LMFDB - Embedded newform 91.2.e.b.53.2

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:	$4$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			53.2
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	91.53
Dual form			91.2.e.b.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 + 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(-1.11803 - 1.93649i) q^{5} +5.85410 q^{6} +(-2.00000 + 1.73205i) q^{7} -7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(1.30902 + 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(-1.11803 - 1.93649i) q^{5} +5.85410 q^{6} +(-2.00000 + 1.73205i) q^{7} -7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(2.92705 - 5.06980i) q^{10} +(1.50000 - 2.59808i) q^{11} +(5.42705 + 9.39993i) q^{12} -1.00000 q^{13} +(-6.54508 - 2.26728i) q^{14} -5.00000 q^{15} +(-4.92705 - 8.53390i) q^{16} +(-0.736068 + 1.27491i) q^{17} +(2.61803 - 4.53457i) q^{18} +(-1.50000 - 2.59808i) q^{19} +10.8541 q^{20} +(1.11803 + 5.80948i) q^{21} +7.85410 q^{22} +(4.11803 + 7.13264i) q^{23} +(-8.35410 + 14.4697i) q^{24} +(-1.30902 - 2.26728i) q^{26} +2.23607 q^{27} +(-2.42705 - 12.6113i) q^{28} +4.47214 q^{29} +(-6.54508 - 11.3364i) q^{30} +(-2.50000 + 4.33013i) q^{31} +(5.42705 - 9.39993i) q^{32} +(-3.35410 - 5.80948i) q^{33} -3.85410 q^{34} +(5.59017 + 1.93649i) q^{35} +9.70820 q^{36} +(-2.35410 - 4.07742i) q^{37} +(3.92705 - 6.80185i) q^{38} +(-1.11803 + 1.93649i) q^{39} +(8.35410 + 14.4697i) q^{40} -4.47214 q^{41} +(-11.7082 + 10.1396i) q^{42} -8.00000 q^{43} +(7.28115 + 12.6113i) q^{44} +(-2.23607 + 3.87298i) q^{45} +(-10.7812 + 18.6735i) q^{46} +(3.73607 + 6.47106i) q^{47} -22.0344 q^{48} +(1.00000 - 6.92820i) q^{49} +(1.64590 + 2.85078i) q^{51} +(2.42705 - 4.20378i) q^{52} +(3.73607 - 6.47106i) q^{53} +(2.92705 + 5.06980i) q^{54} -6.70820 q^{55} +(14.9443 - 12.9421i) q^{56} -6.70820 q^{57} +(5.85410 + 10.1396i) q^{58} +(0.736068 - 1.27491i) q^{59} +(12.1353 - 21.0189i) q^{60} +(-1.50000 - 2.59808i) q^{61} -13.0902 q^{62} +(5.00000 + 1.73205i) q^{63} +8.70820 q^{64} +(1.11803 + 1.93649i) q^{65} +(8.78115 - 15.2094i) q^{66} +(1.50000 - 2.59808i) q^{67} +(-3.57295 - 6.18853i) q^{68} +18.4164 q^{69} +(2.92705 + 15.2094i) q^{70} -8.94427 q^{71} +(7.47214 + 12.9421i) q^{72} +(1.35410 - 2.34537i) q^{73} +(6.16312 - 10.6748i) q^{74} +14.5623 q^{76} +(1.50000 + 7.79423i) q^{77} -5.85410 q^{78} +(1.35410 + 2.34537i) q^{79} +(-11.0172 + 19.0824i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-5.85410 - 10.1396i) q^{82} +(-27.1353 - 9.39993i) q^{84} +3.29180 q^{85} +(-10.4721 - 18.1383i) q^{86} +(5.00000 - 8.66025i) q^{87} +(-11.2082 + 19.4132i) q^{88} +(-1.11803 - 1.93649i) q^{89} -11.7082 q^{90} +(2.00000 - 1.73205i) q^{91} -39.9787 q^{92} +(5.59017 + 9.68246i) q^{93} +(-9.78115 + 16.9415i) q^{94} +(-3.35410 + 5.80948i) q^{95} +(-12.1353 - 21.0189i) q^{96} +9.41641 q^{97} +(17.0172 - 6.80185i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 3 * q^4 + 10 * q^6 - 8 * q^7 - 12 * q^8 - 4 * q^9	$ 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9} + 5 q^{10} + 6 q^{11} + 15 q^{12} - 4 q^{13} - 15 q^{14} - 20 q^{15} - 13 q^{16} + 6 q^{17} + 6 q^{18} - 6 q^{19} + 30 q^{20} + 18 q^{22} + 12 q^{23} - 20 q^{24} - 3 q^{26} - 3 q^{28} - 15 q^{30} - 10 q^{31} + 15 q^{32} - 2 q^{34} + 12 q^{36} + 4 q^{37} + 9 q^{38} + 20 q^{40} - 20 q^{42} - 32 q^{43} + 9 q^{44} - 23 q^{46} + 6 q^{47} - 30 q^{48} + 4 q^{49} + 20 q^{51} + 3 q^{52} + 6 q^{53} + 5 q^{54} + 24 q^{56} + 10 q^{58} - 6 q^{59} + 15 q^{60} - 6 q^{61} - 30 q^{62} + 20 q^{63} + 8 q^{64} + 15 q^{66} + 6 q^{67} - 21 q^{68} + 20 q^{69} + 5 q^{70} + 12 q^{72} - 8 q^{73} + 9 q^{74} + 18 q^{76} + 6 q^{77} - 10 q^{78} - 8 q^{79} - 15 q^{80} + 22 q^{81} - 10 q^{82} - 75 q^{84} + 40 q^{85} - 24 q^{86} + 20 q^{87} - 18 q^{88} - 20 q^{90} + 8 q^{91} - 66 q^{92} - 19 q^{94} - 15 q^{96} - 16 q^{97} + 39 q^{98} - 24 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - 3 * q^4 + 10 * q^6 - 8 * q^7 - 12 * q^8 - 4 * q^9 + 5 * q^10 + 6 * q^11 + 15 * q^12 - 4 * q^13 - 15 * q^14 - 20 * q^15 - 13 * q^16 + 6 * q^17 + 6 * q^18 - 6 * q^19 + 30 * q^20 + 18 * q^22 + 12 * q^23 - 20 * q^24 - 3 * q^26 - 3 * q^28 - 15 * q^30 - 10 * q^31 + 15 * q^32 - 2 * q^34 + 12 * q^36 + 4 * q^37 + 9 * q^38 + 20 * q^40 - 20 * q^42 - 32 * q^43 + 9 * q^44 - 23 * q^46 + 6 * q^47 - 30 * q^48 + 4 * q^49 + 20 * q^51 + 3 * q^52 + 6 * q^53 + 5 * q^54 + 24 * q^56 + 10 * q^58 - 6 * q^59 + 15 * q^60 - 6 * q^61 - 30 * q^62 + 20 * q^63 + 8 * q^64 + 15 * q^66 + 6 * q^67 - 21 * q^68 + 20 * q^69 + 5 * q^70 + 12 * q^72 - 8 * q^73 + 9 * q^74 + 18 * q^76 + 6 * q^77 - 10 * q^78 - 8 * q^79 - 15 * q^80 + 22 * q^81 - 10 * q^82 - 75 * q^84 + 40 * q^85 - 24 * q^86 + 20 * q^87 - 18 * q^88 - 20 * q^90 + 8 * q^91 - 66 * q^92 - 19 * q^94 - 15 * q^96 - 16 * q^97 + 39 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.30902	+	2.26728i	0.925615	+	1.60321i	0.790569	+	0.612372i	$0.209785\pi$
$2$	1.30902	+	2.26728i	0.925615	+	1.60321i	0.135045	+	0.990839i	$0.456882\pi$
$3$	1.11803	−	1.93649i	0.645497	−	1.11803i	−0.338689	−	0.940898i	$-0.609984\pi$
$3$	1.11803	−	1.93649i	0.645497	−	1.11803i	0.984186	−	0.177136i	$-0.0566831\pi$
$4$	−2.42705	+	4.20378i	−1.21353	+	2.10189i
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i	−1.00000			$\pi$
$6$	5.85410			2.38993
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	−7.47214			−2.64180
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$	2.92705	−	5.06980i	0.925615	−	1.60321i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	5.42705	+	9.39993i	1.56665	+	2.71353i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−6.54508	−	2.26728i	−1.74925	−	0.605957i
$15$	−5.00000			−1.29099
$16$	−4.92705	−	8.53390i	−1.23176	−	2.13348i
$17$	−0.736068	+	1.27491i	−0.178523	+	0.309210i	−0.941375	−	0.337363i	$-0.890465\pi$
$17$	−0.736068	+	1.27491i	−0.178523	+	0.309210i	0.762852	+	0.646573i	$0.223798\pi$
$18$	2.61803	−	4.53457i	0.617077	−	1.06881i
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$	10.8541			2.42705
$21$	1.11803	+	5.80948i	0.243975	+	1.26773i
$22$	7.85410			1.67450
$23$	4.11803	+	7.13264i	0.858669	+	1.48726i	0.873199	+	0.487365i	$0.162042\pi$
$23$	4.11803	+	7.13264i	0.858669	+	1.48726i	−0.0145291	+	0.999894i	$0.504625\pi$
$24$	−8.35410	+	14.4697i	−1.70527	+	2.95362i
$25$		0			0
$26$	−1.30902	−	2.26728i	−0.256719	−	0.444651i
$27$	2.23607			0.430331
$28$	−2.42705	−	12.6113i	−0.458670	−	2.38332i
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$	−6.54508	−	11.3364i	−1.19496	−	2.06974i
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	5.42705	−	9.39993i	0.959376	−	1.66169i
$33$	−3.35410	−	5.80948i	−0.583874	−	1.01130i
$34$	−3.85410			−0.660973
$35$	5.59017	+	1.93649i	0.944911	+	0.327327i
$36$	9.70820			1.61803
$37$	−2.35410	−	4.07742i	−0.387012	−	0.670324i	0.605034	−	0.796200i	$-0.293159\pi$
$37$	−2.35410	−	4.07742i	−0.387012	−	0.670324i	−0.992046	+	0.125875i	$0.959826\pi$
$38$	3.92705	−	6.80185i	0.637052	−	1.10341i
$39$	−1.11803	+	1.93649i	−0.179029	+	0.310087i
$40$	8.35410	+	14.4697i	1.32090	+	2.28787i
$41$	−4.47214			−0.698430			−0.349215	−	0.937043i	$-0.613552\pi$
$41$	−4.47214			−0.698430			−0.349215	+	0.937043i	$0.613552\pi$
$42$	−11.7082	+	10.1396i	−1.80662	+	1.56457i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	7.28115	+	12.6113i	1.09768	+	1.90123i
$45$	−2.23607	+	3.87298i	−0.333333	+	0.577350i
$46$	−10.7812	+	18.6735i	−1.58959	+	2.75326i
$47$	3.73607	+	6.47106i	0.544962	+	0.943901i	0.998609	+	0.0527200i	$0.0167891\pi$
$47$	3.73607	+	6.47106i	0.544962	+	0.943901i	−0.453648	+	0.891181i	$0.649878\pi$
$48$	−22.0344			−3.18040
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	1.64590	+	2.85078i	0.230472	+	0.399189i
$52$	2.42705	−	4.20378i	0.336571	−	0.582959i
$53$	3.73607	−	6.47106i	0.513188	−	0.888868i	−0.486695	−	0.873572i	$-0.661798\pi$
$53$	3.73607	−	6.47106i	0.513188	−	0.888868i	0.999883	−	0.0152962i	$-0.00486912\pi$
$54$	2.92705	+	5.06980i	0.398321	+	0.689913i
$55$	−6.70820			−0.904534
$56$	14.9443	−	12.9421i	1.99701	−	1.72946i
$57$	−6.70820			−0.888523
$58$	5.85410	+	10.1396i	0.768681	+	1.33139i
$59$	0.736068	−	1.27491i	0.0958279	−	0.165979i	−0.814126	−	0.580688i	$-0.802783\pi$
$59$	0.736068	−	1.27491i	0.0958279	−	0.165979i	0.909954	+	0.414710i	$0.136117\pi$
$60$	12.1353	−	21.0189i	1.56665	−	2.71353i
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	0.753876	−	0.657017i	$-0.228182\pi$
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	−0.945931	+	0.324367i	$0.894849\pi$
$62$	−13.0902			−1.66245
$63$	5.00000	+	1.73205i	0.629941	+	0.218218i
$64$	8.70820			1.08853
$65$	1.11803	+	1.93649i	0.138675	+	0.240192i
$66$	8.78115	−	15.2094i	1.08089	−	1.87215i
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	−3.57295	−	6.18853i	−0.433284	−	0.750469i
$69$	18.4164			2.21707
$70$	2.92705	+	15.2094i	0.349850	+	1.81787i
$71$	−8.94427			−1.06149			−0.530745	−	0.847532i	$-0.678088\pi$
$71$	−8.94427			−1.06149			−0.530745	+	0.847532i	$0.678088\pi$
$72$	7.47214	+	12.9421i	0.880600	+	1.52524i
$73$	1.35410	−	2.34537i	0.158486	−	0.274505i	−0.775837	−	0.630933i	$-0.782672\pi$
$73$	1.35410	−	2.34537i	0.158486	−	0.274505i	0.934323	+	0.356428i	$0.116006\pi$
$74$	6.16312	−	10.6748i	0.716448	−	1.24092i
$75$		0			0
$76$	14.5623			1.67041
$77$	1.50000	+	7.79423i	0.170941	+	0.888235i
$78$	−5.85410			−0.662847
$79$	1.35410	+	2.34537i	0.152348	+	0.263875i	0.932090	−	0.362226i	$-0.117983\pi$
$79$	1.35410	+	2.34537i	0.152348	+	0.263875i	−0.779742	+	0.626101i	$0.784650\pi$
$80$	−11.0172	+	19.0824i	−1.23176	+	2.13348i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−5.85410	−	10.1396i	−0.646477	−	1.11973i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−27.1353	−	9.39993i	−2.96070	−	1.02562i
$85$	3.29180			0.357045
$86$	−10.4721	−	18.1383i	−1.12924	−	1.95590i
$87$	5.00000	−	8.66025i	0.536056	−	0.928477i
$88$	−11.2082	+	19.4132i	−1.19480	+	2.06945i
$89$	−1.11803	−	1.93649i	−0.118511	−	0.205268i	0.800667	−	0.599110i	$-0.204479\pi$
$89$	−1.11803	−	1.93649i	−0.118511	−	0.205268i	−0.919178	+	0.393842i	$0.871146\pi$
$90$	−11.7082			−1.23415
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	−39.9787			−4.16807
$93$	5.59017	+	9.68246i	0.579674	+	1.00402i
$94$	−9.78115	+	16.9415i	−1.00885	+	1.74738i
$95$	−3.35410	+	5.80948i	−0.344124	+	0.596040i
$96$	−12.1353	−	21.0189i	−1.23855	−	2.14523i
$97$	9.41641			0.956091			0.478046	−	0.878335i	$-0.341345\pi$
$97$	9.41641			0.956091			0.478046	+	0.878335i	$0.341345\pi$
$98$	17.0172	−	6.80185i	1.71900	−	0.687091i
$99$	−6.00000			−0.603023
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	−4.30902	+	7.46344i	−0.426656	+	0.738990i
$103$	1.35410	+	2.34537i	0.133424	+	0.231097i	0.924994	−	0.379981i	$-0.124070\pi$
$103$	1.35410	+	2.34537i	0.133424	+	0.231097i	−0.791571	+	0.611078i	$0.790736\pi$
$104$	7.47214			0.732703
$105$	10.0000	−	8.66025i	0.975900	−	0.845154i
$106$	19.5623			1.90006
$107$	4.88197	+	8.45581i	0.471957	+	0.817454i	0.999485	−	0.0320835i	$-0.0102142\pi$
$107$	4.88197	+	8.45581i	0.471957	+	0.817454i	−0.527528	+	0.849538i	$0.676881\pi$
$108$	−5.42705	+	9.39993i	−0.522218	+	0.904508i
$109$	1.35410	−	2.34537i	0.129699	−	0.224646i	−0.793861	−	0.608100i	$-0.791932\pi$
$109$	1.35410	−	2.34537i	0.129699	−	0.224646i	0.923560	+	0.383454i	$0.125265\pi$
$110$	−8.78115	−	15.2094i	−0.837250	−	1.45016i
$111$	−10.5279			−0.999261
$112$	24.6353	+	8.53390i	2.32781	+	0.806378i
$113$	2.94427			0.276974			0.138487	−	0.990364i	$-0.455776\pi$
$113$	2.94427			0.276974			0.138487	+	0.990364i	$0.455776\pi$
$114$	−8.78115	−	15.2094i	−0.822430	−	1.42449i
$115$	9.20820	−	15.9491i	0.858669	−	1.48726i
$116$	−10.8541	+	18.7999i	−1.00778	+	1.74552i
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$	3.85410			0.354799
$119$	−0.736068	−	3.82472i	−0.0674752	−	0.350612i
$120$	37.3607			3.41055
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	3.92705	−	6.80185i	0.355538	−	0.615811i
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$	−12.1353	−	21.0189i	−1.08978	−	1.88755i
$125$	−11.1803			−1.00000
$126$	2.61803	+	13.6037i	0.233233	+	1.21191i
$127$	−11.4164			−1.01304			−0.506521	−	0.862228i	$-0.669069\pi$
$127$	−11.4164			−1.01304			−0.506521	+	0.862228i	$0.669069\pi$
$128$	0.545085	+	0.944115i	0.0481792	+	0.0834488i
$129$	−8.94427	+	15.4919i	−0.787499	+	1.36399i
$130$	−2.92705	+	5.06980i	−0.256719	+	0.444651i
$131$	4.11803	+	7.13264i	0.359794	+	0.623182i	0.987926	−	0.154925i	$-0.0495135\pi$
$131$	4.11803	+	7.13264i	0.359794	+	0.623182i	−0.628132	+	0.778107i	$0.716180\pi$
$132$	32.5623			2.83418
$133$	7.50000	+	2.59808i	0.650332	+	0.225282i
$134$	7.85410			0.678491
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$	5.50000	−	9.52628i	0.471621	−	0.816872i
$137$	4.11803	−	7.13264i	0.351827	−	0.609383i	−0.634742	−	0.772724i	$-0.718894\pi$
$137$	4.11803	−	7.13264i	0.351827	−	0.609383i	0.986570	+	0.163341i	$0.0522271\pi$
$138$	24.1074	+	41.7552i	2.05216	+	3.55444i
$139$	−23.4164			−1.98615			−0.993077	−	0.117466i	$-0.962523\pi$
$139$	−23.4164			−1.98615			−0.993077	+	0.117466i	$0.962523\pi$
$140$	−21.7082	+	18.7999i	−1.83468	+	1.58888i
$141$	16.7082			1.40708
$142$	−11.7082	−	20.2792i	−0.982531	−	1.70179i
$143$	−1.50000	+	2.59808i	−0.125436	+	0.217262i
$144$	−9.85410	+	17.0678i	−0.821175	+	1.42232i
$145$	−5.00000	−	8.66025i	−0.415227	−	0.719195i
$146$	7.09017			0.586787
$147$	−12.2984	−	9.68246i	−1.01435	−	0.798596i
$148$	22.8541			1.87860
$149$	−0.354102	−	0.613323i	−0.0290092	−	0.0502453i	0.851156	−	0.524912i	$-0.175902\pi$
$149$	−0.354102	−	0.613323i	−0.0290092	−	0.0502453i	−0.880166	+	0.474667i	$0.842569\pi$
$150$		0			0
$151$	−10.2082	+	17.6811i	−0.830732	+	1.43887i	0.0667268	+	0.997771i	$0.478744\pi$
$151$	−10.2082	+	17.6811i	−0.830732	+	1.43887i	−0.897459	+	0.441098i	$0.854589\pi$
$152$	11.2082	+	19.4132i	0.909105	+	1.57462i
$153$	2.94427			0.238030
$154$	−15.7082	+	13.6037i	−1.26580	+	1.09622i
$155$	11.1803			0.898027
$156$	−5.42705	−	9.39993i	−0.434512	−	0.752597i
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	−3.54508	+	6.14027i	−0.282032	+	0.488493i
$159$	−8.35410	−	14.4697i	−0.662523	−	1.14752i
$160$	−24.2705			−1.91875
$161$	−20.5902	−	7.13264i	−1.62273	−	0.562131i
$162$	28.7984			2.26261
$163$	8.20820	+	14.2170i	0.642916	+	1.11356i	0.984779	+	0.173813i	$0.0556090\pi$
$163$	8.20820	+	14.2170i	0.642916	+	1.11356i	−0.341862	+	0.939750i	$0.611058\pi$
$164$	10.8541	−	18.7999i	0.847563	−	1.46802i
$165$	−7.50000	+	12.9904i	−0.583874	+	1.01130i
$166$		0			0
$167$	22.4721			1.73895			0.869473	−	0.493980i	$-0.164459\pi$
$167$	22.4721			1.73895			0.869473	+	0.493980i	$0.164459\pi$
$168$	−8.35410	−	43.4092i	−0.644533	−	3.34909i
$169$	1.00000			0.0769231
$170$	4.30902	+	7.46344i	0.330487	+	0.572419i
$171$	−3.00000	+	5.19615i	−0.229416	+	0.397360i
$172$	19.4164	−	33.6302i	1.48049	−	2.56428i
$173$	8.20820	+	14.2170i	0.624058	+	1.08090i	0.988722	+	0.149761i	$0.0478505\pi$
$173$	8.20820	+	14.2170i	0.624058	+	1.08090i	−0.364664	+	0.931139i	$0.618816\pi$
$174$	26.1803			1.98473
$175$		0			0
$176$	−29.5623			−2.22834
$177$	−1.64590	−	2.85078i	−0.123713	−	0.214278i
$178$	2.92705	−	5.06980i	0.219392	−	0.379998i
$179$	10.0623	−	17.4284i	0.752092	−	1.30266i	−0.194715	−	0.980860i	$-0.562378\pi$
$179$	10.0623	−	17.4284i	0.752092	−	1.30266i	0.946807	−	0.321802i	$-0.104288\pi$
$180$	−10.8541	−	18.7999i	−0.809017	−	1.40126i
$181$	−25.4164			−1.88919			−0.944593	−	0.328243i	$-0.893544\pi$
$181$	−25.4164			−1.88919			−0.944593	+	0.328243i	$0.893544\pi$
$182$	6.54508	+	2.26728i	0.485154	+	0.168062i
$183$	−6.70820			−0.495885
$184$	−30.7705	−	53.2961i	−2.26843	−	3.92904i
$185$	−5.26393	+	9.11740i	−0.387012	+	0.670324i
$186$	−14.6353	+	25.3490i	−1.07311	+	1.85868i
$187$	2.20820	+	3.82472i	0.161480	+	0.279691i
$188$	−36.2705			−2.64530
$189$	−4.47214	+	3.87298i	−0.325300	+	0.281718i
$190$	−17.5623			−1.27410
$191$	−5.59017	−	9.68246i	−0.404491	−	0.700598i	0.589772	−	0.807570i	$-0.299218\pi$
$191$	−5.59017	−	9.68246i	−0.404491	−	0.700598i	−0.994262	+	0.106972i	$0.965884\pi$
$192$	9.73607	−	16.8634i	0.702640	−	1.21701i
$193$	−0.354102	+	0.613323i	−0.0254888	+	0.0441479i	−0.878488	−	0.477764i	$-0.841448\pi$
$193$	−0.354102	+	0.613323i	−0.0254888	+	0.0441479i	0.853000	+	0.521912i	$0.174781\pi$
$194$	12.3262	+	21.3497i	0.884972	+	1.53282i
$195$	5.00000			0.358057
$196$	26.6976	+	21.0189i	1.90697	+	1.50135i
$197$	−9.05573			−0.645194			−0.322597	−	0.946536i	$-0.604556\pi$
$197$	−9.05573			−0.645194			−0.322597	+	0.946536i	$0.604556\pi$
$198$	−7.85410	−	13.6037i	−0.558167	−	0.966773i
$199$	10.3541	−	17.9338i	0.733983	−	1.27130i	−0.221185	−	0.975232i	$-0.570993\pi$
$199$	10.3541	−	17.9338i	0.733983	−	1.27130i	0.955168	−	0.296064i	$-0.0956741\pi$
$200$		0			0
$201$	−3.35410	−	5.80948i	−0.236580	−	0.409769i
$202$	23.5623			1.65784
$203$	−8.94427	+	7.74597i	−0.627765	+	0.543660i
$204$	−15.9787			−1.11873
$205$	5.00000	+	8.66025i	0.349215	+	0.604858i
$206$	−3.54508	+	6.14027i	−0.246998	+	0.427813i
$207$	8.23607	−	14.2653i	0.572446	−	0.991506i
$208$	4.92705	+	8.53390i	0.341630	+	0.591720i
$209$	−9.00000			−0.622543
$210$	32.7254	+	11.3364i	2.25827	+	0.782287i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	18.1353	+	31.4112i	1.24553	+	2.15733i
$213$	−10.0000	+	17.3205i	−0.685189	+	1.18678i
$214$	−12.7812	+	22.1376i	−0.873702	+	1.51330i
$215$	8.94427	+	15.4919i	0.609994	+	1.05654i
$216$	−16.7082			−1.13685
$217$	−2.50000	−	12.9904i	−0.169711	−	0.881845i
$218$	7.09017			0.480207
$219$	−3.02786	−	5.24441i	−0.204604	−	0.354385i
$220$	16.2812	−	28.1998i	1.09768	−	1.90123i
$221$	0.736068	−	1.27491i	0.0495133	−	0.0857595i
$222$	−13.7812	−	23.8697i	−0.924930	−	1.60203i
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$	5.42705	+	28.1998i	0.362610	+	1.88418i
$225$		0			0
$226$	3.85410	+	6.67550i	0.256371	+	0.444048i
$227$	−2.97214	+	5.14789i	−0.197268	+	0.341677i	−0.947642	−	0.319336i	$-0.896540\pi$
$227$	−2.97214	+	5.14789i	−0.197268	+	0.341677i	0.750374	+	0.661014i	$0.229873\pi$
$228$	16.2812	−	28.1998i	1.07825	−	1.86758i
$229$	−12.0623	−	20.8925i	−0.797100	−	1.38062i	−0.921497	−	0.388385i	$-0.873033\pi$
$229$	−12.0623	−	20.8925i	−0.797100	−	1.38062i	0.124398	−	0.992232i	$-0.460300\pi$
$230$	48.2148			3.17919
$231$	16.7705	+	5.80948i	1.10342	+	0.382235i
$232$	−33.4164			−2.19389
$233$	−5.97214	−	10.3440i	−0.391248	−	0.677661i	0.601367	−	0.798973i	$-0.294623\pi$
$233$	−5.97214	−	10.3440i	−0.391248	−	0.677661i	−0.992614	+	0.121312i	$0.961290\pi$
$234$	−2.61803	+	4.53457i	−0.171146	+	0.296434i
$235$	8.35410	−	14.4697i	0.544962	−	0.943901i
$236$	3.57295	+	6.18853i	0.232579	+	0.402839i
$237$	6.05573			0.393362
$238$	7.70820	−	6.67550i	0.499649	−	0.432708i
$239$	19.4164			1.25594			0.627972	−	0.778236i	$-0.283885\pi$
$239$	19.4164			1.25594			0.627972	+	0.778236i	$0.283885\pi$
$240$	24.6353	+	42.6695i	1.59020	+	2.75431i
$241$	−2.35410	+	4.07742i	−0.151641	+	0.262650i	−0.931831	−	0.362893i	$-0.881789\pi$
$241$	−2.35410	+	4.07742i	−0.151641	+	0.262650i	0.780190	+	0.625543i	$0.215122\pi$
$242$	−2.61803	+	4.53457i	−0.168294	+	0.291493i
$243$	−8.94427	−	15.4919i	−0.573775	−	0.993808i
$244$	14.5623			0.932256
$245$	−14.5344	+	5.80948i	−0.928571	+	0.371154i
$246$	−26.1803			−1.66920
$247$	1.50000	+	2.59808i	0.0954427	+	0.165312i
$248$	18.6803	−	32.3553i	1.18620	−	2.05456i
$249$		0			0
$250$	−14.6353	−	25.3490i	−0.925615	−	1.60321i
$251$	1.52786			0.0964379			0.0482190	−	0.998837i	$-0.484645\pi$
$251$	1.52786			0.0964379			0.0482190	+	0.998837i	$0.484645\pi$
$252$	−19.4164	+	16.8151i	−1.22312	+	1.05925i
$253$	24.7082			1.55339
$254$	−14.9443	−	25.8842i	−0.937687	−	1.62412i
$255$	3.68034	−	6.37454i	0.230472	−	0.399189i
$256$	7.28115	−	12.6113i	0.455072	−	0.788208i
$257$	0.0278640	+	0.0482619i	0.00173811	+	0.00301050i	0.866893	−	0.498494i	$-0.166113\pi$
$257$	0.0278640	+	0.0482619i	0.00173811	+	0.00301050i	−0.865155	+	0.501504i	$0.832780\pi$
$258$	−46.8328			−2.91568
$259$	11.7705	+	4.07742i	0.731384	+	0.253359i
$260$	−10.8541			−0.673143
$261$	−4.47214	−	7.74597i	−0.276818	−	0.479463i
$262$	−10.7812	+	18.6735i	−0.666062	+	1.15365i
$263$	−13.0623	+	22.6246i	−0.805456	+	1.39509i	0.110526	+	0.993873i	$0.464746\pi$
$263$	−13.0623	+	22.6246i	−0.805456	+	1.39509i	−0.915983	+	0.401218i	$0.868587\pi$
$264$	25.0623	+	43.4092i	1.54248	+	2.67165i
$265$	−16.7082			−1.02638
$266$	3.92705	+	20.4056i	0.240783	+	1.25114i
$267$	−5.00000			−0.305995
$268$	7.28115	+	12.6113i	0.444767	+	0.770359i
$269$	−6.73607	+	11.6672i	−0.410705	+	0.711362i	−0.994967	−	0.100203i	$-0.968051\pi$
$269$	−6.73607	+	11.6672i	−0.410705	+	0.711362i	0.584262	+	0.811565i	$0.301384\pi$
$270$	6.54508	−	11.3364i	0.398321	−	0.689913i
$271$	10.2082	+	17.6811i	0.620104	+	1.07405i	0.989466	+	0.144766i	$0.0462430\pi$
$271$	10.2082	+	17.6811i	0.620104	+	1.07405i	−0.369362	+	0.929286i	$0.620424\pi$
$272$	14.5066			0.879590
$273$	−1.11803	−	5.80948i	−0.0676665	−	0.351605i
$274$	21.5623			1.30263
$275$		0			0
$276$	−44.6976	+	77.4184i	−2.69048	+	4.66004i
$277$	0.208204	−	0.360620i	0.0125098	−	0.0216675i	−0.859703	−	0.510795i	$-0.829351\pi$
$277$	0.208204	−	0.360620i	0.0125098	−	0.0216675i	0.872213	+	0.489127i	$0.162685\pi$
$278$	−30.6525	−	53.0916i	−1.83841	−	3.18423i
$279$	10.0000			0.598684
$280$	−41.7705	−	14.4697i	−2.49627	−	0.864732i
$281$	26.9443			1.60736			0.803680	−	0.595061i	$-0.202872\pi$
$281$	26.9443			1.60736			0.803680	+	0.595061i	$0.202872\pi$
$282$	21.8713	+	37.8822i	1.30242	+	2.25585i
$283$	−13.0623	+	22.6246i	−0.776473	+	1.34489i	0.157489	+	0.987521i	$0.449660\pi$
$283$	−13.0623	+	22.6246i	−0.776473	+	1.34489i	−0.933963	+	0.357371i	$0.883673\pi$
$284$	21.7082	−	37.5997i	1.28814	−	2.23113i
$285$	7.50000	+	12.9904i	0.444262	+	0.769484i
$286$	−7.85410			−0.464423
$287$	8.94427	−	7.74597i	0.527964	−	0.457230i
$288$	−21.7082			−1.27917
$289$	7.41641	+	12.8456i	0.436259	+	0.755623i
$290$	13.0902	−	22.6728i	0.768681	−	1.33139i
$291$	10.5279	−	18.2348i	0.617154	−	1.06894i
$292$	6.57295	+	11.3847i	0.384653	+	0.666238i
$293$	−14.9443			−0.873054			−0.436527	−	0.899691i	$-0.643792\pi$
$293$	−14.9443			−0.873054			−0.436527	+	0.899691i	$0.643792\pi$
$294$	5.85410	−	40.5584i	0.341418	−	2.36541i
$295$	−3.29180			−0.191656
$296$	17.5902	+	30.4671i	1.02241	+	1.77086i
$297$	3.35410	−	5.80948i	0.194625	−	0.337100i
$298$	0.927051	−	1.60570i	0.0537026	−	0.0930157i
$299$	−4.11803	−	7.13264i	−0.238152	−	0.412491i
$300$		0			0
$301$	16.0000	−	13.8564i	0.922225	−	0.798670i
$302$	−53.4508			−3.07575
$303$	−10.0623	−	17.4284i	−0.578064	−	1.00124i
$304$	−14.7812	+	25.6017i	−0.847757	+	1.46836i
$305$	−3.35410	+	5.80948i	−0.192055	+	0.332650i
$306$	3.85410	+	6.67550i	0.220324	+	0.381613i
$307$	19.4164			1.10815			0.554076	−	0.832466i	$-0.313072\pi$
$307$	19.4164			1.10815			0.554076	+	0.832466i	$0.313072\pi$
$308$	−36.4058	−	12.6113i	−2.07441	−	0.718597i
$309$	6.05573			0.344498
$310$	14.6353	+	25.3490i	0.831227	+	1.43973i
$311$	13.8820	−	24.0443i	0.787174	−	1.36343i	−0.140518	−	0.990078i	$-0.544877\pi$
$311$	13.8820	−	24.0443i	0.787174	−	1.36343i	0.927692	−	0.373347i	$-0.121790\pi$
$312$	8.35410	−	14.4697i	0.472958	−	0.819187i
$313$	2.79180	+	4.83553i	0.157802	+	0.273320i	0.934076	−	0.357075i	$-0.116226\pi$
$313$	2.79180	+	4.83553i	0.157802	+	0.273320i	−0.776274	+	0.630396i	$0.782893\pi$
$314$	−18.3262			−1.03421
$315$	−2.23607	−	11.6190i	−0.125988	−	0.654654i
$316$	−13.1459			−0.739515
$317$	4.11803	+	7.13264i	0.231292	+	0.400609i	0.958189	−	0.286138i	$-0.0923714\pi$
$317$	4.11803	+	7.13264i	0.231292	+	0.400609i	−0.726897	+	0.686747i	$0.759038\pi$
$318$	21.8713	−	37.8822i	1.22648	−	2.12433i
$319$	6.70820	−	11.6190i	0.375587	−	0.650536i
$320$	−9.73607	−	16.8634i	−0.544263	−	0.942691i
$321$	21.8328			1.21859
$322$	−10.7812	−	56.0205i	−0.600810	−	3.12190i
$323$	4.41641			0.245736
$324$	26.6976	+	46.2415i	1.48320	+	2.56897i
$325$		0			0
$326$	−21.4894	+	37.2207i	−1.19019	+	2.06146i
$327$	−3.02786	−	5.24441i	−0.167441	−	0.290017i
$328$	33.4164			1.84511
$329$	−18.6803	−	6.47106i	−1.02988	−	0.356761i
$330$	−39.2705			−2.16177
$331$	0.791796	+	1.37143i	0.0435210	+	0.0753807i	0.886965	−	0.461836i	$-0.152809\pi$
$331$	0.791796	+	1.37143i	0.0435210	+	0.0753807i	−0.843444	+	0.537217i	$0.819476\pi$
$332$		0			0
$333$	−4.70820	+	8.15485i	−0.258008	+	0.446883i
$334$	29.4164	+	50.9507i	1.60959	+	2.78790i
$335$	−6.70820			−0.366508
$336$	44.0689	−	38.1648i	2.40415	−	2.08206i
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	1.30902	+	2.26728i	0.0712011	+	0.123324i
$339$	3.29180	−	5.70156i	0.178786	−	0.309666i
$340$	−7.98936	+	13.8380i	−0.433284	+	0.750469i
$341$	7.50000	+	12.9904i	0.406148	+	0.703469i
$342$	−15.7082			−0.849402
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	59.7771			3.22296
$345$	−20.5902	−	35.6632i	−1.10854	−	1.92004i
$346$	−21.4894	+	37.2207i	−1.15527	+	2.00099i
$347$	−11.5344	+	19.9782i	−0.619201	+	1.07249i	0.370430	+	0.928860i	$0.379210\pi$
$347$	−11.5344	+	19.9782i	−0.619201	+	1.07249i	−0.989632	+	0.143628i	$0.954123\pi$
$348$	24.2705	+	42.0378i	1.30104	+	2.25346i
$349$	−29.4164			−1.57462			−0.787312	−	0.616555i	$-0.788528\pi$
$349$	−29.4164			−1.57462			−0.787312	+	0.616555i	$0.788528\pi$
$350$		0			0
$351$	−2.23607			−0.119352
$352$	−16.2812	−	28.1998i	−0.867788	−	1.50305i
$353$	−8.64590	+	14.9751i	−0.460175	+	0.797046i	−0.998969	−	0.0453912i	$-0.985547\pi$
$353$	−8.64590	+	14.9751i	−0.460175	+	0.797046i	0.538795	+	0.842437i	$0.318880\pi$
$354$	4.30902	−	7.46344i	0.229022	−	0.396677i
$355$	10.0000	+	17.3205i	0.530745	+	0.919277i
$356$	10.8541			0.575266
$357$	−8.22949	−	2.85078i	−0.435551	−	0.150879i
$358$	52.6869			2.78459
$359$	−5.97214	−	10.3440i	−0.315197	−	0.545938i	0.664282	−	0.747482i	$-0.268737\pi$
$359$	−5.97214	−	10.3440i	−0.315197	−	0.545938i	−0.979479	+	0.201544i	$0.935404\pi$
$360$	16.7082	−	28.9395i	0.880600	−	1.52524i
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	−33.2705	−	57.6262i	−1.74866	−	3.02877i
$363$	4.47214			0.234726
$364$	2.42705	+	12.6113i	0.127212	+	0.661013i
$365$	−6.05573			−0.316971
$366$	−8.78115	−	15.2094i	−0.458998	−	0.795008i
$367$	6.35410	−	11.0056i	0.331681	−	0.574489i	−0.651160	−	0.758940i	$-0.725717\pi$
$367$	6.35410	−	11.0056i	0.331681	−	0.574489i	0.982842	+	0.184451i	$0.0590508\pi$
$368$	40.5795	−	70.2858i	2.11535	−	3.66390i
$369$	4.47214	+	7.74597i	0.232810	+	0.403239i
$370$	−27.5623			−1.43290
$371$	3.73607	+	19.4132i	0.193967	+	1.00788i
$372$	−54.2705			−2.81379
$373$	0.791796	+	1.37143i	0.0409976	+	0.0710100i	0.885796	−	0.464075i	$-0.153613\pi$
$373$	0.791796	+	1.37143i	0.0409976	+	0.0710100i	−0.844798	+	0.535085i	$0.820280\pi$
$374$	−5.78115	+	10.0133i	−0.298936	+	0.517773i
$375$	−12.5000	+	21.6506i	−0.645497	+	1.11803i
$376$	−27.9164	−	48.3526i	−1.43968	−	2.49360i
$377$	−4.47214			−0.230327
$378$	−14.6353	−	5.06980i	−0.752756	−	0.260762i
$379$	−15.4164			−0.791888			−0.395944	−	0.918275i	$-0.629583\pi$
$379$	−15.4164			−0.791888			−0.395944	+	0.918275i	$0.629583\pi$
$380$	−16.2812	−	28.1998i	−0.835206	−	1.44662i
$381$	−12.7639	+	22.1078i	−0.653916	+	1.13262i
$382$	14.6353	−	25.3490i	0.748805	−	1.29697i
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	0.608290	−	0.793715i	$-0.291856\pi$
$383$	−7.50000	−	12.9904i	−0.383232	−	0.663777i	−0.991522	+	0.129937i	$0.958522\pi$
$384$	2.43769			0.124398
$385$	13.4164	−	11.6190i	0.683763	−	0.592157i
$386$	−1.85410			−0.0943713
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	−22.8541	+	39.5845i	−1.16024	+	2.00960i
$389$	−0.736068	+	1.27491i	−0.0373201	+	0.0646404i	−0.884082	−	0.467332i	$-0.845215\pi$
$389$	−0.736068	+	1.27491i	−0.0373201	+	0.0646404i	0.846762	+	0.531972i	$0.178549\pi$
$390$	6.54508	+	11.3364i	0.331423	+	0.574042i
$391$	−12.1246			−0.613168
$392$	−7.47214	+	51.7685i	−0.377400	+	2.61470i
$393$	18.4164			0.928985
$394$	−11.8541	−	20.5319i	−0.597201	−	1.03438i
$395$	3.02786	−	5.24441i	0.152348	−	0.263875i
$396$	14.5623	−	25.2227i	0.731783	−	1.26749i
$397$	13.0623	+	22.6246i	0.655578	+	1.13549i	0.981748	+	0.190184i	$0.0609084\pi$
$397$	13.0623	+	22.6246i	0.655578	+	1.13549i	−0.326170	+	0.945311i	$0.605758\pi$
$398$	54.2148			2.71754
$399$	13.4164	−	11.6190i	0.671660	−	0.581675i
$400$		0			0
$401$	−7.11803	−	12.3288i	−0.355458	−	0.615671i	0.631739	−	0.775182i	$-0.282342\pi$
$401$	−7.11803	−	12.3288i	−0.355458	−	0.615671i	−0.987196	+	0.159511i	$0.949008\pi$
$402$	8.78115	−	15.2094i	0.437964	−	0.758576i
$403$	2.50000	−	4.33013i	0.124534	−	0.215699i
$404$	21.8435	+	37.8340i	1.08675	+	1.88231i
$405$	−24.5967			−1.22222
$406$	−29.2705	−	10.1396i	−1.45267	−	0.503220i
$407$	−14.1246			−0.700131
$408$	−12.2984	−	21.3014i	−0.608860	−	1.05458i
$409$	−4.35410	+	7.54153i	−0.215296	+	0.372904i	−0.953364	−	0.301822i	$-0.902405\pi$
$409$	−4.35410	+	7.54153i	−0.215296	+	0.372904i	0.738068	+	0.674727i	$0.235738\pi$
$410$	−13.0902	+	22.6728i	−0.646477	+	1.11973i
$411$	−9.20820	−	15.9491i	−0.454207	−	0.786710i
$412$	−13.1459			−0.647652
$413$	0.736068	+	3.82472i	0.0362195	+	0.188202i
$414$	43.1246			2.11946
$415$		0			0
$416$	−5.42705	+	9.39993i	−0.266083	+	0.460869i
$417$	−26.1803	+	45.3457i	−1.28206	+	2.22059i
$418$	−11.7812	−	20.4056i	−0.576235	−	0.998068i
$419$	32.9443			1.60943			0.804717	−	0.593659i	$-0.202317\pi$
$419$	32.9443			1.60943			0.804717	+	0.593659i	$0.202317\pi$
$420$	12.1353	+	63.0566i	0.592140	+	3.07685i
$421$	13.4164			0.653876			0.326938	−	0.945046i	$-0.393983\pi$
$421$	13.4164			0.653876			0.326938	+	0.945046i	$0.393983\pi$
$422$	5.23607	+	9.06914i	0.254888	+	0.441479i
$423$	7.47214	−	12.9421i	0.363308	−	0.629267i
$424$	−27.9164	+	48.3526i	−1.35574	+	2.34821i
$425$		0			0
$426$	−52.3607			−2.53688
$427$	7.50000	+	2.59808i	0.362950	+	0.125730i
$428$	−47.3951			−2.29093
$429$	3.35410	+	5.80948i	0.161938	+	0.280484i
$430$	−23.4164	+	40.5584i	−1.12924	+	1.95590i
$431$	15.6803	−	27.1591i	0.755295	−	1.30821i	−0.189932	−	0.981797i	$-0.560827\pi$
$431$	15.6803	−	27.1591i	0.755295	−	1.30821i	0.945227	−	0.326413i	$-0.105840\pi$
$432$	−11.0172	−	19.0824i	−0.530066	−	0.918102i
$433$	29.4164			1.41366			0.706831	−	0.707382i	$-0.250124\pi$
$433$	29.4164			1.41366			0.706831	+	0.707382i	$0.250124\pi$
$434$	26.1803	−	22.6728i	1.25670	−	1.08833i
$435$	−22.3607			−1.07211
$436$	6.57295	+	11.3847i	0.314787	+	0.545227i
$437$	12.3541	−	21.3979i	0.590977	−	1.02360i
$438$	7.92705	−	13.7301i	0.378769	−	0.656047i
$439$	−12.0623	−	20.8925i	−0.575702	−	0.997146i	−0.995965	−	0.0897433i	$-0.971395\pi$
$439$	−12.0623	−	20.8925i	−0.575702	−	0.997146i	0.420262	−	0.907403i	$-0.361938\pi$
$440$	50.1246			2.38960
$441$	−13.0000	+	5.19615i	−0.619048	+	0.247436i
$442$	3.85410			0.183321
$443$	−1.11803	−	1.93649i	−0.0531194	−	0.0920055i	0.838243	−	0.545297i	$-0.183583\pi$
$443$	−1.11803	−	1.93649i	−0.0531194	−	0.0920055i	−0.891362	+	0.453291i	$0.850250\pi$
$444$	25.5517	−	44.2568i	1.21263	−	2.10033i
$445$	−2.50000	+	4.33013i	−0.118511	+	0.205268i
$446$	−5.23607	−	9.06914i	−0.247935	−	0.429436i
$447$	−1.58359			−0.0749013
$448$	−17.4164	+	15.0831i	−0.822848	+	0.712607i
$449$	−34.3607			−1.62158			−0.810790	−	0.585337i	$-0.800962\pi$
$449$	−34.3607			−1.62158			−0.810790	+	0.585337i	$0.800962\pi$
$450$		0			0
$451$	−6.70820	+	11.6190i	−0.315877	+	0.547115i
$452$	−7.14590	+	12.3771i	−0.336115	+	0.582168i
$453$	22.8262	+	39.5362i	1.07247	+	1.85757i
$454$	−15.5623			−0.730375
$455$	−5.59017	−	1.93649i	−0.262071	−	0.0907841i
$456$	50.1246			2.34730
$457$	3.06231	+	5.30407i	0.143249	+	0.248114i	0.928718	−	0.370786i	$-0.120912\pi$
$457$	3.06231	+	5.30407i	0.143249	+	0.248114i	−0.785470	+	0.618900i	$0.787578\pi$
$458$	31.5795	−	54.6973i	1.47561	−	2.55584i
$459$	−1.64590	+	2.85078i	−0.0768239	+	0.133063i
$460$	44.6976	+	77.4184i	2.08403	+	3.60965i
$461$	34.3607			1.60034			0.800168	−	0.599776i	$-0.204744\pi$
$461$	34.3607			1.60034			0.800168	+	0.599776i	$0.204744\pi$
$462$	8.78115	+	45.6282i	0.408536	+	2.12282i
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$	−22.0344	−	38.1648i	−1.02292	−	1.77176i
$465$	12.5000	−	21.6506i	0.579674	−	1.00402i
$466$	15.6353	−	27.0811i	0.724289	−	1.25451i
$467$	−4.82624	−	8.35929i	−0.223332	−	0.386822i	0.732486	−	0.680782i	$-0.238360\pi$
$467$	−4.82624	−	8.35929i	−0.223332	−	0.386822i	−0.955818	+	0.293960i	$0.905027\pi$
$468$	−9.70820			−0.448762
$469$	1.50000	+	7.79423i	0.0692636	+	0.359904i
$470$	43.7426			2.01770
$471$	7.82624	+	13.5554i	0.360614	+	0.624602i
$472$	−5.50000	+	9.52628i	−0.253158	+	0.438483i
$473$	−12.0000	+	20.7846i	−0.551761	+	0.955677i
$474$	7.92705	+	13.7301i	0.364102	+	0.630642i
$475$		0			0
$476$	17.8647	+	6.18853i	0.818829	+	0.283651i
$477$	−14.9443			−0.684251
$478$	25.4164	+	44.0225i	1.16252	+	2.01354i
$479$	−11.9164	+	20.6398i	−0.544475	+	0.943058i	0.454165	+	0.890917i	$0.349938\pi$
$479$	−11.9164	+	20.6398i	−0.544475	+	0.943058i	−0.998640	+	0.0521401i	$0.983396\pi$
$480$	−27.1353	+	46.9996i	−1.23855	+	2.14523i
$481$	2.35410	+	4.07742i	0.107338	+	0.185915i
$482$	−12.3262			−0.561445
$483$	−36.8328	+	31.8982i	−1.67595	+	1.45142i
$484$	−9.70820			−0.441282
$485$	−10.5279	−	18.2348i	−0.478046	−	0.827999i
$486$	23.4164	−	40.5584i	1.06219	−	1.83977i
$487$	10.9164	−	18.9078i	0.494670	−	0.856793i	−0.505311	−	0.862937i	$-0.668622\pi$
$487$	10.9164	−	18.9078i	0.494670	−	0.856793i	0.999981	+	0.00614405i	$0.00195572\pi$
$488$	11.2082	+	19.4132i	0.507372	+	0.878793i
$489$	36.7082			1.66000
$490$	−32.1976	−	25.3490i	−1.45454	−	1.14515i
$491$	−25.5279			−1.15206			−0.576028	−	0.817430i	$-0.695398\pi$
$491$	−25.5279			−1.15206			−0.576028	+	0.817430i	$0.695398\pi$
$492$	−24.2705	−	42.0378i	−1.09420	−	1.89521i
$493$	−3.29180	+	5.70156i	−0.148255	+	0.256785i
$494$	−3.92705	+	6.80185i	−0.176686	+	0.306030i
$495$	6.70820	+	11.6190i	0.301511	+	0.522233i
$496$	49.2705			2.21231
$497$	17.8885	−	15.4919i	0.802411	−	0.694908i
$498$		0			0
$499$	−13.2082	−	22.8773i	−0.591280	−	1.02413i	−0.994060	−	0.108831i	$-0.965289\pi$
$499$	−13.2082	−	22.8773i	−0.591280	−	1.02413i	0.402780	−	0.915297i	$-0.368044\pi$
$500$	27.1353	−	46.9996i	1.21353	−	2.10189i
$501$	25.1246	−	43.5171i	1.12248	−	1.94420i
$502$	2.00000	+	3.46410i	0.0892644	+	0.154610i
$503$	20.9443			0.933859			0.466929	−	0.884295i	$-0.345360\pi$
$503$	20.9443			0.933859			0.466929	+	0.884295i	$0.345360\pi$
$504$	−37.3607	−	12.9421i	−1.66418	−	0.576488i
$505$	−20.1246			−0.895533
$506$	32.3435	+	56.0205i	1.43784	+	2.49042i
$507$	1.11803	−	1.93649i	0.0496536	−	0.0860026i
$508$	27.7082	−	47.9920i	1.22935	−	2.12930i
$509$	10.1180	+	17.5249i	0.448474	+	0.776780i	0.998287	−	0.0585081i	$-0.0186343\pi$
$509$	10.1180	+	17.5249i	0.448474	+	0.776780i	−0.549813	+	0.835288i	$0.685301\pi$
$510$	19.2705			0.853313
$511$	1.35410	+	7.03612i	0.0599019	+	0.311260i
$512$	40.3050			1.78124
$513$	−3.35410	−	5.80948i	−0.148087	−	0.256495i
$514$	−0.0729490	+	0.126351i	−0.00321764	+	0.00557312i
$515$	3.02786	−	5.24441i	0.133424	−	0.231097i
$516$	−43.4164	−	75.1994i	−1.91130	−	3.31047i
$517$	22.4164			0.985872
$518$	6.16312	+	32.0245i	0.270792	+	1.40708i
$519$	36.7082			1.61131
$520$	−8.35410	−	14.4697i	−0.366352	−	0.634540i
$521$	8.97214	−	15.5402i	0.393076	−	0.680828i	−0.599777	−	0.800167i	$-0.704744\pi$
$521$	8.97214	−	15.5402i	0.393076	−	0.680828i	0.992854	+	0.119339i	$0.0380775\pi$
$522$	11.7082	−	20.2792i	0.512454	−	0.887597i
$523$	−16.3541	−	28.3261i	−0.715115	−	1.23862i	−0.962915	−	0.269804i	$-0.913041\pi$
$523$	−16.3541	−	28.3261i	−0.715115	−	1.23862i	0.247800	−	0.968811i	$-0.420292\pi$
$524$	−39.9787			−1.74648
$525$		0			0
$526$	−68.3951			−2.98217
$527$	−3.68034	−	6.37454i	−0.160318	−	0.277679i
$528$	−33.0517	+	57.2472i	−1.43839	+	2.49136i
$529$	−22.4164	+	38.8264i	−0.974626	+	1.68810i
$530$	−21.8713	−	37.8822i	−0.950030	−	1.64550i
$531$	−2.94427			−0.127771
$532$	−29.1246	+	25.2227i	−1.26271	+	1.09354i
$533$	4.47214			0.193710
$534$	−6.54508	−	11.3364i	−0.283234	−	0.490575i
$535$	10.9164	−	18.9078i	0.471957	−	0.817454i
$536$	−11.2082	+	19.4132i	−0.484121	+	0.838522i
$537$	−22.5000	−	38.9711i	−0.970947	−	1.68173i
$538$	−35.2705			−1.52062
$539$	−16.5000	−	12.9904i	−0.710705	−	0.559535i
$540$	24.2705			1.04444
$541$	−0.645898	−	1.11873i	−0.0277693	−	0.0480979i	0.851807	−	0.523856i	$-0.175507\pi$
$541$	−0.645898	−	1.11873i	−0.0277693	−	0.0480979i	−0.879576	+	0.475758i	$0.842174\pi$
$542$	−26.7254	+	46.2898i	−1.14796	+	1.98832i
$543$	−28.4164	+	49.2187i	−1.21946	+	2.11217i
$544$	7.98936	+	13.8380i	0.342541	+	0.593298i
$545$	−6.05573			−0.259399
$546$	11.7082	−	10.1396i	0.501065	−	0.433935i
$547$	−4.58359			−0.195980			−0.0979901	−	0.995187i	$-0.531241\pi$
$547$	−4.58359			−0.195980			−0.0979901	+	0.995187i	$0.531241\pi$
$548$	19.9894	+	34.6226i	0.853903	+	1.47900i
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	−6.70820	−	11.6190i	−0.285779	−	0.494984i
$552$	−137.610			−5.85707
$553$	−6.77051	−	2.34537i	−0.287911	−	0.0997354i
$554$	1.09017			0.0463169
$555$	11.7705	+	20.3871i	0.499630	+	0.865385i
$556$	56.8328	−	98.4373i	2.41025	−	4.17467i
$557$	9.35410	−	16.2018i	0.396346	−	0.686491i	−0.596926	−	0.802296i	$-0.703611\pi$
$557$	9.35410	−	16.2018i	0.396346	−	0.686491i	0.993272	+	0.115805i	$0.0369447\pi$
$558$	13.0902	+	22.6728i	0.554151	+	0.959818i
$559$	8.00000			0.338364
$560$	−11.0172	−	57.2472i	−0.465563	−	2.41913i
$561$	9.87539			0.416939
$562$	35.2705	+	61.0903i	1.48780	+	2.57694i
$563$	−6.29837	+	10.9091i	−0.265445	+	0.459764i	−0.967680	−	0.252181i	$-0.918852\pi$
$563$	−6.29837	+	10.9091i	−0.265445	+	0.459764i	0.702235	+	0.711945i	$0.252185\pi$
$564$	−40.5517	+	70.2375i	−1.70753	+	2.95753i
$565$	−3.29180	−	5.70156i	−0.138487	−	0.239866i
$566$	−68.3951			−2.87486
$567$	5.50000	+	28.5788i	0.230978	+	1.20020i
$568$	66.8328			2.80424
$569$	−12.7361	−	22.0595i	−0.533924	−	0.924783i	−0.999215	−	0.0396252i	$-0.987384\pi$
$569$	−12.7361	−	22.0595i	−0.533924	−	0.924783i	0.465291	−	0.885158i	$-0.345950\pi$
$570$	−19.6353	+	34.0093i	−0.822430	+	1.42449i
$571$	18.0623	−	31.2848i	0.755884	−	1.30923i	−0.189050	−	0.981968i	$-0.560541\pi$
$571$	18.0623	−	31.2848i	0.755884	−	1.30923i	0.944934	−	0.327262i	$-0.106126\pi$
$572$	−7.28115	−	12.6113i	−0.304440	−	0.527306i
$573$	−25.0000			−1.04439
$574$	29.2705	+	10.1396i	1.22173	+	0.423219i
$575$		0			0
$576$	−8.70820	−	15.0831i	−0.362842	−	0.628460i
$577$	9.64590	−	16.7072i	0.401564	−	0.695529i	−0.592351	−	0.805680i	$-0.701800\pi$
$577$	9.64590	−	16.7072i	0.401564	−	0.695529i	0.993915	+	0.110151i	$0.0351334\pi$
$578$	−19.4164	+	33.6302i	−0.807616	+	1.39883i
$579$	0.791796	+	1.37143i	0.0329059	+	0.0569947i
$580$	48.5410			2.01556
$581$		0			0
$582$	55.1246			2.28499
$583$	−11.2082	−	19.4132i	−0.464196	−	0.804012i
$584$	−10.1180	+	17.5249i	−0.418687	+	0.725188i
$585$	2.23607	−	3.87298i	0.0924500	−	0.160128i
$586$	−19.5623	−	33.8829i	−0.808111	−	1.39969i
$587$	−6.11146			−0.252247			−0.126123	−	0.992015i	$-0.540254\pi$
$587$	−6.11146			−0.252247			−0.126123	+	0.992015i	$0.540254\pi$
$588$	70.5517	−	28.1998i	2.90950	−	1.16294i
$589$	15.0000			0.618064
$590$	−4.30902	−	7.46344i	−0.177399	−	0.307265i
$591$	−10.1246	+	17.5363i	−0.416471	+	0.721349i
$592$	−23.1976	+	40.1794i	−0.953414	+	1.65136i
$593$	−13.8820	−	24.0443i	−0.570064	−	0.987380i	−0.996559	−	0.0828898i	$-0.973585\pi$
$593$	−13.8820	−	24.0443i	−0.570064	−	0.987380i	0.426495	−	0.904490i	$-0.359748\pi$
$594$	17.5623			0.720590
$595$	−6.58359	+	5.70156i	−0.269901	+	0.233741i
$596$	3.43769			0.140813
$597$	−23.1525	−	40.1013i	−0.947568	−	1.64124i
$598$	10.7812	−	18.6735i	0.440874	−	0.763616i
$599$	8.53444	−	14.7821i	0.348708	−	0.603980i	−0.637312	−	0.770606i	$-0.719954\pi$
$599$	8.53444	−	14.7821i	0.348708	−	0.603980i	0.986020	+	0.166626i	$0.0532872\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	52.3607	+	18.1383i	2.13406	+	0.739261i
$603$	−6.00000			−0.244339
$604$	−49.5517	−	85.8260i	−2.01623	−	3.49221i
$605$	2.23607	−	3.87298i	0.0909091	−	0.157459i
$606$	26.3435	−	45.6282i	1.07013	−	1.85352i
$607$	−12.0623	−	20.8925i	−0.489594	−	0.848001i	0.510334	−	0.859976i	$-0.329522\pi$
$607$	−12.0623	−	20.8925i	−0.489594	−	0.848001i	−0.999928	+	0.0119745i	$0.996188\pi$
$608$	−32.5623			−1.32058
$609$	5.00000	+	25.9808i	0.202610	+	1.05279i
$610$	−17.5623			−0.711077
$611$	−3.73607	−	6.47106i	−0.151145	−	0.261791i
$612$	−7.14590	+	12.3771i	−0.288856	+	0.500313i
$613$	9.06231	−	15.6964i	0.366023	−	0.633971i	−0.622917	−	0.782288i	$-0.714052\pi$
$613$	9.06231	−	15.6964i	0.366023	−	0.633971i	0.988940	+	0.148318i	$0.0473858\pi$
$614$	25.4164	+	44.0225i	1.02572	+	1.77660i
$615$	22.3607			0.901670
$616$	−11.2082	−	58.2395i	−0.451591	−	2.34654i
$617$	−4.47214			−0.180041			−0.0900207	−	0.995940i	$-0.528693\pi$
$617$	−4.47214			−0.180041			−0.0900207	+	0.995940i	$0.528693\pi$
$618$	7.92705	+	13.7301i	0.318873	+	0.552304i
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−8.50000	+	14.7224i	−0.341644	+	0.591744i	0.643094	+	0.765787i	$0.277650\pi$
$620$	−27.1353	+	46.9996i	−1.08978	+	1.88755i
$621$	9.20820	+	15.9491i	0.369512	+	0.640014i
$622$	72.6869			2.91448
$623$	5.59017	+	1.93649i	0.223965	+	0.0775839i
$624$	22.0344			0.882084
$625$	12.5000	+	21.6506i	0.500000	+	0.866025i
$626$	−7.30902	+	12.6596i	−0.292127	+	0.505979i
$627$	−10.0623	+	17.4284i	−0.401850	+	0.696024i
$628$	−16.9894	−	29.4264i	−0.677949	−	1.17424i
$629$	6.93112			0.276362
$630$	23.4164	−	20.2792i	0.932932	−	0.807943i
$631$	22.8328			0.908960			0.454480	−	0.890757i	$-0.349825\pi$
$631$	22.8328			0.908960			0.454480	+	0.890757i	$0.349825\pi$
$632$	−10.1180	−	17.5249i	−0.402474	−	0.697105i
$633$	4.47214	−	7.74597i	0.177751	−	0.307875i
$634$	−10.7812	+	18.6735i	−0.428174	+	0.741620i
$635$	12.7639	+	22.1078i	0.506521	+	0.877320i
$636$	81.1033			3.21596
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$	35.1246			1.39060
$639$	8.94427	+	15.4919i	0.353830	+	0.612851i
$640$	1.21885	−	2.11111i	0.0481792	−	0.0834488i
$641$	−5.97214	+	10.3440i	−0.235885	+	0.408565i	−0.959530	−	0.281608i	$-0.909132\pi$
$641$	−5.97214	+	10.3440i	−0.235885	+	0.408565i	0.723644	+	0.690173i	$0.242466\pi$
$642$	28.5795	+	49.5012i	1.12794	+	1.95366i
$643$	34.8328			1.37367			0.686836	−	0.726812i	$-0.258999\pi$
$643$	34.8328			1.37367			0.686836	+	0.726812i	$0.258999\pi$
$644$	79.9574	−	69.2452i	3.15076	−	2.72864i
$645$	40.0000			1.57500
$646$	5.78115	+	10.0133i	0.227456	+	0.393966i
$647$	−10.1180	+	17.5249i	−0.397781	+	0.688977i	−0.993452	−	0.114252i	$-0.963553\pi$
$647$	−10.1180	+	17.5249i	−0.397781	+	0.688977i	0.595671	+	0.803229i	$0.296886\pi$
$648$	−41.0967	+	71.1817i	−1.61443	+	2.79628i
$649$	−2.20820	−	3.82472i	−0.0866796	−	0.150133i
$650$		0			0
$651$	−27.9508	−	9.68246i	−1.09548	−	0.379485i
$652$	−79.6869			−3.12078
$653$	−2.26393	−	3.92125i	−0.0885945	−	0.153450i	0.818323	−	0.574759i	$-0.194904\pi$
$653$	−2.26393	−	3.92125i	−0.0885945	−	0.153450i	−0.906917	+	0.421309i	$0.861571\pi$
$654$	7.92705	−	13.7301i	0.309972	−	0.536888i
$655$	9.20820	−	15.9491i	0.359794	−	0.623182i
$656$	22.0344	+	38.1648i	0.860300	+	1.49008i
$657$	−5.41641			−0.211314
$658$	−9.78115	−	50.8244i	−0.381309	−	1.98134i
$659$	−8.94427			−0.348419			−0.174210	−	0.984709i	$-0.555737\pi$
$659$	−8.94427			−0.348419			−0.174210	+	0.984709i	$0.555737\pi$
$660$	−36.4058	−	63.0566i	−1.41709	−	2.45448i
$661$	3.35410	−	5.80948i	0.130459	−	0.225962i	−0.793394	−	0.608708i	$-0.791688\pi$
$661$	3.35410	−	5.80948i	0.130459	−	0.225962i	0.923854	+	0.382746i	$0.125021\pi$
$662$	−2.07295	+	3.59045i	−0.0805675	+	0.139547i
$663$	−1.64590	−	2.85078i	−0.0639214	−	0.110715i
$664$		0			0
$665$	−3.35410	−	17.4284i	−0.130066	−	0.675845i
$666$	−24.6525			−0.955264
$667$	18.4164	+	31.8982i	0.713086	+	1.23510i
$668$	−54.5410	+	94.4678i	−2.11026	+	3.65507i
$669$	−4.47214	+	7.74597i	−0.172903	+	0.299476i
$670$	−8.78115	−	15.2094i	−0.339246	−	0.587591i
$671$	−9.00000			−0.347441
$672$	60.6763	+	21.0189i	2.34064	+	0.810821i
$673$	−9.41641			−0.362976			−0.181488	−	0.983393i	$-0.558091\pi$
$673$	−9.41641			−0.362976			−0.181488	+	0.983393i	$0.558091\pi$
$674$	23.5623	+	40.8111i	0.907586	+	1.57199i
$675$		0			0
$676$	−2.42705	+	4.20378i	−0.0933481	+	0.161684i
$677$	1.44427	+	2.50155i	0.0555079	+	0.0961425i	0.892444	−	0.451158i	$-0.148989\pi$
$677$	1.44427	+	2.50155i	0.0555079	+	0.0961425i	−0.836936	+	0.547300i	$0.815656\pi$
$678$	17.2361			0.661947
$679$	−18.8328	+	16.3097i	−0.722737	+	0.625909i
$680$	−24.5967			−0.943242
$681$	6.64590	+	11.5110i	0.254671	+	0.441104i
$682$	−19.6353	+	34.0093i	−0.751873	+	1.30228i
$683$	6.73607	−	11.6672i	0.257748	−	0.446433i	−0.707890	−	0.706323i	$-0.750353\pi$
$683$	6.73607	−	11.6672i	0.257748	−	0.446433i	0.965638	+	0.259889i	$0.0836861\pi$
$684$	−14.5623	−	25.2227i	−0.556804	−	0.964412i
$685$	−18.4164			−0.703655
$686$	−22.2533	+	43.0784i	−0.849635	+	1.64474i
$687$	−53.9443			−2.05810
$688$	39.4164	+	68.2712i	1.50274	+	2.60282i
$689$	−3.73607	+	6.47106i	−0.142333	+	0.246528i
$690$	53.9058	−	93.3675i	2.05216	−	3.55444i
$691$	25.9164	+	44.8885i	0.985907	+	1.70764i	0.637836	+	0.770172i	$0.279830\pi$
$691$	25.9164	+	44.8885i	0.985907	+	1.70764i	0.348070	+	0.937468i	$0.386837\pi$
$692$	−79.6869			−3.02924
$693$	12.0000	−	10.3923i	0.455842	−	0.394771i
$694$	−60.3951			−2.29257
$695$	26.1803	+	45.3457i	0.993077	+	1.72006i
$696$	−37.3607	+	64.7106i	−1.41615	+	2.45285i
$697$	3.29180	−	5.70156i	0.124686	−	0.215962i
$698$	−38.5066	−	66.6953i	−1.45750	−	2.52446i
$699$	−26.7082			−1.01020
$700$		0			0
$701$	−22.3607			−0.844551			−0.422276	−	0.906467i	$-0.638769\pi$
$701$	−22.3607			−0.844551			−0.422276	+	0.906467i	$0.638769\pi$
$702$	−2.92705	−	5.06980i	−0.110474	−	0.191347i
$703$	−7.06231	+	12.2323i	−0.266360	+	0.461349i
$704$	13.0623	−	22.6246i	0.492304	−	0.852696i
$705$	−18.6803	−	32.3553i	−0.703542	−	1.21857i
$706$	−45.2705			−1.70378
$707$	4.50000	+	23.3827i	0.169240	+	0.879396i
$708$	15.9787			0.600517
$709$	25.0623	+	43.4092i	0.941235	+	1.63027i	0.763120	+	0.646256i	$0.223666\pi$
$709$	25.0623	+	43.4092i	0.941235	+	1.63027i	0.178114	+	0.984010i	$0.443000\pi$
$710$	−26.1803	+	45.3457i	−0.982531	+	1.70179i
$711$	2.70820	−	4.69075i	0.101566	−	0.175917i
$712$	8.35410	+	14.4697i	0.313083	+	0.542276i
$713$	−41.1803			−1.54222
$714$	−4.30902	−	22.3903i	−0.161261	−	0.837936i
$715$	6.70820			0.250873
$716$	48.8435	+	84.5994i	1.82537	+	3.16163i
$717$	21.7082	−	37.5997i	0.810708	−	1.40419i
$718$	15.6353	−	27.0811i	0.583503	−	1.01066i
$719$	−12.3541	−	21.3979i	−0.460730	−	0.798008i	0.538267	−	0.842774i	$-0.319079\pi$
$719$	−12.3541	−	21.3979i	−0.460730	−	0.798008i	−0.998998	+	0.0447660i	$0.985746\pi$
$720$	44.0689			1.64235
$721$	−6.77051	−	2.34537i	−0.252147	−	0.0873463i
$722$	26.1803			0.974331
$723$	5.26393	+	9.11740i	0.195768	+	0.339080i
$724$	61.6869	−	106.845i	2.29258	−	3.97086i
$725$		0			0
$726$	5.85410	+	10.1396i	0.217266	+	0.376316i
$727$	−38.8328			−1.44023			−0.720115	−	0.693855i	$-0.755911\pi$
$727$	−38.8328			−1.44023			−0.720115	+	0.693855i	$0.755911\pi$
$728$	−14.9443	+	12.9421i	−0.553872	+	0.479667i
$729$	−7.00000			−0.259259
$730$	−7.92705	−	13.7301i	−0.293393	−	0.508172i
$731$	5.88854	−	10.1993i	0.217796	−	0.377233i
$732$	16.2812	−	28.1998i	0.601769	−	1.04229i
$733$	−14.3541	−	24.8620i	−0.530181	−	0.918300i	−0.999380	−	0.0352078i	$-0.988791\pi$
$733$	−14.3541	−	24.8620i	−0.530181	−	0.918300i	0.469199	−	0.883092i	$-0.344543\pi$
$734$	33.2705			1.22804
$735$	−5.00000	+	34.6410i	−0.184428	+	1.27775i
$736$	89.3951			3.29515
$737$	−4.50000	−	7.79423i	−0.165760	−	0.287104i
$738$	−11.7082	+	20.2792i	−0.430985	+	0.746488i
$739$	8.91641	−	15.4437i	0.327995	−	0.568105i	−0.654119	−	0.756392i	$-0.726960\pi$
$739$	8.91641	−	15.4437i	0.327995	−	0.568105i	0.982114	+	0.188287i	$0.0602936\pi$
$740$	−25.5517	−	44.2568i	−0.939298	−	1.62691i
$741$	6.70820			0.246432
$742$	−39.1246	+	33.8829i	−1.43631	+	1.24388i
$743$	32.9443			1.20861			0.604304	−	0.796754i	$-0.293451\pi$
$743$	32.9443			1.20861			0.604304	+	0.796754i	$0.293451\pi$
$744$	−41.7705	−	72.3486i	−1.53138	−	2.65243i
$745$	−0.791796	+	1.37143i	−0.0290092	+	0.0502453i
$746$	−2.07295	+	3.59045i	−0.0758961	+	0.131456i
$747$		0			0
$748$	−21.4377			−0.783840
$749$	−24.4098	−	8.45581i	−0.891916	−	0.308969i
$750$	−65.4508			−2.38993
$751$	5.06231	+	8.76817i	0.184726	+	0.319955i	0.943484	−	0.331417i	$-0.107527\pi$
$751$	5.06231	+	8.76817i	0.184726	+	0.319955i	−0.758758	+	0.651373i	$0.774194\pi$
$752$	36.8156	−	63.7665i	1.34253	−	2.32532i
$753$	1.70820	−	2.95870i	0.0622504	−	0.107821i
$754$	−5.85410	−	10.1396i	−0.213194	−	0.369263i
$755$	45.6525			1.66146
$756$	−5.42705	−	28.1998i	−0.197380	−	1.02562i
$757$	−52.8328			−1.92024			−0.960121	−	0.279586i	$-0.909803\pi$
$757$	−52.8328			−1.92024			−0.960121	+	0.279586i	$0.909803\pi$
$758$	−20.1803	−	34.9534i	−0.732983	−	1.26956i
$759$	27.6246	−	47.8472i	1.00271	−	1.73674i
$760$	25.0623	−	43.4092i	0.909105	−	1.57462i
$761$	16.7705	+	29.0474i	0.607931	+	1.05297i	0.991581	+	0.129488i	$0.0413334\pi$
$761$	16.7705	+	29.0474i	0.607931	+	1.05297i	−0.383650	+	0.923478i	$0.625333\pi$
$762$	−66.8328			−2.42110
$763$	1.35410	+	7.03612i	0.0490218	+	0.254725i
$764$	54.2705			1.96344
$765$	−3.29180	−	5.70156i	−0.119015	−	0.206140i
$766$	19.6353	−	34.0093i	0.709451	−	1.22880i
$767$	−0.736068	+	1.27491i	−0.0265779	+	0.0460342i
$768$	−16.2812	−	28.1998i	−0.587496	−	1.01757i
$769$	46.0000			1.65880			0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000			1.65880			0.829401	+	0.558653i	$0.188682\pi$
$770$	43.9058	+	15.2094i	1.58225	+	0.548109i
$771$	0.124612

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)

\(f(q)\)	\(=\)	\(q+(1.30902 + 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(-1.11803 - 1.93649i) q^{5} +5.85410 q^{6} +(-2.00000 + 1.73205i) q^{7} -7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(1.30902 + 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(-1.11803 - 1.93649i) q^{5} +5.85410 q^{6} +(-2.00000 + 1.73205i) q^{7} -7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(2.92705 - 5.06980i) q^{10} +(1.50000 - 2.59808i) q^{11} +(5.42705 + 9.39993i) q^{12} -1.00000 q^{13} +(-6.54508 - 2.26728i) q^{14} -5.00000 q^{15} +(-4.92705 - 8.53390i) q^{16} +(-0.736068 + 1.27491i) q^{17} +(2.61803 - 4.53457i) q^{18} +(-1.50000 - 2.59808i) q^{19} +10.8541 q^{20} +(1.11803 + 5.80948i) q^{21} +7.85410 q^{22} +(4.11803 + 7.13264i) q^{23} +(-8.35410 + 14.4697i) q^{24} +(-1.30902 - 2.26728i) q^{26} +2.23607 q^{27} +(-2.42705 - 12.6113i) q^{28} +4.47214 q^{29} +(-6.54508 - 11.3364i) q^{30} +(-2.50000 + 4.33013i) q^{31} +(5.42705 - 9.39993i) q^{32} +(-3.35410 - 5.80948i) q^{33} -3.85410 q^{34} +(5.59017 + 1.93649i) q^{35} +9.70820 q^{36} +(-2.35410 - 4.07742i) q^{37} +(3.92705 - 6.80185i) q^{38} +(-1.11803 + 1.93649i) q^{39} +(8.35410 + 14.4697i) q^{40} -4.47214 q^{41} +(-11.7082 + 10.1396i) q^{42} -8.00000 q^{43} +(7.28115 + 12.6113i) q^{44} +(-2.23607 + 3.87298i) q^{45} +(-10.7812 + 18.6735i) q^{46} +(3.73607 + 6.47106i) q^{47} -22.0344 q^{48} +(1.00000 - 6.92820i) q^{49} +(1.64590 + 2.85078i) q^{51} +(2.42705 - 4.20378i) q^{52} +(3.73607 - 6.47106i) q^{53} +(2.92705 + 5.06980i) q^{54} -6.70820 q^{55} +(14.9443 - 12.9421i) q^{56} -6.70820 q^{57} +(5.85410 + 10.1396i) q^{58} +(0.736068 - 1.27491i) q^{59} +(12.1353 - 21.0189i) q^{60} +(-1.50000 - 2.59808i) q^{61} -13.0902 q^{62} +(5.00000 + 1.73205i) q^{63} +8.70820 q^{64} +(1.11803 + 1.93649i) q^{65} +(8.78115 - 15.2094i) q^{66} +(1.50000 - 2.59808i) q^{67} +(-3.57295 - 6.18853i) q^{68} +18.4164 q^{69} +(2.92705 + 15.2094i) q^{70} -8.94427 q^{71} +(7.47214 + 12.9421i) q^{72} +(1.35410 - 2.34537i) q^{73} +(6.16312 - 10.6748i) q^{74} +14.5623 q^{76} +(1.50000 + 7.79423i) q^{77} -5.85410 q^{78} +(1.35410 + 2.34537i) q^{79} +(-11.0172 + 19.0824i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-5.85410 - 10.1396i) q^{82} +(-27.1353 - 9.39993i) q^{84} +3.29180 q^{85} +(-10.4721 - 18.1383i) q^{86} +(5.00000 - 8.66025i) q^{87} +(-11.2082 + 19.4132i) q^{88} +(-1.11803 - 1.93649i) q^{89} -11.7082 q^{90} +(2.00000 - 1.73205i) q^{91} -39.9787 q^{92} +(5.59017 + 9.68246i) q^{93} +(-9.78115 + 16.9415i) q^{94} +(-3.35410 + 5.80948i) q^{95} +(-12.1353 - 21.0189i) q^{96} +9.41641 q^{97} +(17.0172 - 6.80185i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 3 * q^4 + 10 * q^6 - 8 * q^7 - 12 * q^8 - 4 * q^9	\( 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9} + 5 q^{10} + 6 q^{11} + 15 q^{12} - 4 q^{13} - 15 q^{14} - 20 q^{15} - 13 q^{16} + 6 q^{17} + 6 q^{18} - 6 q^{19} + 30 q^{20} + 18 q^{22} + 12 q^{23} - 20 q^{24} - 3 q^{26} - 3 q^{28} - 15 q^{30} - 10 q^{31} + 15 q^{32} - 2 q^{34} + 12 q^{36} + 4 q^{37} + 9 q^{38} + 20 q^{40} - 20 q^{42} - 32 q^{43} + 9 q^{44} - 23 q^{46} + 6 q^{47} - 30 q^{48} + 4 q^{49} + 20 q^{51} + 3 q^{52} + 6 q^{53} + 5 q^{54} + 24 q^{56} + 10 q^{58} - 6 q^{59} + 15 q^{60} - 6 q^{61} - 30 q^{62} + 20 q^{63} + 8 q^{64} + 15 q^{66} + 6 q^{67} - 21 q^{68} + 20 q^{69} + 5 q^{70} + 12 q^{72} - 8 q^{73} + 9 q^{74} + 18 q^{76} + 6 q^{77} - 10 q^{78} - 8 q^{79} - 15 q^{80} + 22 q^{81} - 10 q^{82} - 75 q^{84} + 40 q^{85} - 24 q^{86} + 20 q^{87} - 18 q^{88} - 20 q^{90} + 8 q^{91} - 66 q^{92} - 19 q^{94} - 15 q^{96} - 16 q^{97} + 39 q^{98} - 24 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 3 * q^4 + 10 * q^6 - 8 * q^7 - 12 * q^8 - 4 * q^9 + 5 * q^10 + 6 * q^11 + 15 * q^12 - 4 * q^13 - 15 * q^14 - 20 * q^15 - 13 * q^16 + 6 * q^17 + 6 * q^18 - 6 * q^19 + 30 * q^20 + 18 * q^22 + 12 * q^23 - 20 * q^24 - 3 * q^26 - 3 * q^28 - 15 * q^30 - 10 * q^31 + 15 * q^32 - 2 * q^34 + 12 * q^36 + 4 * q^37 + 9 * q^38 + 20 * q^40 - 20 * q^42 - 32 * q^43 + 9 * q^44 - 23 * q^46 + 6 * q^47 - 30 * q^48 + 4 * q^49 + 20 * q^51 + 3 * q^52 + 6 * q^53 + 5 * q^54 + 24 * q^56 + 10 * q^58 - 6 * q^59 + 15 * q^60 - 6 * q^61 - 30 * q^62 + 20 * q^63 + 8 * q^64 + 15 * q^66 + 6 * q^67 - 21 * q^68 + 20 * q^69 + 5 * q^70 + 12 * q^72 - 8 * q^73 + 9 * q^74 + 18 * q^76 + 6 * q^77 - 10 * q^78 - 8 * q^79 - 15 * q^80 + 22 * q^81 - 10 * q^82 - 75 * q^84 + 40 * q^85 - 24 * q^86 + 20 * q^87 - 18 * q^88 - 20 * q^90 + 8 * q^91 - 66 * q^92 - 19 * q^94 - 15 * q^96 - 16 * q^97 + 39 * q^98 - 24 * q^99

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