LMFDB - Embedded newform 10.24.b.a.9.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,24,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	10.b (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:	$33.5204037345$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 190890377806 x^{10} + \cdots + 13\!\cdots\!01 $ x^12 + 190890377806x^10 + 11891747400203387380815x^8 + 259162984456772175500044188641220x^6 + 1380478075454165034166946607317389971466815x^4 + 2513795111640504034920397565484668273464192364644206*x^2 + 1334759269199828356976682814310061172000907474614558584815601
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{88}\cdot 3^{8}\cdot 5^{27}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.10
Root			$30251.3i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.24.b.a.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2048.00i q^{2} +60502.7i q^{3} -4.19430e6 q^{4} +(-1.08542e8 + 1.18165e7i) q^{5} -1.23909e8 q^{6} -6.68031e9i q^{7} -8.58993e9i q^{8} +9.04826e10 q^{9} +(-2.42001e10 - 2.22293e11i) q^{10} -3.84250e11 q^{11} -2.53767e11i q^{12} +5.33401e12i q^{13} +1.36813e13 q^{14} +(-7.14928e11 - 6.56706e12i) q^{15} +1.75922e13 q^{16} -6.29715e13i q^{17} +1.85308e14i q^{18} +3.05310e14 q^{19} +(4.55257e14 - 4.95619e13i) q^{20} +4.04177e14 q^{21} -7.86944e14i q^{22} +2.45373e15i q^{23} +5.19714e14 q^{24} +(1.16417e16 - 2.56516e15i) q^{25} -1.09241e16 q^{26} +1.11704e16i q^{27} +2.80192e16i q^{28} -1.18489e16 q^{29} +(1.34493e16 - 1.46417e15i) q^{30} -2.04263e17 q^{31} +3.60288e16i q^{32} -2.32482e16i q^{33} +1.28966e17 q^{34} +(7.89377e16 + 7.25092e17i) q^{35} -3.79512e17 q^{36} +1.51532e18i q^{37} +6.25274e17i q^{38} -3.22722e17 q^{39} +(1.01503e17 + 9.32366e17i) q^{40} +5.01414e18 q^{41} +8.27754e17i q^{42} +8.67774e18i q^{43} +1.61166e18 q^{44} +(-9.82114e18 + 1.06918e18i) q^{45} -5.02524e18 q^{46} +2.54387e19i q^{47} +1.06437e18i q^{48} -1.72578e19 q^{49} +(5.25345e18 + 2.38421e19i) q^{50} +3.80994e18 q^{51} -2.23725e19i q^{52} -8.84115e19i q^{53} -2.28769e19 q^{54} +(4.17071e19 - 4.54048e18i) q^{55} -5.73834e19 q^{56} +1.84720e19i q^{57} -2.42666e19i q^{58} +3.41052e20 q^{59} +(2.99863e18 + 2.75443e19i) q^{60} -2.73047e19 q^{61} -4.18331e20i q^{62} -6.04452e20i q^{63} -7.37870e19 q^{64} +(-6.30292e19 - 5.78963e20i) q^{65} +4.76122e19 q^{66} -1.26642e20i q^{67} +2.64122e20i q^{68} -1.48457e20 q^{69} +(-1.48499e21 + 1.61664e20i) q^{70} +1.89393e21 q^{71} -7.77240e20i q^{72} +2.61372e21i q^{73} -3.10338e21 q^{74} +(1.55199e20 + 7.04352e20i) q^{75} -1.28056e21 q^{76} +2.56691e21i q^{77} -6.60935e20i q^{78} +6.16012e21 q^{79} +(-1.90949e21 + 2.07877e20i) q^{80} +7.84248e21 q^{81} +1.02690e22i q^{82} +1.13570e22i q^{83} -1.69524e21 q^{84} +(7.44101e20 + 6.83503e21i) q^{85} -1.77720e22 q^{86} -7.16891e20i q^{87} +3.30068e21i q^{88} +6.13209e21 q^{89} +(-2.18969e21 - 2.01137e22i) q^{90} +3.56329e22 q^{91} -1.02917e22i q^{92} -1.23585e22i q^{93} -5.20985e22 q^{94} +(-3.31388e22 + 3.60768e21i) q^{95} -2.17984e21 q^{96} -6.63696e22i q^{97} -3.53439e22i q^{98} -3.47679e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 50331648 q^{4} - 153465660 q^{5} + 1496219648 q^{6} - 397404876524 q^{9} + 515607920640 q^{10} + 1618708468464 q^{11} - 18612479361024 q^{14} + 56360859857360 q^{15} + 211106232532992 q^{16} - 11\!\cdots\!80 q^{19}+ \cdots - 49\!\cdots\!28 q^{99}+O(q^{100}) $ 12 * q - 50331648 * q^4 - 153465660 * q^5 + 1496219648 * q^6 - 397404876524 * q^9 + 515607920640 * q^10 + 1618708468464 * q^11 - 18612479361024 * q^14 + 56360859857360 * q^15 + 211106232532992 * q^16 - 1100262406554480 * q^19 + 643681631600640 * q^20 + 2454694989205424 * q^21 - 6275600054484992 * q^24 + 18348046596119100 * q^25 + 47412135014105088 * q^26 - 191332118394850680 * q^29 + 69062266581647360 * q^30 + 314531620762193664 * q^31 - 27202419348209664 * q^34 - 132973567506049680 * q^35 + 1666836863224119296 * q^36 + 16801243916907657312 * q^39 - 2162616363972034560 * q^40 - 334736513821173096 * q^41 - 6789355404112429056 * q^44 + 44571509177637873820 * q^45 + 37044797625677611008 * q^46 - 61353034749652271196 * q^49 - 11488666440926822400 * q^50 + 21794418357272939264 * q^51 - 64483243481607372800 * q^54 + 33608617917590982480 * q^55 + 78066396633860407296 * q^56 - 792491082249081738960 * q^59 - 236394579943164477440 * q^60 + 396873789531683516904 * q^61 - 885443715538058477568 * q^64 - 1103464906421517591840 * q^65 - 1919302523514221625344 * q^66 - 5004088166299913161808 * q^69 + 1549427758140305080320 * q^70 + 11216046927623429218464 * q^71 - 7698848775986662539264 * q^74 + 2698057827395500242400 * q^75 + 4614835012861081681920 * q^76 - 13308383509524480375360 * q^79 - 2699796442149090754560 * q^80 + 80031139288718178809852 * q^81 - 10295737012004266704896 * q^84 - 53931318208690956660480 * q^85 + 70834920401828427890688 * q^86 + 26549329728846280565880 * q^89 - 149835156254250257121280 * q^90 + 213312013693120420064544 * q^91 - 110687147549581976961024 * q^94 - 333982981030300532283600 * q^95 + 26321774410926619885568 * q^96 - 497641983005968176470128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$-1$

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 $

$2$			2048.00i			0.707107i
$2$			2048.00i			0.707107i
$3$			60502.7i			0.197188i	0.995128	+	0.0985939i	$0.0314345\pi$
$3$			60502.7i			0.197188i	−0.995128	+	0.0985939i	$0.968566\pi$
$4$	−4.19430e6			−0.500000
$5$	−1.08542e8	+	1.18165e7i	−0.994126	+	0.108226i
$5$	−1.08542e8	+	1.18165e7i	−0.994126	+	0.108226i
$6$	−1.23909e8			−0.139433
$7$		−	6.68031e9i		−	1.27694i	−0.769648	−	0.638468i	$-0.779568\pi$
$7$		−	6.68031e9i		−	1.27694i	0.769648	−	0.638468i	$-0.220432\pi$
$8$		−	8.58993e9i		−	0.353553i
$9$	9.04826e10			0.961117
$10$	−2.42001e10	−	2.22293e11i	−0.0765275	−	0.702953i
$11$	−3.84250e11			−0.406067			−0.203034	−	0.979172i	$-0.565080\pi$
$11$	−3.84250e11			−0.406067			−0.203034	+	0.979172i	$0.565080\pi$
$12$		−	2.53767e11i		−	0.0985939i
$13$			5.33401e12i			0.825478i	0.910849	+	0.412739i	$0.135428\pi$
$13$			5.33401e12i			0.825478i	−0.910849	+	0.412739i	$0.864572\pi$
$14$	1.36813e13			0.902930
$15$	−7.14928e11	−	6.56706e12i	−0.0213409	−	0.196030i
$16$	1.75922e13			0.250000
$17$		−	6.29715e13i		−	0.445637i	−0.974860	−	0.222819i	$-0.928474\pi$
$17$		−	6.29715e13i		−	0.445637i	0.974860	−	0.222819i	$-0.0715257\pi$
$18$			1.85308e14i			0.679612i
$19$	3.05310e14			0.601276			0.300638	−	0.953738i	$-0.402800\pi$
$19$	3.05310e14			0.601276			0.300638	+	0.953738i	$0.402800\pi$
$20$	4.55257e14	−	4.95619e13i	0.497063	−	0.0541131i
$21$	4.04177e14			0.251796
$22$		−	7.86944e14i		−	0.287133i
$23$			2.45373e15i			0.536978i	0.963283	+	0.268489i	$0.0865243\pi$
$23$			2.45373e15i			0.536978i	−0.963283	+	0.268489i	$0.913476\pi$
$24$	5.19714e14			0.0697164
$25$	1.16417e16	−	2.56516e15i	0.976574	−	0.215181i
$26$	−1.09241e16			−0.583701
$27$			1.11704e16i			0.386708i
$28$			2.80192e16i			0.638468i
$29$	−1.18489e16			−0.180344			−0.0901720	−	0.995926i	$-0.528742\pi$
$29$	−1.18489e16			−0.180344			−0.0901720	+	0.995926i	$0.528742\pi$
$30$	1.34493e16	−	1.46417e15i	0.138614	−	0.0150903i
$31$	−2.04263e17			−1.44388			−0.721939	−	0.691957i	$-0.756749\pi$
$31$	−2.04263e17			−1.44388			−0.721939	+	0.691957i	$0.756749\pi$
$32$			3.60288e16i			0.176777i
$33$		−	2.32482e16i		−	0.0800715i
$34$	1.28966e17			0.315113
$35$	7.89377e16	+	7.25092e17i	0.138198	+	1.26944i
$36$	−3.79512e17			−0.480558
$37$			1.51532e18i			1.40018i	0.714053	+	0.700092i	$0.246857\pi$
$37$			1.51532e18i			1.40018i	−0.714053	+	0.700092i	$0.753143\pi$
$38$			6.25274e17i			0.425166i
$39$	−3.22722e17			−0.162774
$40$	1.01503e17	+	9.32366e17i	0.0382638	+	0.351477i
$41$	5.01414e18			1.42293			0.711463	−	0.702723i	$-0.248033\pi$
$41$	5.01414e18			1.42293			0.711463	+	0.702723i	$0.248033\pi$
$42$			8.27754e17i			0.178047i
$43$			8.67774e18i			1.42403i	0.702164	+	0.712015i	$0.252217\pi$
$43$			8.67774e18i			1.42403i	−0.702164	+	0.712015i	$0.747783\pi$
$44$	1.61166e18			0.203034
$45$	−9.82114e18	+	1.06918e18i	−0.955472	+	0.104018i
$46$	−5.02524e18			−0.379701
$47$			2.54387e19i			1.50096i	0.660892	+	0.750481i	$0.270178\pi$
$47$			2.54387e19i			1.50096i	−0.660892	+	0.750481i	$0.729822\pi$
$48$			1.06437e18i			0.0492970i
$49$	−1.72578e19			−0.630565
$50$	5.25345e18	+	2.38421e19i	0.152156	+	0.690542i
$51$	3.80994e18			0.0878742
$52$		−	2.23725e19i		−	0.412739i
$53$		−	8.84115e19i		−	1.31020i	−0.755544	−	0.655098i	$-0.772627\pi$
$53$		−	8.84115e19i		−	1.31020i	0.755544	−	0.655098i	$-0.227373\pi$
$54$	−2.28769e19			−0.273444
$55$	4.17071e19	−	4.54048e18i	0.403682	−	0.0439471i
$56$	−5.73834e19			−0.451465
$57$			1.84720e19i			0.118564i
$58$		−	2.42666e19i		−	0.127522i
$59$	3.41052e20			1.47239			0.736195	−	0.676770i	$-0.236621\pi$
$59$	3.41052e20			1.47239			0.736195	+	0.676770i	$0.236621\pi$
$60$	2.99863e18	+	2.75443e19i	0.0106705	+	0.0980148i
$61$	−2.73047e19			−0.0803424			−0.0401712	−	0.999193i	$-0.512790\pi$
$61$	−2.73047e19			−0.0803424			−0.0401712	+	0.999193i	$0.512790\pi$
$62$		−	4.18331e20i		−	1.02098i
$63$		−	6.04452e20i		−	1.22728i
$64$	−7.37870e19			−0.125000
$65$	−6.30292e19	−	5.78963e20i	−0.0893384	−	0.820629i
$66$	4.76122e19			0.0566191
$67$		−	1.26642e20i		−	0.126682i	−0.997992	−	0.0633412i	$-0.979824\pi$
$67$		−	1.26642e20i		−	0.126682i	0.997992	−	0.0633412i	$-0.0201756\pi$
$68$			2.64122e20i			0.222819i
$69$	−1.48457e20			−0.105886
$70$	−1.48499e21	+	1.61664e20i	−0.897627	+	0.0977207i
$71$	1.89393e21			0.972507			0.486253	−	0.873818i	$-0.338363\pi$
$71$	1.89393e21			0.972507			0.486253	+	0.873818i	$0.338363\pi$
$72$		−	7.77240e20i		−	0.339806i
$73$			2.61372e21i			0.975095i	0.873096	+	0.487548i	$0.162108\pi$
$73$			2.61372e21i			0.975095i	−0.873096	+	0.487548i	$0.837892\pi$
$74$	−3.10338e21			−0.990079
$75$	1.55199e20	+	7.04352e20i	0.0424311	+	0.192569i
$76$	−1.28056e21			−0.300638
$77$			2.56691e21i			0.518522i
$78$		−	6.60935e20i		−	0.115099i
$79$	6.16012e21			0.926568			0.463284	−	0.886210i	$-0.346671\pi$
$79$	6.16012e21			0.926568			0.463284	+	0.886210i	$0.346671\pi$
$80$	−1.90949e21	+	2.07877e20i	−0.248532	+	0.0270566i
$81$	7.84248e21			0.884863
$82$			1.02690e22i			1.00616i
$83$			1.13570e22i			0.967974i	0.875075	+	0.483987i	$0.160812\pi$
$83$			1.13570e22i			0.967974i	−0.875075	+	0.483987i	$0.839188\pi$
$84$	−1.69524e21			−0.125898
$85$	7.44101e20	+	6.83503e21i	0.0482296	+	0.443020i
$86$	−1.77720e22			−1.00694
$87$		−	7.16891e20i		−	0.0355616i
$88$			3.30068e21i			0.143566i
$89$	6.13209e21			0.234220			0.117110	−	0.993119i	$-0.462637\pi$
$89$	6.13209e21			0.234220			0.117110	+	0.993119i	$0.462637\pi$
$90$	−2.18969e21	−	2.01137e22i	−0.0735519	−	0.675620i
$91$	3.56329e22			1.05408
$92$		−	1.02917e22i		−	0.268489i
$93$		−	1.23585e22i		−	0.284715i
$94$	−5.20985e22			−1.06134
$95$	−3.31388e22	+	3.60768e21i	−0.597744	+	0.0650739i
$96$	−2.17984e21			−0.0348582
$97$		−	6.63696e22i		−	0.942094i	−0.882108	−	0.471047i	$-0.843876\pi$
$97$		−	6.63696e22i		−	0.942094i	0.882108	−	0.471047i	$-0.156124\pi$
$98$		−	3.53439e22i		−	0.445877i
$99$	−3.47679e22			−0.390278
$100$	−4.88287e22	+	1.07591e22i	−0.488287	+	0.107591i
$101$	2.10699e23			1.87917			0.939587	−	0.342311i	$-0.111210\pi$
$101$	2.10699e23			1.87917			0.939587	+	0.342311i	$0.111210\pi$
$102$			7.80276e21i			0.0621365i
$103$		−	2.18079e23i		−	1.55233i	−0.630528	−	0.776167i	$-0.717162\pi$
$103$		−	2.18079e23i		−	1.55233i	0.630528	−	0.776167i	$-0.282838\pi$
$104$	4.58188e22			0.291851
$105$	−4.38700e22	+	4.77594e21i	−0.250317	+	0.0272510i
$106$	1.81067e23			0.926449
$107$			1.05974e23i			0.486726i	0.969935	+	0.243363i	$0.0782507\pi$
$107$			1.05974e23i			0.486726i	−0.969935	+	0.243363i	$0.921749\pi$
$108$		−	4.68519e22i		−	0.193354i
$109$	−1.28513e23			−0.477026			−0.238513	−	0.971139i	$-0.576660\pi$
$109$	−1.28513e23			−0.477026			−0.238513	+	0.971139i	$0.576660\pi$
$110$	9.29890e21	+	8.54162e22i	0.0310753	+	0.285446i
$111$	−9.16810e22			−0.276099
$112$		−	1.17521e23i		−	0.319234i
$113$			3.81423e23i			0.935416i	0.883883	+	0.467708i	$0.154920\pi$
$113$			3.81423e23i			0.935416i	−0.883883	+	0.467708i	$0.845080\pi$
$114$	−3.78308e22			−0.0838377
$115$	−2.89944e22	−	2.66332e23i	−0.0581151	−	0.533824i
$116$	4.96979e22			0.0901720
$117$			4.82635e23i			0.793381i
$118$			6.98475e23i			1.04114i
$119$	−4.20669e23			−0.569050
$120$	−5.64106e22	+	6.14118e21i	−0.0693069	+	0.00754515i
$121$	−7.47782e23			−0.835109
$122$		−	5.59201e22i		−	0.0568107i
$123$			3.03369e23i			0.280584i
$124$	8.56741e23			0.721939
$125$	−1.23330e24	+	4.15990e23i	−0.947550	+	0.319608i
$126$	1.23792e24			0.867821
$127$			1.29360e24i			0.828052i	0.910265	+	0.414026i	$0.135878\pi$
$127$			1.29360e24i			0.828052i	−0.910265	+	0.414026i	$0.864122\pi$
$128$		−	1.51116e23i		−	0.0883883i
$129$	−5.25027e23			−0.280802
$130$	1.18572e24	−	1.29084e23i	0.580273	−	0.0631718i
$131$	1.87614e24			0.840706			0.420353	−	0.907361i	$-0.361906\pi$
$131$	1.87614e24			0.840706			0.420353	+	0.907361i	$0.361906\pi$
$132$			9.75098e22i			0.0400358i
$133$		−	2.03956e24i		−	0.767791i
$134$	2.59362e23			0.0895779
$135$	−1.31994e23	−	1.21245e24i	−0.0418520	−	0.384437i
$136$	−5.40921e23			−0.157557
$137$		−	4.36628e24i		−	1.16903i	−0.811384	−	0.584514i	$-0.801285\pi$
$137$		−	4.36628e24i		−	1.16903i	0.811384	−	0.584514i	$-0.198715\pi$
$138$		−	3.04040e23i		−	0.0748724i
$139$	−9.66182e23			−0.218972			−0.109486	−	0.993988i	$-0.534920\pi$
$139$	−9.66182e23			−0.218972			−0.109486	+	0.993988i	$0.534920\pi$
$140$	−3.31089e23	−	3.04126e24i	−0.0690990	−	0.634718i
$141$	−1.53911e24			−0.295971
$142$			3.87877e24i			0.687666i
$143$		−	2.04959e24i		−	0.335200i
$144$	1.59179e24			0.240279
$145$	1.28610e24	−	1.40012e23i	0.179285	−	0.0195179i
$146$	−5.35291e24			−0.689496
$147$		−	1.04414e24i		−	0.124340i
$148$		−	6.35572e24i		−	0.700092i
$149$	1.07102e25			1.09183			0.545916	−	0.837840i	$-0.316182\pi$
$149$	1.07102e25			1.09183			0.545916	+	0.837840i	$0.316182\pi$
$150$	−1.44251e24	+	3.17848e23i	−0.136167	+	0.0300033i
$151$	−1.90748e25			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$151$	−1.90748e25			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$152$		−	2.62259e24i		−	0.212583i
$153$		−	5.69782e24i		−	0.428309i
$154$	−5.25703e24			−0.366650
$155$	2.21711e25	−	2.41367e24i	1.43540	−	0.156265i
$156$	1.35359e24			0.0813871
$157$			3.35050e25i			1.87182i	0.352242	+	0.935909i	$0.385419\pi$
$157$			3.35050e25i			1.87182i	−0.352242	+	0.935909i	$0.614581\pi$
$158$			1.26159e25i			0.655183i
$159$	5.34913e24			0.258355
$160$	−4.25733e23	−	3.91063e24i	−0.0191319	−	0.175738i
$161$	1.63917e25			0.685687
$162$			1.60614e25i			0.625692i
$163$			4.14955e24i			0.150606i	0.997161	+	0.0753032i	$0.0239925\pi$
$163$			4.14955e24i			0.150606i	−0.997161	+	0.0753032i	$0.976008\pi$
$164$	−2.10308e25			−0.711463
$165$	2.74711e23	+	2.52339e24i	0.00866584	+	0.0796012i
$166$	−2.32590e25			−0.684461
$167$			5.39583e25i			1.48190i	0.671561	+	0.740950i	$0.265624\pi$
$167$			5.39583e25i			1.48190i	−0.671561	+	0.740950i	$0.734376\pi$
$168$		−	3.47185e24i		−	0.0890234i
$169$	1.33022e25			0.318586
$170$	−1.39981e25	+	1.52392e24i	−0.313262	+	0.0341035i
$171$	2.76252e25			0.577897
$172$		−	3.63971e25i		−	0.712015i
$173$		−	1.31784e25i		−	0.241175i	−0.992703	−	0.120587i	$-0.961522\pi$
$173$		−	1.31784e25i		−	0.241175i	0.992703	−	0.120587i	$-0.0384778\pi$
$174$	1.46819e24			0.0251459
$175$	−1.71361e25	−	7.77700e25i	−0.274773	−	1.24702i
$176$	−6.75980e24			−0.101517
$177$			2.06346e25i			0.290337i
$178$			1.25585e25i			0.165618i
$179$	−4.40683e25			−0.544900			−0.272450	−	0.962170i	$-0.587834\pi$
$179$	−4.40683e25			−0.544900			−0.272450	+	0.962170i	$0.587834\pi$
$180$	4.11928e25	−	4.48449e24i	0.477736	−	0.0520090i
$181$	−5.87133e25			−0.638900			−0.319450	−	0.947603i	$-0.603498\pi$
$181$	−5.87133e25			−0.638900			−0.319450	+	0.947603i	$0.603498\pi$
$182$			7.29761e25i			0.745349i
$183$		−	1.65201e24i		−	0.0158426i
$184$	2.10774e25			0.189850
$185$	−1.79057e25	−	1.64476e26i	−0.151537	−	1.39196i
$186$	2.53101e25			0.201324
$187$			2.41968e25i			0.180959i
$188$		−	1.06698e26i		−	0.750481i
$189$	7.46214e25			0.493802
$190$	−7.38853e24	−	6.78683e25i	−0.0460142	−	0.422669i
$191$	8.64925e25			0.507101			0.253551	−	0.967322i	$-0.418402\pi$
$191$	8.64925e25			0.507101			0.253551	+	0.967322i	$0.418402\pi$
$192$		−	4.46431e24i		−	0.0246485i
$193$		−	3.29744e26i		−	1.71502i	−0.514470	−	0.857508i	$-0.672011\pi$
$193$		−	3.29744e26i		−	1.71502i	0.514470	−	0.857508i	$-0.327989\pi$
$194$	1.35925e26			0.666161
$195$	3.50288e25	−	3.81343e24i	0.161818	−	0.0176164i
$196$	7.23844e25			0.315283
$197$			4.20477e26i			1.72735i	0.504046	+	0.863677i	$0.331844\pi$
$197$			4.20477e26i			1.72735i	−0.504046	+	0.863677i	$0.668156\pi$
$198$		−	7.12047e25i		−	0.275968i
$199$	−2.93623e26			−1.07394			−0.536970	−	0.843602i	$-0.680431\pi$
$199$	−2.93623e26			−1.07394			−0.536970	+	0.843602i	$0.680431\pi$
$200$	−2.20345e25	−	1.00001e26i	−0.0760780	−	0.345271i
$201$	7.66215e24			0.0249802
$202$			4.31512e26i			1.32878i
$203$			7.91544e25i			0.230288i
$204$	−1.59801e25			−0.0439371
$205$	−5.44244e26	+	5.92495e25i	−1.41457	+	0.153998i
$206$	4.46625e26			1.09767
$207$			2.22020e26i			0.516099i
$208$			9.38369e25i			0.206369i
$209$	−1.17315e26			−0.244159
$210$	−9.78112e24	−	8.98458e25i	−0.0192693	−	0.177001i
$211$	−5.56452e25			−0.103796			−0.0518979	−	0.998652i	$-0.516527\pi$
$211$	−5.56452e25			−0.103796			−0.0518979	+	0.998652i	$0.516527\pi$
$212$			3.70825e26i			0.655098i
$213$			1.14588e26i			0.191767i
$214$	−2.17034e26			−0.344167
$215$	−1.02540e26	−	9.41897e26i	−0.154118	−	1.41567i
$216$	9.59526e25			0.136722
$217$			1.36454e27i			1.84374i
$218$		−	2.63194e26i		−	0.337308i
$219$	−1.58137e26			−0.192277
$220$	−1.74932e26	+	1.90441e25i	−0.201841	+	0.0219736i
$221$	3.35891e26			0.367864
$222$		−	1.87763e26i		−	0.195232i
$223$			2.02216e26i			0.199669i	0.995004	+	0.0998343i	$0.0318313\pi$
$223$			2.02216e26i			0.199669i	−0.995004	+	0.0998343i	$0.968169\pi$
$224$	2.40684e26			0.225733
$225$	1.05337e27	−	2.32102e26i	0.938602	−	0.206814i
$226$	−7.81154e26			−0.661439
$227$			9.87174e26i			0.794504i	0.917709	+	0.397252i	$0.130036\pi$
$227$			9.87174e26i			0.794504i	−0.917709	+	0.397252i	$0.869964\pi$
$228$		−	7.74774e25i		−	0.0592822i
$229$	2.06231e27			1.50054			0.750268	−	0.661134i	$-0.229924\pi$
$229$	2.06231e27			1.50054			0.750268	+	0.661134i	$0.229924\pi$
$230$	5.45448e26	−	5.93806e25i	0.377471	−	0.0410936i
$231$	−1.55305e26			−0.102246
$232$			1.01781e26i			0.0637612i
$233$		−	3.21738e27i		−	1.91827i	−0.282949	−	0.959135i	$-0.591313\pi$
$233$		−	3.21738e27i		−	1.91827i	0.282949	−	0.959135i	$-0.408687\pi$
$234$	−9.88437e26			−0.561005
$235$	−3.00596e26	−	2.76116e27i	−0.162443	−	1.49215i
$236$	−1.43048e27			−0.736195
$237$			3.72703e26i			0.182708i
$238$		−	8.61530e26i		−	0.402379i
$239$	−1.38476e27			−0.616308			−0.308154	−	0.951336i	$-0.599711\pi$
$239$	−1.38476e27			−0.616308			−0.308154	+	0.951336i	$0.599711\pi$
$240$	−1.25771e25	−	1.15529e26i	−0.00533523	−	0.0490074i
$241$	3.93371e26			0.159077			0.0795384	−	0.996832i	$-0.474655\pi$
$241$	3.93371e26			0.159077			0.0795384	+	0.996832i	$0.474655\pi$
$242$		−	1.53146e27i		−	0.590512i
$243$			1.52610e27i			0.561193i
$244$	1.14524e26			0.0401712
$245$	1.87319e27	−	2.03926e26i	0.626862	−	0.0682437i
$246$	−6.21300e26			−0.198403
$247$			1.62853e27i			0.496340i
$248$			1.75461e27i			0.510488i
$249$	−6.87126e26			−0.190873
$250$	−8.51948e26	−	2.52579e27i	−0.225997	−	0.670019i
$251$	−4.83844e26			−0.122591			−0.0612954	−	0.998120i	$-0.519523\pi$
$251$	−4.83844e26			−0.122591			−0.0612954	+	0.998120i	$0.519523\pi$
$252$			2.53525e27i			0.613642i
$253$		−	9.42846e26i		−	0.218049i
$254$	−2.64929e27			−0.585521
$255$	−4.13538e26	+	4.50201e25i	−0.0873581	+	0.00951030i
$256$	3.09485e26			0.0625000
$257$			2.11895e27i			0.409158i	0.978850	+	0.204579i	$0.0655825\pi$
$257$			2.11895e27i			0.409158i	−0.978850	+	0.204579i	$0.934418\pi$
$258$		−	1.07525e27i		−	0.198557i
$259$	1.01228e28			1.78794
$260$	2.64364e26	+	2.42835e27i	0.0446692	+	0.410315i
$261$	−1.07212e27			−0.173332
$262$			3.84233e27i			0.594469i
$263$			1.55026e27i			0.229569i	0.993390	+	0.114785i	$0.0366178\pi$
$263$			1.55026e27i			0.229569i	−0.993390	+	0.114785i	$0.963382\pi$
$264$	−1.99700e26			−0.0283096
$265$	1.04471e27	+	9.59633e27i	0.141798	+	1.30250i
$266$	4.17702e27			0.542910
$267$			3.71008e26i			0.0461853i
$268$			5.31173e26i			0.0633412i
$269$	−1.77612e27			−0.202919			−0.101459	−	0.994840i	$-0.532351\pi$
$269$	−1.77612e27			−0.202919			−0.101459	+	0.994840i	$0.532351\pi$
$270$	2.48310e27	−	2.70324e26i	0.271838	−	0.0295938i
$271$	−1.82544e28			−1.91523			−0.957614	−	0.288055i	$-0.906992\pi$
$271$	−1.82544e28			−1.91523			−0.957614	+	0.288055i	$0.906992\pi$
$272$		−	1.10781e27i		−	0.111409i
$273$			2.15588e27i			0.207852i
$274$	8.94213e27			0.826627
$275$	−4.47331e27	+	9.85662e26i	−0.396555	+	0.0873780i
$276$	6.22675e26			0.0529428
$277$		−	7.40227e27i		−	0.603737i	−0.953350	−	0.301868i	$-0.902390\pi$
$277$		−	7.40227e27i		−	0.603737i	0.953350	−	0.301868i	$-0.0976103\pi$
$278$		−	1.97874e27i		−	0.154837i
$279$	−1.84823e28			−1.38773
$280$	6.22849e27	−	6.78069e26i	0.448813	−	0.0488604i
$281$	9.45987e27			0.654278			0.327139	−	0.944976i	$-0.393915\pi$
$281$	9.45987e27			0.654278			0.327139	+	0.944976i	$0.393915\pi$
$282$		−	3.15210e27i		−	0.209283i
$283$			5.97197e27i			0.380692i	0.981717	+	0.190346i	$0.0609609\pi$
$283$			5.97197e27i			0.380692i	−0.981717	+	0.190346i	$0.939039\pi$
$284$	−7.94371e27			−0.486253
$285$	−2.18274e26	−	2.00499e27i	−0.0128318	−	0.117868i
$286$	4.19757e27			0.237022
$287$		−	3.34960e28i		−	1.81699i
$288$			3.25998e27i			0.169903i
$289$	1.60022e28			0.801408
$290$	2.86745e26	+	2.63394e27i	0.0138013	+	0.126773i
$291$	4.01554e27			0.185769
$292$		−	1.09628e28i		−	0.487548i
$293$		−	1.87349e28i		−	0.801074i	−0.916281	−	0.400537i	$-0.868824\pi$
$293$		−	1.87349e28i		−	0.801074i	0.916281	−	0.400537i	$-0.131176\pi$
$294$	2.13840e27			0.0879216
$295$	−3.70184e28	+	4.03003e27i	−1.46374	+	0.159351i
$296$	1.30165e28			0.495039
$297$		−	4.29221e27i		−	0.157030i
$298$			2.19345e28i			0.772042i
$299$	−1.30882e28			−0.443264
$300$	−6.50952e26	−	2.95427e27i	−0.0212156	−	0.0962843i
$301$	5.79700e28			1.81840
$302$		−	3.90653e28i		−	1.17954i
$303$			1.27479e28i			0.370550i
$304$	5.37106e27			0.150319
$305$	2.96370e27	−	3.22646e26i	0.0798705	−	0.00869516i
$306$	1.16691e28			0.302860
$307$		−	2.17274e28i		−	0.543145i	−0.962418	−	0.271572i	$-0.912456\pi$
$307$		−	2.17274e28i		−	0.543145i	0.962418	−	0.271572i	$-0.0875436\pi$
$308$		−	1.07664e28i		−	0.259261i
$309$	1.31943e28			0.306101
$310$	4.94319e27	+	4.54063e28i	0.110496	+	1.01498i
$311$	−3.83810e28			−0.826745			−0.413373	−	0.910562i	$-0.635649\pi$
$311$	−3.83810e28			−0.826745			−0.413373	+	0.910562i	$0.635649\pi$
$312$			2.77216e27i			0.0575494i
$313$			6.70552e28i			1.34175i	0.741569	+	0.670877i	$0.234082\pi$
$313$			6.70552e28i			1.34175i	−0.741569	+	0.670877i	$0.765918\pi$
$314$	−6.86182e28			−1.32358
$315$	7.14248e27	+	6.56082e28i	0.132824	+	1.22008i
$316$	−2.58374e28			−0.463284
$317$		−	3.91952e28i		−	0.677722i	−0.940836	−	0.338861i	$-0.889958\pi$
$317$		−	3.91952e28i		−	0.677722i	0.940836	−	0.338861i	$-0.110042\pi$
$318$			1.09550e28i			0.182684i
$319$	4.55294e27			0.0732318
$320$	8.00896e27	−	8.71901e26i	0.124266	−	0.0135283i
$321$	−6.41169e27			−0.0959765
$322$			3.35702e28i			0.484854i
$323$		−	1.92258e28i		−	0.267951i
$324$	−3.28938e28			−0.442431
$325$	1.36826e28	+	6.20968e28i	0.177627	+	0.806140i
$326$	−8.49828e27			−0.106495
$327$		−	7.77537e27i		−	0.0940637i
$328$		−	4.30712e28i		−	0.503081i
$329$	1.69938e29			1.91663
$330$	−5.16791e27	+	5.62608e26i	−0.0562866	+	0.00612767i
$331$	−6.80670e28			−0.716003			−0.358002	−	0.933721i	$-0.616542\pi$
$331$	−6.80670e28			−0.716003			−0.358002	+	0.933721i	$0.616542\pi$
$332$		−	4.76345e28i		−	0.483987i
$333$			1.37110e29i			1.34574i
$334$	−1.10507e29			−1.04786
$335$	1.49646e27	+	1.37459e28i	0.0137104	+	0.125938i
$336$	7.11035e27			0.0629491
$337$		−	6.85617e28i		−	0.586594i	−0.956021	−	0.293297i	$-0.905247\pi$
$337$		−	6.85617e28i		−	0.586594i	0.956021	−	0.293297i	$-0.0947525\pi$
$338$			2.72429e28i			0.225274i
$339$	−2.30771e28			−0.184453
$340$	−3.12098e27	−	2.86682e28i	−0.0241148	−	0.221510i
$341$	7.84881e28			0.586311
$342$			5.65764e28i			0.408635i
$343$		−	6.75443e28i		−	0.471744i
$344$	7.45412e28			0.503471
$345$	1.61138e28	−	1.75424e27i	0.105264	−	0.0114596i
$346$	2.69893e28			0.170536
$347$		−	2.40923e29i		−	1.47262i	−0.676647	−	0.736308i	$-0.736567\pi$
$347$		−	2.40923e29i		−	1.47262i	0.676647	−	0.736308i	$-0.263433\pi$
$348$			3.00686e27i			0.0177808i
$349$	1.40701e29			0.805017			0.402509	−	0.915416i	$-0.368138\pi$
$349$	1.40701e29			0.805017			0.402509	+	0.915416i	$0.368138\pi$
$350$	1.59273e29	−	3.50946e28i	0.881778	−	0.194294i
$351$	−5.95828e28			−0.319219
$352$		−	1.38441e28i		−	0.0717832i
$353$		−	2.37954e29i		−	1.19422i	−0.802160	−	0.597110i	$-0.796316\pi$
$353$		−	2.37954e29i		−	1.19422i	0.802160	−	0.597110i	$-0.203684\pi$
$354$	−4.22596e28			−0.205300
$355$	−2.05570e29	+	2.23795e28i	−0.966794	+	0.105251i
$356$	−2.57198e28			−0.117110
$357$		−	2.54516e28i		−	0.112210i
$358$		−	9.02519e28i		−	0.385302i
$359$	−5.34603e28			−0.221027			−0.110514	−	0.993875i	$-0.535250\pi$
$359$	−5.34603e28			−0.221027			−0.110514	+	0.993875i	$0.535250\pi$
$360$	9.18423e27	+	8.43629e28i	0.0367759	+	0.337810i
$361$	−1.64616e29			−0.638467
$362$		−	1.20245e29i		−	0.451771i
$363$		−	4.52428e28i		−	0.164673i
$364$	−1.49455e29			−0.527041
$365$	−3.08850e28	−	2.83698e29i	−0.105531	−	0.969368i
$366$	3.38332e27			0.0112024
$367$			5.64288e29i			1.81068i	0.424691	+	0.905338i	$0.360383\pi$
$367$			5.64288e29i			1.81068i	−0.424691	+	0.905338i	$0.639617\pi$
$368$			4.31665e28i			0.134245i
$369$	4.53693e29			1.36760
$370$	3.36846e29	−	3.66710e28i	0.984264	−	0.107153i
$371$	−5.90616e29			−1.67304
$372$			5.18351e28i			0.142358i
$373$			6.14546e29i			1.63645i	0.574897	+	0.818226i	$0.305042\pi$
$373$			6.14546e29i			1.63645i	−0.574897	+	0.818226i	$0.694958\pi$
$374$	−4.95550e28			−0.127957
$375$	−2.51685e28	−	7.46177e28i	−0.0630228	−	0.186845i
$376$	2.18517e29			0.530670
$377$		−	6.32023e28i		−	0.148870i
$378$			1.52825e29i			0.349171i
$379$	−4.75016e29			−1.05283			−0.526414	−	0.850228i	$-0.676464\pi$
$379$	−4.75016e29			−1.05283			−0.526414	+	0.850228i	$0.676464\pi$
$380$	1.38994e29	−	1.51317e28i	0.298872	−	0.0325369i
$381$	−7.82663e28			−0.163282
$382$			1.77137e29i			0.358575i
$383$		−	4.76430e29i		−	0.935865i	−0.883764	−	0.467933i	$-0.844999\pi$
$383$		−	4.76430e29i		−	0.935865i	0.883764	−	0.467933i	$-0.155001\pi$
$384$	9.14291e27			0.0174291
$385$	−3.03318e28	−	2.78617e29i	−0.0561177	−	0.515476i
$386$	6.75317e29			1.21270
$387$			7.85185e29i			1.36866i
$388$			2.78374e29i			0.471047i
$389$	7.97621e29			1.31032			0.655158	−	0.755491i	$-0.272602\pi$
$389$	7.97621e29			1.31032			0.655158	+	0.755491i	$0.272602\pi$
$390$	7.80991e27	+	7.17390e28i	0.0124567	+	0.114423i
$391$	1.54515e29			0.239297
$392$			1.48243e29i			0.222939i
$393$			1.13511e29i			0.165777i
$394$	−8.61138e29			−1.22142
$395$	−6.68629e29	+	7.27908e28i	−0.921126	+	0.100279i
$396$	1.45827e29			0.195139
$397$			1.41292e30i			1.83665i	0.395831	+	0.918323i	$0.370457\pi$
$397$			1.41292e30i			1.83665i	−0.395831	+	0.918323i	$0.629543\pi$
$398$		−	6.01340e29i		−	0.759390i
$399$	1.23399e29			0.151399
$400$	2.04802e29	−	4.51268e28i	0.244144	−	0.0537953i
$401$	7.58271e29			0.878342			0.439171	−	0.898403i	$-0.355272\pi$
$401$	7.58271e29			0.878342			0.439171	+	0.898403i	$0.355272\pi$
$402$			1.56921e28i			0.0176637i
$403$		−	1.08954e30i		−	1.19189i
$404$	−8.83736e29			−0.939587
$405$	−8.51236e29	+	9.26704e28i	−0.879665	+	0.0957654i
$406$	−1.62108e29			−0.162838
$407$		−	5.82262e29i		−	0.568568i
$408$		−	3.27272e28i		−	0.0310682i
$409$	−1.16756e29			−0.107761			−0.0538805	−	0.998547i	$-0.517159\pi$
$409$	−1.16756e29			−0.107761			−0.0538805	+	0.998547i	$0.517159\pi$
$410$	−1.21343e29	−	1.11461e30i	−0.108893	−	1.00025i
$411$	2.64171e29			0.230518
$412$			9.14688e29i			0.776167i
$413$		−	2.27833e30i		−	1.88015i
$414$	−4.54697e29			−0.364937
$415$	−1.34199e29	−	1.23270e30i	−0.104760	−	0.962288i
$416$	−1.92178e29			−0.145925
$417$		−	5.84566e28i		−	0.0431786i
$418$		−	2.40262e29i		−	0.172646i
$419$	2.26689e30			1.58478			0.792389	−	0.610016i	$-0.208837\pi$
$419$	2.26689e30			1.58478			0.792389	+	0.610016i	$0.208837\pi$
$420$	1.84004e29	−	2.00317e28i	0.125159	−	0.0136255i
$421$	5.10785e29			0.338060			0.169030	−	0.985611i	$-0.445937\pi$
$421$	5.10785e29			0.338060			0.169030	+	0.985611i	$0.445937\pi$
$422$		−	1.13961e29i		−	0.0733947i
$423$			2.30176e30i			1.44260i
$424$	−7.59449e29			−0.463224
$425$	−1.61532e29	−	7.33093e29i	−0.0958927	−	0.435198i
$426$	−2.34676e29			−0.135599
$427$			1.82404e29i			0.102592i
$428$		−	4.44486e29i		−	0.243363i
$429$	1.24006e29			0.0660973
$430$	1.92900e30	−	2.10002e29i	1.00103	−	0.108978i
$431$	1.43432e28			0.00724701			0.00362350	−	0.999993i	$-0.498847\pi$
$431$	1.43432e28			0.00724701			0.00362350	+	0.999993i	$0.498847\pi$
$432$			1.96511e29i			0.0966771i
$433$			6.68888e29i			0.320437i	0.987082	+	0.160219i	$0.0512199\pi$
$433$			6.68888e29i			0.320437i	−0.987082	+	0.160219i	$0.948780\pi$
$434$	−2.79458e30			−1.30372
$435$	8.47112e27	+	7.78126e28i	0.00384870	+	0.0353528i
$436$	5.39022e29			0.238513
$437$			7.49147e29i			0.322872i
$438$		−	3.23865e29i		−	0.135960i
$439$	4.08803e30			1.67175			0.835877	−	0.548917i	$-0.184960\pi$
$439$	4.08803e30			1.67175			0.835877	+	0.548917i	$0.184960\pi$
$440$	−3.90024e28	−	3.58262e29i	−0.0155377	−	0.142723i
$441$	−1.56153e30			−0.606047
$442$			6.87904e29i			0.260119i
$443$			8.93064e29i			0.329033i	0.986374	+	0.164517i	$0.0526064\pi$
$443$			8.93064e29i			0.329033i	−0.986374	+	0.164517i	$0.947394\pi$
$444$	3.84538e29			0.138050
$445$	−6.65587e29	+	7.24596e28i	−0.232844	+	0.0253487i
$446$	−4.14139e29			−0.141187
$447$			6.47997e29i			0.215296i
$448$			4.92920e29i			0.159617i
$449$	−1.33604e28			−0.00421683			−0.00210842	−	0.999998i	$-0.500671\pi$
$449$	−1.33604e28			−0.00421683			−0.00210842	+	0.999998i	$0.500671\pi$
$450$	4.75345e29	+	2.15730e30i	0.146240	+	0.663692i
$451$	−1.92668e30			−0.577804
$452$		−	1.59980e30i		−	0.467708i
$453$		−	1.15408e30i		−	0.328932i
$454$	−2.02173e30			−0.561800
$455$	−3.86765e30	+	4.21054e29i	−1.04789	+	0.114079i
$456$	1.58674e29			0.0419188
$457$			5.23101e30i			1.34756i	0.738930	+	0.673782i	$0.235331\pi$
$457$			5.23101e30i			1.34756i	−0.738930	+	0.673782i	$0.764669\pi$
$458$			4.22362e30i			1.06104i
$459$	7.03414e29			0.172332
$460$	1.21611e29	+	1.11708e30i	0.0290576	+	0.266912i
$461$	−3.71072e30			−0.864764			−0.432382	−	0.901691i	$-0.642327\pi$
$461$	−3.71072e30			−0.864764			−0.432382	+	0.901691i	$0.642327\pi$
$462$		−	3.18064e29i		−	0.0722990i
$463$			2.38552e30i			0.528935i	0.964395	+	0.264468i	$0.0851962\pi$
$463$			2.38552e30i			0.528935i	−0.964395	+	0.264468i	$0.914804\pi$
$464$	−2.08448e29			−0.0450860
$465$	1.46033e29	+	1.34141e30i	0.0308136	+	0.283043i
$466$	6.58920e30			1.35642
$467$		−	3.98348e30i		−	0.800053i	−0.916504	−	0.400026i	$-0.869001\pi$
$467$		−	3.98348e30i		−	0.800053i	0.916504	−	0.400026i	$-0.130999\pi$
$468$		−	2.02432e30i		−	0.396690i
$469$	−8.46005e29			−0.161765
$470$	5.65486e30	−	6.15620e29i	1.05511	−	0.114865i
$471$	−2.02714e30			−0.369100
$472$		−	2.92962e30i		−	0.520568i
$473$		−	3.33442e30i		−	0.578252i
$474$	−7.63297e29			−0.129194
$475$	3.55431e30	−	7.83168e29i	0.587191	−	0.129383i
$476$	1.76441e30			0.284525
$477$		−	7.99970e30i		−	1.25925i
$478$		−	2.83598e30i		−	0.435796i
$479$	3.29159e30			0.493796			0.246898	−	0.969041i	$-0.420589\pi$
$479$	3.29159e30			0.493796			0.246898	+	0.969041i	$0.420589\pi$
$480$	2.36603e29	−	2.57580e28i	0.0346535	−	0.00377257i
$481$	−8.08274e30			−1.15582
$482$			8.05624e29i			0.112484i
$483$			9.91740e29i			0.135209i
$484$	3.13643e30			0.417555
$485$	7.84254e29	+	7.20387e30i	0.101959	+	0.936560i
$486$	−3.12546e30			−0.396823
$487$		−	1.12121e31i		−	1.39029i	−0.718871	−	0.695144i	$-0.755341\pi$
$487$		−	1.12121e31i		−	1.39029i	0.718871	−	0.695144i	$-0.244659\pi$
$488$			2.34546e29i			0.0284053i
$489$	−2.51059e29			−0.0296978
$490$	4.17641e29	+	3.83629e30i	0.0482556	+	0.443258i
$491$	3.90173e30			0.440372			0.220186	−	0.975458i	$-0.429334\pi$
$491$	3.90173e30			0.440372			0.220186	+	0.975458i	$0.429334\pi$
$492$		−	1.27242e30i		−	0.140292i
$493$			7.46144e29i			0.0803680i
$494$	−3.33522e30			−0.350966
$495$	3.77377e30	−	4.10834e29i	0.387986	−	0.0422383i
$496$	−3.59343e30			−0.360969
$497$		−	1.26520e31i		−	1.24183i
$498$		−	1.40723e30i		−	0.134967i
$499$	8.79960e30			0.824720			0.412360	−	0.911021i	$-0.364705\pi$
$499$	8.79960e30			0.824720			0.412360	+	0.911021i	$0.364705\pi$
$500$	5.17282e30	−	1.74479e30i	0.473775	−	0.159804i
$501$	−3.26462e30			−0.292213
$502$		−	9.90913e29i		−	0.0866848i
$503$			7.44866e30i			0.636864i	0.947946	+	0.318432i	$0.103156\pi$
$503$			7.44866e30i			0.636864i	−0.947946	+	0.318432i	$0.896844\pi$
$504$	−5.19220e30			−0.433911
$505$	−2.28696e31	+	2.48972e30i	−1.86814	+	0.203376i
$506$	1.93095e30			0.154184
$507$			8.04820e29i			0.0628213i
$508$		−	5.42576e30i		−	0.414026i
$509$	−1.16630e31			−0.870074			−0.435037	−	0.900412i	$-0.643265\pi$
$509$	−1.16630e31			−0.870074			−0.435037	+	0.900412i	$0.643265\pi$
$510$	−9.22011e28	−	8.46925e29i	−0.00672480	−	0.0617715i
$511$	1.74605e31			1.24513
$512$			6.33825e29i			0.0441942i
$513$			3.41042e30i			0.232519i
$514$	−4.33962e30			−0.289318
$515$	2.57692e30	+	2.36706e31i	0.168003	+	1.54322i
$516$	2.20212e30			0.140401
$517$		−	9.77482e30i		−	0.609491i
$518$			2.07315e31i			1.26427i
$519$	7.97327e29			0.0475567
$520$	−4.97325e30	+	5.41417e29i	−0.290136	+	0.0315859i
$521$	8.10652e30			0.462595			0.231297	−	0.972883i	$-0.425703\pi$
$521$	8.10652e30			0.462595			0.231297	+	0.972883i	$0.425703\pi$
$522$		−	2.19570e30i		−	0.122564i
$523$			6.74977e30i			0.368569i	0.982873	+	0.184285i	$0.0589968\pi$
$523$			6.74977e30i			0.368569i	−0.982873	+	0.184285i	$0.941003\pi$
$524$	−7.86908e30			−0.420353
$525$	4.70529e30	−	1.03678e30i	0.245898	−	0.0541818i
$526$	−3.17493e30			−0.162330
$527$			1.28627e31i			0.643445i
$528$		−	4.08986e29i		−	0.0200179i
$529$	1.48597e31			0.711654
$530$	−1.96533e31	+	2.13957e30i	−0.921007	+	0.100266i
$531$	3.08593e31			1.41514
$532$			8.55455e30i			0.383896i
$533$			2.67455e31i			1.17459i
$534$	−7.59824e29			−0.0326579
$535$	−1.25223e30	−	1.15026e31i	−0.0526765	−	0.483867i
$536$	−1.08784e30			−0.0447890
$537$		−	2.66625e30i		−	0.107448i
$538$		−	3.63750e30i		−	0.143485i
$539$	6.63130e30			0.256052
$540$	5.53623e29	+	5.08538e30i	0.0209260	+	0.192219i
$541$	−2.62998e31			−0.973160			−0.486580	−	0.873636i	$-0.661756\pi$
$541$	−2.62998e31			−0.973160			−0.486580	+	0.873636i	$0.661756\pi$
$542$		−	3.73850e31i		−	1.35427i
$543$		−	3.55231e30i		−	0.125983i
$544$	2.26879e30			0.0787783
$545$	1.39490e31	−	1.51857e30i	0.474224	−	0.0516267i
$546$	−4.41525e30			−0.146974
$547$		−	1.27193e31i		−	0.414581i	−0.978279	−	0.207290i	$-0.933536\pi$
$547$		−	1.27193e31i		−	0.414581i	0.978279	−	0.207290i	$-0.0664645\pi$
$548$			1.83135e31i			0.584514i
$549$	−2.47060e30			−0.0772185
$550$	−2.01864e30	−	9.16134e30i	−0.0617856	−	0.280407i
$551$	−3.61759e30			−0.108437
$552$			1.27524e30i			0.0374362i
$553$		−	4.11515e31i		−	1.18317i
$554$	1.51598e31			0.426906
$555$	9.95121e30	−	1.08335e30i	0.274477	−	0.0298812i
$556$	4.05246e30			0.109486
$557$			6.50155e31i			1.72061i	0.509780	+	0.860305i	$0.329727\pi$
$557$			6.50155e31i			1.72061i	−0.509780	+	0.860305i	$0.670273\pi$
$558$		−	3.78516e31i		−	0.981277i
$559$	−4.62872e31			−1.17551
$560$	1.38869e30	+	1.27560e31i	0.0345495	+	0.317359i
$561$	−1.46397e30			−0.0356828
$562$			1.93738e31i			0.462644i
$563$		−	8.02470e31i		−	1.87751i	−0.344586	−	0.938755i	$-0.611981\pi$
$563$		−	8.02470e31i		−	1.87751i	0.344586	−	0.938755i	$-0.388019\pi$
$564$	6.45549e30			0.147986
$565$	−4.50707e30	−	4.14003e31i	−0.101237	−	0.929922i
$566$	−1.22306e31			−0.269190
$567$		−	5.23902e31i		−	1.12991i
$568$		−	1.62687e31i		−	0.343833i
$569$	−2.41323e31			−0.499813			−0.249907	−	0.968270i	$-0.580400\pi$
$569$	−2.41323e31			−0.499813			−0.249907	+	0.968270i	$0.580400\pi$
$570$	4.10621e30	−	4.47026e29i	0.0833452	−	0.00907344i
$571$	−4.16020e31			−0.827559			−0.413779	−	0.910377i	$-0.635792\pi$
$571$	−4.16020e31			−0.827559			−0.413779	+	0.910377i	$0.635792\pi$
$572$			8.59662e30i			0.167600i
$573$			5.23303e30i			0.0999942i
$574$	6.85999e31			1.28480
$575$	6.29421e30	+	2.85655e31i	0.115548	+	0.524399i
$576$	−6.67644e30			−0.120140
$577$			9.97989e30i			0.176037i	0.996119	+	0.0880185i	$0.0280535\pi$
$577$			9.97989e30i			0.176037i	−0.996119	+	0.0880185i	$0.971947\pi$
$578$			3.27724e31i			0.566681i
$579$	1.99504e31			0.338181
$580$	−5.39430e30	+	5.87254e29i	−0.0896423	+	0.00975897i
$581$	7.58679e31			1.23604
$582$			8.22382e30i			0.131359i
$583$			3.39721e31i			0.532028i
$584$	2.24517e31			0.344748
$585$	−5.70304e30	−	5.23861e31i	−0.0858646	−	0.788721i
$586$	3.83690e31			0.566445
$587$			1.20724e32i			1.74765i	0.486243	+	0.873824i	$0.338367\pi$
$587$			1.20724e32i			1.74765i	−0.486243	+	0.873824i	$0.661633\pi$
$588$			4.37945e30i			0.0621699i
$589$	−6.23635e31			−0.868169
$590$	−8.25351e30	−	7.58137e31i	−0.112678	−	1.03502i
$591$	−2.54400e31			−0.340613
$592$			2.66578e31i			0.350046i
$593$			7.24341e31i			0.932855i	0.884560	+	0.466427i	$0.154459\pi$
$593$			7.24341e31i			0.932855i	−0.884560	+	0.466427i	$0.845541\pi$
$594$	8.79044e30			0.111037
$595$	4.56601e31	−	4.97082e30i	0.565708	−	0.0615862i
$596$	−4.49219e31			−0.545916
$597$		−	1.77650e31i		−	0.211768i
$598$		−	2.68047e31i		−	0.313435i
$599$	−7.77648e31			−0.892020			−0.446010	−	0.895028i	$-0.647155\pi$
$599$	−7.77648e31			−0.892020			−0.446010	+	0.895028i	$0.647155\pi$
$600$	6.05034e30	−	1.33315e30i	0.0680833	−	0.0150017i
$601$	−3.19111e31			−0.352278			−0.176139	−	0.984365i	$-0.556361\pi$
$601$	−3.19111e31			−0.352278			−0.176139	+	0.984365i	$0.556361\pi$
$602$			1.18723e32i			1.28580i
$603$		−	1.14589e31i		−	0.121757i
$604$	8.00057e31			0.834058
$605$	8.11656e31	−	8.83614e30i	0.830204	−	0.0903808i
$606$	−2.61076e31			−0.262019
$607$			8.74076e31i			0.860754i	0.902649	+	0.430377i	$0.141619\pi$
$607$			8.74076e31i			0.860754i	−0.902649	+	0.430377i	$0.858381\pi$
$608$			1.09999e31i			0.106292i
$609$	−4.78905e30			−0.0454099
$610$	6.60778e29	+	6.06966e30i	0.00614841	+	0.0564770i
$611$	−1.35690e32			−1.23901
$612$			2.38984e31i			0.214155i
$613$		−	3.89732e31i		−	0.342744i	−0.985206	−	0.171372i	$-0.945180\pi$
$613$		−	3.89732e31i		−	0.342744i	0.985206	−	0.171372i	$-0.0548200\pi$
$614$	4.44976e31			0.384061
$615$	−3.58475e30	−	3.29282e31i	−0.0303665	−	0.278936i
$616$	2.20496e31			0.183325
$617$			1.39691e32i			1.13996i	0.821658	+	0.569981i	$0.193049\pi$
$617$			1.39691e32i			1.13996i	−0.821658	+	0.569981i	$0.806951\pi$
$618$			2.70220e31i			0.216446i
$619$	−1.17702e32			−0.925422			−0.462711	−	0.886509i	$-0.653123\pi$
$619$	−1.17702e32			−0.925422			−0.462711	+	0.886509i	$0.653123\pi$
$620$	−9.29921e31	+	1.01237e31i	−0.717698	+	0.0781327i
$621$	−2.74090e31			−0.207654
$622$		−	7.86043e31i		−	0.584597i
$623$		−	4.09642e31i		−	0.299083i
$624$	−5.67739e30			−0.0406936
$625$	1.28948e32	−	5.97255e31i	0.907394	−	0.420281i
$626$	−1.37329e32			−0.948763
$627$		−	7.09788e30i		−	0.0481451i
$628$		−	1.40530e32i		−	0.935909i
$629$	9.54220e31			0.623974
$630$	−1.34366e32	+	1.46278e31i	−0.862724	+	0.0939211i
$631$	2.19477e32			1.38373			0.691864	−	0.722028i	$-0.256790\pi$
$631$	2.19477e32			1.38373			0.691864	+	0.722028i	$0.256790\pi$
$632$		−	5.29150e31i		−	0.327591i
$633$		−	3.36669e30i		−	0.0204673i
$634$	8.02718e31			0.479222
$635$	−1.52858e31	−	1.40410e32i	−0.0896169	−	0.823188i
$636$	−2.24359e31			−0.129177
$637$		−	9.20533e31i		−	0.520518i
$638$			9.32443e30i			0.0517827i
$639$	1.71368e32			0.934693
$640$	1.78565e30	+	1.64024e31i	0.00956594	+	0.0878692i
$641$	3.18119e32			1.67387			0.836937	−	0.547299i	$-0.184344\pi$
$641$	3.18119e32			1.67387			0.836937	+	0.547299i	$0.184344\pi$
$642$		−	1.31311e31i		−	0.0678656i
$643$		−	3.31419e31i		−	0.168249i	−0.996455	−	0.0841243i	$-0.973191\pi$
$643$		−	3.31419e31i		−	0.168249i	0.996455	−	0.0841243i	$-0.0268093\pi$
$644$	−6.87517e31			−0.342843
$645$	5.69873e31	−	6.20396e30i	0.279152	−	0.0303901i
$646$	3.93744e31			0.189470
$647$		−	1.50921e32i		−	0.713427i	−0.934214	−	0.356714i	$-0.883897\pi$
$647$		−	1.50921e32i		−	0.713427i	0.934214	−	0.356714i	$-0.116103\pi$
$648$		−	6.73664e31i		−	0.312846i
$649$	−1.31049e32			−0.597889
$650$	−1.27174e32	+	2.80219e31i	−0.570027	+	0.125601i
$651$	−8.25583e31			−0.363563
$652$		−	1.74045e31i		−	0.0753032i
$653$		−	2.06051e32i		−	0.875937i	−0.898990	−	0.437969i	$-0.855698\pi$
$653$		−	2.06051e32i		−	0.875937i	0.898990	−	0.437969i	$-0.144302\pi$
$654$	1.59240e31			0.0665131
$655$	−2.03639e32	+	2.21693e31i	−0.835768	+	0.0909865i
$656$	8.82098e31			0.355732
$657$			2.36497e32i			0.937180i
$658$			3.48034e32i			1.35526i
$659$	−3.85077e32			−1.47355			−0.736776	−	0.676137i	$-0.763653\pi$
$659$	−3.85077e32			−1.47355			−0.736776	+	0.676137i	$0.763653\pi$
$660$	−1.15222e30	−	1.05839e31i	−0.00433292	−	0.0398006i
$661$	4.04090e32			1.49335			0.746674	−	0.665190i	$-0.231649\pi$
$661$	4.04090e32			1.49335			0.746674	+	0.665190i	$0.231649\pi$
$662$		−	1.39401e32i		−	0.506291i
$663$			2.03223e31i			0.0725382i
$664$	9.75555e31			0.342230
$665$	2.41004e31	+	2.21378e32i	0.0830952	+	0.763281i
$666$	−2.80802e32			−0.951582
$667$		−	2.90740e31i		−	0.0968408i
$668$		−	2.26317e32i		−	0.740950i
$669$	−1.22346e31			−0.0393722
$670$	−2.81516e31	+	3.06474e30i	−0.0890518	+	0.00969468i
$671$	1.04918e31			0.0326244
$672$			1.45620e31i			0.0445117i
$673$			7.40902e31i			0.222632i	0.993785	+	0.111316i	$0.0355066\pi$
$673$			7.40902e31i			0.222632i	−0.993785	+	0.111316i	$0.964493\pi$
$674$	1.40414e32			0.414785
$675$	2.86537e31	+	1.30042e32i	0.0832124	+	0.377649i
$676$	−5.57935e31			−0.159293
$677$		−	3.37541e32i		−	0.947452i	−0.880672	−	0.473726i	$-0.842909\pi$
$677$		−	3.37541e32i		−	0.947452i	0.880672	−	0.473726i	$-0.157091\pi$
$678$		−	4.72619e31i		−	0.130428i
$679$	−4.43369e32			−1.20299
$680$	5.87125e31	−	6.39177e30i	0.156631	−	0.0170518i
$681$	−5.97267e31			−0.156667
$682$			1.60744e32i			0.414585i
$683$			5.02656e32i			1.27477i	0.770545	+	0.637386i	$0.219984\pi$
$683$			5.02656e32i			1.27477i	−0.770545	+	0.637386i	$0.780016\pi$
$684$	−1.15869e32			−0.288948
$685$	5.15940e31	+	4.73923e32i	0.126519	+	1.16216i
$686$	1.38331e32			0.333574
$687$			1.24775e32i			0.295888i
$688$			1.52660e32i			0.356008i
$689$	4.71588e32			1.08154
$690$	3.59268e30	+	3.30011e31i	0.00810316	+	0.0744326i
$691$	−6.53513e32			−1.44963			−0.724814	−	0.688944i	$-0.758074\pi$
$691$	−6.53513e32			−1.44963			−0.724814	+	0.688944i	$0.758074\pi$
$692$			5.52741e31i			0.120587i
$693$			2.32261e32i			0.498360i
$694$	4.93411e32			1.04130
$695$	1.04871e32	−	1.14169e31i	0.217686	−	0.0236985i
$696$	−6.15805e30			−0.0125729
$697$		−	3.15748e32i		−	0.634109i
$698$			2.88156e32i			0.569233i
$699$	1.94660e32			0.378260
$700$	7.18738e31	+	3.26191e32i	0.137386	+	0.623511i
$701$	−5.68983e31			−0.106990			−0.0534949	−	0.998568i	$-0.517036\pi$
$701$	−5.68983e31			−0.106990			−0.0534949	+	0.998568i	$0.517036\pi$
$702$		−	1.22026e32i		−	0.225722i
$703$			4.62642e32i			0.841897i
$704$	2.83526e31			0.0507584
$705$	1.67058e32	−	1.81868e31i	0.294233	−	0.0320319i
$706$	4.87330e32			0.844441
$707$		−	1.40754e33i		−	2.39958i
$708$		−	8.65477e31i		−	0.145169i
$709$	−7.15763e32			−1.18124			−0.590619	−	0.806950i	$-0.701116\pi$
$709$	−7.15763e32			−1.18124			−0.590619	+	0.806950i	$0.701116\pi$
$710$	−4.58333e31	−	4.21008e32i	−0.0744235	−	0.683627i
$711$	5.57383e32			0.890540
$712$		−	5.26742e31i		−	0.0828091i
$713$		−	5.01206e32i		−	0.775331i
$714$	5.21249e31			0.0793443
$715$	2.42190e31	+	2.22466e32i	0.0362774	+	0.333231i
$716$	1.84836e32			0.272450
$717$		−	8.37815e31i		−	0.121528i
$718$		−	1.09487e32i		−	0.156290i
$719$	−6.10174e32			−0.857179			−0.428589	−	0.903499i	$-0.640989\pi$
$719$	−6.10174e32			−0.857179			−0.428589	+	0.903499i	$0.640989\pi$
$720$	−1.72775e32	+	1.88093e31i	−0.238868	+	0.0260045i
$721$	−1.45683e33			−1.98223
$722$		−	3.37133e32i		−	0.451464i
$723$			2.38000e31i			0.0313680i
$724$	2.46262e32			0.319450
$725$	−1.37941e32	+	3.03943e31i	−0.176119	+	0.0388066i
$726$	9.26573e31			0.116442
$727$		−	6.09058e32i		−	0.753378i	−0.926340	−	0.376689i	$-0.877063\pi$
$727$		−	6.09058e32i		−	0.753378i	0.926340	−	0.376689i	$-0.122937\pi$
$728$		−	3.06084e32i		−	0.372674i
$729$	6.45983e32			0.774202
$730$	5.81014e32	−	6.32525e31i	0.685446	−	0.0746216i
$731$	5.46450e32			0.634601
$732$			6.92903e30i			0.00792128i
$733$		−	5.77845e31i		−	0.0650302i	−0.999471	−	0.0325151i	$-0.989648\pi$
$733$		−	5.77845e31i		−	0.0650302i	0.999471	−	0.0325151i	$-0.0103517\pi$
$734$	−1.15566e33			−1.28034
$735$	1.23381e31	+	1.13333e32i	0.0134568	+	0.123610i
$736$	−8.84049e31			−0.0949252
$737$			4.86620e31i			0.0514415i
$738$			9.29163e32i			0.967038i
$739$	1.46332e33			1.49943			0.749717	−	0.661758i	$-0.230190\pi$
$739$	1.46332e33			1.49943			0.749717	+	0.661758i	$0.230190\pi$
$740$	7.51021e31	+	6.89860e32i	0.0757683	+	0.695979i
$741$	−9.85301e31			−0.0978723
$742$		−	1.20958e33i		−	1.18302i
$743$		−	1.28767e33i		−	1.24003i	−0.784591	−	0.620014i	$-0.787127\pi$
$743$		−	1.28767e33i		−	1.24003i	0.784591	−	0.620014i	$-0.212873\pi$
$744$	−1.06158e32			−0.100662
$745$	−1.16250e33	+	1.26557e32i	−1.08542	+	0.118165i
$746$	−1.25859e33			−1.15715
$747$			1.02761e33i			0.930336i
$748$		−	1.01489e32i		−	0.0904793i
$749$	7.07937e32			0.621518
$750$	1.52817e32	−	5.15451e31i	0.132120	−	0.0445639i
$751$	−1.02292e33			−0.870932			−0.435466	−	0.900205i	$-0.643416\pi$
$751$	−1.02292e33			−0.870932			−0.435466	+	0.900205i	$0.643416\pi$
$752$			4.47522e32i			0.375240i
$753$		−	2.92739e31i		−	0.0241734i
$754$	1.29438e32			0.105267
$755$	2.07042e33	−	2.25397e32i	1.65832	−	0.180534i
$756$	−3.12985e32			−0.246901
$757$			6.10268e31i			0.0474153i	0.999719	+	0.0237076i	$0.00754708\pi$
$757$			6.10268e31i			0.0474153i	−0.999719	+	0.0237076i	$0.992453\pi$
$758$		−	9.72833e32i		−	0.744462i
$759$	5.70447e31			0.0429967
$760$	3.09897e31	+	2.84660e32i	0.0230071	+	0.211335i
$761$	1.30709e33			0.955833			0.477917	−	0.878405i	$-0.341392\pi$
$761$	1.30709e33			0.955833			0.477917	+	0.878405i	$0.341392\pi$
$762$		−	1.60289e32i		−	0.115458i
$763$			8.58506e32i			0.609131i
$764$	−3.62776e32			−0.253551
$765$	6.73282e31	+	6.18452e32i	0.0463543	+	0.425794i
$766$	9.75729e32			0.661757
$767$			1.81918e33i			1.21543i
$768$			1.87247e31i			0.0123242i
$769$	3.99129e32			0.258798			0.129399	−	0.991593i	$-0.458695\pi$
$769$	3.99129e32			0.258798			0.129399	+	0.991593i	$0.458695\pi$
$770$	5.70607e32	−	6.21195e31i	0.364497	−	0.0396812i
$771$	−1.28202e32			−0.0806809
$772$			1.38305e33i			0.857508i
$773$			1.87338e33i			1.14436i	0.820129	+	0.572178i	$0.193901\pi$
$773$			1.87338e33i			1.14436i	−0.820129	+	0.572178i	$0.806099\pi$
$774$	−1.60806e33			−0.967789
$775$	−2.37796e33	+	5.23967e32i	−1.41005	+	0.310695i
$776$	−5.70110e32			−0.333080
$777$			6.12457e32i			0.352561i
$778$			1.63353e33i			0.926534i
$779$	1.53087e33			0.855572
$780$	−1.46921e32	+	1.59947e31i	−0.0809091	+	0.00880822i
$781$	−7.27742e32			−0.394903
$782$			3.16447e32i			0.169209i
$783$		−	1.32357e32i		−	0.0697405i
$784$	−3.03602e32			−0.157641
$785$	−3.95911e32	−	3.63669e33i	−0.202580	−	1.86082i
$786$	−2.32471e32			−0.117222
$787$			9.78666e32i			0.486323i	0.969986	+	0.243162i	$0.0781845\pi$
$787$			9.78666e32i			0.486323i	−0.969986	+	0.243162i	$0.921815\pi$
$788$		−	1.76361e33i		−	0.863677i
$789$	−9.37949e31			−0.0452683
$790$	−1.49076e32	−	1.36935e33i	−0.0709079	−	0.651334i
$791$	2.54802e33			1.19447
$792$			2.98654e32i			0.137984i
$793$		−	1.45644e32i		−	0.0663209i
$794$	−2.89365e33			−1.29871
$795$	−5.80604e32	+	6.32079e31i	−0.256837	+	0.0279608i
$796$	1.23154e33			0.536970
$797$		−	2.12925e33i		−	0.915072i	−0.889191	−	0.457536i	$-0.848732\pi$
$797$		−	2.12925e33i		−	0.915072i	0.889191	−	0.457536i	$-0.151268\pi$
$798$			2.52721e32i			0.107055i
$799$	1.60191e33			0.668884
$800$	9.24196e31	+	4.19435e32i	0.0380390	+	0.172636i
$801$	5.54847e32			0.225112
$802$			1.55294e33i			0.621082i
$803$		−	1.00432e33i		−	0.395954i
$804$	−3.21374e31			−0.0124901
$805$	−1.77918e33	+	1.93692e32i	−0.681659	+	0.0742093i
$806$	2.23138e33			0.842793
$807$		−	1.07460e32i		−	0.0400131i
$808$		−	1.80989e33i		−	0.664388i
$809$	−5.01643e33			−1.81546			−0.907730	−	0.419556i	$-0.862186\pi$
$809$	−5.01643e33			−1.81546			−0.907730	+	0.419556i	$0.862186\pi$
$810$	−1.89789e32	−	1.74333e33i	−0.0677163	−	0.622017i
$811$	8.00102e32			0.281453			0.140726	−	0.990049i	$-0.455056\pi$
$811$	8.00102e32			0.281453			0.140726	+	0.990049i	$0.455056\pi$
$812$		−	3.31998e32i		−	0.115144i
$813$		−	1.10444e33i		−	0.377660i
$814$	1.19247e33			0.402039
$815$	−4.90330e31	−	4.50399e32i	−0.0162996	−	0.149722i
$816$	6.70252e31			0.0219686
$817$			2.64940e33i			0.856236i
$818$		−	2.39116e32i		−	0.0761985i
$819$	3.22415e33			1.01310
$820$	2.28272e33	−	2.48510e32i	0.707284	−	0.0769990i
$821$	−4.06858e33			−1.24307			−0.621536	−	0.783386i	$-0.713491\pi$
$821$	−4.06858e33			−1.24307			−0.621536	+	0.783386i	$0.713491\pi$
$822$			5.41023e32i			0.163001i
$823$		−	5.68706e33i		−	1.68962i	−0.535064	−	0.844811i	$-0.679713\pi$
$823$		−	5.68706e33i		−	1.68962i	0.535064	−	0.844811i	$-0.320287\pi$
$824$	−1.87328e33			−0.548833
$825$	−5.96352e31	−	2.70647e32i	−0.0172299	−	0.0781958i
$826$	4.66603e33			1.32946
$827$			2.87691e33i			0.808376i	0.914676	+	0.404188i	$0.132446\pi$
$827$			2.87691e33i			0.808376i	−0.914676	+	0.404188i	$0.867554\pi$
$828$		−	9.31219e32i		−	0.258049i
$829$	1.56663e33			0.428144			0.214072	−	0.976818i	$-0.431327\pi$
$829$	1.56663e33			0.428144			0.214072	+	0.976818i	$0.431327\pi$
$830$	2.52458e33	−	2.74840e32i	0.680441	−	0.0740766i
$831$	4.47857e32			0.119050
$832$		−	3.93581e32i		−	0.103185i
$833$			1.08675e33i			0.281003i
$834$	1.19719e32			0.0305319
$835$	−6.37596e32	−	5.85672e33i	−0.160380	−	1.47320i
$836$	4.92056e32			0.122079
$837$		−	2.28169e33i		−	0.558360i
$838$			4.64259e33i			1.12061i
$839$	3.71863e33			0.885362			0.442681	−	0.896679i	$-0.354027\pi$
$839$	3.71863e33			0.885362			0.442681	+	0.896679i	$0.354027\pi$
$840$	4.10250e31	+	3.76841e32i	0.00963467	+	0.0885005i
$841$	−4.17632e33			−0.967476
$842$			1.04609e33i			0.239044i
$843$			5.72347e32i			0.129016i
$844$	2.33393e32			0.0518979
$845$	−1.44385e33	+	1.57185e32i	−0.316715	+	0.0344794i
$846$	−4.71400e33			−1.02007
$847$			4.99542e33i			1.06638i
$848$		−	1.55535e33i		−	0.327549i
$849$	−3.61320e32			−0.0750678
$850$	1.50138e33	−	3.30817e32i	0.307731	−	0.0678064i
$851$	−3.71819e33			−0.751868
$852$		−	4.80616e32i		−	0.0958833i
$853$			1.01387e33i			0.199558i	0.995010	+	0.0997792i	$0.0318136\pi$
$853$			1.01387e33i			0.199558i	−0.995010	+	0.0997792i	$0.968186\pi$
$854$	−3.73564e32			−0.0725436
$855$	−2.99849e33	+	3.26432e32i	−0.574502	+	0.0625436i
$856$	9.10307e32			0.172084
$857$			7.44523e33i			1.38867i	0.719652	+	0.694335i	$0.244301\pi$
$857$			7.44523e33i			1.38867i	−0.719652	+	0.694335i	$0.755699\pi$
$858$			2.53964e32i			0.0467378i
$859$	−1.76949e33			−0.321312			−0.160656	−	0.987010i	$-0.551361\pi$
$859$	−1.76949e33			−0.321312			−0.160656	+	0.987010i	$0.551361\pi$
$860$	4.30085e32	+	3.95060e33i	0.0770588	+	0.707833i
$861$	2.02660e33			0.358288
$862$			2.93750e31i			0.00512441i
$863$			6.17332e33i			1.06266i	0.847165	+	0.531331i	$0.178308\pi$
$863$			6.17332e33i			1.06266i	−0.847165	+	0.531331i	$0.821692\pi$
$864$	−4.02454e32			−0.0683610
$865$	1.55722e32	+	1.43040e33i	0.0261014	+	0.239758i
$866$	−1.36988e33			−0.226583
$867$			9.68174e32i			0.158028i
$868$		−	5.72330e33i		−	0.921869i
$869$	−2.36702e33			−0.376249
$870$	−1.59360e32	+	1.73489e31i	−0.0249982	+	0.00272144i
$871$	6.75508e32			0.104573
$872$			1.10392e33i			0.168654i
$873$		−	6.00529e33i		−	0.905462i
$874$	−1.53425e33			−0.228305
$875$	2.77894e33	+	8.23880e33i	0.408119	+	1.20996i
$876$	6.63276e32			0.0961385
$877$		−	4.24175e33i		−	0.606806i	−0.952862	−	0.303403i	$-0.901877\pi$
$877$		−	4.24175e33i		−	0.606806i	0.952862	−	0.303403i	$-0.0981229\pi$
$878$			8.37229e33i			1.18211i
$879$	1.13351e33			0.157962
$880$	7.33720e32	−	7.98769e31i	0.100921	−	0.0109868i
$881$	5.11821e33			0.694857			0.347428	−	0.937707i	$-0.387055\pi$
$881$	5.11821e33			0.694857			0.347428	+	0.937707i	$0.387055\pi$
$882$		−	3.19801e33i		−	0.428540i
$883$		−	5.65800e33i		−	0.748367i	−0.927355	−	0.374184i	$-0.877923\pi$
$883$		−	5.65800e33i		−	0.748367i	0.927355	−	0.374184i	$-0.122077\pi$
$884$	−1.40883e33			−0.183932
$885$	−2.43828e32	−	2.23971e33i	−0.0314221	−	0.288632i
$886$	−1.82899e33			−0.232662
$887$		−	3.49394e33i		−	0.438726i	−0.975643	−	0.219363i	$-0.929602\pi$
$887$		−	3.49394e33i		−	0.438726i	0.975643	−	0.219363i	$-0.0703979\pi$
$888$			7.87534e32i			0.0976158i
$889$	8.64165e33			1.05737
$890$	−1.48397e32	−	1.36312e33i	−0.0179242	−	0.164645i
$891$	−3.01347e33			−0.359314
$892$		−	8.48156e32i		−	0.0998343i
$893$			7.76668e33i			0.902493i
$894$	−1.32710e33			−0.152237
$895$	4.78325e33	−	5.20732e32i	0.541699	−	0.0589725i
$896$	−1.00950e33			−0.112866
$897$		−	7.91873e32i		−	0.0874062i
$898$		−	2.73621e31i		−	0.00298175i
$899$	2.42029e33			0.260395
$900$	−4.41815e33	+	9.73507e32i	−0.469301	+	0.103407i
$901$	−5.56740e33			−0.583872
$902$		−	3.94585e33i		−	0.408569i
$903$			3.50734e33i			0.358566i
$904$	3.27640e33			0.330720
$905$	6.37284e33	−	6.93784e32i	0.635148	−	0.0691458i
$906$	2.36355e33			0.232590
$907$		−	1.65586e34i		−	1.60894i	−0.593997	−	0.804468i	$-0.702451\pi$
$907$		−	1.65586e34i		−	1.60894i	0.593997	−	0.804468i	$-0.297549\pi$
$908$		−	4.14051e33i		−	0.397252i
$909$	1.90646e34			1.80611
$910$	−8.62319e32	−	7.92095e33i	−0.0806663	−	0.740971i
$911$	−1.19977e33			−0.110825			−0.0554125	−	0.998464i	$-0.517647\pi$
$911$	−1.19977e33			−0.110825			−0.0554125	+	0.998464i	$0.517647\pi$
$912$			3.24964e32i			0.0296411i
$913$		−	4.36391e33i		−	0.393062i
$914$	−1.07131e34			−0.952872
$915$	1.95209e31	+	1.79312e32i	0.00171458	+	0.0157495i
$916$	−8.64997e33			−0.750268
$917$		−	1.25332e34i		−	1.07353i
$918$			1.44059e33i			0.121857i
$919$	−1.66669e34			−1.39228			−0.696140	−	0.717906i	$-0.745101\pi$
$919$	−1.66669e34			−1.39228			−0.696140	+	0.717906i	$0.745101\pi$
$920$	−2.28777e33	+	2.49060e32i	−0.188735	+	0.0205468i
$921$	1.31456e33			0.107102
$922$		−	7.59955e33i		−	0.611480i
$923$			1.01022e34i			0.802783i
$924$	6.51396e32			0.0511231
$925$	3.88704e33	+	1.76409e34i	0.301293	+	1.36738i
$926$	−4.88555e33			−0.374014
$927$		−	1.97323e34i		−	1.49197i
$928$		−	4.26902e32i		−	0.0318806i
$929$	−9.13449e33			−0.673757			−0.336879	−	0.941548i	$-0.609371\pi$
$929$	−9.13449e33			−0.673757			−0.336879	+	0.941548i	$0.609371\pi$
$930$	−2.74720e33	+	2.99076e32i	−0.200141	+	0.0217885i
$931$	−5.26897e33			−0.379144
$932$			1.34947e34i			0.959135i
$933$		−	2.32215e33i		−	0.163024i
$934$	8.15817e33			0.565723
$935$	−2.85921e32	−	2.62636e33i	−0.0195845	−	0.179896i
$936$	4.14581e33			0.280502
$937$			6.97063e32i			0.0465872i	0.999729	+	0.0232936i	$0.00741526\pi$
$937$			6.97063e32i			0.0465872i	−0.999729	+	0.0232936i	$0.992585\pi$
$938$		−	1.73262e33i		−	0.114385i
$939$	−4.05702e33			−0.264577
$940$	1.26079e33	+	1.15811e34i	0.0812217	+	0.746073i
$941$	2.43621e34			1.55036			0.775182	−	0.631739i	$-0.217658\pi$
$941$	2.43621e34			1.55036			0.775182	+	0.631739i	$0.217658\pi$
$942$		−	4.15159e33i		−	0.260993i
$943$			1.23034e34i			0.764081i
$944$	5.99985e33			0.368097
$945$	−8.09954e33	+	8.81762e32i	−0.490901	+	0.0534423i
$946$	6.82889e33			0.408886
$947$			5.79468e33i			0.342772i	0.985204	+	0.171386i	$0.0548244\pi$
$947$			5.79468e33i			0.342772i	−0.985204	+	0.171386i	$0.945176\pi$
$948$		−	1.56323e33i		−	0.0913540i
$949$	−1.39416e34			−0.804919
$950$	1.60393e33	+	7.27923e33i	0.0914878	+	0.415207i
$951$	2.37142e33			0.133639
$952$			3.61352e33i			0.201190i
$953$		−	5.83767e33i		−	0.321123i	−0.987026	−	0.160561i	$-0.948670\pi$
$953$		−	5.83767e33i		−	0.321123i	0.987026	−	0.160561i	$-0.0513304\pi$
$954$	1.63834e34			0.890425
$955$	−9.38804e33	+	1.02204e33i	−0.504123	+	0.0548817i
$956$	5.80809e33			0.308154
$957$			2.75465e32i			0.0144404i
$958$			6.74118e33i			0.349167i
$959$	−2.91681e34			−1.49277
$960$	5.27524e31	+	4.84564e32i	0.00266761	+	0.0245037i
$961$	2.17101e34			1.08478
$962$		−	1.65535e34i		−	0.817288i
$963$			9.58878e33i			0.467801i
$964$	−1.64992e33			−0.0795384
$965$	3.89641e33	+	3.57910e34i	0.185610	+	1.70494i
$966$	−2.03108e33			−0.0956073
$967$			1.33898e34i			0.622832i	0.950274	+	0.311416i	$0.100803\pi$
$967$			1.33898e34i			0.622832i	−0.950274	+	0.311416i	$0.899197\pi$
$968$			6.42340e33i			0.295256i
$969$	1.16321e33			0.0528367
$970$	−1.47535e34	+	1.60615e33i	−0.662248	+	0.0720961i
$971$	1.76979e34			0.785057			0.392529	−	0.919740i	$-0.371600\pi$
$971$	1.76979e34			0.785057			0.392529	+	0.919740i	$0.371600\pi$
$972$		−	6.40094e33i		−	0.280596i
$973$			6.45439e33i			0.279613i
$974$	2.29624e34			0.983082
$975$	−3.75702e33	+	8.27833e32i	−0.158961	+	0.0350259i
$976$	−4.80350e32			−0.0200856
$977$			1.05901e34i			0.437634i	0.975766	+	0.218817i	$0.0702198\pi$
$977$			1.05901e34i			0.437634i	−0.975766	+	0.218817i	$0.929780\pi$
$978$		−	5.14168e32i		−	0.0209995i
$979$	−2.35625e33			−0.0951089
$980$	−7.85673e33	+	8.55328e32i	−0.313431	+	0.0341219i
$981$	−1.16282e34			−0.458478
$982$			7.99074e33i			0.311390i
$983$		−	1.04769e34i		−	0.403522i	−0.979435	−	0.201761i	$-0.935334\pi$
$983$		−	1.04769e34i		−	0.403522i	0.979435	−	0.201761i	$-0.0646664\pi$
$984$	2.60592e33			0.0992014
$985$	−4.96856e33	−	4.56393e34i	−0.186945	−	1.71721i
$986$	−1.52810e33			−0.0568287
$987$			1.02817e34i			0.377937i
$988$		−	6.83053e33i		−	0.248170i
$989$	−2.12928e34			−0.764674
$990$	8.41388e32	+	7.72868e33i	0.0298670	+	0.274347i
$991$	−4.99669e34			−1.75322			−0.876609	−	0.481204i	$-0.840200\pi$
$991$	−4.99669e34			−1.75322			−0.876609	+	0.481204i	$0.840200\pi$
$992$		−	7.35935e33i		−	0.255244i
$993$		−	4.11824e33i		−	0.141187i
$994$	2.59114e34			0.878106
$995$	3.18703e34	−	3.46959e33i	1.06763	−	0.116228i
$996$	2.88202e33			0.0954364
$997$		−	4.02448e34i		−	1.31739i	−0.752409	−	0.658696i	$-0.771108\pi$
$997$		−	4.02448e34i		−	1.31739i	0.752409	−	0.658696i	$-0.228892\pi$
$998$			1.80216e34i			0.583165i
$999$	−1.69267e34			−0.541463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.24.b.a.9.10	yes	12
5.2	odd	4		50.24.a.j.1.4		6
5.3	odd	4		50.24.a.k.1.3		6
5.4	even	2	inner	10.24.b.a.9.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.24.b.a.9.3	✓	12	5.4	even	2	inner
10.24.b.a.9.10	yes	12	1.1	even	1	trivial
50.24.a.j.1.4		6	5.2	odd	4
50.24.a.k.1.3		6	5.3	odd	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2048.00i q^{2} +60502.7i q^{3} -4.19430e6 q^{4} +(-1.08542e8 + 1.18165e7i) q^{5} -1.23909e8 q^{6} -6.68031e9i q^{7} -8.58993e9i q^{8} +9.04826e10 q^{9} +(-2.42001e10 - 2.22293e11i) q^{10} -3.84250e11 q^{11} -2.53767e11i q^{12} +5.33401e12i q^{13} +1.36813e13 q^{14} +(-7.14928e11 - 6.56706e12i) q^{15} +1.75922e13 q^{16} -6.29715e13i q^{17} +1.85308e14i q^{18} +3.05310e14 q^{19} +(4.55257e14 - 4.95619e13i) q^{20} +4.04177e14 q^{21} -7.86944e14i q^{22} +2.45373e15i q^{23} +5.19714e14 q^{24} +(1.16417e16 - 2.56516e15i) q^{25} -1.09241e16 q^{26} +1.11704e16i q^{27} +2.80192e16i q^{28} -1.18489e16 q^{29} +(1.34493e16 - 1.46417e15i) q^{30} -2.04263e17 q^{31} +3.60288e16i q^{32} -2.32482e16i q^{33} +1.28966e17 q^{34} +(7.89377e16 + 7.25092e17i) q^{35} -3.79512e17 q^{36} +1.51532e18i q^{37} +6.25274e17i q^{38} -3.22722e17 q^{39} +(1.01503e17 + 9.32366e17i) q^{40} +5.01414e18 q^{41} +8.27754e17i q^{42} +8.67774e18i q^{43} +1.61166e18 q^{44} +(-9.82114e18 + 1.06918e18i) q^{45} -5.02524e18 q^{46} +2.54387e19i q^{47} +1.06437e18i q^{48} -1.72578e19 q^{49} +(5.25345e18 + 2.38421e19i) q^{50} +3.80994e18 q^{51} -2.23725e19i q^{52} -8.84115e19i q^{53} -2.28769e19 q^{54} +(4.17071e19 - 4.54048e18i) q^{55} -5.73834e19 q^{56} +1.84720e19i q^{57} -2.42666e19i q^{58} +3.41052e20 q^{59} +(2.99863e18 + 2.75443e19i) q^{60} -2.73047e19 q^{61} -4.18331e20i q^{62} -6.04452e20i q^{63} -7.37870e19 q^{64} +(-6.30292e19 - 5.78963e20i) q^{65} +4.76122e19 q^{66} -1.26642e20i q^{67} +2.64122e20i q^{68} -1.48457e20 q^{69} +(-1.48499e21 + 1.61664e20i) q^{70} +1.89393e21 q^{71} -7.77240e20i q^{72} +2.61372e21i q^{73} -3.10338e21 q^{74} +(1.55199e20 + 7.04352e20i) q^{75} -1.28056e21 q^{76} +2.56691e21i q^{77} -6.60935e20i q^{78} +6.16012e21 q^{79} +(-1.90949e21 + 2.07877e20i) q^{80} +7.84248e21 q^{81} +1.02690e22i q^{82} +1.13570e22i q^{83} -1.69524e21 q^{84} +(7.44101e20 + 6.83503e21i) q^{85} -1.77720e22 q^{86} -7.16891e20i q^{87} +3.30068e21i q^{88} +6.13209e21 q^{89} +(-2.18969e21 - 2.01137e22i) q^{90} +3.56329e22 q^{91} -1.02917e22i q^{92} -1.23585e22i q^{93} -5.20985e22 q^{94} +(-3.31388e22 + 3.60768e21i) q^{95} -2.17984e21 q^{96} -6.63696e22i q^{97} -3.53439e22i q^{98} -3.47679e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 50331648 q^{4} - 153465660 q^{5} + 1496219648 q^{6} - 397404876524 q^{9} + 515607920640 q^{10} + 1618708468464 q^{11} - 18612479361024 q^{14} + 56360859857360 q^{15} + 211106232532992 q^{16} - 11\!\cdots\!80 q^{19}+ \cdots - 49\!\cdots\!28 q^{99}+O(q^{100}) \) 12 * q - 50331648 * q^4 - 153465660 * q^5 + 1496219648 * q^6 - 397404876524 * q^9 + 515607920640 * q^10 + 1618708468464 * q^11 - 18612479361024 * q^14 + 56360859857360 * q^15 + 211106232532992 * q^16 - 1100262406554480 * q^19 + 643681631600640 * q^20 + 2454694989205424 * q^21 - 6275600054484992 * q^24 + 18348046596119100 * q^25 + 47412135014105088 * q^26 - 191332118394850680 * q^29 + 69062266581647360 * q^30 + 314531620762193664 * q^31 - 27202419348209664 * q^34 - 132973567506049680 * q^35 + 1666836863224119296 * q^36 + 16801243916907657312 * q^39 - 2162616363972034560 * q^40 - 334736513821173096 * q^41 - 6789355404112429056 * q^44 + 44571509177637873820 * q^45 + 37044797625677611008 * q^46 - 61353034749652271196 * q^49 - 11488666440926822400 * q^50 + 21794418357272939264 * q^51 - 64483243481607372800 * q^54 + 33608617917590982480 * q^55 + 78066396633860407296 * q^56 - 792491082249081738960 * q^59 - 236394579943164477440 * q^60 + 396873789531683516904 * q^61 - 885443715538058477568 * q^64 - 1103464906421517591840 * q^65 - 1919302523514221625344 * q^66 - 5004088166299913161808 * q^69 + 1549427758140305080320 * q^70 + 11216046927623429218464 * q^71 - 7698848775986662539264 * q^74 + 2698057827395500242400 * q^75 + 4614835012861081681920 * q^76 - 13308383509524480375360 * q^79 - 2699796442149090754560 * q^80 + 80031139288718178809852 * q^81 - 10295737012004266704896 * q^84 - 53931318208690956660480 * q^85 + 70834920401828427890688 * q^86 + 26549329728846280565880 * q^89 - 149835156254250257121280 * q^90 + 213312013693120420064544 * q^91 - 110687147549581976961024 * q^94 - 333982981030300532283600 * q^95 + 26321774410926619885568 * q^96 - 497641983005968176470128 * q^99

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