LMFDB - Embedded newform 722.2.c.m.429.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(429,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("722.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.c (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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.324000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 20x^{4} + 25x^{2} + 25 $ x^8 + 5x^6 + 20x^4 + 25*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			429.4
Root			$-0.587785 + 1.01807i$ of defining polynomial
Character	$\chi$	$=$	722.429
Dual form			722.2.c.m.653.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.26007 - 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} +1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.26007 - 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} +1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +(1.22982 + 2.13012i) q^{10} -1.67853 q^{11} -2.52015 q^{12} +(-3.17229 - 5.49456i) q^{13} +(1.39680 - 2.41933i) q^{14} +(-3.09934 - 5.36821i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.48459 + 4.30343i) q^{17} +3.35114 q^{18} -2.45965 q^{20} +(-3.52015 + 6.09707i) q^{21} +(0.839266 - 1.45365i) q^{22} +(1.24945 + 2.16411i) q^{23} +(1.26007 - 2.18251i) q^{24} +(-0.524938 - 0.909219i) q^{25} +6.34458 q^{26} -0.884927 q^{27} +(1.39680 + 2.41933i) q^{28} +(-2.96589 - 5.13708i) q^{29} +6.19868 q^{30} +7.28408 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.11507 + 3.66341i) q^{33} +(-2.48459 - 4.30343i) q^{34} +(-3.43564 + 5.95071i) q^{35} +(-1.67557 + 2.90217i) q^{36} +0.550972 q^{37} -15.9893 q^{39} +(1.22982 - 2.13012i) q^{40} +(1.30371 - 2.25809i) q^{41} +(-3.52015 - 6.09707i) q^{42} +(-1.43564 + 2.48661i) q^{43} +(0.839266 + 1.45365i) q^{44} -8.24263 q^{45} -2.49890 q^{46} +(-0.372797 - 0.645703i) q^{47} +(1.26007 + 2.18251i) q^{48} +0.804226 q^{49} +1.04988 q^{50} +(6.26153 + 10.8453i) q^{51} +(-3.17229 + 5.49456i) q^{52} +(0.735136 + 1.27329i) q^{53} +(0.442463 - 0.766369i) q^{54} +(-2.06430 + 3.57547i) q^{55} -2.79360 q^{56} +5.93179 q^{58} +(2.48131 - 4.29775i) q^{59} +(-3.09934 + 5.36821i) q^{60} +(-4.66843 - 8.08596i) q^{61} +(-3.64204 + 6.30820i) q^{62} +(4.68088 + 8.10752i) q^{63} +1.00000 q^{64} -15.6054 q^{65} +(-2.11507 - 3.66341i) q^{66} +(-5.78022 - 10.0116i) q^{67} +4.96917 q^{68} +6.29761 q^{69} +(-3.43564 - 5.95071i) q^{70} +(3.49849 - 6.05956i) q^{71} +(-1.67557 - 2.90217i) q^{72} +(3.09310 - 5.35740i) q^{73} +(-0.275486 + 0.477156i) q^{74} -2.64584 q^{75} +4.68915 q^{77} +(7.99463 - 13.8471i) q^{78} +(2.95579 - 5.11958i) q^{79} +(1.22982 + 2.13012i) q^{80} +(3.91164 - 6.77516i) q^{81} +(1.30371 + 2.25809i) q^{82} +15.1773 q^{83} +7.04029 q^{84} +(6.11121 + 10.5849i) q^{85} +(-1.43564 - 2.48661i) q^{86} -14.9490 q^{87} -1.67853 q^{88} +(-3.45251 - 5.97992i) q^{89} +(4.12132 - 7.13833i) q^{90} +(8.86212 + 15.3496i) q^{91} +(1.24945 - 2.16411i) q^{92} +(9.17848 - 15.8976i) q^{93} +0.745593 q^{94} -2.52015 q^{96} +(-7.19369 + 12.4598i) q^{97} +(-0.402113 + 0.696480i) q^{98} +(2.81250 + 4.87139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 18 q^{13} + 2 q^{14} - 4 q^{15} - 4 q^{16} - 6 q^{17} + 8 q^{18} - 4 q^{20} - 4 q^{21} - 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} - 8 q^{27} + 2 q^{28} + 2 q^{29} + 8 q^{30} + 52 q^{31} - 4 q^{32} - 16 q^{33} - 6 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} - 20 q^{46} + 12 q^{47} - 2 q^{48} - 24 q^{49} + 12 q^{50} + 2 q^{51} - 18 q^{52} - 8 q^{53} + 4 q^{54} + 26 q^{55} - 4 q^{56} - 4 q^{58} + 8 q^{59} - 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} - 8 q^{65} - 16 q^{66} - 10 q^{67} + 12 q^{68} - 40 q^{69} - 6 q^{70} - 4 q^{72} + 14 q^{73} - 4 q^{74} + 16 q^{75} + 8 q^{77} + 6 q^{78} - 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} + 8 q^{84} + 18 q^{85} + 10 q^{86} - 52 q^{87} + 4 q^{88} + 16 q^{89} + 22 q^{90} + 4 q^{91} + 10 q^{92} - 8 q^{93} - 24 q^{94} + 4 q^{96} - 28 q^{97} + 12 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 18 * q^13 + 2 * q^14 - 4 * q^15 - 4 * q^16 - 6 * q^17 + 8 * q^18 - 4 * q^20 - 4 * q^21 - 2 * q^22 + 10 * q^23 - 2 * q^24 - 6 * q^25 + 36 * q^26 - 8 * q^27 + 2 * q^28 + 2 * q^29 + 8 * q^30 + 52 * q^31 - 4 * q^32 - 16 * q^33 - 6 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 44 * q^45 - 20 * q^46 + 12 * q^47 - 2 * q^48 - 24 * q^49 + 12 * q^50 + 2 * q^51 - 18 * q^52 - 8 * q^53 + 4 * q^54 + 26 * q^55 - 4 * q^56 - 4 * q^58 + 8 * q^59 - 4 * q^60 - 26 * q^62 + 22 * q^63 + 8 * q^64 - 8 * q^65 - 16 * q^66 - 10 * q^67 + 12 * q^68 - 40 * q^69 - 6 * q^70 - 4 * q^72 + 14 * q^73 - 4 * q^74 + 16 * q^75 + 8 * q^77 + 6 * q^78 - 22 * q^79 + 2 * q^80 + 4 * q^81 + 12 * q^82 - 24 * q^83 + 8 * q^84 + 18 * q^85 + 10 * q^86 - 52 * q^87 + 4 * q^88 + 16 * q^89 + 22 * q^90 + 4 * q^91 + 10 * q^92 - 8 * q^93 - 24 * q^94 + 4 * q^96 - 28 * q^97 + 12 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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
$3$	1.26007	−	2.18251i	0.727504	−	1.26007i	−0.230431	−	0.973089i	$-0.574014\pi$
$3$	1.26007	−	2.18251i	0.727504	−	1.26007i	0.957935	−	0.286985i	$-0.0926530\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.22982	−	2.13012i	0.549994	−	0.952618i	−0.448280	−	0.893893i	$-0.647963\pi$
$5$	1.22982	−	2.13012i	0.549994	−	0.952618i	0.998274	−	0.0587249i	$-0.0187035\pi$
$6$	1.26007	+	2.18251i	0.514423	+	0.891007i
$7$	−2.79360			−1.05588			−0.527942	−	0.849281i	$-0.677036\pi$
$7$	−2.79360			−1.05588			−0.527942	+	0.849281i	$0.677036\pi$
$8$	1.00000			0.353553
$9$	−1.67557	−	2.90217i	−0.558524	−	0.967391i
$10$	1.22982	+	2.13012i	0.388905	+	0.673603i
$11$	−1.67853			−0.506096			−0.253048	−	0.967454i	$-0.581433\pi$
$11$	−1.67853			−0.506096			−0.253048	+	0.967454i	$0.581433\pi$
$12$	−2.52015			−0.727504
$13$	−3.17229	−	5.49456i	−0.879834	−	1.52392i	−0.851522	−	0.524319i	$-0.824320\pi$
$13$	−3.17229	−	5.49456i	−0.879834	−	1.52392i	−0.0283125	−	0.999599i	$-0.509013\pi$
$14$	1.39680	−	2.41933i	0.373311	−	0.646594i
$15$	−3.09934	−	5.36821i	−0.800246	−	1.38607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.48459	+	4.30343i	−0.602601	+	1.04374i	0.389825	+	0.920889i	$0.372536\pi$
$17$	−2.48459	+	4.30343i	−0.602601	+	1.04374i	−0.992426	+	0.122846i	$0.960798\pi$
$18$	3.35114			0.789872
$19$		0			0
$19$		0			0
$20$	−2.45965			−0.549994
$21$	−3.52015	+	6.09707i	−0.768159	+	1.33049i
$22$	0.839266	−	1.45365i	0.178932	−	0.309919i
$23$	1.24945	+	2.16411i	0.260529	+	0.451249i	0.966383	−	0.257109i	$-0.0827698\pi$
$23$	1.24945	+	2.16411i	0.260529	+	0.451249i	−0.705854	+	0.708358i	$0.749436\pi$
$24$	1.26007	−	2.18251i	0.257211	−	0.445503i
$25$	−0.524938	−	0.909219i	−0.104988	−	0.181844i
$26$	6.34458			1.24427
$27$	−0.884927			−0.170304
$28$	1.39680	+	2.41933i	0.263971	+	0.457211i
$29$	−2.96589	−	5.13708i	−0.550752	−	0.953931i	−0.998220	−	0.0596313i	$-0.981007\pi$
$29$	−2.96589	−	5.13708i	−0.550752	−	0.953931i	0.447468	−	0.894300i	$-0.352326\pi$
$30$	6.19868			1.13172
$31$	7.28408			1.30826			0.654130	−	0.756382i	$-0.273035\pi$
$31$	7.28408			1.30826			0.654130	+	0.756382i	$0.273035\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.11507	+	3.66341i	−0.368187	+	0.637719i
$34$	−2.48459	−	4.30343i	−0.426103	−	0.738032i
$35$	−3.43564	+	5.95071i	−0.580730	+	1.00585i
$36$	−1.67557	+	2.90217i	−0.279262	+	0.483696i
$37$	0.550972			0.0905792			0.0452896	−	0.998974i	$-0.485579\pi$
$37$	0.550972			0.0905792			0.0452896	+	0.998974i	$0.485579\pi$
$38$		0			0
$39$	−15.9893			−2.56033
$40$	1.22982	−	2.13012i	0.194452	−	0.336801i
$41$	1.30371	−	2.25809i	0.203605	−	0.352654i	−0.746083	−	0.665853i	$-0.768068\pi$
$41$	1.30371	−	2.25809i	0.203605	−	0.352654i	0.949687	+	0.313200i	$0.101401\pi$
$42$	−3.52015	−	6.09707i	−0.543170	−	0.940799i
$43$	−1.43564	+	2.48661i	−0.218934	+	0.379204i	−0.954482	−	0.298268i	$-0.903591\pi$
$43$	−1.43564	+	2.48661i	−0.218934	+	0.379204i	0.735549	+	0.677472i	$0.236924\pi$
$44$	0.839266	+	1.45365i	0.126524	+	0.219146i
$45$	−8.24263			−1.22874
$46$	−2.49890			−0.368443
$47$	−0.372797	−	0.645703i	−0.0543780	−	0.0941854i	0.837555	−	0.546353i	$-0.183984\pi$
$47$	−0.372797	−	0.645703i	−0.0543780	−	0.0941854i	−0.891933	+	0.452167i	$0.850651\pi$
$48$	1.26007	+	2.18251i	0.181876	+	0.315018i
$49$	0.804226			0.114889
$50$	1.04988			0.148475
$51$	6.26153	+	10.8453i	0.876789	+	1.51864i
$52$	−3.17229	+	5.49456i	−0.439917	+	0.761959i
$53$	0.735136	+	1.27329i	0.100979	+	0.174900i	0.912088	−	0.409994i	$-0.134469\pi$
$53$	0.735136	+	1.27329i	0.100979	+	0.174900i	−0.811109	+	0.584894i	$0.801136\pi$
$54$	0.442463	−	0.766369i	0.0602117	−	0.104290i
$55$	−2.06430	+	3.57547i	−0.278350	+	0.482117i
$56$	−2.79360			−0.373311
$57$		0			0
$58$	5.93179			0.778882
$59$	2.48131	−	4.29775i	0.323038	−	0.559519i	−0.658075	−	0.752952i	$-0.728629\pi$
$59$	2.48131	−	4.29775i	0.323038	−	0.559519i	0.981113	+	0.193433i	$0.0619624\pi$
$60$	−3.09934	+	5.36821i	−0.400123	+	0.693033i
$61$	−4.66843	−	8.08596i	−0.597731	−	1.03530i	−0.993155	−	0.116802i	$-0.962736\pi$
$61$	−4.66843	−	8.08596i	−0.597731	−	1.03530i	0.395424	−	0.918499i	$-0.370598\pi$
$62$	−3.64204	+	6.30820i	−0.462539	+	0.801142i
$63$	4.68088	+	8.10752i	0.589736	+	1.02145i
$64$	1.00000			0.125000
$65$	−15.6054			−1.93562
$66$	−2.11507	−	3.66341i	−0.260347	−	0.450935i
$67$	−5.78022	−	10.0116i	−0.706166	−	1.22312i	−0.966269	−	0.257535i	$-0.917090\pi$
$67$	−5.78022	−	10.0116i	−0.706166	−	1.22312i	0.260103	−	0.965581i	$-0.416244\pi$
$68$	4.96917			0.602601
$69$	6.29761			0.758143
$70$	−3.43564	−	5.95071i	−0.410638	−	0.711246i
$71$	3.49849	−	6.05956i	0.415195	−	0.719138i	−0.580254	−	0.814435i	$-0.697047\pi$
$71$	3.49849	−	6.05956i	0.415195	−	0.719138i	0.995449	+	0.0952973i	$0.0303802\pi$
$72$	−1.67557	−	2.90217i	−0.197468	−	0.342024i
$73$	3.09310	−	5.35740i	0.362020	−	0.627036i	−0.626274	−	0.779603i	$-0.715421\pi$
$73$	3.09310	−	5.35740i	0.362020	−	0.627036i	0.988293	+	0.152567i	$0.0487540\pi$
$74$	−0.275486	+	0.477156i	−0.0320246	+	0.0554682i
$75$	−2.64584			−0.305515
$76$		0			0
$77$	4.68915			0.534379
$78$	7.99463	−	13.8471i	0.905214	−	1.56788i
$79$	2.95579	−	5.11958i	0.332552	−	0.575998i	−0.650459	−	0.759541i	$-0.725423\pi$
$79$	2.95579	−	5.11958i	0.332552	−	0.575998i	0.983012	+	0.183543i	$0.0587568\pi$
$80$	1.22982	+	2.13012i	0.137499	+	0.238155i
$81$	3.91164	−	6.77516i	0.434626	−	0.752795i
$82$	1.30371	+	2.25809i	0.143970	+	0.249364i
$83$	15.1773			1.66593			0.832964	−	0.553328i	$-0.186642\pi$
$83$	15.1773			1.66593			0.832964	+	0.553328i	$0.186642\pi$
$84$	7.04029			0.768159
$85$	6.11121	+	10.5849i	0.662854	+	1.14810i
$86$	−1.43564	−	2.48661i	−0.154809	−	0.268138i
$87$	−14.9490			−1.60270
$88$	−1.67853			−0.178932
$89$	−3.45251	−	5.97992i	−0.365965	−	0.633870i	0.622965	−	0.782249i	$-0.285928\pi$
$89$	−3.45251	−	5.97992i	−0.365965	−	0.633870i	−0.988931	+	0.148379i	$0.952594\pi$
$90$	4.12132	−	7.13833i	0.434425	−	0.752446i
$91$	8.86212	+	15.3496i	0.929002	+	1.60908i
$92$	1.24945	−	2.16411i	0.130264	−	0.225625i
$93$	9.17848	−	15.8976i	0.951764	−	1.64850i
$94$	0.745593			0.0769021
$95$		0			0
$96$	−2.52015			−0.257211
$97$	−7.19369	+	12.4598i	−0.730408	+	1.26510i	0.226300	+	0.974058i	$0.427337\pi$
$97$	−7.19369	+	12.4598i	−0.730408	+	1.26510i	−0.956709	+	0.291047i	$0.905996\pi$
$98$	−0.402113	+	0.696480i	−0.0406196	+	0.0703551i
$99$	2.81250	+	4.87139i	0.282667	+	0.489593i
$100$	−0.524938	+	0.909219i	−0.0524938	+	0.0909219i
$101$	−5.64146	−	9.77130i	−0.561347	−	0.972281i	−0.997379	−	0.0723500i	$-0.976950\pi$
$101$	−5.64146	−	9.77130i	−0.561347	−	0.972281i	0.436033	−	0.899931i	$-0.356383\pi$
$102$	−12.5231			−1.23997
$103$	14.8280			1.46104			0.730522	−	0.682889i	$-0.239277\pi$
$103$	14.8280			1.46104			0.730522	+	0.682889i	$0.239277\pi$
$104$	−3.17229	−	5.49456i	−0.311068	−	0.538786i
$105$	8.65833	+	14.9967i	0.844966	+	1.46352i
$106$	−1.47027			−0.142805
$107$	−2.82849			−0.273440			−0.136720	−	0.990610i	$-0.543656\pi$
$107$	−2.82849			−0.273440			−0.136720	+	0.990610i	$0.543656\pi$
$108$	0.442463	+	0.766369i	0.0425761	+	0.0737439i
$109$	−0.862695	+	1.49423i	−0.0826312	+	0.143121i	−0.904379	−	0.426729i	$-0.859666\pi$
$109$	−0.862695	+	1.49423i	−0.0826312	+	0.143121i	0.821748	+	0.569851i	$0.192999\pi$
$110$	−2.06430	−	3.57547i	−0.196823	−	0.340908i
$111$	0.694265	−	1.20250i	0.0658967	−	0.114137i
$112$	1.39680	−	2.41933i	0.131985	−	0.228605i
$113$	−0.427785			−0.0402426			−0.0201213	−	0.999798i	$-0.506405\pi$
$113$	−0.427785			−0.0402426			−0.0201213	+	0.999798i	$0.506405\pi$
$114$		0			0
$115$	6.14643			0.573157
$116$	−2.96589	+	5.13708i	−0.275376	+	0.476966i
$117$	−10.6308	+	18.4131i	−0.982816	+	1.70229i
$118$	2.48131	+	4.29775i	0.228423	+	0.395640i
$119$	6.94095	−	12.0221i	0.636276	−	1.10206i
$120$	−3.09934	−	5.36821i	−0.282930	−	0.490049i
$121$	−8.18253			−0.743867
$122$	9.33686			0.845320
$123$	−3.28553	−	5.69071i	−0.296246	−	0.513114i
$124$	−3.64204	−	6.30820i	−0.327065	−	0.566493i
$125$	9.71592			0.869018
$126$	−9.36176			−0.834012
$127$	0.568158	+	0.984079i	0.0504159	+	0.0873229i	0.890132	−	0.455703i	$-0.150612\pi$
$127$	0.568158	+	0.984079i	0.0504159	+	0.0873229i	−0.839716	+	0.543026i	$0.817279\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	3.61803	+	6.26662i	0.318550	+	0.551745i
$130$	7.80272	−	13.5147i	0.684344	−	1.18532i
$131$	8.92075	−	15.4512i	0.779410	−	1.34998i	−0.152873	−	0.988246i	$-0.548852\pi$
$131$	8.92075	−	15.4512i	0.779410	−	1.34998i	0.932282	−	0.361731i	$-0.117814\pi$
$132$	4.23015			0.368187
$133$		0			0
$134$	11.5604			0.998670
$135$	−1.08831	+	1.88500i	−0.0936664	+	0.162235i
$136$	−2.48459	+	4.30343i	−0.213052	+	0.369016i
$137$	7.95782	+	13.7833i	0.679882	+	1.17759i	0.975016	+	0.222135i	$0.0713025\pi$
$137$	7.95782	+	13.7833i	0.679882	+	1.17759i	−0.295134	+	0.955456i	$0.595364\pi$
$138$	−3.14880	+	5.45389i	−0.268044	+	0.464266i
$139$	−5.06008	−	8.76432i	−0.429191	−	0.743380i	0.567611	−	0.823297i	$-0.307868\pi$
$139$	−5.06008	−	8.76432i	−0.429191	−	0.743380i	−0.996802	+	0.0799168i	$0.974535\pi$
$140$	6.87129			0.580730
$141$	−1.87901			−0.158241
$142$	3.49849	+	6.05956i	0.293587	+	0.508507i
$143$	5.32479	+	9.22280i	0.445281	+	0.771249i
$144$	3.35114			0.279262
$145$	−14.5901			−1.21164
$146$	3.09310	+	5.35740i	0.255986	+	0.443382i
$147$	1.01338	−	1.75523i	0.0835825	−	0.144769i
$148$	−0.275486	−	0.477156i	−0.0226448	−	0.0392220i
$149$	−4.69925	+	8.13935i	−0.384978	+	0.666801i	−0.991766	−	0.128062i	$-0.959124\pi$
$149$	−4.69925	+	8.13935i	−0.384978	+	0.666801i	0.606788	+	0.794864i	$0.292458\pi$
$150$	1.32292	−	2.29137i	0.108016	−	0.187089i
$151$	−10.2632			−0.835210			−0.417605	−	0.908629i	$-0.637130\pi$
$151$	−10.2632			−0.835210			−0.417605	+	0.908629i	$0.637130\pi$
$152$		0			0
$153$	16.6524			1.34627
$154$	−2.34458	+	4.06093i	−0.188931	+	0.327239i
$155$	8.95814	−	15.5160i	0.719535	−	1.24627i
$156$	7.99463	+	13.8471i	0.640083	+	1.10866i
$157$	−1.48694	+	2.57545i	−0.118671	+	0.205543i	−0.919241	−	0.393695i	$-0.871197\pi$
$157$	−1.48694	+	2.57545i	−0.118671	+	0.205543i	0.800571	+	0.599239i	$0.204530\pi$
$158$	2.95579	+	5.11958i	0.235150	+	0.407292i
$159$	3.70530			0.293849
$160$	−2.45965			−0.194452
$161$	−3.49047	−	6.04568i	−0.275088	−	0.476466i
$162$	3.91164	+	6.77516i	0.307327	+	0.532307i
$163$	5.59191			0.437992			0.218996	−	0.975726i	$-0.429722\pi$
$163$	5.59191			0.437992			0.218996	+	0.975726i	$0.429722\pi$
$164$	−2.60741			−0.203605
$165$	5.20234	+	9.01071i	0.405001	+	0.701483i
$166$	−7.58866	+	13.1439i	−0.588994	+	1.02017i
$167$	3.54180	+	6.13458i	0.274073	+	0.474708i	0.969901	−	0.243500i	$-0.0782957\pi$
$167$	3.54180	+	6.13458i	0.274073	+	0.474708i	−0.695828	+	0.718209i	$0.744962\pi$
$168$	−3.52015	+	6.09707i	−0.271585	+	0.470399i
$169$	−13.6268	+	23.6024i	−1.04822	+	1.81557i
$170$	−12.2224			−0.937418
$171$		0			0
$172$	2.87129			0.218934
$173$	11.5104	−	19.9366i	0.875120	−	1.51575i	0.0184843	−	0.999829i	$-0.494116\pi$
$173$	11.5104	−	19.9366i	0.875120	−	1.51575i	0.856635	−	0.515922i	$-0.172551\pi$
$174$	7.47449	−	12.9462i	0.566639	−	0.981448i
$175$	1.46647	+	2.54000i	0.110855	+	0.192006i
$176$	0.839266	−	1.45365i	0.0632620	−	0.109573i
$177$	−6.25325	−	10.8310i	−0.470023	−	0.814104i
$178$	6.90502			0.517553
$179$	8.21471			0.613996			0.306998	−	0.951710i	$-0.400675\pi$
$179$	8.21471			0.613996			0.306998	+	0.951710i	$0.400675\pi$
$180$	4.12132	+	7.13833i	0.307185	+	0.532060i
$181$	6.49994	+	11.2582i	0.483137	+	0.836818i	0.999813	−	0.0193635i	$-0.00616397\pi$
$181$	6.49994	+	11.2582i	0.483137	+	0.836818i	−0.516676	+	0.856181i	$0.672831\pi$
$182$	−17.7242			−1.31381
$183$	−23.5303			−1.73941
$184$	1.24945	+	2.16411i	0.0921108	+	0.159541i
$185$	0.677599	−	1.17364i	0.0498181	−	0.0862874i
$186$	9.17848	+	15.8976i	0.672998	+	1.16567i
$187$	4.17046	−	7.22345i	0.304974	−	0.528231i
$188$	−0.372797	+	0.645703i	−0.0271890	+	0.0470927i
$189$	2.47214			0.179821
$190$		0			0
$191$	6.57479			0.475735			0.237868	−	0.971298i	$-0.423552\pi$
$191$	6.57479			0.475735			0.237868	+	0.971298i	$0.423552\pi$
$192$	1.26007	−	2.18251i	0.0909380	−	0.157509i
$193$	−13.4413	+	23.2810i	−0.967527	+	1.67581i	−0.264859	+	0.964287i	$0.585325\pi$
$193$	−13.4413	+	23.2810i	−0.967527	+	1.67581i	−0.702667	+	0.711518i	$0.748008\pi$
$194$	−7.19369	−	12.4598i	−0.516477	−	0.894564i
$195$	−19.6640	+	34.0590i	−1.40817	+	2.43902i
$196$	−0.402113	−	0.696480i	−0.0287224	−	0.0497486i
$197$	−9.84940			−0.701741			−0.350870	−	0.936424i	$-0.614114\pi$
$197$	−9.84940			−0.701741			−0.350870	+	0.936424i	$0.614114\pi$
$198$	−5.62500			−0.399751
$199$	10.2331	+	17.7242i	0.725402	+	1.25643i	0.958808	+	0.284053i	$0.0916793\pi$
$199$	10.2331	+	17.7242i	0.725402	+	1.25643i	−0.233407	+	0.972379i	$0.574987\pi$
$200$	−0.524938	−	0.909219i	−0.0371187	−	0.0642915i
$201$	−29.1340			−2.05495
$202$	11.2829			0.793864
$203$	8.28553	+	14.3510i	0.581530	+	1.00724i
$204$	6.26153	−	10.8453i	0.438394	−	0.759322i
$205$	−3.20666	−	5.55410i	−0.223963	−	0.387915i
$206$	−7.41399	+	12.8414i	−0.516557	+	0.894703i
$207$	4.18709	−	7.25225i	0.291023	−	0.504066i
$208$	6.34458			0.439917
$209$		0			0
$210$	−17.3167			−1.19496
$211$	−4.05815	+	7.02892i	−0.279374	+	0.483891i	−0.971229	−	0.238146i	$-0.923460\pi$
$211$	−4.05815	+	7.02892i	−0.279374	+	0.483891i	0.691855	+	0.722036i	$0.256794\pi$
$212$	0.735136	−	1.27329i	0.0504893	−	0.0874501i
$213$	−8.81671	−	15.2710i	−0.604111	−	1.04635i
$214$	1.41424	−	2.44954i	0.0966757	−	0.167447i
$215$	3.53118	+	6.11619i	0.240825	+	0.417120i
$216$	−0.884927			−0.0602117
$217$	−20.3488			−1.38137
$218$	−0.862695	−	1.49423i	−0.0584291	−	0.101202i
$219$	−7.79506	−	13.5014i	−0.526741	−	0.912342i
$220$	4.12860			0.278350
$221$	31.5273			2.12076
$222$	0.694265	+	1.20250i	0.0465960	+	0.0807067i
$223$	−5.37701	+	9.31326i	−0.360071	+	0.623662i	−0.987972	−	0.154631i	$-0.950581\pi$
$223$	−5.37701	+	9.31326i	−0.360071	+	0.623662i	0.627901	+	0.778293i	$0.283914\pi$
$224$	1.39680	+	2.41933i	0.0933278	+	0.161648i
$225$	−1.75914	+	3.04692i	−0.117276	+	0.203128i
$226$	0.213892	−	0.370473i	0.0142279	−	0.0246435i
$227$	27.0936			1.79827			0.899133	−	0.437676i	$-0.144198\pi$
$227$	27.0936			1.79827			0.899133	+	0.437676i	$0.144198\pi$
$228$		0			0
$229$	9.46557			0.625503			0.312751	−	0.949835i	$-0.398749\pi$
$229$	9.46557			0.625503			0.312751	+	0.949835i	$0.398749\pi$
$230$	−3.07321	+	5.32296i	−0.202642	+	0.350986i
$231$	5.90868	−	10.2341i	0.388762	−	0.673356i
$232$	−2.96589	−	5.13708i	−0.194720	−	0.337266i
$233$	−11.4311	+	19.7992i	−0.748873	+	1.29709i	0.199490	+	0.979900i	$0.436071\pi$
$233$	−11.4311	+	19.7992i	−0.748873	+	1.29709i	−0.948363	+	0.317186i	$0.897262\pi$
$234$	−10.6308	−	18.4131i	−0.694956	−	1.20370i
$235$	−1.83390			−0.119630
$236$	−4.96261			−0.323038
$237$	−7.44903	−	12.9021i	−0.483866	−	0.838081i
$238$	6.94095	+	12.0221i	0.449915	+	0.779276i
$239$	8.66611			0.560564			0.280282	−	0.959918i	$-0.409572\pi$
$239$	8.66611			0.560564			0.280282	+	0.959918i	$0.409572\pi$
$240$	6.19868			0.400123
$241$	−2.82913	−	4.90020i	−0.182240	−	0.315649i	0.760403	−	0.649452i	$-0.225002\pi$
$241$	−2.82913	−	4.90020i	−0.182240	−	0.315649i	−0.942643	+	0.333802i	$0.891668\pi$
$242$	4.09127	−	7.08628i	0.262997	−	0.455523i
$243$	−11.1853	−	19.3735i	−0.717537	−	1.24281i
$244$	−4.66843	+	8.08596i	−0.298866	+	0.517650i
$245$	0.989057	−	1.71310i	0.0631885	−	0.109446i
$246$	6.57106			0.418956
$247$		0			0
$248$	7.28408			0.462539
$249$	19.1245	−	33.1247i	1.21197	−	2.09919i
$250$	−4.85796	+	8.41423i	−0.307244	+	0.532163i
$251$	6.77762	+	11.7392i	0.427799	+	0.740970i	0.996677	−	0.0814518i	$-0.0259557\pi$
$251$	6.77762	+	11.7392i	0.427799	+	0.740970i	−0.568878	+	0.822422i	$0.692622\pi$
$252$	4.68088	−	8.10752i	0.294868	−	0.510726i
$253$	−2.09724	−	3.63253i	−0.131853	−	0.228375i
$254$	−1.13632			−0.0712988
$255$	30.8023			1.92892
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.01963	−	8.69425i	−0.313116	−	0.542332i	0.665919	−	0.746024i	$-0.268039\pi$
$257$	−5.01963	−	8.69425i	−0.313116	−	0.542332i	−0.979035	+	0.203691i	$0.934706\pi$
$258$	−7.23607			−0.450498
$259$	−1.53920			−0.0956411
$260$	7.80272	+	13.5147i	0.483904	+	0.838146i
$261$	−9.93912	+	17.2151i	−0.615216	+	1.06559i
$262$	8.92075	+	15.4512i	0.551126	+	0.954578i
$263$	9.41309	−	16.3040i	0.580436	−	1.00534i	−0.414992	−	0.909825i	$-0.636215\pi$
$263$	9.41309	−	16.3040i	0.580436	−	1.00534i	0.995428	−	0.0955194i	$-0.0304512\pi$
$264$	−2.11507	+	3.66341i	−0.130174	+	0.225468i
$265$	3.61635			0.222151
$266$		0			0
$267$	−17.4017			−1.06496
$268$	−5.78022	+	10.0116i	−0.353083	+	0.611558i
$269$	8.19134	−	14.1878i	0.499435	−	0.865046i	−0.500565	−	0.865699i	$-0.666874\pi$
$269$	8.19134	−	14.1878i	0.499435	−	0.865046i	1.00000		0.000652557i	$0.000207715\pi$
$270$	−1.08831	−	1.88500i	−0.0662321	−	0.114717i
$271$	1.38342	−	2.39615i	0.0840367	−	0.145556i	−0.820944	−	0.571009i	$-0.806552\pi$
$271$	1.38342	−	2.39615i	0.0840367	−	0.145556i	0.904980	+	0.425453i	$0.139885\pi$
$272$	−2.48459	−	4.30343i	−0.150650	−	0.260934i
$273$	44.6677			2.70341
$274$	−15.9156			−0.961499
$275$	0.881125	+	1.52615i	0.0531338	+	0.0920305i
$276$	−3.14880	−	5.45389i	−0.189536	−	0.328285i
$277$	24.5321			1.47399			0.736996	−	0.675897i	$-0.236244\pi$
$277$	24.5321			1.47399			0.736996	+	0.675897i	$0.236244\pi$
$278$	10.1202			0.606967
$279$	−12.2050	−	21.1397i	−0.730694	−	1.26560i
$280$	−3.43564	+	5.95071i	−0.205319	+	0.355623i
$281$	−5.08518	−	8.80779i	−0.303356	−	0.525429i	0.673538	−	0.739153i	$-0.264774\pi$
$281$	−5.08518	−	8.80779i	−0.303356	−	0.525429i	−0.976894	+	0.213724i	$0.931441\pi$
$282$	0.939503	−	1.62727i	0.0559466	−	0.0969023i
$283$	−13.8339	+	23.9610i	−0.822340	+	1.42433i	0.0815955	+	0.996666i	$0.473998\pi$
$283$	−13.8339	+	23.9610i	−0.822340	+	1.42433i	−0.903935	+	0.427669i	$0.859335\pi$
$284$	−6.99698			−0.415195
$285$		0			0
$286$	−10.6496			−0.629722
$287$	−3.64204	+	6.30820i	−0.214983	+	0.372361i
$288$	−1.67557	+	2.90217i	−0.0987339	+	0.171012i
$289$	−3.84635	−	6.66207i	−0.226256	−	0.391887i
$290$	7.29506	−	12.6354i	0.428380	−	0.741977i
$291$	18.1292	+	31.4006i	1.06275	+	1.84074i
$292$	−6.18619			−0.362020
$293$	23.8386			1.39267			0.696333	−	0.717719i	$-0.254814\pi$
$293$	23.8386			1.39267			0.696333	+	0.717719i	$0.254814\pi$
$294$	1.01338	+	1.75523i	0.0591018	+	0.102367i
$295$	−6.10314	−	10.5710i	−0.355339	−	0.615465i
$296$	0.550972			0.0320246
$297$	1.48538			0.0861904
$298$	−4.69925	−	8.13935i	−0.272221	−	0.471500i
$299$	7.92724	−	13.7304i	0.458444	−	0.794049i
$300$	1.32292	+	2.29137i	0.0763789	+	0.132292i
$301$	4.01062	−	6.94660i	0.231168	−	0.400395i
$302$	5.13162	−	8.88822i	0.295291	−	0.511460i
$303$	−28.4346			−1.63353
$304$		0			0
$305$	−22.9654			−1.31500
$306$	−8.32620	+	14.4214i	−0.475977	+	0.824417i
$307$	−12.9942	+	22.5066i	−0.741619	+	1.28452i	0.210138	+	0.977672i	$0.432609\pi$
$307$	−12.9942	+	22.5066i	−0.741619	+	1.28452i	−0.951758	+	0.306851i	$0.900725\pi$
$308$	−2.34458	−	4.06093i	−0.133595	−	0.231393i
$309$	18.6843	−	32.3622i	1.06291	−	1.84102i
$310$	8.95814	+	15.5160i	0.508788	+	0.881247i
$311$	−23.1043			−1.31013			−0.655063	−	0.755574i	$-0.727358\pi$
$311$	−23.1043			−1.31013			−0.655063	+	0.755574i	$0.727358\pi$
$312$	−15.9893			−0.905214
$313$	−6.13235	−	10.6215i	−0.346621	−	0.600365i	0.639026	−	0.769185i	$-0.279338\pi$
$313$	−6.13235	−	10.6215i	−0.346621	−	0.600365i	−0.985647	+	0.168820i	$0.946004\pi$
$314$	−1.48694	−	2.57545i	−0.0839127	−	0.145341i
$315$	23.0267			1.29741
$316$	−5.91158			−0.332552
$317$	0.136152	+	0.235823i	0.00764708	+	0.0132451i	0.869824	−	0.493363i	$-0.164233\pi$
$317$	0.136152	+	0.235823i	0.00764708	+	0.0132451i	−0.862177	+	0.506608i	$0.830899\pi$
$318$	−1.85265	+	3.20888i	−0.103891	+	0.179945i
$319$	4.97834	+	8.62275i	0.278734	+	0.482781i
$320$	1.22982	−	2.13012i	0.0687493	−	0.119077i
$321$	−3.56410	+	6.17320i	−0.198929	+	0.344555i
$322$	6.98095			0.389033
$323$		0			0
$324$	−7.82328			−0.434626
$325$	−3.33051	+	5.76861i	−0.184743	+	0.319985i
$326$	−2.79595	+	4.84273i	−0.154854	+	0.268214i
$327$	2.17412	+	3.76568i	0.120229	+	0.208243i
$328$	1.30371	−	2.25809i	0.0719851	−	0.124682i
$329$	1.04145	+	1.80384i	0.0574168	+	0.0994488i
$330$	−10.4047			−0.572759
$331$	−19.9930			−1.09891			−0.549457	−	0.835522i	$-0.685165\pi$
$331$	−19.9930			−1.09891			−0.549457	+	0.835522i	$0.685165\pi$
$332$	−7.58866	−	13.1439i	−0.416482	−	0.721368i
$333$	−0.923192	−	1.59902i	−0.0505906	−	0.0876256i
$334$	−7.08361			−0.387598
$335$	−28.4346			−1.55355
$336$	−3.52015	−	6.09707i	−0.192040	−	0.332623i
$337$	8.64121	−	14.9670i	0.470717	−	0.815305i	−0.528722	−	0.848795i	$-0.677329\pi$
$337$	8.64121	−	14.9670i	0.470717	−	0.815305i	0.999439	+	0.0334897i	$0.0106621\pi$
$338$	−13.6268	−	23.6024i	−0.741202	−	1.28380i
$339$	−0.539040	+	0.933645i	−0.0292767	+	0.0507086i
$340$	6.11121	−	10.5849i	0.331427	−	0.574049i
$341$	−12.2266			−0.662105
$342$		0			0
$343$	17.3085			0.934573
$344$	−1.43564	+	2.48661i	−0.0774047	+	0.134069i
$345$	7.74495	−	13.4146i	0.416974	−	0.722220i
$346$	11.5104	+	19.9366i	0.618803	+	1.07180i
$347$	9.27279	−	16.0609i	0.497789	−	0.862197i	−0.502207	−	0.864747i	$-0.667479\pi$
$347$	9.27279	−	16.0609i	0.497789	−	0.862197i	0.999997	+	0.00255065i	$0.000811898\pi$
$348$	7.47449	+	12.9462i	0.400674	+	0.693989i
$349$	−20.1210			−1.07705			−0.538527	−	0.842609i	$-0.681019\pi$
$349$	−20.1210			−1.07705			−0.538527	+	0.842609i	$0.681019\pi$
$350$	−2.93294			−0.156772
$351$	2.80724	+	4.86229i	0.149840	+	0.259530i
$352$	0.839266	+	1.45365i	0.0447330	+	0.0774799i
$353$	24.0557			1.28035			0.640177	−	0.768227i	$-0.278861\pi$
$353$	24.0557			1.28035			0.640177	+	0.768227i	$0.278861\pi$
$354$	12.5065			0.664713
$355$	−8.60506	−	14.9044i	−0.456709	−	0.791044i
$356$	−3.45251	+	5.97992i	−0.182983	+	0.316935i
$357$	−17.4922	−	30.2974i	−0.925787	−	1.60351i
$358$	−4.10736	+	7.11415i	−0.217081	+	0.375994i
$359$	5.42673	−	9.39937i	0.286412	−	0.496080i	−0.686539	−	0.727093i	$-0.740871\pi$
$359$	5.42673	−	9.39937i	0.286412	−	0.496080i	0.972951	+	0.231013i	$0.0742041\pi$
$360$	−8.24263			−0.434425
$361$		0			0
$362$	−12.9999			−0.683259
$363$	−10.3106	+	17.8585i	−0.541166	+	0.937327i
$364$	8.86212	−	15.3496i	0.464501	−	0.804540i
$365$	−7.60793	−	13.1773i	−0.398217	−	0.689733i
$366$	11.7651	−	20.3778i	0.614973	−	1.06516i
$367$	16.3060	+	28.2429i	0.851168	+	1.47427i	0.880155	+	0.474687i	$0.157439\pi$
$367$	16.3060	+	28.2429i	0.851168	+	1.47427i	−0.0289868	+	0.999580i	$0.509228\pi$
$368$	−2.49890			−0.130264
$369$	−8.73781			−0.454872
$370$	0.677599	+	1.17364i	0.0352267	+	0.0610144i
$371$	−2.05368	−	3.55707i	−0.106622	−	0.184674i
$372$	−18.3570			−0.951764
$373$	−5.30198			−0.274526			−0.137263	−	0.990535i	$-0.543831\pi$
$373$	−5.30198			−0.274526			−0.137263	+	0.990535i	$0.543831\pi$
$374$	4.17046	+	7.22345i	0.215649	+	0.373515i
$375$	12.2428	−	21.2051i	0.632214	−	1.09503i
$376$	−0.372797	−	0.645703i	−0.0192255	−	0.0332996i
$377$	−18.8173	+	32.5926i	−0.969142	+	1.67860i
$378$	−1.23607	+	2.14093i	−0.0635765	+	0.110118i
$379$	24.6656			1.26699			0.633494	−	0.773748i	$-0.281620\pi$
$379$	24.6656			1.26699			0.633494	+	0.773748i	$0.281620\pi$
$380$		0			0
$381$	2.86368			0.146711
$382$	−3.28740	+	5.69394i	−0.168198	+	0.291327i
$383$	−1.82208	+	3.15593i	−0.0931039	+	0.161261i	−0.908816	−	0.417198i	$-0.863012\pi$
$383$	−1.82208	+	3.15593i	−0.0931039	+	0.161261i	0.815712	+	0.578459i	$0.196346\pi$
$384$	1.26007	+	2.18251i	0.0643029	+	0.111376i
$385$	5.76684	−	9.98845i	0.293905	−	0.509059i
$386$	−13.4413	−	23.2810i	−0.684145	−	1.18497i
$387$	9.62209			0.489118
$388$	14.3874			0.730408
$389$	−1.39677	−	2.41927i	−0.0708189	−	0.122662i	0.828442	−	0.560076i	$-0.189228\pi$
$389$	−1.39677	−	2.41927i	−0.0708189	−	0.122662i	−0.899260	+	0.437414i	$0.855895\pi$
$390$	−19.6640	−	34.0590i	−0.995725	−	1.72465i
$391$	−12.4175			−0.627979
$392$	0.804226			0.0406196
$393$	−22.4816	−	38.9393i	−1.13405	−	1.96423i
$394$	4.92470	−	8.52983i	0.248103	−	0.429727i
$395$	−7.27021	−	12.5924i	−0.365804	−	0.633591i
$396$	2.81250	−	4.87139i	0.141333	−	0.244797i
$397$	19.7551	−	34.2168i	0.991478	−	1.71729i	0.382919	−	0.923782i	$-0.374919\pi$
$397$	19.7551	−	34.2168i	0.991478	−	1.71729i	0.608559	−	0.793509i	$-0.291748\pi$
$398$	−20.4661			−1.02587
$399$		0			0
$400$	1.04988			0.0524938
$401$	9.31073	−	16.1267i	0.464956	−	0.805327i	−0.534244	−	0.845331i	$-0.679404\pi$
$401$	9.31073	−	16.1267i	0.464956	−	0.805327i	0.999200	+	0.0400033i	$0.0127369\pi$
$402$	14.5670	−	25.2308i	0.726536	−	1.25840i
$403$	−23.1072	−	40.0228i	−1.15105	−	1.99368i
$404$	−5.64146	+	9.77130i	−0.280673	+	0.486140i
$405$	−9.62126	−	16.6645i	−0.478084	−	0.828066i
$406$	−16.5711			−0.822408
$407$	−0.924824			−0.0458418
$408$	6.26153	+	10.8453i	0.309992	+	0.536921i
$409$	8.57164	+	14.8465i	0.423840	+	0.734113i	0.996311	−	0.0858120i	$-0.0273485\pi$
$409$	8.57164	+	14.8465i	0.423840	+	0.734113i	−0.572471	+	0.819925i	$0.694015\pi$
$410$	6.41332			0.316731
$411$	40.1098			1.97847
$412$	−7.41399	−	12.8414i	−0.365261	−	0.632651i
$413$	−6.93179	+	12.0062i	−0.341091	+	0.590787i
$414$	4.18709	+	7.25225i	0.205784	+	0.356429i
$415$	18.6654	−	32.3295i	0.916251	−	1.58699i
$416$	−3.17229	+	5.49456i	−0.155534	+	0.269393i
$417$	−25.5043			−1.24895
$418$		0			0
$419$	−18.5042			−0.903989			−0.451995	−	0.892021i	$-0.649287\pi$
$419$	−18.5042			−0.903989			−0.451995	+	0.892021i	$0.649287\pi$
$420$	8.65833	−	14.9967i	0.422483	−	0.731762i
$421$	8.09980	−	14.0293i	0.394760	−	0.683745i	−0.598310	−	0.801264i	$-0.704161\pi$
$421$	8.09980	−	14.0293i	0.394760	−	0.683745i	0.993071	+	0.117520i	$0.0374943\pi$
$422$	−4.05815	−	7.02892i	−0.197548	−	0.342162i
$423$	−1.24929	+	2.16384i	−0.0607428	+	0.105210i
$424$	0.735136	+	1.27329i	0.0357013	+	0.0618365i
$425$	5.21702			0.253062
$426$	17.6334			0.854342
$427$	13.0417	+	22.5890i	0.631134	+	1.09316i
$428$	1.41424	+	2.44954i	0.0683600	+	0.118403i
$429$	26.8385			1.29577
$430$	−7.06236			−0.340577
$431$	−6.34983	−	10.9982i	−0.305861	−	0.529766i	0.671592	−	0.740921i	$-0.265611\pi$
$431$	−6.34983	−	10.9982i	−0.305861	−	0.529766i	−0.977453	+	0.211155i	$0.932277\pi$
$432$	0.442463	−	0.766369i	0.0212880	−	0.0368720i
$433$	−7.11751	−	12.3279i	−0.342046	−	0.592441i	0.642767	−	0.766062i	$-0.277787\pi$
$433$	−7.11751	−	12.3279i	−0.342046	−	0.592441i	−0.984813	+	0.173621i	$0.944453\pi$
$434$	10.1744	−	17.6226i	0.488388	−	0.845912i
$435$	−18.3846	+	31.8431i	−0.881475	+	1.52676i
$436$	1.72539			0.0826312
$437$		0			0
$438$	15.5901			0.744924
$439$	−14.0950	+	24.4133i	−0.672718	+	1.16518i	0.304412	+	0.952540i	$0.401540\pi$
$439$	−14.0950	+	24.4133i	−0.672718	+	1.16518i	−0.977130	+	0.212642i	$0.931793\pi$
$440$	−2.06430	+	3.57547i	−0.0984116	+	0.170454i
$441$	−1.34754	−	2.33400i	−0.0641685	−	0.111143i
$442$	−15.7637	+	27.3035i	−0.749801	+	1.29869i
$443$	16.4972	+	28.5740i	0.783805	+	1.35759i	0.929711	+	0.368291i	$0.120057\pi$
$443$	16.4972	+	28.5740i	0.783805	+	1.35759i	−0.145906	+	0.989298i	$0.546610\pi$
$444$	−1.38853			−0.0658967
$445$	−16.9839			−0.805115
$446$	−5.37701	−	9.31326i	−0.254609	−	0.440995i
$447$	11.8428	+	20.5124i	0.560146	+	0.970201i
$448$	−2.79360			−0.131985
$449$	−17.1975			−0.811601			−0.405801	−	0.913962i	$-0.633007\pi$
$449$	−17.1975			−0.811601			−0.405801	+	0.913962i	$0.633007\pi$
$450$	−1.75914	−	3.04692i	−0.0829267	−	0.143633i
$451$	−2.18831	+	3.79027i	−0.103044	+	0.178477i
$452$	0.213892	+	0.370473i	0.0100607	+	0.0174256i
$453$	−12.9324	+	22.3996i	−0.607618	+	1.05243i
$454$	−13.5468	+	23.4637i	−0.635783	+	1.10121i
$455$	43.5954			2.04378
$456$		0			0
$457$	−31.1517			−1.45722			−0.728608	−	0.684931i	$-0.759832\pi$
$457$	−31.1517			−1.45722			−0.728608	+	0.684931i	$0.759832\pi$
$458$	−4.73279	+	8.19743i	−0.221149	+	0.383041i
$459$	2.19868	−	3.80822i	0.102626	−	0.177753i
$460$	−3.07321	−	5.32296i	−0.143289	−	0.248184i
$461$	−7.77050	+	13.4589i	−0.361908	+	0.626843i	−0.988275	−	0.152685i	$-0.951208\pi$
$461$	−7.77050	+	13.4589i	−0.361908	+	0.626843i	0.626367	+	0.779528i	$0.284541\pi$
$462$	5.90868	+	10.2341i	0.274897	+	0.476135i
$463$	20.6648			0.960374			0.480187	−	0.877166i	$-0.340569\pi$
$463$	20.6648			0.960374			0.480187	+	0.877166i	$0.340569\pi$
$464$	5.93179			0.275376
$465$	−22.5758	−	39.1025i	−1.04693	−	1.81333i
$466$	−11.4311	−	19.7992i	−0.529533	−	0.917178i
$467$	−28.4830			−1.31803			−0.659017	−	0.752128i	$-0.729028\pi$
$467$	−28.4830			−1.31803			−0.659017	+	0.752128i	$0.729028\pi$
$468$	21.2616			0.982816
$469$	16.1477	+	27.9686i	0.745629	+	1.29147i
$470$	0.916949	−	1.58820i	0.0422957	−	0.0732583i
$471$	3.74730	+	6.49052i	0.172667	+	0.299067i
$472$	2.48131	−	4.29775i	0.114211	−	0.197820i
$473$	2.40977	−	4.17385i	0.110802	−	0.191914i
$474$	14.8981			0.684290
$475$		0			0
$476$	−13.8819			−0.636276
$477$	2.46354	−	4.26698i	0.112798	−	0.195372i
$478$	−4.33306	+	7.50508i	−0.198189	+	0.343274i
$479$	5.23632	+	9.06958i	0.239254	+	0.414400i	0.960500	−	0.278279i	$-0.0897639\pi$
$479$	5.23632	+	9.06958i	0.239254	+	0.414400i	−0.721247	+	0.692678i	$0.756431\pi$
$480$	−3.09934	+	5.36821i	−0.141465	+	0.245024i
$481$	−1.74784	−	3.02735i	−0.0796947	−	0.138035i
$482$	5.65826			0.257727
$483$	−17.5930			−0.800510
$484$	4.09127	+	7.08628i	0.185967	+	0.322104i
$485$	17.6940	+	30.6468i	0.803441	+	1.39160i
$486$	22.3706			1.01475
$487$	2.29894			0.104175			0.0520875	−	0.998643i	$-0.483413\pi$
$487$	2.29894			0.104175			0.0520875	+	0.998643i	$0.483413\pi$
$488$	−4.66843	−	8.08596i	−0.211330	−	0.366034i
$489$	7.04622	−	12.2044i	0.318641	−	0.551902i
$490$	0.989057	+	1.71310i	0.0446810	+	0.0773898i
$491$	−6.08059	+	10.5319i	−0.274413	+	0.475297i	−0.969987	−	0.243157i	$-0.921817\pi$
$491$	−6.08059	+	10.5319i	−0.274413	+	0.475297i	0.695574	+	0.718455i	$0.255150\pi$
$492$	−3.28553	+	5.69071i	−0.148123	+	0.256557i
$493$	29.4761			1.32754
$494$		0			0
$495$	13.8355			0.621860
$496$	−3.64204	+	6.30820i	−0.163532	+	0.283246i
$497$	−9.77340	+	16.9280i	−0.438397	+	0.759326i
$498$	19.1245	+	33.1247i	0.856991	+	1.48435i
$499$	−7.56742	+	13.1072i	−0.338764	+	0.586757i	−0.984201	−	0.177057i	$-0.943342\pi$
$499$	−7.56742	+	13.1072i	−0.338764	+	0.586757i	0.645436	+	0.763814i	$0.276676\pi$
$500$	−4.85796	−	8.41423i	−0.217255	−	0.376296i
$501$	17.8517			0.797556
$502$	−13.5552			−0.605000
$503$	0.286841	+	0.496824i	0.0127896	+	0.0221523i	0.872349	−	0.488883i	$-0.162595\pi$
$503$	0.286841	+	0.496824i	0.0127896	+	0.0221523i	−0.859560	+	0.511035i	$0.829262\pi$
$504$	4.68088	+	8.10752i	0.208503	+	0.361138i
$505$	−27.7520			−1.23495
$506$	4.19449			0.186468
$507$	34.3416	+	59.4814i	1.52516	+	2.64166i
$508$	0.568158	−	0.984079i	0.0252079	−	0.0436614i
$509$	13.1081	+	22.7039i	0.581008	+	1.00633i	0.995360	+	0.0962184i	$0.0306747\pi$
$509$	13.1081	+	22.7039i	0.581008	+	1.00633i	−0.414353	+	0.910116i	$0.635992\pi$
$510$	−15.4012	+	26.6756i	−0.681975	+	1.18121i
$511$	−8.64089	+	14.9665i	−0.382250	+	0.662077i
$512$	1.00000			0.0441942
$513$		0			0
$514$	10.0393			0.442813
$515$	18.2358	−	31.5854i	0.803566	−	1.39182i
$516$	3.61803	−	6.26662i	0.159275	−	0.275873i
$517$	0.625751	+	1.08383i	0.0275205	+	0.0476669i
$518$	0.769599	−	1.33298i	0.0338142	−	0.0585680i
$519$	−29.0079	−	50.2432i	−1.27331	−	2.20543i
$520$	−15.6054			−0.684344
$521$	−12.9637			−0.567948			−0.283974	−	0.958832i	$-0.591653\pi$
$521$	−12.9637			−0.567948			−0.283974	+	0.958832i	$0.591653\pi$
$522$	−9.93912	−	17.2151i	−0.435024	−	0.753483i
$523$	−8.88963	−	15.3973i	−0.388716	−	0.673276i	0.603561	−	0.797317i	$-0.293748\pi$
$523$	−8.88963	−	15.3973i	−0.388716	−	0.673276i	−0.992277	+	0.124041i	$0.960415\pi$
$524$	−17.8415			−0.779410
$525$	7.39144			0.322589
$526$	9.41309	+	16.3040i	0.410430	+	0.710886i
$527$	−18.0979	+	31.3465i	−0.788358	+	1.36548i
$528$	−2.11507	−	3.66341i	−0.0920467	−	0.159430i
$529$	8.37774	−	14.5107i	0.364250	−	0.630899i
$530$	−1.80818	+	3.13185i	−0.0785421	+	0.136039i
$531$	−16.6304			−0.721698
$532$		0			0
$533$	−16.5429			−0.716554
$534$	8.70083	−	15.0703i	0.376522	−	0.652155i
$535$	−3.47854	+	6.02501i	−0.150391	+	0.260484i
$536$	−5.78022	−	10.0116i	−0.249668	−	0.432437i
$537$	10.3511	−	17.9287i	0.446685	−	0.773681i
$538$	8.19134	+	14.1878i	0.353154	+	0.611680i
$539$	−1.34992			−0.0581451
$540$	2.17661			0.0936664
$541$	2.67209	+	4.62820i	0.114882	+	0.198982i	0.917733	−	0.397199i	$-0.130018\pi$
$541$	2.67209	+	4.62820i	0.114882	+	0.198982i	−0.802851	+	0.596180i	$0.796684\pi$
$542$	1.38342	+	2.39615i	0.0594229	+	0.102923i
$543$	32.7616			1.40594
$544$	4.96917			0.213052
$545$	2.12193	+	3.67529i	0.0908934	+	0.157432i
$546$	−22.3338	+	38.6833i	−0.955800	+	1.65549i
$547$	−2.55056	−	4.41770i	−0.109054	−	0.188887i	0.806333	−	0.591461i	$-0.201449\pi$
$547$	−2.55056	−	4.41770i	−0.109054	−	0.188887i	−0.915387	+	0.402574i	$0.868115\pi$
$548$	7.95782	−	13.7833i	0.339941	−	0.588795i
$549$	−15.6446	+	27.0972i	−0.667694	+	1.15648i
$550$	−1.76225			−0.0751426
$551$		0			0
$552$	6.29761			0.268044
$553$	−8.25731	+	14.3021i	−0.351137	+	0.608186i
$554$	−12.2661	+	21.2454i	−0.521135	+	0.902632i
$555$	−1.70765	−	2.95774i	−0.0724857	−	0.125549i
$556$	−5.06008	+	8.76432i	−0.214595	+	0.371690i
$557$	5.36176	+	9.28685i	0.227185	+	0.393496i	0.956973	−	0.290178i	$-0.0937144\pi$
$557$	5.36176	+	9.28685i	0.227185	+	0.393496i	−0.729788	+	0.683674i	$0.760381\pi$
$558$	24.4100			1.03336
$559$	18.2171			0.770502
$560$	−3.43564	−	5.95071i	−0.145182	−	0.251463i
$561$	−10.5102	−	18.2041i	−0.443740	−	0.768580i
$562$	10.1704			0.429011
$563$	9.76285			0.411455			0.205728	−	0.978609i	$-0.434044\pi$
$563$	9.76285			0.411455			0.205728	+	0.978609i	$0.434044\pi$
$564$	0.939503	+	1.62727i	0.0395602	+	0.0685203i
$565$	−0.526100	+	0.911233i	−0.0221332	+	0.0383358i
$566$	−13.8339	−	23.9610i	−0.581482	−	1.00716i
$567$	−10.9276	+	18.9271i	−0.458915	+	0.794864i
$568$	3.49849	−	6.05956i	0.146793	−	0.254254i
$569$	−8.84194			−0.370674			−0.185337	−	0.982675i	$-0.559338\pi$
$569$	−8.84194			−0.370674			−0.185337	+	0.982675i	$0.559338\pi$
$570$		0			0
$571$	22.8411			0.955871			0.477935	−	0.878395i	$-0.341385\pi$
$571$	22.8411			0.955871			0.477935	+	0.878395i	$0.341385\pi$
$572$	5.32479	−	9.22280i	0.222640	−	0.385625i
$573$	8.28472	−	14.3496i	0.346099	−	0.599461i
$574$	−3.64204	−	6.30820i	−0.152016	−	0.263299i
$575$	1.31177	−	2.27205i	0.0547046	−	0.0947511i
$576$	−1.67557	−	2.90217i	−0.0698154	−	0.120924i
$577$	−14.0176			−0.583560			−0.291780	−	0.956486i	$-0.594247\pi$
$577$	−14.0176			−0.583560			−0.291780	+	0.956486i	$0.594247\pi$
$578$	7.69270			0.319974
$579$	33.8741	+	58.6716i	1.40776	+	2.43831i
$580$	7.29506	+	12.6354i	0.302911	+	0.524657i
$581$	−42.3994			−1.75903
$582$	−36.2583			−1.50296
$583$	−1.23395	−	2.13726i	−0.0511049	−	0.0885163i
$584$	3.09310	−	5.35740i	0.127993	−	0.221691i
$585$	26.1480	+	45.2897i	1.08109	+	1.87250i
$586$	−11.9193	+	20.6448i	−0.492382	+	0.852830i
$587$	−10.5178	+	18.2174i	−0.434116	+	0.751911i	−0.997223	−	0.0744731i	$-0.976273\pi$
$587$	−10.5178	+	18.2174i	−0.434116	+	0.751911i	0.563107	+	0.826384i	$0.309606\pi$
$588$	−2.02677			−0.0835825
$589$		0			0
$590$	12.2063			0.502525
$591$	−12.4110	+	21.4964i	−0.510519	+	0.884245i
$592$	−0.275486	+	0.477156i	−0.0113224	+	0.0196110i
$593$	17.4596	+	30.2410i	0.716981	+	1.24185i	0.962190	+	0.272377i	$0.0878099\pi$
$593$	17.4596	+	30.2410i	0.716981	+	1.24185i	−0.245210	+	0.969470i	$0.578857\pi$
$594$	−0.742689	+	1.28637i	−0.0304729	+	0.0527806i
$595$	−17.0723	−	29.5701i	−0.699897	−	1.21226i
$596$	9.39851			0.384978
$597$	51.5776			2.11093
$598$	7.92724	+	13.7304i	0.324169	+	0.561477i
$599$	−10.7553	−	18.6288i	−0.439450	−	0.761150i	0.558197	−	0.829709i	$-0.311493\pi$
$599$	−10.7553	−	18.6288i	−0.439450	−	0.761150i	−0.997647	+	0.0685583i	$0.978160\pi$
$600$	−2.64584			−0.108016
$601$	−14.3417			−0.585012			−0.292506	−	0.956264i	$-0.594489\pi$
$601$	−14.3417			−0.585012			−0.292506	+	0.956264i	$0.594489\pi$
$602$	4.01062	+	6.94660i	0.163461	+	0.283122i
$603$	−19.3703	+	33.5504i	−0.788821	+	1.36628i
$604$	5.13162	+	8.88822i	0.208803	+	0.361657i
$605$	−10.0631	+	17.4298i	−0.409122	+	0.708621i
$606$	14.2173	−	24.6251i	0.577539	−	1.00033i
$607$	−10.3488			−0.420046			−0.210023	−	0.977696i	$-0.567354\pi$
$607$	−10.3488			−0.420046			−0.210023	+	0.977696i	$0.567354\pi$
$608$		0			0
$609$	41.7615			1.69226
$610$	11.4827	−	19.8886i	0.464921	−	0.805267i
$611$	−2.36524	+	4.09671i	−0.0956873	+	0.165735i
$612$	−8.32620	−	14.4214i	−0.336567	−	0.582951i
$613$	−9.78370	+	16.9459i	−0.395160	+	0.684437i	−0.993122	−	0.117088i	$-0.962644\pi$
$613$	−9.78370	+	16.9459i	−0.395160	+	0.684437i	0.597962	+	0.801525i	$0.295978\pi$
$614$	−12.9942	−	22.5066i	−0.524404	−	0.908294i
$615$	−16.1625			−0.651735
$616$	4.68915			0.188931
$617$	2.96261	+	5.13139i	0.119270	+	0.206582i	0.919479	−	0.393140i	$-0.128611\pi$
$617$	2.96261	+	5.13139i	0.119270	+	0.206582i	−0.800208	+	0.599722i	$0.795278\pi$
$618$	18.6843	+	32.3622i	0.751594	+	1.30180i
$619$	8.03958			0.323138			0.161569	−	0.986861i	$-0.448345\pi$
$619$	8.03958			0.323138			0.161569	+	0.986861i	$0.448345\pi$
$620$	−17.9163			−0.719535
$621$	−1.10567	−	1.91508i	−0.0443692	−	0.0768496i
$622$	11.5522	−	20.0089i	0.463200	−	0.802286i
$623$	9.64494	+	16.7055i	0.386417	+	0.669293i
$624$	7.99463	−	13.8471i	0.320041	−	0.554328i
$625$	14.5736	−	25.2422i	0.582943	−	1.00969i
$626$	12.2647			0.490196
$627$		0			0
$628$	2.97387			0.118671
$629$	−1.36894	+	2.37107i	−0.0545831	+	0.0945408i
$630$	−11.5133	+	19.9417i	−0.458702	+	0.794495i
$631$	6.45032	+	11.1723i	0.256783	+	0.444762i	0.965378	−	0.260854i	$-0.0840040\pi$
$631$	6.45032	+	11.1723i	0.256783	+	0.444762i	−0.708595	+	0.705615i	$0.750671\pi$
$632$	2.95579	−	5.11958i	0.117575	−	0.203646i
$633$	10.2271	+	17.7139i	0.406492	+	0.704065i
$634$	−0.272305			−0.0108146
$635$	2.79494			0.110914
$636$	−1.85265	−	3.20888i	−0.0734623	−	0.127241i
$637$	−2.55124	−	4.41887i	−0.101084	−	0.175082i
$638$	−9.95669			−0.394189
$639$	−23.4479			−0.927584
$640$	1.22982	+	2.13012i	0.0486131	+	0.0842003i
$641$	14.4319	−	24.9969i	0.570028	−	0.987317i	−0.426535	−	0.904471i	$-0.640266\pi$
$641$	14.4319	−	24.9969i	0.570028	−	0.987317i	0.996562	−	0.0828458i	$-0.0264009\pi$
$642$	−3.56410	−	6.17320i	−0.140664	−	0.243637i
$643$	−13.1697	+	22.8106i	−0.519363	+	0.899563i	0.480384	+	0.877058i	$0.340497\pi$
$643$	−13.1697	+	22.8106i	−0.519363	+	0.899563i	−0.999747	+	0.0225047i	$0.992836\pi$
$644$	−3.49047	+	6.04568i	−0.137544	+	0.238233i
$645$	17.7982			0.700803
$646$		0			0
$647$	−3.04601			−0.119751			−0.0598756	−	0.998206i	$-0.519070\pi$
$647$	−3.04601			−0.119751			−0.0598756	+	0.998206i	$0.519070\pi$
$648$	3.91164	−	6.77516i	0.153664	−	0.266153i
$649$	−4.16495	+	7.21390i	−0.163489	+	0.283170i
$650$	−3.33051	−	5.76861i	−0.130633	−	0.226264i
$651$	−25.6410	+	44.4116i	−1.00495	+	1.74063i
$652$	−2.79595	−	4.84273i	−0.109498	−	0.189656i
$653$	−15.1973			−0.594717			−0.297359	−	0.954766i	$-0.596106\pi$
$653$	−15.1973			−0.594717			−0.297359	+	0.954766i	$0.596106\pi$
$654$	−4.34824			−0.170030
$655$	−21.9419	−	38.0045i	−0.857342	−	1.48496i
$656$	1.30371	+	2.25809i	0.0509012	+	0.0881634i
$657$	−20.7308			−0.808786
$658$	−2.08289			−0.0811996
$659$	−8.93704	−	15.4794i	−0.348138	−	0.602992i	0.637781	−	0.770218i	$-0.279852\pi$
$659$	−8.93704	−	15.4794i	−0.348138	−	0.602992i	−0.985919	+	0.167226i	$0.946519\pi$
$660$	5.20234	−	9.01071i	0.202501	−	0.350742i
$661$	−18.9263	−	32.7812i	−0.736146	−	1.27504i	−0.954219	−	0.299110i	$-0.903310\pi$
$661$	−18.9263	−	32.7812i	−0.736146	−	1.27504i	0.218072	−	0.975933i	$-0.430023\pi$
$662$	9.99650	−	17.3144i	0.388525	−	0.672945i
$663$	39.7267	−	68.8087i	1.54286	−	2.67231i
$664$	15.1773			0.588994
$665$		0			0
$666$	1.84638			0.0715460
$667$	7.41148	−	12.8371i	0.286974	−	0.497053i
$668$	3.54180	−	6.13458i	0.137036	−	0.237354i
$669$	13.5509	+	23.4708i	0.523906	+	0.907433i
$670$	14.2173	−	24.6251i	0.549263	−	0.951351i
$671$	7.83611	+	13.5725i	0.302510	+	0.523962i
$672$	7.04029			0.271585
$673$	−8.28461			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$673$	−8.28461			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$674$	8.64121	+	14.9670i	0.332847	+	0.576508i
$675$	0.464532	+	0.804593i	0.0178798	+	0.0309688i
$676$	27.2537			1.04822
$677$	−18.3233			−0.704223			−0.352111	−	0.935958i	$-0.614536\pi$
$677$	−18.3233			−0.704223			−0.352111	+	0.935958i	$0.614536\pi$
$678$	−0.539040	−	0.933645i	−0.0207017	−	0.0358564i
$679$	20.0963	−	34.8079i	0.771226	−	1.33580i
$680$	6.11121	+	10.5849i	0.234354	+	0.405914i
$681$	34.1399	−	59.1321i	1.30825	−	2.26595i
$682$	6.11328	−	10.5885i	0.234090	−	0.405455i
$683$	−49.2217			−1.88342			−0.941709	−	0.336429i	$-0.890781\pi$
$683$	−49.2217			−1.88342			−0.941709	+	0.336429i	$0.890781\pi$
$684$		0			0
$685$	39.1469			1.49573
$686$	−8.65427	+	14.9896i	−0.330422	+	0.572307i
$687$	11.9273	−	20.6587i	0.455055	−	0.788179i
$688$	−1.43564	−	2.48661i	−0.0547334	−	0.0948011i
$689$	4.66412	−	8.07850i	0.177689	−	0.307766i
$690$	7.74495	+	13.4146i	0.294845	+	0.510687i
$691$	16.6779			0.634458			0.317229	−	0.948349i	$-0.397248\pi$
$691$	16.6779			0.634458			0.317229	+	0.948349i	$0.397248\pi$
$692$	−23.0208			−0.875120
$693$	−7.85701	−	13.6087i	−0.298463	−	0.516953i
$694$	9.27279	+	16.0609i	0.351990	+	0.609665i
$695$	−24.8921			−0.944210
$696$	−14.9490			−0.566639
$697$	6.47834	+	11.2208i	0.245385	+	0.425019i
$698$	10.0605	−	17.4253i	0.380796	−	0.659558i
$699$	28.8079	+	49.8968i	1.08962	+	1.88727i
$700$	1.46647	−	2.54000i	0.0554273	−	0.0960029i
$701$	15.4533	−	26.7659i	0.583663	−	1.01093i	−0.411378	−	0.911465i	$-0.634952\pi$
$701$	15.4533	−	26.7659i	0.583663	−	1.01093i	0.995041	−	0.0994688i	$-0.0317143\pi$
$702$	−5.61449			−0.211905
$703$		0			0
$704$	−1.67853			−0.0632620
$705$	−2.31085	+	4.00250i	−0.0870315	+	0.150743i
$706$	−12.0278	+	20.8328i	−0.452674	+	0.784054i
$707$	15.7600	+	27.2972i	0.592716	+	1.02661i
$708$	−6.25325	+	10.8310i	−0.235012	+	0.407052i
$709$	−20.0528	−	34.7325i	−0.753098	−	1.30440i	−0.946314	−	0.323248i	$-0.895225\pi$
$709$	−20.0528	−	34.7325i	−0.753098	−	1.30440i	0.193216	−	0.981156i	$-0.438108\pi$
$710$	17.2101			0.645884
$711$	−19.8105			−0.742953
$712$	−3.45251	−	5.97992i	−0.129388	−	0.224107i
$713$	9.10111	+	15.7636i	0.340839	+	0.590351i
$714$	34.9845			1.30926
$715$	26.1942			0.979608
$716$	−4.10736	−	7.11415i	−0.153499	−	0.265868i
$717$	10.9199	−	18.9139i	0.407813	−	0.706352i
$718$	5.42673	+	9.39937i	0.202524	+	0.350781i
$719$	22.8264	−	39.5365i	0.851282	−	1.47446i	−0.0287690	−	0.999586i	$-0.509159\pi$
$719$	22.8264	−	39.5365i	0.851282	−	1.47446i	0.880051	−	0.474878i	$-0.157508\pi$
$720$	4.12132	−	7.13833i	0.153592	−	0.266030i
$721$	−41.4235			−1.54269
$722$		0			0
$723$	−14.2596			−0.530322
$724$	6.49994	−	11.2582i	0.241569	−	0.418409i
$725$	−3.11382	+	5.39329i	−0.115644	+	0.200302i
$726$	−10.3106	−	17.8585i	−0.382662	−	0.662790i
$727$	7.59053	−	13.1472i	0.281517	−	0.487602i	−0.690242	−	0.723579i	$-0.742496\pi$
$727$	7.59053	−	13.1472i	0.281517	−	0.487602i	0.971759	+	0.235977i	$0.0758291\pi$
$728$	8.86212	+	15.3496i	0.328452	+	0.568896i
$729$	−32.9073			−1.21879
$730$	15.2159			0.563164
$731$	−7.13397	−	12.3564i	−0.263859	−	0.457018i
$732$	11.7651	+	20.3778i	0.434852	+	0.753185i
$733$	−26.9986			−0.997217			−0.498608	−	0.866827i	$-0.666155\pi$
$733$	−26.9986			−0.997217			−0.498608	+	0.866827i	$0.666155\pi$
$734$	−32.6121			−1.20373
$735$	−2.49257	−	4.31726i	−0.0919398	−	0.159244i
$736$	1.24945	−	2.16411i	0.0460554	−	0.0797703i
$737$	9.70228	+	16.8048i	0.357388	+	0.619014i
$738$	4.36890	−	7.56716i	0.160822	−	0.278551i
$739$	2.60391	−	4.51010i	0.0957864	−	0.165907i	−0.814150	−	0.580654i	$-0.802797\pi$
$739$	2.60391	−	4.51010i	0.0957864	−	0.165907i	0.909937	+	0.414748i	$0.136130\pi$
$740$	−1.35520			−0.0498181
$741$		0			0
$742$	4.10736			0.150786
$743$	−11.0539	+	19.1460i	−0.405529	+	0.702398i	−0.994383	−	0.105842i	$-0.966246\pi$
$743$	−11.0539	+	19.1460i	−0.405529	+	0.702398i	0.588853	+	0.808240i	$0.299580\pi$
$744$	9.17848	−	15.8976i	0.336499	−	0.582834i
$745$	11.5585	+	20.0199i	0.423471	+	0.733474i
$746$	2.65099	−	4.59165i	0.0970596	−	0.168112i
$747$	−25.4307	−	44.0472i	−0.930460	−	1.61160i
$748$	−8.34092			−0.304974
$749$	7.90167			0.288721
$750$	12.2428	+	21.2051i	0.447043	+	0.774301i
$751$	6.24798	+	10.8218i	0.227992	+	0.394894i	0.957213	−	0.289384i	$-0.0934506\pi$
$751$	6.24798	+	10.8218i	0.227992	+	0.394894i	−0.729221	+	0.684279i	$0.760117\pi$
$752$	0.745593			0.0271890
$753$	34.1612			1.24490
$754$	−18.8173	−	32.5926i	−0.685287	−	1.18695i
$755$	−12.6220	+	21.8619i	−0.459361	+	0.795636i
$756$	−1.23607	−	2.14093i	−0.0449554	−	0.0778650i
$757$	15.4994	−	26.8458i	0.563336	−	0.975727i	−0.433866	−	0.900977i	$-0.642851\pi$
$757$	15.4994	−	26.8458i	0.563336	−	0.975727i	0.997202	−	0.0747495i	$-0.0238157\pi$
$758$	−12.3328	+	21.3610i	−0.447948	+	0.775868i
$759$	−10.5707			−0.383693
$760$		0			0
$761$	1.96398			0.0711941			0.0355971	−	0.999366i	$-0.488667\pi$
$761$	1.96398			0.0711941			0.0355971	+	0.999366i	$0.488667\pi$
$762$	−1.43184	+	2.48002i	−0.0518702	+	0.0898418i
$763$	2.41003	−	4.17429i	0.0872489	−	0.151120i
$764$	−3.28740	−	5.69394i	−0.118934	−	0.205999i
$765$	20.4795	−	35.4716i	0.740439	−	1.28248i
$766$	−1.82208	−	3.15593i	−0.0658344	−	0.114029i
$767$	−31.4857			−1.13688
$768$	−2.52015			−0.0909380
$769$	11.1661	+	19.3402i	0.402659	+	0.697426i	0.994046	−	0.108962i	$-0.0347527\pi$
$769$	11.1661	+	19.3402i	0.402659	+	0.697426i	−0.591387	+	0.806388i	$0.701419\pi$
$770$	5.76684	+	9.98845i	0.207822	+	0.359959i
$771$	−25.3004			−0.911172
$772$	26.8826			0.967527
$773$	−13.6776	−	23.6904i	−0.491951	−	0.852084i	0.508006	−	0.861353i	$-0.330383\pi$
$773$	−13.6776	−	23.6904i	−0.491951	−	0.852084i	−0.999957	+	0.00926978i	$0.997049\pi$
$774$	−4.81105	+	8.33298i	−0.172929	+	0.299523i
$775$	−3.82369	−	6.62282i	−0.137351	−	0.237899i
$776$	−7.19369	+	12.4598i	−0.258238	+	0.447282i
$777$	−1.93950	+	3.35932i	−0.0695793	+	0.120515i
$778$	2.79353			0.100153
$779$		0			0
$780$	39.3280			1.40817
$781$	−5.87233	+	10.1712i	−0.210128	+	0.363953i
$782$	6.20875	−	10.7539i	0.222024	−	0.384557i
$783$	2.62460	+	4.54594i	0.0937955	+	0.162459i
$784$	−0.402113	+	0.696480i	−0.0143612	+	0.0248743i
$785$	3.65734	+	6.33471i	0.130536	+	0.226095i
$786$	44.9632			1.60378
$787$	7.78962			0.277670			0.138835	−	0.990316i	$-0.455664\pi$
$787$	7.78962			0.277670			0.138835	+	0.990316i	$0.455664\pi$
$788$	4.92470	+	8.52983i	0.175435	+	0.303863i
$789$	−23.7224	−	41.0884i	−0.844539	−	1.46278i
$790$	14.5404			0.517325
$791$	1.19506			0.0424915
$792$	2.81250	+	4.87139i	0.0999378	+	0.173097i
$793$	−29.6192	+	51.3020i	−1.05181	+	1.82179i
$794$	19.7551	+	34.2168i	0.701081	+	1.21431i
$795$	4.55687	−	7.89273i	0.161615	−	0.279926i
$796$	10.2331	−	17.7242i	0.362701	−	0.628216i
$797$	−6.09655			−0.215951			−0.107975	−	0.994154i	$-0.534437\pi$
$797$	−6.09655			−0.215951			−0.107975	+	0.994154i	$0.534437\pi$
$798$		0			0
$799$	3.70498			0.131073
$800$	−0.524938	+	0.909219i	−0.0185594	+	0.0321458i
$801$	−11.5698	+	20.0396i	−0.408800	+	0.708063i
$802$	9.31073	+	16.1267i	0.328773	+	0.569452i
$803$	−5.19186	+	8.99256i	−0.183217	+	0.317341i
$804$	14.5670	+	25.2308i	0.513739	+	0.889821i
$805$	−17.1707			−0.605187
$806$	46.2144			1.62783
$807$	−20.6434	−	35.7554i	−0.726681	−	1.25865i
$808$	−5.64146	−	9.77130i	−0.198466	−	0.343753i
$809$	56.8455			1.99858			0.999291	−	0.0376413i	$-0.0119844\pi$
$809$	56.8455			1.99858			0.999291	+	0.0376413i	$0.0119844\pi$
$810$	19.2425			0.676113
$811$	10.4604	+	18.1180i	0.367316	+	0.636209i	0.989145	−	0.146944i	$-0.0469436\pi$
$811$	10.4604	+	18.1180i	0.367316	+	0.636209i	−0.621829	+	0.783153i	$0.713610\pi$
$812$	8.28553	−	14.3510i	0.290765	−	0.503620i
$813$	−3.48642	−	6.03865i	−0.122274	−	0.211785i
$814$	0.462412	−	0.800921i	0.0162075	−	0.0280723i
$815$	6.87707	−	11.9114i	0.240893	−	0.417239i
$816$	−12.5231			−0.438394
$817$		0			0
$818$	−17.1433			−0.599401
$819$	29.6982	−	51.4388i	1.03774	−	1.79742i
$820$	−3.20666	+	5.55410i	−0.111981	+	0.193958i
$821$	−8.12912	−	14.0800i	−0.283708	−	0.491397i	0.688587	−	0.725154i	$-0.258231\pi$
$821$	−8.12912	−	14.0800i	−0.283708	−	0.491397i	−0.972295	+	0.233757i	$0.924898\pi$
$822$	−20.0549	+	34.7361i	−0.699494	+	1.21156i
$823$	8.76642	+	15.1839i	0.305578	+	0.529277i	0.977390	−	0.211445i	$-0.0678169\pi$
$823$	8.76642	+	15.1839i	0.305578	+	0.529277i	−0.671812	+	0.740722i	$0.734484\pi$
$824$	14.8280			0.516557
$825$	4.44113			0.154620
$826$	−6.93179	−	12.0062i	−0.241188	−	0.417749i
$827$	8.51268	+	14.7444i	0.296015	+	0.512713i	0.975221	−	0.221235i	$-0.0710088\pi$
$827$	8.51268	+	14.7444i	0.296015	+	0.512713i	−0.679205	+	0.733948i	$0.737675\pi$
$828$	−8.37418			−0.291023
$829$	−5.76207			−0.200125			−0.100062	−	0.994981i	$-0.531904\pi$
$829$	−5.76207			−0.200125			−0.100062	+	0.994981i	$0.531904\pi$
$830$	18.6654	+	32.3295i	0.647887	+	1.12217i
$831$	30.9123	−	53.5416i	1.07234	−	1.85734i
$832$	−3.17229	−	5.49456i	−0.109979	−	0.190490i
$833$	−1.99817	+	3.46093i	−0.0692325	+	0.119914i
$834$	12.7522	−	22.0874i	0.441571	−	0.764824i
$835$	17.4232			0.602954
$836$		0			0
$837$	−6.44588			−0.222802
$838$	9.25210	−	16.0251i	0.319609	−	0.553578i
$839$	−4.44977	+	7.70722i	−0.153623	+	0.266083i	−0.932557	−	0.361023i	$-0.882427\pi$
$839$	−4.44977	+	7.70722i	−0.153623	+	0.266083i	0.778934	+	0.627106i	$0.215761\pi$
$840$	8.65833	+	14.9967i	0.298741	+	0.517434i
$841$	−3.09304	+	5.35730i	−0.106657	+	0.184735i
$842$	8.09980	+	14.0293i	0.279138	+	0.483481i
$843$	−25.6308			−0.882772
$844$	8.11630			0.279374
$845$	33.5172	+	58.0535i	1.15303	+	1.99710i
$846$	−1.24929	−	2.16384i	−0.0429516	−	0.0743944i
$847$	22.8588			0.785436
$848$	−1.47027			−0.0504893
$849$	34.8635	+	60.3853i	1.19651	+	2.07242i
$850$	−2.60851	+	4.51807i	−0.0894711	+	0.154968i
$851$	0.688413	+	1.19237i	0.0235985	+	0.0408738i
$852$	−8.81671	+	15.2710i	−0.302056	+	0.523176i
$853$	−1.39458	+	2.41547i	−0.0477493	+	0.0827043i	−0.888912	−	0.458078i	$-0.848538\pi$
$853$	−1.39458	+	2.41547i	−0.0477493	+	0.0827043i	0.841163	+	0.540782i	$0.181872\pi$
$854$	−26.0835			−0.892559
$855$		0			0
$856$	−2.82849			−0.0966757
$857$	−8.19724	+	14.1980i	−0.280012	+	0.484995i	−0.971387	−	0.237500i	$-0.923672\pi$
$857$	−8.19724	+	14.1980i	−0.280012	+	0.484995i	0.691375	+	0.722496i	$0.257005\pi$
$858$	−13.4192	+	23.2428i	−0.458125	+	0.793496i
$859$	−4.76252	−	8.24893i	−0.162495	−	0.281450i	0.773268	−	0.634080i	$-0.218621\pi$
$859$	−4.76252	−	8.24893i	−0.162495	−	0.281450i	−0.935763	+	0.352630i	$0.885288\pi$
$860$	3.53118	−	6.11619i	0.120412	−	0.208560i
$861$	9.17848	+	15.8976i	0.312802	+	0.541788i
$862$	12.6997			0.432552
$863$	−50.6764			−1.72505			−0.862523	−	0.506018i	$-0.831117\pi$
$863$	−50.6764			−1.72505			−0.862523	+	0.506018i	$0.831117\pi$
$864$	0.442463	+	0.766369i	0.0150529	+	0.0260724i
$865$	−28.3116	−	49.0370i	−0.962622	−	1.66731i
$866$	14.2350			0.483726
$867$	−19.3867			−0.658408
$868$	10.1744	+	17.6226i	0.345342	+	0.598150i
$869$	−4.96139	+	8.59338i	−0.168304	+	0.291510i
$870$	−18.3846	−	31.8431i	−0.623297	−	1.07958i
$871$	−36.6731	+	63.5196i	−1.24262	+	2.15228i
$872$	−0.862695	+	1.49423i	−0.0292145	+	0.0506011i
$873$	48.2141			1.63180
$874$		0			0
$875$	−27.1424			−0.917582
$876$	−7.79506	+	13.5014i	−0.263371	+	0.456171i
$877$	−9.62892	+	16.6778i	−0.325146	+	0.563169i	−0.981542	−	0.191248i	$-0.938747\pi$
$877$	−9.62892	+	16.6778i	−0.325146	+	0.563169i	0.656396	+	0.754416i	$0.272080\pi$
$878$	−14.0950	−	24.4133i	−0.475684	−	0.823908i
$879$	30.0384	−	52.0280i	1.01317	−	1.75486i
$880$	−2.06430	−	3.57547i	−0.0695875	−	0.120529i
$881$	19.1076			0.643750			0.321875	−	0.946782i	$-0.395687\pi$
$881$	19.1076			0.643750			0.321875	+	0.946782i	$0.395687\pi$
$882$	2.69507			0.0907479
$883$	−24.9990	−	43.2995i	−0.841283	−	1.45714i	−0.888810	−	0.458275i	$-0.848468\pi$
$883$	−24.9990	−	43.2995i	−0.841283	−	1.45714i	0.0475275	−	0.998870i	$-0.484866\pi$
$884$	−15.7637	−	27.3035i	−0.530189	−	0.918314i
$885$	−30.7616			−1.03404
$886$	−32.9944			−1.10847
$887$	−19.8097	−	34.3115i	−0.665146	−	1.15207i	−0.979246	−	0.202676i	$-0.935036\pi$
$887$	−19.8097	−	34.3115i	−0.665146	−	1.15207i	0.314100	−	0.949390i	$-0.398297\pi$
$888$	0.694265	−	1.20250i	0.0232980	−	0.0403533i
$889$	−1.58721	−	2.74913i	−0.0532333	−	0.0922027i
$890$	8.49196	−	14.7085i	0.284651	−	0.493030i
$891$	−6.56581	+	11.3723i	−0.219963	+	0.380987i
$892$	10.7540			0.360071
$893$		0			0
$894$	−23.6856			−0.792166
$895$	10.1027	−	17.4983i	0.337695	−	0.584904i
$896$	1.39680	−	2.41933i	0.0466639	−	0.0808242i
$897$	−19.9778	−	34.6026i	−0.667040	−	1.15535i
$898$	8.59876	−	14.8935i	0.286944	−	0.497002i
$899$	−21.6038	−	37.4189i	−0.720527	−	1.24799i
$900$	3.51828			0.117276
$901$	−7.30603			−0.243399
$902$	−2.18831	−	3.79027i	−0.0728628	−	0.126202i
$903$	−10.1074	−	17.5065i	−0.336352	−	0.582578i
$904$	−0.427785			−0.0142279
$905$	31.9752			1.06289
$906$	−12.9324	−	22.3996i	−0.429651	−	0.744178i
$907$	−27.6272	+	47.8518i	−0.917348	+	1.58889i	−0.113921	+	0.993490i	$0.536341\pi$
$907$	−27.6272	+	47.8518i	−0.917348	+	1.58889i	−0.803427	+	0.595403i	$0.796992\pi$
$908$	−13.5468	−	23.4637i	−0.449566	−	0.778672i
$909$	−18.9053	+	32.7450i	−0.627051	+	1.08608i
$910$	−21.7977	+	37.7547i	−0.722587	+	1.25156i
$911$	27.7087			0.918031			0.459015	−	0.888428i	$-0.348202\pi$
$911$	27.7087			0.918031			0.459015	+	0.888428i	$0.348202\pi$
$912$		0			0
$913$	−25.4756			−0.843120
$914$	15.5759	−	26.9782i	0.515203	−	0.892359i
$915$	−28.9381	+	50.1223i	−0.956664	+	1.65699i
$916$	−4.73279	−	8.19743i	−0.156376	−	0.270851i
$917$	−24.9211	+	43.1645i	−0.822966	+	1.42542i
$918$	2.19868	+	3.80822i	0.0725672	+	0.125690i
$919$	27.2500			0.898894			0.449447	−	0.893307i	$-0.351621\pi$
$919$	27.2500			0.898894			0.449447	+	0.893307i	$0.351621\pi$
$920$	6.14643			0.202642
$921$	32.7473	+	56.7201i	1.07906	+	1.86899i
$922$	−7.77050	−	13.4589i	−0.255908	−	0.443245i
$923$	−44.3929			−1.46121
$924$	−11.8174			−0.388762
$925$	−0.289226	−	0.500954i	−0.00950970	−	0.0164713i
$926$	−10.3324	+	17.8962i	−0.339543	+	0.588106i
$927$	−24.8453	−	43.0334i	−0.816027	−	1.41340i
$928$	−2.96589	+	5.13708i	−0.0973602	+	0.168633i
$929$	−22.2205	+	38.4870i	−0.729031	+	1.26272i	0.228263	+	0.973600i	$0.426695\pi$
$929$	−22.2205	+	38.4870i	−0.729031	+	1.26272i	−0.957293	+	0.289118i	$0.906638\pi$
$930$	45.1517			1.48058
$931$		0			0
$932$	22.8621			0.748873
$933$	−29.1132	+	50.4255i	−0.953122	+	1.65086i
$934$	14.2415	−	24.6670i	0.465995	−	0.807128i
$935$	−10.2579	−	17.7671i	−0.335468	−	0.581048i
$936$	−10.6308	+	18.4131i	−0.347478	+	0.601850i
$937$	9.10485	+	15.7701i	0.297442	+	0.515185i	0.975550	−	0.219777i	$-0.0705330\pi$
$937$	9.10485	+	15.7701i	0.297442	+	0.515185i	−0.678108	+	0.734963i	$0.737200\pi$
$938$	−32.2953			−1.05448
$939$	−30.9088			−1.00867
$940$	0.916949	+	1.58820i	0.0299076	+	0.0518015i
$941$	20.1340	+	34.8731i	0.656350	+	1.13683i	0.981554	+	0.191188i	$0.0612339\pi$
$941$	20.1340	+	34.8731i	0.656350	+	1.13683i	−0.325204	+	0.945644i	$0.605433\pi$
$942$	−7.49460			−0.244187
$943$	6.51567			0.212180
$944$	2.48131	+	4.29775i	0.0807596	+	0.139880i
$945$	3.04029	−	5.26594i	0.0989008	−	0.171301i
$946$	2.40977	+	4.17385i	0.0783485	+	0.135704i
$947$	−3.18280	+	5.51278i	−0.103427	+	0.179141i	−0.913095	−	0.407748i	$-0.866314\pi$
$947$	−3.18280	+	5.51278i	−0.103427	+	0.179141i	0.809667	+	0.586889i	$0.199648\pi$
$948$	−7.44903	+	12.9021i	−0.241933	+	0.419041i
$949$	−39.2488			−1.27407
$950$		0			0
$951$	0.686248			0.0222531
$952$	6.94095	−	12.0221i	0.224958	−	0.389638i
$953$	16.3472	−	28.3142i	0.529537	−	0.917186i	−0.469869	−	0.882736i	$-0.655699\pi$
$953$	16.3472	−	28.3142i	0.529537	−	0.917186i	0.999406	−	0.0344496i	$-0.0109678\pi$
$954$	2.46354	+	4.26698i	0.0797601	+	0.138149i
$955$	8.08584	−	14.0051i	0.261652	−	0.453194i
$956$	−4.33306	−	7.50508i	−0.140141	−	0.242731i
$957$	25.0923			0.811119
$958$	−10.4726			−0.338356
$959$	−22.2310	−	38.5052i	−0.717876	−	1.24340i
$960$	−3.09934	−	5.36821i	−0.100031	−	0.173258i
$961$	22.0578			0.711542
$962$	3.49568			0.112705
$963$	4.73933	+	8.20876i	0.152723	+	0.264524i
$964$	−2.82913	+	4.90020i	−0.0911201	+	0.157825i
$965$	33.0609	+	57.2632i	1.06427	+	1.84337i
$966$	8.79651	−	15.2360i	0.283023	−	0.490210i
$967$	−4.27968	+	7.41262i	−0.137625	+	0.238374i	−0.926597	−	0.376055i	$-0.877280\pi$
$967$	−4.27968	+	7.41262i	−0.137625	+	0.238374i	0.788972	+	0.614429i	$0.210614\pi$
$968$	−8.18253			−0.262997
$969$		0			0
$970$	−35.3879			−1.13624
$971$	20.9394	−	36.2682i	0.671978	−	1.16390i	−0.305364	−	0.952236i	$-0.598778\pi$
$971$	20.9394	−	36.2682i	0.671978	−	1.16390i	0.977342	−	0.211665i	$-0.0678886\pi$
$972$	−11.1853	+	19.3735i	−0.358768	+	0.621405i
$973$	14.1359	+	24.4841i	0.453175	+	0.784923i
$974$	−1.14947	+	1.99094i	−0.0368314	+	0.0637939i
$975$	8.39337	+	14.5377i	0.268803	+	0.465581i
$976$	9.33686			0.298866
$977$	−6.18021			−0.197722			−0.0988612	−	0.995101i	$-0.531520\pi$
$977$	−6.18021			−0.197722			−0.0988612	+	0.995101i	$0.531520\pi$
$978$	7.04622	+	12.2044i	0.225313	+	0.390254i
$979$	5.79514	+	10.0375i	0.185214	+	0.320799i
$980$	−1.97811			−0.0631885
$981$	5.78203			0.184606
$982$	−6.08059	−	10.5319i	−0.194039	−	0.336086i
$983$	−16.7871	+	29.0761i	−0.535425	+	0.927383i	0.463718	+	0.885983i	$0.346515\pi$
$983$	−16.7871	+	29.0761i	−0.535425	+	0.927383i	−0.999143	+	0.0414001i	$0.986818\pi$
$984$	−3.28553	−	5.69071i	−0.104739	−	0.181413i
$985$	−12.1130	+	20.9804i	−0.385954	+	0.668491i
$986$	−14.7380	+	25.5270i	−0.469355	+	0.812946i
$987$	5.24920			0.167084
$988$		0			0
$989$	−7.17507			−0.228154
$990$	−6.91776	+	11.9819i	−0.219861	+	0.380810i
$991$	23.0873	−	39.9884i	0.733393	−	1.27027i	−0.222032	−	0.975039i	$-0.571269\pi$
$991$	23.0873	−	39.9884i	0.733393	−	1.27027i	0.955425	−	0.295234i	$-0.0953976\pi$
$992$	−3.64204	−	6.30820i	−0.115635	−	0.200285i
$993$	−25.1926	+	43.6349i	−0.799464	+	1.38471i
$994$	−9.77340	−	16.9280i	−0.309993	−	0.536924i
$995$	50.3394			1.59587
$996$	−38.2491			−1.21197
$997$	0.409565	+	0.709388i	0.0129711	+	0.0224665i	0.872438	−	0.488725i	$-0.162538\pi$
$997$	0.409565	+	0.709388i	0.0129711	+	0.0224665i	−0.859467	+	0.511191i	$0.829204\pi$
$998$	−7.56742	−	13.1072i	−0.239542	−	0.414900i
$999$	−0.487570			−0.0154260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.c.m.429.4		8
19.2	odd	18		722.2.e.s.595.1		24
19.3	odd	18		722.2.e.s.99.4		24
19.4	even	9		722.2.e.r.423.1		24
19.5	even	9		722.2.e.r.389.1		24
19.6	even	9		722.2.e.r.415.4		24
19.7	even	3	inner	722.2.c.m.653.4		8
19.8	odd	6		722.2.a.m.1.4	✓	4
19.9	even	9		722.2.e.r.245.1		24
19.10	odd	18		722.2.e.s.245.4		24
19.11	even	3		722.2.a.n.1.1	yes	4
19.12	odd	6		722.2.c.n.653.1		8
19.13	odd	18		722.2.e.s.415.1		24
19.14	odd	18		722.2.e.s.389.4		24
19.15	odd	18		722.2.e.s.423.4		24
19.16	even	9		722.2.e.r.99.1		24
19.17	even	9		722.2.e.r.595.4		24
19.18	odd	2		722.2.c.n.429.1		8
57.8	even	6		6498.2.a.ca.1.4		4
57.11	odd	6		6498.2.a.bx.1.4		4
76.11	odd	6		5776.2.a.bt.1.4		4
76.27	even	6		5776.2.a.bv.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.4	✓	4	19.8	odd	6
722.2.a.n.1.1	yes	4	19.11	even	3
722.2.c.m.429.4		8	1.1	even	1	trivial
722.2.c.m.653.4		8	19.7	even	3	inner
722.2.c.n.429.1		8	19.18	odd	2
722.2.c.n.653.1		8	19.12	odd	6
722.2.e.r.99.1		24	19.16	even	9
722.2.e.r.245.1		24	19.9	even	9
722.2.e.r.389.1		24	19.5	even	9
722.2.e.r.415.4		24	19.6	even	9
722.2.e.r.423.1		24	19.4	even	9
722.2.e.r.595.4		24	19.17	even	9
722.2.e.s.99.4		24	19.3	odd	18
722.2.e.s.245.4		24	19.10	odd	18
722.2.e.s.389.4		24	19.14	odd	18
722.2.e.s.415.1		24	19.13	odd	18
722.2.e.s.423.4		24	19.15	odd	18
722.2.e.s.595.1		24	19.2	odd	18
5776.2.a.bt.1.4		4	76.11	odd	6
5776.2.a.bv.1.1		4	76.27	even	6
6498.2.a.bx.1.4		4	57.11	odd	6
6498.2.a.ca.1.4		4	57.8	even	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.26007 - 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} +1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.26007 - 2.18251i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22982 - 2.13012i) q^{5} +(1.26007 + 2.18251i) q^{6} -2.79360 q^{7} +1.00000 q^{8} +(-1.67557 - 2.90217i) q^{9} +(1.22982 + 2.13012i) q^{10} -1.67853 q^{11} -2.52015 q^{12} +(-3.17229 - 5.49456i) q^{13} +(1.39680 - 2.41933i) q^{14} +(-3.09934 - 5.36821i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.48459 + 4.30343i) q^{17} +3.35114 q^{18} -2.45965 q^{20} +(-3.52015 + 6.09707i) q^{21} +(0.839266 - 1.45365i) q^{22} +(1.24945 + 2.16411i) q^{23} +(1.26007 - 2.18251i) q^{24} +(-0.524938 - 0.909219i) q^{25} +6.34458 q^{26} -0.884927 q^{27} +(1.39680 + 2.41933i) q^{28} +(-2.96589 - 5.13708i) q^{29} +6.19868 q^{30} +7.28408 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.11507 + 3.66341i) q^{33} +(-2.48459 - 4.30343i) q^{34} +(-3.43564 + 5.95071i) q^{35} +(-1.67557 + 2.90217i) q^{36} +0.550972 q^{37} -15.9893 q^{39} +(1.22982 - 2.13012i) q^{40} +(1.30371 - 2.25809i) q^{41} +(-3.52015 - 6.09707i) q^{42} +(-1.43564 + 2.48661i) q^{43} +(0.839266 + 1.45365i) q^{44} -8.24263 q^{45} -2.49890 q^{46} +(-0.372797 - 0.645703i) q^{47} +(1.26007 + 2.18251i) q^{48} +0.804226 q^{49} +1.04988 q^{50} +(6.26153 + 10.8453i) q^{51} +(-3.17229 + 5.49456i) q^{52} +(0.735136 + 1.27329i) q^{53} +(0.442463 - 0.766369i) q^{54} +(-2.06430 + 3.57547i) q^{55} -2.79360 q^{56} +5.93179 q^{58} +(2.48131 - 4.29775i) q^{59} +(-3.09934 + 5.36821i) q^{60} +(-4.66843 - 8.08596i) q^{61} +(-3.64204 + 6.30820i) q^{62} +(4.68088 + 8.10752i) q^{63} +1.00000 q^{64} -15.6054 q^{65} +(-2.11507 - 3.66341i) q^{66} +(-5.78022 - 10.0116i) q^{67} +4.96917 q^{68} +6.29761 q^{69} +(-3.43564 - 5.95071i) q^{70} +(3.49849 - 6.05956i) q^{71} +(-1.67557 - 2.90217i) q^{72} +(3.09310 - 5.35740i) q^{73} +(-0.275486 + 0.477156i) q^{74} -2.64584 q^{75} +4.68915 q^{77} +(7.99463 - 13.8471i) q^{78} +(2.95579 - 5.11958i) q^{79} +(1.22982 + 2.13012i) q^{80} +(3.91164 - 6.77516i) q^{81} +(1.30371 + 2.25809i) q^{82} +15.1773 q^{83} +7.04029 q^{84} +(6.11121 + 10.5849i) q^{85} +(-1.43564 - 2.48661i) q^{86} -14.9490 q^{87} -1.67853 q^{88} +(-3.45251 - 5.97992i) q^{89} +(4.12132 - 7.13833i) q^{90} +(8.86212 + 15.3496i) q^{91} +(1.24945 - 2.16411i) q^{92} +(9.17848 - 15.8976i) q^{93} +0.745593 q^{94} -2.52015 q^{96} +(-7.19369 + 12.4598i) q^{97} +(-0.402113 + 0.696480i) q^{98} +(2.81250 + 4.87139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 18 q^{13} + 2 q^{14} - 4 q^{15} - 4 q^{16} - 6 q^{17} + 8 q^{18} - 4 q^{20} - 4 q^{21} - 2 q^{22} + 10 q^{23} - 2 q^{24} - 6 q^{25} + 36 q^{26} - 8 q^{27} + 2 q^{28} + 2 q^{29} + 8 q^{30} + 52 q^{31} - 4 q^{32} - 16 q^{33} - 6 q^{34} - 6 q^{35} - 4 q^{36} + 8 q^{37} - 12 q^{39} + 2 q^{40} + 12 q^{41} - 4 q^{42} + 10 q^{43} - 2 q^{44} - 44 q^{45} - 20 q^{46} + 12 q^{47} - 2 q^{48} - 24 q^{49} + 12 q^{50} + 2 q^{51} - 18 q^{52} - 8 q^{53} + 4 q^{54} + 26 q^{55} - 4 q^{56} - 4 q^{58} + 8 q^{59} - 4 q^{60} - 26 q^{62} + 22 q^{63} + 8 q^{64} - 8 q^{65} - 16 q^{66} - 10 q^{67} + 12 q^{68} - 40 q^{69} - 6 q^{70} - 4 q^{72} + 14 q^{73} - 4 q^{74} + 16 q^{75} + 8 q^{77} + 6 q^{78} - 22 q^{79} + 2 q^{80} + 4 q^{81} + 12 q^{82} - 24 q^{83} + 8 q^{84} + 18 q^{85} + 10 q^{86} - 52 q^{87} + 4 q^{88} + 16 q^{89} + 22 q^{90} + 4 q^{91} + 10 q^{92} - 8 q^{93} - 24 q^{94} + 4 q^{96} - 28 q^{97} + 12 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 18 * q^13 + 2 * q^14 - 4 * q^15 - 4 * q^16 - 6 * q^17 + 8 * q^18 - 4 * q^20 - 4 * q^21 - 2 * q^22 + 10 * q^23 - 2 * q^24 - 6 * q^25 + 36 * q^26 - 8 * q^27 + 2 * q^28 + 2 * q^29 + 8 * q^30 + 52 * q^31 - 4 * q^32 - 16 * q^33 - 6 * q^34 - 6 * q^35 - 4 * q^36 + 8 * q^37 - 12 * q^39 + 2 * q^40 + 12 * q^41 - 4 * q^42 + 10 * q^43 - 2 * q^44 - 44 * q^45 - 20 * q^46 + 12 * q^47 - 2 * q^48 - 24 * q^49 + 12 * q^50 + 2 * q^51 - 18 * q^52 - 8 * q^53 + 4 * q^54 + 26 * q^55 - 4 * q^56 - 4 * q^58 + 8 * q^59 - 4 * q^60 - 26 * q^62 + 22 * q^63 + 8 * q^64 - 8 * q^65 - 16 * q^66 - 10 * q^67 + 12 * q^68 - 40 * q^69 - 6 * q^70 - 4 * q^72 + 14 * q^73 - 4 * q^74 + 16 * q^75 + 8 * q^77 + 6 * q^78 - 22 * q^79 + 2 * q^80 + 4 * q^81 + 12 * q^82 - 24 * q^83 + 8 * q^84 + 18 * q^85 + 10 * q^86 - 52 * q^87 + 4 * q^88 + 16 * q^89 + 22 * q^90 + 4 * q^91 + 10 * q^92 - 8 * q^93 - 24 * q^94 + 4 * q^96 - 28 * q^97 + 12 * q^98 - 22 * q^99

Introduction

L-functions

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