LMFDB - Embedded newform 273.2.bw.b.11.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(11,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("273.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bw (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	273.11
Dual form			273.2.bw.b.149.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00573734 - 0.0214121i) q^{2} +(-1.43178 - 0.974676i) q^{3} +(1.73163 - 0.999754i) q^{4} +(2.15869 + 0.578419i) q^{5} +(-0.0126552 + 0.0362495i) q^{6} +(1.44048 + 2.21924i) q^{7} +(-0.0626912 - 0.0626912i) q^{8} +(1.10001 + 2.79105i) q^{9} +O(q^{10})$	\(q+(-0.00573734 - 0.0214121i) q^{2} +(-1.43178 - 0.974676i) q^{3} +(1.73163 - 0.999754i) q^{4} +(2.15869 + 0.578419i) q^{5} +(-0.0126552 + 0.0362495i) q^{6} +(1.44048 + 2.21924i) q^{7} +(-0.0626912 - 0.0626912i) q^{8} +(1.10001 + 2.79105i) q^{9} -0.0495405i q^{10} +(-3.61079 - 3.61079i) q^{11} +(-3.45375 - 0.256341i) q^{12} +(3.17766 + 1.70367i) q^{13} +(0.0392540 - 0.0435761i) q^{14} +(-2.52700 - 2.93219i) q^{15} +(1.99853 - 3.46155i) q^{16} +(0.253331 + 0.438783i) q^{17} +(0.0534510 - 0.0395668i) q^{18} +(1.23862 + 1.23862i) q^{19} +(4.31631 - 1.15655i) q^{20} +(0.100591 - 4.58147i) q^{21} +(-0.0565981 + 0.0980307i) q^{22} +(3.78050 - 6.54801i) q^{23} +(0.0286566 + 0.150864i) q^{24} +(-0.00476183 - 0.00274924i) q^{25} +(0.0182479 - 0.0778147i) q^{26} +(1.14539 - 5.06834i) q^{27} +(4.71306 + 2.40277i) q^{28} +(-8.79466 + 5.07760i) q^{29} +(-0.0482860 + 0.0709314i) q^{30} +(0.211677 - 0.0567187i) q^{31} +(-0.256861 - 0.0688256i) q^{32} +(1.65052 + 8.68921i) q^{33} +(0.00794180 - 0.00794180i) q^{34} +(1.82589 + 5.62385i) q^{35} +(4.69518 + 3.73331i) q^{36} +(0.0820203 + 0.306104i) q^{37} +(0.0194150 - 0.0336277i) q^{38} +(-2.88919 - 5.53648i) q^{39} +(-0.0990689 - 0.171592i) q^{40} +(1.21605 + 0.325838i) q^{41} +(-0.0986759 + 0.0241316i) q^{42} +(-7.35892 - 4.24867i) q^{43} +(-9.86243 - 2.64263i) q^{44} +(0.760188 + 6.66128i) q^{45} +(-0.161896 - 0.0433800i) q^{46} +(-1.84390 + 6.88152i) q^{47} +(-6.23535 + 3.00828i) q^{48} +(-2.85006 + 6.39352i) q^{49} +(-3.15467e-5 + 0.000117734i) q^{50} +(0.0649552 - 0.875158i) q^{51} +(7.20576 - 0.226750i) q^{52} +(5.68942 + 3.28479i) q^{53} +(-0.115095 + 0.00455364i) q^{54} +(-5.70601 - 9.88311i) q^{55} +(0.0488217 - 0.229432i) q^{56} +(-0.566182 - 2.98068i) q^{57} +(0.159180 + 0.159180i) q^{58} +(-1.63897 + 6.11671i) q^{59} +(-7.30730 - 2.55107i) q^{60} -12.3384 q^{61} +(-0.00242893 - 0.00420703i) q^{62} +(-4.60948 + 6.46164i) q^{63} -7.98821i q^{64} +(5.87413 + 5.51572i) q^{65} +(0.176584 - 0.0851941i) q^{66} +(4.13223 + 4.13223i) q^{67} +(0.877350 + 0.506538i) q^{68} +(-11.7950 + 5.69058i) q^{69} +(0.109942 - 0.0713619i) q^{70} +(-0.744738 - 2.77940i) q^{71} +(0.106013 - 0.243935i) q^{72} +(0.193342 + 0.721562i) q^{73} +(0.00608374 - 0.00351245i) q^{74} +(0.00413829 + 0.00857757i) q^{75} +(3.38313 + 0.906508i) q^{76} +(2.81196 - 13.2145i) q^{77} +(-0.101971 + 0.0936281i) q^{78} +(1.05053 + 1.81957i) q^{79} +(6.31642 - 6.31642i) q^{80} +(-6.57994 + 6.14039i) q^{81} -0.0279075i q^{82} +(-7.73187 + 7.73187i) q^{83} +(-4.40616 - 8.03396i) q^{84} +(0.293063 + 1.09373i) q^{85} +(-0.0487522 + 0.181946i) q^{86} +(17.5411 + 1.30192i) q^{87} +0.452729i q^{88} +(11.9130 - 3.19208i) q^{89} +(0.138270 - 0.0544952i) q^{90} +(0.796471 + 9.50608i) q^{91} -15.1183i q^{92} +(-0.358358 - 0.125108i) q^{93} +0.157927 q^{94} +(1.95735 + 3.39023i) q^{95} +(0.300686 + 0.348899i) q^{96} +(10.2262 - 2.74010i) q^{97} +(0.153250 + 0.0243438i) q^{98} +(6.10598 - 14.0498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 16 q^{9}+O(q^{10}) $ 128 * q - 4 * q^3 - 12 * q^4 - 4 * q^6 - 16 * q^7 - 16 * q^9	$ 128 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 16 q^{9} - 48 q^{12} - 16 q^{13} - 6 q^{15} + 32 q^{16} + 22 q^{18} - 16 q^{19} - 18 q^{21} - 8 q^{22} - 4 q^{24} - 40 q^{27} - 76 q^{28} - 4 q^{31} + 50 q^{33} - 48 q^{34} - 60 q^{36} + 28 q^{37} + 40 q^{39} + 44 q^{40} + 44 q^{42} - 144 q^{43} + 58 q^{45} + 48 q^{46} - 64 q^{48} + 24 q^{49} + 36 q^{51} - 22 q^{54} - 16 q^{55} + 40 q^{57} - 28 q^{58} - 4 q^{60} - 40 q^{61} + 20 q^{63} - 34 q^{66} + 96 q^{67} - 54 q^{69} + 64 q^{70} - 98 q^{72} + 48 q^{73} - 12 q^{75} + 144 q^{76} + 82 q^{78} - 24 q^{79} - 48 q^{81} + 4 q^{84} + 56 q^{85} - 2 q^{87} - 24 q^{91} + 10 q^{93} + 32 q^{94} - 54 q^{96} + 52 q^{97} - 10 q^{99}+O(q^{100}) $ 128 * q - 4 * q^3 - 12 * q^4 - 4 * q^6 - 16 * q^7 - 16 * q^9 - 48 * q^12 - 16 * q^13 - 6 * q^15 + 32 * q^16 + 22 * q^18 - 16 * q^19 - 18 * q^21 - 8 * q^22 - 4 * q^24 - 40 * q^27 - 76 * q^28 - 4 * q^31 + 50 * q^33 - 48 * q^34 - 60 * q^36 + 28 * q^37 + 40 * q^39 + 44 * q^40 + 44 * q^42 - 144 * q^43 + 58 * q^45 + 48 * q^46 - 64 * q^48 + 24 * q^49 + 36 * q^51 - 22 * q^54 - 16 * q^55 + 40 * q^57 - 28 * q^58 - 4 * q^60 - 40 * q^61 + 20 * q^63 - 34 * q^66 + 96 * q^67 - 54 * q^69 + 64 * q^70 - 98 * q^72 + 48 * q^73 - 12 * q^75 + 144 * q^76 + 82 * q^78 - 24 * q^79 - 48 * q^81 + 4 * q^84 + 56 * q^85 - 2 * q^87 - 24 * q^91 + 10 * q^93 + 32 * q^94 - 54 * q^96 + 52 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.00573734	−	0.0214121i	−0.00405692	−	0.0151406i	0.963868	−	0.266381i	$-0.0858281\pi$
$2$	−0.00573734	−	0.0214121i	−0.00405692	−	0.0151406i	−0.967925	+	0.251241i	$0.919161\pi$
$3$	−1.43178	−	0.974676i	−0.826641	−	0.562730i
$3$	−1.43178	−	0.974676i	−0.826641	−	0.562730i
$4$	1.73163	−	0.999754i	0.865813	−	0.499877i
$5$	2.15869	+	0.578419i	0.965395	+	0.258677i	0.706882	−	0.707331i	$-0.250101\pi$
$5$	2.15869	+	0.578419i	0.965395	+	0.258677i	0.258512	+	0.966008i	$0.416768\pi$
$6$	−0.0126552	+	0.0362495i	−0.00516646	+	0.0147988i
$7$	1.44048	+	2.21924i	0.544448	+	0.838794i
$7$	1.44048	+	2.21924i	0.544448	+	0.838794i
$8$	−0.0626912	−	0.0626912i	−0.0221647	−	0.0221647i
$9$	1.10001	+	2.79105i	0.366671	+	0.930351i
$10$		−	0.0495405i		−	0.0156661i
$11$	−3.61079	−	3.61079i	−1.08869	−	1.08869i	−0.995663	−	0.0930297i	$-0.970345\pi$
$11$	−3.61079	−	3.61079i	−1.08869	−	1.08869i	−0.0930297	−	0.995663i	$-0.529655\pi$
$12$	−3.45375	−	0.256341i	−0.997012	−	0.0739994i
$13$	3.17766	+	1.70367i	0.881323	+	0.472514i
$13$	3.17766	+	1.70367i	0.881323	+	0.472514i
$14$	0.0392540	−	0.0435761i	0.0104911	−	0.0116462i
$15$	−2.52700	−	2.93219i	−0.652470	−	0.757089i
$16$	1.99853	−	3.46155i	0.499631	−	0.865387i
$17$	0.253331	+	0.438783i	0.0614419	+	0.106420i	0.895110	−	0.445845i	$-0.147097\pi$
$17$	0.253331	+	0.438783i	0.0614419	+	0.106420i	−0.833668	+	0.552266i	$0.813763\pi$
$18$	0.0534510	−	0.0395668i	0.0125985	−	0.00932598i
$19$	1.23862	+	1.23862i	0.284158	+	0.284158i	0.834765	−	0.550607i	$-0.185604\pi$
$19$	1.23862	+	1.23862i	0.284158	+	0.284158i	−0.550607	+	0.834765i	$0.685604\pi$
$20$	4.31631	−	1.15655i	0.965157	−	0.258613i
$21$	0.100591	−	4.58147i	0.0219508	−	0.999759i
$22$	−0.0565981	+	0.0980307i	−0.0120667	+	0.0209002i
$23$	3.78050	−	6.54801i	0.788288	−	1.36535i	−0.138727	−	0.990331i	$-0.544301\pi$
$23$	3.78050	−	6.54801i	0.788288	−	1.36535i	0.927015	−	0.375024i	$-0.122365\pi$
$24$	0.0286566	+	0.150864i	0.00584951	+	0.0307949i
$25$	−0.00476183	−	0.00274924i	−0.000952366	−	0.000549849i
$26$	0.0182479	−	0.0778147i	0.00357870	−	0.0152607i
$27$	1.14539	−	5.06834i	0.220431	−	0.975403i
$28$	4.71306	+	2.40277i	0.890684	+	0.454081i
$29$	−8.79466	+	5.07760i	−1.63313	+	0.942886i	−0.650006	+	0.759929i	$0.725234\pi$
$29$	−8.79466	+	5.07760i	−1.63313	+	0.942886i	−0.983121	+	0.182957i	$0.941433\pi$
$30$	−0.0482860	+	0.0709314i	−0.00881578	+	0.0129502i
$31$	0.211677	−	0.0567187i	0.0380183	−	0.0101870i	−0.239760	−	0.970832i	$-0.577069\pi$
$31$	0.211677	−	0.0567187i	0.0380183	−	0.0101870i	0.277778	+	0.960645i	$0.410402\pi$
$32$	−0.256861	−	0.0688256i	−0.0454070	−	0.0121668i
$33$	1.65052	+	8.68921i	0.287319	+	1.51260i
$34$	0.00794180	−	0.00794180i	0.00136201	−	0.00136201i
$35$	1.82589	+	5.62385i	0.308631	+	0.950604i
$36$	4.69518	+	3.73331i	0.782529	+	0.622219i
$37$	0.0820203	+	0.306104i	0.0134841	+	0.0503232i	0.972340	−	0.233570i	$-0.0750407\pi$
$37$	0.0820203	+	0.306104i	0.0134841	+	0.0503232i	−0.958856	+	0.283893i	$0.908374\pi$
$38$	0.0194150	−	0.0336277i	0.00314952	−	0.00545514i
$39$	−2.88919	−	5.53648i	−0.462640	−	0.886546i
$40$	−0.0990689	−	0.171592i	−0.0156642	−	0.0271311i
$41$	1.21605	+	0.325838i	0.189914	+	0.0508874i	0.352523	−	0.935803i	$-0.385324\pi$
$41$	1.21605	+	0.325838i	0.189914	+	0.0508874i	−0.162608	+	0.986691i	$0.551991\pi$
$42$	−0.0986759	+	0.0241316i	−0.0152260	+	0.00372359i
$43$	−7.35892	−	4.24867i	−1.12222	−	0.647917i	−0.180257	−	0.983620i	$-0.557693\pi$
$43$	−7.35892	−	4.24867i	−1.12222	−	0.647917i	−0.941968	+	0.335703i	$0.891026\pi$
$44$	−9.86243	−	2.64263i	−1.48682	−	0.398391i
$45$	0.760188	+	6.66128i	0.113322	+	0.993005i
$46$	−0.161896	−	0.0433800i	−0.0238703	−	0.00639603i
$47$	−1.84390	+	6.88152i	−0.268960	+	1.00377i	0.690821	+	0.723026i	$0.257249\pi$
$47$	−1.84390	+	6.88152i	−0.268960	+	1.00377i	−0.959782	+	0.280748i	$0.909418\pi$
$48$	−6.23535	+	3.00828i	−0.899995	+	0.434207i
$49$	−2.85006	+	6.39352i	−0.407152	+	0.913361i
$50$	−3.15467e−5	0	0.000117734i	−4.46138e−6	0	1.66501e-5i
$51$	0.0649552	−	0.875158i	0.00909555	−	0.122547i
$52$	7.20576	−	0.226750i	0.999260	−	0.0314446i
$53$	5.68942	+	3.28479i	0.781501	+	0.451200i	0.836962	−	0.547261i	$-0.184329\pi$
$53$	5.68942	+	3.28479i	0.781501	+	0.451200i	−0.0554608	+	0.998461i	$0.517663\pi$
$54$	−0.115095	+	0.00455364i	−0.0156625	+	0.000619672i
$55$	−5.70601	−	9.88311i	−0.769399	−	1.33264i
$56$	0.0488217	−	0.229432i	0.00652408	−	0.0306591i
$57$	−0.566182	−	2.98068i	−0.0749926	−	0.394801i
$58$	0.159180	+	0.159180i	0.0209013	+	0.0209013i
$59$	−1.63897	+	6.11671i	−0.213376	+	0.796328i	0.773357	+	0.633971i	$0.218576\pi$
$59$	−1.63897	+	6.11671i	−0.213376	+	0.796328i	−0.986732	+	0.162357i	$0.948090\pi$
$60$	−7.30730	−	2.55107i	−0.943368	−	0.329342i
$61$	−12.3384			−1.57978			−0.789888	−	0.613251i	$-0.789861\pi$
$61$	−12.3384			−1.57978			−0.789888	+	0.613251i	$0.789861\pi$
$62$	−0.00242893	−	0.00420703i	−0.000308474	−	0.000534293i
$63$	−4.60948	+	6.46164i	−0.580739	+	0.814090i
$64$		−	7.98821i		−	0.998526i
$65$	5.87413	+	5.51572i	0.728596	+	0.684140i
$66$	0.176584	−	0.0851941i	0.0217360	−	0.0104867i
$67$	4.13223	+	4.13223i	0.504832	+	0.504832i	0.912936	−	0.408103i	$-0.133810\pi$
$67$	4.13223	+	4.13223i	0.504832	+	0.504832i	−0.408103	+	0.912936i	$0.633810\pi$
$68$	0.877350	+	0.506538i	0.106394	+	0.0614268i
$69$	−11.7950	+	5.69058i	−1.41996	+	0.685065i
$70$	0.109942	−	0.0713619i	0.0131406	−	0.00852938i
$71$	−0.744738	−	2.77940i	−0.0883841	−	0.329854i	0.907549	−	0.419945i	$-0.137951\pi$
$71$	−0.744738	−	2.77940i	−0.0883841	−	0.329854i	−0.995934	+	0.0900913i	$0.971284\pi$
$72$	0.106013	−	0.243935i	0.0124938	−	0.0287481i
$73$	0.193342	+	0.721562i	0.0226290	+	0.0844525i	0.976317	−	0.216345i	$-0.0694137\pi$
$73$	0.193342	+	0.721562i	0.0226290	+	0.0844525i	−0.953688	+	0.300798i	$0.902747\pi$
$74$	0.00608374	−	0.00351245i	0.000707220	−	0.000408314i
$75$	0.00413829	+	0.00857757i	0.000477849	+	0.000990452i
$76$	3.38313	+	0.906508i	0.388072	+	0.103984i
$77$	2.81196	−	13.2145i	0.320452	−	1.50593i
$78$	−0.101971	+	0.0936281i	−0.0115460	+	0.0106013i
$79$	1.05053	+	1.81957i	0.118194	+	0.204718i	0.919052	−	0.394136i	$-0.128956\pi$
$79$	1.05053	+	1.81957i	0.118194	+	0.204718i	−0.800858	+	0.598854i	$0.795623\pi$
$80$	6.31642	−	6.31642i	0.706197	−	0.706197i
$81$	−6.57994	+	6.14039i	−0.731105	+	0.682265i
$82$		−	0.0279075i		−	0.00308187i
$83$	−7.73187	+	7.73187i	−0.848683	+	0.848683i	−0.989969	−	0.141285i	$-0.954876\pi$
$83$	−7.73187	+	7.73187i	−0.848683	+	0.848683i	0.141285	+	0.989969i	$0.454876\pi$
$84$	−4.40616	−	8.03396i	−0.480751	−	0.876577i
$85$	0.293063	+	1.09373i	0.0317872	+	0.118631i
$86$	−0.0487522	+	0.181946i	−0.00525709	+	0.0196197i
$87$	17.5411	+	1.30192i	1.88060	+	0.139580i
$88$			0.452729i			0.0482611i
$89$	11.9130	−	3.19208i	1.26278	−	0.338360i	0.435517	−	0.900180i	$-0.356565\pi$
$89$	11.9130	−	3.19208i	1.26278	−	0.338360i	0.827259	+	0.561820i	$0.189899\pi$
$90$	0.138270	−	0.0544952i	0.0145750	−	0.00574430i
$91$	0.796471	+	9.50608i	0.0834929	+	0.996508i
$92$		−	15.1183i		−	1.57619i
$93$	−0.358358	−	0.125108i	−0.0371600	−	0.0129731i
$94$	0.157927			0.0162889
$95$	1.95735	+	3.39023i	0.200820	+	0.347830i
$96$	0.300686	+	0.348899i	0.0306887	+	0.0356094i
$97$	10.2262	−	2.74010i	1.03831	−	0.278215i	0.300899	−	0.953656i	$-0.402713\pi$
$97$	10.2262	−	2.74010i	1.03831	−	0.278215i	0.737414	+	0.675441i	$0.236047\pi$
$98$	0.153250	+	0.0243438i	0.0154806	+	0.00245910i
$99$	6.10598	−	14.0498i	0.613674	−	1.41206i
$100$	−0.0109943			−0.00109943
$101$	−6.03254			−0.600260			−0.300130	−	0.953898i	$-0.597030\pi$
$101$	−6.03254			−0.600260			−0.300130	+	0.953898i	$0.597030\pi$
$102$	−0.0191116	+	0.00363026i	−0.00189233	+	0.000359449i
$103$	−3.19510	+	1.84469i	−0.314823	+	0.181763i	−0.649082	−	0.760718i	$-0.724847\pi$
$103$	−3.19510	+	1.84469i	−0.314823	+	0.181763i	0.334260	+	0.942481i	$0.391514\pi$
$104$	−0.0924056	−	0.306016i	−0.00906112	−	0.0300074i
$105$	2.86715	−	9.83178i	0.279806	−	0.959484i
$106$	0.0376919	−	0.140668i	0.00366096	−	0.0136629i
$107$	−2.31100	−	1.33426i	−0.223413	−	0.128987i	0.384117	−	0.923285i	$-0.374506\pi$
$107$	−2.31100	−	1.33426i	−0.223413	−	0.128987i	−0.607530	+	0.794297i	$0.707839\pi$
$108$	−3.08371	−	9.92158i	−0.296730	−	0.954704i
$109$	−9.65515	+	2.58709i	−0.924796	+	0.247798i	−0.689634	−	0.724158i	$-0.742229\pi$
$109$	−9.65515	+	2.58709i	−0.924796	+	0.247798i	−0.235162	+	0.971956i	$0.575562\pi$
$110$	−0.178880	+	0.178880i	−0.0170556	+	0.0170556i
$111$	0.180917	−	0.518218i	0.0171719	−	0.0491871i
$112$	10.5608	−	0.551064i	0.997905	−	0.0520707i
$113$	9.40140	+	5.42790i	0.884409	+	0.510614i	0.872110	−	0.489310i	$-0.162751\pi$
$113$	9.40140	+	5.42790i	0.884409	+	0.510614i	0.0122996	+	0.999924i	$0.496085\pi$
$114$	−0.0605742	+	0.0292243i	−0.00567329	+	0.00273711i
$115$	11.9484	−	11.9484i	1.11419	−	1.11419i
$116$	−10.1527	+	17.5850i	−0.942654	+	1.63273i
$117$	−1.25958	+	10.7431i	−0.116448	+	0.993197i
$118$	0.140375			0.0129225
$119$	−0.608847	+	1.19426i	−0.0558129	+	0.109478i
$120$	−0.0254017	+	0.342243i	−0.00231885	+	0.0312424i
$121$			15.0756i			1.37050i
$122$	0.0707899	+	0.264191i	0.00640902	+	0.0239188i
$123$	−1.42353	−	1.65178i	−0.128355	−	0.148936i
$124$	0.309841	−	0.309841i	0.0278245	−	0.0278245i
$125$	−7.91004	−	7.91004i	−0.707495	−	0.707495i
$126$	0.164803	+	0.0616258i	0.0146818	+	0.00549006i
$127$	−9.44764	+	5.45460i	−0.838343	+	0.484017i	−0.856701	−	0.515814i	$-0.827490\pi$
$127$	−9.44764	+	5.45460i	−0.838343	+	0.484017i	0.0183577	+	0.999831i	$0.494156\pi$
$128$	−0.684765	+	0.183482i	−0.0605253	+	0.0162177i
$129$	6.39530	+	13.2557i	0.563075	+	1.16710i
$130$	0.0844009	−	0.157423i	0.00740245	−	0.0138069i
$131$	−12.1741	+	7.02869i	−1.06365	+	0.614100i	−0.926440	−	0.376442i	$-0.877147\pi$
$131$	−12.1741	+	7.02869i	−1.06365	+	0.614100i	−0.137212	+	0.990542i	$0.543814\pi$
$132$	11.5452	+	13.3963i	1.00488	+	1.16600i
$133$	−0.964592	+	4.53299i	−0.0836408	+	0.393060i
$134$	0.0647716	−	0.112188i	0.00559541	−	0.00969153i
$135$	5.40416	−	10.2785i	0.465116	−	0.884628i
$136$	0.0116262	−	0.0433894i	0.000996936	−	0.00372061i
$137$	4.07025	−	15.1904i	0.347745	−	1.29780i	−0.541628	−	0.840618i	$-0.682192\pi$
$137$	4.07025	−	15.1904i	0.347745	−	1.29780i	0.889373	−	0.457183i	$-0.151141\pi$
$138$	0.189519	+	0.219907i	0.0161330	+	0.0187198i
$139$	2.80733	−	4.86244i	0.238115	−	0.412427i	−0.722059	−	0.691832i	$-0.756804\pi$
$139$	2.80733	−	4.86244i	0.238115	−	0.412427i	0.960173	+	0.279405i	$0.0901373\pi$
$140$	8.78422	+	7.91296i	0.742402	+	0.668767i
$141$	9.34732	−	8.05565i	0.787187	−	0.678408i
$142$	−0.0552399	+	0.0318927i	−0.00463563	+	0.00267638i
$143$	−5.32223	−	17.6254i	−0.445067	−	1.47391i
$144$	11.8598	+	1.77024i	0.988314	+	0.147520i
$145$	−21.9219	+	5.87395i	−1.82051	+	0.487805i
$146$	0.0143409	−	0.00827971i	0.00118686	−	0.000685233i
$147$	10.3123	−	6.37626i	0.850543	−	0.525905i
$148$	0.448057	+	0.448057i	0.0368301	+	0.0368301i
$149$	−6.26675	+	6.26675i	−0.513392	+	0.513392i	−0.915564	−	0.402172i	$-0.868255\pi$
$149$	−6.26675	+	6.26675i	−0.513392	+	0.513392i	0.402172	+	0.915564i	$0.368255\pi$
$150$	0.000159921	0	0.000137822i	1.30575e−5	0	1.12531e-5i
$151$	−4.51925	−	16.8661i	−0.367772	−	1.37254i	−0.863624	−	0.504136i	$-0.831811\pi$
$151$	−4.51925	−	16.8661i	−0.367772	−	1.37254i	0.495853	−	0.868407i	$-0.334856\pi$
$152$		−	0.155301i		−	0.0125965i
$153$	−0.945998	+	1.18973i	−0.0764794	+	0.0961838i
$154$	−0.299082	+	0.0156061i	−0.0241007	+	0.00125757i
$155$	0.489752			0.0393378
$156$	−10.5381	−	6.69863i	−0.843724	−	0.536320i
$157$	4.58689	−	7.94472i	0.366073	−	0.634058i	−0.622874	−	0.782322i	$-0.714035\pi$
$157$	4.58689	−	7.94472i	0.366073	−	0.634058i	0.988948	+	0.148264i	$0.0473686\pi$
$158$	0.0329335	−	0.0329335i	0.00262005	−	0.00262005i
$159$	−4.94441	−	10.2484i	−0.392118	−	0.812754i
$160$	−0.514672	−	0.297146i	−0.0406884	−	0.0234914i
$161$	19.9773	−	1.04242i	1.57443	−	0.0821539i
$162$	0.169230	+	0.105661i	0.0132959	+	0.00830149i
$163$	8.11999	−	8.11999i	0.636007	−	0.636007i	−0.313561	−	0.949568i	$-0.601522\pi$
$163$	8.11999	−	8.11999i	0.636007	−	0.636007i	0.949568	+	0.313561i	$0.101522\pi$
$164$	2.43149	−	0.651517i	0.189868	−	0.0508749i
$165$	−1.46305	+	19.7120i	−0.113898	+	1.53458i
$166$	0.209916	+	0.121195i	0.0162926	+	0.00940655i
$167$	2.62822	−	9.80866i	0.203378	−	0.759017i	−0.786560	−	0.617514i	$-0.788140\pi$
$167$	2.62822	−	9.80866i	0.203378	−	0.759017i	0.989938	−	0.141503i	$-0.0451934\pi$
$168$	−0.293524	+	0.280912i	−0.0226459	+	0.0216728i
$169$	7.19499	+	10.8274i	0.553461	+	0.832875i
$170$	0.0217375	−	0.0125502i	0.00166719	−	0.000962554i
$171$	−2.09455	+	4.81954i	−0.160174	+	0.368559i
$172$	−16.9905			−1.29551
$173$	2.12483			0.161548			0.0807738	−	0.996732i	$-0.474261\pi$
$173$	2.12483			0.161548			0.0807738	+	0.996732i	$0.474261\pi$
$174$	−0.0727624	−	0.383060i	−0.00551610	−	0.0290397i
$175$	−0.000758064	−	0.0145279i	−5.73043e−5	−	0.00109820i
$176$	−19.7152	+	5.28266i	−1.48609	+	0.398196i
$177$	8.30847	−	7.16035i	0.624502	−	0.538205i
$178$	−0.136698	−	0.236768i	−0.0102460	−	0.0177465i
$179$	8.05614			0.602144			0.301072	−	0.953601i	$-0.402655\pi$
$179$	8.05614			0.602144			0.301072	+	0.953601i	$0.402655\pi$
$180$	7.97600	+	10.7748i	0.594496	+	0.803109i
$181$		−	12.0600i		−	0.896410i	−0.893931	−	0.448205i	$-0.852063\pi$
$181$		−	12.0600i		−	0.896410i	0.893931	−	0.448205i	$-0.147937\pi$
$182$	0.198975	−	0.0715938i	0.0147490	−	0.00530688i
$183$	17.6660	+	12.0260i	1.30591	+	0.888986i
$184$	−0.647506	+	0.173499i	−0.0477348	+	0.0127905i
$185$			0.708225i			0.0520697i
$186$	−0.000622788		0.00839098i	−4.56650e−5		0.000615256i
$187$	0.669625	−	2.49908i	0.0489679	−	0.182751i
$188$	3.68689	+	13.7597i	0.268894	+	1.00353i
$189$	12.8978	−	4.75892i	0.938175	−	0.346161i
$190$	0.0613618	−	0.0613618i	0.00445165	−	0.00445165i
$191$		−	6.38823i		−	0.462236i	−0.972926	−	0.231118i	$-0.925762\pi$
$191$		−	6.38823i		−	0.462236i	0.972926	−	0.231118i	$-0.0742383\pi$
$192$	−7.78592	+	11.4374i	−0.561900	+	0.825423i
$193$	9.53905	−	9.53905i	0.686636	−	0.686636i	−0.274851	−	0.961487i	$-0.588629\pi$
$193$	9.53905	−	9.53905i	0.686636	−	0.686636i	0.961487	+	0.274851i	$0.0886285\pi$
$194$	−0.117343	−	0.203243i	−0.00842470	−	0.0145920i
$195$	−3.03445	−	13.6227i	−0.217301	−	0.975541i
$196$	1.45671	+	13.9205i	0.104051	+	0.994325i
$197$	−0.653855	−	0.175200i	−0.0465852	−	0.0124825i	0.235451	−	0.971886i	$-0.424343\pi$
$197$	−0.653855	−	0.175200i	−0.0465852	−	0.0124825i	−0.282036	+	0.959404i	$0.591010\pi$
$198$	−0.335867	−	0.0501331i	−0.0238691	−	0.00356280i
$199$	−17.9225	+	10.3475i	−1.27049	+	0.733518i	−0.975080	−	0.221852i	$-0.928790\pi$
$199$	−17.9225	+	10.3475i	−1.27049	+	0.733518i	−0.295410	+	0.955370i	$0.595456\pi$
$200$	0.000126171	0	0.000470878i	8.92167e−6	0	3.32961e-5i
$201$	−1.88888	−	9.94405i	−0.133231	−	0.701399i
$202$	0.0346107	+	0.129169i	0.00243520	+	0.00908830i
$203$	−23.9369	−	12.2033i	−1.68004	−	0.856504i
$204$	−0.762465	−	1.58039i	−0.0533832	−	0.110649i
$205$	2.43659	+	1.40677i	0.170179	+	0.0982529i
$206$	0.0578300	+	0.0578300i	0.00402921	+	0.00402921i
$207$	22.4344	+	3.34866i	1.55930	+	0.232748i
$208$	12.2480	−	7.59477i	0.849244	−	0.526603i
$209$		−	8.94476i		−	0.618722i
$210$	−0.226969	−	0.00498335i	−0.0156623	−	0.000343884i
$211$	−7.78226	−	13.4793i	−0.535753	−	0.927951i	−0.999127	−	0.0417879i	$-0.986695\pi$
$211$	−7.78226	−	13.4793i	−0.535753	−	0.927951i	0.463374	−	0.886163i	$-0.346639\pi$
$212$	13.1359			0.902178
$213$	−1.64271	+	4.70538i	−0.112557	+	0.322407i
$214$	−0.0153102	+	0.0571384i	−0.00104658	+	0.00390590i
$215$	−13.4281	−	13.4281i	−0.915789	−	0.915789i
$216$	−0.389546	+	0.245934i	−0.0265053	+	0.0167337i
$217$	0.430788	+	0.388061i	0.0292438	+	0.0263433i
$218$	0.110790	+	0.191894i	0.00750363	+	0.0129967i
$219$	0.426466	−	1.22157i	0.0288179	−	0.0825459i
$220$	−19.7614	−	11.4092i	−1.33231	−	0.769210i
$221$	0.0574570	+	1.82589i	0.00386497	+	0.122823i
$222$	−0.0121341		0.000900607i	−0.000814388		6.04448e-5i
$223$	−3.31360	+	12.3665i	−0.221895	+	0.828124i	0.761730	+	0.647895i	$0.224350\pi$
$223$	−3.31360	+	12.3665i	−0.221895	+	0.828124i	−0.983625	+	0.180229i	$0.942316\pi$
$224$	−0.217261	−	0.669177i	−0.0145163	−	0.0447113i
$225$	0.00243521	−	0.0163147i	0.000162347	−	0.00108765i
$226$	0.0622835	−	0.232445i	0.00414304	−	0.0154620i
$227$	21.8666	+	5.85913i	1.45134	+	0.388884i	0.896488	−	0.443067i	$-0.146110\pi$
$227$	21.8666	+	5.85913i	1.45134	+	0.388884i	0.554848	+	0.831952i	$0.312776\pi$
$228$	−3.96036	−	4.59538i	−0.262282	−	0.304337i
$229$	0.314417	+	0.0842478i	0.0207773	+	0.00556725i	0.269193	−	0.963086i	$-0.413243\pi$
$229$	0.314417	+	0.0842478i	0.0207773	+	0.00556725i	−0.248415	+	0.968654i	$0.579910\pi$
$230$	−0.324392	−	0.187288i	−0.0213898	−	0.0123494i
$231$	−16.9059	+	16.1795i	−1.11233	+	1.06453i
$232$	0.869668	+	0.233027i	0.0570965	+	0.0152990i
$233$	5.50880	+	9.54151i	0.360893	+	0.625085i	0.988108	−	0.153761i	$-0.0491385\pi$
$233$	5.50880	+	9.54151i	0.360893	+	0.625085i	−0.627215	+	0.778846i	$0.715805\pi$
$234$	0.237258	−	0.0346664i	0.0155100	−	0.00226622i
$235$	−7.96080	+	13.7885i	−0.519306	+	0.899464i
$236$	3.27713	+	12.2304i	0.213323	+	0.796133i
$237$	0.269360	−	3.62916i	0.0174968	−	0.235739i
$238$	0.0290647	+	0.00618480i	0.00188399	+	0.000400901i
$239$	1.73546	−	1.73546i	0.112257	−	0.112257i	−0.648747	−	0.761004i	$-0.724707\pi$
$239$	1.73546	−	1.73546i	0.112257	−	0.112257i	0.761004	+	0.648747i	$0.224707\pi$
$240$	−15.2002	+	2.88729i	−0.981169	+	0.186374i
$241$	−10.8927	−	2.91870i	−0.701662	−	0.188010i	−0.109687	−	0.993966i	$-0.534985\pi$
$241$	−10.8927	−	2.91870i	−0.701662	−	0.188010i	−0.591975	+	0.805956i	$0.701652\pi$
$242$	0.322799	−	0.0864937i	0.0207503	−	0.00556002i
$243$	15.4059	−	2.37839i	0.988292	−	0.152574i
$244$	−21.3656	+	12.3354i	−1.36779	+	0.789694i
$245$	−9.85053	+	12.1531i	−0.629327	+	0.776433i
$246$	−0.0272008	+	0.0399575i	−0.00173426	+	0.00254760i
$247$	1.82570	+	6.04610i	0.116166	+	0.384704i
$248$	−0.0168261	−	0.00971453i	−0.00106846	−	0.000616873i
$249$	18.6064	−	3.53430i	1.17914	−	0.223977i
$250$	−0.123988	+	0.214753i	−0.00784166	+	0.0135822i
$251$	−8.41027	+	14.5670i	−0.530852	+	0.919462i	0.468500	+	0.883463i	$0.344794\pi$
$251$	−8.41027	+	14.5670i	−0.530852	+	0.919462i	−0.999352	+	0.0359985i	$0.988539\pi$
$252$	−1.52184	+	15.7975i	−0.0958668	+	0.995147i
$253$	−37.2940	+	9.99290i	−2.34466	+	0.628248i
$254$	0.170999	+	0.170999i	0.0107294	+	0.0107294i
$255$	0.646426	−	1.85162i	0.0404808	−	0.115953i
$256$	−7.98035	−	13.8224i	−0.498772	−	0.863898i
$257$	−7.91130	+	13.7028i	−0.493493	+	0.854755i	−0.999972	−	0.00749733i	$-0.997614\pi$
$257$	−7.91130	+	13.7028i	−0.493493	+	0.854755i	0.506479	+	0.862252i	$0.330947\pi$
$258$	0.247141	−	0.212989i	0.0153863	−	0.0132601i
$259$	−0.561170	+	0.622958i	−0.0348694	+	0.0387087i
$260$	15.6862	+	3.67847i	0.972814	+	0.228129i
$261$	−23.8461	−	18.9609i	−1.47603	−	1.17365i
$262$	0.220346	+	0.220346i	0.0136130	+	0.0136130i
$263$			13.3523i			0.823341i	0.911333	+	0.411670i	$0.135054\pi$
$263$			13.3523i			0.823341i	−0.911333	+	0.411670i	$0.864946\pi$
$264$	0.441264	−	0.648210i	0.0271579	−	0.0398946i
$265$	10.3817	+	10.3817i	0.637742	+	0.637742i
$266$	0.102595	−	0.00535339i	0.00629049	−	0.000328238i
$267$	−20.1681	−	7.04096i	−1.23427	−	0.430899i
$268$	11.2867	+	3.02426i	0.689444	+	0.184736i
$269$	0.126981	−	0.0733126i	0.00774217	−	0.00446995i	−0.496124	−	0.868252i	$-0.665244\pi$
$269$	0.126981	−	0.0733126i	0.00774217	−	0.00446995i	0.503866	+	0.863782i	$0.331911\pi$
$270$	−0.251088	−	0.0567433i	−0.0152808	−	0.00345329i
$271$	−1.02334	−	3.81915i	−0.0621633	−	0.231997i	0.927854	−	0.372944i	$-0.121652\pi$
$271$	−1.02334	−	3.81915i	−0.0621633	−	0.231997i	−0.990017	+	0.140948i	$0.954985\pi$
$272$	2.02516			0.122793
$273$	8.12498	−	14.3870i	0.491746	−	0.870739i
$274$	−0.348610			−0.0210603
$275$	0.00726702	+	0.0271209i	0.000438218	+	0.00163545i
$276$	−14.7354	+	21.6461i	−0.886968	+	1.30294i
$277$	1.15367	−	0.666072i	0.0693174	−	0.0400204i	−0.464941	−	0.885342i	$-0.653924\pi$
$277$	1.15367	−	0.666072i	0.0693174	−	0.0400204i	0.534258	+	0.845321i	$0.320591\pi$
$278$	−0.120221	−	0.0322132i	−0.00721040	−	0.00193202i
$279$	0.391153	+	0.528411i	0.0234177	+	0.0316351i
$280$	0.238099	−	0.467032i	0.0142291	−	0.0279105i
$281$	12.1579	+	12.1579i	0.725278	+	0.725278i	0.969675	−	0.244397i	$-0.0785901\pi$
$281$	12.1579	+	12.1579i	0.725278	+	0.725278i	−0.244397	+	0.969675i	$0.578590\pi$
$282$	−0.226117	−	0.153927i	−0.0134651	−	0.00916624i
$283$		−	16.5655i		−	0.984718i	−0.870392	−	0.492359i	$-0.836135\pi$
$283$		−	16.5655i		−	0.984718i	0.870392	−	0.492359i	$-0.163865\pi$
$284$	−4.06832	−	4.06832i	−0.241411	−	0.241411i
$285$	0.501872	−	6.76185i	0.0297284	−	0.400538i
$286$	−0.346861	+	0.215083i	−0.0205103	+	0.0127181i
$287$	1.02857	+	3.16806i	0.0607146	+	0.187005i
$288$	−0.0904541	−	0.792620i	−0.00533006	−	0.0467056i
$289$	8.37165	−	14.5001i	0.492450	−	0.852948i
$290$	0.251547	+	0.435692i	0.0147713	+	0.0255847i
$291$	−17.3124	−	6.04400i	−1.01487	−	0.354306i
$292$	1.05618	+	1.05618i	0.0618083	+	0.0618083i
$293$	17.6380	−	4.72608i	1.03042	−	0.276101i	0.296283	−	0.955100i	$-0.404253\pi$
$293$	17.6380	−	4.72608i	1.03042	−	0.276101i	0.734139	+	0.678999i	$0.237586\pi$
$294$	−0.195694	−	0.184225i	−0.0114131	−	0.0107442i
$295$	−7.07604	+	12.2561i	−0.411983	+	0.713576i
$296$	0.0140481	−	0.0243320i	0.000816527	−	0.00141427i
$297$	−22.4365	+	14.1649i	−1.30190	+	0.821933i
$298$	0.170139	+	0.0982296i	0.00985587	+	0.00569029i
$299$	23.1688	−	14.3666i	1.33989	−	0.830841i
$300$	0.0157414	+	0.0107159i	0.000908832	+	0.000618680i
$301$	−1.17151	−	22.4513i	−0.0675247	−	1.29407i
$302$	−0.335209	+	0.193533i	−0.0192891	+	0.0111366i
$303$	8.63729	+	5.87977i	0.496199	+	0.337784i
$304$	6.76294	−	1.81212i	0.387881	−	0.103932i
$305$	−26.6348	−	7.13678i	−1.52511	−	0.408651i
$306$	0.0309020	+	0.0134299i	0.00176655	+	0.000767736i
$307$	0.941330	−	0.941330i	0.0537245	−	0.0537245i	−0.679734	−	0.733459i	$-0.737905\pi$
$307$	0.941330	−	0.941330i	0.0537245	−	0.0537245i	0.733459	+	0.679734i	$0.237905\pi$
$308$	−8.34195	−	25.6937i	−0.475327	−	1.46404i
$309$	6.37267	+	0.472987i	0.362529	+	0.0269073i
$310$	−0.00280988	−	0.0104866i	−0.000159590	−	0.000595599i
$311$	0.0446914	−	0.0774078i	0.00253422	−	0.00438940i	−0.864756	−	0.502193i	$-0.832527\pi$
$311$	0.0446914	−	0.0774078i	0.00253422	−	0.00438940i	0.867290	+	0.497804i	$0.165860\pi$
$312$	−0.165962	+	0.528215i	−0.00939574	+	0.0299043i
$313$	−2.46373	−	4.26730i	−0.139258	−	0.241202i	0.787958	−	0.615729i	$-0.211138\pi$
$313$	−2.46373	−	4.26730i	−0.139258	−	0.241202i	−0.927216	+	0.374527i	$0.877805\pi$
$314$	−0.196429	−	0.0526331i	−0.0110852	−	0.00297026i
$315$	−13.6880	+	11.2824i	−0.771229	+	0.635694i
$316$	3.63825	+	2.10054i	0.204667	+	0.118165i
$317$	−18.1376	−	4.85995i	−1.01871	−	0.272962i	−0.289445	−	0.957195i	$-0.593471\pi$
$317$	−18.1376	−	4.85995i	−1.01871	−	0.272962i	−0.729264	+	0.684232i	$0.760137\pi$
$318$	−0.191072	+	0.164669i	−0.0107148	+	0.00923418i
$319$	50.0897	+	13.4215i	2.80449	+	0.751460i
$320$	4.62053	−	17.2440i	0.258295	−	0.963972i
$321$	2.00839	+	4.16284i	0.112097	+	0.232347i
$322$	−0.136937	−	0.421775i	−0.00763120	−	0.0235046i
$323$	−0.229703	+	0.857264i	−0.0127810	+	0.0476995i
$324$	−5.25512	+	17.2112i	−0.291951	+	0.956176i
$325$	−0.0104476	−	0.0168488i	−0.000579531	−	0.000934601i
$326$	−0.220453	−	0.127279i	−0.0122098	−	0.00704931i
$327$	16.3457	+	5.70649i	0.903917	+	0.315570i
$328$	−0.0558081	−	0.0966625i	−0.00308149	−	0.00533729i
$329$	−17.9279	+	5.82061i	−0.988394	+	0.320901i
$330$	0.430468	−	0.0817677i	0.0236965	−	0.00450116i
$331$	21.6629	+	21.6629i	1.19070	+	1.19070i	0.976871	+	0.213831i	$0.0685942\pi$
$331$	21.6629	+	21.6629i	1.19070	+	1.19070i	0.213831	+	0.976871i	$0.431406\pi$
$332$	−5.65873	+	21.1187i	−0.310563	+	1.15904i
$333$	−0.764129	+	0.565641i	−0.0418740	+	0.0309970i
$334$	−0.225103			−0.0123171
$335$	6.53004	+	11.3104i	0.356774	+	0.617951i
$336$	−15.6580	−	9.50439i	−0.854211	−	0.518507i
$337$			15.1629i			0.825976i	0.910737	+	0.412988i	$0.135515\pi$
$337$			15.1629i			0.825976i	−0.910737	+	0.412988i	$0.864485\pi$
$338$	0.190556	−	0.216180i	0.0103649	−	0.0117586i
$339$	−8.17033	−	16.9349i	−0.443752	−	0.919778i
$340$	1.60093	+	1.60093i	0.0868228	+	0.0868228i
$341$	−0.969120	−	0.559522i	−0.0524808	−	0.0302998i
$342$	0.115213	+	0.0171973i	0.00623003	+	0.000929922i
$343$	−18.2942	+	2.88474i	−0.987795	+	0.155761i
$344$	0.194985	+	0.727693i	0.0105129	+	0.0392346i
$345$	−28.7534	+	5.46171i	−1.54803	+	0.294049i
$346$	−0.0121909	−	0.0454969i	−0.000655385	−	0.00244593i
$347$	4.52778	−	2.61412i	0.243064	−	0.140333i	−0.373520	−	0.927622i	$-0.621849\pi$
$347$	4.52778	−	2.61412i	0.243064	−	0.140333i	0.616584	+	0.787289i	$0.288516\pi$
$348$	31.6761	−	15.2823i	1.69802	−	0.819218i
$349$	31.5501	+	8.45382i	1.68884	+	0.452523i	0.970089	−	0.242748i	$-0.0780488\pi$
$349$	31.5501	+	8.45382i	1.68884	+	0.452523i	0.718748	+	0.695271i	$0.244715\pi$
$350$	−0.000306722	0	9.95831e-5i	−1.63950e−5	0	5.32294e-6i
$351$	12.2745	−	14.1541i	0.655162	−	0.755488i
$352$	0.678954	+	1.17598i	0.0361884	+	0.0626801i
$353$	−9.54213	+	9.54213i	−0.507876	+	0.507876i	−0.913874	−	0.405998i	$-0.866924\pi$
$353$	−9.54213	+	9.54213i	−0.507876	+	0.507876i	0.405998	+	0.913874i	$0.366924\pi$
$354$	−0.200986	−	0.136820i	−0.0106823	−	0.00727190i
$355$		−	6.43063i		−	0.341302i
$356$	17.4376	−	17.4376i	0.924190	−	0.924190i
$357$	2.03575	−	1.11649i	0.107744	−	0.0590911i
$358$	−0.0462209	−	0.172499i	−0.00244285	−	0.00911684i
$359$	1.48522	−	5.54292i	0.0783869	−	0.292544i	−0.915593	−	0.402106i	$-0.868278\pi$
$359$	1.48522	−	5.54292i	0.0783869	−	0.292544i	0.993980	+	0.109562i	$0.0349449\pi$
$360$	0.369946	−	0.465260i	0.0194979	−	0.0245214i
$361$		−	15.9317i		−	0.838508i
$362$	−0.258229	+	0.0691922i	−0.0135722	+	0.00363666i
$363$	14.6938	−	21.5849i	0.771224	−	1.13292i
$364$	10.8829	+	15.6647i	0.570421	+	0.821053i
$365$			1.66946i			0.0873836i
$366$	0.156145	−	0.447262i	0.00816184	−	0.0233788i
$367$	25.4420			1.32806			0.664031	−	0.747705i	$-0.268844\pi$
$367$	25.4420			1.32806			0.664031	+	0.747705i	$0.268844\pi$
$368$	−15.1108	−	26.1727i	−0.787707	−	1.36435i
$369$	0.428234	+	3.75247i	0.0222930	+	0.195346i
$370$	0.0151646	−	0.00406333i	0.000788368	−	0.000211243i
$371$	0.905732	+	17.3578i	0.0470232	+	0.901174i
$372$	−0.745619	+	0.141631i	−0.0386586	+	0.00734321i
$373$	−5.43429			−0.281377			−0.140688	−	0.990054i	$-0.544932\pi$
$373$	−5.43429			−0.281377			−0.140688	+	0.990054i	$0.544932\pi$
$374$	−0.0573523			−0.00296561
$375$	3.61574	+	19.0352i	0.186716	+	0.982973i
$376$	0.547007	−	0.315815i	0.0282097	−	0.0162869i
$377$	−36.5970	+	1.15163i	−1.88484	+	0.0593118i
$378$	−0.175897	−	0.248864i	−0.00904718	−	0.0128002i
$379$	−1.46724	+	5.47583i	−0.0753672	+	0.281274i	−0.993316	−	0.115424i	$-0.963177\pi$
$379$	−1.46724	+	5.47583i	−0.0753672	+	0.281274i	0.917949	+	0.396698i	$0.129844\pi$
$380$	6.77879	+	3.91373i	0.347744	+	0.200770i
$381$	18.8435	+	1.39858i	0.965380	+	0.0716516i
$382$	−0.136785	+	0.0366515i	−0.00699854	+	0.00187525i
$383$	10.1934	−	10.1934i	0.520859	−	0.520859i	−0.396972	−	0.917831i	$-0.629939\pi$
$383$	10.1934	−	10.1934i	0.520859	−	0.520859i	0.917831	+	0.396972i	$0.129939\pi$
$384$	1.15927	+	0.404717i	0.0591588	+	0.0206531i
$385$	13.7136	−	26.8994i	0.698911	−	1.37092i
$386$	−0.258980	−	0.149522i	−0.0131817	−	0.00761047i
$387$	3.76336	−	25.2127i	0.191303	−	1.28163i
$388$	14.9685	−	14.9685i	0.759912	−	0.759912i
$389$	13.9948	−	24.2397i	0.709564	−	1.22900i	−0.255454	−	0.966821i	$-0.582225\pi$
$389$	13.9948	−	24.2397i	0.709564	−	1.22900i	0.965019	−	0.262181i	$-0.0844416\pi$
$390$	−0.274280	+	0.143132i	−0.0138887	+	0.00724777i
$391$	3.83087			0.193736
$392$	0.579491	−	0.222144i	0.0292687	−	0.0112200i
$393$	24.2813	+	1.80219i	1.22483	+	0.0909083i
$394$			0.0150056i			0.000755969i
$395$	1.21529	+	4.53553i	0.0611480	+	0.228207i
$396$	−3.47308	−	30.4335i	−0.174529	−	1.52934i
$397$	15.0584	−	15.0584i	0.755761	−	0.755761i	−0.219787	−	0.975548i	$-0.570536\pi$
$397$	15.0584	−	15.0584i	0.755761	−	0.755761i	0.975548	+	0.219787i	$0.0705363\pi$
$398$	0.324390	+	0.324390i	0.0162602	+	0.0162602i
$399$	5.79928	−	5.55009i	0.290327	−	0.277852i
$400$	−0.0190333	+	0.0109889i	−0.000951664	+	0.000549444i
$401$	9.60225	−	2.57292i	0.479514	−	0.128485i	−0.0109625	−	0.999940i	$-0.503490\pi$
$401$	9.60225	−	2.57292i	0.479514	−	0.128485i	0.490476	+	0.871455i	$0.336823\pi$
$402$	−0.202085	+	0.0974972i	−0.0100791	+	0.00486272i
$403$	0.769267	+	0.180396i	0.0383199	+	0.00898618i
$404$	−10.4461	+	6.03105i	−0.519712	+	0.300056i
$405$	−17.7558	+	9.44921i	−0.882291	+	0.469535i
$406$	−0.123964	+	0.582553i	−0.00615222	+	0.0289116i
$407$	0.809118	−	1.40143i	0.0401065	−	0.0694665i
$408$	−0.0589368	+	0.0507926i	−0.00291781	+	0.00251461i
$409$	−3.02543	+	11.2911i	−0.149598	+	0.558307i	0.849910	+	0.526928i	$0.176656\pi$
$409$	−3.02543	+	11.2911i	−0.149598	+	0.558307i	−0.999508	+	0.0313785i	$0.990010\pi$
$410$	0.0161422	−	0.0602436i	0.000797207	−	0.00297522i
$411$	−20.6334	+	17.7822i	−1.01777	+	0.877129i
$412$	−3.68848	+	6.38863i	−0.181718	+	0.314745i
$413$	−15.9354	+	5.17371i	−0.784128	+	0.254582i
$414$	−0.0570122	−	0.499580i	−0.00280200	−	0.0245530i
$415$	−21.1630	+	12.2184i	−1.03885	+	0.599780i
$416$	−0.698958	−	0.656311i	−0.0342692	−	0.0321783i
$417$	−8.75879	+	4.22572i	−0.428920	+	0.206935i
$418$	−0.191526	+	0.0513192i	−0.00936783	+	0.00251010i
$419$	6.57161	−	3.79412i	0.321044	−	0.185355i	−0.330814	−	0.943696i	$-0.607323\pi$
$419$	6.57161	−	3.79412i	0.321044	−	0.185355i	0.651858	+	0.758341i	$0.273990\pi$
$420$	−4.86453	−	19.8914i	−0.237365	−	0.970602i
$421$	6.77694	+	6.77694i	0.330288	+	0.330288i	0.852696	−	0.522408i	$-0.174966\pi$
$421$	6.77694	+	6.77694i	0.330288	+	0.330288i	−0.522408	+	0.852696i	$0.674966\pi$
$422$	−0.243969	+	0.243969i	−0.0118762	+	0.0118762i
$423$	−21.2350	+	2.42335i	−1.03248	+	0.117827i
$424$	−0.150749	−	0.562603i	−0.00732102	−	0.0273224i
$425$		−	0.00278588i		−	0.000135135i
$426$	0.110177	+	0.00817744i	0.00533808	+	0.000396198i
$427$	−17.7732	−	27.3820i	−0.860106	−	1.32511i
$428$	−5.33571			−0.257911
$429$	−9.55880	+	30.4233i	−0.461503	+	1.46885i
$430$	−0.210482	+	0.364565i	−0.0101503	+	0.0175809i
$431$	8.86838	−	8.86838i	0.427175	−	0.427175i	−0.460490	−	0.887665i	$-0.652326\pi$
$431$	8.86838	−	8.86838i	0.427175	−	0.427175i	0.887665	+	0.460490i	$0.152326\pi$
$432$	−15.2552	−	14.0940i	−0.733967	−	0.678100i
$433$	−22.9588	−	13.2553i	−1.10333	−	0.637009i	−0.166238	−	0.986086i	$-0.553162\pi$
$433$	−22.9588	−	13.2553i	−1.10333	−	0.637009i	−0.937094	+	0.349077i	$0.886495\pi$
$434$	0.00583760	−	0.0114505i	0.000280214	−	0.000549642i
$435$	37.1126	+	12.9565i	1.77941	+	0.621217i
$436$	−14.1326	+	14.1326i	−0.676831	+	0.676831i
$437$	12.7931	−	3.42789i	0.611975	−	0.163978i
$438$	−0.0286031	−	0.00212295i	−0.00136671	−	0.000101439i
$439$	21.0036	+	12.1264i	1.00245	+	0.578762i	0.908971	−	0.416859i	$-0.136869\pi$
$439$	21.0036	+	12.1264i	1.00245	+	0.578762i	0.0934748	+	0.995622i	$0.470203\pi$
$440$	−0.261867	+	0.977300i	−0.0124840	+	0.0465910i
$441$	−20.9798	−	0.921713i	−0.999036	−	0.0438911i
$442$	0.0387665	−	0.0117061i	0.00184394	−	0.000556800i
$443$	−11.0334	+	6.37012i	−0.524212	+	0.302654i	−0.738656	−	0.674082i	$-0.764539\pi$
$443$	−11.0334	+	6.37012i	−0.524212	+	0.302654i	0.214444	+	0.976736i	$0.431206\pi$
$444$	−0.204811	−	1.07823i	−0.00971988	−	0.0511706i
$445$	27.5628			1.30660
$446$	0.283804			0.0134385
$447$	15.0807	−	2.86458i	0.713292	−	0.135490i
$448$	17.7278	−	11.5068i	0.837558	−	0.543646i
$449$	38.8364	−	10.4062i	1.83280	−	0.491098i	0.834592	−	0.550868i	$-0.185703\pi$
$449$	38.8364	−	10.4062i	1.83280	−	0.491098i	0.998212	+	0.0597698i	$0.0190367\pi$
$450$	−0.000363304	0	4.14603e-5i	−1.71263e−5	0	1.95446e-6i
$451$	−3.21435	−	5.56741i	−0.151358	−	0.262159i
$452$	21.7063			1.02098
$453$	−9.96837	+	28.5534i	−0.468355	+	1.34156i
$454$		−	0.501825i		−	0.0235518i
$455$	−3.77916	+	20.9814i	−0.177170	+	0.983621i
$456$	−0.151368	+	0.222357i	−0.00708845	+	0.0104128i
$457$	27.9677	−	7.49392i	1.30827	−	0.350551i	0.463701	−	0.885992i	$-0.346521\pi$
$457$	27.9677	−	7.49392i	1.30827	−	0.350551i	0.844573	+	0.535441i	$0.179855\pi$
$458$		−	0.00721567i		−	0.000337166i
$459$	2.51406	−	0.781392i	0.117346	−	0.0364723i
$460$	8.74469	−	32.6356i	0.407723	−	1.52164i
$461$	−8.16601	−	30.4760i	−0.380329	−	1.41941i	−0.845400	−	0.534134i	$-0.820638\pi$
$461$	−8.16601	−	30.4760i	−0.380329	−	1.41941i	0.465071	−	0.885274i	$-0.346029\pi$
$462$	0.443432	+	0.269163i	0.0206303	+	0.0125226i
$463$	−23.6315	+	23.6315i	−1.09825	+	1.09825i	−0.103634	+	0.994615i	$0.533047\pi$
$463$	−23.6315	+	23.6315i	−1.09825	+	1.09825i	−0.994615	+	0.103634i	$0.966953\pi$
$464$			40.5908i			1.88438i
$465$	−0.701219	−	0.477350i	−0.0325183	−	0.0221366i
$466$	0.172698	−	0.172698i	0.00800006	−	0.00800006i
$467$	−2.75550	−	4.77266i	−0.127509	−	0.220852i	0.795202	−	0.606345i	$-0.207365\pi$
$467$	−2.75550	−	4.77266i	−0.127509	−	0.220852i	−0.922711	+	0.385493i	$0.874032\pi$
$468$	8.55930	+	19.8622i	0.395654	+	0.918132i
$469$	−3.21804	+	15.1228i	−0.148595	+	0.698306i
$470$	0.340914	+	0.0913478i	0.0157252	+	0.00421356i
$471$	−14.3110	+	6.90440i	−0.659414	+	0.318138i
$472$	0.486213	−	0.280715i	0.0223798	−	0.0129210i
$473$	11.2304	+	41.9125i	0.516376	+	1.92714i
$474$	−0.0792532	+	0.0150542i	−0.00364022	+	0.000691461i
$475$	−0.00249282	−	0.00930335i	−0.000114379	−	0.000426867i
$476$	0.139671	+	2.67671i	0.00640179	+	0.122687i
$477$	−2.90958	+	19.4928i	−0.133220	+	0.892512i
$478$	−0.0471166	−	0.0272028i	−0.00215506	−	0.00124423i
$479$	−25.8860	−	25.8860i	−1.18276	−	1.18276i	−0.979025	−	0.203738i	$-0.934691\pi$
$479$	−25.8860	−	25.8860i	−1.18276	−	1.18276i	−0.203738	−	0.979025i	$-0.565309\pi$
$480$	0.447278	+	0.927087i	0.0204154	+	0.0423155i
$481$	−0.260869	+	1.11243i	−0.0118946	+	0.0507224i
$482$			0.249981i			0.0113863i
$483$	−29.6192	−	17.9789i	−1.34772	−	0.818068i
$484$	15.0718	+	26.1052i	0.685084	+	1.18660i
$485$	23.6601			1.07435
$486$	−0.139316	−	0.316227i	−0.00631948	−	0.0143444i
$487$	−8.23755	+	30.7430i	−0.373279	+	1.39310i	0.482564	+	0.875861i	$0.339706\pi$
$487$	−8.23755	+	30.7430i	−0.373279	+	1.39310i	−0.855843	+	0.517236i	$0.826961\pi$
$488$	0.773511	+	0.773511i	0.0350152	+	0.0350152i
$489$	−19.5404	+	3.71172i	−0.883649	+	0.167850i
$490$	0.316739	+	0.141194i	0.0143088	+	0.00637848i
$491$	−16.4064	−	28.4167i	−0.740411	−	1.28243i	−0.952309	−	0.305137i	$-0.901298\pi$
$491$	−16.4064	−	28.4167i	−0.740411	−	1.28243i	0.211898	−	0.977292i	$-0.432036\pi$
$492$	−4.11639	−	1.43709i	−0.185581	−	0.0647889i
$493$	−4.45592	−	2.57263i	−0.200685	−	0.115865i
$494$	0.118985	−	0.0737805i	0.00535338	−	0.00331954i
$495$	21.3076	−	26.7973i	0.957704	−	1.20445i
$496$	0.226708	−	0.846085i	0.0101795	−	0.0379903i
$497$	5.09538	−	5.65641i	0.228559	−	0.253725i
$498$	−0.182428	−	0.378125i	−0.00817481	−	0.0169442i
$499$	1.58919	−	5.93095i	0.0711421	−	0.265506i	−0.921189	−	0.389116i	$-0.872781\pi$
$499$	1.58919	−	5.93095i	0.0711421	−	0.265506i	0.992331	+	0.123610i	$0.0394472\pi$
$500$	−21.6053	−	5.78912i	−0.966219	−	0.258898i
$501$	−13.3233	+	11.4822i	−0.595242	+	0.512988i
$502$	0.360162	+	0.0965052i	0.0160748	+	0.00430724i
$503$	13.5178	+	7.80449i	0.602727	+	0.347985i	0.770114	−	0.637907i	$-0.220199\pi$
$503$	13.5178	+	7.80449i	0.602727	+	0.347985i	−0.167386	+	0.985891i	$0.553533\pi$
$504$	0.694061	−	0.116114i	0.0309159	−	0.00517213i
$505$	−13.0224	−	3.48933i	−0.579487	−	0.155273i
$506$	0.427937	+	0.741209i	0.0190241	+	0.0329508i
$507$	0.251514	−	22.5153i	0.0111701	−	0.999938i
$508$	−10.9065	+	18.8906i	−0.483899	+	0.838137i
$509$	−3.66252	−	13.6687i	−0.162338	−	0.605855i	−0.998365	−	0.0571656i	$-0.981794\pi$
$509$	−3.66252	−	13.6687i	−0.162338	−	0.605855i	0.836026	−	0.548689i	$-0.184873\pi$
$510$	−0.0433558	−	0.00321792i	−0.00191983	−	0.000142492i
$511$	−1.32282	+	1.46847i	−0.0585180	+	0.0649611i
$512$	−1.25275	+	1.25275i	−0.0553640	+	0.0553640i
$513$	7.69643	−	4.85903i	0.339806	−	0.214531i
$514$	0.338794	+	0.0907797i	0.0149436	+	0.00400412i
$515$	−7.96423	+	2.13401i	−0.350946	+	0.0940356i
$516$	24.3268	+	16.5603i	1.07093	+	0.729024i
$517$	31.5056	−	18.1898i	1.38562	−	0.799986i
$518$	0.0165584	+	0.00844169i	0.000727536	+	0.000370907i
$519$	−3.04229	−	2.07102i	−0.133542	−	0.0909076i
$520$	−0.0224694	−	0.714043i	−0.000985348	−	0.0313128i
$521$	14.9447	+	8.62833i	0.654739	+	0.378014i	0.790270	−	0.612759i	$-0.209940\pi$
$521$	14.9447	+	8.62833i	0.654739	+	0.378014i	−0.135530	+	0.990773i	$0.543274\pi$
$522$	−0.269179	+	0.619379i	−0.0117817	+	0.0271095i
$523$	−0.326033	+	0.564706i	−0.0142564	+	0.0246929i	−0.873066	−	0.487603i	$-0.837871\pi$
$523$	−0.326033	+	0.564706i	−0.0142564	+	0.0246929i	0.858809	+	0.512296i	$0.171205\pi$
$524$	−14.0539	+	24.3421i	−0.613949	+	1.06339i
$525$	−0.0130746	+	0.0215396i	−0.000570622	+	0.000940067i
$526$	0.285901	−	0.0766070i	0.0124659	−	0.00334022i
$527$	0.0785117	+	0.0785117i	0.00342002	+	0.00342002i
$528$	33.3767	+	11.6523i	1.45254	+	0.507100i
$529$	−17.0843	−	29.5909i	−0.742795	−	1.28656i
$530$	0.162730	−	0.281857i	0.00706854	−	0.0122431i
$531$	−18.8750	+	2.15402i	−0.819103	+	0.0934764i
$532$	2.86156	+	8.81379i	0.124064	+	0.382126i
$533$	3.30905	+	3.10715i	0.143331	+	0.134586i
$534$	−0.0350500	+	0.472237i	−0.00151676	+	0.0204357i
$535$	−4.21697	−	4.21697i	−0.182315	−	0.182315i
$536$		−	0.518109i		−	0.0223789i
$537$	−11.5347	−	7.85213i	−0.497757	−	0.338844i
$538$	−0.00229831	−	0.00229831i	−9.90871e−5	−	9.90871e-5i
$539$	33.3766	−	12.7947i	1.43763	−	0.551106i
$540$	−0.917938	−	23.2013i	−0.0395017	−	0.998423i
$541$	15.7886	+	4.23054i	0.678804	+	0.181885i	0.581718	−	0.813391i	$-0.302381\pi$
$541$	15.7886	+	4.23054i	0.678804	+	0.181885i	0.0970868	+	0.995276i	$0.469048\pi$
$542$	−0.0759046	+	0.0438235i	−0.00326038	+	0.00188238i
$543$	−11.7546	+	17.2673i	−0.504436	+	0.741009i
$544$	−0.0348714	−	0.130142i	−0.00149510	−	0.00557978i
$545$	−22.3389			−0.956892
$546$	−0.354670	−	0.0914296i	−0.0151785	−	0.00391282i
$547$	12.1821			0.520870			0.260435	−	0.965491i	$-0.416134\pi$
$547$	12.1821			0.520870			0.260435	+	0.965491i	$0.416134\pi$
$548$	−8.13850	−	30.3733i	−0.347659	−	1.29748i
$549$	−13.5724	−	34.4372i	−0.579258	−	1.46975i
$550$	0.000539021	0	0.000311204i	2.29839e−5	0	1.32698e-5i
$551$	−17.1824	−	4.60401i	−0.731995	−	0.196138i
$552$	1.09619	+	0.382696i	0.0466571	+	0.0162886i
$553$	−2.52480	+	4.95242i	−0.107366	+	0.210598i
$554$	−0.0208810	−	0.0208810i	−0.000887148	−	0.000887148i
$555$	0.690290	−	1.01403i	0.0293012	−	0.0430430i
$556$		−	11.2266i		−	0.476112i
$557$	24.0227	+	24.0227i	1.01787	+	1.01787i	0.999837	+	0.0180366i	$0.00574152\pi$
$557$	24.0227	+	24.0227i	1.01787	+	1.01787i	0.0180366	+	0.999837i	$0.494258\pi$
$558$	0.00907019	−	0.0114071i	0.000383972	−	0.000482899i
$559$	−16.1458	−	26.0380i	−0.682893	−	1.10129i
$560$	23.1163	+	4.91901i	0.976842	+	0.207866i
$561$	−3.39455	+	2.92547i	−0.143318	+	0.123513i
$562$	0.190571	−	0.330079i	0.00803876	−	0.0139235i
$563$	−0.658951	−	1.14134i	−0.0277715	−	0.0481016i	0.851806	−	0.523858i	$-0.175508\pi$
$563$	−0.658951	−	1.14134i	−0.0277715	−	0.0481016i	−0.879577	+	0.475756i	$0.842174\pi$
$564$	8.13238	−	23.2944i	0.342435	−	0.980871i
$565$	17.1551	+	17.1551i	0.721720	+	0.721720i
$566$	−0.354702	+	0.0950421i	−0.0149092	+	0.00399492i
$567$	−23.1052	−	5.75741i	−0.970329	−	0.241788i
$568$	−0.127555	+	0.220932i	−0.00535210	+	0.00927011i
$569$	3.95059	−	6.84262i	0.165617	−	0.286857i	−0.771257	−	0.636524i	$-0.780372\pi$
$569$	3.95059	−	6.84262i	0.165617	−	0.286857i	0.936874	+	0.349666i	$0.113705\pi$
$570$	−0.147665	+	0.0280490i	−0.00618499	+	0.00117484i
$571$	13.1002	+	7.56338i	0.548224	+	0.316518i	0.748406	−	0.663241i	$-0.230820\pi$
$571$	13.1002	+	7.56338i	0.548224	+	0.316518i	−0.200181	+	0.979759i	$0.564153\pi$
$572$	−26.8372	−	25.1997i	−1.12212	−	1.05365i
$573$	−6.22645	+	9.14656i	−0.260114	+	0.382103i
$574$	0.0619335	−	0.0402001i	0.00258505	−	0.00167792i
$575$	−0.0360042	+	0.0207870i	−0.00150148	+	0.000866878i
$576$	22.2955	−	8.78713i	0.928979	−	0.366130i
$577$	−18.7903	+	5.03484i	−0.782249	+	0.209603i	−0.627776	−	0.778394i	$-0.716035\pi$
$577$	−18.7903	+	5.03484i	−0.782249	+	0.209603i	−0.154473	+	0.987997i	$0.549368\pi$
$578$	−0.358508	−	0.0960620i	−0.0149120	−	0.00399565i
$579$	−22.9553	+	4.36038i	−0.953992	+	0.181211i
$580$	−32.0880	+	32.0880i	−1.33238	+	1.33238i
$581$	−28.2965	−	6.02132i	−1.17394	−	0.249806i
$582$	−0.0300871	+	0.405371i	−0.00124715	+	0.0168032i
$583$	−8.68260	−	32.4039i	−0.359597	−	1.34203i
$584$	0.0331148	−	0.0573564i	0.00137030	−	0.00237343i
$585$	−8.93303	+	22.4624i	−0.369335	+	0.928704i
$586$	−0.202390	−	0.350550i	−0.00836067	−	0.0144811i
$587$	27.7466	+	7.43467i	1.14522	+	0.306862i	0.781049	−	0.624469i	$-0.214685\pi$
$587$	27.7466	+	7.43467i	1.14522	+	0.306862i	0.364174	+	0.931331i	$0.381351\pi$
$588$	11.4823	−	21.3510i	0.473523	−	0.880502i
$589$	0.332440	+	0.191934i	0.0136979	+	0.00790851i
$590$	0.303025	+	0.0811954i	0.0124754	+	0.00334276i
$591$	0.765416	+	0.888145i	0.0314850	+	0.0365334i
$592$	1.22351	+	0.327839i	0.0502861	+	0.0134741i
$593$	−6.60367	+	24.6452i	−0.271180	+	1.01206i	0.687178	+	0.726489i	$0.258849\pi$
$593$	−6.60367	+	24.6452i	−0.271180	+	1.01206i	−0.958358	+	0.285569i	$0.907817\pi$
$594$	0.432026	+	0.399142i	0.0177262	+	0.0163770i
$595$	−2.00509	+	2.22586i	−0.0822008	+	0.0912515i
$596$	−4.58645	+	17.1169i	−0.187868	+	0.701135i
$597$	35.7466	+	2.65316i	1.46301	+	0.108586i
$598$	−0.440546	−	0.413665i	−0.0180152	−	0.0169160i
$599$	7.67535	+	4.43137i	0.313606	+	0.181061i	0.648539	−	0.761181i	$-0.275380\pi$
$599$	7.67535	+	4.43137i	0.313606	+	0.181061i	−0.334933	+	0.942242i	$0.608714\pi$
$600$	0.000278303	0	0.000797172i	1.13617e−5	0	3.25444e-5i
$601$	9.61701	+	16.6571i	0.392286	+	0.679459i	0.992751	−	0.120192i	$-0.0383511\pi$
$601$	9.61701	+	16.6571i	0.392286	+	0.679459i	−0.600465	+	0.799651i	$0.705018\pi$
$602$	−0.474008	+	0.153895i	−0.0193191	+	0.00627231i
$603$	−6.98777	+	16.0788i	−0.284564	+	0.654778i
$604$	−24.6876	−	24.6876i	−1.00452	−	1.00452i
$605$	−8.71998	+	32.5434i	−0.354518	+	1.32308i
$606$	0.0763429	−	0.218676i	0.00310122	−	0.00888312i
$607$	−18.7015			−0.759069			−0.379534	−	0.925178i	$-0.623916\pi$
$607$	−18.7015			−0.759069			−0.379534	+	0.925178i	$0.623916\pi$
$608$	−0.232903	−	0.403400i	−0.00944548	−	0.0163600i
$609$	22.3782	+	40.8032i	0.906810	+	1.65343i
$610$			0.611253i			0.0247489i
$611$	−17.5831	+	18.7257i	−0.711338	+	0.757561i
$612$	−0.448678	+	3.00593i	−0.0181368	+	0.121507i
$613$	−16.8943	−	16.8943i	−0.682356	−	0.682356i	0.278174	−	0.960531i	$-0.410271\pi$
$613$	−16.8943	−	16.8943i	−0.682356	−	0.682356i	−0.960531	+	0.278174i	$0.910271\pi$
$614$	−0.0255565	−	0.0147551i	−0.00103138	−	0.000595466i
$615$	−2.11753	−	4.38908i	−0.0853871	−	0.176985i
$616$	−1.00471	+	0.652145i	−0.0404811	+	0.0262757i
$617$	7.10167	+	26.5038i	0.285903	+	1.06700i	0.948177	+	0.317742i	$0.102925\pi$
$617$	7.10167	+	26.5038i	0.285903	+	1.06700i	−0.662275	+	0.749261i	$0.730409\pi$
$618$	−0.0264346	−	0.139166i	−0.00106335	−	0.00559807i
$619$	1.63066	+	6.08572i	0.0655419	+	0.244606i	0.990923	−	0.134433i	$-0.0429213\pi$
$619$	1.63066	+	6.08572i	0.0655419	+	0.244606i	−0.925381	+	0.379039i	$0.876255\pi$
$620$	0.848067	−	0.489632i	0.0340592	−	0.0196641i
$621$	−28.8574	−	26.6609i	−1.15801	−	1.06986i
$622$	−0.00191387		0.000512820i	−7.67393e−5		2.05622e-5i
$623$	24.2444	+	21.8397i	0.971331	+	0.874990i
$624$	−24.9389	−	1.06374i	−0.998355	−	0.0425835i
$625$	−12.4862	−	21.6268i	−0.499450	−	0.865072i
$626$	−0.0772365	+	0.0772365i	−0.00308699	+	0.00308699i
$627$	−8.71825	+	12.8070i	−0.348173	+	0.511461i
$628$		−	18.3430i		−	0.731967i
$629$	−0.113535	+	0.113535i	−0.00452693	+	0.00452693i
$630$	0.320113	+	0.228356i	0.0127536	+	0.00909792i
$631$	3.03163	+	11.3142i	0.120687	+	0.450411i	0.999649	−	0.0264805i	$-0.00843000\pi$
$631$	3.03163	+	11.3142i	0.120687	+	0.450411i	−0.878962	+	0.476892i	$0.841763\pi$
$632$	0.0482121	−	0.179930i	0.00191777	−	0.00715723i
$633$	−1.99540	+	26.8846i	−0.0793102	+	1.06857i
$634$			0.416247i			0.0165313i
$635$	−23.5496	+	6.31008i	−0.934536	+	0.250408i
$636$	−18.8078	−	12.8033i	−0.745778	−	0.507682i
$637$	−19.9490	+	15.4608i	−0.790408	+	0.612581i
$638$		−	1.14953i		−	0.0455103i
$639$	6.93823	−	5.13598i	0.274472	−	0.203176i
$640$	−1.58432			−0.0626259
$641$	−10.2130	−	17.6894i	−0.403388	−	0.698688i	0.590745	−	0.806859i	$-0.298834\pi$
$641$	−10.2130	−	17.6894i	−0.403388	−	0.698688i	−0.994132	+	0.108171i	$0.965501\pi$
$642$	0.0776123	−	0.0668873i	0.00306311	−	0.00263983i
$643$	−12.3698	+	3.31448i	−0.487817	+	0.130710i	−0.494340	−	0.869269i	$-0.664590\pi$
$643$	−12.3698	+	3.31448i	−0.487817	+	0.130710i	0.00652305	+	0.999979i	$0.497924\pi$
$644$	33.5511	−	21.7775i	1.32210	−	0.858153i
$645$	6.13809	+	32.3142i	0.241687	+	1.27237i
$646$	0.0196737			0.000774051
$647$	−38.9058			−1.52954			−0.764772	−	0.644301i	$-0.777148\pi$
$647$	−38.9058			−1.52954			−0.764772	+	0.644301i	$0.777148\pi$
$648$	0.797452	+	0.0275564i	0.0313269	+	0.00108252i
$649$	28.0041	−	16.1682i	1.09926	−	0.634657i
$650$	−0.000300825	0	0.000320373i	−1.17993e−5	0	1.25661e-5i
$651$	−0.238562	−	0.975498i	−0.00935000	−	0.0382328i
$652$	5.94279	−	22.1788i	0.232738	−	0.868588i
$653$	−31.3149	−	18.0797i	−1.22545	−	0.707512i	−0.259373	−	0.965777i	$-0.583516\pi$
$653$	−31.3149	−	18.0797i	−1.22545	−	0.707512i	−0.966074	+	0.258265i	$0.916849\pi$
$654$	0.0284070	−	0.382734i	0.00111080	−	0.0149661i
$655$	−30.3455	+	8.13106i	−1.18570	+	0.317707i
$656$	3.55820	−	3.55820i	0.138925	−	0.138925i
$657$	−1.80124	+	1.33336i	−0.0702731	+	0.0520192i
$658$	0.227490	+	0.350477i	0.00886846	+	0.0136630i
$659$	−23.6766	−	13.6697i	−0.922309	−	0.532495i	−0.0379381	−	0.999280i	$-0.512079\pi$
$659$	−23.6766	−	13.6697i	−0.922309	−	0.532495i	−0.884371	+	0.466785i	$0.845412\pi$
$660$	17.1737	+	35.5965i	0.668485	+	1.38559i
$661$	−9.19640	+	9.19640i	−0.357698	+	0.357698i	−0.862964	−	0.505266i	$-0.831395\pi$
$661$	−9.19640	+	9.19640i	−0.357698	+	0.357698i	0.505266	+	0.862964i	$0.331395\pi$
$662$	0.339560	−	0.588135i	0.0131974	−	0.0228585i
$663$	1.69739	−	2.67029i	0.0659212	−	0.103705i
$664$	0.969440			0.0376216
$665$	−4.70422	+	9.22736i	−0.182422	+	0.357822i
$666$	0.0164956	+	0.0131163i	0.000639192	+	0.000508246i
$667$			76.7833i			2.97306i
$668$	−5.25515	−	19.6125i	−0.203328	−	0.758830i
$669$	16.7977	−	14.4765i	0.649437	−	0.559694i
$670$	0.204713	−	0.204713i	0.00790875	−	0.00790875i
$671$	44.5515	+	44.5515i	1.71989	+	1.71989i
$672$	−0.341160	+	1.16988i	−0.0131605	+	0.0451290i
$673$	15.8762	−	9.16613i	0.611983	−	0.353328i	−0.161758	−	0.986830i	$-0.551717\pi$
$673$	15.8762	−	9.16613i	0.611983	−	0.353328i	0.773741	+	0.633502i	$0.218383\pi$
$674$	0.324669	−	0.0869948i	0.0125058	−	0.00335091i
$675$	−0.0193883	+	0.0209856i	−0.000746255	+	0.000807737i
$676$	23.2837	+	11.5557i	0.895529	+	0.444452i
$677$	12.4515	−	7.18887i	0.478550	−	0.276291i	−0.241262	−	0.970460i	$-0.577561\pi$
$677$	12.4515	−	7.18887i	0.478550	−	0.276291i	0.719812	+	0.694169i	$0.244228\pi$
$678$	−0.315735	+	0.272105i	−0.0121257	+	0.0104501i
$679$	20.8115	+	18.7474i	0.798674	+	0.719458i
$680$	0.0501945	−	0.0869395i	0.00192487	−	0.00333398i
$681$	−25.5975	−	29.7019i	−0.980897	−	1.13818i
$682$	−0.00642034	+	0.0239610i	−0.000245847	+	0.000917515i
$683$	4.90238	−	18.2959i	0.187584	−	0.700074i	−0.806478	−	0.591264i	$-0.798629\pi$
$683$	4.90238	−	18.2959i	0.187584	−	0.700074i	0.994063	−	0.108810i	$-0.0347041\pi$
$684$	1.19138	+	10.4397i	0.0455535	+	0.399171i
$685$	17.5728	−	30.4370i	0.671422	−	1.16294i
$686$	0.166728	+	0.375166i	0.00636572	+	0.0143239i
$687$	−0.368063	−	0.427079i	−0.0140425	−	0.0162941i
$688$	−29.4140	+	16.9822i	−1.12140	+	0.647439i
$689$	12.4828	+	20.1308i	0.475557	+	0.766923i
$690$	0.281914	+	0.584333i	0.0107323	+	0.0222452i
$691$	−15.9753	+	4.28057i	−0.607729	+	0.162841i	−0.549543	−	0.835465i	$-0.685198\pi$
$691$	−15.9753	+	4.28057i	−0.607729	+	0.162841i	−0.0581860	+	0.998306i	$0.518532\pi$
$692$	3.67940	−	2.12430i	0.139870	−	0.0807539i
$693$	39.9754	−	6.68775i	1.51854	−	0.254047i
$694$	−0.0819511	−	0.0819511i	−0.00311082	−	0.00311082i
$695$	8.87267	−	8.87267i	0.336560	−	0.336560i
$696$	−1.01805	−	1.18129i	−0.0385891	−	0.0447766i
$697$	0.165090	+	0.616125i	0.00625324	+	0.0233374i
$698$		−	0.724055i		−	0.0274059i
$699$	1.41248	−	19.0307i	0.0534249	−	0.719807i
$700$	−0.0158370	−	0.0243990i	−0.000598582	−	0.000922194i
$701$	−23.0828			−0.871826			−0.435913	−	0.899989i	$-0.643574\pi$
$701$	−23.0828			−0.871826			−0.435913	+	0.899989i	$0.643574\pi$
$702$	−0.373491	−	0.181615i	−0.0140965	−	0.00685461i
$703$	−0.277554	+	0.480737i	−0.0104681	+	0.0181314i
$704$	−28.8437	+	28.8437i	−1.08709	+	1.08709i
$705$	24.8375	−	11.9830i	0.935434	−	0.451305i
$706$	0.259063	+	0.149570i	0.00974997	+	0.00562915i
$707$	−8.68972	−	13.3877i	−0.326811	−	0.503494i
$708$	7.22856	−	20.7055i	0.271666	−	0.778159i
$709$	4.92652	−	4.92652i	0.185020	−	0.185020i	−0.608519	−	0.793539i	$-0.708236\pi$
$709$	4.92652	−	4.92652i	0.185020	−	0.185020i	0.793539	+	0.608519i	$0.208236\pi$
$710$	−0.137693	+	0.0368947i	−0.00516753	+	0.00138463i
$711$	−3.92292	+	4.93363i	−0.147121	+	0.185026i
$712$	−0.946956	−	0.546725i	−0.0354887	−	0.0204894i
$713$	0.428850	−	1.60049i	0.0160605	−	0.0599388i
$714$	−0.0355862	−	0.0371840i	−0.00133178	−	0.00139158i
$715$	−1.29416	−	41.1263i	−0.0483987	−	1.53804i
$716$	13.9502	−	8.05416i	0.521344	−	0.300998i
$717$	−4.17630	+	0.793291i	−0.155967	+	0.0296260i
$718$	−0.127206			−0.00474730
$719$	19.5482			0.729024			0.364512	−	0.931199i	$-0.381236\pi$
$719$	19.5482			0.729024			0.364512	+	0.931199i	$0.381236\pi$
$720$	24.5776	+	10.6813i	0.915953	+	0.398069i
$721$	−8.69628	−	4.43346i	−0.323866	−	0.165111i
$722$	−0.341130	+	0.0914054i	−0.0126955	+	0.00340176i
$723$	12.7512	+	14.7958i	0.474224	+	0.550262i
$724$	−12.0570	−	20.8833i	−0.448095	−	0.776123i
$725$	0.0558382			0.00207378
$726$	−0.546481	−	0.190784i	−0.0202818	−	0.00708066i
$727$			23.0323i			0.854219i	0.904200	+	0.427110i	$0.140468\pi$
$727$			23.0323i			0.854219i	−0.904200	+	0.427110i	$0.859532\pi$
$728$	0.546016	−	0.645879i	0.0202367	−	0.0239379i
$729$	−24.3762	−	11.6105i	−0.902821	−	0.430017i
$730$	0.0357466	−	0.00957827i	0.00132304	−	0.000354508i
$731$		−	4.30529i		−	0.159237i
$732$	42.6139	+	3.16285i	1.57505	+	0.116902i
$733$	−11.2072	+	41.8258i	−0.413947	+	1.54487i	0.372988	+	0.927836i	$0.378333\pi$
$733$	−11.2072	+	41.8258i	−0.413947	+	1.54487i	−0.786935	+	0.617035i	$0.788334\pi$
$734$	−0.145970	−	0.544766i	−0.00538784	−	0.0201077i
$735$	25.9492	−	7.79954i	0.957149	−	0.287690i
$736$	−1.42173	+	1.42173i	−0.0524057	+	0.0524057i
$737$		−	29.8412i		−	1.09921i
$738$	0.0778913	−	0.0306986i	0.00286722	−	0.00113003i
$739$	−7.64901	+	7.64901i	−0.281373	+	0.281373i	−0.833657	−	0.552283i	$-0.813757\pi$
$739$	−7.64901	+	7.64901i	−0.281373	+	0.281373i	0.552283	+	0.833657i	$0.313757\pi$
$740$	0.708051	+	1.22638i	0.0260285	+	0.0450826i
$741$	3.27898	−	10.4362i	0.120456	−	0.383382i
$742$	0.366471	−	0.118981i	0.0134536	−	0.00436795i
$743$	7.62029	+	2.04185i	0.279561	+	0.0749083i	0.395875	−	0.918304i	$-0.370441\pi$
$743$	7.62029	+	2.04185i	0.279561	+	0.0749083i	−0.116314	+	0.993212i	$0.537108\pi$
$744$	0.0146228	+	0.0303091i	0.000536096	+	0.00111118i
$745$	−17.1528	+	9.90316i	−0.628429	+	0.362824i
$746$	0.0311784	+	0.116359i	0.00114152	+	0.00426022i
$747$	−30.0852	−	13.0749i	−1.10076	−	0.478386i
$748$	−1.33892	−	4.99692i	−0.0489558	−	0.182706i
$749$	−0.367902	−	7.05063i	−0.0134428	−	0.257624i
$750$	0.386838	−	0.186632i	0.0141253	−	0.00681483i
$751$	0.619065	+	0.357417i	0.0225900	+	0.0130423i	0.511252	−	0.859431i	$-0.329182\pi$
$751$	0.619065	+	0.357417i	0.0225900	+	0.0130423i	−0.488662	+	0.872473i	$0.662515\pi$
$752$	20.1356	+	20.1356i	0.734272	+	0.734272i
$753$	26.2398	−	12.6595i	0.956232	−	0.461339i
$754$	0.234628	+	0.777009i	0.00854465	+	0.0282970i
$755$		−	39.0226i		−	1.42018i
$756$	17.5764	−	21.1353i	0.639246	−	0.768683i
$757$	−4.88834	−	8.46685i	−0.177670	−	0.307733i	0.763412	−	0.645912i	$-0.223523\pi$
$757$	−4.88834	−	8.46685i	−0.177670	−	0.307733i	−0.941082	+	0.338179i	$0.890189\pi$
$758$	0.125667			0.00456442
$759$	63.1368	+	22.0419i	2.29172	+	0.800071i
$760$	0.0898288	−	0.335246i	0.00325843	−	0.0121606i
$761$	10.8806	+	10.8806i	0.394421	+	0.394421i	0.876260	−	0.481839i	$-0.160031\pi$
$761$	10.8806	+	10.8806i	0.394421	+	0.394421i	−0.481839	+	0.876260i	$0.660031\pi$
$762$	−0.0781649	−	0.411501i	−0.00283161	−	0.0149071i
$763$	−19.6494	−	17.7005i	−0.711355	−	0.640800i
$764$	−6.38666	−	11.0620i	−0.231061	−	0.400210i
$765$	−2.73027	+	2.02107i	−0.0987133	+	0.0730719i
$766$	−0.276745	−	0.159779i	−0.00999920	−	0.00577304i
$767$	−15.6290	+	16.6445i	−0.564329	+	0.601000i
$768$	−2.04620	+	27.5689i	−0.0738358	+	0.994808i
$769$	9.26070	−	34.5614i	0.333949	−	1.24632i	−0.571054	−	0.820912i	$-0.693465\pi$
$769$	9.26070	−	34.5614i	0.333949	−	1.24632i	0.905004	−	0.425404i	$-0.139868\pi$
$770$	−0.654651	−	0.139306i	−0.0235920	−	0.00502023i
$771$	24.6830	−	11.9085i	0.888938	−	0.428873i
$772$	6.98135	−	26.0548i	0.251264	−	0.937732i
$773$	33.2547	+	8.91057i	1.19609	+	0.320491i	0.801290	−	0.598276i	$-0.204148\pi$
$773$	33.2547	+	8.91057i	1.19609	+	0.320491i	0.394799	+	0.918767i	$0.370814\pi$
$774$	−0.561448	+	0.0640727i	−0.0201808	+	0.00230304i
$775$	−0.00116390		0.000311867i	−4.18087e−5		1.12026e-5i
$776$	−0.812873	−	0.469312i	−0.0291804	−	0.0168473i
$777$	1.41066	−	0.344982i	0.0506071	−	0.0123762i
$778$	−0.599315	−	0.160586i	−0.0214865	−	0.00575729i
$779$	1.10263	+	1.90980i	0.0395057	+	0.0684258i
$780$	−18.8739	−	20.5557i	−0.675793	−	0.736012i
$781$	−7.34673	+	12.7249i	−0.262887	+	0.455333i
$782$	−0.0219790	−	0.0820269i	−0.000785969	−	0.00293328i
$783$	15.6617	+	50.3902i	0.559703	+	1.80080i
$784$	16.4356	+	22.6433i	0.586985	+	0.808688i
$785$	14.4970	−	14.4970i	0.517421	−	0.517421i
$786$	−0.100722	−	0.530253i	−0.00359263	−	0.0189135i
$787$	−14.2902	−	3.82904i	−0.509390	−	0.136491i	−0.00503542	−	0.999987i	$-0.501603\pi$
$787$	−14.2902	−	3.82904i	−0.509390	−	0.136491i	−0.504354	+	0.863497i	$0.668269\pi$
$788$	−1.30739	+	0.350314i	−0.0465738	+	0.0124794i
$789$	13.0142	−	19.1177i	0.463318	−	0.680607i
$790$	0.0901425	−	0.0520438i	0.00320713	−	0.00185164i
$791$	1.49666	+	28.6827i	0.0532153	+	1.01984i
$792$	−1.26359	+	0.498007i	−0.0448997	+	0.0176959i
$793$	−39.2073	−	21.0207i	−1.39229	−	0.746466i
$794$	−0.408827	−	0.236037i	−0.0145087	−	0.00837663i
$795$	−4.74556	−	24.9831i	−0.168308	−	0.886060i
$796$	−20.6900	+	35.8361i	−0.733338	+	1.27018i
$797$	14.0517	−	24.3382i	0.497736	−	0.862104i	−0.502261	−	0.864716i	$-0.667498\pi$
$797$	14.0517	−	24.3382i	0.497736	−	0.862104i	0.999997	+	0.00261256i	$0.000831604\pi$
$798$	−0.152111	−	0.0923318i	−0.00538469	−	0.00326851i
$799$	−3.48661	+	0.934235i	−0.123347	+	0.0330508i
$800$	0.00103391	+	0.00103391i	3.65542e−5	+	3.65542e-5i
$801$	22.0137	+	29.7385i	0.777817	+	1.05076i
$802$	−0.110183	−	0.190842i	−0.00389069	−	0.00673888i
$803$	1.90729	−	3.30352i	0.0673068	−	0.116579i
$804$	−13.2124	−	15.3310i	−0.465967	−	0.540681i
$805$	43.7278	+	9.30500i	1.54120	+	0.327958i
$806$	−0.000550895	−	0.0175066i	−1.94044e−5	−	0.000616644i
$807$	−0.253266	−	0.0187977i	−0.00891537	−	0.000661709i
$808$	0.378187	+	0.378187i	0.0133046	+	0.0133046i
$809$		−	49.9234i		−	1.75521i	−0.479383	−	0.877606i	$-0.659139\pi$
$809$		−	49.9234i		−	1.75521i	0.479383	−	0.877606i	$-0.340861\pi$
$810$	0.304198	+	0.325974i	0.0106884	+	0.0114536i
$811$	21.3148	+	21.3148i	0.748463	+	0.748463i	0.974191	−	0.225727i	$-0.0724758\pi$
$811$	21.3148	+	21.3148i	0.748463	+	0.748463i	−0.225727	+	0.974191i	$0.572476\pi$
$812$	−53.6500	+	2.79946i	−1.88275	+	0.0982417i
$813$	−2.25723	+	6.46562i	−0.0791646	+	0.226759i
$814$	−0.0346498	−	0.00928438i	−0.00121447	−	0.000325417i
$815$	22.2253	−	12.8318i	0.778518	−	0.449478i
$816$	−2.89959	−	1.97387i	−0.101506	−	0.0690994i
$817$	−3.85240	−	14.3774i	−0.134778	−	0.503000i
$818$	0.259123			0.00906001
$819$	−25.6558	+	12.6798i	−0.896488	+	0.443068i
$820$	5.62569			0.196457
$821$	0.443388	+	1.65475i	0.0154744	+	0.0577511i	0.973231	−	0.229828i	$-0.0738163\pi$
$821$	0.443388	+	1.65475i	0.0154744	+	0.0577511i	−0.957757	+	0.287579i	$0.907150\pi$
$822$	0.499134	+	0.339781i	0.0174093	+	0.0118512i
$823$	35.6226	−	20.5667i	1.24172	−	0.716910i	0.272279	−	0.962218i	$-0.412223\pi$
$823$	35.6226	−	20.5667i	1.24172	−	0.716910i	0.969445	+	0.245308i	$0.0788892\pi$
$824$	0.315950	+	0.0846587i	0.0110067	+	0.00294922i
$825$	0.0160293	−	0.0459143i	0.000558068	−	0.00159853i
$826$	0.202206	+	0.311526i	0.00703566	+	0.0108394i
$827$	−11.3816	−	11.3816i	−0.395778	−	0.395778i	0.480963	−	0.876741i	$-0.340287\pi$
$827$	−11.3816	−	11.3816i	−0.395778	−	0.395778i	−0.876741	+	0.480963i	$0.840287\pi$
$828$	42.1959	−	16.6303i	1.46641	−	0.577942i
$829$		−	15.2726i		−	0.530438i	−0.964188	−	0.265219i	$-0.914556\pi$
$829$		−	15.2726i		−	0.530438i	0.964188	−	0.265219i	$-0.0854443\pi$
$830$	0.383041	+	0.383041i	0.0132956	+	0.0132956i
$831$	−2.30101	−	0.170784i	−0.0798212	−	0.00592442i
$832$	13.6093	−	25.3838i	0.471818	−	0.880024i
$833$	−3.52738	+	0.369122i	−0.122216	+	0.0127893i
$834$	0.140734	+	0.163299i	0.00487321	+	0.00565459i
$835$	11.3470	−	19.6536i	0.392680	−	0.680141i
$836$	−8.94256	−	15.4890i	−0.309285	−	0.535697i
$837$	−0.0450167	−	1.13782i	−0.00155601	−	0.0393287i
$838$	−0.118944	−	0.118944i	−0.00410884	−	0.00410884i
$839$	−53.3362	+	14.2914i	−1.84137	+	0.493393i	−0.998966	−	0.0454555i	$-0.985526\pi$
$839$	−53.3362	+	14.2914i	−1.84137	+	0.493393i	−0.842402	+	0.538849i	$0.818859\pi$
$840$	−0.796111	+	0.436621i	−0.0274684	+	0.0150648i
$841$	37.0640	−	64.1967i	1.27807	−	2.21368i
$842$	0.106227	−	0.183990i	0.00366081	−	0.00634071i
$843$	−5.55746	−	29.2574i	−0.191409	−	1.00768i
$844$	−26.9519	−	15.5607i	−0.927723	−	0.535621i
$845$	9.26898	+	27.5346i	0.318863	+	0.947221i
$846$	0.173721	+	0.440782i	0.00597266	+	0.0151544i
$847$	−33.4563	+	21.7160i	−1.14957	+	0.746169i
$848$	22.7409	−	13.1295i	0.780925	−	0.450867i
$849$	−16.1460	+	23.7182i	−0.554130	+	0.814008i
$850$	−5.96514e−5	0	1.59836e-5i	−2.04603e−6	0	5.48231e-7i
$851$	2.31445	+	0.620155i	0.0793383	+	0.0212586i
$852$	1.85966	+	9.79026i	0.0637110	+	0.335409i
$853$	−34.8338	+	34.8338i	−1.19269	+	1.19269i	−0.216378	+	0.976310i	$0.569424\pi$
$853$	−34.8338	+	34.8338i	−1.19269	+	1.19269i	−0.976310	+	0.216378i	$0.930576\pi$
$854$	−0.484333	+	0.537661i	−0.0165736	+	0.0183984i
$855$	−7.30919	+	9.19235i	−0.249969	+	0.314372i
$856$	0.0612332	+	0.228525i	0.00209291	+	0.00781084i
$857$	10.8381	−	18.7721i	0.370222	−	0.641244i	−0.619377	−	0.785093i	$-0.712615\pi$
$857$	10.8381	−	18.7721i	0.370222	−	0.641244i	0.989600	+	0.143850i	$0.0459482\pi$
$858$	0.706267	+	0.0301249i	0.0241116	+	0.00102845i
$859$	15.0629	+	26.0897i	0.513938	+	0.890167i	0.999869	+	0.0161701i	$0.00514734\pi$
$859$	15.0629	+	26.0897i	0.513938	+	0.890167i	−0.485931	+	0.873997i	$0.661519\pi$
$860$	−36.6772	−	9.82763i	−1.25068	−	0.335120i
$861$	1.61514	−	5.53850i	0.0550439	−	0.188752i
$862$	−0.240771	−	0.139009i	−0.00820070	−	0.00473468i
$863$	15.8765	+	4.25408i	0.540441	+	0.144811i	0.518705	−	0.854953i	$-0.326414\pi$
$863$	15.8765	+	4.25408i	0.540441	+	0.144811i	0.0217355	+	0.999764i	$0.493081\pi$
$864$	−0.643037	+	1.22302i	−0.0218766	+	0.0416081i
$865$	4.58684	+	1.22904i	0.155957	+	0.0417886i
$866$	−0.152100	+	0.567646i	−0.00516858	+	0.0192894i
$867$	−26.1193	+	12.6014i	−0.887058	+	0.427966i
$868$	1.13393	+	0.241293i	0.0384881	+	0.00819003i
$869$	2.77684	−	10.3633i	0.0941979	−	0.351551i
$870$	0.0644977	−	0.868994i	0.00218668	−	0.0294617i
$871$	6.09083	+	20.1708i	0.206380	+	0.683461i
$872$	0.767480	+	0.443105i	0.0259902	+	0.0150054i
$873$	18.8967	+	25.5277i	0.639557	+	0.863982i
$874$	−0.146796	−	0.254259i	−0.00496546	−	0.00860043i
$875$	6.16006	−	28.9485i	0.208248	−	0.978637i
$876$	−0.482789	−	2.54166i	−0.0163119	−	0.0858747i
$877$	1.32005	+	1.32005i	0.0445748	+	0.0445748i	0.729043	−	0.684468i	$-0.239965\pi$
$877$	1.32005	+	1.32005i	0.0445748	+	0.0445748i	−0.684468	+	0.729043i	$0.739965\pi$
$878$	0.139147	−	0.519303i	0.00469598	−	0.0175256i
$879$	−29.8602	−	10.4246i	−1.00716	−	0.351613i
$880$	−45.6145			−1.53766
$881$	7.40677	+	12.8289i	0.249540	+	0.432217i	0.963398	−	0.268074i	$-0.0863871\pi$
$881$	7.40677	+	12.8289i	0.249540	+	0.432217i	−0.713858	+	0.700291i	$0.753054\pi$
$882$	0.100632	+	0.454508i	0.00338847	+	0.0153041i
$883$		−	23.7386i		−	0.798868i	−0.916762	−	0.399434i	$-0.869207\pi$
$883$		−	23.7386i		−	0.798868i	0.916762	−	0.399434i	$-0.130793\pi$
$884$	1.92494	+	3.10432i	0.0647427	+	0.104410i
$885$	22.0771	−	10.6512i	0.742112	−	0.358036i
$886$	0.199700	+	0.199700i	0.00670905	+	0.00670905i
$887$	48.6425	+	28.0838i	1.63325	+	0.942960i	0.983080	+	0.183176i	$0.0586377\pi$
$887$	48.6425	+	28.0838i	1.63325	+	0.942960i	0.650175	+	0.759785i	$0.274696\pi$
$888$	−0.0438296	+	0.0211458i	−0.00147082	+	0.000709607i
$889$	−25.7142	−	13.1094i	−0.862426	−	0.439675i
$890$	−0.158137	−	0.590177i	−0.00530078	−	0.0197828i
$891$	45.9304	+	1.58715i	1.53873	+	0.0531715i
$892$	6.62557	+	24.7270i	0.221841	+	0.827920i
$893$	−10.8075	+	6.23969i	−0.361658	+	0.208803i
$894$	−0.147860	−	0.306474i	−0.00494517	−	0.0102500i
$895$	17.3907	+	4.65982i	0.581307	+	0.155761i
$896$	−1.39358	−	1.25536i	−0.0465562	−	0.0419385i
$897$	−47.1755	−	2.01221i	−1.57514	−	0.0671856i
$898$	−0.445636	−	0.771864i	−0.0148711	−	0.0257574i
$899$	−1.57363	+	1.57363i	−0.0524836	+	0.0524836i
$900$	−0.0120938	−	0.0306856i	−0.000403128	−	0.00102285i
$901$			3.32856i			0.110890i
$902$	−0.100768	+	0.100768i	−0.00335521	+	0.00335521i
$903$	−20.2054	+	33.2873i	−0.672394	+	1.10773i
$904$	−0.249103	−	0.929666i	−0.00828505	−	0.0309202i
$905$	6.97571	−	26.0337i	0.231880	−	0.865389i
$906$	0.668579	+	0.0496227i	0.0222121	+	0.00164860i
$907$		−	18.4717i		−	0.613344i	−0.951815	−	0.306672i	$-0.900785\pi$
$907$		−	18.4717i		−	0.613344i	0.951815	−	0.306672i	$-0.0992154\pi$
$908$	43.7224	−	11.7154i	1.45098	−	0.388789i
$909$	−6.63587	−	16.8371i	−0.220098	−	0.558452i
$910$	0.470937	−	0.0394576i	0.0156114	−	0.00130801i
$911$			26.5459i			0.879504i	0.898119	+	0.439752i	$0.144934\pi$
$911$			26.5459i			0.879504i	−0.898119	+	0.439752i	$0.855066\pi$
$912$	−11.4493	−	3.99711i	−0.379124	−	0.132357i
$913$	55.8363			1.84791
$914$	−0.320921	−	0.555851i	−0.0106151	−	0.0183859i
$915$	31.1793	+	36.1787i	1.03076	+	1.19603i
$916$	0.628679	−	0.168454i	0.0207721	−	0.00556588i
$917$	−33.1348	−	16.8925i	−1.09421	−	0.557840i
$918$	−0.0311553	−	0.0493482i	−0.00102828	−	0.00162873i
$919$	15.4725			0.510389			0.255195	−	0.966890i	$-0.417860\pi$
$919$	15.4725			0.510389			0.255195	+	0.966890i	$0.417860\pi$
$920$	−1.49812			−0.0493915
$921$	−2.26527	+	0.430289i	−0.0746433	+	0.0141785i
$922$	−0.605702	+	0.349702i	−0.0199477	+	0.0115168i
$923$	2.36867	−	10.1008i	0.0779657	−	0.332471i
$924$	−13.0992	+	44.9186i	−0.430932	+	1.47771i
$925$	0.000450988	−	0.00168311i	1.48284e−5	−	5.53403e-5i
$926$	0.641582	+	0.370417i	0.0210837	+	0.0121727i
$927$	−8.66328	−	6.88851i	−0.284539	−	0.226248i
$928$	2.60847	−	0.698937i	0.0856272	−	0.0229437i
$929$	−39.7906	+	39.7906i	−1.30549	+	1.30549i	−0.380848	+	0.924638i	$0.624368\pi$
$929$	−39.7906	+	39.7906i	−1.30549	+	1.30549i	−0.924638	+	0.380848i	$0.875632\pi$
$930$	−0.00619790	+	0.0177533i	−0.000203237	+	0.000582153i
$931$	−11.4493	+	4.38899i	−0.375234	+	0.143843i
$932$	19.0783	+	11.0149i	0.624932	+	0.360805i
$933$	−0.139436	+	0.0672717i	−0.00456493	+	0.00220238i
$934$	−0.0863832	+	0.0863832i	−0.00282655	+	0.00282655i
$935$	2.89102	−	5.00740i	0.0945466	−	0.163760i
$936$	0.752460	−	0.594531i	0.0245949	−	0.0194328i
$937$	51.3488			1.67749			0.838746	−	0.544523i	$-0.183289\pi$
$937$	51.3488			1.67749			0.838746	+	0.544523i	$0.183289\pi$
$938$	0.342273	−	0.0178598i	0.0111756	−	0.000583143i
$939$	−0.631711	+	8.51120i	−0.0206151	+	0.277752i
$940$			31.8354i			1.03836i
$941$	−9.93719	−	37.0861i	−0.323943	−	1.20897i	−0.915370	−	0.402613i	$-0.868102\pi$
$941$	−9.93719	−	37.0861i	−0.323943	−	1.20897i	0.591427	−	0.806358i	$-0.298565\pi$
$942$	0.229944	+	0.266814i	0.00749199	+	0.00869328i
$943$	6.73085	−	6.73085i	0.219187	−	0.219187i
$944$	17.8978	+	17.8978i	0.582523	+	0.582523i
$945$	30.5949	−	2.81271i	0.995253	−	0.0914975i
$946$	0.833001	−	0.480933i	0.0270832	−	0.0156365i
$947$	−22.8271	+	6.11649i	−0.741780	+	0.198759i	−0.609869	−	0.792502i	$-0.708778\pi$
$947$	−22.8271	+	6.11649i	−0.741780	+	0.198759i	−0.131911	+	0.991262i	$0.542111\pi$
$948$	−3.16184	−	6.55364i	−0.102692	−	0.212852i
$949$	−0.614933	+	2.62227i	−0.0199616	+	0.0851224i
$950$	−0.000184902	0	0.000106753i	−5.99900e−6	0	3.46352e-6i
$951$	21.2322	+	24.6367i	0.688503	+	0.798899i
$952$	0.113039	−	0.0367002i	0.00366361	−	0.00118946i
$953$	−15.3472	+	26.5822i	−0.497146	+	0.861082i	−0.999995	−	0.00329261i	$-0.998952\pi$
$953$	−15.3472	+	26.5822i	−0.497146	+	0.861082i	0.502849	+	0.864374i	$0.332285\pi$
$954$	0.434073	−	0.0495366i	0.0140536	−	0.00160381i
$955$	3.69507	−	13.7902i	0.119570	−	0.446240i
$956$	1.27013	−	4.74019i	0.0410789	−	0.153309i
$957$	−58.6361	−	68.0380i	−1.89544	−	2.19936i
$958$	−0.405756	+	0.702791i	−0.0131094	+	0.0227061i
$959$	39.5742	−	12.8485i	1.27792	−	0.414900i
$960$	−23.4230	+	20.1862i	−0.755973	+	0.651508i
$961$	−26.8052	+	15.4760i	−0.864684	+	0.499225i
$962$	0.0253161		0.000796643i	0.000816224		2.56848e-5i
$963$	1.18185	−	7.91782i	0.0380846	−	0.255148i
$964$	−21.7801	+	5.83596i	−0.701490	+	0.187964i
$965$	26.1094	−	15.0743i	0.840491	−	0.485258i
$966$	−0.215030	+	0.737360i	−0.00691847	+	0.0237242i
$967$	10.8854	+	10.8854i	0.350050	+	0.350050i	0.860128	−	0.510078i	$-0.170384\pi$
$967$	10.8854	+	10.8854i	0.350050	+	0.350050i	−0.510078	+	0.860128i	$0.670384\pi$
$968$	0.945104	−	0.945104i	0.0303768	−	0.0303768i
$969$	1.16444	−	1.00353i	0.0374072	−	0.0322381i
$970$	−0.135746	−	0.506612i	−0.00435855	−	0.0162663i
$971$			33.0222i			1.05973i	0.848082	+	0.529866i	$0.177758\pi$
$971$			33.0222i			1.05973i	−0.848082	+	0.529866i	$0.822242\pi$
$972$	24.2995	−	19.5207i	0.779407	−	0.626125i
$973$	14.8348	−	0.774080i	0.475582	−	0.0248159i
$974$	0.705532			0.0226067
$975$	−0.00146331	+	0.0343069i	−4.68635e−5	+	0.00109870i
$976$	−24.6587	+	42.7101i	−0.789306	+	1.36712i
$977$	−30.8391	+	30.8391i	−0.986631	+	0.986631i	−0.999912	−	0.0132803i	$-0.995773\pi$
$977$	−30.8391	+	30.8391i	−0.986631	+	0.986631i	0.0132803	+	0.999912i	$0.495773\pi$
$978$	0.191586	+	0.397106i	0.00612624	+	0.0126980i
$979$	−54.5413	−	31.4894i	−1.74315	−	1.00641i
$980$	−4.90731	+	30.8927i	−0.156758	+	0.986831i
$981$	−17.8415	−	24.1022i	−0.569635	−	0.769524i
$982$	−0.514331	+	0.514331i	−0.0164130	+	0.0164130i
$983$	24.5844	−	6.58738i	0.784122	−	0.210105i	0.155521	−	0.987833i	$-0.450294\pi$
$983$	24.5844	−	6.58738i	0.784122	−	0.210105i	0.628601	+	0.777728i	$0.283628\pi$
$984$	−0.0143094	+	0.192795i	−0.000456168	+	0.00614607i
$985$	−1.31013	−	0.756404i	−0.0417442	−	0.0241010i
$986$	−0.0295201	+	0.110171i	−0.000940112	+	0.00350855i
$987$	31.3420	+	9.13999i	0.997628	+	0.290929i
$988$	9.20604	+	8.64432i	0.292883	+	0.275013i
$989$	−55.6407	+	32.1242i	−1.76927	+	1.02149i
$990$	−0.696035	−	0.302494i	−0.0221214	−	0.00961388i
$991$	13.5561			0.430623			0.215312	−	0.976545i	$-0.430923\pi$
$991$	13.5561			0.430623			0.215312	+	0.976545i	$0.430923\pi$
$992$	−0.0582752			−0.00185024
$993$	−9.90230	−	52.1310i	−0.314240	−	1.65433i
$994$	−0.150349	−	0.0766499i	−0.00476879	−	0.00243119i
$995$	−44.6742	+	11.9704i	−1.41627	+	0.379488i
$996$	28.6860	−	24.7220i	0.908949	−	0.783345i
$997$	26.5027	+	45.9041i	0.839350	+	1.45380i	0.890439	+	0.455103i	$0.150397\pi$
$997$	26.5027	+	45.9041i	0.839350	+	1.45380i	−0.0510891	+	0.998694i	$0.516269\pi$
$998$	−0.136112			−0.00430854
$999$	1.64538	−	0.0650982i	0.0520577	−	0.00205962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bw.b.11.16	yes	128
3.2	odd	2	inner	273.2.bw.b.11.17	yes	128
7.2	even	3		273.2.bv.b.128.16	yes	128
13.6	odd	12		273.2.bv.b.32.17	yes	128
21.2	odd	6		273.2.bv.b.128.17	yes	128
39.32	even	12		273.2.bv.b.32.16	✓	128
91.58	odd	12	inner	273.2.bw.b.149.17	yes	128
273.149	even	12	inner	273.2.bw.b.149.16	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bv.b.32.16	✓	128	39.32	even	12
273.2.bv.b.32.17	yes	128	13.6	odd	12
273.2.bv.b.128.16	yes	128	7.2	even	3
273.2.bv.b.128.17	yes	128	21.2	odd	6
273.2.bw.b.11.16	yes	128	1.1	even	1	trivial
273.2.bw.b.11.17	yes	128	3.2	odd	2	inner
273.2.bw.b.149.16	yes	128	273.149	even	12	inner
273.2.bw.b.149.17	yes	128	91.58	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00573734 - 0.0214121i) q^{2} +(-1.43178 - 0.974676i) q^{3} +(1.73163 - 0.999754i) q^{4} +(2.15869 + 0.578419i) q^{5} +(-0.0126552 + 0.0362495i) q^{6} +(1.44048 + 2.21924i) q^{7} +(-0.0626912 - 0.0626912i) q^{8} +(1.10001 + 2.79105i) q^{9} +O(q^{10})\)	\(q+(-0.00573734 - 0.0214121i) q^{2} +(-1.43178 - 0.974676i) q^{3} +(1.73163 - 0.999754i) q^{4} +(2.15869 + 0.578419i) q^{5} +(-0.0126552 + 0.0362495i) q^{6} +(1.44048 + 2.21924i) q^{7} +(-0.0626912 - 0.0626912i) q^{8} +(1.10001 + 2.79105i) q^{9} -0.0495405i q^{10} +(-3.61079 - 3.61079i) q^{11} +(-3.45375 - 0.256341i) q^{12} +(3.17766 + 1.70367i) q^{13} +(0.0392540 - 0.0435761i) q^{14} +(-2.52700 - 2.93219i) q^{15} +(1.99853 - 3.46155i) q^{16} +(0.253331 + 0.438783i) q^{17} +(0.0534510 - 0.0395668i) q^{18} +(1.23862 + 1.23862i) q^{19} +(4.31631 - 1.15655i) q^{20} +(0.100591 - 4.58147i) q^{21} +(-0.0565981 + 0.0980307i) q^{22} +(3.78050 - 6.54801i) q^{23} +(0.0286566 + 0.150864i) q^{24} +(-0.00476183 - 0.00274924i) q^{25} +(0.0182479 - 0.0778147i) q^{26} +(1.14539 - 5.06834i) q^{27} +(4.71306 + 2.40277i) q^{28} +(-8.79466 + 5.07760i) q^{29} +(-0.0482860 + 0.0709314i) q^{30} +(0.211677 - 0.0567187i) q^{31} +(-0.256861 - 0.0688256i) q^{32} +(1.65052 + 8.68921i) q^{33} +(0.00794180 - 0.00794180i) q^{34} +(1.82589 + 5.62385i) q^{35} +(4.69518 + 3.73331i) q^{36} +(0.0820203 + 0.306104i) q^{37} +(0.0194150 - 0.0336277i) q^{38} +(-2.88919 - 5.53648i) q^{39} +(-0.0990689 - 0.171592i) q^{40} +(1.21605 + 0.325838i) q^{41} +(-0.0986759 + 0.0241316i) q^{42} +(-7.35892 - 4.24867i) q^{43} +(-9.86243 - 2.64263i) q^{44} +(0.760188 + 6.66128i) q^{45} +(-0.161896 - 0.0433800i) q^{46} +(-1.84390 + 6.88152i) q^{47} +(-6.23535 + 3.00828i) q^{48} +(-2.85006 + 6.39352i) q^{49} +(-3.15467e-5 + 0.000117734i) q^{50} +(0.0649552 - 0.875158i) q^{51} +(7.20576 - 0.226750i) q^{52} +(5.68942 + 3.28479i) q^{53} +(-0.115095 + 0.00455364i) q^{54} +(-5.70601 - 9.88311i) q^{55} +(0.0488217 - 0.229432i) q^{56} +(-0.566182 - 2.98068i) q^{57} +(0.159180 + 0.159180i) q^{58} +(-1.63897 + 6.11671i) q^{59} +(-7.30730 - 2.55107i) q^{60} -12.3384 q^{61} +(-0.00242893 - 0.00420703i) q^{62} +(-4.60948 + 6.46164i) q^{63} -7.98821i q^{64} +(5.87413 + 5.51572i) q^{65} +(0.176584 - 0.0851941i) q^{66} +(4.13223 + 4.13223i) q^{67} +(0.877350 + 0.506538i) q^{68} +(-11.7950 + 5.69058i) q^{69} +(0.109942 - 0.0713619i) q^{70} +(-0.744738 - 2.77940i) q^{71} +(0.106013 - 0.243935i) q^{72} +(0.193342 + 0.721562i) q^{73} +(0.00608374 - 0.00351245i) q^{74} +(0.00413829 + 0.00857757i) q^{75} +(3.38313 + 0.906508i) q^{76} +(2.81196 - 13.2145i) q^{77} +(-0.101971 + 0.0936281i) q^{78} +(1.05053 + 1.81957i) q^{79} +(6.31642 - 6.31642i) q^{80} +(-6.57994 + 6.14039i) q^{81} -0.0279075i q^{82} +(-7.73187 + 7.73187i) q^{83} +(-4.40616 - 8.03396i) q^{84} +(0.293063 + 1.09373i) q^{85} +(-0.0487522 + 0.181946i) q^{86} +(17.5411 + 1.30192i) q^{87} +0.452729i q^{88} +(11.9130 - 3.19208i) q^{89} +(0.138270 - 0.0544952i) q^{90} +(0.796471 + 9.50608i) q^{91} -15.1183i q^{92} +(-0.358358 - 0.125108i) q^{93} +0.157927 q^{94} +(1.95735 + 3.39023i) q^{95} +(0.300686 + 0.348899i) q^{96} +(10.2262 - 2.74010i) q^{97} +(0.153250 + 0.0243438i) q^{98} +(6.10598 - 14.0498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 16 q^{9}+O(q^{10}) \) 128 * q - 4 * q^3 - 12 * q^4 - 4 * q^6 - 16 * q^7 - 16 * q^9	\( 128 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 16 q^{9} - 48 q^{12} - 16 q^{13} - 6 q^{15} + 32 q^{16} + 22 q^{18} - 16 q^{19} - 18 q^{21} - 8 q^{22} - 4 q^{24} - 40 q^{27} - 76 q^{28} - 4 q^{31} + 50 q^{33} - 48 q^{34} - 60 q^{36} + 28 q^{37} + 40 q^{39} + 44 q^{40} + 44 q^{42} - 144 q^{43} + 58 q^{45} + 48 q^{46} - 64 q^{48} + 24 q^{49} + 36 q^{51} - 22 q^{54} - 16 q^{55} + 40 q^{57} - 28 q^{58} - 4 q^{60} - 40 q^{61} + 20 q^{63} - 34 q^{66} + 96 q^{67} - 54 q^{69} + 64 q^{70} - 98 q^{72} + 48 q^{73} - 12 q^{75} + 144 q^{76} + 82 q^{78} - 24 q^{79} - 48 q^{81} + 4 q^{84} + 56 q^{85} - 2 q^{87} - 24 q^{91} + 10 q^{93} + 32 q^{94} - 54 q^{96} + 52 q^{97} - 10 q^{99}+O(q^{100}) \) 128 * q - 4 * q^3 - 12 * q^4 - 4 * q^6 - 16 * q^7 - 16 * q^9 - 48 * q^12 - 16 * q^13 - 6 * q^15 + 32 * q^16 + 22 * q^18 - 16 * q^19 - 18 * q^21 - 8 * q^22 - 4 * q^24 - 40 * q^27 - 76 * q^28 - 4 * q^31 + 50 * q^33 - 48 * q^34 - 60 * q^36 + 28 * q^37 + 40 * q^39 + 44 * q^40 + 44 * q^42 - 144 * q^43 + 58 * q^45 + 48 * q^46 - 64 * q^48 + 24 * q^49 + 36 * q^51 - 22 * q^54 - 16 * q^55 + 40 * q^57 - 28 * q^58 - 4 * q^60 - 40 * q^61 + 20 * q^63 - 34 * q^66 + 96 * q^67 - 54 * q^69 + 64 * q^70 - 98 * q^72 + 48 * q^73 - 12 * q^75 + 144 * q^76 + 82 * q^78 - 24 * q^79 - 48 * q^81 + 4 * q^84 + 56 * q^85 - 2 * q^87 - 24 * q^91 + 10 * q^93 + 32 * q^94 - 54 * q^96 + 52 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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