LMFDB - Embedded newform 16.9.f.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,9,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, 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:	$6.51805776098$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	16.11
Dual form			16.9.f.a.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.4426 - 8.67733i) q^{2} +(-4.15109 - 4.15109i) q^{3} +(105.408 + 233.292i) q^{4} +(178.569 + 178.569i) q^{5} +(19.7811 + 91.8219i) q^{6} +678.560 q^{7} +(607.393 - 4050.71i) q^{8} -6526.54i q^{9} +O(q^{10})$	\(q+(-13.4426 - 8.67733i) q^{2} +(-4.15109 - 4.15109i) q^{3} +(105.408 + 233.292i) q^{4} +(178.569 + 178.569i) q^{5} +(19.7811 + 91.8219i) q^{6} +678.560 q^{7} +(607.393 - 4050.71i) q^{8} -6526.54i q^{9} +(-850.931 - 3949.93i) q^{10} +(10827.2 - 10827.2i) q^{11} +(530.858 - 1405.97i) q^{12} +(13725.9 - 13725.9i) q^{13} +(-9121.62 - 5888.09i) q^{14} -1482.51i q^{15} +(-43314.3 + 49181.7i) q^{16} +54329.7 q^{17} +(-56632.9 + 87733.7i) q^{18} +(44874.7 + 44874.7i) q^{19} +(-22836.1 + 60481.1i) q^{20} +(-2816.77 - 2816.77i) q^{21} +(-239497. + 51594.8i) q^{22} +156491. q^{23} +(-19336.2 + 14293.5i) q^{24} -326852. i q^{25} +(-303617. + 65408.0i) q^{26} +(-54327.6 + 54327.6i) q^{27} +(71525.6 + 158303. i) q^{28} +(535058. - 535058. i) q^{29} +(-12864.2 + 19928.8i) q^{30} +860087. i q^{31} +(1.00902e6 - 285278. i) q^{32} -89889.5 q^{33} +(-730333. - 471436. i) q^{34} +(121169. + 121169. i) q^{35} +(1.52259e6 - 687949. i) q^{36} +(-1.51155e6 - 1.51155e6i) q^{37} +(-213841. - 992626. i) q^{38} -113955. q^{39} +(831791. - 614869. i) q^{40} -420120. i q^{41} +(13422.7 + 62306.7i) q^{42} +(-3.94167e6 + 3.94167e6i) q^{43} +(3.66718e6 + 1.38463e6i) q^{44} +(1.16543e6 - 1.16543e6i) q^{45} +(-2.10365e6 - 1.35792e6i) q^{46} +7.69996e6i q^{47} +(383959. - 24355.8i) q^{48} -5.30436e6 q^{49} +(-2.83620e6 + 4.39374e6i) q^{50} +(-225527. - 225527. i) q^{51} +(4.64897e6 + 1.75533e6i) q^{52} +(-526972. - 526972. i) q^{53} +(1.20172e6 - 258887. i) q^{54} +3.86680e6 q^{55} +(412153. - 2.74865e6i) q^{56} -372558. i q^{57} +(-1.18355e7 + 2.54971e6i) q^{58} +(5.40369e6 - 5.40369e6i) q^{59} +(345857. - 156268. i) q^{60} +(1.64146e7 - 1.64146e7i) q^{61} +(7.46326e6 - 1.15618e7i) q^{62} -4.42865e6i q^{63} +(-1.60394e7 - 4.92075e6i) q^{64} +4.90204e6 q^{65} +(1.20835e6 + 780000. i) q^{66} +(-1.82967e7 - 1.82967e7i) q^{67} +(5.72678e6 + 1.26747e7i) q^{68} +(-649608. - 649608. i) q^{69} +(-577408. - 2.68026e6i) q^{70} +4.30921e7 q^{71} +(-2.64371e7 - 3.96417e6i) q^{72} +4.60961e7i q^{73} +(7.20299e6 + 3.34355e7i) q^{74} +(-1.35679e6 + 1.35679e6i) q^{75} +(-5.73876e6 + 1.51991e7i) q^{76} +(7.34691e6 - 7.34691e6i) q^{77} +(1.53186e6 + 988827. i) q^{78} +9.29789e6i q^{79} +(-1.65169e7 + 1.04772e6i) q^{80} -4.23696e7 q^{81} +(-3.64552e6 + 5.64751e6i) q^{82} +(-4.69383e7 - 4.69383e7i) q^{83} +(360219. - 954038. i) q^{84} +(9.70157e6 + 9.70157e6i) q^{85} +(8.71896e7 - 1.87832e7i) q^{86} -4.44215e6 q^{87} +(-3.72816e7 - 5.04343e7i) q^{88} +9.80626e7i q^{89} +(-2.57793e7 + 5.55363e6i) q^{90} +(9.31387e6 - 9.31387e6i) q^{91} +(1.64954e7 + 3.65081e7i) q^{92} +(3.57030e6 - 3.57030e6i) q^{93} +(6.68151e7 - 1.03508e8i) q^{94} +1.60264e7i q^{95} +(-5.37276e6 - 3.00434e6i) q^{96} -6.70976e7 q^{97} +(7.13044e7 + 4.60276e7i) q^{98} +(-7.06642e7 - 7.06642e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) $ 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−13.4426	−	8.67733i	−0.840164	−	0.542333i
$2$	−13.4426	−	8.67733i	−0.840164	−	0.542333i
$3$	−4.15109	−	4.15109i	−0.0512480	−	0.0512480i	0.681018	−	0.732266i	$-0.261537\pi$
$3$	−4.15109	−	4.15109i	−0.0512480	−	0.0512480i	−0.732266	+	0.681018i	$0.761537\pi$
$4$	105.408	+	233.292i	0.411750	+	0.911297i
$5$	178.569	+	178.569i	0.285710	+	0.285710i	0.835381	−	0.549671i	$-0.185247\pi$
$5$	178.569	+	178.569i	0.285710	+	0.285710i	−0.549671	+	0.835381i	$0.685247\pi$
$6$	19.7811	+	91.8219i	0.0152632	+	0.0708502i
$7$	678.560			0.282616			0.141308	−	0.989966i	$-0.454869\pi$
$7$	678.560			0.282616			0.141308	+	0.989966i	$0.454869\pi$
$8$	607.393	−	4050.71i	0.148289	−	0.988944i
$9$		−	6526.54i		−	0.994747i
$10$	−850.931	−	3949.93i	−0.0850931	−	0.394993i
$11$	10827.2	−	10827.2i	0.739513	−	0.739513i	−0.232971	−	0.972484i	$-0.574845\pi$
$11$	10827.2	−	10827.2i	0.739513	−	0.739513i	0.972484	+	0.232971i	$0.0748447\pi$
$12$	530.858	−	1405.97i	0.0256008	−	0.0678035i
$13$	13725.9	−	13725.9i	0.480583	−	0.480583i	−0.424735	−	0.905318i	$-0.639633\pi$
$13$	13725.9	−	13725.9i	0.480583	−	0.480583i	0.905318	+	0.424735i	$0.139633\pi$
$14$	−9121.62	−	5888.09i	−0.237443	−	0.153272i
$15$		−	1482.51i		−	0.0292841i
$16$	−43314.3	+	49181.7i	−0.660924	+	0.750453i
$17$	54329.7			0.650491			0.325246	−	0.945630i	$-0.394553\pi$
$17$	54329.7			0.650491			0.325246	+	0.945630i	$0.394553\pi$
$18$	−56632.9	+	87733.7i	−0.539484	+	0.835750i
$19$	44874.7	+	44874.7i	0.344340	+	0.344340i	0.857996	−	0.513656i	$-0.171709\pi$
$19$	44874.7	+	44874.7i	0.344340	+	0.344340i	−0.513656	+	0.857996i	$0.671709\pi$
$20$	−22836.1	+	60481.1i	−0.142725	+	0.378007i
$21$	−2816.77	−	2816.77i	−0.0144835	−	0.0144835i
$22$	−239497.	+	51594.8i	−1.02237	+	0.220250i
$23$	156491.			0.559214			0.279607	−	0.960115i	$-0.409796\pi$
$23$	156491.			0.559214			0.279607	+	0.960115i	$0.409796\pi$
$24$	−19336.2	+	14293.5i	−0.0582810	+	0.0430819i
$25$		−	326852.i		−	0.836740i
$26$	−303617.	+	65408.0i	−0.664404	+	0.143132i
$27$	−54327.6	+	54327.6i	−0.102227	+	0.102227i
$28$	71525.6	+	158303.i	0.116367	+	0.257547i
$29$	535058.	−	535058.i	0.756500	−	0.756500i	−0.219183	−	0.975684i	$-0.570339\pi$
$29$	535058.	−	535058.i	0.756500	−	0.756500i	0.975684	+	0.219183i	$0.0703393\pi$
$30$	−12864.2	+	19928.8i	−0.0158817	+	0.0246034i
$31$			860087.i			0.931313i	0.884965	+	0.465657i	$0.154182\pi$
$31$			860087.i			0.931313i	−0.884965	+	0.465657i	$0.845818\pi$
$32$	1.00902e6	−	285278.i	0.962280	−	0.272062i
$33$	−89889.5			−0.0757972
$34$	−730333.	−	471436.i	−0.546519	−	0.352783i
$35$	121169.	+	121169.i	0.0807460	+	0.0807460i
$36$	1.52259e6	−	687949.i	0.906510	−	0.409587i
$37$	−1.51155e6	−	1.51155e6i	−0.806523	−	0.806523i	0.177583	−	0.984106i	$-0.443172\pi$
$37$	−1.51155e6	−	1.51155e6i	−0.806523	−	0.806523i	−0.984106	+	0.177583i	$0.943172\pi$
$38$	−213841.	−	992626.i	−0.102555	−	0.476048i
$39$	−113955.			−0.0492579
$40$	831791.	−	614869.i	0.324918	−	0.240183i
$41$		−	420120.i		−	0.148675i	−0.997233	−	0.0743375i	$-0.976316\pi$
$41$		−	420120.i		−	0.148675i	0.997233	−	0.0743375i	$-0.0236842\pi$
$42$	13422.7	+	62306.7i	0.00431363	+	0.0200234i
$43$	−3.94167e6	+	3.94167e6i	−1.15294	+	1.15294i	−0.166980	+	0.985960i	$0.553402\pi$
$43$	−3.94167e6	+	3.94167e6i	−1.15294	+	1.15294i	−0.985960	+	0.166980i	$0.946598\pi$
$44$	3.66718e6	+	1.38463e6i	0.978410	+	0.369422i
$45$	1.16543e6	−	1.16543e6i	0.284209	−	0.284209i
$46$	−2.10365e6	−	1.35792e6i	−0.469831	−	0.303280i
$47$			7.69996e6i			1.57796i	0.614416	+	0.788982i	$0.289392\pi$
$47$			7.69996e6i			1.57796i	−0.614416	+	0.788982i	$0.710608\pi$
$48$	383959.	−	24355.8i	0.0723303	−	0.00458815i
$49$	−5.30436e6			−0.920128
$50$	−2.83620e6	+	4.39374e6i	−0.453792	+	0.702999i
$51$	−225527.	−	225527.i	−0.0333364	−	0.0333364i
$52$	4.64897e6	+	1.75533e6i	0.635834	+	0.240074i
$53$	−526972.	−	526972.i	−0.0667857	−	0.0667857i	0.672925	−	0.739711i	$-0.265038\pi$
$53$	−526972.	−	526972.i	−0.0667857	−	0.0667857i	−0.739711	+	0.672925i	$0.765038\pi$
$54$	1.20172e6	−	258887.i	0.141328	−	0.0304463i
$55$	3.86680e6			0.422572
$56$	412153.	−	2.74865e6i	0.0419089	−	0.279491i
$57$		−	372558.i		−	0.0352935i
$58$	−1.18355e7	+	2.54971e6i	−1.04586	+	0.225309i
$59$	5.40369e6	−	5.40369e6i	0.445946	−	0.445946i	−0.448058	−	0.894004i	$-0.647884\pi$
$59$	5.40369e6	−	5.40369e6i	0.445946	−	0.445946i	0.894004	+	0.448058i	$0.147884\pi$
$60$	345857.	−	156268.i	0.0266865	−	0.0120577i
$61$	1.64146e7	−	1.64146e7i	1.18553	−	1.18553i	0.207237	−	0.978291i	$-0.433553\pi$
$61$	1.64146e7	−	1.64146e7i	1.18553	−	1.18553i	0.978291	−	0.207237i	$-0.0664471\pi$
$62$	7.46326e6	−	1.15618e7i	0.505082	−	0.782455i
$63$		−	4.42865e6i		−	0.281131i
$64$	−1.60394e7	−	4.92075e6i	−0.956021	−	0.293300i
$65$	4.90204e6			0.274614
$66$	1.20835e6	+	780000.i	0.0636820	+	0.0411073i
$67$	−1.82967e7	−	1.82967e7i	−0.907973	−	0.907973i	0.0881354	−	0.996109i	$-0.471909\pi$
$67$	−1.82967e7	−	1.82967e7i	−0.907973	−	0.907973i	−0.996109	+	0.0881354i	$0.971909\pi$
$68$	5.72678e6	+	1.26747e7i	0.267840	+	0.592791i
$69$	−649608.	−	649608.i	−0.0286586	−	0.0286586i
$70$	−577408.	−	2.68026e6i	−0.0240486	−	0.111631i
$71$	4.30921e7			1.69576			0.847880	−	0.530188i	$-0.177879\pi$
$71$	4.30921e7			1.69576			0.847880	+	0.530188i	$0.177879\pi$
$72$	−2.64371e7	−	3.96417e6i	−0.983749	−	0.147510i
$73$			4.60961e7i			1.62320i	0.584211	+	0.811602i	$0.301404\pi$
$73$			4.60961e7i			1.62320i	−0.584211	+	0.811602i	$0.698596\pi$
$74$	7.20299e6	+	3.34355e7i	0.240207	+	1.11502i
$75$	−1.35679e6	+	1.35679e6i	−0.0428813	+	0.0428813i
$76$	−5.73876e6	+	1.51991e7i	−0.172014	+	0.455577i
$77$	7.34691e6	−	7.34691e6i	0.208998	−	0.208998i
$78$	1.53186e6	+	988827.i	0.0413847	+	0.0267142i
$79$			9.29789e6i			0.238713i	0.992851	+	0.119357i	$0.0380831\pi$
$79$			9.29789e6i			0.238713i	−0.992851	+	0.119357i	$0.961917\pi$
$80$	−1.65169e7	+	1.04772e6i	−0.403244	+	0.0255791i
$81$	−4.23696e7			−0.984269
$82$	−3.64552e6	+	5.64751e6i	−0.0806313	+	0.124911i
$83$	−4.69383e7	−	4.69383e7i	−0.989043	−	0.989043i	0.0108980	−	0.999941i	$-0.496531\pi$
$83$	−4.69383e7	−	4.69383e7i	−0.989043	−	0.989043i	−0.999941	+	0.0108980i	$0.996531\pi$
$84$	360219.	−	954038.i	0.00723519	−	0.0191623i
$85$	9.70157e6	+	9.70157e6i	0.185852	+	0.185852i
$86$	8.71896e7	−	1.87832e7i	1.59394	−	0.343381i
$87$	−4.44215e6			−0.0775383
$88$	−3.72816e7	−	5.04343e7i	−0.621675	−	0.840999i
$89$			9.80626e7i			1.56294i	0.623941	+	0.781472i	$0.285531\pi$
$89$			9.80626e7i			1.56294i	−0.623941	+	0.781472i	$0.714469\pi$
$90$	−2.57793e7	+	5.55363e6i	−0.392918	+	0.0846461i
$91$	9.31387e6	−	9.31387e6i	0.135820	−	0.135820i
$92$	1.64954e7	+	3.65081e7i	0.230256	+	0.509610i
$93$	3.57030e6	−	3.57030e6i	0.0477280	−	0.0477280i
$94$	6.68151e7	−	1.03508e8i	0.855782	−	1.32575i
$95$			1.60264e7i			0.196762i
$96$	−5.37276e6	−	3.00434e6i	−0.0632576	−	0.0353723i
$97$	−6.70976e7			−0.757914			−0.378957	−	0.925414i	$-0.623717\pi$
$97$	−6.70976e7			−0.757914			−0.378957	+	0.925414i	$0.623717\pi$
$98$	7.13044e7	+	4.60276e7i	0.773058	+	0.499016i
$99$	−7.06642e7	−	7.06642e7i	−0.735628	−	0.735628i
$100$	7.62519e7	−	3.44528e7i	0.762519	−	0.344528i
$101$	1.18901e7	+	1.18901e7i	0.114261	+	0.114261i	0.761926	−	0.647664i	$-0.224254\pi$
$101$	1.18901e7	+	1.18901e7i	0.114261	+	0.114261i	−0.647664	+	0.761926i	$0.724254\pi$
$102$	1.07470e6	+	4.98865e6i	0.00992860	+	0.0460875i
$103$	7.07595e7			0.628689			0.314344	−	0.949309i	$-0.398215\pi$
$103$	7.07595e7			0.628689			0.314344	+	0.949309i	$0.398215\pi$
$104$	−4.72628e7	−	6.39369e7i	−0.404004	−	0.546535i
$105$		−	1.00597e6i		−	0.00827615i
$106$	2.51117e6	+	1.16566e7i	0.0198908	+	0.0923310i
$107$	−3.07804e7	+	3.07804e7i	−0.234822	+	0.234822i	−0.814702	−	0.579880i	$-0.803099\pi$
$107$	−3.07804e7	+	3.07804e7i	−0.234822	+	0.234822i	0.579880	+	0.814702i	$0.303099\pi$
$108$	−1.84007e7	−	6.94763e6i	−0.135251	−	0.0510672i
$109$	5.61903e7	−	5.61903e7i	0.398067	−	0.398067i	−0.479484	−	0.877551i	$-0.659176\pi$
$109$	5.61903e7	−	5.61903e7i	0.398067	−	0.398067i	0.877551	+	0.479484i	$0.159176\pi$
$110$	−5.19799e7	−	3.35535e7i	−0.355030	−	0.229175i
$111$			1.25492e7i			0.0826655i
$112$	−2.93914e7	+	3.33727e7i	−0.186788	+	0.212090i
$113$	5.02028e7			0.307903			0.153952	−	0.988078i	$-0.450800\pi$
$113$	5.02028e7			0.307903			0.153952	+	0.988078i	$0.450800\pi$
$114$	−3.23281e6	+	5.00815e6i	−0.0191408	+	0.0296523i
$115$	2.79443e7	+	2.79443e7i	0.159773	+	0.159773i
$116$	1.81224e8	+	6.84254e7i	1.00089	+	0.377908i
$117$	−8.95828e7	−	8.95828e7i	−0.478059	−	0.478059i
$118$	−1.19529e8	+	2.57502e7i	−0.616519	+	0.132816i
$119$	3.68660e7			0.183839
$120$	−6.00522e6	−	900465.i	−0.0289603	−	0.00434252i
$121$		−	2.00980e7i		−	0.0937588i
$122$	−3.63091e8	+	7.82205e7i	−1.63899	+	0.353086i
$123$	−1.74396e6	+	1.74396e6i	−0.00761930	+	0.00761930i
$124$	−2.00652e8	+	9.06600e7i	−0.848703	+	0.383468i
$125$	1.28119e8	−	1.28119e8i	0.524774	−	0.524774i
$126$	−3.84288e7	+	5.95326e7i	−0.152467	+	0.236196i
$127$			2.51755e8i			0.967750i	0.875137	+	0.483875i	$0.160771\pi$
$127$			2.51755e8i			0.967750i	−0.875137	+	0.483875i	$0.839229\pi$
$128$	1.72912e8	+	2.05327e8i	0.644148	+	0.764901i
$129$	3.27245e7			0.118172
$130$	−6.58962e7	−	4.25366e7i	−0.230721	−	0.148932i
$131$	2.15256e8	+	2.15256e8i	0.730919	+	0.730919i	0.970802	−	0.239883i	$-0.0771090\pi$
$131$	2.15256e8	+	2.15256e8i	0.730919	+	0.730919i	−0.239883	+	0.970802i	$0.577109\pi$
$132$	−9.47506e6	−	2.09705e7i	−0.0312095	−	0.0690737i
$133$	3.04502e7	+	3.04502e7i	0.0973158	+	0.0973158i
$134$	8.71890e7	+	4.04722e8i	0.270422	+	1.25527i
$135$	−1.94024e7			−0.0584144
$136$	3.29995e7	−	2.20074e8i	0.0964609	−	0.643299i
$137$		−	4.81060e8i		−	1.36558i	−0.730615	−	0.682790i	$-0.760766\pi$
$137$		−	4.81060e8i		−	1.36558i	0.730615	−	0.682790i	$-0.239234\pi$
$138$	3.09557e6	+	1.43693e7i	0.00853541	+	0.0396204i
$139$	−4.83884e7	+	4.83884e7i	−0.129623	+	0.129623i	−0.768942	−	0.639319i	$-0.779216\pi$
$139$	−4.83884e7	+	4.83884e7i	−0.129623	+	0.129623i	0.639319	+	0.768942i	$0.279216\pi$
$140$	−1.54956e7	+	4.10401e7i	−0.0403364	+	0.106831i
$141$	3.19632e7	−	3.19632e7i	0.0808676	−	0.0808676i
$142$	−5.79271e8	−	3.73925e8i	−1.42472	−	0.919667i
$143$		−	2.97227e8i		−	0.710795i
$144$	3.20986e8	+	2.82693e8i	0.746511	+	0.657453i
$145$	1.91089e8			0.432279
$146$	3.99991e8	−	6.19653e8i	0.880317	−	1.36376i
$147$	2.20189e7	+	2.20189e7i	0.0471548	+	0.0471548i
$148$	1.93304e8	−	5.11963e8i	0.402896	−	1.06707i
$149$	−1.01648e8	−	1.01648e8i	−0.206232	−	0.206232i	0.596432	−	0.802664i	$-0.296585\pi$
$149$	−1.01648e8	−	1.01648e8i	−0.206232	−	0.206232i	−0.802664	+	0.596432i	$0.796585\pi$
$150$	3.00121e7	−	6.46550e6i	0.0592832	−	0.0127714i
$151$	−2.60553e8			−0.501173			−0.250586	−	0.968094i	$-0.580623\pi$
$151$	−2.60553e8			−0.501173			−0.250586	+	0.968094i	$0.580623\pi$
$152$	2.09031e8	−	1.54518e8i	0.391594	−	0.289471i
$153$		−	3.54585e8i		−	0.647074i
$154$	−1.62513e8	+	3.50102e7i	−0.288939	+	0.0622460i
$155$	−1.53585e8	+	1.53585e8i	−0.266085	+	0.266085i
$156$	−1.20118e7	−	2.65848e7i	−0.0202819	−	0.0448885i
$157$	−6.41838e8	+	6.41838e8i	−1.05640	+	1.05640i	−0.0580843	+	0.998312i	$0.518499\pi$
$157$	−6.41838e8	+	6.41838e8i	−1.05640	+	1.05640i	−0.998312	+	0.0580843i	$0.981501\pi$
$158$	8.06809e7	−	1.24988e8i	0.129462	−	0.200558i
$159$			4.37501e6i			0.00684528i
$160$	2.31121e8	+	1.29238e8i	0.352663	+	0.197202i
$161$	1.06188e8			0.158043
$162$	5.69558e8	+	3.67655e8i	0.826947	+	0.533802i
$163$	7.01086e8	+	7.01086e8i	0.993164	+	0.993164i	0.999977	−	0.00681276i	$-0.00216859\pi$
$163$	7.01086e8	+	7.01086e8i	0.993164	+	0.993164i	−0.00681276	+	0.999977i	$0.502169\pi$
$164$	9.80106e7	−	4.42840e7i	0.135487	−	0.0612169i
$165$	−1.60514e7	−	1.60514e7i	−0.0216560	−	0.0216560i
$166$	2.23675e8	+	1.03827e9i	0.294567	+	1.36735i
$167$	−1.27166e9			−1.63495			−0.817475	−	0.575964i	$-0.804627\pi$
$167$	−1.27166e9			−1.63495			−0.817475	+	0.575964i	$0.804627\pi$
$168$	−1.31208e7	+	9.69903e6i	−0.0164711	+	0.0121756i
$169$			4.38928e8i			0.538080i
$170$	−4.62308e7	−	2.14598e8i	−0.0553523	−	0.256939i
$171$	2.92876e8	−	2.92876e8i	0.342531	−	0.342531i
$172$	−1.33504e9	−	5.04077e8i	−1.52539	−	0.575948i
$173$	−9.00534e8	+	9.00534e8i	−1.00535	+	1.00535i	−0.00536097	+	0.999986i	$0.501706\pi$
$173$	−9.00534e8	+	9.00534e8i	−1.00535	+	1.00535i	−0.999986	+	0.00536097i	$0.998294\pi$
$174$	5.97141e7	+	3.85460e7i	0.0651449	+	0.0420516i
$175$		−	2.21788e8i		−	0.236476i
$176$	6.35268e7	+	1.00147e9i	0.0662074	+	1.04373i
$177$	−4.48624e7			−0.0457077
$178$	8.50921e8	−	1.31822e9i	0.847636	−	1.31313i
$179$	−3.52076e8	−	3.52076e8i	−0.342945	−	0.342945i	0.514528	−	0.857473i	$-0.327967\pi$
$179$	−3.52076e8	−	3.52076e8i	−0.342945	−	0.342945i	−0.857473	+	0.514528i	$0.827967\pi$
$180$	3.94732e8	+	1.49040e8i	0.376022	+	0.141976i
$181$	1.01087e9	+	1.01087e9i	0.941850	+	0.941850i	0.998400	−	0.0565495i	$-0.0180099\pi$
$181$	1.01087e9	+	1.01087e9i	0.941850	+	0.941850i	−0.0565495	+	0.998400i	$0.518010\pi$
$182$	−2.06022e8	+	4.43833e7i	−0.187771	+	0.0404514i
$183$	−1.36277e8			−0.121512
$184$	9.50515e7	−	6.33900e8i	0.0829254	−	0.553031i
$185$		−	5.39832e8i		−	0.460863i
$186$	−7.89749e7	+	1.70135e7i	−0.0659838	+	0.0142149i
$187$	5.88239e8	−	5.88239e8i	0.481047	−	0.481047i
$188$	−1.79634e9	+	8.11637e8i	−1.43799	+	0.649726i
$189$	−3.68645e7	+	3.68645e7i	−0.0288909	+	0.0288909i
$190$	1.39066e8	−	2.15437e8i	0.106711	−	0.165312i
$191$		−	2.15168e9i		−	1.61676i	−0.588664	−	0.808378i	$-0.700346\pi$
$191$		−	2.15168e9i		−	1.61676i	0.588664	−	0.808378i	$-0.299654\pi$
$192$	4.61544e7	+	8.70073e7i	0.0339631	+	0.0640252i
$193$	1.05246e9			0.758533			0.379266	−	0.925287i	$-0.376176\pi$
$193$	1.05246e9			0.758533			0.379266	+	0.925287i	$0.376176\pi$
$194$	9.01967e8	+	5.82228e8i	0.636772	+	0.411042i
$195$	−2.03488e7	−	2.03488e7i	−0.0140734	−	0.0140734i
$196$	−5.59121e8	−	1.23746e9i	−0.378863	−	0.838510i
$197$	−3.43435e8	−	3.43435e8i	−0.228024	−	0.228024i	0.583843	−	0.811867i	$-0.301548\pi$
$197$	−3.43435e8	−	3.43435e8i	−0.228024	−	0.228024i	−0.811867	+	0.583843i	$0.801548\pi$
$198$	3.36735e8	+	1.56309e9i	0.219093	+	1.01700i
$199$	1.82886e9			1.16619			0.583093	−	0.812405i	$-0.301842\pi$
$199$	1.82886e9			1.16619			0.583093	+	0.812405i	$0.301842\pi$
$200$	−1.32398e9	−	1.98527e8i	−0.827489	−	0.124080i
$201$			1.51902e8i			0.0930637i
$202$	−5.66597e7	−	2.63008e8i	−0.0340305	−	0.157966i
$203$	3.63069e8	−	3.63069e8i	0.213799	−	0.213799i
$204$	2.88414e7	−	7.63861e7i	0.0166531	−	0.0441056i
$205$	7.50202e7	−	7.50202e7i	0.0424778	−	0.0424778i
$206$	−9.51192e8	−	6.14003e8i	−0.528201	−	0.340959i
$207$		−	1.02134e9i		−	0.556276i
$208$	8.05345e7	+	1.26959e9i	0.0430258	+	0.678284i
$209$	9.71735e8			0.509287
$210$	−8.72914e6	+	1.35229e7i	−0.00448843	+	0.00695332i
$211$	1.07562e9	+	1.07562e9i	0.542662	+	0.542662i	0.924308	−	0.381647i	$-0.124643\pi$
$211$	1.07562e9	+	1.07562e9i	0.542662	+	0.542662i	−0.381647	+	0.924308i	$0.624643\pi$
$212$	6.73913e7	−	1.78485e8i	0.0333626	−	0.0883606i
$213$	−1.78879e8	−	1.78879e8i	−0.0869044	−	0.0869044i
$214$	6.80860e8	−	1.46677e8i	0.324641	−	0.0699372i
$215$	−1.40772e9			−0.658812
$216$	1.87067e8	+	2.53064e8i	0.0859375	+	0.116256i
$217$			5.83621e8i			0.263204i
$218$	−1.24293e9	+	2.67763e8i	−0.550326	+	0.118556i
$219$	1.91349e8	−	1.91349e8i	0.0831860	−	0.0831860i
$220$	4.07591e8	+	9.02093e8i	0.173994	+	0.385088i
$221$	7.45725e8	−	7.45725e8i	0.312615	−	0.312615i
$222$	1.08894e8	−	1.68694e8i	0.0448322	−	0.0694525i
$223$			2.39285e9i			0.967602i	0.875178	+	0.483801i	$0.160744\pi$
$223$			2.39285e9i			0.967602i	−0.875178	+	0.483801i	$0.839256\pi$
$224$	6.84683e8	−	1.93578e8i	0.271955	−	0.0768889i
$225$	−2.13321e9			−0.832345
$226$	−6.74857e8	−	4.35626e8i	−0.258689	−	0.166986i
$227$	−2.01769e9	−	2.01769e9i	−0.759890	−	0.759890i	0.216412	−	0.976302i	$-0.430564\pi$
$227$	−2.01769e9	−	2.01769e9i	−0.759890	−	0.759890i	−0.976302	+	0.216412i	$0.930564\pi$
$228$	8.69148e7	−	3.92705e7i	0.0321628	−	0.0145321i
$229$	5.08872e8	+	5.08872e8i	0.185041	+	0.185041i	0.793548	−	0.608508i	$-0.208231\pi$
$229$	5.08872e8	+	5.08872e8i	0.185041	+	0.185041i	−0.608508	+	0.793548i	$0.708231\pi$
$230$	−1.33163e8	−	6.18127e8i	−0.0475852	−	0.220885i
$231$	−6.09954e7			−0.0214215
$232$	−1.84238e9	−	2.49236e9i	−0.635956	−	0.860317i
$233$		−	1.34476e8i		−	0.0456269i	−0.999740	−	0.0228135i	$-0.992738\pi$
$233$		−	1.34476e8i		−	0.0456269i	0.999740	−	0.0228135i	$-0.00726238\pi$
$234$	4.26888e8	+	1.98157e9i	0.142380	+	0.660914i
$235$	−1.37497e9	+	1.37497e9i	−0.450840	+	0.450840i
$236$	1.83023e9	+	6.91046e8i	0.590008	+	0.222771i
$237$	3.85964e7	−	3.85964e7i	0.0122336	−	0.0122336i
$238$	−4.95575e8	−	3.19898e8i	−0.154455	−	0.0997020i
$239$			4.59261e9i			1.40756i	0.710416	+	0.703782i	$0.248507\pi$
$239$			4.59261e9i			1.40756i	−0.710416	+	0.703782i	$0.751493\pi$
$240$	7.29122e7	+	6.42139e7i	0.0219763	+	0.0193546i
$241$	−2.53957e9			−0.752823			−0.376411	−	0.926453i	$-0.622842\pi$
$241$	−2.53957e9			−0.752823			−0.376411	+	0.926453i	$0.622842\pi$
$242$	−1.74397e8	+	2.70170e8i	−0.0508485	+	0.0787727i
$243$	5.32323e8	+	5.32323e8i	0.152669	+	0.152669i
$244$	5.55963e9	+	2.09917e9i	1.56851	+	0.592227i
$245$	−9.47191e8	−	9.47191e8i	−0.262890	−	0.262890i
$246$	3.85762e7	−	8.31045e6i	0.0105337	−	0.00226926i
$247$	1.23189e9			0.330968
$248$	3.48397e9	+	5.22411e8i	0.921017	+	0.138104i
$249$			3.89690e8i			0.101373i
$250$	−2.83398e9	+	6.10523e8i	−0.725499	+	0.156294i
$251$	−3.33378e9	+	3.33378e9i	−0.839929	+	0.839929i	−0.988849	−	0.148920i	$-0.952420\pi$
$251$	−3.33378e9	+	3.33378e9i	−0.839929	+	0.839929i	0.148920	+	0.988849i	$0.452420\pi$
$252$	1.03317e9	−	4.66815e8i	0.256194	−	0.115756i
$253$	1.69436e9	−	1.69436e9i	0.413546	−	0.413546i
$254$	2.18456e9	−	3.38425e9i	0.524843	−	0.813069i
$255$		−	8.05442e7i		−	0.0190491i
$256$	−5.42704e8	−	4.26054e9i	−0.126358	−	0.991985i
$257$	−3.51521e7			−0.00805785			−0.00402892	−	0.999992i	$-0.501282\pi$
$257$	−3.51521e7			−0.00805785			−0.00402892	+	0.999992i	$0.501282\pi$
$258$	−4.39903e8	−	2.83961e8i	−0.0992837	−	0.0640885i
$259$	−1.02568e9	−	1.02568e9i	−0.227936	−	0.227936i
$260$	5.16714e8	+	1.14361e9i	0.113072	+	0.250255i
$261$	−3.49208e9	−	3.49208e9i	−0.752527	−	0.752527i
$262$	−1.02576e9	−	4.76144e9i	−0.217690	−	1.01049i
$263$	3.00154e9			0.627366			0.313683	−	0.949528i	$-0.398437\pi$
$263$	3.00154e9			0.627366			0.313683	+	0.949528i	$0.398437\pi$
$264$	−5.45982e7	+	3.64117e8i	−0.0112399	+	0.0749592i
$265$		−	1.88201e8i		−	0.0381626i
$266$	−1.45104e8	−	6.73556e8i	−0.0289836	−	0.134539i
$267$	4.07067e8	−	4.07067e8i	0.0800978	−	0.0800978i
$268$	2.33985e9	−	6.19708e9i	0.453575	−	1.20129i
$269$	7.15031e9	−	7.15031e9i	1.36558	−	1.36558i	0.498940	−	0.866637i	$-0.333723\pi$
$269$	7.15031e9	−	7.15031e9i	1.36558	−	1.36558i	0.866637	−	0.498940i	$-0.166277\pi$
$270$	2.60819e8	+	1.68361e8i	0.0490777	+	0.0316801i
$271$			4.20161e9i			0.779001i	0.921026	+	0.389501i	$0.127352\pi$
$271$			4.20161e9i			0.779001i	−0.921026	+	0.389501i	$0.872648\pi$
$272$	−2.35325e9	+	2.67202e9i	−0.429925	+	0.488163i
$273$	−7.73254e7			−0.0139210
$274$	−4.17432e9	+	6.46671e9i	−0.740599	+	1.14731i
$275$	−3.53889e9	−	3.53889e9i	−0.618780	−	0.618780i
$276$	8.30745e7	−	2.20022e8i	0.0143163	−	0.0379167i
$277$	−2.32439e9	−	2.32439e9i	−0.394811	−	0.394811i	0.481587	−	0.876398i	$-0.340060\pi$
$277$	−2.32439e9	−	2.32439e9i	−0.394811	−	0.394811i	−0.876398	+	0.481587i	$0.840060\pi$
$278$	1.07035e9	−	2.30585e8i	0.179203	−	0.0386057i
$279$	5.61339e9			0.926421
$280$	5.64420e8	−	4.17226e8i	0.0918270	−	0.0678795i
$281$			5.06198e9i			0.811885i	0.913899	+	0.405943i	$0.133057\pi$
$281$			5.06198e9i			0.811885i	−0.913899	+	0.405943i	$0.866943\pi$
$282$	−7.07025e8	+	1.52314e8i	−0.111799	+	0.0240848i
$283$	1.19377e9	−	1.19377e9i	0.186113	−	0.186113i	−0.607901	−	0.794013i	$-0.707988\pi$
$283$	1.19377e9	−	1.19377e9i	0.186113	−	0.186113i	0.794013	+	0.607901i	$0.207988\pi$
$284$	4.54225e9	+	1.00530e10i	0.698229	+	1.54534i
$285$	6.65271e7	−	6.65271e7i	0.0100837	−	0.0100837i
$286$	−2.57914e9	+	3.99551e9i	−0.385487	+	0.597184i
$287$		−	2.85077e8i		−	0.0420179i
$288$	−1.86187e9	−	6.58543e9i	−0.270633	−	0.957225i
$289$	−4.02404e9			−0.576861
$290$	−2.56874e9	−	1.65814e9i	−0.363185	−	0.234439i
$291$	2.78528e8	+	2.78528e8i	0.0388416	+	0.0388416i
$292$	−1.07539e10	+	4.85890e9i	−1.47922	+	0.668354i
$293$	8.21280e9	+	8.21280e9i	1.11435	+	1.11435i	0.992556	+	0.121792i	$0.0388642\pi$
$293$	8.21280e9	+	8.21280e9i	1.11435	+	1.11435i	0.121792	+	0.992556i	$0.461136\pi$
$294$	−1.04926e8	−	4.87056e8i	−0.0140441	−	0.0651913i
$295$	1.92986e9			0.254822
$296$	−7.04098e9	+	5.20477e9i	−0.917205	+	0.678007i
$297$			1.17643e9i			0.151196i
$298$	4.84384e8	+	2.24846e9i	0.0614222	+	0.285115i
$299$	2.14798e9	−	2.14798e9i	0.268749	−	0.268749i
$300$	−4.59545e8	−	1.73512e8i	−0.0567339	−	0.0214212i
$301$	−2.67466e9	+	2.67466e9i	−0.325839	+	0.325839i
$302$	3.50251e9	+	2.26090e9i	0.421067	+	0.271803i
$303$		−	9.87136e7i		−	0.0117113i
$304$	−4.15073e9	+	2.63294e8i	−0.485993	+	0.0308281i
$305$	5.86227e9			0.677433
$306$	−3.07685e9	+	4.76655e9i	−0.350930	+	0.543648i
$307$	−4.52981e9	−	4.52981e9i	−0.509948	−	0.509948i	0.404562	−	0.914510i	$-0.367424\pi$
$307$	−4.52981e9	−	4.52981e9i	−0.509948	−	0.509948i	−0.914510	+	0.404562i	$0.867424\pi$
$308$	2.48840e9	+	9.39553e8i	0.276514	+	0.104404i
$309$	−2.93729e8	−	2.93729e8i	−0.0322191	−	0.0322191i
$310$	3.39728e9	−	7.31875e8i	0.367862	−	0.0792483i
$311$	−3.43362e9			−0.367038			−0.183519	−	0.983016i	$-0.558749\pi$
$311$	−3.43362e9			−0.367038			−0.183519	+	0.983016i	$0.558749\pi$
$312$	−6.92156e7	+	4.61600e8i	−0.00730441	+	0.0487133i
$313$			1.68643e9i			0.175708i	0.996133	+	0.0878538i	$0.0280008\pi$
$313$			1.68643e9i			0.175708i	−0.996133	+	0.0878538i	$0.971999\pi$
$314$	1.41974e10	−	3.05854e9i	1.46046	−	0.314627i
$315$	7.90817e8	−	7.90817e8i	0.0803219	−	0.0803219i
$316$	−2.16912e9	+	9.80072e8i	−0.217538	+	0.0982900i
$317$	1.98043e9	−	1.98043e9i	0.196120	−	0.196120i	−0.602214	−	0.798334i	$-0.705715\pi$
$317$	1.98043e9	−	1.98043e9i	0.196120	−	0.196120i	0.798334	+	0.602214i	$0.205715\pi$
$318$	3.79634e7	−	5.88116e7i	0.00371242	−	0.00575115i
$319$		−	1.15864e10i		−	1.11888i
$320$	−1.98543e9	−	3.74282e9i	−0.189346	−	0.356943i
$321$	2.55544e8			0.0240683
$322$	−1.42745e9	−	9.21432e8i	−0.132782	−	0.0857117i
$323$	2.43803e9	+	2.43803e9i	0.223990	+	0.223990i
$324$	−4.46609e9	−	9.88448e9i	−0.405273	−	0.896962i
$325$	−4.48634e9	−	4.48634e9i	−0.402123	−	0.402123i
$326$	−3.34088e9	−	1.55080e10i	−0.295795	−	1.37305i
$327$	−4.66503e8			−0.0408003
$328$	−1.70179e9	−	2.55178e8i	−0.147031	−	0.0220469i
$329$			5.22489e9i			0.445957i
$330$	7.64897e7	+	3.55057e8i	0.00644981	+	0.0299393i
$331$	9.28588e9	−	9.28588e9i	0.773590	−	0.773590i	−0.205142	−	0.978732i	$-0.565766\pi$
$331$	9.28588e9	−	9.28588e9i	0.773590	−	0.773590i	0.978732	+	0.205142i	$0.0657655\pi$
$332$	6.00266e9	−	1.58980e10i	0.494073	−	1.30855i
$333$	−9.86521e9	+	9.86521e9i	−0.802287	+	0.802287i
$334$	1.70944e10	+	1.10346e10i	1.37363	+	0.886687i
$335$		−	6.53442e9i		−	0.518833i
$336$	2.60539e8	−	1.65269e7i	0.0204417	−	0.00129668i
$337$	−1.15121e10			−0.892558			−0.446279	−	0.894894i	$-0.647251\pi$
$337$	−1.15121e10			−0.892558			−0.446279	+	0.894894i	$0.647251\pi$
$338$	3.80873e9	−	5.90035e9i	0.291819	−	0.452075i
$339$	−2.08396e8	−	2.08396e8i	−0.0157794	−	0.0157794i
$340$	−1.24068e9	+	3.28592e9i	−0.0928416	+	0.245890i
$341$	9.31235e9	+	9.31235e9i	0.688718	+	0.688718i
$342$	−6.47841e9	+	1.39564e9i	−0.473548	+	0.102016i
$343$	−7.51109e9			−0.542658
$344$	1.35724e10	+	1.83607e10i	0.969225	+	1.31116i
$345$		−	2.31999e8i		−	0.0163761i
$346$	1.99198e10	−	4.29131e9i	1.38989	−	0.299423i
$347$	−1.30618e10	+	1.30618e10i	−0.900915	+	0.900915i	−0.995515	−	0.0946007i	$-0.969843\pi$
$347$	−1.30618e10	+	1.30618e10i	−0.900915	+	0.900915i	0.0946007	+	0.995515i	$0.469843\pi$
$348$	−4.68238e8	−	1.03632e9i	−0.0319264	−	0.0706604i
$349$	−9.13341e9	+	9.13341e9i	−0.615646	+	0.615646i	−0.944412	−	0.328765i	$-0.893367\pi$
$349$	−9.13341e9	+	9.13341e9i	−0.615646	+	0.615646i	0.328765	+	0.944412i	$0.393367\pi$
$350$	−1.92453e9	+	2.98142e9i	−0.128249	+	0.198678i
$351$			1.49139e9i			0.0982570i
$352$	7.83615e9	−	1.40137e10i	0.510425	−	0.912812i
$353$	1.58332e10			1.01969			0.509847	−	0.860265i	$-0.329702\pi$
$353$	1.58332e10			1.01969			0.509847	+	0.860265i	$0.329702\pi$
$354$	6.03069e8	+	3.89286e8i	0.0384020	+	0.0247888i
$355$	7.69490e9	+	7.69490e9i	0.484495	+	0.484495i
$356$	−2.28772e10	+	1.03366e10i	−1.42431	+	0.643541i
$357$	−1.53034e8	−	1.53034e8i	−0.00942139	−	0.00942139i
$358$	1.67774e9	+	7.78790e9i	0.102139	+	0.474120i
$359$	−1.68599e10			−1.01502			−0.507512	−	0.861645i	$-0.669435\pi$
$359$	−1.68599e10			−1.01502			−0.507512	+	0.861645i	$0.669435\pi$
$360$	−4.01296e9	−	5.42872e9i	−0.238922	−	0.323212i
$361$		−	1.29561e10i		−	0.762860i
$362$	−4.81710e9	−	2.23604e10i	−0.280512	−	1.30210i
$363$	−8.34288e7	+	8.34288e7i	−0.00480496	+	0.00480496i
$364$	3.15461e9	+	1.19110e9i	0.179697	+	0.0678486i
$365$	−8.23132e9	+	8.23132e9i	−0.463765	+	0.463765i
$366$	1.83192e9	+	1.18252e9i	0.102090	+	0.0658999i
$367$		−	4.30112e8i		−	0.0237092i	−0.999930	−	0.0118546i	$-0.996226\pi$
$367$		−	4.30112e8i		−	0.0237092i	0.999930	−	0.0118546i	$-0.00377353\pi$
$368$	−6.77830e9	+	7.69648e9i	−0.369598	+	0.419663i
$369$	−2.74193e9			−0.147894
$370$	−4.68430e9	+	7.25675e9i	−0.249941	+	0.387200i
$371$	−3.57582e8	−	3.57582e8i	−0.0188747	−	0.0188747i
$372$	1.20926e9	+	4.56585e8i	0.0631463	+	0.0238424i
$373$	−2.00789e9	−	2.00789e9i	−0.103730	−	0.103730i	0.653337	−	0.757067i	$-0.273368\pi$
$373$	−2.00789e9	−	2.00789e9i	−0.103730	−	0.103730i	−0.757067	+	0.653337i	$0.773368\pi$
$374$	−1.30118e10	+	2.80313e9i	−0.665045	+	0.143270i
$375$	−1.06366e9			−0.0537873
$376$	3.11904e10	+	4.67690e9i	1.56052	+	0.233995i
$377$		−	1.46883e10i		−	0.727122i
$378$	8.15441e8	−	1.75670e8i	0.0399416	−	0.00860460i
$379$	7.16515e9	−	7.16515e9i	0.347271	−	0.347271i	−0.511821	−	0.859092i	$-0.671029\pi$
$379$	7.16515e9	−	7.16515e9i	0.347271	−	0.347271i	0.859092	+	0.511821i	$0.171029\pi$
$380$	−3.73883e9	+	1.68931e9i	−0.179309	+	0.0810168i
$381$	1.04506e9	−	1.04506e9i	0.0495953	−	0.0495953i
$382$	−1.86708e10	+	2.89242e10i	−0.876820	+	1.35834i
$383$			4.08810e9i			0.189988i	0.995478	+	0.0949941i	$0.0302832\pi$
$383$			4.08810e9i			0.189988i	−0.995478	+	0.0949941i	$0.969717\pi$
$384$	1.34556e8	−	1.57010e9i	0.00618838	−	0.0722110i
$385$	2.62385e9			0.119425
$386$	−1.41478e10	−	9.13250e9i	−0.637292	−	0.411377i
$387$	2.57255e10	+	2.57255e10i	1.14688	+	1.14688i
$388$	−7.07261e9	−	1.56533e10i	−0.312071	−	0.690684i
$389$	−7.29821e9	−	7.29821e9i	−0.318726	−	0.318726i	0.529551	−	0.848278i	$-0.322360\pi$
$389$	−7.29821e9	−	7.29821e9i	−0.318726	−	0.318726i	−0.848278	+	0.529551i	$0.822360\pi$
$390$	9.69679e7	+	4.50114e8i	0.00419150	+	0.0194565i
$391$	8.50210e9			0.363764
$392$	−3.22183e9	+	2.14864e10i	−0.136445	+	0.909955i
$393$		−	1.78709e9i		−	0.0749163i
$394$	1.63657e9	+	7.59676e9i	0.0679124	+	0.315242i
$395$	−1.66031e9	+	1.66031e9i	−0.0682026	+	0.0682026i
$396$	9.03682e9	−	2.39340e10i	0.367481	−	0.973271i
$397$	1.06028e10	−	1.06028e10i	0.426833	−	0.426833i	−0.460715	−	0.887548i	$-0.652407\pi$
$397$	1.06028e10	−	1.06028e10i	0.426833	−	0.426833i	0.887548	+	0.460715i	$0.152407\pi$
$398$	−2.45847e10	−	1.58696e10i	−0.979788	−	0.632462i
$399$		−	2.52803e8i		−	0.00997448i
$400$	1.60751e10	+	1.41574e10i	0.627934	+	0.553022i
$401$	4.39373e10			1.69925			0.849623	−	0.527391i	$-0.176830\pi$
$401$	4.39373e10			1.69925			0.849623	+	0.527391i	$0.176830\pi$
$402$	1.31811e9	−	2.04197e9i	0.0504715	−	0.0781887i
$403$	1.18055e10	+	1.18055e10i	0.447573	+	0.447573i
$404$	−1.52055e9	+	4.02717e9i	−0.0570789	+	0.151173i
$405$	−7.56587e9	−	7.56587e9i	−0.281215	−	0.281215i
$406$	−8.03107e9	+	1.73013e9i	−0.295576	+	0.0636758i
$407$	−3.27318e10			−1.19287
$408$	−1.05053e9	+	7.76563e8i	−0.0379113	+	0.0280244i
$409$		−	5.24796e10i		−	1.87542i	−0.347425	−	0.937708i	$-0.612944\pi$
$409$		−	5.24796e10i		−	1.87542i	0.347425	−	0.937708i	$-0.387056\pi$
$410$	−1.65944e9	+	3.57493e8i	−0.0587255	+	0.0126512i
$411$	−1.99692e9	+	1.99692e9i	−0.0699833	+	0.0699833i
$412$	7.45861e9	+	1.65076e10i	0.258862	+	0.572922i
$413$	3.66673e9	−	3.66673e9i	0.126031	−	0.126031i
$414$	−8.86253e9	+	1.37295e10i	−0.301687	+	0.467363i
$415$		−	1.67634e10i		−	0.565158i
$416$	9.93409e9	−	1.77655e10i	0.331707	−	0.593204i
$417$	4.01729e8			0.0132858
$418$	−1.30627e10	−	8.43206e9i	−0.427885	−	0.276203i
$419$	−1.74286e9	−	1.74286e9i	−0.0565467	−	0.0565467i	0.678268	−	0.734815i	$-0.262731\pi$
$419$	−1.74286e9	−	1.74286e9i	−0.0565467	−	0.0565467i	−0.734815	+	0.678268i	$0.762731\pi$
$420$	2.34685e8	−	1.06037e8i	0.00754203	−	0.00340770i
$421$	7.46104e9	+	7.46104e9i	0.237504	+	0.237504i	0.815816	−	0.578312i	$-0.196288\pi$
$421$	7.46104e9	+	7.46104e9i	0.237504	+	0.237504i	−0.578312	+	0.815816i	$0.696288\pi$
$422$	−5.12564e9	−	2.37927e10i	−0.161621	−	0.750228i
$423$	5.02541e10			1.56968
$424$	−2.45469e9	+	1.81453e9i	−0.0759510	+	0.0561437i
$425$		−	1.77577e10i		−	0.544292i
$426$	8.52412e8	+	3.95680e9i	0.0258828	+	0.120145i
$427$	1.11383e10	−	1.11383e10i	0.335049	−	0.335049i
$428$	−1.04253e10	−	3.93632e9i	−0.310680	−	0.117305i
$429$	−1.23382e9	+	1.23382e9i	−0.0364268	+	0.0364268i
$430$	1.89234e10	+	1.22152e10i	0.553510	+	0.357296i
$431$			2.14187e10i			0.620704i	0.950622	+	0.310352i	$0.100447\pi$
$431$			2.14187e10i			0.620704i	−0.950622	+	0.310352i	$0.899553\pi$
$432$	−3.18758e8	−	5.02508e9i	−0.00915220	−	0.144281i
$433$	−4.12749e10			−1.17418			−0.587090	−	0.809522i	$-0.699726\pi$
$433$	−4.12749e10			−1.17418			−0.587090	+	0.809522i	$0.699726\pi$
$434$	5.06427e9	−	7.84539e9i	0.142744	−	0.221134i
$435$	−7.93228e8	−	7.93228e8i	−0.0221534	−	0.0221534i
$436$	1.90317e10	+	7.18585e9i	0.526661	+	0.198853i
$437$	7.02248e9	+	7.02248e9i	0.192559	+	0.192559i
$438$	−4.23263e9	+	9.11834e8i	−0.115004	+	0.0247753i
$439$	−4.91495e10			−1.32331			−0.661654	−	0.749809i	$-0.730145\pi$
$439$	−4.91495e10			−1.32331			−0.661654	+	0.749809i	$0.730145\pi$
$440$	2.34867e9	−	1.56633e10i	0.0626629	−	0.417900i
$441$			3.46191e10i			0.915295i
$442$	−1.64954e10	+	3.55360e9i	−0.432189	+	0.0931063i
$443$	−2.76039e10	+	2.76039e10i	−0.716731	+	0.716731i	−0.967934	−	0.251203i	$-0.919174\pi$
$443$	−2.76039e10	+	2.76039e10i	−0.716731	+	0.716731i	0.251203	+	0.967934i	$0.419174\pi$
$444$	−2.92763e9	+	1.32279e9i	−0.0753328	+	0.0340375i
$445$	−1.75109e10	+	1.75109e10i	−0.446548	+	0.446548i
$446$	2.07636e10	−	3.21662e10i	0.524763	−	0.812944i
$447$			8.43904e8i			0.0211380i
$448$	−1.08837e10	−	3.33903e9i	−0.270186	−	0.0828911i
$449$	−1.10940e10			−0.272962			−0.136481	−	0.990643i	$-0.543579\pi$
$449$	−1.10940e10			−0.272962			−0.136481	+	0.990643i	$0.543579\pi$
$450$	2.86759e10	+	1.85106e10i	0.699306	+	0.451408i
$451$	−4.54872e9	−	4.54872e9i	−0.109947	−	0.109947i
$452$	5.29177e9	+	1.17119e10i	0.126779	+	0.280591i
$453$	1.08158e9	+	1.08158e9i	0.0256841	+	0.0256841i
$454$	9.61487e9	+	4.46311e10i	0.226318	+	1.05054i
$455$	3.32633e9			0.0776103
$456$	−1.50913e9	−	2.26289e8i	−0.0349033	−	0.00523364i
$457$			4.18321e10i			0.959059i	0.877526	+	0.479529i	$0.159193\pi$
$457$			4.18321e10i			0.959059i	−0.877526	+	0.479529i	$0.840807\pi$
$458$	−2.42492e9	−	1.12562e10i	−0.0551107	−	0.255818i
$459$	−2.95160e9	+	2.95160e9i	−0.0664977	+	0.0664977i
$460$	−3.57364e9	+	9.46475e9i	−0.0798140	+	0.211387i
$461$	9.08702e9	−	9.08702e9i	0.201195	−	0.201195i	−0.599317	−	0.800512i	$-0.704561\pi$
$461$	9.08702e9	−	9.08702e9i	0.201195	−	0.201195i	0.800512	+	0.599317i	$0.204561\pi$
$462$	8.19938e8	+	5.29277e8i	0.0179975	+	0.0116176i
$463$			7.06745e10i			1.53794i	0.639286	+	0.768969i	$0.279230\pi$
$463$			7.06745e10i			1.53794i	−0.639286	+	0.768969i	$0.720770\pi$
$464$	3.13936e9	+	4.94908e10i	0.0677282	+	1.06771i
$465$	1.27509e9			0.0272727
$466$	−1.16689e9	+	1.80771e9i	−0.0247450	+	0.0383341i
$467$	−4.37255e10	−	4.37255e10i	−0.919320	−	0.919320i	0.0776598	−	0.996980i	$-0.475255\pi$
$467$	−4.37255e10	−	4.37255e10i	−0.919320	−	0.919320i	−0.996980	+	0.0776598i	$0.975255\pi$
$468$	1.14562e10	−	3.03417e10i	0.238813	−	0.632494i
$469$	−1.24154e10	−	1.24154e10i	−0.256607	−	0.256607i
$470$	3.04143e10	−	6.55213e9i	0.623284	−	0.134274i
$471$	5.32866e9			0.108276
$472$	−1.86066e10	−	2.51710e10i	−0.374887	−	0.507145i
$473$			8.53546e10i			1.70523i
$474$	−8.53750e8	+	1.83923e8i	−0.0169129	+	0.00364353i
$475$	1.46674e10	−	1.46674e10i	0.288123	−	0.288123i
$476$	3.88596e9	+	8.60053e9i	0.0756957	+	0.167532i
$477$	−3.43930e9	+	3.43930e9i	−0.0664349	+	0.0664349i
$478$	3.98516e10	−	6.17367e10i	0.763368	−	1.18258i
$479$		−	9.89699e10i		−	1.88001i	−0.341156	−	0.940007i	$-0.610818\pi$
$479$		−	9.89699e10i		−	1.88001i	0.341156	−	0.940007i	$-0.389182\pi$
$480$	−4.22926e8	−	1.49589e9i	−0.00796709	−	0.0281795i
$481$	−4.14950e10			−0.775203
$482$	3.41385e10	+	2.20367e10i	0.632494	+	0.408281i
$483$	−4.40798e8	−	4.40798e8i	−0.00809937	−	0.00809937i
$484$	4.68871e9	−	2.11849e9i	0.0854421	−	0.0386052i
$485$	−1.19815e10	−	1.19815e10i	−0.216543	−	0.216543i
$486$	−2.53667e9	−	1.17750e10i	−0.0454694	−	0.211064i
$487$	8.02107e10			1.42599			0.712995	−	0.701169i	$-0.247338\pi$
$487$	8.02107e10			1.42599			0.712995	+	0.701169i	$0.247338\pi$
$488$	−5.65208e10	−	7.64611e10i	−0.996620	−	1.34822i
$489$		−	5.82055e9i		−	0.101795i
$490$	4.51364e9	+	2.09518e10i	0.0782965	+	0.363444i
$491$	−2.27057e9	+	2.27057e9i	−0.0390669	+	0.0390669i	−0.726370	−	0.687303i	$-0.758794\pi$
$491$	−2.27057e9	+	2.27057e9i	−0.0390669	+	0.0390669i	0.687303	+	0.726370i	$0.258794\pi$
$492$	−5.90678e8	−	2.23024e8i	−0.0100807	−	0.00380620i
$493$	2.90695e10	−	2.90695e10i	0.492097	−	0.492097i
$494$	−1.65599e10	−	1.06895e10i	−0.278067	−	0.179495i
$495$		−	2.52368e10i		−	0.420352i
$496$	−4.23005e10	−	3.72541e10i	−0.698906	−	0.615528i
$497$	2.92406e10			0.479248
$498$	3.38147e9	−	5.23846e9i	0.0549779	−	0.0851699i
$499$	−7.93375e10	−	7.93375e10i	−1.27961	−	1.27961i	−0.940887	−	0.338719i	$-0.890006\pi$
$499$	−7.93375e10	−	7.93375e10i	−1.27961	−	1.27961i	−0.338719	−	0.940887i	$-0.609994\pi$
$500$	4.33938e10	+	1.63843e10i	0.694301	+	0.262150i
$501$	5.27877e9	+	5.27877e9i	0.0837880	+	0.0837880i
$502$	7.37431e10	−	1.58864e10i	1.16120	−	0.250157i
$503$	3.58098e10			0.559410			0.279705	−	0.960086i	$-0.409763\pi$
$503$	3.58098e10			0.559410			0.279705	+	0.960086i	$0.409763\pi$
$504$	−1.79392e10	−	2.68993e9i	−0.278023	−	0.0416887i
$505$			4.24639e9i			0.0652911i
$506$	−3.74791e10	+	8.07411e9i	−0.571726	+	0.123167i
$507$	1.82203e9	−	1.82203e9i	0.0275755	−	0.0275755i
$508$	−5.87325e10	+	2.65370e10i	−0.881908	+	0.398471i
$509$	3.59639e10	−	3.59639e10i	0.535791	−	0.535791i	−0.386499	−	0.922290i	$-0.626316\pi$
$509$	3.59639e10	−	3.59639e10i	0.535791	−	0.535791i	0.922290	+	0.386499i	$0.126316\pi$
$510$	−6.98908e8	+	1.08272e9i	−0.0103309	+	0.0160043i
$511$			3.12790e10i			0.458743i
$512$	−2.96748e10	+	6.19821e10i	−0.431825	+	0.901958i
$513$	−4.87586e9			−0.0704015
$514$	4.72537e8	+	3.05027e8i	0.00676991	+	0.00437004i
$515$	1.26354e10	+	1.26354e10i	0.179622	+	0.179622i
$516$	3.44942e9	+	7.63436e9i	0.0486572	+	0.107690i
$517$	8.33691e10	+	8.33691e10i	1.16693	+	1.16693i
$518$	4.88766e9	+	2.26880e10i	0.0678863	+	0.315121i
$519$	7.47640e9			0.103044
$520$	2.97746e9	−	1.98568e10i	0.0407224	−	0.271578i
$521$			4.61839e10i			0.626815i	0.949619	+	0.313408i	$0.101471\pi$
$521$			4.61839e10i			0.626815i	−0.949619	+	0.313408i	$0.898529\pi$
$522$	1.66408e10	+	7.72446e10i	0.224125	+	1.04037i
$523$	8.94782e10	−	8.94782e10i	1.19594	−	1.19594i	0.220572	−	0.975371i	$-0.429207\pi$
$523$	8.94782e10	−	8.94782e10i	1.19594	−	1.19594i	0.975371	−	0.220572i	$-0.0707925\pi$
$524$	−2.75278e10	+	7.29071e10i	−0.365129	+	0.967040i
$525$	−9.20664e8	+	9.20664e8i	−0.0121189	+	0.0121189i
$526$	−4.03485e10	−	2.60453e10i	−0.527090	−	0.340241i
$527$			4.67283e10i			0.605811i
$528$	3.89350e9	−	4.42091e9i	0.0500962	−	0.0568822i
$529$	−5.38216e10			−0.687280
$530$	−1.63308e9	+	2.52991e9i	−0.0206969	+	0.0320629i
$531$	−3.52674e10	−	3.52674e10i	−0.443604	−	0.443604i
$532$	−3.89409e9	+	1.03135e10i	−0.0486138	+	0.128753i
$533$	−5.76653e9	−	5.76653e9i	−0.0714506	−	0.0714506i
$534$	−9.00429e9	+	1.93979e9i	−0.110735	+	0.0238556i
$535$	−1.09928e10			−0.134182
$536$	−8.52279e10	+	6.30013e10i	−1.03258	+	0.763292i
$537$			2.92300e9i			0.0351505i
$538$	−1.58165e11	+	3.40733e10i	−1.88790	+	0.406710i
$539$	−5.74314e10	+	5.74314e10i	−0.680447	+	0.680447i
$540$	−2.04517e9	−	4.52642e9i	−0.0240521	−	0.0532329i
$541$	3.59861e10	−	3.59861e10i	0.420093	−	0.420093i	−0.465143	−	0.885236i	$-0.653997\pi$
$541$	3.59861e10	−	3.59861e10i	0.420093	−	0.420093i	0.885236	+	0.465143i	$0.153997\pi$
$542$	3.64587e10	−	5.64806e10i	0.422478	−	0.654488i
$543$		−	8.39244e9i		−	0.0965360i
$544$	5.48199e10	−	1.54990e10i	0.625954	−	0.176974i
$545$	2.00677e10			0.227463
$546$	1.03946e9	+	6.70978e8i	0.0116960	+	0.00754984i
$547$	5.06362e10	+	5.06362e10i	0.565603	+	0.565603i	0.930894	−	0.365291i	$-0.119030\pi$
$547$	5.06362e10	+	5.06362e10i	0.565603	+	0.565603i	−0.365291	+	0.930894i	$0.619030\pi$
$548$	1.12228e11	−	5.07076e10i	1.24445	−	0.562277i
$549$	−1.07131e11	−	1.07131e11i	−1.17930	−	1.17930i
$550$	1.68638e10	+	7.82801e10i	0.184292	+	0.855461i
$551$	4.80211e10			0.520986
$552$	−3.02594e9	+	2.23681e9i	−0.0325915	+	0.0240920i
$553$			6.30918e9i			0.0674640i
$554$	1.10764e10	+	5.14153e10i	0.117587	+	0.545825i
$555$	−2.24089e9	+	2.24089e9i	−0.0236183	+	0.0236183i
$556$	−1.63891e10	−	6.18811e9i	−0.171497	−	0.0647528i
$557$	1.31189e10	−	1.31189e10i	0.136294	−	0.136294i	−0.635668	−	0.771962i	$-0.719275\pi$
$557$	1.31189e10	−	1.31189e10i	0.136294	−	0.136294i	0.771962	+	0.635668i	$0.219275\pi$
$558$	−7.54587e10	−	4.87092e10i	−0.778345	−	0.502429i
$559$			1.08206e11i			1.10817i
$560$	−1.12077e10	+	7.10941e8i	−0.113963	+	0.00722905i
$561$	−4.88367e9			−0.0493054
$562$	4.39244e10	−	6.80462e10i	0.440312	−	0.682117i
$563$	1.39489e10	+	1.39489e10i	0.138837	+	0.138837i	0.773110	−	0.634272i	$-0.218700\pi$
$563$	1.39489e10	+	1.39489e10i	0.138837	+	0.138837i	−0.634272	+	0.773110i	$0.718700\pi$
$564$	1.08260e10	+	4.08759e9i	0.106992	+	0.0403972i
$565$	8.96464e9	+	8.96464e9i	0.0879709	+	0.0879709i
$566$	−2.64062e10	+	5.68867e9i	−0.257300	+	0.0554300i
$567$	−2.87503e10			−0.278170
$568$	2.61739e10	−	1.74554e11i	0.251463	−	1.67701i
$569$		−	8.39272e10i		−	0.800670i	−0.916369	−	0.400335i	$-0.868894\pi$
$569$		−	8.39272e10i		−	0.800670i	0.916369	−	0.400335i	$-0.131106\pi$
$570$	−1.47158e9	+	3.17021e8i	−0.0139407	+	0.00300323i
$571$	−9.90663e10	+	9.90663e10i	−0.931926	+	0.931926i	−0.997826	−	0.0659001i	$-0.979008\pi$
$571$	−9.90663e10	+	9.90663e10i	−0.931926	+	0.931926i	0.0659001	+	0.997826i	$0.479008\pi$
$572$	6.93407e10	−	3.13301e10i	0.647745	−	0.292670i
$573$	−8.93182e9	+	8.93182e9i	−0.0828556	+	0.0828556i
$574$	−2.47370e9	+	3.83217e9i	−0.0227877	+	0.0353019i
$575$		−	5.11493e10i		−	0.467916i
$576$	−3.21155e10	+	1.04681e11i	−0.291759	+	0.950999i
$577$	4.80099e10			0.433139			0.216570	−	0.976267i	$-0.430513\pi$
$577$	4.80099e10			0.433139			0.216570	+	0.976267i	$0.430513\pi$
$578$	5.40937e10	+	3.49180e10i	0.484658	+	0.312851i
$579$	−4.36884e9	−	4.36884e9i	−0.0388733	−	0.0388733i
$580$	2.01423e10	+	4.45796e10i	0.177991	+	0.393934i
$581$	−3.18505e10	−	3.18505e10i	−0.279519	−	0.279519i
$582$	−1.32727e9	−	6.16103e9i	−0.0115682	−	0.0536984i
$583$	−1.14113e10			−0.0987778
$584$	1.86722e11	+	2.79985e10i	1.60526	+	0.240704i
$585$		−	3.19933e10i		−	0.273172i
$586$	−3.91364e10	−	1.81667e11i	−0.331887	−	1.54058i
$587$	2.73385e10	−	2.73385e10i	0.230262	−	0.230262i	−0.582540	−	0.812802i	$-0.697941\pi$
$587$	2.73385e10	−	2.73385e10i	0.230262	−	0.230262i	0.812802	+	0.582540i	$0.197941\pi$
$588$	−2.81586e9	+	7.45779e9i	−0.0235560	+	0.0623880i
$589$	−3.85961e10	+	3.85961e10i	−0.320688	+	0.320688i
$590$	−2.59423e10	−	1.67460e10i	−0.214092	−	0.138199i
$591$			2.85126e9i			0.0233715i
$592$	1.39813e11	−	8.86878e9i	1.13831	−	0.0722067i
$593$	−2.71697e10			−0.219718			−0.109859	−	0.993947i	$-0.535040\pi$
$593$	−2.71697e10			−0.219718			−0.109859	+	0.993947i	$0.535040\pi$
$594$	1.02083e10	−	1.58143e10i	0.0819987	−	0.127030i
$595$	6.58310e9	+	6.58310e9i	0.0525246	+	0.0525246i
$596$	1.29992e10	−	3.44283e10i	0.103023	−	0.272854i
$597$	−7.59176e9	−	7.59176e9i	−0.0597648	−	0.0597648i
$598$	−4.75133e10	+	1.02358e10i	−0.371544	+	0.0800415i
$599$	−9.11423e10			−0.707966			−0.353983	−	0.935252i	$-0.615173\pi$
$599$	−9.11423e10			−0.707966			−0.353983	+	0.935252i	$0.615173\pi$
$600$	4.67187e9	+	6.32008e9i	0.0360484	+	0.0487660i
$601$		−	6.40542e10i		−	0.490964i	−0.969401	−	0.245482i	$-0.921054\pi$
$601$		−	6.40542e10i		−	0.490964i	0.969401	−	0.245482i	$-0.0789462\pi$
$602$	5.91634e10	−	1.27455e10i	0.450471	−	0.0970448i
$603$	−1.19414e11	+	1.19414e11i	−0.903204	+	0.903204i
$604$	−2.74643e10	−	6.07848e10i	−0.206358	−	0.456717i
$605$	3.58888e9	−	3.58888e9i	0.0267878	−	0.0267878i
$606$	−8.56570e8	+	1.32697e9i	−0.00635145	+	0.00983944i
$607$			6.38127e10i			0.470059i	0.971988	+	0.235029i	$0.0755186\pi$
$607$			6.38127e10i			0.470059i	−0.971988	+	0.235029i	$0.924481\pi$
$608$	5.80813e10	+	3.24779e10i	0.425033	+	0.237669i
$609$	−3.01427e9			−0.0219135
$610$	−7.88043e10	−	5.08689e10i	−0.569155	−	0.367394i
$611$	1.05689e11	+	1.05689e11i	0.758343	+	0.758343i
$612$	8.27218e10	−	3.73760e10i	0.589677	−	0.266433i
$613$	7.80041e10	+	7.80041e10i	0.552428	+	0.552428i	0.927141	−	0.374713i	$-0.122259\pi$
$613$	7.80041e10	+	7.80041e10i	0.552428	+	0.552428i	−0.374713	+	0.927141i	$0.622259\pi$
$614$	2.15858e10	+	1.00199e11i	0.151878	+	0.705002i
$615$	−6.22831e8			−0.00435381
$616$	−2.52978e10	−	3.42227e10i	−0.175695	−	0.237679i
$617$		−	6.99146e10i		−	0.482422i	−0.970473	−	0.241211i	$-0.922455\pi$
$617$		−	6.99146e10i		−	0.482422i	0.970473	−	0.241211i	$-0.0775446\pi$
$618$	1.39970e9	+	6.49727e9i	0.00959582	+	0.0445427i
$619$	1.59428e11	−	1.59428e11i	1.08593	−	1.08593i	0.0899908	−	0.995943i	$-0.471316\pi$
$619$	1.59428e11	−	1.59428e11i	1.08593	−	1.08593i	0.995943	−	0.0899908i	$-0.0286838\pi$
$620$	−5.20191e10	−	1.96410e10i	−0.352043	−	0.132922i
$621$	−8.50177e9	+	8.50177e9i	−0.0571667	+	0.0571667i
$622$	4.61568e10	+	2.97946e10i	0.308372	+	0.199057i
$623$			6.65413e10i			0.441712i
$624$	4.93589e9	−	5.60451e9i	0.0325557	−	0.0369657i
$625$	−8.19205e10			−0.536874
$626$	1.46337e10	−	2.26700e10i	0.0952920	−	0.147623i
$627$	−4.03376e9	−	4.03376e9i	−0.0261000	−	0.0261000i
$628$	−2.17390e11	−	8.20809e10i	−1.39766	−	0.527720i
$629$	−8.21222e10	−	8.21222e10i	−0.524636	−	0.524636i
$630$	−1.74928e10	+	3.76847e9i	−0.111045	+	0.0239223i
$631$	−2.73276e11			−1.72379			−0.861895	−	0.507086i	$-0.830723\pi$
$631$	−2.73276e11			−1.72379			−0.861895	+	0.507086i	$0.830723\pi$
$632$	3.76631e10	+	5.64747e9i	0.236074	+	0.0353986i
$633$		−	8.92999e9i		−	0.0556207i
$634$	−4.38070e10	+	9.43731e9i	−0.271135	+	0.0584106i
$635$	−4.49555e10	+	4.49555e10i	−0.276496	+	0.276496i
$636$	−1.02066e9	+	4.61161e8i	−0.00623808	+	0.00281854i
$637$	−7.28072e10	+	7.28072e10i	−0.442198	+	0.442198i
$638$	−1.00539e11	+	1.55751e11i	−0.606808	+	0.940045i
$639$		−	2.81242e11i		−	1.68685i
$640$	−5.78822e9	+	6.75415e10i	−0.0345005	+	0.402579i
$641$	1.45498e11			0.861836			0.430918	−	0.902391i	$-0.358190\pi$
$641$	1.45498e11			0.861836			0.430918	+	0.902391i	$0.358190\pi$
$642$	−3.43518e9	−	2.21744e9i	−0.0202213	−	0.0130531i
$643$	2.10255e11	+	2.10255e11i	1.22999	+	1.22999i	0.963965	+	0.266030i	$0.0857119\pi$
$643$	2.10255e11	+	2.10255e11i	1.22999	+	1.22999i	0.266030	+	0.963965i	$0.414288\pi$
$644$	1.11931e10	+	2.47729e10i	0.0650740	+	0.144024i
$645$	5.84356e9	+	5.84356e9i	0.0337628	+	0.0337628i
$646$	−1.16179e10	−	5.39290e10i	−0.0667110	−	0.309665i
$647$	1.62249e11			0.925903			0.462951	−	0.886384i	$-0.346790\pi$
$647$	1.62249e11			0.925903			0.462951	+	0.886384i	$0.346790\pi$
$648$	−2.57350e10	+	1.71627e11i	−0.145957	+	0.973387i
$649$		−	1.17014e11i		−	0.659566i
$650$	2.13787e10	+	9.92376e10i	0.119765	+	0.555934i
$651$	2.42266e9	−	2.42266e9i	0.0134887	−	0.0134887i
$652$	−8.96578e10	+	2.37458e11i	−0.496132	+	1.31400i
$653$	−1.94136e11	+	1.94136e11i	−1.06771	+	1.06771i	−0.0701735	+	0.997535i	$0.522355\pi$
$653$	−1.94136e11	+	1.94136e11i	−1.06771	+	1.06771i	−0.997535	+	0.0701735i	$0.977645\pi$
$654$	6.27101e9	+	4.04800e9i	0.0342789	+	0.0221273i
$655$			7.68758e10i			0.417661i
$656$	2.06622e10	+	1.81972e10i	0.111573	+	0.0982629i
$657$	3.00848e11			1.61468
$658$	4.53381e10	−	7.02362e10i	0.241857	−	0.374677i
$659$	−6.94908e10	−	6.94908e10i	−0.368456	−	0.368456i	0.498458	−	0.866914i	$-0.333900\pi$
$659$	−6.94908e10	−	6.94908e10i	−0.368456	−	0.368456i	−0.866914	+	0.498458i	$0.833900\pi$
$660$	2.05272e9	−	5.43662e9i	0.0108182	−	0.0286519i
$661$	2.27327e11	+	2.27327e11i	1.19082	+	1.19082i	0.976839	+	0.213976i	$0.0686416\pi$
$661$	2.27327e11	+	2.27327e11i	1.19082	+	1.19082i	0.213976	+	0.976839i	$0.431358\pi$
$662$	−2.05403e11	+	4.42499e10i	−1.06949	+	0.230399i
$663$	−6.19115e9			−0.0320418
$664$	−2.18644e11	+	1.61624e11i	−1.12477	+	0.831443i
$665$			1.08749e10i			0.0556081i
$666$	2.18218e11	−	4.70106e10i	1.10916	−	0.238945i
$667$	8.37318e10	−	8.37318e10i	0.423045	−	0.423045i
$668$	−1.34043e11	−	2.96668e11i	−0.673190	−	1.48992i
$669$	9.93296e9	−	9.93296e9i	0.0495877	−	0.0495877i
$670$	−5.67013e10	+	8.78397e10i	−0.281380	+	0.435905i
$671$		−	3.55449e11i		−	1.75343i
$672$	−3.64574e9	−	2.03862e9i	−0.0178776	−	0.00999677i
$673$	−7.78148e10			−0.379317			−0.189658	−	0.981850i	$-0.560738\pi$
$673$	−7.78148e10			−0.379317			−0.189658	+	0.981850i	$0.560738\pi$
$674$	1.54753e11	+	9.98946e10i	0.749895	+	0.484064i
$675$	1.77570e10	+	1.77570e10i	0.0855373	+	0.0855373i
$676$	−1.02398e11	+	4.62665e10i	−0.490351	+	0.221554i
$677$	−6.62929e10	−	6.62929e10i	−0.315582	−	0.315582i	0.531485	−	0.847068i	$-0.321634\pi$
$677$	−6.62929e10	−	6.62929e10i	−0.315582	−	0.315582i	−0.847068	+	0.531485i	$0.821634\pi$
$678$	9.93069e8	+	4.60972e9i	0.00469960	+	0.0218150i
$679$	−4.55297e10			−0.214198
$680$	4.51910e10	−	3.34056e10i	0.211357	−	0.156237i
$681$			1.67512e10i			0.0778857i
$682$	−4.43760e10	−	2.05989e11i	−0.205121	−	0.952151i
$683$	2.16613e11	−	2.16613e11i	0.995411	−	0.995411i	−0.00457872	−	0.999990i	$-0.501457\pi$
$683$	2.16613e11	−	2.16613e11i	0.995411	−	0.995411i	0.999990	+	0.00457872i	$0.00145746\pi$
$684$	9.91972e10	+	3.74542e10i	0.453184	+	0.171110i
$685$	8.59022e10	−	8.59022e10i	0.390159	−	0.390159i
$686$	1.00969e11	+	6.51762e10i	0.455922	+	0.294302i
$687$		−	4.22475e9i		−	0.0189659i
$688$	−2.31271e10	−	3.64589e11i	−0.103221	−	1.62723i
$689$	−1.44663e10			−0.0641922
$690$	−2.01313e9	+	3.11867e9i	−0.00888129	+	0.0137586i
$691$	−1.17927e11	−	1.17927e11i	−0.517251	−	0.517251i	0.399487	−	0.916739i	$-0.369188\pi$
$691$	−1.17927e11	−	1.17927e11i	−0.517251	−	0.517251i	−0.916739	+	0.399487i	$0.869188\pi$
$692$	−3.05011e11	−	1.15164e11i	−1.33012	−	0.502218i
$693$	−4.79499e10	−	4.79499e10i	−0.207900	−	0.207900i
$694$	2.88925e11	−	6.22430e10i	1.24551	−	0.268320i
$695$	−1.72813e10			−0.0740691
$696$	−2.69813e9	+	1.79939e10i	−0.0114981	+	0.0766811i
$697$		−	2.28250e10i		−	0.0967117i
$698$	2.02030e11	−	4.35233e10i	0.851129	−	0.183358i
$699$	−5.58222e8	+	5.58222e8i	−0.00233829	+	0.00233829i
$700$	5.17415e10	−	2.33783e10i	0.215500	−	0.0973689i
$701$	−1.50464e11	+	1.50464e11i	−0.623104	+	0.623104i	−0.946324	−	0.323220i	$-0.895235\pi$
$701$	−1.50464e11	+	1.50464e11i	−0.623104	+	0.623104i	0.323220	+	0.946324i	$0.395235\pi$
$702$	1.29413e10	−	2.00482e10i	0.0532880	−	0.0825520i
$703$		−	1.35661e11i		−	0.555436i
$704$	−2.26940e11	+	1.20384e11i	−0.923888	+	0.490091i
$705$	1.14153e10			0.0462093
$706$	−2.12840e11	−	1.37390e11i	−0.856710	−	0.553014i
$707$	8.06814e9	+	8.06814e9i	0.0322920	+	0.0322920i
$708$	−4.72886e9	−	1.04660e10i	−0.0188202	−	0.0416533i
$709$	2.06291e11	+	2.06291e11i	0.816386	+	0.816386i	0.985582	−	0.169197i	$-0.0541173\pi$
$709$	2.06291e11	+	2.06291e11i	0.816386	+	0.816386i	−0.169197	+	0.985582i	$0.554117\pi$
$710$	−3.66684e10	−	1.70211e11i	−0.144297	−	0.669813i
$711$	6.06830e10			0.237459
$712$	3.97223e11	+	5.95625e10i	1.54566	+	0.231768i
$713$			1.34596e11i			0.520803i
$714$	7.29251e8	+	3.38510e9i	0.00280598	+	0.0130250i
$715$	5.30754e10	−	5.30754e10i	0.203081	−	0.203081i
$716$	4.50249e10	−	1.19248e11i	0.171317	−	0.453732i
$717$	1.90643e10	−	1.90643e10i	0.0721349	−	0.0721349i
$718$	2.26641e11	+	1.46299e11i	0.852786	+	0.550481i
$719$			1.31229e11i			0.491036i	0.969392	+	0.245518i	$0.0789581\pi$
$719$			1.31229e11i			0.491036i	−0.969392	+	0.245518i	$0.921042\pi$
$720$	6.83798e9	+	1.07798e11i	0.0254447	+	0.401126i
$721$	4.80146e10			0.177677
$722$	−1.12424e11	+	1.74164e11i	−0.413724	+	0.640928i
$723$	1.05420e10	+	1.05420e10i	0.0385807	+	0.0385807i
$724$	−1.29274e11	+	3.42382e11i	−0.470499	+	1.24611i
$725$	−1.74885e11	−	1.74885e11i	−0.632994	−	0.632994i
$726$	1.84544e9	−	3.97562e8i	0.00664283	−	0.00143106i
$727$	−4.41837e11			−1.58170			−0.790850	−	0.612010i	$-0.790361\pi$
$727$	−4.41837e11			−1.58170			−0.790850	+	0.612010i	$0.790361\pi$
$728$	−3.20707e10	−	4.33850e10i	−0.114178	−	0.154459i
$729$			2.73567e11i			0.968621i
$730$	1.82076e11	−	3.92246e10i	0.641153	−	0.138123i
$731$	−2.14150e11	+	2.14150e11i	−0.749977	+	0.749977i
$732$	−1.43647e10	−	3.17924e10i	−0.0500325	−	0.110733i
$733$	−8.84393e10	+	8.84393e10i	−0.306358	+	0.306358i	−0.843495	−	0.537137i	$-0.819506\pi$
$733$	−8.84393e10	+	8.84393e10i	−0.306358	+	0.306358i	0.537137	+	0.843495i	$0.319506\pi$
$734$	−3.73222e9	+	5.78183e9i	−0.0128583	+	0.0199196i
$735$			7.86375e9i			0.0269451i
$736$	1.57903e11	−	4.46433e10i	0.538120	−	0.152141i
$737$	−3.96204e11			−1.34292
$738$	3.68587e10	+	2.37926e10i	0.124255	+	0.0802078i
$739$	−6.56728e10	−	6.56728e10i	−0.220195	−	0.220195i	0.588385	−	0.808581i	$-0.299764\pi$
$739$	−6.56728e10	−	6.56728e10i	−0.220195	−	0.220195i	−0.808581	+	0.588385i	$0.799764\pi$
$740$	1.25938e11	−	5.69026e10i	0.419983	−	0.189760i
$741$	−5.11370e9	−	5.11370e9i	−0.0169614	−	0.0169614i
$742$	1.70398e9	+	7.90969e9i	0.00562146	+	0.0260942i
$743$	4.56048e11			1.49643			0.748213	−	0.663458i	$-0.230912\pi$
$743$	4.56048e11			1.49643			0.748213	+	0.663458i	$0.230912\pi$
$744$	−1.22937e10	−	1.66308e10i	−0.0401227	−	0.0542778i
$745$		−	3.63024e10i		−	0.117845i
$746$	9.56818e9	+	4.44144e10i	0.0308940	+	0.143406i
$747$	−3.06345e11	+	3.06345e11i	−0.983847	+	0.983847i
$748$	1.99236e11	+	7.52264e10i	0.636447	+	0.240306i
$749$	−2.08863e10	+	2.08863e10i	−0.0663644	+	0.0663644i
$750$	1.42984e10	+	9.22977e9i	0.0451901	+	0.0291706i
$751$			4.80079e11i			1.50922i	0.656172	+	0.754611i	$0.272174\pi$
$751$			4.80079e11i			1.50922i	−0.656172	+	0.754611i	$0.727826\pi$
$752$	−3.78697e11	−	3.33519e11i	−1.18419	−	1.04292i
$753$	2.76777e10			0.0860895
$754$	−1.27456e11	+	1.97450e11i	−0.394342	+	0.610902i
$755$	−4.65265e10	−	4.65265e10i	−0.143190	−	0.143190i
$756$	−1.24860e10	−	4.71439e9i	−0.0382240	−	0.0144324i
$757$	9.74187e10	+	9.74187e10i	0.296660	+	0.296660i	0.839704	−	0.543044i	$-0.182728\pi$
$757$	9.74187e10	+	9.74187e10i	0.296660	+	0.296660i	−0.543044	+	0.839704i	$0.682728\pi$
$758$	−1.58493e11	+	3.41440e10i	−0.480101	+	0.103428i
$759$	−1.40669e10			−0.0423868
$760$	6.49184e10	+	9.73433e9i	0.194587	+	0.0291777i
$761$			1.09915e11i			0.327731i	0.986483	+	0.163866i	$0.0523964\pi$
$761$			1.09915e11i			0.327731i	−0.986483	+	0.163866i	$0.947604\pi$
$762$	−2.31166e10	+	4.98000e9i	−0.0685654	+	0.0147710i
$763$	3.81285e10	−	3.81285e10i	0.112500	−	0.112500i
$764$	5.01970e11	−	2.26804e11i	1.47334	−	0.665699i
$765$	6.33176e10	−	6.33176e10i	0.184875	−	0.184875i
$766$	3.54738e10	−	5.49548e10i	0.103037	−	0.159621i
$767$		−	1.48341e11i		−	0.428628i
$768$	−1.54331e10	+	1.99387e10i	−0.0443617	+	0.0573129i
$769$	−8.99610e10			−0.257246			−0.128623	−	0.991694i	$-0.541056\pi$
$769$	−8.99610e10			−0.257246			−0.128623	+	0.991694i	$0.541056\pi$
$770$	−3.52715e10	−	2.27680e10i	−0.100337	−	0.0647684i
$771$	1.45920e8	+	1.45920e8i	0.000412949	+	0.000412949i
$772$	1.10937e11	+	2.45529e11i	0.312326	+	0.691249i
$773$	−3.11524e11	−	3.11524e11i	−0.872517	−	0.872517i	0.120230	−	0.992746i	$-0.461637\pi$
$773$	−3.11524e11	−	3.11524e11i	−0.872517	−	0.872517i	−0.992746	+	0.120230i	$0.961637\pi$
$774$	−1.22589e11	−	5.69046e11i	−0.341577	−	1.58556i
$775$	2.81121e11			0.779267
$776$	−4.07546e10	+	2.71793e11i	−0.112390	+	0.749534i
$777$			8.51539e9i			0.0233626i
$778$	3.47781e10	+	1.61436e11i	0.0949265	+	0.440638i
$779$	1.88527e10	−	1.88527e10i	0.0511947	−	0.0511947i
$780$	2.60229e9	−	6.89214e9i	0.00703035	−	0.0186198i
$781$	4.66567e11	−	4.66567e11i	1.25404	−	1.25404i
$782$	−1.14290e11	−	7.37755e10i	−0.305621	−	0.197281i
$783$			5.81368e10i			0.154669i
$784$	2.29755e11	−	2.60877e11i	0.608135	−	0.690513i
$785$	−2.29224e11			−0.603645
$786$	−1.55072e10	+	2.40232e10i	−0.0406296	+	0.0629420i
$787$	−4.31725e11	−	4.31725e11i	−1.12540	−	1.12540i	−0.990915	−	0.134487i	$-0.957061\pi$
$787$	−4.31725e11	−	4.31725e11i	−1.12540	−	1.12540i	−0.134487	−	0.990915i	$-0.542939\pi$
$788$	4.39199e10	−	1.16321e11i	0.113909	−	0.301686i
$789$	−1.24597e10	−	1.24597e10i	−0.0321513	−	0.0321513i
$790$	3.67260e10	−	7.91186e9i	0.0942899	−	0.0203128i
$791$	3.40656e10			0.0870183
$792$	−3.29161e11	+	2.43320e11i	−0.836581	+	0.618410i
$793$		−	4.50612e11i		−	1.13949i
$794$	−2.34533e11	+	5.05254e10i	−0.590096	+	0.127124i
$795$	−7.81240e8	+	7.81240e8i	−0.00195576	+	0.00195576i
$796$	1.92776e11	+	4.26658e11i	0.480177	+	1.06274i
$797$	3.60338e11	−	3.60338e11i	0.893051	−	0.893051i	−0.101758	−	0.994809i	$-0.532447\pi$
$797$	3.60338e11	−	3.60338e11i	0.893051	−	0.893051i	0.994809	+	0.101758i	$0.0324468\pi$
$798$	−2.19365e9	+	3.39833e9i	−0.00540949	+	0.00838020i
$799$			4.18336e11i			1.02645i
$800$	−9.32434e10	−	3.29801e11i	−0.227645	−	0.805178i
$801$	6.40009e11			1.55473
$802$	−5.90633e11	−	3.81259e11i	−1.42764	−	0.921557i
$803$	4.99092e11	+	4.99092e11i	1.20038	+	1.20038i
$804$	−3.54376e10	+	1.60117e10i	−0.0848087	+	0.0383190i
$805$	1.89619e10	+	1.89619e10i	0.0451543	+	0.0451543i
$806$	−5.62566e10	−	2.61137e11i	−0.133301	−	0.618769i
$807$	−5.93632e10			−0.139966
$808$	5.53853e10	−	4.09414e10i	0.129942	−	0.0960543i
$809$			1.49178e11i			0.348267i	0.984722	+	0.174133i	$0.0557124\pi$
$809$			1.49178e11i			0.348267i	−0.984722	+	0.174133i	$0.944288\pi$
$810$	3.60536e10	+	1.67357e11i	0.0837545	+	0.388779i
$811$	3.90317e11	−	3.90317e11i	0.902265	−	0.902265i	−0.0933672	−	0.995632i	$-0.529763\pi$
$811$	3.90317e11	−	3.90317e11i	0.902265	−	0.902265i	0.995632	+	0.0933672i	$0.0297631\pi$
$812$	1.22972e11	+	4.64308e10i	0.282866	+	0.106803i
$813$	1.74412e10	−	1.74412e10i	0.0399223	−	0.0399223i
$814$	4.40001e11	+	2.84025e11i	1.00220	+	0.646932i
$815$			2.50384e11i			0.567513i
$816$	2.08604e10	−	1.32324e9i	0.0470502	−	0.00298455i
$817$	−3.53763e11			−0.794006
$818$	−4.55383e11	+	7.05464e11i	−1.01710	+	1.57566i
$819$	−6.07873e10	−	6.07873e10i	−0.135107	−	0.135107i
$820$	2.54093e10	+	9.59388e9i	0.0562002	+	0.0212197i
$821$	−4.34741e10	−	4.34741e10i	−0.0956881	−	0.0956881i	0.657642	−	0.753330i	$-0.271554\pi$
$821$	−4.34741e10	−	4.34741e10i	−0.0956881	−	0.0956881i	−0.753330	+	0.657642i	$0.771554\pi$
$822$	4.41719e10	−	9.51592e9i	0.0967517	−	0.0208432i
$823$	1.14053e11			0.248604			0.124302	−	0.992244i	$-0.460331\pi$
$823$	1.14053e11			0.248604			0.124302	+	0.992244i	$0.460331\pi$
$824$	4.29788e10	−	2.86626e11i	0.0932278	−	0.621738i
$825$			2.93805e10i			0.0634225i
$826$	−8.11079e10	+	1.74730e10i	−0.174238	+	0.0375360i
$827$	−3.14159e11	+	3.14159e11i	−0.671626	+	0.671626i	−0.958091	−	0.286465i	$-0.907520\pi$
$827$	−3.14159e11	+	3.14159e11i	−0.671626	+	0.671626i	0.286465	+	0.958091i	$0.407520\pi$
$828$	2.38271e11	−	1.07658e11i	0.506933	−	0.229047i
$829$	4.44301e11	−	4.44301e11i	0.940718	−	0.940718i	−0.0576210	−	0.998339i	$-0.518352\pi$
$829$	4.44301e11	−	4.44301e11i	0.940718	−	0.940718i	0.998339	+	0.0576210i	$0.0183515\pi$
$830$	−1.45462e11	+	2.25344e11i	−0.306504	+	0.474825i
$831$			1.92975e10i			0.0404666i
$832$	−2.87697e11	+	1.52613e11i	−0.600402	+	0.318492i
$833$	−2.88184e11			−0.598535
$834$	−5.40029e9	−	3.48594e9i	−0.0111623	−	0.00720535i
$835$	−2.27078e11	−	2.27078e11i	−0.467121	−	0.467121i
$836$	1.02429e11	+	2.26698e11i	0.209699	+	0.464112i
$837$	−4.67264e10	−	4.67264e10i	−0.0952053	−	0.0952053i
$838$	8.30525e9	+	3.85521e10i	0.0168413	+	0.0781757i
$839$	8.71585e11			1.75898			0.879492	−	0.475914i	$-0.157883\pi$
$839$	8.71585e11			1.75898			0.879492	+	0.475914i	$0.157883\pi$
$840$	−4.07490e9	−	6.11020e8i	−0.00818465	−	0.00122726i
$841$		−	7.23284e10i		−	0.144585i
$842$	−3.55540e10	−	1.65038e11i	−0.0707360	−	0.328349i
$843$	2.10127e10	−	2.10127e10i	0.0416075	−	0.0416075i
$844$	−1.37555e11	+	3.64313e11i	−0.271085	+	0.717967i
$845$	−7.83788e10	+	7.83788e10i	−0.153735	+	0.153735i
$846$	−6.75547e11	−	4.36071e11i	−1.31878	−	0.851287i
$847$		−	1.36377e10i		−	0.0264977i
$848$	4.87428e10	−	3.09191e9i	0.0942598	−	0.00597921i
$849$	−9.91092e9			−0.0190758
$850$	−1.54090e11	+	2.38710e11i	−0.295188	+	0.457294i
$851$	−2.36544e11	−	2.36544e11i	−0.451019	−	0.451019i
$852$	2.28758e10	−	6.05864e10i	0.0434129	−	0.114979i
$853$	−1.79994e10	−	1.79994e10i	−0.0339987	−	0.0339987i	0.689903	−	0.723902i	$-0.257653\pi$
$853$	−1.79994e10	−	1.79994e10i	−0.0339987	−	0.0339987i	−0.723902	+	0.689903i	$0.757653\pi$
$854$	−2.46379e11	+	5.30773e10i	−0.463204	+	0.0997877i
$855$	1.04597e11			0.195729
$856$	1.05987e11	+	1.43378e11i	0.197404	+	0.267047i
$857$			3.07684e11i			0.570402i	0.958468	+	0.285201i	$0.0920603\pi$
$857$			3.07684e11i			0.570402i	−0.958468	+	0.285201i	$0.907940\pi$
$858$	2.72920e10	−	5.87949e9i	0.0503600	−	0.0108490i
$859$	−3.33076e11	+	3.33076e11i	−0.611746	+	0.611746i	−0.943401	−	0.331655i	$-0.892393\pi$
$859$	−3.33076e11	+	3.33076e11i	−0.611746	+	0.611746i	0.331655	+	0.943401i	$0.392393\pi$
$860$	−1.48385e11	−	3.28409e11i	−0.271266	−	0.600374i
$861$	−1.18338e9	+	1.18338e9i	−0.00215333	+	0.00215333i
$862$	1.85857e11	−	2.87924e11i	0.336628	−	0.521493i
$863$		−	3.58359e10i		−	0.0646063i	−0.999478	−	0.0323031i	$-0.989716\pi$
$863$		−	3.58359e10i		−	0.0646063i	0.999478	−	0.0323031i	$-0.0102842\pi$
$864$	−3.93193e10	+	7.03162e10i	−0.0705588	+	0.126183i
$865$	−3.21614e11			−0.574474
$866$	5.54843e11	+	3.58156e11i	0.986503	+	0.636796i
$867$	1.67042e10	+	1.67042e10i	0.0295630	+	0.0295630i
$868$	−1.36154e11	+	6.15183e10i	−0.239857	+	0.108374i
$869$	1.00670e11	+	1.00670e11i	0.176531	+	0.176531i
$870$	3.77996e9	+	1.75462e10i	0.00659797	+	0.0306271i
$871$	−5.02278e11			−0.872713
$872$	−1.93481e11	−	2.61741e11i	−0.334637	−	0.452695i
$873$			4.37915e11i			0.753933i
$874$	−3.34641e10	−	1.55337e11i	−0.0573501	−	0.266213i
$875$	8.69363e10	−	8.69363e10i	0.148309	−	0.148309i
$876$	6.48100e10	+	2.44705e10i	0.110059	+	0.0415553i
$877$	−4.07544e11	+	4.07544e11i	−0.688931	+	0.688931i	−0.961996	−	0.273065i	$-0.911963\pi$
$877$	−4.07544e11	+	4.07544e11i	−0.688931	+	0.688931i	0.273065	+	0.961996i	$0.411963\pi$
$878$	6.60698e11	+	4.26486e11i	1.11180	+	0.717674i
$879$		−	6.81842e10i		−	0.114216i
$880$	−1.67488e11	+	1.90176e11i	−0.279288	+	0.317120i
$881$	7.43998e11			1.23500			0.617502	−	0.786570i	$-0.288145\pi$
$881$	7.43998e11			1.23500			0.617502	+	0.786570i	$0.288145\pi$
$882$	3.00401e11	−	4.65371e11i	0.496395	−	0.768998i
$883$	−3.51745e11	−	3.51745e11i	−0.578608	−	0.578608i	0.355911	−	0.934520i	$-0.384170\pi$
$883$	−3.51745e11	−	3.51745e11i	−0.578608	−	0.578608i	−0.934520	+	0.355911i	$0.884170\pi$
$884$	2.52577e11	+	9.53664e10i	0.413604	+	0.156166i
$885$	−8.01102e9	−	8.01102e9i	−0.0130591	−	0.0130591i
$886$	6.10598e11	−	1.31541e11i	0.990878	−	0.213464i
$887$	−2.51972e11			−0.407060			−0.203530	−	0.979069i	$-0.565241\pi$
$887$	−2.51972e11			−0.407060			−0.203530	+	0.979069i	$0.565241\pi$
$888$	5.08332e10	+	7.62229e9i	0.0817515	+	0.0122584i
$889$			1.70831e11i			0.273501i
$890$	3.87340e11	−	8.34444e10i	0.617351	−	0.132996i
$891$	−4.58744e11	+	4.58744e11i	−0.727880	+	0.727880i
$892$	−5.58234e11	+	2.52226e11i	−0.881773	+	0.398410i
$893$	−3.45533e11	+	3.45533e11i	−0.543356	+	0.543356i
$894$	7.32284e9	−	1.13443e10i	0.0114638	−	0.0177593i
$895$		−	1.25739e11i		−	0.195965i
$896$	1.17331e11	+	1.39326e11i	0.182046	+	0.216173i
$897$	−1.78329e10			−0.0275457
$898$	1.49132e11	+	9.62662e10i	0.229333	+	0.148036i
$899$	4.60197e11	+	4.60197e11i	0.704539	+	0.704539i
$900$	−2.24857e11	−	4.97661e11i	−0.342718	−	0.758513i
$901$	−2.86302e10	−	2.86302e10i	−0.0434435	−	0.0434435i
$902$	2.16760e10	+	1.00618e11i	0.0327456	+	0.152001i
$903$	2.22055e10			0.0333972
$904$	3.04928e10	−	2.03357e11i	0.0456587	−	0.304499i
$905$			3.61020e11i			0.538191i
$906$	−5.15403e9	−	2.39244e10i	−0.00764952	−	0.0355082i
$907$	6.97475e11	−	6.97475e11i	1.03062	−	1.03062i	0.0311055	−	0.999516i	$-0.490097\pi$
$907$	6.97475e11	−	6.97475e11i	1.03062	−	1.03062i	0.999516	−	0.0311055i	$-0.00990279\pi$
$908$	2.58030e11	−	6.83391e11i	0.379601	−	1.00537i
$909$	7.76010e10	−	7.76010e10i	0.113661	−	0.113661i
$910$	−4.47146e10	−	2.88636e10i	−0.0652054	−	0.0420906i
$911$		−	4.42216e11i		−	0.642038i	−0.947073	−	0.321019i	$-0.895975\pi$
$911$		−	4.42216e11i		−	0.642038i	0.947073	−	0.321019i	$-0.104025\pi$
$912$	1.83230e10	+	1.61371e10i	0.0264861	+	0.0233263i
$913$	−1.01642e12			−1.46282
$914$	3.62991e11	−	5.62333e11i	0.520129	−	0.805766i
$915$	−2.43348e10	−	2.43348e10i	−0.0347171	−	0.0347171i
$916$	−6.50767e10	+	1.72355e11i	−0.0924365	+	0.244817i
$917$	1.46064e11	+	1.46064e11i	0.206569	+	0.206569i
$918$	6.52892e10	−	1.40652e10i	0.0919328	−	0.0198050i
$919$	−8.75081e11			−1.22683			−0.613417	−	0.789759i	$-0.710206\pi$
$919$	−8.75081e11			−1.22683			−0.613417	+	0.789759i	$0.710206\pi$
$920$	1.30168e11	−	9.62214e10i	0.181699	−	0.134314i
$921$			3.76073e10i			0.0522677i
$922$	−2.01004e11	+	4.33023e10i	−0.278152	+	0.0599221i
$923$	5.91480e11	−	5.91480e11i	0.814954	−	0.814954i
$924$	−6.42940e9	−	1.42297e10i	−0.00882028	−	0.0195213i
$925$	−4.94054e11	+	4.94054e11i	−0.674850	+	0.674850i
$926$	6.13266e11	−	9.50051e11i	0.834075	−	1.29212i
$927$		−	4.61814e11i		−	0.625386i
$928$	3.87246e11	−	6.92527e11i	0.522150	−	0.933780i
$929$	7.76510e11			1.04252			0.521260	−	0.853398i	$-0.325462\pi$
$929$	7.76510e11			1.04252			0.521260	+	0.853398i	$0.325462\pi$
$930$	−1.71405e10	−	1.10643e10i	−0.0229135	−	0.0147909i
$931$	−2.38031e11	−	2.38031e11i	−0.316837	−	0.316837i
$932$	3.13722e10	−	1.41748e10i	0.0415797	−	0.0187869i
$933$	1.42533e10	+	1.42533e10i	0.0188100	+	0.0188100i
$934$	2.08364e11	+	9.67205e11i	0.273802	+	1.27096i
$935$	2.10082e11			0.274879
$936$	−4.17286e11	+	3.08462e11i	−0.543664	+	0.401882i
$937$		−	9.96991e11i		−	1.29340i	−0.762744	−	0.646700i	$-0.776149\pi$
$937$		−	9.96991e11i		−	1.29340i	0.762744	−	0.646700i	$-0.223851\pi$
$938$	5.91630e10	+	2.74628e11i	0.0764255	+	0.354759i
$939$	7.00052e9	−	7.00052e9i	0.00900467	−	0.00900467i
$940$	−4.65703e11	−	1.75837e11i	−0.596482	−	0.225216i
$941$	−3.88579e11	+	3.88579e11i	−0.495588	+	0.495588i	−0.910062	−	0.414473i	$-0.863966\pi$
$941$	−3.88579e11	+	3.88579e11i	−0.495588	+	0.495588i	0.414473	+	0.910062i	$0.363966\pi$
$942$	−7.16311e10	−	4.62385e10i	−0.0909699	−	0.0587219i
$943$		−	6.57449e10i		−	0.0831410i
$944$	3.17052e10	+	4.99820e11i	0.0399248	+	0.629398i
$945$	−1.31657e10			−0.0165088
$946$	7.40650e11	−	1.14739e12i	0.924802	−	1.43267i
$947$	1.46397e11	+	1.46397e11i	0.182026	+	0.182026i	0.792238	−	0.610212i	$-0.208916\pi$
$947$	1.46397e11	+	1.46397e11i	0.182026	+	0.182026i	−0.610212	+	0.792238i	$0.708916\pi$
$948$	1.30726e10	+	4.93586e9i	0.0161856	+	0.00611125i
$949$	6.32712e11	+	6.32712e11i	0.780084	+	0.780084i
$950$	−3.24441e11	+	6.98942e10i	−0.398329	+	0.0858118i
$951$	−1.64419e10			−0.0201015
$952$	2.23921e10	−	1.49333e11i	0.0272614	−	0.181806i
$953$		−	3.38980e11i		−	0.410963i	−0.978661	−	0.205481i	$-0.934124\pi$
$953$		−	3.38980e11i		−	0.410963i	0.978661	−	0.205481i	$-0.0658760\pi$
$954$	7.60771e10	−	1.63893e10i	0.0918461	−	0.0197864i
$955$	3.84223e11	−	3.84223e11i	0.461923	−	0.461923i
$956$	−1.07142e12	+	4.84098e11i	−1.28271	+	0.579564i
$957$	−4.80961e10	+	4.80961e10i	−0.0573406	+	0.0573406i
$958$	−8.58794e11	+	1.33041e12i	−1.01959	+	1.57952i
$959$		−	3.26428e11i		−	0.385934i
$960$	−7.29505e9	+	2.37785e10i	−0.00858902	+	0.0279962i
$961$	1.13141e11			0.132656
$962$	5.57801e11	+	3.60066e11i	0.651297	+	0.420418i
$963$	2.00889e11	+	2.00889e11i	0.233589	+	0.233589i
$964$	−2.67691e11	−	5.92463e11i	−0.309975	−	0.686045i
$965$	1.87935e11	+	1.87935e11i	0.216720	+	0.216720i
$966$	2.10053e9	+	9.75043e9i	0.00241224	+	0.0111974i
$967$	−9.68146e11			−1.10722			−0.553611	−	0.832775i	$-0.686751\pi$
$967$	−9.68146e11			−1.10722			−0.553611	+	0.832775i	$0.686751\pi$
$968$	−8.14114e10	−	1.22074e10i	−0.0927222	−	0.0139034i
$969$		−	2.02409e10i		−	0.0229581i
$970$	5.70954e10	+	2.65030e11i	0.0644932	+	0.299370i
$971$	−9.31711e11	+	9.31711e11i	−1.04810	+	1.04810i	−0.0493211	+	0.998783i	$0.515706\pi$
$971$	−9.31711e11	+	9.31711e11i	−1.04810	+	1.04810i	−0.998783	+	0.0493211i	$0.984294\pi$
$972$	−6.80756e10	+	1.80298e11i	−0.0762653	+	0.201988i
$973$	−3.28344e10	+	3.28344e10i	−0.0366335	+	0.0366335i
$974$	−1.07824e12	−	6.96015e11i	−1.19806	−	0.773361i
$975$			3.72464e10i			0.0412160i
$976$	9.63100e10	+	1.51829e12i	0.106138	+	1.67323i
$977$	9.75225e11			1.07035			0.535176	−	0.844741i	$-0.320245\pi$
$977$	9.75225e11			1.07035			0.535176	+	0.844741i	$0.320245\pi$
$978$	−5.05068e10	+	7.82434e10i	−0.0552070	+	0.0855248i
$979$	1.06174e12	+	1.06174e12i	1.15582	+	1.15582i
$980$	1.21131e11	−	3.20814e11i	0.131326	−	0.347815i
$981$	−3.66728e11	−	3.66728e11i	−0.395976	−	0.395976i
$982$	5.02249e10	−	1.08199e10i	0.0540099	−	0.0116353i
$983$	6.33928e11			0.678932			0.339466	−	0.940618i	$-0.389754\pi$
$983$	6.33928e11			0.678932			0.339466	+	0.940618i	$0.389754\pi$
$984$	6.00500e9	+	8.12353e9i	0.00640520	+	0.00866492i
$985$		−	1.22653e11i		−	0.130297i
$986$	−6.43017e11	+	1.38525e11i	−0.680322	+	0.146561i
$987$	2.16890e10	−	2.16890e10i	0.0228544	−	0.0228544i
$988$	1.29851e11	+	2.87391e11i	0.136276	+	0.301610i
$989$	−6.16836e11	+	6.16836e11i	−0.644740	+	0.644740i
$990$	−2.18988e11	+	3.39249e11i	−0.227971	+	0.353165i
$991$		−	8.73961e11i		−	0.906145i	−0.891474	−	0.453072i	$-0.850328\pi$
$991$		−	8.73961e11i		−	0.906145i	0.891474	−	0.453072i	$-0.149672\pi$
$992$	2.45364e11	+	8.67848e11i	0.253375	+	0.896184i
$993$	−7.70931e10			−0.0792900
$994$	−3.93070e11	−	2.53730e11i	−0.402647	−	0.259912i
$995$	3.26577e11	+	3.26577e11i	0.333191	+	0.333191i
$996$	−9.09116e10	+	4.10765e10i	−0.0923809	+	0.0417403i
$997$	5.84957e11	+	5.84957e11i	0.592029	+	0.592029i	0.938179	−	0.346150i	$-0.112511\pi$
$997$	5.84957e11	+	5.84957e11i	0.592029	+	0.592029i	−0.346150	+	0.938179i	$0.612511\pi$
$998$	3.78066e11	+	1.75494e12i	0.381106	+	1.76905i
$999$	1.64238e11			0.164897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.9.f.a.11.4	yes	30
4.3	odd	2		64.9.f.a.15.8		30
8.3	odd	2		128.9.f.a.31.8		30
8.5	even	2		128.9.f.b.31.8		30
16.3	odd	4	inner	16.9.f.a.3.4	✓	30
16.5	even	4		128.9.f.a.95.8		30
16.11	odd	4		128.9.f.b.95.8		30
16.13	even	4		64.9.f.a.47.8		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.9.f.a.3.4	✓	30	16.3	odd	4	inner
16.9.f.a.11.4	yes	30	1.1	even	1	trivial
64.9.f.a.15.8		30	4.3	odd	2
64.9.f.a.47.8		30	16.13	even	4
128.9.f.a.31.8		30	8.3	odd	2
128.9.f.a.95.8		30	16.5	even	4
128.9.f.b.31.8		30	8.5	even	2
128.9.f.b.95.8		30	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.4426 - 8.67733i) q^{2} +(-4.15109 - 4.15109i) q^{3} +(105.408 + 233.292i) q^{4} +(178.569 + 178.569i) q^{5} +(19.7811 + 91.8219i) q^{6} +678.560 q^{7} +(607.393 - 4050.71i) q^{8} -6526.54i q^{9} +O(q^{10})\)	\(q+(-13.4426 - 8.67733i) q^{2} +(-4.15109 - 4.15109i) q^{3} +(105.408 + 233.292i) q^{4} +(178.569 + 178.569i) q^{5} +(19.7811 + 91.8219i) q^{6} +678.560 q^{7} +(607.393 - 4050.71i) q^{8} -6526.54i q^{9} +(-850.931 - 3949.93i) q^{10} +(10827.2 - 10827.2i) q^{11} +(530.858 - 1405.97i) q^{12} +(13725.9 - 13725.9i) q^{13} +(-9121.62 - 5888.09i) q^{14} -1482.51i q^{15} +(-43314.3 + 49181.7i) q^{16} +54329.7 q^{17} +(-56632.9 + 87733.7i) q^{18} +(44874.7 + 44874.7i) q^{19} +(-22836.1 + 60481.1i) q^{20} +(-2816.77 - 2816.77i) q^{21} +(-239497. + 51594.8i) q^{22} +156491. q^{23} +(-19336.2 + 14293.5i) q^{24} -326852. i q^{25} +(-303617. + 65408.0i) q^{26} +(-54327.6 + 54327.6i) q^{27} +(71525.6 + 158303. i) q^{28} +(535058. - 535058. i) q^{29} +(-12864.2 + 19928.8i) q^{30} +860087. i q^{31} +(1.00902e6 - 285278. i) q^{32} -89889.5 q^{33} +(-730333. - 471436. i) q^{34} +(121169. + 121169. i) q^{35} +(1.52259e6 - 687949. i) q^{36} +(-1.51155e6 - 1.51155e6i) q^{37} +(-213841. - 992626. i) q^{38} -113955. q^{39} +(831791. - 614869. i) q^{40} -420120. i q^{41} +(13422.7 + 62306.7i) q^{42} +(-3.94167e6 + 3.94167e6i) q^{43} +(3.66718e6 + 1.38463e6i) q^{44} +(1.16543e6 - 1.16543e6i) q^{45} +(-2.10365e6 - 1.35792e6i) q^{46} +7.69996e6i q^{47} +(383959. - 24355.8i) q^{48} -5.30436e6 q^{49} +(-2.83620e6 + 4.39374e6i) q^{50} +(-225527. - 225527. i) q^{51} +(4.64897e6 + 1.75533e6i) q^{52} +(-526972. - 526972. i) q^{53} +(1.20172e6 - 258887. i) q^{54} +3.86680e6 q^{55} +(412153. - 2.74865e6i) q^{56} -372558. i q^{57} +(-1.18355e7 + 2.54971e6i) q^{58} +(5.40369e6 - 5.40369e6i) q^{59} +(345857. - 156268. i) q^{60} +(1.64146e7 - 1.64146e7i) q^{61} +(7.46326e6 - 1.15618e7i) q^{62} -4.42865e6i q^{63} +(-1.60394e7 - 4.92075e6i) q^{64} +4.90204e6 q^{65} +(1.20835e6 + 780000. i) q^{66} +(-1.82967e7 - 1.82967e7i) q^{67} +(5.72678e6 + 1.26747e7i) q^{68} +(-649608. - 649608. i) q^{69} +(-577408. - 2.68026e6i) q^{70} +4.30921e7 q^{71} +(-2.64371e7 - 3.96417e6i) q^{72} +4.60961e7i q^{73} +(7.20299e6 + 3.34355e7i) q^{74} +(-1.35679e6 + 1.35679e6i) q^{75} +(-5.73876e6 + 1.51991e7i) q^{76} +(7.34691e6 - 7.34691e6i) q^{77} +(1.53186e6 + 988827. i) q^{78} +9.29789e6i q^{79} +(-1.65169e7 + 1.04772e6i) q^{80} -4.23696e7 q^{81} +(-3.64552e6 + 5.64751e6i) q^{82} +(-4.69383e7 - 4.69383e7i) q^{83} +(360219. - 954038. i) q^{84} +(9.70157e6 + 9.70157e6i) q^{85} +(8.71896e7 - 1.87832e7i) q^{86} -4.44215e6 q^{87} +(-3.72816e7 - 5.04343e7i) q^{88} +9.80626e7i q^{89} +(-2.57793e7 + 5.55363e6i) q^{90} +(9.31387e6 - 9.31387e6i) q^{91} +(1.64954e7 + 3.65081e7i) q^{92} +(3.57030e6 - 3.57030e6i) q^{93} +(6.68151e7 - 1.03508e8i) q^{94} +1.60264e7i q^{95} +(-5.37276e6 - 3.00434e6i) q^{96} -6.70976e7 q^{97} +(7.13044e7 + 4.60276e7i) q^{98} +(-7.06642e7 - 7.06642e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Introduction

L-functions

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