LMFDB - Embedded newform 225.2.q.a.106.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.4
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27906 - 0.484430i) q^{2} +(-1.66084 - 0.491525i) q^{3} +(3.13236 + 1.39462i) q^{4} +(-1.74691 + 1.39582i) q^{5} +(3.54706 + 1.92478i) q^{6} +(-0.0399999 + 0.0692819i) q^{7} +(-2.69327 - 1.95678i) q^{8} +(2.51681 + 1.63269i) q^{9} +O(q^{10})$	\(q+(-2.27906 - 0.484430i) q^{2} +(-1.66084 - 0.491525i) q^{3} +(3.13236 + 1.39462i) q^{4} +(-1.74691 + 1.39582i) q^{5} +(3.54706 + 1.92478i) q^{6} +(-0.0399999 + 0.0692819i) q^{7} +(-2.69327 - 1.95678i) q^{8} +(2.51681 + 1.63269i) q^{9} +(4.65750 - 2.33489i) q^{10} +(0.117280 + 0.0249287i) q^{11} +(-4.51688 - 3.85588i) q^{12} +(0.896805 - 0.190622i) q^{13} +(0.124725 - 0.138521i) q^{14} +(3.58743 - 1.45958i) q^{15} +(0.601591 + 0.668134i) q^{16} +(-2.65368 - 1.92801i) q^{17} +(-4.94504 - 4.94022i) q^{18} +(-2.09128 - 1.51940i) q^{19} +(-7.41859 + 1.93593i) q^{20} +(0.100487 - 0.0954055i) q^{21} +(-0.255213 - 0.113628i) q^{22} +(4.80528 - 5.33681i) q^{23} +(3.51130 + 4.57371i) q^{24} +(1.10340 - 4.87673i) q^{25} -2.13622 q^{26} +(-3.37752 - 3.94872i) q^{27} +(-0.221916 + 0.161231i) q^{28} +(-0.650369 - 6.18784i) q^{29} +(-8.88303 + 1.58862i) q^{30} +(0.644990 - 6.13667i) q^{31} +(2.28167 + 3.95197i) q^{32} +(-0.182531 - 0.0990488i) q^{33} +(5.11392 + 5.67959i) q^{34} +(-0.0268284 - 0.176862i) q^{35} +(5.60657 + 8.62417i) q^{36} +(-3.64504 + 11.2183i) q^{37} +(4.03010 + 4.47588i) q^{38} +(-1.58315 - 0.124209i) q^{39} +(7.43621 - 0.340995i) q^{40} +(6.21021 - 1.32002i) q^{41} +(-0.275234 + 0.168756i) q^{42} +(6.13162 - 10.6203i) q^{43} +(0.332599 + 0.241647i) q^{44} +(-6.67558 + 0.660830i) q^{45} +(-13.5368 + 9.83509i) q^{46} +(0.401436 + 3.81941i) q^{47} +(-0.670744 - 1.40536i) q^{48} +(3.49680 + 6.05664i) q^{49} +(-4.87715 + 10.5799i) q^{50} +(3.45969 + 4.50648i) q^{51} +(3.07496 + 0.653604i) q^{52} +(6.52099 - 4.73778i) q^{53} +(5.78469 + 10.6355i) q^{54} +(-0.239674 + 0.120153i) q^{55} +(0.243300 - 0.108324i) q^{56} +(2.72646 + 3.55140i) q^{57} +(-1.51534 + 14.4175i) q^{58} +(-1.33884 + 0.284579i) q^{59} +(13.2727 + 0.431147i) q^{60} +(-9.81061 - 2.08531i) q^{61} +(-4.44276 + 13.6734i) q^{62} +(-0.213788 + 0.109062i) q^{63} +(-3.84127 - 11.8222i) q^{64} +(-1.30057 + 1.58477i) q^{65} +(0.368018 + 0.314162i) q^{66} +(0.885569 - 8.42563i) q^{67} +(-5.62346 - 9.74012i) q^{68} +(-10.6040 + 6.50169i) q^{69} +(-0.0245335 + 0.416076i) q^{70} +(5.54404 - 4.02798i) q^{71} +(-3.58364 - 9.32212i) q^{72} +(1.36759 + 4.20901i) q^{73} +(13.7417 - 23.8014i) q^{74} +(-4.22961 + 7.55714i) q^{75} +(-4.43165 - 7.67584i) q^{76} +(-0.00641831 + 0.00712825i) q^{77} +(3.54792 + 1.05000i) q^{78} +(-0.223694 - 2.12830i) q^{79} +(-1.98352 - 0.327462i) q^{80} +(3.66864 + 8.21834i) q^{81} -14.7929 q^{82} +(2.75244 - 1.22546i) q^{83} +(0.447817 - 0.158703i) q^{84} +(7.32690 - 0.335983i) q^{85} +(-19.1191 + 21.2339i) q^{86} +(-1.96132 + 10.5967i) q^{87} +(-0.267088 - 0.296631i) q^{88} +(-4.33323 - 13.3363i) q^{89} +(15.5342 + 1.72777i) q^{90} +(-0.0226655 + 0.0697572i) q^{91} +(22.4947 - 10.0153i) q^{92} +(-4.08755 + 9.87502i) q^{93} +(0.935338 - 8.89915i) q^{94} +(5.77407 - 0.264776i) q^{95} +(-1.84701 - 7.68510i) q^{96} +(-1.27656 - 12.1456i) q^{97} +(-5.03541 - 15.4974i) q^{98} +(0.254471 + 0.254223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−2.27906	−	0.484430i	−1.61154	−	0.342544i	−0.687901	−	0.725805i	$-0.741468\pi$
$2$	−2.27906	−	0.484430i	−1.61154	−	0.342544i	−0.923640	+	0.383261i	$0.874801\pi$
$3$	−1.66084	−	0.491525i	−0.958889	−	0.283782i
$3$	−1.66084	−	0.491525i	−0.958889	−	0.283782i
$4$	3.13236	+	1.39462i	1.56618	+	0.697309i
$5$	−1.74691	+	1.39582i	−0.781243	+	0.624228i
$5$	−1.74691	+	1.39582i	−0.781243	+	0.624228i
$6$	3.54706	+	1.92478i	1.44808	+	0.785787i
$7$	−0.0399999	+	0.0692819i	−0.0151185	+	0.0261861i	−0.873486	−	0.486850i	$-0.838146\pi$
$7$	−0.0399999	+	0.0692819i	−0.0151185	+	0.0261861i	0.858367	+	0.513036i	$0.171479\pi$
$8$	−2.69327	−	1.95678i	−0.952216	−	0.691826i
$9$	2.51681	+	1.63269i	0.838936	+	0.544231i
$10$	4.65750	−	2.33489i	1.47283	−	0.738359i
$11$	0.117280	+	0.0249287i	0.0353613	+	0.00751628i	0.225558	−	0.974230i	$-0.427579\pi$
$11$	0.117280	+	0.0249287i	0.0353613	+	0.00751628i	−0.190197	+	0.981746i	$0.560913\pi$
$12$	−4.51688	−	3.85588i	−1.30391	−	1.11310i
$13$	0.896805	−	0.190622i	0.248729	−	0.0528690i	−0.0818599	−	0.996644i	$-0.526086\pi$
$13$	0.896805	−	0.190622i	0.248729	−	0.0528690i	0.330589	+	0.943775i	$0.392753\pi$
$14$	0.124725	−	0.138521i	0.0333340	−	0.0370212i
$15$	3.58743	−	1.45958i	0.926269	−	0.376862i
$16$	0.601591	+	0.668134i	0.150398	+	0.167034i
$17$	−2.65368	−	1.92801i	−0.643613	−	0.467612i	0.217477	−	0.976066i	$-0.430217\pi$
$17$	−2.65368	−	1.92801i	−0.643613	−	0.467612i	−0.861090	+	0.508453i	$0.830217\pi$
$18$	−4.94504	−	4.94022i	−1.16556	−	1.16442i
$19$	−2.09128	−	1.51940i	−0.479771	−	0.348574i	0.321466	−	0.946921i	$-0.395824\pi$
$19$	−2.09128	−	1.51940i	−0.479771	−	0.348574i	−0.801237	+	0.598347i	$0.795824\pi$
$20$	−7.41859	+	1.93593i	−1.65885	+	0.432886i
$21$	0.100487	−	0.0954055i	0.0219281	−	0.0208192i
$22$	−0.255213	−	0.113628i	−0.0544116	−	0.0242256i
$23$	4.80528	−	5.33681i	1.00197	−	1.11280i	0.00835697	−	0.999965i	$-0.497340\pi$
$23$	4.80528	−	5.33681i	1.00197	−	1.11280i	0.993614	−	0.112836i	$-0.0359935\pi$
$24$	3.51130	+	4.57371i	0.716742	+	0.933606i
$25$	1.10340	−	4.87673i	0.220680	−	0.975346i
$26$	−2.13622			−0.418947
$27$	−3.37752	−	3.94872i	−0.650003	−	0.759931i
$28$	−0.221916	+	0.161231i	−0.0419382	+	0.0304699i
$29$	−0.650369	−	6.18784i	−0.120770	−	1.14905i	−0.872169	−	0.489205i	$-0.837287\pi$
$29$	−0.650369	−	6.18784i	−0.120770	−	1.14905i	0.751398	−	0.659849i	$-0.229380\pi$
$30$	−8.88303	+	1.58862i	−1.62181	+	0.290042i
$31$	0.644990	−	6.13667i	0.115844	−	1.10218i	−0.769952	−	0.638102i	$-0.779720\pi$
$31$	0.644990	−	6.13667i	0.115844	−	1.10218i	0.885795	−	0.464076i	$-0.153614\pi$
$32$	2.28167	+	3.95197i	0.403346	+	0.698616i
$33$	−0.182531	−	0.0990488i	−0.0317746	−	0.0172422i
$34$	5.11392	+	5.67959i	0.877031	+	0.974041i
$35$	−0.0268284	−	0.176862i	−0.00453483	−	0.0298951i
$36$	5.60657	+	8.62417i	0.934429	+	1.43736i
$37$	−3.64504	+	11.2183i	−0.599241	+	1.84427i	−0.0668736	+	0.997761i	$0.521302\pi$
$37$	−3.64504	+	11.2183i	−0.599241	+	1.84427i	−0.532368	+	0.846513i	$0.678698\pi$
$38$	4.03010	+	4.47588i	0.653769	+	0.726084i
$39$	−1.58315	−	0.124209i	−0.253507	−	0.0198893i
$40$	7.43621	−	0.340995i	1.17577	−	0.0539161i
$41$	6.21021	−	1.32002i	0.969872	−	0.206153i	0.304374	−	0.952552i	$-0.401553\pi$
$41$	6.21021	−	1.32002i	0.969872	−	0.206153i	0.665498	+	0.746400i	$0.268219\pi$
$42$	−0.275234	+	0.168756i	−0.0424696	+	0.0260396i
$43$	6.13162	−	10.6203i	0.935064	−	1.61958i	0.160543	−	0.987029i	$-0.448675\pi$
$43$	6.13162	−	10.6203i	0.935064	−	1.61958i	0.774520	−	0.632549i	$-0.217991\pi$
$44$	0.332599	+	0.241647i	0.0501411	+	0.0364297i
$45$	−6.67558	+	0.660830i	−0.995136	+	0.0985108i
$46$	−13.5368	+	9.83509i	−1.99590	+	1.45011i
$47$	0.401436	+	3.81941i	0.0585555	+	0.557118i	0.983992	+	0.178215i	$0.0570322\pi$
$47$	0.401436	+	3.81941i	0.0585555	+	0.557118i	−0.925436	+	0.378904i	$0.876301\pi$
$48$	−0.670744	−	1.40536i	−0.0968136	−	0.202847i
$49$	3.49680	+	6.05664i	0.499543	+	0.865234i
$50$	−4.87715	+	10.5799i	−0.689733	+	1.49622i
$51$	3.45969	+	4.50648i	0.484453	+	0.631034i
$52$	3.07496	+	0.653604i	0.426421	+	0.0906385i
$53$	6.52099	−	4.73778i	0.895727	−	0.650784i	−0.0416378	−	0.999133i	$-0.513258\pi$
$53$	6.52099	−	4.73778i	0.895727	−	0.650784i	0.937365	+	0.348349i	$0.113258\pi$
$54$	5.78469	+	10.6355i	0.787197	+	1.44731i
$55$	−0.239674	+	0.120153i	−0.0323177	+	0.0162015i
$56$	0.243300	−	0.108324i	0.0325123	−	0.0144754i
$57$	2.72646	+	3.55140i	0.361128	+	0.470394i
$58$	−1.51534	+	14.4175i	−0.198975	+	1.89312i
$59$	−1.33884	+	0.284579i	−0.174302	+	0.0370490i	−0.294236	−	0.955733i	$-0.595065\pi$
$59$	−1.33884	+	0.284579i	−0.174302	+	0.0370490i	0.119934	+	0.992782i	$0.461732\pi$
$60$	13.2727	+	0.431147i	1.71350	+	0.0556609i
$61$	−9.81061	−	2.08531i	−1.25612	−	0.266996i	−0.468669	−	0.883374i	$-0.655266\pi$
$61$	−9.81061	−	2.08531i	−1.25612	−	0.266996i	−0.787451	+	0.616378i	$0.788599\pi$
$62$	−4.44276	+	13.6734i	−0.564231	+	1.73652i
$63$	−0.213788	+	0.109062i	−0.0269348	+	0.0137405i
$64$	−3.84127	−	11.8222i	−0.480159	−	1.47778i
$65$	−1.30057	+	1.58477i	−0.161315	+	0.196567i
$66$	0.368018	+	0.314162i	0.0452999	+	0.0386707i
$67$	0.885569	−	8.42563i	0.108190	−	1.02935i	−0.796894	−	0.604120i	$-0.793525\pi$
$67$	0.885569	−	8.42563i	0.108190	−	1.02935i	0.905083	−	0.425235i	$-0.139808\pi$
$68$	−5.62346	−	9.74012i	−0.681945	−	1.18116i
$69$	−10.6040	+	6.50169i	−1.27657	+	0.782711i
$70$	−0.0245335	+	0.416076i	−0.00293231	+	0.0497305i
$71$	5.54404	−	4.02798i	0.657957	−	0.478034i	−0.208016	−	0.978126i	$-0.566700\pi$
$71$	5.54404	−	4.02798i	0.657957	−	0.478034i	0.865972	+	0.500092i	$0.166700\pi$
$72$	−3.58364	−	9.32212i	−0.422336	−	1.09862i
$73$	1.36759	+	4.20901i	0.160064	+	0.492627i	0.998639	−	0.0521600i	$-0.0166106\pi$
$73$	1.36759	+	4.20901i	0.160064	+	0.492627i	−0.838575	+	0.544787i	$0.816611\pi$
$74$	13.7417	−	23.8014i	1.59745	−	2.76686i
$75$	−4.22961	+	7.55714i	−0.488393	+	0.872624i
$76$	−4.43165	−	7.67584i	−0.508345	−	0.880480i
$77$	−0.00641831	+	0.00712825i	−0.000731434	+	0.000812340i
$78$	3.54792	+	1.05000i	0.401723	+	0.118889i
$79$	−0.223694	−	2.12830i	−0.0251675	−	0.239453i	−0.999873	−	0.0159582i	$-0.994920\pi$
$79$	−0.223694	−	2.12830i	−0.0251675	−	0.239453i	0.974705	−	0.223495i	$-0.0717465\pi$
$80$	−1.98352	−	0.327462i	−0.221764	−	0.0366113i
$81$	3.66864	+	8.21834i	0.407626	+	0.913149i
$82$	−14.7929			−1.63360
$83$	2.75244	−	1.22546i	0.302119	−	0.134512i	−0.250078	−	0.968226i	$-0.580456\pi$
$83$	2.75244	−	1.22546i	0.302119	−	0.134512i	0.552197	+	0.833714i	$0.313790\pi$
$84$	0.447817	−	0.158703i	0.0488609	−	0.0173159i
$85$	7.32690	−	0.335983i	0.794714	−	0.0364424i
$86$	−19.1191	+	21.2339i	−2.06167	+	2.28972i
$87$	−1.96132	+	10.5967i	−0.210275	+	1.13609i
$88$	−0.267088	−	0.296631i	−0.0284717	−	0.0316210i
$89$	−4.33323	−	13.3363i	−0.459321	−	1.41364i	−0.865986	−	0.500068i	$-0.833308\pi$
$89$	−4.33323	−	13.3363i	−0.459321	−	1.41364i	0.406665	−	0.913577i	$-0.366692\pi$
$90$	15.5342	+	1.72777i	1.63745	+	0.182123i
$91$	−0.0226655	+	0.0697572i	−0.00237599	+	0.00731254i
$92$	22.4947	−	10.0153i	2.34523	−	1.04417i
$93$	−4.08755	+	9.87502i	−0.423859	+	1.02399i
$94$	0.935338	−	8.89915i	0.0964728	−	0.917877i
$95$	5.77407	−	0.264776i	0.592408	−	0.0271655i
$96$	−1.84701	−	7.68510i	−0.188510	−	0.784358i
$97$	−1.27656	−	12.1456i	−0.129615	−	1.23320i	−0.845114	−	0.534586i	$-0.820467\pi$
$97$	−1.27656	−	12.1456i	−0.129615	−	1.23320i	0.715499	−	0.698613i	$-0.246199\pi$
$98$	−5.03541	−	15.4974i	−0.508653	−	1.56547i
$99$	0.254471	+	0.254223i	0.0255753	+	0.0255504i
$100$	10.2574	−	13.7369i	1.02574	−	1.37369i
$101$	−3.17409	+	5.49768i	−0.315833	+	0.547039i	−0.979614	−	0.200888i	$-0.935617\pi$
$101$	−3.17409	+	5.49768i	−0.315833	+	0.547039i	0.663781	+	0.747927i	$0.268951\pi$
$102$	−5.70177	−	11.9465i	−0.564560	−	1.18288i
$103$	6.49051	+	2.88976i	0.639529	+	0.284737i	0.700771	−	0.713386i	$-0.252839\pi$
$103$	6.49051	+	2.88976i	0.639529	+	0.284737i	−0.0612421	+	0.998123i	$0.519506\pi$
$104$	−2.78835	−	1.24145i	−0.273420	−	0.121734i
$105$	−0.0423741	+	0.306927i	−0.00413529	+	0.0299530i
$106$	−17.1569	+	7.63873i	−1.66642	+	0.741939i
$107$	−7.25662			−0.701524			−0.350762	−	0.936465i	$-0.614077\pi$
$107$	−7.25662			−0.701524			−0.350762	+	0.936465i	$0.614077\pi$
$108$	−5.07265	−	17.0792i	−0.488116	−	1.64344i
$109$	0.254477	−	0.783199i	0.0243744	−	0.0750168i	−0.938129	−	0.346285i	$-0.887443\pi$
$109$	0.254477	−	0.783199i	0.0243744	−	0.0750168i	0.962504	+	0.271268i	$0.0874430\pi$
$110$	0.604438	−	0.157732i	0.0576309	−	0.0150391i
$111$	11.5679	−	16.8402i	1.09798	−	1.59840i
$112$	−0.0703532	+	0.0149540i	−0.00664775	+	0.00141302i
$113$	−11.5629	+	2.45777i	−1.08775	+	0.231207i	−0.716682	−	0.697400i	$-0.754340\pi$
$113$	−11.5629	+	2.45777i	−1.08775	+	0.231207i	−0.371063	+	0.928607i	$0.621007\pi$
$114$	−4.49337	−	9.41464i	−0.420842	−	0.881762i
$115$	−0.945206	+	16.0302i	−0.0881409	+	1.49483i
$116$	6.59249	−	20.2896i	0.612097	−	1.88384i
$117$	2.56831	+	0.984448i	0.237440	+	0.0910122i
$118$	3.18916			0.293586
$119$	0.239724	−	0.106732i	0.0219754	−	0.00978409i
$120$	−12.5180	−	3.08874i	−1.14273	−	0.281962i
$121$	−10.0359	−	4.46826i	−0.912352	−	0.406205i
$122$	21.3488	+	9.50510i	1.93283	+	0.860551i
$123$	−10.9630	−	0.860122i	−0.988502	−	0.0775546i
$124$	10.5787	−	18.3228i	0.949991	−	1.64543i
$125$	4.87948	+	10.0594i	0.436434	+	0.899736i
$126$	0.540069	−	0.144993i	0.0481132	−	0.0129170i
$127$	−1.06234	−	3.26956i	−0.0942677	−	0.290126i	0.892794	−	0.450464i	$-0.148742\pi$
$127$	−1.06234	−	3.26956i	−0.0942677	−	0.290126i	−0.987062	+	0.160338i	$0.948742\pi$
$128$	2.07347	+	19.7277i	0.183270	+	1.74370i
$129$	−15.4038	+	14.6248i	−1.35623	+	1.28764i
$130$	3.73178	−	2.98176i	0.327299	−	0.261518i
$131$	−0.663522	+	6.31299i	−0.0579722	+	0.551569i	0.926533	+	0.376213i	$0.122774\pi$
$131$	−0.663522	+	6.31299i	−0.0579722	+	0.551569i	−0.984505	+	0.175355i	$0.943893\pi$
$132$	−0.433619	−	0.564818i	−0.0377417	−	0.0491611i
$133$	0.188918	−	0.0841116i	0.0163812	−	0.00729340i
$134$	−6.09989	+	18.7735i	−0.526951	+	1.62179i
$135$	11.4119	+	2.18367i	0.982180	+	0.187941i
$136$	3.37440	+	10.3853i	0.289353	+	0.890536i
$137$	8.09601	+	8.99153i	0.691689	+	0.768199i	0.982030	−	0.188725i	$-0.0604354\pi$
$137$	8.09601	+	8.99153i	0.691689	+	0.768199i	−0.290341	+	0.956923i	$0.593769\pi$
$138$	27.3168	−	9.68087i	2.32536	−	0.824090i
$139$	−7.40708	+	8.22640i	−0.628261	+	0.697754i	−0.970293	−	0.241934i	$-0.922218\pi$
$139$	−7.40708	+	8.22640i	−0.628261	+	0.697754i	0.342032	+	0.939688i	$0.388885\pi$
$140$	0.162618	−	0.591411i	0.0137438	−	0.0499833i
$141$	1.21061	−	6.54076i	0.101952	−	0.550832i
$142$	−14.5865	+	6.49433i	−1.22407	+	0.544992i
$143$	0.109929			0.00919277
$144$	0.423231	+	2.66378i	0.0352692	+	0.221982i
$145$	9.77322	+	9.90182i	0.811622	+	0.822301i
$146$	−1.07785	−	10.2551i	−0.0892038	−	0.848717i
$147$	−2.83065	−	11.7779i	−0.233468	−	0.971424i
$148$	−27.0628	+	30.0563i	−2.22455	+	2.47061i
$149$	2.97995	+	5.16142i	0.244127	+	0.422840i	0.961886	−	0.273452i	$-0.0881653\pi$
$149$	2.97995	+	5.16142i	0.244127	+	0.422840i	−0.717759	+	0.696292i	$0.754832\pi$
$150$	13.3004	−	15.1743i	1.08598	−	1.23897i
$151$	10.4787	−	18.1497i	0.852746	−	1.47700i	−0.0259746	−	0.999663i	$-0.508269\pi$
$151$	10.4787	−	18.1497i	0.852746	−	1.47700i	0.878721	−	0.477337i	$-0.158398\pi$
$152$	2.65925	+	8.18432i	0.215693	+	0.663836i
$153$	−3.53096	−	9.18509i	−0.285461	−	0.742570i
$154$	0.0180809	−	0.0131365i	0.00145700	−	0.00105857i
$155$	7.43892	+	11.6205i	0.597508	+	0.933381i
$156$	−4.78577	−	2.59695i	−0.383169	−	0.207923i
$157$	0.0806568	+	0.139702i	0.00643711	+	0.0111494i	0.869226	−	0.494415i	$-0.164618\pi$
$157$	0.0806568	+	0.139702i	0.00643711	+	0.0111494i	−0.862789	+	0.505564i	$0.831284\pi$
$158$	−0.521201	+	4.95890i	−0.0414646	+	0.394509i
$159$	−13.1591	+	4.66348i	−1.04358	+	0.369838i
$160$	−9.50210	−	3.71895i	−0.751207	−	0.294009i
$161$	0.177533	+	0.546391i	0.0139916	+	0.0430616i
$162$	−4.37984	−	20.5073i	−0.344113	−	1.61121i
$163$	−1.94428	+	5.98388i	−0.152288	+	0.468693i	−0.997876	−	0.0651422i	$-0.979250\pi$
$163$	−1.94428	+	5.98388i	−0.152288	+	0.468693i	0.845588	+	0.533836i	$0.179250\pi$
$164$	21.2936	+	4.52609i	1.66275	+	0.353428i
$165$	0.457120	−	0.0817504i	0.0355867	−	0.00636426i
$166$	−6.86663	+	1.45955i	−0.532954	+	0.113283i
$167$	1.65522	−	15.7484i	0.128085	−	1.21865i	−0.721960	−	0.691935i	$-0.756758\pi$
$167$	1.65522	−	15.7484i	0.128085	−	1.21865i	0.850044	−	0.526711i	$-0.176575\pi$
$168$	−0.457327	+	0.0603216i	−0.0352836	+	0.00465391i
$169$	−11.1082	+	4.94568i	−0.854475	+	0.380437i
$170$	−16.8612	−	2.78364i	−1.29320	−	0.213496i
$171$	−2.78262	−	7.23844i	−0.212793	−	0.553538i
$172$	34.0177	−	24.7153i	2.59383	−	1.88452i
$173$	−19.6306	−	4.17261i	−1.49248	−	0.317237i	−0.611827	−	0.790991i	$-0.709565\pi$
$173$	−19.6306	−	4.17261i	−1.49248	−	0.317237i	−0.880657	+	0.473754i	$0.842899\pi$
$174$	9.60333	−	23.2005i	0.728026	−	1.75882i
$175$	0.293733	+	0.271514i	0.0222041	+	0.0205246i
$176$	0.0538990	+	0.0933559i	0.00406279	+	0.00703697i
$177$	2.36348	+	0.185431i	0.177650	+	0.0139378i
$178$	3.41519	+	32.4934i	0.255980	+	2.43548i
$179$	5.67257	−	4.12136i	0.423987	−	0.308045i	−0.355253	−	0.934770i	$-0.615605\pi$
$179$	5.67257	−	4.12136i	0.423987	−	0.308045i	0.779240	+	0.626725i	$0.215605\pi$
$180$	−21.8319	−	7.23992i	−1.62726	−	0.539632i
$181$	15.8020	+	11.4808i	1.17455	+	0.853362i	0.991547	−	0.129750i	$-0.0414173\pi$
$181$	15.8020	+	11.4808i	1.17455	+	0.853362i	0.183006	+	0.983112i	$0.441417\pi$
$182$	0.0854485	−	0.148001i	0.00633386	−	0.0109706i
$183$	15.2689	+	8.28553i	1.12871	+	0.612484i
$184$	−23.3849	+	4.97061i	−1.72396	+	0.366438i
$185$	−9.29109	−	24.6852i	−0.683094	−	1.81489i
$186$	14.0995	−	20.5257i	1.03383	−	1.50501i
$187$	−0.263162	−	0.292271i	−0.0192443	−	0.0213730i
$188$	−4.06918	+	12.5236i	−0.296775	+	0.913380i
$189$	0.408675	−	0.0760523i	0.0297267	−	0.00553199i
$190$	−13.2877	−	2.19369i	−0.963994	−	0.159147i
$191$	8.37417	+	9.30046i	0.605934	+	0.672958i	0.965573	−	0.260134i	$-0.0837667\pi$
$191$	8.37417	+	9.30046i	0.605934	+	0.672958i	−0.359639	+	0.933092i	$0.617100\pi$
$192$	0.568842	+	21.5229i	0.0410527	+	1.55328i
$193$	2.25962	+	3.91377i	0.162651	+	0.281720i	0.935819	−	0.352482i	$-0.114662\pi$
$193$	2.25962	+	3.91377i	0.162651	+	0.281720i	−0.773168	+	0.634202i	$0.781329\pi$
$194$	−2.97435	+	28.2990i	−0.213546	+	2.03175i
$195$	2.93899	−	1.99280i	0.210466	−	0.142707i
$196$	2.50656	+	23.8483i	0.179040	+	1.70345i
$197$	−5.64856	+	4.10392i	−0.402444	+	0.292392i	−0.770536	−	0.637397i	$-0.780011\pi$
$197$	−5.64856	+	4.10392i	−0.402444	+	0.292392i	0.368092	+	0.929789i	$0.380011\pi$
$198$	−0.456802	−	0.702664i	−0.0324635	−	0.0499362i
$199$	5.63769			0.399646			0.199823	−	0.979832i	$-0.435963\pi$
$199$	5.63769			0.399646			0.199823	+	0.979832i	$0.435963\pi$
$200$	−12.5144	+	10.9753i	−0.884904	+	0.776069i
$201$	−5.61220	+	13.5584i	−0.395854	+	0.956334i
$202$	9.89718	−	10.9919i	0.696363	−	0.773390i
$203$	0.454720	+	0.202454i	0.0319151	+	0.0142095i
$204$	4.55218	+	18.9409i	0.318717	+	1.32613i
$205$	−9.00618	+	10.9743i	−0.629019	+	0.766476i
$206$	−13.3924	−	9.73014i	−0.933092	−	0.677931i
$207$	20.8073	−	5.58617i	1.44621	−	0.388266i
$208$	0.666871	+	0.484510i	0.0462392	+	0.0335947i
$209$	−0.207389	−	0.230328i	−0.0143454	−	0.0159322i
$210$	0.245258	−	0.678978i	0.0169244	−	0.0468539i
$211$	6.14696	−	6.82689i	0.423174	−	0.469982i	−0.493426	−	0.869788i	$-0.664256\pi$
$211$	6.14696	−	6.82689i	0.423174	−	0.469982i	0.916600	+	0.399805i	$0.130922\pi$
$212$	27.0335	−	5.74615i	1.85667	−	0.394647i
$213$	−11.1876	+	3.96482i	−0.766565	+	0.271665i
$214$	16.5383	+	3.51532i	1.13053	+	0.240303i
$215$	4.11255	+	27.1113i	0.280474	+	1.84898i
$216$	1.36981	+	17.2440i	0.0932038	+	1.17331i
$217$	0.399360	+	0.290152i	0.0271103	+	0.0196968i
$218$	−0.959373	+	1.66168i	−0.0649769	+	0.112543i
$219$	−0.202522	−	7.66271i	−0.0136852	−	0.517798i
$220$	−0.918315	+	0.0421103i	−0.0619128	+	0.00283907i
$221$	−2.74736	−	1.22320i	−0.184807	−	0.0822815i
$222$	−34.5219	+	32.7760i	−2.31696	+	2.19978i
$223$	16.1144	+	3.42522i	1.07910	+	0.229370i	0.712970	−	0.701194i	$-0.247349\pi$
$223$	16.1144	+	3.42522i	1.07910	+	0.229370i	0.366129	+	0.930564i	$0.380683\pi$
$224$	−0.365067			−0.0243920
$225$	10.7392	−	10.4723i	0.715949	−	0.698152i
$226$	27.5432			1.83214
$227$	−22.4446	−	4.77074i	−1.48970	−	0.316645i	−0.610085	−	0.792336i	$-0.708865\pi$
$227$	−22.4446	−	4.77074i	−1.48970	−	0.316645i	−0.879612	+	0.475691i	$0.842198\pi$
$228$	3.58742	+	14.9266i	0.237582	+	0.988541i
$229$	13.1563	+	5.85755i	0.869391	+	0.387078i	0.792435	−	0.609957i	$-0.208813\pi$
$229$	13.1563	+	5.85755i	0.869391	+	0.387078i	0.0769564	+	0.997034i	$0.475480\pi$
$230$	9.91970	−	36.0760i	0.654085	−	2.37878i
$231$	0.0141635	−	0.00868416i	0.000931891	−	0.000571376i
$232$	−10.3566	+	17.9382i	−0.679945	+	1.17770i
$233$	4.93126	+	3.58277i	0.323058	+	0.234715i	0.737479	−	0.675370i	$-0.236016\pi$
$233$	4.93126	+	3.58277i	0.323058	+	0.234715i	−0.414421	+	0.910085i	$0.636016\pi$
$234$	−5.37645	−	3.48778i	−0.351469	−	0.228004i
$235$	−6.03247	−	6.11184i	−0.393515	−	0.398693i
$236$	−4.59061	−	0.975765i	−0.298823	−	0.0635169i
$237$	−0.674593	+	3.64473i	−0.0438195	+	0.236751i
$238$	−0.598049	+	0.127119i	−0.0387658	+	0.00823992i
$239$	−3.49373	+	3.88018i	−0.225990	+	0.250988i	−0.845467	−	0.534027i	$-0.820678\pi$
$239$	−3.49373	+	3.88018i	−0.225990	+	0.250988i	0.619477	+	0.785015i	$0.287345\pi$
$240$	3.13336	+	1.51881i	0.202258	+	0.0980388i
$241$	2.95328	+	3.27995i	0.190237	+	0.211280i	0.830717	−	0.556695i	$-0.187931\pi$
$241$	2.95328	+	3.27995i	0.190237	+	0.211280i	−0.640479	+	0.767975i	$0.721264\pi$
$242$	20.7078	+	15.0451i	1.33115	+	0.967136i
$243$	−2.05352	−	15.4526i	−0.131733	−	0.991285i
$244$	−27.8222	−	20.2140i	−1.78113	−	1.29407i
$245$	−14.5625	−	5.69952i	−0.930367	−	0.364129i
$246$	24.5687	+	7.27108i	1.56645	+	0.463587i
$247$	−2.16510	−	0.963963i	−0.137762	−	0.0613355i
$248$	−13.7452	+	15.2656i	−0.872823	+	0.969368i
$249$	−5.17371	+	0.682414i	−0.327871	+	0.0432462i
$250$	−6.24758	−	25.2897i	−0.395132	−	1.59946i
$251$	−21.8640			−1.38004			−0.690021	−	0.723790i	$-0.742399\pi$
$251$	−21.8640			−1.38004			−0.690021	+	0.723790i	$0.742399\pi$
$252$	−0.821761	+	0.0434680i	−0.0517661	+	0.00273822i
$253$	0.696605	−	0.506113i	0.0437952	−	0.0318190i
$254$	0.837276	+	7.96615i	0.0525354	+	0.499841i
$255$	−12.3340	−	3.04334i	−0.772384	−	0.190581i
$256$	2.23242	−	21.2401i	0.139527	−	1.32751i
$257$	−8.09823	−	14.0265i	−0.505154	−	0.874952i	−0.999982	−	0.00596115i	$-0.998102\pi$
$257$	−8.09823	−	14.0265i	−0.505154	−	0.874952i	0.494829	−	0.868991i	$-0.335231\pi$
$258$	42.1909	−	25.8688i	2.62669	−	1.61052i
$259$	−0.631423	−	0.701266i	−0.0392347	−	0.0435745i
$260$	−6.28400	+	3.15029i	−0.389717	+	0.195373i
$261$	8.46599	−	16.6355i	0.524032	−	1.02971i
$262$	4.57041	−	14.0663i	0.282361	−	0.869017i
$263$	−17.9584	−	19.9449i	−1.10736	−	1.22985i	−0.970971	−	0.239199i	$-0.923115\pi$
$263$	−17.9584	−	19.9449i	−1.10736	−	1.22985i	−0.136394	−	0.990655i	$-0.543551\pi$
$264$	0.297790	+	0.623939i	0.0183277	+	0.0384008i
$265$	−4.77853	+	17.3786i	−0.293543	+	1.06756i
$266$	−0.471301	+	0.100178i	−0.0288973	+	0.00614232i
$267$	0.641695	+	24.2794i	0.0392711	+	1.48588i
$268$	14.5245	−	25.1571i	0.887223	−	1.53671i
$269$	−0.482020	−	0.350208i	−0.0293893	−	0.0213525i	0.572994	−	0.819560i	$-0.305782\pi$
$269$	−0.482020	−	0.350208i	−0.0293893	−	0.0213525i	−0.602383	+	0.798207i	$0.705782\pi$
$270$	−24.9506	−	10.5050i	−1.51845	−	0.639314i
$271$	−13.5684	+	9.85799i	−0.824219	+	0.598830i	−0.917918	−	0.396771i	$-0.870131\pi$
$271$	−13.5684	+	9.85799i	−0.824219	+	0.598830i	0.0936990	+	0.995601i	$0.470131\pi$
$272$	−0.308260	−	2.93289i	−0.0186910	−	0.177833i
$273$	0.0719312	−	0.104715i	0.00435347	−	0.00633765i
$274$	−14.0956	−	24.4142i	−0.851544	−	1.47492i
$275$	0.250978	−	0.544438i	0.0151345	−	0.0328309i
$276$	−42.2829	+	5.57713i	−2.54513	+	0.335704i
$277$	17.9293	+	3.81098i	1.07726	+	0.228980i	0.712182	−	0.701995i	$-0.247707\pi$
$277$	17.9293	+	3.81098i	1.07726	+	0.228980i	0.365083	+	0.930975i	$0.381041\pi$
$278$	20.8663	−	15.1603i	1.25148	−	0.909252i
$279$	11.6426	−	14.3917i	0.697024	−	0.861611i
$280$	−0.273823	+	0.528835i	−0.0163641	+	0.0316039i
$281$	26.8130	−	11.9379i	1.59953	−	0.712156i	0.603186	−	0.797600i	$-0.293898\pi$
$281$	26.8130	−	11.9379i	1.59953	−	0.712156i	0.996343	+	0.0854442i	$0.0272309\pi$
$282$	−5.92760	+	14.3204i	−0.352983	+	0.852765i
$283$	2.60480	−	24.7830i	0.154839	−	1.47320i	−0.590785	−	0.806829i	$-0.701182\pi$
$283$	2.60480	−	24.7830i	0.154839	−	1.47320i	0.745624	−	0.666367i	$-0.232152\pi$
$284$	22.9835	−	4.88528i	1.36382	−	0.289888i
$285$	−9.71998	−	2.39835i	−0.575762	−	0.142066i
$286$	−0.250536	−	0.0532531i	−0.0148145	−	0.00314892i
$287$	−0.156954	+	0.483056i	−0.00926472	+	0.0285139i
$288$	−0.709823	+	13.6716i	−0.0418267	+	0.805607i
$289$	−1.92849	−	5.93528i	−0.113441	−	0.349134i
$290$	−17.4771	−	27.3013i	−1.02629	−	1.60319i
$291$	−3.84971	+	20.7994i	−0.225674	+	1.21928i
$292$	−1.58617	+	15.0914i	−0.0928236	+	0.883157i
$293$	−12.3483	−	21.3878i	−0.721394	−	1.24949i	−0.960441	−	0.278483i	$-0.910169\pi$
$293$	−12.3483	−	21.3878i	−0.721394	−	1.24949i	0.239048	−	0.971008i	$-0.423165\pi$
$294$	0.745679	+	28.2138i	0.0434889	+	1.64546i
$295$	1.94161	−	2.36591i	0.113045	−	0.137748i
$296$	31.7688	−	23.0814i	1.84652	−	1.34158i
$297$	−0.297680	−	0.547304i	−0.0172731	−	0.0317578i
$298$	−4.29114	−	13.2068i	−0.248579	−	0.765048i
$299$	3.29209	−	5.70207i	0.190386	−	0.329759i
$300$	−23.7880	+	17.7730i	−1.37340	+	1.02613i
$301$	0.490529	+	0.849621i	0.0282736	+	0.0489713i
$302$	−32.6739	+	36.2880i	−1.88017	+	2.08814i
$303$	7.97391	−	7.57065i	0.458089	−	0.434922i
$304$	−0.242929	−	2.31131i	−0.0139329	−	0.132563i
$305$	20.0490	−	10.0509i	1.14800	−	0.575515i
$306$	3.59775	+	22.6439i	0.205669	+	1.29447i
$307$	−2.26067			−0.129023			−0.0645116	−	0.997917i	$-0.520549\pi$
$307$	−2.26067			−0.129023			−0.0645116	+	0.997917i	$0.520549\pi$
$308$	−0.0300457	+	0.0133772i	−0.00171201	+	0.000762236i
$309$	−9.35934	−	7.98969i	−0.532434	−	0.454517i
$310$	−11.3244	−	30.0875i	−0.643185	−	1.70885i
$311$	−0.205373	+	0.228090i	−0.0116456	+	0.0129338i	−0.748940	−	0.662638i	$-0.769437\pi$
$311$	−0.205373	+	0.228090i	−0.0116456	+	0.0129338i	0.737294	+	0.675572i	$0.236103\pi$
$312$	4.02080	+	3.43240i	0.227633	+	0.194321i
$313$	−0.847833	−	0.941614i	−0.0479224	−	0.0532232i	0.718707	−	0.695313i	$-0.244734\pi$
$313$	−0.847833	−	0.941614i	−0.0479224	−	0.0532232i	−0.766629	+	0.642090i	$0.778068\pi$
$314$	−0.116146	−	0.357461i	−0.00655451	−	0.0201727i
$315$	0.221239	−	0.488930i	0.0124654	−	0.0275481i
$316$	2.26748	−	6.97859i	0.127556	−	0.392576i
$317$	−3.94679	+	1.75722i	−0.221674	+	0.0986955i	−0.514569	−	0.857449i	$-0.672048\pi$
$317$	−3.94679	+	1.75722i	−0.221674	+	0.0986955i	0.292895	+	0.956145i	$0.405381\pi$
$318$	32.2495	−	4.25372i	1.80846	−	0.238537i
$319$	0.0779795	−	0.741925i	0.00436601	−	0.0415398i
$320$	23.2120	+	15.2907i	1.29759	+	0.854774i
$321$	12.0521	+	3.56681i	0.672684	+	0.199080i
$322$	−0.139921	−	1.33126i	−0.00779750	−	0.0741883i
$323$	2.62016	+	8.06402i	0.145789	+	0.448694i
$324$	0.0300565	+	30.8592i	0.00166981	+	1.71440i
$325$	0.0599226	−	4.58381i	0.00332391	−	0.254264i
$326$	7.32990	−	12.6958i	0.405966	−	0.703153i
$327$	−0.807608	+	1.17569i	−0.0446608	+	0.0650158i
$328$	−19.3088	−	8.59683i	−1.06615	−	0.474680i
$329$	−0.280673	−	0.124964i	−0.0154740	−	0.00688948i
$330$	−1.08141	−	0.0351282i	−0.0595295	−	0.00193375i
$331$	−16.1914	+	7.20887i	−0.889959	+	0.396235i	−0.800204	−	0.599729i	$-0.795275\pi$
$331$	−16.1914	+	7.20887i	−0.889959	+	0.396235i	−0.0897555	+	0.995964i	$0.528609\pi$
$332$	10.3307			0.566970
$333$	−27.4899	+	22.2830i	−1.50644	+	1.22110i
$334$	−11.4013	+	35.0897i	−0.623853	+	1.92002i
$335$	10.2136	+	15.9549i	0.558029	+	0.871711i
$336$	0.124196	+	0.00974401i	0.00677545	+	0.000531579i
$337$	18.1991	−	3.86833i	0.991366	−	0.210721i	0.316445	−	0.948611i	$-0.397511\pi$
$337$	18.1991	−	3.86833i	0.991366	−	0.210721i	0.674921	+	0.737890i	$0.264178\pi$
$338$	27.7120	−	5.89038i	1.50734	−	0.320394i
$339$	20.4122	+	1.60148i	1.10864	+	0.0869802i
$340$	23.4191	+	9.16581i	1.27008	+	0.497086i
$341$	0.228624	−	0.703632i	0.0123807	−	0.0381038i
$342$	2.83526	+	17.8449i	0.153313	+	0.964939i
$343$	−1.11949			−0.0604465
$344$	−37.2957	+	16.6051i	−2.01085	+	0.895287i
$345$	9.44909	−	26.1591i	0.508722	−	1.40836i
$346$	42.7180	+	19.0193i	2.29653	+	1.02248i
$347$	3.43437	+	1.52908i	0.184366	+	0.0820852i	0.496844	−	0.867840i	$-0.334492\pi$
$347$	3.43437	+	1.52908i	0.184366	+	0.0820852i	−0.312477	+	0.949925i	$0.601159\pi$
$348$	−20.9219	+	30.4575i	−1.12153	+	1.63269i
$349$	−8.67968	+	15.0336i	−0.464613	+	0.804733i	−0.999184	−	0.0403906i	$-0.987140\pi$
$349$	−8.67968	+	15.0336i	−0.464613	+	0.804733i	0.534571	+	0.845123i	$0.320473\pi$
$350$	−0.537907	−	0.761091i	−0.0287523	−	0.0406820i
$351$	−3.78169	−	2.89740i	−0.201851	−	0.154652i
$352$	0.169078	+	0.520367i	0.00901186	+	0.0277357i
$353$	2.36154	+	22.4685i	0.125692	+	1.19588i	0.857542	+	0.514414i	$0.171990\pi$
$353$	2.36154	+	22.4685i	0.125692	+	1.19588i	−0.731850	+	0.681466i	$0.761343\pi$
$354$	−5.29669	−	1.56755i	−0.281516	−	0.0833143i
$355$	−4.06263	+	14.7750i	−0.215622	+	0.784175i
$356$	5.02580	−	47.8173i	0.266367	−	2.53431i
$357$	−0.450605	+	0.0594349i	−0.0238485	+	0.00314563i
$358$	−14.9246	+	6.64488i	−0.788792	+	0.351193i
$359$	4.89466	−	15.0642i	0.258330	−	0.795059i	−0.734825	−	0.678257i	$-0.762736\pi$
$359$	4.89466	−	15.0642i	0.258330	−	0.795059i	0.993155	−	0.116802i	$-0.0372643\pi$
$360$	19.2723	+	11.2828i	1.01574	+	0.594657i
$361$	−3.80647	−	11.7151i	−0.200340	−	0.616585i
$362$	−30.4521	−	33.8204i	−1.60053	−	1.77756i
$363$	14.4718	+	12.3540i	0.759570	+	0.648414i
$364$	−0.168281	+	0.186895i	−0.00882033	+	0.00979597i
$365$	−8.26405	−	5.44386i	−0.432560	−	0.284945i
$366$	−30.7850	−	26.2799i	−1.60916	−	1.37367i
$367$	−17.8242	+	7.93586i	−0.930417	+	0.414248i	−0.815258	−	0.579099i	$-0.803405\pi$
$367$	−17.8242	+	7.93586i	−0.930417	+	0.414248i	−0.115160	+	0.993347i	$0.536738\pi$
$368$	6.45652			0.336569
$369$	17.7851	+	6.81712i	0.925855	+	0.354885i
$370$	9.21675	+	60.7599i	0.479156	+	3.15876i
$371$	0.0674031	+	0.641297i	0.00349939	+	0.0332945i
$372$	−26.5756	+	25.2316i	−1.37788	+	1.30820i
$373$	15.0111	−	16.6715i	0.777243	−	0.863216i	−0.216340	−	0.976318i	$-0.569412\pi$
$373$	15.0111	−	16.6715i	0.777243	−	0.863216i	0.993583	+	0.113102i	$0.0360786\pi$
$374$	0.458178	+	0.793587i	0.0236918	+	0.0410354i
$375$	−3.15963	−	19.1054i	−0.163162	−	0.986599i
$376$	6.39256	−	11.0722i	0.329671	−	0.571008i
$377$	−1.76279	−	5.42531i	−0.0907884	−	0.279418i
$378$	−0.968238	−	0.0246464i	−0.0498008	−	0.00126768i
$379$	−28.9193	+	21.0111i	−1.48548	+	1.07927i	−0.509746	+	0.860325i	$0.670261\pi$
$379$	−28.9193	+	21.0111i	−1.48548	+	1.07927i	−0.975738	+	0.218942i	$0.929739\pi$
$380$	18.4558	+	7.22325i	0.946761	+	0.370545i
$381$	0.157319	+	5.95239i	0.00805971	+	0.304950i
$382$	−14.5798	−	25.2530i	−0.745970	−	1.29206i
$383$	−3.78092	+	35.9730i	−0.193196	+	1.83814i	0.283385	+	0.959006i	$0.408543\pi$
$383$	−3.78092	+	35.9730i	−0.193196	+	1.83814i	−0.476581	+	0.879131i	$0.658124\pi$
$384$	6.25295	−	33.7838i	0.319095	−	1.72402i
$385$	0.00126249	−	0.0214112i	6.43425e−5	−	0.00109122i
$386$	−3.25386	−	10.0144i	−0.165617	−	0.509718i
$387$	32.7718	−	16.7182i	1.66588	−	0.849831i
$388$	12.9399	−	39.8248i	0.656922	−	2.02180i
$389$	18.1432	+	3.85646i	0.919897	+	0.195530i	0.643440	−	0.765496i	$-0.277506\pi$
$389$	18.1432	+	3.85646i	0.919897	+	0.195530i	0.276457	+	0.961026i	$0.410840\pi$
$390$	−7.66352	+	3.11798i	−0.388057	+	0.157885i
$391$	−23.0411	+	4.89755i	−1.16524	+	0.247680i
$392$	2.43365	−	23.1546i	0.122918	−	1.16949i
$393$	4.20500	−	10.1588i	0.212114	−	0.512442i
$394$	14.8615	−	6.61676i	0.748711	−	0.333348i
$395$	3.36149	+	3.40572i	0.169135	+	0.171360i
$396$	0.442551	+	1.15121i	0.0222390	+	0.0578505i
$397$	29.8077	−	21.6566i	1.49601	−	1.08691i	0.524069	−	0.851676i	$-0.324413\pi$
$397$	29.8077	−	21.6566i	1.49601	−	1.08691i	0.971938	−	0.235237i	$-0.0755868\pi$
$398$	−12.8487	−	2.73107i	−0.644045	−	0.136896i
$399$	−0.355106	+	0.0468385i	−0.0177775	+	0.00234486i
$400$	3.92211	−	2.19658i	0.196105	−	0.109829i
$401$	5.69134	+	9.85769i	0.284212	+	0.492270i	0.972418	−	0.233246i	$-0.0749347\pi$
$401$	5.69134	+	9.85769i	0.284212	+	0.492270i	−0.688206	+	0.725516i	$0.741601\pi$
$402$	19.3586	−	28.1817i	0.965521	−	1.40557i
$403$	−0.591353	−	5.62634i	−0.0294574	−	0.280268i
$404$	−17.6096	+	12.7941i	−0.876108	+	0.636530i
$405$	−17.8801	−	9.23597i	−0.888468	−	0.458939i
$406$	−0.938261	−	0.681686i	−0.0465651	−	0.0338315i
$407$	−0.707149	+	1.22482i	−0.0350521	+	0.0607120i
$408$	−0.499705	−	18.9070i	−0.0247391	−	0.936038i
$409$	−5.81648	+	1.23633i	−0.287607	+	0.0611327i	−0.349456	−	0.936953i	$-0.613634\pi$
$409$	−5.81648	+	1.23633i	−0.287607	+	0.0611327i	0.0618493	+	0.998086i	$0.480300\pi$
$410$	25.8419	−	20.6482i	1.27624	−	1.01974i
$411$	−9.02666	−	18.9129i	−0.445252	−	0.932906i
$412$	16.3005	+	18.1036i	0.803069	+	0.891899i
$413$	0.0338373	−	0.104140i	0.00166502	−	0.00512442i
$414$	−50.1273	+	2.65154i	−2.46362	+	0.130316i
$415$	−3.09774	+	5.98267i	−0.152062	+	0.293678i
$416$	2.79954	+	3.10921i	0.137259	+	0.152442i
$417$	16.3455	−	10.0220i	0.800442	−	0.490780i
$418$	0.361074	+	0.625398i	0.0176607	+	0.0305892i
$419$	0.225553	−	2.14600i	0.0110190	−	0.104839i	−0.987630	−	0.156803i	$-0.949881\pi$
$419$	0.225553	−	2.14600i	0.0110190	−	0.104839i	0.998649	+	0.0519638i	$0.0165480\pi$
$420$	−0.560777	+	0.902310i	−0.0273631	+	0.0440282i
$421$	−0.566044	−	5.38555i	−0.0275873	−	0.262476i	−0.999618	−	0.0276234i	$-0.991206\pi$
$421$	−0.566044	−	5.38555i	−0.0275873	−	0.262476i	0.972031	−	0.234852i	$-0.0754606\pi$
$422$	−17.3165	+	12.5811i	−0.842952	+	0.612440i
$423$	−5.22558	+	10.2681i	−0.254077	+	0.499254i
$424$	−26.8336			−1.30315
$425$	−12.3305	+	10.8139i	−0.598116	+	0.524553i
$426$	27.4180	−	3.61644i	1.32841	−	0.175217i
$427$	0.536897	−	0.596285i	0.0259823	−	0.0288563i
$428$	−22.7304	−	10.1202i	−1.09871	−	0.489179i
$429$	−0.182576	−	0.0540331i	−0.00881484	−	0.00260874i
$430$	3.76076	−	63.7806i	0.181360	−	3.07577i
$431$	16.1355	+	11.7231i	0.777218	+	0.564682i	0.904143	−	0.427230i	$-0.140511\pi$
$431$	16.1355	+	11.7231i	0.777218	+	0.564682i	−0.126925	+	0.991912i	$0.540511\pi$
$432$	0.606392	−	4.63215i	0.0291750	−	0.222864i
$433$	−6.10893	−	4.43840i	−0.293577	−	0.213296i	0.431241	−	0.902237i	$-0.358076\pi$
$433$	−6.10893	−	4.43840i	−0.293577	−	0.213296i	−0.724817	+	0.688941i	$0.758076\pi$
$434$	−0.769609	−	0.854737i	−0.0369424	−	0.0410287i
$435$	−11.3648	−	21.2492i	−0.544901	−	1.01882i
$436$	1.88938	−	2.09837i	0.0904847	−	0.100493i
$437$	−18.1579	+	3.85958i	−0.868611	+	0.184629i
$438$	−3.25048	+	17.5619i	−0.155314	+	0.839140i
$439$	17.1715	+	3.64991i	0.819551	+	0.174201i	0.598563	−	0.801076i	$-0.295739\pi$
$439$	17.1715	+	3.64991i	0.819551	+	0.174201i	0.220988	+	0.975277i	$0.429072\pi$
$440$	0.880622	+	0.145383i	0.0419820	+	0.00693087i
$441$	−1.08785	+	20.9526i	−0.0518022	+	0.997742i
$442$	5.66885	+	4.11866i	0.269639	+	0.195905i
$443$	−15.3170	+	26.5299i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$443$	−15.3170	+	26.5299i	−0.727734	+	1.26047i	−0.957839	+	0.287306i	$0.907240\pi$
$444$	59.7205	−	36.6168i	2.83421	−	1.73776i
$445$	26.1848	+	17.2489i	1.24128	+	0.817679i
$446$	−35.0664	−	15.6126i	−1.66044	−	0.739277i
$447$	−2.41226	−	10.0370i	−0.114096	−	0.474735i
$448$	0.972716	+	0.206757i	0.0459565	+	0.00976836i
$449$	−14.3285			−0.676205			−0.338102	−	0.941109i	$-0.609785\pi$
$449$	−14.3285			−0.676205			−0.338102	+	0.941109i	$0.609785\pi$
$450$	−29.5485	+	18.6646i	−1.39293	+	0.879857i
$451$	0.761242			0.0358455
$452$	−39.6468	−	8.42720i	−1.86483	−	0.396382i
$453$	−26.3245	+	24.9932i	−1.23683	+	1.17428i
$454$	48.8415	+	21.7456i	2.29224	+	1.02057i
$455$	−0.0577736	−	0.153496i	−0.00270847	−	0.00719602i
$456$	−0.393800	−	14.9000i	−0.0184414	−	0.697755i
$457$	−2.41930	+	4.19035i	−0.113170	+	0.196017i	−0.917047	−	0.398780i	$-0.869434\pi$
$457$	−2.41930	+	4.19035i	−0.113170	+	0.196017i	0.803877	+	0.594796i	$0.202767\pi$
$458$	−27.1464	−	19.7230i	−1.26847	−	0.921596i
$459$	1.34967	+	16.9906i	0.0629974	+	0.793051i
$460$	−25.3168	+	48.8943i	−1.18040	+	2.27971i
$461$	9.18177	+	1.95165i	0.427638	+	0.0908972i	0.416702	−	0.909043i	$-0.363186\pi$
$461$	9.18177	+	1.95165i	0.427638	+	0.0908972i	0.0109354	+	0.999940i	$0.496519\pi$
$462$	−0.0364864	+	0.0129305i	−0.00169750	+	0.000601582i
$463$	2.35193	−	0.499919i	0.109304	−	0.0232332i	−0.152935	−	0.988236i	$-0.548873\pi$
$463$	2.35193	−	0.499919i	0.109304	−	0.0232332i	0.262239	+	0.965003i	$0.415539\pi$
$464$	3.74306	−	4.15708i	0.173767	−	0.192988i
$465$	−6.64312	−	22.9563i	−0.308067	−	1.06457i
$466$	−9.50306	−	10.5542i	−0.440221	−	0.488915i
$467$	−18.8087	−	13.6654i	−0.870365	−	0.632357i	0.0603199	−	0.998179i	$-0.480788\pi$
$467$	−18.8087	−	13.6654i	−0.870365	−	0.632357i	−0.930685	+	0.365822i	$0.880788\pi$
$468$	6.67196	+	6.66546i	0.308411	+	0.308111i
$469$	0.548321	+	0.398378i	0.0253191	+	0.0183954i
$470$	10.7876	+	16.8516i	0.497595	+	0.777305i
$471$	−0.0652916	−	0.271668i	−0.00300848	−	0.0125178i
$472$	4.16272	+	1.85336i	0.191605	+	0.0853079i
$473$	0.983868	−	1.09270i	0.0452383	−	0.0502422i
$474$	3.30306	−	7.97978i	0.151714	−	0.366523i
$475$	−9.71722	+	8.52208i	−0.445857	+	0.391020i
$476$	0.899752			0.0412400
$477$	24.1474	−	1.27730i	1.10563	−	0.0584837i
$478$	9.84210	−	7.15070i	0.450167	−	0.327065i
$479$	−2.50686	−	23.8511i	−0.114541	−	1.08979i	−0.889235	−	0.457450i	$-0.848763\pi$
$479$	−2.50686	−	23.8511i	−0.114541	−	1.08979i	0.774694	−	0.632336i	$-0.217904\pi$
$480$	13.9535	+	10.8471i	0.636889	+	0.495101i
$481$	−1.13044	+	10.7554i	−0.0515437	+	0.490406i
$482$	−5.14180	−	8.90586i	−0.234203	−	0.405651i
$483$	−0.0262904	−	0.994732i	−0.00119625	−	0.0452619i
$484$	−25.2045	−	27.9924i	−1.14566	−	1.27238i
$485$	19.1831	+	19.4355i	0.871058	+	0.882519i
$486$	−2.80561	+	36.2122i	−0.127265	+	1.64262i
$487$	0.662529	−	2.03906i	0.0300221	−	0.0923984i	−0.934923	−	0.354851i	$-0.884531\pi$
$487$	0.662529	−	2.03906i	0.0300221	−	0.0923984i	0.964945	+	0.262453i	$0.0845315\pi$
$488$	22.3422	+	24.8135i	1.01138	+	1.12325i
$489$	6.17037	−	8.98263i	0.279034	−	0.406208i
$490$	30.4279	+	20.0441i	1.37459	+	0.905500i
$491$	13.2181	−	2.80960i	0.596526	−	0.126796i	0.100253	−	0.994962i	$-0.468035\pi$
$491$	13.2181	−	2.80960i	0.596526	−	0.126796i	0.496273	+	0.868166i	$0.334701\pi$
$492$	−33.1406	−	17.9834i	−1.49409	−	0.810756i
$493$	−10.2044	+	17.6745i	−0.459582	+	0.796020i
$494$	4.46742	+	3.24577i	0.200999	+	0.146034i
$495$	−0.799387	−	0.0889110i	−0.0359298	−	0.00399625i
$496$	4.48814	−	3.26082i	0.201523	−	0.146415i
$497$	0.0573050	+	0.545221i	0.00257048	+	0.0244565i
$498$	12.1218	+	0.951036i	0.543191	+	0.0426170i
$499$	6.61074	+	11.4501i	0.295937	+	0.512579i	0.975203	−	0.221314i	$-0.0710347\pi$
$499$	6.61074	+	11.4501i	0.295937	+	0.512579i	−0.679265	+	0.733893i	$0.737701\pi$
$500$	1.25533	+	38.3146i	0.0561400	+	1.71348i
$501$	−10.4898	+	25.3420i	−0.468649	+	1.13220i
$502$	49.8294	+	10.5916i	2.22399	+	0.472724i
$503$	11.6115	−	8.43628i	0.517733	−	0.376155i	−0.298016	−	0.954561i	$-0.596325\pi$
$503$	11.6115	−	8.43628i	0.517733	−	0.376155i	0.815749	+	0.578406i	$0.196325\pi$
$504$	0.789199	+	0.124603i	0.0351537	+	0.00555026i
$505$	−2.12890	−	14.0344i	−0.0947347	−	0.624522i
$506$	−1.83278	+	0.816007i	−0.0814771	+	0.0362759i
$507$	20.8799	−	2.75406i	0.927307	−	0.122312i
$508$	1.23214	−	11.7230i	0.0546672	−	0.520124i
$509$	14.8920	−	3.16540i	0.660078	−	0.140304i	0.134320	−	0.990938i	$-0.457115\pi$
$509$	14.8920	−	3.16540i	0.660078	−	0.140304i	0.525758	+	0.850634i	$0.323782\pi$
$510$	26.6356	+	12.9109i	1.17945	+	0.571705i
$511$	−0.346311	−	0.0736107i	−0.0153199	−	0.00325635i
$512$	−3.11762	+	9.59504i	−0.137781	+	0.424045i
$513$	1.06363	+	13.3897i	0.0469605	+	0.591168i
$514$	11.6615	+	35.8904i	0.514367	+	1.58306i
$515$	−15.3719	+	4.01140i	−0.677368	+	0.176763i
$516$	−68.6463	+	24.3277i	−3.02198	+	1.07097i
$517$	−0.0481324	+	0.457949i	−0.00211686	+	0.0201406i
$518$	1.09934	+	1.90411i	0.0483021	+	0.0836617i
$519$	30.5524	+	16.5790i	1.34110	+	0.727736i
$520$	6.60383	−	1.72331i	0.289597	−	0.0755721i
$521$	−20.5999	+	14.9667i	−0.902500	+	0.655704i	−0.939107	−	0.343625i	$-0.888345\pi$
$521$	−20.5999	+	14.9667i	−0.902500	+	0.655704i	0.0366072	+	0.999330i	$0.488345\pi$
$522$	−27.3532	+	33.8121i	−1.19722	+	1.47991i
$523$	−12.3971	−	38.1544i	−0.542088	−	1.66838i	−0.727814	−	0.685775i	$-0.759464\pi$
$523$	−12.3971	−	38.1544i	−0.542088	−	1.66838i	0.185726	−	0.982602i	$-0.440536\pi$
$524$	−10.8826	+	18.8492i	−0.475409	+	0.823432i
$525$	−0.354389	−	0.595320i	−0.0154668	−	0.0259819i
$526$	31.2665	+	54.1552i	1.36329	+	2.36128i
$527$	−13.5432	+	15.0412i	−0.589950	+	0.655206i
$528$	−0.0436312	−	0.181542i	−0.00189880	−	0.00790061i
$529$	−2.98661	−	28.4157i	−0.129853	−	1.23547i
$530$	19.3093	−	37.2920i	0.838741	−	1.61986i
$531$	−3.83423	−	1.46968i	−0.166391	−	0.0637787i
$532$	0.709063			0.0307418
$533$	5.31772	−	2.36760i	0.230336	−	0.102552i
$534$	10.2992	−	55.6451i	0.445690	−	2.40800i
$535$	12.6767	−	10.1289i	0.548061	−	0.437911i
$536$	−18.8722	+	20.9597i	−0.815154	+	0.905320i
$537$	−11.4470	+	4.05673i	−0.493974	+	0.175061i
$538$	0.928902	+	1.03165i	0.0400478	+	0.0444776i
$539$	0.259122	+	0.797495i	0.0111612	+	0.0343505i
$540$	32.7008	+	22.7553i	1.40722	+	0.979233i
$541$	8.54221	−	26.2902i	0.367258	−	1.13030i	−0.581297	−	0.813692i	$-0.697454\pi$
$541$	8.54221	−	26.2902i	0.367258	−	1.13030i	0.948555	−	0.316613i	$-0.102546\pi$
$542$	35.6986	−	15.8941i	1.53339	−	0.682708i
$543$	−20.6015	−	26.8349i	−0.884096	−	1.15160i
$544$	1.56462	−	14.8864i	0.0670826	−	0.638248i
$545$	0.648652	+	1.72338i	0.0277852	+	0.0738215i
$546$	−0.214663	+	0.203807i	−0.00918672	+	0.00872213i
$547$	−0.948368	−	9.02311i	−0.0405493	−	0.385801i	−0.995909	−	0.0903569i	$-0.971199\pi$
$547$	−0.948368	−	9.02311i	−0.0405493	−	0.385801i	0.955360	−	0.295444i	$-0.0954674\pi$
$548$	12.8199	+	39.4556i	0.547639	+	1.68546i
$549$	−21.2867	−	21.2660i	−0.908496	−	0.907611i
$550$	−0.835736	+	1.11923i	−0.0356359	+	0.0477240i
$551$	−8.04171	+	13.9287i	−0.342588	+	0.593381i
$552$	41.2818	+	3.23884i	1.75707	+	0.137854i
$553$	0.156401	+	0.0696340i	0.00665083	+	0.00296114i
$554$	−39.0157	−	17.3709i	−1.65762	−	0.738020i
$555$	3.29769	+	45.5650i	0.139979	+	1.93413i
$556$	−34.6744	+	15.4380i	−1.47052	+	0.654718i
$557$	14.0755			0.596397			0.298199	−	0.954504i	$-0.403614\pi$
$557$	14.0755			0.596397			0.298199	+	0.954504i	$0.403614\pi$
$558$	−33.5060	+	27.1597i	−1.41842	+	1.14976i
$559$	3.47441	−	10.6931i	0.146952	−	0.452272i
$560$	0.102028	−	0.124323i	0.00431146	−	0.00525362i
$561$	0.293413	+	0.614767i	0.0123879	+	0.0259555i
$562$	−66.8916	+	14.2182i	−2.82165	+	0.599760i
$563$	32.1147	−	6.82619i	1.35347	−	0.287690i	0.526617	−	0.850103i	$-0.323460\pi$
$563$	32.1147	−	6.82619i	1.35347	−	0.287690i	0.826856	+	0.562413i	$0.190127\pi$
$564$	12.9139	−	18.7997i	0.543775	−	0.791611i
$565$	16.7688	−	20.4332i	0.705467	−	0.859630i
$566$	−17.9421	+	55.2202i	−0.754164	+	2.32108i
$567$	−0.716127	−	0.0745629i	−0.0300745	−	0.00313135i
$568$	−22.8135			−0.957233
$569$	3.74547	−	1.66759i	0.157018	−	0.0699091i	−0.326723	−	0.945120i	$-0.605944\pi$
$569$	3.74547	−	1.66759i	0.157018	−	0.0699091i	0.483741	+	0.875211i	$0.339278\pi$
$570$	20.9906	+	10.1746i	0.879200	+	0.426169i
$571$	−30.4423	−	13.5538i	−1.27397	−	0.567209i	−0.345433	−	0.938443i	$-0.612268\pi$
$571$	−30.4423	−	13.5538i	−1.27397	−	0.567209i	−0.928539	+	0.371235i	$0.878935\pi$
$572$	0.344339	+	0.153310i	0.0143975	+	0.00641020i
$573$	−9.33679	−	19.5627i	−0.390050	−	0.817245i
$574$	0.591715	−	1.02488i	0.0246977	−	0.0427777i
$575$	−20.7240	−	29.3227i	−0.864252	−	1.22284i
$576$	9.63430	−	36.0258i	0.401429	−	1.50108i
$577$	12.2872	+	37.8160i	0.511522	+	1.57430i	0.789523	+	0.613721i	$0.210328\pi$
$577$	12.2872	+	37.8160i	0.511522	+	1.57430i	−0.278001	+	0.960581i	$0.589672\pi$
$578$	1.51992	+	14.4611i	0.0632204	+	0.601502i
$579$	−1.82916	−	7.61083i	−0.0760172	−	0.316295i
$580$	16.8040	+	44.6460i	0.697749	+	1.85382i
$581$	−0.0251948	+	0.239712i	−0.00104526	+	0.00994495i
$582$	18.8496	−	45.5383i	0.781340	−	1.88762i
$583$	0.882890	−	0.393088i	0.0365656	−	0.0162800i
$584$	4.55280	−	14.0121i	0.188396	−	0.579824i
$585$	−5.86072	+	1.86515i	−0.242311	+	0.0771143i
$586$	17.7816	+	54.7261i	0.734550	+	2.26071i
$587$	2.62542	+	2.91582i	0.108363	+	0.120349i	0.794886	−	0.606759i	$-0.207531\pi$
$587$	2.62542	+	2.91582i	0.108363	+	0.120349i	−0.686523	+	0.727108i	$0.740864\pi$
$588$	7.55902	−	40.8403i	0.311729	−	1.68423i
$589$	−10.6729	+	11.8535i	−0.439769	+	0.488413i
$590$	−5.57118	+	4.45148i	−0.229362	+	0.183264i
$591$	11.3986	−	4.03957i	0.468874	−	0.166166i
$592$	−9.68815	+	4.31344i	−0.398180	+	0.177281i
$593$	5.32290			0.218585			0.109293	−	0.994010i	$-0.465141\pi$
$593$	5.32290			0.218585			0.109293	+	0.994010i	$0.465141\pi$
$594$	0.413300	+	1.39155i	0.0169579	+	0.0570958i
$595$	−0.269798	+	0.521061i	−0.0110606	+	0.0213614i
$596$	2.13607	+	20.3233i	0.0874968	+	0.832476i
$597$	−9.36333	−	2.77107i	−0.383216	−	0.113412i
$598$	−10.2651	+	11.4006i	−0.419772	+	0.466204i
$599$	13.4381	+	23.2754i	0.549064	+	0.951007i	0.998339	+	0.0576132i	$0.0183490\pi$
$599$	13.4381	+	23.2754i	0.549064	+	0.951007i	−0.449275	+	0.893394i	$0.648318\pi$
$600$	26.1791	−	12.0771i	1.06876	−	0.493044i
$601$	10.8178	−	18.7369i	0.441266	−	0.764294i	−0.556518	−	0.830835i	$-0.687863\pi$
$601$	10.8178	−	18.7369i	0.441266	−	0.764294i	0.997784	+	0.0665411i	$0.0211963\pi$
$602$	−0.706364	−	2.17397i	−0.0287893	−	0.0886042i
$603$	15.9853	−	19.7598i	0.650970	−	0.804682i
$604$	58.1350	−	42.2376i	2.36548	−	1.71862i
$605$	23.7686	−	6.20257i	0.966332	−	0.252170i
$606$	−21.8405	+	13.3912i	−0.887209	+	0.543979i
$607$	−4.31032	−	7.46569i	−0.174950	−	0.303023i	0.765194	−	0.643800i	$-0.222643\pi$
$607$	−4.31032	−	7.46569i	−0.174950	−	0.303023i	−0.940144	+	0.340777i	$0.889310\pi$
$608$	1.23302	−	11.7314i	0.0500057	−	0.475772i
$609$	−0.655708	−	0.559751i	−0.0265706	−	0.0226823i
$610$	−50.5618	+	13.1944i	−2.04719	+	0.534226i
$611$	1.08807	+	3.34874i	0.0440187	+	0.135476i
$612$	1.74945	−	33.6954i	0.0707171	−	1.36205i
$613$	−14.3490	+	44.1615i	−0.579549	+	1.78367i	0.0405907	+	0.999176i	$0.487076\pi$
$613$	−14.3490	+	44.1615i	−0.579549	+	1.78367i	−0.620139	+	0.784492i	$0.712924\pi$
$614$	5.15221	+	1.09514i	0.207926	+	0.0441961i
$615$	20.3520	−	13.7998i	0.820672	−	0.556461i
$616$	0.0312347	−	0.00663914i	0.00125848	−	0.000267498i
$617$	1.91480	−	18.2181i	0.0770869	−	0.733433i	−0.885899	−	0.463879i	$-0.846457\pi$
$617$	1.91480	−	18.2181i	0.0770869	−	0.733433i	0.962985	−	0.269553i	$-0.0868761\pi$
$618$	17.4601	+	22.7429i	0.702347	+	0.914855i
$619$	−10.5904	+	4.71516i	−0.425665	+	0.189518i	−0.608377	−	0.793648i	$-0.708179\pi$
$619$	−10.5904	+	4.71516i	−0.425665	+	0.189518i	0.182712	+	0.983167i	$0.441513\pi$
$620$	7.09522	+	46.7741i	0.284951	+	1.87849i
$621$	−37.3035	−	0.949558i	−1.49694	−	0.0381044i
$622$	0.578552	−	0.420343i	0.0231978	−	0.0168542i
$623$	1.09729	+	0.233237i	0.0439621	+	0.00934443i
$624$	−0.869420	−	1.13248i	−0.0348046	−	0.0453354i
$625$	−22.5650	−	10.7620i	−0.902601	−	0.430478i
$626$	1.47612	+	2.55671i	0.0589976	+	0.102187i
$627$	0.231228	+	0.484476i	0.00923436	+	0.0193481i
$628$	0.0578159	+	0.550082i	0.00230711	+	0.0219507i
$629$	31.3018	−	22.7421i	1.24808	−	0.906787i
$630$	−0.741069	+	1.00713i	−0.0295249	+	0.0401249i
$631$	−4.86948	−	3.53788i	−0.193851	−	0.140841i	0.486626	−	0.873610i	$-0.338227\pi$
$631$	−4.86948	−	3.53788i	−0.193851	−	0.140841i	−0.680477	+	0.732769i	$0.738227\pi$
$632$	−3.56215	+	6.16982i	−0.141695	+	0.245422i
$633$	−13.5647	+	8.31702i	−0.539149	+	0.330572i
$634$	9.84623	−	2.09288i	0.391044	−	0.0831189i
$635$	6.41951	+	4.22879i	0.254751	+	0.167814i
$636$	−47.7228	−	3.74418i	−1.89233	−	0.148466i
$637$	4.29047	+	4.76505i	0.169995	+	0.188798i
$638$	−0.537131	+	1.65312i	−0.0212652	+	0.0654476i
$639$	20.5297	−	1.08594i	0.812144	−	0.0429593i
$640$	−31.1584	−	31.5684i	−1.23164	−	1.24785i
$641$	−1.23699	−	1.37381i	−0.0488580	−	0.0542623i	0.718220	−	0.695816i	$-0.244957\pi$
$641$	−1.23699	−	1.37381i	−0.0488580	−	0.0542623i	−0.767078	+	0.641553i	$0.778290\pi$
$642$	−25.7397	−	13.9674i	−1.01586	−	0.551249i
$643$	−1.14078	−	1.97588i	−0.0449878	−	0.0779212i	0.842655	−	0.538454i	$-0.180992\pi$
$643$	−1.14078	−	1.97588i	−0.0449878	−	0.0779212i	−0.887643	+	0.460533i	$0.847658\pi$
$644$	−0.205908	+	1.95909i	−0.00811392	+	0.0771988i
$645$	6.49557	−	47.0491i	0.255763	−	1.85256i
$646$	−2.06505	−	19.6477i	−0.0812485	−	0.773028i
$647$	21.2655	−	15.4503i	0.836034	−	0.607414i	−0.0852263	−	0.996362i	$-0.527161\pi$
$647$	21.2655	−	15.4503i	0.836034	−	0.607414i	0.921260	+	0.388948i	$0.127161\pi$
$648$	6.20083	−	29.3130i	0.243591	−	1.15152i
$649$	−0.164114			−0.00644203
$650$	−2.35710	+	10.4178i	−0.0924531	+	0.408618i
$651$	−0.520658	−	0.678193i	−0.0204062	−	0.0265805i
$652$	−14.4354	+	16.0321i	−0.565334	+	0.627867i
$653$	−15.4993	−	6.90073i	−0.606535	−	0.270047i	0.0804036	−	0.996762i	$-0.474379\pi$
$653$	−15.4993	−	6.90073i	−0.606535	−	0.270047i	−0.686938	+	0.726716i	$0.741046\pi$
$654$	2.41013	−	2.28824i	0.0942434	−	0.0894773i
$655$	−7.65266	−	11.9544i	−0.299014	−	0.467097i
$656$	4.61796	+	3.35514i	0.180301	+	0.130996i
$657$	−3.43005	+	12.8261i	−0.133819	+	0.500394i
$658$	0.579136	+	0.420767i	0.0225771	+	0.0164032i
$659$	3.26005	+	3.62065i	0.126993	+	0.141040i	0.803288	−	0.595591i	$-0.203082\pi$
$659$	3.26005	+	3.62065i	0.126993	+	0.141040i	−0.676295	+	0.736631i	$0.736415\pi$
$660$	1.54588	+	0.381436i	0.0601731	+	0.0148474i
$661$	−3.50644	+	3.89429i	−0.136385	+	0.151470i	−0.807468	−	0.589911i	$-0.799163\pi$
$661$	−3.50644	+	3.89429i	−0.136385	+	0.151470i	0.671083	+	0.741382i	$0.265829\pi$
$662$	40.3934	−	8.58588i	1.56993	−	0.333700i
$663$	3.96170	+	3.38194i	0.153860	+	0.131344i
$664$	−9.81103	−	2.08540i	−0.380742	−	0.0809291i
$665$	−0.212618	+	0.410630i	−0.00824498	+	0.0159235i
$666$	73.4457	−	37.4675i	2.84596	−	1.45184i
$667$	−36.1485	−	26.2634i	−1.39968	−	1.01692i
$668$	27.1477	−	47.0212i	1.05038	−	1.81931i
$669$	−25.0799	−	13.6094i	−0.969646	−	0.526169i
$670$	−15.5484	−	41.3100i	−0.600688	−	1.59595i
$671$	−1.09861	−	0.489131i	−0.0424112	−	0.0188827i
$672$	0.606319	+	0.179439i	0.0233892	+	0.00692202i
$673$	6.92100	+	1.47110i	0.266785	+	0.0567069i	0.339362	−	0.940656i	$-0.389789\pi$
$673$	6.92100	+	1.47110i	0.266785	+	0.0567069i	−0.0725769	+	0.997363i	$0.523122\pi$
$674$	−43.3507			−1.66981
$675$	−22.9836	+	12.1142i	−0.884639	+	0.466277i
$676$	−41.6922			−1.60354
$677$	27.5562	+	5.85726i	1.05907	+	0.225113i	0.704346	−	0.709857i	$-0.251241\pi$
$677$	27.5562	+	5.85726i	1.05907	+	0.225113i	0.354727	+	0.934970i	$0.384574\pi$
$678$	−45.7449	−	13.5381i	−1.75682	−	0.519929i
$679$	0.892533	+	0.397381i	0.0342523	+	0.0152501i
$680$	−20.3908	−	13.4322i	−0.781952	−	0.515103i
$681$	34.9320	+	18.9555i	1.33860	+	0.726376i
$682$	−0.861908	+	1.49287i	−0.0330042	+	0.0571649i
$683$	19.5504	+	14.2042i	0.748075	+	0.543508i	0.895230	−	0.445605i	$-0.147012\pi$
$683$	19.5504	+	14.2042i	0.748075	+	0.543508i	−0.147155	+	0.989113i	$0.547012\pi$
$684$	1.37868	−	26.5541i	0.0527150	−	1.01532i
$685$	−26.6935	−	4.40687i	−1.01991	−	0.168378i
$686$	2.55138	+	0.542312i	0.0974121	+	0.0207056i
$687$	−18.9714	−	16.1951i	−0.723804	−	0.617882i
$688$	10.7845	−	2.29232i	0.411155	−	0.0873938i
$689$	4.94493	−	5.49191i	0.188387	−	0.209225i
$690$	−34.2073	+	55.0408i	−1.30225	+	2.09537i
$691$	14.2462	+	15.8220i	0.541952	+	0.601898i	0.950456	−	0.310858i	$-0.100616\pi$
$691$	14.2462	+	15.8220i	0.541952	+	0.601898i	−0.408505	+	0.912756i	$0.633950\pi$
$692$	−55.6709	−	40.4473i	−2.11629	−	1.53757i
$693$	−0.0277919	+	0.00746132i	−0.00105573	+	0.000283432i
$694$	−7.08640	−	5.14857i	−0.268996	−	0.195437i
$695$	1.45698	−	24.7097i	0.0552665	−	0.937293i
$696$	26.0178	−	24.7020i	0.986202	−	0.936327i
$697$	−19.0250	−	8.47046i	−0.720622	−	0.320841i
$698$	27.0643	−	30.0579i	1.02440	−	1.13771i
$699$	−6.42904	−	8.37427i	−0.243169	−	0.316744i
$700$	0.541420	+	1.26013i	0.0204638	+	0.0476283i
$701$	46.9741			1.77419			0.887095	−	0.461588i	$-0.152720\pi$
$701$	46.9741			1.77419			0.887095	+	0.461588i	$0.152720\pi$
$702$	7.21511	+	8.43532i	0.272317	+	0.318371i
$703$	24.6679	−	17.9222i	0.930366	−	0.675950i
$704$	−0.155793	−	1.48227i	−0.00587167	−	0.0558652i
$705$	7.01487	+	13.1159i	0.264195	+	0.493974i
$706$	5.50233	−	52.3512i	0.207083	−	1.97026i
$707$	−0.253926	−	0.439813i	−0.00954988	−	0.0165409i
$708$	7.14468	+	3.87699i	0.268513	+	0.145706i
$709$	−16.1094	−	17.8913i	−0.605002	−	0.671923i	0.360367	−	0.932811i	$-0.382651\pi$
$709$	−16.1094	−	17.8913i	−0.605002	−	0.671923i	−0.965369	+	0.260888i	$0.915985\pi$
$710$	16.4164	−	31.7051i	0.616098	−	1.18987i
$711$	2.91187	−	5.72175i	0.109204	−	0.214582i
$712$	−14.4256	+	44.3975i	−0.540623	+	1.66387i
$713$	−29.6509	−	32.9306i	−1.11043	−	1.23326i
$714$	1.05575	+	0.0828306i	0.0395104	+	0.00309986i
$715$	−0.192037	+	0.153441i	−0.00718178	+	0.00573838i
$716$	23.5163	−	4.99854i	0.878844	−	0.186804i
$717$	7.70974	−	4.72712i	0.287925	−	0.176537i
$718$	−18.4528	+	31.9612i	−0.688652	+	1.19278i
$719$	19.5095	+	14.1745i	0.727582	+	0.528619i	0.888798	−	0.458300i	$-0.151541\pi$
$719$	19.5095	+	14.1745i	0.727582	+	0.528619i	−0.161216	+	0.986919i	$0.551541\pi$
$720$	−4.45749	−	4.06263i	−0.166121	−	0.151405i
$721$	−0.459828	+	0.334085i	−0.0171249	+	0.0124420i
$722$	3.00004	+	28.5434i	0.111650	+	1.06228i
$723$	−3.29276	−	6.89909i	−0.122459	−	0.256580i
$724$	33.4862	+	57.9998i	1.24451	+	2.15555i
$725$	−30.8941	−	3.65599i	−1.14738	−	0.135780i
$726$	−26.9974	−	35.1660i	−1.00197	−	1.30513i
$727$	−24.4031	−	5.18703i	−0.905060	−	0.192376i	−0.268207	−	0.963361i	$-0.586431\pi$
$727$	−24.4031	−	5.18703i	−0.905060	−	0.192376i	−0.636853	+	0.770985i	$0.719764\pi$
$728$	0.197544	−	0.143524i	0.00732146	−	0.00531935i
$729$	−4.18477	+	26.6737i	−0.154991	+	0.987916i
$730$	16.1971	+	16.4102i	0.599482	+	0.607370i
$731$	−36.7474	+	16.3610i	−1.35915	+	0.605134i
$732$	36.2726	+	47.2476i	1.34067	+	1.74632i
$733$	3.49195	−	33.2237i	0.128978	−	1.22715i	−0.718200	−	0.695837i	$-0.755034\pi$
$733$	3.49195	−	33.2237i	0.128978	−	1.22715i	0.847178	−	0.531309i	$-0.178300\pi$
$734$	44.4669	−	9.45173i	1.64130	−	0.348870i
$735$	21.3847	+	16.6239i	0.788785	+	0.613180i
$736$	32.0550	+	6.81349i	1.18156	+	0.251149i
$737$	0.313900	−	0.966084i	0.0115626	−	0.0355862i
$738$	−37.2309	−	24.1523i	−1.37049	−	0.889058i
$739$	6.22346	+	19.1538i	0.228934	+	0.704586i	0.997868	+	0.0652583i	$0.0207871\pi$
$739$	6.22346	+	19.1538i	0.228934	+	0.704586i	−0.768935	+	0.639327i	$0.779213\pi$
$740$	5.32330	−	90.2804i	0.195688	−	3.31877i
$741$	3.12208	+	2.66519i	0.114692	+	0.0979082i
$742$	0.157048	−	1.49421i	0.00576540	−	0.0548541i
$743$	7.12565	+	12.3420i	0.261415	+	0.452784i	0.966618	−	0.256222i	$-0.0824777\pi$
$743$	7.12565	+	12.3420i	0.261415	+	0.452784i	−0.705203	+	0.709005i	$0.749144\pi$
$744$	30.3321	−	18.5977i	1.11203	−	0.681825i
$745$	−12.4101	−	4.85709i	−0.454671	−	0.177950i
$746$	−42.2873	+	30.7235i	−1.54825	+	1.12487i
$747$	8.92816	+	1.40962i	0.326664	+	0.0515755i
$748$	−0.416713	−	1.28251i	−0.0152365	−	0.0468932i
$749$	0.290264	−	0.502752i	0.0106060	−	0.0183702i
$750$	−2.05424	+	45.0730i	−0.0750103	+	1.64584i
$751$	−7.92393	−	13.7247i	−0.289148	−	0.500820i	0.684458	−	0.729052i	$-0.260039\pi$
$751$	−7.92393	−	13.7247i	−0.289148	−	0.500820i	−0.973607	+	0.228232i	$0.926705\pi$
$752$	−2.31038	+	2.56594i	−0.0842509	+	0.0935701i
$753$	36.3127	+	10.7467i	1.32331	+	0.391631i
$754$	1.38933	+	13.2186i	0.0505964	+	0.481392i
$755$	7.02820	+	46.3322i	0.255782	+	1.68620i
$756$	1.38618	+	0.331722i	0.0504150	+	0.0120646i
$757$	20.8659			0.758385			0.379192	−	0.925318i	$-0.376202\pi$
$757$	20.8659			0.758385			0.379192	+	0.925318i	$0.376202\pi$
$758$	76.0873	−	33.8762i	2.76361	−	1.23044i
$759$	−1.40572	+	0.498176i	−0.0510244	+	0.0180827i
$760$	−16.0693	−	10.5855i	−0.582894	−	0.383975i
$761$	13.7889	−	15.3142i	0.499849	−	0.555138i	−0.439437	−	0.898273i	$-0.644822\pi$
$761$	13.7889	−	15.3142i	0.499849	−	0.555138i	0.939286	+	0.343135i	$0.111489\pi$
$762$	2.52497	−	13.6421i	0.0914702	−	0.494200i
$763$	0.0440824	+	0.0489585i	0.00159589	+	0.00177242i
$764$	13.2604	+	40.8112i	0.479743	+	1.47650i
$765$	18.9890	+	11.1170i	0.686547	+	0.401935i
$766$	26.0434	−	80.1532i	0.940985	−	2.89605i
$767$	−1.14643	+	0.510424i	−0.0413952	+	0.0184303i
$768$	−14.1477	+	34.1792i	−0.510513	+	1.23334i
$769$	−0.706683	+	6.72364i	−0.0254837	+	0.242461i	0.974364	+	0.224979i	$0.0722315\pi$
$769$	−0.706683	+	6.72364i	−0.0254837	+	0.242461i	−0.999847	+	0.0174814i	$0.994435\pi$
$770$	−0.0132495	+	0.0481859i	−0.000477479	+	0.00173650i
$771$	6.55550	+	27.2764i	0.236091	+	0.982335i
$772$	1.61973	+	15.4107i	0.0582952	+	0.554642i
$773$	9.42167	+	28.9969i	0.338874	+	1.04295i	0.964782	+	0.263050i	$0.0847285\pi$
$773$	9.42167	+	28.9969i	0.338874	+	1.04295i	−0.625908	+	0.779897i	$0.715272\pi$
$774$	−82.7877	+	22.2261i	−2.97574	+	0.798901i
$775$	−29.2152	−	9.91664i	−1.04944	−	0.356216i
$776$	−20.3282	+	35.2094i	−0.729738	+	1.26394i
$777$	0.704005	+	1.47505i	0.0252560	+	0.0529172i
$778$	−39.4813	−	17.5782i	−1.41547	−	0.630210i
$779$	−14.9929	−	6.67527i	−0.537176	−	0.239166i
$780$	11.9852	−	2.14341i	0.429139	−	0.0767463i
$781$	0.750619	−	0.334197i	0.0268593	−	0.0119585i
$782$	54.8847			1.96267
$783$	−22.2374	+	23.4677i	−0.794701	+	0.838666i
$784$	−1.94300	+	5.97995i	−0.0693930	+	0.213570i
$785$	−0.335898	−	0.131464i	−0.0119887	−	0.00469217i
$786$	−14.5047	+	21.1154i	−0.517364	+	0.753162i
$787$	−36.9391	+	7.85165i	−1.31674	+	0.279881i	−0.812134	−	0.583471i	$-0.801694\pi$
$787$	−36.9391	+	7.85165i	−1.31674	+	0.279881i	−0.504603	+	0.863352i	$0.668361\pi$
$788$	−23.4168	+	4.97739i	−0.834188	+	0.177312i
$789$	20.0228	+	41.9523i	0.712830	+	1.49354i
$790$	−6.01122	−	9.39026i	−0.213869	−	0.334090i
$791$	0.292236	−	0.899410i	0.0103907	−	0.0319793i
$792$	−0.187902	−	1.18264i	−0.00667679	−	0.0420232i
$793$	−9.19570			−0.326549
$794$	−78.4248	+	34.9170i	−2.78319	+	1.23916i
$795$	16.4784	−	26.5143i	0.584428	−	0.940367i
$796$	17.6593	+	7.86243i	0.625918	+	0.278676i
$797$	2.47483	+	1.10186i	0.0876629	+	0.0390301i	0.450100	−	0.892978i	$-0.351388\pi$
$797$	2.47483	+	1.10186i	0.0876629	+	0.0390301i	−0.362437	+	0.932008i	$0.618055\pi$
$798$	0.831998	+	0.0652759i	0.0294524	+	0.00231074i
$799$	6.29860	−	10.9095i	0.222828	−	0.385950i
$800$	21.7903	−	6.76650i	0.770403	−	0.239232i
$801$	10.8682	−	40.6397i	0.384008	−	1.43593i
$802$	−8.19556	−	25.2233i	−0.289395	−	0.890667i
$803$	0.0554662	+	0.527726i	0.00195736	+	0.0186230i
$804$	−36.4882	+	34.6429i	−1.28684	+	1.22176i
$805$	−1.07280	−	0.706693i	−0.0378111	−	0.0249076i
$806$	−1.37784	+	13.1093i	−0.0485323	+	0.461754i
$807$	0.628424	+	0.818565i	0.0221216	+	0.0288149i
$808$	19.3064	−	8.59577i	0.679198	−	0.302398i
$809$	−7.45430	+	22.9420i	−0.262079	+	0.806597i	0.730273	+	0.683156i	$0.239393\pi$
$809$	−7.45430	+	22.9420i	−0.262079	+	0.806597i	−0.992352	+	0.123441i	$0.960607\pi$
$810$	36.2756	+	29.7110i	1.27460	+	1.04394i
$811$	6.27979	+	19.3272i	0.220513	+	0.678670i	0.998716	+	0.0506570i	$0.0161315\pi$
$811$	6.27979	+	19.3272i	0.220513	+	0.678670i	−0.778203	+	0.628013i	$0.783868\pi$
$812$	1.14200	+	1.26832i	0.0400764	+	0.0445094i
$813$	27.3804	−	9.70340i	0.960271	−	0.340313i
$814$	2.20497	−	2.44887i	0.0772843	−	0.0858329i
$815$	−4.95590	−	13.1672i	−0.173598	−	0.461225i
$816$	−0.929618	+	5.02260i	−0.0325432	+	0.175826i
$817$	−28.9594	+	12.8935i	−1.01316	+	0.451088i
$818$	13.8550			0.484430
$819$	−0.170937	+	0.138560i	−0.00597301	+	0.00484167i
$820$	−43.5156	+	21.8152i	−1.51963	+	0.761820i
$821$	−4.47424	−	42.5695i	−0.156152	−	1.48569i	−0.739331	−	0.673342i	$-0.764858\pi$
$821$	−4.47424	−	42.5695i	−0.156152	−	1.48569i	0.583179	−	0.812344i	$-0.301809\pi$
$822$	11.4103	+	47.4765i	0.397981	+	1.65593i
$823$	−11.9680	+	13.2918i	−0.417179	+	0.463324i	−0.914703	−	0.404126i	$-0.867576\pi$
$823$	−11.9680	+	13.2918i	−0.417179	+	0.463324i	0.497524	+	0.867450i	$0.334243\pi$
$824$	−11.8261	−	20.4834i	−0.411982	−	0.713573i
$825$	−0.684439	+	0.780865i	−0.0238291	+	0.0271862i
$826$	−0.127566	+	0.220951i	−0.00443859	+	0.00768786i
$827$	−3.27396	−	10.0762i	−0.113847	−	0.350384i	0.877858	−	0.478921i	$-0.158972\pi$
$827$	−3.27396	−	10.0762i	−0.113847	−	0.350384i	−0.991705	+	0.128537i	$0.958972\pi$
$828$	72.9667	+	11.5204i	2.53577	+	0.400360i
$829$	19.9022	−	14.4598i	0.691231	−	0.502209i	−0.185834	−	0.982581i	$-0.559499\pi$
$829$	19.9022	−	14.4598i	0.691231	−	0.502209i	0.877064	+	0.480373i	$0.159499\pi$
$830$	9.95813	−	12.1342i	0.345652	−	0.421186i
$831$	−27.9045	−	15.1421i	−0.967997	−	0.525274i
$832$	−5.69844	−	9.86999i	−0.197558	−	0.342180i
$833$	2.39788	−	22.8143i	0.0830815	−	0.790468i
$834$	−42.1073	+	14.9225i	−1.45806	+	0.516725i
$835$	19.0903	+	29.8214i	0.660647	+	1.03201i
$836$	−0.328397	−	1.01070i	−0.0113578	−	0.0349558i
$837$	−26.4104	+	18.1798i	−0.912878	+	0.628386i
$838$	−1.55363	+	4.78159i	−0.0536694	+	0.165177i
$839$	0.0375639	+	0.00798446i	0.00129685	+	0.000275654i	0.208560	−	0.978010i	$-0.433122\pi$
$839$	0.0375639	+	0.00798446i	0.00129685	+	0.000275654i	−0.207263	+	0.978285i	$0.566456\pi$
$840$	0.714713	−	0.743721i	0.0246599	−	0.0256608i
$841$	−9.50015	+	2.01932i	−0.327591	+	0.0696317i
$842$	−1.31887	+	12.5482i	−0.0454513	+	0.432440i
$843$	−50.4000	+	6.64777i	−1.73587	+	0.228961i
$844$	28.7754	−	12.8116i	0.990491	−	0.440995i
$845$	12.5017	−	24.1446i	0.430073	−	0.830600i
$846$	16.8836	−	20.8703i	0.580471	−	0.717536i
$847$	0.711003	−	0.516574i	0.0244303	−	0.0177497i
$848$	7.08844	+	1.50670i	0.243418	+	0.0517401i
$849$	−16.5076	+	39.8804i	−0.566540	+	1.36869i
$850$	33.3405	−	18.6724i	1.14357	−	0.640458i
$851$	42.3544	+	73.3599i	1.45189	+	2.51475i
$852$	−40.5732	−	3.18324i	−1.39001	−	0.109056i
$853$	3.13826	+	29.8585i	0.107452	+	1.02234i	0.906827	+	0.421503i	$0.138497\pi$
$853$	3.13826	+	29.8585i	0.107452	+	1.02234i	−0.799375	+	0.600832i	$0.794836\pi$
$854$	−1.51248	+	1.09888i	−0.0517560	+	0.0376030i
$855$	14.9645	+	8.76089i	0.511776	+	0.299616i
$856$	19.5441	+	14.1996i	0.668003	+	0.485332i
$857$	−22.6490	+	39.2291i	−0.773673	+	1.34004i	0.161864	+	0.986813i	$0.448250\pi$
$857$	−22.6490	+	39.2291i	−0.773673	+	1.34004i	−0.935537	+	0.353229i	$0.885084\pi$
$858$	0.389926	+	0.211590i	0.0133119	+	0.00722356i
$859$	15.0829	−	3.20596i	0.514621	−	0.109386i	0.0567216	−	0.998390i	$-0.481935\pi$
$859$	15.0829	−	3.20596i	0.514621	−	0.109386i	0.457900	+	0.889004i	$0.348602\pi$
$860$	−24.9279	+	90.6579i	−0.850035	+	3.09141i
$861$	0.498111	−	0.725134i	0.0169756	−	0.0247125i
$862$	−31.0947	−	34.5342i	−1.05909	−	1.17624i
$863$	−3.41163	+	10.4999i	−0.116133	+	0.357421i	−0.992182	−	0.124802i	$-0.960171\pi$
$863$	−3.41163	+	10.4999i	−0.116133	+	0.357421i	0.876048	+	0.482223i	$0.160171\pi$
$864$	7.89884	−	22.3575i	0.268724	−	0.760618i
$865$	40.1171	−	20.1115i	1.36402	−	0.683811i
$866$	11.7725	+	13.0747i	0.400047	+	0.444298i
$867$	0.285584	+	10.8055i	0.00969895	+	0.366973i
$868$	0.846290	+	1.46582i	0.0287250	+	0.0497531i
$869$	0.0268210	−	0.255184i	0.000909839	−	0.00865654i
$870$	15.6074	+	53.9336i	0.529140	+	1.82852i
$871$	−0.811926	−	7.72496i	−0.0275110	−	0.261750i
$872$	−2.21792	+	1.61141i	−0.0751083	+	0.0545694i
$873$	16.6172	−	32.6524i	0.562407	−	1.10512i
$874$	43.2527			1.46304
$875$	−0.892110	−	0.0643142i	−0.0301588	−	0.00217422i
$876$	10.0522	−	24.2848i	0.339632	−	0.820508i
$877$	−2.33615	+	2.59456i	−0.0788862	+	0.0876120i	−0.781296	−	0.624161i	$-0.785441\pi$
$877$	−2.33615	+	2.59456i	−0.0788862	+	0.0876120i	0.702409	+	0.711773i	$0.252108\pi$
$878$	−37.3668	−	16.6368i	−1.26107	−	0.561464i
$879$	9.99591	+	41.5913i	0.337154	+	1.40284i
$880$	−0.224464	−	0.0878514i	−0.00756670	−	0.00296147i
$881$	23.4739	+	17.0548i	0.790855	+	0.574590i	0.908217	−	0.418499i	$-0.137444\pi$
$881$	23.4739	+	17.0548i	0.790855	+	0.574590i	−0.117362	+	0.993089i	$0.537444\pi$
$882$	12.6293	−	47.2253i	0.425251	−	1.59016i
$883$	28.7635	+	20.8979i	0.967969	+	0.703270i	0.954988	−	0.296645i	$-0.0958680\pi$
$883$	28.7635	+	20.8979i	0.967969	+	0.703270i	0.0129808	+	0.999916i	$0.495868\pi$
$884$	−6.89982	−	7.66303i	−0.232066	−	0.257736i
$885$	−4.38762	+	2.97505i	−0.147488	+	0.100005i
$886$	47.7603	−	53.0432i	1.60454	−	1.78202i
$887$	0.799916	−	0.170027i	0.0268586	−	0.00570896i	−0.194463	−	0.980910i	$-0.562296\pi$
$887$	0.799916	−	0.170027i	0.0268586	−	0.00570896i	0.221321	+	0.975201i	$0.428963\pi$
$888$	−64.1081	+	22.7194i	−2.15133	+	0.762414i
$889$	0.269015	+	0.0571808i	0.00902246	+	0.00191778i
$890$	−51.3208	−	51.9961i	−1.72028	−	1.74291i
$891$	0.225386	+	1.05530i	0.00755072	+	0.0353540i
$892$	45.6993	+	33.2025i	1.53012	+	1.11170i
$893$	4.96370	−	8.59738i	0.166104	−	0.287700i
$894$	0.635462	+	24.0436i	0.0212530	+	0.804138i
$895$	−4.15681	+	15.1175i	−0.138947	+	0.505322i
$896$	−1.44971	−	0.645453i	−0.0484315	−	0.0215631i
$897$	−8.27035	+	7.85210i	−0.276139	+	0.262174i
$898$	32.6556	+	6.94116i	1.08973	+	0.231630i
$899$	−38.3922			−1.28045
$900$	48.2440	−	17.8259i	1.60813	−	0.594195i
$901$	−26.4392			−0.880816
$902$	−1.73492	−	0.368768i	−0.0577665	−	0.0122786i
$903$	−0.397082	−	1.65219i	−0.0132141	−	0.0549816i
$904$	35.9514	+	16.0066i	1.19572	+	0.532371i
$905$	−43.6298	+	2.00069i	−1.45030	+	0.0665051i
$906$	72.1027	−	44.2087i	2.39545	−	1.46874i
$907$	−23.0912	+	39.9952i	−0.766732	+	1.32802i	0.172594	+	0.984993i	$0.444785\pi$
$907$	−23.0912	+	39.9952i	−0.766732	+	1.32802i	−0.939326	+	0.343026i	$0.888548\pi$
$908$	−63.6511	−	46.2453i	−2.11234	−	1.53470i
$909$	−16.9646	+	8.65429i	−0.562679	+	0.287045i
$910$	0.0573113	+	0.377815i	0.00189985	+	0.0125245i
$911$	−27.1978	−	5.78106i	−0.901102	−	0.191535i	−0.266009	−	0.963971i	$-0.585705\pi$
$911$	−27.1978	−	5.78106i	−0.901102	−	0.191535i	−0.635093	+	0.772435i	$0.719038\pi$
$912$	−0.732600	+	3.95813i	−0.0242588	+	0.131067i
$913$	0.353356	−	0.0751081i	0.0116944	−	0.00248571i
$914$	7.54367	−	8.37810i	0.249523	−	0.277123i
$915$	−38.2385	+	6.83849i	−1.26413	+	0.226074i
$916$	33.0412	+	36.6960i	1.09171	+	1.21247i
$917$	−0.410835	−	0.298489i	−0.0135670	−	0.00985698i
$918$	5.15474	−	39.3764i	0.170132	−	1.29961i
$919$	−0.974020	−	0.707667i	−0.0321299	−	0.0233438i	0.571604	−	0.820529i	$-0.306321\pi$
$919$	−0.974020	−	0.707667i	−0.0321299	−	0.0233438i	−0.603734	+	0.797186i	$0.706321\pi$
$920$	33.9133	−	41.3242i	1.11809	−	1.36242i
$921$	3.75462	+	1.11117i	0.123719	+	0.0366145i
$922$	−19.9804	−	8.89584i	−0.658019	−	0.292969i
$923$	4.20410	−	4.66913i	0.138380	−	0.153686i
$924$	0.0564764	−	0.00744925i	0.00185794	−	0.000245062i
$925$	50.6866	+	30.1541i	1.66657	+	0.991462i
$926$	−5.60238			−0.184106
$927$	11.6173	+	17.8700i	0.381561	+	0.586927i
$928$	22.9702	−	16.6889i	0.754035	−	0.547839i
$929$	4.89897	+	46.6106i	0.160730	+	1.52924i	0.716310	+	0.697782i	$0.245829\pi$
$929$	4.89897	+	46.6106i	0.160730	+	1.52924i	−0.555580	+	0.831463i	$0.687504\pi$
$930$	4.01939	+	55.5369i	0.131801	+	1.82113i
$931$	1.88968	−	17.9791i	0.0619318	−	0.589242i
$932$	10.4499	+	18.0998i	0.342298	+	0.592878i
$933$	0.453205	−	0.277876i	0.0148373	−	0.00909726i
$934$	36.2464	+	40.2557i	1.18602	+	1.31721i
$935$	0.867677	+	0.143246i	0.0283761	+	0.00468464i
$936$	−4.99082	−	7.67700i	−0.163130	−	0.250931i
$937$	−2.37863	+	7.32067i	−0.0777065	+	0.239156i	−0.982362	−	0.186987i	$-0.940128\pi$
$937$	−2.37863	+	7.32067i	−0.0777065	+	0.239156i	0.904656	+	0.426143i	$0.140128\pi$
$938$	−1.05667	−	1.17355i	−0.0345015	−	0.0383178i
$939$	0.945292	+	1.98061i	0.0308484	+	0.0646346i
$940$	−10.3722	−	27.5575i	−0.338304	−	0.898827i
$941$	6.30608	−	1.34040i	0.205572	−	0.0436958i	−0.103974	−	0.994580i	$-0.533156\pi$
$941$	6.30608	−	1.34040i	0.205572	−	0.0436958i	0.309547	+	0.950884i	$0.399823\pi$
$942$	0.0171998	+	0.650776i	0.000560398	+	0.0212034i
$943$	22.7971	−	39.4858i	0.742376	−	1.28583i
$944$	−0.995571	−	0.723325i	−0.0324031	−	0.0235422i
$945$	−0.607764	+	0.703291i	−0.0197706	+	0.0228781i
$946$	−2.77163	+	2.01371i	−0.0901135	+	0.0654713i
$947$	1.47551	+	14.0385i	0.0479477	+	0.456192i	0.991985	+	0.126354i	$0.0403274\pi$
$947$	1.47551	+	14.0385i	0.0479477	+	0.456192i	−0.944038	+	0.329838i	$0.893006\pi$
$948$	−7.19608	+	10.4758i	−0.233718	+	0.340239i
$949$	2.02879	+	3.51396i	0.0658573	+	0.114068i
$950$	26.2745	−	14.7151i	0.852457	−	0.477419i
$951$	7.41872	−	0.978530i	0.240568	−	0.0317310i
$952$	−0.854492	−	0.181628i	−0.0276942	−	0.00588659i
$953$	−39.7413	+	28.8737i	−1.28735	+	0.935312i	−0.999748	−	0.0224398i	$-0.992857\pi$
$953$	−39.7413	+	28.8737i	−1.28735	+	0.935312i	−0.287598	+	0.957751i	$0.592857\pi$
$954$	−55.6522	−	8.78667i	−1.80181	−	0.284479i
$955$	−27.6107	−	4.55828i	−0.893460	−	0.147503i
$956$	−16.3550	+	7.28171i	−0.528958	+	0.235507i
$957$	−0.494186	+	1.19389i	−0.0159748	+	0.0385931i
$958$	−5.84092	+	55.5726i	−0.188712	+	1.79547i
$959$	−0.946790	+	0.201246i	−0.0305734	+	0.00649859i
$960$	−31.0358	−	36.8047i	−1.00168	−	1.18787i
$961$	−6.92011	−	1.47092i	−0.223229	−	0.0474489i
$962$	7.78660	−	23.9647i	0.251050	−	0.772653i
$963$	−18.2635	−	11.8478i	−0.588534	−	0.381791i
$964$	4.67647	+	14.3927i	0.150619	+	0.463557i
$965$	−9.41026	−	3.68301i	−0.302927	−	0.118560i
$966$	−0.421960	+	2.27979i	−0.0135764	+	0.0733511i
$967$	−4.29570	+	40.8708i	−0.138140	+	1.31432i	0.677399	+	0.735616i	$0.263107\pi$
$967$	−4.29570	+	40.8708i	−0.138140	+	1.31432i	−0.815539	+	0.578701i	$0.803560\pi$
$968$	18.2860	+	31.6722i	0.587733	+	1.01798i
$969$	−0.388011	−	14.6809i	−0.0124647	−	0.471620i
$970$	−34.3043	−	53.5875i	−1.10144	−	1.72059i
$971$	−14.7679	+	10.7295i	−0.473925	+	0.344327i	−0.798969	−	0.601372i	$-0.794621\pi$
$971$	−14.7679	+	10.7295i	−0.473925	+	0.344327i	0.325044	+	0.945699i	$0.394621\pi$
$972$	15.1181	−	51.2671i	0.484914	−	1.64439i
$973$	−0.273658	−	0.842232i	−0.00877306	−	0.0270007i
$974$	−2.49773	+	4.32619i	−0.0800323	+	0.138620i
$975$	−2.35258	+	7.58354i	−0.0753428	+	0.242868i
$976$	−4.50871	−	7.80931i	−0.144320	−	0.249970i
$977$	−21.6077	+	23.9978i	−0.691293	+	0.767758i	−0.981965	−	0.189065i	$-0.939454\pi$
$977$	−21.6077	+	23.9978i	−0.691293	+	0.767758i	0.290672	+	0.956823i	$0.406121\pi$
$978$	−18.4141	+	17.4829i	−0.588818	+	0.559040i
$979$	−0.175746	−	1.67211i	−0.00561685	−	0.0534408i
$980$	−37.6665	−	38.1622i	−1.20321	−	1.21905i
$981$	1.91919	−	1.55568i	0.0612750	−	0.0496690i
$982$	−31.4860			−1.00476
$983$	31.0537	−	13.8260i	0.990458	−	0.440980i	0.153441	−	0.988158i	$-0.450964\pi$
$983$	31.0537	−	13.8260i	0.990458	−	0.440980i	0.837017	+	0.547177i	$0.184298\pi$
$984$	27.8433	+	23.7687i	0.887613	+	0.757720i
$985$	4.13922	−	15.0535i	0.131887	−	0.479646i
$986$	31.8185	−	35.3380i	1.01331	−	1.12539i
$987$	0.404732	+	0.345503i	0.0128828	+	0.0109975i
$988$	−5.43751	−	6.03897i	−0.172990	−	0.192125i
$989$	−27.2142	−	83.7567i	−0.865362	−	2.66331i
$990$	1.77878	+	0.589881i	0.0565334	+	0.0187476i
$991$	8.29122	−	25.5177i	0.263379	−	0.810598i	−0.728683	−	0.684851i	$-0.759867\pi$
$991$	8.29122	−	25.5177i	0.263379	−	0.810598i	0.992062	−	0.125747i	$-0.0401327\pi$
$992$	25.7236	−	11.4529i	0.816725	−	0.363629i
$993$	30.4347	−	4.01434i	0.965816	−	0.127391i
$994$	0.133519	−	1.27035i	0.00423498	−	0.0402931i
$995$	−9.84855	+	7.86918i	−0.312220	+	0.249470i
$996$	−17.1577	−	5.07779i	−0.543661	−	0.160896i
$997$	1.81440	+	17.2629i	0.0574627	+	0.546721i	0.984947	+	0.172858i	$0.0553003\pi$
$997$	1.81440	+	17.2629i	0.0574627	+	0.546721i	−0.927484	+	0.373863i	$0.878033\pi$
$998$	−9.51950	−	29.2980i	−0.301335	−	0.927413i
$999$	56.6090	−	23.4967i	1.79103	−	0.743403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.4	yes	224
3.2	odd	2		675.2.r.a.181.25		224
9.4	even	3	inner	225.2.q.a.31.25	✓	224
9.5	odd	6		675.2.r.a.631.4		224
25.21	even	5	inner	225.2.q.a.196.25	yes	224
75.71	odd	10		675.2.r.a.46.4		224
225.121	even	15	inner	225.2.q.a.121.4	yes	224
225.221	odd	30		675.2.r.a.496.25		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.25	✓	224	9.4	even	3	inner
225.2.q.a.106.4	yes	224	1.1	even	1	trivial
225.2.q.a.121.4	yes	224	225.121	even	15	inner
225.2.q.a.196.25	yes	224	25.21	even	5	inner
675.2.r.a.46.4		224	75.71	odd	10
675.2.r.a.181.25		224	3.2	odd	2
675.2.r.a.496.25		224	225.221	odd	30
675.2.r.a.631.4		224	9.5	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27906 - 0.484430i) q^{2} +(-1.66084 - 0.491525i) q^{3} +(3.13236 + 1.39462i) q^{4} +(-1.74691 + 1.39582i) q^{5} +(3.54706 + 1.92478i) q^{6} +(-0.0399999 + 0.0692819i) q^{7} +(-2.69327 - 1.95678i) q^{8} +(2.51681 + 1.63269i) q^{9} +O(q^{10})\)	\(q+(-2.27906 - 0.484430i) q^{2} +(-1.66084 - 0.491525i) q^{3} +(3.13236 + 1.39462i) q^{4} +(-1.74691 + 1.39582i) q^{5} +(3.54706 + 1.92478i) q^{6} +(-0.0399999 + 0.0692819i) q^{7} +(-2.69327 - 1.95678i) q^{8} +(2.51681 + 1.63269i) q^{9} +(4.65750 - 2.33489i) q^{10} +(0.117280 + 0.0249287i) q^{11} +(-4.51688 - 3.85588i) q^{12} +(0.896805 - 0.190622i) q^{13} +(0.124725 - 0.138521i) q^{14} +(3.58743 - 1.45958i) q^{15} +(0.601591 + 0.668134i) q^{16} +(-2.65368 - 1.92801i) q^{17} +(-4.94504 - 4.94022i) q^{18} +(-2.09128 - 1.51940i) q^{19} +(-7.41859 + 1.93593i) q^{20} +(0.100487 - 0.0954055i) q^{21} +(-0.255213 - 0.113628i) q^{22} +(4.80528 - 5.33681i) q^{23} +(3.51130 + 4.57371i) q^{24} +(1.10340 - 4.87673i) q^{25} -2.13622 q^{26} +(-3.37752 - 3.94872i) q^{27} +(-0.221916 + 0.161231i) q^{28} +(-0.650369 - 6.18784i) q^{29} +(-8.88303 + 1.58862i) q^{30} +(0.644990 - 6.13667i) q^{31} +(2.28167 + 3.95197i) q^{32} +(-0.182531 - 0.0990488i) q^{33} +(5.11392 + 5.67959i) q^{34} +(-0.0268284 - 0.176862i) q^{35} +(5.60657 + 8.62417i) q^{36} +(-3.64504 + 11.2183i) q^{37} +(4.03010 + 4.47588i) q^{38} +(-1.58315 - 0.124209i) q^{39} +(7.43621 - 0.340995i) q^{40} +(6.21021 - 1.32002i) q^{41} +(-0.275234 + 0.168756i) q^{42} +(6.13162 - 10.6203i) q^{43} +(0.332599 + 0.241647i) q^{44} +(-6.67558 + 0.660830i) q^{45} +(-13.5368 + 9.83509i) q^{46} +(0.401436 + 3.81941i) q^{47} +(-0.670744 - 1.40536i) q^{48} +(3.49680 + 6.05664i) q^{49} +(-4.87715 + 10.5799i) q^{50} +(3.45969 + 4.50648i) q^{51} +(3.07496 + 0.653604i) q^{52} +(6.52099 - 4.73778i) q^{53} +(5.78469 + 10.6355i) q^{54} +(-0.239674 + 0.120153i) q^{55} +(0.243300 - 0.108324i) q^{56} +(2.72646 + 3.55140i) q^{57} +(-1.51534 + 14.4175i) q^{58} +(-1.33884 + 0.284579i) q^{59} +(13.2727 + 0.431147i) q^{60} +(-9.81061 - 2.08531i) q^{61} +(-4.44276 + 13.6734i) q^{62} +(-0.213788 + 0.109062i) q^{63} +(-3.84127 - 11.8222i) q^{64} +(-1.30057 + 1.58477i) q^{65} +(0.368018 + 0.314162i) q^{66} +(0.885569 - 8.42563i) q^{67} +(-5.62346 - 9.74012i) q^{68} +(-10.6040 + 6.50169i) q^{69} +(-0.0245335 + 0.416076i) q^{70} +(5.54404 - 4.02798i) q^{71} +(-3.58364 - 9.32212i) q^{72} +(1.36759 + 4.20901i) q^{73} +(13.7417 - 23.8014i) q^{74} +(-4.22961 + 7.55714i) q^{75} +(-4.43165 - 7.67584i) q^{76} +(-0.00641831 + 0.00712825i) q^{77} +(3.54792 + 1.05000i) q^{78} +(-0.223694 - 2.12830i) q^{79} +(-1.98352 - 0.327462i) q^{80} +(3.66864 + 8.21834i) q^{81} -14.7929 q^{82} +(2.75244 - 1.22546i) q^{83} +(0.447817 - 0.158703i) q^{84} +(7.32690 - 0.335983i) q^{85} +(-19.1191 + 21.2339i) q^{86} +(-1.96132 + 10.5967i) q^{87} +(-0.267088 - 0.296631i) q^{88} +(-4.33323 - 13.3363i) q^{89} +(15.5342 + 1.72777i) q^{90} +(-0.0226655 + 0.0697572i) q^{91} +(22.4947 - 10.0153i) q^{92} +(-4.08755 + 9.87502i) q^{93} +(0.935338 - 8.89915i) q^{94} +(5.77407 - 0.264776i) q^{95} +(-1.84701 - 7.68510i) q^{96} +(-1.27656 - 12.1456i) q^{97} +(-5.03541 - 15.4974i) q^{98} +(0.254471 + 0.254223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more