LMFDB - Embedded newform 30.10.c.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,10,Mod(19,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("30.19");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	30.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.4510750849$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{889})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 445x^{2} + 49284 $ x^4 + 445*x^2 + 49284
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$14.4081i$ of defining polynomial
Character	$\chi$	$=$	30.19
Dual form			30.10.c.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000i q^{2} -81.0000i q^{3} -256.000 q^{4} +(1396.52 + 53.3623i) q^{5} -1296.00 q^{6} +11525.9i q^{7} +4096.00i q^{8} -6561.00 q^{9} +O(q^{10})$	\(q-16.0000i q^{2} -81.0000i q^{3} -256.000 q^{4} +(1396.52 + 53.3623i) q^{5} -1296.00 q^{6} +11525.9i q^{7} +4096.00i q^{8} -6561.00 q^{9} +(853.797 - 22344.4i) q^{10} +23630.6 q^{11} +20736.0i q^{12} +179922. i q^{13} +184415. q^{14} +(4322.35 - 113118. i) q^{15} +65536.0 q^{16} -376774. i q^{17} +104976. i q^{18} +344256. q^{19} +(-357510. - 13660.8i) q^{20} +933602. q^{21} -378090. i q^{22} +422945. i q^{23} +331776. q^{24} +(1.94743e6 + 149043. i) q^{25} +2.87875e6 q^{26} +531441. i q^{27} -2.95064e6i q^{28} +6.01502e6 q^{29} +(-1.80989e6 - 69157.6i) q^{30} -5.39931e6 q^{31} -1.04858e6i q^{32} -1.91408e6i q^{33} -6.02838e6 q^{34} +(-615051. + 1.60963e7i) q^{35} +1.67962e6 q^{36} +922766. i q^{37} -5.50810e6i q^{38} +1.45737e7 q^{39} +(-218572. + 5.72016e6i) q^{40} -2.15643e7 q^{41} -1.49376e7i q^{42} +1.66892e6i q^{43} -6.04944e6 q^{44} +(-9.16259e6 - 350110. i) q^{45} +6.76711e6 q^{46} +3.02283e7i q^{47} -5.30842e6i q^{48} -9.24938e7 q^{49} +(2.38470e6 - 3.11589e7i) q^{50} -3.05187e7 q^{51} -4.60599e7i q^{52} +3.64412e7i q^{53} +8.50306e6 q^{54} +(3.30007e7 + 1.26099e6i) q^{55} -4.72103e7 q^{56} -2.78848e7i q^{57} -9.62403e7i q^{58} +1.10359e8 q^{59} +(-1.10652e6 + 2.89583e7i) q^{60} +1.21913e8 q^{61} +8.63889e7i q^{62} -7.56217e7i q^{63} -1.67772e7 q^{64} +(-9.60104e6 + 2.51265e8i) q^{65} -3.06253e7 q^{66} +1.26022e8i q^{67} +9.64540e7i q^{68} +3.42585e7 q^{69} +(2.57540e8 + 9.84082e6i) q^{70} -5.01662e7 q^{71} -2.68739e7i q^{72} -4.06246e8i q^{73} +1.47643e7 q^{74} +(1.20725e7 - 1.57742e8i) q^{75} -8.81297e7 q^{76} +2.72365e8i q^{77} -2.33178e8i q^{78} +5.87351e8 q^{79} +(9.15226e7 + 3.49715e6i) q^{80} +4.30467e7 q^{81} +3.45029e8i q^{82} -3.11987e7i q^{83} -2.39002e8 q^{84} +(2.01055e7 - 5.26173e8i) q^{85} +2.67026e7 q^{86} -4.87216e8i q^{87} +9.67911e7i q^{88} +8.18411e7 q^{89} +(-5.60176e6 + 1.46601e8i) q^{90} -2.07377e9 q^{91} -1.08274e8i q^{92} +4.37344e8i q^{93} +4.83653e8 q^{94} +(4.80762e8 + 1.83703e7i) q^{95} -8.49347e7 q^{96} -9.14396e8i q^{97} +1.47990e9i q^{98} -1.55041e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 1024 q^{4} + 1710 q^{5} - 5184 q^{6} - 26244 q^{9}+O(q^{10}) $ 4 * q - 1024 * q^4 + 1710 * q^5 - 5184 * q^6 - 26244 * q^9	\( 4 q - 1024 q^{4} + 1710 q^{5} - 5184 q^{6} - 26244 q^{9} - 39520 q^{10} + 900 q^{11} + 270144 q^{14} - 200070 q^{15} + 262144 q^{16} + 840336 q^{19} - 437760 q^{20} + 1367604 q^{21} + 1327104 q^{24} + 1161600 q^{25} + 4444992 q^{26} + 8920044 q^{29} - 2216160 q^{30} - 11689928 q^{31} + 16064 q^{34} - 9176580 q^{35} + 6718464 q^{36} + 22502772 q^{39} + 10117120 q^{40} - 94900464 q^{41} - 230400 q^{44} - 11219310 q^{45} + 59699200 q^{46} - 123301836 q^{49} + 49420800 q^{50} + 81324 q^{51} + 34012224 q^{54} + 91107200 q^{55} - 69156864 q^{56} - 44259300 q^{59} + 51217920 q^{60} + 94450760 q^{61} - 67108864 q^{64} - 124888140 q^{65} - 1166400 q^{66} + 302227200 q^{69} + 568520960 q^{70} - 912569400 q^{71} - 316377792 q^{74} + 250192800 q^{75} - 215126016 q^{76} + 1963018008 q^{79} + 112066560 q^{80} + 172186884 q^{81} - 350106624 q^{84} + 1012346420 q^{85} - 1056294144 q^{86} + 1733458248 q^{89} + 259290720 q^{90} - 4400514552 q^{91} + 42544000 q^{94} + 879308640 q^{95} - 339738624 q^{96} - 5904900 q^{99}+O(q^{100}) \) 4 * q - 1024 * q^4 + 1710 * q^5 - 5184 * q^6 - 26244 * q^9 - 39520 * q^10 + 900 * q^11 + 270144 * q^14 - 200070 * q^15 + 262144 * q^16 + 840336 * q^19 - 437760 * q^20 + 1367604 * q^21 + 1327104 * q^24 + 1161600 * q^25 + 4444992 * q^26 + 8920044 * q^29 - 2216160 * q^30 - 11689928 * q^31 + 16064 * q^34 - 9176580 * q^35 + 6718464 * q^36 + 22502772 * q^39 + 10117120 * q^40 - 94900464 * q^41 - 230400 * q^44 - 11219310 * q^45 + 59699200 * q^46 - 123301836 * q^49 + 49420800 * q^50 + 81324 * q^51 + 34012224 * q^54 + 91107200 * q^55 - 69156864 * q^56 - 44259300 * q^59 + 51217920 * q^60 + 94450760 * q^61 - 67108864 * q^64 - 124888140 * q^65 - 1166400 * q^66 + 302227200 * q^69 + 568520960 * q^70 - 912569400 * q^71 - 316377792 * q^74 + 250192800 * q^75 - 215126016 * q^76 + 1963018008 * q^79 + 112066560 * q^80 + 172186884 * q^81 - 350106624 * q^84 + 1012346420 * q^85 - 1056294144 * q^86 + 1733458248 * q^89 + 259290720 * q^90 - 4400514552 * q^91 + 42544000 * q^94 + 879308640 * q^95 - 339738624 * q^96 - 5904900 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	16.0000i		−	0.707107i
$2$		−	16.0000i		−	0.707107i
$3$		−	81.0000i		−	0.577350i
$3$		−	81.0000i		−	0.577350i
$4$	−256.000			−0.500000
$5$	1396.52	+	53.3623i	0.999271	+	0.0381830i
$5$	1396.52	+	53.3623i	0.999271	+	0.0381830i
$6$	−1296.00			−0.408248
$7$			11525.9i			1.81441i	0.420689	+	0.907205i	$0.361788\pi$
$7$			11525.9i			1.81441i	−0.420689	+	0.907205i	$0.638212\pi$
$8$			4096.00i			0.353553i
$9$	−6561.00			−0.333333
$10$	853.797	−	22344.4i	0.0269994	−	0.706591i
$11$	23630.6			0.486641			0.243320	−	0.969946i	$-0.421763\pi$
$11$	23630.6			0.486641			0.243320	+	0.969946i	$0.421763\pi$
$12$			20736.0i			0.288675i
$13$			179922.i			1.74718i	0.486660	+	0.873591i	$0.338215\pi$
$13$			179922.i			1.74718i	−0.486660	+	0.873591i	$0.661785\pi$
$14$	184415.			1.28298
$15$	4322.35	−	113118.i	0.0220449	−	0.576929i
$16$	65536.0			0.250000
$17$		−	376774.i		−	1.09411i	−0.837097	−	0.547054i	$-0.815749\pi$
$17$		−	376774.i		−	1.09411i	0.837097	−	0.547054i	$-0.184251\pi$
$18$			104976.i			0.235702i
$19$	344256.			0.606026			0.303013	−	0.952987i	$-0.402008\pi$
$19$	344256.			0.606026			0.303013	+	0.952987i	$0.402008\pi$
$20$	−357510.	−	13660.8i	−0.499635	−	0.0190915i
$21$	933602.			1.04755
$22$		−	378090.i		−	0.344107i
$23$			422945.i			0.315143i	0.987508	+	0.157572i	$0.0503665\pi$
$23$			422945.i			0.315143i	−0.987508	+	0.157572i	$0.949633\pi$
$24$	331776.			0.204124
$25$	1.94743e6	+	149043.i	0.997084	+	0.0763102i
$26$	2.87875e6			1.23544
$27$			531441.i			0.192450i
$28$		−	2.95064e6i		−	0.907205i
$29$	6.01502e6			1.57923			0.789616	−	0.613602i	$-0.210280\pi$
$29$	6.01502e6			1.57923			0.789616	+	0.613602i	$0.210280\pi$
$30$	−1.80989e6	−	69157.6i	−0.407951	−	0.0155881i
$31$	−5.39931e6			−1.05005			−0.525025	−	0.851087i	$-0.675944\pi$
$31$	−5.39931e6			−1.05005			−0.525025	+	0.851087i	$0.675944\pi$
$32$		−	1.04858e6i		−	0.176777i
$33$		−	1.91408e6i		−	0.280962i
$34$	−6.02838e6			−0.773651
$35$	−615051.	+	1.60963e7i	−0.0692795	+	1.81309i
$36$	1.67962e6			0.166667
$37$			922766.i			0.0809439i	0.999181	+	0.0404719i	$0.0128861\pi$
$37$			922766.i			0.0809439i	−0.999181	+	0.0404719i	$0.987114\pi$
$38$		−	5.50810e6i		−	0.428525i
$39$	1.45737e7			1.00874
$40$	−218572.	+	5.72016e6i	−0.0134997	+	0.353296i
$41$	−2.15643e7			−1.19182			−0.595908	−	0.803053i	$-0.703208\pi$
$41$	−2.15643e7			−1.19182			−0.595908	+	0.803053i	$0.703208\pi$
$42$		−	1.49376e7i		−	0.740730i
$43$			1.66892e6i			0.0744434i	0.999307	+	0.0372217i	$0.0118508\pi$
$43$			1.66892e6i			0.0744434i	−0.999307	+	0.0372217i	$0.988149\pi$
$44$	−6.04944e6			−0.243320
$45$	−9.16259e6	−	350110.i	−0.333090	−	0.0127277i
$46$	6.76711e6			0.222840
$47$			3.02283e7i			0.903594i	0.892121	+	0.451797i	$0.149217\pi$
$47$			3.02283e7i			0.903594i	−0.892121	+	0.451797i	$0.850783\pi$
$48$		−	5.30842e6i		−	0.144338i
$49$	−9.24938e7			−2.29208
$50$	2.38470e6	−	3.11589e7i	0.0539595	−	0.705045i
$51$	−3.05187e7			−0.631684
$52$		−	4.60599e7i		−	0.873591i
$53$			3.64412e7i			0.634383i	0.948361	+	0.317192i	$0.102740\pi$
$53$			3.64412e7i			0.634383i	−0.948361	+	0.317192i	$0.897260\pi$
$54$	8.50306e6			0.136083
$55$	3.30007e7	+	1.26099e6i	0.486286	+	0.0185814i
$56$	−4.72103e7			−0.641491
$57$		−	2.78848e7i		−	0.349889i
$58$		−	9.62403e7i		−	1.11669i
$59$	1.10359e8			1.18569			0.592847	−	0.805315i	$-0.298004\pi$
$59$	1.10359e8			1.18569			0.592847	+	0.805315i	$0.298004\pi$
$60$	−1.10652e6	+	2.89583e7i	−0.0110225	+	0.288465i
$61$	1.21913e8			1.12737			0.563683	−	0.825991i	$-0.309384\pi$
$61$	1.21913e8			1.12737			0.563683	+	0.825991i	$0.309384\pi$
$62$			8.63889e7i			0.742498i
$63$		−	7.56217e7i		−	0.604803i
$64$	−1.67772e7			−0.125000
$65$	−9.60104e6	+	2.51265e8i	−0.0667126	+	1.74591i
$66$	−3.06253e7			−0.198670
$67$			1.26022e8i			0.764027i	0.924157	+	0.382013i	$0.124769\pi$
$67$			1.26022e8i			0.764027i	−0.924157	+	0.382013i	$0.875231\pi$
$68$			9.64540e7i			0.547054i
$69$	3.42585e7			0.181948
$70$	2.57540e8	+	9.84082e6i	1.28205	+	0.0489880i
$71$	−5.01662e7			−0.234287			−0.117144	−	0.993115i	$-0.537374\pi$
$71$	−5.01662e7			−0.234287			−0.117144	+	0.993115i	$0.537374\pi$
$72$		−	2.68739e7i		−	0.117851i
$73$		−	4.06246e8i		−	1.67431i	−0.546965	−	0.837155i	$-0.684217\pi$
$73$		−	4.06246e8i		−	1.67431i	0.546965	−	0.837155i	$-0.315783\pi$
$74$	1.47643e7			0.0572360
$75$	1.20725e7	−	1.57742e8i	0.0440577	−	0.575667i
$76$	−8.81297e7			−0.303013
$77$			2.72365e8i			0.882966i
$78$		−	2.33178e8i		−	0.713284i
$79$	5.87351e8			1.69658			0.848292	−	0.529528i	$-0.177631\pi$
$79$	5.87351e8			1.69658			0.848292	+	0.529528i	$0.177631\pi$
$80$	9.15226e7	+	3.49715e6i	0.249818	+	0.00954574i
$81$	4.30467e7			0.111111
$82$			3.45029e8i			0.842741i
$83$		−	3.11987e7i		−	0.0721580i	−0.999349	−	0.0360790i	$-0.988513\pi$
$83$		−	3.11987e7i		−	0.0721580i	0.999349	−	0.0360790i	$-0.0114868\pi$
$84$	−2.39002e8			−0.523775
$85$	2.01055e7	−	5.26173e8i	0.0417763	−	1.09331i
$86$	2.67026e7			0.0526394
$87$		−	4.87216e8i		−	0.911770i
$88$			9.67911e7i			0.172053i
$89$	8.18411e7			0.138266			0.0691331	−	0.997607i	$-0.477977\pi$
$89$	8.18411e7			0.138266			0.0691331	+	0.997607i	$0.477977\pi$
$90$	−5.60176e6	+	1.46601e8i	−0.00899981	+	0.235530i
$91$	−2.07377e9			−3.17011
$92$		−	1.08274e8i		−	0.157572i
$93$			4.37344e8i			0.606247i
$94$	4.83653e8			0.638938
$95$	4.80762e8	+	1.83703e7i	0.605584	+	0.0231399i
$96$	−8.49347e7			−0.102062
$97$		−	9.14396e8i		−	1.04872i	−0.851495	−	0.524362i	$-0.824304\pi$
$97$		−	9.14396e8i		−	1.04872i	0.851495	−	0.524362i	$-0.175696\pi$
$98$			1.47990e9i			1.62075i
$99$	−1.55041e8			−0.162214
$100$	−4.98542e8	−	3.81551e7i	−0.498542	−	0.0381551i
$101$	−1.47476e9			−1.41018			−0.705092	−	0.709116i	$-0.749094\pi$
$101$	−1.47476e9			−1.41018			−0.705092	+	0.709116i	$0.749094\pi$
$102$			4.88299e8i			0.446668i
$103$			1.24081e9i			1.08627i	0.839645	+	0.543136i	$0.182763\pi$
$103$			1.24081e9i			1.08627i	−0.839645	+	0.543136i	$0.817237\pi$
$104$	−7.36959e8			−0.617722
$105$	1.30380e9	+	4.98191e7i	1.04679	+	0.0399986i
$106$	5.83060e8			0.448577
$107$			8.09960e7i			0.0597361i	0.999554	+	0.0298680i	$0.00950871\pi$
$107$			8.09960e7i			0.0597361i	−0.999554	+	0.0298680i	$0.990491\pi$
$108$		−	1.36049e8i		−	0.0962250i
$109$	−8.73687e8			−0.592839			−0.296419	−	0.955058i	$-0.595793\pi$
$109$	−8.73687e8			−0.592839			−0.296419	+	0.955058i	$0.595793\pi$
$110$	2.01758e7	−	5.28012e8i	0.0131390	−	0.343856i
$111$	7.47441e7			0.0467330
$112$			7.55364e8i			0.453602i
$113$		−	2.20607e9i		−	1.27282i	−0.771352	−	0.636409i	$-0.780419\pi$
$113$		−	2.20607e9i		−	1.27282i	0.771352	−	0.636409i	$-0.219581\pi$
$114$	−4.46156e8			−0.247409
$115$	−2.25693e7	+	5.90652e8i	−0.0120331	+	0.314914i
$116$	−1.53984e9			−0.789616
$117$		−	1.18047e9i		−	0.582394i
$118$		−	1.76574e9i		−	0.838412i
$119$	4.34267e9			1.98516
$120$	4.63333e8	+	1.77043e7i	0.203975	+	0.00779407i
$121$	−1.79954e9			−0.763181
$122$		−	1.95060e9i		−	0.797168i
$123$			1.74671e9i			0.688095i
$124$	1.38222e9			0.525025
$125$	2.71168e9	+	3.12062e8i	0.993443	+	0.114326i
$126$	−1.20995e9			−0.427660
$127$			6.92970e8i			0.236373i	0.992991	+	0.118186i	$0.0377081\pi$
$127$			6.92970e8i			0.236373i	−0.992991	+	0.118186i	$0.962292\pi$
$128$			2.68435e8i			0.0883883i
$129$	1.35182e8			0.0429799
$130$	4.02024e9	+	1.53617e8i	1.23454	+	0.0471730i
$131$	−1.40216e9			−0.415984			−0.207992	−	0.978131i	$-0.566693\pi$
$131$	−1.40216e9			−0.415984			−0.207992	+	0.978131i	$0.566693\pi$
$132$			4.90005e8i			0.140481i
$133$			3.96788e9i			1.09958i
$134$	2.01635e9			0.540249
$135$	−2.83589e7	+	7.42170e8i	−0.00734832	+	0.192310i
$136$	1.54326e9			0.386826
$137$		−	6.38679e9i		−	1.54896i	−0.632599	−	0.774480i	$-0.718012\pi$
$137$		−	6.38679e9i		−	1.54896i	0.632599	−	0.774480i	$-0.281988\pi$
$138$		−	5.48136e8i		−	0.128657i
$139$	−2.32882e9			−0.529139			−0.264569	−	0.964367i	$-0.585230\pi$
$139$	−2.32882e9			−0.529139			−0.264569	+	0.964367i	$0.585230\pi$
$140$	1.57453e8	−	4.12064e9i	0.0346398	−	0.906543i
$141$	2.44849e9			0.521690
$142$			8.02658e8i			0.165666i
$143$			4.25166e9i			0.850250i
$144$	−4.29982e8			−0.0833333
$145$	8.40011e9	+	3.20975e8i	1.57808	+	0.0602997i
$146$	−6.49993e9			−1.18392
$147$			7.49200e9i			1.32333i
$148$		−	2.36228e8i		−	0.0404719i
$149$	1.21121e9			0.201317			0.100659	−	0.994921i	$-0.467905\pi$
$149$	1.21121e9			0.201317			0.100659	+	0.994921i	$0.467905\pi$
$150$	−2.52387e9	−	1.93160e8i	−0.407058	−	0.0311535i
$151$	−4.40101e9			−0.688900			−0.344450	−	0.938805i	$-0.611935\pi$
$151$	−4.40101e9			−0.688900			−0.344450	+	0.938805i	$0.611935\pi$
$152$			1.41007e9i			0.214262i
$153$			2.47201e9i			0.364703i
$154$	4.35785e9			0.624351
$155$	−7.54026e9	−	2.88119e8i	−1.04929	−	0.0400941i
$156$	−3.73086e9			−0.504368
$157$			2.54037e9i			0.333694i	0.985983	+	0.166847i	$0.0533586\pi$
$157$			2.54037e9i			0.333694i	−0.985983	+	0.166847i	$0.946641\pi$
$158$		−	9.39761e9i		−	1.19967i
$159$	2.95174e9			0.366261
$160$	5.59544e7	−	1.46436e9i	0.00674986	−	0.176648i
$161$	−4.87484e9			−0.571799
$162$		−	6.88748e8i		−	0.0785674i
$163$		−	5.04588e9i		−	0.559877i	−0.960018	−	0.279939i	$-0.909686\pi$
$163$		−	5.04588e9i		−	0.559877i	0.960018	−	0.279939i	$-0.0903142\pi$
$164$	5.52047e9			0.595908
$165$	1.02140e8	−	2.67306e9i	0.0107280	−	0.280757i
$166$	−4.99179e8			−0.0510234
$167$			1.34715e8i			0.0134027i	0.999978	+	0.00670134i	$0.00213312\pi$
$167$			1.34715e8i			0.0134027i	−0.999978	+	0.00670134i	$0.997867\pi$
$168$			3.82403e9i			0.370365i
$169$	−2.17673e10			−2.05265
$170$	−8.41877e9	−	3.21688e8i	−0.773087	−	0.0295403i
$171$	−2.25867e9			−0.202009
$172$		−	4.27242e8i		−	0.0372217i
$173$		−	1.31036e10i		−	1.11220i	−0.831115	−	0.556100i	$-0.812297\pi$
$173$		−	1.31036e10i		−	1.11220i	0.831115	−	0.556100i	$-0.187703\pi$
$174$	−7.79546e9			−0.644719
$175$	−1.71787e9	+	2.24460e10i	−0.138458	+	1.80912i
$176$	1.54866e9			0.121660
$177$		−	8.93906e9i		−	0.684561i
$178$		−	1.30946e9i		−	0.0977690i
$179$	1.93107e10			1.40592			0.702960	−	0.711230i	$-0.251861\pi$
$179$	1.93107e10			1.40592			0.702960	+	0.711230i	$0.251861\pi$
$180$	2.34562e9	+	8.96282e7i	0.166545	+	0.00636383i
$181$	4.50186e8			0.0311773			0.0155887	−	0.999878i	$-0.495038\pi$
$181$	4.50186e8			0.0311773			0.0155887	+	0.999878i	$0.495038\pi$
$182$			3.31803e10i			2.24160i
$183$		−	9.87494e9i		−	0.650885i
$184$	−1.73238e9			−0.111420
$185$	−4.92409e7	+	1.28866e9i	−0.00309068	+	0.0808848i
$186$	6.99750e9			0.428681
$187$		−	8.90340e9i		−	0.532438i
$188$		−	7.73845e9i		−	0.451797i
$189$	−6.12536e9			−0.349183
$190$	2.93925e8	−	7.69220e9i	0.0163623	−	0.428212i
$191$	4.97205e7			0.00270325			0.00135162	−	0.999999i	$-0.499570\pi$
$191$	4.97205e7			0.00270325			0.00135162	+	0.999999i	$0.499570\pi$
$192$			1.35895e9i			0.0721688i
$193$		−	3.43079e10i		−	1.77986i	−0.456097	−	0.889930i	$-0.650753\pi$
$193$		−	3.43079e10i		−	1.77986i	0.456097	−	0.889930i	$-0.349247\pi$
$194$	−1.46303e10			−0.741561
$195$	2.03524e10	+	7.77684e8i	1.00800	+	0.0385166i
$196$	2.36784e10			1.14604
$197$		−	1.13593e10i		−	0.537343i	−0.963232	−	0.268672i	$-0.913415\pi$
$197$		−	1.13593e10i		−	0.537343i	0.963232	−	0.268672i	$-0.0865847\pi$
$198$			2.48065e9i			0.114702i
$199$	1.14503e10			0.517580			0.258790	−	0.965934i	$-0.416676\pi$
$199$	1.14503e10			0.517580			0.258790	+	0.965934i	$0.416676\pi$
$200$	−6.10482e8	+	7.97667e9i	−0.0269797	+	0.352522i
$201$	1.02078e10			0.441111
$202$			2.35962e10i			0.997150i
$203$			6.93287e10i			2.86537i
$204$	7.81278e9			0.315842
$205$	−3.01151e10	−	1.15072e9i	−1.19095	−	0.0455070i
$206$	1.98530e10			0.768110
$207$		−	2.77494e9i		−	0.105048i
$208$			1.17913e10i			0.436796i
$209$	8.13500e9			0.294917
$210$	7.97106e8	−	2.08607e10i	0.0282833	−	0.740190i
$211$	1.79789e10			0.624443			0.312221	−	0.950009i	$-0.398927\pi$
$211$	1.79789e10			0.624443			0.312221	+	0.950009i	$0.398927\pi$
$212$		−	9.32896e9i		−	0.317192i
$213$			4.06346e9i			0.135266i
$214$	1.29594e9			0.0422398
$215$	−8.90572e7	+	2.33068e9i	−0.00284247	+	0.0743891i
$216$	−2.17678e9			−0.0680414
$217$		−	6.22321e10i		−	1.90522i
$218$			1.39790e10i			0.419200i
$219$	−3.29059e10			−0.966664
$220$	−8.44819e9	−	3.22812e8i	−0.243143	−	0.00929069i
$221$	6.77897e10			1.91161
$222$		−	1.19590e9i		−	0.0330452i
$223$		−	1.93336e9i		−	0.0523530i	−0.999657	−	0.0261765i	$-0.991667\pi$
$223$		−	1.93336e9i		−	0.0523530i	0.999657	−	0.0261765i	$-0.00833320\pi$
$224$	1.20858e10			0.320745
$225$	−1.27771e10	−	9.77874e8i	−0.332361	−	0.0254367i
$226$	−3.52971e10			−0.900018
$227$		−	3.00235e10i		−	0.750489i	−0.926926	−	0.375244i	$-0.877559\pi$
$227$		−	3.00235e10i		−	0.750489i	0.926926	−	0.375244i	$-0.122441\pi$
$228$			7.13850e9i			0.174944i
$229$	1.93100e10			0.464005			0.232003	−	0.972715i	$-0.425472\pi$
$229$	1.93100e10			0.464005			0.232003	+	0.972715i	$0.425472\pi$
$230$	9.45043e9	+	3.61109e8i	0.222678	+	0.00850869i
$231$	2.20616e10			0.509780
$232$			2.46375e10i			0.558343i
$233$			2.03630e10i			0.452626i	0.974055	+	0.226313i	$0.0726672\pi$
$233$			2.03630e10i			0.452626i	−0.974055	+	0.226313i	$0.927333\pi$
$234$	−1.88875e10			−0.411815
$235$	−1.61305e9	+	4.22145e10i	−0.0345019	+	0.902935i
$236$	−2.82518e10			−0.592847
$237$		−	4.75754e10i		−	0.979524i
$238$		−	6.94828e10i		−	1.40372i
$239$	−8.60068e10			−1.70507			−0.852535	−	0.522671i	$-0.824936\pi$
$239$	−8.60068e10			−1.70507			−0.852535	+	0.522671i	$0.824936\pi$
$240$	2.83269e8	−	7.41333e9i	0.00551124	−	0.144232i
$241$	5.58126e10			1.06575			0.532875	−	0.846194i	$-0.321111\pi$
$241$	5.58126e10			1.06575			0.532875	+	0.846194i	$0.321111\pi$
$242$			2.87926e10i			0.539650i
$243$		−	3.48678e9i		−	0.0641500i
$244$	−3.12097e10			−0.563683
$245$	−1.29170e11	−	4.93568e9i	−2.29041	−	0.0875185i
$246$	2.79474e10			0.486556
$247$			6.19392e10i			1.05884i
$248$		−	2.21156e10i		−	0.371249i
$249$	−2.52709e9			−0.0416604
$250$	4.99299e9	−	4.33868e10i	0.0808408	−	0.702470i
$251$	−4.48289e10			−0.712896			−0.356448	−	0.934315i	$-0.616012\pi$
$251$	−4.48289e10			−0.712896			−0.356448	+	0.934315i	$0.616012\pi$
$252$			1.93592e10i			0.302402i
$253$			9.99445e9i			0.153362i
$254$	1.10875e10			0.167141
$255$	−4.26200e10	−	1.62855e9i	−0.631223	−	0.0241196i
$256$	4.29497e9			0.0625000
$257$			3.99412e10i			0.571114i	0.958362	+	0.285557i	$0.0921785\pi$
$257$			3.99412e10i			0.571114i	−0.958362	+	0.285557i	$0.907821\pi$
$258$		−	2.16291e9i		−	0.0303914i
$259$	−1.06358e10			−0.146865
$260$	2.45787e9	−	6.43238e10i	0.0333563	−	0.872954i
$261$	−3.94645e10			−0.526411
$262$			2.24345e10i			0.294145i
$263$			9.01083e10i			1.16135i	0.814135	+	0.580676i	$0.197212\pi$
$263$			9.01083e10i			1.16135i	−0.814135	+	0.580676i	$0.802788\pi$
$264$	7.84008e9			0.0993351
$265$	−1.94459e9	+	5.08911e10i	−0.0242226	+	0.633921i
$266$	6.34861e10			0.777519
$267$		−	6.62913e9i		−	0.0798281i
$268$		−	3.22615e10i		−	0.382013i
$269$	1.14771e11			1.33643			0.668217	−	0.743966i	$-0.267058\pi$
$269$	1.14771e11			1.33643			0.668217	+	0.743966i	$0.267058\pi$
$270$	1.18747e10	+	4.53743e8i	0.135984	+	0.00519604i
$271$	9.34587e10			1.05259			0.526293	−	0.850303i	$-0.323581\pi$
$271$	9.34587e10			1.05259			0.526293	+	0.850303i	$0.323581\pi$
$272$		−	2.46922e10i		−	0.273527i
$273$			1.67975e11i			1.83026i
$274$	−1.02189e11			−1.09528
$275$	4.60190e10	+	3.52199e9i	0.485222	+	0.0371357i
$276$	−8.77018e9			−0.0909741
$277$			4.20391e9i			0.0429037i	0.999770	+	0.0214519i	$0.00682886\pi$
$277$			4.20391e9i			0.0429037i	−0.999770	+	0.0214519i	$0.993171\pi$
$278$			3.72611e10i			0.374158i
$279$	3.54248e10			0.350017
$280$	−6.59302e10	−	2.51925e9i	−0.641023	−	0.0244940i
$281$	−3.09270e10			−0.295910			−0.147955	−	0.988994i	$-0.547269\pi$
$281$	−3.09270e10			−0.295910			−0.147955	+	0.988994i	$0.547269\pi$
$282$		−	3.91759e10i		−	0.368891i
$283$		−	9.06447e10i		−	0.840047i	−0.907513	−	0.420023i	$-0.862022\pi$
$283$		−	9.06447e10i		−	0.840047i	0.907513	−	0.420023i	$-0.137978\pi$
$284$	1.28425e10			0.117144
$285$	1.48800e9	−	3.89417e10i	0.0133598	−	0.349634i
$286$	6.80266e10			0.601218
$287$		−	2.48549e11i		−	2.16244i
$288$			6.87971e9i			0.0589256i
$289$	−2.33705e10			−0.197073
$290$	5.13560e9	−	1.34402e11i	0.0426384	−	1.11587i
$291$	−7.40661e10			−0.605482
$292$			1.03999e11i			0.837155i
$293$		−	1.41313e11i		−	1.12015i	−0.828440	−	0.560077i	$-0.810771\pi$
$293$		−	1.41313e11i		−	1.12015i	0.828440	−	0.560077i	$-0.189229\pi$
$294$	1.19872e11			0.935739
$295$	1.54119e11	+	5.88900e9i	1.18483	+	0.0452733i
$296$	−3.77965e9			−0.0286180
$297$			1.25583e10i			0.0936540i
$298$		−	1.93793e10i		−	0.142353i
$299$	−7.60969e10			−0.550613
$300$	−3.09056e9	+	4.03819e10i	−0.0220289	+	0.287833i
$301$	−1.92358e10			−0.135071
$302$			7.04162e10i			0.487126i
$303$			1.19456e11i			0.814170i
$304$	2.25612e10			0.151506
$305$	1.70254e11	+	6.50555e9i	1.12654	+	0.0430462i
$306$	3.95522e10			0.257884
$307$			1.66025e11i			1.06672i	0.845888	+	0.533361i	$0.179071\pi$
$307$			1.66025e11i			1.06672i	−0.845888	+	0.533361i	$0.820929\pi$
$308$		−	6.97256e10i		−	0.441483i
$309$	1.00506e11			0.627159
$310$	−4.60991e9	+	1.20644e11i	−0.0283508	+	0.741957i
$311$	1.38804e11			0.841359			0.420679	−	0.907209i	$-0.361792\pi$
$311$	1.38804e11			0.841359			0.420679	+	0.907209i	$0.361792\pi$
$312$			5.96937e10i			0.356642i
$313$		−	1.16787e11i		−	0.687773i	−0.939011	−	0.343886i	$-0.888257\pi$
$313$		−	1.16787e11i		−	0.687773i	0.939011	−	0.343886i	$-0.111743\pi$
$314$	4.06459e10			0.235957
$315$	4.03535e9	−	1.05608e11i	0.0230932	−	0.604362i
$316$	−1.50362e11			−0.848292
$317$		−	7.67758e10i		−	0.427029i	−0.976940	−	0.213515i	$-0.931509\pi$
$317$		−	7.67758e10i		−	0.427029i	0.976940	−	0.213515i	$-0.0684911\pi$
$318$		−	4.72279e10i		−	0.258986i
$319$	1.42139e11			0.768518
$320$	−2.34298e10	−	8.95271e8i	−0.124909	−	0.00477287i
$321$	6.56068e9			0.0344886
$322$			7.79974e10i			0.404323i
$323$		−	1.29707e11i		−	0.663058i
$324$	−1.10200e10			−0.0555556
$325$	−2.68161e10	+	3.50385e11i	−0.133328	+	1.74209i
$326$	−8.07341e10			−0.395893
$327$			7.07687e10i			0.342276i
$328$		−	8.83275e10i		−	0.421370i
$329$	−3.48410e11			−1.63949
$330$	−4.27690e10	−	1.63424e9i	−0.198525	−	0.00758582i
$331$	−3.72820e11			−1.70716			−0.853579	−	0.520963i	$-0.825573\pi$
$331$	−3.72820e11			−1.70716			−0.853579	+	0.520963i	$0.825573\pi$
$332$			7.98686e9i			0.0360790i
$333$		−	6.05427e9i		−	0.0269813i
$334$	2.15544e9			0.00947712
$335$	−6.72481e9	+	1.75992e11i	−0.0291728	+	0.763470i
$336$	6.11845e10			0.261887
$337$		−	2.56831e10i		−	0.108471i	−0.998528	−	0.0542354i	$-0.982728\pi$
$337$		−	2.56831e10i		−	0.108471i	0.998528	−	0.0542354i	$-0.0172721\pi$
$338$			3.48277e11i			1.45144i
$339$	−1.78692e11			−0.734861
$340$	−5.14701e9	+	1.34700e11i	−0.0208882	+	0.546655i
$341$	−1.27589e11			−0.510997
$342$			3.61387e10i			0.142842i
$343$		−	6.00965e11i		−	2.34437i
$344$	−6.83588e9			−0.0263197
$345$	4.78428e10	+	1.82811e9i	0.181815	+	0.00694732i
$346$	−2.09658e11			−0.786445
$347$		−	2.42556e11i		−	0.898111i	−0.893504	−	0.449056i	$-0.851761\pi$
$347$		−	2.42556e11i		−	0.898111i	0.893504	−	0.449056i	$-0.148239\pi$
$348$			1.24727e11i			0.455885i
$349$	1.15225e11			0.415750			0.207875	−	0.978155i	$-0.433345\pi$
$349$	1.15225e11			0.415750			0.207875	+	0.978155i	$0.433345\pi$
$350$	3.59136e11	+	2.74859e10i	1.27924	+	0.0979046i
$351$	−9.56177e10			−0.336246
$352$		−	2.47785e10i		−	0.0860267i
$353$			3.14641e11i			1.07852i	0.842138	+	0.539262i	$0.181297\pi$
$353$			3.14641e11i			1.07852i	−0.842138	+	0.539262i	$0.818703\pi$
$354$	−1.43025e11			−0.484058
$355$	−7.00582e10	−	2.67698e9i	−0.234116	−	0.00894577i
$356$	−2.09513e10			−0.0691331
$357$		−	3.51756e11i		−	1.14613i
$358$		−	3.08972e11i		−	0.994135i
$359$	3.66236e10			0.116369			0.0581844	−	0.998306i	$-0.481469\pi$
$359$	3.66236e10			0.116369			0.0581844	+	0.998306i	$0.481469\pi$
$360$	1.43405e9	−	3.75300e10i	0.00449991	−	0.117765i
$361$	−2.04175e11			−0.632733
$362$		−	7.20298e9i		−	0.0220457i
$363$			1.45763e11i			0.440623i
$364$	5.30884e11			1.58505
$365$	2.16782e10	−	5.67332e11i	0.0639302	−	1.67309i
$366$	−1.57999e11			−0.460245
$367$		−	3.50305e11i		−	1.00797i	−0.863711	−	0.503987i	$-0.831866\pi$
$367$		−	3.50305e11i		−	1.00797i	0.863711	−	0.503987i	$-0.168134\pi$
$368$			2.77181e10i			0.0787859i
$369$	1.41484e11			0.397272
$370$	2.06186e10	+	7.87855e8i	0.0571942	+	0.00218544i
$371$	−4.20020e11			−1.15103
$372$		−	1.11960e11i		−	0.303124i
$373$			3.18411e11i			0.851722i	0.904789	+	0.425861i	$0.140029\pi$
$373$			3.18411e11i			0.851722i	−0.904789	+	0.425861i	$0.859971\pi$
$374$	−1.42454e11			−0.376490
$375$	2.52770e10	−	2.19646e11i	0.0660063	−	0.573565i
$376$	−1.23815e11			−0.319469
$377$			1.08223e12i			2.75921i
$378$			9.80058e10i			0.246910i
$379$	7.75004e11			1.92942			0.964712	−	0.263308i	$-0.0848136\pi$
$379$	7.75004e11			1.92942			0.964712	+	0.263308i	$0.0848136\pi$
$380$	−1.23075e11	−	4.70280e9i	−0.302792	−	0.0115699i
$381$	5.61306e10			0.136470
$382$		−	7.95528e8i		−	0.00191148i
$383$			2.57843e11i			0.612295i	0.951984	+	0.306148i	$0.0990401\pi$
$383$			2.57843e11i			0.612295i	−0.951984	+	0.306148i	$0.900960\pi$
$384$	2.17433e10			0.0510310
$385$	−1.45341e10	+	3.80365e11i	−0.0337142	+	0.882322i
$386$	−5.48926e11			−1.25855
$387$		−	1.09498e10i		−	0.0248145i
$388$			2.34085e11i			0.524362i
$389$	−2.08420e11			−0.461494			−0.230747	−	0.973014i	$-0.574117\pi$
$389$	−2.08420e11			−0.461494			−0.230747	+	0.973014i	$0.574117\pi$
$390$	1.24429e10	−	3.25639e11i	0.0272353	−	0.712764i
$391$	1.59354e11			0.344801
$392$		−	3.78855e11i		−	0.810374i
$393$			1.13575e11i			0.240168i
$394$	−1.81748e11			−0.379959
$395$	8.20249e11	+	3.13424e10i	1.69535	+	0.0647806i
$396$	3.96904e10			0.0811068
$397$			2.71957e11i			0.549469i	0.961520	+	0.274734i	$0.0885899\pi$
$397$			2.71957e11i			0.549469i	−0.961520	+	0.274734i	$0.911410\pi$
$398$		−	1.83204e11i		−	0.365984i
$399$	3.21398e11			0.634842
$400$	1.27627e11	+	9.76771e9i	0.249271	+	0.0190776i
$401$	9.91322e11			1.91454			0.957271	−	0.289192i	$-0.0933866\pi$
$401$	9.91322e11			1.91454			0.957271	+	0.289192i	$0.0933866\pi$
$402$		−	1.63324e11i		−	0.311913i
$403$		−	9.71452e11i		−	1.83463i
$404$	3.77539e11			0.705092
$405$	6.01158e10	+	2.29707e9i	0.111030	+	0.00424255i
$406$	1.10926e12			2.02612
$407$			2.18056e10i			0.0393906i
$408$		−	1.25004e11i		−	0.223334i
$409$	−8.27520e11			−1.46226			−0.731128	−	0.682240i	$-0.761006\pi$
$409$	−8.27520e11			−1.46226			−0.731128	+	0.682240i	$0.761006\pi$
$410$	−1.84116e10	+	4.81842e11i	−0.0321783	+	0.842126i
$411$	−5.17330e11			−0.894292
$412$		−	3.17648e11i		−	0.543136i
$413$			1.27199e12i			2.15133i
$414$	−4.43990e10			−0.0742800
$415$	1.66483e9	−	4.35697e10i	0.00275521	−	0.0721054i
$416$	1.88662e11			0.308861
$417$			1.88635e11i			0.305498i
$418$		−	1.30160e11i		−	0.208538i
$419$	5.74138e11			0.910025			0.455013	−	0.890485i	$-0.349635\pi$
$419$	5.74138e11			0.910025			0.455013	+	0.890485i	$0.349635\pi$
$420$	−3.33772e11	−	1.27537e10i	−0.523393	−	0.0199993i
$421$	−7.22096e11			−1.12028			−0.560138	−	0.828399i	$-0.689252\pi$
$421$	−7.22096e11			−1.12028			−0.560138	+	0.828399i	$0.689252\pi$
$422$		−	2.87663e11i		−	0.441548i
$423$		−	1.98328e11i		−	0.301198i
$424$	−1.49263e11			−0.224288
$425$	5.61556e10	−	7.33740e11i	0.0834917	−	1.09092i
$426$	6.50153e10			0.0956473
$427$			1.40516e12i			2.04550i
$428$		−	2.07350e10i		−	0.0298680i
$429$	3.44385e11			0.490892
$430$	3.72909e10	+	1.42491e9i	0.0526010	+	0.00200993i
$431$	−6.48320e11			−0.904986			−0.452493	−	0.891768i	$-0.649465\pi$
$431$	−6.48320e11			−0.904986			−0.452493	+	0.891768i	$0.649465\pi$
$432$			3.48285e10i			0.0481125i
$433$		−	1.17824e12i		−	1.61078i	−0.592743	−	0.805391i	$-0.701955\pi$
$433$		−	1.17824e12i		−	1.61078i	0.592743	−	0.805391i	$-0.298045\pi$
$434$	−9.95714e11			−1.34720
$435$	2.59990e10	−	6.80409e11i	0.0348141	−	0.911105i
$436$	2.23664e11			0.296419
$437$			1.45601e11i			0.190985i
$438$			5.26495e11i			0.683534i
$439$	−7.89728e11			−1.01482			−0.507408	−	0.861706i	$-0.669396\pi$
$439$	−7.89728e11			−1.01482			−0.507408	+	0.861706i	$0.669396\pi$
$440$	−5.16500e9	+	1.35171e11i	−0.00656951	+	0.171928i
$441$	6.06852e11			0.764028
$442$		−	1.08464e12i		−	1.35171i
$443$			2.57150e11i			0.317227i	0.987341	+	0.158613i	$0.0507024\pi$
$443$			2.57150e11i			0.317227i	−0.987341	+	0.158613i	$0.949298\pi$
$444$	−1.91345e10			−0.0233665
$445$	1.14293e11	+	4.36723e9i	0.138165	+	0.00527942i
$446$	−3.09338e10			−0.0370192
$447$		−	9.81078e10i		−	0.116230i
$448$		−	1.93373e11i		−	0.226801i
$449$	6.64748e11			0.771878			0.385939	−	0.922524i	$-0.373878\pi$
$449$	6.64748e11			0.771878			0.385939	+	0.922524i	$0.373878\pi$
$450$	−1.56460e10	+	2.04433e11i	−0.0179865	+	0.235015i
$451$	−5.09579e11			−0.579986
$452$			5.64754e11i			0.636409i
$453$			3.56482e11i			0.397737i
$454$	−4.80375e11			−0.530676
$455$	−2.89606e12	−	1.10661e11i	−3.16779	−	0.121044i
$456$	1.14216e11			0.123704
$457$			1.35061e11i			0.144846i	0.997374	+	0.0724232i	$0.0230732\pi$
$457$			1.35061e11i			0.144846i	−0.997374	+	0.0724232i	$0.976927\pi$
$458$		−	3.08960e11i		−	0.328101i
$459$	2.00233e11			0.210561
$460$	5.77774e9	−	1.51207e11i	0.00601656	−	0.157457i
$461$	1.39045e12			1.43384			0.716921	−	0.697154i	$-0.245551\pi$
$461$	1.39045e12			1.43384			0.716921	+	0.697154i	$0.245551\pi$
$462$		−	3.52986e11i		−	0.360469i
$463$			1.26409e12i			1.27839i	0.769043	+	0.639197i	$0.220733\pi$
$463$			1.26409e12i			1.27839i	−0.769043	+	0.639197i	$0.779267\pi$
$464$	3.94200e11			0.394808
$465$	−2.33377e10	+	6.10761e11i	−0.0231483	+	0.605805i
$466$	3.25808e11			0.320055
$467$		−	1.68750e12i		−	1.64179i	−0.571077	−	0.820896i	$-0.693474\pi$
$467$		−	1.68750e12i		−	1.64179i	0.571077	−	0.820896i	$-0.306526\pi$
$468$			3.02199e11i			0.291197i
$469$	−1.45252e12			−1.38626
$470$	6.75433e11	+	2.58088e10i	0.638472	+	0.0243965i
$471$	2.05770e11			0.192658
$472$			4.52029e11i			0.419206i
$473$			3.94375e10i			0.0362272i
$474$	−7.61206e11			−0.692628
$475$	6.70415e11	+	5.13092e10i	0.604258	+	0.0462460i
$476$	−1.11172e12			−0.992580
$477$		−	2.39091e11i		−	0.211461i
$478$			1.37611e12i			1.20567i
$479$	−1.29843e12			−1.12696			−0.563481	−	0.826129i	$-0.690538\pi$
$479$	−1.29843e12			−1.12696			−0.563481	+	0.826129i	$0.690538\pi$
$480$	−1.18613e11	−	4.53231e9i	−0.101988	−	0.00389703i
$481$	−1.66026e11			−0.141424
$482$		−	8.93002e11i		−	0.753600i
$483$			3.94862e11i			0.330128i
$484$	4.60682e11			0.381590
$485$	4.87943e10	−	1.27698e12i	0.0400434	−	1.04796i
$486$	−5.57886e10			−0.0453609
$487$			9.96552e11i			0.802823i	0.915898	+	0.401411i	$0.131480\pi$
$487$			9.96552e11i			0.802823i	−0.915898	+	0.401411i	$0.868520\pi$
$488$			4.99355e11i			0.398584i
$489$	−4.08717e11			−0.323245
$490$	−7.89709e10	+	2.06672e12i	−0.0618849	+	1.61957i
$491$	2.35972e12			1.83229			0.916145	−	0.400846i	$-0.131284\pi$
$491$	2.35972e12			1.83229			0.916145	+	0.400846i	$0.131284\pi$
$492$		−	4.47158e11i		−	0.344047i
$493$		−	2.26630e12i		−	1.72785i
$494$	9.91027e11			0.748711
$495$	−2.16518e11	−	8.27333e9i	−0.162095	−	0.00619380i
$496$	−3.53849e11			−0.262513
$497$		−	5.78212e11i		−	0.425093i
$498$			4.04335e10i			0.0294584i
$499$	1.62292e12			1.17178			0.585889	−	0.810391i	$-0.300746\pi$
$499$	1.62292e12			1.17178			0.585889	+	0.810391i	$0.300746\pi$
$500$	−6.94190e11	−	7.98879e10i	−0.496722	−	0.0571631i
$501$	1.09119e10			0.00773804
$502$			7.17262e11i			0.504093i
$503$		−	2.54673e12i		−	1.77389i	−0.461874	−	0.886945i	$-0.652823\pi$
$503$		−	2.54673e12i		−	1.77389i	0.461874	−	0.886945i	$-0.347177\pi$
$504$	3.09747e11			0.213830
$505$	−2.05954e12	−	7.86967e10i	−1.40916	−	0.0538450i
$506$	1.59911e11			0.108443
$507$			1.76315e12i			1.18510i
$508$		−	1.77400e11i		−	0.118186i
$509$	8.17390e11			0.539758			0.269879	−	0.962894i	$-0.413016\pi$
$509$	8.17390e11			0.539758			0.269879	+	0.962894i	$0.413016\pi$
$510$	−2.60567e10	+	6.81920e11i	−0.0170551	+	0.446342i
$511$	4.68237e12			3.03789
$512$		−	6.87195e10i		−	0.0441942i
$513$			1.82952e11i			0.116630i
$514$	6.39060e11			0.403838
$515$	−6.62126e10	+	1.73282e12i	−0.0414771	+	1.08548i
$516$	−3.46066e10			−0.0214900
$517$			7.14314e11i			0.439726i
$518$			1.70172e11i			0.103849i
$519$	−1.06139e12			−0.642129
$520$	−1.02918e12	−	3.93258e10i	−0.617272	−	0.0235865i
$521$	−1.18857e12			−0.706733			−0.353366	−	0.935485i	$-0.614963\pi$
$521$	−1.18857e12			−0.706733			−0.353366	+	0.935485i	$0.614963\pi$
$522$			6.31432e11i			0.372228i
$523$		−	1.85559e12i		−	1.08448i	−0.840222	−	0.542242i	$-0.817575\pi$
$523$		−	1.85559e12i		−	1.08448i	0.840222	−	0.542242i	$-0.182425\pi$
$524$	3.58953e11			0.207992
$525$	1.81812e12	+	1.39147e11i	1.04450	+	0.0799388i
$526$	1.44173e12			0.821200
$527$			2.03432e12i			1.14887i
$528$		−	1.25441e11i		−	0.0702405i
$529$	1.62227e12			0.900685
$530$	8.14257e11	+	3.11134e10i	0.448250	+	0.0171280i
$531$	−7.24064e11			−0.395231
$532$		−	1.01578e12i		−	0.549789i
$533$		−	3.87989e12i		−	2.08232i
$534$	−1.06066e11			−0.0564470
$535$	−4.32214e9	+	1.13113e11i	−0.00228090	+	0.0596925i
$536$	−5.16185e11			−0.270124
$537$		−	1.56417e12i		−	0.811708i
$538$		−	1.83634e12i		−	0.945002i
$539$	−2.18569e12			−1.11542
$540$	7.25988e9	−	1.89995e11i	0.00367416	−	0.0961549i
$541$	−9.66487e11			−0.485074			−0.242537	−	0.970142i	$-0.577980\pi$
$541$	−9.66487e11			−0.485074			−0.242537	+	0.970142i	$0.577980\pi$
$542$		−	1.49534e12i		−	0.744291i
$543$		−	3.64651e10i		−	0.0180002i
$544$	−3.95076e11			−0.193413
$545$	−1.22012e12	−	4.66220e10i	−0.592407	−	0.0226364i
$546$	2.68760e12			1.29419
$547$		−	1.31778e12i		−	0.629359i	−0.949198	−	0.314680i	$-0.898103\pi$
$547$		−	1.31778e12i		−	0.629359i	0.949198	−	0.314680i	$-0.101897\pi$
$548$			1.63502e12i			0.774480i
$549$	−7.99870e11			−0.375789
$550$	5.63519e10	−	7.36304e11i	0.0262589	−	0.343104i
$551$	2.07071e12			0.957055
$552$			1.40323e11i			0.0643284i
$553$			6.76977e12i			3.07830i
$554$	6.72626e10			0.0303375
$555$	1.04382e11	+	3.98852e9i	0.0466989	+	0.00178440i
$556$	5.96178e11			0.264569
$557$			1.10028e11i			0.0484347i	0.999707	+	0.0242173i	$0.00770937\pi$
$557$			1.10028e11i			0.0484347i	−0.999707	+	0.0242173i	$0.992291\pi$
$558$		−	5.66798e11i		−	0.247499i
$559$	−3.00274e11			−0.130066
$560$	−4.03080e10	+	1.05488e12i	−0.0173199	+	0.453272i
$561$	−7.21176e11			−0.307403
$562$			4.94832e11i			0.209240i
$563$			2.32028e12i			0.973314i	0.873593	+	0.486657i	$0.161784\pi$
$563$			2.32028e12i			0.973314i	−0.873593	+	0.486657i	$0.838216\pi$
$564$	−6.26814e11			−0.260845
$565$	1.17721e11	−	3.08083e12i	0.0485999	−	1.27189i
$566$	−1.45032e12			−0.594003
$567$			4.96154e11i			0.201601i
$568$		−	2.05481e11i		−	0.0828330i
$569$	1.95405e12			0.781501			0.390751	−	0.920497i	$-0.372216\pi$
$569$	1.95405e12			0.781501			0.390751	+	0.920497i	$0.372216\pi$
$570$	−6.23068e11	−	2.38079e10i	−0.247228	−	0.00944680i
$571$	−1.91313e12			−0.753151			−0.376575	−	0.926386i	$-0.622898\pi$
$571$	−1.91313e12			−0.753151			−0.376575	+	0.926386i	$0.622898\pi$
$572$		−	1.08843e12i		−	0.425125i
$573$		−	4.02736e9i		−	0.00156072i
$574$	−3.97679e12			−1.52908
$575$	−6.30371e10	+	8.23655e11i	−0.0240487	+	0.314225i
$576$	1.10075e11			0.0416667
$577$			7.00977e11i			0.263277i	0.991298	+	0.131638i	$0.0420238\pi$
$577$			7.00977e11i			0.263277i	−0.991298	+	0.131638i	$0.957976\pi$
$578$			3.73928e11i			0.139352i
$579$	−2.77894e12			−1.02760
$580$	−2.15043e12	−	8.21697e10i	−0.789040	−	0.0301499i
$581$	3.59594e11			0.130924
$582$			1.18506e12i			0.428140i
$583$			8.61130e11i			0.308717i
$584$	1.66398e12			0.591958
$585$	6.29924e10	−	1.64855e12i	0.0222375	−	0.581970i
$586$	−2.26101e12			−0.792069
$587$			4.12852e12i			1.43524i	0.696437	+	0.717618i	$0.254768\pi$
$587$			4.12852e12i			1.43524i	−0.696437	+	0.717618i	$0.745232\pi$
$588$		−	1.91795e12i		−	0.661667i
$589$	−1.85875e12			−0.636358
$590$	9.42240e10	−	2.46590e12i	0.0320131	−	0.837801i
$591$	−9.20100e11			−0.310235
$592$			6.04744e10i			0.0202360i
$593$			1.42543e12i			0.473367i	0.971587	+	0.236684i	$0.0760605\pi$
$593$			1.42543e12i			0.473367i	−0.971587	+	0.236684i	$0.923939\pi$
$594$	2.00933e11			0.0662234
$595$	6.06464e12	+	2.31735e11i	1.98371	+	0.0757993i
$596$	−3.10069e11			−0.100659
$597$		−	9.27473e11i		−	0.298825i
$598$			1.21755e12i			0.389342i
$599$	−1.53586e12			−0.487452			−0.243726	−	0.969844i	$-0.578370\pi$
$599$	−1.53586e12			−0.487452			−0.243726	+	0.969844i	$0.578370\pi$
$600$	6.46111e11	+	4.94490e10i	0.203529	+	0.0155768i
$601$	−5.17710e12			−1.61864			−0.809322	−	0.587365i	$-0.800165\pi$
$601$	−5.17710e12			−1.61864			−0.809322	+	0.587365i	$0.800165\pi$
$602$			3.07773e11i			0.0955095i
$603$		−	8.26828e11i		−	0.254676i
$604$	1.12666e12			0.344450
$605$	−2.51310e12	−	9.60277e10i	−0.762624	−	0.0291405i
$606$	1.91129e12			0.575705
$607$			6.84196e11i			0.204565i	0.994755	+	0.102283i	$0.0326146\pi$
$607$			6.84196e11i			0.204565i	−0.994755	+	0.102283i	$0.967385\pi$
$608$		−	3.60979e11i		−	0.107131i
$609$	5.61563e12			1.65432
$610$	1.04089e11	−	2.72407e12i	0.0304383	−	0.796587i
$611$	−5.43873e12			−1.57874
$612$		−	6.32835e11i		−	0.182351i
$613$		−	9.34376e11i		−	0.267270i	−0.991031	−	0.133635i	$-0.957335\pi$
$613$		−	9.34376e11i		−	0.267270i	0.991031	−	0.133635i	$-0.0426649\pi$
$614$	2.65640e12			0.754287
$615$	−9.32086e10	+	2.43932e12i	−0.0262735	+	0.687593i
$616$	−1.11561e12			−0.312175
$617$			1.90293e12i			0.528614i	0.964439	+	0.264307i	$0.0851432\pi$
$617$			1.90293e12i			0.528614i	−0.964439	+	0.264307i	$0.914857\pi$
$618$		−	1.60809e12i		−	0.443469i
$619$	−7.94806e11			−0.217597			−0.108799	−	0.994064i	$-0.534700\pi$
$619$	−7.94806e11			−0.217597			−0.108799	+	0.994064i	$0.534700\pi$
$620$	1.93031e12	+	7.37586e10i	0.524643	+	0.0200470i
$621$	−2.24770e11			−0.0606494
$622$		−	2.22087e12i		−	0.594931i
$623$			9.43296e11i			0.250872i
$624$	9.55099e11			0.252184
$625$	3.77027e12	+	5.80503e11i	0.988353	+	0.152175i
$626$	−1.86859e12			−0.486329
$627$		−	6.58935e11i		−	0.170270i
$628$		−	6.50335e11i		−	0.166847i
$629$	3.47674e11			0.0885614
$630$	−1.68972e12	−	6.45656e10i	−0.427349	−	0.0163293i
$631$	4.87329e12			1.22374			0.611872	−	0.790957i	$-0.290417\pi$
$631$	4.87329e12			1.22374			0.611872	+	0.790957i	$0.290417\pi$
$632$			2.40579e12i			0.599833i
$633$		−	1.45629e12i		−	0.360522i
$634$	−1.22841e12			−0.301955
$635$	−3.69785e10	+	9.67749e11i	−0.00902542	+	0.236201i
$636$	−7.55646e11			−0.183131
$637$		−	1.66416e13i		−	4.00469i
$638$		−	2.27422e12i		−	0.543425i
$639$	3.29140e11			0.0780957
$640$	−1.43243e10	+	3.74876e11i	−0.00337493	+	0.0883239i
$641$	4.51469e12			1.05625			0.528125	−	0.849166i	$-0.322895\pi$
$641$	4.51469e12			1.05625			0.528125	+	0.849166i	$0.322895\pi$
$642$		−	1.04971e11i		−	0.0243872i
$643$			2.91863e12i			0.673332i	0.941624	+	0.336666i	$0.109299\pi$
$643$			2.91863e12i			0.673332i	−0.941624	+	0.336666i	$0.890701\pi$
$644$	1.24796e12			0.285900
$645$	1.88785e11	+	7.21363e9i	0.0429486	+	0.00164110i
$646$	−2.07531e12			−0.468853
$647$			1.79049e12i			0.401700i	0.979622	+	0.200850i	$0.0643705\pi$
$647$			1.79049e12i			0.401700i	−0.979622	+	0.200850i	$0.935630\pi$
$648$			1.76319e11i			0.0392837i
$649$	2.60785e12			0.577007
$650$	5.60616e12	+	4.29058e11i	1.23184	+	0.0942771i
$651$	−5.04080e12			−1.09998
$652$			1.29175e12i			0.279939i
$653$			2.18547e12i			0.470366i	0.971951	+	0.235183i	$0.0755690\pi$
$653$			2.18547e12i			0.470366i	−0.971951	+	0.235183i	$0.924431\pi$
$654$	1.13230e12			0.242025
$655$	−1.95815e12	−	7.48225e10i	−0.415680	−	0.0158835i
$656$	−1.41324e12			−0.297954
$657$			2.66538e12i			0.558104i
$658$			5.57456e12i			1.15929i
$659$	6.06885e12			1.25349			0.626747	−	0.779223i	$-0.284386\pi$
$659$	6.06885e12			1.25349			0.626747	+	0.779223i	$0.284386\pi$
$660$	−2.61478e10	+	6.84303e11i	−0.00536398	+	0.140379i
$661$	−1.27039e12			−0.258839			−0.129419	−	0.991590i	$-0.541311\pi$
$661$	−1.27039e12			−0.258839			−0.129419	+	0.991590i	$0.541311\pi$
$662$			5.96513e12i			1.20714i
$663$		−	5.49097e12i		−	1.10367i
$664$	1.27790e11			0.0255117
$665$	−2.11735e11	+	5.54124e12i	−0.0419852	+	1.09878i
$666$	−9.68683e10			−0.0190787
$667$			2.54402e12i			0.497684i
$668$		−	3.44870e10i		−	0.00670134i
$669$	−1.56603e11			−0.0302260
$670$	2.81588e12	+	1.07597e11i	0.539855	+	0.0206283i
$671$	2.88088e12			0.548622
$672$		−	9.78952e11i		−	0.185182i
$673$			9.68837e12i			1.82047i	0.414096	+	0.910233i	$0.364098\pi$
$673$			9.68837e12i			1.82047i	−0.414096	+	0.910233i	$0.635902\pi$
$674$	−4.10929e11			−0.0767004
$675$	−7.92078e10	+	1.03494e12i	−0.0146859	+	0.191889i
$676$	5.57243e12			1.02632
$677$		−	9.59636e12i		−	1.75573i	−0.478909	−	0.877865i	$-0.658968\pi$
$677$		−	9.59636e12i		−	1.75573i	0.478909	−	0.877865i	$-0.341032\pi$
$678$			2.85907e12i			0.519625i
$679$	1.05393e13			1.90282
$680$	2.15521e12	+	8.23522e10i	0.386544	+	0.0147702i
$681$	−2.43190e12			−0.433295
$682$			2.04142e12i			0.361330i
$683$		−	2.46916e12i		−	0.434167i	−0.976153	−	0.217083i	$-0.930346\pi$
$683$		−	2.46916e12i		−	0.434167i	0.976153	−	0.217083i	$-0.0696544\pi$
$684$	5.78219e11			0.101004
$685$	3.40814e11	−	8.91930e12i	0.0591439	−	1.54783i
$686$	−9.61544e12			−1.65772
$687$		−	1.56411e12i		−	0.267893i
$688$			1.09374e11i			0.0186108i
$689$	−6.55657e12			−1.10838
$690$	2.92498e10	−	7.65485e11i	0.00491250	−	0.128563i
$691$	−3.70532e12			−0.618264			−0.309132	−	0.951019i	$-0.600039\pi$
$691$	−3.70532e12			−0.618264			−0.309132	+	0.951019i	$0.600039\pi$
$692$			3.35452e12i			0.556100i
$693$		−	1.78699e12i		−	0.294322i
$694$	−3.88090e12			−0.635060
$695$	−3.25225e12	−	1.24271e11i	−0.528753	−	0.0202041i
$696$	1.99564e12			0.322359
$697$			8.12488e12i			1.30397i
$698$		−	1.84360e12i		−	0.293980i
$699$	1.64940e12			0.261324
$700$	4.39774e11	−	5.74617e12i	0.0692290	−	0.904560i
$701$	−6.08652e11			−0.0952002			−0.0476001	−	0.998866i	$-0.515157\pi$
$701$	−6.08652e11			−0.0952002			−0.0476001	+	0.998866i	$0.515157\pi$
$702$			1.52988e12i			0.237761i
$703$			3.17668e11i			0.0490540i
$704$	−3.96456e11			−0.0608301
$705$	3.41938e12	+	1.30657e11i	0.521310	+	0.0199197i
$706$	5.03426e12			0.762631
$707$		−	1.69980e13i		−	2.55865i
$708$			2.28840e12i			0.342280i
$709$	−1.89628e12			−0.281835			−0.140918	−	0.990021i	$-0.545005\pi$
$709$	−1.89628e12			−0.281835			−0.140918	+	0.990021i	$0.545005\pi$
$710$	−4.28317e10	+	1.12093e12i	−0.00632562	+	0.165545i
$711$	−3.85361e12			−0.565528
$712$			3.35221e11i			0.0488845i
$713$		−	2.28361e12i		−	0.330917i
$714$	−5.62810e12			−0.810439
$715$	−2.26879e11	+	5.93755e12i	−0.0324651	+	0.849630i
$716$	−4.94355e12			−0.702960
$717$			6.96655e12i			0.984422i
$718$		−	5.85978e11i		−	0.0822851i
$719$	−1.06984e13			−1.49293			−0.746463	−	0.665427i	$-0.768250\pi$
$719$	−1.06984e13			−1.49293			−0.746463	+	0.665427i	$0.768250\pi$
$720$	−6.00479e11	−	2.29448e10i	−0.0832726	−	0.00318191i
$721$	−1.43015e13			−1.97094
$722$			3.26680e12i			0.447410i
$723$		−	4.52082e12i		−	0.615312i
$724$	−1.15248e11			−0.0155887
$725$	1.17138e13	+	8.96499e11i	1.57463	+	0.120512i
$726$	2.33220e12			0.311567
$727$		−	1.34110e13i		−	1.78055i	−0.455420	−	0.890277i	$-0.650511\pi$
$727$		−	1.34110e13i		−	1.78055i	0.455420	−	0.890277i	$-0.349489\pi$
$728$		−	8.49415e12i		−	1.12080i
$729$	−2.82430e11			−0.0370370
$730$	−9.07731e12	−	3.46852e11i	−1.18305	−	0.0452054i
$731$	6.28803e11			0.0814491
$732$			2.52798e12i			0.325443i
$733$			5.27165e12i			0.674495i	0.941416	+	0.337248i	$0.109496\pi$
$733$			5.27165e12i			0.674495i	−0.941416	+	0.337248i	$0.890504\pi$
$734$	−5.60488e12			−0.712745
$735$	−3.99790e11	+	1.04628e13i	−0.0505288	+	1.32237i
$736$	4.43490e11			0.0557100
$737$			2.97797e12i			0.371807i
$738$		−	2.26374e12i		−	0.280914i
$739$	3.37965e12			0.416842			0.208421	−	0.978039i	$-0.433168\pi$
$739$	3.37965e12			0.416842			0.208421	+	0.978039i	$0.433168\pi$
$740$	1.26057e10	−	3.29898e11i	0.00154534	−	0.0404424i
$741$	5.01707e12			0.611320
$742$			6.72032e12i			0.813902i
$743$		−	1.43051e13i		−	1.72203i	−0.508578	−	0.861016i	$-0.669829\pi$
$743$		−	1.43051e13i		−	1.72203i	0.508578	−	0.861016i	$-0.330171\pi$
$744$	−1.79136e12			−0.214341
$745$	1.69148e12	+	6.46329e10i	0.201170	+	0.00768688i
$746$	5.09457e12			0.602259
$747$			2.04694e11i			0.0240527i
$748$			2.27927e12i			0.266219i
$749$	−9.33556e11			−0.108386
$750$	−3.51433e12	−	4.04432e11i	−0.405572	−	0.0466735i
$751$	−1.04305e13			−1.19654			−0.598269	−	0.801295i	$-0.704145\pi$
$751$	−1.04305e13			−1.19654			−0.598269	+	0.801295i	$0.704145\pi$
$752$			1.98104e12i			0.225899i
$753$			3.63114e12i			0.411591i
$754$	1.73157e13			1.95105
$755$	−6.14612e12	−	2.34848e11i	−0.688398	−	0.0263043i
$756$	1.56809e12			0.174592
$757$			3.71920e12i			0.411641i	0.978590	+	0.205820i	$0.0659863\pi$
$757$			3.71920e12i			0.411641i	−0.978590	+	0.205820i	$0.934014\pi$
$758$		−	1.24001e13i		−	1.36431i
$759$	8.09551e11			0.0885434
$760$	−7.52448e10	+	1.96920e12i	−0.00818117	+	0.214106i
$761$	9.97542e12			1.07820			0.539101	−	0.842241i	$-0.318764\pi$
$761$	9.97542e12			1.07820			0.539101	+	0.842241i	$0.318764\pi$
$762$		−	8.98089e11i		−	0.0964989i
$763$		−	1.00701e13i		−	1.07565i
$764$	−1.27285e10			−0.00135162
$765$	−1.31912e11	+	3.45222e12i	−0.0139254	+	0.364437i
$766$	4.12549e12			0.432958
$767$			1.98559e13i			2.07162i
$768$		−	3.47892e11i		−	0.0360844i
$769$	−7.29892e12			−0.752645			−0.376322	−	0.926489i	$-0.622812\pi$
$769$	−7.29892e12			−0.752645			−0.376322	+	0.926489i	$0.622812\pi$
$770$	6.08584e12	+	2.32545e11i	0.623896	+	0.0238396i
$771$	3.23524e12			0.329733
$772$			8.78281e12i			0.889930i
$773$			4.61615e12i			0.465021i	0.972594	+	0.232511i	$0.0746940\pi$
$773$			4.61615e12i			0.465021i	−0.972594	+	0.232511i	$0.925306\pi$
$774$	−1.75196e11			−0.0175465
$775$	−1.05148e13	−	8.04731e11i	−1.04699	−	0.0801296i
$776$	3.74537e12			0.370780
$777$			8.61496e11i			0.0847927i
$778$			3.33472e12i			0.326325i
$779$	−7.42366e12			−0.722270
$780$	−5.21023e12	−	1.99087e11i	−0.504000	−	0.0192583i
$781$	−1.18546e12			−0.114014
$782$		−	2.54967e12i		−	0.243811i
$783$			3.19663e12i			0.303923i
$784$	−6.06167e12			−0.573021
$785$	−1.35560e11	+	3.54769e12i	−0.0127414	+	0.333451i
$786$	1.81720e12			0.169825
$787$			9.56490e12i			0.888780i	0.895834	+	0.444390i	$0.146579\pi$
$787$			9.56490e12i			0.888780i	−0.895834	+	0.444390i	$0.853421\pi$
$788$			2.90797e12i			0.268672i
$789$	7.29877e12			0.670507
$790$	5.01478e11	−	1.31240e13i	0.0458068	−	1.19879i
$791$	2.54270e13			2.30941
$792$		−	6.35046e11i		−	0.0573512i
$793$			2.19348e13i			1.96972i
$794$	4.35131e12			0.388533
$795$	4.12218e12	+	1.57512e11i	0.365994	+	0.0139849i
$796$	−2.93127e12			−0.258790
$797$		−	1.33590e13i		−	1.17277i	−0.810034	−	0.586384i	$-0.800551\pi$
$797$		−	1.33590e13i		−	1.17277i	0.810034	−	0.586384i	$-0.199449\pi$
$798$		−	5.14237e12i		−	0.448901i
$799$	1.13892e13			0.988630
$800$	1.56283e11	−	2.04203e12i	0.0134899	−	0.176261i
$801$	−5.36959e11			−0.0460888
$802$		−	1.58611e13i		−	1.35379i
$803$		−	9.59985e12i		−	0.814788i
$804$	−2.61319e12			−0.220556
$805$	−6.80782e12	−	2.60133e11i	−0.571382	−	0.0218330i
$806$	−1.55432e13			−1.29728
$807$		−	9.29647e12i		−	0.771591i
$808$		−	6.04062e12i		−	0.498575i
$809$	−1.09742e12			−0.0900753			−0.0450376	−	0.998985i	$-0.514341\pi$
$809$	−1.09742e12			−0.0900753			−0.0450376	+	0.998985i	$0.514341\pi$
$810$	3.67532e10	−	9.61852e11i	0.00299994	−	0.0785101i
$811$	2.33541e13			1.89570			0.947851	−	0.318715i	$-0.103251\pi$
$811$	2.33541e13			1.89570			0.947851	+	0.318715i	$0.103251\pi$
$812$		−	1.77482e13i		−	1.43269i
$813$		−	7.57015e12i		−	0.607711i
$814$	3.48889e11			0.0278533
$815$	2.69260e11	−	7.04669e12i	0.0213778	−	0.559469i
$816$	−2.00007e12			−0.157921
$817$			5.74535e11i			0.0451146i
$818$			1.32403e13i			1.03397i
$819$	1.36060e13			1.05670
$820$	7.70947e12	+	2.94585e11i	0.595473	+	0.0227535i
$821$	1.04183e13			0.800298			0.400149	−	0.916450i	$-0.368958\pi$
$821$	1.04183e13			0.800298			0.400149	+	0.916450i	$0.368958\pi$
$822$			8.27728e12i			0.632360i
$823$			8.51504e12i			0.646975i	0.946232	+	0.323487i	$0.104855\pi$
$823$			8.51504e12i			0.646975i	−0.946232	+	0.323487i	$0.895145\pi$
$824$	−5.08237e12			−0.384055
$825$	2.85281e11	−	3.72754e12i	0.0214403	−	0.280143i
$826$	2.03518e13			1.52122
$827$			4.37509e12i			0.325246i	0.986688	+	0.162623i	$0.0519955\pi$
$827$			4.37509e12i			0.325246i	−0.986688	+	0.162623i	$0.948005\pi$
$828$			7.10385e11i			0.0525239i
$829$	−1.90430e13			−1.40036			−0.700179	−	0.713967i	$-0.746897\pi$
$829$	−1.90430e13			−1.40036			−0.700179	+	0.713967i	$0.746897\pi$
$830$	−6.97114e11	−	2.66373e10i	−0.0509862	−	0.00194823i
$831$	3.40517e11			0.0247705
$832$		−	3.01858e12i		−	0.218398i
$833$			3.48492e13i			2.50779i
$834$	3.01815e12			0.216020
$835$	−7.18870e9	+	1.88133e11i	−0.000511754	+	0.0133929i
$836$	−2.08256e12			−0.147458
$837$		−	2.86941e12i		−	0.202082i
$838$		−	9.18621e12i		−	0.643485i
$839$	2.92417e12			0.203739			0.101870	−	0.994798i	$-0.467518\pi$
$839$	2.92417e12			0.203739			0.101870	+	0.994798i	$0.467518\pi$
$840$	−2.04059e11	+	5.34035e12i	−0.0141416	+	0.370095i
$841$	2.16733e13			1.49397
$842$			1.15535e13i			0.792155i
$843$			2.50509e12i			0.170844i
$844$	−4.60261e12			−0.312221
$845$	−3.03985e13	−	1.16155e12i	−2.05115	−	0.0783762i
$846$	−3.17325e12			−0.212979
$847$		−	2.07414e13i		−	1.38472i
$848$			2.38821e12i			0.158596i
$849$	−7.34222e12			−0.485001
$850$	−1.17398e13	−	8.98490e11i	−0.771396	−	0.0590375i
$851$	−3.90279e11			−0.0255089
$852$		−	1.04025e12i		−	0.0676328i
$853$			2.94793e12i			0.190654i	0.995446	+	0.0953272i	$0.0303897\pi$
$853$			2.94793e12i			0.190654i	−0.995446	+	0.0953272i	$0.969610\pi$
$854$	2.24826e13			1.44639
$855$	−3.15428e12	−	1.20528e11i	−0.201861	−	0.00771328i
$856$	−3.31760e11			−0.0211199
$857$		−	5.74771e12i		−	0.363983i	−0.983300	−	0.181991i	$-0.941746\pi$
$857$		−	5.74771e12i		−	0.363983i	0.983300	−	0.181991i	$-0.0582543\pi$
$858$		−	5.51016e12i		−	0.347113i
$859$	−2.62167e13			−1.64289			−0.821445	−	0.570288i	$-0.806832\pi$
$859$	−2.62167e13			−1.64289			−0.821445	+	0.570288i	$0.806832\pi$
$860$	2.27986e10	−	5.96654e11i	0.00142123	−	0.0371946i
$861$	−2.01325e13			−1.24849
$862$			1.03731e13i			0.639922i
$863$		−	2.71367e13i		−	1.66536i	−0.553756	−	0.832679i	$-0.686806\pi$
$863$		−	2.71367e13i		−	1.66536i	0.553756	−	0.832679i	$-0.313194\pi$
$864$	5.57256e11			0.0340207
$865$	6.99238e11	−	1.82995e13i	0.0424671	−	1.11139i
$866$	−1.88518e13			−1.13900
$867$			1.89301e12i			0.113780i
$868$			1.59314e13i			0.952611i
$869$	1.38795e13			0.825627
$870$	−1.08865e13	−	4.15984e11i	−0.644248	−	0.0246173i
$871$	−2.26740e13			−1.33489
$872$		−	3.57862e12i		−	0.209600i
$873$			5.99935e12i			0.349575i
$874$	2.32962e12			0.135047
$875$	−3.59681e12	+	3.12547e13i	−0.207435	+	1.80251i
$876$	8.42391e12			0.483332
$877$			3.20448e12i			0.182919i	0.995809	+	0.0914597i	$0.0291533\pi$
$877$			3.20448e12i			0.182919i	−0.995809	+	0.0914597i	$0.970847\pi$
$878$			1.26357e13i			0.717583i
$879$	−1.14464e13			−0.646722
$880$	2.16274e12	+	8.26400e10i	0.121571	+	0.00464535i
$881$	2.42828e13			1.35802			0.679011	−	0.734128i	$-0.262409\pi$
$881$	2.42828e13			1.35802			0.679011	+	0.734128i	$0.262409\pi$
$882$		−	9.70963e12i		−	0.540249i
$883$		−	1.99599e13i		−	1.10493i	−0.833536	−	0.552465i	$-0.813687\pi$
$883$		−	1.99599e13i		−	1.10493i	0.833536	−	0.552465i	$-0.186313\pi$
$884$	−1.73542e13			−0.955804
$885$	4.77009e11	−	1.24836e13i	0.0261386	−	0.684062i
$886$	4.11440e12			0.224313
$887$			3.21110e13i			1.74180i	0.491461	+	0.870900i	$0.336463\pi$
$887$			3.21110e13i			1.74180i	−0.491461	+	0.870900i	$0.663537\pi$
$888$			3.06152e11i			0.0165226i
$889$	−7.98714e12			−0.428877
$890$	6.98757e10	−	1.82869e12i	0.00373311	−	0.0976977i
$891$	1.01722e12			0.0540712
$892$			4.94941e11i			0.0261765i
$893$			1.04063e13i			0.547601i
$894$	−1.56973e12			−0.0821873
$895$	2.69679e13	+	1.03047e12i	1.40489	+	0.0536822i
$896$	−3.09397e12			−0.160373
$897$			6.16385e12i			0.317897i
$898$		−	1.06360e13i		−	0.545800i
$899$	−3.24769e13			−1.65827
$900$	3.27093e12	+	2.50336e11i	0.166181	+	0.0127184i
$901$	1.37301e13			0.694084
$902$			8.15327e12i			0.410112i
$903$			1.55810e12i			0.0779832i
$904$	9.03606e12			0.450009
$905$	6.28695e11	+	2.40230e10i	0.0311546	+	0.00119044i
$906$	5.70371e12			0.281242
$907$		−	2.31616e13i		−	1.13641i	−0.822887	−	0.568206i	$-0.807638\pi$
$907$		−	2.31616e13i		−	1.13641i	0.822887	−	0.568206i	$-0.192362\pi$
$908$			7.68600e12i			0.375244i
$909$	9.67591e12			0.470061
$910$	−1.77058e12	+	4.63370e13i	−0.0855911	+	2.23997i
$911$	−2.01248e13			−0.968054			−0.484027	−	0.875053i	$-0.660826\pi$
$911$	−2.01248e13			−0.968054			−0.484027	+	0.875053i	$0.660826\pi$
$912$		−	1.82746e12i		−	0.0874722i
$913$		−	7.37244e11i		−	0.0351150i
$914$	2.16098e12			0.102422
$915$	5.26950e11	−	1.37906e13i	0.0248527	−	0.650411i
$916$	−4.94336e12			−0.232003
$917$		−	1.61612e13i		−	0.754765i
$918$		−	3.20373e12i		−	0.148889i
$919$	6.30423e12			0.291549			0.145775	−	0.989318i	$-0.453433\pi$
$919$	6.30423e12			0.291549			0.145775	+	0.989318i	$0.453433\pi$
$920$	−2.41931e12	−	9.24439e10i	−0.111339	−	0.00425435i
$921$	1.34480e13			0.615873
$922$		−	2.22472e13i		−	1.01388i
$923$		−	9.02598e12i		−	0.409342i
$924$	−5.64777e12			−0.254890
$925$	−1.37532e11	+	1.79702e12i	−0.00617685	+	0.0807078i
$926$	2.02255e13			0.903961
$927$		−	8.14097e12i		−	0.362091i
$928$		−	6.30720e12i		−	0.279171i
$929$	−1.68246e13			−0.741097			−0.370549	−	0.928813i	$-0.620830\pi$
$929$	−1.68246e13			−0.741097			−0.370549	+	0.928813i	$0.620830\pi$
$930$	9.77217e12	+	3.73403e11i	0.428369	+	0.0163683i
$931$	−3.18416e13			−1.38906
$932$		−	5.21292e12i		−	0.226313i
$933$		−	1.12432e13i		−	0.485759i
$934$	−2.70000e13			−1.16092
$935$	4.75106e11	−	1.24338e13i	0.0203300	−	0.532049i
$936$	4.83519e12			0.205907
$937$			1.16791e13i			0.494972i	0.968891	+	0.247486i	$0.0796044\pi$
$937$			1.16791e13i			0.494972i	−0.968891	+	0.247486i	$0.920396\pi$
$938$			2.32403e13i			0.980232i
$939$	−9.45975e12			−0.397086
$940$	4.12941e11	−	1.08069e13i	0.0172510	−	0.451468i
$941$	−2.04936e13			−0.852049			−0.426024	−	0.904712i	$-0.640086\pi$
$941$	−2.04936e13			−0.852049			−0.426024	+	0.904712i	$0.640086\pi$
$942$		−	3.29232e12i		−	0.136230i
$943$		−	9.12052e12i		−	0.375593i
$944$	7.23247e12			0.296423
$945$	−8.55421e12	−	3.26863e11i	−0.348929	−	0.0133329i
$946$	6.31001e11			0.0256165
$947$			1.76453e13i			0.712942i	0.934306	+	0.356471i	$0.116020\pi$
$947$			1.76453e13i			0.712942i	−0.934306	+	0.356471i	$0.883980\pi$
$948$			1.21793e13i			0.489762i
$949$	7.30924e13			2.92533
$950$	8.20947e11	−	1.07266e13i	0.0327008	−	0.427275i
$951$	−6.21884e12			−0.246546
$952$			1.77876e13i			0.701860i
$953$			1.92532e13i			0.756111i	0.925783	+	0.378055i	$0.123407\pi$
$953$			1.92532e13i			0.756111i	−0.925783	+	0.378055i	$0.876593\pi$
$954$	−3.82546e12			−0.149526
$955$	6.94359e10	+	2.65320e9i	0.00270127	+	0.000103218i
$956$	2.20177e13			0.852535
$957$		−	1.15132e13i		−	0.443704i
$958$			2.07749e13i			0.796883i
$959$	7.36138e13			2.81045
$960$	−7.25170e10	+	1.89781e12i	−0.00275562	+	0.0721162i
$961$	2.71288e12			0.102607
$962$			2.65641e12i			0.100002i
$963$		−	5.31415e11i		−	0.0199120i
$964$	−1.42880e13			−0.532875
$965$	1.83075e12	−	4.79117e13i	0.0679603	−	1.77856i
$966$	6.31779e12			0.233436
$967$			4.08261e13i			1.50148i	0.660599	+	0.750739i	$0.270302\pi$
$967$			4.08261e13i			1.50148i	−0.660599	+	0.750739i	$0.729698\pi$
$968$		−	7.37092e12i		−	0.269825i
$969$	−1.05062e13			−0.382816
$970$	−2.04316e13	−	7.80709e11i	−0.741020	−	0.0283150i
$971$	3.20884e13			1.15841			0.579204	−	0.815183i	$-0.303364\pi$
$971$	3.20884e13			1.15841			0.579204	+	0.815183i	$0.303364\pi$
$972$			8.92617e11i			0.0320750i
$973$		−	2.68419e13i		−	0.960075i
$974$	1.59448e13			0.567681
$975$	2.83812e13	+	2.17211e12i	1.00580	+	0.0769769i
$976$	7.98968e12			0.281842
$977$			9.36548e12i			0.328855i	0.986389	+	0.164428i	$0.0525777\pi$
$977$			9.36548e12i			0.328855i	−0.986389	+	0.164428i	$0.947422\pi$
$978$			6.53947e12i			0.228569i
$979$	1.93396e12			0.0672860
$980$	3.30675e13	+	1.26354e12i	1.14521	+	0.0437593i
$981$	5.73226e12			0.197613
$982$		−	3.77556e13i		−	1.29563i
$983$		−	3.94997e13i		−	1.34928i	−0.738145	−	0.674642i	$-0.764298\pi$
$983$		−	3.94997e13i		−	1.34928i	0.738145	−	0.674642i	$-0.235702\pi$
$984$	−7.15453e12			−0.243278
$985$	6.06156e11	−	1.58635e13i	0.0205174	−	0.536951i
$986$	−3.62608e13			−1.22177
$987$			2.82212e13i			0.946560i
$988$		−	1.58564e13i		−	0.529419i
$989$	−7.05859e11			−0.0234603
$990$	−1.32373e11	+	3.46429e12i	−0.00437967	+	0.114619i
$991$	−9.82588e12			−0.323623			−0.161812	−	0.986822i	$-0.551734\pi$
$991$	−9.82588e12			−0.323623			−0.161812	+	0.986822i	$0.551734\pi$
$992$			5.66158e12i			0.185625i
$993$			3.01985e13i			0.985628i
$994$	−9.25140e12			−0.300586
$995$	1.59906e13	+	6.11013e11i	0.517202	+	0.0197627i
$996$	6.46935e11			0.0208302
$997$			1.26229e13i			0.404606i	0.979323	+	0.202303i	$0.0648425\pi$
$997$			1.26229e13i			0.404606i	−0.979323	+	0.202303i	$0.935157\pi$
$998$		−	2.59668e13i		−	0.828572i
$999$	−4.90396e11			−0.0155777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.10.c.a.19.2	✓	4
3.2	odd	2		90.10.c.a.19.3		4
4.3	odd	2		240.10.f.a.49.4		4
5.2	odd	4		150.10.a.o.1.1		2
5.3	odd	4		150.10.a.n.1.2		2
5.4	even	2	inner	30.10.c.a.19.4	yes	4
15.14	odd	2		90.10.c.a.19.1		4
20.19	odd	2		240.10.f.a.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.10.c.a.19.2	✓	4	1.1	even	1	trivial
30.10.c.a.19.4	yes	4	5.4	even	2	inner
90.10.c.a.19.1		4	15.14	odd	2
90.10.c.a.19.3		4	3.2	odd	2
150.10.a.n.1.2		2	5.3	odd	4
150.10.a.o.1.1		2	5.2	odd	4
240.10.f.a.49.2		4	20.19	odd	2
240.10.f.a.49.4		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	30.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-16.0000i q^{2} -81.0000i q^{3} -256.000 q^{4} +(1396.52 + 53.3623i) q^{5} -1296.00 q^{6} +11525.9i q^{7} +4096.00i q^{8} -6561.00 q^{9} +O(q^{10})\)	\(q-16.0000i q^{2} -81.0000i q^{3} -256.000 q^{4} +(1396.52 + 53.3623i) q^{5} -1296.00 q^{6} +11525.9i q^{7} +4096.00i q^{8} -6561.00 q^{9} +(853.797 - 22344.4i) q^{10} +23630.6 q^{11} +20736.0i q^{12} +179922. i q^{13} +184415. q^{14} +(4322.35 - 113118. i) q^{15} +65536.0 q^{16} -376774. i q^{17} +104976. i q^{18} +344256. q^{19} +(-357510. - 13660.8i) q^{20} +933602. q^{21} -378090. i q^{22} +422945. i q^{23} +331776. q^{24} +(1.94743e6 + 149043. i) q^{25} +2.87875e6 q^{26} +531441. i q^{27} -2.95064e6i q^{28} +6.01502e6 q^{29} +(-1.80989e6 - 69157.6i) q^{30} -5.39931e6 q^{31} -1.04858e6i q^{32} -1.91408e6i q^{33} -6.02838e6 q^{34} +(-615051. + 1.60963e7i) q^{35} +1.67962e6 q^{36} +922766. i q^{37} -5.50810e6i q^{38} +1.45737e7 q^{39} +(-218572. + 5.72016e6i) q^{40} -2.15643e7 q^{41} -1.49376e7i q^{42} +1.66892e6i q^{43} -6.04944e6 q^{44} +(-9.16259e6 - 350110. i) q^{45} +6.76711e6 q^{46} +3.02283e7i q^{47} -5.30842e6i q^{48} -9.24938e7 q^{49} +(2.38470e6 - 3.11589e7i) q^{50} -3.05187e7 q^{51} -4.60599e7i q^{52} +3.64412e7i q^{53} +8.50306e6 q^{54} +(3.30007e7 + 1.26099e6i) q^{55} -4.72103e7 q^{56} -2.78848e7i q^{57} -9.62403e7i q^{58} +1.10359e8 q^{59} +(-1.10652e6 + 2.89583e7i) q^{60} +1.21913e8 q^{61} +8.63889e7i q^{62} -7.56217e7i q^{63} -1.67772e7 q^{64} +(-9.60104e6 + 2.51265e8i) q^{65} -3.06253e7 q^{66} +1.26022e8i q^{67} +9.64540e7i q^{68} +3.42585e7 q^{69} +(2.57540e8 + 9.84082e6i) q^{70} -5.01662e7 q^{71} -2.68739e7i q^{72} -4.06246e8i q^{73} +1.47643e7 q^{74} +(1.20725e7 - 1.57742e8i) q^{75} -8.81297e7 q^{76} +2.72365e8i q^{77} -2.33178e8i q^{78} +5.87351e8 q^{79} +(9.15226e7 + 3.49715e6i) q^{80} +4.30467e7 q^{81} +3.45029e8i q^{82} -3.11987e7i q^{83} -2.39002e8 q^{84} +(2.01055e7 - 5.26173e8i) q^{85} +2.67026e7 q^{86} -4.87216e8i q^{87} +9.67911e7i q^{88} +8.18411e7 q^{89} +(-5.60176e6 + 1.46601e8i) q^{90} -2.07377e9 q^{91} -1.08274e8i q^{92} +4.37344e8i q^{93} +4.83653e8 q^{94} +(4.80762e8 + 1.83703e7i) q^{95} -8.49347e7 q^{96} -9.14396e8i q^{97} +1.47990e9i q^{98} -1.55041e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 1024 q^{4} + 1710 q^{5} - 5184 q^{6} - 26244 q^{9}+O(q^{10}) \) 4 * q - 1024 * q^4 + 1710 * q^5 - 5184 * q^6 - 26244 * q^9	\( 4 q - 1024 q^{4} + 1710 q^{5} - 5184 q^{6} - 26244 q^{9} - 39520 q^{10} + 900 q^{11} + 270144 q^{14} - 200070 q^{15} + 262144 q^{16} + 840336 q^{19} - 437760 q^{20} + 1367604 q^{21} + 1327104 q^{24} + 1161600 q^{25} + 4444992 q^{26} + 8920044 q^{29} - 2216160 q^{30} - 11689928 q^{31} + 16064 q^{34} - 9176580 q^{35} + 6718464 q^{36} + 22502772 q^{39} + 10117120 q^{40} - 94900464 q^{41} - 230400 q^{44} - 11219310 q^{45} + 59699200 q^{46} - 123301836 q^{49} + 49420800 q^{50} + 81324 q^{51} + 34012224 q^{54} + 91107200 q^{55} - 69156864 q^{56} - 44259300 q^{59} + 51217920 q^{60} + 94450760 q^{61} - 67108864 q^{64} - 124888140 q^{65} - 1166400 q^{66} + 302227200 q^{69} + 568520960 q^{70} - 912569400 q^{71} - 316377792 q^{74} + 250192800 q^{75} - 215126016 q^{76} + 1963018008 q^{79} + 112066560 q^{80} + 172186884 q^{81} - 350106624 q^{84} + 1012346420 q^{85} - 1056294144 q^{86} + 1733458248 q^{89} + 259290720 q^{90} - 4400514552 q^{91} + 42544000 q^{94} + 879308640 q^{95} - 339738624 q^{96} - 5904900 q^{99}+O(q^{100}) \) 4 * q - 1024 * q^4 + 1710 * q^5 - 5184 * q^6 - 26244 * q^9 - 39520 * q^10 + 900 * q^11 + 270144 * q^14 - 200070 * q^15 + 262144 * q^16 + 840336 * q^19 - 437760 * q^20 + 1367604 * q^21 + 1327104 * q^24 + 1161600 * q^25 + 4444992 * q^26 + 8920044 * q^29 - 2216160 * q^30 - 11689928 * q^31 + 16064 * q^34 - 9176580 * q^35 + 6718464 * q^36 + 22502772 * q^39 + 10117120 * q^40 - 94900464 * q^41 - 230400 * q^44 - 11219310 * q^45 + 59699200 * q^46 - 123301836 * q^49 + 49420800 * q^50 + 81324 * q^51 + 34012224 * q^54 + 91107200 * q^55 - 69156864 * q^56 - 44259300 * q^59 + 51217920 * q^60 + 94450760 * q^61 - 67108864 * q^64 - 124888140 * q^65 - 1166400 * q^66 + 302227200 * q^69 + 568520960 * q^70 - 912569400 * q^71 - 316377792 * q^74 + 250192800 * q^75 - 215126016 * q^76 + 1963018008 * q^79 + 112066560 * q^80 + 172186884 * q^81 - 350106624 * q^84 + 1012346420 * q^85 - 1056294144 * q^86 + 1733458248 * q^89 + 259290720 * q^90 - 4400514552 * q^91 + 42544000 * q^94 + 879308640 * q^95 - 339738624 * q^96 - 5904900 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more