LMFDB - Embedded newform 430.2.k.b.21.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(11,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("430.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.k (of order $7$, degree $6$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 17 x^{16} - 43 x^{15} + 90 x^{14} - 114 x^{13} + 135 x^{12} + 2 x^{11} + 313 x^{10} + \cdots + 169 $ x^18 - 5x^17 + 17x^16 - 43x^15 + 90x^14 - 114x^13 + 135x^12 + 2x^11 + 313x^10 - 632x^9 + 2382x^8 - 1755x^7 + 2203x^6 - 3817x^5 + 4882x^4 - 4217x^3 + 2612x^2 - 871*x + 169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			21.2
Root			$0.257241 - 0.322570i$ of defining polynomial
Character	$\chi$	$=$	430.21
Dual form			430.2.k.b.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 - 0.433884i) q^{2} +(0.371724 - 0.179013i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.222521 + 0.974928i) q^{5} -0.412583 q^{6} -2.38473 q^{7} +(-0.222521 - 0.974928i) q^{8} +(-1.76434 + 2.21241i) q^{9} +O(q^{10})$	\(q+(-0.900969 - 0.433884i) q^{2} +(0.371724 - 0.179013i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.222521 + 0.974928i) q^{5} -0.412583 q^{6} -2.38473 q^{7} +(-0.222521 - 0.974928i) q^{8} +(-1.76434 + 2.21241i) q^{9} +(0.222521 - 0.974928i) q^{10} +(1.90541 - 2.38931i) q^{11} +(0.371724 + 0.179013i) q^{12} +(1.49265 + 6.53974i) q^{13} +(2.14857 + 1.03470i) q^{14} +(0.257241 + 0.322570i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-1.01754 + 4.45813i) q^{17} +(2.54954 - 1.22779i) q^{18} +(-2.18757 - 2.74313i) q^{19} +(-0.623490 + 0.781831i) q^{20} +(-0.886463 + 0.426898i) q^{21} +(-2.75340 + 1.32597i) q^{22} +(-2.15933 + 2.70771i) q^{23} +(-0.257241 - 0.322570i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(1.49265 - 6.53974i) q^{26} +(-0.535222 + 2.34496i) q^{27} +(-1.48686 - 1.86446i) q^{28} +(0.583267 + 0.280886i) q^{29} +(-0.0918083 - 0.402238i) q^{30} +(2.69801 + 1.29929i) q^{31} +(0.623490 - 0.781831i) q^{32} +(0.280570 - 1.22926i) q^{33} +(2.85108 - 3.57514i) q^{34} +(-0.530653 - 2.32494i) q^{35} -2.82978 q^{36} -6.29157 q^{37} +(0.780736 + 3.42063i) q^{38} +(1.72555 + 2.16377i) q^{39} +(0.900969 - 0.433884i) q^{40} +(7.21820 + 3.47610i) q^{41} +0.983900 q^{42} +(3.21291 + 5.71640i) q^{43} +3.05604 q^{44} +(-2.54954 - 1.22779i) q^{45} +(3.12032 - 1.50267i) q^{46} +(7.22293 + 9.05726i) q^{47} +(0.0918083 + 0.402238i) q^{48} -1.31305 q^{49} +1.00000 q^{50} +(0.419819 + 1.83935i) q^{51} +(-4.18232 + 5.24446i) q^{52} +(1.43260 - 6.27663i) q^{53} +(1.49966 - 1.88051i) q^{54} +(2.75340 + 1.32597i) q^{55} +(0.530653 + 2.32494i) q^{56} +(-1.30423 - 0.628084i) q^{57} +(-0.403633 - 0.506140i) q^{58} +(0.208882 - 0.915173i) q^{59} +(-0.0918083 + 0.402238i) q^{60} +(-2.54241 + 1.22436i) q^{61} +(-1.86708 - 2.34125i) q^{62} +(4.20747 - 5.27600i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-6.04363 + 2.91046i) q^{65} +(-0.786140 + 0.985789i) q^{66} +(-6.91275 - 8.66831i) q^{67} +(-4.11993 + 1.98405i) q^{68} +(-0.317959 + 1.39307i) q^{69} +(-0.530653 + 2.32494i) q^{70} +(2.78264 + 3.48932i) q^{71} +(2.54954 + 1.22779i) q^{72} +(-2.99578 - 13.1254i) q^{73} +(5.66850 + 2.72981i) q^{74} +(-0.257241 + 0.322570i) q^{75} +(0.780736 - 3.42063i) q^{76} +(-4.54390 + 5.69787i) q^{77} +(-0.615843 - 2.69818i) q^{78} +0.820024 q^{79} -1.00000 q^{80} +(-1.66823 - 7.30899i) q^{81} +(-4.99515 - 6.26372i) q^{82} +(6.12377 - 2.94905i) q^{83} +(-0.886463 - 0.426898i) q^{84} -4.57277 q^{85} +(-0.414474 - 6.54433i) q^{86} +0.267097 q^{87} +(-2.75340 - 1.32597i) q^{88} +(8.98332 - 4.32614i) q^{89} +(1.76434 + 2.21241i) q^{90} +(-3.55958 - 15.5955i) q^{91} -3.46329 q^{92} +1.23551 q^{93} +(-2.57783 - 11.2942i) q^{94} +(2.18757 - 2.74313i) q^{95} +(0.0918083 - 0.402238i) q^{96} +(-5.31364 + 6.66310i) q^{97} +(1.18301 + 0.569709i) q^{98} +(1.92434 + 8.43110i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) $ 18 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^7 - 3 * q^8 - 7 * q^9	\( 18 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{7} - 3 q^{8} - 7 q^{9} + 3 q^{10} + 9 q^{11} + 2 q^{12} + 4 q^{13} + 13 q^{14} + 5 q^{15} - 3 q^{16} - q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 2 q^{21} - 12 q^{22} - 19 q^{23} - 5 q^{24} - 3 q^{25} + 4 q^{26} + 17 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} - 13 q^{31} - 3 q^{32} - 42 q^{33} - 8 q^{34} + 15 q^{35} + 2 q^{37} + 12 q^{38} - 39 q^{39} + 3 q^{40} - 4 q^{41} - 2 q^{42} - 13 q^{43} - 12 q^{44} - 7 q^{45} + 16 q^{46} + 16 q^{47} + 2 q^{48} + 4 q^{49} + 18 q^{50} + 7 q^{51} - 10 q^{52} + 14 q^{53} - 4 q^{54} + 12 q^{55} - 15 q^{56} + 45 q^{57} + 24 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} + 50 q^{62} - 33 q^{63} - 3 q^{64} - 4 q^{65} + 5 q^{67} + 13 q^{68} + 4 q^{69} + 15 q^{70} - 3 q^{71} + 7 q^{72} - 22 q^{73} - 12 q^{74} - 5 q^{75} + 12 q^{76} - 24 q^{77} + 31 q^{78} - 38 q^{79} - 18 q^{80} + 22 q^{81} - 11 q^{82} - 26 q^{83} - 2 q^{84} + 8 q^{85} - 41 q^{86} - 22 q^{87} - 12 q^{88} + 52 q^{89} + 7 q^{90} - 14 q^{91} + 2 q^{92} - 6 q^{93} + 2 q^{94} + 2 q^{95} + 2 q^{96} + 27 q^{97} + 32 q^{98} + 36 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^7 - 3 * q^8 - 7 * q^9 + 3 * q^10 + 9 * q^11 + 2 * q^12 + 4 * q^13 + 13 * q^14 + 5 * q^15 - 3 * q^16 - q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 2 * q^21 - 12 * q^22 - 19 * q^23 - 5 * q^24 - 3 * q^25 + 4 * q^26 + 17 * q^27 - q^28 - 4 * q^29 - 2 * q^30 - 13 * q^31 - 3 * q^32 - 42 * q^33 - 8 * q^34 + 15 * q^35 + 2 * q^37 + 12 * q^38 - 39 * q^39 + 3 * q^40 - 4 * q^41 - 2 * q^42 - 13 * q^43 - 12 * q^44 - 7 * q^45 + 16 * q^46 + 16 * q^47 + 2 * q^48 + 4 * q^49 + 18 * q^50 + 7 * q^51 - 10 * q^52 + 14 * q^53 - 4 * q^54 + 12 * q^55 - 15 * q^56 + 45 * q^57 + 24 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 + 50 * q^62 - 33 * q^63 - 3 * q^64 - 4 * q^65 + 5 * q^67 + 13 * q^68 + 4 * q^69 + 15 * q^70 - 3 * q^71 + 7 * q^72 - 22 * q^73 - 12 * q^74 - 5 * q^75 + 12 * q^76 - 24 * q^77 + 31 * q^78 - 38 * q^79 - 18 * q^80 + 22 * q^81 - 11 * q^82 - 26 * q^83 - 2 * q^84 + 8 * q^85 - 41 * q^86 - 22 * q^87 - 12 * q^88 + 52 * q^89 + 7 * q^90 - 14 * q^91 + 2 * q^92 - 6 * q^93 + 2 * q^94 + 2 * q^95 + 2 * q^96 + 27 * q^97 + 32 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−0.900969	−	0.433884i	−0.637081	−	0.306802i
$2$	−0.900969	−	0.433884i	−0.637081	−	0.306802i
$3$	0.371724	−	0.179013i	0.214615	−	0.103353i	−0.323488	−	0.946232i	$-0.604855\pi$
$3$	0.371724	−	0.179013i	0.214615	−	0.103353i	0.538103	+	0.842879i	$0.319141\pi$
$4$	0.623490	+	0.781831i	0.311745	+	0.390916i
$5$	0.222521	+	0.974928i	0.0995144	+	0.436001i
$5$	0.222521	+	0.974928i	0.0995144	+	0.436001i
$6$	−0.412583			−0.168436
$7$	−2.38473			−0.901345			−0.450672	−	0.892689i	$-0.648816\pi$
$7$	−2.38473			−0.901345			−0.450672	+	0.892689i	$0.648816\pi$
$8$	−0.222521	−	0.974928i	−0.0786730	−	0.344689i
$9$	−1.76434	+	2.21241i	−0.588112	+	0.737469i
$10$	0.222521	−	0.974928i	0.0703673	−	0.308299i
$11$	1.90541	−	2.38931i	0.574504	−	0.720405i	−0.406661	−	0.913579i	$-0.633307\pi$
$11$	1.90541	−	2.38931i	0.574504	−	0.720405i	0.981164	+	0.193174i	$0.0618783\pi$
$12$	0.371724	+	0.179013i	0.107308	+	0.0516766i
$13$	1.49265	+	6.53974i	0.413987	+	1.81380i	0.564792	+	0.825233i	$0.308956\pi$
$13$	1.49265	+	6.53974i	0.413987	+	1.81380i	−0.150804	+	0.988564i	$0.548186\pi$
$14$	2.14857	+	1.03470i	0.574230	+	0.276534i
$15$	0.257241	+	0.322570i	0.0664194	+	0.0832873i
$16$	−0.222521	+	0.974928i	−0.0556302	+	0.243732i
$17$	−1.01754	+	4.45813i	−0.246789	+	1.08125i	0.687905	+	0.725801i	$0.258531\pi$
$17$	−1.01754	+	4.45813i	−0.246789	+	1.08125i	−0.934694	+	0.355453i	$0.884326\pi$
$18$	2.54954	−	1.22779i	0.600932	−	0.289394i
$19$	−2.18757	−	2.74313i	−0.501864	−	0.629317i	0.464785	−	0.885424i	$-0.346132\pi$
$19$	−2.18757	−	2.74313i	−0.501864	−	0.629317i	−0.966649	+	0.256106i	$0.917560\pi$
$20$	−0.623490	+	0.781831i	−0.139417	+	0.174823i
$21$	−0.886463	+	0.426898i	−0.193442	+	0.0931568i
$22$	−2.75340	+	1.32597i	−0.587027	+	0.282697i
$23$	−2.15933	+	2.70771i	−0.450251	+	0.564597i	−0.954213	−	0.299129i	$-0.903304\pi$
$23$	−2.15933	+	2.70771i	−0.450251	+	0.564597i	0.503962	+	0.863726i	$0.331875\pi$
$24$	−0.257241	−	0.322570i	−0.0525091	−	0.0658444i
$25$	−0.900969	+	0.433884i	−0.180194	+	0.0867767i
$26$	1.49265	−	6.53974i	0.292733	−	1.28255i
$27$	−0.535222	+	2.34496i	−0.103003	+	0.451288i
$28$	−1.48686	−	1.86446i	−0.280990	−	0.352350i
$29$	0.583267	+	0.280886i	0.108310	+	0.0521593i	0.487254	−	0.873260i	$-0.337999\pi$
$29$	0.583267	+	0.280886i	0.108310	+	0.0521593i	−0.378944	+	0.925419i	$0.623713\pi$
$30$	−0.0918083	−	0.402238i	−0.0167618	−	0.0734384i
$31$	2.69801	+	1.29929i	0.484577	+	0.233360i	0.660189	−	0.751099i	$-0.270476\pi$
$31$	2.69801	+	1.29929i	0.484577	+	0.233360i	−0.175612	+	0.984459i	$0.556190\pi$
$32$	0.623490	−	0.781831i	0.110218	−	0.138210i
$33$	0.280570	−	1.22926i	0.0488410	−	0.213986i
$34$	2.85108	−	3.57514i	0.488956	−	0.613131i
$35$	−0.530653	−	2.32494i	−0.0896968	−	0.392987i
$36$	−2.82978			−0.471629
$37$	−6.29157			−1.03433			−0.517164	−	0.855887i	$-0.673012\pi$
$37$	−6.29157			−1.03433			−0.517164	+	0.855887i	$0.673012\pi$
$38$	0.780736	+	3.42063i	0.126652	+	0.554899i
$39$	1.72555	+	2.16377i	0.276310	+	0.346481i
$40$	0.900969	−	0.433884i	0.142456	−	0.0686030i
$41$	7.21820	+	3.47610i	1.12729	+	0.542876i	0.902138	−	0.431447i	$-0.141997\pi$
$41$	7.21820	+	3.47610i	1.12729	+	0.542876i	0.225155	+	0.974323i	$0.427711\pi$
$42$	0.983900			0.151819
$43$	3.21291	+	5.71640i	0.489963	+	0.871743i
$43$	3.21291	+	5.71640i	0.489963	+	0.871743i
$44$	3.05604			0.460716
$45$	−2.54954	−	1.22779i	−0.380063	−	0.183029i
$46$	3.12032	−	1.50267i	0.460066	−	0.221556i
$47$	7.22293	+	9.05726i	1.05357	+	1.32114i	0.945008	+	0.327048i	$0.106054\pi$
$47$	7.22293	+	9.05726i	1.05357	+	1.32114i	0.108564	+	0.994089i	$0.465375\pi$
$48$	0.0918083	+	0.402238i	0.0132514	+	0.0580581i
$49$	−1.31305			−0.187578
$50$	1.00000			0.141421
$51$	0.419819	+	1.83935i	0.0587864	+	0.257560i
$52$	−4.18232	+	5.24446i	−0.579983	+	0.727276i
$53$	1.43260	−	6.27663i	0.196783	−	0.862161i	−0.776054	−	0.630667i	$-0.782781\pi$
$53$	1.43260	−	6.27663i	0.196783	−	0.862161i	0.972836	−	0.231494i	$-0.0743614\pi$
$54$	1.49966	−	1.88051i	0.204078	−	0.255905i
$55$	2.75340	+	1.32597i	0.371269	+	0.178794i
$56$	0.530653	+	2.32494i	0.0709115	+	0.310684i
$57$	−1.30423	−	0.628084i	−0.172749	−	0.0831918i
$58$	−0.403633	−	0.506140i	−0.0529996	−	0.0664594i
$59$	0.208882	−	0.915173i	0.0271942	−	0.119145i	−0.959509	−	0.281678i	$-0.909109\pi$
$59$	0.208882	−	0.915173i	0.0271942	−	0.119145i	0.986703	+	0.162532i	$0.0519662\pi$
$60$	−0.0918083	+	0.402238i	−0.0118524	+	0.0519288i
$61$	−2.54241	+	1.22436i	−0.325522	+	0.156763i	−0.589506	−	0.807764i	$-0.700678\pi$
$61$	−2.54241	+	1.22436i	−0.325522	+	0.156763i	0.263984	+	0.964527i	$0.414963\pi$
$62$	−1.86708	−	2.34125i	−0.237120	−	0.297339i
$63$	4.20747	−	5.27600i	0.530092	−	0.664714i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	−6.04363	+	2.91046i	−0.749620	+	0.360998i
$66$	−0.786140	+	0.985789i	−0.0967672	+	0.121342i
$67$	−6.91275	−	8.66831i	−0.844527	−	1.05900i	−0.997493	−	0.0707714i	$-0.977454\pi$
$67$	−6.91275	−	8.66831i	−0.844527	−	1.05900i	0.152966	−	0.988231i	$-0.451118\pi$
$68$	−4.11993	+	1.98405i	−0.499615	+	0.240602i
$69$	−0.317959	+	1.39307i	−0.0382778	+	0.167706i
$70$	−0.530653	+	2.32494i	−0.0634252	+	0.277884i
$71$	2.78264	+	3.48932i	0.330238	+	0.414106i	0.919035	−	0.394175i	$-0.128970\pi$
$71$	2.78264	+	3.48932i	0.330238	+	0.414106i	−0.588797	+	0.808281i	$0.700398\pi$
$72$	2.54954	+	1.22779i	0.300466	+	0.144697i
$73$	−2.99578	−	13.1254i	−0.350629	−	1.53621i	−0.775732	−	0.631062i	$-0.782619\pi$
$73$	−2.99578	−	13.1254i	−0.350629	−	1.53621i	0.425103	−	0.905145i	$-0.360238\pi$
$74$	5.66850	+	2.72981i	0.658950	+	0.317334i
$75$	−0.257241	+	0.322570i	−0.0297036	+	0.0372472i
$76$	0.780736	−	3.42063i	0.0895566	−	0.392373i
$77$	−4.54390	+	5.69787i	−0.517826	+	0.649333i
$78$	−0.615843	−	2.69818i	−0.0697305	−	0.305509i
$79$	0.820024			0.0922599			0.0461300	−	0.998935i	$-0.485311\pi$
$79$	0.820024			0.0922599			0.0461300	+	0.998935i	$0.485311\pi$
$80$	−1.00000			−0.111803
$81$	−1.66823	−	7.30899i	−0.185359	−	0.812110i
$82$	−4.99515	−	6.26372i	−0.551622	−	0.691712i
$83$	6.12377	−	2.94905i	0.672171	−	0.323700i	−0.0664808	−	0.997788i	$-0.521177\pi$
$83$	6.12377	−	2.94905i	0.672171	−	0.323700i	0.738652	+	0.674087i	$0.235463\pi$
$84$	−0.886463	−	0.426898i	−0.0967211	−	0.0465784i
$85$	−4.57277			−0.495987
$86$	−0.414474	−	6.54433i	−0.0446939	−	0.705693i
$87$	0.267097			0.0286358
$88$	−2.75340	−	1.32597i	−0.293514	−	0.141349i
$89$	8.98332	−	4.32614i	0.952230	−	0.458570i	0.107762	−	0.994177i	$-0.465631\pi$
$89$	8.98332	−	4.32614i	0.952230	−	0.458570i	0.844467	+	0.535607i	$0.179917\pi$
$90$	1.76434	+	2.21241i	0.185977	+	0.233208i
$91$	−3.55958	−	15.5955i	−0.373145	−	1.63486i
$92$	−3.46329			−0.361073
$93$	1.23551			0.128116
$94$	−2.57783	−	11.2942i	−0.265883	−	1.16491i
$95$	2.18757	−	2.74313i	0.224440	−	0.281439i
$96$	0.0918083	−	0.402238i	0.00937014	−	0.0410533i
$97$	−5.31364	+	6.66310i	−0.539519	+	0.676535i	−0.974625	−	0.223844i	$-0.928139\pi$
$97$	−5.31364	+	6.66310i	−0.539519	+	0.676535i	0.435106	+	0.900379i	$0.356711\pi$
$98$	1.18301	+	0.569709i	0.119502	+	0.0575493i
$99$	1.92434	+	8.43110i	0.193404	+	0.847357i
$100$	−0.900969	−	0.433884i	−0.0900969	−	0.0433884i
$101$	−1.53076	−	1.91951i	−0.152316	−	0.190998i	0.699819	−	0.714320i	$-0.253264\pi$
$101$	−1.53076	−	1.91951i	−0.152316	−	0.190998i	−0.852135	+	0.523322i	$0.824693\pi$
$102$	0.419819	−	1.83935i	0.0415682	−	0.182122i
$103$	0.618057	−	2.70788i	0.0608989	−	0.266816i	−0.935308	−	0.353836i	$-0.884877\pi$
$103$	0.618057	−	2.70788i	0.0608989	−	0.266816i	0.996207	+	0.0870199i	$0.0277344\pi$
$104$	6.04363	−	2.91046i	0.592626	−	0.285394i
$105$	−0.613452	−	0.769244i	−0.0598667	−	0.0750705i
$106$	−4.01405	+	5.03346i	−0.389879	+	0.488893i
$107$	−1.74818	+	0.841879i	−0.169003	+	0.0813875i	−0.516473	−	0.856304i	$-0.672755\pi$
$107$	−1.74818	+	0.841879i	−0.169003	+	0.0813875i	0.347470	+	0.937691i	$0.387041\pi$
$108$	−2.16707	+	1.04361i	−0.208526	+	0.100421i
$109$	−0.0894965	+	0.112225i	−0.00857221	+	0.0107492i	−0.786099	−	0.618100i	$-0.787902\pi$
$109$	−0.0894965	+	0.112225i	−0.00857221	+	0.0107492i	0.777527	+	0.628850i	$0.216474\pi$
$110$	−1.90541	−	2.38931i	−0.181674	−	0.227812i
$111$	−2.33873	+	1.12627i	−0.221982	+	0.106901i
$112$	0.530653	−	2.32494i	0.0501420	−	0.219686i
$113$	0.550828	−	2.41334i	0.0518176	−	0.227028i	−0.942388	−	0.334521i	$-0.891425\pi$
$113$	0.550828	−	2.41334i	0.0518176	−	0.227028i	0.994206	+	0.107494i	$0.0342825\pi$
$114$	0.902555	+	1.13177i	0.0845320	+	0.106000i
$115$	−3.12032	−	1.50267i	−0.290971	−	0.140124i
$116$	0.144055	+	0.631146i	0.0133752	+	0.0586004i
$117$	−17.1021	−	8.23594i	−1.58109	−	0.761413i
$118$	−0.585275	+	0.733912i	−0.0538789	+	0.0675621i
$119$	2.42656	−	10.6314i	0.222442	−	0.974583i
$120$	0.257241	−	0.322570i	0.0234828	−	0.0294465i
$121$	0.369516	+	1.61895i	0.0335923	+	0.147178i
$122$	2.82186			0.255479
$123$	3.30545			0.298042
$124$	0.666354	+	2.91949i	0.0598403	+	0.262178i
$125$	−0.623490	−	0.781831i	−0.0557666	−	0.0699291i
$126$	−6.07997	+	2.92796i	−0.541647	+	0.260843i
$127$	−14.7701	−	7.11292i	−1.31064	−	0.631170i	−0.357558	−	0.933891i	$-0.616391\pi$
$127$	−14.7701	−	7.11292i	−1.31064	−	0.631170i	−0.953079	+	0.302721i	$0.902105\pi$
$128$	1.00000			0.0883883
$129$	2.21762	+	1.54977i	0.195251	+	0.136450i
$130$	6.70792			0.588323
$131$	−5.69741	−	2.74373i	−0.497785	−	0.239721i	0.168107	−	0.985769i	$-0.446235\pi$
$131$	−5.69741	−	2.74373i	−0.497785	−	0.239721i	−0.665892	+	0.746048i	$0.731949\pi$
$132$	1.13601	−	0.547072i	0.0988766	−	0.0476165i
$133$	5.21678	+	6.54164i	0.452352	+	0.567232i
$134$	2.46713	+	10.8092i	0.213128	+	0.933773i
$135$	−2.40526			−0.207012
$136$	4.57277			0.392112
$137$	1.59203	+	6.97513i	0.136016	+	0.595925i	0.996287	+	0.0860889i	$0.0274369\pi$
$137$	1.59203	+	6.97513i	0.136016	+	0.595925i	−0.860271	+	0.509836i	$0.829706\pi$
$138$	0.890901	−	1.11716i	0.0758386	−	0.0950986i
$139$	3.83699	−	16.8110i	0.325449	−	1.42589i	−0.502253	−	0.864720i	$-0.667496\pi$
$139$	3.83699	−	16.8110i	0.325449	−	1.42589i	0.827703	−	0.561167i	$-0.189647\pi$
$140$	1.48686	−	1.86446i	0.125662	−	0.157576i
$141$	4.30630	+	2.07381i	0.362656	+	0.174646i
$142$	−0.993112	−	4.35111i	−0.0833401	−	0.365137i
$143$	18.4696	+	8.89449i	1.54451	+	0.743794i
$144$	−1.76434	−	2.21241i	−0.147028	−	0.184367i
$145$	−0.144055	+	0.631146i	−0.0119631	+	0.0524138i
$146$	−2.99578	+	13.1254i	−0.247932	+	1.08626i
$147$	−0.488091	+	0.235052i	−0.0402571	+	0.0193868i
$148$	−3.92273	−	4.91894i	−0.322446	−	0.404335i
$149$	10.5875	−	13.2763i	0.867362	−	1.08764i	−0.128032	−	0.991770i	$-0.540866\pi$
$149$	10.5875	−	13.2763i	0.867362	−	1.08764i	0.995394	−	0.0958680i	$-0.0305627\pi$
$150$	0.371724	−	0.179013i	0.0303512	−	0.0146163i
$151$	7.29482	−	3.51300i	0.593644	−	0.285884i	−0.112840	−	0.993613i	$-0.535995\pi$
$151$	7.29482	−	3.51300i	0.593644	−	0.285884i	0.706484	+	0.707729i	$0.250280\pi$
$152$	−2.18757	+	2.74313i	−0.177436	+	0.222497i
$153$	−8.06791	−	10.1168i	−0.652252	−	0.817898i
$154$	6.56613	−	3.16208i	0.529114	−	0.254808i
$155$	−0.666354	+	2.91949i	−0.0535228	+	0.234499i
$156$	−0.615843	+	2.69818i	−0.0493069	+	0.216028i
$157$	15.4309	+	19.3498i	1.23152	+	1.54428i	0.738486	+	0.674269i	$0.235541\pi$
$157$	15.4309	+	19.3498i	1.23152	+	1.54428i	0.493035	+	0.870009i	$0.335887\pi$
$158$	−0.738816	−	0.355795i	−0.0587771	−	0.0283055i
$159$	−0.591066	−	2.58963i	−0.0468746	−	0.205371i
$160$	0.900969	+	0.433884i	0.0712278	+	0.0343015i
$161$	5.14942	−	6.45717i	0.405831	−	0.508896i
$162$	−1.66823	+	7.30899i	−0.131068	+	0.574249i
$163$	−2.49545	+	3.12920i	−0.195459	+	0.245098i	−0.869897	−	0.493234i	$-0.835815\pi$
$163$	−2.49545	+	3.12920i	−0.195459	+	0.245098i	0.674438	+	0.738332i	$0.264386\pi$
$164$	1.78275	+	7.81073i	0.139209	+	0.609915i
$165$	1.26087			0.0981587
$166$	−6.79687			−0.527539
$167$	−3.41832	−	14.9766i	−0.264517	−	1.15893i	−0.916291	−	0.400513i	$-0.868832\pi$
$167$	−3.41832	−	14.9766i	−0.264517	−	1.15893i	0.651774	−	0.758414i	$-0.274025\pi$
$168$	0.613452	+	0.769244i	0.0473288	+	0.0593485i
$169$	−28.8276	+	13.8826i	−2.21751	+	1.06789i
$170$	4.11993	+	1.98405i	0.315984	+	0.152170i
$171$	9.92854			0.759254
$172$	−2.46605	+	6.07607i	−0.188034	+	0.463296i
$173$	17.8980			1.36076			0.680379	−	0.732860i	$-0.261815\pi$
$173$	17.8980			1.36076			0.680379	+	0.732860i	$0.261815\pi$
$174$	−0.240646	−	0.115889i	−0.0182433	−	0.00878551i
$175$	2.14857	−	1.03470i	0.162417	−	0.0782158i
$176$	1.90541	+	2.38931i	0.143626	+	0.180101i
$177$	−0.0861812	−	0.377585i	−0.00647778	−	0.0283810i
$178$	−9.97073			−0.747338
$179$	−11.8338			−0.884499			−0.442250	−	0.896892i	$-0.645819\pi$
$179$	−11.8338			−0.884499			−0.442250	+	0.896892i	$0.645819\pi$
$180$	−0.629684	−	2.75883i	−0.0469339	−	0.205631i
$181$	−7.53819	+	9.45259i	−0.560309	+	0.702605i	−0.978615	−	0.205701i	$-0.934053\pi$
$181$	−7.53819	+	9.45259i	−0.560309	+	0.702605i	0.418306	+	0.908306i	$0.362624\pi$
$182$	−3.55958	+	15.5955i	−0.263854	+	1.15602i
$183$	−0.725898	+	0.910247i	−0.0536599	+	0.0672874i
$184$	3.12032	+	1.50267i	0.230033	+	0.110778i
$185$	−1.40001	−	6.13382i	−0.102930	−	0.450968i
$186$	−1.11315	−	0.536066i	−0.0816203	−	0.0393063i
$187$	8.71302	+	10.9258i	0.637159	+	0.798973i
$188$	−2.57783	+	11.2942i	−0.188008	+	0.823716i
$189$	1.27636	−	5.59210i	0.0928416	−	0.406766i
$190$	−3.16114	+	1.52232i	−0.229333	+	0.110441i
$191$	16.2961	+	20.4347i	1.17914	+	1.47860i	0.843926	+	0.536459i	$0.180238\pi$
$191$	16.2961	+	20.4347i	1.17914	+	1.47860i	0.335218	+	0.942141i	$0.391190\pi$
$192$	−0.257241	+	0.322570i	−0.0185648	+	0.0232795i
$193$	−13.7803	+	6.63623i	−0.991926	+	0.477686i	−0.858191	−	0.513331i	$-0.828411\pi$
$193$	−13.7803	+	6.63623i	−0.991926	+	0.477686i	−0.133735	+	0.991017i	$0.542697\pi$
$194$	7.67844	−	3.69774i	0.551280	−	0.265482i
$195$	−1.72555	+	2.16377i	−0.123569	+	0.154951i
$196$	−0.818671	−	1.02658i	−0.0584765	−	0.0733272i
$197$	16.2993	−	7.84933i	1.16128	−	0.559241i	0.248874	−	0.968536i	$-0.419939\pi$
$197$	16.2993	−	7.84933i	1.16128	−	0.559241i	0.912402	+	0.409294i	$0.134225\pi$
$198$	1.92434	−	8.43110i	0.136757	−	0.599172i
$199$	1.48993	−	6.52781i	0.105618	−	0.462744i	−0.894266	−	0.447536i	$-0.852302\pi$
$199$	1.48993	−	6.52781i	0.105618	−	0.462744i	0.999884	−	0.0152084i	$-0.00484116\pi$
$200$	0.623490	+	0.781831i	0.0440874	+	0.0552838i
$201$	−4.12138	−	1.98475i	−0.290699	−	0.139993i
$202$	0.546321	+	2.39359i	0.0384390	+	0.168412i
$203$	−1.39094	−	0.669839i	−0.0976245	−	0.0470135i
$204$	−1.17631	+	1.47504i	−0.0823579	+	0.103274i
$205$	−1.78275	+	7.81073i	−0.124513	+	0.545525i
$206$	−1.73176	+	2.17155i	−0.120657	+	0.151299i
$207$	−2.18078	−	9.55463i	−0.151575	−	0.664092i
$208$	−6.70792			−0.465111
$209$	−10.7224			−0.741686
$210$	0.218938	+	0.959231i	0.0151082	+	0.0661933i
$211$	13.9965	+	17.5511i	0.963560	+	1.20827i	0.978050	+	0.208371i	$0.0668162\pi$
$211$	13.9965	+	17.5511i	0.963560	+	1.20827i	−0.0144896	+	0.999895i	$0.504612\pi$
$212$	5.80048	−	2.79336i	0.398378	−	0.191849i
$213$	1.65901	+	0.798935i	0.113673	+	0.0547421i
$214$	1.94033			0.132638
$215$	−4.85814	+	4.40437i	−0.331322	+	0.300376i
$216$	2.40526			0.163658
$217$	−6.43404	−	3.09847i	−0.436771	−	0.210338i
$218$	0.129326	−	0.0622802i	0.00875907	−	0.00421815i
$219$	−3.46321	−	4.34273i	−0.234022	−	0.293455i
$220$	0.680034	+	2.97942i	0.0458479	+	0.200873i
$221$	−30.6738			−2.06334
$222$	2.59579			0.174218
$223$	4.21273	+	18.4572i	0.282105	+	1.23598i	0.895089	+	0.445888i	$0.147112\pi$
$223$	4.21273	+	18.4572i	0.282105	+	1.23598i	−0.612984	+	0.790095i	$0.710031\pi$
$224$	−1.48686	+	1.86446i	−0.0993448	+	0.124574i
$225$	0.629684	−	2.75883i	0.0419790	−	0.183922i
$226$	−1.54339	+	1.93535i	−0.102665	+	0.128737i
$227$	4.44604	+	2.14110i	0.295094	+	0.142110i	0.575573	−	0.817750i	$-0.304779\pi$
$227$	4.44604	+	2.14110i	0.295094	+	0.142110i	−0.280479	+	0.959860i	$0.590493\pi$
$228$	−0.322118	−	1.41129i	−0.0213328	−	0.0934651i
$229$	17.6458	+	8.49775i	1.16606	+	0.561547i	0.913821	−	0.406116i	$-0.133117\pi$
$229$	17.6458	+	8.49775i	1.16606	+	0.561547i	0.252244	+	0.967664i	$0.418832\pi$
$230$	2.15933	+	2.70771i	0.142382	+	0.178541i
$231$	−0.669085	+	2.93145i	−0.0440226	+	0.192876i
$232$	0.144055	−	0.631146i	0.00945767	−	0.0414368i
$233$	4.85784	−	2.33941i	0.318248	−	0.153260i	−0.267939	−	0.963436i	$-0.586343\pi$
$233$	4.85784	−	2.33941i	0.318248	−	0.153260i	0.586187	+	0.810176i	$0.300628\pi$
$234$	11.8350	+	14.8407i	0.773680	+	0.970164i
$235$	−7.22293	+	9.05726i	−0.471172	+	0.590831i
$236$	0.845747	−	0.407290i	0.0550534	−	0.0265123i
$237$	0.304823	−	0.146795i	0.0198004	−	0.00953536i
$238$	−6.79906	+	8.52576i	−0.440718	+	0.552643i
$239$	17.8783	+	22.4187i	1.15645	+	1.45015i	0.870680	+	0.491850i	$0.163679\pi$
$239$	17.8783	+	22.4187i	1.15645	+	1.45015i	0.285773	+	0.958297i	$0.407750\pi$
$240$	−0.371724	+	0.179013i	−0.0239947	+	0.0115552i
$241$	1.78409	−	7.81662i	0.114923	−	0.503513i	−0.884400	−	0.466730i	$-0.845432\pi$
$241$	1.78409	−	7.81662i	0.114923	−	0.503513i	0.999323	−	0.0367826i	$-0.0117109\pi$
$242$	0.369516	−	1.61895i	0.0237534	−	0.104070i
$243$	−6.42750	−	8.05983i	−0.412324	−	0.517038i
$244$	−2.54241	−	1.22436i	−0.162761	−	0.0783815i
$245$	−0.292180	−	1.28012i	−0.0186667	−	0.0817842i
$246$	−2.97810	−	1.43418i	−0.189877	−	0.0914399i
$247$	14.6741	−	18.4007i	0.933689	−	1.17081i
$248$	0.666354	−	2.91949i	0.0423135	−	0.185388i
$249$	1.74843	−	2.19247i	0.110803	−	0.138942i
$250$	0.222521	+	0.974928i	0.0140735	+	0.0616599i
$251$	14.4569			0.912514			0.456257	−	0.889848i	$-0.349190\pi$
$251$	14.4569			0.912514			0.456257	+	0.889848i	$0.349190\pi$
$252$	6.74826			0.425100
$253$	2.35516	+	10.3186i	0.148067	+	0.648726i
$254$	10.2212	+	12.8170i	0.641338	+	0.804212i
$255$	−1.69981	+	0.818586i	−0.106446	+	0.0512618i
$256$	−0.900969	−	0.433884i	−0.0563106	−	0.0271177i
$257$	−0.118139			−0.00736930			−0.00368465	−	0.999993i	$-0.501173\pi$
$257$	−0.118139			−0.00736930			−0.00368465	+	0.999993i	$0.501173\pi$
$258$	−1.32559	−	2.35849i	−0.0825276	−	0.146833i
$259$	15.0037			0.932285
$260$	−6.04363	−	2.91046i	−0.374810	−	0.180499i
$261$	−1.65051	+	0.794845i	−0.102164	+	0.0491997i
$262$	3.94273	+	4.94403i	0.243583	+	0.305443i
$263$	−3.32393	−	14.5631i	−0.204962	−	0.897998i	−0.967862	−	0.251481i	$-0.919082\pi$
$263$	−3.32393	−	14.5631i	−0.204962	−	0.897998i	0.762900	−	0.646517i	$-0.223775\pi$
$264$	−1.26087			−0.0776013
$265$	6.43804			0.395486
$266$	−1.86185	−	8.15729i	−0.114157	−	0.500155i
$267$	2.56488	−	3.21626i	0.156968	−	0.196832i
$268$	2.46713	−	10.8092i	0.150704	−	0.660277i
$269$	−16.8998	+	21.1917i	−1.03040	+	1.29208i	−0.0748647	+	0.997194i	$0.523852\pi$
$269$	−16.8998	+	21.1917i	−1.03040	+	1.29208i	−0.955533	+	0.294884i	$0.904719\pi$
$270$	2.16707	+	1.04361i	0.131884	+	0.0635118i
$271$	−4.64206	−	20.3382i	−0.281985	−	1.23546i	−0.895244	−	0.445576i	$-0.852999\pi$
$271$	−4.64206	−	20.3382i	−0.281985	−	1.23546i	0.613259	−	0.789882i	$-0.289858\pi$
$272$	−4.11993	−	1.98405i	−0.249807	−	0.120301i
$273$	−4.11498	−	5.16003i	−0.249050	−	0.312299i
$274$	1.59203	−	6.97513i	0.0961779	−	0.421383i
$275$	−0.680034	+	2.97942i	−0.0410076	+	0.179666i
$276$	−1.28739	+	0.619974i	−0.0774918	+	0.0373181i
$277$	5.87958	+	7.37276i	0.353270	+	0.442986i	0.926436	−	0.376453i	$-0.122856\pi$
$277$	5.87958	+	7.37276i	0.353270	+	0.442986i	−0.573166	+	0.819439i	$0.694285\pi$
$278$	−10.7510	+	13.4813i	−0.644803	+	0.808557i
$279$	−7.63477	+	3.67671i	−0.457081	+	0.220119i
$280$	−2.14857	+	1.03470i	−0.128402	+	0.0618350i
$281$	−9.74202	+	12.2161i	−0.581160	+	0.728752i	−0.982310	−	0.187260i	$-0.940039\pi$
$281$	−9.74202	+	12.2161i	−0.581160	+	0.728752i	0.401150	+	0.916012i	$0.368611\pi$
$282$	−2.98005	−	3.73687i	−0.177460	−	0.222527i
$283$	16.6638	−	8.02486i	0.990560	−	0.477028i	0.132835	−	0.991138i	$-0.457592\pi$
$283$	16.6638	−	8.02486i	0.990560	−	0.477028i	0.857724	+	0.514110i	$0.171878\pi$
$284$	−0.993112	+	4.35111i	−0.0589303	+	0.258191i
$285$	0.322118	−	1.41129i	0.0190806	−	0.0835977i
$286$	−12.7814	−	16.0273i	−0.755777	−	0.947715i
$287$	−17.2135	−	8.28958i	−1.01608	−	0.489318i
$288$	0.629684	+	2.75883i	0.0371045	+	0.162565i
$289$	−3.52303	−	1.69660i	−0.207237	−	0.0998002i
$290$	0.403633	−	0.506140i	0.0237021	−	0.0297216i
$291$	−0.782429	+	3.42805i	−0.0458668	+	0.200956i
$292$	8.39398	−	10.5257i	0.491221	−	0.615971i
$293$	5.22194	+	22.8788i	0.305069	+	1.33660i	0.862367	+	0.506283i	$0.168981\pi$
$293$	5.22194	+	22.8788i	0.305069	+	1.33660i	−0.557298	+	0.830312i	$0.688162\pi$
$294$	0.541740			0.0315949
$295$	0.938708			0.0546537
$296$	1.40001	+	6.13382i	0.0813736	+	0.356521i
$297$	4.58302	+	5.74693i	0.265934	+	0.333471i
$298$	−15.2994	+	7.36780i	−0.886270	+	0.426805i
$299$	−20.9309	−	10.0798i	−1.21046	−	0.582928i
$300$	−0.412583			−0.0238205
$301$	−7.66192	−	13.6321i	−0.441626	−	0.785741i
$302$	−8.09664			−0.465909
$303$	−0.912637	−	0.439503i	−0.0524296	−	0.0252488i
$304$	3.16114	−	1.52232i	0.181304	−	0.0873112i
$305$	−1.75940	−	2.20622i	−0.100743	−	0.126328i
$306$	2.87940	+	12.6155i	0.164605	+	0.721180i
$307$	10.4196			0.594681			0.297340	−	0.954772i	$-0.403900\pi$
$307$	10.4196			0.594681			0.297340	+	0.954772i	$0.403900\pi$
$308$	−7.28785			−0.415264
$309$	−0.255000	−	1.11723i	−0.0145064	−	0.0635568i
$310$	1.86708	−	2.34125i	0.106043	−	0.132974i
$311$	−6.01539	+	26.3552i	−0.341102	+	1.49446i	0.455651	+	0.890159i	$0.349407\pi$
$311$	−6.01539	+	26.3552i	−0.341102	+	1.49446i	−0.796753	+	0.604306i	$0.793451\pi$
$312$	1.72555	−	2.16377i	0.0976902	−	0.122500i
$313$	−22.7419	−	10.9519i	−1.28545	−	0.619040i	−0.338665	−	0.940907i	$-0.609975\pi$
$313$	−22.7419	−	10.9519i	−1.28545	−	0.619040i	−0.946785	+	0.321867i	$0.895690\pi$
$314$	−5.50723	−	24.1287i	−0.310791	−	1.36166i
$315$	6.07997	+	2.92796i	0.342568	+	0.164972i
$316$	0.511277	+	0.641121i	0.0287616	+	0.0360659i
$317$	3.94301	−	17.2754i	0.221461	−	0.970285i	−0.734918	−	0.678156i	$-0.762779\pi$
$317$	3.94301	−	17.2754i	0.221461	−	0.970285i	0.956379	−	0.292129i	$-0.0943637\pi$
$318$	−0.591066	+	2.58963i	−0.0331453	+	0.145219i
$319$	1.78249	−	0.858401i	0.0998002	−	0.0480613i
$320$	−0.623490	−	0.781831i	−0.0348541	−	0.0437057i
$321$	−0.499133	+	0.625893i	−0.0278589	+	0.0349340i
$322$	−7.44113	+	3.58346i	−0.414678	+	0.199698i
$323$	14.4552	−	6.96124i	0.804307	−	0.387334i
$324$	4.67428	−	5.86136i	0.259682	−	0.325631i
$325$	−4.18232	−	5.24446i	−0.231993	−	0.290910i
$326$	3.60604	−	1.73658i	0.199720	−	0.0961800i
$327$	−0.0131783	+	0.0577378i	−0.000728760	+	0.00319291i
$328$	1.78275	−	7.81073i	0.0984358	−	0.431275i
$329$	−17.2248	−	21.5992i	−0.949631	−	1.19080i
$330$	−1.13601	−	0.547072i	−0.0625351	−	0.0301153i
$331$	−0.822845	−	3.60512i	−0.0452277	−	0.198155i	0.947267	−	0.320447i	$-0.103833\pi$
$331$	−0.822845	−	3.60512i	−0.0452277	−	0.198155i	−0.992494	+	0.122291i	$0.960976\pi$
$332$	6.12377	+	2.94905i	0.336085	+	0.161850i
$333$	11.1004	−	13.9195i	0.608300	−	0.762784i
$334$	−3.41832	+	14.9766i	−0.187042	+	0.819485i
$335$	6.91275	−	8.66831i	0.377684	−	0.473600i
$336$	−0.218938	−	0.959231i	−0.0119441	−	0.0523304i
$337$	35.5428			1.93614			0.968069	−	0.250683i	$-0.0806553\pi$
$337$	35.5428			1.93614			0.968069	+	0.250683i	$0.0806553\pi$
$338$	31.9962			1.74036
$339$	−0.227262	−	0.995701i	−0.0123432	−	0.0540791i
$340$	−2.85108	−	3.57514i	−0.154621	−	0.193889i
$341$	8.24524	−	3.97070i	0.446505	−	0.215025i
$342$	−8.94530	−	4.30783i	−0.483707	−	0.232941i
$343$	19.8244			1.07042
$344$	4.85814	−	4.40437i	0.261933	−	0.237468i
$345$	−1.42889			−0.0769291
$346$	−16.1255	−	7.76564i	−0.866914	−	0.417484i
$347$	−2.55840	+	1.23206i	−0.137342	+	0.0661404i	−0.501293	−	0.865278i	$-0.667142\pi$
$347$	−2.55840	+	1.23206i	−0.137342	+	0.0661404i	0.363951	+	0.931418i	$0.381428\pi$
$348$	0.166532	+	0.208825i	0.00892705	+	0.0111942i
$349$	−0.556336	−	2.43747i	−0.0297800	−	0.130475i	0.957853	−	0.287259i	$-0.0927442\pi$
$349$	−0.556336	−	2.43747i	−0.0297800	−	0.130475i	−0.987633	+	0.156785i	$0.949887\pi$
$350$	−2.38473			−0.127469
$351$	−16.1343			−0.861186
$352$	−0.680034	−	2.97942i	−0.0362459	−	0.158804i
$353$	−16.2293	+	20.3509i	−0.863800	+	1.08317i	0.131967	+	0.991254i	$0.457871\pi$
$353$	−16.2293	+	20.3509i	−0.863800	+	1.08317i	−0.995767	+	0.0919167i	$0.970701\pi$
$354$	−0.0861812	+	0.377585i	−0.00458048	+	0.0200684i
$355$	−2.78264	+	3.48932i	−0.147687	+	0.185194i
$356$	8.98332	+	4.32614i	0.476115	+	0.229285i
$357$	−1.00116	−	4.38635i	−0.0529868	−	0.232150i
$358$	10.6619	+	5.13449i	0.563498	+	0.271366i
$359$	−9.19262	−	11.5272i	−0.485168	−	0.608381i	0.477644	−	0.878553i	$-0.341491\pi$
$359$	−9.19262	−	11.5272i	−0.485168	−	0.608381i	−0.962812	+	0.270172i	$0.912919\pi$
$360$	−0.629684	+	2.75883i	−0.0331873	+	0.145403i
$361$	1.48861	−	6.52203i	0.0783479	−	0.343265i
$362$	10.8930	−	5.24579i	0.572523	−	0.275713i
$363$	0.427172	+	0.535656i	0.0224207	+	0.0281147i
$364$	9.97372	−	12.5066i	0.522765	−	0.655526i
$365$	12.1297	−	5.84133i	0.634895	−	0.305749i
$366$	1.04895	−	0.505149i	0.0548297	−	0.0264046i
$367$	15.8851	−	19.9193i	0.829196	−	1.03978i	−0.169333	−	0.985559i	$-0.554161\pi$
$367$	15.8851	−	19.9193i	0.829196	−	1.03978i	0.998529	−	0.0542204i	$-0.0172674\pi$
$368$	−2.15933	−	2.70771i	−0.112563	−	0.141149i
$369$	−20.4259	+	9.83659i	−1.06333	+	0.512072i
$370$	−1.40001	+	6.13382i	−0.0727828	+	0.318882i
$371$	−3.41637	+	14.9681i	−0.177369	+	0.777104i
$372$	0.770326	+	0.965958i	0.0399395	+	0.0500826i
$373$	13.6221	+	6.56004i	0.705324	+	0.339666i	0.751926	−	0.659247i	$-0.229125\pi$
$373$	13.6221	+	6.56004i	0.705324	+	0.339666i	−0.0466021	+	0.998914i	$0.514839\pi$
$374$	−3.10964	−	13.6242i	−0.160796	−	0.704492i
$375$	−0.371724	−	0.179013i	−0.0191958	−	0.00924419i
$376$	7.22293	−	9.05726i	0.372494	−	0.467093i
$377$	−0.966309	+	4.23368i	−0.0497674	+	0.218045i
$378$	−3.57628	+	4.48452i	−0.183944	+	0.230659i
$379$	−1.77116	−	7.75995i	−0.0909783	−	0.398602i	0.908850	−	0.417123i	$-0.136961\pi$
$379$	−1.77116	−	7.75995i	−0.0909783	−	0.398602i	−0.999828	+	0.0185208i	$0.994104\pi$
$380$	3.50860			0.179987
$381$	−6.76372			−0.346516
$382$	−5.81601	−	25.4816i	−0.297573	−	1.30375i
$383$	−11.4175	−	14.3171i	−0.583408	−	0.731571i	0.399282	−	0.916828i	$-0.369260\pi$
$383$	−11.4175	−	14.3171i	−0.583408	−	0.731571i	−0.982690	+	0.185257i	$0.940688\pi$
$384$	0.371724	−	0.179013i	0.0189695	−	0.00913522i
$385$	−6.56613	−	3.16208i	−0.334641	−	0.161155i
$386$	15.2949			0.778492
$387$	−18.3157	−	2.97740i	−0.931037	−	0.151350i
$388$	−8.52242			−0.432660
$389$	−25.0471	−	12.0620i	−1.26994	−	0.611569i	−0.327152	−	0.944972i	$-0.606089\pi$
$389$	−25.0471	−	12.0620i	−1.26994	−	0.611569i	−0.942784	+	0.333403i	$0.891803\pi$
$390$	2.49350	−	1.20080i	0.126263	−	0.0608051i
$391$	−9.87412	−	12.3818i	−0.499356	−	0.626172i
$392$	0.292180	+	1.28012i	0.0147573	+	0.0646561i
$393$	−2.60903			−0.131608
$394$	−18.0909			−0.911404
$395$	0.182473	+	0.799465i	0.00918119	+	0.0402254i
$396$	−5.39189	+	6.76122i	−0.270953	+	0.339764i
$397$	−8.08037	+	35.4024i	−0.405542	+	1.77680i	0.198768	+	0.980047i	$0.436306\pi$
$397$	−8.08037	+	35.4024i	−0.405542	+	1.77680i	−0.604310	+	0.796749i	$0.706551\pi$
$398$	−4.17469	+	5.23490i	−0.209258	+	0.262402i
$399$	3.11024	+	1.49781i	0.155707	+	0.0749844i
$400$	−0.222521	−	0.974928i	−0.0111260	−	0.0487464i
$401$	6.24204	+	3.00601i	0.311713	+	0.150113i	0.583199	−	0.812329i	$-0.301801\pi$
$401$	6.24204	+	3.00601i	0.311713	+	0.150113i	−0.271486	+	0.962442i	$0.587515\pi$
$402$	2.85208	+	3.57640i	0.142249	+	0.178374i
$403$	−4.46985	+	19.5837i	−0.222659	+	0.975533i
$404$	0.546321	−	2.39359i	0.0271805	−	0.119085i
$405$	6.75452	−	3.25281i	0.335635	−	0.161633i
$406$	0.962557	+	1.20701i	0.0477709	+	0.0599028i
$407$	−11.9880	+	15.0325i	−0.594225	+	0.745134i
$408$	1.69981	−	0.818586i	0.0841532	−	0.0405260i
$409$	−13.7143	+	6.60446i	−0.678128	+	0.326569i	−0.741051	−	0.671449i	$-0.765672\pi$
$409$	−13.7143	+	6.60446i	−0.678128	+	0.326569i	0.0629225	+	0.998018i	$0.479958\pi$
$410$	4.99515	−	6.26372i	0.246693	−	0.309343i
$411$	1.84043	+	2.30783i	0.0907819	+	0.113837i
$412$	2.50246	−	1.20512i	0.123287	−	0.0593721i
$413$	−0.498129	+	2.18244i	−0.0245113	+	0.107391i
$414$	−2.18078	+	9.55463i	−0.107180	+	0.469584i
$415$	4.23778	+	5.31401i	0.208024	+	0.260854i
$416$	6.04363	+	2.91046i	0.296313	+	0.142697i
$417$	−1.58308	−	6.93591i	−0.0775236	−	0.339653i
$418$	9.66057	+	4.65229i	0.472514	+	0.227551i
$419$	−6.75455	+	8.46993i	−0.329981	+	0.413783i	−0.918951	−	0.394372i	$-0.870962\pi$
$419$	−6.75455	+	8.46993i	−0.329981	+	0.413783i	0.588970	+	0.808155i	$0.299534\pi$
$420$	0.218938	−	0.959231i	0.0106831	−	0.0468057i
$421$	14.9615	−	18.7611i	0.729178	−	0.914360i	−0.269640	−	0.962961i	$-0.586905\pi$
$421$	14.9615	−	18.7611i	0.729178	−	0.914360i	0.998818	+	0.0486010i	$0.0154763\pi$
$422$	−4.99530	−	21.8858i	−0.243167	−	1.06539i
$423$	−32.7820			−1.59392
$424$	−6.43804			−0.312659
$425$	−1.01754	−	4.45813i	−0.0493578	−	0.216251i
$426$	−1.14807	−	1.43963i	−0.0556241	−	0.0697504i
$427$	6.06296	−	2.91977i	0.293407	−	0.141298i
$428$	−1.74818	−	0.841879i	−0.0845014	−	0.0406937i
$429$	8.45782			0.408348
$430$	6.28802	−	1.86033i	0.303235	−	0.0897132i
$431$	−7.93133			−0.382039			−0.191019	−	0.981586i	$-0.561179\pi$
$431$	−7.93133			−0.382039			−0.191019	+	0.981586i	$0.561179\pi$
$432$	−2.16707	−	1.04361i	−0.104263	−	0.0502105i
$433$	−6.70273	+	3.22787i	−0.322113	+	0.155121i	−0.587951	−	0.808896i	$-0.700065\pi$
$433$	−6.70273	+	3.22787i	−0.322113	+	0.155121i	0.265839	+	0.964018i	$0.414351\pi$
$434$	4.45249	+	5.58325i	0.213726	+	0.268005i
$435$	0.0594346	+	0.260400i	0.00284967	+	0.0124852i
$436$	−0.143541			−0.00687438
$437$	12.1513			0.581275
$438$	1.23601	+	5.41530i	0.0590587	+	0.258753i
$439$	−10.4873	+	13.1506i	−0.500530	+	0.627645i	−0.966349	−	0.257235i	$-0.917188\pi$
$439$	−10.4873	+	13.1506i	−0.500530	+	0.627645i	0.465819	+	0.884880i	$0.345760\pi$
$440$	0.680034	−	2.97942i	0.0324193	−	0.142038i
$441$	2.31665	−	2.90499i	0.110317	−	0.138333i
$442$	27.6361	+	13.3089i	1.31452	+	0.633038i
$443$	−6.99257	−	30.6364i	−0.332227	−	1.45558i	−0.814809	−	0.579730i	$-0.803158\pi$
$443$	−6.99257	−	30.6364i	−0.332227	−	1.45558i	0.482582	−	0.875851i	$-0.339699\pi$
$444$	−2.33873	−	1.12627i	−0.110991	−	0.0534505i
$445$	6.21665	+	7.79543i	0.294697	+	0.369539i
$446$	4.21273	−	18.4572i	0.199478	−	0.873972i
$447$	1.55900	−	6.83043i	0.0737382	−	0.323068i
$448$	2.14857	−	1.03470i	0.101510	−	0.0488848i
$449$	11.6972	+	14.6678i	0.552025	+	0.692218i	0.977061	−	0.212959i	$-0.0683100\pi$
$449$	11.6972	+	14.6678i	0.552025	+	0.692218i	−0.425036	+	0.905176i	$0.639739\pi$
$450$	−1.76434	+	2.21241i	−0.0831716	+	0.104294i
$451$	22.0591	−	10.6231i	1.03872	−	0.500223i
$452$	2.23026	−	1.07404i	0.104903	−	0.0505184i
$453$	2.08279	−	2.61173i	0.0978579	−	0.122710i
$454$	−3.07675	−	3.85812i	−0.144399	−	0.181071i
$455$	14.4124	−	6.94067i	0.675666	−	0.325383i
$456$	−0.322118	+	1.41129i	−0.0150846	+	0.0660898i
$457$	1.90693	−	8.35479i	0.0892022	−	0.390821i	−0.910542	−	0.413416i	$-0.864336\pi$
$457$	1.90693	−	8.35479i	0.0892022	−	0.390821i	0.999745	+	0.0225950i	$0.00719282\pi$
$458$	−12.2112	−	15.3124i	−0.570594	−	0.715502i
$459$	−9.90952	−	4.77217i	−0.462537	−	0.222746i
$460$	−0.770655	−	3.37646i	−0.0359320	−	0.157428i
$461$	11.7538	+	5.66033i	0.547429	+	0.263628i	0.687091	−	0.726571i	$-0.258887\pi$
$461$	11.7538	+	5.66033i	0.547429	+	0.263628i	−0.139662	+	0.990199i	$0.544602\pi$
$462$	1.87474	−	2.35084i	0.0872206	−	0.109371i
$463$	−9.02530	+	39.5424i	−0.419441	+	1.83769i	0.116171	+	0.993229i	$0.462938\pi$
$463$	−9.02530	+	39.5424i	−0.419441	+	1.83769i	−0.535613	+	0.844464i	$0.679919\pi$
$464$	−0.403633	+	0.506140i	−0.0187382	+	0.0234969i
$465$	0.274926	+	1.20453i	0.0127494	+	0.0558587i
$466$	−5.39180			−0.249770
$467$	23.8236			1.10243			0.551214	−	0.834364i	$-0.314165\pi$
$467$	23.8236			1.10243			0.551214	+	0.834364i	$0.314165\pi$
$468$	−4.22387	−	18.5060i	−0.195249	−	0.855440i
$469$	16.4851	+	20.6716i	0.761209	+	0.954526i
$470$	10.4374	−	5.02640i	0.481443	−	0.231851i
$471$	9.19990	+	4.43044i	0.423909	+	0.204144i
$472$	−0.938708			−0.0432076
$473$	19.7802	+	3.21547i	0.909494	+	0.147847i
$474$	−0.338328			−0.0155399
$475$	3.16114	+	1.52232i	0.145043	+	0.0698490i
$476$	9.82493	−	4.73144i	0.450325	−	0.216865i
$477$	11.3589	+	14.2436i	0.520087	+	0.652168i
$478$	−6.38070	−	27.9557i	−0.291847	−	1.27866i
$479$	−14.9174			−0.681593			−0.340797	−	0.940137i	$-0.610697\pi$
$479$	−14.9174			−0.681593			−0.340797	+	0.940137i	$0.610697\pi$
$480$	0.412583			0.0188317
$481$	−9.39112	−	41.1452i	−0.428198	−	1.87606i
$482$	−4.99891	+	6.26844i	−0.227694	+	0.285520i
$483$	0.758248	−	3.32210i	0.0345015	−	0.151161i
$484$	−1.03536	+	1.29830i	−0.0470618	+	0.0590137i
$485$	−7.67844	−	3.69774i	−0.348660	−	0.167906i
$486$	2.29395	+	10.0504i	0.104056	+	0.455897i
$487$	13.9766	+	6.73076i	0.633339	+	0.305000i	0.722870	−	0.690984i	$-0.242823\pi$
$487$	13.9766	+	6.73076i	0.633339	+	0.305000i	−0.0895311	+	0.995984i	$0.528537\pi$
$488$	1.75940	+	2.20622i	0.0796443	+	0.0998708i
$489$	−0.367453	+	1.60992i	−0.0166168	+	0.0728030i
$490$	−0.292180	+	1.28012i	−0.0131994	+	0.0578301i
$491$	2.26472	−	1.09063i	0.102205	−	0.0492195i	−0.382083	−	0.924128i	$-0.624793\pi$
$491$	2.26472	−	1.09063i	0.102205	−	0.0492195i	0.484288	+	0.874909i	$0.339079\pi$
$492$	2.06091	+	2.58430i	0.0929131	+	0.116509i
$493$	−1.84572	+	2.31446i	−0.0831272	+	0.104238i
$494$	−21.2046	+	10.2116i	−0.954042	+	0.459442i
$495$	−7.79151	+	3.75219i	−0.350202	+	0.168649i
$496$	−1.86708	+	2.34125i	−0.0838344	+	0.105125i
$497$	−6.63585	−	8.32109i	−0.297658	−	0.373252i
$498$	−2.52656	+	1.21673i	−0.113218	+	0.0545229i
$499$	−7.62470	+	33.4060i	−0.341329	+	1.49546i	0.454944	+	0.890520i	$0.349659\pi$
$499$	−7.62470	+	33.4060i	−0.341329	+	1.49546i	−0.796273	+	0.604938i	$0.793198\pi$
$500$	0.222521	−	0.974928i	0.00995144	−	0.0436001i
$501$	−3.95168	−	4.95525i	−0.176548	−	0.221384i
$502$	−13.0253	−	6.27263i	−0.581345	−	0.279961i
$503$	−8.35021	−	36.5847i	−0.372318	−	1.63123i	−0.720253	−	0.693711i	$-0.755974\pi$
$503$	−8.35021	−	36.5847i	−0.372318	−	1.63123i	0.347935	−	0.937518i	$-0.386883\pi$
$504$	−6.07997	−	2.92796i	−0.270824	−	0.130422i
$505$	1.53076	−	1.91951i	0.0681178	−	0.0854170i
$506$	2.35516	−	10.3186i	0.104700	−	0.458718i
$507$	−8.23074	+	10.3210i	−0.365540	+	0.458372i
$508$	−3.64792	−	15.9826i	−0.161850	−	0.709113i
$509$	32.4082			1.43647			0.718233	−	0.695803i	$-0.244951\pi$
$509$	32.4082			1.43647			0.718233	+	0.695803i	$0.244951\pi$
$510$	1.88665			0.0835422
$511$	7.14413	+	31.3005i	0.316038	+	1.38465i
$512$	0.623490	+	0.781831i	0.0275546	+	0.0345524i
$513$	7.60337	−	3.66159i	0.335697	−	0.161663i
$514$	0.106439	+	0.0512585i	0.00469484	+	0.00226092i
$515$	2.77752			0.122392
$516$	0.171005	+	2.70008i	0.00752807	+	0.118864i
$517$	35.4033			1.55703
$518$	−13.5179	−	6.50987i	−0.593941	−	0.286027i
$519$	6.65311	−	3.20397i	0.292039	−	0.140639i
$520$	4.18232	+	5.24446i	0.183407	+	0.229985i
$521$	−3.37517	−	14.7876i	−0.147869	−	0.647855i	−0.993475	−	0.114048i	$-0.963618\pi$
$521$	−3.37517	−	14.7876i	−0.147869	−	0.647855i	0.845607	−	0.533807i	$-0.179239\pi$
$522$	1.83193			0.0801815
$523$	−29.6289			−1.29558			−0.647791	−	0.761818i	$-0.724307\pi$
$523$	−29.6289			−1.29558			−0.647791	+	0.761818i	$0.724307\pi$
$524$	−1.40714	−	6.16510i	−0.0614714	−	0.269324i
$525$	0.613452	−	0.769244i	0.0267732	−	0.0335726i
$526$	−3.32393	+	14.5631i	−0.144930	+	0.634981i
$527$	−8.53774	+	10.7060i	−0.371910	+	0.466360i
$528$	1.13601	+	0.547072i	0.0494383	+	0.0238082i
$529$	2.44898	+	10.7297i	0.106477	+	0.466507i
$530$	−5.80048	−	2.79336i	−0.251957	−	0.121336i
$531$	1.65620	+	2.07681i	0.0718728	+	0.0901257i
$532$	−1.86185	+	8.15729i	−0.0807213	+	0.353663i
$533$	−11.9585	+	52.3937i	−0.517981	+	2.26942i
$534$	−3.70636	+	1.78489i	−0.160390	+	0.0772397i
$535$	−1.20978	−	1.51701i	−0.0523032	−	0.0655862i
$536$	−6.91275	+	8.66831i	−0.298585	+	0.374414i
$537$	−4.39891	+	2.11840i	−0.189827	+	0.0914158i
$538$	24.4209	−	11.7605i	1.05286	−	0.507030i
$539$	−2.50189	+	3.13728i	−0.107764	+	0.135132i
$540$	−1.49966	−	1.88051i	−0.0645350	−	0.0809243i
$541$	−6.35788	+	3.06180i	−0.273347	+	0.131637i	−0.565536	−	0.824724i	$-0.691331\pi$
$541$	−6.35788	+	3.06180i	−0.273347	+	0.131637i	0.292189	+	0.956361i	$0.405616\pi$
$542$	−4.64206	+	20.3382i	−0.199394	+	0.873601i
$543$	−1.10999	+	4.86319i	−0.0476343	+	0.208699i
$544$	2.85108	+	3.57514i	0.122239	+	0.153283i
$545$	−0.129326	−	0.0622802i	−0.00553972	−	0.00266779i
$546$	1.46862	+	6.43445i	0.0628512	+	0.275369i
$547$	−37.0589	−	17.8466i	−1.58452	−	0.763067i	−0.585653	−	0.810562i	$-0.699162\pi$
$547$	−37.0589	−	17.8466i	−1.58452	−	0.763067i	−0.998871	+	0.0474955i	$0.984876\pi$
$548$	−4.46076	+	5.59362i	−0.190554	+	0.238947i
$549$	1.77688	−	7.78502i	0.0758354	−	0.332257i
$550$	1.90541	−	2.38931i	0.0812471	−	0.101881i
$551$	−0.505431	−	2.21444i	−0.0215321	−	0.0943382i
$552$	1.42889			0.0608178
$553$	−1.95554			−0.0831580
$554$	−2.09840	−	9.19368i	−0.0891524	−	0.390602i
$555$	−1.61845	−	2.02947i	−0.0686994	−	0.0861463i
$556$	15.5357	−	7.48158i	0.658859	−	0.317290i
$557$	27.5944	+	13.2887i	1.16921	+	0.563062i	0.914750	−	0.404021i	$-0.132388\pi$
$557$	27.5944	+	13.2887i	1.16921	+	0.563062i	0.254461	+	0.967083i	$0.418102\pi$
$558$	8.47395			0.358731
$559$	−32.5880	+	29.5442i	−1.37833	+	1.24958i
$560$	2.38473			0.100773
$561$	5.19470	+	2.50164i	0.219320	+	0.105619i
$562$	14.0776	−	6.77943i	0.593829	−	0.285973i
$563$	6.79300	+	8.51815i	0.286291	+	0.358997i	0.904093	−	0.427336i	$-0.140548\pi$
$563$	6.79300	+	8.51815i	0.286291	+	0.358997i	−0.617802	+	0.786334i	$0.711977\pi$
$564$	1.06357	+	4.65980i	0.0447843	+	0.196213i
$565$	2.47540			0.104141
$566$	−18.4954			−0.777420
$567$	3.97828	+	17.4300i	0.167072	+	0.731991i
$568$	2.78264	−	3.48932i	0.116757	−	0.146408i
$569$	−0.552498	+	2.42065i	−0.0231619	+	0.101479i	−0.985188	−	0.171480i	$-0.945145\pi$
$569$	−0.552498	+	2.42065i	−0.0231619	+	0.101479i	0.962026	+	0.272959i	$0.0880023\pi$
$570$	−0.902555	+	1.13177i	−0.0378039	+	0.0474046i
$571$	20.9649	+	10.0962i	0.877356	+	0.422512i	0.817658	−	0.575704i	$-0.195272\pi$
$571$	20.9649	+	10.0962i	0.877356	+	0.422512i	0.0596977	+	0.998217i	$0.480986\pi$
$572$	4.56161	+	19.9857i	0.190731	+	0.835646i
$573$	9.71572	+	4.67884i	0.405880	+	0.195462i
$574$	11.9121	+	14.9373i	0.497201	+	0.623471i
$575$	0.770655	−	3.37646i	0.0321385	−	0.140808i
$576$	0.629684	−	2.75883i	0.0262368	−	0.114951i
$577$	−21.0073	+	10.1166i	−0.874546	+	0.421159i	−0.816629	−	0.577162i	$-0.804160\pi$
$577$	−21.0073	+	10.1166i	−0.874546	+	0.421159i	−0.0579164	+	0.998321i	$0.518446\pi$
$578$	2.43801	+	3.05717i	0.101408	+	0.127162i
$579$	−3.93449	+	4.93369i	−0.163512	+	0.205037i
$580$	−0.583267	+	0.280886i	−0.0242188	+	0.0116632i
$581$	−14.6036	+	7.03270i	−0.605858	+	0.291766i
$582$	2.19232	−	2.74908i	0.0908745	−	0.113953i
$583$	−12.2671	−	15.3825i	−0.508053	−	0.637078i
$584$	−12.1297	+	5.84133i	−0.501929	+	0.241716i
$585$	4.22387	−	18.5060i	0.174636	−	0.765129i
$586$	5.22194	−	22.8788i	0.215716	−	0.945116i
$587$	−9.43496	−	11.8311i	−0.389423	−	0.488321i	0.548018	−	0.836467i	$-0.315383\pi$
$587$	−9.43496	−	11.8311i	−0.389423	−	0.488321i	−0.937440	+	0.348146i	$0.886811\pi$
$588$	−0.488091	−	0.235052i	−0.0201285	−	0.00969339i
$589$	−2.33797	−	10.2433i	−0.0963342	−	0.422068i
$590$	−0.845747	−	0.407290i	−0.0348189	−	0.0167679i
$591$	4.65371	−	5.83557i	0.191428	−	0.240043i
$592$	1.40001	−	6.13382i	0.0575399	−	0.252099i
$593$	18.9519	−	23.7649i	0.778262	−	0.975909i	−0.221738	−	0.975106i	$-0.571173\pi$
$593$	18.9519	−	23.7649i	0.778262	−	0.975909i	1.00000		0.000802921i	$-0.000255578\pi$
$594$	−1.63566	−	7.16630i	−0.0671120	−	0.294037i
$595$	10.9049			0.447055
$596$	16.9810			0.695571
$597$	−0.614719	−	2.69326i	−0.0251588	−	0.110228i
$598$	14.4846	+	18.1631i	0.592319	+	0.742745i
$599$	4.59872	−	2.21463i	0.187899	−	0.0904873i	−0.337569	−	0.941301i	$-0.609605\pi$
$599$	4.59872	−	2.21463i	0.187899	−	0.0904873i	0.525468	+	0.850814i	$0.323890\pi$
$600$	0.371724	+	0.179013i	0.0151756	+	0.00730817i
$601$	14.6741			0.598570			0.299285	−	0.954164i	$-0.403252\pi$
$601$	14.6741			0.598570			0.299285	+	0.954164i	$0.403252\pi$
$602$	0.988411	+	15.6065i	0.0402846	+	0.636072i
$603$	31.3742			1.27766
$604$	7.29482	+	3.51300i	0.296822	+	0.142942i
$605$	−1.49614	+	0.720503i	−0.0608267	+	0.0292926i
$606$	0.631564	+	0.791956i	0.0256555	+	0.0321710i
$607$	−10.5572	−	46.2542i	−0.428504	−	1.87740i	−0.477551	−	0.878604i	$-0.658475\pi$
$607$	−10.5572	−	46.2542i	−0.428504	−	1.87740i	0.0490464	−	0.998796i	$-0.484382\pi$
$608$	−3.50860			−0.142292
$609$	−0.636954			−0.0258107
$610$	0.627923	+	2.75111i	0.0254238	+	0.111389i
$611$	−48.4508	+	60.7554i	−1.96011	+	2.45790i
$612$	2.87940	−	12.6155i	0.116393	−	0.509951i
$613$	−5.86032	+	7.34861i	−0.236696	+	0.296807i	−0.885966	−	0.463751i	$-0.846503\pi$
$613$	−5.86032	+	7.34861i	−0.236696	+	0.296807i	0.649270	+	0.760558i	$0.275075\pi$
$614$	−9.38778	−	4.52092i	−0.378860	−	0.182449i
$615$	0.735531	+	3.22257i	0.0296595	+	0.129947i
$616$	6.56613	+	3.16208i	0.264557	+	0.127404i
$617$	−19.0212	−	23.8518i	−0.765765	−	0.960239i	0.234164	−	0.972197i	$-0.424765\pi$
$617$	−19.0212	−	23.8518i	−0.765765	−	0.960239i	−0.999928	+	0.0119585i	$0.996193\pi$
$618$	−0.255000	+	1.11723i	−0.0102576	+	0.0449414i
$619$	1.52548	−	6.68356i	0.0613141	−	0.268635i	−0.934974	−	0.354716i	$-0.884577\pi$
$619$	1.52548	−	6.68356i	0.0613141	−	0.268635i	0.996288	+	0.0860816i	$0.0274346\pi$
$620$	−2.69801	+	1.29929i	−0.108355	+	0.0521809i
$621$	−5.19376	−	6.51276i	−0.208418	−	0.261348i
$622$	16.8548	−	21.1352i	0.675814	−	0.847444i
$623$	−21.4228	+	10.3167i	−0.858287	+	0.413329i
$624$	−2.49350	+	1.20080i	−0.0998197	+	0.0480706i
$625$	0.623490	−	0.781831i	0.0249396	−	0.0312733i
$626$	15.7379	+	19.7347i	0.629013	+	0.788757i
$627$	−3.98579	+	1.91945i	−0.159177	+	0.0766556i
$628$	−5.50723	+	24.1287i	−0.219762	+	0.962842i
$629$	6.40191	−	28.0486i	0.255261	−	1.11837i
$630$	−4.20747	−	5.27600i	−0.167630	−	0.210201i
$631$	27.7786	+	13.3775i	1.10585	+	0.532549i	0.895493	−	0.445075i	$-0.146823\pi$
$631$	27.7786	+	13.3775i	1.10585	+	0.532549i	0.210357	+	0.977625i	$0.432537\pi$
$632$	−0.182473	−	0.799465i	−0.00725837	−	0.0318010i
$633$	8.34472	+	4.01860i	0.331673	+	0.159725i
$634$	−11.0481	+	13.8538i	−0.438774	+	0.550206i
$635$	3.64792	−	15.9826i	0.144763	−	0.634250i
$636$	1.65613	−	2.07672i	0.0656698	−	0.0823473i
$637$	−1.95992	−	8.58697i	−0.0776549	−	0.340228i
$638$	−1.97841			−0.0783261
$639$	−12.6293			−0.499607
$640$	0.222521	+	0.974928i	0.00879591	+	0.0385374i
$641$	−21.5861	−	27.0682i	−0.852601	−	1.06913i	−0.996828	−	0.0795834i	$-0.974641\pi$
$641$	−21.5861	−	27.0682i	−0.852601	−	1.06913i	0.144227	−	0.989545i	$-0.453930\pi$
$642$	0.721269	−	0.347345i	0.0284662	−	0.0137086i
$643$	−24.6124	−	11.8527i	−0.970619	−	0.467426i	−0.119751	−	0.992804i	$-0.538209\pi$
$643$	−24.6124	−	11.8527i	−0.970619	−	0.467426i	−0.850869	+	0.525378i	$0.823924\pi$
$644$	8.25903			0.325451
$645$	−1.01745	+	2.50688i	−0.0400620	+	0.0987083i
$646$	−16.0440			−0.631243
$647$	7.79692	+	3.75480i	0.306529	+	0.147616i	0.580824	−	0.814029i	$-0.302730\pi$
$647$	7.79692	+	3.75480i	0.306529	+	0.147616i	−0.274296	+	0.961645i	$0.588445\pi$
$648$	−6.75452	+	3.25281i	−0.265343	+	0.127782i
$649$	−1.78863	−	2.24287i	−0.0702098	−	0.0880403i
$650$	1.49265	+	6.53974i	0.0585467	+	0.256510i
$651$	−2.94635			−0.115477
$652$	−4.00240			−0.156746
$653$	−0.358852	−	1.57223i	−0.0140430	−	0.0615263i	0.967421	−	0.253173i	$-0.0814743\pi$
$653$	−0.358852	−	1.57223i	−0.0140430	−	0.0615263i	−0.981464	+	0.191647i	$0.938617\pi$
$654$	0.0369247	−	0.0463021i	0.00144387	−	0.00181056i
$655$	1.40714	−	6.16510i	0.0549817	−	0.240891i
$656$	−4.99515	+	6.26372i	−0.195028	+	0.244557i
$657$	34.3242	+	16.5297i	1.33911	+	0.644884i
$658$	6.14744	+	26.9337i	0.239652	+	1.04999i
$659$	17.2572	+	8.31061i	0.672243	+	0.323735i	0.738681	−	0.674055i	$-0.235449\pi$
$659$	17.2572	+	8.31061i	0.672243	+	0.323735i	−0.0664375	+	0.997791i	$0.521163\pi$
$660$	0.786140	+	0.985789i	0.0306005	+	0.0383718i
$661$	−1.94773	+	8.53355i	−0.0757578	+	0.331916i	−0.998578	−	0.0533150i	$-0.983021\pi$
$661$	−1.94773	+	8.53355i	−0.0757578	+	0.331916i	0.922820	+	0.385231i	$0.125878\pi$
$662$	−0.822845	+	3.60512i	−0.0319808	+	0.140117i
$663$	−11.4022	+	5.49101i	−0.442825	+	0.213253i
$664$	−4.23778	−	5.31401i	−0.164458	−	0.206223i
$665$	−5.21678	+	6.54164i	−0.202298	+	0.253674i
$666$	−16.0406	+	7.72474i	−0.621560	+	0.299328i
$667$	−2.02002	+	0.972792i	−0.0782156	+	0.0376667i
$668$	9.57792	−	12.0103i	0.370581	−	0.464694i
$669$	4.87004	+	6.10684i	0.188287	+	0.236104i
$670$	−9.98921	+	4.81055i	−0.385917	+	0.185848i
$671$	−1.91896	+	8.40751i	−0.0740806	+	0.324568i
$672$	−0.218938	+	0.959231i	−0.00844573	+	0.0370032i
$673$	1.38495	+	1.73667i	0.0533858	+	0.0669437i	0.807808	−	0.589446i	$-0.200654\pi$
$673$	1.38495	+	1.73667i	0.0533858	+	0.0669437i	−0.754422	+	0.656390i	$0.772083\pi$
$674$	−32.0229	−	15.4214i	−1.23348	−	0.594011i
$675$	−0.535222	−	2.34496i	−0.0206007	−	0.0902575i
$676$	−28.8276	−	13.8826i	−1.10875	−	0.533947i
$677$	−1.90843	+	2.39309i	−0.0733467	+	0.0919739i	−0.817151	−	0.576423i	$-0.804448\pi$
$677$	−1.90843	+	2.39309i	−0.0733467	+	0.0919739i	0.743804	+	0.668397i	$0.233019\pi$
$678$	−0.227262	+	0.995701i	−0.00872796	+	0.0382397i
$679$	12.6716	−	15.8897i	0.486292	−	0.609791i
$680$	1.01754	+	4.45813i	0.0390208	+	0.170961i
$681$	2.03598			0.0780190
$682$	−9.15153			−0.350430
$683$	2.93640	+	12.8652i	0.112358	+	0.492274i	0.999525	+	0.0308247i	$0.00981335\pi$
$683$	2.93640	+	12.8652i	0.112358	+	0.492274i	−0.887166	+	0.461450i	$0.847330\pi$
$684$	6.19034	+	7.76244i	0.236694	+	0.296804i
$685$	−6.44599	+	3.10422i	−0.246288	+	0.118606i
$686$	−17.8612	−	8.60148i	−0.681943	−	0.328406i
$687$	8.08057			0.308293
$688$	−6.28802	+	1.86033i	−0.239728	+	0.0709245i
$689$	43.1859			1.64525
$690$	1.28739	+	0.619974i	0.0490101	+	0.0236020i
$691$	43.2061	−	20.8070i	1.64364	−	0.791535i	0.643990	−	0.765034i	$-0.277278\pi$
$691$	43.2061	−	20.8070i	1.64364	−	0.791535i	0.999649	−	0.0265003i	$-0.00843630\pi$
$692$	11.1592	+	13.9932i	0.424209	+	0.531942i
$693$	−4.58905	−	20.1059i	−0.174323	−	0.763761i
$694$	2.83960			0.107790
$695$	17.2433			0.654075
$696$	−0.0594346	−	0.260400i	−0.00225286	−	0.00987043i
$697$	−22.8417	+	28.6426i	−0.865191	+	1.08491i
$698$	−0.556336	+	2.43747i	−0.0210576	+	0.0922595i
$699$	1.38699	−	1.73923i	0.0524609	−	0.0657838i
$700$	2.14857	+	1.03470i	0.0812083	+	0.0391079i
$701$	−4.48507	−	19.6504i	−0.169399	−	0.742184i	−0.986240	−	0.165321i	$-0.947134\pi$
$701$	−4.48507	−	19.6504i	−0.169399	−	0.742184i	0.816841	−	0.576863i	$-0.195723\pi$
$702$	14.5365	+	7.00042i	0.548646	+	0.264214i
$703$	13.7633	+	17.2586i	0.519091	+	0.650920i
$704$	−0.680034	+	2.97942i	−0.0256297	+	0.112291i
$705$	−1.06357	+	4.65980i	−0.0400563	+	0.175498i
$706$	23.4521	−	11.2939i	0.882630	−	0.425052i
$707$	3.65045	+	4.57752i	0.137289	+	0.172155i
$708$	0.241474	−	0.302799i	0.00907516	−	0.0113799i
$709$	12.8551	−	6.19070i	0.482784	−	0.232497i	−0.176629	−	0.984278i	$-0.556519\pi$
$709$	12.8551	−	6.19070i	0.482784	−	0.232497i	0.659413	+	0.751781i	$0.270805\pi$
$710$	4.02103	−	1.93642i	0.150906	−	0.0726727i
$711$	−1.44680	+	1.81423i	−0.0542592	+	0.0680389i
$712$	−6.21665	−	7.79543i	−0.232979	−	0.292146i
$713$	−9.34400	+	4.49983i	−0.349936	+	0.168520i
$714$	−1.00116	+	4.38635i	−0.0374673	+	0.164155i
$715$	−4.56161	+	19.9857i	−0.170595	+	0.747424i
$716$	−7.37825	−	9.25203i	−0.275738	−	0.345765i
$717$	10.6591	+	5.13313i	0.398070	+	0.191700i
$718$	3.28081	+	14.3742i	0.122439	+	0.536439i
$719$	−15.2552	−	7.34650i	−0.568922	−	0.273978i	0.127230	−	0.991873i	$-0.459392\pi$
$719$	−15.2552	−	7.34650i	−0.568922	−	0.273978i	−0.696151	+	0.717895i	$0.745106\pi$
$720$	1.76434	−	2.21241i	0.0657529	−	0.0824516i
$721$	−1.47390	+	6.45758i	−0.0548909	+	0.240493i
$722$	−4.17099	+	5.23026i	−0.155228	+	0.194650i
$723$	−0.736086	−	3.22500i	−0.0273753	−	0.119939i
$724$	−12.0903			−0.449333
$725$	−0.647377			−0.0240430
$726$	−0.152456	−	0.667953i	−0.00565817	−	0.0247901i
$727$	14.3959	+	18.0518i	0.533913	+	0.669506i	0.973498	−	0.228695i	$-0.0734460\pi$
$727$	14.3959	+	18.0518i	0.533913	+	0.669506i	−0.439585	+	0.898201i	$0.644875\pi$
$728$	−14.4124	+	6.94067i	−0.534161	+	0.257238i
$729$	16.4315	+	7.91299i	0.608574	+	0.293074i
$730$	−13.4629			−0.498284
$731$	−28.7537	+	8.50688i	−1.06349	+	0.314638i
$732$	−1.16425			−0.0430319
$733$	6.33843	+	3.05243i	0.234115	+	0.112744i	0.547264	−	0.836960i	$-0.315669\pi$
$733$	6.33843	+	3.05243i	0.234115	+	0.112744i	−0.313149	+	0.949704i	$0.601384\pi$
$734$	−22.9547	+	11.0544i	−0.847272	+	0.408025i
$735$	−0.337769	−	0.423549i	−0.0124588	−	0.0156229i
$736$	0.770655	+	3.37646i	0.0284067	+	0.124458i
$737$	−33.8829			−1.24809
$738$	22.6710			0.834532
$739$	−2.99291	−	13.1128i	−0.110096	−	0.482361i	−0.999673	−	0.0255762i	$-0.991858\pi$
$739$	−2.99291	−	13.1128i	−0.110096	−	0.482361i	0.889577	−	0.456785i	$-0.150999\pi$
$740$	3.92273	−	4.91894i	0.144202	−	0.180824i
$741$	2.16074	−	9.46683i	0.0793769	−	0.347773i
$742$	9.57245	−	12.0035i	0.351416	−	0.440661i
$743$	−13.1254	−	6.32085i	−0.481523	−	0.231889i	0.177344	−	0.984149i	$-0.443250\pi$
$743$	−13.1254	−	6.32085i	−0.481523	−	0.231889i	−0.658867	+	0.752260i	$0.728964\pi$
$744$	−0.274926	−	1.20453i	−0.0100793	−	0.0441602i
$745$	15.2994	+	7.36780i	0.560526	+	0.269935i
$746$	−9.42676	−	11.8208i	−0.345138	−	0.432790i
$747$	−4.27988	+	18.7514i	−0.156593	+	0.686078i
$748$	−3.10964	+	13.6242i	−0.113700	+	0.498151i
$749$	4.16894	−	2.00766i	0.152330	−	0.0733582i
$750$	0.257241	+	0.322570i	0.00939312	+	0.0117786i
$751$	−5.62390	+	7.05214i	−0.205219	+	0.257336i	−0.873781	−	0.486320i	$-0.838339\pi$
$751$	−5.62390	+	7.05214i	−0.205219	+	0.257336i	0.668562	+	0.743657i	$0.266910\pi$
$752$	−10.4374	+	5.02640i	−0.380614	+	0.183294i
$753$	5.37399	−	2.58798i	0.195839	−	0.0943112i
$754$	2.70754	−	3.39515i	0.0986027	−	0.123644i
$755$	5.04817	+	6.33021i	0.183722	+	0.230380i
$756$	5.16788	−	2.48872i	0.187954	−	0.0905139i
$757$	−5.41119	+	23.7080i	−0.196673	+	0.861682i	0.776227	+	0.630454i	$0.217131\pi$
$757$	−5.41119	+	23.7080i	−0.196673	+	0.861682i	−0.972900	+	0.231227i	$0.925726\pi$
$758$	−1.77116	+	7.75995i	−0.0643314	+	0.281854i
$759$	2.72263	+	3.41408i	0.0988254	+	0.123923i
$760$	−3.16114	−	1.52232i	−0.114666	−	0.0552204i
$761$	−10.6163	−	46.5130i	−0.384840	−	1.68609i	−0.682069	−	0.731287i	$-0.738920\pi$
$761$	−10.6163	−	46.5130i	−0.384840	−	1.68609i	0.297230	−	0.954806i	$-0.403937\pi$
$762$	6.09390	+	2.93467i	0.220759	+	0.106312i
$763$	0.213425	−	0.267627i	0.00772651	−	0.00968874i
$764$	−5.81601	+	25.4816i	−0.210416	+	0.921892i
$765$	8.06791	−	10.1168i	0.291696	−	0.365775i
$766$	4.07487	+	17.8532i	0.147231	+	0.645061i
$767$	6.29678			0.227364
$768$	−0.412583			−0.0148878
$769$	3.42010	+	14.9845i	0.123332	+	0.540353i	0.998410	+	0.0563709i	$0.0179529\pi$
$769$	3.42010	+	14.9845i	0.123332	+	0.540353i	−0.875078	+	0.483982i	$0.839190\pi$
$770$	4.54390	+	5.69787i	0.163751	+	0.205337i
$771$	−0.0439151	+	0.0211484i	−0.00158156	+	0.000761640i
$772$	−13.7803	−	6.63623i	−0.495963	−	0.238843i
$773$	−20.6867			−0.744047			−0.372024	−	0.928223i	$-0.621336\pi$
$773$	−20.6867			−0.744047			−0.372024	+	0.928223i	$0.621336\pi$
$774$	15.2100	+	10.6294i	0.546712	+	0.382066i
$775$	−2.99457			−0.107568
$776$	7.67844	+	3.69774i	0.275640	+	0.132741i
$777$	5.57724	−	2.68586i	0.200082	−	0.0963546i
$778$	17.3331	+	21.7350i	0.621422	+	0.779238i
$779$	−6.25494	−	27.4047i	−0.224107	−	0.981875i
$780$	−2.76757			−0.0990950
$781$	13.6391			0.488047
$782$	3.52403	+	15.4398i	0.126019	+	0.552126i
$783$	−0.970844	+	1.21740i	−0.0346951	+	0.0435063i
$784$	0.292180	−	1.28012i	0.0104350	−	0.0457187i
$785$	−15.4309	+	19.3498i	−0.550753	+	0.690622i
$786$	2.35065	+	1.13202i	0.0838451	+	0.0403777i
$787$	−2.91349	−	12.7648i	−0.103855	−	0.455017i	−0.999938	−	0.0111315i	$-0.996457\pi$
$787$	−2.91349	−	12.7648i	−0.103855	−	0.455017i	0.896083	−	0.443886i	$-0.146400\pi$
$788$	16.2993	+	7.84933i	0.580638	+	0.279621i
$789$	−3.84256	−	4.81842i	−0.136799	−	0.171540i
$790$	0.182473	−	0.799465i	0.00649208	−	0.0284437i
$791$	−1.31358	+	5.75517i	−0.0467055	+	0.204630i
$792$	7.79151	−	3.75219i	0.276859	−	0.133328i
$793$	−11.8019	−	14.7991i	−0.419098	−	0.525533i
$794$	22.6407	−	28.3905i	0.803488	−	1.00754i
$795$	2.39318	−	1.15249i	0.0848772	−	0.0408747i
$796$	6.03260	−	2.90515i	0.213820	−	0.102970i
$797$	29.8947	−	37.4868i	1.05893	−	1.32785i	0.116590	−	0.993180i	$-0.462804\pi$
$797$	29.8947	−	37.4868i	1.05893	−	1.32785i	0.942335	−	0.334670i	$-0.108625\pi$
$798$	−2.15235	−	2.69897i	−0.0761925	−	0.0955424i
$799$	−47.7280	+	22.9846i	−1.68850	+	0.813137i
$800$	−0.222521	+	0.974928i	−0.00786730	+	0.0344689i
$801$	−6.27841	+	27.5075i	−0.221837	+	0.971930i
$802$	−4.31963	−	5.41664i	−0.152531	−	0.191268i
$803$	−37.0688	−	17.8514i	−1.30813	−	0.629962i
$804$	−1.01790	−	4.45969i	−0.0358984	−	0.157281i
$805$	7.44113	+	3.58346i	0.262265	+	0.126300i
$806$	12.5242	−	15.7049i	0.441147	−	0.553181i
$807$	−2.48848	+	10.9027i	−0.0875985	+	0.383794i
$808$	−1.53076	+	1.91951i	−0.0538519	+	0.0675281i
$809$	−1.20016	−	5.25826i	−0.0421955	−	0.184871i	0.949438	−	0.313954i	$-0.101654\pi$
$809$	−1.20016	−	5.25826i	−0.0421955	−	0.184871i	−0.991634	+	0.129083i	$0.958797\pi$
$810$	−7.49696			−0.263416
$811$	−39.2788			−1.37926			−0.689632	−	0.724160i	$-0.742228\pi$
$811$	−39.2788			−1.37926			−0.689632	+	0.724160i	$0.742228\pi$
$812$	−0.343533	−	1.50512i	−0.0120556	−	0.0528192i
$813$	−5.36637	−	6.72922i	−0.188207	−	0.236004i
$814$	17.3232	−	8.34242i	0.607178	−	0.292402i
$815$	−3.60604	−	1.73658i	−0.126314	−	0.0608296i
$816$	−1.88665			−0.0660459
$817$	8.65237	−	21.3185i	0.302708	−	0.745839i
$818$	15.2217			0.532215
$819$	40.7840	+	19.6405i	1.42511	+	0.686295i
$820$	−7.21820	+	3.47610i	−0.252070	+	0.121391i
$821$	25.8199	+	32.3772i	0.901122	+	1.12997i	0.990979	+	0.134017i	$0.0427875\pi$
$821$	25.8199	+	32.3772i	0.901122	+	1.12997i	−0.0898572	+	0.995955i	$0.528641\pi$
$822$	−0.656843	−	2.87782i	−0.0229100	−	0.100375i
$823$	29.0698			1.01331			0.506655	−	0.862149i	$-0.330882\pi$
$823$	29.0698			1.01331			0.506655	+	0.862149i	$0.330882\pi$
$824$	−2.77752			−0.0967596
$825$	0.280570	+	1.22926i	0.00976820	+	0.0427973i
$826$	1.39573	−	1.75018i	0.0485635	−	0.0608967i
$827$	6.93595	−	30.3884i	0.241187	−	1.05671i	−0.698752	−	0.715364i	$-0.746261\pi$
$827$	6.93595	−	30.3884i	0.241187	−	1.05671i	0.939939	−	0.341344i	$-0.110882\pi$
$828$	6.11041	−	7.66222i	0.212352	−	0.266280i
$829$	11.5401	+	5.55740i	0.400803	+	0.193016i	0.623416	−	0.781890i	$-0.285744\pi$
$829$	11.5401	+	5.55740i	0.400803	+	0.193016i	−0.222613	+	0.974907i	$0.571459\pi$
$830$	−1.51245	−	6.62646i	−0.0524978	−	0.230008i
$831$	3.50540	+	1.68811i	0.121601	+	0.0585600i
$832$	−4.18232	−	5.24446i	−0.144996	−	0.181819i
$833$	1.33607	−	5.85372i	0.0462922	−	0.202819i
$834$	−1.58308	+	6.93591i	−0.0548175	+	0.240171i
$835$	13.8405	−	6.66523i	0.478970	−	0.230660i
$836$	−6.68532	−	8.38313i	−0.231217	−	0.289937i
$837$	−4.49083	+	5.63132i	−0.155226	+	0.194647i
$838$	9.76060	−	4.70046i	0.337174	−	0.162375i
$839$	29.7457	−	14.3248i	1.02693	−	0.494546i	0.156941	−	0.987608i	$-0.449837\pi$
$839$	29.7457	−	14.3248i	1.02693	−	0.494546i	0.869994	+	0.493062i	$0.164123\pi$
$840$	−0.613452	+	0.769244i	−0.0211661	+	0.0265414i
$841$	−17.8199	−	22.3454i	−0.614479	−	0.770533i
$842$	−21.6200	+	10.4116i	−0.745073	+	0.358808i
$843$	−1.43450	+	6.28497i	−0.0494069	+	0.216466i
$844$	−4.99530	+	21.8858i	−0.171945	+	0.753342i
$845$	−19.9493	−	25.0156i	−0.686277	−	0.860564i
$846$	29.5356	+	14.2236i	1.01545	+	0.489017i
$847$	−0.881197	−	3.86078i	−0.0302783	−	0.132658i
$848$	5.80048	+	2.79336i	0.199189	+	0.0959245i
$849$	4.75778	−	5.96607i	0.163287	−	0.204755i
$850$	−1.01754	+	4.45813i	−0.0349013	+	0.152912i
$851$	13.5856	−	17.0357i	0.465707	−	0.583978i
$852$	0.409741	+	1.79519i	0.0140375	+	0.0615022i
$853$	−5.00384			−0.171328			−0.0856641	−	0.996324i	$-0.527301\pi$
$853$	−5.00384			−0.171328			−0.0856641	+	0.996324i	$0.527301\pi$
$854$	−6.72938			−0.230275
$855$	2.20931	+	9.67961i	0.0755567	+	0.331036i
$856$	1.20978	+	1.51701i	0.0413493	+	0.0518504i
$857$	−15.9325	+	7.67267i	−0.544242	+	0.262093i	−0.685742	−	0.727845i	$-0.740522\pi$
$857$	−15.9325	+	7.67267i	−0.544242	+	0.262093i	0.141499	+	0.989938i	$0.454808\pi$
$858$	−7.62024	−	3.66971i	−0.260151	−	0.125282i
$859$	−3.69033			−0.125912			−0.0629562	−	0.998016i	$-0.520053\pi$
$859$	−3.69033			−0.125912			−0.0629562	+	0.998016i	$0.520053\pi$
$860$	−6.47248	−	1.05217i	−0.220710	−	0.0358786i
$861$	−7.88261			−0.268639
$862$	7.14588	+	3.44128i	0.243390	+	0.117210i
$863$	21.8792	−	10.5365i	0.744778	−	0.358666i	−0.0226995	−	0.999742i	$-0.507226\pi$
$863$	21.8792	−	10.5365i	0.744778	−	0.358666i	0.767477	+	0.641076i	$0.221512\pi$
$864$	1.49966	+	1.88051i	0.0510194	+	0.0639763i
$865$	3.98268	+	17.4492i	0.135415	+	0.593292i
$866$	7.43947			0.252804
$867$	−1.61331			−0.0547909
$868$	−1.58908	−	6.96220i	−0.0539368	−	0.236312i
$869$	1.56248	−	1.95929i	0.0530037	−	0.0664645i
$870$	0.0594346	−	0.260400i	0.00201502	−	0.00882838i
$871$	46.3702	−	58.1463i	1.57119	−	1.97021i
$872$	0.129326	+	0.0622802i	0.00437954	+	0.00210907i
$873$	−5.36644	−	23.5119i	−0.181626	−	0.795757i
$874$	−10.9479	−	5.27225i	−0.370320	−	0.178337i
$875$	1.48686	+	1.86446i	0.0502649	+	0.0630302i
$876$	1.23601	−	5.41530i	0.0417608	−	0.182966i
$877$	−2.17425	+	9.52603i	−0.0734194	+	0.321671i	−0.998279	−	0.0586364i	$-0.981325\pi$
$877$	−2.17425	+	9.52603i	−0.0734194	+	0.321671i	0.924860	+	0.380308i	$0.124182\pi$
$878$	15.1545	−	7.29804i	0.511441	−	0.246297i
$879$	6.03673	+	7.56982i	0.203614	+	0.255324i
$880$	−1.90541	+	2.38931i	−0.0642315	+	0.0805437i
$881$	−18.1406	+	8.73605i	−0.611172	+	0.294325i	−0.713751	−	0.700400i	$-0.753005\pi$
$881$	−18.1406	+	8.73605i	−0.611172	+	0.294325i	0.102578	+	0.994725i	$0.467291\pi$
$882$	−3.34766	+	1.61215i	−0.112722	+	0.0542839i
$883$	−1.82917	+	2.29370i	−0.0615564	+	0.0771892i	−0.811656	−	0.584135i	$-0.801434\pi$
$883$	−1.82917	+	2.29370i	−0.0615564	+	0.0771892i	0.750100	+	0.661324i	$0.230005\pi$
$884$	−19.1248	−	23.9817i	−0.643237	−	0.806593i
$885$	0.348941	−	0.168041i	0.0117295	−	0.00564864i
$886$	−6.99257	+	30.6364i	−0.234920	+	1.02925i
$887$	8.85513	−	38.7969i	0.297326	−	1.30267i	−0.576765	−	0.816910i	$-0.695685\pi$
$887$	8.85513	−	38.7969i	0.297326	−	1.30267i	0.874091	−	0.485761i	$-0.161458\pi$
$888$	1.61845	+	2.02947i	0.0543116	+	0.0681046i
$889$	35.2228	+	16.9624i	1.18134	+	0.568901i
$890$	−2.21870	−	9.72074i	−0.0743708	−	0.325840i
$891$	−20.6421	−	9.94073i	−0.691537	−	0.333027i
$892$	−11.8038	+	14.8015i	−0.395220	+	0.495591i
$893$	9.04457	−	39.6269i	0.302665	−	1.32606i
$894$	−4.36822	+	5.47758i	−0.146095	+	0.183198i
$895$	−2.63327	−	11.5371i	−0.0880204	−	0.385643i
$896$	−2.38473			−0.0796684
$897$	−9.58491			−0.320031
$898$	−4.17468	−	18.2905i	−0.139311	−	0.610361i
$899$	1.20871	+	1.51567i	0.0403126	+	0.0505504i
$900$	2.54954	−	1.22779i	0.0849847	−	0.0409265i
$901$	26.5243	+	12.7734i	0.883652	+	0.425544i
$902$	−24.4838			−0.815221
$903$	−5.28844	−	3.69580i	−0.175988	−	0.122988i
$904$	−2.47540			−0.0823306
$905$	−10.8930	−	5.24579i	−0.362096	−	0.174376i
$906$	−3.00972	+	1.44940i	−0.0999911	+	0.0481532i
$907$	−19.6605	−	24.6535i	−0.652816	−	0.818605i	0.339724	−	0.940525i	$-0.389666\pi$
$907$	−19.6605	−	24.6535i	−0.652816	−	0.818605i	−0.992540	+	0.121920i	$0.961095\pi$
$908$	1.09808	+	4.81100i	0.0364411	+	0.159659i
$909$	6.94751			0.230434
$910$	−15.9966			−0.530282
$911$	9.86002	+	43.1996i	0.326677	+	1.43127i	0.825422	+	0.564517i	$0.190937\pi$
$911$	9.86002	+	43.1996i	0.326677	+	1.43127i	−0.498745	+	0.866749i	$0.666205\pi$
$912$	0.902555	−	1.13177i	0.0298866	−	0.0374766i
$913$	4.62210	−	20.2508i	0.152969	−	0.670202i
$914$	−5.34309	+	6.70002i	−0.176734	+	0.221617i
$915$	−1.04895	−	0.505149i	−0.0346773	−	0.0166997i
$916$	4.35814	+	19.0943i	0.143997	+	0.630893i
$917$	13.5868	+	6.54306i	0.448676	+	0.216071i
$918$	6.85760	+	8.59916i	0.226334	+	0.283814i
$919$	6.85182	−	30.0198i	0.226021	−	0.990261i	−0.726829	−	0.686819i	$-0.759007\pi$
$919$	6.85182	−	30.0198i	0.226021	−	0.990261i	0.952850	−	0.303443i	$-0.0981361\pi$
$920$	−0.770655	+	3.37646i	−0.0254078	+	0.111319i
$921$	3.87324	−	1.86525i	0.127627	−	0.0614621i
$922$	−8.13388	−	10.1996i	−0.267875	−	0.335905i
$923$	−18.6657	+	23.4061i	−0.614389	+	0.770420i
$924$	−2.70907	+	1.30462i	−0.0891219	+	0.0429188i
$925$	5.66850	−	2.72981i	0.186379	−	0.0897555i
$926$	25.2883	−	31.7106i	0.831026	−	1.04207i
$927$	4.90048	+	6.14501i	0.160953	+	0.201829i
$928$	0.583267	−	0.280886i	0.0191467	−	0.00922055i
$929$	1.69299	−	7.41747i	0.0555452	−	0.243359i	−0.939532	−	0.342461i	$-0.888740\pi$
$929$	1.69299	−	7.41747i	0.0555452	−	0.243359i	0.995077	+	0.0991013i	$0.0315968\pi$
$930$	0.274926	−	1.20453i	0.00901518	−	0.0394981i
$931$	2.87238	+	3.60186i	0.0941386	+	0.118046i
$932$	4.85784	+	2.33941i	0.159124	+	0.0766300i
$933$	2.48185	+	10.8737i	0.0812521	+	0.355989i
$934$	−21.4644	−	10.3367i	−0.702336	−	0.338227i
$935$	−8.71302	+	10.9258i	−0.284946	+	0.357311i
$936$	−4.22387	+	18.5060i	−0.138062	+	0.604887i
$937$	−0.0396944	+	0.0497752i	−0.00129676	+	0.00162608i	−0.782479	−	0.622676i	$-0.786045\pi$
$937$	−0.0396944	+	0.0497752i	−0.00129676	+	0.00162608i	0.781183	+	0.624303i	$0.214617\pi$
$938$	−5.88345	−	25.7771i	−0.192101	−	0.841652i
$939$	−10.4143			−0.339857
$940$	−11.5847			−0.377850
$941$	5.03659	+	22.0667i	0.164188	+	0.719355i	0.988249	+	0.152854i	$0.0488463\pi$
$941$	5.03659	+	22.0667i	0.164188	+	0.719355i	−0.824061	+	0.566502i	$0.808297\pi$
$942$	−6.36653	−	7.98337i	−0.207433	−	0.260112i
$943$	−24.9987	+	12.0388i	−0.814071	+	0.392036i
$944$	0.845747	+	0.407290i	0.0275267	+	0.0132562i
$945$	5.73592			0.186589
$946$	−16.4262	−	11.4793i	−0.534061	−	0.373225i
$947$	−25.6382			−0.833128			−0.416564	−	0.909106i	$-0.636766\pi$
$947$	−25.6382			−0.833128			−0.416564	+	0.909106i	$0.636766\pi$
$948$	0.304823	+	0.146795i	0.00990019	+	0.00476768i
$949$	81.3648	−	39.1832i	2.64121	−	1.27194i
$950$	−2.18757	−	2.74313i	−0.0709743	−	0.0889989i
$951$	−1.62682	−	7.12755i	−0.0527531	−	0.231127i
$952$	−10.9049			−0.353428
$953$	43.4157			1.40637			0.703187	−	0.711005i	$-0.251760\pi$
$953$	43.4157			1.40637			0.703187	+	0.711005i	$0.251760\pi$
$954$	−4.05393	−	17.7614i	−0.131251	−	0.575048i
$955$	−16.2961	+	20.4347i	−0.527329	+	0.661250i
$956$	−6.38070	+	27.9557i	−0.206367	+	0.904152i
$957$	0.508929	−	0.638177i	0.0164513	−	0.0206293i
$958$	13.4401	+	6.47241i	0.434230	+	0.209114i
$959$	−3.79656	−	16.6338i	−0.122597	−	0.537134i
$960$	−0.371724	−	0.179013i	−0.0119973	−	0.00577762i
$961$	−13.7371	−	17.2258i	−0.443132	−	0.555670i
$962$	−9.39112	+	41.1452i	−0.302782	+	1.32657i
$963$	1.22180	−	5.35304i	0.0393719	−	0.172499i
$964$	7.22364	−	3.47872i	0.232658	−	0.112042i
$965$	−9.53624	−	11.9581i	−0.306983	−	0.384944i
$966$	−2.12456	+	2.66412i	−0.0683567	+	0.0857166i
$967$	−29.2092	+	14.0664i	−0.939305	+	0.452346i	−0.839924	−	0.542704i	$-0.817401\pi$
$967$	−29.2092	+	14.0664i	−0.939305	+	0.452346i	−0.0993812	+	0.995049i	$0.531686\pi$
$968$	1.49614	−	0.720503i	0.0480877	−	0.0231578i
$969$	4.12718	−	5.17532i	0.132584	−	0.166255i
$970$	5.31364	+	6.66310i	0.170611	+	0.213939i
$971$	39.9146	−	19.2218i	1.28092	−	0.616858i	0.335293	−	0.942114i	$-0.391165\pi$
$971$	39.9146	−	19.2218i	1.28092	−	0.616858i	0.945626	+	0.325256i	$0.105450\pi$
$972$	2.29395	−	10.0504i	0.0735784	−	0.322368i
$973$	−9.15020	+	40.0897i	−0.293342	+	1.28522i
$974$	−9.67209	−	12.1284i	−0.309914	−	0.388619i
$975$	−2.49350	−	1.20080i	−0.0798558	−	0.0384565i
$976$	−0.627923	−	2.75111i	−0.0200993	−	0.0880608i
$977$	−7.55896	−	3.64020i	−0.241832	−	0.116460i	0.309042	−	0.951048i	$-0.399992\pi$
$977$	−7.55896	−	3.64020i	−0.241832	−	0.116460i	−0.550875	+	0.834588i	$0.685706\pi$
$978$	1.02958	−	1.29105i	0.0329224	−	0.0412834i
$979$	6.78043	−	29.7070i	0.216704	−	0.949441i
$980$	0.818671	−	1.02658i	0.0261515	−	0.0327929i
$981$	−0.0903856	−	0.396005i	−0.00288579	−	0.0126435i
$982$	−2.51365			−0.0802137
$983$	−43.0399			−1.37276			−0.686380	−	0.727243i	$-0.740801\pi$
$983$	−43.0399			−1.37276			−0.686380	+	0.727243i	$0.740801\pi$
$984$	−0.735531	−	3.22257i	−0.0234479	−	0.102732i
$985$	11.2795	+	14.1440i	0.359394	+	0.450665i
$986$	2.66715	−	1.28443i	0.0849393	−	0.0409046i
$987$	−10.2694	−	4.94548i	−0.326878	−	0.157416i
$988$	23.5354			0.748760
$989$	−22.4161	−	3.64396i	−0.712790	−	0.115871i
$990$	8.64792			0.274849
$991$	−50.4196	−	24.2808i	−1.60163	−	0.771305i	−0.602001	−	0.798495i	$-0.705630\pi$
$991$	−50.4196	−	24.2808i	−1.60163	−	0.771305i	−0.999630	+	0.0271901i	$0.991344\pi$
$992$	2.69801	−	1.29929i	0.0856619	−	0.0412526i
$993$	−0.951235	−	1.19281i	−0.0301865	−	0.0378527i
$994$	2.36831	+	10.3762i	0.0751181	+	0.329114i
$995$	6.69568			0.212267
$996$	2.80427			0.0888567
$997$	−9.13291	−	40.0139i	−0.289242	−	1.26725i	−0.885568	−	0.464510i	$-0.846230\pi$
$997$	−9.13291	−	40.0139i	−0.289242	−	1.26725i	0.596325	−	0.802743i	$-0.296627\pi$
$998$	21.3639	−	26.7895i	0.676264	−	0.848008i
$999$	3.36738	−	14.7535i	0.106539	−	0.466779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.k.b.21.2	✓	18
43.41	even	7	inner	430.2.k.b.41.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.k.b.21.2	✓	18	1.1	even	1	trivial
430.2.k.b.41.2	yes	18	43.41	even	7	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 - 0.433884i) q^{2} +(0.371724 - 0.179013i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.222521 + 0.974928i) q^{5} -0.412583 q^{6} -2.38473 q^{7} +(-0.222521 - 0.974928i) q^{8} +(-1.76434 + 2.21241i) q^{9} +O(q^{10})\)	\(q+(-0.900969 - 0.433884i) q^{2} +(0.371724 - 0.179013i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.222521 + 0.974928i) q^{5} -0.412583 q^{6} -2.38473 q^{7} +(-0.222521 - 0.974928i) q^{8} +(-1.76434 + 2.21241i) q^{9} +(0.222521 - 0.974928i) q^{10} +(1.90541 - 2.38931i) q^{11} +(0.371724 + 0.179013i) q^{12} +(1.49265 + 6.53974i) q^{13} +(2.14857 + 1.03470i) q^{14} +(0.257241 + 0.322570i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-1.01754 + 4.45813i) q^{17} +(2.54954 - 1.22779i) q^{18} +(-2.18757 - 2.74313i) q^{19} +(-0.623490 + 0.781831i) q^{20} +(-0.886463 + 0.426898i) q^{21} +(-2.75340 + 1.32597i) q^{22} +(-2.15933 + 2.70771i) q^{23} +(-0.257241 - 0.322570i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(1.49265 - 6.53974i) q^{26} +(-0.535222 + 2.34496i) q^{27} +(-1.48686 - 1.86446i) q^{28} +(0.583267 + 0.280886i) q^{29} +(-0.0918083 - 0.402238i) q^{30} +(2.69801 + 1.29929i) q^{31} +(0.623490 - 0.781831i) q^{32} +(0.280570 - 1.22926i) q^{33} +(2.85108 - 3.57514i) q^{34} +(-0.530653 - 2.32494i) q^{35} -2.82978 q^{36} -6.29157 q^{37} +(0.780736 + 3.42063i) q^{38} +(1.72555 + 2.16377i) q^{39} +(0.900969 - 0.433884i) q^{40} +(7.21820 + 3.47610i) q^{41} +0.983900 q^{42} +(3.21291 + 5.71640i) q^{43} +3.05604 q^{44} +(-2.54954 - 1.22779i) q^{45} +(3.12032 - 1.50267i) q^{46} +(7.22293 + 9.05726i) q^{47} +(0.0918083 + 0.402238i) q^{48} -1.31305 q^{49} +1.00000 q^{50} +(0.419819 + 1.83935i) q^{51} +(-4.18232 + 5.24446i) q^{52} +(1.43260 - 6.27663i) q^{53} +(1.49966 - 1.88051i) q^{54} +(2.75340 + 1.32597i) q^{55} +(0.530653 + 2.32494i) q^{56} +(-1.30423 - 0.628084i) q^{57} +(-0.403633 - 0.506140i) q^{58} +(0.208882 - 0.915173i) q^{59} +(-0.0918083 + 0.402238i) q^{60} +(-2.54241 + 1.22436i) q^{61} +(-1.86708 - 2.34125i) q^{62} +(4.20747 - 5.27600i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-6.04363 + 2.91046i) q^{65} +(-0.786140 + 0.985789i) q^{66} +(-6.91275 - 8.66831i) q^{67} +(-4.11993 + 1.98405i) q^{68} +(-0.317959 + 1.39307i) q^{69} +(-0.530653 + 2.32494i) q^{70} +(2.78264 + 3.48932i) q^{71} +(2.54954 + 1.22779i) q^{72} +(-2.99578 - 13.1254i) q^{73} +(5.66850 + 2.72981i) q^{74} +(-0.257241 + 0.322570i) q^{75} +(0.780736 - 3.42063i) q^{76} +(-4.54390 + 5.69787i) q^{77} +(-0.615843 - 2.69818i) q^{78} +0.820024 q^{79} -1.00000 q^{80} +(-1.66823 - 7.30899i) q^{81} +(-4.99515 - 6.26372i) q^{82} +(6.12377 - 2.94905i) q^{83} +(-0.886463 - 0.426898i) q^{84} -4.57277 q^{85} +(-0.414474 - 6.54433i) q^{86} +0.267097 q^{87} +(-2.75340 - 1.32597i) q^{88} +(8.98332 - 4.32614i) q^{89} +(1.76434 + 2.21241i) q^{90} +(-3.55958 - 15.5955i) q^{91} -3.46329 q^{92} +1.23551 q^{93} +(-2.57783 - 11.2942i) q^{94} +(2.18757 - 2.74313i) q^{95} +(0.0918083 - 0.402238i) q^{96} +(-5.31364 + 6.66310i) q^{97} +(1.18301 + 0.569709i) q^{98} +(1.92434 + 8.43110i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) \) 18 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^7 - 3 * q^8 - 7 * q^9	\( 18 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{7} - 3 q^{8} - 7 q^{9} + 3 q^{10} + 9 q^{11} + 2 q^{12} + 4 q^{13} + 13 q^{14} + 5 q^{15} - 3 q^{16} - q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 2 q^{21} - 12 q^{22} - 19 q^{23} - 5 q^{24} - 3 q^{25} + 4 q^{26} + 17 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} - 13 q^{31} - 3 q^{32} - 42 q^{33} - 8 q^{34} + 15 q^{35} + 2 q^{37} + 12 q^{38} - 39 q^{39} + 3 q^{40} - 4 q^{41} - 2 q^{42} - 13 q^{43} - 12 q^{44} - 7 q^{45} + 16 q^{46} + 16 q^{47} + 2 q^{48} + 4 q^{49} + 18 q^{50} + 7 q^{51} - 10 q^{52} + 14 q^{53} - 4 q^{54} + 12 q^{55} - 15 q^{56} + 45 q^{57} + 24 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} + 50 q^{62} - 33 q^{63} - 3 q^{64} - 4 q^{65} + 5 q^{67} + 13 q^{68} + 4 q^{69} + 15 q^{70} - 3 q^{71} + 7 q^{72} - 22 q^{73} - 12 q^{74} - 5 q^{75} + 12 q^{76} - 24 q^{77} + 31 q^{78} - 38 q^{79} - 18 q^{80} + 22 q^{81} - 11 q^{82} - 26 q^{83} - 2 q^{84} + 8 q^{85} - 41 q^{86} - 22 q^{87} - 12 q^{88} + 52 q^{89} + 7 q^{90} - 14 q^{91} + 2 q^{92} - 6 q^{93} + 2 q^{94} + 2 q^{95} + 2 q^{96} + 27 q^{97} + 32 q^{98} + 36 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^7 - 3 * q^8 - 7 * q^9 + 3 * q^10 + 9 * q^11 + 2 * q^12 + 4 * q^13 + 13 * q^14 + 5 * q^15 - 3 * q^16 - q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 2 * q^21 - 12 * q^22 - 19 * q^23 - 5 * q^24 - 3 * q^25 + 4 * q^26 + 17 * q^27 - q^28 - 4 * q^29 - 2 * q^30 - 13 * q^31 - 3 * q^32 - 42 * q^33 - 8 * q^34 + 15 * q^35 + 2 * q^37 + 12 * q^38 - 39 * q^39 + 3 * q^40 - 4 * q^41 - 2 * q^42 - 13 * q^43 - 12 * q^44 - 7 * q^45 + 16 * q^46 + 16 * q^47 + 2 * q^48 + 4 * q^49 + 18 * q^50 + 7 * q^51 - 10 * q^52 + 14 * q^53 - 4 * q^54 + 12 * q^55 - 15 * q^56 + 45 * q^57 + 24 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 + 50 * q^62 - 33 * q^63 - 3 * q^64 - 4 * q^65 + 5 * q^67 + 13 * q^68 + 4 * q^69 + 15 * q^70 - 3 * q^71 + 7 * q^72 - 22 * q^73 - 12 * q^74 - 5 * q^75 + 12 * q^76 - 24 * q^77 + 31 * q^78 - 38 * q^79 - 18 * q^80 + 22 * q^81 - 11 * q^82 - 26 * q^83 - 2 * q^84 + 8 * q^85 - 41 * q^86 - 22 * q^87 - 12 * q^88 + 52 * q^89 + 7 * q^90 - 14 * q^91 + 2 * q^92 - 6 * q^93 + 2 * q^94 + 2 * q^95 + 2 * q^96 + 27 * q^97 + 32 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more