LMFDB - Embedded newform 966.2.i.l.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1768034304.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - x^{6} - 6x^{5} + 14x^{4} + 18x^{3} - 31x^{2} - 14x + 49 $ x^8 - 2x^7 - x^6 - 6x^5 + 14x^4 + 18x^3 - 31x^2 - 14x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.4
Root			$-1.17927 + 0.441707i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.l.415.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.91421 + 3.31552i) q^{5} +1.00000 q^{6} +(1.16774 - 2.37411i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.91421 + 3.31552i) q^{5} +1.00000 q^{6} +(1.16774 - 2.37411i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.91421 - 3.31552i) q^{10} +(2.55412 - 4.42387i) q^{11} +(-0.500000 - 0.866025i) q^{12} +0.0556701 q^{13} +(-2.63991 + 0.175759i) q^{14} -3.82843 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.38638 - 5.86538i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.08196 - 3.60605i) q^{19} -3.82843 q^{20} +(1.47216 + 2.19835i) q^{21} -5.10824 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.82843 + 8.36308i) q^{25} +(-0.0278351 - 0.0482117i) q^{26} +1.00000 q^{27} +(1.47216 + 2.19835i) q^{28} +2.94433 q^{29} +(1.91421 + 3.31552i) q^{30} +(1.60979 - 2.78824i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.55412 + 4.42387i) q^{33} -6.77276 q^{34} +(10.1067 - 0.672879i) q^{35} +1.00000 q^{36} +(4.02629 + 6.97373i) q^{37} +(-2.08196 + 3.60605i) q^{38} +(-0.0278351 + 0.0482117i) q^{39} +(1.91421 + 3.31552i) q^{40} -4.16391 q^{41} +(1.16774 - 2.37411i) q^{42} +12.5596 q^{43} +(2.55412 + 4.42387i) q^{44} +(1.91421 - 3.31552i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-5.99845 - 10.3896i) q^{47} +1.00000 q^{48} +(-4.27276 - 5.54469i) q^{49} +9.65685 q^{50} +(3.38638 + 5.86538i) q^{51} +(-0.0278351 + 0.0482117i) q^{52} +(-2.85854 + 4.95114i) q^{53} +(-0.500000 - 0.866025i) q^{54} +19.5565 q^{55} +(1.16774 - 2.37411i) q^{56} +4.16391 q^{57} +(-1.47216 - 2.54986i) q^{58} +(-4.30059 + 7.44884i) q^{59} +(1.91421 - 3.31552i) q^{60} +(2.88866 + 5.00331i) q^{61} -3.21958 q^{62} +(-2.63991 + 0.175759i) q^{63} +1.00000 q^{64} +(0.106565 + 0.184575i) q^{65} +(2.55412 - 4.42387i) q^{66} +(-6.07718 + 10.5260i) q^{67} +(3.38638 + 5.86538i) q^{68} +1.00000 q^{69} +(-5.63608 - 8.41621i) q^{70} +11.9443 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.10979 - 1.92221i) q^{73} +(4.02629 - 6.97373i) q^{74} +(-4.82843 - 8.36308i) q^{75} +4.16391 q^{76} +(-7.52017 - 11.2297i) q^{77} +0.0556701 q^{78} +(1.47216 + 2.54986i) q^{79} +(1.91421 - 3.31552i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.08196 + 3.60605i) q^{82} -14.7651 q^{83} +(-2.63991 + 0.175759i) q^{84} +25.9290 q^{85} +(-6.27981 - 10.8770i) q^{86} +(-1.47216 + 2.54986i) q^{87} +(2.55412 - 4.42387i) q^{88} +(-1.19786 - 2.07475i) q^{89} -3.82843 q^{90} +(0.0650084 - 0.132167i) q^{91} +1.00000 q^{92} +(1.60979 + 2.78824i) q^{93} +(-5.99845 + 10.3896i) q^{94} +(7.97062 - 13.8055i) q^{95} +(-0.500000 - 0.866025i) q^{96} +4.60118 q^{97} +(-2.66546 + 6.47266i) q^{98} -5.10824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9	$ 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} - 6 q^{14} - 8 q^{15} - 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} - 8 q^{20} + 6 q^{21} + 12 q^{22} - 4 q^{23} - 4 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{27} + 6 q^{28} + 12 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 6 q^{33} - 20 q^{34} - 10 q^{35} + 8 q^{36} + 4 q^{38} - 6 q^{39} + 4 q^{40} + 8 q^{41} + 40 q^{43} - 6 q^{44} + 4 q^{45} - 4 q^{46} - 10 q^{47} + 8 q^{48} + 32 q^{50} + 10 q^{51} - 6 q^{52} - 4 q^{54} + 20 q^{55} - 8 q^{57} - 6 q^{58} - 6 q^{59} + 4 q^{60} + 4 q^{62} - 6 q^{63} + 8 q^{64} + 14 q^{65} - 6 q^{66} - 18 q^{67} + 10 q^{68} + 8 q^{69} + 2 q^{70} + 84 q^{71} - 4 q^{72} - 6 q^{73} - 16 q^{75} - 8 q^{76} - 2 q^{77} + 12 q^{78} + 6 q^{79} + 4 q^{80} - 4 q^{81} - 4 q^{82} - 20 q^{83} - 6 q^{84} + 68 q^{85} - 20 q^{86} - 6 q^{87} - 6 q^{88} - 8 q^{90} + 10 q^{91} + 8 q^{92} - 2 q^{93} - 10 q^{94} + 20 q^{95} - 4 q^{96} - 20 q^{97} - 18 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 - 6 * q^14 - 8 * q^15 - 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 - 8 * q^20 + 6 * q^21 + 12 * q^22 - 4 * q^23 - 4 * q^24 - 16 * q^25 - 6 * q^26 + 8 * q^27 + 6 * q^28 + 12 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 6 * q^33 - 20 * q^34 - 10 * q^35 + 8 * q^36 + 4 * q^38 - 6 * q^39 + 4 * q^40 + 8 * q^41 + 40 * q^43 - 6 * q^44 + 4 * q^45 - 4 * q^46 - 10 * q^47 + 8 * q^48 + 32 * q^50 + 10 * q^51 - 6 * q^52 - 4 * q^54 + 20 * q^55 - 8 * q^57 - 6 * q^58 - 6 * q^59 + 4 * q^60 + 4 * q^62 - 6 * q^63 + 8 * q^64 + 14 * q^65 - 6 * q^66 - 18 * q^67 + 10 * q^68 + 8 * q^69 + 2 * q^70 + 84 * q^71 - 4 * q^72 - 6 * q^73 - 16 * q^75 - 8 * q^76 - 2 * q^77 + 12 * q^78 + 6 * q^79 + 4 * q^80 - 4 * q^81 - 4 * q^82 - 20 * q^83 - 6 * q^84 + 68 * q^85 - 20 * q^86 - 6 * q^87 - 6 * q^88 - 8 * q^90 + 10 * q^91 + 8 * q^92 - 2 * q^93 - 10 * q^94 + 20 * q^95 - 4 * q^96 - 20 * q^97 - 18 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.91421	+	3.31552i	0.856062	+	1.48274i	0.875656	+	0.482935i	$0.160429\pi$
$5$	1.91421	+	3.31552i	0.856062	+	1.48274i	−0.0195936	+	0.999808i	$0.506237\pi$
$6$	1.00000			0.408248
$7$	1.16774	−	2.37411i	0.441365	−	0.897328i
$7$	1.16774	−	2.37411i	0.441365	−	0.897328i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.91421	−	3.31552i	0.605327	−	1.04846i
$11$	2.55412	−	4.42387i	0.770096	−	1.33385i	−0.167413	−	0.985887i	$-0.553541\pi$
$11$	2.55412	−	4.42387i	0.770096	−	1.33385i	0.937510	−	0.347959i	$-0.113125\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.0556701			0.0154401			0.00772006	−	0.999970i	$-0.497543\pi$
$13$	0.0556701			0.0154401			0.00772006	+	0.999970i	$0.497543\pi$
$14$	−2.63991	+	0.175759i	−0.705545	+	0.0469735i
$15$	−3.82843			−0.988496
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.38638	−	5.86538i	0.821317	−	1.42256i	−0.0833841	−	0.996517i	$-0.526573\pi$
$17$	3.38638	−	5.86538i	0.821317	−	1.42256i	0.904701	−	0.426046i	$-0.140094\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−2.08196	−	3.60605i	−0.477633	−	0.827285i	0.522038	−	0.852922i	$-0.325172\pi$
$19$	−2.08196	−	3.60605i	−0.477633	−	0.827285i	−0.999671	+	0.0256370i	$0.991839\pi$
$20$	−3.82843			−0.856062
$21$	1.47216	+	2.19835i	0.321253	+	0.479719i
$22$	−5.10824			−1.08908
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.82843	+	8.36308i	−0.965685	+	1.67262i
$26$	−0.0278351	−	0.0482117i	−0.00545891	−	0.00945510i
$27$	1.00000			0.192450
$28$	1.47216	+	2.19835i	0.278213	+	0.415449i
$29$	2.94433			0.546748			0.273374	−	0.961908i	$-0.411860\pi$
$29$	2.94433			0.546748			0.273374	+	0.961908i	$0.411860\pi$
$30$	1.91421	+	3.31552i	0.349486	+	0.605327i
$31$	1.60979	−	2.78824i	0.289127	−	0.500783i	−0.684475	−	0.729037i	$-0.739968\pi$
$31$	1.60979	−	2.78824i	0.289127	−	0.500783i	0.973602	+	0.228254i	$0.0733017\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.55412	+	4.42387i	0.444615	+	0.770096i
$34$	−6.77276			−1.16152
$35$	10.1067	−	0.672879i	1.70834	−	0.113737i
$36$	1.00000			0.166667
$37$	4.02629	+	6.97373i	0.661917	+	1.14647i	0.980111	+	0.198449i	$0.0635903\pi$
$37$	4.02629	+	6.97373i	0.661917	+	1.14647i	−0.318194	+	0.948026i	$0.603076\pi$
$38$	−2.08196	+	3.60605i	−0.337738	+	0.584979i
$39$	−0.0278351	+	0.0482117i	−0.00445718	+	0.00772006i
$40$	1.91421	+	3.31552i	0.302664	+	0.524229i
$41$	−4.16391			−0.650294			−0.325147	−	0.945664i	$-0.605414\pi$
$41$	−4.16391			−0.650294			−0.325147	+	0.945664i	$0.605414\pi$
$42$	1.16774	−	2.37411i	0.180187	−	0.366332i
$43$	12.5596			1.91533			0.957663	−	0.287893i	$-0.0929547\pi$
$43$	12.5596			1.91533			0.957663	+	0.287893i	$0.0929547\pi$
$44$	2.55412	+	4.42387i	0.385048	+	0.666923i
$45$	1.91421	−	3.31552i	0.285354	−	0.494248i
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	−5.99845	−	10.3896i	−0.874964	−	1.51548i	−0.856801	−	0.515647i	$-0.827552\pi$
$47$	−5.99845	−	10.3896i	−0.874964	−	1.51548i	−0.0181627	−	0.999835i	$-0.505782\pi$
$48$	1.00000			0.144338
$49$	−4.27276	−	5.54469i	−0.610394	−	0.792098i
$50$	9.65685			1.36569
$51$	3.38638	+	5.86538i	0.474188	+	0.821317i
$52$	−0.0278351	+	0.0482117i	−0.00386003	+	0.00668577i
$53$	−2.85854	+	4.95114i	−0.392651	+	0.680092i	−0.992798	−	0.119798i	$-0.961775\pi$
$53$	−2.85854	+	4.95114i	−0.392651	+	0.680092i	0.600147	+	0.799890i	$0.295109\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	19.5565			2.63700
$56$	1.16774	−	2.37411i	0.156046	−	0.317253i
$57$	4.16391			0.551524
$58$	−1.47216	−	2.54986i	−0.193305	−	0.334814i
$59$	−4.30059	+	7.44884i	−0.559889	+	0.969757i	0.437616	+	0.899162i	$0.355823\pi$
$59$	−4.30059	+	7.44884i	−0.559889	+	0.969757i	−0.997505	+	0.0705948i	$0.977510\pi$
$60$	1.91421	−	3.31552i	0.247124	−	0.428031i
$61$	2.88866	+	5.00331i	0.369855	+	0.640608i	0.989543	−	0.144241i	$-0.0460740\pi$
$61$	2.88866	+	5.00331i	0.369855	+	0.640608i	−0.619688	+	0.784849i	$0.712741\pi$
$62$	−3.21958			−0.408887
$63$	−2.63991	+	0.175759i	−0.332597	+	0.0221435i
$64$	1.00000			0.125000
$65$	0.106565	+	0.184575i	0.0132177	+	0.0228937i
$66$	2.55412	−	4.42387i	0.314391	−	0.544540i
$67$	−6.07718	+	10.5260i	−0.742446	+	1.28595i	0.208933	+	0.977930i	$0.433001\pi$
$67$	−6.07718	+	10.5260i	−0.742446	+	1.28595i	−0.951379	+	0.308024i	$0.900332\pi$
$68$	3.38638	+	5.86538i	0.410659	+	0.711282i
$69$	1.00000			0.120386
$70$	−5.63608	−	8.41621i	−0.673640	−	1.00593i
$71$	11.9443			1.41753			0.708766	−	0.705444i	$-0.249252\pi$
$71$	11.9443			1.41753			0.708766	+	0.705444i	$0.249252\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	1.10979	−	1.92221i	0.129891	−	0.224978i	−0.793743	−	0.608253i	$-0.791871\pi$
$73$	1.10979	−	1.92221i	0.129891	−	0.224978i	0.923634	+	0.383275i	$0.125204\pi$
$74$	4.02629	−	6.97373i	0.468046	−	0.810680i
$75$	−4.82843	−	8.36308i	−0.557539	−	0.965685i
$76$	4.16391			0.477633
$77$	−7.52017	−	11.2297i	−0.857003	−	1.27974i
$78$	0.0556701			0.00630340
$79$	1.47216	+	2.54986i	0.165631	+	0.286882i	0.936879	−	0.349653i	$-0.113700\pi$
$79$	1.47216	+	2.54986i	0.165631	+	0.286882i	−0.771248	+	0.636535i	$0.780367\pi$
$80$	1.91421	−	3.31552i	0.214016	−	0.370686i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.08196	+	3.60605i	0.229914	+	0.398222i
$83$	−14.7651			−1.62068			−0.810340	−	0.585960i	$-0.800718\pi$
$83$	−14.7651			−1.62068			−0.810340	+	0.585960i	$0.800718\pi$
$84$	−2.63991	+	0.175759i	−0.288037	+	0.0191768i
$85$	25.9290			2.81240
$86$	−6.27981	−	10.8770i	−0.677170	−	1.17289i
$87$	−1.47216	+	2.54986i	−0.157833	+	0.273374i
$88$	2.55412	−	4.42387i	0.272270	−	0.471586i
$89$	−1.19786	−	2.07475i	−0.126973	−	0.219923i	0.795530	−	0.605915i	$-0.207193\pi$
$89$	−1.19786	−	2.07475i	−0.126973	−	0.219923i	−0.922502	+	0.385991i	$0.873859\pi$
$90$	−3.82843			−0.403552
$91$	0.0650084	−	0.132167i	0.00681473	−	0.0138548i
$92$	1.00000			0.104257
$93$	1.60979	+	2.78824i	0.166928	+	0.289127i
$94$	−5.99845	+	10.3896i	−0.618693	+	1.07161i
$95$	7.97062	−	13.8055i	0.817768	−	1.41642i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	4.60118			0.467179			0.233590	−	0.972335i	$-0.424953\pi$
$97$	4.60118			0.467179			0.233590	+	0.972335i	$0.424953\pi$
$98$	−2.66546	+	6.47266i	−0.269252	+	0.653837i
$99$	−5.10824			−0.513398
$100$	−4.82843	−	8.36308i	−0.482843	−	0.836308i
$101$	7.44373	−	12.8929i	0.740678	−	1.28289i	−0.211508	−	0.977376i	$-0.567838\pi$
$101$	7.44373	−	12.8929i	0.740678	−	1.28289i	0.952187	−	0.305516i	$-0.0988291\pi$
$102$	3.38638	−	5.86538i	0.335301	−	0.580759i
$103$	−3.07718	−	5.32983i	−0.303204	−	0.525164i	0.673656	−	0.739045i	$-0.264723\pi$
$103$	−3.07718	−	5.32983i	−0.303204	−	0.525164i	−0.976860	+	0.213881i	$0.931390\pi$
$104$	0.0556701			0.00545891
$105$	−4.47062	+	9.08909i	−0.436287	+	0.887004i
$106$	5.71709			0.555293
$107$	−2.06118	−	3.57006i	−0.199262	−	0.345131i	0.749028	−	0.662539i	$-0.230521\pi$
$107$	−2.06118	−	3.57006i	−0.199262	−	0.345131i	−0.948289	+	0.317408i	$0.897188\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−10.0480	+	17.4037i	−0.962425	+	1.66697i	−0.246044	+	0.969259i	$0.579131\pi$
$109$	−10.0480	+	17.4037i	−0.962425	+	1.66697i	−0.716381	+	0.697710i	$0.754203\pi$
$110$	−9.77826	−	16.9365i	−0.932321	−	1.61483i
$111$	−8.05257			−0.764316
$112$	−2.63991	+	0.175759i	−0.249448	+	0.0166076i
$113$	−5.33238			−0.501629			−0.250814	−	0.968035i	$-0.580698\pi$
$113$	−5.33238			−0.501629			−0.250814	+	0.968035i	$0.580698\pi$
$114$	−2.08196	−	3.60605i	−0.194993	−	0.337738i
$115$	1.91421	−	3.31552i	0.178501	−	0.309173i
$116$	−1.47216	+	2.54986i	−0.136687	+	0.236749i
$117$	−0.0278351	−	0.0482117i	−0.00257335	−	0.00445718i
$118$	8.60118			0.791803
$119$	−9.97062	−	14.8889i	−0.914005	−	1.36486i
$120$	−3.82843			−0.349486
$121$	−7.54706	−	13.0719i	−0.686097	−	1.18835i
$122$	2.88866	−	5.00331i	0.261527	−	0.452978i
$123$	2.08196	−	3.60605i	0.187724	−	0.325147i
$124$	1.60979	+	2.78824i	0.144563	+	0.250391i
$125$	−17.8284			−1.59462
$126$	1.47216	+	2.19835i	0.131151	+	0.195844i
$127$	8.54861			0.758567			0.379283	−	0.925281i	$-0.376171\pi$
$127$	8.54861			0.758567			0.379283	+	0.925281i	$0.376171\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−6.27981	+	10.8770i	−0.552907	+	0.957663i
$130$	0.106565	−	0.184575i	0.00934633	−	0.0161883i
$131$	3.47062	+	6.01128i	0.303229	+	0.525208i	0.976865	−	0.213855i	$-0.0686019\pi$
$131$	3.47062	+	6.01128i	0.303229	+	0.525208i	−0.673636	+	0.739063i	$0.735269\pi$
$132$	−5.10824			−0.444615
$133$	−10.9923	+	0.731843i	−0.953157	+	0.0634589i
$134$	12.1544			1.04998
$135$	1.91421	+	3.31552i	0.164749	+	0.285354i
$136$	3.38638	−	5.86538i	0.290380	−	0.502952i
$137$	−2.63991	+	4.57245i	−0.225542	+	0.390651i	−0.956482	−	0.291791i	$-0.905749\pi$
$137$	−2.63991	+	4.57245i	−0.225542	+	0.390651i	0.730940	+	0.682442i	$0.239082\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	9.31371			0.789978			0.394989	−	0.918686i	$-0.370748\pi$
$139$	9.31371			0.789978			0.394989	+	0.918686i	$0.370748\pi$
$140$	−4.47062	+	9.08909i	−0.377836	+	0.768168i
$141$	11.9969			1.01032
$142$	−5.97216	−	10.3441i	−0.501173	−	0.868057i
$143$	0.142188	−	0.246277i	0.0118904	−	0.0205947i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	5.63608	+	9.76197i	0.468051	+	0.810688i
$146$	−2.21958			−0.183694
$147$	6.93822	−	0.927973i	0.572255	−	0.0765379i
$148$	−8.05257			−0.661917
$149$	5.85949	+	10.1489i	0.480028	+	0.831433i	0.999738	−	0.0229102i	$-0.00729317\pi$
$149$	5.85949	+	10.1489i	0.480028	+	0.831433i	−0.519710	+	0.854343i	$0.673960\pi$
$150$	−4.82843	+	8.36308i	−0.394239	+	0.682843i
$151$	−8.77826	+	15.2044i	−0.714365	+	1.23732i	0.248839	+	0.968545i	$0.419951\pi$
$151$	−8.77826	+	15.2044i	−0.714365	+	1.23732i	−0.963204	+	0.268772i	$0.913382\pi$
$152$	−2.08196	−	3.60605i	−0.168869	−	0.292490i
$153$	−6.77276			−0.547545
$154$	−5.96511	+	12.1275i	−0.480682	+	0.977262i
$155$	12.3259			0.990043
$156$	−0.0278351	−	0.0482117i	−0.00222859	−	0.00386003i
$157$	4.57946	−	7.93186i	0.365481	−	0.633031i	−0.623372	−	0.781925i	$-0.714238\pi$
$157$	4.57946	−	7.93186i	0.365481	−	0.633031i	0.988853	+	0.148894i	$0.0475713\pi$
$158$	1.47216	−	2.54986i	0.117119	−	0.202856i
$159$	−2.85854	−	4.95114i	−0.226697	−	0.392651i
$160$	−3.82843			−0.302664
$161$	−2.63991	+	0.175759i	−0.208054	+	0.0138517i
$162$	1.00000			0.0785674
$163$	6.08652	+	10.5422i	0.476733	+	0.825726i	0.999645	−	0.0266613i	$-0.00848756\pi$
$163$	6.08652	+	10.5422i	0.476733	+	0.825726i	−0.522912	+	0.852387i	$0.675154\pi$
$164$	2.08196	−	3.60605i	0.162573	−	0.281585i
$165$	−9.77826	+	16.9365i	−0.761237	+	1.31850i
$166$	7.38255	+	12.7869i	0.572997	+	0.992460i
$167$	21.0788			1.63113			0.815563	−	0.578668i	$-0.196427\pi$
$167$	21.0788			1.63113			0.815563	+	0.578668i	$0.196427\pi$
$168$	1.47216	+	2.19835i	0.113580	+	0.169606i
$169$	−12.9969			−0.999762
$170$	−12.9645	−	22.4552i	−0.994332	−	1.72223i
$171$	−2.08196	+	3.60605i	−0.159211	+	0.275762i
$172$	−6.27981	+	10.8770i	−0.478831	+	0.829360i
$173$	−6.71252	−	11.6264i	−0.510344	−	0.883941i	−0.999928	−	0.0119854i	$-0.996185\pi$
$173$	−6.71252	−	11.6264i	−0.510344	−	0.883941i	0.489584	−	0.871956i	$-0.337149\pi$
$174$	2.94433			0.223209
$175$	14.2165	+	21.2291i	1.07467	+	1.60477i
$176$	−5.10824			−0.385048
$177$	−4.30059	−	7.44884i	−0.323252	−	0.559889i
$178$	−1.19786	+	2.07475i	−0.0897833	+	0.155509i
$179$	−0.998450	+	1.72937i	−0.0746277	+	0.129259i	−0.900924	−	0.433976i	$-0.857110\pi$
$179$	−0.998450	+	1.72937i	−0.0746277	+	0.129259i	0.826297	+	0.563235i	$0.190444\pi$
$180$	1.91421	+	3.31552i	0.142677	+	0.247124i
$181$	20.5443			1.52705			0.763523	−	0.645781i	$-0.223468\pi$
$181$	20.5443			1.52705			0.763523	+	0.645781i	$0.223468\pi$
$182$	−0.146964	+	0.00978451i	−0.0108937	+	0.000725276i
$183$	−5.77732			−0.427072
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	−15.4143	+	26.6984i	−1.13328	+	1.96291i
$186$	1.60979	−	2.78824i	0.118036	−	0.204444i
$187$	−17.2984	−	29.9618i	−1.26499	−	2.19102i
$188$	11.9969			0.874964
$189$	1.16774	−	2.37411i	0.0849407	−	0.172691i
$190$	−15.9412			−1.15650
$191$	0.973715	+	1.68652i	0.0704555	+	0.122033i	0.899101	−	0.437741i	$-0.144221\pi$
$191$	0.973715	+	1.68652i	0.0704555	+	0.122033i	−0.828646	+	0.559774i	$0.810888\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−2.22019	+	3.84547i	−0.159812	+	0.276803i	−0.934801	−	0.355172i	$-0.884422\pi$
$193$	−2.22019	+	3.84547i	−0.159812	+	0.276803i	0.774988	+	0.631975i	$0.217756\pi$
$194$	−2.30059	−	3.98474i	−0.165173	−	0.286088i
$195$	−0.213129			−0.0152625
$196$	6.93822	−	0.927973i	0.495587	−	0.0662838i
$197$	−15.7620			−1.12300			−0.561498	−	0.827478i	$-0.689775\pi$
$197$	−15.7620			−1.12300			−0.561498	+	0.827478i	$0.689775\pi$
$198$	2.55412	+	4.42387i	0.181513	+	0.314391i
$199$	−9.93667	+	17.2108i	−0.704392	+	1.22004i	0.262519	+	0.964927i	$0.415447\pi$
$199$	−9.93667	+	17.2108i	−0.704392	+	1.22004i	−0.966911	+	0.255115i	$0.917887\pi$
$200$	−4.82843	+	8.36308i	−0.341421	+	0.591359i
$201$	−6.07718	−	10.5260i	−0.428651	−	0.742446i
$202$	−14.8875			−1.04748
$203$	3.43822	−	6.99015i	0.241316	−	0.490612i
$204$	−6.77276			−0.474188
$205$	−7.97062	−	13.8055i	−0.556692	−	0.964219i
$206$	−3.07718	+	5.32983i	−0.214397	+	0.371347i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	−0.0278351	−	0.0482117i	−0.00193001	−	0.00334288i
$209$	−21.2703			−1.47129
$210$	10.1067	−	0.672879i	0.697428	−	0.0464331i
$211$	−10.6427			−0.732676			−0.366338	−	0.930482i	$-0.619389\pi$
$211$	−10.6427			−0.732676			−0.366338	+	0.930482i	$0.619389\pi$
$212$	−2.85854	−	4.95114i	−0.196326	−	0.340046i
$213$	−5.97216	+	10.3441i	−0.409206	+	0.708766i
$214$	−2.06118	+	3.57006i	−0.140899	+	0.244045i
$215$	24.0418	+	41.6416i	1.63964	+	2.83994i
$216$	1.00000			0.0680414
$217$	−4.73975	−	7.07776i	−0.321756	−	0.480469i
$218$	20.0960			1.36107
$219$	1.10979	+	1.92221i	0.0749927	+	0.129891i
$220$	−9.77826	+	16.9365i	−0.659250	+	1.14186i
$221$	0.188520	−	0.326526i	0.0126812	−	0.0219645i
$222$	4.02629	+	6.97373i	0.270227	+	0.468046i
$223$	−28.5424			−1.91134			−0.955671	−	0.294438i	$-0.904868\pi$
$223$	−28.5424			−1.91134			−0.955671	+	0.294438i	$0.904868\pi$
$224$	1.47216	+	2.19835i	0.0983632	+	0.146883i
$225$	9.65685			0.643790
$226$	2.66619	+	4.61798i	0.177352	+	0.307184i
$227$	1.84160	−	3.18974i	0.122231	−	0.211710i	−0.798416	−	0.602106i	$-0.794328\pi$
$227$	1.84160	−	3.18974i	0.122231	−	0.211710i	0.920647	+	0.390396i	$0.127662\pi$
$228$	−2.08196	+	3.60605i	−0.137881	+	0.238817i
$229$	6.08196	+	10.5343i	0.401907	+	0.696123i	0.993956	−	0.109779i	$-0.0350142\pi$
$229$	6.08196	+	10.5343i	0.401907	+	0.696123i	−0.592049	+	0.805902i	$0.701681\pi$
$230$	−3.82843			−0.252439
$231$	13.4853	−	0.897817i	0.887266	−	0.0590721i
$232$	2.94433			0.193305
$233$	0.746472	+	1.29293i	0.0489030	+	0.0847024i	0.889441	−	0.457051i	$-0.151094\pi$
$233$	0.746472	+	1.29293i	0.0489030	+	0.0847024i	−0.840538	+	0.541753i	$0.817761\pi$
$234$	−0.0278351	+	0.0482117i	−0.00181964	+	0.00315170i
$235$	22.9646	−	39.7759i	1.49805	−	2.59469i
$236$	−4.30059	−	7.44884i	−0.279945	−	0.484878i
$237$	−2.94433			−0.191255
$238$	−7.90883	+	16.0792i	−0.512654	+	1.04226i
$239$	25.1193			1.62483			0.812415	−	0.583080i	$-0.198153\pi$
$239$	25.1193			1.62483			0.812415	+	0.583080i	$0.198153\pi$
$240$	1.91421	+	3.31552i	0.123562	+	0.214016i
$241$	−5.92355	+	10.2599i	−0.381570	+	0.660898i	−0.991287	−	0.131721i	$-0.957950\pi$
$241$	−5.92355	+	10.2599i	−0.381570	+	0.660898i	0.609717	+	0.792619i	$0.291283\pi$
$242$	−7.54706	+	13.0719i	−0.485144	+	0.840293i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−5.77732			−0.369855
$245$	10.2045	−	24.7801i	0.651943	−	1.58314i
$246$	−4.16391			−0.265481
$247$	−0.115903	−	0.200749i	−0.00737471	−	0.0127734i
$248$	1.60979	−	2.78824i	0.102222	−	0.177053i
$249$	7.38255	−	12.7869i	0.467850	−	0.810340i
$250$	8.91421	+	15.4399i	0.563784	+	0.976503i
$251$	8.09413			0.510897			0.255448	−	0.966823i	$-0.417777\pi$
$251$	8.09413			0.510897			0.255448	+	0.966823i	$0.417777\pi$
$252$	1.16774	−	2.37411i	0.0735608	−	0.149555i
$253$	−5.10824			−0.321152
$254$	−4.27431	−	7.40332i	−0.268194	−	0.464525i
$255$	−12.9645	+	22.4552i	−0.811869	+	1.40620i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.970615	−	1.68116i	−0.0605453	−	0.104868i	0.834164	−	0.551517i	$-0.185951\pi$
$257$	−0.970615	−	1.68116i	−0.0605453	−	0.104868i	−0.894709	+	0.446649i	$0.852617\pi$
$258$	12.5596			0.781928
$259$	21.2580	−	1.41531i	1.32091	−	0.0879430i
$260$	−0.213129			−0.0132177
$261$	−1.47216	−	2.54986i	−0.0911247	−	0.157833i
$262$	3.47062	−	6.01128i	0.214415	−	0.371378i
$263$	14.6538	−	25.3810i	0.903589	−	1.56506i	0.0807894	−	0.996731i	$-0.474256\pi$
$263$	14.6538	−	25.3810i	0.903589	−	1.56506i	0.822800	−	0.568331i	$-0.192411\pi$
$264$	2.55412	+	4.42387i	0.157195	+	0.272270i
$265$	−21.8875			−1.34454
$266$	6.12996	+	9.15372i	0.375852	+	0.561251i
$267$	2.39572			0.146615
$268$	−6.07718	−	10.5260i	−0.371223	−	0.642977i
$269$	−1.31471	+	2.27714i	−0.0801590	+	0.138840i	−0.903318	−	0.428971i	$-0.858876\pi$
$269$	−1.31471	+	2.27714i	−0.0801590	+	0.138840i	0.823159	+	0.567811i	$0.192209\pi$
$270$	1.91421	−	3.31552i	0.116495	−	0.201776i
$271$	−1.60979	−	2.78824i	−0.0977878	−	0.169373i	0.812981	−	0.582290i	$-0.197843\pi$
$271$	−1.60979	−	2.78824i	−0.0977878	−	0.169373i	−0.910769	+	0.412917i	$0.864510\pi$
$272$	−6.77276			−0.410659
$273$	0.0819556	+	0.122382i	0.00496018	+	0.00740691i
$274$	5.27981			0.318965
$275$	24.6648	+	42.7206i	1.48734	+	2.57615i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	−7.38504	+	12.7913i	−0.443724	+	0.768553i	−0.997962	−	0.0638053i	$-0.979676\pi$
$277$	−7.38504	+	12.7913i	−0.443724	+	0.768553i	0.554238	+	0.832358i	$0.313010\pi$
$278$	−4.65685	−	8.06591i	−0.279300	−	0.483761i
$279$	−3.21958			−0.192751
$280$	10.1067	−	0.672879i	0.603990	−	0.0402122i
$281$	3.44992			0.205805			0.102903	−	0.994691i	$-0.467187\pi$
$281$	3.44992			0.205805			0.102903	+	0.994691i	$0.467187\pi$
$282$	−5.99845	−	10.3896i	−0.357203	−	0.618693i
$283$	−0.475996	+	0.824449i	−0.0282950	+	0.0490084i	−0.879826	−	0.475296i	$-0.842341\pi$
$283$	−0.475996	+	0.824449i	−0.0282950	+	0.0490084i	0.851531	+	0.524304i	$0.175674\pi$
$284$	−5.97216	+	10.3441i	−0.354383	+	0.613809i
$285$	7.97062	+	13.8055i	0.472139	+	0.817768i
$286$	−0.284376			−0.0168155
$287$	−4.86237	+	9.88557i	−0.287017	+	0.583527i
$288$	1.00000			0.0589256
$289$	−14.4351	−	25.0024i	−0.849125	−	1.47073i
$290$	5.63608	−	9.76197i	0.330962	−	0.573243i
$291$	−2.30059	+	3.98474i	−0.134863	+	0.233590i
$292$	1.10979	+	1.92221i	0.0649456	+	0.112489i
$293$	−14.5147			−0.847959			−0.423979	−	0.905672i	$-0.639367\pi$
$293$	−14.5147			−0.847959			−0.423979	+	0.905672i	$0.639367\pi$
$294$	−4.27276	−	5.54469i	−0.249192	−	0.323373i
$295$	−32.9290			−1.91720
$296$	4.02629	+	6.97373i	0.234023	+	0.405340i
$297$	2.55412	−	4.42387i	0.148205	−	0.256699i
$298$	5.85949	−	10.1489i	0.339431	−	0.587912i
$299$	−0.0278351	−	0.0482117i	−0.00160974	−	0.00278816i
$300$	9.65685			0.557539
$301$	14.6664	−	29.8179i	0.845358	−	1.71867i
$302$	17.5565			1.01026
$303$	7.44373	+	12.8929i	0.427631	+	0.740678i
$304$	−2.08196	+	3.60605i	−0.119408	+	0.206821i
$305$	−11.0590	+	19.1548i	−0.633238	+	1.09680i
$306$	3.38638	+	5.86538i	0.193586	+	0.335301i
$307$	17.2611			0.985145			0.492573	−	0.870271i	$-0.336057\pi$
$307$	17.2611			0.985145			0.492573	+	0.870271i	$0.336057\pi$
$308$	13.4853	−	0.897817i	0.768395	−	0.0511579i
$309$	6.15436			0.350109
$310$	−6.16297	−	10.6746i	−0.350033	−	0.606275i
$311$	−1.18529	+	2.05299i	−0.0672119	+	0.116414i	−0.897673	−	0.440662i	$-0.854744\pi$
$311$	−1.18529	+	2.05299i	−0.0672119	+	0.116414i	0.830461	+	0.557077i	$0.188077\pi$
$312$	−0.0278351	+	0.0482117i	−0.00157585	+	0.00272945i
$313$	2.91899	+	5.05584i	0.164991	+	0.285773i	0.936652	−	0.350261i	$-0.113907\pi$
$313$	2.91899	+	5.05584i	0.164991	+	0.285773i	−0.771661	+	0.636034i	$0.780574\pi$
$314$	−9.15892			−0.516868
$315$	−5.63608	−	8.41621i	−0.317557	−	0.474200i
$316$	−2.94433			−0.165631
$317$	−0.314706	−	0.545087i	−0.0176757	−	0.0306151i	0.857052	−	0.515229i	$-0.172293\pi$
$317$	−0.314706	−	0.545087i	−0.0176757	−	0.0306151i	−0.874728	+	0.484614i	$0.838960\pi$
$318$	−2.85854	+	4.95114i	−0.160299	+	0.277646i
$319$	7.52017	−	13.0253i	0.421049	−	0.729278i
$320$	1.91421	+	3.31552i	0.107008	+	0.185343i
$321$	4.12236			0.230087
$322$	1.47216	+	2.19835i	0.0820405	+	0.122509i
$323$	−28.2012			−1.56915
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−0.268799	+	0.465574i	−0.0149103	+	0.0258254i
$326$	6.08652	−	10.5422i	0.337101	−	0.583876i
$327$	−10.0480	−	17.4037i	−0.555656	−	0.962425i
$328$	−4.16391			−0.229914
$329$	−31.6707	+	2.10856i	−1.74606	+	0.116249i
$330$	19.5565			1.07655
$331$	−6.85015	−	11.8648i	−0.376518	−	0.652149i	0.614035	−	0.789279i	$-0.289545\pi$
$331$	−6.85015	−	11.8648i	−0.376518	−	0.652149i	−0.990553	+	0.137130i	$0.956212\pi$
$332$	7.38255	−	12.7869i	0.405170	−	0.701775i
$333$	4.02629	−	6.97373i	0.220639	−	0.382158i
$334$	−10.5394	−	18.2548i	−0.576690	−	0.998857i
$335$	−46.5321			−2.54232
$336$	1.16774	−	2.37411i	0.0637056	−	0.129518i
$337$	−19.8318			−1.08031			−0.540153	−	0.841567i	$-0.681634\pi$
$337$	−19.8318			−1.08031			−0.540153	+	0.841567i	$0.681634\pi$
$338$	6.49845	+	11.2556i	0.353469	+	0.612226i
$339$	2.66619	−	4.61798i	0.144808	−	0.250814i
$340$	−12.9645	+	22.4552i	−0.703099	+	1.21780i
$341$	−8.22320	−	14.2430i	−0.445311	−	0.771302i
$342$	4.16391			0.225159
$343$	−18.1532	+	3.66921i	−0.980178	+	0.198119i
$344$	12.5596			0.677170
$345$	1.91421	+	3.31552i	0.103058	+	0.178501i
$346$	−6.71252	+	11.6264i	−0.360868	+	0.625041i
$347$	−2.77887	+	4.81314i	−0.149178	+	0.258383i	−0.930924	−	0.365214i	$-0.880996\pi$
$347$	−2.77887	+	4.81314i	−0.149178	+	0.258383i	0.781746	+	0.623597i	$0.214329\pi$
$348$	−1.47216	−	2.54986i	−0.0789163	−	0.136687i
$349$	−15.5027			−0.829843			−0.414922	−	0.909857i	$-0.636191\pi$
$349$	−15.5027			−0.829843			−0.414922	+	0.909857i	$0.636191\pi$
$350$	11.2767	−	22.9264i	0.602766	−	1.22547i
$351$	0.0556701			0.00297145
$352$	2.55412	+	4.42387i	0.136135	+	0.235793i
$353$	−7.97062	+	13.8055i	−0.424233	+	0.734793i	−0.996348	−	0.0853799i	$-0.972790\pi$
$353$	−7.97062	+	13.8055i	−0.424233	+	0.734793i	0.572115	+	0.820173i	$0.306123\pi$
$354$	−4.30059	+	7.44884i	−0.228574	+	0.395902i
$355$	22.8640	+	39.6016i	1.21350	+	2.10184i
$356$	2.39572			0.126973
$357$	17.8794	−	1.19037i	0.946281	−	0.0630011i
$358$	1.99690			0.105539
$359$	−16.2024	−	28.0633i	−0.855128	−	1.48113i	−0.876526	−	0.481355i	$-0.840145\pi$
$359$	−16.2024	−	28.0633i	−0.855128	−	1.48113i	0.0213977	−	0.999771i	$-0.493188\pi$
$360$	1.91421	−	3.31552i	0.100888	−	0.174743i
$361$	0.830922	−	1.43920i	0.0437327	−	0.0757473i
$362$	−10.2722	−	17.7919i	−0.539892	−	0.935121i
$363$	15.0941			0.792236
$364$	0.0819556	+	0.122382i	0.00429564	+	0.00641457i
$365$	8.49751			0.444780
$366$	2.88866	+	5.00331i	0.150993	+	0.261527i
$367$	−5.43344	+	9.41100i	−0.283623	+	0.491250i	−0.972274	−	0.233843i	$-0.924870\pi$
$367$	−5.43344	+	9.41100i	−0.283623	+	0.491250i	0.688651	+	0.725093i	$0.258203\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	2.08196	+	3.60605i	0.108382	+	0.187724i
$370$	30.8287			1.60271
$371$	8.41649	+	12.5681i	0.436963	+	0.652505i
$372$	−3.21958			−0.166928
$373$	0.108241	+	0.187479i	0.00560451	+	0.00970730i	0.868814	−	0.495138i	$-0.164883\pi$
$373$	0.108241	+	0.187479i	0.00560451	+	0.00970730i	−0.863210	+	0.504846i	$0.831549\pi$
$374$	−17.2984	+	29.9618i	−0.894481	+	1.54929i
$375$	8.91421	−	15.4399i	0.460328	−	0.797311i
$376$	−5.99845	−	10.3896i	−0.309346	−	0.535804i
$377$	0.163911			0.00844186
$378$	−2.63991	+	0.175759i	−0.135782	+	0.00904005i
$379$	8.93667			0.459046			0.229523	−	0.973303i	$-0.426283\pi$
$379$	8.93667			0.459046			0.229523	+	0.973303i	$0.426283\pi$
$380$	7.97062	+	13.8055i	0.408884	+	0.708208i
$381$	−4.27431	+	7.40332i	−0.218979	+	0.379283i
$382$	0.973715	−	1.68652i	0.0498196	−	0.0862900i
$383$	−13.4143	−	23.2343i	−0.685441	−	1.18722i	−0.973298	−	0.229545i	$-0.926276\pi$
$383$	−13.4143	−	23.2343i	−0.685441	−	1.18722i	0.287857	−	0.957673i	$-0.407057\pi$
$384$	1.00000			0.0510310
$385$	22.8370	−	46.4293i	1.16388	−	2.36625i
$386$	4.44037			0.226009
$387$	−6.27981	−	10.8770i	−0.319221	−	0.552907i
$388$	−2.30059	+	3.98474i	−0.116795	+	0.202295i
$389$	1.83299	−	3.17483i	0.0929363	−	0.160970i	−0.815809	−	0.578321i	$-0.803708\pi$
$389$	1.83299	−	3.17483i	0.0929363	−	0.160970i	0.908745	+	0.417351i	$0.137041\pi$
$390$	0.106565	+	0.184575i	0.00539610	+	0.00934633i
$391$	−6.77276			−0.342513
$392$	−4.27276	−	5.54469i	−0.215807	−	0.280049i
$393$	−6.94123			−0.350139
$394$	7.88100	+	13.6503i	0.397039	+	0.687692i
$395$	−5.63608	+	9.76197i	−0.283582	+	0.491178i
$396$	2.55412	−	4.42387i	0.128349	−	0.222308i
$397$	−9.97862	−	17.2835i	−0.500812	−	0.867433i	−1.00000		0.000938384i	$-0.999701\pi$
$397$	−9.97862	−	17.2835i	−0.500812	−	0.867433i	0.499187	−	0.866494i	$-0.333632\pi$
$398$	19.8733			0.996160
$399$	4.86237	−	9.88557i	0.243423	−	0.494897i
$400$	9.65685			0.482843
$401$	−0.193083	−	0.334429i	−0.00964209	−	0.0167006i	0.861164	−	0.508327i	$-0.169736\pi$
$401$	−0.193083	−	0.334429i	−0.00964209	−	0.0167006i	−0.870806	+	0.491626i	$0.836403\pi$
$402$	−6.07718	+	10.5260i	−0.303102	+	0.524988i
$403$	0.0896173	−	0.155222i	0.00446415	−	0.00773214i
$404$	7.44373	+	12.8929i	0.370339	+	0.641446i
$405$	−3.82843			−0.190236
$406$	−7.77276	+	0.517491i	−0.385755	+	0.0256827i
$407$	41.1345			2.03896
$408$	3.38638	+	5.86538i	0.167651	+	0.290380i
$409$	7.76570	−	13.4506i	0.383989	−	0.665089i	−0.607639	−	0.794213i	$-0.707883\pi$
$409$	7.76570	−	13.4506i	0.383989	−	0.665089i	0.991628	+	0.129124i	$0.0412167\pi$
$410$	−7.97062	+	13.8055i	−0.393641	+	0.681806i
$411$	−2.63991	−	4.57245i	−0.130217	−	0.225542i
$412$	6.15436			0.303204
$413$	12.6624	+	18.9084i	0.623074	+	0.930421i
$414$	1.00000			0.0491473
$415$	−28.2635	−	48.9539i	−1.38740	−	2.40305i
$416$	−0.0278351	+	0.0482117i	−0.00136473	+	0.00236378i
$417$	−4.65685	+	8.06591i	−0.228047	+	0.394989i
$418$	10.6351	+	18.4206i	0.520181	+	0.900980i
$419$	0.559628			0.0273396			0.0136698	−	0.999907i	$-0.495649\pi$
$419$	0.559628			0.0273396			0.0136698	+	0.999907i	$0.495649\pi$
$420$	−5.63608	−	8.41621i	−0.275012	−	0.410669i
$421$	17.2024			0.838392			0.419196	−	0.907896i	$-0.362312\pi$
$421$	17.2024			0.838392			0.419196	+	0.907896i	$0.362312\pi$
$422$	5.32137	+	9.21688i	0.259040	+	0.448671i
$423$	−5.99845	+	10.3896i	−0.291655	+	0.505161i
$424$	−2.85854	+	4.95114i	−0.138823	+	0.240449i
$425$	32.7018	+	56.6411i	1.58627	+	2.74750i
$426$	11.9443			0.578705
$427$	15.2516	−	1.01541i	0.738076	−	0.0491393i
$428$	4.12236			0.199262
$429$	0.142188	+	0.246277i	0.00686491	+	0.0118904i
$430$	24.0418	−	41.6416i	1.15940	−	2.00814i
$431$	−9.42505	+	16.3247i	−0.453989	+	0.786331i	−0.998629	−	0.0523381i	$-0.983333\pi$
$431$	−9.42505	+	16.3247i	−0.453989	+	0.786331i	0.544641	+	0.838669i	$0.316666\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	0.435383			0.0209232			0.0104616	−	0.999945i	$-0.496670\pi$
$433$	0.435383			0.0209232			0.0104616	+	0.999945i	$0.496670\pi$
$434$	−3.75964	+	7.64363i	−0.180469	+	0.366906i
$435$	−11.2722			−0.540458
$436$	−10.0480	−	17.4037i	−0.481212	−	0.833484i
$437$	−2.08196	+	3.60605i	−0.0995934	+	0.172501i
$438$	1.10979	−	1.92221i	0.0530278	−	0.0918469i
$439$	17.0024	+	29.4490i	0.811481	+	1.40553i	0.911828	+	0.410573i	$0.134671\pi$
$439$	17.0024	+	29.4490i	0.811481	+	1.40553i	−0.100347	+	0.994953i	$0.531995\pi$
$440$	19.5565			0.932321
$441$	−2.66546	+	6.47266i	−0.126927	+	0.308222i
$442$	−0.377040			−0.0179340
$443$	−8.47062	−	14.6715i	−0.402451	−	0.697066i	0.591570	−	0.806254i	$-0.298508\pi$
$443$	−8.47062	−	14.6715i	−0.402451	−	0.697066i	−0.994021	+	0.109188i	$0.965175\pi$
$444$	4.02629	−	6.97373i	0.191079	−	0.330959i
$445$	4.58591	−	7.94304i	0.217393	−	0.376536i
$446$	14.2712	+	24.7185i	0.675761	+	1.17045i
$447$	−11.7190			−0.554289
$448$	1.16774	−	2.37411i	0.0551706	−	0.112166i
$449$	5.28937			0.249621			0.124810	−	0.992181i	$-0.460168\pi$
$449$	5.28937			0.249621			0.124810	+	0.992181i	$0.460168\pi$
$450$	−4.82843	−	8.36308i	−0.227614	−	0.394239i
$451$	−10.6351	+	18.4206i	−0.500789	+	0.867392i
$452$	2.66619	−	4.61798i	0.125407	−	0.217212i
$453$	−8.77826	−	15.2044i	−0.412439	−	0.714365i
$454$	−3.68319			−0.172861
$455$	0.562641	−	0.0374593i	0.0263770	−	0.00175612i
$456$	4.16391			0.194993
$457$	−3.47862	−	6.02514i	−0.162723	−	0.281844i	0.773121	−	0.634258i	$-0.218694\pi$
$457$	−3.47862	−	6.02514i	−0.162723	−	0.281844i	−0.935844	+	0.352414i	$0.885361\pi$
$458$	6.08196	−	10.5343i	0.284191	−	0.492233i
$459$	3.38638	−	5.86538i	0.158063	−	0.273772i
$460$	1.91421	+	3.31552i	0.0892507	+	0.154587i
$461$	6.65564			0.309984			0.154992	−	0.987916i	$-0.450465\pi$
$461$	6.65564			0.309984			0.154992	+	0.987916i	$0.450465\pi$
$462$	−7.52017	−	11.2297i	−0.349870	−	0.522452i
$463$	19.8604			0.922993			0.461496	−	0.887142i	$-0.347313\pi$
$463$	19.8604			0.922993			0.461496	+	0.887142i	$0.347313\pi$
$464$	−1.47216	−	2.54986i	−0.0683435	−	0.118374i
$465$	−6.16297	+	10.6746i	−0.285801	+	0.495021i
$466$	0.746472	−	1.29293i	0.0345796	−	0.0598937i
$467$	−9.27215	−	16.0598i	−0.429064	−	0.743161i	0.567726	−	0.823217i	$-0.307823\pi$
$467$	−9.27215	−	16.0598i	−0.429064	−	0.743161i	−0.996790	+	0.0800567i	$0.974490\pi$
$468$	0.0556701			0.00257335
$469$	17.8932	+	26.7195i	0.826232	+	1.23379i
$470$	−45.9293			−2.11856
$471$	4.57946	+	7.93186i	0.211010	+	0.365481i
$472$	−4.30059	+	7.44884i	−0.197951	+	0.342861i
$473$	32.0788	−	55.5621i	1.47498	−	2.55475i
$474$	1.47216	+	2.54986i	0.0676188	+	0.117119i
$475$	40.2103			1.84497
$476$	17.8794	−	1.19037i	0.819503	−	0.0545605i
$477$	5.71709			0.261767
$478$	−12.5596	−	21.7539i	−0.574464	−	0.995001i
$479$	−4.64158	+	8.03946i	−0.212079	+	0.367332i	−0.952365	−	0.304960i	$-0.901357\pi$
$479$	−4.64158	+	8.03946i	−0.212079	+	0.367332i	0.740286	+	0.672292i	$0.234690\pi$
$480$	1.91421	−	3.31552i	0.0873715	−	0.151332i
$481$	0.224144	+	0.388229i	0.0102201	+	0.0177017i
$482$	11.8471			0.539621
$483$	1.16774	−	2.37411i	0.0531341	−	0.108026i
$484$	15.0941			0.686097
$485$	8.80765	+	15.2553i	0.399935	+	0.692707i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−4.93116	+	8.54102i	−0.223452	+	0.387031i	−0.955854	−	0.293842i	$-0.905066\pi$
$487$	−4.93116	+	8.54102i	−0.223452	+	0.387031i	0.732402	+	0.680873i	$0.238399\pi$
$488$	2.88866	+	5.00331i	0.130763	+	0.226489i
$489$	−12.1730			−0.550484
$490$	−26.5625	+	3.55268i	−1.19997	+	0.160494i
$491$	−41.3368			−1.86551			−0.932753	−	0.360517i	$-0.882600\pi$
$491$	−41.3368			−1.86551			−0.932753	+	0.360517i	$0.882600\pi$
$492$	2.08196	+	3.60605i	0.0938618	+	0.162573i
$493$	9.97062	−	17.2696i	0.449054	−	0.777784i
$494$	−0.115903	+	0.200749i	−0.00521471	+	0.00903214i
$495$	−9.77826	−	16.9365i	−0.439500	−	0.761237i
$496$	−3.21958			−0.144563
$497$	13.9479	−	28.3571i	0.625649	−	1.27199i
$498$	−14.7651			−0.661640
$499$	2.22724	+	3.85770i	0.0997051	+	0.172694i	0.911563	−	0.411161i	$-0.134877\pi$
$499$	2.22724	+	3.85770i	0.0997051	+	0.172694i	−0.811857	+	0.583856i	$0.801543\pi$
$500$	8.91421	−	15.4399i	0.398656	−	0.690492i
$501$	−10.5394	+	18.2548i	−0.470866	+	0.815563i
$502$	−4.04706	−	7.00972i	−0.180629	−	0.312859i
$503$	−9.67596			−0.431430			−0.215715	−	0.976456i	$-0.569208\pi$
$503$	−9.67596			−0.431430			−0.215715	+	0.976456i	$0.569208\pi$
$504$	−2.63991	+	0.175759i	−0.117591	+	0.00782891i
$505$	56.9955			2.53627
$506$	2.55412	+	4.42387i	0.113545	+	0.196665i
$507$	6.49845	−	11.2556i	0.288606	−	0.499881i
$508$	−4.27431	+	7.40332i	−0.189642	+	0.328469i
$509$	−2.29293	−	3.97147i	−0.101632	−	0.176032i	0.810725	−	0.585427i	$-0.199073\pi$
$509$	−2.29293	−	3.97147i	−0.101632	−	0.176032i	−0.912357	+	0.409395i	$0.865740\pi$
$510$	25.9290			1.14816
$511$	−3.26759	−	4.87941i	−0.144550	−	0.215852i
$512$	1.00000			0.0441942
$513$	−2.08196	−	3.60605i	−0.0919206	−	0.159211i
$514$	−0.970615	+	1.68116i	−0.0428120	+	0.0741526i
$515$	11.7808	−	20.4049i	0.519122	−	0.899146i
$516$	−6.27981	−	10.8770i	−0.276453	−	0.478831i
$517$	−61.2831			−2.69523
$518$	−11.8547	−	17.7023i	−0.520866	−	0.777796i
$519$	13.4250			0.589294
$520$	0.106565	+	0.184575i	0.00467316	+	0.00809416i
$521$	11.4652	−	19.8584i	0.502301	−	0.870011i	−0.497695	−	0.867352i	$-0.665820\pi$
$521$	11.4652	−	19.8584i	0.502301	−	0.870011i	0.999996	−	0.00265908i	$-0.000846412\pi$
$522$	−1.47216	+	2.54986i	−0.0644349	+	0.111605i
$523$	−1.52857	−	2.64756i	−0.0668396	−	0.115770i	0.830669	−	0.556767i	$-0.187958\pi$
$523$	−1.52857	−	2.64756i	−0.0668396	−	0.115770i	−0.897509	+	0.440997i	$0.854625\pi$
$524$	−6.94123			−0.303229
$525$	−25.4932	+	1.69728i	−1.11261	+	0.0740752i
$526$	−29.3075			−1.27787
$527$	−10.9027	−	18.8841i	−0.474930	−	0.822603i
$528$	2.55412	−	4.42387i	0.111154	−	0.192524i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	10.9437	+	18.9551i	0.475365	+	0.823356i
$531$	8.60118			0.373260
$532$	4.86237	−	9.88557i	0.210811	−	0.428594i
$533$	−0.231805			−0.0100406
$534$	−1.19786	−	2.07475i	−0.0518364	−	0.0897833i
$535$	7.89107	−	13.6677i	0.341161	−	0.590908i
$536$	−6.07718	+	10.5260i	−0.262494	+	0.454653i
$537$	−0.998450	−	1.72937i	−0.0430863	−	0.0746277i
$538$	2.62941			0.113362
$539$	−35.4421	+	4.74031i	−1.52660	+	0.204180i
$540$	−3.82843			−0.164749
$541$	19.6675	+	34.0651i	0.845571	+	1.46457i	0.885125	+	0.465354i	$0.154073\pi$
$541$	19.6675	+	34.0651i	0.845571	+	1.46457i	−0.0395537	+	0.999217i	$0.512594\pi$
$542$	−1.60979	+	2.78824i	−0.0691464	+	0.119765i
$543$	−10.2722	+	17.7919i	−0.440820	+	0.763523i
$544$	3.38638	+	5.86538i	0.145190	+	0.251476i
$545$	−76.9361			−3.29558
$546$	0.0650084	−	0.132167i	0.00278210	−	0.00565622i
$547$	−12.4019			−0.530268			−0.265134	−	0.964212i	$-0.585416\pi$
$547$	−12.4019			−0.530268			−0.265134	+	0.964212i	$0.585416\pi$
$548$	−2.63991	−	4.57245i	−0.112771	−	0.195326i
$549$	2.88866	−	5.00331i	0.123285	−	0.213536i
$550$	24.6648	−	42.7206i	1.05171	−	1.82161i
$551$	−6.12996	−	10.6174i	−0.261145	−	0.452317i
$552$	1.00000			0.0425628
$553$	7.77276	−	0.517491i	0.330531	−	0.0220060i
$554$	14.7701			0.627521
$555$	−15.4143	−	26.6984i	−0.654302	−	1.13328i
$556$	−4.65685	+	8.06591i	−0.197495	+	0.342071i
$557$	15.5419	−	26.9194i	0.658531	−	1.14061i	−0.322465	−	0.946581i	$-0.604511\pi$
$557$	15.5419	−	26.9194i	0.658531	−	1.14061i	0.980996	−	0.194028i	$-0.0621553\pi$
$558$	1.60979	+	2.78824i	0.0681479	+	0.118036i
$559$	0.699196			0.0295728
$560$	−5.63608	−	8.41621i	−0.238168	−	0.355650i
$561$	34.5969			1.46068
$562$	−1.72496	−	2.98772i	−0.0727631	−	0.126029i
$563$	17.0951	−	29.6095i	0.720471	−	1.24789i	−0.240340	−	0.970689i	$-0.577259\pi$
$563$	17.0951	−	29.6095i	0.720471	−	1.24789i	0.960811	−	0.277204i	$-0.0894078\pi$
$564$	−5.99845	+	10.3896i	−0.252580	+	0.437482i
$565$	−10.2073	−	17.6796i	−0.429425	−	0.743786i
$566$	0.951992			0.0400152
$567$	1.47216	+	2.19835i	0.0618251	+	0.0923219i
$568$	11.9443			0.501173
$569$	19.2411	+	33.3265i	0.806629	+	1.39712i	0.915186	+	0.403031i	$0.132043\pi$
$569$	19.2411	+	33.3265i	0.806629	+	1.39712i	−0.108558	+	0.994090i	$0.534623\pi$
$570$	7.97062	−	13.8055i	0.333852	−	0.578249i
$571$	13.5407	−	23.4532i	0.566662	−	0.981488i	−0.430231	−	0.902719i	$-0.641568\pi$
$571$	13.5407	−	23.4532i	0.566662	−	0.981488i	0.996893	−	0.0787688i	$-0.0250989\pi$
$572$	0.142188	+	0.246277i	0.00594519	+	0.0102974i
$573$	−1.94743			−0.0813550
$574$	10.9923	−	0.731843i	0.458811	−	0.0305466i
$575$	9.65685			0.402719
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	4.16942	−	7.22164i	0.173575	−	0.300641i	−0.766092	−	0.642731i	$-0.777801\pi$
$577$	4.16942	−	7.22164i	0.173575	−	0.300641i	0.939667	+	0.342090i	$0.111135\pi$
$578$	−14.4351	+	25.0024i	−0.600422	+	1.03996i
$579$	−2.22019	−	3.84547i	−0.0922678	−	0.159812i
$580$	−11.2722			−0.468051
$581$	−17.2418	+	35.0539i	−0.715311	+	1.45428i
$582$	4.60118			0.190725
$583$	14.6021	+	25.2916i	0.604758	+	1.04747i
$584$	1.10979	−	1.92221i	0.0459235	−	0.0795418i
$585$	0.106565	−	0.184575i	0.00440590	−	0.00763124i
$586$	7.25736	+	12.5701i	0.299799	+	0.519267i
$587$	40.4714			1.67043			0.835217	−	0.549920i	$-0.185342\pi$
$587$	40.4714			1.67043			0.835217	+	0.549920i	$0.185342\pi$
$588$	−2.66546	+	6.47266i	−0.109922	+	0.266928i
$589$	−13.4061			−0.552387
$590$	16.4645	+	28.5174i	0.677833	+	1.17404i
$591$	7.88100	−	13.6503i	0.324181	−	0.561498i
$592$	4.02629	−	6.97373i	0.165479	−	0.286619i
$593$	15.1685	+	26.2726i	0.622895	+	1.07889i	0.988944	+	0.148290i	$0.0473768\pi$
$593$	15.1685	+	26.2726i	0.622895	+	1.07889i	−0.366049	+	0.930595i	$0.619290\pi$
$594$	−5.10824			−0.209594
$595$	30.2784	−	61.5582i	1.24129	−	2.52364i
$596$	−11.7190			−0.480028
$597$	−9.93667	−	17.2108i	−0.406681	−	0.704392i
$598$	−0.0278351	+	0.0482117i	−0.00113826	+	0.00197153i
$599$	3.39721	−	5.88415i	0.138806	−	0.240420i	−0.788239	−	0.615370i	$-0.789007\pi$
$599$	3.39721	−	5.88415i	0.138806	−	0.240420i	0.927045	+	0.374950i	$0.122340\pi$
$600$	−4.82843	−	8.36308i	−0.197120	−	0.341421i
$601$	21.0251			0.857633			0.428816	−	0.903392i	$-0.358931\pi$
$601$	21.0251			0.857633			0.428816	+	0.903392i	$0.358931\pi$
$602$	−33.1562	+	2.20746i	−1.35135	+	0.0899695i
$603$	12.1544			0.494964
$604$	−8.77826	−	15.2044i	−0.357183	−	0.618658i
$605$	28.8934	−	50.0448i	1.17468	−	2.03461i
$606$	7.44373	−	12.8929i	0.302381	−	0.523739i
$607$	−1.21864	−	2.11074i	−0.0494629	−	0.0856723i	0.840234	−	0.542224i	$-0.182418\pi$
$607$	−1.21864	−	2.11074i	−0.0494629	−	0.0856723i	−0.889697	+	0.456552i	$0.849084\pi$
$608$	4.16391			0.168869
$609$	4.33454	+	6.47266i	0.175644	+	0.262285i
$610$	22.1180			0.895534
$611$	−0.333935	−	0.578392i	−0.0135095	−	0.0233992i
$612$	3.38638	−	5.86538i	0.136886	−	0.237094i
$613$	−2.15436	+	3.73146i	−0.0870138	+	0.150712i	−0.906248	−	0.422747i	$-0.861066\pi$
$613$	−2.15436	+	3.73146i	−0.0870138	+	0.150712i	0.819234	+	0.573460i	$0.194399\pi$
$614$	−8.63057	−	14.9486i	−0.348301	−	0.603276i
$615$	15.9412			0.642812
$616$	−7.52017	−	11.2297i	−0.302996	−	0.452457i
$617$	−12.0621			−0.485603			−0.242801	−	0.970076i	$-0.578066\pi$
$617$	−12.0621			−0.485603			−0.242801	+	0.970076i	$0.578066\pi$
$618$	−3.07718	−	5.32983i	−0.123782	−	0.214397i
$619$	−19.5472	+	33.8567i	−0.785668	+	1.36082i	0.142931	+	0.989733i	$0.454347\pi$
$619$	−19.5472	+	33.8567i	−0.785668	+	1.36082i	−0.928599	+	0.371084i	$0.878986\pi$
$620$	−6.16297	+	10.6746i	−0.247511	+	0.428701i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	2.37059			0.0950519
$623$	−6.32447	+	0.421068i	−0.253385	+	0.0168697i
$624$	0.0556701			0.00222859
$625$	−9.98528	−	17.2950i	−0.399411	−	0.691801i
$626$	2.91899	−	5.05584i	0.116666	−	0.202072i
$627$	10.6351	−	18.4206i	0.424726	−	0.735647i
$628$	4.57946	+	7.93186i	0.182740	+	0.316516i
$629$	54.5381			2.17458
$630$	−4.47062	+	9.08909i	−0.178114	+	0.362118i
$631$	13.1947			0.525273			0.262636	−	0.964895i	$-0.415408\pi$
$631$	13.1947			0.525273			0.262636	+	0.964895i	$0.415408\pi$
$632$	1.47216	+	2.54986i	0.0585596	+	0.101428i
$633$	5.32137	−	9.21688i	0.211505	−	0.366338i
$634$	−0.314706	+	0.545087i	−0.0124986	+	0.0216482i
$635$	16.3639	+	28.3431i	0.649380	+	1.12476i
$636$	5.71709			0.226697
$637$	−0.237865	−	0.308673i	−0.00942455	−	0.0122301i
$638$	−15.0403			−0.595453
$639$	−5.97216	−	10.3441i	−0.236255	−	0.409206i
$640$	1.91421	−	3.31552i	0.0756659	−	0.131057i
$641$	−22.2597	+	38.5550i	−0.879206	+	1.52283i	−0.0269920	+	0.999636i	$0.508593\pi$
$641$	−22.2597	+	38.5550i	−0.879206	+	1.52283i	−0.852214	+	0.523194i	$0.824740\pi$
$642$	−2.06118	−	3.57006i	−0.0813482	−	0.140899i
$643$	4.30348			0.169713			0.0848563	−	0.996393i	$-0.472957\pi$
$643$	4.30348			0.169713			0.0848563	+	0.996393i	$0.472957\pi$
$644$	1.16774	−	2.37411i	0.0460155	−	0.0935529i
$645$	−48.0836			−1.89329
$646$	14.1006	+	24.4229i	0.554780	+	0.960907i
$647$	−11.8189	+	20.4709i	−0.464648	+	0.804794i	−0.999186	−	0.0403508i	$-0.987152\pi$
$647$	−11.8189	+	20.4709i	−0.464648	+	0.804794i	0.534538	+	0.845145i	$0.320486\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	21.9685	+	38.0505i	0.862338	+	1.49361i
$650$	0.537598			0.0210863
$651$	8.49940	−	0.565869i	0.333118	−	0.0221782i
$652$	−12.1730			−0.476733
$653$	8.52017	+	14.7574i	0.333420	+	0.577501i	0.983180	−	0.182639i	$-0.0584639\pi$
$653$	8.52017	+	14.7574i	0.333420	+	0.577501i	−0.649760	+	0.760139i	$0.725131\pi$
$654$	−10.0480	+	17.4037i	−0.392908	+	0.680537i
$655$	−13.2870	+	23.0138i	−0.519166	+	0.899222i
$656$	2.08196	+	3.60605i	0.0812867	+	0.140793i
$657$	−2.21958			−0.0865941
$658$	17.6614	+	26.3734i	0.688514	+	1.02814i
$659$	0.998791			0.0389074			0.0194537	−	0.999811i	$-0.493807\pi$
$659$	0.998791			0.0389074			0.0194537	+	0.999811i	$0.493807\pi$
$660$	−9.77826	−	16.9365i	−0.380618	−	0.659250i
$661$	−13.1826	+	22.8329i	−0.512743	+	0.888097i	0.487148	+	0.873320i	$0.338037\pi$
$661$	−13.1826	+	22.8329i	−0.512743	+	0.888097i	−0.999891	+	0.0147777i	$0.995296\pi$
$662$	−6.85015	+	11.8648i	−0.266239	+	0.461139i
$663$	0.188520	+	0.326526i	0.00732152	+	0.0126812i
$664$	−14.7651			−0.572997
$665$	−23.4681	−	35.0444i	−0.910055	−	1.35896i
$666$	−8.05257			−0.312031
$667$	−1.47216	−	2.54986i	−0.0570025	−	0.0987311i
$668$	−10.5394	+	18.2548i	−0.407782	+	0.706299i
$669$	14.2712	−	24.7185i	0.551757	−	0.955671i
$670$	23.2660	+	40.2980i	0.898846	+	1.55685i
$671$	29.5119			1.13930
$672$	−2.63991	+	0.175759i	−0.101837	+	0.00678004i
$673$	−20.3388			−0.784005			−0.392002	−	0.919964i	$-0.628217\pi$
$673$	−20.3388			−0.784005			−0.392002	+	0.919964i	$0.628217\pi$
$674$	9.91589	+	17.1748i	0.381946	+	0.661550i
$675$	−4.82843	+	8.36308i	−0.185846	+	0.321895i
$676$	6.49845	−	11.2556i	0.249940	−	0.432909i
$677$	−15.2882	−	26.4799i	−0.587572	−	1.01770i	−0.994549	−	0.104266i	$-0.966751\pi$
$677$	−15.2882	−	26.4799i	−0.587572	−	1.01770i	0.406978	−	0.913438i	$-0.366583\pi$
$678$	−5.33238			−0.204789
$679$	5.37300	−	10.9237i	0.206197	−	0.419213i
$680$	25.9290			0.994332
$681$	1.84160	+	3.18974i	0.0705701	+	0.122231i
$682$	−8.22320	+	14.2430i	−0.314883	+	0.545393i
$683$	−20.0180	+	34.6722i	−0.765968	+	1.32670i	0.173765	+	0.984787i	$0.444407\pi$
$683$	−20.0180	+	34.6722i	−0.765968	+	1.32670i	−0.939733	+	0.341909i	$0.888927\pi$
$684$	−2.08196	−	3.60605i	−0.0796056	−	0.137881i
$685$	−20.2134			−0.772314
$686$	12.2542	+	13.8865i	0.467868	+	0.530188i
$687$	−12.1639			−0.464082
$688$	−6.27981	−	10.8770i	−0.239416	−	0.414680i
$689$	−0.159135	+	0.275631i	−0.00606258	+	0.0105007i
$690$	1.91421	−	3.31552i	0.0728729	−	0.126220i
$691$	−10.3431	−	17.9148i	−0.393470	−	0.681510i	0.599435	−	0.800424i	$-0.295392\pi$
$691$	−10.3431	−	17.9148i	−0.393470	−	0.681510i	−0.992905	+	0.118914i	$0.962059\pi$
$692$	13.4250			0.510344
$693$	−5.96511	+	12.1275i	−0.226596	+	0.460686i
$694$	5.55774			0.210969
$695$	17.8284	+	30.8797i	0.676271	+	1.17134i
$696$	−1.47216	+	2.54986i	−0.0558023	+	0.0966524i
$697$	−14.1006	+	24.4229i	−0.534098	+	0.925084i
$698$	7.75137	+	13.4258i	0.293394	+	0.508173i
$699$	−1.49294			−0.0564683
$700$	−25.4932	+	1.69728i	−0.963552	+	0.0641510i
$701$	−18.5954			−0.702339			−0.351170	−	0.936312i	$-0.614216\pi$
$701$	−18.5954			−0.702339			−0.351170	+	0.936312i	$0.614216\pi$
$702$	−0.0278351	−	0.0482117i	−0.00105057	−	0.00181964i
$703$	16.7651	−	29.0380i	0.632308	−	1.09519i
$704$	2.55412	−	4.42387i	0.0962620	−	0.166731i
$705$	22.9646	+	39.7759i	0.864898	+	1.49805i
$706$	15.9412			0.599956
$707$	−21.9168	−	32.7278i	−0.824265	−	1.23086i
$708$	8.60118			0.323252
$709$	9.94428	+	17.2240i	0.373465	+	0.646861i	0.990096	−	0.140392i	$-0.0448362\pi$
$709$	9.94428	+	17.2240i	0.373465	+	0.646861i	−0.616631	+	0.787252i	$0.711503\pi$
$710$	22.8640	−	39.6016i	0.858071	−	1.48622i
$711$	1.47216	−	2.54986i	0.0552105	−	0.0956274i
$712$	−1.19786	−	2.07475i	−0.0448916	−	0.0777546i
$713$	−3.21958			−0.120574
$714$	−9.97062	−	14.8889i	−0.373141	−	0.557202i
$715$	1.08871			0.0407156
$716$	−0.998450	−	1.72937i	−0.0373138	−	0.0646295i
$717$	−12.5596	+	21.7539i	−0.469048	+	0.812415i
$718$	−16.2024	+	28.0633i	−0.604667	+	1.04731i
$719$	14.2706	+	24.7174i	0.532204	+	0.921804i	0.999293	+	0.0375937i	$0.0119693\pi$
$719$	14.2706	+	24.7174i	0.532204	+	0.921804i	−0.467089	+	0.884210i	$0.654697\pi$
$720$	−3.82843			−0.142677
$721$	−16.2469	+	1.08168i	−0.605068	+	0.0402839i
$722$	−1.66184			−0.0618474
$723$	−5.92355	−	10.2599i	−0.220299	−	0.381570i
$724$	−10.2722	+	17.7919i	−0.381762	+	0.661230i
$725$	−14.2165	+	24.6237i	−0.527987	+	0.914500i
$726$	−7.54706	−	13.0719i	−0.280098	−	0.485144i
$727$	−24.4745			−0.907710			−0.453855	−	0.891076i	$-0.649952\pi$
$727$	−24.4745			−0.907710			−0.453855	+	0.891076i	$0.649952\pi$
$728$	0.0650084	−	0.132167i	0.00240937	−	0.00489843i
$729$	1.00000			0.0370370
$730$	−4.24875	−	7.35906i	−0.157253	−	0.272371i
$731$	42.5317	−	73.6670i	1.57309	−	2.72467i
$732$	2.88866	−	5.00331i	0.106768	−	0.184927i
$733$	−14.9584	−	25.9087i	−0.552501	−	0.956959i	−0.998093	−	0.0617235i	$-0.980340\pi$
$733$	−14.9584	−	25.9087i	−0.552501	−	0.956959i	0.445592	−	0.895236i	$-0.352993\pi$
$734$	10.8669			0.401104
$735$	16.3579	+	21.2274i	0.603372	+	0.782985i
$736$	1.00000			0.0368605
$737$	31.0437	+	53.7693i	1.14351	+	1.98062i
$738$	2.08196	−	3.60605i	0.0766378	−	0.132741i
$739$	−2.48984	+	4.31254i	−0.0915904	+	0.158639i	−0.908180	−	0.418579i	$-0.862528\pi$
$739$	−2.48984	+	4.31254i	−0.0915904	+	0.158639i	0.816590	+	0.577218i	$0.195862\pi$
$740$	−15.4143	−	26.6984i	−0.566642	−	0.981453i
$741$	0.231805			0.00851559
$742$	6.67608	−	13.5730i	0.245087	−	0.498279i
$743$	34.0502			1.24918			0.624589	−	0.780953i	$-0.285266\pi$
$743$	34.0502			1.24918			0.624589	+	0.780953i	$0.285266\pi$
$744$	1.60979	+	2.78824i	0.0590178	+	0.102222i
$745$	−22.4326	+	38.8544i	−0.821868	+	1.42352i
$746$	0.108241	−	0.187479i	0.00396299	−	0.00686410i
$747$	7.38255	+	12.7869i	0.270113	+	0.467850i
$748$	34.5969			1.26499
$749$	−10.8826	+	0.724539i	−0.397643	+	0.0264741i
$750$	−17.8284			−0.651002
$751$	22.9082	+	39.6782i	0.835933	+	1.44788i	0.893268	+	0.449524i	$0.148406\pi$
$751$	22.9082	+	39.6782i	0.835933	+	1.44788i	−0.0573353	+	0.998355i	$0.518260\pi$
$752$	−5.99845	+	10.3896i	−0.218741	+	0.378870i
$753$	−4.04706	+	7.00972i	−0.147483	+	0.255448i
$754$	−0.0819556	−	0.141951i	−0.00298465	−	0.00516956i
$755$	−67.2139			−2.44616
$756$	1.47216	+	2.19835i	0.0535421	+	0.0799531i
$757$	17.0256			0.618804			0.309402	−	0.950931i	$-0.399871\pi$
$757$	17.0256			0.618804			0.309402	+	0.950931i	$0.399871\pi$
$758$	−4.46833	−	7.73938i	−0.162297	−	0.281107i
$759$	2.55412	−	4.42387i	0.0927087	−	0.160576i
$760$	7.97062	−	13.8055i	0.289125	−	0.500779i
$761$	22.6480	+	39.2275i	0.820991	+	1.42200i	0.904945	+	0.425528i	$0.139912\pi$
$761$	22.6480	+	39.2275i	0.820991	+	1.42200i	−0.0839546	+	0.996470i	$0.526755\pi$
$762$	8.54861			0.309684
$763$	29.5847	+	44.1780i	1.07104	+	1.59935i
$764$	−1.94743			−0.0704555
$765$	−12.9645	−	22.4552i	−0.468733	−	0.811869i
$766$	−13.4143	+	23.2343i	−0.484680	+	0.839490i
$767$	−0.239415	+	0.414678i	−0.00864476	+	0.0149732i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	13.8318			0.498787			0.249393	−	0.968402i	$-0.419769\pi$
$769$	13.8318			0.498787			0.249393	+	0.968402i	$0.419769\pi$
$770$	−51.6274	+	3.43723i	−1.86052	+	0.123869i
$771$	1.94123			0.0699117
$772$	−2.22019	−	3.84547i	−0.0799062	−	0.138402i
$773$	−3.58734	+	6.21345i	−0.129028	+	0.223482i	−0.923300	−	0.384079i	$-0.874519\pi$
$773$	−3.58734	+	6.21345i	−0.129028	+	0.223482i	0.794273	+	0.607562i	$0.207852\pi$
$774$	−6.27981	+	10.8770i	−0.225723	+	0.390964i
$775$	15.5455	+	26.9256i	0.558411	+	0.967197i
$776$	4.60118			0.165173
$777$	−9.40333	+	19.1177i	−0.337342	+	0.685842i
$778$	−3.66598			−0.131432
$779$	8.66908	+	15.0153i	0.310602	+	0.537978i
$780$	0.106565	−	0.184575i	0.00381562	−	0.00660885i
$781$	30.5073	−	52.8401i	1.09164	−	1.89077i
$782$	3.38638	+	5.86538i	0.121097	+	0.209746i
$783$	2.94433			0.105222
$784$	−2.66546	+	6.47266i	−0.0951950	+	0.231166i
$785$	35.0643			1.25150
$786$	3.47062	+	6.01128i	0.123793	+	0.214415i
$787$	3.57012	−	6.18363i	0.127261	−	0.220423i	−0.795353	−	0.606146i	$-0.792715\pi$
$787$	3.57012	−	6.18363i	0.127261	−	0.220423i	0.922615	+	0.385723i	$0.126048\pi$
$788$	7.88100	−	13.6503i	0.280749	−	0.486271i
$789$	14.6538	+	25.3810i	0.521687	+	0.903589i
$790$	11.2722			0.401045
$791$	−6.22685	+	12.6596i	−0.221401	+	0.450125i
$792$	−5.10824			−0.181513
$793$	0.160812	+	0.278535i	0.00571060	+	0.00989106i
$794$	−9.97862	+	17.2835i	−0.354128	+	0.613367i
$795$	10.9437	−	18.9551i	0.388134	−	0.672268i
$796$	−9.93667	−	17.2108i	−0.352196	−	0.610021i
$797$	1.94889			0.0690333			0.0345167	−	0.999404i	$-0.489011\pi$
$797$	1.94889			0.0690333			0.0345167	+	0.999404i	$0.489011\pi$
$798$	−10.9923	+	0.731843i	−0.389125	+	0.0259070i
$799$	−81.2521			−2.87449
$800$	−4.82843	−	8.36308i	−0.170711	−	0.295680i
$801$	−1.19786	+	2.07475i	−0.0423242	+	0.0733077i
$802$	−0.193083	+	0.334429i	−0.00681798	+	0.0118091i
$803$	−5.66908	−	9.81913i	−0.200057	−	0.346510i
$804$	12.1544			0.428651
$805$	−5.63608	−	8.41621i	−0.198646	−	0.296632i
$806$	−0.179235			−0.00631327
$807$	−1.31471	−	2.27714i	−0.0462798	−	0.0801590i
$808$	7.44373	−	12.8929i	0.261869	−	0.453571i
$809$	−19.9675	+	34.5848i	−0.702020	+	1.21594i	0.265736	+	0.964046i	$0.414385\pi$
$809$	−19.9675	+	34.5848i	−0.702020	+	1.21594i	−0.967756	+	0.251889i	$0.918948\pi$
$810$	1.91421	+	3.31552i	0.0672586	+	0.116495i
$811$	−39.4035			−1.38364			−0.691822	−	0.722068i	$-0.743192\pi$
$811$	−39.4035			−1.38364			−0.691822	+	0.722068i	$0.743192\pi$
$812$	4.33454	+	6.47266i	0.152113	+	0.227146i
$813$	3.21958			0.112916
$814$	−20.5672	−	35.6235i	−0.720881	−	1.24860i
$815$	−23.3018	+	40.3599i	−0.816226	+	1.41375i
$816$	3.38638	−	5.86538i	0.118547	−	0.205329i
$817$	−26.1486	−	45.2907i	−0.914823	−	1.58452i
$818$	−15.5314			−0.543043
$819$	−0.146964	+	0.00978451i	−0.00513534	+	0.000341898i
$820$	15.9412			0.556692
$821$	19.7489	+	34.2061i	0.689241	+	1.19380i	0.972084	+	0.234634i	$0.0753891\pi$
$821$	19.7489	+	34.2061i	0.689241	+	1.19380i	−0.282843	+	0.959166i	$0.591278\pi$
$822$	−2.63991	+	4.57245i	−0.0920773	+	0.159483i
$823$	−4.40527	+	7.63015i	−0.153558	+	0.265970i	−0.932533	−	0.361085i	$-0.882407\pi$
$823$	−4.40527	+	7.63015i	−0.153558	+	0.265970i	0.778975	+	0.627055i	$0.215740\pi$
$824$	−3.07718	−	5.32983i	−0.107199	−	0.185673i
$825$	−49.3295			−1.71743
$826$	10.0440	−	20.4201i	0.349474	−	0.710507i
$827$	26.5271			0.922437			0.461219	−	0.887286i	$-0.347412\pi$
$827$	26.5271			0.922437			0.461219	+	0.887286i	$0.347412\pi$
$828$	−0.500000	−	0.866025i	−0.0173762	−	0.0300965i
$829$	8.55352	−	14.8151i	0.297076	−	0.514551i	−0.678390	−	0.734702i	$-0.737322\pi$
$829$	8.55352	−	14.8151i	0.297076	−	0.514551i	0.975466	+	0.220152i	$0.0706552\pi$
$830$	−28.2635	+	48.9539i	−0.981042	+	1.69921i
$831$	−7.38504	−	12.7913i	−0.256184	−	0.443724i
$832$	0.0556701			0.00193001
$833$	−46.9909	+	6.28493i	−1.62814	+	0.217760i
$834$	9.31371			0.322507
$835$	40.3493	+	69.8871i	1.39635	+	2.41854i
$836$	10.6351	−	18.4206i	0.367824	−	0.637089i
$837$	1.60979	−	2.78824i	0.0556425	−	0.0963756i
$838$	−0.279814	−	0.484652i	−0.00966601	−	0.0167420i
$839$	−13.4585			−0.464640			−0.232320	−	0.972639i	$-0.574632\pi$
$839$	−13.4585			−0.464640			−0.232320	+	0.972639i	$0.574632\pi$
$840$	−4.47062	+	9.08909i	−0.154251	+	0.313603i
$841$	−20.3309			−0.701066
$842$	−8.60118	−	14.8977i	−0.296416	−	0.513408i
$843$	−1.72496	+	2.98772i	−0.0594108	+	0.102903i
$844$	5.32137	−	9.21688i	0.183169	−	0.317258i
$845$	−24.8788	−	43.0914i	−0.855858	−	1.48239i
$846$	11.9969			0.412462
$847$	−39.8471	+	2.65292i	−1.36916	+	0.0911555i
$848$	5.71709			0.196326
$849$	−0.475996	−	0.824449i	−0.0163361	−	0.0282950i
$850$	32.7018	−	56.6411i	1.12166	−	1.94277i
$851$	4.02629	−	6.97373i	0.138019	−	0.239056i
$852$	−5.97216	−	10.3441i	−0.204603	−	0.354383i
$853$	38.3278			1.31232			0.656160	−	0.754622i	$-0.272180\pi$
$853$	38.3278			1.31232			0.656160	+	0.754622i	$0.272180\pi$
$854$	−8.50517	−	12.7006i	−0.291041	−	0.434604i
$855$	−15.9412			−0.545179
$856$	−2.06118	−	3.57006i	−0.0704496	−	0.122022i
$857$	−22.7978	+	39.4870i	−0.778759	+	1.34885i	0.153898	+	0.988087i	$0.450817\pi$
$857$	−22.7978	+	39.4870i	−0.778759	+	1.34885i	−0.932657	+	0.360764i	$0.882516\pi$
$858$	0.142188	−	0.246277i	0.00485423	−	0.00840777i
$859$	−13.6210	−	23.5923i	−0.464743	−	0.804959i	0.534447	−	0.845202i	$-0.320520\pi$
$859$	−13.6210	−	23.5923i	−0.464743	−	0.804959i	−0.999190	+	0.0402434i	$0.987187\pi$
$860$	−48.0836			−1.63964
$861$	−6.12996	−	9.15372i	−0.208909	−	0.311958i
$862$	18.8501			0.642037
$863$	−28.2317	−	48.8987i	−0.961017	−	1.66453i	−0.719955	−	0.694021i	$-0.755838\pi$
$863$	−28.2317	−	48.8987i	−0.961017	−	1.66453i	−0.241062	−	0.970510i	$-0.577496\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	25.6984	−	44.5110i	0.873772	−	1.51342i
$866$	−0.217692	−	0.377053i	−0.00739746	−	0.0128128i
$867$	28.8702			0.980485
$868$	8.49940	−	0.565869i	0.288488	−	0.0192069i
$869$	15.0403			0.510209
$870$	5.63608	+	9.76197i	0.191081	+	0.330962i
$871$	−0.338317	+	0.585983i	−0.0114634	+	0.0198553i
$872$	−10.0480	+	17.4037i	−0.340269	+	0.589362i
$873$	−2.30059	−	3.98474i	−0.0778632	−	0.134863i
$874$	4.16391			0.140846
$875$	−20.8190	+	42.3266i	−0.703811	+	1.43090i
$876$	−2.21958			−0.0749927
$877$	−7.59512	−	13.1551i	−0.256469	−	0.444218i	0.708824	−	0.705385i	$-0.249226\pi$
$877$	−7.59512	−	13.1551i	−0.256469	−	0.444218i	−0.965294	+	0.261167i	$0.915893\pi$
$878$	17.0024	−	29.4490i	0.573803	−	0.993857i
$879$	7.25736	−	12.5701i	0.244785	−	0.423979i
$880$	−9.77826	−	16.9365i	−0.329625	−	0.570928i
$881$	2.60885			0.0878942			0.0439471	−	0.999034i	$-0.486007\pi$
$881$	2.60885			0.0878942			0.0439471	+	0.999034i	$0.486007\pi$
$882$	6.93822	−	0.927973i	0.233622	−	0.0312465i
$883$	−25.7863			−0.867779			−0.433890	−	0.900966i	$-0.642859\pi$
$883$	−25.7863			−0.867779			−0.433890	+	0.900966i	$0.642859\pi$
$884$	0.188520	+	0.326526i	0.00634062	+	0.0109823i
$885$	16.4645	−	28.5174i	0.553448	−	0.958600i
$886$	−8.47062	+	14.6715i	−0.284576	+	0.492900i
$887$	−7.13458	−	12.3575i	−0.239556	−	0.414923i	0.721031	−	0.692903i	$-0.243668\pi$
$887$	−7.13458	−	12.3575i	−0.239556	−	0.414923i	−0.960587	+	0.277980i	$0.910335\pi$
$888$	−8.05257			−0.270227
$889$	9.98258	−	20.2953i	0.334805	−	0.680683i
$890$	−9.17183			−0.307440
$891$	2.55412	+	4.42387i	0.0855663	+	0.148205i
$892$	14.2712	−	24.7185i	0.477835	−	0.827635i
$893$	−24.9770	+	43.2615i	−0.835824	+	1.44769i
$894$	5.85949	+	10.1489i	0.195971	+	0.339431i
$895$	−7.64499			−0.255544
$896$	−2.63991	+	0.175759i	−0.0881931	+	0.00587168i
$897$	0.0556701			0.00185877
$898$	−2.64468	−	4.58072i	−0.0882542	−	0.152861i
$899$	4.73975	−	8.20950i	0.158080	−	0.273802i
$900$	−4.82843	+	8.36308i	−0.160948	+	0.278769i
$901$	19.3602	+	33.5329i	0.644982	+	1.11714i
$902$	21.2703			0.708222
$903$	18.4898	+	27.6104i	0.615303	+	0.918817i
$904$	−5.33238			−0.177352
$905$	39.3262	+	68.1150i	1.30725	+	2.26422i
$906$	−8.77826	+	15.2044i	−0.291638	+	0.505132i
$907$	20.7603	−	35.9579i	0.689335	−	1.19396i	−0.282718	−	0.959203i	$-0.591236\pi$
$907$	20.7603	−	35.9579i	0.689335	−	1.19396i	0.972053	−	0.234760i	$-0.0754306\pi$
$908$	1.84160	+	3.18974i	0.0611155	+	0.105855i
$909$	−14.8875			−0.493786
$910$	−0.313761	−	0.468532i	−0.0104011	−	0.0155317i
$911$	8.50317			0.281723			0.140861	−	0.990029i	$-0.455013\pi$
$911$	8.50317			0.281723			0.140861	+	0.990029i	$0.455013\pi$
$912$	−2.08196	−	3.60605i	−0.0689404	−	0.119408i
$913$	−37.7118	+	65.3188i	−1.24808	+	2.16174i
$914$	−3.47862	+	6.02514i	−0.115062	+	0.199294i
$915$	−11.0590	−	19.1548i	−0.365600	−	0.633238i
$916$	−12.1639			−0.401907
$917$	18.3242	−	1.21998i	0.605119	−	0.0402873i
$918$	−6.77276			−0.223534
$919$	−7.29366	−	12.6330i	−0.240596	−	0.416724i	0.720288	−	0.693675i	$-0.244009\pi$
$919$	−7.29366	−	12.6330i	−0.240596	−	0.416724i	−0.960884	+	0.276951i	$0.910676\pi$
$920$	1.91421	−	3.31552i	0.0631098	−	0.109309i
$921$	−8.63057	+	14.9486i	−0.284387	+	0.492573i
$922$	−3.32782	−	5.76396i	−0.109596	−	0.189826i
$923$	0.664942			0.0218868
$924$	−5.96511	+	12.1275i	−0.196238	+	0.398966i
$925$	−77.7625			−2.55682
$926$	−9.93022	−	17.1996i	−0.326327	−	0.565215i
$927$	−3.07718	+	5.32983i	−0.101068	+	0.175055i
$928$	−1.47216	+	2.54986i	−0.0483262	+	0.0837034i
$929$	15.6908	+	27.1773i	0.514798	+	0.891657i	0.999853	+	0.0171730i	$0.00546659\pi$
$929$	15.6908	+	27.1773i	0.514798	+	0.891657i	−0.485054	+	0.874484i	$0.661200\pi$
$930$	12.3259			0.404183
$931$	−11.0987	+	26.9516i	−0.363747	+	0.883302i
$932$	−1.49294			−0.0489030
$933$	−1.18529	−	2.05299i	−0.0388048	−	0.0672119i
$934$	−9.27215	+	16.0598i	−0.303394	+	0.525494i
$935$	66.2258	−	114.706i	2.16582	−	3.75130i
$936$	−0.0278351	−	0.0482117i	−0.000909818	−	0.00157585i
$937$	−12.9726			−0.423795			−0.211897	−	0.977292i	$-0.567964\pi$
$937$	−12.9726			−0.423795			−0.211897	+	0.977292i	$0.567964\pi$
$938$	14.1932	−	28.8557i	0.463423	−	0.942173i
$939$	−5.83798			−0.190515
$940$	22.9646	+	39.7759i	0.749024	+	1.29735i
$941$	−4.94071	+	8.55756i	−0.161063	+	0.278969i	−0.935250	−	0.353988i	$-0.884825\pi$
$941$	−4.94071	+	8.55756i	−0.161063	+	0.278969i	0.774187	+	0.632956i	$0.218159\pi$
$942$	4.57946	−	7.93186i	0.149207	−	0.258434i
$943$	2.08196	+	3.60605i	0.0677978	+	0.117429i
$944$	8.60118			0.279945
$945$	10.1067	−	0.672879i	0.328771	−	0.0218888i
$946$	−64.1576			−2.08594
$947$	−13.0804	−	22.6558i	−0.425054	−	0.736216i	0.571371	−	0.820692i	$-0.306412\pi$
$947$	−13.0804	−	22.6558i	−0.425054	−	0.736216i	−0.996426	+	0.0844760i	$0.973078\pi$
$948$	1.47216	−	2.54986i	0.0478137	−	0.0828157i
$949$	0.0617822	−	0.107010i	0.00200553	−	0.00347369i
$950$	−20.1051	−	34.8231i	−0.652297	−	1.12981i
$951$	0.629412			0.0204101
$952$	−9.97062	−	14.8889i	−0.323149	−	0.482551i
$953$	11.8360			0.383405			0.191703	−	0.981453i	$-0.438599\pi$
$953$	11.8360			0.383405			0.191703	+	0.981453i	$0.438599\pi$
$954$	−2.85854	−	4.95114i	−0.0925488	−	0.160299i
$955$	−3.72780	+	6.45673i	−0.120629	+	0.208935i
$956$	−12.5596	+	21.7539i	−0.406207	+	0.703572i
$957$	7.52017	+	13.0253i	0.243093	+	0.421049i
$958$	9.28317			0.299926
$959$	7.77276	+	11.6069i	0.250995	+	0.374805i
$960$	−3.82843			−0.123562
$961$	10.3171	+	17.8698i	0.332811	+	0.576446i
$962$	0.224144	−	0.388229i	0.00722669	−	0.0125170i
$963$	−2.06118	+	3.57006i	−0.0664205	+	0.115044i
$964$	−5.92355	−	10.2599i	−0.190785	−	0.330449i
$965$	−16.9996			−0.547238
$966$	−2.63991	+	0.175759i	−0.0849376	+	0.00565494i
$967$	−23.7730			−0.764488			−0.382244	−	0.924061i	$-0.624849\pi$
$967$	−23.7730			−0.764488			−0.382244	+	0.924061i	$0.624849\pi$
$968$	−7.54706	−	13.0719i	−0.242572	−	0.420147i
$969$	14.1006	−	24.4229i	0.452976	−	0.784577i
$970$	8.80765	−	15.2553i	0.282797	−	0.489818i
$971$	−2.78903	−	4.83073i	−0.0895041	−	0.155026i	0.817798	−	0.575506i	$-0.195195\pi$
$971$	−2.78903	−	4.83073i	−0.0895041	−	0.155026i	−0.907302	+	0.420480i	$0.861862\pi$
$972$	1.00000			0.0320750
$973$	10.8760	−	22.1117i	0.348669	−	0.708870i
$974$	9.86232			0.316009
$975$	−0.268799	−	0.465574i	−0.00860846	−	0.0149103i
$976$	2.88866	−	5.00331i	0.0924637	−	0.160152i
$977$	18.7328	−	32.4462i	0.599316	−	1.03805i	−0.393606	−	0.919279i	$-0.628773\pi$
$977$	18.7328	−	32.4462i	0.599316	−	1.03805i	0.992922	−	0.118767i	$-0.0378941\pi$
$978$	6.08652	+	10.5422i	0.194625	+	0.337101i
$979$	−12.2379			−0.391125
$980$	16.3579	+	21.2274i	0.522535	+	0.678085i
$981$	20.0960			0.641616
$982$	20.6684	+	35.7988i	0.659556	+	1.14238i
$983$	−4.62747	+	8.01501i	−0.147593	+	0.255639i	−0.930337	−	0.366704i	$-0.880486\pi$
$983$	−4.62747	+	8.01501i	−0.147593	+	0.255639i	0.782744	+	0.622344i	$0.213819\pi$
$984$	2.08196	−	3.60605i	0.0663703	−	0.114957i
$985$	−30.1718	−	52.2591i	−0.961354	−	1.66511i
$986$	−19.9412			−0.635058
$987$	14.0093	−	28.4819i	0.445920	−	0.906589i
$988$	0.231805			0.00737471
$989$	−6.27981	−	10.8770i	−0.199686	−	0.345867i
$990$	−9.77826	+	16.9365i	−0.310774	+	0.538276i
$991$	1.67957	−	2.90911i	0.0533535	−	0.0924109i	−0.838115	−	0.545493i	$-0.816342\pi$
$991$	1.67957	−	2.90911i	0.0533535	−	0.0924109i	0.891469	+	0.453082i	$0.149676\pi$
$992$	1.60979	+	2.78824i	0.0511109	+	0.0885267i
$993$	13.7003			0.434766
$994$	−31.5319	+	2.09932i	−1.00013	+	0.0665864i
$995$	−76.0836			−2.41201
$996$	7.38255	+	12.7869i	0.233925	+	0.405170i
$997$	1.67669	−	2.90411i	0.0531012	−	0.0919740i	−0.838253	−	0.545282i	$-0.816423\pi$
$997$	1.67669	−	2.90411i	0.0531012	−	0.0919740i	0.891354	+	0.453308i	$0.149756\pi$
$998$	2.22724	−	3.85770i	0.0705021	−	0.122113i
$999$	4.02629	+	6.97373i	0.127386	+	0.220639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.l.277.4	✓	8
7.2	even	3	inner	966.2.i.l.415.4	yes	8
7.3	odd	6		6762.2.a.cm.1.3		4
7.4	even	3		6762.2.a.cp.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.l.277.4	✓	8	1.1	even	1	trivial
966.2.i.l.415.4	yes	8	7.2	even	3	inner
6762.2.a.cm.1.3		4	7.3	odd	6
6762.2.a.cp.1.1		4	7.4	even	3

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.91421 + 3.31552i) q^{5} +1.00000 q^{6} +(1.16774 - 2.37411i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.91421 + 3.31552i) q^{5} +1.00000 q^{6} +(1.16774 - 2.37411i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.91421 - 3.31552i) q^{10} +(2.55412 - 4.42387i) q^{11} +(-0.500000 - 0.866025i) q^{12} +0.0556701 q^{13} +(-2.63991 + 0.175759i) q^{14} -3.82843 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.38638 - 5.86538i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.08196 - 3.60605i) q^{19} -3.82843 q^{20} +(1.47216 + 2.19835i) q^{21} -5.10824 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.82843 + 8.36308i) q^{25} +(-0.0278351 - 0.0482117i) q^{26} +1.00000 q^{27} +(1.47216 + 2.19835i) q^{28} +2.94433 q^{29} +(1.91421 + 3.31552i) q^{30} +(1.60979 - 2.78824i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.55412 + 4.42387i) q^{33} -6.77276 q^{34} +(10.1067 - 0.672879i) q^{35} +1.00000 q^{36} +(4.02629 + 6.97373i) q^{37} +(-2.08196 + 3.60605i) q^{38} +(-0.0278351 + 0.0482117i) q^{39} +(1.91421 + 3.31552i) q^{40} -4.16391 q^{41} +(1.16774 - 2.37411i) q^{42} +12.5596 q^{43} +(2.55412 + 4.42387i) q^{44} +(1.91421 - 3.31552i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-5.99845 - 10.3896i) q^{47} +1.00000 q^{48} +(-4.27276 - 5.54469i) q^{49} +9.65685 q^{50} +(3.38638 + 5.86538i) q^{51} +(-0.0278351 + 0.0482117i) q^{52} +(-2.85854 + 4.95114i) q^{53} +(-0.500000 - 0.866025i) q^{54} +19.5565 q^{55} +(1.16774 - 2.37411i) q^{56} +4.16391 q^{57} +(-1.47216 - 2.54986i) q^{58} +(-4.30059 + 7.44884i) q^{59} +(1.91421 - 3.31552i) q^{60} +(2.88866 + 5.00331i) q^{61} -3.21958 q^{62} +(-2.63991 + 0.175759i) q^{63} +1.00000 q^{64} +(0.106565 + 0.184575i) q^{65} +(2.55412 - 4.42387i) q^{66} +(-6.07718 + 10.5260i) q^{67} +(3.38638 + 5.86538i) q^{68} +1.00000 q^{69} +(-5.63608 - 8.41621i) q^{70} +11.9443 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.10979 - 1.92221i) q^{73} +(4.02629 - 6.97373i) q^{74} +(-4.82843 - 8.36308i) q^{75} +4.16391 q^{76} +(-7.52017 - 11.2297i) q^{77} +0.0556701 q^{78} +(1.47216 + 2.54986i) q^{79} +(1.91421 - 3.31552i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.08196 + 3.60605i) q^{82} -14.7651 q^{83} +(-2.63991 + 0.175759i) q^{84} +25.9290 q^{85} +(-6.27981 - 10.8770i) q^{86} +(-1.47216 + 2.54986i) q^{87} +(2.55412 - 4.42387i) q^{88} +(-1.19786 - 2.07475i) q^{89} -3.82843 q^{90} +(0.0650084 - 0.132167i) q^{91} +1.00000 q^{92} +(1.60979 + 2.78824i) q^{93} +(-5.99845 + 10.3896i) q^{94} +(7.97062 - 13.8055i) q^{95} +(-0.500000 - 0.866025i) q^{96} +4.60118 q^{97} +(-2.66546 + 6.47266i) q^{98} -5.10824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} - 6 q^{14} - 8 q^{15} - 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} - 8 q^{20} + 6 q^{21} + 12 q^{22} - 4 q^{23} - 4 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{27} + 6 q^{28} + 12 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 6 q^{33} - 20 q^{34} - 10 q^{35} + 8 q^{36} + 4 q^{38} - 6 q^{39} + 4 q^{40} + 8 q^{41} + 40 q^{43} - 6 q^{44} + 4 q^{45} - 4 q^{46} - 10 q^{47} + 8 q^{48} + 32 q^{50} + 10 q^{51} - 6 q^{52} - 4 q^{54} + 20 q^{55} - 8 q^{57} - 6 q^{58} - 6 q^{59} + 4 q^{60} + 4 q^{62} - 6 q^{63} + 8 q^{64} + 14 q^{65} - 6 q^{66} - 18 q^{67} + 10 q^{68} + 8 q^{69} + 2 q^{70} + 84 q^{71} - 4 q^{72} - 6 q^{73} - 16 q^{75} - 8 q^{76} - 2 q^{77} + 12 q^{78} + 6 q^{79} + 4 q^{80} - 4 q^{81} - 4 q^{82} - 20 q^{83} - 6 q^{84} + 68 q^{85} - 20 q^{86} - 6 q^{87} - 6 q^{88} - 8 q^{90} + 10 q^{91} + 8 q^{92} - 2 q^{93} - 10 q^{94} + 20 q^{95} - 4 q^{96} - 20 q^{97} - 18 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 - 6 * q^14 - 8 * q^15 - 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 - 8 * q^20 + 6 * q^21 + 12 * q^22 - 4 * q^23 - 4 * q^24 - 16 * q^25 - 6 * q^26 + 8 * q^27 + 6 * q^28 + 12 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 6 * q^33 - 20 * q^34 - 10 * q^35 + 8 * q^36 + 4 * q^38 - 6 * q^39 + 4 * q^40 + 8 * q^41 + 40 * q^43 - 6 * q^44 + 4 * q^45 - 4 * q^46 - 10 * q^47 + 8 * q^48 + 32 * q^50 + 10 * q^51 - 6 * q^52 - 4 * q^54 + 20 * q^55 - 8 * q^57 - 6 * q^58 - 6 * q^59 + 4 * q^60 + 4 * q^62 - 6 * q^63 + 8 * q^64 + 14 * q^65 - 6 * q^66 - 18 * q^67 + 10 * q^68 + 8 * q^69 + 2 * q^70 + 84 * q^71 - 4 * q^72 - 6 * q^73 - 16 * q^75 - 8 * q^76 - 2 * q^77 + 12 * q^78 + 6 * q^79 + 4 * q^80 - 4 * q^81 - 4 * q^82 - 20 * q^83 - 6 * q^84 + 68 * q^85 - 20 * q^86 - 6 * q^87 - 6 * q^88 - 8 * q^90 + 10 * q^91 + 8 * q^92 - 2 * q^93 - 10 * q^94 + 20 * q^95 - 4 * q^96 - 20 * q^97 - 18 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more