LMFDB - Embedded newform 273.2.l.b.256.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 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			256.7
Root			$-1.02737 + 1.77946i$ of defining polynomial
Character	$\chi$	$=$	273.256
Dual form			273.2.l.b.16.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.05474 q^{2} +(0.500000 + 0.866025i) q^{3} +2.22196 q^{4} +(-0.274662 - 0.475728i) q^{5} +(1.02737 + 1.77946i) q^{6} +(2.59269 + 0.527227i) q^{7} +0.456078 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+2.05474 q^{2} +(0.500000 + 0.866025i) q^{3} +2.22196 q^{4} +(-0.274662 - 0.475728i) q^{5} +(1.02737 + 1.77946i) q^{6} +(2.59269 + 0.527227i) q^{7} +0.456078 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.564359 - 0.977499i) q^{10} +(-2.34912 - 4.06880i) q^{11} +(1.11098 + 1.92428i) q^{12} +(-0.663964 + 3.54389i) q^{13} +(5.32730 + 1.08331i) q^{14} +(0.274662 - 0.475728i) q^{15} -3.50680 q^{16} -0.603612 q^{17} +(-1.02737 + 1.77946i) q^{18} +(-0.280555 + 0.485935i) q^{19} +(-0.610289 - 1.05705i) q^{20} +(0.839752 + 2.50895i) q^{21} +(-4.82684 - 8.36033i) q^{22} +0.376699 q^{23} +(0.228039 + 0.394976i) q^{24} +(2.34912 - 4.06880i) q^{25} +(-1.36427 + 7.28178i) q^{26} -1.00000 q^{27} +(5.76086 + 1.17148i) q^{28} +(2.09200 - 3.62344i) q^{29} +(0.564359 - 0.977499i) q^{30} +(-0.577330 + 0.999965i) q^{31} -8.11773 q^{32} +(2.34912 - 4.06880i) q^{33} -1.24027 q^{34} +(-0.461296 - 1.37822i) q^{35} +(-1.11098 + 1.92428i) q^{36} -8.80232 q^{37} +(-0.576468 + 0.998472i) q^{38} +(-3.40108 + 1.19694i) q^{39} +(-0.125267 - 0.216969i) q^{40} +(-3.96001 + 6.85894i) q^{41} +(1.72547 + 5.15524i) q^{42} +(-0.747200 - 1.29419i) q^{43} +(-5.21966 - 9.04072i) q^{44} +0.549324 q^{45} +0.774020 q^{46} +(-1.09885 - 1.90326i) q^{47} +(-1.75340 - 3.03698i) q^{48} +(6.44406 + 2.73387i) q^{49} +(4.82684 - 8.36033i) q^{50} +(-0.301806 - 0.522743i) q^{51} +(-1.47530 + 7.87439i) q^{52} +(4.52338 - 7.83473i) q^{53} -2.05474 q^{54} +(-1.29043 + 2.23509i) q^{55} +(1.18247 + 0.240457i) q^{56} -0.561110 q^{57} +(4.29851 - 7.44524i) q^{58} +8.53654 q^{59} +(0.610289 - 1.05705i) q^{60} +(-3.71212 + 6.42958i) q^{61} +(-1.18626 + 2.05467i) q^{62} +(-1.75294 + 1.98172i) q^{63} -9.66624 q^{64} +(1.86829 - 0.657505i) q^{65} +(4.82684 - 8.36033i) q^{66} +(4.79936 + 8.31274i) q^{67} -1.34120 q^{68} +(0.188350 + 0.326231i) q^{69} +(-0.947844 - 2.83190i) q^{70} +(2.88877 + 5.00350i) q^{71} +(-0.228039 + 0.394976i) q^{72} +(7.24668 - 12.5516i) q^{73} -18.0865 q^{74} +4.69824 q^{75} +(-0.623383 + 1.07973i) q^{76} +(-3.94536 - 11.7876i) q^{77} +(-6.98834 + 2.45939i) q^{78} +(7.31102 + 12.6631i) q^{79} +(0.963186 + 1.66829i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.13680 + 14.0934i) q^{82} -14.8750 q^{83} +(1.86590 + 5.57479i) q^{84} +(0.165789 + 0.287155i) q^{85} +(-1.53530 - 2.65922i) q^{86} +4.18399 q^{87} +(-1.07138 - 1.85569i) q^{88} +9.18353 q^{89} +1.12872 q^{90} +(-3.58988 + 8.83814i) q^{91} +0.837013 q^{92} -1.15466 q^{93} +(-2.25784 - 3.91070i) q^{94} +0.308231 q^{95} +(-4.05887 - 7.03016i) q^{96} +(3.15034 + 5.45655i) q^{97} +(13.2409 + 5.61740i) q^{98} +4.69824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.05474			1.45292			0.726461	−	0.687208i	$-0.241164\pi$
$2$	2.05474			1.45292			0.726461	+	0.687208i	$0.241164\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	2.22196			1.11098
$5$	−0.274662	−	0.475728i	−0.122833	−	0.212752i	0.798051	−	0.602590i	$-0.205864\pi$
$5$	−0.274662	−	0.475728i	−0.122833	−	0.212752i	−0.920884	+	0.389838i	$0.872531\pi$
$6$	1.02737	+	1.77946i	0.419422	+	0.726461i
$7$	2.59269	+	0.527227i	0.979944	+	0.199273i
$7$	2.59269	+	0.527227i	0.979944	+	0.199273i
$8$	0.456078			0.161248
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.564359	−	0.977499i	−0.178466	−	0.309112i
$11$	−2.34912	−	4.06880i	−0.708287	−	1.22679i	−0.965492	−	0.260432i	$-0.916135\pi$
$11$	−2.34912	−	4.06880i	−0.708287	−	1.22679i	0.257205	−	0.966357i	$-0.417198\pi$
$12$	1.11098	+	1.92428i	0.320713	+	0.555491i
$13$	−0.663964	+	3.54389i	−0.184150	+	0.982898i
$13$	−0.663964	+	3.54389i	−0.184150	+	0.982898i
$14$	5.32730	+	1.08331i	1.42378	+	0.289528i
$15$	0.274662	−	0.475728i	0.0709174	−	0.122833i
$16$	−3.50680			−0.876701
$17$	−0.603612			−0.146397			−0.0731987	−	0.997317i	$-0.523321\pi$
$17$	−0.603612			−0.146397			−0.0731987	+	0.997317i	$0.523321\pi$
$18$	−1.02737	+	1.77946i	−0.242154	+	0.419422i
$19$	−0.280555	+	0.485935i	−0.0643637	+	0.111481i	−0.896412	−	0.443223i	$-0.853835\pi$
$19$	−0.280555	+	0.485935i	−0.0643637	+	0.111481i	0.832048	+	0.554704i	$0.187168\pi$
$20$	−0.610289	−	1.05705i	−0.136465	−	0.236364i
$21$	0.839752	+	2.50895i	0.183249	+	0.547497i
$22$	−4.82684	−	8.36033i	−1.02909	−	1.78243i
$23$	0.376699			0.0785473			0.0392736	−	0.999228i	$-0.487496\pi$
$23$	0.376699			0.0785473			0.0392736	+	0.999228i	$0.487496\pi$
$24$	0.228039	+	0.394976i	0.0465483	+	0.0806240i
$25$	2.34912	−	4.06880i	0.469824	−	0.813760i
$26$	−1.36427	+	7.28178i	−0.267556	+	1.42807i
$27$	−1.00000			−0.192450
$28$	5.76086	+	1.17148i	1.08870	+	0.221389i
$29$	2.09200	−	3.62344i	0.388474	−	0.672856i	−0.603771	−	0.797158i	$-0.706336\pi$
$29$	2.09200	−	3.62344i	0.388474	−	0.672856i	0.992244	+	0.124302i	$0.0396691\pi$
$30$	0.564359	−	0.977499i	0.103037	−	0.178466i
$31$	−0.577330	+	0.999965i	−0.103691	+	0.179599i	−0.913203	−	0.407505i	$-0.866399\pi$
$31$	−0.577330	+	0.999965i	−0.103691	+	0.179599i	0.809511	+	0.587104i	$0.199732\pi$
$32$	−8.11773			−1.43503
$33$	2.34912	−	4.06880i	0.408930	−	0.708287i
$34$	−1.24027			−0.212704
$35$	−0.461296	−	1.37822i	−0.0779732	−	0.232962i
$36$	−1.11098	+	1.92428i	−0.185164	+	0.320713i
$37$	−8.80232			−1.44709			−0.723547	−	0.690276i	$-0.757489\pi$
$37$	−8.80232			−1.44709			−0.723547	+	0.690276i	$0.757489\pi$
$38$	−0.576468	+	0.998472i	−0.0935154	+	0.161973i
$39$	−3.40108	+	1.19694i	−0.544609	+	0.191663i
$40$	−0.125267	−	0.216969i	−0.0198065	−	0.0343059i
$41$	−3.96001	+	6.85894i	−0.618450	+	1.07119i	0.371319	+	0.928506i	$0.378906\pi$
$41$	−3.96001	+	6.85894i	−0.618450	+	1.07119i	−0.989769	+	0.142681i	$0.954428\pi$
$42$	1.72547	+	5.15524i	0.266246	+	0.795471i
$43$	−0.747200	−	1.29419i	−0.113947	−	0.197362i	0.803411	−	0.595424i	$-0.203016\pi$
$43$	−0.747200	−	1.29419i	−0.113947	−	0.197362i	−0.917358	+	0.398062i	$0.869683\pi$
$44$	−5.21966	−	9.04072i	−0.786894	−	1.36294i
$45$	0.549324			0.0818884
$46$	0.774020			0.114123
$47$	−1.09885	−	1.90326i	−0.160283	−	0.277619i	0.774687	−	0.632345i	$-0.217907\pi$
$47$	−1.09885	−	1.90326i	−0.160283	−	0.277619i	−0.934970	+	0.354726i	$0.884574\pi$
$48$	−1.75340	−	3.03698i	−0.253082	−	0.438351i
$49$	6.44406	+	2.73387i	0.920581	+	0.390553i
$50$	4.82684	−	8.36033i	0.682618	−	1.18233i
$51$	−0.301806	−	0.522743i	−0.0422613	−	0.0731987i
$52$	−1.47530	+	7.87439i	−0.204588	+	1.09198i
$53$	4.52338	−	7.83473i	0.621334	−	1.07618i	−0.367903	−	0.929864i	$-0.619924\pi$
$53$	4.52338	−	7.83473i	0.621334	−	1.07618i	0.989238	−	0.146318i	$-0.0467424\pi$
$54$	−2.05474			−0.279615
$55$	−1.29043	+	2.23509i	−0.174001	+	0.301379i
$56$	1.18247	+	0.240457i	0.158014	+	0.0321324i
$57$	−0.561110			−0.0743208
$58$	4.29851	−	7.44524i	0.564422	−	0.977608i
$59$	8.53654			1.11136			0.555681	−	0.831395i	$-0.312457\pi$
$59$	8.53654			1.11136			0.555681	+	0.831395i	$0.312457\pi$
$60$	0.610289	−	1.05705i	0.0787879	−	0.136465i
$61$	−3.71212	+	6.42958i	−0.475288	+	0.823223i	−0.999599	−	0.0283034i	$-0.990990\pi$
$61$	−3.71212	+	6.42958i	−0.475288	+	0.823223i	0.524311	+	0.851527i	$0.324323\pi$
$62$	−1.18626	+	2.05467i	−0.150656	+	0.260943i
$63$	−1.75294	+	1.98172i	−0.220849	+	0.249673i
$64$	−9.66624			−1.20828
$65$	1.86829	−	0.657505i	0.231733	−	0.0815535i
$66$	4.82684	−	8.36033i	0.594143	−	1.02909i
$67$	4.79936	+	8.31274i	0.586336	+	1.01556i	0.994707	+	0.102747i	$0.0327634\pi$
$67$	4.79936	+	8.31274i	0.586336	+	1.01556i	−0.408372	+	0.912816i	$0.633903\pi$
$68$	−1.34120			−0.162645
$69$	0.188350	+	0.326231i	0.0226746	+	0.0392736i
$70$	−0.947844	−	2.83190i	−0.113289	−	0.338476i
$71$	2.88877	+	5.00350i	0.342834	+	0.593806i	0.984958	−	0.172795i	$-0.0552799\pi$
$71$	2.88877	+	5.00350i	0.342834	+	0.593806i	−0.642124	+	0.766601i	$0.721947\pi$
$72$	−0.228039	+	0.394976i	−0.0268747	+	0.0465483i
$73$	7.24668	−	12.5516i	0.848160	−	1.46906i	−0.0346892	−	0.999398i	$-0.511044\pi$
$73$	7.24668	−	12.5516i	0.848160	−	1.46906i	0.882849	−	0.469657i	$-0.155623\pi$
$74$	−18.0865			−2.10251
$75$	4.69824			0.542506
$76$	−0.623383	+	1.07973i	−0.0715069	+	0.123854i
$77$	−3.94536	−	11.7876i	−0.449616	−	1.34333i
$78$	−6.98834	+	2.45939i	−0.791274	+	0.278471i
$79$	7.31102	+	12.6631i	0.822554	+	1.42471i	0.903774	+	0.428009i	$0.140785\pi$
$79$	7.31102	+	12.6631i	0.822554	+	1.42471i	−0.0812206	+	0.996696i	$0.525882\pi$
$80$	0.963186	+	1.66829i	0.107687	+	0.186520i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.13680	+	14.0934i	−0.898560	+	1.55635i
$83$	−14.8750			−1.63274			−0.816371	−	0.577528i	$-0.804017\pi$
$83$	−14.8750			−1.63274			−0.816371	+	0.577528i	$0.804017\pi$
$84$	1.86590	+	5.57479i	0.203586	+	0.608259i
$85$	0.165789	+	0.287155i	0.0179824	+	0.0311464i
$86$	−1.53530	−	2.65922i	−0.165556	−	0.286751i
$87$	4.18399			0.448571
$88$	−1.07138	−	1.85569i	−0.114210	−	0.197817i
$89$	9.18353			0.973452			0.486726	−	0.873555i	$-0.338191\pi$
$89$	9.18353			0.973452			0.486726	+	0.873555i	$0.338191\pi$
$90$	1.12872			0.118977
$91$	−3.58988	+	8.83814i	−0.376322	+	0.926489i
$92$	0.837013			0.0872646
$93$	−1.15466			−0.119733
$94$	−2.25784	−	3.91070i	−0.232879	−	0.403358i
$95$	0.308231			0.0316238
$96$	−4.05887	−	7.03016i	−0.414256	−	0.717513i
$97$	3.15034	+	5.45655i	0.319869	+	0.554029i	0.980460	−	0.196717i	$-0.0630279\pi$
$97$	3.15034	+	5.45655i	0.319869	+	0.554029i	−0.660592	+	0.750745i	$0.729695\pi$
$98$	13.2409	+	5.61740i	1.33753	+	0.567443i
$99$	4.69824			0.472191
$100$	5.21966	−	9.04072i	0.521966	−	0.904072i
$101$	−2.22194	−	3.84851i	−0.221091	−	0.382941i	0.734049	−	0.679097i	$-0.237628\pi$
$101$	−2.22194	−	3.84851i	−0.221091	−	0.382941i	−0.955140	+	0.296156i	$0.904295\pi$
$102$	−0.620133	−	1.07410i	−0.0614023	−	0.106352i
$103$	8.31431	+	14.4008i	0.819234	+	1.41895i	0.906248	+	0.422747i	$0.138934\pi$
$103$	8.31431	+	14.4008i	0.819234	+	1.41895i	−0.0870141	+	0.996207i	$0.527733\pi$
$104$	−0.302820	+	1.61629i	−0.0296939	+	0.158490i
$105$	0.962929	−	1.08861i	0.0939723	−	0.106237i
$106$	9.29438	−	16.0983i	0.902750	−	1.56361i
$107$	17.8721			1.72776			0.863881	−	0.503696i	$-0.168027\pi$
$107$	17.8721			1.72776			0.863881	+	0.503696i	$0.168027\pi$
$108$	−2.22196			−0.213809
$109$	−5.07774	+	8.79490i	−0.486359	+	0.842399i	−0.999877	−	0.0156799i	$-0.995009\pi$
$109$	−5.07774	+	8.79490i	−0.486359	+	0.842399i	0.513518	+	0.858079i	$0.328342\pi$
$110$	−2.65150	+	4.59253i	−0.252810	+	0.437880i
$111$	−4.40116	−	7.62304i	−0.417740	−	0.723547i
$112$	−9.09205	−	1.84888i	−0.859118	−	0.174703i
$113$	−3.74505	−	6.48662i	−0.352305	−	0.610210i	0.634348	−	0.773048i	$-0.281269\pi$
$113$	−3.74505	−	6.48662i	−0.352305	−	0.610210i	−0.986653	+	0.162838i	$0.947935\pi$
$114$	−1.15294			−0.107982
$115$	−0.103465	−	0.179207i	−0.00964816	−	0.0167111i
$116$	4.64834	−	8.05116i	0.431587	−	0.747531i
$117$	−2.73712	−	2.34695i	−0.253046	−	0.216976i
$118$	17.5404			1.61472
$119$	−1.56498	−	0.318240i	−0.143461	−	0.0291730i
$120$	0.125267	−	0.216969i	0.0114353	−	0.0198065i
$121$	−5.53675	+	9.58992i	−0.503340	+	0.871811i
$122$	−7.62745	+	13.2111i	−0.690557	+	1.19608i
$123$	−7.92003			−0.714125
$124$	−1.28281	+	2.22189i	−0.115199	+	0.199531i
$125$	−5.32748			−0.476504
$126$	−3.60183	+	4.07192i	−0.320877	+	0.362756i
$127$	2.36612	−	4.09824i	0.209959	−	0.363660i	−0.741742	−	0.670685i	$-0.766000\pi$
$127$	2.36612	−	4.09824i	0.209959	−	0.363660i	0.951702	+	0.307025i	$0.0993335\pi$
$128$	−3.62616			−0.320510
$129$	0.747200	−	1.29419i	0.0657873	−	0.113947i
$130$	3.83886	−	1.35100i	0.336691	−	0.118491i
$131$	−1.78705	−	3.09527i	−0.156136	−	0.270435i	0.777336	−	0.629085i	$-0.216570\pi$
$131$	−1.78705	−	3.09527i	−0.156136	−	0.270435i	−0.933472	+	0.358650i	$0.883237\pi$
$132$	5.21966	−	9.04072i	0.454313	−	0.786894i
$133$	−0.983589	+	1.11196i	−0.0852880	+	0.0964194i
$134$	9.86145	+	17.0805i	0.851900	+	1.47553i
$135$	0.274662	+	0.475728i	0.0236391	+	0.0409442i
$136$	−0.275294			−0.0236063
$137$	−19.2576			−1.64529			−0.822644	−	0.568557i	$-0.807502\pi$
$137$	−19.2576			−1.64529			−0.822644	+	0.568557i	$0.807502\pi$
$138$	0.387010	+	0.670321i	0.0329445	+	0.0570615i
$139$	−4.83155	−	8.36849i	−0.409807	−	0.709806i	0.585061	−	0.810989i	$-0.301070\pi$
$139$	−4.83155	−	8.36849i	−0.409807	−	0.709806i	−0.994868	+	0.101183i	$0.967737\pi$
$140$	−1.02498	−	3.06236i	−0.0866269	−	0.258817i
$141$	1.09885	−	1.90326i	0.0925395	−	0.160283i
$142$	5.93568	+	10.2809i	0.498111	+	0.862753i
$143$	15.9791	−	5.62349i	1.33624	−	0.470260i
$144$	1.75340	−	3.03698i	0.146117	−	0.253082i
$145$	−2.29837			−0.190869
$146$	14.8901	−	25.7903i	1.23231	−	2.13442i
$147$	0.854431	+	6.94766i	0.0704723	+	0.573033i
$148$	−19.5584			−1.60769
$149$	−3.56248	+	6.17039i	−0.291850	+	0.505498i	−0.974247	−	0.225483i	$-0.927604\pi$
$149$	−3.56248	+	6.17039i	−0.291850	+	0.505498i	0.682398	+	0.730981i	$0.260937\pi$
$150$	9.65368			0.788219
$151$	9.82744	−	17.0216i	0.799746	−	1.38520i	−0.120036	−	0.992770i	$-0.538301\pi$
$151$	9.82744	−	17.0216i	0.799746	−	1.38520i	0.919781	−	0.392431i	$-0.128366\pi$
$152$	−0.127955	+	0.221625i	−0.0103785	+	0.0179761i
$153$	0.301806	−	0.522743i	0.0243996	−	0.0422613i
$154$	−8.10670	−	24.2206i	−0.653256	−	1.95175i
$155$	0.634282			0.0509468
$156$	−7.55708	+	2.65955i	−0.605050	+	0.212934i
$157$	2.60509	−	4.51215i	0.207909	−	0.360109i	−0.743147	−	0.669129i	$-0.766668\pi$
$157$	2.60509	−	4.51215i	0.207909	−	0.360109i	0.951056	+	0.309020i	$0.100001\pi$
$158$	15.0223	+	26.0193i	1.19511	+	2.06999i
$159$	9.04676			0.717455
$160$	2.22963	+	3.86184i	0.176268	+	0.305305i
$161$	0.976664	+	0.198606i	0.0769719	+	0.0156523i
$162$	−1.02737	−	1.77946i	−0.0807179	−	0.139807i
$163$	2.08690	−	3.61461i	0.163458	−	0.283118i	−0.772648	−	0.634834i	$-0.781068\pi$
$163$	2.08690	−	3.61461i	0.163458	−	0.283118i	0.936107	+	0.351716i	$0.114402\pi$
$164$	−8.79901	+	15.2403i	−0.687087	+	1.19007i
$165$	−2.58086			−0.200919
$166$	−30.5642			−2.37225
$167$	−2.52335	+	4.37058i	−0.195263	+	0.338205i	−0.946987	−	0.321273i	$-0.895889\pi$
$167$	−2.52335	+	4.37058i	−0.195263	+	0.338205i	0.751724	+	0.659478i	$0.229223\pi$
$168$	0.382993	+	1.14428i	0.0295485	+	0.0882829i
$169$	−12.1183	−	4.70603i	−0.932177	−	0.362002i
$170$	0.340654	+	0.590030i	0.0261270	+	0.0452532i
$171$	−0.280555	−	0.485935i	−0.0214546	−	0.0371604i
$172$	−1.66025	−	2.87564i	−0.126593	−	0.219265i
$173$	−1.36949	+	2.37202i	−0.104120	+	0.180341i	−0.913378	−	0.407112i	$-0.866536\pi$
$173$	−1.36949	+	2.37202i	−0.104120	+	0.180341i	0.809258	+	0.587453i	$0.199869\pi$
$174$	8.59702			0.651738
$175$	8.23572	−	9.31060i	0.622562	−	0.703816i
$176$	8.23791	+	14.2685i	0.620956	+	1.07553i
$177$	4.26827	+	7.39286i	0.320823	+	0.555681i
$178$	18.8698			1.41435
$179$	6.34782	+	10.9948i	0.474459	+	0.821787i	0.999572	−	0.0292456i	$-0.00931049\pi$
$179$	6.34782	+	10.9948i	0.474459	+	0.821787i	−0.525114	+	0.851032i	$0.675977\pi$
$180$	1.22058			0.0909765
$181$	7.95691			0.591432			0.295716	−	0.955276i	$-0.404442\pi$
$181$	7.95691			0.591432			0.295716	+	0.955276i	$0.404442\pi$
$182$	−7.37629	+	18.1601i	−0.546767	+	1.34612i
$183$	−7.42424			−0.548816
$184$	0.171805			0.0126656
$185$	2.41766	+	4.18752i	0.177750	+	0.307872i
$186$	−2.37253			−0.173962
$187$	1.41796	+	2.45597i	0.103691	+	0.179599i
$188$	−2.44160	−	4.22897i	−0.178072	−	0.308429i
$189$	−2.59269	−	0.527227i	−0.188590	−	0.0383501i
$190$	0.633335			0.0459469
$191$	−1.53989	+	2.66717i	−0.111423	+	0.192990i	−0.916344	−	0.400392i	$-0.868874\pi$
$191$	−1.53989	+	2.66717i	−0.111423	+	0.192990i	0.804921	+	0.593382i	$0.202207\pi$
$192$	−4.83312	−	8.37121i	−0.348800	−	0.604140i
$193$	1.69587	+	2.93734i	0.122072	+	0.211434i	0.920584	−	0.390543i	$-0.127713\pi$
$193$	1.69587	+	2.93734i	0.122072	+	0.211434i	−0.798513	+	0.601978i	$0.794380\pi$
$194$	6.47314	+	11.2118i	0.464744	+	0.804961i
$195$	1.50356	+	1.28924i	0.107672	+	0.0923242i
$196$	14.3185	+	6.07456i	1.02275	+	0.433897i
$197$	2.06163	−	3.57085i	0.146885	−	0.254413i	−0.783189	−	0.621783i	$-0.786409\pi$
$197$	2.06163	−	3.57085i	0.146885	−	0.254413i	0.930075	+	0.367370i	$0.119742\pi$
$198$	9.65368			0.686057
$199$	−1.14828			−0.0813997			−0.0406998	−	0.999171i	$-0.512959\pi$
$199$	−1.14828			−0.0813997			−0.0406998	+	0.999171i	$0.512959\pi$
$200$	1.07138	−	1.85569i	0.0757583	−	0.131217i
$201$	−4.79936	+	8.31274i	−0.338521	+	0.586336i
$202$	−4.56551	−	7.90769i	−0.321228	−	0.556383i
$203$	7.33427	−	8.29150i	0.514765	−	0.581949i
$204$	−0.670602	−	1.16152i	−0.0469515	−	0.0813224i
$205$	4.35066			0.303863
$206$	17.0838	+	29.5900i	1.19028	+	2.06163i
$207$	−0.188350	+	0.326231i	−0.0130912	+	0.0226746i
$208$	2.32839	−	12.4277i	0.161445	−	0.861708i
$209$	2.63623			0.182352
$210$	1.97857	−	2.23680i	0.136534	−	0.154354i
$211$	−2.28300	+	3.95427i	−0.157168	+	0.272223i	−0.933846	−	0.357674i	$-0.883570\pi$
$211$	−2.28300	+	3.95427i	−0.157168	+	0.272223i	0.776678	+	0.629898i	$0.216903\pi$
$212$	10.0508	−	17.4085i	0.690291	−	1.19562i
$213$	−2.88877	+	5.00350i	−0.197935	+	0.342834i
$214$	36.7226			2.51030
$215$	−0.410455	+	0.710929i	−0.0279928	+	0.0484849i
$216$	−0.456078			−0.0310322
$217$	−2.02404	+	2.28821i	−0.137401	+	0.155334i
$218$	−10.4334	+	18.0713i	−0.706642	+	1.22394i
$219$	14.4934			0.979370
$220$	−2.86729	+	4.96628i	−0.193312	+	0.334827i
$221$	0.400776	−	2.13913i	0.0269591	−	0.143894i
$222$	−9.04325	−	15.6634i	−0.606943	−	1.05126i
$223$	8.42312	−	14.5893i	0.564054	−	0.976970i	−0.433083	−	0.901354i	$-0.642574\pi$
$223$	8.42312	−	14.5893i	0.564054	−	0.976970i	0.997137	−	0.0756163i	$-0.0240924\pi$
$224$	−21.0468	−	4.27989i	−1.40625	−	0.285962i
$225$	2.34912	+	4.06880i	0.156608	+	0.271253i
$226$	−7.69512	−	13.3283i	−0.511872	−	0.886588i
$227$	−28.4730			−1.88982			−0.944909	−	0.327333i	$-0.893850\pi$
$227$	−28.4730			−1.88982			−0.944909	+	0.327333i	$0.893850\pi$
$228$	−1.24677			−0.0825691
$229$	−13.1373	−	22.7545i	−0.868137	−	1.50366i	−0.863899	−	0.503666i	$-0.831984\pi$
$229$	−13.1373	−	22.7545i	−0.868137	−	1.50366i	−0.00423787	−	0.999991i	$-0.501349\pi$
$230$	−0.212594	−	0.368223i	−0.0140180	−	0.0242799i
$231$	8.23572	−	9.31060i	0.541871	−	0.612593i
$232$	0.954114	−	1.65257i	0.0626406	−	0.108497i
$233$	−11.0974	−	19.2212i	−0.727014	−	1.25922i	−0.958140	−	0.286301i	$-0.907574\pi$
$233$	−11.0974	−	19.2212i	−0.727014	−	1.25922i	0.231126	−	0.972924i	$-0.425759\pi$
$234$	−5.62407	−	4.82238i	−0.367657	−	0.315249i
$235$	−0.603622	+	1.04550i	−0.0393760	+	0.0682012i
$236$	18.9679			1.23470
$237$	−7.31102	+	12.6631i	−0.474902	+	0.822554i
$238$	−3.21562	−	0.653902i	−0.208438	−	0.0423862i
$239$	27.3213			1.76727			0.883633	−	0.468180i	$-0.155090\pi$
$239$	27.3213			1.76727			0.883633	+	0.468180i	$0.155090\pi$
$240$	−0.963186	+	1.66829i	−0.0621734	+	0.107687i
$241$	−23.7831			−1.53200			−0.766001	−	0.642839i	$-0.777756\pi$
$241$	−23.7831			−1.53200			−0.766001	+	0.642839i	$0.777756\pi$
$242$	−11.3766	+	19.7048i	−0.731314	+	1.26667i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−8.24820	+	14.2863i	−0.528037	+	0.914586i
$245$	−0.469360	−	3.81651i	−0.0299863	−	0.243828i
$246$	−16.2736			−1.03757
$247$	−1.53582	−	1.31690i	−0.0977221	−	0.0837923i
$248$	−0.263308	+	0.456062i	−0.0167201	+	0.0289600i
$249$	−7.43749	−	12.8821i	−0.471332	−	0.816371i
$250$	−10.9466			−0.692323
$251$	4.16795	+	7.21910i	0.263079	+	0.455666i	0.967058	−	0.254554i	$-0.0819288\pi$
$251$	4.16795	+	7.21910i	0.263079	+	0.455666i	−0.703980	+	0.710220i	$0.748595\pi$
$252$	−3.89496	+	4.40331i	−0.245359	+	0.277383i
$253$	−0.884913	−	1.53271i	−0.0556340	−	0.0963609i
$254$	4.86177	−	8.42084i	0.305055	−	0.528370i
$255$	−0.165789	+	0.287155i	−0.0103821	+	0.0179824i
$256$	11.8817			0.742604
$257$	−13.7742			−0.859214			−0.429607	−	0.903016i	$-0.641348\pi$
$257$	−13.7742			−0.859214			−0.429607	+	0.903016i	$0.641348\pi$
$258$	1.53530	−	2.65922i	0.0955838	−	0.165556i
$259$	−22.8217	−	4.64082i	−1.41807	−	0.288367i
$260$	4.15128	−	1.46095i	0.257452	−	0.0906044i
$261$	2.09200	+	3.62344i	0.129491	+	0.224285i
$262$	−3.67193	−	6.35998i	−0.226853	−	0.392921i
$263$	4.52282	+	7.83375i	0.278889	+	0.483050i	0.971109	−	0.238637i	$-0.0767005\pi$
$263$	4.52282	+	7.83375i	0.278889	+	0.483050i	−0.692220	+	0.721687i	$0.743367\pi$
$264$	1.07138	−	1.85569i	0.0659391	−	0.114210i
$265$	−4.96960			−0.305280
$266$	−2.02102	+	2.28480i	−0.123917	+	0.140090i
$267$	4.59177	+	7.95317i	0.281012	+	0.486726i
$268$	10.6640	+	18.4706i	0.651408	+	1.12827i
$269$	2.28856			0.139536			0.0697681	−	0.997563i	$-0.477774\pi$
$269$	2.28856			0.139536			0.0697681	+	0.997563i	$0.477774\pi$
$270$	0.564359	+	0.977499i	0.0343458	+	0.0594887i
$271$	3.98115			0.241838			0.120919	−	0.992662i	$-0.461416\pi$
$271$	3.98115			0.241838			0.120919	+	0.992662i	$0.461416\pi$
$272$	2.11675			0.128347
$273$	−9.44900	+	1.31014i	−0.571879	+	0.0792932i
$274$	−39.5694			−2.39047
$275$	−22.0735			−1.33108
$276$	0.418506	+	0.724874i	0.0251911	+	0.0436323i
$277$	−8.39999			−0.504706			−0.252353	−	0.967635i	$-0.581204\pi$
$277$	−8.39999			−0.504706			−0.252353	+	0.967635i	$0.581204\pi$
$278$	−9.92758	−	17.1951i	−0.595417	−	1.03129i
$279$	−0.577330	−	0.999965i	−0.0345638	−	0.0598663i
$280$	−0.210387	−	0.628579i	−0.0125730	−	0.0375648i
$281$	−12.9559			−0.772884			−0.386442	−	0.922314i	$-0.626296\pi$
$281$	−12.9559			−0.772884			−0.386442	+	0.922314i	$0.626296\pi$
$282$	2.25784	−	3.91070i	0.134453	−	0.232879i
$283$	−12.8026	−	22.1747i	−0.761033	−	1.31815i	−0.942319	−	0.334717i	$-0.891359\pi$
$283$	−12.8026	−	22.1747i	−0.761033	−	1.31815i	0.181286	−	0.983431i	$-0.441974\pi$
$284$	6.41874	+	11.1176i	0.380882	+	0.659707i
$285$	0.154115	+	0.266936i	0.00912901	+	0.0158119i
$286$	32.8329	−	11.5548i	1.94145	−	0.683251i
$287$	−13.8833	+	15.6953i	−0.819505	+	0.926463i
$288$	4.05887	−	7.03016i	0.239171	−	0.414256i
$289$	−16.6357			−0.978568
$290$	−4.72255			−0.277318
$291$	−3.15034	+	5.45655i	−0.184676	+	0.319869i
$292$	16.1019	−	27.8892i	0.942290	−	1.63209i
$293$	−12.3943	−	21.4675i	−0.724081	−	1.25415i	−0.959351	−	0.282215i	$-0.908931\pi$
$293$	−12.3943	−	21.4675i	−0.724081	−	1.25415i	0.235270	−	0.971930i	$-0.424403\pi$
$294$	1.75564	+	14.2756i	0.102391	+	0.832572i
$295$	−2.34466	−	4.06107i	−0.136511	−	0.236445i
$296$	−4.01455			−0.233341
$297$	2.34912	+	4.06880i	0.136310	+	0.236096i
$298$	−7.31997	+	12.6786i	−0.424035	+	0.734450i
$299$	−0.250115	+	1.33498i	−0.0144645	+	0.0772040i
$300$	10.4393			0.602715
$301$	−1.25493	−	3.74937i	−0.0723327	−	0.216110i
$302$	20.1929	−	34.9751i	1.16197	−	2.01259i
$303$	2.22194	−	3.84851i	0.127647	−	0.221091i
$304$	0.983851	−	1.70408i	0.0564277	−	0.0977357i
$305$	4.07831			0.233523
$306$	0.620133	−	1.07410i	0.0354507	−	0.0614023i
$307$	−25.2086			−1.43873			−0.719365	−	0.694632i	$-0.755567\pi$
$307$	−25.2086			−1.43873			−0.719365	+	0.694632i	$0.755567\pi$
$308$	−8.76645	−	26.1917i	−0.499515	−	1.49241i
$309$	−8.31431	+	14.4008i	−0.472985	+	0.819234i
$310$	1.30329			0.0740217
$311$	−2.06640	+	3.57911i	−0.117175	+	0.202953i	−0.918647	−	0.395079i	$-0.870717\pi$
$311$	−2.06640	+	3.57911i	−0.117175	+	0.202953i	0.801472	+	0.598032i	$0.204050\pi$
$312$	−1.55116	+	0.545896i	−0.0878171	+	0.0309053i
$313$	15.0691	+	26.1005i	0.851758	+	1.47529i	0.879620	+	0.475676i	$0.157797\pi$
$313$	15.0691	+	26.1005i	0.851758	+	1.47529i	−0.0278626	+	0.999612i	$0.508870\pi$
$314$	5.35279	−	9.27131i	0.302076	−	0.523210i
$315$	1.42423	+	0.289618i	0.0802460	+	0.0163181i
$316$	16.2448	+	28.1369i	0.913843	+	1.58282i
$317$	−5.76330	−	9.98233i	−0.323699	−	0.560663i	0.657549	−	0.753412i	$-0.271593\pi$
$317$	−5.76330	−	9.98233i	−0.323699	−	0.560663i	−0.981248	+	0.192748i	$0.938260\pi$
$318$	18.5888			1.04241
$319$	−19.6574			−1.10060
$320$	2.65495	+	4.59850i	0.148416	+	0.257064i
$321$	8.93605	+	15.4777i	0.498762	+	0.863881i
$322$	2.00679	+	0.408084i	0.111834	+	0.0227416i
$323$	0.169346	−	0.293316i	0.00942268	−	0.0163206i
$324$	−1.11098	−	1.92428i	−0.0617212	−	0.106904i
$325$	12.8596	+	11.0266i	0.713324	+	0.611644i
$326$	4.28803	−	7.42709i	0.237492	−	0.411348i
$327$	−10.1555			−0.561599
$328$	−1.80608	+	3.12822i	−0.0997239	+	0.172727i
$329$	−1.84552	−	5.51389i	−0.101747	−	0.303991i
$330$	−5.30299			−0.291920
$331$	0.567695	−	0.983277i	0.0312033	−	0.0540458i	−0.850002	−	0.526779i	$-0.823399\pi$
$331$	0.567695	−	0.983277i	0.0312033	−	0.0540458i	0.881205	+	0.472734i	$0.156733\pi$
$332$	−33.0517			−1.81395
$333$	4.40116	−	7.62304i	0.241182	−	0.417740i
$334$	−5.18484	+	8.98041i	−0.283702	+	0.491386i
$335$	2.63640	−	4.56639i	0.144042	−	0.249488i
$336$	−2.94485	−	8.79839i	−0.160655	−	0.479991i
$337$	23.3181			1.27022			0.635110	−	0.772421i	$-0.280955\pi$
$337$	23.3181			1.27022			0.635110	+	0.772421i	$0.280955\pi$
$338$	−24.9000	−	9.66967i	−1.35438	−	0.525961i
$339$	3.74505	−	6.48662i	0.203403	−	0.352305i
$340$	0.368378	+	0.638049i	0.0199781	+	0.0346030i
$341$	5.42487			0.293773
$342$	−0.576468	−	0.998472i	−0.0311718	−	0.0539912i
$343$	15.2661	+	10.4856i	0.824291	+	0.566167i
$344$	−0.340782	−	0.590252i	−0.0183737	−	0.0318242i
$345$	0.103465	−	0.179207i	0.00557037	−	0.00964816i
$346$	−2.81394	+	4.87389i	−0.151279	+	0.262022i
$347$	2.53822			0.136259			0.0681294	−	0.997676i	$-0.478297\pi$
$347$	2.53822			0.136259			0.0681294	+	0.997676i	$0.478297\pi$
$348$	9.29667			0.498354
$349$	−5.34353	+	9.25527i	−0.286033	+	0.495423i	−0.972859	−	0.231398i	$-0.925670\pi$
$349$	−5.34353	+	9.25527i	−0.286033	+	0.495423i	0.686826	+	0.726822i	$0.259003\pi$
$350$	16.9223	−	19.1309i	0.904534	−	1.02259i
$351$	0.663964	−	3.54389i	0.0354398	−	0.189159i
$352$	19.0695	+	33.0294i	1.01641	+	1.76047i
$353$	−11.1203	−	19.2610i	−0.591875	−	1.02516i	−0.993980	−	0.109564i	$-0.965054\pi$
$353$	−11.1203	−	19.2610i	−0.591875	−	1.02516i	0.402105	−	0.915594i	$-0.368279\pi$
$354$	8.77019	+	15.1904i	0.466130	+	0.807361i
$355$	1.58687	−	2.74854i	0.0842223	−	0.145877i
$356$	20.4055			1.08149
$357$	−0.506884	−	1.51443i	−0.0268272	−	0.0801521i
$358$	13.0431	+	22.5914i	0.689351	+	1.19399i
$359$	8.38142	+	14.5170i	0.442354	+	0.766180i	0.997864	−	0.0653300i	$-0.0208100\pi$
$359$	8.38142	+	14.5170i	0.442354	+	0.766180i	−0.555509	+	0.831510i	$0.687477\pi$
$360$	0.250535			0.0132043
$361$	9.34258	+	16.1818i	0.491715	+	0.851675i
$362$	16.3494			0.859305
$363$	−11.0735			−0.581208
$364$	−7.97659	+	19.6380i	−0.418087	+	1.02931i
$365$	−7.96155			−0.416726
$366$	−15.2549			−0.797386
$367$	2.34097	+	4.05468i	0.122198	+	0.211653i	0.920634	−	0.390427i	$-0.127672\pi$
$367$	2.34097	+	4.05468i	0.122198	+	0.211653i	−0.798436	+	0.602079i	$0.794339\pi$
$368$	−1.32101			−0.0688625
$369$	−3.96001	−	6.85894i	−0.206150	−	0.357062i
$370$	4.96767	+	8.60426i	0.258257	+	0.447314i
$371$	15.8584	−	17.9282i	0.823327	−	0.930783i
$372$	−2.56561			−0.133021
$373$	3.38086	−	5.85582i	0.175054	−	0.303203i	−0.765126	−	0.643881i	$-0.777323\pi$
$373$	3.38086	−	5.85582i	0.175054	−	0.303203i	0.940180	+	0.340678i	$0.110657\pi$
$374$	2.91354	+	5.04639i	0.150655	+	0.260943i
$375$	−2.66374	−	4.61373i	−0.137555	−	0.238252i
$376$	−0.501160	−	0.868034i	−0.0258453	−	0.0447655i
$377$	11.4521	+	9.81963i	0.589811	+	0.505737i
$378$	−5.32730	−	1.08331i	−0.274007	−	0.0557197i
$379$	9.62497	−	16.6709i	0.494402	−	0.856329i	−0.505578	−	0.862781i	$-0.668721\pi$
$379$	9.62497	−	16.6709i	0.494402	−	0.856329i	0.999979	+	0.00645256i	$0.00205393\pi$
$380$	0.684878			0.0351335
$381$	4.73225			0.242440
$382$	−3.16408	+	5.48036i	−0.161889	+	0.280399i
$383$	−6.74254	+	11.6784i	−0.344528	+	0.596740i	−0.985268	−	0.171018i	$-0.945294\pi$
$383$	−6.74254	+	11.6784i	−0.344528	+	0.596740i	0.640740	+	0.767758i	$0.278628\pi$
$384$	−1.81308	−	3.14034i	−0.0925233	−	0.160255i
$385$	−4.52408	+	5.11454i	−0.230568	+	0.260661i
$386$	3.48458	+	6.03547i	0.177361	+	0.307198i
$387$	1.49440			0.0759646
$388$	6.99994	+	12.1243i	0.355368	+	0.615516i
$389$	16.4229	−	28.4453i	0.832675	−	1.44224i	−0.0632336	−	0.997999i	$-0.520141\pi$
$389$	16.4229	−	28.4453i	0.832675	−	1.44224i	0.895909	−	0.444238i	$-0.146525\pi$
$390$	3.08943	+	2.64905i	0.156440	+	0.134140i
$391$	−0.227380			−0.0114991
$392$	2.93900	+	1.24686i	0.148442	+	0.0629759i
$393$	1.78705	−	3.09527i	0.0901449	−	0.156136i
$394$	4.23612	−	7.33718i	0.213413	−	0.369642i
$395$	4.01612	−	6.95612i	0.202073	−	0.350000i
$396$	10.4393			0.524596
$397$	13.3054	−	23.0457i	0.667781	−	1.15663i	−0.310743	−	0.950494i	$-0.600578\pi$
$397$	13.3054	−	23.0457i	0.667781	−	1.15663i	0.978523	−	0.206136i	$-0.0660889\pi$
$398$	−2.35943			−0.118267
$399$	−1.45478	−	0.295832i	−0.0728302	−	0.0148101i
$400$	−8.23791	+	14.2685i	−0.411895	+	0.713424i
$401$	−23.1117			−1.15414			−0.577071	−	0.816694i	$-0.695805\pi$
$401$	−23.1117			−1.15414			−0.577071	+	0.816694i	$0.695805\pi$
$402$	−9.86145	+	17.0805i	−0.491845	+	0.851900i
$403$	−3.16044	−	2.70993i	−0.157433	−	0.134991i
$404$	−4.93706	−	8.55124i	−0.245628	−	0.425440i
$405$	−0.274662	+	0.475728i	−0.0136481	+	0.0236391i
$406$	15.0700	−	17.0369i	0.747913	−	0.845527i
$407$	20.6777	+	35.8149i	1.02496	+	1.77528i
$408$	−0.137647	−	0.238412i	−0.00681455	−	0.0118031i
$409$	−7.24147			−0.358067			−0.179034	−	0.983843i	$-0.557297\pi$
$409$	−7.24147			−0.358067			−0.179034	+	0.983843i	$0.557297\pi$
$410$	8.93948			0.441489
$411$	−9.62880	−	16.6776i	−0.474954	−	0.822644i
$412$	18.4741	+	31.9981i	0.910154	+	1.57643i
$413$	22.1326	+	4.50069i	1.08907	+	0.221465i
$414$	−0.387010	+	0.670321i	−0.0190205	+	0.0329445i
$415$	4.08559	+	7.07645i	0.200554	+	0.347369i
$416$	5.38988	−	28.7684i	0.264261	−	1.41048i
$417$	4.83155	−	8.36849i	0.236602	−	0.409807i
$418$	5.41677			0.264943
$419$	−17.5550	+	30.4062i	−0.857618	+	1.48544i	0.0165759	+	0.999863i	$0.494723\pi$
$419$	−17.5550	+	30.4062i	−0.857618	+	1.48544i	−0.874194	+	0.485576i	$0.838610\pi$
$420$	2.13959	−	2.41884i	0.104402	−	0.118027i
$421$	25.2731			1.23174			0.615868	−	0.787849i	$-0.288805\pi$
$421$	25.2731			1.23174			0.615868	+	0.787849i	$0.288805\pi$
$422$	−4.69098	+	8.12501i	−0.228353	+	0.395519i
$423$	2.19769			0.106855
$424$	2.06302	−	3.57325i	0.100189	−	0.173532i
$425$	−1.41796	+	2.45597i	−0.0687810	+	0.119132i
$426$	−5.93568	+	10.2809i	−0.287584	+	0.498111i
$427$	−13.0142	+	14.7128i	−0.629802	+	0.712001i
$428$	39.7112			1.91951
$429$	12.8596	+	11.0266i	0.620869	+	0.532367i
$430$	−0.843379	+	1.46077i	−0.0406713	+	0.0704448i
$431$	−8.78466	−	15.2155i	−0.423142	−	0.732904i	0.573103	−	0.819484i	$-0.305740\pi$
$431$	−8.78466	−	15.2155i	−0.423142	−	0.732904i	−0.996245	+	0.0865796i	$0.972406\pi$
$432$	3.50680			0.168721
$433$	−3.02011	−	5.23098i	−0.145137	−	0.251385i	0.784287	−	0.620398i	$-0.213029\pi$
$433$	−3.02011	−	5.23098i	−0.145137	−	0.251385i	−0.929424	+	0.369013i	$0.879696\pi$
$434$	−4.15889	+	4.70169i	−0.199633	+	0.225688i
$435$	−1.14918	−	1.99044i	−0.0550991	−	0.0954344i
$436$	−11.2826	+	19.5420i	−0.540336	+	0.935890i
$437$	−0.105685	+	0.183052i	−0.00505559	+	0.00875654i
$438$	29.7801			1.42295
$439$	24.8563			1.18633			0.593164	−	0.805081i	$-0.297878\pi$
$439$	24.8563			1.18633			0.593164	+	0.805081i	$0.297878\pi$
$440$	−0.588537	+	1.01938i	−0.0280574	+	0.0485968i
$441$	−5.58963	+	4.21379i	−0.266173	+	0.200657i
$442$	0.823492	−	4.39537i	0.0391695	−	0.209066i
$443$	15.8094	+	27.3826i	0.751126	+	1.30099i	0.947278	+	0.320414i	$0.103822\pi$
$443$	15.8094	+	27.3826i	0.751126	+	1.30099i	−0.196152	+	0.980574i	$0.562845\pi$
$444$	−9.77922	−	16.9381i	−0.464101	−	0.803847i
$445$	−2.52237	−	4.36887i	−0.119572	−	0.207104i
$446$	17.3073	−	29.9772i	0.819527	−	1.41946i
$447$	−7.12496			−0.336999
$448$	−25.0615	−	5.09630i	−1.18405	−	0.240778i
$449$	−2.63384	−	4.56194i	−0.124298	−	0.215291i	0.797160	−	0.603768i	$-0.206335\pi$
$449$	−2.63384	−	4.56194i	−0.124298	−	0.215291i	−0.921459	+	0.388477i	$0.873001\pi$
$450$	4.82684	+	8.36033i	0.227539	+	0.394110i
$451$	37.2102			1.75216
$452$	−8.32137	−	14.4130i	−0.391404	−	0.677932i
$453$	19.6549			0.923467
$454$	−58.5046			−2.74576
$455$	5.19056	−	0.719691i	0.243337	−	0.0337396i
$456$	−0.255910			−0.0119841
$457$	−18.4895			−0.864902			−0.432451	−	0.901658i	$-0.642351\pi$
$457$	−18.4895			−0.864902			−0.432451	+	0.901658i	$0.642351\pi$
$458$	−26.9937	−	46.7545i	−1.26133	−	2.18470i
$459$	0.603612			0.0281742
$460$	−0.229895	−	0.398191i	−0.0107189	−	0.0185657i
$461$	4.79101	+	8.29827i	0.223140	+	0.386489i	0.955760	−	0.294149i	$-0.0950361\pi$
$461$	4.79101	+	8.29827i	0.223140	+	0.386489i	−0.732620	+	0.680638i	$0.761703\pi$
$462$	16.9223	−	19.1309i	0.787296	−	0.890049i
$463$	2.22178			0.103255			0.0516275	−	0.998666i	$-0.483559\pi$
$463$	2.22178			0.103255			0.0516275	+	0.998666i	$0.483559\pi$
$464$	−7.33622	+	12.7067i	−0.340575	+	0.589894i
$465$	0.317141	+	0.549304i	0.0147071	+	0.0254734i
$466$	−22.8023	−	39.4947i	−1.05629	−	1.82956i
$467$	6.76331	+	11.7144i	0.312969	+	0.542078i	0.979004	−	0.203843i	$-0.0653431\pi$
$467$	6.76331	+	11.7144i	0.312969	+	0.542078i	−0.666035	+	0.745921i	$0.732010\pi$
$468$	−6.08177	−	5.21485i	−0.281130	−	0.241056i
$469$	8.06055	+	24.0827i	0.372202	+	1.11204i
$470$	−1.24029	+	2.14824i	−0.0572102	+	0.0990910i
$471$	5.21018			0.240073
$472$	3.89333			0.179205
$473$	−3.51053	+	6.08041i	−0.161414	+	0.279578i
$474$	−15.0223	+	26.0193i	−0.689995	+	1.19511i
$475$	1.31812	+	2.28304i	0.0604793	+	0.104753i
$476$	−3.47732	−	0.707119i	−0.159383	−	0.0324107i
$477$	4.52338	+	7.83473i	0.207111	+	0.358727i
$478$	56.1382			2.56770
$479$	7.29355	+	12.6328i	0.333251	+	0.577207i	0.983147	−	0.182816i	$-0.0585211\pi$
$479$	7.29355	+	12.6328i	0.333251	+	0.577207i	−0.649897	+	0.760023i	$0.725188\pi$
$480$	−2.22963	+	3.86184i	−0.101768	+	0.176268i
$481$	5.84442	−	31.1945i	0.266483	−	1.42235i
$482$	−48.8681			−2.22588
$483$	0.316334	+	0.945119i	0.0143937	+	0.0430044i
$484$	−12.3024	+	21.3085i	−0.559202	+	0.968567i
$485$	1.73056	−	2.99741i	0.0785806	−	0.136106i
$486$	1.02737	−	1.77946i	0.0466025	−	0.0807179i
$487$	−1.50126			−0.0680284			−0.0340142	−	0.999421i	$-0.510829\pi$
$487$	−1.50126			−0.0680284			−0.0340142	+	0.999421i	$0.510829\pi$
$488$	−1.69302	+	2.93239i	−0.0766393	+	0.132743i
$489$	4.17379			0.188745
$490$	−0.964413	−	7.84195i	−0.0435677	−	0.354263i
$491$	14.1980	−	24.5917i	0.640748	−	1.10981i	−0.344518	−	0.938780i	$-0.611958\pi$
$491$	14.1980	−	24.5917i	0.640748	−	1.10981i	0.985266	−	0.171028i	$-0.0547089\pi$
$492$	−17.5980			−0.793380
$493$	−1.26275	+	2.18715i	−0.0568715	+	0.0985044i
$494$	−3.15572	−	2.70589i	−0.141983	−	0.121744i
$495$	−1.29043	−	2.23509i	−0.0580004	−	0.100460i
$496$	2.02458	−	3.50668i	0.0909064	−	0.157455i
$497$	4.85170	+	14.4955i	0.217629	+	0.650214i
$498$	−15.2821	−	26.4694i	−0.684808	−	1.18612i
$499$	−10.5569	−	18.2851i	−0.472593	−	0.818554i	0.526915	−	0.849918i	$-0.323348\pi$
$499$	−10.5569	−	18.2851i	−0.472593	−	0.818554i	−0.999508	+	0.0313633i	$0.990015\pi$
$500$	−11.8375			−0.529387
$501$	−5.04671			−0.225470
$502$	8.56406	+	14.8334i	0.382233	+	0.662046i
$503$	14.2618	+	24.7022i	0.635903	+	1.10142i	0.986323	+	0.164824i	$0.0527056\pi$
$503$	14.2618	+	24.7022i	0.635903	+	1.10142i	−0.350420	+	0.936593i	$0.613961\pi$
$504$	−0.799476	+	0.903820i	−0.0356115	+	0.0402593i
$505$	−1.22056	+	2.11408i	−0.0543143	+	0.0940752i
$506$	−1.81827	−	3.14933i	−0.0808318	−	0.140005i
$507$	−1.98361	−	12.8478i	−0.0880953	−	0.570590i
$508$	5.25744	−	9.10615i	0.233261	−	0.404020i
$509$	34.2589			1.51850			0.759250	−	0.650800i	$-0.225566\pi$
$509$	34.2589			1.51850			0.759250	+	0.650800i	$0.225566\pi$
$510$	−0.340654	+	0.590030i	−0.0150844	+	0.0261270i
$511$	25.4059	−	28.7218i	1.12389	−	1.27058i
$512$	31.6661			1.39946
$513$	0.280555	−	0.485935i	0.0123868	−	0.0214546i
$514$	−28.3025			−1.24837
$515$	4.56725	−	7.91071i	0.201257	−	0.348587i
$516$	1.66025	−	2.87564i	0.0730885	−	0.126593i
$517$	−5.16264	+	8.94196i	−0.227053	+	0.393267i
$518$	−46.8927	−	9.53569i	−2.06035	−	0.418974i
$519$	−2.73897			−0.120228
$520$	0.852089	−	0.299874i	0.0373666	−	0.0131503i
$521$	−17.2434	+	29.8665i	−0.755448	+	1.30847i	0.189703	+	0.981841i	$0.439247\pi$
$521$	−17.2434	+	29.8665i	−0.755448	+	1.30847i	−0.945151	+	0.326633i	$0.894086\pi$
$522$	4.29851	+	7.44524i	0.188141	+	0.325869i
$523$	31.3896			1.37257			0.686285	−	0.727332i	$-0.259240\pi$
$523$	31.3896			1.37257			0.686285	+	0.727332i	$0.259240\pi$
$524$	−3.97077	−	6.87757i	−0.173464	−	0.300448i
$525$	12.1811	+	2.47704i	0.531626	+	0.108107i
$526$	9.29323	+	16.0963i	0.405204	+	0.701834i
$527$	0.348483	−	0.603590i	0.0151802	−	0.0262928i
$528$	−8.23791	+	14.2685i	−0.358509	+	0.620956i
$529$	−22.8581			−0.993830
$530$	−10.2112			−0.443548
$531$	−4.26827	+	7.39286i	−0.185227	+	0.320823i
$532$	−2.18550	+	2.47074i	−0.0947534	+	0.107120i
$533$	−21.6780	−	18.5879i	−0.938980	−	0.805133i
$534$	9.43489	+	16.3417i	0.408288	+	0.707175i
$535$	−4.90879	−	8.50227i	−0.212225	−	0.367585i
$536$	2.18889	+	3.79126i	0.0945455	+	0.163758i
$537$	−6.34782	+	10.9948i	−0.273929	+	0.474459i
$538$	4.70241			0.202735
$539$	−4.01433	−	32.6418i	−0.172909	−	1.40598i
$540$	0.610289	+	1.05705i	0.0262626	+	0.0454882i
$541$	−4.55013	−	7.88106i	−0.195626	−	0.338833i	0.751480	−	0.659756i	$-0.229340\pi$
$541$	−4.55013	−	7.88106i	−0.195626	−	0.338833i	−0.947105	+	0.320923i	$0.896007\pi$
$542$	8.18023			0.351371
$543$	3.97845	+	6.89089i	0.170732	+	0.295716i
$544$	4.89996			0.210084
$545$	5.57865			0.238963
$546$	−19.4152	+	2.69200i	−0.830896	+	0.115207i
$547$	−35.9950			−1.53903			−0.769517	−	0.638626i	$-0.779503\pi$
$547$	−35.9950			−1.53903			−0.769517	+	0.638626i	$0.779503\pi$
$548$	−42.7897			−1.82789
$549$	−3.71212	−	6.42958i	−0.158429	−	0.274408i
$550$	−45.3553			−1.93396
$551$	1.17384	+	2.03315i	0.0500072	+	0.0866150i
$552$	0.0859023	+	0.148787i	0.00365624	+	0.00633280i
$553$	12.2789	+	36.6859i	0.522151	+	1.56004i
$554$	−17.2598			−0.733299
$555$	−2.41766	+	4.18752i	−0.102624	+	0.177750i
$556$	−10.7355	−	18.5945i	−0.455288	−	0.788581i
$557$	7.95708	+	13.7821i	0.337152	+	0.583965i	0.983896	−	0.178743i	$-0.0572030\pi$
$557$	7.95708	+	13.7821i	0.337152	+	0.583965i	−0.646744	+	0.762707i	$0.723870\pi$
$558$	−1.18626	−	2.05467i	−0.0502185	−	0.0869811i
$559$	5.08257	−	1.78870i	0.214970	−	0.0756540i
$560$	1.61767	+	4.83316i	0.0683592	+	0.204238i
$561$	−1.41796	+	2.45597i	−0.0598662	+	0.103691i
$562$	−26.6210			−1.12294
$563$	−25.2247			−1.06310			−0.531548	−	0.847028i	$-0.678390\pi$
$563$	−25.2247			−1.06310			−0.531548	+	0.847028i	$0.678390\pi$
$564$	2.44160	−	4.22897i	0.102810	−	0.178072i
$565$	−2.05725	+	3.56326i	−0.0865490	+	0.149907i
$566$	−26.3059	−	45.5632i	−1.10572	−	1.91517i
$567$	−0.839752	−	2.50895i	−0.0352663	−	0.105366i
$568$	1.31751	+	2.28199i	0.0552813	+	0.0957501i
$569$	34.1685			1.43242			0.716208	−	0.697886i	$-0.245876\pi$
$569$	34.1685			1.43242			0.716208	+	0.697886i	$0.245876\pi$
$570$	0.316667	+	0.548484i	0.0132637	+	0.0229735i
$571$	−7.15867	+	12.3992i	−0.299581	+	0.518889i	−0.976040	−	0.217591i	$-0.930180\pi$
$571$	−7.15867	+	12.3992i	−0.299581	+	0.518889i	0.676459	+	0.736480i	$0.263514\pi$
$572$	35.5050	−	12.4952i	1.48454	−	0.522450i
$573$	−3.07979			−0.128660
$574$	−28.5266	+	32.2497i	−1.19068	+	1.34608i
$575$	0.884913	−	1.53271i	0.0369034	−	0.0639186i
$576$	4.83312	−	8.37121i	0.201380	−	0.348800i
$577$	5.34662	−	9.26061i	0.222583	−	0.385524i	−0.733009	−	0.680219i	$-0.761885\pi$
$577$	5.34662	−	9.26061i	0.222583	−	0.385524i	0.955591	+	0.294695i	$0.0952180\pi$
$578$	−34.1820			−1.42178
$579$	−1.69587	+	2.93734i	−0.0704781	+	0.122072i
$580$	−5.10688			−0.212052
$581$	−38.5662	−	7.84249i	−1.59999	−	0.325361i
$582$	−6.47314	+	11.2118i	−0.268320	+	0.464744i
$583$	−42.5039			−1.76033
$584$	3.30505	−	5.72452i	0.136764	−	0.236882i
$585$	−0.364731	+	1.94674i	−0.0150798	+	0.0804879i
$586$	−25.4670	−	44.1102i	−1.05203	−	1.82217i
$587$	−21.3592	+	36.9951i	−0.881587	+	1.52695i	−0.0320103	+	0.999488i	$0.510191\pi$
$587$	−21.3592	+	36.9951i	−0.881587	+	1.52695i	−0.849576	+	0.527465i	$0.823142\pi$
$588$	1.89852	+	15.4374i	0.0782935	+	0.636629i
$589$	−0.323945	−	0.561090i	−0.0133479	−	0.0231193i
$590$	−4.81767	−	8.34446i	−0.198341	−	0.343536i
$591$	4.12327			0.169608
$592$	30.8680			1.26867
$593$	14.0922	+	24.4084i	0.578697	+	1.00233i	0.995629	+	0.0933948i	$0.0297719\pi$
$593$	14.0922	+	24.4084i	0.578697	+	1.00233i	−0.416932	+	0.908938i	$0.636895\pi$
$594$	4.82684	+	8.36033i	0.198048	+	0.343028i
$595$	0.278444	+	0.831913i	0.0114151	+	0.0341051i
$596$	−7.91570	+	13.7104i	−0.324240	+	0.561599i
$597$	−0.574142	−	0.994443i	−0.0234981	−	0.0406998i
$598$	−0.513921	+	2.74304i	−0.0210158	+	0.112171i
$599$	15.7857	−	27.3417i	0.644987	−	1.11715i	−0.339317	−	0.940672i	$-0.610196\pi$
$599$	15.7857	−	27.3417i	0.644987	−	1.11715i	0.984304	−	0.176479i	$-0.0564707\pi$
$600$	2.14277			0.0874781
$601$	16.0445	−	27.7899i	0.654469	−	1.13357i	−0.327558	−	0.944831i	$-0.606226\pi$
$601$	16.0445	−	27.7899i	0.654469	−	1.13357i	0.982027	−	0.188742i	$-0.0604409\pi$
$602$	−2.57855	−	7.70399i	−0.105094	−	0.313991i
$603$	−9.59873			−0.390890
$604$	21.8362	−	37.8214i	0.888503	−	1.53893i
$605$	6.08293			0.247306
$606$	4.56551	−	7.90769i	0.185461	−	0.321228i
$607$	9.33324	−	16.1657i	0.378825	−	0.656144i	−0.612067	−	0.790806i	$-0.709662\pi$
$607$	9.33324	−	16.1657i	0.378825	−	0.656144i	0.990892	+	0.134662i	$0.0429950\pi$
$608$	2.27747	−	3.94469i	0.0923636	−	0.159978i
$609$	10.8478	+	2.20591i	0.439574	+	0.0893881i
$610$	8.37988			0.339291
$611$	7.47452	−	2.63049i	0.302387	−	0.106418i
$612$	0.670602	−	1.16152i	0.0271075	−	0.0469515i
$613$	−8.96569	−	15.5290i	−0.362121	−	0.627211i	0.626189	−	0.779671i	$-0.284614\pi$
$613$	−8.96569	−	15.5290i	−0.362121	−	0.627211i	−0.988310	+	0.152460i	$0.951281\pi$
$614$	−51.7971			−2.09036
$615$	2.17533	+	3.76778i	0.0877177	+	0.151932i
$616$	−1.79939	−	5.37609i	−0.0724997	−	0.216609i
$617$	−15.8059	−	27.3765i	−0.636320	−	1.10214i	−0.986234	−	0.165356i	$-0.947123\pi$
$617$	−15.8059	−	27.3765i	−0.636320	−	1.10214i	0.349914	−	0.936782i	$-0.386211\pi$
$618$	−17.0838	+	29.5900i	−0.687210	+	1.19028i
$619$	16.3184	−	28.2644i	0.655894	−	1.13604i	−0.325775	−	0.945447i	$-0.605625\pi$
$619$	16.3184	−	28.2644i	0.655894	−	1.13604i	0.981669	−	0.190594i	$-0.0610413\pi$
$620$	1.40935			0.0566009
$621$	−0.376699			−0.0151164
$622$	−4.24592	+	7.35415i	−0.170246	+	0.294875i
$623$	23.8100	+	4.84180i	0.953929	+	0.193983i
$624$	11.9269	−	4.19742i	0.477459	−	0.168031i
$625$	−10.2824	−	17.8096i	−0.411294	−	0.712382i
$626$	30.9632	+	53.6298i	1.23754	+	2.14348i
$627$	1.31812	+	2.28304i	0.0526404	+	0.0911759i
$628$	5.78842	−	10.0258i	0.230983	−	0.400075i
$629$	5.31319			0.211851
$630$	2.92642	+	0.595091i	0.116591	+	0.0237090i
$631$	12.7985	+	22.1676i	0.509500	+	0.882480i	0.999939	+	0.0110045i	$0.00350290\pi$
$631$	12.7985	+	22.1676i	0.509500	+	0.882480i	−0.490440	+	0.871475i	$0.663164\pi$
$632$	3.33440	+	5.77535i	0.132635	+	0.229731i
$633$	−4.56600			−0.181482
$634$	−11.8421	−	20.5111i	−0.470310	−	0.814600i
$635$	−2.59954			−0.103159
$636$	20.1016			0.797080
$637$	−13.9672	+	21.0219i	−0.553399	+	0.832916i
$638$	−40.3909			−1.59909
$639$	−5.77754			−0.228556
$640$	0.995967	+	1.72507i	0.0393691	+	0.0681892i
$641$	43.2415			1.70794			0.853969	−	0.520324i	$-0.174189\pi$
$641$	43.2415			1.70794			0.853969	+	0.520324i	$0.174189\pi$
$642$	18.3613	+	31.8027i	0.724662	+	1.25515i
$643$	2.25709	+	3.90939i	0.0890108	+	0.154171i	0.907093	−	0.420930i	$-0.138296\pi$
$643$	2.25709	+	3.90939i	0.0890108	+	0.154171i	−0.818082	+	0.575101i	$0.804963\pi$
$644$	2.17011	+	0.441295i	0.0855144	+	0.0173895i
$645$	−0.820910			−0.0323233
$646$	0.347963	−	0.602689i	0.0136904	−	0.0237125i
$647$	5.72020	+	9.90769i	0.224884	+	0.389511i	0.956285	−	0.292437i	$-0.0944662\pi$
$647$	5.72020	+	9.90769i	0.224884	+	0.389511i	−0.731400	+	0.681948i	$0.761133\pi$
$648$	−0.228039	−	0.394976i	−0.00895823	−	0.0155161i
$649$	−20.0534	−	34.7334i	−0.787163	−	1.36341i
$650$	26.4232	+	22.6567i	1.03640	+	0.888670i
$651$	−2.99367	−	0.608768i	−0.117331	−	0.0238595i
$652$	4.63701	−	8.03153i	0.181599	−	0.314539i
$653$	−21.7515			−0.851201			−0.425600	−	0.904911i	$-0.639937\pi$
$653$	−21.7515			−0.851201			−0.425600	+	0.904911i	$0.639937\pi$
$654$	−20.8669			−0.815960
$655$	−0.981671	+	1.70030i	−0.0383571	+	0.0664364i
$656$	13.8870	−	24.0530i	0.542196	−	0.939111i
$657$	7.24668	+	12.5516i	0.282720	+	0.489685i
$658$	−3.79206	−	11.3296i	−0.147830	−	0.441675i
$659$	3.28320	+	5.68668i	0.127895	+	0.221521i	0.922861	−	0.385133i	$-0.125844\pi$
$659$	3.28320	+	5.68668i	0.127895	+	0.221521i	−0.794966	+	0.606655i	$0.792511\pi$
$660$	−5.73457			−0.223218
$661$	23.0777	+	39.9718i	0.897619	+	1.55472i	0.830529	+	0.556975i	$0.188038\pi$
$661$	23.0777	+	39.9718i	0.897619	+	1.55472i	0.0670899	+	0.997747i	$0.478629\pi$
$662$	1.16647	−	2.02038i	0.0453360	−	0.0785243i
$663$	2.05293	−	0.722484i	0.0797293	−	0.0280590i
$664$	−6.78416			−0.263276
$665$	0.799147	+	0.162508i	0.0309896	+	0.00630177i
$666$	9.04325	−	15.6634i	0.350419	−	0.606943i
$667$	0.788053	−	1.36495i	0.0305135	−	0.0528510i
$668$	−5.60680	+	9.71127i	−0.216934	+	0.375740i
$669$	16.8462			0.651314
$670$	5.41713	−	9.38275i	0.209282	−	0.362487i
$671$	34.8809			1.34656
$672$	−6.81689	−	20.3670i	−0.262967	−	0.785673i
$673$	−5.50174	+	9.52930i	−0.212077	+	0.367327i	−0.952364	−	0.304963i	$-0.901356\pi$
$673$	−5.50174	+	9.52930i	−0.212077	+	0.367327i	0.740288	+	0.672290i	$0.234689\pi$
$674$	47.9128			1.84553
$675$	−2.34912	+	4.06880i	−0.0904177	+	0.156608i
$676$	−26.9264	−	10.4566i	−1.03563	−	0.402178i
$677$	−11.0575	−	19.1522i	−0.424976	−	0.736080i	0.571442	−	0.820642i	$-0.306384\pi$
$677$	−11.0575	−	19.1522i	−0.424976	−	0.736080i	−0.996418	+	0.0845623i	$0.973051\pi$
$678$	7.69512	−	13.3283i	0.295529	−	0.511872i
$679$	5.29101	+	15.8081i	0.203050	+	0.606658i
$680$	0.0756129	+	0.130965i	0.00289962	+	0.00502229i
$681$	−14.2365	−	24.6583i	−0.545544	−	0.944909i
$682$	11.1467			0.426830
$683$	−8.47618			−0.324332			−0.162166	−	0.986763i	$-0.551848\pi$
$683$	−8.47618			−0.324332			−0.162166	+	0.986763i	$0.551848\pi$
$684$	−0.623383	−	1.07973i	−0.0238356	−	0.0412845i
$685$	5.28933	+	9.16139i	0.202095	+	0.350039i
$686$	31.3678	+	21.5451i	1.19763	+	0.822596i
$687$	13.1373	−	22.7545i	0.501219	−	0.868137i
$688$	2.62028	+	4.53847i	0.0998974	+	0.173027i
$689$	24.7620	+	21.2323i	0.943359	+	0.808888i
$690$	0.212594	−	0.368223i	0.00809331	−	0.0140180i
$691$	1.91943			0.0730185			0.0365092	−	0.999333i	$-0.488376\pi$
$691$	1.91943			0.0730185			0.0365092	+	0.999333i	$0.488376\pi$
$692$	−3.04295	+	5.27055i	−0.115676	+	0.200356i
$693$	12.1811	+	2.47704i	0.462721	+	0.0940950i
$694$	5.21539			0.197973
$695$	−2.65408	+	4.59701i	−0.100675	+	0.174374i
$696$	1.90823			0.0723312
$697$	2.39031	−	4.14014i	0.0905395	−	0.156819i
$698$	−10.9796	+	19.0172i	−0.415583	+	0.719811i
$699$	11.0974	−	19.2212i	0.419742	−	0.727014i
$700$	18.2995	−	20.6878i	0.691655	−	0.781926i
$701$	−18.1080			−0.683929			−0.341965	−	0.939713i	$-0.611092\pi$
$701$	−18.1080			−0.683929			−0.341965	+	0.939713i	$0.611092\pi$
$702$	1.36427	−	7.28178i	0.0514912	−	0.274833i
$703$	2.46953	−	4.27736i	0.0931403	−	0.161324i
$704$	22.7072	+	39.3300i	0.855809	+	1.48230i
$705$	−1.20724			−0.0454674
$706$	−22.8494	−	39.5763i	−0.859948	−	1.48947i
$707$	−3.73175	−	11.1494i	−0.140347	−	0.419318i
$708$	9.48394	+	16.4267i	0.356428	+	0.617352i
$709$	14.1884	−	24.5751i	0.532857	−	0.922936i	−0.466407	−	0.884570i	$-0.654452\pi$
$709$	14.1884	−	24.5751i	0.532857	−	0.922936i	0.999264	−	0.0383652i	$-0.0122150\pi$
$710$	3.26061	−	5.64754i	0.122368	−	0.211948i
$711$	−14.6220			−0.548369
$712$	4.18841			0.156967
$713$	−0.217480	+	0.376686i	−0.00814468	+	0.0141070i
$714$	−1.04152	−	3.11176i	−0.0389778	−	0.116455i
$715$	−7.06411	−	6.05715i	−0.264183	−	0.226525i
$716$	14.1046	+	24.4299i	0.527115	+	0.912990i
$717$	13.6606	+	23.6609i	0.510166	+	0.883633i
$718$	17.2217	+	29.8288i	0.642706	+	1.11320i
$719$	−22.1741	+	38.4067i	−0.826955	+	1.43233i	0.0734616	+	0.997298i	$0.476595\pi$
$719$	−22.1741	+	38.4067i	−0.826955	+	1.43233i	−0.900416	+	0.435029i	$0.856738\pi$
$720$	−1.92637			−0.0717916
$721$	13.9639	+	41.7203i	0.520044	+	1.55375i
$722$	19.1966	+	33.2495i	0.714423	+	1.23742i
$723$	−11.8915	−	20.5967i	−0.442251	−	0.766001i
$724$	17.6800			0.657071
$725$	−9.82870	−	17.0238i	−0.365029	−	0.632248i
$726$	−22.7532			−0.844449
$727$	24.1298			0.894924			0.447462	−	0.894303i	$-0.352328\pi$
$727$	24.1298			0.894924			0.447462	+	0.894303i	$0.352328\pi$
$728$	−1.63727	+	4.03089i	−0.0606812	+	0.149395i
$729$	1.00000			0.0370370
$730$	−16.3589			−0.605471
$731$	0.451019	+	0.781187i	0.0166815	+	0.0288933i
$732$	−16.4964			−0.609724
$733$	16.7734	+	29.0524i	0.619540	+	1.07308i	0.989570	+	0.144055i	$0.0460143\pi$
$733$	16.7734	+	29.0524i	0.619540	+	1.07308i	−0.370029	+	0.929020i	$0.620652\pi$
$734$	4.81009	+	8.33132i	0.177544	+	0.307515i
$735$	3.07052	−	2.31473i	0.113258	−	0.0853803i
$736$	−3.05795			−0.112717
$737$	22.5486	−	39.0553i	0.830588	−	1.43862i
$738$	−8.13680	−	14.0934i	−0.299520	−	0.518784i
$739$	8.41105	+	14.5684i	0.309405	+	0.535906i	0.978232	−	0.207512i	$-0.0665367\pi$
$739$	8.41105	+	14.5684i	0.309405	+	0.535906i	−0.668827	+	0.743418i	$0.733203\pi$
$740$	5.37196	+	9.30451i	0.197477	+	0.342041i
$741$	0.372557	−	1.98851i	0.0136862	−	0.0730498i
$742$	32.5849	−	36.8377i	1.19623	−	1.35236i
$743$	−16.5645	+	28.6906i	−0.607694	+	1.05256i	0.383926	+	0.923364i	$0.374572\pi$
$743$	−16.5645	+	28.6906i	−0.607694	+	1.05256i	−0.991620	+	0.129192i	$0.958761\pi$
$744$	−0.526615			−0.0193067
$745$	3.91391			0.143394
$746$	6.94680	−	12.0322i	0.254340	−	0.440530i
$747$	7.43749	−	12.8821i	0.272124	−	0.471332i
$748$	3.15065	+	5.45709i	0.115199	+	0.199531i
$749$	46.3368	+	9.42265i	1.69311	+	0.344296i
$750$	−5.47329	−	9.48002i	−0.199856	−	0.346161i
$751$	−29.7949			−1.08723			−0.543616	−	0.839334i	$-0.682945\pi$
$751$	−29.7949			−1.08723			−0.543616	+	0.839334i	$0.682945\pi$
$752$	3.85344	+	6.67435i	0.140520	+	0.243388i
$753$	−4.16795	+	7.21910i	−0.151889	+	0.263079i
$754$	23.5310	+	20.1768i	0.856950	+	0.734796i
$755$	−10.7969			−0.392939
$756$	−5.76086	−	1.17148i	−0.209520	−	0.0426063i
$757$	−11.0742	+	19.1810i	−0.402498	+	0.697147i	−0.994027	−	0.109137i	$-0.965191\pi$
$757$	−11.0742	+	19.1810i	−0.402498	+	0.697147i	0.591529	+	0.806284i	$0.298525\pi$
$758$	19.7768	−	34.2545i	0.718327	−	1.24418i
$759$	0.884913	−	1.53271i	0.0321203	−	0.0556340i
$760$	0.140577			0.00509928
$761$	−21.4467	+	37.1468i	−0.777443	+	1.34657i	0.155969	+	0.987762i	$0.450150\pi$
$761$	−21.4467	+	37.1468i	−0.777443	+	1.34657i	−0.933411	+	0.358808i	$0.883183\pi$
$762$	9.72354			0.352247
$763$	−17.8019	+	20.1253i	−0.644472	+	0.728586i
$764$	−3.42159	+	5.92637i	−0.123789	+	0.214408i
$765$	−0.331578			−0.0119882
$766$	−13.8542	+	23.9961i	−0.500572	+	0.867016i
$767$	−5.66795	+	30.2525i	−0.204658	+	1.09236i
$768$	5.94083	+	10.2898i	0.214371	+	0.371302i
$769$	25.5865	−	44.3171i	0.922671	−	1.59811i	0.127407	−	0.991850i	$-0.459334\pi$
$769$	25.5865	−	44.3171i	0.922671	−	1.59811i	0.795264	−	0.606263i	$-0.207332\pi$
$770$	−9.29581	+	10.5091i	−0.334998	+	0.378720i
$771$	−6.88712	−	11.9288i	−0.248034	−	0.429607i
$772$	3.76817	+	6.52666i	0.135619	+	0.234900i
$773$	−36.3249			−1.30652			−0.653259	−	0.757135i	$-0.726599\pi$
$773$	−36.3249			−1.30652			−0.653259	+	0.757135i	$0.726599\pi$
$774$	3.07061			0.110371
$775$	2.71244	+	4.69808i	0.0974336	+	0.168760i
$776$	1.43680	+	2.48862i	0.0515782	+	0.0893361i
$777$	−7.39177	−	22.0846i	−0.265178	−	0.792279i
$778$	33.7449	−	58.4478i	1.20981	−	2.09546i
$779$	−2.22200	−	3.84862i	−0.0796115	−	0.137891i
$780$	3.34086	+	2.86464i	0.119622	+	0.102571i
$781$	13.5721	−	23.5076i	0.485650	−	0.841170i
$782$	−0.467208			−0.0167073
$783$	−2.09200	+	3.62344i	−0.0747618	+	0.129491i
$784$	−22.5981	−	9.58715i	−0.807074	−	0.342398i
$785$	−2.86208			−0.102152
$786$	3.67193	−	6.35998i	0.130974	−	0.226853i
$787$	−54.3948			−1.93896			−0.969482	−	0.245162i	$-0.921159\pi$
$787$	−54.3948			−1.93896			−0.969482	+	0.245162i	$0.921159\pi$
$788$	4.58087	−	7.93431i	0.163187	−	0.282648i
$789$	−4.52282	+	7.83375i	−0.161017	+	0.278889i
$790$	8.25208	−	14.2930i	0.293596	−	0.508523i
$791$	−6.28983	−	18.7923i	−0.223641	−	0.668177i
$792$	2.14277			0.0761399
$793$	−20.3210	−	17.4243i	−0.721620	−	0.618757i
$794$	27.3392	−	47.3529i	0.970233	−	1.68049i
$795$	−2.48480	−	4.30380i	−0.0881268	−	0.152640i
$796$	−2.55145			−0.0904336
$797$	15.9900	+	27.6955i	0.566396	+	0.981026i	0.996918	+	0.0784465i	$0.0249960\pi$
$797$	15.9900	+	27.6955i	0.566396	+	0.981026i	−0.430522	+	0.902580i	$0.641671\pi$
$798$	−2.98920	−	0.607859i	−0.105817	−	0.0215180i
$799$	0.663276	+	1.14883i	0.0234650	+	0.0406426i
$800$	−19.0695	+	33.0294i	−0.674210	+	1.16777i
$801$	−4.59177	+	7.95317i	−0.162242	+	0.281012i
$802$	−47.4886			−1.67688
$803$	−68.0933			−2.40296
$804$	−10.6640	+	18.4706i	−0.376091	+	0.651408i
$805$	−0.173770	−	0.519176i	−0.00612458	−	0.0182986i
$806$	−6.49388	−	5.56821i	−0.228737	−	0.196132i
$807$	1.14428	+	1.98196i	0.0402806	+	0.0697681i
$808$	−1.01338	−	1.75522i	−0.0356505	−	0.0617485i
$809$	0.0423933	+	0.0734274i	0.00149047	+	0.00258157i	0.866770	−	0.498709i	$-0.166192\pi$
$809$	0.0423933	+	0.0734274i	0.00149047	+	0.00258157i	−0.865279	+	0.501290i	$0.832859\pi$
$810$	−0.564359	+	0.977499i	−0.0198296	+	0.0343458i
$811$	2.81654			0.0989019			0.0494510	−	0.998777i	$-0.484253\pi$
$811$	2.81654			0.0989019			0.0494510	+	0.998777i	$0.484253\pi$
$812$	16.2965	−	18.4234i	0.571894	−	0.646535i
$813$	1.99057	+	3.44778i	0.0698125	+	0.120919i
$814$	42.4874	+	73.5903i	1.48918	+	2.57934i
$815$	−2.29276			−0.0803120
$816$	1.05837	+	1.83316i	0.0370505	+	0.0641734i
$817$	0.838522			0.0293362
$818$	−14.8793			−0.520244
$819$	−5.85911	−	7.52800i	−0.204734	−	0.263050i
$820$	9.66701			0.337586
$821$	16.7031			0.582943			0.291471	−	0.956580i	$-0.405855\pi$
$821$	16.7031			0.582943			0.291471	+	0.956580i	$0.405855\pi$
$822$	−19.7847	−	34.2681i	−0.690071	−	1.19524i
$823$	−26.3739			−0.919336			−0.459668	−	0.888091i	$-0.652032\pi$
$823$	−26.3739			−0.919336			−0.459668	+	0.888091i	$0.652032\pi$
$824$	3.79198	+	6.56790i	0.132100	+	0.228804i
$825$	−11.0367	−	19.1162i	−0.384250	−	0.665541i
$826$	45.4767	+	9.24776i	1.58234	+	0.321771i
$827$	−36.8372			−1.28095			−0.640477	−	0.767977i	$-0.721263\pi$
$827$	−36.8372			−1.28095			−0.640477	+	0.767977i	$0.721263\pi$
$828$	−0.418506	+	0.724874i	−0.0145441	+	0.0251911i
$829$	−12.4027	−	21.4822i	−0.430765	−	0.746107i	0.566174	−	0.824286i	$-0.308423\pi$
$829$	−12.4027	−	21.4822i	−0.430765	−	0.746107i	−0.996939	+	0.0781784i	$0.975090\pi$
$830$	8.39483	+	14.5403i	0.291389	+	0.504700i
$831$	−4.19999	−	7.27460i	−0.145696	−	0.252353i
$832$	6.41803	−	34.2561i	0.222505	−	1.18762i
$833$	−3.88971	−	1.65020i	−0.134771	−	0.0571759i
$834$	9.92758	−	17.1951i	0.343764	−	0.595417i
$835$	2.77228			0.0959386
$836$	5.85761			0.202590
$837$	0.577330	−	0.999965i	0.0199554	−	0.0345638i
$838$	−36.0710	+	62.4768i	−1.24605	+	2.15823i
$839$	−11.4460	−	19.8250i	−0.395159	−	0.684435i	0.597963	−	0.801524i	$-0.295977\pi$
$839$	−11.4460	−	19.8250i	−0.395159	−	0.684435i	−0.993121	+	0.117089i	$0.962644\pi$
$840$	0.439171	−	0.496490i	0.0151529	−	0.0171305i
$841$	5.74711	+	9.95429i	0.198176	+	0.343251i
$842$	51.9297			1.78962
$843$	−6.47795	−	11.2201i	−0.223112	−	0.386442i
$844$	−5.07274	+	8.78625i	−0.174611	+	0.302435i
$845$	1.08965	+	7.05759i	0.0374849	+	0.242788i
$846$	4.51569			0.155253
$847$	−19.4111	+	21.9446i	−0.666974	+	0.754024i
$848$	−15.8626	+	27.4749i	−0.544724	+	0.943490i
$849$	12.8026	−	22.1747i	0.439383	−	0.761033i
$850$	−2.91354	+	5.04639i	−0.0999335	+	0.173090i
$851$	−3.31583			−0.113665
$852$	−6.41874	+	11.1176i	−0.219902	+	0.380882i
$853$	0.727097			0.0248953			0.0124477	−	0.999923i	$-0.496038\pi$
$853$	0.727097			0.0248953			0.0124477	+	0.999923i	$0.496038\pi$
$854$	−26.7409	+	30.2309i	−0.915053	+	1.03448i
$855$	−0.154115	+	0.266936i	−0.00527064	+	0.00912901i
$856$	8.15108			0.278598
$857$	6.16106	−	10.6713i	0.210458	−	0.364524i	−0.741400	−	0.671063i	$-0.765838\pi$
$857$	6.16106	−	10.6713i	0.210458	−	0.364524i	0.951858	+	0.306540i	$0.0991712\pi$
$858$	26.4232	+	22.6567i	0.902074	+	0.773488i
$859$	−17.1581	−	29.7187i	−0.585427	−	1.01399i	−0.994822	−	0.101632i	$-0.967594\pi$
$859$	−17.1581	−	29.7187i	−0.585427	−	1.01399i	0.409395	−	0.912357i	$-0.365740\pi$
$860$	−0.912016	+	1.57966i	−0.0310995	+	0.0538659i
$861$	−20.5342	−	4.17565i	−0.699802	−	0.142306i
$862$	−18.0502	−	31.2639i	−0.614793	−	1.06485i
$863$	17.8997	+	31.0032i	0.609313	+	1.05536i	0.991354	+	0.131216i	$0.0418881\pi$
$863$	17.8997	+	31.0032i	0.609313	+	1.05536i	−0.382041	+	0.924146i	$0.624779\pi$
$864$	8.11773			0.276171
$865$	1.50458			0.0511574
$866$	−6.20554	−	10.7483i	−0.210873	−	0.365242i
$867$	−8.31783	−	14.4069i	−0.282488	−	0.489284i
$868$	−4.49735	+	5.08433i	−0.152650	+	0.172573i
$869$	34.3489	−	59.4941i	1.16521	−	2.01820i
$870$	−2.36127	−	4.08985i	−0.0800547	−	0.138659i
$871$	−32.6460	+	11.4891i	−1.10617	+	0.389292i
$872$	−2.31585	+	4.01117i	−0.0784245	+	0.135835i
$873$	−6.30068			−0.213246
$874$	−0.217155	+	0.376124i	−0.00734538	+	0.0127226i
$875$	−13.8125	−	2.80879i	−0.466947	−	0.0949544i
$876$	32.2037			1.08806
$877$	−14.9040	+	25.8145i	−0.503272	+	0.871693i	0.496721	+	0.867910i	$0.334537\pi$
$877$	−14.9040	+	25.8145i	−0.503272	+	0.871693i	−0.999993	+	0.00378256i	$0.998796\pi$
$878$	51.0734			1.72364
$879$	12.3943	−	21.4675i	0.418048	−	0.724081i
$880$	4.52528	−	7.83801i	0.152547	−	0.264219i
$881$	11.3524	−	19.6629i	0.382470	−	0.662458i	−0.608944	−	0.793213i	$-0.708407\pi$
$881$	11.3524	−	19.6629i	0.382470	−	0.662458i	0.991415	+	0.130755i	$0.0417400\pi$
$882$	−11.4853	+	8.65825i	−0.386729	+	0.291538i
$883$	51.4418			1.73115			0.865577	−	0.500776i	$-0.166952\pi$
$883$	51.4418			1.73115			0.865577	+	0.500776i	$0.166952\pi$
$884$	0.890511	−	4.75308i	0.0299511	−	0.159863i
$885$	2.34466	−	4.06107i	0.0788149	−	0.136511i
$886$	32.4842	+	56.2642i	1.09133	+	1.89023i
$887$	14.8077			0.497194			0.248597	−	0.968607i	$-0.420031\pi$
$887$	14.8077			0.497194			0.248597	+	0.968607i	$0.420031\pi$
$888$	−2.00728	−	3.47670i	−0.0673598	−	0.116671i
$889$	8.29532	−	9.37799i	0.278216	−	0.314528i
$890$	−5.18281	−	8.97689i	−0.173728	−	0.300906i
$891$	−2.34912	+	4.06880i	−0.0786985	+	0.136310i
$892$	18.7159	−	32.4169i	0.626654	−	1.08540i
$893$	1.23315			0.0412657
$894$	−14.6399			−0.489633
$895$	3.48701	−	6.03968i	0.116558	−	0.201884i
$896$	−9.40150	−	1.91181i	−0.314082	−	0.0638690i
$897$	−1.28118	+	0.450885i	−0.0427775	+	0.0150546i
$898$	−5.41186	−	9.37361i	−0.180596	−	0.312801i
$899$	2.41554	+	4.18384i	0.0805628	+	0.139539i
$900$	5.21966	+	9.04072i	0.173989	+	0.301357i
$901$	−2.73037	+	4.72913i	−0.0909617	+	0.157550i
$902$	76.4574			2.54575
$903$	2.61959	−	2.96148i	0.0871744	−	0.0985520i
$904$	−1.70804	−	2.95841i	−0.0568085	−	0.0983952i
$905$	−2.18546	−	3.78533i	−0.0726471	−	0.125829i
$906$	40.3857			1.34173
$907$	1.11175	+	1.92561i	0.0369151	+	0.0639389i	0.883893	−	0.467690i	$-0.154914\pi$
$907$	1.11175	+	1.92561i	0.0369151	+	0.0639389i	−0.846978	+	0.531629i	$0.821580\pi$
$908$	−63.2659			−2.09955
$909$	4.44387			0.147394
$910$	10.6653	−	1.47878i	0.353550	−	0.0490210i
$911$	−29.3786			−0.973355			−0.486678	−	0.873582i	$-0.661791\pi$
$911$	−29.3786			−0.973355			−0.486678	+	0.873582i	$0.661791\pi$
$912$	1.96770			0.0651571
$913$	34.9431	+	60.5233i	1.15645	+	2.00303i
$914$	−37.9911			−1.25663
$915$	2.03916	+	3.53192i	0.0674124	+	0.116762i
$916$	−29.1906	−	50.5596i	−0.964484	−	1.67054i
$917$	−3.00137	−	8.96725i	−0.0991138	−	0.296125i
$918$	1.24027			0.0409349
$919$	10.8455	−	18.7850i	0.357761	−	0.619661i	−0.629825	−	0.776737i	$-0.716874\pi$
$919$	10.8455	−	18.7850i	0.357761	−	0.619661i	0.987586	+	0.157076i	$0.0502069\pi$
$920$	−0.0471882	−	0.0817323i	−0.00155575	−	0.00269463i
$921$	−12.6043	−	21.8313i	−0.415326	−	0.719365i
$922$	9.84429	+	17.0508i	0.324204	+	0.561538i
$923$	−19.6499	+	6.91534i	−0.646784	+	0.227621i
$924$	18.2995	−	20.6878i	0.602008	−	0.680580i
$925$	−20.6777	+	35.8149i	−0.679880	+	1.17759i
$926$	4.56519			0.150021
$927$	−16.6286			−0.546156
$928$	−16.9823	+	29.4141i	−0.557470	+	0.965566i
$929$	15.5615	−	26.9534i	0.510557	−	0.884311i	−0.489368	−	0.872077i	$-0.662773\pi$
$929$	15.5615	−	26.9534i	0.510557	−	0.884311i	0.999925	−	0.0122336i	$-0.00389416\pi$
$930$	0.651643	+	1.12868i	0.0213682	+	0.0370108i
$931$	−3.13640	+	2.36440i	−0.102791	+	0.0774900i
$932$	−24.6580	−	42.7089i	−0.807699	−	1.39898i
$933$	−4.13280			−0.135302
$934$	13.8969	+	24.0701i	0.454719	+	0.787597i
$935$	0.778918	−	1.34913i	0.0254733	−	0.0441211i
$936$	−1.24834	−	1.07040i	−0.0408033	−	0.0349870i
$937$	13.1250			0.428777			0.214388	−	0.976749i	$-0.431224\pi$
$937$	13.1250			0.428777			0.214388	+	0.976749i	$0.431224\pi$
$938$	16.5624	+	49.4837i	0.540780	+	1.61570i
$939$	−15.0691	+	26.1005i	−0.491763	+	0.851758i
$940$	−1.34123	+	2.32307i	−0.0437460	+	0.0757703i
$941$	−23.5806	+	40.8428i	−0.768705	+	1.33144i	0.169560	+	0.985520i	$0.445765\pi$
$941$	−23.5806	+	40.8428i	−0.768705	+	1.33144i	−0.938265	+	0.345917i	$0.887568\pi$
$942$	10.7056			0.348807
$943$	−1.49173	+	2.58376i	−0.0485776	+	0.0841388i
$944$	−29.9360			−0.974333
$945$	0.461296	+	1.37822i	0.0150060	+	0.0448336i
$946$	−7.21323	+	12.4937i	−0.234522	+	0.406204i
$947$	4.31484			0.140214			0.0701068	−	0.997539i	$-0.477666\pi$
$947$	4.31484			0.140214			0.0701068	+	0.997539i	$0.477666\pi$
$948$	−16.2448	+	28.1369i	−0.527607	+	0.913843i
$949$	39.6700	+	34.0152i	1.28774	+	1.10418i
$950$	2.70839	+	4.69106i	0.0878716	+	0.152198i
$951$	5.76330	−	9.98233i	0.186888	−	0.323699i
$952$	−0.713752	−	0.145143i	−0.0231328	−	0.00470410i
$953$	−5.09812	−	8.83020i	−0.165144	−	0.286038i	0.771562	−	0.636154i	$-0.219476\pi$
$953$	−5.09812	−	8.83020i	−0.165144	−	0.286038i	−0.936707	+	0.350116i	$0.886142\pi$
$954$	9.29438	+	16.0983i	0.300917	+	0.521203i
$955$	1.69180			0.0547454
$956$	60.7069			1.96340
$957$	−9.82870	−	17.0238i	−0.317717	−	0.550302i
$958$	14.9864	+	25.9571i	0.484187	+	0.838637i
$959$	−49.9290	−	10.1531i	−1.61229	−	0.327861i
$960$	−2.65495	+	4.59850i	−0.0856881	+	0.148416i
$961$	14.8334	+	25.6922i	0.478496	+	0.828780i
$962$	12.0088	−	64.0966i	0.387179	−	2.06656i
$963$	−8.93605	+	15.4777i	−0.287960	+	0.498762i
$964$	−52.8451			−1.70203
$965$	0.931584	−	1.61355i	0.0299887	−	0.0519420i
$966$	0.649985	+	1.94198i	0.0209129	+	0.0624820i
$967$	14.3246			0.460649			0.230324	−	0.973114i	$-0.426021\pi$
$967$	14.3246			0.460649			0.230324	+	0.973114i	$0.426021\pi$
$968$	−2.52519	+	4.37376i	−0.0811627	+	0.140578i
$969$	0.338692			0.0108804
$970$	3.55585	−	6.15891i	0.114171	−	0.197751i
$971$	8.54294	−	14.7968i	0.274156	−	0.474852i	−0.695766	−	0.718269i	$-0.744935\pi$
$971$	8.54294	−	14.7968i	0.274156	−	0.474852i	0.969922	+	0.243416i	$0.0782682\pi$
$972$	1.11098	−	1.92428i	0.0356348	−	0.0617212i
$973$	−8.11461	−	24.2442i	−0.260142	−	0.777233i
$974$	−3.08469			−0.0988400
$975$	−3.11946	+	16.6501i	−0.0999028	+	0.533229i
$976$	13.0177	−	22.5473i	0.416686	−	0.721721i
$977$	25.0285	+	43.3507i	0.800733	+	1.38691i	0.919134	+	0.393945i	$0.128890\pi$
$977$	25.0285	+	43.3507i	0.800733	+	1.38691i	−0.118401	+	0.992966i	$0.537777\pi$
$978$	8.57606			0.274232
$979$	−21.5732	−	37.3659i	−0.689484	−	1.19422i
$980$	−1.04290	−	8.48016i	−0.0333142	−	0.270889i
$981$	−5.07774	−	8.79490i	−0.162120	−	0.280800i
$982$	29.1733	−	50.5296i	0.930956	−	1.61246i
$983$	20.6067	−	35.6919i	0.657252	−	1.13839i	−0.324072	−	0.946032i	$-0.605052\pi$
$983$	20.6067	−	35.6919i	0.657252	−	1.13839i	0.981324	−	0.192362i	$-0.0616147\pi$
$984$	−3.61215			−0.115151
$985$	−2.26501			−0.0721692
$986$	−2.59463	+	4.49403i	−0.0826299	+	0.143119i
$987$	3.85241	−	4.35521i	0.122624	−	0.138628i
$988$	−3.41254	−	2.92610i	−0.108567	−	0.0930917i
$989$	−0.281470	−	0.487520i	−0.00895022	−	0.0155022i
$990$	−2.65150	−	4.59253i	−0.0842701	−	0.145960i
$991$	−5.01241	−	8.68175i	−0.159225	−	0.275785i	0.775365	−	0.631514i	$-0.217566\pi$
$991$	−5.01241	−	8.68175i	−0.159225	−	0.275785i	−0.934589	+	0.355729i	$0.884233\pi$
$992$	4.68661	−	8.11745i	0.148800	−	0.257729i
$993$	1.13539			0.0360305
$994$	9.96900	+	29.7846i	0.316197	+	0.944710i
$995$	0.315390	+	0.546271i	0.00999853	+	0.0173180i
$996$	−16.5258	−	28.6236i	−0.523641	−	0.906973i
$997$	−43.8518			−1.38880			−0.694401	−	0.719588i	$-0.744330\pi$
$997$	−43.8518			−1.38880			−0.694401	+	0.719588i	$0.744330\pi$
$998$	−21.6917	−	37.5712i	−0.686640	−	1.18930i
$999$	8.80232			0.278493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.b.256.7	yes	16
3.2	odd	2		819.2.s.e.802.2		16
7.2	even	3		273.2.j.b.100.2	✓	16
13.3	even	3		273.2.j.b.172.2	yes	16
21.2	odd	6		819.2.n.e.100.7		16
39.29	odd	6		819.2.n.e.172.7		16
91.16	even	3	inner	273.2.l.b.16.7	yes	16
273.107	odd	6		819.2.s.e.289.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.2	✓	16	7.2	even	3
273.2.j.b.172.2	yes	16	13.3	even	3
273.2.l.b.16.7	yes	16	91.16	even	3	inner
273.2.l.b.256.7	yes	16	1.1	even	1	trivial
819.2.n.e.100.7		16	21.2	odd	6
819.2.n.e.172.7		16	39.29	odd	6
819.2.s.e.289.2		16	273.107	odd	6
819.2.s.e.802.2		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.05474 q^{2} +(0.500000 + 0.866025i) q^{3} +2.22196 q^{4} +(-0.274662 - 0.475728i) q^{5} +(1.02737 + 1.77946i) q^{6} +(2.59269 + 0.527227i) q^{7} +0.456078 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+2.05474 q^{2} +(0.500000 + 0.866025i) q^{3} +2.22196 q^{4} +(-0.274662 - 0.475728i) q^{5} +(1.02737 + 1.77946i) q^{6} +(2.59269 + 0.527227i) q^{7} +0.456078 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.564359 - 0.977499i) q^{10} +(-2.34912 - 4.06880i) q^{11} +(1.11098 + 1.92428i) q^{12} +(-0.663964 + 3.54389i) q^{13} +(5.32730 + 1.08331i) q^{14} +(0.274662 - 0.475728i) q^{15} -3.50680 q^{16} -0.603612 q^{17} +(-1.02737 + 1.77946i) q^{18} +(-0.280555 + 0.485935i) q^{19} +(-0.610289 - 1.05705i) q^{20} +(0.839752 + 2.50895i) q^{21} +(-4.82684 - 8.36033i) q^{22} +0.376699 q^{23} +(0.228039 + 0.394976i) q^{24} +(2.34912 - 4.06880i) q^{25} +(-1.36427 + 7.28178i) q^{26} -1.00000 q^{27} +(5.76086 + 1.17148i) q^{28} +(2.09200 - 3.62344i) q^{29} +(0.564359 - 0.977499i) q^{30} +(-0.577330 + 0.999965i) q^{31} -8.11773 q^{32} +(2.34912 - 4.06880i) q^{33} -1.24027 q^{34} +(-0.461296 - 1.37822i) q^{35} +(-1.11098 + 1.92428i) q^{36} -8.80232 q^{37} +(-0.576468 + 0.998472i) q^{38} +(-3.40108 + 1.19694i) q^{39} +(-0.125267 - 0.216969i) q^{40} +(-3.96001 + 6.85894i) q^{41} +(1.72547 + 5.15524i) q^{42} +(-0.747200 - 1.29419i) q^{43} +(-5.21966 - 9.04072i) q^{44} +0.549324 q^{45} +0.774020 q^{46} +(-1.09885 - 1.90326i) q^{47} +(-1.75340 - 3.03698i) q^{48} +(6.44406 + 2.73387i) q^{49} +(4.82684 - 8.36033i) q^{50} +(-0.301806 - 0.522743i) q^{51} +(-1.47530 + 7.87439i) q^{52} +(4.52338 - 7.83473i) q^{53} -2.05474 q^{54} +(-1.29043 + 2.23509i) q^{55} +(1.18247 + 0.240457i) q^{56} -0.561110 q^{57} +(4.29851 - 7.44524i) q^{58} +8.53654 q^{59} +(0.610289 - 1.05705i) q^{60} +(-3.71212 + 6.42958i) q^{61} +(-1.18626 + 2.05467i) q^{62} +(-1.75294 + 1.98172i) q^{63} -9.66624 q^{64} +(1.86829 - 0.657505i) q^{65} +(4.82684 - 8.36033i) q^{66} +(4.79936 + 8.31274i) q^{67} -1.34120 q^{68} +(0.188350 + 0.326231i) q^{69} +(-0.947844 - 2.83190i) q^{70} +(2.88877 + 5.00350i) q^{71} +(-0.228039 + 0.394976i) q^{72} +(7.24668 - 12.5516i) q^{73} -18.0865 q^{74} +4.69824 q^{75} +(-0.623383 + 1.07973i) q^{76} +(-3.94536 - 11.7876i) q^{77} +(-6.98834 + 2.45939i) q^{78} +(7.31102 + 12.6631i) q^{79} +(0.963186 + 1.66829i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.13680 + 14.0934i) q^{82} -14.8750 q^{83} +(1.86590 + 5.57479i) q^{84} +(0.165789 + 0.287155i) q^{85} +(-1.53530 - 2.65922i) q^{86} +4.18399 q^{87} +(-1.07138 - 1.85569i) q^{88} +9.18353 q^{89} +1.12872 q^{90} +(-3.58988 + 8.83814i) q^{91} +0.837013 q^{92} -1.15466 q^{93} +(-2.25784 - 3.91070i) q^{94} +0.308231 q^{95} +(-4.05887 - 7.03016i) q^{96} +(3.15034 + 5.45655i) q^{97} +(13.2409 + 5.61740i) q^{98} +4.69824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Introduction

L-functions

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