LMFDB - Embedded newform 108.2.l.a.23.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(11,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("108.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	108.23
Dual form			108.2.l.a.47.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654159 + 1.25382i) q^{2} +(1.71606 + 0.234845i) q^{3} +(-1.14415 + 1.64040i) q^{4} +(0.137245 + 0.0242000i) q^{5} +(0.828118 + 2.30526i) q^{6} +(-2.98823 - 3.56123i) q^{7} +(-2.80523 - 0.361485i) q^{8} +(2.88970 + 0.806015i) q^{9} +O(q^{10})$	\(q+(0.654159 + 1.25382i) q^{2} +(1.71606 + 0.234845i) q^{3} +(-1.14415 + 1.64040i) q^{4} +(0.137245 + 0.0242000i) q^{5} +(0.828118 + 2.30526i) q^{6} +(-2.98823 - 3.56123i) q^{7} +(-2.80523 - 0.361485i) q^{8} +(2.88970 + 0.806015i) q^{9} +(0.0594376 + 0.187912i) q^{10} +(-0.182573 - 1.03542i) q^{11} +(-2.34867 + 2.54632i) q^{12} +(-1.46220 + 0.532196i) q^{13} +(2.51039 - 6.07633i) q^{14} +(0.229837 + 0.0737600i) q^{15} +(-1.38183 - 3.75374i) q^{16} +(5.25631 + 3.03473i) q^{17} +(0.879718 + 4.15043i) q^{18} +(-3.80088 + 2.19444i) q^{19} +(-0.196727 + 0.197449i) q^{20} +(-4.29163 - 6.81305i) q^{21} +(1.17880 - 0.906244i) q^{22} +(1.94128 + 1.62893i) q^{23} +(-4.72904 - 1.27912i) q^{24} +(-4.68021 - 1.70346i) q^{25} +(-1.62379 - 1.48520i) q^{26} +(4.76959 + 2.06180i) q^{27} +(9.26084 - 0.827297i) q^{28} +(0.210458 - 0.578229i) q^{29} +(0.0578679 + 0.336426i) q^{30} +(3.18818 - 3.79952i) q^{31} +(3.80260 - 4.18811i) q^{32} +(-0.0701412 - 1.81972i) q^{33} +(-0.366562 + 8.57569i) q^{34} +(-0.323938 - 0.561078i) q^{35} +(-4.62844 + 3.81805i) q^{36} +(-1.43991 + 2.49400i) q^{37} +(-5.23782 - 3.33012i) q^{38} +(-2.63420 + 0.569889i) q^{39} +(-0.376257 - 0.117499i) q^{40} +(-2.25297 - 6.18999i) q^{41} +(5.73496 - 9.83776i) q^{42} +(2.15530 - 0.380038i) q^{43} +(1.90740 + 0.885188i) q^{44} +(0.377091 + 0.180553i) q^{45} +(-0.772484 + 3.49960i) q^{46} +(-8.46639 + 7.10414i) q^{47} +(-1.48975 - 6.76614i) q^{48} +(-2.53733 + 14.3899i) q^{49} +(-0.925763 - 6.98250i) q^{50} +(8.30743 + 6.44219i) q^{51} +(0.799963 - 3.00750i) q^{52} +8.73360i q^{53} +(0.534935 + 7.32897i) q^{54} -0.146525i q^{55} +(7.09534 + 11.0703i) q^{56} +(-7.03787 + 2.87316i) q^{57} +(0.862670 - 0.114376i) q^{58} +(-1.42477 + 8.08025i) q^{59} +(-0.383965 + 0.292632i) q^{60} +(8.56477 - 7.18670i) q^{61} +(6.84951 + 1.51193i) q^{62} +(-5.76467 - 12.6994i) q^{63} +(7.73866 + 2.02810i) q^{64} +(-0.213559 + 0.0376562i) q^{65} +(2.23572 - 1.27833i) q^{66} +(1.93034 + 5.30357i) q^{67} +(-10.9922 + 5.15026i) q^{68} +(2.94880 + 3.25123i) q^{69} +(0.491586 - 0.773196i) q^{70} +(2.33277 - 4.04048i) q^{71} +(-7.81490 - 3.30564i) q^{72} +(-5.64518 - 9.77774i) q^{73} +(-4.06898 - 0.173925i) q^{74} +(-7.63146 - 4.02235i) q^{75} +(0.749029 - 8.74574i) q^{76} +(-3.14181 + 3.74426i) q^{77} +(-2.43772 - 2.93002i) q^{78} +(0.572755 - 1.57363i) q^{79} +(-0.0988087 - 0.548623i) q^{80} +(7.70068 + 4.65828i) q^{81} +(6.28736 - 6.87406i) q^{82} +(2.20553 + 0.802749i) q^{83} +(16.0864 + 0.755175i) q^{84} +(0.647964 + 0.543706i) q^{85} +(1.88641 + 2.45377i) q^{86} +(0.496952 - 0.942848i) q^{87} +(0.137869 + 2.97059i) q^{88} +(7.63741 - 4.40946i) q^{89} +(0.0202964 + 0.590917i) q^{90} +(6.26466 + 3.61690i) q^{91} +(-4.89321 + 1.32073i) q^{92} +(6.36339 - 5.77146i) q^{93} +(-14.4457 - 5.96813i) q^{94} +(-0.574758 + 0.209195i) q^{95} +(7.50902 - 6.29401i) q^{96} +(-0.978443 - 5.54902i) q^{97} +(-19.7022 + 6.23192i) q^{98} +(0.306985 - 3.13921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.654159	+	1.25382i	0.462560	+	0.886588i
$2$	0.654159	+	1.25382i	0.462560	+	0.886588i
$3$	1.71606	+	0.234845i	0.990765	+	0.135588i
$3$	1.71606	+	0.234845i	0.990765	+	0.135588i
$4$	−1.14415	+	1.64040i	−0.572077	+	0.820200i
$5$	0.137245	+	0.0242000i	0.0613780	+	0.0108226i	0.204253	−	0.978918i	$-0.434524\pi$
$5$	0.137245	+	0.0242000i	0.0613780	+	0.0108226i	−0.142875	+	0.989741i	$0.545635\pi$
$6$	0.828118	+	2.30526i	0.338078	+	0.941118i
$7$	−2.98823	−	3.56123i	−1.12944	−	1.34602i	−0.930621	−	0.365984i	$-0.880732\pi$
$7$	−2.98823	−	3.56123i	−1.12944	−	1.34602i	−0.198824	−	0.980035i	$-0.563712\pi$
$8$	−2.80523	−	0.361485i	−0.991799	−	0.127804i
$9$	2.88970	+	0.806015i	0.963232	+	0.268672i
$10$	0.0594376	+	0.187912i	0.0187958	+	0.0594231i
$11$	−0.182573	−	1.03542i	−0.0550477	−	0.312191i	0.944834	−	0.327549i	$-0.106223\pi$
$11$	−0.182573	−	1.03542i	−0.0550477	−	0.312191i	−0.999882	+	0.0153574i	$0.995111\pi$
$12$	−2.34867	+	2.54632i	−0.678003	+	0.735059i
$13$	−1.46220	+	0.532196i	−0.405541	+	0.147605i	−0.536733	−	0.843752i	$-0.680342\pi$
$13$	−1.46220	+	0.532196i	−0.405541	+	0.147605i	0.131192	+	0.991357i	$0.458119\pi$
$14$	2.51039	−	6.07633i	0.670929	−	1.62397i
$15$	0.229837	+	0.0737600i	0.0593437	+	0.0190448i
$16$	−1.38183	−	3.75374i	−0.345457	−	0.938435i
$17$	5.25631	+	3.03473i	1.27484	+	0.736031i	0.975895	−	0.218238i	$-0.0700310\pi$
$17$	5.25631	+	3.03473i	1.27484	+	0.736031i	0.298948	+	0.954269i	$0.403364\pi$
$18$	0.879718	+	4.15043i	0.207351	+	0.978267i
$19$	−3.80088	+	2.19444i	−0.871981	+	0.503439i	−0.868006	−	0.496553i	$-0.834599\pi$
$19$	−3.80088	+	2.19444i	−0.871981	+	0.503439i	−0.00397518	+	0.999992i	$0.501265\pi$
$20$	−0.196727	+	0.197449i	−0.0439896	+	0.0441509i
$21$	−4.29163	−	6.81305i	−0.936510	−	1.48673i
$22$	1.17880	−	0.906244i	0.251322	−	0.193212i
$23$	1.94128	+	1.62893i	0.404785	+	0.339655i	0.822340	−	0.568997i	$-0.192668\pi$
$23$	1.94128	+	1.62893i	0.404785	+	0.339655i	−0.417555	+	0.908652i	$0.637113\pi$
$24$	−4.72904	−	1.27912i	−0.965312	−	0.261100i
$25$	−4.68021	−	1.70346i	−0.936042	−	0.340692i
$26$	−1.62379	−	1.48520i	−0.318451	−	0.291271i
$27$	4.76959	+	2.06180i	0.917908	+	0.396793i
$28$	9.26084	−	0.827297i	1.75013	−	0.156345i
$29$	0.210458	−	0.578229i	0.0390811	−	0.107374i	−0.918617	−	0.395149i	$-0.870693\pi$
$29$	0.210458	−	0.578229i	0.0390811	−	0.107374i	0.957698	+	0.287774i	$0.0929153\pi$
$30$	0.0578679	+	0.336426i	0.0105652	+	0.0614228i
$31$	3.18818	−	3.79952i	0.572613	−	0.682414i	−0.399552	−	0.916711i	$-0.630834\pi$
$31$	3.18818	−	3.79952i	0.572613	−	0.682414i	0.972165	+	0.234297i	$0.0752787\pi$
$32$	3.80260	−	4.18811i	0.672210	−	0.740360i
$33$	−0.0701412	−	1.81972i	−0.0122100	−	0.316772i
$34$	−0.366562	+	8.57569i	−0.0628648	+	1.47072i
$35$	−0.323938	−	0.561078i	−0.0547556	−	0.0948394i
$36$	−4.62844	+	3.81805i	−0.771407	+	0.636342i
$37$	−1.43991	+	2.49400i	−0.236720	+	0.410012i	−0.959771	−	0.280783i	$-0.909406\pi$
$37$	−1.43991	+	2.49400i	−0.236720	+	0.410012i	0.723051	+	0.690795i	$0.242739\pi$
$38$	−5.23782	−	3.33012i	−0.849686	−	0.540218i
$39$	−2.63420	+	0.569889i	−0.421809	+	0.0912552i
$40$	−0.376257	−	0.117499i	−0.0594914	−	0.0185782i
$41$	−2.25297	−	6.18999i	−0.351855	−	0.966713i	−0.981774	−	0.190053i	$-0.939134\pi$
$41$	−2.25297	−	6.18999i	−0.351855	−	0.966713i	0.629919	−	0.776661i	$-0.283088\pi$
$42$	5.73496	−	9.83776i	0.884923	−	1.51800i
$43$	2.15530	−	0.380038i	0.328681	−	0.0579553i	−0.00687300	−	0.999976i	$-0.502188\pi$
$43$	2.15530	−	0.380038i	0.328681	−	0.0579553i	0.335554	+	0.942021i	$0.391077\pi$
$44$	1.90740	+	0.885188i	0.287551	+	0.133447i
$45$	0.377091	+	0.180553i	0.0562135	+	0.0269152i
$46$	−0.772484	+	3.49960i	−0.113897	+	0.515988i
$47$	−8.46639	+	7.10414i	−1.23495	+	1.03625i	−0.237048	+	0.971498i	$0.576180\pi$
$47$	−8.46639	+	7.10414i	−1.23495	+	1.03625i	−0.997902	+	0.0647475i	$0.979376\pi$
$48$	−1.48975	−	6.76614i	−0.215026	−	0.976608i
$49$	−2.53733	+	14.3899i	−0.362476	+	2.05570i
$50$	−0.925763	−	6.98250i	−0.130923	−	0.987474i
$51$	8.30743	+	6.44219i	1.16327	+	0.902087i
$52$	0.799963	−	3.00750i	0.110935	−	0.417066i
$53$			8.73360i			1.19965i	0.800130	+	0.599826i	$0.204764\pi$
$53$			8.73360i			1.19965i	−0.800130	+	0.599826i	$0.795236\pi$
$54$	0.534935	+	7.32897i	0.0727955	+	0.997347i
$55$		−	0.146525i		−	0.0197574i
$56$	7.09534	+	11.0703i	0.948155	+	1.47933i
$57$	−7.03787	+	2.87316i	−0.932189	+	0.380559i
$58$	0.862670	−	0.114376i	0.113274	−	0.0150183i
$59$	−1.42477	+	8.08025i	−0.185489	+	1.05196i	0.739837	+	0.672786i	$0.234903\pi$
$59$	−1.42477	+	8.08025i	−0.185489	+	1.05196i	−0.925326	+	0.379173i	$0.876208\pi$
$60$	−0.383965	+	0.292632i	−0.0495697	+	0.0377787i
$61$	8.56477	−	7.18670i	1.09661	−	0.920162i	0.0994142	−	0.995046i	$-0.468303\pi$
$61$	8.56477	−	7.18670i	1.09661	−	0.920162i	0.997192	+	0.0748840i	$0.0238587\pi$
$62$	6.84951	+	1.51193i	0.869888	+	0.192015i
$63$	−5.76467	−	12.6994i	−0.726280	−	1.59998i
$64$	7.73866	+	2.02810i	0.967332	+	0.253513i
$65$	−0.213559	+	0.0376562i	−0.0264887	+	0.00467068i
$66$	2.23572	−	1.27833i	0.275198	−	0.157351i
$67$	1.93034	+	5.30357i	0.235829	+	0.647934i	0.999996	+	0.00291580i	$0.000928130\pi$
$67$	1.93034	+	5.30357i	0.235829	+	0.647934i	−0.764167	+	0.645019i	$0.776850\pi$
$68$	−10.9922	+	5.15026i	−1.33300	+	0.624561i
$69$	2.94880	+	3.25123i	0.354994	+	0.391402i
$70$	0.491586	−	0.773196i	0.0587558	−	0.0924146i
$71$	2.33277	−	4.04048i	0.276849	−	0.479517i	−0.693751	−	0.720215i	$-0.744043\pi$
$71$	2.33277	−	4.04048i	0.276849	−	0.479517i	0.970600	+	0.240698i	$0.0773764\pi$
$72$	−7.81490	−	3.30564i	−0.920995	−	0.389574i
$73$	−5.64518	−	9.77774i	−0.660718	−	1.14440i	−0.980427	−	0.196882i	$-0.936918\pi$
$73$	−5.64518	−	9.77774i	−0.660718	−	1.14440i	0.319709	−	0.947516i	$-0.396415\pi$
$74$	−4.06898	−	0.173925i	−0.473009	−	0.0202184i
$75$	−7.63146	−	4.02235i	−0.881205	−	0.464461i
$76$	0.749029	−	8.74574i	0.0859195	−	1.00320i
$77$	−3.14181	+	3.74426i	−0.358042	+	0.426698i
$78$	−2.43772	−	2.93002i	−0.276018	−	0.331760i
$79$	0.572755	−	1.57363i	0.0644400	−	0.177047i	−0.903294	−	0.429023i	$-0.858858\pi$
$79$	0.572755	−	1.57363i	0.0644400	−	0.177047i	0.967734	+	0.251975i	$0.0810802\pi$
$80$	−0.0988087	−	0.548623i	−0.0110471	−	0.0613379i
$81$	7.70068	+	4.65828i	0.855631	+	0.517586i
$82$	6.28736	−	6.87406i	0.694322	−	0.759113i
$83$	2.20553	+	0.802749i	0.242089	+	0.0881131i	0.460215	−	0.887807i	$-0.347772\pi$
$83$	2.20553	+	0.802749i	0.242089	+	0.0881131i	−0.218126	+	0.975921i	$0.569994\pi$
$84$	16.0864	+	0.755175i	1.75517	+	0.0823964i
$85$	0.647964	+	0.543706i	0.0702815	+	0.0589732i
$86$	1.88641	+	2.45377i	0.203417	+	0.264596i
$87$	0.496952	−	0.942848i	0.0532788	−	0.101084i
$88$	0.137869	+	2.97059i	0.0146969	+	0.316666i
$89$	7.63741	−	4.40946i	0.809564	−	0.467402i	−0.0372408	−	0.999306i	$-0.511857\pi$
$89$	7.63741	−	4.40946i	0.809564	−	0.467402i	0.846804	+	0.531905i	$0.178524\pi$
$90$	0.0202964	+	0.590917i	0.00213943	+	0.0622881i
$91$	6.26466	+	3.61690i	0.656715	+	0.379154i
$92$	−4.89321	+	1.32073i	−0.510153	+	0.137696i
$93$	6.36339	−	5.77146i	0.659853	−	0.598473i
$94$	−14.4457	−	5.96813i	−1.48996	−	0.615566i
$95$	−0.574758	+	0.209195i	−0.0589689	+	0.0214629i
$96$	7.50902	−	6.29401i	0.766387	−	0.642380i
$97$	−0.978443	−	5.54902i	−0.0993458	−	0.563418i	−0.993329	−	0.115317i	$-0.963212\pi$
$97$	−0.978443	−	5.54902i	−0.0993458	−	0.563418i	0.893983	−	0.448101i	$-0.147899\pi$
$98$	−19.7022	+	6.23192i	−1.99023	+	0.629519i
$99$	0.306985	−	3.13921i	0.0308532	−	0.315502i
$100$	8.14923	−	5.72841i	0.814923	−	0.572841i
$101$	−6.72190	−	8.01085i	−0.668854	−	0.797109i	0.319773	−	0.947494i	$-0.396393\pi$
$101$	−6.72190	−	8.01085i	−0.668854	−	0.797109i	−0.988628	+	0.150385i	$0.951949\pi$
$102$	−2.64300	+	14.6303i	−0.261696	+	1.44861i
$103$	−1.52148	−	0.268277i	−0.149915	−	0.0264341i	0.0981867	−	0.995168i	$-0.468696\pi$
$103$	−1.52148	−	0.268277i	−0.149915	−	0.0264341i	−0.248102	+	0.968734i	$0.579807\pi$
$104$	4.29419	−	0.964372i	0.421080	−	0.0945644i
$105$	−0.424130	−	1.03892i	−0.0413908	−	0.101388i
$106$	−10.9504	+	5.71316i	−1.06360	+	0.554911i
$107$	7.89051			0.762805			0.381402	−	0.924409i	$-0.375441\pi$
$107$	7.89051			0.762805			0.381402	+	0.924409i	$0.375441\pi$
$108$	−8.83932	+	5.46503i	−0.850563	+	0.525872i
$109$	1.78550			0.171020			0.0855098	−	0.996337i	$-0.472748\pi$
$109$	1.78550			0.171020			0.0855098	+	0.996337i	$0.472748\pi$
$110$	0.183717	−	0.0958505i	0.0175167	−	0.00913899i
$111$	−3.05668	+	3.94169i	−0.290127	+	0.374129i
$112$	−9.23872	+	16.1380i	−0.872977	+	1.52490i
$113$	−10.4607	−	1.84450i	−0.984057	−	0.173516i	−0.341607	−	0.939843i	$-0.610971\pi$
$113$	−10.4607	−	1.84450i	−0.984057	−	0.173516i	−0.642451	+	0.766327i	$0.722082\pi$
$114$	−8.20633	−	6.94476i	−0.768593	−	0.650436i
$115$	0.227011	+	0.270542i	0.0211689	+	0.0252281i
$116$	0.707730	+	1.00682i	0.0657111	+	0.0934807i
$117$	−4.65426	+	0.359332i	−0.430287	+	0.0332203i
$118$	−11.0632	+	3.49936i	−1.01845	+	0.322142i
$119$	−4.89968	−	27.7874i	−0.449152	−	2.54727i
$120$	−0.618084	−	0.289997i	−0.0564231	−	0.0264730i
$121$	9.29786	−	3.38414i	0.845260	−	0.307649i
$122$	14.6136	+	6.03748i	1.32305	+	0.546608i
$123$	−2.41253	−	11.1515i	−0.217531	−	1.00549i
$124$	2.58497	+	9.57712i	0.232138	+	0.860051i
$125$	−1.20457	−	0.695459i	−0.107740	−	0.0622038i
$126$	12.1519	−	15.5353i	1.08257	−	1.38400i
$127$	−2.89596	+	1.67198i	−0.256975	+	0.148364i	−0.622954	−	0.782259i	$-0.714067\pi$
$127$	−2.89596	+	1.67198i	−0.256975	+	0.148364i	0.365979	+	0.930623i	$0.380734\pi$
$128$	2.51943	+	11.0296i	0.222688	+	0.974890i
$129$	3.78787	−	0.146004i	0.333503	−	0.0128549i
$130$	−0.186916	−	0.243132i	−0.0163936	−	0.0213241i
$131$	2.00847	+	1.68531i	0.175481	+	0.147246i	0.726298	−	0.687380i	$-0.241239\pi$
$131$	2.00847	+	1.68531i	0.175481	+	0.147246i	−0.550817	+	0.834626i	$0.685684\pi$
$132$	3.06532	+	1.96697i	0.266802	+	0.171203i
$133$	19.1728	+	6.97833i	1.66249	+	0.605098i
$134$	−5.38700	+	5.88969i	−0.465366	+	0.508791i
$135$	0.604708	+	0.398396i	0.0520450	+	0.0342885i
$136$	−13.6482	−	10.4132i	−1.17032	−	0.892926i
$137$	3.04906	−	8.37723i	0.260499	−	0.715715i	−0.738635	−	0.674106i	$-0.764529\pi$
$137$	3.04906	−	8.37723i	0.260499	−	0.715715i	0.999134	−	0.0416094i	$-0.0132485\pi$
$138$	−2.14749	+	5.82409i	−0.182806	+	0.495780i
$139$	9.64531	−	11.4948i	0.818105	−	0.974979i	−0.181860	−	0.983324i	$-0.558212\pi$
$139$	9.64531	−	11.4948i	0.818105	−	0.974979i	0.999965	+	0.00834505i	$0.00265634\pi$
$140$	1.29103	+	0.110570i	0.109112	+	0.00934488i
$141$	−16.1972	+	10.2028i	−1.36405	+	0.859232i
$142$	6.59206	+	0.281773i	0.553193	+	0.0236458i
$143$	0.818005	+	1.41683i	0.0684050	+	0.118481i
$144$	−0.967492	−	11.9609i	−0.0806243	−	0.996745i
$145$	0.0428775	−	0.0742661i	0.00356079	−	0.00616746i
$146$	8.56673	−	13.4743i	0.708987	−	1.11514i
$147$	−7.73360	+	24.0980i	−0.637857	+	1.98757i
$148$	−2.44368	−	5.21556i	−0.200870	−	0.428716i
$149$	6.19266	+	17.0142i	0.507323	+	1.39386i	0.883989	+	0.467509i	$0.154848\pi$
$149$	6.19266	+	17.0142i	0.507323	+	1.39386i	−0.376666	+	0.926349i	$0.622929\pi$
$150$	0.0511443	−	12.1998i	0.00417591	−	0.996107i
$151$	−14.3804	+	2.53565i	−1.17026	+	0.206348i	−0.724803	−	0.688956i	$-0.758069\pi$
$151$	−14.3804	+	2.53565i	−1.17026	+	0.206348i	−0.445456	+	0.895304i	$0.646958\pi$
$152$	11.4556	−	4.78195i	0.929172	−	0.387867i
$153$	12.7431	+	13.0061i	1.03022	+	1.05148i
$154$	−6.74988	−	1.48994i	−0.543921	−	0.120062i
$155$	0.529511	−	0.444312i	0.0425313	−	0.0356880i
$156$	2.07908	−	4.97318i	0.166460	−	0.398173i
$157$	0.0237965	−	0.134957i	0.00189917	−	0.0107707i	−0.983843	−	0.179031i	$-0.942704\pi$
$157$	0.0237965	−	0.134957i	0.00189917	−	0.0107707i	0.985743	+	0.168260i	$0.0538149\pi$
$158$	2.34773	−	0.311270i	0.186776	−	0.0247633i
$159$	−2.05104	+	14.9873i	−0.162658	+	1.18857i
$160$	0.623241	−	0.482775i	0.0492715	−	0.0381667i
$161$		−	11.7810i		−	0.928469i
$162$	−0.803195	+	12.7026i	−0.0631050	+	0.998007i
$163$			12.0210i			0.941554i	0.882252	+	0.470777i	$0.156026\pi$
$163$			12.0210i			0.941554i	−0.882252	+	0.470777i	$0.843974\pi$
$164$	12.7318	+	3.38652i	0.994186	+	0.264443i
$165$	0.0344107	−	0.251445i	0.00267887	−	0.0195750i
$166$	0.436263	+	3.29048i	0.0338606	+	0.255391i
$167$	1.95387	−	11.0810i	0.151195	−	0.857471i	−0.810987	−	0.585064i	$-0.801069\pi$
$167$	1.95387	−	11.0810i	0.151195	−	0.857471i	0.962182	−	0.272407i	$-0.0878196\pi$
$168$	9.57620	+	20.6635i	0.738820	+	1.59423i
$169$	−8.10379	+	6.79989i	−0.623368	+	0.523068i
$170$	−0.257841	+	1.16810i	−0.0197755	+	0.0895894i
$171$	−12.7521	+	3.27769i	−0.975180	+	0.250651i
$172$	−1.84258	+	3.97038i	−0.140496	+	0.302739i
$173$	5.61630	−	0.990305i	0.426999	−	0.0752915i	0.0439813	−	0.999032i	$-0.485996\pi$
$173$	5.61630	−	0.990305i	0.426999	−	0.0752915i	0.383018	+	0.923741i	$0.374885\pi$
$174$	1.50725	+	0.00631875i	0.114264	+	0.000479023i
$175$	7.91914	+	21.7577i	0.598631	+	1.64472i
$176$	−3.63442	+	2.11610i	−0.273954	+	0.159507i
$177$	−4.34259	+	13.5316i	−0.326409	+	1.01709i
$178$	10.5248	+	6.69148i	0.788864	+	0.501548i
$179$	6.20187	−	10.7419i	0.463549	−	0.802891i	−0.535585	−	0.844481i	$-0.679909\pi$
$179$	6.20187	−	10.7419i	0.463549	−	0.802891i	0.999135	+	0.0415901i	$0.0132424\pi$
$180$	−0.727629	+	0.412001i	−0.0542342	+	0.0307088i
$181$	0.582122	+	1.00827i	0.0432688	+	0.0749437i	0.886849	−	0.462060i	$-0.152889\pi$
$181$	0.582122	+	1.00827i	0.0432688	+	0.0749437i	−0.843580	+	0.537004i	$0.819556\pi$
$182$	−0.436881	+	10.2208i	−0.0323838	+	0.757617i
$183$	16.3854	−	10.3214i	1.21124	−	0.762978i
$184$	−4.85691	−	5.27126i	−0.358056	−	0.388603i
$185$	−0.257976	+	0.307444i	−0.0189668	+	0.0226037i
$186$	11.3991	+	4.20312i	0.835820	+	0.308188i
$187$	2.18257	−	5.99656i	0.159605	−	0.438512i
$188$	−1.96680	−	22.0165i	−0.143443	−	1.60572i
$189$	−6.91009	−	23.1467i	−0.502635	−	1.68368i
$190$	−0.638277	−	0.583799i	−0.0463055	−	0.0423533i
$191$	13.5161	+	4.91947i	0.977993	+	0.355960i	0.781060	−	0.624456i	$-0.214679\pi$
$191$	13.5161	+	4.91947i	0.977993	+	0.355960i	0.196934	+	0.980417i	$0.436902\pi$
$192$	12.8037	+	5.29772i	0.924026	+	0.382330i
$193$	−14.0915	−	11.8242i	−1.01433	−	0.851125i	−0.0254271	−	0.999677i	$-0.508095\pi$
$193$	−14.0915	−	11.8242i	−1.01433	−	0.851125i	−0.988905	+	0.148551i	$0.952539\pi$
$194$	6.31745	−	4.85674i	0.453566	−	0.348693i
$195$	−0.375322	+	0.0144669i	−0.0268774	+	0.00103599i
$196$	−20.7021	−	20.6265i	−1.47872	−	1.47332i
$197$	−18.3471	+	10.5927i	−1.30718	+	0.754699i	−0.981624	−	0.190825i	$-0.938884\pi$
$197$	−18.3471	+	10.5927i	−1.30718	+	0.754699i	−0.325553	+	0.945524i	$0.605550\pi$
$198$	4.13683	−	1.66863i	0.293992	−	0.118585i
$199$	−5.80763	−	3.35304i	−0.411692	−	0.237691i	0.279824	−	0.960051i	$-0.409724\pi$
$199$	−5.80763	−	3.35304i	−0.411692	−	0.237691i	−0.691517	+	0.722361i	$0.743057\pi$
$200$	12.5133	+	6.47042i	0.884825	+	0.457528i
$201$	2.06706	+	9.55456i	0.145799	+	0.673926i
$202$	5.64701	−	13.6685i	0.397322	−	0.961709i
$203$	−2.68810	+	0.978390i	−0.188668	+	0.0686695i
$204$	−20.0728	+	6.25667i	−1.40537	+	0.438054i
$205$	−0.159412	−	0.904068i	−0.0111338	−	0.0631429i
$206$	−0.658914	−	2.08316i	−0.0459087	−	0.145141i
$207$	4.29677	+	6.27180i	0.298646	+	0.435920i
$208$	4.01823	+	4.75330i	0.278614	+	0.329582i
$209$	2.96610	+	3.53486i	0.205170	+	0.244512i
$210$	1.02517	−	1.21140i	0.0707435	−	0.0835946i
$211$	−17.3303	−	3.05581i	−1.19307	−	0.210370i	−0.458369	−	0.888762i	$-0.651566\pi$
$211$	−17.3303	−	3.05581i	−1.19307	−	0.210370i	−0.734701	+	0.678391i	$0.762677\pi$
$212$	−14.3266	−	9.99257i	−0.983955	−	0.686293i
$213$	4.95205	−	6.38585i	0.339309	−	0.437551i
$214$	5.16165	+	9.89332i	0.352843	+	0.676293i
$215$	0.305002			0.0208010
$216$	−12.6345	−	7.50796i	−0.859669	−	0.510852i
$217$	−23.0580			−1.56528
$218$	1.16800	+	2.23870i	0.0791069	+	0.151624i
$219$	−7.39119	−	18.1049i	−0.499450	−	1.22341i
$220$	0.240360	+	0.167647i	0.0162050	+	0.0113028i
$221$	−9.30084	−	1.63999i	−0.625643	−	0.110318i
$222$	−6.94174	−	1.25404i	−0.465899	−	0.0841660i
$223$	5.95915	+	7.10184i	0.399054	+	0.475574i	0.927731	−	0.373249i	$-0.121756\pi$
$223$	5.95915	+	7.10184i	0.399054	+	0.475574i	−0.528677	+	0.848823i	$0.677312\pi$
$224$	−26.2779	−	1.02690i	−1.75576	−	0.0686123i
$225$	−12.1514	−	8.69480i	−0.810092	−	0.579653i
$226$	−4.53026	−	14.3224i	−0.301348	−	0.952715i
$227$	3.87558	+	21.9795i	0.257231	+	1.45883i	0.790280	+	0.612746i	$0.209935\pi$
$227$	3.87558	+	21.9795i	0.257231	+	1.45883i	−0.533049	+	0.846085i	$0.678954\pi$
$228$	3.33927	−	14.8323i	0.221149	−	0.982291i
$229$	24.7476	−	9.00740i	1.63537	−	0.595226i	0.649149	−	0.760661i	$-0.275125\pi$
$229$	24.7476	−	9.00740i	1.63537	−	0.595226i	0.986221	+	0.165435i	$0.0529028\pi$
$230$	−0.190710	+	0.461609i	−0.0125751	+	0.0304376i
$231$	−6.27084	+	5.68752i	−0.412591	+	0.374211i
$232$	−0.799405	+	1.54599i	−0.0524835	+	0.101499i
$233$	−6.49629	−	3.75063i	−0.425586	−	0.245712i	0.271878	−	0.962332i	$-0.412355\pi$
$233$	−6.49629	−	3.75063i	−0.425586	−	0.245712i	−0.697464	+	0.716619i	$0.745688\pi$
$234$	−3.49517	−	5.60057i	−0.228486	−	0.366121i
$235$	−1.33389	+	0.770123i	−0.0870135	+	0.0502373i
$236$	−11.6247	−	11.5822i	−0.756704	−	0.753939i
$237$	1.35244	−	2.56593i	0.0878504	−	0.166675i
$238$	31.6354	−	24.3207i	2.05062	−	1.57648i
$239$	2.63068	+	2.20740i	0.170165	+	0.142785i	0.723893	−	0.689912i	$-0.242351\pi$
$239$	2.63068	+	2.20740i	0.170165	+	0.142785i	−0.553728	+	0.832697i	$0.686795\pi$
$240$	−0.0407197	−	0.964673i	−0.00262845	−	0.0622694i
$241$	1.59962	+	0.582213i	0.103040	+	0.0375036i	0.393026	−	0.919527i	$-0.371428\pi$
$241$	1.59962	+	0.582213i	0.103040	+	0.0375036i	−0.289986	+	0.957031i	$0.593650\pi$
$242$	10.3254	+	9.44411i	0.663741	+	0.607091i
$243$	12.1208	+	9.80233i	0.777551	+	0.628820i
$244$	1.98965	+	22.2723i	0.127374	+	1.42584i
$245$	−0.696473	+	1.91354i	−0.0444960	+	0.122252i
$246$	12.4038	−	10.3197i	0.790837	−	0.657961i
$247$	4.38976	−	5.23152i	0.279314	−	0.332873i
$248$	−10.3170	+	9.50606i	−0.655133	+	0.603635i
$249$	3.59630	+	1.89552i	0.227906	+	0.120124i
$250$	0.0840037	−	1.96526i	0.00531286	−	0.124294i
$251$	−7.79783	−	13.5062i	−0.492195	−	0.852506i	0.507765	−	0.861496i	$-0.330472\pi$
$251$	−7.79783	−	13.5062i	−0.492195	−	0.852506i	−0.999960	+	0.00898943i	$0.997139\pi$
$252$	27.4278	+	5.07374i	1.72779	+	0.319615i
$253$	1.33220	−	2.30744i	0.0837547	−	0.145067i
$254$	−3.99079	−	2.53728i	−0.250404	−	0.159203i
$255$	0.984255	+	1.08520i	0.0616364	+	0.0679579i
$256$	−12.1811	+	10.3740i	−0.761319	+	0.648377i
$257$	−3.39598	−	9.33039i	−0.211836	−	0.582014i	0.787579	−	0.616213i	$-0.211334\pi$
$257$	−3.39598	−	9.33039i	−0.211836	−	0.582014i	−0.999415	+	0.0341995i	$0.989112\pi$
$258$	2.66093	+	4.65382i	0.165662	+	0.289734i
$259$	13.1845	−	2.32479i	0.819246	−	0.144455i
$260$	0.182573	−	0.393407i	0.0113227	−	0.0243980i
$261$	1.07422	−	1.50127i	0.0664926	−	0.0929264i
$262$	−0.799223	+	3.62074i	−0.0493761	+	0.223690i
$263$	−20.0312	+	16.8082i	−1.23518	+	1.03644i	−0.237292	+	0.971438i	$0.576260\pi$
$263$	−20.0312	+	16.8082i	−1.23518	+	1.03644i	−0.997885	+	0.0649985i	$0.979296\pi$
$264$	−0.461038	+	5.13008i	−0.0283749	+	0.315735i
$265$	−0.211354	+	1.19865i	−0.0129833	+	0.0736322i
$266$	3.79245	+	28.6043i	0.232530	+	1.75384i
$267$	14.1418	−	5.77327i	0.865462	−	0.353318i
$268$	−10.9086	−	2.90156i	−0.666348	−	0.177241i
$269$		−	0.465194i		−	0.0283634i	−0.999899	−	0.0141817i	$-0.995486\pi$
$269$		−	0.465194i		−	0.0283634i	0.999899	−	0.0141817i	$-0.00451432\pi$
$270$	−0.103944	+	1.01881i	−0.00632584	+	0.0620029i
$271$		−	15.6578i		−	0.951143i	−0.879677	−	0.475571i	$-0.842241\pi$
$271$		−	15.6578i		−	0.951143i	0.879677	−	0.475571i	$-0.157759\pi$
$272$	4.12828	−	23.9243i	0.250314	−	1.45062i
$273$	9.90109	+	7.67803i	0.599241	+	0.464696i
$274$	12.4981	−	1.65705i	0.755041	−	0.100106i
$275$	−0.909317	+	5.15699i	−0.0548339	+	0.310978i
$276$	−8.70719	+	1.11731i	−0.524111	+	0.0672539i
$277$	−7.55460	+	6.33906i	−0.453912	+	0.380877i	−0.840885	−	0.541214i	$-0.817965\pi$
$277$	−7.55460	+	6.33906i	−0.453912	+	0.380877i	0.386973	+	0.922091i	$0.373521\pi$
$278$	20.7221	+	4.57409i	1.24283	+	0.274335i
$279$	12.2753	−	8.40974i	0.734905	−	0.503478i
$280$	0.705901	+	1.69105i	0.0421857	+	0.101060i
$281$	16.8051	−	2.96320i	1.00251	−	0.176770i	0.351783	−	0.936081i	$-0.385575\pi$
$281$	16.8051	−	2.96320i	1.00251	−	0.176770i	0.650727	+	0.759312i	$0.274464\pi$
$282$	−23.3881	−	13.6341i	−1.39274	−	0.811902i
$283$	−3.24599	−	8.91828i	−0.192954	−	0.530137i	0.805056	−	0.593199i	$-0.202135\pi$
$283$	−3.24599	−	8.91828i	−0.192954	−	0.530137i	−0.998010	+	0.0630625i	$0.979913\pi$
$284$	3.95896	+	8.44961i	0.234921	+	0.501392i
$285$	−1.03545	+	0.224011i	−0.0613345	+	0.0132693i
$286$	−1.24135	+	1.95246i	−0.0734023	+	0.115452i
$287$	−15.3116	+	26.5204i	−0.903814	+	1.56545i
$288$	14.3640	−	9.03741i	0.846408	−	0.532535i
$289$	9.91922	+	17.1806i	0.583484	+	1.01062i
$290$	0.121165	+	0.00517913i	0.00711507	+	0.000304129i
$291$	−0.375901	−	9.75222i	−0.0220357	−	0.571685i
$292$	22.4984	+	1.92687i	1.31662	+	0.112762i
$293$	1.45797	−	1.73754i	0.0851753	−	0.101508i	−0.721774	−	0.692129i	$-0.756673\pi$
$293$	1.45797	−	1.73754i	0.0851753	−	0.101508i	0.806949	+	0.590621i	$0.201117\pi$
$294$	−35.2737	+	6.06734i	−2.05720	+	0.353855i
$295$	−0.391085	+	1.07450i	−0.0227699	+	0.0625597i
$296$	4.94084	−	6.47575i	0.287180	−	0.376395i
$297$	1.26403	−	5.31496i	0.0733466	−	0.308405i
$298$	−17.2818	+	18.8945i	−1.00111	+	1.09453i
$299$	−3.70544	−	1.34867i	−0.214291	−	0.0779957i
$300$	15.3298	−	7.91646i	0.885068	−	0.457057i
$301$	−7.79394	−	6.53989i	−0.449235	−	0.376953i
$302$	−12.5863	−	16.3718i	−0.724261	−	0.942089i
$303$	−9.65385	−	15.3257i	−0.554599	−	0.880437i
$304$	13.4895	+	11.2352i	0.773676	+	0.644381i
$305$	1.34939	−	0.779072i	0.0772660	−	0.0446095i
$306$	−7.97139	+	24.4857i	−0.455694	+	1.39975i
$307$	−10.5153	−	6.07100i	−0.600138	−	0.346490i	0.168958	−	0.985623i	$-0.445960\pi$
$307$	−10.5153	−	6.07100i	−0.600138	−	0.346490i	−0.769096	+	0.639133i	$0.779293\pi$
$308$	−2.54738	−	9.43783i	−0.145150	−	0.537770i
$309$	−2.54793	−	0.817690i	−0.144947	−	0.0465168i
$310$	0.903474	+	0.373263i	0.0513139	+	0.0211999i
$311$	16.3253	−	5.94192i	0.925723	−	0.336936i	0.165210	−	0.986258i	$-0.447170\pi$
$311$	16.3253	−	5.94192i	0.925723	−	0.336936i	0.760513	+	0.649323i	$0.224948\pi$
$312$	7.59554	−	0.646447i	0.430013	−	0.0365979i
$313$	2.82602	+	16.0272i	0.159736	+	0.905909i	0.954327	+	0.298764i	$0.0965743\pi$
$313$	2.82602	+	16.0272i	0.159736	+	0.905909i	−0.794591	+	0.607145i	$0.792315\pi$
$314$	0.184779	−	0.0584465i	0.0104277	−	0.00329832i
$315$	−0.483846	−	1.88244i	−0.0272616	−	0.106064i
$316$	1.92607	+	2.74002i	0.108350	+	0.154138i
$317$	18.7298	+	22.3213i	1.05197	+	1.25369i	0.966314	+	0.257366i	$0.0828547\pi$
$317$	18.7298	+	22.3213i	1.05197	+	1.25369i	0.0856578	+	0.996325i	$0.472701\pi$
$318$	−20.1332	+	7.23245i	−1.12901	+	0.405576i
$319$	−0.637134	−	0.112344i	−0.0356727	−	0.00629005i
$320$	1.01301	+	0.465623i	0.0566292	+	0.0260291i
$321$	13.5406	+	1.85305i	0.755760	+	0.103427i
$322$	14.7713	−	7.70661i	0.823170	−	0.429473i
$323$	−26.6381			−1.48219
$324$	−16.4522	+	7.30242i	−0.914011	+	0.405690i
$325$	7.74997			0.429891
$326$	−15.0722	+	7.86361i	−0.834770	+	0.435525i
$327$	3.06401	+	0.419316i	0.169440	+	0.0231882i
$328$	4.08252	+	18.1788i	0.225419	+	1.00375i
$329$	50.5990	+	8.92197i	2.78961	+	0.491884i
$330$	0.337778	−	0.121340i	0.0185941	−	0.00667954i
$331$	−1.75836	−	2.09553i	−0.0966481	−	0.115181i	0.715553	−	0.698559i	$-0.246175\pi$
$331$	−1.75836	−	2.09553i	−0.0966481	−	0.115181i	−0.812201	+	0.583378i	$0.801731\pi$
$332$	−3.84030	+	2.69949i	−0.210764	+	0.148154i
$333$	−6.17112	+	6.04632i	−0.338175	+	0.331336i
$334$	15.1717	−	4.79889i	0.830160	−	0.262584i
$335$	0.136584	+	0.774604i	0.00746236	+	0.0423212i
$336$	−19.6441	+	25.5241i	−1.07167	+	1.39245i
$337$	−6.48096	+	2.35888i	−0.353040	+	0.128496i	−0.512452	−	0.858716i	$-0.671263\pi$
$337$	−6.48096	+	2.35888i	−0.353040	+	0.128496i	0.159411	+	0.987212i	$0.449040\pi$
$338$	−13.8270	−	5.71253i	−0.752091	−	0.310720i
$339$	−17.5179	−	5.62190i	−0.951443	−	0.305340i
$340$	−1.63326	+	0.440837i	−0.0885762	+	0.0239077i
$341$	−4.51618	−	2.60742i	−0.244565	−	0.141199i
$342$	−12.4516	−	13.8448i	−0.673304	−	0.748641i
$343$	30.6457	−	17.6933i	1.65471	−	0.955349i
$344$	−6.18350	+	0.286985i	−0.333392	+	0.0154732i
$345$	0.326029	+	0.517577i	0.0175528	+	0.0278654i
$346$	4.91562	+	6.39404i	0.264265	+	0.343746i
$347$	−17.5469	−	14.7236i	−0.941964	−	0.790402i	0.0359618	−	0.999353i	$-0.488551\pi$
$347$	−17.5469	−	14.7236i	−0.941964	−	0.790402i	−0.977926	+	0.208951i	$0.932995\pi$
$348$	0.978059	+	1.89396i	0.0524295	+	0.101527i
$349$	−25.4917	−	9.27824i	−1.36454	−	0.496653i	−0.447086	−	0.894491i	$-0.647538\pi$
$349$	−25.4917	−	9.27824i	−1.36454	−	0.496653i	−0.917456	+	0.397838i	$0.869760\pi$
$350$	−22.0999	+	24.1622i	−1.18129	+	1.29152i
$351$	−8.07137	−	0.476397i	−0.430818	−	0.0254282i
$352$	−5.03071	−	3.17265i	−0.268138	−	0.169103i
$353$	−2.30370	+	6.32935i	−0.122613	+	0.336877i	−0.985780	−	0.168042i	$-0.946256\pi$
$353$	−2.30370	+	6.32935i	−0.122613	+	0.336877i	0.863166	+	0.504919i	$0.168478\pi$
$354$	−19.8070	+	3.40695i	−1.05273	+	0.181077i
$355$	0.417942	−	0.498084i	0.0221820	−	0.0264355i
$356$	−1.50508	+	17.5735i	−0.0797693	+	0.931394i
$357$	−1.88237	−	48.8355i	−0.0996256	−	2.58465i
$358$	17.5255	+	0.749116i	0.926253	+	0.0395920i
$359$	14.3604	+	24.8729i	0.757913	+	1.31274i	0.943913	+	0.330194i	$0.107114\pi$
$359$	14.3604	+	24.8729i	0.757913	+	1.31274i	−0.186000	+	0.982550i	$0.559552\pi$
$360$	−0.992562	−	0.642805i	−0.0523126	−	0.0338788i
$361$	0.131118	−	0.227104i	0.00690097	−	0.0119528i
$362$	−0.883387	+	1.38944i	−0.0464298	+	0.0730276i
$363$	16.7504	−	3.62382i	0.879167	−	0.190201i
$364$	−13.1009	+	6.13826i	−0.686674	+	0.321732i
$365$	−0.538153	−	1.47856i	−0.0281682	−	0.0773915i
$366$	23.6598	+	13.7926i	1.23672	+	0.720950i
$367$	−3.84637	+	0.678219i	−0.200779	+	0.0354027i	−0.273133	−	0.961976i	$-0.588060\pi$
$367$	−3.84637	+	0.678219i	−0.200779	+	0.0354027i	0.0723541	+	0.997379i	$0.476949\pi$
$368$	3.43205	−	9.53795i	0.178908	−	0.497200i
$369$	−1.52118	−	19.7031i	−0.0791894	−	1.02570i
$370$	−0.554239	−	0.122340i	−0.0288135	−	0.00636014i
$371$	31.1024	−	26.0980i	1.61476	−	1.35494i
$372$	2.18682	+	17.0419i	0.113381	+	0.883583i
$373$	−1.89369	+	10.7397i	−0.0980518	+	0.556079i	0.895718	+	0.444623i	$0.146662\pi$
$373$	−1.89369	+	10.7397i	−0.0980518	+	0.556079i	−0.993769	+	0.111456i	$0.964449\pi$
$374$	8.94638	−	1.18614i	0.462606	−	0.0613339i
$375$	−1.90379	−	1.47633i	−0.0983111	−	0.0762376i
$376$	26.3182	−	16.8683i	1.35726	−	0.869916i
$377$			0.957490i			0.0493132i
$378$	24.5017	−	23.8057i	1.26023	−	1.22443i
$379$			5.95264i			0.305766i	0.988244	+	0.152883i	$0.0488558\pi$
$379$			5.95264i			0.305766i	−0.988244	+	0.152883i	$0.951144\pi$
$380$	0.314448	−	1.18218i	0.0161308	−	0.0606448i
$381$	−5.36228	+	2.18911i	−0.274718	+	0.112152i
$382$	2.67354	+	20.1650i	0.136790	+	1.03173i
$383$	−1.15926	+	6.57451i	−0.0592356	+	0.335942i	−0.999995	−	0.00313275i	$-0.999003\pi$
$383$	−1.15926	+	6.57451i	−0.0592356	+	0.335942i	0.940759	+	0.339075i	$0.110114\pi$
$384$	1.73322	+	19.5191i	0.0884482	+	0.996081i
$385$	−0.521809	+	0.437850i	−0.0265939	+	0.0223149i
$386$	5.60738	−	25.4032i	0.285408	−	1.29299i
$387$	6.53448	+	0.639012i	0.332167	+	0.0324828i
$388$	10.2221	+	4.74389i	0.518949	+	0.240835i
$389$	−30.0164	+	5.29270i	−1.52189	+	0.268351i	−0.871176	−	0.490970i	$-0.836642\pi$
$389$	−30.0164	+	5.29270i	−1.52189	+	0.268351i	−0.650716	+	0.759321i	$0.725531\pi$
$390$	−0.263659	−	0.461125i	−0.0133509	−	0.0233500i
$391$	5.26061	+	14.4534i	0.266041	+	0.730941i
$392$	12.3195	−	39.4498i	0.622231	−	1.99252i
$393$	3.05087	+	3.36377i	0.153896	+	0.169680i
$394$	−25.2833	−	16.0747i	−1.27375	−	0.809834i
$395$	0.116690	−	0.202113i	0.00587131	−	0.0101694i
$396$	4.79832	+	4.09531i	0.241125	+	0.205797i
$397$	7.87633	+	13.6422i	0.395302	+	0.684683i	0.993140	−	0.116934i	$-0.0373067\pi$
$397$	7.87633	+	13.6422i	0.395302	+	0.684683i	−0.597838	+	0.801617i	$0.703973\pi$
$398$	0.405009	−	9.47517i	0.0203013	−	0.474947i
$399$	31.2628	+	16.4778i	1.56510	+	0.824924i
$400$	0.0729116	+	19.9222i	0.00364558	+	0.996109i
$401$	−1.99200	+	2.37398i	−0.0994758	+	0.118551i	−0.813486	−	0.581585i	$-0.802433\pi$
$401$	−1.99200	+	2.37398i	−0.0994758	+	0.118551i	0.714010	+	0.700136i	$0.246877\pi$
$402$	−10.6276	+	8.84192i	−0.530054	+	0.440995i
$403$	−2.63965	+	7.25239i	−0.131490	+	0.361267i
$404$	20.8319	−	1.86097i	1.03643	−	0.0925868i
$405$	0.944151	+	0.825683i	0.0469153	+	0.0410285i
$406$	−2.98518	−	2.73039i	−0.148152	−	0.135507i
$407$	2.84523	+	1.03558i	0.141033	+	0.0513318i
$408$	−20.9755	−	21.0749i	−1.03844	−	1.04336i
$409$	−20.1116	−	16.8756i	−0.994454	−	0.834446i	−0.00824757	−	0.999966i	$-0.502625\pi$
$409$	−20.1116	−	16.8756i	−0.994454	−	0.834446i	−0.986206	+	0.165520i	$0.947070\pi$
$410$	1.02926	−	0.791278i	0.0508317	−	0.0390784i
$411$	7.19971	−	13.6597i	0.355136	−	0.673785i
$412$	2.18088	−	2.18888i	0.107444	−	0.107838i
$413$	33.0332	−	19.0717i	1.62546	−	0.938458i
$414$	−5.05297	+	9.49014i	−0.248340	+	0.466415i
$415$	0.283273	+	0.163547i	0.0139053	+	0.00802823i
$416$	−3.33125	+	8.14757i	−0.163328	+	0.399468i
$417$	19.2514	−	17.4606i	0.942745	−	0.855051i
$418$	−2.49180	+	6.03134i	−0.121878	+	0.295002i
$419$	−33.9869	+	12.3702i	−1.66037	+	0.604325i	−0.990421	−	0.138082i	$-0.955906\pi$
$419$	−33.9869	+	12.3702i	−1.66037	+	0.604325i	−0.669949	+	0.742407i	$0.733684\pi$
$420$	2.18951	+	0.492936i	0.106837	+	0.0240528i
$421$	2.20155	+	12.4856i	0.107297	+	0.608511i	0.990278	+	0.139103i	$0.0444218\pi$
$421$	2.20155	+	12.4856i	0.107297	+	0.608511i	−0.882981	+	0.469409i	$0.844467\pi$
$422$	−7.50535	−	23.7282i	−0.365355	−	1.15507i
$423$	−30.1913	+	13.7048i	−1.46795	+	0.666349i
$424$	3.15707	−	24.4998i	0.153321	−	1.18981i
$425$	−19.4311	−	23.1571i	−0.942548	−	1.12328i
$426$	11.2462	+	2.03165i	0.544878	+	0.0984338i
$427$	−51.1870	−	9.02565i	−2.47711	−	0.436782i
$428$	−9.02795	+	12.9436i	−0.436383	+	0.625652i
$429$	1.07101	+	2.62346i	0.0517087	+	0.126662i
$430$	0.199520	+	0.382419i	0.00962169	+	0.0184419i
$431$	11.3033			0.544463			0.272231	−	0.962232i	$-0.412238\pi$
$431$	11.3033			0.544463			0.272231	+	0.962232i	$0.412238\pi$
$432$	1.14870	−	20.7528i	0.0552667	−	0.998472i
$433$	18.1058			0.870111			0.435056	−	0.900404i	$-0.356729\pi$
$433$	18.1058			0.870111			0.435056	+	0.900404i	$0.356729\pi$
$434$	−15.0836	−	28.9107i	−0.724035	−	1.38776i
$435$	0.0910213	−	0.117375i	0.00436414	−	0.00562771i
$436$	−2.04288	+	2.92893i	−0.0978363	+	0.140270i
$437$	−10.9531	−	1.93133i	−0.523960	−	0.0923883i
$438$	17.8653	−	21.1107i	0.853639	−	1.00871i
$439$	−8.79038	−	10.4760i	−0.419542	−	0.499991i	0.514333	−	0.857591i	$-0.328040\pi$
$439$	−8.79038	−	10.4760i	−0.419542	−	0.499991i	−0.933875	+	0.357600i	$0.883595\pi$
$440$	−0.0529666	+	0.411036i	−0.00252508	+	0.0195954i
$441$	−18.9306	+	39.5373i	−0.901457	+	1.88273i
$442$	−4.02797	−	12.7344i	−0.191591	−	0.605716i
$443$	1.88953	+	10.7160i	0.0897742	+	0.509135i	0.996224	+	0.0868210i	$0.0276708\pi$
$443$	1.88953	+	10.7160i	0.0897742	+	0.509135i	−0.906450	+	0.422314i	$0.861218\pi$
$444$	−2.96865	−	9.52407i	−0.140886	−	0.451993i
$445$	1.15491	−	0.420352i	0.0547479	−	0.0199266i
$446$	−5.00623	+	12.1175i	−0.237052	+	0.573778i
$447$	6.63125	+	30.6516i	0.313647	+	1.44977i
$448$	−15.9023	−	33.6196i	−0.751315	−	1.58838i
$449$	−6.10203	−	3.52301i	−0.287973	−	0.166261i	0.349055	−	0.937102i	$-0.386503\pi$
$449$	−6.10203	−	3.52301i	−0.287973	−	0.166261i	−0.637027	+	0.770841i	$0.719836\pi$
$450$	2.95282	−	20.9235i	0.139197	−	0.986342i
$451$	−5.99791	+	3.46289i	−0.282431	+	0.163061i
$452$	14.9943	−	15.0493i	0.705274	−	0.707860i
$453$	−25.2730	+	0.974152i	−1.18743	+	0.0457697i
$454$	−25.0232	+	19.2374i	−1.17440	+	0.902855i
$455$	0.772266	+	0.648008i	0.0362044	+	0.0303791i
$456$	20.7815	−	5.51580i	0.973182	−	0.258301i
$457$	−23.9184	−	8.70557i	−1.11885	−	0.407229i	−0.284620	−	0.958641i	$-0.591867\pi$
$457$	−23.9184	−	8.70557i	−1.11885	−	0.407229i	−0.834234	+	0.551411i	$0.814090\pi$
$458$	27.4826	+	25.1369i	1.28418	+	1.17457i
$459$	18.8135	+	25.3119i	0.878137	+	1.18146i
$460$	−0.703532	+	0.0628485i	−0.0328024	+	0.00293033i
$461$	−13.4094	+	36.8420i	−0.624538	+	1.71590i	0.0710586	+	0.997472i	$0.477362\pi$
$461$	−13.4094	+	36.8420i	−0.624538	+	1.71590i	−0.695597	+	0.718432i	$0.744860\pi$
$462$	−11.2333	−	4.14199i	−0.522619	−	0.192703i
$463$	4.80801	−	5.72997i	0.223447	−	0.266294i	−0.642661	−	0.766151i	$-0.722170\pi$
$463$	4.80801	−	5.72997i	0.223447	−	0.266294i	0.866108	+	0.499857i	$0.166614\pi$
$464$	−2.46134	+	0.00900805i	−0.114265	+	0.000418188i
$465$	1.01301	−	0.638112i	0.0469774	−	0.0295917i
$466$	0.453034	−	10.5987i	0.0209864	−	0.490976i
$467$	0.689932	+	1.19500i	0.0319262	+	0.0552979i	0.881547	−	0.472096i	$-0.156502\pi$
$467$	0.689932	+	1.19500i	0.0319262	+	0.0552979i	−0.849621	+	0.527394i	$0.823169\pi$
$468$	4.73574	−	8.04599i	0.218910	−	0.371926i
$469$	13.1189	−	22.7227i	0.605777	−	1.04924i
$470$	−1.83818	−	1.16868i	−0.0847887	−	0.0539074i
$471$	0.0725301	−	0.226005i	0.00334201	−	0.0104138i
$472$	6.91769	−	22.1520i	0.318413	−	1.01963i
$473$	−0.786999	−	2.16226i	−0.0361862	−	0.0994209i
$474$	4.10194	+	0.0171963i	0.188408	+	0.000789852i
$475$	21.5271	−	3.79580i	0.987729	−	0.174163i
$476$	51.1885	+	23.7557i	2.34622	+	1.08884i
$477$	−7.03941	+	25.2374i	−0.322313	+	1.15554i
$478$	−1.04681	+	4.74241i	−0.0478802	+	0.216913i
$479$	9.74905	−	8.18042i	0.445445	−	0.373773i	−0.392297	−	0.919839i	$-0.628319\pi$
$479$	9.74905	−	8.18042i	0.445445	−	0.373773i	0.837742	+	0.546066i	$0.183875\pi$
$480$	1.18289	−	0.682104i	0.0539915	−	0.0311337i
$481$	0.778139	−	4.41304i	0.0354801	−	0.201217i
$482$	0.316410	+	2.38650i	0.0144121	+	0.108702i
$483$	2.76670	−	20.2168i	0.125889	−	0.919895i
$484$	−5.08682	+	19.1242i	−0.231219	+	0.869281i
$485$		−	0.785256i		−	0.0356566i
$486$	−4.36146	+	21.6097i	−0.197840	+	0.980234i
$487$		−	12.3932i		−	0.561588i	−0.959768	−	0.280794i	$-0.909402\pi$
$487$		−	12.3932i		−	0.561588i	0.959768	−	0.280794i	$-0.0905979\pi$
$488$	−26.6241	+	17.0643i	−1.20521	+	0.772465i
$489$	−2.82306	+	20.6286i	−0.127663	+	0.932859i
$490$	−2.85485	+	0.378506i	−0.128969	+	0.0170992i
$491$	4.61221	−	26.1572i	0.208146	−	1.18046i	−0.684265	−	0.729233i	$-0.739877\pi$
$491$	4.61221	−	26.1572i	0.208146	−	1.18046i	0.892411	−	0.451223i	$-0.149012\pi$
$492$	21.0532	+	8.80145i	0.949150	+	0.396800i
$493$	2.86100	−	2.40067i	0.128853	−	0.108121i
$494$	9.43101	+	2.08175i	0.424321	+	0.0936625i
$495$	0.118101	−	0.423412i	0.00530826	−	0.0190310i
$496$	−18.6679	−	6.71730i	−0.838214	−	0.301616i
$497$	−21.3599	+	3.76634i	−0.958125	+	0.168943i
$498$	−0.0241016	+	5.74910i	−0.00108002	+	0.257623i
$499$	−3.29755	−	9.05994i	−0.147619	−	0.405579i	0.843741	−	0.536750i	$-0.180348\pi$
$499$	−3.29755	−	9.05994i	−0.147619	−	0.405579i	−0.991360	+	0.131172i	$0.958126\pi$
$500$	2.51904	−	1.18027i	0.112655	−	0.0527831i
$501$	5.95527	−	18.5567i	0.266062	−	0.829052i
$502$	11.8334	−	18.6123i	0.528152	−	0.830709i
$503$	−4.28642	+	7.42429i	−0.191122	+	0.331033i	−0.945622	−	0.325267i	$-0.894546\pi$
$503$	−4.28642	+	7.42429i	−0.191122	+	0.331033i	0.754500	+	0.656300i	$0.227879\pi$
$504$	11.5806	+	37.7087i	0.515839	+	1.67968i
$505$	−0.728686	−	1.26212i	−0.0324261	−	0.0561637i
$506$	3.76459	+	0.160915i	0.167357	+	0.00715354i
$507$	−15.5035	+	9.76585i	−0.688533	+	0.433717i
$508$	0.570698	−	6.66353i	0.0253206	−	0.295646i
$509$	19.9295	−	23.7511i	0.883360	−	1.05275i	−0.114876	−	0.993380i	$-0.536647\pi$
$509$	19.9295	−	23.7511i	0.883360	−	1.05275i	0.998236	−	0.0593674i	$-0.0189083\pi$
$510$	−0.716793	+	1.94398i	−0.0317401	+	0.0860807i
$511$	−17.9517	+	49.3219i	−0.794137	+	2.18187i
$512$	−20.9756	−	8.48670i	−0.926999	−	0.375063i
$513$	−22.6531	+	2.62993i	−1.00016	+	0.116114i
$514$	9.47716	−	10.3615i	0.418020	−	0.457027i
$515$	−0.202323	−	0.0736396i	−0.00891542	−	0.00324495i
$516$	−4.09440	+	6.38067i	−0.180246	+	0.280894i
$517$	8.90151	+	7.46925i	0.391488	+	0.328497i
$518$	11.5396	+	15.0103i	0.507023	+	0.659515i
$519$	9.87045	−	0.380458i	0.433265	−	0.0167003i
$520$	0.612695	−	0.0284360i	0.0268684	−	0.00124700i
$521$	−25.2374	+	14.5708i	−1.10567	+	0.638359i	−0.937705	−	0.347433i	$-0.887053\pi$
$521$	−25.2374	+	14.5708i	−1.10567	+	0.638359i	−0.167966	+	0.985793i	$0.553720\pi$
$522$	2.58504	+	0.364814i	0.113144	+	0.0159675i
$523$	−4.50959	−	2.60361i	−0.197190	−	0.113848i	0.398154	−	0.917319i	$-0.369651\pi$
$523$	−4.50959	−	2.60361i	−0.197190	−	0.113848i	−0.595344	+	0.803471i	$0.702984\pi$
$524$	−5.06259	+	1.36645i	−0.221160	+	0.0596936i
$525$	8.48000	+	39.1971i	0.370098	+	1.71070i
$526$	−34.1781	−	14.1204i	−1.49024	−	0.615679i
$527$	28.2886	−	10.2962i	1.23227	−	0.448510i
$528$	−6.73382	+	2.77783i	−0.293052	+	0.120889i
$529$	−2.87875	−	16.3262i	−0.125163	−	0.709834i
$530$	−1.64115	+	0.519104i	−0.0712870	+	0.0225484i
$531$	−10.6299	+	22.2011i	−0.461300	+	0.963445i
$532$	−33.3839	+	23.4668i	−1.44737	+	1.01741i
$533$	6.58858	+	7.85196i	0.285383	+	0.340106i
$534$	16.4896	+	13.9547i	0.713576	+	0.603877i
$535$	1.08294	+	0.190951i	0.0468194	+	0.00825552i
$536$	−3.49790	−	15.5755i	−0.151086	−	0.672761i
$537$	13.1654	−	16.9773i	0.568131	−	0.732625i
$538$	0.583272	−	0.304311i	0.0251466	−	0.0131198i
$539$	15.3629			0.661725
$540$	−1.34541	+	0.536137i	−0.0578971	+	0.0230717i
$541$	24.3664			1.04759			0.523797	−	0.851843i	$-0.324515\pi$
$541$	24.3664			1.04759			0.523797	+	0.851843i	$0.324515\pi$
$542$	19.6321	−	10.2427i	0.843272	−	0.439961i
$543$	0.762168	+	1.86695i	0.0327078	+	0.0801184i
$544$	32.6974	−	10.4742i	1.40189	−	0.449076i
$545$	0.245051	+	0.0432091i	0.0104968	+	0.00185088i
$546$	−3.15002	+	17.4369i	−0.134808	+	0.746230i
$547$	22.9927	+	27.4016i	0.983097	+	1.17161i	0.985165	+	0.171611i	$0.0548974\pi$
$547$	22.9927	+	27.4016i	0.983097	+	1.17161i	−0.00206780	+	0.999998i	$0.500658\pi$
$548$	10.2534	+	14.5865i	0.438004	+	0.623105i
$549$	30.5422	−	13.8640i	1.30351	−	0.591702i
$550$	−7.06081	+	2.23337i	−0.301074	+	0.0952311i
$551$	0.468962	+	2.65961i	0.0199784	+	0.113303i
$552$	−7.09679	−	10.1864i	−0.302059	−	0.433562i
$553$	−7.31560	+	2.66266i	−0.311091	+	0.113228i
$554$	−12.8900	−	5.32539i	−0.547643	−	0.226254i
$555$	−0.514904	+	0.467007i	−0.0218564	+	0.0198233i
$556$	7.82042	+	28.9740i	0.331660	+	1.22877i
$557$	10.4040	+	6.00674i	0.440831	+	0.254514i	0.703950	−	0.710250i	$-0.251418\pi$
$557$	10.4040	+	6.00674i	0.440831	+	0.254514i	−0.263119	+	0.964763i	$0.584751\pi$
$558$	18.5744	+	9.88981i	0.786315	+	0.418669i
$559$	−2.94922	+	1.70274i	−0.124739	+	0.0720180i
$560$	−1.65851	+	1.99129i	−0.0700849	+	0.0841475i
$561$	5.15367	−	9.77786i	0.217588	−	0.412822i
$562$	14.7086	+	19.1323i	0.620443	+	0.807047i
$563$	3.65854	+	3.06988i	0.154189	+	0.129380i	0.716619	−	0.697465i	$-0.245689\pi$
$563$	3.65854	+	3.06988i	0.154189	+	0.129380i	−0.562430	+	0.826845i	$0.690133\pi$
$564$	1.79533	−	38.2434i	0.0755972	−	1.61034i
$565$	−1.39104	−	0.506297i	−0.0585215	−	0.0213001i
$566$	9.05857	−	9.90387i	0.380760	−	0.416291i
$567$	−6.42219	−	41.3439i	−0.269707	−	1.73628i
$568$	−8.00454	+	10.4912i	−0.335863	+	0.440202i
$569$	2.71384	−	7.45620i	0.113770	−	0.312580i	−0.869719	−	0.493547i	$-0.835700\pi$
$569$	2.71384	−	7.45620i	0.113770	−	0.312580i	0.983489	+	0.180966i	$0.0579225\pi$
$570$	−0.958216	−	1.15173i	−0.0401353	−	0.0482406i
$571$	−10.4105	+	12.4067i	−0.435666	+	0.519206i	−0.938548	−	0.345149i	$-0.887828\pi$
$571$	−10.4105	+	12.4067i	−0.435666	+	0.519206i	0.502882	+	0.864355i	$0.332273\pi$
$572$	−3.26008	−	0.279210i	−0.136311	−	0.0116744i
$573$	22.0391	+	11.6163i	0.920698	+	0.485277i
$574$	−43.2682	−	1.84947i	−1.80598	−	0.0771953i
$575$	−6.31079	−	10.9306i	−0.263178	−	0.455838i
$576$	20.7277	+	12.0981i	0.863653	+	0.504086i
$577$	−8.09164	+	14.0151i	−0.336859	+	0.583458i	−0.983840	−	0.179049i	$-0.942698\pi$
$577$	−8.09164	+	14.0151i	−0.336859	+	0.583458i	0.646981	+	0.762506i	$0.276031\pi$
$578$	−15.0527	+	23.6758i	−0.626110	+	0.984783i
$579$	−21.4050	−	23.6003i	−0.889562	−	0.980797i
$580$	0.0727676	+	0.155308i	0.00302151	+	0.00644882i
$581$	−3.73187	−	10.2532i	−0.154824	−	0.425375i
$582$	11.9817	−	6.85081i	0.496656	−	0.283975i
$583$	9.04295	−	1.59452i	0.374521	−	0.0660381i
$584$	12.3015	+	29.4695i	0.509041	+	1.21946i
$585$	−0.647472	−	0.0633167i	−0.0267697	−	0.00261782i
$586$	3.13231	+	0.691410i	0.129394	+	0.0285619i
$587$	19.9180	−	16.7132i	0.822103	−	0.689826i	−0.131361	−	0.991335i	$-0.541935\pi$
$587$	19.9180	−	16.7132i	0.822103	−	0.689826i	0.953464	+	0.301508i	$0.0974901\pi$
$588$	−30.6820	−	40.2580i	−1.26530	−	1.66021i
$589$	−3.78006	+	21.4378i	−0.155755	+	0.883328i
$590$	−1.60306	+	0.212540i	−0.0659971	+	0.00875012i
$591$	−33.9723	+	13.8689i	−1.39743	+	0.570492i
$592$	11.3515	+	1.95878i	0.466546	+	0.0805052i
$593$		−	7.68968i		−	0.315778i	−0.987457	−	0.157889i	$-0.949531\pi$
$593$		−	7.68968i		−	0.315778i	0.987457	−	0.157889i	$-0.0504687\pi$
$594$	7.49091	−	1.89195i	0.307356	−	0.0776278i
$595$		−	3.93227i		−	0.161207i
$596$	−34.9955	−	9.30840i	−1.43347	−	0.381287i
$597$	−9.17878	−	7.11789i	−0.375662	−	0.291316i
$598$	−0.732950	−	5.52822i	−0.0299726	−	0.226066i
$599$	5.26567	−	29.8631i	0.215150	−	1.22017i	−0.665497	−	0.746400i	$-0.731780\pi$
$599$	5.26567	−	29.8631i	0.215150	−	1.22017i	0.880647	−	0.473773i	$-0.157108\pi$
$600$	19.9540	+	14.0423i	0.814618	+	0.573274i
$601$	14.0780	−	11.8129i	0.574254	−	0.481857i	−0.308800	−	0.951127i	$-0.599927\pi$
$601$	14.0780	−	11.8129i	0.574254	−	0.481857i	0.883055	+	0.469270i	$0.155483\pi$
$602$	3.10141	−	14.0504i	0.126404	−	0.572650i
$603$	1.30334	+	16.8816i	0.0530762	+	0.687471i
$604$	12.2939	−	26.4908i	0.500231	−	1.07789i
$605$	1.35798	−	0.239449i	0.0552099	−	0.00973499i
$606$	12.9006	−	22.1297i	0.524049	−	0.898956i
$607$	1.94501	+	5.34387i	0.0789455	+	0.216901i	0.972886	−	0.231284i	$-0.0742927\pi$
$607$	1.94501	+	5.34387i	0.0789455	+	0.216901i	−0.893941	+	0.448185i	$0.852070\pi$
$608$	−5.26265	+	24.2631i	−0.213429	+	0.983997i
$609$	−4.84271	+	1.04768i	−0.196236	+	0.0424543i
$610$	1.85954	+	1.18227i	0.0752904	+	0.0478685i
$611$	8.59873	−	14.8934i	0.347867	−	0.602524i
$612$	−35.9153	+	6.02280i	−1.45179	+	0.243457i
$613$	−4.98728	−	8.63823i	−0.201434	−	0.348895i	0.747556	−	0.664198i	$-0.231227\pi$
$613$	−4.98728	−	8.63823i	−0.201434	−	0.348895i	−0.948991	+	0.315304i	$0.897894\pi$
$614$	0.733308	−	17.1557i	0.0295939	−	0.692348i
$615$	−0.0612432	−	1.58887i	−0.00246956	−	0.0640694i
$616$	10.1670	−	9.36780i	0.409640	−	0.377439i
$617$	12.6243	−	15.0451i	0.508236	−	0.605692i	−0.449521	−	0.893270i	$-0.648405\pi$
$617$	12.6243	−	15.0451i	0.508236	−	0.605692i	0.957757	+	0.287577i	$0.0928498\pi$
$618$	−0.641513	−	3.72956i	−0.0258054	−	0.150025i
$619$	11.9916	−	32.9466i	0.481983	−	1.32424i	−0.425808	−	0.904814i	$-0.640010\pi$
$619$	11.9916	−	32.9466i	0.481983	−	1.32424i	0.907791	−	0.419423i	$-0.137768\pi$
$620$	0.123009	+	1.37697i	0.00494015	+	0.0553005i
$621$	5.90059	+	11.7718i	0.236782	+	0.472388i
$622$	18.1295	+	16.5821i	0.726926	+	0.664882i
$623$	−38.5254	−	14.0221i	−1.54349	−	0.561784i
$624$	5.77922	+	9.10060i	0.231354	+	0.364315i
$625$	18.9282	+	15.8827i	0.757129	+	0.635307i
$626$	−18.2466	+	14.0276i	−0.729280	+	0.560657i
$627$	4.25985	+	6.76260i	0.170122	+	0.270072i
$628$	0.194156	+	0.193447i	0.00774768	+	0.00771938i
$629$	−15.1373	+	8.73951i	−0.603563	+	0.348467i
$630$	2.04374	−	1.83807i	0.0814246	−	0.0732306i
$631$	20.6478	+	11.9210i	0.821976	+	0.474568i	0.851097	−	0.525008i	$-0.175938\pi$
$631$	20.6478	+	11.9210i	0.821976	+	0.474568i	−0.0291214	+	0.999576i	$0.509271\pi$
$632$	−2.17556	+	4.20736i	−0.0865390	+	0.167360i
$633$	−29.0222	−	9.31389i	−1.15353	−	0.370194i
$634$	−15.7348	+	38.0856i	−0.624907	+	1.51257i
$635$	−0.437918	+	0.159389i	−0.0173783	+	0.00632517i
$636$	−22.2385	−	20.5123i	−0.881816	−	0.813368i
$637$	−3.94818	−	22.3913i	−0.156433	−	0.887174i
$638$	−0.275927	−	0.872345i	−0.0109241	−	0.0345365i
$639$	9.99769	−	9.79551i	0.395502	−	0.387504i
$640$	0.0788622	+	1.57473i	0.00311730	+	0.0622468i
$641$	11.9138	+	14.1983i	0.470568	+	0.560801i	0.948165	−	0.317778i	$-0.102937\pi$
$641$	11.9138	+	14.1983i	0.470568	+	0.560801i	−0.477598	+	0.878579i	$0.658492\pi$
$642$	6.53427	+	18.1897i	0.257887	+	0.717889i
$643$	35.2470	+	6.21500i	1.39001	+	0.245096i	0.818031	−	0.575175i	$-0.195066\pi$
$643$	35.2470	+	6.21500i	1.39001	+	0.245096i	0.571976	+	0.820270i	$0.306177\pi$
$644$	19.3255	+	13.4792i	0.761531	+	0.531155i
$645$	0.523401	+	0.0716283i	0.0206089	+	0.00282036i
$646$	−17.4256	−	33.3996i	−0.685600	−	1.31409i
$647$	−31.4863			−1.23785			−0.618926	−	0.785449i	$-0.712432\pi$
$647$	−31.4863			−1.23785			−0.618926	+	0.785449i	$0.712432\pi$
$648$	−19.9183	−	15.8512i	−0.782465	−	0.622695i
$649$	8.62659			0.338623
$650$	5.06971	+	9.71711i	0.198850	+	0.381136i
$651$	−39.5688	−	5.41506i	−1.55082	−	0.212233i
$652$	−19.7192	−	13.7538i	−0.772263	−	0.538641i
$653$	−26.5025	−	4.67310i	−1.03712	−	0.182873i	−0.370936	−	0.928658i	$-0.620963\pi$
$653$	−26.5025	−	4.67310i	−1.03712	−	0.182873i	−0.666186	+	0.745786i	$0.732074\pi$
$654$	1.47860	+	4.11604i	0.0578180	+	0.160950i
$655$	0.234869	+	0.279906i	0.00917709	+	0.0109368i
$656$	−20.1224	+	17.0106i	−0.785647	+	0.664151i
$657$	−8.43185	−	32.8048i	−0.328958	−	1.27984i
$658$	21.9132	+	69.2787i	0.854265	+	2.70076i
$659$	7.78431	+	44.1470i	0.303234	+	1.71972i	0.631705	+	0.775209i	$0.282355\pi$
$659$	7.78431	+	44.1470i	0.303234	+	1.71972i	−0.328471	+	0.944514i	$0.606533\pi$
$660$	0.373099	+	0.344139i	0.0145229	+	0.0133956i
$661$	19.0048	−	6.91718i	0.739201	−	0.269047i	0.0551465	−	0.998478i	$-0.482437\pi$
$661$	19.0048	−	6.91718i	0.739201	−	0.269047i	0.684054	+	0.729431i	$0.260215\pi$
$662$	1.47718	−	3.57548i	0.0574123	−	0.138965i
$663$	−15.5756	−	4.99857i	−0.604907	−	0.194128i
$664$	−5.89685	−	3.04916i	−0.228842	−	0.118331i
$665$	2.46250	+	1.42173i	0.0954917	+	0.0551322i
$666$	−11.6179	−	3.78225i	−0.450185	−	0.146559i
$667$	1.35045	−	0.779683i	0.0522896	−	0.0301894i
$668$	15.9417	+	15.8835i	0.616803	+	0.614549i
$669$	8.55840	+	13.5866i	0.330887	+	0.525289i
$670$	−0.881871	+	0.677966i	−0.0340696	+	0.0261921i
$671$	−9.00495	−	7.55605i	−0.347632	−	0.291698i
$672$	−44.8531	−	7.93344i	−1.73025	−	0.306039i
$673$	40.4201	+	14.7117i	1.55808	+	0.567094i	0.970295	−	0.241924i	$-0.0777784\pi$
$673$	40.4201	+	14.7117i	1.55808	+	0.567094i	0.587784	+	0.809018i	$0.300001\pi$
$674$	−7.19720	−	6.58291i	−0.277226	−	0.253564i
$675$	−18.8105	−	17.7744i	−0.724017	−	0.684139i
$676$	−1.88256	−	21.0736i	−0.0724062	−	0.810522i
$677$	6.79083	−	18.6577i	0.260993	−	0.717072i	−0.738108	−	0.674682i	$-0.764281\pi$
$677$	6.79083	−	18.6577i	0.260993	−	0.717072i	0.999101	−	0.0423898i	$-0.0134971\pi$
$678$	−4.41062	−	25.6420i	−0.169389	−	0.984776i
$679$	−16.8376	+	20.0662i	−0.646166	+	0.770071i
$680$	−1.62115	−	1.75945i	−0.0621681	−	0.0674719i
$681$	1.48893	+	38.6282i	0.0570559	+	1.48024i
$682$	0.314947	−	7.36816i	0.0120599	−	0.282141i
$683$	−16.6637	−	28.8624i	−0.637618	−	1.10439i	−0.985954	−	0.167017i	$-0.946586\pi$
$683$	−16.6637	−	28.8624i	−0.637618	−	1.10439i	0.348336	−	0.937370i	$-0.386747\pi$
$684$	9.21366	−	24.6688i	0.352293	−	0.943235i
$685$	0.621199	−	1.07595i	0.0237348	−	0.0411098i
$686$	42.2315	+	26.8501i	1.61241	+	1.02514i
$687$	44.5837	−	9.64534i	1.70097	−	0.367993i
$688$	−4.40482	−	7.56529i	−0.167932	−	0.288424i
$689$	−4.64799	−	12.7703i	−0.177074	−	0.486508i
$690$	−0.435676	+	0.747360i	−0.0165859	+	0.0284515i
$691$	−1.92394	+	0.339243i	−0.0731902	+	0.0129054i	−0.210123	−	0.977675i	$-0.567387\pi$
$691$	−1.92394	+	0.339243i	−0.0731902	+	0.0129054i	0.136933	+	0.990580i	$0.456275\pi$
$692$	−4.80141	+	10.3460i	−0.182522	+	0.393297i
$693$	−12.0968	+	8.28743i	−0.459519	+	0.314813i
$694$	6.98234	−	31.6322i	0.265046	−	1.20074i
$695$	1.60195	−	1.34420i	0.0607654	−	0.0509882i
$696$	−1.73489	+	2.46527i	−0.0657609	+	0.0934457i
$697$	6.94264	−	39.3737i	0.262971	−	1.49138i
$698$	−5.04236	−	38.0316i	−0.190856	−	1.43952i
$699$	−10.2672	−	7.96192i	−0.388340	−	0.301147i
$700$	−44.7520	−	11.9035i	−1.69147	−	0.449911i
$701$		−	15.9132i		−	0.601032i	−0.953777	−	0.300516i	$-0.902841\pi$
$701$		−	15.9132i		−	0.601032i	0.953777	−	0.300516i	$-0.0971588\pi$
$702$	−4.68263	−	10.4317i	−0.176735	−	0.393720i
$703$		−	12.6392i		−	0.476697i
$704$	0.687070	−	8.38304i	0.0258949	−	0.315948i
$705$	−2.46989	+	1.00832i	−0.0930216	+	0.0379754i
$706$	−9.44288	+	1.25197i	−0.355388	+	0.0471185i
$707$	−8.44192	+	47.8765i	−0.317491	+	1.80058i
$708$	−17.2286	−	22.6058i	−0.647491	−	0.849577i
$709$	−25.2965	+	21.2262i	−0.950028	+	0.797169i	−0.979302	−	0.202403i	$-0.935125\pi$
$709$	−25.2965	+	21.2262i	−0.950028	+	0.797169i	0.0292739	+	0.999571i	$0.490681\pi$
$710$	0.897910	+	0.198200i	0.0336980	+	0.00743832i
$711$	2.92346	−	4.08567i	0.109638	−	0.153225i
$712$	−23.0187	+	9.60875i	−0.862661	+	0.360103i
$713$	12.3783	−	2.18262i	0.463570	−	0.0817399i
$714$	59.9997	−	34.3063i	2.24543	−	1.28388i
$715$	0.0779800	+	0.214248i	0.00291629	+	0.00801244i
$716$	10.5252	+	22.4640i	0.393346	+	0.839518i
$717$	3.99600	+	4.40583i	0.149233	+	0.164539i
$718$	−21.7923	+	34.2763i	−0.813283	+	1.27918i
$719$	4.06158	−	7.03487i	0.151471	−	0.262356i	−0.780297	−	0.625409i	$-0.784932\pi$
$719$	4.06158	−	7.03487i	0.151471	−	0.262356i	0.931769	+	0.363053i	$0.118266\pi$
$720$	0.156671	−	1.66500i	0.00583880	−	0.0620507i
$721$	3.59112	+	6.22000i	0.133740	+	0.231645i
$722$	0.370521	+	0.0158376i	0.0137893	+	0.000589416i
$723$	2.60830	+	1.37477i	0.0970038	+	0.0511283i
$724$	−2.32000	−	0.198696i	−0.0862219	−	0.00738448i
$725$	−1.96998	+	2.34773i	−0.0731631	+	0.0871924i
$726$	15.5010	+	18.6315i	0.575298	+	0.691480i
$727$	12.8952	−	35.4294i	0.478258	−	1.31400i	−0.432713	−	0.901532i	$-0.642444\pi$
$727$	12.8952	−	35.4294i	0.478258	−	1.31400i	0.910971	−	0.412470i	$-0.135334\pi$
$728$	−16.2664	−	12.4108i	−0.602872	−	0.459976i
$729$	18.4980	+	19.6679i	0.685110	+	0.728439i
$730$	1.50182	−	1.64196i	0.0555849	−	0.0607718i
$731$	12.4823	+	4.54317i	0.461673	+	0.168035i
$732$	−1.81620	+	38.6878i	−0.0671286	+	1.42994i
$733$	−22.3955	−	18.7921i	−0.827198	−	0.694101i	0.127448	−	0.991845i	$-0.459321\pi$
$733$	−22.3955	−	18.7921i	−0.827198	−	0.694101i	−0.954646	+	0.297744i	$0.903766\pi$
$734$	−3.36650	−	4.37901i	−0.124260	−	0.161632i
$735$	−1.64457	+	3.12018i	−0.0606610	+	0.115090i
$736$	14.2040	−	1.93614i	0.523567	−	0.0713671i
$737$	5.13900	−	2.96700i	0.189298	−	0.109291i
$738$	23.7091	−	14.7962i	0.872746	−	0.544657i
$739$	34.0829	+	19.6778i	1.25376	+	0.723858i	0.971854	−	0.235584i	$-0.0757002\pi$
$739$	34.0829	+	19.6778i	1.25376	+	0.723858i	0.281905	+	0.959442i	$0.409034\pi$
$740$	−0.209167	−	0.774948i	−0.00768914	−	0.0284876i
$741$	8.76168	−	7.94666i	0.321868	−	0.291928i
$742$	53.0682	+	21.9247i	1.94820	+	0.804881i
$743$	10.4717	−	3.81140i	0.384171	−	0.139827i	−0.142713	−	0.989764i	$-0.545583\pi$
$743$	10.4717	−	3.81140i	0.384171	−	0.139827i	0.526884	+	0.849937i	$0.323360\pi$
$744$	−19.9371	+	13.8900i	−0.730929	+	0.509233i
$745$	0.438169	+	2.48498i	0.0160533	+	0.0910427i
$746$	−14.7044	+	4.65109i	−0.538368	+	0.170288i
$747$	5.72629	+	4.09739i	0.209514	+	0.149916i
$748$	7.33956	+	10.4413i	0.268361	+	0.381770i
$749$	−23.5787	−	28.0999i	−0.861545	−	1.02675i
$750$	0.605687	−	3.35277i	0.0221166	−	0.122426i
$751$	28.7902	+	5.07650i	1.05057	+	0.185244i	0.672169	−	0.740397i	$-0.265363\pi$
$751$	28.7902	+	5.07650i	1.05057	+	0.185244i	0.378402	+	0.925641i	$0.376474\pi$
$752$	38.3662	+	21.9639i	1.39907	+	0.800941i
$753$	−10.2096	−	25.0087i	−0.372060	−	0.911369i
$754$	−1.20052	+	0.626350i	−0.0437205	+	0.0228103i
$755$	−2.03500			−0.0740613
$756$	45.8761	+	15.1481i	1.66850	+	0.550931i
$757$	−8.57552			−0.311682			−0.155841	−	0.987782i	$-0.549809\pi$
$757$	−8.57552			−0.311682			−0.155841	+	0.987782i	$0.549809\pi$
$758$	−7.46356	+	3.89397i	−0.271089	+	0.141435i
$759$	2.82802	−	3.64683i	0.102651	−	0.132372i
$760$	1.68795	−	0.379074i	0.0612284	−	0.0137504i
$761$	−5.54033	−	0.976910i	−0.200837	−	0.0354130i	0.0723247	−	0.997381i	$-0.476958\pi$
$761$	−5.54033	−	0.976910i	−0.200837	−	0.0354130i	−0.273161	+	0.961968i	$0.588069\pi$
$762$	−6.25254	−	5.29133i	−0.226506	−	0.191685i
$763$	−5.33548	−	6.35857i	−0.193157	−	0.230196i
$764$	−23.5344	+	16.5432i	−0.851446	+	0.598514i
$765$	1.43418	+	2.09341i	0.0518530	+	0.0756875i
$766$	−9.00163	+	2.84726i	−0.325242	+	0.102876i
$767$	−2.21699	−	12.5732i	−0.0800509	−	0.453991i
$768$	−23.3397	+	14.9418i	−0.842201	+	0.539164i
$769$	−2.35854	+	0.858439i	−0.0850512	+	0.0309561i	−0.384195	−	0.923252i	$-0.625521\pi$
$769$	−2.35854	+	0.858439i	−0.0850512	+	0.0309561i	0.299144	+	0.954208i	$0.403299\pi$
$770$	−0.890333	−	0.367834i	−0.0320854	−	0.0132558i
$771$	−3.63650	−	16.8090i	−0.130965	−	0.605361i
$772$	35.5193	−	9.58707i	1.27837	−	0.345046i
$773$	0.0355587	+	0.0205298i	0.00127896	+	0.000738407i	0.500639	−	0.865656i	$-0.333098\pi$
$773$	0.0355587	+	0.0205298i	0.00127896	+	0.000738407i	−0.499360	+	0.866394i	$0.666432\pi$
$774$	3.47338	+	8.61111i	0.124848	+	0.309520i
$775$	−21.3937	+	12.3516i	−0.768483	+	0.443684i
$776$	0.738869	+	15.9200i	0.0265238	+	0.571494i
$777$	23.1713	−	0.893143i	0.831267	−	0.0320413i
$778$	−26.2716	−	34.1731i	−0.941883	−	1.22516i
$779$	22.1468	+	18.5834i	0.793492	+	0.665819i
$780$	0.405695	−	0.632231i	0.0145262	−	0.0226375i
$781$	−4.60950	−	1.67772i	−0.164941	−	0.0600335i
$782$	−14.6808	+	16.0507i	−0.524983	+	0.573972i
$783$	2.19599	−	2.32399i	0.0784783	−	0.0830527i
$784$	57.5221	−	10.3599i	2.05436	−	0.369997i
$785$	0.00653192	−	0.0179463i	0.000233134	−	0.000640531i
$786$	−2.22182	+	6.02569i	−0.0792498	+	0.214929i
$787$	27.9726	−	33.3365i	0.997116	−	1.18832i	0.0150289	−	0.999887i	$-0.495216\pi$
$787$	27.9726	−	33.3365i	0.997116	−	1.18832i	0.982087	−	0.188429i	$-0.0603396\pi$
$788$	3.61561	−	42.2163i	0.128801	−	1.50389i
$789$	−38.3220	+	24.1395i	−1.36430	+	0.859391i
$790$	0.329748	+	0.0140948i	0.0117319	+	0.000501472i
$791$	24.6902	+	42.7647i	0.877882	+	1.52054i
$792$	−1.99594	+	8.69524i	−0.0709227	+	0.308972i
$793$	−8.69865	+	15.0665i	−0.308898	+	0.535028i
$794$	−11.9526	+	18.7997i	−0.424181	+	0.667177i
$795$	−0.644191	+	2.00731i	−0.0228471	+	0.0711918i
$796$	12.1451	−	5.69045i	0.430473	−	0.201693i
$797$	15.3705	+	42.2300i	0.544450	+	1.49586i	0.841102	+	0.540877i	$0.181908\pi$
$797$	15.3705	+	42.2300i	0.544450	+	1.49586i	−0.296652	+	0.954986i	$0.595870\pi$
$798$	−0.209516	+	49.9772i	−0.00741678	+	1.76917i
$799$	−66.0612	+	11.6484i	−2.33708	+	0.412090i
$800$	−24.9312	+	13.1237i	−0.881452	+	0.463992i
$801$	25.6239	−	6.58613i	0.905375	−	0.232709i
$802$	−4.27963	−	0.944665i	−0.151119	−	0.0333573i
$803$	−9.09342	+	7.63028i	−0.320900	+	0.269267i
$804$	−18.0383	−	7.54107i	−0.636163	−	0.265953i
$805$	0.285100	−	1.61688i	0.0100484	−	0.0569875i
$806$	−10.8200	+	1.43455i	−0.381117	+	0.0505298i
$807$	0.109249	−	0.798299i	0.00384573	−	0.0281014i
$808$	15.9607	+	24.9022i	0.561495	+	0.876055i
$809$			39.4534i			1.38711i	0.720405	+	0.693553i	$0.243956\pi$
$809$			39.4534i			1.38711i	−0.720405	+	0.693553i	$0.756044\pi$
$810$	−0.417637	+	1.72393i	−0.0146743	+	0.0605727i
$811$			49.4348i			1.73589i	0.496659	+	0.867946i	$0.334560\pi$
$811$			49.4348i			1.73589i	−0.496659	+	0.867946i	$0.665440\pi$
$812$	1.47065	−	5.52900i	0.0516097	−	0.194030i
$813$	3.67716	−	26.8696i	0.128964	−	0.942359i
$814$	0.562798	+	4.24486i	0.0197260	+	0.148782i
$815$	−0.290908	+	1.64982i	−0.0101900	+	0.0577906i
$816$	12.7029	−	40.0859i	0.444689	−	1.40329i
$817$	−7.35807	+	6.17416i	−0.257426	+	0.216006i
$818$	8.00291	−	36.2557i	0.279815	−	1.26765i
$819$	15.1877	+	15.5012i	0.530700	+	0.541654i
$820$	1.66543	+	0.772894i	0.0581592	+	0.0269906i
$821$	21.7656	−	3.83786i	0.759624	−	0.133942i	0.219598	−	0.975590i	$-0.429525\pi$
$821$	21.7656	−	3.83786i	0.759624	−	0.133942i	0.540026	+	0.841648i	$0.318414\pi$
$822$	21.8367	+	0.0915444i	0.761641	+	0.00319298i
$823$	6.69131	+	18.3842i	0.233244	+	0.640833i	0.999999	−	0.00110635i	$-0.000352162\pi$
$823$	6.69131	+	18.3842i	0.233244	+	0.640833i	−0.766755	+	0.641940i	$0.778130\pi$
$824$	4.17112	+	1.30257i	0.145308	+	0.0453772i
$825$	−2.77153	+	8.63614i	−0.0964925	+	0.300672i
$826$	45.5216	+	28.9419i	1.58390	+	1.00702i
$827$	−8.39197	+	14.5353i	−0.291817	+	0.505442i	−0.974239	−	0.225516i	$-0.927593\pi$
$827$	−8.39197	+	14.5353i	−0.291817	+	0.505442i	0.682422	+	0.730958i	$0.260927\pi$
$828$	−15.2044	−	0.127483i	−0.528390	−	0.00443035i
$829$	−18.8116	−	32.5827i	−0.653355	−	1.13164i	−0.982304	−	0.187296i	$-0.940028\pi$
$829$	−18.8116	−	32.5827i	−0.653355	−	1.13164i	0.328949	−	0.944348i	$-0.393306\pi$
$830$	−0.0197547	+	0.462160i	−0.000685696	+	0.0160418i
$831$	−14.4528	+	9.10402i	−0.501363	+	0.315815i
$832$	−12.3948	+	1.15300i	−0.429712	+	0.0399732i
$833$	−57.0065	+	67.9377i	−1.97516	+	2.35390i
$834$	34.4860	+	12.7159i	1.19415	+	0.440314i
$835$	0.536320	−	1.47353i	0.0185601	−	0.0509935i
$836$	−9.19227	+	0.821172i	−0.317921	+	0.0284008i
$837$	23.0401	−	11.5488i	0.796384	−	0.399184i
$838$	−37.7429	−	34.5215i	−1.30381	−	1.19253i
$839$	−51.7302	−	18.8283i	−1.78592	−	0.650024i	−0.999476	−	0.0323683i	$-0.989695\pi$
$839$	−51.7302	−	18.8283i	−1.78592	−	0.650024i	−0.786449	−	0.617655i	$-0.788083\pi$
$840$	0.814230	+	3.06772i	0.0280936	+	0.105846i
$841$	21.9252	+	18.3975i	0.756043	+	0.634395i
$842$	−14.2146	+	10.9279i	−0.489868	+	0.376601i
$843$	29.5344	−	1.13841i	1.01722	−	0.0392089i
$844$	24.8413	−	24.9324i	0.855073	−	0.858209i
$845$	−1.27676	+	0.737140i	−0.0439220	+	0.0253584i
$846$	−36.9333	−	28.8895i	−1.26979	−	0.993243i
$847$	−39.8358	−	22.9992i	−1.36878	−	0.790263i
$848$	32.7836	−	12.0683i	1.12580	−	0.414428i
$849$	−3.47588	−	16.0666i	−0.119292	−	0.551404i
$850$	16.3239	−	39.5116i	0.559906	−	1.35524i
$851$	−6.85782	+	2.49604i	−0.235083	+	0.0855633i
$852$	4.80944	+	15.4297i	0.164769	+	0.528614i
$853$	1.97889	+	11.2229i	0.0677560	+	0.384263i	0.999762	+	0.0218204i	$0.00694619\pi$
$853$	1.97889	+	11.2229i	0.0677560	+	0.384263i	−0.932006	+	0.362443i	$0.881943\pi$
$854$	−22.1678	−	70.0837i	−0.758568	−	2.39822i
$855$	−1.82949	+	0.141246i	−0.0625672	+	0.00483050i
$856$	−22.1347	−	2.85230i	−0.756549	−	0.0974897i
$857$	17.0466	+	20.3153i	0.582300	+	0.693958i	0.974106	−	0.226090i	$-0.0725943\pi$
$857$	17.0466	+	20.3153i	0.582300	+	0.693958i	−0.391807	+	0.920048i	$0.628150\pi$
$858$	−2.58875	+	3.05901i	−0.0883783	+	0.104433i
$859$	7.71712	+	1.36074i	0.263305	+	0.0464277i	0.303742	−	0.952754i	$-0.401764\pi$
$859$	7.71712	+	1.36074i	0.263305	+	0.0464277i	−0.0404372	+	0.999182i	$0.512875\pi$
$860$	−0.348969	+	0.500326i	−0.0118997	+	0.0170610i
$861$	−32.5037	+	41.9147i	−1.10772	+	1.42845i
$862$	7.39417	+	14.1724i	0.251847	+	0.482714i
$863$	32.9090			1.12023			0.560117	−	0.828413i	$-0.310756\pi$
$863$	32.9090			1.12023			0.560117	+	0.828413i	$0.310756\pi$
$864$	26.7719	−	12.1354i	0.910797	−	0.412854i
$865$	0.794776			0.0270232
$866$	11.8441	+	22.7016i	0.402479	+	0.771430i
$867$	12.9872	+	31.8123i	0.441067	+	1.08040i
$868$	26.3819	−	37.8243i	0.895459	−	1.28384i
$869$	−1.73394	−	0.305741i	−0.0588199	−	0.0103715i
$870$	0.206710	+	0.0373428i	0.00700813	+	0.00126604i
$871$	−5.64508	−	6.72755i	−0.191276	−	0.227954i
$872$	−5.00874	−	0.645431i	−0.169617	−	0.0218571i
$873$	1.64519	−	16.8236i	0.0556814	−	0.569394i
$874$	−4.74354	−	14.9967i	−0.160453	−	0.507272i
$875$	1.12284	+	6.36795i	0.0379590	+	0.215276i
$876$	38.1559	+	8.59025i	1.28917	+	0.290238i
$877$	−37.2032	+	13.5408i	−1.25626	+	0.457242i	−0.882513	−	0.470288i	$-0.844150\pi$
$877$	−37.2032	+	13.5408i	−1.25626	+	0.457242i	−0.373748	+	0.927530i	$0.621928\pi$
$878$	7.38472	−	17.8745i	0.249222	−	0.603237i
$879$	2.91000	−	2.63931i	0.0981520	−	0.0890219i
$880$	−0.550016	+	0.202472i	−0.0185410	+	0.00682534i
$881$	−20.1797	−	11.6507i	−0.679870	−	0.392523i	0.119936	−	0.992782i	$-0.461731\pi$
$881$	−20.1797	−	11.6507i	−0.679870	−	0.392523i	−0.799806	+	0.600259i	$0.795064\pi$
$882$	−61.9565	+	2.12804i	−2.08618	+	0.0716549i
$883$	−44.2753	+	25.5624i	−1.48998	+	0.860242i	−0.999934	−	0.0114524i	$-0.996355\pi$
$883$	−44.2753	+	25.5624i	−1.48998	+	0.860242i	−0.490049	+	0.871695i	$0.663021\pi$
$884$	13.3318	−	13.3807i	0.448398	−	0.450042i
$885$	−0.923464	+	1.75205i	−0.0310419	+	0.0588946i
$886$	−12.2000	+	9.37913i	−0.409867	+	0.315098i
$887$	−5.23482	−	4.39254i	−0.175768	−	0.147487i	0.550659	−	0.834730i	$-0.314376\pi$
$887$	−5.23482	−	4.39254i	−0.175768	−	0.147487i	−0.726428	+	0.687243i	$0.758821\pi$
$888$	9.99955	−	9.95242i	0.335563	−	0.333981i
$889$	14.6081	+	5.31691i	0.489940	+	0.178324i
$890$	1.28254	+	1.17307i	0.0429908	+	0.0393215i
$891$	3.41734	−	8.82392i	0.114485	−	0.295612i
$892$	−18.4680	+	1.64980i	−0.618356	+	0.0552395i
$893$	16.5901	−	45.5809i	0.555167	−	1.52531i
$894$	−34.0939	+	28.3655i	−1.14027	+	0.948683i
$895$	1.11113	−	1.32420i	0.0371411	−	0.0442630i
$896$	31.7504	−	41.9313i	1.06071	−	1.40083i
$897$	−6.04202	−	3.18460i	−0.201737	−	0.106331i
$898$	0.425540	−	9.95549i	0.0142005	−	0.332219i
$899$	−1.52601	−	2.64313i	−0.0508954	−	0.0881535i
$900$	28.1660	−	9.98495i	0.938866	−	0.332832i
$901$	−26.5042	+	45.9065i	−0.882981	+	1.52937i
$902$	−8.26545	−	5.25505i	−0.275209	−	0.174974i
$903$	−11.8390	−	13.0532i	−0.393977	−	0.434383i
$904$	28.6779	+	8.95563i	0.953811	+	0.297860i
$905$	0.0554934	+	0.152467i	0.00184466	+	0.00506817i
$906$	−17.7540	−	31.0507i	−0.589837	−	1.03159i
$907$	7.37773	−	1.30089i	0.244974	−	0.0431955i	−0.0498130	−	0.998759i	$-0.515863\pi$
$907$	7.37773	−	1.30089i	0.244974	−	0.0431955i	0.294787	+	0.955563i	$0.404751\pi$
$908$	−40.4894	−	18.7904i	−1.34369	−	0.623582i
$909$	−12.9674	−	28.5669i	−0.430101	−	0.947503i
$910$	−0.307304	+	1.39219i	−0.0101870	+	0.0461505i
$911$	19.8453	−	16.6521i	0.657503	−	0.551710i	−0.251835	−	0.967770i	$-0.581034\pi$
$911$	19.8453	−	16.6521i	0.657503	−	0.551710i	0.909337	+	0.416060i	$0.136589\pi$
$912$	20.5102	+	22.4481i	0.679161	+	0.743332i
$913$	0.428513	−	2.43022i	0.0141817	−	0.0804284i
$914$	−4.73114	−	35.6842i	−0.156492	−	1.18033i
$915$	2.49859	−	1.02003i	0.0826010	−	0.0337213i
$916$	−13.5393	+	50.9019i	−0.447352	+	1.68185i
$917$		−	12.1887i		−	0.402508i
$918$	−19.4297	+	40.1468i	−0.641275	+	1.32504i
$919$		−	37.4197i		−	1.23436i	−0.786821	−	0.617182i	$-0.788274\pi$
$919$		−	37.4197i		−	1.23436i	0.786821	−	0.617182i	$-0.211726\pi$
$920$	−0.539023	−	0.840993i	−0.0177710	−	0.0277267i
$921$	−16.6191	−	12.8876i	−0.547616	−	0.424662i
$922$	−54.9653	+	7.28749i	−1.81019	+	0.240001i
$923$	−1.26065	+	7.14947i	−0.0414946	+	0.235328i
$924$	−2.15501	−	16.7941i	−0.0708947	−	0.552485i
$925$	10.9875	−	9.21963i	0.361268	−	0.303140i
$926$	10.3296	+	2.28010i	0.339451	+	0.0749287i
$927$	−4.18037	−	2.00157i	−0.137301	−	0.0657403i
$928$	−1.62140	−	3.08019i	−0.0532250	−	0.101112i
$929$	−12.0979	+	2.13318i	−0.396919	+	0.0699875i	−0.368545	−	0.929610i	$-0.620144\pi$
$929$	−12.0979	+	2.13318i	−0.396919	+	0.0699875i	−0.0283738	+	0.999597i	$0.509033\pi$
$930$	1.46275	+	0.852717i	0.0479655	+	0.0279617i
$931$	−21.9337	−	60.2623i	−0.718848	−	1.97502i
$932$	13.5853	−	6.36521i	0.445001	−	0.208500i
$933$	29.4106	−	6.36276i	0.962859	−	0.208307i
$934$	−1.04699	+	1.64677i	−0.0342586	+	0.0538840i
$935$	0.444664	−	0.770181i	0.0145421	−	0.0251876i
$936$	13.1862	+	0.674437i	0.431004	+	0.0220447i
$937$	−20.8028	−	36.0316i	−0.679599	−	1.17710i	−0.975102	−	0.221758i	$-0.928821\pi$
$937$	−20.8028	−	36.0316i	−0.679599	−	1.17710i	0.295503	−	0.955342i	$-0.404513\pi$
$938$	37.0721	+	1.58462i	1.21045	+	0.0517397i
$939$	1.08571	+	28.1672i	0.0354308	+	0.919202i
$940$	0.262867	−	3.06926i	0.00857376	−	0.100108i
$941$	33.5803	−	40.0194i	1.09469	−	1.30460i	0.145682	−	0.989331i	$-0.453462\pi$
$941$	33.5803	−	40.0194i	1.09469	−	1.30460i	0.949004	−	0.315265i	$-0.102093\pi$
$942$	0.330817	−	0.0569030i	0.0107786	−	0.00185400i
$943$	5.70939	−	15.6864i	0.185923	−	0.510820i
$944$	32.2999	−	5.81732i	1.05127	−	0.189338i
$945$	−0.388224	−	3.34401i	−0.0126289	−	0.108781i
$946$	2.19627	−	2.40122i	0.0714070	−	0.0780704i
$947$	16.5986	+	6.04138i	0.539380	+	0.196318i	0.597322	−	0.802002i	$-0.296231\pi$
$947$	16.5986	+	6.04138i	0.539380	+	0.196318i	−0.0579415	+	0.998320i	$0.518454\pi$
$948$	2.66176	+	5.15436i	0.0864499	+	0.167406i
$949$	13.4580	+	11.2926i	0.436867	+	0.366575i
$950$	18.8414	+	24.5081i	0.611295	+	0.795148i
$951$	26.8994	+	42.7033i	0.872272	+	1.38475i
$952$	3.69998	+	79.7214i	0.119917	+	2.58378i
$953$	47.6750	−	27.5252i	1.54435	−	0.891628i	0.545788	−	0.837923i	$-0.316230\pi$
$953$	47.6750	−	27.5252i	1.54435	−	0.891628i	0.998557	−	0.0537052i	$-0.0171031\pi$
$954$	−36.2482	+	7.68310i	−1.17358	+	0.248750i
$955$	1.73597	+	1.00227i	0.0561748	+	0.0324325i
$956$	−6.63093	+	1.78976i	−0.214460	+	0.0578851i
$957$	−1.06697	−	0.342416i	−0.0344904	−	0.0110687i
$958$	16.6342	+	6.87230i	0.537428	+	0.222034i
$959$	−38.9446	+	14.1747i	−1.25759	+	0.457724i
$960$	1.62904	+	1.03694i	0.0525770	+	0.0334670i
$961$	1.11121	+	6.30196i	0.0358453	+	0.203289i
$962$	6.04221	−	1.91118i	0.194809	−	0.0616189i
$963$	22.8012	+	6.35987i	0.734758	+	0.204944i
$964$	−2.78527	+	1.95787i	−0.0897075	+	0.0630588i
$965$	−1.64785	−	1.96383i	−0.0530462	−	0.0632180i
$966$	27.1582	−	9.75602i	0.873799	−	0.313895i
$967$	16.5590	+	2.91980i	0.532502	+	0.0938945i	0.433433	−	0.901186i	$-0.357302\pi$
$967$	16.5590	+	2.91980i	0.532502	+	0.0938945i	0.0990696	+	0.995081i	$0.468413\pi$
$968$	−27.3060	+	6.13227i	−0.877647	+	0.197099i
$969$	−45.7125	−	6.25584i	−1.46850	−	0.200967i
$970$	0.984573	−	0.513682i	0.0316127	−	0.0164933i
$971$	22.4986			0.722013			0.361007	−	0.932563i	$-0.382433\pi$
$971$	22.4986			0.722013			0.361007	+	0.932563i	$0.382433\pi$
$972$	−29.9478	+	8.66764i	−0.960577	+	0.278015i
$973$	−69.7582			−2.23635
$974$	15.5389	−	8.10710i	0.497898	−	0.259768i
$975$	13.2994	+	1.82004i	0.425921	+	0.0582880i
$976$	−38.8120	−	22.2191i	−1.24234	−	0.711217i
$977$	8.62912	+	1.52155i	0.276070	+	0.0486786i	0.309969	−	0.950747i	$-0.399681\pi$
$977$	8.62912	+	1.52155i	0.276070	+	0.0486786i	−0.0338989	+	0.999425i	$0.510792\pi$
$978$	−27.7114	+	9.95477i	−0.886113	+	0.318318i
$979$	−5.96003	−	7.10288i	−0.190483	−	0.227009i
$980$	−2.34211	−	3.33188i	−0.0748158	−	0.106433i
$981$	5.15955	+	1.43914i	0.164732	+	0.0459481i
$982$	35.8136	−	11.3280i	1.14286	−	0.361492i
$983$	1.90169	+	10.7850i	0.0606544	+	0.343988i	0.999999	+	0.00101465i	$0.000322973\pi$
$983$	1.90169	+	10.7850i	0.0606544	+	0.343988i	−0.939345	+	0.342973i	$0.888566\pi$
$984$	2.73663	+	32.1545i	0.0872407	+	1.02505i
$985$	−2.77440	+	1.00980i	−0.0883996	+	0.0321748i
$986$	4.88157	+	2.01678i	0.155461	+	0.0642274i
$987$	84.7354	+	27.1935i	2.69716	+	0.865580i
$988$	3.55922	+	13.1866i	0.113234	+	0.419522i
$989$	4.80310	+	2.77307i	0.152730	+	0.0881785i
$990$	0.608142	−	0.128901i	0.0193280	−	0.00409673i
$991$	31.9842	−	18.4661i	1.01601	−	0.586594i	0.103065	−	0.994675i	$-0.467135\pi$
$991$	31.9842	−	18.4661i	1.01601	−	0.586594i	0.912946	+	0.408081i	$0.133802\pi$
$992$	−3.78947	−	27.8005i	−0.120316	−	0.882666i
$993$	−2.52532	−	4.00899i	−0.0801385	−	0.127221i
$994$	−18.6951	−	24.3179i	−0.592973	−	0.771315i
$995$	−0.715926	−	0.600734i	−0.0226964	−	0.0190445i
$996$	−7.22413	+	3.73060i	−0.228905	+	0.118209i
$997$	35.4190	+	12.8915i	1.12173	+	0.408276i	0.835283	−	0.549820i	$-0.185304\pi$
$997$	35.4190	+	12.8915i	1.12173	+	0.408276i	0.286447	+	0.958096i	$0.407526\pi$
$998$	9.20246	−	10.0612i	0.291299	−	0.318481i
$999$	−12.0099	+	8.92656i	−0.379977	+	0.282424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.l.a.23.11	yes	96
3.2	odd	2		324.2.l.a.179.6		96
4.3	odd	2	inner	108.2.l.a.23.3	✓	96
9.2	odd	6		972.2.l.b.215.6		96
9.4	even	3		972.2.l.d.863.1		96
9.5	odd	6		972.2.l.a.863.16		96
9.7	even	3		972.2.l.c.215.11		96
12.11	even	2		324.2.l.a.179.14		96
27.2	odd	18		972.2.l.d.107.9		96
27.7	even	9		324.2.l.a.143.14		96
27.11	odd	18		972.2.l.c.755.13		96
27.16	even	9		972.2.l.b.755.4		96
27.20	odd	18	inner	108.2.l.a.47.3	yes	96
27.25	even	9		972.2.l.a.107.8		96
36.7	odd	6		972.2.l.c.215.13		96
36.11	even	6		972.2.l.b.215.4		96
36.23	even	6		972.2.l.a.863.8		96
36.31	odd	6		972.2.l.d.863.9		96
108.7	odd	18		324.2.l.a.143.6		96
108.11	even	18		972.2.l.c.755.11		96
108.43	odd	18		972.2.l.b.755.6		96
108.47	even	18	inner	108.2.l.a.47.11	yes	96
108.79	odd	18		972.2.l.a.107.16		96
108.83	even	18		972.2.l.d.107.1		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.3	✓	96	4.3	odd	2	inner
108.2.l.a.23.11	yes	96	1.1	even	1	trivial
108.2.l.a.47.3	yes	96	27.20	odd	18	inner
108.2.l.a.47.11	yes	96	108.47	even	18	inner
324.2.l.a.143.6		96	108.7	odd	18
324.2.l.a.143.14		96	27.7	even	9
324.2.l.a.179.6		96	3.2	odd	2
324.2.l.a.179.14		96	12.11	even	2
972.2.l.a.107.8		96	27.25	even	9
972.2.l.a.107.16		96	108.79	odd	18
972.2.l.a.863.8		96	36.23	even	6
972.2.l.a.863.16		96	9.5	odd	6
972.2.l.b.215.4		96	36.11	even	6
972.2.l.b.215.6		96	9.2	odd	6
972.2.l.b.755.4		96	27.16	even	9
972.2.l.b.755.6		96	108.43	odd	18
972.2.l.c.215.11		96	9.7	even	3
972.2.l.c.215.13		96	36.7	odd	6
972.2.l.c.755.11		96	108.11	even	18
972.2.l.c.755.13		96	27.11	odd	18
972.2.l.d.107.1		96	108.83	even	18
972.2.l.d.107.9		96	27.2	odd	18
972.2.l.d.863.1		96	9.4	even	3
972.2.l.d.863.9		96	36.31	odd	6

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654159 + 1.25382i) q^{2} +(1.71606 + 0.234845i) q^{3} +(-1.14415 + 1.64040i) q^{4} +(0.137245 + 0.0242000i) q^{5} +(0.828118 + 2.30526i) q^{6} +(-2.98823 - 3.56123i) q^{7} +(-2.80523 - 0.361485i) q^{8} +(2.88970 + 0.806015i) q^{9} +O(q^{10})\)	\(q+(0.654159 + 1.25382i) q^{2} +(1.71606 + 0.234845i) q^{3} +(-1.14415 + 1.64040i) q^{4} +(0.137245 + 0.0242000i) q^{5} +(0.828118 + 2.30526i) q^{6} +(-2.98823 - 3.56123i) q^{7} +(-2.80523 - 0.361485i) q^{8} +(2.88970 + 0.806015i) q^{9} +(0.0594376 + 0.187912i) q^{10} +(-0.182573 - 1.03542i) q^{11} +(-2.34867 + 2.54632i) q^{12} +(-1.46220 + 0.532196i) q^{13} +(2.51039 - 6.07633i) q^{14} +(0.229837 + 0.0737600i) q^{15} +(-1.38183 - 3.75374i) q^{16} +(5.25631 + 3.03473i) q^{17} +(0.879718 + 4.15043i) q^{18} +(-3.80088 + 2.19444i) q^{19} +(-0.196727 + 0.197449i) q^{20} +(-4.29163 - 6.81305i) q^{21} +(1.17880 - 0.906244i) q^{22} +(1.94128 + 1.62893i) q^{23} +(-4.72904 - 1.27912i) q^{24} +(-4.68021 - 1.70346i) q^{25} +(-1.62379 - 1.48520i) q^{26} +(4.76959 + 2.06180i) q^{27} +(9.26084 - 0.827297i) q^{28} +(0.210458 - 0.578229i) q^{29} +(0.0578679 + 0.336426i) q^{30} +(3.18818 - 3.79952i) q^{31} +(3.80260 - 4.18811i) q^{32} +(-0.0701412 - 1.81972i) q^{33} +(-0.366562 + 8.57569i) q^{34} +(-0.323938 - 0.561078i) q^{35} +(-4.62844 + 3.81805i) q^{36} +(-1.43991 + 2.49400i) q^{37} +(-5.23782 - 3.33012i) q^{38} +(-2.63420 + 0.569889i) q^{39} +(-0.376257 - 0.117499i) q^{40} +(-2.25297 - 6.18999i) q^{41} +(5.73496 - 9.83776i) q^{42} +(2.15530 - 0.380038i) q^{43} +(1.90740 + 0.885188i) q^{44} +(0.377091 + 0.180553i) q^{45} +(-0.772484 + 3.49960i) q^{46} +(-8.46639 + 7.10414i) q^{47} +(-1.48975 - 6.76614i) q^{48} +(-2.53733 + 14.3899i) q^{49} +(-0.925763 - 6.98250i) q^{50} +(8.30743 + 6.44219i) q^{51} +(0.799963 - 3.00750i) q^{52} +8.73360i q^{53} +(0.534935 + 7.32897i) q^{54} -0.146525i q^{55} +(7.09534 + 11.0703i) q^{56} +(-7.03787 + 2.87316i) q^{57} +(0.862670 - 0.114376i) q^{58} +(-1.42477 + 8.08025i) q^{59} +(-0.383965 + 0.292632i) q^{60} +(8.56477 - 7.18670i) q^{61} +(6.84951 + 1.51193i) q^{62} +(-5.76467 - 12.6994i) q^{63} +(7.73866 + 2.02810i) q^{64} +(-0.213559 + 0.0376562i) q^{65} +(2.23572 - 1.27833i) q^{66} +(1.93034 + 5.30357i) q^{67} +(-10.9922 + 5.15026i) q^{68} +(2.94880 + 3.25123i) q^{69} +(0.491586 - 0.773196i) q^{70} +(2.33277 - 4.04048i) q^{71} +(-7.81490 - 3.30564i) q^{72} +(-5.64518 - 9.77774i) q^{73} +(-4.06898 - 0.173925i) q^{74} +(-7.63146 - 4.02235i) q^{75} +(0.749029 - 8.74574i) q^{76} +(-3.14181 + 3.74426i) q^{77} +(-2.43772 - 2.93002i) q^{78} +(0.572755 - 1.57363i) q^{79} +(-0.0988087 - 0.548623i) q^{80} +(7.70068 + 4.65828i) q^{81} +(6.28736 - 6.87406i) q^{82} +(2.20553 + 0.802749i) q^{83} +(16.0864 + 0.755175i) q^{84} +(0.647964 + 0.543706i) q^{85} +(1.88641 + 2.45377i) q^{86} +(0.496952 - 0.942848i) q^{87} +(0.137869 + 2.97059i) q^{88} +(7.63741 - 4.40946i) q^{89} +(0.0202964 + 0.590917i) q^{90} +(6.26466 + 3.61690i) q^{91} +(-4.89321 + 1.32073i) q^{92} +(6.36339 - 5.77146i) q^{93} +(-14.4457 - 5.96813i) q^{94} +(-0.574758 + 0.209195i) q^{95} +(7.50902 - 6.29401i) q^{96} +(-0.978443 - 5.54902i) q^{97} +(-19.7022 + 6.23192i) q^{98} +(0.306985 - 3.13921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

Varieties

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