LMFDB - Embedded newform 43.2.g.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, 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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	43.13
Dual form			43.2.g.a.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.581275 - 2.54673i) q^{2} +(-1.40948 + 1.30780i) q^{3} +(-4.34603 - 2.09294i) q^{4} +(2.95419 + 0.445272i) q^{5} +(2.51133 + 4.34976i) q^{6} +(-0.339884 + 0.588696i) q^{7} +(-4.59900 + 5.76696i) q^{8} +(0.0520854 - 0.695032i) q^{9} +O(q^{10})$	\(q+(0.581275 - 2.54673i) q^{2} +(-1.40948 + 1.30780i) q^{3} +(-4.34603 - 2.09294i) q^{4} +(2.95419 + 0.445272i) q^{5} +(2.51133 + 4.34976i) q^{6} +(-0.339884 + 0.588696i) q^{7} +(-4.59900 + 5.76696i) q^{8} +(0.0520854 - 0.695032i) q^{9} +(2.85118 - 7.26470i) q^{10} +(-1.98321 + 0.955063i) q^{11} +(8.86279 - 2.73381i) q^{12} +(-0.884105 - 2.25266i) q^{13} +(1.30168 + 1.20779i) q^{14} +(-4.74619 + 3.23590i) q^{15} +(5.99853 + 7.52192i) q^{16} +(-2.49942 + 0.376727i) q^{17} +(-1.73978 - 0.536652i) q^{18} +(-0.122786 - 1.63846i) q^{19} +(-11.9071 - 8.11809i) q^{20} +(-0.290840 - 1.27425i) q^{21} +(1.27950 + 5.60586i) q^{22} +(0.0324711 + 0.0221384i) q^{23} +(-1.05987 - 14.1430i) q^{24} +(3.75109 + 1.15706i) q^{25} +(-6.25084 + 0.942162i) q^{26} +(-2.76090 - 3.46206i) q^{27} +(2.70925 - 1.84713i) q^{28} +(5.57974 + 5.17724i) q^{29} +(5.48212 + 13.9682i) q^{30} +(8.56546 - 2.64209i) q^{31} +(9.35164 - 4.50351i) q^{32} +(1.54625 - 3.93979i) q^{33} +(-0.493428 + 6.58434i) q^{34} +(-1.26621 + 1.58778i) q^{35} +(-1.68102 + 2.91162i) q^{36} +(-5.57614 - 9.65816i) q^{37} +(-4.24410 - 0.639696i) q^{38} +(4.19217 + 2.01884i) q^{39} +(-16.1542 + 14.9889i) q^{40} +(0.555724 - 2.43478i) q^{41} -3.41424 q^{42} +(-6.51074 - 0.781227i) q^{43} +10.6180 q^{44} +(0.463348 - 2.03006i) q^{45} +(0.0752553 - 0.0698267i) q^{46} +(7.92075 + 3.81443i) q^{47} +(-18.2920 - 2.75708i) q^{48} +(3.26896 + 5.66200i) q^{49} +(5.12713 - 8.88045i) q^{50} +(3.03019 - 3.79974i) q^{51} +(-0.872336 + 11.6405i) q^{52} +(-2.23834 + 5.70320i) q^{53} +(-10.4218 + 5.01886i) q^{54} +(-6.28403 + 1.93837i) q^{55} +(-1.83186 - 4.66750i) q^{56} +(2.31586 + 2.14880i) q^{57} +(16.4284 - 11.2007i) q^{58} +(2.97714 + 3.73321i) q^{59} +(27.3996 - 4.12983i) q^{60} +(-4.87717 - 1.50441i) q^{61} +(-1.74982 - 23.3497i) q^{62} +(0.391459 + 0.266892i) q^{63} +(-1.75166 - 7.67453i) q^{64} +(-1.60876 - 7.04845i) q^{65} +(-9.13479 - 6.22799i) q^{66} +(0.194013 + 2.58893i) q^{67} +(11.6510 + 3.59386i) q^{68} +(-0.0747200 + 0.0112622i) q^{69} +(3.30762 + 4.14763i) q^{70} +(-7.71099 + 5.25726i) q^{71} +(3.76868 + 3.49682i) q^{72} +(-1.43804 - 3.66406i) q^{73} +(-27.8380 + 8.58689i) q^{74} +(-6.80028 + 3.27484i) q^{75} +(-2.89557 + 7.37780i) q^{76} +(0.111819 - 1.49212i) q^{77} +(7.57825 - 9.50283i) q^{78} +(3.10044 - 5.37012i) q^{79} +(14.3715 + 24.8921i) q^{80} +(10.4867 + 1.58062i) q^{81} +(-5.87772 - 2.83056i) q^{82} +(3.97087 - 3.68443i) q^{83} +(-1.40293 + 6.14666i) q^{84} -7.55150 q^{85} +(-5.77411 + 16.1270i) q^{86} -14.6353 q^{87} +(3.61296 - 15.8294i) q^{88} +(7.30600 - 6.77898i) q^{89} +(-4.90069 - 2.36005i) q^{90} +(1.62662 + 0.245174i) q^{91} +(-0.0947861 - 0.164174i) q^{92} +(-8.61749 + 14.9259i) q^{93} +(14.3185 - 17.9548i) q^{94} +(0.366830 - 4.89500i) q^{95} +(-7.29122 + 18.5777i) q^{96} +(-0.852010 + 0.410306i) q^{97} +(16.3198 - 5.03398i) q^{98} +(0.560503 + 1.42814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{16}{21}\right)$

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 $

$2$	0.581275	−	2.54673i	0.411024	−	1.80081i	−0.168324	−	0.985732i	$-0.553836\pi$
$2$	0.581275	−	2.54673i	0.411024	−	1.80081i	0.579348	−	0.815080i	$-0.303307\pi$
$3$	−1.40948	+	1.30780i	−0.813762	+	0.755061i	−0.972660	−	0.232234i	$-0.925397\pi$
$3$	−1.40948	+	1.30780i	−0.813762	+	0.755061i	0.158898	+	0.987295i	$0.449206\pi$
$4$	−4.34603	−	2.09294i	−2.17301	−	1.04647i
$5$	2.95419	+	0.445272i	1.32115	+	0.199132i	0.771483	−	0.636250i	$-0.219515\pi$
$5$	2.95419	+	0.445272i	1.32115	+	0.199132i	0.549670	+	0.835382i	$0.314754\pi$
$6$	2.51133	+	4.34976i	1.02525	+	1.77578i
$7$	−0.339884	+	0.588696i	−0.128464	+	0.222506i	−0.923082	−	0.384604i	$-0.874338\pi$
$7$	−0.339884	+	0.588696i	−0.128464	+	0.222506i	0.794618	+	0.607110i	$0.207671\pi$
$8$	−4.59900	+	5.76696i	−1.62599	+	2.03893i
$9$	0.0520854	−	0.695032i	0.0173618	−	0.231677i
$10$	2.85118	−	7.26470i	0.901624	−	2.29730i
$11$	−1.98321	+	0.955063i	−0.597960	+	0.287962i	−0.708278	−	0.705934i	$-0.750527\pi$
$11$	−1.98321	+	0.955063i	−0.597960	+	0.287962i	0.110318	+	0.993896i	$0.464813\pi$
$12$	8.86279	−	2.73381i	2.55847	−	0.789182i
$13$	−0.884105	−	2.25266i	−0.245207	−	0.624776i	0.754289	−	0.656543i	$-0.227982\pi$
$13$	−0.884105	−	2.25266i	−0.245207	−	0.624776i	−0.999495	+	0.0317667i	$0.989887\pi$
$14$	1.30168	+	1.20779i	0.347890	+	0.322795i
$15$	−4.74619	+	3.23590i	−1.22546	+	0.835505i
$16$	5.99853	+	7.52192i	1.49963	+	1.88048i
$17$	−2.49942	+	0.376727i	−0.606199	+	0.0913697i	−0.444967	−	0.895547i	$-0.646785\pi$
$17$	−2.49942	+	0.376727i	−0.606199	+	0.0913697i	−0.161231	+	0.986917i	$0.551547\pi$
$18$	−1.73978	−	0.536652i	−0.410071	−	0.126490i
$19$	−0.122786	−	1.63846i	−0.0281690	−	0.375890i	−0.993417	−	0.114554i	$-0.963456\pi$
$19$	−0.122786	−	1.63846i	−0.0281690	−	0.375890i	0.965248	−	0.261336i	$-0.0841629\pi$
$20$	−11.9071	−	8.11809i	−2.66250	−	1.81526i
$21$	−0.290840	−	1.27425i	−0.0634666	−	0.278065i
$22$	1.27950	+	5.60586i	0.272790	+	1.19517i
$23$	0.0324711	+	0.0221384i	0.00677069	+	0.00461618i	0.566701	−	0.823924i	$-0.308220\pi$
$23$	0.0324711	+	0.0221384i	0.00677069	+	0.00461618i	−0.559930	+	0.828540i	$0.689172\pi$
$24$	−1.05987	−	14.1430i	−0.216345	−	2.88693i
$25$	3.75109	+	1.15706i	0.750217	+	0.231411i
$26$	−6.25084	+	0.942162i	−1.22589	+	0.184773i
$27$	−2.76090	−	3.46206i	−0.531335	−	0.666273i
$28$	2.70925	−	1.84713i	0.511999	−	0.349075i
$29$	5.57974	+	5.17724i	1.03613	+	0.961389i	0.999280	−	0.0379317i	$-0.0120769\pi$
$29$	5.57974	+	5.17724i	1.03613	+	0.961389i	0.0368507	+	0.999321i	$0.488267\pi$
$30$	5.48212	+	13.9682i	1.00089	+	2.55024i
$31$	8.56546	−	2.64209i	1.53840	−	0.474534i	0.594316	−	0.804232i	$-0.297423\pi$
$31$	8.56546	−	2.64209i	1.53840	−	0.474534i	0.944087	+	0.329698i	$0.106947\pi$
$32$	9.35164	−	4.50351i	1.65315	−	0.796116i
$33$	1.54625	−	3.93979i	0.269168	−	0.685829i
$34$	−0.493428	+	6.58434i	−0.0846222	+	1.12920i
$35$	−1.26621	+	1.58778i	−0.214028	+	0.268383i
$36$	−1.68102	+	2.91162i	−0.280170	+	0.485269i
$37$	−5.57614	−	9.65816i	−0.916712	−	1.58779i	−0.804376	−	0.594121i	$-0.797500\pi$
$37$	−5.57614	−	9.65816i	−0.916712	−	1.58779i	−0.112336	−	0.993670i	$-0.535833\pi$
$38$	−4.24410	−	0.639696i	−0.688485	−	0.103772i
$39$	4.19217	+	2.01884i	0.671284	+	0.323273i
$40$	−16.1542	+	14.9889i	−2.55420	+	2.36995i
$41$	0.555724	−	2.43478i	0.0867894	−	0.380249i	−0.912815	−	0.408373i	$-0.866096\pi$
$41$	0.555724	−	2.43478i	0.0867894	−	0.380249i	0.999604	+	0.0281239i	$0.00895331\pi$
$42$	−3.41424			−0.526829
$43$	−6.51074	−	0.781227i	−0.992878	−	0.119136i
$43$	−6.51074	−	0.781227i	−0.992878	−	0.119136i
$44$	10.6180			1.60072
$45$	0.463348	−	2.03006i	0.0690719	−	0.302624i
$46$	0.0752553	−	0.0698267i	0.0110958	−	0.0102954i
$47$	7.92075	+	3.81443i	1.15536	+	0.556392i	0.910640	−	0.413202i	$-0.135590\pi$
$47$	7.92075	+	3.81443i	1.15536	+	0.556392i	0.244720	+	0.969594i	$0.421304\pi$
$48$	−18.2920	−	2.75708i	−2.64022	−	0.397950i
$49$	3.26896	+	5.66200i	0.466994	+	0.808857i
$50$	5.12713	−	8.88045i	0.725085	−	1.25588i
$51$	3.03019	−	3.79974i	0.424312	−	0.532070i
$52$	−0.872336	+	11.6405i	−0.120971	+	1.61425i
$53$	−2.23834	+	5.70320i	−0.307460	+	0.783395i	0.690722	+	0.723120i	$0.257293\pi$
$53$	−2.23834	+	5.70320i	−0.307460	+	0.783395i	−0.998182	+	0.0602746i	$0.980802\pi$
$54$	−10.4218	+	5.01886i	−1.41822	+	0.682981i
$55$	−6.28403	+	1.93837i	−0.847338	+	0.261369i
$56$	−1.83186	−	4.66750i	−0.244793	−	0.623721i
$57$	2.31586	+	2.14880i	0.306743	+	0.284616i
$58$	16.4284	−	11.2007i	2.15716	−	1.47072i
$59$	2.97714	+	3.73321i	0.387590	+	0.486023i	0.936901	−	0.349596i	$-0.113681\pi$
$59$	2.97714	+	3.73321i	0.387590	+	0.486023i	−0.549311	+	0.835618i	$0.685110\pi$
$60$	27.3996	−	4.12983i	3.53727	−	0.533158i
$61$	−4.87717	−	1.50441i	−0.624458	−	0.192620i	−0.0336523	−	0.999434i	$-0.510714\pi$
$61$	−4.87717	−	1.50441i	−0.624458	−	0.192620i	−0.590806	+	0.806814i	$0.701190\pi$
$62$	−1.74982	−	23.3497i	−0.222227	−	2.96542i
$63$	0.391459	+	0.266892i	0.0493192	+	0.0336253i
$64$	−1.75166	−	7.67453i	−0.218958	−	0.959317i
$65$	−1.60876	−	7.04845i	−0.199543	−	0.874253i
$66$	−9.13479	−	6.22799i	−1.12441	−	0.766613i
$67$	0.194013	+	2.58893i	0.0237025	+	0.316288i	0.996435	+	0.0843595i	$0.0268844\pi$
$67$	0.194013	+	2.58893i	0.0237025	+	0.316288i	−0.972733	+	0.231928i	$0.925497\pi$
$68$	11.6510	+	3.59386i	1.41289	+	0.435820i
$69$	−0.0747200	+	0.0112622i	−0.00899524	+	0.00135581i
$70$	3.30762	+	4.14763i	0.395337	+	0.495737i
$71$	−7.71099	+	5.25726i	−0.915126	+	0.623922i	−0.926615	−	0.376012i	$-0.877295\pi$
$71$	−7.71099	+	5.25726i	−0.915126	+	0.623922i	0.0114889	+	0.999934i	$0.496343\pi$
$72$	3.76868	+	3.49682i	0.444143	+	0.412105i
$73$	−1.43804	−	3.66406i	−0.168310	−	0.428846i	0.821687	−	0.569940i	$-0.193033\pi$
$73$	−1.43804	−	3.66406i	−0.168310	−	0.428846i	−0.989996	+	0.141093i	$0.954938\pi$
$74$	−27.8380	+	8.58689i	−3.23610	+	0.998206i
$75$	−6.80028	+	3.27484i	−0.785229	+	0.378146i
$76$	−2.89557	+	7.37780i	−0.332145	+	0.846292i
$77$	0.111819	−	1.49212i	0.0127429	−	0.170042i
$78$	7.57825	−	9.50283i	0.858068	−	1.07598i
$79$	3.10044	−	5.37012i	0.348827	−	0.604186i	−0.637215	−	0.770686i	$-0.719914\pi$
$79$	3.10044	−	5.37012i	0.348827	−	0.604186i	0.986041	+	0.166501i	$0.0532469\pi$
$80$	14.3715	+	24.8921i	1.60678	+	2.78303i
$81$	10.4867	+	1.58062i	1.16519	+	0.175624i
$82$	−5.87772	−	2.83056i	−0.649085	−	0.312583i
$83$	3.97087	−	3.68443i	0.435860	−	0.404419i	−0.431490	−	0.902118i	$-0.642012\pi$
$83$	3.97087	−	3.68443i	0.435860	−	0.404419i	0.867350	+	0.497699i	$0.165821\pi$
$84$	−1.40293	+	6.14666i	−0.153073	+	0.670655i
$85$	−7.55150			−0.819075
$86$	−5.77411	+	16.1270i	−0.622638	+	1.73902i
$87$	−14.6353			−1.56907
$88$	3.61296	−	15.8294i	0.385143	−	1.68742i
$89$	7.30600	−	6.77898i	0.774435	−	0.718570i	−0.190320	−	0.981722i	$-0.560952\pi$
$89$	7.30600	−	6.77898i	0.774435	−	0.718570i	0.964754	+	0.263152i	$0.0847620\pi$
$90$	−4.90069	−	2.36005i	−0.516578	−	0.248771i
$91$	1.62662	+	0.245174i	0.170517	+	0.0257012i
$92$	−0.0947861	−	0.164174i	−0.00988213	−	0.0171163i
$93$	−8.61749	+	14.9259i	−0.893592	+	1.54775i
$94$	14.3185	−	17.9548i	1.47684	−	1.85190i
$95$	0.366830	−	4.89500i	0.0376359	−	0.502217i
$96$	−7.29122	+	18.5777i	−0.744157	+	1.89608i
$97$	−0.852010	+	0.410306i	−0.0865085	+	0.0416603i	−0.476638	−	0.879100i	$-0.658145\pi$
$97$	−0.852010	+	0.410306i	−0.0865085	+	0.0416603i	0.390129	+	0.920760i	$0.372430\pi$
$98$	16.3198	−	5.03398i	1.64855	−	0.508509i
$99$	0.560503	+	1.42814i	0.0563326	+	0.143533i
$100$	−13.8807	−	12.8794i	−1.38807	−	1.28794i
$101$	−12.0268	+	8.19971i	−1.19671	+	0.815901i	−0.986820	−	0.161824i	$-0.948262\pi$
$101$	−12.0268	+	8.19971i	−1.19671	+	0.815901i	−0.209888	+	0.977725i	$0.567310\pi$
$102$	−7.91555	−	9.92579i	−0.783757	−	0.982800i
$103$	−0.475530	+	0.0716747i	−0.0468554	+	0.00706231i	−0.172428	−	0.985022i	$-0.555161\pi$
$103$	−0.475530	+	0.0716747i	−0.0468554	+	0.00706231i	0.125573	+	0.992084i	$0.459923\pi$
$104$	17.0570	+	5.26139i	1.67258	+	0.515922i
$105$	−0.291807	−	3.89389i	−0.0284774	−	0.380005i
$106$	13.2234	+	9.01559i	1.28437	+	0.875671i
$107$	−0.415643	−	1.82105i	−0.0401817	−	0.176047i	0.950855	−	0.309636i	$-0.100207\pi$
$107$	−0.415643	−	1.82105i	−0.0401817	−	0.176047i	−0.991037	+	0.133588i	$0.957350\pi$
$108$	4.75308	+	20.8246i	0.457365	+	2.00385i
$109$	3.78562	+	2.58100i	0.362597	+	0.247214i	0.730890	−	0.682495i	$-0.239105\pi$
$109$	3.78562	+	2.58100i	0.362597	+	0.247214i	−0.368293	+	0.929710i	$0.620058\pi$
$110$	1.28375	+	17.1305i	0.122401	+	1.63333i
$111$	20.4904	+	6.32046i	1.94486	+	0.599911i
$112$	−6.46693	+	0.974732i	−0.611067	+	0.0921035i
$113$	8.37826	+	10.5060i	0.788161	+	0.988322i	0.999939	+	0.0110047i	$0.00350297\pi$
$113$	8.37826	+	10.5060i	0.788161	+	0.988322i	−0.211779	+	0.977318i	$0.567926\pi$
$114$	6.81857	−	4.64882i	0.638618	−	0.435402i
$115$	0.0860681	+	0.0798595i	0.00802589	+	0.00744694i
$116$	−13.4141	−	34.1785i	−1.24546	−	3.17339i
$117$	−1.61172	+	0.497150i	−0.149004	+	0.0459615i
$118$	11.2380	−	5.41195i	1.03454	−	0.498210i
$119$	0.627734	−	1.59944i	0.0575443	−	0.146621i
$120$	3.16642	−	42.2530i	0.289054	−	3.85715i
$121$	−3.83742	+	4.81197i	−0.348856	+	0.437452i
$122$	−6.66631	+	11.5464i	−0.603539	+	1.04536i
$123$	2.40094	+	4.15855i	0.216486	+	0.374964i
$124$	−42.7555	−	6.44435i	−3.83956	−	0.578720i
$125$	−2.89227	−	1.39284i	−0.258692	−	0.124580i
$126$	0.907249	−	0.841804i	0.0808241	−	0.0749938i
$127$	0.0467262	−	0.204721i	0.00414628	−	0.0181660i	−0.972812	−	0.231594i	$-0.925606\pi$
$127$	0.0467262	−	0.204721i	0.00414628	−	0.0181660i	0.976959	+	0.213428i	$0.0684630\pi$
$128$	0.195885			0.0173140
$129$	10.1984	−	7.41365i	0.897922	−	0.652735i
$130$	−18.8857			−1.65638
$131$	2.11433	−	9.26347i	0.184730	−	0.809353i	−0.794608	−	0.607122i	$-0.792324\pi$
$131$	2.11433	−	9.26347i	0.184730	−	0.809353i	0.979338	−	0.202231i	$-0.0648191\pi$
$132$	−14.9658	+	13.8862i	−1.30261	+	1.20864i
$133$	1.00629	+	0.484604i	0.0872564	+	0.0420205i
$134$	6.70608	+	1.01078i	0.579317	+	0.0873180i
$135$	−6.61465	−	11.4569i	−0.569299	−	0.986054i
$136$	9.32226	−	16.1466i	0.799377	−	1.38456i
$137$	3.69528	−	4.63374i	0.315709	−	0.395887i	−0.598504	−	0.801120i	$-0.704238\pi$
$137$	3.69528	−	4.63374i	0.315709	−	0.395887i	0.914214	+	0.405233i	$0.132809\pi$
$138$	−0.0147510	+	0.196838i	−0.00125569	+	0.0167560i
$139$	3.99725	−	10.1848i	0.339043	−	0.863866i	−0.655075	−	0.755563i	$-0.727363\pi$
$139$	3.99725	−	10.1848i	0.339043	−	0.863866i	0.994118	−	0.108303i	$-0.0345416\pi$
$140$	8.82610	−	4.25042i	0.745941	−	0.359226i
$141$	−16.1527	+	4.98243i	−1.36030	+	0.419597i
$142$	8.90664	+	22.6937i	0.747429	+	1.90442i
$143$	3.90480	+	3.62312i	0.326536	+	0.302981i
$144$	5.54041	−	3.77739i	0.461701	−	0.314782i
$145$	14.1783	+	17.7790i	1.17744	+	1.47647i
$146$	−10.1673	+	1.53247i	−0.841451	+	0.126828i
$147$	−12.0123	−	3.70531i	−0.990759	−	0.305609i
$148$	4.02015	+	53.6451i	0.330454	+	4.40960i
$149$	−8.61865	−	5.87610i	−0.706068	−	0.481389i	0.156275	−	0.987714i	$-0.450051\pi$
$149$	−8.61865	−	5.87610i	−0.706068	−	0.481389i	−0.862343	+	0.506325i	$0.831004\pi$
$150$	4.38731	+	19.2221i	0.358223	+	1.56948i
$151$	−2.08440	−	9.13237i	−0.169626	−	0.743181i	−0.986148	−	0.165867i	$-0.946958\pi$
$151$	−2.08440	−	9.13237i	−0.169626	−	0.743181i	0.816522	−	0.577315i	$-0.195899\pi$
$152$	10.0137	+	6.82719i	0.812215	+	0.553759i
$153$	0.131654	+	1.75680i	0.0106436	+	0.142029i
$154$	−3.73502	−	1.15210i	−0.300977	−	0.0928390i
$155$	26.4804	−	3.99128i	2.12696	−	0.320587i
$156$	−13.9940	−	17.5479i	−1.12041	−	1.40496i
$157$	−5.96209	+	4.06488i	−0.475827	+	0.324413i	−0.777375	−	0.629038i	$-0.783449\pi$
$157$	−5.96209	+	4.06488i	−0.475827	+	0.324413i	0.301548	+	0.953451i	$0.402497\pi$
$158$	−11.8740	−	11.0175i	−0.944649	−	0.876506i
$159$	−4.30378	−	10.9659i	−0.341312	−	0.869648i
$160$	29.6318	−	9.14019i	2.34260	−	0.722596i
$161$	−0.0240692	+	0.0115911i	−0.00189692	+	0.000913507i
$162$	10.1211	−	25.7881i	0.795187	−	2.02610i
$163$	−0.580643	+	7.74814i	−0.0454795	+	0.606881i	0.927176	+	0.374627i	$0.122229\pi$
$163$	−0.580643	+	7.74814i	−0.0454795	+	0.606881i	−0.972655	+	0.232254i	$0.925390\pi$
$164$	−7.51104	+	9.41855i	−0.586514	+	0.735465i
$165$	6.32220	−	10.9504i	0.492182	−	0.852485i
$166$	−7.07510	−	12.2544i	−0.549134	−	0.951128i
$167$	11.5269	+	1.73741i	0.891981	+	0.134445i	0.579012	−	0.815319i	$-0.303438\pi$
$167$	11.5269	+	1.73741i	0.891981	+	0.134445i	0.312969	+	0.949763i	$0.398676\pi$
$168$	8.68615	+	4.18303i	0.670151	+	0.322728i
$169$	5.23683	−	4.85907i	0.402833	−	0.373774i
$170$	−4.38950	+	19.2317i	−0.336659	+	1.47500i
$171$	−1.14518			−0.0875741
$172$	26.6608	+	17.0218i	2.03287	+	1.29790i
$173$	−5.35127			−0.406849			−0.203425	−	0.979091i	$-0.565207\pi$
$173$	−5.35127			−0.406849			−0.203425	+	0.979091i	$0.565207\pi$
$174$	−8.50715	+	37.2723i	−0.644926	+	2.82560i
$175$	−1.95609	+	1.81498i	−0.147866	+	0.137200i
$176$	−19.0803	−	9.18856i	−1.43823	−	0.692614i
$177$	−9.07852	−	1.36837i	−0.682383	−	0.102853i
$178$	−13.0175	−	22.5469i	−0.975699	−	1.68996i
$179$	−7.01753	+	12.1547i	−0.524515	+	0.908487i	0.475078	+	0.879944i	$0.342420\pi$
$179$	−7.01753	+	12.1547i	−0.524515	+	0.908487i	−0.999593	+	0.0285427i	$0.990913\pi$
$180$	−6.26252	+	7.85295i	−0.466780	+	0.585324i
$181$	−1.45930	+	19.4730i	−0.108469	+	1.44742i	0.631814	+	0.775120i	$0.282311\pi$
$181$	−1.45930	+	19.4730i	−0.108469	+	1.44742i	−0.740283	+	0.672296i	$0.765308\pi$
$182$	1.56991	−	4.00007i	0.116369	−	0.296505i
$183$	8.84174	−	4.25796i	0.653600	−	0.314757i
$184$	−0.277006	+	0.0854450i	−0.0204212	+	0.00629909i
$185$	−12.1724	−	31.0149i	−0.894936	−	2.28026i
$186$	33.0032	+	30.6225i	2.41991	+	2.24535i
$187$	4.59707	−	3.13423i	0.336171	−	0.229198i
$188$	−26.4404	−	33.1553i	−1.92837	−	2.41810i
$189$	2.97648	−	0.448632i	0.216507	−	0.0326332i
$190$	−12.2530	−	3.77956i	−0.888929	−	0.274198i
$191$	0.651998	+	8.70031i	0.0471769	+	0.629533i	0.969811	+	0.243857i	$0.0784127\pi$
$191$	0.651998	+	8.70031i	0.0471769	+	0.629533i	−0.922634	+	0.385676i	$0.873968\pi$
$192$	12.5057	+	8.52626i	0.902523	+	0.615329i
$193$	4.33067	+	18.9739i	0.311729	+	1.36577i	0.851674	+	0.524072i	$0.175588\pi$
$193$	4.33067	+	18.9739i	0.311729	+	1.36577i	−0.539945	+	0.841700i	$0.681555\pi$
$194$	0.549688	+	2.40834i	0.0394653	+	0.172909i
$195$	11.4855	+	7.83069i	0.822495	+	0.560767i
$196$	−2.35677	−	31.4490i	−0.168341	−	2.24635i
$197$	−22.2716	−	6.86986i	−1.58678	−	0.489458i	−0.629110	−	0.777317i	$-0.716580\pi$
$197$	−22.2716	−	6.86986i	−1.58678	−	0.489458i	−0.957673	+	0.287859i	$0.907057\pi$
$198$	3.96289	−	0.597310i	0.281630	−	0.0424489i
$199$	−11.7392	−	14.7205i	−0.832169	−	1.04351i	−0.998351	−	0.0574120i	$-0.981715\pi$
$199$	−11.7392	−	14.7205i	−0.832169	−	1.04351i	0.166181	−	0.986095i	$-0.446856\pi$
$200$	−23.9239	+	16.3111i	−1.69168	+	1.15337i
$201$	−3.65927	−	3.39530i	−0.258105	−	0.239486i
$202$	13.8916	+	35.3952i	0.977410	+	2.49040i
$203$	−4.94428	+	1.52511i	−0.347020	+	0.107042i
$204$	−21.1219	+	10.1718i	−1.47883	+	0.712168i
$205$	2.72585	−	6.94536i	0.190382	−	0.485085i
$206$	−0.0938777	+	1.25271i	−0.00654077	+	0.0872805i
$207$	0.0170782	−	0.0214154i	0.00118702	−	0.00148847i
$208$	11.6410	−	20.1628i	0.807160	−	1.39804i
$209$	1.80835	+	3.13215i	0.125086	+	0.216655i
$210$	−10.0863	−	1.52027i	−0.696022	−	0.104908i
$211$	−14.0286	−	6.75583i	−0.965770	−	0.465090i	−0.116582	−	0.993181i	$-0.537194\pi$
$211$	−14.0286	−	6.75583i	−0.965770	−	0.465090i	−0.849188	+	0.528091i	$0.822908\pi$
$212$	21.6643	−	20.1016i	1.48791	−	1.38058i
$213$	3.99300	−	17.4945i	0.273596	−	1.19870i
$214$	−4.87933			−0.333544
$215$	−18.8861	−	5.20694i	−1.28802	−	0.355110i
$216$	32.6629			2.22243
$217$	−1.35587	+	5.94045i	−0.0920424	+	0.403264i
$218$	8.77359	−	8.14071i	0.594223	−	0.551358i
$219$	6.81876	+	3.28374i	0.460769	+	0.221895i
$220$	31.3675	+	4.72788i	2.11479	+	0.318754i
$221$	3.05839	+	5.29729i	0.205730	+	0.356334i
$222$	28.0071	−	48.5097i	1.87971	−	3.25576i
$223$	−11.3004	+	14.1702i	−0.756730	+	0.948909i	−0.999777	−	0.0211054i	$-0.993281\pi$
$223$	−11.3004	+	14.1702i	−0.756730	+	0.948909i	0.243048	+	0.970014i	$0.421853\pi$
$224$	−0.527271	+	7.03594i	−0.0352297	+	0.470108i
$225$	0.999568	−	2.54686i	0.0666379	−	0.169791i
$226$	31.6261	−	15.2303i	2.10374	−	1.01311i
$227$	23.8281	−	7.34998i	1.58152	−	0.487836i	0.625279	−	0.780402i	$-0.284985\pi$
$227$	23.8281	−	7.34998i	1.58152	−	0.487836i	0.956245	+	0.292566i	$0.0945091\pi$
$228$	−5.56747	−	14.1857i	−0.368715	−	0.939470i
$229$	−0.350174	−	0.324914i	−0.0231402	−	0.0214709i	0.668518	−	0.743696i	$-0.266929\pi$
$229$	−0.350174	−	0.324914i	−0.0231402	−	0.0214709i	−0.691658	+	0.722225i	$0.743119\pi$
$230$	0.253410	−	0.172772i	0.0167094	−	0.0113923i
$231$	1.79379	+	2.24934i	0.118023	+	0.147996i
$232$	−55.5181	+	8.36801i	−3.64494	+	0.549387i
$233$	−10.0428	−	3.09778i	−0.657924	−	0.202943i	−0.0522233	−	0.998635i	$-0.516631\pi$
$233$	−10.0428	−	3.09778i	−0.657924	−	0.202943i	−0.605700	+	0.795693i	$0.707107\pi$
$234$	0.329255	+	4.39360i	0.0215241	+	0.287219i
$235$	21.7009	+	14.7954i	1.41561	+	0.965147i
$236$	−5.12535	−	22.4556i	−0.333632	−	1.46174i
$237$	2.65306	+	11.6238i	0.172335	+	0.755049i
$238$	−3.70846	−	2.52839i	−0.240384	−	0.163891i
$239$	0.952467	+	12.7098i	0.0616099	+	0.822127i	0.939343	+	0.342978i	$0.111436\pi$
$239$	0.952467	+	12.7098i	0.0616099	+	0.822127i	−0.877733	+	0.479149i	$0.840945\pi$
$240$	−52.8103	−	16.2898i	−3.40889	−	1.05150i
$241$	4.44144	−	0.669439i	0.286098	−	0.0431224i	−0.00442537	−	0.999990i	$-0.501409\pi$
$241$	4.44144	−	0.669439i	0.286098	−	0.0431224i	0.290524	+	0.956868i	$0.406171\pi$
$242$	10.0242	+	12.5700i	0.644380	+	0.808027i
$243$	−5.87182	+	4.00334i	−0.376678	+	0.256815i
$244$	18.0477	+	16.7458i	1.15539	+	1.07204i
$245$	7.13598	+	18.1822i	0.455901	+	1.16162i
$246$	11.9863	−	3.69729i	0.764220	−	0.235731i
$247$	−3.58235	+	1.72517i	−0.227940	+	0.109770i
$248$	−24.1557	+	61.5477i	−1.53389	+	3.90828i
$249$	−0.778342	+	10.3863i	−0.0493254	+	0.658202i
$250$	−5.22840	+	6.55620i	−0.330673	+	0.414651i
$251$	1.16008	−	2.00931i	0.0732233	−	0.126827i	−0.827089	−	0.562071i	$-0.810005\pi$
$251$	1.16008	−	2.00931i	0.0732233	−	0.126827i	0.900312	+	0.435245i	$0.143338\pi$
$252$	−1.14270	−	1.97922i	−0.0719836	−	0.124679i
$253$	−0.0855406	−	0.0128932i	−0.00537789	−	0.000810586i
$254$	−0.494208	−	0.237998i	−0.0310094	−	0.0149333i
$255$	10.6437	−	9.87589i	0.666533	−	0.618452i
$256$	3.61719	−	15.8479i	0.226074	−	0.990496i
$257$	0.450674			0.0281123			0.0140561	−	0.999901i	$-0.495526\pi$
$257$	0.450674			0.0281123			0.0140561	+	0.999901i	$0.495526\pi$
$258$	−12.9525	−	30.2820i	−0.806386	−	1.88528i
$259$	7.58095			0.471057
$260$	−7.76024	+	33.9998i	−0.481269	+	2.10858i
$261$	3.88897	−	3.60843i	0.240721	−	0.223357i
$262$	−22.3626	−	10.7692i	−1.38156	−	0.665326i
$263$	−7.56220	−	1.13982i	−0.466305	−	0.0702842i	−0.0883127	−	0.996093i	$-0.528147\pi$
$263$	−7.56220	−	1.13982i	−0.466305	−	0.0702842i	−0.377993	+	0.925809i	$0.623386\pi$
$264$	15.6094	+	27.0363i	0.960692	+	1.66397i
$265$	−9.15195	+	15.8517i	−0.562200	+	0.973759i
$266$	1.81909	−	2.28106i	0.111535	−	0.139861i
$267$	−1.43207	+	19.1096i	−0.0876413	+	1.16949i
$268$	4.57527	−	11.6576i	0.279479	−	0.712102i
$269$	20.2042	−	9.72982i	1.23187	−	0.593238i	0.299277	−	0.954166i	$-0.403255\pi$
$269$	20.2042	−	9.72982i	1.23187	−	0.593238i	0.932593	+	0.360929i	$0.117540\pi$
$270$	−33.0226	+	10.1861i	−2.00969	+	0.619908i
$271$	−2.35324	−	5.99596i	−0.142949	−	0.364229i	0.841411	−	0.540396i	$-0.181725\pi$
$271$	−2.35324	−	5.99596i	−0.142949	−	0.364229i	−0.984360	+	0.176167i	$0.943630\pi$
$272$	−17.8266	−	16.5406i	−1.08089	−	1.00292i
$273$	−2.61333	+	1.78174i	−0.158166	+	0.107836i
$274$	−9.65292	−	12.1044i	−0.583154	−	0.731252i
$275$	−8.54425	+	1.28784i	−0.515238	+	0.0776596i
$276$	0.348307	+	0.107438i	0.0209656	+	0.00646703i
$277$	−1.04050	−	13.8845i	−0.0625177	−	0.834240i	−0.937033	−	0.349242i	$-0.886439\pi$
$277$	−1.04050	−	13.8845i	−0.0625177	−	0.834240i	0.874515	−	0.484999i	$-0.161180\pi$
$278$	−23.6145	−	16.1001i	−1.41631	−	0.965621i
$279$	−1.39020	−	6.09088i	−0.0832293	−	0.364652i
$280$	−3.33335	−	14.6044i	−0.199206	−	0.872777i
$281$	−5.10601	−	3.48122i	−0.304599	−	0.207672i	0.401368	−	0.915917i	$-0.368535\pi$
$281$	−5.10601	−	3.48122i	−0.304599	−	0.207672i	−0.705967	+	0.708245i	$0.749487\pi$
$282$	3.29979	+	44.0327i	0.196500	+	2.62211i
$283$	−1.04493	−	0.322319i	−0.0621148	−	0.0191599i	0.263542	−	0.964648i	$-0.415109\pi$
$283$	−1.04493	−	0.322319i	−0.0621148	−	0.0191599i	−0.325657	+	0.945488i	$0.605585\pi$
$284$	44.5153	−	6.70960i	2.64150	−	0.398142i
$285$	5.88467	+	7.37914i	0.348578	+	0.437103i
$286$	11.4969	−	7.83845i	0.679825	−	0.463497i
$287$	1.24447	+	1.15469i	0.0734585	+	0.0681595i
$288$	−2.64300	−	6.73425i	−0.155740	−	0.396820i
$289$	−10.1396	+	3.12764i	−0.596444	+	0.183979i
$290$	53.5199	−	25.7738i	3.14280	−	1.51349i
$291$	0.664289	−	1.69258i	0.0389413	−	0.0992208i
$292$	−1.41890	+	18.9339i	−0.0830346	+	1.10802i
$293$	11.3840	−	14.2751i	0.665059	−	0.833958i	−0.328824	−	0.944391i	$-0.606652\pi$
$293$	11.3840	−	14.2751i	0.665059	−	0.833958i	0.993884	+	0.110433i	$0.0352238\pi$
$294$	−16.4189	+	28.4384i	−0.957569	+	1.65856i
$295$	7.13272	+	12.3542i	0.415283	+	0.719292i
$296$	81.3429	+	12.2605i	4.72796	+	0.712625i
$297$	8.78192	+	4.22915i	0.509579	+	0.245400i
$298$	−19.9747	+	18.5338i	−1.15710	+	1.07363i
$299$	0.0211625	−	0.0927191i	0.00122386	−	0.00536209i
$300$	36.4082			2.10203
$301$	2.67280	−	3.56731i	0.154057	−	0.205617i
$302$	−24.4693			−1.40805
$303$	6.22784	−	27.2860i	0.357780	−	1.56754i
$304$	11.5879	−	10.7520i	0.664610	−	0.616668i
$305$	−13.7382	−	6.61597i	−0.786648	−	0.378830i
$306$	4.55062	+	0.685896i	0.260142	+	0.0392101i
$307$	−9.05158	−	15.6778i	−0.516601	−	0.894779i	−0.999814	−	0.0192762i	$-0.993864\pi$
$307$	−9.05158	−	15.6778i	−0.516601	−	0.894779i	0.483213	−	0.875503i	$-0.339470\pi$
$308$	−3.60887	+	6.25075i	−0.205635	+	0.356170i
$309$	0.576513	−	0.722925i	0.0327967	−	0.0411257i
$310$	5.22768	−	69.7586i	0.296912	−	3.96202i
$311$	−6.32352	+	16.1121i	−0.358574	+	0.913631i	0.631790	+	0.775140i	$0.282321\pi$
$311$	−6.32352	+	16.1121i	−0.358574	+	0.913631i	−0.990364	+	0.138491i	$0.955775\pi$
$312$	−30.9224	+	14.8914i	−1.75063	+	0.843061i
$313$	6.21930	−	1.91840i	0.351535	−	0.108434i	−0.113958	−	0.993486i	$-0.536353\pi$
$313$	6.21930	−	1.91840i	0.351535	−	0.108434i	0.465494	+	0.885051i	$0.345877\pi$
$314$	6.88656	+	17.5467i	0.388631	+	0.990216i
$315$	1.03760	+	0.962755i	0.0584623	+	0.0542451i
$316$	−24.7139	+	16.8497i	−1.39027	+	0.947868i
$317$	8.24997	+	10.3451i	0.463365	+	0.581041i	0.957532	−	0.288326i	$-0.0930985\pi$
$317$	8.24997	+	10.3451i	0.463365	+	0.581041i	−0.494168	+	0.869367i	$0.664527\pi$
$318$	−30.4288	+	4.58640i	−1.70636	+	0.257192i
$319$	−16.0104	−	4.93854i	−0.896409	−	0.276505i
$320$	−1.75748	−	23.4520i	−0.0982463	−	1.31101i
$321$	2.96741	+	2.02315i	0.165625	+	0.112921i
$322$	0.0155286	+	0.0680354i	0.000865377	+	0.00379147i
$323$	0.924148	+	4.04896i	0.0514210	+	0.225290i
$324$	−42.2674	−	28.8174i	−2.34819	−	1.60097i
$325$	−0.709895	−	9.47289i	−0.0393779	−	0.525462i
$326$	19.3949	+	5.98254i	1.07419	+	0.331342i
$327$	−8.71119	+	1.31300i	−0.481730	+	0.0726091i
$328$	11.4855	+	14.4024i	0.634182	+	0.795240i
$329$	−4.93767	+	3.36645i	−0.272223	+	0.185598i
$330$	−24.2127	−	22.4661i	−1.33287	−	1.23672i
$331$	−3.89417	−	9.92219i	−0.214043	−	0.545373i	0.783017	−	0.622001i	$-0.213680\pi$
$331$	−3.89417	−	9.92219i	−0.214043	−	0.545373i	−0.997060	+	0.0766279i	$0.975585\pi$
$332$	−24.9688	+	7.70186i	−1.37034	+	0.422695i
$333$	−7.00316	+	3.37254i	−0.383771	+	0.184814i
$334$	11.1250	−	28.3461i	0.608735	−	1.55103i
$335$	−0.579625	+	7.73456i	−0.0316683	+	0.422584i
$336$	7.84023	−	9.83134i	0.427720	−	0.536343i
$337$	15.8233	−	27.4068i	0.861953	−	1.49295i	−0.00808906	−	0.999967i	$-0.502575\pi$
$337$	15.8233	−	27.4068i	0.861953	−	1.49295i	0.870042	−	0.492978i	$-0.164092\pi$
$338$	−9.33070	−	16.1613i	−0.507523	−	0.879056i
$339$	−25.5488	−	3.85086i	−1.38762	−	0.209150i
$340$	32.8191	+	15.8048i	1.77986	+	0.857137i
$341$	−14.4637	+	13.4204i	−0.783255	+	0.726754i
$342$	−0.665665	+	2.91647i	−0.0359950	+	0.157705i
$343$	−9.20263			−0.496895
$344$	34.4482	−	33.9543i	1.85732	−	1.83069i
$345$	−0.225752			−0.0121541
$346$	−3.11056	+	13.6283i	−0.167225	+	0.732659i
$347$	−24.8966	+	23.1007i	−1.33652	+	1.24011i	−0.388679	+	0.921373i	$0.627068\pi$
$347$	−24.8966	+	23.1007i	−1.33652	+	1.24011i	−0.947843	+	0.318738i	$0.896741\pi$
$348$	63.6056	+	30.6308i	3.40962	+	1.64199i
$349$	34.7537	+	5.23828i	1.86032	+	0.280399i	0.980736	−	0.195336i	$-0.0625799\pi$
$349$	34.7537	+	5.23828i	1.86032	+	0.280399i	0.879589	+	0.475735i	$0.157818\pi$
$350$	3.48525	+	6.03664i	0.186295	+	0.322672i
$351$	−5.35792	+	9.28020i	−0.285985	+	0.495340i
$352$	−14.2451	+	17.8628i	−0.759267	+	0.952091i
$353$	0.821043	−	10.9561i	0.0436997	−	0.583132i	−0.931777	−	0.363030i	$-0.881742\pi$
$353$	0.821043	−	10.9561i	0.0436997	−	0.583132i	0.975477	−	0.220101i	$-0.0706388\pi$
$354$	−8.76198	+	22.3252i	−0.465694	+	1.18657i
$355$	−25.1206	+	12.0974i	−1.33326	+	0.642066i
$356$	−45.9401	+	14.1706i	−2.43482	+	0.751042i
$357$	1.20698	+	3.07533i	0.0638801	+	0.162764i
$358$	26.8757	+	24.9370i	1.42043	+	1.31796i
$359$	−11.5329	+	7.86296i	−0.608681	+	0.414991i	−0.828053	−	0.560650i	$-0.810551\pi$
$359$	−11.5329	+	7.86296i	−0.608681	+	0.414991i	0.219372	+	0.975641i	$0.429599\pi$
$360$	9.57634	+	12.0084i	0.504718	+	0.632896i
$361$	16.1183	−	2.42944i	0.848331	−	0.127865i
$362$	48.7442	+	15.0356i	2.56194	+	0.790254i
$363$	−0.884359	−	11.8010i	−0.0464168	−	0.619390i
$364$	−6.55623	−	4.46996i	−0.343640	−	0.234289i
$365$	−2.61673	−	11.4646i	−0.136966	−	0.600087i
$366$	−5.70440	−	24.9926i	−0.298174	−	1.30638i
$367$	23.0999	+	15.7492i	1.20580	+	0.822104i	0.988085	−	0.153908i	$-0.0491859\pi$
$367$	23.0999	+	15.7492i	1.20580	+	0.822104i	0.217719	+	0.976011i	$0.430138\pi$
$368$	0.0282555	+	0.377043i	0.00147292	+	0.0196547i
$369$	−1.66331	−	0.513062i	−0.0865883	−	0.0267090i
$370$	−86.0622	+	12.9718i	−4.47416	+	0.674371i
$371$	−2.59667	−	3.25613i	−0.134813	−	0.169050i
$372$	68.6909	−	46.8326i	3.56146	−	2.42816i
$373$	−0.876784	−	0.813537i	−0.0453982	−	0.0421234i	0.657147	−	0.753762i	$-0.271763\pi$
$373$	−0.876784	−	0.813537i	−0.0453982	−	0.0421234i	−0.702546	+	0.711639i	$0.747953\pi$
$374$	−5.30989	−	13.5294i	−0.274568	−	0.699587i
$375$	5.89815	−	1.81934i	0.304579	−	0.0939502i
$376$	−58.4252	+	28.1361i	−3.01305	+	1.45101i
$377$	6.72950	−	17.1465i	0.346587	−	0.883089i
$378$	0.587608	−	7.84108i	0.0302233	−	0.403302i
$379$	20.5142	−	25.7239i	1.05374	−	1.32135i	0.108817	−	0.994062i	$-0.465294\pi$
$379$	20.5142	−	25.7239i	1.05374	−	1.32135i	0.944925	−	0.327288i	$-0.106135\pi$
$380$	−11.8392	+	20.5061i	−0.607338	+	1.05194i
$381$	0.201875	+	0.349658i	0.0103424	+	0.0179135i
$382$	22.5364	+	3.39681i	1.15306	+	0.173796i
$383$	0.101772	+	0.0490107i	0.00520029	+	0.00250433i	0.436482	−	0.899713i	$-0.356224\pi$
$383$	0.101772	+	0.0490107i	0.00520029	+	0.00250433i	−0.431282	+	0.902217i	$0.641939\pi$
$384$	−0.276096	+	0.256180i	−0.0140895	+	0.0130731i
$385$	0.994730	−	4.35820i	0.0506962	−	0.222114i
$386$	50.8388			2.58763
$387$	−0.882092	+	4.48448i	−0.0448393	+	0.227959i
$388$	4.56161			0.231580
$389$	3.94066	−	17.2652i	0.199800	−	0.875379i	−0.771256	−	0.636525i	$-0.780371\pi$
$389$	3.94066	−	17.2652i	0.199800	−	0.875379i	0.971056	−	0.238854i	$-0.0767717\pi$
$390$	26.6189	−	24.6987i	1.34790	−	1.25067i
$391$	−0.0894991	−	0.0431005i	−0.00452617	−	0.00217969i
$392$	−47.6865	−	7.18758i	−2.40853	−	0.363028i
$393$	9.13471	+	15.8218i	0.460785	+	0.798103i
$394$	−30.4416	+	52.7264i	−1.53363	+	2.65632i
$395$	11.5504	−	14.4838i	0.581166	−	0.728759i
$396$	0.553041	−	7.37982i	0.0277914	−	0.370850i
$397$	3.79333	−	9.66525i	0.190382	−	0.485085i	−0.803530	−	0.595264i	$-0.797047\pi$
$397$	3.79333	−	9.66525i	0.190382	−	0.485085i	0.993912	+	0.110179i	$0.0351425\pi$
$398$	−44.3128	+	21.3399i	−2.22120	+	1.06967i
$399$	−2.05211	+	0.632992i	−0.102734	+	0.0316892i
$400$	13.7977	+	35.1560i	0.689886	+	1.75780i
$401$	−26.5760	−	24.6589i	−1.32714	−	1.23141i	−0.952610	−	0.304194i	$-0.901613\pi$
$401$	−26.5760	−	24.6589i	−1.32714	−	1.23141i	−0.374532	−	0.927214i	$-0.622197\pi$
$402$	−10.7740	+	7.34557i	−0.537357	+	0.366364i
$403$	−13.5245	−	16.9592i	−0.673704	−	0.844798i
$404$	69.4301	−	10.4649i	3.45428	−	0.520649i
$405$	30.2759	+	9.33888i	1.50442	+	0.464052i
$406$	1.01006	+	13.4783i	0.0501282	+	0.668915i
$407$	20.2828	+	13.8286i	1.00538	+	0.685457i
$408$	7.97711	+	34.9500i	0.394926	+	1.73028i
$409$	4.39223	+	19.2436i	0.217182	+	0.951535i	0.959549	+	0.281542i	$0.0908458\pi$
$409$	4.39223	+	19.2436i	0.217182	+	0.951535i	−0.742367	+	0.669993i	$0.766297\pi$
$410$	−16.1035	−	10.9792i	−0.795295	−	0.542223i
$411$	0.851604	+	11.3639i	0.0420065	+	0.560538i
$412$	2.21668	+	0.683755i	0.109208	+	0.0336862i
$413$	−3.20960	+	0.483770i	−0.157934	+	0.0238048i
$414$	−0.0446121	−	0.0559418i	−0.00219256	−	0.00274939i
$415$	13.3713	−	9.11638i	0.656370	−	0.447506i
$416$	−18.4127	−	17.0845i	−0.902758	−	0.837637i
$417$	7.68573	+	19.5829i	0.376372	+	0.958980i
$418$	9.02789	−	2.78474i	0.441569	−	0.136206i
$419$	−13.3314	+	6.42007i	−0.651282	+	0.313641i	−0.730193	−	0.683241i	$-0.760570\pi$
$419$	−13.3314	+	6.42007i	−0.651282	+	0.313641i	0.0789110	+	0.996882i	$0.474856\pi$
$420$	−6.88146	+	17.5337i	−0.335781	+	0.855556i
$421$	1.94811	−	25.9957i	0.0949450	−	1.26695i	−0.722672	−	0.691191i	$-0.757086\pi$
$421$	1.94811	−	25.9957i	0.0949450	−	1.26695i	0.817617	−	0.575762i	$-0.195295\pi$
$422$	−25.3598	+	31.8001i	−1.23449	+	1.54801i
$423$	3.06371	−	5.30650i	0.148963	−	0.258011i
$424$	−22.5960	−	39.1374i	−1.09736	−	1.90068i
$425$	−9.81144	−	1.47884i	−0.475925	−	0.0717341i
$426$	−42.2327	−	20.3382i	−2.04618	−	0.985389i
$427$	2.54331	−	2.35985i	0.123079	−	0.114201i
$428$	−2.00495	+	8.78425i	−0.0969128	+	0.424603i
$429$	−10.2421			−0.494491
$430$	−24.2387	+	45.0711i	−1.16889	+	2.17352i
$431$	22.7264			1.09469			0.547345	−	0.836907i	$-0.315638\pi$
$431$	22.7264			1.09469			0.547345	+	0.836907i	$0.315638\pi$
$432$	9.47999	−	41.5345i	0.456106	−	1.99833i
$433$	8.63794	−	8.01484i	0.415113	−	0.385169i	−0.444782	−	0.895639i	$-0.646719\pi$
$433$	8.63794	−	8.01484i	0.415113	−	0.385169i	0.859896	+	0.510470i	$0.170529\pi$
$434$	14.3406	+	6.90608i	0.688371	+	0.331502i
$435$	−43.2355	−	6.51670i	−2.07298	−	0.312452i
$436$	−11.0506	−	19.1402i	−0.529227	−	0.916647i
$437$	0.0322860	−	0.0559211i	0.00154445	−	0.00267507i
$438$	12.3264	−	15.4568i	0.588978	−	0.738555i
$439$	−1.27757	+	17.0480i	−0.0609753	+	0.813659i	0.879955	+	0.475058i	$0.157573\pi$
$439$	−1.27757	+	17.0480i	−0.0609753	+	0.813659i	−0.940930	+	0.338601i	$0.890046\pi$
$440$	17.7218	−	45.1543i	0.844852	−	2.15265i
$441$	4.10554	−	1.97712i	0.195502	−	0.0941487i
$442$	15.2685	−	4.70972i	0.726250	−	0.224019i
$443$	14.5169	+	36.9885i	0.689719	+	1.75738i	0.652161	+	0.758081i	$0.273863\pi$
$443$	14.5169	+	36.9885i	0.689719	+	1.75738i	0.0375580	+	0.999294i	$0.488042\pi$
$444$	−75.8237	−	70.3541i	−3.59843	−	3.33886i
$445$	24.6018	−	16.7732i	1.16624	−	0.795127i
$446$	29.5192	+	37.0159i	1.39777	+	1.75275i
$447$	19.8326	−	2.98928i	0.938049	−	0.141388i
$448$	5.11333	+	1.57725i	0.241582	+	0.0745181i
$449$	−1.53481	−	20.4806i	−0.0724321	−	0.966539i	−0.908492	−	0.417901i	$-0.862766\pi$
$449$	−1.53481	−	20.4806i	−0.0724321	−	0.966539i	0.836060	−	0.548638i	$-0.184853\pi$
$450$	−5.90514	−	4.02606i	−0.278371	−	0.189790i
$451$	1.22326	+	5.35943i	0.0576009	+	0.252366i
$452$	−14.4238	−	63.1946i	−0.678436	−	2.97242i
$453$	14.8813	+	10.1459i	0.699183	+	0.476695i
$454$	−4.86778	−	64.9561i	−0.228456	−	3.04854i
$455$	4.69618	+	1.44858i	0.220161	+	0.0679105i
$456$	−23.0427	+	3.47312i	−1.07907	+	0.162644i
$457$	13.7826	+	17.2829i	0.644724	+	0.808458i	0.991585	−	0.129458i	$-0.0413238\pi$
$457$	13.7826	+	17.2829i	0.644724	+	0.808458i	−0.346861	+	0.937917i	$0.612752\pi$
$458$	−1.03102	+	0.702936i	−0.0481763	+	0.0328460i
$459$	8.20490	+	7.61304i	0.382972	+	0.355346i
$460$	−0.206913	−	0.527207i	−0.00964739	−	0.0245812i
$461$	4.74602	−	1.46395i	0.221044	−	0.0681831i	−0.182255	−	0.983251i	$-0.558340\pi$
$461$	4.74602	−	1.46395i	0.221044	−	0.0681831i	0.403299	+	0.915068i	$0.367863\pi$
$462$	6.77116	−	3.26082i	0.315023	−	0.151707i
$463$	−14.6914	+	37.4330i	−0.682766	+	1.73966i	−0.00983742	+	0.999952i	$0.503131\pi$
$463$	−14.6914	+	37.4330i	−0.682766	+	1.73966i	−0.672928	+	0.739708i	$0.734964\pi$
$464$	−5.47256	+	73.0262i	−0.254057	+	3.39016i
$465$	−32.1038	+	40.2568i	−1.48878	+	1.86687i
$466$	−13.7268	+	23.7756i	−0.635884	+	1.10138i
$467$	−9.69685	−	16.7954i	−0.448717	−	0.777200i	0.549586	−	0.835437i	$-0.314785\pi$
$467$	−9.69685	−	16.7954i	−0.448717	−	0.777200i	−0.998303	+	0.0582371i	$0.981452\pi$
$468$	8.04509	+	1.21260i	0.371884	+	0.0560526i
$469$	−1.59003	−	0.765719i	−0.0734208	−	0.0353576i
$470$	50.2942	−	46.6662i	2.31990	−	2.15255i
$471$	3.08736	−	13.5266i	0.142258	−	0.623273i
$472$	−35.2211			−1.62118
$473$	13.6583	−	4.66882i	0.628008	−	0.214673i
$474$	31.1450			1.43054
$475$	1.43522	−	6.28809i	0.0658523	−	0.288518i
$476$	−6.07568	+	5.63741i	−0.278478	+	0.258390i
$477$	3.84732	+	1.85277i	0.176157	+	0.0848326i
$478$	32.9221	+	4.96220i	1.50582	+	0.226966i
$479$	−1.26895	−	2.19788i	−0.0579796	−	0.100424i	0.835579	−	0.549371i	$-0.185133\pi$
$479$	−1.26895	−	2.19788i	−0.0579796	−	0.100424i	−0.893558	+	0.448947i	$0.851799\pi$
$480$	−29.8117	+	51.6355i	−1.36071	+	2.35683i
$481$	−16.8267	+	21.1000i	−0.767230	+	0.962076i
$482$	0.876815	−	11.7003i	0.0399378	−	0.532933i
$483$	0.0187661	−	0.0478152i	0.000853886	−	0.00217567i
$484$	26.7487	−	12.8815i	1.21585	−	0.585522i
$485$	−2.69969	+	0.832745i	−0.122587	+	0.0378130i
$486$	6.78230	+	17.2810i	0.307651	+	0.783883i
$487$	−0.530064	−	0.491827i	−0.0240195	−	0.0222868i	0.668072	−	0.744097i	$-0.267120\pi$
$487$	−0.530064	−	0.491827i	−0.0240195	−	0.0222868i	−0.692091	+	0.721810i	$0.743310\pi$
$488$	31.1060	−	21.2077i	1.40810	−	0.960027i
$489$	−9.31465	−	11.6802i	−0.421223	−	0.528197i
$490$	50.4531	−	7.60459i	2.27924	−	0.343540i
$491$	−4.96897	−	1.53273i	−0.224247	−	0.0691709i	0.180596	−	0.983557i	$-0.442197\pi$
$491$	−4.96897	−	1.53273i	−0.224247	−	0.0691709i	−0.404842	+	0.914386i	$0.632674\pi$
$492$	−1.73097	−	23.0982i	−0.0780382	−	1.04135i
$493$	−15.8965	−	10.8381i	−0.715943	−	0.488122i
$494$	2.31121	+	10.1261i	0.103986	+	0.455595i
$495$	1.01992	+	4.46856i	0.0458420	+	0.200847i
$496$	71.2538	+	48.5800i	3.19939	+	2.18131i
$497$	−0.474089	−	6.32628i	−0.0212658	−	0.283773i
$498$	25.9986	+	8.01950i	1.16502	+	0.359362i
$499$	−0.153922	+	0.0232000i	−0.00689050	+	0.00103858i	−0.152487	−	0.988306i	$-0.548728\pi$
$499$	−0.153922	+	0.0232000i	−0.00689050	+	0.00103858i	0.145596	+	0.989344i	$0.453490\pi$
$500$	9.65474	+	12.1067i	0.431773	+	0.541426i
$501$	−18.5192	+	12.6261i	−0.827375	+	0.564095i
$502$	−4.44285	−	4.12237i	−0.198294	−	0.183990i
$503$	−7.28863	−	18.5711i	−0.324984	−	0.828046i	−0.996225	−	0.0868067i	$-0.972334\pi$
$503$	−7.28863	−	18.5711i	−0.324984	−	0.828046i	0.671241	−	0.741239i	$-0.265761\pi$
$504$	−3.33948	+	1.03009i	−0.148752	+	0.0458839i
$505$	−39.1804	+	18.8683i	−1.74350	+	0.839628i
$506$	−0.0825580	+	0.210354i	−0.00367015	+	0.00935140i
$507$	−1.02649	+	13.6975i	−0.0455878	+	0.608327i
$508$	−0.631541	+	0.791927i	−0.0280201	+	0.0351361i
$509$	−9.32749	+	16.1557i	−0.413434	+	0.716089i	−0.995263	−	0.0972228i	$-0.969004\pi$
$509$	−9.32749	+	16.1557i	−0.413434	+	0.716089i	0.581829	+	0.813311i	$0.302337\pi$
$510$	−18.9643	−	32.8472i	−0.839755	−	1.45450i
$511$	2.64578	+	0.398788i	0.117043	+	0.0176413i
$512$	−37.9049	−	18.2540i	−1.67518	−	0.806722i
$513$	−5.33346	+	4.94873i	−0.235478	+	0.218492i
$514$	0.261966	−	1.14775i	0.0115548	−	0.0506249i
$515$	−1.43672			−0.0633094
$516$	−59.8390	+	10.8752i	−2.63426	+	0.478756i
$517$	−19.3515			−0.851079
$518$	4.40662	−	19.3067i	0.193616	−	0.848286i
$519$	7.54250	−	6.99841i	0.331079	−	0.307196i
$520$	48.0468	+	23.1381i	2.10699	+	1.01467i
$521$	−13.8523	−	2.08790i	−0.606880	−	0.0914724i	−0.161589	−	0.986858i	$-0.551662\pi$
$521$	−13.8523	−	2.08790i	−0.606880	−	0.0914724i	−0.445291	+	0.895386i	$0.646900\pi$
$522$	−6.92916	−	12.0017i	−0.303281	−	0.525298i
$523$	16.1137	−	27.9097i	0.704602	−	1.22041i	−0.262234	−	0.965004i	$-0.584459\pi$
$523$	16.1137	−	27.9097i	0.704602	−	1.22041i	0.966835	−	0.255401i	$-0.0822076\pi$
$524$	−28.5768	+	35.8342i	−1.24838	+	1.56542i
$525$	0.383418	−	5.11636i	0.0167337	−	0.223296i
$526$	−7.29854	+	18.5964i	−0.318231	+	0.810840i
$527$	−20.4133	+	9.83055i	−0.889219	+	0.428225i
$528$	38.9100	−	12.0022i	1.69334	−	0.522327i
$529$	−8.40228	−	21.4087i	−0.365316	−	0.930811i
$530$	35.0501	+	32.5218i	1.52248	+	1.41265i
$531$	2.74977	−	1.87476i	0.119330	−	0.0813576i
$532$	−3.35912	−	4.21220i	−0.145636	−	0.182622i
$533$	−5.97606	+	0.900747i	−0.258852	+	0.0390157i
$534$	47.8347	+	14.7551i	2.07001	+	0.638514i
$535$	−0.417024	−	5.56479i	−0.0180295	−	0.240587i
$536$	−15.8225	−	10.7876i	−0.683428	−	0.465953i
$537$	−6.00494	−	26.3094i	−0.259132	−	1.13533i
$538$	−13.0351	−	57.1103i	−0.561981	−	2.46220i
$539$	−11.8906	−	8.10687i	−0.512164	−	0.349188i
$540$	4.76887	+	63.6361i	0.205219	+	2.73846i
$541$	−24.2850	−	7.49094i	−1.04409	−	0.322061i	−0.275167	−	0.961396i	$-0.588733\pi$
$541$	−24.2850	−	7.49094i	−1.04409	−	0.322061i	−0.768928	+	0.639336i	$0.779209\pi$
$542$	−16.6380	+	2.50777i	−0.714663	+	0.107718i
$543$	−23.4100	−	29.3552i	−1.00462	−	1.25975i
$544$	−21.6771	+	14.7792i	−0.929398	+	0.633652i
$545$	10.0342	+	9.31037i	0.429818	+	0.398813i
$546$	3.01855	+	7.69114i	0.129182	+	0.329150i
$547$	5.19488	−	1.60241i	0.222117	−	0.0685141i	−0.181699	−	0.983354i	$-0.558160\pi$
$547$	5.19488	−	1.60241i	0.222117	−	0.0685141i	0.403816	+	0.914840i	$0.367683\pi$
$548$	−25.7579	+	12.4044i	−1.10032	+	0.529889i
$549$	−1.29964	+	3.31143i	−0.0554673	+	0.141328i
$550$	−1.68678	+	22.5085i	−0.0719245	+	0.959766i
$551$	7.79761	−	9.77790i	0.332189	−	0.416552i
$552$	0.278688	−	0.482703i	0.0118618	−	0.0205452i
$553$	2.10758	+	3.65043i	0.0896233	+	0.155232i
$554$	−35.9650	−	5.42085i	−1.52801	−	0.230310i
$555$	57.7182	+	27.7956i	2.45000	+	1.17986i
$556$	−38.6884	+	35.8976i	−1.64075	+	1.52240i
$557$	−9.31439	+	40.8090i	−0.394664	+	1.72913i	0.253233	+	0.967405i	$0.418506\pi$
$557$	−9.31439	+	40.8090i	−0.394664	+	1.72913i	−0.647896	+	0.761729i	$0.724351\pi$
$558$	−16.3199			−0.690878
$559$	3.99633	+	15.3572i	0.169027	+	0.649539i
$560$	−19.5385			−0.825653
$561$	−2.38051	+	10.4297i	−0.100505	+	0.440343i
$562$	−11.8337	+	10.9801i	−0.499176	+	0.463168i
$563$	25.0303	+	12.0540i	1.05490	+	0.508013i	0.879211	−	0.476432i	$-0.158070\pi$
$563$	25.0303	+	12.0540i	1.05490	+	0.508013i	0.175690	+	0.984446i	$0.443784\pi$
$564$	80.6278	+	12.1527i	3.39504	+	0.511721i
$565$	20.0729	+	34.7673i	0.844474	+	1.46267i
$566$	−1.42825	+	2.47381i	−0.0600339	+	0.103982i
$567$	−4.49476	+	5.63625i	−0.188762	+	0.236700i
$568$	5.14439	−	68.6471i	0.215854	−	2.88037i
$569$	−9.42162	+	24.0059i	−0.394975	+	1.00638i	0.585664	+	0.810554i	$0.300834\pi$
$569$	−9.42162	+	24.0059i	−0.394975	+	1.00638i	−0.980639	+	0.195825i	$0.937261\pi$
$570$	22.2133	−	10.6974i	0.930413	−	0.448063i
$571$	38.3172	−	11.8193i	1.60353	−	0.494622i	0.641395	−	0.767211i	$-0.278356\pi$
$571$	38.3172	−	11.8193i	1.60353	−	0.494622i	0.962131	+	0.272588i	$0.0878797\pi$
$572$	−9.38740	−	23.9187i	−0.392507	−	1.00009i
$573$	−12.2973	−	11.4102i	−0.513727	−	0.476669i
$574$	3.66408	−	2.49812i	0.152936	−	0.104270i
$575$	0.0961865	+	0.120614i	0.00401126	+	0.00502996i
$576$	−5.42528	+	0.817729i	−0.226053	+	0.0340721i
$577$	19.2792	+	5.94684i	0.802603	+	0.247570i	0.668805	−	0.743438i	$-0.266806\pi$
$577$	19.2792	+	5.94684i	0.802603	+	0.247570i	0.133799	+	0.991009i	$0.457282\pi$
$578$	2.07139	+	27.6408i	0.0861584	+	1.14970i
$579$	−30.9182	−	21.0796i	−1.28491	−	0.876040i
$580$	−24.4089	−	106.942i	−1.01353	−	4.44054i
$581$	0.819374	+	3.58991i	0.0339934	+	0.148935i
$582$	−3.92441	−	2.67562i	−0.162672	−	0.110908i
$583$	−1.00782	−	13.4484i	−0.0417395	−	0.556976i
$584$	27.7441	+	8.55791i	1.14806	+	0.354129i
$585$	−4.98269	+	0.751020i	−0.206009	+	0.0310508i
$586$	−29.7375	−	37.2897i	−1.22845	−	1.54042i
$587$	9.57940	−	6.53112i	0.395384	−	0.269568i	−0.349266	−	0.937024i	$-0.613569\pi$
$587$	9.57940	−	6.53112i	0.395384	−	0.269568i	0.744650	+	0.667455i	$0.232617\pi$
$588$	44.4509	+	41.2444i	1.83312	+	1.70089i
$589$	−5.38070	−	13.7098i	−0.221708	−	0.564902i
$590$	35.6090	−	10.9839i	1.46600	−	0.452201i
$591$	40.3757	−	19.4439i	1.66083	−	0.799816i
$592$	39.1992	−	99.8781i	1.61108	−	4.10496i
$593$	0.913090	−	12.1843i	0.0374961	−	0.500351i	−0.946564	−	0.322516i	$-0.895472\pi$
$593$	0.913090	−	12.1843i	0.0374961	−	0.500351i	0.984060	−	0.177835i	$-0.0569094\pi$
$594$	15.8752	−	19.9069i	0.651368	−	0.816790i
$595$	2.56663	−	4.44554i	0.105222	−	0.182249i
$596$	25.1586	+	43.5760i	1.03054	+	1.78494i
$597$	35.7976	+	5.39563i	1.46510	+	0.220828i
$598$	−0.223830	−	0.107791i	−0.00915307	−	0.00440789i
$599$	−7.00317	+	6.49799i	−0.286142	+	0.265501i	−0.810163	−	0.586204i	$-0.800622\pi$
$599$	−7.00317	+	6.49799i	−0.286142	+	0.265501i	0.524022	+	0.851705i	$0.324431\pi$
$600$	12.3886	−	54.2779i	0.505762	−	2.21589i
$601$	−9.69294			−0.395383			−0.197692	−	0.980264i	$-0.563344\pi$
$601$	−9.69294			−0.395383			−0.197692	+	0.980264i	$0.563344\pi$
$602$	−7.53137	−	8.88049i	−0.306956	−	0.361942i
$603$	1.80949			0.0736882
$604$	−10.0546	+	44.0521i	−0.409116	+	1.79245i
$605$	−13.4791	+	12.5068i	−0.548003	+	0.508472i
$606$	−65.8699	−	31.7213i	−2.67578	−	1.28859i
$607$	1.91366	+	0.288437i	0.0776729	+	0.0117073i	0.187764	−	0.982214i	$-0.439876\pi$
$607$	1.91366	+	0.288437i	0.0776729	+	0.0117073i	−0.110091	+	0.993922i	$0.535114\pi$
$608$	−8.52710	−	14.7694i	−0.345819	−	0.598977i
$609$	4.97431	−	8.61575i	0.201569	−	0.349128i
$610$	−24.8348	+	31.1418i	−1.00553	+	1.26090i
$611$	1.58985	−	21.2151i	0.0643186	−	0.858272i
$612$	3.10470	−	7.91064i	0.125500	−	0.319769i
$613$	−14.0264	+	6.75474i	−0.566519	+	0.272821i	−0.695142	−	0.718872i	$-0.744659\pi$
$613$	−14.0264	+	6.75474i	−0.566519	+	0.272821i	0.128623	+	0.991694i	$0.458944\pi$
$614$	−45.1886	+	13.9388i	−1.82366	+	0.562526i
$615$	5.24114	+	13.3542i	0.211343	+	0.538494i
$616$	8.09072	+	7.50709i	0.325984	+	0.302469i
$617$	17.3090	−	11.8011i	0.696835	−	0.475094i	−0.162367	−	0.986730i	$-0.551913\pi$
$617$	17.3090	−	11.8011i	0.696835	−	0.475094i	0.859202	+	0.511636i	$0.170961\pi$
$618$	−1.50598	−	1.88844i	−0.0605795	−	0.0759643i
$619$	−45.0405	+	6.78876i	−1.81033	+	0.272863i	−0.965165	−	0.261643i	$-0.915736\pi$
$619$	−45.0405	+	6.78876i	−1.81033	+	0.272863i	−0.845165	+	0.534506i	$0.820498\pi$
$620$	−123.438	−	38.0756i	−4.95740	−	1.52915i
$621$	−0.0130049	−	0.173539i	−0.000521870	−	0.00696387i
$622$	37.3574	+	25.4699i	1.49790	+	1.02125i
$623$	1.50757	+	6.60507i	0.0603993	+	0.264627i
$624$	9.96129	+	43.6433i	0.398771	+	1.74713i
$625$	−24.1410	−	16.4591i	−0.965642	−	0.658363i
$626$	−1.27053	−	16.9540i	−0.0507805	−	0.677618i
$627$	−6.64506	−	2.04973i	−0.265378	−	0.0818584i
$628$	34.4190	−	5.18782i	1.37347	−	0.207017i
$629$	17.5756	+	22.0391i	0.700785	+	0.878757i
$630$	3.05501	−	2.08287i	0.121715	−	0.0829836i
$631$	7.91485	+	7.34390i	0.315085	+	0.292356i	0.821822	−	0.569745i	$-0.192958\pi$
$631$	7.91485	+	7.34390i	0.315085	+	0.292356i	−0.506737	+	0.862101i	$0.669148\pi$
$632$	16.7103	+	42.5773i	0.664702	+	1.69363i
$633$	28.6083	−	8.82450i	1.13708	−	0.350742i
$634$	31.1418	−	14.9971i	1.23680	−	0.595611i
$635$	0.229194	−	0.583977i	0.00909530	−	0.0231744i
$636$	−4.24649	+	56.6654i	−0.168384	+	2.24693i
$637$	9.86448	−	12.3697i	0.390845	−	0.490104i
$638$	−21.8836	+	37.9035i	−0.866379	+	1.50061i
$639$	3.25233	+	5.63321i	0.128660	+	0.222846i
$640$	0.578682	+	0.0872223i	0.0228744	+	0.00344776i
$641$	5.95986	+	2.87012i	0.235400	+	0.113363i	0.547866	−	0.836566i	$-0.315440\pi$
$641$	5.95986	+	2.87012i	0.235400	+	0.113363i	−0.312465	+	0.949929i	$0.601155\pi$
$642$	6.87730	−	6.38121i	0.271426	−	0.251846i
$643$	−8.62182	+	37.7747i	−0.340012	+	1.48969i	0.459035	+	0.888418i	$0.348195\pi$
$643$	−8.62182	+	37.7747i	−0.340012	+	1.48969i	−0.799046	+	0.601270i	$0.794662\pi$
$644$	0.128865			0.00507799
$645$	33.4292	−	17.3602i	1.31627	−	0.683558i
$646$	10.8488			0.426840
$647$	−5.10650	+	22.3730i	−0.200757	+	0.879575i	0.769720	+	0.638382i	$0.220396\pi$
$647$	−5.10650	+	22.3730i	−0.200757	+	0.879575i	−0.970477	+	0.241193i	$0.922461\pi$
$648$	−57.3437	+	53.2072i	−2.25267	+	2.09018i
$649$	−9.46973	−	4.56038i	−0.371720	−	0.179011i
$650$	−24.5376	−	3.69844i	−0.962443	−	0.145065i
$651$	−5.85788	−	10.1461i	−0.229589	−	0.397659i
$652$	18.7399	−	32.4584i	0.733910	−	1.27117i
$653$	17.8010	−	22.3217i	0.696606	−	0.873516i	−0.300159	−	0.953889i	$-0.597040\pi$
$653$	17.8010	−	22.3217i	0.696606	−	0.873516i	0.996765	+	0.0803731i	$0.0256112\pi$
$654$	−1.71974	+	22.9483i	−0.0672470	+	0.897349i
$655$	10.3709	−	26.4246i	0.405224	−	1.03249i
$656$	21.6478	−	10.4250i	0.845204	−	0.407029i
$657$	−2.62154	+	0.808639i	−0.102276	+	0.0315480i
$658$	5.70330	+	14.5318i	0.222338	+	0.566507i
$659$	−12.3638	−	11.4720i	−0.481627	−	0.446884i	0.401611	−	0.915810i	$-0.368450\pi$
$659$	−12.3638	−	11.4720i	−0.481627	−	0.446884i	−0.883237	+	0.468926i	$0.844641\pi$
$660$	−50.3949	+	34.3587i	−1.96162	+	1.33741i
$661$	5.61134	+	7.03640i	0.218256	+	0.273684i	0.878891	−	0.477023i	$-0.158284\pi$
$661$	5.61134	+	7.03640i	0.218256	+	0.273684i	−0.660635	+	0.750707i	$0.729713\pi$
$662$	−27.5327	+	4.14989i	−1.07009	+	0.161290i
$663$	−11.2385	−	3.46663i	−0.436469	−	0.134633i
$664$	2.98594	+	39.8446i	0.115877	+	1.54627i
$665$	2.75699	+	1.87968i	0.106911	+	0.0728910i
$666$	4.51821	+	19.7956i	0.175077	+	0.767062i
$667$	0.0665643	+	0.291637i	0.00257738	+	0.0112922i
$668$	−46.4601	−	31.6760i	−1.79760	−	1.22558i
$669$	−2.60425	−	34.7513i	−0.100686	−	1.34356i
$670$	19.3609	+	5.97206i	0.747978	+	0.230721i
$671$	11.1093	−	1.67445i	0.428868	−	0.0646415i
$672$	−8.45845	−	10.6066i	−0.326292	−	0.409157i
$673$	−9.88152	+	6.73710i	−0.380904	+	0.259696i	−0.738603	−	0.674141i	$-0.764514\pi$
$673$	−9.88152	+	6.73710i	−0.380904	+	0.259696i	0.357698	+	0.933837i	$0.383562\pi$
$674$	−60.6002	−	56.2287i	−2.33423	−	2.16585i
$675$	−6.35057	−	16.1810i	−0.244434	−	0.622807i
$676$	−32.9291	+	10.1573i	−1.26650	+	0.390665i
$677$	39.1303	−	18.8442i	1.50390	−	0.724240i	0.512944	−	0.858422i	$-0.328555\pi$
$677$	39.1303	−	18.8442i	1.50390	−	0.724240i	0.990957	+	0.134182i	$0.0428407\pi$
$678$	−24.6580	+	62.8275i	−0.946984	+	2.41288i
$679$	0.0480386	−	0.641031i	0.00184355	−	0.0246005i
$680$	34.7293	−	43.5492i	1.33181	−	1.67004i
$681$	−23.9728	+	41.5221i	−0.918639	+	1.59113i
$682$	25.7707	+	44.6362i	0.986812	+	1.70921i
$683$	7.26911	+	1.09564i	0.278145	+	0.0419236i	0.286633	−	0.958040i	$-0.407464\pi$
$683$	7.26911	+	1.09564i	0.278145	+	0.0419236i	−0.00848853	+	0.999964i	$0.502702\pi$
$684$	4.97699	+	2.39679i	0.190300	+	0.0916436i
$685$	12.9798	−	12.0435i	0.495934	−	0.460159i
$686$	−5.34926	+	23.4366i	−0.204236	+	0.894815i
$687$	0.918487			0.0350425
$688$	−33.1785	−	53.6595i	−1.26492	−	2.04575i
$689$	14.8263			0.564838
$690$	−0.131224	+	0.574929i	−0.00499561	+	0.0218872i
$691$	0.0567156	−	0.0526244i	0.00215756	−	0.00200193i	−0.679093	−	0.734052i	$-0.737627\pi$
$691$	0.0567156	−	0.0526244i	0.00215756	−	0.00200193i	0.681251	+	0.732050i	$0.261436\pi$
$692$	23.2568	+	11.1999i	0.884090	+	0.425755i
$693$	−1.03124	−	0.155435i	−0.0391737	−	0.00590449i
$694$	44.3595	+	76.8330i	1.68386	+	2.91654i
$695$	16.3436	−	28.3080i	0.619950	−	1.07378i
$696$	67.3079	−	84.4014i	2.55130	−	3.19923i
$697$	−0.471738	+	6.29491i	−0.0178684	+	0.238437i
$698$	33.5420	−	85.4636i	1.26958	−	3.23484i
$699$	18.2064	−	8.76772i	0.688628	−	0.331626i
$700$	12.2999	−	3.79400i	0.464891	−	0.143400i
$701$	−2.64824	−	6.74761i	−0.100023	−	0.254854i	0.872099	−	0.489329i	$-0.162758\pi$
$701$	−2.64824	−	6.74761i	−0.100023	−	0.254854i	−0.972122	+	0.234475i	$0.924663\pi$
$702$	20.5198	+	19.0395i	0.774468	+	0.718601i
$703$	−15.1399	+	10.3222i	−0.571011	+	0.389309i
$704$	10.8036	+	13.5473i	0.407175	+	0.510581i
$705$	−49.9365	+	7.52671i	−1.88072	+	0.283472i
$706$	−27.4249	−	8.45946i	−1.03215	−	0.318376i
$707$	−0.739433	−	9.86704i	−0.0278092	−	0.371088i
$708$	36.5916	+	24.9477i	1.37520	+	0.937593i
$709$	4.06410	+	17.8060i	0.152630	+	0.668717i	0.992115	+	0.125333i	$0.0400000\pi$
$709$	4.06410	+	17.8060i	0.152630	+	0.668717i	−0.839484	+	0.543384i	$0.817143\pi$
$710$	16.2070	+	71.0074i	0.608237	+	2.66486i
$711$	−3.57091	−	2.43461i	−0.133920	−	0.0913049i
$712$	5.49382	+	73.3099i	0.205890	+	2.74741i
$713$	0.336622	+	0.103834i	0.0126066	+	0.00388862i
$714$	8.53363	−	1.28624i	0.319363	−	0.0481363i
$715$	9.92223	+	12.4421i	0.371070	+	0.465307i
$716$	55.9375	−	38.1375i	2.09048	−	1.42527i
$717$	−17.9644	−	16.6685i	−0.670892	−	0.622497i
$718$	13.3211	+	33.9416i	0.497139	+	1.26669i
$719$	23.5212	−	7.25534i	0.877194	−	0.270578i	0.176724	−	0.984260i	$-0.443450\pi$
$719$	23.5212	−	7.25534i	0.877194	−	0.270578i	0.700470	+	0.713682i	$0.252974\pi$
$720$	18.0494	−	8.69212i	0.672660	−	0.323936i
$721$	0.119430	−	0.304304i	0.00444782	−	0.0113329i
$722$	3.18202	−	42.4612i	0.118423	−	1.58024i
$723$	−5.38461	+	6.75209i	−0.200256	+	0.251113i
$724$	47.0979	−	81.5760i	1.75038	−	3.03175i
$725$	14.9397	+	25.8763i	0.554847	+	0.961023i
$726$	−30.5679	−	4.60738i	−1.13448	−	0.170996i
$727$	−31.0316	−	14.9441i	−1.15090	−	0.554244i	−0.241596	−	0.970377i	$-0.577671\pi$
$727$	−31.0316	−	14.9441i	−1.15090	−	0.554244i	−0.909304	+	0.416133i	$0.863385\pi$
$728$	−8.89475	+	8.25313i	−0.329662	+	0.305881i
$729$	−4.03899	+	17.6960i	−0.149592	+	0.655407i
$730$	−30.7184			−1.13694
$731$	16.5674	−	0.500154i	0.612767	−	0.0184989i
$732$	−47.3381			−1.74967
$733$	−6.10947	+	26.7673i	−0.225658	+	0.988674i	0.727478	+	0.686131i	$0.240692\pi$
$733$	−6.10947	+	26.7673i	−0.225658	+	0.988674i	−0.953136	+	0.302542i	$0.902165\pi$
$734$	53.5365	−	49.6746i	1.97607	−	1.83352i
$735$	−33.8368	−	16.2949i	−1.24809	−	0.601047i
$736$	0.403359	+	0.0607965i	0.0148680	+	0.00224099i
$737$	−2.85736	−	4.94909i	−0.105252	−	0.182302i
$738$	−2.27347	+	3.93777i	−0.0836876	+	0.144951i
$739$	−26.8699	+	33.6938i	−0.988425	+	1.23945i	−0.0175538	+	0.999846i	$0.505588\pi$
$739$	−26.8699	+	33.6938i	−0.988425	+	1.23945i	−0.970872	+	0.239600i	$0.922984\pi$
$740$	−12.0104	+	160.268i	−0.441511	+	5.89156i
$741$	2.79306	−	7.11661i	0.102606	−	0.261435i
$742$	−9.80186	+	4.72033i	−0.359838	+	0.173289i
$743$	−24.3219	+	7.50232i	−0.892284	+	0.275233i	−0.706800	−	0.707414i	$-0.749862\pi$
$743$	−24.3219	+	7.50232i	−0.892284	+	0.275233i	−0.185485	+	0.982647i	$0.559386\pi$
$744$	−46.4454	−	118.341i	−1.70277	−	4.33859i
$745$	−22.8446	−	21.1967i	−0.836963	−	0.776588i
$746$	−2.58151	+	1.76005i	−0.0945160	+	0.0644399i
$747$	−2.35397	−	2.95179i	−0.0861274	−	0.108000i
$748$	−26.5388	+	4.00008i	−0.970354	+	0.146257i
$749$	1.21331	+	0.374258i	0.0443335	+	0.0136751i
$750$	−1.20492	−	16.0785i	−0.0439975	−	0.587105i
$751$	28.1091	+	19.1645i	1.02572	+	0.699322i	0.954522	−	0.298140i	$-0.0963664\pi$
$751$	28.1091	+	19.1645i	1.02572	+	0.699322i	0.0711949	+	0.997462i	$0.477319\pi$
$752$	18.8210	+	82.4603i	0.686332	+	3.00702i
$753$	0.992684	+	4.34923i	0.0361754	+	0.158495i
$754$	−39.7558	−	27.1051i	−1.44782	−	0.987108i
$755$	−2.09133	−	27.9068i	−0.0761112	−	1.01563i
$756$	−13.8748	−	4.27982i	−0.504623	−	0.155656i
$757$	−0.383633	+	0.0578234i	−0.0139434	+	0.00210163i	−0.156010	−	0.987755i	$-0.549863\pi$
$757$	−0.383633	+	0.0578234i	−0.0139434	+	0.00210163i	0.142067	+	0.989857i	$0.454625\pi$
$758$	−53.5876	−	67.1968i	−1.94639	−	2.44070i
$759$	0.137429	−	0.0936977i	0.00498837	−	0.00340101i
$760$	26.5422	+	24.6276i	0.962789	+	0.893337i
$761$	−2.93530	−	7.47902i	−0.106405	−	0.271114i	0.867748	−	0.497004i	$-0.165566\pi$
$761$	−2.93530	−	7.47902i	−0.106405	−	0.271114i	−0.974153	+	0.225889i	$0.927471\pi$
$762$	1.00783	−	0.310875i	0.0365099	−	0.0112618i
$763$	−2.80609	+	1.35134i	−0.101587	+	0.0489219i
$764$	15.3756	−	39.1764i	0.556270	−	1.41735i
$765$	−0.393323	+	5.24853i	−0.0142206	+	0.189761i
$766$	0.183974	−	0.230697i	0.00664727	−	0.00833541i
$767$	5.77756	−	10.0070i	0.208616	−	0.361333i
$768$	15.6277	+	27.0679i	0.563914	+	0.976728i
$769$	−20.3218	−	3.06301i	−0.732821	−	0.110455i	−0.227978	−	0.973666i	$-0.573212\pi$
$769$	−20.3218	−	3.06301i	−0.732821	−	0.110455i	−0.504843	+	0.863211i	$0.668450\pi$
$770$	−10.5210	−	5.06663i	−0.379149	−	0.182589i
$771$	−0.635215	+	0.589394i	−0.0228767	+	0.0212265i
$772$	20.8900	−	91.5250i	0.751847	−	3.29406i
$773$	−20.6462			−0.742592			−0.371296	−	0.928515i	$-0.621086\pi$
$773$	−20.6462			−0.742592			−0.371296	+	0.928515i	$0.621086\pi$
$774$	10.9080	+	4.85317i	0.392081	+	0.174444i
$775$	35.1868			1.26395
$776$	1.55217	−	6.80051i	0.0557197	−	0.244124i
$777$	−10.6852	+	9.91440i	−0.383329	+	0.355677i
$778$	−41.6792	−	20.0716i	−1.49427	−	0.719603i
$779$	−4.05754	−	0.611576i	−0.145377	−	0.0219120i
$780$	−33.5272	−	58.0709i	−1.20047	−	2.07927i
$781$	10.2715	−	17.7907i	0.367542	−	0.636602i
$782$	−0.161789	+	0.202877i	−0.00578557	+	0.00725487i
$783$	2.51881	−	33.6112i	0.0900150	−	1.20117i
$784$	−22.9802	+	58.5526i	−0.820721	+	2.09116i
$785$	−19.4231	+	9.35367i	−0.693240	+	0.333847i
$786$	45.6036	−	14.0669i	1.62663	−	0.501748i
$787$	12.2749	+	31.2760i	0.437553	+	1.11487i	0.964292	+	0.264840i	$0.0853192\pi$
$787$	12.2749	+	31.2760i	0.437553	+	1.11487i	−0.526739	+	0.850027i	$0.676586\pi$
$788$	82.4146	+	76.4696i	2.93590	+	2.72412i
$789$	12.1494	−	8.28333i	0.432531	−	0.294895i
$790$	−30.1724	−	37.8350i	−1.07348	−	1.34611i
$791$	−9.03247	+	1.36143i	−0.321158	+	0.0484068i
$792$	−10.8138	−	3.33560i	−0.384250	−	0.118526i
$793$	0.923008	+	12.3167i	0.0327770	+	0.437378i
$794$	−22.4098	−	15.2788i	−0.795296	−	0.542223i
$795$	−7.83138	−	34.3115i	−0.277750	−	1.21690i
$796$	20.2098	+	88.5450i	0.716318	+	3.13840i
$797$	19.2517	+	13.1256i	0.681930	+	0.464932i	0.854082	−	0.520138i	$-0.174120\pi$
$797$	19.2517	+	13.1256i	0.681930	+	0.464932i	−0.172152	+	0.985070i	$0.555072\pi$
$798$	0.419221	+	5.59412i	0.0148403	+	0.198030i
$799$	−21.2343	−	6.54991i	−0.751215	−	0.231719i
$800$	40.2896	−	6.07268i	1.42445	−	0.214702i
$801$	−4.33107	−	5.43099i	−0.153031	−	0.191895i
$802$	−78.2477	+	53.3483i	−2.76302	+	1.88380i
$803$	6.35134	+	5.89319i	0.224134	+	0.207966i
$804$	8.79712	+	22.4147i	0.310251	+	0.790506i
$805$	−0.0762661	+	0.0235250i	−0.00268803	+	0.000829146i
$806$	−51.0520	+	24.5854i	−1.79823	+	0.865982i
$807$	−15.7526	+	40.1371i	−0.554519	+	1.41289i
$808$	8.02366	−	107.068i	0.282271	−	3.76665i
$809$	11.8573	−	14.8686i	0.416882	−	0.522753i	−0.528406	−	0.848992i	$-0.677210\pi$
$809$	11.8573	−	14.8686i	0.416882	−	0.522753i	0.945287	+	0.326239i	$0.105781\pi$
$810$	41.3822	−	71.6761i	1.45402	−	2.51844i
$811$	−4.29128	−	7.43271i	−0.150687	−	0.260998i	0.780793	−	0.624790i	$-0.214815\pi$
$811$	−4.29128	−	7.43271i	−0.150687	−	0.260998i	−0.931480	+	0.363792i	$0.881482\pi$
$812$	24.6799	+	3.71990i	0.866096	+	0.130543i
$813$	11.1584	+	5.37360i	0.391342	+	0.188460i
$814$	47.0076	−	43.6166i	1.64761	−	1.52876i
$815$	−5.16536	+	22.6309i	−0.180935	+	0.792726i
$816$	46.7581			1.63686
$817$	−0.480587	+	10.7635i	−0.0168136	+	0.376568i
$818$	51.5614			1.80280
$819$	0.255127	−	1.11779i	0.00891487	−	0.0390586i
$820$	−26.3828	+	24.4797i	−0.921329	+	0.854868i
$821$	24.0723	+	11.5926i	0.840130	+	0.404585i	0.803904	−	0.594758i	$-0.202752\pi$
$821$	24.0723	+	11.5926i	0.840130	+	0.404585i	0.0362253	+	0.999344i	$0.488467\pi$
$822$	29.4357	+	4.43672i	1.02669	+	0.154749i
$823$	−5.12770	−	8.88144i	−0.178740	−	0.309588i	0.762709	−	0.646742i	$-0.223869\pi$
$823$	−5.12770	−	8.88144i	−0.178740	−	0.309588i	−0.941449	+	0.337154i	$0.890536\pi$
$824$	1.77362	−	3.07200i	0.0617869	−	0.107018i
$825$	10.3587	−	12.9894i	0.360643	−	0.452232i
$826$	−0.633630	+	8.45521i	−0.0220468	+	0.294194i
$827$	−12.9951	+	33.1111i	−0.451886	+	1.15139i	0.505565	+	0.862789i	$0.331284\pi$
$827$	−12.9951	+	33.1111i	−0.451886	+	1.15139i	−0.957451	+	0.288597i	$0.906811\pi$
$828$	−0.119043	+	0.0573282i	−0.00413704	+	0.00199229i
$829$	−18.5452	+	5.72042i	−0.644100	+	0.198678i	−0.599561	−	0.800329i	$-0.704658\pi$
$829$	−18.5452	+	5.72042i	−0.644100	+	0.198678i	−0.0445390	+	0.999008i	$0.514182\pi$
$830$	−15.4446	−	39.3522i	−0.536090	−	1.36593i
$831$	19.6248	+	18.2092i	0.680777	+	0.631669i
$832$	−15.7395	+	10.7310i	−0.545668	+	0.372030i
$833$	−10.3035	−	12.9202i	−0.356996	−	0.447659i
$834$	54.3400	−	8.19044i	1.88164	−	0.283612i
$835$	33.2791	+	10.2652i	1.15167	+	0.355243i
$836$	−1.30374	−	17.3972i	−0.0450907	−	0.601694i
$837$	−32.7955	−	22.3596i	−1.13358	−	0.772860i
$838$	8.60099	+	37.6834i	0.297116	+	1.30175i
$839$	−9.15974	−	40.1315i	−0.316229	−	1.38549i	−0.844109	−	0.536172i	$-0.819870\pi$
$839$	−9.15974	−	40.1315i	−0.316229	−	1.38549i	0.527879	−	0.849320i	$-0.322987\pi$
$840$	23.7979	+	16.2251i	0.821106	+	0.559821i
$841$	2.16248	+	28.8563i	0.0745684	+	0.995046i
$842$	−65.0717	−	20.0720i	−2.24252	−	0.691726i
$843$	11.7496	−	1.77096i	0.404677	−	0.0609952i
$844$	46.8293	+	58.7220i	1.61193	+	2.02130i
$845$	17.6342	−	12.0228i	0.606634	−	0.413596i
$846$	−11.7334	−	10.8870i	−0.403402	−	0.374302i
$847$	−1.52851	−	3.89458i	−0.0525202	−	0.133819i
$848$	−56.3258	+	17.3742i	−1.93424	+	0.596633i
$849$	1.89434	−	0.912265i	0.0650135	−	0.0313089i
$850$	−9.46935	+	24.1275i	−0.324796	+	0.827567i
$851$	0.0327530	−	0.437058i	0.00112276	−	0.0149822i
$852$	−53.9685	+	67.6744i	−1.84893	+	2.31849i
$853$	−12.0504	+	20.8719i	−0.412598	+	0.714640i	−0.995173	−	0.0981366i	$-0.968712\pi$
$853$	−12.0504	+	20.8719i	−0.412598	+	0.714640i	0.582575	+	0.812777i	$0.302045\pi$
$854$	−4.53154	−	7.84885i	−0.155066	−	0.268582i
$855$	−3.38308	−	0.509917i	−0.115699	−	0.0174388i
$856$	12.4135	+	5.97801i	0.424283	+	0.204324i
$857$	−18.3284	+	17.0062i	−0.626085	+	0.580922i	−0.928077	−	0.372388i	$-0.878539\pi$
$857$	−18.3284	+	17.0062i	−0.626085	+	0.580922i	0.301992	+	0.953311i	$0.402349\pi$
$858$	−5.95346	+	26.0838i	−0.203248	+	0.890486i
$859$	49.1887			1.67830			0.839148	−	0.543904i	$-0.183054\pi$
$859$	49.1887			1.67830			0.839148	+	0.543904i	$0.183054\pi$
$860$	71.1816	+	62.1569i	2.42727	+	2.11953i
$861$	−3.26416			−0.111242
$862$	13.2103	−	57.8780i	0.449944	−	1.97133i
$863$	18.6697	−	17.3230i	0.635525	−	0.589681i	−0.295184	−	0.955440i	$-0.595381\pi$
$863$	18.6697	−	17.3230i	0.635525	−	0.589681i	0.930710	+	0.365759i	$0.119191\pi$
$864$	−41.4104	−	19.9422i	−1.40881	−	0.678447i
$865$	−15.8086	−	2.38277i	−0.537510	−	0.0810166i
$866$	−15.3906	−	26.6574i	−0.522995	−	0.905854i
$867$	10.2011	−	17.6689i	0.346449	−	0.600067i
$868$	18.3256	−	22.9796i	0.622013	−	0.779980i
$869$	−1.02002	+	13.6112i	−0.0346017	+	0.461728i
$870$	−41.7280	+	106.321i	−1.41471	+	3.60463i
$871$	5.66045	−	2.72593i	0.191797	−	0.0923646i
$872$	−32.2946	+	9.96156i	−1.09363	+	0.337341i
$873$	0.240799	+	0.613545i	0.00814980	+	0.0207653i
$874$	−0.123649	−	0.114729i	−0.00418249	−	0.00388078i
$875$	1.80299	−	1.22926i	0.0609523	−	0.0415566i
$876$	−22.7619	−	28.5425i	−0.769053	−	0.964362i
$877$	44.1742	−	6.65819i	1.49166	−	0.224831i	0.647970	−	0.761666i	$-0.275618\pi$
$877$	44.1742	−	6.65819i	1.49166	−	0.224831i	0.843687	+	0.536835i	$0.180380\pi$
$878$	42.6742	+	13.1632i	1.44018	+	0.444238i
$879$	2.62352	+	35.0084i	0.0884890	+	1.18080i
$880$	−52.2752	−	35.6406i	−1.76220	−	1.20145i
$881$	2.11123	+	9.24989i	0.0711291	+	0.311637i	0.997960	−	0.0638421i	$-0.0203354\pi$
$881$	2.11123	+	9.24989i	0.0711291	+	0.311637i	−0.926831	+	0.375479i	$0.877478\pi$
$882$	−2.64876	−	11.6050i	−0.0891882	−	0.390759i
$883$	14.5862	+	9.94471i	0.490865	+	0.334666i	0.783326	−	0.621611i	$-0.213522\pi$
$883$	14.5862	+	9.94471i	0.490865	+	0.334666i	−0.292461	+	0.956278i	$0.594474\pi$
$884$	−2.20496	−	29.4232i	−0.0741609	−	0.989609i
$885$	−26.2103	−	8.08482i	−0.881051	−	0.271768i
$886$	102.638	−	15.4702i	3.44819	−	0.519731i
$887$	−25.0000	−	31.3490i	−0.839419	−	1.05260i	−0.997870	−	0.0652308i	$-0.979222\pi$
$887$	−25.0000	−	31.3490i	−0.839419	−	1.05260i	0.158452	−	0.987367i	$-0.449350\pi$
$888$	−130.685	+	89.0997i	−4.38551	+	2.98999i
$889$	0.104637	+	0.0970887i	0.00350940	+	0.00325625i
$890$	−28.4165	−	72.4040i	−0.952523	−	2.42699i
$891$	−22.3069	+	6.88077i	−0.747310	+	0.230515i
$892$	78.7692	−	37.9333i	2.63739	−	1.27010i
$893$	5.27726	−	13.4462i	0.176597	−	0.449961i
$894$	3.91529	−	52.2459i	0.130947	−	1.74736i
$895$	−26.1433	+	32.7826i	−0.873873	+	1.09580i
$896$	−0.0665782	+	0.115317i	−0.00222422	+	0.00385247i
$897$	0.0914304	+	0.158362i	0.00305277	+	0.00528755i
$898$	−53.0507	−	7.99611i	−1.77033	−	0.266834i
$899$	61.4718	+	29.6032i	2.05020	+	0.987323i
$900$	−9.67457	+	8.97669i	−0.322486	+	0.299223i
$901$	3.44601	−	15.0979i	0.114803	−	0.502986i
$902$	14.3601			0.478139
$903$	0.898102	+	8.52355i	0.0298870	+	0.283646i
$904$	−99.1194			−3.29666
$905$	−12.9818	+	56.8771i	−0.431530	+	1.89066i
$906$	34.4890	−	32.0011i	1.14582	−	1.06316i
$907$	−27.1369	−	13.0684i	−0.901065	−	0.433930i	−0.0747914	−	0.997199i	$-0.523829\pi$
$907$	−27.1369	−	13.0684i	−0.901065	−	0.433930i	−0.826273	+	0.563269i	$0.809543\pi$
$908$	−118.941	−	17.9274i	−3.94718	−	0.594942i
$909$	5.07264	+	8.78606i	0.168249	+	0.291415i
$910$	6.41892	−	11.1179i	0.212785	−	0.368555i
$911$	−24.7828	+	31.0766i	−0.821090	+	1.02961i	0.177872	+	0.984054i	$0.443079\pi$
$911$	−24.7828	+	31.0766i	−0.821090	+	1.02961i	−0.998962	+	0.0455601i	$0.985493\pi$
$912$	−2.27137	+	30.3093i	−0.0752126	+	1.00364i
$913$	−4.35621	+	11.0994i	−0.144169	+	0.367338i
$914$	52.0263	−	25.0546i	1.72088	−	0.828731i
$915$	28.0161	−	8.64182i	0.926184	−	0.285690i
$916$	0.841842	+	2.14498i	0.0278153	+	0.0708721i
$917$	4.73474	+	4.39319i	0.156355	+	0.145076i
$918$	24.1577	−	16.4704i	0.797322	−	0.543605i
$919$	−0.240240	−	0.301251i	−0.00792478	−	0.00993736i	0.777853	−	0.628446i	$-0.216309\pi$
$919$	−0.240240	−	0.301251i	−0.00792478	−	0.00993736i	−0.785778	+	0.618509i	$0.787737\pi$
$920$	−0.856374	+	0.129078i	−0.0282338	+	0.00425556i
$921$	33.2615	+	10.2598i	1.09600	+	0.338072i
$922$	−0.969555	−	12.9378i	−0.0319306	−	0.426084i
$923$	18.6602	+	12.7223i	0.614207	+	0.418759i
$924$	−3.08813	−	13.5300i	−0.101592	−	0.445104i
$925$	−9.74154	−	42.6805i	−0.320300	−	1.40333i
$926$	86.7921	+	59.1739i	2.85217	+	1.94457i
$927$	0.0250480	+	0.334242i	0.000822683	+	0.0109779i
$928$	75.4954	+	23.2873i	2.47826	+	0.764442i
$929$	−37.8857	+	5.71035i	−1.24299	+	0.187350i	−0.737419	−	0.675435i	$-0.763956\pi$
$929$	−37.8857	+	5.71035i	−1.24299	+	0.187350i	−0.505570	+	0.862786i	$0.668718\pi$
$930$	83.8623	+	105.160i	2.74995	+	3.44833i
$931$	8.87561	−	6.05129i	0.290886	−	0.198323i
$932$	37.1627	+	34.4819i	1.21730	+	1.12949i
$933$	−12.1586	−	30.9795i	−0.398054	−	1.01422i
$934$	−48.4100	+	14.9325i	−1.58402	+	0.488607i
$935$	14.9762	−	7.21216i	0.489774	−	0.235863i
$936$	4.54526	−	11.5811i	0.148566	−	0.378541i
$937$	3.22968	−	43.0971i	0.105509	−	1.40792i	−0.653542	−	0.756890i	$-0.726718\pi$
$937$	3.22968	−	43.0971i	0.105509	−	1.40792i	0.759051	−	0.651031i	$-0.225663\pi$
$938$	−2.87433	+	3.60429i	−0.0938501	+	0.117684i
$939$	−6.25707	+	10.8376i	−0.204192	+	0.353671i
$940$	−63.3469	−	109.720i	−2.06615	−	3.57867i
$941$	−19.7415	−	2.97555i	−0.643553	−	0.0970001i	−0.180846	−	0.983511i	$-0.557884\pi$
$941$	−19.7415	−	2.97555i	−0.643553	−	0.0970001i	−0.462707	+	0.886511i	$0.653122\pi$
$942$	−32.6541	−	15.7254i	−1.06393	−	0.512360i
$943$	0.0719473	−	0.0667573i	0.00234292	−	0.00217392i
$944$	−10.2225	+	44.7876i	−0.332713	+	1.45771i
$945$	8.99285			0.292537
$946$	−3.95104	−	37.4978i	−0.128459	−	1.21916i
$947$	−58.8426			−1.91213			−0.956064	−	0.293159i	$-0.905293\pi$
$947$	−58.8426			−1.91213			−0.956064	+	0.293159i	$0.905293\pi$
$948$	12.7977	−	56.0702i	0.415649	−	1.82108i
$949$	−6.98252	+	6.47883i	−0.226662	+	0.210312i
$950$	−15.1798	−	7.31023i	−0.492499	−	0.237175i
$951$	−25.1576	−	3.79189i	−0.815790	−	0.122961i
$952$	6.33697	+	10.9759i	0.205382	+	0.355732i
$953$	−1.59117	+	2.75598i	−0.0515429	+	0.0892749i	−0.890646	−	0.454698i	$-0.849747\pi$
$953$	−1.59117	+	2.75598i	−0.0515429	+	0.0892749i	0.839103	+	0.543973i	$0.183081\pi$
$954$	6.95487	−	8.72113i	0.225172	−	0.282357i
$955$	−1.94788	+	25.9927i	−0.0630320	+	0.841103i
$956$	22.4613	−	57.2305i	0.726451	−	1.85097i
$957$	29.0249	−	13.9777i	0.938242	−	0.451834i
$958$	−6.33502	+	1.95409i	−0.204675	+	0.0631339i
$959$	1.47190	+	3.75033i	0.0475300	+	0.121104i
$960$	33.1477	+	30.7566i	1.06984	+	0.992665i
$961$	40.7731	−	27.7986i	1.31526	−	0.896729i
$962$	43.9551	+	55.1179i	1.41717	+	1.77707i
$963$	−1.28734	+	0.194035i	−0.0414838	+	0.00625268i
$964$	−20.7037	−	6.38625i	−0.666822	−	0.205687i
$965$	4.34506	+	57.9808i	0.139872	+	1.86647i
$966$	−0.110864	−	0.0755860i	−0.00356700	−	0.00243194i
$967$	−8.07351	−	35.3724i	−0.259627	−	1.13750i	−0.921652	−	0.388017i	$-0.873160\pi$
$967$	−8.07351	−	35.3724i	−0.259627	−	1.13750i	0.662026	−	0.749481i	$-0.269697\pi$
$968$	−10.1022	−	44.2605i	−0.324696	−	1.42259i
$969$	−6.59781	−	4.49831i	−0.211952	−	0.144507i
$970$	0.551515	+	7.35945i	0.0177081	+	0.236298i
$971$	9.37157	+	2.89075i	0.300748	+	0.0927684i	0.441457	−	0.897283i	$-0.354462\pi$
$971$	9.37157	+	2.89075i	0.300748	+	0.0927684i	−0.140709	+	0.990051i	$0.544938\pi$
$972$	33.8979	−	5.10928i	1.08727	−	0.163880i
$973$	4.63716	+	5.81482i	0.148661	+	0.186415i
$974$	−1.56067	+	1.06404i	−0.0500070	+	0.0340942i
$975$	13.3893	+	12.4234i	0.428800	+	0.397868i
$976$	−17.9398	−	45.7100i	−0.574240	−	1.46314i
$977$	41.6328	−	12.8420i	1.33195	−	0.410852i	0.454597	−	0.890697i	$-0.349783\pi$
$977$	41.6328	−	12.8420i	1.33195	−	0.410852i	0.877353	+	0.479845i	$0.159307\pi$
$978$	−35.1607	+	16.9325i	−1.12432	+	0.541442i
$979$	−8.01497	+	20.4218i	−0.256160	+	0.652684i
$980$	7.04099	−	93.9555i	0.224916	−	3.00130i
$981$	1.99105	−	2.49670i	0.0635693	−	0.0797134i
$982$	−6.79178	+	11.7637i	−0.216734	+	0.375395i
$983$	−4.07894	−	7.06494i	−0.130098	−	0.225336i	0.793616	−	0.608419i	$-0.208196\pi$
$983$	−4.07894	−	7.06494i	−0.130098	−	0.225336i	−0.923714	+	0.383082i	$0.874863\pi$
$984$	−35.0241	−	5.27904i	−1.11653	−	0.168290i
$985$	−62.7354	−	30.2118i	−1.99891	−	0.962627i
$986$	−36.8419	+	34.1843i	−1.17329	+	1.08865i
$987$	2.55688	−	11.2024i	0.0813865	−	0.356578i
$988$	19.1797			0.610187
$989$	−0.194116	−	0.169505i	−0.00617252	−	0.00538994i
$990$	11.9731			0.380530
$991$	9.71748	−	42.5751i	0.308686	−	1.35244i	−0.547946	−	0.836514i	$-0.684590\pi$
$991$	9.71748	−	42.5751i	0.308686	−	1.35244i	0.856632	−	0.515928i	$-0.172553\pi$
$992$	68.2024	−	63.2826i	2.16543	−	2.00922i
$993$	18.4650	+	8.89229i	0.585970	+	0.282188i
$994$	−16.3869	−	2.46993i	−0.519762	−	0.0783415i
$995$	−28.1251	−	48.7142i	−0.891627	−	1.54434i
$996$	25.1205	−	43.5099i	0.795973	−	1.37867i
$997$	28.0427	−	35.1644i	0.888121	−	1.11367i	−0.104753	−	0.994498i	$-0.533405\pi$
$997$	28.0427	−	35.1644i	0.888121	−	1.11367i	0.992874	−	0.119170i	$-0.0380234\pi$
$998$	−0.0303868	+	0.405484i	−0.000961878	+	0.0128354i
$999$	−18.0419	+	45.9701i	−0.570822	+	1.45443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.13.3	yes	36
3.2	odd	2		387.2.y.c.271.1		36
4.3	odd	2		688.2.bg.c.529.3		36
43.10	even	21	inner	43.2.g.a.10.3	✓	36
43.15	even	21		1849.2.a.n.1.2		18
43.28	odd	42		1849.2.a.o.1.17		18
129.53	odd	42		387.2.y.c.10.1		36
172.139	odd	42		688.2.bg.c.225.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.10.3	✓	36	43.10	even	21	inner
43.2.g.a.13.3	yes	36	1.1	even	1	trivial
387.2.y.c.10.1		36	129.53	odd	42
387.2.y.c.271.1		36	3.2	odd	2
688.2.bg.c.225.3		36	172.139	odd	42
688.2.bg.c.529.3		36	4.3	odd	2
1849.2.a.n.1.2		18	43.15	even	21
1849.2.a.o.1.17		18	43.28	odd	42

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.581275 - 2.54673i) q^{2} +(-1.40948 + 1.30780i) q^{3} +(-4.34603 - 2.09294i) q^{4} +(2.95419 + 0.445272i) q^{5} +(2.51133 + 4.34976i) q^{6} +(-0.339884 + 0.588696i) q^{7} +(-4.59900 + 5.76696i) q^{8} +(0.0520854 - 0.695032i) q^{9} +O(q^{10})\)	\(q+(0.581275 - 2.54673i) q^{2} +(-1.40948 + 1.30780i) q^{3} +(-4.34603 - 2.09294i) q^{4} +(2.95419 + 0.445272i) q^{5} +(2.51133 + 4.34976i) q^{6} +(-0.339884 + 0.588696i) q^{7} +(-4.59900 + 5.76696i) q^{8} +(0.0520854 - 0.695032i) q^{9} +(2.85118 - 7.26470i) q^{10} +(-1.98321 + 0.955063i) q^{11} +(8.86279 - 2.73381i) q^{12} +(-0.884105 - 2.25266i) q^{13} +(1.30168 + 1.20779i) q^{14} +(-4.74619 + 3.23590i) q^{15} +(5.99853 + 7.52192i) q^{16} +(-2.49942 + 0.376727i) q^{17} +(-1.73978 - 0.536652i) q^{18} +(-0.122786 - 1.63846i) q^{19} +(-11.9071 - 8.11809i) q^{20} +(-0.290840 - 1.27425i) q^{21} +(1.27950 + 5.60586i) q^{22} +(0.0324711 + 0.0221384i) q^{23} +(-1.05987 - 14.1430i) q^{24} +(3.75109 + 1.15706i) q^{25} +(-6.25084 + 0.942162i) q^{26} +(-2.76090 - 3.46206i) q^{27} +(2.70925 - 1.84713i) q^{28} +(5.57974 + 5.17724i) q^{29} +(5.48212 + 13.9682i) q^{30} +(8.56546 - 2.64209i) q^{31} +(9.35164 - 4.50351i) q^{32} +(1.54625 - 3.93979i) q^{33} +(-0.493428 + 6.58434i) q^{34} +(-1.26621 + 1.58778i) q^{35} +(-1.68102 + 2.91162i) q^{36} +(-5.57614 - 9.65816i) q^{37} +(-4.24410 - 0.639696i) q^{38} +(4.19217 + 2.01884i) q^{39} +(-16.1542 + 14.9889i) q^{40} +(0.555724 - 2.43478i) q^{41} -3.41424 q^{42} +(-6.51074 - 0.781227i) q^{43} +10.6180 q^{44} +(0.463348 - 2.03006i) q^{45} +(0.0752553 - 0.0698267i) q^{46} +(7.92075 + 3.81443i) q^{47} +(-18.2920 - 2.75708i) q^{48} +(3.26896 + 5.66200i) q^{49} +(5.12713 - 8.88045i) q^{50} +(3.03019 - 3.79974i) q^{51} +(-0.872336 + 11.6405i) q^{52} +(-2.23834 + 5.70320i) q^{53} +(-10.4218 + 5.01886i) q^{54} +(-6.28403 + 1.93837i) q^{55} +(-1.83186 - 4.66750i) q^{56} +(2.31586 + 2.14880i) q^{57} +(16.4284 - 11.2007i) q^{58} +(2.97714 + 3.73321i) q^{59} +(27.3996 - 4.12983i) q^{60} +(-4.87717 - 1.50441i) q^{61} +(-1.74982 - 23.3497i) q^{62} +(0.391459 + 0.266892i) q^{63} +(-1.75166 - 7.67453i) q^{64} +(-1.60876 - 7.04845i) q^{65} +(-9.13479 - 6.22799i) q^{66} +(0.194013 + 2.58893i) q^{67} +(11.6510 + 3.59386i) q^{68} +(-0.0747200 + 0.0112622i) q^{69} +(3.30762 + 4.14763i) q^{70} +(-7.71099 + 5.25726i) q^{71} +(3.76868 + 3.49682i) q^{72} +(-1.43804 - 3.66406i) q^{73} +(-27.8380 + 8.58689i) q^{74} +(-6.80028 + 3.27484i) q^{75} +(-2.89557 + 7.37780i) q^{76} +(0.111819 - 1.49212i) q^{77} +(7.57825 - 9.50283i) q^{78} +(3.10044 - 5.37012i) q^{79} +(14.3715 + 24.8921i) q^{80} +(10.4867 + 1.58062i) q^{81} +(-5.87772 - 2.83056i) q^{82} +(3.97087 - 3.68443i) q^{83} +(-1.40293 + 6.14666i) q^{84} -7.55150 q^{85} +(-5.77411 + 16.1270i) q^{86} -14.6353 q^{87} +(3.61296 - 15.8294i) q^{88} +(7.30600 - 6.77898i) q^{89} +(-4.90069 - 2.36005i) q^{90} +(1.62662 + 0.245174i) q^{91} +(-0.0947861 - 0.164174i) q^{92} +(-8.61749 + 14.9259i) q^{93} +(14.3185 - 17.9548i) q^{94} +(0.366830 - 4.89500i) q^{95} +(-7.29122 + 18.5777i) q^{96} +(-0.852010 + 0.410306i) q^{97} +(16.3198 - 5.03398i) q^{98} +(0.560503 + 1.42814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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