LMFDB - Embedded newform 91.10.h.a.16.2

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			16.2
Character	$\chi$	$=$	91.16
Dual form			91.10.h.a.74.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-42.8048 q^{2} +(136.894 - 237.108i) q^{3} +1320.25 q^{4} +(98.6739 - 170.908i) q^{5} +(-5859.74 + 10149.4i) q^{6} +(4801.69 + 4159.02i) q^{7} -34597.0 q^{8} +(-27638.7 - 47871.6i) q^{9} +O(q^{10})$	\(q-42.8048 q^{2} +(136.894 - 237.108i) q^{3} +1320.25 q^{4} +(98.6739 - 170.908i) q^{5} +(-5859.74 + 10149.4i) q^{6} +(4801.69 + 4159.02i) q^{7} -34597.0 q^{8} +(-27638.7 - 47871.6i) q^{9} +(-4223.72 + 7315.69i) q^{10} +(-16216.3 + 28087.5i) q^{11} +(180735. - 313042. i) q^{12} +(40492.4 + 94683.0i) q^{13} +(-205535. - 178026. i) q^{14} +(-27015.8 - 46792.8i) q^{15} +804951. q^{16} -270741. q^{17} +(1.18307e6 + 2.04914e6i) q^{18} +(322957. + 559378. i) q^{19} +(130274. - 225642. i) q^{20} +(1.64346e6 - 569172. i) q^{21} +(694137. - 1.20228e6i) q^{22} +1.09953e6 q^{23} +(-4.73614e6 + 8.20324e6i) q^{24} +(957089. + 1.65773e6i) q^{25} +(-1.73327e6 - 4.05289e6i) q^{26} -9.74535e6 q^{27} +(6.33943e6 + 5.49095e6i) q^{28} +(-1.60721e6 - 2.78378e6i) q^{29} +(1.15641e6 + 2.00296e6i) q^{30} +(249771. + 432616. i) q^{31} -1.67421e7 q^{32} +(4.43986e6 + 7.69006e6i) q^{33} +1.15890e7 q^{34} +(1.18461e6 - 410261. i) q^{35} +(-3.64900e7 - 6.32026e7i) q^{36} -4.54277e6 q^{37} +(-1.38241e7 - 2.39441e7i) q^{38} +(2.79933e7 + 3.36050e6i) q^{39} +(-3.41382e6 + 5.91292e6i) q^{40} +(1.27584e7 + 2.20981e7i) q^{41} +(-7.03480e7 + 2.43633e7i) q^{42} +(-1.56441e7 + 2.70964e7i) q^{43} +(-2.14096e7 + 3.70826e7i) q^{44} -1.09089e7 q^{45} -4.70652e7 q^{46} +(-7.28961e6 + 1.26260e7i) q^{47} +(1.10193e8 - 1.90860e8i) q^{48} +(5.75876e6 + 3.99406e7i) q^{49} +(-4.09680e7 - 7.09587e7i) q^{50} +(-3.70629e7 + 6.41948e7i) q^{51} +(5.34601e7 + 1.25005e8i) q^{52} +(3.38445e7 + 5.86204e7i) q^{53} +4.17148e8 q^{54} +(3.20026e6 + 5.54301e6i) q^{55} +(-1.66124e8 - 1.43890e8i) q^{56} +1.76844e8 q^{57} +(6.87964e7 + 1.19159e8i) q^{58} +1.87085e7 q^{59} +(-3.56677e7 - 6.17782e7i) q^{60} +(3.61089e7 + 6.25425e7i) q^{61} +(-1.06914e7 - 1.85181e7i) q^{62} +(6.63866e7 - 3.44814e8i) q^{63} +3.04506e8 q^{64} +(2.01776e7 + 2.42225e6i) q^{65} +(-1.90047e8 - 3.29171e8i) q^{66} +(-2.68350e7 + 4.64796e7i) q^{67} -3.57446e8 q^{68} +(1.50520e8 - 2.60708e8i) q^{69} +(-5.07070e7 + 1.75611e7i) q^{70} +(-3.88412e7 + 6.72749e7i) q^{71} +(9.56217e8 + 1.65622e9i) q^{72} +(-1.05202e8 - 1.82215e8i) q^{73} +1.94452e8 q^{74} +5.24081e8 q^{75} +(4.26385e8 + 7.38520e8i) q^{76} +(-1.94682e8 + 6.74234e7i) q^{77} +(-1.19825e9 - 1.43845e8i) q^{78} +(4.67474e7 - 8.09689e7i) q^{79} +(7.94276e7 - 1.37573e8i) q^{80} +(-7.90073e8 + 1.36845e9i) q^{81} +(-5.46119e8 - 9.45906e8i) q^{82} +7.26828e8 q^{83} +(2.16978e9 - 7.51451e8i) q^{84} +(-2.67150e7 + 4.62718e7i) q^{85} +(6.69642e8 - 1.15985e9i) q^{86} -8.80075e8 q^{87} +(5.61037e8 - 9.71745e8i) q^{88} -9.05926e8 q^{89} +4.66952e8 q^{90} +(-1.99356e8 + 6.23046e8i) q^{91} +1.45166e9 q^{92} +1.36769e8 q^{93} +(3.12030e8 - 5.40452e8i) q^{94} +1.27470e8 q^{95} +(-2.29190e9 + 3.96968e9i) q^{96} +(-7.83512e6 + 1.35708e7i) q^{97} +(-2.46503e8 - 1.70965e9i) q^{98} +1.79279e9 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 $

$2$	−42.8048			−1.89172			−0.945861	−	0.324571i	$-0.894780\pi$
$2$	−42.8048			−1.89172			−0.945861	+	0.324571i	$0.894780\pi$
$3$	136.894	−	237.108i	0.975754	−	1.69006i	0.298330	−	0.954463i	$-0.403571\pi$
$3$	136.894	−	237.108i	0.975754	−	1.69006i	0.677424	−	0.735592i	$-0.263096\pi$
$4$	1320.25			2.57862
$5$	98.6739	−	170.908i	0.0706053	−	0.122292i	−0.828561	−	0.559898i	$-0.810840\pi$
$5$	98.6739	−	170.908i	0.0706053	−	0.122292i	0.899167	+	0.437606i	$0.144174\pi$
$6$	−5859.74	+	10149.4i	−1.84586	+	3.19712i
$7$	4801.69	+	4159.02i	0.755879	+	0.654711i
$7$	4801.69	+	4159.02i	0.755879	+	0.654711i
$8$	−34597.0			−2.98630
$9$	−27638.7	−	47871.6i	−1.40419	−	2.43213i
$10$	−4223.72	+	7315.69i	−0.133566	+	0.231342i
$11$	−16216.3	+	28087.5i	−0.333953	+	0.578424i	−0.983283	−	0.182083i	$-0.941716\pi$
$11$	−16216.3	+	28087.5i	−0.333953	+	0.578424i	0.649330	+	0.760507i	$0.275049\pi$
$12$	180735.	−	313042.i	2.51609	−	4.35800i
$13$	40492.4	+	94683.0i	0.393214	+	0.919447i
$13$	40492.4	+	94683.0i	0.393214	+	0.919447i
$14$	−205535.	−	178026.i	−1.42991	−	1.23853i
$15$	−27015.8	−	46792.8i	−0.137787	−	0.238654i
$16$	804951.			3.07064
$17$	−270741.			−0.786200			−0.393100	−	0.919496i	$-0.628597\pi$
$17$	−270741.			−0.786200			−0.393100	+	0.919496i	$0.628597\pi$
$18$	1.18307e6	+	2.04914e6i	2.65634	+	4.60092i
$19$	322957.	+	559378.i	0.568530	+	0.984724i	0.996712	+	0.0810307i	$0.0258212\pi$
$19$	322957.	+	559378.i	0.568530	+	0.984724i	−0.428181	+	0.903693i	$0.640845\pi$
$20$	130274.	−	225642.i	0.182064	−	0.315344i
$21$	1.64346e6	−	569172.i	1.84405	−	0.638641i
$22$	694137.	−	1.20228e6i	0.631747	−	1.09422i
$23$	1.09953e6			0.819279			0.409640	−	0.912247i	$-0.365654\pi$
$23$	1.09953e6			0.819279			0.409640	+	0.912247i	$0.365654\pi$
$24$	−4.73614e6	+	8.20324e6i	−2.91390	+	5.04702i
$25$	957089.	+	1.65773e6i	0.490030	+	0.848756i
$26$	−1.73327e6	−	4.05289e6i	−0.743851	−	1.73934i
$27$	−9.74535e6			−3.52907
$28$	6.33943e6	+	5.49095e6i	1.94912	+	1.68825i
$29$	−1.60721e6	−	2.78378e6i	−0.421971	−	0.730875i	0.574161	−	0.818742i	$-0.305328\pi$
$29$	−1.60721e6	−	2.78378e6i	−0.421971	−	0.730875i	−0.996132	+	0.0878671i	$0.971995\pi$
$30$	1.15641e6	+	2.00296e6i	0.260654	+	0.451467i
$31$	249771.	+	432616.i	0.0485752	+	0.0841347i	0.889291	−	0.457342i	$-0.151199\pi$
$31$	249771.	+	432616.i	0.0485752	+	0.0841347i	−0.840715	+	0.541477i	$0.817865\pi$
$32$	−1.67421e7			−2.82250
$33$	4.43986e6	+	7.69006e6i	0.651713	+	1.12880i
$34$	1.15890e7			1.48727
$35$	1.18461e6	−	410261.i	0.133435	−	0.0462119i
$36$	−3.64900e7	−	6.32026e7i	−3.62087	−	6.27153i
$37$	−4.54277e6			−0.398486			−0.199243	−	0.979950i	$-0.563848\pi$
$37$	−4.54277e6			−0.398486			−0.199243	+	0.979950i	$0.563848\pi$
$38$	−1.38241e7	−	2.39441e7i	−1.07550	−	1.86282i
$39$	2.79933e7	+	3.36050e6i	1.93760	+	0.232602i
$40$	−3.41382e6	+	5.91292e6i	−0.210849	+	0.365201i
$41$	1.27584e7	+	2.20981e7i	0.705127	+	1.22132i	0.966646	+	0.256118i	$0.0824435\pi$
$41$	1.27584e7	+	2.20981e7i	0.705127	+	1.22132i	−0.261518	+	0.965198i	$0.584223\pi$
$42$	−7.03480e7	+	2.43633e7i	−3.48843	+	1.20813i
$43$	−1.56441e7	+	2.70964e7i	−0.697818	+	1.20866i	0.271403	+	0.962466i	$0.412512\pi$
$43$	−1.56441e7	+	2.70964e7i	−0.697818	+	1.20866i	−0.969221	+	0.246191i	$0.920821\pi$
$44$	−2.14096e7	+	3.70826e7i	−0.861138	+	1.49153i
$45$	−1.09089e7			−0.396573
$46$	−4.70652e7			−1.54985
$47$	−7.28961e6	+	1.26260e7i	−0.217903	+	0.377420i	−0.954167	−	0.299275i	$-0.903255\pi$
$47$	−7.28961e6	+	1.26260e7i	−0.217903	+	0.377420i	0.736263	+	0.676695i	$0.236588\pi$
$48$	1.10193e8	−	1.90860e8i	2.99619	−	5.18956i
$49$	5.75876e6	+	3.99406e7i	0.142707	+	0.989765i
$50$	−4.09680e7	−	7.09587e7i	−0.927001	−	1.60561i
$51$	−3.70629e7	+	6.41948e7i	−0.767138	+	1.32872i
$52$	5.34601e7	+	1.25005e8i	1.01395	+	2.37090i
$53$	3.38445e7	+	5.86204e7i	0.589178	+	1.02049i	0.994340	+	0.106242i	$0.0338818\pi$
$53$	3.38445e7	+	5.86204e7i	0.589178	+	1.02049i	−0.405162	+	0.914245i	$0.632785\pi$
$54$	4.17148e8			6.67603
$55$	3.20026e6	+	5.54301e6i	0.0471577	+	0.0816796i
$56$	−1.66124e8	−	1.43890e8i	−2.25729	−	1.95517i
$57$	1.76844e8			2.21898
$58$	6.87964e7	+	1.19159e8i	0.798252	+	1.38261i
$59$	1.87085e7			0.201004			0.100502	−	0.994937i	$-0.467955\pi$
$59$	1.87085e7			0.201004			0.100502	+	0.994937i	$0.467955\pi$
$60$	−3.56677e7	−	6.17782e7i	−0.355299	−	0.615396i
$61$	3.61089e7	+	6.25425e7i	0.333911	+	0.578350i	0.983275	−	0.182127i	$-0.0582983\pi$
$61$	3.61089e7	+	6.25425e7i	0.333911	+	0.578350i	−0.649364	+	0.760477i	$0.724965\pi$
$62$	−1.06914e7	−	1.85181e7i	−0.0918908	−	0.159160i
$63$	6.63866e7	−	3.44814e8i	0.530943	−	2.75774i
$64$	3.04506e8			2.26875
$65$	2.01776e7	+	2.42225e6i	0.140204	+	0.0168310i
$66$	−1.90047e8	−	3.29171e8i	−1.23286	−	2.13538i
$67$	−2.68350e7	+	4.64796e7i	−0.162691	+	0.281790i	−0.935833	−	0.352444i	$-0.885351\pi$
$67$	−2.68350e7	+	4.64796e7i	−0.162691	+	0.281790i	0.773142	+	0.634233i	$0.218684\pi$
$68$	−3.57446e8			−2.02731
$69$	1.50520e8	−	2.60708e8i	0.799415	−	1.38463i
$70$	−5.07070e7	+	1.75611e7i	−0.252422	+	0.0874201i
$71$	−3.88412e7	+	6.72749e7i	−0.181397	+	0.314189i	−0.942356	−	0.334611i	$-0.891395\pi$
$71$	−3.88412e7	+	6.72749e7i	−0.181397	+	0.314189i	0.760960	+	0.648799i	$0.224729\pi$
$72$	9.56217e8	+	1.65622e9i	4.19334	+	7.26308i
$73$	−1.05202e8	−	1.82215e8i	−0.433582	−	0.750985i	0.563597	−	0.826050i	$-0.309417\pi$
$73$	−1.05202e8	−	1.82215e8i	−0.433582	−	0.750985i	−0.997179	+	0.0750645i	$0.976084\pi$
$74$	1.94452e8			0.753824
$75$	5.24081e8			1.91259
$76$	4.26385e8	+	7.38520e8i	1.46602	+	2.53922i
$77$	−1.94682e8	+	6.74234e7i	−0.631129	+	0.218576i
$78$	−1.19825e9	−	1.43845e8i	−3.66540	−	0.440018i
$79$	4.67474e7	−	8.09689e7i	0.135032	−	0.233882i	−0.790578	−	0.612361i	$-0.790220\pi$
$79$	4.67474e7	−	8.09689e7i	0.135032	−	0.233882i	0.925610	+	0.378480i	$0.123553\pi$
$80$	7.94276e7	−	1.37573e8i	0.216804	−	0.375515i
$81$	−7.90073e8	+	1.36845e9i	−2.03932	+	3.53220i
$82$	−5.46119e8	−	9.45906e8i	−1.33391	−	2.31039i
$83$	7.26828e8			1.68105			0.840524	−	0.541774i	$-0.182247\pi$
$83$	7.26828e8			1.68105			0.840524	+	0.541774i	$0.182247\pi$
$84$	2.16978e9	−	7.51451e8i	4.75510	−	1.64681i
$85$	−2.67150e7	+	4.62718e7i	−0.0555099	+	0.0961459i
$86$	6.69642e8	−	1.15985e9i	1.32008	−	2.28644i
$87$	−8.80075e8			−1.64696
$88$	5.61037e8	−	9.71745e8i	0.997286	−	1.72735i
$89$	−9.05926e8			−1.53052			−0.765258	−	0.643724i	$-0.777389\pi$
$89$	−9.05926e8			−1.53052			−0.765258	+	0.643724i	$0.777389\pi$
$90$	4.66952e8			0.750207
$91$	−1.99356e8	+	6.23046e8i	−0.304750	+	0.952432i
$92$	1.45166e9			2.11261
$93$	1.36769e8			0.189590
$94$	3.12030e8	−	5.40452e8i	0.412213	−	0.713973i
$95$	1.27470e8			0.160565
$96$	−2.29190e9	+	3.96968e9i	−2.75407	+	4.77019i
$97$	−7.83512e6	+	1.35708e7i	−0.00898613	+	0.0155644i	−0.870484	−	0.492198i	$-0.836194\pi$
$97$	−7.83512e6	+	1.35708e7i	−0.00898613	+	0.0155644i	0.861497	+	0.507762i	$0.169527\pi$
$98$	−2.46503e8	−	1.70965e9i	−0.269963	−	1.87236i
$99$	1.79279e9			1.87574
$100$	1.26360e9	+	2.18862e9i	1.26360	+	2.18862i
$101$	−1.30692e8	+	2.26366e8i	−0.124969	+	0.216453i	−0.921721	−	0.387854i	$-0.873217\pi$
$101$	−1.30692e8	+	2.26366e8i	−0.124969	+	0.216453i	0.796752	+	0.604307i	$0.206550\pi$
$102$	1.58647e9	−	2.74785e9i	1.45121	−	2.51357i
$103$	7.72722e8	−	1.33839e9i	0.676481	−	1.17170i	−0.299553	−	0.954080i	$-0.596837\pi$
$103$	7.72722e8	−	1.33839e9i	0.676481	−	1.17170i	0.976034	−	0.217620i	$-0.0698293\pi$
$104$	−1.40092e9	−	3.27575e9i	−1.17425	−	2.74575i
$105$	6.48905e7	−	3.37043e8i	0.0520990	−	0.270604i
$106$	−1.44871e9	−	2.50923e9i	−1.11456	−	1.93048i
$107$	5.18893e7			0.0382693			0.0191347	−	0.999817i	$-0.493909\pi$
$107$	5.18893e7			0.0382693			0.0191347	+	0.999817i	$0.493909\pi$
$108$	−1.28663e10			−9.10012
$109$	1.24921e9	+	2.16369e9i	0.847647	+	1.46817i	0.883303	+	0.468803i	$0.155315\pi$
$109$	1.24921e9	+	2.16369e9i	0.847647	+	1.46817i	−0.0356562	+	0.999364i	$0.511352\pi$
$110$	−1.36986e8	−	2.37268e8i	−0.0892094	−	0.154515i
$111$	−6.21880e8	+	1.07713e9i	−0.388824	+	0.673463i
$112$	3.86512e9	+	3.34780e9i	2.32104	+	2.01038i
$113$	1.16550e8	−	2.01871e8i	0.0672450	−	0.116472i	−0.830443	−	0.557104i	$-0.811912\pi$
$113$	1.16550e8	−	2.01871e8i	0.0672450	−	0.116472i	0.897688	+	0.440632i	$0.145246\pi$
$114$	−7.56978e9			−4.19770
$115$	1.08495e8	−	1.87919e8i	0.0578454	−	0.100191i
$116$	−2.12193e9	−	3.67528e9i	−1.08810	−	1.88465i
$117$	3.41347e9	−	4.55535e9i	1.68407	−	2.24743i
$118$	−8.00815e8			−0.380245
$119$	−1.30001e9	−	1.12601e9i	−0.594273	−	0.514734i
$120$	9.34667e8	+	1.61889e9i	0.411473	+	0.712692i
$121$	6.53034e8	+	1.13109e9i	0.276950	+	0.479692i
$122$	−1.54564e9	−	2.67712e9i	−0.631667	−	1.09408i
$123$	6.98620e9			2.75212
$124$	3.29761e8	+	5.71162e8i	0.125257	+	0.216951i
$125$	7.63204e8			0.279605
$126$	−2.84167e9	+	1.47597e10i	−1.00440	+	5.21687i
$127$	−1.24984e9	−	2.16478e9i	−0.426321	−	0.738410i	0.570222	−	0.821491i	$-0.306857\pi$
$127$	−1.24984e9	−	2.16478e9i	−0.426321	−	0.738410i	−0.996543	+	0.0830810i	$0.973524\pi$
$128$	−4.46240e9			−1.46934
$129$	4.28318e9	+	7.41868e9i	1.36180	+	2.35870i
$130$	−8.63700e8	−	1.03684e8i	−0.265227	−	0.0318396i
$131$	1.27790e9	−	2.21339e9i	0.379119	−	0.656653i	−0.611815	−	0.791001i	$-0.709560\pi$
$131$	1.27790e9	−	2.21339e9i	0.379119	−	0.656653i	0.990934	+	0.134347i	$0.0428938\pi$
$132$	5.86173e9	+	1.01528e10i	1.68052	+	2.91074i
$133$	−7.75725e8	+	4.02914e9i	−0.214969	+	1.11656i
$134$	1.14867e9	−	1.98955e9i	0.307767	−	0.533068i
$135$	−9.61612e8	+	1.66556e9i	−0.249171	+	0.431577i
$136$	9.36682e9			2.34783
$137$	−3.38232e9			−0.820298			−0.410149	−	0.912019i	$-0.634523\pi$
$137$	−3.38232e9			−0.820298			−0.410149	+	0.912019i	$0.634523\pi$
$138$	−6.44296e9	+	1.11595e10i	−1.51227	+	2.61933i
$139$	3.65850e9	−	6.33671e9i	0.831260	−	1.43978i	−0.0657794	−	0.997834i	$-0.520953\pi$
$139$	3.65850e9	−	6.33671e9i	0.831260	−	1.43978i	0.897039	−	0.441950i	$-0.145713\pi$
$140$	1.56398e9	−	5.41647e8i	0.344077	−	0.119163i
$141$	1.99581e9	+	3.45685e9i	0.425240	+	0.736537i
$142$	1.66259e9	−	2.87969e9i	0.343153	−	0.594358i
$143$	−3.31605e9	−	3.98080e8i	−0.663146	−	0.0796083i
$144$	−2.22478e10	−	3.85343e10i	−4.31177	−	7.46821i
$145$	−6.34360e8			−0.119173
$146$	4.50315e9	+	7.79968e9i	0.820216	+	1.42066i
$147$	1.02586e10	+	4.10220e9i	1.81200	+	0.724584i
$148$	−5.99759e9			−1.02754
$149$	−2.17231e9	−	3.76255e9i	−0.361064	−	0.625381i	0.627072	−	0.778961i	$-0.284253\pi$
$149$	−2.17231e9	−	3.76255e9i	−0.361064	−	0.625381i	−0.988136	+	0.153580i	$0.950920\pi$
$150$	−2.24332e10			−3.61810
$151$	−3.26772e9	−	5.65985e9i	−0.511503	−	0.885950i	−0.999911	−	0.0133341i	$-0.995756\pi$
$151$	−3.26772e9	−	5.65985e9i	−0.511503	−	0.885950i	0.488408	−	0.872615i	$-0.337578\pi$
$152$	−1.11734e10	−	1.93528e10i	−1.69780	−	2.94068i
$153$	7.48292e9	+	1.29608e10i	1.10398	+	1.91214i
$154$	8.33334e9	−	2.88605e9i	1.19392	−	0.413485i
$155$	9.85835e7			0.0137187
$156$	3.69582e10	+	4.43670e9i	4.99632	+	0.599790i
$157$	−1.63599e8	−	2.83362e8i	−0.0214898	−	0.0372215i	0.855080	−	0.518495i	$-0.173508\pi$
$157$	−1.63599e8	−	2.83362e8i	−0.0214898	−	0.0372215i	−0.876570	+	0.481274i	$0.840174\pi$
$158$	−2.00101e9	+	3.46586e9i	−0.255442	+	0.442439i
$159$	1.85325e10			2.29957
$160$	−1.65200e9	+	2.86136e9i	−0.199284	+	0.345169i
$161$	5.27960e9	+	4.57297e9i	0.619276	+	0.536391i
$162$	3.38189e10	−	5.85761e10i	3.85782	−	6.68194i
$163$	5.37709e9	+	9.31340e9i	0.596628	+	1.03339i	0.993315	+	0.115435i	$0.0368263\pi$
$163$	5.37709e9	+	9.31340e9i	0.596628	+	1.03339i	−0.396687	+	0.917954i	$0.629840\pi$
$164$	1.68442e10	+	2.91751e10i	1.81825	+	3.14930i
$165$	1.75239e9			0.184057
$166$	−3.11117e10			−3.18008
$167$	−1.81116e9	−	3.13702e9i	−0.180191	−	0.312100i	0.761755	−	0.647866i	$-0.224338\pi$
$167$	−1.81116e9	−	3.13702e9i	−0.180191	−	0.312100i	−0.941945	+	0.335766i	$0.891005\pi$
$168$	−5.68589e10	+	1.96917e10i	−5.50689	+	1.90718i
$169$	−7.32523e9	+	7.66788e9i	−0.690766	+	0.723078i
$170$	1.14353e9	−	1.98065e9i	0.105009	−	0.181881i
$171$	1.78522e10	−	3.09210e10i	1.59665	−	2.76548i
$172$	−2.06541e10	+	3.57740e10i	−1.79940	+	3.11666i
$173$	−1.44795e9	−	2.50792e9i	−0.122898	−	0.212866i	0.798011	−	0.602643i	$-0.205886\pi$
$173$	−1.44795e9	−	2.50792e9i	−0.122898	−	0.212866i	−0.920909	+	0.389777i	$0.872552\pi$
$174$	3.76714e10			3.11559
$175$	−2.29887e9	+	1.19404e10i	−0.185287	+	0.962385i
$176$	−1.30534e10	+	2.26091e10i	−1.02545	+	1.77613i
$177$	2.56110e9	−	4.43595e9i	0.196131	−	0.339709i
$178$	3.87780e10			2.89531
$179$	−1.03653e10	+	1.79533e10i	−0.754647	+	1.30709i	0.190902	+	0.981609i	$0.438859\pi$
$179$	−1.03653e10	+	1.79533e10i	−0.754647	+	1.30709i	−0.945549	+	0.325479i	$0.894475\pi$
$180$	−1.44024e10			−1.02261
$181$	−2.28739e10			−1.58412			−0.792059	−	0.610445i	$-0.790991\pi$
$181$	−2.28739e10			−1.58412			−0.792059	+	0.610445i	$0.790991\pi$
$182$	8.53341e9	−	2.66694e10i	0.576503	−	1.80174i
$183$	1.97725e10			1.30326
$184$	−3.80405e10			−2.44662
$185$	−4.48252e8	+	7.76396e8i	−0.0281352	+	0.0487316i
$186$	−5.85438e9			−0.358651
$187$	4.39042e9	−	7.60443e9i	0.262554	−	0.454757i
$188$	−9.62411e9	+	1.66695e10i	−0.561889	+	0.973220i
$189$	−4.67941e10	−	4.05311e10i	−2.66755	−	2.31052i
$190$	−5.45632e9			−0.303744
$191$	−9.30769e9	−	1.61214e10i	−0.506048	−	0.876501i	−0.999976	−	0.00699771i	$-0.997773\pi$
$191$	−9.30769e9	−	1.61214e10i	−0.506048	−	0.876501i	0.493928	−	0.869503i	$-0.335561\pi$
$192$	4.16852e10	−	7.22010e10i	2.21374	−	3.83431i
$193$	4.54473e9	−	7.87170e9i	0.235776	−	0.408376i	−0.723722	−	0.690092i	$-0.757570\pi$
$193$	4.54473e9	−	7.87170e9i	0.235776	−	0.408376i	0.959498	+	0.281715i	$0.0909034\pi$
$194$	3.35381e8	−	5.80896e8i	0.0169993	−	0.0294436i
$195$	3.33654e9	−	4.45269e9i	0.165250	−	0.220529i
$196$	7.60301e9	+	5.27316e10i	0.367988	+	2.55222i
$197$	5.80492e9	+	1.00544e10i	0.274599	+	0.475619i	0.970034	−	0.242970i	$-0.0781217\pi$
$197$	5.80492e9	+	1.00544e10i	0.274599	+	0.475619i	−0.695435	+	0.718589i	$0.744788\pi$
$198$	−7.67402e10			−3.54838
$199$	3.80412e9			0.171955			0.0859777	−	0.996297i	$-0.472599\pi$
$199$	3.80412e9			0.171955			0.0859777	+	0.996297i	$0.472599\pi$
$200$	−3.31125e10	−	5.73525e10i	−1.46338	−	2.53464i
$201$	7.34712e9	+	1.27256e10i	0.317494	+	0.549915i
$202$	5.59425e9	−	9.68953e9i	0.236407	−	0.409470i
$203$	3.86044e9	−	2.00512e10i	0.159553	−	0.828722i
$204$	−4.89323e10	+	8.47533e10i	−1.97815	+	3.42626i
$205$	5.03567e9			0.199143
$206$	−3.30762e10	+	5.72897e10i	−1.27971	+	2.21653i
$207$	−3.03896e10	−	5.26363e10i	−1.15043	−	1.99259i
$208$	3.25944e10	+	7.62151e10i	1.20742	+	2.82329i
$209$	−2.09487e10			−0.759451
$210$	−2.77762e9	+	1.44271e10i	−0.0985568	+	0.511907i
$211$	1.50417e10	+	2.60531e10i	0.522429	+	0.904874i	0.999659	+	0.0260954i	$0.00830737\pi$
$211$	1.50417e10	+	2.60531e10i	0.522429	+	0.904874i	−0.477230	+	0.878778i	$0.658359\pi$
$212$	4.46832e10	+	7.73937e10i	1.51926	+	2.63144i
$213$	1.06343e10	+	1.84191e10i	0.353998	+	0.613142i
$214$	−2.22111e9			−0.0723949
$215$	3.08733e9	+	5.34740e9i	0.0985393	+	0.170675i
$216$	3.37160e11			10.5389
$217$	−5.99936e8	+	3.11609e9i	−0.0183669	+	0.0953984i
$218$	−5.34720e10	−	9.26163e10i	−1.60351	−	2.77737i
$219$	−5.76063e10			−1.69228
$220$	4.22515e9	+	7.31817e9i	0.121602	+	0.210620i
$221$	−1.09629e10	−	2.56345e10i	−0.309145	−	0.722870i
$222$	2.66194e10	−	4.61062e10i	0.735547	−	1.27400i
$223$	−4.17999e9	−	7.23995e9i	−0.113189	−	0.196049i	0.803866	−	0.594811i	$-0.202773\pi$
$223$	−4.17999e9	−	7.23995e9i	−0.113189	−	0.196049i	−0.917054	+	0.398762i	$0.869440\pi$
$224$	−8.03902e10	−	6.96306e10i	−2.13347	−	1.84792i
$225$	5.29054e10	−	9.16349e10i	1.37619	−	2.38363i
$226$	−4.98891e9	+	8.64104e9i	−0.127209	+	0.220332i
$227$	3.27712e10			0.819173			0.409586	−	0.912271i	$-0.365673\pi$
$227$	3.27712e10			0.819173			0.409586	+	0.912271i	$0.365673\pi$
$228$	2.33479e11			5.72190
$229$	1.84387e10	−	3.19368e10i	0.443069	−	0.767419i	−0.554846	−	0.831953i	$-0.687223\pi$
$229$	1.84387e10	−	3.19368e10i	0.443069	−	0.767419i	0.997915	+	0.0645343i	$0.0205562\pi$
$230$	−4.64410e9	+	8.04382e9i	−0.109428	+	0.189534i
$231$	−1.06643e10	+	5.53907e10i	−0.246421	+	1.27992i
$232$	5.56048e10	+	9.63104e10i	1.26013	+	2.18261i
$233$	3.40358e10	−	5.89517e10i	0.756544	−	1.31037i	−0.188059	−	0.982158i	$-0.560220\pi$
$233$	3.40358e10	−	5.89517e10i	0.756544	−	1.31037i	0.944603	−	0.328215i	$-0.106447\pi$
$234$	−1.46113e11	+	1.94991e11i	−3.18579	+	4.25151i
$235$	1.43859e9	+	2.49171e9i	0.0307702	+	0.0532956i
$236$	2.47000e10			0.518313
$237$	−1.27989e10	−	2.21684e10i	−0.263515	−	0.456422i
$238$	5.56467e10	+	4.81988e10i	1.12420	+	0.973734i
$239$	2.10530e9			0.0417371			0.0208686	−	0.999782i	$-0.493357\pi$
$239$	2.10530e9			0.0417371			0.0208686	+	0.999782i	$0.493357\pi$
$240$	−2.17464e10	−	3.76659e10i	−0.423094	−	0.732820i
$241$	−8.26795e9			−0.157878			−0.0789389	−	0.996879i	$-0.525153\pi$
$241$	−8.26795e9			−0.157878			−0.0789389	+	0.996879i	$0.525153\pi$
$242$	−2.79530e10	−	4.84160e10i	−0.523913	−	0.907444i
$243$	1.20404e11	+	2.08546e11i	2.21520	+	3.83685i
$244$	4.76729e10	+	8.25718e10i	0.861027	+	1.49134i
$245$	7.39441e9	+	2.95687e9i	0.131116	+	0.0524307i
$246$	−2.99043e11			−5.20625
$247$	−3.98863e10	+	5.32291e10i	−0.681847	+	0.909940i
$248$	−8.64134e9	−	1.49672e10i	−0.145060	−	0.251252i
$249$	9.94988e10	−	1.72337e11i	1.64029	−	2.84107i
$250$	−3.26688e10			−0.528936
$251$	1.53799e10	−	2.66389e10i	0.244581	−	0.423627i	−0.717433	−	0.696628i	$-0.754683\pi$
$251$	1.53799e10	−	2.66389e10i	0.244581	−	0.423627i	0.962014	+	0.273001i	$0.0880162\pi$
$252$	8.76470e10	−	4.55242e11i	1.36910	−	7.11114i
$253$	−1.78304e10	+	3.08831e10i	−0.273601	+	0.473891i
$254$	5.34991e10	+	9.26631e10i	0.806482	+	1.39687i
$255$	7.31428e9	+	1.26687e10i	0.108328	+	0.187630i
$256$	3.51047e10			0.510840
$257$	−1.01690e10			−0.145406			−0.0727028	−	0.997354i	$-0.523162\pi$
$257$	−1.01690e10			−0.145406			−0.0727028	+	0.997354i	$0.523162\pi$
$258$	−1.83341e11	−	3.17555e11i	−2.57614	−	4.46201i
$259$	−2.18129e10	−	1.88934e10i	−0.301207	−	0.260893i
$260$	2.66395e10	+	3.19798e9i	0.361532	+	0.0434006i
$261$	−8.88426e10	+	1.53880e11i	−1.18506	+	2.05258i
$262$	−5.47002e10	+	9.47435e10i	−0.717188	+	1.24221i
$263$	−8.71897e9	+	1.51017e10i	−0.112374	+	0.194637i	−0.916727	−	0.399515i	$-0.869179\pi$
$263$	−8.71897e9	+	1.51017e10i	−0.112374	+	0.194637i	0.804353	+	0.594151i	$0.202512\pi$
$264$	−1.53606e11	−	2.66053e11i	−1.94621	−	3.37094i
$265$	1.33583e10			0.166396
$266$	3.32048e10	−	1.72467e11i	0.406661	−	2.11221i
$267$	−1.24016e11	+	2.14803e11i	−1.49341	+	2.58666i
$268$	−3.54289e10	+	6.13647e10i	−0.419519	+	0.726628i
$269$	−9.58272e9			−0.111584			−0.0557922	−	0.998442i	$-0.517768\pi$
$269$	−9.58272e9			−0.111584			−0.0557922	+	0.998442i	$0.517768\pi$
$270$	4.11616e10	−	7.12940e10i	0.471363	−	0.816424i
$271$	8.19491e10			0.922959			0.461480	−	0.887151i	$-0.347319\pi$
$271$	8.19491e10			0.922959			0.461480	+	0.887151i	$0.347319\pi$
$272$	−2.17933e11			−2.41414
$273$	1.20439e11	+	1.32561e11i	1.31230	+	1.44438i
$274$	1.44779e11			1.55178
$275$	−6.20820e10			−0.654589
$276$	1.98724e11	−	3.44200e11i	2.06138	−	3.57042i
$277$	9.01546e10			0.920087			0.460043	−	0.887896i	$-0.347834\pi$
$277$	9.01546e10			0.920087			0.460043	+	0.887896i	$0.347834\pi$
$278$	−1.56602e11	+	2.71242e11i	−1.57251	+	2.72367i
$279$	1.38067e10	−	2.39139e10i	0.136418	−	0.236283i
$280$	−4.09840e10	+	1.41938e10i	−0.398477	+	0.138003i
$281$	1.10737e9			0.0105953			0.00529765	−	0.999986i	$-0.498314\pi$
$281$	1.10737e9			0.0105953			0.00529765	+	0.999986i	$0.498314\pi$
$282$	−8.54304e10	−	1.47970e11i	−0.804436	−	1.39332i
$283$	−9.25166e10	+	1.60243e11i	−0.857395	+	1.48505i	0.0170108	+	0.999855i	$0.494585\pi$
$283$	−9.25166e10	+	1.60243e11i	−0.857395	+	1.48505i	−0.874405	+	0.485196i	$0.838748\pi$
$284$	−5.12801e10	+	8.88198e10i	−0.467753	+	0.810172i
$285$	1.74499e10	−	3.02241e10i	0.156672	−	0.271364i
$286$	1.41943e11	+	1.70397e10i	1.25449	+	0.150597i
$287$	−3.06449e10	+	1.59170e11i	−0.266618	+	1.38482i
$288$	4.62729e11	+	8.01470e11i	3.96333	+	6.86470i
$289$	−4.52874e10			−0.381889
$290$	2.71536e10			0.225443
$291$	2.14517e9	+	3.71554e9i	0.0175365	+	0.0303741i
$292$	−1.38893e11	−	2.40570e11i	−1.11804	−	1.93650i
$293$	−7.00988e10	+	1.21415e11i	−0.555657	+	0.962425i	0.442196	+	0.896919i	$0.354200\pi$
$293$	−7.00988e10	+	1.21415e11i	−0.555657	+	0.962425i	−0.997852	+	0.0655068i	$0.979134\pi$
$294$	−4.39117e11	−	1.75594e11i	−3.42781	−	1.37071i
$295$	1.84604e9	−	3.19744e9i	0.0141920	−	0.0245812i
$296$	1.57166e11			1.19000
$297$	1.58034e11	−	2.73723e11i	1.17855	−	2.04130i
$298$	9.29854e10	+	1.61055e11i	0.683033	+	1.18305i
$299$	4.45226e10	+	1.04107e11i	0.322152	+	0.753284i
$300$	6.91919e11			4.93184
$301$	−1.87812e11	+	6.50441e10i	−1.31879	+	0.456729i
$302$	1.39874e11	+	2.42269e11i	0.967622	+	1.67597i
$303$	3.57821e10	+	6.19764e10i	0.243879	+	0.422410i
$304$	2.59965e11	+	4.50272e11i	1.74575	+	3.02373i
$305$	1.42520e10			0.0943034
$306$	−3.20305e11	−	5.54784e11i	−2.08842	−	3.61724i
$307$	6.82074e10			0.438237			0.219118	−	0.975698i	$-0.429682\pi$
$307$	6.82074e10			0.438237			0.219118	+	0.975698i	$0.429682\pi$
$308$	−2.57030e11	+	8.90159e10i	−1.62744	+	0.563624i
$309$	−2.11563e11	−	3.66437e11i	−1.32016	−	2.28658i
$310$	−4.21985e9			−0.0259519
$311$	2.23415e10	+	3.86966e10i	0.135422	+	0.234558i	0.925759	−	0.378115i	$-0.123428\pi$
$311$	2.23415e10	+	3.86966e10i	0.135422	+	0.234558i	−0.790336	+	0.612673i	$0.790094\pi$
$312$	−9.68485e11	−	1.16263e11i	−5.78625	−	0.694619i
$313$	9.43093e10	−	1.63349e11i	0.555399	−	0.961979i	−0.442473	−	0.896782i	$-0.645899\pi$
$313$	9.43093e10	−	1.63349e11i	0.555399	−	0.961979i	0.997872	−	0.0651975i	$-0.0207677\pi$
$314$	7.00283e9	+	1.21293e10i	0.0406528	+	0.0704127i
$315$	−5.23810e10	−	4.53702e10i	−0.299762	−	0.259641i
$316$	6.17183e10	−	1.06899e11i	0.348195	−	0.603091i
$317$	1.20861e11	−	2.09337e11i	0.672230	−	1.16434i	−0.305041	−	0.952339i	$-0.598670\pi$
$317$	1.20861e11	−	2.09337e11i	0.672230	−	1.16434i	0.977270	−	0.211997i	$-0.0679966\pi$
$318$	−7.93280e11			−4.35015
$319$	1.04253e11			0.563675
$320$	3.00468e10	−	5.20426e10i	0.160186	−	0.277450i
$321$	7.10336e9	−	1.23034e10i	0.0373414	−	0.0646773i
$322$	−2.25992e11	−	1.95745e11i	−1.17150	−	1.01470i
$323$	−8.74376e10	−	1.51446e11i	−0.446979	−	0.774190i
$324$	−1.04309e12	+	1.80669e12i	−5.25861	+	9.10818i
$325$	−1.18204e11	+	1.57745e11i	−0.587700	+	0.784299i
$326$	−2.30165e11	−	3.98658e11i	−1.12865	−	1.95489i
$327$	6.84038e11			3.30838
$328$	−4.41401e11	−	7.64530e11i	−2.10572	−	3.64722i
$329$	−8.75140e10	+	3.03083e10i	−0.411809	+	0.142620i
$330$	−7.50108e10			−0.348186
$331$	−1.91067e11	−	3.30938e11i	−0.874903	−	1.51538i	−0.856866	−	0.515539i	$-0.827592\pi$
$331$	−1.91067e11	−	3.30938e11i	−0.874903	−	1.51538i	−0.0180366	−	0.999837i	$-0.505742\pi$
$332$	9.59596e11			4.33478
$333$	1.25556e11	+	2.17470e11i	0.559550	+	0.969169i
$334$	7.75264e10	+	1.34280e11i	0.340871	+	0.590407i
$335$	5.29582e9	+	9.17263e9i	0.0229737	+	0.0397917i
$336$	1.32291e12	−	4.58156e11i	5.66242	−	1.96104i
$337$	2.21248e11			0.934425			0.467213	−	0.884145i	$-0.345258\pi$
$337$	2.21248e11			0.934425			0.467213	+	0.884145i	$0.345258\pi$
$338$	3.13555e11	−	3.28222e11i	1.30674	−	1.36786i
$339$	−3.19101e10	−	5.52700e10i	−0.131229	−	0.227295i
$340$	−3.52705e10	+	6.10904e10i	−0.143139	+	0.247923i
$341$	−1.62015e10			−0.0648874
$342$	−7.64161e11	+	1.32357e12i	−3.02042	+	5.23152i
$343$	−1.38462e11	+	2.15733e11i	−0.540140	+	0.841575i
$344$	5.41239e11	−	9.37454e11i	2.08390	−	3.60941i
$345$	−2.97047e10	−	5.14501e10i	−0.112886	−	0.195524i
$346$	6.19791e10	+	1.07351e11i	0.232489	+	0.402683i
$347$	−1.10819e11			−0.410327			−0.205163	−	0.978728i	$-0.565773\pi$
$347$	−1.10819e11			−0.410327			−0.205163	+	0.978728i	$0.565773\pi$
$348$	−1.16192e12			−4.24687
$349$	5.26762e10	+	9.12379e10i	0.190064	+	0.329201i	0.945271	−	0.326285i	$-0.105797\pi$
$349$	5.26762e10	+	9.12379e10i	0.190064	+	0.329201i	−0.755207	+	0.655486i	$0.772464\pi$
$350$	9.84029e10	−	5.11108e11i	0.350511	−	1.82057i
$351$	−3.94613e11	−	9.22719e11i	−1.38768	−	3.24480i
$352$	2.71495e11	−	4.70244e11i	0.942584	−	1.63260i
$353$	−2.49046e11	+	4.31360e11i	−0.853677	+	1.47861i	0.0241906	+	0.999707i	$0.492299\pi$
$353$	−2.49046e11	+	4.31360e11i	−0.853677	+	1.47861i	−0.877867	+	0.478904i	$0.841034\pi$
$354$	−1.09627e11	+	1.89880e11i	−0.371025	+	0.642635i
$355$	7.66522e9	+	1.32766e10i	0.0256152	+	0.0443668i
$356$	−1.19605e12			−3.94661
$357$	−4.44952e11	+	1.54098e11i	−1.44979	+	0.502100i
$358$	4.43685e11	−	7.68486e11i	1.42758	−	2.47265i
$359$	−5.01949e10	+	8.69401e10i	−0.159490	+	0.276245i	−0.934685	−	0.355477i	$-0.884318\pi$
$359$	−5.01949e10	+	8.69401e10i	−0.159490	+	0.276245i	0.775195	+	0.631722i	$0.217652\pi$
$360$	3.77415e11			1.18429
$361$	−4.72588e10	+	8.18547e10i	−0.146454	+	0.253665i
$362$	9.79114e11			2.99671
$363$	3.57587e11			1.08094
$364$	−2.63200e11	+	8.22578e11i	−0.785833	+	2.45596i
$365$	−4.15227e10			−0.122453
$366$	−8.46356e11			−2.46540
$367$	9.41734e10	−	1.63113e11i	0.270976	−	0.469344i	−0.698136	−	0.715965i	$-0.745987\pi$
$367$	9.41734e10	−	1.63113e11i	0.270976	−	0.469344i	0.969112	+	0.246621i	$0.0793203\pi$
$368$	8.85068e11			2.51571
$369$	7.05249e11	−	1.22153e12i	1.98027	−	3.42992i
$370$	1.91873e10	−	3.32335e10i	0.0532240	−	0.0921866i
$371$	−8.12926e10	+	4.22237e11i	−0.222776	+	1.15711i
$372$	1.80570e11			0.488879
$373$	6.18895e10	+	1.07196e11i	0.165549	+	0.286740i	0.936850	−	0.349731i	$-0.113727\pi$
$373$	6.18895e10	+	1.07196e11i	0.165549	+	0.286740i	−0.771301	+	0.636471i	$0.780394\pi$
$374$	−1.87931e11	+	3.25506e11i	−0.496680	+	0.860275i
$375$	1.04478e11	−	1.80962e11i	0.272826	−	0.472548i
$376$	2.52199e11	−	4.36821e11i	0.650725	−	1.12709i
$377$	1.98496e11	−	2.64897e11i	0.506076	−	0.675370i
$378$	2.00301e12	+	1.73493e12i	5.04627	+	4.37087i
$379$	5.96331e10	+	1.03287e11i	0.148460	+	0.257141i	0.930659	−	0.365889i	$-0.119235\pi$
$379$	5.96331e10	+	1.03287e11i	0.148460	+	0.257141i	−0.782198	+	0.623030i	$0.785902\pi$
$380$	1.68292e11			0.414035
$381$	−6.84384e11			−1.66394
$382$	3.98414e11	+	6.90073e11i	0.957303	+	1.65810i
$383$	3.30994e11	+	5.73298e11i	0.786006	+	1.36140i	0.928396	+	0.371591i	$0.121188\pi$
$383$	3.30994e11	+	5.73298e11i	0.786006	+	1.36140i	−0.142391	+	0.989811i	$0.545479\pi$
$384$	−6.10877e11	+	1.05807e12i	−1.43372	+	2.48327i
$385$	−7.68684e9	+	3.99257e10i	−0.0178310	+	0.0926146i
$386$	−1.94536e11	+	3.36947e11i	−0.446023	+	0.772535i
$387$	1.72953e12			3.91948
$388$	−1.03443e10	+	1.79169e10i	−0.0231718	+	0.0401347i
$389$	5.61430e10	+	9.72426e10i	0.124315	+	0.215319i	0.921465	−	0.388462i	$-0.126993\pi$
$389$	5.61430e10	+	9.72426e10i	0.124315	+	0.215319i	−0.797150	+	0.603781i	$0.793660\pi$
$390$	−1.42820e11	+	1.90596e11i	−0.312607	+	0.417181i
$391$	−2.97687e11			−0.644118
$392$	−1.99236e11	−	1.38183e12i	−0.426168	−	2.95574i
$393$	−3.49875e11	−	6.06000e11i	−0.739854	−	1.28146i
$394$	−2.48479e11	−	4.30377e11i	−0.519464	−	0.899739i
$395$	−9.22549e9	−	1.59790e10i	−0.0190679	−	0.0330266i
$396$	2.36694e12			4.83681
$397$	2.96753e11	+	5.13991e11i	0.599567	+	1.03848i	0.992885	+	0.119078i	$0.0379937\pi$
$397$	2.96753e11	+	5.13991e11i	0.599567	+	1.03848i	−0.393318	+	0.919402i	$0.628673\pi$
$398$	−1.62835e11			−0.325292
$399$	8.49150e11	+	7.35498e11i	1.67728	+	1.45279i
$400$	7.70410e11	+	1.33439e12i	1.50471	+	2.60623i
$401$	−8.94348e11			−1.72726			−0.863629	−	0.504129i	$-0.831814\pi$
$401$	−8.94348e11			−1.72726			−0.863629	+	0.504129i	$0.831814\pi$
$402$	−3.14492e11	−	5.44716e11i	−0.600610	−	1.04029i
$403$	−3.08476e10	+	4.11667e10i	−0.0582570	+	0.0777453i
$404$	−1.72547e11	+	2.98859e11i	−0.322248	+	0.558150i
$405$	1.55919e11	+	2.70060e11i	0.287973	+	0.498784i
$406$	−1.65245e11	+	8.58289e11i	−0.301829	+	1.56771i
$407$	7.36671e10	−	1.27595e11i	0.133076	−	0.230494i
$408$	1.28227e12	−	2.22095e12i	2.29091	−	3.96797i
$409$	−1.34939e11			−0.238441			−0.119221	−	0.992868i	$-0.538040\pi$
$409$	−1.34939e11			−0.238441			−0.119221	+	0.992868i	$0.538040\pi$
$410$	−2.15551e11			−0.376723
$411$	−4.63020e11	+	8.01975e11i	−0.800409	+	1.38635i
$412$	1.02019e12	−	1.76702e12i	1.74438	−	3.02136i
$413$	8.98325e10	+	7.78091e10i	0.151935	+	0.131600i
$414$	1.30082e12	+	2.25309e12i	2.17629	+	3.76944i
$415$	7.17189e10	−	1.24221e11i	0.118691	−	0.205579i
$416$	−6.77927e11	−	1.58519e12i	−1.10985	−	2.59514i
$417$	−1.00166e12	−	1.73492e12i	−1.62221	−	2.80975i
$418$	8.96707e11			1.43667
$419$	−1.60103e11	−	2.77307e11i	−0.253768	−	0.439540i	0.710792	−	0.703402i	$-0.248337\pi$
$419$	−1.60103e11	−	2.77307e11i	−0.253768	−	0.439540i	−0.964560	+	0.263863i	$0.915003\pi$
$420$	8.56717e10	−	4.44982e11i	0.134343	−	0.697783i
$421$	9.19475e11			1.42650			0.713248	−	0.700912i	$-0.247223\pi$
$421$	9.19475e11			1.42650			0.713248	+	0.700912i	$0.247223\pi$
$422$	−6.43859e11	−	1.11520e12i	−0.988291	−	1.71177i
$423$	8.05901e11			1.22391
$424$	−1.17092e12	−	2.02809e12i	−1.75947	−	3.04748i
$425$	−2.59123e11	−	4.48814e11i	−0.385262	−	0.667292i
$426$	−4.55199e11	−	7.88427e11i	−0.669665	−	1.15989i
$427$	−8.67316e10	+	4.50487e11i	−0.126256	+	0.655778i
$428$	6.85069e10			0.0986819
$429$	−5.48337e11	+	7.31768e11i	−0.781609	+	1.04307i
$430$	−1.32152e11	−	2.28895e11i	−0.186409	−	0.322870i
$431$	−5.67269e11	+	9.82538e11i	−0.791846	+	1.37152i	0.132976	+	0.991119i	$0.457547\pi$
$431$	−5.67269e11	+	9.82538e11i	−0.791846	+	1.37152i	−0.924822	+	0.380399i	$0.875787\pi$
$432$	−7.84453e12			−10.8365
$433$	−4.53595e11	+	7.85650e11i	−0.620116	+	1.07407i	0.369347	+	0.929291i	$0.379581\pi$
$433$	−4.53595e11	+	7.85650e11i	−0.620116	+	1.07407i	−0.989464	+	0.144782i	$0.953752\pi$
$434$	2.56802e10	−	1.33384e11i	0.0347451	−	0.180467i
$435$	−8.68404e10	+	1.50412e11i	−0.116284	+	0.201410i
$436$	1.64927e12	+	2.85661e12i	2.18575	+	3.78584i
$437$	3.55101e11	+	6.15053e11i	0.465785	+	0.806764i
$438$	2.46582e12			3.20132
$439$	−3.98425e11			−0.511983			−0.255992	−	0.966679i	$-0.582402\pi$
$439$	−3.98425e11			−0.511983			−0.255992	+	0.966679i	$0.582402\pi$
$440$	−1.10719e11	−	1.91772e11i	−0.140827	−	0.243920i
$441$	1.75286e12	−	1.37959e12i	2.20685	−	1.73690i
$442$	4.69266e11	+	1.09728e12i	0.584816	+	1.36747i
$443$	3.81889e11	−	6.61451e11i	0.471108	−	0.815983i	−0.528346	−	0.849029i	$-0.677188\pi$
$443$	3.81889e11	−	6.61451e11i	0.471108	−	0.815983i	0.999454	+	0.0330463i	$0.0105209\pi$
$444$	−8.21037e11	+	1.42208e12i	−1.00263	+	1.73660i
$445$	−8.93912e10	+	1.54830e11i	−0.108062	+	0.187170i
$446$	1.78924e11	+	3.09905e11i	0.214122	+	0.370870i
$447$	−1.18951e12			−1.40924
$448$	1.46214e12	+	1.26645e12i	1.71490	+	1.48537i
$449$	−4.34599e11	+	7.52748e11i	−0.504639	+	0.874060i	0.495347	+	0.868695i	$0.335041\pi$
$449$	−4.34599e11	+	7.52748e11i	−0.504639	+	0.874060i	−0.999986	+	0.00536471i	$0.998292\pi$
$450$	−2.26461e12	+	3.92241e12i	−2.60337	+	4.50917i
$451$	−8.27576e11			−0.941919
$452$	1.53875e11	−	2.66520e11i	0.173399	−	0.300336i
$453$	−1.78933e12			−1.99641
$454$	−1.40276e12			−1.54965
$455$	8.68125e10	+	9.55500e10i	0.0949578	+	0.104515i
$456$	−6.11829e12			−6.62656
$457$	1.04279e12			1.11834			0.559171	−	0.829052i	$-0.311119\pi$
$457$	1.04279e12			1.11834			0.559171	+	0.829052i	$0.311119\pi$
$458$	−7.89267e11	+	1.36705e12i	−0.838165	+	1.45174i
$459$	2.63846e12			2.77456
$460$	1.43241e11	−	2.48100e11i	0.149161	−	0.258355i
$461$	7.14924e10	−	1.23828e11i	0.0737234	−	0.127693i	−0.826807	−	0.562486i	$-0.809845\pi$
$461$	7.14924e10	−	1.23828e11i	0.0737234	−	0.127693i	0.900530	+	0.434793i	$0.143178\pi$
$462$	4.56483e11	−	2.37099e12i	0.466160	−	2.42125i
$463$	1.47492e12			1.49161			0.745804	−	0.666165i	$-0.232065\pi$
$463$	1.47492e12			1.49161			0.745804	+	0.666165i	$0.232065\pi$
$464$	−1.29373e12	−	2.24080e12i	−1.29572	−	2.24426i
$465$	1.34955e10	−	2.33750e10i	0.0133860	−	0.0231853i
$466$	−1.45690e12	+	2.52342e12i	−1.43117	+	2.47886i
$467$	5.70249e11	−	9.87701e11i	0.554803	−	0.960947i	−0.443116	−	0.896464i	$-0.646127\pi$
$467$	5.70249e11	−	9.87701e11i	0.554803	−	0.960947i	0.997919	−	0.0644826i	$-0.0205397\pi$
$468$	4.50664e12	−	6.01421e12i	4.34257	−	5.79525i
$469$	−3.22162e11	+	1.11573e11i	−0.307466	+	0.106483i
$470$	−6.15785e10	−	1.06657e11i	−0.0582088	−	0.100821i
$471$	−8.95833e10			−0.0838751
$472$	−6.47260e11			−0.600260
$473$	−5.07380e11	−	8.78808e11i	−0.466077	−	0.807270i
$474$	5.47855e11	+	9.48913e11i	0.498498	+	0.863424i
$475$	−6.18198e11	+	1.07075e12i	−0.557194	+	0.965088i
$476$	−1.71634e12	−	1.48662e12i	−1.53240	−	1.32730i
$477$	1.87084e12	−	3.24038e12i	1.65464	−	2.86592i
$478$	−9.01168e10			−0.0789551
$479$	−5.10791e11	+	8.84715e11i	−0.443336	+	0.767881i	−0.997935	−	0.0642375i	$-0.979538\pi$
$479$	−5.10791e11	+	8.84715e11i	−0.443336	+	0.767881i	0.554599	+	0.832118i	$0.312872\pi$
$480$	4.52301e11	+	7.83408e11i	0.388903	+	0.673600i
$481$	−1.83947e11	−	4.30123e11i	−0.156690	−	0.366386i
$482$	3.53908e11			0.298661
$483$	1.80704e12	−	6.25822e11i	1.51079	−	0.523226i
$484$	8.62169e11	+	1.49332e12i	0.714148	+	1.23694i
$485$	1.54624e9	+	2.67817e9i	0.00126894	+	0.00219786i
$486$	−5.15388e12	−	8.92679e12i	−4.19055	−	7.25825i
$487$	−5.09909e11			−0.410783			−0.205392	−	0.978680i	$-0.565847\pi$
$487$	−5.09909e11			−0.410783			−0.205392	+	0.978680i	$0.565847\pi$
$488$	−1.24926e12	−	2.16378e12i	−0.997159	−	1.72713i
$489$	2.94438e12			2.32865
$490$	−3.16516e11	−	1.26568e11i	−0.248035	−	0.0991843i
$491$	−1.17079e12	−	2.02787e12i	−0.909103	−	1.57461i	−0.815313	−	0.579020i	$-0.803435\pi$
$491$	−1.17079e12	−	2.02787e12i	−0.909103	−	1.57461i	−0.0937897	−	0.995592i	$-0.529898\pi$
$492$	9.22353e12			7.09667
$493$	4.35138e11	+	7.53681e11i	0.331754	+	0.574614i
$494$	1.70732e12	−	2.27846e12i	1.28987	−	1.72136i
$495$	1.76902e11	−	3.06403e11i	0.132437	−	0.229388i
$496$	2.01053e11	+	3.48235e11i	0.149157	+	0.258348i
$497$	−4.66301e11	+	1.61492e11i	−0.342817	+	0.118726i
$498$	−4.25903e12	+	7.37685e12i	−3.10297	+	5.37451i
$499$	−5.35306e11	+	9.27178e11i	−0.386500	+	0.669438i	−0.991976	−	0.126426i	$-0.959650\pi$
$499$	−5.35306e11	+	9.27178e11i	−0.386500	+	0.669438i	0.605476	+	0.795864i	$0.292983\pi$
$500$	1.00762e12			0.720995
$501$	−9.91752e11			−0.703288
$502$	−6.58336e11	+	1.14027e12i	−0.462680	+	0.801385i
$503$	−1.12497e12	+	1.94851e12i	−0.783584	+	1.35721i	0.146258	+	0.989247i	$0.453277\pi$
$503$	−1.12497e12	+	1.94851e12i	−0.783584	+	1.35721i	−0.929842	+	0.367960i	$0.880056\pi$
$504$	−2.29678e12	+	1.19296e13i	−1.58556	+	8.23544i
$505$	2.57918e10	+	4.46727e10i	0.0176470	+	0.0305655i
$506$	7.63225e11	−	1.32195e12i	0.517578	−	0.896471i
$507$	8.15334e11	+	2.78656e12i	0.548024	+	1.87298i
$508$	−1.65010e12	−	2.85806e12i	−1.09932	−	1.90408i
$509$	−1.50276e12			−0.992340			−0.496170	−	0.868225i	$-0.665261\pi$
$509$	−1.50276e12			−0.992340			−0.496170	+	0.868225i	$0.665261\pi$
$510$	−3.13086e11	−	5.42281e11i	−0.204926	−	0.354943i
$511$	2.52689e11	−	1.31248e12i	0.163943	−	0.851525i
$512$	7.82097e11			0.502975
$513$	−3.14733e12	−	5.45134e12i	−2.00639	−	3.47516i
$514$	4.35284e11			0.275067
$515$	−1.52495e11	−	2.64129e11i	−0.0955263	−	0.165456i
$516$	5.65487e12	+	9.79453e12i	3.51155	+	6.08219i
$517$	−2.36422e11	−	4.09494e11i	−0.145539	−	0.252081i
$518$	9.33698e11	+	8.08730e11i	0.569800	+	0.493537i
$519$	−7.92864e11			−0.479674
$520$	−6.98086e11	−	8.38028e10i	−0.418691	−	0.0502624i
$521$	1.35052e11	+	2.33916e11i	0.0803026	+	0.139088i	0.903380	−	0.428841i	$-0.141078\pi$
$521$	1.35052e11	+	2.33916e11i	0.0803026	+	0.139088i	−0.823077	+	0.567929i	$0.807745\pi$
$522$	3.80289e12	−	6.58680e12i	2.24180	−	3.88291i
$523$	−6.67348e11			−0.390027			−0.195014	−	0.980801i	$-0.562475\pi$
$523$	−6.67348e11			−0.390027			−0.195014	+	0.980801i	$0.562475\pi$
$524$	1.68715e12	−	2.92222e12i	0.977602	−	1.69326i
$525$	2.51647e12	+	2.17966e12i	1.44569	+	1.25220i
$526$	3.73214e11	−	6.46425e11i	0.212580	−	0.368199i
$527$	−6.76232e10	−	1.17127e11i	−0.0381898	−	0.0661467i
$528$	3.57387e12	+	6.19012e12i	2.00118	+	3.46614i
$529$	−5.92185e11			−0.328781
$530$	−5.71798e11			−0.314776
$531$	−5.17080e11	−	8.95608e11i	−0.282249	−	0.488869i
$532$	−1.02415e12	+	5.31948e12i	−0.554322	+	2.87917i
$533$	−1.57570e12	+	2.10281e12i	−0.845670	+	1.12857i
$534$	5.30849e12	−	9.19458e12i	2.82511	−	4.89324i
$535$	5.12012e9	−	8.86830e9i	0.00270202	−	0.00468003i
$536$	9.28411e11	−	1.60805e12i	0.485846	−	0.841510i
$537$	2.83791e12	+	4.91540e12i	1.47270	+	2.55079i
$538$	4.10186e11			0.211087
$539$	−1.21522e12	−	4.85941e11i	−0.620162	−	0.247990i
$540$	−1.26957e12	+	2.19896e12i	−0.642517	+	1.11287i
$541$	−1.03167e12	+	1.78691e12i	−0.517791	+	0.896840i	0.481996	+	0.876174i	$0.339912\pi$
$541$	−1.03167e12	+	1.78691e12i	−0.517791	+	0.896840i	−0.999786	+	0.0206665i	$0.993421\pi$
$542$	−3.50782e12			−1.74598
$543$	−3.13132e12	+	5.42360e12i	−1.54571	+	2.67725i
$544$	4.53276e12			2.21905
$545$	4.93056e11			0.239393
$546$	−5.15535e12	−	5.67423e12i	−2.48251	−	2.73237i
$547$	8.94903e11			0.427399			0.213699	−	0.976899i	$-0.431449\pi$
$547$	8.94903e11			0.427399			0.213699	+	0.976899i	$0.431449\pi$
$548$	−4.46551e12			−2.11523
$549$	1.99601e12	−	3.45719e12i	0.937749	−	1.62423i
$550$	2.65741e12			1.23830
$551$	1.03812e12	−	1.79808e12i	0.479807	−	0.831049i
$552$	−5.20753e12	+	9.01971e12i	−2.38730	+	4.13492i
$553$	5.61217e11	−	1.94364e11i	0.255193	−	0.0883797i
$554$	−3.85905e12			−1.74055
$555$	1.22727e11	+	2.12569e11i	0.0549060	+	0.0951000i
$556$	4.83014e12	−	8.36605e12i	2.14350	−	3.71265i
$557$	−1.80584e12	+	3.12781e12i	−0.794933	+	1.37686i	0.127948	+	0.991781i	$0.459161\pi$
$557$	−1.80584e12	+	3.12781e12i	−0.794933	+	1.37686i	−0.922882	+	0.385084i	$0.874172\pi$
$558$	−5.90993e11	+	1.02363e12i	−0.258065	+	0.446981i
$559$	−3.19903e12	−	3.84032e11i	−1.38569	−	0.166347i
$560$	9.53553e11	−	3.30240e11i	0.409731	−	0.141900i
$561$	−1.20205e12	−	2.08201e12i	−0.512377	−	0.887462i
$562$	−4.74006e10			−0.0200434
$563$	4.39744e12			1.84464			0.922321	−	0.386425i	$-0.126290\pi$
$563$	4.39744e12			1.84464			0.922321	+	0.386425i	$0.126290\pi$
$564$	2.63498e12	+	4.56391e12i	1.09653	+	1.89925i
$565$	−2.30009e10	−	3.98387e10i	−0.00949570	−	0.0164470i
$566$	3.96016e12	−	6.85919e12i	1.62195	−	2.80931i
$567$	−9.48507e12	+	3.28492e12i	−3.85405	+	1.33475i
$568$	1.34379e12	−	2.32751e12i	0.541706	−	0.938263i
$569$	3.83651e12			1.53437			0.767187	−	0.641424i	$-0.221656\pi$
$569$	3.83651e12			1.53437			0.767187	+	0.641424i	$0.221656\pi$
$570$	−7.46940e11	+	1.29374e12i	−0.296380	+	0.513345i
$571$	−6.17836e11	−	1.07012e12i	−0.243226	−	0.421280i	0.718405	−	0.695625i	$-0.244872\pi$
$571$	−6.17836e11	−	1.07012e12i	−0.243226	−	0.421280i	−0.961631	+	0.274345i	$0.911539\pi$
$572$	−4.37802e12	−	5.25566e11i	−1.71000	−	0.205279i
$573$	−5.09668e12			−1.97511
$574$	1.31175e12	−	6.81326e12i	0.504367	−	2.61970i
$575$	1.05235e12	+	1.82272e12i	0.401471	+	0.695369i
$576$	−8.41616e12	−	1.45772e13i	−3.18576	−	5.51790i
$577$	−1.40308e12	−	2.43021e12i	−0.526978	−	0.912753i	−0.999506	−	0.0314373i	$-0.989992\pi$
$577$	−1.40308e12	−	2.43021e12i	−0.526978	−	0.912753i	0.472527	−	0.881316i	$-0.343342\pi$
$578$	1.93852e12			0.722429
$579$	−1.24430e12	−	2.15519e12i	−0.460119	−	0.796950i
$580$	−8.37514e11			−0.307303
$581$	3.49000e12	+	3.02289e12i	1.27067	+	1.10060i
$582$	−9.18235e10	−	1.59043e11i	−0.0331742	−	0.0574594i
$583$	−2.19534e12			−0.787032
$584$	3.63967e12	+	6.30410e12i	1.29481	+	2.24267i
$585$	−4.41726e11	−	1.03288e12i	−0.155938	−	0.364628i
$586$	3.00057e12	−	5.19713e12i	1.05115	−	1.82064i
$587$	2.48793e12	+	4.30923e12i	0.864903	+	1.49806i	0.867144	+	0.498058i	$0.165953\pi$
$587$	2.48793e12	+	4.30923e12i	0.864903	+	1.49806i	−0.00224138	+	0.999997i	$0.500713\pi$
$588$	1.35439e13	+	5.41593e12i	4.67246	+	1.86842i
$589$	−1.61331e11	+	2.79433e11i	−0.0552330	+	0.0956663i
$590$	−7.90195e10	+	1.36866e11i	−0.0268473	+	0.0465009i
$591$	3.17865e12			1.07176
$592$	−3.65670e12			−1.22361
$593$	1.02286e12	−	1.77164e12i	0.339679	−	0.588342i	−0.644693	−	0.764442i	$-0.723015\pi$
$593$	1.02286e12	−	1.77164e12i	0.339679	−	0.588342i	0.984372	+	0.176100i	$0.0563481\pi$
$594$	−6.76462e12	+	1.17167e13i	−2.22948	+	3.86158i
$595$	−3.20722e11	+	1.11074e11i	−0.104907	+	0.0363318i
$596$	−2.86800e12	−	4.96752e12i	−0.931045	−	1.61262i
$597$	5.20763e11	−	9.01989e11i	0.167786	−	0.290614i
$598$	−1.90578e12	−	4.45627e12i	−0.609422	−	1.42500i
$599$	1.95711e12	+	3.38981e12i	0.621147	+	1.07586i	0.989273	+	0.146082i	$0.0466662\pi$
$599$	1.95711e12	+	3.38981e12i	0.621147	+	1.07586i	−0.368126	+	0.929776i	$0.620000\pi$
$600$	−1.81317e13			−5.71159
$601$	1.65908e11	+	2.87360e11i	0.0518718	+	0.0898446i	0.890795	−	0.454405i	$-0.150148\pi$
$601$	1.65908e11	+	2.87360e11i	0.0518718	+	0.0898446i	−0.838924	+	0.544249i	$0.816815\pi$
$602$	8.03926e12	−	2.78420e12i	2.49478	−	0.864006i
$603$	2.96674e12			0.913800
$604$	−4.31421e12	−	7.47243e12i	−1.31897	−	2.28452i
$605$	2.57750e11			0.0782166
$606$	−1.53165e12	−	2.65289e12i	−0.461351	−	0.799083i
$607$	−2.41988e12	−	4.19135e12i	−0.723510	−	1.25316i	−0.959584	−	0.281421i	$-0.909194\pi$
$607$	−2.41988e12	−	4.19135e12i	−0.723510	−	1.25316i	0.236075	−	0.971735i	$-0.424139\pi$
$608$	−5.40697e12	−	9.36515e12i	−1.60468	−	2.77938i
$609$	−4.22584e12	−	3.66025e12i	−1.24490	−	1.07828i
$610$	−6.10055e11			−0.178396
$611$	−1.49064e12	−	1.78946e11i	−0.432700	−	0.0519441i
$612$	9.87933e12	+	1.71115e13i	2.84673	+	4.93068i
$613$	1.44247e12	−	2.49843e12i	0.412605	−	0.714653i	−0.582569	−	0.812781i	$-0.697952\pi$
$613$	1.44247e12	−	2.49843e12i	0.412605	−	0.714653i	0.995174	+	0.0981286i	$0.0312857\pi$
$614$	−2.91960e12			−0.829022
$615$	6.89355e11	−	1.19400e12i	0.194314	−	0.336562i
$616$	6.73543e12	−	2.33265e12i	1.88474	−	0.652735i
$617$	−1.67848e12	+	2.90721e12i	−0.466264	+	0.807593i	−0.999258	−	0.0385261i	$-0.987734\pi$
$617$	−1.67848e12	+	2.90721e12i	−0.466264	+	0.807593i	0.532993	+	0.846119i	$0.321067\pi$
$618$	9.05590e12	+	1.56853e13i	2.49737	+	4.32558i
$619$	−1.93678e12	−	3.35460e12i	−0.530240	−	0.918403i	−0.999378	−	0.0352775i	$-0.988768\pi$
$619$	−1.93678e12	−	3.35460e12i	−0.530240	−	0.918403i	0.469138	−	0.883125i	$-0.344565\pi$
$620$	1.30155e11			0.0353752
$621$	−1.07153e13			−2.89130
$622$	−9.56323e11	−	1.65640e12i	−0.256182	−	0.443720i
$623$	−4.34997e12	−	3.76776e12i	−1.15689	−	1.00205i
$624$	2.25332e13	+	2.70503e12i	5.94967	+	0.714236i
$625$	−1.79401e12	+	3.10731e12i	−0.470288	+	0.814563i
$626$	−4.03689e12	+	6.99210e12i	−1.05066	+	1.81980i
$627$	−2.86777e12	+	4.96712e12i	−0.741037	+	1.28351i
$628$	−2.15992e11	−	3.74109e11i	−0.0554140	−	0.0959799i
$629$	1.22991e12			0.313289
$630$	2.24216e12	+	1.94206e12i	0.567066	+	0.491168i
$631$	1.17266e12	−	2.03110e12i	0.294468	−	0.510034i	−0.680393	−	0.732847i	$-0.738191\pi$
$631$	1.17266e12	−	2.03110e12i	0.294468	−	0.510034i	0.974861	+	0.222814i	$0.0715242\pi$
$632$	−1.61732e12	+	2.80128e12i	−0.403246	+	0.698442i
$633$	8.23653e12			2.03905
$634$	−5.17341e12	+	8.96061e12i	−1.27167	+	2.20260i
$635$	−4.93305e11			−0.120402
$636$	2.44676e13			5.92971
$637$	−3.54851e12	+	2.16255e12i	−0.853922	+	0.520401i
$638$	−4.46251e12			−1.06632
$639$	4.29408e12			1.01886
$640$	−4.40322e11	+	7.62660e11i	−0.103743	+	0.179689i
$641$	1.47602e12			0.345328			0.172664	−	0.984981i	$-0.444763\pi$
$641$	1.47602e12			0.345328			0.172664	+	0.984981i	$0.444763\pi$
$642$	−3.04058e11	+	5.26644e11i	−0.0706396	+	0.122351i
$643$	1.17469e12	−	2.03462e12i	0.271002	−	0.469389i	−0.698117	−	0.715984i	$-0.745978\pi$
$643$	1.17469e12	−	2.03462e12i	0.271002	−	0.469389i	0.969119	+	0.246595i	$0.0793117\pi$
$644$	6.97040e12	+	6.03746e12i	1.59688	+	1.38315i
$645$	1.69055e12			0.384600
$646$	3.74275e12	+	6.48263e12i	0.845560	+	1.46455i
$647$	1.52191e12	−	2.63603e12i	0.341445	−	0.591400i	−0.643257	−	0.765651i	$-0.722417\pi$
$647$	1.52191e12	−	2.63603e12i	0.341445	−	0.591400i	0.984701	+	0.174251i	$0.0557505\pi$
$648$	2.73342e13	−	4.73442e13i	6.09002	−	10.5482i
$649$	−3.03384e11	+	5.25477e11i	−0.0671261	+	0.116266i
$650$	5.05969e12	−	6.75226e12i	1.11177	−	1.48368i
$651$	6.56723e11	+	5.68825e11i	0.143307	+	0.124126i
$652$	7.09911e12	+	1.22960e13i	1.53847	+	2.66471i
$653$	−4.25727e12			−0.916267			−0.458133	−	0.888883i	$-0.651482\pi$
$653$	−4.25727e12			−0.916267			−0.458133	+	0.888883i	$0.651482\pi$
$654$	−2.92801e13			−6.25853
$655$	−2.52190e11	−	4.36807e11i	−0.0535356	−	0.0927264i
$656$	1.02698e13	+	1.77879e13i	2.16519	+	3.75023i
$657$	−5.81529e12	+	1.00724e13i	−1.21766	+	2.10905i
$658$	3.74602e12	−	1.29734e12i	0.779029	−	0.269798i
$659$	−1.52715e12	+	2.64511e12i	−0.315426	+	0.546335i	−0.979528	−	0.201308i	$-0.935481\pi$
$659$	−1.52715e12	+	2.64511e12i	−0.315426	+	0.546335i	0.664102	+	0.747642i	$0.268814\pi$
$660$	2.31360e12			0.474613
$661$	1.35725e10	−	2.35082e10i	0.00276537	−	0.00478975i	−0.864639	−	0.502393i	$-0.832453\pi$
$661$	1.35725e10	−	2.35082e10i	0.00276537	−	0.00478975i	0.867405	+	0.497603i	$0.165786\pi$
$662$	8.17859e12	+	1.41657e13i	1.65507	+	2.86667i
$663$	−7.57892e12	−	9.09822e11i	−1.52334	−	0.182871i
$664$	−2.51461e13			−5.02012
$665$	6.12070e11	+	5.30149e11i	0.121368	+	0.105124i
$666$	−5.37441e12	−	9.30874e12i	−1.05851	−	1.83340i
$667$	−1.76718e12	−	3.06085e12i	−0.345712	−	0.598791i
$668$	−2.39119e12	−	4.14166e12i	−0.464643	−	0.804786i
$669$	−2.28887e12			−0.441777
$670$	−2.26687e11	−	3.92633e11i	−0.0434600	−	0.0752749i
$671$	−2.34222e12			−0.446042
$672$	−2.75149e13	+	9.52913e12i	−5.20484	+	1.80257i
$673$	3.07256e12	+	5.32183e12i	0.577342	+	0.999985i	0.995783	+	0.0917411i	$0.0292432\pi$
$673$	3.07256e12	+	5.32183e12i	0.577342	+	0.999985i	−0.418441	+	0.908244i	$0.637423\pi$
$674$	−9.47047e12			−1.76767
$675$	−9.32718e12	−	1.61551e13i	−1.72935	−	2.99532i
$676$	−9.67114e12	+	1.01235e13i	−1.78122	+	1.86454i
$677$	1.89316e11	−	3.27905e11i	0.0346368	−	0.0599927i	−0.848187	−	0.529696i	$-0.822306\pi$
$677$	1.89316e11	−	3.27905e11i	0.0346368	−	0.0599927i	0.882824	+	0.469704i	$0.155639\pi$
$678$	1.36591e12	+	2.36582e12i	0.248249	+	0.429980i
$679$	−9.40630e10	+	3.25764e10i	−0.0169826	+	0.00588152i
$680$	9.24260e11	−	1.60087e12i	0.165769	−	0.287121i
$681$	4.48619e12	−	7.77031e12i	0.799311	−	1.38445i
$682$	6.93502e11			0.122749
$683$	−3.35747e12			−0.590362			−0.295181	−	0.955441i	$-0.595380\pi$
$683$	−3.35747e12			−0.590362			−0.295181	+	0.955441i	$0.595380\pi$
$684$	2.35694e13	−	4.08235e13i	4.11715	−	7.13111i
$685$	−3.33746e11	+	5.78065e11i	−0.0579173	+	0.100316i
$686$	5.92683e12	−	9.23440e12i	1.02180	−	1.59203i
$687$	−5.04833e12	−	8.74396e12i	−0.864653	−	1.49762i
$688$	−1.25927e13	+	2.18112e13i	−2.14275	+	3.71135i
$689$	−4.17991e12	+	5.57818e12i	−0.706611	+	0.942988i
$690$	1.27150e12	+	2.20231e12i	0.213549	+	0.369877i
$691$	5.80842e12			0.969185			0.484592	−	0.874740i	$-0.338968\pi$
$691$	5.80842e12			0.969185			0.484592	+	0.874740i	$0.338968\pi$
$692$	−1.91166e12	−	3.31108e12i	−0.316907	−	0.548899i
$693$	8.60844e12	+	7.45626e12i	1.41783	+	1.22807i
$694$	4.74357e12			0.776225
$695$	−7.21997e11	−	1.25054e12i	−0.117383	−	0.203313i
$696$	3.04480e13			4.91832
$697$	−3.45421e12	−	5.98286e12i	−0.554371	−	0.960199i
$698$	−2.25479e12	−	3.90542e12i	−0.359549	−	0.622757i
$699$	−9.31862e12	−	1.61403e13i	−1.47640	−	2.55720i
$700$	−3.03509e12	+	1.57644e13i	−0.477783	+	2.48162i
$701$	4.44738e12			0.695622			0.347811	−	0.937565i	$-0.386925\pi$
$701$	4.44738e12			0.695622			0.347811	+	0.937565i	$0.386925\pi$
$702$	1.68913e13	+	3.94968e13i	2.62510	+	6.13826i
$703$	−1.46712e12	−	2.54112e12i	−0.226551	−	0.392398i
$704$	−4.93798e12	+	8.55283e12i	−0.757657	+	1.31230i
$705$	7.87739e11			0.120097
$706$	1.06604e13	−	1.84643e13i	1.61492	−	2.79712i
$707$	−1.56900e12	+	5.43385e11i	−0.236176	+	0.0817938i
$708$	3.38129e12	−	5.85656e12i	0.505746	−	0.875978i
$709$	−1.35163e12	−	2.34110e12i	−0.200887	−	0.347946i	0.747928	−	0.663780i	$-0.231049\pi$
$709$	−1.35163e12	−	2.34110e12i	−0.200887	−	0.347946i	−0.948814	+	0.315834i	$0.897716\pi$
$710$	−3.28108e11	−	5.68300e11i	−0.0484568	−	0.0839296i
$711$	−5.16815e12			−0.758441
$712$	3.13424e13			4.57058
$713$	2.74631e11	+	4.75675e11i	0.0397967	+	0.0689298i
$714$	1.90461e13	−	6.59614e12i	2.74261	−	0.949834i
$715$	−3.95243e11	+	5.27460e11i	−0.0565570	+	0.0754766i
$716$	−1.36848e13	+	2.37028e13i	−1.94595	+	3.37048i
$717$	2.88203e11	−	4.99183e11i	0.0407252	−	0.0705381i
$718$	2.14858e12	−	3.72145e12i	0.301712	−	0.522580i
$719$	5.18601e12	+	8.98244e12i	0.723692	+	1.25347i	0.959510	+	0.281674i	$0.0908895\pi$
$719$	5.18601e12	+	8.98244e12i	0.723692	+	1.25347i	−0.235819	+	0.971797i	$0.575777\pi$
$720$	−8.78110e12			−1.21773
$721$	9.27677e12	−	3.21278e12i	1.27846	−	0.442764i
$722$	2.02290e12	−	3.50377e12i	0.277050	−	0.479864i
$723$	−1.13184e12	+	1.96040e12i	−0.154050	+	0.266822i
$724$	−3.01993e13			−4.08483
$725$	3.07649e12	−	5.32864e12i	0.413557	−	0.716301i
$726$	−1.53064e13			−2.04484
$727$	6.87496e12			0.912778			0.456389	−	0.889780i	$-0.349142\pi$
$727$	6.87496e12			0.912778			0.456389	+	0.889780i	$0.349142\pi$
$728$	6.89714e12	−	2.15556e13i	0.910076	−	2.84425i
$729$	3.48287e13			4.56734
$730$	1.77737e12			0.231646
$731$	4.23549e12	−	7.33608e12i	0.548625	−	0.950246i
$732$	2.61046e13			3.36060
$733$	−1.26337e12	+	2.18822e12i	−0.161645	+	0.279977i	−0.935459	−	0.353436i	$-0.885013\pi$
$733$	−1.26337e12	+	2.18822e12i	−0.161645	+	0.279977i	0.773814	+	0.633413i	$0.218347\pi$
$734$	−4.03107e12	+	6.98202e12i	−0.512611	+	0.887869i
$735$	1.71335e12	−	1.34850e12i	0.216548	−	0.170434i
$736$	−1.84084e13			−2.31242
$737$	−8.70331e11	−	1.50746e12i	−0.108663	−	0.188209i
$738$	−3.01880e13	+	5.22872e13i	−3.74612	+	6.48846i
$739$	−3.00244e12	+	5.20038e12i	−0.370318	+	0.641409i	−0.989614	−	0.143748i	$-0.954084\pi$
$739$	−3.00244e12	+	5.20038e12i	−0.370318	+	0.641409i	0.619297	+	0.785157i	$0.287418\pi$
$740$	−5.91806e11	+	1.02504e12i	−0.0725498	+	0.125660i
$741$	7.16085e12	+	1.67441e13i	0.872534	+	2.04024i
$742$	3.47971e12	−	1.80738e13i	0.421430	−	2.18892i
$743$	−8.05788e11	−	1.39567e12i	−0.0969999	−	0.168009i	0.813442	−	0.581647i	$-0.197591\pi$
$743$	−8.05788e11	−	1.39567e12i	−0.0969999	−	0.168009i	−0.910442	+	0.413638i	$0.864258\pi$
$744$	−4.73181e12			−0.566173
$745$	−8.57402e11			−0.101972
$746$	−2.64917e12	−	4.58849e12i	−0.313173	−	0.542432i
$747$	−2.00886e13	−	3.47945e13i	−2.36051	−	4.08853i
$748$	5.79646e12	−	1.00398e13i	0.677026	−	1.17264i
$749$	2.49156e11	+	2.15808e11i	0.0289270	+	0.0250553i
$750$	−4.47218e12	+	7.74604e12i	−0.516111	+	0.893931i
$751$	1.03821e13			1.19098			0.595490	−	0.803363i	$-0.296958\pi$
$751$	1.03821e13			1.19098			0.595490	+	0.803363i	$0.296958\pi$
$752$	−5.86778e12	+	1.01633e13i	−0.669103	+	1.15892i
$753$	−4.21086e12	−	7.29342e12i	−0.477302	−	0.826712i
$754$	−8.49659e12	+	1.13389e13i	−0.957356	+	1.27761i
$755$	−1.28975e12			−0.144459
$756$	−6.17800e13	−	5.35112e13i	−6.87860	−	5.95795i
$757$	3.05998e12	+	5.30004e12i	0.338678	+	0.586607i	0.984184	−	0.177148i	$-0.0566870\pi$
$757$	3.05998e12	+	5.30004e12i	0.338678	+	0.586607i	−0.645506	+	0.763755i	$0.723354\pi$
$758$	−2.55258e12	−	4.42120e12i	−0.280846	−	0.486439i
$759$	4.88176e12	+	8.45545e12i	0.533935	+	0.924802i
$760$	−4.41007e12			−0.479496
$761$	6.64885e12	+	1.15161e13i	0.718647	+	1.24473i	0.961536	+	0.274679i	$0.0885715\pi$
$761$	6.64885e12	+	1.15161e13i	0.718647	+	1.24473i	−0.242889	+	0.970054i	$0.578095\pi$
$762$	2.92949e13			3.14771
$763$	−3.00052e12	+	1.55848e13i	−0.320506	+	1.66472i
$764$	−1.22885e13	−	2.12843e13i	−1.30490	−	2.26016i
$765$	2.95347e12			0.311786
$766$	−1.41681e13	−	2.45399e13i	−1.48690	−	2.57539i
$767$	7.57554e11	+	1.77138e12i	0.0790377	+	0.184813i
$768$	4.80564e12	−	8.32361e12i	0.498454	−	0.863348i
$769$	−4.84521e12	−	8.39215e12i	−0.499625	−	0.865376i	0.500375	−	0.865809i	$-0.333195\pi$
$769$	−4.84521e12	−	8.39215e12i	−0.499625	−	0.865376i	−1.00000		0.000433165i	$0.999862\pi$
$770$	3.29034e11	−	1.70901e12i	0.0337312	−	0.175201i
$771$	−1.39209e12	+	2.41116e12i	−0.141880	+	0.245744i
$772$	6.00018e12	−	1.03926e13i	0.607976	−	1.05305i
$773$	3.26544e12			0.328953			0.164477	−	0.986381i	$-0.447406\pi$
$773$	3.26544e12			0.328953			0.164477	+	0.986381i	$0.447406\pi$
$774$	−7.40322e13			−7.41457
$775$	−4.78107e11	+	8.28105e11i	−0.0476066	+	0.0824570i
$776$	2.71072e11	−	4.69510e11i	0.0268353	−	0.0464801i
$777$	−7.46586e12	+	2.58562e12i	−0.734827	+	0.254489i
$778$	−2.40319e12	−	4.16245e12i	−0.235169	−	0.407325i
$779$	−8.24081e12	+	1.42735e13i	−0.801773	+	1.38871i
$780$	4.40507e12	−	5.87867e12i	0.426116	−	0.568661i
$781$	−1.25972e12	−	2.18191e12i	−0.121156	−	0.209849i
$782$	1.27425e13			1.21849
$783$	1.56629e13	+	2.71289e13i	1.48917	+	2.57931i
$784$	4.63552e12	+	3.21502e13i	0.438204	+	3.03921i
$785$	−6.45719e10			−0.00606918
$786$	1.49763e13	+	2.59397e13i	1.39960	+	2.42418i
$787$	−1.01089e12			−0.0939326			−0.0469663	−	0.998896i	$-0.514955\pi$
$787$	−1.01089e12			−0.0939326			−0.0469663	+	0.998896i	$0.514955\pi$
$788$	7.66395e12	+	1.32744e13i	0.708084	+	1.22644i
$789$	2.38716e12	+	4.13468e12i	0.219298	+	0.379835i
$790$	3.94895e11	+	6.83979e11i	0.0360712	+	0.0624771i
$791$	1.39922e12	−	4.84586e11i	0.127084	−	0.0440126i
$792$	−6.20254e13			−5.60152
$793$	−4.45957e12	+	5.95140e12i	−0.400464	+	0.534428i
$794$	−1.27024e13	−	2.20013e13i	−1.13421	−	1.96452i
$795$	1.82867e12	−	3.16736e12i	0.162362	−	0.281219i
$796$	5.02240e12			0.443407
$797$	−2.82742e12	+	4.89724e12i	−0.248215	+	0.429921i	−0.963031	−	0.269392i	$-0.913177\pi$
$797$	−2.82742e12	+	4.89724e12i	−0.248215	+	0.429921i	0.714816	+	0.699313i	$0.246511\pi$
$798$	−3.63477e13	−	3.14829e13i	−3.17296	−	2.74828i
$799$	1.97359e12	−	3.41836e12i	0.171316	−	0.296727i
$800$	−1.60237e13	−	2.77538e13i	−1.38311	−	2.39562i
$801$	2.50386e13	+	4.33682e13i	2.14914	+	3.72241i
$802$	3.82824e13			3.26749
$803$	6.82396e12			0.579184
$804$	9.70005e12	+	1.68010e13i	0.818694	+	1.41802i
$805$	1.30252e12	−	4.51094e11i	0.109320	−	0.0378605i
$806$	1.32042e12	−	1.76213e12i	0.110206	−	0.147072i
$807$	−1.31182e12	+	2.27214e12i	−0.108879	+	0.188584i
$808$	4.52156e12	−	7.83158e12i	0.373196	−	0.646395i
$809$	5.87520e12	−	1.01761e13i	0.482230	−	0.835247i	−0.517562	−	0.855646i	$-0.673160\pi$
$809$	5.87520e12	−	1.01761e13i	0.482230	−	0.835247i	0.999792	+	0.0203989i	$0.00649363\pi$
$810$	−6.67408e12	−	1.15599e13i	−0.544765	−	0.943560i
$811$	6.76028e11			0.0548745			0.0274373	−	0.999624i	$-0.491265\pi$
$811$	6.76028e11			0.0548745			0.0274373	+	0.999624i	$0.491265\pi$
$812$	5.09674e12	−	2.64727e13i	0.411425	−	2.13696i
$813$	1.12184e13	−	1.94308e13i	0.900581	−	1.55985i
$814$	−3.15330e12	+	5.46168e12i	−0.251742	+	0.436030i
$815$	2.12231e12			0.168500
$816$	−2.98338e13	+	5.16736e13i	−2.35561	+	4.08003i
$817$	−2.02095e13			−1.58692
$818$	5.77602e12			0.451065
$819$	3.53362e13	−	7.67668e12i	2.74437	−	0.596205i
$820$	6.64834e12			0.513513
$821$	7.90499e12			0.607235			0.303618	−	0.952794i	$-0.401805\pi$
$821$	7.90499e12			0.607235			0.303618	+	0.952794i	$0.401805\pi$
$822$	1.98195e13	−	3.43284e13i	1.51415	−	2.62259i
$823$	−4.67264e11			−0.0355028			−0.0177514	−	0.999842i	$-0.505651\pi$
$823$	−4.67264e11			−0.0355028			−0.0177514	+	0.999842i	$0.505651\pi$
$824$	−2.67339e13	+	4.63044e13i	−2.02018	+	3.49905i
$825$	−8.49868e12	+	1.47201e13i	−0.638717	+	1.10629i
$826$	−3.84526e12	−	3.33060e12i	−0.287419	−	0.248950i
$827$	8.23951e12			0.612529			0.306264	−	0.951946i	$-0.400921\pi$
$827$	8.23951e12			0.612529			0.306264	+	0.951946i	$0.400921\pi$
$828$	−4.01219e13	−	6.94932e13i	−2.96650	−	5.13814i
$829$	1.18638e13	−	2.05487e13i	0.872427	−	1.51109i	0.0129476	−	0.999916i	$-0.495879\pi$
$829$	1.18638e13	−	2.05487e13i	0.872427	−	1.51109i	0.859479	−	0.511171i	$-0.170788\pi$
$830$	−3.06992e12	+	5.31725e12i	−0.224530	+	0.388898i
$831$	1.23417e13	−	2.13764e13i	0.897778	−	1.55500i
$832$	1.23302e13	+	2.88316e13i	0.892103	+	2.08600i
$833$	−1.55913e12	−	1.08135e13i	−0.112197	−	0.778153i
$834$	4.28758e13	+	7.42630e13i	3.06877	+	5.31527i
$835$	−7.14857e11			−0.0508897
$836$	−2.76576e13			−1.95833
$837$	−2.43411e12	−	4.21600e12i	−0.171425	−	0.296918i
$838$	6.85320e12	+	1.18701e13i	0.480060	+	0.831488i
$839$	1.90171e12	−	3.29386e12i	0.132500	−	0.229497i	−0.792140	−	0.610340i	$-0.791033\pi$
$839$	1.90171e12	−	3.29386e12i	0.132500	−	0.229497i	0.924640	+	0.380843i	$0.124366\pi$
$840$	−2.24502e12	+	1.16607e13i	−0.155583	+	0.808105i
$841$	2.08730e12	−	3.61532e12i	0.143881	−	0.249209i
$842$	−3.93579e13			−2.69853
$843$	1.51592e11	−	2.62566e11i	0.0103384	−	0.0179066i
$844$	1.98589e13	+	3.43966e13i	1.34714	+	2.33332i
$845$	5.87695e11	+	2.00856e12i	0.0396549	+	0.135528i
$846$	−3.44964e13			−2.31530
$847$	−1.56855e12	+	8.14711e12i	−0.104718	+	0.543912i
$848$	2.72432e13	+	4.71865e13i	1.80916	+	3.13355i
$849$	2.53300e13	+	4.38729e13i	1.67321	+	2.89809i
$850$	1.10917e13	+	1.92114e13i	0.728808	+	1.26233i
$851$	−4.99491e12			−0.326471
$852$	1.40399e13	+	2.43179e13i	0.912824	+	1.58106i
$853$	−1.35495e13			−0.876297			−0.438148	−	0.898903i	$-0.644366\pi$
$853$	−1.35495e13			−0.876297			−0.438148	+	0.898903i	$0.644366\pi$
$854$	3.71253e12	−	1.92830e13i	0.238841	−	1.24055i
$855$	−3.52310e12	−	6.10218e12i	−0.225464	−	0.390515i
$856$	−1.79522e12			−0.114284
$857$	−3.51026e12	−	6.07996e12i	−0.222293	−	0.385023i	0.733211	−	0.680001i	$-0.238021\pi$
$857$	−3.51026e12	−	6.07996e12i	−0.222293	−	0.385023i	−0.955504	+	0.294978i	$0.904688\pi$
$858$	2.34715e13	−	3.13232e13i	1.47859	−	1.97321i
$859$	−1.81338e12	+	3.14087e12i	−0.113637	+	0.196825i	−0.917234	−	0.398349i	$-0.869583\pi$
$859$	−1.81338e12	+	3.14087e12i	−0.113637	+	0.196825i	0.803597	+	0.595174i	$0.202917\pi$
$860$	4.07605e12	+	7.05992e12i	0.254095	+	0.440105i
$861$	3.35455e13	+	2.90557e13i	2.08027	+	1.80184i
$862$	2.42818e13	−	4.20573e13i	1.49795	−	2.59453i
$863$	1.01587e13	−	1.75954e13i	0.623433	−	1.07982i	−0.365409	−	0.930847i	$-0.619071\pi$
$863$	1.01587e13	−	1.75954e13i	0.623433	−	1.07982i	0.988842	−	0.148971i	$-0.0475960\pi$
$864$	1.63157e14			9.96082
$865$	−5.71499e11			−0.0347090
$866$	1.94161e13	−	3.36296e13i	1.17309	−	2.03185i
$867$	−6.19960e12	+	1.07380e13i	−0.372630	+	0.645414i
$868$	−7.92067e11	+	4.11402e12i	−0.0473612	+	0.245996i
$869$	1.51614e12	+	2.62604e12i	0.0901886	+	0.156211i
$870$	3.71718e12	−	6.43835e12i	0.219977	−	0.381012i
$871$	−5.48744e12	−	6.58747e11i	−0.323063	−	0.0387826i
$872$	−4.32188e13	−	7.48572e13i	−2.53133	−	4.38439i
$873$	8.66210e11			0.0504730
$874$	−1.52000e13	−	2.63272e13i	−0.881137	−	1.52617i
$875$	3.66466e12	+	3.17418e12i	0.211348	+	0.183061i
$876$	−7.60547e13			−4.36373
$877$	−2.10837e12	−	3.65180e12i	−0.120350	−	0.208453i	0.799555	−	0.600592i	$-0.205068\pi$
$877$	−2.10837e12	−	3.65180e12i	−0.120350	−	0.208453i	−0.919906	+	0.392139i	$0.871735\pi$
$878$	1.70545e13			0.968531
$879$	1.91923e13	+	3.32420e13i	1.08437	+	1.87818i
$880$	2.57605e12	+	4.46185e12i	0.144805	+	0.250809i
$881$	−4.20225e12	−	7.27850e12i	−0.235012	−	0.407052i	0.724264	−	0.689522i	$-0.242180\pi$
$881$	−4.20225e12	−	7.27850e12i	−0.235012	−	0.407052i	−0.959276	+	0.282470i	$0.908846\pi$
$882$	−7.50307e13	+	5.90530e13i	−4.17475	+	3.28574i
$883$	−5.89788e12			−0.326492			−0.163246	−	0.986585i	$-0.552196\pi$
$883$	−5.89788e12			−0.326492			−0.163246	+	0.986585i	$0.552196\pi$
$884$	−1.44738e13	−	3.38440e13i	−0.797165	−	1.86400i
$885$	−5.05426e11	−	8.75424e11i	−0.0276958	−	0.0479705i
$886$	−1.63467e13	+	2.83133e13i	−0.891206	+	1.54361i
$887$	9.93590e12			0.538953			0.269477	−	0.963007i	$-0.413149\pi$
$887$	9.93590e12			0.538953			0.269477	+	0.963007i	$0.413149\pi$
$888$	2.15152e13	−	3.72654e13i	1.16115	−	2.01116i
$889$	3.00204e12	−	1.55927e13i	0.161198	−	0.837266i
$890$	3.82637e12	−	6.62748e12i	0.204424	−	0.354073i
$891$	−2.56242e13	−	4.43824e13i	−1.36207	−	2.35918i
$892$	−5.51863e12	−	9.55855e12i	−0.291870	−	0.505534i
$893$	−9.41693e12			−0.495539
$894$	5.09167e13			2.66589
$895$	2.04557e12	+	3.54304e12i	0.106564	+	0.184575i
$896$	−2.14270e13	−	1.85592e13i	−1.11065	−	0.961995i
$897$	3.07795e13	+	3.69497e12i	1.58743	+	0.190566i
$898$	1.86029e13	−	3.22212e13i	0.954637	−	1.65348i
$899$	8.02871e11	−	1.39061e12i	0.0409946	−	0.0710048i
$900$	6.98484e13	−	1.20981e14i	3.54867	−	6.14647i
$901$	−9.16308e12	−	1.58709e13i	−0.463212	−	0.802307i
$902$	3.54242e13			1.78185
$903$	−1.02880e13	+	5.34360e13i	−0.514913	+	2.67448i
$904$	−4.03229e12	+	6.98413e12i	−0.200814	+	0.347820i
$905$	−2.25706e12	+	3.90934e12i	−0.111847	+	0.193725i
$906$	7.65919e13			3.77665
$907$	−5.06905e12	+	8.77985e12i	−0.248710	+	0.430779i	−0.963168	−	0.268900i	$-0.913340\pi$
$907$	−5.06905e12	+	8.77985e12i	−0.248710	+	0.430779i	0.714458	+	0.699678i	$0.246673\pi$
$908$	4.32662e13			2.11233
$909$	1.44487e13			0.701924
$910$	−3.71599e12	−	4.09000e12i	−0.179634	−	0.197714i
$911$	−3.73468e13			−1.79647			−0.898237	−	0.439512i	$-0.855151\pi$
$911$	−3.73468e13			−1.79647			−0.898237	+	0.439512i	$0.855151\pi$
$912$	1.42351e14			6.81371
$913$	−1.17865e13	+	2.04148e13i	−0.561392	+	0.972360i
$914$	−4.46365e13			−2.11559
$915$	1.95102e12	−	3.37927e12i	0.0920169	−	0.159378i
$916$	2.43438e13	−	4.21647e13i	1.14251	−	1.97888i
$917$	1.53416e13	−	5.31318e12i	0.716486	−	0.248137i
$918$	−1.12939e14			−5.24870
$919$	−1.96854e13	−	3.40960e13i	−0.910382	−	1.57683i	−0.813525	−	0.581529i	$-0.802455\pi$
$919$	−1.96854e13	−	3.40960e13i	−0.910382	−	1.57683i	−0.0968564	−	0.995298i	$-0.530879\pi$
$920$	−3.75360e12	+	6.50143e12i	−0.172744	+	0.299201i
$921$	9.33722e12	−	1.61725e13i	0.427611	−	0.740644i
$922$	−3.06022e12	+	5.30045e12i	−0.139464	+	0.241559i
$923$	−7.94256e12	−	9.53476e11i	−0.360208	−	0.0432417i
$924$	−1.40795e13	+	7.31296e13i	−0.635425	+	3.30042i
$925$	−4.34783e12	−	7.53067e12i	−0.195270	−	0.338217i
$926$	−6.31338e13			−2.82171
$927$	−8.54281e13			−3.79964
$928$	2.69081e13	+	4.66062e13i	1.19101	+	2.06290i
$929$	6.69414e12	+	1.15946e13i	0.294865	+	0.510722i	0.974954	−	0.222408i	$-0.0713919\pi$
$929$	6.69414e12	+	1.15946e13i	0.294865	+	0.510722i	−0.680088	+	0.733130i	$0.738059\pi$
$930$	−5.77674e11	+	1.00056e12i	−0.0253227	+	0.0438602i
$931$	−2.04821e13	+	1.61204e13i	−0.893511	+	0.703239i
$932$	4.49358e13	−	7.78311e13i	1.95084	−	3.37895i
$933$	1.22337e13			0.528556
$934$	−2.44094e13	+	4.22783e13i	−1.04953	+	1.81785i
$935$	−8.66440e11	−	1.50072e12i	−0.0370754	−	0.0642165i
$936$	−1.18096e14	+	1.57602e14i	−5.02914	+	6.71150i
$937$	4.10161e13			1.73831			0.869153	−	0.494544i	$-0.164665\pi$
$937$	4.10161e13			1.73831			0.869153	+	0.494544i	$0.164665\pi$
$938$	1.37901e13	−	4.77586e12i	0.581640	−	0.201437i
$939$	−2.58208e13	−	4.47230e13i	−1.08387	−	1.87731i
$940$	1.89930e12	+	3.28968e12i	0.0793446	+	0.137429i
$941$	1.05429e13	+	1.82609e13i	0.438338	+	0.759223i	0.997561	−	0.0697936i	$-0.0222341\pi$
$941$	1.05429e13	+	1.82609e13i	0.438338	+	0.759223i	−0.559224	+	0.829017i	$0.688901\pi$
$942$	3.83460e12			0.158668
$943$	1.40282e13	+	2.42976e13i	0.577696	+	1.00060i
$944$	1.50594e13			0.617213
$945$	−1.15445e13	+	3.99814e12i	−0.470902	+	0.163085i
$946$	2.17183e13	+	3.76172e13i	0.881689	+	1.52713i
$947$	2.61515e13			1.05663			0.528314	−	0.849049i	$-0.322824\pi$
$947$	2.61515e13			1.05663			0.528314	+	0.849049i	$0.322824\pi$
$948$	−1.68978e13	−	2.92678e13i	−0.679505	−	1.17694i
$949$	1.29928e13	−	1.73392e13i	0.520001	−	0.693953i
$950$	2.64618e13	−	4.58332e13i	1.05406	−	1.82568i
$951$	−3.30903e13	−	5.73140e13i	−1.31186	−	2.27221i
$952$	4.49765e13	+	3.89568e13i	1.77468	+	1.53715i
$953$	7.97305e10	−	1.38097e11i	0.00313117	−	0.00542335i	−0.864456	−	0.502709i	$-0.832337\pi$
$953$	7.97305e10	−	1.38097e11i	0.00313117	−	0.00542335i	0.867587	+	0.497286i	$0.165670\pi$
$954$	−8.00808e13	+	1.38704e14i	−3.13012	+	5.42152i
$955$	−3.67370e12			−0.142919
$956$	2.77952e12			0.107624
$957$	1.42716e13	−	2.47191e13i	0.550008	−	0.952641i
$958$	2.18643e13	−	3.78701e13i	0.838669	−	1.45262i
$959$	−1.62408e13	−	1.40671e13i	−0.620046	−	0.537058i
$960$	−8.22649e12	−	1.42487e13i	−0.312604	−	0.541445i
$961$	1.30950e13	−	2.26813e13i	0.495281	−	0.857852i
$962$	7.87384e12	+	1.84113e13i	0.296414	+	0.693102i
$963$	−1.43415e12	−	2.48402e12i	−0.0537374	−	0.0930760i
$964$	−1.09158e13			−0.407106
$965$	−8.96892e11	−	1.55346e12i	−0.0332941	−	0.0576671i
$966$	−7.73498e13	+	2.67882e13i	−2.85800	+	0.989798i
$967$	−2.60487e13			−0.958004			−0.479002	−	0.877814i	$-0.659001\pi$
$967$	−2.60487e13			−0.958004			−0.479002	+	0.877814i	$0.659001\pi$
$968$	−2.25930e13	−	3.91323e13i	−0.827057	−	1.43251i
$969$	−4.78789e13			−1.74456
$970$	−6.61866e10	−	1.14639e11i	−0.00240048	−	0.00415775i
$971$	−6.16732e12	−	1.06821e13i	−0.222643	−	0.385630i	0.732966	−	0.680265i	$-0.238135\pi$
$971$	−6.16732e12	−	1.06821e13i	−0.222643	−	0.385630i	−0.955610	+	0.294635i	$0.904802\pi$
$972$	1.58964e14	+	2.75334e14i	5.71216	+	9.89375i
$973$	4.39215e13	−	1.52111e13i	1.57097	−	0.544069i
$974$	2.18266e13			0.777088
$975$	2.12213e13	+	4.96216e13i	0.752058	+	1.75853i
$976$	2.90659e13	+	5.03436e13i	1.02532	+	1.77591i
$977$	−1.61599e12	+	2.79898e12i	−0.0567431	+	0.0982820i	−0.893002	−	0.450053i	$-0.851405\pi$
$977$	−1.61599e12	+	2.79898e12i	−0.0567431	+	0.0982820i	0.836259	+	0.548335i	$0.184738\pi$
$978$	−1.26033e14			−4.40515
$979$	1.46908e13	−	2.54452e13i	0.511121	−	0.885288i
$980$	9.76248e12	+	3.90382e12i	0.338098	+	0.135199i
$981$	6.90529e13	−	1.19603e14i	2.38052	−	4.12317i
$982$	5.01155e13	+	8.68026e13i	1.71977	+	2.97873i
$983$	−1.47179e13	−	2.54922e13i	−0.502754	−	0.870796i	−0.999995	−	0.00318325i	$-0.998987\pi$
$983$	−1.47179e13	−	2.54922e13i	−0.502754	−	0.870796i	0.497241	−	0.867613i	$-0.334347\pi$
$984$	−2.41702e14			−8.21867
$985$	2.29118e12			0.0775524
$986$	−1.86260e13	−	3.22612e13i	−0.627586	−	1.08701i
$987$	−4.79383e12	+	2.48993e13i	−0.160789	+	0.835143i
$988$	−5.26599e13	+	7.02758e13i	−1.75822	+	2.34639i
$989$	−1.72012e13	+	2.97933e13i	−0.571708	+	0.990227i
$990$	−7.57226e12	+	1.31155e13i	−0.250534	+	0.433938i
$991$	−1.10475e13	+	1.91348e13i	−0.363859	+	0.630222i	−0.988592	−	0.150616i	$-0.951874\pi$
$991$	−1.10475e13	+	1.91348e13i	−0.363859	+	0.630222i	0.624733	+	0.780838i	$0.285208\pi$
$992$	−4.18169e12	−	7.24289e12i	−0.137104	−	0.237470i
$993$	−1.04624e14			−3.41476
$994$	1.99599e13	−	6.91263e12i	0.648515	−	0.224597i
$995$	3.75368e11	−	6.50156e11i	0.0121410	−	0.0210287i
$996$	1.31363e14	−	2.27528e14i	4.22968	−	7.32602i
$997$	2.28800e13			0.733379			0.366690	−	0.930343i	$-0.380491\pi$
$997$	2.28800e13			0.733379			0.366690	+	0.930343i	$0.380491\pi$
$998$	2.29137e13	−	3.96877e13i	0.731152	−	1.26639i
$999$	4.42709e13			1.40628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.h.a.16.2	yes	164
7.4	even	3		91.10.g.a.81.81	yes	164
13.9	even	3		91.10.g.a.9.81	✓	164
91.74	even	3	inner	91.10.h.a.74.2	yes	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.g.a.9.81	✓	164	13.9	even	3
91.10.g.a.81.81	yes	164	7.4	even	3
91.10.h.a.16.2	yes	164	1.1	even	1	trivial
91.10.h.a.74.2	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)

\(f(q)\)	\(=\)	\(q-42.8048 q^{2} +(136.894 - 237.108i) q^{3} +1320.25 q^{4} +(98.6739 - 170.908i) q^{5} +(-5859.74 + 10149.4i) q^{6} +(4801.69 + 4159.02i) q^{7} -34597.0 q^{8} +(-27638.7 - 47871.6i) q^{9} +O(q^{10})\)	\(q-42.8048 q^{2} +(136.894 - 237.108i) q^{3} +1320.25 q^{4} +(98.6739 - 170.908i) q^{5} +(-5859.74 + 10149.4i) q^{6} +(4801.69 + 4159.02i) q^{7} -34597.0 q^{8} +(-27638.7 - 47871.6i) q^{9} +(-4223.72 + 7315.69i) q^{10} +(-16216.3 + 28087.5i) q^{11} +(180735. - 313042. i) q^{12} +(40492.4 + 94683.0i) q^{13} +(-205535. - 178026. i) q^{14} +(-27015.8 - 46792.8i) q^{15} +804951. q^{16} -270741. q^{17} +(1.18307e6 + 2.04914e6i) q^{18} +(322957. + 559378. i) q^{19} +(130274. - 225642. i) q^{20} +(1.64346e6 - 569172. i) q^{21} +(694137. - 1.20228e6i) q^{22} +1.09953e6 q^{23} +(-4.73614e6 + 8.20324e6i) q^{24} +(957089. + 1.65773e6i) q^{25} +(-1.73327e6 - 4.05289e6i) q^{26} -9.74535e6 q^{27} +(6.33943e6 + 5.49095e6i) q^{28} +(-1.60721e6 - 2.78378e6i) q^{29} +(1.15641e6 + 2.00296e6i) q^{30} +(249771. + 432616. i) q^{31} -1.67421e7 q^{32} +(4.43986e6 + 7.69006e6i) q^{33} +1.15890e7 q^{34} +(1.18461e6 - 410261. i) q^{35} +(-3.64900e7 - 6.32026e7i) q^{36} -4.54277e6 q^{37} +(-1.38241e7 - 2.39441e7i) q^{38} +(2.79933e7 + 3.36050e6i) q^{39} +(-3.41382e6 + 5.91292e6i) q^{40} +(1.27584e7 + 2.20981e7i) q^{41} +(-7.03480e7 + 2.43633e7i) q^{42} +(-1.56441e7 + 2.70964e7i) q^{43} +(-2.14096e7 + 3.70826e7i) q^{44} -1.09089e7 q^{45} -4.70652e7 q^{46} +(-7.28961e6 + 1.26260e7i) q^{47} +(1.10193e8 - 1.90860e8i) q^{48} +(5.75876e6 + 3.99406e7i) q^{49} +(-4.09680e7 - 7.09587e7i) q^{50} +(-3.70629e7 + 6.41948e7i) q^{51} +(5.34601e7 + 1.25005e8i) q^{52} +(3.38445e7 + 5.86204e7i) q^{53} +4.17148e8 q^{54} +(3.20026e6 + 5.54301e6i) q^{55} +(-1.66124e8 - 1.43890e8i) q^{56} +1.76844e8 q^{57} +(6.87964e7 + 1.19159e8i) q^{58} +1.87085e7 q^{59} +(-3.56677e7 - 6.17782e7i) q^{60} +(3.61089e7 + 6.25425e7i) q^{61} +(-1.06914e7 - 1.85181e7i) q^{62} +(6.63866e7 - 3.44814e8i) q^{63} +3.04506e8 q^{64} +(2.01776e7 + 2.42225e6i) q^{65} +(-1.90047e8 - 3.29171e8i) q^{66} +(-2.68350e7 + 4.64796e7i) q^{67} -3.57446e8 q^{68} +(1.50520e8 - 2.60708e8i) q^{69} +(-5.07070e7 + 1.75611e7i) q^{70} +(-3.88412e7 + 6.72749e7i) q^{71} +(9.56217e8 + 1.65622e9i) q^{72} +(-1.05202e8 - 1.82215e8i) q^{73} +1.94452e8 q^{74} +5.24081e8 q^{75} +(4.26385e8 + 7.38520e8i) q^{76} +(-1.94682e8 + 6.74234e7i) q^{77} +(-1.19825e9 - 1.43845e8i) q^{78} +(4.67474e7 - 8.09689e7i) q^{79} +(7.94276e7 - 1.37573e8i) q^{80} +(-7.90073e8 + 1.36845e9i) q^{81} +(-5.46119e8 - 9.45906e8i) q^{82} +7.26828e8 q^{83} +(2.16978e9 - 7.51451e8i) q^{84} +(-2.67150e7 + 4.62718e7i) q^{85} +(6.69642e8 - 1.15985e9i) q^{86} -8.80075e8 q^{87} +(5.61037e8 - 9.71745e8i) q^{88} -9.05926e8 q^{89} +4.66952e8 q^{90} +(-1.99356e8 + 6.23046e8i) q^{91} +1.45166e9 q^{92} +1.36769e8 q^{93} +(3.12030e8 - 5.40452e8i) q^{94} +1.27470e8 q^{95} +(-2.29190e9 + 3.96968e9i) q^{96} +(-7.83512e6 + 1.35708e7i) q^{97} +(-2.46503e8 - 1.70965e9i) q^{98} +1.79279e9 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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