LMFDB - Embedded newform 91.10.h.a.16.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(16,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, degree $2$, 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:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$164$
Relative dimension:	$82$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.9
Character	$\chi$	$=$	91.16
Dual form			91.10.h.a.74.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-39.3517 q^{2} +(-134.908 + 233.667i) q^{3} +1036.55 q^{4} +(-1292.21 + 2238.17i) q^{5} +(5308.84 - 9195.18i) q^{6} +(797.607 - 6302.18i) q^{7} -20642.1 q^{8} +(-26558.7 - 46000.9i) q^{9} +O(q^{10})$	\(q-39.3517 q^{2} +(-134.908 + 233.667i) q^{3} +1036.55 q^{4} +(-1292.21 + 2238.17i) q^{5} +(5308.84 - 9195.18i) q^{6} +(797.607 - 6302.18i) q^{7} -20642.1 q^{8} +(-26558.7 - 46000.9i) q^{9} +(50850.6 - 88075.8i) q^{10} +(989.006 - 1713.01i) q^{11} +(-139839. + 242208. i) q^{12} +(89126.5 + 51584.5i) q^{13} +(-31387.2 + 248001. i) q^{14} +(-348658. - 603893. i) q^{15} +281585. q^{16} -130872. q^{17} +(1.04513e6 + 1.81021e6i) q^{18} +(40886.3 + 70817.2i) q^{19} +(-1.33944e6 + 2.31999e6i) q^{20} +(1.36501e6 + 1.03659e6i) q^{21} +(-38919.0 + 67409.8i) q^{22} +828097. q^{23} +(2.78477e6 - 4.82337e6i) q^{24} +(-2.36305e6 - 4.09292e6i) q^{25} +(-3.50728e6 - 2.02994e6i) q^{26} +9.02109e6 q^{27} +(826763. - 6.53255e6i) q^{28} +(2.44130e6 + 4.22845e6i) q^{29} +(1.37203e7 + 2.37642e7i) q^{30} +(-770884. - 1.33521e6i) q^{31} -512080. q^{32} +(266849. + 462196. i) q^{33} +5.15002e6 q^{34} +(1.30747e7 + 9.92891e6i) q^{35} +(-2.75295e7 - 4.76825e7i) q^{36} +3.10213e6 q^{37} +(-1.60894e6 - 2.78677e6i) q^{38} +(-2.40774e7 + 1.38668e7i) q^{39} +(2.66739e7 - 4.62005e7i) q^{40} +(1.08273e7 + 1.87534e7i) q^{41} +(-5.37153e7 - 4.07914e7i) q^{42} +(371566. - 643571. i) q^{43} +(1.02516e6 - 1.77563e6i) q^{44} +1.37277e8 q^{45} -3.25870e7 q^{46} +(5.55290e6 - 9.61790e6i) q^{47} +(-3.79879e7 + 6.57970e7i) q^{48} +(-3.90813e7 - 1.00533e7i) q^{49} +(9.29899e7 + 1.61063e8i) q^{50} +(1.76556e7 - 3.05804e7i) q^{51} +(9.23845e7 + 5.34701e7i) q^{52} +(1.06555e6 + 1.84558e6i) q^{53} -3.54995e8 q^{54} +(2.55601e6 + 4.42713e6i) q^{55} +(-1.64643e7 + 1.30090e8i) q^{56} -2.20635e7 q^{57} +(-9.60691e7 - 1.66397e8i) q^{58} +5.05608e7 q^{59} +(-3.61403e8 - 6.25968e8i) q^{60} +(9.67515e7 + 1.67578e8i) q^{61} +(3.03356e7 + 5.25428e7i) q^{62} +(-3.11089e8 + 1.30687e8i) q^{63} -1.24020e8 q^{64} +(-2.30625e8 + 1.32823e8i) q^{65} +(-1.05010e7 - 1.81882e7i) q^{66} +(7.50625e7 - 1.30012e8i) q^{67} -1.35656e8 q^{68} +(-1.11717e8 + 1.93499e8i) q^{69} +(-5.14511e8 - 3.90719e8i) q^{70} +(-8.06295e7 + 1.39654e8i) q^{71} +(5.48226e8 + 9.49555e8i) q^{72} +(1.43686e8 + 2.48871e8i) q^{73} -1.22074e8 q^{74} +1.27517e9 q^{75} +(4.23809e7 + 7.34058e7i) q^{76} +(-1.00068e7 - 7.59920e6i) q^{77} +(9.47488e8 - 5.45681e8i) q^{78} +(2.00649e8 - 3.47534e8i) q^{79} +(-3.63866e8 + 6.30235e8i) q^{80} +(-6.94260e8 + 1.20249e9i) q^{81} +(-4.26071e8 - 7.37976e8i) q^{82} +2.64758e8 q^{83} +(1.41490e9 + 1.07448e9i) q^{84} +(1.69114e8 - 2.92914e8i) q^{85} +(-1.46217e7 + 2.53256e7i) q^{86} -1.31740e9 q^{87} +(-2.04151e7 + 3.53601e7i) q^{88} -1.06327e8 q^{89} -5.40210e9 q^{90} +(3.96182e8 - 5.20547e8i) q^{91} +8.58367e8 q^{92} +4.15993e8 q^{93} +(-2.18516e8 + 3.78481e8i) q^{94} -2.11335e8 q^{95} +(6.90836e7 - 1.19656e8i) q^{96} +(6.03467e8 - 1.04523e9i) q^{97} +(1.53791e9 + 3.95615e8i) q^{98} -1.05067e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9}+O(q^{10}) $ 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9	\( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9} + 38977 q^{10} - 59285 q^{11} + 44088 q^{12} + 232454 q^{13} + 17108 q^{14} - 407531 q^{15} + 10497654 q^{16} - 1395086 q^{17} - 76575 q^{18} + 1207545 q^{19} + 713618 q^{20} + 1790137 q^{21} + 199216 q^{22} + 2148062 q^{23} + 3435832 q^{24} - 29660780 q^{25} - 6096660 q^{26} - 9655538 q^{27} - 5996877 q^{28} + 996812 q^{29} + 4910674 q^{30} + 7678612 q^{31} - 13584366 q^{32} - 3082415 q^{33} + 32705872 q^{34} + 11865077 q^{35} - 134627249 q^{36} - 25237130 q^{37} + 25519874 q^{38} + 30627737 q^{39} + 45727182 q^{40} - 13667582 q^{41} - 81628563 q^{42} + 26867814 q^{43} - 75673614 q^{44} + 29593550 q^{45} - 70893356 q^{46} - 23074040 q^{47} + 29166348 q^{48} - 13541447 q^{49} + 77715962 q^{50} - 94065066 q^{51} + 139792121 q^{52} + 46529776 q^{53} - 14474550 q^{54} + 218800681 q^{55} - 649788015 q^{56} - 143710238 q^{57} + 1142701 q^{58} + 439131230 q^{59} - 557690411 q^{60} + 508694743 q^{61} + 307731320 q^{62} - 355730647 q^{63} + 1713678376 q^{64} + 148754944 q^{65} + 278425259 q^{66} + 37418955 q^{67} - 1290484830 q^{68} + 290468024 q^{69} - 182370322 q^{70} - 415622020 q^{71} + 720832393 q^{72} + 514120432 q^{73} + 128989762 q^{74} + 241348444 q^{75} + 985961470 q^{76} - 1189530907 q^{77} + 2167273673 q^{78} - 376448286 q^{79} - 482394712 q^{80} - 3131306974 q^{81} - 971561072 q^{82} + 971157612 q^{83} + 3735517629 q^{84} + 538436691 q^{85} + 1470174876 q^{86} - 912549686 q^{87} - 629673387 q^{88} + 699403942 q^{89} - 8083448244 q^{90} + 2740572083 q^{91} + 2309185554 q^{92} + 820704894 q^{93} + 419356886 q^{94} - 5283246 q^{95} - 4707829686 q^{96} + 1339771120 q^{97} - 1961676608 q^{98} + 1482300132 q^{99}+O(q^{100}) \) 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9 + 38977 * q^10 - 59285 * q^11 + 44088 * q^12 + 232454 * q^13 + 17108 * q^14 - 407531 * q^15 + 10497654 * q^16 - 1395086 * q^17 - 76575 * q^18 + 1207545 * q^19 + 713618 * q^20 + 1790137 * q^21 + 199216 * q^22 + 2148062 * q^23 + 3435832 * q^24 - 29660780 * q^25 - 6096660 * q^26 - 9655538 * q^27 - 5996877 * q^28 + 996812 * q^29 + 4910674 * q^30 + 7678612 * q^31 - 13584366 * q^32 - 3082415 * q^33 + 32705872 * q^34 + 11865077 * q^35 - 134627249 * q^36 - 25237130 * q^37 + 25519874 * q^38 + 30627737 * q^39 + 45727182 * q^40 - 13667582 * q^41 - 81628563 * q^42 + 26867814 * q^43 - 75673614 * q^44 + 29593550 * q^45 - 70893356 * q^46 - 23074040 * q^47 + 29166348 * q^48 - 13541447 * q^49 + 77715962 * q^50 - 94065066 * q^51 + 139792121 * q^52 + 46529776 * q^53 - 14474550 * q^54 + 218800681 * q^55 - 649788015 * q^56 - 143710238 * q^57 + 1142701 * q^58 + 439131230 * q^59 - 557690411 * q^60 + 508694743 * q^61 + 307731320 * q^62 - 355730647 * q^63 + 1713678376 * q^64 + 148754944 * q^65 + 278425259 * q^66 + 37418955 * q^67 - 1290484830 * q^68 + 290468024 * q^69 - 182370322 * q^70 - 415622020 * q^71 + 720832393 * q^72 + 514120432 * q^73 + 128989762 * q^74 + 241348444 * q^75 + 985961470 * q^76 - 1189530907 * q^77 + 2167273673 * q^78 - 376448286 * q^79 - 482394712 * q^80 - 3131306974 * q^81 - 971561072 * q^82 + 971157612 * q^83 + 3735517629 * q^84 + 538436691 * q^85 + 1470174876 * q^86 - 912549686 * q^87 - 629673387 * q^88 + 699403942 * q^89 - 8083448244 * q^90 + 2740572083 * q^91 + 2309185554 * q^92 + 820704894 * q^93 + 419356886 * q^94 - 5283246 * q^95 - 4707829686 * q^96 + 1339771120 * q^97 - 1961676608 * q^98 + 1482300132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−39.3517			−1.73911			−0.869557	−	0.493832i	$-0.835596\pi$
$2$	−39.3517			−1.73911			−0.869557	+	0.493832i	$0.835596\pi$
$3$	−134.908	+	233.667i	−0.961592	+	1.66553i	−0.243088	+	0.970004i	$0.578160\pi$
$3$	−134.908	+	233.667i	−0.961592	+	1.66553i	−0.718504	+	0.695523i	$0.755173\pi$
$4$	1036.55			2.02452
$5$	−1292.21	+	2238.17i	−0.924630	+	1.60151i	−0.132475	+	0.991186i	$0.542292\pi$
$5$	−1292.21	+	2238.17i	−0.924630	+	1.60151i	−0.792155	+	0.610319i	$0.791041\pi$
$6$	5308.84	−	9195.18i	1.67232	−	2.89654i
$7$	797.607	−	6302.18i	0.125559	−	0.992086i
$7$	797.607	−	6302.18i	0.125559	−	0.992086i
$8$	−20642.1			−1.78176
$9$	−26558.7	−	46000.9i	−1.34932	−	2.33709i
$10$	50850.6	−	88075.8i	1.60804	−	2.78520i
$11$	989.006	−	1713.01i	0.0203672	−	0.0352771i	−0.855662	−	0.517535i	$-0.826850\pi$
$11$	989.006	−	1713.01i	0.0203672	−	0.0352771i	0.876029	+	0.482258i	$0.160183\pi$
$12$	−139839.	+	242208.i	−1.94676	+	3.37189i
$13$	89126.5	+	51584.5i	0.865490	+	0.500927i
$13$	89126.5	+	51584.5i	0.865490	+	0.500927i
$14$	−31387.2	+	248001.i	−0.218361	+	1.72535i
$15$	−348658.	−	603893.i	−1.77823	−	3.07999i
$16$	281585.			1.07416
$17$	−130872.			−0.380037			−0.190018	−	0.981781i	$-0.560855\pi$
$17$	−130872.			−0.380037			−0.190018	+	0.981781i	$0.560855\pi$
$18$	1.04513e6	+	1.81021e6i	2.34662	+	4.06447i
$19$	40886.3	+	70817.2i	0.0719758	+	0.124666i	0.899767	−	0.436370i	$-0.143736\pi$
$19$	40886.3	+	70817.2i	0.0719758	+	0.124666i	−0.827791	+	0.561036i	$0.810403\pi$
$20$	−1.33944e6	+	2.31999e6i	−1.87193	+	3.24228i
$21$	1.36501e6	+	1.03659e6i	1.53161	+	1.16310i
$22$	−38919.0	+	67409.8i	−0.0354209	+	0.0613509i
$23$	828097.			0.617029			0.308515	−	0.951220i	$-0.400168\pi$
$23$	828097.			0.617029			0.308515	+	0.951220i	$0.400168\pi$
$24$	2.78477e6	−	4.82337e6i	1.71332	−	2.96756i
$25$	−2.36305e6	−	4.09292e6i	−1.20988	−	2.09557i
$26$	−3.50728e6	−	2.02994e6i	−1.50519	−	0.871169i
$27$	9.02109e6			3.26680
$28$	826763.	−	6.53255e6i	0.254197	−	2.00850i
$29$	2.44130e6	+	4.22845e6i	0.640958	+	1.11017i	0.985219	+	0.171298i	$0.0547960\pi$
$29$	2.44130e6	+	4.22845e6i	0.640958	+	1.11017i	−0.344261	+	0.938874i	$0.611871\pi$
$30$	1.37203e7	+	2.37642e7i	3.09255	+	5.35646i
$31$	−770884.	−	1.33521e6i	−0.149921	−	0.259670i	0.781277	−	0.624184i	$-0.214569\pi$
$31$	−770884.	−	1.33521e6i	−0.149921	−	0.259670i	−0.931198	+	0.364514i	$0.881235\pi$
$32$	−512080.			−0.0863303
$33$	266849.	+	462196.i	0.0391699	+	0.0678443i
$34$	5.15002e6			0.660928
$35$	1.30747e7	+	9.92891e6i	1.47274	+	1.11840i
$36$	−2.75295e7	−	4.76825e7i	−2.73172	−	4.73148i
$37$	3.10213e6			0.272115			0.136057	−	0.990701i	$-0.456557\pi$
$37$	3.10213e6			0.272115			0.136057	+	0.990701i	$0.456557\pi$
$38$	−1.60894e6	−	2.78677e6i	−0.125174	−	0.216808i
$39$	−2.40774e7	+	1.38668e7i	−1.66655	+	0.959809i
$40$	2.66739e7	−	4.62005e7i	1.64747	−	2.85349i
$41$	1.08273e7	+	1.87534e7i	0.598399	+	1.03646i	0.993058	+	0.117630i	$0.0375297\pi$
$41$	1.08273e7	+	1.87534e7i	0.598399	+	1.03646i	−0.394658	+	0.918828i	$0.629137\pi$
$42$	−5.37153e7	−	4.07914e7i	−2.66364	−	2.02277i
$43$	371566.	−	643571.i	0.0165740	−	0.0287070i	−0.857619	−	0.514285i	$-0.828057\pi$
$43$	371566.	−	643571.i	0.0165740	−	0.0287070i	0.874193	+	0.485578i	$0.161391\pi$
$44$	1.02516e6	−	1.77563e6i	0.0412338	−	0.0714191i
$45$	1.37277e8			4.99048
$46$	−3.25870e7			−1.07308
$47$	5.55290e6	−	9.61790e6i	0.165989	−	0.287501i	−0.771017	−	0.636815i	$-0.780252\pi$
$47$	5.55290e6	−	9.61790e6i	0.165989	−	0.287501i	0.937006	+	0.349313i	$0.113585\pi$
$48$	−3.79879e7	+	6.57970e7i	−1.03290	+	1.78904i
$49$	−3.90813e7	−	1.00533e7i	−0.968470	−	0.249131i
$50$	9.29899e7	+	1.61063e8i	2.10412	+	3.64445i
$51$	1.76556e7	−	3.05804e7i	0.365441	−	0.632962i
$52$	9.23845e7	+	5.34701e7i	1.75220	+	1.01414i
$53$	1.06555e6	+	1.84558e6i	0.0185494	+	0.0321286i	0.875151	−	0.483850i	$-0.160762\pi$
$53$	1.06555e6	+	1.84558e6i	0.0185494	+	0.0321286i	−0.856602	+	0.515978i	$0.827429\pi$
$54$	−3.54995e8			−5.68133
$55$	2.55601e6	+	4.42713e6i	0.0376643	+	0.0652365i
$56$	−1.64643e7	+	1.30090e8i	−0.223716	+	1.76766i
$57$	−2.20635e7			−0.276846
$58$	−9.60691e7	−	1.66397e8i	−1.11470	−	1.93072i
$59$	5.05608e7			0.543225			0.271613	−	0.962407i	$-0.412443\pi$
$59$	5.05608e7			0.543225			0.271613	+	0.962407i	$0.412443\pi$
$60$	−3.61403e8	−	6.25968e8i	−3.60007	−	6.23550i
$61$	9.67515e7	+	1.67578e8i	0.894692	+	1.54965i	0.834186	+	0.551483i	$0.185938\pi$
$61$	9.67515e7	+	1.67578e8i	0.894692	+	1.54965i	0.0605057	+	0.998168i	$0.480729\pi$
$62$	3.03356e7	+	5.25428e7i	0.260729	+	0.451596i
$63$	−3.11089e8	+	1.30687e8i	−2.48801	+	1.04520i
$64$	−1.24020e8			−0.924022
$65$	−2.30625e8	+	1.32823e8i	−1.60249	+	0.922915i
$66$	−1.05010e7	−	1.81882e7i	−0.0681210	−	0.117989i
$67$	7.50625e7	−	1.30012e8i	0.455078	−	0.788219i	−0.543614	−	0.839335i	$-0.682945\pi$
$67$	7.50625e7	−	1.30012e8i	0.455078	−	0.788219i	0.998693	+	0.0511162i	$0.0162779\pi$
$68$	−1.35656e8			−0.769392
$69$	−1.11717e8	+	1.93499e8i	−0.593331	+	1.02768i
$70$	−5.14511e8	−	3.90719e8i	−2.56126	−	1.94502i
$71$	−8.06295e7	+	1.39654e8i	−0.376557	+	0.652217i	−0.990559	−	0.137088i	$-0.956226\pi$
$71$	−8.06295e7	+	1.39654e8i	−0.376557	+	0.652217i	0.614001	+	0.789305i	$0.289559\pi$
$72$	5.48226e8	+	9.49555e8i	2.40416	+	4.16413i
$73$	1.43686e8	+	2.48871e8i	0.592189	+	1.02570i	0.993937	+	0.109952i	$0.0350696\pi$
$73$	1.43686e8	+	2.48871e8i	0.592189	+	1.02570i	−0.401748	+	0.915750i	$0.631597\pi$
$74$	−1.22074e8			−0.473239
$75$	1.27517e9			4.65365
$76$	4.23809e7	+	7.34058e7i	0.145717	+	0.252388i
$77$	−1.00068e7	−	7.59920e6i	−0.0324406	−	0.0246354i
$78$	9.47488e8	−	5.45681e8i	2.89833	−	1.66922i
$79$	2.00649e8	−	3.47534e8i	0.579582	−	1.00387i	−0.415945	−	0.909390i	$-0.636549\pi$
$79$	2.00649e8	−	3.47534e8i	0.579582	−	1.00387i	0.995527	−	0.0944758i	$-0.0301175\pi$
$80$	−3.63866e8	+	6.30235e8i	−0.993200	+	1.72027i
$81$	−6.94260e8	+	1.20249e9i	−1.79201	+	3.10385i
$82$	−4.26071e8	−	7.37976e8i	−1.04068	−	1.80252i
$83$	2.64758e8			0.612346			0.306173	−	0.951976i	$-0.400951\pi$
$83$	2.64758e8			0.612346			0.306173	+	0.951976i	$0.400951\pi$
$84$	1.41490e9	+	1.07448e9i	3.10077	+	2.35473i
$85$	1.69114e8	−	2.92914e8i	0.351394	−	0.608631i
$86$	−1.46217e7	+	2.53256e7i	−0.0288241	+	0.0499248i
$87$	−1.31740e9			−2.46536
$88$	−2.04151e7	+	3.53601e7i	−0.0362894	+	0.0628552i
$89$	−1.06327e8			−0.179633			−0.0898166	−	0.995958i	$-0.528628\pi$
$89$	−1.06327e8			−0.179633			−0.0898166	+	0.995958i	$0.528628\pi$
$90$	−5.40210e9			−8.67902
$91$	3.96182e8	−	5.20547e8i	0.605632	−	0.795745i
$92$	8.58367e8			1.24919
$93$	4.15993e8			0.576650
$94$	−2.18516e8	+	3.78481e8i	−0.288674	+	0.499998i
$95$	−2.11335e8			−0.266204
$96$	6.90836e7	−	1.19656e8i	0.0830146	−	0.143785i
$97$	6.03467e8	−	1.04523e9i	0.692118	−	1.19878i	−0.279024	−	0.960284i	$-0.590011\pi$
$97$	6.03467e8	−	1.04523e9i	0.692118	−	1.19878i	0.971142	−	0.238500i	$-0.0766557\pi$
$98$	1.53791e9	+	3.95615e8i	1.68428	+	0.433267i
$99$	−1.05067e8			−0.109928
$100$	−2.44943e9	−	4.24253e9i	−2.44943	−	4.24253i
$101$	7.26391e8	−	1.25815e9i	0.694584	−	1.20305i	−0.275737	−	0.961233i	$-0.588922\pi$
$101$	7.26391e8	−	1.25815e9i	0.694584	−	1.20305i	0.970321	−	0.241821i	$-0.0777447\pi$
$102$	−6.94778e8	+	1.20339e9i	−0.635543	+	1.10079i
$103$	7.80815e8	−	1.35241e9i	0.683566	−	1.18397i	−0.290319	−	0.956930i	$-0.593761\pi$
$103$	7.80815e8	−	1.35241e9i	0.683566	−	1.18397i	0.973885	−	0.227042i	$-0.0729054\pi$
$104$	−1.83976e9	−	1.06481e9i	−1.54209	−	0.892529i
$105$	−4.08393e9	+	1.71563e9i	−3.27889	+	1.37744i
$106$	−4.19310e7	−	7.26267e7i	−0.0322596	−	0.0558753i
$107$	−1.29895e9			−0.957999			−0.478999	−	0.877815i	$-0.659000\pi$
$107$	−1.29895e9			−0.957999			−0.478999	+	0.877815i	$0.659000\pi$
$108$	9.35085e9			6.61369
$109$	1.02340e8	+	1.77258e8i	0.0694426	+	0.120278i	0.898656	−	0.438654i	$-0.144545\pi$
$109$	1.02340e8	+	1.77258e8i	0.0694426	+	0.120278i	−0.829213	+	0.558932i	$0.811211\pi$
$110$	−1.00583e8	−	1.74215e8i	−0.0655025	−	0.113454i
$111$	−4.18501e8	+	7.24865e8i	−0.261663	+	0.453214i
$112$	2.24594e8	−	1.77460e9i	0.134870	−	1.06566i
$113$	4.65753e8	−	8.06707e8i	0.268721	−	0.465439i	−0.699810	−	0.714329i	$-0.746732\pi$
$113$	4.65753e8	−	8.06707e8i	0.268721	−	0.465439i	0.968532	+	0.248889i	$0.0800655\pi$
$114$	8.68236e8			0.481466
$115$	−1.07007e9	+	1.85342e9i	−0.570524	+	0.988176i
$116$	2.53054e9	+	4.38302e9i	1.29763	+	2.24756i
$117$	5.85376e6	−	5.46992e9i	0.00288801	−	2.69864i
$118$	−1.98965e9			−0.944731
$119$	−1.04384e8	+	8.24777e8i	−0.0477171	+	0.377029i
$120$	7.19702e9	+	1.24656e10i	3.16838	+	5.48780i
$121$	1.17702e9	+	2.03865e9i	0.499170	+	0.864588i
$122$	−3.80733e9	−	6.59449e9i	−1.55597	−	2.69502i
$123$	−5.84272e9			−2.30166
$124$	−7.99063e8	−	1.38402e9i	−0.303517	−	0.525708i
$125$	7.16652e9			2.62551
$126$	1.22419e10	−	5.14274e9i	4.32694	−	1.81772i
$127$	−9.89448e8	−	1.71377e9i	−0.337502	−	0.584570i	0.646460	−	0.762948i	$-0.276249\pi$
$127$	−9.89448e8	−	1.71377e9i	−0.337502	−	0.584570i	−0.983962	+	0.178377i	$0.942915\pi$
$128$	5.14258e9			1.69331
$129$	1.00254e8	+	1.73645e8i	0.0318749	+	0.0552089i
$130$	9.07548e9	−	5.22679e9i	2.78692	−	1.60506i
$131$	−3.08030e8	+	5.33523e8i	−0.0913844	+	0.158282i	−0.908094	−	0.418767i	$-0.862463\pi$
$131$	−3.08030e8	+	5.33523e8i	−0.0913844	+	0.158282i	0.816709	+	0.577049i	$0.195796\pi$
$132$	2.76603e8	+	4.79091e8i	0.0793003	+	0.137352i
$133$	4.78914e8	−	2.01189e8i	0.132716	−	0.0557533i
$134$	−2.95383e9	+	5.11619e9i	−0.791434	+	1.37080i
$135$	−1.16571e10	+	2.01908e10i	−3.02058	+	5.23179i
$136$	2.70147e9			0.677133
$137$	3.11159e9			0.754639			0.377320	−	0.926083i	$-0.376846\pi$
$137$	3.11159e9			0.754639			0.377320	+	0.926083i	$0.376846\pi$
$138$	4.39623e9	−	7.61450e9i	1.03187	−	1.78725i
$139$	−4.72642e8	+	8.18640e8i	−0.107391	+	0.186006i	−0.914712	−	0.404106i	$-0.867583\pi$
$139$	−4.72642e8	+	8.18640e8i	−0.107391	+	0.186006i	0.807322	+	0.590111i	$0.200916\pi$
$140$	1.35526e10	+	1.02919e10i	2.98158	+	2.26421i
$141$	1.49826e9	+	2.59506e9i	0.319228	+	0.552918i
$142$	3.17290e9	−	5.49563e9i	0.654877	−	1.13428i
$143$	1.76511e8	−	1.01657e8i	0.0352988	−	0.0203295i
$144$	−7.47851e9	−	1.29532e10i	−1.44939	−	2.51041i
$145$	−1.26187e10			−2.37060
$146$	−5.65427e9	−	9.79349e9i	−1.02989	−	1.78381i
$147$	7.62149e9	−	7.77573e9i	1.34621	−	1.37345i
$148$	3.21552e9			0.550901
$149$	−2.72316e9	−	4.71666e9i	−0.452622	−	0.783964i	0.545926	−	0.837833i	$-0.316178\pi$
$149$	−2.72316e9	−	4.71666e9i	−0.452622	−	0.783964i	−0.998548	+	0.0538694i	$0.982845\pi$
$150$	−5.01802e10			−8.09323
$151$	4.13160e9	+	7.15614e9i	0.646728	+	1.12017i	0.983900	+	0.178723i	$0.0571964\pi$
$151$	4.13160e9	+	7.15614e9i	0.646728	+	1.12017i	−0.337171	+	0.941443i	$0.609470\pi$
$152$	−8.43978e8	−	1.46181e9i	−0.128243	−	0.222124i
$153$	3.47578e9	+	6.02022e9i	0.512791	+	0.888181i
$154$	3.93786e8	+	2.99041e8i	0.0564179	+	0.0428438i
$155$	3.98458e9			0.554485
$156$	−2.49576e10	+	1.43737e10i	−3.37397	+	1.94315i
$157$	−5.52756e9	−	9.57402e9i	−0.726081	−	1.25761i	−0.958527	−	0.285000i	$-0.908006\pi$
$157$	−5.52756e9	−	9.57402e9i	−0.726081	−	1.25761i	0.232446	−	0.972609i	$-0.425327\pi$
$158$	−7.89587e9	+	1.36760e10i	−1.00796	+	1.74584i
$159$	−5.75001e8			−0.0713480
$160$	6.61715e8	−	1.14612e9i	0.0798236	−	0.138259i
$161$	6.60496e8	−	5.21881e9i	0.0774736	−	0.612146i
$162$	2.73203e10	−	4.73202e10i	3.11651	−	5.39795i
$163$	4.56829e9	+	7.91252e9i	0.506886	+	0.877952i	0.999968	+	0.00796909i	$0.00253667\pi$
$163$	4.56829e9	+	7.91252e9i	0.506886	+	0.877952i	−0.493083	+	0.869982i	$0.664130\pi$
$164$	1.12230e10	+	1.94389e10i	1.21147	+	2.09833i
$165$	−1.37930e9			−0.144871
$166$	−1.04187e10			−1.06494
$167$	7.69679e8	+	1.33312e9i	0.0765748	+	0.132631i	0.901770	−	0.432216i	$-0.142268\pi$
$167$	7.69679e8	+	1.33312e9i	0.0765748	+	0.132631i	−0.825195	+	0.564848i	$0.808935\pi$
$168$	−2.81766e10	−	2.13973e10i	−2.72896	−	2.07237i
$169$	5.28258e9	+	9.19509e9i	0.498145	+	0.867094i
$170$	−6.65491e9	+	1.15266e10i	−0.611114	+	1.05848i
$171$	2.17177e9	−	3.76162e9i	0.194237	−	0.336428i
$172$	3.85148e8	−	6.67096e8i	0.0335544	−	0.0581180i
$173$	3.60785e9	+	6.24897e9i	0.306225	+	0.530397i	0.977533	−	0.210781i	$-0.0676007\pi$
$173$	3.60785e9	+	6.24897e9i	0.306225	+	0.530397i	−0.671308	+	0.741178i	$0.734267\pi$
$174$	5.18418e10			4.28754
$175$	−2.76791e10	+	1.16278e10i	−2.23090	+	0.937188i
$176$	2.78489e8	−	4.82357e8i	0.0218777	−	0.0378932i
$177$	−6.82104e9	+	1.18144e10i	−0.522361	+	0.904757i
$178$	4.18413e9			0.312403
$179$	−5.45644e8	+	9.45082e8i	−0.0397256	+	0.0688067i	−0.885205	−	0.465202i	$-0.845982\pi$
$179$	−5.45644e8	+	9.45082e8i	−0.0397256	+	0.0688067i	0.845479	+	0.534009i	$0.179315\pi$
$180$	1.42295e11			10.1033
$181$	−2.50155e9			−0.173243			−0.0866214	−	0.996241i	$-0.527607\pi$
$181$	−2.50155e9			−0.173243			−0.0866214	+	0.996241i	$0.527607\pi$
$182$	−1.55904e10	+	2.04844e10i	−1.05326	+	1.38389i
$183$	−5.22101e10			−3.44131
$184$	−1.70936e10			−1.09940
$185$	−4.00860e9	+	6.94310e9i	−0.251605	+	0.435793i
$186$	−1.63700e10			−1.00286
$187$	−1.29433e8	+	2.24184e8i	−0.00774030	+	0.0134066i
$188$	5.75588e9	−	9.96948e9i	0.336048	−	0.582052i
$189$	7.19529e9	−	5.68525e10i	0.410176	−	3.24094i
$190$	8.31638e9			0.462959
$191$	−4.43878e9	−	7.68819e9i	−0.241331	−	0.417998i	0.719763	−	0.694220i	$-0.244251\pi$
$191$	−4.43878e9	−	7.68819e9i	−0.241331	−	0.417998i	−0.961094	+	0.276222i	$0.910917\pi$
$192$	1.67313e10	−	2.89794e10i	0.888532	−	1.53898i
$193$	1.16873e10	−	2.02430e10i	0.606326	−	1.05019i	−0.385515	−	0.922702i	$-0.625976\pi$
$193$	1.16873e10	−	2.02430e10i	0.606326	−	1.05019i	0.991840	−	0.127485i	$-0.0406905\pi$
$194$	−2.37474e10	+	4.11317e10i	−1.20367	+	2.08482i
$195$	7.68473e7	−	7.18083e10i	0.00380604	−	3.55647i
$196$	−4.05098e10	−	1.04208e10i	−1.96069	−	0.504370i
$197$	1.93497e10	+	3.35147e10i	0.915328	+	1.58539i	0.806421	+	0.591342i	$0.201402\pi$
$197$	1.93497e10	+	3.35147e10i	0.915328	+	1.58539i	0.108907	+	0.994052i	$0.465265\pi$
$198$	4.13455e9			0.191177
$199$	6.16990e9			0.278894			0.139447	−	0.990230i	$-0.455467\pi$
$199$	6.16990e9			0.278894			0.139447	+	0.990230i	$0.455467\pi$
$200$	4.87782e10	+	8.44864e10i	2.15571	+	3.73381i
$201$	2.02530e10	+	3.50792e10i	0.875200	+	1.51589i
$202$	−2.85847e10	+	4.95102e10i	−1.20796	+	2.09225i
$203$	2.85956e10	−	1.20128e10i	1.18186	−	0.496493i
$204$	1.83010e10	−	3.16982e10i	0.739842	−	1.28144i
$205$	−5.59643e10			−2.21319
$206$	−3.07264e10	+	5.32197e10i	−1.18880	+	2.05906i
$207$	−2.19931e10	−	3.80932e10i	−0.832570	−	1.44205i
$208$	2.50967e10	+	1.45254e10i	0.929675	+	0.538075i
$209$	1.61747e8			0.00586379
$210$	1.60710e11	−	6.75131e10i	5.70237	−	2.39553i
$211$	−1.32866e10	−	2.30131e10i	−0.461469	−	0.799288i	0.537565	−	0.843222i	$-0.319344\pi$
$211$	−1.32866e10	−	2.30131e10i	−0.461469	−	0.799288i	−0.999034	+	0.0439338i	$0.986011\pi$
$212$	1.10450e9	+	1.91304e9i	0.0375537	+	0.0650449i
$213$	−2.17551e10	−	3.76809e10i	−0.724189	−	1.25433i
$214$	5.11158e10			1.66607
$215$	9.60282e8	+	1.66326e9i	0.0306497	+	0.0530868i
$216$	−1.86214e11			−5.82064
$217$	−9.02960e9	+	3.79328e9i	−0.276439	+	0.116130i
$218$	−4.02725e9	−	6.97540e9i	−0.120769	−	0.209178i
$219$	−7.75372e10			−2.27778
$220$	2.64944e9	+	4.58896e9i	0.0762521	+	0.132072i
$221$	−1.16641e10	−	6.75095e9i	−0.328918	−	0.190371i
$222$	1.64687e10	−	2.85246e10i	0.455063	−	0.788191i
$223$	−6.13056e9	−	1.06184e10i	−0.166008	−	0.287534i	0.771005	−	0.636829i	$-0.219754\pi$
$223$	−6.13056e9	−	1.06184e10i	−0.166008	−	0.287534i	−0.937013	+	0.349295i	$0.886421\pi$
$224$	−4.08439e8	+	3.22722e9i	−0.0108395	+	0.0856471i
$225$	−1.25519e11	+	2.17405e11i	−3.26503	+	5.65520i
$226$	−1.83281e10	+	3.17453e10i	−0.467337	+	0.809452i
$227$	3.04090e10			0.760126			0.380063	−	0.924961i	$-0.375902\pi$
$227$	3.04090e10			0.760126			0.380063	+	0.924961i	$0.375902\pi$
$228$	−2.28700e10			−0.560479
$229$	−1.05991e10	+	1.83582e10i	−0.254689	+	0.441135i	−0.964811	−	0.262944i	$-0.915307\pi$
$229$	−1.05991e10	+	1.83582e10i	−0.254689	+	0.441135i	0.710122	+	0.704079i	$0.248640\pi$
$230$	4.21092e10	−	7.29353e10i	0.992206	−	1.71855i
$231$	3.12568e9	−	1.31308e9i	0.0722255	−	0.0303415i
$232$	−5.03934e10	−	8.72840e10i	−1.14203	−	1.97806i
$233$	1.30874e10	−	2.26681e10i	0.290906	−	0.503864i	−0.683118	−	0.730308i	$-0.739377\pi$
$233$	1.30874e10	−	2.26681e10i	0.290906	−	0.503864i	0.974024	+	0.226444i	$0.0727100\pi$
$234$	−2.30355e8	+	2.15250e11i	−0.00502258	+	4.69324i
$235$	1.43510e10	+	2.48567e10i	0.306957	+	0.531665i
$236$	5.24090e10			1.09977
$237$	5.41382e10	+	9.37700e10i	1.11464	+	1.93062i
$238$	4.10769e9	−	3.24564e10i	0.0829854	−	0.655697i
$239$	8.03903e10			1.59372			0.796862	−	0.604161i	$-0.206492\pi$
$239$	8.03903e10			1.59372			0.796862	+	0.604161i	$0.206492\pi$
$240$	−9.81767e10	−	1.70047e11i	−1.91011	−	3.30840i
$241$	7.51248e10			1.43452			0.717260	−	0.696806i	$-0.245396\pi$
$241$	7.51248e10			1.43452			0.717260	+	0.696806i	$0.245396\pi$
$242$	−4.63176e10	−	8.02245e10i	−0.868114	−	1.50362i
$243$	−9.85410e10	−	1.70678e11i	−1.81296	−	3.14014i
$244$	1.00288e11	+	1.73704e11i	1.81132	+	3.13730i
$245$	7.30022e10	−	7.44796e10i	1.29446	−	1.32066i
$246$	2.29921e11			4.00286
$247$	−9.01170e6	+	8.42079e9i	−0.000154053	+	0.143952i
$248$	1.59127e10	+	2.75615e10i	0.267122	+	0.462669i
$249$	−3.57178e10	+	6.18651e10i	−0.588828	+	1.01988i
$250$	−2.82015e11			−4.56606
$251$	−6.10516e9	+	1.05744e10i	−0.0970879	+	0.168161i	−0.910478	−	0.413557i	$-0.864286\pi$
$251$	−6.10516e9	+	1.05744e10i	−0.0970879	+	0.168161i	0.813390	+	0.581718i	$0.197619\pi$
$252$	−3.22461e11	+	1.35464e11i	−5.03703	+	2.11603i
$253$	8.18993e8	−	1.41854e9i	0.0125672	−	0.0217670i
$254$	3.89364e10	+	6.74399e10i	0.586954	+	1.01663i
$255$	4.56295e10	+	7.90326e10i	0.675795	+	1.17051i
$256$	−1.38871e11			−2.02084
$257$	−2.66161e10			−0.380579			−0.190289	−	0.981728i	$-0.560943\pi$
$257$	−2.66161e10			−0.380579			−0.190289	+	0.981728i	$0.560943\pi$
$258$	−3.94517e9	−	6.83323e9i	−0.0554341	−	0.0960147i
$259$	2.47428e9	−	1.95502e10i	0.0341664	−	0.269961i
$260$	−2.39055e11	+	1.37678e11i	−3.24428	+	1.86846i
$261$	1.29675e11	−	2.24604e11i	1.72971	−	2.99595i
$262$	1.21215e10	−	2.09950e10i	0.158928	−	0.275271i
$263$	1.20085e10	−	2.07994e10i	0.154771	−	0.268071i	−0.778205	−	0.628011i	$-0.783869\pi$
$263$	1.20085e10	−	2.07994e10i	0.154771	−	0.268071i	0.932976	+	0.359940i	$0.117203\pi$
$264$	−5.50832e9	−	9.54069e9i	−0.0697913	−	0.120882i
$265$	−5.50764e9			−0.0686055
$266$	−1.88460e10	+	7.91710e9i	−0.230809	+	0.0969614i
$267$	1.43443e10	−	2.48450e10i	0.172734	−	0.299184i
$268$	7.78063e10	−	1.34764e11i	0.921315	−	1.59576i
$269$	−8.78810e10			−1.02332			−0.511658	−	0.859189i	$-0.670969\pi$
$269$	−8.78810e10			−1.02332			−0.511658	+	0.859189i	$0.670969\pi$
$270$	4.58728e11	−	7.94540e11i	5.25313	−	9.09869i
$271$	1.00252e11			1.12910			0.564550	−	0.825399i	$-0.309050\pi$
$271$	1.00252e11			1.12910			0.564550	+	0.825399i	$0.309050\pi$
$272$	−3.68515e10			−0.408220
$273$	6.81866e10	+	1.62801e11i	0.742963	+	1.77388i
$274$	−1.22446e11			−1.31240
$275$	−9.34828e9			−0.0985677
$276$	−1.15800e11	+	2.00572e11i	−1.20121	+	2.08056i
$277$	9.12483e10			0.931249			0.465624	−	0.884982i	$-0.345830\pi$
$277$	9.12483e10			0.931249			0.465624	+	0.884982i	$0.345830\pi$
$278$	1.85993e10	−	3.22149e10i	0.186764	−	0.323485i
$279$	−4.09473e10	+	7.09228e10i	−0.404582	+	0.700756i
$280$	−2.69889e11	−	2.04953e11i	−2.62406	−	1.99271i
$281$	1.14850e10			0.109888			0.0549441	−	0.998489i	$-0.482502\pi$
$281$	1.14850e10			0.109888			0.0549441	+	0.998489i	$0.482502\pi$
$282$	−5.89589e10	−	1.02120e11i	−0.555173	−	0.961588i
$283$	−3.42593e10	+	5.93388e10i	−0.317497	+	0.549920i	−0.979965	−	0.199170i	$-0.936176\pi$
$283$	−3.42593e10	+	5.93388e10i	−0.317497	+	0.549920i	0.662468	+	0.749090i	$0.269509\pi$
$284$	−8.35768e10	+	1.44759e11i	−0.762348	+	1.32043i
$285$	2.85107e10	−	4.93819e10i	0.255980	−	0.443370i
$286$	−6.94602e9	+	4.00038e9i	−0.0613887	+	0.0353553i
$287$	1.26823e11	−	5.32775e10i	1.10339	−	0.463527i
$288$	1.36002e10	+	2.35562e10i	0.116487	+	0.201762i
$289$	−1.01460e11			−0.855572
$290$	4.96566e11			4.12274
$291$	1.62825e11	+	2.82020e11i	1.33107	+	2.30548i
$292$	1.48938e11	+	2.57968e11i	1.19890	+	2.07655i
$293$	−8.33876e10	+	1.44432e11i	−0.660994	+	1.14487i	0.319361	+	0.947633i	$0.396532\pi$
$293$	−8.33876e10	+	1.44432e11i	−0.660994	+	1.14487i	−0.980355	+	0.197241i	$0.936802\pi$
$294$	−2.99918e11	+	3.05988e11i	−2.34121	+	2.38859i
$295$	−6.53352e10	+	1.13164e11i	−0.502282	+	0.869979i
$296$	−6.40344e10			−0.484842
$297$	8.92191e9	−	1.54532e10i	0.0665356	−	0.115243i
$298$	1.07161e11	+	1.85608e11i	0.787161	+	1.36340i
$299$	7.38054e10	+	4.27169e10i	0.534033	+	0.309086i
$300$	1.32179e12			9.42140
$301$	−3.75953e9	−	2.85499e9i	−0.0263988	−	0.0200473i
$302$	−1.62585e11	−	2.81606e11i	−1.12473	−	1.94810i
$303$	1.95992e11	+	3.39467e11i	1.33581	+	2.31370i
$304$	1.15130e10	+	1.99410e10i	0.0773136	+	0.133911i
$305$	−5.00093e11			−3.30903
$306$	−1.36778e11	−	2.36906e11i	−0.891803	−	1.54465i
$307$	1.44779e10			0.0930215			0.0465107	−	0.998918i	$-0.485190\pi$
$307$	1.44779e10			0.0930215			0.0465107	+	0.998918i	$0.485190\pi$
$308$	−1.03726e10	−	7.87698e9i	−0.0656766	−	0.0498748i
$309$	2.10676e11	+	3.64901e11i	1.31462	+	2.27700i
$310$	−1.56800e11			−0.964312
$311$	−1.19491e11	−	2.06964e11i	−0.724290	−	1.25451i	−0.959266	−	0.282506i	$-0.908834\pi$
$311$	−1.19491e11	−	2.06964e11i	−0.724290	−	1.25451i	0.234976	−	0.972001i	$-0.424499\pi$
$312$	4.97008e11	−	2.86239e11i	2.96940	−	1.71015i
$313$	−5.98501e10	+	1.03663e11i	−0.352464	+	0.610486i	−0.986681	−	0.162669i	$-0.947990\pi$
$313$	−5.98501e10	+	1.03663e11i	−0.352464	+	0.610486i	0.634216	+	0.773156i	$0.281323\pi$
$314$	2.17519e11	+	3.76754e11i	1.26274	+	2.18713i
$315$	1.09493e11	−	8.65146e11i	0.626600	−	4.95099i
$316$	2.07983e11	−	3.60238e11i	1.17338	−	2.03235i
$317$	3.73123e10	−	6.46267e10i	0.207532	−	0.359456i	−0.743405	−	0.668842i	$-0.766790\pi$
$317$	3.73123e10	−	6.46267e10i	0.207532	−	0.359456i	0.950936	+	0.309386i	$0.100124\pi$
$318$	2.26273e10			0.124082
$319$	9.65783e9			0.0522181
$320$	1.60260e11	−	2.77578e11i	0.854378	−	1.47983i
$321$	1.75238e11	−	3.03521e11i	0.921204	−	1.59557i
$322$	−2.59916e10	+	2.05369e11i	−0.134735	+	1.06459i
$323$	−5.35086e9	−	9.26797e9i	−0.0273535	−	0.0473776i
$324$	−7.19638e11	+	1.24645e12i	−3.62795	+	6.28380i
$325$	5.20837e8	−	4.86684e11i	0.00258956	−	2.41976i
$326$	−1.79770e11	−	3.11371e11i	−0.881532	−	1.52686i
$327$	−5.52258e10			−0.267102
$328$	−2.23497e11	−	3.87108e11i	−1.06620	−	1.84672i
$329$	−5.61847e10	−	4.26667e10i	−0.264385	−	0.200774i
$330$	5.42777e10			0.251947
$331$	2.07214e11	+	3.58904e11i	0.948838	+	1.64344i	0.747878	+	0.663837i	$0.231073\pi$
$331$	2.07214e11	+	3.58904e11i	0.948838	+	1.64344i	0.200961	+	0.979599i	$0.435594\pi$
$332$	2.74436e11			1.23971
$333$	−8.23883e10	−	1.42701e11i	−0.367170	−	0.635956i
$334$	−3.02882e10	−	5.24607e10i	−0.133172	−	0.230661i
$335$	1.93993e11	+	3.36006e11i	0.841558	+	1.45762i
$336$	3.84365e11	+	2.91887e11i	1.64519	+	1.24936i
$337$	−3.04862e11			−1.28756			−0.643782	−	0.765209i	$-0.722635\pi$
$337$	−3.04862e11			−1.28756			−0.643782	+	0.765209i	$0.722635\pi$
$338$	−2.07878e11	−	3.61842e11i	−0.866332	−	1.50798i
$339$	1.25667e11	+	2.17662e11i	0.516801	+	0.895126i
$340$	1.75296e11	−	3.03621e11i	0.711403	−	1.23219i
$341$	−3.04964e9			−0.0122139
$342$	−8.54628e10	+	1.48026e11i	−0.337800	+	0.585087i
$343$	−9.45293e10	+	2.38278e11i	−0.368759	+	0.929525i
$344$	−7.66989e9	+	1.32846e10i	−0.0295309	+	0.0511490i
$345$	−2.88722e11	−	5.00082e11i	−1.09722	−	1.90044i
$346$	−1.41975e11	−	2.45908e11i	−0.532560	−	0.922421i
$347$	−2.70786e11			−1.00264			−0.501319	−	0.865263i	$-0.667152\pi$
$347$	−2.70786e11			−1.00264			−0.501319	+	0.865263i	$0.667152\pi$
$348$	−1.36555e12			−4.99117
$349$	3.99260e10	+	6.91539e10i	0.144059	+	0.249518i	0.929022	−	0.370025i	$-0.120651\pi$
$349$	3.99260e10	+	6.91539e10i	0.144059	+	0.249518i	−0.784962	+	0.619544i	$0.787318\pi$
$350$	1.08922e12	−	4.57574e11i	3.87979	−	1.62988i
$351$	8.04019e11	+	4.65348e11i	2.82738	+	1.63643i
$352$	−5.06451e8	+	8.77198e8i	−0.00175831	+	0.00304548i
$353$	−5.22627e10	+	9.05216e10i	−0.179145	+	0.310289i	−0.941588	−	0.336767i	$-0.890667\pi$
$353$	−5.22627e10	+	9.05216e10i	−0.179145	+	0.310289i	0.762443	+	0.647056i	$0.224000\pi$
$354$	2.68419e11	−	4.64916e11i	0.908446	−	1.57348i
$355$	−2.08380e11	−	3.60925e11i	−0.696352	−	1.20612i
$356$	−1.10213e11			−0.363671
$357$	−1.78641e11	−	1.35660e11i	−0.582068	−	0.442023i
$358$	2.14720e10	−	3.71906e10i	0.0690874	−	0.119663i
$359$	−2.81925e11	+	4.88309e11i	−0.895796	+	1.55156i	−0.0629800	+	0.998015i	$0.520060\pi$
$359$	−2.81925e11	+	4.88309e11i	−0.895796	+	1.55156i	−0.832816	+	0.553550i	$0.813273\pi$
$360$	−2.83369e12			−8.89183
$361$	1.58000e11	−	2.73665e11i	0.489639	−	0.848080i
$362$	9.84401e10			0.301289
$363$	−6.35155e11			−1.91999
$364$	4.10665e11	−	5.39575e11i	1.22611	−	1.61100i
$365$	−7.42688e11			−2.19022
$366$	2.05455e12			5.98484
$367$	1.47921e11	−	2.56206e11i	0.425629	−	0.737211i	−0.570850	−	0.821054i	$-0.693386\pi$
$367$	1.47921e11	−	2.56206e11i	0.425629	−	0.737211i	0.996479	+	0.0838435i	$0.0267196\pi$
$368$	2.33179e11			0.662788
$369$	5.75115e11	−	9.96128e11i	1.61486	−	2.79703i
$370$	1.57745e11	−	2.73222e11i	0.437570	−	0.757894i
$371$	1.24811e10	−	5.24321e9i	0.0342034	−	0.0143686i
$372$	4.31199e11			1.16744
$373$	5.02877e10	+	8.71009e10i	0.134515	+	0.232988i	0.925412	−	0.378962i	$-0.123719\pi$
$373$	5.02877e10	+	8.71009e10i	0.134515	+	0.232988i	−0.790897	+	0.611950i	$0.790386\pi$
$374$	5.09340e9	−	8.82203e9i	0.0134613	−	0.0233156i
$375$	−9.66819e11	+	1.67458e12i	−2.52467	+	4.37285i
$376$	−1.14623e11	+	1.98533e11i	−0.295752	+	0.512258i
$377$	−5.38083e8	+	5.02800e11i	−0.00137187	+	1.28191i
$378$	−2.83147e11	+	2.23724e12i	−0.713343	+	5.63637i
$379$	1.17870e11	+	2.04158e11i	0.293446	+	0.508264i	0.974622	−	0.223856i	$-0.0718645\pi$
$379$	1.17870e11	+	2.04158e11i	0.293446	+	0.508264i	−0.681176	+	0.732120i	$0.738531\pi$
$380$	−2.19060e11			−0.538935
$381$	5.33936e11			1.29816
$382$	1.74673e11	+	3.02543e11i	0.419703	+	0.726946i
$383$	−3.63563e11	−	6.29710e11i	−0.863348	−	1.49536i	−0.868679	−	0.495376i	$-0.835030\pi$
$383$	−3.63563e11	−	6.29710e11i	−0.863348	−	1.49536i	0.00533080	−	0.999986i	$-0.498303\pi$
$384$	−6.93774e11	+	1.20165e12i	−1.62827	+	2.82025i
$385$	2.99393e10	−	1.25773e10i	0.0694493	−	0.0291752i
$386$	−4.59914e11	+	7.96595e11i	−1.05447	+	1.82639i
$387$	−3.94732e10			−0.0894546
$388$	6.25526e11	−	1.08344e12i	1.40121	−	2.42696i
$389$	1.44844e10	+	2.50877e10i	0.0320721	+	0.0555506i	0.881616	−	0.471967i	$-0.156456\pi$
$389$	1.44844e10	+	2.50877e10i	0.0320721	+	0.0555506i	−0.849544	+	0.527518i	$0.823123\pi$
$390$	−3.02407e9	+	2.82578e12i	−0.00661913	+	6.18510i
$391$	−1.08374e11			−0.234494
$392$	8.06718e11	+	2.07521e11i	1.72558	+	0.443890i
$393$	−8.31112e10	−	1.43953e11i	−0.175749	−	0.304406i
$394$	−7.61444e11	−	1.31886e12i	−1.59186	−	2.75718i
$395$	5.18561e11	+	8.98174e11i	1.07180	+	1.85641i
$396$	−1.08907e11			−0.222551
$397$	−2.31638e11	−	4.01209e11i	−0.468008	−	0.810613i	0.531324	−	0.847169i	$-0.321695\pi$
$397$	−2.31638e11	−	4.01209e11i	−0.468008	−	0.810613i	−0.999332	+	0.0365554i	$0.988361\pi$
$398$	−2.42796e11			−0.485029
$399$	−1.75980e10	+	1.39048e11i	−0.0347605	+	0.274655i
$400$	−6.65398e11	−	1.15250e12i	−1.29961	−	2.25098i
$401$	−4.89675e11			−0.945712			−0.472856	−	0.881140i	$-0.656777\pi$
$401$	−4.89675e11			−0.945712			−0.472856	+	0.881140i	$0.656777\pi$
$402$	−7.96990e11	−	1.38043e12i	−1.52207	−	2.63631i
$403$	1.69910e8	−	1.58768e11i	0.000320882	−	0.299841i
$404$	7.52944e11	−	1.30414e12i	1.40620	−	2.43561i
$405$	−1.79426e12	−	3.10775e12i	−3.31389	−	5.73982i
$406$	−1.12529e12	+	4.72725e11i	−2.05540	+	0.863459i
$407$	3.06802e9	−	5.31397e9i	0.00554222	−	0.00959941i
$408$	−3.64448e11	+	6.31243e11i	−0.651126	+	1.12778i
$409$	−5.31288e11			−0.938804			−0.469402	−	0.882984i	$-0.655531\pi$
$409$	−5.31288e11			−0.938804			−0.469402	+	0.882984i	$0.655531\pi$
$410$	2.20229e12			3.84899
$411$	−4.19777e11	+	7.27075e11i	−0.725655	+	1.25687i
$412$	8.09357e11	−	1.40185e12i	1.38389	−	2.39697i
$413$	4.03277e10	−	3.18643e11i	0.0682068	−	0.538926i
$414$	8.65467e11	+	1.49903e12i	1.44793	+	2.50790i
$415$	−3.42122e11	+	5.92573e11i	−0.566194	+	0.980676i
$416$	−4.56400e10	−	2.64154e10i	−0.0747180	−	0.0432451i
$417$	−1.27526e11	−	2.20882e11i	−0.206532	−	0.357724i
$418$	−6.36502e9			−0.0101978
$419$	5.87869e11	+	1.01822e12i	0.931789	+	1.61391i	0.780262	+	0.625453i	$0.215086\pi$
$419$	5.87869e11	+	1.01822e12i	0.931789	+	1.61391i	0.151527	+	0.988453i	$0.451581\pi$
$420$	−4.23322e12	+	1.77835e12i	−6.63818	+	2.78866i
$421$	−3.81333e11			−0.591609			−0.295804	−	0.955249i	$-0.595588\pi$
$421$	−3.81333e11			−0.591609			−0.295804	+	0.955249i	$0.595588\pi$
$422$	5.22850e11	+	9.05603e11i	0.802548	+	1.39005i
$423$	−5.89910e11			−0.895889
$424$	−2.19951e10	−	3.80966e10i	−0.0330506	−	0.0572453i
$425$	3.09256e11	+	5.35648e11i	0.459799	+	0.796396i
$426$	8.56098e11	+	1.48281e12i	1.25945	+	2.18143i
$427$	1.13328e12	−	4.76083e11i	1.64972	−	0.693038i
$428$	−1.34643e12			−1.93949
$429$	−5.88159e7	+	5.49592e10i	−8.38372e−5	+	0.0783398i
$430$	−3.77887e10	−	6.54520e10i	−0.0533033	−	0.0923240i
$431$	5.92805e11	−	1.02677e12i	0.827493	−	1.43326i	−0.0725060	−	0.997368i	$-0.523100\pi$
$431$	5.92805e11	−	1.02677e12i	0.827493	−	1.43326i	0.899999	−	0.435892i	$-0.143567\pi$
$432$	2.54020e12			3.50906
$433$	9.02979e10	−	1.56401e11i	0.123447	−	0.213817i	−0.797678	−	0.603084i	$-0.793938\pi$
$433$	9.02979e10	−	1.56401e11i	0.123447	−	0.213817i	0.921125	+	0.389267i	$0.127272\pi$
$434$	3.55330e11	−	1.49272e11i	0.480759	−	0.201964i
$435$	1.70235e12	−	2.94856e12i	2.27955	−	3.94829i
$436$	1.06081e11	+	1.83738e11i	0.140588	+	0.243506i
$437$	3.38578e10	+	5.86435e10i	0.0444112	+	0.0769225i
$438$	3.05122e12			3.96132
$439$	−1.31100e11			−0.168466			−0.0842331	−	0.996446i	$-0.526844\pi$
$439$	−1.31100e11			−0.168466			−0.0842331	+	0.996446i	$0.526844\pi$
$440$	−5.27613e10	−	9.13852e10i	−0.0671086	−	0.116236i
$441$	5.75483e11	+	2.06478e12i	0.724535	+	2.59956i
$442$	4.59004e11	+	2.65661e11i	0.572026	+	0.331076i
$443$	−2.48805e11	+	4.30943e11i	−0.306932	+	0.531622i	−0.977690	−	0.210055i	$-0.932636\pi$
$443$	−2.48805e11	+	4.30943e11i	−0.306932	+	0.531622i	0.670757	+	0.741677i	$0.265969\pi$
$444$	−4.33799e11	+	7.51361e11i	−0.529743	+	0.917541i
$445$	1.37396e11	−	2.37977e11i	0.166094	−	0.287684i
$446$	2.41248e11	+	4.17853e11i	0.288706	+	0.500054i
$447$	1.46950e12			1.74095
$448$	−9.89193e10	+	7.81596e11i	−0.116019	+	0.916709i
$449$	−1.99339e11	+	3.45265e11i	−0.231464	+	0.400907i	−0.958239	−	0.285968i	$-0.907685\pi$
$449$	−1.99339e11	+	3.45265e11i	−0.231464	+	0.400907i	0.726775	+	0.686875i	$0.241018\pi$
$450$	4.93937e12	−	8.55525e12i	5.67826	−	9.83504i
$451$	4.28329e10			0.0487509
$452$	4.82778e11	−	8.36196e11i	0.544032	−	0.942291i
$453$	−2.22954e12			−2.48755
$454$	−1.19664e12			−1.32195
$455$	6.53123e11	+	1.55938e12i	0.714404	+	1.70569i
$456$	4.55437e11			0.493272
$457$	−1.29871e12			−1.39280			−0.696402	−	0.717652i	$-0.745217\pi$
$457$	−1.29871e12			−1.39280			−0.696402	+	0.717652i	$0.745217\pi$
$458$	4.17093e11	−	7.22427e11i	0.442934	−	0.767184i
$459$	−1.18061e12			−1.24150
$460$	−1.10919e12	+	1.92117e12i	−1.15504	+	2.00058i
$461$	−6.91597e11	+	1.19788e12i	−0.713180	+	1.23526i	0.250478	+	0.968122i	$0.419412\pi$
$461$	−6.91597e11	+	1.19788e12i	−0.713180	+	1.23526i	−0.963657	+	0.267141i	$0.913921\pi$
$462$	−1.23001e11	+	5.16718e10i	−0.125609	+	0.0527673i
$463$	−2.87774e11			−0.291030			−0.145515	−	0.989356i	$-0.546484\pi$
$463$	−2.87774e11			−0.291030			−0.145515	+	0.989356i	$0.546484\pi$
$464$	6.87431e11	+	1.19067e12i	0.688491	+	1.19250i
$465$	−5.37550e11	+	9.31064e11i	−0.533188	+	0.923509i
$466$	−5.15012e11	+	8.92027e11i	−0.505919	+	0.876277i
$467$	7.55265e11	−	1.30816e12i	0.734808	−	1.27272i	−0.220000	−	0.975500i	$-0.570606\pi$
$467$	7.55265e11	−	1.30816e12i	0.734808	−	1.27272i	0.954808	−	0.297224i	$-0.0960609\pi$
$468$	6.06774e9	−	5.66987e12i	0.00584683	−	5.46344i
$469$	−7.59488e11	−	5.76755e11i	−0.724842	−	0.550445i
$470$	−5.64736e11	−	9.78152e11i	−0.533833	−	0.924626i
$471$	2.98284e12			2.79278
$472$	−1.04368e12			−0.967896
$473$	−7.34962e8	−	1.27299e9i	−0.000675134	−	0.00116937i
$474$	−2.13043e12	−	3.69001e12i	−1.93849	−	3.35757i
$475$	1.93233e11	−	3.34689e11i	0.174164	−	0.301662i
$476$	−1.08200e11	+	8.54926e11i	−0.0966041	+	0.763303i
$477$	5.65990e10	−	9.80323e10i	0.0500583	−	0.0867034i
$478$	−3.16349e12			−2.77167
$479$	−6.67472e11	+	1.15610e12i	−0.579327	+	1.00342i	0.416230	+	0.909259i	$0.363351\pi$
$479$	−6.67472e11	+	1.15610e12i	−0.579327	+	1.00342i	−0.995557	+	0.0941637i	$0.969982\pi$
$480$	1.78541e11	+	3.09242e11i	0.153515	+	0.265897i
$481$	2.76482e11	+	1.60022e11i	0.235512	+	0.136309i
$482$	−2.95629e12			−2.49479
$483$	1.13036e12	+	8.58394e11i	0.945048	+	0.717669i
$484$	1.22004e12	+	2.11318e12i	1.01058	+	1.75038i
$485$	1.55961e12	+	2.70132e12i	1.27991	+	2.21686i
$486$	3.87775e12	+	6.71647e12i	3.15295	+	5.46107i
$487$	−2.33420e11			−0.188043			−0.0940215	−	0.995570i	$-0.529972\pi$
$487$	−2.33420e11			−0.188043			−0.0940215	+	0.995570i	$0.529972\pi$
$488$	−1.99715e12	−	3.45917e12i	−1.59412	−	2.76110i
$489$	−2.46519e12			−1.94967
$490$	−2.87276e12	+	2.93090e12i	−2.25121	+	2.29677i
$491$	−5.22926e11	−	9.05734e11i	−0.406044	−	0.703289i	0.588398	−	0.808571i	$-0.299759\pi$
$491$	−5.22926e11	−	9.05734e11i	−0.406044	−	0.703289i	−0.994442	+	0.105282i	$0.966425\pi$
$492$	−6.05629e12			−4.65976
$493$	−3.19497e11	−	5.53385e11i	−0.243588	−	0.421906i
$494$	3.54626e8	−	3.31372e11i	0.000267916	−	0.250348i
$495$	1.35768e11	−	2.35157e11i	0.101642	−	0.176050i
$496$	−2.17069e11	−	3.75975e11i	−0.161039	−	0.278927i
$497$	8.15816e11	+	6.19530e11i	0.599775	+	0.455469i
$498$	1.40556e12	−	2.43450e12i	1.02404	−	1.77369i
$499$	−1.88511e11	+	3.26510e11i	−0.136108	+	0.235746i	−0.926020	−	0.377474i	$-0.876793\pi$
$499$	−1.88511e11	+	3.26510e11i	−0.136108	+	0.235746i	0.789912	+	0.613220i	$0.210126\pi$
$500$	7.42849e12			5.31539
$501$	−4.15343e11			−0.294535
$502$	2.40248e11	−	4.16122e11i	0.168847	−	0.292452i
$503$	5.94340e11	−	1.02943e12i	0.413980	−	0.717034i	−0.581341	−	0.813660i	$-0.697472\pi$
$503$	5.94340e11	−	1.02943e12i	0.413980	−	0.717034i	0.995321	+	0.0966262i	$0.0308051\pi$
$504$	6.42153e12	−	2.69764e12i	4.43304	−	1.86229i
$505$	1.87730e12	+	3.25158e12i	1.28447	+	2.22476i
$506$	−3.22287e10	+	5.58218e10i	−0.0218558	+	0.0378553i
$507$	−2.86125e12	−	6.12407e9i	−1.92318	−	0.00411628i
$508$	−1.02562e12	−	1.77642e12i	−0.683279	−	1.18347i
$509$	−8.33921e11			−0.550674			−0.275337	−	0.961348i	$-0.588790\pi$
$509$	−8.33921e11			−0.550674			−0.275337	+	0.961348i	$0.588790\pi$
$510$	−1.79560e12	−	3.11006e12i	−1.17528	−	2.03565i
$511$	1.68303e12	−	7.07031e11i	1.09194	−	0.458717i
$512$	2.83180e12			1.82116
$513$	3.68839e11	+	6.38848e11i	0.235130	+	0.407258i
$514$	1.04739e12			0.661870
$515$	2.01795e12	+	3.49520e12i	1.26409	+	2.18947i
$516$	1.03919e11	+	1.79993e11i	0.0645314	+	0.111772i
$517$	−1.09837e10	−	1.90243e10i	−0.00676147	−	0.0117112i
$518$	−9.73670e10	+	7.69331e11i	−0.0594193	+	0.469493i
$519$	−1.94690e12			−1.17785
$520$	4.76058e12	−	2.74173e12i	2.85526	−	1.64441i
$521$	4.11368e11	+	7.12510e11i	0.244602	+	0.423664i	0.962020	−	0.272980i	$-0.0880092\pi$
$521$	4.11368e11	+	7.12510e11i	0.244602	+	0.423664i	−0.717417	+	0.696644i	$0.754676\pi$
$522$	−5.10293e12	+	8.83854e12i	−3.00817	+	5.21030i
$523$	8.71284e11			0.509216			0.254608	−	0.967044i	$-0.418054\pi$
$523$	8.71284e11			0.509216			0.254608	+	0.967044i	$0.418054\pi$
$524$	−3.19290e11	+	5.53026e11i	−0.185009	+	0.320446i
$525$	1.01709e12	−	8.03637e12i	0.584307	−	4.61682i
$526$	−4.72556e11	+	8.18492e11i	−0.269165	+	0.466207i
$527$	1.00887e11	+	1.74741e11i	0.0569754	+	0.0986843i
$528$	7.51406e10	+	1.30147e11i	0.0420748	+	0.0728757i
$529$	−1.11541e12			−0.619275
$530$	2.16735e11			0.119313
$531$	−1.34283e12	−	2.32585e12i	−0.732985	−	1.26957i
$532$	4.96420e11	−	2.08543e11i	0.268687	−	0.112874i
$533$	−2.38642e9	+	2.22994e12i	−0.00128078	+	1.19680i
$534$	−5.64471e11	+	9.77692e11i	−0.300404	+	0.520315i
$535$	1.67851e12	−	2.90727e12i	0.885794	−	1.53424i
$536$	−1.54945e12	+	2.68372e12i	−0.810839	+	1.40441i
$537$	−1.47223e11	−	2.54998e11i	−0.0763996	−	0.132328i
$538$	3.45827e12			1.77966
$539$	−5.58730e10	+	5.70037e10i	−0.0285136	+	0.0290907i
$540$	−1.20833e13	+	2.09288e13i	−6.11522	+	10.5919i
$541$	1.88203e12	−	3.25976e12i	0.944578	−	1.63606i	0.187983	−	0.982172i	$-0.439805\pi$
$541$	1.88203e12	−	3.25976e12i	0.944578	−	1.63606i	0.756594	−	0.653885i	$-0.226862\pi$
$542$	−3.94509e12			−1.96363
$543$	3.37478e11	−	5.84529e11i	0.166589	−	0.288540i
$544$	6.70169e10			0.0328087
$545$	−5.28979e11			−0.256835
$546$	−2.68326e12	−	6.40647e12i	−1.29210	−	3.08498i
$547$	2.52516e12			1.20599			0.602997	−	0.797743i	$-0.293973\pi$
$547$	2.52516e12			1.20599			0.602997	+	0.797743i	$0.293973\pi$
$548$	3.22533e12			1.52778
$549$	5.13918e12	−	8.90132e12i	2.41445	−	4.18195i
$550$	3.67870e11			0.171420
$551$	−1.99631e11	+	3.45771e11i	−0.0922670	+	0.159811i
$552$	2.30606e12	−	3.99422e12i	1.05717	−	1.83107i
$553$	−2.03018e12	−	1.54172e12i	−0.923149	−	0.701040i
$554$	−3.59077e12			−1.61955
$555$	−1.08158e12	−	1.87335e12i	−0.483883	−	0.838111i
$556$	−4.89919e11	+	8.48565e11i	−0.217414	+	0.376572i
$557$	−3.79007e11	+	6.56459e11i	−0.166839	+	0.288974i	−0.937307	−	0.348505i	$-0.886689\pi$
$557$	−3.79007e11	+	6.56459e11i	−0.166839	+	0.288974i	0.770468	+	0.637479i	$0.220023\pi$
$558$	1.61135e12	−	2.79093e12i	0.703614	−	1.21870i
$559$	6.63147e10	−	3.81922e10i	0.0287248	−	0.0165433i
$560$	3.68163e12	+	2.79583e12i	1.58195	+	1.20134i
$561$	−3.49230e10	−	6.04884e10i	−0.0148860	−	0.0257833i
$562$	−4.51952e11			−0.191108
$563$	−2.20982e11			−0.0926976			−0.0463488	−	0.998925i	$-0.514759\pi$
$563$	−2.20982e11			−0.0926976			−0.0463488	+	0.998925i	$0.514759\pi$
$564$	1.55302e12	+	2.68992e12i	0.646282	+	1.11939i
$565$	1.20370e12	+	2.08487e12i	0.496936	+	0.860718i
$566$	1.34816e12	−	2.33508e12i	0.552163	−	0.956374i
$567$	7.02458e12	+	5.33447e12i	2.85428	+	2.16754i
$568$	1.66436e12	−	2.88276e12i	0.670934	−	1.16209i
$569$	−3.50851e12			−1.40319			−0.701596	−	0.712575i	$-0.747529\pi$
$569$	−3.50851e12			−1.40319			−0.701596	+	0.712575i	$0.747529\pi$
$570$	−1.12194e12	+	1.94326e12i	−0.445178	+	0.771071i
$571$	1.69261e12	+	2.93169e12i	0.666338	+	1.15413i	0.978921	+	0.204241i	$0.0654725\pi$
$571$	1.69261e12	+	2.93169e12i	0.666338	+	1.15413i	−0.312583	+	0.949891i	$0.601194\pi$
$572$	1.82964e11	−	1.05373e11i	0.0714632	−	0.0411574i
$573$	2.39530e12			0.928249
$574$	−4.99069e12	+	2.09656e12i	−1.91892	+	0.806127i
$575$	−1.95683e12	−	3.38933e12i	−0.746532	−	1.29303i
$576$	3.29381e12	+	5.70504e12i	1.24680	+	2.15952i
$577$	−6.21266e11	−	1.07606e12i	−0.233338	−	0.404154i	0.725450	−	0.688275i	$-0.241632\pi$
$577$	−6.21266e11	−	1.07606e12i	−0.233338	−	0.404154i	−0.958788	+	0.284121i	$0.908298\pi$
$578$	3.99264e12			1.48794
$579$	3.15341e12	+	5.46187e12i	1.16608	+	2.01970i
$580$	−1.30799e13			−4.79932
$581$	2.11173e11	−	1.66855e12i	0.0768856	−	0.607500i
$582$	−6.40742e12	−	1.10980e13i	−2.31489	−	4.00950i
$583$	4.21533e9			0.00151120
$584$	−2.96597e12	−	5.13721e12i	−1.05514	−	1.82755i
$585$	1.22351e13	+	7.08138e12i	4.31921	+	2.49987i
$586$	3.28144e12	−	5.68362e12i	1.14954	−	1.99107i
$587$	2.11993e12	+	3.67182e12i	0.736969	+	1.27647i	0.953854	+	0.300270i	$0.0970769\pi$
$587$	2.11993e12	+	3.67182e12i	0.736969	+	1.27647i	−0.216885	+	0.976197i	$0.569590\pi$
$588$	7.90009e12	−	8.05996e12i	2.72542	−	2.78058i
$589$	6.30373e10	−	1.09184e11i	0.0215813	−	0.0373800i
$590$	2.57105e12	−	4.45319e12i	0.873527	−	1.51299i
$591$	−1.04417e13			−3.52069
$592$	8.73511e11			0.292295
$593$	−1.06909e12	+	1.85171e12i	−0.355032	+	0.614933i	−0.987123	−	0.159961i	$-0.948863\pi$
$593$	−1.06909e12	+	1.85171e12i	−0.355032	+	0.614933i	0.632092	+	0.774894i	$0.282197\pi$
$594$	−3.51092e11	+	6.08110e11i	−0.115713	+	0.200421i
$595$	−1.71111e12	−	1.29941e12i	−0.559694	−	0.425032i
$596$	−2.82271e12	−	4.88907e12i	−0.916342	−	1.58715i
$597$	−8.32367e11	+	1.44170e12i	−0.268183	+	0.464506i
$598$	−2.90437e12	−	1.68098e12i	−0.928744	−	0.537536i
$599$	−1.37192e12	−	2.37623e12i	−0.435419	−	0.754167i	0.561911	−	0.827198i	$-0.310066\pi$
$599$	−1.37192e12	−	2.37623e12i	−0.435419	−	0.754167i	−0.997330	+	0.0730303i	$0.976733\pi$
$600$	−2.63222e13			−8.29167
$601$	2.97057e12	+	5.14518e12i	0.928762	+	1.60866i	0.785396	+	0.618994i	$0.212460\pi$
$601$	2.97057e12	+	5.14518e12i	0.928762	+	1.60866i	0.143367	+	0.989670i	$0.454207\pi$
$602$	1.47944e11	+	1.12349e11i	0.0459106	+	0.0348645i
$603$	−7.97423e12			−2.45618
$604$	4.28262e12	+	7.41772e12i	1.30931	+	2.26780i
$605$	−6.08381e12			−1.84619
$606$	−7.71259e12	−	1.33586e13i	−2.32313	−	4.02378i
$607$	3.01683e12	+	5.22530e12i	0.901989	+	1.56229i	0.824908	+	0.565267i	$0.191227\pi$
$607$	3.01683e12	+	5.22530e12i	0.901989	+	1.56229i	0.0770810	+	0.997025i	$0.475440\pi$
$608$	−2.09371e10	−	3.62641e10i	−0.00621370	−	0.0107624i
$609$	−1.05077e12	+	8.30248e12i	−0.309548	+	2.44585i
$610$	1.96795e13			5.75479
$611$	9.91045e11	−	5.70767e11i	0.287679	−	0.165681i
$612$	3.60283e12	+	6.24029e12i	1.03816	+	1.79814i
$613$	2.98573e12	−	5.17144e12i	0.854041	−	1.47924i	−0.0234916	−	0.999724i	$-0.507478\pi$
$613$	2.98573e12	−	5.17144e12i	0.854041	−	1.47924i	0.877532	−	0.479518i	$-0.159188\pi$
$614$	−5.69730e11			−0.161775
$615$	7.55002e12	−	1.30770e13i	2.12819	−	3.68613i
$616$	2.06562e11	+	1.56863e11i	0.0578013	+	0.0438943i
$617$	1.25382e12	−	2.17168e12i	0.348298	−	0.603271i	−0.637649	−	0.770327i	$-0.720093\pi$
$617$	1.25382e12	−	2.17168e12i	0.348298	−	0.603271i	0.985947	+	0.167057i	$0.0534262\pi$
$618$	−8.29045e12	−	1.43595e13i	−2.28628	−	3.95996i
$619$	5.82215e10	+	1.00843e11i	0.0159395	+	0.0276081i	0.873885	−	0.486132i	$-0.161593\pi$
$619$	5.82215e10	+	1.00843e11i	0.0159395	+	0.0276081i	−0.857946	+	0.513741i	$0.828259\pi$
$620$	4.13023e12			1.12257
$621$	7.47033e12			2.01571
$622$	4.70216e12	+	8.14438e12i	1.25962	+	2.18173i
$623$	−8.48068e10	+	6.70089e11i	−0.0225546	+	0.178212i
$624$	−6.77984e12	+	3.90467e12i	−1.79015	+	1.03099i
$625$	−4.64532e12	+	8.04593e12i	−1.21774	+	2.10919i
$626$	2.35520e12	−	4.07933e12i	0.612976	−	1.06171i
$627$	−2.18209e10	+	3.77950e10i	−0.00563858	+	0.00976630i
$628$	−5.72962e12	−	9.92399e12i	−1.46997	−	2.54606i
$629$	−4.05981e11			−0.103414
$630$	−4.30875e12	+	3.40450e13i	−1.08973	+	8.61034i
$631$	2.10032e12	−	3.63786e12i	0.527416	−	0.913511i	−0.472074	−	0.881559i	$-0.656494\pi$
$631$	2.10032e12	−	3.63786e12i	0.527416	−	0.913511i	0.999489	−	0.0319517i	$-0.0101723\pi$
$632$	−4.14181e12	+	7.17383e12i	−1.03267	+	1.78864i
$633$	7.16986e12			1.77498
$634$	−1.46830e12	+	2.54317e12i	−0.360922	+	0.625135i
$635$	5.11430e12			1.24826
$636$	−5.96020e11			−0.144445
$637$	−2.96458e12	−	2.91200e12i	−0.713405	−	0.700752i
$638$	−3.80052e11			−0.0908133
$639$	8.56564e12			2.03239
$640$	−6.64529e12	+	1.15100e13i	−1.56568	+	2.71185i
$641$	−1.79247e12			−0.419364			−0.209682	−	0.977770i	$-0.567243\pi$
$641$	−1.79247e12			−0.419364			−0.209682	+	0.977770i	$0.567243\pi$
$642$	−6.89591e12	+	1.19441e13i	−1.60208	+	2.77488i
$643$	−2.41790e12	+	4.18792e12i	−0.557813	+	0.966160i	0.439866	+	0.898063i	$0.355026\pi$
$643$	−2.41790e12	+	4.18792e12i	−0.557813	+	0.966160i	−0.997679	+	0.0680965i	$0.978307\pi$
$644$	6.84639e11	−	5.40958e12i	0.156847	−	1.23930i
$645$	−5.18198e11			−0.117890
$646$	2.10565e11	+	3.64710e11i	0.0475708	+	0.0823951i
$647$	1.08222e12	−	1.87445e12i	0.242798	−	0.420538i	−0.718712	−	0.695308i	$-0.755268\pi$
$647$	1.08222e12	−	1.87445e12i	0.242798	−	0.420538i	0.961510	+	0.274769i	$0.0886015\pi$
$648$	1.43310e13	−	2.48220e13i	3.19292	−	5.53030i
$649$	5.00050e10	−	8.66111e10i	0.0110640	−	0.0191634i
$650$	−2.04958e10	+	1.91518e13i	−0.00450355	+	4.20824i
$651$	3.31799e11	−	2.62166e12i	0.0724037	−	0.572087i
$652$	4.73528e12	+	8.20175e12i	1.02620	+	1.77743i
$653$	−5.93927e12			−1.27827			−0.639137	−	0.769093i	$-0.720708\pi$
$653$	−5.93927e12			−1.27827			−0.639137	+	0.769093i	$0.720708\pi$
$654$	2.17323e12			0.464521
$655$	−7.96078e11	−	1.37885e12i	−0.168993	−	0.292705i
$656$	3.04879e12	+	5.28066e12i	0.642777	+	1.11332i
$657$	7.63220e12	−	1.32194e13i	1.59811	−	2.76800i
$658$	2.21096e12	+	1.67900e12i	0.459795	+	0.349169i
$659$	−9.68812e10	+	1.67803e11i	−0.0200104	+	0.0346590i	−0.875857	−	0.482570i	$-0.839703\pi$
$659$	−9.68812e10	+	1.67803e11i	−0.0200104	+	0.0346590i	0.855847	+	0.517229i	$0.173037\pi$
$660$	−1.42972e12			−0.293294
$661$	−2.55795e12	+	4.43049e12i	−0.521177	+	0.902704i	0.478520	+	0.878077i	$0.341173\pi$
$661$	−2.55795e12	+	4.43049e12i	−0.521177	+	0.902704i	−0.999697	+	0.0246278i	$0.992160\pi$
$662$	−8.15420e12	−	1.41235e13i	−1.65014	−	2.85812i
$663$	3.15106e12	−	1.81477e12i	0.633352	−	0.364763i
$664$	−5.46515e12			−1.09105
$665$	−1.68562e11	+	1.33187e12i	−0.0334243	+	0.264097i
$666$	3.24212e12	+	5.61551e12i	0.638550	+	1.10600i
$667$	2.02163e12	+	3.50156e12i	0.395490	+	0.685008i
$668$	7.97814e11	+	1.38186e12i	0.155027	+	0.268515i
$669$	3.30824e12			0.638527
$670$	−7.63394e12	−	1.32224e13i	−1.46357	−	2.53497i
$671$	3.82751e11			0.0728895
$672$	−6.98993e11	−	5.30816e11i	−0.132224	−	0.100411i
$673$	4.50438e11	+	7.80182e11i	0.0846384	+	0.146598i	0.905237	−	0.424907i	$-0.139693\pi$
$673$	4.50438e11	+	7.80182e11i	0.0846384	+	0.146598i	−0.820599	+	0.571505i	$0.806360\pi$
$674$	1.19968e13			2.23922
$675$	−2.13173e13	−	3.69226e13i	−3.95243	−	6.84582i
$676$	5.47568e12	+	9.53121e12i	1.00850	+	1.75545i
$677$	7.18397e11	−	1.24430e12i	0.131436	−	0.227655i	−0.792794	−	0.609490i	$-0.791374\pi$
$677$	7.18397e11	−	1.24430e12i	0.131436	−	0.227655i	0.924230	+	0.381835i	$0.124708\pi$
$678$	−4.94522e12	−	8.56536e12i	−0.898776	−	1.55673i
$679$	−6.10592e12	−	4.63684e12i	−1.10240	−	0.837159i
$680$	−3.49086e12	+	6.04635e12i	−0.626098	+	1.08443i
$681$	−4.10241e12	+	7.10558e12i	−0.730931	+	1.26601i
$682$	1.20008e11			0.0212413
$683$	5.44070e12			0.956669			0.478334	−	0.878178i	$-0.341241\pi$
$683$	5.44070e12			0.956669			0.478334	+	0.878178i	$0.341241\pi$
$684$	2.25116e12	−	3.89912e12i	0.393236	−	0.681105i
$685$	−4.02082e12	+	6.96427e12i	−0.697762	+	1.20856i
$686$	3.71989e12	−	9.37665e12i	0.641314	−	1.61655i
$687$	−2.85981e12	−	4.95333e12i	−0.489814	−	0.848383i
$688$	1.04627e11	−	1.81220e11i	0.0178031	−	0.0308360i
$689$	−2.34856e8	+	2.19456e11i	−3.97022e−5	+	0.0370989i
$690$	1.13617e13	+	1.96791e13i	1.90820	+	3.30509i
$691$	1.01548e12			0.169442			0.0847209	−	0.996405i	$-0.473000\pi$
$691$	1.01548e12			0.169442			0.0847209	+	0.996405i	$0.473000\pi$
$692$	3.73973e12	+	6.47740e12i	0.619958	+	1.07380i
$693$	−8.38019e10	+	6.62149e11i	−0.0138024	+	0.109058i
$694$	1.06559e13			1.74370
$695$	−1.22151e12	−	2.11571e12i	−0.198593	−	0.343973i
$696$	2.71938e13			4.39267
$697$	−1.41698e12	−	2.45428e12i	−0.227414	−	0.393892i
$698$	−1.57116e12	−	2.72132e12i	−0.250536	−	0.433941i
$699$	3.53119e12	+	6.11620e12i	0.559466	+	0.969023i
$700$	−2.86909e13	+	1.20528e13i	−4.51651	+	1.89735i
$701$	−8.61830e11			−0.134800			−0.0674001	−	0.997726i	$-0.521470\pi$
$701$	−8.61830e11			−0.134800			−0.0674001	+	0.997726i	$0.521470\pi$
$702$	−3.16395e13	−	1.83122e13i	−4.91714	−	2.84593i
$703$	1.26835e11	+	2.19684e11i	0.0195857	+	0.0339234i
$704$	−1.22657e11	+	2.12447e11i	−0.0188198	+	0.0325968i
$705$	−7.74425e12			−1.18067
$706$	2.05662e12	−	3.56218e12i	0.311554	−	0.539628i
$707$	−7.34969e12	−	5.58135e12i	−1.10632	−	0.840141i
$708$	−7.07038e12	+	1.22463e13i	−1.05753	+	1.83170i
$709$	−3.81902e11	−	6.61474e11i	−0.0567602	−	0.0983116i	0.836249	−	0.548350i	$-0.184744\pi$
$709$	−3.81902e11	−	6.61474e11i	−0.0567602	−	0.0983116i	−0.893009	+	0.450038i	$0.851410\pi$
$710$	8.20011e12	+	1.42030e13i	1.21104	+	2.09758i
$711$	−2.13159e13			−3.12817
$712$	2.19480e12			0.320063
$713$	−6.38367e11	−	1.10568e12i	−0.0925055	−	0.160224i
$714$	7.02982e12	+	5.33844e12i	1.01228	+	0.768728i
$715$	−5.63366e8	+	5.26425e11i	−8.06146e−5	+	0.0753285i
$716$	−5.65589e11	+	9.79629e11i	−0.0804252	+	0.139301i
$717$	−1.08453e13	+	1.87846e13i	−1.53251	+	2.65439i
$718$	1.10942e13	−	1.92158e13i	1.55789	−	2.69835i
$719$	−1.88448e12	−	3.26401e12i	−0.262973	−	0.455482i	0.704058	−	0.710143i	$-0.251370\pi$
$719$	−1.88448e12	−	3.26401e12i	−0.262973	−	0.455482i	−0.967030	+	0.254661i	$0.918036\pi$
$720$	3.86552e13			5.36058
$721$	−7.90035e12	−	5.99953e12i	−1.08877	−	0.826815i
$722$	−6.21758e12	+	1.07692e13i	−0.851538	+	1.47491i
$723$	−1.01349e13	+	1.75542e13i	−1.37942	+	2.38923i
$724$	−2.59299e12			−0.350733
$725$	1.15378e13	−	1.99841e13i	1.55097	−	2.68635i
$726$	2.49944e13			3.33909
$727$	1.04476e13			1.38711			0.693556	−	0.720403i	$-0.256043\pi$
$727$	1.04476e13			1.38711			0.693556	+	0.720403i	$0.256043\pi$
$728$	−8.17803e12	+	1.07452e13i	−1.07909	+	1.41782i
$729$	2.58455e13			3.38931
$730$	2.92260e13			3.80905
$731$	−4.86275e10	+	8.42253e10i	−0.00629874	+	0.0109097i
$732$	−5.41186e13			−6.96701
$733$	−8.34391e11	+	1.44521e12i	−0.106758	+	0.184911i	−0.914455	−	0.404687i	$-0.867380\pi$
$733$	−8.34391e11	+	1.44521e12i	−0.106758	+	0.184911i	0.807697	+	0.589598i	$0.200714\pi$
$734$	−5.82092e12	+	1.00821e13i	−0.740217	+	1.28209i
$735$	7.55486e12	+	2.71061e13i	0.954846	+	3.42589i
$736$	−4.24052e11			−0.0532683
$737$	−1.48474e11	−	2.57165e11i	−0.0185374	−	0.0321077i
$738$	−2.26317e13	+	3.91993e13i	−2.80843	+	4.86435i
$739$	−2.40776e12	+	4.17037e12i	−0.296971	+	0.514368i	−0.975441	−	0.220259i	$-0.929310\pi$
$739$	−2.40776e12	+	4.17037e12i	−0.296971	+	0.514368i	0.678471	+	0.734628i	$0.262643\pi$
$740$	−4.15513e12	+	7.19689e12i	−0.509380	+	0.882272i
$741$	−1.96644e12	−	1.13813e12i	−0.239607	−	0.138679i
$742$	−4.91151e11	+	2.06329e11i	−0.0594836	+	0.0249887i
$743$	−1.26788e12	−	2.19603e12i	−0.152626	−	0.264355i	0.779566	−	0.626320i	$-0.215440\pi$
$743$	−1.26788e12	−	2.19603e12i	−0.152626	−	0.264355i	−0.932192	+	0.361964i	$0.882106\pi$
$744$	−8.58696e12			−1.02745
$745$	1.40756e13			1.67403
$746$	−1.97891e12	−	3.42756e12i	−0.233938	−	0.405192i
$747$	−7.03161e12	−	1.21791e13i	−0.826251	−	1.43111i
$748$	−1.34164e11	+	2.32379e11i	−0.0156704	+	0.0271419i
$749$	−1.03605e12	+	8.18620e12i	−0.120285	+	0.950417i
$750$	3.80459e13	−	6.58975e13i	4.39069	−	7.60489i
$751$	−2.77099e11			−0.0317874			−0.0158937	−	0.999874i	$-0.505059\pi$
$751$	−2.77099e11			−0.0317874			−0.0158937	+	0.999874i	$0.505059\pi$
$752$	1.56361e12	−	2.70825e12i	0.178299	−	0.308823i
$753$	−1.64727e12	−	2.85315e12i	−0.186718	−	0.323405i
$754$	2.11745e10	−	1.97860e13i	0.00238584	−	2.22940i
$755$	−2.13556e13			−2.39194
$756$	7.45830e12	−	5.89307e13i	0.830409	−	6.56135i
$757$	−5.93702e12	−	1.02832e13i	−0.657109	−	1.13815i	−0.981361	−	0.192175i	$-0.938446\pi$
$757$	−5.93702e12	−	1.02832e13i	−0.657109	−	1.13815i	0.324252	−	0.945971i	$-0.394888\pi$
$758$	−4.63840e12	−	8.03394e12i	−0.510337	−	0.883929i
$759$	2.20977e11	+	3.82743e11i	0.0241690	+	0.0418619i
$760$	4.36239e12			0.474311
$761$	3.77772e12	+	6.54320e12i	0.408318	+	0.707228i	0.994701	−	0.102806i	$-0.0327821\pi$
$761$	3.77772e12	+	6.54320e12i	0.408318	+	0.707228i	−0.586383	+	0.810034i	$0.699449\pi$
$762$	−2.10113e13			−2.25764
$763$	1.19874e12	−	5.03583e11i	0.128045	−	0.0537911i
$764$	−4.60104e12	−	7.96923e12i	−0.488580	−	0.846245i
$765$	−1.79657e13			−1.89657
$766$	1.43068e13	+	2.47802e13i	1.50146	+	2.60061i
$767$	4.50631e12	+	2.60815e12i	0.470156	+	0.272116i
$768$	1.87348e13	−	3.24495e13i	1.94322	−	3.36576i
$769$	−3.46226e12	−	5.99682e12i	−0.357019	−	0.618375i	0.630442	−	0.776236i	$-0.282874\pi$
$769$	−3.46226e12	−	5.99682e12i	−0.357019	−	0.618375i	−0.987461	+	0.157861i	$0.949540\pi$
$770$	−1.17816e12	+	4.94937e11i	−0.120780	+	0.0507390i
$771$	3.59071e12	−	6.21929e12i	0.365962	−	0.633864i
$772$	1.21145e13	−	2.09829e13i	1.22752	−	2.12612i
$773$	−7.40171e12			−0.745632			−0.372816	−	0.927905i	$-0.621608\pi$
$773$	−7.40171e12			−0.745632			−0.372816	+	0.927905i	$0.621608\pi$
$774$	1.55334e12			0.155572
$775$	−3.64327e12	+	6.31034e12i	−0.362772	+	0.628340i
$776$	−1.24568e13	+	2.15758e13i	−1.23319	+	2.13594i
$777$	4.23443e12	+	3.21562e12i	0.416773	+	0.316498i
$778$	−5.69986e11	−	9.87245e11i	−0.0557771	−	0.0966088i
$779$	−8.85373e11	+	1.53351e12i	−0.0861406	+	0.149200i
$780$	7.96564e10	−	7.44331e13i	0.00770539	−	7.20013i
$781$	1.59486e11	+	2.76238e11i	0.0153389	+	0.0265677i
$782$	4.26472e12			0.407812
$783$	2.20232e13	+	3.81452e13i	2.09388	+	3.62670i
$784$	−1.10047e13	−	2.83086e12i	−1.04029	−	0.267606i
$785$	2.85711e13			2.68543
$786$	3.27056e12	+	5.66478e12i	0.305648	+	0.529397i
$787$	1.89594e13			1.76173			0.880864	−	0.473370i	$-0.156963\pi$
$787$	1.89594e13			1.76173			0.880864	+	0.473370i	$0.156963\pi$
$788$	2.00570e13	+	3.47398e13i	1.85310	+	3.20966i
$789$	3.24009e12	+	5.61200e12i	0.297653	+	0.515551i
$790$	−2.04062e13	−	3.53446e13i	−1.86398	−	3.22851i
$791$	−4.71252e12	−	3.57869e12i	−0.428015	−	0.325035i
$792$	2.16879e12			0.195864
$793$	−2.13249e10	+	1.99266e13i	−0.00191495	+	1.78938i
$794$	9.11536e12	+	1.57883e13i	0.813919	+	1.40975i
$795$	7.43022e11	−	1.28695e12i	0.0659705	−	0.114264i
$796$	6.39544e12			0.564627
$797$	9.13238e12	−	1.58177e13i	0.801718	−	1.38862i	−0.116767	−	0.993159i	$-0.537253\pi$
$797$	9.13238e12	−	1.58177e13i	0.801718	−	1.38862i	0.918485	−	0.395457i	$-0.129414\pi$
$798$	6.92511e11	−	5.47178e12i	0.0604524	−	0.477656i
$799$	−7.26718e11	+	1.25871e12i	−0.0630820	+	0.109261i
$800$	1.21007e12	+	2.09590e12i	0.104449	+	0.180912i
$801$	2.82389e12	+	4.89112e12i	0.242383	+	0.419819i
$802$	1.92695e13			1.64470
$803$	5.68424e11			0.0482450
$804$	2.09933e13	+	3.63615e13i	1.77186	+	3.06895i
$805$	1.08271e13	+	8.22210e12i	0.908721	+	0.690083i
$806$	−6.68623e9	+	6.24780e12i	−0.000558051	+	0.521458i
$807$	1.18558e13	−	2.05349e13i	0.984013	−	1.70436i
$808$	−1.49942e13	+	2.59708e13i	−1.23758	+	2.14355i
$809$	1.36282e12	−	2.36048e12i	0.111859	−	0.193746i	−0.804661	−	0.593735i	$-0.797653\pi$
$809$	1.36282e12	−	2.36048e12i	0.111859	−	0.193746i	0.916520	+	0.399989i	$0.130986\pi$
$810$	7.06071e13	+	1.22295e14i	5.76323	+	9.98220i
$811$	−7.75034e12			−0.629110			−0.314555	−	0.949239i	$-0.601855\pi$
$811$	−7.75034e12			−0.629110			−0.314555	+	0.949239i	$0.601855\pi$
$812$	2.96409e13	−	1.24520e13i	2.39271	−	1.00516i
$813$	−1.35248e13	+	2.34256e13i	−1.08573	+	1.88055i
$814$	−1.20732e11	+	2.09114e11i	−0.00963856	+	0.0166945i
$815$	−2.36128e13			−1.87473
$816$	4.97155e12	−	8.61097e12i	0.392542	−	0.679902i
$817$	6.07678e10			0.00477172
$818$	2.09071e13			1.63269
$819$	−3.44677e13	−	4.39974e12i	−2.67692	−	0.341703i
$820$	−5.80101e13			−4.48065
$821$	3.29272e12			0.252936			0.126468	−	0.991971i	$-0.459636\pi$
$821$	3.29272e12			0.252936			0.126468	+	0.991971i	$0.459636\pi$
$822$	1.65189e13	−	2.86116e13i	1.26200	−	2.18584i
$823$	1.94161e13			1.47524			0.737621	−	0.675215i	$-0.235949\pi$
$823$	1.94161e13			1.47524			0.737621	+	0.675215i	$0.235949\pi$
$824$	−1.61176e13	+	2.79166e13i	−1.21795	+	2.10955i
$825$	1.26115e12	−	2.18438e12i	0.0947819	−	0.164167i
$826$	−1.58696e12	+	1.25391e13i	−0.118620	+	0.937255i
$827$	1.42778e13			1.06142			0.530708	−	0.847555i	$-0.321926\pi$
$827$	1.42778e13			1.06142			0.530708	+	0.847555i	$0.321926\pi$
$828$	−2.27971e13	−	3.94857e13i	−1.68555	−	2.91946i
$829$	−1.00984e13	+	1.74909e13i	−0.742603	+	1.28623i	0.208703	+	0.977979i	$0.433076\pi$
$829$	−1.00984e13	+	1.74909e13i	−0.742603	+	1.28623i	−0.951306	+	0.308248i	$0.900257\pi$
$830$	1.34631e13	−	2.33188e13i	0.984676	−	1.70551i
$831$	−1.23101e13	+	2.13217e13i	−0.895482	+	1.55102i
$832$	−1.10535e13	−	6.39751e12i	−0.799731	−	0.462867i
$833$	5.11463e12	+	1.31570e12i	0.368054	+	0.0946789i
$834$	5.01837e12	+	8.69207e12i	0.359182	+	0.622122i
$835$	−3.97835e12			−0.283213
$836$	1.67660e11			0.0118714
$837$	−6.95422e12	−	1.20451e13i	−0.489761	−	0.848290i
$838$	−2.31336e13	−	4.00686e13i	−1.62049	−	2.80677i
$839$	−6.31000e12	+	1.09292e13i	−0.439644	+	0.761485i	−0.997662	−	0.0683435i	$-0.978229\pi$
$839$	−6.31000e12	+	1.09292e13i	−0.439644	+	0.761485i	0.558018	+	0.829829i	$0.311562\pi$
$840$	8.43009e13	−	3.54143e13i	5.84219	−	2.45426i
$841$	−4.66628e12	+	8.08223e12i	−0.321654	+	0.557121i
$842$	1.50061e13			1.02888
$843$	−1.54941e12	+	2.68366e12i	−0.105668	+	0.183022i
$844$	−1.37723e13	−	2.38543e13i	−0.934254	−	1.61818i
$845$	−2.74064e13	−	5.86593e10i	−1.84926	−	0.00395805i
$846$	2.32139e13			1.55805
$847$	1.37868e13	−	5.79173e12i	0.920422	−	0.386663i
$848$	3.00041e11	+	5.19687e11i	0.0199251	+	0.0345112i
$849$	−9.24368e12	−	1.60105e13i	−0.610605	−	1.05760i
$850$	−1.21698e13	−	2.10786e13i	−0.799644	−	1.38502i
$851$	2.56886e12			0.167903
$852$	−2.25503e13	−	3.90583e13i	−1.46614	−	2.53942i
$853$	2.15302e13			1.39244			0.696222	−	0.717827i	$-0.254863\pi$
$853$	2.15302e13			1.39244			0.696222	+	0.717827i	$0.254863\pi$
$854$	−4.45964e13	+	1.87347e13i	−2.86906	+	1.20527i
$855$	5.61277e12	+	9.72160e12i	0.359194	+	0.622143i
$856$	2.68130e13			1.70692
$857$	5.64307e12	+	9.77409e12i	0.357357	+	0.618960i	0.987518	−	0.157504i	$-0.0503448\pi$
$857$	5.64307e12	+	9.77409e12i	0.357357	+	0.618960i	−0.630162	+	0.776464i	$0.717011\pi$
$858$	2.31450e9	−	2.16274e12i	0.000145802	−	0.136242i
$859$	6.31673e12	−	1.09409e13i	0.395843	−	0.685620i	−0.597366	−	0.801969i	$-0.703786\pi$
$859$	6.31673e12	−	1.09409e13i	0.395843	−	0.685620i	0.993208	+	0.116349i	$0.0371192\pi$
$860$	9.95384e11	+	1.72406e12i	0.0620508	+	0.107475i
$861$	−4.66019e12	+	3.68218e13i	−0.288995	+	2.28345i
$862$	−2.33279e13	+	4.04051e13i	−1.43911	+	2.49260i
$863$	−9.78798e12	+	1.69533e13i	−0.600682	+	1.04041i	0.392036	+	0.919950i	$0.371771\pi$
$863$	−9.78798e12	+	1.69533e13i	−0.600682	+	1.04041i	−0.992718	+	0.120462i	$0.961562\pi$
$864$	−4.61952e12			−0.282024
$865$	−1.86484e13			−1.13258
$866$	−3.55337e12	+	6.15462e12i	−0.214689	+	0.371853i
$867$	1.36878e13	−	2.37080e13i	0.822711	−	1.42498i
$868$	−9.35967e12	+	3.93194e12i	−0.559657	+	0.235108i
$869$	−3.96886e11	−	6.87427e11i	−0.0236090	−	0.0408919i
$870$	−6.69905e13	+	1.16031e14i	−3.96439	+	6.86653i
$871$	1.33967e13	−	7.71546e12i	0.788706	−	0.454235i
$872$	−2.11251e12	−	3.65898e12i	−0.123730	−	0.214307i
$873$	−6.41090e13			−3.73556
$874$	−1.33236e12	−	2.30772e12i	−0.0772362	−	0.133777i
$875$	5.71607e12	−	4.51647e13i	0.329656	−	2.60473i
$876$	−8.03715e13			−4.61141
$877$	3.88113e12	+	6.72232e12i	0.221544	+	0.383726i	0.955277	−	0.295712i	$-0.0955569\pi$
$877$	3.88113e12	+	6.72232e12i	0.221544	+	0.383726i	−0.733733	+	0.679438i	$0.762224\pi$
$878$	5.15901e12			0.292982
$879$	−2.24993e13	−	3.89699e13i	−1.27121	−	2.20180i
$880$	7.19732e11	+	1.24661e12i	0.0404575	+	0.0700744i
$881$	1.44932e13	+	2.51030e13i	0.810539	+	1.40389i	0.912488	+	0.409105i	$0.134159\pi$
$881$	1.44932e13	+	2.51030e13i	0.810539	+	1.40389i	−0.101949	+	0.994790i	$0.532508\pi$
$882$	−2.26462e13	−	8.12524e13i	−1.26005	−	4.52093i
$883$	−1.23599e13			−0.684211			−0.342106	−	0.939662i	$-0.611140\pi$
$883$	−1.23599e13			−0.684211			−0.342106	+	0.939662i	$0.611140\pi$
$884$	−1.20905e13	−	6.99773e12i	−0.665901	−	0.385409i
$885$	−1.76284e13	−	3.05333e13i	−0.965982	−	1.67313i
$886$	9.79090e12	−	1.69583e13i	0.533790	−	0.924552i
$887$	2.94160e13			1.59561			0.797807	−	0.602912i	$-0.205993\pi$
$887$	2.94160e13			1.59561			0.797807	+	0.602912i	$0.205993\pi$
$888$	8.63873e12	−	1.49627e13i	0.466220	−	0.807518i
$889$	−1.15897e13	+	4.86876e12i	−0.622321	+	0.261433i
$890$	−5.40677e12	+	9.36480e12i	−0.288857	+	0.500315i
$891$	1.37326e12	+	2.37855e12i	0.0729964	+	0.126434i
$892$	−6.35466e12	−	1.10066e13i	−0.336086	−	0.582118i
$893$	9.08150e11			0.0477888
$894$	−5.78274e13			−3.02771
$895$	−1.41017e12	−	2.44249e12i	−0.0734629	−	0.127242i
$896$	4.10176e12	−	3.24095e13i	0.212610	−	1.67991i
$897$	−1.99384e13	+	1.14830e13i	−1.02831	+	0.592230i
$898$	7.84431e12	−	1.35868e13i	0.402542	−	0.697224i
$899$	3.76391e12	−	6.51929e12i	0.192186	−	0.332875i
$900$	−1.30107e14	+	2.25352e14i	−6.61012	+	11.4491i
$901$	−1.39450e11	−	2.41534e11i	−0.00704947	−	0.0122100i
$902$	−1.68555e12			−0.0847835
$903$	1.17431e12	−	4.93319e11i	0.0587742	−	0.0246907i
$904$	−9.61410e12	+	1.66521e13i	−0.478796	+	0.829300i
$905$	3.23252e12	−	5.59889e12i	0.160185	−	0.277449i
$906$	8.77360e13			4.32614
$907$	−1.46499e13	+	2.53743e13i	−0.718788	+	1.24498i	0.242692	+	0.970103i	$0.421970\pi$
$907$	−1.46499e13	+	2.53743e13i	−0.718788	+	1.24498i	−0.961480	+	0.274874i	$0.911364\pi$
$908$	3.15206e13			1.53889
$909$	−7.71679e13			−3.74886
$910$	−2.57015e13	−	6.13642e13i	−1.24243	−	2.96640i
$911$	−2.45327e13			−1.18008			−0.590041	−	0.807373i	$-0.700888\pi$
$911$	−2.45327e13			−1.18008			−0.590041	+	0.807373i	$0.700888\pi$
$912$	−6.21274e12			−0.297377
$913$	2.61847e11	−	4.53532e11i	0.0124718	−	0.0216018i
$914$	5.11065e13			2.42225
$915$	6.74663e13	−	1.16855e14i	3.18194	−	5.51129i
$916$	−1.09866e13	+	1.90293e13i	−0.515623	+	0.893086i
$917$	3.11667e12	+	2.36680e12i	0.145556	+	0.110535i
$918$	4.64588e13			2.15912
$919$	−8.97164e12	−	1.55393e13i	−0.414908	−	0.718642i	0.580511	−	0.814253i	$-0.302853\pi$
$919$	−8.97164e12	−	1.55393e13i	−0.414908	−	0.718642i	−0.995419	+	0.0956105i	$0.969520\pi$
$920$	2.20886e13	−	3.82585e13i	1.01653	−	1.76069i
$921$	−1.95318e12	+	3.38301e12i	−0.0894488	+	0.154930i
$922$	2.72155e13	−	4.71386e13i	1.24030	−	2.14827i
$923$	−1.43902e13	+	8.28768e12i	−0.652619	+	0.375859i
$924$	3.23994e12	−	1.36108e12i	0.146222	−	0.0614269i
$925$	−7.33048e12	−	1.26968e13i	−0.329226	−	0.570237i
$926$	1.13244e13			0.506134
$927$	−8.29496e13			−3.68940
$928$	−1.25014e12	−	2.16531e12i	−0.0553341	−	0.0958415i
$929$	−2.37165e12	−	4.10781e12i	−0.104467	−	0.180942i	0.809053	−	0.587735i	$-0.199980\pi$
$929$	−2.37165e12	−	4.10781e12i	−0.104467	−	0.180942i	−0.913520	+	0.406793i	$0.866647\pi$
$930$	2.11535e13	−	3.66389e13i	0.927275	−	1.60609i
$931$	−8.85941e11	−	3.17867e12i	−0.0386484	−	0.138666i
$932$	1.35658e13	−	2.34967e13i	0.588945	−	1.02008i
$933$	6.44809e13			2.78589
$934$	−2.97210e13	+	5.14782e13i	−1.27791	+	2.21341i
$935$	−3.34509e11	−	5.79387e11i	−0.0143138	−	0.0247923i
$936$	−1.20834e11	+	1.12911e14i	−0.00514573	+	4.80832i
$937$	−9.68517e12			−0.410468			−0.205234	−	0.978713i	$-0.565796\pi$
$937$	−9.68517e12			−0.410468			−0.205234	+	0.978713i	$0.565796\pi$
$938$	2.98871e13	+	2.26963e13i	1.26058	+	0.957287i
$939$	−1.61485e13	−	2.79700e13i	−0.677854	−	1.17408i
$940$	1.48756e13	+	2.57653e13i	0.621440	+	1.07637i
$941$	−1.03110e13	−	1.78593e13i	−0.428696	−	0.742523i	0.568062	−	0.822986i	$-0.307693\pi$
$941$	−1.03110e13	−	1.78593e13i	−0.428696	−	0.742523i	−0.996758	+	0.0804629i	$0.974360\pi$
$942$	−1.17380e14			−4.85696
$943$	8.96601e12	+	1.55296e13i	0.369230	+	0.639525i
$944$	1.42371e13			0.583511
$945$	1.17948e14	+	8.95696e13i	4.81113	+	3.65357i
$946$	2.89220e10	+	5.00943e10i	0.00117413	+	0.00203366i
$947$	−2.51300e13			−1.01535			−0.507676	−	0.861548i	$-0.669495\pi$
$947$	−2.51300e13			−1.01535			−0.507676	+	0.861548i	$0.669495\pi$
$948$	5.61171e13	+	9.71977e13i	2.25662	+	3.90858i
$949$	−3.16696e10	+	2.95930e13i	−0.00126749	+	1.18438i
$950$	−7.60403e12	+	1.31706e13i	−0.302892	+	0.524624i
$951$	1.00674e13	+	1.74373e13i	0.399122	+	0.691300i
$952$	2.15471e12	−	1.70251e13i	0.0850202	−	0.671775i
$953$	2.11728e13	−	3.66724e13i	0.831498	−	1.44020i	−0.0653521	−	0.997862i	$-0.520817\pi$
$953$	2.11728e13	−	3.66724e13i	0.831498	−	1.44020i	0.896850	−	0.442335i	$-0.145850\pi$
$954$	−2.22726e12	+	3.85773e12i	−0.0870570	+	0.150787i
$955$	2.29433e13			0.892568
$956$	8.33289e13			3.22653
$957$	−1.30291e12	+	2.25671e12i	−0.0502126	+	0.0869707i
$958$	2.62662e13	−	4.54943e13i	1.00752	−	1.74507i
$959$	2.48182e12	−	1.96098e13i	0.0947518	−	0.748667i
$960$	4.32406e13	+	7.48949e13i	1.64313	+	2.84598i
$961$	1.20313e13	−	2.08388e13i	0.455048	−	0.788165i
$962$	−1.08800e13	−	6.29712e12i	−0.409583	−	0.237058i
$963$	3.44983e13	+	5.97529e13i	1.29265	+	2.23893i
$964$	7.78709e13			2.90421
$965$	3.02049e13	+	5.23163e13i	1.12125	+	1.94207i
$966$	−4.44815e13	−	3.37792e13i	−1.64355	−	1.24811i
$967$	4.30653e13			1.58383			0.791915	−	0.610631i	$-0.209084\pi$
$967$	4.30653e13			1.58383			0.791915	+	0.610631i	$0.209084\pi$
$968$	−2.42961e13	−	4.20821e13i	−0.889400	−	1.54049i
$969$	2.88749e12			0.105212
$970$	−6.13733e13	−	1.06302e14i	−2.22590	−	3.85538i
$971$	−9.75553e12	−	1.68971e13i	−0.352180	−	0.609993i	0.634451	−	0.772963i	$-0.281226\pi$
$971$	−9.75553e12	−	1.68971e13i	−0.352180	−	0.609993i	−0.986631	+	0.162970i	$0.947893\pi$
$972$	−1.02143e14	−	1.76917e14i	−3.67038	−	6.35728i
$973$	4.78223e12	+	3.63163e12i	0.171050	+	0.129895i
$974$	9.18545e12			0.327028
$975$	1.13652e14	+	6.57792e13i	4.02769	+	2.33114i
$976$	2.72437e13	+	4.71875e13i	0.961042	+	1.66457i
$977$	1.33823e13	−	2.31789e13i	0.469901	−	0.813893i	−0.529507	−	0.848306i	$-0.677623\pi$
$977$	1.33823e13	−	2.31789e13i	0.469901	−	0.813893i	0.999408	+	0.0344132i	$0.0109562\pi$
$978$	9.70094e13			3.39070
$979$	−1.05158e11	+	1.82138e11i	−0.00365863	+	0.00633694i
$980$	7.56708e13	−	7.72021e13i	2.62066	−	2.67370i
$981$	5.43603e12	−	9.41547e12i	0.187401	−	0.324587i
$982$	2.05780e13	+	3.56421e13i	0.706157	+	1.22310i
$983$	−6.89372e12	−	1.19403e13i	−0.235485	−	0.407872i	0.723929	−	0.689875i	$-0.242334\pi$
$983$	−6.89372e12	−	1.19403e13i	−0.235485	−	0.407872i	−0.959413	+	0.282003i	$0.909001\pi$
$984$	1.20606e14			4.10101
$985$	−1.00016e14			−3.38536
$986$	1.25727e13	+	2.17766e13i	0.423627	+	0.733743i
$987$	1.75495e13	−	7.37245e12i	0.588625	−	0.247277i
$988$	−9.34112e9	+	8.72860e12i	−0.000311884	+	0.291433i
$989$	3.07692e11	−	5.32939e11i	0.0102267	−	0.0177131i
$990$	−5.34270e12	+	9.25384e12i	−0.176768	+	0.306171i
$991$	−1.48858e13	+	2.57829e13i	−0.490276	+	0.849182i	−0.999937	−	0.0111927i	$-0.996437\pi$
$991$	−1.48858e13	+	2.57829e13i	−0.490276	+	0.849182i	0.509662	+	0.860375i	$0.329771\pi$
$992$	3.94755e11	+	6.83736e11i	0.0129427	+	0.0224174i
$993$	−1.11819e14			−3.64958
$994$	−3.21037e13	−	2.43796e13i	−1.04308	−	0.792113i
$995$	−7.97281e12	+	1.38093e13i	−0.257874	+	0.446651i
$996$	−3.70235e13	+	6.41265e13i	−1.19209	+	2.06477i
$997$	−3.86932e12			−0.124024			−0.0620122	−	0.998075i	$-0.519752\pi$
$997$	−3.86932e12			−0.124024			−0.0620122	+	0.998075i	$0.519752\pi$
$998$	7.41821e12	−	1.28487e13i	0.236707	−	0.409989i
$999$	2.79846e13			0.888943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.h.a.16.9	yes	164
7.4	even	3		91.10.g.a.81.74	yes	164
13.9	even	3		91.10.g.a.9.74	✓	164
91.74	even	3	inner	91.10.h.a.74.9	yes	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.g.a.9.74	✓	164	13.9	even	3
91.10.g.a.81.74	yes	164	7.4	even	3
91.10.h.a.16.9	yes	164	1.1	even	1	trivial
91.10.h.a.74.9	yes	164	91.74	even	3	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-39.3517 q^{2} +(-134.908 + 233.667i) q^{3} +1036.55 q^{4} +(-1292.21 + 2238.17i) q^{5} +(5308.84 - 9195.18i) q^{6} +(797.607 - 6302.18i) q^{7} -20642.1 q^{8} +(-26558.7 - 46000.9i) q^{9} +O(q^{10})\)	\(q-39.3517 q^{2} +(-134.908 + 233.667i) q^{3} +1036.55 q^{4} +(-1292.21 + 2238.17i) q^{5} +(5308.84 - 9195.18i) q^{6} +(797.607 - 6302.18i) q^{7} -20642.1 q^{8} +(-26558.7 - 46000.9i) q^{9} +(50850.6 - 88075.8i) q^{10} +(989.006 - 1713.01i) q^{11} +(-139839. + 242208. i) q^{12} +(89126.5 + 51584.5i) q^{13} +(-31387.2 + 248001. i) q^{14} +(-348658. - 603893. i) q^{15} +281585. q^{16} -130872. q^{17} +(1.04513e6 + 1.81021e6i) q^{18} +(40886.3 + 70817.2i) q^{19} +(-1.33944e6 + 2.31999e6i) q^{20} +(1.36501e6 + 1.03659e6i) q^{21} +(-38919.0 + 67409.8i) q^{22} +828097. q^{23} +(2.78477e6 - 4.82337e6i) q^{24} +(-2.36305e6 - 4.09292e6i) q^{25} +(-3.50728e6 - 2.02994e6i) q^{26} +9.02109e6 q^{27} +(826763. - 6.53255e6i) q^{28} +(2.44130e6 + 4.22845e6i) q^{29} +(1.37203e7 + 2.37642e7i) q^{30} +(-770884. - 1.33521e6i) q^{31} -512080. q^{32} +(266849. + 462196. i) q^{33} +5.15002e6 q^{34} +(1.30747e7 + 9.92891e6i) q^{35} +(-2.75295e7 - 4.76825e7i) q^{36} +3.10213e6 q^{37} +(-1.60894e6 - 2.78677e6i) q^{38} +(-2.40774e7 + 1.38668e7i) q^{39} +(2.66739e7 - 4.62005e7i) q^{40} +(1.08273e7 + 1.87534e7i) q^{41} +(-5.37153e7 - 4.07914e7i) q^{42} +(371566. - 643571. i) q^{43} +(1.02516e6 - 1.77563e6i) q^{44} +1.37277e8 q^{45} -3.25870e7 q^{46} +(5.55290e6 - 9.61790e6i) q^{47} +(-3.79879e7 + 6.57970e7i) q^{48} +(-3.90813e7 - 1.00533e7i) q^{49} +(9.29899e7 + 1.61063e8i) q^{50} +(1.76556e7 - 3.05804e7i) q^{51} +(9.23845e7 + 5.34701e7i) q^{52} +(1.06555e6 + 1.84558e6i) q^{53} -3.54995e8 q^{54} +(2.55601e6 + 4.42713e6i) q^{55} +(-1.64643e7 + 1.30090e8i) q^{56} -2.20635e7 q^{57} +(-9.60691e7 - 1.66397e8i) q^{58} +5.05608e7 q^{59} +(-3.61403e8 - 6.25968e8i) q^{60} +(9.67515e7 + 1.67578e8i) q^{61} +(3.03356e7 + 5.25428e7i) q^{62} +(-3.11089e8 + 1.30687e8i) q^{63} -1.24020e8 q^{64} +(-2.30625e8 + 1.32823e8i) q^{65} +(-1.05010e7 - 1.81882e7i) q^{66} +(7.50625e7 - 1.30012e8i) q^{67} -1.35656e8 q^{68} +(-1.11717e8 + 1.93499e8i) q^{69} +(-5.14511e8 - 3.90719e8i) q^{70} +(-8.06295e7 + 1.39654e8i) q^{71} +(5.48226e8 + 9.49555e8i) q^{72} +(1.43686e8 + 2.48871e8i) q^{73} -1.22074e8 q^{74} +1.27517e9 q^{75} +(4.23809e7 + 7.34058e7i) q^{76} +(-1.00068e7 - 7.59920e6i) q^{77} +(9.47488e8 - 5.45681e8i) q^{78} +(2.00649e8 - 3.47534e8i) q^{79} +(-3.63866e8 + 6.30235e8i) q^{80} +(-6.94260e8 + 1.20249e9i) q^{81} +(-4.26071e8 - 7.37976e8i) q^{82} +2.64758e8 q^{83} +(1.41490e9 + 1.07448e9i) q^{84} +(1.69114e8 - 2.92914e8i) q^{85} +(-1.46217e7 + 2.53256e7i) q^{86} -1.31740e9 q^{87} +(-2.04151e7 + 3.53601e7i) q^{88} -1.06327e8 q^{89} -5.40210e9 q^{90} +(3.96182e8 - 5.20547e8i) q^{91} +8.58367e8 q^{92} +4.15993e8 q^{93} +(-2.18516e8 + 3.78481e8i) q^{94} -2.11335e8 q^{95} +(6.90836e7 - 1.19656e8i) q^{96} +(6.03467e8 - 1.04523e9i) q^{97} +(1.53791e9 + 3.95615e8i) q^{98} -1.05067e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9}+O(q^{10}) \) 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9	\( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9} + 38977 q^{10} - 59285 q^{11} + 44088 q^{12} + 232454 q^{13} + 17108 q^{14} - 407531 q^{15} + 10497654 q^{16} - 1395086 q^{17} - 76575 q^{18} + 1207545 q^{19} + 713618 q^{20} + 1790137 q^{21} + 199216 q^{22} + 2148062 q^{23} + 3435832 q^{24} - 29660780 q^{25} - 6096660 q^{26} - 9655538 q^{27} - 5996877 q^{28} + 996812 q^{29} + 4910674 q^{30} + 7678612 q^{31} - 13584366 q^{32} - 3082415 q^{33} + 32705872 q^{34} + 11865077 q^{35} - 134627249 q^{36} - 25237130 q^{37} + 25519874 q^{38} + 30627737 q^{39} + 45727182 q^{40} - 13667582 q^{41} - 81628563 q^{42} + 26867814 q^{43} - 75673614 q^{44} + 29593550 q^{45} - 70893356 q^{46} - 23074040 q^{47} + 29166348 q^{48} - 13541447 q^{49} + 77715962 q^{50} - 94065066 q^{51} + 139792121 q^{52} + 46529776 q^{53} - 14474550 q^{54} + 218800681 q^{55} - 649788015 q^{56} - 143710238 q^{57} + 1142701 q^{58} + 439131230 q^{59} - 557690411 q^{60} + 508694743 q^{61} + 307731320 q^{62} - 355730647 q^{63} + 1713678376 q^{64} + 148754944 q^{65} + 278425259 q^{66} + 37418955 q^{67} - 1290484830 q^{68} + 290468024 q^{69} - 182370322 q^{70} - 415622020 q^{71} + 720832393 q^{72} + 514120432 q^{73} + 128989762 q^{74} + 241348444 q^{75} + 985961470 q^{76} - 1189530907 q^{77} + 2167273673 q^{78} - 376448286 q^{79} - 482394712 q^{80} - 3131306974 q^{81} - 971561072 q^{82} + 971157612 q^{83} + 3735517629 q^{84} + 538436691 q^{85} + 1470174876 q^{86} - 912549686 q^{87} - 629673387 q^{88} + 699403942 q^{89} - 8083448244 q^{90} + 2740572083 q^{91} + 2309185554 q^{92} + 820704894 q^{93} + 419356886 q^{94} - 5283246 q^{95} - 4707829686 q^{96} + 1339771120 q^{97} - 1961676608 q^{98} + 1482300132 q^{99}+O(q^{100}) \) 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9 + 38977 * q^10 - 59285 * q^11 + 44088 * q^12 + 232454 * q^13 + 17108 * q^14 - 407531 * q^15 + 10497654 * q^16 - 1395086 * q^17 - 76575 * q^18 + 1207545 * q^19 + 713618 * q^20 + 1790137 * q^21 + 199216 * q^22 + 2148062 * q^23 + 3435832 * q^24 - 29660780 * q^25 - 6096660 * q^26 - 9655538 * q^27 - 5996877 * q^28 + 996812 * q^29 + 4910674 * q^30 + 7678612 * q^31 - 13584366 * q^32 - 3082415 * q^33 + 32705872 * q^34 + 11865077 * q^35 - 134627249 * q^36 - 25237130 * q^37 + 25519874 * q^38 + 30627737 * q^39 + 45727182 * q^40 - 13667582 * q^41 - 81628563 * q^42 + 26867814 * q^43 - 75673614 * q^44 + 29593550 * q^45 - 70893356 * q^46 - 23074040 * q^47 + 29166348 * q^48 - 13541447 * q^49 + 77715962 * q^50 - 94065066 * q^51 + 139792121 * q^52 + 46529776 * q^53 - 14474550 * q^54 + 218800681 * q^55 - 649788015 * q^56 - 143710238 * q^57 + 1142701 * q^58 + 439131230 * q^59 - 557690411 * q^60 + 508694743 * q^61 + 307731320 * q^62 - 355730647 * q^63 + 1713678376 * q^64 + 148754944 * q^65 + 278425259 * q^66 + 37418955 * q^67 - 1290484830 * q^68 + 290468024 * q^69 - 182370322 * q^70 - 415622020 * q^71 + 720832393 * q^72 + 514120432 * q^73 + 128989762 * q^74 + 241348444 * q^75 + 985961470 * q^76 - 1189530907 * q^77 + 2167273673 * q^78 - 376448286 * q^79 - 482394712 * q^80 - 3131306974 * q^81 - 971561072 * q^82 + 971157612 * q^83 + 3735517629 * q^84 + 538436691 * q^85 + 1470174876 * q^86 - 912549686 * q^87 - 629673387 * q^88 + 699403942 * q^89 - 8083448244 * q^90 + 2740572083 * q^91 + 2309185554 * q^92 + 820704894 * q^93 + 419356886 * q^94 - 5283246 * q^95 - 4707829686 * q^96 + 1339771120 * q^97 - 1961676608 * q^98 + 1482300132 * q^99

Introduction

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