} -2187.00i q^{9} -3926.69 q^{11} +(-21388.2 - 21388.2i) q^{12} +(3479.04 - 3479.04i) q^{13} -79132.5i q^{14} -187225. q^{16} +(-100058. - 100058. i) q^{17} +(46465.2 - 46465.2i) q^{18} +152908. i q^{19} +123164. q^{21} +(-83426.7 - 83426.7i) q^{22} +(76182.9 - 76182.9i) q^{23} -549116. i q^{24} +147832. q^{26} +(72320.0 + 72320.0i) q^{27} +(1.20451e6 - 1.20451e6i) q^{28} +935605. i q^{29} -273508. q^{31} +(-1.85228e6 - 1.85228e6i) q^{32} +(129848. - 129848. i) q^{33} -4.25168e6i q^{34} +1.41453e6 q^{36} +(-1.05800e6 - 1.05800e6i) q^{37} +(-3.24869e6 + 3.24869e6i) q^{38} +230091. i q^{39} -2.83041e6 q^{41} +(2.61676e6 + 2.61676e6i) q^{42} +(382541. - 382541. i) q^{43} -2.53975e6i q^{44} +3.23718e6 q^{46} +(2.79713e6 + 2.79713e6i) q^{47} +(6.19118e6 - 6.19118e6i) q^{48} +1.17140e6i q^{49} +6.61745e6 q^{51} +(2.25021e6 + 2.25021e6i) q^{52} +(1.27793e6 - 1.27793e6i) q^{53} +3.07303e6i q^{54} +3.09243e7 q^{56} +(-5.05637e6 - 5.05637e6i) q^{57} +(-1.98779e7 + 1.98779e7i) q^{58} +9.64312e6i q^{59} -8.78687e6 q^{61} +(-5.81097e6 - 5.81097e6i) q^{62} +(-4.07282e6 + 4.07282e6i) q^{63} -3.07779e7i q^{64} +5.51753e6 q^{66} +(-1.74595e7 - 1.74595e7i) q^{67} +(6.47166e7 - 6.47166e7i) q^{68} +5.03845e6i q^{69} -2.53806e7 q^{71} +(1.81582e7 + 1.81582e7i) q^{72} +(-3.10129e7 + 3.10129e7i) q^{73} -4.49568e7i q^{74} -9.88995e7 q^{76} +(7.31261e6 + 7.31261e6i) q^{77} +(-4.88852e6 + 4.88852e6i) q^{78} -3.27530e7i q^{79} -4.78297e6 q^{81} +(-6.01351e7 - 6.01351e7i) q^{82} +(-1.57518e7 + 1.57518e7i) q^{83} +7.96618e7i q^{84} +1.62550e7 q^{86} +(-3.09387e7 - 3.09387e7i) q^{87} +(3.26025e7 - 3.26025e7i) q^{88} +2.96432e7i q^{89} -1.29579e7 q^{91} +(4.92745e7 + 4.92745e7i) q^{92} +(9.04439e6 - 9.04439e6i) q^{93} +1.18856e8i q^{94} +1.22503e8 q^{96} +(7.80155e7 + 7.80155e7i) q^{97} +(-2.48877e7 + 2.48877e7i) q^{98} +8.58766e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 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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