LMFDB - Embedded newform 75.9.f.e.43.5

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			43.5
Root			$0.963769 - 0.963769i$ of defining polynomial
Character	$\chi$	$=$	75.43
Dual form			75.9.f.e.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.41326 + 3.41326i) q^{2} +(33.0681 + 33.0681i) q^{3} +232.699i q^{4} -225.740 q^{6} +(-2986.31 + 2986.31i) q^{7} +(-1668.06 - 1668.06i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(-3.41326 + 3.41326i) q^{2} +(33.0681 + 33.0681i) q^{3} +232.699i q^{4} -225.740 q^{6} +(-2986.31 + 2986.31i) q^{7} +(-1668.06 - 1668.06i) q^{8} +2187.00i q^{9} +3718.40 q^{11} +(-7694.93 + 7694.93i) q^{12} +(-26540.0 - 26540.0i) q^{13} -20386.1i q^{14} -48184.0 q^{16} +(21318.8 - 21318.8i) q^{17} +(-7464.80 - 7464.80i) q^{18} +12769.7i q^{19} -197503. q^{21} +(-12691.9 + 12691.9i) q^{22} +(357866. + 357866. i) q^{23} -110319. i q^{24} +181176. q^{26} +(-72320.0 + 72320.0i) q^{27} +(-694911. - 694911. i) q^{28} -492861. i q^{29} +594889. q^{31} +(591487. - 591487. i) q^{32} +(122960. + 122960. i) q^{33} +145533. i q^{34} -508913. q^{36} +(303865. - 303865. i) q^{37} +(-43586.3 - 43586.3i) q^{38} -1.75526e6i q^{39} -5.33801e6 q^{41} +(674129. - 674129. i) q^{42} +(-309949. - 309949. i) q^{43} +865269. i q^{44} -2.44298e6 q^{46} +(1.95806e6 - 1.95806e6i) q^{47} +(-1.59335e6 - 1.59335e6i) q^{48} -1.20712e7i q^{49} +1.40994e6 q^{51} +(6.17584e6 - 6.17584e6i) q^{52} +(-5.56394e6 - 5.56394e6i) q^{53} -493694. i q^{54} +9.96266e6 q^{56} +(-422270. + 422270. i) q^{57} +(1.68226e6 + 1.68226e6i) q^{58} -1.11543e7i q^{59} -6.20517e6 q^{61} +(-2.03051e6 + 2.03051e6i) q^{62} +(-6.53105e6 - 6.53105e6i) q^{63} -8.29731e6i q^{64} -839391. q^{66} +(-911525. + 911525. i) q^{67} +(4.96086e6 + 4.96086e6i) q^{68} +2.36679e7i q^{69} -2.89373e7 q^{71} +(3.64804e6 - 3.64804e6i) q^{72} +(1.28737e7 + 1.28737e7i) q^{73} +2.07434e6i q^{74} -2.97150e6 q^{76} +(-1.11043e7 + 1.11043e7i) q^{77} +(5.99114e6 + 5.99114e6i) q^{78} +4.05256e7i q^{79} -4.78297e6 q^{81} +(1.82200e7 - 1.82200e7i) q^{82} +(-2.54585e6 - 2.54585e6i) q^{83} -4.59588e7i q^{84} +2.11587e6 q^{86} +(1.62980e7 - 1.62980e7i) q^{87} +(-6.20250e6 - 6.20250e6i) q^{88} +5.88015e7i q^{89} +1.58513e8 q^{91} +(-8.32752e7 + 8.32752e7i) q^{92} +(1.96719e7 + 1.96719e7i) q^{93} +1.33668e7i q^{94} +3.91187e7 q^{96} +(-6.57476e7 + 6.57476e7i) q^{97} +(4.12023e7 + 4.12023e7i) q^{98} +8.13214e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−3.41326	+	3.41326i	−0.213329	+	0.213329i	−0.805680	−	0.592351i	$-0.798200\pi$
$2$	−3.41326	+	3.41326i	−0.213329	+	0.213329i	0.592351	+	0.805680i	$0.298200\pi$
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$			232.699i			0.908982i
$5$		0			0
$5$		0			0
$6$	−225.740			−0.174182
$7$	−2986.31	+	2986.31i	−1.24378	+	1.24378i	−0.285353	+	0.958422i	$0.592111\pi$
$7$	−2986.31	+	2986.31i	−1.24378	+	1.24378i	−0.958422	+	0.285353i	$0.907889\pi$
$8$	−1668.06	−	1668.06i	−0.407241	−	0.407241i
$9$			2187.00i			0.333333i
$10$		0			0
$11$	3718.40			0.253972			0.126986	−	0.991905i	$-0.459470\pi$
$11$	3718.40			0.253972			0.126986	+	0.991905i	$0.459470\pi$
$12$	−7694.93	+	7694.93i	−0.371090	+	0.371090i
$13$	−26540.0	−	26540.0i	−0.929239	−	0.929239i	0.0684174	−	0.997657i	$-0.478205\pi$
$13$	−26540.0	−	26540.0i	−0.929239	−	0.929239i	−0.997657	+	0.0684174i	$0.978205\pi$
$14$		−	20386.1i		−	0.530666i
$15$		0			0
$16$	−48184.0			−0.735230
$17$	21318.8	−	21318.8i	0.255250	−	0.255250i	−0.567869	−	0.823119i	$-0.692232\pi$
$17$	21318.8	−	21318.8i	0.255250	−	0.255250i	0.823119	+	0.567869i	$0.192232\pi$
$18$	−7464.80	−	7464.80i	−0.0711096	−	0.0711096i
$19$			12769.7i			0.0979866i	0.998799	+	0.0489933i	$0.0156013\pi$
$19$			12769.7i			0.0979866i	−0.998799	+	0.0489933i	$0.984399\pi$
$20$		0			0
$21$	−197503.			−1.01554
$22$	−12691.9	+	12691.9i	−0.0541794	+	0.0541794i
$23$	357866.	+	357866.i	1.27882	+	1.27882i	0.941329	+	0.337491i	$0.109578\pi$
$23$	357866.	+	357866.i	1.27882	+	1.27882i	0.337491	+	0.941329i	$0.390422\pi$
$24$		−	110319.i		−	0.332511i
$25$		0			0
$26$	181176.			0.396467
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	−694911.	−	694911.i	−1.13057	−	1.13057i
$29$		−	492861.i		−	0.696839i	−0.937339	−	0.348419i	$-0.886719\pi$
$29$		−	492861.i		−	0.696839i	0.937339	−	0.348419i	$-0.113281\pi$
$30$		0			0
$31$	594889.			0.644154			0.322077	−	0.946714i	$-0.395619\pi$
$31$	594889.			0.644154			0.322077	+	0.946714i	$0.395619\pi$
$32$	591487.	−	591487.i	0.564086	−	0.564086i
$33$	122960.	+	122960.i	0.103683	+	0.103683i
$34$			145533.i			0.108904i
$35$		0			0
$36$	−508913.			−0.302994
$37$	303865.	−	303865.i	0.162134	−	0.162134i	−0.621378	−	0.783511i	$-0.713427\pi$
$37$	303865.	−	303865.i	0.162134	−	0.162134i	0.783511	+	0.621378i	$0.213427\pi$
$38$	−43586.3	−	43586.3i	−0.0209034	−	0.0209034i
$39$		−	1.75526e6i		−	0.758721i
$40$		0			0
$41$	−5.33801e6			−1.88905			−0.944527	−	0.328435i	$-0.893479\pi$
$41$	−5.33801e6			−1.88905			−0.944527	+	0.328435i	$0.893479\pi$
$42$	674129.	−	674129.i	0.216644	−	0.216644i
$43$	−309949.	−	309949.i	−0.0906602	−	0.0906602i	0.660322	−	0.750982i	$-0.270420\pi$
$43$	−309949.	−	309949.i	−0.0906602	−	0.0906602i	−0.750982	+	0.660322i	$0.770420\pi$
$44$			865269.i			0.230856i
$45$		0			0
$46$	−2.44298e6			−0.545618
$47$	1.95806e6	−	1.95806e6i	0.401269	−	0.401269i	−0.477411	−	0.878680i	$-0.658425\pi$
$47$	1.95806e6	−	1.95806e6i	0.401269	−	0.401269i	0.878680	+	0.477411i	$0.158425\pi$
$48$	−1.59335e6	−	1.59335e6i	−0.300156	−	0.300156i
$49$		−	1.20712e7i		−	2.09396i
$50$		0			0
$51$	1.40994e6			0.208411
$52$	6.17584e6	−	6.17584e6i	0.844662	−	0.844662i
$53$	−5.56394e6	−	5.56394e6i	−0.705146	−	0.705146i	0.260364	−	0.965510i	$-0.416157\pi$
$53$	−5.56394e6	−	5.56394e6i	−0.705146	−	0.705146i	−0.965510	+	0.260364i	$0.916157\pi$
$54$		−	493694.i		−	0.0580607i
$55$		0			0
$56$	9.96266e6			1.01303
$57$	−422270.	+	422270.i	−0.0400029	+	0.0400029i
$58$	1.68226e6	+	1.68226e6i	0.148656	+	0.148656i
$59$		−	1.11543e7i		−	0.920521i	−0.887784	−	0.460260i	$-0.847756\pi$
$59$		−	1.11543e7i		−	0.920521i	0.887784	−	0.460260i	$-0.152244\pi$
$60$		0			0
$61$	−6.20517e6			−0.448161			−0.224081	−	0.974571i	$-0.571938\pi$
$61$	−6.20517e6			−0.448161			−0.224081	+	0.974571i	$0.571938\pi$
$62$	−2.03051e6	+	2.03051e6i	−0.137416	+	0.137416i
$63$	−6.53105e6	−	6.53105e6i	−0.414592	−	0.414592i
$64$		−	8.29731e6i		−	0.494558i
$65$		0			0
$66$	−839391.			−0.0442373
$67$	−911525.	+	911525.i	−0.0452345	+	0.0452345i	−0.729362	−	0.684128i	$-0.760183\pi$
$67$	−911525.	+	911525.i	−0.0452345	+	0.0452345i	0.684128	+	0.729362i	$0.260183\pi$
$68$	4.96086e6	+	4.96086e6i	0.232018	+	0.232018i
$69$			2.36679e7i			1.04415i
$70$		0			0
$71$	−2.89373e7			−1.13874			−0.569371	−	0.822081i	$-0.692813\pi$
$71$	−2.89373e7			−1.13874			−0.569371	+	0.822081i	$0.692813\pi$
$72$	3.64804e6	−	3.64804e6i	0.135747	−	0.135747i
$73$	1.28737e7	+	1.28737e7i	0.453327	+	0.453327i	0.896457	−	0.443130i	$-0.146132\pi$
$73$	1.28737e7	+	1.28737e7i	0.453327	+	0.453327i	−0.443130	+	0.896457i	$0.646132\pi$
$74$			2.07434e6i			0.0691756i
$75$		0			0
$76$	−2.97150e6			−0.0890680
$77$	−1.11043e7	+	1.11043e7i	−0.315884	+	0.315884i
$78$	5.99114e6	+	5.99114e6i	0.161857	+	0.161857i
$79$			4.05256e7i			1.04045i	0.854029	+	0.520225i	$0.174152\pi$
$79$			4.05256e7i			1.04045i	−0.854029	+	0.520225i	$0.825848\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	1.82200e7	−	1.82200e7i	0.402989	−	0.402989i
$83$	−2.54585e6	−	2.54585e6i	−0.0536439	−	0.0536439i	0.679776	−	0.733420i	$-0.262077\pi$
$83$	−2.54585e6	−	2.54585e6i	−0.0536439	−	0.0536439i	−0.733420	+	0.679776i	$0.762077\pi$
$84$		−	4.59588e7i		−	0.923106i
$85$		0			0
$86$	2.11587e6			0.0386808
$87$	1.62980e7	−	1.62980e7i	0.284483	−	0.284483i
$88$	−6.20250e6	−	6.20250e6i	−0.103428	−	0.103428i
$89$			5.88015e7i			0.937192i	0.883413	+	0.468596i	$0.155240\pi$
$89$			5.88015e7i			0.937192i	−0.883413	+	0.468596i	$0.844760\pi$
$90$		0			0
$91$	1.58513e8			2.31153
$92$	−8.32752e7	+	8.32752e7i	−1.16242	+	1.16242i
$93$	1.96719e7	+	1.96719e7i	0.262975	+	0.262975i
$94$			1.33668e7i			0.171204i
$95$		0			0
$96$	3.91187e7			0.460574
$97$	−6.57476e7	+	6.57476e7i	−0.742664	+	0.742664i	−0.973090	−	0.230425i	$-0.925988\pi$
$97$	−6.57476e7	+	6.57476e7i	−0.742664	+	0.742664i	0.230425	+	0.973090i	$0.425988\pi$
$98$	4.12023e7	+	4.12023e7i	0.446701	+	0.446701i
$99$			8.13214e6i			0.0846572i
$100$		0			0
$101$	−1.16082e8			−1.11553			−0.557763	−	0.830000i	$-0.688340\pi$
$101$	−1.16082e8			−1.11553			−0.557763	+	0.830000i	$0.688340\pi$
$102$	−4.81250e6	+	4.81250e6i	−0.0444601	+	0.0444601i
$103$	−7.41173e7	−	7.41173e7i	−0.658523	−	0.658523i	0.296508	−	0.955030i	$-0.404178\pi$
$103$	−7.41173e7	−	7.41173e7i	−0.658523	−	0.658523i	−0.955030	+	0.296508i	$0.904178\pi$
$104$			8.85405e7i			0.756848i
$105$		0			0
$106$	3.79824e7			0.300856
$107$	−4.84024e7	+	4.84024e7i	−0.369260	+	0.369260i	−0.867207	−	0.497948i	$-0.834087\pi$
$107$	−4.84024e7	+	4.84024e7i	−0.369260	+	0.369260i	0.497948	+	0.867207i	$0.334087\pi$
$108$	−1.68288e7	−	1.68288e7i	−0.123697	−	0.123697i
$109$		−	2.53999e7i		−	0.179940i	−0.995944	−	0.0899698i	$-0.971323\pi$
$109$		−	2.53999e7i		−	0.179940i	0.995944	−	0.0899698i	$-0.0286771\pi$
$110$		0			0
$111$	2.00965e7			0.132382
$112$	1.43892e8	−	1.43892e8i	0.914461	−	0.914461i
$113$	1.22374e8	+	1.22374e8i	0.750542	+	0.750542i	0.974580	−	0.224038i	$-0.0719241\pi$
$113$	1.22374e8	+	1.22374e8i	0.750542	+	0.750542i	−0.224038	+	0.974580i	$0.571924\pi$
$114$		−	2.88264e6i		−	0.0170675i
$115$		0			0
$116$	1.14688e8			0.633413
$117$	5.80430e7	−	5.80430e7i	0.309746	−	0.309746i
$118$	3.80724e7	+	3.80724e7i	0.196373	+	0.196373i
$119$			1.27329e8i			0.634949i
$120$		0			0
$121$	−2.00532e8			−0.935498
$122$	2.11798e7	−	2.11798e7i	0.0956056	−	0.0956056i
$123$	−1.76518e8	−	1.76518e8i	−0.771203	−	0.771203i
$124$			1.38430e8i			0.585524i
$125$		0			0
$126$	4.45843e7			0.176889
$127$	−8.10562e7	+	8.10562e7i	−0.311581	+	0.311581i	−0.845522	−	0.533941i	$-0.820711\pi$
$127$	−8.10562e7	+	8.10562e7i	−0.311581	+	0.311581i	0.533941	+	0.845522i	$0.320711\pi$
$128$	1.79742e8	+	1.79742e8i	0.669590	+	0.669590i
$129$		−	2.04989e7i		−	0.0740237i
$130$		0			0
$131$	2.38187e7			0.0808786			0.0404393	−	0.999182i	$-0.487124\pi$
$131$	2.38187e7			0.0808786			0.0404393	+	0.999182i	$0.487124\pi$
$132$	−2.86128e7	+	2.86128e7i	−0.0942464	+	0.0942464i
$133$	−3.81343e7	−	3.81343e7i	−0.121873	−	0.121873i
$134$		−	6.22254e6i		−	0.0192996i
$135$		0			0
$136$	−7.11219e7			−0.207897
$137$	−2.83037e8	+	2.83037e8i	−0.803453	+	0.803453i	−0.983634	−	0.180180i	$-0.942332\pi$
$137$	−2.83037e8	+	2.83037e8i	−0.803453	+	0.803453i	0.180180	+	0.983634i	$0.442332\pi$
$138$	−8.07847e7	−	8.07847e7i	−0.222748	−	0.222748i
$139$		−	6.63736e8i		−	1.77802i	−0.457891	−	0.889008i	$-0.651395\pi$
$139$		−	6.63736e8i		−	1.77802i	0.457891	−	0.889008i	$-0.348605\pi$
$140$		0			0
$141$	1.29499e8			0.327634
$142$	9.87706e7	−	9.87706e7i	0.242926	−	0.242926i
$143$	−9.86863e7	−	9.86863e7i	−0.236000	−	0.236000i
$144$		−	1.05378e8i		−	0.245077i
$145$		0			0
$146$	−8.78824e7			−0.193415
$147$	3.99173e8	−	3.99173e8i	0.854854	−	0.854854i
$148$	7.07091e7	+	7.07091e7i	0.147377	+	0.147377i
$149$			1.37220e8i			0.278403i	0.990264	+	0.139201i	$0.0444535\pi$
$149$			1.37220e8i			0.278403i	−0.990264	+	0.139201i	$0.955546\pi$
$150$		0			0
$151$	1.36764e8			0.263066			0.131533	−	0.991312i	$-0.458010\pi$
$151$	1.36764e8			0.263066			0.131533	+	0.991312i	$0.458010\pi$
$152$	2.13006e7	−	2.13006e7i	0.0399041	−	0.0399041i
$153$	4.66242e7	+	4.66242e7i	0.0850835	+	0.0850835i
$154$		−	7.58035e7i		−	0.134774i
$155$		0			0
$156$	4.08447e8			0.689663
$157$	5.97367e8	−	5.97367e8i	0.983202	−	0.983202i	−0.0166592	−	0.999861i	$-0.505303\pi$
$157$	5.97367e8	−	5.97367e8i	0.983202	−	0.983202i	0.999861	+	0.0166592i	$0.00530305\pi$
$158$	−1.38324e8	−	1.38324e8i	−0.221958	−	0.221958i
$159$		−	3.67978e8i		−	0.575750i
$160$		0			0
$161$	−2.13740e9			−3.18113
$162$	1.63255e7	−	1.63255e7i	0.0237032	−	0.0237032i
$163$	−5.59706e8	−	5.59706e8i	−0.792883	−	0.792883i	0.189079	−	0.981962i	$-0.439450\pi$
$163$	−5.59706e8	−	5.59706e8i	−0.792883	−	0.792883i	−0.981962	+	0.189079i	$0.939450\pi$
$164$		−	1.24215e9i		−	1.71712i
$165$		0			0
$166$	1.73793e7			0.0228876
$167$	−5.95014e8	+	5.95014e8i	−0.765000	+	0.765000i	−0.977222	−	0.212221i	$-0.931930\pi$
$167$	−5.95014e8	+	5.95014e8i	−0.765000	+	0.765000i	0.212221	+	0.977222i	$0.431930\pi$
$168$	3.29446e8	+	3.29446e8i	0.413568	+	0.413568i
$169$			5.93013e8i			0.726972i
$170$		0			0
$171$	−2.79274e7			−0.0326622
$172$	7.21249e7	−	7.21249e7i	0.0824084	−	0.0824084i
$173$	6.46506e7	+	6.46506e7i	0.0721752	+	0.0721752i	0.742273	−	0.670098i	$-0.233748\pi$
$173$	6.46506e7	+	6.46506e7i	0.0721752	+	0.0721752i	−0.670098	+	0.742273i	$0.733748\pi$
$174$			1.11258e8i			0.121377i
$175$		0			0
$176$	−1.79167e8			−0.186727
$177$	3.68851e8	−	3.68851e8i	0.375801	−	0.375801i
$178$	−2.00705e8	−	2.00705e8i	−0.199930	−	0.199930i
$179$			1.42994e9i			1.39285i	0.717630	+	0.696425i	$0.245227\pi$
$179$			1.42994e9i			1.39285i	−0.717630	+	0.696425i	$0.754773\pi$
$180$		0			0
$181$	9.17748e6			0.00855085			0.00427542	−	0.999991i	$-0.498639\pi$
$181$	9.17748e6			0.00855085			0.00427542	+	0.999991i	$0.498639\pi$
$182$	−5.41046e8	+	5.41046e8i	−0.493116	+	0.493116i
$183$	−2.05193e8	−	2.05193e8i	−0.182961	−	0.182961i
$184$		−	1.19388e9i		−	1.04157i
$185$		0			0
$186$	−1.34290e8			−0.112200
$187$	7.92717e7	−	7.92717e7i	0.0648264	−	0.0648264i
$188$	4.55640e8	+	4.55640e8i	0.364746	+	0.364746i
$189$		−	4.31939e8i		−	0.338513i
$190$		0			0
$191$	1.93740e9			1.45574			0.727872	−	0.685713i	$-0.240510\pi$
$191$	1.93740e9			1.45574			0.727872	+	0.685713i	$0.240510\pi$
$192$	2.74376e8	−	2.74376e8i	0.201902	−	0.201902i
$193$	−8.51391e8	−	8.51391e8i	−0.613621	−	0.613621i	0.330267	−	0.943888i	$-0.392861\pi$
$193$	−8.51391e8	−	8.51391e8i	−0.613621	−	0.613621i	−0.943888	+	0.330267i	$0.892861\pi$
$194$		−	4.48827e8i		−	0.316863i
$195$		0			0
$196$	2.80897e9			1.90337
$197$	2.68094e8	−	2.68094e8i	0.178001	−	0.178001i	−0.612483	−	0.790484i	$-0.709829\pi$
$197$	2.68094e8	−	2.68094e8i	0.178001	−	0.178001i	0.790484	+	0.612483i	$0.209829\pi$
$198$	−2.77571e7	−	2.77571e7i	−0.0180598	−	0.0180598i
$199$			1.96767e9i			1.25470i	0.778736	+	0.627352i	$0.215861\pi$
$199$			1.96767e9i			1.25470i	−0.778736	+	0.627352i	$0.784139\pi$
$200$		0			0
$201$	−6.02848e7			−0.0369338
$202$	3.96218e8	−	3.96218e8i	0.237974	−	0.237974i
$203$	1.47183e9	+	1.47183e9i	0.866711	+	0.866711i
$204$			3.28093e8i			0.189442i
$205$		0			0
$206$	5.05963e8			0.280964
$207$	−7.82653e8	+	7.82653e8i	−0.426273	+	0.426273i
$208$	1.27880e9	+	1.27880e9i	0.683204	+	0.683204i
$209$			4.74829e7i			0.0248858i
$210$		0			0
$211$	−2.88243e9			−1.45422			−0.727108	−	0.686523i	$-0.759136\pi$
$211$	−2.88243e9			−1.45422			−0.727108	+	0.686523i	$0.759136\pi$
$212$	1.29473e9	−	1.29473e9i	0.640965	−	0.640965i
$213$	−9.56903e8	−	9.56903e8i	−0.464889	−	0.464889i
$214$		−	3.30420e8i		−	0.157547i
$215$		0			0
$216$	2.41268e8			0.110837
$217$	−1.77652e9	+	1.77652e9i	−0.801183	+	0.801183i
$218$	8.66966e7	+	8.66966e7i	0.0383863	+	0.0383863i
$219$			8.51417e8i			0.370140i
$220$		0			0
$221$	−1.13160e9			−0.474378
$222$	−6.85944e7	+	6.85944e7i	−0.0282408	+	0.0282408i
$223$	1.80381e9	+	1.80381e9i	0.729410	+	0.729410i	0.970502	−	0.241092i	$-0.0775055\pi$
$223$	1.80381e9	+	1.80381e9i	0.729410	+	0.729410i	−0.241092	+	0.970502i	$0.577506\pi$
$224$			3.53272e9i			1.40319i
$225$		0			0
$226$	−8.35388e8			−0.320224
$227$	−2.83002e9	+	2.83002e9i	−1.06582	+	1.06582i	−0.0681495	+	0.997675i	$0.521709\pi$
$227$	−2.83002e9	+	2.83002e9i	−1.06582	+	1.06582i	−0.997675	+	0.0681495i	$0.978291\pi$
$228$	−9.82620e7	−	9.82620e7i	−0.0363619	−	0.0363619i
$229$		−	2.49944e8i		−	0.0908867i	−0.998967	−	0.0454433i	$-0.985530\pi$
$229$		−	2.49944e8i		−	0.0908867i	0.998967	−	0.0454433i	$-0.0144700\pi$
$230$		0			0
$231$	−7.34395e8			−0.257918
$232$	−8.22120e8	+	8.22120e8i	−0.283781	+	0.283781i
$233$	−2.03413e9	−	2.03413e9i	−0.690167	−	0.690167i	0.272102	−	0.962269i	$-0.412281\pi$
$233$	−2.03413e9	−	2.03413e9i	−0.690167	−	0.690167i	−0.962269	+	0.272102i	$0.912281\pi$
$234$			3.96232e8i			0.132156i
$235$		0			0
$236$	2.59559e9			0.836736
$237$	−1.34011e9	+	1.34011e9i	−0.424762	+	0.424762i
$238$	−4.34606e8	−	4.34606e8i	−0.135453	−	0.135453i
$239$			1.62375e9i			0.497653i	0.968548	+	0.248826i	$0.0800449\pi$
$239$			1.62375e9i			0.497653i	−0.968548	+	0.248826i	$0.919955\pi$
$240$		0			0
$241$	2.87994e9			0.853720			0.426860	−	0.904318i	$-0.359620\pi$
$241$	2.87994e9			0.853720			0.426860	+	0.904318i	$0.359620\pi$
$242$	6.84469e8	−	6.84469e8i	0.199569	−	0.199569i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$		−	1.44394e9i		−	0.407370i
$245$		0			0
$246$	1.20500e9			0.329039
$247$	3.38908e8	−	3.38908e8i	0.0910530	−	0.0910530i
$248$	−9.92310e8	−	9.92310e8i	−0.262326	−	0.262326i
$249$		−	1.68373e8i		−	0.0438001i
$250$		0			0
$251$	−1.05347e9			−0.265415			−0.132708	−	0.991155i	$-0.542367\pi$
$251$	−1.05347e9			−0.265415			−0.132708	+	0.991155i	$0.542367\pi$
$252$	1.51977e9	−	1.51977e9i	0.376856	−	0.376856i
$253$	1.33069e9	+	1.33069e9i	0.324784	+	0.324784i
$254$		−	5.53332e8i		−	0.132938i
$255$		0			0
$256$	8.97101e8			0.208873
$257$	1.46753e9	−	1.46753e9i	0.336399	−	0.336399i	−0.518611	−	0.855010i	$-0.673551\pi$
$257$	1.46753e9	−	1.46753e9i	0.336399	−	0.336399i	0.855010	+	0.518611i	$0.173551\pi$
$258$	6.99679e7	+	6.99679e7i	0.0157914	+	0.0157914i
$259$			1.81487e9i			0.403316i
$260$		0			0
$261$	1.07789e9			0.232280
$262$	−8.12995e7	+	8.12995e7i	−0.0172537	+	0.0172537i
$263$	−5.69296e8	−	5.69296e8i	−0.118991	−	0.118991i	0.645104	−	0.764095i	$-0.276814\pi$
$263$	−5.69296e8	−	5.69296e8i	−0.118991	−	0.118991i	−0.764095	+	0.645104i	$0.776814\pi$
$264$		−	4.10210e8i		−	0.0844482i
$265$		0			0
$266$	2.60324e8			0.0519982
$267$	−1.94446e9	+	1.94446e9i	−0.382607	+	0.382607i
$268$	−2.12111e8	−	2.12111e8i	−0.0411173	−	0.0411173i
$269$		−	4.20262e9i		−	0.802622i	−0.915942	−	0.401311i	$-0.868555\pi$
$269$		−	4.20262e9i		−	0.802622i	0.915942	−	0.401311i	$-0.131445\pi$
$270$		0			0
$271$	−4.34712e9			−0.805980			−0.402990	−	0.915204i	$-0.632029\pi$
$271$	−4.34712e9			−0.805980			−0.402990	+	0.915204i	$0.632029\pi$
$272$	−1.02722e9	+	1.02722e9i	−0.187668	+	0.187668i
$273$	5.24173e9	+	5.24173e9i	0.943678	+	0.943678i
$274$		−	1.93216e9i		−	0.342799i
$275$		0			0
$276$	−5.50751e9			−0.949115
$277$	3.17706e9	−	3.17706e9i	0.539643	−	0.539643i	−0.383781	−	0.923424i	$-0.625378\pi$
$277$	3.17706e9	−	3.17706e9i	0.539643	−	0.539643i	0.923424	+	0.383781i	$0.125378\pi$
$278$	2.26550e9	+	2.26550e9i	0.379302	+	0.379302i
$279$			1.30102e9i			0.214718i
$280$		0			0
$281$	1.69869e9			0.272451			0.136225	−	0.990678i	$-0.456503\pi$
$281$	1.69869e9			0.272451			0.136225	+	0.990678i	$0.456503\pi$
$282$	−4.42013e8	+	4.42013e8i	−0.0698938	+	0.0698938i
$283$	−1.40099e9	−	1.40099e9i	−0.218418	−	0.218418i	0.589413	−	0.807832i	$-0.299359\pi$
$283$	−1.40099e9	−	1.40099e9i	−0.218418	−	0.218418i	−0.807832	+	0.589413i	$0.799359\pi$
$284$		−	6.73370e9i		−	1.03510i
$285$		0			0
$286$	6.73684e8			0.100691
$287$	1.59409e10	−	1.59409e10i	2.34956	−	2.34956i
$288$	1.29358e9	+	1.29358e9i	0.188029	+	0.188029i
$289$			6.06678e9i			0.869694i
$290$		0			0
$291$	−4.34829e9			−0.606383
$292$	−2.99570e9	+	2.99570e9i	−0.412066	+	0.412066i
$293$	−8.47944e9	−	8.47944e9i	−1.15053	−	1.15053i	−0.986447	−	0.164079i	$-0.947535\pi$
$293$	−8.47944e9	−	8.47944e9i	−1.15053	−	1.15053i	−0.164079	−	0.986447i	$-0.552465\pi$
$294$			2.72496e9i			0.364730i
$295$		0			0
$296$	−1.01373e9			−0.132055
$297$	−2.68914e8	+	2.68914e8i	−0.0345612	+	0.0345612i
$298$	−4.68369e8	−	4.68369e8i	−0.0593913	−	0.0593913i
$299$		−	1.89955e10i		−	2.37666i
$300$		0			0
$301$	1.85121e9			0.225522
$302$	−4.66813e8	+	4.66813e8i	−0.0561196	+	0.0561196i
$303$	−3.83861e9	−	3.83861e9i	−0.455411	−	0.455411i
$304$		−	6.15296e8i		−	0.0720426i
$305$		0			0
$306$	−3.18281e8			−0.0363015
$307$	−4.87814e9	+	4.87814e9i	−0.549162	+	0.549162i	−0.926198	−	0.377036i	$-0.876943\pi$
$307$	−4.87814e9	+	4.87814e9i	−0.549162	+	0.549162i	0.377036	+	0.926198i	$0.376943\pi$
$308$	−2.58396e9	−	2.58396e9i	−0.287132	−	0.287132i
$309$		−	4.90184e9i		−	0.537682i
$310$		0			0
$311$	7.32957e9			0.783496			0.391748	−	0.920073i	$-0.371870\pi$
$311$	7.32957e9			0.783496			0.391748	+	0.920073i	$0.371870\pi$
$312$	−2.92787e9	+	2.92787e9i	−0.308982	+	0.308982i
$313$	−1.09178e10	−	1.09178e10i	−1.13752	−	1.13752i	−0.988894	−	0.148625i	$-0.952515\pi$
$313$	−1.09178e10	−	1.09178e10i	−1.13752	−	1.13752i	−0.148625	−	0.988894i	$-0.547485\pi$
$314$			4.07794e9i			0.419490i
$315$		0			0
$316$	−9.43028e9			−0.945750
$317$	−5.67267e9	+	5.67267e9i	−0.561759	+	0.561759i	−0.929807	−	0.368048i	$-0.880026\pi$
$317$	−5.67267e9	+	5.67267e9i	−0.561759	+	0.561759i	0.368048	+	0.929807i	$0.380026\pi$
$318$	1.25601e9	+	1.25601e9i	0.122824	+	0.122824i
$319$		−	1.83265e9i		−	0.176977i
$320$		0			0
$321$	−3.20115e9			−0.301499
$322$	7.29548e9	−	7.29548e9i	0.678626	−	0.678626i
$323$	2.72235e8	+	2.72235e8i	0.0250111	+	0.0250111i
$324$		−	1.11299e9i		−	0.100998i
$325$		0			0
$326$	3.82084e9			0.338289
$327$	8.39928e8	−	8.39928e8i	0.0734601	−	0.0734601i
$328$	8.90411e9	+	8.90411e9i	0.769299	+	0.769299i
$329$			1.16947e10i			0.998176i
$330$		0			0
$331$	−1.49297e10			−1.24377			−0.621883	−	0.783110i	$-0.713632\pi$
$331$	−1.49297e10			−1.24377			−0.621883	+	0.783110i	$0.713632\pi$
$332$	5.92418e8	−	5.92418e8i	0.0487613	−	0.0487613i
$333$	6.64552e8	+	6.64552e8i	0.0540446	+	0.0540446i
$334$		−	4.06188e9i		−	0.326393i
$335$		0			0
$336$	9.51648e9			0.746654
$337$	−1.16331e10	+	1.16331e10i	−0.901939	+	0.901939i	−0.995604	−	0.0936652i	$-0.970142\pi$
$337$	−1.16331e10	+	1.16331e10i	−0.901939	+	0.901939i	0.0936652	+	0.995604i	$0.470142\pi$
$338$	−2.02411e9	−	2.02411e9i	−0.155084	−	0.155084i
$339$			8.09335e9i			0.612815i
$340$		0			0
$341$	2.21204e9			0.163597
$342$	9.53233e7	−	9.53233e7i	0.00696778	−	0.00696778i
$343$	1.88329e10	+	1.88329e10i	1.36064	+	1.36064i
$344$			1.03403e9i			0.0738410i
$345$		0			0
$346$	−4.41338e8			−0.0307941
$347$	1.62365e10	−	1.62365e10i	1.11988	−	1.11988i	0.128127	−	0.991758i	$-0.459103\pi$
$347$	1.62365e10	−	1.62365e10i	1.11988	−	1.11988i	0.991758	−	0.128127i	$-0.0408966\pi$
$348$	3.79253e9	+	3.79253e9i	0.258590	+	0.258590i
$349$		−	1.99031e10i		−	1.34159i	−0.741645	−	0.670793i	$-0.765954\pi$
$349$		−	1.99031e10i		−	1.34159i	0.741645	−	0.670793i	$-0.234046\pi$
$350$		0			0
$351$	3.83874e9			0.252907
$352$	2.19938e9	−	2.19938e9i	0.143262	−	0.143262i
$353$	1.08087e10	+	1.08087e10i	0.696106	+	0.696106i	0.963568	−	0.267463i	$-0.0861852\pi$
$353$	1.08087e10	+	1.08087e10i	0.696106	+	0.696106i	−0.267463	+	0.963568i	$0.586185\pi$
$354$			2.51797e9i			0.160338i
$355$		0			0
$356$	−1.36831e10			−0.851891
$357$	−4.21052e9	+	4.21052e9i	−0.259217	+	0.259217i
$358$	−4.88074e9	−	4.88074e9i	−0.297135	−	0.297135i
$359$			1.31053e10i			0.788987i	0.918899	+	0.394494i	$0.129080\pi$
$359$			1.31053e10i			0.788987i	−0.918899	+	0.394494i	$0.870920\pi$
$360$		0			0
$361$	1.68205e10			0.990399
$362$	−3.13251e7	+	3.13251e7i	−0.00182414	+	0.00182414i
$363$	−6.63123e9	−	6.63123e9i	−0.381916	−	0.381916i
$364$			3.68859e10i			2.10114i
$365$		0			0
$366$	1.40076e9			0.0780617
$367$	1.18302e9	−	1.18302e9i	0.0652120	−	0.0652120i	−0.673749	−	0.738961i	$-0.735317\pi$
$367$	1.18302e9	−	1.18302e9i	0.0652120	−	0.0652120i	0.738961	+	0.673749i	$0.235317\pi$
$368$	−1.72434e10	−	1.72434e10i	−0.940226	−	0.940226i
$369$		−	1.16742e10i		−	0.629684i
$370$		0			0
$371$	3.32313e10			1.75409
$372$	−4.57763e9	+	4.57763e9i	−0.239039	+	0.239039i
$373$	5.06748e9	+	5.06748e9i	0.261792	+	0.261792i	0.825782	−	0.563990i	$-0.190734\pi$
$373$	5.06748e9	+	5.06748e9i	0.261792	+	0.261792i	−0.563990	+	0.825782i	$0.690734\pi$
$374$			5.41150e8i			0.0276586i
$375$		0			0
$376$	−6.53232e9			−0.326826
$377$	−1.30805e10	+	1.30805e10i	−0.647530	+	0.647530i
$378$	1.47432e9	+	1.47432e9i	0.0722145	+	0.0722145i
$379$		−	3.93866e9i		−	0.190894i	−0.995435	−	0.0954470i	$-0.969572\pi$
$379$		−	3.93866e9i		−	0.190894i	0.995435	−	0.0954470i	$-0.0304280\pi$
$380$		0			0
$381$	−5.36075e9			−0.254405
$382$	−6.61283e9	+	6.61283e9i	−0.310552	+	0.310552i
$383$	2.28411e10	+	2.28411e10i	1.06150	+	1.06150i	0.997980	+	0.0635221i	$0.0202333\pi$
$383$	2.28411e10	+	2.28411e10i	1.06150	+	1.06150i	0.0635221	+	0.997980i	$0.479767\pi$
$384$			1.18874e10i			0.546718i
$385$		0			0
$386$	5.81204e9			0.261806
$387$	6.77859e8	−	6.77859e8i	0.0302201	−	0.0302201i
$388$	−1.52994e10	−	1.52994e10i	−0.675068	−	0.675068i
$389$			2.99063e10i			1.30607i	0.757330	+	0.653033i	$0.226504\pi$
$389$			2.99063e10i			1.30607i	−0.757330	+	0.653033i	$0.773496\pi$
$390$		0			0
$391$	1.52585e10			0.652839
$392$	−2.01355e10	+	2.01355e10i	−0.852744	+	0.852744i
$393$	7.87640e8	+	7.87640e8i	0.0330185	+	0.0330185i
$394$			1.83015e9i			0.0759454i
$395$		0			0
$396$	−1.89234e9			−0.0769518
$397$	−1.79942e10	+	1.79942e10i	−0.724385	+	0.724385i	−0.969495	−	0.245110i	$-0.921176\pi$
$397$	−1.79942e10	+	1.79942e10i	−0.724385	+	0.724385i	0.245110	+	0.969495i	$0.421176\pi$
$398$	−6.71618e9	−	6.71618e9i	−0.267664	−	0.267664i
$399$		−	2.52206e9i		−	0.0995092i
$400$		0			0
$401$	−7.45517e9			−0.288323			−0.144162	−	0.989554i	$-0.546049\pi$
$401$	−7.45517e9			−0.288323			−0.144162	+	0.989554i	$0.546049\pi$
$402$	2.05768e8	−	2.05768e8i	0.00787903	−	0.00787903i
$403$	−1.57884e10	−	1.57884e10i	−0.598573	−	0.598573i
$404$		−	2.70122e10i		−	1.01399i
$405$		0			0
$406$	−1.00475e10			−0.369789
$407$	1.12989e9	−	1.12989e9i	0.0411774	−	0.0411774i
$408$	−2.35187e9	−	2.35187e9i	−0.0848735	−	0.0848735i
$409$			2.73971e10i			0.979065i	0.871985	+	0.489533i	$0.162833\pi$
$409$			2.73971e10i			0.979065i	−0.871985	+	0.489533i	$0.837167\pi$
$410$		0			0
$411$	−1.87190e10			−0.656017
$412$	1.72471e10	−	1.72471e10i	0.598585	−	0.598585i
$413$	3.33101e10	+	3.33101e10i	1.14492	+	1.14492i
$414$		−	5.34280e9i		−	0.181873i
$415$		0			0
$416$	−3.13961e10			−1.04834
$417$	2.19485e10	−	2.19485e10i	0.725872	−	0.725872i
$418$	−1.62071e8	−	1.62071e8i	−0.00530886	−	0.00530886i
$419$		−	2.45940e10i		−	0.797947i	−0.916963	−	0.398973i	$-0.869367\pi$
$419$		−	2.45940e10i		−	0.797947i	0.916963	−	0.398973i	$-0.130633\pi$
$420$		0			0
$421$	4.95943e10			1.57871			0.789356	−	0.613935i	$-0.210414\pi$
$421$	4.95943e10			1.57871			0.789356	+	0.613935i	$0.210414\pi$
$422$	9.83848e9	−	9.83848e9i	0.310226	−	0.310226i
$423$	4.28228e9	+	4.28228e9i	0.133756	+	0.133756i
$424$			1.85620e10i			0.574328i
$425$		0			0
$426$	6.53231e9			0.198348
$427$	1.85305e10	−	1.85305e10i	0.557412	−	0.557412i
$428$	−1.12632e10	−	1.12632e10i	−0.335650	−	0.335650i
$429$		−	6.52674e9i		−	0.192694i
$430$		0			0
$431$	−8.93548e9			−0.258946			−0.129473	−	0.991583i	$-0.541329\pi$
$431$	−8.93548e9			−0.258946			−0.129473	+	0.991583i	$0.541329\pi$
$432$	3.48467e9	−	3.48467e9i	0.100052	−	0.100052i
$433$	−4.09306e9	−	4.09306e9i	−0.116439	−	0.116439i	0.646487	−	0.762925i	$-0.276238\pi$
$433$	−4.09306e9	−	4.09306e9i	−0.116439	−	0.116439i	−0.762925	+	0.646487i	$0.776238\pi$
$434$		−	1.21275e10i		−	0.341830i
$435$		0			0
$436$	5.91055e9			0.163562
$437$	−4.56985e9	+	4.56985e9i	−0.125307	+	0.125307i
$438$	−2.90611e9	−	2.90611e9i	−0.0789614	−	0.0789614i
$439$		−	6.34014e10i		−	1.70703i	−0.521070	−	0.853514i	$-0.674467\pi$
$439$		−	6.34014e10i		−	1.70703i	0.521070	−	0.853514i	$-0.325533\pi$
$440$		0			0
$441$	2.63998e10			0.697985
$442$	3.86245e9	−	3.86245e9i	0.101198	−	0.101198i
$443$	−2.73590e10	−	2.73590e10i	−0.710371	−	0.710371i	0.256242	−	0.966613i	$-0.417516\pi$
$443$	−2.73590e10	−	2.73590e10i	−0.710371	−	0.710371i	−0.966613	+	0.256242i	$0.917516\pi$
$444$			4.67643e9i			0.120332i
$445$		0			0
$446$	−1.23138e10			−0.311208
$447$	−4.53762e9	+	4.53762e9i	−0.113657	+	0.113657i
$448$	2.47783e10	+	2.47783e10i	0.615119	+	0.615119i
$449$			1.56376e10i			0.384755i	0.981321	+	0.192377i	$0.0616197\pi$
$449$			1.56376e10i			0.384755i	−0.981321	+	0.192377i	$0.938380\pi$
$450$		0			0
$451$	−1.98489e10			−0.479766
$452$	−2.84763e10	+	2.84763e10i	−0.682229	+	0.682229i
$453$	4.52254e9	+	4.52254e9i	0.107396	+	0.107396i
$454$		−	1.93192e10i		−	0.454742i
$455$		0			0
$456$	1.40874e9			0.0325816
$457$	4.45561e10	−	4.45561e10i	1.02151	−	1.02151i	0.0217466	−	0.999764i	$-0.493077\pi$
$457$	4.45561e10	−	4.45561e10i	1.02151	−	1.02151i	0.999764	−	0.0217466i	$-0.00692271\pi$
$458$	8.53123e8	+	8.53123e8i	0.0193887	+	0.0193887i
$459$			3.08355e9i			0.0694704i
$460$		0			0
$461$	−7.09502e10			−1.57091			−0.785453	−	0.618922i	$-0.787570\pi$
$461$	−7.09502e10			−1.57091			−0.785453	+	0.618922i	$0.787570\pi$
$462$	2.50668e9	−	2.50668e9i	0.0550213	−	0.0550213i
$463$	5.16781e9	+	5.16781e9i	0.112456	+	0.112456i	0.761096	−	0.648640i	$-0.224662\pi$
$463$	5.16781e9	+	5.16781e9i	0.112456	+	0.112456i	−0.648640	+	0.761096i	$0.724662\pi$
$464$			2.37480e10i			0.512336i
$465$		0			0
$466$	1.38860e10			0.294465
$467$	−5.20025e10	+	5.20025e10i	−1.09334	+	1.09334i	−0.0981747	+	0.995169i	$0.531300\pi$
$467$	−5.20025e10	+	5.20025e10i	−1.09334	+	1.09334i	−0.995169	+	0.0981747i	$0.968700\pi$
$468$	1.35066e10	+	1.35066e10i	0.281554	+	0.281554i
$469$		−	5.44418e9i		−	0.112523i
$470$		0			0
$471$	3.95076e10			0.802781
$472$	−1.86060e10	+	1.86060e10i	−0.374873	+	0.374873i
$473$	−1.15251e9	−	1.15251e9i	−0.0230251	−	0.0230251i
$474$		−	9.14825e9i		−	0.181228i
$475$		0			0
$476$	−2.96293e10			−0.577157
$477$	1.21683e10	−	1.21683e10i	0.235049	−	0.235049i
$478$	−5.54227e9	−	5.54227e9i	−0.106164	−	0.106164i
$479$			6.51302e10i			1.23720i	0.785706	+	0.618601i	$0.212300\pi$
$479$			6.51302e10i			1.23720i	−0.785706	+	0.618601i	$0.787700\pi$
$480$		0			0
$481$	−1.61291e10			−0.301322
$482$	−9.82999e9	+	9.82999e9i	−0.182123	+	0.182123i
$483$	−7.06796e10	−	7.06796e10i	−1.29869	−	1.29869i
$484$		−	4.66638e10i		−	0.850351i
$485$		0			0
$486$	1.07971e9			0.0193536
$487$	2.48309e10	−	2.48309e10i	0.441445	−	0.441445i	−0.451053	−	0.892497i	$-0.648951\pi$
$487$	2.48309e10	−	2.48309e10i	0.441445	−	0.441445i	0.892497	+	0.451053i	$0.148951\pi$
$488$	1.03506e10	+	1.03506e10i	0.182509	+	0.182509i
$489$		−	3.70168e10i		−	0.647386i
$490$		0			0
$491$	9.96236e9			0.171410			0.0857050	−	0.996321i	$-0.472686\pi$
$491$	9.96236e9			0.171410			0.0857050	+	0.996321i	$0.472686\pi$
$492$	4.10756e10	−	4.10756e10i	0.701009	−	0.701009i
$493$	−1.05072e10	−	1.05072e10i	−0.177868	−	0.177868i
$494$			2.31356e9i			0.0388484i
$495$		0			0
$496$	−2.86642e10			−0.473601
$497$	8.64157e10	−	8.64157e10i	1.41634	−	1.41634i
$498$	5.74700e8	+	5.74700e8i	0.00934381	+	0.00934381i
$499$		−	9.64141e10i		−	1.55503i	−0.628865	−	0.777514i	$-0.716480\pi$
$499$		−	9.64141e10i		−	1.55503i	0.628865	−	0.777514i	$-0.283520\pi$
$500$		0			0
$501$	−3.93520e10			−0.624620
$502$	3.59575e9	−	3.59575e9i	0.0566207	−	0.0566207i
$503$	1.79788e10	+	1.79788e10i	0.280860	+	0.280860i	0.833452	−	0.552592i	$-0.186361\pi$
$503$	1.79788e10	+	1.79788e10i	0.280860	+	0.280860i	−0.552592	+	0.833452i	$0.686361\pi$
$504$			2.17883e10i			0.337677i
$505$		0			0
$506$	−9.08397e9			−0.138571
$507$	−1.96098e10	+	1.96098e10i	−0.296785	+	0.296785i
$508$	−1.88617e10	−	1.88617e10i	−0.283222	−	0.283222i
$509$		−	7.61419e10i		−	1.13436i	−0.823592	−	0.567182i	$-0.808034\pi$
$509$		−	7.61419e10i		−	1.13436i	0.823592	−	0.567182i	$-0.191966\pi$
$510$		0			0
$511$	−7.68895e10			−1.12767
$512$	−4.90759e10	+	4.90759e10i	−0.714148	+	0.714148i
$513$	−9.23505e8	−	9.23505e8i	−0.0133343	−	0.0133343i
$514$			1.00181e10i			0.143527i
$515$		0			0
$516$	4.77007e9			0.0672862
$517$	7.28086e9	−	7.28086e9i	0.101911	−	0.101911i
$518$	−6.19461e9	−	6.19461e9i	−0.0860389	−	0.0860389i
$519$			4.27575e9i			0.0589308i
$520$		0			0
$521$	8.59219e10			1.16615			0.583073	−	0.812420i	$-0.301850\pi$
$521$	8.59219e10			1.16615			0.583073	+	0.812420i	$0.301850\pi$
$522$	−3.67910e9	+	3.67910e9i	−0.0495519	+	0.0495519i
$523$	2.70058e9	+	2.70058e9i	0.0360953	+	0.0360953i	0.724924	−	0.688829i	$-0.241875\pi$
$523$	2.70058e9	+	2.70058e9i	0.0360953	+	0.0360953i	−0.688829	+	0.724924i	$0.741875\pi$
$524$			5.54260e9i			0.0735171i
$525$		0			0
$526$	3.88631e9			0.0507685
$527$	1.26823e10	−	1.26823e10i	0.164420	−	0.164420i
$528$	−5.92472e9	−	5.92472e9i	−0.0762311	−	0.0762311i
$529$			1.77825e11i			2.27076i
$530$		0			0
$531$	2.43944e10			0.306840
$532$	8.87382e9	−	8.87382e9i	0.110781	−	0.110781i
$533$	1.41671e11	+	1.41671e11i	1.75538	+	1.75538i
$534$		−	1.32739e10i		−	0.163242i
$535$		0			0
$536$	3.04095e9			0.0368426
$537$	−4.72853e10	+	4.72853e10i	−0.568628	+	0.568628i
$538$	1.43446e10	+	1.43446e10i	0.171222	+	0.171222i
$539$		−	4.48857e10i		−	0.531805i
$540$		0			0
$541$	1.15164e11			1.34440			0.672199	−	0.740371i	$-0.265350\pi$
$541$	1.15164e11			1.34440			0.672199	+	0.740371i	$0.265350\pi$
$542$	1.48378e10	−	1.48378e10i	0.171939	−	0.171939i
$543$	3.03482e8	+	3.03482e8i	0.00349087	+	0.00349087i
$544$		−	2.52196e10i		−	0.287966i
$545$		0			0
$546$	−3.57828e10			−0.402627
$547$	−1.03711e11	+	1.03711e11i	−1.15845	+	1.15845i	−0.173640	+	0.984809i	$0.555553\pi$
$547$	−1.03711e11	+	1.03711e11i	−1.15845	+	1.15845i	−0.984809	+	0.173640i	$0.944447\pi$
$548$	−6.58625e10	−	6.58625e10i	−0.730324	−	0.730324i
$549$		−	1.35707e10i		−	0.149387i
$550$		0			0
$551$	6.29369e9			0.0682808
$552$	3.94794e10	−	3.94794e10i	0.425221	−	0.425221i
$553$	−1.21022e11	−	1.21022e11i	−1.29409	−	1.29409i
$554$			2.16883e10i			0.230243i
$555$		0			0
$556$	1.54451e11			1.61618
$557$	−6.32848e10	+	6.32848e10i	−0.657474	+	0.657474i	−0.954782	−	0.297308i	$-0.903911\pi$
$557$	−6.32848e10	+	6.32848e10i	−0.657474	+	0.657474i	0.297308	+	0.954782i	$0.403911\pi$
$558$	−4.44073e9	−	4.44073e9i	−0.0458055	−	0.0458055i
$559$			1.64521e10i			0.168490i
$560$		0			0
$561$	5.24273e9			0.0529305
$562$	−5.79805e9	+	5.79805e9i	−0.0581215	+	0.0581215i
$563$	2.35869e9	+	2.35869e9i	0.0234767	+	0.0234767i	0.718748	−	0.695271i	$-0.244716\pi$
$563$	2.35869e9	+	2.35869e9i	0.0234767	+	0.0234767i	−0.695271	+	0.718748i	$0.744716\pi$
$564$			3.01343e10i			0.297814i
$565$		0			0
$566$	9.56387e9			0.0931897
$567$	1.42834e10	−	1.42834e10i	0.138197	−	0.138197i
$568$	4.82691e10	+	4.82691e10i	0.463742	+	0.463742i
$569$			1.72859e11i			1.64908i	0.565802	+	0.824541i	$0.308567\pi$
$569$			1.72859e11i			1.64908i	−0.565802	+	0.824541i	$0.691433\pi$
$570$		0			0
$571$	−1.00753e11			−0.947792			−0.473896	−	0.880581i	$-0.657153\pi$
$571$	−1.00753e11			−0.947792			−0.473896	+	0.880581i	$0.657153\pi$
$572$	2.29642e10	−	2.29642e10i	0.214520	−	0.214520i
$573$	6.40660e10	+	6.40660e10i	0.594305	+	0.594305i
$574$			1.08821e11i			1.00246i
$575$		0			0
$576$	1.81462e10			0.164853
$577$	3.96749e10	−	3.96749e10i	0.357942	−	0.357942i	−0.505112	−	0.863054i	$-0.668549\pi$
$577$	3.96749e10	−	3.96749e10i	0.357942	−	0.357942i	0.863054	+	0.505112i	$0.168549\pi$
$578$	−2.07075e10	−	2.07075e10i	−0.185531	−	0.185531i
$579$		−	5.63078e10i		−	0.501019i
$580$		0			0
$581$	1.52054e10			0.133442
$582$	1.48419e10	−	1.48419e10i	0.129359	−	0.129359i
$583$	−2.06890e10	−	2.06890e10i	−0.179087	−	0.179087i
$584$		−	4.29481e10i		−	0.369226i
$585$		0			0
$586$	5.78850e10			0.490880
$587$	−2.04147e10	+	2.04147e10i	−0.171946	+	0.171946i	−0.787834	−	0.615888i	$-0.788797\pi$
$587$	−2.04147e10	+	2.04147e10i	−0.171946	+	0.171946i	0.615888	+	0.787834i	$0.288797\pi$
$588$	9.28873e10	+	9.28873e10i	0.777046	+	0.777046i
$589$			7.59657e9i			0.0631184i
$590$		0			0
$591$	1.77307e10			0.145337
$592$	−1.46414e10	+	1.46414e10i	−0.119206	+	0.119206i
$593$	−4.33841e9	−	4.33841e9i	−0.0350842	−	0.0350842i	0.689347	−	0.724431i	$-0.257898\pi$
$593$	−4.33841e9	−	4.33841e9i	−0.0350842	−	0.0350842i	−0.724431	+	0.689347i	$0.757898\pi$
$594$		−	1.83575e9i		−	0.0147458i
$595$		0			0
$596$	−3.19311e10			−0.253063
$597$	−6.50673e10	+	6.50673e10i	−0.512230	+	0.512230i
$598$	6.48367e10	+	6.48367e10i	0.507010	+	0.507010i
$599$			7.57336e10i			0.588276i	0.955763	+	0.294138i	$0.0950326\pi$
$599$			7.57336e10i			0.588276i	−0.955763	+	0.294138i	$0.904967\pi$
$600$		0			0
$601$	−1.77282e11			−1.35883			−0.679416	−	0.733753i	$-0.737767\pi$
$601$	−1.77282e11			−1.35883			−0.679416	+	0.733753i	$0.737767\pi$
$602$	−6.31864e9	+	6.31864e9i	−0.0481103	+	0.0481103i
$603$	−1.99350e9	−	1.99350e9i	−0.0150782	−	0.0150782i
$604$			3.18250e10i			0.239123i
$605$		0			0
$606$	2.62044e10			0.194305
$607$	5.36913e10	−	5.36913e10i	0.395503	−	0.395503i	−0.481141	−	0.876643i	$-0.659777\pi$
$607$	5.36913e10	−	5.36913e10i	0.395503	−	0.395503i	0.876643	+	0.481141i	$0.159777\pi$
$608$	7.55312e9	+	7.55312e9i	0.0552729	+	0.0552729i
$609$			9.73414e10i			0.707666i
$610$		0			0
$611$	−1.03934e11			−0.745749
$612$	−1.08494e10	+	1.08494e10i	−0.0773393	+	0.0773393i
$613$	8.48533e10	+	8.48533e10i	0.600934	+	0.600934i	0.940560	−	0.339627i	$-0.110301\pi$
$613$	8.48533e10	+	8.48533e10i	0.600934	+	0.600934i	−0.339627	+	0.940560i	$0.610301\pi$
$614$		−	3.33007e10i		−	0.234304i
$615$		0			0
$616$	3.70451e10			0.257281
$617$	−4.57825e10	+	4.57825e10i	−0.315907	+	0.315907i	−0.847193	−	0.531286i	$-0.821709\pi$
$617$	−4.57825e10	+	4.57825e10i	−0.315907	+	0.315907i	0.531286	+	0.847193i	$0.321709\pi$
$618$	1.67313e10	+	1.67313e10i	0.114703	+	0.114703i
$619$			7.33128e9i			0.0499364i	0.999688	+	0.0249682i	$0.00794845\pi$
$619$			7.33128e9i			0.0499364i	−0.999688	+	0.0249682i	$0.992052\pi$
$620$		0			0
$621$	−5.17617e10			−0.348051
$622$	−2.50177e10	+	2.50177e10i	−0.167142	+	0.167142i
$623$	−1.75599e11	−	1.75599e11i	−1.16566	−	1.16566i
$624$			8.45752e10i			0.557834i
$625$		0			0
$626$	7.45307e10			0.485331
$627$	−1.57017e9	+	1.57017e9i	−0.0101596	+	0.0101596i
$628$	1.39007e11	+	1.39007e11i	0.893713	+	0.893713i
$629$		−	1.29560e10i		−	0.0827694i
$630$		0			0
$631$	1.33496e10			0.0842077			0.0421038	−	0.999113i	$-0.486594\pi$
$631$	1.33496e10			0.0842077			0.0421038	+	0.999113i	$0.486594\pi$
$632$	6.75990e10	−	6.75990e10i	0.423713	−	0.423713i
$633$	−9.53165e10	−	9.53165e10i	−0.593681	−	0.593681i
$634$		−	3.87246e10i		−	0.239679i
$635$		0			0
$636$	8.56283e10			0.523346
$637$	−3.20371e11	+	3.20371e11i	−1.94579	+	1.94579i
$638$	6.25532e9	+	6.25532e9i	0.0377543	+	0.0377543i
$639$		−	6.32859e10i		−	0.379580i
$640$		0			0
$641$	1.83871e11			1.08913			0.544565	−	0.838718i	$-0.316695\pi$
$641$	1.83871e11			1.08913			0.544565	+	0.838718i	$0.316695\pi$
$642$	1.09264e10	−	1.09264e10i	0.0643184	−	0.0643184i
$643$	−5.67204e10	−	5.67204e10i	−0.331815	−	0.331815i	0.521461	−	0.853275i	$-0.325387\pi$
$643$	−5.67204e10	−	5.67204e10i	−0.331815	−	0.331815i	−0.853275	+	0.521461i	$0.825387\pi$
$644$		−	4.97370e11i		−	2.89159i
$645$		0			0
$646$	−1.85841e9			−0.0106712
$647$	1.95804e11	−	1.95804e11i	1.11739	−	1.11739i	0.125264	−	0.992123i	$-0.460022\pi$
$647$	1.95804e11	−	1.95804e11i	1.11739	−	1.11739i	0.992123	−	0.125264i	$-0.0399778\pi$
$648$	7.97827e9	+	7.97827e9i	0.0452490	+	0.0452490i
$649$		−	4.14761e10i		−	0.233786i
$650$		0			0
$651$	−1.17492e11			−0.654163
$652$	1.30243e11	−	1.30243e11i	0.720716	−	0.720716i
$653$	−6.70806e10	−	6.70806e10i	−0.368930	−	0.368930i	0.498157	−	0.867087i	$-0.334010\pi$
$653$	−6.70806e10	−	6.70806e10i	−0.368930	−	0.368930i	−0.867087	+	0.498157i	$0.834010\pi$
$654$			5.73379e9i			0.0313423i
$655$		0			0
$656$	2.57207e11			1.38889
$657$	−2.81547e10	+	2.81547e10i	−0.151109	+	0.151109i
$658$	−3.99172e10	−	3.99172e10i	−0.212940	−	0.212940i
$659$			7.10757e10i			0.376860i	0.982087	+	0.188430i	$0.0603398\pi$
$659$			7.10757e10i			0.376860i	−0.982087	+	0.188430i	$0.939660\pi$
$660$		0			0
$661$	−1.11906e11			−0.586205			−0.293102	−	0.956081i	$-0.594688\pi$
$661$	−1.11906e11			−0.586205			−0.293102	+	0.956081i	$0.594688\pi$
$662$	5.09589e10	−	5.09589e10i	0.265331	−	0.265331i
$663$	−3.74199e10	−	3.74199e10i	−0.193664	−	0.193664i
$664$			8.49325e9i			0.0436920i
$665$		0			0
$666$	−4.53658e9			−0.0230585
$667$	1.76378e11	−	1.76378e11i	0.891131	−	0.891131i
$668$	−1.38459e11	−	1.38459e11i	−0.695371	−	0.695371i
$669$			1.19297e11i			0.595561i
$670$		0			0
$671$	−2.30733e10			−0.113820
$672$	−1.16820e11	+	1.16820e11i	−0.572851	+	0.572851i
$673$	−2.80577e10	−	2.80577e10i	−0.136771	−	0.136771i	0.635407	−	0.772177i	$-0.280832\pi$
$673$	−2.80577e10	−	2.80577e10i	−0.136771	−	0.136771i	−0.772177	+	0.635407i	$0.780832\pi$
$674$		−	7.94138e10i		−	0.384819i
$675$		0			0
$676$	−1.37994e11			−0.660804
$677$	1.20579e11	−	1.20579e11i	0.574005	−	0.574005i	−0.359240	−	0.933245i	$-0.616964\pi$
$677$	1.20579e11	−	1.20579e11i	0.574005	−	0.574005i	0.933245	+	0.359240i	$0.116964\pi$
$678$	−2.76247e10	−	2.76247e10i	−0.130731	−	0.130731i
$679$		−	3.92685e11i		−	1.84742i
$680$		0			0
$681$	−1.87167e11			−0.870242
$682$	−7.55025e9	+	7.55025e9i	−0.0348999	+	0.0348999i
$683$	1.10674e11	+	1.10674e11i	0.508584	+	0.508584i	0.914092	−	0.405508i	$-0.132905\pi$
$683$	1.10674e11	+	1.10674e11i	0.508584	+	0.508584i	−0.405508	+	0.914092i	$0.632905\pi$
$684$		−	6.49868e9i		−	0.0296893i
$685$		0			0
$686$	−1.28563e11			−0.580525
$687$	8.26517e9	−	8.26517e9i	0.0371043	−	0.0371043i
$688$	1.49346e10	+	1.49346e10i	0.0666560	+	0.0666560i
$689$			2.95334e11i			1.31050i
$690$		0			0
$691$	−3.83799e11			−1.68342			−0.841708	−	0.539933i	$-0.818450\pi$
$691$	−3.83799e11			−1.68342			−0.841708	+	0.539933i	$0.818450\pi$
$692$	−1.50441e10	+	1.50441e10i	−0.0656059	+	0.0656059i
$693$	−2.42850e10	−	2.42850e10i	−0.105295	−	0.105295i
$694$			1.10838e11i			0.477807i
$695$		0			0
$696$	−5.43719e10			−0.231706
$697$	−1.13800e11	+	1.13800e11i	−0.482182	+	0.482182i
$698$	6.79344e10	+	6.79344e10i	0.286199	+	0.286199i
$699$		−	1.34529e11i		−	0.563519i
$700$		0			0
$701$	2.12708e11			0.880871			0.440435	−	0.897784i	$-0.354824\pi$
$701$	2.12708e11			0.880871			0.440435	+	0.897784i	$0.354824\pi$
$702$	−1.31026e10	+	1.31026e10i	−0.0539523	+	0.0539523i
$703$	3.88027e9	+	3.88027e9i	0.0158869	+	0.0158869i
$704$		−	3.08527e10i		−	0.125604i
$705$		0			0
$706$	−7.37859e10			−0.296999
$707$	3.46656e11	−	3.46656e11i	1.38746	−	1.38746i
$708$	8.58314e10	+	8.58314e10i	0.341596	+	0.341596i
$709$			1.39198e11i			0.550868i	0.961320	+	0.275434i	$0.0888216\pi$
$709$			1.39198e11i			0.550868i	−0.961320	+	0.275434i	$0.911178\pi$
$710$		0			0
$711$	−8.86295e10			−0.346817
$712$	9.80844e10	−	9.80844e10i	0.381663	−	0.381663i
$713$	2.12891e11	+	2.12891e11i	0.823756	+	0.823756i
$714$		−	2.87432e10i		−	0.110597i
$715$		0			0
$716$	−3.32745e11			−1.26607
$717$	−5.36942e10	+	5.36942e10i	−0.203166	+	0.203166i
$718$	−4.47319e10	−	4.47319e10i	−0.168314	−	0.168314i
$719$		−	1.85015e11i		−	0.692294i	−0.938180	−	0.346147i	$-0.887490\pi$
$719$		−	1.85015e11i		−	0.692294i	0.938180	−	0.346147i	$-0.112510\pi$
$720$		0			0
$721$	4.42674e11			1.63811
$722$	−5.74127e10	+	5.74127e10i	−0.211280	+	0.211280i
$723$	9.52342e10	+	9.52342e10i	0.348530	+	0.348530i
$724$			2.13559e9i			0.00777257i
$725$		0			0
$726$	4.52682e10			0.162947
$727$	6.36461e10	−	6.36461e10i	0.227842	−	0.227842i	−0.583948	−	0.811791i	$-0.698493\pi$
$727$	6.36461e10	−	6.36461e10i	0.227842	−	0.227842i	0.811791	+	0.583948i	$0.198493\pi$
$728$	−2.64409e11	−	2.64409e11i	−0.941349	−	0.941349i
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	−1.32155e10			−0.0462821
$732$	4.77483e10	−	4.77483e10i	0.166308	−	0.166308i
$733$	−1.39320e11	−	1.39320e11i	−0.482611	−	0.482611i	0.423354	−	0.905964i	$-0.360853\pi$
$733$	−1.39320e11	−	1.39320e11i	−0.482611	−	0.482611i	−0.905964	+	0.423354i	$0.860853\pi$
$734$			8.07590e9i			0.0278232i
$735$		0			0
$736$	4.23347e11			1.44273
$737$	−3.38941e9	+	3.38941e9i	−0.0114883	+	0.0114883i
$738$	3.98472e10	+	3.98472e10i	0.134330	+	0.134330i
$739$		−	2.08330e11i		−	0.698513i	−0.937027	−	0.349256i	$-0.886434\pi$
$739$		−	2.08330e11i		−	0.698513i	0.937027	−	0.349256i	$-0.113566\pi$
$740$		0			0
$741$	2.24141e10			0.0743445
$742$	−1.13427e11	+	1.13427e11i	−0.374197	+	0.374197i
$743$	−2.39321e11	−	2.39321e11i	−0.785282	−	0.785282i	0.195434	−	0.980717i	$-0.437388\pi$
$743$	−2.39321e11	−	2.39321e11i	−0.785282	−	0.785282i	−0.980717	+	0.195434i	$0.937388\pi$
$744$		−	6.56276e10i		−	0.214188i
$745$		0			0
$746$	−3.45932e10			−0.111696
$747$	5.56778e9	−	5.56778e9i	0.0178813	−	0.0178813i
$748$	1.84465e10	+	1.84465e10i	0.0589260	+	0.0589260i
$749$		−	2.89089e11i		−	0.918552i
$750$		0			0
$751$	2.71597e11			0.853819			0.426909	−	0.904294i	$-0.359602\pi$
$751$	2.71597e11			0.853819			0.426909	+	0.904294i	$0.359602\pi$
$752$	−9.43473e10	+	9.43473e10i	−0.295025	+	0.295025i
$753$	−3.48361e10	−	3.48361e10i	−0.108355	−	0.108355i
$754$		−	8.92944e10i		−	0.276273i
$755$		0			0
$756$	1.00512e11			0.307702
$757$	−9.65225e10	+	9.65225e10i	−0.293931	+	0.293931i	−0.838631	−	0.544700i	$-0.816643\pi$
$757$	−9.65225e10	+	9.65225e10i	−0.293931	+	0.293931i	0.544700	+	0.838631i	$0.316643\pi$
$758$	1.34437e10	+	1.34437e10i	0.0407232	+	0.0407232i
$759$			8.80067e10i			0.265185i
$760$		0			0
$761$	8.48394e10			0.252964			0.126482	−	0.991969i	$-0.459631\pi$
$761$	8.48394e10			0.252964			0.126482	+	0.991969i	$0.459631\pi$
$762$	1.82976e10	−	1.82976e10i	0.0542719	−	0.0542719i
$763$	7.58520e10	+	7.58520e10i	0.223805	+	0.223805i
$764$			4.50831e11i			1.32324i
$765$		0			0
$766$	−1.55925e11			−0.452898
$767$	−2.96035e11	+	2.96035e11i	−0.855384	+	0.855384i
$768$	2.96654e10	+	2.96654e10i	0.0852719	+	0.0852719i
$769$			3.19744e11i			0.914318i	0.889385	+	0.457159i	$0.151133\pi$
$769$			3.19744e11i			0.914318i	−0.889385	+	0.457159i	$0.848867\pi$
$770$		0			0
$771$	9.70568e10			0.274668
$772$	1.98118e11	−	1.98118e11i	0.557770	−	0.557770i
$773$	3.14922e11	+	3.14922e11i	0.882034	+	0.882034i	0.993741	−	0.111707i	$-0.0356318\pi$
$773$	3.14922e11	+	3.14922e11i	0.882034	+	0.882034i	−0.111707	+	0.993741i	$0.535632\pi$
$774$			4.62741e9i			0.0128936i
$775$		0			0
$776$	2.19341e11			0.604886
$777$	−6.00142e10	+	6.00142e10i	−0.164653	+	0.164653i
$778$	−1.02078e11	−	1.02078e11i	−0.278621	−	0.278621i
$779$		−	6.81649e10i		−	0.185102i
$780$		0			0
$781$	−1.07601e11			−0.289208
$782$	−5.20813e10	+	5.20813e10i	−0.139269	+	0.139269i
$783$	3.56437e10	+	3.56437e10i	0.0948277	+	0.0948277i
$784$			5.81640e11i			1.53954i
$785$		0			0
$786$	−5.37684e9			−0.0140876
$787$	−3.26040e11	+	3.26040e11i	−0.849908	+	0.849908i	−0.990121	−	0.140213i	$-0.955221\pi$
$787$	−3.26040e11	+	3.26040e11i	−0.849908	+	0.849908i	0.140213	+	0.990121i	$0.455221\pi$
$788$	6.23853e10	+	6.23853e10i	0.161799	+	0.161799i
$789$		−	3.76511e10i		−	0.0971559i
$790$		0			0
$791$	−7.30892e11			−1.86701
$792$	1.35649e10	−	1.35649e10i	0.0344758	−	0.0344758i
$793$	1.64685e11	+	1.64685e11i	0.416449	+	0.416449i
$794$		−	1.22837e11i		−	0.309064i
$795$		0			0
$796$	−4.57877e11			−1.14050
$797$	−1.46875e11	+	1.46875e11i	−0.364012	+	0.364012i	−0.865288	−	0.501276i	$-0.832864\pi$
$797$	−1.46875e11	+	1.46875e11i	−0.364012	+	0.364012i	0.501276	+	0.865288i	$0.332864\pi$
$798$	8.60843e9	+	8.60843e9i	0.0212282	+	0.0212282i
$799$		−	8.34870e10i		−	0.204848i
$800$		0			0
$801$	−1.28599e11			−0.312397
$802$	2.54464e10	−	2.54464e10i	0.0615077	−	0.0615077i
$803$	4.78695e10	+	4.78695e10i	0.115132	+	0.115132i
$804$		−	1.40282e10i		−	0.0335721i
$805$		0			0
$806$	1.07780e11			0.255386
$807$	1.38973e11	−	1.38973e11i	0.327669	−	0.327669i
$808$	1.93632e11	+	1.93632e11i	0.454287	+	0.454287i
$809$			4.77326e11i			1.11435i	0.830395	+	0.557174i	$0.188115\pi$
$809$			4.77326e11i			1.11435i	−0.830395	+	0.557174i	$0.811885\pi$
$810$		0			0
$811$	2.18590e11			0.505297			0.252649	−	0.967558i	$-0.418698\pi$
$811$	2.18590e11			0.505297			0.252649	+	0.967558i	$0.418698\pi$
$812$	−3.42494e11	+	3.42494e11i	−0.787824	+	0.787824i
$813$	−1.43751e11	−	1.43751e11i	−0.329040	−	0.329040i
$814$			7.71321e9i			0.0175686i
$815$		0			0
$816$	−6.79367e10			−0.153230
$817$	3.95796e9	−	3.95796e9i	0.00888348	−	0.00888348i
$818$	−9.35135e10	−	9.35135e10i	−0.208863	−	0.208863i
$819$			3.46668e11i			0.770510i
$820$		0			0
$821$	7.72694e11			1.70073			0.850364	−	0.526195i	$-0.176382\pi$
$821$	7.72694e11			1.70073			0.850364	+	0.526195i	$0.176382\pi$
$822$	6.38928e10	−	6.38928e10i	0.139947	−	0.139947i
$823$	1.35869e11	+	1.35869e11i	0.296157	+	0.296157i	0.839507	−	0.543349i	$-0.182844\pi$
$823$	1.35869e11	+	1.35869e11i	0.296157	+	0.296157i	−0.543349	+	0.839507i	$0.682844\pi$
$824$			2.47264e11i			0.536354i
$825$		0			0
$826$	−2.27392e11			−0.488489
$827$	4.73937e11	−	4.73937e11i	1.01321	−	1.01321i	0.0132954	−	0.999912i	$-0.495768\pi$
$827$	4.73937e11	−	4.73937e11i	1.01321	−	1.01321i	0.999912	−	0.0132954i	$-0.00423218\pi$
$828$	−1.82123e11	−	1.82123e11i	−0.387475	−	0.387475i
$829$			2.22869e10i			0.0471881i	0.999722	+	0.0235940i	$0.00751091\pi$
$829$			2.22869e10i			0.0471881i	−0.999722	+	0.0235940i	$0.992489\pi$
$830$		0			0
$831$	2.10119e11			0.440617
$832$	−2.20211e11	+	2.20211e11i	−0.459563	+	0.459563i
$833$	−2.57344e11	−	2.57344e11i	−0.534483	−	0.534483i
$834$			1.49832e11i			0.309699i
$835$		0			0
$836$	−1.10492e10			−0.0226208
$837$	−4.30224e10	+	4.30224e10i	−0.0876582	+	0.0876582i
$838$	8.39458e10	+	8.39458e10i	0.170225	+	0.170225i
$839$		−	1.02047e11i		−	0.205945i	−0.994684	−	0.102973i	$-0.967165\pi$
$839$		−	1.02047e11i		−	0.205945i	0.994684	−	0.102973i	$-0.0328354\pi$
$840$		0			0
$841$	2.57335e11			0.514416
$842$	−1.69278e11	+	1.69278e11i	−0.336785	+	0.336785i
$843$	5.61723e10	+	5.61723e10i	0.111227	+	0.111227i
$844$		−	6.70740e11i		−	1.32186i
$845$		0			0
$846$	−2.92331e10			−0.0570681
$847$	5.98851e11	−	5.98851e11i	1.16355	−	1.16355i
$848$	2.68093e11	+	2.68093e11i	0.518444	+	0.518444i
$849$		−	9.26561e10i		−	0.178338i
$850$		0			0
$851$	2.17486e11			0.414680
$852$	2.22671e11	−	2.22671e11i	0.422576	−	0.422576i
$853$	−5.93009e10	−	5.93009e10i	−0.112012	−	0.112012i	0.648879	−	0.760891i	$-0.275238\pi$
$853$	−5.93009e10	−	5.93009e10i	−0.112012	−	0.112012i	−0.760891	+	0.648879i	$0.775238\pi$
$854$			1.26499e11i			0.237824i
$855$		0			0
$856$	1.61476e11			0.300755
$857$	−5.32423e11	+	5.32423e11i	−0.987038	+	0.987038i	−0.999917	−	0.0128791i	$-0.995900\pi$
$857$	−5.32423e11	+	5.32423e11i	−0.987038	+	0.987038i	0.0128791	+	0.999917i	$0.495900\pi$
$858$	2.22775e10	+	2.22775e10i	0.0411071	+	0.0411071i
$859$			6.20242e11i			1.13917i	0.821932	+	0.569585i	$0.192896\pi$
$859$			6.20242e11i			1.13917i	−0.821932	+	0.569585i	$0.807104\pi$
$860$		0			0
$861$	1.05427e12			1.91841
$862$	3.04991e10	−	3.04991e10i	0.0552406	−	0.0552406i
$863$	3.83679e11	+	3.83679e11i	0.691711	+	0.691711i	0.962608	−	0.270897i	$-0.0873203\pi$
$863$	3.83679e11	+	3.83679e11i	0.691711	+	0.691711i	−0.270897	+	0.962608i	$0.587320\pi$
$864$			8.55527e10i			0.153525i
$865$		0			0
$866$	2.79414e10			0.0496794
$867$	−2.00617e11	+	2.00617e11i	−0.355051	+	0.355051i
$868$	−4.13395e11	−	4.13395e11i	−0.728260	−	0.728260i
$869$			1.50690e11i			0.264245i
$870$		0			0
$871$	4.83838e10			0.0840673
$872$	−4.23686e10	+	4.23686e10i	−0.0732787	+	0.0732787i
$873$	−1.43790e11	−	1.43790e11i	−0.247555	−	0.247555i
$874$		−	3.11962e10i		−	0.0534632i
$875$		0			0
$876$	−1.98124e11			−0.336450
$877$	2.02189e11	−	2.02189e11i	0.341790	−	0.341790i	−0.515250	−	0.857040i	$-0.672301\pi$
$877$	2.02189e11	−	2.02189e11i	0.341790	−	0.341790i	0.857040	+	0.515250i	$0.172301\pi$
$878$	2.16405e11	+	2.16405e11i	0.364158	+	0.364158i
$879$		−	5.60798e11i		−	0.939401i
$880$		0			0
$881$	−4.18447e11			−0.694604			−0.347302	−	0.937753i	$-0.612902\pi$
$881$	−4.18447e11			−0.694604			−0.347302	+	0.937753i	$0.612902\pi$
$882$	−9.01093e10	+	9.01093e10i	−0.148900	+	0.148900i
$883$	4.16343e10	+	4.16343e10i	0.0684871	+	0.0684871i	0.740521	−	0.672034i	$-0.234579\pi$
$883$	4.16343e10	+	4.16343e10i	0.0684871	+	0.0684871i	−0.672034	+	0.740521i	$0.734579\pi$
$884$		−	2.63323e11i		−	0.431200i
$885$		0			0
$886$	1.86767e11			0.303085
$887$	−1.20656e11	+	1.20656e11i	−0.194918	+	0.194918i	−0.797817	−	0.602899i	$-0.794012\pi$
$887$	−1.20656e11	+	1.20656e11i	−0.194918	+	0.194918i	0.602899	+	0.797817i	$0.294012\pi$
$888$	−3.35221e10	−	3.35221e10i	−0.0539112	−	0.0539112i
$889$		−	4.84117e11i		−	0.775075i
$890$		0			0
$891$	−1.77850e10			−0.0282191
$892$	−4.19746e11	+	4.19746e11i	−0.663021	+	0.663021i
$893$	2.50039e10	+	2.50039e10i	0.0393189	+	0.0393189i
$894$		−	3.09761e10i		−	0.0484928i
$895$		0			0
$896$	−1.07353e12			−1.66564
$897$	6.28147e11	−	6.28147e11i	0.970267	−	0.970267i
$898$	−5.33751e10	−	5.33751e10i	−0.0820792	−	0.0820792i
$899$		−	2.93198e11i		−	0.448871i
$900$		0			0
$901$	−2.37233e11			−0.359978
$902$	6.77493e10	−	6.77493e10i	0.102348	−	0.102348i
$903$	6.12159e10	+	6.12159e10i	0.0920689	+	0.0920689i
$904$		−	4.08253e11i		−	0.611302i
$905$		0			0
$906$	−3.08732e10			−0.0458215
$907$	3.06605e11	−	3.06605e11i	0.453054	−	0.453054i	−0.443313	−	0.896367i	$-0.646197\pi$
$907$	3.06605e11	−	3.06605e11i	0.453054	−	0.453054i	0.896367	+	0.443313i	$0.146197\pi$
$908$	−6.58543e11	−	6.58543e11i	−0.968815	−	0.968815i
$909$		−	2.53871e11i		−	0.371842i
$910$		0			0
$911$	−6.24402e11			−0.906548			−0.453274	−	0.891371i	$-0.649744\pi$
$911$	−6.24402e11			−0.906548			−0.453274	+	0.891371i	$0.649744\pi$
$912$	2.03467e10	−	2.03467e10i	0.0294113	−	0.0294113i
$913$	−9.46649e9	−	9.46649e9i	−0.0136240	−	0.0136240i
$914$			3.04163e11i			0.435835i
$915$		0			0
$916$	5.81617e10			0.0826143
$917$	−7.11300e10	+	7.11300e10i	−0.100595	+	0.100595i
$918$	−1.05249e10	−	1.05249e10i	−0.0148200	−	0.0148200i
$919$			1.41399e11i			0.198236i	0.995076	+	0.0991181i	$0.0316022\pi$
$919$			1.41399e11i			0.198236i	−0.995076	+	0.0991181i	$0.968398\pi$
$920$		0			0
$921$	−3.22622e11			−0.448389
$922$	2.42171e11	−	2.42171e11i	0.335119	−	0.335119i
$923$	7.67997e11	+	7.67997e11i	1.05816	+	1.05816i
$924$		−	1.70893e11i		−	0.234443i
$925$		0			0
$926$	−3.52781e10			−0.0479802
$927$	1.62095e11	−	1.62095e11i	0.219508	−	0.219508i
$928$	−2.91521e11	−	2.91521e11i	−0.393077	−	0.393077i
$929$			5.68335e11i			0.763030i	0.924363	+	0.381515i	$0.124598\pi$
$929$			5.68335e11i			0.763030i	−0.924363	+	0.381515i	$0.875402\pi$
$930$		0			0
$931$	1.54146e11			0.205180
$932$	4.73340e11	−	4.73340e11i	0.627349	−	0.627349i
$933$	2.42375e11	+	2.42375e11i	0.319861	+	0.319861i
$934$		−	3.54996e11i		−	0.466483i
$935$		0			0
$936$	−1.93638e11			−0.252283
$937$	4.77324e11	−	4.77324e11i	0.619234	−	0.619234i	−0.326101	−	0.945335i	$-0.605735\pi$
$937$	4.77324e11	−	4.77324e11i	0.619234	−	0.619234i	0.945335	+	0.326101i	$0.105735\pi$
$938$	1.85824e10	+	1.85824e10i	0.0240044	+	0.0240044i
$939$		−	7.22063e11i		−	0.928780i
$940$		0			0
$941$	−4.47168e11			−0.570312			−0.285156	−	0.958481i	$-0.592045\pi$
$941$	−4.47168e11			−0.570312			−0.285156	+	0.958481i	$0.592045\pi$
$942$	−1.34850e11	+	1.34850e11i	−0.171256	+	0.171256i
$943$	−1.91029e12	−	1.91029e12i	−2.41576	−	2.41576i
$944$			5.37458e11i			0.676794i
$945$		0			0
$946$	7.86766e9			0.00982383
$947$	−5.32643e11	+	5.32643e11i	−0.662272	+	0.662272i	−0.955915	−	0.293643i	$-0.905132\pi$
$947$	−5.32643e11	+	5.32643e11i	−0.662272	+	0.662272i	0.293643	+	0.955915i	$0.405132\pi$
$948$	−3.11842e11	−	3.11842e11i	−0.386101	−	0.386101i
$949$		−	6.83335e11i		−	0.842498i
$950$		0			0
$951$	−3.75169e11			−0.458674
$952$	2.12392e11	−	2.12392e11i	0.258577	−	0.258577i
$953$	2.19524e11	+	2.19524e11i	0.266140	+	0.266140i	0.827543	−	0.561403i	$-0.189738\pi$
$953$	2.19524e11	+	2.19524e11i	0.266140	+	0.266140i	−0.561403	+	0.827543i	$0.689738\pi$
$954$			8.30674e10i			0.100285i
$955$		0			0
$956$	−3.77845e11			−0.452357
$957$	6.06023e10	−	6.06023e10i	0.0722506	−	0.0722506i
$958$	−2.22306e11	−	2.22306e11i	−0.263931	−	0.263931i
$959$		−	1.69047e12i		−	1.99863i
$960$		0			0
$961$	−4.98998e11			−0.585066
$962$	5.50529e10	−	5.50529e10i	0.0642807	−	0.0642807i
$963$	−1.05856e11	−	1.05856e11i	−0.123087	−	0.123087i
$964$			6.70161e11i			0.776016i
$965$		0			0
$966$	4.82496e11			0.554096
$967$	−9.42137e11	+	9.42137e11i	−1.07748	+	1.07748i	−0.0807427	+	0.996735i	$0.525729\pi$
$967$	−9.42137e11	+	9.42137e11i	−1.07748	+	1.07748i	−0.996735	+	0.0807427i	$0.974271\pi$
$968$	3.34500e11	+	3.34500e11i	0.380973	+	0.380973i
$969$			1.80046e10i			0.0204215i
$970$		0			0
$971$	5.07947e11			0.571401			0.285701	−	0.958319i	$-0.407774\pi$
$971$	5.07947e11			0.571401			0.285701	+	0.958319i	$0.407774\pi$
$972$	3.68046e10	−	3.68046e10i	0.0412322	−	0.0412322i
$973$	1.98212e12	+	1.98212e12i	2.21145	+	2.21145i
$974$			1.69509e11i			0.188346i
$975$		0			0
$976$	2.98990e11			0.329501
$977$	−1.46420e11	+	1.46420e11i	−0.160703	+	0.160703i	−0.782878	−	0.622175i	$-0.786249\pi$
$977$	−1.46420e11	+	1.46420e11i	−0.160703	+	0.160703i	0.622175	+	0.782878i	$0.286249\pi$
$978$	1.26348e11	+	1.26348e11i	0.138106	+	0.138106i
$979$			2.18648e11i			0.238020i
$980$		0			0
$981$	5.55497e10			0.0599799
$982$	−3.40041e10	+	3.40041e10i	−0.0365667	+	0.0365667i
$983$	−4.76804e11	−	4.76804e11i	−0.510653	−	0.510653i	0.404074	−	0.914726i	$-0.367594\pi$
$983$	−4.76804e11	−	4.76804e11i	−0.510653	−	0.510653i	−0.914726	+	0.404074i	$0.867594\pi$
$984$			5.88884e11i			0.628130i
$985$		0			0
$986$	7.17275e10			0.0758888
$987$	−3.86723e11	+	3.86723e11i	−0.407504	+	0.407504i
$988$	7.88637e10	+	7.88637e10i	0.0827655	+	0.0827655i
$989$		−	2.21841e11i		−	0.231876i
$990$		0			0
$991$	8.56658e11			0.888204			0.444102	−	0.895976i	$-0.353523\pi$
$991$	8.56658e11			0.888204			0.444102	+	0.895976i	$0.353523\pi$
$992$	3.51869e11	−	3.51869e11i	0.363358	−	0.363358i
$993$	−4.93696e11	−	4.93696e11i	−0.507765	−	0.507765i
$994$			5.89918e11i			0.604291i
$995$		0			0
$996$	3.91803e10			0.0398135
$997$	3.83959e11	−	3.83959e11i	0.388601	−	0.388601i	−0.485587	−	0.874188i	$-0.661394\pi$
$997$	3.83959e11	−	3.83959e11i	0.388601	−	0.388601i	0.874188	+	0.485587i	$0.161394\pi$
$998$	3.29086e11	+	3.29086e11i	0.331732	+	0.331732i
$999$			4.39510e10i			0.0441272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.e.43.5		16
5.2	odd	4	inner	75.9.f.e.7.5		16
5.3	odd	4		15.9.f.a.7.4	✓	16
5.4	even	2		15.9.f.a.13.4	yes	16
15.8	even	4		45.9.g.c.37.5		16
15.14	odd	2		45.9.g.c.28.5		16
20.3	even	4		240.9.bg.d.97.8		16
20.19	odd	2		240.9.bg.d.193.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.f.a.7.4	✓	16	5.3	odd	4
15.9.f.a.13.4	yes	16	5.4	even	2
45.9.g.c.28.5		16	15.14	odd	2
45.9.g.c.37.5		16	15.8	even	4
75.9.f.e.7.5		16	5.2	odd	4	inner
75.9.f.e.43.5		16	1.1	even	1	trivial
240.9.bg.d.97.8		16	20.3	even	4
240.9.bg.d.193.8		16	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.41326 + 3.41326i) q^{2} +(33.0681 + 33.0681i) q^{3} +232.699i q^{4} -225.740 q^{6} +(-2986.31 + 2986.31i) q^{7} +(-1668.06 - 1668.06i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(-3.41326 + 3.41326i) q^{2} +(33.0681 + 33.0681i) q^{3} +232.699i q^{4} -225.740 q^{6} +(-2986.31 + 2986.31i) q^{7} +(-1668.06 - 1668.06i) q^{8} +2187.00i q^{9} +3718.40 q^{11} +(-7694.93 + 7694.93i) q^{12} +(-26540.0 - 26540.0i) q^{13} -20386.1i q^{14} -48184.0 q^{16} +(21318.8 - 21318.8i) q^{17} +(-7464.80 - 7464.80i) q^{18} +12769.7i q^{19} -197503. q^{21} +(-12691.9 + 12691.9i) q^{22} +(357866. + 357866. i) q^{23} -110319. i q^{24} +181176. q^{26} +(-72320.0 + 72320.0i) q^{27} +(-694911. - 694911. i) q^{28} -492861. i q^{29} +594889. q^{31} +(591487. - 591487. i) q^{32} +(122960. + 122960. i) q^{33} +145533. i q^{34} -508913. q^{36} +(303865. - 303865. i) q^{37} +(-43586.3 - 43586.3i) q^{38} -1.75526e6i q^{39} -5.33801e6 q^{41} +(674129. - 674129. i) q^{42} +(-309949. - 309949. i) q^{43} +865269. i q^{44} -2.44298e6 q^{46} +(1.95806e6 - 1.95806e6i) q^{47} +(-1.59335e6 - 1.59335e6i) q^{48} -1.20712e7i q^{49} +1.40994e6 q^{51} +(6.17584e6 - 6.17584e6i) q^{52} +(-5.56394e6 - 5.56394e6i) q^{53} -493694. i q^{54} +9.96266e6 q^{56} +(-422270. + 422270. i) q^{57} +(1.68226e6 + 1.68226e6i) q^{58} -1.11543e7i q^{59} -6.20517e6 q^{61} +(-2.03051e6 + 2.03051e6i) q^{62} +(-6.53105e6 - 6.53105e6i) q^{63} -8.29731e6i q^{64} -839391. q^{66} +(-911525. + 911525. i) q^{67} +(4.96086e6 + 4.96086e6i) q^{68} +2.36679e7i q^{69} -2.89373e7 q^{71} +(3.64804e6 - 3.64804e6i) q^{72} +(1.28737e7 + 1.28737e7i) q^{73} +2.07434e6i q^{74} -2.97150e6 q^{76} +(-1.11043e7 + 1.11043e7i) q^{77} +(5.99114e6 + 5.99114e6i) q^{78} +4.05256e7i q^{79} -4.78297e6 q^{81} +(1.82200e7 - 1.82200e7i) q^{82} +(-2.54585e6 - 2.54585e6i) q^{83} -4.59588e7i q^{84} +2.11587e6 q^{86} +(1.62980e7 - 1.62980e7i) q^{87} +(-6.20250e6 - 6.20250e6i) q^{88} +5.88015e7i q^{89} +1.58513e8 q^{91} +(-8.32752e7 + 8.32752e7i) q^{92} +(1.96719e7 + 1.96719e7i) q^{93} +1.33668e7i q^{94} +3.91187e7 q^{96} +(-6.57476e7 + 6.57476e7i) q^{97} +(4.12023e7 + 4.12023e7i) q^{98} +8.13214e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 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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Database

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