LMFDB - Embedded newform 75.9.c.g.26.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(26,75)]

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, 0]))

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

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

chi := DirichletCharacter("75.26");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 433 x^{8} - 2220 x^{7} + 49747 x^{6} + 744964 x^{5} + 4580249 x^{4} + 16418988 x^{3} + \cdots + 53656344 $ x^10 - 4x^9 - 433x^8 - 2220x^7 + 49747x^6 + 744964x^5 + 4580249x^4 + 16418988x^3 + 38943804x^2 + 57910464*x + 53656344
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3^{11}\cdot 5^{10} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.9
Root			$-0.616448 - 2.23607i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.9.c.g.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+23.7888i q^{2} +(80.3707 + 10.0775i) q^{3} -309.906 q^{4} +(-239.732 + 1911.92i) q^{6} +692.753 q^{7} -1282.36i q^{8} +(6357.89 + 1619.88i) q^{9} +O(q^{10})$	\(q+23.7888i q^{2} +(80.3707 + 10.0775i) q^{3} -309.906 q^{4} +(-239.732 + 1911.92i) q^{6} +692.753 q^{7} -1282.36i q^{8} +(6357.89 + 1619.88i) q^{9} +15881.8i q^{11} +(-24907.4 - 3123.09i) q^{12} +48870.9 q^{13} +16479.8i q^{14} -48830.2 q^{16} -41025.6i q^{17} +(-38534.9 + 151246. i) q^{18} -108213. q^{19} +(55677.0 + 6981.24i) q^{21} -377809. q^{22} +433886. i q^{23} +(12923.0 - 103064. i) q^{24} +1.16258e6i q^{26} +(494663. + 194262. i) q^{27} -214688. q^{28} +377879. i q^{29} -408921. q^{31} -1.48989e6i q^{32} +(-160049. + 1.27643e6i) q^{33} +975949. q^{34} +(-1.97035e6 - 502009. i) q^{36} -2.31002e6 q^{37} -2.57425e6i q^{38} +(3.92778e6 + 492497. i) q^{39} -2.15170e6i q^{41} +(-166075. + 1.32449e6i) q^{42} +2.42811e6 q^{43} -4.92187e6i q^{44} -1.03216e7 q^{46} +8.18110e6i q^{47} +(-3.92451e6 - 492087. i) q^{48} -5.28489e6 q^{49} +(413437. - 3.29725e6i) q^{51} -1.51454e7 q^{52} -1.36324e7i q^{53} +(-4.62126e6 + 1.17674e7i) q^{54} -888360. i q^{56} +(-8.69714e6 - 1.09052e6i) q^{57} -8.98929e6 q^{58} -1.23667e7i q^{59} -1.15129e6 q^{61} -9.72773e6i q^{62} +(4.40445e6 + 1.12217e6i) q^{63} +2.29423e7 q^{64} +(-3.03647e7 - 3.80738e6i) q^{66} +1.55586e7 q^{67} +1.27141e7i q^{68} +(-4.37250e6 + 3.48717e7i) q^{69} +2.52525e7i q^{71} +(2.07727e6 - 8.15311e6i) q^{72} +2.29182e7 q^{73} -5.49526e7i q^{74} +3.35358e7 q^{76} +1.10022e7i q^{77} +(-1.17159e7 + 9.34372e7i) q^{78} +4.49938e7 q^{79} +(3.77987e7 + 2.05980e7i) q^{81} +5.11864e7 q^{82} -2.12119e7i q^{83} +(-1.72547e7 - 2.16353e6i) q^{84} +5.77618e7i q^{86} +(-3.80809e6 + 3.03704e7i) q^{87} +2.03662e7 q^{88} +4.87898e7i q^{89} +3.38555e7 q^{91} -1.34464e8i q^{92} +(-3.28652e7 - 4.12091e6i) q^{93} -1.94618e8 q^{94} +(1.50145e7 - 1.19744e8i) q^{96} -2.91619e7 q^{97} -1.25721e8i q^{98} +(-2.57265e7 + 1.00975e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 112 q^{3} - 786 q^{4} - 5282 q^{6} - 7156 q^{7} + 3922 q^{9}+O(q^{10}) $ 10 * q + 112 * q^3 - 786 * q^4 - 5282 * q^6 - 7156 * q^7 + 3922 * q^9	$ 10 q + 112 q^{3} - 786 q^{4} - 5282 q^{6} - 7156 q^{7} + 3922 q^{9} + 3812 q^{12} + 55464 q^{13} + 280386 q^{16} + 419800 q^{18} - 231516 q^{19} + 289572 q^{21} - 1129940 q^{22} + 1136334 q^{24} + 335512 q^{27} + 3340724 q^{28} + 881620 q^{31} - 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} - 4672616 q^{37} + 1826792 q^{39} + 5392860 q^{42} - 7731336 q^{43} - 25424604 q^{46} - 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} - 21064016 q^{52} - 7979798 q^{54} + 2856304 q^{57} + 4351100 q^{58} + 22417020 q^{61} - 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} + 46646024 q^{67} + 33562632 q^{69} - 54175560 q^{72} + 129964884 q^{73} + 198922436 q^{76} - 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} - 202877560 q^{82} - 197346768 q^{84} + 168322540 q^{87} + 484775700 q^{88} + 444288464 q^{91} - 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} + 258825724 q^{97} - 33965200 q^{99}+O(q^{100}) $ 10 * q + 112 * q^3 - 786 * q^4 - 5282 * q^6 - 7156 * q^7 + 3922 * q^9 + 3812 * q^12 + 55464 * q^13 + 280386 * q^16 + 419800 * q^18 - 231516 * q^19 + 289572 * q^21 - 1129940 * q^22 + 1136334 * q^24 + 335512 * q^27 + 3340724 * q^28 + 881620 * q^31 - 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 - 4672616 * q^37 + 1826792 * q^39 + 5392860 * q^42 - 7731336 * q^43 - 25424604 * q^46 - 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 - 21064016 * q^52 - 7979798 * q^54 + 2856304 * q^57 + 4351100 * q^58 + 22417020 * q^61 - 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 + 46646024 * q^67 + 33562632 * q^69 - 54175560 * q^72 + 129964884 * q^73 + 198922436 * q^76 - 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 - 202877560 * q^82 - 197346768 * q^84 + 168322540 * q^87 + 484775700 * q^88 + 444288464 * q^91 - 463412376 * q^93 - 92050036 * q^94 - 360807406 * q^96 + 258825724 * q^97 - 33965200 * 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 $

$2$			23.7888i			1.48680i	0.668848	+	0.743399i	$0.266788\pi$
$2$			23.7888i			1.48680i	−0.668848	+	0.743399i	$0.733212\pi$
$3$	80.3707	+	10.0775i	0.992230	+	0.124414i
$3$	80.3707	+	10.0775i	0.992230	+	0.124414i
$4$	−309.906			−1.21057
$5$		0			0
$5$		0			0
$6$	−239.732	+	1911.92i	−0.184978	+	1.47525i
$7$	692.753			0.288527			0.144263	−	0.989539i	$-0.453919\pi$
$7$	692.753			0.288527			0.144263	+	0.989539i	$0.453919\pi$
$8$		−	1282.36i		−	0.313077i
$9$	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	$0.817525\pi$
$12$	−24907.4	−	3123.09i	−1.20117	−	0.150612i
$13$	48870.9			1.71110			0.855552	−	0.517716i	$-0.173218\pi$
$13$	48870.9			1.71110			0.855552	+	0.517716i	$0.173218\pi$
$14$			16479.8i			0.428982i
$15$		0			0
$16$	−48830.2			−0.745089
$17$		−	41025.6i		−	0.491201i	−0.969371	−	0.245600i	$-0.921015\pi$
$17$		−	41025.6i		−	0.491201i	0.969371	−	0.245600i	$-0.0789851\pi$
$18$	−38534.9	+	151246.i	−0.367083	+	1.44077i
$19$	−108213.			−0.830356			−0.415178	−	0.909740i	$-0.636281\pi$
$19$	−108213.			−0.830356			−0.415178	+	0.909740i	$0.636281\pi$
$20$		0			0
$21$	55677.0	+	6981.24i	0.286285	+	0.0358968i
$22$	−377809.			−1.61280
$23$			433886.i			1.55047i	0.631671	+	0.775237i	$0.282369\pi$
$23$			433886.i			1.55047i	−0.631671	+	0.775237i	$0.717631\pi$
$24$	12923.0	−	103064.i	0.0389511	−	0.310644i
$25$		0			0
$26$			1.16258e6i			2.54407i
$27$	494663.	+	194262.i	0.930796	+	0.365539i
$28$	−214688.			−0.349282
$29$			377879.i			0.534270i	0.963659	+	0.267135i	$0.0860770\pi$
$29$			377879.i			0.534270i	−0.963659	+	0.267135i	$0.913923\pi$
$30$		0			0
$31$	−408921.			−0.442784			−0.221392	−	0.975185i	$-0.571060\pi$
$31$	−408921.			−0.442784			−0.221392	+	0.975185i	$0.571060\pi$
$32$		−	1.48989e6i		−	1.42087i
$33$	−160049.	+	1.27643e6i	−0.134958	+	1.07632i
$34$	975949.			0.730317
$35$		0			0
$36$	−1.97035e6	−	502009.i	−1.17309	−	0.298883i
$37$	−2.31002e6			−1.23256			−0.616282	−	0.787526i	$-0.711362\pi$
$37$	−2.31002e6			−1.23256			−0.616282	+	0.787526i	$0.711362\pi$
$38$		−	2.57425e6i		−	1.23457i
$39$	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	$-0.124327\pi$
$42$	−166075.	+	1.32449e6i	−0.0533713	+	0.425649i
$43$	2.42811e6			0.710223			0.355111	−	0.934824i	$-0.384443\pi$
$43$	2.42811e6			0.710223			0.355111	+	0.934824i	$0.384443\pi$
$44$		−	4.92187e6i		−	1.31317i
$45$		0			0
$46$	−1.03216e7			−2.30524
$47$			8.18110e6i			1.67656i	0.545237	+	0.838282i	$0.316440\pi$
$47$			8.18110e6i			1.67656i	−0.545237	+	0.838282i	$0.683560\pi$
$48$	−3.92451e6	−	492087.i	−0.739300	−	0.0926994i
$49$	−5.28489e6			−0.916752
$50$		0			0
$51$	413437.	−	3.29725e6i	0.0611122	−	0.487385i
$52$	−1.51454e7			−2.07141
$53$		−	1.36324e7i		−	1.72770i	−0.503748	−	0.863850i	$-0.668046\pi$
$53$		−	1.36324e7i		−	1.72770i	0.503748	−	0.863850i	$-0.331954\pi$
$54$	−4.62126e6	+	1.17674e7i	−0.543482	+	1.38391i
$55$		0			0
$56$		−	888360.i		−	0.0903310i
$57$	−8.69714e6	−	1.09052e6i	−0.823904	−	0.103308i
$58$	−8.98929e6			−0.794353
$59$		−	1.23667e7i		−	1.02057i	−0.860004	−	0.510287i	$-0.829539\pi$
$59$		−	1.23667e7i		−	1.02057i	0.860004	−	0.510287i	$-0.170461\pi$
$60$		0			0
$61$	−1.15129e6			−0.0831509			−0.0415755	−	0.999135i	$-0.513238\pi$
$61$	−1.15129e6			−0.0831509			−0.0415755	+	0.999135i	$0.513238\pi$
$62$		−	9.72773e6i		−	0.658331i
$63$	4.40445e6	+	1.12217e6i	0.279595	+	0.0712357i
$64$	2.29423e7			1.36746
$65$		0			0
$66$	−3.03647e7	−	3.80738e6i	−1.60027	−	0.200655i
$67$	1.55586e7			0.772096			0.386048	−	0.922479i	$-0.373840\pi$
$67$	1.55586e7			0.772096			0.386048	+	0.922479i	$0.373840\pi$
$68$			1.27141e7i			0.594634i
$69$	−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	$0.834483\pi$
$72$	2.07727e6	−	8.15311e6i	0.0772969	−	0.303384i
$73$	2.29182e7			0.807030			0.403515	−	0.914973i	$-0.367788\pi$
$73$	2.29182e7			0.807030			0.403515	+	0.914973i	$0.367788\pi$
$74$		−	5.49526e7i		−	1.83257i
$75$		0			0
$76$	3.35358e7			1.00520
$77$			1.10022e7i			0.312979i
$78$	−1.17159e7	+	9.34372e7i	−0.316518	+	2.52430i
$79$	4.49938e7			1.15517			0.577583	−	0.816332i	$-0.303996\pi$
$79$	4.49938e7			1.15517			0.577583	+	0.816332i	$0.303996\pi$
$80$		0			0
$81$	3.77987e7	+	2.05980e7i	0.878086	+	0.478503i
$82$	5.11864e7			1.13214
$83$		−	2.12119e7i		−	0.446957i	−0.974709	−	0.223479i	$-0.928259\pi$
$83$		−	2.12119e7i		−	0.446957i	0.974709	−	0.223479i	$-0.0717413\pi$
$84$	−1.72547e7	−	2.16353e6i	−0.346569	−	0.0434556i
$85$		0			0
$86$			5.77618e7i			1.05596i
$87$	−3.80809e6	+	3.03704e7i	−0.0664707	+	0.530119i
$88$	2.03662e7			0.339609
$89$			4.87898e7i			0.777622i	0.921317	+	0.388811i	$0.127114\pi$
$89$			4.87898e7i			0.777622i	−0.921317	+	0.388811i	$0.872886\pi$
$90$		0			0
$91$	3.38555e7			0.493700
$92$		−	1.34464e8i		−	1.87696i
$93$	−3.28652e7	−	4.12091e6i	−0.439344	−	0.0550885i
$94$	−1.94618e8			−2.49271
$95$		0			0
$96$	1.50145e7	−	1.19744e8i	0.176777	−	1.40983i
$97$	−2.91619e7			−0.329404			−0.164702	−	0.986343i	$-0.552666\pi$
$97$	−2.91619e7			−0.329404			−0.164702	+	0.986343i	$0.552666\pi$
$98$		−	1.25721e8i		−	1.36303i
$99$	−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	$-0.0982111\pi$
$102$	7.84377e7	+	9.83515e6i	0.724643	+	0.0908616i
$103$	6.94350e7			0.616921			0.308461	−	0.951237i	$-0.400186\pi$
$103$	6.94350e7			0.616921			0.308461	+	0.951237i	$0.400186\pi$
$104$		−	6.26701e7i		−	0.535707i
$105$		0			0
$106$	3.24298e8			2.56874
$107$			2.16211e8i			1.64946i	0.565523	+	0.824732i	$0.308674\pi$
$107$			2.16211e8i			1.64946i	−0.565523	+	0.824732i	$0.691326\pi$
$108$	−1.53299e8	−	6.02031e7i	−1.12679	−	0.442510i
$109$	7.00475e7			0.496234			0.248117	−	0.968730i	$-0.420188\pi$
$109$	7.00475e7			0.496234			0.248117	+	0.968730i	$0.420188\pi$
$110$		0			0
$111$	−1.85658e8	−	2.32793e7i	−1.22299	−	0.153348i
$112$	−3.38272e7			−0.214978
$113$		−	4.56013e7i		−	0.279681i	−0.990174	−	0.139841i	$-0.955341\pi$
$113$		−	4.56013e7i		−	0.279681i	0.990174	−	0.139841i	$-0.0446590\pi$
$114$	2.59421e7	−	2.06894e8i	0.153598	−	1.22498i
$115$		0			0
$116$		−	1.17107e8i		−	0.646772i
$117$	3.10715e8	+	7.91647e7i	1.65813	+	0.422462i
$118$	2.94188e8			1.51739
$119$		−	2.84206e7i		−	0.141725i
$120$		0			0
$121$	−3.78728e7			−0.176679
$122$		−	2.73879e7i		−	0.123629i
$123$	2.16839e7	−	1.72934e8i	0.0947362	−	0.755544i
$124$	1.26727e8			0.536022
$125$		0			0
$126$	−2.66951e7	+	1.04776e8i	−0.105913	+	0.415701i
$127$	−1.07871e7			−0.0414660			−0.0207330	−	0.999785i	$-0.506600\pi$
$127$	−1.07871e7			−0.0414660			−0.0207330	+	0.999785i	$0.506600\pi$
$128$			1.64355e8i			0.612271i
$129$	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	$-0.162801\pi$
$132$	4.96003e7	−	3.95574e8i	0.163376	−	1.30296i
$133$	−7.49648e7			−0.239580
$134$			3.70120e8i			1.14795i
$135$		0			0
$136$	−5.26097e7			−0.153784
$137$		−	7.39800e7i		−	0.210006i	−0.994472	−	0.105003i	$-0.966515\pi$
$137$		−	7.39800e7i		−	0.210006i	0.994472	−	0.105003i	$-0.0334852\pi$
$138$	−8.29555e8	−	1.04016e8i	−2.28733	−	0.286804i
$139$	−4.00966e7			−0.107411			−0.0537054	−	0.998557i	$-0.517103\pi$
$139$	−4.00966e7			−0.107411			−0.0537054	+	0.998557i	$0.517103\pi$
$140$		0			0
$141$	−8.24452e7	+	6.57520e8i	−0.208588	+	1.66354i
$142$	−6.00726e8			−1.47748
$143$			7.76158e8i			1.85612i
$144$	−3.10457e8	−	7.90987e7i	−0.722023	−	0.183958i
$145$		0			0
$146$			5.45197e8i			1.19989i
$147$	−4.24750e8	−	5.32587e7i	−0.909629	−	0.114057i
$148$	7.15890e8			1.49211
$149$			1.80649e8i			0.366515i	0.983065	+	0.183257i	$0.0586641\pi$
$149$			1.80649e8i			0.366515i	−0.983065	+	0.183257i	$0.941336\pi$
$150$		0			0
$151$	−4.33011e7			−0.0832898			−0.0416449	−	0.999132i	$-0.513260\pi$
$151$	−4.33011e7			−0.0832898			−0.0416449	+	0.999132i	$0.513260\pi$
$152$			1.38768e8i			0.259965i
$153$	6.64563e7	−	2.60836e8i	0.121275	−	0.475995i
$154$	−2.61728e8			−0.465337
$155$		0			0
$156$	−1.21724e9	−	1.52628e8i	−2.05532	−	0.257713i
$157$	−9.98639e7			−0.164365			−0.0821826	−	0.996617i	$-0.526189\pi$
$157$	−9.98639e7			−0.164365			−0.0821826	+	0.996617i	$0.526189\pi$
$158$			1.07035e9i			1.71750i
$159$	1.37381e8	−	1.09564e9i	0.214950	−	1.71428i
$160$		0			0
$161$			3.00576e8i			0.447353i
$162$	−4.90000e8	+	8.99186e8i	−0.711437	+	1.30554i
$163$	4.15495e8			0.588594			0.294297	−	0.955714i	$-0.404915\pi$
$163$	4.15495e8			0.588594			0.294297	+	0.955714i	$0.404915\pi$
$164$			6.66826e8i			0.921801i
$165$		0			0
$166$	5.04604e8			0.664536
$167$		−	2.00570e8i		−	0.257869i	−0.991653	−	0.128935i	$-0.958844\pi$
$167$		−	2.00570e8i		−	0.257869i	0.991653	−	0.128935i	$-0.0411557\pi$
$168$	8.95247e6	−	7.13981e7i	0.0112384	−	0.0896292i
$169$	1.57263e9			1.92788
$170$		0			0
$171$	−6.88005e8	−	1.75291e8i	−0.804650	−	0.205010i
$172$	−7.52487e8			−0.859775
$173$		−	1.07943e9i		−	1.20507i	−0.798093	−	0.602534i	$-0.794158\pi$
$173$		−	1.07943e9i		−	1.20507i	0.798093	−	0.602534i	$-0.205842\pi$
$174$	−7.22475e8	−	9.05898e7i	−0.788181	−	0.0988285i
$175$		0			0
$176$		−	7.75511e8i		−	0.808234i
$177$	1.24626e8	−	9.93918e8i	0.126974	−	1.01265i
$178$	−1.16065e9			−1.15617
$179$			4.03427e8i			0.392964i	0.980507	+	0.196482i	$0.0629517\pi$
$179$			4.03427e8i			0.392964i	−0.980507	+	0.196482i	$0.937048\pi$
$180$		0			0
$181$	−9.48830e8			−0.884045			−0.442022	−	0.897004i	$-0.645739\pi$
$181$	−9.48830e8			−0.884045			−0.442022	+	0.897004i	$0.645739\pi$
$182$			8.05380e8i			0.734032i
$183$	−9.25303e7	−	1.16022e7i	−0.0825049	−	0.0103451i
$184$	5.56399e8			0.485417
$185$		0			0
$186$	9.80314e7	−	7.81824e8i	0.0819056	−	0.653216i
$187$	6.51560e8			0.532830
$188$		−	2.53537e9i		−	2.02960i
$189$	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	$-0.134584\pi$
$192$	1.84388e9	+	2.31201e8i	1.35684	+	0.170132i
$193$	2.66289e9			1.91921			0.959607	−	0.281342i	$-0.0907797\pi$
$193$	2.66289e9			1.91921			0.959607	+	0.281342i	$0.0907797\pi$
$194$		−	6.93725e8i		−	0.489757i
$195$		0			0
$196$	1.63782e9			1.10979
$197$		−	2.31610e9i		−	1.53777i	−0.639386	−	0.768886i	$-0.720811\pi$
$197$		−	2.31610e9i		−	1.53777i	0.639386	−	0.768886i	$-0.279189\pi$
$198$	−2.40207e9	−	6.12003e8i	−1.56287	−	0.398192i
$199$	−9.37508e8			−0.597809			−0.298905	−	0.954283i	$-0.596621\pi$
$199$	−9.37508e8			−0.597809			−0.298905	+	0.954283i	$0.596621\pi$
$200$		0			0
$201$	1.25046e9	+	1.56792e8i	0.766097	+	0.0960595i
$202$	1.50344e9			0.902984
$203$			2.61777e8i			0.154151i
$204$	−1.28127e8	+	1.02184e9i	−0.0739807	+	0.590014i
$205$		0			0
$206$			1.65177e9i			0.917238i
$207$	−7.02841e8	+	2.75860e9i	−0.382803	+	1.50247i
$208$	−2.38637e9			−1.27493
$209$		−	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	$0.317828\pi$
$212$			4.22476e9i			2.09150i
$213$	−2.54483e8	+	2.02956e9i	−0.123634	+	0.986014i
$214$	−5.14340e9			−2.45242
$215$		0			0
$216$	2.49114e8	−	6.34337e8i	0.114442	−	0.291411i
$217$	−2.83281e8			−0.127755
$218$			1.66634e9i			0.737800i
$219$	1.84195e9	+	2.30959e8i	0.800759	+	0.100406i
$220$		0			0
$221$		−	2.00496e9i		−	0.840496i
$222$	5.53787e8	−	4.41658e9i	0.227998	−	1.81834i
$223$	3.70772e9			1.49929			0.749647	−	0.661838i	$-0.230223\pi$
$223$	3.70772e9			1.49929			0.749647	+	0.661838i	$0.230223\pi$
$224$		−	1.03213e9i		−	0.409960i
$225$		0			0
$226$	1.08480e9			0.415830
$227$		−	3.97024e9i		−	1.49525i	−0.664122	−	0.747624i	$-0.731194\pi$
$227$		−	3.97024e9i		−	1.49525i	0.664122	−	0.747624i	$-0.268806\pi$
$228$	2.69530e9	+	3.37958e8i	0.997395	+	0.125061i
$229$	2.84129e9			1.03317			0.516587	−	0.856235i	$-0.327202\pi$
$229$	2.84129e9			1.03317			0.516587	+	0.856235i	$0.327202\pi$
$230$		0			0
$231$	−1.10875e8	+	8.84252e8i	−0.0389390	+	0.310547i
$232$	4.84578e8			0.167268
$233$			3.80946e8i			0.129253i	0.997910	+	0.0646264i	$0.0205856\pi$
$233$			3.80946e8i			0.129253i	−0.997910	+	0.0646264i	$0.979414\pi$
$234$	−1.88323e9	+	7.39154e9i	−0.628117	+	2.46531i
$235$		0			0
$236$			3.83251e9i			1.23548i
$237$	3.61618e9	+	4.53426e8i	1.14619	+	0.143719i
$238$	6.76092e8			0.210716
$239$		−	3.08542e9i		−	0.945633i	−0.881161	−	0.472817i	$-0.843237\pi$
$239$		−	3.08542e9i		−	0.945633i	0.881161	−	0.472817i	$-0.156763\pi$
$240$		0			0
$241$	−1.83623e9			−0.544326			−0.272163	−	0.962251i	$-0.587739\pi$
$241$	−1.83623e9			−0.544326			−0.272163	+	0.962251i	$0.587739\pi$
$242$		−	9.00948e8i		−	0.262687i
$243$	2.83033e9	+	2.03639e9i	0.811731	+	0.584031i
$244$	3.56793e8			0.100660
$245$		0			0
$246$	4.11389e9	+	5.15833e8i	1.12334	+	0.140854i
$247$	−5.28845e9			−1.42083
$248$			5.24384e8i			0.138625i
$249$	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	$0.825184\pi$
$252$	−1.36497e9	−	3.47769e8i	−0.338469	−	0.0862359i
$253$	−6.89089e9			−1.68187
$254$		−	2.56613e8i		−	0.0616515i
$255$		0			0
$256$	1.96340e9			0.457141
$257$			1.12642e9i			0.258207i	0.991631	+	0.129104i	$0.0412100\pi$
$257$			1.12642e9i			0.258207i	−0.991631	+	0.129104i	$0.958790\pi$
$258$	−5.82096e8	+	4.64235e9i	−0.131376	+	1.04775i
$259$	−1.60028e9			−0.355628
$260$		0			0
$261$	−6.12117e8	+	2.40251e9i	−0.131908	+	0.517731i
$262$	6.85793e9			1.45542
$263$		−	6.91865e9i		−	1.44610i	−0.690796	−	0.723050i	$-0.742740\pi$
$263$		−	6.91865e9i		−	1.44610i	0.690796	−	0.723050i	$-0.257260\pi$
$264$	1.63685e9	+	2.05241e8i	0.336971	+	0.0422521i
$265$		0			0
$266$		−	1.78332e9i		−	0.356207i
$267$	−4.91680e8	+	3.92127e9i	−0.0967470	+	0.771581i
$268$	−4.82171e9			−0.934677
$269$			1.04065e9i			0.198744i	0.995050	+	0.0993720i	$0.0316834\pi$
$269$			1.04065e9i			0.198744i	−0.995050	+	0.0993720i	$0.968317\pi$
$270$		0			0
$271$	−4.30357e9			−0.797906			−0.398953	−	0.916971i	$-0.630626\pi$
$271$	−4.30357e9			−0.797906			−0.398953	+	0.916971i	$0.630626\pi$
$272$			2.00329e9i			0.365988i
$273$	2.72099e9	+	3.41179e8i	0.489864	+	0.0614231i
$274$	1.75989e9			0.312237
$275$		0			0
$276$	1.35506e9	−	1.08070e10i	0.233520	−	1.86237i
$277$	1.01360e10			1.72166			0.860832	−	0.508889i	$-0.169944\pi$
$277$	1.01360e10			1.72166			0.860832	+	0.508889i	$0.169944\pi$
$278$		−	9.53848e8i		−	0.159698i
$279$	−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	$-0.250310\pi$
$282$	−1.56416e10	−	1.96127e9i	−2.47335	−	0.310128i
$283$	−1.58051e9			−0.246405			−0.123203	−	0.992382i	$-0.539317\pi$
$283$	−1.58051e9			−0.246405			−0.123203	+	0.992382i	$0.539317\pi$
$284$		−	7.82590e9i		−	1.20299i
$285$		0			0
$286$	−1.84638e10			−2.75967
$287$		−	1.49060e9i		−	0.219702i
$288$	2.41344e9	−	9.47258e9i	0.350806	−	1.37689i
$289$	5.29266e9			0.758722
$290$		0			0
$291$	−2.34376e9	−	2.93880e8i	−0.326844	−	0.0409824i
$292$	−7.10250e9			−0.976967
$293$		−	7.30987e8i		−	0.0991835i	−0.998770	−	0.0495917i	$-0.984208\pi$
$293$		−	7.30987e8i		−	0.0991835i	0.998770	−	0.0495917i	$-0.0157920\pi$
$294$	1.26696e9	−	1.01043e10i	0.169579	−	1.35244i
$295$		0			0
$296$			2.96228e9i			0.385887i
$297$	−3.08523e9	+	7.85614e9i	−0.396517	+	1.00968i
$298$	−4.29743e9			−0.544934
$299$			2.12044e10i			2.65302i
$300$		0			0
$301$	1.68208e9			0.204918
$302$		−	1.03008e9i		−	0.123835i
$303$	6.36894e8	−	5.07938e9i	0.0755609	−	0.602616i
$304$	5.28405e9			0.618689
$305$		0			0
$306$	6.20497e9	+	1.58092e9i	0.707708	+	0.180311i
$307$	−8.05460e9			−0.906757			−0.453378	−	0.891318i	$-0.649781\pi$
$307$	−8.05460e9			−0.906757			−0.453378	+	0.891318i	$0.649781\pi$
$308$		−	3.40964e9i		−	0.378884i
$309$	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	$-0.0389157\pi$
$312$	6.31560e8	−	5.03684e9i	0.0666494	−	0.531545i
$313$	−3.40795e9			−0.355072			−0.177536	−	0.984114i	$-0.556813\pi$
$313$	−3.40795e9			−0.355072			−0.177536	+	0.984114i	$0.556813\pi$
$314$		−	2.37564e9i		−	0.244378i
$315$		0			0
$316$	−1.39439e10			−1.39841
$317$			2.80342e9i			0.277620i	0.990319	+	0.138810i	$0.0443278\pi$
$317$			2.80342e9i			0.277620i	−0.990319	+	0.138810i	$0.955672\pi$
$318$	2.60640e10	+	3.26812e9i	2.54879	+	0.319587i
$319$	−6.00140e9			−0.579549
$320$		0			0
$321$	−2.17887e9	+	1.73770e10i	−0.205216	+	1.63665i
$322$	−7.15034e9			−0.665125
$323$			4.43950e9i			0.407872i
$324$	−1.17141e10	−	6.38344e9i	−1.06299	−	0.579261i
$325$		0			0
$326$			9.88412e9i			0.875120i
$327$	5.62976e9	+	7.05906e8i	0.492379	+	0.0617384i
$328$	−2.75926e9			−0.238395
$329$			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	$0.551378\pi$
$332$			6.57368e9i			0.541074i
$333$	−1.46869e10	−	3.74195e9i	−1.19441	−	0.304313i
$334$	4.77131e9			0.383400
$335$		0			0
$336$	−2.71872e9	−	3.40895e8i	−0.213308	−	0.0267463i
$337$	−4.33270e9			−0.335922			−0.167961	−	0.985794i	$-0.553718\pi$
$337$	−4.33270e9			−0.335922			−0.167961	+	0.985794i	$0.553718\pi$
$338$			3.74110e10i			2.86637i
$339$	4.59548e8	−	3.66500e9i	0.0347962	−	0.277508i
$340$		0			0
$341$		−	6.49440e9i		−	0.480310i
$342$	4.16997e9	−	1.63668e10i	0.304809	−	1.19635i
$343$	−7.65471e9			−0.553035
$344$		−	3.11372e9i		−	0.222354i
$345$		0			0
$346$	2.56784e10			1.79169
$347$			1.49997e9i			0.103458i	0.998661	+	0.0517291i	$0.0164732\pi$
$347$			1.49997e9i			0.103458i	−0.998661	+	0.0517291i	$0.983527\pi$
$348$	1.18015e9	−	9.41198e9i	0.0804675	−	0.641747i
$349$	−1.91502e10			−1.29084			−0.645418	−	0.763830i	$-0.723317\pi$
$349$	−1.91502e10			−1.29084			−0.645418	+	0.763830i	$0.723317\pi$
$350$		0			0
$351$	2.41746e10	+	9.49376e9i	1.59269	+	0.625475i
$352$	2.36622e10			1.54129
$353$			2.74321e10i			1.76669i	0.468723	+	0.883345i	$0.344714\pi$
$353$			2.74321e10i			1.76669i	−0.468723	+	0.883345i	$0.655286\pi$
$354$	2.36441e10	+	2.96469e9i	1.50560	+	0.188784i
$355$		0			0
$356$		−	1.51202e10i		−	0.941367i
$357$	2.86410e8	−	2.28418e9i	0.0176325	−	0.140624i
$358$	−9.59704e9			−0.584258
$359$			7.34907e9i			0.442440i	0.975224	+	0.221220i	$0.0710039\pi$
$359$			7.34907e9i			0.442440i	−0.975224	+	0.221220i	$0.928996\pi$
$360$		0			0
$361$	−5.27355e9			−0.310509
$362$		−	2.25715e10i		−	1.31440i
$363$	−3.04386e9	−	3.81664e8i	−0.175307	−	0.0219814i
$364$	−1.04920e10			−0.597659
$365$		0			0
$366$	2.76002e8	−	2.20118e9i	0.0153811	−	0.122668i
$367$	6.53522e9			0.360243			0.180122	−	0.983644i	$-0.442351\pi$
$367$	6.53522e9			0.360243			0.180122	+	0.983644i	$0.442351\pi$
$368$		−	2.11867e10i		−	1.15524i
$369$	3.48549e9	−	1.36803e10i	0.188000	−	0.737887i
$370$		0			0
$371$		−	9.44388e9i		−	0.498488i
$372$	1.01851e10	+	1.27710e9i	0.531857	+	0.0666886i
$373$	3.22724e10			1.66723			0.833615	−	0.552346i	$-0.186267\pi$
$373$	3.22724e10			1.66723			0.833615	+	0.552346i	$0.186267\pi$
$374$			1.54998e10i			0.792210i
$375$		0			0
$376$	1.04911e10			0.524893
$377$			1.84673e10i			0.914193i
$378$	−3.20139e9	+	8.15193e9i	−0.156809	+	0.399294i
$379$	−2.00937e10			−0.973875			−0.486938	−	0.873437i	$-0.661886\pi$
$379$	−2.00937e10			−0.973875			−0.486938	+	0.873437i	$0.661886\pi$
$380$		0			0
$381$	−8.66970e8	−	1.08708e8i	−0.0411438	−	0.00515894i
$382$	2.59813e10			1.22013
$383$		−	2.64566e10i		−	1.22953i	−0.788711	−	0.614765i	$-0.789251\pi$
$383$		−	2.64566e10i		−	1.22953i	0.788711	−	0.614765i	$-0.210749\pi$
$384$	−1.65630e9	+	1.32093e10i	−0.0761751	+	0.607514i
$385$		0			0
$386$			6.33469e10i			2.85349i
$387$	1.54377e10	+	3.93324e9i	0.688236	+	0.175350i
$388$	9.03744e9			0.398766
$389$		−	2.69010e10i		−	1.17482i	−0.809291	−	0.587408i	$-0.800149\pi$
$389$		−	2.69010e10i		−	1.17482i	0.809291	−	0.587408i	$-0.199851\pi$
$390$		0			0
$391$	1.78004e10			0.761594
$392$			6.77715e9i			0.287014i
$393$	2.90519e9	−	2.31696e10i	0.121788	−	0.971288i
$394$	5.50971e10			2.28636
$395$		0			0
$396$	7.97281e9	−	3.12927e10i	0.324213	−	1.27251i
$397$	−2.18233e10			−0.878533			−0.439266	−	0.898357i	$-0.644762\pi$
$397$	−2.18233e10			−0.878533			−0.439266	+	0.898357i	$0.644762\pi$
$398$		−	2.23022e10i		−	0.888822i
$399$	−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	$-0.268560\pi$
$402$	−3.72990e9	+	2.97468e10i	−0.142821	+	1.13903i
$403$	−1.99843e10			−0.757651
$404$			1.95859e10i			0.735222i
$405$		0			0
$406$	−6.22736e9			−0.229192
$407$		−	3.66873e10i		−	1.33702i
$408$	−4.22827e9	−	5.30175e8i	−0.152589	−	0.0191328i
$409$	−1.02245e10			−0.365385			−0.182692	−	0.983170i	$-0.558481\pi$
$409$	−1.02245e10			−0.365385			−0.182692	+	0.983170i	$0.558481\pi$
$410$		0			0
$411$	7.45535e8	−	5.94582e9i	0.0261277	−	0.208375i
$412$	−2.15183e10			−0.746827
$413$		−	8.56705e9i		−	0.294463i
$414$	−6.56237e10	−	1.67197e10i	−2.23388	−	0.569152i
$415$		0			0
$416$		−	7.28124e10i		−	2.43126i
$417$	−3.22259e9	−	4.04074e8i	−0.106576	−	0.0133634i
$418$	4.08838e10			1.33920
$419$		−	3.03535e10i		−	0.984812i	−0.870366	−	0.492406i	$-0.836118\pi$
$419$		−	3.03535e10i		−	0.984812i	0.870366	−	0.492406i	$-0.163882\pi$
$420$		0			0
$421$	3.94064e10			1.25441			0.627203	−	0.778856i	$-0.284200\pi$
$421$	3.94064e10			1.25441			0.627203	+	0.778856i	$0.284200\pi$
$422$			5.10729e10i			1.61043i
$423$	−1.32524e10	+	5.20145e10i	−0.413934	+	1.62466i
$424$	−1.74817e10			−0.540903
$425$		0			0
$426$	−4.82807e10	−	6.05383e9i	−1.46600	−	0.183820i
$427$	−7.97563e8			−0.0239913
$428$		−	6.70052e10i		−	1.99679i
$429$	−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	$0.905964\pi$
$432$	−2.41545e10	−	9.48585e9i	−0.693526	−	0.272359i
$433$	−4.76129e10			−1.35448			−0.677241	−	0.735761i	$-0.736824\pi$
$433$	−4.76129e10			−1.35448			−0.677241	+	0.735761i	$0.736824\pi$
$434$		−	6.73891e9i		−	0.189946i
$435$		0			0
$436$	−2.17082e10			−0.600727
$437$		−	4.69520e10i		−	1.28744i
$438$	−5.49423e9	+	4.38178e10i	−0.149283	+	1.19057i
$439$	−2.80845e10			−0.756151			−0.378076	−	0.925775i	$-0.623414\pi$
$439$	−2.80845e10			−0.756151			−0.378076	+	0.925775i	$0.623414\pi$
$440$		0			0
$441$	−3.36008e10	−	8.56087e9i	−0.888372	−	0.226341i
$442$	4.76955e10			1.24965
$443$			3.22901e9i			0.0838407i	0.999121	+	0.0419204i	$0.0133476\pi$
$443$			3.22901e9i			0.0838407i	−0.999121	+	0.0419204i	$0.986652\pi$
$444$	5.75366e10	+	7.21440e9i	1.48051	+	0.185639i
$445$		0			0
$446$			8.82020e10i			2.22915i
$447$	−1.82050e9	+	1.45189e10i	−0.0455995	+	0.363667i
$448$	1.58933e10			0.394551
$449$		−	4.21051e10i		−	1.03598i	−0.855388	−	0.517988i	$-0.826681\pi$
$449$		−	4.21051e10i		−	1.03598i	0.855388	−	0.517988i	$-0.173319\pi$
$450$		0			0
$451$	3.41729e10			0.825993
$452$			1.41321e10i			0.338574i
$453$	−3.48014e9	−	4.36368e8i	−0.0826426	−	0.0103624i
$454$	9.44472e10			2.22313
$455$		0			0
$456$	−1.39844e9	+	1.11529e10i	−0.0323433	+	0.257945i
$457$	−4.14329e10			−0.949905			−0.474952	−	0.880011i	$-0.657535\pi$
$457$	−4.14329e10			−0.949905			−0.474952	+	0.880011i	$0.657535\pi$
$458$			6.75908e10i			1.53612i
$459$	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	$0.691814\pi$
$462$	−2.10353e10	−	2.63757e9i	−0.461722	−	0.0578944i
$463$	4.57191e10			0.994887			0.497444	−	0.867496i	$-0.334272\pi$
$463$	4.57191e10			0.994887			0.497444	+	0.867496i	$0.334272\pi$
$464$		−	1.84519e10i		−	0.398079i
$465$		0			0
$466$	−9.06225e9			−0.192173
$467$			2.76952e9i			0.0582286i	0.999576	+	0.0291143i	$0.00926868\pi$
$467$			2.76952e9i			0.0582286i	−0.999576	+	0.0291143i	$0.990731\pi$
$468$	−9.62926e10	−	2.45336e10i	−2.00729	−	0.511421i
$469$	1.07783e10			0.222771
$470$		0			0
$471$	−8.02613e9	−	1.00638e9i	−0.163088	−	0.0204493i
$472$	−1.58586e10			−0.319518
$473$			3.85628e10i			0.770413i
$474$	−1.07865e10	+	8.60245e10i	−0.213681	+	1.70415i
$475$		0			0
$476$			8.80772e9i			0.171568i
$477$	2.20828e10	−	8.66732e10i	0.426560	−	1.67422i
$478$	7.33984e10			1.40597
$479$			3.82055e10i			0.725744i	0.931839	+	0.362872i	$0.118204\pi$
$479$			3.82055e10i			0.725744i	−0.931839	+	0.362872i	$0.881796\pi$
$480$		0			0
$481$	−1.12893e11			−2.10905
$482$		−	4.36817e10i		−	0.809303i
$483$	−3.02906e9	+	2.41575e10i	−0.0556570	+	0.443878i
$484$	1.17370e10			0.213883
$485$		0			0
$486$	−4.84432e10	+	6.73302e10i	−0.868336	+	1.20688i
$487$	−2.79097e10			−0.496179			−0.248090	−	0.968737i	$-0.579803\pi$
$487$	−2.79097e10			−0.496179			−0.248090	+	0.968737i	$0.579803\pi$
$488$			1.47638e9i			0.0260326i
$489$	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	$-0.100945\pi$
$492$	−6.71996e9	+	5.35933e10i	−0.114685	+	0.914639i
$493$	1.55027e10			0.262434
$494$		−	1.25806e11i		−	2.11248i
$495$		0			0
$496$	1.99677e10			0.329914
$497$			1.74937e10i			0.286719i
$498$	4.05554e10	+	5.08516e9i	0.659373	+	0.0826775i
$499$	−1.31298e10			−0.211765			−0.105883	−	0.994379i	$-0.533767\pi$
$499$	−1.31298e10			−0.211765			−0.105883	+	0.994379i	$0.533767\pi$
$500$		0			0
$501$	2.02125e9	−	1.61199e10i	0.0320825	−	0.255866i
$502$	−9.85762e10			−1.55223
$503$			1.84778e10i			0.288654i	0.989530	+	0.144327i	$0.0461017\pi$
$503$			1.84778e10i			0.288654i	−0.989530	+	0.144327i	$0.953898\pi$
$504$	1.43903e9	−	5.64809e9i	0.0223022	−	0.0875346i
$505$		0			0
$506$		−	1.63926e11i		−	2.50061i
$507$	1.26393e11	+	1.58482e10i	1.91290	+	0.239855i
$508$	3.34300e9			0.0501975
$509$			7.39108e10i			1.10112i	0.834794	+	0.550562i	$0.185587\pi$
$509$			7.39108e10i			1.10112i	−0.834794	+	0.550562i	$0.814413\pi$
$510$		0			0
$511$	1.58767e10			0.232850
$512$			8.87820e10i			1.29195i
$513$	−5.35289e10	−	2.10217e10i	−0.772892	−	0.303527i
$514$	−2.67962e10			−0.383902
$515$		0			0
$516$	−6.04778e10	−	7.58320e9i	−0.853095	−	0.106968i
$517$	−1.29931e11			−1.81865
$518$		−	3.80686e10i		−	0.528747i
$519$	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	$0.818639\pi$
$522$	−5.71529e10	−	1.45615e10i	−0.769761	−	0.196121i
$523$	−3.03522e10			−0.405680			−0.202840	−	0.979212i	$-0.565017\pi$
$523$	−3.03522e10			−0.405680			−0.202840	+	0.979212i	$0.565017\pi$
$524$			8.93410e10i			1.18502i
$525$		0			0
$526$	1.64586e11			2.15006
$527$			1.67762e10i			0.217496i
$528$	7.81523e9	−	6.23283e10i	0.100556	−	0.801955i
$529$	−1.09946e11			−1.40397
$530$		0			0
$531$	2.00325e10	−	7.86259e10i	0.251974	−	0.988980i
$532$	2.32320e10			0.290029
$533$		−	1.05156e11i		−	1.30294i
$534$	−9.32821e10	−	1.16965e10i	−1.14719	−	0.143843i
$535$		0			0
$536$		−	1.99518e10i		−	0.241725i
$537$	−4.06555e9	+	3.24237e10i	−0.0488902	+	0.389911i
$538$	−2.47557e10			−0.295492
$539$		−	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	$0.566108\pi$
$542$		−	1.02377e11i		−	1.18633i
$543$	−7.62581e10	−	9.56187e9i	−0.877176	−	0.109987i
$544$	−6.11238e10			−0.697935
$545$		0			0
$546$	−8.11624e9	+	6.47289e10i	−0.0913239	+	0.728329i
$547$	1.62586e11			1.81607			0.908036	−	0.418891i	$-0.137581\pi$
$547$	1.62586e11			1.81607			0.908036	+	0.418891i	$0.137581\pi$
$548$			2.29269e10i			0.254227i
$549$	−7.31980e9	−	1.86495e9i	−0.0805768	−	0.0205295i
$550$		0			0
$551$		−	4.08914e10i		−	0.443635i
$552$	4.47181e10	+	5.60712e9i	0.481645	+	0.0603926i
$553$	3.11696e10			0.333296
$554$			2.41124e11i			2.55977i
$555$		0			0
$556$	1.24262e10			0.130028
$557$			1.81639e11i			1.88707i	0.331273	+	0.943535i	$0.392522\pi$
$557$			1.81639e11i			1.88707i	−0.331273	+	0.943535i	$0.607478\pi$
$558$	1.57577e10	−	6.18478e10i	0.162538	−	0.637951i
$559$	1.18664e11			1.21527
$560$		0			0
$561$	5.23663e10	+	6.56612e9i	0.528690	+	0.0662914i
$562$	2.09959e11			2.10470
$563$		−	6.38376e10i		−	0.635394i	−0.948192	−	0.317697i	$-0.897090\pi$
$563$		−	6.38376e10i		−	0.635394i	0.948192	−	0.317697i	$-0.102910\pi$
$564$	2.55503e10	−	2.03770e11i	0.252510	−	2.01383i
$565$		0			0
$566$		−	3.75983e10i		−	0.366355i
$567$	2.61852e10	+	1.42693e10i	0.253352	+	0.138061i
$568$	3.23828e10			0.311115
$569$			1.31605e10i			0.125552i	0.998028	+	0.0627760i	$0.0199954\pi$
$569$			1.31605e10i			0.125552i	−0.998028	+	0.0627760i	$0.980005\pi$
$570$		0			0
$571$	7.09445e10			0.667382			0.333691	−	0.942683i	$-0.391706\pi$
$571$	7.09445e10			0.667382			0.333691	+	0.942683i	$0.391706\pi$
$572$		−	2.40536e11i		−	2.24696i
$573$	1.10063e10	−	8.77780e10i	0.102099	−	0.814267i
$574$	3.54596e10			0.326652
$575$		0			0
$576$	1.45864e11	+	3.71636e10i	1.32513	+	0.337620i
$577$	−1.05284e11			−0.949859			−0.474929	−	0.880024i	$-0.657526\pi$
$577$	−1.05284e11			−0.949859			−0.474929	+	0.880024i	$0.657526\pi$
$578$			1.25906e11i			1.12807i
$579$	2.14018e11	+	2.68353e10i	1.90430	+	0.238777i
$580$		0			0
$581$		−	1.46946e10i		−	0.128959i
$582$	6.99104e9	−	5.57552e10i	0.0609326	−	0.485952i
$583$	2.16507e11			1.87412
$584$		−	2.93895e10i		−	0.252662i
$585$		0			0
$586$	1.73893e10			0.147466
$587$		−	3.67507e10i		−	0.309538i	−0.987951	−	0.154769i	$-0.950537\pi$
$587$		−	3.67507e10i		−	0.309538i	0.987951	−	0.154769i	$-0.0494633\pi$
$588$	1.31633e11	+	1.65052e10i	1.10117	+	0.138074i
$589$	4.42505e10			0.367669
$590$		0			0
$591$	2.33405e10	−	1.86146e11i	0.191320	−	1.52582i
$592$	1.12799e11			0.918370
$593$			2.06347e11i			1.66870i	0.551234	+	0.834351i	$0.314157\pi$
$593$			2.06347e11i			1.66870i	−0.551234	+	0.834351i	$0.685843\pi$
$594$	−1.86888e11	−	7.33940e10i	−1.50119	−	0.589542i
$595$		0			0
$596$		−	5.59843e10i		−	0.443692i
$597$	−7.53481e10	−	9.44776e9i	−0.593164	−	0.0743758i
$598$	−5.04427e11			−3.94451
$599$			1.66792e11i			1.29559i	0.761813	+	0.647797i	$0.224310\pi$
$599$			1.66792e11i			1.29559i	−0.761813	+	0.647797i	$0.775690\pi$
$600$		0			0
$601$	−1.53051e11			−1.17311			−0.586555	−	0.809909i	$-0.699516\pi$
$601$	−1.53051e11			−1.17311			−0.586555	+	0.809909i	$0.699516\pi$
$602$			4.00147e10i			0.304673i
$603$	9.89199e10	+	2.52030e10i	0.748194	+	0.190626i
$604$	1.34193e10			0.100828
$605$		0			0
$606$	1.20832e11	+	1.51509e10i	0.895969	+	0.112344i
$607$	2.06970e11			1.52459			0.762293	−	0.647233i	$-0.224074\pi$
$607$	2.06970e11			1.52459			0.762293	+	0.647233i	$0.224074\pi$
$608$			1.61226e11i			1.17983i
$609$	−2.63807e9	+	2.10392e10i	−0.0191786	+	0.152954i
$610$		0			0
$611$			3.99817e11i			2.86878i
$612$	−2.05952e10	+	8.08347e10i	−0.146812	+	0.576225i
$613$	1.06596e11			0.754913			0.377457	−	0.926027i	$-0.376799\pi$
$613$	1.06596e11			0.754913			0.377457	+	0.926027i	$0.376799\pi$
$614$		−	1.91609e11i		−	1.34816i
$615$		0			0
$616$	1.41088e10			0.0979865
$617$			1.06362e11i			0.733914i	0.930238	+	0.366957i	$0.119600\pi$
$617$			1.06362e11i			0.733914i	−0.930238	+	0.366957i	$0.880400\pi$
$618$	−1.66458e10	+	1.32754e11i	−0.114117	+	0.910111i
$619$	−1.57576e11			−1.07332			−0.536659	−	0.843799i	$-0.680314\pi$
$619$	−1.57576e11			−1.07332			−0.536659	+	0.843799i	$0.680314\pi$
$620$		0			0
$621$	−8.42877e10	+	2.14627e11i	−0.566758	+	1.44317i
$622$	5.42795e10			0.362639
$623$			3.37993e10i			0.224365i
$624$	−1.91794e11	−	2.40487e10i	−1.26502	−	0.158618i
$625$		0			0
$626$		−	8.10711e10i		−	0.527920i
$627$	1.73194e10	−	1.38126e11i	0.112063	−	0.893729i
$628$	3.09484e10			0.198976
$629$			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	$0.165850\pi$
$632$		−	5.76983e10i		−	0.361655i
$633$	1.72550e11	+	2.16358e10i	1.07473	+	0.134759i
$634$	−6.66900e10			−0.412766
$635$		0			0
$636$	−4.25752e10	+	3.39547e11i	−0.260212	+	2.07525i
$637$	−2.58277e11			−1.56866
$638$		−	1.42766e11i		−	0.861673i
$639$	−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	$-0.325673\pi$
$642$	−4.13379e11	−	5.18328e10i	−2.43337	−	0.305116i
$643$	−2.34011e11			−1.36896			−0.684481	−	0.729030i	$-0.739971\pi$
$643$	−2.34011e11			−1.36896			−0.684481	+	0.729030i	$0.739971\pi$
$644$		−	9.31503e10i		−	0.541553i
$645$		0			0
$646$	−1.05610e11			−0.606423
$647$			1.59734e11i			0.911551i	0.890095	+	0.455775i	$0.150638\pi$
$647$			1.59734e11i			0.911551i	−0.890095	+	0.455775i	$0.849362\pi$
$648$	2.64140e10	−	4.84716e10i	0.149808	−	0.274908i
$649$	1.96405e11			1.10707
$650$		0			0
$651$	−2.27675e10	−	2.85477e9i	−0.126763	−	0.0158945i
$652$	−1.28765e11			−0.712534
$653$		−	1.20294e11i		−	0.661596i	−0.943702	−	0.330798i	$-0.892682\pi$
$653$		−	1.20294e11i		−	0.661596i	0.943702	−	0.330798i	$-0.107318\pi$
$654$	−1.67926e10	+	1.33925e11i	−0.0917926	+	0.732068i
$655$		0			0
$656$			1.05068e11i			0.567356i
$657$	1.45711e11	+	3.71247e10i	0.782046	+	0.199251i
$658$	−1.34822e11			−0.719215
$659$			9.51290e10i			0.504396i	0.967676	+	0.252198i	$0.0811534\pi$
$659$			9.51290e10i			0.504396i	−0.967676	+	0.252198i	$0.918847\pi$
$660$		0			0
$661$	−3.37799e11			−1.76951			−0.884755	−	0.466056i	$-0.845674\pi$
$661$	−3.37799e11			−1.76951			−0.884755	+	0.466056i	$0.845674\pi$
$662$		−	9.17811e10i		−	0.477882i
$663$	2.02050e10	−	1.61140e11i	0.104569	−	0.833966i
$664$	−2.72013e10			−0.139932
$665$		0			0
$666$	8.90164e10	−	3.49383e11i	0.452453	−	1.77584i
$667$	−1.63957e11			−0.828372
$668$			6.21578e10i			0.312169i
$669$	2.97992e11	+	3.73646e10i	1.48765	+	0.186533i
$670$		0			0
$671$		−	1.82846e10i		−	0.0901978i
$672$	1.04013e10	−	8.29529e10i	0.0510048	−	0.406775i
$673$	1.01484e11			0.494693			0.247347	−	0.968927i	$-0.420441\pi$
$673$	1.01484e11			0.494693			0.247347	+	0.968927i	$0.420441\pi$
$674$		−	1.03070e11i		−	0.499449i
$675$		0			0
$676$	−4.87368e11			−2.33384
$677$		−	1.58724e11i		−	0.755595i	−0.925888	−	0.377797i	$-0.876682\pi$
$677$		−	1.58724e11i		−	0.755595i	0.925888	−	0.377797i	$-0.123318\pi$
$678$	8.71860e10	+	1.09321e10i	0.412599	+	0.0517350i
$679$	−2.02020e10			−0.0950418
$680$		0			0
$681$	4.00102e10	−	3.19091e11i	0.186030	−	1.48363i
$682$	1.54494e11			0.714124
$683$		−	1.30156e11i		−	0.598110i	−0.954236	−	0.299055i	$-0.903329\pi$
$683$		−	1.30156e11i		−	0.598110i	0.954236	−	0.299055i	$-0.0966714\pi$
$684$	2.13217e11	+	5.43238e10i	0.974086	+	0.248180i
$685$		0			0
$686$		−	1.82096e11i		−	0.822251i
$687$	2.28356e11	+	2.86332e10i	1.02515	+	0.128541i
$688$	−1.18565e11			−0.529179
$689$		−	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	$0.501585\pi$
$692$			3.34523e11i			1.45882i
$693$	−1.78221e10	+	6.99506e10i	−0.0772729	+	0.303290i
$694$	−3.56825e10			−0.153821
$695$		0			0
$696$	3.89459e10	+	4.88335e9i	0.165968	+	0.0208104i
$697$	−8.82750e10			−0.374030
$698$		−	4.55559e11i		−	1.91921i
$699$	−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	$0.806958\pi$
$702$	−2.25845e11	+	5.75085e11i	−0.929955	+	2.36801i
$703$	2.49974e11			1.02347
$704$			3.64364e11i			1.48336i
$705$		0			0
$706$	−6.52577e11			−2.62671
$707$		−	4.37816e10i		−	0.175232i
$708$	−3.86222e10	+	3.08021e11i	−0.153711	+	1.22588i
$709$	1.38692e11			0.548865			0.274433	−	0.961606i	$-0.411510\pi$
$709$	1.38692e11			0.548865			0.274433	+	0.961606i	$0.411510\pi$
$710$		0			0
$711$	2.86065e11	+	7.28843e10i	1.11940	+	0.285204i
$712$	6.25661e10			0.243455
$713$		−	1.77425e11i		−	0.686525i
$714$	5.43379e10	+	6.81333e9i	0.209079	+	0.0262160i
$715$		0			0
$716$		−	1.25024e11i		−	0.475711i
$717$	3.10934e10	−	2.47977e11i	0.117650	−	0.938286i
$718$	−1.74825e11			−0.657820
$719$		−	5.06730e11i		−	1.89610i	−0.318125	−	0.948049i	$-0.603053\pi$
$719$		−	5.06730e11i		−	1.89610i	0.318125	−	0.948049i	$-0.396947\pi$
$720$		0			0
$721$	4.81013e10			0.177998
$722$		−	1.25451e11i		−	0.461664i
$723$	−1.47579e11	−	1.85047e10i	−0.540097	−	0.0677217i
$724$	2.94048e11			1.07020
$725$		0			0
$726$	9.07933e9	−	7.24098e10i	0.0326819	−	0.260646i
$727$	−2.19798e11			−0.786840			−0.393420	−	0.919359i	$-0.628708\pi$
$727$	−2.19798e11			−0.786840			−0.393420	+	0.919359i	$0.628708\pi$
$728$		−	4.34149e10i		−	0.154566i
$729$	2.06954e11	+	1.92189e11i	0.732763	+	0.680484i
$730$		0			0
$731$		−	9.96147e10i		−	0.348862i
$732$	2.86757e10	+	3.59559e9i	0.0998780	+	0.0125235i
$733$	−3.34443e11			−1.15853			−0.579263	−	0.815140i	$-0.696660\pi$
$733$	−3.34443e11			−1.15853			−0.579263	+	0.815140i	$0.696660\pi$
$734$			1.55465e11i			0.535609i
$735$		0			0
$736$	6.46444e11			2.20303
$737$			2.47099e11i			0.837530i
$738$	3.25437e11	+	8.29156e10i	1.09709	+	0.279519i
$739$	−4.18860e11			−1.40440			−0.702201	−	0.711979i	$-0.747799\pi$
$739$	−4.18860e11			−1.40440			−0.702201	+	0.711979i	$0.747799\pi$
$740$		0			0
$741$	−4.25037e11	−	5.32945e10i	−1.40979	−	0.176771i
$742$	2.24658e11			0.741152
$743$			1.94993e11i			0.639830i	0.947446	+	0.319915i	$0.103654\pi$
$743$			1.94993e11i			0.639830i	−0.947446	+	0.319915i	$0.896346\pi$
$744$	−5.28450e9	+	4.21451e10i	−0.0172469	+	0.137548i
$745$		0			0
$746$			7.67721e11i			2.47884i
$747$	3.43606e10	−	1.34863e11i	0.110351	−	0.433121i
$748$	−2.01923e11			−0.645028
$749$			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	$0.489312\pi$
$752$		−	3.99484e11i		−	1.24919i
$753$	−4.17594e10	+	3.33041e11i	−0.129889	+	1.03590i
$754$	−4.39314e11			−1.35922
$755$		0			0
$756$	−1.06199e11	−	4.17059e10i	−0.325111	−	0.127676i
$757$	9.33494e10			0.284268			0.142134	−	0.989847i	$-0.454604\pi$
$757$	9.33494e10			0.284268			0.142134	+	0.989847i	$0.454604\pi$
$758$		−	4.78005e11i		−	1.44796i
$759$	−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	$-0.0342118\pi$
$762$	2.58603e9	−	2.06242e10i	0.00767031	−	0.0611725i
$763$	4.85256e10			0.143177
$764$			3.38468e11i			0.993447i
$765$		0			0
$766$	6.29370e11			1.82806
$767$		−	6.04370e11i		−	1.74631i
$768$	1.57800e11	+	1.97863e10i	0.453589	+	0.0568747i
$769$	−1.60418e11			−0.458720			−0.229360	−	0.973342i	$-0.573663\pi$
$769$	−1.60418e11			−0.458720			−0.229360	+	0.973342i	$0.573663\pi$
$770$		0			0
$771$	−1.13515e10	+	9.05313e10i	−0.0321246	+	0.256201i
$772$	−8.25245e11			−2.32335
$773$			3.72166e11i			1.04236i	0.853446	+	0.521181i	$0.174508\pi$
$773$			3.72166e11i			1.04236i	−0.853446	+	0.521181i	$0.825492\pi$
$774$	−9.35669e10	+	3.67243e11i	−0.260710	+	1.02327i
$775$		0			0
$776$			3.73961e10i			0.103129i
$777$	−1.28615e11	−	1.61268e10i	−0.352865	−	0.0442451i
$778$	6.39941e11			1.74671
$779$			2.32842e11i			0.632283i
$780$		0			0
$781$	−4.01055e11			−1.07795
$782$			4.23451e11i			1.13234i
$783$	−7.34077e10	+	1.86923e11i	−0.195296	+	0.497297i
$784$	2.58062e11			0.683062
$785$		0			0
$786$	5.51176e11	+	6.91110e10i	1.44411	+	0.181074i
$787$	5.18916e11			1.35269			0.676345	−	0.736585i	$-0.263563\pi$
$787$	5.18916e11			1.35269			0.676345	+	0.736585i	$0.263563\pi$
$788$			7.17773e11i			1.86158i
$789$	6.97229e10	−	5.56056e11i	0.179915	−	1.43486i
$790$		0			0
$791$		−	3.15904e10i		−	0.0806956i
$792$	1.29486e11	+	3.29907e10i	0.329096	+	0.0838477i
$793$	−5.62648e10			−0.142280
$794$		−	5.19149e11i		−	1.30620i
$795$		0			0
$796$	2.90539e11			0.723690
$797$			1.05184e11i			0.260686i	0.991469	+	0.130343i	$0.0416078\pi$
$797$			1.05184e11i			0.260686i	−0.991469	+	0.130343i	$0.958392\pi$
$798$	1.79715e10	−	1.43327e11i	0.0443172	−	0.353440i
$799$	3.35634e11			0.823530
$800$		0			0
$801$	−7.90333e10	+	3.10200e11i	−0.191991	+	0.753549i
$802$	9.19105e11			2.22161
$803$			3.63983e11i			0.875424i
$804$	−3.87524e11	−	4.85909e10i	−0.927415	−	0.116287i
$805$		0			0
$806$		−	4.75402e11i		−	1.12647i
$807$	−1.04871e10	+	8.36375e10i	−0.0247265	+	0.197200i
$808$	−8.10446e10			−0.190142
$809$		−	1.09572e10i		−	0.0255804i	−0.999918	−	0.0127902i	$-0.995929\pi$
$809$		−	1.09572e10i		−	0.0255804i	0.999918	−	0.0127902i	$-0.00407135\pi$
$810$		0			0
$811$	1.31782e11			0.304630			0.152315	−	0.988332i	$-0.451327\pi$
$811$	1.31782e11			0.304630			0.152315	+	0.988332i	$0.451327\pi$
$812$		−	8.11263e10i		−	0.186611i
$813$	−3.45881e11	−	4.33694e10i	−0.791707	−	0.0992706i
$814$	8.72747e11			1.98788
$815$		0			0
$816$	−2.01882e10	+	1.61005e11i	−0.0455341	+	0.363145i
$817$	−2.62753e11			−0.589738
$818$		−	2.43229e11i		−	0.543254i
$819$	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	$0.987197\pi$
$822$	1.41444e11	+	1.77354e10i	0.309811	+	0.0388466i
$823$	4.11792e11			0.897591			0.448795	−	0.893635i	$-0.351853\pi$
$823$	4.11792e11			0.897591			0.448795	+	0.893635i	$0.351853\pi$
$824$		−	8.90408e10i		−	0.193144i
$825$		0			0
$826$	2.03800e11			0.437808
$827$			1.78687e11i			0.382007i	0.981589	+	0.191004i	$0.0611742\pi$
$827$			1.78687e11i			0.382007i	−0.981589	+	0.191004i	$0.938826\pi$
$828$	2.17815e11	−	8.54907e11i	0.463411	−	1.81885i
$829$	−3.65541e11			−0.773960			−0.386980	−	0.922088i	$-0.626482\pi$
$829$	−3.65541e11			−0.773960			−0.386980	+	0.922088i	$0.626482\pi$
$830$		0			0
$831$	8.14639e11	+	1.02146e11i	1.70829	+	0.214199i
$832$	1.12121e12			2.33988
$833$			2.16816e11i			0.450310i
$834$	9.61243e9	−	7.66614e10i	0.0198687	−	0.158457i
$835$		0			0
$836$			5.32609e11i			1.09039i
$837$	−2.02278e11	−	7.94378e10i	−0.412142	−	0.161855i
$838$	7.22074e11			1.46422
$839$			5.20766e11i			1.05098i	0.850799	+	0.525491i	$0.176118\pi$
$839$			5.20766e11i			1.05098i	−0.850799	+	0.525491i	$0.823882\pi$
$840$		0			0
$841$	3.57454e11			0.714555
$842$			9.37429e11i			1.86505i
$843$	8.89440e10	−	7.09349e11i	0.176119	−	1.40459i
$844$	−6.65348e11			−1.31123
$845$		0			0
$846$	−1.23736e12	−	3.15257e11i	−2.41554	−	0.615437i
$847$	−2.62365e10			−0.0509768
$848$			6.65672e11i			1.28729i
$849$	−1.27026e11	−	1.59276e10i	−0.244491	−	0.0306563i
$850$		0			0
$851$		−	1.00229e12i		−	1.91106i
$852$	7.88657e10	−	6.28973e11i	0.149668	−	1.19364i
$853$	−5.21152e11			−0.984392			−0.492196	−	0.870484i	$-0.663806\pi$
$853$	−5.21152e11			−0.984392			−0.492196	+	0.870484i	$0.663806\pi$
$854$		−	1.89731e10i		−	0.0356702i
$855$		0			0
$856$	2.77261e11			0.516409
$857$		−	8.67435e11i		−	1.60810i	−0.594560	−	0.804051i	$-0.702674\pi$
$857$		−	8.67435e11i		−	1.60810i	0.594560	−	0.804051i	$-0.297326\pi$
$858$	−1.48395e12	−	1.86070e11i	−2.73823	−	0.343342i
$859$	−6.24921e11			−1.14776			−0.573882	−	0.818938i	$-0.694563\pi$
$859$	−6.24921e11			−1.14776			−0.573882	+	0.818938i	$0.694563\pi$
$860$		0			0
$861$	1.50216e10	−	1.19801e11i	0.0273340	−	0.217995i
$862$	−4.77990e11			−0.865745
$863$		−	8.65555e11i		−	1.56046i	−0.625495	−	0.780228i	$-0.715103\pi$
$863$		−	8.65555e11i		−	1.56046i	0.625495	−	0.780228i	$-0.284897\pi$
$864$	2.89430e11	−	7.36996e11i	0.519384	−	1.32254i
$865$		0			0
$866$		−	1.13265e12i		−	2.01384i
$867$	4.25374e11	+	5.33369e10i	0.752827	+	0.0943955i
$868$	8.77906e10			0.154657
$869$			7.14583e11i			1.25306i
$870$		0			0
$871$	7.60363e11			1.32114
$872$		−	8.98262e10i		−	0.155359i
$873$	−1.85408e11	−	4.72386e10i	−0.319206	−	0.0813280i
$874$	1.11693e12			1.91417
$875$		0			0
$876$	−5.70833e11	−	7.15756e10i	−0.969376	−	0.121548i
$877$	−3.45290e10			−0.0583694			−0.0291847	−	0.999574i	$-0.509291\pi$
$877$	−3.45290e10			−0.0583694			−0.0291847	+	0.999574i	$0.509291\pi$
$878$		−	6.68096e11i		−	1.12424i
$879$	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	$0.984806\pi$
$882$	2.03653e11	−	7.99321e11i	0.336524	−	1.32083i
$883$	−7.36663e11			−1.21179			−0.605893	−	0.795546i	$-0.707184\pi$
$883$	−7.36663e11			−1.21179			−0.605893	+	0.795546i	$0.707184\pi$
$884$			6.21348e11i			1.01748i
$885$		0			0
$886$	−7.68143e10			−0.124654
$887$			1.56687e11i			0.253126i	0.991959	+	0.126563i	$0.0403947\pi$
$887$			1.56687e11i			0.253126i	−0.991959	+	0.126563i	$0.959605\pi$
$888$	−2.98525e10	+	2.38081e11i	−0.0480097	+	0.382889i
$889$	−7.47283e9			−0.0119640
$890$		0			0
$891$	−3.27133e11	+	6.00312e11i	−0.519055	+	0.952503i
$892$	−1.14904e12			−1.81500
$893$		−	8.85300e11i		−	1.39214i
$894$	−3.45387e11	−	4.33074e10i	−0.540700	−	0.0677973i
$895$		0			0
$896$			1.13858e11i			0.176657i
$897$	−2.13688e11	+	1.70421e12i	−0.330073	+	2.63241i
$898$	1.00163e12			1.54029
$899$		−	1.54523e11i		−	0.236567i
$900$		0			0
$901$	−5.59277e11			−0.848648
$902$			8.12933e11i			1.22809i
$903$	1.35190e11	+	1.69512e10i	0.203326	+	0.0254947i
$904$	−5.84773e10			−0.0875616
$905$		0			0
$906$	1.03807e10	−	8.27883e10i	0.0154068	−	0.122873i
$907$	−5.78430e11			−0.854716			−0.427358	−	0.904083i	$-0.640556\pi$
$907$	−5.78430e11			−0.854716			−0.427358	+	0.904083i	$0.640556\pi$
$908$			1.23040e12i			1.81010i
$909$	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	$0.981107\pi$
$912$	4.24682e11	+	5.32501e10i	0.613882	+	0.0769735i
$913$	3.36882e11			0.484836
$914$		−	9.85637e11i		−	1.41232i
$915$		0			0
$916$	−8.80533e11			−1.25073
$917$		−	1.99710e11i		−	0.282437i
$918$	4.82766e11	+	1.89590e11i	0.679776	+	0.266959i
$919$	−8.52245e11			−1.19482			−0.597410	−	0.801936i	$-0.703803\pi$
$919$	−8.52245e11			−1.19482			−0.597410	+	0.801936i	$0.703803\pi$
$920$		0			0
$921$	−6.47354e11	−	8.11705e10i	−0.899711	−	0.112813i
$922$	−1.77036e12			−2.44984
$923$			1.23411e12i			1.70038i
$924$	3.43607e10	−	2.74035e11i	0.0471384	−	0.375940i
$925$		0			0
$926$			1.08760e12i			1.47920i
$927$	4.41460e11	+	1.12476e11i	0.597823	+	0.152314i
$928$	5.63000e11			0.759131
$929$			4.58591e11i			0.615691i	0.951436	+	0.307845i	$0.0996079\pi$
$929$			4.58591e11i			0.615691i	−0.951436	+	0.307845i	$0.900392\pi$
$930$		0			0
$931$	5.71893e11			0.761231
$932$		−	1.18058e11i		−	0.156470i
$933$	2.29942e10	−	1.83384e11i	0.0303453	−	0.242011i
$934$	−6.58834e10			−0.0865742
$935$		0			0
$936$	1.01518e11	−	3.98450e11i	0.132263	−	0.519123i
$937$	1.32495e11			0.171886			0.0859432	−	0.996300i	$-0.472610\pi$
$937$	1.32495e11			0.171886			0.0859432	+	0.996300i	$0.472610\pi$
$938$			2.56402e11i			0.331215i
$939$	−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	$0.833636\pi$
$942$	2.39406e10	−	1.90932e11i	0.0304040	−	0.242479i
$943$	9.33594e11			1.18062
$944$			6.03867e11i			0.760419i
$945$		0			0
$946$	−9.17362e11			−1.14545
$947$			7.18981e11i			0.893959i	0.894544	+	0.446980i	$0.147500\pi$
$947$			7.18981e11i			0.893959i	−0.894544	+	0.446980i	$0.852500\pi$
$948$	−1.12068e12	−	1.40520e11i	−1.38754	−	0.173982i
$949$	1.12003e12			1.38091
$950$		0			0
$951$	−2.82516e10	+	2.25313e11i	−0.0345398	+	0.275463i
$952$	−3.64455e10			−0.0443707
$953$		−	3.21954e11i		−	0.390321i	−0.980771	−	0.195160i	$-0.937477\pi$
$953$		−	3.21954e11i		−	0.390321i	0.980771	−	0.195160i	$-0.0625228\pi$
$954$	2.06185e12	+	5.25322e11i	2.48922	+	0.634209i
$955$		0			0
$956$			9.56191e11i			1.14476i
$957$	−4.82337e11	−	6.04793e10i	−0.575046	−	0.0721040i
$958$	−9.08862e11			−1.07904
$959$		−	5.12499e10i		−	0.0605924i
$960$		0			0
$961$	−6.85675e11			−0.803942
$962$		−	2.68558e12i		−	3.13573i
$963$	−3.50235e11	+	1.37465e12i	−0.407244	+	1.59840i
$964$	5.69059e11			0.658945
$965$		0			0
$966$	−5.74677e11	−	7.20577e10i	−0.659957	−	0.0827507i
$967$	−4.20589e11			−0.481008			−0.240504	−	0.970648i	$-0.577313\pi$
$967$	−4.20589e11			−0.481008			−0.240504	+	0.970648i	$0.577313\pi$
$968$			4.85666e10i			0.0553142i
$969$	−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	$-0.167664\pi$
$972$	−8.77137e11	−	6.31090e11i	−0.982658	−	0.707011i
$973$	−2.77770e10			−0.0309909
$974$		−	6.63937e11i		−	0.737719i
$975$		0			0
$976$	5.62179e10			0.0619548
$977$		−	8.04509e11i		−	0.882983i	−0.897265	−	0.441492i	$-0.854449\pi$
$977$		−	8.04509e11i		−	0.882983i	0.897265	−	0.441492i	$-0.145551\pi$
$978$	−9.96075e10	+	7.94394e11i	−0.108877	+	0.868321i
$979$	−7.74869e11			−0.843525
$980$		0			0
$981$	4.45354e11	+	1.13468e11i	0.480872	+	0.122518i
$982$	8.62300e11			0.927283
$983$		−	7.12126e11i		−	0.762681i	−0.924435	−	0.381340i	$-0.875463\pi$
$983$		−	7.12126e11i		−	0.762681i	0.924435	−	0.381340i	$-0.124537\pi$
$984$	−2.21764e11	−	2.78066e10i	−0.236543	−	0.0296597i
$985$		0			0
$986$			3.68791e11i			0.390187i
$987$	−5.71142e10	+	4.55499e11i	−0.0601832	+	0.479975i
$988$	1.63892e12			1.72001
$989$			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	$0.285700\pi$
$992$			6.09249e11i			0.629141i
$993$	−3.10083e11	−	3.88808e10i	−0.318920	−	0.0399887i
$994$	−4.16155e11			−0.426294
$995$		0			0
$996$	−6.62465e10	+	5.28331e11i	−0.0673171	+	0.536870i
$997$	−2.28898e11			−0.231665			−0.115833	−	0.993269i	$-0.536954\pi$
$997$	−2.28898e11			−0.231665			−0.115833	+	0.993269i	$0.536954\pi$
$998$		−	3.12341e11i		−	0.314852i
$999$	−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.c.g.26.9		10
3.2	odd	2	inner	75.9.c.g.26.2		10
5.2	odd	4		75.9.d.c.74.3		20
5.3	odd	4		75.9.d.c.74.18		20
5.4	even	2		15.9.c.a.11.2	✓	10
15.2	even	4		75.9.d.c.74.17		20
15.8	even	4		75.9.d.c.74.4		20
15.14	odd	2		15.9.c.a.11.9	yes	10
20.19	odd	2		240.9.l.b.161.10		10
60.59	even	2		240.9.l.b.161.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.c.a.11.2	✓	10	5.4	even	2
15.9.c.a.11.9	yes	10	15.14	odd	2
75.9.c.g.26.2		10	3.2	odd	2	inner
75.9.c.g.26.9		10	1.1	even	1	trivial
75.9.d.c.74.3		20	5.2	odd	4
75.9.d.c.74.4		20	15.8	even	4
75.9.d.c.74.17		20	15.2	even	4
75.9.d.c.74.18		20	5.3	odd	4
240.9.l.b.161.9		10	60.59	even	2
240.9.l.b.161.10		10	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+23.7888i q^{2} +(80.3707 + 10.0775i) q^{3} -309.906 q^{4} +(-239.732 + 1911.92i) q^{6} +692.753 q^{7} -1282.36i q^{8} +(6357.89 + 1619.88i) q^{9} +O(q^{10})\)	\(q+23.7888i q^{2} +(80.3707 + 10.0775i) q^{3} -309.906 q^{4} +(-239.732 + 1911.92i) q^{6} +692.753 q^{7} -1282.36i q^{8} +(6357.89 + 1619.88i) q^{9} +15881.8i q^{11} +(-24907.4 - 3123.09i) q^{12} +48870.9 q^{13} +16479.8i q^{14} -48830.2 q^{16} -41025.6i q^{17} +(-38534.9 + 151246. i) q^{18} -108213. q^{19} +(55677.0 + 6981.24i) q^{21} -377809. q^{22} +433886. i q^{23} +(12923.0 - 103064. i) q^{24} +1.16258e6i q^{26} +(494663. + 194262. i) q^{27} -214688. q^{28} +377879. i q^{29} -408921. q^{31} -1.48989e6i q^{32} +(-160049. + 1.27643e6i) q^{33} +975949. q^{34} +(-1.97035e6 - 502009. i) q^{36} -2.31002e6 q^{37} -2.57425e6i q^{38} +(3.92778e6 + 492497. i) q^{39} -2.15170e6i q^{41} +(-166075. + 1.32449e6i) q^{42} +2.42811e6 q^{43} -4.92187e6i q^{44} -1.03216e7 q^{46} +8.18110e6i q^{47} +(-3.92451e6 - 492087. i) q^{48} -5.28489e6 q^{49} +(413437. - 3.29725e6i) q^{51} -1.51454e7 q^{52} -1.36324e7i q^{53} +(-4.62126e6 + 1.17674e7i) q^{54} -888360. i q^{56} +(-8.69714e6 - 1.09052e6i) q^{57} -8.98929e6 q^{58} -1.23667e7i q^{59} -1.15129e6 q^{61} -9.72773e6i q^{62} +(4.40445e6 + 1.12217e6i) q^{63} +2.29423e7 q^{64} +(-3.03647e7 - 3.80738e6i) q^{66} +1.55586e7 q^{67} +1.27141e7i q^{68} +(-4.37250e6 + 3.48717e7i) q^{69} +2.52525e7i q^{71} +(2.07727e6 - 8.15311e6i) q^{72} +2.29182e7 q^{73} -5.49526e7i q^{74} +3.35358e7 q^{76} +1.10022e7i q^{77} +(-1.17159e7 + 9.34372e7i) q^{78} +4.49938e7 q^{79} +(3.77987e7 + 2.05980e7i) q^{81} +5.11864e7 q^{82} -2.12119e7i q^{83} +(-1.72547e7 - 2.16353e6i) q^{84} +5.77618e7i q^{86} +(-3.80809e6 + 3.03704e7i) q^{87} +2.03662e7 q^{88} +4.87898e7i q^{89} +3.38555e7 q^{91} -1.34464e8i q^{92} +(-3.28652e7 - 4.12091e6i) q^{93} -1.94618e8 q^{94} +(1.50145e7 - 1.19744e8i) q^{96} -2.91619e7 q^{97} -1.25721e8i q^{98} +(-2.57265e7 + 1.00975e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 112 q^{3} - 786 q^{4} - 5282 q^{6} - 7156 q^{7} + 3922 q^{9}+O(q^{10}) \) 10 * q + 112 * q^3 - 786 * q^4 - 5282 * q^6 - 7156 * q^7 + 3922 * q^9	\( 10 q + 112 q^{3} - 786 q^{4} - 5282 q^{6} - 7156 q^{7} + 3922 q^{9} + 3812 q^{12} + 55464 q^{13} + 280386 q^{16} + 419800 q^{18} - 231516 q^{19} + 289572 q^{21} - 1129940 q^{22} + 1136334 q^{24} + 335512 q^{27} + 3340724 q^{28} + 881620 q^{31} - 1266460 q^{33} - 1111276 q^{34} - 668662 q^{36} - 4672616 q^{37} + 1826792 q^{39} + 5392860 q^{42} - 7731336 q^{43} - 25424604 q^{46} - 22413388 q^{48} + 9354214 q^{49} - 27732692 q^{51} - 21064016 q^{52} - 7979798 q^{54} + 2856304 q^{57} + 4351100 q^{58} + 22417020 q^{61} - 8830596 q^{63} - 22935002 q^{64} - 27419800 q^{66} + 46646024 q^{67} + 33562632 q^{69} - 54175560 q^{72} + 129964884 q^{73} + 198922436 q^{76} - 60388360 q^{78} + 162310924 q^{79} - 93575390 q^{81} - 202877560 q^{82} - 197346768 q^{84} + 168322540 q^{87} + 484775700 q^{88} + 444288464 q^{91} - 463412376 q^{93} - 92050036 q^{94} - 360807406 q^{96} + 258825724 q^{97} - 33965200 q^{99}+O(q^{100}) \) 10 * q + 112 * q^3 - 786 * q^4 - 5282 * q^6 - 7156 * q^7 + 3922 * q^9 + 3812 * q^12 + 55464 * q^13 + 280386 * q^16 + 419800 * q^18 - 231516 * q^19 + 289572 * q^21 - 1129940 * q^22 + 1136334 * q^24 + 335512 * q^27 + 3340724 * q^28 + 881620 * q^31 - 1266460 * q^33 - 1111276 * q^34 - 668662 * q^36 - 4672616 * q^37 + 1826792 * q^39 + 5392860 * q^42 - 7731336 * q^43 - 25424604 * q^46 - 22413388 * q^48 + 9354214 * q^49 - 27732692 * q^51 - 21064016 * q^52 - 7979798 * q^54 + 2856304 * q^57 + 4351100 * q^58 + 22417020 * q^61 - 8830596 * q^63 - 22935002 * q^64 - 27419800 * q^66 + 46646024 * q^67 + 33562632 * q^69 - 54175560 * q^72 + 129964884 * q^73 + 198922436 * q^76 - 60388360 * q^78 + 162310924 * q^79 - 93575390 * q^81 - 202877560 * q^82 - 197346768 * q^84 + 168322540 * q^87 + 484775700 * q^88 + 444288464 * q^91 - 463412376 * q^93 - 92050036 * q^94 - 360807406 * q^96 + 258825724 * q^97 - 33965200 * q^99

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