LMFDB - Embedded newform 14.11.b.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,11,Mod(13,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("14.13");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	14.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.89500153743$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14130x^{6} + 61043589x^{4} + 87066375930x^{2} + 12363031798119 $ x^8 + 14130x^6 + 61043589x^4 + 87066375930*x^2 + 12363031798119
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{2}\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.8
Root			$54.6993i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.11.b.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.6274 q^{2} +469.394i q^{3} +512.000 q^{4} +1370.18i q^{5} +10621.2i q^{6} +(-12242.6 - 11514.9i) q^{7} +11585.2 q^{8} -161282. q^{9} +O(q^{10})$	\(q+22.6274 q^{2} +469.394i q^{3} +512.000 q^{4} +1370.18i q^{5} +10621.2i q^{6} +(-12242.6 - 11514.9i) q^{7} +11585.2 q^{8} -161282. q^{9} +31003.6i q^{10} +214362. q^{11} +240330. i q^{12} +420232. i q^{13} +(-277019. - 260553. i) q^{14} -643153. q^{15} +262144. q^{16} -75204.7i q^{17} -3.64940e6 q^{18} +2.33351e6i q^{19} +701530. i q^{20} +(5.40504e6 - 5.74662e6i) q^{21} +4.85046e6 q^{22} +662126. q^{23} +5.43805e6i q^{24} +7.88824e6 q^{25} +9.50875e6i q^{26} -4.79877e7i q^{27} +(-6.26822e6 - 5.89564e6i) q^{28} +6.60603e6 q^{29} -1.45529e7 q^{30} +8.54507e6i q^{31} +5.93164e6 q^{32} +1.00620e8i q^{33} -1.70169e6i q^{34} +(1.57775e7 - 1.67746e7i) q^{35} -8.25765e7 q^{36} +7.29148e7 q^{37} +5.28014e7i q^{38} -1.97254e8 q^{39} +1.58738e7i q^{40} +1.10803e7i q^{41} +(1.22302e8 - 1.30031e8i) q^{42} -6.62029e7 q^{43} +1.09753e8 q^{44} -2.20985e8i q^{45} +1.49822e7 q^{46} +2.19417e7i q^{47} +1.23049e8i q^{48} +(1.72883e7 + 2.81946e8i) q^{49} +1.78491e8 q^{50} +3.53007e7 q^{51} +2.15159e8i q^{52} +5.63633e8 q^{53} -1.08584e9i q^{54} +2.93714e8i q^{55} +(-1.41834e8 - 1.33403e8i) q^{56} -1.09534e9 q^{57} +1.49477e8 q^{58} -6.33264e8i q^{59} -3.29294e8 q^{60} -7.67594e8i q^{61} +1.93353e8i q^{62} +(1.97452e9 + 1.85715e9i) q^{63} +1.34218e8 q^{64} -5.75791e8 q^{65} +2.27678e9i q^{66} -1.30480e9 q^{67} -3.85048e7i q^{68} +3.10798e8i q^{69} +(3.57004e8 - 3.79565e8i) q^{70} -1.25444e9 q^{71} -1.86849e9 q^{72} -4.03787e9i q^{73} +1.64987e9 q^{74} +3.70270e9i q^{75} +1.19476e9i q^{76} +(-2.62435e9 - 2.46836e9i) q^{77} -4.46336e9 q^{78} +8.20678e7 q^{79} +3.59184e8i q^{80} +1.30016e10 q^{81} +2.50719e8i q^{82} -3.58618e9i q^{83} +(2.76738e9 - 2.94227e9i) q^{84} +1.03044e8 q^{85} -1.49800e9 q^{86} +3.10083e9i q^{87} +2.48343e9 q^{88} +4.23634e9i q^{89} -5.00032e9i q^{90} +(4.83893e9 - 5.14474e9i) q^{91} +3.39008e8 q^{92} -4.01101e9 q^{93} +4.96485e8i q^{94} -3.19732e9 q^{95} +2.78428e9i q^{96} -9.87038e9i q^{97} +(3.91191e8 + 6.37970e9i) q^{98} -3.45727e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4096 q^{4} + 18376 q^{7} - 246456 q^{9}+O(q^{10}) $ 8 * q + 4096 * q^4 + 18376 * q^7 - 246456 * q^9	$ 8 q + 4096 q^{4} + 18376 q^{7} - 246456 q^{9} + 430800 q^{11} - 136704 q^{14} - 1896960 q^{15} + 2097152 q^{16} - 4512768 q^{18} + 5339136 q^{21} + 13228032 q^{22} + 6265488 q^{23} - 28719160 q^{25} + 9408512 q^{28} - 46431408 q^{29} + 28584960 q^{30} + 184450560 q^{35} - 126185472 q^{36} + 360932816 q^{37} - 836120064 q^{39} + 308382720 q^{42} + 32112848 q^{43} + 220569600 q^{44} - 769191936 q^{46} + 853888904 q^{49} - 53836800 q^{50} + 1737904128 q^{51} - 1132258608 q^{53} - 69992448 q^{56} - 2040889344 q^{57} + 352352256 q^{58} - 971243520 q^{60} + 2661283080 q^{63} + 1073741824 q^{64} - 143001600 q^{65} - 2254742192 q^{67} + 402662400 q^{70} + 2121911184 q^{71} - 2310537216 q^{72} + 4970207232 q^{74} - 17516185008 q^{77} + 1916728320 q^{78} - 5257367792 q^{79} + 24706423944 q^{81} + 2733637632 q^{84} + 4331212800 q^{85} - 14424637440 q^{86} + 6772752384 q^{88} - 8536548864 q^{91} + 3207929856 q^{92} - 20748386304 q^{93} + 30330078720 q^{95} - 802977792 q^{98} - 16331376816 q^{99}+O(q^{100}) $ 8 * q + 4096 * q^4 + 18376 * q^7 - 246456 * q^9 + 430800 * q^11 - 136704 * q^14 - 1896960 * q^15 + 2097152 * q^16 - 4512768 * q^18 + 5339136 * q^21 + 13228032 * q^22 + 6265488 * q^23 - 28719160 * q^25 + 9408512 * q^28 - 46431408 * q^29 + 28584960 * q^30 + 184450560 * q^35 - 126185472 * q^36 + 360932816 * q^37 - 836120064 * q^39 + 308382720 * q^42 + 32112848 * q^43 + 220569600 * q^44 - 769191936 * q^46 + 853888904 * q^49 - 53836800 * q^50 + 1737904128 * q^51 - 1132258608 * q^53 - 69992448 * q^56 - 2040889344 * q^57 + 352352256 * q^58 - 971243520 * q^60 + 2661283080 * q^63 + 1073741824 * q^64 - 143001600 * q^65 - 2254742192 * q^67 + 402662400 * q^70 + 2121911184 * q^71 - 2310537216 * q^72 + 4970207232 * q^74 - 17516185008 * q^77 + 1916728320 * q^78 - 5257367792 * q^79 + 24706423944 * q^81 + 2733637632 * q^84 + 4331212800 * q^85 - 14424637440 * q^86 + 6772752384 * q^88 - 8536548864 * q^91 + 3207929856 * q^92 - 20748386304 * q^93 + 30330078720 * q^95 - 802977792 * q^98 - 16331376816 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	22.6274			0.707107
$2$	22.6274			0.707107
$3$			469.394i			1.93166i	0.259168	+	0.965832i	$0.416552\pi$
$3$			469.394i			1.93166i	−0.259168	+	0.965832i	$0.583448\pi$
$4$	512.000			0.500000
$5$			1370.18i			0.438457i	0.975674	+	0.219228i	$0.0703539\pi$
$5$			1370.18i			0.438457i	−0.975674	+	0.219228i	$0.929646\pi$
$6$			10621.2i			1.36589i
$7$	−12242.6	−	11514.9i	−0.728424	−	0.685127i
$7$	−12242.6	−	11514.9i	−0.728424	−	0.685127i
$8$	11585.2			0.353553
$9$	−161282.			−2.73133
$10$			31003.6i			0.310036i
$11$	214362.			1.33102			0.665509	−	0.746389i	$-0.268214\pi$
$11$	214362.			1.33102			0.665509	+	0.746389i	$0.268214\pi$
$12$			240330.i			0.965832i
$13$			420232.i			1.13181i	0.824472	+	0.565903i	$0.191472\pi$
$13$			420232.i			1.13181i	−0.824472	+	0.565903i	$0.808528\pi$
$14$	−277019.	−	260553.i	−0.515074	−	0.484458i
$15$	−643153.			−0.846951
$16$	262144.			0.250000
$17$		−	75204.7i		−	0.0529664i	−0.999649	−	0.0264832i	$-0.991569\pi$
$17$		−	75204.7i		−	0.0529664i	0.999649	−	0.0264832i	$-0.00843085\pi$
$18$	−3.64940e6			−1.93134
$19$			2.33351e6i			0.942415i	0.882022	+	0.471207i	$0.156182\pi$
$19$			2.33351e6i			0.942415i	−0.882022	+	0.471207i	$0.843818\pi$
$20$			701530.i			0.219228i
$21$	5.40504e6	−	5.74662e6i	1.32343	−	1.40707i
$22$	4.85046e6			0.941172
$23$	662126.			0.102873			0.0514365	−	0.998676i	$-0.483620\pi$
$23$	662126.			0.102873			0.0514365	+	0.998676i	$0.483620\pi$
$24$			5.43805e6i			0.682946i
$25$	7.88824e6			0.807756
$26$			9.50875e6i			0.800307i
$27$		−	4.79877e7i		−	3.34434i
$28$	−6.26822e6	−	5.89564e6i	−0.364212	−	0.342563i
$29$	6.60603e6			0.322070			0.161035	−	0.986949i	$-0.448517\pi$
$29$	6.60603e6			0.322070			0.161035	+	0.986949i	$0.448517\pi$
$30$	−1.45529e7			−0.598885
$31$			8.54507e6i			0.298475i	0.988801	+	0.149237i	$0.0476818\pi$
$31$			8.54507e6i			0.298475i	−0.988801	+	0.149237i	$0.952318\pi$
$32$	5.93164e6			0.176777
$33$			1.00620e8i			2.57108i
$34$		−	1.70169e6i		−	0.0374529i
$35$	1.57775e7	−	1.67746e7i	0.300398	−	0.319382i
$36$	−8.25765e7			−1.36566
$37$	7.29148e7			1.05149			0.525747	−	0.850641i	$-0.323786\pi$
$37$	7.29148e7			1.05149			0.525747	+	0.850641i	$0.323786\pi$
$38$			5.28014e7i			0.666388i
$39$	−1.97254e8			−2.18627
$40$			1.58738e7i			0.155018i
$41$			1.10803e7i			0.0956387i	0.998856	+	0.0478194i	$0.0152272\pi$
$41$			1.10803e7i			0.0956387i	−0.998856	+	0.0478194i	$0.984773\pi$
$42$	1.22302e8	−	1.30031e8i	0.935810	−	0.994949i
$43$	−6.62029e7			−0.450334			−0.225167	−	0.974320i	$-0.572293\pi$
$43$	−6.62029e7			−0.450334			−0.225167	+	0.974320i	$0.572293\pi$
$44$	1.09753e8			0.665509
$45$		−	2.20985e8i		−	1.19757i
$46$	1.49822e7			0.0727422
$47$			2.19417e7i			0.0956713i	0.998855	+	0.0478356i	$0.0152324\pi$
$47$			2.19417e7i			0.0956713i	−0.998855	+	0.0478356i	$0.984768\pi$
$48$			1.23049e8i			0.482916i
$49$	1.72883e7	+	2.81946e8i	0.0612030	+	0.998125i
$50$	1.78491e8			0.571170
$51$	3.53007e7			0.102313
$52$			2.15159e8i			0.565903i
$53$	5.63633e8			1.34777			0.673887	−	0.738834i	$-0.264623\pi$
$53$	5.63633e8			1.34777			0.673887	+	0.738834i	$0.264623\pi$
$54$		−	1.08584e9i		−	2.36481i
$55$			2.93714e8i			0.583594i
$56$	−1.41834e8	−	1.33403e8i	−0.257537	−	0.242229i
$57$	−1.09534e9			−1.82043
$58$	1.49477e8			0.227738
$59$		−	6.33264e8i		−	0.885778i	−0.896576	−	0.442889i	$-0.853954\pi$
$59$		−	6.33264e8i		−	0.885778i	0.896576	−	0.442889i	$-0.146046\pi$
$60$	−3.29294e8			−0.423475
$61$		−	7.67594e8i		−	0.908830i	−0.890790	−	0.454415i	$-0.849848\pi$
$61$		−	7.67594e8i		−	0.908830i	0.890790	−	0.454415i	$-0.150152\pi$
$62$			1.93353e8i			0.211053i
$63$	1.97452e9	+	1.85715e9i	1.98956	+	1.87131i
$64$	1.34218e8			0.125000
$65$	−5.75791e8			−0.496248
$66$			2.27678e9i			1.81803i
$67$	−1.30480e9			−0.966432			−0.483216	−	0.875501i	$-0.660531\pi$
$67$	−1.30480e9			−0.966432			−0.483216	+	0.875501i	$0.660531\pi$
$68$		−	3.85048e7i		−	0.0264832i
$69$			3.10798e8i			0.198716i
$70$	3.57004e8	−	3.79565e8i	0.212414	−	0.225837i
$71$	−1.25444e9			−0.695276			−0.347638	−	0.937629i	$-0.613016\pi$
$71$	−1.25444e9			−0.695276			−0.347638	+	0.937629i	$0.613016\pi$
$72$	−1.86849e9			−0.965670
$73$		−	4.03787e9i		−	1.94777i	−0.227033	−	0.973887i	$-0.572903\pi$
$73$		−	4.03787e9i		−	1.94777i	0.227033	−	0.973887i	$-0.427097\pi$
$74$	1.64987e9			0.743519
$75$			3.70270e9i			1.56031i
$76$			1.19476e9i			0.471207i
$77$	−2.62435e9	−	2.46836e9i	−0.969546	−	0.911916i
$78$	−4.46336e9			−1.54593
$79$	8.20678e7			0.0266709			0.0133354	−	0.999911i	$-0.495755\pi$
$79$	8.20678e7			0.0266709			0.0133354	+	0.999911i	$0.495755\pi$
$80$			3.59184e8i			0.109614i
$81$	1.30016e10			3.72882
$82$			2.50719e8i			0.0676268i
$83$		−	3.58618e9i		−	0.910419i	−0.890384	−	0.455209i	$-0.849564\pi$
$83$		−	3.58618e9i		−	0.910419i	0.890384	−	0.455209i	$-0.150436\pi$
$84$	2.76738e9	−	2.94227e9i	0.661717	−	0.703535i
$85$	1.03044e8			0.0232235
$86$	−1.49800e9			−0.318434
$87$			3.10083e9i			0.622131i
$88$	2.48343e9			0.470586
$89$			4.23634e9i			0.758648i	0.925264	+	0.379324i	$0.123843\pi$
$89$			4.23634e9i			0.758648i	−0.925264	+	0.379324i	$0.876157\pi$
$90$		−	5.00032e9i		−	0.846809i
$91$	4.83893e9	−	5.14474e9i	0.775430	−	0.824434i
$92$	3.39008e8			0.0514365
$93$	−4.01101e9			−0.576553
$94$			4.96485e8i			0.0676498i
$95$	−3.19732e9			−0.413208
$96$			2.78428e9i			0.341473i
$97$		−	9.87038e9i		−	1.14941i	−0.818360	−	0.574705i	$-0.805117\pi$
$97$		−	9.87038e9i		−	1.14941i	0.818360	−	0.574705i	$-0.194883\pi$
$98$	3.91191e8	+	6.37970e9i	0.0432771	+	0.705781i
$99$	−3.45727e10			−3.63545
$100$	4.03878e9			0.403878
$101$			1.91532e10i			1.82236i	0.412008	+	0.911180i	$0.364828\pi$
$101$			1.91532e10i			1.82236i	−0.412008	+	0.911180i	$0.635172\pi$
$102$	7.98763e8			0.0723464
$103$			1.46696e9i			0.126541i	0.997996	+	0.0632707i	$0.0201532\pi$
$103$			1.46696e9i			0.126541i	−0.997996	+	0.0632707i	$0.979847\pi$
$104$			4.86848e9i			0.400154i
$105$	7.87388e9	+	7.40586e9i	0.616939	+	0.580269i
$106$	1.27536e10			0.953021
$107$	−6.33759e9			−0.451861			−0.225931	−	0.974143i	$-0.572542\pi$
$107$	−6.33759e9			−0.451861			−0.225931	+	0.974143i	$0.572542\pi$
$108$		−	2.45697e10i		−	1.67217i
$109$	2.43948e10			1.58550			0.792748	−	0.609550i	$-0.208650\pi$
$109$	2.43948e10			1.58550			0.792748	+	0.609550i	$0.208650\pi$
$110$			6.64598e9i			0.412663i
$111$			3.42258e10i			2.03113i
$112$	−3.20933e9	−	3.01857e9i	−0.182106	−	0.171282i
$113$	−7.29151e9			−0.395754			−0.197877	−	0.980227i	$-0.563405\pi$
$113$	−7.29151e9			−0.395754			−0.197877	+	0.980227i	$0.563405\pi$
$114$	−2.47847e10			−1.28724
$115$			9.07229e8i			0.0451053i
$116$	3.38229e9			0.161035
$117$		−	6.77758e10i		−	3.09133i
$118$		−	1.43291e10i		−	0.626340i
$119$	−8.65976e8	+	9.20703e8i	−0.0362887	+	0.0385820i
$120$	−7.45108e9			−0.299442
$121$	2.00136e10			0.771611
$122$		−	1.73687e10i		−	0.642640i
$123$	−5.20105e9			−0.184742
$124$			4.37508e9i			0.149237i
$125$			2.41889e10i			0.792622i
$126$	4.46782e10	+	4.20225e10i	1.40683	+	1.32321i
$127$	1.40056e10			0.423920			0.211960	−	0.977278i	$-0.432015\pi$
$127$	1.40056e10			0.423920			0.211960	+	0.977278i	$0.432015\pi$
$128$	3.03700e9			0.0883883
$129$		−	3.10753e10i		−	0.869894i
$130$	−1.30287e10			−0.350900
$131$			5.01875e9i			0.130088i	0.997882	+	0.0650442i	$0.0207188\pi$
$131$			5.01875e9i			0.130088i	−0.997882	+	0.0650442i	$0.979281\pi$
$132$			5.15176e10i			1.28554i
$133$	2.68702e10	−	2.85683e10i	0.645673	−	0.686477i
$134$	−2.95244e10			−0.683371
$135$	6.57516e10			1.46635
$136$		−	8.71264e8i		−	0.0187264i
$137$	−8.44903e10			−1.75067			−0.875335	−	0.483517i	$-0.839359\pi$
$137$	−8.44903e10			−1.75067			−0.875335	+	0.483517i	$0.839359\pi$
$138$			7.03256e9i			0.140513i
$139$		−	6.83986e10i		−	1.31818i	−0.752066	−	0.659088i	$-0.770942\pi$
$139$		−	6.83986e10i		−	1.31818i	0.752066	−	0.659088i	$-0.229058\pi$
$140$	8.07807e9	−	8.58857e9i	0.150199	−	0.159691i
$141$	−1.02993e10			−0.184805
$142$	−2.83847e10			−0.491635
$143$			9.00816e10i			1.50645i
$144$	−4.22791e10			−0.682832
$145$			9.05142e9i			0.141214i
$146$		−	9.13667e10i		−	1.37728i
$147$	−1.32344e11	+	8.11505e9i	−1.92804	+	0.118224i
$148$	3.73324e10			0.525747
$149$	7.38033e10			1.00495			0.502475	−	0.864592i	$-0.332423\pi$
$149$	7.38033e10			1.00495			0.502475	+	0.864592i	$0.332423\pi$
$150$			8.37825e10i			1.10331i
$151$	1.08121e11			1.37729			0.688644	−	0.725100i	$-0.258206\pi$
$151$	1.08121e11			1.37729			0.688644	+	0.725100i	$0.258206\pi$
$152$			2.70343e10i			0.333194i
$153$			1.21292e10i			0.144669i
$154$	−5.93823e10	−	5.58526e10i	−0.685573	−	0.644822i
$155$	−1.17083e10			−0.130868
$156$	−1.00994e11			−1.09313
$157$		−	5.27093e9i		−	0.0552572i	−0.999618	−	0.0276286i	$-0.991204\pi$
$157$		−	5.27093e9i		−	0.0552572i	0.999618	−	0.0276286i	$-0.00879558\pi$
$158$	1.85698e9			0.0188592
$159$			2.64566e11i			2.60345i
$160$			8.12740e9i			0.0775089i
$161$	−8.10615e9	−	7.62433e9i	−0.0749351	−	0.0704810i
$162$	2.94193e11			2.63667
$163$	−5.05438e10			−0.439268			−0.219634	−	0.975582i	$-0.570486\pi$
$163$	−5.05438e10			−0.439268			−0.219634	+	0.975582i	$0.570486\pi$
$164$			5.67313e9i			0.0478194i
$165$	−1.37868e11			−1.12731
$166$		−	8.11459e10i		−	0.643763i
$167$		−	1.54791e11i		−	1.19169i	−0.803099	−	0.595846i	$-0.796817\pi$
$167$		−	1.54791e11i		−	1.19169i	0.803099	−	0.595846i	$-0.203183\pi$
$168$	6.26187e10	−	6.65759e10i	0.467905	−	0.497475i
$169$	−3.87361e10			−0.280984
$170$	2.33161e9			0.0164215
$171$		−	3.76354e11i		−	2.57404i
$172$	−3.38959e10			−0.225167
$173$			5.52740e9i			0.0356690i	0.999841	+	0.0178345i	$0.00567720\pi$
$173$			5.52740e9i			0.0356690i	−0.999841	+	0.0178345i	$0.994323\pi$
$174$			7.01638e10i			0.439913i
$175$	−9.65728e10	−	9.08325e10i	−0.588389	−	0.553415i
$176$	5.61937e10			0.332755
$177$	2.97251e11			1.71103
$178$			9.58574e10i			0.536445i
$179$	−1.01646e9			−0.00553126			−0.00276563	−	0.999996i	$-0.500880\pi$
$179$	−1.01646e9			−0.00553126			−0.00276563	+	0.999996i	$0.500880\pi$
$180$		−	1.13144e11i		−	0.598784i
$181$			2.73254e11i			1.40661i	0.710888	+	0.703306i	$0.248293\pi$
$181$			2.73254e11i			1.40661i	−0.710888	+	0.703306i	$0.751707\pi$
$182$	1.09493e11	−	1.16412e11i	0.548312	−	0.582963i
$183$	3.60305e11			1.75555
$184$	7.67088e9			0.0363711
$185$			9.99061e10i			0.461035i
$186$	−9.07588e10			−0.407684
$187$		−	1.61210e10i		−	0.0704993i
$188$			1.12342e10i			0.0478356i
$189$	−5.52574e11	+	5.87495e11i	−2.29130	+	2.43610i
$190$	−7.23472e10			−0.292182
$191$	−1.46596e11			−0.576709			−0.288354	−	0.957524i	$-0.593108\pi$
$191$	−1.46596e11			−0.576709			−0.288354	+	0.957524i	$0.593108\pi$
$192$			6.30011e10i			0.241458i
$193$	6.86373e10			0.256315			0.128157	−	0.991754i	$-0.459094\pi$
$193$	6.86373e10			0.256315			0.128157	+	0.991754i	$0.459094\pi$
$194$		−	2.23341e11i		−	0.812756i
$195$		−	2.70273e11i		−	0.958584i
$196$	8.85163e9	+	1.44356e11i	0.0306015	+	0.499063i
$197$	2.21534e11			0.746637			0.373319	−	0.927703i	$-0.378220\pi$
$197$	2.21534e11			0.746637			0.373319	+	0.927703i	$0.378220\pi$
$198$	−7.82292e11			−2.57065
$199$			2.25367e11i			0.722147i	0.932537	+	0.361073i	$0.117590\pi$
$199$			2.25367e11i			0.722147i	−0.932537	+	0.361073i	$0.882410\pi$
$200$	9.13871e10			0.285585
$201$		−	6.12468e11i		−	1.86682i
$202$			4.33387e11i			1.28860i
$203$	−8.08751e10	−	7.60679e10i	−0.234604	−	0.220659i
$204$	1.80739e10			0.0511566
$205$	−1.51820e10			−0.0419334
$206$			3.31936e10i			0.0894783i
$207$	−1.06789e11			−0.280980
$208$			1.10161e11i			0.282951i
$209$			5.00216e11i			1.25437i
$210$	1.78166e11	+	1.67575e11i	0.436242	+	0.410312i
$211$	−2.62773e11			−0.628303			−0.314151	−	0.949373i	$-0.601720\pi$
$211$	−2.62773e11			−0.628303			−0.314151	+	0.949373i	$0.601720\pi$
$212$	2.88580e11			0.673887
$213$		−	5.88826e11i		−	1.34304i
$214$	−1.43403e11			−0.319514
$215$		−	9.07096e10i		−	0.197452i
$216$		−	5.55949e11i		−	1.18240i
$217$	9.83959e10	−	1.04614e11i	0.204493	−	0.217416i
$218$	5.51992e11			1.12111
$219$	1.89536e12			3.76245
$220$			1.50381e11i			0.291797i
$221$	3.16034e10			0.0599477
$222$			7.74441e11i			1.43623i
$223$		−	3.16854e11i		−	0.574559i	−0.957847	−	0.287279i	$-0.907249\pi$
$223$		−	3.16854e11i		−	0.574559i	0.957847	−	0.287279i	$-0.0927508\pi$
$224$	−7.26188e10	−	6.83024e10i	−0.128768	−	0.121114i
$225$	−1.27223e12			−2.20625
$226$	−1.64988e11			−0.279840
$227$			6.34796e11i			1.05319i	0.850118	+	0.526593i	$0.176531\pi$
$227$			6.34796e11i			1.05319i	−0.850118	+	0.526593i	$0.823469\pi$
$228$	−5.60813e11			−0.910214
$229$		−	4.69653e11i		−	0.745761i	−0.927879	−	0.372880i	$-0.878370\pi$
$229$		−	4.69653e11i		−	0.745761i	0.927879	−	0.372880i	$-0.121630\pi$
$230$			2.05283e10i			0.0318943i
$231$	1.15863e12	−	1.23186e12i	1.76152	−	1.87284i
$232$	7.65324e10			0.113869
$233$	−6.86561e11			−0.999769			−0.499885	−	0.866092i	$-0.666624\pi$
$233$	−6.86561e11			−0.999769			−0.499885	+	0.866092i	$0.666624\pi$
$234$		−	1.53359e12i		−	2.18590i
$235$	−3.00640e10			−0.0419477
$236$		−	3.24231e11i		−	0.442889i
$237$			3.85222e10i			0.0515192i
$238$	−1.95948e10	+	2.08331e10i	−0.0256600	+	0.0272816i
$239$	−6.20590e11			−0.795820			−0.397910	−	0.917424i	$-0.630264\pi$
$239$	−6.20590e11			−0.795820			−0.397910	+	0.917424i	$0.630264\pi$
$240$	−1.68599e11			−0.211738
$241$			1.11075e12i			1.36625i	0.730301	+	0.683126i	$0.239380\pi$
$241$			1.11075e12i			1.36625i	−0.730301	+	0.683126i	$0.760620\pi$
$242$	4.52856e11			0.545611
$243$			3.26925e12i			3.85849i
$244$		−	3.93008e11i		−	0.454415i
$245$	−3.86315e11	+	2.36881e10i	−0.437635	+	0.0268349i
$246$	−1.17686e11			−0.130632
$247$	−9.80615e11			−1.06663
$248$			9.89967e10i			0.105527i
$249$	1.68333e12			1.75862
$250$			5.47333e11i			0.560469i
$251$		−	5.61035e11i		−	0.563146i	−0.959540	−	0.281573i	$-0.909144\pi$
$251$		−	5.61035e11i		−	0.563146i	0.959540	−	0.281573i	$-0.0908562\pi$
$252$	1.01095e12	+	9.50862e11i	0.994782	+	0.935653i
$253$	1.41935e11			0.136926
$254$	3.16911e11			0.299757
$255$			4.83681e10i			0.0448599i
$256$	6.87195e10			0.0625000
$257$		−	1.82570e12i		−	1.62841i	−0.580576	−	0.814206i	$-0.697173\pi$
$257$		−	1.82570e12i		−	1.62841i	0.580576	−	0.814206i	$-0.302827\pi$
$258$		−	7.03153e11i		−	0.615108i
$259$	−8.92668e11	−	8.39608e11i	−0.765934	−	0.720407i
$260$	−2.94805e11			−0.248124
$261$	−1.06543e12			−0.879679
$262$			1.13561e11i			0.0919864i
$263$	−2.00325e12			−1.59205			−0.796023	−	0.605266i	$-0.793067\pi$
$263$	−2.00325e12			−1.59205			−0.796023	+	0.605266i	$0.793067\pi$
$264$			1.16571e12i			0.909015i
$265$			7.72277e11i			0.590941i
$266$	6.08003e11	−	6.46427e11i	0.456560	−	0.485413i
$267$	−1.98851e12			−1.46545
$268$	−6.68060e11			−0.483216
$269$			8.89778e11i			0.631714i	0.948807	+	0.315857i	$0.102292\pi$
$269$			8.89778e11i			0.631714i	−0.948807	+	0.315857i	$0.897708\pi$
$270$	1.48779e12			1.03687
$271$		−	1.64755e12i		−	1.12718i	−0.826056	−	0.563588i	$-0.809421\pi$
$271$		−	1.64755e12i		−	1.12718i	0.826056	−	0.563588i	$-0.190579\pi$
$272$		−	1.97145e10i		−	0.0132416i
$273$	2.41491e12	+	2.27137e12i	1.59253	+	1.49787i
$274$	−1.91180e12			−1.23791
$275$	1.69094e12			1.07514
$276$			1.59129e11i			0.0993580i
$277$	6.91448e11			0.423995			0.211997	−	0.977270i	$-0.432003\pi$
$277$	6.91448e11			0.423995			0.211997	+	0.977270i	$0.432003\pi$
$278$		−	1.54768e12i		−	0.932091i
$279$		−	1.37817e12i		−	0.815232i
$280$	1.82786e11	−	1.94337e11i	0.106207	−	0.112919i
$281$	7.81630e11			0.446138			0.223069	−	0.974803i	$-0.428392\pi$
$281$	7.81630e11			0.446138			0.223069	+	0.974803i	$0.428392\pi$
$282$	−2.33047e11			−0.130677
$283$			1.25222e12i			0.689842i	0.938632	+	0.344921i	$0.112094\pi$
$283$			1.25222e12i			0.689842i	−0.938632	+	0.344921i	$0.887906\pi$
$284$	−6.42272e11			−0.347638
$285$		−	1.50081e12i		−	0.798179i
$286$			2.03831e12i			1.06522i
$287$	1.27589e11	−	1.35652e11i	0.0655246	−	0.0696655i
$288$	−9.56668e11			−0.482835
$289$	2.01034e12			0.997195
$290$			2.04810e11i			0.0998532i
$291$	4.63310e12			2.22028
$292$		−	2.06739e12i		−	0.973887i
$293$			3.97245e12i			1.83959i	0.392405	+	0.919793i	$0.371643\pi$
$293$			3.97245e12i			1.83959i	−0.392405	+	0.919793i	$0.628357\pi$
$294$	−2.99460e12	+	1.83623e11i	−1.36333	+	0.0835968i
$295$	8.67684e11			0.388375
$296$	8.44735e11			0.371759
$297$		−	1.02867e13i		−	4.45138i
$298$	1.66998e12			0.710607
$299$			2.78246e11i			0.116432i
$300$			1.89578e12i			0.780157i
$301$	8.10497e11	+	7.62321e11i	0.328034	+	0.308536i
$302$	2.44650e12			0.973890
$303$	−8.99040e12			−3.52019
$304$			6.11716e11i			0.235604i
$305$	1.05174e12			0.398482
$306$			2.74452e11i			0.102296i
$307$		−	9.37011e11i		−	0.343600i	−0.985132	−	0.171800i	$-0.945042\pi$
$307$		−	9.37011e11i		−	0.343600i	0.985132	−	0.171800i	$-0.0549583\pi$
$308$	−1.34367e12	−	1.26380e12i	−0.484773	−	0.455958i
$309$	−6.88584e11			−0.244436
$310$	−2.64928e11			−0.0925377
$311$			2.83127e12i			0.973149i	0.873639	+	0.486575i	$0.161754\pi$
$311$			2.83127e12i			0.973149i	−0.873639	+	0.486575i	$0.838246\pi$
$312$	−2.28524e12			−0.772963
$313$		−	1.33109e12i		−	0.443085i	−0.975151	−	0.221543i	$-0.928891\pi$
$313$		−	1.33109e12i		−	0.443085i	0.975151	−	0.221543i	$-0.0711092\pi$
$314$		−	1.19268e11i		−	0.0390728i
$315$	−2.54463e12	+	2.70544e12i	−0.820486	+	0.872337i
$316$	4.20187e10			0.0133354
$317$	9.06962e11			0.283330			0.141665	−	0.989915i	$-0.454754\pi$
$317$	9.06962e11			0.283330			0.141665	+	0.989915i	$0.454754\pi$
$318$			5.98645e12i			1.84092i
$319$	1.41608e12			0.428681
$320$			1.83902e11i			0.0548071i
$321$		−	2.97483e12i		−	0.872845i
$322$	−1.83421e11	−	1.72519e11i	−0.0529871	−	0.0498376i
$323$	1.75491e11			0.0499163
$324$	6.65682e12			1.86441
$325$			3.31489e12i			0.914223i
$326$	−1.14368e12			−0.310610
$327$			1.14508e13i			3.06265i
$328$			1.28368e11i			0.0338134i
$329$	2.52657e11	−	2.68624e11i	0.0655469	−	0.0696893i
$330$	−3.11959e12			−0.797127
$331$	2.05042e12			0.516064			0.258032	−	0.966136i	$-0.416926\pi$
$331$	2.05042e12			0.516064			0.258032	+	0.966136i	$0.416926\pi$
$332$		−	1.83612e12i		−	0.455209i
$333$	−1.17599e13			−2.87198
$334$		−	3.50252e12i		−	0.842653i
$335$		−	1.78781e12i		−	0.423739i
$336$	1.41690e12	−	1.50644e12i	0.330859	−	0.351768i
$337$	2.22911e12			0.512840			0.256420	−	0.966565i	$-0.417457\pi$
$337$	2.22911e12			0.512840			0.256420	+	0.966565i	$0.417457\pi$
$338$	−8.76497e11			−0.198686
$339$		−	3.42259e12i		−	0.764464i
$340$	5.27584e10			0.0116117
$341$			1.83174e12i			0.397275i
$342$		−	8.51592e12i		−	1.82012i
$343$	3.03493e12	−	3.65083e12i	0.639260	−	0.768990i
$344$	−7.66976e11			−0.159217
$345$	−4.25848e11			−0.0871283
$346$			1.25071e11i			0.0252218i
$347$	−5.98763e12			−1.19017			−0.595083	−	0.803665i	$-0.702881\pi$
$347$	−5.98763e12			−1.19017			−0.595083	+	0.803665i	$0.702881\pi$
$348$			1.58763e12i			0.311066i
$349$		−	6.61887e12i		−	1.27837i	−0.769053	−	0.639185i	$-0.779272\pi$
$349$		−	6.61887e12i		−	1.27837i	0.769053	−	0.639185i	$-0.220728\pi$
$350$	−2.18519e12	−	2.05530e12i	−0.416054	−	0.391324i
$351$	2.01659e13			3.78515
$352$	1.27152e12			0.235293
$353$			4.77897e12i			0.871889i	0.899974	+	0.435944i	$0.143586\pi$
$353$			4.77897e12i			0.871889i	−0.899974	+	0.435944i	$0.856414\pi$
$354$	6.72602e12			1.20988
$355$		−	1.71880e12i		−	0.304848i
$356$			2.16900e12i			0.379324i
$357$	−4.32173e11	−	4.06484e11i	−0.0745275	−	0.0700976i
$358$	−2.29998e10			−0.00391119
$359$	−6.34383e12			−1.06385			−0.531924	−	0.846792i	$-0.678531\pi$
$359$	−6.34383e12			−1.06385			−0.531924	+	0.846792i	$0.678531\pi$
$360$		−	2.56016e12i		−	0.423404i
$361$	6.85788e11			0.111855
$362$			6.18304e12i			0.994624i
$363$			9.39427e12i			1.49049i
$364$	2.47753e12	−	2.63410e12i	0.387715	−	0.412217i
$365$	5.53260e12			0.854014
$366$	8.15276e12			1.24136
$367$		−	3.33553e12i		−	0.500997i	−0.968117	−	0.250498i	$-0.919406\pi$
$367$		−	3.33553e12i		−	0.500997i	0.968117	−	0.250498i	$-0.0805945\pi$
$368$	1.73572e11			0.0257182
$369$		−	1.78706e12i		−	0.261221i
$370$			2.26062e12i			0.326001i
$371$	−6.90035e12	−	6.49019e12i	−0.981751	−	0.923396i
$372$	−2.05364e12			−0.288276
$373$	8.95696e11			0.124056			0.0620278	−	0.998074i	$-0.480243\pi$
$373$	8.95696e11			0.124056			0.0620278	+	0.998074i	$0.480243\pi$
$374$		−	3.64777e11i		−	0.0498505i
$375$	−1.13541e13			−1.53108
$376$			2.54200e11i			0.0338249i
$377$			2.77606e12i			0.364521i
$378$	−1.25033e13	+	1.32935e13i	−1.62019	+	1.72258i
$379$	−9.51666e12			−1.21699			−0.608497	−	0.793556i	$-0.708227\pi$
$379$	−9.51666e12			−1.21699			−0.608497	+	0.793556i	$0.708227\pi$
$380$	−1.63703e12			−0.206604
$381$			6.57416e12i			0.818871i
$382$	−3.31710e12			−0.407795
$383$		−	1.16463e13i		−	1.41316i	−0.707631	−	0.706582i	$-0.750236\pi$
$383$		−	1.16463e13i		−	1.41316i	0.707631	−	0.706582i	$-0.249764\pi$
$384$			1.42555e12i			0.170737i
$385$	3.38209e12	−	3.59583e12i	0.399836	−	0.425104i
$386$	1.55308e12			0.181242
$387$	1.06773e13			1.23001
$388$		−	5.05363e12i		−	0.574705i
$389$	1.10283e12			0.123811			0.0619054	−	0.998082i	$-0.480282\pi$
$389$	1.10283e12			0.123811			0.0619054	+	0.998082i	$0.480282\pi$
$390$		−	6.11559e12i		−	0.677821i
$391$		−	4.97950e10i		−	0.00544881i
$392$	2.00290e11	+	3.26641e12i	0.0216385	+	0.352891i
$393$	−2.35577e12			−0.251287
$394$	5.01275e12			0.527952
$395$			1.12447e11i			0.0116940i
$396$	−1.77012e13			−1.81772
$397$			5.84211e12i			0.592403i	0.955125	+	0.296202i	$0.0957200\pi$
$397$			5.84211e12i			0.592403i	−0.955125	+	0.296202i	$0.904280\pi$
$398$			5.09948e12i			0.510635i
$399$	1.34098e13	+	1.26127e13i	1.32604	+	1.24722i
$400$	2.06786e12			0.201939
$401$	−6.39957e12			−0.617205			−0.308602	−	0.951191i	$-0.599861\pi$
$401$	−6.39957e12			−0.617205			−0.308602	+	0.951191i	$0.599861\pi$
$402$		−	1.38586e13i		−	1.32004i
$403$	−3.59091e12			−0.337815
$404$			9.80644e12i			0.911180i
$405$			1.78145e13i			1.63493i
$406$	−1.82999e12	−	1.72122e12i	−0.165890	−	0.156029i
$407$	1.56302e13			1.39956
$408$	4.08967e11			0.0361732
$409$			9.41361e12i			0.822507i	0.911521	+	0.411254i	$0.134909\pi$
$409$			9.41361e12i			0.822507i	−0.911521	+	0.411254i	$0.865091\pi$
$410$	−3.43530e11			−0.0296514
$411$		−	3.96593e13i		−	3.38171i
$412$			7.51085e11i			0.0632707i
$413$	−7.29199e12	+	7.75282e12i	−0.606870	+	0.645222i
$414$	−2.41636e12			−0.198683
$415$	4.91370e12			0.399179
$416$			2.49266e12i			0.200077i
$417$	3.21059e13			2.54627
$418$			1.13186e13i			0.886975i
$419$		−	1.88608e13i		−	1.46046i	−0.683202	−	0.730230i	$-0.739413\pi$
$419$		−	1.88608e13i		−	1.46046i	0.683202	−	0.730230i	$-0.260587\pi$
$420$	4.03143e12	+	3.79180e12i	0.308470	+	0.290134i
$421$	−1.52281e13			−1.15143			−0.575714	−	0.817651i	$-0.695276\pi$
$421$	−1.52281e13			−1.15143			−0.575714	+	0.817651i	$0.695276\pi$
$422$	−5.94588e12			−0.444277
$423$		−	3.53881e12i		−	0.261310i
$424$	6.52983e12			0.476510
$425$		−	5.93233e11i		−	0.0427839i
$426$		−	1.33236e13i		−	0.949673i
$427$	−8.83879e12	+	9.39737e12i	−0.622664	+	0.662013i
$428$	−3.24485e12			−0.225931
$429$	−4.22838e13			−2.90996
$430$		−	2.05252e12i		−	0.139620i
$431$	4.63050e12			0.311345			0.155672	−	0.987809i	$-0.450246\pi$
$431$	4.63050e12			0.311345			0.155672	+	0.987809i	$0.450246\pi$
$432$		−	1.25797e13i		−	0.836086i
$433$		−	1.60023e13i		−	1.05134i	−0.850689	−	0.525669i	$-0.823815\pi$
$433$		−	1.60023e13i		−	1.05134i	0.850689	−	0.525669i	$-0.176185\pi$
$434$	2.22644e12	−	2.36715e12i	0.144598	−	0.153736i
$435$	−4.24869e12			−0.272777
$436$	1.24901e13			0.792748
$437$			1.54508e12i			0.0969490i
$438$	4.28870e13			2.66045
$439$			1.53469e13i			0.941233i	0.882338	+	0.470616i	$0.155968\pi$
$439$			1.53469e13i			0.941233i	−0.882338	+	0.470616i	$0.844032\pi$
$440$			3.40274e12i			0.206332i
$441$	−2.78830e12	−	4.54728e13i	−0.167166	−	2.72621i
$442$	7.15103e11			0.0423894
$443$	2.38107e13			1.39558			0.697789	−	0.716303i	$-0.254167\pi$
$443$	2.38107e13			1.39558			0.697789	+	0.716303i	$0.254167\pi$
$444$			1.75236e13i			1.01557i
$445$	−5.80453e12			−0.332634
$446$		−	7.16958e12i		−	0.406275i
$447$			3.46429e13i			1.94123i
$448$	−1.64318e12	−	1.54551e12i	−0.0910530	−	0.0856408i
$449$	2.78505e13			1.52616			0.763082	−	0.646302i	$-0.223685\pi$
$449$	2.78505e13			1.52616			0.763082	+	0.646302i	$0.223685\pi$
$450$	−2.87873e13			−1.56005
$451$			2.37520e12i			0.127297i
$452$	−3.73325e12			−0.197877
$453$			5.07513e13i			2.66046i
$454$			1.43638e13i			0.744714i
$455$	7.04920e12	+	6.63019e12i	0.361479	+	0.339992i
$456$	−1.26897e13			−0.643619
$457$	−7.00071e11			−0.0351205			−0.0175603	−	0.999846i	$-0.505590\pi$
$457$	−7.00071e11			−0.0351205			−0.0175603	+	0.999846i	$0.505590\pi$
$458$		−	1.06270e13i		−	0.527333i
$459$	−3.60890e12			−0.177138
$460$			4.64501e11i			0.0225527i
$461$		−	3.39820e13i		−	1.63209i	−0.577989	−	0.816045i	$-0.696162\pi$
$461$		−	3.39820e13i		−	1.63209i	0.577989	−	0.816045i	$-0.303838\pi$
$462$	2.62169e13	−	2.78737e13i	1.24558	−	1.32430i
$463$	−3.51140e13			−1.65035			−0.825173	−	0.564880i	$-0.808923\pi$
$463$	−3.51140e13			−1.65035			−0.825173	+	0.564880i	$0.808923\pi$
$464$	1.73173e12			0.0805175
$465$		−	5.49579e12i		−	0.252793i
$466$	−1.55351e13			−0.706943
$467$			2.50436e13i			1.12749i	0.825949	+	0.563745i	$0.190640\pi$
$467$			2.50436e13i			1.12749i	−0.825949	+	0.563745i	$0.809360\pi$
$468$		−	3.47012e13i		−	1.54567i
$469$	1.59742e13	+	1.50247e13i	0.703972	+	0.662128i
$470$	−6.80272e11			−0.0296615
$471$	2.47415e12			0.106738
$472$		−	7.33652e12i		−	0.313170i
$473$	−1.41914e13			−0.599403
$474$			8.71657e11i			0.0364296i
$475$			1.84073e13i			0.761241i
$476$	−4.43380e11	+	4.71400e11i	−0.0181443	+	0.0192910i
$477$	−9.09040e13			−3.68121
$478$	−1.40423e13			−0.562730
$479$		−	2.52899e13i		−	1.00293i	−0.865179	−	0.501463i	$-0.832795\pi$
$479$		−	2.52899e13i		−	1.00293i	0.865179	−	0.501463i	$-0.167205\pi$
$480$	−3.81495e12			−0.149721
$481$			3.06411e13i			1.19009i
$482$			2.51334e13i			0.966086i
$483$	3.57882e12	−	3.80498e12i	0.136146	−	0.144750i
$484$	1.02470e13			0.385805
$485$	1.35242e13			0.503967
$486$			7.39748e13i			2.72836i
$487$	4.28135e13			1.56292			0.781459	−	0.623957i	$-0.214476\pi$
$487$	4.28135e13			1.56292			0.781459	+	0.623957i	$0.214476\pi$
$488$		−	8.89276e12i		−	0.321320i
$489$		−	2.37250e13i		−	0.848519i
$490$	−8.74132e12	+	5.36000e11i	−0.309454	+	0.0189751i
$491$	1.82600e13			0.639871			0.319935	−	0.947439i	$-0.396339\pi$
$491$	1.82600e13			0.639871			0.319935	+	0.947439i	$0.396339\pi$
$492$	−2.66294e12			−0.0923709
$493$		−	4.96804e11i		−	0.0170589i
$494$	−2.21888e13			−0.754222
$495$		−	4.73708e13i		−	1.59399i
$496$			2.24004e12i			0.0746186i
$497$	1.53576e13	+	1.44448e13i	0.506456	+	0.476352i
$498$	3.80894e13			1.24353
$499$	−3.56690e13			−1.15289			−0.576445	−	0.817136i	$-0.695561\pi$
$499$	−3.56690e13			−1.15289			−0.576445	+	0.817136i	$0.695561\pi$
$500$			1.23847e13i			0.396311i
$501$	7.26581e13			2.30195
$502$		−	1.26948e13i		−	0.398205i
$503$		−	3.41113e13i		−	1.05940i	−0.848186	−	0.529699i	$-0.822305\pi$
$503$		−	3.41113e13i		−	1.05940i	0.848186	−	0.529699i	$-0.177695\pi$
$504$	2.28752e13	+	2.15155e13i	0.703417	+	0.661606i
$505$	−2.62433e13			−0.799026
$506$	3.21161e12			0.0968212
$507$		−	1.81825e13i		−	0.542767i
$508$	7.17088e12			0.211960
$509$		−	2.43934e13i		−	0.713975i	−0.934109	−	0.356988i	$-0.883804\pi$
$509$		−	2.43934e13i		−	0.713975i	0.934109	−	0.356988i	$-0.116196\pi$
$510$			1.09445e12i			0.0317208i
$511$	−4.64958e13	+	4.94342e13i	−1.33447	+	1.41881i
$512$	1.55494e12			0.0441942
$513$	1.11980e14			3.15176
$514$		−	4.13109e13i		−	1.15146i
$515$	−2.01000e12			−0.0554829
$516$		−	1.59105e13i		−	0.434947i
$517$			4.70347e12i			0.127340i
$518$	−2.01988e13	−	1.89982e13i	−0.541597	−	0.509404i
$519$	−2.59453e12			−0.0689005
$520$	−6.67068e12			−0.175450
$521$		−	5.96383e13i		−	1.55359i	−0.629753	−	0.776795i	$-0.716844\pi$
$521$		−	5.96383e13i		−	1.55359i	0.629753	−	0.776795i	$-0.283156\pi$
$522$	−2.41080e13			−0.622027
$523$		−	6.05353e13i		−	1.54703i	−0.633775	−	0.773517i	$-0.718496\pi$
$523$		−	6.05353e13i		−	1.54703i	0.633775	−	0.773517i	$-0.281504\pi$
$524$			2.56960e12i			0.0650442i
$525$	4.26363e13	−	4.53307e13i	1.06901	−	1.13657i
$526$	−4.53283e13			−1.12575
$527$	6.42630e11			0.0158091
$528$			2.63770e13i			0.642770i
$529$	−4.09881e13			−0.989417
$530$			1.74746e13i			0.417858i
$531$			1.02134e14i			2.41935i
$532$	1.37575e13	−	1.46270e13i	0.322837	−	0.343239i
$533$	−4.65631e12			−0.108244
$534$	−4.49949e13			−1.03623
$535$		−	8.68362e12i		−	0.198122i
$536$	−1.51165e13			−0.341685
$537$		−	4.77120e11i		−	0.0106845i
$538$			2.01334e13i			0.446689i
$539$	3.70596e12	+	6.04384e13i	0.0814624	+	1.32852i
$540$	3.36648e13			0.733175
$541$	6.76116e13			1.45893			0.729465	−	0.684018i	$-0.239769\pi$
$541$	6.76116e13			1.45893			0.729465	+	0.684018i	$0.239769\pi$
$542$		−	3.72797e13i		−	0.797033i
$543$	−1.28264e14			−2.71710
$544$		−	4.46087e11i		−	0.00936322i
$545$			3.34252e13i			0.695171i
$546$	5.46432e13	+	5.13952e13i	1.12609	+	1.05915i
$547$	6.48737e13			1.32474			0.662372	−	0.749175i	$-0.269550\pi$
$547$	6.48737e13			1.32474			0.662372	+	0.749175i	$0.269550\pi$
$548$	−4.32591e13			−0.875335
$549$			1.23799e14i			2.48231i
$550$	3.82616e13			0.760238
$551$			1.54152e13i			0.303523i
$552$			3.60067e12i			0.0702567i
$553$	−1.00473e12	−	9.45005e11i	−0.0194277	−	0.0182729i
$554$	1.56457e13			0.299810
$555$	−4.68954e13			−0.890564
$556$		−	3.50201e13i		−	0.659088i
$557$	−5.02847e13			−0.937907			−0.468954	−	0.883223i	$-0.655369\pi$
$557$	−5.02847e13			−0.937907			−0.468954	+	0.883223i	$0.655369\pi$
$558$		−	3.11844e13i		−	0.576456i
$559$		−	2.78205e13i		−	0.509690i
$560$	4.13597e12	−	4.39735e12i	0.0750996	−	0.0798456i
$561$	7.56712e12			0.136181
$562$	1.76863e13			0.315467
$563$			6.83913e13i			1.20909i	0.796571	+	0.604545i	$0.206645\pi$
$563$			6.83913e13i			1.20909i	−0.796571	+	0.604545i	$0.793355\pi$
$564$	−5.27326e12			−0.0924024
$565$		−	9.99065e12i		−	0.173521i
$566$			2.83346e13i			0.487792i
$567$	−1.59174e14	−	1.49712e14i	−2.71616	−	2.55471i
$568$	−1.45330e13			−0.245817
$569$	−6.44588e13			−1.08074			−0.540370	−	0.841428i	$-0.681716\pi$
$569$	−6.44588e13			−1.08074			−0.540370	+	0.841428i	$0.681716\pi$
$570$		−	3.39594e13i		−	0.564398i
$571$	4.92785e13			0.811853			0.405926	−	0.913906i	$-0.366949\pi$
$571$	4.92785e13			0.811853			0.405926	+	0.913906i	$0.366949\pi$
$572$			4.61218e13i			0.753227i
$573$		−	6.88116e13i		−	1.11401i
$574$	2.88701e12	−	3.06946e12i	0.0463329	−	0.0492610i
$575$	5.22301e12			0.0830962
$576$	−2.16469e13			−0.341416
$577$		−	7.31912e13i		−	1.14440i	−0.820112	−	0.572202i	$-0.806089\pi$
$577$		−	7.31912e13i		−	1.14440i	0.820112	−	0.572202i	$-0.193911\pi$
$578$	4.54888e13			0.705123
$579$			3.22180e13i			0.495114i
$580$			4.63433e12i			0.0706068i
$581$	−4.12945e13	+	4.39042e13i	−0.623752	+	0.663171i
$582$	1.04835e14			1.56997
$583$	1.20822e14			1.79391
$584$		−	4.67797e13i		−	0.688642i
$585$	9.28649e13			1.35541
$586$			8.98862e13i			1.30078i
$587$			1.73014e13i			0.248251i	0.992267	+	0.124126i	$0.0396125\pi$
$587$			1.73014e13i			0.248251i	−0.992267	+	0.124126i	$0.960387\pi$
$588$	−6.77600e13	+	4.15491e12i	−0.964022	+	0.0591119i
$589$	−1.99400e13			−0.281287
$590$	1.96335e13			0.274623
$591$			1.03987e14i			1.44225i
$592$	1.91142e13			0.262874
$593$			2.16135e13i			0.294749i	0.989081	+	0.147374i	$0.0470822\pi$
$593$			2.16135e13i			0.294749i	−0.989081	+	0.147374i	$0.952918\pi$
$594$		−	2.32762e14i		−	3.14760i
$595$	−1.26153e12	−	1.18654e12i	−0.0169165	−	0.0159110i
$596$	3.77873e13			0.502475
$597$	−1.05786e14			−1.39494
$598$			6.29599e12i			0.0823300i
$599$	2.30454e13			0.298848			0.149424	−	0.988773i	$-0.452258\pi$
$599$	2.30454e13			0.298848			0.149424	+	0.988773i	$0.452258\pi$
$600$			4.28966e13i			0.551654i
$601$		−	8.34214e13i		−	1.06391i	−0.846772	−	0.531955i	$-0.821457\pi$
$601$		−	8.34214e13i		−	1.06391i	0.846772	−	0.531955i	$-0.178543\pi$
$602$	1.83394e13	+	1.72494e13i	0.231955	+	0.218168i
$603$	2.10442e14			2.63964
$604$	5.53579e13			0.688644
$605$			2.74222e13i			0.338318i
$606$	−2.03430e14			−2.48915
$607$			5.85876e13i			0.710988i	0.934679	+	0.355494i	$0.115687\pi$
$607$			5.85876e13i			0.710988i	−0.934679	+	0.355494i	$0.884313\pi$
$608$			1.38416e13i			0.166597i
$609$	3.57058e13	−	3.79623e13i	0.426239	−	0.453175i
$610$	2.37982e13			0.281770
$611$	−9.22061e12			−0.108281
$612$			6.21014e12i			0.0723343i
$613$	7.23051e13			0.835347			0.417673	−	0.908597i	$-0.362846\pi$
$613$	7.23051e13			0.835347			0.417673	+	0.908597i	$0.362846\pi$
$614$		−	2.12021e13i		−	0.242962i
$615$		−	7.12636e12i		−	0.0810013i
$616$	−3.04037e13	−	2.85965e13i	−0.342786	−	0.322411i
$617$	−5.49660e13			−0.614707			−0.307354	−	0.951595i	$-0.599443\pi$
$617$	−5.49660e13			−0.614707			−0.307354	+	0.951595i	$0.599443\pi$
$618$	−1.55809e13			−0.172842
$619$			3.30735e13i			0.363938i	0.983304	+	0.181969i	$0.0582470\pi$
$619$			3.30735e13i			0.363938i	−0.983304	+	0.181969i	$0.941753\pi$
$620$	−5.99463e12			−0.0654341
$621$		−	3.17739e13i		−	0.344042i
$622$			6.40644e13i			0.688121i
$623$	4.87811e13	−	5.18639e13i	0.519770	−	0.552618i
$624$	−5.17090e13			−0.546567
$625$	4.38905e13			0.460225
$626$		−	3.01192e13i		−	0.313309i
$627$	−2.34799e14			−2.42303
$628$		−	2.69872e12i		−	0.0276286i
$629$		−	5.48353e12i		−	0.0556939i
$630$	−5.75783e13	+	6.12170e13i	−0.580171	+	0.616836i
$631$	−6.40040e13			−0.639824			−0.319912	−	0.947447i	$-0.603653\pi$
$631$	−6.40040e13			−0.639824			−0.319912	+	0.947447i	$0.603653\pi$
$632$	9.50775e11			0.00942958
$633$		−	1.23344e14i		−	1.21367i
$634$	2.05222e13			0.200345
$635$			1.91902e13i			0.185870i
$636$			1.35458e14i			1.30172i
$637$	−1.18482e14	+	7.26511e12i	−1.12968	+	0.0692700i
$638$	3.20422e13			0.303123
$639$	2.02318e14			1.89903
$640$			4.16123e12i			0.0387544i
$641$	1.92579e13			0.177959			0.0889794	−	0.996033i	$-0.471639\pi$
$641$	1.92579e13			0.177959			0.0889794	+	0.996033i	$0.471639\pi$
$642$		−	6.73127e13i		−	0.617194i
$643$		−	1.43089e14i		−	1.30182i	−0.759154	−	0.650911i	$-0.774387\pi$
$643$		−	1.43089e14i		−	1.30182i	0.759154	−	0.650911i	$-0.225613\pi$
$644$	−4.15035e12	−	3.90365e12i	−0.0374676	−	0.0352405i
$645$	4.25786e13			0.381411
$646$	3.97091e12			0.0352962
$647$		−	3.10422e13i		−	0.273798i	−0.990585	−	0.136899i	$-0.956286\pi$
$647$		−	3.10422e13i		−	0.273798i	0.990585	−	0.136899i	$-0.0437136\pi$
$648$	1.50627e14			1.31834
$649$		−	1.35748e14i		−	1.17899i
$650$			7.50073e13i			0.646453i
$651$	4.91053e13	+	4.61865e13i	0.419975	+	0.395012i
$652$	−2.58784e13			−0.219634
$653$	−2.06274e14			−1.73731			−0.868657	−	0.495415i	$-0.835016\pi$
$653$	−2.06274e14			−1.73731			−0.868657	+	0.495415i	$0.835016\pi$
$654$			2.59102e14i			2.16562i
$655$	−6.87657e12			−0.0570381
$656$			2.90464e12i			0.0239097i
$657$			6.51237e14i			5.32001i
$658$	5.71698e12	−	6.07827e12i	0.0463487	−	0.0492777i
$659$	5.30609e13			0.426921			0.213460	−	0.976952i	$-0.431527\pi$
$659$	5.30609e13			0.426921			0.213460	+	0.976952i	$0.431527\pi$
$660$	−7.05882e13			−0.563654
$661$		−	3.66882e13i		−	0.290750i	−0.989377	−	0.145375i	$-0.953561\pi$
$661$		−	3.66882e13i		−	0.290750i	0.989377	−	0.145375i	$-0.0464388\pi$
$662$	4.63958e13			0.364912
$663$			1.48345e13i			0.115799i
$664$		−	4.15467e13i		−	0.321882i
$665$	3.91436e13	+	3.68169e13i	0.300991	+	0.283100i
$666$	−2.66095e14			−2.03079
$667$	4.37402e12			0.0331323
$668$		−	7.92531e13i		−	0.595846i
$669$	1.48729e14			1.10986
$670$		−	4.04536e13i		−	0.299628i
$671$		−	1.64543e14i		−	1.20967i
$672$	3.20608e13	−	3.40869e13i	0.233952	−	0.248737i
$673$	1.95048e12			0.0141276			0.00706378	−	0.999975i	$-0.497752\pi$
$673$	1.95048e12			0.0141276			0.00706378	+	0.999975i	$0.497752\pi$
$674$	5.04390e13			0.362633
$675$		−	3.78538e14i		−	2.70141i
$676$	−1.98329e13			−0.140492
$677$		−	8.60193e13i		−	0.604856i	−0.953172	−	0.302428i	$-0.902203\pi$
$677$		−	8.60193e13i		−	0.604856i	0.953172	−	0.302428i	$-0.0977973\pi$
$678$		−	7.74444e13i		−	0.540557i
$679$	−1.13657e14	+	1.20839e14i	−0.787492	+	0.837258i
$680$	1.19379e12			0.00821073
$681$	−2.97970e14			−2.03440
$682$			4.14475e13i			0.280916i
$683$	−2.30166e14			−1.54860			−0.774298	−	0.632821i	$-0.781897\pi$
$683$	−2.30166e14			−1.54860			−0.774298	+	0.632821i	$0.781897\pi$
$684$		−	1.92693e14i		−	1.28702i
$685$		−	1.15767e14i		−	0.767593i
$686$	6.86726e13	−	8.26088e13i	0.452025	−	0.543758i
$687$	2.20452e14			1.44056
$688$	−1.73547e13			−0.112583
$689$			2.36856e14i			1.52542i
$690$	−9.63585e12			−0.0616090
$691$			2.40345e13i			0.152562i	0.997086	+	0.0762808i	$0.0243046\pi$
$691$			2.40345e13i			0.152562i	−0.997086	+	0.0762808i	$0.975695\pi$
$692$			2.83003e12i			0.0178345i
$693$	4.23261e14	+	3.98103e14i	2.64815	+	2.49074i
$694$	−1.35484e14			−0.841574
$695$	9.37182e13			0.577963
$696$			3.59239e13i			0.219957i
$697$	8.33293e11			0.00506564
$698$		−	1.49768e14i		−	0.903944i
$699$		−	3.22268e14i		−	1.93122i
$700$	−4.94452e13	−	4.65062e13i	−0.294194	−	0.276708i
$701$	−1.38404e14			−0.817633			−0.408816	−	0.912617i	$-0.634058\pi$
$701$	−1.38404e14			−0.817633			−0.408816	+	0.912617i	$0.634058\pi$
$702$	4.56303e14			2.67650
$703$			1.70148e14i			0.990944i
$704$	2.87712e13			0.166377
$705$		−	1.41119e13i		−	0.0810289i
$706$			1.08136e14i			0.616518i
$707$	2.20548e14	−	2.34485e14i	1.24855	−	1.32745i
$708$	1.52192e14			0.855513
$709$	3.24989e14			1.81400			0.907000	−	0.421131i	$-0.138367\pi$
$709$	3.24989e14			1.81400			0.907000	+	0.421131i	$0.138367\pi$
$710$		−	3.88920e13i		−	0.215560i
$711$	−1.32361e13			−0.0728469
$712$			4.90790e13i			0.268223i
$713$			5.65791e12i			0.0307050i
$714$	−9.77895e12	−	9.19769e12i	−0.0526989	−	0.0495665i
$715$	−1.23428e14			−0.660515
$716$	−5.20426e11			−0.00276563
$717$		−	2.91301e14i		−	1.53726i
$718$	−1.43545e14			−0.752254
$719$			2.59709e14i			1.35158i	0.737093	+	0.675792i	$0.236198\pi$
$719$			2.59709e14i			1.35158i	−0.737093	+	0.675792i	$0.763802\pi$
$720$		−	5.79299e13i		−	0.299392i
$721$	1.68920e13	−	1.79595e13i	0.0866969	−	0.0921758i
$722$	1.55176e13			0.0790931
$723$	−5.21379e14			−2.63914
$724$			1.39906e14i			0.703306i
$725$	5.21099e13			0.260154
$726$			2.12568e14i			1.05394i
$727$			2.98811e14i			1.47138i	0.677319	+	0.735690i	$0.263142\pi$
$727$			2.98811e14i			1.47138i	−0.677319	+	0.735690i	$0.736858\pi$
$728$	5.60602e13	−	5.96030e13i	0.274156	−	0.291482i
$729$	−7.66838e14			−3.72448
$730$	1.25188e14			0.603879
$731$			4.97877e12i			0.0238526i
$732$	1.84476e14			0.877777
$733$		−	4.16290e13i		−	0.196732i	−0.995150	−	0.0983662i	$-0.968638\pi$
$733$		−	4.16290e13i		−	0.196732i	0.995150	−	0.0983662i	$-0.0313617\pi$
$734$		−	7.54745e13i		−	0.354258i
$735$	−1.11191e13	−	1.81334e14i	−0.0518360	−	0.845363i
$736$	3.92749e12			0.0181855
$737$	−2.79700e14			−1.28634
$738$		−	4.04366e13i		−	0.184711i
$739$	2.74676e14			1.24623			0.623114	−	0.782131i	$-0.285867\pi$
$739$	2.74676e14			1.24623			0.623114	+	0.782131i	$0.285867\pi$
$740$			5.11519e13i			0.230517i
$741$		−	4.60295e14i		−	2.06037i
$742$	−1.56137e14	−	1.46856e14i	−0.694203	−	0.652940i
$743$	1.53590e14			0.678295			0.339147	−	0.940733i	$-0.389861\pi$
$743$	1.53590e14			0.678295			0.339147	+	0.940733i	$0.389861\pi$
$744$	−4.64685e13			−0.203842
$745$			1.01124e14i			0.440627i
$746$	2.02673e13			0.0877206
$747$			5.78386e14i			2.48665i
$748$		−	8.25396e12i		−	0.0352496i
$749$	7.75887e13	+	7.29769e13i	0.329147	+	0.309582i
$750$	−2.56915e14			−1.08264
$751$	4.39239e13			0.183866			0.0919330	−	0.995765i	$-0.470695\pi$
$751$	4.39239e13			0.183866			0.0919330	+	0.995765i	$0.470695\pi$
$752$			5.75189e12i			0.0239178i
$753$	2.63347e14			1.08781
$754$			6.28151e13i			0.257755i
$755$			1.48145e14i			0.603881i
$756$	−2.82918e14	+	3.00797e14i	−1.14565	+	1.21805i
$757$	−2.96395e14			−1.19231			−0.596157	−	0.802868i	$-0.703307\pi$
$757$	−2.96395e14			−1.19231			−0.596157	+	0.802868i	$0.703307\pi$
$758$	−2.15338e14			−0.860545
$759$			6.66233e13i			0.264495i
$760$	−3.70418e13			−0.146091
$761$			1.38268e14i			0.541750i	0.962615	+	0.270875i	$0.0873130\pi$
$761$			1.38268e14i			0.541750i	−0.962615	+	0.270875i	$0.912687\pi$
$762$			1.48756e14i			0.579029i
$763$	−2.98657e14	−	2.80904e14i	−1.15491	−	1.08627i
$764$	−7.50574e13			−0.288354
$765$	−1.66191e13			−0.0634309
$766$		−	2.63525e14i		−	0.999258i
$767$	2.66118e14			1.00253
$768$			3.22565e13i			0.120729i
$769$			2.26479e14i			0.842163i	0.907023	+	0.421081i	$0.138349\pi$
$769$			2.26479e14i			0.842163i	−0.907023	+	0.421081i	$0.861651\pi$
$770$	7.65280e13	−	8.13642e13i	0.282727	−	0.300594i
$771$	8.56974e14			3.14554
$772$	3.51423e13			0.128157
$773$			3.90332e14i			1.41428i	0.707072	+	0.707141i	$0.250016\pi$
$773$			3.90332e14i			1.41428i	−0.707072	+	0.707141i	$0.749984\pi$
$774$	2.41601e14			0.869748
$775$			6.74056e13i			0.241095i
$776$		−	1.14351e14i		−	0.406378i
$777$	3.94107e14	−	4.19013e14i	1.39158	−	1.47953i
$778$	2.49541e13			0.0875475
$779$	−2.58561e13			−0.0901313
$780$		−	1.38380e14i		−	0.479292i
$781$	−2.68904e14			−0.925426
$782$		−	1.12673e12i		−	0.00385289i
$783$		−	3.17008e14i		−	1.07711i
$784$	4.53204e12	+	7.39104e13i	0.0153008	+	0.249531i
$785$	7.22211e12			0.0242279
$786$	−5.33050e13			−0.177687
$787$			3.07942e14i			1.01999i	0.860178	+	0.509994i	$0.170353\pi$
$787$			3.07942e14i			1.01999i	−0.860178	+	0.509994i	$0.829647\pi$
$788$	1.13425e14			0.373319
$789$		−	9.40313e14i		−	3.07530i
$790$			2.54439e12i			0.00826892i
$791$	8.92672e13	+	8.39611e13i	0.288277	+	0.271141i
$792$	−4.00533e14			−1.28532
$793$	3.22567e14			1.02862
$794$			1.32192e14i			0.418892i
$795$	−3.62503e14			−1.14150
$796$			1.15388e14i			0.361073i
$797$			7.45545e13i			0.231837i	0.993259	+	0.115918i	$0.0369811\pi$
$797$			7.45545e13i			0.231837i	−0.993259	+	0.115918i	$0.963019\pi$
$798$	3.03429e14	+	2.85393e14i	0.937655	+	0.881921i
$799$	1.65012e12			0.00506736
$800$	4.67902e13			0.142792
$801$		−	6.83246e14i		−	2.07212i
$802$	−1.44806e14			−0.436430
$803$		−	8.65567e14i		−	2.59252i
$804$		−	3.13584e14i		−	0.933411i
$805$	1.04467e13	−	1.11069e13i	0.0309029	−	0.0328558i
$806$	−8.12530e13			−0.238871
$807$	−4.17657e14			−1.22026
$808$			2.21894e14i			0.644302i
$809$	1.02308e14			0.295235			0.147618	−	0.989045i	$-0.452840\pi$
$809$	1.02308e14			0.295235			0.147618	+	0.989045i	$0.452840\pi$
$810$			4.03096e14i			1.15607i
$811$			4.43418e13i			0.126389i	0.998001	+	0.0631944i	$0.0201288\pi$
$811$			4.43418e13i			0.126389i	−0.998001	+	0.0631944i	$0.979871\pi$
$812$	−4.14080e13	−	3.89468e13i	−0.117302	−	0.110329i
$813$	7.73350e14			2.17732
$814$	3.53670e14			0.989637
$815$		−	6.92539e13i		−	0.192600i
$816$	9.25386e12			0.0255783
$817$		−	1.54485e14i		−	0.424401i
$818$			2.13006e14i			0.581601i
$819$	−7.80434e14	+	8.29754e14i	−2.11795	+	2.25180i
$820$	−7.77319e12			−0.0209667
$821$	1.64163e14			0.440109			0.220054	−	0.975488i	$-0.429376\pi$
$821$	1.64163e14			0.440109			0.220054	+	0.975488i	$0.429376\pi$
$822$		−	8.97387e14i		−	2.39123i
$823$	−1.41067e14			−0.373616			−0.186808	−	0.982396i	$-0.559814\pi$
$823$	−1.41067e14			−0.373616			−0.186808	+	0.982396i	$0.559814\pi$
$824$			1.69951e13i			0.0447392i
$825$			7.93717e14i			2.07681i
$826$	−1.64999e14	+	1.75426e14i	−0.429122	+	0.456241i
$827$	−2.65758e14			−0.687003			−0.343502	−	0.939152i	$-0.611613\pi$
$827$	−2.65758e14			−0.687003			−0.343502	+	0.939152i	$0.611613\pi$
$828$	−5.46760e13			−0.140490
$829$			6.75658e14i			1.72566i	0.505498	+	0.862828i	$0.331309\pi$
$829$			6.75658e14i			1.72566i	−0.505498	+	0.862828i	$0.668691\pi$
$830$	1.11184e14			0.282262
$831$			3.24562e14i			0.819015i
$832$			5.64025e13i			0.141476i
$833$	2.12036e13	−	1.30016e12i	0.0528671	−	0.00324170i
$834$	7.26474e14			1.80049
$835$	2.12091e14			0.522505
$836$			2.56111e14i			0.627186i
$837$	4.10058e14			0.998201
$838$		−	4.26771e14i		−	1.03270i
$839$		−	1.55720e14i		−	0.374572i	−0.982305	−	0.187286i	$-0.940031\pi$
$839$		−	1.55720e14i		−	0.374572i	0.982305	−	0.187286i	$-0.0599690\pi$
$840$	9.12208e13	+	8.57987e13i	0.218121	+	0.205156i
$841$	−3.77068e14			−0.896271
$842$	−3.44574e14			−0.814182
$843$			3.66893e14i			0.861789i
$844$	−1.34540e14			−0.314151
$845$		−	5.30752e13i		−	0.123199i
$846$		−	8.00741e13i		−	0.184774i
$847$	−2.45019e14	−	2.30455e14i	−0.562060	−	0.528651i
$848$	1.47753e14			0.336944
$849$	−5.87787e14			−1.33254
$850$		−	1.34233e13i		−	0.0302528i
$851$	4.82787e13			0.108170
$852$		−	3.01479e14i		−	0.671520i
$853$		−	3.97170e14i		−	0.879491i	−0.898122	−	0.439746i	$-0.855069\pi$
$853$		−	3.97170e14i		−	0.879491i	0.898122	−	0.439746i	$-0.144931\pi$
$854$	−1.99999e14	+	2.12638e14i	−0.440290	+	0.468114i
$855$	5.15671e14			1.12861
$856$	−7.34225e13			−0.159757
$857$		−	5.08562e14i		−	1.10012i	−0.835126	−	0.550059i	$-0.814605\pi$
$857$		−	5.08562e14i		−	1.10012i	0.835126	−	0.550059i	$-0.185395\pi$
$858$	−9.56774e14			−2.05766
$859$		−	1.97810e14i		−	0.422944i	−0.977384	−	0.211472i	$-0.932174\pi$
$859$		−	1.97810e14i		−	0.422944i	0.977384	−	0.211472i	$-0.0678258\pi$
$860$		−	4.64433e13i		−	0.0987259i
$861$	6.36745e13	+	5.98897e13i	0.134570	+	0.126572i
$862$	1.04776e14			0.220154
$863$	−7.11404e14			−1.48615			−0.743074	−	0.669209i	$-0.766633\pi$
$863$	−7.11404e14			−1.48615			−0.743074	+	0.669209i	$0.766633\pi$
$864$		−	2.84646e14i		−	0.591202i
$865$	−7.57352e12			−0.0156393
$866$		−	3.62090e14i		−	0.743409i
$867$			9.43642e14i			1.92625i
$868$	5.03787e13	−	5.35624e13i	0.102246	−	0.108708i
$869$	1.75922e13			0.0354995
$870$	−9.61368e13			−0.192883
$871$		−	5.48320e14i		−	1.09381i
$872$	2.82620e14			0.560557
$873$			1.59192e15i			3.13942i
$874$			3.49611e13i			0.0685533i
$875$	2.78533e14	−	2.96136e14i	0.543047	−	0.577365i
$876$	9.70422e14			1.88122
$877$	9.04137e14			1.74275			0.871377	−	0.490614i	$-0.163228\pi$
$877$	9.04137e14			1.74275			0.871377	+	0.490614i	$0.163228\pi$
$878$			3.47260e14i			0.665552i
$879$	−1.86464e15			−3.55346
$880$			7.69953e13i			0.145898i
$881$			2.80487e14i			0.528486i	0.964456	+	0.264243i	$0.0851221\pi$
$881$			2.80487e14i			0.528486i	−0.964456	+	0.264243i	$0.914878\pi$
$882$	−6.30921e13	−	1.02893e15i	−0.118204	−	1.92772i
$883$	−8.80449e14			−1.64021			−0.820107	−	0.572210i	$-0.806086\pi$
$883$	−8.80449e14			−1.64021			−0.820107	+	0.572210i	$0.806086\pi$
$884$	1.61809e13			0.0299738
$885$			4.07286e14i			0.750211i
$886$	5.38775e14			0.986823
$887$		−	5.06209e14i		−	0.921960i	−0.887411	−	0.460980i	$-0.847498\pi$
$887$		−	5.06209e14i		−	0.921960i	0.887411	−	0.460980i	$-0.152502\pi$
$888$			3.96514e14i			0.718114i
$889$	−1.71466e14	−	1.61274e14i	−0.308793	−	0.290439i
$890$	−1.31342e14			−0.235208
$891$	2.78705e15			4.96313
$892$		−	1.62229e14i		−	0.287279i
$893$	−5.12013e13			−0.0901620
$894$			7.83878e14i			1.37265i
$895$		−	1.39273e12i		−	0.00242522i
$896$	−3.71808e13	−	3.49708e13i	−0.0643842	−	0.0605572i
$897$	−1.30607e14			−0.224908
$898$	6.30184e14			1.07916
$899$			5.64490e13i			0.0961297i
$900$	−6.51383e14			−1.10312
$901$		−	4.23879e13i		−	0.0713868i
$902$			5.37447e13i			0.0900125i
$903$	−3.57829e14	+	3.80443e14i	−0.595987	+	0.633651i
$904$	−8.44738e13			−0.139920
$905$	−3.74407e14			−0.616738
$906$			1.14837e15i			1.88123i
$907$	−5.58963e14			−0.910640			−0.455320	−	0.890328i	$-0.650475\pi$
$907$	−5.58963e14			−0.910640			−0.455320	+	0.890328i	$0.650475\pi$
$908$			3.25015e14i			0.526593i
$909$		−	3.08907e15i		−	4.97746i
$910$	1.59505e14	+	1.50024e14i	0.255604	+	0.240411i
$911$	9.62012e14			1.53316			0.766582	−	0.642147i	$-0.221956\pi$
$911$	9.62012e14			1.53316			0.766582	+	0.642147i	$0.221956\pi$
$912$	−2.87136e14			−0.455107
$913$		−	7.68740e14i		−	1.21178i
$914$	−1.58408e13			−0.0248340
$915$			4.93681e14i			0.769734i
$916$		−	2.40462e14i		−	0.372880i
$917$	5.77905e13	−	6.14426e13i	0.0891271	−	0.0947595i
$918$	−8.16600e13			−0.125255
$919$	5.05270e14			0.770807			0.385403	−	0.922748i	$-0.374062\pi$
$919$	5.05270e14			0.770807			0.385403	+	0.922748i	$0.374062\pi$
$920$			1.05105e13i			0.0159471i
$921$	4.39828e14			0.663720
$922$		−	7.68924e14i		−	1.15406i
$923$		−	5.27154e14i		−	0.786918i
$924$	5.93221e14	−	6.30710e14i	0.880758	−	0.936419i
$925$	5.75169e14			0.849351
$926$	−7.94539e14			−1.16697
$927$		−	2.36595e14i		−	0.345626i
$928$	3.91846e13			0.0569345
$929$			8.72533e14i			1.26097i	0.776203	+	0.630483i	$0.217143\pi$
$929$			8.72533e14i			1.26097i	−0.776203	+	0.630483i	$0.782857\pi$
$930$		−	1.24356e14i		−	0.178752i
$931$	−6.57924e14	+	4.03426e13i	−0.940648	+	0.0576787i
$932$	−3.51519e14			−0.499885
$933$	−1.32898e15			−1.87980
$934$			5.66673e14i			0.797256i
$935$	2.20886e13			0.0309109
$936$		−	7.85199e14i		−	1.09295i
$937$			7.65368e14i			1.05967i	0.848100	+	0.529837i	$0.177747\pi$
$937$			7.65368e14i			1.05967i	−0.848100	+	0.529837i	$0.822253\pi$
$938$	3.61456e14	+	3.39971e14i	0.497784	+	0.468196i
$939$	6.24809e14			0.855892
$940$	−1.53928e13			−0.0209739
$941$			4.22666e14i			0.572861i	0.958101	+	0.286431i	$0.0924688\pi$
$941$			4.22666e14i			0.572861i	−0.958101	+	0.286431i	$0.907531\pi$
$942$	5.59835e13			0.0754755
$943$			7.33658e12i			0.00983864i
$944$		−	1.66006e14i		−	0.221445i
$945$	−8.04972e14	−	7.57124e14i	−1.06812	−	1.00463i
$946$	−3.21114e14			−0.423842
$947$	6.87404e14			0.902530			0.451265	−	0.892390i	$-0.350973\pi$
$947$	6.87404e14			0.902530			0.451265	+	0.892390i	$0.350973\pi$
$948$			1.97234e13i			0.0257596i
$949$	1.69684e15			2.20450
$950$			4.16510e14i			0.538279i
$951$			4.25723e14i			0.547298i
$952$	−1.00325e13	+	1.06666e13i	−0.0128300	+	0.0136408i
$953$	−5.03843e14			−0.640960			−0.320480	−	0.947255i	$-0.603844\pi$
$953$	−5.03843e14			−0.640960			−0.320480	+	0.947255i	$0.603844\pi$
$954$	−2.05692e15			−2.60301
$955$		−	2.00863e14i		−	0.252862i
$956$	−3.17742e14			−0.397910
$957$			6.64700e14i			0.828068i
$958$		−	5.72245e14i		−	0.709176i
$959$	1.03438e15	+	9.72900e14i	1.27523	+	1.19943i
$960$	−8.63226e13			−0.105869
$961$	7.46610e14			0.910913
$962$			6.93329e14i			0.841519i
$963$	1.02214e15			1.23418
$964$			5.68703e14i			0.683126i
$965$			9.40452e13i			0.112383i
$966$	8.09794e13	−	8.60970e13i	0.0962695	−	0.102353i
$967$	5.68178e14			0.671974			0.335987	−	0.941867i	$-0.390930\pi$
$967$	5.68178e14			0.671974			0.335987	+	0.941867i	$0.390930\pi$
$968$	2.31862e14			0.272806
$969$			8.23745e13i			0.0964215i
$970$	3.06017e14			0.356358
$971$		−	9.01977e14i		−	1.04496i	−0.852652	−	0.522479i	$-0.825007\pi$
$971$		−	9.01977e14i		−	1.04496i	0.852652	−	0.522479i	$-0.174993\pi$
$972$			1.67386e15i			1.92924i
$973$	−7.87605e14	+	8.37379e14i	−0.903117	+	0.960191i
$974$	9.68759e14			1.10515
$975$	−1.55599e15			−1.76597
$976$		−	2.01220e14i		−	0.227207i
$977$	−1.45946e15			−1.63954			−0.819768	−	0.572696i	$-0.805897\pi$
$977$	−1.45946e15			−1.63954			−0.819768	+	0.572696i	$0.805897\pi$
$978$		−	5.36835e14i		−	0.599994i
$979$			9.08109e14i			1.00978i
$980$	−1.97793e14	+	1.21283e13i	−0.218817	+	0.0134174i
$981$	−3.93445e15			−4.33051
$982$	4.13176e14			0.452457
$983$		−	9.57054e14i		−	1.04272i	−0.853336	−	0.521361i	$-0.825424\pi$
$983$		−	9.57054e14i		−	1.04272i	0.853336	−	0.521361i	$-0.174576\pi$
$984$	−6.02554e13			−0.0653161
$985$			3.03541e14i			0.327368i
$986$		−	1.12414e13i		−	0.0120625i
$987$	1.26091e14	+	1.18596e14i	0.134616	+	0.126615i
$988$	−5.02075e14			−0.533315
$989$	−4.38346e13			−0.0463272
$990$		−	1.07188e15i		−	1.12712i
$991$	−1.51529e14			−0.158536			−0.0792681	−	0.996853i	$-0.525258\pi$
$991$	−1.51529e14			−0.158536			−0.0792681	+	0.996853i	$0.525258\pi$
$992$			5.06863e13i			0.0527633i
$993$			9.62457e14i			0.996862i
$994$	3.47503e14	+	3.26847e14i	0.358118	+	0.336832i
$995$	−3.08793e14			−0.316630
$996$	8.61866e14			0.879312
$997$		−	9.47806e14i		−	0.962152i	−0.876679	−	0.481076i	$-0.840246\pi$
$997$		−	9.47806e14i		−	0.962152i	0.876679	−	0.481076i	$-0.159754\pi$
$998$	−8.07097e14			−0.815217
$999$		−	3.49901e15i		−	3.51656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.11.b.a.13.8	yes	8
3.2	odd	2		126.11.c.a.55.2		8
4.3	odd	2		112.11.c.d.97.1		8
7.2	even	3		98.11.d.c.31.1		16
7.3	odd	6		98.11.d.c.19.1		16
7.4	even	3		98.11.d.c.19.4		16
7.5	odd	6		98.11.d.c.31.4		16
7.6	odd	2	inner	14.11.b.a.13.5	✓	8
21.20	even	2		126.11.c.a.55.3		8
28.27	even	2		112.11.c.d.97.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.11.b.a.13.5	✓	8	7.6	odd	2	inner
14.11.b.a.13.8	yes	8	1.1	even	1	trivial
98.11.d.c.19.1		16	7.3	odd	6
98.11.d.c.19.4		16	7.4	even	3
98.11.d.c.31.1		16	7.2	even	3
98.11.d.c.31.4		16	7.5	odd	6
112.11.c.d.97.1		8	4.3	odd	2
112.11.c.d.97.8		8	28.27	even	2
126.11.c.a.55.2		8	3.2	odd	2
126.11.c.a.55.3		8	21.20	even	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+22.6274 q^{2} +469.394i q^{3} +512.000 q^{4} +1370.18i q^{5} +10621.2i q^{6} +(-12242.6 - 11514.9i) q^{7} +11585.2 q^{8} -161282. q^{9} +O(q^{10})\)	\(q+22.6274 q^{2} +469.394i q^{3} +512.000 q^{4} +1370.18i q^{5} +10621.2i q^{6} +(-12242.6 - 11514.9i) q^{7} +11585.2 q^{8} -161282. q^{9} +31003.6i q^{10} +214362. q^{11} +240330. i q^{12} +420232. i q^{13} +(-277019. - 260553. i) q^{14} -643153. q^{15} +262144. q^{16} -75204.7i q^{17} -3.64940e6 q^{18} +2.33351e6i q^{19} +701530. i q^{20} +(5.40504e6 - 5.74662e6i) q^{21} +4.85046e6 q^{22} +662126. q^{23} +5.43805e6i q^{24} +7.88824e6 q^{25} +9.50875e6i q^{26} -4.79877e7i q^{27} +(-6.26822e6 - 5.89564e6i) q^{28} +6.60603e6 q^{29} -1.45529e7 q^{30} +8.54507e6i q^{31} +5.93164e6 q^{32} +1.00620e8i q^{33} -1.70169e6i q^{34} +(1.57775e7 - 1.67746e7i) q^{35} -8.25765e7 q^{36} +7.29148e7 q^{37} +5.28014e7i q^{38} -1.97254e8 q^{39} +1.58738e7i q^{40} +1.10803e7i q^{41} +(1.22302e8 - 1.30031e8i) q^{42} -6.62029e7 q^{43} +1.09753e8 q^{44} -2.20985e8i q^{45} +1.49822e7 q^{46} +2.19417e7i q^{47} +1.23049e8i q^{48} +(1.72883e7 + 2.81946e8i) q^{49} +1.78491e8 q^{50} +3.53007e7 q^{51} +2.15159e8i q^{52} +5.63633e8 q^{53} -1.08584e9i q^{54} +2.93714e8i q^{55} +(-1.41834e8 - 1.33403e8i) q^{56} -1.09534e9 q^{57} +1.49477e8 q^{58} -6.33264e8i q^{59} -3.29294e8 q^{60} -7.67594e8i q^{61} +1.93353e8i q^{62} +(1.97452e9 + 1.85715e9i) q^{63} +1.34218e8 q^{64} -5.75791e8 q^{65} +2.27678e9i q^{66} -1.30480e9 q^{67} -3.85048e7i q^{68} +3.10798e8i q^{69} +(3.57004e8 - 3.79565e8i) q^{70} -1.25444e9 q^{71} -1.86849e9 q^{72} -4.03787e9i q^{73} +1.64987e9 q^{74} +3.70270e9i q^{75} +1.19476e9i q^{76} +(-2.62435e9 - 2.46836e9i) q^{77} -4.46336e9 q^{78} +8.20678e7 q^{79} +3.59184e8i q^{80} +1.30016e10 q^{81} +2.50719e8i q^{82} -3.58618e9i q^{83} +(2.76738e9 - 2.94227e9i) q^{84} +1.03044e8 q^{85} -1.49800e9 q^{86} +3.10083e9i q^{87} +2.48343e9 q^{88} +4.23634e9i q^{89} -5.00032e9i q^{90} +(4.83893e9 - 5.14474e9i) q^{91} +3.39008e8 q^{92} -4.01101e9 q^{93} +4.96485e8i q^{94} -3.19732e9 q^{95} +2.78428e9i q^{96} -9.87038e9i q^{97} +(3.91191e8 + 6.37970e9i) q^{98} -3.45727e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4096 q^{4} + 18376 q^{7} - 246456 q^{9}+O(q^{10}) \) 8 * q + 4096 * q^4 + 18376 * q^7 - 246456 * q^9	\( 8 q + 4096 q^{4} + 18376 q^{7} - 246456 q^{9} + 430800 q^{11} - 136704 q^{14} - 1896960 q^{15} + 2097152 q^{16} - 4512768 q^{18} + 5339136 q^{21} + 13228032 q^{22} + 6265488 q^{23} - 28719160 q^{25} + 9408512 q^{28} - 46431408 q^{29} + 28584960 q^{30} + 184450560 q^{35} - 126185472 q^{36} + 360932816 q^{37} - 836120064 q^{39} + 308382720 q^{42} + 32112848 q^{43} + 220569600 q^{44} - 769191936 q^{46} + 853888904 q^{49} - 53836800 q^{50} + 1737904128 q^{51} - 1132258608 q^{53} - 69992448 q^{56} - 2040889344 q^{57} + 352352256 q^{58} - 971243520 q^{60} + 2661283080 q^{63} + 1073741824 q^{64} - 143001600 q^{65} - 2254742192 q^{67} + 402662400 q^{70} + 2121911184 q^{71} - 2310537216 q^{72} + 4970207232 q^{74} - 17516185008 q^{77} + 1916728320 q^{78} - 5257367792 q^{79} + 24706423944 q^{81} + 2733637632 q^{84} + 4331212800 q^{85} - 14424637440 q^{86} + 6772752384 q^{88} - 8536548864 q^{91} + 3207929856 q^{92} - 20748386304 q^{93} + 30330078720 q^{95} - 802977792 q^{98} - 16331376816 q^{99}+O(q^{100}) \) 8 * q + 4096 * q^4 + 18376 * q^7 - 246456 * q^9 + 430800 * q^11 - 136704 * q^14 - 1896960 * q^15 + 2097152 * q^16 - 4512768 * q^18 + 5339136 * q^21 + 13228032 * q^22 + 6265488 * q^23 - 28719160 * q^25 + 9408512 * q^28 - 46431408 * q^29 + 28584960 * q^30 + 184450560 * q^35 - 126185472 * q^36 + 360932816 * q^37 - 836120064 * q^39 + 308382720 * q^42 + 32112848 * q^43 + 220569600 * q^44 - 769191936 * q^46 + 853888904 * q^49 - 53836800 * q^50 + 1737904128 * q^51 - 1132258608 * q^53 - 69992448 * q^56 - 2040889344 * q^57 + 352352256 * q^58 - 971243520 * q^60 + 2661283080 * q^63 + 1073741824 * q^64 - 143001600 * q^65 - 2254742192 * q^67 + 402662400 * q^70 + 2121911184 * q^71 - 2310537216 * q^72 + 4970207232 * q^74 - 17516185008 * q^77 + 1916728320 * q^78 - 5257367792 * q^79 + 24706423944 * q^81 + 2733637632 * q^84 + 4331212800 * q^85 - 14424637440 * q^86 + 6772752384 * q^88 - 8536548864 * q^91 + 3207929856 * q^92 - 20748386304 * q^93 + 30330078720 * q^95 - 802977792 * q^98 - 16331376816 * q^99

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