LMFDB - Embedded newform 70.10.c.a.29.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,10,Mod(29,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("70.29");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	70.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:	$36.0525085315$
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} - 4 x^{11} + 8 x^{10} - 58350 x^{9} + 119678049 x^{8} - 1684868742 x^{7} + 7484411826 x^{6} + \cdots + 34\!\cdots\!56 $ x^12 - 4x^11 + 8x^10 - 58350x^9 + 119678049x^8 - 1684868742x^7 + 7484411826x^6 + 7978617913968x^5 + 1924116888185856x^4 + 10336829823710208x^3 + 1378923955763328x^2 - 3098302776323629056*x + 3480786613958252691456
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{4}\cdot 5^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.12
Root			$-30.8787 - 30.8787i$ of defining polynomial
Character	$\chi$	$=$	70.29
Dual form			70.10.c.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000i q^{2} +201.043i q^{3} -256.000 q^{4} +(-1353.09 + 349.677i) q^{5} -3216.69 q^{6} -2401.00i q^{7} -4096.00i q^{8} -20735.3 q^{9} +O(q^{10})$	\(q+16.0000i q^{2} +201.043i q^{3} -256.000 q^{4} +(-1353.09 + 349.677i) q^{5} -3216.69 q^{6} -2401.00i q^{7} -4096.00i q^{8} -20735.3 q^{9} +(-5594.82 - 21649.4i) q^{10} -15618.5 q^{11} -51467.0i q^{12} -29286.1i q^{13} +38416.0 q^{14} +(-70300.0 - 272029. i) q^{15} +65536.0 q^{16} -139809. i q^{17} -331765. i q^{18} +271017. q^{19} +(346391. - 89517.2i) q^{20} +482704. q^{21} -249896. i q^{22} -873473. i q^{23} +823472. q^{24} +(1.70858e6 - 946287. i) q^{25} +468577. q^{26} -211557. i q^{27} +614656. i q^{28} -3.31307e6 q^{29} +(4.35247e6 - 1.12480e6i) q^{30} -6.25069e6 q^{31} +1.04858e6i q^{32} -3.13999e6i q^{33} +2.23695e6 q^{34} +(839573. + 3.24877e6i) q^{35} +5.30824e6 q^{36} +6.37553e6i q^{37} +4.33627e6i q^{38} +5.88776e6 q^{39} +(1.43228e6 + 5.54225e6i) q^{40} +7.91273e6 q^{41} +7.72327e6i q^{42} +2.12455e7i q^{43} +3.99833e6 q^{44} +(2.80567e7 - 7.25065e6i) q^{45} +1.39756e7 q^{46} -4.02228e6i q^{47} +1.31756e7i q^{48} -5.76480e6 q^{49} +(1.51406e7 + 2.73372e7i) q^{50} +2.81077e7 q^{51} +7.49723e6i q^{52} -9.13777e7i q^{53} +3.38492e6 q^{54} +(2.11332e7 - 5.46142e6i) q^{55} -9.83450e6 q^{56} +5.44861e7i q^{57} -5.30091e7i q^{58} +7.49792e7 q^{59} +(1.79968e7 + 6.96395e7i) q^{60} +1.59662e8 q^{61} -1.00011e8i q^{62} +4.97855e7i q^{63} -1.67772e7 q^{64} +(1.02407e7 + 3.96267e7i) q^{65} +5.02398e7 q^{66} +1.57308e8i q^{67} +3.57912e7i q^{68} +1.75606e8 q^{69} +(-5.19803e7 + 1.34332e7i) q^{70} -3.29592e7 q^{71} +8.49318e7i q^{72} -3.35788e8i q^{73} -1.02009e8 q^{74} +(1.90244e8 + 3.43498e8i) q^{75} -6.93804e7 q^{76} +3.75000e7i q^{77} +9.42042e7i q^{78} +5.93256e7 q^{79} +(-8.86761e7 + 2.29164e7i) q^{80} -3.65601e8 q^{81} +1.26604e8i q^{82} -3.97437e8i q^{83} -1.23572e8 q^{84} +(4.88881e7 + 1.89175e8i) q^{85} -3.39928e8 q^{86} -6.66069e8i q^{87} +6.39733e7i q^{88} +8.36174e8 q^{89} +(1.16010e8 + 4.48907e8i) q^{90} -7.03159e7 q^{91} +2.23609e8i q^{92} -1.25666e9i q^{93} +6.43565e7 q^{94} +(-3.66710e8 + 9.47683e7i) q^{95} -2.10809e8 q^{96} -7.45068e8i q^{97} -9.22368e7i q^{98} +3.23854e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3072 q^{4} + 4010 q^{5} - 2464 q^{6} - 24506 q^{9}+O(q^{10}) $ 12 * q - 3072 * q^4 + 4010 * q^5 - 2464 * q^6 - 24506 * q^9	\( 12 q - 3072 q^{4} + 4010 q^{5} - 2464 q^{6} - 24506 q^{9} - 50080 q^{10} + 30806 q^{11} + 460992 q^{14} - 109450 q^{15} + 786432 q^{16} + 907064 q^{19} - 1026560 q^{20} + 369754 q^{21} + 630784 q^{24} + 1375500 q^{25} - 1020192 q^{26} - 5975006 q^{29} + 8624000 q^{30} - 20971700 q^{31} - 1283360 q^{34} + 7515130 q^{35} + 6273536 q^{36} - 774774 q^{39} + 12820480 q^{40} - 81549584 q^{41} - 7886336 q^{44} + 7857730 q^{45} - 41064000 q^{46} - 69177612 q^{49} + 15262400 q^{50} - 266346046 q^{51} - 145368608 q^{54} - 38302660 q^{55} - 118013952 q^{56} - 2784020 q^{59} + 28019200 q^{60} - 446750772 q^{61} - 201326592 q^{64} + 14974470 q^{65} - 344900000 q^{66} + 635592700 q^{69} + 154048160 q^{70} - 532489184 q^{71} - 736948544 q^{74} + 796780600 q^{75} - 232208384 q^{76} + 1455238758 q^{79} + 262799360 q^{80} - 1291761292 q^{81} - 94657024 q^{84} + 746117890 q^{85} - 899491968 q^{86} + 2979792428 q^{89} + 658842560 q^{90} + 153092562 q^{91} - 414904288 q^{94} - 1056284100 q^{95} - 161480704 q^{96} + 5383147148 q^{99}+O(q^{100}) \) 12 * q - 3072 * q^4 + 4010 * q^5 - 2464 * q^6 - 24506 * q^9 - 50080 * q^10 + 30806 * q^11 + 460992 * q^14 - 109450 * q^15 + 786432 * q^16 + 907064 * q^19 - 1026560 * q^20 + 369754 * q^21 + 630784 * q^24 + 1375500 * q^25 - 1020192 * q^26 - 5975006 * q^29 + 8624000 * q^30 - 20971700 * q^31 - 1283360 * q^34 + 7515130 * q^35 + 6273536 * q^36 - 774774 * q^39 + 12820480 * q^40 - 81549584 * q^41 - 7886336 * q^44 + 7857730 * q^45 - 41064000 * q^46 - 69177612 * q^49 + 15262400 * q^50 - 266346046 * q^51 - 145368608 * q^54 - 38302660 * q^55 - 118013952 * q^56 - 2784020 * q^59 + 28019200 * q^60 - 446750772 * q^61 - 201326592 * q^64 + 14974470 * q^65 - 344900000 * q^66 + 635592700 * q^69 + 154048160 * q^70 - 532489184 * q^71 - 736948544 * q^74 + 796780600 * q^75 - 232208384 * q^76 + 1455238758 * q^79 + 262799360 * q^80 - 1291761292 * q^81 - 94657024 * q^84 + 746117890 * q^85 - 899491968 * q^86 + 2979792428 * q^89 + 658842560 * q^90 + 153092562 * q^91 - 414904288 * q^94 - 1056284100 * q^95 - 161480704 * q^96 + 5383147148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$1$	$-1$

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
$3$			201.043i			1.43299i	0.697592	+	0.716495i	$0.254255\pi$
$3$			201.043i			1.43299i	−0.697592	+	0.716495i	$0.745745\pi$
$4$	−256.000			−0.500000
$5$	−1353.09	+	349.677i	−0.968192	+	0.250208i
$5$	−1353.09	+	349.677i	−0.968192	+	0.250208i
$6$	−3216.69			−1.01328
$7$		−	2401.00i		−	0.377964i
$7$		−	2401.00i		−	0.377964i
$8$		−	4096.00i		−	0.353553i
$9$	−20735.3			−1.05346
$10$	−5594.82	−	21649.4i	−0.176924	−	0.684615i
$11$	−15618.5			−0.321641			−0.160821	−	0.986984i	$-0.551414\pi$
$11$	−15618.5			−0.321641			−0.160821	+	0.986984i	$0.551414\pi$
$12$		−	51467.0i		−	0.716495i
$13$		−	29286.1i		−	0.284391i	−0.989839	−	0.142196i	$-0.954584\pi$
$13$		−	29286.1i		−	0.284391i	0.989839	−	0.142196i	$-0.0454162\pi$
$14$	38416.0			0.267261
$15$	−70300.0	−	272029.i	−0.358546	−	1.38741i
$16$	65536.0			0.250000
$17$		−	139809.i		−	0.405991i	−0.979180	−	0.202995i	$-0.934932\pi$
$17$		−	139809.i		−	0.405991i	0.979180	−	0.202995i	$-0.0650677\pi$
$18$		−	331765.i		−	0.744910i
$19$	271017.			0.477096			0.238548	−	0.971131i	$-0.423329\pi$
$19$	271017.			0.477096			0.238548	+	0.971131i	$0.423329\pi$
$20$	346391.	−	89517.2i	0.484096	−	0.125104i
$21$	482704.			0.541620
$22$		−	249896.i		−	0.227435i
$23$		−	873473.i		−	0.650840i	−0.945570	−	0.325420i	$-0.894494\pi$
$23$		−	873473.i		−	0.650840i	0.945570	−	0.325420i	$-0.105506\pi$
$24$	823472.			0.506639
$25$	1.70858e6	−	946287.i	0.874792	−	0.484499i
$26$	468577.			0.201095
$27$		−	211557.i		−	0.0766110i
$28$			614656.i			0.188982i
$29$	−3.31307e6			−0.869840			−0.434920	−	0.900469i	$-0.643223\pi$
$29$	−3.31307e6			−0.869840			−0.434920	+	0.900469i	$0.643223\pi$
$30$	4.35247e6	−	1.12480e6i	0.981047	−	0.253530i
$31$	−6.25069e6			−1.21563			−0.607813	−	0.794080i	$-0.707953\pi$
$31$	−6.25069e6			−1.21563			−0.607813	+	0.794080i	$0.707953\pi$
$32$			1.04858e6i			0.176777i
$33$		−	3.13999e6i		−	0.460909i
$34$	2.23695e6			0.287079
$35$	839573.	+	3.24877e6i	0.0945698	+	0.365942i
$36$	5.30824e6			0.526731
$37$			6.37553e6i			0.559253i	0.960109	+	0.279627i	$0.0902107\pi$
$37$			6.37553e6i			0.559253i	−0.960109	+	0.279627i	$0.909789\pi$
$38$			4.33627e6i			0.337358i
$39$	5.88776e6			0.407530
$40$	1.43228e6	+	5.54225e6i	0.0884619	+	0.342308i
$41$	7.91273e6			0.437320			0.218660	−	0.975801i	$-0.429831\pi$
$41$	7.91273e6			0.437320			0.218660	+	0.975801i	$0.429831\pi$
$42$			7.72327e6i			0.382983i
$43$			2.12455e7i			0.947674i	0.880612	+	0.473837i	$0.157131\pi$
$43$			2.12455e7i			0.947674i	−0.880612	+	0.473837i	$0.842869\pi$
$44$	3.99833e6			0.160821
$45$	2.80567e7	−	7.25065e6i	1.01995	−	0.263585i
$46$	1.39756e7			0.460214
$47$		−	4.02228e6i		−	0.120235i	−0.998191	−	0.0601177i	$-0.980852\pi$
$47$		−	4.02228e6i		−	0.120235i	0.998191	−	0.0601177i	$-0.0191476\pi$
$48$			1.31756e7i			0.358248i
$49$	−5.76480e6			−0.142857
$50$	1.51406e7	+	2.73372e7i	0.342593	+	0.618571i
$51$	2.81077e7			0.581781
$52$			7.49723e6i			0.142196i
$53$		−	9.13777e7i		−	1.59074i	−0.606125	−	0.795370i	$-0.707277\pi$
$53$		−	9.13777e7i		−	1.59074i	0.606125	−	0.795370i	$-0.292723\pi$
$54$	3.38492e6			0.0541722
$55$	2.11332e7	−	5.46142e6i	0.311411	−	0.0804773i
$56$	−9.83450e6			−0.133631
$57$			5.44861e7i			0.683674i
$58$		−	5.30091e7i		−	0.615070i
$59$	7.49792e7			0.805576			0.402788	−	0.915293i	$-0.368041\pi$
$59$	7.49792e7			0.805576			0.402788	+	0.915293i	$0.368041\pi$
$60$	1.79968e7	+	6.96395e7i	0.179273	+	0.693705i
$61$	1.59662e8			1.47645			0.738224	−	0.674556i	$-0.235665\pi$
$61$	1.59662e8			1.47645			0.738224	+	0.674556i	$0.235665\pi$
$62$		−	1.00011e8i		−	0.859578i
$63$			4.97855e7i			0.398171i
$64$	−1.67772e7			−0.125000
$65$	1.02407e7	+	3.96267e7i	0.0711570	+	0.275345i
$66$	5.02398e7			0.325912
$67$			1.57308e8i			0.953702i	0.878984	+	0.476851i	$0.158222\pi$
$67$			1.57308e8i			0.953702i	−0.878984	+	0.476851i	$0.841778\pi$
$68$			3.57912e7i			0.202995i
$69$	1.75606e8			0.932648
$70$	−5.19803e7	+	1.34332e7i	−0.258760	+	0.0668709i
$71$	−3.29592e7			−0.153927			−0.0769633	−	0.997034i	$-0.524522\pi$
$71$	−3.29592e7			−0.153927			−0.0769633	+	0.997034i	$0.524522\pi$
$72$			8.49318e7i			0.372455i
$73$		−	3.35788e8i		−	1.38393i	−0.721933	−	0.691963i	$-0.756746\pi$
$73$		−	3.35788e8i		−	1.38393i	0.721933	−	0.691963i	$-0.243254\pi$
$74$	−1.02009e8			−0.395452
$75$	1.90244e8	+	3.43498e8i	0.694283	+	1.25357i
$76$	−6.93804e7			−0.238548
$77$			3.75000e7i			0.121569i
$78$			9.42042e7i			0.288167i
$79$	5.93256e7			0.171364			0.0856822	−	0.996323i	$-0.472693\pi$
$79$	5.93256e7			0.171364			0.0856822	+	0.996323i	$0.472693\pi$
$80$	−8.86761e7	+	2.29164e7i	−0.242048	+	0.0625520i
$81$	−3.65601e8			−0.943679
$82$			1.26604e8i			0.309232i
$83$		−	3.97437e8i		−	0.919213i	−0.888123	−	0.459607i	$-0.847990\pi$
$83$		−	3.97437e8i		−	0.919213i	0.888123	−	0.459607i	$-0.152010\pi$
$84$	−1.23572e8			−0.270810
$85$	4.88881e7	+	1.89175e8i	0.101582	+	0.393077i
$86$	−3.39928e8			−0.670107
$87$		−	6.66069e8i		−	1.24647i
$88$			6.39733e7i			0.113717i
$89$	8.36174e8			1.41267			0.706336	−	0.707877i	$-0.250347\pi$
$89$	8.36174e8			1.41267			0.706336	+	0.707877i	$0.250347\pi$
$90$	1.16010e8	+	4.48907e8i	0.186383	+	0.721216i
$91$	−7.03159e7			−0.107490
$92$			2.23609e8i			0.325420i
$93$		−	1.25666e9i		−	1.74198i
$94$	6.43565e7			0.0850193
$95$	−3.66710e8	+	9.47683e7i	−0.461920	+	0.119373i
$96$	−2.10809e8			−0.253319
$97$		−	7.45068e8i		−	0.854521i	−0.904128	−	0.427261i	$-0.859479\pi$
$97$		−	7.45068e8i		−	0.854521i	0.904128	−	0.427261i	$-0.140521\pi$
$98$		−	9.22368e7i		−	0.101015i
$99$	3.23854e8			0.338837
$100$	−4.37396e8	+	2.42250e8i	−0.437396	+	0.242250i
$101$	−1.72732e9			−1.65168			−0.825840	−	0.563905i	$-0.809298\pi$
$101$	−1.72732e9			−1.65168			−0.825840	+	0.563905i	$0.809298\pi$
$102$			4.49723e8i			0.411381i
$103$		−	6.28769e8i		−	0.550457i	−0.961379	−	0.275229i	$-0.911246\pi$
$103$		−	6.28769e8i		−	0.550457i	0.961379	−	0.275229i	$-0.0887535\pi$
$104$	−1.19956e8			−0.100547
$105$	−6.53142e8	+	1.68790e8i	−0.524392	+	0.135518i
$106$	1.46204e9			1.12482
$107$		−	1.64943e9i		−	1.21648i	−0.793753	−	0.608241i	$-0.791875\pi$
$107$		−	1.64943e9i		−	1.21648i	0.793753	−	0.608241i	$-0.208125\pi$
$108$			5.41587e7i			0.0383055i
$109$	−1.48709e9			−1.00907			−0.504533	−	0.863393i	$-0.668335\pi$
$109$	−1.48709e9			−1.00907			−0.504533	+	0.863393i	$0.668335\pi$
$110$	8.73827e7	+	3.38131e8i	0.0569060	+	0.220201i
$111$	−1.28176e9			−0.801405
$112$		−	1.57352e8i		−	0.0944911i
$113$		−	1.66416e9i		−	0.960158i	−0.877225	−	0.480079i	$-0.840608\pi$
$113$		−	1.66416e9i		−	0.960158i	0.877225	−	0.480079i	$-0.159392\pi$
$114$	−8.71777e8			−0.483430
$115$	3.05433e8	+	1.18189e9i	0.162846	+	0.630138i
$116$	8.48145e8			0.434920
$117$			6.07255e8i			0.299595i
$118$			1.19967e9i			0.569629i
$119$	−3.35682e8			−0.153450
$120$	−1.11423e9	+	2.87949e8i	−0.490524	+	0.126765i
$121$	−2.11401e9			−0.896547
$122$			2.55460e9i			1.04401i
$123$			1.59080e9i			0.626675i
$124$	1.60018e9			0.607813
$125$	−1.98096e9	+	1.87786e9i	−0.725741	+	0.687968i
$126$	−7.96567e8			−0.281550
$127$			1.45106e9i			0.494958i	0.968893	+	0.247479i	$0.0796021\pi$
$127$			1.45106e9i			0.494958i	−0.968893	+	0.247479i	$0.920398\pi$
$128$		−	2.68435e8i		−	0.0883883i
$129$	−4.27126e9			−1.35801
$130$	−6.34027e8	+	1.63850e8i	−0.194698	+	0.0503156i
$131$	6.23775e9			1.85058			0.925289	−	0.379263i	$-0.123822\pi$
$131$	6.23775e9			1.85058			0.925289	+	0.379263i	$0.123822\pi$
$132$			8.03837e8i			0.230455i
$133$		−	6.50712e8i		−	0.180325i
$134$	−2.51692e9			−0.674369
$135$	7.39767e7	+	2.86256e8i	0.0191687	+	0.0741742i
$136$	−5.72659e8			−0.143539
$137$		−	7.14761e9i		−	1.73348i	−0.498761	−	0.866739i	$-0.666212\pi$
$137$		−	7.14761e9i		−	1.73348i	0.498761	−	0.866739i	$-0.333788\pi$
$138$			2.80969e9i			0.659482i
$139$	2.17548e9			0.494298			0.247149	−	0.968978i	$-0.420506\pi$
$139$	2.17548e9			0.494298			0.247149	+	0.968978i	$0.420506\pi$
$140$	−2.14931e8	−	8.31685e8i	−0.0472849	−	0.182971i
$141$	8.08652e8			0.172296
$142$		−	5.27346e8i		−	0.108842i
$143$			4.57404e8i			0.0914719i
$144$	−1.35891e9			−0.263366
$145$	4.48288e9	−	1.15850e9i	0.842172	−	0.217641i
$146$	5.37261e9			0.978583
$147$		−	1.15897e9i		−	0.204713i
$148$		−	1.63214e9i		−	0.279627i
$149$	2.76925e9			0.460282			0.230141	−	0.973157i	$-0.426081\pi$
$149$	2.76925e9			0.460282			0.230141	+	0.973157i	$0.426081\pi$
$150$	−5.49596e9	+	3.04391e9i	−0.886407	+	0.490932i
$151$	9.61745e8			0.150544			0.0752720	−	0.997163i	$-0.476017\pi$
$151$	9.61745e8			0.150544			0.0752720	+	0.997163i	$0.476017\pi$
$152$		−	1.11009e9i		−	0.168679i
$153$			2.89899e9i			0.427696i
$154$	−6.00000e8			−0.0859623
$155$	8.45774e9	−	2.18572e9i	1.17696	−	0.304160i
$156$	−1.50727e9			−0.203765
$157$		−	7.42184e9i		−	0.974907i	−0.873149	−	0.487454i	$-0.837926\pi$
$157$		−	7.42184e9i		−	0.974907i	0.873149	−	0.487454i	$-0.162074\pi$
$158$			9.49210e8i			0.121173i
$159$	1.83709e10			2.27951
$160$	−3.66662e8	−	1.41882e9i	−0.0442310	−	0.171154i
$161$	−2.09721e9			−0.245995
$162$		−	5.84961e9i		−	0.667282i
$163$		−	5.13802e8i		−	0.0570100i	−0.999594	−	0.0285050i	$-0.990925\pi$
$163$		−	5.13802e8i		−	0.0570100i	0.999594	−	0.0285050i	$-0.00907466\pi$
$164$	−2.02566e9			−0.218660
$165$	1.09798e9	+	4.24869e9i	0.115323	+	0.446249i
$166$	6.35898e9			0.649982
$167$		−	1.71805e10i		−	1.70927i	−0.519228	−	0.854636i	$-0.673780\pi$
$167$		−	1.71805e10i		−	1.70927i	0.519228	−	0.854636i	$-0.326220\pi$
$168$		−	1.97716e9i		−	0.191491i
$169$	9.74683e9			0.919122
$170$	−3.02679e9	+	7.82209e8i	−0.277948	+	0.0718295i
$171$	−5.61962e9			−0.502602
$172$		−	5.43885e9i		−	0.473837i
$173$			7.60367e9i			0.645380i	0.946505	+	0.322690i	$0.104587\pi$
$173$			7.60367e9i			0.645380i	−0.946505	+	0.322690i	$0.895413\pi$
$174$	1.06571e10			0.881389
$175$	−2.27204e9	−	4.10229e9i	−0.183123	−	0.330640i
$176$	−1.02357e9			−0.0804103
$177$			1.50740e10i			1.15438i
$178$			1.33788e10i			0.998910i
$179$	1.61995e10			1.17941			0.589703	−	0.807620i	$-0.299245\pi$
$179$	1.61995e10			1.17941			0.589703	+	0.807620i	$0.299245\pi$
$180$	−7.18252e9	+	1.85617e9i	−0.509977	+	0.131792i
$181$	−2.00837e10			−1.39088			−0.695441	−	0.718583i	$-0.744791\pi$
$181$	−2.00837e10			−1.39088			−0.695441	+	0.718583i	$0.744791\pi$
$182$		−	1.12505e9i		−	0.0760067i
$183$			3.20990e10i			2.11574i
$184$	−3.57775e9			−0.230107
$185$	−2.22937e9	−	8.62667e9i	−0.139930	−	0.541465i
$186$	2.01065e10			1.23177
$187$			2.18361e9i			0.130583i
$188$			1.02970e9i			0.0601177i
$189$	−5.07949e8			−0.0289562
$190$	−1.51629e9	−	5.86737e9i	−0.0844096	−	0.326627i
$191$	−4.08580e9			−0.222140			−0.111070	−	0.993813i	$-0.535428\pi$
$191$	−4.08580e9			−0.222140			−0.111070	+	0.993813i	$0.535428\pi$
$192$		−	3.37294e9i		−	0.179124i
$193$			2.35391e10i			1.22119i	0.791944	+	0.610594i	$0.209069\pi$
$193$			2.35391e10i			1.22119i	−0.791944	+	0.610594i	$0.790931\pi$
$194$	1.19211e10			0.604238
$195$	−7.96667e9	+	2.05881e9i	−0.394567	+	0.101967i
$196$	1.47579e9			0.0714286
$197$			2.49930e10i			1.18228i	0.806569	+	0.591140i	$0.201322\pi$
$197$			2.49930e10i			1.18228i	−0.806569	+	0.591140i	$0.798678\pi$
$198$			5.18166e9i			0.239594i
$199$	5.92459e9			0.267805			0.133903	−	0.990994i	$-0.457249\pi$
$199$	5.92459e9			0.267805			0.133903	+	0.990994i	$0.457249\pi$
$200$	−3.87599e9	−	6.99833e9i	−0.171296	−	0.309286i
$201$	−3.16256e10			−1.36665
$202$		−	2.76371e10i		−	1.16791i
$203$			7.95467e9i			0.328769i
$204$	−7.19557e9			−0.290891
$205$	−1.07066e10	+	2.76690e9i	−0.423410	+	0.109421i
$206$	1.00603e10			0.389232
$207$			1.81117e10i			0.685636i
$208$		−	1.91929e9i		−	0.0710978i
$209$	−4.23288e9			−0.153454
$210$	−2.70065e9	−	1.04503e10i	−0.0958254	−	0.370801i
$211$	−5.00436e10			−1.73811			−0.869055	−	0.494716i	$-0.835272\pi$
$211$	−5.00436e10			−1.73811			−0.869055	+	0.494716i	$0.835272\pi$
$212$			2.33927e10i			0.795370i
$213$		−	6.62621e9i		−	0.220575i
$214$	2.63908e10			0.860182
$215$	−7.42906e9	−	2.87471e10i	−0.237116	−	0.917531i
$216$	−8.66539e8			−0.0270861
$217$			1.50079e10i			0.459464i
$218$		−	2.37935e10i		−	0.713517i
$219$	6.75079e10			1.98315
$220$	−5.41010e9	+	1.39812e9i	−0.155705	+	0.0402386i
$221$	−4.09447e9			−0.115460
$222$		−	2.05081e10i		−	0.566679i
$223$		−	9.17747e9i		−	0.248514i	−0.992250	−	0.124257i	$-0.960345\pi$
$223$		−	9.17747e9i		−	0.248514i	0.992250	−	0.124257i	$-0.0396548\pi$
$224$	2.51763e9			0.0668153
$225$	−3.54279e10	+	1.96215e10i	−0.921560	+	0.510402i
$226$	2.66266e10			0.678935
$227$		−	4.88804e10i		−	1.22185i	−0.791688	−	0.610926i	$-0.790797\pi$
$227$		−	4.88804e10i		−	1.22185i	0.791688	−	0.610926i	$-0.209203\pi$
$228$		−	1.39484e10i		−	0.341837i
$229$	−1.07277e10			−0.257778			−0.128889	−	0.991659i	$-0.541141\pi$
$229$	−1.07277e10			−0.257778			−0.128889	+	0.991659i	$0.541141\pi$
$230$	−1.89102e10	+	4.88693e9i	−0.445575	+	0.115149i
$231$	−7.53911e9			−0.174207
$232$			1.35703e10i			0.307535i
$233$		−	7.90863e10i		−	1.75792i	−0.476895	−	0.878961i	$-0.658238\pi$
$233$		−	7.90863e10i		−	1.75792i	0.476895	−	0.878961i	$-0.341762\pi$
$234$	−9.71609e9			−0.211846
$235$	1.40650e9	+	5.44251e9i	0.0300839	+	0.116411i
$236$	−1.91947e10			−0.402788
$237$			1.19270e10i			0.245564i
$238$		−	5.37092e9i		−	0.108506i
$239$	−7.03817e10			−1.39530			−0.697652	−	0.716436i	$-0.745772\pi$
$239$	−7.03817e10			−1.39530			−0.697652	+	0.716436i	$0.745772\pi$
$240$	−4.60718e9	−	1.78277e10i	−0.0896365	−	0.346853i
$241$	3.22499e9			0.0615816			0.0307908	−	0.999526i	$-0.490197\pi$
$241$	3.22499e9			0.0615816			0.0307908	+	0.999526i	$0.490197\pi$
$242$		−	3.38242e10i		−	0.633954i
$243$		−	7.76656e10i		−	1.42889i
$244$	−4.08735e10			−0.738224
$245$	7.80029e9	−	2.01582e9i	0.138313	−	0.0357440i
$246$	−2.54528e10			−0.443126
$247$		−	7.93702e9i		−	0.135682i
$248$			2.56028e10i			0.429789i
$249$	7.99018e10			1.31722
$250$	−3.00458e10	−	3.16954e10i	−0.486467	−	0.513176i
$251$	−1.09992e11			−1.74916			−0.874580	−	0.484881i	$-0.838863\pi$
$251$	−1.09992e11			−1.74916			−0.874580	+	0.484881i	$0.838863\pi$
$252$		−	1.27451e10i		−	0.199086i
$253$			1.36423e10i			0.209337i
$254$	−2.32169e10			−0.349988
$255$	−3.80323e10	+	9.82861e9i	−0.563276	+	0.145566i
$256$	4.29497e9			0.0625000
$257$		−	1.98467e10i		−	0.283785i	−0.989882	−	0.141892i	$-0.954681\pi$
$257$		−	1.98467e10i		−	0.283785i	0.989882	−	0.141892i	$-0.0453187\pi$
$258$		−	6.83402e10i		−	0.960257i
$259$	1.53077e10			0.211378
$260$	−2.62161e9	−	1.01444e10i	−0.0355785	−	0.137673i
$261$	6.86974e10			0.916343
$262$			9.98040e10i			1.30856i
$263$			8.60804e10i			1.10944i	0.832038	+	0.554719i	$0.187174\pi$
$263$			8.60804e10i			1.10944i	−0.832038	+	0.554719i	$0.812826\pi$
$264$	−1.28614e10			−0.162956
$265$	3.19527e10	+	1.23642e11i	0.398016	+	1.54014i
$266$	1.04114e10			0.127509
$267$			1.68107e11i			2.02435i
$268$		−	4.02707e10i		−	0.476851i
$269$	1.06232e11			1.23700			0.618498	−	0.785786i	$-0.287741\pi$
$269$	1.06232e11			1.23700			0.618498	+	0.785786i	$0.287741\pi$
$270$	−4.58010e9	+	1.18363e9i	−0.0524491	+	0.0135543i
$271$	−2.66290e10			−0.299912			−0.149956	−	0.988693i	$-0.547913\pi$
$271$	−2.66290e10			−0.299912			−0.149956	+	0.988693i	$0.547913\pi$
$272$		−	9.16255e9i		−	0.101498i
$273$		−	1.41365e10i		−	0.154032i
$274$	1.14362e11			1.22575
$275$	−2.66854e10	+	1.47796e10i	−0.281369	+	0.155835i
$276$	−4.49551e10			−0.466324
$277$			1.59378e11i			1.62655i	0.581878	+	0.813276i	$0.302318\pi$
$277$			1.59378e11i			1.62655i	−0.581878	+	0.813276i	$0.697682\pi$
$278$			3.48077e10i			0.349521i
$279$	1.29610e11			1.28062
$280$	1.33070e10	−	3.43889e9i	0.129380	−	0.0334355i
$281$	−5.32719e10			−0.509706			−0.254853	−	0.966980i	$-0.582027\pi$
$281$	−5.32719e10			−0.509706			−0.254853	+	0.966980i	$0.582027\pi$
$282$			1.29384e10i			0.121832i
$283$			2.09521e10i			0.194173i	0.995276	+	0.0970863i	$0.0309523\pi$
$283$			2.09521e10i			0.194173i	−0.995276	+	0.0970863i	$0.969048\pi$
$284$	8.43754e9			0.0769633
$285$	−1.90525e10	−	7.37246e10i	−0.171061	−	0.661927i
$286$	−7.31847e9			−0.0646804
$287$		−	1.89985e10i		−	0.165291i
$288$		−	2.17425e10i		−	0.186228i
$289$	9.90412e10			0.835171
$290$	1.85360e10	+	7.17260e10i	0.153895	+	0.595505i
$291$	1.49791e11			1.22452
$292$			8.59618e10i			0.691963i
$293$		−	1.50217e11i		−	1.19073i	−0.803455	−	0.595366i	$-0.797007\pi$
$293$		−	1.50217e11i		−	1.19073i	0.803455	−	0.595366i	$-0.202993\pi$
$294$	1.85436e10			0.144754
$295$	−1.01454e11	+	2.62185e10i	−0.779953	+	0.201562i
$296$	2.61142e10			0.197726
$297$			3.30421e9i			0.0246413i
$298$			4.43080e10i			0.325468i
$299$	−2.55806e10			−0.185093
$300$	−4.87026e10	−	8.79354e10i	−0.347141	−	0.626784i
$301$	5.10105e10			0.358187
$302$			1.53879e10i			0.106451i
$303$		−	3.47265e11i		−	2.36684i
$304$	1.77614e10			0.119274
$305$	−2.16037e11	+	5.58301e10i	−1.42948	+	0.369419i
$306$	−4.63838e10			−0.302427
$307$		−	6.95420e10i		−	0.446812i	−0.974725	−	0.223406i	$-0.928282\pi$
$307$		−	6.95420e10i		−	0.446812i	0.974725	−	0.223406i	$-0.0717175\pi$
$308$		−	9.60000e9i		−	0.0607845i
$309$	1.26410e11			0.788800
$310$	3.49715e10	+	1.35324e11i	0.215073	+	0.832236i
$311$	−1.35026e11			−0.818455			−0.409228	−	0.912432i	$-0.634202\pi$
$311$	−1.35026e11			−0.818455			−0.409228	+	0.912432i	$0.634202\pi$
$312$		−	2.41163e10i		−	0.144084i
$313$		−	2.79797e10i		−	0.164776i	−0.996600	−	0.0823881i	$-0.973745\pi$
$313$		−	2.79797e10i		−	0.164776i	0.996600	−	0.0823881i	$-0.0262547\pi$
$314$	1.18749e11			0.689364
$315$	−1.74088e10	−	6.73642e10i	−0.0996257	−	0.385506i
$316$	−1.51874e10			−0.0856822
$317$			6.80226e9i			0.0378344i	0.999821	+	0.0189172i	$0.00602189\pi$
$317$			6.80226e9i			0.0378344i	−0.999821	+	0.0189172i	$0.993978\pi$
$318$			2.93934e11i			1.61186i
$319$	5.17451e10			0.279776
$320$	2.27011e10	−	5.86660e9i	0.121024	−	0.0312760i
$321$	3.31605e11			1.74321
$322$		−	3.35554e10i		−	0.173944i
$323$		−	3.78907e10i		−	0.193696i
$324$	9.35938e10			0.471840
$325$	−2.77130e10	−	5.00375e10i	−0.137787	−	0.248783i
$326$	8.22083e9			0.0403122
$327$		−	2.98970e11i		−	1.44598i
$328$		−	3.24106e10i		−	0.154616i
$329$	−9.65750e9			−0.0454447
$330$	−6.79790e10	+	1.75677e10i	−0.315545	+	0.0815458i
$331$	6.81462e10			0.312044			0.156022	−	0.987754i	$-0.450133\pi$
$331$	6.81462e10			0.312044			0.156022	+	0.987754i	$0.450133\pi$
$332$			1.01744e11i			0.459607i
$333$		−	1.32199e11i		−	0.589152i
$334$	2.74888e11			1.20864
$335$	−5.50067e10	−	2.12851e11i	−0.238624	−	0.923367i
$336$	3.16345e10			0.135405
$337$			4.12449e11i			1.74195i	0.491327	+	0.870975i	$0.336512\pi$
$337$			4.12449e11i			1.74195i	−0.491327	+	0.870975i	$0.663488\pi$
$338$			1.55949e11i			0.649917i
$339$	3.34568e11			1.37590
$340$	−1.25153e10	−	4.84287e10i	−0.0507911	−	0.196539i
$341$	9.76263e10			0.390996
$342$		−	8.99139e10i		−	0.355393i
$343$			1.38413e10i			0.0539949i
$344$	8.70216e10			0.335053
$345$	−2.37610e11	+	6.14052e10i	−0.902982	+	0.233356i
$346$	−1.21659e11			−0.456353
$347$		−	9.76937e10i		−	0.361730i	−0.983508	−	0.180865i	$-0.942110\pi$
$347$		−	9.76937e10i		−	0.361730i	0.983508	−	0.180865i	$-0.0578896\pi$
$348$			1.70514e11i			0.623236i
$349$	1.77906e11			0.641913			0.320956	−	0.947094i	$-0.395996\pi$
$349$	1.77906e11			0.641913			0.320956	+	0.947094i	$0.395996\pi$
$350$	6.56367e10	−	3.63526e10i	0.233798	−	0.129488i
$351$	−6.19569e9			−0.0217875
$352$		−	1.63772e10i		−	0.0568587i
$353$			5.05930e11i			1.73422i	0.498117	+	0.867110i	$0.334025\pi$
$353$			5.05930e11i			1.73422i	−0.498117	+	0.867110i	$0.665975\pi$
$354$	−2.41185e11			−0.816272
$355$	4.45967e10	−	1.15250e10i	0.149030	−	0.0385137i
$356$	−2.14060e11			−0.706336
$357$		−	6.74866e10i		−	0.219893i
$358$			2.59192e11i			0.833965i
$359$	−2.26820e11			−0.720702			−0.360351	−	0.932817i	$-0.617343\pi$
$359$	−2.26820e11			−0.720702			−0.360351	+	0.932817i	$0.617343\pi$
$360$	−2.96987e10	−	1.14920e11i	−0.0931913	−	0.360608i
$361$	−2.49237e11			−0.772380
$362$		−	3.21339e11i		−	0.983503i
$363$		−	4.25007e11i		−	1.28474i
$364$	1.80009e10			0.0537449
$365$	1.17417e11	+	4.54352e11i	0.346270	+	1.33991i
$366$	−5.13584e11			−1.49605
$367$		−	8.91653e10i		−	0.256566i	−0.991738	−	0.128283i	$-0.959053\pi$
$367$		−	8.91653e10i		−	0.256566i	0.991738	−	0.128283i	$-0.0409465\pi$
$368$		−	5.72440e10i		−	0.162710i
$369$	−1.64073e11			−0.460700
$370$	1.38027e11	−	3.56700e10i	0.382873	−	0.0989453i
$371$	−2.19398e11			−0.601243
$372$			3.21704e11i			0.870991i
$373$		−	2.45130e11i		−	0.655703i	−0.944729	−	0.327852i	$-0.893675\pi$
$373$		−	2.45130e11i		−	0.655703i	0.944729	−	0.327852i	$-0.106325\pi$
$374$	−3.49378e10			−0.0923365
$375$	−3.77531e11	−	3.98259e11i	−0.985852	−	1.03998i
$376$	−1.64753e10			−0.0425096
$377$			9.70267e10i			0.247375i
$378$		−	8.12719e9i		−	0.0204752i
$379$	3.41880e11			0.851133			0.425567	−	0.904927i	$-0.360075\pi$
$379$	3.41880e11			0.851133			0.425567	+	0.904927i	$0.360075\pi$
$380$	9.38778e10	−	2.42607e10i	0.230960	−	0.0596866i
$381$	−2.91725e11			−0.709270
$382$		−	6.53728e10i		−	0.157077i
$383$		−	1.39360e11i		−	0.330935i	−0.986215	−	0.165468i	$-0.947087\pi$
$383$		−	1.39360e11i		−	0.330935i	0.986215	−	0.165468i	$-0.0529133\pi$
$384$	5.39671e10			0.126660
$385$	−1.31129e10	−	5.07408e10i	−0.0304176	−	0.117702i
$386$	−3.76626e11			−0.863510
$387$		−	4.40532e11i		−	0.998339i
$388$			1.90737e11i			0.427261i
$389$	−7.50059e11			−1.66082			−0.830410	−	0.557153i	$-0.811894\pi$
$389$	−7.50059e11			−1.66082			−0.830410	+	0.557153i	$0.811894\pi$
$390$	−3.29410e10	−	1.27467e11i	−0.0721018	−	0.279001i
$391$	−1.22120e11			−0.264235
$392$			2.36126e10i			0.0505076i
$393$			1.25406e12i			2.65186i
$394$	−3.99888e11			−0.835999
$395$	−8.02729e10	+	2.07448e10i	−0.165914	+	0.0428768i
$396$	−8.29066e10			−0.169419
$397$		−	6.29880e11i		−	1.27262i	−0.771432	−	0.636312i	$-0.780459\pi$
$397$		−	6.29880e11i		−	1.27262i	0.771432	−	0.636312i	$-0.219541\pi$
$398$			9.47934e10i			0.189367i
$399$	1.30821e11			0.258404
$400$	1.11973e11	−	6.20159e10i	0.218698	−	0.121125i
$401$	−1.63259e11			−0.315303			−0.157652	−	0.987495i	$-0.550392\pi$
$401$	−1.63259e11			−0.315303			−0.157652	+	0.987495i	$0.550392\pi$
$402$		−	5.06009e11i		−	0.966365i
$403$			1.83058e11i			0.345713i
$404$	4.42193e11			0.825840
$405$	4.94691e11	−	1.27842e11i	0.913663	−	0.236116i
$406$	−1.27275e11			−0.232474
$407$		−	9.95762e10i		−	0.179879i
$408$		−	1.15129e11i		−	0.205691i
$409$	−6.51936e11			−1.15199			−0.575996	−	0.817452i	$-0.695386\pi$
$409$	−6.51936e11			−1.15199			−0.575996	+	0.817452i	$0.695386\pi$
$410$	−4.42704e10	−	1.71306e11i	−0.0773723	−	0.299396i
$411$	1.43698e12			2.48406
$412$			1.60965e11i			0.275229i
$413$		−	1.80025e11i		−	0.304479i
$414$	−2.89788e11			−0.484818
$415$	1.38974e11	+	5.37767e11i	0.229995	+	0.889975i
$416$	3.07087e10			0.0502737
$417$			4.37365e11i			0.708324i
$418$		−	6.77260e10i		−	0.108508i
$419$	4.74478e11			0.752060			0.376030	−	0.926607i	$-0.377289\pi$
$419$	4.74478e11			0.752060			0.376030	+	0.926607i	$0.377289\pi$
$420$	1.67204e11	−	4.32103e10i	0.262196	−	0.0677588i
$421$	1.46001e11			0.226510			0.113255	−	0.993566i	$-0.463872\pi$
$421$	1.46001e11			0.226510			0.113255	+	0.993566i	$0.463872\pi$
$422$		−	8.00697e11i		−	1.22903i
$423$			8.34033e10i			0.126663i
$424$	−3.74283e11			−0.562411
$425$	−1.32300e11	−	2.38875e11i	−0.196702	−	0.355158i
$426$	1.06019e11			0.155970
$427$		−	3.83349e11i		−	0.558045i
$428$			4.22253e11i			0.608241i
$429$	−9.19579e10			−0.131078
$430$	4.59953e11	−	1.18865e11i	0.648792	−	0.167666i
$431$	−4.41387e11			−0.616129			−0.308064	−	0.951365i	$-0.599681\pi$
$431$	−4.41387e11			−0.616129			−0.308064	+	0.951365i	$0.599681\pi$
$432$		−	1.38646e10i		−	0.0191528i
$433$		−	1.35346e11i		−	0.185033i	−0.995711	−	0.0925165i	$-0.970509\pi$
$433$		−	1.35346e11i		−	0.185033i	0.995711	−	0.0925165i	$-0.0294911\pi$
$434$	−2.40126e11			−0.324890
$435$	2.32909e11	+	9.01251e11i	0.311878	+	1.20682i
$436$	3.80696e11			0.504533
$437$		−	2.36726e11i		−	0.310513i
$438$			1.08013e12i			1.40230i
$439$	−7.39550e10			−0.0950336			−0.0475168	−	0.998870i	$-0.515131\pi$
$439$	−7.39550e10			−0.0950336			−0.0475168	+	0.998870i	$0.515131\pi$
$440$	−2.23700e10	−	8.65616e10i	−0.0284530	−	0.110100i
$441$	1.19535e11			0.150495
$442$		−	6.55115e10i		−	0.0816427i
$443$			9.68867e10i			0.119522i	0.998213	+	0.0597610i	$0.0190338\pi$
$443$			9.68867e10i			0.119522i	−0.998213	+	0.0597610i	$0.980966\pi$
$444$	3.28130e11			0.400702
$445$	−1.13142e12	+	2.92390e11i	−1.36774	+	0.353462i
$446$	1.46840e11			0.175726
$447$			5.56738e11i			0.659579i
$448$			4.02821e10i			0.0472456i
$449$	−1.31869e12			−1.53120			−0.765602	−	0.643314i	$-0.777559\pi$
$449$	−1.31869e12			−1.53120			−0.765602	+	0.643314i	$0.777559\pi$
$450$	−3.13945e11	−	5.66846e11i	−0.360908	−	0.651641i
$451$	−1.23585e11			−0.140660
$452$			4.26026e11i			0.480079i
$453$			1.93352e11i			0.215728i
$454$	7.82087e11			0.863980
$455$	9.51436e10	−	2.45878e10i	0.104071	−	0.0268948i
$456$	2.23175e11			0.241715
$457$		−	3.66535e11i		−	0.393091i	−0.980495	−	0.196546i	$-0.937028\pi$
$457$		−	3.66535e11i		−	0.393091i	0.980495	−	0.196546i	$-0.0629723\pi$
$458$		−	1.71643e11i		−	0.182276i
$459$	−2.95777e10			−0.0311034
$460$	−7.81909e10	−	3.02563e11i	−0.0814228	−	0.315069i
$461$	−1.09415e12			−1.12829			−0.564146	−	0.825675i	$-0.690795\pi$
$461$	−1.09415e12			−1.12829			−0.564146	+	0.825675i	$0.690795\pi$
$462$		−	1.20626e11i		−	0.123183i
$463$		−	1.06833e12i		−	1.08042i	−0.841530	−	0.540210i	$-0.818345\pi$
$463$		−	1.06833e12i		−	1.08042i	0.841530	−	0.540210i	$-0.181655\pi$
$464$	−2.17125e11			−0.217460
$465$	4.39423e11	+	1.70037e12i	0.435858	+	1.68657i
$466$	1.26538e12			1.24304
$467$		−	4.76995e11i		−	0.464074i	−0.972707	−	0.232037i	$-0.925461\pi$
$467$		−	4.76995e11i		−	0.464074i	0.972707	−	0.232037i	$-0.0745391\pi$
$468$		−	1.55457e11i		−	0.149798i
$469$	3.77695e11			0.360466
$470$	−8.70802e10	+	2.25040e10i	−0.0823150	+	0.0212725i
$471$	1.49211e12			1.39703
$472$		−	3.07115e11i		−	0.284814i
$473$		−	3.31823e11i		−	0.304811i
$474$	−1.90832e11			−0.173640
$475$	4.63054e11	−	2.56460e11i	0.417359	−	0.231152i
$476$	8.59347e10			0.0767251
$477$			1.89474e12i			1.67578i
$478$		−	1.12611e12i		−	0.986629i
$479$	4.85334e11			0.421241			0.210621	−	0.977568i	$-0.432452\pi$
$479$	4.85334e11			0.421241			0.210621	+	0.977568i	$0.432452\pi$
$480$	2.85243e11	−	7.37149e10i	0.245262	−	0.0633826i
$481$	1.86714e11			0.159047
$482$			5.15998e10i			0.0435448i
$483$		−	4.21629e11i		−	0.352508i
$484$	5.41187e11			0.448273
$485$	2.60533e11	+	1.00814e12i	0.213808	+	0.827341i
$486$	1.24265e12			1.01038
$487$			6.47331e11i			0.521490i	0.965408	+	0.260745i	$0.0839682\pi$
$487$			6.47331e11i			0.521490i	−0.965408	+	0.260745i	$0.916032\pi$
$488$		−	6.53977e11i		−	0.522003i
$489$	1.03296e11			0.0816948
$490$	3.22530e10	+	1.24805e11i	0.0252748	+	0.0978022i
$491$	−3.97775e11			−0.308866			−0.154433	−	0.988003i	$-0.549355\pi$
$491$	−3.97775e11			−0.308866			−0.154433	+	0.988003i	$0.549355\pi$
$492$		−	4.07245e11i		−	0.313338i
$493$			4.63198e11i			0.353147i
$494$	1.26992e11			0.0959415
$495$	−4.38203e11	+	1.13244e11i	−0.328059	+	0.0847798i
$496$	−4.09645e11			−0.303907
$497$			7.91349e10i			0.0581788i
$498$			1.27843e12i			0.931418i
$499$	2.18635e12			1.57859			0.789293	−	0.614017i	$-0.210447\pi$
$499$	2.18635e12			1.57859			0.789293	+	0.614017i	$0.210447\pi$
$500$	5.07127e11	−	4.80732e11i	0.362870	−	0.343984i
$501$	3.45402e12			2.44937
$502$		−	1.75987e12i		−	1.23684i
$503$		−	2.69639e12i		−	1.87814i	−0.343730	−	0.939068i	$-0.611691\pi$
$503$		−	2.69639e12i		−	1.87814i	0.343730	−	0.939068i	$-0.388309\pi$
$504$	2.03921e11			0.140775
$505$	2.33721e12	−	6.04002e11i	1.59914	−	0.413264i
$506$	−2.18277e11			−0.148024
$507$			1.95953e12i			1.31709i
$508$		−	3.71471e11i		−	0.247479i
$509$	−2.82393e12			−1.86476			−0.932381	−	0.361476i	$-0.882273\pi$
$509$	−2.82393e12			−1.86476			−0.932381	+	0.361476i	$0.882273\pi$
$510$	−1.57258e11	−	6.08516e11i	−0.102931	−	0.398296i
$511$	−8.06228e11			−0.523075
$512$			6.87195e10i			0.0441942i
$513$		−	5.73357e10i		−	0.0365508i
$514$	3.17547e11			0.200666
$515$	2.19866e11	+	8.50781e11i	0.137729	+	0.532948i
$516$	1.09344e12			0.679004
$517$			6.28220e10i			0.0386727i
$518$			2.44922e11i			0.149467i
$519$	−1.52866e12			−0.924824
$520$	1.62311e11	−	4.19457e10i	0.0973492	−	0.0251578i
$521$	−2.82836e12			−1.68176			−0.840882	−	0.541219i	$-0.817963\pi$
$521$	−2.82836e12			−1.68176			−0.840882	+	0.541219i	$0.817963\pi$
$522$			1.09916e12i			0.647953i
$523$		−	2.81319e12i		−	1.64415i	−0.569380	−	0.822074i	$-0.692817\pi$
$523$		−	2.81319e12i		−	1.64415i	0.569380	−	0.822074i	$-0.307183\pi$
$524$	−1.59686e12			−0.925289
$525$	8.24738e11	−	4.56777e11i	0.473804	−	0.262414i
$526$	−1.37729e12			−0.784492
$527$			8.73905e11i			0.493533i
$528$		−	2.05782e11i		−	0.115227i
$529$	1.03820e12			0.576407
$530$	−1.97828e12	+	5.11242e11i	−1.08904	+	0.281440i
$531$	−1.55472e12			−0.848644
$532$			1.66582e11i			0.0901626i
$533$		−	2.31733e11i		−	0.124370i
$534$	−2.68971e12			−1.43143
$535$	5.76765e11	+	2.23182e12i	0.304374	+	1.17779i
$536$	6.44332e11			0.337185
$537$			3.25680e12i			1.69008i
$538$			1.69971e12i			0.874689i
$539$	9.00375e10			0.0459488
$540$	−1.89380e10	−	7.32816e10i	−0.00958435	−	0.0370871i
$541$	1.96722e12			0.987337			0.493668	−	0.869650i	$-0.335656\pi$
$541$	1.96722e12			0.987337			0.493668	+	0.869650i	$0.335656\pi$
$542$		−	4.26065e11i		−	0.212070i
$543$		−	4.03769e12i		−	1.99312i
$544$	1.46601e11			0.0717697
$545$	2.01217e12	−	5.20002e11i	0.976969	−	0.252476i
$546$	2.26184e11			0.108917
$547$		−	1.89427e11i		−	0.0904689i	−0.998976	−	0.0452345i	$-0.985597\pi$
$547$		−	1.89427e11i		−	0.0904689i	0.998976	−	0.0452345i	$-0.0144035\pi$
$548$			1.82979e12i			0.866739i
$549$	−3.31065e12			−1.55538
$550$	−2.36473e11	−	4.26966e11i	−0.110192	−	0.198958i
$551$	−8.97898e11			−0.414997
$552$		−	7.19281e11i		−	0.329741i
$553$		−	1.42441e11i		−	0.0647696i
$554$	−2.55004e12			−1.15015
$555$	1.73433e12	−	4.48200e11i	0.775914	−	0.200518i
$556$	−5.56923e11			−0.247149
$557$		−	7.51468e10i		−	0.0330797i	−0.999863	−	0.0165399i	$-0.994735\pi$
$557$		−	7.51468e10i		−	0.0330797i	0.999863	−	0.0165399i	$-0.00526504\pi$
$558$			2.07376e12i			0.905533i
$559$	6.22197e11			0.269510
$560$	5.50223e10	+	2.12911e11i	0.0236424	+	0.0914856i
$561$	−4.39000e11			−0.187125
$562$		−	8.52350e11i		−	0.360417i
$563$			7.92094e11i			0.332268i	0.986103	+	0.166134i	$0.0531285\pi$
$563$			7.92094e11i			0.332268i	−0.986103	+	0.166134i	$0.946872\pi$
$564$	−2.07015e11			−0.0861481
$565$	5.81919e11	+	2.25176e12i	0.240239	+	0.929618i
$566$	−3.35233e11			−0.137301
$567$			8.77807e11i			0.356677i
$568$			1.35001e11i			0.0544212i
$569$	−1.81892e12			−0.727459			−0.363730	−	0.931505i	$-0.618497\pi$
$569$	−1.81892e12			−0.727459			−0.363730	+	0.931505i	$0.618497\pi$
$570$	1.17959e12	−	3.04840e11i	0.468053	−	0.120958i
$571$	4.05446e12			1.59614			0.798068	−	0.602567i	$-0.205855\pi$
$571$	4.05446e12			1.59614			0.798068	+	0.602567i	$0.205855\pi$
$572$		−	1.17095e11i		−	0.0457360i
$573$		−	8.21422e11i		−	0.318325i
$574$	3.03976e11			0.116879
$575$	−8.26557e11	−	1.49240e12i	−0.315332	−	0.569350i
$576$	3.47881e11			0.131683
$577$			1.08566e12i			0.407758i	0.978996	+	0.203879i	$0.0653549\pi$
$577$			1.08566e12i			0.407758i	−0.978996	+	0.203879i	$0.934645\pi$
$578$			1.58466e12i			0.590555i
$579$	−4.73238e12			−1.74995
$580$	−1.14762e12	+	2.96576e11i	−0.421086	+	0.108820i
$581$	−9.54245e11			−0.347430
$582$			2.39665e12i			0.865867i
$583$			1.42718e12i			0.511648i
$584$	−1.37539e12			−0.489292
$585$	−2.12343e11	−	8.21671e11i	−0.0749612	−	0.290066i
$586$	2.40347e12			0.841974
$587$		−	3.71279e12i		−	1.29071i	−0.763882	−	0.645355i	$-0.776709\pi$
$587$		−	3.71279e12i		−	1.29071i	0.763882	−	0.645355i	$-0.223291\pi$
$588$			2.96697e11i			0.102356i
$589$	−1.69404e12			−0.579970
$590$	−4.19495e11	−	1.62326e12i	−0.142526	−	0.551510i
$591$	−5.02467e12			−1.69420
$592$			4.17827e11i			0.139813i
$593$		−	7.00484e11i		−	0.232623i	−0.993213	−	0.116311i	$-0.962893\pi$
$593$		−	7.00484e11i		−	0.232623i	0.993213	−	0.116311i	$-0.0371070\pi$
$594$	−5.28673e10			−0.0174240
$595$	4.54208e11	−	1.17380e11i	0.148569	−	0.0383945i
$596$	−7.08928e11			−0.230141
$597$			1.19110e12i			0.383763i
$598$		−	4.09290e11i		−	0.130881i
$599$	−4.49331e12			−1.42609			−0.713043	−	0.701120i	$-0.752684\pi$
$599$	−4.49331e12			−1.42609			−0.713043	+	0.701120i	$0.752684\pi$
$600$	1.40697e12	−	7.79241e11i	0.443203	−	0.245466i
$601$	−2.44210e12			−0.763534			−0.381767	−	0.924259i	$-0.624684\pi$
$601$	−2.44210e12			−0.763534			−0.381767	+	0.924259i	$0.624684\pi$
$602$			8.16168e11i			0.253277i
$603$		−	3.26182e12i		−	1.00469i
$604$	−2.46207e11			−0.0752720
$605$	2.86045e12	−	7.39220e11i	0.868030	−	0.224323i
$606$	5.55624e12			1.67361
$607$		−	3.54731e12i		−	1.06060i	−0.847811	−	0.530299i	$-0.822080\pi$
$607$		−	3.54731e12i		−	1.06060i	0.847811	−	0.530299i	$-0.177920\pi$
$608$			2.84182e11i			0.0843394i
$609$	−1.59923e12			−0.471122
$610$	−8.93282e11	−	3.45660e12i	−0.261219	−	1.01080i
$611$	−1.17797e11			−0.0341939
$612$		−	7.42142e11i		−	0.213848i
$613$			2.08138e12i			0.595359i	0.954666	+	0.297679i	$0.0962126\pi$
$613$			2.08138e12i			0.595359i	−0.954666	+	0.297679i	$0.903787\pi$
$614$	1.11267e12			0.315944
$615$	−5.56265e11	−	2.15249e12i	−0.156799	−	0.606742i
$616$	1.53600e11			0.0429811
$617$		−	2.42245e12i		−	0.672933i	−0.941695	−	0.336467i	$-0.890768\pi$
$617$		−	2.42245e12i		−	0.672933i	0.941695	−	0.336467i	$-0.109232\pi$
$618$			2.02255e12i			0.557766i
$619$	5.86646e12			1.60608			0.803042	−	0.595922i	$-0.203213\pi$
$619$	5.86646e12			1.60608			0.803042	+	0.595922i	$0.203213\pi$
$620$	−2.16518e12	+	5.59544e11i	−0.588480	+	0.152080i
$621$	−1.84790e11			−0.0498615
$622$		−	2.16041e12i		−	0.578735i
$623$		−	2.00765e12i		−	0.533940i
$624$	3.85860e11			0.101882
$625$	2.02378e12	−	3.23361e12i	0.530521	−	0.847672i
$626$	4.47676e11			0.116514
$627$		−	8.50990e11i		−	0.219898i
$628$			1.89999e12i			0.487454i
$629$	8.91359e11			0.227052
$630$	1.07783e12	−	2.78541e11i	0.272594	−	0.0704460i
$631$	−3.08036e12			−0.773515			−0.386758	−	0.922181i	$-0.626405\pi$
$631$	−3.08036e12			−0.773515			−0.386758	+	0.922181i	$0.626405\pi$
$632$		−	2.42998e11i		−	0.0605865i
$633$		−	1.00609e13i		−	2.49070i
$634$	−1.08836e11			−0.0267529
$635$	−5.07401e11	−	1.96341e12i	−0.123842	−	0.479214i
$636$	−4.70294e12			−1.13976
$637$			1.68828e11i			0.0406273i
$638$			8.27922e11i			0.197832i
$639$	6.83418e11			0.162156
$640$	9.38656e10	+	3.63217e11i	0.0221155	+	0.0855769i
$641$	8.02920e12			1.87850			0.939250	−	0.343233i	$-0.111522\pi$
$641$	8.02920e12			1.87850			0.939250	+	0.343233i	$0.111522\pi$
$642$			5.30569e12i			1.23263i
$643$			8.21210e12i			1.89454i	0.320430	+	0.947272i	$0.396173\pi$
$643$			8.21210e12i			1.89454i	−0.320430	+	0.947272i	$0.603827\pi$
$644$	5.36886e11			0.122997
$645$	5.77940e12	−	1.49356e12i	1.31481	−	0.339785i
$646$	6.06252e11			0.136964
$647$		−	5.88696e12i		−	1.32075i	−0.750934	−	0.660377i	$-0.770396\pi$
$647$		−	5.88696e12i		−	1.32075i	0.750934	−	0.660377i	$-0.229604\pi$
$648$			1.49750e12i			0.333641i
$649$	−1.17106e12			−0.259107
$650$	8.00600e11	−	4.43409e11i	0.175916	−	0.0974303i
$651$	−3.01723e12			−0.658407
$652$			1.31533e11i			0.0285050i
$653$			3.10572e12i			0.668425i	0.942498	+	0.334213i	$0.108470\pi$
$653$			3.10572e12i			0.668425i	−0.942498	+	0.334213i	$0.891530\pi$
$654$	4.78352e12			1.02246
$655$	−8.44024e12	+	2.18120e12i	−1.79171	+	0.463030i
$656$	5.18569e11			0.109330
$657$			6.96267e12i			1.45791i
$658$		−	1.54520e11i		−	0.0321343i
$659$	6.48568e12			1.33959			0.669793	−	0.742547i	$-0.266383\pi$
$659$	6.48568e12			1.33959			0.669793	+	0.742547i	$0.266383\pi$
$660$	−2.81083e11	−	1.08766e12i	−0.0576616	−	0.223124i
$661$	−3.76148e12			−0.766394			−0.383197	−	0.923667i	$-0.625177\pi$
$661$	−3.76148e12			−0.766394			−0.383197	+	0.923667i	$0.625177\pi$
$662$			1.09034e12i			0.220648i
$663$		−	8.23164e11i		−	0.165453i
$664$	−1.62790e12			−0.324991
$665$	2.27539e11	+	8.80472e11i	0.0451188	+	0.174589i
$666$	2.11518e12			0.416594
$667$			2.89388e12i			0.566127i
$668$			4.39820e12i			0.854636i
$669$	1.84507e12			0.356119
$670$	3.40562e12	−	8.80108e11i	0.652919	−	0.168733i
$671$	−2.49368e12			−0.474887
$672$			5.06152e11i			0.0957457i
$673$			1.57852e12i			0.296607i	0.988942	+	0.148303i	$0.0473812\pi$
$673$			1.57852e12i			0.296607i	−0.988942	+	0.148303i	$0.952619\pi$
$674$	−6.59919e12			−1.23175
$675$	−2.00194e11	−	3.61462e11i	−0.0371180	−	0.0670187i
$676$	−2.49519e12			−0.459561
$677$			6.10156e12i			1.11633i	0.829730	+	0.558164i	$0.188494\pi$
$677$			6.10156e12i			1.11633i	−0.829730	+	0.558164i	$0.811506\pi$
$678$			5.35309e12i			0.972907i
$679$	−1.78891e12			−0.322979
$680$	7.74859e11	−	2.00246e11i	0.138974	−	0.0359147i
$681$	9.82707e12			1.75090
$682$			1.56202e12i			0.276476i
$683$			2.97384e12i			0.522907i	0.965216	+	0.261454i	$0.0842019\pi$
$683$			2.97384e12i			0.522907i	−0.965216	+	0.261454i	$0.915798\pi$
$684$	1.43862e12			0.251301
$685$	2.49935e12	+	9.67136e12i	0.433730	+	1.67834i
$686$	−2.21461e11			−0.0381802
$687$		−	2.15672e12i		−	0.369393i
$688$			1.39235e12i			0.236919i
$689$	−2.67610e12			−0.452392
$690$	−9.82483e11	−	3.80176e12i	−0.165008	−	0.638505i
$691$	1.10345e13			1.84121			0.920603	−	0.390500i	$-0.127698\pi$
$691$	1.10345e13			1.84121			0.920603	+	0.390500i	$0.127698\pi$
$692$		−	1.94654e12i		−	0.322690i
$693$		−	7.77574e11i		−	0.128068i
$694$	1.56310e12			0.255781
$695$	−2.94362e12	+	7.60715e11i	−0.478575	+	0.123677i
$696$	−2.72822e12			−0.440694
$697$		−	1.10627e12i		−	0.177548i
$698$			2.84650e12i			0.453901i
$699$	1.58997e13			2.51908
$700$	5.81641e11	+	1.05019e12i	0.0915617	+	0.165320i
$701$	−1.06601e12			−0.166737			−0.0833684	−	0.996519i	$-0.526568\pi$
$701$	−1.06601e12			−0.166737			−0.0833684	+	0.996519i	$0.526568\pi$
$702$		−	9.91310e10i		−	0.0154061i
$703$			1.72788e12i			0.266817i
$704$	2.62035e11			0.0402052
$705$	−1.09418e12	+	2.82767e11i	−0.166816	+	0.0431099i
$706$	−8.09488e12			−1.22628
$707$			4.14729e12i			0.624276i
$708$		−	3.85896e12i		−	0.577192i
$709$	−5.15092e12			−0.765556			−0.382778	−	0.923840i	$-0.625033\pi$
$709$	−5.15092e12			−0.765556			−0.382778	+	0.923840i	$0.625033\pi$
$710$	1.84401e11	+	7.13547e11i	0.0272333	+	0.105380i
$711$	−1.23013e12			−0.180526
$712$		−	3.42497e12i		−	0.499455i
$713$			5.45981e12i			0.791179i
$714$	1.07979e12			0.155488
$715$	−1.59943e11	−	6.18909e11i	−0.0228870	−	0.0885624i
$716$	−4.14707e12			−0.589703
$717$		−	1.41497e13i		−	1.99946i
$718$		−	3.62912e12i		−	0.509613i
$719$	7.14930e12			0.997662			0.498831	−	0.866699i	$-0.333763\pi$
$719$	7.14930e12			0.997662			0.498831	+	0.866699i	$0.333763\pi$
$720$	1.83872e12	−	4.75178e11i	0.254988	−	0.0658962i
$721$	−1.50967e12			−0.208053
$722$		−	3.98780e12i		−	0.546155i
$723$			6.48361e11i			0.0882459i
$724$	5.14143e12			0.695441
$725$	−5.66063e12	+	3.13511e12i	−0.760929	+	0.421437i
$726$	6.80011e12			0.908451
$727$			6.60804e12i			0.877340i	0.898648	+	0.438670i	$0.144550\pi$
$727$			6.60804e12i			0.877340i	−0.898648	+	0.438670i	$0.855450\pi$
$728$			2.88014e11i			0.0380034i
$729$	8.41800e12			1.10391
$730$	−7.26963e12	+	1.87868e12i	−0.947457	+	0.244850i
$731$	2.97032e12			0.384747
$732$		−	8.21734e12i		−	1.05787i
$733$			3.15031e12i			0.403075i	0.979481	+	0.201537i	$0.0645938\pi$
$733$			3.15031e12i			0.403075i	−0.979481	+	0.201537i	$0.935406\pi$
$734$	1.42664e12			0.181419
$735$	4.05266e11	+	1.56819e12i	0.0512208	+	0.198201i
$736$	9.15903e11			0.115053
$737$		−	2.45691e12i		−	0.306750i
$738$		−	2.62517e12i		−	0.325764i
$739$	−8.91714e12			−1.09983			−0.549915	−	0.835221i	$-0.685340\pi$
$739$	−8.91714e12			−1.09983			−0.549915	+	0.835221i	$0.685340\pi$
$740$	5.70720e11	+	2.20843e12i	0.0699649	+	0.270732i
$741$	1.59568e12			0.194431
$742$		−	3.51037e12i		−	0.425143i
$743$		−	2.01761e12i		−	0.242878i	−0.992599	−	0.121439i	$-0.961249\pi$
$743$		−	2.01761e12i		−	0.242878i	0.992599	−	0.121439i	$-0.0387509\pi$
$744$	−5.14727e12			−0.615883
$745$	−3.74704e12	+	9.68341e11i	−0.445641	+	0.115166i
$746$	3.92209e12			0.463652
$747$			8.24096e12i			0.968357i
$748$		−	5.59005e11i		−	0.0652917i
$749$	−3.96027e12			−0.459787
$750$	6.37214e12	−	6.04049e12i	0.735377	−	0.697103i
$751$	5.57535e12			0.639576			0.319788	−	0.947489i	$-0.396388\pi$
$751$	5.57535e12			0.639576			0.319788	+	0.947489i	$0.396388\pi$
$752$		−	2.63604e11i		−	0.0300588i
$753$		−	2.21131e13i		−	2.50653i
$754$	−1.55243e12			−0.174920
$755$	−1.30133e12	+	3.36300e11i	−0.145756	+	0.0376673i
$756$	1.30035e11			0.0144781
$757$		−	9.24800e12i		−	1.02357i	−0.859115	−	0.511783i	$-0.828985\pi$
$757$		−	9.24800e12i		−	1.02357i	0.859115	−	0.511783i	$-0.171015\pi$
$758$			5.47008e12i			0.601842i
$759$	−2.74270e12			−0.299978
$760$	3.88171e11	+	1.50205e12i	0.0422048	+	0.163313i
$761$	5.63867e12			0.609461			0.304730	−	0.952439i	$-0.401434\pi$
$761$	5.63867e12			0.609461			0.304730	+	0.952439i	$0.401434\pi$
$762$		−	4.66760e12i		−	0.501530i
$763$			3.57051e12i			0.381391i
$764$	1.04597e12			0.111070
$765$	−1.01371e12	−	3.92259e12i	−0.107013	−	0.414092i
$766$	2.22976e12			0.234007
$767$		−	2.19585e12i		−	0.229099i
$768$			8.63473e11i			0.0895619i
$769$	3.02171e12			0.311591			0.155795	−	0.987789i	$-0.450206\pi$
$769$	3.02171e12			0.311591			0.155795	+	0.987789i	$0.450206\pi$
$770$	8.11854e11	−	2.09806e11i	0.0832280	−	0.0215085i
$771$	3.99004e12			0.406661
$772$		−	6.02602e12i		−	0.610594i
$773$		−	1.04201e13i		−	1.04970i	−0.851196	−	0.524848i	$-0.824122\pi$
$773$		−	1.04201e13i		−	1.04970i	0.851196	−	0.524848i	$-0.175878\pi$
$774$	7.04851e12			0.705932
$775$	−1.06798e13	+	5.91495e12i	−1.06342	+	0.588970i
$776$	−3.05180e12			−0.302119
$777$			3.07750e12i			0.302903i
$778$		−	1.20010e13i		−	1.17438i
$779$	2.14449e12			0.208643
$780$	2.03947e12	−	5.27056e11i	0.197284	−	0.0509836i
$781$	5.14772e11			0.0495091
$782$		−	1.95392e12i		−	0.186843i
$783$			7.00904e11i			0.0666393i
$784$	−3.77802e11			−0.0357143
$785$	2.59524e12	+	1.00424e13i	0.243930	+	0.943898i
$786$	−2.00649e13			−1.87515
$787$			5.20975e12i			0.484095i	0.970264	+	0.242047i	$0.0778189\pi$
$787$			5.20975e12i			0.484095i	−0.970264	+	0.242047i	$0.922181\pi$
$788$		−	6.39821e12i		−	0.591140i
$789$	−1.73059e13			−1.58982
$790$	−3.31917e11	−	1.28437e12i	−0.0303184	−	0.117319i
$791$	−3.99566e12			−0.362906
$792$		−	1.32651e12i		−	0.119797i
$793$		−	4.67588e12i		−	0.419889i
$794$	1.00781e13			0.899881
$795$	−2.48574e13	+	6.42386e12i	−2.20701	+	0.570353i
$796$	−1.51670e12			−0.133903
$797$		−	4.43164e12i		−	0.389047i	−0.980898	−	0.194523i	$-0.937684\pi$
$797$		−	4.43164e12i		−	0.389047i	0.980898	−	0.194523i	$-0.0623160\pi$
$798$			2.09314e12i			0.182719i
$799$	−5.62353e11			−0.0488145
$800$	9.92254e11	+	1.79157e12i	0.0856481	+	0.154643i
$801$	−1.73383e13			−1.48820
$802$		−	2.61215e12i		−	0.222953i
$803$			5.24451e12i			0.445128i
$804$	8.09615e12			0.683323
$805$	2.83771e12	−	7.33345e11i	0.238170	−	0.0615498i
$806$	−2.92893e12			−0.244456
$807$			2.13571e13i			1.77260i
$808$			7.07509e12i			0.583957i
$809$	−1.51138e13			−1.24052			−0.620261	−	0.784396i	$-0.712973\pi$
$809$	−1.51138e13			−1.24052			−0.620261	+	0.784396i	$0.712973\pi$
$810$	2.04547e12	+	7.91505e12i	0.166959	+	0.646057i
$811$	−1.54577e13			−1.25473			−0.627364	−	0.778726i	$-0.715866\pi$
$811$	−1.54577e13			−1.25473			−0.627364	+	0.778726i	$0.715866\pi$
$812$		−	2.03640e12i		−	0.164384i
$813$		−	5.35358e12i		−	0.429771i
$814$	1.59322e12			0.127194
$815$	1.79664e11	+	6.95220e11i	0.0142644	+	0.0551967i
$816$	1.84207e12			0.145445
$817$			5.75790e12i			0.452131i
$818$		−	1.04310e13i		−	0.814582i
$819$	1.45802e12			0.113236
$820$	2.74090e12	−	7.08326e11i	0.211705	−	0.0547105i
$821$	1.35717e13			1.04253			0.521267	−	0.853394i	$-0.325460\pi$
$821$	1.35717e13			1.04253			0.521267	+	0.853394i	$0.325460\pi$
$822$			2.29916e13i			1.75649i
$823$			1.26218e13i			0.959011i	0.877539	+	0.479506i	$0.159184\pi$
$823$			1.26218e13i			0.959011i	−0.877539	+	0.479506i	$0.840816\pi$
$824$	−2.57544e12			−0.194616
$825$	−2.97133e12	−	5.36491e12i	−0.223310	−	0.403199i
$826$	2.88040e12			0.215299
$827$		−	2.20948e13i		−	1.64254i	−0.570540	−	0.821270i	$-0.693266\pi$
$827$		−	2.20948e13i		−	1.64254i	0.570540	−	0.821270i	$-0.306734\pi$
$828$		−	4.63660e12i		−	0.342818i
$829$	7.09788e12			0.521955			0.260978	−	0.965345i	$-0.415955\pi$
$829$	7.09788e12			0.521955			0.260978	+	0.965345i	$0.415955\pi$
$830$	−8.60427e12	+	2.22359e12i	−0.629307	+	0.162631i
$831$	−3.20417e13			−2.33083
$832$			4.91339e11i			0.0355489i
$833$			8.05974e11i			0.0579987i
$834$	−6.99785e12			−0.500861
$835$	6.00761e12	+	2.32467e13i	0.427674	+	1.65490i
$836$	1.08362e12			0.0767268
$837$			1.32238e12i			0.0931304i
$838$			7.59164e12i			0.531787i
$839$	2.47192e13			1.72229			0.861144	−	0.508362i	$-0.169749\pi$
$839$	2.47192e13			1.72229			0.861144	+	0.508362i	$0.169749\pi$
$840$	6.91365e11	+	2.67527e12i	0.0479127	+	0.185400i
$841$	−3.53073e12			−0.243379
$842$			2.33602e12i			0.160166i
$843$		−	1.07099e13i		−	0.730404i
$844$	1.28112e13			0.869055
$845$	−1.31883e13	+	3.40824e12i	−0.889886	+	0.229972i
$846$	−1.33445e12			−0.0895646
$847$			5.07574e12i			0.338863i
$848$		−	5.98853e12i		−	0.397685i
$849$	−4.21227e12			−0.278248
$850$	3.82200e12	−	2.11680e12i	0.251134	−	0.139089i
$851$	5.56886e12			0.363985
$852$			1.69631e12i			0.110288i
$853$		−	8.35049e12i		−	0.540059i	−0.962852	−	0.270030i	$-0.912966\pi$
$853$		−	8.35049e12i		−	0.540059i	0.962852	−	0.270030i	$-0.0870335\pi$
$854$	6.13359e12			0.394597
$855$	7.60385e12	−	1.96505e12i	0.486616	−	0.125755i
$856$	−6.75605e12			−0.430091
$857$		−	5.66058e12i		−	0.358465i	−0.983807	−	0.179233i	$-0.942639\pi$
$857$		−	5.66058e12i		−	0.358465i	0.983807	−	0.179233i	$-0.0573615\pi$
$858$		−	1.47133e12i		−	0.0926865i
$859$	9.99170e12			0.626138			0.313069	−	0.949730i	$-0.398643\pi$
$859$	9.99170e12			0.626138			0.313069	+	0.949730i	$0.398643\pi$
$860$	1.90184e12	+	7.35925e12i	0.118558	+	0.458765i
$861$	3.81951e12			0.236861
$862$		−	7.06219e12i		−	0.435669i
$863$			9.53908e12i			0.585407i	0.956203	+	0.292704i	$0.0945549\pi$
$863$			9.53908e12i			0.585407i	−0.956203	+	0.292704i	$0.905445\pi$
$864$	2.21834e11			0.0135430
$865$	−2.65882e12	−	1.02884e13i	−0.161479	−	0.624852i
$866$	2.16553e12			0.130838
$867$			1.99115e13i			1.19679i
$868$		−	3.84202e12i		−	0.229732i
$869$	−9.26577e11			−0.0551179
$870$	−1.44200e13	+	3.72654e12i	−0.853354	+	0.220531i
$871$	4.60692e12			0.271224
$872$			6.09114e12i			0.356758i
$873$			1.54492e13i			0.900206i
$874$	3.78762e12			0.219566
$875$	4.50874e12	+	4.75629e12i	0.260028	+	0.274304i
$876$	−1.72820e13			−0.991576
$877$		−	1.27850e13i		−	0.729799i	−0.931047	−	0.364900i	$-0.881103\pi$
$877$		−	1.27850e13i		−	0.729799i	0.931047	−	0.364900i	$-0.118897\pi$
$878$		−	1.18328e12i		−	0.0671989i
$879$	3.02000e13			1.70631
$880$	1.38499e12	−	3.57920e11i	0.0778527	−	0.0201193i
$881$	−1.50900e13			−0.843913			−0.421957	−	0.906616i	$-0.638657\pi$
$881$	−1.50900e13			−0.843913			−0.421957	+	0.906616i	$0.638657\pi$
$882$			1.91256e12i			0.106416i
$883$			1.48974e12i			0.0824685i	0.999150	+	0.0412342i	$0.0131290\pi$
$883$			1.48974e12i			0.0824685i	−0.999150	+	0.0412342i	$0.986871\pi$
$884$	1.04818e12			0.0577301
$885$	−5.27104e12	−	2.03965e13i	−0.288836	−	1.11767i
$886$	−1.55019e12			−0.0845148
$887$		−	1.92566e13i		−	1.04453i	−0.852782	−	0.522267i	$-0.825086\pi$
$887$		−	1.92566e13i		−	1.04453i	0.852782	−	0.522267i	$-0.174914\pi$
$888$			5.25007e12i			0.283339i
$889$	3.48399e12			0.187076
$890$	−4.67824e12	−	1.81027e13i	−0.249935	−	0.967137i
$891$	5.71013e12			0.303526
$892$			2.34943e12i			0.124257i
$893$		−	1.09011e12i		−	0.0573638i
$894$	−8.90781e12			−0.466393
$895$	−2.19194e13	+	5.66459e12i	−1.14189	+	0.295097i
$896$	−6.44514e11			−0.0334077
$897$		−	5.14280e12i		−	0.265237i
$898$		−	2.10990e13i		−	1.08273i
$899$	2.07089e13			1.05740
$900$	9.06953e12	−	5.02312e12i	0.460780	−	0.255201i
$901$	−1.27755e13			−0.645826
$902$		−	1.97736e12i		−	0.0994618i
$903$			1.02553e13i			0.513279i
$904$	−6.81641e12			−0.339467
$905$	2.71751e13	−	7.02280e12i	1.34664	−	0.348010i
$906$	−3.09363e12			−0.152543
$907$		−	4.29875e12i		−	0.210916i	−0.994424	−	0.105458i	$-0.966369\pi$
$907$		−	4.29875e12i		−	0.210916i	0.994424	−	0.105458i	$-0.0336309\pi$
$908$			1.25134e13i			0.610926i
$909$	3.58164e13			1.73998
$910$	3.93405e11	+	1.52230e12i	0.0190175	+	0.0735891i
$911$	1.55780e13			0.749339			0.374669	−	0.927158i	$-0.377756\pi$
$911$	1.55780e13			0.749339			0.374669	+	0.927158i	$0.377756\pi$
$912$			3.57080e12i			0.170918i
$913$			6.20736e12i			0.295657i
$914$	5.86457e12			0.277957
$915$	−1.12243e13	−	4.34328e13i	−0.529374	−	2.04844i
$916$	2.74628e12			0.128889
$917$		−	1.49768e13i		−	0.699453i
$918$		−	4.73244e11i		−	0.0219934i
$919$	3.15200e13			1.45769			0.728846	−	0.684677i	$-0.240057\pi$
$919$	3.15200e13			1.45769			0.728846	+	0.684677i	$0.240057\pi$
$920$	4.84101e12	−	1.25105e12i	0.222788	−	0.0575746i
$921$	1.39809e13			0.640277
$922$		−	1.75064e13i		−	0.797823i
$923$			9.65244e11i			0.0437753i
$924$	1.93001e12			0.0871036
$925$	6.03308e12	+	1.08931e13i	0.270958	+	0.489230i
$926$	1.70933e13			0.763972
$927$			1.30377e13i			0.579886i
$928$		−	3.47400e12i		−	0.153767i
$929$	−1.29506e13			−0.570453			−0.285227	−	0.958460i	$-0.592069\pi$
$929$	−1.29506e13			−0.570453			−0.285227	+	0.958460i	$0.592069\pi$
$930$	−2.72059e13	+	7.03077e12i	−1.19259	+	0.308198i
$931$	−1.56236e12			−0.0681565
$932$			2.02461e13i			0.878961i
$933$		−	2.71460e13i		−	1.17284i
$934$	7.63192e12			0.328150
$935$	−7.63558e11	−	2.95462e12i	−0.0326730	−	0.126430i
$936$	2.48732e12			0.105923
$937$			3.67767e13i			1.55864i	0.626628	+	0.779318i	$0.284434\pi$
$937$			3.67767e13i			1.55864i	−0.626628	+	0.779318i	$0.715566\pi$
$938$			6.04313e12i			0.254888i
$939$	5.62513e12			0.236123
$940$	−3.60064e11	−	1.39328e12i	−0.0150419	−	0.0582055i
$941$	2.14183e13			0.890494			0.445247	−	0.895408i	$-0.353116\pi$
$941$	2.14183e13			0.890494			0.445247	+	0.895408i	$0.353116\pi$
$942$			2.38738e13i			0.987852i
$943$		−	6.91156e12i		−	0.284625i
$944$	4.91384e12			0.201394
$945$	6.87301e11	−	1.77618e11i	0.0280352	−	0.00724509i
$946$	5.30916e12			0.215534
$947$			4.33771e12i			0.175261i	0.996153	+	0.0876306i	$0.0279295\pi$
$947$			4.33771e12i			0.175261i	−0.996153	+	0.0876306i	$0.972071\pi$
$948$		−	3.05331e12i		−	0.122782i
$949$	−9.83392e12			−0.393576
$950$	4.10336e12	+	7.40886e12i	0.163449	+	0.295118i
$951$	−1.36755e12			−0.0542163
$952$			1.37496e12i			0.0542528i
$953$			3.24424e13i			1.27408i	0.770833	+	0.637038i	$0.219840\pi$
$953$			3.24424e13i			1.27408i	−0.770833	+	0.637038i	$0.780160\pi$
$954$	−3.03159e13			−1.18496
$955$	5.52846e12	−	1.42871e12i	0.215074	−	0.0555813i
$956$	1.80177e13			0.697652
$957$			1.04030e13i			0.400917i
$958$			7.76534e12i			0.297863i
$959$	−1.71614e13			−0.655193
$960$	1.17944e12	+	4.56389e12i	0.0448182	+	0.173426i
$961$	1.26315e13			0.477747
$962$			2.98743e12i			0.112463i
$963$			3.42013e13i			1.28152i
$964$	−8.25596e11			−0.0307908
$965$	−8.23108e12	−	3.18506e13i	−0.305551	−	1.18234i
$966$	6.74607e12			0.249261
$967$		−	3.83198e13i		−	1.40930i	−0.709553	−	0.704652i	$-0.751103\pi$
$967$		−	3.83198e13i		−	1.40930i	0.709553	−	0.704652i	$-0.248897\pi$
$968$			8.65899e12i			0.316977i
$969$	7.61767e12			0.277565
$970$	−1.61303e13	+	4.16852e12i	−0.585018	+	0.151185i
$971$	6.62920e12			0.239317			0.119659	−	0.992815i	$-0.461820\pi$
$971$	6.62920e12			0.239317			0.119659	+	0.992815i	$0.461820\pi$
$972$			1.98824e13i			0.714447i
$973$		−	5.22333e12i		−	0.186827i
$974$	−1.03573e13			−0.368749
$975$	1.00597e13	−	5.57151e12i	0.356504	−	0.197448i
$976$	1.04636e13			0.369112
$977$		−	2.52226e13i		−	0.885655i	−0.896607	−	0.442828i	$-0.853975\pi$
$977$		−	2.52226e13i		−	0.885655i	0.896607	−	0.442828i	$-0.146025\pi$
$978$			1.65274e12i			0.0577670i
$979$	−1.30598e13			−0.454374
$980$	−1.99687e12	+	5.16049e11i	−0.0691566	+	0.0178720i
$981$	3.08353e13			1.06301
$982$		−	6.36440e12i		−	0.218401i
$983$			2.73832e13i			0.935391i	0.883890	+	0.467695i	$0.154916\pi$
$983$			2.73832e13i			0.935391i	−0.883890	+	0.467695i	$0.845084\pi$
$984$	6.51592e12			0.221563
$985$	−8.73947e12	−	3.38178e13i	−0.295816	−	1.14467i
$986$	−7.41117e12			−0.249713
$987$		−	1.94157e12i		−	0.0651218i
$988$			2.03188e12i			0.0678409i
$989$	1.85574e13			0.616785
$990$	−1.81191e12	−	7.01126e12i	−0.0599484	−	0.231973i
$991$	−2.54798e13			−0.839197			−0.419599	−	0.907710i	$-0.637829\pi$
$991$	−2.54798e13			−0.839197			−0.419599	+	0.907710i	$0.637829\pi$
$992$		−	6.55432e12i		−	0.214894i
$993$			1.37003e13i			0.447156i
$994$	−1.26616e12			−0.0411386
$995$	−8.01650e12	+	2.07169e12i	−0.259287	+	0.0670071i
$996$	−2.04549e13			−0.658612
$997$		−	2.00966e13i		−	0.644162i	−0.946712	−	0.322081i	$-0.895618\pi$
$997$		−	2.00966e13i		−	0.644162i	0.946712	−	0.322081i	$-0.104382\pi$
$998$			3.49817e13i			1.11623i
$999$	1.34879e12			0.0428450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.10.c.a.29.12	yes	12
5.2	odd	4		350.10.a.u.1.6		6
5.3	odd	4		350.10.a.v.1.1		6
5.4	even	2	inner	70.10.c.a.29.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.10.c.a.29.1	✓	12	5.4	even	2	inner
70.10.c.a.29.12	yes	12	1.1	even	1	trivial
350.10.a.u.1.6		6	5.2	odd	4
350.10.a.v.1.1		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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	70.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+16.0000i q^{2} +201.043i q^{3} -256.000 q^{4} +(-1353.09 + 349.677i) q^{5} -3216.69 q^{6} -2401.00i q^{7} -4096.00i q^{8} -20735.3 q^{9} +O(q^{10})\)	\(q+16.0000i q^{2} +201.043i q^{3} -256.000 q^{4} +(-1353.09 + 349.677i) q^{5} -3216.69 q^{6} -2401.00i q^{7} -4096.00i q^{8} -20735.3 q^{9} +(-5594.82 - 21649.4i) q^{10} -15618.5 q^{11} -51467.0i q^{12} -29286.1i q^{13} +38416.0 q^{14} +(-70300.0 - 272029. i) q^{15} +65536.0 q^{16} -139809. i q^{17} -331765. i q^{18} +271017. q^{19} +(346391. - 89517.2i) q^{20} +482704. q^{21} -249896. i q^{22} -873473. i q^{23} +823472. q^{24} +(1.70858e6 - 946287. i) q^{25} +468577. q^{26} -211557. i q^{27} +614656. i q^{28} -3.31307e6 q^{29} +(4.35247e6 - 1.12480e6i) q^{30} -6.25069e6 q^{31} +1.04858e6i q^{32} -3.13999e6i q^{33} +2.23695e6 q^{34} +(839573. + 3.24877e6i) q^{35} +5.30824e6 q^{36} +6.37553e6i q^{37} +4.33627e6i q^{38} +5.88776e6 q^{39} +(1.43228e6 + 5.54225e6i) q^{40} +7.91273e6 q^{41} +7.72327e6i q^{42} +2.12455e7i q^{43} +3.99833e6 q^{44} +(2.80567e7 - 7.25065e6i) q^{45} +1.39756e7 q^{46} -4.02228e6i q^{47} +1.31756e7i q^{48} -5.76480e6 q^{49} +(1.51406e7 + 2.73372e7i) q^{50} +2.81077e7 q^{51} +7.49723e6i q^{52} -9.13777e7i q^{53} +3.38492e6 q^{54} +(2.11332e7 - 5.46142e6i) q^{55} -9.83450e6 q^{56} +5.44861e7i q^{57} -5.30091e7i q^{58} +7.49792e7 q^{59} +(1.79968e7 + 6.96395e7i) q^{60} +1.59662e8 q^{61} -1.00011e8i q^{62} +4.97855e7i q^{63} -1.67772e7 q^{64} +(1.02407e7 + 3.96267e7i) q^{65} +5.02398e7 q^{66} +1.57308e8i q^{67} +3.57912e7i q^{68} +1.75606e8 q^{69} +(-5.19803e7 + 1.34332e7i) q^{70} -3.29592e7 q^{71} +8.49318e7i q^{72} -3.35788e8i q^{73} -1.02009e8 q^{74} +(1.90244e8 + 3.43498e8i) q^{75} -6.93804e7 q^{76} +3.75000e7i q^{77} +9.42042e7i q^{78} +5.93256e7 q^{79} +(-8.86761e7 + 2.29164e7i) q^{80} -3.65601e8 q^{81} +1.26604e8i q^{82} -3.97437e8i q^{83} -1.23572e8 q^{84} +(4.88881e7 + 1.89175e8i) q^{85} -3.39928e8 q^{86} -6.66069e8i q^{87} +6.39733e7i q^{88} +8.36174e8 q^{89} +(1.16010e8 + 4.48907e8i) q^{90} -7.03159e7 q^{91} +2.23609e8i q^{92} -1.25666e9i q^{93} +6.43565e7 q^{94} +(-3.66710e8 + 9.47683e7i) q^{95} -2.10809e8 q^{96} -7.45068e8i q^{97} -9.22368e7i q^{98} +3.23854e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3072 q^{4} + 4010 q^{5} - 2464 q^{6} - 24506 q^{9}+O(q^{10}) \) 12 * q - 3072 * q^4 + 4010 * q^5 - 2464 * q^6 - 24506 * q^9	\( 12 q - 3072 q^{4} + 4010 q^{5} - 2464 q^{6} - 24506 q^{9} - 50080 q^{10} + 30806 q^{11} + 460992 q^{14} - 109450 q^{15} + 786432 q^{16} + 907064 q^{19} - 1026560 q^{20} + 369754 q^{21} + 630784 q^{24} + 1375500 q^{25} - 1020192 q^{26} - 5975006 q^{29} + 8624000 q^{30} - 20971700 q^{31} - 1283360 q^{34} + 7515130 q^{35} + 6273536 q^{36} - 774774 q^{39} + 12820480 q^{40} - 81549584 q^{41} - 7886336 q^{44} + 7857730 q^{45} - 41064000 q^{46} - 69177612 q^{49} + 15262400 q^{50} - 266346046 q^{51} - 145368608 q^{54} - 38302660 q^{55} - 118013952 q^{56} - 2784020 q^{59} + 28019200 q^{60} - 446750772 q^{61} - 201326592 q^{64} + 14974470 q^{65} - 344900000 q^{66} + 635592700 q^{69} + 154048160 q^{70} - 532489184 q^{71} - 736948544 q^{74} + 796780600 q^{75} - 232208384 q^{76} + 1455238758 q^{79} + 262799360 q^{80} - 1291761292 q^{81} - 94657024 q^{84} + 746117890 q^{85} - 899491968 q^{86} + 2979792428 q^{89} + 658842560 q^{90} + 153092562 q^{91} - 414904288 q^{94} - 1056284100 q^{95} - 161480704 q^{96} + 5383147148 q^{99}+O(q^{100}) \) 12 * q - 3072 * q^4 + 4010 * q^5 - 2464 * q^6 - 24506 * q^9 - 50080 * q^10 + 30806 * q^11 + 460992 * q^14 - 109450 * q^15 + 786432 * q^16 + 907064 * q^19 - 1026560 * q^20 + 369754 * q^21 + 630784 * q^24 + 1375500 * q^25 - 1020192 * q^26 - 5975006 * q^29 + 8624000 * q^30 - 20971700 * q^31 - 1283360 * q^34 + 7515130 * q^35 + 6273536 * q^36 - 774774 * q^39 + 12820480 * q^40 - 81549584 * q^41 - 7886336 * q^44 + 7857730 * q^45 - 41064000 * q^46 - 69177612 * q^49 + 15262400 * q^50 - 266346046 * q^51 - 145368608 * q^54 - 38302660 * q^55 - 118013952 * q^56 - 2784020 * q^59 + 28019200 * q^60 - 446750772 * q^61 - 201326592 * q^64 + 14974470 * q^65 - 344900000 * q^66 + 635592700 * q^69 + 154048160 * q^70 - 532489184 * q^71 - 736948544 * q^74 + 796780600 * q^75 - 232208384 * q^76 + 1455238758 * q^79 + 262799360 * q^80 - 1291761292 * q^81 - 94657024 * q^84 + 746117890 * q^85 - 899491968 * q^86 + 2979792428 * q^89 + 658842560 * q^90 + 153092562 * q^91 - 414904288 * q^94 - 1056284100 * q^95 - 161480704 * q^96 + 5383147148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more