LMFDB - Embedded newform 430.2.q.c.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			181.1
Character	$\chi$	$=$	430.181
Dual form			430.2.q.c.411.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.623490 - 0.781831i) q^{2} +(-3.32148 - 0.500633i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.826239 + 0.563320i) q^{5} +(1.67950 + 2.90898i) q^{6} +(-0.871475 + 1.50944i) q^{7} +(0.900969 - 0.433884i) q^{8} +(7.91489 + 2.44142i) q^{9} +O(q^{10})$	\(q+(-0.623490 - 0.781831i) q^{2} +(-3.32148 - 0.500633i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.826239 + 0.563320i) q^{5} +(1.67950 + 2.90898i) q^{6} +(-0.871475 + 1.50944i) q^{7} +(0.900969 - 0.433884i) q^{8} +(7.91489 + 2.44142i) q^{9} +(-0.0747301 - 0.997204i) q^{10} +(-0.296819 - 1.30045i) q^{11} +(1.22718 - 3.12680i) q^{12} +(0.276493 - 3.68954i) q^{13} +(1.72348 - 0.259773i) q^{14} +(-2.46232 - 2.28470i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(0.528983 - 0.360654i) q^{17} +(-3.02607 - 7.71031i) q^{18} +(-0.715661 + 0.220752i) q^{19} +(-0.733052 + 0.680173i) q^{20} +(3.65026 - 4.57728i) q^{21} +(-0.831667 + 1.04288i) q^{22} +(-5.37625 + 4.98843i) q^{23} +(-3.20977 + 0.990082i) q^{24} +(0.365341 + 0.930874i) q^{25} +(-3.05699 + 2.08422i) q^{26} +(-15.9878 - 7.69934i) q^{27} +(-1.27767 - 1.18551i) q^{28} +(-2.86116 + 0.431250i) q^{29} +(-0.251018 + 3.34961i) q^{30} +(1.79184 - 4.56553i) q^{31} +(0.222521 + 0.974928i) q^{32} +(0.334831 + 4.46801i) q^{33} +(-0.611786 - 0.188711i) q^{34} +(-1.57034 + 0.756238i) q^{35} +(-4.14144 + 7.17318i) q^{36} +(-4.24005 - 7.34399i) q^{37} +(0.618798 + 0.421889i) q^{38} +(-2.76547 + 12.1163i) q^{39} +(0.988831 + 0.149042i) q^{40} +(-6.87166 - 8.61679i) q^{41} -5.85457 q^{42} +(5.14937 - 4.06005i) q^{43} +1.33389 q^{44} +(5.16429 + 6.47581i) q^{45} +(7.25215 + 1.09309i) q^{46} +(2.39319 - 10.4852i) q^{47} +(2.77534 + 1.89219i) q^{48} +(1.98106 + 3.43130i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-1.93756 + 0.933081i) q^{51} +(3.53551 + 1.09056i) q^{52} +(-0.218853 - 2.92039i) q^{53} +(3.94867 + 17.3003i) q^{54} +(0.487325 - 1.24168i) q^{55} +(-0.130251 + 1.73808i) q^{56} +(2.48757 - 0.374941i) q^{57} +(2.12107 + 1.96806i) q^{58} +(-2.94897 - 1.42015i) q^{59} +(2.77534 - 1.89219i) q^{60} +(-3.59900 - 9.17010i) q^{61} +(-4.68667 + 1.44564i) q^{62} +(-10.5828 + 9.81941i) q^{63} +(0.623490 - 0.781831i) q^{64} +(2.30684 - 2.89269i) q^{65} +(3.28447 - 3.04754i) q^{66} +(1.15852 - 0.357357i) q^{67} +(0.233902 + 0.595973i) q^{68} +(20.3545 - 13.8775i) q^{69} +(1.57034 + 0.756238i) q^{70} +(-5.28111 - 4.90015i) q^{71} +(8.19036 - 1.23450i) q^{72} +(-0.768814 + 10.2591i) q^{73} +(-3.09813 + 7.89391i) q^{74} +(-0.747448 - 3.27478i) q^{75} +(-0.0559679 - 0.746840i) q^{76} +(2.22162 + 0.685278i) q^{77} +(11.1972 - 5.39227i) q^{78} +(-1.81601 + 3.14543i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(28.7179 + 19.5795i) q^{81} +(-2.45247 + 10.7450i) q^{82} +(5.48911 + 0.827350i) q^{83} +(3.65026 + 4.57728i) q^{84} +0.640230 q^{85} +(-6.38485 - 1.49454i) q^{86} +9.71917 q^{87} +(-0.831667 - 1.04288i) q^{88} +(-2.95788 - 0.445829i) q^{89} +(1.84311 - 8.07521i) q^{90} +(5.32818 + 3.63269i) q^{91} +(-3.66703 - 6.35149i) q^{92} +(-8.23721 + 14.2673i) q^{93} +(-9.68981 + 4.66637i) q^{94} +(-0.715661 - 0.220752i) q^{95} +(-0.251018 - 3.34961i) q^{96} +(2.40648 + 10.5435i) q^{97} +(1.44753 - 3.68824i) q^{98} +(0.825651 - 11.0176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{21}\right)$

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 $

$2$	−0.623490	−	0.781831i	−0.440874	−	0.552838i
$2$	−0.623490	−	0.781831i	−0.440874	−	0.552838i
$3$	−3.32148	−	0.500633i	−1.91766	−	0.289040i	−0.922394	−	0.386249i	$-0.873770\pi$
$3$	−3.32148	−	0.500633i	−1.91766	−	0.289040i	−0.995264	+	0.0972089i	$0.969009\pi$
$4$	−0.222521	+	0.974928i	−0.111260	+	0.487464i
$5$	0.826239	+	0.563320i	0.369505	+	0.251924i
$5$	0.826239	+	0.563320i	0.369505	+	0.251924i
$6$	1.67950	+	2.90898i	0.685653	+	1.18759i
$7$	−0.871475	+	1.50944i	−0.329387	+	0.570514i	−0.982390	−	0.186840i	$-0.940175\pi$
$7$	−0.871475	+	1.50944i	−0.329387	+	0.570514i	0.653004	+	0.757355i	$0.273509\pi$
$8$	0.900969	−	0.433884i	0.318541	−	0.153401i
$9$	7.91489	+	2.44142i	2.63830	+	0.813807i
$10$	−0.0747301	−	0.997204i	−0.0236317	−	0.315344i
$11$	−0.296819	−	1.30045i	−0.0894942	−	0.392100i	0.910265	−	0.414025i	$-0.135877\pi$
$11$	−0.296819	−	1.30045i	−0.0894942	−	0.392100i	−0.999760	+	0.0219256i	$0.993020\pi$
$12$	1.22718	−	3.12680i	0.354256	−	0.902631i
$13$	0.276493	−	3.68954i	0.0766853	−	1.02329i	−0.817597	−	0.575791i	$-0.804694\pi$
$13$	0.276493	−	3.68954i	0.0766853	−	1.02329i	0.894282	−	0.447503i	$-0.147687\pi$
$14$	1.72348	−	0.259773i	0.460620	−	0.0694273i
$15$	−2.46232	−	2.28470i	−0.635768	−	0.589907i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	0.528983	−	0.360654i	0.128297	−	0.0874716i	−0.497471	−	0.867481i	$-0.665738\pi$
$17$	0.528983	−	0.360654i	0.128297	−	0.0874716i	0.625768	+	0.780009i	$0.284786\pi$
$18$	−3.02607	−	7.71031i	−0.713252	−	1.81734i
$19$	−0.715661	+	0.220752i	−0.164184	+	0.0506440i	−0.375757	−	0.926718i	$-0.622617\pi$
$19$	−0.715661	+	0.220752i	−0.164184	+	0.0506440i	0.211574	+	0.977362i	$0.432141\pi$
$20$	−0.733052	+	0.680173i	−0.163915	+	0.152091i
$21$	3.65026	−	4.57728i	0.796553	−	0.998845i
$22$	−0.831667	+	1.04288i	−0.177312	+	0.222342i
$23$	−5.37625	+	4.98843i	−1.12103	+	1.04016i	−0.122162	+	0.992510i	$0.538983\pi$
$23$	−5.37625	+	4.98843i	−1.12103	+	1.04016i	−0.998864	+	0.0476502i	$0.984827\pi$
$24$	−3.20977	+	0.990082i	−0.655191	+	0.202100i
$25$	0.365341	+	0.930874i	0.0730682	+	0.186175i
$26$	−3.05699	+	2.08422i	−0.599525	+	0.408749i
$27$	−15.9878	−	7.69934i	−3.07686	−	1.48174i
$28$	−1.27767	−	1.18551i	−0.241457	−	0.224040i
$29$	−2.86116	+	0.431250i	−0.531303	+	0.0800811i	−0.409215	−	0.912438i	$-0.634197\pi$
$29$	−2.86116	+	0.431250i	−0.531303	+	0.0800811i	−0.122089	+	0.992519i	$0.538959\pi$
$30$	−0.251018	+	3.34961i	−0.0458295	+	0.611552i
$31$	1.79184	−	4.56553i	0.321824	−	0.819993i	−0.674809	−	0.737993i	$-0.735774\pi$
$31$	1.79184	−	4.56553i	0.321824	−	0.819993i	0.996632	−	0.0820003i	$-0.0261309\pi$
$32$	0.222521	+	0.974928i	0.0393365	+	0.172345i
$33$	0.334831	+	4.46801i	0.0582866	+	0.777780i
$34$	−0.611786	−	0.188711i	−0.104921	−	0.0323637i
$35$	−1.57034	+	0.756238i	−0.265436	+	0.127827i
$36$	−4.14144	+	7.17318i	−0.690240	+	1.19553i
$37$	−4.24005	−	7.34399i	−0.697060	−	1.20734i	−0.969481	−	0.245166i	$-0.921158\pi$
$37$	−4.24005	−	7.34399i	−0.697060	−	1.20734i	0.272421	−	0.962178i	$-0.412176\pi$
$38$	0.618798	+	0.421889i	0.100382	+	0.0684395i
$39$	−2.76547	+	12.1163i	−0.442830	+	1.94016i
$40$	0.988831	+	0.149042i	0.156348	+	0.0235657i
$41$	−6.87166	−	8.61679i	−1.07317	−	1.34572i	−0.934735	−	0.355346i	$-0.884363\pi$
$41$	−6.87166	−	8.61679i	−1.07317	−	1.34572i	−0.138438	−	0.990371i	$-0.544208\pi$
$42$	−5.85457			−0.903379
$43$	5.14937	−	4.06005i	0.785272	−	0.619151i
$43$	5.14937	−	4.06005i	0.785272	−	0.619151i
$44$	1.33389			0.201092
$45$	5.16429	+	6.47581i	0.769847	+	0.965357i
$46$	7.25215	+	1.09309i	1.06927	+	0.161167i
$47$	2.39319	−	10.4852i	0.349082	−	1.52943i	−0.430188	−	0.902739i	$-0.641553\pi$
$47$	2.39319	−	10.4852i	0.349082	−	1.52943i	0.779270	−	0.626689i	$-0.215590\pi$
$48$	2.77534	+	1.89219i	0.400585	+	0.273114i
$49$	1.98106	+	3.43130i	0.283009	+	0.490186i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−1.93756	+	0.933081i	−0.271313	+	0.130657i
$52$	3.53551	+	1.09056i	0.490287	+	0.151233i
$53$	−0.218853	−	2.92039i	−0.0300618	−	0.401146i	−0.991855	−	0.127370i	$-0.959346\pi$
$53$	−0.218853	−	2.92039i	−0.0300618	−	0.401146i	0.961793	−	0.273776i	$-0.0882727\pi$
$54$	3.94867	+	17.3003i	0.537346	+	2.35427i
$55$	0.487325	−	1.24168i	0.0657109	−	0.167429i
$56$	−0.130251	+	1.73808i	−0.0174055	+	0.232260i
$57$	2.48757	−	0.374941i	0.329487	−	0.0496621i
$58$	2.12107	+	1.96806i	0.278510	+	0.258419i
$59$	−2.94897	−	1.42015i	−0.383924	−	0.184888i	0.231959	−	0.972725i	$-0.425486\pi$
$59$	−2.94897	−	1.42015i	−0.383924	−	0.184888i	−0.615883	+	0.787838i	$0.711201\pi$
$60$	2.77534	−	1.89219i	0.358294	−	0.244281i
$61$	−3.59900	−	9.17010i	−0.460805	−	1.17411i	−0.952823	−	0.303527i	$-0.901836\pi$
$61$	−3.59900	−	9.17010i	−0.460805	−	1.17411i	0.492018	−	0.870585i	$-0.336259\pi$
$62$	−4.68667	+	1.44564i	−0.595207	+	0.183597i
$63$	−10.5828	+	9.81941i	−1.33331	+	1.23713i
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	2.30684	−	2.89269i	0.286128	−	0.358794i
$66$	3.28447	−	3.04754i	0.404290	−	0.375126i
$67$	1.15852	−	0.357357i	0.141536	−	0.0436581i	−0.223178	−	0.974778i	$-0.571643\pi$
$67$	1.15852	−	0.357357i	0.141536	−	0.0436581i	0.364714	+	0.931120i	$0.381167\pi$
$68$	0.233902	+	0.595973i	0.0283648	+	0.0722724i
$69$	20.3545	−	13.8775i	2.45039	−	1.67065i
$70$	1.57034	+	0.756238i	0.187692	+	0.0903877i
$71$	−5.28111	−	4.90015i	−0.626752	−	0.581541i	0.301512	−	0.953462i	$-0.402509\pi$
$71$	−5.28111	−	4.90015i	−0.626752	−	0.581541i	−0.928264	+	0.371921i	$0.878699\pi$
$72$	8.19036	−	1.23450i	0.965243	−	0.145487i
$73$	−0.768814	+	10.2591i	−0.0899829	+	1.20074i	0.751232	+	0.660038i	$0.229460\pi$
$73$	−0.768814	+	10.2591i	−0.0899829	+	1.20074i	−0.841215	+	0.540700i	$0.818159\pi$
$74$	−3.09813	+	7.89391i	−0.360150	+	0.917648i
$75$	−0.747448	−	3.27478i	−0.0863078	−	0.378139i
$76$	−0.0559679	−	0.746840i	−0.00641996	−	0.0856684i
$77$	2.22162	+	0.685278i	0.253177	+	0.0780946i
$78$	11.1972	−	5.39227i	1.26783	−	0.610554i
$79$	−1.81601	+	3.14543i	−0.204318	+	0.353888i	−0.949915	−	0.312508i	$-0.898831\pi$
$79$	−1.81601	+	3.14543i	−0.204318	+	0.353888i	0.745598	+	0.666396i	$0.232164\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	28.7179	+	19.5795i	3.19088	+	2.17550i
$82$	−2.45247	+	10.7450i	−0.270830	+	1.18658i
$83$	5.48911	+	0.827350i	0.602508	+	0.0908135i	0.443211	−	0.896417i	$-0.353839\pi$
$83$	5.48911	+	0.827350i	0.602508	+	0.0908135i	0.159297	+	0.987231i	$0.449077\pi$
$84$	3.65026	+	4.57728i	0.398276	+	0.499423i
$85$	0.640230			0.0694427
$86$	−6.38485	−	1.49454i	−0.688496	−	0.161161i
$87$	9.71917			1.04200
$88$	−0.831667	−	1.04288i	−0.0886560	−	0.111171i
$89$	−2.95788	−	0.445829i	−0.313535	−	0.0472577i	−0.00961003	−	0.999954i	$-0.503059\pi$
$89$	−2.95788	−	0.445829i	−0.313535	−	0.0472577i	−0.303925	+	0.952696i	$0.598297\pi$
$90$	1.84311	−	8.07521i	0.194281	−	0.851201i
$91$	5.32818	+	3.63269i	0.558545	+	0.380809i
$92$	−3.66703	−	6.35149i	−0.382315	−	0.662189i
$93$	−8.23721	+	14.2673i	−0.854159	+	1.47945i
$94$	−9.68981	+	4.66637i	−0.999428	+	0.481299i
$95$	−0.715661	−	0.220752i	−0.0734252	−	0.0226487i
$96$	−0.251018	−	3.34961i	−0.0256194	−	0.341868i
$97$	2.40648	+	10.5435i	0.244341	+	1.07053i	0.937019	+	0.349279i	$0.113573\pi$
$97$	2.40648	+	10.5435i	0.244341	+	1.07053i	−0.692678	+	0.721247i	$0.743569\pi$
$98$	1.44753	−	3.68824i	0.146222	−	0.372568i
$99$	0.825651	−	11.0176i	0.0829811	−	1.10731i
$100$	−0.988831	+	0.149042i	−0.0988831	+	0.0149042i
$101$	0.624762	+	0.579694i	0.0621661	+	0.0576817i	0.710644	−	0.703552i	$-0.248404\pi$
$101$	0.624762	+	0.579694i	0.0621661	+	0.0576817i	−0.648478	+	0.761233i	$0.724594\pi$
$102$	1.93756	+	0.933081i	0.191847	+	0.0923888i
$103$	15.2246	−	10.3800i	1.50013	−	1.02277i	0.513812	−	0.857903i	$-0.328233\pi$
$103$	15.2246	−	10.3800i	1.50013	−	1.02277i	0.986316	−	0.164867i	$-0.0527196\pi$
$104$	−1.35172	−	3.44413i	−0.132547	−	0.337724i
$105$	5.59446	−	1.72566i	0.545964	−	0.168408i
$106$	−2.14680	+	1.99194i	−0.208516	+	0.193474i
$107$	−2.93785	+	3.68395i	−0.284013	+	0.356141i	−0.903289	−	0.429032i	$-0.858855\pi$
$107$	−2.93785	+	3.68395i	−0.284013	+	0.356141i	0.619276	+	0.785173i	$0.287426\pi$
$108$	11.0639	−	13.8737i	1.06463	−	1.33500i
$109$	1.40069	−	1.29965i	0.134162	−	0.124484i	−0.610238	−	0.792218i	$-0.708926\pi$
$109$	1.40069	−	1.29965i	0.134162	−	0.124484i	0.744400	+	0.667734i	$0.232736\pi$
$110$	−1.27463	+	0.393171i	−0.121531	+	0.0374874i
$111$	10.4066	+	26.5156i	0.987752	+	2.51675i
$112$	1.44009	−	0.981839i	0.136076	−	0.0927750i
$113$	−18.6651	−	8.98865i	−1.75587	−	0.845581i	−0.975418	−	0.220362i	$-0.929276\pi$
$113$	−18.6651	−	8.98865i	−1.75587	−	0.845581i	−0.780449	−	0.625219i	$-0.785010\pi$
$114$	−1.84411	−	1.71109i	−0.172717	−	0.160258i
$115$	−7.25215	+	1.09309i	−0.676267	+	0.101931i
$116$	0.216230	−	2.88538i	0.0200764	−	0.267901i
$117$	11.1961	−	28.5273i	1.03508	−	2.63735i
$118$	0.728337	+	3.19105i	0.0670488	+	0.293760i
$119$	0.0833905	+	1.11277i	0.00764439	+	0.102007i
$120$	−3.20977	−	0.990082i	−0.293010	−	0.0903817i
$121$	8.30760	−	4.00073i	0.755236	−	0.363703i
$122$	−4.92554	+	8.53128i	−0.445937	+	0.772386i
$123$	18.5102	+	32.0607i	1.66901	+	2.89082i
$124$	4.05234	+	2.76284i	0.363911	+	0.248110i
$125$	−0.222521	+	0.974928i	−0.0199029	+	0.0872002i
$126$	14.2754	+	2.15167i	1.27175	+	0.191686i
$127$	−11.2399	−	14.0943i	−0.997377	−	1.25067i	−0.967960	−	0.251104i	$-0.919206\pi$
$127$	−11.2399	−	14.0943i	−0.997377	−	1.25067i	−0.0294167	−	0.999567i	$-0.509365\pi$
$128$	−1.00000			−0.0883883
$129$	−19.1361	+	10.9074i	−1.68484	+	0.960346i
$130$	−3.69988			−0.324501
$131$	−11.2896	−	14.1567i	−0.986377	−	1.23688i	−0.971512	−	0.236989i	$-0.923840\pi$
$131$	−11.2896	−	14.1567i	−0.986377	−	1.23688i	−0.0148651	−	0.999890i	$-0.504732\pi$
$132$	−4.43049	−	0.667789i	−0.385625	−	0.0581236i
$133$	0.290469	−	1.27263i	0.0251868	−	0.110351i
$134$	−1.00172	−	0.682961i	−0.0865354	−	0.0589989i
$135$	−8.87259	−	15.3678i	−0.763631	−	1.32265i
$136$	0.320115	−	0.554456i	0.0274496	−	0.0475442i
$137$	−11.2192	+	5.40288i	−0.958520	+	0.461599i	−0.846665	−	0.532126i	$-0.821393\pi$
$137$	−11.2192	+	5.40288i	−0.958520	+	0.461599i	−0.111854	+	0.993725i	$0.535679\pi$
$138$	−23.5407	−	7.26133i	−2.00391	−	0.618126i
$139$	−1.30220	−	17.3766i	−0.110451	−	1.47387i	−0.727048	−	0.686586i	$-0.759108\pi$
$139$	−1.30220	−	17.3766i	−0.110451	−	1.47387i	0.616597	−	0.787279i	$-0.288511\pi$
$140$	−0.387843	−	1.69925i	−0.0327787	−	0.143613i
$141$	−13.1982	+	33.6284i	−1.11149	+	2.83202i
$142$	−0.538376	+	7.18413i	−0.0451795	+	0.602879i
$143$	−4.88012	+	0.735560i	−0.408096	+	0.0615106i
$144$	−6.07178	−	5.63379i	−0.505981	−	0.469482i
$145$	−2.60693	−	1.25543i	−0.216494	−	0.104258i
$146$	8.50024	−	5.79537i	0.703485	−	0.479628i
$147$	−4.86224	−	12.3888i	−0.401031	−	1.02181i
$148$	8.10336	−	2.49956i	0.666092	−	0.205462i
$149$	6.32253	−	5.86645i	0.517962	−	0.480598i	−0.377330	−	0.926079i	$-0.623158\pi$
$149$	6.32253	−	5.86645i	0.517962	−	0.480598i	0.895292	+	0.445481i	$0.146967\pi$
$150$	−2.09430	+	2.62617i	−0.170999	+	0.214426i
$151$	−14.1298	+	17.7183i	−1.14987	+	1.44189i	−0.272449	+	0.962170i	$0.587834\pi$
$151$	−14.1298	+	17.7183i	−1.14987	+	1.44189i	−0.877421	+	0.479721i	$0.840738\pi$
$152$	−0.549007	+	0.509404i	−0.0445304	+	0.0413181i
$153$	5.06735	−	1.56307i	0.409671	−	0.126367i
$154$	−0.849383	−	2.16419i	−0.0684452	−	0.174396i
$155$	4.05234	−	2.76284i	0.325492	−	0.221916i
$156$	−11.1972	−	5.39227i	−0.896490	−	0.431727i
$157$	13.3725	+	12.4078i	1.06724	+	0.990253i	0.999972	−	0.00748164i	$-0.00238150\pi$
$157$	13.3725	+	12.4078i	1.06724	+	0.990253i	0.0672673	+	0.997735i	$0.478572\pi$
$158$	3.59146	−	0.541326i	0.285721	−	0.0430656i
$159$	−0.735127	+	9.80958i	−0.0582993	+	0.777951i
$160$	−0.365341	+	0.930874i	−0.0288827	+	0.0735920i
$161$	−2.84447	−	12.4624i	−0.224175	−	0.982176i
$162$	−2.59742	−	34.6602i	−0.204073	−	2.72316i
$163$	8.60680	+	2.65485i	0.674136	+	0.207944i	0.612877	−	0.790178i	$-0.290012\pi$
$163$	8.60680	+	2.65485i	0.674136	+	0.207944i	0.0612594	+	0.998122i	$0.480488\pi$
$164$	9.92984	−	4.78196i	0.775390	−	0.373408i
$165$	−2.24027	+	3.88026i	−0.174405	+	0.302078i
$166$	−2.77556	−	4.80740i	−0.215425	−	0.373127i
$167$	8.67587	+	5.91511i	0.671359	+	0.457725i	0.850414	−	0.526114i	$-0.176352\pi$
$167$	8.67587	+	5.91511i	0.671359	+	0.457725i	−0.179055	+	0.983839i	$0.557304\pi$
$168$	1.30276	−	5.70778i	0.100510	−	0.440365i
$169$	−0.681450	−	0.102712i	−0.0524193	−	0.00790093i
$170$	−0.399177	−	0.500552i	−0.0306155	−	0.0383906i
$171$	−6.20332			−0.474380
$172$	2.81241	+	5.92371i	0.214444	+	0.451679i
$173$	5.11967			0.389241			0.194621	−	0.980879i	$-0.437652\pi$
$173$	5.11967			0.389241			0.194621	+	0.980879i	$0.437652\pi$
$174$	−6.05981	−	7.59876i	−0.459393	−	0.576060i
$175$	−1.72348	−	0.259773i	−0.130283	−	0.0196370i
$176$	−0.296819	+	1.30045i	−0.0223735	+	0.0980249i
$177$	9.08399	+	6.19336i	0.682795	+	0.465521i
$178$	1.49565	+	2.59053i	0.112103	+	0.194169i
$179$	−6.55970	+	11.3617i	−0.490295	+	0.849215i	−0.999938	−	0.0111706i	$-0.996444\pi$
$179$	−6.55970	+	11.3617i	−0.490295	+	0.849215i	0.509643	+	0.860386i	$0.329778\pi$
$180$	−7.46261	+	3.59380i	−0.556230	+	0.267866i
$181$	−1.57192	−	0.484872i	−0.116840	−	0.0360403i	0.235784	−	0.971805i	$-0.424234\pi$
$181$	−1.57192	−	0.484872i	−0.116840	−	0.0360403i	−0.352624	+	0.935765i	$0.614710\pi$
$182$	−0.481913	−	6.43068i	−0.0357218	−	0.476674i
$183$	7.36316	+	32.2601i	0.544300	+	2.38474i
$184$	−2.67944	+	6.82709i	−0.197531	+	0.503300i
$185$	0.633719	−	8.45639i	0.0465920	−	0.621726i
$186$	16.2904	−	2.45538i	1.19447	−	0.180038i
$187$	−0.626024	−	0.580865i	−0.0457794	−	0.0424771i
$188$	9.68981	+	4.66637i	0.706702	+	0.340330i
$189$	25.5547	−	17.4229i	1.85883	−	1.26733i
$190$	0.273616	+	0.697163i	0.0198502	+	0.0505775i
$191$	−5.92006	+	1.82610i	−0.428360	+	0.132132i	−0.501436	−	0.865195i	$-0.667195\pi$
$191$	−5.92006	+	1.82610i	−0.428360	+	0.132132i	0.0730757	+	0.997326i	$0.476719\pi$
$192$	−2.46232	+	2.28470i	−0.177703	+	0.164884i
$193$	−5.70799	+	7.15760i	−0.410870	+	0.515215i	−0.943608	−	0.331065i	$-0.892592\pi$
$193$	−5.70799	+	7.15760i	−0.410870	+	0.515215i	0.532737	+	0.846281i	$0.321163\pi$
$194$	6.74279	−	8.45520i	0.484104	−	0.607048i
$195$	−9.11030	+	8.45313i	−0.652402	+	0.605341i
$196$	−3.78610	+	1.16786i	−0.270436	+	0.0834184i
$197$	0.101689	+	0.259098i	0.00724501	+	0.0184600i	0.934450	−	0.356093i	$-0.115891\pi$
$197$	0.101689	+	0.259098i	0.00724501	+	0.0184600i	−0.927205	+	0.374553i	$0.877796\pi$
$198$	−9.12866	+	6.22381i	−0.648745	+	0.442307i
$199$	24.2075	+	11.6577i	1.71603	+	0.826394i	0.990388	+	0.138317i	$0.0441694\pi$
$199$	24.2075	+	11.6577i	1.71603	+	0.826394i	0.725638	+	0.688077i	$0.241545\pi$
$200$	0.733052	+	0.680173i	0.0518346	+	0.0480955i
$201$	−4.02692	+	0.606960i	−0.284037	+	0.0428117i
$202$	0.0636906	−	0.849891i	0.00448125	−	0.0597982i
$203$	1.84248	−	4.69456i	0.129317	−	0.329494i
$204$	−0.478538	−	2.09661i	−0.0335044	−	0.146792i
$205$	−0.823622	−	10.9905i	−0.0575243	−	0.767608i
$206$	−17.6078	−	5.43129i	−1.22679	−	0.378416i
$207$	−54.7313	+	26.3572i	−3.80409	+	1.83195i
$208$	−1.84994	+	3.20419i	−0.128270	+	0.222171i
$209$	0.499498	+	0.865155i	0.0345510	+	0.0598441i
$210$	−4.83727	−	3.29799i	−0.333803	−	0.227583i
$211$	1.26513	−	5.54290i	0.0870952	−	0.381589i	−0.912529	−	0.409013i	$-0.865873\pi$
$211$	1.26513	−	5.54290i	0.0870952	−	0.381589i	0.999624	+	0.0274236i	$0.00873030\pi$
$212$	2.89587	+	0.436482i	0.198889	+	0.0299777i
$213$	15.0879	+	18.9197i	1.03381	+	1.29635i
$214$	4.71195			0.322102
$215$	6.54172	−	0.453825i	0.446141	−	0.0309506i
$216$	−17.7452			−1.20741
$217$	5.32984	+	6.68341i	0.361813	+	0.453700i
$218$	−1.88942	−	0.284785i	−0.127968	−	0.0192881i
$219$	7.68965	−	33.6906i	0.519618	−	2.27660i
$220$	1.10211	+	0.751407i	0.0743044	+	0.0506599i
$221$	−1.18439	−	2.05142i	−0.0796706	−	0.137994i
$222$	14.2423	−	24.6684i	0.955883	−	1.65564i
$223$	14.0898	−	6.78528i	0.943522	−	0.454376i	0.102111	−	0.994773i	$-0.467440\pi$
$223$	14.0898	−	6.78528i	0.943522	−	0.454376i	0.841410	+	0.540397i	$0.181726\pi$
$224$	−1.66552	−	0.513743i	−0.111282	−	0.0343259i
$225$	0.618980	+	8.25971i	0.0412653	+	0.550648i
$226$	4.60991	+	20.1973i	0.306646	+	1.34351i
$227$	−1.15524	+	2.94351i	−0.0766762	+	0.195368i	−0.964072	−	0.265640i	$-0.914417\pi$
$227$	−1.15524	+	2.94351i	−0.0766762	+	0.195368i	0.887396	+	0.461008i	$0.152512\pi$
$228$	−0.187996	+	2.50863i	−0.0124503	+	0.166138i
$229$	−27.2655	+	4.10961i	−1.80175	+	0.271570i	−0.962325	−	0.271902i	$-0.912347\pi$
$229$	−27.2655	+	4.10961i	−1.80175	+	0.271570i	−0.839427	+	0.543472i	$0.817109\pi$
$230$	5.37625	+	4.98843i	0.354500	+	0.328928i
$231$	−7.03598	−	3.38835i	−0.462934	−	0.222937i
$232$	−2.39070	+	1.62995i	−0.156957	+	0.107012i
$233$	3.68626	+	9.39244i	0.241495	+	0.615319i	0.999310	−	0.0371505i	$-0.0118281\pi$
$233$	3.68626	+	9.39244i	0.241495	+	0.615319i	−0.757815	+	0.652470i	$0.773733\pi$
$234$	−29.2842	+	9.03297i	−1.91437	+	0.590504i
$235$	7.88388	−	7.31518i	0.514288	−	0.477189i
$236$	2.04075	−	2.55902i	0.132842	−	0.166578i
$237$	7.60656	−	9.53833i	0.494099	−	0.619581i
$238$	0.818004	−	0.758997i	0.0530234	−	0.0491985i
$239$	−17.9239	+	5.52879i	−1.15940	+	0.357628i	−0.814021	−	0.580835i	$-0.802726\pi$
$239$	−17.9239	+	5.52879i	−1.15940	+	0.357628i	−0.345380	+	0.938463i	$0.612250\pi$
$240$	1.22718	+	3.12680i	0.0792141	+	0.201834i
$241$	2.06232	−	1.40606i	0.132845	−	0.0905725i	−0.495074	−	0.868851i	$-0.664859\pi$
$241$	2.06232	−	1.40606i	0.132845	−	0.0905725i	0.627919	+	0.778278i	$0.283907\pi$
$242$	−8.30760	−	4.00073i	−0.534033	−	0.257177i
$243$	−46.5594	−	43.2008i	−2.98679	−	2.77134i
$244$	9.74104	−	1.46823i	0.623606	−	0.0939935i
$245$	−0.296090	+	3.95105i	−0.0189165	+	0.252423i
$246$	13.5251	−	34.4614i	0.862329	−	2.19718i
$247$	0.616598	+	2.70149i	0.0392332	+	0.171892i
$248$	−0.366518	−	4.89085i	−0.0232739	−	0.310569i
$249$	−17.8178	−	5.49606i	−1.12916	−	0.348298i
$250$	0.900969	−	0.433884i	0.0569823	−	0.0274412i
$251$	5.05237	−	8.75097i	0.318903	−	0.552356i	−0.661356	−	0.750072i	$-0.730019\pi$
$251$	5.05237	−	8.75097i	0.318903	−	0.552356i	0.980259	+	0.197716i	$0.0633523\pi$
$252$	−7.21832	−	12.5025i	−0.454711	−	0.787583i
$253$	8.08297	+	5.51087i	0.508172	+	0.346466i
$254$	−4.01146	+	17.5754i	−0.251702	+	1.10278i
$255$	−2.12651	−	0.320520i	−0.133167	−	0.0200718i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	−22.9694			−1.43279			−0.716395	−	0.697695i	$-0.754209\pi$
$257$	−22.9694			−1.43279			−0.716395	+	0.697695i	$0.754209\pi$
$258$	20.4590	+	8.16056i	1.27372	+	0.508054i
$259$	14.7804			0.918409
$260$	2.30684	+	2.89269i	0.143064	+	0.179397i
$261$	−23.6986	−	3.57199i	−1.46691	−	0.221101i
$262$	−4.02921	+	17.6531i	−0.248926	+	1.09061i
$263$	15.4049	+	10.5029i	0.949904	+	0.647633i	0.935899	−	0.352268i	$-0.114590\pi$
$263$	15.4049	+	10.5029i	0.949904	+	0.647633i	0.0140049	+	0.999902i	$0.495542\pi$
$264$	2.24027	+	3.88026i	0.137879	+	0.238813i
$265$	1.46429	−	2.53622i	0.0899506	−	0.155799i
$266$	−1.17608	+	0.566372i	−0.0721103	+	0.0347265i
$267$	9.60135	+	2.96162i	0.587593	+	0.181248i
$268$	0.0906017	+	1.20900i	0.00553438	+	0.0738512i
$269$	−3.98676	−	17.4672i	−0.243077	−	1.06499i	−0.938198	−	0.346099i	$-0.887506\pi$
$269$	−3.98676	−	17.4672i	−0.243077	−	1.06499i	0.695121	−	0.718893i	$-0.255351\pi$
$270$	−6.48304	+	16.5185i	−0.394545	+	1.00528i
$271$	1.26198	−	16.8399i	0.0766596	−	1.02295i	−0.817712	−	0.575627i	$-0.804758\pi$
$271$	1.26198	−	16.8399i	0.0766596	−	1.02295i	0.894372	−	0.447324i	$-0.147623\pi$
$272$	−0.633079	+	0.0954213i	−0.0383861	+	0.00578577i
$273$	−15.8788	−	14.7334i	−0.961029	−	0.891704i
$274$	11.2192	+	5.40288i	0.677776	+	0.326400i
$275$	1.10211	−	0.751407i	0.0664599	−	0.0453116i
$276$	9.00022	+	22.9322i	0.541750	+	1.38036i
$277$	11.9612	−	3.68955i	0.718680	−	0.221683i	0.0862195	−	0.996276i	$-0.472521\pi$
$277$	11.9612	−	3.68955i	0.718680	−	0.221683i	0.632460	+	0.774593i	$0.282045\pi$
$278$	−12.7737	+	11.8522i	−0.766114	+	0.710850i
$279$	25.3286	−	31.7610i	1.51638	−	1.90148i
$280$	−1.08671	+	1.36269i	−0.0649434	+	0.0814365i
$281$	14.1000	−	13.0829i	0.841134	−	0.780459i	−0.136529	−	0.990636i	$-0.543595\pi$
$281$	14.1000	−	13.0829i	0.841134	−	0.780459i	0.977663	+	0.210177i	$0.0674042\pi$
$282$	34.5207	−	10.6482i	2.05568	−	0.634092i
$283$	−8.30609	−	21.1636i	−0.493746	−	1.25804i	−0.933063	−	0.359712i	$-0.882875\pi$
$283$	−8.30609	−	21.1636i	−0.493746	−	1.25804i	0.439318	−	0.898332i	$-0.355220\pi$
$284$	5.95245	−	4.05831i	0.353213	−	0.240816i
$285$	2.26654	+	1.09151i	0.134258	+	0.0646553i
$286$	3.61779	+	3.35682i	0.213924	+	0.198493i
$287$	18.9950	−	2.86304i	1.12124	−	0.169000i
$288$	−0.618980	+	8.25971i	−0.0364737	+	0.486708i
$289$	−6.06105	+	15.4433i	−0.356532	+	0.908429i
$290$	0.643858	+	2.82093i	0.0378087	+	0.165651i
$291$	−2.71466	−	36.2247i	−0.159136	−	2.12353i
$292$	−9.83082	−	3.03241i	−0.575305	−	0.177458i
$293$	−17.6066	+	8.47889i	−1.02859	+	0.495342i	−0.870545	−	0.492090i	$-0.836233\pi$
$293$	−17.6066	+	8.47889i	−1.02859	+	0.495342i	−0.158044	+	0.987432i	$0.550519\pi$
$294$	−6.65439	+	11.5257i	−0.388092	+	0.672195i
$295$	−1.63656	−	2.83460i	−0.0952841	−	0.165037i
$296$	−7.00659	−	4.77701i	−0.407250	−	0.277658i
$297$	−5.26710	+	23.0767i	−0.305628	+	1.33904i
$298$	−8.52861	−	1.28548i	−0.494049	−	0.0744659i
$299$	16.9185	+	21.2152i	0.978424	+	1.22690i
$300$	3.35900			0.193932
$301$	1.64085	+	11.3109i	0.0945768	+	0.651949i
$302$	22.6625			1.30408
$303$	−1.78492	−	2.23822i	−0.102541	−	0.128582i
$304$	0.740569	+	0.111623i	0.0424745	+	0.00640201i
$305$	2.19207	−	9.60409i	0.125518	−	0.549928i
$306$	−4.38150	−	2.98726i	−0.250474	−	0.170770i
$307$	7.97084	+	13.8059i	0.454920	+	0.787944i	0.998684	−	0.0512942i	$-0.0163346\pi$
$307$	7.97084	+	13.8059i	0.454920	+	0.787944i	−0.543764	+	0.839238i	$0.683001\pi$
$308$	−1.16245	+	2.01343i	−0.0662369	+	0.114726i
$309$	−55.7649	+	26.8550i	−3.17236	+	1.52773i
$310$	−4.68667	−	1.44564i	−0.266185	−	0.0821071i
$311$	0.0904189	+	1.20656i	0.00512719	+	0.0684176i	0.999180	−	0.0404773i	$-0.0128879\pi$
$311$	0.0904189	+	1.20656i	0.00512719	+	0.0684176i	−0.994053	+	0.108895i	$0.965269\pi$
$312$	2.76547	+	12.1163i	0.156564	+	0.685951i
$313$	7.08837	−	18.0609i	0.400658	−	1.02086i	−0.578123	−	0.815950i	$-0.696214\pi$
$313$	7.08837	−	18.0609i	0.400658	−	1.02086i	0.978781	−	0.204910i	$-0.0656903\pi$
$314$	1.36324	−	18.1912i	0.0769321	−	1.02659i
$315$	−14.2754	+	2.15167i	−0.804327	+	0.121233i
$316$	−2.66246	−	2.47041i	−0.149775	−	0.138971i
$317$	22.0760	+	10.6312i	1.23991	+	0.597109i	0.934789	−	0.355204i	$-0.115589\pi$
$317$	22.0760	+	10.6312i	1.23991	+	0.597109i	0.305121	+	0.952313i	$0.401303\pi$
$318$	8.12779	−	5.54143i	0.455784	−	0.310748i
$319$	1.41006	+	3.59278i	0.0789483	+	0.201157i
$320$	0.955573	−	0.294755i	0.0534181	−	0.0164773i
$321$	11.6023	−	10.7654i	0.647579	−	0.600866i
$322$	−7.97002	+	9.99408i	−0.444152	+	0.556949i
$323$	−0.298957	+	0.374880i	−0.0166344	+	0.0208589i
$324$	−25.4790	+	23.6410i	−1.41550	+	1.31339i
$325$	3.53551	−	1.09056i	0.196115	−	0.0604934i
$326$	−3.29061	−	8.38433i	−0.182250	−	0.464365i
$327$	−5.30302	+	3.61554i	−0.293258	+	0.199940i
$328$	−9.92984	−	4.78196i	−0.548284	−	0.264039i
$329$	13.7412	+	12.7500i	0.757578	+	0.702929i
$330$	4.43049	−	0.667789i	0.243891	−	0.0367606i
$331$	−0.329002	+	4.39023i	−0.0180836	+	0.241309i	0.980836	+	0.194836i	$0.0624173\pi$
$331$	−0.329002	+	4.39023i	−0.0180836	+	0.241309i	−0.998920	+	0.0464734i	$0.985202\pi$
$332$	−2.02805	+	5.16738i	−0.111304	+	0.283597i
$333$	−15.6298	−	68.4786i	−0.856507	−	3.75260i
$334$	−0.784699	−	10.4711i	−0.0429368	−	0.572952i
$335$	1.15852	+	0.357357i	0.0632969	+	0.0195245i
$336$	−5.27478	+	2.54020i	−0.287763	+	0.138579i
$337$	9.61044	−	16.6458i	0.523514	−	0.906753i	−0.476111	−	0.879385i	$-0.657954\pi$
$337$	9.61044	−	16.6458i	0.523514	−	0.906753i	0.999625	−	0.0273682i	$-0.00871267\pi$
$338$	0.344574	+	0.596819i	0.0187423	+	0.0324627i
$339$	57.4959	+	39.2000i	3.12275	+	2.12905i
$340$	−0.142465	+	0.624178i	−0.00772623	+	0.0338508i
$341$	−6.46908	−	0.975057i	−0.350320	−	0.0528023i
$342$	3.86771	+	4.84995i	0.209142	+	0.262255i
$343$	−19.1064			−1.03165
$344$	2.87783	−	5.89220i	0.155162	−	0.317686i
$345$	24.6351			1.32631
$346$	−3.19206	−	4.00272i	−0.171606	−	0.215188i
$347$	0.160211	+	0.0241480i	0.00860060	+	0.00129633i	0.153341	−	0.988173i	$-0.450997\pi$
$347$	0.160211	+	0.0241480i	0.00860060	+	0.00129633i	−0.144741	+	0.989470i	$0.546235\pi$
$348$	−2.16272	+	9.47549i	−0.115934	+	0.507940i
$349$	−6.40412	−	4.36625i	−0.342805	−	0.233720i	0.379663	−	0.925125i	$-0.376040\pi$
$349$	−6.40412	−	4.36625i	−0.342805	−	0.233720i	−0.722468	+	0.691405i	$0.756992\pi$
$350$	0.871475	+	1.50944i	0.0465823	+	0.0806829i
$351$	−32.8275	+	56.8590i	−1.75220	+	3.03491i
$352$	1.20179	−	0.578753i	0.0640558	−	0.0308477i
$353$	−25.5382	−	7.87750i	−1.35926	−	0.419277i	−0.472430	−	0.881368i	$-0.656623\pi$
$353$	−25.5382	−	7.87750i	−1.35926	−	0.419277i	−0.886832	+	0.462091i	$0.847099\pi$
$354$	−0.821612	−	10.9636i	−0.0436682	−	0.582711i
$355$	−1.60310	−	7.02365i	−0.0850838	−	0.372776i
$356$	1.09284	−	2.78451i	0.0579205	−	0.147579i
$357$	0.280109	−	3.73779i	0.0148249	−	0.197825i
$358$	12.9729	−	1.95534i	0.685637	−	0.103343i
$359$	23.5583	+	21.8589i	1.24336	+	1.15367i	0.982092	+	0.188403i	$0.0603311\pi$
$359$	23.5583	+	21.8589i	1.24336	+	1.15367i	0.261268	+	0.965266i	$0.415859\pi$
$360$	7.46261	+	3.59380i	0.393314	+	0.189410i
$361$	−15.2351	+	10.3871i	−0.801847	+	0.546690i
$362$	0.600986	+	1.53129i	0.0315871	+	0.0804827i
$363$	−29.5964	+	9.12929i	−1.55341	+	0.479163i
$364$	−4.72724	+	4.38624i	−0.247775	+	0.229901i
$365$	−6.41439	+	8.04339i	−0.335744	+	0.421010i
$366$	20.6311	−	25.8706i	1.07841	−	1.35228i
$367$	1.86910	−	1.73427i	0.0975661	−	0.0905281i	−0.629882	−	0.776691i	$-0.716897\pi$
$367$	1.86910	−	1.73427i	0.0975661	−	0.0905281i	0.727448	+	0.686163i	$0.240706\pi$
$368$	7.00824	−	2.16175i	0.365330	−	0.112689i
$369$	−33.3512	−	84.9776i	−1.73620	−	4.42375i
$370$	−7.00659	+	4.77701i	−0.364255	+	0.248345i
$371$	4.59887	+	2.21470i	0.238762	+	0.114982i
$372$	−12.0766	−	11.2054i	−0.626143	−	0.580975i
$373$	10.7400	−	1.61879i	0.556095	−	0.0838179i	0.135019	−	0.990843i	$-0.456890\pi$
$373$	10.7400	−	1.61879i	0.556095	−	0.0838179i	0.421077	+	0.907025i	$0.361652\pi$
$374$	−0.0638193	+	0.851609i	−0.00330002	+	0.0440356i
$375$	1.22718	−	3.12680i	0.0633713	−	0.161467i
$376$	−2.39319	−	10.4852i	−0.123419	−	0.540735i
$377$	0.800024	+	10.6756i	0.0412034	+	0.549821i
$378$	−29.5549	−	9.11647i	−1.52014	−	0.468900i
$379$	−5.83062	+	2.80788i	−0.299499	+	0.144231i	−0.577598	−	0.816321i	$-0.696010\pi$
$379$	−5.83062	+	2.80788i	−0.299499	+	0.144231i	0.278099	+	0.960552i	$0.410296\pi$
$380$	0.374467	−	0.648596i	0.0192097	−	0.0332723i
$381$	30.2769	+	52.4412i	1.55113	+	2.68664i
$382$	5.11879	+	3.48993i	0.261900	+	0.178561i
$383$	1.50138	−	6.57798i	0.0767169	−	0.336119i	−0.921975	−	0.387249i	$-0.873425\pi$
$383$	1.50138	−	6.57798i	0.0767169	−	0.336119i	0.998692	+	0.0511304i	$0.0162824\pi$
$384$	3.32148	+	0.500633i	0.169499	+	0.0255478i
$385$	1.44955	+	1.81768i	0.0738761	+	0.0926377i
$386$	9.15491			0.465973
$387$	50.6690	−	19.5630i	2.57565	−	0.994446i
$388$	−10.8146			−0.549028
$389$	2.99890	+	3.76050i	0.152050	+	0.190665i	0.852023	−	0.523505i	$-0.175376\pi$
$389$	2.99890	+	3.76050i	0.152050	+	0.190665i	−0.699972	+	0.714170i	$0.746804\pi$
$390$	12.2891	+	1.85228i	0.622283	+	0.0937940i
$391$	−1.04485	+	4.57777i	−0.0528401	+	0.231508i
$392$	3.27366	+	2.23195i	0.165345	+	0.112730i
$393$	30.4109	+	52.6732i	1.53403	+	2.65701i
$394$	0.139169	−	0.241048i	0.00701125	−	0.0121438i
$395$	−3.27234	+	1.57588i	−0.164649	+	0.0792910i
$396$	10.5576	+	3.25659i	0.530539	+	0.163650i
$397$	0.443428	+	5.91713i	0.0222550	+	0.296972i	0.997214	+	0.0745892i	$0.0237646\pi$
$397$	0.443428	+	5.91713i	0.0222550	+	0.296972i	−0.974959	+	0.222383i	$0.928616\pi$
$398$	−5.97876	−	26.1947i	−0.299688	−	1.31302i
$399$	−1.60190	+	4.08159i	−0.0801955	+	0.204335i
$400$	0.0747301	−	0.997204i	0.00373650	−	0.0498602i
$401$	−1.42210	+	0.214346i	−0.0710161	+	0.0107039i	−0.184454	−	0.982841i	$-0.559052\pi$
$401$	−1.42210	+	0.214346i	−0.0710161	+	0.0107039i	0.113438	+	0.993545i	$0.463814\pi$
$402$	2.98528	+	2.76994i	0.148892	+	0.138152i
$403$	−16.3493	−	7.87339i	−0.814415	−	0.392201i
$404$	−0.704182	+	0.480103i	−0.0350344	+	0.0238860i
$405$	12.6983	+	32.3547i	0.630984	+	1.60772i
$406$	−4.81912	+	1.48650i	−0.239169	+	0.0737739i
$407$	−8.29194	+	7.69380i	−0.411016	+	0.381367i
$408$	−1.34083	+	1.68135i	−0.0663812	+	0.0832394i
$409$	13.2227	−	16.5807i	0.653819	−	0.819863i	−0.338836	−	0.940846i	$-0.610033\pi$
$409$	13.2227	−	16.5807i	0.653819	−	0.819863i	0.992655	+	0.120983i	$0.0386046\pi$
$410$	−8.07918	+	7.49638i	−0.399002	+	0.370220i
$411$	39.9692	−	12.3289i	1.97153	−	0.608138i
$412$	6.73193	+	17.1527i	0.331659	+	0.845052i
$413$	4.71359	−	3.21367i	0.231941	−	0.158134i
$414$	54.7313	+	26.3572i	2.68990	+	1.29539i
$415$	4.06925	+	3.77571i	0.199752	+	0.185343i
$416$	3.65856	−	0.551439i	0.179376	−	0.0270365i
$417$	−4.37408	+	58.3680i	−0.214200	+	2.85829i
$418$	0.364974	−	0.929939i	0.0178515	−	0.0454848i
$419$	−2.09813	−	9.19253i	−0.102501	−	0.449084i	−0.999968	−	0.00800361i	$-0.997452\pi$
$419$	−2.09813	−	9.19253i	−0.102501	−	0.449084i	0.897467	−	0.441081i	$-0.145405\pi$
$420$	0.437512	+	5.83820i	0.0213484	+	0.284875i
$421$	7.93786	+	2.44851i	0.386868	+	0.119333i	0.482087	−	0.876123i	$-0.339879\pi$
$421$	7.93786	+	2.44851i	0.386868	+	0.119333i	−0.0952190	+	0.995456i	$0.530355\pi$
$422$	−5.12241	+	2.46682i	−0.249355	+	0.120083i
$423$	44.5407	−	77.1467i	2.16564	−	3.75100i
$424$	−1.46429	−	2.53622i	−0.0711122	−	0.123170i
$425$	0.528983	+	0.360654i	0.0256594	+	0.0174943i
$426$	5.38482	−	23.5924i	0.260895	−	1.14306i
$427$	16.9782	+	2.55904i	0.821630	+	0.123841i
$428$	−2.93785	−	3.68395i	−0.142007	−	0.178071i
$429$	16.5775			0.800368
$430$	−4.43351	−	4.83156i	−0.213803	−	0.232999i
$431$	25.2239			1.21499			0.607496	−	0.794323i	$-0.292174\pi$
$431$	25.2239			1.21499			0.607496	+	0.794323i	$0.292174\pi$
$432$	11.0639	+	13.8737i	0.532314	+	0.667500i
$433$	0.173176	+	0.0261020i	0.00832230	+	0.00125438i	0.153202	−	0.988195i	$-0.451041\pi$
$433$	0.173176	+	0.0261020i	0.00832230	+	0.00125438i	−0.144880	+	0.989449i	$0.546280\pi$
$434$	1.90220	−	8.33408i	0.0913085	−	0.400049i
$435$	8.03036	+	5.47501i	0.385026	+	0.262506i
$436$	0.955383	+	1.65477i	0.0457546	+	0.0792492i
$437$	2.74637	−	4.75685i	0.131376	−	0.227551i
$438$	−31.1348	+	14.9937i	−1.48768	+	0.716427i
$439$	17.8149	+	5.49515i	0.850257	+	0.262269i	0.689106	−	0.724660i	$-0.258003\pi$
$439$	17.8149	+	5.49515i	0.850257	+	0.262269i	0.161150	+	0.986930i	$0.448480\pi$
$440$	−0.0996818	−	1.33016i	−0.00475214	−	0.0634129i
$441$	7.30265	+	31.9950i	0.347745	+	1.52357i
$442$	−0.865412	+	2.20503i	−0.0411634	+	0.104883i
$443$	−1.88736	+	25.1851i	−0.0896713	+	1.19658i	0.752951	+	0.658076i	$0.228629\pi$
$443$	−1.88736	+	25.1851i	−0.0896713	+	1.19658i	−0.842623	+	0.538504i	$0.818990\pi$
$444$	−28.1665	+	4.24542i	−1.33672	+	0.201479i
$445$	−2.19277	−	2.03459i	−0.103947	−	0.0964490i
$446$	−14.0898	−	6.78528i	−0.667171	−	0.321292i
$447$	−23.9371	+	16.3200i	−1.13219	+	0.771912i
$448$	0.636771	+	1.62247i	0.0300846	+	0.0766543i
$449$	6.61731	−	2.04117i	0.312290	−	0.0963287i	−0.134648	−	0.990893i	$-0.542991\pi$
$449$	6.61731	−	2.04117i	0.312290	−	0.0963287i	0.446938	+	0.894565i	$0.352514\pi$
$450$	6.07178	−	5.63379i	0.286226	−	0.265579i
$451$	−9.16604	+	11.4939i	−0.431612	+	0.541224i
$452$	12.9167	−	16.1970i	0.607549	−	0.761842i
$453$	55.8024	−	51.7770i	2.62182	−	2.43270i
$454$	3.02161	−	0.932044i	0.141811	−	0.0437430i
$455$	2.35598	+	6.00294i	0.110450	+	0.281422i
$456$	2.07854	−	1.41713i	0.0973367	−	0.0663630i
$457$	−20.8353	−	10.0338i	−0.974635	−	0.469359i	−0.122378	−	0.992484i	$-0.539052\pi$
$457$	−20.8353	−	10.0338i	−0.974635	−	0.469359i	−0.852257	+	0.523124i	$0.824766\pi$
$458$	20.2128	+	18.7547i	0.944480	+	0.876349i
$459$	−11.2341	+	1.69327i	−0.524363	+	0.0790350i
$460$	0.548076	−	7.31356i	0.0255542	−	0.340997i
$461$	−0.824591	+	2.10102i	−0.0384050	+	0.0978544i	−0.948790	−	0.315909i	$-0.897691\pi$
$461$	−0.824591	+	2.10102i	−0.0384050	+	0.0978544i	0.910385	+	0.413763i	$0.135786\pi$
$462$	1.73774	+	7.61355i	0.0808472	+	0.354215i
$463$	−0.349536	−	4.66424i	−0.0162443	−	0.216766i	−0.999419	−	0.0340954i	$-0.989145\pi$
$463$	−0.349536	−	4.66424i	−0.0162443	−	0.216766i	0.983174	−	0.182670i	$-0.0584740\pi$
$464$	2.76492	+	0.852866i	0.128358	+	0.0395933i
$465$	−14.8429	+	7.14798i	−0.688325	+	0.331480i
$466$	5.04496	−	8.73813i	0.233703	−	0.404786i
$467$	−7.43740	−	12.8820i	−0.344162	−	0.596106i	0.641039	−	0.767508i	$-0.278504\pi$
$467$	−7.43740	−	12.8820i	−0.344162	−	0.596106i	−0.985201	+	0.171402i	$0.945170\pi$
$468$	25.3207	+	17.2633i	1.17045	+	0.797998i
$469$	−0.470215	+	2.06015i	−0.0217125	+	0.0951287i
$470$	−10.6348	−	1.60293i	−0.490545	−	0.0739377i
$471$	−38.2046	−	47.9071i	−1.76038	−	2.20744i
$472$	−3.27311			−0.150657
$473$	−6.80831	−	5.49139i	−0.313046	−	0.252494i
$474$	−12.2000			−0.560364
$475$	−0.466953	−	0.585540i	−0.0214253	−	0.0268664i
$476$	−1.10343	−	0.166315i	−0.0505754	−	0.00762302i
$477$	5.39770	−	23.6489i	0.247144	−	1.08281i
$478$	15.4980	+	10.5663i	0.708860	+	0.483293i
$479$	1.87753	+	3.25197i	0.0857864	+	0.148586i	0.905726	−	0.423864i	$-0.139326\pi$
$479$	1.87753	+	3.25197i	0.0857864	+	0.148586i	−0.819940	+	0.572450i	$0.805993\pi$
$480$	1.67950	−	2.90898i	0.0766583	−	0.132776i
$481$	−28.2683	+	13.6133i	−1.28892	+	0.620712i
$482$	−2.38514	−	0.735717i	−0.108640	−	0.0335110i
$483$	3.20875	+	42.8177i	0.146003	+	1.94827i
$484$	2.05181	+	8.98955i	0.0932639	+	0.408616i
$485$	−3.95102	+	10.0670i	−0.179406	+	0.457120i
$486$	−4.74645	+	63.3369i	−0.215303	+	2.87302i
$487$	−26.5496	+	4.00171i	−1.20308	+	0.181335i	−0.719831	−	0.694149i	$-0.755781\pi$
$487$	−26.5496	+	4.00171i	−1.20308	+	0.181335i	−0.483247	+	0.875484i	$0.660543\pi$
$488$	−7.22135	−	6.70043i	−0.326895	−	0.303314i
$489$	−27.2582	−	13.1269i	−1.23266	−	0.593617i
$490$	3.27366	−	2.23195i	0.147889	−	0.100829i
$491$	−8.00791	−	20.4038i	−0.361392	−	0.920811i	−0.989740	−	0.142879i	$-0.954364\pi$
$491$	−8.00791	−	20.4038i	−0.361392	−	0.920811i	0.628348	−	0.777932i	$-0.283731\pi$
$492$	−35.3758	+	10.9120i	−1.59486	+	0.491950i
$493$	−1.35797	+	1.26001i	−0.0611599	+	0.0567481i
$494$	1.72767	−	2.16643i	0.0777316	−	0.0974723i
$495$	6.88859	−	8.63802i	0.309619	−	0.388250i
$496$	−3.59530	+	3.33595i	−0.161434	+	0.149789i
$497$	11.9988	−	3.70115i	0.538221	−	0.166019i
$498$	6.81221	+	17.3572i	0.305263	+	0.777796i
$499$	−29.5387	+	20.1392i	−1.32233	+	0.901552i	−0.998999	−	0.0447321i	$-0.985757\pi$
$499$	−29.5387	+	20.1392i	−1.32233	+	0.901552i	−0.323335	+	0.946284i	$0.604804\pi$
$500$	−0.900969	−	0.433884i	−0.0402926	−	0.0194039i
$501$	−25.8555	−	23.9904i	−1.15514	−	1.07181i
$502$	−9.99188	+	1.50603i	−0.445960	+	0.0672176i
$503$	0.802150	−	10.7039i	0.0357661	−	0.477265i	−0.950347	−	0.311192i	$-0.899272\pi$
$503$	0.802150	−	10.7039i	0.0357661	−	0.477265i	0.986113	−	0.166074i	$-0.0531090\pi$
$504$	−5.27429	+	13.4387i	−0.234936	+	0.598607i
$505$	0.189649	+	0.830906i	0.00843927	+	0.0369748i
$506$	−0.731073	−	9.75549i	−0.0325002	−	0.433684i
$507$	2.21200	+	0.682313i	0.0982386	+	0.0303026i
$508$	16.2421	−	7.82177i	0.720626	−	0.347035i
$509$	−11.4042	+	19.7527i	−0.505484	+	0.875524i	0.494496	+	0.869180i	$0.335353\pi$
$509$	−11.4042	+	19.7527i	−0.505484	+	0.875524i	−0.999980	+	0.00634416i	$0.997981\pi$
$510$	1.07527	+	1.86242i	0.0476136	+	0.0824692i
$511$	−14.8155	−	10.1010i	−0.655399	−	0.446844i
$512$	0.222521	−	0.974928i	0.00983413	−	0.0430861i
$513$	13.1415	+	1.98077i	0.580212	+	0.0874529i
$514$	14.3212	+	17.9582i	0.631679	+	0.792101i
$515$	18.4264			0.811966
$516$	−6.37577	−	21.0835i	−0.280677	−	0.928149i
$517$	−14.3458			−0.630929
$518$	−9.21543	−	11.5558i	−0.404903	−	0.507732i
$519$	−17.0049	−	2.56308i	−0.746432	−	0.112507i
$520$	0.823302	−	3.60712i	0.0361042	−	0.158183i
$521$	26.3887	+	17.9915i	1.15611	+	0.788222i	0.980554	−	0.196247i	$-0.0628756\pi$
$521$	26.3887	+	17.9915i	1.15611	+	0.788222i	0.175555	+	0.984470i	$0.443828\pi$
$522$	11.9831	+	20.7554i	0.524488	+	0.908439i
$523$	−13.2725	+	22.9887i	−0.580366	+	1.00522i	0.415069	+	0.909790i	$0.363757\pi$
$523$	−13.2725	+	22.9887i	−0.580366	+	1.00522i	−0.995436	+	0.0954341i	$0.969576\pi$
$524$	16.3140	−	7.85639i	0.712678	−	0.343208i
$525$	5.59446	+	1.72566i	0.244162	+	0.0753141i
$526$	−1.39331	−	18.5924i	−0.0607512	−	0.810668i
$527$	−0.698726	−	3.06132i	−0.0304370	−	0.133353i
$528$	1.63692	−	4.17081i	0.0712380	−	0.181511i
$529$	2.30083	−	30.7025i	0.100036	−	1.33489i
$530$	−2.89587	+	0.436482i	−0.125788	+	0.0189596i
$531$	−19.8736	−	18.4400i	−0.862442	−	0.800229i
$532$	1.17608	+	0.566372i	0.0509897	+	0.0245553i
$533$	−33.6920	+	22.9708i	−1.45936	+	0.994975i
$534$	−3.67085	−	9.35318i	−0.158853	−	0.404752i
$535$	−4.50261	+	1.38887i	−0.194665	+	0.0600462i
$536$	0.888742	−	0.824632i	0.0383878	−	0.0356187i
$537$	27.4760	−	34.4538i	1.18568	−	1.48679i
$538$	−11.1707	+	14.0076i	−0.481602	+	0.603909i
$539$	3.87421	−	3.59474i	0.166874	−	0.154836i
$540$	16.9568	−	5.23048i	0.729705	−	0.225084i
$541$	−1.18909	−	3.02976i	−0.0511232	−	0.130260i	0.903031	−	0.429576i	$-0.141337\pi$
$541$	−1.18909	−	3.02976i	−0.0511232	−	0.130260i	−0.954154	+	0.299316i	$0.903242\pi$
$542$	−13.9528	+	9.51286i	−0.599324	+	0.408612i
$543$	4.97835	+	2.39745i	0.213641	+	0.102884i
$544$	0.469322	+	0.435467i	0.0201220	+	0.0186705i
$545$	1.88942	−	0.284785i	0.0809341	−	0.0121988i
$546$	−1.61875	+	21.6007i	−0.0692759	+	0.924423i
$547$	−1.22683	+	3.12592i	−0.0524557	+	0.133655i	−0.954700	−	0.297571i	$-0.903824\pi$
$547$	−1.22683	+	3.12592i	−0.0524557	+	0.133655i	0.902244	+	0.431226i	$0.141919\pi$
$548$	−2.77091	−	12.1402i	−0.118367	−	0.518602i
$549$	−6.09762	−	81.3670i	−0.260240	−	3.47266i
$550$	−1.27463	−	0.393171i	−0.0543504	−	0.0167649i
$551$	1.95242	−	0.940235i	0.0831758	−	0.0400553i
$552$	12.3176	−	21.3346i	0.524270	−	0.908063i
$553$	−3.16522	−	5.48232i	−0.134599	−	0.233132i
$554$	−10.3423	−	7.05126i	−0.439402	−	0.299579i
$555$	−6.33843	+	27.7705i	−0.269052	+	1.17879i
$556$	17.2307	+	2.59711i	0.730745	+	0.110142i
$557$	−9.68273	−	12.1418i	−0.410270	−	0.514463i	0.533169	−	0.846009i	$-0.321001\pi$
$557$	−9.68273	−	12.1418i	−0.410270	−	0.514463i	−0.943439	+	0.331546i	$0.892430\pi$
$558$	−40.6239			−1.71975
$559$	−13.5559	−	20.1214i	−0.573355	−	0.851044i
$560$	1.74295			0.0736531
$561$	1.78853	+	2.24274i	0.0755117	+	0.0946886i
$562$	−19.0198	−	2.86677i	−0.802302	−	0.120928i
$563$	−9.61803	+	42.1393i	−0.405351	+	1.77596i	0.199786	+	0.979840i	$0.435975\pi$
$563$	−9.61803	+	42.1393i	−0.405351	+	1.77596i	−0.605137	+	0.796121i	$0.706882\pi$
$564$	−29.8484	−	20.3503i	−1.25684	−	0.856902i
$565$	−10.3584	−	17.9412i	−0.435780	−	0.754793i
$566$	−11.3676	+	19.6892i	−0.477815	+	0.827600i
$567$	−54.5810	+	26.2848i	−2.29219	+	1.10386i
$568$	−6.88421	−	2.12350i	−0.288855	−	0.0890999i
$569$	2.17754	+	29.0572i	0.0912870	+	1.21814i	0.835231	+	0.549899i	$0.185334\pi$
$569$	2.17754	+	29.0572i	0.0912870	+	1.21814i	−0.743944	+	0.668242i	$0.767047\pi$
$570$	−0.559789	−	2.45259i	−0.0234470	−	0.102728i
$571$	1.97120	−	5.02253i	0.0824920	−	0.210186i	−0.883676	−	0.468098i	$-0.844939\pi$
$571$	1.97120	−	5.02253i	0.0824920	−	0.210186i	0.966168	+	0.257912i	$0.0830345\pi$
$572$	0.368811	−	4.92144i	0.0154208	−	0.205776i
$573$	20.5776	−	3.10157i	0.859640	−	0.129570i
$574$	−14.0816	−	13.0658i	−0.587755	−	0.545357i
$575$	−6.60777	−	3.18213i	−0.275563	−	0.132704i
$576$	6.84363	−	4.66591i	0.285151	−	0.194413i
$577$	11.1487	+	28.4063i	0.464125	+	1.18257i	0.951025	+	0.309113i	$0.100032\pi$
$577$	11.1487	+	28.4063i	0.464125	+	1.18257i	−0.486901	+	0.873457i	$0.661873\pi$
$578$	15.8531	−	4.89002i	0.659400	−	0.203398i
$579$	22.5423	−	20.9162i	0.936827	−	0.869248i
$580$	1.80405	−	2.26221i	0.0749092	−	0.0939331i
$581$	−6.03246	+	7.56446i	−0.250268	+	0.313827i
$582$	−26.6290	+	24.7081i	−1.10381	+	1.02418i
$583$	−3.73285	+	1.15143i	−0.154599	+	0.0476875i
$584$	3.75858	+	9.57672i	0.155531	+	0.396287i
$585$	25.3207	−	17.2633i	1.04688	−	0.713751i
$586$	17.6066	+	8.47889i	0.727322	+	0.350260i
$587$	3.64390	+	3.38104i	0.150400	+	0.139551i	0.751784	−	0.659409i	$-0.229194\pi$
$587$	3.64390	+	3.38104i	0.150400	+	0.139551i	−0.601384	+	0.798960i	$0.705384\pi$
$588$	13.1601	−	1.98357i	0.542715	−	0.0818011i
$589$	−0.274498	+	3.66292i	−0.0113105	+	0.150928i
$590$	−1.19580	+	3.04686i	−0.0492304	+	0.125437i
$591$	−0.208044	−	0.911499i	−0.00855777	−	0.0374940i
$592$	0.633719	+	8.45639i	0.0260457	+	0.347556i
$593$	−26.3825	−	8.13792i	−1.08340	−	0.334184i	−0.298881	−	0.954290i	$-0.596613\pi$
$593$	−26.3825	−	8.13792i	−1.08340	−	0.334184i	−0.784518	+	0.620106i	$0.787090\pi$
$594$	21.3260	−	10.2701i	0.875018	−	0.421386i
$595$	−0.557944	+	0.966388i	−0.0228735	+	0.0396181i
$596$	4.31247	+	7.46942i	0.176646	+	0.305959i
$597$	−74.5686	−	50.8400i	−3.05189	−	2.08074i
$598$	6.03815	−	26.4549i	0.246918	−	1.08182i
$599$	32.0926	+	4.83718i	1.31127	+	0.197642i	0.767204	−	0.641403i	$-0.221647\pi$
$599$	32.0926	+	4.83718i	1.31127	+	0.197642i	0.544063	+	0.839044i	$0.316885\pi$
$600$	−2.09430	−	2.62617i	−0.0854995	−	0.107213i
$601$	39.7238			1.62037			0.810184	−	0.586176i	$-0.199367\pi$
$601$	39.7238			1.62037			0.810184	+	0.586176i	$0.199367\pi$
$602$	7.82016	−	8.33509i	0.318726	−	0.339713i
$603$	10.0420			0.408943
$604$	−14.1298	−	17.7183i	−0.574935	−	0.720946i
$605$	9.11775	+	1.37428i	0.370689	+	0.0558724i
$606$	−0.637031	+	2.79101i	−0.0258776	+	0.113377i
$607$	17.6655	+	12.0441i	0.717021	+	0.488856i	0.866038	−	0.499978i	$-0.166659\pi$
$607$	17.6655	+	12.0441i	0.717021	+	0.488856i	−0.149017	+	0.988835i	$0.547611\pi$
$608$	−0.374467	−	0.648596i	−0.0151866	−	0.0263040i
$609$	−8.47002	+	14.6705i	−0.343222	+	0.594479i
$610$	−8.87551	+	4.27422i	−0.359359	+	0.173058i
$611$	−38.0240	−	11.7288i	−1.53829	−	0.474498i
$612$	0.396290	+	5.28812i	0.0160191	+	0.213759i
$613$	−3.43486	−	15.0491i	−0.138733	−	0.607828i	−0.995714	−	0.0924810i	$-0.970520\pi$
$613$	−3.43486	−	15.0491i	−0.138733	−	0.607828i	0.856982	−	0.515347i	$-0.172337\pi$
$614$	5.82415	−	14.8397i	0.235043	−	0.598881i
$615$	−2.76655	+	36.9170i	−0.111558	+	1.48864i
$616$	2.29894	−	0.346509i	0.0926268	−	0.0139612i
$617$	7.72111	+	7.16414i	0.310840	+	0.288417i	0.820130	−	0.572178i	$-0.193901\pi$
$617$	7.72111	+	7.16414i	0.310840	+	0.288417i	−0.509290	+	0.860595i	$0.670092\pi$
$618$	55.7649	+	26.8550i	2.24319	+	1.08027i
$619$	−23.4380	+	15.9798i	−0.942055	+	0.642282i	−0.933843	−	0.357684i	$-0.883566\pi$
$619$	−23.4380	+	15.9798i	−0.942055	+	0.642282i	−0.00821214	+	0.999966i	$0.502614\pi$
$620$	1.79184	+	4.56553i	0.0719619	+	0.183356i
$621$	124.362	−	38.3607i	4.99049	−	1.53936i
$622$	0.886949	−	0.822968i	0.0355634	−	0.0329980i
$623$	3.25067	−	4.07621i	0.130235	−	0.163310i
$624$	7.74867	−	9.71653i	0.310195	−	0.388973i
$625$	−0.733052	+	0.680173i	−0.0293221	+	0.0272069i
$626$	−18.5401	+	5.71886i	−0.741010	+	0.228571i
$627$	−1.22595	−	3.12366i	−0.0489596	−	0.124747i
$628$	−15.0724	+	10.2762i	−0.601454	+	0.410065i
$629$	−4.89156	−	2.35565i	−0.195039	−	0.0939259i
$630$	10.5828	+	9.81941i	0.421629	+	0.391214i
$631$	9.52818	−	1.43614i	0.379311	−	0.0571719i	0.0433801	−	0.999059i	$-0.486187\pi$
$631$	9.52818	−	1.43614i	0.379311	−	0.0571719i	0.335931	+	0.941887i	$0.390949\pi$
$632$	−0.271422	+	3.62187i	−0.0107966	+	0.144070i
$633$	−6.97707	+	17.7773i	−0.277314	+	0.706584i
$634$	−5.45232	−	23.8882i	−0.216539	−	0.948720i
$635$	−1.34719	−	17.9769i	−0.0534614	−	0.713393i
$636$	−9.40006	−	2.89953i	−0.372736	−	0.114974i
$637$	13.2077	−	6.36048i	0.523307	−	0.252011i
$638$	1.92979	−	3.34249i	0.0764011	−	0.132331i
$639$	−29.8360	−	51.6775i	−1.18030	−	2.04433i
$640$	−0.826239	−	0.563320i	−0.0326600	−	0.0222672i
$641$	5.20508	−	22.8050i	0.205588	−	0.900742i	−0.761874	−	0.647726i	$-0.775720\pi$
$641$	5.20508	−	22.8050i	0.205588	−	0.900742i	0.967462	−	0.253016i	$-0.0814225\pi$
$642$	−15.6507	−	2.35896i	−0.617682	−	0.0931006i
$643$	−15.4794	−	19.4106i	−0.610448	−	0.765478i	0.376517	−	0.926410i	$-0.377122\pi$
$643$	−15.4794	−	19.4106i	−0.610448	−	0.765478i	−0.986966	+	0.160932i	$0.948550\pi$
$644$	12.7829			0.503717
$645$	−21.9554	−	1.76763i	−0.864493	−	0.0696002i
$646$	0.479490			0.0188653
$647$	−0.520993	−	0.653305i	−0.0204824	−	0.0256841i	0.771485	−	0.636248i	$-0.219514\pi$
$647$	−0.520993	−	0.653305i	−0.0204824	−	0.0256841i	−0.791967	+	0.610564i	$0.790943\pi$
$648$	34.3692	+	5.18032i	1.35015	+	0.203502i
$649$	−0.971521	+	4.25651i	−0.0381355	+	0.167083i
$650$	−3.05699	−	2.08422i	−0.119905	−	0.0817498i
$651$	−14.3570	−	24.8671i	−0.562697	−	0.974619i
$652$	−4.50347	+	7.80025i	−0.176370	+	0.305481i
$653$	12.0953	−	5.82477i	0.473324	−	0.227941i	−0.181986	−	0.983301i	$-0.558252\pi$
$653$	12.0953	−	5.82477i	0.473324	−	0.227941i	0.655310	+	0.755360i	$0.272538\pi$
$654$	6.13312	+	1.89182i	0.239824	+	0.0739759i
$655$	−1.35315	−	18.0565i	−0.0528718	−	0.705526i
$656$	2.45247	+	10.7450i	0.0957528	+	0.419520i
$657$	−31.1319	+	79.3227i	−1.21457	+	3.09467i
$658$	1.40083	−	18.6928i	0.0546101	−	0.728721i
$659$	−26.5656	+	4.00413i	−1.03485	+	0.155979i	−0.644434	−	0.764660i	$-0.722907\pi$
$659$	−26.5656	+	4.00413i	−1.03485	+	0.155979i	−0.390416	+	0.920638i	$0.627669\pi$
$660$	−3.28447	−	3.04754i	−0.127848	−	0.118625i
$661$	7.64951	+	3.68381i	0.297532	+	0.143284i	0.576694	−	0.816960i	$-0.304343\pi$
$661$	7.64951	+	3.68381i	0.297532	+	0.143284i	−0.279162	+	0.960244i	$0.590057\pi$
$662$	3.63755	−	2.48004i	0.141377	−	0.0963895i
$663$	2.90692	+	7.40670i	0.112895	+	0.287653i
$664$	5.30449	−	1.63622i	0.205854	−	0.0634976i
$665$	0.956892	−	0.887866i	0.0371067	−	0.0344300i
$666$	−43.7937	+	54.9156i	−1.69697	+	2.12794i
$667$	13.2310	−	16.5912i	0.512308	−	0.642414i
$668$	−7.69737	+	7.14212i	−0.297820	+	0.276337i
$669$	−50.1959	+	15.4834i	−1.94069	+	0.598622i
$670$	−0.442934	−	1.12858i	−0.0171120	−	0.0436008i
$671$	−10.8570	+	7.40217i	−0.419129	+	0.285757i
$672$	5.27478	+	2.54020i	0.203479	+	0.0979904i
$673$	−27.5694	−	25.5807i	−1.06272	−	0.986062i	−0.0627935	−	0.998027i	$-0.520001\pi$
$673$	−27.5694	−	25.5807i	−1.06272	−	0.986062i	−0.999928	+	0.0119647i	$0.996191\pi$
$674$	−19.0062	+	2.86472i	−0.732092	+	0.110345i
$675$	1.32610	−	17.6956i	0.0510415	−	0.681102i
$676$	0.251774	−	0.641509i	0.00968361	−	0.0246734i
$677$	−3.89966	−	17.0855i	−0.149876	−	0.656650i	−0.992918	−	0.118802i	$-0.962095\pi$
$677$	−3.89966	−	17.0855i	−0.149876	−	0.656650i	0.843042	−	0.537848i	$-0.180763\pi$
$678$	−5.20028	−	69.3929i	−0.199715	−	2.66502i
$679$	−18.0119	−	5.55593i	−0.691233	−	0.213217i
$680$	0.576827	−	0.277785i	0.0221203	−	0.0106526i
$681$	5.31074	−	9.19847i	0.203508	−	0.352486i
$682$	3.27107	+	5.66567i	0.125256	+	0.216950i
$683$	21.7526	+	14.8306i	0.832339	+	0.567479i	0.902812	−	0.430035i	$-0.141499\pi$
$683$	21.7526	+	14.8306i	0.832339	+	0.567479i	−0.0704736	+	0.997514i	$0.522451\pi$
$684$	1.38037	−	6.04779i	0.0527797	−	0.231243i
$685$	−12.3133	−	1.85593i	−0.470466	−	0.0709113i
$686$	11.9127	+	14.9380i	0.454828	+	0.570336i
$687$	92.6191			3.53364
$688$	−6.40101	+	1.42375i	−0.244036	+	0.0542799i
$689$	−10.8354			−0.412796
$690$	−15.3598	−	19.2605i	−0.584736	−	0.733236i
$691$	14.1828	+	2.13772i	0.539540	+	0.0813225i	0.413158	−	0.910659i	$-0.364426\pi$
$691$	14.1828	+	2.13772i	0.539540	+	0.0813225i	0.126381	+	0.991982i	$0.459664\pi$
$692$	−1.13923	+	4.99131i	−0.0433072	+	0.189741i
$693$	15.9108	+	10.8478i	0.604401	+	0.412074i
$694$	−0.0810105	−	0.140314i	−0.00307512	−	0.00532626i
$695$	8.71267	−	15.0908i	0.330490	−	0.572426i
$696$	8.75667	−	4.21699i	0.331921	−	0.159845i
$697$	−6.74268	−	2.07984i	−0.255397	−	0.0787796i
$698$	0.579228	+	7.72926i	0.0219241	+	0.292557i
$699$	−7.54169	−	33.0423i	−0.285253	−	1.24977i
$700$	0.636771	−	1.62247i	0.0240677	−	0.0613235i
$701$	0.600189	−	8.00897i	0.0226688	−	0.302495i	−0.974333	−	0.225113i	$-0.927725\pi$
$701$	0.600189	−	8.00897i	0.0226688	−	0.302495i	0.997002	−	0.0773817i	$-0.0246560\pi$
$702$	64.9218	−	9.78538i	2.45031	−	0.369325i
$703$	4.65564	+	4.31980i	0.175591	+	0.162924i
$704$	−1.20179	−	0.578753i	−0.0452943	−	0.0218126i
$705$	−29.8484	+	20.3503i	−1.12416	+	0.766436i
$706$	9.76394	+	24.8781i	0.367471	+	0.936301i
$707$	−1.41948	+	0.437851i	−0.0533849	+	0.0164671i
$708$	−8.05946	+	7.47808i	−0.302893	+	0.281044i
$709$	0.601207	−	0.753890i	0.0225788	−	0.0283129i	−0.770414	−	0.637544i	$-0.779950\pi$
$709$	0.601207	−	0.753890i	0.0225788	−	0.0283129i	0.792993	+	0.609231i	$0.208522\pi$
$710$	−4.49179	+	5.63253i	−0.168574	+	0.211385i
$711$	−22.0529	+	20.4621i	−0.827047	+	0.767387i
$712$	−2.85840	+	0.881698i	−0.107123	+	0.0330430i
$713$	13.1415	+	33.4839i	0.492152	+	1.25398i
$714$	−3.09697	+	2.11148i	−0.115901	+	0.0790200i
$715$	−4.44650	−	2.14132i	−0.166290	−	0.0800809i
$716$	−9.61720	−	8.92345i	−0.359411	−	0.333485i
$717$	62.3018	−	9.39049i	2.32670	−	0.350694i
$718$	2.40162	−	32.0474i	0.0896278	−	1.19600i
$719$	−2.80091	+	7.13659i	−0.104456	+	0.266150i	−0.973541	−	0.228514i	$-0.926613\pi$
$719$	−2.80091	+	7.13659i	−0.104456	+	0.266150i	0.869085	+	0.494664i	$0.164709\pi$
$720$	−1.84311	−	8.07521i	−0.0686888	−	0.300945i
$721$	2.40006	+	32.0266i	0.0893828	+	1.19273i
$722$	17.6199	+	5.43502i	0.655745	+	0.202270i
$723$	−7.55386	+	3.63775i	−0.280931	+	0.135289i
$724$	0.822500	−	1.42461i	0.0305680	−	0.0529453i
$725$	−1.44674	−	2.50582i	−0.0537305	−	0.0930639i
$726$	25.5906	+	17.4474i	0.949758	+	0.647534i
$727$	−1.94808	+	8.53509i	−0.0722503	+	0.316549i	−0.998120	−	0.0612944i	$-0.980477\pi$
$727$	−1.94808	+	8.53509i	−0.0722503	+	0.316549i	0.925869	+	0.377844i	$0.123334\pi$
$728$	6.37669	+	0.961131i	0.236336	+	0.0356219i
$729$	68.0059	+	85.2767i	2.51874	+	3.15840i
$730$	10.2879			0.380771
$731$	1.25965	−	4.00484i	0.0465900	−	0.148124i
$732$	−33.0897			−1.22303
$733$	−27.8008	−	34.8611i	−1.02684	−	1.28762i	−0.957007	−	0.290064i	$-0.906323\pi$
$733$	−27.8008	−	34.8611i	−1.02684	−	1.28762i	−0.0698376	−	0.997558i	$-0.522248\pi$
$734$	−2.52127	−	0.380020i	−0.0930617	−	0.0140268i
$735$	2.96148	−	12.9751i	0.109236	−	0.478594i
$736$	−6.05969	−	4.13143i	−0.223363	−	0.152286i
$737$	−0.808595	−	1.40053i	−0.0297850	−	0.0515891i
$738$	−45.6440	+	79.0577i	−1.68018	+	2.91015i
$739$	−8.85830	+	4.26593i	−0.325858	+	0.156925i	−0.589659	−	0.807652i	$-0.700738\pi$
$739$	−8.85830	+	4.26593i	−0.325858	+	0.156925i	0.263801	+	0.964577i	$0.415024\pi$
$740$	8.10336	+	2.49956i	0.297885	+	0.0918855i
$741$	−0.695564	−	9.28165i	−0.0255522	−	0.340970i
$742$	−1.13583	−	4.97639i	−0.0416976	−	0.182689i
$743$	5.10967	−	13.0192i	0.187456	−	0.477629i	−0.805991	−	0.591928i	$-0.798367\pi$
$743$	5.10967	−	13.0192i	0.187456	−	0.477629i	0.993446	+	0.114299i	$0.0364621\pi$
$744$	−1.23113	+	16.4284i	−0.0451356	+	0.602293i
$745$	8.52861	−	1.28548i	0.312464	−	0.0470964i
$746$	−7.96190	−	7.38756i	−0.291506	−	0.270478i
$747$	41.4258	+	19.9496i	1.51569	+	0.729918i
$748$	0.705605	−	0.481074i	0.0257995	−	0.0175898i
$749$	−3.00043	−	7.64498i	−0.109634	−	0.279342i
$750$	−3.20977	+	0.990082i	−0.117204	+	0.0361527i
$751$	−1.44766	+	1.34323i	−0.0528258	+	0.0490152i	−0.706144	−	0.708068i	$-0.749567\pi$
$751$	−1.44766	+	1.34323i	−0.0528258	+	0.0490152i	0.653318	+	0.757083i	$0.273376\pi$
$752$	−6.70556	+	8.40850i	−0.244527	+	0.306627i
$753$	−21.1624	+	26.5368i	−0.771200	+	0.967055i
$754$	7.84770	−	7.28160i	0.285796	−	0.265180i
$755$	−21.6557	+	6.67989i	−0.788131	+	0.243106i
$756$	11.2996	+	28.7909i	0.410963	+	1.04712i
$757$	38.0928	−	25.9712i	1.38451	−	0.943940i	0.384725	−	0.923031i	$-0.374296\pi$
$757$	38.0928	−	25.9712i	1.38451	−	0.943940i	0.999781	−	0.0209092i	$-0.00665608\pi$
$758$	5.83062	+	2.80788i	0.211778	+	0.101987i
$759$	−24.0885	−	22.3509i	−0.874357	−	0.811285i
$760$	−0.740569	+	0.111623i	−0.0268633	+	0.00404898i
$761$	0.259717	−	3.46569i	0.00941475	−	0.125631i	−0.990516	−	0.137397i	$-0.956126\pi$
$761$	0.259717	−	3.46569i	0.00941475	−	0.125631i	0.999931	+	0.0117661i	$0.00374536\pi$
$762$	22.1228	−	56.3680i	0.801425	−	2.04200i
$763$	0.741077	+	3.24687i	0.0268288	+	0.117545i
$764$	−0.462975	−	6.17797i	−0.0167499	−	0.223511i
$765$	5.06735	+	1.56307i	0.183210	+	0.0565129i
$766$	−6.07896	+	2.92747i	−0.219642	+	0.105774i
$767$	−6.05507	+	10.4877i	−0.218636	+	0.378689i
$768$	−1.67950	−	2.90898i	−0.0606037	−	0.104969i
$769$	14.5758	+	9.93763i	0.525618	+	0.358360i	0.796872	−	0.604148i	$-0.206486\pi$
$769$	14.5758	+	9.93763i	0.525618	+	0.358360i	−0.271255	+	0.962508i	$0.587439\pi$
$770$	0.517340	−	2.26661i	0.0186436	−	0.0816831i
$771$	76.2923	+	11.4992i	2.74760	+	0.414134i
$772$	−5.70799	−	7.15760i	−0.205435	−	0.257608i
$773$	7.72503			0.277850			0.138925	−	0.990303i	$-0.455635\pi$
$773$	7.72503			0.277850			0.138925	+	0.990303i	$0.455635\pi$
$774$	−46.8866	−	27.4172i	−1.68530	−	0.985492i
$775$	4.90456			0.176177
$776$	6.74279	+	8.45520i	0.242052	+	0.303524i
$777$	−49.0928	−	7.39955i	−1.76120	−	0.265457i
$778$	1.07030	−	4.68927i	0.0383720	−	0.168119i
$779$	6.81995	+	4.64976i	0.244350	+	0.166595i
$780$	−6.21395	−	10.7629i	−0.222495	−	0.385373i
$781$	−4.80486	+	8.32225i	−0.171931	+	0.297794i
$782$	4.23049	−	2.03730i	0.151282	−	0.0728536i
$783$	49.0641	+	15.1343i	1.75341	+	0.540854i
$784$	−0.296090	−	3.95105i	−0.0105746	−	0.141109i
$785$	4.05927	+	17.7848i	0.144882	+	0.634767i
$786$	22.2207	−	56.6174i	0.792586	−	2.01948i
$787$	2.14354	−	28.6036i	0.0764091	−	1.01961i	−0.818834	−	0.574030i	$-0.805379\pi$
$787$	2.14354	−	28.6036i	0.0764091	−	1.01961i	0.895243	−	0.445578i	$-0.147002\pi$
$788$	−0.275230	+	0.0414842i	−0.00980466	+	0.00147781i
$789$	−45.9089	−	42.5972i	−1.63440	−	1.51650i
$790$	3.27234	+	1.57588i	0.116425	+	0.0560672i
$791$	29.8340	−	20.3405i	1.06078	−	0.723224i
$792$	−4.03645	−	10.2847i	−0.143429	−	0.365451i
$793$	−34.8286	+	10.7432i	−1.23680	+	0.381502i
$794$	4.34973	−	4.03596i	0.154366	−	0.143231i
$795$	−6.13333	+	7.69095i	−0.217527	+	0.272770i
$796$	−16.7521	+	21.0065i	−0.593763	+	0.744556i
$797$	−6.29793	+	5.84362i	−0.223084	+	0.206992i	−0.783795	−	0.621020i	$-0.786718\pi$
$797$	−6.29793	+	5.84362i	−0.223084	+	0.206992i	0.560711	+	0.828012i	$0.310528\pi$
$798$	4.18988	−	1.29241i	0.148320	−	0.0457507i
$799$	−2.51559	−	6.40962i	−0.0889952	−	0.226756i
$800$	−0.826239	+	0.563320i	−0.0292120	+	0.0199164i
$801$	−22.3228	−	10.7501i	−0.788739	−	0.379837i
$802$	1.05424	+	0.978196i	0.0372267	+	0.0345413i
$803$	13.5696	−	2.04529i	0.478862	−	0.0721768i
$804$	0.304331	−	4.06102i	0.0107329	−	0.143221i
$805$	4.67012	−	11.8993i	0.164600	−	0.419394i
$806$	4.03793	+	17.6913i	0.142230	+	0.623151i
$807$	4.49733	+	60.0128i	0.158314	+	2.11255i
$808$	0.814410	+	0.251212i	0.0286509	+	0.00883762i
$809$	−37.1949	+	17.9121i	−1.30770	+	0.629757i	−0.952359	−	0.304978i	$-0.901351\pi$
$809$	−37.1949	+	17.9121i	−1.30770	+	0.629757i	−0.355345	+	0.934735i	$0.615637\pi$
$810$	17.3787	−	30.1008i	0.610625	−	1.05763i
$811$	10.4005	+	18.0142i	0.365211	+	0.632563i	0.988810	−	0.149181i	$-0.0476637\pi$
$811$	10.4005	+	18.0142i	0.365211	+	0.632563i	−0.623599	+	0.781744i	$0.714330\pi$
$812$	4.16687	+	2.84092i	0.146228	+	0.0996969i
$813$	−12.6222	+	55.3017i	−0.442681	+	1.93951i
$814$	11.1852	+	1.68590i	0.392041	+	0.0590906i
$815$	5.61574	+	7.04192i	0.196711	+	0.246668i
$816$	2.15053			0.0752837
$817$	−2.78894	+	4.04235i	−0.0975726	+	0.141424i
$818$	−21.2075			−0.741503
$819$	33.3030	+	41.7607i	1.16370	+	1.45924i
$820$	10.8982	+	1.64264i	0.380581	+	0.0573634i
$821$	2.48888	−	10.9045i	0.0868627	−	0.380570i	−0.912746	−	0.408526i	$-0.866043\pi$
$821$	2.48888	−	10.9045i	0.0868627	−	0.380570i	0.999609	+	0.0279563i	$0.00889992\pi$
$822$	−34.5595	−	23.5622i	−1.20540	−	0.821828i
$823$	−4.52247	−	7.83314i	−0.157643	−	0.273046i	0.776375	−	0.630271i	$-0.217056\pi$
$823$	−4.52247	−	7.83314i	−0.157643	−	0.273046i	−0.934018	+	0.357225i	$0.883723\pi$
$824$	9.21322	−	15.9578i	0.320958	−	0.555915i
$825$	−4.03682	+	1.94403i	−0.140544	+	0.0676825i
$826$	−5.45142	−	1.68154i	−0.189679	−	0.0585083i
$827$	1.54497	+	20.6161i	0.0537237	+	0.716893i	0.957416	+	0.288711i	$0.0932268\pi$
$827$	1.54497	+	20.6161i	0.0537237	+	0.716893i	−0.903692	+	0.428182i	$0.859154\pi$
$828$	−13.5175	−	59.2241i	−0.469766	−	2.05818i
$829$	10.6419	−	27.1152i	0.369609	−	0.941748i	−0.618192	−	0.786027i	$-0.712135\pi$
$829$	10.6419	−	27.1152i	0.369609	−	0.941748i	0.987801	−	0.155721i	$-0.0497702\pi$
$830$	0.414835	−	5.53559i	0.0143991	−	0.192143i
$831$	−41.5761	+	6.26658i	−1.44226	+	0.217385i
$832$	−2.71221	−	2.51656i	−0.0940289	−	0.0872460i
$833$	2.28546	+	1.10062i	0.0791866	+	0.0381343i
$834$	48.3612	−	32.9721i	1.67461	−	1.14173i
$835$	3.83624	+	9.77459i	0.132759	+	0.338264i
$836$	−0.954613	+	0.294459i	−0.0330160	+	0.0101841i
$837$	−63.7992	+	59.1970i	−2.20522	+	2.04615i
$838$	−5.87884	+	7.37184i	−0.203081	+	0.254656i
$839$	−1.01371	+	1.27115i	−0.0349972	+	0.0438851i	−0.799022	−	0.601302i	$-0.794649\pi$
$839$	−1.01371	+	1.27115i	−0.0349972	+	0.0438851i	0.764025	+	0.645187i	$0.223220\pi$
$840$	4.29170	−	3.98212i	0.148078	−	0.137396i
$841$	−19.7114	+	6.08015i	−0.679703	+	0.209660i
$842$	−3.03486	−	7.73269i	−0.104588	−	0.266486i
$843$	−53.3825	+	36.3956i	−1.83859	+	1.25353i
$844$	5.12241	+	2.46682i	0.176321	+	0.0849116i
$845$	−0.505181	−	0.468739i	−0.0173788	−	0.0161251i
$846$	−88.0863	+	13.2769i	−3.02847	+	0.456469i
$847$	−1.20101	+	16.0263i	−0.0412671	+	0.550672i
$848$	−1.06993	+	2.72614i	−0.0367415	+	0.0936159i
$849$	16.9933	+	74.4527i	0.583210	+	2.55521i
$850$	−0.0478445	−	0.638440i	−0.00164105	−	0.0218983i
$851$	59.4306	+	18.3319i	2.03725	+	0.628410i
$852$	−21.8027	+	10.4996i	−0.746947	+	0.359711i
$853$	10.5058	−	18.1966i	0.359712	−	0.623039i	−0.628201	−	0.778051i	$-0.716208\pi$
$853$	10.5058	−	18.1966i	0.359712	−	0.623039i	0.987913	+	0.155012i	$0.0495417\pi$
$854$	−8.58496	−	14.8696i	−0.293771	−	0.508827i
$855$	−5.12543	−	3.49446i	−0.175286	−	0.119508i
$856$	−1.04851	+	4.59381i	−0.0358373	+	0.157013i
$857$	−33.8526	−	5.10245i	−1.15638	−	0.174297i	−0.457283	−	0.889321i	$-0.651177\pi$
$857$	−33.8526	−	5.10245i	−1.15638	−	0.174297i	−0.699099	+	0.715025i	$0.746415\pi$
$858$	−10.3359	−	12.9608i	−0.352861	−	0.442474i
$859$	−42.6433			−1.45497			−0.727486	−	0.686123i	$-0.759311\pi$
$859$	−42.6433			−1.45497			−0.727486	+	0.686123i	$0.759311\pi$
$860$	−1.01322	+	6.47869i	−0.0345506	+	0.220921i
$861$	−64.5249			−2.19900
$862$	−15.7268	−	19.7208i	−0.535658	−	0.671694i
$863$	55.2658	+	8.32997i	1.88127	+	0.283556i	0.986598	−	0.163171i	$-0.0521722\pi$
$863$	55.2658	+	8.32997i	1.88127	+	0.283556i	0.894671	+	0.446727i	$0.147410\pi$
$864$	3.94867	−	17.3003i	0.134337	−	0.588567i
$865$	4.23007	+	2.88401i	0.143827	+	0.0980594i
$866$	−0.0875659	−	0.151669i	−0.00297561	−	0.00515391i
$867$	27.8631	−	48.2603i	0.946280	−	1.63900i
$868$	−7.70185	+	3.70901i	−0.261418	+	0.125892i
$869$	4.62949	+	1.42801i	0.157045	+	0.0484419i
$870$	−0.726315	−	9.69200i	−0.0246244	−	0.328590i
$871$	−0.998159	−	4.37322i	−0.0338213	−	0.148181i
$872$	0.698081	−	1.77868i	0.0236400	−	0.0602338i
$873$	−6.69402	+	89.3255i	−0.226558	+	3.02321i
$874$	−5.43138	+	0.818649i	−0.183719	+	0.0276912i
$875$	−1.27767	−	1.18551i	−0.0431932	−	0.0400774i
$876$	31.1348	+	14.9937i	1.05195	+	0.506590i
$877$	−27.1776	+	18.5294i	−0.917723	+	0.625693i	−0.927324	−	0.374261i	$-0.877897\pi$
$877$	−27.1776	+	18.5294i	−0.917723	+	0.625693i	0.00960012	+	0.999954i	$0.496944\pi$
$878$	−6.81109	−	17.3544i	−0.229863	−	0.585682i
$879$	62.7248	−	19.3480i	2.11566	−	0.652593i
$880$	−0.977811	+	0.907276i	−0.0329620	+	0.0305843i
$881$	−18.5761	+	23.2937i	−0.625846	+	0.784786i	−0.989154	−	0.146883i	$-0.953076\pi$
$881$	−18.5761	+	23.2937i	−0.625846	+	0.784786i	0.363308	+	0.931669i	$0.381647\pi$
$882$	20.4616	−	25.6580i	0.688977	−	0.863949i
$883$	−3.65849	+	3.39458i	−0.123118	+	0.114237i	−0.739329	−	0.673344i	$-0.764857\pi$
$883$	−3.65849	+	3.39458i	−0.123118	+	0.114237i	0.616211	+	0.787581i	$0.288667\pi$
$884$	2.26354	−	0.698209i	0.0761311	−	0.0234833i
$885$	4.01670	+	10.2344i	0.135020	+	0.344025i
$886$	20.8673	−	14.2271i	0.701049	−	0.477967i
$887$	−47.6636	−	22.9536i	−1.60039	−	0.770706i	−0.600798	−	0.799401i	$-0.705151\pi$
$887$	−47.6636	−	22.9536i	−1.60039	−	0.770706i	−0.999588	+	0.0286950i	$0.990865\pi$
$888$	20.8807	+	19.3745i	0.700712	+	0.650165i
$889$	31.0698	−	4.68302i	1.04205	−	0.157063i
$890$	−0.223539	+	2.98293i	−0.00749306	+	0.0999879i
$891$	16.9381	−	43.1577i	0.567449	−	1.44584i
$892$	3.47989	+	15.2464i	0.116515	+	0.510487i
$893$	0.601928	+	8.03217i	0.0201427	+	0.268786i
$894$	27.6841	+	8.53940i	0.925894	+	0.285600i
$895$	−11.8202	+	5.69229i	−0.395105	+	0.190272i
$896$	0.871475	−	1.50944i	0.0291139	−	0.0504268i
$897$	−45.5736	−	78.9357i	−1.52166	−	2.63559i
$898$	−5.72167	−	3.90097i	−0.190935	−	0.130177i
$899$	−3.15784	+	13.8354i	−0.105320	+	0.461437i
$900$	−8.19036	−	1.23450i	−0.273012	−	0.0411499i
$901$	−1.16902	−	1.46591i	−0.0389457	−	0.0488364i
$902$	14.7012			0.489496
$903$	0.212563	−	38.3904i	0.00707365	−	1.27755i
$904$	−20.7167			−0.689028
$905$	−1.02564	−	1.28611i	−0.0340934	−	0.0427518i
$906$	−75.2731	−	11.3456i	−2.50078	−	0.376932i
$907$	−3.73907	+	16.3820i	−0.124154	+	0.543954i	0.874146	+	0.485664i	$0.161422\pi$
$907$	−3.73907	+	16.3820i	−0.124154	+	0.543954i	−0.998300	+	0.0582902i	$0.981435\pi$
$908$	−2.61265	−	1.78127i	−0.0867037	−	0.0591136i
$909$	3.52964	+	6.11352i	0.117071	+	0.202773i
$910$	3.22436	−	5.58475i	0.106886	−	0.185133i
$911$	0.991853	−	0.477651i	0.0328616	−	0.0158253i	−0.417381	−	0.908732i	$-0.637052\pi$
$911$	0.991853	−	0.477651i	0.0328616	−	0.0158253i	0.450242	+	0.892906i	$0.351338\pi$
$912$	−2.40390	−	0.741506i	−0.0796012	−	0.0245537i
$913$	−0.553344	−	7.38387i	−0.0183130	−	0.244370i
$914$	5.14590	+	22.5457i	0.170211	+	0.745744i
$915$	−12.0890	+	30.8024i	−0.399651	+	1.01830i
$916$	2.06057	−	27.4963i	0.0680830	−	0.908504i
$917$	31.2073	−	4.70374i	1.03056	−	0.155331i
$918$	8.32820	+	7.72744i	0.274871	+	0.255043i
$919$	13.2843	+	6.39736i	0.438207	+	0.211029i	0.639962	−	0.768407i	$-0.278950\pi$
$919$	13.2843	+	6.39736i	0.438207	+	0.211029i	−0.201755	+	0.979436i	$0.564664\pi$
$920$	−6.05969	+	4.13143i	−0.199782	+	0.136209i
$921$	−19.5633	−	49.8465i	−0.644633	−	1.64250i
$922$	2.15677	−	0.665276i	0.0710295	−	0.0219097i
$923$	−19.5395	+	18.1300i	−0.643150	+	0.596756i
$924$	4.86905	−	6.10560i	0.160180	−	0.200859i
$925$	5.28726	−	6.63001i	0.173844	−	0.217994i
$926$	−3.42872	+	3.18138i	−0.112675	+	0.104547i
$927$	145.843	−	44.9867i	4.79012	−	1.47756i
$928$	−1.05710	−	2.69346i	−0.0347012	−	0.0884171i
$929$	11.4827	−	7.82877i	0.376735	−	0.256854i	−0.360118	−	0.932907i	$-0.617263\pi$
$929$	11.4827	−	7.82877i	0.376735	−	0.256854i	0.736853	+	0.676053i	$0.236311\pi$
$930$	14.8429	+	7.14798i	0.486719	+	0.234392i
$931$	−2.17524	−	2.01832i	−0.0712905	−	0.0661479i
$932$	−9.97723	+	1.50382i	−0.326815	+	0.0492594i
$933$	0.303717	−	4.05282i	0.00994325	−	0.132683i
$934$	−5.43437	+	13.8466i	−0.177818	+	0.453073i
$935$	−0.190032	−	0.832585i	−0.00621472	−	0.0272285i
$936$	−2.29015	−	30.5600i	−0.0748560	−	0.998885i
$937$	35.9881	+	11.1009i	1.17568	+	0.362650i	0.820224	−	0.572043i	$-0.193849\pi$
$937$	35.9881	+	11.1009i	1.17568	+	0.362650i	0.355457	+	0.934692i	$0.384325\pi$
$938$	1.90386	−	0.916852i	0.0621633	−	0.0299363i
$939$	−32.5857	+	56.4402i	−1.06340	+	1.84185i
$940$	5.37744	+	9.31400i	0.175393	+	0.303789i
$941$	−12.8454	−	8.75783i	−0.418747	−	0.285497i	0.335560	−	0.942019i	$-0.391075\pi$
$941$	−12.8454	−	8.75783i	−0.418747	−	0.285497i	−0.754307	+	0.656522i	$0.772027\pi$
$942$	−13.6351	+	59.7392i	−0.444255	+	1.94641i
$943$	79.9281	+	12.0472i	2.60282	+	0.392311i
$944$	2.04075	+	2.55902i	0.0664209	+	0.0832891i
$945$	30.9289			1.00612
$946$	−0.0484298	+	8.74677i	−0.00157459	+	0.284382i
$947$	38.9613			1.26607			0.633035	−	0.774123i	$-0.281809\pi$
$947$	38.9613			1.26607			0.633035	+	0.774123i	$0.281809\pi$
$948$	7.60656	+	9.53833i	0.247050	+	0.309790i
$949$	37.6388	+	5.67314i	1.22181	+	0.184158i
$950$	−0.166653	+	0.730156i	−0.00540695	+	0.0236894i
$951$	−68.0026	−	46.3634i	−2.20514	−	1.50344i
$952$	0.557944	+	0.966388i	0.0180831	+	0.0313208i
$953$	25.5902	−	44.3236i	0.828949	−	1.43578i	−0.0699139	−	0.997553i	$-0.522272\pi$
$953$	25.5902	−	44.3236i	0.828949	−	1.43578i	0.898863	−	0.438229i	$-0.144394\pi$
$954$	−21.8548	+	10.5247i	−0.707577	+	0.340751i
$955$	−5.92006	−	1.82610i	−0.191569	−	0.0590911i
$956$	−1.40173	−	18.7048i	−0.0453352	−	0.604956i
$957$	−2.88483	−	12.6393i	−0.0932534	−	0.408570i
$958$	1.37187	−	3.49548i	0.0443233	−	0.112934i
$959$	1.62193	−	21.6431i	0.0523748	−	0.698894i
$960$	−3.32148	+	0.500633i	−0.107200	+	0.0161579i
$961$	5.09125	+	4.72399i	0.164234	+	0.152387i
$962$	28.2683	+	13.6133i	0.911406	+	0.438910i
$963$	−32.2469	+	21.9855i	−1.03914	+	0.708474i
$964$	0.911902	+	2.32349i	0.0293704	+	0.0748345i
$965$	−8.74818	+	2.69846i	−0.281614	+	0.0868664i
$966$	31.4756	−	29.2051i	1.01271	−	0.939659i
$967$	26.5103	−	33.2429i	0.852515	−	1.06902i	−0.144320	−	0.989531i	$-0.546100\pi$
$967$	26.5103	−	33.2429i	0.852515	−	1.06902i	0.996836	−	0.0794894i	$-0.0253290\pi$
$968$	5.74904	−	7.20906i	0.184781	−	0.231708i
$969$	1.18066	−	1.09549i	0.0379282	−	0.0351922i
$970$	10.3341	−	3.18766i	0.331809	−	0.102350i
$971$	−0.0573652	−	0.146164i	−0.00184094	−	0.00469063i	0.929950	−	0.367685i	$-0.119850\pi$
$971$	−0.0573652	−	0.146164i	−0.00184094	−	0.00469063i	−0.931791	+	0.362995i	$0.881754\pi$
$972$	52.4782	−	35.7790i	1.68324	−	1.14761i
$973$	27.3638	+	13.1777i	0.877242	+	0.422458i
$974$	19.6821	+	18.2623i	0.630655	+	0.585162i
$975$	−12.2891	+	1.85228i	−0.393566	+	0.0593206i
$976$	−0.736172	+	9.82353i	−0.0235643	+	0.314443i
$977$	−7.80859	+	19.8960i	−0.249819	+	0.636528i	−0.999686	−	0.0250604i	$-0.992022\pi$
$977$	−7.80859	+	19.8960i	−0.249819	+	0.636528i	0.749867	+	0.661589i	$0.230117\pi$
$978$	6.73222	+	29.4958i	0.215273	+	0.943172i
$979$	0.298177	+	3.97890i	0.00952978	+	0.127166i
$980$	−3.78610	−	1.16786i	−0.120943	−	0.0373058i
$981$	14.2593	−	6.86692i	0.455265	−	0.219244i
$982$	−10.9595	+	18.9824i	−0.349732	+	0.605753i
$983$	−13.3448	−	23.1139i	−0.425634	−	0.737220i	0.570845	−	0.821058i	$-0.306616\pi$
$983$	−13.3448	−	23.1139i	−0.425634	−	0.737220i	−0.996479	+	0.0838379i	$0.973282\pi$
$984$	30.5878	+	20.8544i	0.975103	+	0.664814i
$985$	−0.0619362	+	0.271360i	−0.00197345	+	0.00864625i
$986$	1.83180	+	0.276099i	0.0583363	+	0.00879279i
$987$	−39.2581	−	49.2281i	−1.24960	−	1.56695i
$988$	−2.77097			−0.0881562
$989$	−7.43104	+	47.5151i	−0.236293	+	1.51089i
$990$	−11.0484			−0.351143
$991$	−0.798960	−	1.00186i	−0.0253798	−	0.0318253i	0.768980	−	0.639273i	$-0.220765\pi$
$991$	−0.798960	−	1.00186i	−0.0253798	−	0.0318253i	−0.794359	+	0.607448i	$0.792193\pi$
$992$	4.84978	+	0.730987i	0.153981	+	0.0232089i
$993$	3.29067	−	14.4174i	0.104426	−	0.457521i
$994$	−10.3748	−	7.07343i	−0.329069	−	0.224356i
$995$	13.4342	+	23.2686i	0.425892	+	0.737666i
$996$	9.32309	−	16.1481i	0.295413	−	0.511671i
$997$	−18.2669	+	8.79686i	−0.578517	+	0.278599i	−0.700173	−	0.713973i	$-0.746894\pi$
$997$	−18.2669	+	8.79686i	−0.578517	+	0.278599i	0.121656	+	0.992572i	$0.461180\pi$
$998$	34.1625	+	10.5377i	1.08140	+	0.333566i
$999$	11.2455	+	150.060i	0.355790	+	4.74769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.181.1	✓	48
43.24	even	21	inner	430.2.q.c.411.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.181.1	✓	48	1.1	even	1	trivial
430.2.q.c.411.1	yes	48	43.24	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.623490 - 0.781831i) q^{2} +(-3.32148 - 0.500633i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.826239 + 0.563320i) q^{5} +(1.67950 + 2.90898i) q^{6} +(-0.871475 + 1.50944i) q^{7} +(0.900969 - 0.433884i) q^{8} +(7.91489 + 2.44142i) q^{9} +O(q^{10})\)	\(q+(-0.623490 - 0.781831i) q^{2} +(-3.32148 - 0.500633i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.826239 + 0.563320i) q^{5} +(1.67950 + 2.90898i) q^{6} +(-0.871475 + 1.50944i) q^{7} +(0.900969 - 0.433884i) q^{8} +(7.91489 + 2.44142i) q^{9} +(-0.0747301 - 0.997204i) q^{10} +(-0.296819 - 1.30045i) q^{11} +(1.22718 - 3.12680i) q^{12} +(0.276493 - 3.68954i) q^{13} +(1.72348 - 0.259773i) q^{14} +(-2.46232 - 2.28470i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(0.528983 - 0.360654i) q^{17} +(-3.02607 - 7.71031i) q^{18} +(-0.715661 + 0.220752i) q^{19} +(-0.733052 + 0.680173i) q^{20} +(3.65026 - 4.57728i) q^{21} +(-0.831667 + 1.04288i) q^{22} +(-5.37625 + 4.98843i) q^{23} +(-3.20977 + 0.990082i) q^{24} +(0.365341 + 0.930874i) q^{25} +(-3.05699 + 2.08422i) q^{26} +(-15.9878 - 7.69934i) q^{27} +(-1.27767 - 1.18551i) q^{28} +(-2.86116 + 0.431250i) q^{29} +(-0.251018 + 3.34961i) q^{30} +(1.79184 - 4.56553i) q^{31} +(0.222521 + 0.974928i) q^{32} +(0.334831 + 4.46801i) q^{33} +(-0.611786 - 0.188711i) q^{34} +(-1.57034 + 0.756238i) q^{35} +(-4.14144 + 7.17318i) q^{36} +(-4.24005 - 7.34399i) q^{37} +(0.618798 + 0.421889i) q^{38} +(-2.76547 + 12.1163i) q^{39} +(0.988831 + 0.149042i) q^{40} +(-6.87166 - 8.61679i) q^{41} -5.85457 q^{42} +(5.14937 - 4.06005i) q^{43} +1.33389 q^{44} +(5.16429 + 6.47581i) q^{45} +(7.25215 + 1.09309i) q^{46} +(2.39319 - 10.4852i) q^{47} +(2.77534 + 1.89219i) q^{48} +(1.98106 + 3.43130i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-1.93756 + 0.933081i) q^{51} +(3.53551 + 1.09056i) q^{52} +(-0.218853 - 2.92039i) q^{53} +(3.94867 + 17.3003i) q^{54} +(0.487325 - 1.24168i) q^{55} +(-0.130251 + 1.73808i) q^{56} +(2.48757 - 0.374941i) q^{57} +(2.12107 + 1.96806i) q^{58} +(-2.94897 - 1.42015i) q^{59} +(2.77534 - 1.89219i) q^{60} +(-3.59900 - 9.17010i) q^{61} +(-4.68667 + 1.44564i) q^{62} +(-10.5828 + 9.81941i) q^{63} +(0.623490 - 0.781831i) q^{64} +(2.30684 - 2.89269i) q^{65} +(3.28447 - 3.04754i) q^{66} +(1.15852 - 0.357357i) q^{67} +(0.233902 + 0.595973i) q^{68} +(20.3545 - 13.8775i) q^{69} +(1.57034 + 0.756238i) q^{70} +(-5.28111 - 4.90015i) q^{71} +(8.19036 - 1.23450i) q^{72} +(-0.768814 + 10.2591i) q^{73} +(-3.09813 + 7.89391i) q^{74} +(-0.747448 - 3.27478i) q^{75} +(-0.0559679 - 0.746840i) q^{76} +(2.22162 + 0.685278i) q^{77} +(11.1972 - 5.39227i) q^{78} +(-1.81601 + 3.14543i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(28.7179 + 19.5795i) q^{81} +(-2.45247 + 10.7450i) q^{82} +(5.48911 + 0.827350i) q^{83} +(3.65026 + 4.57728i) q^{84} +0.640230 q^{85} +(-6.38485 - 1.49454i) q^{86} +9.71917 q^{87} +(-0.831667 - 1.04288i) q^{88} +(-2.95788 - 0.445829i) q^{89} +(1.84311 - 8.07521i) q^{90} +(5.32818 + 3.63269i) q^{91} +(-3.66703 - 6.35149i) q^{92} +(-8.23721 + 14.2673i) q^{93} +(-9.68981 + 4.66637i) q^{94} +(-0.715661 - 0.220752i) q^{95} +(-0.251018 - 3.34961i) q^{96} +(2.40648 + 10.5435i) q^{97} +(1.44753 - 3.68824i) q^{98} +(0.825651 - 11.0176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

L-functions

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