LMFDB - Embedded newform 483.2.q.d.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	483.127
Dual form			483.2.q.d.232.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.112067 + 0.0720210i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.823458 + 1.80312i) q^{4} +(-0.784721 + 0.230415i) q^{5} +(0.0553392 + 0.121176i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0754970 - 0.525093i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.112067 + 0.0720210i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.823458 + 1.80312i) q^{4} +(-0.784721 + 0.230415i) q^{5} +(0.0553392 + 0.121176i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0754970 - 0.525093i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.0713466 - 0.0823383i) q^{10} +(-4.07573 - 2.61931i) q^{11} +(1.66758 + 1.07169i) q^{12} +(4.49713 - 5.18996i) q^{13} +(0.127818 + 0.0375308i) q^{14} +(0.116392 + 0.809525i) q^{15} +(-2.54992 - 2.94277i) q^{16} +(0.998945 + 2.18738i) q^{17} +(0.127818 - 0.0375308i) q^{18} +(2.63472 - 5.76923i) q^{19} +(0.230719 - 1.60468i) q^{20} +(-0.841254 + 0.540641i) q^{21} +0.645401 q^{22} +(4.48602 - 1.69576i) q^{23} -0.530493 q^{24} +(-3.64357 + 2.34158i) q^{25} +(-0.130193 + 0.905511i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(1.90196 - 0.558465i) q^{28} +(-1.96882 - 4.31113i) q^{29} +(-0.0713466 - 0.0823383i) q^{30} +(-0.366899 - 2.55184i) q^{31} +(1.51571 + 0.445053i) q^{32} +(-3.17269 + 3.66148i) q^{33} +(-0.269486 - 0.173188i) q^{34} +(0.688019 + 0.442163i) q^{35} +(1.29810 - 1.49809i) q^{36} +(4.67265 + 1.37202i) q^{37} +(0.120241 + 0.836295i) q^{38} +(-4.49713 - 5.18996i) q^{39} +(0.180233 + 0.394656i) q^{40} +(-6.42483 + 1.88650i) q^{41} +(0.0553392 - 0.121176i) q^{42} +(0.0472946 - 0.328941i) q^{43} +(8.07914 - 5.19215i) q^{44} +0.817850 q^{45} +(-0.380604 + 0.513127i) q^{46} -11.9814 q^{47} +(-3.27571 + 2.10517i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.239681 - 0.524828i) q^{50} +(2.30729 - 0.677480i) q^{51} +(5.65493 + 12.3826i) q^{52} +(-4.06815 - 4.69490i) q^{53} +(-0.0189584 - 0.131858i) q^{54} +(3.80184 + 1.11632i) q^{55} +(-0.347399 + 0.400920i) q^{56} +(-5.33555 - 3.42895i) q^{57} +(0.531132 + 0.341338i) q^{58} +(-0.138849 + 0.160241i) q^{59} +(-1.55552 - 0.456741i) q^{60} +(0.113286 + 0.787921i) q^{61} +(0.224903 + 0.259552i) q^{62} +(0.415415 + 0.909632i) q^{63} +(7.27031 - 2.13475i) q^{64} +(-2.33315 + 5.10888i) q^{65} +(0.0918501 - 0.638831i) q^{66} +(2.86214 - 1.83938i) q^{67} -4.76671 q^{68} +(-1.04007 - 4.68169i) q^{69} -0.108949 q^{70} +(-5.60905 + 3.60472i) q^{71} +(-0.0754970 + 0.525093i) q^{72} +(-4.16581 + 9.12186i) q^{73} +(-0.622464 + 0.182772i) q^{74} +(1.79921 + 3.93973i) q^{75} +(8.23304 + 9.50144i) q^{76} +(0.689492 + 4.79552i) q^{77} +(0.877766 + 0.257735i) q^{78} +(7.76108 - 8.95677i) q^{79} +(2.67903 + 1.72171i) q^{80} +(0.841254 + 0.540641i) q^{81} +(0.584143 - 0.674138i) q^{82} +(7.49464 + 2.20063i) q^{83} +(-0.282104 - 1.96208i) q^{84} +(-1.28790 - 1.48632i) q^{85} +(0.0183905 + 0.0402696i) q^{86} +(-4.54744 + 1.33525i) q^{87} +(-1.06768 + 2.33789i) q^{88} +(-0.473210 + 3.29125i) q^{89} +(-0.0916539 + 0.0589024i) q^{90} -6.86730 q^{91} +(-0.636387 + 9.48523i) q^{92} -2.57808 q^{93} +(1.34272 - 0.862912i) q^{94} +(-0.738203 + 5.13431i) q^{95} +(0.656231 - 1.43695i) q^{96} +(5.05491 - 1.48426i) q^{97} +(-0.0553392 - 0.121176i) q^{98} +(3.17269 + 3.66148i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−0.112067	+	0.0720210i	−0.0792433	+	0.0509266i	−0.579662	−	0.814857i	$-0.696816\pi$
$2$	−0.112067	+	0.0720210i	−0.0792433	+	0.0509266i	0.500419	+	0.865783i	$0.333179\pi$
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	−0.823458	+	1.80312i	−0.411729	+	0.901561i
$5$	−0.784721	+	0.230415i	−0.350938	+	0.103045i	−0.452450	−	0.891790i	$-0.649450\pi$
$5$	−0.784721	+	0.230415i	−0.350938	+	0.103045i	0.101512	+	0.994834i	$0.467632\pi$
$6$	0.0553392	+	0.121176i	0.0225921	+	0.0494699i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.0754970	−	0.525093i	−0.0266922	−	0.185648i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	0.0713466	−	0.0823383i	0.0225618	−	0.0260377i
$11$	−4.07573	−	2.61931i	−1.22888	−	0.789753i	−0.245163	−	0.969482i	$-0.578842\pi$
$11$	−4.07573	−	2.61931i	−1.22888	−	0.789753i	−0.983716	+	0.179729i	$0.942478\pi$
$12$	1.66758	+	1.07169i	0.481388	+	0.309370i
$13$	4.49713	−	5.18996i	1.24728	−	1.43944i	0.393067	−	0.919510i	$-0.371414\pi$
$13$	4.49713	−	5.18996i	1.24728	−	1.43944i	0.854211	−	0.519926i	$-0.174041\pi$
$14$	0.127818	+	0.0375308i	0.0341608	+	0.0100305i
$15$	0.116392	+	0.809525i	0.0300523	+	0.209018i
$16$	−2.54992	−	2.94277i	−0.637481	−	0.735692i
$17$	0.998945	+	2.18738i	0.242280	+	0.530519i	0.991236	−	0.132100i	$-0.0421721\pi$
$17$	0.998945	+	2.18738i	0.242280	+	0.530519i	−0.748957	+	0.662619i	$0.769445\pi$
$18$	0.127818	−	0.0375308i	0.0301270	−	0.00884609i
$19$	2.63472	−	5.76923i	0.604446	−	1.32355i	−0.321863	−	0.946786i	$-0.604309\pi$
$19$	2.63472	−	5.76923i	0.604446	−	1.32355i	0.926309	−	0.376766i	$-0.122964\pi$
$20$	0.230719	−	1.60468i	0.0515903	−	0.358818i
$21$	−0.841254	+	0.540641i	−0.183577	+	0.117977i
$22$	0.645401			0.137600
$23$	4.48602	−	1.69576i	0.935400	−	0.353591i
$23$	4.48602	−	1.69576i	0.935400	−	0.353591i
$24$	−0.530493			−0.108286
$25$	−3.64357	+	2.34158i	−0.728714	+	0.468316i
$26$	−0.130193	+	0.905511i	−0.0255329	+	0.177585i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	1.90196	−	0.558465i	0.359436	−	0.105540i
$29$	−1.96882	−	4.31113i	−0.365602	−	0.800556i	−0.999629	−	0.0272451i	$-0.991327\pi$
$29$	−1.96882	−	4.31113i	−0.365602	−	0.800556i	0.634027	−	0.773311i	$-0.281401\pi$
$30$	−0.0713466	−	0.0823383i	−0.0130260	−	0.0150329i
$31$	−0.366899	−	2.55184i	−0.0658970	−	0.458324i	−0.995877	−	0.0907137i	$-0.971085\pi$
$31$	−0.366899	−	2.55184i	−0.0658970	−	0.458324i	0.929980	−	0.367610i	$-0.119824\pi$
$32$	1.51571	+	0.445053i	0.267942	+	0.0786750i
$33$	−3.17269	+	3.66148i	−0.552294	+	0.637382i
$34$	−0.269486	−	0.173188i	−0.0462166	−	0.0297016i
$35$	0.688019	+	0.442163i	0.116296	+	0.0747392i
$36$	1.29810	−	1.49809i	0.216350	−	0.249681i
$37$	4.67265	+	1.37202i	0.768180	+	0.225558i	0.642264	−	0.766483i	$-0.277995\pi$
$37$	4.67265	+	1.37202i	0.768180	+	0.225558i	0.125915	+	0.992041i	$0.459813\pi$
$38$	0.120241	+	0.836295i	0.0195057	+	0.135665i
$39$	−4.49713	−	5.18996i	−0.720116	−	0.831059i
$40$	0.180233	+	0.394656i	0.0284974	+	0.0624006i
$41$	−6.42483	+	1.88650i	−1.00339	+	0.294622i	−0.741847	−	0.670570i	$-0.766050\pi$
$41$	−6.42483	+	1.88650i	−1.00339	+	0.294622i	−0.261544	+	0.965192i	$0.584232\pi$
$42$	0.0553392	−	0.121176i	0.00853902	−	0.0186979i
$43$	0.0472946	−	0.328941i	0.00721236	−	0.0501631i	−0.985897	−	0.167351i	$-0.946479\pi$
$43$	0.0472946	−	0.328941i	0.00721236	−	0.0501631i	0.993110	+	0.117188i	$0.0373879\pi$
$44$	8.07914	−	5.19215i	1.21798	−	0.782745i
$45$	0.817850			0.121918
$46$	−0.380604	+	0.513127i	−0.0561170	+	0.0756564i
$47$	−11.9814			−1.74766			−0.873832	−	0.486227i	$-0.838373\pi$
$47$	−11.9814			−1.74766			−0.873832	+	0.486227i	$0.838373\pi$
$48$	−3.27571	+	2.10517i	−0.472807	+	0.303855i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	0.239681	−	0.524828i	0.0338960	−	0.0742218i
$51$	2.30729	−	0.677480i	0.323085	−	0.0948662i
$52$	5.65493	+	12.3826i	0.784198	+	1.71715i
$53$	−4.06815	−	4.69490i	−0.558804	−	0.644894i	0.404108	−	0.914711i	$-0.367582\pi$
$53$	−4.06815	−	4.69490i	−0.558804	−	0.644894i	−0.962911	+	0.269817i	$0.913037\pi$
$54$	−0.0189584	−	0.131858i	−0.00257991	−	0.0179436i
$55$	3.80184	+	1.11632i	0.512640	+	0.150525i
$56$	−0.347399	+	0.400920i	−0.0464231	+	0.0535752i
$57$	−5.33555	−	3.42895i	−0.706710	−	0.454175i
$58$	0.531132	+	0.341338i	0.0697410	+	0.0448198i
$59$	−0.138849	+	0.160241i	−0.0180766	+	0.0208616i	−0.764716	−	0.644368i	$-0.777121\pi$
$59$	−0.138849	+	0.160241i	−0.0180766	+	0.0208616i	0.746639	+	0.665229i	$0.231666\pi$
$60$	−1.55552	−	0.456741i	−0.200816	−	0.0589650i
$61$	0.113286	+	0.787921i	0.0145048	+	0.100883i	0.995788	−	0.0916885i	$-0.0292264\pi$
$61$	0.113286	+	0.787921i	0.0145048	+	0.100883i	−0.981283	+	0.192571i	$0.938317\pi$
$62$	0.224903	+	0.259552i	0.0285628	+	0.0329632i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	7.27031	−	2.13475i	0.908788	−	0.266844i
$65$	−2.33315	+	5.10888i	−0.289391	+	0.633678i
$66$	0.0918501	−	0.638831i	0.0113060	−	0.0786347i
$67$	2.86214	−	1.83938i	0.349666	−	0.224717i	−0.354004	−	0.935244i	$-0.615180\pi$
$67$	2.86214	−	1.83938i	0.349666	−	0.224717i	0.703670	+	0.710527i	$0.251544\pi$
$68$	−4.76671			−0.578049
$69$	−1.04007	−	4.68169i	−0.125210	−	0.563610i
$70$	−0.108949			−0.0130219
$71$	−5.60905	+	3.60472i	−0.665671	+	0.427801i	−0.829363	−	0.558711i	$-0.811296\pi$
$71$	−5.60905	+	3.60472i	−0.665671	+	0.427801i	0.163691	+	0.986512i	$0.447660\pi$
$72$	−0.0754970	+	0.525093i	−0.00889741	+	0.0618828i
$73$	−4.16581	+	9.12186i	−0.487572	+	1.06763i	0.492740	+	0.870177i	$0.335995\pi$
$73$	−4.16581	+	9.12186i	−0.487572	+	1.06763i	−0.980312	+	0.197457i	$0.936732\pi$
$74$	−0.622464	+	0.182772i	−0.0723600	+	0.0212468i
$75$	1.79921	+	3.93973i	0.207755	+	0.454920i
$76$	8.23304	+	9.50144i	0.944395	+	1.08989i
$77$	0.689492	+	4.79552i	0.0785748	+	0.546500i
$78$	0.877766	+	0.257735i	0.0993874	+	0.0291828i
$79$	7.76108	−	8.95677i	0.873190	−	1.00771i	−0.126686	−	0.991943i	$-0.540434\pi$
$79$	7.76108	−	8.95677i	0.873190	−	1.00771i	0.999876	−	0.0157719i	$-0.00502057\pi$
$80$	2.67903	+	1.72171i	0.299525	+	0.192493i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	0.584143	−	0.674138i	0.0645079	−	0.0744460i
$83$	7.49464	+	2.20063i	0.822644	+	0.241550i	0.665854	−	0.746082i	$-0.268067\pi$
$83$	7.49464	+	2.20063i	0.822644	+	0.241550i	0.156790	+	0.987632i	$0.449885\pi$
$84$	−0.282104	−	1.96208i	−0.0307801	−	0.214080i
$85$	−1.28790	−	1.48632i	−0.139692	−	0.161214i
$86$	0.0183905	+	0.0402696i	0.00198310	+	0.00434239i
$87$	−4.54744	+	1.33525i	−0.487536	+	0.143154i
$88$	−1.06768	+	2.33789i	−0.113815	+	0.249220i
$89$	−0.473210	+	3.29125i	−0.0501602	+	0.348872i	0.949250	+	0.314523i	$0.101845\pi$
$89$	−0.473210	+	3.29125i	−0.0501602	+	0.348872i	−0.999410	+	0.0343484i	$0.989064\pi$
$90$	−0.0916539	+	0.0589024i	−0.00966117	+	0.00620886i
$91$	−6.86730			−0.719889
$92$	−0.636387	+	9.48523i	−0.0663479	+	0.988904i
$93$	−2.57808			−0.267335
$94$	1.34272	−	0.862912i	0.138491	−	0.0890026i
$95$	−0.738203	+	5.13431i	−0.0757380	+	0.526769i
$96$	0.656231	−	1.43695i	0.0669763	−	0.146658i
$97$	5.05491	−	1.48426i	0.513248	−	0.150703i	−0.0148448	−	0.999890i	$-0.504725\pi$
$97$	5.05491	−	1.48426i	0.513248	−	0.150703i	0.528093	+	0.849187i	$0.322907\pi$
$98$	−0.0553392	−	0.121176i	−0.00559010	−	0.0122406i
$99$	3.17269	+	3.66148i	0.318867	+	0.367993i
$100$	−1.22183	−	8.49800i	−0.122183	−	0.849800i
$101$	3.79714	+	1.11494i	0.377830	+	0.110941i	0.465133	−	0.885241i	$-0.346007\pi$
$101$	3.79714	+	1.11494i	0.377830	+	0.110941i	−0.0873028	+	0.996182i	$0.527825\pi$
$102$	−0.209778	+	0.242096i	−0.0207711	+	0.0239711i
$103$	2.10878	+	1.35523i	0.207784	+	0.133535i	0.640394	−	0.768046i	$-0.278771\pi$
$103$	2.10878	+	1.35523i	0.207784	+	0.133535i	−0.432610	+	0.901581i	$0.642407\pi$
$104$	−3.06473	−	1.96958i	−0.300522	−	0.193134i
$105$	0.535578	−	0.618090i	0.0522670	−	0.0603194i
$106$	0.794037	+	0.233150i	0.0771237	+	0.0226456i
$107$	−2.62185	−	18.2354i	−0.253464	−	1.76288i	−0.577078	−	0.816689i	$-0.695807\pi$
$107$	−2.62185	−	18.2354i	−0.253464	−	1.76288i	0.323614	−	0.946189i	$-0.395102\pi$
$108$	−1.29810	−	1.49809i	−0.124910	−	0.144154i
$109$	5.19851	+	11.3831i	0.497927	+	1.09031i	0.977138	+	0.212608i	$0.0681956\pi$
$109$	5.19851	+	11.3831i	0.497927	+	1.09031i	−0.479211	+	0.877700i	$0.659077\pi$
$110$	−0.506459	+	0.148710i	−0.0482890	+	0.0141789i
$111$	2.02304	−	4.42984i	0.192018	−	0.420461i
$112$	−0.554151	+	3.85421i	−0.0523624	+	0.364188i
$113$	11.7857	−	7.57421i	1.10871	−	0.712522i	0.147695	−	0.989033i	$-0.452814\pi$
$113$	11.7857	−	7.57421i	1.10871	−	0.712522i	0.961011	+	0.276511i	$0.0891781\pi$
$114$	0.844895			0.0791316
$115$	−3.12955	+	2.36435i	−0.291832	+	0.220476i
$116$	9.39473			0.872279
$117$	−5.77714	+	3.71274i	−0.534097	+	0.343243i
$118$	0.00401972	−	0.0279578i	0.000370045	−	0.00257372i
$119$	0.998945	−	2.18738i	0.0915732	−	0.200517i
$120$	0.416289	−	0.122233i	0.0380018	−	0.0111583i
$121$	5.18122	+	11.3453i	0.471020	+	1.03139i
$122$	−0.0694425	−	0.0801409i	−0.00628703	−	0.00725562i
$123$	0.952950	+	6.62791i	0.0859246	+	0.597619i
$124$	4.90340	+	1.43977i	0.440339	+	0.129295i
$125$	4.99754	−	5.76747i	0.446994	−	0.515858i
$126$	−0.112067	−	0.0720210i	−0.00998372	−	0.00641614i
$127$	−5.80129	−	3.72826i	−0.514781	−	0.330830i	0.257323	−	0.966325i	$-0.417160\pi$
$127$	−5.80129	−	3.72826i	−0.514781	−	0.330830i	−0.772105	+	0.635495i	$0.780796\pi$
$128$	−2.72998	+	3.15057i	−0.241299	+	0.278473i
$129$	−0.318862	−	0.0936264i	−0.0280743	−	0.00824335i
$130$	−0.106478	−	0.740572i	−0.00933875	−	0.0649524i
$131$	14.7876	+	17.0658i	1.29200	+	1.49105i	0.769907	+	0.638157i	$0.220303\pi$
$131$	14.7876	+	17.0658i	1.29200	+	1.49105i	0.522092	+	0.852889i	$0.325152\pi$
$132$	−3.98952	−	8.73582i	−0.347243	−	0.760356i
$133$	−6.08547	+	1.78685i	−0.527677	+	0.154940i
$134$	−0.188277	+	0.412268i	−0.0162646	+	0.0356146i
$135$	0.116392	−	0.809525i	0.0100174	−	0.0696728i
$136$	1.07316	−	0.689680i	0.0920230	−	0.0591396i
$137$	−12.1035			−1.03407			−0.517035	−	0.855964i	$-0.672964\pi$
$137$	−12.1035			−1.03407			−0.517035	+	0.855964i	$0.672964\pi$
$138$	0.453738	+	0.449756i	0.0386248	+	0.0382858i
$139$	−1.41432			−0.119961			−0.0599804	−	0.998200i	$-0.519104\pi$
$139$	−1.41432			−0.119961			−0.0599804	+	0.998200i	$0.519104\pi$
$140$	−1.36383	+	0.876479i	−0.115265	+	0.0740760i
$141$	−1.70513	+	11.8594i	−0.143598	+	0.998744i
$142$	0.368973	−	0.807939i	0.0309636	−	0.0678007i
$143$	−31.9232	+	9.37350i	−2.66955	+	0.783852i
$144$	1.61756	+	3.54196i	0.134797	+	0.295163i
$145$	2.53833	+	2.92938i	0.210796	+	0.243272i
$146$	−0.190116	−	1.32229i	−0.0157341	−	0.109433i
$147$	0.959493	+	0.281733i	0.0791376	+	0.0232369i
$148$	−6.32164	+	7.29557i	−0.519636	+	0.599692i
$149$	8.72553	+	5.60756i	0.714823	+	0.459389i	0.846833	−	0.531859i	$-0.178507\pi$
$149$	8.72553	+	5.60756i	0.714823	+	0.459389i	−0.132009	+	0.991248i	$0.542143\pi$
$150$	−0.485376	−	0.311932i	−0.0396307	−	0.0254691i
$151$	−5.82089	+	6.71766i	−0.473697	+	0.546675i	−0.941436	−	0.337191i	$-0.890523\pi$
$151$	−5.82089	+	6.71766i	−0.473697	+	0.546675i	0.467739	+	0.883867i	$0.345069\pi$
$152$	−3.22830	−	0.947913i	−0.261849	−	0.0768859i
$153$	−0.342223	−	2.38022i	−0.0276671	−	0.192429i
$154$	−0.422647	−	0.487761i	−0.0340579	−	0.0393049i
$155$	0.875895	+	1.91794i	0.0703536	+	0.154053i
$156$	13.0613	−	3.83515i	1.04574	−	0.307058i
$157$	−2.61945	+	5.73579i	−0.209055	+	0.457766i	−0.984893	−	0.173166i	$-0.944600\pi$
$157$	−2.61945	+	5.73579i	−0.209055	+	0.457766i	0.775838	+	0.630932i	$0.217327\pi$
$158$	−0.224685	+	1.56272i	−0.0178750	+	0.124323i
$159$	−5.22607	+	3.35859i	−0.414454	+	0.266354i
$160$	−1.29196			−0.102138
$161$	−4.21929	−	2.27982i	−0.332527	−	0.179675i
$162$	−0.133214			−0.0104663
$163$	−4.25664	+	2.73558i	−0.333406	+	0.214267i	−0.696623	−	0.717438i	$-0.745315\pi$
$163$	−4.25664	+	2.73558i	−0.333406	+	0.214267i	0.363217	+	0.931705i	$0.381678\pi$
$164$	1.88899	−	13.1382i	0.147505	−	1.02592i
$165$	1.64602	−	3.60428i	0.128142	−	0.280592i
$166$	−0.998393	+	0.293155i	−0.0774903	+	0.0227532i
$167$	−3.84558	−	8.42065i	−0.297580	−	0.651609i	0.700493	−	0.713659i	$-0.252964\pi$
$167$	−3.84558	−	8.42065i	−0.297580	−	0.651609i	−0.998073	+	0.0620498i	$0.980236\pi$
$168$	0.347399	+	0.400920i	0.0268024	+	0.0309316i
$169$	−4.86145	−	33.8121i	−0.373958	−	2.60093i
$170$	0.251377	+	0.0738109i	0.0192797	+	0.00566104i
$171$	−4.15337	+	4.79325i	−0.317616	+	0.366549i
$172$	0.554176	+	0.356147i	0.0422555	+	0.0271560i
$173$	9.86277	+	6.33842i	0.749852	+	0.481901i	0.858905	−	0.512135i	$-0.171145\pi$
$173$	9.86277	+	6.33842i	0.749852	+	0.481901i	−0.109053	+	0.994036i	$0.534782\pi$
$174$	0.413451	−	0.477148i	0.0313437	−	0.0361725i
$175$	4.15568	+	1.22022i	0.314140	+	0.0922398i
$176$	2.68477	+	18.6730i	0.202372	+	1.40753i
$177$	0.138849	+	0.160241i	0.0104366	+	0.0120444i
$178$	−0.184008	−	0.402921i	−0.0137920	−	0.0302002i
$179$	−11.4534	+	3.36301i	−0.856064	+	0.251363i	−0.680177	−	0.733048i	$-0.738097\pi$
$179$	−11.4534	+	3.36301i	−0.856064	+	0.251363i	−0.175886	+	0.984411i	$0.556279\pi$
$180$	−0.673465	+	1.47468i	−0.0501971	+	0.109916i
$181$	0.600138	−	4.17405i	0.0446079	−	0.310255i	−0.955286	−	0.295684i	$-0.904453\pi$
$181$	0.600138	−	4.17405i	0.0446079	−	0.310255i	0.999894	−	0.0145711i	$-0.00463830\pi$
$182$	0.769597	−	0.494590i	0.0570464	−	0.0366615i
$183$	0.796023			0.0588437
$184$	−1.22911	−	2.22755i	−0.0906115	−	0.164218i
$185$	−3.98286			−0.292826
$186$	0.288918	−	0.185676i	0.0211845	−	0.0136144i
$187$	1.65801	−	11.5317i	0.121246	−	0.843285i
$188$	9.86617	−	21.6039i	0.719564	−	1.57563i
$189$	0.959493	−	0.281733i	0.0697928	−	0.0204930i
$190$	−0.287051	−	0.628553i	−0.0208248	−	0.0456000i
$191$	−0.824948	−	0.952040i	−0.0596911	−	0.0688872i	0.725119	−	0.688624i	$-0.241785\pi$
$191$	−0.824948	−	0.952040i	−0.0596911	−	0.0688872i	−0.784810	+	0.619737i	$0.787239\pi$
$192$	−1.07835	−	7.50011i	−0.0778235	−	0.541274i
$193$	12.0469	+	3.53728i	0.867153	+	0.254619i	0.684904	−	0.728633i	$-0.259844\pi$
$193$	12.0469	+	3.53728i	0.867153	+	0.254619i	0.182249	+	0.983252i	$0.441662\pi$
$194$	−0.459591	+	0.530396i	−0.0329967	+	0.0380802i
$195$	4.72483	+	3.03647i	0.338352	+	0.217446i
$196$	−1.66758	−	1.07169i	−0.119113	−	0.0765491i
$197$	1.17313	−	1.35387i	0.0835824	−	0.0964592i	−0.712418	−	0.701755i	$-0.752400\pi$
$197$	1.17313	−	1.35387i	0.0835824	−	0.0964592i	0.796000	+	0.605296i	$0.206945\pi$
$198$	−0.619257	−	0.181830i	−0.0440087	−	0.0129221i
$199$	−2.79617	−	19.4478i	−0.198215	−	1.37862i	−0.809459	−	0.587176i	$-0.800240\pi$
$199$	−2.79617	−	19.4478i	−0.198215	−	1.37862i	0.611244	−	0.791442i	$-0.290670\pi$
$200$	1.50463	+	1.73643i	0.106393	+	0.122784i
$201$	−1.41334	−	3.09478i	−0.0996892	−	0.218289i
$202$	−0.505834	+	0.148526i	−0.0355903	+	0.0104503i
$203$	−1.96882	+	4.31113i	−0.138184	+	0.302582i
$204$	−0.678374	+	4.71819i	−0.0474957	+	0.330340i
$205$	4.60702	−	2.96075i	0.321768	−	0.206788i
$206$	−0.333930			−0.0232660
$207$	−4.78206	+	0.363213i	−0.332376	+	0.0252450i
$208$	−26.7402			−1.85410
$209$	−25.8498	+	16.6127i	−1.78807	+	1.14912i
$210$	−0.0155051	+	0.107840i	−0.00106995	+	0.00744169i
$211$	11.7236	−	25.6710i	0.807083	−	1.76726i	0.187614	−	0.982243i	$-0.439925\pi$
$211$	11.7236	−	25.6710i	0.807083	−	1.76726i	0.619469	−	0.785022i	$-0.287348\pi$
$212$	11.8154	−	3.46932i	0.811487	−	0.238274i
$213$	2.76977	+	6.06496i	0.189782	+	0.415564i
$214$	1.60715	+	1.85475i	0.109863	+	0.126788i
$215$	0.0386799	+	0.269024i	0.00263795	+	0.0183473i
$216$	0.509004	+	0.149457i	0.0346333	+	0.0101693i
$217$	−1.68828	+	1.94838i	−0.114608	+	0.132265i
$218$	−1.40241	−	0.901272i	−0.0949830	−	0.0610418i
$219$	8.43616	+	5.42159i	0.570063	+	0.366357i
$220$	−5.14352	+	5.93594i	−0.346776	+	0.400201i
$221$	15.8448	+	4.65246i	1.06584	+	0.312958i
$222$	0.0923257	+	0.642139i	0.00619650	+	0.0430976i
$223$	13.9300	+	16.0760i	0.932820	+	1.07653i	0.996907	+	0.0785872i	$0.0250409\pi$
$223$	13.9300	+	16.0760i	0.932820	+	1.07653i	−0.0640874	+	0.997944i	$0.520414\pi$
$224$	−0.656231	−	1.43695i	−0.0438463	−	0.0960100i
$225$	4.15568	−	1.22022i	0.277045	−	0.0813479i
$226$	−0.775285	+	1.69764i	−0.0515712	+	0.112925i
$227$	0.363345	−	2.52712i	0.0241161	−	0.167731i	−0.974204	−	0.225669i	$-0.927543\pi$
$227$	0.363345	−	2.52712i	0.0241161	−	0.167731i	0.998320	+	0.0579377i	$0.0184525\pi$
$228$	10.5764	−	6.79705i	0.700440	−	0.450145i
$229$	−21.8026			−1.44075			−0.720377	−	0.693582i	$-0.756031\pi$
$229$	−21.8026			−1.44075			−0.720377	+	0.693582i	$0.756031\pi$
$230$	0.180436	−	0.490358i	0.0118976	−	0.0323333i
$231$	4.84483			0.318767
$232$	−2.11510	+	1.35929i	−0.138863	+	0.0892420i
$233$	2.92507	−	20.3443i	0.191628	−	1.33280i	−0.636073	−	0.771629i	$-0.719442\pi$
$233$	2.92507	−	20.3443i	0.191628	−	1.33280i	0.827701	−	0.561170i	$-0.189649\pi$
$234$	0.380031	−	0.832152i	0.0248434	−	0.0543995i
$235$	9.40204	−	2.76069i	0.613322	−	0.180088i
$236$	−0.174597	−	0.382314i	−0.0113653	−	0.0248865i
$237$	−7.76108	−	8.95677i	−0.504136	−	0.581804i
$238$	0.0455890	+	0.317079i	0.00295510	+	0.0205532i
$239$	19.1828	+	5.63259i	1.24083	+	0.364342i	0.835329	−	0.549751i	$-0.185277\pi$
$239$	19.1828	+	5.63259i	1.24083	+	0.364342i	0.405506	+	0.914092i	$0.367095\pi$
$240$	2.08545	−	2.40674i	0.134615	−	0.155354i
$241$	9.82626	+	6.31495i	0.632965	+	0.406782i	0.817406	−	0.576062i	$-0.195411\pi$
$241$	9.82626	+	6.31495i	0.632965	+	0.406782i	−0.184441	+	0.982844i	$0.559048\pi$
$242$	−1.39774	−	0.898275i	−0.0898504	−	0.0577433i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	−1.51400	−	0.444551i	−0.0969241	−	0.0284595i
$245$	−0.116392	−	0.809525i	−0.00743602	−	0.0517187i
$246$	−0.584143	−	0.674138i	−0.0372436	−	0.0429814i
$247$	−18.0934	−	39.6190i	−1.15126	−	2.52090i
$248$	−1.31225	+	0.385312i	−0.0833282	+	0.0244674i
$249$	3.24483	−	7.10518i	0.205633	−	0.450272i
$250$	−0.144680	+	1.00627i	−0.00915036	+	0.0636421i
$251$	16.6445	−	10.6968i	1.05059	−	0.675175i	0.103009	−	0.994680i	$-0.467153\pi$
$251$	16.6445	−	10.6968i	1.05059	−	0.675175i	0.947584	+	0.319505i	$0.103517\pi$
$252$	−1.98225			−0.124870
$253$	−22.7256	−	4.83883i	−1.42874	−	0.304215i
$254$	0.918647			0.0576410
$255$	−1.65447	+	1.06327i	−0.103607	+	0.0665843i
$256$	−2.07767	+	14.4505i	−0.129855	+	0.903159i
$257$	−1.46390	+	3.20549i	−0.0913154	+	0.199953i	−0.949779	−	0.312922i	$-0.898692\pi$
$257$	−1.46390	+	3.20549i	−0.0913154	+	0.199953i	0.858463	+	0.512875i	$0.171419\pi$
$258$	0.0424770	−	0.0124724i	0.00264450	−	0.000776496i
$259$	−2.02304	−	4.42984i	−0.125705	−	0.275257i
$260$	−7.29068	−	8.41389i	−0.452149	−	0.521807i
$261$	0.674489	+	4.69118i	0.0417498	+	0.290377i
$262$	−2.88630	−	0.847493i	−0.178316	−	0.0523583i
$263$	16.9754	−	19.5907i	1.04675	−	1.20801i	0.0691338	−	0.997607i	$-0.477976\pi$
$263$	16.9754	−	19.5907i	1.04675	−	1.20801i	0.977614	−	0.210404i	$-0.0674781\pi$
$264$	2.16215	+	1.38953i	0.133071	+	0.0855195i
$265$	4.27414	+	2.74682i	0.262558	+	0.168736i
$266$	0.553288	−	0.638529i	0.0339243	−	0.0391507i
$267$	3.19041	+	0.936787i	0.195250	+	0.0573305i
$268$	0.959783	+	6.67544i	0.0586281	+	0.407767i
$269$	−1.17279	−	1.35347i	−0.0715060	−	0.0825223i	0.718869	−	0.695145i	$-0.244660\pi$
$269$	−1.17279	−	1.35347i	−0.0715060	−	0.0825223i	−0.790375	+	0.612623i	$0.790114\pi$
$270$	0.0452591	+	0.0991037i	0.00275438	+	0.00603126i
$271$	6.71653	−	1.97215i	0.408000	−	0.119800i	−0.0712911	−	0.997456i	$-0.522712\pi$
$271$	6.71653	−	1.97215i	0.408000	−	0.119800i	0.479291	+	0.877656i	$0.340894\pi$
$272$	3.88973	−	8.51732i	0.235850	−	0.516439i
$273$	−0.977319	+	6.79740i	−0.0591500	+	0.411397i
$274$	1.35640	−	0.871706i	0.0819432	−	0.0526617i
$275$	20.9836			1.26536
$276$	9.29812	+	1.97980i	0.559681	+	0.119170i
$277$	−1.85664			−0.111555			−0.0557773	−	0.998443i	$-0.517764\pi$
$277$	−1.85664			−0.111555			−0.0557773	+	0.998443i	$0.517764\pi$
$278$	0.158498	−	0.101861i	0.00950609	−	0.00610919i
$279$	−0.366899	+	2.55184i	−0.0219657	+	0.152775i
$280$	0.180233	−	0.394656i	0.0107710	−	0.0235852i
$281$	−11.4851	+	3.37233i	−0.685143	+	0.201176i	−0.605736	−	0.795666i	$-0.707121\pi$
$281$	−11.4851	+	3.37233i	−0.685143	+	0.201176i	−0.0794077	+	0.996842i	$0.525303\pi$
$282$	−0.663040	−	1.45186i	−0.0394835	−	0.0864567i
$283$	−21.0365	−	24.2774i	−1.25049	−	1.44314i	−0.849952	−	0.526860i	$-0.823369\pi$
$283$	−21.0365	−	24.2774i	−1.25049	−	1.44314i	−0.400536	−	0.916281i	$-0.631176\pi$
$284$	−1.88093	−	13.0821i	−0.111612	−	0.776281i
$285$	4.97700	+	1.46138i	0.294812	+	0.0865646i
$286$	2.90245	−	3.34960i	0.171625	−	0.198066i
$287$	5.63309	+	3.62017i	0.332511	+	0.213692i
$288$	−1.32893	−	0.854051i	−0.0783079	−	0.0503254i
$289$	7.34587	−	8.47759i	0.432110	−	0.498682i
$290$	−0.495440	−	0.145474i	−0.0290932	−	0.00854254i
$291$	−0.749759	−	5.21469i	−0.0439517	−	0.305690i
$292$	−13.0175	−	15.0229i	−0.761789	−	0.879151i
$293$	6.74623	+	14.7722i	0.394119	+	0.863000i	0.997833	+	0.0657991i	$0.0209596\pi$
$293$	6.74623	+	14.7722i	0.394119	+	0.863000i	−0.603714	+	0.797201i	$0.706313\pi$
$294$	−0.127818	+	0.0375308i	−0.00745450	+	0.00218884i
$295$	0.0720362	−	0.157737i	0.00419411	−	0.00918381i
$296$	0.367664	−	2.55716i	0.0213701	−	0.148632i
$297$	4.07573	−	2.61931i	0.236498	−	0.151988i
$298$	−1.38171			−0.0800401
$299$	11.3733	−	30.9083i	0.657733	−	1.78747i
$300$	−8.58538			−0.495677
$301$	−0.279569	+	0.179668i	−0.0161141	+	0.0103559i
$302$	0.168516	−	1.17205i	0.00969700	−	0.0674441i
$303$	1.64398	−	3.59982i	0.0944444	−	0.206804i
$304$	−23.6958	+	6.95772i	−1.35905	+	0.399053i
$305$	−0.270446	−	0.592195i	−0.0154857	−	0.0339090i
$306$	0.209778	+	0.242096i	0.0119922	+	0.0138397i
$307$	2.31081	+	16.0720i	0.131885	+	0.917280i	0.943095	+	0.332524i	$0.107900\pi$
$307$	2.31081	+	16.0720i	0.131885	+	0.917280i	−0.811210	+	0.584755i	$0.801191\pi$
$308$	−9.21467	−	2.70567i	−0.525055	−	0.154170i
$309$	1.64155	−	1.89445i	0.0933843	−	0.107771i
$310$	−0.236291	−	0.151855i	−0.0134204	−	0.00862479i
$311$	18.5588	+	11.9270i	1.05238	+	0.676320i	0.948017	−	0.318219i	$-0.103085\pi$
$311$	18.5588	+	11.9270i	1.05238	+	0.676320i	0.104358	+	0.994540i	$0.466721\pi$
$312$	−2.38569	+	2.75324i	−0.135063	+	0.155871i
$313$	−3.81889	−	1.12133i	−0.215857	−	0.0633812i	0.172016	−	0.985094i	$-0.444972\pi$
$313$	−3.81889	−	1.12133i	−0.215857	−	0.0633812i	−0.387873	+	0.921713i	$0.626790\pi$
$314$	−0.119544	−	0.831448i	−0.00674627	−	0.0469213i
$315$	−0.535578	−	0.618090i	−0.0301764	−	0.0348254i
$316$	9.75921	+	21.3697i	0.548999	+	1.20214i
$317$	−27.0441	+	7.94086i	−1.51895	+	0.446003i	−0.931646	−	0.363366i	$-0.881627\pi$
$317$	−27.0441	+	7.94086i	−1.51895	+	0.446003i	−0.587300	+	0.809369i	$0.699809\pi$
$318$	0.343780	−	0.752774i	0.0192782	−	0.0422135i
$319$	−3.26779	+	22.7280i	−0.182961	+	1.27252i
$320$	−5.21328	+	3.35037i	−0.291431	+	0.187292i
$321$	−18.4229			−1.02826
$322$	0.637038	−	0.0483851i	0.0355007	−	0.00269640i
$323$	15.2515			0.848614
$324$	−1.66758	+	1.07169i	−0.0926432	+	0.0595382i
$325$	−4.23289	+	29.4404i	−0.234798	+	1.63306i
$326$	0.280010	−	0.613136i	0.0155083	−	0.0339584i
$327$	12.0071	−	3.52560i	0.663994	−	0.194966i
$328$	1.47564	+	3.23121i	0.0814788	+	0.178414i
$329$	7.84614	+	9.05493i	0.432572	+	0.499214i
$330$	0.0751196	+	0.522468i	0.00413520	+	0.0287609i
$331$	−13.4441	−	3.94756i	−0.738957	−	0.216977i	−0.109472	−	0.993990i	$-0.534916\pi$
$331$	−13.4441	−	3.94756i	−0.738957	−	0.216977i	−0.629485	+	0.777012i	$0.716734\pi$
$332$	−10.1395	+	11.7016i	−0.556479	+	0.642211i
$333$	−4.09684	−	2.63288i	−0.224505	−	0.144281i
$334$	1.03743	+	0.666714i	0.0567655	+	0.0364809i
$335$	−1.82216	+	2.10288i	−0.0995552	+	0.114893i
$336$	3.73611	+	1.09702i	0.203822	+	0.0598474i
$337$	4.47212	+	31.1043i	0.243612	+	1.69436i	0.633698	+	0.773581i	$0.281536\pi$
$337$	4.47212	+	31.1043i	0.243612	+	1.69436i	−0.390085	+	0.920779i	$0.627555\pi$
$338$	2.97999	+	3.43910i	0.162090	+	0.187062i
$339$	−5.81984	−	12.7437i	−0.316090	−	0.692141i
$340$	3.74054	−	1.09832i	0.202859	−	0.0595648i
$341$	−5.18869	+	11.3616i	−0.280983	+	0.615267i
$342$	0.120241	−	0.836295i	0.00650189	−	0.0452217i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	−0.176295			−0.00950521
$345$	1.89490	+	3.43417i	0.102018	+	0.184890i
$346$	−1.56179			−0.0839623
$347$	−15.6044	+	10.0283i	−0.837686	+	0.538348i	−0.887712	−	0.460400i	$-0.847706\pi$
$347$	−15.6044	+	10.0283i	−0.837686	+	0.538348i	0.0500254	+	0.998748i	$0.484070\pi$
$348$	1.33701	−	9.29910i	0.0716712	−	0.498484i
$349$	−4.69796	+	10.2871i	−0.251476	+	0.550655i	−0.992701	−	0.120601i	$-0.961518\pi$
$349$	−4.69796	+	10.2871i	−0.251476	+	0.550655i	0.741225	+	0.671256i	$0.234245\pi$
$350$	−0.553596	+	0.162550i	−0.0295909	+	0.00868868i
$351$	2.85278	+	6.24672i	0.152270	+	0.333425i
$352$	−5.01190	−	5.78404i	−0.267135	−	0.308290i
$353$	−3.35304	−	23.3209i	−0.178464	−	1.24125i	−0.860318	−	0.509758i	$-0.829735\pi$
$353$	−3.35304	−	23.3209i	−0.178464	−	1.24125i	0.681853	−	0.731489i	$-0.261174\pi$
$354$	−0.0271011	−	0.00795761i	−0.00144041	−	0.000422942i
$355$	3.57096	−	4.12110i	0.189527	−	0.218725i
$356$	−5.54486	−	3.56346i	−0.293877	−	0.188863i
$357$	−2.02296	−	1.30007i	−0.107066	−	0.0688073i
$358$	1.04133	−	1.20176i	0.0550362	−	0.0635152i
$359$	23.1937	+	6.81030i	1.22412	+	0.359434i	0.829027	−	0.559208i	$-0.188895\pi$
$359$	23.1937	+	6.81030i	1.22412	+	0.359434i	0.395091	+	0.918642i	$0.370713\pi$
$360$	−0.0617452	−	0.429447i	−0.00325426	−	0.0226339i
$361$	−13.8999	−	16.0413i	−0.731574	−	0.844281i
$362$	0.233364	+	0.510996i	0.0122653	+	0.0268573i
$363$	11.9672	−	3.51388i	0.628114	−	0.184431i
$364$	5.65493	−	12.3826i	0.296399	−	0.649024i
$365$	1.16719	−	8.11798i	0.0610935	−	0.424915i
$366$	−0.0892079	+	0.0573304i	−0.00466297	+	0.00299671i
$367$	35.3755			1.84659			0.923293	−	0.384096i	$-0.125487\pi$
$367$	35.3755			1.84659			0.923293	+	0.384096i	$0.125487\pi$
$368$	−16.4292	−	8.87726i	−0.856433	−	0.462759i
$369$	6.69607			0.348583
$370$	0.446347	−	0.286850i	0.0232045	−	0.0149126i
$371$	−0.884094	+	6.14901i	−0.0458999	+	0.319241i
$372$	2.12294	−	4.64859i	0.110069	−	0.241018i
$373$	−8.31042	+	2.44016i	−0.430297	+	0.126347i	−0.489707	−	0.871887i	$-0.662896\pi$
$373$	−8.31042	+	2.44016i	−0.430297	+	0.126347i	0.0594100	+	0.998234i	$0.481078\pi$
$374$	0.644720	+	1.41174i	0.0333377	+	0.0729993i
$375$	−4.99754	−	5.76747i	−0.258072	−	0.297831i
$376$	0.904559	+	6.29134i	0.0466491	+	0.324451i
$377$	−31.2286	−	9.16955i	−1.60836	−	0.472256i
$378$	−0.0872368	+	0.100677i	−0.00448697	+	0.00517825i
$379$	−14.4540	−	9.28904i	−0.742454	−	0.477146i	0.113928	−	0.993489i	$-0.463657\pi$
$379$	−14.4540	−	9.28904i	−0.742454	−	0.477146i	−0.856382	+	0.516343i	$0.827293\pi$
$380$	−8.64991	−	5.55896i	−0.443731	−	0.285169i
$381$	−4.51593	+	5.21166i	−0.231358	+	0.267001i
$382$	0.161016	+	0.0472787i	0.00823831	+	0.00241899i
$383$	0.938698	+	6.52879i	0.0479653	+	0.333606i	0.999648	+	0.0265233i	$0.00844362\pi$
$383$	0.938698	+	6.52879i	0.0479653	+	0.333606i	−0.951683	+	0.307082i	$0.900647\pi$
$384$	2.72998	+	3.15057i	0.139314	+	0.160777i
$385$	−1.64602	−	3.60428i	−0.0838888	−	0.183691i
$386$	−1.60481	+	0.471216i	−0.0816829	+	0.0239843i
$387$	−0.138052	+	0.302292i	−0.00701759	+	0.0153664i
$388$	−1.48621	+	10.3368i	−0.0754510	+	0.524773i
$389$	−9.88141	+	6.35039i	−0.501007	+	0.321978i	−0.766619	−	0.642102i	$-0.778062\pi$
$389$	−9.88141	+	6.35039i	−0.501007	+	0.321978i	0.265612	+	0.964080i	$0.414426\pi$
$390$	−0.748187			−0.0378859
$391$	8.19057	+	8.11868i	0.414215	+	0.410580i
$392$	0.530493			0.0267939
$393$	18.9966	−	12.2084i	0.958251	−	0.615831i
$394$	−0.0339625	+	0.236214i	−0.00171101	+	0.0119003i
$395$	−4.02651	+	8.81683i	−0.202596	+	0.443623i
$396$	−9.21467	+	2.70567i	−0.463055	+	0.135965i
$397$	12.0600	+	26.4077i	0.605273	+	1.32536i	0.925761	+	0.378110i	$0.123426\pi$
$397$	12.0600	+	26.4077i	0.605273	+	1.32536i	−0.320488	+	0.947253i	$0.603847\pi$
$398$	1.71401	+	1.97807i	0.0859156	+	0.0991518i
$399$	0.902614	+	6.27782i	0.0451872	+	0.314284i
$400$	16.1816	+	4.75133i	0.809078	+	0.237567i
$401$	−13.7666	+	15.8875i	−0.687473	+	0.793386i	−0.987003	−	0.160701i	$-0.948625\pi$
$401$	−13.7666	+	15.8875i	−0.687473	+	0.793386i	0.299530	+	0.954087i	$0.403170\pi$
$402$	0.381278	+	0.245032i	0.0190164	+	0.0122211i
$403$	−14.8939	−	9.57175i	−0.741920	−	0.476803i
$404$	−5.13717	+	5.92861i	−0.255584	+	0.294959i
$405$	−0.784721	−	0.230415i	−0.0389931	−	0.0114494i
$406$	−0.0898516	−	0.624931i	−0.00445926	−	0.0310148i
$407$	−15.4507	−	17.8311i	−0.765865	−	0.883856i
$408$	−0.529933	−	1.16039i	−0.0262356	−	0.0574480i
$409$	−4.80918	+	1.41210i	−0.237799	+	0.0698240i	−0.398460	−	0.917186i	$-0.630455\pi$
$409$	−4.80918	+	1.41210i	−0.237799	+	0.0698240i	0.160662	+	0.987010i	$0.448637\pi$
$410$	−0.303058	+	0.663605i	−0.0149670	+	0.0327731i
$411$	−1.72251	+	11.9803i	−0.0849650	+	0.590944i
$412$	−4.18014	+	2.68641i	−0.205941	+	0.132350i
$413$	0.212029			0.0104333
$414$	0.509752	−	0.385113i	0.0250529	−	0.0189273i
$415$	−6.38826			−0.313587
$416$	9.12615	−	5.86502i	0.447446	−	0.287556i
$417$	−0.201278	+	1.39992i	−0.00985664	+	0.0685545i
$418$	1.70045	−	3.72346i	0.0831717	−	0.182121i
$419$	21.2111	−	6.22815i	1.03623	−	0.304265i	0.280989	−	0.959711i	$-0.409337\pi$
$419$	21.2111	−	6.22815i	1.03623	−	0.304265i	0.755242	+	0.655446i	$0.227519\pi$
$420$	0.673465	+	1.47468i	0.0328617	+	0.0719571i
$421$	−7.62482	−	8.79951i	−0.371611	−	0.428862i	0.538885	−	0.842379i	$-0.318846\pi$
$421$	−7.62482	−	8.79951i	−0.371611	−	0.428862i	−0.910496	+	0.413517i	$0.864300\pi$
$422$	0.535030	+	3.72121i	0.0260448	+	0.181146i
$423$	11.4961	+	3.37555i	0.558957	+	0.164125i
$424$	−2.15813	+	2.49061i	−0.104808	+	0.120955i
$425$	−8.76167	−	5.63078i	−0.425003	−	0.273133i
$426$	−0.747205	−	0.480199i	−0.0362022	−	0.0232657i
$427$	0.521284	−	0.601594i	0.0252267	−	0.0291132i
$428$	35.0396	+	10.2885i	1.69370	+	0.497315i
$429$	4.73495	+	32.9323i	0.228605	+	1.58999i
$430$	−0.0237102	−	0.0273630i	−0.00114341	−	0.00131956i
$431$	7.44035	+	16.2921i	0.358389	+	0.784762i	0.999845	+	0.0176027i	$0.00560340\pi$
$431$	7.44035	+	16.2921i	0.358389	+	0.784762i	−0.641456	+	0.767160i	$0.721669\pi$
$432$	3.73611	−	1.09702i	0.179754	−	0.0527805i
$433$	6.92436	−	15.1622i	0.332764	−	0.728651i	−0.667103	−	0.744965i	$-0.732466\pi$
$433$	6.92436	−	15.1622i	0.332764	−	0.728651i	0.999867	+	0.0163145i	$0.00519331\pi$
$434$	0.0488762	−	0.339941i	0.00234613	−	0.0163177i
$435$	3.26081	−	2.09559i	0.156344	−	0.100476i
$436$	−24.8059			−1.18799
$437$	2.03617	−	30.3487i	0.0974032	−	1.45178i
$438$	−1.33588			−0.0638310
$439$	−21.2412	+	13.6509i	−1.01379	+	0.651521i	−0.938370	−	0.345631i	$-0.887665\pi$
$439$	−21.2412	+	13.6509i	−1.01379	+	0.651521i	−0.0754159	+	0.997152i	$0.524028\pi$
$440$	0.299145	−	2.08060i	0.0142612	−	0.0991887i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	−2.11076	+	0.619774i	−0.100398	+	0.0294796i
$443$	14.5908	+	31.9495i	0.693232	+	1.51797i	0.847989	+	0.530014i	$0.177813\pi$
$443$	14.5908	+	31.9495i	0.693232	+	1.51797i	−0.154757	+	0.987953i	$0.549459\pi$
$444$	6.32164	+	7.29557i	0.300012	+	0.346232i
$445$	−0.387015	−	2.69175i	−0.0183463	−	0.127601i
$446$	−2.71890	−	0.798342i	−0.128744	−	0.0378026i
$447$	6.79225	−	7.83868i	0.321263	−	0.370757i
$448$	−6.37438	−	4.09656i	−0.301161	−	0.193544i
$449$	17.1222	+	11.0037i	0.808044	+	0.519299i	0.878232	−	0.478235i	$-0.158723\pi$
$449$	17.1222	+	11.0037i	0.808044	+	0.519299i	−0.0701874	+	0.997534i	$0.522360\pi$
$450$	−0.377833	+	0.436043i	−0.0178112	+	0.0205552i
$451$	31.1272	+	9.13978i	1.46572	+	0.430375i
$452$	3.95219	+	27.4881i	0.185896	+	1.29293i
$453$	5.82089	+	6.71766i	0.273489	+	0.315623i
$454$	0.141287	+	0.309375i	0.00663092	+	0.0145197i
$455$	5.38892	−	1.58233i	0.252636	−	0.0741807i
$456$	−1.39770	+	3.06053i	−0.0654533	+	0.143323i
$457$	2.20029	−	15.3034i	0.102925	−	0.715861i	−0.871377	−	0.490615i	$-0.836772\pi$
$457$	2.20029	−	15.3034i	0.102925	−	0.715861i	0.974302	−	0.225246i	$-0.0723186\pi$
$458$	2.44335	−	1.57024i	0.114170	−	0.0733727i
$459$	−2.40469			−0.112241
$460$	−1.68615	−	7.58989i	−0.0786173	−	0.353881i
$461$	6.75967			0.314829			0.157415	−	0.987533i	$-0.449684\pi$
$461$	6.75967			0.314829			0.157415	+	0.987533i	$0.449684\pi$
$462$	−0.542945	+	0.348930i	−0.0252601	+	0.0162337i
$463$	−2.01867	+	14.0402i	−0.0938158	+	0.652503i	0.887601	+	0.460614i	$0.152371\pi$
$463$	−2.01867	+	14.0402i	−0.0938158	+	0.652503i	−0.981417	+	0.191889i	$0.938538\pi$
$464$	−7.66629	+	16.7868i	−0.355898	+	0.779309i
$465$	2.02307	−	0.594028i	0.0938178	−	0.0275474i
$466$	1.13741	+	2.49059i	0.0526897	+	0.115374i
$467$	22.2535	+	25.6819i	1.02977	+	1.18842i	0.981869	+	0.189563i	$0.0607072\pi$
$467$	22.2535	+	25.6819i	1.02977	+	1.18842i	0.0478993	+	0.998852i	$0.484747\pi$
$468$	−1.93729	−	13.4742i	−0.0895515	−	0.622844i
$469$	−3.26442	−	0.958519i	−0.150737	−	0.0442603i
$470$	−0.854831	+	0.986527i	−0.0394304	+	0.0455051i
$471$	5.30463	+	3.40908i	0.244424	+	0.157082i
$472$	0.0946240	+	0.0608112i	0.00435542	+	0.00279906i
$473$	−1.05436	+	1.21680i	−0.0484796	+	0.0559484i
$474$	1.51484	+	0.444796i	0.0695787	+	0.0204302i
$475$	3.90933	+	27.1900i	0.179372	+	1.24756i
$476$	3.12153	+	3.60244i	0.143075	+	0.165118i
$477$	2.58066	+	5.65085i	0.118160	+	0.258735i
$478$	−2.55543	+	0.750341i	−0.116883	+	0.0343198i
$479$	14.7000	−	32.1885i	0.671659	−	1.47073i	−0.199586	−	0.979880i	$-0.563960\pi$
$479$	14.7000	−	32.1885i	0.671659	−	1.47073i	0.871245	−	0.490848i	$-0.163313\pi$
$480$	−0.183865	+	1.27881i	−0.00839224	+	0.0583693i
$481$	28.1342	−	18.0808i	1.28281	−	0.824412i
$482$	−1.55601			−0.0708742
$483$	−2.85708	+	3.85189i	−0.130002	+	0.175267i
$484$	−24.7235			−1.12379
$485$	−3.62470	+	2.32945i	−0.164589	+	0.105775i
$486$	−0.0189584	+	0.131858i	−0.000859969	+	0.00598121i
$487$	5.34217	−	11.6977i	0.242077	−	0.530075i	−0.749126	−	0.662428i	$-0.769526\pi$
$487$	5.34217	−	11.6977i	0.242077	−	0.530075i	0.991203	+	0.132353i	$0.0422534\pi$
$488$	0.405179	−	0.118971i	0.0183416	−	0.00538558i
$489$	2.10195	+	4.60263i	0.0950535	+	0.208138i
$490$	0.0713466	+	0.0823383i	0.00322311	+	0.00371967i
$491$	−6.06621	−	42.1915i	−0.273764	−	1.90407i	−0.407756	−	0.913091i	$-0.633689\pi$
$491$	−6.06621	−	42.1915i	−0.273764	−	1.90407i	0.133991	−	0.990982i	$-0.457221\pi$
$492$	−12.7356	−	3.73952i	−0.574167	−	0.168591i
$493$	7.46334	−	8.61316i	0.336132	−	0.387917i
$494$	4.88108	+	3.13688i	0.219610	+	0.141135i
$495$	−3.33334	−	2.14221i	−0.149822	−	0.0962850i
$496$	−6.57390	+	7.58669i	−0.295177	+	0.340652i
$497$	6.39741	+	1.87845i	0.286963	+	0.0842599i
$498$	0.148085	+	1.02995i	0.00663583	+	0.0461532i
$499$	−11.6046	−	13.3925i	−0.519495	−	0.599529i	0.434010	−	0.900908i	$-0.357098\pi$
$499$	−11.6046	−	13.3925i	−0.519495	−	0.599529i	−0.953504	+	0.301380i	$0.902553\pi$
$500$	6.28418	+	13.7604i	0.281037	+	0.615386i
$501$	−8.88222	+	2.60806i	−0.396828	+	0.116519i
$502$	−1.09491	+	2.39751i	−0.0488681	+	0.107006i
$503$	0.327456	−	2.27750i	0.0146005	−	0.101549i	−0.981218	−	0.192902i	$-0.938210\pi$
$503$	0.327456	−	2.27750i	0.0146005	−	0.101549i	0.995819	+	0.0913530i	$0.0291192\pi$
$504$	0.446279	−	0.286806i	0.0198788	−	0.0127754i
$505$	−3.23660			−0.144027
$506$	2.89528	−	1.09445i	0.128711	−	0.0486540i
$507$	−34.1598			−1.51709
$508$	11.4996	−	7.39037i	0.510214	−	0.327895i
$509$	0.276905	−	1.92592i	0.0122736	−	0.0853649i	−0.982764	−	0.184865i	$-0.940815\pi$
$509$	0.276905	−	1.92592i	0.0122736	−	0.0853649i	0.995038	+	0.0995000i	$0.0317243\pi$
$510$	0.108834	−	0.238314i	0.00481926	−	0.0105527i
$511$	9.62187	−	2.82524i	0.425647	−	0.124981i
$512$	−4.27147	−	9.35321i	−0.188774	−	0.413357i
$513$	4.15337	+	4.79325i	0.183376	+	0.211627i
$514$	−0.0668081	−	0.464660i	−0.00294678	−	0.0204953i
$515$	−1.96707	−	0.577584i	−0.0866794	−	0.0254514i
$516$	0.431390	−	0.497850i	0.0189909	−	0.0219166i
$517$	48.8329	+	31.3830i	2.14767	+	1.38022i
$518$	0.545757	+	0.350737i	0.0239792	+	0.0154105i
$519$	7.67752	−	8.86033i	0.337006	−	0.388925i
$520$	2.85878	+	0.839414i	0.125366	+	0.0368107i
$521$	3.29896	+	22.9448i	0.144530	+	1.00523i	0.924981	+	0.380013i	$0.124080\pi$
$521$	3.29896	+	22.9448i	0.144530	+	1.00523i	−0.780451	+	0.625217i	$0.785010\pi$
$522$	−0.413451	−	0.477148i	−0.0180963	−	0.0208842i
$523$	−8.94029	−	19.5765i	−0.390931	−	0.856020i	−0.998110	−	0.0614549i	$-0.980426\pi$
$523$	−8.94029	−	19.5765i	−0.390931	−	0.856020i	0.607178	−	0.794565i	$-0.292301\pi$
$524$	−42.9487	+	12.6109i	−1.87622	+	0.550908i
$525$	1.79921	−	3.93973i	0.0785241	−	0.171944i
$526$	−0.491442	+	3.41805i	−0.0214279	+	0.149034i
$527$	5.21534	−	3.35170i	0.227184	−	0.146002i
$528$	18.8650			0.820994
$529$	17.2488	−	15.2144i	0.749947	−	0.661498i
$530$	−0.676819			−0.0293991
$531$	0.178370	−	0.114631i	0.00774060	−	0.00497458i
$532$	1.78921	−	12.4442i	0.0775721	−	0.539526i
$533$	−19.1024	+	41.8285i	−0.827417	+	1.81179i
$534$	−0.425007	+	0.124793i	−0.0183919	+	0.00540034i
$535$	6.25912	+	13.7056i	0.270605	+	0.592543i
$536$	−1.18193	−	1.36402i	−0.0510517	−	0.0589168i
$537$	1.69879	+	11.8154i	0.0733084	+	0.509871i
$538$	0.228908	+	0.0672136i	0.00986894	+	0.00289778i
$539$	3.17269	−	3.66148i	0.136657	−	0.157711i
$540$	1.36383	+	0.876479i	0.0586898	+	0.0377177i
$541$	23.0892	+	14.8385i	0.992683	+	0.637959i	0.932856	−	0.360250i	$-0.117309\pi$
$541$	23.0892	+	14.8385i	0.992683	+	0.637959i	0.0598273	+	0.998209i	$0.480945\pi$
$542$	−0.610665	+	0.704744i	−0.0262303	+	0.0302714i
$543$	−4.04616	−	1.18806i	−0.173637	−	0.0509845i
$544$	0.540610	+	3.76003i	0.0231785	+	0.161210i
$545$	−6.70222	−	7.73478i	−0.287092	−	0.331321i
$546$	−0.380031	−	0.832152i	−0.0162638	−	0.0356128i
$547$	−19.6495	+	5.76961i	−0.840152	+	0.246691i	−0.673372	−	0.739303i	$-0.735155\pi$
$547$	−19.6495	+	5.76961i	−0.840152	+	0.246691i	−0.166779	+	0.985994i	$0.553337\pi$
$548$	9.96672	−	21.8241i	0.425757	−	0.932278i
$549$	0.113286	−	0.787921i	0.00483492	−	0.0336276i
$550$	−2.35156	+	1.51126i	−0.100271	+	0.0644403i
$551$	−30.0592			−1.28056
$552$	−2.37980	+	0.899589i	−0.101291	+	0.0382891i
$553$	−11.8515			−0.503977
$554$	0.208068	−	0.133717i	0.00883995	−	0.00568109i
$555$	−0.566820	+	3.94232i	−0.0240602	+	0.167342i
$556$	1.16463	−	2.55019i	0.0493914	−	0.108152i
$557$	17.4734	−	5.13065i	0.740371	−	0.217393i	0.110266	−	0.993902i	$-0.464830\pi$
$557$	17.4734	−	5.13065i	0.740371	−	0.217393i	0.630105	+	0.776510i	$0.283012\pi$
$558$	−0.142669	−	0.312401i	−0.00603966	−	0.0132250i
$559$	−1.49450	−	1.72475i	−0.0632107	−	0.0729490i
$560$	−0.453212	−	3.15216i	−0.0191517	−	0.133203i
$561$	−11.1784	−	3.28228i	−0.471953	−	0.138578i
$562$	1.04422	−	1.20509i	0.0440478	−	0.0508339i
$563$	22.1686	+	14.2469i	0.934297	+	0.600436i	0.916772	−	0.399410i	$-0.130785\pi$
$563$	22.1686	+	14.2469i	0.934297	+	0.600436i	0.0175248	+	0.999846i	$0.494421\pi$
$564$	−19.9799	−	12.8403i	−0.841305	−	0.540674i
$565$	−7.50328	+	8.65925i	−0.315665	+	0.364297i
$566$	4.10598	+	1.20562i	0.172587	+	0.0506761i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	2.31628	+	2.67313i	0.0971889	+	0.112162i
$569$	3.76162	+	8.23681i	0.157696	+	0.345305i	0.971944	−	0.235211i	$-0.0755781\pi$
$569$	3.76162	+	8.23681i	0.157696	+	0.345305i	−0.814249	+	0.580516i	$0.802851\pi$
$570$	−0.663007	+	0.194676i	−0.0277703	+	0.00815409i
$571$	5.82537	−	12.7558i	0.243784	−	0.533813i	−0.747701	−	0.664036i	$-0.768842\pi$
$571$	5.82537	−	12.7558i	0.243784	−	0.533813i	0.991485	+	0.130223i	$0.0415694\pi$
$572$	9.38587	−	65.2801i	0.392443	−	2.72950i
$573$	−1.05975	+	0.681062i	−0.0442718	+	0.0284518i
$574$	−0.892012			−0.0372319
$575$	−12.3744	+	16.6830i	−0.516047	+	0.695730i
$576$	−7.57724			−0.315718
$577$	12.8463	−	8.25580i	0.534797	−	0.343693i	−0.245204	−	0.969472i	$-0.578855\pi$
$577$	12.8463	−	8.25580i	0.534797	−	0.343693i	0.780001	+	0.625778i	$0.215218\pi$
$578$	−0.212665	+	1.47911i	−0.00884568	+	0.0615231i
$579$	5.21573	−	11.4208i	0.216758	−	0.474634i
$580$	−7.37224	+	2.16469i	−0.306116	+	0.0898837i
$581$	−3.24483	−	7.10518i	−0.134618	−	0.294772i
$582$	0.459591	+	0.530396i	0.0190506	+	0.0219856i
$583$	4.28329	+	29.7909i	0.177396	+	1.23381i
$584$	5.10433	+	1.49877i	0.211219	+	0.0620195i
$585$	3.67797	−	4.24461i	0.152065	−	0.175493i
$586$	−1.81994	−	1.16960i	−0.0751809	−	0.0483158i
$587$	−16.8097	−	10.8029i	−0.693811	−	0.445885i	0.145628	−	0.989339i	$-0.453480\pi$
$587$	−16.8097	−	10.8029i	−0.693811	−	0.445885i	−0.839439	+	0.543454i	$0.817116\pi$
$588$	−1.29810	+	1.49809i	−0.0535328	+	0.0617801i
$589$	−15.6888	−	4.60665i	−0.646447	−	0.189814i
$590$	0.00328753	+	0.0228652i	0.000135345	+	0.000941347i
$591$	−1.17313	−	1.35387i	−0.0482563	−	0.0556908i
$592$	−7.87738	−	17.2491i	−0.323758	−	0.708932i
$593$	−15.4089	+	4.52446i	−0.632768	+	0.185797i	−0.582360	−	0.812931i	$-0.697870\pi$
$593$	−15.4089	+	4.52446i	−0.632768	+	0.185797i	−0.0504084	+	0.998729i	$0.516052\pi$
$594$	−0.268109	+	0.587077i	−0.0110006	+	0.0240881i
$595$	−0.279887	+	1.94666i	−0.0114743	+	0.0798052i
$596$	−17.2962	+	11.1156i	−0.708481	+	0.455313i
$597$	−19.6478			−0.804131
$598$	0.951482	+	4.28292i	0.0389090	+	0.175141i
$599$	16.8476			0.688374			0.344187	−	0.938901i	$-0.388155\pi$
$599$	16.8476			0.688374			0.344187	+	0.938901i	$0.388155\pi$
$600$	1.93289	−	1.24219i	0.0789099	−	0.0507123i
$601$	−2.82915	+	19.6771i	−0.115403	+	0.802647i	0.847111	+	0.531416i	$0.178340\pi$
$601$	−2.82915	+	19.6771i	−0.115403	+	0.802647i	−0.962514	+	0.271231i	$0.912569\pi$
$602$	0.0183905	−	0.0402696i	0.000749542	−	0.00164127i
$603$	−3.26442	+	0.958519i	−0.132937	+	0.0390339i
$604$	−7.31950	−	16.0275i	−0.297826	−	0.652149i
$605$	−6.67994	−	7.70906i	−0.271578	−	0.313418i
$606$	0.0750267	+	0.521823i	0.00304775	+	0.0211976i
$607$	−25.4077	−	7.46037i	−1.03127	−	0.302807i	−0.278040	−	0.960569i	$-0.589685\pi$
$607$	−25.4077	−	7.46037i	−1.03127	−	0.302807i	−0.753225	+	0.657763i	$0.771503\pi$
$608$	6.56109	−	7.57190i	0.266087	−	0.307081i
$609$	3.98705	+	2.56232i	0.161563	+	0.103831i
$610$	0.0729586	+	0.0468877i	0.00295401	+	0.00189843i
$611$	−53.8818	+	62.1829i	−2.17982	+	2.51565i
$612$	4.57363	+	1.34294i	0.184878	+	0.0542850i
$613$	4.87546	+	33.9095i	0.196918	+	1.36959i	0.813162	+	0.582038i	$0.197744\pi$
$613$	4.87546	+	33.9095i	0.196918	+	1.36959i	−0.616244	+	0.787555i	$0.711346\pi$
$614$	−1.41649	−	1.63472i	−0.0571649	−	0.0659718i
$615$	−2.27497	−	4.98149i	−0.0917356	−	0.200873i
$616$	2.46604	−	0.724095i	0.0993596	−	0.0291746i
$617$	−2.57279	+	5.63363i	−0.103577	+	0.226801i	−0.954324	−	0.298773i	$-0.903422\pi$
$617$	−2.57279	+	5.63363i	−0.103577	+	0.226801i	0.850747	+	0.525575i	$0.176150\pi$
$618$	−0.0475231	+	0.330531i	−0.00191166	+	0.0132959i
$619$	23.4297	−	15.0574i	0.941719	−	0.605206i	0.0228374	−	0.999739i	$-0.492730\pi$
$619$	23.4297	−	15.0574i	0.941719	−	0.605206i	0.918882	+	0.394533i	$0.129094\pi$
$620$	−4.17955			−0.167855
$621$	−0.321042	+	4.78507i	−0.0128830	+	0.192018i
$622$	−2.93883			−0.117836
$623$	2.79725	−	1.79768i	0.112069	−	0.0720226i
$624$	−3.80552	+	26.4680i	−0.152343	+	1.05957i
$625$	6.40330	−	14.0213i	0.256132	−	0.560851i
$626$	0.508731	−	0.149377i	0.0203330	−	0.00597030i
$627$	12.7648	+	27.9509i	0.509776	+	1.11625i
$628$	−8.18533	−	9.44637i	−0.326630	−	0.376951i
$629$	1.66660	+	11.5915i	0.0664517	+	0.462182i
$630$	0.104536	+	0.0306945i	0.00416481	+	0.00122290i
$631$	2.12627	−	2.45385i	0.0846456	−	0.0976863i	−0.711847	−	0.702335i	$-0.752141\pi$
$631$	2.12627	−	2.45385i	0.0846456	−	0.0976863i	0.796492	+	0.604649i	$0.206686\pi$
$632$	−5.28908	−	3.39908i	−0.210388	−	0.135208i
$633$	−23.7413	−	15.2576i	−0.943631	−	0.606435i
$634$	2.45884	−	2.83765i	0.0976529	−	0.112697i
$635$	5.41144	+	1.58894i	0.214747	+	0.0630553i
$636$	−1.75250	−	12.1889i	−0.0694911	−	0.483321i
$637$	4.49713	+	5.18996i	0.178183	+	0.205634i
$638$	−1.27068	−	2.78240i	−0.0503067	−	0.110156i
$639$	6.39741	−	1.87845i	0.253077	−	0.0743103i
$640$	1.41634	−	3.10134i	0.0559856	−	0.122591i
$641$	5.50442	−	38.2841i	0.217411	−	1.51213i	−0.530131	−	0.847916i	$-0.677857\pi$
$641$	5.50442	−	38.2841i	0.217411	−	1.51213i	0.747542	−	0.664214i	$-0.231234\pi$
$642$	2.06460	−	1.32683i	0.0814831	−	0.0523660i
$643$	−17.2595			−0.680647			−0.340323	−	0.940308i	$-0.610537\pi$
$643$	−17.2595			−0.680647			−0.340323	+	0.940308i	$0.610537\pi$
$644$	7.58520	−	5.73056i	0.298899	−	0.225816i
$645$	0.271791			0.0107018
$646$	−1.70918	+	1.09843i	−0.0672470	+	0.0432170i
$647$	−1.84731	+	12.8483i	−0.0726253	+	0.505120i	0.920745	+	0.390164i	$0.127582\pi$
$647$	−1.84731	+	12.8483i	−0.0726253	+	0.505120i	−0.993371	+	0.114956i	$0.963327\pi$
$648$	0.220375	−	0.482553i	0.00865714	−	0.0189565i
$649$	0.985633	−	0.289408i	0.0386895	−	0.0113603i
$650$	−1.64596	−	3.60415i	−0.0645599	−	0.141366i
$651$	1.68828	+	1.94838i	0.0661691	+	0.0763632i
$652$	−1.42741	−	9.92788i	−0.0559018	−	0.388806i
$653$	13.9121	+	4.08496i	0.544423	+	0.159857i	0.542368	−	0.840141i	$-0.317528\pi$
$653$	13.9121	+	4.08496i	0.544423	+	0.159857i	0.00205467	+	0.999998i	$0.499346\pi$
$654$	−1.09168	+	1.25987i	−0.0426881	+	0.0492647i
$655$	−15.5364	−	9.98461i	−0.607056	−	0.390131i
$656$	21.9344	+	14.0964i	0.856393	+	0.550370i
$657$	6.56700	−	7.57872i	0.256203	−	0.295674i
$658$	−1.53144	−	0.449671i	−0.0597017	−	0.0175300i
$659$	−2.11073	−	14.6805i	−0.0822225	−	0.571870i	−0.988733	−	0.149688i	$-0.952173\pi$
$659$	−2.11073	−	14.6805i	−0.0822225	−	0.571870i	0.906511	−	0.422183i	$-0.138736\pi$
$660$	5.14352	+	5.93594i	0.200211	+	0.231056i
$661$	−11.0001	−	24.0868i	−0.427854	−	0.936869i	−0.993670	−	0.112337i	$-0.964166\pi$
$661$	−11.0001	−	24.0868i	−0.427854	−	0.936869i	0.565817	−	0.824531i	$-0.308561\pi$
$662$	1.79095	−	0.525871i	0.0696073	−	0.0204386i
$663$	6.86006	−	15.0214i	0.266423	−	0.583384i
$664$	0.589711	−	4.10153i	0.0228852	−	0.159170i
$665$	4.36368	−	2.80436i	0.169216	−	0.108749i
$666$	0.648743			0.0251383
$667$	−16.1428	−	16.0011i	−0.625053	−	0.619567i
$668$	18.3501			0.709988
$669$	17.8949	−	11.5003i	0.691855	−	0.444628i
$670$	0.0527519	−	0.366897i	0.00203798	−	0.0141745i
$671$	1.60209	−	3.50809i	0.0618480	−	0.135428i
$672$	−1.51571	+	0.445053i	−0.0584698	+	0.0171683i
$673$	−10.2716	−	22.4917i	−0.395941	−	0.866990i	−0.997666	−	0.0682863i	$-0.978247\pi$
$673$	−10.2716	−	22.4917i	−0.395941	−	0.866990i	0.601725	−	0.798703i	$-0.294480\pi$
$674$	−2.74134	−	3.16368i	−0.105593	−	0.121860i
$675$	−0.616383	−	4.28704i	−0.0237246	−	0.165008i
$676$	64.9706	+	19.0771i	2.49887	+	0.733734i
$677$	21.0969	−	24.3472i	0.810821	−	0.935738i	−0.188101	−	0.982150i	$-0.560233\pi$
$677$	21.0969	−	24.3472i	0.810821	−	0.935738i	0.998922	+	0.0464119i	$0.0147787\pi$
$678$	1.57002	+	1.00899i	0.0602964	+	0.0387501i
$679$	−4.43199	−	2.84826i	−0.170084	−	0.109306i
$680$	−0.683221	+	0.788480i	−0.0262003	+	0.0302368i
$681$	−2.44969	−	0.719293i	−0.0938722	−	0.0275634i
$682$	−0.236797	−	1.64696i	−0.00906742	−	0.0630653i
$683$	−32.0639	−	37.0037i	−1.22689	−	1.41591i	−0.877942	−	0.478768i	$-0.841084\pi$
$683$	−32.0639	−	37.0037i	−1.22689	−	1.41591i	−0.348950	−	0.937141i	$-0.613462\pi$
$684$	−5.22268	−	11.4361i	−0.199694	−	0.437269i
$685$	9.49786	−	2.78882i	0.362895	−	0.106555i
$686$	−0.0553392	+	0.121176i	−0.00211286	+	0.00462652i
$687$	−3.10283	+	21.5807i	−0.118380	+	0.823353i
$688$	−1.08860	+	0.699598i	−0.0415023	+	0.0266719i
$689$	−42.6613			−1.62527
$690$	−0.459688	−	0.248385i	−0.0175000	−	0.00945585i
$691$	47.5693			1.80962			0.904810	−	0.425815i	$-0.140013\pi$
$691$	47.5693			1.80962			0.904810	+	0.425815i	$0.140013\pi$
$692$	−19.5505	+	12.5643i	−0.743199	+	0.477625i
$693$	0.689492	−	4.79552i	0.0261916	−	0.182167i
$694$	1.02648	−	2.24769i	0.0389648	−	0.0853210i
$695$	1.10984	−	0.325880i	0.0420988	−	0.0123613i
$696$	1.04445	+	2.28702i	0.0395897	+	0.0866893i
$697$	−10.5446	−	12.1691i	−0.399404	−	0.460936i
$698$	−0.214401	−	1.49119i	−0.00811521	−	0.0564425i
$699$	−19.7209	−	5.79059i	−0.745914	−	0.219020i
$700$	−5.62223	+	6.48840i	−0.212500	+	0.245238i
$701$	29.0586	+	18.6748i	1.09753	+	0.705338i	0.958540	−	0.284957i	$-0.0919793\pi$
$701$	29.0586	+	18.6748i	1.09753	+	0.705338i	0.138986	+	0.990294i	$0.455616\pi$
$702$	−0.769597	−	0.494590i	−0.0290466	−	0.0186671i
$703$	20.2266	−	23.3427i	0.762861	−	0.880388i
$704$	−35.2234	−	10.3425i	−1.32753	−	0.389799i
$705$	−1.39454	−	9.69923i	−0.0525214	−	0.365294i
$706$	2.05536	+	2.37201i	0.0773546	+	0.0892719i
$707$	−1.64398	−	3.59982i	−0.0618284	−	0.135385i
$708$	−0.403270	+	0.118411i	−0.0151558	+	0.00445015i
$709$	−5.34682	+	11.7079i	−0.200804	+	0.439699i	−0.983066	−	0.183250i	$-0.941338\pi$
$709$	−5.34682	+	11.7079i	−0.200804	+	0.439699i	0.782262	+	0.622949i	$0.214066\pi$
$710$	−0.103380	+	0.719024i	−0.00387978	+	0.0269845i
$711$	−9.97012	+	6.40740i	−0.373909	+	0.240296i
$712$	1.76394			0.0661064
$713$	−5.97323	−	10.8254i	−0.223699	−	0.405416i
$714$	0.320339			0.0119884
$715$	22.8910	−	14.7112i	0.856076	−	0.550167i
$716$	3.36744	−	23.4211i	0.125847	−	0.875287i
$717$	8.30526	−	18.1860i	0.310166	−	0.679168i
$718$	−3.08974	+	0.907228i	−0.115308	+	0.0338575i
$719$	9.79160	+	21.4406i	0.365165	+	0.799600i	0.999645	+	0.0266602i	$0.00848721\pi$
$719$	9.79160	+	21.4406i	0.365165	+	0.799600i	−0.634480	+	0.772940i	$0.718786\pi$
$720$	−2.08545	−	2.40674i	−0.0777202	−	0.0896939i
$721$	−0.356742	−	2.48120i	−0.0132858	−	0.0924046i
$722$	2.71303	+	0.796619i	0.100969	+	0.0296471i
$723$	7.64910	−	8.82753i	0.284473	−	0.328299i
$724$	7.03213	+	4.51928i	0.261347	+	0.167958i
$725$	17.2684	+	11.0977i	0.641332	+	0.412159i
$726$	−1.08805	+	1.25568i	−0.0403814	+	0.0466026i
$727$	−4.75850	−	1.39722i	−0.176483	−	0.0518201i	0.192297	−	0.981337i	$-0.438406\pi$
$727$	−4.75850	−	1.39722i	−0.176483	−	0.0518201i	−0.368780	+	0.929517i	$0.620224\pi$
$728$	0.518461	+	3.60597i	0.0192154	+	0.133646i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	0.453862	+	0.993820i	0.0167982	+	0.0367829i
$731$	0.766766	−	0.225143i	0.0283599	−	0.00832721i
$732$	−0.655492	+	1.43533i	−0.0242277	+	0.0530512i
$733$	−3.55595	+	24.7321i	−0.131342	+	0.913503i	0.812466	+	0.583008i	$0.198125\pi$
$733$	−3.55595	+	24.7321i	−0.131342	+	0.913503i	−0.943808	+	0.330494i	$0.892785\pi$
$734$	−3.96443	+	2.54778i	−0.146330	+	0.0940403i
$735$	−0.817850			−0.0301668
$736$	7.55422	−	0.573767i	0.278452	−	0.0211493i
$737$	−16.4832			−0.607168
$738$	−0.750408	+	0.482258i	−0.0276229	+	0.0177522i
$739$	2.98558	−	20.7652i	0.109826	−	0.763860i	−0.858255	−	0.513224i	$-0.828451\pi$
$739$	2.98558	−	20.7652i	0.109826	−	0.763860i	0.968081	−	0.250636i	$-0.0806398\pi$
$740$	3.27972	−	7.18159i	0.120565	−	0.264000i
$741$	−41.7907	+	12.2709i	−1.53522	+	0.450782i
$742$	−0.343780	−	0.752774i	−0.0126206	−	0.0276352i
$743$	−27.1198	−	31.2980i	−0.994930	−	1.14821i	−0.988953	−	0.148228i	$-0.952643\pi$
$743$	−27.1198	−	31.2980i	−0.994930	−	1.14821i	−0.00597691	−	0.999982i	$-0.501903\pi$
$744$	0.194637	+	1.35373i	0.00713575	+	0.0496302i
$745$	−8.13917	−	2.38988i	−0.298196	−	0.0875583i
$746$	0.755580	−	0.871986i	0.0276638	−	0.0319257i
$747$	−6.57107	−	4.22297i	−0.240423	−	0.154510i
$748$	19.4278	+	12.4855i	0.710352	+	0.456516i
$749$	−12.0644	+	13.9231i	−0.440824	+	0.508738i
$750$	0.975438	+	0.286414i	0.0356180	+	0.0104584i
$751$	1.85710	+	12.9164i	0.0677666	+	0.471327i	0.995241	+	0.0974410i	$0.0310657\pi$
$751$	1.85710	+	12.9164i	0.0677666	+	0.471327i	−0.927475	+	0.373886i	$0.878025\pi$
$752$	30.5516	+	35.2584i	1.11410	+	1.28574i
$753$	−8.21915	−	17.9974i	−0.299522	−	0.655862i
$754$	4.16010	−	1.22151i	0.151502	−	0.0444849i
$755$	3.01992	−	6.61271i	0.109906	−	0.240661i
$756$	−0.282104	+	1.96208i	−0.0102600	+	0.0713601i
$757$	16.5103	−	10.6105i	0.600076	−	0.385646i	−0.205048	−	0.978752i	$-0.565735\pi$
$757$	16.5103	−	10.6105i	0.600076	−	0.385646i	0.805124	+	0.593106i	$0.202099\pi$
$758$	2.28883			0.0831339
$759$	−8.02376	+	21.8056i	−0.291244	+	0.791493i
$760$	2.75173			0.0998156
$761$	31.7570	−	20.4090i	1.15119	−	0.739824i	0.181314	−	0.983425i	$-0.441965\pi$
$761$	31.7570	−	20.4090i	1.15119	−	0.739824i	0.969876	+	0.243601i	$0.0783287\pi$
$762$	0.130737	−	0.909296i	0.00473610	−	0.0329403i
$763$	5.19851	−	11.3831i	0.188199	−	0.412097i
$764$	2.39595	−	0.703516i	0.0866826	−	0.0254523i
$765$	0.816987	+	1.78895i	0.0295382	+	0.0646797i
$766$	−0.575407	−	0.664056i	−0.0207903	−	0.0239933i
$767$	0.207220	+	1.44125i	0.00748227	+	0.0520403i
$768$	14.0078	+	4.11305i	0.505462	+	0.148417i
$769$	−31.3656	+	36.1979i	−1.13107	+	1.30533i	−0.184503	+	0.982832i	$0.559068\pi$
$769$	−31.3656	+	36.1979i	−1.13107	+	1.30533i	−0.946571	+	0.322496i	$0.895478\pi$
$770$	0.444048	+	0.285372i	0.0160024	+	0.0102841i
$771$	2.96452	+	1.90518i	0.106765	+	0.0686135i
$772$	−16.2982	+	18.8092i	−0.586587	+	0.676957i
$773$	−39.5770	−	11.6209i	−1.42349	−	0.417973i	−0.522804	−	0.852453i	$-0.675114\pi$
$773$	−39.5770	−	11.6209i	−1.42349	−	0.417973i	−0.900682	+	0.434480i	$0.856932\pi$
$774$	−0.00630031	−	0.0438197i	−0.000226460	−	0.00157506i
$775$	7.31216	+	8.43869i	0.262661	+	0.303127i
$776$	−1.16100	−	2.54224i	−0.0416776	−	0.0912612i
$777$	−4.67265	+	1.37202i	−0.167631	+	0.0492208i
$778$	0.650017	−	1.42334i	0.0233042	−	0.0510291i
$779$	−6.04397	+	42.0367i	−0.216548	+	1.50612i
$780$	−9.36582	+	6.01905i	−0.335350	+	0.215516i
$781$	32.3029			1.15589
$782$	−1.50261	−	0.319942i	−0.0537332	−	0.0114411i
$783$	4.73942			0.169373
$784$	3.27571	−	2.10517i	0.116989	−	0.0751846i
$785$	0.733925	−	5.10456i	0.0261949	−	0.182189i
$786$	−1.24963	+	2.73631i	−0.0445728	+	0.0976009i
$787$	32.8748	−	9.65292i	1.17186	−	0.344089i	0.362830	−	0.931855i	$-0.381811\pi$
$787$	32.8748	−	9.65292i	1.17186	−	0.344089i	0.809031	+	0.587766i	$0.199992\pi$
$788$	1.47516	+	3.23016i	0.0525506	+	0.115070i
$789$	−16.9754	−	19.5907i	−0.604340	−	0.697446i
$790$	−0.183759	−	1.27807i	−0.00653784	−	0.0454716i
$791$	−13.4422	−	3.94699i	−0.477950	−	0.140339i
$792$	1.68309	−	1.94239i	0.0598060	−	0.0690198i
$793$	4.59874	+	2.95543i	0.163306	+	0.104950i
$794$	−3.25343	−	2.09085i	−0.115460	−	0.0742016i
$795$	3.32714	−	3.83972i	0.118001	−	0.136181i
$796$	37.3693	+	10.9726i	1.32452	+	0.388914i
$797$	−7.41155	−	51.5485i	−0.262531	−	1.82594i	−0.513669	−	0.857989i	$-0.671714\pi$
$797$	−7.41155	−	51.5485i	−0.262531	−	1.82594i	0.251138	−	0.967951i	$-0.419195\pi$
$798$	−0.553288	−	0.638529i	−0.0195862	−	0.0226037i
$799$	−11.9687	−	26.2079i	−0.423424	−	0.927169i
$800$	−6.56473	+	1.92758i	−0.232098	+	0.0681502i
$801$	1.38129	−	3.02461i	0.0488056	−	0.106869i
$802$	0.398547	−	2.77196i	0.0140732	−	0.0978811i
$803$	40.8718	−	26.2667i	1.44233	−	0.926931i
$804$	6.74409			0.237846
$805$	3.83627	+	0.816837i	0.135211	+	0.0287897i
$806$	2.35849			0.0830741
$807$	−1.50659	+	0.968229i	−0.0530346	+	0.0340833i
$808$	0.298776	−	2.07803i	0.0105109	−	0.0731048i
$809$	18.1070	−	39.6487i	0.636607	−	1.39398i	−0.266195	−	0.963919i	$-0.585766\pi$
$809$	18.1070	−	39.6487i	0.636607	−	1.39398i	0.902802	−	0.430056i	$-0.141506\pi$
$810$	0.104536	−	0.0306945i	0.00367302	−	0.00107850i
$811$	21.1674	+	46.3502i	0.743289	+	1.62758i	0.778068	+	0.628180i	$0.216200\pi$
$811$	21.1674	+	46.3502i	0.743289	+	1.62758i	−0.0347791	+	0.999395i	$0.511073\pi$
$812$	−6.15224	−	7.10006i	−0.215901	−	0.249163i
$813$	−0.996216	−	6.92883i	−0.0349388	−	0.243005i
$814$	3.01573	+	0.885499i	0.105701	+	0.0310367i
$815$	2.70996	−	3.12746i	0.0949257	−	0.109550i
$816$	−7.87706	−	5.06228i	−0.275752	−	0.177215i
$817$	−1.77313	−	1.13952i	−0.0620339	−	0.0398668i
$818$	0.437249	−	0.504612i	0.0152881	−	0.0176434i
$819$	6.58913	+	1.93474i	0.230243	+	0.0676054i
$820$	1.54491	+	10.7451i	0.0539506	+	0.375234i
$821$	−9.13352	−	10.5406i	−0.318762	−	0.367871i	0.573644	−	0.819105i	$-0.305529\pi$
$821$	−9.13352	−	10.5406i	−0.318762	−	0.367871i	−0.892406	+	0.451234i	$0.850984\pi$
$822$	−0.669797	−	1.46665i	−0.0233619	−	0.0511553i
$823$	−7.05076	+	2.07029i	−0.245774	+	0.0721657i	−0.402299	−	0.915508i	$-0.631789\pi$
$823$	−7.05076	+	2.07029i	−0.245774	+	0.0721657i	0.156525	+	0.987674i	$0.449971\pi$
$824$	0.552416	−	1.20962i	0.0192443	−	0.0421392i
$825$	2.98627	−	20.7700i	0.103969	−	0.723118i
$826$	−0.0237614	+	0.0152705i	−0.000826766	+	0.000531330i
$827$	20.1829			0.701830			0.350915	−	0.936407i	$-0.385871\pi$
$827$	20.1829			0.701830			0.350915	+	0.936407i	$0.385871\pi$
$828$	3.28291	−	8.92172i	0.114089	−	0.310051i
$829$	35.7743			1.24249			0.621247	−	0.783615i	$-0.286626\pi$
$829$	35.7743			1.24249			0.621247	+	0.783615i	$0.286626\pi$
$830$	0.715913	−	0.460089i	0.0248497	−	0.0159699i
$831$	−0.264227	+	1.83774i	−0.00916594	+	0.0637505i
$832$	21.6162	−	47.3329i	0.749407	−	1.64097i
$833$	−2.30729	+	0.677480i	−0.0799427	+	0.0234733i
$834$	−0.0782672	−	0.171381i	−0.00271017	−	0.00593445i
$835$	4.95795	+	5.72178i	0.171577	+	0.198010i
$836$	−8.66843	−	60.2902i	−0.299804	−	2.08518i
$837$	2.47365	+	0.726329i	0.0855019	+	0.0251056i
$838$	−1.92851	+	2.22562i	−0.0666192	+	0.0768827i
$839$	9.00760	+	5.78883i	0.310977	+	0.199853i	0.686814	−	0.726833i	$-0.259009\pi$
$839$	9.00760	+	5.78883i	0.310977	+	0.199853i	−0.375837	+	0.926686i	$0.622645\pi$
$840$	−0.364989	−	0.234564i	−0.0125933	−	0.00809324i
$841$	4.28143	−	4.94103i	0.147636	−	0.170381i
$842$	1.48824	+	0.436987i	0.0512881	+	0.0150596i
$843$	1.70350	+	11.8481i	0.0586718	+	0.408071i
$844$	36.6341	+	42.2780i	1.26100	+	1.45527i
$845$	11.6057	+	25.4129i	0.399248	+	0.874232i
$846$	−1.53144	+	0.449671i	−0.0526519	+	0.0154600i
$847$	5.18122	−	11.3453i	0.178029	−	0.389829i
$848$	−3.44252	+	23.9433i	−0.118217	+	0.822215i
$849$	−27.0241	+	17.3673i	−0.927464	+	0.596045i
$850$	1.38743			0.0475884
$851$	23.2882	−	1.76882i	0.798311	−	0.0606343i
$852$	−13.2167			−0.452795
$853$	−24.6575	+	15.8464i	−0.844256	+	0.542570i	−0.889778	−	0.456393i	$-0.849141\pi$
$853$	−24.6575	+	15.8464i	−0.844256	+	0.542570i	0.0455224	+	0.998963i	$0.485505\pi$
$854$	−0.0150913	+	0.104962i	−0.000516413	+	0.00359173i
$855$	2.15480	−	4.71836i	0.0736927	−	0.161365i
$856$	−9.37732	+	2.75343i	−0.320510	+	0.0941103i
$857$	−22.7361	−	49.7851i	−0.776651	−	1.70063i	−0.711430	−	0.702757i	$-0.751952\pi$
$857$	−22.7361	−	49.7851i	−0.776651	−	1.70063i	−0.0652203	−	0.997871i	$-0.520775\pi$
$858$	−2.90245	−	3.34960i	−0.0990879	−	0.114354i
$859$	2.50933	+	17.4528i	0.0856172	+	0.595481i	0.986788	+	0.162017i	$0.0517999\pi$
$859$	2.50933	+	17.4528i	0.0856172	+	0.595481i	−0.901171	+	0.433464i	$0.857291\pi$
$860$	−0.516935	−	0.151786i	−0.0176273	−	0.00517585i
$861$	4.38499	−	5.06055i	0.149440	−	0.172463i
$862$	−2.00719	−	1.28994i	−0.0683652	−	0.0439356i
$863$	−22.2355	−	14.2899i	−0.756904	−	0.486433i	0.104392	−	0.994536i	$-0.466710\pi$
$863$	−22.2355	−	14.2899i	−0.756904	−	0.486433i	−0.861296	+	0.508103i	$0.830347\pi$
$864$	−1.03448	+	1.19386i	−0.0351939	+	0.0406159i
$865$	−9.19999	−	2.70136i	−0.312809	−	0.0918490i
$866$	0.316008	+	2.19789i	0.0107384	+	0.0746872i
$867$	−7.34587	−	8.47759i	−0.249479	−	0.287914i
$868$	−2.12294	−	4.64859i	−0.0720573	−	0.157784i
$869$	−55.0927	+	16.1767i	−1.86889	+	0.548756i
$870$	−0.214502	+	0.469694i	−0.00727230	+	0.0159241i
$871$	3.32506	−	23.1263i	0.112666	−	0.783606i
$872$	5.58474	−	3.58909i	0.189123	−	0.121542i
$873$	−5.26831			−0.178305
$874$	1.95756	+	3.54774i	0.0662155	+	0.120004i
$875$	−7.63146			−0.257990
$876$	−16.7226	+	10.7470i	−0.565005	+	0.363106i
$877$	−5.00163	+	34.7871i	−0.168893	+	1.17468i	0.712285	+	0.701891i	$0.247660\pi$
$877$	−5.00163	+	34.7871i	−0.168893	+	1.17468i	−0.881178	+	0.472785i	$0.843249\pi$
$878$	1.39728	−	3.05962i	0.0471560	−	0.103257i
$879$	15.5819	−	4.57526i	0.525565	−	0.154320i
$880$	−6.40933	−	14.0345i	−0.216058	−	0.473102i
$881$	17.1183	+	19.7555i	0.576729	+	0.665581i	0.966898	−	0.255162i	$-0.0821289\pi$
$881$	17.1183	+	19.7555i	0.576729	+	0.665581i	−0.390169	+	0.920743i	$0.627583\pi$
$882$	0.0189584	+	0.131858i	0.000638361	+	0.00443990i
$883$	−18.0033	−	5.28625i	−0.605859	−	0.177896i	−0.0356069	−	0.999366i	$-0.511336\pi$
$883$	−18.0033	−	5.28625i	−0.605859	−	0.177896i	−0.570252	+	0.821470i	$0.693155\pi$
$884$	−21.4365	+	24.7390i	−0.720987	+	0.832064i
$885$	−0.145880	−	0.0937513i	−0.00490370	−	0.00315141i
$886$	−3.93619	−	2.52963i	−0.132239	−	0.0849847i
$887$	−10.1289	+	11.6894i	−0.340096	+	0.392491i	−0.899873	−	0.436152i	$-0.856341\pi$
$887$	−10.1289	+	11.6894i	−0.340096	+	0.392491i	0.559778	+	0.828643i	$0.310887\pi$
$888$	−2.47881	−	0.727844i	−0.0831834	−	0.0244249i
$889$	0.981405	+	6.82582i	0.0329153	+	0.228931i
$890$	0.237234	+	0.273783i	0.00795210	+	0.00917722i
$891$	−2.01262	−	4.40701i	−0.0674252	−	0.147641i
$892$	−40.4578	+	11.8795i	−1.35463	+	0.397755i
$893$	−31.5676	+	69.1234i	−1.05637	+	2.31312i
$894$	−0.196637	+	1.36764i	−0.00657653	+	0.0457408i
$895$	8.21280	−	5.27804i	0.274524	−	0.176426i
$896$	4.16880			0.139270
$897$	−28.9751	−	15.6562i	−0.967452	−	0.522746i
$898$	−2.71133			−0.0904782
$899$	−10.2789	+	6.60587i	−0.342822	+	0.220318i
$900$	−1.22183	+	8.49800i	−0.0407276	+	0.283267i
$901$	6.20569	−	13.5886i	0.206741	−	0.452701i
$902$	−4.14659	+	1.21755i	−0.138066	+	0.0405399i
$903$	0.138052	+	0.302292i	0.00459409	+	0.0100597i
$904$	−4.86695	−	5.61676i	−0.161872	−	0.186811i
$905$	0.490822	+	3.41375i	0.0163155	+	0.113477i
$906$	−1.13614	−	0.333601i	−0.0377458	−	0.0110832i
$907$	9.45016	−	10.9061i	0.313787	−	0.362130i	−0.576845	−	0.816853i	$-0.695716\pi$
$907$	9.45016	−	10.9061i	0.313787	−	0.362130i	0.890633	+	0.454724i	$0.150262\pi$
$908$	4.25751	+	2.73613i	0.141290	+	0.0908017i
$909$	−3.32922	−	2.13956i	−0.110423	−	0.0709647i
$910$	−0.489958	+	0.565442i	−0.0162420	+	0.0187442i
$911$	−4.96344	−	1.45740i	−0.164446	−	0.0482858i	0.198473	−	0.980106i	$-0.436402\pi$
$911$	−4.96344	−	1.45740i	−0.164446	−	0.0482858i	−0.362919	+	0.931821i	$0.618220\pi$
$912$	3.51463	+	24.4448i	0.116381	+	0.809449i
$913$	−24.7820	−	28.6000i	−0.820166	−	0.946522i
$914$	0.855584	+	1.87347i	0.0283002	+	0.0619688i
$915$	−0.624656	+	0.183416i	−0.0206505	+	0.00606353i
$916$	17.9535	−	39.3127i	0.593201	−	1.29893i
$917$	3.21365	−	22.3514i	0.106124	−	0.738110i
$918$	0.269486	−	0.173188i	0.00889438	−	0.00571607i
$919$	−21.3790			−0.705227			−0.352613	−	0.935769i	$-0.614707\pi$
$919$	−21.3790			−0.705227			−0.352613	+	0.935769i	$0.614707\pi$
$920$	1.47777	+	1.46480i	0.0487207	+	0.0482931i
$921$	16.2373			0.535038
$922$	−0.757536	+	0.486839i	−0.0249481	+	0.0160332i
$923$	−6.51626	+	45.3216i	−0.214485	+	1.49178i
$924$	−3.98952	+	8.73582i	−0.131245	+	0.287387i
$925$	−20.2378	+	5.94236i	−0.665416	+	0.195384i
$926$	−0.784963	−	1.71883i	−0.0257955	−	0.0564842i
$927$	−1.64155	−	1.89445i	−0.0539155	−	0.0622218i
$928$	−1.06549	−	7.41065i	−0.0349765	−	0.243267i
$929$	−25.7958	−	7.57432i	−0.846332	−	0.248505i	−0.170313	−	0.985390i	$-0.554478\pi$
$929$	−25.7958	−	7.57432i	−0.846332	−	0.248505i	−0.676019	+	0.736885i	$0.736296\pi$
$930$	−0.183937	+	0.212275i	−0.00603154	+	0.00696077i
$931$	5.33555	+	3.42895i	0.174865	+	0.112379i
$932$	34.2746	+	22.0269i	1.12270	+	0.721516i
$933$	14.4468	−	16.6725i	0.472968	−	0.545834i
$934$	−4.34351	−	1.27537i	−0.142124	−	0.0417314i
$935$	1.35601	+	9.43124i	0.0443462	+	0.308434i
$936$	2.38569	+	2.75324i	0.0779788	+	0.0899924i
$937$	0.467332	+	1.02331i	0.0152671	+	0.0334302i	0.917112	−	0.398630i	$-0.130514\pi$
$937$	0.467332	+	1.02331i	0.0152671	+	0.0334302i	−0.901845	+	0.432060i	$0.857787\pi$
$938$	0.434867	−	0.127688i	0.0141989	−	0.00416917i
$939$	−1.65340	+	3.62044i	−0.0539567	+	0.118149i
$940$	−2.76433	+	19.2263i	−0.0901625	+	0.627094i
$941$	−0.829943	+	0.533372i	−0.0270554	+	0.0173874i	−0.554099	−	0.832451i	$-0.686937\pi$
$941$	−0.829943	+	0.533372i	−0.0270554	+	0.0173874i	0.527043	+	0.849838i	$0.323301\pi$
$942$	−0.839998			−0.0273686
$943$	−25.6229	+	19.3579i	−0.834396	+	0.630379i
$944$	0.825606			0.0268712
$945$	−0.688019	+	0.442163i	−0.0223813	+	0.0143836i
$946$	0.0305240	−	0.212299i	0.000992420	−	0.00690243i
$947$	22.7666	−	49.8520i	0.739817	−	1.61997i	−0.0440392	−	0.999030i	$-0.514023\pi$
$947$	22.7666	−	49.8520i	0.739817	−	1.61997i	0.783856	−	0.620943i	$-0.213250\pi$
$948$	22.5411	−	6.61865i	0.732100	−	0.214964i
$949$	28.6079	+	62.6426i	0.928652	+	2.03346i
$950$	−2.39636	−	2.76555i	−0.0777482	−	0.0897262i
$951$	4.01126	+	27.8989i	0.130074	+	0.904684i
$952$	−1.22400	−	0.359398i	−0.0396700	−	0.0116482i
$953$	4.84492	−	5.59134i	0.156942	−	0.181121i	−0.671833	−	0.740703i	$-0.734493\pi$
$953$	4.84492	−	5.59134i	0.156942	−	0.181121i	0.828775	+	0.559582i	$0.189038\pi$
$954$	−0.696187	−	0.447412i	−0.0225399	−	0.0144855i
$955$	0.866718	+	0.557006i	0.0280463	+	0.0180243i
$956$	−25.9525	+	29.9508i	−0.839364	+	0.968678i
$957$	22.0316	+	6.46905i	0.712180	+	0.209115i
$958$	0.670865	+	4.66597i	0.0216747	+	0.150751i
$959$	7.92610	+	9.14721i	0.255947	+	0.295379i
$960$	2.57434	+	5.63703i	0.0830866	+	0.181934i
$961$	23.3670	−	6.86117i	0.753775	−	0.221328i
$962$	−1.85072	+	4.05251i	−0.0596696	+	0.130658i
$963$	−2.62185	+	18.2354i	−0.0844879	+	0.587626i
$964$	−19.4781	+	12.5178i	−0.627348	+	0.403172i
$965$	−10.2685			−0.330554
$966$	0.0427674	−	0.637440i	0.00137602	−	0.0205093i
$967$	−37.4561			−1.20451			−0.602254	−	0.798304i	$-0.705731\pi$
$967$	−37.4561			−1.20451			−0.602254	+	0.798304i	$0.705731\pi$
$968$	5.56617	−	3.57716i	0.178903	−	0.114974i
$969$	2.17051	−	15.0962i	0.0697268	−	0.484961i
$970$	0.238439	−	0.522109i	0.00765582	−	0.0167639i
$971$	−32.2454	+	9.46811i	−1.03480	+	0.303846i	−0.754663	−	0.656112i	$-0.772200\pi$
$971$	−32.2454	+	9.46811i	−1.03480	+	0.303846i	−0.280142	+	0.959959i	$0.590381\pi$
$972$	0.823458	+	1.80312i	0.0264124	+	0.0578352i
$973$	0.926181	+	1.06887i	0.0296920	+	0.0342664i
$974$	0.243802	+	1.69568i	0.00781191	+	0.0543330i
$975$	28.5383	+	8.37961i	0.913958	+	0.268362i
$976$	2.02980	−	2.34251i	0.0649722	−	0.0749819i
$977$	29.6302	+	19.0422i	0.947953	+	0.609213i	0.920639	−	0.390414i	$-0.127668\pi$
$977$	29.6302	+	19.0422i	0.947953	+	0.609213i	0.0273141	+	0.999627i	$0.491305\pi$
$978$	−0.567045	−	0.364418i	−0.0181321	−	0.0116528i
$979$	10.5495	−	12.1748i	0.337163	−	0.389107i
$980$	1.55552	+	0.456741i	0.0496891	+	0.0145901i
$981$	−1.78093	−	12.3866i	−0.0568607	−	0.395475i
$982$	3.71849	+	4.29137i	0.118662	+	0.136943i
$983$	10.3576	+	22.6800i	0.330356	+	0.723379i	0.999810	−	0.0194741i	$-0.00619918\pi$
$983$	10.3576	+	22.6800i	0.330356	+	0.723379i	−0.669454	+	0.742853i	$0.733472\pi$
$984$	3.40833	−	1.00078i	0.108654	−	0.0319036i
$985$	−0.608632	+	1.33272i	−0.0193926	+	0.0424639i
$986$	−0.216065	+	1.50277i	−0.00688092	+	0.0478579i
$987$	10.0794	−	6.47763i	0.320830	−	0.206185i
$988$	86.3371			2.74675
$989$	−0.345641	−	1.55584i	−0.0109908	−	0.0494728i
$990$	0.527841			0.0167759
$991$	−33.0573	+	21.2447i	−1.05010	+	0.674859i	−0.947465	−	0.319860i	$-0.896364\pi$
$991$	−33.0573	+	21.2447i	−1.05010	+	0.674859i	−0.102636	+	0.994719i	$0.532728\pi$
$992$	0.579591	−	4.03114i	0.0184020	−	0.127989i
$993$	−5.82068	+	12.7455i	−0.184714	+	0.404467i
$994$	−0.852226	+	0.250236i	−0.0270310	+	0.00793700i
$995$	6.67528	+	14.6168i	0.211621	+	0.463384i
$996$	10.1395	+	11.7016i	0.321283	+	0.370780i
$997$	4.98970	+	34.7041i	0.158025	+	1.09909i	0.902266	+	0.431180i	$0.141902\pi$
$997$	4.98970	+	34.7041i	0.158025	+	1.09909i	−0.744241	+	0.667912i	$0.767188\pi$
$998$	2.26503	+	0.665074i	0.0716984	+	0.0210525i
$999$	−3.18912	+	3.68044i	−0.100899	+	0.116444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.d.127.4	✓	60
23.2	even	11	inner	483.2.q.d.232.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.d.127.4	✓	60	1.1	even	1	trivial
483.2.q.d.232.4	yes	60	23.2	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.112067 + 0.0720210i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.823458 + 1.80312i) q^{4} +(-0.784721 + 0.230415i) q^{5} +(0.0553392 + 0.121176i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0754970 - 0.525093i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.112067 + 0.0720210i) q^{2} +(0.142315 - 0.989821i) q^{3} +(-0.823458 + 1.80312i) q^{4} +(-0.784721 + 0.230415i) q^{5} +(0.0553392 + 0.121176i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.0754970 - 0.525093i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.0713466 - 0.0823383i) q^{10} +(-4.07573 - 2.61931i) q^{11} +(1.66758 + 1.07169i) q^{12} +(4.49713 - 5.18996i) q^{13} +(0.127818 + 0.0375308i) q^{14} +(0.116392 + 0.809525i) q^{15} +(-2.54992 - 2.94277i) q^{16} +(0.998945 + 2.18738i) q^{17} +(0.127818 - 0.0375308i) q^{18} +(2.63472 - 5.76923i) q^{19} +(0.230719 - 1.60468i) q^{20} +(-0.841254 + 0.540641i) q^{21} +0.645401 q^{22} +(4.48602 - 1.69576i) q^{23} -0.530493 q^{24} +(-3.64357 + 2.34158i) q^{25} +(-0.130193 + 0.905511i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(1.90196 - 0.558465i) q^{28} +(-1.96882 - 4.31113i) q^{29} +(-0.0713466 - 0.0823383i) q^{30} +(-0.366899 - 2.55184i) q^{31} +(1.51571 + 0.445053i) q^{32} +(-3.17269 + 3.66148i) q^{33} +(-0.269486 - 0.173188i) q^{34} +(0.688019 + 0.442163i) q^{35} +(1.29810 - 1.49809i) q^{36} +(4.67265 + 1.37202i) q^{37} +(0.120241 + 0.836295i) q^{38} +(-4.49713 - 5.18996i) q^{39} +(0.180233 + 0.394656i) q^{40} +(-6.42483 + 1.88650i) q^{41} +(0.0553392 - 0.121176i) q^{42} +(0.0472946 - 0.328941i) q^{43} +(8.07914 - 5.19215i) q^{44} +0.817850 q^{45} +(-0.380604 + 0.513127i) q^{46} -11.9814 q^{47} +(-3.27571 + 2.10517i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(0.239681 - 0.524828i) q^{50} +(2.30729 - 0.677480i) q^{51} +(5.65493 + 12.3826i) q^{52} +(-4.06815 - 4.69490i) q^{53} +(-0.0189584 - 0.131858i) q^{54} +(3.80184 + 1.11632i) q^{55} +(-0.347399 + 0.400920i) q^{56} +(-5.33555 - 3.42895i) q^{57} +(0.531132 + 0.341338i) q^{58} +(-0.138849 + 0.160241i) q^{59} +(-1.55552 - 0.456741i) q^{60} +(0.113286 + 0.787921i) q^{61} +(0.224903 + 0.259552i) q^{62} +(0.415415 + 0.909632i) q^{63} +(7.27031 - 2.13475i) q^{64} +(-2.33315 + 5.10888i) q^{65} +(0.0918501 - 0.638831i) q^{66} +(2.86214 - 1.83938i) q^{67} -4.76671 q^{68} +(-1.04007 - 4.68169i) q^{69} -0.108949 q^{70} +(-5.60905 + 3.60472i) q^{71} +(-0.0754970 + 0.525093i) q^{72} +(-4.16581 + 9.12186i) q^{73} +(-0.622464 + 0.182772i) q^{74} +(1.79921 + 3.93973i) q^{75} +(8.23304 + 9.50144i) q^{76} +(0.689492 + 4.79552i) q^{77} +(0.877766 + 0.257735i) q^{78} +(7.76108 - 8.95677i) q^{79} +(2.67903 + 1.72171i) q^{80} +(0.841254 + 0.540641i) q^{81} +(0.584143 - 0.674138i) q^{82} +(7.49464 + 2.20063i) q^{83} +(-0.282104 - 1.96208i) q^{84} +(-1.28790 - 1.48632i) q^{85} +(0.0183905 + 0.0402696i) q^{86} +(-4.54744 + 1.33525i) q^{87} +(-1.06768 + 2.33789i) q^{88} +(-0.473210 + 3.29125i) q^{89} +(-0.0916539 + 0.0589024i) q^{90} -6.86730 q^{91} +(-0.636387 + 9.48523i) q^{92} -2.57808 q^{93} +(1.34272 - 0.862912i) q^{94} +(-0.738203 + 5.13431i) q^{95} +(0.656231 - 1.43695i) q^{96} +(5.05491 - 1.48426i) q^{97} +(-0.0553392 - 0.121176i) q^{98} +(3.17269 + 3.66148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Introduction

L-functions

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