LMFDB - Embedded newform 91.2.e.c.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(53,91)]

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([4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("91.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.e (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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			53.5
Root			$1.50426 + 2.60546i$ of defining polynomial
Character	$\chi$	$=$	91.53
Dual form			91.2.e.c.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00426 + 1.73943i) q^{2} +(-0.879528 + 1.52339i) q^{3} +(-1.01709 + 1.76164i) q^{4} +(-0.452861 - 0.784378i) q^{5} -3.53311 q^{6} +(0.237709 - 2.63505i) q^{7} -0.0686323 q^{8} +(-0.0471392 - 0.0816475i) q^{9} +O(q^{10})$	\(q+(1.00426 + 1.73943i) q^{2} +(-0.879528 + 1.52339i) q^{3} +(-1.01709 + 1.76164i) q^{4} +(-0.452861 - 0.784378i) q^{5} -3.53311 q^{6} +(0.237709 - 2.63505i) q^{7} -0.0686323 q^{8} +(-0.0471392 - 0.0816475i) q^{9} +(0.909582 - 1.57544i) q^{10} +(-0.358181 + 0.620387i) q^{11} +(-1.78911 - 3.09883i) q^{12} +1.00000 q^{13} +(4.82222 - 2.23280i) q^{14} +1.59322 q^{15} +(1.96525 + 3.40391i) q^{16} +(-1.17614 + 2.03713i) q^{17} +(0.0946802 - 0.163991i) q^{18} +(-3.31796 - 5.74687i) q^{19} +1.84239 q^{20} +(3.80513 + 2.67972i) q^{21} -1.43883 q^{22} +(-1.87953 - 3.25544i) q^{23} +(0.0603641 - 0.104554i) q^{24} +(2.08983 - 3.61970i) q^{25} +(1.00426 + 1.73943i) q^{26} -5.11133 q^{27} +(4.40025 + 3.09883i) q^{28} +3.25799 q^{29} +(1.60001 + 2.77129i) q^{30} +(-0.785250 + 1.36009i) q^{31} +(-4.01588 + 6.95570i) q^{32} +(-0.630060 - 1.09130i) q^{33} -4.72459 q^{34} +(-2.17452 + 1.00686i) q^{35} +0.191778 q^{36} +(-2.60441 - 4.51098i) q^{37} +(6.66419 - 11.5427i) q^{38} +(-0.879528 + 1.52339i) q^{39} +(0.0310809 + 0.0538337i) q^{40} +4.92168 q^{41} +(-0.839850 + 9.30992i) q^{42} -9.43766 q^{43} +(-0.728600 - 1.26197i) q^{44} +(-0.0426950 + 0.0739499i) q^{45} +(3.77508 - 6.53863i) q^{46} +(4.15993 + 7.20521i) q^{47} -6.91395 q^{48} +(-6.88699 - 1.25275i) q^{49} +8.39497 q^{50} +(-2.06889 - 3.58342i) q^{51} +(-1.01709 + 1.76164i) q^{52} +(-7.04163 + 12.1965i) q^{53} +(-5.13311 - 8.89081i) q^{54} +0.648824 q^{55} +(-0.0163145 + 0.180850i) q^{56} +11.6729 q^{57} +(3.27188 + 5.66706i) q^{58} +(-0.358181 + 0.620387i) q^{59} +(-1.62044 + 2.80668i) q^{60} +(5.82633 + 10.0915i) q^{61} -3.15439 q^{62} +(-0.226351 + 0.104806i) q^{63} -8.27099 q^{64} +(-0.452861 - 0.784378i) q^{65} +(1.26549 - 2.19189i) q^{66} +(-4.69587 + 8.13349i) q^{67} +(-2.39246 - 4.14386i) q^{68} +6.61239 q^{69} +(-3.93516 - 2.77129i) q^{70} +10.9914 q^{71} +(0.00323527 + 0.00560366i) q^{72} +(1.73650 - 3.00771i) q^{73} +(5.23103 - 9.06041i) q^{74} +(3.67614 + 6.36725i) q^{75} +13.4986 q^{76} +(1.54961 + 1.09130i) q^{77} -3.53311 q^{78} +(-6.50408 - 11.2654i) q^{79} +(1.77997 - 3.08299i) q^{80} +(4.63697 - 8.03147i) q^{81} +(4.94265 + 8.56093i) q^{82} +3.54083 q^{83} +(-8.59086 + 3.97778i) q^{84} +2.13050 q^{85} +(-9.47789 - 16.4162i) q^{86} +(-2.86550 + 4.96318i) q^{87} +(0.0245828 - 0.0425786i) q^{88} +(-6.02503 - 10.4357i) q^{89} -0.171508 q^{90} +(0.237709 - 2.63505i) q^{91} +7.64656 q^{92} +(-1.38130 - 2.39248i) q^{93} +(-8.35532 + 14.4718i) q^{94} +(-3.00514 + 5.20506i) q^{95} +(-7.06415 - 12.2355i) q^{96} +7.43766 q^{97} +(-4.73727 - 13.2375i) q^{98} +0.0675374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 18 * q^8 - 3 * q^9	\( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9} + 5 q^{10} - 11 q^{11} - 5 q^{12} + 10 q^{13} + 10 q^{14} - 10 q^{16} + 5 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 2 q^{21} + 16 q^{22} - 10 q^{23} - 9 q^{25} - 4 q^{26} + 37 q^{28} - 6 q^{29} + 13 q^{30} + 6 q^{31} - 22 q^{32} - 8 q^{33} - 44 q^{34} - 4 q^{35} + 14 q^{36} - 4 q^{37} + 10 q^{38} - 28 q^{40} + 28 q^{41} + 52 q^{42} + 4 q^{43} + 32 q^{45} - 3 q^{46} - q^{47} - 46 q^{48} - 11 q^{49} + 18 q^{50} + 8 q^{51} - 8 q^{52} - 17 q^{53} - 23 q^{54} - 21 q^{56} - 32 q^{57} + 27 q^{58} - 11 q^{59} + 29 q^{60} + 11 q^{61} - 46 q^{62} + 5 q^{63} + 18 q^{64} - 2 q^{65} - 21 q^{66} - 13 q^{67} + 32 q^{68} + 36 q^{69} + 49 q^{70} + 30 q^{71} + 19 q^{72} + 33 q^{74} + 20 q^{75} + 16 q^{76} - 46 q^{77} - 10 q^{78} - 2 q^{79} - 55 q^{80} + 19 q^{81} - 34 q^{82} + 12 q^{83} - 23 q^{84} - 44 q^{85} - 28 q^{86} + 8 q^{87} + 3 q^{88} + 4 q^{89} - 68 q^{90} + q^{91} + 42 q^{92} - 18 q^{93} - 20 q^{94} + 12 q^{95} + 37 q^{96} - 24 q^{97} - 7 q^{98} + 22 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 18 * q^8 - 3 * q^9 + 5 * q^10 - 11 * q^11 - 5 * q^12 + 10 * q^13 + 10 * q^14 - 10 * q^16 + 5 * q^17 - 9 * q^18 - 9 * q^19 + 2 * q^20 + 2 * q^21 + 16 * q^22 - 10 * q^23 - 9 * q^25 - 4 * q^26 + 37 * q^28 - 6 * q^29 + 13 * q^30 + 6 * q^31 - 22 * q^32 - 8 * q^33 - 44 * q^34 - 4 * q^35 + 14 * q^36 - 4 * q^37 + 10 * q^38 - 28 * q^40 + 28 * q^41 + 52 * q^42 + 4 * q^43 + 32 * q^45 - 3 * q^46 - q^47 - 46 * q^48 - 11 * q^49 + 18 * q^50 + 8 * q^51 - 8 * q^52 - 17 * q^53 - 23 * q^54 - 21 * q^56 - 32 * q^57 + 27 * q^58 - 11 * q^59 + 29 * q^60 + 11 * q^61 - 46 * q^62 + 5 * q^63 + 18 * q^64 - 2 * q^65 - 21 * q^66 - 13 * q^67 + 32 * q^68 + 36 * q^69 + 49 * q^70 + 30 * q^71 + 19 * q^72 + 33 * q^74 + 20 * q^75 + 16 * q^76 - 46 * q^77 - 10 * q^78 - 2 * q^79 - 55 * q^80 + 19 * q^81 - 34 * q^82 + 12 * q^83 - 23 * q^84 - 44 * q^85 - 28 * q^86 + 8 * q^87 + 3 * q^88 + 4 * q^89 - 68 * q^90 + q^91 + 42 * q^92 - 18 * q^93 - 20 * q^94 + 12 * q^95 + 37 * q^96 - 24 * q^97 - 7 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$	$66$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00426	+	1.73943i	0.710121	+	1.22997i	0.964812	+	0.262942i	$0.0846930\pi$
$2$	1.00426	+	1.73943i	0.710121	+	1.22997i	−0.254691	+	0.967023i	$0.581974\pi$
$3$	−0.879528	+	1.52339i	−0.507796	+	0.879528i	0.492164	+	0.870503i	$0.336206\pi$
$3$	−0.879528	+	1.52339i	−0.507796	+	0.879528i	−0.999959	+	0.00902528i	$0.997127\pi$
$4$	−1.01709	+	1.76164i	−0.508543	+	0.880822i
$5$	−0.452861	−	0.784378i	−0.202526	−	0.350784i	0.746816	−	0.665031i	$-0.231582\pi$
$5$	−0.452861	−	0.784378i	−0.202526	−	0.350784i	−0.949342	+	0.314246i	$0.898248\pi$
$6$	−3.53311			−1.44238
$7$	0.237709	−	2.63505i	0.0898454	−	0.995956i
$7$	0.237709	−	2.63505i	0.0898454	−	0.995956i
$8$	−0.0686323			−0.0242652
$9$	−0.0471392	−	0.0816475i	−0.0157131	−	0.0272158i
$10$	0.909582	−	1.57544i	0.287635	−	0.498199i
$11$	−0.358181	+	0.620387i	−0.107996	+	0.187054i	−0.914958	−	0.403549i	$-0.867777\pi$
$11$	−0.358181	+	0.620387i	−0.107996	+	0.187054i	0.806963	+	0.590603i	$0.201110\pi$
$12$	−1.78911	−	3.09883i	−0.516472	−	0.894555i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	4.82222	−	2.23280i	1.28879	−	0.596742i
$15$	1.59322			0.411366
$16$	1.96525	+	3.40391i	0.491311	+	0.850976i
$17$	−1.17614	+	2.03713i	−0.285255	+	0.494076i	−0.972671	−	0.232188i	$-0.925412\pi$
$17$	−1.17614	+	2.03713i	−0.285255	+	0.494076i	0.687416	+	0.726264i	$0.258745\pi$
$18$	0.0946802	−	0.163991i	0.0223163	−	0.0386530i
$19$	−3.31796	−	5.74687i	−0.761191	−	1.31842i	−0.942237	−	0.334947i	$-0.891282\pi$
$19$	−3.31796	−	5.74687i	−0.761191	−	1.31842i	0.181046	−	0.983475i	$-0.442052\pi$
$20$	1.84239			0.411971
$21$	3.80513	+	2.67972i	0.830348	+	0.584764i
$22$	−1.43883			−0.306759
$23$	−1.87953	−	3.25544i	−0.391909	−	0.678806i	0.600793	−	0.799405i	$-0.294852\pi$
$23$	−1.87953	−	3.25544i	−0.391909	−	0.678806i	−0.992701	+	0.120599i	$0.961518\pi$
$24$	0.0603641	−	0.104554i	0.0123218	−	0.0213419i
$25$	2.08983	−	3.61970i	0.417967	−	0.723940i
$26$	1.00426	+	1.73943i	0.196952	+	0.341131i
$27$	−5.11133			−0.983675
$28$	4.40025	+	3.09883i	0.831569	+	0.585624i
$29$	3.25799			0.604994			0.302497	−	0.953150i	$-0.402180\pi$
$29$	3.25799			0.604994			0.302497	+	0.953150i	$0.402180\pi$
$30$	1.60001	+	2.77129i	0.292120	+	0.505966i
$31$	−0.785250	+	1.36009i	−0.141035	+	0.244280i	−0.927887	−	0.372862i	$-0.878376\pi$
$31$	−0.785250	+	1.36009i	−0.141035	+	0.244280i	0.786852	+	0.617142i	$0.211710\pi$
$32$	−4.01588	+	6.95570i	−0.709913	+	1.22961i
$33$	−0.630060	−	1.09130i	−0.109679	−	0.189970i
$34$	−4.72459			−0.810261
$35$	−2.17452	+	1.00686i	−0.367562	+	0.170190i
$36$	0.191778			0.0319631
$37$	−2.60441	−	4.51098i	−0.428163	−	0.741600i	0.568547	−	0.822651i	$-0.307506\pi$
$37$	−2.60441	−	4.51098i	−0.428163	−	0.741600i	−0.996710	+	0.0810508i	$0.974172\pi$
$38$	6.66419	−	11.5427i	1.08108	−	1.87248i
$39$	−0.879528	+	1.52339i	−0.140837	+	0.243937i
$40$	0.0310809	+	0.0538337i	0.00491432	+	0.00851185i
$41$	4.92168			0.768637			0.384318	−	0.923201i	$-0.374437\pi$
$41$	4.92168			0.768637			0.384318	+	0.923201i	$0.374437\pi$
$42$	−0.839850	+	9.30992i	−0.129592	+	1.43655i
$43$	−9.43766			−1.43923			−0.719615	−	0.694373i	$-0.755682\pi$
$43$	−9.43766			−1.43923			−0.719615	+	0.694373i	$0.755682\pi$
$44$	−0.728600	−	1.26197i	−0.109841	−	0.190250i
$45$	−0.0426950	+	0.0739499i	−0.00636459	+	0.0110238i
$46$	3.77508	−	6.53863i	0.556605	−	0.964068i
$47$	4.15993	+	7.20521i	0.606788	+	1.05099i	0.991766	+	0.128062i	$0.0408758\pi$
$47$	4.15993	+	7.20521i	0.606788	+	1.05099i	−0.384978	+	0.922926i	$0.625791\pi$
$48$	−6.91395			−0.997943
$49$	−6.88699	−	1.25275i	−0.983856	−	0.178964i
$50$	8.39497			1.18723
$51$	−2.06889	−	3.58342i	−0.289702	−	0.501779i
$52$	−1.01709	+	1.76164i	−0.141044	+	0.244296i
$53$	−7.04163	+	12.1965i	−0.967243	+	1.67531i	−0.263777	+	0.964584i	$0.584968\pi$
$53$	−7.04163	+	12.1965i	−0.967243	+	1.67531i	−0.703465	+	0.710729i	$0.748365\pi$
$54$	−5.13311	−	8.89081i	−0.698528	−	1.20989i
$55$	0.648824			0.0874874
$56$	−0.0163145	+	0.180850i	−0.00218012	+	0.0241671i
$57$	11.6729			1.54612
$58$	3.27188	+	5.66706i	0.429619	+	0.744122i
$59$	−0.358181	+	0.620387i	−0.0466311	+	0.0807675i	−0.888399	−	0.459072i	$-0.848182\pi$
$59$	−0.358181	+	0.620387i	−0.0466311	+	0.0807675i	0.841768	+	0.539840i	$0.181515\pi$
$60$	−1.62044	+	2.80668i	−0.209197	+	0.362340i
$61$	5.82633	+	10.0915i	0.745986	+	1.29208i	0.949733	+	0.313061i	$0.101355\pi$
$61$	5.82633	+	10.0915i	0.745986	+	1.29208i	−0.203747	+	0.979024i	$0.565312\pi$
$62$	−3.15439			−0.400607
$63$	−0.226351	+	0.104806i	−0.0285175	+	0.0132043i
$64$	−8.27099			−1.03387
$65$	−0.452861	−	0.784378i	−0.0561705	−	0.0972901i
$66$	1.26549	−	2.19189i	0.155771	−	0.269803i
$67$	−4.69587	+	8.13349i	−0.573692	+	0.993664i	0.422490	+	0.906367i	$0.361156\pi$
$67$	−4.69587	+	8.13349i	−0.573692	+	0.993664i	−0.996182	+	0.0872964i	$0.972177\pi$
$68$	−2.39246	−	4.14386i	−0.290128	−	0.502517i
$69$	6.61239			0.796038
$70$	−3.93516	−	2.77129i	−0.470341	−	0.331233i
$71$	10.9914			1.30444			0.652220	−	0.758030i	$-0.273838\pi$
$71$	10.9914			1.30444			0.652220	+	0.758030i	$0.273838\pi$
$72$	0.00323527	+	0.00560366i	0.000381281	+	0.000660397i
$73$	1.73650	−	3.00771i	0.203242	−	0.352025i	−0.746329	−	0.665577i	$-0.768186\pi$
$73$	1.73650	−	3.00771i	0.203242	−	0.352025i	0.949571	+	0.313552i	$0.101519\pi$
$74$	5.23103	−	9.06041i	0.608095	−	1.05325i
$75$	3.67614	+	6.36725i	0.424484	+	0.735227i
$76$	13.4986			1.54839
$77$	1.54961	+	1.09130i	0.176594	+	0.124365i
$78$	−3.53311			−0.400046
$79$	−6.50408	−	11.2654i	−0.731766	−	1.26746i	−0.956128	−	0.292950i	$-0.905363\pi$
$79$	−6.50408	−	11.2654i	−0.731766	−	1.26746i	0.224361	−	0.974506i	$-0.427970\pi$
$80$	1.77997	−	3.08299i	0.199006	−	0.344689i
$81$	4.63697	−	8.03147i	0.515219	−	0.892386i
$82$	4.94265	+	8.56093i	0.545825	+	0.945396i
$83$	3.54083			0.388656			0.194328	−	0.980937i	$-0.437747\pi$
$83$	3.54083			0.388656			0.194328	+	0.980937i	$0.437747\pi$
$84$	−8.59086	+	3.97778i	−0.937340	+	0.434011i
$85$	2.13050			0.231085
$86$	−9.47789	−	16.4162i	−1.02203	−	1.77020i
$87$	−2.86550	+	4.96318i	−0.307213	+	0.532109i
$88$	0.0245828	−	0.0425786i	0.00262053	−	0.00453889i
$89$	−6.02503	−	10.4357i	−0.638651	−	1.10618i	−0.985729	−	0.168340i	$-0.946159\pi$
$89$	−6.02503	−	10.4357i	−0.638651	−	1.10618i	0.347077	−	0.937836i	$-0.387174\pi$
$90$	−0.171508			−0.0180785
$91$	0.237709	−	2.63505i	0.0249186	−	0.276228i
$92$	7.64656			0.797209
$93$	−1.38130	−	2.39248i	−0.143234	−	0.248088i
$94$	−8.35532	+	14.4718i	−0.861786	+	1.49266i
$95$	−3.00514	+	5.20506i	−0.308321	+	0.534028i
$96$	−7.06415	−	12.2355i	−0.720982	−	1.24878i
$97$	7.43766			0.755180			0.377590	−	0.925973i	$-0.376753\pi$
$97$	7.43766			0.755180			0.377590	+	0.925973i	$0.376753\pi$
$98$	−4.73727	−	13.2375i	−0.478537	−	1.33719i
$99$	0.0675374			0.00678776
$100$	4.25108	+	7.36309i	0.425108	+	0.736309i
$101$	0.599526	−	1.03841i	0.0596551	−	0.103326i	−0.834656	−	0.550772i	$-0.814333\pi$
$101$	0.599526	−	1.03841i	0.0596551	−	0.103326i	0.894311	+	0.447447i	$0.147667\pi$
$102$	4.15541	−	7.19739i	0.411447	−	0.712647i
$103$	7.20615	+	12.4814i	0.710043	+	1.22983i	0.964840	+	0.262837i	$0.0846580\pi$
$103$	7.20615	+	12.4814i	0.710043	+	1.22983i	−0.254797	+	0.966995i	$0.582009\pi$
$104$	−0.0686323			−0.00672995
$105$	0.378721	−	4.19820i	0.0369594	−	0.409703i
$106$	−28.2866			−2.74744
$107$	−6.79661	−	11.7721i	−0.657053	−	1.13805i	−0.981375	−	0.192102i	$-0.938469\pi$
$107$	−6.79661	−	11.7721i	−0.657053	−	1.13805i	0.324322	−	0.945947i	$-0.394864\pi$
$108$	5.19866	−	9.00434i	0.500241	−	0.866443i
$109$	6.86241	−	11.8860i	0.657299	−	1.13848i	−0.324013	−	0.946053i	$-0.605032\pi$
$109$	6.86241	−	11.8860i	0.657299	−	1.13848i	0.981312	−	0.192423i	$-0.0616346\pi$
$110$	0.651589	+	1.12859i	0.0621266	+	0.107606i
$111$	9.16262			0.869677
$112$	9.43662	−	4.36939i	0.891677	−	0.412868i
$113$	−3.25799			−0.306486			−0.153243	−	0.988189i	$-0.548972\pi$
$113$	−3.25799			−0.306486			−0.153243	+	0.988189i	$0.548972\pi$
$114$	11.7227	+	20.3043i	1.09793	+	1.90167i
$115$	−1.70233	+	2.94852i	−0.158743	+	0.274951i
$116$	−3.31366	+	5.73942i	−0.307665	+	0.532892i
$117$	−0.0471392	−	0.0816475i	−0.00435802	−	0.00754831i
$118$	−1.43883			−0.132455
$119$	5.08836	+	3.58342i	0.466449	+	0.328492i
$120$	−0.109346			−0.00998189
$121$	5.24341	+	9.08186i	0.476674	+	0.825623i
$122$	−11.7023	+	20.2690i	−1.05948	+	1.83507i
$123$	−4.32875	+	7.49762i	−0.390310	+	0.676037i
$124$	−1.59733	−	2.76666i	−0.143445	−	0.248453i
$125$	−8.31422			−0.743647
$126$	−0.409618	−	0.288469i	−0.0364917	−	0.0256989i
$127$	−0.950834			−0.0843729			−0.0421865	−	0.999110i	$-0.513432\pi$
$127$	−0.950834			−0.0843729			−0.0421865	+	0.999110i	$0.513432\pi$
$128$	−0.274489	−	0.475429i	−0.0242617	−	0.0420224i
$129$	8.30069	−	14.3772i	0.730835	−	1.26584i
$130$	0.909582	−	1.57544i	0.0797756	−	0.138175i
$131$	9.40980	+	16.2983i	0.822138	+	1.42399i	0.904087	+	0.427349i	$0.140552\pi$
$131$	9.40980	+	16.2983i	0.822138	+	1.42399i	−0.0819487	+	0.996637i	$0.526114\pi$
$132$	2.56330			0.223106
$133$	−15.9320	+	7.37690i	−1.38148	+	0.639658i
$134$	−18.8635			−1.62956
$135$	2.31472	+	4.00921i	0.199219	+	0.345058i
$136$	0.0807209	−	0.139813i	0.00692176	−	0.0119888i
$137$	−3.09090	+	5.35359i	−0.264073	+	0.457388i	−0.967320	−	0.253557i	$-0.918399\pi$
$137$	−3.09090	+	5.35359i	−0.264073	+	0.457388i	0.703247	+	0.710945i	$0.251733\pi$
$138$	6.64057	+	11.5018i	0.565283	+	0.979099i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	0.437952	−	4.85480i	0.0370137	−	0.410305i
$141$	−14.6351			−1.23250
$142$	11.0383	+	19.1188i	0.926309	+	1.60441i
$143$	−0.358181	+	0.620387i	−0.0299526	+	0.0518794i
$144$	0.185280	−	0.320915i	0.0154400	−	0.0267429i
$145$	−1.47542	−	2.55550i	−0.122527	−	0.212223i
$146$	6.97560			0.577305
$147$	7.96572	−	9.38972i	0.657002	−	0.774451i
$148$	10.5956			0.870956
$149$	10.5385	+	18.2533i	0.863351	+	1.49537i	0.868675	+	0.495382i	$0.164972\pi$
$149$	10.5385	+	18.2533i	0.863351	+	1.49537i	−0.00532425	+	0.999986i	$0.501695\pi$
$150$	−7.38361	+	12.7888i	−0.602869	+	1.04420i
$151$	7.86171	−	13.6169i	0.639777	−	1.10813i	−0.345704	−	0.938344i	$-0.612360\pi$
$151$	7.86171	−	13.6169i	0.639777	−	1.10813i	0.985481	−	0.169783i	$-0.0543067\pi$
$152$	0.227719	+	0.394421i	0.0184705	+	0.0319918i
$153$	0.221768			0.0179289
$154$	−0.342022	+	3.79139i	−0.0275609	+	0.305519i
$155$	1.42244			0.114253
$156$	−1.78911	−	3.09883i	−0.143243	−	0.248105i
$157$	3.89250	−	6.74200i	0.310655	−	0.538070i	−0.667849	−	0.744297i	$-0.732785\pi$
$157$	3.89250	−	6.74200i	0.310655	−	0.538070i	0.978504	+	0.206226i	$0.0661183\pi$
$158$	13.0636	−	22.6268i	1.03928	−	1.80009i
$159$	−12.3866	−	21.4543i	−0.982323	−	1.70143i
$160$	7.27453			0.575102
$161$	−9.02503	+	4.17881i	−0.711272	+	0.329336i
$162$	18.6269			1.46347
$163$	−0.844956	−	1.46351i	−0.0661820	−	0.114631i	0.831036	−	0.556219i	$-0.187748\pi$
$163$	−0.844956	−	1.46351i	−0.0661820	−	0.114631i	−0.897218	+	0.441588i	$0.854415\pi$
$164$	−5.00576	+	8.67024i	−0.390884	+	0.677032i
$165$	−0.570659	+	0.988410i	−0.0444257	+	0.0769476i
$166$	3.55592	+	6.15903i	0.275993	+	0.478034i
$167$	−21.8667			−1.69210			−0.846049	−	0.533105i	$-0.821025\pi$
$167$	−21.8667			−1.69210			−0.846049	+	0.533105i	$0.821025\pi$
$168$	−0.261155	−	0.183916i	−0.0201486	−	0.0141894i
$169$	1.00000			0.0769231
$170$	2.13958	+	3.70587i	0.164099	+	0.284227i
$171$	−0.312812	+	0.541805i	−0.0239213	+	0.0414329i
$172$	9.59891	−	16.6258i	0.731910	−	1.26770i
$173$	−2.92061	−	5.05865i	−0.222050	−	0.384602i	0.733380	−	0.679819i	$-0.237942\pi$
$173$	−2.92061	−	5.05865i	−0.222050	−	0.384602i	−0.955430	+	0.295217i	$0.904608\pi$
$174$	−11.5108			−0.872634
$175$	−9.04132	−	6.36725i	−0.683460	−	0.481319i
$176$	−2.81565			−0.212238
$177$	−0.630060	−	1.09130i	−0.0473582	−	0.0820268i
$178$	12.1014	−	20.9603i	0.907039	−	1.57104i
$179$	−1.26714	+	2.19475i	−0.0947103	+	0.164043i	−0.909488	−	0.415731i	$-0.863526\pi$
$179$	−1.26714	+	2.19475i	−0.0947103	+	0.164043i	0.814777	+	0.579774i	$0.196859\pi$
$180$	−0.0868489	−	0.150427i	−0.00647333	−	0.0112121i
$181$	−10.7248			−0.797169			−0.398585	−	0.917132i	$-0.630498\pi$
$181$	−10.7248			−0.797169			−0.398585	+	0.917132i	$0.630498\pi$
$182$	4.82222	−	2.23280i	0.357447	−	0.165506i
$183$	−20.4977			−1.51523
$184$	0.128996	+	0.223428i	0.00950974	+	0.0164714i
$185$	−2.35887	+	4.08569i	−0.173428	+	0.300386i
$186$	2.77437	−	4.80535i	0.203427	−	0.352345i
$187$	−0.842538	−	1.45932i	−0.0616125	−	0.106716i
$188$	−16.9240			−1.23431
$189$	−1.21501	+	13.4686i	−0.0883787	+	0.979697i
$190$	−12.0718			−0.875781
$191$	0.839303	+	1.45371i	0.0607298	+	0.105187i	0.894792	−	0.446484i	$-0.147324\pi$
$191$	0.839303	+	1.45371i	0.0607298	+	0.105187i	−0.834062	+	0.551671i	$0.813991\pi$
$192$	7.27457	−	12.5999i	0.524997	−	0.909321i
$193$	3.22408	−	5.58427i	0.232074	−	0.401964i	−0.726344	−	0.687331i	$-0.758782\pi$
$193$	3.22408	−	5.58427i	0.232074	−	0.401964i	0.958418	+	0.285367i	$0.0921154\pi$
$194$	7.46936	+	12.9373i	0.536269	+	0.928845i
$195$	1.59322			0.114093
$196$	9.21155	−	10.8583i	0.657968	−	0.775590i
$197$	1.87251			0.133411			0.0667054	−	0.997773i	$-0.478751\pi$
$197$	1.87251			0.133411			0.0667054	+	0.997773i	$0.478751\pi$
$198$	0.0678252	+	0.117477i	0.00482013	+	0.00834871i
$199$	5.69833	−	9.86979i	0.403944	−	0.699651i	−0.590254	−	0.807217i	$-0.700972\pi$
$199$	5.69833	−	9.86979i	0.403944	−	0.699651i	0.994198	+	0.107566i	$0.0343058\pi$
$200$	−0.143430	+	0.248428i	−0.0101420	+	0.0175665i
$201$	−8.26030	−	14.3073i	−0.582637	−	1.00916i
$202$	2.40833			0.169449
$203$	0.774453	−	8.58498i	0.0543559	−	0.602547i
$204$	8.41694			0.589304
$205$	−2.22883	−	3.86045i	−0.155669	−	0.269626i
$206$	−14.4737	+	25.0692i	−1.00843	+	1.74666i
$207$	−0.177199	+	0.306918i	−0.0123162	+	0.0213322i
$208$	1.96525	+	3.40391i	0.136265	+	0.236018i
$209$	4.75371			0.328821
$210$	7.68283	−	3.55734i	0.530166	−	0.245480i
$211$	7.53599			0.518799			0.259400	−	0.965770i	$-0.416475\pi$
$211$	7.53599			0.518799			0.259400	+	0.965770i	$0.416475\pi$
$212$	−14.3239	−	24.8097i	−0.983768	−	1.70394i
$213$	−9.66725	+	16.7442i	−0.662389	+	1.14729i
$214$	13.6512	−	23.6445i	0.933174	−	1.61630i
$215$	4.27395	+	7.40269i	0.291481	+	0.504859i
$216$	0.350802			0.0238691
$217$	3.39725	+	2.39248i	0.230621	+	0.162412i
$218$	27.5666			1.86705
$219$	3.05460	+	5.29072i	0.206411	+	0.357514i
$220$	−0.659909	+	1.14300i	−0.0444911	+	0.0770608i
$221$	−1.17614	+	2.03713i	−0.0791154	+	0.137032i
$222$	9.20167	+	15.9378i	0.617576	+	1.06967i
$223$	17.6349			1.18092			0.590459	−	0.807067i	$-0.298947\pi$
$223$	17.6349			1.18092			0.590459	+	0.807067i	$0.298947\pi$
$224$	17.3740	+	12.2355i	1.16085	+	0.817517i
$225$	−0.394052			−0.0262702
$226$	−3.27188	−	5.66706i	−0.217642	−	0.376967i
$227$	2.66452	−	4.61509i	0.176851	−	0.306314i	−0.763950	−	0.645276i	$-0.776742\pi$
$227$	2.66452	−	4.61509i	0.176851	−	0.306314i	0.940800	+	0.338962i	$0.110076\pi$
$228$	−11.8724	+	20.5636i	−0.786267	+	1.36185i
$229$	4.25950	+	7.37767i	0.281476	+	0.487530i	0.971748	−	0.236019i	$-0.0758428\pi$
$229$	4.25950	+	7.37767i	0.281476	+	0.487530i	−0.690273	+	0.723549i	$0.742509\pi$
$230$	−6.83834			−0.450907
$231$	−3.02539	+	1.40083i	−0.199056	+	0.0921678i
$232$	−0.223604			−0.0146803
$233$	−2.37685	−	4.11683i	−0.155713	−	0.269703i	0.777605	−	0.628752i	$-0.216434\pi$
$233$	−2.37685	−	4.11683i	−0.155713	−	0.269703i	−0.933318	+	0.359050i	$0.883101\pi$
$234$	0.0946802	−	0.163991i	0.00618944	−	0.0107204i
$235$	3.76774	−	6.52592i	0.245780	−	0.425704i
$236$	−0.728600	−	1.26197i	−0.0474278	−	0.0821474i
$237$	22.8821			1.48635
$238$	−1.12308	+	12.4495i	−0.0727983	+	0.806984i
$239$	14.8314			0.959365			0.479682	−	0.877442i	$-0.340752\pi$
$239$	14.8314			0.959365			0.479682	+	0.877442i	$0.340752\pi$
$240$	3.13106	+	5.42315i	0.202109	+	0.350063i
$241$	3.06066	−	5.30121i	0.197154	−	0.341481i	−0.750450	−	0.660927i	$-0.770163\pi$
$241$	3.06066	−	5.30121i	0.197154	−	0.341481i	0.947605	+	0.319446i	$0.103497\pi$
$242$	−10.5315	+	18.2411i	−0.676992	+	1.17258i
$243$	0.489705	+	0.848195i	0.0314146	+	0.0544117i
$244$	−23.7035			−1.51746
$245$	2.13622	+	5.96932i	0.136478	+	0.381366i
$246$	−17.3888			−1.10867
$247$	−3.31796	−	5.74687i	−0.211116	−	0.365664i
$248$	0.0538935	−	0.0933463i	0.00342224	−	0.00592750i
$249$	−3.11426	+	5.39405i	−0.197358	+	0.341834i
$250$	−8.34966	−	14.4620i	−0.528079	−	0.914660i
$251$	−13.9708			−0.881832			−0.440916	−	0.897548i	$-0.645346\pi$
$251$	−13.9708			−0.881832			−0.440916	+	0.897548i	$0.645346\pi$
$252$	0.0455874	−	0.505346i	0.00287173	−	0.0318338i
$253$	2.69284			0.169298
$254$	−0.954887	−	1.65391i	−0.0599149	−	0.103776i
$255$	−1.87384	+	3.24558i	−0.117344	+	0.203246i
$256$	−7.71967	+	13.3709i	−0.482479	+	0.835679i
$257$	−8.63253	−	14.9520i	−0.538482	−	0.932679i	−0.998986	−	0.0450210i	$-0.985665\pi$
$257$	−8.63253	−	14.9520i	−0.538482	−	0.932679i	0.460504	−	0.887658i	$-0.347669\pi$
$258$	33.3443			2.07592
$259$	−12.5057	+	5.79047i	−0.777069	+	0.359802i
$260$	1.84239			0.114260
$261$	−0.153579	−	0.266007i	−0.00950631	−	0.0164654i
$262$	−18.8998	+	32.7354i	−1.16763	+	2.02240i
$263$	1.30336	−	2.25749i	0.0803687	−	0.139203i	−0.823040	−	0.567984i	$-0.807724\pi$
$263$	1.30336	−	2.25749i	0.0803687	−	0.139203i	0.903408	+	0.428781i	$0.141057\pi$
$264$	0.0432425	+	0.0748982i	0.00266139	+	0.00460966i
$265$	12.7555			0.783565
$266$	−28.8315	−	20.3043i	−1.76777	−	1.24494i
$267$	21.1967			1.29722
$268$	−9.55221	−	16.5449i	−0.583494	−	1.01064i
$269$	7.24477	−	12.5483i	0.441721	−	0.765084i	−0.556096	−	0.831118i	$-0.687701\pi$
$269$	7.24477	−	12.5483i	0.441721	−	0.765084i	0.997817	+	0.0660343i	$0.0210347\pi$
$270$	−4.64917	+	8.05260i	−0.282940	+	0.490066i
$271$	4.31796	+	7.47892i	0.262297	+	0.454312i	0.966852	−	0.255338i	$-0.0821866\pi$
$271$	4.31796	+	7.47892i	0.262297	+	0.454312i	−0.704555	+	0.709650i	$0.748853\pi$
$272$	−9.24558			−0.560596
$273$	3.80513	+	2.67972i	0.230297	+	0.162184i
$274$	−12.4163			−0.750095
$275$	1.49708	+	2.59301i	0.0902771	+	0.156364i
$276$	−6.72537	+	11.6487i	−0.404819	+	0.701168i
$277$	−6.11349	+	10.5889i	−0.367324	+	0.636223i	−0.989146	−	0.146935i	$-0.953059\pi$
$277$	−6.11349	+	10.5889i	−0.367324	+	0.636223i	0.621822	+	0.783158i	$0.286393\pi$
$278$	−4.01705	−	6.95773i	−0.240927	−	0.417297i
$279$	0.148064			0.00886437
$280$	0.149243	−	0.0691030i	0.00891896	−	0.00412970i
$281$	−24.1822			−1.44259			−0.721293	−	0.692630i	$-0.756452\pi$
$281$	−24.1822			−1.44259			−0.721293	+	0.692630i	$0.756452\pi$
$282$	−14.6975	−	25.4568i	−0.875222	−	1.51593i
$283$	15.3842	−	26.6461i	0.914493	−	1.58395i	0.106851	−	0.994275i	$-0.465923\pi$
$283$	15.3842	−	26.6461i	0.914493	−	1.58395i	0.807642	−	0.589674i	$-0.200744\pi$
$284$	−11.1792	+	19.3629i	−0.663363	+	1.14898i
$285$	−5.28622	−	9.15599i	−0.313128	−	0.542354i
$286$	−1.43883			−0.0850797
$287$	1.16992	−	12.9689i	0.0690585	−	0.765528i
$288$	0.757221			0.0446197
$289$	5.73341	+	9.93056i	0.337259	+	0.584150i
$290$	2.96341	−	5.13278i	0.174018	−	0.301407i
$291$	−6.54163	+	11.3304i	−0.383477	+	0.664202i
$292$	3.53234	+	6.11819i	0.206714	+	0.358040i
$293$	−31.8295			−1.85950			−0.929749	−	0.368193i	$-0.879976\pi$
$293$	−31.8295			−1.85950			−0.929749	+	0.368193i	$0.879976\pi$
$294$	24.3325	+	4.42610i	1.41910	+	0.258135i
$295$	0.648824			0.0377760
$296$	0.178747	+	0.309599i	0.0103895	+	0.0179951i
$297$	1.83078	−	3.17100i	0.106233	−	0.184000i
$298$	−21.1669	+	36.6622i	−1.22617	+	2.12378i
$299$	−1.87953	−	3.25544i	−0.108696	−	0.188267i
$300$	−14.9558			−0.863472
$301$	−2.24341	+	24.8687i	−0.129308	+	1.43341i
$302$	31.5809			1.81728
$303$	1.05460	+	1.82662i	0.0605852	+	0.104937i
$304$	13.0412	−	22.5880i	0.747964	−	1.29551i
$305$	5.27704	−	9.14010i	0.302162	−	0.523360i
$306$	0.222714	+	0.385751i	0.0127317	+	0.0220519i
$307$	28.7884			1.64304			0.821520	−	0.570179i	$-0.193126\pi$
$307$	28.7884			1.64304			0.821520	+	0.570179i	$0.193126\pi$
$308$	−3.49856	+	1.61992i	−0.199349	+	0.0923034i
$309$	−25.3521			−1.44223
$310$	1.42850	+	2.47423i	0.0811332	+	0.140527i
$311$	−2.75931	+	4.77927i	−0.156466	+	0.271007i	−0.933592	−	0.358338i	$-0.883344\pi$
$311$	−2.75931	+	4.77927i	−0.156466	+	0.271007i	0.777126	+	0.629345i	$0.216677\pi$
$312$	0.0603641	−	0.104554i	0.00341744	−	0.00591918i
$313$	2.42399	+	4.19848i	0.137012	+	0.237312i	0.926364	−	0.376629i	$-0.122917\pi$
$313$	2.42399	+	4.19848i	0.137012	+	0.237312i	−0.789352	+	0.613941i	$0.789583\pi$
$314$	15.6363			0.882410
$315$	0.184713	+	0.130082i	0.0104074	+	0.00732929i
$316$	26.4608			1.48854
$317$	3.82756	+	6.62952i	0.214977	+	0.372351i	0.953265	−	0.302134i	$-0.0976990\pi$
$317$	3.82756	+	6.62952i	0.214977	+	0.372351i	−0.738288	+	0.674485i	$0.764366\pi$
$318$	24.8788	−	43.0914i	1.39514	−	2.41645i
$319$	−1.16695	+	2.02122i	−0.0653366	+	0.113166i
$320$	3.74561	+	6.48758i	0.209386	+	0.362667i
$321$	23.9112			1.33459
$322$	−16.3322	−	11.5018i	−0.910161	−	0.640971i
$323$	15.6095			0.868534
$324$	9.43239	+	16.3374i	0.524022	+	0.907633i
$325$	2.08983	−	3.61970i	0.115923	−	0.200785i
$326$	1.69711	−	2.93949i	0.0939945	−	0.162803i
$327$	12.0714	+	20.9082i	0.667548	+	1.15623i
$328$	−0.337786			−0.0186511
$329$	19.9750	−	9.24889i	1.10125	−	0.509908i
$330$	−2.29236			−0.126190
$331$	−5.67159	−	9.82348i	−0.311739	−	0.539947i	0.667000	−	0.745058i	$-0.267578\pi$
$331$	−5.67159	−	9.82348i	−0.311739	−	0.539947i	−0.978739	+	0.205110i	$0.934245\pi$
$332$	−3.60132	+	6.23768i	−0.197648	+	0.342337i
$333$	−0.245540	+	0.425288i	−0.0134555	+	0.0233056i
$334$	−21.9599	−	38.0357i	−1.20159	−	2.08122i
$335$	8.50631			0.464749
$336$	−1.64351	+	18.2186i	−0.0896606	+	0.993907i
$337$	1.74149			0.0948649			0.0474324	−	0.998874i	$-0.484896\pi$
$337$	1.74149			0.0948649			0.0474324	+	0.998874i	$0.484896\pi$
$338$	1.00426	+	1.73943i	0.0546247	+	0.0946127i
$339$	2.86550	−	4.96318i	0.155632	−	0.269563i
$340$	−2.16690	+	3.75319i	−0.117517	+	0.203545i
$341$	−0.562522	−	0.974317i	−0.0304623	−	0.0527622i
$342$	−1.25658			−0.0679480
$343$	−4.93815	+	17.8498i	−0.266635	+	0.963798i
$344$	0.647729			0.0349232
$345$	−2.99449	−	5.18661i	−0.161218	−	0.279238i
$346$	5.86612	−	10.1604i	0.315365	−	0.546228i
$347$	−10.5251	+	18.2301i	−0.565019	+	0.978641i	0.432029	+	0.901860i	$0.357798\pi$
$347$	−10.5251	+	18.2301i	−0.565019	+	0.978641i	−0.997048	+	0.0767814i	$0.975536\pi$
$348$	−5.82891	−	10.0960i	−0.312462	−	0.541200i
$349$	−8.35601			−0.447287			−0.223643	−	0.974671i	$-0.571795\pi$
$349$	−8.35601			−0.447287			−0.223643	+	0.974671i	$0.571795\pi$
$350$	1.99556	−	22.1212i	0.106667	−	1.18243i
$351$	−5.11133			−0.272822
$352$	−2.87682	−	4.98279i	−0.153335	−	0.265584i
$353$	4.26677	−	7.39027i	0.227097	−	0.393344i	−0.729849	−	0.683608i	$-0.760410\pi$
$353$	4.26677	−	7.39027i	0.227097	−	0.393344i	0.956947	+	0.290264i	$0.0937431\pi$
$354$	1.26549	−	2.19189i	0.0672601	−	0.116498i
$355$	−4.97758	−	8.62141i	−0.264182	−	0.457577i
$356$	24.5119			1.29913
$357$	−9.93429	+	4.59982i	−0.525778	+	0.243448i
$358$	−5.09015			−0.269023
$359$	8.08565	+	14.0047i	0.426744	+	0.739142i	0.996582	−	0.0826150i	$-0.0263272\pi$
$359$	8.08565	+	14.0047i	0.426744	+	0.739142i	−0.569837	+	0.821757i	$0.692994\pi$
$360$	0.00293026	−	0.00507535i	0.000154438	−	0.000267495i
$361$	−12.5177	+	21.6812i	−0.658824	+	1.14112i
$362$	−10.7705	−	18.6551i	−0.566086	−	0.980490i
$363$	−18.4469			−0.968212
$364$	4.40025	+	3.09883i	0.230636	+	0.162423i
$365$	−3.14557			−0.164647
$366$	−20.5851	−	35.6544i	−1.07600	−	1.86368i
$367$	−14.0770	+	24.3821i	−0.734813	+	1.27273i	0.219992	+	0.975502i	$0.429397\pi$
$367$	−14.0770	+	24.3821i	−0.734813	+	1.27273i	−0.954805	+	0.297232i	$0.903936\pi$
$368$	7.38747	−	12.7955i	0.385098	−	0.667010i
$369$	−0.232004	−	0.401842i	−0.0120776	−	0.0209191i
$370$	−9.47571			−0.492619
$371$	30.4644	+	21.4543i	1.58164	+	1.11385i
$372$	5.61959			0.291362
$373$	14.2518	+	24.6849i	0.737932	+	1.27814i	0.953425	+	0.301630i	$0.0975308\pi$
$373$	14.2518	+	24.6849i	0.737932	+	1.27814i	−0.215493	+	0.976505i	$0.569136\pi$
$374$	1.69226	−	2.93108i	0.0875046	−	0.151562i
$375$	7.31259	−	12.6658i	0.377621	−	0.654058i
$376$	−0.285506	−	0.494511i	−0.0147238	−	0.0255024i
$377$	3.25799			0.167795
$378$	−24.6479	+	11.4126i	−1.26775	+	0.587000i
$379$	−7.26263			−0.373056			−0.186528	−	0.982450i	$-0.559724\pi$
$379$	−7.26263			−0.373056			−0.186528	+	0.982450i	$0.559724\pi$
$380$	−6.11297	−	10.5880i	−0.313589	−	0.543152i
$381$	0.836286	−	1.44849i	0.0428442	−	0.0742083i
$382$	−1.68576	+	2.91982i	−0.0862510	+	0.149391i
$383$	−6.46627	−	11.1999i	−0.330411	−	0.572289i	0.652181	−	0.758063i	$-0.273854\pi$
$383$	−6.46627	−	11.1999i	−0.330411	−	0.572289i	−0.982592	+	0.185774i	$0.940521\pi$
$384$	0.965684			0.0492799
$385$	0.154231	−	1.70968i	0.00786034	−	0.0871336i
$386$	12.9513			0.659203
$387$	0.444884	+	0.770561i	0.0226147	+	0.0391698i
$388$	−7.56474	+	13.1025i	−0.384041	+	0.665179i
$389$	10.5679	−	18.3041i	0.535811	−	0.928053i	−0.463312	−	0.886195i	$-0.653339\pi$
$389$	10.5679	−	18.3041i	0.535811	−	0.928053i	0.999124	−	0.0418574i	$-0.0133275\pi$
$390$	1.60001	+	2.77129i	0.0810194	+	0.140330i
$391$	8.84232			0.447175
$392$	0.472670	+	0.0859791i	0.0238734	+	0.00434260i
$393$	−33.1047			−1.66991
$394$	1.88049	+	3.25711i	0.0947378	+	0.164091i
$395$	−5.89089	+	10.2033i	−0.296403	+	0.513384i
$396$	−0.0686913	+	0.118977i	−0.00345187	+	0.00597881i
$397$	−9.60366	−	16.6340i	−0.481994	−	0.834838i	0.517792	−	0.855506i	$-0.326754\pi$
$397$	−9.60366	−	16.6340i	−0.481994	−	0.834838i	−0.999786	+	0.0206683i	$0.993421\pi$
$398$	22.8905			1.14740
$399$	2.77476	−	30.7588i	0.138912	−	1.53987i
$400$	16.4282			0.821408
$401$	−8.33460	−	14.4360i	−0.416210	−	0.720897i	0.579344	−	0.815083i	$-0.303309\pi$
$401$	−8.33460	−	14.4360i	−0.416210	−	0.720897i	−0.995555	+	0.0941856i	$0.969975\pi$
$402$	16.5910	−	28.7365i	0.827485	−	1.43325i
$403$	−0.785250	+	1.36009i	−0.0391161	+	0.0677510i
$404$	1.21954	+	2.11230i	0.0606743	+	0.105091i
$405$	−8.39961			−0.417380
$406$	15.7107	−	7.27446i	0.779711	−	0.361025i
$407$	3.73140			0.184959
$408$	0.141993	+	0.245939i	0.00702968	+	0.0121758i
$409$	−6.17416	+	10.6940i	−0.305293	+	0.528782i	−0.977326	−	0.211738i	$-0.932088\pi$
$409$	−6.17416	+	10.6940i	−0.305293	+	0.528782i	0.672034	+	0.740520i	$0.265421\pi$
$410$	4.47667	−	7.75382i	0.221087	−	0.382934i
$411$	−5.43706	−	9.41727i	−0.268190	−	0.464520i
$412$	−29.3171			−1.44435
$413$	1.54961	+	1.09130i	0.0762513	+	0.0536991i
$414$	−0.711817			−0.0349839
$415$	−1.60350	−	2.77735i	−0.0787128	−	0.136335i
$416$	−4.01588	+	6.95570i	−0.196895	+	0.341031i
$417$	3.51811	−	6.09355i	0.172283	−	0.298402i
$418$	4.77397	+	8.26876i	0.233502	+	0.404438i
$419$	4.35934			0.212968			0.106484	−	0.994314i	$-0.466041\pi$
$419$	4.35934			0.212968			0.106484	+	0.994314i	$0.466041\pi$
$420$	7.01055	+	4.93710i	0.342080	+	0.240906i
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	7.56811	+	13.1084i	0.368410	+	0.638105i
$423$	0.392192	−	0.679296i	0.0190690	−	0.0330285i
$424$	0.483284	−	0.837072i	0.0234703	−	0.0406518i
$425$	4.91586	+	8.51451i	0.238454	+	0.413015i
$426$	−38.8338			−1.88150
$427$	27.9766	−	12.9538i	1.35388	−	0.626881i
$428$	27.6509			1.33656
$429$	−0.630060	−	1.09130i	−0.0304196	−	0.0526882i
$430$	−8.58433	+	14.8685i	−0.413973	+	0.717022i
$431$	11.6813	−	20.2326i	0.562667	−	0.974569i	−0.434595	−	0.900626i	$-0.643109\pi$
$431$	11.6813	−	20.2326i	0.562667	−	0.974569i	0.997262	−	0.0739426i	$-0.0235582\pi$
$432$	−10.0450	−	17.3985i	−0.483291	−	0.837084i
$433$	−2.71285			−0.130371			−0.0651856	−	0.997873i	$-0.520764\pi$
$433$	−2.71285			−0.130371			−0.0651856	+	0.997873i	$0.520764\pi$
$434$	−0.749825	+	8.31197i	−0.0359927	+	0.398987i
$435$	5.19068			0.248874
$436$	13.9593	+	24.1782i	0.668529	+	1.15793i
$437$	−12.4724	+	21.6028i	−0.596635	+	1.03340i
$438$	−6.13524	+	10.6265i	−0.293153	+	0.507756i
$439$	4.41760	+	7.65150i	0.210840	+	0.365186i	0.951978	−	0.306167i	$-0.0990467\pi$
$439$	4.41760	+	7.65150i	0.210840	+	0.365186i	−0.741137	+	0.671353i	$0.765713\pi$
$440$	−0.0445303			−0.00212290
$441$	0.222363	+	0.621359i	0.0105887	+	0.0295885i
$442$	−4.72459			−0.224726
$443$	1.45279	+	2.51630i	0.0690240	+	0.119553i	0.898472	−	0.439031i	$-0.144678\pi$
$443$	1.45279	+	2.51630i	0.0690240	+	0.119553i	−0.829448	+	0.558584i	$0.811345\pi$
$444$	−9.31917	+	16.1413i	−0.442268	+	0.766031i
$445$	−5.45700	+	9.45179i	−0.258686	+	0.448058i
$446$	17.7100	+	30.6747i	0.838595	+	1.45249i
$447$	−37.0758			−1.75362
$448$	−1.96609	+	21.7945i	−0.0928888	+	1.02969i
$449$	−15.2777			−0.720998			−0.360499	−	0.932760i	$-0.617394\pi$
$449$	−15.2777			−0.720998			−0.360499	+	0.932760i	$0.617394\pi$
$450$	−0.395732	−	0.685428i	−0.0186550	−	0.0323114i
$451$	−1.76285	+	3.05334i	−0.0830093	+	0.143776i
$452$	3.31366	−	5.73942i	0.155861	−	0.269960i
$453$	13.8292	+	23.9529i	0.649752	+	1.12540i
$454$	10.7035			0.502341
$455$	−2.17452	+	1.00686i	−0.101943	+	0.0472022i
$456$	−0.801141			−0.0375169
$457$	−11.8300	−	20.4902i	−0.553384	−	0.958489i	−0.998027	−	0.0627815i	$-0.980003\pi$
$457$	−11.8300	−	20.4902i	−0.553384	−	0.958489i	0.444643	−	0.895708i	$-0.353330\pi$
$458$	−8.55531	+	14.8182i	−0.399763	+	0.692410i
$459$	6.01161	−	10.4124i	0.280598	−	0.486010i
$460$	−3.46283	−	5.99779i	−0.161455	−	0.279649i
$461$	−26.6170			−1.23968			−0.619839	−	0.784729i	$-0.712802\pi$
$461$	−26.6170			−1.23968			−0.619839	+	0.784729i	$0.712802\pi$
$462$	−5.47493	−	3.85566i	−0.254717	−	0.179382i
$463$	−1.44250			−0.0670385			−0.0335193	−	0.999438i	$-0.510672\pi$
$463$	−1.44250			−0.0670385			−0.0335193	+	0.999438i	$0.510672\pi$
$464$	6.40276	+	11.0899i	0.297240	+	0.514836i
$465$	−1.25107	+	2.16692i	−0.0580171	+	0.100488i
$466$	4.77397	−	8.26876i	0.221150	−	0.383043i
$467$	4.19480	+	7.26560i	0.194112	+	0.336212i	0.946609	−	0.322384i	$-0.104484\pi$
$467$	4.19480	+	7.26560i	0.194112	+	0.336212i	−0.752497	+	0.658596i	$0.771151\pi$
$468$	0.191778			0.00886496
$469$	20.3159	+	14.3073i	0.938102	+	0.660648i
$470$	15.1352			0.698135
$471$	6.84712	+	11.8596i	0.315499	+	0.546460i
$472$	0.0245828	−	0.0425786i	0.00113151	−	0.00195984i
$473$	3.38039	−	5.85500i	0.155430	−	0.269213i
$474$	22.9796	+	39.8019i	1.05549	+	1.82816i
$475$	−27.7359			−1.27261
$476$	−11.4880	+	5.31922i	−0.526552	+	0.243806i
$477$	1.32775			0.0607934
$478$	14.8946	+	25.7983i	0.681265	+	1.17999i
$479$	−6.30608	+	10.9225i	−0.288132	+	0.499060i	−0.973364	−	0.229265i	$-0.926368\pi$
$479$	−6.30608	+	10.9225i	−0.288132	+	0.499060i	0.685232	+	0.728325i	$0.259701\pi$
$480$	−6.39815	+	11.0819i	−0.292034	+	0.505819i
$481$	−2.60441	−	4.51098i	−0.118751	−	0.205683i
$482$	12.2948			0.560013
$483$	1.57182	−	17.4240i	0.0715204	−	0.792819i
$484$	−21.3320			−0.969636
$485$	−3.36823	−	5.83394i	−0.152943	−	0.264905i
$486$	−0.983585	+	1.70362i	−0.0446163	+	0.0772778i
$487$	−10.7840	+	18.6785i	−0.488671	+	0.846403i	−0.999915	−	0.0130329i	$-0.995851\pi$
$487$	−10.7840	+	18.6785i	−0.488671	+	0.846403i	0.511244	+	0.859435i	$0.329185\pi$
$488$	−0.399875	−	0.692604i	−0.0181015	−	0.0313527i
$489$	2.97265			0.134428
$490$	−8.23791	+	9.71058i	−0.372151	+	0.438679i
$491$	39.2347			1.77064			0.885318	−	0.464987i	$-0.153941\pi$
$491$	39.2347			1.77064			0.885318	+	0.464987i	$0.153941\pi$
$492$	−8.80542	−	15.2514i	−0.396979	−	0.687588i
$493$	−3.83184	+	6.63694i	−0.172577	+	0.298913i
$494$	6.66419	−	11.5427i	0.299836	−	0.519332i
$495$	−0.0305850	−	0.0529748i	−0.00137469	−	0.00238104i
$496$	−6.17283			−0.277168
$497$	2.61275	−	28.9629i	0.117198	−	1.29916i
$498$	−12.5101			−0.560592
$499$	−4.58407	−	7.93984i	−0.205211	−	0.355436i	0.744989	−	0.667077i	$-0.232455\pi$
$499$	−4.58407	−	7.93984i	−0.205211	−	0.355436i	−0.950200	+	0.311641i	$0.899121\pi$
$500$	8.45627	−	14.6467i	0.378176	−	0.655020i
$501$	19.2324	−	33.3115i	0.859240	−	1.48825i
$502$	−14.0304	−	24.3013i	−0.626207	−	1.08462i
$503$	24.9370			1.11188			0.555942	−	0.831221i	$-0.312358\pi$
$503$	24.9370			1.11188			0.555942	+	0.831221i	$0.312358\pi$
$504$	0.0155350	−	0.00719307i	0.000691983	−	0.000320405i
$505$	−1.08601			−0.0483267
$506$	2.70432	+	4.68402i	0.120222	+	0.208230i
$507$	−0.879528	+	1.52339i	−0.0390612	+	0.0676560i
$508$	0.967080	−	1.67503i	0.0429072	−	0.0743175i
$509$	−2.94904	−	5.10788i	−0.130714	−	0.226403i	0.793238	−	0.608912i	$-0.208394\pi$
$509$	−2.94904	−	5.10788i	−0.130714	−	0.226403i	−0.923952	+	0.382509i	$0.875060\pi$
$510$	−7.52730			−0.333314
$511$	−7.51268	−	5.29072i	−0.332341	−	0.234048i
$512$	−32.1083			−1.41900
$513$	16.9592	+	29.3741i	0.748765	+	1.29690i
$514$	17.3386	−	30.0314i	0.764775	−	1.32463i
$515$	6.52677	−	11.3047i	0.287604	−	0.498144i
$516$	16.8850	+	29.2457i	0.743321	+	1.28747i
$517$	−5.96003			−0.262122
$518$	−22.6312	−	15.9378i	−0.994357	−	0.700265i
$519$	10.2750			0.451024
$520$	0.0310809	+	0.0538337i	0.00136299	+	0.00236076i
$521$	18.5948	−	32.2071i	0.814652	−	1.41102i	−0.0949259	−	0.995484i	$-0.530261\pi$
$521$	18.5948	−	32.2071i	0.814652	−	1.41102i	0.909578	−	0.415534i	$-0.136405\pi$
$522$	0.308468	−	0.534281i	0.0135013	−	0.0233849i
$523$	2.54540	+	4.40876i	0.111303	+	0.192782i	0.916296	−	0.400502i	$-0.131164\pi$
$523$	2.54540	+	4.40876i	0.111303	+	0.192782i	−0.804993	+	0.593284i	$0.797831\pi$
$524$	−38.2823			−1.67237
$525$	17.6519	−	8.17325i	0.770392	−	0.356710i
$526$	5.23567			0.228286
$527$	−1.84712	−	3.19931i	−0.0804618	−	0.139364i
$528$	2.47644	−	4.28933i	0.107773	−	0.186669i
$529$	4.43475	−	7.68121i	0.192815	−	0.333966i
$530$	12.8099	+	22.1874i	0.556426	+	0.963758i
$531$	0.0675374			0.00293087
$532$	3.20873	−	35.5694i	0.139116	−	1.54213i
$533$	4.92168			0.213181
$534$	21.2871	+	36.8703i	0.921181	+	1.59553i
$535$	−6.15583	+	10.6622i	−0.266140	+	0.460968i
$536$	0.322289	−	0.558220i	0.0139208	−	0.0241114i
$537$	−2.22897	−	3.86068i	−0.0961870	−	0.166601i
$538$	29.1026			1.25470
$539$	3.24397	−	3.82389i	0.139728	−	0.164707i
$540$	−9.41707			−0.405246
$541$	0.383425	+	0.664111i	0.0164847	+	0.0285524i	0.874150	−	0.485656i	$-0.161419\pi$
$541$	0.383425	+	0.664111i	0.0164847	+	0.0285524i	−0.857665	+	0.514208i	$0.828086\pi$
$542$	−8.67272	+	15.0216i	−0.372525	+	0.645232i
$543$	9.43277	−	16.3380i	0.404799	−	0.701133i
$544$	−9.44643	−	16.3617i	−0.405012	−	0.701502i
$545$	−12.4309			−0.532480
$546$	−0.839850	+	9.30992i	−0.0359423	+	0.398428i
$547$	14.1428			0.604702			0.302351	−	0.953197i	$-0.402229\pi$
$547$	14.1428			0.604702			0.302351	+	0.953197i	$0.402229\pi$
$548$	−6.28741	−	10.8901i	−0.268585	−	0.465203i
$549$	0.549297	−	0.951411i	0.0234434	−	0.0406052i
$550$	−3.00691	+	5.20813i	−0.128215	+	0.222075i
$551$	−10.8099	−	18.7233i	−0.460516	−	0.797637i
$552$	−0.453824			−0.0193160
$553$	−31.2310	+	14.4607i	−1.32808	+	0.614932i
$554$	−24.5582			−1.04338
$555$	−4.14939	−	7.18696i	−0.176132	−	0.305069i
$556$	4.06834	−	7.04657i	0.172536	−	0.298841i
$557$	12.4314	−	21.5317i	0.526733	−	0.912329i	−0.472782	−	0.881180i	$-0.656750\pi$
$557$	12.4314	−	21.5317i	0.526733	−	0.912329i	0.999515	−	0.0311490i	$-0.00991664\pi$
$558$	0.148695	+	0.257548i	0.00629477	+	0.0109029i
$559$	−9.43766			−0.399171
$560$	−7.70072	−	5.42315i	−0.325415	−	0.229170i
$561$	2.96414			0.125146
$562$	−24.2852	−	42.0633i	−1.02441	−	1.77433i
$563$	−22.0047	+	38.1133i	−0.927388	+	1.60628i	−0.139713	+	0.990192i	$0.544618\pi$
$563$	−22.0047	+	38.1133i	−0.927388	+	1.60628i	−0.787675	+	0.616091i	$0.788715\pi$
$564$	14.8852	−	25.7818i	0.626778	−	1.08561i
$565$	1.47542	+	2.55550i	0.0620713	+	0.107511i
$566$	61.7989			2.59760
$567$	−20.0611	−	14.1278i	−0.842487	−	0.593312i
$568$	−0.754366			−0.0316525
$569$	16.6308	+	28.8054i	0.697199	+	1.20758i	0.969434	+	0.245353i	$0.0789040\pi$
$569$	16.6308	+	28.8054i	0.697199	+	1.20758i	−0.272235	+	0.962231i	$0.587763\pi$
$570$	10.6175	−	18.3900i	0.444718	−	0.770274i
$571$	6.17699	−	10.6989i	0.258499	−	0.447734i	−0.707341	−	0.706873i	$-0.750105\pi$
$571$	6.17699	−	10.6989i	0.258499	−	0.447734i	0.965840	+	0.259139i	$0.0834387\pi$
$572$	−0.728600	−	1.26197i	−0.0304643	−	0.0527657i
$573$	−2.95276			−0.123353
$574$	23.7334	−	10.9891i	0.990613	−	0.458678i
$575$	−15.7116			−0.655219
$576$	0.389888	+	0.675306i	0.0162453	+	0.0281377i
$577$	12.9829	−	22.4871i	0.540486	−	0.936150i	−0.458390	−	0.888751i	$-0.651574\pi$
$577$	12.9829	−	22.4871i	0.540486	−	0.936150i	0.998876	−	0.0473984i	$-0.0150930\pi$
$578$	−11.5157	+	19.9458i	−0.478990	+	0.829635i
$579$	5.67133	+	9.82304i	0.235693	+	0.408232i
$580$	6.00250			0.249240
$581$	0.841685	−	9.33026i	0.0349190	−	0.387085i
$582$	−26.2781			−1.08926
$583$	−5.04435	−	8.73707i	−0.208916	−	0.361853i
$584$	−0.119180	+	0.206426i	−0.00493171	+	0.00854196i
$585$	−0.0426950	+	0.0739499i	−0.00176522	+	0.00305745i
$586$	−31.9652	−	55.3653i	−1.32047	−	2.28712i
$587$	−23.9747			−0.989543			−0.494771	−	0.869023i	$-0.664748\pi$
$587$	−23.9747			−0.989543			−0.494771	+	0.869023i	$0.664748\pi$
$588$	8.43953	+	23.5829i	0.348040	+	0.972543i
$589$	10.4217			0.429418
$590$	0.651589	+	1.12859i	0.0268255	+	0.0464631i
$591$	−1.64693	+	2.85256i	−0.0677454	+	0.117339i
$592$	10.2366	−	17.7304i	0.420723	−	0.728713i
$593$	−23.5240	−	40.7448i	−0.966015	−	1.67319i	−0.706862	−	0.707352i	$-0.749890\pi$
$593$	−23.5240	−	40.7448i	−0.966015	−	1.67319i	−0.259154	−	0.965836i	$-0.583444\pi$
$594$	7.35433			0.301752
$595$	0.506439	−	5.61398i	0.0207620	−	0.230151i
$596$	−42.8744			−1.75620
$597$	10.0237	+	17.3615i	0.410242	+	0.710560i
$598$	3.77508	−	6.53863i	0.154374	−	0.267384i
$599$	−10.0868	+	17.4708i	−0.412135	+	0.713840i	−0.995123	−	0.0986415i	$-0.968550\pi$
$599$	−10.0868	+	17.4708i	−0.412135	+	0.713840i	0.582988	+	0.812481i	$0.301884\pi$
$600$	−0.252302	−	0.437000i	−0.0103002	−	0.0178404i
$601$	29.5773			1.20648			0.603242	−	0.797558i	$-0.293875\pi$
$601$	29.5773			1.20648			0.603242	+	0.797558i	$0.293875\pi$
$602$	−45.5105	+	21.0724i	−1.85487	+	0.858849i
$603$	0.885439			0.0360579
$604$	15.9921	+	27.6991i	0.650708	+	1.12706i
$605$	4.74907	−	8.22564i	0.193077	−	0.334420i
$606$	−2.11819	+	3.66881i	−0.0860456	+	0.149035i
$607$	7.72099	+	13.3732i	0.313385	+	0.542799i	0.979093	−	0.203413i	$-0.0652035\pi$
$607$	7.72099	+	13.3732i	0.313385	+	0.542799i	−0.665708	+	0.746213i	$0.731870\pi$
$608$	53.2980			2.16152
$609$	12.3971	+	8.73052i	0.502356	+	0.353779i
$610$	21.1981			0.858287
$611$	4.15993	+	7.20521i	0.168293	+	0.291492i
$612$	−0.225557	+	0.390677i	−0.00911762	+	0.0157922i
$613$	−0.997423	+	1.72759i	−0.0402855	+	0.0697766i	−0.885465	−	0.464706i	$-0.846160\pi$
$613$	−0.997423	+	1.72759i	−0.0402855	+	0.0697766i	0.845180	+	0.534482i	$0.179493\pi$
$614$	28.9111	+	50.0755i	1.16676	+	2.02088i
$615$	7.84129			0.316191
$616$	−0.106353	−	0.0748982i	−0.00428510	−	0.00301773i
$617$	−2.85584			−0.114972			−0.0574858	−	0.998346i	$-0.518308\pi$
$617$	−2.85584			−0.114972			−0.0574858	+	0.998346i	$0.518308\pi$
$618$	−25.4601	−	44.0982i	−1.02416	−	1.77389i
$619$	−15.9911	+	27.6975i	−0.642738	+	1.11326i	0.342080	+	0.939671i	$0.388868\pi$
$619$	−15.9911	+	27.6975i	−0.642738	+	1.11326i	−0.984819	+	0.173585i	$0.944465\pi$
$620$	−1.44674	+	2.50582i	−0.0581024	+	0.100636i
$621$	9.60688	+	16.6396i	0.385511	+	0.667725i
$622$	−11.0843			−0.444440
$623$	−28.9307	+	13.3956i	−1.15908	+	0.536684i
$624$	−6.91395			−0.276780
$625$	−6.68398	−	11.5770i	−0.267359	−	0.463080i
$626$	−4.86865	+	8.43275i	−0.194590	+	0.337040i
$627$	−4.18102	+	7.24174i	−0.166974	+	0.289207i
$628$	7.91800	+	13.7144i	0.315963	+	0.547263i
$629$	12.2526			0.488542
$630$	−0.0407689	+	0.451932i	−0.00162427	+	0.0180054i
$631$	32.1115			1.27834			0.639169	−	0.769066i	$-0.279278\pi$
$631$	32.1115			1.27834			0.639169	+	0.769066i	$0.279278\pi$
$632$	0.446390	+	0.773171i	0.0177565	+	0.0307551i
$633$	−6.62812	+	11.4802i	−0.263444	+	0.456298i
$634$	−7.68774	+	13.3156i	−0.305319	+	0.528828i
$635$	0.430596	+	0.745814i	0.0170877	+	0.0295967i
$636$	50.3930			1.99821
$637$	−6.88699	−	1.25275i	−0.272872	−	0.0496357i
$638$	−4.68769			−0.185588
$639$	−0.518126	−	0.897420i	−0.0204967	−	0.0355014i
$640$	−0.248611	+	0.430607i	−0.00982721	+	0.0170212i
$641$	−16.5124	+	28.6003i	−0.652200	+	1.12964i	0.330387	+	0.943845i	$0.392821\pi$
$641$	−16.5124	+	28.6003i	−0.652200	+	1.12964i	−0.982588	+	0.185799i	$0.940513\pi$
$642$	24.0131	+	41.5920i	0.947723	+	1.64150i
$643$	15.7942			0.622863			0.311432	−	0.950269i	$-0.399192\pi$
$643$	15.7942			0.622863			0.311432	+	0.950269i	$0.399192\pi$
$644$	1.81765	−	20.1491i	0.0716256	−	0.793985i
$645$	−15.0362			−0.592051
$646$	15.6760	+	27.1516i	0.616764	+	1.06827i
$647$	2.32036	−	4.01898i	0.0912227	−	0.158002i	−0.816803	−	0.576916i	$-0.804256\pi$
$647$	2.32036	−	4.01898i	0.0912227	−	0.158002i	0.908026	+	0.418914i	$0.137589\pi$
$648$	−0.318246	+	0.551219i	−0.0125019	+	0.0216539i
$649$	−0.256587	−	0.444421i	−0.0100719	−	0.0174451i
$650$	8.39497			0.329278
$651$	−6.63265	+	3.07108i	−0.259954	+	0.120365i
$652$	3.43757			0.134626
$653$	−13.4143	−	23.2342i	−0.524941	−	0.909225i	−0.999578	−	0.0290430i	$-0.990754\pi$
$653$	−13.4143	−	23.2342i	−0.524941	−	0.909225i	0.474637	−	0.880182i	$-0.342579\pi$
$654$	−24.2456	+	41.9946i	−0.948079	+	1.64212i
$655$	8.52266	−	14.7617i	0.333008	−	0.576787i
$656$	9.67230	+	16.7529i	0.377640	+	0.654092i
$657$	−0.327429			−0.0127742
$658$	36.1479	+	25.4568i	1.40919	+	0.992409i
$659$	−42.9889			−1.67461			−0.837306	−	0.546735i	$-0.815871\pi$
$659$	−42.9889			−1.67461			−0.837306	+	0.546735i	$0.815871\pi$
$660$	−1.16082	−	2.01059i	−0.0451847	−	0.0782623i
$661$	14.7349	−	25.5216i	0.573122	−	0.992676i	−0.423121	−	0.906073i	$-0.639066\pi$
$661$	14.7349	−	25.5216i	0.573122	−	0.992676i	0.996243	−	0.0866030i	$-0.0276012\pi$
$662$	11.3915	−	19.7307i	0.442744	−	0.766855i
$663$	−2.06889	−	3.58342i	−0.0803490	−	0.139169i
$664$	−0.243015			−0.00943082
$665$	13.0013	+	9.15599i	0.504167	+	0.355054i
$666$	−0.986346			−0.0382201
$667$	−6.12349	−	10.6062i	−0.237102	−	0.410673i
$668$	22.2403	−	38.5214i	0.860504	−	1.49044i
$669$	−15.5104	+	26.8647i	−0.599666	+	1.03865i
$670$	8.54256	+	14.7962i	0.330028	+	0.571625i
$671$	−8.34752			−0.322252
$672$	−33.9203	+	15.7059i	−1.30850	+	0.605869i
$673$	−20.1702			−0.777504			−0.388752	−	0.921342i	$-0.627094\pi$
$673$	−20.1702			−0.777504			−0.388752	+	0.921342i	$0.627094\pi$
$674$	1.74891	+	3.02920i	0.0673655	+	0.116680i
$675$	−10.6818	+	18.5015i	−0.411144	+	0.712122i
$676$	−1.01709	+	1.76164i	−0.0391187	+	0.0677555i
$677$	3.10241	+	5.37353i	0.119235	+	0.206521i	0.919465	−	0.393172i	$-0.128622\pi$
$677$	3.10241	+	5.37353i	0.119235	+	0.206521i	−0.800230	+	0.599694i	$0.795289\pi$
$678$	11.5108			0.442071
$679$	1.76800	−	19.5986i	0.0678495	−	0.752126i
$680$	−0.146221			−0.00560733
$681$	4.68704	+	8.11820i	0.179608	+	0.311090i
$682$	1.12984	−	1.95694i	0.0432638	−	0.0749351i
$683$	0.884758	−	1.53245i	0.0338543	−	0.0586374i	−0.848602	−	0.529032i	$-0.822555\pi$
$683$	0.884758	−	1.53245i	0.0338543	−	0.0586374i	0.882456	+	0.470395i	$0.155888\pi$
$684$	−0.636312	−	1.10212i	−0.0243300	−	0.0421408i
$685$	5.59899			0.213926
$686$	−36.0077	+	9.33627i	−1.37478	+	0.356460i
$687$	−14.9854			−0.571729
$688$	−18.5473	−	32.1249i	−0.707110	−	1.22475i
$689$	−7.04163	+	12.1965i	−0.268265	+	0.464648i
$690$	6.01451	−	10.4174i	0.228969	−	0.396585i
$691$	−22.4658	−	38.9120i	−0.854641	−	1.48028i	−0.876977	−	0.480531i	$-0.840444\pi$
$691$	−22.4658	−	38.9120i	−0.854641	−	1.48028i	0.0223363	−	0.999751i	$-0.492890\pi$
$692$	11.8820			0.451688
$693$	0.0160542	−	0.177964i	0.000609849	−	0.00676031i
$694$	−42.2800			−1.60493
$695$	1.81144	+	3.13751i	0.0687120	+	0.119013i
$696$	0.196666	−	0.340635i	0.00745459	−	0.0129117i
$697$	−5.78856	+	10.0261i	−0.219257	+	0.379765i
$698$	−8.39162	−	14.5347i	−0.317628	−	0.550147i
$699$	8.36204			0.316281
$700$	20.4126	−	9.45154i	0.771525	−	0.357235i
$701$	38.5707			1.45679			0.728397	−	0.685156i	$-0.240266\pi$
$701$	38.5707			1.45679			0.728397	+	0.685156i	$0.240266\pi$
$702$	−5.13311	−	8.89081i	−0.193737	−	0.335562i
$703$	−17.2827	+	29.9344i	−0.651828	+	1.12900i
$704$	2.96251	−	5.13121i	0.111654	−	0.193390i
$705$	6.62767	+	11.4795i	0.249612	+	0.432341i
$706$	17.1398			0.645066
$707$	−2.59375	−	1.82662i	−0.0975480	−	0.0686972i
$708$	2.56330			0.0963346
$709$	−4.38866	−	7.60137i	−0.164819	−	0.285476i	0.771772	−	0.635900i	$-0.219371\pi$
$709$	−4.38866	−	7.60137i	−0.164819	−	0.285476i	−0.936591	+	0.350424i	$0.886037\pi$
$710$	9.99758	−	17.3163i	0.375203	−	0.649870i
$711$	−0.613194	+	1.06208i	−0.0229966	+	0.0398312i
$712$	0.413512	+	0.716223i	0.0154970	+	0.0268416i
$713$	5.90360			0.221091
$714$	−17.9777	−	12.6606i	−0.672799	−	0.473811i
$715$	0.648824			0.0242646
$716$	−2.57757	−	4.46449i	−0.0963284	−	0.166846i
$717$	−13.0447	+	22.5940i	−0.487161	+	0.843788i
$718$	−16.2402	+	28.1289i	−0.606080	+	1.04976i
$719$	−2.10218	−	3.64109i	−0.0783982	−	0.135790i	0.824161	−	0.566356i	$-0.191647\pi$
$719$	−2.10218	−	3.64109i	−0.0783982	−	0.135790i	−0.902559	+	0.430566i	$0.858314\pi$
$720$	−0.335625			−0.0125080
$721$	34.6022	−	16.0216i	1.28865	−	0.596677i
$722$	−50.2840			−1.87138
$723$	5.38386	+	9.32513i	0.200228	+	0.346805i
$724$	10.9080	−	18.8933i	0.405394	−	0.702164i
$725$	6.80866	−	11.7930i	0.252867	−	0.437979i
$726$	−18.5255	−	32.0872i	−0.687547	−	1.19087i
$727$	−28.9856			−1.07502			−0.537509	−	0.843258i	$-0.680634\pi$
$727$	−28.9856			−1.07502			−0.537509	+	0.843258i	$0.680634\pi$
$728$	−0.0163145	+	0.180850i	−0.000604656	+	0.00670274i
$729$	26.0990			0.966630
$730$	−3.15898	−	5.47151i	−0.116919	−	0.202510i
$731$	11.1000	−	19.2257i	0.410547	−	0.711089i
$732$	20.8479	−	36.1096i	0.770561	−	1.33465i
$733$	12.0172	+	20.8145i	0.443867	+	0.768800i	0.997972	−	0.0636467i	$-0.0202731\pi$
$733$	12.0172	+	20.8145i	0.443867	+	0.768800i	−0.554106	+	0.832446i	$0.686940\pi$
$734$	−56.5480			−2.08722
$735$	−10.9725	−	1.99590i	−0.404725	−	0.0736198i
$736$	30.1918			1.11288
$737$	−3.36394	−	5.82652i	−0.123912	−	0.214622i
$738$	0.465985	−	0.807110i	0.0171532	−	0.0297101i
$739$	−5.90276	+	10.2239i	−0.217136	+	0.376091i	−0.953931	−	0.300025i	$-0.903005\pi$
$739$	−5.90276	+	10.2239i	−0.217136	+	0.376091i	0.736795	+	0.676116i	$0.236338\pi$
$740$	−4.79835	−	8.31099i	−0.176391	−	0.305518i
$741$	11.6729			0.428816
$742$	−6.72396	+	74.5366i	−0.246844	+	2.73632i
$743$	47.2786			1.73448			0.867241	−	0.497888i	$-0.165891\pi$
$743$	47.2786			1.73448			0.867241	+	0.497888i	$0.165891\pi$
$744$	0.0948017	+	0.164201i	0.00347560	+	0.00601992i
$745$	9.54499	−	16.5324i	0.349701	−	0.605700i
$746$	−28.6252	+	49.5802i	−1.04804	+	1.81526i
$747$	−0.166912	−	0.289100i	−0.00610698	−	0.0105776i
$748$	3.42773			0.125330
$749$	−32.6356	+	15.1111i	−1.19248	+	0.552147i
$750$	29.3750			1.07262
$751$	−2.73850	−	4.74322i	−0.0999294	−	0.173083i	0.811726	−	0.584039i	$-0.198528\pi$
$751$	−2.73850	−	4.74322i	−0.0999294	−	0.173083i	−0.911655	+	0.410956i	$0.865195\pi$
$752$	−16.3506	+	28.3200i	−0.596244	+	1.03273i
$753$	12.2877	−	21.2830i	0.447790	−	0.775596i
$754$	3.27188	+	5.66706i	0.119155	+	0.206382i
$755$	−14.2410			−0.518285
$756$	−22.4911	−	15.8391i	−0.817994	−	0.576064i
$757$	10.7453			0.390546			0.195273	−	0.980749i	$-0.437441\pi$
$757$	10.7453			0.390546			0.195273	+	0.980749i	$0.437441\pi$
$758$	−7.29358	−	12.6329i	−0.264915	−	0.458846i
$759$	−2.36843	+	4.10224i	−0.0859686	+	0.148902i
$760$	0.206250	−	0.357236i	0.00748148	−	0.0129583i
$761$	16.5200	+	28.6134i	0.598848	+	1.03724i	0.992991	+	0.118186i	$0.0377080\pi$
$761$	16.5200	+	28.6134i	0.598848	+	1.03724i	−0.394143	+	0.919049i	$0.628959\pi$
$762$	3.35940			0.121698
$763$	−29.6891	−	20.9082i	−1.07482	−	0.756928i
$764$	−3.41457			−0.123535
$765$	−0.100430	−	0.173950i	−0.00363106	−	0.00628918i
$766$	12.9877	−	22.4953i	0.469263	−	0.812788i
$767$	−0.358181	+	0.620387i	−0.0129332	+	0.0224009i
$768$	−13.5793	−	23.5201i	−0.490002	−	0.848708i
$769$	2.98332			0.107581			0.0537907	−	0.998552i	$-0.482870\pi$
$769$	2.98332			0.107581			0.0537907	+	0.998552i	$0.482870\pi$
$770$	3.12877	−	1.44870i	0.112753	−	0.0522074i
$771$	30.3702			1.09376
$772$	6.55833	+	11.3594i	0.236039	+	0.408832i
$773$	10.9543	−	18.9733i	0.393998	−	0.682424i	−0.598975	−	0.800768i	$-0.704425\pi$
$773$	10.9543	−	18.9733i	0.393998	−	0.682424i	0.992973	+	0.118344i	$0.0377585\pi$
$774$	−0.893560	+	1.54769i	−0.0321184	+	0.0556306i
$775$	3.28208	+	5.68473i	0.117896	+	0.204202i
$776$	−0.510464			−0.0183246
$777$	2.17803	−	24.1440i	0.0781365	−	0.866160i
$778$	42.4516			1.52196
$779$	−16.3299	−	28.2842i	−0.585079	−	1.01339i
$780$	−1.62044	+	2.80668i	−0.0580209	+	0.100495i
$781$	−3.93691	+	6.81892i	−0.140874	+	0.244000i
$782$	8.88001	+	15.3806i	0.317548	+	0.550010i
$783$	−16.6527			−0.595118
$784$	−9.27039	−	25.9046i	−0.331085	−	0.925165i
$785$	−7.05104			−0.251662
$786$	−33.2458	−	57.5835i	−1.18584	−	2.05393i
$787$	6.68161	−	11.5729i	0.238174	−	0.412529i	−0.722017	−	0.691876i	$-0.756785\pi$
$787$	6.68161	−	11.5729i	0.238174	−	0.412529i	0.960190	+	0.279347i	$0.0901179\pi$
$788$	−1.90450	+	3.29869i	−0.0678451	+	0.117511i
$789$	2.29269	+	3.97105i	0.0816218	+	0.141373i
$790$	−23.6640			−0.841927
$791$	−0.774453	+	8.58498i	−0.0275364	+	0.305247i
$792$	−0.00463525			−0.000164706
$793$	5.82633	+	10.0915i	0.206899	+	0.358360i
$794$	19.2892	−	33.4099i	0.684548	−	1.18567i
$795$	−11.2188	+	19.4316i	−0.397891	+	0.689167i
$796$	11.5914	+	20.0768i	0.410845	+	0.711605i
$797$	32.5388			1.15258			0.576292	−	0.817244i	$-0.304499\pi$
$797$	32.5388			1.15258			0.576292	+	0.817244i	$0.304499\pi$
$798$	56.2894	−	26.0634i	1.99262	−	0.922634i
$799$	−19.5706			−0.692357
$800$	16.7850	+	29.0725i	0.593440	+	1.02787i
$801$	−0.568030	+	0.983857i	−0.0200703	+	0.0347629i
$802$	16.7403	−	28.9950i	0.591119	−	1.02385i
$803$	1.24396	+	2.15460i	0.0438984	+	0.0760343i
$804$	33.6057			1.18518
$805$	7.36484	+	5.18661i	0.259577	+	0.182804i
$806$	−3.15439			−0.111109
$807$	12.7440	+	22.0732i	0.448608	+	0.777013i
$808$	−0.0411469	+	0.0712685i	−0.00144754	+	0.00250722i
$809$	−3.84413	+	6.65824i	−0.135153	+	0.234091i	−0.925656	−	0.378367i	$-0.876486\pi$
$809$	−3.84413	+	6.65824i	−0.135153	+	0.234091i	0.790503	+	0.612458i	$0.209819\pi$
$810$	−8.43542	−	14.6106i	−0.296390	−	0.513363i
$811$	−48.3178			−1.69667			−0.848334	−	0.529461i	$-0.822394\pi$
$811$	−48.3178			−1.69667			−0.848334	+	0.529461i	$0.822394\pi$
$812$	14.3360	+	10.0960i	0.503094	+	0.354299i
$813$	−15.1911			−0.532773
$814$	3.74731	+	6.49052i	0.131343	+	0.227493i
$815$	−0.765295	+	1.32553i	−0.0268071	+	0.0464313i
$816$	8.13175	−	14.0846i	0.284668	−	0.493060i
$817$	31.3137	+	54.2370i	1.09553	+	1.89751i
$818$	−24.8019			−0.867178
$819$	−0.226351	+	0.104806i	−0.00790933	+	0.00366221i
$820$	9.06766			0.316656
$821$	1.86721	+	3.23410i	0.0651661	+	0.112871i	0.896768	−	0.442502i	$-0.145909\pi$
$821$	1.86721	+	3.23410i	0.0651661	+	0.112871i	−0.831602	+	0.555373i	$0.812576\pi$
$822$	10.9205	−	18.9148i	0.380895	−	0.659730i
$823$	−7.11590	+	12.3251i	−0.248045	+	0.429626i	−0.962983	−	0.269561i	$-0.913121\pi$
$823$	−7.11590	+	12.3251i	−0.248045	+	0.429626i	0.714939	+	0.699187i	$0.246455\pi$
$824$	−0.494575	−	0.856629i	−0.0172293	−	0.0298421i
$825$	−5.26688			−0.183369
$826$	−0.342022	+	3.79139i	−0.0119005	+	0.131919i
$827$	48.3016			1.67961			0.839805	−	0.542888i	$-0.182669\pi$
$827$	48.3016			1.67961			0.839805	+	0.542888i	$0.182669\pi$
$828$	−0.360453	−	0.624323i	−0.0125266	−	0.0216967i
$829$	−5.75506	+	9.96806i	−0.199882	+	0.346205i	−0.948490	−	0.316808i	$-0.897389\pi$
$829$	−5.75506	+	9.96806i	−0.199882	+	0.346205i	0.748608	+	0.663013i	$0.230722\pi$
$830$	3.22067	−	5.57837i	0.111791	−	0.193628i
$831$	−10.7540	−	18.6264i	−0.373051	−	0.646143i
$832$	−8.27099			−0.286745
$833$	10.6520	−	12.5563i	0.369071	−	0.435049i
$834$	14.1324			0.489366
$835$	9.90258	+	17.1518i	0.342693	+	0.593562i
$836$	−4.83493	+	8.37434i	−0.167219	+	0.289633i
$837$	4.01367	−	6.95188i	0.138733	−	0.240292i
$838$	4.37792	+	7.58278i	0.151233	+	0.261943i
$839$	13.1103			0.452616			0.226308	−	0.974056i	$-0.427334\pi$
$839$	13.1103			0.452616			0.226308	+	0.974056i	$0.427334\pi$
$840$	−0.0259925	+	0.288133i	−0.000896827	+	0.00994152i
$841$	−18.3855			−0.633982
$842$	−10.0426	−	17.3943i	−0.346092	−	0.599448i
$843$	21.2689	−	36.8388i	0.732539	−	1.26880i
$844$	−7.66475	+	13.2757i	−0.263831	+	0.456969i
$845$	−0.452861	−	0.784378i	−0.0155789	−	0.0269834i
$846$	1.57545			0.0541652
$847$	25.1776	−	11.6578i	0.865111	−	0.400568i
$848$	−55.3541			−1.90087
$849$	27.0616	+	46.8721i	0.928751	+	1.60864i
$850$	−9.87362	+	17.1016i	−0.338662	+	0.586580i
$851$	−9.79014	+	16.9570i	−0.335602	+	0.581279i
$852$	−19.6648	−	34.0605i	−0.673706	−	1.16689i
$853$	8.80346			0.301425			0.150712	−	0.988578i	$-0.451843\pi$
$853$	8.80346			0.301425			0.150712	+	0.988578i	$0.451843\pi$
$854$	50.6282	+	35.6544i	1.73246	+	1.22007i
$855$	0.566640			0.0193787
$856$	0.466467	+	0.807945i	0.0159435	+	0.0276150i
$857$	−8.48254	+	14.6922i	−0.289758	+	0.501876i	−0.973752	−	0.227612i	$-0.926908\pi$
$857$	−8.48254	+	14.6922i	−0.289758	+	0.501876i	0.683994	+	0.729488i	$0.260242\pi$
$858$	1.26549	−	2.19189i	0.0432031	−	0.0748300i
$859$	−7.27049	−	12.5929i	−0.248066	−	0.429663i	0.714923	−	0.699203i	$-0.246462\pi$
$859$	−7.27049	−	12.5929i	−0.248066	−	0.429663i	−0.962989	+	0.269540i	$0.913128\pi$
$860$	−17.3879			−0.592922
$861$	18.7276	+	13.1887i	0.638236	+	0.449471i
$862$	46.9243			1.59825
$863$	−19.5222	−	33.8135i	−0.664544	−	1.15102i	−0.979409	−	0.201887i	$-0.935293\pi$
$863$	−19.5222	−	33.8135i	−0.664544	−	1.15102i	0.314865	−	0.949136i	$-0.398041\pi$
$864$	20.5265	−	35.5529i	0.698324	−	1.20953i
$865$	−2.64526	+	4.58173i	−0.0899416	+	0.155783i
$866$	−2.72441	−	4.71882i	−0.0925793	−	0.160352i
$867$	−20.1708			−0.685036
$868$	−7.66999	+	3.55139i	−0.260336	+	0.120542i
$869$	9.31854			0.316110
$870$	5.21281	+	9.02885i	0.176731	+	0.306107i
$871$	−4.69587	+	8.13349i	−0.159114	+	0.275593i
$872$	−0.470983	+	0.815767i	−0.0159495	+	0.0276253i
$873$	−0.350605	−	0.607266i	−0.0118662	−	0.0205529i
$874$	−50.1022			−1.69473
$875$	−1.97636	+	21.9084i	−0.0668133	+	0.740639i
$876$	−12.4272			−0.419875
$877$	−16.2971	−	28.2273i	−0.550312	−	0.953169i	−0.998252	−	0.0591051i	$-0.981175\pi$
$877$	−16.2971	−	28.2273i	−0.550312	−	0.953169i	0.447939	−	0.894064i	$-0.352158\pi$
$878$	−8.87285	+	15.3682i	−0.299444	+	0.518652i
$879$	27.9949	−	48.4886i	0.944245	−	1.63548i
$880$	1.27510	+	2.20853i	0.0429835	+	0.0744497i
$881$	−43.4141			−1.46266			−0.731330	−	0.682024i	$-0.761100\pi$
$881$	−43.4141			−1.46266			−0.731330	+	0.682024i	$0.761100\pi$
$882$	−0.857501	+	1.01079i	−0.0288736	+	0.0340352i
$883$	28.2902			0.952040			0.476020	−	0.879434i	$-0.342079\pi$
$883$	28.2902			0.952040			0.476020	+	0.879434i	$0.342079\pi$
$884$	−2.39246	−	4.14386i	−0.0804672	−	0.139373i
$885$	−0.570659	+	0.988410i	−0.0191825	+	0.0332250i
$886$	−2.91796	+	5.05406i	−0.0980308	+	0.169794i
$887$	25.1325	+	43.5307i	0.843866	+	1.46162i	0.886602	+	0.462532i	$0.153059\pi$
$887$	25.1325	+	43.5307i	0.843866	+	1.46162i	−0.0427364	+	0.999086i	$0.513608\pi$
$888$	−0.628852			−0.0211029
$889$	−0.226022	+	2.50550i	−0.00758052	+	0.0840317i
$890$	−21.9210			−0.734794
$891$	3.32175	+	5.75344i	0.111283	+	0.192747i
$892$	−17.9362	+	31.0664i	−0.600548	+	1.04018i
$893$	27.6049	−	47.8131i	0.923764	−	1.60001i
$894$	−37.2338	−	64.4908i	−1.24528	−	2.15690i
$895$	2.29535			0.0767250
$896$	−1.31803	+	0.610280i	−0.0440323	+	0.0203880i
$897$	6.61239			0.220781
$898$	−15.3428	−	26.5745i	−0.511996	−	0.886803i
$899$	−2.55834	+	4.43117i	−0.0853253	+	0.147788i
$900$	0.400785	−	0.694180i	0.0133595	−	0.0231393i
$901$	−16.5638	−	28.6894i	−0.551821	−	0.955782i
$902$	−7.08145			−0.235786
$903$	−35.9115	−	25.2903i	−1.19506	−	0.841609i
$904$	0.223604			0.00743695
$905$	4.85685	+	8.41231i	0.161447	+	0.279635i
$906$	−27.7763	+	48.1099i	−0.922805	+	1.59835i
$907$	−13.4138	+	23.2334i	−0.445399	+	0.771453i	−0.998080	−	0.0619394i	$-0.980271\pi$
$907$	−13.4138	+	23.2334i	−0.445399	+	0.771453i	0.552681	+	0.833393i	$0.313605\pi$
$908$	5.42009	+	9.38787i	0.179872	+	0.311548i
$909$	−0.113045			−0.00374946
$910$	−3.93516	−	2.77129i	−0.130449	−	0.0918674i
$911$	−22.3560			−0.740687			−0.370344	−	0.928895i	$-0.620760\pi$
$911$	−22.3560			−0.740687			−0.370344	+	0.928895i	$0.620760\pi$
$912$	22.9402	+	39.7336i	0.759626	+	1.31571i
$913$	−1.26826	+	2.19668i	−0.0419731	+	0.0726996i
$914$	23.7608	−	41.1550i	0.785939	−	1.36129i
$915$	9.28260	+	16.0779i	0.306873	+	0.531520i
$916$	−17.3291			−0.572569
$917$	45.1835	−	20.9211i	1.49209	−	0.690875i
$918$	24.1489			0.797034
$919$	4.31122	+	7.46725i	0.142214	+	0.246322i	0.928330	−	0.371757i	$-0.121245\pi$
$919$	4.31122	+	7.46725i	0.142214	+	0.246322i	−0.786116	+	0.618079i	$0.787911\pi$
$920$	0.116835	−	0.202364i	0.00385193	−	0.00667174i
$921$	−25.3202	+	43.8559i	−0.834329	+	1.44510i
$922$	−26.7305	−	46.2985i	−0.880321	−	1.52476i
$923$	10.9914			0.361786
$924$	0.609318	−	6.75442i	0.0200451	−	0.222204i
$925$	−21.7712			−0.715832
$926$	−1.44865	−	2.50913i	−0.0476054	−	0.0824550i
$927$	0.679385	−	1.17673i	0.0223139	−	0.0386488i
$928$	−13.0837	+	22.6616i	−0.429493	+	0.743904i
$929$	−20.6930	−	35.8414i	−0.678916	−	1.17592i	−0.975308	−	0.220851i	$-0.929117\pi$
$929$	−20.6930	−	35.8414i	−0.678916	−	1.17592i	0.296391	−	0.955067i	$-0.404217\pi$
$930$	−5.02562			−0.164796
$931$	15.6513	+	43.7352i	0.512952	+	1.43336i
$932$	9.66985			0.316747
$933$	−4.85379	−	8.40700i	−0.158906	−	0.275233i
$934$	−8.42535	+	14.5931i	−0.275686	+	0.477502i
$935$	−0.763105	+	1.32174i	−0.0249562	+	0.0432254i
$936$	0.00323527	+	0.00560366i	0.000105748	+	0.000183161i
$937$	21.3818			0.698514			0.349257	−	0.937027i	$-0.386434\pi$
$937$	21.3818			0.698514			0.349257	+	0.937027i	$0.386434\pi$
$938$	−4.48403	+	49.7064i	−0.146409	+	1.62297i
$939$	−8.52788			−0.278297
$940$	7.66423	+	13.2748i	0.249979	+	0.432977i
$941$	26.5740	−	46.0275i	0.866288	−	1.50046i	0.000525658	−	1.00000i	$-0.499833\pi$
$941$	26.5740	−	46.0275i	0.866288	−	1.50046i	0.865762	−	0.500455i	$-0.166834\pi$
$942$	−13.7526	+	23.8202i	−0.448084	+	0.776105i
$943$	−9.25043	−	16.0222i	−0.301235	−	0.521755i
$944$	−2.81565			−0.0916416
$945$	11.1147	−	5.14638i	0.361561	−	0.167412i
$946$	13.5792			0.441497
$947$	4.43468	+	7.68109i	0.144108	+	0.249602i	0.929040	−	0.369980i	$-0.120635\pi$
$947$	4.43468	+	7.68109i	0.144108	+	0.249602i	−0.784932	+	0.619582i	$0.787302\pi$
$948$	−23.2730	+	40.3101i	−0.755873	+	1.30921i
$949$	1.73650	−	3.00771i	0.0563692	−	0.0976343i
$950$	−27.8541	−	48.2448i	−0.903707	−	1.56527i
$951$	−13.4658			−0.436658
$952$	−0.349226	−	0.245939i	−0.0113185	−	0.00797091i
$953$	−39.8167			−1.28979			−0.644894	−	0.764272i	$-0.723099\pi$
$953$	−39.8167			−1.28979			−0.644894	+	0.764272i	$0.723099\pi$
$954$	1.33341	+	2.30953i	0.0431706	+	0.0747737i
$955$	0.760174	−	1.31666i	0.0245987	−	0.0426061i
$956$	−15.0848	+	26.1277i	−0.487878	+	0.845029i
$957$	−2.05273	−	3.55543i	−0.0663553	−	0.114931i
$958$	−25.3319			−0.818435
$959$	13.3723	+	9.41727i	0.431813	+	0.304099i
$960$	−13.1775			−0.425301
$961$	14.2668	+	24.7108i	0.460218	+	0.797121i
$962$	5.23103	−	9.06041i	0.168655	−	0.292119i
$963$	−0.640773	+	1.10985i	−0.0206486	+	0.0357645i
$964$	6.22589	+	10.7836i	0.200523	+	0.347315i
$965$	−5.84024			−0.188004
$966$	31.8864	−	14.7642i	1.02593	−	0.475029i
$967$	−22.1611			−0.712652			−0.356326	−	0.934362i	$-0.615971\pi$
$967$	−22.1611			−0.712652			−0.356326	+	0.934362i	$0.615971\pi$
$968$	−0.359868	−	0.623309i	−0.0115666	−	0.0200339i
$969$	−13.7290	+	23.7793i	−0.441038	+	0.763900i
$970$	6.76516	−	11.7176i	0.217216	−	0.376230i
$971$	−18.0212	−	31.2136i	−0.578327	−	1.00169i	−0.995671	−	0.0929428i	$-0.970373\pi$
$971$	−18.0212	−	31.2136i	−0.578327	−	1.00169i	0.417345	−	0.908748i	$-0.362961\pi$
$972$	−1.99229			−0.0639027
$973$	−0.950834	+	10.5402i	−0.0304824	+	0.337903i
$974$	−43.3199			−1.38806
$975$	3.67614	+	6.36725i	0.117731	+	0.203915i
$976$	−22.9004	+	39.6646i	−0.733022	+	1.26963i
$977$	−16.4708	+	28.5283i	−0.526947	+	0.912700i	0.472559	+	0.881299i	$0.343330\pi$
$977$	−16.4708	+	28.5283i	−0.526947	+	0.912700i	−0.999507	+	0.0314009i	$0.990003\pi$
$978$	2.98532	+	5.17072i	0.0954600	+	0.165342i
$979$	8.63219			0.275886
$980$	−12.6885	−	2.30805i	−0.405320	−	0.0737281i
$981$	−1.29395			−0.0413128
$982$	39.4019	+	68.2461i	1.25736	+	2.17782i
$983$	2.09973	−	3.63683i	0.0669709	−	0.115997i	−0.830596	−	0.556876i	$-0.812000\pi$
$983$	2.09973	−	3.63683i	0.0669709	−	0.115997i	0.897567	+	0.440879i	$0.145333\pi$
$984$	0.297092	−	0.514579i	0.00947096	−	0.0164042i
$985$	−0.847986	−	1.46876i	−0.0270191	−	0.0467984i
$986$	−15.3927			−0.490203
$987$	−3.47889	+	38.5643i	−0.110734	+	1.22751i
$988$	13.4986			0.429447
$989$	17.7383	+	30.7237i	0.564047	+	0.976958i
$990$	0.0614308	−	0.106401i	0.00195240	−	0.00338165i
$991$	6.70693	−	11.6167i	0.213053	−	0.369018i	−0.739616	−	0.673029i	$-0.764993\pi$
$991$	6.70693	−	11.6167i	0.213053	−	0.369018i	0.952668	+	0.304011i	$0.0983261\pi$
$992$	−6.30693	−	10.9239i	−0.200245	−	0.346835i
$993$	19.9533			0.633198
$994$	53.0029	−	24.5416i	1.68115	−	0.778414i
$995$	−10.3222			−0.327236
$996$	−6.33493	−	10.9724i	−0.200730	−	0.347675i
$997$	23.9434	−	41.4712i	0.758295	−	1.31341i	−0.185424	−	0.982659i	$-0.559366\pi$
$997$	23.9434	−	41.4712i	0.758295	−	1.31341i	0.943719	−	0.330747i	$-0.107301\pi$
$998$	9.20722	−	15.9474i	0.291449	−	0.504805i
$999$	13.3120	+	23.0571i	0.421173	+	0.729494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.e.c.53.5	✓	10
3.2	odd	2		819.2.j.h.235.1		10
4.3	odd	2		1456.2.r.p.417.4		10
7.2	even	3	inner	91.2.e.c.79.5	yes	10
7.3	odd	6		637.2.a.k.1.1		5
7.4	even	3		637.2.a.l.1.1		5
7.5	odd	6		637.2.e.m.79.5		10
7.6	odd	2		637.2.e.m.508.5		10
13.12	even	2		1183.2.e.f.508.1		10
21.2	odd	6		819.2.j.h.352.1		10
21.11	odd	6		5733.2.a.bl.1.5		5
21.17	even	6		5733.2.a.bm.1.5		5
28.23	odd	6		1456.2.r.p.625.4		10
91.25	even	6		8281.2.a.bw.1.5		5
91.38	odd	6		8281.2.a.bx.1.5		5
91.51	even	6		1183.2.e.f.170.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.5	✓	10	1.1	even	1	trivial
91.2.e.c.79.5	yes	10	7.2	even	3	inner
637.2.a.k.1.1		5	7.3	odd	6
637.2.a.l.1.1		5	7.4	even	3
637.2.e.m.79.5		10	7.5	odd	6
637.2.e.m.508.5		10	7.6	odd	2
819.2.j.h.235.1		10	3.2	odd	2
819.2.j.h.352.1		10	21.2	odd	6
1183.2.e.f.170.1		10	91.51	even	6
1183.2.e.f.508.1		10	13.12	even	2
1456.2.r.p.417.4		10	4.3	odd	2
1456.2.r.p.625.4		10	28.23	odd	6
5733.2.a.bl.1.5		5	21.11	odd	6
5733.2.a.bm.1.5		5	21.17	even	6
8281.2.a.bw.1.5		5	91.25	even	6
8281.2.a.bx.1.5		5	91.38	odd	6

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00426 + 1.73943i) q^{2} +(-0.879528 + 1.52339i) q^{3} +(-1.01709 + 1.76164i) q^{4} +(-0.452861 - 0.784378i) q^{5} -3.53311 q^{6} +(0.237709 - 2.63505i) q^{7} -0.0686323 q^{8} +(-0.0471392 - 0.0816475i) q^{9} +O(q^{10})\)	\(q+(1.00426 + 1.73943i) q^{2} +(-0.879528 + 1.52339i) q^{3} +(-1.01709 + 1.76164i) q^{4} +(-0.452861 - 0.784378i) q^{5} -3.53311 q^{6} +(0.237709 - 2.63505i) q^{7} -0.0686323 q^{8} +(-0.0471392 - 0.0816475i) q^{9} +(0.909582 - 1.57544i) q^{10} +(-0.358181 + 0.620387i) q^{11} +(-1.78911 - 3.09883i) q^{12} +1.00000 q^{13} +(4.82222 - 2.23280i) q^{14} +1.59322 q^{15} +(1.96525 + 3.40391i) q^{16} +(-1.17614 + 2.03713i) q^{17} +(0.0946802 - 0.163991i) q^{18} +(-3.31796 - 5.74687i) q^{19} +1.84239 q^{20} +(3.80513 + 2.67972i) q^{21} -1.43883 q^{22} +(-1.87953 - 3.25544i) q^{23} +(0.0603641 - 0.104554i) q^{24} +(2.08983 - 3.61970i) q^{25} +(1.00426 + 1.73943i) q^{26} -5.11133 q^{27} +(4.40025 + 3.09883i) q^{28} +3.25799 q^{29} +(1.60001 + 2.77129i) q^{30} +(-0.785250 + 1.36009i) q^{31} +(-4.01588 + 6.95570i) q^{32} +(-0.630060 - 1.09130i) q^{33} -4.72459 q^{34} +(-2.17452 + 1.00686i) q^{35} +0.191778 q^{36} +(-2.60441 - 4.51098i) q^{37} +(6.66419 - 11.5427i) q^{38} +(-0.879528 + 1.52339i) q^{39} +(0.0310809 + 0.0538337i) q^{40} +4.92168 q^{41} +(-0.839850 + 9.30992i) q^{42} -9.43766 q^{43} +(-0.728600 - 1.26197i) q^{44} +(-0.0426950 + 0.0739499i) q^{45} +(3.77508 - 6.53863i) q^{46} +(4.15993 + 7.20521i) q^{47} -6.91395 q^{48} +(-6.88699 - 1.25275i) q^{49} +8.39497 q^{50} +(-2.06889 - 3.58342i) q^{51} +(-1.01709 + 1.76164i) q^{52} +(-7.04163 + 12.1965i) q^{53} +(-5.13311 - 8.89081i) q^{54} +0.648824 q^{55} +(-0.0163145 + 0.180850i) q^{56} +11.6729 q^{57} +(3.27188 + 5.66706i) q^{58} +(-0.358181 + 0.620387i) q^{59} +(-1.62044 + 2.80668i) q^{60} +(5.82633 + 10.0915i) q^{61} -3.15439 q^{62} +(-0.226351 + 0.104806i) q^{63} -8.27099 q^{64} +(-0.452861 - 0.784378i) q^{65} +(1.26549 - 2.19189i) q^{66} +(-4.69587 + 8.13349i) q^{67} +(-2.39246 - 4.14386i) q^{68} +6.61239 q^{69} +(-3.93516 - 2.77129i) q^{70} +10.9914 q^{71} +(0.00323527 + 0.00560366i) q^{72} +(1.73650 - 3.00771i) q^{73} +(5.23103 - 9.06041i) q^{74} +(3.67614 + 6.36725i) q^{75} +13.4986 q^{76} +(1.54961 + 1.09130i) q^{77} -3.53311 q^{78} +(-6.50408 - 11.2654i) q^{79} +(1.77997 - 3.08299i) q^{80} +(4.63697 - 8.03147i) q^{81} +(4.94265 + 8.56093i) q^{82} +3.54083 q^{83} +(-8.59086 + 3.97778i) q^{84} +2.13050 q^{85} +(-9.47789 - 16.4162i) q^{86} +(-2.86550 + 4.96318i) q^{87} +(0.0245828 - 0.0425786i) q^{88} +(-6.02503 - 10.4357i) q^{89} -0.171508 q^{90} +(0.237709 - 2.63505i) q^{91} +7.64656 q^{92} +(-1.38130 - 2.39248i) q^{93} +(-8.35532 + 14.4718i) q^{94} +(-3.00514 + 5.20506i) q^{95} +(-7.06415 - 12.2355i) q^{96} +7.43766 q^{97} +(-4.73727 - 13.2375i) q^{98} +0.0675374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 18 * q^8 - 3 * q^9	\( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9} + 5 q^{10} - 11 q^{11} - 5 q^{12} + 10 q^{13} + 10 q^{14} - 10 q^{16} + 5 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 2 q^{21} + 16 q^{22} - 10 q^{23} - 9 q^{25} - 4 q^{26} + 37 q^{28} - 6 q^{29} + 13 q^{30} + 6 q^{31} - 22 q^{32} - 8 q^{33} - 44 q^{34} - 4 q^{35} + 14 q^{36} - 4 q^{37} + 10 q^{38} - 28 q^{40} + 28 q^{41} + 52 q^{42} + 4 q^{43} + 32 q^{45} - 3 q^{46} - q^{47} - 46 q^{48} - 11 q^{49} + 18 q^{50} + 8 q^{51} - 8 q^{52} - 17 q^{53} - 23 q^{54} - 21 q^{56} - 32 q^{57} + 27 q^{58} - 11 q^{59} + 29 q^{60} + 11 q^{61} - 46 q^{62} + 5 q^{63} + 18 q^{64} - 2 q^{65} - 21 q^{66} - 13 q^{67} + 32 q^{68} + 36 q^{69} + 49 q^{70} + 30 q^{71} + 19 q^{72} + 33 q^{74} + 20 q^{75} + 16 q^{76} - 46 q^{77} - 10 q^{78} - 2 q^{79} - 55 q^{80} + 19 q^{81} - 34 q^{82} + 12 q^{83} - 23 q^{84} - 44 q^{85} - 28 q^{86} + 8 q^{87} + 3 q^{88} + 4 q^{89} - 68 q^{90} + q^{91} + 42 q^{92} - 18 q^{93} - 20 q^{94} + 12 q^{95} + 37 q^{96} - 24 q^{97} - 7 q^{98} + 22 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 18 * q^8 - 3 * q^9 + 5 * q^10 - 11 * q^11 - 5 * q^12 + 10 * q^13 + 10 * q^14 - 10 * q^16 + 5 * q^17 - 9 * q^18 - 9 * q^19 + 2 * q^20 + 2 * q^21 + 16 * q^22 - 10 * q^23 - 9 * q^25 - 4 * q^26 + 37 * q^28 - 6 * q^29 + 13 * q^30 + 6 * q^31 - 22 * q^32 - 8 * q^33 - 44 * q^34 - 4 * q^35 + 14 * q^36 - 4 * q^37 + 10 * q^38 - 28 * q^40 + 28 * q^41 + 52 * q^42 + 4 * q^43 + 32 * q^45 - 3 * q^46 - q^47 - 46 * q^48 - 11 * q^49 + 18 * q^50 + 8 * q^51 - 8 * q^52 - 17 * q^53 - 23 * q^54 - 21 * q^56 - 32 * q^57 + 27 * q^58 - 11 * q^59 + 29 * q^60 + 11 * q^61 - 46 * q^62 + 5 * q^63 + 18 * q^64 - 2 * q^65 - 21 * q^66 - 13 * q^67 + 32 * q^68 + 36 * q^69 + 49 * q^70 + 30 * q^71 + 19 * q^72 + 33 * q^74 + 20 * q^75 + 16 * q^76 - 46 * q^77 - 10 * q^78 - 2 * q^79 - 55 * q^80 + 19 * q^81 - 34 * q^82 + 12 * q^83 - 23 * q^84 - 44 * q^85 - 28 * q^86 + 8 * q^87 + 3 * q^88 + 4 * q^89 - 68 * q^90 + q^91 + 42 * q^92 - 18 * q^93 - 20 * q^94 + 12 * q^95 + 37 * q^96 - 24 * q^97 - 7 * q^98 + 22 * q^99

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