LMFDB - Embedded newform 1014.2.e.n.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.e (of order $3$, degree $2$, not 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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.3
Root			$-0.623490 - 1.07992i$ of defining polynomial
Character	$\chi$	$=$	1014.529
Dual form			1014.2.e.n.991.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +4.29590 q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.17845 + 3.77318i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +4.29590 q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.17845 + 3.77318i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.14795 - 3.72036i) q^{10} +(-0.579417 + 1.00358i) q^{11} -1.00000 q^{12} +4.35690 q^{14} +(2.14795 - 3.72036i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.246980 - 0.427781i) q^{17} -1.00000 q^{18} +(-0.890084 - 1.54167i) q^{19} +(-2.14795 - 3.72036i) q^{20} +4.35690 q^{21} +(0.579417 + 1.00358i) q^{22} +(-1.69202 + 2.93067i) q^{23} +(-0.500000 + 0.866025i) q^{24} +13.4547 q^{25} -1.00000 q^{27} +(2.17845 - 3.77318i) q^{28} +(-3.46950 + 6.00935i) q^{29} +(-2.14795 - 3.72036i) q^{30} -2.22521 q^{31} +(0.500000 + 0.866025i) q^{32} +(0.579417 + 1.00358i) q^{33} -0.493959 q^{34} +(9.35839 + 16.2092i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.93900 - 3.35845i) q^{37} -1.78017 q^{38} -4.29590 q^{40} +(3.15883 - 5.47126i) q^{41} +(2.17845 - 3.77318i) q^{42} +(-3.69202 - 6.39477i) q^{43} +1.15883 q^{44} +(-2.14795 - 3.72036i) q^{45} +(1.69202 + 2.93067i) q^{46} -1.78017 q^{47} +(0.500000 + 0.866025i) q^{48} +(-5.99127 + 10.3772i) q^{49} +(6.72737 - 11.6521i) q^{50} -0.493959 q^{51} -2.51573 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.48911 + 4.31127i) q^{55} +(-2.17845 - 3.77318i) q^{56} -1.78017 q^{57} +(3.46950 + 6.00935i) q^{58} +(-3.31551 - 5.74263i) q^{59} -4.29590 q^{60} +(-5.24698 - 9.08804i) q^{61} +(-1.11260 + 1.92709i) q^{62} +(2.17845 - 3.77318i) q^{63} +1.00000 q^{64} +1.15883 q^{66} +(-2.04892 + 3.54883i) q^{67} +(-0.246980 + 0.427781i) q^{68} +(1.69202 + 2.93067i) q^{69} +18.7168 q^{70} +(-4.69202 - 8.12682i) q^{71} +(0.500000 + 0.866025i) q^{72} +0.374354 q^{73} +(-1.93900 - 3.35845i) q^{74} +(6.72737 - 11.6521i) q^{75} +(-0.890084 + 1.54167i) q^{76} -5.04892 q^{77} +2.65519 q^{79} +(-2.14795 + 3.72036i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.15883 - 5.47126i) q^{82} -14.2784 q^{83} +(-2.17845 - 3.77318i) q^{84} +(-1.06100 - 1.83770i) q^{85} -7.38404 q^{86} +(3.46950 + 6.00935i) q^{87} +(0.579417 - 1.00358i) q^{88} +(-0.417895 + 0.723815i) q^{89} -4.29590 q^{90} +3.38404 q^{92} +(-1.11260 + 1.92709i) q^{93} +(-0.890084 + 1.54167i) q^{94} +(-3.82371 - 6.62286i) q^{95} +1.00000 q^{96} +(-9.19687 - 15.9294i) q^{97} +(5.99127 + 10.3772i) q^{98} +1.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 5 q^{11} - 6 q^{12} + 18 q^{14} - q^{15} - 3 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + q^{20} + 18 q^{21} - 5 q^{22} - 3 q^{24} + 36 q^{25} - 6 q^{27} + 9 q^{28} - 11 q^{29} + q^{30} - 10 q^{31} + 3 q^{32} - 5 q^{33} + 16 q^{34} + 4 q^{35} - 3 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{40} + 2 q^{41} + 9 q^{42} - 12 q^{43} - 10 q^{44} + q^{45} - 8 q^{47} + 3 q^{48} - 20 q^{49} + 18 q^{50} + 16 q^{51} + 10 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 8 q^{57} + 11 q^{58} - 5 q^{59} + 2 q^{60} - 22 q^{61} - 5 q^{62} + 9 q^{63} + 6 q^{64} - 10 q^{66} + 6 q^{67} + 8 q^{68} + 8 q^{70} - 18 q^{71} + 3 q^{72} + 26 q^{73} + 8 q^{74} + 18 q^{75} - 4 q^{76} - 12 q^{77} + 62 q^{79} + q^{80} - 3 q^{81} - 2 q^{82} - 26 q^{83} - 9 q^{84} - 26 q^{85} - 24 q^{86} + 11 q^{87} - 5 q^{88} - 14 q^{89} + 2 q^{90} - 5 q^{93} - 4 q^{94} - 8 q^{95} + 6 q^{96} - 23 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 5 * q^11 - 6 * q^12 + 18 * q^14 - q^15 - 3 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + q^20 + 18 * q^21 - 5 * q^22 - 3 * q^24 + 36 * q^25 - 6 * q^27 + 9 * q^28 - 11 * q^29 + q^30 - 10 * q^31 + 3 * q^32 - 5 * q^33 + 16 * q^34 + 4 * q^35 - 3 * q^36 - 8 * q^37 - 8 * q^38 + 2 * q^40 + 2 * q^41 + 9 * q^42 - 12 * q^43 - 10 * q^44 + q^45 - 8 * q^47 + 3 * q^48 - 20 * q^49 + 18 * q^50 + 16 * q^51 + 10 * q^53 - 3 * q^54 - 18 * q^55 - 9 * q^56 - 8 * q^57 + 11 * q^58 - 5 * q^59 + 2 * q^60 - 22 * q^61 - 5 * q^62 + 9 * q^63 + 6 * q^64 - 10 * q^66 + 6 * q^67 + 8 * q^68 + 8 * q^70 - 18 * q^71 + 3 * q^72 + 26 * q^73 + 8 * q^74 + 18 * q^75 - 4 * q^76 - 12 * q^77 + 62 * q^79 + q^80 - 3 * q^81 - 2 * q^82 - 26 * q^83 - 9 * q^84 - 26 * q^85 - 24 * q^86 + 11 * q^87 - 5 * q^88 - 14 * q^89 + 2 * q^90 - 5 * q^93 - 4 * q^94 - 8 * q^95 + 6 * q^96 - 23 * q^97 + 20 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	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
$5$	4.29590			1.92118			0.960592	−	0.277963i	$-0.0896593\pi$
$5$	4.29590			1.92118			0.960592	+	0.277963i	$0.0896593\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	2.17845	+	3.77318i	0.823376	+	1.42613i	0.903154	+	0.429316i	$0.141245\pi$
$7$	2.17845	+	3.77318i	0.823376	+	1.42613i	−0.0797783	+	0.996813i	$0.525421\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.14795	−	3.72036i	0.679241	−	1.17648i
$11$	−0.579417	+	1.00358i	−0.174701	+	0.302591i	−0.940058	−	0.341016i	$-0.889229\pi$
$11$	−0.579417	+	1.00358i	−0.174701	+	0.302591i	0.765357	+	0.643606i	$0.222562\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	4.35690			1.16443
$15$	2.14795	−	3.72036i	0.554598	−	0.960592i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.246980	−	0.427781i	−0.0599014	−	0.103752i	0.834520	−	0.550978i	$-0.185745\pi$
$17$	−0.246980	−	0.427781i	−0.0599014	−	0.103752i	−0.894421	+	0.447226i	$0.852412\pi$
$18$	−1.00000			−0.235702
$19$	−0.890084	−	1.54167i	−0.204199	−	0.353683i	0.745678	−	0.666306i	$-0.232126\pi$
$19$	−0.890084	−	1.54167i	−0.204199	−	0.353683i	−0.949877	+	0.312623i	$0.898792\pi$
$20$	−2.14795	−	3.72036i	−0.480296	−	0.831897i
$21$	4.35690			0.950753
$22$	0.579417	+	1.00358i	0.123532	+	0.213964i
$23$	−1.69202	+	2.93067i	−0.352811	+	0.611086i	−0.986741	−	0.162304i	$-0.948107\pi$
$23$	−1.69202	+	2.93067i	−0.352811	+	0.611086i	0.633930	+	0.773391i	$0.281441\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	13.4547			2.69095
$26$		0			0
$27$	−1.00000			−0.192450
$28$	2.17845	−	3.77318i	0.411688	−	0.713064i
$29$	−3.46950	+	6.00935i	−0.644270	+	1.11591i	0.340200	+	0.940353i	$0.389505\pi$
$29$	−3.46950	+	6.00935i	−0.644270	+	1.11591i	−0.984470	+	0.175555i	$0.943828\pi$
$30$	−2.14795	−	3.72036i	−0.392160	−	0.679241i
$31$	−2.22521			−0.399659			−0.199830	−	0.979831i	$-0.564039\pi$
$31$	−2.22521			−0.399659			−0.199830	+	0.979831i	$0.564039\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.579417	+	1.00358i	0.100864	+	0.174701i
$34$	−0.493959			−0.0847133
$35$	9.35839	+	16.2092i	1.58186	+	2.73986i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.93900	−	3.35845i	0.318770	−	0.552126i	−0.661462	−	0.749979i	$-0.730064\pi$
$37$	1.93900	−	3.35845i	0.318770	−	0.552126i	0.980232	+	0.197853i	$0.0633970\pi$
$38$	−1.78017			−0.288781
$39$		0			0
$40$	−4.29590			−0.679241
$41$	3.15883	−	5.47126i	0.493327	−	0.854467i	−0.506644	−	0.862156i	$-0.669114\pi$
$41$	3.15883	−	5.47126i	0.493327	−	0.854467i	0.999970	+	0.00768834i	$0.00244730\pi$
$42$	2.17845	−	3.77318i	0.336142	−	0.582215i
$43$	−3.69202	−	6.39477i	−0.563028	−	0.975193i	−0.997230	−	0.0743776i	$-0.976303\pi$
$43$	−3.69202	−	6.39477i	−0.563028	−	0.975193i	0.434202	−	0.900815i	$-0.357030\pi$
$44$	1.15883			0.174701
$45$	−2.14795	−	3.72036i	−0.320197	−	0.554598i
$46$	1.69202	+	2.93067i	0.249475	+	0.432103i
$47$	−1.78017			−0.259664			−0.129832	−	0.991536i	$-0.541444\pi$
$47$	−1.78017			−0.259664			−0.129832	+	0.991536i	$0.541444\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−5.99127	+	10.3772i	−0.855896	+	1.48246i
$50$	6.72737	−	11.6521i	0.951393	−	1.64786i
$51$	−0.493959			−0.0691681
$52$		0			0
$53$	−2.51573			−0.345562			−0.172781	−	0.984960i	$-0.555275\pi$
$53$	−2.51573			−0.345562			−0.172781	+	0.984960i	$0.555275\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−2.48911	+	4.31127i	−0.335632	+	0.581332i
$56$	−2.17845	−	3.77318i	−0.291107	−	0.504213i
$57$	−1.78017			−0.235789
$58$	3.46950	+	6.00935i	0.455568	+	0.789066i
$59$	−3.31551	−	5.74263i	−0.431643	−	0.747627i	0.565372	−	0.824836i	$-0.308733\pi$
$59$	−3.31551	−	5.74263i	−0.431643	−	0.747627i	−0.997015	+	0.0772087i	$0.975399\pi$
$60$	−4.29590			−0.554598
$61$	−5.24698	−	9.08804i	−0.671807	−	1.16360i	−0.977391	−	0.211439i	$-0.932185\pi$
$61$	−5.24698	−	9.08804i	−0.671807	−	1.16360i	0.305584	−	0.952165i	$-0.401148\pi$
$62$	−1.11260	+	1.92709i	−0.141301	+	0.244740i
$63$	2.17845	−	3.77318i	0.274459	−	0.475376i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.15883			0.142643
$67$	−2.04892	+	3.54883i	−0.250315	+	0.433558i	−0.963613	−	0.267303i	$-0.913868\pi$
$67$	−2.04892	+	3.54883i	−0.250315	+	0.433558i	0.713297	+	0.700861i	$0.247201\pi$
$68$	−0.246980	+	0.427781i	−0.0299507	+	0.0518761i
$69$	1.69202	+	2.93067i	0.203695	+	0.352811i
$70$	18.7168			2.23708
$71$	−4.69202	−	8.12682i	−0.556841	−	0.964476i	−0.997758	−	0.0669283i	$-0.978680\pi$
$71$	−4.69202	−	8.12682i	−0.556841	−	0.964476i	0.440917	−	0.897548i	$-0.354653\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	0.374354			0.0438149			0.0219074	−	0.999760i	$-0.493026\pi$
$73$	0.374354			0.0438149			0.0219074	+	0.999760i	$0.493026\pi$
$74$	−1.93900	−	3.35845i	−0.225404	−	0.390412i
$75$	6.72737	−	11.6521i	0.776809	−	1.34547i
$76$	−0.890084	+	1.54167i	−0.102100	+	0.176842i
$77$	−5.04892			−0.575378
$78$		0			0
$79$	2.65519			0.298732			0.149366	−	0.988782i	$-0.452277\pi$
$79$	2.65519			0.298732			0.149366	+	0.988782i	$0.452277\pi$
$80$	−2.14795	+	3.72036i	−0.240148	+	0.415948i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.15883	−	5.47126i	−0.348835	−	0.604200i
$83$	−14.2784			−1.56726			−0.783631	−	0.621226i	$-0.786635\pi$
$83$	−14.2784			−1.56726			−0.783631	+	0.621226i	$0.786635\pi$
$84$	−2.17845	−	3.77318i	−0.237688	−	0.411688i
$85$	−1.06100	−	1.83770i	−0.115081	−	0.199327i
$86$	−7.38404			−0.796242
$87$	3.46950	+	6.00935i	0.371970	+	0.644270i
$88$	0.579417	−	1.00358i	0.0617660	−	0.106982i
$89$	−0.417895	+	0.723815i	−0.0442968	+	0.0767242i	−0.887324	−	0.461147i	$-0.847438\pi$
$89$	−0.417895	+	0.723815i	−0.0442968	+	0.0767242i	0.843027	+	0.537871i	$0.180771\pi$
$90$	−4.29590			−0.452827
$91$		0			0
$92$	3.38404			0.352811
$93$	−1.11260	+	1.92709i	−0.115372	+	0.199830i
$94$	−0.890084	+	1.54167i	−0.0918051	+	0.159011i
$95$	−3.82371	−	6.62286i	−0.392304	−	0.679491i
$96$	1.00000			0.102062
$97$	−9.19687	−	15.9294i	−0.933800	−	1.61739i	−0.776759	−	0.629797i	$-0.783138\pi$
$97$	−9.19687	−	15.9294i	−0.933800	−	1.61739i	−0.157041	−	0.987592i	$-0.550195\pi$
$98$	5.99127	+	10.3772i	0.605210	+	1.04825i
$99$	1.15883			0.116467
$100$	−6.72737	−	11.6521i	−0.672737	−	1.16521i
$101$	2.73341	−	4.73440i	0.271984	−	0.471090i	−0.697386	−	0.716696i	$-0.745654\pi$
$101$	2.73341	−	4.73440i	0.271984	−	0.471090i	0.969370	+	0.245606i	$0.0789869\pi$
$102$	−0.246980	+	0.427781i	−0.0244546	+	0.0423567i
$103$	7.00969			0.690685			0.345343	−	0.938477i	$-0.387763\pi$
$103$	7.00969			0.690685			0.345343	+	0.938477i	$0.387763\pi$
$104$		0			0
$105$	18.7168			1.82657
$106$	−1.25786	+	2.17869i	−0.122175	+	0.211613i
$107$	0.958615	−	1.66037i	0.0926728	−	0.160514i	−0.815962	−	0.578105i	$-0.803792\pi$
$107$	0.958615	−	1.66037i	0.0926728	−	0.160514i	0.908635	+	0.417591i	$0.137126\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	18.7681			1.79766			0.898828	−	0.438301i	$-0.144420\pi$
$109$	18.7681			1.79766			0.898828	+	0.438301i	$0.144420\pi$
$110$	2.48911	+	4.31127i	0.237328	+	0.411064i
$111$	−1.93900	−	3.35845i	−0.184042	−	0.318770i
$112$	−4.35690			−0.411688
$113$	−5.20775	−	9.02009i	−0.489904	−	0.848539i	0.510028	−	0.860158i	$-0.329635\pi$
$113$	−5.20775	−	9.02009i	−0.489904	−	0.848539i	−0.999932	+	0.0116189i	$0.996302\pi$
$114$	−0.890084	+	1.54167i	−0.0833640	+	0.144391i
$115$	−7.26875	+	12.5898i	−0.677814	+	1.17401i
$116$	6.93900			0.644270
$117$		0			0
$118$	−6.63102			−0.610435
$119$	1.07606	−	1.86380i	0.0986427	−	0.170854i
$120$	−2.14795	+	3.72036i	−0.196080	+	0.339620i
$121$	4.82855	+	8.36330i	0.438959	+	0.760300i
$122$	−10.4940			−0.950078
$123$	−3.15883	−	5.47126i	−0.284822	−	0.493327i
$124$	1.11260	+	1.92709i	0.0999148	+	0.173058i
$125$	36.3207			3.24862
$126$	−2.17845	−	3.77318i	−0.194072	−	0.336142i
$127$	−4.19687	+	7.26918i	−0.372412	+	0.645036i	−0.989936	−	0.141516i	$-0.954802\pi$
$127$	−4.19687	+	7.26918i	−0.372412	+	0.645036i	0.617524	+	0.786552i	$0.288136\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−7.38404			−0.650129
$130$		0			0
$131$	−13.5036			−1.17982			−0.589910	−	0.807469i	$-0.700837\pi$
$131$	−13.5036			−1.17982			−0.589910	+	0.807469i	$0.700837\pi$
$132$	0.579417	−	1.00358i	0.0504318	−	0.0873504i
$133$	3.87800	−	6.71690i	0.336265	−	0.582429i
$134$	2.04892	+	3.54883i	0.176999	+	0.306572i
$135$	−4.29590			−0.369732
$136$	0.246980	+	0.427781i	0.0211783	+	0.0366819i
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	0.767853	−	0.640626i	$-0.221325\pi$
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	−0.938725	+	0.344668i	$0.887992\pi$
$138$	3.38404			0.288069
$139$	7.51573	+	13.0176i	0.637476	+	1.10414i	0.985985	+	0.166835i	$0.0533548\pi$
$139$	7.51573	+	13.0176i	0.637476	+	1.10414i	−0.348509	+	0.937305i	$0.613312\pi$
$140$	9.35839	−	16.2092i	0.790928	−	1.36993i
$141$	−0.890084	+	1.54167i	−0.0749586	+	0.129832i
$142$	−9.38404			−0.787491
$143$		0			0
$144$	1.00000			0.0833333
$145$	−14.9046	+	25.8156i	−1.23776	+	2.14387i
$146$	0.187177	−	0.324200i	0.0154909	−	0.0268310i
$147$	5.99127	+	10.3772i	0.494152	+	0.855896i
$148$	−3.87800			−0.318770
$149$	1.96346	+	3.40081i	0.160853	+	0.278605i	0.935175	−	0.354187i	$-0.115242\pi$
$149$	1.96346	+	3.40081i	0.160853	+	0.278605i	−0.774322	+	0.632792i	$0.781909\pi$
$150$	−6.72737	−	11.6521i	−0.549287	−	0.951393i
$151$	9.62863			0.783567			0.391783	−	0.920057i	$-0.371858\pi$
$151$	9.62863			0.783567			0.391783	+	0.920057i	$0.371858\pi$
$152$	0.890084	+	1.54167i	0.0721953	+	0.125046i
$153$	−0.246980	+	0.427781i	−0.0199671	+	0.0345841i
$154$	−2.52446	+	4.37249i	−0.203427	+	0.352345i
$155$	−9.55927			−0.767819
$156$		0			0
$157$	−17.3840			−1.38740			−0.693699	−	0.720265i	$-0.744020\pi$
$157$	−17.3840			−1.38740			−0.693699	+	0.720265i	$0.744020\pi$
$158$	1.32759	−	2.29946i	0.105618	−	0.182935i
$159$	−1.25786	+	2.17869i	−0.0997552	+	0.172781i
$160$	2.14795	+	3.72036i	0.169810	+	0.294120i
$161$	−14.7439			−1.16198
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	11.2349	+	19.4594i	0.879985	+	1.52418i	0.851356	+	0.524589i	$0.175781\pi$
$163$	11.2349	+	19.4594i	0.879985	+	1.52418i	0.0286294	+	0.999590i	$0.490886\pi$
$164$	−6.31767			−0.493327
$165$	2.48911	+	4.31127i	0.193777	+	0.335632i
$166$	−7.13922	+	12.3655i	−0.554111	+	0.959748i
$167$	0.417895	−	0.723815i	0.0323377	−	0.0560105i	−0.849404	−	0.527744i	$-0.823038\pi$
$167$	0.417895	−	0.723815i	0.0323377	−	0.0560105i	0.881741	+	0.471733i	$0.156371\pi$
$168$	−4.35690			−0.336142
$169$		0			0
$170$	−2.12200			−0.162750
$171$	−0.890084	+	1.54167i	−0.0680664	+	0.117894i
$172$	−3.69202	+	6.39477i	−0.281514	+	0.487597i
$173$	2.08546	+	3.61212i	0.158554	+	0.274624i	0.934348	−	0.356363i	$-0.115983\pi$
$173$	2.08546	+	3.61212i	0.158554	+	0.274624i	−0.775793	+	0.630987i	$0.782650\pi$
$174$	6.93900			0.526044
$175$	29.3104	+	50.7672i	2.21566	+	3.83764i
$176$	−0.579417	−	1.00358i	−0.0436752	−	0.0756476i
$177$	−6.63102			−0.498418
$178$	0.417895	+	0.723815i	0.0313225	+	0.0542522i
$179$	−11.4438	+	19.8213i	−0.855353	+	1.48152i	0.0209638	+	0.999780i	$0.493327\pi$
$179$	−11.4438	+	19.8213i	−0.855353	+	1.48152i	−0.876317	+	0.481735i	$0.840007\pi$
$180$	−2.14795	+	3.72036i	−0.160099	+	0.277299i
$181$	11.6039			0.862509			0.431255	−	0.902230i	$-0.358071\pi$
$181$	11.6039			0.862509			0.431255	+	0.902230i	$0.358071\pi$
$182$		0			0
$183$	−10.4940			−0.775736
$184$	1.69202	−	2.93067i	0.124737	−	0.216052i
$185$	8.32975	−	14.4275i	0.612415	−	1.06073i
$186$	1.11260	+	1.92709i	0.0815801	+	0.141301i
$187$	0.572417			0.0418592
$188$	0.890084	+	1.54167i	0.0649160	+	0.112438i
$189$	−2.17845	−	3.77318i	−0.158459	−	0.274459i
$190$	−7.64742			−0.554802
$191$	−8.34481	−	14.4536i	−0.603810	−	1.04583i	−0.992238	−	0.124350i	$-0.960315\pi$
$191$	−8.34481	−	14.4536i	−0.603810	−	1.04583i	0.388429	−	0.921479i	$-0.373018\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	4.82371	−	8.35491i	0.347218	−	0.601399i	−0.638536	−	0.769592i	$-0.720460\pi$
$193$	4.82371	−	8.35491i	0.347218	−	0.601399i	0.985754	+	0.168193i	$0.0537930\pi$
$194$	−18.3937			−1.32059
$195$		0			0
$196$	11.9825			0.855896
$197$	9.81916	−	17.0073i	0.699586	−	1.21172i	−0.269024	−	0.963133i	$-0.586701\pi$
$197$	9.81916	−	17.0073i	0.699586	−	1.21172i	0.968610	−	0.248585i	$-0.0799656\pi$
$198$	0.579417	−	1.00358i	0.0411774	−	0.0713213i
$199$	9.21044	+	15.9529i	0.652911	+	1.13087i	0.982413	+	0.186720i	$0.0597857\pi$
$199$	9.21044	+	15.9529i	0.652911	+	1.13087i	−0.329502	+	0.944155i	$0.606881\pi$
$200$	−13.4547			−0.951393
$201$	2.04892	+	3.54883i	0.144519	+	0.250315i
$202$	−2.73341	−	4.73440i	−0.192322	−	0.333111i
$203$	−30.2325			−2.12191
$204$	0.246980	+	0.427781i	0.0172920	+	0.0299507i
$205$	13.5700	−	23.5040i	0.947772	−	1.64159i
$206$	3.50484	−	6.07057i	0.244194	−	0.422957i
$207$	3.38404			0.235207
$208$		0			0
$209$	2.06292			0.142695
$210$	9.35839	−	16.2092i	0.645790	−	1.11854i
$211$	−7.96077	+	13.7885i	−0.548042	+	0.949237i	0.450367	+	0.892844i	$0.351293\pi$
$211$	−7.96077	+	13.7885i	−0.548042	+	0.949237i	−0.998409	+	0.0563930i	$0.982040\pi$
$212$	1.25786	+	2.17869i	0.0863905	+	0.149633i
$213$	−9.38404			−0.642984
$214$	−0.958615	−	1.66037i	−0.0655296	−	0.113501i
$215$	−15.8605	−	27.4713i	−1.08168	−	1.87352i
$216$	1.00000			0.0680414
$217$	−4.84750	−	8.39612i	−0.329070	−	0.569966i
$218$	9.38404	−	16.2536i	0.635568	−	1.10084i
$219$	0.187177	−	0.324200i	0.0126483	−	0.0219074i
$220$	4.97823			0.335632
$221$		0			0
$222$	−3.87800			−0.260274
$223$	−2.59179	+	4.48912i	−0.173559	+	0.300614i	−0.939662	−	0.342105i	$-0.888860\pi$
$223$	−2.59179	+	4.48912i	−0.173559	+	0.300614i	0.766102	+	0.642719i	$0.222194\pi$
$224$	−2.17845	+	3.77318i	−0.145554	+	0.252106i
$225$	−6.72737	−	11.6521i	−0.448491	−	0.776809i
$226$	−10.4155			−0.692829
$227$	7.44385	+	12.8931i	0.494065	+	0.855746i	0.999977	−	0.00683921i	$-0.00217701\pi$
$227$	7.44385	+	12.8931i	0.494065	+	0.855746i	−0.505911	+	0.862586i	$0.668844\pi$
$228$	0.890084	+	1.54167i	0.0589472	+	0.102100i
$229$	−23.4577			−1.55013			−0.775065	−	0.631882i	$-0.782283\pi$
$229$	−23.4577			−1.55013			−0.775065	+	0.631882i	$0.782283\pi$
$230$	7.26875	+	12.5898i	0.479287	+	0.830150i
$231$	−2.52446	+	4.37249i	−0.166097	+	0.287689i
$232$	3.46950	−	6.00935i	0.227784	−	0.394533i
$233$	−11.8780			−0.778154			−0.389077	−	0.921205i	$-0.627206\pi$
$233$	−11.8780			−0.778154			−0.389077	+	0.921205i	$0.627206\pi$
$234$		0			0
$235$	−7.64742			−0.498862
$236$	−3.31551	+	5.74263i	−0.215821	+	0.373814i
$237$	1.32759	−	2.29946i	0.0862364	−	0.149366i
$238$	−1.07606	−	1.86380i	−0.0697509	−	0.120812i
$239$	25.3599			1.64039			0.820197	−	0.572081i	$-0.193864\pi$
$239$	25.3599			1.64039			0.820197	+	0.572081i	$0.193864\pi$
$240$	2.14795	+	3.72036i	0.138649	+	0.240148i
$241$	6.01089	+	10.4112i	0.387195	+	0.670642i	0.992071	−	0.125678i	$-0.0401106\pi$
$241$	6.01089	+	10.4112i	0.387195	+	0.670642i	−0.604876	+	0.796320i	$0.706777\pi$
$242$	9.65710			0.620782
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.24698	+	9.08804i	−0.335903	+	0.581802i
$245$	−25.7379	+	44.5793i	−1.64433	+	2.84807i
$246$	−6.31767			−0.402800
$247$		0			0
$248$	2.22521			0.141301
$249$	−7.13922	+	12.3655i	−0.452430	+	0.783631i
$250$	18.1603	−	31.4546i	1.14856	−	1.98936i
$251$	7.67241	+	13.2890i	0.484278	+	0.838794i	0.999837	−	0.0180600i	$-0.00574899\pi$
$251$	7.67241	+	13.2890i	0.484278	+	0.838794i	−0.515559	+	0.856854i	$0.672416\pi$
$252$	−4.35690			−0.274459
$253$	−1.96077	−	3.39616i	−0.123273	−	0.213514i
$254$	4.19687	+	7.26918i	0.263335	+	0.456109i
$255$	−2.12200			−0.132885
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.75302	−	6.50042i	0.234107	−	0.405485i	−0.724906	−	0.688848i	$-0.758117\pi$
$257$	3.75302	−	6.50042i	0.234107	−	0.405485i	0.959013	+	0.283363i	$0.0914501\pi$
$258$	−3.69202	+	6.39477i	−0.229855	+	0.398121i
$259$	16.8961			1.04987
$260$		0			0
$261$	6.93900			0.429513
$262$	−6.75182	+	11.6945i	−0.417129	+	0.722489i
$263$	6.11529	−	10.5920i	0.377085	−	0.653131i	−0.613552	−	0.789655i	$-0.710260\pi$
$263$	6.11529	−	10.5920i	0.377085	−	0.653131i	0.990637	+	0.136524i	$0.0435931\pi$
$264$	−0.579417	−	1.00358i	−0.0356606	−	0.0617660i
$265$	−10.8073			−0.663888
$266$	−3.87800	−	6.71690i	−0.237776	−	0.411839i
$267$	0.417895	+	0.723815i	0.0255747	+	0.0442968i
$268$	4.09783			0.250315
$269$	−1.35809	−	2.35228i	−0.0828044	−	0.143421i	0.821649	−	0.569994i	$-0.193054\pi$
$269$	−1.35809	−	2.35228i	−0.0828044	−	0.143421i	−0.904453	+	0.426572i	$0.859721\pi$
$270$	−2.14795	+	3.72036i	−0.130720	+	0.226414i
$271$	6.19687	−	10.7333i	0.376433	−	0.652001i	−0.614108	−	0.789222i	$-0.710484\pi$
$271$	6.19687	−	10.7333i	0.376433	−	0.652001i	0.990540	+	0.137222i	$0.0438172\pi$
$272$	0.493959			0.0299507
$273$		0			0
$274$	−4.00000			−0.241649
$275$	−7.79590	+	13.5029i	−0.470110	+	0.814255i
$276$	1.69202	−	2.93067i	0.101848	−	0.176405i
$277$	12.0640	+	20.8954i	0.724854	+	1.25548i	0.959034	+	0.283291i	$0.0914264\pi$
$277$	12.0640	+	20.8954i	0.724854	+	1.25548i	−0.234179	+	0.972193i	$0.575240\pi$
$278$	15.0315			0.901527
$279$	1.11260	+	1.92709i	0.0666099	+	0.115372i
$280$	−9.35839	−	16.2092i	−0.559271	−	0.968685i
$281$	−12.8358			−0.765719			−0.382860	−	0.923807i	$-0.625061\pi$
$281$	−12.8358			−0.765719			−0.382860	+	0.923807i	$0.625061\pi$
$282$	0.890084	+	1.54167i	0.0530037	+	0.0918051i
$283$	−2.82371	+	4.89081i	−0.167852	+	0.290728i	−0.937664	−	0.347542i	$-0.887016\pi$
$283$	−2.82371	+	4.89081i	−0.167852	+	0.290728i	0.769812	+	0.638270i	$0.220350\pi$
$284$	−4.69202	+	8.12682i	−0.278420	+	0.482238i
$285$	−7.64742			−0.452994
$286$		0			0
$287$	27.5254			1.62477
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	8.37800	−	14.5111i	0.492824	−	0.853596i
$290$	14.9046	+	25.8156i	0.875229	+	1.51594i
$291$	−18.3937			−1.07826
$292$	−0.187177	−	0.324200i	−0.0109537	−	0.0189724i
$293$	10.6826	+	18.5029i	0.624086	+	1.08095i	0.988717	+	0.149796i	$0.0478618\pi$
$293$	10.6826	+	18.5029i	0.624086	+	1.08095i	−0.364631	+	0.931152i	$0.618805\pi$
$294$	11.9825			0.698836
$295$	−14.2431	−	24.6698i	−0.829265	−	1.43633i
$296$	−1.93900	+	3.35845i	−0.112702	+	0.195206i
$297$	0.579417	−	1.00358i	0.0336212	−	0.0582336i
$298$	3.92692			0.227480
$299$		0			0
$300$	−13.4547			−0.776809
$301$	16.0858	−	27.8613i	0.927167	−	1.60590i
$302$	4.81431	−	8.33864i	0.277033	−	0.479835i
$303$	−2.73341	−	4.73440i	−0.157030	−	0.271984i
$304$	1.78017			0.102100
$305$	−22.5405	−	39.0413i	−1.29066	−	2.23550i
$306$	0.246980	+	0.427781i	0.0141189	+	0.0244546i
$307$	28.8853			1.64857			0.824286	−	0.566174i	$-0.191577\pi$
$307$	28.8853			1.64857			0.824286	+	0.566174i	$0.191577\pi$
$308$	2.52446	+	4.37249i	0.143844	+	0.249146i
$309$	3.50484	−	6.07057i	0.199384	−	0.345343i
$310$	−4.77963	+	8.27857i	−0.271465	+	0.470191i
$311$	3.38404			0.191891			0.0959457	−	0.995387i	$-0.469412\pi$
$311$	3.38404			0.191891			0.0959457	+	0.995387i	$0.469412\pi$
$312$		0			0
$313$	14.3502			0.811121			0.405560	−	0.914068i	$-0.367076\pi$
$313$	14.3502			0.811121			0.405560	+	0.914068i	$0.367076\pi$
$314$	−8.69202	+	15.0550i	−0.490519	+	0.849604i
$315$	9.35839	−	16.2092i	0.527285	−	0.913285i
$316$	−1.32759	−	2.29946i	−0.0746829	−	0.129355i
$317$	18.5332			1.04093			0.520464	−	0.853884i	$-0.325759\pi$
$317$	18.5332			1.04093			0.520464	+	0.853884i	$0.325759\pi$
$318$	1.25786	+	2.17869i	0.0705376	+	0.122175i
$319$	−4.02057	−	6.96384i	−0.225109	−	0.389900i
$320$	4.29590			0.240148
$321$	−0.958615	−	1.66037i	−0.0535047	−	0.0926728i
$322$	−7.37196	+	12.7686i	−0.410823	+	0.711567i
$323$	−0.439665	+	0.761522i	−0.0244636	+	0.0423722i
$324$	1.00000			0.0555556
$325$		0			0
$326$	22.4698			1.24449
$327$	9.38404	−	16.2536i	0.518939	−	0.898828i
$328$	−3.15883	+	5.47126i	−0.174417	+	0.302100i
$329$	−3.87800	−	6.71690i	−0.213801	−	0.370315i
$330$	4.97823			0.274043
$331$	3.93900	+	6.82255i	0.216507	+	0.375001i	0.953738	−	0.300640i	$-0.0972002\pi$
$331$	3.93900	+	6.82255i	0.216507	+	0.375001i	−0.737231	+	0.675641i	$0.763867\pi$
$332$	7.13922	+	12.3655i	0.391816	+	0.678644i
$333$	−3.87800			−0.212513
$334$	−0.417895	−	0.723815i	−0.0228662	−	0.0396054i
$335$	−8.80194	+	15.2454i	−0.480901	+	0.832945i
$336$	−2.17845	+	3.77318i	−0.118844	+	0.205844i
$337$	−13.7265			−0.747728			−0.373864	−	0.927484i	$-0.621967\pi$
$337$	−13.7265			−0.747728			−0.373864	+	0.927484i	$0.621967\pi$
$338$		0			0
$339$	−10.4155			−0.565692
$340$	−1.06100	+	1.83770i	−0.0575407	+	0.0996635i
$341$	1.28932	−	2.23317i	0.0698208	−	0.120933i
$342$	0.890084	+	1.54167i	0.0481302	+	0.0833640i
$343$	−21.7084			−1.17214
$344$	3.69202	+	6.39477i	0.199060	+	0.344783i
$345$	7.26875	+	12.5898i	0.391336	+	0.677814i
$346$	4.17092			0.224230
$347$	2.42543	+	4.20096i	0.130204	+	0.225520i	0.923755	−	0.382984i	$-0.125104\pi$
$347$	2.42543	+	4.20096i	0.130204	+	0.225520i	−0.793551	+	0.608503i	$0.791770\pi$
$348$	3.46950	−	6.00935i	0.185985	−	0.322135i
$349$	−14.1739	+	24.5499i	−0.758711	+	1.31413i	0.184797	+	0.982777i	$0.440837\pi$
$349$	−14.1739	+	24.5499i	−0.758711	+	1.31413i	−0.943508	+	0.331350i	$0.892496\pi$
$350$	58.6209			3.13342
$351$		0			0
$352$	−1.15883			−0.0617660
$353$	−14.2228	+	24.6346i	−0.757004	+	1.31117i	0.187368	+	0.982290i	$0.440004\pi$
$353$	−14.2228	+	24.6346i	−0.757004	+	1.31117i	−0.944372	+	0.328880i	$0.893329\pi$
$354$	−3.31551	+	5.74263i	−0.176217	+	0.305218i
$355$	−20.1564	−	34.9120i	−1.06979	−	1.85294i
$356$	0.835790			0.0442968
$357$	−1.07606	−	1.86380i	−0.0569514	−	0.0986427i
$358$	11.4438	+	19.8213i	0.604826	+	1.04759i
$359$	−11.2271			−0.592545			−0.296273	−	0.955103i	$-0.595744\pi$
$359$	−11.2271			−0.592545			−0.296273	+	0.955103i	$0.595744\pi$
$360$	2.14795	+	3.72036i	0.113207	+	0.196080i
$361$	7.91550	−	13.7101i	0.416605	−	0.721582i
$362$	5.80194	−	10.0493i	0.304943	−	0.528177i
$363$	9.65710			0.506867
$364$		0			0
$365$	1.60819			0.0841764
$366$	−5.24698	+	9.08804i	−0.274264	+	0.475039i
$367$	−8.41335	+	14.5723i	−0.439173	+	0.760670i	−0.997626	−	0.0688662i	$-0.978062\pi$
$367$	−8.41335	+	14.5723i	−0.439173	+	0.760670i	0.558453	+	0.829536i	$0.311395\pi$
$368$	−1.69202	−	2.93067i	−0.0882027	−	0.152772i
$369$	−6.31767			−0.328885
$370$	−8.32975	−	14.4275i	−0.433043	−	0.750053i
$371$	−5.48039	−	9.49231i	−0.284527	−	0.492816i
$372$	2.22521			0.115372
$373$	13.2664	+	22.9780i	0.686906	+	1.18976i	0.972834	+	0.231505i	$0.0743649\pi$
$373$	13.2664	+	22.9780i	0.686906	+	1.18976i	−0.285928	+	0.958251i	$0.592302\pi$
$374$	0.286208	−	0.495727i	0.0147995	−	0.0256334i
$375$	18.1603	−	31.4546i	0.937795	−	1.62431i
$376$	1.78017			0.0918051
$377$		0			0
$378$	−4.35690			−0.224095
$379$	10.9879	−	19.0316i	0.564411	−	0.977589i	−0.432693	−	0.901541i	$-0.642436\pi$
$379$	10.9879	−	19.0316i	0.564411	−	0.977589i	0.997104	−	0.0760479i	$-0.0242302\pi$
$380$	−3.82371	+	6.62286i	−0.196152	+	0.339745i
$381$	4.19687	+	7.26918i	0.215012	+	0.372412i
$382$	−16.6896			−0.853916
$383$	−0.307979	−	0.533434i	−0.0157370	−	0.0272572i	0.858050	−	0.513567i	$-0.171676\pi$
$383$	−0.307979	−	0.533434i	−0.0157370	−	0.0272572i	−0.873787	+	0.486309i	$0.838343\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−21.6896			−1.10541
$386$	−4.82371	−	8.35491i	−0.245520	−	0.425254i
$387$	−3.69202	+	6.39477i	−0.187676	+	0.325064i
$388$	−9.19687	+	15.9294i	−0.466900	+	0.808695i
$389$	−35.5260			−1.80124			−0.900620	−	0.434607i	$-0.856887\pi$
$389$	−35.5260			−1.80124			−0.900620	+	0.434607i	$0.856887\pi$
$390$		0			0
$391$	1.67158			0.0845354
$392$	5.99127	−	10.3772i	0.302605	−	0.524127i
$393$	−6.75182	+	11.6945i	−0.340584	+	0.589910i
$394$	−9.81916	−	17.0073i	−0.494682	−	0.856815i
$395$	11.4064			0.573918
$396$	−0.579417	−	1.00358i	−0.0291168	−	0.0504318i
$397$	−8.03923	−	13.9244i	−0.403477	−	0.698843i	0.590666	−	0.806916i	$-0.298865\pi$
$397$	−8.03923	−	13.9244i	−0.403477	−	0.698843i	−0.994143	+	0.108073i	$0.965532\pi$
$398$	18.4209			0.923355
$399$	−3.87800	−	6.71690i	−0.194143	−	0.336265i
$400$	−6.72737	+	11.6521i	−0.336368	+	0.582607i
$401$	11.4547	−	19.8402i	0.572022	−	0.990771i	−0.424336	−	0.905505i	$-0.639493\pi$
$401$	11.4547	−	19.8402i	0.572022	−	0.990771i	0.996358	−	0.0852664i	$-0.0271741\pi$
$402$	4.09783			0.204381
$403$		0			0
$404$	−5.46681			−0.271984
$405$	−2.14795	+	3.72036i	−0.106732	+	0.184866i
$406$	−15.1163	+	26.1821i	−0.750207	+	1.29940i
$407$	2.24698	+	3.89188i	0.111379	+	0.192913i
$408$	0.493959			0.0244546
$409$	−0.623490	−	1.07992i	−0.0308296	−	0.0533984i	0.850199	−	0.526462i	$-0.176482\pi$
$409$	−0.623490	−	1.07992i	−0.0308296	−	0.0533984i	−0.881029	+	0.473063i	$0.843148\pi$
$410$	−13.5700	−	23.5040i	−0.670176	−	1.16078i
$411$	−4.00000			−0.197305
$412$	−3.50484	−	6.07057i	−0.172671	−	0.299075i
$413$	14.4453	−	25.0201i	0.710809	−	1.23116i
$414$	1.69202	−	2.93067i	0.0831583	−	0.144034i
$415$	−61.3387			−3.01100
$416$		0			0
$417$	15.0315			0.736094
$418$	1.03146	−	1.78654i	0.0504503	−	0.0873825i
$419$	−14.7315	+	25.5158i	−0.719683	+	1.24653i	0.241442	+	0.970415i	$0.422380\pi$
$419$	−14.7315	+	25.5158i	−0.719683	+	1.24653i	−0.961125	+	0.276112i	$0.910954\pi$
$420$	−9.35839	−	16.2092i	−0.456643	−	0.790928i
$421$	17.3491			0.845545			0.422772	−	0.906236i	$-0.361057\pi$
$421$	17.3491			0.845545			0.422772	+	0.906236i	$0.361057\pi$
$422$	7.96077	+	13.7885i	0.387524	+	0.671212i
$423$	0.890084	+	1.54167i	0.0432774	+	0.0749586i
$424$	2.51573			0.122175
$425$	−3.32304	−	5.75568i	−0.161191	−	0.279192i
$426$	−4.69202	+	8.12682i	−0.227329	+	0.393746i
$427$	22.8605	−	39.5956i	1.10630	−	1.91617i
$428$	−1.91723			−0.0926728
$429$		0			0
$430$	−31.7211			−1.52973
$431$	12.6920	−	21.9832i	0.611353	−	1.05889i	−0.379659	−	0.925126i	$-0.623959\pi$
$431$	12.6920	−	21.9832i	0.611353	−	1.05889i	0.991013	−	0.133768i	$-0.0427078\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−10.0027	−	17.3252i	−0.480699	−	0.832594i	0.519056	−	0.854740i	$-0.326284\pi$
$433$	−10.0027	−	17.3252i	−0.480699	−	0.832594i	−0.999755	+	0.0221458i	$0.992950\pi$
$434$	−9.69501			−0.465375
$435$	14.9046	+	25.8156i	0.714622	+	1.23776i
$436$	−9.38404	−	16.2536i	−0.449414	−	0.778408i
$437$	6.02416			0.288175
$438$	−0.187177	−	0.324200i	−0.00894367	−	0.0154909i
$439$	−0.271971	+	0.471067i	−0.0129805	+	0.0224828i	−0.872443	−	0.488716i	$-0.837465\pi$
$439$	−0.271971	+	0.471067i	−0.0129805	+	0.0224828i	0.859462	+	0.511199i	$0.170799\pi$
$440$	2.48911	−	4.31127i	0.118664	−	0.205532i
$441$	11.9825			0.570597
$442$		0			0
$443$	−18.1360			−0.861667			−0.430834	−	0.902431i	$-0.641780\pi$
$443$	−18.1360			−0.861667			−0.430834	+	0.902431i	$0.641780\pi$
$444$	−1.93900	+	3.35845i	−0.0920209	+	0.159385i
$445$	−1.79523	+	3.10943i	−0.0851022	+	0.147401i
$446$	2.59179	+	4.48912i	0.122725	+	0.212566i
$447$	3.92692			0.185737
$448$	2.17845	+	3.77318i	0.102922	+	0.178266i
$449$	14.6896	+	25.4432i	0.693246	+	1.20074i	0.970768	+	0.240019i	$0.0771536\pi$
$449$	14.6896	+	25.4432i	0.693246	+	1.20074i	−0.277522	+	0.960719i	$0.589513\pi$
$450$	−13.4547			−0.634262
$451$	3.66056	+	6.34028i	0.172369	+	0.298552i
$452$	−5.20775	+	9.02009i	−0.244952	+	0.424269i
$453$	4.81431	−	8.33864i	0.226196	−	0.391783i
$454$	14.8877			0.698714
$455$		0			0
$456$	1.78017			0.0833640
$457$	−4.17360	+	7.22889i	−0.195233	+	0.338153i	−0.946977	−	0.321302i	$-0.895880\pi$
$457$	−4.17360	+	7.22889i	−0.195233	+	0.338153i	0.751744	+	0.659455i	$0.229213\pi$
$458$	−11.7289	+	20.3150i	−0.548054	+	0.949257i
$459$	0.246980	+	0.427781i	0.0115280	+	0.0199671i
$460$	14.5375			0.677814
$461$	10.7485	+	18.6169i	0.500606	+	0.867075i	1.00000		0.000700154i	$0.000222866\pi$
$461$	10.7485	+	18.6169i	0.500606	+	0.867075i	−0.499394	+	0.866375i	$0.666444\pi$
$462$	2.52446	+	4.37249i	0.117448	+	0.203427i
$463$	−26.1715			−1.21629			−0.608147	−	0.793825i	$-0.708087\pi$
$463$	−26.1715			−1.21629			−0.608147	+	0.793825i	$0.708087\pi$
$464$	−3.46950	−	6.00935i	−0.161068	−	0.278977i
$465$	−4.77963	+	8.27857i	−0.221650	+	0.383910i
$466$	−5.93900	+	10.2867i	−0.275119	+	0.476520i
$467$	−9.81269			−0.454077			−0.227039	−	0.973886i	$-0.572904\pi$
$467$	−9.81269			−0.454077			−0.227039	+	0.973886i	$0.572904\pi$
$468$		0			0
$469$	−17.8538			−0.824414
$470$	−3.82371	+	6.62286i	−0.176374	+	0.305490i
$471$	−8.69202	+	15.0550i	−0.400507	+	0.693699i
$472$	3.31551	+	5.74263i	0.152609	+	0.264326i
$473$	8.55688			0.393446
$474$	−1.32759	−	2.29946i	−0.0609784	−	0.105618i
$475$	−11.9758	−	20.7428i	−0.549489	−	0.951743i
$476$	−2.15213			−0.0986427
$477$	1.25786	+	2.17869i	0.0575937	+	0.0997552i
$478$	12.6799	−	21.9623i	0.579967	−	1.00453i
$479$	8.64071	−	14.9662i	0.394804	−	0.683821i	−0.598272	−	0.801293i	$-0.704146\pi$
$479$	8.64071	−	14.9662i	0.394804	−	0.683821i	0.993076	+	0.117472i	$0.0374791\pi$
$480$	4.29590			0.196080
$481$		0			0
$482$	12.0218			0.547577
$483$	−7.37196	+	12.7686i	−0.335436	+	0.580992i
$484$	4.82855	−	8.36330i	0.219480	−	0.380150i
$485$	−39.5088	−	68.4312i	−1.79400	−	3.10730i
$486$	1.00000			0.0453609
$487$	−15.8443	−	27.4431i	−0.717973	−	1.24357i	−0.961802	−	0.273747i	$-0.911737\pi$
$487$	−15.8443	−	27.4431i	−0.717973	−	1.24357i	0.243829	−	0.969818i	$-0.421597\pi$
$488$	5.24698	+	9.08804i	0.237520	+	0.411396i
$489$	22.4698			1.01612
$490$	25.7379	+	44.5793i	1.16272	+	2.01389i
$491$	−1.15183	+	1.99503i	−0.0519815	+	0.0900346i	−0.890845	−	0.454307i	$-0.849887\pi$
$491$	−1.15183	+	1.99503i	−0.0519815	+	0.0900346i	0.838864	+	0.544341i	$0.183220\pi$
$492$	−3.15883	+	5.47126i	−0.142411	+	0.246663i
$493$	3.42758			0.154371
$494$		0			0
$495$	4.97823			0.223755
$496$	1.11260	−	1.92709i	0.0499574	−	0.0865288i
$497$	20.4426	−	35.4077i	0.916978	−	1.58825i
$498$	7.13922	+	12.3655i	0.319916	+	0.554111i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−18.1603	−	31.4546i	−0.812154	−	1.40669i
$501$	−0.417895	−	0.723815i	−0.0186702	−	0.0323377i
$502$	15.3448			0.684873
$503$	17.6843	+	30.6300i	0.788502	+	1.36573i	0.926885	+	0.375346i	$0.122476\pi$
$503$	17.6843	+	30.6300i	0.788502	+	1.36573i	−0.138383	+	0.990379i	$0.544190\pi$
$504$	−2.17845	+	3.77318i	−0.0970358	+	0.168071i
$505$	11.7424	−	20.3385i	0.522531	−	0.905051i
$506$	−3.92154			−0.174334
$507$		0			0
$508$	8.39373			0.372412
$509$	14.3056	−	24.7780i	0.634084	−	1.09827i	−0.352624	−	0.935765i	$-0.614711\pi$
$509$	14.3056	−	24.7780i	0.634084	−	1.09827i	0.986708	−	0.162501i	$-0.0519560\pi$
$510$	−1.06100	+	1.83770i	−0.0469818	+	0.0813749i
$511$	0.815511	+	1.41251i	0.0360761	+	0.0624856i
$512$	−1.00000			−0.0441942
$513$	0.890084	+	1.54167i	0.0392982	+	0.0680664i
$514$	−3.75302	−	6.50042i	−0.165539	−	0.286721i
$515$	30.1129			1.32693
$516$	3.69202	+	6.39477i	0.162532	+	0.281514i
$517$	1.03146	−	1.78654i	0.0453635	−	0.0785719i
$518$	8.44803	−	14.6324i	0.371185	−	0.642911i
$519$	4.17092			0.183083
$520$		0			0
$521$	−17.1594			−0.751768			−0.375884	−	0.926667i	$-0.622661\pi$
$521$	−17.1594			−0.751768			−0.375884	+	0.926667i	$0.622661\pi$
$522$	3.46950	−	6.00935i	0.151856	−	0.263022i
$523$	−8.25667	+	14.3010i	−0.361039	+	0.625338i	−0.988132	−	0.153607i	$-0.950911\pi$
$523$	−8.25667	+	14.3010i	−0.361039	+	0.625338i	0.627093	+	0.778944i	$0.284245\pi$
$524$	6.75182	+	11.6945i	0.294955	+	0.510877i
$525$	58.6209			2.55842
$526$	−6.11529	−	10.5920i	−0.266639	−	0.461833i
$527$	0.549581	+	0.951903i	0.0239401	+	0.0414655i
$528$	−1.15883			−0.0504318
$529$	5.77413	+	10.0011i	0.251049	+	0.434830i
$530$	−5.40366	+	9.35941i	−0.234720	+	0.406547i
$531$	−3.31551	+	5.74263i	−0.143881	+	0.249209i
$532$	−7.75600			−0.336265
$533$		0			0
$534$	0.835790			0.0361682
$535$	4.11811	−	7.13278i	0.178042	−	0.308377i
$536$	2.04892	−	3.54883i	0.0884997	−	0.153286i
$537$	11.4438	+	19.8213i	0.493838	+	0.855353i
$538$	−2.71618			−0.117103
$539$	−6.94289	−	12.0254i	−0.299051	−	0.517972i
$540$	2.14795	+	3.72036i	0.0924330	+	0.160099i
$541$	25.0858			1.07852			0.539260	−	0.842139i	$-0.318704\pi$
$541$	25.0858			1.07852			0.539260	+	0.842139i	$0.318704\pi$
$542$	−6.19687	−	10.7333i	−0.266178	−	0.461034i
$543$	5.80194	−	10.0493i	0.248985	−	0.431255i
$544$	0.246980	−	0.427781i	0.0105892	−	0.0183410i
$545$	80.6258			3.45363
$546$		0			0
$547$	31.1594			1.33228			0.666140	−	0.745826i	$-0.267945\pi$
$547$	31.1594			1.33228			0.666140	+	0.745826i	$0.267945\pi$
$548$	−2.00000	+	3.46410i	−0.0854358	+	0.147979i
$549$	−5.24698	+	9.08804i	−0.223936	+	0.387868i
$550$	7.79590	+	13.5029i	0.332418	+	0.575765i
$551$	12.3526			0.526238
$552$	−1.69202	−	2.93067i	−0.0720172	−	0.124737i
$553$	5.78418	+	10.0185i	0.245969	+	0.426030i
$554$	24.1280			1.02510
$555$	−8.32975	−	14.4275i	−0.353578	−	0.612415i
$556$	7.51573	−	13.0176i	0.318738	−	0.552070i
$557$	1.98792	−	3.44318i	0.0842308	−	0.145892i	−0.820832	−	0.571169i	$-0.806490\pi$
$557$	1.98792	−	3.44318i	0.0842308	−	0.145892i	0.905063	+	0.425277i	$0.139823\pi$
$558$	2.22521			0.0942006
$559$		0			0
$560$	−18.7168			−0.790928
$561$	0.286208	−	0.495727i	0.0120837	−	0.0209296i
$562$	−6.41789	+	11.1161i	−0.270723	+	0.468905i
$563$	−0.301405	−	0.522049i	−0.0127027	−	0.0220018i	0.859604	−	0.510961i	$-0.170710\pi$
$563$	−0.301405	−	0.522049i	−0.0127027	−	0.0220018i	−0.872307	+	0.488959i	$0.837377\pi$
$564$	1.78017			0.0749586
$565$	−22.3720	−	38.7494i	−0.941195	−	1.63020i
$566$	2.82371	+	4.89081i	0.118689	+	0.205576i
$567$	−4.35690			−0.182972
$568$	4.69202	+	8.12682i	0.196873	+	0.340994i
$569$	−1.10992	+	1.92243i	−0.0465301	+	0.0805925i	−0.888352	−	0.459162i	$-0.848150\pi$
$569$	−1.10992	+	1.92243i	−0.0465301	+	0.0805925i	0.841822	+	0.539755i	$0.181483\pi$
$570$	−3.82371	+	6.62286i	−0.160158	+	0.277401i
$571$	24.4155			1.02176			0.510878	−	0.859653i	$-0.329320\pi$
$571$	24.4155			1.02176			0.510878	+	0.859653i	$0.329320\pi$
$572$		0			0
$573$	−16.6896			−0.697219
$574$	13.7627	−	23.8377i	0.574444	−	0.994967i
$575$	−22.7657	+	39.4313i	−0.949395	+	1.64440i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	20.7375			0.863313			0.431656	−	0.902038i	$-0.357929\pi$
$577$	20.7375			0.863313			0.431656	+	0.902038i	$0.357929\pi$
$578$	−8.37800	−	14.5111i	−0.348479	−	0.603583i
$579$	−4.82371	−	8.35491i	−0.200466	−	0.347218i
$580$	29.8092			1.23776
$581$	−31.1048	−	53.8752i	−1.29045	−	2.23512i
$582$	−9.19687	+	15.9294i	−0.381222	+	0.660296i
$583$	1.45766	−	2.52473i	0.0603699	−	0.104564i
$584$	−0.374354			−0.0154909
$585$		0			0
$586$	21.3653			0.882591
$587$	−5.68396	+	9.84490i	−0.234602	+	0.406343i	−0.959157	−	0.282874i	$-0.908712\pi$
$587$	−5.68396	+	9.84490i	−0.234602	+	0.406343i	0.724555	+	0.689217i	$0.242045\pi$
$588$	5.99127	−	10.3772i	0.247076	−	0.427948i
$589$	1.98062	+	3.43054i	0.0816101	+	0.141353i
$590$	−28.4862			−1.17276
$591$	−9.81916	−	17.0073i	−0.403906	−	0.699586i
$592$	1.93900	+	3.35845i	0.0796925	+	0.138031i
$593$	−36.7198			−1.50790			−0.753950	−	0.656932i	$-0.771854\pi$
$593$	−36.7198			−1.50790			−0.753950	+	0.656932i	$0.771854\pi$
$594$	−0.579417	−	1.00358i	−0.0237738	−	0.0411774i
$595$	4.62266	−	8.00669i	0.189511	−	0.328242i
$596$	1.96346	−	3.40081i	0.0804264	−	0.139303i
$597$	18.4209			0.753916
$598$		0			0
$599$	−47.4965			−1.94065			−0.970327	−	0.241798i	$-0.922263\pi$
$599$	−47.4965			−1.94065			−0.970327	+	0.241798i	$0.922263\pi$
$600$	−6.72737	+	11.6521i	−0.274644	+	0.475697i
$601$	−3.87531	+	6.71224i	−0.158077	+	0.273798i	−0.934175	−	0.356814i	$-0.883863\pi$
$601$	−3.87531	+	6.71224i	−0.158077	+	0.273798i	0.776098	+	0.630612i	$0.217196\pi$
$602$	−16.0858	−	27.8613i	−0.655606	−	1.13554i
$603$	4.09783			0.166877
$604$	−4.81431	−	8.33864i	−0.195892	−	0.339294i
$605$	20.7430	+	35.9279i	0.843321	+	1.46068i
$606$	−5.46681			−0.222074
$607$	−1.82155	−	3.15502i	−0.0739345	−	0.128058i	0.826688	−	0.562661i	$-0.190222\pi$
$607$	−1.82155	−	3.15502i	−0.0739345	−	0.128058i	−0.900622	+	0.434602i	$0.856889\pi$
$608$	0.890084	−	1.54167i	0.0360977	−	0.0625230i
$609$	−15.1163	+	26.1821i	−0.612541	+	1.06095i
$610$	−45.0810			−1.82528
$611$		0			0
$612$	0.493959			0.0199671
$613$	−15.2131	+	26.3499i	−0.614452	+	1.06426i	0.376028	+	0.926608i	$0.377290\pi$
$613$	−15.2131	+	26.3499i	−0.614452	+	1.06426i	−0.990480	+	0.137654i	$0.956044\pi$
$614$	14.4426	−	25.0154i	0.582858	−	1.00954i
$615$	−13.5700	−	23.5040i	−0.547196	−	0.947772i
$616$	5.04892			0.203427
$617$	4.08277	+	7.07156i	0.164366	+	0.284690i	0.936430	−	0.350854i	$-0.114109\pi$
$617$	4.08277	+	7.07156i	0.164366	+	0.284690i	−0.772064	+	0.635545i	$0.780775\pi$
$618$	−3.50484	−	6.07057i	−0.140986	−	0.244194i
$619$	−7.95646			−0.319797			−0.159899	−	0.987133i	$-0.551117\pi$
$619$	−7.95646			−0.319797			−0.159899	+	0.987133i	$0.551117\pi$
$620$	4.77963	+	8.27857i	0.191955	+	0.332475i
$621$	1.69202	−	2.93067i	0.0678985	−	0.117604i
$622$	1.69202	−	2.93067i	0.0678439	−	0.117509i
$623$	−3.64145			−0.145892
$624$		0			0
$625$	88.7561			3.55024
$626$	7.17510	−	12.4276i	0.286774	−	0.496708i
$627$	1.03146	−	1.78654i	0.0411925	−	0.0713475i
$628$	8.69202	+	15.0550i	0.346849	+	0.600761i
$629$	−1.91557			−0.0763790
$630$	−9.35839	−	16.2092i	−0.372847	−	0.645790i
$631$	−7.61679	−	13.1927i	−0.303219	−	0.525191i	0.673644	−	0.739056i	$-0.264728\pi$
$631$	−7.61679	−	13.1927i	−0.303219	−	0.525191i	−0.976863	+	0.213865i	$0.931395\pi$
$632$	−2.65519			−0.105618
$633$	7.96077	+	13.7885i	0.316412	+	0.548042i
$634$	9.26659	−	16.0502i	0.368023	−	0.637435i
$635$	−18.0293	+	31.2277i	−0.715471	+	1.23923i
$636$	2.51573			0.0997552
$637$		0			0
$638$	−8.04115			−0.318352
$639$	−4.69202	+	8.12682i	−0.185614	+	0.321492i
$640$	2.14795	−	3.72036i	0.0849051	−	0.147060i
$641$	7.09544	+	12.2897i	0.280253	+	0.485413i	0.971447	−	0.237257i	$-0.0762483\pi$
$641$	7.09544	+	12.2897i	0.280253	+	0.485413i	−0.691194	+	0.722669i	$0.742915\pi$
$642$	−1.91723			−0.0756671
$643$	−11.2784	−	19.5348i	−0.444778	−	0.770378i	0.553259	−	0.833010i	$-0.313384\pi$
$643$	−11.2784	−	19.5348i	−0.444778	−	0.770378i	−0.998037	+	0.0626312i	$0.980051\pi$
$644$	7.37196	+	12.7686i	0.290496	+	0.503154i
$645$	−31.7211			−1.24902
$646$	0.439665	+	0.761522i	0.0172984	+	0.0299617i
$647$	18.4523	−	31.9604i	0.725436	−	1.25649i	−0.233358	−	0.972391i	$-0.574971\pi$
$647$	18.4523	−	31.9604i	0.725436	−	1.25649i	0.958794	−	0.284102i	$-0.0916953\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	7.68425			0.301633
$650$		0			0
$651$	−9.69501			−0.379977
$652$	11.2349	−	19.4594i	0.439993	−	0.762089i
$653$	0.924764	−	1.60174i	0.0361888	−	0.0626808i	−0.847364	−	0.531013i	$-0.821812\pi$
$653$	0.924764	−	1.60174i	0.0361888	−	0.0626808i	0.883553	+	0.468332i	$0.155145\pi$
$654$	−9.38404	−	16.2536i	−0.366945	−	0.635568i
$655$	−58.0103			−2.26665
$656$	3.15883	+	5.47126i	0.123332	+	0.213617i
$657$	−0.187177	−	0.324200i	−0.00730248	−	0.0126483i
$658$	−7.75600			−0.302361
$659$	−9.13922	−	15.8296i	−0.356013	−	0.616633i	0.631277	−	0.775557i	$-0.282531\pi$
$659$	−9.13922	−	15.8296i	−0.356013	−	0.616633i	−0.987291	+	0.158924i	$0.949198\pi$
$660$	2.48911	−	4.31127i	0.0968887	−	0.167816i
$661$	−1.81700	+	3.14714i	−0.0706732	+	0.122410i	−0.899197	−	0.437545i	$-0.855848\pi$
$661$	−1.81700	+	3.14714i	−0.0706732	+	0.122410i	0.828523	+	0.559955i	$0.189181\pi$
$662$	7.87800			0.306187
$663$		0			0
$664$	14.2784			0.554111
$665$	16.6595	−	28.8551i	0.646028	−	1.11895i
$666$	−1.93900	+	3.35845i	−0.0751348	+	0.130137i
$667$	−11.7409	−	20.3359i	−0.454611	−	0.787409i
$668$	−0.835790			−0.0323377
$669$	2.59179	+	4.48912i	0.100205	+	0.173559i
$670$	8.80194	+	15.2454i	0.340049	+	0.588981i
$671$	12.1608			0.469461
$672$	2.17845	+	3.77318i	0.0840355	+	0.145554i
$673$	3.07391	−	5.32417i	0.118490	−	0.205232i	−0.800679	−	0.599093i	$-0.795528\pi$
$673$	3.07391	−	5.32417i	0.118490	−	0.205232i	0.919170	+	0.393862i	$0.128861\pi$
$674$	−6.86323	+	11.8875i	−0.264362	+	0.457888i
$675$	−13.4547			−0.517873
$676$		0			0
$677$	−18.2892			−0.702911			−0.351455	−	0.936205i	$-0.614313\pi$
$677$	−18.2892			−0.702911			−0.351455	+	0.936205i	$0.614313\pi$
$678$	−5.20775	+	9.02009i	−0.200002	+	0.346414i
$679$	40.0698	−	69.4029i	1.53774	−	2.66344i
$680$	1.06100	+	1.83770i	0.0406875	+	0.0704727i
$681$	14.8877			0.570498
$682$	−1.28932	−	2.23317i	−0.0493708	−	0.0855127i
$683$	−1.79643	−	3.11151i	−0.0687385	−	0.119059i	0.829608	−	0.558347i	$-0.188564\pi$
$683$	−1.79643	−	3.11151i	−0.0687385	−	0.119059i	−0.898346	+	0.439288i	$0.855231\pi$
$684$	1.78017			0.0680664
$685$	−8.59179	−	14.8814i	−0.328276	−	0.568590i
$686$	−10.8542	+	18.8000i	−0.414416	+	0.717789i
$687$	−11.7289	+	20.3150i	−0.447484	+	0.775065i
$688$	7.38404			0.281514
$689$		0			0
$690$	14.5375			0.553433
$691$	9.90946	−	17.1637i	0.376974	−	0.652938i	−0.613647	−	0.789581i	$-0.710298\pi$
$691$	9.90946	−	17.1637i	0.376974	−	0.652938i	0.990620	+	0.136643i	$0.0436314\pi$
$692$	2.08546	−	3.61212i	0.0792772	−	0.137312i
$693$	2.52446	+	4.37249i	0.0958963	+	0.166097i
$694$	4.85086			0.184136
$695$	32.2868	+	55.9224i	1.22471	+	2.12126i
$696$	−3.46950	−	6.00935i	−0.131511	−	0.227784i
$697$	−3.12067			−0.118204
$698$	14.1739	+	24.5499i	0.536490	+	0.929228i
$699$	−5.93900	+	10.2867i	−0.224634	+	0.389077i
$700$	29.3104	−	50.7672i	1.10783	−	1.91882i
$701$	5.25608			0.198519			0.0992596	−	0.995062i	$-0.468353\pi$
$701$	5.25608			0.198519			0.0992596	+	0.995062i	$0.468353\pi$
$702$		0			0
$703$	−6.90349			−0.260370
$704$	−0.579417	+	1.00358i	−0.0218376	+	0.0378238i
$705$	−3.82371	+	6.62286i	−0.144009	+	0.249431i
$706$	14.2228	+	24.6346i	0.535283	+	0.927137i
$707$	23.8183			0.895781
$708$	3.31551	+	5.74263i	0.124605	+	0.215821i
$709$	−13.0489	−	22.6014i	−0.490062	−	0.848813i	0.509872	−	0.860250i	$-0.329693\pi$
$709$	−13.0489	−	22.6014i	−0.490062	−	0.848813i	−0.999935	+	0.0114372i	$0.996359\pi$
$710$	−40.3129			−1.51292
$711$	−1.32759	−	2.29946i	−0.0497886	−	0.0862364i
$712$	0.417895	−	0.723815i	0.0156613	−	0.0271261i
$713$	3.76510	−	6.52135i	0.141004	−	0.244226i
$714$	−2.15213			−0.0805414
$715$		0			0
$716$	22.8877			0.855353
$717$	12.6799	−	21.9623i	0.473541	−	0.820197i
$718$	−5.61356	+	9.72298i	−0.209496	+	0.362858i
$719$	−25.4155	−	44.0209i	−0.947838	−	1.64170i	−0.749966	−	0.661476i	$-0.769930\pi$
$719$	−25.4155	−	44.0209i	−0.947838	−	1.64170i	−0.197872	−	0.980228i	$-0.563403\pi$
$720$	4.29590			0.160099
$721$	15.2702	+	26.4488i	0.568694	+	0.985006i
$722$	−7.91550	−	13.7101i	−0.294584	−	0.510235i
$723$	12.0218			0.447094
$724$	−5.80194	−	10.0493i	−0.215627	−	0.373477i
$725$	−46.6812	+	80.8542i	−1.73370	+	3.00285i
$726$	4.82855	−	8.36330i	0.179204	−	0.310391i
$727$	−20.5042			−0.760460			−0.380230	−	0.924892i	$-0.624155\pi$
$727$	−20.5042			−0.760460			−0.380230	+	0.924892i	$0.624155\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	0.804094	−	1.39273i	0.0297608	−	0.0515473i
$731$	−1.82371	+	3.15875i	−0.0674523	+	0.116831i
$732$	5.24698	+	9.08804i	0.193934	+	0.335903i
$733$	3.26205			0.120486			0.0602432	−	0.998184i	$-0.480812\pi$
$733$	3.26205			0.120486			0.0602432	+	0.998184i	$0.480812\pi$
$734$	8.41335	+	14.5723i	0.310542	+	0.537875i
$735$	25.7379	+	44.5793i	0.949356	+	1.64433i
$736$	−3.38404			−0.124737
$737$	−2.37435	−	4.11250i	−0.0874605	−	0.151486i
$738$	−3.15883	+	5.47126i	−0.116278	+	0.201400i
$739$	16.4101	−	28.4232i	0.603656	−	1.04556i	−0.388606	−	0.921404i	$-0.627043\pi$
$739$	16.4101	−	28.4232i	0.603656	−	1.04556i	0.992262	−	0.124159i	$-0.0396234\pi$
$740$	−16.6595			−0.612415
$741$		0			0
$742$	−10.9608			−0.402383
$743$	−17.4765	+	30.2702i	−0.641151	+	1.11051i	0.344026	+	0.938960i	$0.388209\pi$
$743$	−17.4765	+	30.2702i	−0.641151	+	1.11051i	−0.985176	+	0.171545i	$0.945124\pi$
$744$	1.11260	−	1.92709i	0.0407901	−	0.0706505i
$745$	8.43482	+	14.6095i	0.309028	+	0.535252i
$746$	26.5327			0.971432
$747$	7.13922	+	12.3655i	0.261210	+	0.452430i
$748$	−0.286208	−	0.495727i	−0.0104648	−	0.0181256i
$749$	8.35317			0.305218
$750$	−18.1603	−	31.4546i	−0.663121	−	1.14856i
$751$	5.08306	−	8.80413i	0.185484	−	0.321267i	−0.758256	−	0.651957i	$-0.773948\pi$
$751$	5.08306	−	8.80413i	0.185484	−	0.321267i	0.943739	+	0.330690i	$0.107281\pi$
$752$	0.890084	−	1.54167i	0.0324580	−	0.0562189i
$753$	15.3448			0.559196
$754$		0			0
$755$	41.3636			1.50538
$756$	−2.17845	+	3.77318i	−0.0792294	+	0.137229i
$757$	1.23191	−	2.13374i	0.0447747	−	0.0775520i	−0.842770	−	0.538275i	$-0.819076\pi$
$757$	1.23191	−	2.13374i	0.0447747	−	0.0775520i	0.887544	+	0.460723i	$0.152410\pi$
$758$	−10.9879	−	19.0316i	−0.399099	−	0.691260i
$759$	−3.92154			−0.142343
$760$	3.82371	+	6.62286i	0.138700	+	0.240236i
$761$	−21.4034	−	37.0718i	−0.775873	−	1.34385i	−0.934302	−	0.356482i	$-0.883976\pi$
$761$	−21.4034	−	37.0718i	−0.775873	−	1.34385i	0.158429	−	0.987370i	$-0.449357\pi$
$762$	8.39373			0.304073
$763$	40.8853	+	70.8154i	1.48015	+	2.56369i
$764$	−8.34481	+	14.4536i	−0.301905	+	0.522914i
$765$	−1.06100	+	1.83770i	−0.0383605	+	0.0664423i
$766$	−0.615957			−0.0222554
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	12.7017	−	22.0000i	0.458035	−	0.793341i	−0.540822	−	0.841137i	$-0.681887\pi$
$769$	12.7017	−	22.0000i	0.458035	−	0.793341i	0.998857	+	0.0477967i	$0.0152200\pi$
$770$	−10.8448	+	18.7838i	−0.390820	+	0.676920i
$771$	−3.75302	−	6.50042i	−0.135162	−	0.234107i
$772$	−9.64742			−0.347218
$773$	2.23945	+	3.87884i	0.0805473	+	0.139512i	0.903485	−	0.428619i	$-0.141000\pi$
$773$	2.23945	+	3.87884i	0.0805473	+	0.139512i	−0.822938	+	0.568131i	$0.807667\pi$
$774$	3.69202	+	6.39477i	0.132707	+	0.229855i
$775$	−29.9396			−1.07546
$776$	9.19687	+	15.9294i	0.330148	+	0.571834i
$777$	8.44803	−	14.6324i	0.303071	−	0.524935i
$778$	−17.7630	+	30.7664i	−0.636835	+	1.10303i
$779$	−11.2465			−0.402948
$780$		0			0
$781$	10.8745			0.389122
$782$	0.835790	−	1.44763i	0.0298878	−	0.0517671i
$783$	3.46950	−	6.00935i	0.123990	−	0.214757i
$784$	−5.99127	−	10.3772i	−0.213974	−	0.370614i
$785$	−74.6801			−2.66545
$786$	6.75182	+	11.6945i	0.240830	+	0.417129i
$787$	4.71917	+	8.17384i	0.168220	+	0.291366i	0.937794	−	0.347192i	$-0.112865\pi$
$787$	4.71917	+	8.17384i	0.168220	+	0.291366i	−0.769574	+	0.638558i	$0.779531\pi$
$788$	−19.6383			−0.699586
$789$	−6.11529	−	10.5920i	−0.217710	−	0.377085i
$790$	5.70320	−	9.87824i	0.202911	−	0.351452i
$791$	22.6896	−	39.2996i	0.806750	−	1.39733i
$792$	−1.15883			−0.0411774
$793$		0			0
$794$	−16.0785			−0.570603
$795$	−5.40366	+	9.35941i	−0.191648	+	0.331944i
$796$	9.21044	−	15.9529i	0.326455	−	0.565437i
$797$	12.6230	+	21.8636i	0.447128	+	0.774449i	0.998198	−	0.0600107i	$-0.0191135\pi$
$797$	12.6230	+	21.8636i	0.447128	+	0.774449i	−0.551070	+	0.834459i	$0.685780\pi$
$798$	−7.75600			−0.274560
$799$	0.439665	+	0.761522i	0.0155542	+	0.0269407i
$800$	6.72737	+	11.6521i	0.237848	+	0.411965i
$801$	0.835790			0.0295312
$802$	−11.4547	−	19.8402i	−0.404481	−	0.700581i
$803$	−0.216907	+	0.375694i	−0.00765449	+	0.0132580i
$804$	2.04892	−	3.54883i	0.0722597	−	0.125158i
$805$	−63.3384			−2.23238
$806$		0			0
$807$	−2.71618			−0.0956142
$808$	−2.73341	+	4.73440i	−0.0961609	+	0.166556i
$809$	−5.85325	+	10.1381i	−0.205789	+	0.356437i	−0.950384	−	0.311079i	$-0.899309\pi$
$809$	−5.85325	+	10.1381i	−0.205789	+	0.356437i	0.744595	+	0.667517i	$0.232643\pi$
$810$	2.14795	+	3.72036i	0.0754712	+	0.130720i
$811$	−30.5628			−1.07321			−0.536603	−	0.843835i	$-0.680293\pi$
$811$	−30.5628			−1.07321			−0.536603	+	0.843835i	$0.680293\pi$
$812$	15.1163	+	26.1821i	0.530476	+	0.918812i
$813$	−6.19687	−	10.7333i	−0.217334	−	0.376433i
$814$	4.49396			0.157513
$815$	48.2640	+	83.5956i	1.69061	+	2.92823i
$816$	0.246980	−	0.427781i	0.00864602	−	0.0149753i
$817$	−6.57242	+	11.3838i	−0.229940	+	0.398267i
$818$	−1.24698			−0.0435996
$819$		0			0
$820$	−27.1400			−0.947772
$821$	−11.2796	+	19.5369i	−0.393662	+	0.681843i	−0.992929	−	0.118706i	$-0.962125\pi$
$821$	−11.2796	+	19.5369i	−0.393662	+	0.681843i	0.599267	+	0.800549i	$0.295459\pi$
$822$	−2.00000	+	3.46410i	−0.0697580	+	0.120824i
$823$	7.28836	+	12.6238i	0.254056	+	0.440039i	0.964639	−	0.263575i	$-0.0849018\pi$
$823$	7.28836	+	12.6238i	0.254056	+	0.440039i	−0.710582	+	0.703614i	$0.751568\pi$
$824$	−7.00969			−0.244194
$825$	7.79590	+	13.5029i	0.271418	+	0.470110i
$826$	−14.4453	−	25.0201i	−0.502618	−	0.870559i
$827$	−20.3666			−0.708216			−0.354108	−	0.935205i	$-0.615215\pi$
$827$	−20.3666			−0.708216			−0.354108	+	0.935205i	$0.615215\pi$
$828$	−1.69202	−	2.93067i	−0.0588018	−	0.101848i
$829$	−16.2054	+	28.0685i	−0.562835	+	0.974859i	0.434412	+	0.900714i	$0.356956\pi$
$829$	−16.2054	+	28.0685i	−0.562835	+	0.974859i	−0.997247	+	0.0741452i	$0.976377\pi$
$830$	−30.6694	+	53.1209i	−1.06455	+	1.84385i
$831$	24.1280			0.836990
$832$		0			0
$833$	5.91889			0.205077
$834$	7.51573	−	13.0176i	0.260248	−	0.450763i
$835$	1.79523	−	3.10943i	0.0621266	−	0.107606i
$836$	−1.03146	−	1.78654i	−0.0356738	−	0.0617888i
$837$	2.22521			0.0769145
$838$	14.7315	+	25.5158i	0.508893	+	0.881428i
$839$	−14.9705	−	25.9296i	−0.516838	−	0.895189i	−0.999809	−	0.0195528i	$-0.993776\pi$
$839$	−14.9705	−	25.9296i	−0.516838	−	0.895189i	0.482971	−	0.875636i	$-0.339558\pi$
$840$	−18.7168			−0.645790
$841$	−9.57487	−	16.5842i	−0.330168	−	0.571868i
$842$	8.67456	−	15.0248i	0.298945	−	0.517788i
$843$	−6.41789	+	11.1161i	−0.221044	+	0.382860i
$844$	15.9215			0.548042
$845$		0			0
$846$	1.78017			0.0612034
$847$	−21.0375	+	36.4380i	−0.722857	+	1.25203i
$848$	1.25786	−	2.17869i	0.0431953	−	0.0748164i
$849$	2.82371	+	4.89081i	0.0969094	+	0.167852i
$850$	−6.64609			−0.227959
$851$	6.56166	+	11.3651i	0.224931	+	0.389592i
$852$	4.69202	+	8.12682i	0.160746	+	0.278420i
$853$	41.8780			1.43388			0.716938	−	0.697137i	$-0.245543\pi$
$853$	41.8780			1.43388			0.716938	+	0.697137i	$0.245543\pi$
$854$	−22.8605	−	39.5956i	−0.782272	−	1.35493i
$855$	−3.82371	+	6.62286i	−0.130768	+	0.226497i
$856$	−0.958615	+	1.66037i	−0.0327648	+	0.0567503i
$857$	25.2137			0.861284			0.430642	−	0.902523i	$-0.358287\pi$
$857$	25.2137			0.861284			0.430642	+	0.902523i	$0.358287\pi$
$858$		0			0
$859$	−46.9939			−1.60341			−0.801705	−	0.597719i	$-0.796074\pi$
$859$	−46.9939			−1.60341			−0.801705	+	0.597719i	$0.796074\pi$
$860$	−15.8605	+	27.4713i	−0.540840	+	0.936762i
$861$	13.7627	−	23.8377i	0.469032	−	0.812387i
$862$	−12.6920	−	21.9832i	−0.432292	−	0.748752i
$863$	43.6969			1.48746			0.743730	−	0.668480i	$-0.233055\pi$
$863$	43.6969			1.48746			0.743730	+	0.668480i	$0.233055\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	8.95891	+	15.5173i	0.304612	+	0.527604i
$866$	−20.0054			−0.679810
$867$	−8.37800	−	14.5111i	−0.284532	−	0.492824i
$868$	−4.84750	+	8.39612i	−0.164535	+	0.284983i
$869$	−1.53846	+	2.66469i	−0.0521887	+	0.0903934i
$870$	29.8092			1.01063
$871$		0			0
$872$	−18.7681			−0.635568
$873$	−9.19687	+	15.9294i	−0.311267	+	0.539130i
$874$	3.01208	−	5.21708i	0.101885	−	0.176470i
$875$	79.1226	+	137.044i	2.67483	+	4.63295i
$876$	−0.374354			−0.0126483
$877$	−6.44504	−	11.1631i	−0.217634	−	0.376952i	0.736450	−	0.676491i	$-0.236500\pi$
$877$	−6.44504	−	11.1631i	−0.217634	−	0.376952i	−0.954084	+	0.299539i	$0.903167\pi$
$878$	0.271971	+	0.471067i	0.00917857	+	0.0158977i
$879$	21.3653			0.720632
$880$	−2.48911	−	4.31127i	−0.0839080	−	0.145333i
$881$	7.47889	−	12.9538i	0.251970	−	0.436425i	−0.712098	−	0.702080i	$-0.752255\pi$
$881$	7.47889	−	12.9538i	0.251970	−	0.436425i	0.964068	+	0.265655i	$0.0855881\pi$
$882$	5.99127	−	10.3772i	0.201737	−	0.349418i
$883$	−20.6896			−0.696261			−0.348131	−	0.937446i	$-0.613183\pi$
$883$	−20.6896			−0.696261			−0.348131	+	0.937446i	$0.613183\pi$
$884$		0			0
$885$	−28.4862			−0.957553
$886$	−9.06800	+	15.7062i	−0.304645	+	0.527661i
$887$	−12.0925	+	20.9448i	−0.406025	+	0.703256i	−0.994440	−	0.105303i	$-0.966419\pi$
$887$	−12.0925	+	20.9448i	−0.406025	+	0.703256i	0.588415	+	0.808559i	$0.299752\pi$
$888$	1.93900	+	3.35845i	0.0650686	+	0.112702i
$889$	−36.5706			−1.22654
$890$	1.79523	+	3.10943i	0.0601763	+	0.104228i
$891$	−0.579417	−	1.00358i	−0.0194112	−	0.0336212i
$892$	5.18359			0.173559
$893$	1.58450	+	2.74443i	0.0530232	+	0.0918389i
$894$	1.96346	−	3.40081i	0.0656679	−	0.113740i
$895$	−49.1616	+	85.1504i	−1.64329	+	2.84626i
$896$	4.35690			0.145554
$897$		0			0
$898$	29.3793			0.980399
$899$	7.72037	−	13.3721i	0.257489	−	0.445983i
$900$	−6.72737	+	11.6521i	−0.224246	+	0.388405i
$901$	0.621334	+	1.07618i	0.0206996	+	0.0358528i
$902$	7.32113			0.243767
$903$	−16.0858	−	27.8613i	−0.535300	−	0.927167i
$904$	5.20775	+	9.02009i	0.173207	+	0.300004i
$905$	49.8491			1.65704
$906$	−4.81431	−	8.33864i	−0.159945	−	0.277033i
$907$	−13.6353	+	23.6171i	−0.452754	+	0.784193i	−0.998556	−	0.0537214i	$-0.982892\pi$
$907$	−13.6353	+	23.6171i	−0.452754	+	0.784193i	0.545802	+	0.837914i	$0.316225\pi$
$908$	7.44385	−	12.8931i	0.247033	−	0.427873i
$909$	−5.46681			−0.181323
$910$		0			0
$911$	45.2766			1.50008			0.750041	−	0.661391i	$-0.230034\pi$
$911$	45.2766			1.50008			0.750041	+	0.661391i	$0.230034\pi$
$912$	0.890084	−	1.54167i	0.0294736	−	0.0510498i
$913$	8.27317	−	14.3295i	0.273802	−	0.474239i
$914$	4.17360	+	7.22889i	0.138051	+	0.239111i
$915$	−45.0810			−1.49033
$916$	11.7289	+	20.3150i	0.387532	+	0.671226i
$917$	−29.4170	−	50.9517i	−0.971435	−	1.68257i
$918$	0.493959			0.0163031
$919$	−2.34063	−	4.05410i	−0.0772104	−	0.133732i	0.824835	−	0.565374i	$-0.191268\pi$
$919$	−2.34063	−	4.05410i	−0.0772104	−	0.133732i	−0.902045	+	0.431641i	$0.857935\pi$
$920$	7.26875	−	12.5898i	0.239644	−	0.415075i
$921$	14.4426	−	25.0154i	0.475901	−	0.824286i
$922$	21.4969			0.707964
$923$		0			0
$924$	5.04892			0.166097
$925$	26.0887	−	45.1870i	0.857792	−	1.48574i
$926$	−13.0858	+	22.6652i	−0.430025	+	0.744824i
$927$	−3.50484	−	6.07057i	−0.115114	−	0.199384i
$928$	−6.93900			−0.227784
$929$	1.64550	+	2.85008i	0.0539870	+	0.0935082i	0.891756	−	0.452517i	$-0.149474\pi$
$929$	1.64550	+	2.85008i	0.0539870	+	0.0935082i	−0.837769	+	0.546025i	$0.816140\pi$
$930$	4.77963	+	8.27857i	0.156730	+	0.271465i
$931$	21.3309			0.699093
$932$	5.93900	+	10.2867i	0.194538	+	0.336950i
$933$	1.69202	−	2.93067i	0.0553943	−	0.0959457i
$934$	−4.90635	+	8.49804i	−0.160541	+	0.278064i
$935$	2.45904			0.0804193
$936$		0			0
$937$	6.67563			0.218083			0.109042	−	0.994037i	$-0.465222\pi$
$937$	6.67563			0.218083			0.109042	+	0.994037i	$0.465222\pi$
$938$	−8.92692	+	15.4619i	−0.291474	+	0.504848i
$939$	7.17510	−	12.4276i	0.234150	−	0.405560i
$940$	3.82371	+	6.62286i	0.124716	+	0.216014i
$941$	−38.9778			−1.27064			−0.635319	−	0.772250i	$-0.719131\pi$
$941$	−38.9778			−1.27064			−0.635319	+	0.772250i	$0.719131\pi$
$942$	8.69202	+	15.0550i	0.283201	+	0.490519i
$943$	10.6896	+	18.5150i	0.348102	+	0.602931i
$944$	6.63102			0.215821
$945$	−9.35839	−	16.2092i	−0.304428	−	0.527285i
$946$	4.27844	−	7.41047i	0.139104	−	0.240935i
$947$	−20.3339	+	35.2194i	−0.660764	+	1.14448i	0.319651	+	0.947535i	$0.396434\pi$
$947$	−20.3339	+	35.2194i	−0.660764	+	1.14448i	−0.980415	+	0.196941i	$0.936899\pi$
$948$	−2.65519			−0.0862364
$949$		0			0
$950$	−23.9517			−0.777095
$951$	9.26659	−	16.0502i	0.300490	−	0.520464i
$952$	−1.07606	+	1.86380i	−0.0348754	+	0.0604060i
$953$	22.4252	+	38.8416i	0.726423	+	1.25820i	0.958386	+	0.285477i	$0.0921520\pi$
$953$	22.4252	+	38.8416i	0.726423	+	1.25820i	−0.231962	+	0.972725i	$0.574515\pi$
$954$	2.51573			0.0814497
$955$	−35.8485	−	62.0914i	−1.16003	−	2.00923i
$956$	−12.6799	−	21.9623i	−0.410099	−	0.710312i
$957$	−8.04115			−0.259933
$958$	−8.64071	−	14.9662i	−0.279169	−	0.483534i
$959$	8.71379	−	15.0927i	0.281383	−	0.487370i
$960$	2.14795	−	3.72036i	0.0693247	−	0.120074i
$961$	−26.0484			−0.840272
$962$		0			0
$963$	−1.91723			−0.0617819
$964$	6.01089	−	10.4112i	0.193598	−	0.335321i
$965$	20.7222	−	35.8918i	0.667070	−	1.15540i
$966$	7.37196	+	12.7686i	0.237189	+	0.410823i
$967$	22.4704			0.722599			0.361299	−	0.932450i	$-0.382333\pi$
$967$	22.4704			0.722599			0.361299	+	0.932450i	$0.382333\pi$
$968$	−4.82855	−	8.36330i	−0.155196	−	0.268807i
$969$	0.439665	+	0.761522i	0.0141241	+	0.0244636i
$970$	−79.0176			−2.53710
$971$	−16.9218	−	29.3095i	−0.543048	−	0.940586i	−0.998727	−	0.0504421i	$-0.983937\pi$
$971$	−16.9218	−	29.3095i	−0.543048	−	0.940586i	0.455679	−	0.890144i	$-0.349396\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−32.7453	+	56.7164i	−1.04976	+	1.81825i
$974$	−31.6886			−1.01537
$975$		0			0
$976$	10.4940			0.335903
$977$	−13.6069	+	23.5678i	−0.435322	+	0.754000i	−0.997322	−	0.0731375i	$-0.976699\pi$
$977$	−13.6069	+	23.5678i	−0.435322	+	0.754000i	0.562000	+	0.827137i	$0.310032\pi$
$978$	11.2349	−	19.4594i	0.359252	−	0.622243i
$979$	−0.484271	−	0.838781i	−0.0154774	−	0.0268076i
$980$	51.4758			1.64433
$981$	−9.38404	−	16.2536i	−0.299609	−	0.518939i
$982$	1.15183	+	1.99503i	0.0367565	+	0.0636641i
$983$	−50.9965			−1.62654			−0.813269	−	0.581889i	$-0.802314\pi$
$983$	−50.9965			−1.62654			−0.813269	+	0.581889i	$0.802314\pi$
$984$	3.15883	+	5.47126i	0.100700	+	0.174417i
$985$	42.1821	−	73.0615i	1.34403	−	2.32793i
$986$	1.71379	−	2.96837i	0.0545782	−	0.0945323i
$987$	−7.75600			−0.246876
$988$		0			0
$989$	24.9879			0.794570
$990$	2.48911	−	4.31127i	0.0791093	−	0.137021i
$991$	12.1402	−	21.0274i	0.385645	−	0.667958i	−0.606213	−	0.795302i	$-0.707312\pi$
$991$	12.1402	−	21.0274i	0.385645	−	0.667958i	0.991859	+	0.127345i	$0.0406455\pi$
$992$	−1.11260	−	1.92709i	−0.0353252	−	0.0611851i
$993$	7.87800			0.250001
$994$	−20.4426	−	35.4077i	−0.648401	−	1.12306i
$995$	39.5671	+	68.5322i	1.25436	+	2.17262i
$996$	14.2784			0.452430
$997$	2.03252	+	3.52043i	0.0643707	+	0.111493i	0.896415	−	0.443216i	$-0.146163\pi$
$997$	2.03252	+	3.52043i	0.0643707	+	0.111493i	−0.832044	+	0.554710i	$0.812829\pi$
$998$		0			0
$999$	−1.93900	+	3.35845i	−0.0613473	+	0.106257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.n.529.3		6
13.2	odd	12		1014.2.i.h.361.4		12
13.3	even	3	inner	1014.2.e.n.991.3		6
13.4	even	6		1014.2.a.n.1.1	yes	3
13.5	odd	4		1014.2.i.h.823.1		12
13.6	odd	12		1014.2.b.f.337.4		6
13.7	odd	12		1014.2.b.f.337.3		6
13.8	odd	4		1014.2.i.h.823.6		12
13.9	even	3		1014.2.a.l.1.3	✓	3
13.10	even	6		1014.2.e.l.991.1		6
13.11	odd	12		1014.2.i.h.361.3		12
13.12	even	2		1014.2.e.l.529.1		6
39.17	odd	6		3042.2.a.ba.1.3		3
39.20	even	12		3042.2.b.o.1351.4		6
39.32	even	12		3042.2.b.o.1351.3		6
39.35	odd	6		3042.2.a.bh.1.1		3
52.35	odd	6		8112.2.a.cj.1.3		3
52.43	odd	6		8112.2.a.cm.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.l.1.3	✓	3	13.9	even	3
1014.2.a.n.1.1	yes	3	13.4	even	6
1014.2.b.f.337.3		6	13.7	odd	12
1014.2.b.f.337.4		6	13.6	odd	12
1014.2.e.l.529.1		6	13.12	even	2
1014.2.e.l.991.1		6	13.10	even	6
1014.2.e.n.529.3		6	1.1	even	1	trivial
1014.2.e.n.991.3		6	13.3	even	3	inner
1014.2.i.h.361.3		12	13.11	odd	12
1014.2.i.h.361.4		12	13.2	odd	12
1014.2.i.h.823.1		12	13.5	odd	4
1014.2.i.h.823.6		12	13.8	odd	4
3042.2.a.ba.1.3		3	39.17	odd	6
3042.2.a.bh.1.1		3	39.35	odd	6
3042.2.b.o.1351.3		6	39.32	even	12
3042.2.b.o.1351.4		6	39.20	even	12
8112.2.a.cj.1.3		3	52.35	odd	6
8112.2.a.cm.1.1		3	52.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +4.29590 q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.17845 + 3.77318i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +4.29590 q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.17845 + 3.77318i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.14795 - 3.72036i) q^{10} +(-0.579417 + 1.00358i) q^{11} -1.00000 q^{12} +4.35690 q^{14} +(2.14795 - 3.72036i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.246980 - 0.427781i) q^{17} -1.00000 q^{18} +(-0.890084 - 1.54167i) q^{19} +(-2.14795 - 3.72036i) q^{20} +4.35690 q^{21} +(0.579417 + 1.00358i) q^{22} +(-1.69202 + 2.93067i) q^{23} +(-0.500000 + 0.866025i) q^{24} +13.4547 q^{25} -1.00000 q^{27} +(2.17845 - 3.77318i) q^{28} +(-3.46950 + 6.00935i) q^{29} +(-2.14795 - 3.72036i) q^{30} -2.22521 q^{31} +(0.500000 + 0.866025i) q^{32} +(0.579417 + 1.00358i) q^{33} -0.493959 q^{34} +(9.35839 + 16.2092i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.93900 - 3.35845i) q^{37} -1.78017 q^{38} -4.29590 q^{40} +(3.15883 - 5.47126i) q^{41} +(2.17845 - 3.77318i) q^{42} +(-3.69202 - 6.39477i) q^{43} +1.15883 q^{44} +(-2.14795 - 3.72036i) q^{45} +(1.69202 + 2.93067i) q^{46} -1.78017 q^{47} +(0.500000 + 0.866025i) q^{48} +(-5.99127 + 10.3772i) q^{49} +(6.72737 - 11.6521i) q^{50} -0.493959 q^{51} -2.51573 q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.48911 + 4.31127i) q^{55} +(-2.17845 - 3.77318i) q^{56} -1.78017 q^{57} +(3.46950 + 6.00935i) q^{58} +(-3.31551 - 5.74263i) q^{59} -4.29590 q^{60} +(-5.24698 - 9.08804i) q^{61} +(-1.11260 + 1.92709i) q^{62} +(2.17845 - 3.77318i) q^{63} +1.00000 q^{64} +1.15883 q^{66} +(-2.04892 + 3.54883i) q^{67} +(-0.246980 + 0.427781i) q^{68} +(1.69202 + 2.93067i) q^{69} +18.7168 q^{70} +(-4.69202 - 8.12682i) q^{71} +(0.500000 + 0.866025i) q^{72} +0.374354 q^{73} +(-1.93900 - 3.35845i) q^{74} +(6.72737 - 11.6521i) q^{75} +(-0.890084 + 1.54167i) q^{76} -5.04892 q^{77} +2.65519 q^{79} +(-2.14795 + 3.72036i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.15883 - 5.47126i) q^{82} -14.2784 q^{83} +(-2.17845 - 3.77318i) q^{84} +(-1.06100 - 1.83770i) q^{85} -7.38404 q^{86} +(3.46950 + 6.00935i) q^{87} +(0.579417 - 1.00358i) q^{88} +(-0.417895 + 0.723815i) q^{89} -4.29590 q^{90} +3.38404 q^{92} +(-1.11260 + 1.92709i) q^{93} +(-0.890084 + 1.54167i) q^{94} +(-3.82371 - 6.62286i) q^{95} +1.00000 q^{96} +(-9.19687 - 15.9294i) q^{97} +(5.99127 + 10.3772i) q^{98} +1.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 5 q^{11} - 6 q^{12} + 18 q^{14} - q^{15} - 3 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + q^{20} + 18 q^{21} - 5 q^{22} - 3 q^{24} + 36 q^{25} - 6 q^{27} + 9 q^{28} - 11 q^{29} + q^{30} - 10 q^{31} + 3 q^{32} - 5 q^{33} + 16 q^{34} + 4 q^{35} - 3 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{40} + 2 q^{41} + 9 q^{42} - 12 q^{43} - 10 q^{44} + q^{45} - 8 q^{47} + 3 q^{48} - 20 q^{49} + 18 q^{50} + 16 q^{51} + 10 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 8 q^{57} + 11 q^{58} - 5 q^{59} + 2 q^{60} - 22 q^{61} - 5 q^{62} + 9 q^{63} + 6 q^{64} - 10 q^{66} + 6 q^{67} + 8 q^{68} + 8 q^{70} - 18 q^{71} + 3 q^{72} + 26 q^{73} + 8 q^{74} + 18 q^{75} - 4 q^{76} - 12 q^{77} + 62 q^{79} + q^{80} - 3 q^{81} - 2 q^{82} - 26 q^{83} - 9 q^{84} - 26 q^{85} - 24 q^{86} + 11 q^{87} - 5 q^{88} - 14 q^{89} + 2 q^{90} - 5 q^{93} - 4 q^{94} - 8 q^{95} + 6 q^{96} - 23 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 5 * q^11 - 6 * q^12 + 18 * q^14 - q^15 - 3 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + q^20 + 18 * q^21 - 5 * q^22 - 3 * q^24 + 36 * q^25 - 6 * q^27 + 9 * q^28 - 11 * q^29 + q^30 - 10 * q^31 + 3 * q^32 - 5 * q^33 + 16 * q^34 + 4 * q^35 - 3 * q^36 - 8 * q^37 - 8 * q^38 + 2 * q^40 + 2 * q^41 + 9 * q^42 - 12 * q^43 - 10 * q^44 + q^45 - 8 * q^47 + 3 * q^48 - 20 * q^49 + 18 * q^50 + 16 * q^51 + 10 * q^53 - 3 * q^54 - 18 * q^55 - 9 * q^56 - 8 * q^57 + 11 * q^58 - 5 * q^59 + 2 * q^60 - 22 * q^61 - 5 * q^62 + 9 * q^63 + 6 * q^64 - 10 * q^66 + 6 * q^67 + 8 * q^68 + 8 * q^70 - 18 * q^71 + 3 * q^72 + 26 * q^73 + 8 * q^74 + 18 * q^75 - 4 * q^76 - 12 * q^77 + 62 * q^79 + q^80 - 3 * q^81 - 2 * q^82 - 26 * q^83 - 9 * q^84 - 26 * q^85 - 24 * q^86 + 11 * q^87 - 5 * q^88 - 14 * q^89 + 2 * q^90 - 5 * q^93 - 4 * q^94 - 8 * q^95 + 6 * q^96 - 23 * q^97 + 20 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more