LMFDB - Embedded newform 91.2.f.a.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(22,91)]

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([0, 4]))

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

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.f (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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	91.22
Dual form			91.2.f.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 + 2.26728i) q^{2} +(1.30902 - 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} +2.61803 q^{5} +(3.42705 + 5.93583i) q^{6} +(-0.500000 - 0.866025i) q^{7} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})$	\(q+(-1.30902 + 2.26728i) q^{2} +(1.30902 - 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} +2.61803 q^{5} +(3.42705 + 5.93583i) q^{6} +(-0.500000 - 0.866025i) q^{7} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(-3.42705 + 5.93583i) q^{10} +(-0.927051 + 1.60570i) q^{11} -12.7082 q^{12} +(-2.50000 + 2.59808i) q^{13} +2.61803 q^{14} +(3.42705 - 5.93583i) q^{15} +(-4.92705 + 8.53390i) q^{16} +(0.736068 + 1.27491i) q^{17} +10.0902 q^{18} +(0.927051 + 1.60570i) q^{19} +(-6.35410 - 11.0056i) q^{20} -2.61803 q^{21} +(-2.42705 - 4.20378i) q^{22} +(2.23607 - 3.87298i) q^{23} +(9.78115 - 16.9415i) q^{24} +1.85410 q^{25} +(-2.61803 - 9.06914i) q^{26} -2.23607 q^{27} +(-2.42705 + 4.20378i) q^{28} +(-3.54508 + 6.14027i) q^{29} +(8.97214 + 15.5402i) q^{30} -4.70820 q^{31} +(-5.42705 - 9.39993i) q^{32} +(2.42705 + 4.20378i) q^{33} -3.85410 q^{34} +(-1.30902 - 2.26728i) q^{35} +(-9.35410 + 16.2018i) q^{36} +(-2.00000 + 3.46410i) q^{37} -4.85410 q^{38} +(2.61803 + 9.06914i) q^{39} +19.5623 q^{40} +(-0.381966 + 0.661585i) q^{41} +(3.42705 - 5.93583i) q^{42} +(-6.28115 - 10.8793i) q^{43} +9.00000 q^{44} +(-5.04508 - 8.73834i) q^{45} +(5.85410 + 10.1396i) q^{46} -2.23607 q^{47} +(12.8992 + 22.3420i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.42705 + 4.20378i) q^{50} +3.85410 q^{51} +(16.9894 + 4.20378i) q^{52} +3.76393 q^{53} +(2.92705 - 5.06980i) q^{54} +(-2.42705 + 4.20378i) q^{55} +(-3.73607 - 6.47106i) q^{56} +4.85410 q^{57} +(-9.28115 - 16.0754i) q^{58} +(1.11803 + 1.93649i) q^{59} -33.2705 q^{60} +(3.00000 + 5.19615i) q^{61} +(6.16312 - 10.6748i) q^{62} +(-1.92705 + 3.33775i) q^{63} +8.70820 q^{64} +(-6.54508 + 6.80185i) q^{65} -12.7082 q^{66} +(6.35410 - 11.0056i) q^{67} +(3.57295 - 6.18853i) q^{68} +(-5.85410 - 10.1396i) q^{69} +6.85410 q^{70} +(7.09017 + 12.2805i) q^{71} +(-14.3992 - 24.9401i) q^{72} -2.00000 q^{73} +(-5.23607 - 9.06914i) q^{74} +(2.42705 - 4.20378i) q^{75} +(4.50000 - 7.79423i) q^{76} +1.85410 q^{77} +(-23.9894 - 5.93583i) q^{78} +4.00000 q^{79} +(-12.8992 + 22.3420i) q^{80} +(2.85410 - 4.94345i) q^{81} +(-1.00000 - 1.73205i) q^{82} +6.70820 q^{83} +(6.35410 + 11.0056i) q^{84} +(1.92705 + 3.33775i) q^{85} +32.8885 q^{86} +(9.28115 + 16.0754i) q^{87} +(-6.92705 + 11.9980i) q^{88} +(-2.45492 + 4.25204i) q^{89} +26.4164 q^{90} +(3.50000 + 0.866025i) q^{91} -21.7082 q^{92} +(-6.16312 + 10.6748i) q^{93} +(2.92705 - 5.06980i) q^{94} +(2.42705 + 4.20378i) q^{95} -28.4164 q^{96} +(-9.42705 - 16.3281i) q^{97} +(-1.30902 - 2.26728i) q^{98} +7.14590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 6 q^{5} + 7 q^{6} - 2 q^{7} + 12 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 6 * q^5 + 7 * q^6 - 2 * q^7 + 12 * q^8 - q^9	\( 4 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 6 q^{5} + 7 q^{6} - 2 q^{7} + 12 q^{8} - q^{9} - 7 q^{10} + 3 q^{11} - 24 q^{12} - 10 q^{13} + 6 q^{14} + 7 q^{15} - 13 q^{16} - 6 q^{17} + 18 q^{18} - 3 q^{19} - 12 q^{20} - 6 q^{21} - 3 q^{22} + 19 q^{24} - 6 q^{25} - 6 q^{26} - 3 q^{28} - 3 q^{29} + 18 q^{30} + 8 q^{31} - 15 q^{32} + 3 q^{33} - 2 q^{34} - 3 q^{35} - 24 q^{36} - 8 q^{37} - 6 q^{38} + 6 q^{39} + 38 q^{40} - 6 q^{41} + 7 q^{42} - 5 q^{43} + 36 q^{44} - 9 q^{45} + 10 q^{46} + 27 q^{48} - 2 q^{49} - 3 q^{50} + 2 q^{51} + 21 q^{52} + 24 q^{53} + 5 q^{54} - 3 q^{55} - 6 q^{56} + 6 q^{57} - 17 q^{58} - 66 q^{60} + 12 q^{61} + 9 q^{62} - q^{63} + 8 q^{64} - 15 q^{65} - 24 q^{66} + 12 q^{67} + 21 q^{68} - 10 q^{69} + 14 q^{70} + 6 q^{71} - 33 q^{72} - 8 q^{73} - 12 q^{74} + 3 q^{75} + 18 q^{76} - 6 q^{77} - 49 q^{78} + 16 q^{79} - 27 q^{80} - 2 q^{81} - 4 q^{82} + 12 q^{84} + q^{85} + 60 q^{86} + 17 q^{87} - 21 q^{88} - 21 q^{89} + 52 q^{90} + 14 q^{91} - 60 q^{92} - 9 q^{93} + 5 q^{94} + 3 q^{95} - 60 q^{96} - 31 q^{97} - 3 q^{98} + 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 6 * q^5 + 7 * q^6 - 2 * q^7 + 12 * q^8 - q^9 - 7 * q^10 + 3 * q^11 - 24 * q^12 - 10 * q^13 + 6 * q^14 + 7 * q^15 - 13 * q^16 - 6 * q^17 + 18 * q^18 - 3 * q^19 - 12 * q^20 - 6 * q^21 - 3 * q^22 + 19 * q^24 - 6 * q^25 - 6 * q^26 - 3 * q^28 - 3 * q^29 + 18 * q^30 + 8 * q^31 - 15 * q^32 + 3 * q^33 - 2 * q^34 - 3 * q^35 - 24 * q^36 - 8 * q^37 - 6 * q^38 + 6 * q^39 + 38 * q^40 - 6 * q^41 + 7 * q^42 - 5 * q^43 + 36 * q^44 - 9 * q^45 + 10 * q^46 + 27 * q^48 - 2 * q^49 - 3 * q^50 + 2 * q^51 + 21 * q^52 + 24 * q^53 + 5 * q^54 - 3 * q^55 - 6 * q^56 + 6 * q^57 - 17 * q^58 - 66 * q^60 + 12 * q^61 + 9 * q^62 - q^63 + 8 * q^64 - 15 * q^65 - 24 * q^66 + 12 * q^67 + 21 * q^68 - 10 * q^69 + 14 * q^70 + 6 * q^71 - 33 * q^72 - 8 * q^73 - 12 * q^74 + 3 * q^75 + 18 * q^76 - 6 * q^77 - 49 * q^78 + 16 * q^79 - 27 * q^80 - 2 * q^81 - 4 * q^82 + 12 * q^84 + q^85 + 60 * q^86 + 17 * q^87 - 21 * q^88 - 21 * q^89 + 52 * q^90 + 14 * q^91 - 60 * q^92 - 9 * q^93 + 5 * q^94 + 3 * q^95 - 60 * q^96 - 31 * q^97 - 3 * q^98 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.30902	+	2.26728i	−0.925615	+	1.60321i	−0.135045	+	0.990839i	$0.543118\pi$
$2$	−1.30902	+	2.26728i	−0.925615	+	1.60321i	−0.790569	+	0.612372i	$0.790215\pi$
$3$	1.30902	−	2.26728i	0.755761	−	1.30902i	−0.189234	−	0.981932i	$-0.560600\pi$
$3$	1.30902	−	2.26728i	0.755761	−	1.30902i	0.944995	−	0.327085i	$-0.106066\pi$
$4$	−2.42705	−	4.20378i	−1.21353	−	2.10189i
$5$	2.61803			1.17082			0.585410	−	0.810737i	$-0.300933\pi$
$5$	2.61803			1.17082			0.585410	+	0.810737i	$0.300933\pi$
$6$	3.42705	+	5.93583i	1.39909	+	2.42329i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	7.47214			2.64180
$9$	−1.92705	−	3.33775i	−0.642350	−	1.11258i
$10$	−3.42705	+	5.93583i	−1.08373	+	1.87707i
$11$	−0.927051	+	1.60570i	−0.279516	+	0.484137i	−0.971265	−	0.238002i	$-0.923507\pi$
$11$	−0.927051	+	1.60570i	−0.279516	+	0.484137i	0.691748	+	0.722139i	$0.256841\pi$
$12$	−12.7082			−3.66854
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	2.61803			0.699699
$15$	3.42705	−	5.93583i	0.884861	−	1.53262i
$16$	−4.92705	+	8.53390i	−1.23176	+	2.13348i
$17$	0.736068	+	1.27491i	0.178523	+	0.309210i	0.941375	−	0.337363i	$-0.109535\pi$
$17$	0.736068	+	1.27491i	0.178523	+	0.309210i	−0.762852	+	0.646573i	$0.776202\pi$
$18$	10.0902			2.37828
$19$	0.927051	+	1.60570i	0.212680	+	0.368373i	0.952552	−	0.304375i	$-0.0984475\pi$
$19$	0.927051	+	1.60570i	0.212680	+	0.368373i	−0.739872	+	0.672747i	$0.765114\pi$
$20$	−6.35410	−	11.0056i	−1.42082	−	2.46093i
$21$	−2.61803			−0.571302
$22$	−2.42705	−	4.20378i	−0.517449	−	0.896248i
$23$	2.23607	−	3.87298i	0.466252	−	0.807573i	−0.533005	−	0.846112i	$-0.678937\pi$
$23$	2.23607	−	3.87298i	0.466252	−	0.807573i	0.999257	+	0.0385394i	$0.0122705\pi$
$24$	9.78115	−	16.9415i	1.99657	−	3.45816i
$25$	1.85410			0.370820
$26$	−2.61803	−	9.06914i	−0.513439	−	1.77860i
$27$	−2.23607			−0.430331
$28$	−2.42705	+	4.20378i	−0.458670	+	0.794439i
$29$	−3.54508	+	6.14027i	−0.658306	+	1.14022i	0.322748	+	0.946485i	$0.395393\pi$
$29$	−3.54508	+	6.14027i	−0.658306	+	1.14022i	−0.981054	+	0.193734i	$0.937940\pi$
$30$	8.97214	+	15.5402i	1.63808	+	2.83724i
$31$	−4.70820			−0.845618			−0.422809	−	0.906219i	$-0.638956\pi$
$31$	−4.70820			−0.845618			−0.422809	+	0.906219i	$0.638956\pi$
$32$	−5.42705	−	9.39993i	−0.959376	−	1.66169i
$33$	2.42705	+	4.20378i	0.422495	+	0.731783i
$34$	−3.85410			−0.660973
$35$	−1.30902	−	2.26728i	−0.221264	−	0.383241i
$36$	−9.35410	+	16.2018i	−1.55902	+	2.70030i
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	−4.85410			−0.787439
$39$	2.61803	+	9.06914i	0.419221	+	1.45222i
$40$	19.5623			3.09307
$41$	−0.381966	+	0.661585i	−0.0596531	+	0.103322i	−0.894310	−	0.447449i	$-0.852333\pi$
$41$	−0.381966	+	0.661585i	−0.0596531	+	0.103322i	0.834657	+	0.550771i	$0.185666\pi$
$42$	3.42705	−	5.93583i	0.528805	−	0.915918i
$43$	−6.28115	−	10.8793i	−0.957867	−	1.65907i	−0.727667	−	0.685931i	$-0.759395\pi$
$43$	−6.28115	−	10.8793i	−0.957867	−	1.65907i	−0.230200	−	0.973143i	$-0.573938\pi$
$44$	9.00000			1.35680
$45$	−5.04508	−	8.73834i	−0.752077	−	1.30264i
$46$	5.85410	+	10.1396i	0.863140	+	1.49500i
$47$	−2.23607			−0.326164			−0.163082	−	0.986613i	$-0.552144\pi$
$47$	−2.23607			−0.326164			−0.163082	+	0.986613i	$0.552144\pi$
$48$	12.8992	+	22.3420i	1.86184	+	3.22480i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−2.42705	+	4.20378i	−0.343237	+	0.594504i
$51$	3.85410			0.539682
$52$	16.9894	+	4.20378i	2.35600	+	0.582959i
$53$	3.76393			0.517016			0.258508	−	0.966009i	$-0.416769\pi$
$53$	3.76393			0.517016			0.258508	+	0.966009i	$0.416769\pi$
$54$	2.92705	−	5.06980i	0.398321	−	0.689913i
$55$	−2.42705	+	4.20378i	−0.327263	+	0.566837i
$56$	−3.73607	−	6.47106i	−0.499253	−	0.864732i
$57$	4.85410			0.642942
$58$	−9.28115	−	16.0754i	−1.21868	−	2.11081i
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	0.929580	−	0.368620i	$-0.120170\pi$
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	−0.784024	+	0.620730i	$0.786836\pi$
$60$	−33.2705			−4.29520
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	6.16312	−	10.6748i	0.782717	−	1.35571i
$63$	−1.92705	+	3.33775i	−0.242786	+	0.420517i
$64$	8.70820			1.08853
$65$	−6.54508	+	6.80185i	−0.811818	+	0.843666i
$66$	−12.7082			−1.56427
$67$	6.35410	−	11.0056i	0.776277	−	1.34455i	−0.157797	−	0.987472i	$-0.550439\pi$
$67$	6.35410	−	11.0056i	0.776277	−	1.34455i	0.934074	−	0.357080i	$-0.116228\pi$
$68$	3.57295	−	6.18853i	0.433284	−	0.750469i
$69$	−5.85410	−	10.1396i	−0.704751	−	1.22066i
$70$	6.85410			0.819222
$71$	7.09017	+	12.2805i	0.841448	+	1.45743i	0.888670	+	0.458547i	$0.151630\pi$
$71$	7.09017	+	12.2805i	0.841448	+	1.45743i	−0.0472218	+	0.998884i	$0.515037\pi$
$72$	−14.3992	−	24.9401i	−1.69696	−	2.93922i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	−5.23607	−	9.06914i	−0.608681	−	1.05427i
$75$	2.42705	−	4.20378i	0.280252	−	0.485410i
$76$	4.50000	−	7.79423i	0.516185	−	0.894059i
$77$	1.85410			0.211295
$78$	−23.9894	−	5.93583i	−2.71626	−	0.672100i
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	−12.8992	+	22.3420i	−1.44217	+	2.49792i
$81$	2.85410	−	4.94345i	0.317122	−	0.549272i
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$	6.70820			0.736321			0.368161	−	0.929762i	$-0.379988\pi$
$83$	6.70820			0.736321			0.368161	+	0.929762i	$0.379988\pi$
$84$	6.35410	+	11.0056i	0.693289	+	1.20081i
$85$	1.92705	+	3.33775i	0.209018	+	0.362030i
$86$	32.8885			3.54646
$87$	9.28115	+	16.0754i	0.995044	+	1.72347i
$88$	−6.92705	+	11.9980i	−0.738426	+	1.27899i
$89$	−2.45492	+	4.25204i	−0.260220	+	0.450715i	−0.966300	−	0.257417i	$-0.917129\pi$
$89$	−2.45492	+	4.25204i	−0.260220	+	0.450715i	0.706080	+	0.708132i	$0.250462\pi$
$90$	26.4164			2.78453
$91$	3.50000	+	0.866025i	0.366900	+	0.0907841i
$92$	−21.7082			−2.26324
$93$	−6.16312	+	10.6748i	−0.639086	+	1.10693i
$94$	2.92705	−	5.06980i	0.301902	−	0.522910i
$95$	2.42705	+	4.20378i	0.249010	+	0.431298i
$96$	−28.4164			−2.90024
$97$	−9.42705	−	16.3281i	−0.957172	−	1.65787i	−0.729318	−	0.684175i	$-0.760162\pi$
$97$	−9.42705	−	16.3281i	−0.957172	−	1.65787i	−0.227854	−	0.973695i	$-0.573171\pi$
$98$	−1.30902	−	2.26728i	−0.132231	−	0.229030i
$99$	7.14590			0.718190
$100$	−4.50000	−	7.79423i	−0.450000	−	0.779423i
$101$	5.78115	−	10.0133i	0.575246	−	0.996356i	−0.420769	−	0.907168i	$-0.638240\pi$
$101$	5.78115	−	10.0133i	0.575246	−	0.996356i	0.996015	−	0.0891877i	$-0.0284271\pi$
$102$	−5.04508	+	8.73834i	−0.499538	+	0.865225i
$103$	−8.70820			−0.858045			−0.429022	−	0.903294i	$-0.641142\pi$
$103$	−8.70820			−0.858045			−0.429022	+	0.903294i	$0.641142\pi$
$104$	−18.6803	+	19.4132i	−1.83176	+	1.90362i
$105$	−6.85410			−0.668892
$106$	−4.92705	+	8.53390i	−0.478557	+	0.828886i
$107$	1.69098	−	2.92887i	0.163473	−	0.283144i	−0.772639	−	0.634846i	$-0.781064\pi$
$107$	1.69098	−	2.92887i	0.163473	−	0.283144i	0.936112	+	0.351702i	$0.114397\pi$
$108$	5.42705	+	9.39993i	0.522218	+	0.904508i
$109$	−2.70820			−0.259399			−0.129699	−	0.991553i	$-0.541401\pi$
$109$	−2.70820			−0.259399			−0.129699	+	0.991553i	$0.541401\pi$
$110$	−6.35410	−	11.0056i	−0.605840	−	1.04935i
$111$	5.23607	+	9.06914i	0.496986	+	0.860804i
$112$	9.85410			0.931125
$113$	−0.736068	−	1.27491i	−0.0692435	−	0.119933i	0.829325	−	0.558766i	$-0.188725\pi$
$113$	−0.736068	−	1.27491i	−0.0692435	−	0.119933i	−0.898568	+	0.438833i	$0.855392\pi$
$114$	−6.35410	+	11.0056i	−0.595116	+	1.03077i
$115$	5.85410	−	10.1396i	0.545898	−	0.945523i
$116$	34.4164			3.19548
$117$	13.4894	+	3.33775i	1.24709	+	0.308575i
$118$	−5.85410			−0.538914
$119$	0.736068	−	1.27491i	0.0674752	−	0.116871i
$120$	25.6074	−	44.3533i	2.33762	−	4.04888i
$121$	3.78115	+	6.54915i	0.343741	+	0.595377i
$122$	−15.7082			−1.42215
$123$	1.00000	+	1.73205i	0.0901670	+	0.156174i
$124$	11.4271	+	19.7922i	1.02618	+	1.77739i
$125$	−8.23607			−0.736656
$126$	−5.04508	−	8.73834i	−0.449452	−	0.778474i
$127$	10.4271	−	18.0602i	0.925251	−	1.60258i	0.134094	−	0.990969i	$-0.457187\pi$
$127$	10.4271	−	18.0602i	0.925251	−	1.60258i	0.791157	−	0.611613i	$-0.209479\pi$
$128$	−0.545085	+	0.944115i	−0.0481792	+	0.0834488i
$129$	−32.8885			−2.89567
$130$	−6.85410	−	23.7433i	−0.601145	−	2.08243i
$131$	−15.3262			−1.33906			−0.669530	−	0.742785i	$-0.733504\pi$
$131$	−15.3262			−1.33906			−0.669530	+	0.742785i	$0.733504\pi$
$132$	11.7812	−	20.4056i	1.02542	−	1.77608i
$133$	0.927051	−	1.60570i	0.0803855	−	0.139232i
$134$	16.6353	+	28.8131i	1.43707	+	2.48907i
$135$	−5.85410			−0.503841
$136$	5.50000	+	9.52628i	0.471621	+	0.816872i
$137$	1.30902	+	2.26728i	0.111837	+	0.193707i	0.916511	−	0.400010i	$-0.130993\pi$
$137$	1.30902	+	2.26728i	0.111837	+	0.193707i	−0.804674	+	0.593717i	$0.797660\pi$
$138$	30.6525			2.60931
$139$	−2.28115	−	3.95107i	−0.193485	−	0.335126i	0.752918	−	0.658114i	$-0.228646\pi$
$139$	−2.28115	−	3.95107i	−0.193485	−	0.335126i	−0.946403	+	0.322989i	$0.895312\pi$
$140$	−6.35410	+	11.0056i	−0.537020	+	0.930145i
$141$	−2.92705	+	5.06980i	−0.246502	+	0.426954i
$142$	−37.1246			−3.11543
$143$	−1.85410	−	6.42280i	−0.155048	−	0.537101i
$144$	37.9787			3.16489
$145$	−9.28115	+	16.0754i	−0.770758	+	1.33499i
$146$	2.61803	−	4.53457i	0.216670	−	0.375284i
$147$	1.30902	+	2.26728i	0.107966	+	0.187002i
$148$	19.4164			1.59602
$149$	−0.927051	−	1.60570i	−0.0759470	−	0.131544i	0.825551	−	0.564328i	$-0.190865\pi$
$149$	−0.927051	−	1.60570i	−0.0759470	−	0.131544i	−0.901498	+	0.432784i	$0.857531\pi$
$150$	6.35410	+	11.0056i	0.518810	+	0.898606i
$151$	−1.29180			−0.105125			−0.0525624	−	0.998618i	$-0.516739\pi$
$151$	−1.29180			−0.105125			−0.0525624	+	0.998618i	$0.516739\pi$
$152$	6.92705	+	11.9980i	0.561858	+	0.973167i
$153$	2.83688	−	4.91362i	0.229348	−	0.397243i
$154$	−2.42705	+	4.20378i	−0.195577	+	0.338750i
$155$	−12.3262			−0.990067
$156$	31.7705	−	33.0169i	2.54368	−	2.64347i
$157$	14.8541			1.18549			0.592743	−	0.805392i	$-0.298045\pi$
$157$	14.8541			1.18549			0.592743	+	0.805392i	$0.298045\pi$
$158$	−5.23607	+	9.06914i	−0.416559	+	0.721502i
$159$	4.92705	−	8.53390i	0.390741	−	0.676783i
$160$	−14.2082	−	24.6093i	−1.12326	−	1.94554i
$161$	−4.47214			−0.352454
$162$	7.47214	+	12.9421i	0.587066	+	1.01683i
$163$	1.85410	+	3.21140i	0.145224	+	0.251536i	0.929457	−	0.368931i	$-0.120276\pi$
$163$	1.85410	+	3.21140i	0.145224	+	0.251536i	−0.784232	+	0.620467i	$0.786943\pi$
$164$	3.70820			0.289562
$165$	6.35410	+	11.0056i	0.494666	+	0.856787i
$166$	−8.78115	+	15.2094i	−0.681550	+	1.18048i
$167$	−7.11803	+	12.3288i	−0.550810	+	0.954031i	0.447406	+	0.894331i	$0.352348\pi$
$167$	−7.11803	+	12.3288i	−0.550810	+	0.954031i	−0.998216	+	0.0597001i	$0.980986\pi$
$168$	−19.5623			−1.50926
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	−10.0902			−0.773881
$171$	3.57295	−	6.18853i	0.273230	−	0.473249i
$172$	−30.4894	+	52.8091i	−2.32479	+	4.02666i
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$	−48.5967			−3.68411
$175$	−0.927051	−	1.60570i	−0.0700785	−	0.121379i
$176$	−9.13525	−	15.8227i	−0.688596	−	1.19268i
$177$	5.85410			0.440021
$178$	−6.42705	−	11.1320i	−0.481728	−	0.834377i
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$	−24.4894	+	42.4168i	−1.82533	+	3.16156i
$181$	9.70820			0.721605			0.360803	−	0.932642i	$-0.382503\pi$
$181$	9.70820			0.721605			0.360803	+	0.932642i	$0.382503\pi$
$182$	−6.54508	+	6.80185i	−0.485154	+	0.504187i
$183$	15.7082			1.16118
$184$	16.7082	−	28.9395i	1.23175	−	2.13345i
$185$	−5.23607	+	9.06914i	−0.384963	+	0.666776i
$186$	−16.1353	−	27.9471i	−1.18309	−	2.04918i
$187$	−2.72949			−0.199600
$188$	5.42705	+	9.39993i	0.395808	+	0.685560i
$189$	1.11803	+	1.93649i	0.0813250	+	0.140859i
$190$	−12.7082			−0.921950
$191$	−10.6910	−	18.5173i	−0.773572	−	1.33987i	−0.935593	−	0.353079i	$-0.885135\pi$
$191$	−10.6910	−	18.5173i	−0.773572	−	1.33987i	0.162021	−	0.986787i	$-0.448199\pi$
$192$	11.3992	−	19.7440i	0.822665	−	1.42490i
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$	49.3607			3.54389
$195$	6.85410	+	23.7433i	0.490832	+	1.70029i
$196$	4.85410			0.346722
$197$	8.39919	−	14.5478i	0.598417	−	1.03649i	−0.394638	−	0.918837i	$-0.629130\pi$
$197$	8.39919	−	14.5478i	0.598417	−	1.03649i	0.993055	−	0.117652i	$-0.0375368\pi$
$198$	−9.35410	+	16.2018i	−0.664767	+	1.15141i
$199$	12.2082	+	21.1452i	0.865417	+	1.49895i	0.866633	+	0.498946i	$0.166280\pi$
$199$	12.2082	+	21.1452i	0.865417	+	1.49895i	−0.00121626	+	0.999999i	$0.500387\pi$
$200$	13.8541			0.979633
$201$	−16.6353	−	28.8131i	−1.17336	−	2.03232i
$202$	15.1353	+	26.2150i	1.06491	+	1.84448i
$203$	7.09017			0.497632
$204$	−9.35410	−	16.2018i	−0.654918	−	1.13435i
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	11.3992	−	19.7440i	0.794219	−	1.37563i
$207$	−17.2361			−1.19799
$208$	−9.85410	−	34.1356i	−0.683259	−	2.36688i
$209$	−3.43769			−0.237790
$210$	8.97214	−	15.5402i	0.619136	−	1.07238i
$211$	−2.35410	+	4.07742i	−0.162063	+	0.280701i	−0.935608	−	0.353039i	$-0.885148\pi$
$211$	−2.35410	+	4.07742i	−0.162063	+	0.280701i	0.773545	+	0.633741i	$0.218481\pi$
$212$	−9.13525	−	15.8227i	−0.627412	−	1.08671i
$213$	37.1246			2.54374
$214$	4.42705	+	7.66788i	0.302627	+	0.524165i
$215$	−16.4443	−	28.4823i	−1.12149	−	1.94248i
$216$	−16.7082			−1.13685
$217$	2.35410	+	4.07742i	0.159807	+	0.276794i
$218$	3.54508	−	6.14027i	0.240103	−	0.415871i
$219$	−2.61803	+	4.53457i	−0.176910	+	0.306418i
$220$	23.5623			1.58857
$221$	−5.15248	−	1.27491i	−0.346593	−	0.0857595i
$222$	−27.4164			−1.84007
$223$	−10.1353	+	17.5548i	−0.678707	+	1.17555i	0.296664	+	0.954982i	$0.404126\pi$
$223$	−10.1353	+	17.5548i	−0.678707	+	1.17555i	−0.975371	+	0.220573i	$0.929207\pi$
$224$	−5.42705	+	9.39993i	−0.362610	+	0.628059i
$225$	−3.57295	−	6.18853i	−0.238197	−	0.412569i
$226$	3.85410			0.256371
$227$	−0.736068	−	1.27491i	−0.0488545	−	0.0846186i	0.840564	−	0.541712i	$-0.182224\pi$
$227$	−0.736068	−	1.27491i	−0.0488545	−	0.0846186i	−0.889419	+	0.457094i	$0.848890\pi$
$228$	−11.7812	−	20.4056i	−0.780226	−	1.35139i
$229$	−13.1246			−0.867299			−0.433649	−	0.901082i	$-0.642774\pi$
$229$	−13.1246			−0.867299			−0.433649	+	0.901082i	$0.642774\pi$
$230$	15.3262	+	26.5458i	1.01058	+	1.75038i
$231$	2.42705	−	4.20378i	0.159688	−	0.276588i
$232$	−26.4894	+	45.8809i	−1.73911	+	3.01223i
$233$	2.61803			0.171513			0.0857566	−	0.996316i	$-0.472669\pi$
$233$	2.61803			0.171513			0.0857566	+	0.996316i	$0.472669\pi$
$234$	−25.2254	+	26.2150i	−1.64904	+	1.71373i
$235$	−5.85410			−0.381880
$236$	5.42705	−	9.39993i	0.353271	−	0.611883i
$237$	5.23607	−	9.06914i	0.340119	−	0.589104i
$238$	1.92705	+	3.33775i	0.124912	+	0.216354i
$239$	−24.7082			−1.59824			−0.799120	−	0.601171i	$-0.794701\pi$
$239$	−24.7082			−1.59824			−0.799120	+	0.601171i	$0.794701\pi$
$240$	33.7705	+	58.4922i	2.17988	+	3.77566i
$241$	−12.2812	−	21.2716i	−0.791099	−	1.37022i	−0.925287	−	0.379267i	$-0.876176\pi$
$241$	−12.2812	−	21.2716i	−0.791099	−	1.37022i	0.134189	−	0.990956i	$-0.457157\pi$
$242$	−19.7984			−1.27269
$243$	−10.8262	−	18.7516i	−0.694503	−	1.20292i
$244$	14.5623	−	25.2227i	0.932256	−	1.61471i
$245$	−1.30902	+	2.26728i	−0.0836300	+	0.144851i
$246$	−5.23607			−0.333840
$247$	−6.48936	−	1.60570i	−0.412908	−	0.102168i
$248$	−35.1803			−2.23395
$249$	8.78115	−	15.2094i	0.556483	−	0.963857i
$250$	10.7812	−	18.6735i	0.681860	−	1.18102i
$251$	−0.381966	−	0.661585i	−0.0241095	−	0.0417588i	0.853719	−	0.520734i	$-0.174342\pi$
$251$	−0.381966	−	0.661585i	−0.0241095	−	0.0417588i	−0.877828	+	0.478975i	$0.841008\pi$
$252$	18.7082			1.17851
$253$	4.14590	+	7.18091i	0.260650	+	0.451460i
$254$	27.2984	+	47.2822i	1.71285	+	2.96675i
$255$	10.0902			0.631871
$256$	7.28115	+	12.6113i	0.455072	+	0.788208i
$257$	−8.37132	+	14.4996i	−0.522189	+	0.904457i	0.477478	+	0.878644i	$0.341551\pi$
$257$	−8.37132	+	14.4996i	−0.522189	+	0.904457i	−0.999667	+	0.0258138i	$0.991782\pi$
$258$	43.0517	−	74.5677i	2.68028	−	4.64238i
$259$	4.00000			0.248548
$260$	44.4787	+	11.0056i	2.75845	+	0.682540i
$261$	27.3262			1.69145
$262$	20.0623	−	34.7489i	1.23945	−	2.14680i
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$	18.1353	+	31.4112i	1.11615	+	1.93322i
$265$	9.85410			0.605333
$266$	2.42705	+	4.20378i	0.148812	+	0.257750i
$267$	6.42705	+	11.1320i	0.393329	+	0.681266i
$268$	−61.6869			−3.76813
$269$	14.3713	+	24.8919i	0.876235	+	1.51768i	0.855441	+	0.517900i	$0.173286\pi$
$269$	14.3713	+	24.8919i	0.876235	+	1.51768i	0.0207937	+	0.999784i	$0.493381\pi$
$270$	7.66312	−	13.2729i	0.466363	−	0.807764i
$271$	4.20820	−	7.28882i	0.255630	−	0.442764i	−0.709436	−	0.704770i	$-0.751050\pi$
$271$	4.20820	−	7.28882i	0.255630	−	0.442764i	0.965066	+	0.262005i	$0.0843837\pi$
$272$	−14.5066			−0.879590
$273$	6.54508	−	6.80185i	0.396127	−	0.411667i
$274$	−6.85410			−0.414071
$275$	−1.71885	+	2.97713i	−0.103650	+	0.179528i
$276$	−28.4164	+	49.2187i	−1.71047	+	2.96262i
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	0.931305	−	0.364241i	$-0.118672\pi$
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	−0.781094	+	0.624413i	$0.785338\pi$
$278$	11.9443			0.716370
$279$	9.07295	+	15.7148i	0.543183	+	0.940821i
$280$	−9.78115	−	16.9415i	−0.584536	−	1.01245i
$281$	20.1803			1.20386			0.601929	−	0.798550i	$-0.294399\pi$
$281$	20.1803			1.20386			0.601929	+	0.798550i	$0.294399\pi$
$282$	−7.66312	−	13.2729i	−0.456332	−	0.790390i
$283$	−6.70820	+	11.6190i	−0.398761	+	0.690675i	−0.993573	−	0.113190i	$-0.963893\pi$
$283$	−6.70820	+	11.6190i	−0.398761	+	0.690675i	0.594812	+	0.803865i	$0.297226\pi$
$284$	34.4164	−	59.6110i	2.04224	−	3.53726i
$285$	12.7082			0.752769
$286$	16.9894	+	4.20378i	1.00460	+	0.248574i
$287$	0.763932			0.0450935
$288$	−20.9164	+	36.2283i	−1.23251	+	2.13477i
$289$	7.41641	−	12.8456i	0.436259	−	0.755623i
$290$	−24.2984	−	42.0860i	−1.42685	−	2.47138i
$291$	−49.3607			−2.89357
$292$	4.85410	+	8.40755i	0.284065	+	0.492015i
$293$	3.38197	+	5.85774i	0.197577	+	0.342213i	0.947742	−	0.319037i	$-0.103360\pi$
$293$	3.38197	+	5.85774i	0.197577	+	0.342213i	−0.750166	+	0.661250i	$0.770026\pi$
$294$	−6.85410			−0.399739
$295$	2.92705	+	5.06980i	0.170419	+	0.295175i
$296$	−14.9443	+	25.8842i	−0.868618	+	1.50449i
$297$	2.07295	−	3.59045i	0.120285	−	0.208339i
$298$	4.85410			0.281191
$299$	4.47214	+	15.4919i	0.258630	+	0.895922i
$300$	−23.5623			−1.36037
$301$	−6.28115	+	10.8793i	−0.362040	+	0.627071i
$302$	1.69098	−	2.92887i	0.0973051	−	0.168537i
$303$	−15.1353	−	26.2150i	−0.869498	−	1.50601i
$304$	−18.2705			−1.04789
$305$	7.85410	+	13.6037i	0.449725	+	0.778946i
$306$	7.42705	+	12.8640i	0.424576	+	0.735388i
$307$	−4.85410			−0.277038			−0.138519	−	0.990360i	$-0.544234\pi$
$307$	−4.85410			−0.277038			−0.138519	+	0.990360i	$0.544234\pi$
$308$	−4.50000	−	7.79423i	−0.256411	−	0.444117i
$309$	−11.3992	+	19.7440i	−0.648477	+	1.12320i
$310$	16.1353	−	27.9471i	0.916421	−	1.58729i
$311$	3.32624			0.188614			0.0943068	−	0.995543i	$-0.469937\pi$
$311$	3.32624			0.188614			0.0943068	+	0.995543i	$0.469937\pi$
$312$	19.5623	+	67.7658i	1.10750	+	3.83648i
$313$	25.1246			1.42013			0.710064	−	0.704138i	$-0.248666\pi$
$313$	25.1246			1.42013			0.710064	+	0.704138i	$0.248666\pi$
$314$	−19.4443	+	33.6785i	−1.09730	+	1.90059i
$315$	−5.04508	+	8.73834i	−0.284258	+	0.492350i
$316$	−9.70820	−	16.8151i	−0.546129	−	0.945923i
$317$	26.2361			1.47356			0.736782	−	0.676130i	$-0.236344\pi$
$317$	26.2361			1.47356			0.736782	+	0.676130i	$0.236344\pi$
$318$	12.8992	+	22.3420i	0.723350	+	1.25288i
$319$	−6.57295	−	11.3847i	−0.368014	−	0.637420i
$320$	22.7984			1.27447
$321$	−4.42705	−	7.66788i	−0.247094	−	0.427979i
$322$	5.85410	−	10.1396i	0.326236	−	0.565058i
$323$	−1.36475	+	2.36381i	−0.0759364	+	0.131526i
$324$	−27.7082			−1.53934
$325$	−4.63525	+	4.81710i	−0.257118	+	0.267205i
$326$	−9.70820			−0.537688
$327$	−3.54508	+	6.14027i	−0.196044	+	0.339558i
$328$	−2.85410	+	4.94345i	−0.157591	+	0.272956i
$329$	1.11803	+	1.93649i	0.0616392	+	0.106762i
$330$	−33.2705			−1.83148
$331$	5.07295	+	8.78661i	0.278834	+	0.482956i	0.971095	−	0.238692i	$-0.0767186\pi$
$331$	5.07295	+	8.78661i	0.278834	+	0.482956i	−0.692261	+	0.721647i	$0.743385\pi$
$332$	−16.2812	−	28.1998i	−0.893544	−	1.54766i
$333$	15.4164			0.844814
$334$	−18.6353	−	32.2772i	−1.01968	−	1.76613i
$335$	16.6353	−	28.8131i	0.908881	−	1.57423i
$336$	12.8992	−	22.3420i	0.703708	−	1.21886i
$337$	−11.5623			−0.629839			−0.314919	−	0.949118i	$-0.601978\pi$
$337$	−11.5623			−0.629839			−0.314919	+	0.949118i	$0.601978\pi$
$338$	30.1074	+	15.8710i	1.63763	+	0.863268i
$339$	−3.85410			−0.209326
$340$	9.35410	−	16.2018i	0.507297	−	0.878665i
$341$	4.36475	−	7.55996i	0.236364	−	0.409395i
$342$	9.35410	+	16.2018i	0.505812	+	0.876092i
$343$	1.00000			0.0539949
$344$	−46.9336	−	81.2914i	−2.53049	−	4.38294i
$345$	−15.3262	−	26.5458i	−0.825137	−	1.42918i
$346$	−23.5623			−1.26672
$347$	−15.3820	−	26.6423i	−0.825747	−	1.43024i	−0.901347	−	0.433098i	$-0.857420\pi$
$347$	−15.3820	−	26.6423i	−0.825747	−	1.43024i	0.0755997	−	0.997138i	$-0.475913\pi$
$348$	45.0517	−	78.0318i	2.41502	−	4.18294i
$349$	−10.3541	+	17.9338i	−0.554242	+	0.959976i	0.443720	+	0.896166i	$0.353659\pi$
$349$	−10.3541	+	17.9338i	−0.554242	+	0.959976i	−0.997962	+	0.0638103i	$0.979675\pi$
$350$	4.85410			0.259463
$351$	5.59017	−	5.80948i	0.298381	−	0.310087i
$352$	20.1246			1.07265
$353$	−11.0729	+	19.1789i	−0.589354	+	1.02079i	0.404964	+	0.914333i	$0.367284\pi$
$353$	−11.0729	+	19.1789i	−0.589354	+	1.02079i	−0.994317	+	0.106458i	$0.966049\pi$
$354$	−7.66312	+	13.2729i	−0.407290	+	0.705447i
$355$	18.5623	+	32.1509i	0.985185	+	1.70639i
$356$	23.8328			1.26314
$357$	−1.92705	−	3.33775i	−0.101990	−	0.176652i
$358$	11.7812	+	20.4056i	0.622653	+	1.07847i
$359$	−22.0902			−1.16587			−0.582937	−	0.812517i	$-0.698097\pi$
$359$	−22.0902			−1.16587			−0.582937	+	0.812517i	$0.698097\pi$
$360$	−37.6976	−	65.2941i	−1.98684	−	3.44130i
$361$	7.78115	−	13.4774i	0.409534	−	0.709334i
$362$	−12.7082	+	22.0113i	−0.667928	+	1.15689i
$363$	19.7984			1.03915
$364$	−4.85410	−	16.8151i	−0.254424	−	0.881351i
$365$	−5.23607			−0.274068
$366$	−20.5623	+	35.6150i	−1.07481	+	1.86162i
$367$	0.708204	−	1.22665i	0.0369679	−	0.0640304i	−0.846949	−	0.531673i	$-0.821563\pi$
$367$	0.708204	−	1.22665i	0.0369679	−	0.0640304i	0.883917	+	0.467643i	$0.154897\pi$
$368$	22.0344	+	38.1648i	1.14862	+	1.98948i
$369$	2.94427			0.153273
$370$	−13.7082	−	23.7433i	−0.712656	−	1.23436i
$371$	−1.88197	−	3.25966i	−0.0977068	−	0.169233i
$372$	59.8328			3.10219
$373$	10.2812	+	17.8075i	0.532338	+	0.922036i	0.999287	+	0.0377522i	$0.0120198\pi$
$373$	10.2812	+	17.8075i	0.532338	+	0.922036i	−0.466949	+	0.884284i	$0.654647\pi$
$374$	3.57295	−	6.18853i	0.184753	−	0.320001i
$375$	−10.7812	+	18.6735i	−0.556736	+	0.964296i
$376$	−16.7082			−0.861660
$377$	−7.09017	−	24.5611i	−0.365162	−	1.26496i
$378$	−5.85410			−0.301103
$379$	3.07295	−	5.32250i	0.157847	−	0.273399i	−0.776245	−	0.630431i	$-0.782878\pi$
$379$	3.07295	−	5.32250i	0.157847	−	0.273399i	0.934092	+	0.357032i	$0.116211\pi$
$380$	11.7812	−	20.4056i	0.604360	−	1.04678i
$381$	−27.2984	−	47.2822i	−1.39854	−	2.42234i
$382$	55.9787			2.86412
$383$	10.9894	+	19.0341i	0.561530	+	0.972598i	0.997363	+	0.0725709i	$0.0231204\pi$
$383$	10.9894	+	19.0341i	0.561530	+	0.972598i	−0.435833	+	0.900027i	$0.643546\pi$
$384$	1.42705	+	2.47172i	0.0728239	+	0.126135i
$385$	4.85410			0.247388
$386$	7.85410	+	13.6037i	0.399763	+	0.692410i
$387$	−24.2082	+	41.9298i	−1.23057	+	2.13141i
$388$	−45.7599	+	79.2584i	−2.32311	+	4.02374i
$389$	−11.8885			−0.602773			−0.301387	−	0.953502i	$-0.597449\pi$
$389$	−11.8885			−0.602773			−0.301387	+	0.953502i	$0.597449\pi$
$390$	−62.8050	−	15.5402i	−3.18025	−	0.786908i
$391$	6.58359			0.332947
$392$	−3.73607	+	6.47106i	−0.188700	+	0.326838i
$393$	−20.0623	+	34.7489i	−1.01201	+	1.75285i
$394$	21.9894	+	38.0867i	1.10781	+	1.91878i
$395$	10.4721			0.526910
$396$	−17.3435	−	30.0398i	−0.871542	−	1.50955i
$397$	−0.708204	−	1.22665i	−0.0355437	−	0.0615636i	0.847706	−	0.530466i	$-0.177983\pi$
$397$	−0.708204	−	1.22665i	−0.0355437	−	0.0615636i	−0.883250	+	0.468902i	$0.844650\pi$
$398$	−63.9230			−3.20417
$399$	−2.42705	−	4.20378i	−0.121505	−	0.210452i
$400$	−9.13525	+	15.8227i	−0.456763	+	0.791136i
$401$	−17.7254	+	30.7013i	−0.885165	+	1.53315i	−0.0396416	+	0.999214i	$0.512622\pi$
$401$	−17.7254	+	30.7013i	−0.885165	+	1.53315i	−0.845524	+	0.533938i	$0.820712\pi$
$402$	87.1033			4.34432
$403$	11.7705	−	12.2323i	0.586331	−	0.609333i
$404$	−56.1246			−2.79230
$405$	7.47214	−	12.9421i	0.371293	−	0.643099i
$406$	−9.28115	+	16.0754i	−0.460616	+	0.797810i
$407$	−3.70820	−	6.42280i	−0.183809	−	0.318366i
$408$	28.7984			1.42573
$409$	−7.21885	−	12.5034i	−0.356949	−	0.618254i	0.630500	−	0.776189i	$-0.282850\pi$
$409$	−7.21885	−	12.5034i	−0.356949	−	0.618254i	−0.987450	+	0.157935i	$0.949516\pi$
$410$	−2.61803	−	4.53457i	−0.129295	−	0.223946i
$411$	6.85410			0.338088
$412$	21.1353	+	36.6073i	1.04126	+	1.80351i
$413$	1.11803	−	1.93649i	0.0550149	−	0.0952885i
$414$	22.5623	−	39.0791i	1.10888	−	1.92063i
$415$	17.5623			0.862100
$416$	37.9894	+	9.39993i	1.86258	+	0.460869i
$417$	−11.9443			−0.584914
$418$	4.50000	−	7.79423i	0.220102	−	0.381228i
$419$	5.97214	−	10.3440i	0.291758	−	0.505340i	−0.682468	−	0.730916i	$-0.739093\pi$
$419$	5.97214	−	10.3440i	0.291758	−	0.505340i	0.974226	+	0.225576i	$0.0724265\pi$
$420$	16.6353	+	28.8131i	0.811717	+	1.40594i
$421$	1.41641			0.0690315			0.0345157	−	0.999404i	$-0.489011\pi$
$421$	1.41641			0.0690315			0.0345157	+	0.999404i	$0.489011\pi$
$422$	−6.16312	−	10.6748i	−0.300016	−	0.519643i
$423$	4.30902	+	7.46344i	0.209512	+	0.362885i
$424$	28.1246			1.36585
$425$	1.36475	+	2.36381i	0.0661999	+	0.114662i
$426$	−48.5967	+	84.1720i	−2.35452	+	4.07815i
$427$	3.00000	−	5.19615i	0.145180	−	0.251459i
$428$	−16.4164			−0.793517
$429$	−16.9894	−	4.20378i	−0.820254	−	0.202960i
$430$	86.1033			4.15227
$431$	−3.89919	+	6.75359i	−0.187817	+	0.325309i	−0.944522	−	0.328448i	$-0.893475\pi$
$431$	−3.89919	+	6.75359i	−0.187817	+	0.325309i	0.756705	+	0.653756i	$0.226808\pi$
$432$	11.0172	−	19.0824i	0.530066	−	0.918102i
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	0.853761	−	0.520665i	$-0.174316\pi$
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	−0.877790	+	0.479046i	$0.840983\pi$
$434$	−12.3262			−0.591678
$435$	24.2984	+	42.0860i	1.16502	+	2.01787i
$436$	6.57295	+	11.3847i	0.314787	+	0.545227i
$437$	8.29180			0.396650
$438$	−6.85410	−	11.8717i	−0.327502	−	0.567250i
$439$	−7.42705	+	12.8640i	−0.354474	+	0.613967i	−0.987028	−	0.160550i	$-0.948673\pi$
$439$	−7.42705	+	12.8640i	−0.354474	+	0.613967i	0.632554	+	0.774516i	$0.282007\pi$
$440$	−18.1353	+	31.4112i	−0.864564	+	1.49747i
$441$	3.85410			0.183529
$442$	9.63525	−	10.0133i	0.458302	−	0.476282i
$443$	−5.23607			−0.248773			−0.124387	−	0.992234i	$-0.539696\pi$
$443$	−5.23607			−0.248773			−0.124387	+	0.992234i	$0.539696\pi$
$444$	25.4164	−	44.0225i	1.20621	−	2.08922i
$445$	−6.42705	+	11.1320i	−0.304671	+	0.527706i
$446$	−26.5344	−	45.9590i	−1.25644	−	2.17622i
$447$	−4.85410			−0.229591
$448$	−4.35410	−	7.54153i	−0.205712	−	0.356304i
$449$	−9.76393	−	16.9116i	−0.460788	−	0.798109i	0.538212	−	0.842809i	$-0.319100\pi$
$449$	−9.76393	−	16.9116i	−0.460788	−	0.798109i	−0.999000	+	0.0447005i	$0.985767\pi$
$450$	18.7082			0.881913
$451$	−0.708204	−	1.22665i	−0.0333480	−	0.0577605i
$452$	−3.57295	+	6.18853i	−0.168057	+	0.291084i
$453$	−1.69098	+	2.92887i	−0.0794493	+	0.137610i
$454$	3.85410			0.180882
$455$	9.16312	+	2.26728i	0.429574	+	0.106292i
$456$	36.2705			1.69852
$457$	−7.70820	+	13.3510i	−0.360575	+	0.624533i	−0.988055	−	0.154098i	$-0.950753\pi$
$457$	−7.70820	+	13.3510i	−0.360575	+	0.624533i	0.627481	+	0.778632i	$0.284086\pi$
$458$	17.1803	−	29.7572i	0.802785	−	1.39046i
$459$	−1.64590	−	2.85078i	−0.0768239	−	0.133063i
$460$	−56.8328			−2.64984
$461$	6.10739	+	10.5783i	0.284450	+	0.492681i	0.972476	−	0.233005i	$-0.0748558\pi$
$461$	6.10739	+	10.5783i	0.284450	+	0.492681i	−0.688026	+	0.725686i	$0.741523\pi$
$462$	6.35410	+	11.0056i	0.295620	+	0.512028i
$463$	6.70820			0.311757			0.155878	−	0.987776i	$-0.450179\pi$
$463$	6.70820			0.311757			0.155878	+	0.987776i	$0.450179\pi$
$464$	−34.9336	−	60.5068i	−1.62175	−	2.80896i
$465$	−16.1353	+	27.9471i	−0.748255	+	1.29601i
$466$	−3.42705	+	5.93583i	−0.158755	+	0.274972i
$467$	2.34752			0.108630			0.0543152	−	0.998524i	$-0.482702\pi$
$467$	2.34752			0.108630			0.0543152	+	0.998524i	$0.482702\pi$
$468$	−18.7082	−	64.8071i	−0.864787	−	2.99571i
$469$	−12.7082			−0.586810
$470$	7.66312	−	13.2729i	0.353473	−	0.612234i
$471$	19.4443	−	33.6785i	0.895945	−	1.55182i
$472$	8.35410	+	14.4697i	0.384529	+	0.666023i
$473$	23.2918			1.07096
$474$	13.7082	+	23.7433i	0.629639	+	1.09057i
$475$	1.71885	+	2.97713i	0.0788661	+	0.136600i
$476$	−7.14590			−0.327532
$477$	−7.25329	−	12.5631i	−0.332105	−	0.575223i
$478$	32.3435	−	56.0205i	1.47936	−	2.56232i
$479$	−12.4894	+	21.6322i	−0.570653	+	0.988400i	0.425846	+	0.904796i	$0.359977\pi$
$479$	−12.4894	+	21.6322i	−0.570653	+	0.988400i	−0.996499	+	0.0836047i	$0.973357\pi$
$480$	−74.3951			−3.39566
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$	64.3050			2.92901
$483$	−5.85410	+	10.1396i	−0.266371	+	0.461368i
$484$	18.3541	−	31.7902i	0.834277	−	1.44501i
$485$	−24.6803	−	42.7476i	−1.12068	−	1.94107i
$486$	56.6869			2.57137
$487$	−14.9894	−	25.9623i	−0.679233	−	1.17647i	−0.975212	−	0.221271i	$-0.928979\pi$
$487$	−14.9894	−	25.9623i	−0.679233	−	1.17647i	0.295980	−	0.955194i	$-0.404354\pi$
$488$	22.4164	+	38.8264i	1.01474	+	1.75759i
$489$	9.70820			0.439020
$490$	−3.42705	−	5.93583i	−0.154818	−	0.268153i
$491$	−6.19098	+	10.7231i	−0.279395	+	0.483927i	−0.971235	−	0.238125i	$-0.923467\pi$
$491$	−6.19098	+	10.7231i	−0.279395	+	0.483927i	0.691839	+	0.722051i	$0.256801\pi$
$492$	4.85410	−	8.40755i	0.218840	−	0.379042i
$493$	−10.4377			−0.470090
$494$	12.1353	−	12.6113i	0.545991	−	0.567410i
$495$	18.7082			0.840871
$496$	23.1976	−	40.1794i	1.04160	−	1.80411i
$497$	7.09017	−	12.2805i	0.318038	−	0.550857i
$498$	22.9894	+	39.8187i	1.03018	+	1.78432i
$499$	14.8541			0.664961			0.332480	−	0.943110i	$-0.392114\pi$
$499$	14.8541			0.664961			0.332480	+	0.943110i	$0.392114\pi$
$500$	19.9894	+	34.6226i	0.893951	+	1.54837i
$501$	18.6353	+	32.2772i	0.832562	+	1.44204i
$502$	2.00000			0.0892644
$503$	−13.3090	−	23.0519i	−0.593420	−	1.02783i	−0.993768	−	0.111470i	$-0.964444\pi$
$503$	−13.3090	−	23.0519i	−0.593420	−	1.02783i	0.400348	−	0.916363i	$-0.368889\pi$
$504$	−14.3992	+	24.9401i	−0.641391	+	1.11092i
$505$	15.1353	−	26.2150i	0.673510	−	1.16655i
$506$	−21.7082			−0.965047
$507$	−30.1074	−	15.8710i	−1.33712	−	0.704855i
$508$	−101.228			−4.49126
$509$	9.29837	−	16.1053i	0.412143	−	0.713853i	−0.582981	−	0.812486i	$-0.698114\pi$
$509$	9.29837	−	16.1053i	0.412143	−	0.713853i	0.995124	+	0.0986331i	$0.0314470\pi$
$510$	−13.2082	+	22.8773i	−0.584869	+	1.01302i
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$	−40.3050			−1.78124
$513$	−2.07295	−	3.59045i	−0.0915229	−	0.158522i
$514$	−21.9164	−	37.9603i	−0.966691	−	1.67436i
$515$	−22.7984			−1.00462
$516$	79.8222	+	138.256i	3.51398	+	6.08638i
$517$	2.07295	−	3.59045i	0.0911682	−	0.157908i
$518$	−5.23607	+	9.06914i	−0.230060	+	0.398475i
$519$	23.5623			1.03427
$520$	−48.9058	+	50.8244i	−2.14466	+	2.22880i
$521$	18.6525			0.817180			0.408590	−	0.912718i	$-0.366021\pi$
$521$	18.6525			0.817180			0.408590	+	0.912718i	$0.366021\pi$
$522$	−35.7705	+	61.9563i	−1.56563	+	2.71176i
$523$	−0.562306	+	0.973942i	−0.0245879	+	0.0425875i	−0.878058	−	0.478555i	$-0.841161\pi$
$523$	−0.562306	+	0.973942i	−0.0245879	+	0.0425875i	0.853470	+	0.521143i	$0.174494\pi$
$524$	37.1976	+	64.4281i	1.62498	+	2.81455i
$525$	−4.85410			−0.211850
$526$	−11.7812	−	20.4056i	−0.513683	−	0.889724i
$527$	−3.46556	−	6.00252i	−0.150962	−	0.261474i
$528$	−47.8328			−2.08166
$529$	1.50000	+	2.59808i	0.0652174	+	0.112960i
$530$	−12.8992	+	22.3420i	−0.560305	+	0.970477i
$531$	4.30902	−	7.46344i	0.186995	−	0.323886i
$532$	−9.00000			−0.390199
$533$	−0.763932	−	2.64634i	−0.0330896	−	0.114626i
$534$	−33.6525			−1.45629
$535$	4.42705	−	7.66788i	0.191398	−	0.331511i
$536$	47.4787	−	82.2355i	2.05077	−	3.55203i
$537$	−11.7812	−	20.4056i	−0.508394	−	0.880565i
$538$	−75.2492			−3.24422
$539$	−0.927051	−	1.60570i	−0.0399309	−	0.0691624i
$540$	14.2082	+	24.6093i	0.611424	+	1.05902i
$541$	35.2705			1.51640			0.758199	−	0.652023i	$-0.226080\pi$
$541$	35.2705			1.51640			0.758199	+	0.652023i	$0.226080\pi$
$542$	11.0172	+	19.0824i	0.473230	+	0.819659i
$543$	12.7082	−	22.0113i	0.545361	−	0.944593i
$544$	7.98936	−	13.8380i	0.342541	−	0.593298i
$545$	−7.09017			−0.303710
$546$	6.85410	+	23.7433i	0.293328	+	1.01612i
$547$	−3.00000			−0.128271			−0.0641354	−	0.997941i	$-0.520429\pi$
$547$	−3.00000			−0.128271			−0.0641354	+	0.997941i	$0.520429\pi$
$548$	6.35410	−	11.0056i	0.271434	−	0.470137i
$549$	11.5623	−	20.0265i	0.493467	−	0.854710i
$550$	−4.50000	−	7.79423i	−0.191881	−	0.332347i
$551$	−13.1459			−0.560034
$552$	−43.7426	−	75.7645i	−1.86181	−	3.22475i
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	−13.0902			−0.556148
$555$	13.7082	+	23.7433i	0.581881	+	1.00785i
$556$	−11.0729	+	19.1789i	−0.469598	+	0.813367i
$557$	13.9894	−	24.2303i	0.592748	−	1.02667i	−0.401112	−	0.916029i	$-0.631376\pi$
$557$	13.9894	−	24.2303i	0.592748	−	1.02667i	0.993860	−	0.110641i	$-0.0352904\pi$
$558$	−47.5066			−2.01111
$559$	43.9681	+	10.8793i	1.85965	+	0.460144i
$560$	25.7984			1.09018
$561$	−3.57295	+	6.18853i	−0.150850	+	0.261280i
$562$	−26.4164	+	45.7546i	−1.11431	+	1.93004i
$563$	10.5279	+	18.2348i	0.443697	+	0.768505i	0.997960	−	0.0638360i	$-0.0203335\pi$
$563$	10.5279	+	18.2348i	0.443697	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$564$	28.4164			1.19655
$565$	−1.92705	−	3.33775i	−0.0810716	−	0.140420i
$566$	−17.5623	−	30.4188i	−0.738199	−	1.27860i
$567$	−5.70820			−0.239722
$568$	52.9787	+	91.7618i	2.22294	+	3.85024i
$569$	−7.47214	+	12.9421i	−0.313248	+	0.542562i	−0.979064	−	0.203555i	$-0.934751\pi$
$569$	−7.47214	+	12.9421i	−0.313248	+	0.542562i	0.665815	+	0.746117i	$0.268084\pi$
$570$	−16.6353	+	28.8131i	−0.696774	+	1.20685i
$571$	24.6869			1.03312			0.516558	−	0.856252i	$-0.327213\pi$
$571$	24.6869			1.03312			0.516558	+	0.856252i	$0.327213\pi$
$572$	−22.5000	+	23.3827i	−0.940772	+	0.977679i
$573$	−55.9787			−2.33854
$574$	−1.00000	+	1.73205i	−0.0417392	+	0.0722944i
$575$	4.14590	−	7.18091i	0.172896	−	0.299464i
$576$	−16.7812	−	29.0658i	−0.699215	−	1.21108i
$577$	−43.8328			−1.82478			−0.912392	−	0.409318i	$-0.865767\pi$
$577$	−43.8328			−1.82478			−0.912392	+	0.409318i	$0.865767\pi$
$578$	19.4164	+	33.6302i	0.807616	+	1.39883i
$579$	−7.85410	−	13.6037i	−0.326405	−	0.565351i
$580$	90.1033			3.74134
$581$	−3.35410	−	5.80948i	−0.139152	−	0.241018i
$582$	64.6140	−	111.915i	2.67834	−	4.63901i
$583$	−3.48936	+	6.04374i	−0.144514	+	0.250306i
$584$	−14.9443			−0.618398
$585$	35.3156	+	8.73834i	1.46012	+	0.361286i
$586$	−17.7082			−0.731519
$587$	9.95492	−	17.2424i	0.410883	−	0.711671i	−0.584103	−	0.811679i	$-0.698554\pi$
$587$	9.95492	−	17.2424i	0.410883	−	0.711671i	0.994987	+	0.100009i	$0.0318870\pi$
$588$	6.35410	−	11.0056i	0.262039	−	0.453864i
$589$	−4.36475	−	7.55996i	−0.179846	−	0.311503i
$590$	−15.3262			−0.630971
$591$	−21.9894	−	38.0867i	−0.904521	−	1.56668i
$592$	−19.7082	−	34.1356i	−0.810002	−	1.40296i
$593$	43.7984			1.79858			0.899292	−	0.437349i	$-0.144083\pi$
$593$	43.7984			1.79858			0.899292	+	0.437349i	$0.144083\pi$
$594$	5.42705	+	9.39993i	0.222675	+	0.385684i
$595$	1.92705	−	3.33775i	0.0790014	−	0.136834i
$596$	−4.50000	+	7.79423i	−0.184327	+	0.319264i
$597$	63.9230			2.61619
$598$	−40.9787	−	10.1396i	−1.67574	−	0.414639i
$599$	29.5066			1.20561			0.602803	−	0.797890i	$-0.294050\pi$
$599$	29.5066			1.20561			0.602803	+	0.797890i	$0.294050\pi$
$600$	18.1353	−	31.4112i	0.740369	−	1.28236i
$601$	−20.1976	+	34.9832i	−0.823876	+	1.42699i	0.0788998	+	0.996883i	$0.474859\pi$
$601$	−20.1976	+	34.9832i	−0.823876	+	1.42699i	−0.902776	+	0.430112i	$0.858474\pi$
$602$	−16.4443	−	28.4823i	−0.670218	−	1.16085i
$603$	−48.9787			−1.99457
$604$	3.13525	+	5.43042i	0.127572	+	0.220961i
$605$	9.89919	+	17.1459i	0.402459	+	0.697080i
$606$	79.2492			3.21928
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$	10.0623	−	17.4284i	0.408080	−	0.706816i
$609$	9.28115	−	16.0754i	0.376091	−	0.651409i
$610$	−41.1246			−1.66509
$611$	5.59017	−	5.80948i	0.226154	−	0.235026i
$612$	−27.5410			−1.11328
$613$	−17.2812	+	29.9318i	−0.697979	+	1.20894i	0.271187	+	0.962527i	$0.412584\pi$
$613$	−17.2812	+	29.9318i	−0.697979	+	1.20894i	−0.969166	+	0.246409i	$0.920749\pi$
$614$	6.35410	−	11.0056i	0.256431	−	0.444151i
$615$	2.61803	+	4.53457i	0.105569	+	0.182851i
$616$	13.8541			0.558198
$617$	−0.0278640	−	0.0482619i	−0.00112176	−	0.00194295i	0.865464	−	0.500971i	$-0.167024\pi$
$617$	−0.0278640	−	0.0482619i	−0.00112176	−	0.00194295i	−0.866586	+	0.499028i	$0.833690\pi$
$618$	−29.8435	−	51.6904i	−1.20048	−	2.07929i
$619$	9.41641			0.378477			0.189239	−	0.981931i	$-0.439398\pi$
$619$	9.41641			0.378477			0.189239	+	0.981931i	$0.439398\pi$
$620$	29.9164	+	51.8167i	1.20147	+	2.08101i
$621$	−5.00000	+	8.66025i	−0.200643	+	0.347524i
$622$	−4.35410	+	7.54153i	−0.174584	+	0.302388i
$623$	4.90983			0.196708
$624$	−90.2943	−	22.3420i	−3.61467	−	0.894398i
$625$	−30.8328			−1.23331
$626$	−32.8885	+	56.9646i	−1.31449	+	2.27676i
$627$	−4.50000	+	7.79423i	−0.179713	+	0.311272i
$628$	−36.0517	−	62.4433i	−1.43862	−	2.49176i
$629$	−5.88854			−0.234792
$630$	−13.2082	−	22.8773i	−0.526227	−	0.911453i
$631$	−17.1976	−	29.7870i	−0.684624	−	1.18580i	−0.973555	−	0.228454i	$-0.926633\pi$
$631$	−17.1976	−	29.7870i	−0.684624	−	1.18580i	0.288931	−	0.957350i	$-0.406700\pi$
$632$	29.8885			1.18890
$633$	6.16312	+	10.6748i	0.244962	+	0.424287i
$634$	−34.3435	+	59.4846i	−1.36395	+	2.36244i
$635$	27.2984	−	47.2822i	1.08330	−	1.87634i
$636$	−47.8328			−1.89669
$637$	−1.00000	−	3.46410i	−0.0396214	−	0.137253i
$638$	34.4164			1.36256
$639$	27.3262	−	47.3304i	1.08101	−	1.87236i
$640$	−1.42705	+	2.47172i	−0.0564091	+	0.0977035i
$641$	23.7533	+	41.1419i	0.938199	+	1.62501i	0.768829	+	0.639455i	$0.220840\pi$
$641$	23.7533	+	41.1419i	0.938199	+	1.62501i	0.169370	+	0.985553i	$0.445827\pi$
$642$	23.1803			0.914855
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	0.926750	−	0.375680i	$-0.122591\pi$
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	10.8541	+	18.7999i	0.427712	+	0.740818i
$645$	−86.1033			−3.39032
$646$	−3.57295	−	6.18853i	−0.140576	−	0.243484i
$647$	−12.3820	+	21.4462i	−0.486785	+	0.843137i	−0.999885	−	0.0151924i	$-0.995164\pi$
$647$	−12.3820	+	21.4462i	−0.486785	+	0.843137i	0.513099	+	0.858329i	$0.328497\pi$
$648$	21.3262	−	36.9381i	0.837774	−	1.45107i
$649$	−4.14590			−0.162741
$650$	−4.85410	−	16.8151i	−0.190394	−	0.659543i
$651$	12.3262			0.483103
$652$	9.00000	−	15.5885i	0.352467	−	0.610491i
$653$	0.190983	−	0.330792i	0.00747374	−	0.0129449i	−0.862264	−	0.506458i	$-0.830954\pi$
$653$	0.190983	−	0.330792i	0.00747374	−	0.0129449i	0.869738	+	0.493514i	$0.164288\pi$
$654$	−9.28115	−	16.0754i	−0.362922	−	0.628599i
$655$	−40.1246			−1.56780
$656$	−3.76393	−	6.51932i	−0.146957	−	0.254537i
$657$	3.85410	+	6.67550i	0.150363	+	0.260436i
$658$	−5.85410			−0.228217
$659$	11.9443	+	20.6881i	0.465283	+	0.805893i	0.999214	−	0.0396343i	$-0.0126193\pi$
$659$	11.9443	+	20.6881i	0.465283	+	0.805893i	−0.533931	+	0.845528i	$0.679286\pi$
$660$	30.8435	−	53.4224i	1.20058	−	2.07947i
$661$	24.2705	−	42.0378i	0.944013	−	1.63508i	0.186299	−	0.982493i	$-0.440351\pi$
$661$	24.2705	−	42.0378i	0.944013	−	1.63508i	0.757715	−	0.652586i	$-0.226316\pi$
$662$	−26.5623			−1.03237
$663$	−9.63525	+	10.0133i	−0.374202	+	0.388882i
$664$	50.1246			1.94521
$665$	2.42705	−	4.20378i	0.0941170	−	0.163015i
$666$	−20.1803	+	34.9534i	−0.781972	+	1.35442i
$667$	15.8541	+	27.4601i	0.613873	+	1.06326i
$668$	69.1033			2.67369
$669$	26.5344	+	45.9590i	1.02588	+	1.77688i
$670$	43.5517	+	75.4337i	1.68255	+	2.91426i
$671$	−11.1246			−0.429461
$672$	14.2082	+	24.6093i	0.548093	+	0.949326i
$673$	19.6246	−	33.9908i	0.756473	−	1.31025i	−0.188165	−	0.982137i	$-0.560254\pi$
$673$	19.6246	−	33.9908i	0.756473	−	1.31025i	0.944639	−	0.328113i	$-0.106413\pi$
$674$	15.1353	−	26.2150i	0.582988	−	1.00977i
$675$	−4.14590			−0.159576
$676$	−53.3951	+	33.6302i	−2.05366	+	1.29347i
$677$	43.7426			1.68117			0.840583	−	0.541682i	$-0.182212\pi$
$677$	43.7426			1.68117			0.840583	+	0.541682i	$0.182212\pi$
$678$	5.04508	−	8.73834i	0.193755	−	0.335594i
$679$	−9.42705	+	16.3281i	−0.361777	+	0.626616i
$680$	14.3992	+	24.9401i	0.552184	+	0.956410i
$681$	−3.85410			−0.147690
$682$	11.4271	+	19.7922i	0.437564	+	0.757884i
$683$	−0.736068	−	1.27491i	−0.0281649	−	0.0487830i	0.851599	−	0.524193i	$-0.175633\pi$
$683$	−0.736068	−	1.27491i	−0.0281649	−	0.0487830i	−0.879764	+	0.475410i	$0.842300\pi$
$684$	−34.6869			−1.32629
$685$	3.42705	+	5.93583i	0.130941	+	0.226796i
$686$	−1.30902	+	2.26728i	−0.0499785	+	0.0865653i
$687$	−17.1803	+	29.7572i	−0.655471	+	1.13531i
$688$	123.790			4.71946
$689$	−9.40983	+	9.77898i	−0.358486	+	0.372550i
$690$	80.2492			3.05504
$691$	2.92705	−	5.06980i	0.111350	−	0.192864i	−0.804965	−	0.593323i	$-0.797816\pi$
$691$	2.92705	−	5.06980i	0.111350	−	0.192864i	0.916315	+	0.400458i	$0.131149\pi$
$692$	21.8435	−	37.8340i	0.830364	−	1.43823i
$693$	−3.57295	−	6.18853i	−0.135725	−	0.235083i
$694$	80.5410			3.05730
$695$	−5.97214	−	10.3440i	−0.226536	−	0.392372i
$696$	69.3500	+	120.118i	2.62871	+	4.55305i
$697$	−1.12461			−0.0425977
$698$	−27.1074	−	46.9514i	−1.02603	−	1.77714i
$699$	3.42705	−	5.93583i	0.129623	−	0.224514i
$700$	−4.50000	+	7.79423i	−0.170084	+	0.294594i
$701$	11.2361			0.424380			0.212190	−	0.977228i	$-0.431940\pi$
$701$	11.2361			0.424380			0.212190	+	0.977228i	$0.431940\pi$
$702$	5.85410	+	20.2792i	0.220949	+	0.765389i
$703$	−7.41641			−0.279715
$704$	−8.07295	+	13.9828i	−0.304261	+	0.526995i
$705$	−7.66312	+	13.2729i	−0.288610	+	0.499887i
$706$	−28.9894	−	50.2110i	−1.09103	−	1.88972i
$707$	−11.5623			−0.434845
$708$	−14.2082	−	24.6093i	−0.533977	−	0.924875i
$709$	−11.7812	−	20.4056i	−0.442450	−	0.766347i	0.555420	−	0.831570i	$-0.312557\pi$
$709$	−11.7812	−	20.4056i	−0.442450	−	0.766347i	−0.997871	+	0.0652231i	$0.979224\pi$
$710$	−97.1935			−3.64761
$711$	−7.70820	−	13.3510i	−0.289080	−	0.500702i
$712$	−18.3435	+	31.7718i	−0.687450	+	1.19070i
$713$	−10.5279	+	18.2348i	−0.394272	+	0.682898i
$714$	10.0902			0.377615
$715$	−4.85410	−	16.8151i	−0.181533	−	0.628849i
$716$	−43.6869			−1.63266
$717$	−32.3435	+	56.0205i	−1.20789	+	2.09212i
$718$	28.9164	−	50.0847i	1.07915	−	1.86914i
$719$	−4.06231	−	7.03612i	−0.151498	−	0.262403i	0.780280	−	0.625430i	$-0.215077\pi$
$719$	−4.06231	−	7.03612i	−0.151498	−	0.262403i	−0.931779	+	0.363027i	$0.881743\pi$
$720$	99.4296			3.70552
$721$	4.35410	+	7.54153i	0.162155	+	0.280861i
$722$	20.3713	+	35.2842i	0.758142	+	1.31314i
$723$	−64.3050			−2.39153
$724$	−23.5623	−	40.8111i	−0.875686	−	1.51673i
$725$	−6.57295	+	11.3847i	−0.244113	+	0.422816i
$726$	−25.9164	+	44.8885i	−0.961848	+	1.66597i
$727$	−30.7082			−1.13890			−0.569452	−	0.822025i	$-0.692845\pi$
$727$	−30.7082			−1.13890			−0.569452	+	0.822025i	$0.692845\pi$
$728$	26.1525	+	6.47106i	0.969275	+	0.239833i
$729$	−39.5623			−1.46527
$730$	6.85410	−	11.8717i	0.253682	−	0.439390i
$731$	9.24671	−	16.0158i	0.342002	−	0.592365i
$732$	−38.1246	−	66.0338i	−1.40913	−	2.44068i
$733$	−32.2705			−1.19194			−0.595969	−	0.803007i	$-0.703232\pi$
$733$	−32.2705			−1.19194			−0.595969	+	0.803007i	$0.703232\pi$
$734$	1.85410	+	3.21140i	0.0684362	+	0.118535i
$735$	3.42705	+	5.93583i	0.126409	+	0.218946i
$736$	−48.5410			−1.78925
$737$	11.7812	+	20.4056i	0.433964	+	0.751648i
$738$	−3.85410	+	6.67550i	−0.141871	+	0.245729i
$739$	3.43769	−	5.95426i	0.126458	−	0.219031i	−0.795844	−	0.605502i	$-0.792973\pi$
$739$	3.43769	−	5.95426i	0.126458	−	0.219031i	0.922302	+	0.386470i	$0.126306\pi$
$740$	50.8328			1.86865
$741$	−12.1353	+	12.6113i	−0.445800	+	0.463289i
$742$	9.85410			0.361755
$743$	−19.6631	+	34.0575i	−0.721370	+	1.24945i	0.239081	+	0.971000i	$0.423154\pi$
$743$	−19.6631	+	34.0575i	−0.721370	+	1.24945i	−0.960451	+	0.278450i	$0.910179\pi$
$744$	−46.0517	+	79.7638i	−1.68834	+	2.92428i
$745$	−2.42705	−	4.20378i	−0.0889203	−	0.154014i
$746$	−53.8328			−1.97096
$747$	−12.9271	−	22.3903i	−0.472976	−	0.819219i
$748$	6.62461	+	11.4742i	0.242220	+	0.419537i
$749$	−3.38197			−0.123574
$750$	−28.2254	−	48.8879i	−1.03065	−	1.78513i
$751$	−11.3541	+	19.6659i	−0.414317	+	0.717618i	−0.995356	−	0.0962572i	$-0.969313\pi$
$751$	−11.3541	+	19.6659i	−0.414317	+	0.717618i	0.581039	+	0.813875i	$0.302646\pi$
$752$	11.0172	−	19.0824i	0.401757	−	0.695863i
$753$	−2.00000			−0.0728841
$754$	64.9681	+	16.0754i	2.36600	+	0.585433i
$755$	−3.38197			−0.123082
$756$	5.42705	−	9.39993i	0.197380	−	0.341872i
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	0.491109	+	0.871098i	$0.336592\pi$
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	−0.999948	+	0.0102362i	$0.996742\pi$
$758$	8.04508	+	13.9345i	0.292211	+	0.506124i
$759$	21.7082			0.787958
$760$	18.1353	+	31.4112i	0.657835	+	1.13940i
$761$	14.4271	+	24.9884i	0.522980	+	0.905828i	0.999642	+	0.0267417i	$0.00851317\pi$
$761$	14.4271	+	24.9884i	0.522980	+	0.905828i	−0.476662	+	0.879087i	$0.658154\pi$
$762$	142.936			5.17803
$763$	1.35410	+	2.34537i	0.0490218	+	0.0849082i
$764$	−51.8951	+	89.8850i	−1.87750	+	3.25192i
$765$	7.42705	−	12.8640i	0.268526	−	0.465100i
$766$	−57.5410			−2.07904
$767$	−7.82624	−	1.93649i	−0.282589	−	0.0699227i
$768$	38.1246			1.37570
$769$	9.20820	−	15.9491i	0.332056	−	0.575138i	−0.650859	−	0.759199i	$-0.725591\pi$
$769$	9.20820	−	15.9491i	0.332056	−	0.575138i	0.982915	+	0.184061i	$0.0589243\pi$
$770$	−6.35410	+	11.0056i	−0.228986	+	0.396615i
$771$	21.9164	+	37.9603i	0.789300	+	1.36711i

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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 + 2.26728i) q^{2} +(1.30902 - 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} +2.61803 q^{5} +(3.42705 + 5.93583i) q^{6} +(-0.500000 - 0.866025i) q^{7} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\)	\(q+(-1.30902 + 2.26728i) q^{2} +(1.30902 - 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} +2.61803 q^{5} +(3.42705 + 5.93583i) q^{6} +(-0.500000 - 0.866025i) q^{7} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(-3.42705 + 5.93583i) q^{10} +(-0.927051 + 1.60570i) q^{11} -12.7082 q^{12} +(-2.50000 + 2.59808i) q^{13} +2.61803 q^{14} +(3.42705 - 5.93583i) q^{15} +(-4.92705 + 8.53390i) q^{16} +(0.736068 + 1.27491i) q^{17} +10.0902 q^{18} +(0.927051 + 1.60570i) q^{19} +(-6.35410 - 11.0056i) q^{20} -2.61803 q^{21} +(-2.42705 - 4.20378i) q^{22} +(2.23607 - 3.87298i) q^{23} +(9.78115 - 16.9415i) q^{24} +1.85410 q^{25} +(-2.61803 - 9.06914i) q^{26} -2.23607 q^{27} +(-2.42705 + 4.20378i) q^{28} +(-3.54508 + 6.14027i) q^{29} +(8.97214 + 15.5402i) q^{30} -4.70820 q^{31} +(-5.42705 - 9.39993i) q^{32} +(2.42705 + 4.20378i) q^{33} -3.85410 q^{34} +(-1.30902 - 2.26728i) q^{35} +(-9.35410 + 16.2018i) q^{36} +(-2.00000 + 3.46410i) q^{37} -4.85410 q^{38} +(2.61803 + 9.06914i) q^{39} +19.5623 q^{40} +(-0.381966 + 0.661585i) q^{41} +(3.42705 - 5.93583i) q^{42} +(-6.28115 - 10.8793i) q^{43} +9.00000 q^{44} +(-5.04508 - 8.73834i) q^{45} +(5.85410 + 10.1396i) q^{46} -2.23607 q^{47} +(12.8992 + 22.3420i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.42705 + 4.20378i) q^{50} +3.85410 q^{51} +(16.9894 + 4.20378i) q^{52} +3.76393 q^{53} +(2.92705 - 5.06980i) q^{54} +(-2.42705 + 4.20378i) q^{55} +(-3.73607 - 6.47106i) q^{56} +4.85410 q^{57} +(-9.28115 - 16.0754i) q^{58} +(1.11803 + 1.93649i) q^{59} -33.2705 q^{60} +(3.00000 + 5.19615i) q^{61} +(6.16312 - 10.6748i) q^{62} +(-1.92705 + 3.33775i) q^{63} +8.70820 q^{64} +(-6.54508 + 6.80185i) q^{65} -12.7082 q^{66} +(6.35410 - 11.0056i) q^{67} +(3.57295 - 6.18853i) q^{68} +(-5.85410 - 10.1396i) q^{69} +6.85410 q^{70} +(7.09017 + 12.2805i) q^{71} +(-14.3992 - 24.9401i) q^{72} -2.00000 q^{73} +(-5.23607 - 9.06914i) q^{74} +(2.42705 - 4.20378i) q^{75} +(4.50000 - 7.79423i) q^{76} +1.85410 q^{77} +(-23.9894 - 5.93583i) q^{78} +4.00000 q^{79} +(-12.8992 + 22.3420i) q^{80} +(2.85410 - 4.94345i) q^{81} +(-1.00000 - 1.73205i) q^{82} +6.70820 q^{83} +(6.35410 + 11.0056i) q^{84} +(1.92705 + 3.33775i) q^{85} +32.8885 q^{86} +(9.28115 + 16.0754i) q^{87} +(-6.92705 + 11.9980i) q^{88} +(-2.45492 + 4.25204i) q^{89} +26.4164 q^{90} +(3.50000 + 0.866025i) q^{91} -21.7082 q^{92} +(-6.16312 + 10.6748i) q^{93} +(2.92705 - 5.06980i) q^{94} +(2.42705 + 4.20378i) q^{95} -28.4164 q^{96} +(-9.42705 - 16.3281i) q^{97} +(-1.30902 - 2.26728i) q^{98} +7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 6 q^{5} + 7 q^{6} - 2 q^{7} + 12 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 6 * q^5 + 7 * q^6 - 2 * q^7 + 12 * q^8 - q^9	\( 4 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 6 q^{5} + 7 q^{6} - 2 q^{7} + 12 q^{8} - q^{9} - 7 q^{10} + 3 q^{11} - 24 q^{12} - 10 q^{13} + 6 q^{14} + 7 q^{15} - 13 q^{16} - 6 q^{17} + 18 q^{18} - 3 q^{19} - 12 q^{20} - 6 q^{21} - 3 q^{22} + 19 q^{24} - 6 q^{25} - 6 q^{26} - 3 q^{28} - 3 q^{29} + 18 q^{30} + 8 q^{31} - 15 q^{32} + 3 q^{33} - 2 q^{34} - 3 q^{35} - 24 q^{36} - 8 q^{37} - 6 q^{38} + 6 q^{39} + 38 q^{40} - 6 q^{41} + 7 q^{42} - 5 q^{43} + 36 q^{44} - 9 q^{45} + 10 q^{46} + 27 q^{48} - 2 q^{49} - 3 q^{50} + 2 q^{51} + 21 q^{52} + 24 q^{53} + 5 q^{54} - 3 q^{55} - 6 q^{56} + 6 q^{57} - 17 q^{58} - 66 q^{60} + 12 q^{61} + 9 q^{62} - q^{63} + 8 q^{64} - 15 q^{65} - 24 q^{66} + 12 q^{67} + 21 q^{68} - 10 q^{69} + 14 q^{70} + 6 q^{71} - 33 q^{72} - 8 q^{73} - 12 q^{74} + 3 q^{75} + 18 q^{76} - 6 q^{77} - 49 q^{78} + 16 q^{79} - 27 q^{80} - 2 q^{81} - 4 q^{82} + 12 q^{84} + q^{85} + 60 q^{86} + 17 q^{87} - 21 q^{88} - 21 q^{89} + 52 q^{90} + 14 q^{91} - 60 q^{92} - 9 q^{93} + 5 q^{94} + 3 q^{95} - 60 q^{96} - 31 q^{97} - 3 q^{98} + 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 6 * q^5 + 7 * q^6 - 2 * q^7 + 12 * q^8 - q^9 - 7 * q^10 + 3 * q^11 - 24 * q^12 - 10 * q^13 + 6 * q^14 + 7 * q^15 - 13 * q^16 - 6 * q^17 + 18 * q^18 - 3 * q^19 - 12 * q^20 - 6 * q^21 - 3 * q^22 + 19 * q^24 - 6 * q^25 - 6 * q^26 - 3 * q^28 - 3 * q^29 + 18 * q^30 + 8 * q^31 - 15 * q^32 + 3 * q^33 - 2 * q^34 - 3 * q^35 - 24 * q^36 - 8 * q^37 - 6 * q^38 + 6 * q^39 + 38 * q^40 - 6 * q^41 + 7 * q^42 - 5 * q^43 + 36 * q^44 - 9 * q^45 + 10 * q^46 + 27 * q^48 - 2 * q^49 - 3 * q^50 + 2 * q^51 + 21 * q^52 + 24 * q^53 + 5 * q^54 - 3 * q^55 - 6 * q^56 + 6 * q^57 - 17 * q^58 - 66 * q^60 + 12 * q^61 + 9 * q^62 - q^63 + 8 * q^64 - 15 * q^65 - 24 * q^66 + 12 * q^67 + 21 * q^68 - 10 * q^69 + 14 * q^70 + 6 * q^71 - 33 * q^72 - 8 * q^73 - 12 * q^74 + 3 * q^75 + 18 * q^76 - 6 * q^77 - 49 * q^78 + 16 * q^79 - 27 * q^80 - 2 * q^81 - 4 * q^82 + 12 * q^84 + q^85 + 60 * q^86 + 17 * q^87 - 21 * q^88 - 21 * q^89 + 52 * q^90 + 14 * q^91 - 60 * q^92 - 9 * q^93 + 5 * q^94 + 3 * q^95 - 60 * q^96 - 31 * q^97 - 3 * q^98 + 42 * q^99

Introduction

L-functions

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