LMFDB - Embedded newform 10.24.b.a.9.8

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			9.8
Root			$-179991. i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.24.b.a.9.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2048.00i q^{2} -359983. i q^{3} -4.19430e6 q^{4} +(1.08857e8 - 8.43729e6i) q^{5} +7.37244e8 q^{6} -6.72856e9i q^{7} -8.58993e9i q^{8} -3.54442e10 q^{9} +(1.72796e10 + 2.22938e11i) q^{10} +1.25050e12 q^{11} +1.50988e12i q^{12} +2.11041e12i q^{13} +1.37801e13 q^{14} +(-3.03728e12 - 3.91864e13i) q^{15} +1.75922e13 q^{16} +7.84590e13i q^{17} -7.25898e13i q^{18} -5.95210e14 q^{19} +(-4.56577e14 + 3.53886e13i) q^{20} -2.42217e15 q^{21} +2.56103e15i q^{22} -5.74795e15i q^{23} -3.09223e15 q^{24} +(1.17786e16 - 1.83691e15i) q^{25} -4.32211e15 q^{26} -2.11306e16i q^{27} +2.82216e16i q^{28} +8.07090e16 q^{29} +(8.02538e16 - 6.22034e15i) q^{30} -1.21286e17 q^{31} +3.60288e16i q^{32} -4.50159e17i q^{33} -1.60684e17 q^{34} +(-5.67709e16 - 7.32448e17i) q^{35} +1.48664e17 q^{36} +3.56143e17i q^{37} -1.21899e18i q^{38} +7.59709e17 q^{39} +(-7.24758e16 - 9.35070e17i) q^{40} +2.00008e16 q^{41} -4.96060e18i q^{42} -9.21964e18i q^{43} -5.24499e18 q^{44} +(-3.85833e18 + 2.99053e17i) q^{45} +1.17718e19 q^{46} -1.67794e19i q^{47} -6.33288e18i q^{48} -1.79048e19 q^{49} +(3.76199e18 + 2.41225e19i) q^{50} +2.82439e19 q^{51} -8.85169e18i q^{52} -4.21392e19i q^{53} +4.32755e19 q^{54} +(1.36125e20 - 1.05509e19i) q^{55} -5.77979e19 q^{56} +2.14265e20i q^{57} +1.65292e20i q^{58} -4.09061e20 q^{59} +(1.27393e19 + 1.64360e20i) q^{60} -3.04863e20 q^{61} -2.48394e20i q^{62} +2.38489e20i q^{63} -7.37870e19 q^{64} +(1.78061e19 + 2.29732e20i) q^{65} +9.21926e20 q^{66} +1.70954e21i q^{67} -3.29081e20i q^{68} -2.06916e21 q^{69} +(1.50005e21 - 1.16267e20i) q^{70} +3.47257e21 q^{71} +3.04464e20i q^{72} +2.31870e20i q^{73} -7.29381e20 q^{74} +(-6.61255e20 - 4.24007e21i) q^{75} +2.49649e21 q^{76} -8.41409e21i q^{77} +1.55589e21i q^{78} -1.24820e22 q^{79} +(1.91502e21 - 1.48430e20i) q^{80} -1.09435e22 q^{81} +4.09617e19i q^{82} -6.04644e21i q^{83} +1.01593e22 q^{84} +(6.61982e20 + 8.54078e21i) q^{85} +1.88818e22 q^{86} -2.90538e22i q^{87} -1.07417e22i q^{88} -2.70483e20 q^{89} +(-6.12461e20 - 7.90187e21i) q^{90} +1.42000e22 q^{91} +2.41086e22i q^{92} +4.36610e22i q^{93} +3.43643e22 q^{94} +(-6.47924e22 + 5.02196e21i) q^{95} +1.29697e22 q^{96} +1.39089e23i q^{97} -3.66691e22i q^{98} -4.43231e22 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
$3$		−	359983.i		−	1.17324i	−0.809862	−	0.586620i	$-0.800458\pi$
$3$		−	359983.i		−	1.17324i	0.809862	−	0.586620i	$-0.199542\pi$
$4$	−4.19430e6			−0.500000
$5$	1.08857e8	−	8.43729e6i	0.997010	−	0.0772766i
$5$	1.08857e8	−	8.43729e6i	0.997010	−	0.0772766i
$6$	7.37244e8			0.829606
$7$		−	6.72856e9i		−	1.28616i	−0.765799	−	0.643080i	$-0.777656\pi$
$7$		−	6.72856e9i		−	1.28616i	0.765799	−	0.643080i	$-0.222344\pi$
$8$		−	8.58993e9i		−	0.353553i
$9$	−3.54442e10			−0.376493
$10$	1.72796e10	+	2.22938e11i	0.0546428	+	0.704992i
$11$	1.25050e12			1.32151			0.660753	−	0.750604i	$-0.270237\pi$
$11$	1.25050e12			1.32151			0.660753	+	0.750604i	$0.270237\pi$
$12$			1.50988e12i			0.586620i
$13$			2.11041e12i			0.326601i	0.986576	+	0.163301i	$0.0522140\pi$
$13$			2.11041e12i			0.326601i	−0.986576	+	0.163301i	$0.947786\pi$
$14$	1.37801e13			0.909452
$15$	−3.03728e12	−	3.91864e13i	−0.0906640	−	1.16973i
$16$	1.75922e13			0.250000
$17$			7.84590e13i			0.555240i	0.960691	+	0.277620i	$0.0895455\pi$
$17$			7.84590e13i			0.555240i	−0.960691	+	0.277620i	$0.910454\pi$
$18$		−	7.25898e13i		−	0.266221i
$19$	−5.95210e14			−1.17220			−0.586102	−	0.810237i	$-0.699338\pi$
$19$	−5.95210e14			−1.17220			−0.586102	+	0.810237i	$0.699338\pi$
$20$	−4.56577e14	+	3.53886e13i	−0.498505	+	0.0386383i
$21$	−2.42217e15			−1.50897
$22$			2.56103e15i			0.934445i
$23$		−	5.74795e15i		−	1.25789i	−0.777450	−	0.628945i	$-0.783487\pi$
$23$		−	5.74795e15i		−	1.25789i	0.777450	−	0.628945i	$-0.216513\pi$
$24$	−3.09223e15			−0.414803
$25$	1.17786e16	−	1.83691e15i	0.988057	−	0.154091i
$26$	−4.32211e15			−0.230942
$27$		−	2.11306e16i		−	0.731524i
$28$			2.82216e16i			0.643080i
$29$	8.07090e16			1.22841			0.614207	−	0.789145i	$-0.289476\pi$
$29$	8.07090e16			1.22841			0.614207	+	0.789145i	$0.289476\pi$
$30$	8.02538e16	−	6.22034e15i	0.827125	−	0.0641091i
$31$	−1.21286e17			−0.857339			−0.428669	−	0.903461i	$-0.641017\pi$
$31$	−1.21286e17			−0.857339			−0.428669	+	0.903461i	$0.641017\pi$
$32$			3.60288e16i			0.176777i
$33$		−	4.50159e17i		−	1.55044i
$34$	−1.60684e17			−0.392614
$35$	−5.67709e16	−	7.32448e17i	−0.0993901	−	1.28231i
$36$	1.48664e17			0.188246
$37$			3.56143e17i			0.329082i	0.986370	+	0.164541i	$0.0526144\pi$
$37$			3.56143e17i			0.329082i	−0.986370	+	0.164541i	$0.947386\pi$
$38$		−	1.21899e18i		−	0.828874i
$39$	7.59709e17			0.383182
$40$	−7.24758e16	−	9.35070e17i	−0.0273214	−	0.352496i
$41$	2.00008e16			0.00567589			0.00283794	−	0.999996i	$-0.499097\pi$
$41$	2.00008e16			0.00567589			0.00283794	+	0.999996i	$0.499097\pi$
$42$		−	4.96060e18i		−	1.06701i
$43$		−	9.21964e18i		−	1.51296i	−0.654018	−	0.756479i	$-0.726918\pi$
$43$		−	9.21964e18i		−	1.51296i	0.654018	−	0.756479i	$-0.273082\pi$
$44$	−5.24499e18			−0.660753
$45$	−3.85833e18	+	2.99053e17i	−0.375367	+	0.0290941i
$46$	1.17718e19			0.889462
$47$		−	1.67794e19i		−	0.990038i	−0.868882	−	0.495019i	$-0.835161\pi$
$47$		−	1.67794e19i		−	0.990038i	0.868882	−	0.495019i	$-0.164839\pi$
$48$		−	6.33288e18i		−	0.293310i
$49$	−1.79048e19			−0.654207
$50$	3.76199e18	+	2.41225e19i	0.108959	+	0.698662i
$51$	2.82439e19			0.651429
$52$		−	8.85169e18i		−	0.163301i
$53$		−	4.21392e19i		−	0.624474i	−0.950004	−	0.312237i	$-0.898922\pi$
$53$		−	4.21392e19i		−	0.624474i	0.950004	−	0.312237i	$-0.101078\pi$
$54$	4.32755e19			0.517265
$55$	1.36125e20	−	1.05509e19i	1.31755	−	0.102121i
$56$	−5.77979e19			−0.454726
$57$			2.14265e20i			1.37528i
$58$			1.65292e20i			0.868620i
$59$	−4.09061e20			−1.76600			−0.882999	−	0.469374i	$-0.844480\pi$
$59$	−4.09061e20			−1.76600			−0.882999	+	0.469374i	$0.844480\pi$
$60$	1.27393e19	+	1.64360e20i	0.0453320	+	0.584866i
$61$	−3.04863e20			−0.897039			−0.448520	−	0.893773i	$-0.648049\pi$
$61$	−3.04863e20			−0.897039			−0.448520	+	0.893773i	$0.648049\pi$
$62$		−	2.48394e20i		−	0.606230i
$63$			2.38489e20i			0.484230i
$64$	−7.37870e19			−0.125000
$65$	1.78061e19	+	2.29732e20i	0.0252386	+	0.325624i
$66$	9.21926e20			1.09633
$67$			1.70954e21i			1.71009i	0.518556	+	0.855044i	$0.326470\pi$
$67$			1.70954e21i			1.71009i	−0.518556	+	0.855044i	$0.673530\pi$
$68$		−	3.29081e20i		−	0.277620i
$69$	−2.06916e21			−1.47581
$70$	1.50005e21	−	1.16267e20i	0.906733	−	0.0702794i
$71$	3.47257e21			1.78312			0.891559	−	0.452904i	$-0.149612\pi$
$71$	3.47257e21			1.78312			0.891559	+	0.452904i	$0.149612\pi$
$72$			3.04464e20i			0.133110i
$73$			2.31870e20i			0.0865029i	0.999064	+	0.0432515i	$0.0137717\pi$
$73$			2.31870e20i			0.0865029i	−0.999064	+	0.0432515i	$0.986228\pi$
$74$	−7.29381e20			−0.232696
$75$	−6.61255e20	−	4.24007e21i	−0.180786	−	1.15923i
$76$	2.49649e21			0.586102
$77$		−	8.41409e21i		−	1.69967i
$78$			1.55589e21i			0.270950i
$79$	−1.24820e22			−1.87747			−0.938733	−	0.344646i	$-0.887999\pi$
$79$	−1.24820e22			−1.87747			−0.938733	+	0.344646i	$0.887999\pi$
$80$	1.91502e21	−	1.48430e20i	0.249252	−	0.0193191i
$81$	−1.09435e22			−1.23475
$82$			4.09617e19i			0.00401346i
$83$		−	6.04644e21i		−	0.515349i	−0.966232	−	0.257674i	$-0.917044\pi$
$83$		−	6.04644e21i		−	0.515349i	0.966232	−	0.257674i	$-0.0829562\pi$
$84$	1.01593e22			0.754487
$85$	6.61982e20	+	8.54078e21i	0.0429070	+	0.553579i
$86$	1.88818e22			1.06982
$87$		−	2.90538e22i		−	1.44123i
$88$		−	1.07417e22i		−	0.467223i
$89$	−2.70483e20			−0.0103313			−0.00516565	−	0.999987i	$-0.501644\pi$
$89$	−2.70483e20			−0.0103313			−0.00516565	+	0.999987i	$0.501644\pi$
$90$	−6.12461e20	−	7.90187e21i	−0.0205726	−	0.265424i
$91$	1.42000e22			0.420061
$92$			2.41086e22i			0.628945i
$93$			4.36610e22i			1.00586i
$94$	3.43643e22			0.700063
$95$	−6.47924e22	+	5.02196e21i	−1.16870	+	0.0905840i
$96$	1.29697e22			0.207402
$97$			1.39089e23i			1.97432i	0.159730	+	0.987161i	$0.448938\pi$
$97$			1.39089e23i			1.97432i	−0.159730	+	0.987161i	$0.551062\pi$
$98$		−	3.66691e22i		−	0.462595i
$99$	−4.43231e22			−0.497537
$100$	−4.94028e22	+	7.70455e21i	−0.494028	+	0.0770455i
$101$	6.82072e22			0.608323			0.304161	−	0.952621i	$-0.401624\pi$
$101$	6.82072e22			0.608323			0.304161	+	0.952621i	$0.401624\pi$
$102$			5.78435e22i			0.460630i
$103$		−	8.93495e21i		−	0.0636010i	−0.999494	−	0.0318005i	$-0.989876\pi$
$103$		−	8.93495e21i		−	0.0636010i	0.999494	−	0.0318005i	$-0.0101241\pi$
$104$	1.81283e22			0.115471
$105$	−2.63669e23	+	2.04365e22i	−1.50446	+	0.116608i
$106$	8.63012e22			0.441570
$107$		−	1.33840e23i		−	0.614715i	−0.951594	−	0.307357i	$-0.900555\pi$
$107$		−	1.33840e23i		−	0.614715i	0.951594	−	0.307357i	$-0.0994447\pi$
$108$			8.86281e22i			0.365762i
$109$	3.39151e23			1.25889			0.629446	−	0.777045i	$-0.283282\pi$
$109$	3.39151e23			1.25889			0.629446	+	0.777045i	$0.283282\pi$
$110$	2.16082e22	+	2.78785e23i	0.0722108	+	0.931651i
$111$	1.28205e23			0.386093
$112$		−	1.18370e23i		−	0.321540i
$113$			1.07761e23i			0.264276i	0.991231	+	0.132138i	$0.0421843\pi$
$113$			1.07761e23i			0.264276i	−0.991231	+	0.132138i	$0.957816\pi$
$114$	−4.38815e23			−0.972468
$115$	−4.84971e22	−	6.25701e23i	−0.0972054	−	1.25413i
$116$	−3.38518e23			−0.614207
$117$		−	7.48017e22i		−	0.122963i
$118$		−	8.37758e23i		−	1.24875i
$119$	5.27917e23			0.714127
$120$	−3.36609e23	+	2.60900e22i	−0.413563	+	0.0320546i
$121$	6.68328e23			0.746376
$122$		−	6.24359e23i		−	0.634303i
$123$		−	7.19995e21i		−	0.00665918i
$124$	5.08712e23			0.428669
$125$	1.26667e24	−	2.99339e23i	0.973194	−	0.229984i
$126$	−4.88425e23			−0.342402
$127$		−	4.56390e23i		−	0.292141i	−0.989274	−	0.146071i	$-0.953337\pi$
$127$		−	4.56390e23i		−	0.292141i	0.989274	−	0.146071i	$-0.0466627\pi$
$128$		−	1.51116e23i		−	0.0883883i
$129$	−3.31891e24			−1.77506
$130$	−4.70490e23	+	3.64669e22i	−0.230251	+	0.0178464i
$131$	3.54517e24			1.58861			0.794305	−	0.607520i	$-0.207835\pi$
$131$	3.54517e24			1.58861			0.794305	+	0.607520i	$0.207835\pi$
$132$			1.88810e24i			0.775222i
$133$			4.00491e24i			1.50764i
$134$	−3.50113e24			−1.20921
$135$	−1.78285e23	−	2.30020e24i	−0.0565297	−	0.729336i
$136$	6.73958e23			0.196307
$137$			1.39347e24i			0.373088i	0.982447	+	0.186544i	$0.0597286\pi$
$137$			1.39347e24i			0.373088i	−0.982447	+	0.186544i	$0.940271\pi$
$138$		−	4.23764e24i		−	1.04355i
$139$	2.58956e23			0.0586888			0.0293444	−	0.999569i	$-0.490658\pi$
$139$	2.58956e23			0.0586888			0.0293444	+	0.999569i	$0.490658\pi$
$140$	2.38114e23	+	3.07211e24i	0.0496950	+	0.641157i
$141$	−6.04030e24			−1.16155
$142$			7.11183e24i			1.26086i
$143$			2.63907e24i			0.431605i
$144$	−6.23541e23			−0.0941232
$145$	8.78570e24	−	6.80965e23i	1.22474	−	0.0949277i
$146$	−4.74869e23			−0.0611668
$147$			6.44543e24i			0.767543i
$148$		−	1.49377e24i		−	0.164541i
$149$	9.25805e24			0.943794			0.471897	−	0.881654i	$-0.343569\pi$
$149$	9.25805e24			0.943794			0.471897	+	0.881654i	$0.343569\pi$
$150$	8.68367e24	−	1.35425e24i	0.819698	−	0.127835i
$151$	−7.81021e24			−0.683011			−0.341506	−	0.939880i	$-0.610937\pi$
$151$	−7.81021e24			−0.683011			−0.341506	+	0.939880i	$0.610937\pi$
$152$			5.11281e24i			0.414437i
$153$		−	2.78092e24i		−	0.209044i
$154$	1.72321e25			1.20185
$155$	−1.32028e25	+	1.02333e24i	−0.854775	+	0.0662522i
$156$	−3.18645e24			−0.191591
$157$		−	1.76038e25i		−	0.983469i	−0.870745	−	0.491735i	$-0.836363\pi$
$157$		−	1.76038e25i		−	0.983469i	0.870745	−	0.491735i	$-0.163637\pi$
$158$		−	2.55631e25i		−	1.32757i
$159$	−1.51694e25			−0.732658
$160$	3.03985e23	+	3.92197e24i	0.0136607	+	0.176248i
$161$	−3.86754e25			−1.61785
$162$		−	2.24122e25i		−	0.873097i
$163$			9.67378e24i			0.351107i	0.984470	+	0.175553i	$0.0561714\pi$
$163$			9.67378e24i			0.351107i	−0.984470	+	0.175553i	$0.943829\pi$
$164$	−8.38896e22			−0.00283794
$165$	−3.79812e24	−	4.90028e25i	−0.119813	−	1.54581i
$166$	1.23831e25			0.364407
$167$			3.59273e25i			0.986700i	0.869831	+	0.493350i	$0.164228\pi$
$167$			3.59273e25i			0.986700i	−0.869831	+	0.493350i	$0.835772\pi$
$168$			2.08062e25i			0.533503i
$169$	3.73001e25			0.893332
$170$	−1.74915e25	+	1.35574e24i	−0.391440	+	0.0303398i
$171$	2.10967e25			0.441327
$172$			3.86700e25i			0.756479i
$173$		−	9.99605e25i		−	1.82936i	−0.404182	−	0.914678i	$-0.632444\pi$
$173$		−	9.99605e25i		−	1.82936i	0.404182	−	0.914678i	$-0.367556\pi$
$174$	5.95022e25			1.01910
$175$	−1.23598e25	−	7.92528e25i	−0.198186	−	1.27080i
$176$	2.19991e25			0.330376
$177$			1.47255e26i			2.07194i
$178$		−	5.53950e23i		−	0.00730534i
$179$	2.41224e25			0.298271			0.149136	−	0.988817i	$-0.452351\pi$
$179$	2.41224e25			0.298271			0.149136	+	0.988817i	$0.452351\pi$
$180$	1.61830e25	−	1.25432e24i	0.187683	−	0.0145470i
$181$	−1.91956e25			−0.208880			−0.104440	−	0.994531i	$-0.533305\pi$
$181$	−1.91956e25			−0.208880			−0.104440	+	0.994531i	$0.533305\pi$
$182$			2.90816e25i			0.297028i
$183$			1.09745e26i			1.05244i
$184$	−4.93745e25			−0.444731
$185$	3.00488e24	+	3.87685e25i	0.0254304	+	0.328098i
$186$	−8.94176e25			−0.711253
$187$			9.81133e25i			0.733752i
$188$			7.03781e25i			0.495019i
$189$	−1.42179e26			−0.940857
$190$	−1.02850e25	−	1.32695e26i	−0.0640526	−	0.826395i
$191$	6.61730e24			0.0387969			0.0193985	−	0.999812i	$-0.493825\pi$
$191$	6.61730e24			0.0387969			0.0193985	+	0.999812i	$0.493825\pi$
$192$			2.65620e25i			0.146655i
$193$		−	6.09974e25i		−	0.317251i	−0.987339	−	0.158625i	$-0.949294\pi$
$193$		−	6.09974e25i		−	0.317251i	0.987339	−	0.158625i	$-0.0507062\pi$
$194$	−2.84854e26			−1.39606
$195$	8.26993e25	−	6.40989e24i	0.382036	−	0.0296110i
$196$	7.50983e25			0.327104
$197$			3.29102e26i			1.35198i	0.736912	+	0.675989i	$0.236283\pi$
$197$			3.29102e26i			1.35198i	−0.736912	+	0.675989i	$0.763717\pi$
$198$		−	9.07737e25i		−	0.351812i
$199$	2.18461e26			0.799031			0.399516	−	0.916726i	$-0.369178\pi$
$199$	2.18461e26			0.799031			0.399516	+	0.916726i	$0.369178\pi$
$200$	−1.57789e25	−	1.01177e26i	−0.0544794	−	0.349331i
$201$	6.15404e26			2.00634
$202$			1.39688e26i			0.430149i
$203$		−	5.43056e26i		−	1.57994i
$204$	−1.18463e26			−0.325715
$205$	2.17722e24	−	1.68753e23i	0.00565891	−	0.000438613i
$206$	1.82988e25			0.0449727
$207$			2.03731e26i			0.473586i
$208$			3.71267e25i			0.0816503i
$209$	−7.44311e26			−1.54907
$210$	−4.18540e25	−	5.39993e26i	−0.0824546	−	1.06382i
$211$	5.44633e26			1.01591			0.507955	−	0.861384i	$-0.330402\pi$
$211$	5.44633e26			1.01591			0.507955	+	0.861384i	$0.330402\pi$
$212$			1.76745e26i			0.312237i
$213$		−	1.25006e27i		−	2.09203i
$214$	2.74105e26			0.434669
$215$	−7.77888e25	−	1.00362e27i	−0.116916	−	1.50843i
$216$	−1.81510e26			−0.258633
$217$			8.16083e26i			1.10267i
$218$			6.94581e26i			0.890171i
$219$	8.34690e25			0.101489
$220$	−5.70951e26	+	4.42535e25i	−0.658777	+	0.0510607i
$221$	−1.65580e26			−0.181342
$222$			2.62564e26i			0.273009i
$223$			2.25676e24i			0.00222833i	0.999999	+	0.00111416i	$0.000354649\pi$
$223$			2.25676e24i			0.00222833i	−0.999999	+	0.00111416i	$0.999645\pi$
$224$	2.42422e26			0.227363
$225$	−4.17482e26	+	6.51078e25i	−0.371996	+	0.0580142i
$226$	−2.20694e26			−0.186872
$227$			1.50025e27i			1.20744i	0.797195	+	0.603722i	$0.206316\pi$
$227$			1.50025e27i			1.20744i	−0.797195	+	0.603722i	$0.793684\pi$
$228$		−	8.98693e26i		−	0.687639i
$229$	1.86611e27			1.35778			0.678890	−	0.734240i	$-0.262461\pi$
$229$	1.86611e27			1.35778			0.678890	+	0.734240i	$0.262461\pi$
$230$	1.28144e27	−	9.93220e25i	0.886802	−	0.0687346i
$231$	−3.02893e27			−1.99412
$232$		−	6.93285e26i		−	0.434310i
$233$			9.55839e26i			0.569891i	0.958544	+	0.284945i	$0.0919755\pi$
$233$			9.55839e26i			0.569891i	−0.958544	+	0.284945i	$0.908025\pi$
$234$	1.53194e26			0.0869479
$235$	−1.41573e26	−	1.82655e27i	−0.0765068	−	0.987078i
$236$	1.71573e27			0.882999
$237$			4.49329e27i			2.20272i
$238$			1.08117e27i			0.504964i
$239$	1.01079e27			0.449867			0.224934	−	0.974374i	$-0.427783\pi$
$239$	1.01079e27			0.449867			0.224934	+	0.974374i	$0.427783\pi$
$240$	−5.34323e25	−	6.89375e26i	−0.0226660	−	0.292433i
$241$	−3.28450e27			−1.32823			−0.664114	−	0.747631i	$-0.731191\pi$
$241$	−3.28450e27			−1.32823			−0.664114	+	0.747631i	$0.731191\pi$
$242$			1.36874e27i			0.527768i
$243$			1.95016e27i			0.717130i
$244$	1.27869e27			0.448520
$245$	−1.94906e27	+	1.51068e26i	−0.652251	+	0.0505549i
$246$	1.47455e25			0.00470875
$247$		−	1.25613e27i		−	0.382843i
$248$			1.04184e27i			0.303115i
$249$	−2.17661e27			−0.604628
$250$	6.13045e26	+	2.59415e27i	0.162623	+	0.688152i
$251$	4.51246e27			1.14331			0.571657	−	0.820493i	$-0.306301\pi$
$251$	4.51246e27			1.14331			0.571657	+	0.820493i	$0.306301\pi$
$252$		−	1.00029e27i		−	0.242115i
$253$		−	7.18782e27i		−	1.66231i
$254$	9.34686e26			0.206575
$255$	3.07453e27	−	2.38302e26i	0.649481	−	0.0503402i
$256$	3.09485e26			0.0625000
$257$		−	7.11155e27i		−	1.37320i	−0.727036	−	0.686599i	$-0.759103\pi$
$257$		−	7.11155e27i		−	1.37320i	0.727036	−	0.686599i	$-0.240897\pi$
$258$		−	6.79713e27i		−	1.25516i
$259$	2.39633e27			0.423253
$260$	−7.46843e25	−	9.63564e26i	−0.0126193	−	0.162812i
$261$	−2.86067e27			−0.462489
$262$			7.26051e27i			1.12332i
$263$			8.05472e27i			1.19278i	0.802696	+	0.596388i	$0.203398\pi$
$263$			8.05472e27i			1.19278i	−0.802696	+	0.596388i	$0.796602\pi$
$264$	−3.86684e27			−0.548164
$265$	−3.55541e26	−	4.58713e27i	−0.0482572	−	0.622607i
$266$	−8.20205e27			−1.06606
$267$			9.73693e25i			0.0121211i
$268$		−	7.17032e27i		−	0.855044i
$269$	−7.96530e27			−0.910020			−0.455010	−	0.890486i	$-0.650364\pi$
$269$	−7.96530e27			−0.910020			−0.455010	+	0.890486i	$0.650364\pi$
$270$	4.71082e27	−	3.65128e26i	0.515719	−	0.0399725i
$271$	−3.31998e27			−0.348329			−0.174164	−	0.984717i	$-0.555722\pi$
$271$	−3.31998e27			−0.348329			−0.174164	+	0.984717i	$0.555722\pi$
$272$			1.38027e27i			0.138810i
$273$		−	5.11175e27i		−	0.492833i
$274$	−2.85382e27			−0.263813
$275$	1.47291e28	−	2.29706e27i	1.30572	−	0.203632i
$276$	8.67869e27			0.737903
$277$		−	7.28867e27i		−	0.594471i	−0.954804	−	0.297236i	$-0.903935\pi$
$277$		−	7.28867e27i		−	0.594471i	0.954804	−	0.297236i	$-0.0960647\pi$
$278$			5.30341e26i			0.0414992i
$279$	4.29890e27			0.322782
$280$	−6.29168e27	+	4.87658e26i	−0.453366	+	0.0351397i
$281$	7.45197e27			0.515405			0.257702	−	0.966224i	$-0.417035\pi$
$281$	7.45197e27			0.515405			0.257702	+	0.966224i	$0.417035\pi$
$282$		−	1.23705e28i		−	0.821342i
$283$			2.33655e28i			1.48947i	0.667360	+	0.744735i	$0.267424\pi$
$283$			2.33655e28i			1.48947i	−0.667360	+	0.744735i	$0.732576\pi$
$284$	−1.45650e28			−0.891559
$285$	1.80782e27	+	2.33241e28i	0.106277	+	1.37117i
$286$	−5.40482e27			−0.305191
$287$		−	1.34577e26i		−	0.00730010i
$288$		−	1.27701e27i		−	0.0665551i
$289$	1.38117e28			0.691709
$290$	1.39462e27	+	1.79931e28i	0.0671240	+	0.866023i
$291$	5.00696e28			2.31635
$292$		−	9.72531e26i		−	0.0432515i
$293$			3.42399e28i			1.46404i	0.681281	+	0.732022i	$0.261423\pi$
$293$			3.42399e28i			1.46404i	−0.681281	+	0.732022i	$0.738577\pi$
$294$	−1.32002e28			−0.542735
$295$	−4.45290e28	+	3.45137e27i	−1.76072	+	0.136470i
$296$	3.05925e27			0.116348
$297$		−	2.64239e28i		−	0.966713i
$298$			1.89605e28i			0.667363i
$299$	1.21305e28			0.410828
$300$	2.77350e27	+	1.77842e28i	0.0903929	+	0.579614i
$301$	−6.20350e28			−1.94591
$302$		−	1.59953e28i		−	0.482962i
$303$		−	2.45534e28i		−	0.713709i
$304$	−1.04710e28			−0.293051
$305$	−3.31863e28	+	2.57222e27i	−0.894357	+	0.0693201i
$306$	5.69532e27			0.147816
$307$		−	5.46779e28i		−	1.36685i	−0.730022	−	0.683424i	$-0.760490\pi$
$307$		−	5.46779e28i		−	1.36685i	0.730022	−	0.683424i	$-0.239510\pi$
$308$			3.52913e28i			0.849834i
$309$	−3.21643e27			−0.0746193
$310$	−2.09578e27	−	2.70394e28i	−0.0468474	−	0.604417i
$311$	3.11511e28			0.671010			0.335505	−	0.942038i	$-0.391093\pi$
$311$	3.11511e28			0.671010			0.335505	+	0.942038i	$0.391093\pi$
$312$		−	6.52585e27i		−	0.135475i
$313$		−	7.85021e27i		−	0.157080i	−0.996911	−	0.0785401i	$-0.974974\pi$
$313$		−	7.85021e27i		−	0.157080i	0.996911	−	0.0785401i	$-0.0250259\pi$
$314$	3.60526e28			0.695418
$315$	2.01220e27	+	2.59611e28i	0.0374196	+	0.482782i
$316$	5.23532e28			0.938733
$317$			4.27638e28i			0.739426i	0.929146	+	0.369713i	$0.120544\pi$
$317$			4.27638e28i			0.739426i	−0.929146	+	0.369713i	$0.879456\pi$
$318$		−	3.10669e28i		−	0.518067i
$319$	1.00927e29			1.62336
$320$	−8.03219e27	+	6.22562e26i	−0.124626	+	0.00965957i
$321$	−4.81802e28			−0.721208
$322$		−	7.92073e28i		−	1.14399i
$323$		−	4.66996e28i		−	0.650854i
$324$	4.59003e28			0.617373
$325$	3.87662e27	+	2.48575e28i	0.0503263	+	0.322700i
$326$	−1.98119e28			−0.248270
$327$		−	1.22088e29i		−	1.47698i
$328$		−	1.71806e26i		−	0.00200673i
$329$	−1.12902e29			−1.27335
$330$	1.00358e29	−	7.77856e27i	1.09305	−	0.0847206i
$331$	−2.08280e28			−0.219092			−0.109546	−	0.993982i	$-0.534940\pi$
$331$	−2.08280e28			−0.219092			−0.109546	+	0.993982i	$0.534940\pi$
$332$			2.53606e28i			0.257674i
$333$		−	1.26232e28i		−	0.123897i
$334$	−7.35791e28			−0.697702
$335$	1.44239e28	+	1.86094e29i	0.132150	+	1.70497i
$336$	−4.26112e28			−0.377244
$337$		−	1.66157e29i		−	1.42159i	−0.703399	−	0.710795i	$-0.748335\pi$
$337$		−	1.66157e29i		−	1.42159i	0.703399	−	0.710795i	$-0.251665\pi$
$338$			7.63906e28i			0.631681i
$339$	3.87920e28			0.310060
$340$	−2.77655e27	−	3.58226e28i	−0.0214535	−	0.276790i
$341$	−1.51669e29			−1.13298
$342$			4.32061e28i			0.312065i
$343$		−	6.36785e28i		−	0.444744i
$344$	−7.91961e28			−0.534911
$345$	−2.25242e29	+	1.74581e28i	−1.47139	+	0.114045i
$346$	2.04719e29			1.29355
$347$			2.49311e29i			1.52388i	0.647646	+	0.761942i	$0.275754\pi$
$347$			2.49311e29i			1.52388i	−0.647646	+	0.761942i	$0.724246\pi$
$348$			1.21861e29i			0.720613i
$349$	−3.48584e28			−0.199441			−0.0997205	−	0.995015i	$-0.531795\pi$
$349$	−3.48584e28			−0.199441			−0.0997205	+	0.995015i	$0.531795\pi$
$350$	1.62310e29	−	2.53128e28i	0.898591	−	0.140138i
$351$	4.45942e28			0.238916
$352$			4.50541e28i			0.233611i
$353$			3.30374e29i			1.65805i	0.559214	+	0.829023i	$0.311103\pi$
$353$			3.30374e29i			1.65805i	−0.559214	+	0.829023i	$0.688897\pi$
$354$	−3.01578e29			−1.46508
$355$	3.78012e29	−	2.92991e28i	1.77779	−	0.137793i
$356$	1.13449e27			0.00516565
$357$		−	1.90041e29i		−	0.837842i
$358$			4.94028e28i			0.210910i
$359$	3.98776e29			1.64871			0.824353	−	0.566076i	$-0.191539\pi$
$359$	3.98776e29			1.64871			0.824353	+	0.566076i	$0.191539\pi$
$360$	2.56885e27	+	3.31428e28i	0.0102863	+	0.132712i
$361$	9.64448e28			0.374064
$362$		−	3.93126e28i		−	0.147701i
$363$		−	2.40586e29i		−	0.875679i
$364$	−5.95592e28			−0.210031
$365$	1.95635e27	+	2.52405e28i	0.00668465	+	0.0862443i
$366$	−2.24758e29			−0.744189
$367$			4.16465e29i			1.33634i	0.744007	+	0.668172i	$0.232923\pi$
$367$			4.16465e29i			1.33634i	−0.744007	+	0.668172i	$0.767077\pi$
$368$		−	1.01119e29i		−	0.314472i
$369$	−7.08914e26			−0.00213693
$370$	−7.93979e28	+	6.15400e27i	−0.232001	+	0.0179820i
$371$	−2.83537e29			−0.803173
$372$		−	1.83127e29i		−	0.502932i
$373$		−	3.35562e28i		−	0.0893555i	−0.999001	−	0.0446777i	$-0.985774\pi$
$373$		−	3.35562e28i		−	0.0893555i	0.999001	−	0.0446777i	$-0.0142261\pi$
$374$	−2.00936e29			−0.518841
$375$	−1.07757e29	−	4.55980e29i	−0.269826	−	1.14179i
$376$	−1.44134e29			−0.350031
$377$			1.70329e29i			0.401202i
$378$		−	2.91182e29i		−	0.665286i
$379$	3.54836e29			0.786460			0.393230	−	0.919440i	$-0.371358\pi$
$379$	3.54836e29			0.786460			0.393230	+	0.919440i	$0.371358\pi$
$380$	2.71759e29	−	2.10636e28i	0.584350	−	0.0452920i
$381$	−1.64292e29			−0.342752
$382$			1.35522e28i			0.0274336i
$383$			3.11489e29i			0.611867i	0.952053	+	0.305933i	$0.0989685\pi$
$383$			3.11489e29i			0.611867i	−0.952053	+	0.305933i	$0.901032\pi$
$384$	−5.43990e28			−0.103701
$385$	−7.09921e28	−	9.15929e29i	−0.131344	−	1.69458i
$386$	1.24923e29			0.224330
$387$			3.26783e29i			0.569618i
$388$		−	5.83382e29i		−	0.987161i
$389$	5.19687e29			0.853731			0.426866	−	0.904315i	$-0.359618\pi$
$389$	5.19687e29			0.853731			0.426866	+	0.904315i	$0.359618\pi$
$390$	1.31275e28	+	1.69368e29i	0.0209381	+	0.270140i
$391$	4.50978e29			0.698430
$392$			1.53801e29i			0.231297i
$393$		−	1.27620e30i		−	1.86382i
$394$	−6.74002e29			−0.955992
$395$	−1.35874e30	+	1.05314e29i	−1.87185	+	0.145084i
$396$	1.85905e29			0.248769
$397$			2.15023e29i			0.279508i	0.990186	+	0.139754i	$0.0446312\pi$
$397$			2.15023e29i			0.279508i	−0.990186	+	0.139754i	$0.955369\pi$
$398$			4.47408e29i			0.565000i
$399$	1.44170e30			1.76883
$400$	2.07210e29	−	3.23152e28i	0.247014	−	0.0385228i
$401$	5.62716e28			0.0651822			0.0325911	−	0.999469i	$-0.489624\pi$
$401$	5.62716e28			0.0651822			0.0325911	+	0.999469i	$0.489624\pi$
$402$			1.26035e30i			1.41870i
$403$		−	2.55964e29i		−	0.280008i
$404$	−2.86082e29			−0.304161
$405$	−1.19127e30	+	9.23333e28i	−1.23105	+	0.0954170i
$406$	1.11218e30			1.11718
$407$			4.45358e29i			0.434884i
$408$		−	2.42613e29i		−	0.230315i
$409$	−3.26056e29			−0.300936			−0.150468	−	0.988615i	$-0.548078\pi$
$409$	−3.26056e29			−0.300936			−0.150468	+	0.988615i	$0.548078\pi$
$410$	3.45606e26	+	4.45895e27i	0.000310146	+	0.00400146i
$411$	5.01624e29			0.437721
$412$			3.74759e28i			0.0318005i
$413$			2.75240e30i			2.27136i
$414$	−4.17242e29			−0.334876
$415$	−5.10155e28	−	6.58194e29i	−0.0398244	−	0.513808i
$416$	−7.60354e28			−0.0577355
$417$		−	9.32195e28i		−	0.0688561i
$418$		−	1.52435e30i		−	1.09536i
$419$	−3.41045e29			−0.238424			−0.119212	−	0.992869i	$-0.538037\pi$
$419$	−3.41045e29			−0.238424			−0.119212	+	0.992869i	$0.538037\pi$
$420$	1.10591e30	−	8.57170e28i	0.752231	−	0.0583042i
$421$	−2.52874e30			−1.67363			−0.836816	−	0.547483i	$-0.815586\pi$
$421$	−2.52874e30			−1.67363			−0.836816	+	0.547483i	$0.815586\pi$
$422$			1.11541e30i			0.718357i
$423$			5.94734e29i			0.372742i
$424$	−3.61973e29			−0.220785
$425$	1.44122e29	+	9.24134e29i	0.0855574	+	0.548608i
$426$	2.56013e30			1.47929
$427$			2.05129e30i			1.15374i
$428$			5.61367e29i			0.307357i
$429$	9.50019e29			0.506376
$430$	2.05541e30	−	1.59311e29i	1.06662	−	0.0826723i
$431$	−4.34154e29			−0.219359			−0.109680	−	0.993967i	$-0.534982\pi$
$431$	−4.34154e29			−0.219359			−0.109680	+	0.993967i	$0.534982\pi$
$432$		−	3.71733e29i		−	0.182881i
$433$		−	2.24042e30i		−	1.07329i	−0.843807	−	0.536647i	$-0.819691\pi$
$433$		−	2.24042e30i		−	1.07329i	0.843807	−	0.536647i	$-0.180309\pi$
$434$	−1.67134e30			−0.779709
$435$	−2.45136e29	−	3.16270e30i	−0.111373	−	1.43692i
$436$	−1.42250e30			−0.629446
$437$			3.42123e30i			1.47450i
$438$			1.70944e29i			0.0717634i
$439$	−3.17975e30			−1.30032			−0.650160	−	0.759797i	$-0.725298\pi$
$439$	−3.17975e30			−1.30032			−0.650160	+	0.759797i	$0.725298\pi$
$440$	−9.06312e28	−	1.16931e30i	−0.0361054	−	0.465826i
$441$	6.34623e29			0.246304
$442$		−	3.39109e29i		−	0.128228i
$443$		−	3.68702e30i		−	1.35842i	−0.733946	−	0.679208i	$-0.762323\pi$
$443$		−	3.68702e30i		−	1.35842i	0.733946	−	0.679208i	$-0.237677\pi$
$444$	−5.37732e29			−0.193046
$445$	−2.94439e28	+	2.28215e27i	−0.0103004	+	0.000798368i
$446$	−4.62183e27			−0.00157566
$447$		−	3.33273e30i		−	1.10730i
$448$			4.96480e29i			0.160770i
$449$	3.07040e30			0.969085			0.484542	−	0.874768i	$-0.338986\pi$
$449$	3.07040e30			0.969085			0.484542	+	0.874768i	$0.338986\pi$
$450$	−1.33341e29	−	8.55002e29i	−0.0410222	−	0.263041i
$451$	2.50111e28			0.00750071
$452$		−	4.51981e29i		−	0.132138i
$453$			2.81154e30i			0.801336i
$454$	−3.07251e30			−0.853791
$455$	1.54576e30	−	1.19810e29i	0.418805	−	0.0324609i
$456$	1.84052e30			0.486234
$457$		−	6.83222e30i		−	1.76005i	−0.474925	−	0.880026i	$-0.657525\pi$
$457$		−	6.83222e30i		−	1.76005i	0.474925	−	0.880026i	$-0.342475\pi$
$458$			3.82180e30i			0.960096i
$459$	1.65789e30			0.406171
$460$	2.03412e29	+	2.62438e30i	0.0486027	+	0.627064i
$461$	2.18707e30			0.509686			0.254843	−	0.966982i	$-0.417976\pi$
$461$	2.18707e30			0.509686			0.254843	+	0.966982i	$0.417976\pi$
$462$		−	6.20324e30i		−	1.41005i
$463$		−	4.50181e29i		−	0.0998173i	−0.998754	−	0.0499086i	$-0.984107\pi$
$463$		−	4.50181e29i		−	0.0998173i	0.998754	−	0.0499086i	$-0.0158930\pi$
$464$	1.41985e30			0.307104
$465$	3.68380e29	+	4.75278e30i	0.0777298	+	1.00286i
$466$	−1.95756e30			−0.402974
$467$			2.21548e30i			0.444963i	0.974937	+	0.222482i	$0.0714157\pi$
$467$			2.21548e30i			0.444963i	−0.974937	+	0.222482i	$0.928584\pi$
$468$			3.13741e29i			0.0614815i
$469$	1.15027e31			2.19945
$470$	3.74078e30	−	2.89941e29i	0.697969	−	0.0540985i
$471$	−6.33707e30			−1.15385
$472$			3.51381e30i			0.624375i
$473$		−	1.15292e31i		−	1.99938i
$474$	−9.20227e30			−1.55756
$475$	−7.01071e30	+	1.09335e30i	−1.15820	+	0.180626i
$476$	−2.21424e30			−0.357063
$477$			1.49359e30i			0.235110i
$478$			2.07010e30i			0.318104i
$479$	2.93958e30			0.440989			0.220494	−	0.975388i	$-0.429233\pi$
$479$	2.93958e30			0.440989			0.220494	+	0.975388i	$0.429233\pi$
$480$	1.41184e30	−	1.09429e29i	0.206781	−	0.0160273i
$481$	−7.51607e29			−0.107479
$482$		−	6.72665e30i		−	0.939200i
$483$			1.39225e31i			1.89812i
$484$	−2.80317e30			−0.373188
$485$	1.17353e30	+	1.51407e31i	0.152569	+	1.96842i
$486$	−3.99393e30			−0.507087
$487$			1.09910e31i			1.36287i	0.731879	+	0.681435i	$0.238644\pi$
$487$			1.09910e31i			1.36287i	−0.731879	+	0.681435i	$0.761356\pi$
$488$			2.61875e30i			0.317151i
$489$	3.48239e30			0.411932
$490$	−3.09388e29	−	3.99167e30i	−0.0357477	−	0.461211i
$491$	−1.37843e31			−1.55578			−0.777890	−	0.628400i	$-0.783710\pi$
$491$	−1.37843e31			−1.55578			−0.777890	+	0.628400i	$0.783710\pi$
$492$			3.01988e28i			0.00332959i
$493$			6.33235e30i			0.682065i
$494$	2.57256e30			0.270711
$495$	−4.82486e30	+	3.73967e29i	−0.496049	+	0.0384480i
$496$	−2.13369e30			−0.214335
$497$		−	2.33654e31i		−	2.29338i
$498$		−	4.45770e30i		−	0.427537i
$499$	1.42219e31			1.33291			0.666455	−	0.745546i	$-0.267811\pi$
$499$	1.42219e31			1.33291			0.666455	+	0.745546i	$0.267811\pi$
$500$	−5.31281e30	+	1.25552e30i	−0.486597	+	0.114992i
$501$	1.29332e31			1.15764
$502$			9.24151e30i			0.808444i
$503$		−	3.77197e30i		−	0.322505i	−0.986913	−	0.161253i	$-0.948447\pi$
$503$		−	3.77197e30i		−	0.322505i	0.986913	−	0.161253i	$-0.0515534\pi$
$504$	2.04860e30			0.171201
$505$	7.42479e30	−	5.75484e29i	0.606504	−	0.0470091i
$506$	1.47207e31			1.17543
$507$		−	1.34274e31i		−	1.04809i
$508$			1.91424e30i			0.146071i
$509$	−5.99166e30			−0.446985			−0.223492	−	0.974706i	$-0.571746\pi$
$509$	−5.99166e30			−0.446985			−0.223492	+	0.974706i	$0.571746\pi$
$510$	4.88042e29	+	6.29664e30i	0.0355959	+	0.459253i
$511$	1.56015e30			0.111257
$512$			6.33825e29i			0.0441942i
$513$			1.25771e31i			0.857496i
$514$	1.45645e31			0.970998
$515$	−7.53868e28	−	9.72628e29i	−0.00491487	−	0.0634109i
$516$	1.39205e31			0.887531
$517$		−	2.09827e31i		−	1.30834i
$518$			4.90769e30i			0.299285i
$519$	−3.59840e31			−2.14627
$520$	1.97338e30	−	1.52953e29i	0.115126	−	0.00892320i
$521$	7.13241e30			0.407008			0.203504	−	0.979074i	$-0.434767\pi$
$521$	7.13241e30			0.407008			0.203504	+	0.979074i	$0.434767\pi$
$522$		−	5.85865e30i		−	0.327029i
$523$		−	1.12628e31i		−	0.615003i	−0.951548	−	0.307501i	$-0.900507\pi$
$523$		−	1.12628e31i		−	0.615003i	0.951548	−	0.307501i	$-0.0994929\pi$
$524$	−1.48695e31			−0.794305
$525$	−2.85296e31	+	4.44930e30i	−1.49095	+	0.232519i
$526$	−1.64961e31			−0.843420
$527$		−	9.51601e30i		−	0.476028i
$528$		−	7.91929e30i		−	0.387611i
$529$	−1.21584e31			−0.582286
$530$	9.39445e30	−	7.28148e29i	0.440249	−	0.0341230i
$531$	1.44989e31			0.664886
$532$		−	1.67978e31i		−	0.753821i
$533$			4.22099e28i			0.00185375i
$534$	−1.99412e29			−0.00857092
$535$	−1.12925e30	−	1.45694e31i	−0.0475031	−	0.612877i
$536$	1.46848e31			0.604607
$537$		−	8.68366e30i		−	0.349944i
$538$		−	1.63129e31i		−	0.643481i
$539$	−2.23901e31			−0.864539
$540$	7.47781e29	+	9.64775e30i	0.0282648	+	0.364668i
$541$	1.16570e31			0.431339			0.215669	−	0.976466i	$-0.430807\pi$
$541$	1.16570e31			0.431339			0.215669	+	0.976466i	$0.430807\pi$
$542$		−	6.79933e30i		−	0.246306i
$543$			6.91007e30i			0.245067i
$544$	−2.82678e30			−0.0981534
$545$	3.69188e31	−	2.86151e30i	1.25513	−	0.0972828i
$546$	1.04689e31			0.348485
$547$			5.05504e31i			1.64767i	0.566829	+	0.823835i	$0.308170\pi$
$547$			5.05504e31i			1.64767i	−0.566829	+	0.823835i	$0.691830\pi$
$548$		−	5.84463e30i		−	0.186544i
$549$	1.08056e31			0.337729
$550$	4.70438e30	+	3.01652e31i	0.143990	+	0.923285i
$551$	−4.80388e31			−1.43995
$552$			1.77739e31i			0.521776i
$553$			8.39858e31i			2.41472i
$554$	1.49272e31			0.420355
$555$	1.39560e31	−	1.08171e30i	0.384938	−	0.0298359i
$556$	−1.08614e30			−0.0293444
$557$		−	2.05058e31i		−	0.542677i	−0.962484	−	0.271338i	$-0.912534\pi$
$557$		−	2.05058e31i		−	0.542677i	0.962484	−	0.271338i	$-0.0874663\pi$
$558$			8.80415e30i			0.228241i
$559$	1.94572e31			0.494134
$560$	−9.98724e29	−	1.28854e31i	−0.0248475	−	0.320578i
$561$	3.53191e31			0.860867
$562$			1.52616e31i			0.364446i
$563$		−	6.74592e31i		−	1.57832i	−0.614189	−	0.789159i	$-0.710517\pi$
$563$		−	6.74592e31i		−	1.57832i	0.614189	−	0.789159i	$-0.289483\pi$
$564$	2.53349e31			0.580776
$565$	9.09209e29	+	1.17305e31i	0.0204224	+	0.263486i
$566$	−4.78526e31			−1.05321
$567$			7.36339e31i			1.58808i
$568$		−	2.98292e31i		−	0.630428i
$569$	−1.17162e31			−0.242659			−0.121330	−	0.992612i	$-0.538716\pi$
$569$	−1.17162e31			−0.242659			−0.121330	+	0.992612i	$0.538716\pi$
$570$	−4.77679e31	+	3.70241e30i	−0.969560	+	0.0751490i
$571$	6.13275e30			0.121994			0.0609972	−	0.998138i	$-0.480572\pi$
$571$	6.13275e30			0.121994			0.0609972	+	0.998138i	$0.480572\pi$
$572$		−	1.10691e31i		−	0.215803i
$573$		−	2.38211e30i		−	0.0455181i
$574$	2.75613e29			0.00516195
$575$	−1.05584e31	−	6.77025e31i	−0.193830	−	1.24287i
$576$	2.61532e30			0.0470616
$577$			4.27869e31i			0.754725i	0.926066	+	0.377363i	$0.123169\pi$
$577$			4.27869e31i			0.754725i	−0.926066	+	0.377363i	$0.876831\pi$
$578$			2.82865e31i			0.489112i
$579$	−2.19580e31			−0.372211
$580$	−3.68499e31	+	2.85618e30i	−0.612371	+	0.0474639i
$581$	−4.06838e31			−0.662821
$582$			1.02543e32i			1.63791i
$583$		−	5.26953e31i		−	0.825246i
$584$	1.99174e30			0.0305834
$585$	−6.31124e29	−	8.14266e30i	−0.00950216	−	0.122595i
$586$	−7.01232e31			−1.03524
$587$			2.66497e31i			0.385793i	0.981219	+	0.192897i	$0.0617882\pi$
$587$			2.66497e31i			0.385793i	−0.981219	+	0.192897i	$0.938212\pi$
$588$		−	2.70341e31i		−	0.383771i
$589$	7.21908e31			1.00498
$590$	−7.06841e30	−	9.11954e31i	−0.0964991	−	1.24502i
$591$	1.18471e32			1.58619
$592$			6.26534e30i			0.0822706i
$593$		−	1.92592e31i		−	0.248032i	−0.992280	−	0.124016i	$-0.960423\pi$
$593$		−	1.92592e31i		−	0.248032i	0.992280	−	0.124016i	$-0.0395775\pi$
$594$	5.41161e31			0.683569
$595$	5.74672e31	−	4.45419e30i	0.711991	−	0.0551853i
$596$	−3.88311e31			−0.471897
$597$		−	7.86422e31i		−	0.937456i
$598$			2.48433e31i			0.290499i
$599$	8.70289e31			0.998286			0.499143	−	0.866520i	$-0.333648\pi$
$599$	8.70289e31			0.998286			0.499143	+	0.866520i	$0.333648\pi$
$600$	−3.64220e31	+	5.68014e30i	−0.409849	+	0.0639174i
$601$	−1.25442e32			−1.38480			−0.692398	−	0.721516i	$-0.743446\pi$
$601$	−1.25442e32			−1.38480			−0.692398	+	0.721516i	$0.743446\pi$
$602$		−	1.27048e32i		−	1.37596i
$603$		−	6.05932e31i		−	0.643836i
$604$	3.27584e31			0.341506
$605$	7.27518e31	−	5.63888e30i	0.744144	−	0.0576774i
$606$	5.02853e31			0.504668
$607$			3.32324e31i			0.327259i	0.986522	+	0.163630i	$0.0523202\pi$
$607$			3.32324e31i			0.327259i	−0.986522	+	0.163630i	$0.947680\pi$
$608$		−	2.14447e31i		−	0.207218i
$609$	−1.95491e32			−1.85365
$610$	−5.26790e30	−	6.79656e31i	−0.0490167	−	0.632406i
$611$	3.54114e31			0.323348
$612$			1.16640e31i			0.104522i
$613$			2.65035e31i			0.233082i	0.993186	+	0.116541i	$0.0371806\pi$
$613$			2.65035e31i			0.233082i	−0.993186	+	0.116541i	$0.962819\pi$
$614$	1.11980e32			0.966508
$615$	−6.07481e28	−	7.83761e29i	−0.000514599	−	0.00663926i
$616$	−7.22765e31			−0.600923
$617$			2.28555e31i			0.186514i	0.995642	+	0.0932572i	$0.0297279\pi$
$617$			2.28555e31i			0.186514i	−0.995642	+	0.0932572i	$0.970272\pi$
$618$		−	6.58724e30i		−	0.0527638i
$619$	−6.33662e31			−0.498213			−0.249107	−	0.968476i	$-0.580137\pi$
$619$	−6.33662e31			−0.498213			−0.249107	+	0.968476i	$0.580137\pi$
$620$	5.53766e31	−	4.29215e30i	0.427387	−	0.0331261i
$621$	−1.21458e32			−0.920176
$622$			6.37975e31i			0.474476i
$623$			1.81996e30i			0.0132877i
$624$	1.33650e31			0.0957954
$625$	1.35360e32	−	4.32722e31i	0.952512	−	0.304501i
$626$	1.60772e31			0.111072
$627$			2.67939e32i			1.81744i
$628$			7.38358e31i			0.491735i
$629$	−2.79426e31			−0.182720
$630$	−5.31682e31	+	4.12098e30i	−0.341378	+	0.0264597i
$631$	9.58847e31			0.604521			0.302261	−	0.953225i	$-0.402259\pi$
$631$	9.58847e31			0.604521			0.302261	+	0.953225i	$0.402259\pi$
$632$			1.07219e32i			0.663784i
$633$		−	1.96058e32i		−	1.19191i
$634$	−8.75802e31			−0.522853
$635$	−3.85069e30	−	4.96810e31i	−0.0225757	−	0.291268i
$636$	6.36250e31			0.366329
$637$		−	3.77865e31i		−	0.213665i
$638$			2.06698e32i			1.14789i
$639$	−1.23083e32			−0.671331
$640$	−1.27501e30	−	1.64499e31i	−0.00683035	−	0.0881240i
$641$	1.39689e32			0.735015			0.367508	−	0.930021i	$-0.380211\pi$
$641$	1.39689e32			0.735015			0.367508	+	0.930021i	$0.380211\pi$
$642$		−	9.86730e31i		−	0.509971i
$643$			1.01176e32i			0.513631i	0.966460	+	0.256816i	$0.0826733\pi$
$643$			1.01176e32i			0.513631i	−0.966460	+	0.256816i	$0.917327\pi$
$644$	1.62216e32			0.808924
$645$	−3.61285e32	+	2.80026e31i	−1.76975	+	0.137171i
$646$	9.56407e31			0.460224
$647$			3.99384e32i			1.88796i	0.330008	+	0.943978i	$0.392949\pi$
$647$			3.99384e32i			1.88796i	−0.330008	+	0.943978i	$0.607051\pi$
$648$			9.40038e31i			0.436549i
$649$	−5.11533e32			−2.33378
$650$	−5.09082e31	+	7.93932e30i	−0.228184	+	0.0355861i
$651$	2.93776e32			1.29370
$652$		−	4.05748e31i		−	0.175553i
$653$		−	2.17025e32i		−	0.922589i	−0.887247	−	0.461294i	$-0.847385\pi$
$653$		−	2.17025e32i		−	0.922589i	0.887247	−	0.461294i	$-0.152615\pi$
$654$	2.50037e32			1.04438
$655$	3.85915e32	−	2.99116e31i	1.58386	−	0.122762i
$656$	3.51858e29			0.00141897
$657$		−	8.21844e30i		−	0.0325677i
$658$		−	2.31222e32i		−	0.900393i
$659$	−4.36357e32			−1.66978			−0.834891	−	0.550415i	$-0.814469\pi$
$659$	−4.36357e32			−1.66978			−0.834891	+	0.550415i	$0.814469\pi$
$660$	1.59305e31	+	2.05533e32i	0.0599065	+	0.772903i
$661$	5.27320e31			0.194876			0.0974379	−	0.995242i	$-0.468935\pi$
$661$	5.27320e31			0.194876			0.0974379	+	0.995242i	$0.468935\pi$
$662$		−	4.26558e31i		−	0.154921i
$663$			5.96061e31i			0.212758i
$664$	−5.19385e31			−0.182203
$665$	3.37906e31	+	4.35960e32i	0.116506	+	1.50313i
$666$	2.58523e31			0.0876085
$667$		−	4.63911e32i		−	1.54521i
$668$		−	1.50690e32i		−	0.493350i
$669$	8.12392e29			0.00261436
$670$	−3.81121e32	+	2.95401e31i	−1.20560	+	0.0934440i
$671$	−3.81232e32			−1.18544
$672$		−	8.72677e31i		−	0.266752i
$673$			3.03653e32i			0.912440i	0.889867	+	0.456220i	$0.150797\pi$
$673$			3.03653e32i			0.912440i	−0.889867	+	0.456220i	$0.849203\pi$
$674$	3.40289e32			1.00522
$675$	−3.88150e31	−	2.48888e32i	−0.112721	−	0.722787i
$676$	−1.56448e32			−0.446666
$677$		−	5.62926e32i		−	1.58009i	−0.613049	−	0.790045i	$-0.710057\pi$
$677$		−	5.62926e32i		−	1.58009i	0.613049	−	0.790045i	$-0.289943\pi$
$678$			7.94460e31i			0.219245i
$679$	9.35869e32			2.53929
$680$	7.33647e31	−	5.68638e30i	0.195720	−	0.0151699i
$681$	5.40064e32			1.41662
$682$		−	3.10618e32i		−	0.801136i
$683$			1.74296e32i			0.442029i	0.975271	+	0.221014i	$0.0709368\pi$
$683$			1.74296e32i			0.442029i	−0.975271	+	0.221014i	$0.929063\pi$
$684$	−8.84862e31			−0.220663
$685$	1.17571e31	+	1.51688e32i	0.0288309	+	0.371972i
$686$	1.30414e32			0.314482
$687$		−	6.71768e32i		−	1.59300i
$688$		−	1.62194e32i		−	0.378239i
$689$	8.89310e31			0.203954
$690$	−3.57542e31	−	4.61295e32i	−0.0806422	−	1.04043i
$691$	−1.56242e32			−0.346577			−0.173288	−	0.984871i	$-0.555439\pi$
$691$	−1.56242e32			−0.346577			−0.173288	+	0.984871i	$0.555439\pi$
$692$			4.19265e32i			0.914678i
$693$			2.98231e32i			0.639912i
$694$	−5.10588e32			−1.07755
$695$	2.81890e31	−	2.18488e30i	0.0585133	−	0.00453527i
$696$	−2.49571e32			−0.509550
$697$			1.56925e30i			0.00315148i
$698$		−	7.13899e31i		−	0.141026i
$699$	3.44085e32			0.668619
$700$	5.18406e31	+	3.32410e32i	0.0990929	+	0.635399i
$701$	−7.07181e32			−1.32976			−0.664880	−	0.746950i	$-0.731517\pi$
$701$	−7.07181e32			−1.32976			−0.664880	+	0.746950i	$0.731517\pi$
$702$			9.13288e31i			0.168939i
$703$		−	2.11980e32i		−	0.385752i
$704$	−9.22708e31			−0.165188
$705$	−6.57526e32	+	5.09638e31i	−1.15808	+	0.0897608i
$706$	−6.76606e32			−1.17242
$707$		−	4.58936e32i		−	0.782401i
$708$		−	6.17632e32i		−	1.03597i
$709$	5.15487e32			0.850719			0.425360	−	0.905024i	$-0.360148\pi$
$709$	5.15487e32			0.850719			0.425360	+	0.905024i	$0.360148\pi$
$710$	6.00045e31	+	7.74169e32i	0.0974346	+	1.25708i
$711$	4.42414e32			0.706852
$712$			2.32343e30i			0.00365267i
$713$			6.97147e32i			1.07844i
$714$	3.89204e32			0.592444
$715$	2.22666e31	+	2.87280e32i	0.0333530	+	0.430314i
$716$	−1.01177e32			−0.149136
$717$		−	3.63866e32i		−	0.527802i
$718$			8.16694e32i			1.16581i
$719$	−7.07190e32			−0.993468			−0.496734	−	0.867903i	$-0.665468\pi$
$719$	−7.07190e32			−0.993468			−0.496734	+	0.867903i	$0.665468\pi$
$720$	−6.78765e31	+	5.26100e30i	−0.0938417	+	0.00727352i
$721$	−6.01194e31			−0.0818011
$722$			1.97519e32i			0.264503i
$723$			1.18236e33i			1.55833i
$724$	8.05121e31			0.104440
$725$	9.50635e32	−	1.48255e32i	1.21374	−	0.189288i
$726$	4.92721e32			0.619198
$727$		−	5.40399e32i		−	0.668449i	−0.942493	−	0.334225i	$-0.891526\pi$
$727$		−	5.40399e32i		−	0.668449i	0.942493	−	0.334225i	$-0.108474\pi$
$728$		−	1.21977e32i		−	0.148514i
$729$	−3.28231e32			−0.393380
$730$	−5.16926e31	+	4.00661e30i	−0.0609839	+	0.00472676i
$731$	7.23364e32			0.840054
$732$		−	4.60305e32i		−	0.526221i
$733$		−	7.35726e32i		−	0.827981i	−0.910281	−	0.413991i	$-0.864135\pi$
$733$		−	7.35726e32i		−	0.827981i	0.910281	−	0.413991i	$-0.135865\pi$
$734$	−8.52920e32			−0.944938
$735$	5.43820e31	+	7.01627e32i	0.0593131	+	0.765247i
$736$	2.07092e32			0.222366
$737$			2.13778e33i			2.25989i
$738$		−	1.45186e30i		−	0.00151104i
$739$	1.36373e33			1.39739			0.698695	−	0.715420i	$-0.253765\pi$
$739$	1.36373e33			1.39739			0.698695	+	0.715420i	$0.253765\pi$
$740$	−1.26034e31	−	1.62607e32i	−0.0127152	−	0.164049i
$741$	−4.52186e32			−0.449167
$742$		−	5.80683e32i		−	0.567929i
$743$			1.10539e33i			1.06449i	0.846589	+	0.532247i	$0.178652\pi$
$743$			1.10539e33i			1.06449i	−0.846589	+	0.532247i	$0.821348\pi$
$744$	3.75045e32			0.355627
$745$	1.00780e33	−	7.81128e31i	0.940972	−	0.0729332i
$746$	6.87231e31			0.0631839
$747$			2.14311e32i			0.194025i
$748$		−	4.11517e32i		−	0.366876i
$749$	−9.00553e32			−0.790621
$750$	9.33848e32	−	2.20686e32i	0.807368	−	0.190796i
$751$	−1.15498e33			−0.983363			−0.491682	−	0.870775i	$-0.663618\pi$
$751$	−1.15498e33			−0.983363			−0.491682	+	0.870775i	$0.663618\pi$
$752$		−	2.95187e32i		−	0.247510i
$753$		−	1.62441e33i		−	1.34138i
$754$	−3.48833e32			−0.283692
$755$	−8.50192e32	+	6.58970e31i	−0.680969	+	0.0527808i
$756$	5.96340e32			0.470428
$757$		−	1.13797e33i		−	0.884154i	−0.896977	−	0.442077i	$-0.854242\pi$
$757$		−	1.13797e33i		−	0.884154i	0.896977	−	0.442077i	$-0.145758\pi$
$758$			7.26704e32i			0.556111i
$759$	−2.58749e33			−1.95029
$760$	4.31383e31	+	5.56563e32i	0.0320263	+	0.413198i
$761$	−1.23949e33			−0.906402			−0.453201	−	0.891408i	$-0.649718\pi$
$761$	−1.23949e33			−0.906402			−0.453201	+	0.891408i	$0.649718\pi$
$762$		−	3.36471e32i		−	0.242362i
$763$		−	2.28200e33i		−	1.61914i
$764$	−2.77550e31			−0.0193985
$765$	−2.34634e31	−	3.02721e32i	−0.0161542	−	0.208419i
$766$	−6.37930e32			−0.432655
$767$		−	8.63286e32i		−	0.576777i
$768$		−	1.11409e32i		−	0.0733275i
$769$	1.94873e33			1.26357			0.631783	−	0.775145i	$-0.282323\pi$
$769$	1.94873e33			1.26357			0.631783	+	0.775145i	$0.282323\pi$
$770$	1.87582e33	−	1.45392e32i	1.19825	−	0.0928746i
$771$	−2.56003e33			−1.61109
$772$			2.55842e32i			0.158625i
$773$			6.94776e32i			0.424405i	0.977226	+	0.212203i	$0.0680637\pi$
$773$			6.94776e32i			0.424405i	−0.977226	+	0.212203i	$0.931936\pi$
$774$	−6.69252e32			−0.402780
$775$	−1.42858e33	+	2.22792e32i	−0.847099	+	0.132108i
$776$	1.19477e33			0.698028
$777$		−	8.62638e32i		−	0.496577i
$778$			1.06432e33i			0.603679i
$779$	−1.19047e31			−0.00665330
$780$	−3.46866e32	+	2.68850e31i	−0.191018	+	0.0148055i
$781$	4.34246e33			2.35640
$782$			9.23604e32i			0.493865i
$783$		−	1.70543e33i		−	0.898615i
$784$	−3.14985e32			−0.163552
$785$	−1.48529e32	−	1.91629e33i	−0.0759992	−	0.980528i
$786$	2.61366e33			1.31792
$787$			1.97524e33i			0.981547i	0.871287	+	0.490773i	$0.163286\pi$
$787$			1.97524e33i			0.981547i	−0.871287	+	0.490773i	$0.836714\pi$
$788$		−	1.38036e33i		−	0.675989i
$789$	2.89956e33			1.39941
$790$	−2.15683e32	−	2.78271e33i	−0.102590	−	1.32360i
$791$	7.25075e32			0.339902
$792$			3.80733e32i			0.175906i
$793$		−	6.43385e32i		−	0.292974i
$794$	−4.40367e32			−0.197642
$795$	−1.65129e33	+	1.27989e32i	−0.730467	+	0.0566173i
$796$	−9.16292e32			−0.399516
$797$			2.43925e33i			1.04830i	0.851626	+	0.524150i	$0.175617\pi$
$797$			2.43925e33i			1.04830i	−0.851626	+	0.524150i	$0.824383\pi$
$798$			2.95259e33i			1.25075i
$799$	1.31650e33			0.549708
$800$	6.61816e31	+	4.24367e32i	0.0272397	+	0.174665i
$801$	9.58707e30			0.00388966
$802$			1.15244e32i			0.0460908i
$803$			2.89954e32i			0.114314i
$804$	−2.58119e33			−1.00317
$805$	−4.21007e33	+	3.26316e32i	−1.61301	+	0.125022i
$806$	5.24213e32			0.197995
$807$			2.86737e33i			1.06767i
$808$		−	5.85895e32i		−	0.215075i
$809$	1.16776e33			0.422617			0.211308	−	0.977419i	$-0.432228\pi$
$809$	1.16776e33			0.422617			0.211308	+	0.977419i	$0.432228\pi$
$810$	−1.89099e32	−	2.43972e33i	−0.0674700	−	0.870486i
$811$	5.55308e32			0.195341			0.0976707	−	0.995219i	$-0.468861\pi$
$811$	5.55308e32			0.195341			0.0976707	+	0.995219i	$0.468861\pi$
$812$			2.27774e33i			0.789969i
$813$			1.19514e33i			0.408673i
$814$	−9.12093e32			−0.307510
$815$	8.16205e31	+	1.05305e33i	0.0271323	+	0.350057i
$816$	4.96872e32			0.162857
$817$			5.48762e33i			1.77350i
$818$		−	6.67764e32i		−	0.212794i
$819$	−5.03308e32			−0.158150
$820$	−9.13193e30	+	7.07801e29i	−0.00282946	+	0.000219307i
$821$	−1.64183e33			−0.501628			−0.250814	−	0.968035i	$-0.580698\pi$
$821$	−1.64183e33			−0.501628			−0.250814	+	0.968035i	$0.580698\pi$
$822$			1.02733e33i			0.309516i
$823$			1.72629e33i			0.512879i	0.966560	+	0.256440i	$0.0825495\pi$
$823$			1.72629e33i			0.512879i	−0.966560	+	0.256440i	$0.917451\pi$
$824$	−7.67507e31			−0.0224864
$825$	−8.26901e32	−	5.30222e33i	−0.238909	−	1.53193i
$826$	−5.63691e33			−1.60609
$827$		−	1.81296e33i		−	0.509419i	−0.967018	−	0.254710i	$-0.918020\pi$
$827$		−	1.81296e33i		−	0.509419i	0.967018	−	0.254710i	$-0.0819799\pi$
$828$		−	8.54512e32i		−	0.236793i
$829$	3.71334e33			1.01482			0.507408	−	0.861706i	$-0.330604\pi$
$829$	3.71334e33			1.01482			0.507408	+	0.861706i	$0.330604\pi$
$830$	1.34798e33	−	1.04480e32i	0.363317	−	0.0281601i
$831$	−2.62379e33			−0.697458
$832$		−	1.55721e32i		−	0.0408251i
$833$		−	1.40480e33i		−	0.363242i
$834$	1.90914e32			0.0486886
$835$	3.03129e32	+	3.91092e33i	0.0762488	+	0.983749i
$836$	3.12187e33			0.774537
$837$			2.56285e33i			0.627164i
$838$		−	6.98461e32i		−	0.168592i
$839$	1.13862e33			0.271092			0.135546	−	0.990771i	$-0.456721\pi$
$839$	1.13862e33			0.271092			0.135546	+	0.990771i	$0.456721\pi$
$840$	1.75548e32	+	2.26490e33i	0.0412273	+	0.531908i
$841$	2.19722e33			0.509003
$842$		−	5.17886e33i		−	1.18344i
$843$		−	2.68258e33i		−	0.604693i
$844$	−2.28435e33			−0.507955
$845$	4.06036e33	−	3.14712e32i	0.890660	−	0.0690336i
$846$	−1.21802e33			−0.263569
$847$		−	4.49689e33i		−	0.959959i
$848$		−	7.41321e32i		−	0.156118i
$849$	8.41119e33			1.74751
$850$	−1.89263e33	+	2.95162e32i	−0.387925	+	0.0604982i
$851$	2.04709e33			0.413949
$852$			5.24315e33i			1.04601i
$853$			2.77761e33i			0.546711i	0.961913	+	0.273355i	$0.0881335\pi$
$853$			2.77761e33i			0.546711i	−0.961913	+	0.273355i	$0.911866\pi$
$854$	−4.20104e33			−0.815815
$855$	2.29652e33	−	1.77999e32i	0.440007	−	0.0341042i
$856$	−1.14968e33			−0.217334
$857$			1.34093e33i			0.250108i	0.992150	+	0.125054i	$0.0399104\pi$
$857$			1.34093e33i			0.250108i	−0.992150	+	0.125054i	$0.960090\pi$
$858$			1.94564e33i			0.358062i
$859$	−2.83831e33			−0.515393			−0.257697	−	0.966226i	$-0.582964\pi$
$859$	−2.83831e33			−0.515393			−0.257697	+	0.966226i	$0.582964\pi$
$860$	3.26270e32	+	4.20948e33i	0.0584581	+	0.754217i
$861$	−4.84453e31			−0.00856477
$862$		−	8.89148e32i		−	0.155110i
$863$		−	8.83716e33i		−	1.52121i	−0.649216	−	0.760604i	$-0.724903\pi$
$863$		−	8.83716e33i		−	1.52121i	0.649216	−	0.760604i	$-0.275097\pi$
$864$	7.61310e32			0.129316
$865$	−8.43396e32	−	1.08814e34i	−0.141366	−	1.82389i
$866$	4.58838e33			0.758934
$867$		−	4.97199e33i		−	0.811541i
$868$		−	3.42290e33i		−	0.551337i
$869$	−1.56088e34			−2.48108
$870$	6.47721e33	−	5.02038e32i	1.01605	−	0.0787526i
$871$	−3.60782e33			−0.558517
$872$		−	2.91328e33i		−	0.445085i
$873$		−	4.92990e33i		−	0.743318i
$874$	−7.00668e33			−1.04263
$875$	−2.01412e33	−	8.52290e33i	−0.295796	−	1.25168i
$876$	−3.50094e32			−0.0507444
$877$			9.53398e33i			1.36389i	0.731404	+	0.681944i	$0.238865\pi$
$877$			9.53398e33i			1.36389i	−0.731404	+	0.681944i	$0.761135\pi$
$878$		−	6.51212e33i		−	0.919466i
$879$	1.23257e34			1.71768
$880$	2.39474e33	−	1.85613e32i	0.329388	−	0.0255304i
$881$	8.99539e32			0.122123			0.0610614	−	0.998134i	$-0.480551\pi$
$881$	8.99539e32			0.122123			0.0610614	+	0.998134i	$0.480551\pi$
$882$			1.29971e33i			0.174163i
$883$			9.74617e33i			1.28910i	0.764563	+	0.644549i	$0.222955\pi$
$883$			9.74617e33i			1.28910i	−0.764563	+	0.644549i	$0.777045\pi$
$884$	6.94495e32			0.0906709
$885$	1.24243e33	+	1.60297e34i	0.160113	+	2.06575i
$886$	7.55102e33			0.960545
$887$		−	4.14150e33i		−	0.520039i	−0.965603	−	0.260019i	$-0.916271\pi$
$887$		−	4.14150e33i		−	0.520039i	0.965603	−	0.260019i	$-0.0837289\pi$
$888$		−	1.10127e33i		−	0.136504i
$889$	−3.07085e33			−0.375740
$890$	−4.67384e30	−	6.03010e31i	−0.000564532	−	0.00728349i
$891$	−1.36849e34			−1.63172
$892$		−	9.46552e30i		−	0.00111416i
$893$			9.98728e33i			1.16053i
$894$	6.82544e33			0.782977
$895$	2.62589e33	−	2.03528e32i	0.297379	−	0.0230494i
$896$	−1.01679e33			−0.113682
$897$		−	4.36677e33i		−	0.482000i
$898$			6.28818e33i			0.685247i
$899$	−9.78890e33			−1.05317
$900$	1.75105e33	−	2.73082e32i	0.185998	−	0.0290071i
$901$	3.30620e33			0.346733
$902$			5.12227e31i			0.00530381i
$903$			2.23315e34i			2.28301i
$904$	9.25658e32			0.0934358
$905$	−2.08956e33	+	1.61959e32i	−0.208256	+	0.0161416i
$906$	−5.75803e33			−0.566630
$907$		−	7.15808e33i		−	0.695525i	−0.937583	−	0.347762i	$-0.886942\pi$
$907$		−	7.15808e33i		−	0.695525i	0.937583	−	0.347762i	$-0.113058\pi$
$908$		−	6.29251e33i		−	0.603722i
$909$	−2.41755e33			−0.229029
$910$	2.45370e32	+	3.16572e33i	0.0229533	+	0.296140i
$911$	5.72918e33			0.529214			0.264607	−	0.964356i	$-0.414758\pi$
$911$	5.72918e33			0.529214			0.264607	+	0.964356i	$0.414758\pi$
$912$			3.76939e33i			0.343819i
$913$		−	7.56109e33i		−	0.681036i
$914$	1.39924e34			1.24455
$915$	9.25953e32	+	1.19465e34i	0.0813292	+	1.04930i
$916$	−7.82704e33			−0.678890
$917$		−	2.38539e34i		−	2.04321i
$918$			3.39535e33i			0.287206i
$919$	6.63539e33			0.554292			0.277146	−	0.960828i	$-0.410611\pi$
$919$	6.63539e33			0.554292			0.277146	+	0.960828i	$0.410611\pi$
$920$	−5.37473e33	+	4.16587e32i	−0.443401	+	0.0343673i
$921$	−1.96831e34			−1.60364
$922$			4.47912e33i			0.360402i
$923$			7.32854e33i			0.582368i
$924$	1.27042e34			0.997059
$925$	6.54202e32	+	4.19485e33i	0.0507086	+	0.325152i
$926$	9.21970e32			0.0705815
$927$			3.16693e32i			0.0239453i
$928$			2.90785e33i			0.217155i
$929$	4.55011e33			0.335615			0.167808	−	0.985820i	$-0.446331\pi$
$929$	4.55011e33			0.335615			0.167808	+	0.985820i	$0.446331\pi$
$930$	−9.73369e33	+	7.54443e32i	−0.709127	+	0.0549632i
$931$	1.06571e34			0.766865
$932$		−	4.00908e33i		−	0.284945i
$933$		−	1.12139e34i		−	0.787256i
$934$	−4.53731e33			−0.314636
$935$	8.27810e32	+	1.06803e34i	0.0567019	+	0.731558i
$936$	−6.42542e32			−0.0434740
$937$			1.44423e34i			0.965233i	0.875832	+	0.482617i	$0.160314\pi$
$937$			1.44423e34i			0.965233i	−0.875832	+	0.482617i	$0.839686\pi$
$938$			2.35576e34i			1.55524i
$939$	−2.82594e33			−0.184293
$940$	5.93800e32	+	7.66111e33i	0.0382534	+	0.493539i
$941$	9.16693e33			0.583369			0.291684	−	0.956515i	$-0.405784\pi$
$941$	9.16693e33			0.583369			0.291684	+	0.956515i	$0.405784\pi$
$942$		−	1.29783e34i		−	0.815892i
$943$		−	1.14964e32i		−	0.00713964i
$944$	−7.19629e33			−0.441500
$945$	−1.54771e34	+	1.19960e33i	−0.938043	+	0.0727062i
$946$	2.36118e34			1.41378
$947$		−	1.88703e34i		−	1.11623i	−0.829763	−	0.558116i	$-0.811524\pi$
$947$		−	1.88703e34i		−	1.11623i	0.829763	−	0.558116i	$-0.188476\pi$
$948$		−	1.88462e34i		−	1.10136i
$949$	−4.89339e32			−0.0282519
$950$	−2.23917e33	−	1.43579e34i	−0.127722	−	0.818974i
$951$	1.53942e34			0.867524
$952$		−	4.53477e33i		−	0.252482i
$953$		−	1.79351e34i		−	0.986585i	−0.869864	−	0.493292i	$-0.835793\pi$
$953$		−	1.79351e34i		−	0.986585i	0.869864	−	0.493292i	$-0.164207\pi$
$954$	−3.05888e33			−0.166248
$955$	7.20336e32	−	5.58321e31i	0.0386809	−	0.00299809i
$956$	−4.23955e33			−0.224934
$957$		−	3.63319e34i		−	1.90459i
$958$			6.02027e33i			0.311826i
$959$	9.37605e33			0.479850
$960$	2.24112e32	+	2.89145e33i	0.0113330	+	0.146216i
$961$	−5.30293e33			−0.264970
$962$		−	1.53929e33i		−	0.0759989i
$963$			4.74387e33i			0.231436i
$964$	1.37762e34			0.664114
$965$	−5.14653e32	−	6.63997e33i	−0.0245160	−	0.316302i
$966$	−2.85132e34			−1.34218
$967$			1.99555e33i			0.0928236i	0.998922	+	0.0464118i	$0.0147786\pi$
$967$			1.99555e33i			0.0928236i	−0.998922	+	0.0464118i	$0.985221\pi$
$968$		−	5.74089e33i		−	0.263884i
$969$	−1.68110e34			−0.763609
$970$	−3.10082e34	+	2.40340e33i	−1.39188	+	0.107882i
$971$	3.88582e34			1.72370			0.861850	−	0.507164i	$-0.169306\pi$
$971$	3.88582e34			1.72370			0.861850	+	0.507164i	$0.169306\pi$
$972$		−	8.17956e33i		−	0.358565i
$973$		−	1.74240e33i		−	0.0754832i
$974$	−2.25096e34			−0.963694
$975$	8.94828e33	−	1.39552e33i	0.378605	−	0.0590448i
$976$	−5.36320e33			−0.224260
$977$			3.33629e34i			1.37872i	0.724418	+	0.689361i	$0.242109\pi$
$977$			3.33629e34i			1.37872i	−0.724418	+	0.689361i	$0.757891\pi$
$978$			7.13194e33i			0.291280i
$979$	−3.38240e32			−0.0136529
$980$	8.17494e33	−	6.33627e32i	0.326126	−	0.0252775i
$981$	−1.20209e34			−0.473963
$982$		−	2.82303e34i		−	1.10010i
$983$		−	3.34652e34i		−	1.28893i	−0.764636	−	0.644463i	$-0.777081\pi$
$983$		−	3.34652e34i		−	1.28893i	0.764636	−	0.644463i	$-0.222919\pi$
$984$	−6.18471e31			−0.00235437
$985$	2.77673e33	+	3.58249e34i	0.104476	+	1.34793i
$986$	−1.29687e34			−0.482292
$987$			4.06426e34i			1.49394i
$988$			5.26861e33i			0.191422i
$989$	−5.29940e34			−1.90313
$990$	−7.65884e32	−	9.88131e33i	−0.0271868	−	0.350760i
$991$	3.84793e34			1.35014			0.675072	−	0.737752i	$-0.264112\pi$
$991$	3.84793e34			1.35014			0.675072	+	0.737752i	$0.264112\pi$
$992$		−	4.36980e33i		−	0.151557i
$993$			7.49772e33i			0.257047i
$994$	4.78524e34			1.62166
$995$	2.37809e34	−	1.84322e33i	0.796642	−	0.0617464i
$996$	9.12937e33			0.302314
$997$		−	2.67941e33i		−	0.0877092i	−0.999038	−	0.0438546i	$-0.986036\pi$
$997$		−	2.67941e33i		−	0.0877092i	0.999038	−	0.0438546i	$-0.0139638\pi$
$998$			2.91264e34i			0.942509i
$999$	7.52552e33			0.240732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.24.b.a.9.8	yes	12
5.2	odd	4		50.24.a.j.1.2		6
5.3	odd	4		50.24.a.k.1.5		6
5.4	even	2	inner	10.24.b.a.9.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.24.b.a.9.5	✓	12	5.4	even	2	inner
10.24.b.a.9.8	yes	12	1.1	even	1	trivial
50.24.a.j.1.2		6	5.2	odd	4
50.24.a.k.1.5		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} -359983. i q^{3} -4.19430e6 q^{4} +(1.08857e8 - 8.43729e6i) q^{5} +7.37244e8 q^{6} -6.72856e9i q^{7} -8.58993e9i q^{8} -3.54442e10 q^{9} +(1.72796e10 + 2.22938e11i) q^{10} +1.25050e12 q^{11} +1.50988e12i q^{12} +2.11041e12i q^{13} +1.37801e13 q^{14} +(-3.03728e12 - 3.91864e13i) q^{15} +1.75922e13 q^{16} +7.84590e13i q^{17} -7.25898e13i q^{18} -5.95210e14 q^{19} +(-4.56577e14 + 3.53886e13i) q^{20} -2.42217e15 q^{21} +2.56103e15i q^{22} -5.74795e15i q^{23} -3.09223e15 q^{24} +(1.17786e16 - 1.83691e15i) q^{25} -4.32211e15 q^{26} -2.11306e16i q^{27} +2.82216e16i q^{28} +8.07090e16 q^{29} +(8.02538e16 - 6.22034e15i) q^{30} -1.21286e17 q^{31} +3.60288e16i q^{32} -4.50159e17i q^{33} -1.60684e17 q^{34} +(-5.67709e16 - 7.32448e17i) q^{35} +1.48664e17 q^{36} +3.56143e17i q^{37} -1.21899e18i q^{38} +7.59709e17 q^{39} +(-7.24758e16 - 9.35070e17i) q^{40} +2.00008e16 q^{41} -4.96060e18i q^{42} -9.21964e18i q^{43} -5.24499e18 q^{44} +(-3.85833e18 + 2.99053e17i) q^{45} +1.17718e19 q^{46} -1.67794e19i q^{47} -6.33288e18i q^{48} -1.79048e19 q^{49} +(3.76199e18 + 2.41225e19i) q^{50} +2.82439e19 q^{51} -8.85169e18i q^{52} -4.21392e19i q^{53} +4.32755e19 q^{54} +(1.36125e20 - 1.05509e19i) q^{55} -5.77979e19 q^{56} +2.14265e20i q^{57} +1.65292e20i q^{58} -4.09061e20 q^{59} +(1.27393e19 + 1.64360e20i) q^{60} -3.04863e20 q^{61} -2.48394e20i q^{62} +2.38489e20i q^{63} -7.37870e19 q^{64} +(1.78061e19 + 2.29732e20i) q^{65} +9.21926e20 q^{66} +1.70954e21i q^{67} -3.29081e20i q^{68} -2.06916e21 q^{69} +(1.50005e21 - 1.16267e20i) q^{70} +3.47257e21 q^{71} +3.04464e20i q^{72} +2.31870e20i q^{73} -7.29381e20 q^{74} +(-6.61255e20 - 4.24007e21i) q^{75} +2.49649e21 q^{76} -8.41409e21i q^{77} +1.55589e21i q^{78} -1.24820e22 q^{79} +(1.91502e21 - 1.48430e20i) q^{80} -1.09435e22 q^{81} +4.09617e19i q^{82} -6.04644e21i q^{83} +1.01593e22 q^{84} +(6.61982e20 + 8.54078e21i) q^{85} +1.88818e22 q^{86} -2.90538e22i q^{87} -1.07417e22i q^{88} -2.70483e20 q^{89} +(-6.12461e20 - 7.90187e21i) q^{90} +1.42000e22 q^{91} +2.41086e22i q^{92} +4.36610e22i q^{93} +3.43643e22 q^{94} +(-6.47924e22 + 5.02196e21i) q^{95} +1.29697e22 q^{96} +1.39089e23i q^{97} -3.66691e22i q^{98} -4.43231e22 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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