LMFDB - Embedded newform 22.13.d.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,13,Mod(7,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, 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:	$20.1078639801$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	22.7
Dual form			22.13.d.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-26.6001 + 36.6119i) q^{2} +(103.669 - 319.061i) q^{3} +(-632.867 - 1947.76i) q^{4} +(-5380.08 + 3908.86i) q^{5} +(8923.84 + 12282.6i) q^{6} +(-84352.8 + 27407.9i) q^{7} +(88145.7 + 28640.3i) q^{8} +(338892. + 246219. i) q^{9} -300951. i q^{10} +(-1.77071e6 + 54860.6i) q^{11} -687065. q^{12} +(3.19148e6 - 4.39270e6i) q^{13} +(1.24034e6 - 3.81737e6i) q^{14} +(689417. + 2.12181e6i) q^{15} +(-3.39326e6 + 2.46535e6i) q^{16} +(-2.05258e7 - 2.82514e7i) q^{17} +(-1.80291e7 + 5.85802e6i) q^{18} +(7.64421e7 + 2.48375e7i) q^{19} +(1.10184e7 + 8.00534e6i) q^{20} +2.97551e7i q^{21} +(4.50926e7 - 6.62885e7i) q^{22} +2.43378e8 q^{23} +(1.82760e7 - 2.51548e7i) q^{24} +(-6.17775e7 + 1.90132e8i) q^{25} +(7.59313e7 + 2.33693e8i) q^{26} +(2.57930e8 - 1.87397e8i) q^{27} +(1.06768e8 + 1.46954e8i) q^{28} +(9.32064e8 - 3.02846e8i) q^{29} +(-9.60220e7 - 3.11994e7i) q^{30} +(1.03070e8 + 7.48845e7i) q^{31} -1.89813e8i q^{32} +(-1.66065e8 + 5.70653e8i) q^{33} +1.58033e9 q^{34} +(3.46692e8 - 4.77180e8i) q^{35} +(2.65104e8 - 8.15905e8i) q^{36} +(-1.00458e9 - 3.09178e9i) q^{37} +(-2.94272e9 + 2.13801e9i) q^{38} +(-1.07068e9 - 1.47367e9i) q^{39} +(-5.86182e8 + 1.90462e8i) q^{40} +(5.42123e9 + 1.76146e9i) q^{41} +(-1.08939e9 - 7.91489e8i) q^{42} -9.00405e8i q^{43} +(1.22748e9 + 3.41421e9i) q^{44} -2.78570e9 q^{45} +(-6.47388e9 + 8.91053e9i) q^{46} +(7.71013e8 - 2.37294e9i) q^{47} +(4.34821e8 + 1.33824e9i) q^{48} +(-4.83363e9 + 3.51184e9i) q^{49} +(-5.31779e9 - 7.31932e9i) q^{50} +(-1.11418e10 + 3.62020e9i) q^{51} +(-1.05757e10 - 3.43626e9i) q^{52} +(-6.75615e9 - 4.90863e9i) q^{53} +1.44281e10i q^{54} +(9.31213e9 - 7.21662e9i) q^{55} -8.22031e9 q^{56} +(1.58494e10 - 2.18148e10i) q^{57} +(-1.37052e10 + 4.21804e10i) q^{58} +(-2.12469e10 - 6.53913e10i) q^{59} +(3.69647e9 - 2.68564e9i) q^{60} +(2.37002e10 + 3.26206e10i) q^{61} +(-5.48333e9 + 1.78164e9i) q^{62} +(-3.53349e10 - 1.14810e10i) q^{63} +(6.94940e9 + 5.04904e9i) q^{64} +3.61081e10i q^{65} +(-1.64754e10 - 2.12594e10i) q^{66} +9.38338e10 q^{67} +(-4.20369e10 + 5.78588e10i) q^{68} +(2.52308e10 - 7.76525e10i) q^{69} +(8.24845e9 + 2.53861e10i) q^{70} +(1.23673e11 - 8.98535e10i) q^{71} +(2.28201e10 + 3.14091e10i) q^{72} +(-4.22068e10 + 1.37138e10i) q^{73} +(1.39918e11 + 4.54621e10i) q^{74} +(5.42592e10 + 3.94216e10i) q^{75} -1.64610e11i q^{76} +(1.47861e11 - 5.31591e10i) q^{77} +8.24340e10 q^{78} +(-5.73849e10 + 7.89836e10i) q^{79} +(8.61933e9 - 2.65276e10i) q^{80} +(3.57407e10 + 1.09999e11i) q^{81} +(-2.08696e11 + 1.51626e11i) q^{82} +(1.62315e11 + 2.23407e11i) q^{83} +(5.79559e10 - 1.88310e10i) q^{84} +(2.20861e11 + 7.17622e10i) q^{85} +(3.29656e10 + 2.39509e10i) q^{86} -3.28781e11i q^{87} +(-1.57652e11 - 4.58779e10i) q^{88} -6.25780e11 q^{89} +(7.41001e10 - 1.01990e11i) q^{90} +(-1.48816e11 + 4.58008e11i) q^{91} +(-1.54026e11 - 4.74043e11i) q^{92} +(3.45779e10 - 2.51223e10i) q^{93} +(6.63687e10 + 9.13487e10i) q^{94} +(-5.08351e11 + 1.65173e11i) q^{95} +(-6.05619e10 - 1.96777e10i) q^{96} +(-8.44850e11 - 6.13819e11i) q^{97} -2.70384e11i q^{98} +(-6.13588e11 - 4.17392e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 1240 q^{3} + 24576 q^{4} + 1440 q^{5} - 147200 q^{6} + 439200 q^{7} + 563348 q^{9} - 7317468 q^{11} + 737280 q^{12} + 13341600 q^{13} - 7524864 q^{14} - 29808888 q^{15} - 50331648 q^{16} + 29458800 q^{17}+ \cdots - 5181480396620 q^{99}+O(q^{100}) $ 48 * q + 1240 * q^3 + 24576 * q^4 + 1440 * q^5 - 147200 * q^6 + 439200 * q^7 + 563348 * q^9 - 7317468 * q^11 + 737280 * q^12 + 13341600 * q^13 - 7524864 * q^14 - 29808888 * q^15 - 50331648 * q^16 + 29458800 * q^17 - 96857600 * q^18 + 59195700 * q^19 - 2949120 * q^20 - 147874560 * q^22 + 297521280 * q^23 - 301465600 * q^24 - 349772268 * q^25 + 603191808 * q^26 - 434593340 * q^27 - 981811200 * q^28 + 121665600 * q^29 + 3275650560 * q^30 - 1117400544 * q^31 - 13803991820 * q^33 - 2568870912 * q^34 + 1026283680 * q^35 + 7058374656 * q^36 + 11737565760 * q^37 + 4500864000 * q^38 - 23697921920 * q^39 - 7817134080 * q^40 + 4863244680 * q^41 + 12992468480 * q^42 - 18701991936 * q^44 + 29640403232 * q^45 + 33202391040 * q^46 + 8084031480 * q^47 + 5200936960 * q^48 + 593931516 * q^49 - 13593646080 * q^50 - 30011589660 * q^51 + 55099392000 * q^52 + 40815862920 * q^53 + 29310331992 * q^55 - 7285506048 * q^56 - 98665594300 * q^57 + 81900510720 * q^58 - 156541010940 * q^59 - 30685659136 * q^60 + 255357655680 * q^61 + 67163788800 * q^62 - 429459850400 * q^63 + 103079215104 * q^64 + 460708043264 * q^66 + 76186270200 * q^67 + 60331622400 * q^68 - 1054414688600 * q^69 - 352820375040 * q^70 + 60925955544 * q^71 + 95420416000 * q^72 + 363471756600 * q^73 + 378662860800 * q^74 - 57777629724 * q^75 + 326539185480 * q^77 - 1234846474240 * q^78 + 137547461520 * q^79 - 120795955200 * q^80 - 1017431491848 * q^81 + 613199754240 * q^82 + 715268672100 * q^83 - 354644459520 * q^84 + 1202406730800 * q^85 - 80499776256 * q^86 - 270225899520 * q^88 + 724193830584 * q^89 - 1005067351040 * q^90 + 1925501559192 * q^91 - 608833290240 * q^92 - 2466072811400 * q^93 + 300785049600 * q^94 + 6877125644400 * q^95 + 1350178653780 * q^97 - 5181480396620 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−26.6001	+	36.6119i	−0.415627	+	0.572061i
$2$	−26.6001	+	36.6119i	−0.415627	+	0.572061i
$3$	103.669	−	319.061i	0.142208	−	0.437670i	−0.854434	−	0.519560i	$-0.826096\pi$
$3$	103.669	−	319.061i	0.142208	−	0.437670i	0.996641	+	0.0818904i	$0.0260957\pi$
$4$	−632.867	−	1947.76i	−0.154508	−	0.475528i
$5$	−5380.08	+	3908.86i	−0.344325	+	0.250167i	−0.746485	−	0.665403i	$-0.768260\pi$
$5$	−5380.08	+	3908.86i	−0.344325	+	0.250167i	0.402159	+	0.915570i	$0.368260\pi$
$6$	8923.84	+	12282.6i	0.191269	+	0.263259i
$7$	−84352.8	+	27407.9i	−0.716987	+	0.232963i	−0.644717	−	0.764422i	$-0.723025\pi$
$7$	−84352.8	+	27407.9i	−0.716987	+	0.232963i	−0.0722708	+	0.997385i	$0.523025\pi$
$8$	88145.7	+	28640.3i	0.336249	+	0.109254i
$9$	338892.	+	246219.i	0.637685	+	0.463305i
$10$		−	300951.i		−	0.300951i
$11$	−1.77071e6	+	54860.6i	−0.999520	+	0.0309674i
$11$	−1.77071e6	+	54860.6i	−0.999520	+	0.0309674i
$12$	−687065.			−0.230097
$13$	3.19148e6	−	4.39270e6i	0.661199	−	0.910062i	−0.338321	−	0.941031i	$-0.609859\pi$
$13$	3.19148e6	−	4.39270e6i	0.661199	−	0.910062i	0.999520	+	0.0309684i	$0.00985913\pi$
$14$	1.24034e6	−	3.81737e6i	0.164730	−	0.506987i
$15$	689417.	+	2.12181e6i	0.0605249	+	0.186277i
$16$	−3.39326e6	+	2.46535e6i	−0.202254	+	0.146946i
$17$	−2.05258e7	−	2.82514e7i	−0.850368	−	1.17043i	−0.983781	−	0.179371i	$-0.942594\pi$
$17$	−2.05258e7	−	2.82514e7i	−0.850368	−	1.17043i	0.133413	−	0.991061i	$-0.457406\pi$
$18$	−1.80291e7	+	5.85802e6i	−0.530078	+	0.172233i
$19$	7.64421e7	+	2.48375e7i	1.62484	+	0.527943i	0.973077	−	0.230479i	$-0.0740292\pi$
$19$	7.64421e7	+	2.48375e7i	1.62484	+	0.527943i	0.651764	+	0.758422i	$0.274029\pi$
$20$	1.10184e7	+	8.00534e6i	0.172163	+	0.125084i
$21$			2.97551e7i			0.346933i
$22$	4.50926e7	−	6.62885e7i	0.397712	−	0.584658i
$23$	2.43378e8			1.64405			0.822023	−	0.569454i	$-0.192845\pi$
$23$	2.43378e8			1.64405			0.822023	+	0.569454i	$0.192845\pi$
$24$	1.82760e7	−	2.51548e7i	0.0956344	−	0.131629i
$25$	−6.17775e7	+	1.90132e8i	−0.253041	+	0.778779i
$26$	7.59313e7	+	2.33693e8i	0.245799	+	0.756493i
$27$	2.57930e8	−	1.87397e8i	0.665763	−	0.483705i
$28$	1.06768e8	+	1.46954e8i	0.221561	+	0.304953i
$29$	9.32064e8	−	3.02846e8i	1.56696	−	0.509136i	0.608303	−	0.793705i	$-0.291850\pi$
$29$	9.32064e8	−	3.02846e8i	1.56696	−	0.509136i	0.958656	+	0.284569i	$0.0918504\pi$
$30$	−9.60220e7	−	3.11994e7i	−0.131717	−	0.0427976i
$31$	1.03070e8	+	7.48845e7i	0.116134	+	0.0843766i	0.644336	−	0.764742i	$-0.277134\pi$
$31$	1.03070e8	+	7.48845e7i	0.116134	+	0.0843766i	−0.528202	+	0.849119i	$0.677134\pi$
$32$		−	1.89813e8i		−	0.176777i
$33$	−1.66065e8	+	5.70653e8i	−0.128586	+	0.441864i
$34$	1.58033e9			1.02299
$35$	3.46692e8	−	4.77180e8i	0.188597	−	0.259582i
$36$	2.65104e8	−	8.15905e8i	0.121787	−	0.374822i
$37$	−1.00458e9	−	3.09178e9i	−0.391538	−	1.20503i	−0.931625	−	0.363422i	$-0.881608\pi$
$37$	−1.00458e9	−	3.09178e9i	−0.391538	−	1.20503i	0.540086	−	0.841610i	$-0.318392\pi$
$38$	−2.94272e9	+	2.13801e9i	−0.977344	+	0.710082i
$39$	−1.07068e9	−	1.47367e9i	−0.304279	−	0.418805i
$40$	−5.86182e8	+	1.90462e8i	−0.143111	+	0.0464995i
$41$	5.42123e9	+	1.76146e9i	1.14129	+	0.370826i	0.817854	−	0.575425i	$-0.195163\pi$
$41$	5.42123e9	+	1.76146e9i	1.14129	+	0.370826i	0.323432	+	0.946252i	$0.395163\pi$
$42$	−1.08939e9	−	7.91489e8i	−0.198467	−	0.144195i
$43$		−	9.00405e8i		−	0.142438i	−0.997461	−	0.0712192i	$-0.977311\pi$
$43$		−	9.00405e8i		−	0.142438i	0.997461	−	0.0712192i	$-0.0226890\pi$
$44$	1.22748e9	+	3.41421e9i	0.169160	+	0.470515i
$45$	−2.78570e9			−0.335475
$46$	−6.47388e9	+	8.91053e9i	−0.683310	+	0.940496i
$47$	7.71013e8	−	2.37294e9i	0.0715278	−	0.220140i	−0.908902	−	0.417010i	$-0.863078\pi$
$47$	7.71013e8	−	2.37294e9i	0.0715278	−	0.220140i	0.980430	+	0.196871i	$0.0630779\pi$
$48$	4.34821e8	+	1.33824e9i	0.0355519	+	0.109418i
$49$	−4.83363e9	+	3.51184e9i	−0.349218	+	0.253722i
$50$	−5.31779e9	−	7.31932e9i	−0.340339	−	0.468436i
$51$	−1.11418e10	+	3.62020e9i	−0.633192	+	0.205736i
$52$	−1.05757e10	−	3.43626e9i	−0.534921	−	0.173806i
$53$	−6.75615e9	−	4.90863e9i	−0.304821	−	0.221465i	0.424850	−	0.905264i	$-0.360327\pi$
$53$	−6.75615e9	−	4.90863e9i	−0.304821	−	0.221465i	−0.729671	+	0.683799i	$0.760327\pi$
$54$			1.44281e10i			0.581898i
$55$	9.31213e9	−	7.21662e9i	0.336413	−	0.260710i
$56$	−8.22031e9			−0.266539
$57$	1.58494e10	−	2.18148e10i	0.462130	−	0.636067i
$58$	−1.37052e10	+	4.21804e10i	−0.360013	+	1.10801i
$59$	−2.12469e10	−	6.53913e10i	−0.503714	−	1.55027i	−0.802921	−	0.596085i	$-0.796722\pi$
$59$	−2.12469e10	−	6.53913e10i	−0.503714	−	1.55027i	0.299207	−	0.954188i	$-0.403278\pi$
$60$	3.69647e9	−	2.68564e9i	0.0792281	−	0.0575626i
$61$	2.37002e10	+	3.26206e10i	0.460016	+	0.633158i	0.974512	−	0.224335i	$-0.0720209\pi$
$61$	2.37002e10	+	3.26206e10i	0.460016	+	0.633158i	−0.514496	+	0.857493i	$0.672021\pi$
$62$	−5.48333e9	+	1.78164e9i	−0.0965372	+	0.0313668i
$63$	−3.53349e10	−	1.14810e10i	−0.565145	−	0.183627i
$64$	6.94940e9	+	5.04904e9i	0.101127	+	0.0734732i
$65$			3.61081e10i			0.478768i
$66$	−1.64754e10	−	2.12594e10i	−0.199330	−	0.257210i
$67$	9.38338e10			1.03731			0.518657	−	0.854982i	$-0.326432\pi$
$67$	9.38338e10			1.03731			0.518657	+	0.854982i	$0.326432\pi$
$68$	−4.20369e10	+	5.78588e10i	−0.425184	+	0.585216i
$69$	2.52308e10	−	7.76525e10i	0.233796	−	0.719550i
$70$	8.24845e9	+	2.53861e10i	0.0701106	+	0.215778i
$71$	1.23673e11	−	8.98535e10i	0.965436	−	0.701431i	0.0110295	−	0.999939i	$-0.496489\pi$
$71$	1.23673e11	−	8.98535e10i	0.965436	−	0.701431i	0.954407	+	0.298509i	$0.0964891\pi$
$72$	2.28201e10	+	3.14091e10i	0.163803	+	0.225456i
$73$	−4.22068e10	+	1.37138e10i	−0.278898	+	0.0906195i	−0.445126	−	0.895468i	$-0.646841\pi$
$73$	−4.22068e10	+	1.37138e10i	−0.278898	+	0.0906195i	0.166228	+	0.986087i	$0.446841\pi$
$74$	1.39918e11	+	4.54621e10i	0.852086	+	0.276859i
$75$	5.42592e10	+	3.94216e10i	0.304864	+	0.221497i
$76$		−	1.64610e11i		−	0.854230i
$77$	1.47861e11	−	5.31591e10i	0.709429	−	0.255055i
$78$	8.24340e10			0.366049
$79$	−5.73849e10	+	7.89836e10i	−0.236067	+	0.324918i	−0.910571	−	0.413353i	$-0.864358\pi$
$79$	−5.73849e10	+	7.89836e10i	−0.236067	+	0.324918i	0.674504	+	0.738271i	$0.264358\pi$
$80$	8.61933e9	−	2.65276e10i	0.0328801	−	0.101195i
$81$	3.57407e10	+	1.09999e11i	0.126547	+	0.389473i
$82$	−2.08696e11	+	1.51626e11i	−0.686485	+	0.498760i
$83$	1.62315e11	+	2.23407e11i	0.496466	+	0.683327i	0.981564	−	0.191133i	$-0.0612162\pi$
$83$	1.62315e11	+	2.23407e11i	0.496466	+	0.683327i	−0.485098	+	0.874460i	$0.661216\pi$
$84$	5.79559e10	−	1.88310e10i	0.164976	−	0.0536041i
$85$	2.20861e11	+	7.17622e10i	0.585607	+	0.190275i
$86$	3.29656e10	+	2.39509e10i	0.0814835	+	0.0592012i
$87$		−	3.28781e11i		−	0.758214i
$88$	−1.57652e11	−	4.58779e10i	−0.339471	−	0.0987889i
$89$	−6.25780e11			−1.25916			−0.629581	−	0.776935i	$-0.716773\pi$
$89$	−6.25780e11			−1.25916			−0.629581	+	0.776935i	$0.716773\pi$
$90$	7.41001e10	−	1.01990e11i	0.139432	−	0.191912i
$91$	−1.48816e11	+	4.58008e11i	−0.262060	+	0.806538i
$92$	−1.54026e11	−	4.74043e11i	−0.254019	−	0.781791i
$93$	3.45779e10	−	2.51223e10i	0.0534443	−	0.0388295i
$94$	6.63687e10	+	9.13487e10i	0.0962047	+	0.132414i
$95$	−5.08351e11	+	1.65173e11i	−0.691548	+	0.224698i
$96$	−6.05619e10	−	1.96777e10i	−0.0773699	−	0.0251390i
$97$	−8.44850e11	−	6.13819e11i	−1.01426	−	0.736903i	−0.0491614	−	0.998791i	$-0.515655\pi$
$97$	−8.44850e11	−	6.13819e11i	−1.01426	−	0.736903i	−0.965098	+	0.261888i	$0.915655\pi$
$98$		−	2.70384e11i		−	0.305228i
$99$	−6.13588e11	−	4.17392e11i	−0.651726	−	0.443336i
$100$	4.09428e11			0.409428
$101$	−8.83774e11	+	1.21641e12i	−0.832555	+	1.14591i	0.154887	+	0.987932i	$0.450499\pi$
$101$	−8.83774e11	+	1.21641e12i	−0.832555	+	1.14591i	−0.987442	+	0.157981i	$0.949501\pi$
$102$	1.63831e11	−	5.04221e11i	0.145478	−	0.447734i
$103$	−1.21644e11	−	3.74381e11i	−0.101875	−	0.313538i	0.887110	−	0.461559i	$-0.152710\pi$
$103$	−1.21644e11	−	3.74381e11i	−0.101875	−	0.313538i	−0.988984	+	0.148021i	$0.952710\pi$
$104$	4.07123e11	−	2.95792e11i	0.321756	−	0.233769i
$105$	−1.16309e11	−	1.60085e11i	−0.0867912	−	0.119458i
$106$	3.59429e11	−	1.16786e11i	0.253383	−	0.0823292i
$107$	7.05516e11	+	2.29236e11i	0.470115	+	0.152750i	0.534488	−	0.845176i	$-0.320505\pi$
$107$	7.05516e11	+	2.29236e11i	0.470115	+	0.152750i	−0.0643726	+	0.997926i	$0.520505\pi$
$108$	−5.28241e11	−	3.83790e11i	−0.332881	−	0.241853i
$109$			2.75993e12i			1.64565i	0.568292	+	0.822827i	$0.307604\pi$
$109$			2.75993e12i			1.64565i	−0.568292	+	0.822827i	$0.692396\pi$
$110$	1.65104e10	+	5.32898e11i	0.00931967	+	0.300807i
$111$	−1.09061e12			−0.583086
$112$	2.18661e11	−	3.00961e11i	0.110781	−	0.152476i
$113$	2.96391e11	−	9.12197e11i	0.142362	−	0.438145i	−0.854300	−	0.519780i	$-0.826014\pi$
$113$	2.96391e11	−	9.12197e11i	0.142362	−	0.438145i	0.996662	+	0.0816347i	$0.0260141\pi$
$114$	3.77087e11	+	1.16055e12i	0.171796	+	0.528733i
$115$	−1.30939e12	+	9.51330e11i	−0.566087	+	0.411286i
$116$	−1.17974e12	−	1.62378e12i	−0.484217	−	0.666467i
$117$	2.16313e12	−	7.02845e11i	0.843273	−	0.273996i
$118$	2.95927e12	+	9.61527e11i	1.09621	+	0.356180i
$119$	2.50572e12	+	1.82051e12i	0.882371	+	0.641080i
$120$			2.06773e11i			0.0692479i
$121$	3.13241e12	−	1.94284e11i	0.998082	−	0.0619050i
$122$	−1.82473e12			−0.553401
$123$	1.12403e12	−	1.54709e12i	0.324599	−	0.446772i
$124$	8.06280e10	−	2.48147e11i	0.0221797	−	0.0682621i
$125$	−9.12541e11	−	2.80851e12i	−0.239217	−	0.736234i
$126$	1.36025e12	−	9.88281e11i	0.339935	−	0.246977i
$127$	3.36808e12	+	4.63576e12i	0.802713	+	1.10484i	0.992407	+	0.122996i	$0.0392502\pi$
$127$	3.36808e12	+	4.63576e12i	0.802713	+	1.10484i	−0.189695	+	0.981843i	$0.560750\pi$
$128$	−3.69710e11	+	1.20126e11i	−0.0840623	+	0.0273135i
$129$	−2.87284e11	−	9.33444e10i	−0.0623410	−	0.0202558i
$130$	−1.32199e12	−	9.60481e11i	−0.273884	−	0.198989i
$131$		−	9.24935e12i		−	1.83014i	−0.403298	−	0.915069i	$-0.632136\pi$
$131$		−	9.24935e12i		−	1.83014i	0.403298	−	0.915069i	$-0.367864\pi$
$132$	1.21659e12	−	3.76928e10i	0.229986	−	0.00712549i
$133$	−7.12885e12			−1.28798
$134$	−2.49599e12	+	3.43544e12i	−0.431136	+	0.593408i
$135$	−6.55176e11	+	2.01643e12i	−0.108232	+	0.333104i
$136$	−1.00014e12	−	3.07810e12i	−0.158061	−	0.486463i
$137$	6.32683e12	−	4.59671e12i	0.956892	−	0.695223i	0.00446502	−	0.999990i	$-0.498579\pi$
$137$	6.32683e12	−	4.59671e12i	0.956892	−	0.695223i	0.952427	+	0.304767i	$0.0985787\pi$
$138$	2.17186e12	+	2.98932e12i	0.314455	+	0.432810i
$139$	9.52534e12	−	3.09497e12i	1.32066	−	0.429109i	0.437940	−	0.899004i	$-0.355708\pi$
$139$	9.52534e12	−	3.09497e12i	1.32066	−	0.429109i	0.882722	+	0.469895i	$0.155708\pi$
$140$	−1.14884e12	−	3.73282e11i	−0.152578	−	0.0495757i
$141$	−6.77182e11	−	4.92001e11i	−0.0861768	−	0.0626111i
$142$			6.91801e12i			0.843822i
$143$	−5.41021e12	+	7.95328e12i	−0.632700	+	0.930101i
$144$	−1.75697e12			−0.197055
$145$	−3.83080e12	+	5.27264e12i	−0.412175	+	0.567310i
$146$	6.20617e11	−	1.91006e12i	0.0640777	−	0.197211i
$147$	6.19393e11	+	1.90629e12i	0.0613850	+	0.188923i
$148$	−5.38629e12	+	3.91337e12i	−0.512530	+	0.372375i
$149$	−5.94479e12	−	8.18230e12i	−0.543274	−	0.747752i	0.445807	−	0.895129i	$-0.352917\pi$
$149$	−5.94479e12	−	8.18230e12i	−0.543274	−	0.747752i	−0.989080	+	0.147377i	$0.952917\pi$
$150$	−2.88660e12	+	9.37914e11i	−0.253419	+	0.0823409i
$151$	5.43543e12	+	1.76608e12i	0.458535	+	0.148987i	0.529171	−	0.848515i	$-0.322503\pi$
$151$	5.43543e12	+	1.76608e12i	0.458535	+	0.148987i	−0.0706364	+	0.997502i	$0.522503\pi$
$152$	6.02669e12	+	4.37865e12i	0.488672	+	0.355041i
$153$		−	1.46280e13i		−	1.14035i
$154$	−1.98686e12	+	6.82751e12i	−0.148951	+	0.511845i
$155$	−8.47237e11			−0.0610962
$156$	−2.19276e12	+	3.01807e12i	−0.152140	+	0.209402i
$157$	−7.01460e11	+	2.15887e12i	−0.0468387	+	0.144155i	−0.971741	−	0.236051i	$-0.924147\pi$
$157$	−7.01460e11	+	2.15887e12i	−0.0468387	+	0.144155i	0.924902	+	0.380206i	$0.124147\pi$
$158$	−1.36529e12	−	4.20194e12i	−0.0877574	−	0.270090i
$159$	−2.26656e12	+	1.64675e12i	−0.140276	+	0.101917i
$160$	7.41951e11	+	1.02121e12i	0.0442237	+	0.0608687i
$161$	−2.05296e13	+	6.67048e12i	−1.17876	+	0.383002i
$162$	−4.97797e12	−	1.61744e12i	−0.275399	−	0.0894825i
$163$	−4.99933e12	−	3.63223e12i	−0.266555	−	0.193663i	0.446477	−	0.894795i	$-0.352678\pi$
$163$	−4.99933e12	−	3.63223e12i	−0.266555	−	0.193663i	−0.713032	+	0.701132i	$0.752678\pi$
$164$		−	1.16740e13i		−	0.600009i
$165$	−1.33716e12	−	3.71928e12i	−0.0662644	−	0.184313i
$166$	−1.24970e13			−0.597249
$167$	3.94464e12	−	5.42933e12i	0.181848	−	0.250292i	−0.708355	−	0.705856i	$-0.750562\pi$
$167$	3.94464e12	−	5.42933e12i	0.181848	−	0.250292i	0.890203	+	0.455564i	$0.150562\pi$
$168$	−8.52194e11	+	2.62278e12i	−0.0379038	+	0.116656i
$169$	−1.91073e12	−	5.88061e12i	−0.0820122	−	0.252408i
$170$	−8.50229e12	+	6.17727e12i	−0.352243	+	0.255920i
$171$	1.97901e13	+	2.72388e13i	0.791538	+	1.08946i
$172$	−1.75378e12	+	5.69836e11i	−0.0677335	+	0.0220079i
$173$	3.03267e12	+	9.85376e11i	0.113123	+	0.0367557i	0.365031	−	0.930995i	$-0.381058\pi$
$173$	3.03267e12	+	9.85376e11i	0.113123	+	0.0367557i	−0.251909	+	0.967751i	$0.581058\pi$
$174$	1.20373e13	+	8.74563e12i	0.433745	+	0.315134i
$175$		−	1.77313e13i		−	0.617324i
$176$	5.87324e12	−	4.55158e12i	0.197607	−	0.153139i
$177$	−2.30665e13			−0.750140
$178$	1.66458e13	−	2.29110e13i	0.523341	−	0.720318i
$179$	1.03074e13	−	3.17230e13i	0.313352	−	0.964398i	−0.663075	−	0.748553i	$-0.730749\pi$
$179$	1.03074e13	−	3.17230e13i	0.313352	−	0.964398i	0.976427	−	0.215846i	$-0.0692509\pi$
$180$	1.76298e12	+	5.42589e12i	0.0518337	+	0.159528i
$181$	−3.84560e12	+	2.79399e12i	−0.109368	+	0.0794609i	−0.641125	−	0.767436i	$-0.721532\pi$
$181$	−3.84560e12	+	2.79399e12i	−0.109368	+	0.0794609i	0.531757	+	0.846897i	$0.321532\pi$
$182$	−1.28100e13	−	1.76315e13i	−0.352470	−	0.485133i
$183$	1.28649e13	−	4.18008e12i	0.342532	−	0.111295i
$184$	2.14527e13	+	6.97041e12i	0.552809	+	0.179619i
$185$	1.74901e13	+	1.27073e13i	0.436276	+	0.316973i
$186$			1.93422e12i			0.0467120i
$187$	3.78952e13	+	4.88990e13i	0.886206	+	1.14354i
$188$	−5.10987e12			−0.115734
$189$	−1.66210e13	+	2.28768e13i	−0.364658	+	0.501909i
$190$	7.47489e12	−	2.30054e13i	0.158885	−	0.488998i
$191$	−4.98767e12	−	1.53505e13i	−0.102730	−	0.316171i	0.886461	−	0.462804i	$-0.153156\pi$
$191$	−4.98767e12	−	1.53505e13i	−0.102730	−	0.316171i	−0.989191	+	0.146633i	$0.953156\pi$
$192$	2.33139e12	−	1.69386e12i	0.0465380	−	0.0338119i
$193$	3.38323e13	+	4.65662e13i	0.654617	+	0.901004i	0.999288	−	0.0377199i	$-0.0120095\pi$
$193$	3.38323e13	+	4.65662e13i	0.654617	+	0.901004i	−0.344671	+	0.938724i	$0.612009\pi$
$194$	4.49462e13	−	1.46039e13i	0.843107	−	0.273942i
$195$	1.15207e13	+	3.74331e12i	0.209542	+	0.0680844i
$196$	9.89927e12	+	7.19224e12i	0.174609	+	0.126861i
$197$			8.30837e12i			0.142141i	0.997471	+	0.0710704i	$0.0226415\pi$
$197$			8.30837e12i			0.142141i	−0.997471	+	0.0710704i	$0.977359\pi$
$198$	3.16030e13	−	1.13620e13i	0.524490	−	0.188565i
$199$	1.39191e13			0.224126			0.112063	−	0.993701i	$-0.464254\pi$
$199$	1.39191e13			0.224126			0.112063	+	0.993701i	$0.464254\pi$
$200$	−1.08908e13	+	1.49900e13i	−0.170169	+	0.234218i
$201$	9.72769e12	−	2.99388e13i	0.147514	−	0.454002i
$202$	−2.10266e13	−	6.47133e13i	−0.309501	−	0.952545i
$203$	−7.03219e13	+	5.10918e13i	−1.00488	+	0.730088i
$204$	1.41026e13	+	1.94105e13i	0.195667	+	0.269313i
$205$	−3.60520e13	+	1.17140e13i	−0.485742	+	0.157827i
$206$	1.69425e13	+	5.50496e12i	0.221705	+	0.0720363i
$207$	8.24788e13	+	5.99244e13i	1.04838	+	0.761695i
$208$			2.27737e13i			0.281225i
$209$	−1.36720e14	−	3.97865e13i	−1.64041	−	0.477373i
$210$	8.95484e12			0.104410
$211$	6.93778e13	−	9.54903e13i	0.786187	−	1.08209i	−0.208386	−	0.978047i	$-0.566821\pi$
$211$	6.93778e13	−	9.54903e13i	0.786187	−	1.08209i	0.994572	−	0.104046i	$-0.0331790\pi$
$212$	−5.28511e12	+	1.62659e13i	−0.0582155	+	0.179169i
$213$	−1.58477e13	−	4.87742e13i	−0.169703	−	0.522291i
$214$	−2.71596e13	+	1.97326e13i	−0.282775	+	0.205448i
$215$	3.51956e12	+	4.84425e12i	0.0356334	+	0.0490451i
$216$	2.81026e13	−	9.13107e12i	0.276709	−	0.0899082i
$217$	−1.07466e13	−	3.49180e12i	−0.102924	−	0.0334419i
$218$	−1.01046e14	−	7.34144e13i	−0.941415	−	0.683978i
$219$			1.48883e13i			0.134952i
$220$	−1.99496e13	−	1.35707e13i	−0.175954	−	0.119692i
$221$	−1.89607e14			−1.62743
$222$	2.90104e13	−	3.99294e13i	0.242346	−	0.333561i
$223$	−3.18253e13	+	9.79481e13i	−0.258787	+	0.796465i	0.734273	+	0.678855i	$0.237523\pi$
$223$	−3.18253e13	+	9.79481e13i	−0.258787	+	0.796465i	−0.993060	+	0.117610i	$0.962477\pi$
$224$	5.20236e12	+	1.60112e13i	0.0411825	+	0.126747i
$225$	−6.77500e13	+	4.92232e13i	−0.522172	+	0.379381i
$226$	2.55133e13	+	3.51160e13i	0.191476	+	0.263545i
$227$	−1.89966e12	+	6.17237e11i	−0.0138842	+	0.00451125i	−0.315951	−	0.948776i	$-0.602323\pi$
$227$	−1.89966e12	+	6.17237e11i	−0.0138842	+	0.00451125i	0.302067	+	0.953287i	$0.402323\pi$
$228$	−5.25207e13	−	1.70650e13i	−0.373871	−	0.121478i
$229$	−2.49682e13	−	1.81405e13i	−0.173131	−	0.125787i	0.497845	−	0.867266i	$-0.334125\pi$
$229$	−2.49682e13	−	1.81405e13i	−0.173131	−	0.125787i	−0.670976	+	0.741479i	$0.734125\pi$
$230$		−	7.32449e13i		−	0.494778i
$231$	−1.63238e12	−	5.26877e13i	−0.0107436	−	0.346767i
$232$	9.08310e13			0.582514
$233$	4.29948e13	−	5.91772e13i	0.268708	−	0.369844i	−0.653245	−	0.757146i	$-0.726593\pi$
$233$	4.29948e13	−	5.91772e13i	0.268708	−	0.369844i	0.921953	+	0.387302i	$0.126593\pi$
$234$	−3.18071e13	+	9.78923e13i	−0.193744	+	0.596284i
$235$	5.12735e12	+	1.57804e13i	0.0304429	+	0.0936936i
$236$	−1.13920e14	+	8.27680e13i	−0.659371	+	0.479061i
$237$	1.92516e13	+	2.64975e13i	0.108636	+	0.149525i
$238$	−1.33305e14	+	4.33134e13i	−0.733474	+	0.238320i
$239$	−8.57008e13	−	2.78459e13i	−0.459830	−	0.149408i	0.0699364	−	0.997551i	$-0.477720\pi$
$239$	−8.57008e13	−	2.78459e13i	−0.459830	−	0.149408i	−0.529766	+	0.848144i	$0.677720\pi$
$240$	−7.57037e12	−	5.50019e12i	−0.0396141	−	0.0287813i
$241$		−	3.38514e13i		−	0.172773i	−0.996262	−	0.0863863i	$-0.972468\pi$
$241$		−	3.38514e13i		−	0.172773i	0.996262	−	0.0863863i	$-0.0275319\pi$
$242$	−7.62093e13	+	1.19852e14i	−0.379416	+	0.596694i
$243$	2.08235e14			1.01138
$244$	4.85381e13	−	6.68069e13i	0.230008	−	0.316579i
$245$	1.22780e13	−	3.77879e13i	0.0567718	−	0.174726i
$246$	2.67428e13	+	8.23058e13i	0.120669	+	0.371381i
$247$	3.53067e14	−	2.56518e14i	1.55480	−	1.12963i
$248$	6.94044e12	+	9.55269e12i	0.0298316	+	0.0410597i
$249$	8.81077e13	−	2.86279e13i	0.369673	−	0.120114i
$250$	1.27099e14	+	4.12969e13i	0.520596	+	0.169152i
$251$	3.16763e14	+	2.30141e14i	1.26675	+	0.920349i	0.999068	−	0.0431580i	$-0.0137419\pi$
$251$	3.16763e14	+	2.30141e14i	1.26675	+	0.920349i	0.267683	+	0.963507i	$0.413742\pi$
$252$			7.60899e13i			0.297114i
$253$	−4.30952e14	+	1.33518e13i	−1.64326	+	0.0509118i
$254$	−2.59316e14			−0.965665
$255$	4.57931e13	−	6.30288e13i	0.166555	−	0.229244i
$256$	5.43628e12	−	1.67312e13i	0.0193136	−	0.0594410i
$257$	−1.67783e14	−	5.16382e14i	−0.582302	−	1.79214i	−0.609844	−	0.792521i	$-0.708768\pi$
$257$	−1.67783e14	−	5.16382e14i	−0.582302	−	1.79214i	0.0275418	−	0.999621i	$-0.491232\pi$
$258$	1.10593e13	−	8.03507e12i	0.0374982	−	0.0272440i
$259$	1.69478e14	+	2.33267e14i	0.561456	+	0.772778i
$260$	7.03301e13	−	2.28516e13i	0.227668	−	0.0739737i
$261$	3.90435e14	+	1.26860e14i	1.23511	+	0.401312i
$262$	3.38637e14	+	2.46034e14i	1.04695	+	0.760654i
$263$			7.03069e13i			0.212453i	0.994342	+	0.106227i	$0.0338769\pi$
$263$			7.03069e13i			0.212453i	−0.994342	+	0.106227i	$0.966123\pi$
$264$	−3.09816e13	+	4.55445e13i	−0.0915123	+	0.134528i
$265$	5.55358e13			0.160361
$266$	1.89628e14	−	2.61001e14i	0.535320	−	0.736805i
$267$	−6.48742e13	+	1.99662e14i	−0.179062	+	0.551097i
$268$	−5.93843e13	−	1.82766e14i	−0.160274	−	0.493272i
$269$	−1.38000e14	+	1.00263e14i	−0.364220	+	0.264621i	−0.754810	−	0.655943i	$-0.772271\pi$
$269$	−1.38000e14	+	1.00263e14i	−0.364220	+	0.264621i	0.390590	+	0.920565i	$0.372271\pi$
$270$	−5.63975e13	−	7.76244e13i	−0.145572	−	0.200362i
$271$	−5.34021e13	+	1.73514e13i	−0.134816	+	0.0438045i	−0.375648	−	0.926762i	$-0.622580\pi$
$271$	−5.34021e13	+	1.73514e13i	−0.134816	+	0.0438045i	0.240832	+	0.970567i	$0.422580\pi$
$272$	1.39299e14	+	4.52610e13i	0.343981	+	0.111766i
$273$	1.30705e14	+	9.49628e13i	0.315731	+	0.229392i
$274$			3.53911e14i			0.836354i
$275$	9.89594e13	−	3.40057e14i	0.228802	−	0.786241i
$276$	−1.67216e14			−0.378290
$277$	4.83613e14	−	6.65637e14i	1.07058	−	1.47353i	0.201095	−	0.979572i	$-0.435550\pi$
$277$	4.83613e14	−	6.65637e14i	1.07058	−	1.47353i	0.869486	−	0.493957i	$-0.164450\pi$
$278$	−1.40062e14	+	4.31068e14i	−0.303426	+	0.933849i
$279$	1.64915e13	+	5.07555e13i	0.0349650	+	0.107611i
$280$	4.42260e13	−	3.21320e13i	0.0917760	−	0.0666792i
$281$	−3.15691e14	−	4.34511e14i	−0.641245	−	0.882597i	0.357437	−	0.933937i	$-0.383651\pi$
$281$	−3.15691e14	−	4.34511e14i	−0.641245	−	0.882597i	−0.998681	+	0.0513399i	$0.983651\pi$
$282$	3.60262e13	−	1.17056e13i	0.0716348	−	0.0232756i
$283$	−4.96256e13	−	1.61243e13i	−0.0966022	−	0.0313879i	0.260317	−	0.965523i	$-0.416173\pi$
$283$	−4.96256e13	−	1.61243e13i	−0.0966022	−	0.0313879i	−0.356919	+	0.934135i	$0.616173\pi$
$284$	−2.53282e14	−	1.84020e14i	−0.482718	−	0.350715i
$285$			1.79319e14i			0.334624i
$286$	−1.47273e14	−	4.09636e14i	−0.269108	−	0.748518i
$287$	−5.05574e14			−0.904676
$288$	4.67355e13	−	6.43259e13i	0.0819016	−	0.112728i
$289$	−1.96790e14	+	6.05659e14i	−0.337767	+	1.03954i
$290$	−9.11419e13	−	2.80506e14i	−0.153225	−	0.471578i
$291$	−2.83431e14	+	2.05925e14i	−0.466756	+	0.339118i
$292$	5.34226e13	+	7.35299e13i	0.0861843	+	0.118622i
$293$	−4.94331e14	+	1.60618e14i	−0.781290	+	0.253856i	−0.672391	−	0.740196i	$-0.734733\pi$
$293$	−4.94331e14	+	1.60618e14i	−0.781290	+	0.253856i	−0.108899	+	0.994053i	$0.534733\pi$
$294$	−8.62690e13	−	2.80305e13i	−0.133589	−	0.0434057i
$295$	3.69916e14	+	2.68760e14i	0.561269	+	0.407786i
$296$		−	3.01299e14i		−	0.447968i
$297$	−4.46439e14	+	3.45977e14i	−0.650464	+	0.504090i
$298$	4.57702e14			0.653559
$299$	7.76736e14	−	1.06909e15i	1.08704	−	1.49618i
$300$	4.24452e13	−	1.30633e14i	0.0582238	−	0.179194i
$301$	2.46782e13	+	7.59517e13i	0.0331829	+	0.102127i
$302$	−2.09243e14	+	1.52024e14i	−0.275809	+	0.200387i
$303$	2.96489e14	+	4.08083e14i	0.383136	+	0.527342i
$304$	−3.20621e14	+	1.04176e14i	−0.406210	+	0.131986i
$305$	−2.55018e14	−	8.28605e13i	−0.316791	−	0.102932i
$306$	5.35560e14	+	3.89107e14i	0.652348	+	0.473959i
$307$			3.91520e14i			0.467653i	0.972278	+	0.233826i	$0.0751248\pi$
$307$			3.91520e14i			0.467653i	−0.972278	+	0.233826i	$0.924875\pi$
$308$	−1.97118e14	−	2.54355e14i	−0.230899	−	0.297945i
$309$	−1.32061e14			−0.151714
$310$	2.25366e13	−	3.10190e13i	0.0253932	−	0.0349508i
$311$	−4.68414e14	+	1.44163e15i	−0.517688	+	1.59328i	0.260650	+	0.965433i	$0.416063\pi$
$311$	−4.68414e14	+	1.44163e15i	−0.517688	+	1.59328i	−0.778338	+	0.627846i	$0.783937\pi$
$312$	−5.21698e13	−	1.60562e14i	−0.0565576	−	0.174067i
$313$	−1.23566e15	+	8.97757e14i	−1.31411	+	0.954757i	−0.314125	+	0.949382i	$0.601711\pi$
$313$	−1.23566e15	+	8.97757e14i	−1.31411	+	0.954757i	−0.999986	+	0.00537552i	$0.998289\pi$
$314$	−6.03816e13	−	8.31081e13i	−0.0629980	−	0.0867093i
$315$	2.34982e14	−	7.63503e13i	0.240531	−	0.0781533i
$316$	1.90158e14	+	6.17862e13i	0.190982	+	0.0620539i
$317$	−4.91125e13	−	3.56823e13i	−0.0483990	−	0.0351639i	0.563323	−	0.826237i	$-0.309523\pi$
$317$	−4.91125e13	−	3.56823e13i	−0.0483990	−	0.0351639i	−0.611722	+	0.791073i	$0.709523\pi$
$318$		−	1.26787e14i		−	0.122606i
$319$	−1.63380e15	+	5.87386e14i	−1.55044	+	0.557416i
$320$	−5.71243e13			−0.0532012
$321$	1.46281e14	−	2.01338e14i	0.133708	−	0.184033i
$322$	3.01871e14	−	9.29064e14i	0.270824	−	0.833510i
$323$	−8.67342e14	−	2.66941e15i	−0.763793	−	2.35071i
$324$	1.91632e14	−	1.39229e14i	0.165653	−	0.120354i
$325$	6.38029e14	+	8.78171e14i	0.541427	+	0.745210i
$326$	2.65966e14	−	8.64175e13i	0.221575	−	0.0719939i
$327$	8.80586e14	+	2.86120e14i	0.720253	+	0.234024i
$328$	4.27409e14	+	3.10531e14i	0.343242	+	0.249380i
$329$			2.21296e14i			0.174501i
$330$	1.71739e14	+	4.99774e13i	0.132980	+	0.0386981i
$331$	−9.35876e13			−0.0711624			−0.0355812	−	0.999367i	$-0.511328\pi$
$331$	−9.35876e13			−0.0711624			−0.0355812	+	0.999367i	$0.511328\pi$
$332$	3.32421e14	−	4.57538e14i	0.248233	−	0.341663i
$333$	4.20812e14	−	1.29513e15i	0.308619	−	0.949832i
$334$	9.38504e13	+	2.88842e14i	0.0676017	+	0.208057i
$335$	−5.04834e14	+	3.66783e14i	−0.357174	+	0.259502i
$336$	−7.33567e13	−	1.00967e14i	−0.0509805	−	0.0701687i
$337$	1.65533e15	−	5.37848e14i	1.13007	−	0.367181i	0.316466	−	0.948604i	$-0.397504\pi$
$337$	1.65533e15	−	5.37848e14i	1.13007	−	0.367181i	0.813602	+	0.581423i	$0.197504\pi$
$338$	2.66126e14	+	8.64697e13i	0.178479	+	0.0579914i
$339$	−2.60320e14	−	1.89134e14i	−0.171518	−	0.124615i
$340$		−	4.75602e14i		−	0.307872i
$341$	−1.86615e14	−	1.26944e14i	−0.118692	−	0.0807397i
$342$	−1.52368e15			−0.952222
$343$	1.03306e15	−	1.42189e15i	0.634400	−	0.873176i
$344$	2.57878e13	−	7.93668e13i	0.0155620	−	0.0478948i
$345$	1.67789e14	+	5.16401e14i	0.0995058	+	0.306247i
$346$	−1.16746e14	+	8.48210e13i	−0.0680433	+	0.0494364i
$347$	1.64278e15	+	2.26109e15i	0.941028	+	1.29521i	0.955399	+	0.295317i	$0.0954253\pi$
$347$	1.64278e15	+	2.26109e15i	0.941028	+	1.29521i	−0.0143714	+	0.999897i	$0.504575\pi$
$348$	−6.40389e14	+	2.08075e14i	−0.360552	+	0.117151i
$349$	−8.00951e13	−	2.60245e13i	−0.0443255	−	0.0144022i	0.286770	−	0.957999i	$-0.407418\pi$
$349$	−8.00951e13	−	2.60245e13i	−0.0443255	−	0.0144022i	−0.331096	+	0.943597i	$0.607418\pi$
$350$	6.49178e14	+	4.71656e14i	0.353147	+	0.256576i
$351$		−	1.73108e15i		−	0.925711i
$352$	1.04132e13	+	3.36103e14i	0.00547431	+	0.176692i
$353$	1.37122e14			0.0708696			0.0354348	−	0.999372i	$-0.488718\pi$
$353$	1.37122e14			0.0708696			0.0354348	+	0.999372i	$0.488718\pi$
$354$	6.13572e14	−	8.44510e14i	0.311778	−	0.429126i
$355$	−3.14145e14	+	9.66838e14i	−0.156949	+	0.483041i
$356$	3.96035e14	+	1.21887e15i	0.194551	+	0.598767i
$357$	8.40622e14	−	6.10748e14i	0.406061	−	0.295021i
$358$	8.87262e14	+	1.22121e15i	0.421458	+	0.580087i
$359$	−1.43063e15	+	4.64839e14i	−0.668282	+	0.217138i	−0.623458	−	0.781857i	$-0.714273\pi$
$359$	−1.43063e15	+	4.64839e14i	−0.668282	+	0.217138i	−0.0448243	+	0.998995i	$0.514273\pi$
$360$	−2.45548e14	−	7.97833e13i	−0.112803	−	0.0366520i
$361$	3.43588e15	+	2.49631e15i	1.55237	+	1.12786i
$362$		−	2.15115e14i		−	0.0955916i
$363$	2.62746e14	−	1.01957e15i	0.114841	−	0.445634i
$364$	9.86272e14			0.424022
$365$	1.73471e14	−	2.38762e14i	0.0733617	−	0.100974i
$366$	−1.89169e14	+	5.82201e14i	−0.0786978	+	0.242207i
$367$	−9.25838e14	−	2.84944e15i	−0.378912	−	1.16617i	−0.940801	−	0.338959i	$-0.889925\pi$
$367$	−9.25838e14	−	2.84944e15i	−0.378912	−	1.16617i	0.561889	−	0.827213i	$-0.310075\pi$
$368$	−8.25845e14	+	6.00012e14i	−0.332515	+	0.241587i
$369$	1.40350e15	+	1.93176e15i	0.555975	+	0.765234i
$370$	−9.30476e14	+	3.02330e14i	−0.362656	+	0.117834i
$371$	7.04436e14	+	2.28885e14i	0.270146	+	0.0877757i
$372$	−7.08156e13	−	5.14505e13i	−0.0267221	−	0.0194148i
$373$			1.66723e15i			0.619073i	0.950888	+	0.309536i	$0.100174\pi$
$373$			1.66723e15i			0.619073i	−0.950888	+	0.309536i	$0.899826\pi$
$374$	−2.79830e15	+	8.66976e13i	−1.02250	+	0.0316794i
$375$	−9.90690e14			−0.356246
$376$	1.35923e14	−	1.87082e14i	0.0481023	−	0.0662072i
$377$	1.64435e15	−	5.06080e15i	0.572726	−	1.76267i
$378$	−3.95444e14	−	1.21705e15i	−0.135561	−	0.417214i
$379$	−3.03684e15	+	2.20640e15i	−1.02468	+	0.744472i	−0.967237	−	0.253877i	$-0.918294\pi$
$379$	−3.03684e15	+	2.20640e15i	−1.02468	+	0.744472i	−0.0574411	+	0.998349i	$0.518294\pi$
$380$	6.43437e14	+	8.85616e14i	0.213700	+	0.294133i
$381$	1.82826e15	−	5.94038e14i	0.597707	−	0.194207i
$382$	6.94683e14	+	2.25716e14i	0.223566	+	0.0726412i
$383$	1.60267e15	+	1.16441e15i	0.507753	+	0.368904i	0.811970	−	0.583699i	$-0.198395\pi$
$383$	1.60267e15	+	1.16441e15i	0.507753	+	0.368904i	−0.304218	+	0.952603i	$0.598395\pi$
$384$			1.30414e14i			0.0406757i
$385$	−5.87713e14	+	8.63968e14i	−0.180468	+	0.265298i
$386$	−2.60482e15			−0.787506
$387$	2.21697e14	−	3.05140e14i	0.0659924	−	0.0908308i
$388$	−6.60898e14	+	2.03403e15i	−0.193706	+	0.596167i
$389$	−8.31394e14	−	2.55877e15i	−0.239944	−	0.738471i	−0.996427	−	0.0844579i	$-0.973084\pi$
$389$	−8.31394e14	−	2.55877e15i	−0.239944	−	0.738471i	0.756483	−	0.654013i	$-0.226916\pi$
$390$	−4.43502e14	+	3.22223e14i	−0.126040	+	0.0915733i
$391$	−4.99553e15	−	6.87576e15i	−1.39805	−	1.92424i
$392$	−5.26644e14	+	1.71117e14i	−0.145144	+	0.0471603i
$393$	−2.95111e15	−	9.58875e14i	−0.800996	−	0.260259i
$394$	−3.04186e14	−	2.21004e14i	−0.0813132	−	0.0590775i
$395$		−	6.49248e14i		−	0.170934i
$396$	−4.24661e14	+	1.45928e15i	−0.110121	+	0.378413i
$397$	−5.07626e15			−1.29658			−0.648292	−	0.761392i	$-0.724516\pi$
$397$	−5.07626e15			−1.29658			−0.648292	+	0.761392i	$0.724516\pi$
$398$	−3.70250e14	+	5.09605e14i	−0.0931528	+	0.128214i
$399$	−7.39044e14	+	2.27454e15i	−0.183161	+	0.563711i
$400$	−2.59114e14	−	7.97470e14i	−0.0632601	−	0.194695i
$401$	−6.22264e14	+	4.52101e14i	−0.149661	+	0.108735i	−0.660096	−	0.751181i	$-0.729484\pi$
$401$	−6.22264e14	+	4.52101e14i	−0.149661	+	0.108735i	0.510435	+	0.859916i	$0.329484\pi$
$402$	8.37358e14	+	1.15252e15i	0.198406	+	0.273082i
$403$	6.57890e14	−	2.13761e14i	0.153576	−	0.0498998i
$404$	2.92859e15	+	9.51557e14i	0.673551	+	0.218850i
$405$	−6.22257e14	−	4.52096e14i	−0.141007	−	0.102447i
$406$		−	3.93367e15i		−	0.878297i
$407$	1.94844e15	+	5.41954e15i	0.428667	+	1.19233i
$408$	−1.08579e15			−0.235388
$409$	2.87524e14	−	3.95742e14i	0.0614234	−	0.0845420i	−0.777200	−	0.629253i	$-0.783361\pi$
$409$	2.87524e14	−	3.95742e14i	0.0614234	−	0.0845420i	0.838624	+	0.544711i	$0.183361\pi$
$410$	5.30115e14	−	1.63153e15i	0.111601	−	0.343472i
$411$	−8.10735e14	−	2.49519e15i	−0.168201	−	0.517669i
$412$	−6.52221e14	+	4.73866e14i	−0.133356	+	0.0968886i
$413$	3.58448e15	+	4.93361e15i	0.722313	+	0.994179i
$414$	−4.38789e15	+	1.42571e15i	−0.871473	+	0.283159i
$415$	−1.74653e15	−	5.67483e14i	−0.341892	−	0.111087i
$416$	−8.33789e14	−	6.05783e14i	−0.160878	−	0.116885i
$417$		−	3.36002e15i		−	0.639037i
$418$	5.09342e15	−	3.94724e15i	0.954886	−	0.740007i
$419$	−1.01152e15			−0.186935			−0.0934674	−	0.995622i	$-0.529795\pi$
$419$	−1.01152e15			−0.186935			−0.0934674	+	0.995622i	$0.529795\pi$
$420$	−2.38200e14	+	3.27854e14i	−0.0433956	+	0.0597289i
$421$	−1.06221e15	+	3.26914e15i	−0.190773	+	0.587139i	−1.00000		0.000357284i	$-0.999886\pi$
$421$	−1.06221e15	+	3.26914e15i	−0.190773	+	0.587139i	0.809227	+	0.587496i	$0.199886\pi$
$422$	1.65063e15	+	5.08011e15i	0.292263	+	0.899494i
$423$	8.45553e14	−	6.14330e14i	0.147604	−	0.107241i
$424$	−4.54941e14	−	6.26173e14i	−0.0782997	−	0.107770i
$425$	6.63951e15	−	2.15731e15i	1.12669	−	0.366082i
$426$	2.20727e15	+	7.17186e14i	0.369316	+	0.119998i
$427$	−2.89324e15	−	2.10206e15i	−0.477329	−	0.346800i
$428$		−	1.51925e15i		−	0.247154i
$429$	1.97671e15	+	2.55070e15i	0.317103	+	0.409181i
$430$	−2.70978e14			−0.0428670
$431$	−3.63582e15	+	5.00427e15i	−0.567203	+	0.780688i	−0.992220	−	0.124498i	$-0.960268\pi$
$431$	−3.63582e15	+	5.00427e15i	−0.567203	+	0.780688i	0.425017	+	0.905185i	$0.360268\pi$
$432$	−4.13225e14	+	1.27178e15i	−0.0635747	+	0.195663i
$433$	−6.92122e14	−	2.13013e15i	−0.105016	−	0.323206i	0.884718	−	0.466126i	$-0.154351\pi$
$433$	−6.92122e14	−	2.13013e15i	−0.105016	−	0.323206i	−0.989734	+	0.142920i	$0.954351\pi$
$434$	4.13704e14	−	3.00573e14i	0.0619086	−	0.0449792i
$435$	1.28516e15	+	1.76887e15i	0.189680	+	0.261072i
$436$	5.37568e15	−	1.74667e15i	0.782555	−	0.254267i
$437$	1.86043e16	+	6.04491e15i	2.67132	+	0.867963i
$438$	−5.45089e14	−	3.96030e14i	−0.0772009	−	0.0560898i
$439$			2.70881e15i			0.378436i	0.981935	+	0.189218i	$0.0605952\pi$
$439$			2.70881e15i			0.378436i	−0.981935	+	0.189218i	$0.939405\pi$
$440$	1.02751e15	−	3.69412e14i	0.141602	−	0.0509090i
$441$	−2.50276e15			−0.340242
$442$	5.04358e15	−	6.94190e15i	0.676403	−	0.930989i
$443$	−9.41789e13	+	2.89853e14i	−0.0124604	+	0.0383491i	−0.957093	−	0.289780i	$-0.906418\pi$
$443$	−9.41789e13	+	2.89853e14i	−0.0124604	+	0.0383491i	0.944633	+	0.328129i	$0.106418\pi$
$444$	6.90212e14	+	2.12425e15i	0.0900917	+	0.277274i
$445$	3.36675e15	−	2.44609e15i	0.433561	−	0.315001i
$446$	−2.73951e15	−	3.77062e15i	−0.348068	−	0.479075i
$447$	−3.22695e15	+	1.04850e15i	−0.404526	+	0.131439i
$448$	−7.24585e14	−	2.35432e14i	−0.0896234	−	0.0291204i
$449$	3.97271e15	+	2.88634e15i	0.484852	+	0.352265i	0.803201	−	0.595708i	$-0.203129\pi$
$449$	3.97271e15	+	2.88634e15i	0.484852	+	0.352265i	−0.318349	+	0.947973i	$0.603129\pi$
$450$		−	3.78980e15i		−	0.456395i
$451$	−9.69606e15	−	2.82163e15i	−1.15222	−	0.335306i
$452$	−1.96432e15			−0.230346
$453$	1.12697e15	−	1.55115e15i	0.130414	−	0.179500i
$454$	2.79329e13	−	8.59687e13i	0.00318993	−	0.00981760i
$455$	−9.89648e14	−	3.04582e15i	−0.111535	−	0.343270i
$456$	2.02184e15	−	1.46895e15i	0.224884	−	0.163388i
$457$	1.15998e15	+	1.59657e15i	0.127337	+	0.175264i	0.867925	−	0.496695i	$-0.165453\pi$
$457$	1.15998e15	+	1.59657e15i	0.127337	+	0.175264i	−0.740589	+	0.671959i	$0.765453\pi$
$458$	1.32832e15	−	4.31596e14i	0.143916	−	0.0467611i
$459$	−1.05885e16	−	3.44040e15i	−1.13229	−	0.367902i
$460$	2.68164e15	+	1.94832e15i	0.283043	+	0.205643i
$461$			9.17355e15i			0.955722i	0.878435	+	0.477861i	$0.158588\pi$
$461$			9.17355e15i			0.955722i	−0.878435	+	0.477861i	$0.841412\pi$
$462$	1.97242e15	+	1.34173e15i	0.202837	+	0.137980i
$463$	1.21333e16			1.23166			0.615832	−	0.787878i	$-0.288820\pi$
$463$	1.21333e16			1.23166			0.615832	+	0.787878i	$0.288820\pi$
$464$	−2.41612e15	+	3.32550e15i	−0.242108	+	0.333234i
$465$	−8.78325e13	+	2.70321e14i	−0.00868835	+	0.0267400i
$466$	1.02293e15	+	3.14824e15i	0.0998915	+	0.307434i
$467$	9.51889e15	−	6.91588e15i	0.917667	−	0.666724i	−0.0252752	−	0.999681i	$-0.508046\pi$
$467$	9.51889e15	−	6.91588e15i	0.917667	−	0.666724i	0.942942	+	0.332956i	$0.108046\pi$
$468$	−2.73795e15	−	3.76847e15i	−0.260586	−	0.358665i
$469$	−7.91515e15	+	2.57179e15i	−0.743741	+	0.241656i
$470$	−7.14138e14	−	2.32038e14i	−0.0662514	−	0.0215264i
$471$	6.16093e14	+	4.47618e14i	0.0564314	+	0.0409998i
$472$		−	6.37249e15i		−	0.576311i
$473$	4.93967e13	+	1.59436e15i	0.00441094	+	0.142370i
$474$	−1.48222e15			−0.130690
$475$	−9.44480e15	+	1.29997e16i	−0.822302	+	1.13180i
$476$	1.96014e15	−	6.03270e15i	0.168518	−	0.518645i
$477$	−1.08101e15	−	3.32699e15i	−0.0917735	−	0.282450i
$478$	3.29914e15	−	2.39697e15i	0.276588	−	0.200953i
$479$	−3.20799e15	−	4.41542e15i	−0.265595	−	0.365560i	0.655301	−	0.755367i	$-0.272542\pi$
$479$	−3.20799e15	−	4.41542e15i	−0.265595	−	0.365560i	−0.920896	+	0.389807i	$0.872542\pi$
$480$	4.02745e14	−	1.30860e14i	0.0329294	−	0.0106994i
$481$	−1.67873e16	−	5.45454e15i	−1.35554	−	0.440441i
$482$	1.23937e15	+	9.00452e14i	0.0988365	+	0.0718089i
$483$			7.24173e15i			0.570374i
$484$	−2.36082e15	−	5.97824e15i	−0.183650	−	0.465051i
$485$	6.94470e15			0.533584
$486$	−5.53908e15	+	7.62389e15i	−0.420359	+	0.578574i
$487$	4.06457e15	−	1.25095e16i	0.304678	−	0.937702i	−0.675119	−	0.737709i	$-0.735908\pi$
$487$	4.06457e15	−	1.25095e16i	0.304678	−	0.937702i	0.979797	−	0.199994i	$-0.0640921\pi$
$488$	1.15481e15	+	3.55414e15i	0.0855051	+	0.263158i
$489$	−1.67718e15	+	1.21854e15i	−0.122667	+	0.0891226i
$490$	1.05689e15	+	1.45469e15i	0.0763579	+	0.105098i
$491$	7.88998e15	−	2.56361e15i	0.563102	−	0.182963i	−0.0136147	−	0.999907i	$-0.504334\pi$
$491$	7.88998e15	−	2.56361e15i	0.563102	−	0.182963i	0.576716	+	0.816945i	$0.304334\pi$
$492$	−3.72474e15	−	1.21024e15i	−0.262606	−	0.0853259i
$493$	−2.76872e16	−	2.01159e16i	−1.92840	−	1.40107i
$494$			1.97499e16i			1.35895i
$495$	4.93268e15	−	1.52825e14i	0.335314	−	0.0103888i
$496$	−5.34359e14			−0.0358875
$497$	−7.96945e15	+	1.09690e16i	−0.528798	+	0.727828i
$498$	−1.29555e15	+	3.98730e15i	−0.0849334	+	0.261398i
$499$	6.64918e15	+	2.04641e16i	0.430690	+	1.32553i	0.897440	+	0.441137i	$0.145425\pi$
$499$	6.64918e15	+	2.04641e16i	0.430690	+	1.32553i	−0.466750	+	0.884389i	$0.654575\pi$
$500$	−4.89280e15	+	3.55483e15i	−0.313139	+	0.227509i
$501$	−1.32335e15	−	1.82144e15i	−0.0836853	−	0.115183i
$502$	−1.68518e16	+	5.47550e15i	−1.05299	+	0.342138i
$503$	−1.20142e16	−	3.90364e15i	−0.741797	−	0.241025i	−0.0863494	−	0.996265i	$-0.527520\pi$
$503$	−1.20142e16	−	3.90364e15i	−0.741797	−	0.241025i	−0.655448	+	0.755240i	$0.727520\pi$
$504$	−2.78580e15	−	2.02400e15i	−0.169968	−	0.123489i
$505$		−	9.99894e15i		−	0.602845i
$506$	1.09745e16	−	1.61331e16i	0.653858	−	0.961205i
$507$	−2.07436e15			−0.122134
$508$	6.89783e15	−	9.49405e15i	0.401356	−	0.552420i
$509$	−6.38971e15	+	1.96655e16i	−0.367430	+	1.13083i	0.581015	+	0.813893i	$0.302656\pi$
$509$	−6.38971e15	+	1.96655e16i	−0.367430	+	1.13083i	−0.948445	+	0.316941i	$0.897344\pi$
$510$	1.08950e15	+	3.35315e15i	0.0619167	+	0.190560i
$511$	3.18440e15	−	2.31360e15i	0.178855	−	0.129946i
$512$	4.67954e14	+	6.44084e14i	0.0259767	+	0.0357538i
$513$	2.43712e16	−	7.91869e15i	1.33713	−	0.434459i
$514$	2.33688e16	+	7.59298e15i	1.26724	+	0.411750i
$515$	2.11785e15	+	1.53871e15i	0.113515	+	0.0824734i
$516$			6.18637e14i			0.0327746i
$517$	−1.23506e15	+	4.24408e15i	−0.0646763	+	0.222249i
$518$	−1.30485e16			−0.675433
$519$	6.28791e14	−	8.65456e14i	0.0321738	−	0.0442834i
$520$	−1.03415e15	+	3.18278e15i	−0.0523073	+	0.160985i
$521$	−7.37717e14	−	2.27046e15i	−0.0368862	−	0.113524i	0.930918	−	0.365228i	$-0.119009\pi$
$521$	−7.37717e14	−	2.27046e15i	−0.0368862	−	0.113524i	−0.967804	+	0.251704i	$0.919009\pi$
$522$	−1.50302e16	+	1.09201e16i	−0.742921	+	0.539763i
$523$	−1.83638e14	−	2.52757e14i	−0.00897333	−	0.0123507i	0.804507	−	0.593943i	$-0.202430\pi$
$523$	−1.83638e14	−	2.52757e14i	−0.00897333	−	0.0123507i	−0.813480	+	0.581593i	$0.802430\pi$
$524$	−1.80156e16	+	5.85361e15i	−0.870282	+	0.282772i
$525$	−5.65738e15	−	1.83820e15i	−0.270184	−	0.0877881i
$526$	−2.57407e15	−	1.87017e15i	−0.121536	−	0.0883013i
$527$		−	4.44893e15i		−	0.207678i
$528$	−8.43359e14	−	2.34578e15i	−0.0389232	−	0.108264i
$529$	3.73182e16			1.70289
$530$	−1.47726e15	+	2.03327e15i	−0.0666502	+	0.0917362i
$531$	8.90020e15	−	2.73920e16i	0.397039	−	1.22196i
$532$	4.51161e15	+	1.38853e16i	0.199004	+	0.612472i
$533$	2.50393e16	−	1.81921e16i	1.09209	−	0.793451i
$534$	−5.58436e15	−	7.68621e15i	−0.240838	−	0.331486i
$535$	−4.69178e15	+	1.52445e15i	−0.200085	+	0.0650117i
$536$	8.27105e15	+	2.68743e15i	0.348796	+	0.113331i
$537$	−9.05303e15	−	6.57741e15i	−0.377527	−	0.274290i
$538$		−	7.71943e15i		−	0.318340i
$539$	8.36630e15	−	6.48362e15i	0.341194	−	0.264414i
$540$	4.34216e15			0.175123
$541$	−1.92208e16	+	2.64552e16i	−0.766636	+	1.05518i	0.229997	+	0.973191i	$0.426128\pi$
$541$	−1.92208e16	+	2.64552e16i	−0.766636	+	1.05518i	−0.996633	+	0.0819920i	$0.973872\pi$
$542$	7.85235e14	−	2.41670e15i	0.0309745	−	0.0953296i
$543$	4.92784e14	+	1.51663e15i	0.0192246	+	0.0591673i
$544$	−5.36246e15	+	3.89606e15i	−0.206905	+	0.150325i
$545$	−1.07882e16	−	1.48486e16i	−0.411688	−	0.566640i
$546$	−6.95354e15	+	2.25934e15i	−0.262452	+	0.0852759i
$547$	−1.94665e16	−	6.32505e15i	−0.726714	−	0.236124i	−0.0777825	−	0.996970i	$-0.524784\pi$
$547$	−1.94665e16	−	6.32505e15i	−0.726714	−	0.236124i	−0.648932	+	0.760847i	$0.724784\pi$
$548$	−1.29574e16	−	9.41407e15i	−0.478446	−	0.347611i
$549$			1.68903e16i			0.616884i
$550$	9.81782e15	+	1.26687e16i	0.354682	+	0.457672i
$551$	7.87709e16			2.81485
$552$	4.44798e15	−	6.12212e15i	0.157227	−	0.216405i
$553$	2.67581e15	−	8.23529e15i	0.0935630	−	0.287957i
$554$	1.15061e16	+	3.54120e16i	0.397987	+	1.22488i
$555$	5.86758e15	−	4.26305e15i	0.200771	−	0.145869i
$556$	−1.20565e16	−	1.65944e16i	−0.408107	−	0.561711i
$557$	6.28256e15	−	2.04133e15i	0.210381	−	0.0683568i	−0.201931	−	0.979400i	$-0.564722\pi$
$557$	6.28256e15	−	2.04133e15i	0.210381	−	0.0683568i	0.412311	+	0.911043i	$0.364722\pi$
$558$	−2.29693e15	−	7.46319e14i	−0.0760927	−	0.0247240i
$559$	−3.95520e15	−	2.87362e15i	−0.129628	−	0.0941801i
$560$			2.47391e15i			0.0802152i
$561$	1.95303e16	−	7.02157e15i	0.626517	−	0.225246i
$562$	2.43057e16			0.771418
$563$	8.97711e15	−	1.23559e16i	0.281894	−	0.387994i	−0.644466	−	0.764633i	$-0.722920\pi$
$563$	8.97711e15	−	1.23559e16i	0.281894	−	0.387994i	0.926360	+	0.376639i	$0.122920\pi$
$564$	−5.29737e14	+	1.63036e15i	−0.0164583	+	0.0506535i
$565$	1.97104e15	+	6.06624e15i	0.0605906	+	0.186479i
$566$	1.91039e15	−	1.38798e15i	0.0581063	−	0.0422167i
$567$	−6.02966e15	−	8.29911e15i	−0.181466	−	0.249766i
$568$	1.34746e16	−	4.37818e15i	0.401261	−	0.130378i
$569$	−5.71580e16	−	1.85718e16i	−1.68424	−	0.547242i	−0.698512	−	0.715598i	$-0.746154\pi$
$569$	−5.71580e16	−	1.85718e16i	−1.68424	−	0.547242i	−0.985726	+	0.168356i	$0.946154\pi$
$570$	−6.56521e15	−	4.76990e15i	−0.191425	−	0.139079i
$571$			5.27237e16i			1.52121i	0.649216	+	0.760604i	$0.275097\pi$
$571$			5.27237e16i			1.52121i	−0.649216	+	0.760604i	$0.724903\pi$
$572$	1.89151e16	+	5.50443e15i	0.540047	+	0.157158i
$573$	−5.41481e15			−0.152987
$574$	1.34483e16	−	1.85100e16i	0.376008	−	0.517530i
$575$	−1.50353e16	+	4.62738e16i	−0.416010	+	1.28035i
$576$	1.11193e15	+	3.42216e15i	0.0304467	+	0.0937054i
$577$	−6.39955e15	+	4.64955e15i	−0.173418	+	0.125996i	−0.671109	−	0.741359i	$-0.734182\pi$
$577$	−6.39955e15	+	4.64955e15i	−0.173418	+	0.125996i	0.497690	+	0.867355i	$0.334182\pi$
$578$	−1.69397e16	−	2.33155e16i	−0.454295	−	0.625284i
$579$	1.83648e16	−	5.96710e15i	0.487434	−	0.158377i
$580$	1.26942e16	+	4.12461e15i	0.333456	+	0.108347i
$581$	−1.98148e16	−	1.43963e16i	−0.515150	−	0.374278i
$582$		−	1.58546e16i		−	0.407959i
$583$	1.22325e16	+	8.32113e15i	0.311533	+	0.211919i
$584$	−4.11312e15			−0.103680
$585$	−8.89052e15	+	1.22368e16i	−0.221816	+	0.305303i
$586$	7.26873e15	−	2.23709e16i	0.179504	−	0.552455i
$587$	−8.57504e14	−	2.63913e15i	−0.0209608	−	0.0645107i	0.940029	−	0.341095i	$-0.110798\pi$
$587$	−8.57504e14	−	2.63913e15i	−0.0209608	−	0.0645107i	−0.960990	+	0.276584i	$0.910798\pi$
$588$	3.32102e15	−	2.41286e15i	0.0803540	−	0.0583806i
$589$	6.01892e15	+	8.28433e15i	0.144154	+	0.198411i
$590$	−1.96796e16	+	6.39430e15i	−0.466557	+	0.151594i
$591$	2.65088e15	+	8.61324e14i	0.0622107	+	0.0202135i
$592$	1.10311e16	+	8.01458e15i	0.256265	+	0.186188i
$593$		−	2.94043e16i		−	0.676211i	−0.941108	−	0.338106i	$-0.890214\pi$
$593$		−	2.94043e16i		−	0.676211i	0.941108	−	0.338106i	$-0.109786\pi$
$594$	−7.91534e14	−	2.55480e16i	−0.0180198	−	0.581619i
$595$	−2.05971e16			−0.464200
$596$	−1.21749e16	+	1.67573e16i	−0.271637	+	0.373876i
$597$	1.44298e15	−	4.44105e15i	0.0318724	−	0.0980933i
$598$	1.84800e16	+	5.68756e16i	0.404106	+	1.24371i
$599$	9.22139e15	−	6.69973e15i	0.199634	−	0.145043i	−0.483477	−	0.875357i	$-0.660626\pi$
$599$	9.22139e15	−	6.69973e15i	0.199634	−	0.145043i	0.683111	+	0.730314i	$0.260626\pi$
$600$	3.65367e15	+	5.02885e15i	0.0783109	+	0.107786i
$601$	−5.94489e16	+	1.93161e16i	−1.26153	+	0.409895i	−0.862039	−	0.506843i	$-0.830813\pi$
$601$	−5.94489e16	+	1.93161e16i	−1.26153	+	0.409895i	−0.399489	+	0.916738i	$0.630813\pi$
$602$	−3.43718e15	−	1.11681e15i	−0.0722143	−	0.0234639i
$603$	3.17995e16	+	2.31037e16i	0.661480	+	0.480593i
$604$		−	1.17046e16i		−	0.241066i
$605$	−1.60932e16	+	1.32894e16i	−0.328178	+	0.271003i
$606$	−2.28273e16			−0.460914
$607$	−3.80774e16	+	5.24091e16i	−0.761264	+	1.04779i	0.235844	+	0.971791i	$0.424215\pi$
$607$	−3.80774e16	+	5.24091e16i	−0.761264	+	1.04779i	−0.997108	+	0.0759993i	$0.975785\pi$
$608$	4.71448e15	−	1.45097e16i	0.0933280	−	0.287234i
$609$	9.01121e15	+	2.77336e16i	0.176636	+	0.543630i
$610$	9.81720e15	−	7.13261e15i	0.190550	−	0.138443i
$611$	−7.96291e15	−	1.09600e16i	−0.153047	−	0.210651i
$612$	−2.84919e16	+	9.25759e15i	−0.542267	+	0.176193i
$613$	−6.75790e16	−	2.19578e16i	−1.27365	−	0.413833i	−0.407308	−	0.913291i	$-0.633533\pi$
$613$	−6.75790e16	−	2.19578e16i	−1.27365	−	0.413833i	−0.866338	+	0.499458i	$0.833533\pi$
$614$	−1.43343e16	−	1.04145e16i	−0.267526	−	0.194369i
$615$			1.27172e16i			0.235039i
$616$	1.45558e16	−	4.50971e14i	0.266411	−	0.00825400i
$617$	−5.04531e16			−0.914485			−0.457243	−	0.889342i	$-0.651163\pi$
$617$	−5.04531e16			−0.914485			−0.457243	+	0.889342i	$0.651163\pi$
$618$	3.51284e15	−	4.83502e15i	0.0630562	−	0.0867895i
$619$	4.63220e15	−	1.42564e16i	0.0823461	−	0.253435i	−0.901404	−	0.432979i	$-0.857462\pi$
$619$	4.63220e15	−	1.42564e16i	0.0823461	−	0.253435i	0.983750	+	0.179544i	$0.0574623\pi$
$620$	5.36188e14	+	1.65022e15i	0.00943989	+	0.0290530i
$621$	6.27745e16	−	4.56083e16i	1.09455	−	0.795234i
$622$	−4.03210e16	−	5.54971e16i	−0.696288	−	0.958359i
$623$	5.27863e16	−	1.71513e16i	0.902803	−	0.293338i
$624$	7.26621e15	+	2.36093e15i	0.123084	+	0.0399923i
$625$	−2.35986e16	−	1.71454e16i	−0.395919	−	0.287652i
$626$		−	6.91202e16i		−	1.14857i
$627$	−2.68680e16	+	3.94973e16i	−0.442211	+	0.650073i
$628$	4.64891e15			0.0757867
$629$	−6.67272e16	+	9.18421e16i	−1.07745	+	1.48299i
$630$	−3.45522e15	+	1.06341e16i	−0.0552627	+	0.170081i
$631$	−7.12163e15	−	2.19181e16i	−0.112824	−	0.347238i	0.878663	−	0.477443i	$-0.158436\pi$
$631$	−7.12163e15	−	2.19181e16i	−0.112824	−	0.347238i	−0.991487	+	0.130205i	$0.958436\pi$
$632$	−7.32035e15	+	5.31854e15i	−0.114876	+	0.0834623i
$633$	−2.32749e16	−	3.20352e16i	−0.361798	−	0.497972i
$634$	2.61280e15	−	8.48949e14i	0.0402319	−	0.0130721i
$635$	−3.62411e16	−	1.17754e16i	−0.552789	−	0.179612i
$636$	4.64192e15	+	3.37255e15i	0.0701382	+	0.0509584i
$637$			3.24406e16i			0.485571i
$638$	2.19540e16	−	7.54412e16i	0.325529	−	1.11862i
$639$	6.40353e16			0.940621
$640$	1.51951e15	−	2.09143e15i	0.0221118	−	0.0304343i
$641$	3.57625e16	−	1.10066e17i	0.515560	−	1.58673i	−0.266700	−	0.963780i	$-0.585933\pi$
$641$	3.57625e16	−	1.10066e17i	0.515560	−	1.58673i	0.782260	−	0.622952i	$-0.214067\pi$
$642$	3.48029e15	+	1.07112e16i	0.0497056	+	0.152978i
$643$	2.19815e16	−	1.59705e16i	0.311022	−	0.225971i	−0.421313	−	0.906915i	$-0.638431\pi$
$643$	2.19815e16	−	1.59705e16i	0.311022	−	0.225971i	0.732335	+	0.680945i	$0.238431\pi$
$644$	2.59850e16	+	3.57653e16i	0.364257	+	0.501357i
$645$	1.91048e15	−	6.20754e14i	0.0265329	−	0.00862107i
$646$	1.20804e17	+	3.92514e16i	1.66220	+	0.540083i
$647$	−4.63765e16	−	3.36945e16i	−0.632225	−	0.459339i	0.224945	−	0.974371i	$-0.427780\pi$
$647$	−4.63765e16	−	3.36945e16i	−0.632225	−	0.459339i	−0.857170	+	0.515033i	$0.827780\pi$
$648$			1.07195e16i			0.144786i
$649$	4.12096e16	+	1.14624e17i	0.551481	+	1.53393i
$650$	−4.91232e16			−0.651338
$651$	−2.22820e15	+	3.06685e15i	−0.0292730	+	0.0402909i
$652$	−3.91081e15	+	1.20362e16i	−0.0509074	+	0.156677i
$653$	−2.68296e16	−	8.25730e16i	−0.346047	−	1.06502i	−0.961021	−	0.276475i	$-0.910834\pi$
$653$	−2.68296e16	−	8.25730e16i	−0.346047	−	1.06502i	0.614974	−	0.788547i	$-0.289166\pi$
$654$	−3.38991e16	+	2.46291e16i	−0.433233	+	0.314762i
$655$	3.61544e16	+	4.97623e16i	0.457840	+	0.630163i
$656$	−2.27383e16	+	7.38811e15i	−0.285321	+	0.0927066i
$657$	−1.76802e16	−	5.74464e15i	−0.219834	−	0.0714283i
$658$	−8.10206e15	−	5.88649e15i	−0.0998252	−	0.0725273i
$659$			6.79494e16i			0.829609i	0.909911	+	0.414804i	$0.136150\pi$
$659$			6.79494e16i			0.829609i	−0.909911	+	0.414804i	$0.863850\pi$
$660$	−6.39804e15	+	4.95829e15i	−0.0774076	+	0.0599885i
$661$	8.93574e16			1.07133			0.535663	−	0.844432i	$-0.320062\pi$
$661$	8.93574e16			1.07133			0.535663	+	0.844432i	$0.320062\pi$
$662$	2.48944e15	−	3.42642e15i	0.0295770	−	0.0407092i
$663$	−1.96565e16	+	6.04964e16i	−0.231433	+	0.712277i
$664$	7.90891e15	+	2.43411e16i	0.0922801	+	0.284009i
$665$	3.83538e16	−	2.78657e16i	0.443485	−	0.322211i
$666$	3.62234e16	+	4.98573e16i	0.415092	+	0.571325i
$667$	2.26844e17	−	7.37060e16i	2.57615	−	0.837043i
$668$	−1.30715e16	−	4.24718e15i	−0.147118	−	0.0478016i
$669$	2.79522e16	+	2.03084e16i	0.311787	+	0.226527i
$670$		−	2.82394e16i		−	0.312181i
$671$	−4.37558e16	−	5.64614e16i	−0.479403	−	0.618609i
$672$	5.64789e15			0.0613297
$673$	5.52490e16	−	7.60437e16i	0.594612	−	0.818413i	−0.400590	−	0.916258i	$-0.631195\pi$
$673$	5.52490e16	−	7.60437e16i	0.594612	−	0.818413i	0.995202	+	0.0978442i	$0.0311947\pi$
$674$	−2.43402e16	+	7.49116e16i	−0.259636	+	0.799079i
$675$	1.96959e16	+	6.06176e16i	0.208234	+	0.640879i
$676$	−1.02448e16	+	7.44329e15i	−0.107355	+	0.0779982i
$677$	2.95852e16	+	4.07205e16i	0.307286	+	0.422943i	0.934532	−	0.355878i	$-0.115818\pi$
$677$	2.95852e16	+	4.07205e16i	0.307286	+	0.422943i	−0.627247	+	0.778821i	$0.715818\pi$
$678$	1.38491e16	−	4.49984e15i	0.142575	−	0.0463254i
$679$	8.80890e16	+	2.86218e16i	0.898883	+	0.292065i
$680$	1.74127e16	+	1.26511e16i	0.176121	+	0.127960i
$681$			6.70096e14i			0.00671823i
$682$	9.61166e15	−	3.45559e15i	0.0955195	−	0.0343413i
$683$	−7.14566e16			−0.703912			−0.351956	−	0.936017i	$-0.614483\pi$
$683$	−7.14566e16			−0.703912			−0.351956	+	0.936017i	$0.614483\pi$
$684$	4.05302e16	−	5.57850e16i	0.395769	−	0.544729i
$685$	−1.60710e16	+	4.94614e16i	−0.155560	+	0.478766i
$686$	2.45786e16	+	7.56450e16i	0.235837	+	0.725831i
$687$	−8.37637e15	+	6.08579e15i	−0.0796737	+	0.0578864i
$688$	2.21981e15	+	3.05531e15i	0.0209308	+	0.0288088i
$689$	−4.31243e16	+	1.40119e16i	−0.403094	+	0.130973i
$690$	−2.33696e16	−	7.59325e15i	−0.216550	−	0.0703612i
$691$	−1.10517e17	−	8.02954e16i	−1.01522	−	0.737603i	−0.0499247	−	0.998753i	$-0.515898\pi$
$691$	−1.10517e17	−	8.02954e16i	−1.01522	−	0.737603i	−0.965298	+	0.261150i	$0.915898\pi$
$692$		−	6.53055e15i		−	0.0594720i
$693$	6.31977e16	+	1.83910e16i	0.570561	+	0.166038i
$694$	−1.26481e17			−1.13206
$695$	−3.91493e16	+	5.38844e16i	−0.347389	+	0.478139i
$696$	9.41639e15	−	2.89807e16i	0.0828379	−	0.254949i
$697$	−6.15114e16	−	1.89313e17i	−0.536487	−	1.65114i
$698$	3.08335e15	−	2.24018e15i	0.0266618	−	0.0193709i
$699$	−1.44239e16	−	1.98528e16i	−0.123657	−	0.170200i
$700$	−3.45364e16	+	1.12216e16i	−0.293555	+	0.0953818i
$701$	1.59670e17	+	5.18799e16i	1.34560	+	0.437211i	0.891209	−	0.453593i	$-0.149858\pi$
$701$	1.59670e17	+	5.18799e16i	1.34560	+	0.437211i	0.454388	+	0.890804i	$0.349858\pi$
$702$	6.33783e16	+	4.60470e16i	0.529563	+	0.384750i
$703$		−	2.61293e17i		−	2.16469i
$704$	−1.25824e16	−	8.55914e15i	−0.103354	−	0.0703063i
$705$	5.56646e15			0.0453361
$706$	−3.64747e15	+	5.02031e15i	−0.0294553	+	0.0405417i
$707$	4.12096e16	−	1.26830e17i	0.329976	−	1.01556i
$708$	1.45980e16	+	4.49281e16i	0.115903	+	0.356713i
$709$	−1.82391e17	+	1.32515e17i	−1.43591	+	1.04325i	−0.447031	+	0.894518i	$0.647519\pi$
$709$	−1.82391e17	+	1.32515e17i	−1.43591	+	1.04325i	−0.988878	+	0.148731i	$0.952481\pi$
$710$	−2.70415e16	−	3.72195e16i	−0.211097	−	0.290549i
$711$	−3.88946e16	+	1.26376e16i	−0.301073	+	0.0978244i
$712$	−5.51598e16	−	1.79225e16i	−0.423392	−	0.137568i
$713$	2.50849e16	+	1.82252e16i	0.190930	+	0.138719i
$714$			4.70228e16i			0.354911i
$715$	−1.98091e15	−	6.39371e16i	−0.0148262	−	0.478538i
$716$	−6.83122e16			−0.507014
$717$	−1.77691e16	+	2.44570e16i	−0.130783	+	0.180007i
$718$	2.10362e16	−	6.47428e16i	0.153540	−	0.472547i
$719$	−5.36560e16	−	1.65136e17i	−0.388370	−	1.19528i	−0.934006	−	0.357257i	$-0.883712\pi$
$719$	−5.36560e16	−	1.65136e17i	−0.388370	−	1.19528i	0.545637	−	0.838022i	$-0.316288\pi$
$720$	9.45263e15	−	6.86773e15i	0.0678512	−	0.0492968i
$721$	2.05220e16	+	2.82461e16i	0.146086	+	0.201070i
$722$	−1.82790e17	+	5.93920e16i	−1.29041	+	0.419281i
$723$	−1.08007e16	−	3.50936e15i	−0.0756174	−	0.0245696i
$724$	7.87578e15	+	5.72209e15i	0.0546842	+	0.0397304i
$725$			1.95924e17i			1.34915i
$726$	3.03394e16	+	3.67404e16i	0.207199	+	0.250914i
$727$	−3.42332e16			−0.231868			−0.115934	−	0.993257i	$-0.536986\pi$
$727$	−3.42332e16			−0.231868			−0.115934	+	0.993257i	$0.536986\pi$
$728$	−2.62350e16	+	3.61093e16i	−0.176235	+	0.242567i
$729$	2.59353e15	−	7.98206e15i	0.0172793	−	0.0531802i
$730$	4.12720e15	+	1.27022e16i	0.0272721	+	0.0839348i
$731$	−2.54377e16	+	1.84815e16i	−0.166714	+	0.121125i
$732$	−1.62836e16	−	2.24125e16i	−0.105848	−	0.145688i
$733$	8.59877e16	−	2.79391e16i	0.554386	−	0.180131i	−0.0184074	−	0.999831i	$-0.505860\pi$
$733$	8.59877e16	−	2.79391e16i	0.554386	−	0.180131i	0.572794	+	0.819700i	$0.305860\pi$
$734$	1.28951e17	+	4.18987e16i	0.824608	+	0.267931i
$735$	−1.07838e16	−	7.83490e15i	−0.0683988	−	0.0496946i
$736$		−	4.61962e16i		−	0.290629i
$737$	−1.66153e17	+	5.14778e15i	−1.03682	+	0.0321229i
$738$	−1.08059e17			−0.668839
$739$	−1.66444e17	+	2.29090e17i	−1.02188	+	1.40650i	−0.111008	+	0.993820i	$0.535408\pi$
$739$	−1.66444e17	+	2.29090e17i	−1.02188	+	1.40650i	−0.910875	+	0.412682i	$0.864592\pi$
$740$	1.36819e16	−	4.21085e16i	0.0833212	−	0.256436i
$741$	−4.52429e16	−	1.39243e17i	−0.273301	−	0.841134i
$742$	−2.71180e16	+	1.97024e16i	−0.162493	+	0.118058i
$743$	5.47856e16	+	7.54059e16i	0.325637	+	0.448201i	0.940178	−	0.340684i	$-0.110659\pi$
$743$	5.47856e16	+	7.54059e16i	0.325637	+	0.448201i	−0.614541	+	0.788885i	$0.710659\pi$
$744$	3.76741e15	−	1.22410e15i	0.0222129	−	0.00721740i
$745$	6.39669e16	+	2.07841e16i	0.374126	+	0.121561i
$746$	−6.10404e16	−	4.43484e16i	−0.354148	−	0.257303i
$747$			1.15676e17i			0.665762i
$748$	7.12610e16	−	1.04757e17i	0.406858	−	0.598102i
$749$	−6.57951e16			−0.372652
$750$	2.63525e16	−	3.62711e16i	0.148066	−	0.203795i
$751$	−4.96620e16	+	1.52844e17i	−0.276812	+	0.851939i	0.711923	+	0.702258i	$0.247825\pi$
$751$	−4.96620e16	+	1.52844e17i	−0.276812	+	0.851939i	−0.988734	+	0.149681i	$0.952175\pi$
$752$	3.23386e15	+	9.95281e15i	0.0178819	+	0.0550350i
$753$	1.06268e17	−	7.72081e16i	0.582951	−	0.423539i
$754$	1.41546e17	+	1.94821e17i	0.770315	+	1.06025i
$755$	−3.61464e16	+	1.17447e16i	−0.195157	+	0.0634103i
$756$	5.50775e16	+	1.78958e16i	0.295015	+	0.0958560i
$757$	2.68199e17	+	1.94858e17i	1.42522	+	1.03548i	0.990882	+	0.134735i	$0.0430182\pi$
$757$	2.68199e17	+	1.94858e17i	1.42522	+	1.03548i	0.434339	+	0.900749i	$0.356982\pi$
$758$		−	1.69875e17i		−	0.895601i
$759$	−4.04165e16	+	1.38884e17i	−0.211401	+	0.726445i
$760$	−4.95396e16			−0.257082
$761$	2.05933e17	−	2.83443e17i	1.06028	−	1.45934i	0.180728	−	0.983533i	$-0.442155\pi$
$761$	2.05933e17	−	2.83443e17i	1.06028	−	1.45934i	0.879547	−	0.475811i	$-0.157845\pi$
$762$	−2.68831e16	+	8.27376e16i	−0.137325	+	0.422643i
$763$	−7.56438e16	−	2.32808e17i	−0.383377	−	1.17991i
$764$	−2.67426e16	+	1.94296e16i	−0.134475	+	0.0977021i
$765$	5.71789e16	+	7.87000e16i	0.285277	+	0.392650i
$766$	−8.52626e16	+	2.77035e16i	−0.422071	+	0.137139i
$767$	−3.55054e17	−	1.15364e17i	−1.74390	−	0.566628i
$768$	−4.77469e15	−	3.46902e15i	−0.0232690	−	0.0169059i
$769$		−	1.33468e17i		−	0.645385i	−0.946504	−	0.322692i	$-0.895412\pi$
$769$		−	1.33468e17i		−	0.645385i	0.946504	−	0.322692i	$-0.104588\pi$
$770$	−1.59983e16	−	4.44989e16i	−0.0767591	−	0.213504i
$771$	−1.82152e17			−0.867175
$772$	6.92885e16	−	9.53675e16i	0.327309	−	0.450502i
$773$	−3.82908e16	+	1.17847e17i	−0.179481	+	0.552385i	−0.999810	−	0.0195069i	$-0.993790\pi$
$773$	−3.82908e16	+	1.17847e17i	−0.179481	+	0.552385i	0.820329	+	0.571892i	$0.193790\pi$
$774$	5.27459e15	+	1.62335e16i	0.0245326	+	0.0755035i
$775$	−2.06053e16	+	1.49706e16i	−0.0950974	+	0.0690923i
$776$	−5.68899e16	−	7.83023e16i	−0.260534	−	0.358595i
$777$	9.19962e16	−	2.98914e16i	0.418065	−	0.135838i
$778$	1.15797e17	+	3.76246e16i	0.522178	+	0.169666i
$779$	3.70660e17	+	2.69300e17i	1.65863	+	1.20507i
$780$		−	2.48086e16i		−	0.110163i
$781$	−2.14059e17	+	1.65889e17i	−0.943252	+	0.730991i
$782$	3.84617e17			1.68185
$783$	1.83655e17	−	2.52779e17i	0.796951	−	1.09691i
$784$	7.74387e15	−	2.38332e16i	0.0333474	−	0.102633i
$785$	−4.66482e15	−	1.43568e16i	−0.0199350	−	0.0613537i
$786$	1.13606e17	−	8.25397e16i	0.481800	−	0.350048i
$787$	6.79426e16	+	9.35150e16i	0.285953	+	0.393580i	0.927694	−	0.373341i	$-0.121788\pi$
$787$	6.79426e16	+	9.35150e16i	0.285953	+	0.393580i	−0.641742	+	0.766921i	$0.721788\pi$
$788$	1.61827e16	−	5.25809e15i	0.0675919	−	0.0219620i
$789$	2.24322e16	+	7.28867e15i	0.0929844	+	0.0302125i
$790$	2.37702e16	+	1.72701e16i	0.0977846	+	0.0710447i
$791$			8.50698e16i			0.347309i
$792$	−4.21309e16	−	5.43646e16i	−0.170706	−	0.220275i
$793$	2.18931e17			0.880376
$794$	1.35029e17	−	1.85852e17i	0.538895	−	0.741726i
$795$	5.75736e15	−	1.77193e16i	0.0228045	−	0.0701851i
$796$	−8.80893e15	−	2.71111e16i	−0.0346294	−	0.106578i
$797$	−2.16464e17	+	1.57270e17i	−0.844570	+	0.613616i	−0.923643	−	0.383253i	$-0.874804\pi$
$797$	−2.16464e17	+	1.57270e17i	−0.844570	+	0.613616i	0.0790737	+	0.996869i	$0.474804\pi$
$798$	−6.36167e16	−	8.75609e16i	−0.246351	−	0.339073i
$799$	−8.28644e16	+	2.69243e16i	−0.318484	+	0.103482i
$800$	3.60894e16	+	1.17261e16i	0.137670	+	0.0447317i
$801$	−2.12072e17	−	1.54079e17i	−0.802948	−	0.583376i
$802$		−	3.48082e16i		−	0.130808i
$803$	7.39838e16	−	2.65987e16i	0.275958	−	0.0992128i
$804$	−6.44699e16			−0.238683
$805$	8.43771e16	−	1.16135e17i	0.310063	−	0.426764i
$806$	−9.67374e15	+	2.97727e16i	−0.0352845	+	0.108595i
$807$	1.76836e16	+	5.44245e16i	0.0640220	+	0.197039i
$808$	−1.12739e17	+	8.19098e16i	−0.405142	+	0.294353i
$809$	9.06834e16	+	1.24815e17i	0.323472	+	0.445221i	0.939523	−	0.342485i	$-0.111269\pi$
$809$	9.06834e16	+	1.24815e17i	0.323472	+	0.445221i	−0.616051	+	0.787706i	$0.711269\pi$
$810$	3.31042e16	−	1.07562e16i	0.117212	−	0.0380846i
$811$	−4.28570e16	−	1.39251e16i	−0.150625	−	0.0489410i	0.232734	−	0.972540i	$-0.425233\pi$
$811$	−4.28570e16	−	1.39251e16i	−0.150625	−	0.0489410i	−0.383359	+	0.923599i	$0.625233\pi$
$812$	1.44019e17	+	1.04636e17i	0.502440	+	0.365044i
$813$			1.88374e16i			0.0652345i
$814$	−2.50248e17	−	7.28243e16i	−0.860251	−	0.250340i
$815$	4.10947e16			0.140230
$816$	2.88821e16	−	3.97528e16i	0.0978335	−	0.134656i
$817$	2.23638e16	−	6.88288e16i	0.0751993	−	0.231440i
$818$	6.84073e15	+	2.10536e16i	0.0228340	+	0.0702759i
$819$	−1.63203e17	+	1.18574e17i	−0.540785	+	0.392903i
$820$	4.56322e16	+	6.28073e16i	0.150103	+	0.206598i
$821$	1.29959e17	−	4.22263e16i	0.424373	−	0.137887i	−0.0890415	−	0.996028i	$-0.528380\pi$
$821$	1.29959e17	−	4.22263e16i	0.424373	−	0.137887i	0.513414	+	0.858141i	$0.328380\pi$
$822$	1.12919e17	+	3.66897e16i	0.366047	+	0.118936i
$823$	2.98916e16	+	2.17175e16i	0.0961945	+	0.0698894i	0.634843	−	0.772641i	$-0.281065\pi$
$823$	2.98916e16	+	2.17175e16i	0.0961945	+	0.0698894i	−0.538648	+	0.842531i	$0.681065\pi$
$824$		−	3.64840e16i		−	0.116557i
$825$	−9.82401e16	−	6.68276e16i	−0.311577	−	0.211950i
$826$	−2.75977e17			−0.868945
$827$	1.93477e17	−	2.66298e17i	0.604779	−	0.832407i	−0.391356	−	0.920239i	$-0.627994\pi$
$827$	1.93477e17	−	2.66298e17i	0.604779	−	0.832407i	0.996135	+	0.0878324i	$0.0279940\pi$
$828$	6.45204e16	−	1.98573e17i	0.200223	−	0.616224i
$829$	1.40400e17	+	4.32107e17i	0.432554	+	1.33126i	0.895573	+	0.444915i	$0.146766\pi$
$829$	1.40400e17	+	4.32107e17i	0.432554	+	1.33126i	−0.463019	+	0.886348i	$0.653234\pi$
$830$	6.72347e16	−	4.88488e16i	0.205648	−	0.149412i
$831$	−1.62243e17	−	2.23309e17i	−0.492675	−	0.678108i
$832$	4.43578e16	−	1.44127e16i	0.133730	−	0.0434516i
$833$	1.98428e17	+	6.44733e16i	0.593928	+	0.192979i
$834$	1.23017e17	+	8.93771e16i	0.365568	+	0.265601i
$835$			4.46293e16i			0.131674i
$836$	9.03060e15	+	2.91477e17i	0.0264532	+	0.853820i
$837$	4.06179e16			0.118131
$838$	2.69066e16	−	3.70337e16i	0.0776952	−	0.106938i
$839$	−1.14390e17	+	3.52056e17i	−0.327956	+	1.00935i	0.642132	+	0.766594i	$0.278050\pi$
$839$	−1.14390e17	+	3.52056e17i	−0.327956	+	1.00935i	−0.970088	+	0.242752i	$0.921950\pi$
$840$	−5.66722e15	−	1.74419e16i	−0.0161322	−	0.0496499i
$841$	4.90785e17	−	3.56576e17i	1.38712	−	1.00780i
$842$	−9.14346e16	−	1.25849e17i	−0.256589	−	0.353165i
$843$	−1.71363e17	+	5.56792e16i	−0.477476	+	0.155141i
$844$	−2.29899e17	−	7.46989e16i	−0.636038	−	0.206661i
$845$	3.32664e16	+	2.41694e16i	0.0913829	+	0.0663936i
$846$			4.72986e16i			0.129011i
$847$	−2.58903e17	+	1.02241e17i	−0.701191	+	0.276902i
$848$	3.50269e16			0.0941947
$849$	−1.02893e16	+	1.41620e16i	−0.0274751	+	0.0378163i
$850$	−9.76286e16	+	3.00470e17i	−0.258859	+	0.796687i
$851$	−2.44493e17	−	7.52471e17i	−0.643707	−	1.98113i
$852$	−8.49712e16	+	6.17352e16i	−0.222144	+	0.161397i
$853$	1.56849e17	+	2.15884e17i	0.407180	+	0.560435i	0.962528	−	0.271183i	$-0.0874148\pi$
$853$	1.56849e17	+	2.15884e17i	0.407180	+	0.560435i	−0.555348	+	0.831618i	$0.687415\pi$
$854$	1.53921e17	−	5.00120e16i	0.396781	−	0.128922i
$855$	−2.12945e17	−	6.91900e16i	−0.545093	−	0.177112i
$856$	5.56228e16	+	4.04123e16i	0.141387	+	0.102724i
$857$			2.68787e17i			0.678459i	0.940704	+	0.339230i	$0.110166\pi$
$857$			2.68787e17i			0.678459i	−0.940704	+	0.339230i	$0.889834\pi$
$858$	−1.45967e17	+	4.52238e15i	−0.365873	+	0.0113356i
$859$	−2.71712e17			−0.676316			−0.338158	−	0.941089i	$-0.609804\pi$
$859$	−2.71712e17			−0.676316			−0.338158	+	0.941089i	$0.609804\pi$
$860$	7.20805e15	−	9.92103e15i	0.0178167	−	0.0245226i
$861$	−5.24125e16	+	1.61309e17i	−0.128652	+	0.395950i
$862$	−8.65029e16	−	2.66229e17i	−0.210857	−	0.648950i
$863$	−6.00698e17	+	4.36433e17i	−1.45409	+	1.05646i	−0.469237	+	0.883072i	$0.655471\pi$
$863$	−6.00698e17	+	4.36433e17i	−1.45409	+	1.05646i	−0.984854	+	0.173386i	$0.944529\pi$
$864$	−3.55703e16	−	4.89584e16i	−0.0855078	−	0.117691i
$865$	−2.01677e16	+	6.55290e15i	−0.0481460	+	0.0156436i
$866$	9.63988e16	+	3.13219e16i	0.228541	+	0.0742575i
$867$	1.72841e17	+	1.25576e17i	0.406942	+	0.295661i
$868$			2.31418e16i			0.0541101i
$869$	9.72790e16	−	1.43005e17i	0.225892	−	0.332073i
$870$	−9.89472e16			−0.228186
$871$	2.99469e17	−	4.12183e17i	0.685871	−	0.944021i
$872$	−7.90451e16	+	2.43276e17i	−0.179794	+	0.553350i
$873$	−1.35179e17	−	4.16037e17i	−0.305367	−	0.939824i
$874$	−7.16193e17	+	5.20345e17i	−1.60680	+	1.16741i
$875$	1.53951e17	+	2.11895e17i	0.343031	+	0.472142i
$876$	2.89989e16	−	9.42230e15i	0.0641736	−	0.0208513i
$877$	−3.25786e17	−	1.05854e17i	−0.716036	−	0.232654i	−0.0717324	−	0.997424i	$-0.522853\pi$
$877$	−3.25786e17	−	1.05854e17i	−0.716036	−	0.232654i	−0.644304	+	0.764770i	$0.722853\pi$
$878$	−9.91749e16	−	7.20548e16i	−0.216488	−	0.157288i
$879$			1.74373e17i			0.378047i
$880$	−1.38070e16	+	4.74455e16i	−0.0297306	+	0.102164i
$881$	−2.85292e17			−0.610146			−0.305073	−	0.952329i	$-0.598681\pi$
$881$	−2.85292e17			−0.610146			−0.305073	+	0.952329i	$0.598681\pi$
$882$	6.65737e16	−	9.16309e16i	0.141414	−	0.194639i
$883$	1.00071e17	−	3.07987e17i	0.211127	−	0.649782i	−0.788279	−	0.615318i	$-0.789028\pi$
$883$	1.00071e17	−	3.07987e17i	0.211127	−	0.649782i	0.999406	−	0.0344643i	$-0.0109725\pi$
$884$	1.19996e17	+	3.69311e17i	0.251451	+	0.773888i
$885$	1.24100e17	−	9.01638e16i	0.258292	−	0.187660i
$886$	−8.10690e15	−	1.11582e16i	−0.0167592	−	0.0230670i
$887$	5.57012e17	−	1.80984e17i	1.14373	−	0.371620i	0.324951	−	0.945731i	$-0.394652\pi$
$887$	5.57012e17	−	1.80984e17i	1.14373	−	0.371620i	0.818778	+	0.574111i	$0.194652\pi$
$888$	−9.61328e16	−	3.12354e16i	−0.196062	−	0.0637045i
$889$	−4.11164e17	−	2.98728e17i	−0.832922	−	0.605153i
$890$			1.88329e17i			0.378946i
$891$	−6.93210e16	−	1.92815e17i	−0.138548	−	0.385367i
$892$	2.10921e17			0.418727
$893$	1.17876e17	−	1.62242e17i	0.232443	−	0.319930i
$894$	4.74496e16	−	1.46035e17i	0.0929411	−	0.286043i
$895$	6.85460e16	+	2.10963e17i	0.133366	+	0.410457i
$896$	2.78937e16	−	2.02659e16i	0.0539086	−	0.0391669i
$897$	−2.60580e17	−	3.58658e17i	−0.500250	−	0.688534i
$898$	−2.11349e17	+	6.86715e16i	−0.403035	+	0.130954i
$899$	1.18746e17	+	3.85829e16i	0.224937	+	0.0730864i
$900$	1.38752e17	+	1.00809e17i	0.261086	+	0.189690i
$901$			2.91624e17i			0.545099i
$902$	3.61222e17	−	2.79936e17i	0.670710	−	0.519780i
$903$	2.67916e16			0.0494166
$904$	5.22511e16	−	7.19175e16i	0.0957382	−	0.131772i
$905$	9.76832e15	−	3.00638e16i	0.0177799	−	0.0547208i
$906$	2.68128e16	+	8.25214e16i	0.0484812	+	0.149210i
$907$	3.42536e17	−	2.48867e17i	0.615265	−	0.447016i	−0.236000	−	0.971753i	$-0.575836\pi$
$907$	3.42536e17	−	2.48867e17i	0.615265	−	0.447016i	0.851264	+	0.524737i	$0.175836\pi$
$908$	2.40446e15	+	3.30946e15i	0.00429045	+	0.00590530i
$909$	−5.99008e17	+	1.94629e17i	−1.06182	+	0.345005i
$910$	1.37838e17	+	4.47863e16i	0.242729	+	0.0788674i
$911$	5.96019e17	+	4.33033e17i	1.04268	+	0.757549i	0.970806	−	0.239865i	$-0.0771031\pi$
$911$	5.96019e17	+	4.33033e17i	1.04268	+	0.757549i	0.0718706	+	0.997414i	$0.477103\pi$
$912$			1.13098e17i			0.196556i
$913$	−2.99669e17	−	3.86685e17i	−0.517389	−	0.667625i
$914$	−8.93093e16			−0.153186
$915$	−5.28752e16	+	7.27764e16i	−0.0901001	+	0.124012i
$916$	−1.95318e16	+	6.01127e16i	−0.0330651	+	0.101764i
$917$	2.53505e17	+	7.80209e17i	0.426355	+	1.31219i
$918$	4.07614e17	−	2.96149e17i	0.681072	−	0.494828i
$919$	−3.01697e17	−	4.15250e17i	−0.500816	−	0.689314i	0.481521	−	0.876434i	$-0.340084\pi$
$919$	−3.01697e17	−	4.15250e17i	−0.500816	−	0.689314i	−0.982337	+	0.187121i	$0.940084\pi$
$920$	−1.42664e17	+	4.63543e16i	−0.235281	+	0.0764474i
$921$	1.24919e17	+	4.05886e16i	0.204678	+	0.0665038i
$922$	−3.35861e17	−	2.44017e17i	−0.546732	−	0.397224i
$923$		−	8.30022e17i		−	1.34239i
$924$	−1.01590e17	+	3.65238e16i	−0.163237	+	0.0586873i
$925$	6.49905e17			1.03753
$926$	−3.22747e17	+	4.44223e17i	−0.511913	+	0.704587i
$927$	5.09557e16	−	1.56826e17i	0.0802998	−	0.247138i
$928$	−5.74839e16	−	1.76917e17i	−0.0900033	−	0.277002i
$929$	1.81951e17	−	1.32195e17i	0.283049	−	0.205647i	−0.437197	−	0.899366i	$-0.644029\pi$
$929$	1.81951e17	−	1.32195e17i	0.283049	−	0.205647i	0.720246	+	0.693719i	$0.244029\pi$
$930$	−7.56060e15	−	1.04063e16i	−0.0116858	−	0.0160841i
$931$	−4.56718e17	+	1.48397e17i	−0.701375	+	0.227890i
$932$	−1.42473e17	−	4.62923e16i	−0.217389	−	0.0706340i
$933$	4.11409e17	+	2.98906e17i	0.623711	+	0.453153i
$934$			5.32468e17i			0.802070i
$935$	−3.95019e17	−	1.14954e17i	−0.591218	−	0.172049i
$936$	2.10801e17			0.313485
$937$	5.65610e17	−	7.78495e17i	0.835755	−	1.15032i	−0.151069	−	0.988523i	$-0.548272\pi$
$937$	5.65610e17	−	7.78495e17i	0.835755	−	1.15032i	0.986824	−	0.161796i	$-0.0517285\pi$
$938$	1.16386e17	−	3.58199e17i	0.170877	−	0.525905i
$939$	1.58340e17	+	4.87320e17i	0.230992	+	0.710921i
$940$	2.74915e16	−	1.99738e16i	0.0398503	−	0.0289529i
$941$	5.25486e17	+	7.23270e17i	0.756874	+	1.04175i	0.997468	+	0.0711221i	$0.0226580\pi$
$941$	5.25486e17	+	7.23270e17i	0.756874	+	1.04175i	−0.240593	+	0.970626i	$0.577342\pi$
$942$	−3.27763e16	+	1.06497e16i	−0.0469088	+	0.0152416i
$943$	1.31941e18	+	4.28701e17i	1.87633	+	0.609656i
$944$	2.33309e17	+	1.69509e17i	0.329685	+	0.239530i
$945$		−	1.88048e17i		−	0.264045i
$946$	−5.96864e16	−	4.06016e16i	−0.0832777	−	0.0566495i
$947$	5.95874e17			0.826142			0.413071	−	0.910699i	$-0.364456\pi$
$947$	5.95874e17			0.826142			0.413071	+	0.910699i	$0.364456\pi$
$948$	3.94272e16	−	5.42669e16i	0.0543182	−	0.0747626i
$949$	−7.44616e16	+	2.29169e17i	−0.101938	+	0.313732i
$950$	−2.24710e17	−	6.91585e17i	−0.305689	−	0.940814i
$951$	−1.64763e16	+	1.19707e16i	−0.0222729	+	0.0161822i
$952$	1.68729e17	+	2.32235e17i	0.226656	+	0.311965i
$953$	1.71822e17	−	5.58283e16i	0.229362	−	0.0745241i	−0.192081	−	0.981379i	$-0.561524\pi$
$953$	1.71822e17	−	5.58283e16i	0.229362	−	0.0745241i	0.421443	+	0.906855i	$0.361524\pi$
$954$	1.50562e17	+	4.89207e16i	0.199722	+	0.0648937i
$955$	8.68370e16	+	6.30907e16i	0.114468	+	0.0831659i
$956$			1.84548e17i			0.241747i
$957$	1.80371e16	+	5.82177e17i	0.0234799	+	0.757850i
$958$	2.46990e17			0.319511
$959$	−4.07700e17	+	5.61151e17i	−0.524118	+	0.721386i
$960$	−5.92204e15	+	1.82262e16i	−0.00756561	+	0.0232846i
$961$	−2.38386e17	−	7.33675e17i	−0.302649	−	0.931458i
$962$	6.46247e17	−	4.69526e17i	0.815357	−	0.592392i
$963$	1.82651e17	+	2.51398e17i	0.229016	+	0.315213i
$964$	−6.59346e16	+	2.14234e16i	−0.0821582	+	0.0266948i
$965$	−3.64041e17	−	1.18284e17i	−0.450803	−	0.146475i
$966$	−2.65134e17	−	1.92631e17i	−0.326289	−	0.237063i
$967$		−	7.69379e17i		−	0.940982i	−0.882405	−	0.470491i	$-0.844077\pi$
$967$		−	7.69379e17i		−	0.940982i	0.882405	−	0.470491i	$-0.155923\pi$
$968$	2.81673e17	+	7.25877e16i	0.342368	+	0.0882289i
$969$	−9.41621e17			−1.13745
$970$	−1.84730e17	+	2.54259e17i	−0.221772	+	0.305243i
$971$	−1.97760e17	+	6.08643e17i	−0.235952	+	0.726184i	0.761042	+	0.648702i	$0.224688\pi$
$971$	−1.97760e17	+	6.08643e17i	−0.235952	+	0.726184i	−0.996994	+	0.0774820i	$0.975312\pi$
$972$	−1.31785e17	−	4.05593e17i	−0.156268	−	0.480942i
$973$	−7.18663e17	+	5.22139e17i	−0.846932	+	0.615332i
$974$	3.49878e17	+	4.81565e17i	0.409791	+	0.564029i
$975$	3.46334e17	−	1.12531e17i	0.403151	−	0.130992i
$976$	−1.60842e17	−	5.22608e16i	−0.186081	−	0.0604612i
$977$	−8.95237e17	−	6.50427e17i	−1.02937	−	0.747879i	−0.0611854	−	0.998126i	$-0.519488\pi$
$977$	−8.95237e17	−	6.50427e17i	−1.02937	−	0.747879i	−0.968182	+	0.250247i	$0.919488\pi$
$978$		−	9.38182e16i		−	0.107215i
$979$	1.10808e18	−	3.43306e16i	1.25856	−	0.0389929i
$980$	−8.13724e16			−0.0918587
$981$	−6.79547e17	+	9.35317e17i	−0.762440	+	1.04941i
$982$	−1.16016e17	+	3.57060e17i	−0.129374	+	0.398173i
$983$	1.92068e17	+	5.91124e17i	0.212879	+	0.655175i	0.999297	+	0.0374803i	$0.0119331\pi$
$983$	1.92068e17	+	5.91124e17i	0.212879	+	0.655175i	−0.786418	+	0.617694i	$0.788067\pi$
$984$	1.43388e17	−	1.04177e17i	0.157958	−	0.114763i
$985$	−3.24763e16	−	4.46997e16i	−0.0355589	−	0.0489427i
$986$	1.47297e18	−	4.78595e17i	1.60299	−	0.520843i
$987$	7.06069e16	+	2.29416e16i	0.0763738	+	0.0248154i
$988$	−7.23082e17	−	5.25350e17i	−0.777402	−	0.564816i
$989$		−	2.19139e17i		−	0.234175i
$990$	−1.25615e17	+	1.84660e17i	−0.133422	+	0.196138i
$991$	3.84976e17			0.406436			0.203218	−	0.979134i	$-0.434860\pi$
$991$	3.84976e17			0.406436			0.203218	+	0.979134i	$0.434860\pi$
$992$	1.42140e16	−	1.95639e16i	0.0149158	−	0.0205299i
$993$	−9.70217e15	+	2.98602e16i	−0.0101198	+	0.0311456i
$994$	−1.89608e17	−	5.83554e17i	−0.196580	−	0.605010i
$995$	−7.48859e16	+	5.44078e16i	−0.0771723	+	0.0560690i
$996$	−1.11521e17	−	1.53495e17i	−0.114235	−	0.157231i
$997$	−1.14021e18	+	3.70477e17i	−1.16095	+	0.377217i	−0.825259	−	0.564754i	$-0.808971\pi$
$997$	−1.14021e18	+	3.70477e17i	−1.16095	+	0.377217i	−0.335694	+	0.941971i	$0.608971\pi$
$998$	−9.26098e17	−	3.00907e17i	−0.937289	−	0.304544i
$999$	−8.38503e17	−	6.09208e17i	−0.843551	−	0.612876i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.13.d.a.7.4	✓	48
11.8	odd	10	inner	22.13.d.a.19.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.13.d.a.7.4	✓	48	1.1	even	1	trivial
22.13.d.a.19.4	yes	48	11.8	odd	10	inner

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-26.6001 + 36.6119i) q^{2} +(103.669 - 319.061i) q^{3} +(-632.867 - 1947.76i) q^{4} +(-5380.08 + 3908.86i) q^{5} +(8923.84 + 12282.6i) q^{6} +(-84352.8 + 27407.9i) q^{7} +(88145.7 + 28640.3i) q^{8} +(338892. + 246219. i) q^{9} -300951. i q^{10} +(-1.77071e6 + 54860.6i) q^{11} -687065. q^{12} +(3.19148e6 - 4.39270e6i) q^{13} +(1.24034e6 - 3.81737e6i) q^{14} +(689417. + 2.12181e6i) q^{15} +(-3.39326e6 + 2.46535e6i) q^{16} +(-2.05258e7 - 2.82514e7i) q^{17} +(-1.80291e7 + 5.85802e6i) q^{18} +(7.64421e7 + 2.48375e7i) q^{19} +(1.10184e7 + 8.00534e6i) q^{20} +2.97551e7i q^{21} +(4.50926e7 - 6.62885e7i) q^{22} +2.43378e8 q^{23} +(1.82760e7 - 2.51548e7i) q^{24} +(-6.17775e7 + 1.90132e8i) q^{25} +(7.59313e7 + 2.33693e8i) q^{26} +(2.57930e8 - 1.87397e8i) q^{27} +(1.06768e8 + 1.46954e8i) q^{28} +(9.32064e8 - 3.02846e8i) q^{29} +(-9.60220e7 - 3.11994e7i) q^{30} +(1.03070e8 + 7.48845e7i) q^{31} -1.89813e8i q^{32} +(-1.66065e8 + 5.70653e8i) q^{33} +1.58033e9 q^{34} +(3.46692e8 - 4.77180e8i) q^{35} +(2.65104e8 - 8.15905e8i) q^{36} +(-1.00458e9 - 3.09178e9i) q^{37} +(-2.94272e9 + 2.13801e9i) q^{38} +(-1.07068e9 - 1.47367e9i) q^{39} +(-5.86182e8 + 1.90462e8i) q^{40} +(5.42123e9 + 1.76146e9i) q^{41} +(-1.08939e9 - 7.91489e8i) q^{42} -9.00405e8i q^{43} +(1.22748e9 + 3.41421e9i) q^{44} -2.78570e9 q^{45} +(-6.47388e9 + 8.91053e9i) q^{46} +(7.71013e8 - 2.37294e9i) q^{47} +(4.34821e8 + 1.33824e9i) q^{48} +(-4.83363e9 + 3.51184e9i) q^{49} +(-5.31779e9 - 7.31932e9i) q^{50} +(-1.11418e10 + 3.62020e9i) q^{51} +(-1.05757e10 - 3.43626e9i) q^{52} +(-6.75615e9 - 4.90863e9i) q^{53} +1.44281e10i q^{54} +(9.31213e9 - 7.21662e9i) q^{55} -8.22031e9 q^{56} +(1.58494e10 - 2.18148e10i) q^{57} +(-1.37052e10 + 4.21804e10i) q^{58} +(-2.12469e10 - 6.53913e10i) q^{59} +(3.69647e9 - 2.68564e9i) q^{60} +(2.37002e10 + 3.26206e10i) q^{61} +(-5.48333e9 + 1.78164e9i) q^{62} +(-3.53349e10 - 1.14810e10i) q^{63} +(6.94940e9 + 5.04904e9i) q^{64} +3.61081e10i q^{65} +(-1.64754e10 - 2.12594e10i) q^{66} +9.38338e10 q^{67} +(-4.20369e10 + 5.78588e10i) q^{68} +(2.52308e10 - 7.76525e10i) q^{69} +(8.24845e9 + 2.53861e10i) q^{70} +(1.23673e11 - 8.98535e10i) q^{71} +(2.28201e10 + 3.14091e10i) q^{72} +(-4.22068e10 + 1.37138e10i) q^{73} +(1.39918e11 + 4.54621e10i) q^{74} +(5.42592e10 + 3.94216e10i) q^{75} -1.64610e11i q^{76} +(1.47861e11 - 5.31591e10i) q^{77} +8.24340e10 q^{78} +(-5.73849e10 + 7.89836e10i) q^{79} +(8.61933e9 - 2.65276e10i) q^{80} +(3.57407e10 + 1.09999e11i) q^{81} +(-2.08696e11 + 1.51626e11i) q^{82} +(1.62315e11 + 2.23407e11i) q^{83} +(5.79559e10 - 1.88310e10i) q^{84} +(2.20861e11 + 7.17622e10i) q^{85} +(3.29656e10 + 2.39509e10i) q^{86} -3.28781e11i q^{87} +(-1.57652e11 - 4.58779e10i) q^{88} -6.25780e11 q^{89} +(7.41001e10 - 1.01990e11i) q^{90} +(-1.48816e11 + 4.58008e11i) q^{91} +(-1.54026e11 - 4.74043e11i) q^{92} +(3.45779e10 - 2.51223e10i) q^{93} +(6.63687e10 + 9.13487e10i) q^{94} +(-5.08351e11 + 1.65173e11i) q^{95} +(-6.05619e10 - 1.96777e10i) q^{96} +(-8.44850e11 - 6.13819e11i) q^{97} -2.70384e11i q^{98} +(-6.13588e11 - 4.17392e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 1240 q^{3} + 24576 q^{4} + 1440 q^{5} - 147200 q^{6} + 439200 q^{7} + 563348 q^{9} - 7317468 q^{11} + 737280 q^{12} + 13341600 q^{13} - 7524864 q^{14} - 29808888 q^{15} - 50331648 q^{16} + 29458800 q^{17}+ \cdots - 5181480396620 q^{99}+O(q^{100}) \) 48 * q + 1240 * q^3 + 24576 * q^4 + 1440 * q^5 - 147200 * q^6 + 439200 * q^7 + 563348 * q^9 - 7317468 * q^11 + 737280 * q^12 + 13341600 * q^13 - 7524864 * q^14 - 29808888 * q^15 - 50331648 * q^16 + 29458800 * q^17 - 96857600 * q^18 + 59195700 * q^19 - 2949120 * q^20 - 147874560 * q^22 + 297521280 * q^23 - 301465600 * q^24 - 349772268 * q^25 + 603191808 * q^26 - 434593340 * q^27 - 981811200 * q^28 + 121665600 * q^29 + 3275650560 * q^30 - 1117400544 * q^31 - 13803991820 * q^33 - 2568870912 * q^34 + 1026283680 * q^35 + 7058374656 * q^36 + 11737565760 * q^37 + 4500864000 * q^38 - 23697921920 * q^39 - 7817134080 * q^40 + 4863244680 * q^41 + 12992468480 * q^42 - 18701991936 * q^44 + 29640403232 * q^45 + 33202391040 * q^46 + 8084031480 * q^47 + 5200936960 * q^48 + 593931516 * q^49 - 13593646080 * q^50 - 30011589660 * q^51 + 55099392000 * q^52 + 40815862920 * q^53 + 29310331992 * q^55 - 7285506048 * q^56 - 98665594300 * q^57 + 81900510720 * q^58 - 156541010940 * q^59 - 30685659136 * q^60 + 255357655680 * q^61 + 67163788800 * q^62 - 429459850400 * q^63 + 103079215104 * q^64 + 460708043264 * q^66 + 76186270200 * q^67 + 60331622400 * q^68 - 1054414688600 * q^69 - 352820375040 * q^70 + 60925955544 * q^71 + 95420416000 * q^72 + 363471756600 * q^73 + 378662860800 * q^74 - 57777629724 * q^75 + 326539185480 * q^77 - 1234846474240 * q^78 + 137547461520 * q^79 - 120795955200 * q^80 - 1017431491848 * q^81 + 613199754240 * q^82 + 715268672100 * q^83 - 354644459520 * q^84 + 1202406730800 * q^85 - 80499776256 * q^86 - 270225899520 * q^88 + 724193830584 * q^89 - 1005067351040 * q^90 + 1925501559192 * q^91 - 608833290240 * q^92 - 2466072811400 * q^93 + 300785049600 * q^94 + 6877125644400 * q^95 + 1350178653780 * q^97 - 5181480396620 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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