LMFDB - Embedded newform 91.2.e.c.79.5

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			79.5
Root			$1.50426 - 2.60546i$ of defining polynomial
Character	$\chi$	$=$	91.79
Dual form			91.2.e.c.53.5

$q$-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 $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.00426	−	1.73943i	0.710121	−	1.22997i	−0.254691	−	0.967023i	$-0.581974\pi$
$2$	1.00426	−	1.73943i	0.710121	−	1.22997i	0.964812	−	0.262942i	$-0.0846930\pi$
$3$	−0.879528	−	1.52339i	−0.507796	−	0.879528i	−0.999959	−	0.00902528i	$-0.997127\pi$
$3$	−0.879528	−	1.52339i	−0.507796	−	0.879528i	0.492164	−	0.870503i	$-0.336206\pi$
$4$	−1.01709	−	1.76164i	−0.508543	−	0.880822i
$5$	−0.452861	+	0.784378i	−0.202526	+	0.350784i	−0.949342	−	0.314246i	$-0.898248\pi$
$5$	−0.452861	+	0.784378i	−0.202526	+	0.350784i	0.746816	+	0.665031i	$0.231582\pi$
$6$	−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	0.806963	−	0.590603i	$-0.201110\pi$
$11$	−0.358181	−	0.620387i	−0.107996	−	0.187054i	−0.914958	+	0.403549i	$0.867777\pi$
$12$	−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	0.687416	−	0.726264i	$-0.258745\pi$
$17$	−1.17614	−	2.03713i	−0.285255	−	0.494076i	−0.972671	+	0.232188i	$0.925412\pi$
$18$	0.0946802	+	0.163991i	0.0223163	+	0.0386530i
$19$	−3.31796	+	5.74687i	−0.761191	+	1.31842i	0.181046	+	0.983475i	$0.442052\pi$
$19$	−3.31796	+	5.74687i	−0.761191	+	1.31842i	−0.942237	+	0.334947i	$0.891282\pi$
$20$	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	−0.992701	−	0.120599i	$-0.961518\pi$
$23$	−1.87953	+	3.25544i	−0.391909	+	0.678806i	0.600793	+	0.799405i	$0.294852\pi$
$24$	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	0.786852	−	0.617142i	$-0.211710\pi$
$31$	−0.785250	−	1.36009i	−0.141035	−	0.244280i	−0.927887	+	0.372862i	$0.878376\pi$
$32$	−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	−0.996710	−	0.0810508i	$-0.974172\pi$
$37$	−2.60441	+	4.51098i	−0.428163	+	0.741600i	0.568547	+	0.822651i	$0.307506\pi$
$38$	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	−0.384978	−	0.922926i	$-0.625791\pi$
$47$	4.15993	−	7.20521i	0.606788	−	1.05099i	0.991766	−	0.128062i	$-0.0408758\pi$
$48$	−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	−0.703465	−	0.710729i	$-0.748365\pi$
$53$	−7.04163	−	12.1965i	−0.967243	−	1.67531i	−0.263777	−	0.964584i	$-0.584968\pi$
$54$	−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	0.841768	−	0.539840i	$-0.181515\pi$
$59$	−0.358181	−	0.620387i	−0.0466311	−	0.0807675i	−0.888399	+	0.459072i	$0.848182\pi$
$60$	−1.62044	−	2.80668i	−0.209197	−	0.362340i
$61$	5.82633	−	10.0915i	0.745986	−	1.29208i	−0.203747	−	0.979024i	$-0.565312\pi$
$61$	5.82633	−	10.0915i	0.745986	−	1.29208i	0.949733	−	0.313061i	$-0.101355\pi$
$62$	−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	−0.996182	−	0.0872964i	$-0.972177\pi$
$67$	−4.69587	−	8.13349i	−0.573692	−	0.993664i	0.422490	−	0.906367i	$-0.361156\pi$
$68$	−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	0.949571	−	0.313552i	$-0.101519\pi$
$73$	1.73650	+	3.00771i	0.203242	+	0.352025i	−0.746329	+	0.665577i	$0.768186\pi$
$74$	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	0.224361	+	0.974506i	$0.427970\pi$
$79$	−6.50408	+	11.2654i	−0.731766	+	1.26746i	−0.956128	+	0.292950i	$0.905363\pi$
$80$	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	0.347077	+	0.937836i	$0.387174\pi$
$89$	−6.02503	+	10.4357i	−0.638651	+	1.10618i	−0.985729	+	0.168340i	$0.946159\pi$
$90$	−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	0.894311	−	0.447447i	$-0.147667\pi$
$101$	0.599526	+	1.03841i	0.0596551	+	0.103326i	−0.834656	+	0.550772i	$0.814333\pi$
$102$	4.15541	+	7.19739i	0.411447	+	0.712647i
$103$	7.20615	−	12.4814i	0.710043	−	1.22983i	−0.254797	−	0.966995i	$-0.582009\pi$
$103$	7.20615	−	12.4814i	0.710043	−	1.22983i	0.964840	−	0.262837i	$-0.0846580\pi$
$104$	−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	0.324322	+	0.945947i	$0.394864\pi$
$107$	−6.79661	+	11.7721i	−0.657053	+	1.13805i	−0.981375	+	0.192102i	$0.938469\pi$
$108$	5.19866	+	9.00434i	0.500241	+	0.866443i
$109$	6.86241	+	11.8860i	0.657299	+	1.13848i	0.981312	+	0.192423i	$0.0616346\pi$
$109$	6.86241	+	11.8860i	0.657299	+	1.13848i	−0.324013	+	0.946053i	$0.605032\pi$
$110$	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	−0.0819487	−	0.996637i	$-0.526114\pi$
$131$	9.40980	−	16.2983i	0.822138	−	1.42399i	0.904087	−	0.427349i	$-0.140552\pi$
$132$	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	0.703247	−	0.710945i	$-0.251733\pi$
$137$	−3.09090	−	5.35359i	−0.264073	−	0.457388i	−0.967320	+	0.253557i	$0.918399\pi$
$138$	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	−0.00532425	−	0.999986i	$-0.501695\pi$
$149$	10.5385	−	18.2533i	0.863351	−	1.49537i	0.868675	−	0.495382i	$-0.164972\pi$
$150$	−7.38361	−	12.7888i	−0.602869	−	1.04420i
$151$	7.86171	+	13.6169i	0.639777	+	1.10813i	0.985481	+	0.169783i	$0.0543067\pi$
$151$	7.86171	+	13.6169i	0.639777	+	1.10813i	−0.345704	+	0.938344i	$0.612360\pi$
$152$	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	0.978504	−	0.206226i	$-0.0661183\pi$
$157$	3.89250	+	6.74200i	0.310655	+	0.538070i	−0.667849	+	0.744297i	$0.732785\pi$
$158$	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	−0.897218	−	0.441588i	$-0.854415\pi$
$163$	−0.844956	+	1.46351i	−0.0661820	+	0.114631i	0.831036	+	0.556219i	$0.187748\pi$
$164$	−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	−0.955430	−	0.295217i	$-0.904608\pi$
$173$	−2.92061	+	5.05865i	−0.222050	+	0.384602i	0.733380	+	0.679819i	$0.237942\pi$
$174$	−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	0.814777	−	0.579774i	$-0.196859\pi$
$179$	−1.26714	−	2.19475i	−0.0947103	−	0.164043i	−0.909488	+	0.415731i	$0.863526\pi$
$180$	−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	−0.834062	−	0.551671i	$-0.813991\pi$
$191$	0.839303	−	1.45371i	0.0607298	−	0.105187i	0.894792	+	0.446484i	$0.147324\pi$
$192$	7.27457	+	12.5999i	0.524997	+	0.909321i
$193$	3.22408	+	5.58427i	0.232074	+	0.401964i	0.958418	−	0.285367i	$-0.0921154\pi$
$193$	3.22408	+	5.58427i	0.232074	+	0.401964i	−0.726344	+	0.687331i	$0.758782\pi$
$194$	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	0.994198	−	0.107566i	$-0.0343058\pi$
$199$	5.69833	+	9.86979i	0.403944	+	0.699651i	−0.590254	+	0.807217i	$0.700972\pi$
$200$	−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	0.940800	−	0.338962i	$-0.110076\pi$
$227$	2.66452	+	4.61509i	0.176851	+	0.306314i	−0.763950	+	0.645276i	$0.776742\pi$
$228$	−11.8724	−	20.5636i	−0.786267	−	1.36185i
$229$	4.25950	−	7.37767i	0.281476	−	0.487530i	−0.690273	−	0.723549i	$-0.742509\pi$
$229$	4.25950	−	7.37767i	0.281476	−	0.487530i	0.971748	+	0.236019i	$0.0758428\pi$
$230$	−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	−0.933318	−	0.359050i	$-0.883101\pi$
$233$	−2.37685	+	4.11683i	−0.155713	+	0.269703i	0.777605	+	0.628752i	$0.216434\pi$
$234$	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	0.947605	−	0.319446i	$-0.103497\pi$
$241$	3.06066	+	5.30121i	0.197154	+	0.341481i	−0.750450	+	0.660927i	$0.770163\pi$
$242$	−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	0.460504	+	0.887658i	$0.347669\pi$
$257$	−8.63253	+	14.9520i	−0.538482	+	0.932679i	−0.998986	+	0.0450210i	$0.985665\pi$
$258$	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	0.903408	−	0.428781i	$-0.141057\pi$
$263$	1.30336	+	2.25749i	0.0803687	+	0.139203i	−0.823040	+	0.567984i	$0.807724\pi$
$264$	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	0.997817	−	0.0660343i	$-0.0210347\pi$
$269$	7.24477	+	12.5483i	0.441721	+	0.765084i	−0.556096	+	0.831118i	$0.687701\pi$
$270$	−4.64917	−	8.05260i	−0.282940	−	0.490066i
$271$	4.31796	−	7.47892i	0.262297	−	0.454312i	−0.704555	−	0.709650i	$-0.748853\pi$
$271$	4.31796	−	7.47892i	0.262297	−	0.454312i	0.966852	+	0.255338i	$0.0821866\pi$
$272$	−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	0.621822	−	0.783158i	$-0.286393\pi$
$277$	−6.11349	−	10.5889i	−0.367324	−	0.636223i	−0.989146	+	0.146935i	$0.953059\pi$
$278$	−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	0.807642	+	0.589674i	$0.200744\pi$
$283$	15.3842	+	26.6461i	0.914493	+	1.58395i	0.106851	+	0.994275i	$0.465923\pi$
$284$	−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	0.777126	−	0.629345i	$-0.216677\pi$
$311$	−2.75931	−	4.77927i	−0.156466	−	0.271007i	−0.933592	+	0.358338i	$0.883344\pi$
$312$	0.0603641	+	0.104554i	0.00341744	+	0.00591918i
$313$	2.42399	−	4.19848i	0.137012	−	0.237312i	−0.789352	−	0.613941i	$-0.789583\pi$
$313$	2.42399	−	4.19848i	0.137012	−	0.237312i	0.926364	+	0.376629i	$0.122917\pi$
$314$	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	−0.738288	−	0.674485i	$-0.764366\pi$
$317$	3.82756	−	6.62952i	0.214977	−	0.372351i	0.953265	+	0.302134i	$0.0976990\pi$
$318$	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	−0.978739	−	0.205110i	$-0.934245\pi$
$331$	−5.67159	+	9.82348i	−0.311739	+	0.539947i	0.667000	+	0.745058i	$0.267578\pi$
$332$	−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	−0.997048	−	0.0767814i	$-0.975536\pi$
$347$	−10.5251	−	18.2301i	−0.565019	−	0.978641i	0.432029	−	0.901860i	$-0.357798\pi$
$348$	−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	0.956947	−	0.290264i	$-0.0937431\pi$
$353$	4.26677	+	7.39027i	0.227097	+	0.393344i	−0.729849	+	0.683608i	$0.760410\pi$
$354$	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	−0.569837	−	0.821757i	$-0.692994\pi$
$359$	8.08565	−	14.0047i	0.426744	−	0.739142i	0.996582	+	0.0826150i	$0.0263272\pi$
$360$	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	−0.954805	−	0.297232i	$-0.903936\pi$
$367$	−14.0770	−	24.3821i	−0.734813	−	1.27273i	0.219992	−	0.975502i	$-0.429397\pi$
$368$	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	−0.215493	−	0.976505i	$-0.569136\pi$
$373$	14.2518	−	24.6849i	0.737932	−	1.27814i	0.953425	−	0.301630i	$-0.0975308\pi$
$374$	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	−0.982592	−	0.185774i	$-0.940521\pi$
$383$	−6.46627	+	11.1999i	−0.330411	+	0.572289i	0.652181	+	0.758063i	$0.273854\pi$
$384$	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	0.999124	+	0.0418574i	$0.0133275\pi$
$389$	10.5679	+	18.3041i	0.535811	+	0.928053i	−0.463312	+	0.886195i	$0.653339\pi$
$390$	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	−0.999786	−	0.0206683i	$-0.993421\pi$
$397$	−9.60366	+	16.6340i	−0.481994	+	0.834838i	0.517792	+	0.855506i	$0.326754\pi$
$398$	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	−0.995555	−	0.0941856i	$-0.969975\pi$
$401$	−8.33460	+	14.4360i	−0.416210	+	0.720897i	0.579344	+	0.815083i	$0.303309\pi$
$402$	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	0.672034	−	0.740520i	$-0.265421\pi$
$409$	−6.17416	−	10.6940i	−0.305293	−	0.528782i	−0.977326	+	0.211738i	$0.932088\pi$
$410$	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	0.997262	+	0.0739426i	$0.0235582\pi$
$431$	11.6813	+	20.2326i	0.562667	+	0.974569i	−0.434595	+	0.900626i	$0.643109\pi$
$432$	−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	−0.741137	−	0.671353i	$-0.765713\pi$
$439$	4.41760	−	7.65150i	0.210840	−	0.365186i	0.951978	+	0.306167i	$0.0990467\pi$
$440$	−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	−0.829448	−	0.558584i	$-0.811345\pi$
$443$	1.45279	−	2.51630i	0.0690240	−	0.119553i	0.898472	+	0.439031i	$0.144678\pi$
$444$	−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	0.444643	+	0.895708i	$0.353330\pi$
$457$	−11.8300	+	20.4902i	−0.553384	+	0.958489i	−0.998027	+	0.0627815i	$0.980003\pi$
$458$	−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	−0.752497	−	0.658596i	$-0.771151\pi$
$467$	4.19480	−	7.26560i	0.194112	−	0.336212i	0.946609	+	0.322384i	$0.104484\pi$
$468$	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	0.685232	−	0.728325i	$-0.259701\pi$
$479$	−6.30608	−	10.9225i	−0.288132	−	0.499060i	−0.973364	+	0.229265i	$0.926368\pi$
$480$	−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	0.511244	−	0.859435i	$-0.329185\pi$
$487$	−10.7840	−	18.6785i	−0.488671	−	0.846403i	−0.999915	+	0.0130329i	$0.995851\pi$
$488$	−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	−0.950200	−	0.311641i	$-0.899121\pi$
$499$	−4.58407	+	7.93984i	−0.205211	+	0.355436i	0.744989	+	0.667077i	$0.232455\pi$
$500$	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	−0.923952	−	0.382509i	$-0.875060\pi$
$509$	−2.94904	+	5.10788i	−0.130714	+	0.226403i	0.793238	+	0.608912i	$0.208394\pi$
$510$	−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	0.909578	+	0.415534i	$0.136405\pi$
$521$	18.5948	+	32.2071i	0.814652	+	1.41102i	−0.0949259	+	0.995484i	$0.530261\pi$
$522$	0.308468	+	0.534281i	0.0135013	+	0.0233849i
$523$	2.54540	−	4.40876i	0.111303	−	0.192782i	−0.804993	−	0.593284i	$-0.797831\pi$
$523$	2.54540	−	4.40876i	0.111303	−	0.192782i	0.916296	+	0.400502i	$0.131164\pi$
$524$	−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	−0.857665	−	0.514208i	$-0.828086\pi$
$541$	0.383425	−	0.664111i	0.0164847	−	0.0285524i	0.874150	+	0.485656i	$0.161419\pi$
$542$	−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	0.999515	+	0.0311490i	$0.00991664\pi$
$557$	12.4314	+	21.5317i	0.526733	+	0.912329i	−0.472782	+	0.881180i	$0.656750\pi$
$558$	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	−0.787675	−	0.616091i	$-0.788715\pi$
$563$	−22.0047	−	38.1133i	−0.927388	−	1.60628i	−0.139713	−	0.990192i	$-0.544618\pi$
$564$	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	−0.272235	−	0.962231i	$-0.587763\pi$
$569$	16.6308	−	28.8054i	0.697199	−	1.20758i	0.969434	−	0.245353i	$-0.0789040\pi$
$570$	10.6175	+	18.3900i	0.444718	+	0.770274i
$571$	6.17699	+	10.6989i	0.258499	+	0.447734i	0.965840	−	0.259139i	$-0.0834387\pi$
$571$	6.17699	+	10.6989i	0.258499	+	0.447734i	−0.707341	+	0.706873i	$0.750105\pi$
$572$	−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	0.998876	+	0.0473984i	$0.0150930\pi$
$577$	12.9829	+	22.4871i	0.540486	+	0.936150i	−0.458390	+	0.888751i	$0.651574\pi$
$578$	−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	−0.259154	+	0.965836i	$0.583444\pi$
$593$	−23.5240	+	40.7448i	−0.966015	+	1.67319i	−0.706862	+	0.707352i	$0.749890\pi$
$594$	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	0.582988	−	0.812481i	$-0.301884\pi$
$599$	−10.0868	−	17.4708i	−0.412135	−	0.713840i	−0.995123	+	0.0986415i	$0.968550\pi$
$600$	−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	−0.665708	−	0.746213i	$-0.731870\pi$
$607$	7.72099	−	13.3732i	0.313385	−	0.542799i	0.979093	+	0.203413i	$0.0652035\pi$
$608$	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	0.845180	−	0.534482i	$-0.179493\pi$
$613$	−0.997423	−	1.72759i	−0.0402855	−	0.0697766i	−0.885465	+	0.464706i	$0.846160\pi$
$614$	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	−0.984819	−	0.173585i	$-0.944465\pi$
$619$	−15.9911	−	27.6975i	−0.642738	−	1.11326i	0.342080	−	0.939671i	$-0.388868\pi$
$620$	−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	−0.982588	−	0.185799i	$-0.940513\pi$
$641$	−16.5124	−	28.6003i	−0.652200	−	1.12964i	0.330387	−	0.943845i	$-0.392821\pi$
$642$	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	0.908026	−	0.418914i	$-0.137589\pi$
$647$	2.32036	+	4.01898i	0.0912227	+	0.158002i	−0.816803	+	0.576916i	$0.804256\pi$
$648$	−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	0.474637	+	0.880182i	$0.342579\pi$
$653$	−13.4143	+	23.2342i	−0.524941	+	0.909225i	−0.999578	+	0.0290430i	$0.990754\pi$
$654$	−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	0.996243	+	0.0866030i	$0.0276012\pi$
$661$	14.7349	+	25.5216i	0.573122	+	0.992676i	−0.423121	+	0.906073i	$0.639066\pi$
$662$	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	−0.800230	−	0.599694i	$-0.795289\pi$
$677$	3.10241	−	5.37353i	0.119235	−	0.206521i	0.919465	+	0.393172i	$0.128622\pi$
$678$	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	0.882456	−	0.470395i	$-0.155888\pi$
$683$	0.884758	+	1.53245i	0.0338543	+	0.0586374i	−0.848602	+	0.529032i	$0.822555\pi$
$684$	−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	0.0223363	+	0.999751i	$0.492890\pi$
$691$	−22.4658	+	38.9120i	−0.854641	+	1.48028i	−0.876977	+	0.480531i	$0.840444\pi$
$692$	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	−0.936591	−	0.350424i	$-0.886037\pi$
$709$	−4.38866	+	7.60137i	−0.164819	+	0.285476i	0.771772	+	0.635900i	$0.219371\pi$
$710$	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	−0.902559	−	0.430566i	$-0.858314\pi$
$719$	−2.10218	+	3.64109i	−0.0783982	+	0.135790i	0.824161	+	0.566356i	$0.191647\pi$
$720$	−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	−0.554106	−	0.832446i	$-0.686940\pi$
$733$	12.0172	−	20.8145i	0.443867	−	0.768800i	0.997972	+	0.0636467i	$0.0202731\pi$
$734$	−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	0.736795	−	0.676116i	$-0.236338\pi$
$739$	−5.90276	−	10.2239i	−0.217136	−	0.376091i	−0.953931	+	0.300025i	$0.903005\pi$
$740$	−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	−0.911655	−	0.410956i	$-0.865195\pi$
$751$	−2.73850	+	4.74322i	−0.0999294	+	0.173083i	0.811726	+	0.584039i	$0.198528\pi$
$752$	−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	−0.394143	−	0.919049i	$-0.628959\pi$
$761$	16.5200	−	28.6134i	0.598848	−	1.03724i	0.992991	−	0.118186i	$-0.0377080\pi$
$762$	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	+

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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