LMFDB - Embedded newform 525.2.bg.a.466.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			466.8
Character	$\chi$	$=$	525.466
Dual form			525.2.bg.a.436.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0386614 + 0.367839i) q^{2} +(0.978148 + 0.207912i) q^{3} +(1.82248 + 0.387381i) q^{4} +(1.87660 - 1.21589i) q^{5} +(-0.114295 + 0.351762i) q^{6} +(1.72521 + 2.00591i) q^{7} +(-0.441543 + 1.35893i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.0386614 + 0.367839i) q^{2} +(0.978148 + 0.207912i) q^{3} +(1.82248 + 0.387381i) q^{4} +(1.87660 - 1.21589i) q^{5} +(-0.114295 + 0.351762i) q^{6} +(1.72521 + 2.00591i) q^{7} +(-0.441543 + 1.35893i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.374698 + 0.737293i) q^{10} +(-2.76362 + 1.23044i) q^{11} +(1.70212 + 0.757832i) q^{12} +(-0.201783 + 0.146604i) q^{13} +(-0.804549 + 0.557046i) q^{14} +(2.08839 - 0.799150i) q^{15} +(2.92144 + 1.30071i) q^{16} +(-3.36722 - 3.73967i) q^{17} +(-0.184932 + 0.320312i) q^{18} +(-5.02340 + 1.06776i) q^{19} +(3.89108 - 1.48898i) q^{20} +(1.27045 + 2.32076i) q^{21} +(-0.345759 - 1.06414i) q^{22} +(-0.0747451 + 0.711152i) q^{23} +(-0.714431 + 1.23743i) q^{24} +(2.04324 - 4.56346i) q^{25} +(-0.0461254 - 0.0798915i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.36711 + 4.32405i) q^{28} +(-2.58817 - 7.96556i) q^{29} +(0.213218 + 0.799086i) q^{30} +(-5.52126 - 6.13198i) q^{31} +(-2.02026 + 3.49919i) q^{32} +(-2.95905 + 0.628965i) q^{33} +(1.50578 - 1.09401i) q^{34} +(5.67647 + 1.66663i) q^{35} +(1.50736 + 1.09516i) q^{36} +(6.73789 + 2.99990i) q^{37} +(-0.198551 - 1.88908i) q^{38} +(-0.227854 + 0.101447i) q^{39} +(0.823704 + 3.08703i) q^{40} +(2.64381 - 1.92084i) q^{41} +(-0.902784 + 0.377598i) q^{42} -2.20428 q^{43} +(-5.51330 + 1.17189i) q^{44} +(2.20890 - 0.347486i) q^{45} +(-0.258699 - 0.0549882i) q^{46} +(-0.390190 + 0.433350i) q^{47} +(2.58717 + 1.87969i) q^{48} +(-1.04733 + 6.92121i) q^{49} +(1.59962 + 0.928013i) q^{50} +(-2.51611 - 4.35804i) q^{51} +(-0.424538 + 0.189016i) q^{52} +(1.29692 + 0.275670i) q^{53} +(-0.247488 + 0.274863i) q^{54} +(-3.69012 + 5.66929i) q^{55} +(-3.48764 + 1.45874i) q^{56} -5.13563 q^{57} +(3.03010 - 0.644069i) q^{58} +(0.699053 + 6.65105i) q^{59} +(4.11563 - 0.647436i) q^{60} +(0.230998 - 2.19780i) q^{61} +(2.46904 - 1.79386i) q^{62} +(0.760177 + 2.53419i) q^{63} +(3.96530 + 2.88096i) q^{64} +(-0.200412 + 0.520462i) q^{65} +(-0.116957 - 1.11277i) q^{66} +(9.22816 + 10.2489i) q^{67} +(-4.68802 - 8.11990i) q^{68} +(-0.220968 + 0.680071i) q^{69} +(-0.832511 + 2.02359i) q^{70} +(-3.27981 - 10.0942i) q^{71} +(-0.956095 + 1.06185i) q^{72} +(9.71271 - 4.32438i) q^{73} +(-1.36398 + 2.36247i) q^{74} +(2.94739 - 4.03892i) q^{75} -9.56870 q^{76} +(-7.23596 - 3.42080i) q^{77} +(-0.0285071 - 0.0877357i) q^{78} +(-10.4001 + 11.5505i) q^{79} +(7.06388 - 1.11123i) q^{80} +(0.669131 + 0.743145i) q^{81} +(0.604345 + 1.04676i) q^{82} +(4.42407 - 13.6159i) q^{83} +(1.41636 + 4.72171i) q^{84} +(-10.8659 - 2.92371i) q^{85} +(0.0852206 - 0.810819i) q^{86} +(-0.875477 - 8.32961i) q^{87} +(-0.451827 - 4.29885i) q^{88} +(-0.398777 + 3.79411i) q^{89} +(0.0424196 + 0.825954i) q^{90} +(-0.642191 - 0.151836i) q^{91} +(-0.411708 + 1.26711i) q^{92} +(-4.12570 - 7.14591i) q^{93} +(-0.144318 - 0.160281i) q^{94} +(-8.12864 + 8.11164i) q^{95} +(-2.70364 + 3.00269i) q^{96} +(0.963569 + 2.96556i) q^{97} +(-2.50540 - 0.652833i) q^{98} -3.02516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0386614	+	0.367839i	−0.0273377	+	0.260101i	0.972313	+	0.233681i	$0.0750773\pi$
$2$	−0.0386614	+	0.367839i	−0.0273377	+	0.260101i	−0.999651	+	0.0264197i	$0.991589\pi$
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$4$	1.82248	+	0.387381i	0.911242	+	0.193691i
$5$	1.87660	−	1.21589i	0.839240	−	0.543761i
$5$	1.87660	−	1.21589i	0.839240	−	0.543761i
$6$	−0.114295	+	0.351762i	−0.0466605	+	0.143606i
$7$	1.72521	+	2.00591i	0.652066	+	0.758162i
$7$	1.72521	+	2.00591i	0.652066	+	0.758162i
$8$	−0.441543	+	1.35893i	−0.156109	+	0.480454i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	0.374698	+	0.737293i	0.118490	+	0.233153i
$11$	−2.76362	+	1.23044i	−0.833262	+	0.370992i	−0.778606	−	0.627513i	$-0.784073\pi$
$11$	−2.76362	+	1.23044i	−0.833262	+	0.370992i	−0.0546559	+	0.998505i	$0.517406\pi$
$12$	1.70212	+	0.757832i	0.491359	+	0.218767i
$13$	−0.201783	+	0.146604i	−0.0559645	+	0.0406606i	−0.615416	−	0.788203i	$-0.711012\pi$
$13$	−0.201783	+	0.146604i	−0.0559645	+	0.0406606i	0.559451	+	0.828863i	$0.311012\pi$
$14$	−0.804549	+	0.557046i	−0.215025	+	0.148877i
$15$	2.08839	−	0.799150i	0.539219	−	0.206340i
$16$	2.92144	+	1.30071i	0.730360	+	0.325177i
$17$	−3.36722	−	3.73967i	−0.816670	−	0.907004i	0.180392	−	0.983595i	$-0.442263\pi$
$17$	−3.36722	−	3.73967i	−0.816670	−	0.907004i	−0.997063	+	0.0765904i	$0.975597\pi$
$18$	−0.184932	+	0.320312i	−0.0435890	+	0.0754983i
$19$	−5.02340	+	1.06776i	−1.15245	+	0.244960i	−0.744229	−	0.667924i	$-0.767183\pi$
$19$	−5.02340	+	1.06776i	−1.15245	+	0.244960i	−0.408218	+	0.912884i	$0.633850\pi$
$20$	3.89108	−	1.48898i	0.870073	−	0.332945i
$21$	1.27045	+	2.32076i	0.277236	+	0.506432i
$22$	−0.345759	−	1.06414i	−0.0737160	−	0.226875i
$23$	−0.0747451	+	0.711152i	−0.0155854	+	0.148285i	−0.999547	−	0.0300949i	$-0.990419\pi$
$23$	−0.0747451	+	0.711152i	−0.0155854	+	0.148285i	0.983962	+	0.178380i	$0.0570857\pi$
$24$	−0.714431	+	1.23743i	−0.145833	+	0.252589i
$25$	2.04324	−	4.56346i	0.408648	−	0.912692i
$26$	−0.0461254	−	0.0798915i	−0.00904593	−	0.0156680i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	2.36711	+	4.32405i	0.447342	+	0.817168i
$29$	−2.58817	−	7.96556i	−0.480611	−	1.47917i	−0.838238	−	0.545304i	$-0.816414\pi$
$29$	−2.58817	−	7.96556i	−0.480611	−	1.47917i	0.357628	−	0.933864i	$-0.383586\pi$
$30$	0.213218	+	0.799086i	0.0389281	+	0.145892i
$31$	−5.52126	−	6.13198i	−0.991647	−	1.10134i	−0.994852	−	0.101341i	$-0.967687\pi$
$31$	−5.52126	−	6.13198i	−0.991647	−	1.10134i	0.00320444	−	0.999995i	$-0.498980\pi$
$32$	−2.02026	+	3.49919i	−0.357135	+	0.618576i
$33$	−2.95905	+	0.628965i	−0.515104	+	0.109489i
$34$	1.50578	−	1.09401i	0.258239	−	0.187622i
$35$	5.67647	+	1.66663i	0.959499	+	0.281712i
$36$	1.50736	+	1.09516i	0.251227	+	0.182527i
$37$	6.73789	+	2.99990i	1.10770	+	0.493181i	0.877313	−	0.479918i	$-0.159334\pi$
$37$	6.73789	+	2.99990i	1.10770	+	0.493181i	0.230388	+	0.973099i	$0.426000\pi$
$38$	−0.198551	−	1.88908i	−0.0322092	−	0.306450i
$39$	−0.227854	+	0.101447i	−0.0364859	+	0.0162446i
$40$	0.823704	+	3.08703i	0.130239	+	0.488102i
$41$	2.64381	−	1.92084i	0.412893	−	0.299984i	−0.361879	−	0.932225i	$-0.617865\pi$
$41$	2.64381	−	1.92084i	0.412893	−	0.299984i	0.774772	+	0.632241i	$0.217865\pi$
$42$	−0.902784	+	0.377598i	−0.139303	+	0.0582646i
$43$	−2.20428			−0.336150			−0.168075	−	0.985774i	$-0.553755\pi$
$43$	−2.20428			−0.336150			−0.168075	+	0.985774i	$0.553755\pi$
$44$	−5.51330	+	1.17189i	−0.831161	+	0.176669i
$45$	2.20890	−	0.347486i	0.329284	−	0.0518002i
$46$	−0.258699	−	0.0549882i	−0.0381431	−	0.00810757i
$47$	−0.390190	+	0.433350i	−0.0569151	+	0.0632106i	−0.770930	−	0.636920i	$-0.780208\pi$
$47$	−0.390190	+	0.433350i	−0.0569151	+	0.0632106i	0.714015	+	0.700131i	$0.246875\pi$
$48$	2.58717	+	1.87969i	0.373425	+	0.271309i
$49$	−1.04733	+	6.92121i	−0.149619	+	0.988744i
$50$	1.59962	+	0.928013i	0.226221	+	0.131241i
$51$	−2.51611	−	4.35804i	−0.352326	−	0.610247i
$52$	−0.424538	+	0.189016i	−0.0588728	+	0.0262119i
$53$	1.29692	+	0.275670i	0.178146	+	0.0378662i	0.296121	−	0.955150i	$-0.404307\pi$
$53$	1.29692	+	0.275670i	0.178146	+	0.0378662i	−0.117975	+	0.993017i	$0.537640\pi$
$54$	−0.247488	+	0.274863i	−0.0336788	+	0.0374041i
$55$	−3.69012	+	5.66929i	−0.497576	+	0.764447i
$56$	−3.48764	+	1.45874i	−0.466055	+	0.194932i
$57$	−5.13563			−0.680231
$58$	3.03010	−	0.644069i	0.397872	−	0.0845704i
$59$	0.699053	+	6.65105i	0.0910090	+	0.865892i	0.940843	+	0.338842i	$0.110035\pi$
$59$	0.699053	+	6.65105i	0.0910090	+	0.865892i	−0.849834	+	0.527050i	$0.823298\pi$
$60$	4.11563	−	0.647436i	0.531325	−	0.0835837i
$61$	0.230998	−	2.19780i	0.0295762	−	0.281399i	−0.969731	−	0.244177i	$-0.921482\pi$
$61$	0.230998	−	2.19780i	0.0295762	−	0.281399i	0.999307	−	0.0372224i	$-0.0118510\pi$
$62$	2.46904	−	1.79386i	0.313568	−	0.227821i
$63$	0.760177	+	2.53419i	0.0957734	+	0.319278i
$64$	3.96530	+	2.88096i	0.495663	+	0.360120i
$65$	−0.200412	+	0.520462i	−0.0248580	+	0.0645553i
$66$	−0.116957	−	1.11277i	−0.0143964	−	0.136972i
$67$	9.22816	+	10.2489i	1.12740	+	1.25210i	0.964103	+	0.265527i	$0.0855459\pi$
$67$	9.22816	+	10.2489i	1.12740	+	1.25210i	0.163296	+	0.986577i	$0.447787\pi$
$68$	−4.68802	−	8.11990i	−0.568506	−	0.984682i
$69$	−0.220968	+	0.680071i	−0.0266015	+	0.0818709i
$70$	−0.832511	+	2.02359i	−0.0995041	+	0.241866i
$71$	−3.27981	−	10.0942i	−0.389242	−	1.19796i	−0.933356	−	0.358952i	$-0.883134\pi$
$71$	−3.27981	−	10.0942i	−0.389242	−	1.19796i	0.544115	−	0.839011i	$-0.316866\pi$
$72$	−0.956095	+	1.06185i	−0.112677	+	0.125140i
$73$	9.71271	−	4.32438i	1.13679	−	0.506130i	0.249971	−	0.968253i	$-0.419579\pi$
$73$	9.71271	−	4.32438i	1.13679	−	0.506130i	0.886816	+	0.462123i	$0.152912\pi$
$74$	−1.36398	+	2.36247i	−0.158559	+	0.274632i
$75$	2.94739	−	4.03892i	0.340335	−	0.466375i
$76$	−9.56870			−1.09761
$77$	−7.23596	−	3.42080i	−0.824614	−	0.389836i
$78$	−0.0285071	−	0.0877357i	−0.00322779	−	0.00993411i
$79$	−10.4001	+	11.5505i	−1.17011	+	1.29954i	−0.224409	+	0.974495i	$0.572045\pi$
$79$	−10.4001	+	11.5505i	−1.17011	+	1.29954i	−0.945700	+	0.325042i	$0.894622\pi$
$80$	7.06388	−	1.11123i	0.789766	−	0.124239i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	0.604345	+	1.04676i	0.0667387	+	0.115595i
$83$	4.42407	−	13.6159i	0.485605	−	1.49454i	−0.345498	−	0.938420i	$-0.612290\pi$
$83$	4.42407	−	13.6159i	0.485605	−	1.49454i	0.831103	−	0.556119i	$-0.187710\pi$
$84$	1.41636	+	4.72171i	0.154538	+	0.515180i
$85$	−10.8659	−	2.92371i	−1.17858	−	0.317121i
$86$	0.0852206	−	0.810819i	0.00918957	−	0.0874329i
$87$	−0.875477	−	8.32961i	−0.0938610	−	0.893028i
$88$	−0.451827	−	4.29885i	−0.0481650	−	0.458259i
$89$	−0.398777	+	3.79411i	−0.0422703	+	0.402175i	0.952845	+	0.303457i	$0.0981408\pi$
$89$	−0.398777	+	3.79411i	−0.0422703	+	0.402175i	−0.995115	+	0.0987179i	$0.968526\pi$
$90$	0.0424196	+	0.825954i	0.00447142	+	0.0870632i
$91$	−0.642191	−	0.151836i	−0.0673199	−	0.0159168i
$92$	−0.411708	+	1.26711i	−0.0429236	+	0.132105i
$93$	−4.12570	−	7.14591i	−0.427815	−	0.740997i
$94$	−0.144318	−	0.160281i	−0.0148852	−	0.0165317i
$95$	−8.12864	+	8.11164i	−0.833981	+	0.832237i
$96$	−2.70364	+	3.00269i	−0.275939	+	0.306461i
$97$	0.963569	+	2.96556i	0.0978356	+	0.301107i	0.987982	−	0.154567i	$-0.0493982\pi$
$97$	0.963569	+	2.96556i	0.0978356	+	0.301107i	−0.890147	+	0.455674i	$0.849398\pi$
$98$	−2.50540	−	0.652833i	−0.253083	−	0.0659461i
$99$	−3.02516			−0.304040
$100$	5.49157	−	7.52532i	0.549157	−	0.752532i
$101$	4.35514	−	7.54333i	0.433353	−	0.750589i	−0.563807	−	0.825907i	$-0.690664\pi$
$101$	4.35514	−	7.54333i	0.433353	−	0.750589i	0.997160	+	0.0753174i	$0.0239970\pi$
$102$	1.70033	−	0.757036i	0.168358	−	0.0749578i
$103$	6.32931	−	7.02942i	0.623646	−	0.692629i	−0.345696	−	0.938347i	$-0.612357\pi$
$103$	6.32931	−	7.02942i	0.623646	−	0.692629i	0.969341	+	0.245718i	$0.0790237\pi$
$104$	−0.110128	−	0.338940i	−0.0107990	−	0.0332358i
$105$	5.20592	+	2.81041i	0.508045	+	0.274268i
$106$	−0.151543	+	0.466401i	−0.0147192	+	0.0453009i
$107$	3.98626	+	6.90440i	0.385366	+	0.667473i	0.991820	−	0.127645i	$-0.0407419\pi$
$107$	3.98626	+	6.90440i	0.385366	+	0.667473i	−0.606454	+	0.795119i	$0.707409\pi$
$108$	1.24672	+	1.38463i	0.119966	+	0.133236i
$109$	−1.38655	−	13.1921i	−0.132807	−	1.26357i	−0.834465	−	0.551060i	$-0.814223\pi$
$109$	−1.38655	−	13.1921i	−0.132807	−	1.26357i	0.701658	−	0.712514i	$-0.252443\pi$
$110$	−1.94272	−	1.57655i	−0.185231	−	0.150318i
$111$	5.96693	+	4.33523i	0.566356	+	0.411482i
$112$	2.43098	+	8.10413i	0.229706	+	0.765768i
$113$	−10.3090	+	7.48995i	−0.969792	+	0.704595i	−0.955404	−	0.295301i	$-0.904580\pi$
$113$	−10.3090	+	7.48995i	−0.969792	+	0.704595i	−0.0143880	+	0.999896i	$0.504580\pi$
$114$	0.198551	−	1.88908i	0.0185960	−	0.176929i
$115$	0.724413	+	1.42543i	0.0675519	+	0.132922i
$116$	−1.63119	−	15.5197i	−0.151452	−	1.44097i
$117$	−0.243967	+	0.0518568i	−0.0225548	+	0.00479416i
$118$	−2.47354			−0.227708
$119$	1.69230	−	13.2060i	0.155133	−	1.21060i
$120$	0.163875	+	3.19083i	0.0149597	+	0.291281i
$121$	−1.23684	+	1.37365i	−0.112440	+	0.124878i
$122$	0.799504	+	0.169940i	0.0723837	+	0.0153856i
$123$	2.98540	−	1.32918i	0.269184	−	0.119848i
$124$	−7.68700	−	13.3143i	−0.690313	−	1.19566i
$125$	−1.71431	−	11.0481i	−0.153332	−	0.988175i
$126$	−0.961563	+	0.181647i	−0.0856629	+	0.0161824i
$127$	−7.69553	−	5.59113i	−0.682868	−	0.496133i	0.191440	−	0.981504i	$-0.438684\pi$
$127$	−7.69553	−	5.59113i	−0.682868	−	0.496133i	−0.874308	+	0.485372i	$0.838684\pi$
$128$	−6.62030	+	7.35259i	−0.585158	+	0.649883i
$129$	−2.15611	−	0.458296i	−0.189835	−	0.0403507i
$130$	−0.183698	−	0.0938410i	−0.0161114	−	0.00823040i
$131$	−18.7332	+	3.98187i	−1.63673	+	0.347897i	−0.932246	−	0.361824i	$-0.882154\pi$
$131$	−18.7332	+	3.98187i	−1.63673	+	0.347897i	−0.704482	+	0.709721i	$0.748821\pi$
$132$	−5.63647			−0.490592
$133$	−10.8082	−	8.23438i	−0.937192	−	0.714012i
$134$	−4.12672	+	2.99824i	−0.356494	+	0.259008i
$135$	2.23288	+	0.119364i	0.192176	+	0.0102732i
$136$	6.56872	−	2.92458i	0.563263	−	0.250781i
$137$	0.771711	+	7.34234i	0.0659318	+	0.627299i	0.976734	+	0.214455i	$0.0687977\pi$
$137$	0.771711	+	7.34234i	0.0659318	+	0.627299i	−0.910802	+	0.412843i	$0.864536\pi$
$138$	−0.241613	−	0.107573i	−0.0205675	−	0.00915724i
$139$	−0.635975	−	0.462063i	−0.0539427	−	0.0391917i	0.560487	−	0.828163i	$-0.310614\pi$
$139$	−0.635975	−	0.462063i	−0.0539427	−	0.0391917i	−0.614430	+	0.788971i	$0.710614\pi$
$140$	9.69966	+	5.23636i	0.819771	+	0.442554i
$141$	−0.471762	+	0.342755i	−0.0397296	+	0.0288652i
$142$	3.83984	−	0.816184i	0.322232	−	0.0684926i
$143$	0.377263	−	0.653439i	0.0315483	−	0.0546433i
$144$	2.13982	+	2.37651i	0.178319	+	0.198043i
$145$	−14.5422	−	11.8012i	−1.20766	−	0.980040i
$146$	1.21517	+	3.73990i	0.100568	+	0.309516i
$147$	−2.46345	+	6.55221i	−0.203182	+	0.540417i
$148$	11.1176	+	8.07740i	0.913860	+	0.663958i
$149$	4.40067	+	7.62218i	0.360517	+	0.624433i	0.988046	−	0.154160i	$-0.0492670\pi$
$149$	4.40067	+	7.62218i	0.360517	+	0.624433i	−0.627529	+	0.778593i	$0.715934\pi$
$150$	1.37172	+	1.24031i	0.112001	+	0.101271i
$151$	2.45605	−	4.25400i	0.199870	−	0.346185i	−0.748616	−	0.663004i	$-0.769281\pi$
$151$	2.45605	−	4.25400i	0.199870	−	0.346185i	0.948486	+	0.316819i	$0.102615\pi$
$152$	0.767041	−	7.29791i	0.0622152	−	0.591938i
$153$	−1.55504	−	4.78593i	−0.125718	−	0.386920i
$154$	1.53805	−	2.52941i	0.123940	−	0.203826i
$155$	−17.8170	−	4.79404i	−1.43109	−	0.385066i
$156$	−0.454560	+	0.0966196i	−0.0363939	+	0.00773576i
$157$	0.169557	−	0.293682i	0.0135321	−	0.0234383i	−0.859180	−	0.511673i	$-0.829026\pi$
$157$	0.169557	−	0.293682i	0.0135321	−	0.0234383i	0.872712	+	0.488235i	$0.162359\pi$
$158$	−3.84665	−	4.27214i	−0.306023	−	0.339873i
$159$	1.21127	+	0.539292i	0.0960599	+	0.0427686i
$160$	0.463405	+	9.02298i	0.0366354	+	0.713330i
$161$	−1.55546	+	1.07695i	−0.122587	+	0.0848756i
$162$	−0.299227	+	0.217401i	−0.0235095	+	0.0170806i
$163$	5.82276	+	2.59246i	0.456073	+	0.203057i	0.621898	−	0.783098i	$-0.286362\pi$
$163$	5.82276	+	2.59246i	0.456073	+	0.203057i	−0.165825	+	0.986155i	$0.553029\pi$
$164$	5.56239	−	2.47654i	0.434350	−	0.193385i
$165$	−4.78819	+	4.77818i	−0.372760	+	0.371981i
$166$	4.83741	+	2.15375i	0.375456	+	0.167164i
$167$	−6.25583	+	19.2535i	−0.484090	+	1.48988i	0.349204	+	0.937047i	$0.386452\pi$
$167$	−6.25583	+	19.2535i	−0.484090	+	1.48988i	−0.833294	+	0.552830i	$0.813548\pi$
$168$	−3.71471	+	0.701740i	−0.286596	+	0.0541404i
$169$	−3.99800	+	12.3046i	−0.307538	+	0.946505i
$170$	1.49555	−	3.88388i	0.114703	−	0.297880i
$171$	−5.02340	−	1.06776i	−0.384149	−	0.0816534i
$172$	−4.01727	−	0.853896i	−0.306314	−	0.0651090i
$173$	1.24858	−	11.8794i	0.0949278	−	0.903178i	−0.838618	−	0.544720i	$-0.816636\pi$
$173$	1.24858	−	11.8794i	0.0949278	−	0.903178i	0.933546	−	0.358458i	$-0.116697\pi$
$174$	3.09780			0.234844
$175$	12.6789	−	3.77435i	0.958434	−	0.285314i
$176$	−9.67419			−0.729219
$177$	−0.699053	+	6.65105i	−0.0525440	+	0.499923i
$178$	−1.38020	−	0.293371i	−0.103451	−	0.0219891i
$179$	−11.5391	−	2.45270i	−0.862469	−	0.183324i	−0.244619	−	0.969619i	$-0.578663\pi$
$179$	−11.5391	−	2.45270i	−0.862469	−	0.183324i	−0.617850	+	0.786296i	$0.711996\pi$
$180$	4.16030	+	0.222399i	0.310091	+	0.0165766i
$181$	2.32295	−	7.14930i	0.172663	−	0.531403i	−0.826856	−	0.562414i	$-0.809873\pi$
$181$	2.32295	−	7.14930i	0.172663	−	0.531403i	0.999519	+	0.0310110i	$0.00987269\pi$
$182$	0.0806792	−	0.230353i	0.00598034	−	0.0170749i
$183$	0.682897	−	2.10174i	0.0504812	−	0.155365i
$184$	−0.933401	−	0.415577i	−0.0688112	−	0.0306367i
$185$	16.2918	−	2.56290i	1.19780	−	0.188428i
$186$	2.78805	−	1.24132i	0.204430	−	0.0910179i
$187$	13.9072	+	6.19186i	1.01699	+	0.452794i
$188$	−0.878988	+	0.638622i	−0.0641068	+	0.0465763i
$189$	0.216678	+	2.63686i	0.0157610	+	0.191804i
$190$	−2.66951	−	3.30363i	−0.193667	−	0.239671i
$191$	15.3221	+	6.82182i	1.10867	+	0.493610i	0.877631	−	0.479336i	$-0.159122\pi$
$191$	15.3221	+	6.82182i	1.10867	+	0.493610i	0.231034	+	0.972946i	$0.425789\pi$
$192$	3.27967	+	3.64244i	0.236689	+	0.262870i
$193$	5.55806	−	9.62685i	0.400078	−	0.692956i	−0.593657	−	0.804718i	$-0.702316\pi$
$193$	5.55806	−	9.62685i	0.400078	−	0.692956i	0.993735	+	0.111763i	$0.0356496\pi$
$194$	−1.12810	+	0.239785i	−0.0809929	+	0.0172156i
$195$	−0.304242	+	0.467421i	−0.0217873	+	0.0334727i
$196$	−4.58989	+	12.2081i	−0.327849	+	0.872005i
$197$	5.51769	+	16.9817i	0.393119	+	1.20990i	0.930417	+	0.366504i	$0.119445\pi$
$197$	5.51769	+	16.9817i	0.393119	+	1.20990i	−0.537297	+	0.843393i	$0.680555\pi$
$198$	0.116957	−	1.11277i	0.00831175	−	0.0790811i
$199$	−7.10732	+	12.3102i	−0.503825	+	0.872650i	0.496165	+	0.868228i	$0.334741\pi$
$199$	−7.10732	+	12.3102i	−0.503825	+	0.872650i	−0.999990	+	0.00442211i	$0.998592\pi$
$200$	5.29924	+	4.79158i	0.374713	+	0.338816i
$201$	6.89564	+	11.9436i	0.486381	+	0.842436i
$202$	2.60635	+	1.89363i	0.183382	+	0.133235i
$203$	11.5131	−	18.9339i	0.808059	−	1.32890i
$204$	−2.89736	−	8.91715i	−0.202856	−	0.624326i
$205$	2.62584	−	6.81921i	0.183397	−	0.476274i
$206$	2.34099	+	2.59993i	0.163105	+	0.181146i
$207$	−0.357535	+	0.619268i	−0.0248504	+	0.0430421i
$208$	−0.780186	+	0.165834i	−0.0540962	+	0.0114985i
$209$	12.5689	−	9.13188i	0.869412	−	0.631665i
$210$	−1.23505	+	1.80628i	−0.0852263	+	0.124645i
$211$	−21.1961	−	15.3999i	−1.45920	−	1.06017i	−0.983570	−	0.180526i	$-0.942220\pi$
$211$	−21.1961	−	15.3999i	−1.45920	−	1.06017i	−0.475630	−	0.879645i	$-0.657780\pi$
$212$	2.25684	+	1.00481i	0.155000	+	0.0690105i
$213$	−1.10943	−	10.5555i	−0.0760170	−	0.723254i
$214$	−2.69382	+	1.19937i	−0.184146	+	0.0819869i
$215$	−4.13655	+	2.68015i	−0.282110	+	0.182785i
$216$	−1.15597	+	0.839864i	−0.0786540	+	0.0571455i
$217$	2.77488	−	21.6541i	0.188371	−	1.46997i
$218$	4.90617			0.332288
$219$	10.3996	−	2.21049i	0.702737	−	0.149371i
$220$	−8.92136	+	8.90271i	−0.601478	+	0.600220i
$221$	1.22770	+	0.260955i	0.0825839	+	0.0175538i
$222$	−1.82536	+	2.02726i	−0.122510	+	0.136061i
$223$	18.5531	+	13.4796i	1.24241	+	0.902661i	0.997756	−	0.0669509i	$-0.0213271\pi$
$223$	18.5531	+	13.4796i	1.24241	+	0.902661i	0.244650	+	0.969612i	$0.421327\pi$
$224$	−10.5044	+	1.98437i	−0.701856	+	0.132586i
$225$	3.72272	−	3.33787i	0.248181	−	0.222524i
$226$	−2.35653	−	4.08163i	−0.156754	−	0.271506i
$227$	8.78443	−	3.91108i	0.583043	−	0.259588i	−0.0939499	−	0.995577i	$-0.529949\pi$
$227$	8.78443	−	3.91108i	0.583043	−	0.259588i	0.676993	+	0.735989i	$0.263283\pi$
$228$	−9.35961	−	1.98945i	−0.619855	−	0.131754i
$229$	−14.2600	+	15.8374i	−0.942330	+	1.04656i	0.0565093	+	0.998402i	$0.482003\pi$
$229$	−14.2600	+	15.8374i	−0.942330	+	1.04656i	−0.998840	+	0.0481617i	$0.984664\pi$
$230$	−0.552334	+	0.211358i	−0.0364198	+	0.0139365i
$231$	−6.36661	−	4.85048i	−0.418892	−	0.319138i
$232$	11.9674			0.785699
$233$	−9.38981	+	1.99587i	−0.615147	+	0.130753i	−0.504939	−	0.863155i	$-0.668485\pi$
$233$	−9.38981	+	1.99587i	−0.615147	+	0.130753i	−0.110208	+	0.993909i	$0.535152\pi$
$234$	−0.00964283	−	0.0917454i	−0.000630371	−	0.00599758i
$235$	−0.205326	+	1.28765i	−0.0133940	+	0.0839971i
$236$	−1.30248	+	12.3922i	−0.0847839	+	0.806665i
$237$	−12.5744	+	9.13582i	−0.816793	+	0.593435i
$238$	4.79226	+	1.13306i	0.310636	+	0.0734452i
$239$	8.59024	+	6.24118i	0.555657	+	0.403708i	0.829867	−	0.557962i	$-0.188416\pi$
$239$	8.59024	+	6.24118i	0.555657	+	0.403708i	−0.274210	+	0.961670i	$0.588416\pi$
$240$	7.14056	+	0.381716i	0.460921	+	0.0246396i
$241$	−1.33901	−	12.7398i	−0.0862530	−	0.820643i	−0.949057	−	0.315104i	$-0.897961\pi$
$241$	−1.33901	−	12.7398i	−0.0862530	−	0.820643i	0.862804	−	0.505538i	$-0.168706\pi$
$242$	−0.457465	−	0.508066i	−0.0294070	−	0.0326597i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	1.27237	−	3.91597i	0.0814554	−	0.250694i
$245$	6.44998	+	14.2618i	0.412074	+	0.911150i
$246$	0.373506	+	1.14953i	0.0238139	+	0.0732915i
$247$	0.857100	−	0.951906i	0.0545360	−	0.0605683i
$248$	10.7708	−	4.79546i	0.683946	−	0.304512i
$249$	7.15830	−	12.3985i	0.453639	−	0.785725i
$250$	4.13021	−	0.203452i	0.261217	−	0.0128674i
$251$	10.9005			0.688035			0.344017	−	0.938963i	$-0.388212\pi$
$251$	10.9005			0.688035			0.344017	+	0.938963i	$0.388212\pi$
$252$	0.403714	+	4.91300i	0.0254316	+	0.309490i
$253$	−0.668464	−	2.05732i	−0.0420260	−	0.129343i
$254$	2.35415	−	2.61455i	0.147713	−	0.164052i
$255$	−10.0206	−	5.11898i	−0.627515	−	0.320563i
$256$	4.11071	+	4.56541i	0.256920	+	0.285338i
$257$	4.13610	+	7.16394i	0.258003	+	0.446874i	0.965707	−	0.259635i	$-0.0836022\pi$
$257$	4.13610	+	7.16394i	0.258003	+	0.446874i	−0.707704	+	0.706509i	$0.750269\pi$
$258$	0.251937	−	0.775383i	0.0156849	−	0.0482732i
$259$	5.60671	+	18.6910i	0.348384	+	1.16140i
$260$	−0.566865	+	0.870898i	−0.0351554	+	0.0540108i
$261$	0.875477	−	8.32961i	0.0541907	−	0.515590i
$262$	−0.740433	−	7.04475i	−0.0457441	−	0.435226i
$263$	1.78770	+	17.0088i	0.110234	+	1.04881i	0.900146	+	0.435589i	$0.143460\pi$
$263$	1.78770	+	17.0088i	0.110234	+	1.04881i	−0.789912	+	0.613221i	$0.789874\pi$
$264$	0.451827	−	4.29885i	0.0278080	−	0.264576i
$265$	2.76899	−	1.05959i	0.170098	−	0.0650902i
$266$	3.44679	−	3.65733i	0.211336	−	0.224245i
$267$	−1.17890	+	3.62829i	−0.0721476	+	0.222048i
$268$	12.8480	+	22.2533i	0.784813	+	1.35934i
$269$	8.76071	+	9.72975i	0.534150	+	0.593234i	0.948458	−	0.316903i	$-0.102643\pi$
$269$	8.76071	+	9.72975i	0.534150	+	0.593234i	−0.414308	+	0.910137i	$0.635976\pi$
$270$	−0.130233	+	0.816725i	−0.00792572	+	0.0497043i
$271$	12.0839	−	13.4205i	0.734042	−	0.815236i	−0.254358	−	0.967110i	$-0.581864\pi$
$271$	12.0839	−	13.4205i	0.734042	−	0.815236i	0.988400	+	0.151874i	$0.0485309\pi$
$272$	−4.97290	−	15.3050i	−0.301526	−	0.928002i
$273$	−0.596589	−	0.282037i	−0.0361072	−	0.0170697i
$274$	−2.73063			−0.164964
$275$	−0.0316642	+	15.1257i	−0.00190942	+	0.912117i
$276$	−0.666158	+	1.15382i	−0.0400980	+	0.0694518i
$277$	−8.17089	+	3.63792i	−0.490941	+	0.218581i	−0.637249	−	0.770658i	$-0.719928\pi$
$277$	−8.17089	+	3.63792i	−0.490941	+	0.218581i	0.146308	+	0.989239i	$0.453261\pi$
$278$	0.194552	−	0.216072i	0.0116685	−	0.0129591i
$279$	−2.54982	−	7.84754i	−0.152654	−	0.469820i
$280$	−4.77123	+	6.97803i	−0.285136	+	0.417017i
$281$	−8.31286	+	25.5844i	−0.495904	+	1.52623i	0.319640	+	0.947539i	$0.396438\pi$
$281$	−8.31286	+	25.5844i	−0.495904	+	1.52623i	−0.815544	+	0.578696i	$0.803562\pi$
$282$	−0.107840	−	0.186784i	−0.00642176	−	0.0111228i
$283$	−1.25905	−	1.39831i	−0.0748426	−	0.0831211i	0.704560	−	0.709644i	$-0.251144\pi$
$283$	−1.25905	−	1.39831i	−0.0748426	−	0.0831211i	−0.779403	+	0.626523i	$0.784478\pi$
$284$	−2.06709	−	19.6671i	−0.122659	−	1.16703i
$285$	−9.63751	+	6.24434i	−0.570877	+	0.369883i
$286$	0.225775	+	0.164035i	0.0133503	+	0.00969959i
$287$	8.41413	+	1.98939i	0.496670	+	0.117430i
$288$	−3.26885	+	2.37496i	−0.192619	+	0.139946i
$289$	−0.870024	+	8.27773i	−0.0511779	+	0.486925i
$290$	4.90317	−	4.89292i	0.287924	−	0.287322i
$291$	0.325938	+	3.10109i	0.0191068	+	0.181789i
$292$	19.3764	−	4.11859i	1.13392	−	0.241022i
$293$	−19.3698			−1.13159			−0.565797	−	0.824545i	$-0.691431\pi$
$293$	−19.3698			−1.13159			−0.565797	+	0.824545i	$0.691431\pi$
$294$	−2.31492	−	1.15947i	−0.135009	−	0.0676215i
$295$	9.39876	+	11.6314i	0.547217	+	0.677205i
$296$	−7.05171	+	7.83172i	−0.409872	+	0.455209i
$297$	−2.95905	−	0.628965i	−0.171701	−	0.0364963i
$298$	−2.97387	+	1.32405i	−0.172272	+	0.0767003i
$299$	−0.0891754	−	0.154456i	−0.00515714	−	0.00893244i
$300$	6.93617	−	6.21911i	0.400460	−	0.359061i
$301$	−3.80284	−	4.42158i	−0.219192	−	0.254856i
$302$	1.46983	+	1.06789i	0.0845792	+	0.0614504i
$303$	5.82832	−	6.47301i	0.334828	−	0.371864i
$304$	−16.0644	−	3.41460i	−0.921357	−	0.195841i
$305$	−2.23878	−	4.40525i	−0.128192	−	0.252244i
$306$	1.82057	−	0.386974i	0.104075	−	0.0221219i
$307$	−9.12753			−0.520936			−0.260468	−	0.965483i	$-0.583877\pi$
$307$	−9.12753			−0.520936			−0.260468	+	0.965483i	$0.583877\pi$
$308$	−11.8623	−	9.03742i	−0.675916	−	0.514955i
$309$	7.65250	−	5.55987i	0.435336	−	0.316290i
$310$	2.45226	−	6.36843i	0.139279	−	0.361702i
$311$	−4.15187	+	1.84853i	−0.235431	+	0.104821i	−0.521061	−	0.853519i	$-0.674464\pi$
$311$	−4.15187	+	1.84853i	−0.235431	+	0.104821i	0.285630	+	0.958340i	$0.407797\pi$
$312$	−0.0372522	−	0.354431i	−0.00210899	−	0.0200657i
$313$	2.72014	+	1.21108i	0.153751	+	0.0684545i	0.482170	−	0.876078i	$-0.339849\pi$
$313$	2.72014	+	1.21108i	0.153751	+	0.0684545i	−0.328418	+	0.944532i	$0.606516\pi$
$314$	0.101472	+	0.0737238i	0.00572640	+	0.00416048i
$315$	4.50784	+	3.83137i	0.253988	+	0.215873i
$316$	−23.4286	+	17.0219i	−1.31796	+	0.957554i
$317$	−30.7231	+	6.53040i	−1.72558	+	0.366784i	−0.960743	−	0.277438i	$-0.910515\pi$
$317$	−30.7231	+	6.53040i	−1.72558	+	0.366784i	−0.764839	+	0.644222i	$0.777181\pi$
$318$	−0.245202	+	0.424702i	−0.0137502	+	0.0238161i
$319$	16.9539	+	18.8292i	0.949234	+	1.05423i
$320$	10.9442	+	0.585048i	0.611799	+	0.0327052i
$321$	2.46364	+	7.58231i	0.137507	+	0.423203i
$322$	−0.336008	−	0.613793i	−0.0187250	−	0.0342054i
$323$	20.9080	+	15.1905i	1.16335	+	0.845223i
$324$	0.931600	+	1.61358i	0.0517556	+	0.0896433i
$325$	0.256730	+	1.22038i	0.0142408	+	0.0676943i
$326$	−1.17872	+	2.04161i	−0.0652834	+	0.113074i
$327$	1.38655	−	13.1921i	0.0766761	−	0.729525i
$328$	1.44293	+	4.44087i	0.0796723	+	0.245206i
$329$	−1.54242	−	0.0350676i	−0.0850363	−	0.00193334i
$330$	−1.57248	−	1.94601i	−0.0865623	−	0.107125i
$331$	12.6112	−	2.68058i	0.693172	−	0.147338i	0.152163	−	0.988355i	$-0.451376\pi$
$331$	12.6112	−	2.68058i	0.693172	−	0.147338i	0.541008	+	0.841017i	$0.318043\pi$
$332$	13.3373	−	23.1010i	0.731982	−	1.26783i
$333$	4.93520	+	5.48109i	0.270447	+	0.300362i
$334$	−6.84031	−	3.04550i	−0.374285	−	0.166642i
$335$	29.7791	+	8.01269i	1.62700	+	0.437780i
$336$	0.692916	+	8.43246i	0.0378017	+	0.460029i
$337$	3.29572	−	2.39448i	0.179529	−	0.130436i	−0.494391	−	0.869240i	$-0.664609\pi$
$337$	3.29572	−	2.39448i	0.179529	−	0.130436i	0.673921	+	0.738804i	$0.264609\pi$
$338$	−4.37153	−	1.94633i	−0.237780	−	0.105866i
$339$	−11.6410	+	5.18291i	−0.632253	+	0.281497i
$340$	−18.6704	−	9.53768i	−1.01255	−	0.517253i
$341$	22.8037	+	10.1529i	1.23489	+	0.549808i
$342$	0.586974	−	1.80652i	0.0317399	−	0.0976855i
$343$	−15.6902	+	9.83965i	−0.847189	+	0.531291i
$344$	0.973284	−	2.99546i	0.0524759	−	0.161504i
$345$	0.412220	+	1.54489i	0.0221932	+	0.0831742i
$346$	4.32145	+	0.918552i	0.232322	+	0.0493817i
$347$	16.3371	+	3.47255i	0.877019	+	0.186416i	0.624358	−	0.781139i	$-0.285361\pi$
$347$	16.3371	+	3.47255i	0.877019	+	0.186416i	0.252661	+	0.967555i	$0.418694\pi$
$348$	1.63119	−	15.5197i	0.0874409	−	0.831945i
$349$	14.9074			0.797976			0.398988	−	0.916956i	$-0.369361\pi$
$349$	14.9074			0.797976			0.398988	+	0.916956i	$0.369361\pi$
$350$	0.898169	+	4.80971i	0.0480092	+	0.257090i
$351$	−0.249417			−0.0133129
$352$	1.27767	−	12.1562i	0.0681002	−	0.647930i
$353$	1.84800	+	0.392804i	0.0983589	+	0.0209068i	0.256828	−	0.966457i	$-0.417323\pi$
$353$	1.84800	+	0.392804i	0.0983589	+	0.0209068i	−0.158469	+	0.987364i	$0.550656\pi$
$354$	−2.41949	−	0.514278i	−0.128594	−	0.0273335i
$355$	−18.4283	−	14.9549i	−0.978072	−	0.793724i
$356$	−2.19653	+	6.76023i	−0.116416	+	0.358291i
$357$	4.40101	−	12.5656i	0.232926	−	0.665042i
$358$	1.34831	−	4.14969i	0.0712606	−	0.219318i
$359$	20.0683	+	8.93497i	1.05916	+	0.471570i	0.861003	−	0.508600i	$-0.169837\pi$
$359$	20.0683	+	8.93497i	1.05916	+	0.471570i	0.198160	+	0.980170i	$0.436503\pi$
$360$	−0.503116	+	3.15517i	−0.0265165	+	0.166292i
$361$	6.73711	−	2.99956i	0.354585	−	0.157871i
$362$	2.53998	+	1.13087i	0.133498	+	0.0594373i
$363$	−1.49541	+	1.08648i	−0.0784889	+	0.0570255i
$364$	−1.11156	−	0.525492i	−0.0582618	−	0.0275433i
$365$	12.9689	−	19.9247i	0.678823	−	1.04290i
$366$	0.746700	+	0.332452i	0.0390306	+	0.0173776i
$367$	−22.9507	−	25.4893i	−1.19802	−	1.33053i	−0.930197	−	0.367062i	$-0.880364\pi$
$367$	−22.9507	−	25.4893i	−1.19802	−	1.33053i	−0.267819	−	0.963469i	$-0.586303\pi$
$368$	−1.14336	+	1.98037i	−0.0596020	+	0.103234i
$369$	3.19651	−	0.679439i	0.166404	−	0.0353702i
$370$	0.312867	+	6.09185i	0.0162652	+	0.316700i
$371$	1.68449	+	3.07710i	0.0874545	+	0.159755i
$372$	−4.75082	−	14.6215i	−0.246319	−	0.758091i
$373$	−3.46979	+	33.0128i	−0.179659	+	1.70934i	0.418712	+	0.908119i	$0.362482\pi$
$373$	−3.46979	+	33.0128i	−0.179659	+	1.70934i	−0.598371	+	0.801219i	$0.704185\pi$
$374$	−2.81528	+	4.87620i	−0.145574	+	0.252142i
$375$	0.620190	−	11.1631i	0.0320265	−	0.576461i
$376$	−0.416606	−	0.721583i	−0.0214848	−	0.0372128i
$377$	1.69003	+	1.22788i	0.0870410	+	0.0632390i
$378$	−0.978318	−	0.0222425i	−0.0503192	−	0.00114403i
$379$	−6.12153	−	18.8401i	−0.314442	−	0.967752i	−0.975984	−	0.217844i	$-0.930098\pi$
$379$	−6.12153	−	18.8401i	−0.314442	−	0.967752i	0.661542	−	0.749908i	$-0.269902\pi$
$380$	−17.9566	+	11.6345i	−0.921155	+	0.596835i
$381$	−6.36490	−	7.06894i	−0.326084	−	0.362153i
$382$	−3.10170	+	5.37231i	−0.158697	+	0.274871i
$383$	22.0224	−	4.68100i	1.12529	−	0.239188i	0.392573	−	0.919721i	$-0.371585\pi$
$383$	22.0224	−	4.68100i	1.12529	−	0.239188i	0.732717	+	0.680533i	$0.238252\pi$
$384$	−8.00432	+	5.81548i	−0.408469	+	0.296770i
$385$	−17.7383	+	2.37864i	−0.904027	+	0.121227i
$386$	3.32625	+	2.41666i	0.169301	+	0.123005i
$387$	−2.01371	−	0.896562i	−0.102363	−	0.0455748i
$388$	0.607288	+	5.77796i	0.0308304	+	0.293331i
$389$	25.1213	−	11.1847i	1.27370	−	0.567087i	0.345237	−	0.938516i	$-0.387799\pi$
$389$	25.1213	−	11.1847i	1.27370	−	0.567087i	0.928461	+	0.371429i	$0.121132\pi$
$390$	−0.160173	−	0.129983i	−0.00811067	−	0.00658196i
$391$	2.91116	−	2.11508i	0.147224	−	0.106964i
$392$	−8.94298	−	4.47926i	−0.451689	−	0.226237i
$393$	−19.1517			−0.966077
$394$	−6.45985	+	1.37308i	−0.325443	+	0.0691749i
$395$	−5.47276	+	34.3211i	−0.275365	+	1.72688i
$396$	−5.51330	−	1.17189i	−0.277054	−	0.0588896i
$397$	5.00434	−	5.55789i	0.251161	−	0.278942i	−0.604359	−	0.796712i	$-0.706571\pi$
$397$	5.00434	−	5.55789i	0.251161	−	0.278942i	0.855520	+	0.517769i	$0.173238\pi$
$398$	−4.25340	−	3.09028i	−0.213204	−	0.154902i
$399$	−8.86002	−	10.3016i	−0.443556	−	0.515725i
$400$	11.9049	−	10.6742i	0.595247	−	0.533711i
$401$	−4.68393	−	8.11280i	−0.233904	−	0.405134i	0.725049	−	0.688697i	$-0.241817\pi$
$401$	−4.68393	−	8.11280i	−0.233904	−	0.405134i	−0.958954	+	0.283563i	$0.908484\pi$
$402$	−4.65991	+	2.07473i	−0.232415	+	0.103478i
$403$	2.01307	+	0.427891i	0.100278	+	0.0213148i
$404$	10.8593	−	12.0605i	0.540272	−	0.600032i
$405$	2.15927	+	0.580997i	0.107295	+	0.0288700i
$406$	6.51950	+	4.96696i	0.323557	+	0.246506i
$407$	−22.3121			−1.10597
$408$	7.03323	−	1.49496i	0.348197	−	0.0740115i
$409$	−3.29197	−	31.3210i	−0.162778	−	1.54873i	−0.705437	−	0.708773i	$-0.749249\pi$
$409$	−3.29197	−	31.3210i	−0.162778	−	1.54873i	0.542659	−	0.839953i	$-0.317418\pi$
$410$	2.40685	+	1.22953i	0.118866	+	0.0607219i
$411$	−0.771711	+	7.34234i	−0.0380657	+	0.362171i
$412$	14.2581	−	10.3591i	0.702448	−	0.510358i
$413$	−12.1354	+	12.8767i	−0.597143	+	0.633619i
$414$	−0.213968	−	0.155457i	−0.0105159	−	0.00764028i
$415$	−8.25317	−	30.9307i	−0.405132	−	1.51833i
$416$	−0.105341	−	1.00226i	−0.00516478	−	0.0491396i
$417$	−0.526009	−	0.584192i	−0.0257588	−	0.0286080i
$418$	2.87312	+	4.97640i	0.140529	+	0.243404i
$419$	−6.22040	+	19.1444i	−0.303887	+	0.935267i	0.676204	+	0.736715i	$0.263624\pi$
$419$	−6.22040	+	19.1444i	−0.303887	+	0.935267i	−0.980090	+	0.198552i	$0.936376\pi$
$420$	8.39900	+	7.13861i	0.409829	+	0.348329i
$421$	−7.97680	−	24.5501i	−0.388765	−	1.19650i	−0.933712	−	0.358026i	$-0.883450\pi$
$421$	−7.97680	−	24.5501i	−0.388765	−	1.19650i	0.544947	−	0.838471i	$-0.316550\pi$
$422$	6.48414	−	7.20137i	0.315643	−	0.350557i
$423$	−0.532716	+	0.237180i	−0.0259015	+	0.0115321i
$424$	−0.947263	+	1.64071i	−0.0460032	+	0.0796798i
$425$	−23.9459	+	7.72511i	−1.16155	+	0.374723i
$426$	3.92563			0.190197
$427$	4.80710	−	3.32829i	0.232632	−	0.161067i
$428$	4.59026	+	14.1274i	0.221878	+	0.682872i
$429$	0.504877	−	0.560723i	0.0243757	−	0.0270719i
$430$	−0.825940	−	1.62520i	−0.0398303	−	0.0783741i
$431$	8.58435	+	9.53388i	0.413493	+	0.459231i	0.913529	−	0.406774i	$-0.133346\pi$
$431$	8.58435	+	9.53388i	0.413493	+	0.459231i	−0.500035	+	0.866005i	$0.666680\pi$
$432$	1.59896	+	2.76948i	0.0769299	+	0.133246i
$433$	5.88280	−	18.1054i	0.282709	−	0.870090i	−0.704367	−	0.709836i	$-0.748769\pi$
$433$	5.88280	−	18.1054i	0.282709	−	0.870090i	0.987076	−	0.160253i	$-0.0512311\pi$
$434$	7.85792	+	1.85788i	0.377192	+	0.0891813i
$435$	−11.7708	−	14.5668i	−0.564365	−	0.698427i
$436$	2.58341	−	24.5795i	0.123723	−	1.17715i
$437$	−0.383863	−	3.65221i	−0.0183627	−	0.174709i
$438$	0.411044	+	3.91082i	0.0196404	+	0.186866i
$439$	−2.19088	+	20.8449i	−0.104565	+	0.994871i	0.808898	+	0.587949i	$0.200065\pi$
$439$	−2.19088	+	20.8449i	−0.104565	+	0.994871i	−0.913463	+	0.406922i	$0.866602\pi$
$440$	−6.07481	−	7.51784i	−0.289605	−	0.358399i
$441$	−3.77189	+	5.89685i	−0.179614	+	0.280802i
$442$	−0.143454	+	0.441506i	−0.00682341	+	0.0210003i
$443$	−2.72267	−	4.71581i	−0.129358	−	0.224055i	0.794070	−	0.607826i	$-0.207958\pi$
$443$	−2.72267	−	4.71581i	−0.129358	−	0.224055i	−0.923428	+	0.383772i	$0.874625\pi$
$444$	9.19526	+	10.2124i	0.436388	+	0.484657i
$445$	3.86486	+	7.60488i	0.183212	+	0.360506i
$446$	−5.67561	+	6.30340i	−0.268748	+	0.298475i
$447$	2.71976	+	8.37057i	0.128640	+	0.395914i
$448$	1.06202	+	12.9243i	0.0501757	+	0.610615i
$449$	12.5379			0.591698			0.295849	−	0.955235i	$-0.404397\pi$
$449$	12.5379			0.591698			0.295849	+	0.955235i	$0.404397\pi$
$450$	1.08387	+	1.49841i	0.0510942	+	0.0706356i
$451$	−4.94299	+	8.56151i	−0.232756	+	0.403146i
$452$	−21.6895	+	9.65680i	−1.02019	+	0.454217i
$453$	3.28683	−	3.65040i	0.154429	−	0.171511i
$454$	1.09903	+	3.38246i	0.0515800	+	0.158747i
$455$	−1.38975	+	0.495896i	−0.0651525	+	0.0232480i
$456$	2.26760	−	6.97895i	0.106190	−	0.326819i
$457$	−11.3222	−	19.6107i	−0.529631	−	0.917348i	−0.999403	−	0.0345599i	$-0.988997\pi$
$457$	−11.3222	−	19.6107i	−0.529631	−	0.917348i	0.469772	−	0.882788i	$-0.344336\pi$
$458$	−5.27429	−	5.85769i	−0.246451	−	0.273712i
$459$	−0.526011	−	5.00466i	−0.0245521	−	0.233598i
$460$	0.768048	+	2.87844i	0.0358104	+	0.134208i
$461$	−23.6378	−	17.1738i	−1.10092	−	0.799866i	−0.119711	−	0.992809i	$-0.538197\pi$
$461$	−23.6378	−	17.1738i	−1.10092	−	0.799866i	−0.981210	+	0.192943i	$0.938197\pi$
$462$	2.03034	−	2.15436i	0.0944599	−	0.100230i
$463$	−7.30426	+	5.30686i	−0.339458	+	0.246631i	−0.744433	−	0.667697i	$-0.767280\pi$
$463$	−7.30426	+	5.30686i	−0.339458	+	0.246631i	0.404975	+	0.914328i	$0.367280\pi$
$464$	2.79970	−	26.6374i	0.129973	−	1.23661i
$465$	−16.4309	−	8.39363i	−0.761964	−	0.389245i
$466$	−0.371133	−	3.53110i	−0.0171924	−	0.163575i
$467$	−16.0042	+	3.40179i	−0.740585	+	0.157416i	−0.562730	−	0.826641i	$-0.690249\pi$
$467$	−16.0042	+	3.40179i	−0.740585	+	0.157416i	−0.177855	+	0.984057i	$0.556916\pi$
$468$	−0.464715			−0.0214814
$469$	−4.63790	+	36.1923i	−0.214158	+	1.67121i
$470$	−0.465710	−	0.125309i	−0.0214816	−	0.00578008i
$471$	0.226912	−	0.252011i	0.0104555	−	0.0116121i
$472$	−9.34696	−	1.98676i	−0.430229	−	0.0914479i
$473$	6.09179	−	2.71224i	0.280101	−	0.124709i
$474$	−2.87436	−	4.97854i	−0.132024	−	0.228672i
$475$	−5.39135	+	25.1058i	−0.247372	+	1.15193i
$476$	8.19996	−	23.4122i	0.375844	−	1.07310i
$477$	1.07267	+	0.779344i	0.0491144	+	0.0356837i
$478$	−2.62786	+	2.91853i	−0.120195	+	0.133491i
$479$	40.1305	+	8.53000i	1.83361	+	0.389746i	0.989274	−	0.146069i	$-0.0466622\pi$
$479$	40.1305	+	8.53000i	1.83361	+	0.389746i	0.844335	+	0.535815i	$0.179996\pi$
$480$	−1.42271	+	8.92216i	−0.0649373	+	0.407239i
$481$	−1.79939	+	0.382472i	−0.0820450	+	0.0174392i
$482$	4.73796			0.215808
$483$	−1.74538	+	0.730020i	−0.0794173	+	0.0332171i
$484$	−2.78626	+	2.02433i	−0.126648	+	0.0920152i
$485$	5.41402	+	4.39358i	0.245838	+	0.199502i
$486$	−0.337888	+	0.150438i	−0.0153269	+	0.00682399i
$487$	−1.34108	−	12.7595i	−0.0607700	−	0.578188i	−0.981962	−	0.189079i	$-0.939450\pi$
$487$	−1.34108	−	12.7595i	−0.0607700	−	0.578188i	0.921192	−	0.389109i	$-0.127217\pi$
$488$	2.88465	+	1.28433i	0.130582	+	0.0581389i
$489$	5.15651	+	3.74643i	0.233186	+	0.169419i
$490$	−5.49539	+	1.82117i	−0.248256	+	0.0822722i
$491$	−0.189007	+	0.137322i	−0.00852978	+	0.00619725i	−0.592042	−	0.805907i	$-0.701678\pi$
$491$	−0.189007	+	0.137322i	−0.00852978	+	0.00619725i	0.583512	+	0.812104i	$0.301678\pi$
$492$	5.95574	−	1.26593i	0.268505	−	0.0570726i
$493$	−21.0737	+	36.5007i	−0.949111	+	1.64391i
$494$	0.317011	+	0.352076i	0.0142630	+	0.0158407i
$495$	−5.67700	+	3.67825i	−0.255162	+	0.165325i
$496$	−8.15411	−	25.0958i	−0.366130	−	1.12683i
$497$	14.5897	−	23.9936i	0.654438	−	1.07626i
$498$	4.28391	+	3.11244i	0.191967	+	0.139472i
$499$	−13.5027	−	23.3874i	−0.604465	−	1.04696i	−0.992136	−	0.125166i	$-0.960054\pi$
$499$	−13.5027	−	23.3874i	−0.604465	−	1.04696i	0.387671	−	0.921798i	$-0.373280\pi$
$500$	1.15554	−	20.7991i	0.0516772	−	0.930166i
$501$	−10.1221	+	17.5321i	−0.452224	+	0.783275i
$502$	−0.421429	+	4.00963i	−0.0188093	+	0.178959i
$503$	0.353328	+	1.08743i	0.0157541	+	0.0484862i	0.958625	−	0.284673i	$-0.0918852\pi$
$503$	0.353328	+	1.08743i	0.0157541	+	0.0484862i	−0.942870	+	0.333160i	$0.891885\pi$
$504$	−3.77944	−	0.0859271i	−0.168349	−	0.00382750i
$505$	−0.998978	−	19.4512i	−0.0444539	−	0.865565i
$506$	0.782606	−	0.166348i	0.0347911	−	0.00739507i
$507$	−6.46890	+	11.2045i	−0.287294	+	0.497607i
$508$	−11.8591	−	13.1709i	−0.526162	−	0.584362i
$509$	−35.2830	−	15.7090i	−1.56389	−	0.696289i	−0.571636	−	0.820508i	$-0.693691\pi$
$509$	−35.2830	−	15.7090i	−1.56389	−	0.696289i	−0.992255	+	0.124219i	$0.960358\pi$
$510$	2.27037	−	3.48806i	0.100534	−	0.154454i
$511$	25.4307	+	12.0224i	1.12499	+	0.531838i
$512$	−17.8469	+	12.9665i	−0.788729	+	0.573045i
$513$	−4.69163	−	2.08885i	−0.207141	−	0.0922249i
$514$	−2.79508	+	1.24445i	−0.123286	+	0.0548903i
$515$	3.33061	−	20.8871i	0.146764	−	0.920396i
$516$	−3.75194	−	1.67047i	−0.165170	−	0.0735385i
$517$	0.545124	−	1.67772i	0.0239745	−	0.0737861i
$518$	−7.09204	+	1.33975i	−0.311607	+	0.0588650i
$519$	3.69117	−	11.3603i	0.162024	−	0.498660i
$520$	−0.618780	−	0.502151i	−0.0271353	−	0.0220208i
$521$	24.0892	+	5.12031i	1.05537	+	0.224325i	0.702745	−	0.711442i	$-0.251957\pi$
$521$	24.0892	+	5.12031i	1.05537	+	0.224325i	0.352620	+	0.935766i	$0.385291\pi$
$522$	3.03010	+	0.644069i	0.132624	+	0.0281901i
$523$	2.84191	−	27.0390i	0.124268	−	1.18233i	−0.737614	−	0.675222i	$-0.764048\pi$
$523$	2.84191	−	27.0390i	0.124268	−	1.18233i	0.861882	−	0.507109i	$-0.169286\pi$
$524$	−35.6835			−1.55884
$525$	13.1866	−	1.05579i	0.575509	−	0.0460782i
$526$	−6.32562			−0.275810
$527$	−4.34032	+	41.2954i	−0.189067	+	1.79886i
$528$	−9.46278	−	2.01138i	−0.411815	−	0.0875339i
$529$	21.9972	+	4.67566i	0.956402	+	0.203290i
$530$	0.282706	+	1.05951i	0.0122800	+	0.0460220i
$531$	−2.06661	+	6.36036i	−0.0896831	+	0.276016i
$532$	−16.5080	−	19.1939i	−0.715712	−	0.832163i
$533$	−0.251873	+	0.775184i	−0.0109098	+	0.0335770i
$534$	−1.28905	−	0.573921i	−0.0557825	−	0.0248360i
$535$	15.8756	+	8.10995i	0.686361	+	0.350624i
$536$	−18.0022	+	8.01508i	−0.777575	+	0.346199i
$537$	−10.7770	−	4.79821i	−0.465060	−	0.207058i
$538$	−3.91768	+	2.84636i	−0.168903	+	0.122715i
$539$	−5.62172	−	20.4162i	−0.242144	−	0.879390i
$540$	4.02315	+	1.08251i	0.173129	+	0.0465840i
$541$	−6.40629	−	2.85227i	−0.275428	−	0.122628i	0.264375	−	0.964420i	$-0.414834\pi$
$541$	−6.40629	−	2.85227i	−0.275428	−	0.122628i	−0.539803	+	0.841792i	$0.681501\pi$
$542$	4.46939	+	4.96376i	0.191977	+	0.213212i
$543$	3.75861	−	6.51010i	0.161297	−	0.279375i
$544$	19.8885	−	4.22743i	0.852712	−	0.181250i
$545$	−18.6421	−	23.0704i	−0.798539	−	0.988227i
$546$	0.126809	−	0.208545i	0.00542693	−	0.00892488i
$547$	8.96891	+	27.6035i	0.383483	+	1.18024i	0.937575	+	0.347783i	$0.113065\pi$
$547$	8.96891	+	27.6035i	0.383483	+	1.18024i	−0.554092	+	0.832455i	$0.686935\pi$
$548$	−1.43785	+	13.6803i	−0.0614220	+	0.584392i
$549$	1.10495	−	1.91383i	0.0471582	−	0.0816803i
$550$	−5.56261	−	0.596430i	−0.237190	−	0.0254319i
$551$	21.5067	+	37.2507i	0.916216	+	1.58693i
$552$	−0.826601	−	0.600561i	−0.0351825	−	0.0255616i
$553$	−41.1117	−	0.934693i	−1.74825	−	0.0397472i
$554$	−1.02227	−	3.14622i	−0.0434320	−	0.133670i
$555$	16.4687	+	0.880373i	0.699057	+	0.0373698i
$556$	−0.980060	−	1.08847i	−0.0415638	−	0.0461613i
$557$	21.7634	−	37.6953i	0.922146	−	1.59720i	0.126057	−	0.992023i	$-0.459768\pi$
$557$	21.7634	−	37.6953i	0.922146	−	1.59720i	0.796089	−	0.605180i	$-0.206899\pi$
$558$	2.98521	−	0.634526i	0.126374	−	0.0268616i
$559$	0.444786	−	0.323156i	0.0188125	−	0.0136680i
$560$	14.4157	+	12.2524i	0.609174	+	0.517758i
$561$	12.3159	+	8.94802i	0.519977	+	0.377786i
$562$	−9.08953	−	4.04692i	−0.383419	−	0.170709i
$563$	1.60665	+	15.2863i	0.0677124	+	0.644240i	0.974767	+	0.223226i	$0.0716589\pi$
$563$	1.60665	+	15.2863i	0.0677124	+	0.644240i	−0.907054	+	0.421014i	$0.861674\pi$
$564$	−0.992557	+	0.441915i	−0.0417942	+	0.0186080i
$565$	−10.2390	+	26.5902i	−0.430757	+	1.11866i
$566$	0.563030	−	0.409065i	0.0236659	−	0.0171943i
$567$	−0.336292	+	2.62429i	−0.0141229	+	0.110210i
$568$	15.1655			0.636330
$569$	−19.8414	+	4.21742i	−0.831795	+	0.176804i	−0.604080	−	0.796924i	$-0.706459\pi$
$569$	−19.8414	+	4.21742i	−0.831795	+	0.176804i	−0.227716	+	0.973728i	$0.573126\pi$
$570$	−1.92431	−	3.78646i	−0.0806005	−	0.158598i
$571$	13.2414	+	2.81455i	0.554136	+	0.117785i	0.476465	−	0.879194i	$-0.341918\pi$
$571$	13.2414	+	2.81455i	0.554136	+	0.117785i	0.0776717	+	0.996979i	$0.475251\pi$
$572$	0.940687	−	1.04474i	0.0393321	−	0.0436827i
$573$	13.5689	+	9.85838i	0.566849	+	0.411840i
$574$	−1.05708	+	3.01813i	−0.0441215	+	0.125974i
$575$	3.09259	+	1.79415i	0.128970	+	0.0748212i
$576$	2.45069	+	4.24472i	0.102112	+	0.176863i
$577$	1.77897	−	0.792050i	0.0740596	−	0.0329735i	−0.369373	−	0.929281i	$-0.620427\pi$
$577$	1.77897	−	0.792050i	0.0740596	−	0.0329735i	0.443432	+	0.896308i	$0.353761\pi$
$578$	−3.01123	−	0.640057i	−0.125251	−	0.0266229i
$579$	7.43814	−	8.26089i	0.309119	−	0.343311i
$580$	−21.9313	−	27.1409i	−0.910648	−	1.12697i
$581$	34.9447	−	14.6159i	1.44975	−	0.606371i
$582$	−1.15330			−0.0478060
$583$	−3.92340	+	0.833944i	−0.162491	+	0.0345384i
$584$	1.58794	+	15.1083i	0.0657096	+	0.625185i
$585$	−0.394776	+	0.393951i	−0.0163220	+	0.0162879i
$586$	0.748862	−	7.12495i	0.0309352	−	0.294329i
$587$	−36.0597	+	26.1989i	−1.48834	+	1.08135i	−0.513598	+	0.858031i	$0.671688\pi$
$587$	−36.0597	+	26.1989i	−1.48834	+	1.08135i	−0.974746	+	0.223315i	$0.928312\pi$
$588$	−7.02779	+	10.9870i	−0.289821	+	0.453097i
$589$	34.2830	+	24.9080i	1.41261	+	1.02632i
$590$	−4.64184	+	3.00754i	−0.191101	+	0.123819i
$591$	1.86642	+	17.7578i	0.0767743	+	0.730459i
$592$	15.7823	+	17.5281i	0.648650	+	0.720399i
$593$	−8.23952	−	14.2713i	−0.338356	−	0.586051i	0.645767	−	0.763534i	$-0.276538\pi$
$593$	−8.23952	−	14.2713i	−0.338356	−	0.586051i	−0.984124	+	0.177484i	$0.943204\pi$
$594$	0.345759	−	1.06414i	0.0141867	−	0.0436620i
$595$	−12.8813	−	26.8401i	−0.528081	−	1.10034i
$596$	5.06746	+	15.5960i	0.207571	+	0.638839i
$597$	−9.51145	+	10.5635i	−0.389278	+	0.432337i
$598$	0.0602626	−	0.0268306i	0.00246432	−	0.00109719i
$599$	−0.242946	+	0.420794i	−0.00992650	+	0.0171932i	−0.870946	−	0.491379i	$-0.836493\pi$
$599$	−0.242946	+	0.420794i	−0.00992650	+	0.0171932i	0.861019	+	0.508572i	$0.169826\pi$
$600$	4.18721	+	5.78865i	0.170942	+	0.236320i
$601$	22.1413			0.903164			0.451582	−	0.892230i	$-0.350860\pi$
$601$	22.1413			0.903164			0.451582	+	0.892230i	$0.350860\pi$
$602$	1.77345	−	1.22789i	0.0722805	−	0.0500449i
$603$	4.26174	+	13.1163i	0.173551	+	0.534136i
$604$	6.12402	−	6.80142i	0.249183	−	0.276746i
$605$	−0.650851	+	4.08166i	−0.0264609	+	0.165943i
$606$	2.15569	+	2.39414i	0.0875689	+	0.0972552i
$607$	13.5254	+	23.4268i	0.548981	+	0.950863i	0.998345	+	0.0575140i	$0.0183174\pi$
$607$	13.5254	+	23.4268i	0.548981	+	0.950863i	−0.449364	+	0.893349i	$0.648349\pi$
$608$	6.41229	−	19.7350i	0.260053	−	0.800360i
$609$	15.1980	−	16.1264i	0.615856	−	0.653475i
$610$	1.70697	−	0.653197i	0.0691134	−	0.0264472i
$611$	0.0152029	−	0.144646i	0.000615044	−	0.00585176i
$612$	−0.980064	−	9.32469i	−0.0396167	−	0.376928i
$613$	2.91543	+	27.7385i	0.117753	+	1.12035i	0.880631	+	0.473803i	$0.157119\pi$
$613$	2.91543	+	27.7385i	0.117753	+	1.12035i	−0.762877	+	0.646543i	$0.776214\pi$
$614$	0.352883	−	3.35746i	0.0142412	−	0.135496i
$615$	3.98625	−	6.12425i	0.160741	−	0.246953i
$616$	7.84360	−	8.32272i	0.316028	−	0.335332i
$617$	7.96583	−	24.5163i	0.320692	−	0.986989i	−0.652656	−	0.757655i	$-0.726345\pi$
$617$	7.96583	−	24.5163i	0.320692	−	0.986989i	0.973348	−	0.229334i	$-0.0736549\pi$
$618$	1.74928	+	3.02984i	0.0703663	+	0.121878i
$619$	18.6944	+	20.7622i	0.751390	+	0.834503i	0.990646	−	0.136453i	$-0.0435704\pi$
$619$	18.6944	+	20.7622i	0.751390	+	0.834503i	−0.239257	+	0.970956i	$0.576904\pi$
$620$	−30.6140	−	15.6390i	−1.22949	−	0.628078i
$621$	−0.478475	+	0.531400i	−0.0192005	+	0.0213243i
$622$	−0.519445	−	1.59869i	−0.0208278	−	0.0641015i
$623$	−8.29860	+	5.74571i	−0.332477	+	0.230197i
$624$	−0.797616			−0.0319302
$625$	−16.6503	−	18.6485i	−0.666013	−	0.745940i
$626$	−0.550647	+	0.953749i	−0.0220083	+	0.0381195i
$627$	14.1929	−	6.31909i	0.566810	−	0.252360i
$628$	0.422782	−	0.469547i	0.0168708	−	0.0187370i
$629$	−11.4693	−	35.2988i	−0.457310	−	1.40746i
$630$	−1.58361	+	1.51003i	−0.0630924	+	0.0601611i
$631$	13.1013	−	40.3217i	0.521555	−	1.60518i	−0.249474	−	0.968382i	$-0.580258\pi$
$631$	13.1013	−	40.3217i	0.521555	−	1.60518i	0.771029	−	0.636800i	$-0.219742\pi$
$632$	−11.1042	−	19.2331i	−0.441703	−	0.765052i
$633$	−17.5311	−	19.4703i	−0.696799	−	0.773874i
$634$	−1.21433	−	11.5536i	−0.0482274	−	0.458853i
$635$	−21.2396	−	1.13541i	−0.842868	−	0.0450575i
$636$	1.99861	+	1.45207i	0.0792499	+	0.0575784i
$637$	−0.803342	−	1.55012i	−0.0318296	−	0.0614182i
$638$	−7.58156	+	5.50833i	−0.300157	+	0.218077i
$639$	1.10943	−	10.5555i	0.0438884	−	0.417571i
$640$	−3.48373	+	21.8474i	−0.137707	+	0.863594i
$641$	0.704715	+	6.70491i	0.0278346	+	0.264828i	0.999585	+	0.0288162i	$0.00917377\pi$
$641$	0.704715	+	6.70491i	0.0278346	+	0.264828i	−0.971750	+	0.236012i	$0.924160\pi$
$642$	−2.88431	+	0.613080i	−0.113835	+	0.0241963i
$643$	−25.9778			−1.02446			−0.512232	−	0.858847i	$-0.671181\pi$
$643$	−25.9778			−1.02446			−0.512232	+	0.858847i	$0.671181\pi$
$644$	−3.25198	+	1.36017i	−0.128146	+	0.0535983i
$645$	−4.60339	+	1.76155i	−0.181258	+	0.0693610i
$646$	−6.39599	+	7.10347i	−0.251647	+	0.279482i
$647$	−3.00815	−	0.639402i	−0.118263	−	0.0251375i	0.148400	−	0.988927i	$-0.452588\pi$
$647$	−3.00815	−	0.639402i	−0.118263	−	0.0251375i	−0.266663	+	0.963790i	$0.585921\pi$
$648$	−1.30533	+	0.581170i	−0.0512782	+	0.0228305i
$649$	−10.1156	−	17.5208i	−0.397074	−	0.687752i
$650$	−0.458827	+	0.0472537i	−0.0179967	+	0.00185344i
$651$	7.21637	−	20.6039i	0.282832	−	0.807532i
$652$	9.60761	+	6.98034i	0.376263	+	0.273371i
$653$	7.59779	−	8.43820i	0.297324	−	0.330212i	−0.575910	−	0.817513i	$-0.695352\pi$
$653$	7.59779	−	8.43820i	0.297324	−	0.330212i	0.873234	+	0.487301i	$0.162019\pi$
$654$	4.79896	+	1.02005i	0.187654	+	0.0398871i
$655$	−30.3132	+	30.2498i	−1.18444	+	1.18196i
$656$	10.2222	−	2.17279i	0.399109	−	0.0848332i
$657$	10.6319			0.414789
$658$	0.0725313	−	0.566006i	0.00282756	−	0.0220652i
$659$	38.6857	−	28.1068i	1.50698	−	1.09488i	0.539485	−	0.841995i	$-0.318619\pi$
$659$	38.6857	−	28.1068i	1.50698	−	1.09488i	0.967495	−	0.252890i	$-0.0813810\pi$
$660$	−10.5774	+	6.85331i	−0.411724	+	0.266765i
$661$	18.7208	−	8.33502i	0.728153	−	0.324195i	−0.00896389	−	0.999960i	$-0.502853\pi$
$661$	18.7208	−	8.33502i	0.728153	−	0.324195i	0.737117	+	0.675765i	$0.236187\pi$
$662$	0.498457	+	4.74250i	0.0193731	+	0.184323i
$663$	1.14661	+	0.510506i	0.0445308	+	0.0198264i
$664$	16.5496	+	12.0240i	0.642249	+	0.466621i
$665$	−30.2948	−	2.31105i	−1.17478	−	0.0896188i
$666$	−2.20696	+	1.60345i	−0.0855179	+	0.0621324i
$667$	5.85818	−	1.24519i	0.226830	−	0.0482141i
$668$	−18.8596	+	32.6657i	−0.729699	+	1.26388i
$669$	15.3451	+	17.0424i	0.593275	+	0.658899i
$670$	−4.09868	+	10.6441i	−0.158346	+	0.411218i
$671$	2.06587	+	6.35810i	0.0797521	+	0.245452i
$672$	−10.6874	−	0.242984i	−0.412277	−	0.00937330i
$673$	15.3327	+	11.1399i	0.591033	+	0.429411i	0.842685	−	0.538407i	$-0.180974\pi$
$673$	15.3327	+	11.1399i	0.591033	+	0.429411i	−0.251652	+	0.967818i	$0.580974\pi$
$674$	0.753366	+	1.30487i	0.0290186	+	0.0502616i
$675$	4.33535	−	2.49093i	0.166868	−	0.0958759i
$676$	−12.0528	+	20.8761i	−0.463571	+	0.802929i
$677$	0.154106	−	1.46622i	0.00592279	−	0.0563516i	−0.991161	−	0.132662i	$-0.957647\pi$
$677$	0.154106	−	1.46622i	0.00592279	−	0.0563516i	0.997084	+	0.0763107i	$0.0243141\pi$
$678$	−1.45642	−	4.48239i	−0.0559333	−	0.172145i
$679$	−4.28629	+	7.04903i	−0.164493	+	0.270517i
$680$	8.77089	−	13.4751i	0.336348	−	0.516746i
$681$	9.40563	−	1.99923i	0.360425	−	0.0766106i
$682$	−4.61624	+	7.99555i	−0.176765	+	0.306166i
$683$	−25.2944	−	28.0923i	−0.967863	−	1.07492i	−0.997157	−	0.0753503i	$-0.975993\pi$
$683$	−25.2944	−	28.0923i	−0.967863	−	1.07492i	0.0292938	−	0.999571i	$-0.490674\pi$
$684$	−8.74145	−	3.89194i	−0.334238	−	0.148812i
$685$	10.3756	+	12.8403i	0.396433	+	0.490603i
$686$	−3.01280	−	6.15186i	−0.115029	−	0.234879i
$687$	−17.2412	+	12.5265i	−0.657793	+	0.477915i
$688$	−6.43967	−	2.86713i	−0.245510	−	0.109308i
$689$	−0.302112	+	0.134509i	−0.0115095	+	0.00512438i
$690$	−0.584208	+	0.0919028i	−0.0222404	+	0.00349868i
$691$	27.7086	+	12.3367i	1.05409	+	0.469309i	0.859266	−	0.511530i	$-0.170921\pi$
$691$	27.7086	+	12.3367i	1.05409	+	0.469309i	0.194820	+	0.980839i	$0.437588\pi$
$692$	6.87739	−	21.1664i	0.261439	−	0.804627i
$693$	−5.21901	−	6.06818i	−0.198254	−	0.230511i
$694$	−1.90895	+	5.87515i	−0.0724628	+	0.223018i
$695$	−1.75529	−	0.0938330i	−0.0665818	−	0.00355929i
$696$	11.7059	+	2.48817i	0.443711	+	0.0943137i
$697$	−16.0856	−	3.41909i	−0.609285	−	0.129507i
$698$	−0.576342	+	5.48353i	−0.0218149	+	0.207555i
$699$	−9.59958			−0.363090
$700$	24.5692	−	1.96714i	0.928628	−	0.0743509i
$701$	−2.74962			−0.103852			−0.0519258	−	0.998651i	$-0.516536\pi$
$701$	−2.74962			−0.103852			−0.0519258	+	0.998651i	$0.516536\pi$
$702$	0.00964283	−	0.0917454i	0.000363945	−	0.00346271i
$703$	−37.0503	−	7.87528i	−1.39738	−	0.297022i
$704$	−14.5034	−	3.08280i	−0.546619	−	0.116187i
$705$	−0.468557	+	1.21682i	−0.0176469	+	0.0458282i
$706$	−0.215935	+	0.664578i	−0.00812681	+	0.0250117i
$707$	22.6447	−	4.27778i	0.851643	−	0.160882i
$708$	−3.85050	+	11.8506i	−0.144711	+	0.445374i
$709$	27.4327	+	12.2138i	1.03026	+	0.458701i	0.851036	−	0.525108i	$-0.175975\pi$
$709$	27.4327	+	12.2138i	1.03026	+	0.458701i	0.179223	+	0.983809i	$0.442642\pi$
$710$	6.21346	−	6.20046i	0.233187	−	0.232699i
$711$	−14.1990	+	6.32182i	−0.532505	+	0.237087i
$712$	−4.97984	−	2.21717i	−0.186628	−	0.0830919i
$713$	4.77345	−	3.46812i	0.178767	−	0.129882i
$714$	4.45197	+	2.10466i	0.166611	+	0.0787651i
$715$	−0.0865362	−	1.68495i	−0.00323627	−	0.0630136i
$716$	−20.0796	−	8.94002i	−0.750411	−	0.334104i
$717$	7.10491	+	7.89081i	0.265338	+	0.294688i
$718$	−4.06250	+	7.03645i	−0.151611	+	0.262598i
$719$	−22.3934	+	4.75987i	−0.835134	+	0.177513i	−0.605582	−	0.795783i	$-0.707059\pi$
$719$	−22.3934	+	4.75987i	−0.835134	+	0.177513i	−0.229552	+	0.973296i	$0.573726\pi$
$720$	6.90516	+	1.85798i	0.257340	+	0.0692428i
$721$	25.0197	+	0.568834i	0.931783	+	0.0211845i
$722$	0.842886	+	2.59414i	0.0313690	+	0.0965438i
$723$	1.33901	−	12.7398i	0.0497982	−	0.473798i
$724$	7.00304	−	12.1296i	0.260266	−	0.450794i
$725$	−41.6388	−	4.46456i	−1.54643	−	0.165810i
$726$	−0.341835	−	0.592076i	−0.0126867	−	0.0219740i
$727$	29.5020	+	21.4345i	1.09417	+	0.794961i	0.980099	−	0.198512i	$-0.0636108\pi$
$727$	29.5020	+	21.4345i	1.09417	+	0.794961i	0.114071	+	0.993473i	$0.463611\pi$
$728$	0.489889	−	0.805649i	0.0181565	−	0.0298594i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	6.82767	+	5.54078i	0.252703	+	0.205073i
$731$	7.42229	+	8.24329i	0.274523	+	0.304889i
$732$	2.05875	−	3.56585i	0.0760934	−	0.131798i
$733$	23.4906	−	4.99307i	0.867644	−	0.184423i	0.247477	−	0.968894i	$-0.420398\pi$
$733$	23.4906	−	4.99307i	0.867644	−	0.184423i	0.620166	+	0.784470i	$0.287065\pi$
$734$	10.2633	−	7.45669i	0.378824	−	0.275232i
$735$	3.34384	+	15.2911i	0.123340	+	0.564022i
$736$	−2.33745	−	1.69826i	−0.0861596	−	0.0625986i
$737$	−38.1138	−	16.9694i	−1.40394	−	0.625074i
$738$	0.126342	+	1.20207i	0.00465073	+	0.0442487i
$739$	27.6089	−	12.2923i	1.01561	−	0.452179i	0.169696	−	0.985496i	$-0.445721\pi$
$739$	27.6089	−	12.2923i	1.01561	−	0.452179i	0.845915	+	0.533317i	$0.179055\pi$
$740$	30.6844	+	1.64031i	1.12798	+	0.0602990i
$741$	1.03628	−	0.752903i	0.0380688	−	0.0276586i
$742$	−1.19700	+	0.500657i	−0.0439433	+	0.0183797i
$743$	40.9573			1.50258			0.751288	−	0.659974i	$-0.229433\pi$
$743$	40.9573			1.50258			0.751288	+	0.659974i	$0.229433\pi$
$744$	11.5325	−	2.45130i	0.422800	−	0.0898690i
$745$	17.5260	+	8.95306i	0.642103	+	0.328015i
$746$	−12.0092	−	2.55264i	−0.439689	−	0.0934589i
$747$	9.57967	−	10.6393i	0.350502	−	0.389272i
$748$	22.9470	+	16.6719i	0.839024	+	0.609587i
$749$	−6.97248	+	19.9076i	−0.254769	+	0.727407i
$750$	4.08225	+	0.659712i	0.149063	+	0.0240893i
$751$	11.8421	+	20.5112i	0.432125	+	0.748463i	0.997056	−	0.0766753i	$-0.0244305\pi$
$751$	11.8421	+	20.5112i	0.432125	+	0.748463i	−0.564931	+	0.825138i	$0.691097\pi$
$752$	−1.70358	+	0.758483i	−0.0621232	+	0.0276590i
$753$	10.6623	+	2.26635i	0.388556	+	0.0825902i
$754$	−0.517001	+	0.574187i	−0.0188281	+	0.0209107i
$755$	−0.563365	−	10.9693i	−0.0205030	−	0.399214i
$756$	−0.626580	+	4.88958i	−0.0227885	+	0.177832i
$757$	31.0914			1.13004			0.565019	−	0.825078i	$-0.308869\pi$
$757$	31.0914			1.13004			0.565019	+	0.825078i	$0.308869\pi$
$758$	7.16679	−	1.52335i	0.260310	−	0.0553305i
$759$	−0.226115	−	2.15134i	−0.00820747	−	0.0780889i
$760$	−7.43400	−	14.6279i	−0.269659	−	0.530609i
$761$	−2.64418	+	25.1577i	−0.0958514	+	0.911965i	0.835903	+	0.548877i	$0.184944\pi$
$761$	−2.64418	+	25.1577i	−0.0958514	+	0.911965i	−0.931755	+	0.363088i	$0.881722\pi$
$762$	2.84631	−	2.06796i	0.103111	−	0.0749144i
$763$	24.0701	−	25.5404i	0.871395	−	0.924623i
$764$	25.2816	+	18.3681i	0.914655	+	0.664536i
$765$	−8.73734	−	7.09052i	−0.315899	−	0.256358i
$766$	0.870437	+	8.28165i	0.0314502	+	0.299228i
$767$	−1.11613	−	1.23958i	−0.0403010	−	0.0447588i
$768$	3.07168	+	5.32031i	0.110840	+	0.191980i
$769$	0.0833043	−	0.256384i	0.00300403	−	0.00924546i	−0.949543	−	0.313636i	$-0.898453\pi$
$769$	0.0833043	−	0.256384i	0.00300403	−	0.00924546i	0.952547	+	0.304391i	$0.0984528\pi$
$770$	−0.189170	−	6.61679i	−0.00681723	−	0.238453i
$771$	2.55625	+	7.86733i	0.0920611	+	0.283335i
$772$	13.8587	−	15.3917i	0.498787	−	0.553959i
$773$	−9.04854	+	4.02867i	−0.325453	+	0.144901i	−0.562959	−	0.826485i	$-0.690337\pi$
$773$	−9.04854	+	4.02867i	−0.325453	+	0.144901i	0.237505	+	0.971386i	$0.423670\pi$
$774$	0.407643	−	0.706058i	0.0146524	−	0.0253787i
$775$	−39.2643	+	12.6669i	−1.41042	+	0.455010i
$776$	−4.45544			−0.159941
$777$	1.59811	+	19.4483i	0.0573320	+	0.697703i
$778$	3.14294	+	9.67299i	0.112680	+	0.346793i
$779$	−11.2299	+	12.4721i	−0.402353	+	0.446859i
$780$	−0.735547	+	0.734009i	−0.0263368	+	0.0262817i
$781$	21.4845	+	23.8609i	0.768775	+	0.853811i
$782$	0.665459	+	1.15261i	0.0237968	+	0.0412172i
$783$	2.58817	−	7.96556i	0.0924936	−	0.284666i
$784$	−12.0622	+	18.8576i	−0.430793	+	0.673486i
$785$	−0.0388928	−	0.757285i	−0.00138814	−	0.0270286i
$786$	0.740433	−	7.04475i	0.0264104	−	0.251278i
$787$	−3.63004	−	34.5375i	−0.129397	−	1.23113i	−0.845822	−	0.533466i	$-0.820889\pi$
$787$	−3.63004	−	34.5375i	−0.129397	−	1.23113i	0.716425	−	0.697665i	$-0.245777\pi$
$788$	3.47752	+	33.0863i	0.123881	+	1.17865i
$789$	−1.78770	+	17.0088i	−0.0636438	+	0.605530i
$790$	−12.4130	−	3.34000i	−0.441636	−	0.118832i
$791$	−32.8094	−	7.75727i	−1.16657	−	0.275817i
$792$	1.33573	−	4.11097i	0.0474633	−	0.146077i
$793$	0.275594	+	0.477343i	0.00978664	+	0.0169510i
$794$	1.85093	+	2.05567i	0.0656871	+	0.0729529i
$795$	2.92878	−	0.460732i	0.103873	−	0.0163405i
$796$	−17.7217	+	19.6820i	−0.628131	+	0.697610i
$797$	−1.72542	−	5.31031i	−0.0611176	−	0.188101i	0.915836	−	0.401553i	$-0.131529\pi$
$797$	−1.72542	−	5.31031i	−0.0611176	−	0.188101i	−0.976954	+	0.213452i	$0.931529\pi$
$798$	4.13187	−	2.86078i	0.146266	−	0.101271i
$799$	2.93445			0.103813
$800$	11.8405	+	16.3691i	0.418627	+	0.578734i
$801$	−1.90750	+	3.30389i	−0.0673983	+	0.116737i
$802$	3.16529	−	1.40928i	0.111770	−	0.0497633i
$803$	−21.5213	+	23.9018i	−0.759471	+	0.843478i
$804$	7.94047	+	24.4383i	0.280039	+	0.861871i
$805$	−1.60951	+	3.91226i	−0.0567279	+	0.137889i
$806$	−0.235223	+	0.723941i	−0.00828537	+	0.0254997i
$807$	6.54634	+	11.3386i	0.230442	+	0.399137i
$808$	8.32786	+	9.24903i	0.292973	+	0.325380i
$809$	2.00426	+	19.0693i	0.0704662	+	0.670441i	0.971556	+	0.236809i	$0.0761016\pi$
$809$	2.00426	+	19.0693i	0.0704662	+	0.670441i	−0.901090	+	0.433632i	$0.857232\pi$
$810$	−0.297194	+	0.771800i	−0.0104423	+	0.0271183i
$811$	−22.5661	−	16.3952i	−0.792402	−	0.575714i	0.116273	−	0.993217i	$-0.462905\pi$
$811$	−22.5661	−	16.3952i	−0.792402	−	0.575714i	−0.908675	+	0.417503i	$0.862905\pi$
$812$	28.3170	−	30.0467i	0.993732	−	1.05443i
$813$	14.6101	−	10.6148i	0.512397	−	0.372278i
$814$	0.862619	−	8.20727i	0.0302348	−	0.287665i
$815$	14.0791	−	2.21481i	0.493170	−	0.0775813i
$816$	−1.68214	−	16.0045i	−0.0588866	−	0.560269i
$817$	11.0730	−	2.35364i	0.387395	−	0.0823433i
$818$	11.6484			0.407276
$819$	−0.524913	−	0.399912i	−0.0183420	−	0.0139741i
$820$	7.42718	−	11.4107i	0.259369	−	0.398479i
$821$	15.2741	−	16.9637i	0.533071	−	0.592036i	−0.415108	−	0.909772i	$-0.636256\pi$
$821$	15.2741	−	16.9637i	0.533071	−	0.592036i	0.948179	+	0.317737i	$0.102923\pi$
$822$	−2.67096	−	0.567731i	−0.0931605	−	0.0198019i
$823$	32.4663	−	14.4549i	1.13171	−	0.503868i	0.246535	−	0.969134i	$-0.420708\pi$
$823$	32.4663	−	14.4549i	1.13171	−	0.503868i	0.885171	+	0.465266i	$0.154041\pi$
$824$	6.75781	+	11.7049i	0.235419	+	0.407758i
$825$	−3.17579	+	14.7886i	−0.110567	+	0.514874i
$826$	−4.26736	−	4.96169i	−0.148480	−	0.172639i
$827$	0.542957	+	0.394481i	0.0188805	+	0.0137175i	0.597185	−	0.802103i	$-0.296286\pi$
$827$	0.542957	+	0.394481i	0.0188805	+	0.0137175i	−0.578305	+	0.815821i	$0.696286\pi$
$828$	−0.891494	+	0.990104i	−0.0309816	+	0.0344085i
$829$	−45.6105	−	9.69480i	−1.58412	−	0.336714i	−0.670062	−	0.742305i	$-0.733732\pi$
$829$	−45.6105	−	9.69480i	−1.58412	−	0.336714i	−0.914055	+	0.405591i	$0.867066\pi$
$830$	11.6966	−	1.84001i	0.405995	−	0.0638677i
$831$	−8.74870	+	1.85959i	−0.303489	+	0.0645086i
$832$	−1.22249			−0.0423822
$833$	29.4097	−	19.3885i	1.01898	−	0.671773i
$834$	0.235225	−	0.170901i	0.00814517	−	0.00591781i
$835$	11.6703	+	43.7374i	0.403869	+	1.51359i
$836$	26.4442	−	11.7737i	0.914593	−	0.407203i
$837$	−0.862505	−	8.20619i	−0.0298125	−	0.283647i
$838$	−6.80157	−	3.02826i	−0.234957	−	0.104609i
$839$	0.497188	+	0.361228i	0.0171648	+	0.0124710i	0.596335	−	0.802736i	$-0.296623\pi$
$839$	0.497188	+	0.361228i	0.0171648	+	0.0124710i	−0.579170	+	0.815207i	$0.696623\pi$
$840$	−6.11779	+	5.83355i	−0.211084	+	0.201277i
$841$	−33.2901	+	24.1867i	−1.14793	+	0.834023i
$842$	9.33885	−	1.98503i	0.321838	−	0.0684088i
$843$	−13.4505	+	23.2969i	−0.463260	+	0.802389i
$844$	−32.6640	−	36.2770i	−1.12434	−	1.24871i
$845$	7.45832	+	27.9518i	0.256574	+	0.961573i
$846$	−0.0666486	−	0.205123i	−0.00229143	−	0.00705228i
$847$	−4.88923	−	0.111159i	−0.167996	−	0.00381946i
$848$	3.43032	+	2.49227i	0.117798	+	0.0855851i
$849$	−0.940808	−	1.62953i	−0.0322885	−	0.0559252i
$850$	−1.91581	−	9.10689i	−0.0657118	−	0.312364i
$851$	−2.63701	+	4.56743i	−0.0903955	+	0.156570i
$852$	2.06709	−	19.6671i	0.0708175	−	0.673783i
$853$	12.1938	+	37.5288i	0.417509	+	1.28496i	0.909987	+	0.414636i	$0.136091\pi$
$853$	12.1938	+	37.5288i	0.417509	+	1.28496i	−0.492478	+	0.870325i	$0.663909\pi$
$854$	1.03842	+	1.89691i	0.0355342	+	0.0649110i
$855$	−10.7252	+	4.10414i	−0.366793	+	0.140358i
$856$	−11.1427	+	2.36845i	−0.380849	+	0.0809520i
$857$	−16.3132	+	28.2553i	−0.557248	+	0.965182i	0.440477	+	0.897764i	$0.354809\pi$
$857$	−16.3132	+	28.2553i	−0.557248	+	0.965182i	−0.997725	+	0.0674178i	$0.978524\pi$
$858$	0.186736	+	0.207392i	0.00637507	+	0.00708023i
$859$	−21.4921	−	9.56891i	−0.733302	−	0.326487i	0.00588919	−	0.999983i	$-0.498125\pi$
$859$	−21.4921	−	9.56891i	−0.733302	−	0.326487i	−0.739191	+	0.673496i	$0.764792\pi$
$860$	−8.57704	+	3.28212i	−0.292475	+	0.111919i
$861$	7.81664	+	3.69531i	0.266390	+	0.125936i
$862$	−3.83881	+	2.78906i	−0.130751	+	0.0949958i
$863$	−0.299049	−	0.133145i	−0.0101797	−	0.00453231i	0.401640	−	0.915797i	$-0.368440\pi$
$863$	−0.299049	−	0.133145i	−0.0101797	−	0.00453231i	−0.411820	+	0.911265i	$0.635107\pi$
$864$	−3.69120	+	1.64343i	−0.125577	+	0.0559105i
$865$	−12.1010	−	23.8111i	−0.411445	−	0.809601i
$866$	6.43243	+	2.86390i	0.218583	+	0.0973193i
$867$	−2.57205	+	7.91595i	−0.0873514	+	0.268840i
$868$	13.4455	−	38.3893i	0.456372	−	1.30302i
$869$	14.5298	−	44.7180i	0.492889	−	1.51696i
$870$	5.81332	−	3.76657i	0.197090	−	0.127699i
$871$	−3.36462	−	0.715171i	−0.114006	−	0.0242327i
$872$	18.5393	+	3.94066i	0.627821	+	0.133448i
$873$	−0.325938	+	3.10109i	−0.0110313	+	0.104956i
$874$	1.35827			0.0459440
$875$	19.2040	−	22.4990i	0.649214	−	0.760606i
$876$	19.8093			0.669295
$877$	4.58647	−	43.6373i	0.154874	−	1.47353i	−0.590584	−	0.806976i	$-0.701103\pi$
$877$	4.58647	−	43.6373i	0.154874	−	1.47353i	0.745458	−	0.666552i	$-0.232231\pi$
$878$	−7.58284	−	1.61178i	−0.255909	−	0.0543950i
$879$	−18.9465	−	4.02720i	−0.639049	−	0.135834i
$880$	−18.1546	+	11.7627i	−0.611990	+	0.396521i
$881$	4.99635	−	15.3772i	0.168331	−	0.518071i	−0.830935	−	0.556370i	$-0.812194\pi$
$881$	4.99635	−	15.3772i	0.168331	−	0.518071i	0.999266	+	0.0382988i	$0.0121939\pi$
$882$	−2.02326	−	1.61543i	−0.0681268	−	0.0543943i
$883$	13.9991	−	43.0847i	0.471106	−	1.44991i	−0.380032	−	0.924973i	$-0.624087\pi$
$883$	13.9991	−	43.0847i	0.471106	−	1.44991i	0.851138	−	0.524942i	$-0.175913\pi$
$884$	2.13637	+	0.951174i	0.0718540	+	0.0319914i
$885$	6.77507	+	13.3313i	0.227742	+	0.448127i
$886$	1.83992	−	0.819184i	0.0618133	−	0.0275210i
$887$	45.7920	+	20.3879i	1.53754	+	0.684559i	0.988498	−	0.151233i	$-0.0483244\pi$
$887$	45.7920	+	20.3879i	1.53754	+	0.684559i	0.549046	+	0.835792i	$0.314991\pi$
$888$	−8.52592	+	6.19444i	−0.286111	+	0.207872i
$889$	−2.06108	−	25.0824i	−0.0691264	−	0.841236i
$890$	−2.94679	+	1.12763i	−0.0987767	+	0.0377982i
$891$	−2.76362	−	1.23044i	−0.0925847	−	0.0412213i
$892$	28.5910	+	31.7535i	0.957296	+	1.06318i
$893$	1.49737	−	2.59352i	0.0501076	−	0.0867889i
$894$	−3.18417	+	0.676816i	−0.106495	+	0.0226361i
$895$	−24.6364	+	9.42744i	−0.823503	+	0.315125i
$896$	−26.1700	−	0.594987i	−0.874278	−	0.0198771i
$897$	−0.0551134	−	0.169622i	−0.00184018	−	0.00566350i
$898$	−0.484731	+	4.61191i	−0.0161757	+	0.153901i
$899$	−34.5547	+	59.8505i	−1.15246	+	1.99613i
$900$	8.07763	−	4.64110i	0.269254	−	0.154703i
$901$	−3.33611	−	5.77832i	−0.111142	−	0.192504i
$902$	−2.95815	−	2.14922i	−0.0984956	−	0.0715613i
$903$	−2.80044	−	5.11561i	−0.0931927	−	0.170237i
$904$	−5.62643	−	17.3164i	−0.187132	−	0.575934i
$905$	−4.33349	−	16.2408i	−0.144050	−	0.539862i
$906$	1.21568	+	1.35015i	0.0403884	+	0.0448558i
$907$	−20.9598	+	36.3034i	−0.695958	+	1.20544i	0.273898	+	0.961759i	$0.411687\pi$
$907$	−20.9598	+	36.3034i	−0.695958	+	1.20544i	−0.969857	+	0.243677i	$0.921646\pi$
$908$	17.5246	−	3.72496i	0.581573	−	0.123617i
$909$	7.04677	−	5.11978i	0.233727	−	0.169812i
$910$	−0.128680	−	0.530376i	−0.00426570	−	0.0175818i
$911$	12.5494	+	9.11764i	0.415779	+	0.302081i	0.775937	−	0.630810i	$-0.217277\pi$
$911$	12.5494	+	9.11764i	0.415779	+	0.302081i	−0.360158	+	0.932891i	$0.617277\pi$
$912$	−15.0034	−	6.67996i	−0.496813	−	0.221196i
$913$	4.52712	+	43.0727i	0.149826	+	1.42550i
$914$	7.65129	−	3.40657i	0.253082	−	0.112679i
$915$	−1.27396	−	4.77445i	−0.0421157	−	0.157838i
$916$	−32.1238	+	23.3393i	−1.06140	+	0.771153i
$917$	−40.3059	−	30.7076i	−1.33102	−	1.01405i
$918$	1.86124			0.0614302
$919$	31.0343	−	6.59655i	1.02373	−	0.217600i	0.334693	−	0.942327i	$-0.391368\pi$
$919$	31.0343	−	6.59655i	1.02373	−	0.217600i	0.689036	+	0.724727i	$0.258034\pi$
$920$	−2.25691	+	0.355039i	−0.0744082	+	0.0117053i
$921$	−8.92807	−	1.89772i	−0.294190	−	0.0625320i
$922$	7.23107	−	8.03092i	0.238143	−	0.264484i
$923$	2.14166	+	1.55601i	0.0704936	+	0.0512166i
$924$	−9.72407	−	11.3062i	−0.319898	−	0.371948i
$925$	27.4570	−	24.6186i	0.902782	−	0.809453i
$926$	−1.66967	−	2.89196i	−0.0548689	−	0.0950357i
$927$	8.64124	−	3.84733i	0.283815	−	0.126363i
$928$	33.1018	+	7.03601i	1.08662	+	0.230968i
$929$	19.2008	−	21.3247i	0.629959	−	0.699641i	−0.340680	−	0.940179i	$-0.610657\pi$
$929$	19.2008	−	21.3247i	0.629959	−	0.699641i	0.970640	+	0.240539i	$0.0773241\pi$
$930$	3.72274	−	5.71941i	0.122074	−	0.187547i
$931$	−2.12900	−	35.8863i	−0.0697751	−	1.17613i
$932$	−17.8859			−0.585874
$933$	−4.44548	+	0.944915i	−0.145538	+	0.0309351i
$934$	−0.632567	−	6.01847i	−0.0206982	−	0.196930i
$935$	33.6267	−	5.28988i	1.09971	−	0.172998i
$936$	0.0372522	−	0.354431i	0.00121763	−	0.0115849i
$937$	−12.8621	+	9.34483i	−0.420185	+	0.305282i	−0.777712	−	0.628620i	$-0.783620\pi$
$937$	−12.8621	+	9.34483i	−0.420185	+	0.305282i	0.357527	+	0.933903i	$0.383620\pi$
$938$	−13.1336	−	3.10524i	−0.428828	−	0.101390i
$939$	2.40890	+	1.75017i	0.0786114	+	0.0571145i
$940$	−0.873015	+	2.26719i	−0.0284746	+	0.0739474i
$941$	−0.355455	−	3.38193i	−0.0115875	−	0.110248i	0.987199	−	0.159492i	$-0.0509855\pi$
$941$	−0.355455	−	3.38193i	−0.0115875	−	0.110248i	−0.998787	+	0.0492439i	$0.984319\pi$
$942$	0.0839267	+	0.0932100i	0.00273448	+	0.00303695i
$943$	1.16840	+	2.02372i	0.0380482	+	0.0659014i
$944$	−6.60883	+	20.3399i	−0.215099	+	0.662007i
$945$	3.61274	+	4.68488i	0.117523	+	0.152399i
$946$	0.762149	+	2.34565i	0.0247796	+	0.0762638i
$947$	−0.131071	+	0.145569i	−0.00425923	+	0.00473036i	−0.745271	−	0.666762i	$-0.767680\pi$
$947$	−0.131071	+	0.145569i	−0.00425923	+	0.00473036i	0.741011	+	0.671492i	$0.234346\pi$
$948$	−26.4556	+	11.7788i	−0.859239	+	0.382558i
$949$	−1.32589	+	2.29651i	−0.0430402	+	0.0745478i
$950$	−9.02644	−	2.95377i	−0.292856	−	0.0958331i
$951$	−31.4095			−1.01852
$952$	17.1988	+	8.13074i	0.557417	+	0.263519i
$953$	−0.687248	−	2.11513i	−0.0222622	−	0.0685159i	0.939308	−	0.343074i	$-0.111468\pi$
$953$	−0.687248	−	2.11513i	−0.0222622	−	0.0685159i	−0.961570	+	0.274559i	$0.911468\pi$
$954$	−0.328144	+	0.364441i	−0.0106240	+	0.0117992i
$955$	37.0479	−	5.82807i	1.19884	−	0.188592i
$956$	13.2379	+	14.7021i	0.428143	+	0.475501i
$957$	12.6686	+	21.9426i	0.409517	+	0.709304i
$958$	−4.68917	+	14.4318i	−0.151500	+	0.466269i
$959$	−13.3967	+	14.2150i	−0.432602	+	0.459027i
$960$	10.5834	+	2.84769i	0.341578	+	0.0919088i
$961$	−3.87649	+	36.8823i	−0.125048	+	1.18975i
$962$	−0.0711210	−	0.676671i	−0.00229303	−	0.0218168i
$963$	0.833355	+	7.92884i	0.0268545	+	0.255503i
$964$	2.49484	−	23.7368i	0.0803533	−	0.764511i
$965$	−1.27490	−	24.8237i	−0.0410406	−	0.799103i
$966$	−0.201051	−	0.670240i	−0.00646871	−	0.0215646i
$967$	−8.57944	+	26.4048i	−0.275896	+	0.849121i	0.713085	+	0.701078i	$0.247298\pi$
$967$	−8.57944	+	26.4048i	−0.275896	+	0.849121i	−0.988981	+	0.148043i	$0.952702\pi$
$968$	−1.32058	−	2.28731i	−0.0424450	−	0.0735169i
$969$	17.2928	+	19.2056i	0.555524	+	0.616972i
$970$	−1.82544	+	1.82162i	−0.0586114	+	0.0584888i
$971$	11.2952	−	12.5445i	0.362479	−	0.402573i	−0.534126	−	0.845405i	$-0.679359\pi$
$971$	11.2952	−	12.5445i	0.362479	−	0.402573i	0.896605	+	0.442831i	$0.146026\pi$
$972$	0.575760	+	1.77201i	0.0184675	+	0.0568372i
$973$	−0.170332	−	2.07286i	−0.00546059	−	0.0664529i
$974$	4.74528			0.152049
$975$	−0.00261065	+	1.24708i	−8.36076e−5	+	0.0399387i
$976$	3.53354	−	6.12027i	0.113106	−	0.195905i
$977$	−22.8849	+	10.1890i	−0.732154	+	0.325976i	−0.738729	−	0.674002i	$-0.764574\pi$
$977$	−22.8849	+	10.1890i	−0.732154	+	0.325976i	0.00657505	+	0.999978i	$0.497907\pi$
$978$	−1.57744	+	1.75192i	−0.0504409	+	0.0560203i
$979$	−3.56636	−	10.9761i	−0.113981	−	0.350799i
$980$	6.23025	+	28.4904i	0.199018	+	0.910094i
$981$	4.09904	−	12.6155i	0.130872	−	0.402783i
$982$	−0.0432050	−	0.0748332i	−0.00137873	−	0.00238802i
$983$	−35.8827	−	39.8518i	−1.14448	−	1.27108i	−0.957411	−	0.288729i	$-0.906767\pi$
$983$	−35.8827	−	39.8518i	−1.14448	−	1.27108i	−0.187071	−	0.982346i	$-0.559899\pi$
$984$	0.488086	+	4.64383i	0.0155596	+	0.148040i
$985$	31.0023	+	25.1590i	0.987816	+	0.801631i
$986$	−12.6116	−	9.16289i	−0.401636	−	0.291806i
$987$	−1.50142	−	0.354988i	−0.0477908	−	0.0112994i
$988$	1.93080	−	1.40281i	0.0614270	−	0.0446293i
$989$	0.164759	−	1.56758i	0.00523903	−	0.0498461i
$990$	−1.13352	−	2.23043i	−0.0360256	−	0.0708876i
$991$	−1.41914	−	13.5022i	−0.0450804	−	0.428911i	−0.993665	−	0.112386i	$-0.964151\pi$
$991$	−1.41914	−	13.5022i	−0.0450804	−	0.428911i	0.948584	−	0.316525i	$-0.102516\pi$
$992$	32.6114	−	6.93176i	1.03541	−	0.220083i
$993$	12.8929			0.409144
$994$	8.26171	+	6.29429i	0.262045	+	0.199643i
$995$	1.63027	+	31.7431i	0.0516830	+	1.00632i
$996$	17.8488	−	19.8232i	0.565562	−	0.628121i
$997$	−35.5023	−	7.54625i	−1.12437	−	0.238992i	−0.392044	−	0.919947i	$-0.628232\pi$
$997$	−35.5023	−	7.54625i	−1.12437	−	0.238992i	−0.732326	+	0.680954i	$0.761565\pi$
$998$	9.12482	−	4.06263i	0.288841	−	0.128600i
$999$	3.68777	+	6.38740i	0.116676	+	0.202088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.a.466.8	yes	160
7.2	even	3	inner	525.2.bg.a.16.13	✓	160
25.11	even	5	inner	525.2.bg.a.361.13	yes	160
175.86	even	15	inner	525.2.bg.a.436.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.a.16.13	✓	160	7.2	even	3	inner
525.2.bg.a.361.13	yes	160	25.11	even	5	inner
525.2.bg.a.436.8	yes	160	175.86	even	15	inner
525.2.bg.a.466.8	yes	160	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0386614 + 0.367839i) q^{2} +(0.978148 + 0.207912i) q^{3} +(1.82248 + 0.387381i) q^{4} +(1.87660 - 1.21589i) q^{5} +(-0.114295 + 0.351762i) q^{6} +(1.72521 + 2.00591i) q^{7} +(-0.441543 + 1.35893i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.0386614 + 0.367839i) q^{2} +(0.978148 + 0.207912i) q^{3} +(1.82248 + 0.387381i) q^{4} +(1.87660 - 1.21589i) q^{5} +(-0.114295 + 0.351762i) q^{6} +(1.72521 + 2.00591i) q^{7} +(-0.441543 + 1.35893i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.374698 + 0.737293i) q^{10} +(-2.76362 + 1.23044i) q^{11} +(1.70212 + 0.757832i) q^{12} +(-0.201783 + 0.146604i) q^{13} +(-0.804549 + 0.557046i) q^{14} +(2.08839 - 0.799150i) q^{15} +(2.92144 + 1.30071i) q^{16} +(-3.36722 - 3.73967i) q^{17} +(-0.184932 + 0.320312i) q^{18} +(-5.02340 + 1.06776i) q^{19} +(3.89108 - 1.48898i) q^{20} +(1.27045 + 2.32076i) q^{21} +(-0.345759 - 1.06414i) q^{22} +(-0.0747451 + 0.711152i) q^{23} +(-0.714431 + 1.23743i) q^{24} +(2.04324 - 4.56346i) q^{25} +(-0.0461254 - 0.0798915i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.36711 + 4.32405i) q^{28} +(-2.58817 - 7.96556i) q^{29} +(0.213218 + 0.799086i) q^{30} +(-5.52126 - 6.13198i) q^{31} +(-2.02026 + 3.49919i) q^{32} +(-2.95905 + 0.628965i) q^{33} +(1.50578 - 1.09401i) q^{34} +(5.67647 + 1.66663i) q^{35} +(1.50736 + 1.09516i) q^{36} +(6.73789 + 2.99990i) q^{37} +(-0.198551 - 1.88908i) q^{38} +(-0.227854 + 0.101447i) q^{39} +(0.823704 + 3.08703i) q^{40} +(2.64381 - 1.92084i) q^{41} +(-0.902784 + 0.377598i) q^{42} -2.20428 q^{43} +(-5.51330 + 1.17189i) q^{44} +(2.20890 - 0.347486i) q^{45} +(-0.258699 - 0.0549882i) q^{46} +(-0.390190 + 0.433350i) q^{47} +(2.58717 + 1.87969i) q^{48} +(-1.04733 + 6.92121i) q^{49} +(1.59962 + 0.928013i) q^{50} +(-2.51611 - 4.35804i) q^{51} +(-0.424538 + 0.189016i) q^{52} +(1.29692 + 0.275670i) q^{53} +(-0.247488 + 0.274863i) q^{54} +(-3.69012 + 5.66929i) q^{55} +(-3.48764 + 1.45874i) q^{56} -5.13563 q^{57} +(3.03010 - 0.644069i) q^{58} +(0.699053 + 6.65105i) q^{59} +(4.11563 - 0.647436i) q^{60} +(0.230998 - 2.19780i) q^{61} +(2.46904 - 1.79386i) q^{62} +(0.760177 + 2.53419i) q^{63} +(3.96530 + 2.88096i) q^{64} +(-0.200412 + 0.520462i) q^{65} +(-0.116957 - 1.11277i) q^{66} +(9.22816 + 10.2489i) q^{67} +(-4.68802 - 8.11990i) q^{68} +(-0.220968 + 0.680071i) q^{69} +(-0.832511 + 2.02359i) q^{70} +(-3.27981 - 10.0942i) q^{71} +(-0.956095 + 1.06185i) q^{72} +(9.71271 - 4.32438i) q^{73} +(-1.36398 + 2.36247i) q^{74} +(2.94739 - 4.03892i) q^{75} -9.56870 q^{76} +(-7.23596 - 3.42080i) q^{77} +(-0.0285071 - 0.0877357i) q^{78} +(-10.4001 + 11.5505i) q^{79} +(7.06388 - 1.11123i) q^{80} +(0.669131 + 0.743145i) q^{81} +(0.604345 + 1.04676i) q^{82} +(4.42407 - 13.6159i) q^{83} +(1.41636 + 4.72171i) q^{84} +(-10.8659 - 2.92371i) q^{85} +(0.0852206 - 0.810819i) q^{86} +(-0.875477 - 8.32961i) q^{87} +(-0.451827 - 4.29885i) q^{88} +(-0.398777 + 3.79411i) q^{89} +(0.0424196 + 0.825954i) q^{90} +(-0.642191 - 0.151836i) q^{91} +(-0.411708 + 1.26711i) q^{92} +(-4.12570 - 7.14591i) q^{93} +(-0.144318 - 0.160281i) q^{94} +(-8.12864 + 8.11164i) q^{95} +(-2.70364 + 3.00269i) q^{96} +(0.963569 + 2.96556i) q^{97} +(-2.50540 - 0.652833i) q^{98} -3.02516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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