LMFDB - Embedded newform 75.9.d.c.74.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(74,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("75.74");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.d (of order $2$, degree $1$, not 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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 943 x^{18} + 318815 x^{16} + 48938090 x^{14} + 3842259173 x^{12} + 159675554657 x^{10} + \cdots + 336685801 $ x^20 + 943x^18 + 318815x^16 + 48938090x^14 + 3842259173x^12 + 159675554657x^10 + 3390679484573x^8 + 32981662033730x^6 + 124592584990175x^4 + 133865237486743*x^2 + 336685801
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{22}\cdot 5^{32} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			74.3
Root			$-0.00158591i$ of defining polynomial
Character	$\chi$	$=$	75.74
Dual form			75.9.d.c.74.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-23.7888 q^{2} +(10.0775 - 80.3707i) q^{3} +309.906 q^{4} +(-239.732 + 1911.92i) q^{6} +692.753i q^{7} -1282.36 q^{8} +(-6357.89 - 1619.88i) q^{9} +O(q^{10})$	\(q-23.7888 q^{2} +(10.0775 - 80.3707i) q^{3} +309.906 q^{4} +(-239.732 + 1911.92i) q^{6} +692.753i q^{7} -1282.36 q^{8} +(-6357.89 - 1619.88i) q^{9} +15881.8i q^{11} +(3123.09 - 24907.4i) q^{12} -48870.9i q^{13} -16479.8i q^{14} -48830.2 q^{16} +41025.6 q^{17} +(151246. + 38534.9i) q^{18} +108213. q^{19} +(55677.0 + 6981.24i) q^{21} -377809. i q^{22} +433886. q^{23} +(-12923.0 + 103064. i) q^{24} +1.16258e6i q^{26} +(-194262. + 494663. i) q^{27} +214688. i q^{28} -377879. i q^{29} -408921. q^{31} +1.48989e6 q^{32} +(1.27643e6 + 160049. i) q^{33} -975949. q^{34} +(-1.97035e6 - 502009. i) q^{36} -2.31002e6i q^{37} -2.57425e6 q^{38} +(-3.92778e6 - 492497. i) q^{39} -2.15170e6i q^{41} +(-1.32449e6 - 166075. i) q^{42} -2.42811e6i q^{43} +4.92187e6i q^{44} -1.03216e7 q^{46} -8.18110e6 q^{47} +(-492087. + 3.92451e6i) q^{48} +5.28489e6 q^{49} +(413437. - 3.29725e6i) q^{51} -1.51454e7i q^{52} -1.36324e7 q^{53} +(4.62126e6 - 1.17674e7i) q^{54} -888360. i q^{56} +(1.09052e6 - 8.69714e6i) q^{57} +8.98929e6i q^{58} +1.23667e7i q^{59} -1.15129e6 q^{61} +9.72773e6 q^{62} +(1.12217e6 - 4.40445e6i) q^{63} -2.29423e7 q^{64} +(-3.03647e7 - 3.80738e6i) q^{66} +1.55586e7i q^{67} +1.27141e7 q^{68} +(4.37250e6 - 3.48717e7i) q^{69} +2.52525e7i q^{71} +(8.15311e6 + 2.07727e6i) q^{72} -2.29182e7i q^{73} +5.49526e7i q^{74} +3.35358e7 q^{76} -1.10022e7 q^{77} +(9.34372e7 + 1.17159e7i) q^{78} -4.49938e7 q^{79} +(3.77987e7 + 2.05980e7i) q^{81} +5.11864e7i q^{82} -2.12119e7 q^{83} +(1.72547e7 + 2.16353e6i) q^{84} +5.77618e7i q^{86} +(-3.03704e7 - 3.80809e6i) q^{87} -2.03662e7i q^{88} -4.87898e7i q^{89} +3.38555e7 q^{91} +1.34464e8 q^{92} +(-4.12091e6 + 3.28652e7i) q^{93} +1.94618e8 q^{94} +(1.50145e7 - 1.19744e8i) q^{96} -2.91619e7i q^{97} -1.25721e8 q^{98} +(2.57265e7 - 1.00975e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9}+O(q^{10}) $ 20 * q + 1572 * q^4 - 10564 * q^6 - 7844 * q^9	$ 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9} + 560772 q^{16} + 463032 q^{19} + 579144 q^{21} - 2272668 q^{24} + 1763240 q^{31} + 2222552 q^{34} - 1337324 q^{36} - 3653584 q^{39} - 50849208 q^{46} - 18708428 q^{49} - 55465384 q^{51} + 15959596 q^{54} + 44834040 q^{61} + 45870004 q^{64} - 54839600 q^{66} - 67125264 q^{69} + 397844872 q^{76} - 324621848 q^{79} - 187150780 q^{81} + 394693536 q^{84} + 888576928 q^{91} + 184100072 q^{94} - 721614812 q^{96} + 67930400 q^{99}+O(q^{100}) $ 20 * q + 1572 * q^4 - 10564 * q^6 - 7844 * q^9 + 560772 * q^16 + 463032 * q^19 + 579144 * q^21 - 2272668 * q^24 + 1763240 * q^31 + 2222552 * q^34 - 1337324 * q^36 - 3653584 * q^39 - 50849208 * q^46 - 18708428 * q^49 - 55465384 * q^51 + 15959596 * q^54 + 44834040 * q^61 + 45870004 * q^64 - 54839600 * q^66 - 67125264 * q^69 + 397844872 * q^76 - 324621848 * q^79 - 187150780 * q^81 + 394693536 * q^84 + 888576928 * q^91 + 184100072 * q^94 - 721614812 * q^96 + 67930400 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$26$	$52$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−23.7888			−1.48680			−0.743399	−	0.668848i	$-0.766788\pi$
$2$	−23.7888			−1.48680			−0.743399	+	0.668848i	$0.766788\pi$
$3$	10.0775	−	80.3707i	0.124414	−	0.992230i
$3$	10.0775	−	80.3707i	0.124414	−	0.992230i
$4$	309.906			1.21057
$5$		0			0
$5$		0			0
$6$	−239.732	+	1911.92i	−0.184978	+	1.47525i
$7$			692.753i			0.288527i	0.989539	+	0.144263i	$0.0460813\pi$
$7$			692.753i			0.288527i	−0.989539	+	0.144263i	$0.953919\pi$
$8$	−1282.36			−0.313077
$9$	−6357.89	−	1619.88i	−0.969042	−	0.246895i
$10$		0			0
$11$			15881.8i			1.08475i	0.840137	+	0.542374i	$0.182475\pi$
$11$			15881.8i			1.08475i	−0.840137	+	0.542374i	$0.817525\pi$
$12$	3123.09	−	24907.4i	0.150612	−	1.20117i
$13$		−	48870.9i		−	1.71110i	−0.517716	−	0.855552i	$-0.673218\pi$
$13$		−	48870.9i		−	1.71110i	0.517716	−	0.855552i	$-0.326782\pi$
$14$		−	16479.8i		−	0.428982i
$15$		0			0
$16$	−48830.2			−0.745089
$17$	41025.6			0.491201			0.245600	−	0.969371i	$-0.421015\pi$
$17$	41025.6			0.491201			0.245600	+	0.969371i	$0.421015\pi$
$18$	151246.	+	38534.9i	1.44077	+	0.367083i
$19$	108213.			0.830356			0.415178	−	0.909740i	$-0.363719\pi$
$19$	108213.			0.830356			0.415178	+	0.909740i	$0.363719\pi$
$20$		0			0
$21$	55677.0	+	6981.24i	0.286285	+	0.0358968i
$22$		−	377809.i		−	1.61280i
$23$	433886.			1.55047			0.775237	−	0.631671i	$-0.217631\pi$
$23$	433886.			1.55047			0.775237	+	0.631671i	$0.217631\pi$
$24$	−12923.0	+	103064.i	−0.0389511	+	0.310644i
$25$		0			0
$26$			1.16258e6i			2.54407i
$27$	−194262.	+	494663.i	−0.365539	+	0.930796i
$28$			214688.i			0.349282i
$29$		−	377879.i		−	0.534270i	−0.963659	−	0.267135i	$-0.913923\pi$
$29$		−	377879.i		−	0.534270i	0.963659	−	0.267135i	$-0.0860770\pi$
$30$		0			0
$31$	−408921.			−0.442784			−0.221392	−	0.975185i	$-0.571060\pi$
$31$	−408921.			−0.442784			−0.221392	+	0.975185i	$0.571060\pi$
$32$	1.48989e6			1.42087
$33$	1.27643e6	+	160049.i	1.07632	+	0.134958i
$34$	−975949.			−0.730317
$35$		0			0
$36$	−1.97035e6	−	502009.i	−1.17309	−	0.298883i
$37$		−	2.31002e6i		−	1.23256i	−0.787526	−	0.616282i	$-0.788638\pi$
$37$		−	2.31002e6i		−	1.23256i	0.787526	−	0.616282i	$-0.211362\pi$
$38$	−2.57425e6			−1.23457
$39$	−3.92778e6	−	492497.i	−1.69781	−	0.212885i
$40$		0			0
$41$		−	2.15170e6i		−	0.761460i	−0.924686	−	0.380730i	$-0.875673\pi$
$41$		−	2.15170e6i		−	0.761460i	0.924686	−	0.380730i	$-0.124327\pi$
$42$	−1.32449e6	−	166075.i	−0.425649	−	0.0533713i
$43$		−	2.42811e6i		−	0.710223i	−0.934824	−	0.355111i	$-0.884443\pi$
$43$		−	2.42811e6i		−	0.710223i	0.934824	−	0.355111i	$-0.115557\pi$
$44$			4.92187e6i			1.31317i
$45$		0			0
$46$	−1.03216e7			−2.30524
$47$	−8.18110e6			−1.67656			−0.838282	−	0.545237i	$-0.816440\pi$
$47$	−8.18110e6			−1.67656			−0.838282	+	0.545237i	$0.816440\pi$
$48$	−492087.	+	3.92451e6i	−0.0926994	+	0.739300i
$49$	5.28489e6			0.916752
$50$		0			0
$51$	413437.	−	3.29725e6i	0.0611122	−	0.487385i
$52$		−	1.51454e7i		−	2.07141i
$53$	−1.36324e7			−1.72770			−0.863850	−	0.503748i	$-0.831954\pi$
$53$	−1.36324e7			−1.72770			−0.863850	+	0.503748i	$0.831954\pi$
$54$	4.62126e6	−	1.17674e7i	0.543482	−	1.38391i
$55$		0			0
$56$		−	888360.i		−	0.0903310i
$57$	1.09052e6	−	8.69714e6i	0.103308	−	0.823904i
$58$			8.98929e6i			0.794353i
$59$			1.23667e7i			1.02057i	0.860004	+	0.510287i	$0.170461\pi$
$59$			1.23667e7i			1.02057i	−0.860004	+	0.510287i	$0.829539\pi$
$60$		0			0
$61$	−1.15129e6			−0.0831509			−0.0415755	−	0.999135i	$-0.513238\pi$
$61$	−1.15129e6			−0.0831509			−0.0415755	+	0.999135i	$0.513238\pi$
$62$	9.72773e6			0.658331
$63$	1.12217e6	−	4.40445e6i	0.0712357	−	0.279595i
$64$	−2.29423e7			−1.36746
$65$		0			0
$66$	−3.03647e7	−	3.80738e6i	−1.60027	−	0.200655i
$67$			1.55586e7i			0.772096i	0.922479	+	0.386048i	$0.126160\pi$
$67$			1.55586e7i			0.772096i	−0.922479	+	0.386048i	$0.873840\pi$
$68$	1.27141e7			0.594634
$69$	4.37250e6	−	3.48717e7i	0.192900	−	1.53843i
$70$		0			0
$71$			2.52525e7i			0.993735i	0.867826	+	0.496868i	$0.165517\pi$
$71$			2.52525e7i			0.993735i	−0.867826	+	0.496868i	$0.834483\pi$
$72$	8.15311e6	+	2.07727e6i	0.303384	+	0.0772969i
$73$		−	2.29182e7i		−	0.807030i	−0.914973	−	0.403515i	$-0.867788\pi$
$73$		−	2.29182e7i		−	0.807030i	0.914973	−	0.403515i	$-0.132212\pi$
$74$			5.49526e7i			1.83257i
$75$		0			0
$76$	3.35358e7			1.00520
$77$	−1.10022e7			−0.312979
$78$	9.34372e7	+	1.17159e7i	2.52430	+	0.316518i
$79$	−4.49938e7			−1.15517			−0.577583	−	0.816332i	$-0.696004\pi$
$79$	−4.49938e7			−1.15517			−0.577583	+	0.816332i	$0.696004\pi$
$80$		0			0
$81$	3.77987e7	+	2.05980e7i	0.878086	+	0.478503i
$82$			5.11864e7i			1.13214i
$83$	−2.12119e7			−0.446957			−0.223479	−	0.974709i	$-0.571741\pi$
$83$	−2.12119e7			−0.446957			−0.223479	+	0.974709i	$0.571741\pi$
$84$	1.72547e7	+	2.16353e6i	0.346569	+	0.0434556i
$85$		0			0
$86$			5.77618e7i			1.05596i
$87$	−3.03704e7	−	3.80809e6i	−0.530119	−	0.0664707i
$88$		−	2.03662e7i		−	0.339609i
$89$		−	4.87898e7i		−	0.777622i	−0.921317	−	0.388811i	$-0.872886\pi$
$89$		−	4.87898e7i		−	0.777622i	0.921317	−	0.388811i	$-0.127114\pi$
$90$		0			0
$91$	3.38555e7			0.493700
$92$	1.34464e8			1.87696
$93$	−4.12091e6	+	3.28652e7i	−0.0550885	+	0.439344i
$94$	1.94618e8			2.49271
$95$		0			0
$96$	1.50145e7	−	1.19744e8i	0.176777	−	1.40983i
$97$		−	2.91619e7i		−	0.329404i	−0.986343	−	0.164702i	$-0.947334\pi$
$97$		−	2.91619e7i		−	0.329404i	0.986343	−	0.164702i	$-0.0526662\pi$
$98$	−1.25721e8			−1.36303
$99$	2.57265e7	−	1.00975e8i	0.267818	−	1.05117i
$100$		0			0
$101$		−	6.31995e7i		−	0.607335i	−0.952778	−	0.303667i	$-0.901789\pi$
$101$		−	6.31995e7i		−	0.607335i	0.952778	−	0.303667i	$-0.0982111\pi$
$102$	−9.83515e6	+	7.84377e7i	−0.0908616	+	0.724643i
$103$		−	6.94350e7i		−	0.616921i	−0.951237	−	0.308461i	$-0.900186\pi$
$103$		−	6.94350e7i		−	0.616921i	0.951237	−	0.308461i	$-0.0998138\pi$
$104$			6.26701e7i			0.535707i
$105$		0			0
$106$	3.24298e8			2.56874
$107$	−2.16211e8			−1.64946			−0.824732	−	0.565523i	$-0.808674\pi$
$107$	−2.16211e8			−1.64946			−0.824732	+	0.565523i	$0.808674\pi$
$108$	−6.02031e7	+	1.53299e8i	−0.442510	+	1.12679i
$109$	−7.00475e7			−0.496234			−0.248117	−	0.968730i	$-0.579812\pi$
$109$	−7.00475e7			−0.496234			−0.248117	+	0.968730i	$0.579812\pi$
$110$		0			0
$111$	−1.85658e8	−	2.32793e7i	−1.22299	−	0.153348i
$112$		−	3.38272e7i		−	0.214978i
$113$	−4.56013e7			−0.279681			−0.139841	−	0.990174i	$-0.544659\pi$
$113$	−4.56013e7			−0.279681			−0.139841	+	0.990174i	$0.544659\pi$
$114$	−2.59421e7	+	2.06894e8i	−0.153598	+	1.22498i
$115$		0			0
$116$		−	1.17107e8i		−	0.646772i
$117$	−7.91647e7	+	3.10715e8i	−0.422462	+	1.65813i
$118$		−	2.94188e8i		−	1.51739i
$119$			2.84206e7i			0.141725i
$120$		0			0
$121$	−3.78728e7			−0.176679
$122$	2.73879e7			0.123629
$123$	−1.72934e8	−	2.16839e7i	−0.755544	−	0.0947362i
$124$	−1.26727e8			−0.536022
$125$		0			0
$126$	−2.66951e7	+	1.04776e8i	−0.105913	+	0.415701i
$127$		−	1.07871e7i		−	0.0414660i	−0.999785	−	0.0207330i	$-0.993400\pi$
$127$		−	1.07871e7i		−	0.0414660i	0.999785	−	0.0207330i	$-0.00659998\pi$
$128$	1.64355e8			0.612271
$129$	−1.95149e8	−	2.44694e7i	−0.704705	−	0.0883616i
$130$		0			0
$131$		−	2.88284e8i		−	0.978894i	−0.872033	−	0.489447i	$-0.837199\pi$
$131$		−	2.88284e8i		−	0.978894i	0.872033	−	0.489447i	$-0.162801\pi$
$132$	3.95574e8	+	4.96003e7i	1.30296	+	0.163376i
$133$			7.49648e7i			0.239580i
$134$		−	3.70120e8i		−	1.14795i
$135$		0			0
$136$	−5.26097e7			−0.153784
$137$	7.39800e7			0.210006			0.105003	−	0.994472i	$-0.466515\pi$
$137$	7.39800e7			0.210006			0.105003	+	0.994472i	$0.466515\pi$
$138$	−1.04016e8	+	8.29555e8i	−0.286804	+	2.28733i
$139$	4.00966e7			0.107411			0.0537054	−	0.998557i	$-0.482897\pi$
$139$	4.00966e7			0.107411			0.0537054	+	0.998557i	$0.482897\pi$
$140$		0			0
$141$	−8.24452e7	+	6.57520e8i	−0.208588	+	1.66354i
$142$		−	6.00726e8i		−	1.47748i
$143$	7.76158e8			1.85612
$144$	3.10457e8	+	7.90987e7i	0.722023	+	0.183958i
$145$		0			0
$146$			5.45197e8i			1.19989i
$147$	5.32587e7	−	4.24750e8i	0.114057	−	0.909629i
$148$		−	7.15890e8i		−	1.49211i
$149$		−	1.80649e8i		−	0.366515i	−0.983065	−	0.183257i	$-0.941336\pi$
$149$		−	1.80649e8i		−	0.366515i	0.983065	−	0.183257i	$-0.0586641\pi$
$150$		0			0
$151$	−4.33011e7			−0.0832898			−0.0416449	−	0.999132i	$-0.513260\pi$
$151$	−4.33011e7			−0.0832898			−0.0416449	+	0.999132i	$0.513260\pi$
$152$	−1.38768e8			−0.259965
$153$	−2.60836e8	−	6.64563e7i	−0.475995	−	0.121275i
$154$	2.61728e8			0.465337
$155$		0			0
$156$	−1.21724e9	−	1.52628e8i	−2.05532	−	0.257713i
$157$		−	9.98639e7i		−	0.164365i	−0.996617	−	0.0821826i	$-0.973811\pi$
$157$		−	9.98639e7i		−	0.164365i	0.996617	−	0.0821826i	$-0.0261891\pi$
$158$	1.07035e9			1.71750
$159$	−1.37381e8	+	1.09564e9i	−0.214950	+	1.71428i
$160$		0			0
$161$			3.00576e8i			0.447353i
$162$	−8.99186e8	−	4.90000e8i	−1.30554	−	0.711437i
$163$		−	4.15495e8i		−	0.588594i	−0.955714	−	0.294297i	$-0.904915\pi$
$163$		−	4.15495e8i		−	0.588594i	0.955714	−	0.294297i	$-0.0950854\pi$
$164$		−	6.66826e8i		−	0.921801i
$165$		0			0
$166$	5.04604e8			0.664536
$167$	2.00570e8			0.257869			0.128935	−	0.991653i	$-0.458844\pi$
$167$	2.00570e8			0.257869			0.128935	+	0.991653i	$0.458844\pi$
$168$	−7.13981e7	−	8.95247e6i	−0.0896292	−	0.0112384i
$169$	−1.57263e9			−1.92788
$170$		0			0
$171$	−6.88005e8	−	1.75291e8i	−0.804650	−	0.205010i
$172$		−	7.52487e8i		−	0.859775i
$173$	−1.07943e9			−1.20507			−0.602534	−	0.798093i	$-0.705842\pi$
$173$	−1.07943e9			−1.20507			−0.602534	+	0.798093i	$0.705842\pi$
$174$	7.22475e8	+	9.05898e7i	0.788181	+	0.0988285i
$175$		0			0
$176$		−	7.75511e8i		−	0.808234i
$177$	9.93918e8	+	1.24626e8i	1.01265	+	0.126974i
$178$			1.16065e9i			1.15617i
$179$		−	4.03427e8i		−	0.392964i	−0.980507	−	0.196482i	$-0.937048\pi$
$179$		−	4.03427e8i		−	0.392964i	0.980507	−	0.196482i	$-0.0629517\pi$
$180$		0			0
$181$	−9.48830e8			−0.884045			−0.442022	−	0.897004i	$-0.645739\pi$
$181$	−9.48830e8			−0.884045			−0.442022	+	0.897004i	$0.645739\pi$
$182$	−8.05380e8			−0.734032
$183$	−1.16022e7	+	9.25303e7i	−0.0103451	+	0.0825049i
$184$	−5.56399e8			−0.485417
$185$		0			0
$186$	9.80314e7	−	7.81824e8i	0.0819056	−	0.653216i
$187$			6.51560e8i			0.532830i
$188$	−2.53537e9			−2.02960
$189$	−3.42680e8	−	1.34576e8i	−0.268560	−	0.105468i
$190$		0			0
$191$		−	1.09216e9i		−	0.820643i	−0.911941	−	0.410322i	$-0.865416\pi$
$191$		−	1.09216e9i		−	0.820643i	0.911941	−	0.410322i	$-0.134584\pi$
$192$	−2.31201e8	+	1.84388e9i	−0.170132	+	1.35684i
$193$		−	2.66289e9i		−	1.91921i	−0.281342	−	0.959607i	$-0.590780\pi$
$193$		−	2.66289e9i		−	1.91921i	0.281342	−	0.959607i	$-0.409220\pi$
$194$			6.93725e8i			0.489757i
$195$		0			0
$196$	1.63782e9			1.10979
$197$	2.31610e9			1.53777			0.768886	−	0.639386i	$-0.220811\pi$
$197$	2.31610e9			1.53777			0.768886	+	0.639386i	$0.220811\pi$
$198$	−6.12003e8	+	2.40207e9i	−0.398192	+	1.56287i
$199$	9.37508e8			0.597809			0.298905	−	0.954283i	$-0.403379\pi$
$199$	9.37508e8			0.597809			0.298905	+	0.954283i	$0.403379\pi$
$200$		0			0
$201$	1.25046e9	+	1.56792e8i	0.766097	+	0.0960595i
$202$			1.50344e9i			0.902984i
$203$	2.61777e8			0.154151
$204$	1.28127e8	−	1.02184e9i	0.0739807	−	0.590014i
$205$		0			0
$206$			1.65177e9i			0.917238i
$207$	−2.75860e9	−	7.02841e8i	−1.50247	−	0.382803i
$208$			2.38637e9i			1.27493i
$209$			1.71861e9i			0.900727i
$210$		0			0
$211$	2.14693e9			1.08315			0.541575	−	0.840652i	$-0.317828\pi$
$211$	2.14693e9			1.08315			0.541575	+	0.840652i	$0.317828\pi$
$212$	−4.22476e9			−2.09150
$213$	2.02956e9	+	2.54483e8i	0.986014	+	0.123634i
$214$	5.14340e9			2.45242
$215$		0			0
$216$	2.49114e8	−	6.34337e8i	0.114442	−	0.291411i
$217$		−	2.83281e8i		−	0.127755i
$218$	1.66634e9			0.737800
$219$	−1.84195e9	−	2.30959e8i	−0.800759	−	0.100406i
$220$		0			0
$221$		−	2.00496e9i		−	0.840496i
$222$	4.41658e9	+	5.53787e8i	1.81834	+	0.227998i
$223$		−	3.70772e9i		−	1.49929i	−0.661838	−	0.749647i	$-0.730223\pi$
$223$		−	3.70772e9i		−	1.49929i	0.661838	−	0.749647i	$-0.269777\pi$
$224$			1.03213e9i			0.409960i
$225$		0			0
$226$	1.08480e9			0.415830
$227$	3.97024e9			1.49525			0.747624	−	0.664122i	$-0.231194\pi$
$227$	3.97024e9			1.49525			0.747624	+	0.664122i	$0.231194\pi$
$228$	3.37958e8	−	2.69530e9i	0.125061	−	0.997395i
$229$	−2.84129e9			−1.03317			−0.516587	−	0.856235i	$-0.672798\pi$
$229$	−2.84129e9			−1.03317			−0.516587	+	0.856235i	$0.672798\pi$
$230$		0			0
$231$	−1.10875e8	+	8.84252e8i	−0.0389390	+	0.310547i
$232$			4.84578e8i			0.167268i
$233$	3.80946e8			0.129253			0.0646264	−	0.997910i	$-0.479414\pi$
$233$	3.80946e8			0.129253			0.0646264	+	0.997910i	$0.479414\pi$
$234$	1.88323e9	−	7.39154e9i	0.628117	−	2.46531i
$235$		0			0
$236$			3.83251e9i			1.23548i
$237$	−4.53426e8	+	3.61618e9i	−0.143719	+	1.14619i
$238$		−	6.76092e8i		−	0.210716i
$239$			3.08542e9i			0.945633i	0.881161	+	0.472817i	$0.156763\pi$
$239$			3.08542e9i			0.945633i	−0.881161	+	0.472817i	$0.843237\pi$
$240$		0			0
$241$	−1.83623e9			−0.544326			−0.272163	−	0.962251i	$-0.587739\pi$
$241$	−1.83623e9			−0.544326			−0.272163	+	0.962251i	$0.587739\pi$
$242$	9.00948e8			0.262687
$243$	2.03639e9	−	2.83033e9i	0.584031	−	0.811731i
$244$	−3.56793e8			−0.100660
$245$		0			0
$246$	4.11389e9	+	5.15833e8i	1.12334	+	0.140854i
$247$		−	5.28845e9i		−	1.42083i
$248$	5.24384e8			0.138625
$249$	−2.13763e8	+	1.70481e9i	−0.0556077	+	0.443485i
$250$		0			0
$251$			4.14381e9i			1.04401i	0.852942	+	0.522005i	$0.174816\pi$
$251$			4.14381e9i			1.04401i	−0.852942	+	0.522005i	$0.825184\pi$
$252$	3.47769e8	−	1.36497e9i	0.0862359	−	0.338469i
$253$			6.89089e9i			1.68187i
$254$			2.56613e8i			0.0616515i
$255$		0			0
$256$	1.96340e9			0.457141
$257$	−1.12642e9			−0.258207			−0.129104	−	0.991631i	$-0.541210\pi$
$257$	−1.12642e9			−0.258207			−0.129104	+	0.991631i	$0.541210\pi$
$258$	4.64235e9	+	5.82096e8i	1.04775	+	0.131376i
$259$	1.60028e9			0.355628
$260$		0			0
$261$	−6.12117e8	+	2.40251e9i	−0.131908	+	0.517731i
$262$			6.85793e9i			1.45542i
$263$	−6.91865e9			−1.44610			−0.723050	−	0.690796i	$-0.757260\pi$
$263$	−6.91865e9			−1.44610			−0.723050	+	0.690796i	$0.757260\pi$
$264$	−1.63685e9	−	2.05241e8i	−0.336971	−	0.0422521i
$265$		0			0
$266$		−	1.78332e9i		−	0.356207i
$267$	−3.92127e9	−	4.91680e8i	−0.771581	−	0.0967470i
$268$			4.82171e9i			0.934677i
$269$		−	1.04065e9i		−	0.198744i	−0.995050	−	0.0993720i	$-0.968317\pi$
$269$		−	1.04065e9i		−	0.198744i	0.995050	−	0.0993720i	$-0.0316834\pi$
$270$		0			0
$271$	−4.30357e9			−0.797906			−0.398953	−	0.916971i	$-0.630626\pi$
$271$	−4.30357e9			−0.797906			−0.398953	+	0.916971i	$0.630626\pi$
$272$	−2.00329e9			−0.365988
$273$	3.41179e8	−	2.72099e9i	0.0614231	−	0.489864i
$274$	−1.75989e9			−0.312237
$275$		0			0
$276$	1.35506e9	−	1.08070e10i	0.233520	−	1.86237i
$277$			1.01360e10i			1.72166i	0.508889	+	0.860832i	$0.330056\pi$
$277$			1.01360e10i			1.72166i	−0.508889	+	0.860832i	$0.669944\pi$
$278$	−9.53848e8			−0.159698
$279$	2.59987e9	+	6.62400e8i	0.429077	+	0.109321i
$280$		0			0
$281$		−	8.82598e9i		−	1.41559i	−0.706418	−	0.707795i	$-0.749690\pi$
$281$		−	8.82598e9i		−	1.41559i	0.706418	−	0.707795i	$-0.250310\pi$
$282$	1.96127e9	−	1.56416e10i	0.310128	−	2.47335i
$283$			1.58051e9i			0.246405i	0.992382	+	0.123203i	$0.0393165\pi$
$283$			1.58051e9i			0.246405i	−0.992382	+	0.123203i	$0.960683\pi$
$284$			7.82590e9i			1.20299i
$285$		0			0
$286$	−1.84638e10			−2.75967
$287$	1.49060e9			0.219702
$288$	−9.47258e9	−	2.41344e9i	−1.37689	−	0.350806i
$289$	−5.29266e9			−0.758722
$290$		0			0
$291$	−2.34376e9	−	2.93880e8i	−0.326844	−	0.0409824i
$292$		−	7.10250e9i		−	0.976967i
$293$	−7.30987e8			−0.0991835			−0.0495917	−	0.998770i	$-0.515792\pi$
$293$	−7.30987e8			−0.0991835			−0.0495917	+	0.998770i	$0.515792\pi$
$294$	−1.26696e9	+	1.01043e10i	−0.169579	+	1.35244i
$295$		0			0
$296$			2.96228e9i			0.385887i
$297$	−7.85614e9	−	3.08523e9i	−1.00968	−	0.396517i
$298$			4.29743e9i			0.544934i
$299$		−	2.12044e10i		−	2.65302i
$300$		0			0
$301$	1.68208e9			0.204918
$302$	1.03008e9			0.123835
$303$	−5.07938e9	−	6.36894e8i	−0.602616	−	0.0755609i
$304$	−5.28405e9			−0.618689
$305$		0			0
$306$	6.20497e9	+	1.58092e9i	0.707708	+	0.180311i
$307$		−	8.05460e9i		−	0.906757i	−0.891318	−	0.453378i	$-0.850219\pi$
$307$		−	8.05460e9i		−	0.906757i	0.891318	−	0.453378i	$-0.149781\pi$
$308$	−3.40964e9			−0.378884
$309$	−5.58054e9	−	6.99733e8i	−0.612128	−	0.0767536i
$310$		0			0
$311$		−	2.28173e9i		−	0.243906i	−0.992536	−	0.121953i	$-0.961084\pi$
$311$		−	2.28173e9i		−	0.243906i	0.992536	−	0.121953i	$-0.0389157\pi$
$312$	5.03684e9	+	6.31560e8i	0.531545	+	0.0666494i
$313$			3.40795e9i			0.355072i	0.984114	+	0.177536i	$0.0568126\pi$
$313$			3.40795e9i			0.355072i	−0.984114	+	0.177536i	$0.943187\pi$
$314$			2.37564e9i			0.244378i
$315$		0			0
$316$	−1.39439e10			−1.39841
$317$	−2.80342e9			−0.277620			−0.138810	−	0.990319i	$-0.544328\pi$
$317$	−2.80342e9			−0.277620			−0.138810	+	0.990319i	$0.544328\pi$
$318$	3.26812e9	−	2.60640e10i	0.319587	−	2.54879i
$319$	6.00140e9			0.579549
$320$		0			0
$321$	−2.17887e9	+	1.73770e10i	−0.205216	+	1.63665i
$322$		−	7.15034e9i		−	0.665125i
$323$	4.43950e9			0.407872
$324$	1.17141e10	+	6.38344e9i	1.06299	+	0.579261i
$325$		0			0
$326$			9.88412e9i			0.875120i
$327$	−7.05906e8	+	5.62976e9i	−0.0617384	+	0.492379i
$328$			2.75926e9i			0.238395i
$329$		−	5.66748e9i		−	0.483734i
$330$		0			0
$331$	−3.85817e9			−0.321417			−0.160709	−	0.987002i	$-0.551378\pi$
$331$	−3.85817e9			−0.321417			−0.160709	+	0.987002i	$0.551378\pi$
$332$	−6.57368e9			−0.541074
$333$	−3.74195e9	+	1.46869e10i	−0.304313	+	1.19441i
$334$	−4.77131e9			−0.383400
$335$		0			0
$336$	−2.71872e9	−	3.40895e8i	−0.213308	−	0.0267463i
$337$		−	4.33270e9i		−	0.335922i	−0.985794	−	0.167961i	$-0.946282\pi$
$337$		−	4.33270e9i		−	0.335922i	0.985794	−	0.167961i	$-0.0537183\pi$
$338$	3.74110e10			2.86637
$339$	−4.59548e8	+	3.66500e9i	−0.0347962	+	0.277508i
$340$		0			0
$341$		−	6.49440e9i		−	0.480310i
$342$	1.63668e10	+	4.16997e9i	1.19635	+	0.304809i
$343$			7.65471e9i			0.553035i
$344$			3.11372e9i			0.222354i
$345$		0			0
$346$	2.56784e10			1.79169
$347$	−1.49997e9			−0.103458			−0.0517291	−	0.998661i	$-0.516473\pi$
$347$	−1.49997e9			−0.103458			−0.0517291	+	0.998661i	$0.516473\pi$
$348$	−9.41198e9	−	1.18015e9i	−0.641747	−	0.0804675i
$349$	1.91502e10			1.29084			0.645418	−	0.763830i	$-0.276683\pi$
$349$	1.91502e10			1.29084			0.645418	+	0.763830i	$0.276683\pi$
$350$		0			0
$351$	2.41746e10	+	9.49376e9i	1.59269	+	0.625475i
$352$			2.36622e10i			1.54129i
$353$	2.74321e10			1.76669			0.883345	−	0.468723i	$-0.155286\pi$
$353$	2.74321e10			1.76669			0.883345	+	0.468723i	$0.155286\pi$
$354$	−2.36441e10	−	2.96469e9i	−1.50560	−	0.188784i
$355$		0			0
$356$		−	1.51202e10i		−	0.941367i
$357$	2.28418e9	+	2.86410e8i	0.140624	+	0.0176325i
$358$			9.59704e9i			0.584258i
$359$		−	7.34907e9i		−	0.442440i	−0.975224	−	0.221220i	$-0.928996\pi$
$359$		−	7.34907e9i		−	0.442440i	0.975224	−	0.221220i	$-0.0710039\pi$
$360$		0			0
$361$	−5.27355e9			−0.310509
$362$	2.25715e10			1.31440
$363$	−3.81664e8	+	3.04386e9i	−0.0219814	+	0.175307i
$364$	1.04920e10			0.597659
$365$		0			0
$366$	2.76002e8	−	2.20118e9i	0.0153811	−	0.122668i
$367$			6.53522e9i			0.360243i	0.983644	+	0.180122i	$0.0576492\pi$
$367$			6.53522e9i			0.360243i	−0.983644	+	0.180122i	$0.942351\pi$
$368$	−2.11867e10			−1.15524
$369$	−3.48549e9	+	1.36803e10i	−0.188000	+	0.737887i
$370$		0			0
$371$		−	9.44388e9i		−	0.498488i
$372$	−1.27710e9	+	1.01851e10i	−0.0666886	+	0.531857i
$373$		−	3.22724e10i		−	1.66723i	−0.552346	−	0.833615i	$-0.686267\pi$
$373$		−	3.22724e10i		−	1.66723i	0.552346	−	0.833615i	$-0.313733\pi$
$374$		−	1.54998e10i		−	0.792210i
$375$		0			0
$376$	1.04911e10			0.524893
$377$	−1.84673e10			−0.914193
$378$	8.15193e9	+	3.20139e9i	0.399294	+	0.156809i
$379$	2.00937e10			0.973875			0.486938	−	0.873437i	$-0.338114\pi$
$379$	2.00937e10			0.973875			0.486938	+	0.873437i	$0.338114\pi$
$380$		0			0
$381$	−8.66970e8	−	1.08708e8i	−0.0411438	−	0.00515894i
$382$			2.59813e10i			1.22013i
$383$	−2.64566e10			−1.22953			−0.614765	−	0.788711i	$-0.710749\pi$
$383$	−2.64566e10			−1.22953			−0.614765	+	0.788711i	$0.710749\pi$
$384$	1.65630e9	−	1.32093e10i	0.0761751	−	0.607514i
$385$		0			0
$386$			6.33469e10i			2.85349i
$387$	−3.93324e9	+	1.54377e10i	−0.175350	+	0.688236i
$388$		−	9.03744e9i		−	0.398766i
$389$			2.69010e10i			1.17482i	0.809291	+	0.587408i	$0.199851\pi$
$389$			2.69010e10i			1.17482i	−0.809291	+	0.587408i	$0.800149\pi$
$390$		0			0
$391$	1.78004e10			0.761594
$392$	−6.77715e9			−0.287014
$393$	−2.31696e10	−	2.90519e9i	−0.971288	−	0.121788i
$394$	−5.50971e10			−2.28636
$395$		0			0
$396$	7.97281e9	−	3.12927e10i	0.324213	−	1.27251i
$397$		−	2.18233e10i		−	0.878533i	−0.898357	−	0.439266i	$-0.855238\pi$
$397$		−	2.18233e10i		−	0.878533i	0.898357	−	0.439266i	$-0.144762\pi$
$398$	−2.23022e10			−0.888822
$399$	6.02497e9	+	7.55460e8i	0.237719	+	0.0298071i
$400$		0			0
$401$		−	3.86361e10i		−	1.49422i	−0.664698	−	0.747112i	$-0.731440\pi$
$401$		−	3.86361e10i		−	1.49422i	0.664698	−	0.747112i	$-0.268560\pi$
$402$	−2.97468e10	−	3.72990e9i	−1.13903	−	0.142821i
$403$			1.99843e10i			0.757651i
$404$		−	1.95859e10i		−	0.735222i
$405$		0			0
$406$	−6.22736e9			−0.229192
$407$	3.66873e10			1.33702
$408$	−5.30175e8	+	4.22827e9i	−0.0191328	+	0.152589i
$409$	1.02245e10			0.365385			0.182692	−	0.983170i	$-0.441519\pi$
$409$	1.02245e10			0.365385			0.182692	+	0.983170i	$0.441519\pi$
$410$		0			0
$411$	7.45535e8	−	5.94582e9i	0.0261277	−	0.208375i
$412$		−	2.15183e10i		−	0.746827i
$413$	−8.56705e9			−0.294463
$414$	6.56237e10	+	1.67197e10i	2.23388	+	0.569152i
$415$		0			0
$416$		−	7.28124e10i		−	2.43126i
$417$	4.04074e8	−	3.22259e9i	0.0133634	−	0.106576i
$418$		−	4.08838e10i		−	1.33920i
$419$			3.03535e10i			0.984812i	0.870366	+	0.492406i	$0.163882\pi$
$419$			3.03535e10i			0.984812i	−0.870366	+	0.492406i	$0.836118\pi$
$420$		0			0
$421$	3.94064e10			1.25441			0.627203	−	0.778856i	$-0.284200\pi$
$421$	3.94064e10			1.25441			0.627203	+	0.778856i	$0.284200\pi$
$422$	−5.10729e10			−1.61043
$423$	5.20145e10	+	1.32524e10i	1.62466	+	0.413934i
$424$	1.74817e10			0.540903
$425$		0			0
$426$	−4.82807e10	−	6.05383e9i	−1.46600	−	0.183820i
$427$		−	7.97563e8i		−	0.0239913i
$428$	−6.70052e10			−1.99679
$429$	7.82175e9	−	6.23803e10i	0.230927	−	1.84170i
$430$		0			0
$431$			2.00931e10i			0.582288i	0.956679	+	0.291144i	$0.0940358\pi$
$431$			2.00931e10i			0.582288i	−0.956679	+	0.291144i	$0.905964\pi$
$432$	9.48585e9	−	2.41545e10i	0.272359	−	0.693526i
$433$			4.76129e10i			1.35448i	0.735761	+	0.677241i	$0.236824\pi$
$433$			4.76129e10i			1.35448i	−0.735761	+	0.677241i	$0.763176\pi$
$434$			6.73891e9i			0.189946i
$435$		0			0
$436$	−2.17082e10			−0.600727
$437$	4.69520e10			1.28744
$438$	4.38178e10	+	5.49423e9i	1.19057	+	0.149283i
$439$	2.80845e10			0.756151			0.378076	−	0.925775i	$-0.376586\pi$
$439$	2.80845e10			0.756151			0.378076	+	0.925775i	$0.376586\pi$
$440$		0			0
$441$	−3.36008e10	−	8.56087e9i	−0.888372	−	0.226341i
$442$			4.76955e10i			1.24965i
$443$	3.22901e9			0.0838407			0.0419204	−	0.999121i	$-0.486652\pi$
$443$	3.22901e9			0.0838407			0.0419204	+	0.999121i	$0.486652\pi$
$444$	−5.75366e10	−	7.21440e9i	−1.48051	−	0.185639i
$445$		0			0
$446$			8.82020e10i			2.22915i
$447$	−1.45189e10	−	1.82050e9i	−0.363667	−	0.0455995i
$448$		−	1.58933e10i		−	0.394551i
$449$			4.21051e10i			1.03598i	0.855388	+	0.517988i	$0.173319\pi$
$449$			4.21051e10i			1.03598i	−0.855388	+	0.517988i	$0.826681\pi$
$450$		0			0
$451$	3.41729e10			0.825993
$452$	−1.41321e10			−0.338574
$453$	−4.36368e8	+	3.48014e9i	−0.0103624	+	0.0826426i
$454$	−9.44472e10			−2.22313
$455$		0			0
$456$	−1.39844e9	+	1.11529e10i	−0.0323433	+	0.257945i
$457$		−	4.14329e10i		−	0.949905i	−0.880011	−	0.474952i	$-0.842465\pi$
$457$		−	4.14329e10i		−	0.949905i	0.880011	−	0.474952i	$-0.157535\pi$
$458$	6.75908e10			1.53612
$459$	−7.96972e9	+	2.02939e10i	−0.179553	+	0.457208i
$460$		0			0
$461$			7.44199e10i			1.64773i	0.566789	+	0.823863i	$0.308186\pi$
$461$			7.44199e10i			1.64773i	−0.566789	+	0.823863i	$0.691814\pi$
$462$	2.63757e9	−	2.10353e10i	0.0578944	−	0.461722i
$463$		−	4.57191e10i		−	0.994887i	−0.867496	−	0.497444i	$-0.834272\pi$
$463$		−	4.57191e10i		−	0.994887i	0.867496	−	0.497444i	$-0.165728\pi$
$464$			1.84519e10i			0.398079i
$465$		0			0
$466$	−9.06225e9			−0.192173
$467$	−2.76952e9			−0.0582286			−0.0291143	−	0.999576i	$-0.509269\pi$
$467$	−2.76952e9			−0.0582286			−0.0291143	+	0.999576i	$0.509269\pi$
$468$	−2.45336e10	+	9.62926e10i	−0.511421	+	2.00729i
$469$	−1.07783e10			−0.222771
$470$		0			0
$471$	−8.02613e9	−	1.00638e9i	−0.163088	−	0.0204493i
$472$		−	1.58586e10i		−	0.319518i
$473$	3.85628e10			0.770413
$474$	1.07865e10	−	8.60245e10i	0.213681	−	1.70415i
$475$		0			0
$476$			8.80772e9i			0.171568i
$477$	8.66732e10	+	2.20828e10i	1.67422	+	0.426560i
$478$		−	7.33984e10i		−	1.40597i
$479$		−	3.82055e10i		−	0.725744i	−0.931839	−	0.362872i	$-0.881796\pi$
$479$		−	3.82055e10i		−	0.725744i	0.931839	−	0.362872i	$-0.118204\pi$
$480$		0			0
$481$	−1.12893e11			−2.10905
$482$	4.36817e10			0.809303
$483$	2.41575e10	+	3.02906e9i	0.443878	+	0.0556570i
$484$	−1.17370e10			−0.213883
$485$		0			0
$486$	−4.84432e10	+	6.73302e10i	−0.868336	+	1.20688i
$487$		−	2.79097e10i		−	0.496179i	−0.968737	−	0.248090i	$-0.920197\pi$
$487$		−	2.79097e10i		−	0.496179i	0.968737	−	0.248090i	$-0.0798028\pi$
$488$	1.47638e9			0.0260326
$489$	−3.33936e10	−	4.18716e9i	−0.584021	−	0.0732292i
$490$		0			0
$491$		−	3.62482e10i		−	0.623677i	−0.950135	−	0.311839i	$-0.899055\pi$
$491$		−	3.62482e10i		−	0.623677i	0.950135	−	0.311839i	$-0.100945\pi$
$492$	−5.35933e10	−	6.71996e9i	−0.914639	−	0.114685i
$493$		−	1.55027e10i		−	0.262434i
$494$			1.25806e11i			2.11248i
$495$		0			0
$496$	1.99677e10			0.329914
$497$	−1.74937e10			−0.286719
$498$	5.08516e9	−	4.05554e10i	0.0826775	−	0.659373i
$499$	1.31298e10			0.211765			0.105883	−	0.994379i	$-0.466233\pi$
$499$	1.31298e10			0.211765			0.105883	+	0.994379i	$0.466233\pi$
$500$		0			0
$501$	2.02125e9	−	1.61199e10i	0.0320825	−	0.255866i
$502$		−	9.85762e10i		−	1.55223i
$503$	1.84778e10			0.288654			0.144327	−	0.989530i	$-0.453898\pi$
$503$	1.84778e10			0.288654			0.144327	+	0.989530i	$0.453898\pi$
$504$	−1.43903e9	+	5.64809e9i	−0.0223022	+	0.0875346i
$505$		0			0
$506$		−	1.63926e11i		−	2.50061i
$507$	−1.58482e10	+	1.26393e11i	−0.239855	+	1.91290i
$508$		−	3.34300e9i		−	0.0501975i
$509$		−	7.39108e10i		−	1.10112i	−0.834794	−	0.550562i	$-0.814413\pi$
$509$		−	7.39108e10i		−	1.10112i	0.834794	−	0.550562i	$-0.185587\pi$
$510$		0			0
$511$	1.58767e10			0.232850
$512$	−8.87820e10			−1.29195
$513$	−2.10217e10	+	5.35289e10i	−0.303527	+	0.772892i
$514$	2.67962e10			0.383902
$515$		0			0
$516$	−6.04778e10	−	7.58320e9i	−0.853095	−	0.106968i
$517$		−	1.29931e11i		−	1.81865i
$518$	−3.80686e10			−0.528747
$519$	−1.08780e10	+	8.67548e10i	−0.149927	+	1.19571i
$520$		0			0
$521$			7.94911e10i			1.07887i	0.842029	+	0.539433i	$0.181361\pi$
$521$			7.94911e10i			1.07887i	−0.842029	+	0.539433i	$0.818639\pi$
$522$	1.45615e10	−	5.71529e10i	0.196121	−	0.769761i
$523$			3.03522e10i			0.405680i	0.979212	+	0.202840i	$0.0650171\pi$
$523$			3.03522e10i			0.405680i	−0.979212	+	0.202840i	$0.934983\pi$
$524$		−	8.93410e10i		−	1.18502i
$525$		0			0
$526$	1.64586e11			2.15006
$527$	−1.67762e10			−0.217496
$528$	−6.23283e10	−	7.81523e9i	−0.801955	−	0.100556i
$529$	1.09946e11			1.40397
$530$		0			0
$531$	2.00325e10	−	7.86259e10i	0.251974	−	0.988980i
$532$			2.32320e10i			0.290029i
$533$	−1.05156e11			−1.30294
$534$	9.32821e10	+	1.16965e10i	1.14719	+	0.143843i
$535$		0			0
$536$		−	1.99518e10i		−	0.241725i
$537$	−3.24237e10	−	4.06555e9i	−0.389911	−	0.0488902i
$538$			2.47557e10i			0.295492i
$539$			8.39336e10i			0.994446i
$540$		0			0
$541$	−3.53261e10			−0.412389			−0.206195	−	0.978511i	$-0.566108\pi$
$541$	−3.53261e10			−0.412389			−0.206195	+	0.978511i	$0.566108\pi$
$542$	1.02377e11			1.18633
$543$	−9.56187e9	+	7.62581e10i	−0.109987	+	0.877176i
$544$	6.11238e10			0.697935
$545$		0			0
$546$	−8.11624e9	+	6.47289e10i	−0.0913239	+	0.728329i
$547$			1.62586e11i			1.81607i	0.418891	+	0.908036i	$0.362419\pi$
$547$			1.62586e11i			1.81607i	−0.418891	+	0.908036i	$0.637581\pi$
$548$	2.29269e10			0.254227
$549$	7.31980e9	+	1.86495e9i	0.0805768	+	0.0205295i
$550$		0			0
$551$		−	4.08914e10i		−	0.443635i
$552$	−5.60712e9	+	4.47181e10i	−0.0603926	+	0.481645i
$553$		−	3.11696e10i		−	0.333296i
$554$		−	2.41124e11i		−	2.55977i
$555$		0			0
$556$	1.24262e10			0.130028
$557$	−1.81639e11			−1.88707			−0.943535	−	0.331273i	$-0.892522\pi$
$557$	−1.81639e11			−1.88707			−0.943535	+	0.331273i	$0.892522\pi$
$558$	−6.18478e10	−	1.57577e10i	−0.637951	−	0.162538i
$559$	−1.18664e11			−1.21527
$560$		0			0
$561$	5.23663e10	+	6.56612e9i	0.528690	+	0.0662914i
$562$			2.09959e11i			2.10470i
$563$	−6.38376e10			−0.635394			−0.317697	−	0.948192i	$-0.602910\pi$
$563$	−6.38376e10			−0.635394			−0.317697	+	0.948192i	$0.602910\pi$
$564$	−2.55503e10	+	2.03770e11i	−0.252510	+	2.01383i
$565$		0			0
$566$		−	3.75983e10i		−	0.366355i
$567$	−1.42693e10	+	2.61852e10i	−0.138061	+	0.253352i
$568$		−	3.23828e10i		−	0.311115i
$569$		−	1.31605e10i		−	0.125552i	−0.998028	−	0.0627760i	$-0.980005\pi$
$569$		−	1.31605e10i		−	0.125552i	0.998028	−	0.0627760i	$-0.0199954\pi$
$570$		0			0
$571$	7.09445e10			0.667382			0.333691	−	0.942683i	$-0.391706\pi$
$571$	7.09445e10			0.667382			0.333691	+	0.942683i	$0.391706\pi$
$572$	2.40536e11			2.24696
$573$	−8.77780e10	−	1.10063e10i	−0.814267	−	0.102099i
$574$	−3.54596e10			−0.326652
$575$		0			0
$576$	1.45864e11	+	3.71636e10i	1.32513	+	0.337620i
$577$		−	1.05284e11i		−	0.949859i	−0.880024	−	0.474929i	$-0.842474\pi$
$577$		−	1.05284e11i		−	0.949859i	0.880024	−	0.474929i	$-0.157526\pi$
$578$	1.25906e11			1.12807
$579$	−2.14018e11	−	2.68353e10i	−1.90430	−	0.238777i
$580$		0			0
$581$		−	1.46946e10i		−	0.128959i
$582$	5.57552e10	+	6.99104e9i	0.485952	+	0.0609326i
$583$		−	2.16507e11i		−	1.87412i
$584$			2.93895e10i			0.252662i
$585$		0			0
$586$	1.73893e10			0.147466
$587$	3.67507e10			0.309538			0.154769	−	0.987951i	$-0.450537\pi$
$587$	3.67507e10			0.309538			0.154769	+	0.987951i	$0.450537\pi$
$588$	1.65052e10	−	1.31633e11i	0.138074	−	1.10117i
$589$	−4.42505e10			−0.367669
$590$		0			0
$591$	2.33405e10	−	1.86146e11i	0.191320	−	1.52582i
$592$			1.12799e11i			0.918370i
$593$	2.06347e11			1.66870			0.834351	−	0.551234i	$-0.185843\pi$
$593$	2.06347e11			1.66870			0.834351	+	0.551234i	$0.185843\pi$
$594$	1.86888e11	+	7.33940e10i	1.50119	+	0.589542i
$595$		0			0
$596$		−	5.59843e10i		−	0.443692i
$597$	9.44776e9	−	7.53481e10i	0.0743758	−	0.593164i
$598$			5.04427e11i			3.94451i
$599$		−	1.66792e11i		−	1.29559i	−0.761813	−	0.647797i	$-0.775690\pi$
$599$		−	1.66792e11i		−	1.29559i	0.761813	−	0.647797i	$-0.224310\pi$
$600$		0			0
$601$	−1.53051e11			−1.17311			−0.586555	−	0.809909i	$-0.699516\pi$
$601$	−1.53051e11			−1.17311			−0.586555	+	0.809909i	$0.699516\pi$
$602$	−4.00147e10			−0.304673
$603$	2.52030e10	−	9.89199e10i	0.190626	−	0.748194i
$604$	−1.34193e10			−0.100828
$605$		0			0
$606$	1.20832e11	+	1.51509e10i	0.895969	+	0.112344i
$607$			2.06970e11i			1.52459i	0.647233	+	0.762293i	$0.275926\pi$
$607$			2.06970e11i			1.52459i	−0.647233	+	0.762293i	$0.724074\pi$
$608$	1.61226e11			1.17983
$609$	2.63807e9	−	2.10392e10i	0.0191786	−	0.152954i
$610$		0			0
$611$			3.99817e11i			2.86878i
$612$	−8.08347e10	−	2.05952e10i	−0.576225	−	0.146812i
$613$		−	1.06596e11i		−	0.754913i	−0.926027	−	0.377457i	$-0.876799\pi$
$613$		−	1.06596e11i		−	0.754913i	0.926027	−	0.377457i	$-0.123201\pi$
$614$			1.91609e11i			1.34816i
$615$		0			0
$616$	1.41088e10			0.0979865
$617$	−1.06362e11			−0.733914			−0.366957	−	0.930238i	$-0.619600\pi$
$617$	−1.06362e11			−0.733914			−0.366957	+	0.930238i	$0.619600\pi$
$618$	1.32754e11	+	1.66458e10i	0.910111	+	0.114117i
$619$	1.57576e11			1.07332			0.536659	−	0.843799i	$-0.319686\pi$
$619$	1.57576e11			1.07332			0.536659	+	0.843799i	$0.319686\pi$
$620$		0			0
$621$	−8.42877e10	+	2.14627e11i	−0.566758	+	1.44317i
$622$			5.42795e10i			0.362639i
$623$	3.37993e10			0.224365
$624$	1.91794e11	+	2.40487e10i	1.26502	+	0.158618i
$625$		0			0
$626$		−	8.10711e10i		−	0.527920i
$627$	1.38126e11	+	1.73194e10i	0.893729	+	0.112063i
$628$		−	3.09484e10i		−	0.198976i
$629$		−	9.47701e10i		−	0.605436i
$630$		0			0
$631$	2.74992e11			1.73461			0.867306	−	0.497775i	$-0.165850\pi$
$631$	2.74992e11			1.73461			0.867306	+	0.497775i	$0.165850\pi$
$632$	5.76983e10			0.361655
$633$	2.16358e10	−	1.72550e11i	0.134759	−	1.07473i
$634$	6.66900e10			0.412766
$635$		0			0
$636$	−4.25752e10	+	3.39547e11i	−0.260212	+	2.07525i
$637$		−	2.58277e11i		−	1.56866i
$638$	−1.42766e11			−0.861673
$639$	4.09059e10	−	1.60552e11i	0.245348	−	0.962971i
$640$		0			0
$641$		−	2.88263e11i		−	1.70749i	−0.520695	−	0.853743i	$-0.674327\pi$
$641$		−	2.88263e11i		−	1.70749i	0.520695	−	0.853743i	$-0.325673\pi$
$642$	5.18328e10	−	4.13379e11i	0.305116	−	2.43337i
$643$			2.34011e11i			1.36896i	0.729030	+	0.684481i	$0.239971\pi$
$643$			2.34011e11i			1.36896i	−0.729030	+	0.684481i	$0.760029\pi$
$644$			9.31503e10i			0.541553i
$645$		0			0
$646$	−1.05610e11			−0.606423
$647$	−1.59734e11			−0.911551			−0.455775	−	0.890095i	$-0.650638\pi$
$647$	−1.59734e11			−0.911551			−0.455775	+	0.890095i	$0.650638\pi$
$648$	−4.84716e10	−	2.64140e10i	−0.274908	−	0.149808i
$649$	−1.96405e11			−1.10707
$650$		0			0
$651$	−2.27675e10	−	2.85477e9i	−0.126763	−	0.0158945i
$652$		−	1.28765e11i		−	0.712534i
$653$	−1.20294e11			−0.661596			−0.330798	−	0.943702i	$-0.607318\pi$
$653$	−1.20294e11			−0.661596			−0.330798	+	0.943702i	$0.607318\pi$
$654$	1.67926e10	−	1.33925e11i	0.0917926	−	0.732068i
$655$		0			0
$656$			1.05068e11i			0.567356i
$657$	−3.71247e10	+	1.45711e11i	−0.199251	+	0.782046i
$658$			1.34822e11i			0.719215i
$659$		−	9.51290e10i		−	0.504396i	−0.967676	−	0.252198i	$-0.918847\pi$
$659$		−	9.51290e10i		−	0.504396i	0.967676	−	0.252198i	$-0.0811534\pi$
$660$		0			0
$661$	−3.37799e11			−1.76951			−0.884755	−	0.466056i	$-0.845674\pi$
$661$	−3.37799e11			−1.76951			−0.884755	+	0.466056i	$0.845674\pi$
$662$	9.17811e10			0.477882
$663$	−1.61140e11	−	2.02050e10i	−0.833966	−	0.104569i
$664$	2.72013e10			0.139932
$665$		0			0
$666$	8.90164e10	−	3.49383e11i	0.452453	−	1.77584i
$667$		−	1.63957e11i		−	0.828372i
$668$	6.21578e10			0.312169
$669$	−2.97992e11	−	3.73646e10i	−1.48765	−	0.186533i
$670$		0			0
$671$		−	1.82846e10i		−	0.0901978i
$672$	8.29529e10	+	1.04013e10i	0.406775	+	0.0510048i
$673$		−	1.01484e11i		−	0.494693i	−0.968927	−	0.247347i	$-0.920441\pi$
$673$		−	1.01484e11i		−	0.494693i	0.968927	−	0.247347i	$-0.0795586\pi$
$674$			1.03070e11i			0.499449i
$675$		0			0
$676$	−4.87368e11			−2.33384
$677$	1.58724e11			0.755595			0.377797	−	0.925888i	$-0.376682\pi$
$677$	1.58724e11			0.755595			0.377797	+	0.925888i	$0.376682\pi$
$678$	1.09321e10	−	8.71860e10i	0.0517350	−	0.412599i
$679$	2.02020e10			0.0950418
$680$		0			0
$681$	4.00102e10	−	3.19091e11i	0.186030	−	1.48363i
$682$			1.54494e11i			0.714124i
$683$	−1.30156e11			−0.598110			−0.299055	−	0.954236i	$-0.596671\pi$
$683$	−1.30156e11			−0.598110			−0.299055	+	0.954236i	$0.596671\pi$
$684$	−2.13217e11	−	5.43238e10i	−0.974086	−	0.248180i
$685$		0			0
$686$		−	1.82096e11i		−	0.822251i
$687$	−2.86332e10	+	2.28356e11i	−0.128541	+	1.02515i
$688$			1.18565e11i			0.529179i
$689$			6.66227e11i			2.95628i
$690$		0			0
$691$	−2.27036e9			−0.00995823			−0.00497912	−	0.999988i	$-0.501585\pi$
$691$	−2.27036e9			−0.00995823			−0.00497912	+	0.999988i	$0.501585\pi$
$692$	−3.34523e11			−1.45882
$693$	6.99506e10	+	1.78221e10i	0.303290	+	0.0772729i
$694$	3.56825e10			0.153821
$695$		0			0
$696$	3.89459e10	+	4.88335e9i	0.165968	+	0.0208104i
$697$		−	8.82750e10i		−	0.374030i
$698$	−4.55559e11			−1.91921
$699$	3.83900e9	−	3.06169e10i	0.0160808	−	0.128249i
$700$		0			0
$701$			2.75263e11i			1.13993i	0.821671	+	0.569963i	$0.193042\pi$
$701$			2.75263e11i			1.13993i	−0.821671	+	0.569963i	$0.806958\pi$
$702$	−5.75085e11	−	2.25845e11i	−2.36801	−	0.929955i
$703$		−	2.49974e11i		−	1.02347i
$704$		−	3.64364e11i		−	1.48336i
$705$		0			0
$706$	−6.52577e11			−2.62671
$707$	4.37816e10			0.175232
$708$	3.08021e11	+	3.86222e10i	1.22588	+	0.153711i
$709$	−1.38692e11			−0.548865			−0.274433	−	0.961606i	$-0.588490\pi$
$709$	−1.38692e11			−0.548865			−0.274433	+	0.961606i	$0.588490\pi$
$710$		0			0
$711$	2.86065e11	+	7.28843e10i	1.11940	+	0.285204i
$712$			6.25661e10i			0.243455i
$713$	−1.77425e11			−0.686525
$714$	−5.43379e10	−	6.81333e9i	−0.209079	−	0.0262160i
$715$		0			0
$716$		−	1.25024e11i		−	0.475711i
$717$	2.47977e11	+	3.10934e10i	0.938286	+	0.117650i
$718$			1.74825e11i			0.657820i
$719$			5.06730e11i			1.89610i	0.318125	+	0.948049i	$0.396947\pi$
$719$			5.06730e11i			1.89610i	−0.318125	+	0.948049i	$0.603053\pi$
$720$		0			0
$721$	4.81013e10			0.177998
$722$	1.25451e11			0.461664
$723$	−1.85047e10	+	1.47579e11i	−0.0677217	+	0.540097i
$724$	−2.94048e11			−1.07020
$725$		0			0
$726$	9.07933e9	−	7.24098e10i	0.0326819	−	0.260646i
$727$		−	2.19798e11i		−	0.786840i	−0.919359	−	0.393420i	$-0.871292\pi$
$727$		−	2.19798e11i		−	0.786840i	0.919359	−	0.393420i	$-0.128708\pi$
$728$	−4.34149e10			−0.154566
$729$	−2.06954e11	−	1.92189e11i	−0.732763	−	0.680484i
$730$		0			0
$731$		−	9.96147e10i		−	0.348862i
$732$	−3.59559e9	+	2.86757e10i	−0.0125235	+	0.0998780i
$733$			3.34443e11i			1.15853i	0.815140	+	0.579263i	$0.196660\pi$
$733$			3.34443e11i			1.15853i	−0.815140	+	0.579263i	$0.803340\pi$
$734$		−	1.55465e11i		−	0.535609i
$735$		0			0
$736$	6.46444e11			2.20303
$737$	−2.47099e11			−0.837530
$738$	8.29156e10	−	3.25437e11i	0.279519	−	1.09709i
$739$	4.18860e11			1.40440			0.702201	−	0.711979i	$-0.252201\pi$
$739$	4.18860e11			1.40440			0.702201	+	0.711979i	$0.252201\pi$
$740$		0			0
$741$	−4.25037e11	−	5.32945e10i	−1.40979	−	0.176771i
$742$			2.24658e11i			0.741152i
$743$	1.94993e11			0.639830			0.319915	−	0.947446i	$-0.396346\pi$
$743$	1.94993e11			0.639830			0.319915	+	0.947446i	$0.396346\pi$
$744$	5.28450e9	−	4.21451e10i	0.0172469	−	0.137548i
$745$		0			0
$746$			7.67721e11i			2.47884i
$747$	1.34863e11	+	3.43606e10i	0.433121	+	0.110351i
$748$			2.01923e11i			0.645028i
$749$		−	1.49781e11i		−	0.475915i
$750$		0			0
$751$	2.13581e10			0.0671433			0.0335717	−	0.999436i	$-0.489312\pi$
$751$	2.13581e10			0.0671433			0.0335717	+	0.999436i	$0.489312\pi$
$752$	3.99484e11			1.24919
$753$	3.33041e11	+	4.17594e10i	1.03590	+	0.129889i
$754$	4.39314e11			1.35922
$755$		0			0
$756$	−1.06199e11	−	4.17059e10i	−0.325111	−	0.127676i
$757$			9.33494e10i			0.284268i	0.989847	+	0.142134i	$0.0453964\pi$
$757$			9.33494e10i			0.284268i	−0.989847	+	0.142134i	$0.954604\pi$
$758$	−4.78005e11			−1.44796
$759$	5.53826e11	+	6.94432e10i	1.66881	+	0.209248i
$760$		0			0
$761$		−	7.19545e10i		−	0.214546i	−0.994230	−	0.107273i	$-0.965788\pi$
$761$		−	7.19545e10i		−	0.214546i	0.994230	−	0.107273i	$-0.0342118\pi$
$762$	2.06242e10	+	2.58603e9i	0.0611725	+	0.00767031i
$763$		−	4.85256e10i		−	0.143177i
$764$		−	3.38468e11i		−	0.993447i
$765$		0			0
$766$	6.29370e11			1.82806
$767$	6.04370e11			1.74631
$768$	1.97863e10	−	1.57800e11i	0.0568747	−	0.453589i
$769$	1.60418e11			0.458720			0.229360	−	0.973342i	$-0.426337\pi$
$769$	1.60418e11			0.458720			0.229360	+	0.973342i	$0.426337\pi$
$770$		0			0
$771$	−1.13515e10	+	9.05313e10i	−0.0321246	+	0.256201i
$772$		−	8.25245e11i		−	2.32335i
$773$	3.72166e11			1.04236			0.521181	−	0.853446i	$-0.325492\pi$
$773$	3.72166e11			1.04236			0.521181	+	0.853446i	$0.325492\pi$
$774$	9.35669e10	−	3.67243e11i	0.260710	−	1.02327i
$775$		0			0
$776$			3.73961e10i			0.103129i
$777$	1.61268e10	−	1.28615e11i	0.0442451	−	0.352865i
$778$		−	6.39941e11i		−	1.74671i
$779$		−	2.32842e11i		−	0.632283i
$780$		0			0
$781$	−4.01055e11			−1.07795
$782$	−4.23451e11			−1.13234
$783$	1.86923e11	+	7.34077e10i	0.497297	+	0.195296i
$784$	−2.58062e11			−0.683062
$785$		0			0
$786$	5.51176e11	+	6.91110e10i	1.44411	+	0.181074i
$787$			5.18916e11i			1.35269i	0.736585	+	0.676345i	$0.236437\pi$
$787$			5.18916e11i			1.35269i	−0.736585	+	0.676345i	$0.763563\pi$
$788$	7.17773e11			1.86158
$789$	−6.97229e10	+	5.56056e11i	−0.179915	+	1.43486i
$790$		0			0
$791$		−	3.15904e10i		−	0.0806956i
$792$	−3.29907e10	+	1.29486e11i	−0.0838477	+	0.329096i
$793$			5.62648e10i			0.142280i
$794$			5.19149e11i			1.30620i
$795$		0			0
$796$	2.90539e11			0.723690
$797$	−1.05184e11			−0.260686			−0.130343	−	0.991469i	$-0.541608\pi$
$797$	−1.05184e11			−0.260686			−0.130343	+	0.991469i	$0.541608\pi$
$798$	−1.43327e11	−	1.79715e10i	−0.353440	−	0.0443172i
$799$	−3.35634e11			−0.823530
$800$		0			0
$801$	−7.90333e10	+	3.10200e11i	−0.191991	+	0.753549i
$802$			9.19105e11i			2.22161i
$803$	3.63983e11			0.875424
$804$	3.87524e11	+	4.85909e10i	0.927415	+	0.116287i
$805$		0			0
$806$		−	4.75402e11i		−	1.12647i
$807$	−8.36375e10	−	1.04871e10i	−0.197200	−	0.0247265i
$808$			8.10446e10i			0.190142i
$809$			1.09572e10i			0.0255804i	0.999918	+	0.0127902i	$0.00407135\pi$
$809$			1.09572e10i			0.0255804i	−0.999918	+	0.0127902i	$0.995929\pi$
$810$		0			0
$811$	1.31782e11			0.304630			0.152315	−	0.988332i	$-0.451327\pi$
$811$	1.31782e11			0.304630			0.152315	+	0.988332i	$0.451327\pi$
$812$	8.11263e10			0.186611
$813$	−4.33694e10	+	3.45881e11i	−0.0992706	+	0.791707i
$814$	−8.72747e11			−1.98788
$815$		0			0
$816$	−2.01882e10	+	1.61005e11i	−0.0455341	+	0.363145i
$817$		−	2.62753e11i		−	0.589738i
$818$	−2.43229e11			−0.543254
$819$	−2.15249e11	−	5.48416e10i	−0.478416	−	0.121892i
$820$		0			0
$821$			3.65371e10i			0.0804194i	0.999191	+	0.0402097i	$0.0128026\pi$
$821$			3.65371e10i			0.0804194i	−0.999191	+	0.0402097i	$0.987197\pi$
$822$	−1.77354e10	+	1.41444e11i	−0.0388466	+	0.309811i
$823$		−	4.11792e11i		−	0.897591i	−0.893635	−	0.448795i	$-0.851853\pi$
$823$		−	4.11792e11i		−	0.897591i	0.893635	−	0.448795i	$-0.148147\pi$
$824$			8.90408e10i			0.193144i
$825$		0			0
$826$	2.03800e11			0.437808
$827$	−1.78687e11			−0.382007			−0.191004	−	0.981589i	$-0.561174\pi$
$827$	−1.78687e11			−0.382007			−0.191004	+	0.981589i	$0.561174\pi$
$828$	−8.54907e11	−	2.17815e11i	−1.81885	−	0.463411i
$829$	3.65541e11			0.773960			0.386980	−	0.922088i	$-0.373518\pi$
$829$	3.65541e11			0.773960			0.386980	+	0.922088i	$0.373518\pi$
$830$		0			0
$831$	8.14639e11	+	1.02146e11i	1.70829	+	0.214199i
$832$			1.12121e12i			2.33988i
$833$	2.16816e11			0.450310
$834$	−9.61243e9	+	7.66614e10i	−0.0198687	+	0.158457i
$835$		0			0
$836$			5.32609e11i			1.09039i
$837$	7.94378e10	−	2.02278e11i	0.161855	−	0.412142i
$838$		−	7.22074e11i		−	1.46422i
$839$		−	5.20766e11i		−	1.05098i	−0.850799	−	0.525491i	$-0.823882\pi$
$839$		−	5.20766e11i		−	1.05098i	0.850799	−	0.525491i	$-0.176118\pi$
$840$		0			0
$841$	3.57454e11			0.714555
$842$	−9.37429e11			−1.86505
$843$	−7.09349e11	−	8.89440e10i	−1.40459	−	0.176119i
$844$	6.65348e11			1.31123
$845$		0			0
$846$	−1.23736e12	−	3.15257e11i	−2.41554	−	0.615437i
$847$		−	2.62365e10i		−	0.0509768i
$848$	6.65672e11			1.28729
$849$	1.27026e11	+	1.59276e10i	0.244491	+	0.0306563i
$850$		0			0
$851$		−	1.00229e12i		−	1.91106i
$852$	6.28973e11	+	7.88657e10i	1.19364	+	0.149668i
$853$			5.21152e11i			0.984392i	0.870484	+	0.492196i	$0.163806\pi$
$853$			5.21152e11i			0.984392i	−0.870484	+	0.492196i	$0.836194\pi$
$854$			1.89731e10i			0.0356702i
$855$		0			0
$856$	2.77261e11			0.516409
$857$	8.67435e11			1.60810			0.804051	−	0.594560i	$-0.202674\pi$
$857$	8.67435e11			1.60810			0.804051	+	0.594560i	$0.202674\pi$
$858$	−1.86070e11	+	1.48395e12i	−0.343342	+	2.73823i
$859$	6.24921e11			1.14776			0.573882	−	0.818938i	$-0.305437\pi$
$859$	6.24921e11			1.14776			0.573882	+	0.818938i	$0.305437\pi$
$860$		0			0
$861$	1.50216e10	−	1.19801e11i	0.0273340	−	0.217995i
$862$		−	4.77990e11i		−	0.865745i
$863$	−8.65555e11			−1.56046			−0.780228	−	0.625495i	$-0.784897\pi$
$863$	−8.65555e11			−1.56046			−0.780228	+	0.625495i	$0.784897\pi$
$864$	−2.89430e11	+	7.36996e11i	−0.519384	+	1.32254i
$865$		0			0
$866$		−	1.13265e12i		−	2.01384i
$867$	−5.33369e10	+	4.25374e11i	−0.0943955	+	0.752827i
$868$		−	8.77906e10i		−	0.154657i
$869$		−	7.14583e11i		−	1.25306i
$870$		0			0
$871$	7.60363e11			1.32114
$872$	8.98262e10			0.155359
$873$	−4.72386e10	+	1.85408e11i	−0.0813280	+	0.319206i
$874$	−1.11693e12			−1.91417
$875$		0			0
$876$	−5.70833e11	−	7.15756e10i	−0.969376	−	0.121548i
$877$		−	3.45290e10i		−	0.0583694i	−0.999574	−	0.0291847i	$-0.990709\pi$
$877$		−	3.45290e10i		−	0.0583694i	0.999574	−	0.0291847i	$-0.00929110\pi$
$878$	−6.68096e11			−1.12424
$879$	−7.36654e9	+	5.87499e10i	−0.0123398	+	0.0984129i
$880$		0			0
$881$			5.74904e10i			0.0954316i	0.998861	+	0.0477158i	$0.0151942\pi$
$881$			5.74904e10i			0.0954316i	−0.998861	+	0.0477158i	$0.984806\pi$
$882$	7.99321e11	+	2.03653e11i	1.32083	+	0.336524i
$883$			7.36663e11i			1.21179i	0.795546	+	0.605893i	$0.207184\pi$
$883$			7.36663e11i			1.21179i	−0.795546	+	0.605893i	$0.792816\pi$
$884$		−	6.21348e11i		−	1.01748i
$885$		0			0
$886$	−7.68143e10			−0.124654
$887$	−1.56687e11			−0.253126			−0.126563	−	0.991959i	$-0.540395\pi$
$887$	−1.56687e11			−0.253126			−0.126563	+	0.991959i	$0.540395\pi$
$888$	2.38081e11	+	2.98525e10i	0.382889	+	0.0480097i
$889$	7.47283e9			0.0119640
$890$		0			0
$891$	−3.27133e11	+	6.00312e11i	−0.519055	+	0.952503i
$892$		−	1.14904e12i		−	1.81500i
$893$	−8.85300e11			−1.39214
$894$	3.45387e11	+	4.33074e10i	0.540700	+	0.0677973i
$895$		0			0
$896$			1.13858e11i			0.176657i
$897$	−1.70421e12	−	2.13688e11i	−2.63241	−	0.330073i
$898$		−	1.00163e12i		−	1.54029i
$899$			1.54523e11i			0.236567i
$900$		0			0
$901$	−5.59277e11			−0.848648
$902$	−8.12933e11			−1.22809
$903$	1.69512e10	−	1.35190e11i	0.0254947	−	0.203326i
$904$	5.84773e10			0.0875616
$905$		0			0
$906$	1.03807e10	−	8.27883e10i	0.0154068	−	0.122873i
$907$		−	5.78430e11i		−	0.854716i	−0.904083	−	0.427358i	$-0.859444\pi$
$907$		−	5.78430e11i		−	0.854716i	0.904083	−	0.427358i	$-0.140556\pi$
$908$	1.23040e12			1.81010
$909$	−1.02375e11	+	4.01815e11i	−0.149948	+	0.588533i
$910$		0			0
$911$			8.17142e10i			0.118638i	0.998239	+	0.0593190i	$0.0188929\pi$
$911$			8.17142e10i			0.118638i	−0.998239	+	0.0593190i	$0.981107\pi$
$912$	−5.32501e10	+	4.24682e11i	−0.0769735	+	0.613882i
$913$		−	3.36882e11i		−	0.484836i
$914$			9.85637e11i			1.41232i
$915$		0			0
$916$	−8.80533e11			−1.25073
$917$	1.99710e11			0.282437
$918$	1.89590e11	−	4.82766e11i	0.266959	−	0.679776i
$919$	8.52245e11			1.19482			0.597410	−	0.801936i	$-0.296197\pi$
$919$	8.52245e11			1.19482			0.597410	+	0.801936i	$0.296197\pi$
$920$		0			0
$921$	−6.47354e11	−	8.11705e10i	−0.899711	−	0.112813i
$922$		−	1.77036e12i		−	2.44984i
$923$	1.23411e12			1.70038
$924$	−3.43607e10	+	2.74035e11i	−0.0471384	+	0.375940i
$925$		0			0
$926$			1.08760e12i			1.47920i
$927$	−1.12476e11	+	4.41460e11i	−0.152314	+	0.597823i
$928$		−	5.63000e11i		−	0.759131i
$929$		−	4.58591e11i		−	0.615691i	−0.951436	−	0.307845i	$-0.900392\pi$
$929$		−	4.58591e11i		−	0.615691i	0.951436	−	0.307845i	$-0.0996079\pi$
$930$		0			0
$931$	5.71893e11			0.761231
$932$	1.18058e11			0.156470
$933$	−1.83384e11	−	2.29942e10i	−0.242011	−	0.0303453i
$934$	6.58834e10			0.0865742
$935$		0			0
$936$	1.01518e11	−	3.98450e11i	0.132263	−	0.519123i
$937$			1.32495e11i			0.171886i	0.996300	+	0.0859432i	$0.0273904\pi$
$937$			1.32495e11i			0.171886i	−0.996300	+	0.0859432i	$0.972610\pi$
$938$	2.56402e11			0.331215
$939$	2.73899e11	+	3.43437e10i	0.352313	+	0.0441759i
$940$		0			0
$941$			7.82786e11i			0.998354i	0.866500	+	0.499177i	$0.166364\pi$
$941$			7.82786e11i			0.998354i	−0.866500	+	0.499177i	$0.833636\pi$
$942$	1.90932e11	+	2.39406e10i	0.242479	+	0.0304040i
$943$		−	9.33594e11i		−	1.18062i
$944$		−	6.03867e11i		−	0.760419i
$945$		0			0
$946$	−9.17362e11			−1.14545
$947$	−7.18981e11			−0.893959			−0.446980	−	0.894544i	$-0.647500\pi$
$947$	−7.18981e11			−0.893959			−0.446980	+	0.894544i	$0.647500\pi$
$948$	−1.40520e11	+	1.12068e12i	−0.173982	+	1.38754i
$949$	−1.12003e12			−1.38091
$950$		0			0
$951$	−2.82516e10	+	2.25313e11i	−0.0345398	+	0.275463i
$952$		−	3.64455e10i		−	0.0443707i
$953$	−3.21954e11			−0.390321			−0.195160	−	0.980771i	$-0.562523\pi$
$953$	−3.21954e11			−0.390321			−0.195160	+	0.980771i	$0.562523\pi$
$954$	−2.06185e12	−	5.25322e11i	−2.48922	−	0.634209i
$955$		0			0
$956$			9.56191e11i			1.14476i
$957$	6.04793e10	−	4.82337e11i	0.0721040	−	0.575046i
$958$			9.08862e11i			1.07904i
$959$			5.12499e10i			0.0605924i
$960$		0			0
$961$	−6.85675e11			−0.803942
$962$	2.68558e12			3.13573
$963$	1.37465e12	+	3.50235e11i	1.59840	+	0.407244i
$964$	−5.69059e11			−0.658945
$965$		0			0
$966$	−5.74677e11	−	7.20577e10i	−0.659957	−	0.0827507i
$967$		−	4.20589e11i		−	0.481008i	−0.970648	−	0.240504i	$-0.922687\pi$
$967$		−	4.20589e11i		−	0.481008i	0.970648	−	0.240504i	$-0.0773127\pi$
$968$	4.85666e10			0.0553142
$969$	4.47391e10	−	3.56805e11i	0.0507449	−	0.404703i
$970$		0			0
$971$		−	8.93768e11i		−	1.00542i	−0.864455	−	0.502710i	$-0.832336\pi$
$971$		−	8.93768e11i		−	1.00542i	0.864455	−	0.502710i	$-0.167664\pi$
$972$	6.31090e11	−	8.77137e11i	0.707011	−	0.982658i
$973$			2.77770e10i			0.0309909i
$974$			6.63937e11i			0.737719i
$975$		0			0
$976$	5.62179e10			0.0619548
$977$	8.04509e11			0.882983			0.441492	−	0.897265i	$-0.354449\pi$
$977$	8.04509e11			0.882983			0.441492	+	0.897265i	$0.354449\pi$
$978$	7.94394e11	+	9.96075e10i	0.868321	+	0.108877i
$979$	7.74869e11			0.843525
$980$		0			0
$981$	4.45354e11	+	1.13468e11i	0.480872	+	0.122518i
$982$			8.62300e11i			0.927283i
$983$	−7.12126e11			−0.762681			−0.381340	−	0.924435i	$-0.624537\pi$
$983$	−7.12126e11			−0.762681			−0.381340	+	0.924435i	$0.624537\pi$
$984$	2.21764e11	+	2.78066e10i	0.236543	+	0.0296597i
$985$		0			0
$986$			3.68791e11i			0.390187i
$987$	−4.55499e11	−	5.71142e10i	−0.479975	−	0.0601832i
$988$		−	1.63892e12i		−	1.72001i
$989$		−	1.05352e12i		−	1.10118i
$990$		0			0
$991$	1.20276e12			1.24705			0.623526	−	0.781803i	$-0.285700\pi$
$991$	1.20276e12			1.24705			0.623526	+	0.781803i	$0.285700\pi$
$992$	−6.09249e11			−0.629141
$993$	−3.88808e10	+	3.10083e11i	−0.0399887	+	0.318920i
$994$	4.16155e11			0.426294
$995$		0			0
$996$	−6.62465e10	+	5.28331e11i	−0.0673171	+	0.536870i
$997$		−	2.28898e11i		−	0.231665i	−0.993269	−	0.115833i	$-0.963046\pi$
$997$		−	2.28898e11i		−	0.231665i	0.993269	−	0.115833i	$-0.0369536\pi$
$998$	−3.12341e11			−0.314852
$999$	1.14268e12	+	4.48750e11i	1.14727	+	0.450550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.d.c.74.3		20
3.2	odd	2	inner	75.9.d.c.74.17		20
5.2	odd	4		15.9.c.a.11.2	✓	10
5.3	odd	4		75.9.c.g.26.9		10
5.4	even	2	inner	75.9.d.c.74.18		20
15.2	even	4		15.9.c.a.11.9	yes	10
15.8	even	4		75.9.c.g.26.2		10
15.14	odd	2	inner	75.9.d.c.74.4		20
20.7	even	4		240.9.l.b.161.10		10
60.47	odd	4		240.9.l.b.161.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.c.a.11.2	✓	10	5.2	odd	4
15.9.c.a.11.9	yes	10	15.2	even	4
75.9.c.g.26.2		10	15.8	even	4
75.9.c.g.26.9		10	5.3	odd	4
75.9.d.c.74.3		20	1.1	even	1	trivial
75.9.d.c.74.4		20	15.14	odd	2	inner
75.9.d.c.74.17		20	3.2	odd	2	inner
75.9.d.c.74.18		20	5.4	even	2	inner
240.9.l.b.161.9		10	60.47	odd	4
240.9.l.b.161.10		10	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.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-23.7888 q^{2} +(10.0775 - 80.3707i) q^{3} +309.906 q^{4} +(-239.732 + 1911.92i) q^{6} +692.753i q^{7} -1282.36 q^{8} +(-6357.89 - 1619.88i) q^{9} +O(q^{10})\)	\(q-23.7888 q^{2} +(10.0775 - 80.3707i) q^{3} +309.906 q^{4} +(-239.732 + 1911.92i) q^{6} +692.753i q^{7} -1282.36 q^{8} +(-6357.89 - 1619.88i) q^{9} +15881.8i q^{11} +(3123.09 - 24907.4i) q^{12} -48870.9i q^{13} -16479.8i q^{14} -48830.2 q^{16} +41025.6 q^{17} +(151246. + 38534.9i) q^{18} +108213. q^{19} +(55677.0 + 6981.24i) q^{21} -377809. i q^{22} +433886. q^{23} +(-12923.0 + 103064. i) q^{24} +1.16258e6i q^{26} +(-194262. + 494663. i) q^{27} +214688. i q^{28} -377879. i q^{29} -408921. q^{31} +1.48989e6 q^{32} +(1.27643e6 + 160049. i) q^{33} -975949. q^{34} +(-1.97035e6 - 502009. i) q^{36} -2.31002e6i q^{37} -2.57425e6 q^{38} +(-3.92778e6 - 492497. i) q^{39} -2.15170e6i q^{41} +(-1.32449e6 - 166075. i) q^{42} -2.42811e6i q^{43} +4.92187e6i q^{44} -1.03216e7 q^{46} -8.18110e6 q^{47} +(-492087. + 3.92451e6i) q^{48} +5.28489e6 q^{49} +(413437. - 3.29725e6i) q^{51} -1.51454e7i q^{52} -1.36324e7 q^{53} +(4.62126e6 - 1.17674e7i) q^{54} -888360. i q^{56} +(1.09052e6 - 8.69714e6i) q^{57} +8.98929e6i q^{58} +1.23667e7i q^{59} -1.15129e6 q^{61} +9.72773e6 q^{62} +(1.12217e6 - 4.40445e6i) q^{63} -2.29423e7 q^{64} +(-3.03647e7 - 3.80738e6i) q^{66} +1.55586e7i q^{67} +1.27141e7 q^{68} +(4.37250e6 - 3.48717e7i) q^{69} +2.52525e7i q^{71} +(8.15311e6 + 2.07727e6i) q^{72} -2.29182e7i q^{73} +5.49526e7i q^{74} +3.35358e7 q^{76} -1.10022e7 q^{77} +(9.34372e7 + 1.17159e7i) q^{78} -4.49938e7 q^{79} +(3.77987e7 + 2.05980e7i) q^{81} +5.11864e7i q^{82} -2.12119e7 q^{83} +(1.72547e7 + 2.16353e6i) q^{84} +5.77618e7i q^{86} +(-3.03704e7 - 3.80809e6i) q^{87} -2.03662e7i q^{88} -4.87898e7i q^{89} +3.38555e7 q^{91} +1.34464e8 q^{92} +(-4.12091e6 + 3.28652e7i) q^{93} +1.94618e8 q^{94} +(1.50145e7 - 1.19744e8i) q^{96} -2.91619e7i q^{97} -1.25721e8 q^{98} +(2.57265e7 - 1.00975e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9}+O(q^{10}) \) 20 * q + 1572 * q^4 - 10564 * q^6 - 7844 * q^9	\( 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9} + 560772 q^{16} + 463032 q^{19} + 579144 q^{21} - 2272668 q^{24} + 1763240 q^{31} + 2222552 q^{34} - 1337324 q^{36} - 3653584 q^{39} - 50849208 q^{46} - 18708428 q^{49} - 55465384 q^{51} + 15959596 q^{54} + 44834040 q^{61} + 45870004 q^{64} - 54839600 q^{66} - 67125264 q^{69} + 397844872 q^{76} - 324621848 q^{79} - 187150780 q^{81} + 394693536 q^{84} + 888576928 q^{91} + 184100072 q^{94} - 721614812 q^{96} + 67930400 q^{99}+O(q^{100}) \) 20 * q + 1572 * q^4 - 10564 * q^6 - 7844 * q^9 + 560772 * q^16 + 463032 * q^19 + 579144 * q^21 - 2272668 * q^24 + 1763240 * q^31 + 2222552 * q^34 - 1337324 * q^36 - 3653584 * q^39 - 50849208 * q^46 - 18708428 * q^49 - 55465384 * q^51 + 15959596 * q^54 + 44834040 * q^61 + 45870004 * q^64 - 54839600 * q^66 - 67125264 * q^69 + 397844872 * q^76 - 324621848 * q^79 - 187150780 * q^81 + 394693536 * q^84 + 888576928 * q^91 + 184100072 * q^94 - 721614812 * q^96 + 67930400 * q^99

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