LMFDB - Embedded newform 448.2.bm.a.171.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(3,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([24, 9, 8]))

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

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

chi := DirichletCharacter("448.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.bm (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$62$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			171.11
Character	$\chi$	$=$	448.171
Dual form			448.2.bm.a.131.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19739 - 0.752502i) q^{2} +(0.748476 + 0.254073i) q^{3} +(0.867480 + 1.80208i) q^{4} +(0.629821 - 1.27715i) q^{5} +(-0.705026 - 0.867454i) q^{6} +(-0.189362 + 2.63897i) q^{7} +(0.317355 - 2.81057i) q^{8} +(-1.88440 - 1.44595i) q^{9} +O(q^{10})$	\(q+(-1.19739 - 0.752502i) q^{2} +(0.748476 + 0.254073i) q^{3} +(0.867480 + 1.80208i) q^{4} +(0.629821 - 1.27715i) q^{5} +(-0.705026 - 0.867454i) q^{6} +(-0.189362 + 2.63897i) q^{7} +(0.317355 - 2.81057i) q^{8} +(-1.88440 - 1.44595i) q^{9} +(-1.71520 + 1.05530i) q^{10} +(-4.08203 - 3.57984i) q^{11} +(0.191429 + 1.56921i) q^{12} +(3.62556 - 5.42604i) q^{13} +(2.21257 - 3.01737i) q^{14} +(0.795896 - 0.795896i) q^{15} +(-2.49496 + 3.12653i) q^{16} +(4.17395 - 1.11841i) q^{17} +(1.16828 + 3.14938i) q^{18} +(6.34717 + 0.416015i) q^{19} +(2.84788 + 0.0270820i) q^{20} +(-0.812223 + 1.92709i) q^{21} +(2.19394 + 7.35820i) q^{22} +(-3.45114 - 2.64815i) q^{23} +(0.951622 - 2.02301i) q^{24} +(1.80937 + 2.35801i) q^{25} +(-8.42431 + 3.76883i) q^{26} +(-2.36046 - 3.53267i) q^{27} +(-4.91988 + 1.94801i) q^{28} +(2.19242 - 0.436100i) q^{29} +(-1.55191 + 0.354083i) q^{30} +(5.66081 + 3.26827i) q^{31} +(5.34015 - 1.86621i) q^{32} +(-2.14576 - 3.71656i) q^{33} +(-5.83945 - 1.80174i) q^{34} +(3.25109 + 1.90392i) q^{35} +(0.971032 - 4.65016i) q^{36} +(3.28556 - 6.66246i) q^{37} +(-7.28698 - 5.27439i) q^{38} +(4.09226 - 3.14010i) q^{39} +(-3.38964 - 2.17546i) q^{40} +(-2.26531 + 0.938322i) q^{41} +(2.42269 - 1.69628i) q^{42} +(-0.548601 - 0.109124i) q^{43} +(2.91007 - 10.4616i) q^{44} +(-3.03353 + 1.49597i) q^{45} +(2.13961 + 5.76786i) q^{46} +(-0.750882 - 0.201198i) q^{47} +(-2.66178 + 1.70623i) q^{48} +(-6.92828 - 0.999438i) q^{49} +(-0.392106 - 4.18501i) q^{50} +(3.40826 + 0.223389i) q^{51} +(12.9232 + 1.82656i) q^{52} +(-3.12487 + 3.56323i) q^{53} +(0.168040 + 6.00623i) q^{54} +(-7.14295 + 2.95871i) q^{55} +(7.35690 + 1.36970i) q^{56} +(4.64500 + 1.92402i) q^{57} +(-2.95335 - 1.12762i) q^{58} +(0.221252 + 3.37565i) q^{59} +(2.12469 + 0.743841i) q^{60} +(-6.57381 - 7.49599i) q^{61} +(-4.31881 - 8.17317i) q^{62} +(4.17264 - 4.69905i) q^{63} +(-7.79857 - 1.78389i) q^{64} +(-4.64641 - 8.04782i) q^{65} +(-0.227414 + 6.06485i) q^{66} +(-3.49972 + 10.3098i) q^{67} +(5.63628 + 6.55158i) q^{68} +(-1.91027 - 2.85892i) q^{69} +(-2.46012 - 4.72619i) q^{70} +(3.34785 - 8.08243i) q^{71} +(-4.66196 + 4.83735i) q^{72} +(-0.0483459 - 0.00636486i) q^{73} +(-8.94762 + 5.50517i) q^{74} +(0.755159 + 2.22463i) q^{75} +(4.75635 + 11.7990i) q^{76} +(10.2201 - 10.0944i) q^{77} +(-7.26295 + 0.680487i) q^{78} +(-7.64470 - 2.04839i) q^{79} +(2.42168 + 5.15559i) q^{80} +(0.975079 + 3.63904i) q^{81} +(3.41855 + 0.581115i) q^{82} +(-5.12511 + 7.67026i) q^{83} +(-4.17735 + 0.208025i) q^{84} +(1.20047 - 6.03516i) q^{85} +(0.574774 + 0.543487i) q^{86} +(1.75177 + 0.230625i) q^{87} +(-11.3568 + 10.3367i) q^{88} +(0.574166 + 4.36123i) q^{89} +(4.75803 + 0.491479i) q^{90} +(13.6326 + 10.5952i) q^{91} +(1.77838 - 8.51643i) q^{92} +(3.40660 + 3.88448i) q^{93} +(0.747696 + 0.805953i) q^{94} +(4.52889 - 7.84428i) q^{95} +(4.47113 - 0.0400257i) q^{96} -10.2898 q^{97} +(7.54377 + 6.41027i) q^{98} +(2.51589 + 12.6482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 8 q^{2} - 24 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{7} - 32 q^{8} - 8 q^{9}+O(q^{10}) $ 992 * q - 8 * q^2 - 24 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^7 - 32 * q^8 - 8 * q^9	$ 992 q - 8 q^{2} - 24 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{7} - 32 q^{8} - 8 q^{9} - 24 q^{10} - 8 q^{11} - 24 q^{12} - 16 q^{14} - 32 q^{15} - 8 q^{16} - 24 q^{17} - 8 q^{18} - 24 q^{19} - 16 q^{21} - 48 q^{22} - 8 q^{23} - 24 q^{24} - 8 q^{25} - 24 q^{26} - 56 q^{28} - 32 q^{29} + 72 q^{30} - 48 q^{31} - 8 q^{32} - 16 q^{35} - 192 q^{36} - 8 q^{37} - 24 q^{38} - 8 q^{39} - 24 q^{40} - 56 q^{42} - 32 q^{43} - 24 q^{45} - 8 q^{46} - 24 q^{47} - 16 q^{49} - 80 q^{50} - 8 q^{51} + 120 q^{52} - 8 q^{53} - 24 q^{54} - 16 q^{56} - 32 q^{57} - 8 q^{58} - 216 q^{59} + 88 q^{60} - 24 q^{61} - 224 q^{64} - 16 q^{65} + 264 q^{66} - 88 q^{67} - 24 q^{68} - 16 q^{70} + 96 q^{71} - 8 q^{72} - 24 q^{73} + 48 q^{74} - 24 q^{75} - 16 q^{77} - 128 q^{78} - 8 q^{79} + 48 q^{80} - 8 q^{81} - 264 q^{82} + 96 q^{84} - 32 q^{85} - 8 q^{86} - 24 q^{87} - 8 q^{88} - 24 q^{89} - 16 q^{91} - 32 q^{92} - 56 q^{93} - 24 q^{94} - 16 q^{95} - 432 q^{96} + 120 q^{98} + 16 q^{99}+O(q^{100}) $ 992 * q - 8 * q^2 - 24 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^7 - 32 * q^8 - 8 * q^9 - 24 * q^10 - 8 * q^11 - 24 * q^12 - 16 * q^14 - 32 * q^15 - 8 * q^16 - 24 * q^17 - 8 * q^18 - 24 * q^19 - 16 * q^21 - 48 * q^22 - 8 * q^23 - 24 * q^24 - 8 * q^25 - 24 * q^26 - 56 * q^28 - 32 * q^29 + 72 * q^30 - 48 * q^31 - 8 * q^32 - 16 * q^35 - 192 * q^36 - 8 * q^37 - 24 * q^38 - 8 * q^39 - 24 * q^40 - 56 * q^42 - 32 * q^43 - 24 * q^45 - 8 * q^46 - 24 * q^47 - 16 * q^49 - 80 * q^50 - 8 * q^51 + 120 * q^52 - 8 * q^53 - 24 * q^54 - 16 * q^56 - 32 * q^57 - 8 * q^58 - 216 * q^59 + 88 * q^60 - 24 * q^61 - 224 * q^64 - 16 * q^65 + 264 * q^66 - 88 * q^67 - 24 * q^68 - 16 * q^70 + 96 * q^71 - 8 * q^72 - 24 * q^73 + 48 * q^74 - 24 * q^75 - 16 * q^77 - 128 * q^78 - 8 * q^79 + 48 * q^80 - 8 * q^81 - 264 * q^82 + 96 * q^84 - 32 * q^85 - 8 * q^86 - 24 * q^87 - 8 * q^88 - 24 * q^89 - 16 * q^91 - 32 * q^92 - 56 * q^93 - 24 * q^94 - 16 * q^95 - 432 * q^96 + 120 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−1.19739	−	0.752502i	−0.846682	−	0.532100i
$2$	−1.19739	−	0.752502i	−0.846682	−	0.532100i
$3$	0.748476	+	0.254073i	0.432133	+	0.146689i	0.529026	−	0.848605i	$-0.322557\pi$
$3$	0.748476	+	0.254073i	0.432133	+	0.146689i	−0.0968936	+	0.995295i	$0.530891\pi$
$4$	0.867480	+	1.80208i	0.433740	+	0.901038i
$5$	0.629821	−	1.27715i	0.281665	−	0.571159i	−0.709359	−	0.704848i	$-0.751015\pi$
$5$	0.629821	−	1.27715i	0.281665	−	0.571159i	0.991023	+	0.133688i	$0.0426821\pi$
$6$	−0.705026	−	0.867454i	−0.287826	−	0.354137i
$7$	−0.189362	+	2.63897i	−0.0715719	+	0.997435i
$7$	−0.189362	+	2.63897i	−0.0715719	+	0.997435i
$8$	0.317355	−	2.81057i	0.112202	−	0.993685i
$9$	−1.88440	−	1.44595i	−0.628132	−	0.481983i
$10$	−1.71520	+	1.05530i	−0.542394	+	0.333717i
$11$	−4.08203	−	3.57984i	−1.23078	−	1.07936i	−0.994177	−	0.107756i	$-0.965633\pi$
$11$	−4.08203	−	3.57984i	−1.23078	−	1.07936i	−0.236600	−	0.971607i	$-0.576033\pi$
$12$	0.191429	+	1.56921i	0.0552607	+	0.452993i
$13$	3.62556	−	5.42604i	1.00555	−	1.50491i	0.149007	−	0.988836i	$-0.452392\pi$
$13$	3.62556	−	5.42604i	1.00555	−	1.50491i	0.856543	−	0.516076i	$-0.172608\pi$
$14$	2.21257	−	3.01737i	0.591334	−	0.806427i
$15$	0.795896	−	0.795896i	0.205499	−	0.205499i
$16$	−2.49496	+	3.12653i	−0.623739	+	0.781633i
$17$	4.17395	−	1.11841i	1.01233	−	0.271254i	0.285729	−	0.958311i	$-0.407764\pi$
$17$	4.17395	−	1.11841i	1.01233	−	0.271254i	0.726604	+	0.687057i	$0.241098\pi$
$18$	1.16828	+	3.14938i	0.275365	+	0.742315i
$19$	6.34717	+	0.416015i	1.45614	+	0.0954405i	0.772795	−	0.634655i	$-0.218858\pi$
$19$	6.34717	+	0.416015i	1.45614	+	0.0954405i	0.683345	+	0.730096i	$0.260525\pi$
$20$	2.84788	+	0.0270820i	0.636805	+	0.00605572i
$21$	−0.812223	+	1.92709i	−0.177242	+	0.420526i
$22$	2.19394	+	7.35820i	0.467749	+	1.56877i
$23$	−3.45114	−	2.64815i	−0.719612	−	0.552178i	0.182748	−	0.983160i	$-0.441501\pi$
$23$	−3.45114	−	2.64815i	−0.719612	−	0.552178i	−0.902361	+	0.430982i	$0.858167\pi$
$24$	0.951622	−	2.02301i	0.194249	−	0.412945i
$25$	1.80937	+	2.35801i	0.361873	+	0.471603i
$26$	−8.42431	+	3.76883i	−1.65214	+	0.739129i
$27$	−2.36046	−	3.53267i	−0.454270	−	0.679863i
$28$	−4.91988	+	1.94801i	−0.929771	+	0.368139i
$29$	2.19242	−	0.436100i	0.407122	−	0.0809816i	0.0127190	−	0.999919i	$-0.495951\pi$
$29$	2.19242	−	0.436100i	0.407122	−	0.0809816i	0.394403	+	0.918937i	$0.370951\pi$
$30$	−1.55191	+	0.354083i	−0.283339	+	0.0646465i
$31$	5.66081	+	3.26827i	1.01671	+	0.586999i	0.913150	−	0.407624i	$-0.133643\pi$
$31$	5.66081	+	3.26827i	1.01671	+	0.586999i	0.103562	+	0.994623i	$0.466976\pi$
$32$	5.34015	−	1.86621i	0.944015	−	0.329903i
$33$	−2.14576	−	3.71656i	−0.373528	−	0.646970i
$34$	−5.83945	−	1.80174i	−1.00146	−	0.308996i
$35$	3.25109	+	1.90392i	0.549535	+	0.321821i
$36$	0.971032	−	4.65016i	0.161839	−	0.775027i
$37$	3.28556	−	6.66246i	0.540143	−	1.09530i	−0.440181	−	0.897909i	$-0.645086\pi$
$37$	3.28556	−	6.66246i	0.540143	−	1.09530i	0.980324	−	0.197393i	$-0.0632475\pi$
$38$	−7.28698	−	5.27439i	−1.18210	−	0.855619i
$39$	4.09226	−	3.14010i	0.655285	−	0.502818i
$40$	−3.38964	−	2.17546i	−0.535949	−	0.343971i
$41$	−2.26531	+	0.938322i	−0.353782	+	0.146541i	−0.552495	−	0.833517i	$-0.686324\pi$
$41$	−2.26531	+	0.938322i	−0.353782	+	0.146541i	0.198713	+	0.980058i	$0.436324\pi$
$42$	2.42269	−	1.69628i	0.373829	−	0.261741i
$43$	−0.548601	−	0.109124i	−0.0836609	−	0.0166412i	0.153082	−	0.988213i	$-0.451080\pi$
$43$	−0.548601	−	0.109124i	−0.0836609	−	0.0166412i	−0.236743	+	0.971572i	$0.576080\pi$
$44$	2.91007	−	10.4616i	0.438709	−	1.57714i
$45$	−3.03353	+	1.49597i	−0.452212	+	0.223006i
$46$	2.13961	+	5.76786i	0.315469	+	0.850424i
$47$	−0.750882	−	0.201198i	−0.109527	−	0.0293478i	0.203639	−	0.979046i	$-0.434723\pi$
$47$	−0.750882	−	0.201198i	−0.109527	−	0.0293478i	−0.313166	+	0.949698i	$0.601390\pi$
$48$	−2.66178	+	1.70623i	−0.384195	+	0.246273i
$49$	−6.92828	−	0.999438i	−0.989755	−	0.142777i
$50$	−0.392106	−	4.18501i	−0.0554521	−	0.591850i
$51$	3.40826	+	0.223389i	0.477252	+	0.0312807i
$52$	12.9232	+	1.82656i	1.79213	+	0.253298i
$53$	−3.12487	+	3.56323i	−0.429234	+	0.489447i	−0.925513	−	0.378716i	$-0.876366\pi$
$53$	−3.12487	+	3.56323i	−0.429234	+	0.489447i	0.496279	+	0.868163i	$0.334699\pi$
$54$	0.168040	+	6.00623i	0.0228673	+	0.817344i
$55$	−7.14295	+	2.95871i	−0.963155	+	0.398952i
$56$	7.35690	+	1.36970i	0.983107	+	0.183034i
$57$	4.64500	+	1.92402i	0.615246	+	0.254843i
$58$	−2.95335	−	1.12762i	−0.387793	−	0.148064i
$59$	0.221252	+	3.37565i	0.0288045	+	0.439472i	0.987767	+	0.155938i	$0.0498401\pi$
$59$	0.221252	+	3.37565i	0.0288045	+	0.439472i	−0.958962	+	0.283534i	$0.908493\pi$
$60$	2.12469	+	0.743841i	0.274296	+	0.0960294i
$61$	−6.57381	−	7.49599i	−0.841690	−	0.959764i	0.157926	−	0.987451i	$-0.449519\pi$
$61$	−6.57381	−	7.49599i	−0.841690	−	0.959764i	−0.999617	+	0.0276871i	$0.991186\pi$
$62$	−4.31881	−	8.17317i	−0.548490	−	1.03799i
$63$	4.17264	−	4.69905i	0.525704	−	0.592025i
$64$	−7.79857	−	1.78389i	−0.974821	−	0.222987i
$65$	−4.64641	−	8.04782i	−0.576317	−	0.998210i
$66$	−0.227414	+	6.06485i	−0.0279928	+	0.746532i
$67$	−3.49972	+	10.3098i	−0.427559	+	1.25955i	0.493371	+	0.869819i	$0.335764\pi$
$67$	−3.49972	+	10.3098i	−0.427559	+	1.25955i	−0.920930	+	0.389728i	$0.872569\pi$
$68$	5.63628	+	6.55158i	0.683499	+	0.794496i
$69$	−1.91027	−	2.85892i	−0.229969	−	0.344173i
$70$	−2.46012	−	4.72619i	−0.294041	−	0.564888i
$71$	3.34785	−	8.08243i	0.397317	−	0.959208i	−0.590983	−	0.806684i	$-0.701260\pi$
$71$	3.34785	−	8.08243i	0.397317	−	0.959208i	0.988300	−	0.152524i	$-0.0487402\pi$
$72$	−4.66196	+	4.83735i	−0.549417	+	0.570087i
$73$	−0.0483459	−	0.00636486i	−0.00565846	−	0.000744950i	0.127696	−	0.991813i	$-0.459242\pi$
$73$	−0.0483459	−	0.00636486i	−0.00565846	−	0.000744950i	−0.133355	+	0.991068i	$0.542575\pi$
$74$	−8.94762	+	5.50517i	−1.04014	+	0.639962i
$75$	0.755159	+	2.22463i	0.0871983	+	0.256878i
$76$	4.75635	+	11.7990i	0.545591	+	1.35343i
$77$	10.2201	−	10.0944i	1.16468	−	1.15037i
$78$	−7.26295	+	0.680487i	−0.822368	+	0.0770500i
$79$	−7.64470	−	2.04839i	−0.860096	−	0.230462i	−0.198296	−	0.980142i	$-0.563541\pi$
$79$	−7.64470	−	2.04839i	−0.860096	−	0.230462i	−0.661800	+	0.749680i	$0.730207\pi$
$80$	2.42168	+	5.15559i	0.270752	+	0.576412i
$81$	0.975079	+	3.63904i	0.108342	+	0.404338i
$82$	3.41855	+	0.581115i	0.377515	+	0.0641734i
$83$	−5.12511	+	7.67026i	−0.562553	+	0.841921i	−0.998308	−	0.0581448i	$-0.981481\pi$
$83$	−5.12511	+	7.67026i	−0.562553	+	0.841921i	0.435755	+	0.900065i	$0.356481\pi$
$84$	−4.17735	+	0.208025i	−0.455786	+	0.0226974i
$85$	1.20047	−	6.03516i	0.130209	−	0.654605i
$86$	0.574774	+	0.543487i	0.0619794	+	0.0586057i
$87$	1.75177	+	0.230625i	0.187810	+	0.0247256i
$88$	−11.3568	+	10.3367i	−1.21064	+	1.10190i
$89$	0.574166	+	4.36123i	0.0608615	+	0.462289i	0.994555	+	0.104215i	$0.0332331\pi$
$89$	0.574166	+	4.36123i	0.0608615	+	0.462289i	−0.933693	+	0.358074i	$0.883434\pi$
$90$	4.75803	+	0.491479i	0.501541	+	0.0518064i
$91$	13.6326	+	10.5952i	1.42908	+	1.11068i
$92$	1.77838	−	8.51643i	0.185408	−	0.887900i
$93$	3.40660	+	3.88448i	0.353248	+	0.402802i
$94$	0.747696	+	0.805953i	0.0771190	+	0.0831277i
$95$	4.52889	−	7.84428i	0.464655	−	0.804806i
$96$	4.47113	−	0.0400257i	0.456333	−	0.00408511i
$97$	−10.2898			−1.04477			−0.522386	−	0.852709i	$-0.674958\pi$
$97$	−10.2898			−1.04477			−0.522386	+	0.852709i	$0.674958\pi$
$98$	7.54377	+	6.41027i	0.762036	+	0.647535i
$99$	2.51589	+	12.6482i	0.252857	+	1.27120i
$100$	−2.67973	+	5.30615i	−0.267973	+	0.530615i
$101$	−0.00925178	−	0.141155i	−0.000920587	−	0.0140454i	0.997374	−	0.0724242i	$-0.0230735\pi$
$101$	−0.00925178	−	0.141155i	−0.000920587	−	0.0140454i	−0.998295	+	0.0583788i	$0.981407\pi$
$102$	−3.91291	−	2.83221i	−0.387436	−	0.280430i
$103$	4.55312	−	0.599429i	0.448632	−	0.0590635i	0.0971745	−	0.995267i	$-0.469020\pi$
$103$	4.55312	−	0.599429i	0.448632	−	0.0590635i	0.351458	+	0.936204i	$0.385686\pi$
$104$	−14.0997	−	11.9119i	−1.38258	−	1.16805i
$105$	1.94963	+	2.25105i	0.190264	+	0.219680i
$106$	6.42302	−	1.91510i	0.623859	−	0.186011i
$107$	5.92150	+	17.4442i	0.572453	+	1.68639i	0.717152	+	0.696917i	$0.245445\pi$
$107$	5.92150	+	17.4442i	0.572453	+	1.68639i	−0.144699	+	0.989476i	$0.546221\pi$
$108$	4.31849	−	7.31824i	0.415547	−	0.704198i
$109$	−0.638847	−	1.29545i	−0.0611905	−	0.124082i	0.864129	−	0.503270i	$-0.167870\pi$
$109$	−0.638847	−	1.29545i	−0.0611905	−	0.124082i	−0.925320	+	0.379188i	$0.876203\pi$
$110$	10.7793	+	1.83236i	1.02777	+	0.174709i
$111$	4.15192	−	4.15192i	0.394083	−	0.394083i
$112$	−7.77836	−	7.17615i	−0.734986	−	0.678082i
$113$	0.952470	+	0.952470i	0.0896008	+	0.0896008i	0.750487	−	0.660886i	$-0.229819\pi$
$113$	0.952470	+	0.952470i	0.0896008	+	0.0896008i	−0.660886	+	0.750487i	$0.729819\pi$
$114$	−4.11404	−	5.79918i	−0.385315	−	0.543143i
$115$	−5.55569	+	2.73976i	−0.518071	+	0.255484i
$116$	2.68777	+	3.57260i	0.249553	+	0.331708i
$117$	−14.6778	+	4.98243i	−1.35696	+	0.460626i
$118$	2.27526	−	4.20846i	0.209455	−	0.387420i
$119$	2.16105	+	11.2267i	0.198103	+	1.02915i
$120$	−1.98434	−	2.48950i	−0.181144	−	0.227259i
$121$	2.41189	+	18.3201i	0.219263	+	1.66547i
$122$	2.23065	+	13.9224i	0.201954	+	1.26048i
$123$	−1.93393	+	0.126757i	−0.174377	+	0.0114293i
$124$	−0.979030	+	13.0364i	−0.0879195	+	1.17070i
$125$	11.1343	−	2.21476i	0.995885	−	0.198094i
$126$	−8.53232	+	2.48667i	−0.760120	+	0.221530i
$127$			6.99016i			0.620277i	0.950691	+	0.310138i	$0.100375\pi$
$127$			6.99016i			0.620277i	−0.950691	+	0.310138i	$0.899625\pi$
$128$	7.99554	+	8.00446i	0.706712	+	0.707501i
$129$	−0.382889	−	0.221061i	−0.0337115	−	0.0194634i
$130$	−0.492442	+	13.1328i	−0.0431901	+	1.15182i
$131$	8.20821	−	7.19841i	0.717155	−	0.628928i	−0.220948	−	0.975286i	$-0.570915\pi$
$131$	8.20821	−	7.19841i	0.717155	−	0.628928i	0.938102	+	0.346358i	$0.112582\pi$
$132$	4.83612	−	7.09086i	0.420930	−	0.617180i
$133$	−2.29976	+	16.6712i	−0.199414	+	1.44557i
$134$	11.9487	−	9.71134i	1.03221	−	0.838932i
$135$	−5.99842	+	0.789707i	−0.516262	+	0.0679672i
$136$	−1.81873	−	12.0861i	−0.155955	−	1.03637i
$137$	−0.0591333	+	0.449162i	−0.00505210	+	0.0383745i	−0.993785	−	0.111314i	$-0.964494\pi$
$137$	−0.0591333	+	0.449162i	−0.00505210	+	0.0383745i	0.988733	+	0.149689i	$0.0478272\pi$
$138$	0.135991	+	4.86072i	0.0115763	+	0.413772i
$139$	−0.244810	−	0.0486958i	−0.0207645	−	0.00413032i	0.184697	−	0.982795i	$-0.440870\pi$
$139$	−0.244810	−	0.0486958i	−0.0207645	−	0.00413032i	−0.205462	+	0.978665i	$0.565870\pi$
$140$	−0.610748	+	7.51033i	−0.0516176	+	0.634739i
$141$	−0.510898	−	0.341371i	−0.0430254	−	0.0287486i
$142$	−10.0907	+	7.15855i	−0.846796	+	0.600732i
$143$	−34.2240	+	9.17029i	−2.86195	+	0.766859i
$144$	9.22229	−	2.28405i	0.768524	−	0.190337i
$145$	0.823868	−	3.07472i	0.0684185	−	0.255341i
$146$	0.0530993	+	0.0440016i	0.00439453	+	0.00364160i
$147$	−4.93172	−	2.50835i	−0.406762	−	0.206885i
$148$	14.8564	+	0.141278i	1.22119	+	0.0116130i
$149$	14.8868	−	5.05339i	1.21957	−	0.413989i	0.363867	−	0.931451i	$-0.381456\pi$
$149$	14.8868	−	5.05339i	1.21957	−	0.413989i	0.855707	+	0.517461i	$0.173123\pi$
$150$	0.769818	−	3.23200i	0.0628554	−	0.263892i
$151$	1.97781	−	15.0230i	0.160952	−	1.22255i	−0.700103	−	0.714042i	$-0.746862\pi$
$151$	1.97781	−	15.0230i	0.160952	−	1.22255i	0.861055	−	0.508512i	$-0.169804\pi$
$152$	3.18354	−	17.7071i	0.258219	−	1.43624i
$153$	−9.48254	−	3.92780i	−0.766618	−	0.317544i
$154$	−19.8335	+	4.39636i	−1.59823	+	0.354269i
$155$	7.73938	−	5.17129i	0.621642	−	0.415368i
$156$	9.20865	+	4.65058i	0.737282	+	0.372345i
$157$	10.8736	+	3.69108i	0.867806	+	0.294581i	0.719611	−	0.694378i	$-0.244320\pi$
$157$	10.8736	+	3.69108i	0.867806	+	0.294581i	0.148195	+	0.988958i	$0.452654\pi$
$158$	7.61226	+	8.20538i	0.605599	+	0.652785i
$159$	−3.24421	+	1.87304i	−0.257282	+	0.148542i
$160$	0.979905	−	7.99556i	0.0774683	−	0.632105i
$161$	7.64190	−	8.60598i	0.602266	−	0.678246i
$162$	1.57084	−	5.09110i	0.123417	−	0.399994i
$163$	5.45977	−	4.78809i	0.427642	−	0.375032i	−0.418298	−	0.908310i	$-0.637373\pi$
$163$	5.45977	−	4.78809i	0.427642	−	0.375032i	0.845940	+	0.533278i	$0.179040\pi$
$164$	−3.65604	−	3.26828i	−0.285489	−	0.255210i
$165$	−6.09805	+	0.399687i	−0.474733	+	0.0311156i
$166$	11.9086	−	5.32763i	0.924289	−	0.413505i
$167$	−5.72030	+	13.8100i	−0.442650	+	1.06865i	0.532365	+	0.846515i	$0.321303\pi$
$167$	−5.72030	+	13.8100i	−0.442650	+	1.06865i	−0.975015	+	0.222138i	$0.928697\pi$
$168$	5.15845	+	2.89438i	0.397983	+	0.223306i
$169$	−11.3223	−	27.3344i	−0.870946	−	2.10265i
$170$	−5.97890	+	6.32308i	−0.458561	+	0.484958i
$171$	−11.3590	−	9.96162i	−0.868648	−	0.761784i
$172$	−0.279252	−	1.08328i	−0.0212928	−	0.0825996i
$173$	−0.551979	+	8.42157i	−0.0419662	+	0.640280i	0.924127	+	0.382086i	$0.124794\pi$
$173$	−0.551979	+	8.42157i	−0.0419662	+	0.640280i	−0.966093	+	0.258194i	$0.916873\pi$
$174$	−1.92401	−	1.59436i	−0.145859	−	0.120868i
$175$	−6.56534	+	4.32834i	−0.496293	+	0.327192i
$176$	21.3770	−	3.83104i	1.61135	−	0.288776i
$177$	−0.692061	+	2.58281i	−0.0520185	+	0.194136i
$178$	2.59433	−	5.65415i	0.194453	−	0.423796i
$179$	7.81192	+	15.8410i	0.583891	+	1.18401i	0.965673	+	0.259761i	$0.0836437\pi$
$179$	7.81192	+	15.8410i	0.583891	+	1.18401i	−0.381782	+	0.924252i	$0.624690\pi$
$180$	−5.32738	−	4.16892i	−0.397079	−	0.310733i
$181$	4.51193	−	22.6830i	0.335369	−	1.68601i	−0.333593	−	0.942717i	$-0.608261\pi$
$181$	4.51193	−	22.6830i	0.335369	−	1.68601i	0.668962	−	0.743297i	$-0.266739\pi$
$182$	−8.35058	−	22.9452i	−0.618986	−	1.70081i
$183$	−3.01581	−	7.28080i	−0.222935	−	0.538212i
$184$	−8.53804	+	8.85925i	−0.629433	+	0.653113i
$185$	−6.43965	−	8.39232i	−0.473453	−	0.617016i
$186$	−1.15594	−	7.21471i	−0.0847579	−	0.529009i
$187$	−21.0419	−	10.3767i	−1.53874	−	0.758821i
$188$	−0.288801	−	1.52768i	−0.0210630	−	0.111418i
$189$	9.76958	−	5.56021i	0.710632	−	0.404446i
$190$	−11.3257	+	5.98464i	−0.821651	+	0.434172i
$191$	9.46223	−	5.46302i	0.684663	−	0.395290i	−0.116947	−	0.993138i	$-0.537311\pi$
$191$	9.46223	−	5.46302i	0.684663	−	0.395290i	0.801609	+	0.597848i	$0.203977\pi$
$192$	−5.38380	−	3.31661i	−0.388542	−	0.239356i
$193$	−10.3931	+	18.0013i	−0.748109	+	1.29576i	0.200619	+	0.979669i	$0.435705\pi$
$193$	−10.3931	+	18.0013i	−0.748109	+	1.29576i	−0.948728	+	0.316093i	$0.897629\pi$
$194$	12.3209	+	7.74311i	0.884590	+	0.555923i
$195$	−1.43299	−	7.20413i	−0.102619	−	0.515898i
$196$	−4.20909	−	13.3523i	−0.300649	−	0.953735i
$197$	−17.1669	+	11.4705i	−1.22309	+	0.817242i	−0.987958	−	0.154721i	$-0.950552\pi$
$197$	−17.1669	+	11.4705i	−1.22309	+	0.817242i	−0.235132	+	0.971964i	$0.575552\pi$
$198$	6.50533	−	17.0381i	0.462314	−	1.21084i
$199$	0.0262917	−	0.0201743i	0.00186377	−	0.00143012i	−0.607829	−	0.794068i	$-0.707959\pi$
$199$	0.0262917	−	0.0201743i	0.00186377	−	0.00143012i	0.609693	+	0.792638i	$0.291293\pi$
$200$	7.20157	−	4.33702i	0.509228	−	0.306674i
$201$	−5.23891	+	6.82748i	−0.369524	+	0.481573i
$202$	−0.0951414	+	0.175979i	−0.00669413	+	0.0123819i
$203$	0.735692	+	5.86830i	0.0516354	+	0.411874i
$204$	2.55403	+	6.33573i	0.178818	+	0.443590i
$205$	−0.228361	+	3.48412i	−0.0159494	+	0.243341i
$206$	−5.90292	−	2.70848i	−0.411276	−	0.188709i
$207$	2.67422	+	9.98034i	0.185871	+	0.693682i
$208$	7.91906	+	24.8732i	0.549088	+	1.72464i
$209$	−24.4200	−	24.4200i	−1.68917	−	1.68917i
$210$	−0.640542	−	4.16249i	−0.0442016	−	0.287239i
$211$	1.54125	+	1.02983i	0.106104	+	0.0708966i	0.607490	−	0.794327i	$-0.292176\pi$
$211$	1.54125	+	1.02983i	0.106104	+	0.0708966i	−0.501386	+	0.865224i	$0.667176\pi$
$212$	−9.13197	−	2.54022i	−0.627186	−	0.174463i
$213$	4.55932	−	5.19891i	0.312399	−	0.356223i
$214$	6.03645	−	25.3434i	0.412643	−	1.73244i
$215$	−0.484888	+	0.631919i	−0.0330691	+	0.0430965i
$216$	−10.6779	+	5.51311i	−0.726540	+	0.375120i
$217$	−9.69680	+	14.3198i	−0.658262	+	0.972092i
$218$	−0.209884	+	2.03190i	−0.0142151	+	0.137617i
$219$	−0.0345686	−	0.0170473i	−0.00233593	−	0.00115195i
$220$	−11.5282	−	10.3055i	−0.777230	−	0.694798i
$221$	9.06440	−	26.7029i	0.609738	−	1.79623i
$222$	−8.09579	+	1.84713i	−0.543354	+	0.123971i
$223$			15.0007i			1.00452i	0.864716	+	0.502261i	$0.167498\pi$
$223$			15.0007i			1.00452i	−0.864716	+	0.502261i	$0.832502\pi$
$224$	3.91366	+	14.4459i	0.261492	+	0.965206i
$225$		−	7.05969i		−	0.470646i
$226$	−0.423741	−	1.85721i	−0.0281868	−	0.123540i
$227$	0.963495	−	2.83837i	0.0639494	−	0.188389i	−0.910259	−	0.414040i	$-0.864117\pi$
$227$	0.963495	−	2.83837i	0.0639494	−	0.188389i	0.974208	+	0.225651i	$0.0724508\pi$
$228$	0.562213	+	10.0397i	0.0372335	+	0.664895i
$229$	11.6910	+	5.76537i	0.772564	+	0.380986i	0.785446	−	0.618931i	$-0.212434\pi$
$229$	11.6910	+	5.76537i	0.772564	+	0.380986i	−0.0128817	+	0.999917i	$0.504100\pi$
$230$	8.71400	+	0.900108i	0.574584	+	0.0593513i
$231$	10.2142	−	4.95881i	0.672045	−	0.326265i
$232$	−0.529912	−	6.30034i	−0.0347904	−	0.413638i
$233$	5.42440	−	7.06921i	0.355364	−	0.463119i	−0.581126	−	0.813814i	$-0.697388\pi$
$233$	5.42440	−	7.06921i	0.355364	−	0.463119i	0.936490	+	0.350694i	$0.114054\pi$
$234$	21.3243	+	5.07915i	1.39401	+	0.332034i
$235$	−0.729882	+	0.832271i	−0.0476123	+	0.0542914i
$236$	−5.89125	+	3.32702i	−0.383487	+	0.216571i
$237$	−5.20143	−	3.47549i	−0.337869	−	0.225757i
$238$	5.86050	−	15.0689i	0.379880	−	0.976773i
$239$	1.66544	+	1.66544i	0.107729	+	0.107729i	0.758917	−	0.651188i	$-0.225729\pi$
$239$	1.66544	+	1.66544i	0.107729	+	0.107729i	−0.651188	+	0.758917i	$0.725729\pi$
$240$	0.502669	+	4.47412i	0.0324471	+	0.288803i
$241$	4.25955	+	15.8969i	0.274382	+	1.02401i	0.956254	+	0.292536i	$0.0944992\pi$
$241$	4.25955	+	15.8969i	0.274382	+	1.02401i	−0.681873	+	0.731471i	$0.738834\pi$
$242$	10.8980	−	23.7513i	0.700548	−	1.52679i
$243$	−1.02840	+	15.6903i	−0.0659717	+	1.00653i
$244$	7.80570	−	18.3491i	0.499709	−	1.17468i
$245$	−5.64001	+	8.21900i	−0.360327	+	0.525093i
$246$	2.41105	+	1.30351i	0.153723	+	0.0831089i
$247$	25.2694	−	32.9317i	1.60785	−	2.09539i
$248$	10.9822	−	14.8729i	0.697370	−	0.944430i
$249$	−5.78483	+	4.43885i	−0.366598	+	0.281301i
$250$	−14.9987	−	5.72669i	−0.948603	−	0.362187i
$251$	6.46726	−	4.32129i	0.408210	−	0.272757i	−0.334466	−	0.942408i	$-0.608556\pi$
$251$	6.46726	−	4.32129i	0.408210	−	0.272757i	0.742676	+	0.669650i	$0.233556\pi$
$252$	12.0877	+	3.44308i	0.761456	+	0.216894i
$253$	4.60768	+	23.1644i	0.289682	+	1.45633i
$254$	5.26011	−	8.36994i	0.330049	−	0.525177i
$255$	2.43190	−	4.21217i	0.152291	−	0.263776i
$256$	−3.55040	−	15.6011i	−0.221900	−	0.975069i
$257$	21.0239	−	12.1381i	1.31143	−	0.757156i	0.329099	−	0.944295i	$-0.393255\pi$
$257$	21.0239	−	12.1381i	1.31143	−	0.757156i	0.982333	+	0.187140i	$0.0599216\pi$
$258$	0.292118	+	0.552822i	0.0181865	+	0.0344172i
$259$	16.9599	+	9.93210i	1.05383	+	0.617151i
$260$	10.4721	−	15.3545i	0.649453	−	0.952247i
$261$	−4.76197	−	2.34834i	−0.294758	−	0.145359i
$262$	−15.2452	+	2.44260i	−0.941854	+	0.150904i
$263$	−15.5917	−	20.3195i	−0.961426	−	1.25296i	−0.967473	−	0.252973i	$-0.918591\pi$
$263$	−15.5917	−	20.3195i	−0.961426	−	1.25296i	0.00604691	−	0.999982i	$-0.498075\pi$
$264$	−11.1266	+	4.85132i	−0.684795	+	0.298578i
$265$	2.58267	+	6.23512i	0.158652	+	0.383021i
$266$	15.2988	−	18.2313i	0.938030	−	1.11783i
$267$	−0.678322	+	3.41015i	−0.0415126	+	0.208698i
$268$	−21.6150	+	2.63682i	−1.32035	+	0.161070i
$269$	2.03662	+	4.12987i	0.124175	+	0.251802i	0.950079	−	0.312008i	$-0.101002\pi$
$269$	2.03662	+	4.12987i	0.124175	+	0.251802i	−0.825904	+	0.563810i	$0.809335\pi$
$270$	7.77670	+	3.56824i	0.473275	+	0.217156i
$271$	−0.233855	+	0.872757i	−0.0142057	+	0.0530162i	−0.972665	−	0.232213i	$-0.925403\pi$
$271$	−0.233855	+	0.872757i	−0.0142057	+	0.0530162i	0.958459	+	0.285230i	$0.0920699\pi$
$272$	−6.91709	+	15.8404i	−0.419410	+	0.960463i
$273$	7.51170	+	11.3939i	0.454629	+	0.689593i
$274$	0.408801	−	0.493324i	0.0246966	−	0.0298028i
$275$	1.05543	−	16.1027i	0.0636447	−	0.971031i
$276$	3.49487	−	5.92251i	0.210366	−	0.356493i
$277$	17.3829	+	15.2444i	1.04444	+	0.915949i	0.996558	−	0.0829040i	$-0.0264195\pi$
$277$	17.3829	+	15.2444i	1.04444	+	0.915949i	0.0478821	+	0.998853i	$0.484753\pi$
$278$	0.256490	+	0.242528i	0.0153832	+	0.0145459i
$279$	−5.94147	−	14.3440i	−0.355706	−	0.858751i
$280$	6.38284	−	8.53320i	0.381448	−	0.509956i
$281$	−12.3506	+	29.8170i	−0.736776	+	1.77874i	−0.118231	+	0.992986i	$0.537722\pi$
$281$	−12.3506	+	29.8170i	−0.736776	+	1.77874i	−0.618546	+	0.785749i	$0.712278\pi$
$282$	0.354861	+	0.793206i	0.0211317	+	0.0472347i
$283$	−20.2082	+	1.32451i	−1.20125	+	0.0787341i	−0.652853	−	0.757484i	$-0.726428\pi$
$283$	−20.2082	+	1.32451i	−1.20125	+	0.0787341i	−0.548397	+	0.836218i	$0.684762\pi$
$284$	17.4694	−	0.978267i	1.03662	−	0.0580495i
$285$	5.38279	−	4.72058i	0.318849	−	0.279623i
$286$	47.8801	+	14.7732i	2.83121	+	0.873560i
$287$	−2.04724	−	6.15576i	−0.120845	−	0.363363i
$288$	−12.7614	−	4.20490i	−0.751974	−	0.247776i
$289$	1.44861	−	0.836355i	0.0852124	−	0.0491974i
$290$	−3.30022	+	3.06167i	−0.193796	+	0.179787i
$291$	−7.70168	−	2.61437i	−0.451480	−	0.153257i
$292$	−0.0304692	−	0.0926443i	−0.00178307	−	0.00542160i
$293$	−20.9449	+	13.9949i	−1.22361	+	0.817591i	−0.988030	−	0.154263i	$-0.950700\pi$
$293$	−20.9449	+	13.9949i	−1.22361	+	0.817591i	−0.235582	+	0.971854i	$0.575700\pi$
$294$	4.01765	+	6.71460i	0.234314	+	0.391603i
$295$	4.45056	+	1.84348i	0.259122	+	0.107332i
$296$	−17.6826	−	11.3487i	−1.02778	−	0.659627i
$297$	−3.01096	+	22.8705i	−0.174714	+	1.32708i
$298$	−21.6280	−	5.15148i	−1.25287	−	0.298417i
$299$	−26.8813	+	9.12497i	−1.55459	+	0.527711i
$300$	−3.35386	+	3.29068i	−0.193635	+	0.189987i
$301$	0.391858	−	1.42708i	0.0225863	−	0.0822553i
$302$	−13.6731	+	16.5001i	−0.786796	+	0.949472i
$303$	0.0289390	−	0.108002i	0.00166250	−	0.00620453i
$304$	−17.1366	+	18.8067i	−0.982850	+	1.07864i
$305$	−13.7138	+	3.67461i	−0.785252	+	0.210408i
$306$	8.39862	+	11.8387i	0.480117	+	0.676776i
$307$	11.8945	+	7.94768i	0.678857	+	0.453598i	0.846598	−	0.532233i	$-0.178647\pi$
$307$	11.8945	+	7.94768i	0.678857	+	0.453598i	−0.167740	+	0.985831i	$0.553647\pi$
$308$	27.0567	+	9.66059i	1.54170	+	0.550463i
$309$	3.56020	+	0.708167i	0.202533	+	0.0402862i
$310$	−13.1585	+	0.368142i	−0.747350	+	0.0209091i
$311$	0.0682155	−	0.518148i	0.00386815	−	0.0293815i	−0.989402	−	0.145203i	$-0.953617\pi$
$311$	0.0682155	−	0.518148i	0.00386815	−	0.0293815i	0.993270	+	0.115821i	$0.0369499\pi$
$312$	−7.52676	−	12.4981i	−0.426119	−	0.707565i
$313$	0.885500	−	0.116578i	0.0500514	−	0.00658940i	−0.105459	−	0.994424i	$-0.533631\pi$
$313$	0.885500	−	0.116578i	0.0500514	−	0.00658940i	0.155510	+	0.987834i	$0.450298\pi$
$314$	−10.2424	−	12.6021i	−0.578010	−	0.711175i
$315$	−3.37338	−	8.28866i	−0.190069	−	0.467013i
$316$	−2.94027	−	15.5533i	−0.165403	−	0.874940i
$317$	10.8194	−	9.48834i	0.607677	−	0.532918i	−0.299267	−	0.954169i	$-0.596742\pi$
$317$	10.8194	−	9.48834i	0.607677	−	0.532918i	0.906944	+	0.421251i	$0.138409\pi$
$318$	5.29405	+	0.198512i	0.296876	+	0.0111320i
$319$	−10.5107	−	6.06835i	−0.588486	−	0.339762i
$320$	−7.19001	+	8.83642i	−0.401934	+	0.493971i
$321$			14.5610i			0.812718i
$322$	−15.6263	+	4.55416i	−0.870822	+	0.253793i
$323$	26.9580	−	5.36229i	1.49999	−	0.298366i
$324$	−5.71197	+	4.91396i	−0.317332	+	0.272998i
$325$	19.3546	−	1.26857i	1.07360	−	0.0703676i
$326$	−10.1405	+	1.62472i	−0.561631	+	0.0899847i
$327$	−0.149021	−	1.13193i	−0.00824090	−	0.0625958i
$328$	1.91831	+	6.66459i	0.105921	+	0.367990i
$329$	0.673144	−	1.94345i	0.0371116	−	0.107146i
$330$	7.60250	+	4.11022i	0.418504	+	0.226260i
$331$	11.5066	−	3.90597i	0.632460	−	0.214691i	0.0132447	−	0.999912i	$-0.495784\pi$
$331$	11.5066	−	3.90597i	0.632460	−	0.214691i	0.619216	+	0.785221i	$0.287451\pi$
$332$	−18.2683	−	2.58203i	−1.00260	−	0.141707i
$333$	−15.8249	+	7.80397i	−0.867198	+	0.427655i
$334$	17.2415	−	12.2314i	0.943413	−	0.669275i
$335$	10.9630	+	10.9630i	0.598974	+	0.598974i
$336$	−3.99865	−	7.34745i	−0.218144	−	0.400836i
$337$	21.5579	−	21.5579i	1.17434	−	1.17434i	0.193170	−	0.981165i	$-0.438123\pi$
$337$	21.5579	−	21.5579i	1.17434	−	1.17434i	0.981165	−	0.193170i	$-0.0618769\pi$
$338$	−7.01204	+	41.2500i	−0.381405	+	2.24370i
$339$	0.470903	+	0.954897i	0.0255760	+	0.0518629i
$340$	11.9172	−	3.07205i	0.646301	−	0.166605i
$341$	−11.4077	−	33.6060i	−0.617762	−	1.81987i
$342$	6.10506	+	20.4756i	0.330124	+	1.10720i
$343$	3.94943	−	18.0943i	0.213249	−	0.976998i
$344$	−0.480801	+	1.50725i	−0.0259230	+	0.0812655i
$345$	−4.85440	+	0.639094i	−0.261352	+	0.0344077i
$346$	6.99819	−	9.66853i	0.376225	−	0.519783i
$347$	−1.35760	−	20.7130i	−0.0728800	−	1.11193i	−0.865067	−	0.501656i	$-0.832725\pi$
$347$	−1.35760	−	20.7130i	−0.0728800	−	1.11193i	0.792188	−	0.610278i	$-0.208942\pi$
$348$	1.10403	+	3.35689i	0.0591820	+	0.179948i
$349$	2.79076	+	14.0301i	0.149386	+	0.751013i	0.980747	+	0.195281i	$0.0625620\pi$
$349$	2.79076	+	14.0301i	0.149386	+	0.751013i	−0.831361	+	0.555732i	$0.812438\pi$
$350$	11.1184	−	0.242273i	0.594301	−	0.0129501i
$351$	−27.7264			−1.47993
$352$	−28.4794	−	11.4990i	−1.51796	−	0.612897i
$353$	−17.1985	+	29.7887i	−0.915383	+	1.58549i	−0.109045	+	0.994037i	$0.534779\pi$
$353$	−17.1985	+	29.7887i	−0.915383	+	1.58549i	−0.806339	+	0.591454i	$0.798554\pi$
$354$	2.77223	−	2.57185i	0.147343	−	0.136692i
$355$	−8.21394	−	9.36620i	−0.435951	−	0.497106i
$356$	−7.36118	+	4.81797i	−0.390142	+	0.255352i
$357$	−1.23491	+	8.95198i	−0.0653583	+	0.473789i
$358$	2.56649	−	24.8463i	0.135643	−	1.31317i
$359$	3.76686	+	28.6122i	0.198807	+	1.51009i	0.741952	+	0.670453i	$0.233900\pi$
$359$	3.76686	+	28.6122i	0.198807	+	1.51009i	−0.543145	+	0.839639i	$0.682767\pi$
$360$	3.24182	+	9.00069i	0.170859	+	0.474378i
$361$	21.2760	+	2.80104i	1.11979	+	0.147423i
$362$	−22.4715	+	23.7651i	−1.18108	+	1.24907i
$363$	−2.84941	+	14.3250i	−0.149555	+	0.751866i
$364$	−7.26739	+	33.7581i	−0.380915	+	1.76941i
$365$	−0.0385781	+	0.0577363i	−0.00201927	+	0.00302205i
$366$	−1.86773	+	10.9873i	−0.0976276	+	0.574318i
$367$	−1.77426	−	6.62164i	−0.0926158	−	0.345647i	0.904031	−	0.427466i	$-0.140594\pi$
$367$	−1.77426	−	6.62164i	−0.0926158	−	0.345647i	−0.996647	+	0.0818192i	$0.973927\pi$
$368$	16.8900	−	4.18307i	0.880450	−	0.218058i
$369$	5.62551	+	1.50735i	0.292852	+	0.0784695i
$370$	1.39553	+	14.8947i	0.0725501	+	0.774340i
$371$	−8.81151	−	8.92116i	−0.457471	−	0.463163i
$372$	−4.04498	+	9.50867i	−0.209722	+	0.493002i
$373$	4.64377	+	13.6801i	0.240445	+	0.708329i	0.998428	+	0.0560543i	$0.0178520\pi$
$373$	4.64377	+	13.6801i	0.240445	+	0.708329i	−0.757982	+	0.652275i	$0.773815\pi$
$374$	17.3868	+	28.2591i	0.899052	+	1.46124i
$375$	8.89649	+	1.17124i	0.459413	+	0.0604828i
$376$	−0.803777	+	2.04655i	−0.0414517	+	0.105543i
$377$	5.58246	−	13.4773i	0.287512	−	0.694114i
$378$	−15.8821	−	0.693898i	−0.816885	−	0.0356902i
$379$	−12.3677	−	18.5096i	−0.635287	−	0.950775i	−0.999808	−	0.0195795i	$-0.993767\pi$
$379$	−12.3677	−	18.5096i	−0.635287	−	0.950775i	0.364521	−	0.931195i	$-0.381233\pi$
$380$	18.0647	+	1.35666i	0.926700	+	0.0695950i
$381$	−1.77601	+	5.23197i	−0.0909879	+	0.268042i
$382$	−15.4409	−	0.578989i	−0.790025	−	0.0296237i
$383$	−3.59342	−	6.22399i	−0.183615	−	0.318031i	0.759494	−	0.650515i	$-0.225447\pi$
$383$	−3.59342	−	6.22399i	−0.183615	−	0.318031i	−0.943109	+	0.332484i	$0.892113\pi$
$384$	3.95075	+	8.02260i	0.201611	+	0.409401i
$385$	−6.45532	−	19.4103i	−0.328994	−	0.989238i
$386$	25.9906	−	13.7338i	1.32288	−	0.699030i
$387$	0.875996	+	0.998882i	0.0445294	+	0.0507760i
$388$	−8.92622	−	18.5430i	−0.453160	−	0.941380i
$389$	0.217513	+	3.31861i	0.0110284	+	0.168260i	0.999820	+	0.0189599i	$0.00603549\pi$
$389$	0.217513	+	3.31861i	0.0110284	+	0.168260i	−0.988792	+	0.149300i	$0.952298\pi$
$390$	−3.70528	+	9.70447i	−0.187624	+	0.491405i
$391$	−17.3666	−	7.19348i	−0.878267	−	0.363790i
$392$	−5.00771	+	19.1552i	−0.252928	+	0.967485i
$393$	7.97257	−	3.30235i	0.402163	−	0.166581i
$394$	29.1870	−	0.816583i	1.47042	−	0.0411389i
$395$	−7.43090	+	8.47332i	−0.373889	+	0.426339i
$396$	−20.6106	+	15.5059i	−1.03572	+	0.779203i
$397$	25.9667	+	1.70195i	1.30323	+	0.0854182i	0.701148	−	0.713016i	$-0.252671\pi$
$397$	25.9667	+	1.70195i	1.30323	+	0.0854182i	0.602082	+	0.798434i	$0.294338\pi$
$398$	−0.0466626	+	0.00437195i	−0.00233899	+	0.000219146i
$399$	−5.95702	+	11.8937i	−0.298224	+	0.595428i
$400$	−11.8867	−	0.226094i	−0.594335	−	0.0113047i
$401$	19.1390	+	5.12829i	0.955758	+	0.256094i	0.702804	−	0.711384i	$-0.251931\pi$
$401$	19.1390	+	5.12829i	0.955758	+	0.256094i	0.252954	+	0.967478i	$0.418598\pi$
$402$	11.4107	−	4.23286i	0.569114	−	0.211116i
$403$	38.2574	−	18.8665i	1.90574	−	0.939806i
$404$	0.246346	−	0.139122i	0.0122562	−	0.00692156i
$405$	5.26173	+	1.04662i	0.261458	+	0.0520071i
$406$	3.53500	−	7.58025i	0.175439	−	0.376202i
$407$	−37.2623	+	15.4346i	−1.84702	+	0.765063i
$408$	1.70948	−	9.50825i	0.0846318	−	0.470728i
$409$	−0.718537	+	0.551353i	−0.0355294	+	0.0272626i	−0.626373	−	0.779523i	$-0.715461\pi$
$409$	−0.718537	+	0.551353i	−0.0355294	+	0.0272626i	0.590844	+	0.806786i	$0.298795\pi$
$410$	2.89524	−	4.00000i	0.142986	−	0.197546i
$411$	−0.158380	+	0.321163i	−0.00781231	+	0.0158418i
$412$	5.02996	+	7.68507i	0.247808	+	0.378616i
$413$	−8.95012	−	0.0553424i	−0.440407	−	0.00272322i
$414$	4.30814	−	13.9627i	0.211734	−	0.686230i
$415$	6.56818	+	11.3764i	0.322419	+	0.558447i
$416$	9.23491	−	35.7420i	0.452779	−	1.75239i
$417$	−0.170862	−	0.0986474i	−0.00836716	−	0.00483078i
$418$	10.8642	+	47.6164i	0.531383	+	2.32900i
$419$	14.4982	−	2.88386i	0.708281	−	0.140886i	0.172212	−	0.985060i	$-0.444909\pi$
$419$	14.4982	−	2.88386i	0.708281	−	0.140886i	0.536069	+	0.844174i	$0.319909\pi$
$420$	−2.36530	+	5.46613i	−0.115415	+	0.266720i
$421$	7.09866	+	10.6239i	0.345968	+	0.517777i	0.963122	−	0.269065i	$-0.0867146\pi$
$421$	7.09866	+	10.6239i	0.345968	+	0.517777i	−0.617154	+	0.786842i	$0.711715\pi$
$422$	−1.07053	−	2.39291i	−0.0521125	−	0.116485i
$423$	1.12404	+	1.46488i	0.0546526	+	0.0712247i
$424$	9.02300	+	9.91346i	0.438196	+	0.481440i
$425$	10.1894	+	7.81863i	0.494260	+	0.379259i
$426$	−9.37146	+	2.79421i	−0.454049	+	0.135380i
$427$	21.0265	−	15.9286i	1.01754	−	0.770839i
$428$	−26.2989	+	25.8035i	−1.27121	+	1.24726i
$429$	−27.9458	−	1.83166i	−1.34923	−	0.0884335i
$430$	1.05612	−	0.391773i	0.0509306	−	0.0188930i
$431$	−11.0861	+	2.97052i	−0.534000	+	0.143085i	−0.515735	−	0.856748i	$-0.672481\pi$
$431$	−11.0861	+	2.97052i	−0.534000	+	0.143085i	−0.0182653	+	0.999833i	$0.505814\pi$
$432$	16.9342	+	1.43382i	0.814749	+	0.0689846i
$433$	−4.17047	+	4.17047i	−0.200420	+	0.200420i	−0.800180	−	0.599760i	$-0.795263\pi$
$433$	−4.17047	+	4.17047i	−0.200420	+	0.200420i	0.599760	+	0.800180i	$0.295263\pi$
$434$	22.3865	−	9.84952i	1.07459	−	0.472792i
$435$	1.39785	−	2.09203i	0.0670217	−	0.100305i
$436$	1.78032	−	2.27503i	0.0852618	−	0.108954i
$437$	−20.8033	−	18.2440i	−0.995156	−	0.872728i
$438$	0.0285639	+	0.0464252i	0.00136483	+	0.00221828i
$439$	−19.5754	−	15.0207i	−0.934284	−	0.716901i	0.0248983	−	0.999690i	$-0.492074\pi$
$439$	−19.5754	−	15.0207i	−0.934284	−	0.716901i	−0.959182	+	0.282789i	$0.908740\pi$
$440$	6.04879	+	21.0147i	0.288365	+	1.00184i
$441$	11.6105	+	11.9013i	0.552881	+	0.566728i
$442$	−30.9476	+	25.1527i	−1.47203	+	1.19639i
$443$	1.82892	−	3.70868i	0.0868945	−	0.176205i	−0.849088	−	0.528252i	$-0.822848\pi$
$443$	1.82892	−	3.70868i	0.0868945	−	0.176205i	0.935982	+	0.352047i	$0.114514\pi$
$444$	11.0838	+	3.88036i	0.526013	+	0.184154i
$445$	5.93157	+	2.01350i	0.281183	+	0.0954489i
$446$	11.2881	−	17.9617i	0.534505	−	0.850510i
$447$	12.4263			0.587745
$448$	6.18439	−	20.2424i	0.292185	−	0.956362i
$449$	2.33659			0.110270			0.0551352	−	0.998479i	$-0.482441\pi$
$449$	2.33659			0.110270			0.0551352	+	0.998479i	$0.482441\pi$
$450$	−5.31243	+	8.45319i	−0.250430	+	0.398487i
$451$	12.6061	+	4.27920i	0.593598	+	0.201499i
$452$	−0.890174	+	2.54267i	−0.0418703	+	0.119597i
$453$	5.29729	−	10.7418i	0.248888	−	0.504696i
$454$	−3.28956	+	2.67360i	−0.154386	+	0.125478i
$455$	22.1178	−	10.7378i	1.03690	−	0.503395i
$456$	6.88171	−	12.4445i	0.322266	−	0.582767i
$457$	10.0696	+	7.72666i	0.471035	+	0.361438i	0.816836	−	0.576870i	$-0.195726\pi$
$457$	10.0696	+	7.72666i	0.471035	+	0.361438i	−0.345801	+	0.938308i	$0.612393\pi$
$458$	−9.66024	−	15.7009i	−0.451393	−	0.733655i
$459$	−13.8034	−	12.1053i	−0.644287	−	0.565025i
$460$	−9.75671	−	7.63508i	−0.454909	−	0.355988i
$461$	4.15353	−	6.21619i	0.193449	−	0.289517i	−0.722047	−	0.691844i	$-0.756799\pi$
$461$	4.15353	−	6.21619i	0.193449	−	0.289517i	0.915496	+	0.402327i	$0.131799\pi$
$462$	−15.9619	−	1.74859i	−0.742614	−	0.0813517i
$463$	−7.28740	+	7.28740i	−0.338674	+	0.338674i	−0.855868	−	0.517194i	$-0.826977\pi$
$463$	−7.28740	+	7.28740i	−0.338674	+	0.338674i	0.517194	+	0.855868i	$0.326977\pi$
$464$	−4.10651	+	7.94272i	−0.190640	+	0.368731i
$465$	7.10662	−	1.90421i	0.329562	−	0.0883058i
$466$	−11.8147	+	4.38272i	−0.547306	+	0.203026i
$467$	−15.7511	−	1.03238i	−0.728876	−	0.0477731i	−0.303553	−	0.952815i	$-0.598173\pi$
$467$	−15.7511	−	1.03238i	−0.728876	−	0.0477731i	−0.425323	+	0.905042i	$0.639840\pi$
$468$	−21.7114	−	22.1283i	−1.00361	−	1.02288i
$469$	−26.5446	−	11.1879i	−1.22572	−	0.516610i
$470$	1.50024	−	0.447314i	0.0692009	−	0.0206331i
$471$	7.20081	+	5.52537i	0.331796	+	0.254596i
$472$	9.55770	+	0.449436i	0.439929	+	0.0206870i
$473$	1.84876	+	2.40935i	0.0850061	+	0.110782i
$474$	3.61283	+	8.07560i	0.165943	+	0.370925i
$475$	10.5034	+	15.7194i	0.481928	+	0.721257i
$476$	−18.3567	+	13.6333i	−0.841378	+	0.624882i
$477$	11.0407	−	2.19614i	0.505521	−	0.100554i
$478$	−0.740934	−	3.24744i	−0.0338895	−	0.148534i
$479$	−4.81077	−	2.77750i	−0.219810	−	0.126907i	0.386052	−	0.922477i	$-0.373838\pi$
$479$	−4.81077	−	2.77750i	−0.219810	−	0.126907i	−0.605862	+	0.795570i	$0.707172\pi$
$480$	2.76489	−	5.73552i	0.126200	−	0.261789i
$481$	−24.2388	−	41.9828i	−1.10519	−	1.91425i
$482$	6.86209	−	22.2401i	0.312560	−	1.01301i
$483$	7.90632	−	4.49977i	0.359750	−	0.204746i
$484$	−30.9220	+	20.2388i	−1.40555	+	0.919944i
$485$	−6.48075	+	13.1417i	−0.294276	+	0.596732i
$486$	13.0384	−	18.0135i	0.591433	−	0.817110i
$487$	25.7470	−	19.7564i	1.16671	−	0.895247i	0.170772	−	0.985311i	$-0.445374\pi$
$487$	25.7470	−	19.7564i	1.16671	−	0.895247i	0.995936	+	0.0900640i	$0.0287072\pi$
$488$	−23.1542	+	16.0972i	−1.04814	+	0.728688i
$489$	5.30303	−	2.19659i	0.239811	−	0.0993331i
$490$	12.9381	−	5.59721i	0.584484	−	0.252856i
$491$	16.4118	+	3.26452i	0.740656	+	0.147326i	0.550977	−	0.834520i	$-0.314255\pi$
$491$	16.4118	+	3.26452i	0.740656	+	0.147326i	0.189679	+	0.981846i	$0.439255\pi$
$492$	−1.90607	−	3.37513i	−0.0859324	−	0.152163i
$493$	8.66332	−	4.27228i	0.390176	−	0.192414i
$494$	−55.0384	+	20.4168i	−2.47630	+	0.918594i
$495$	17.7383	+	4.75296i	0.797277	+	0.213630i
$496$	−24.3418	+	9.54452i	−1.09298	+	0.428562i
$497$	20.6953	+	10.3654i	0.928312	+	0.464951i
$498$	10.2669	−	0.961938i	0.460072	−	0.0431055i
$499$	−41.8982	−	2.74615i	−1.87562	−	0.122935i	−0.915464	−	0.402399i	$-0.868176\pi$
$499$	−41.8982	−	2.74615i	−1.87562	−	0.122935i	−0.960156	+	0.279464i	$0.909843\pi$
$500$	13.6500	+	18.1437i	0.610445	+	0.811409i
$501$	−7.79027	+	8.88310i	−0.348044	+	0.396868i
$502$	−10.9956	+	0.307631i	−0.490758	+	0.0137302i
$503$	3.69622	−	1.53103i	0.164806	−	0.0682650i	−0.298755	−	0.954330i	$-0.596571\pi$
$503$	3.69622	−	1.53103i	0.164806	−	0.0682650i	0.463561	+	0.886065i	$0.346571\pi$
$504$	−11.8828	−	13.2188i	−0.529302	−	0.588810i
$505$	−0.186103	−	0.0770864i	−0.00828148	−	0.00343030i
$506$	11.9141	−	31.2040i	0.529644	−	1.38719i
$507$	−1.52951	−	23.3359i	−0.0679280	−	1.03638i
$508$	−12.5968	+	6.06383i	−0.558893	+	0.269039i
$509$	−21.0215	−	23.9705i	−0.931763	−	1.06247i	−0.997907	−	0.0646618i	$-0.979403\pi$
$509$	−21.0215	−	23.9705i	−0.931763	−	1.06247i	0.0661444	−	0.997810i	$-0.478930\pi$
$510$	−6.08159	+	3.21359i	−0.269297	+	0.142300i
$511$	0.0259515	−	0.126378i	0.00114803	−	0.00559063i
$512$	−7.48867	+	21.3523i	−0.330955	+	0.943646i
$513$	−13.5126	−	23.4044i	−0.596594	−	1.03333i
$514$	−34.3077	−	1.28644i	−1.51325	−	0.0567424i
$515$	2.10209	−	6.19255i	0.0926291	−	0.272876i
$516$	0.0662202	−	0.881762i	0.00291518	−	0.0388174i
$517$	2.34486	+	3.50934i	0.103127	+	0.154340i
$518$	−12.8336	−	24.6549i	−0.563876	−	1.08327i
$519$	−2.55284	+	6.16310i	−0.112057	+	0.270530i
$520$	−24.0935	+	10.5050i	−1.05657	+	0.460676i
$521$	37.6651	+	4.95871i	1.65014	+	0.217245i	0.897445	−	0.441126i	$-0.145421\pi$
$521$	37.6651	+	4.95871i	1.65014	+	0.217245i	0.752693	+	0.658371i	$0.228754\pi$
$522$	3.93479	+	6.39527i	0.172221	+	0.279913i
$523$	−6.78370	−	19.9841i	−0.296630	−	0.873845i	−0.988420	−	0.151746i	$-0.951511\pi$
$523$	−6.78370	−	19.9841i	−0.296630	−	0.873845i	0.691789	−	0.722100i	$-0.256823\pi$
$524$	20.0925	+	8.54734i	0.877747	+	0.373392i
$525$	−6.01372	+	1.57158i	−0.262460	+	0.0685894i
$526$	3.37886	+	36.0632i	0.147325	+	1.57243i
$527$	27.2832	+	7.31052i	1.18848	+	0.318451i
$528$	16.9735	+	2.56387i	0.738677	+	0.111578i
$529$	−1.05519	−	3.93801i	−0.0458777	−	0.171218i
$530$	1.59948	−	9.40934i	0.0694770	−	0.408715i
$531$	4.46409	−	6.68098i	0.193725	−	0.289930i
$532$	−32.0377	+	10.3176i	−1.38901	+	0.447324i
$533$	−3.12165	+	15.6936i	−0.135214	+	0.679765i
$534$	3.37836	−	3.57284i	0.146196	−	0.154612i
$535$	26.0083	+	3.42406i	1.12444	+	0.148035i
$536$	27.8658	+	13.1081i	1.20362	+	0.566182i
$537$	1.82226	+	13.8414i	0.0786362	+	0.597301i
$538$	0.669102	−	6.47762i	0.0288470	−	0.279270i
$539$	24.7036	+	28.8819i	1.06406	+	1.24403i
$540$	−6.62662	−	10.1246i	−0.285165	−	0.435691i
$541$	0.472939	+	0.539283i	0.0203332	+	0.0231856i	0.761917	−	0.647675i	$-0.224258\pi$
$541$	0.472939	+	0.539283i	0.0203332	+	0.0231856i	−0.741584	+	0.670860i	$0.765925\pi$
$542$	0.936767	−	0.869054i	0.0402376	−	0.0373290i
$543$	9.14021	−	15.8313i	0.392244	−	0.679387i
$544$	20.2024	−	13.7620i	0.866169	−	0.590039i
$545$	−2.05685			−0.0881057
$546$	−0.420458	−	19.2955i	−0.0179939	−	0.825773i
$547$	5.81192	+	29.2185i	0.248500	+	1.24929i	0.880396	+	0.474240i	$0.157277\pi$
$547$	5.81192	+	29.2185i	0.248500	+	1.24929i	−0.631896	+	0.775053i	$0.717723\pi$
$548$	−0.860721	+	0.283077i	−0.0367682	+	0.0120924i
$549$	1.54885	+	23.6308i	0.0661031	+	1.00854i
$550$	−13.3811	+	18.4870i	−0.570572	+	0.788289i
$551$	14.0971	−	1.85592i	0.600556	−	0.0790647i
$552$	−8.64142	+	4.46165i	−0.367803	+	0.189900i
$553$	6.85325	−	19.7862i	0.291430	−	0.841396i
$554$	−9.34267	−	31.3342i	−0.396932	−	1.33126i
$555$	−2.68766	−	7.91759i	−0.114085	−	0.336083i
$556$	−0.124615	−	0.483410i	−0.00528484	−	0.0205011i
$557$	7.51455	+	15.2380i	0.318402	+	0.645655i	0.995958	−	0.0898158i	$-0.0286278\pi$
$557$	7.51455	+	15.2380i	0.318402	+	0.645655i	−0.677557	+	0.735471i	$0.736961\pi$
$558$	−3.67963	+	21.6463i	−0.155771	+	0.916360i
$559$	−2.58110	+	2.58110i	−0.109169	+	0.109169i
$560$	−14.0640	+	5.41445i	−0.594312	+	0.228802i
$561$	−13.1129	−	13.1129i	−0.553628	−	0.553628i
$562$	37.2259	−	26.4087i	1.57028	−	1.11398i
$563$	−38.3700	+	18.9220i	−1.61710	+	0.797467i	−0.617160	+	0.786837i	$0.711717\pi$
$563$	−38.3700	+	18.9220i	−1.61710	+	0.797467i	−0.999944	+	0.0106299i	$0.996616\pi$
$564$	0.171983	−	1.21681i	0.00724178	−	0.0512369i
$565$	1.81633	−	0.616562i	0.0764137	−	0.0259390i
$566$	25.1937	+	13.6207i	1.05897	+	0.572522i
$567$	−9.78795	+	1.88410i	−0.411055	+	0.0791250i
$568$	−21.6538	−	11.9744i	−0.908572	−	0.502433i
$569$	−3.14033	−	23.8532i	−0.131650	−	0.999978i	−0.921964	−	0.387276i	$-0.873416\pi$
$569$	−3.14033	−	23.8532i	−0.131650	−	0.999978i	0.790314	−	0.612702i	$-0.209917\pi$
$570$	−9.99754	+	1.60181i	−0.418751	+	0.0670923i
$571$	−9.28403	+	0.608507i	−0.388524	+	0.0254652i	−0.258414	−	0.966034i	$-0.583200\pi$
$571$	−9.28403	+	0.608507i	−0.388524	+	0.0254652i	−0.130110	+	0.991500i	$0.541533\pi$
$572$	−46.2142	−	53.7192i	−1.93231	−	2.24611i
$573$	8.47025	−	1.68484i	0.353850	−	0.0703851i
$574$	−2.18088	+	8.91139i	−0.0910283	+	0.371954i
$575$		−	12.9293i		−	0.539190i
$576$	12.1162	+	14.6379i	0.504841	+	0.609913i
$577$	−37.8353	−	21.8442i	−1.57511	−	0.909387i	−0.995528	−	0.0944702i	$-0.969884\pi$
$577$	−37.8353	−	21.8442i	−1.57511	−	0.909387i	−0.579577	−	0.814917i	$-0.696782\pi$
$578$	−2.36391	−	0.0886398i	−0.0983257	−	0.00368693i
$579$	−12.3526	+	10.8329i	−0.513357	+	0.450202i
$580$	6.25556	−	1.18258i	0.259748	−	0.0491041i
$581$	−19.2711	−	14.9774i	−0.799498	−	0.621369i
$582$	7.25459	+	8.92595i	0.300712	+	0.369992i
$583$	25.5116	−	3.35866i	1.05658	−	0.139102i
$584$	−0.0332317	+	0.133859i	−0.00137514	+	0.00553914i
$585$	−2.88105	+	21.8838i	−0.119117	+	0.904783i
$586$	35.6103	−	0.996292i	1.47105	−	0.0411564i
$587$	−29.7847	−	5.92454i	−1.22934	−	0.244532i	−0.462648	−	0.886542i	$-0.653101\pi$
$587$	−29.7847	−	5.92454i	−1.22934	−	0.244532i	−0.766696	+	0.642010i	$0.778101\pi$
$588$	0.242058	−	11.0633i	0.00998231	−	0.456242i
$589$	34.5705	+	23.0993i	1.42445	+	0.951788i
$590$	−3.94183	−	5.55643i	−0.162283	−	0.228754i
$591$	−15.7634	+	4.22378i	−0.648418	+	0.173743i
$592$	12.6331	+	26.8950i	0.519216	+	1.10538i
$593$	−3.19949	+	11.9407i	−0.131387	+	0.490344i	−0.999987	−	0.00517080i	$-0.998354\pi$
$593$	−3.19949	+	11.9407i	−0.131387	+	0.490344i	0.868599	+	0.495515i	$0.165021\pi$
$594$	20.8154	−	25.1192i	0.854067	−	1.03065i
$595$	15.6993	+	4.31082i	0.643607	+	0.176727i
$596$	22.0206	+	22.4434i	0.901998	+	0.919318i
$597$	0.0248045	−	0.00841998i	0.00101518	−	0.000344607i
$598$	39.0539	+	9.30210i	1.59703	+	0.380391i
$599$	−1.46353	+	11.1166i	−0.0597983	+	0.454213i	0.935184	+	0.354162i	$0.115234\pi$
$599$	−1.46353	+	11.1166i	−0.0597983	+	0.454213i	−0.994982	+	0.100051i	$0.968099\pi$
$600$	6.49212	−	1.41643i	0.265040	−	0.0578255i
$601$	10.0321	+	4.15543i	0.409218	+	0.169504i	0.577790	−	0.816186i	$-0.303915\pi$
$601$	10.0321	+	4.15543i	0.409218	+	0.169504i	−0.168572	+	0.985689i	$0.553915\pi$
$602$	−1.54308	+	1.41389i	−0.0628914	+	0.0576260i
$603$	21.5024	−	14.3674i	0.875644	−	0.585086i
$604$	28.7883	−	9.46798i	1.17138	−	0.385247i
$605$	24.9166	+	8.45806i	1.01301	+	0.343869i
$606$	−0.115923	+	0.107543i	−0.00470904	+	0.00436865i
$607$	30.0983	−	17.3773i	1.22165	−	0.705322i	0.256383	−	0.966575i	$-0.417469\pi$
$607$	30.0983	−	17.3773i	1.22165	−	0.705322i	0.965270	+	0.261254i	$0.0841359\pi$
$608$	34.6712	−	9.62359i	1.40610	−	0.390288i
$609$	−0.940332	+	4.57920i	−0.0381042	+	0.185559i
$610$	19.1860	+	5.91976i	0.776817	+	0.239684i
$611$	−3.81408	+	3.34486i	−0.154301	+	0.135318i
$612$	−1.14773	−	20.4956i	−0.0463943	−	0.828484i
$613$	−19.8550	+	1.30137i	−0.801936	+	0.0525617i	−0.460859	−	0.887473i	$-0.652459\pi$
$613$	−19.8550	+	1.30137i	−0.801936	+	0.0525617i	−0.341078	+	0.940035i	$0.610792\pi$
$614$	−8.26174	−	18.4671i	−0.333417	−	0.745273i
$615$	−1.05614	+	2.54976i	−0.0425878	+	0.102816i
$616$	−25.1277	−	31.9277i	−1.01243	−	1.28640i
$617$	1.30076	+	3.14031i	0.0523667	+	0.126424i	0.947898	−	0.318574i	$-0.103204\pi$
$617$	1.30076	+	3.14031i	0.0523667	+	0.126424i	−0.895531	+	0.444999i	$0.853204\pi$
$618$	−3.73004	−	3.52701i	−0.150044	−	0.141877i
$619$	−13.6691	−	11.9874i	−0.549406	−	0.481816i	0.339056	−	0.940766i	$-0.389892\pi$
$619$	−13.6691	−	11.9874i	−0.549406	−	0.481816i	−0.888462	+	0.458950i	$0.848226\pi$
$620$	16.0328	+	9.46096i	0.643893	+	0.379961i
$621$	−1.20879	+	18.4426i	−0.0485071	+	0.740076i
$622$	−0.471588	+	0.569093i	−0.0189090	+	0.0228185i
$623$	−11.6179	+	0.689357i	−0.465460	+	0.0276185i
$624$	−0.392379	+	20.6290i	−0.0157077	+	0.825820i
$625$	0.337735	−	1.26045i	0.0135094	−	0.0504178i
$626$	−1.14801	−	0.526751i	−0.0458838	−	0.0210532i
$627$	−12.0733	−	24.4823i	−0.482162	−	0.977729i
$628$	2.78101	+	22.7970i	0.110974	+	0.909698i
$629$	6.26244	−	31.4834i	0.249700	−	1.25533i
$630$	−2.19798	+	12.4632i	−0.0875698	+	0.496547i
$631$	−10.1954	−	24.6139i	−0.405873	−	0.979864i	−0.986212	−	0.165489i	$-0.947080\pi$
$631$	−10.1954	−	24.6139i	−0.405873	−	0.979864i	0.580339	−	0.814375i	$-0.302920\pi$
$632$	−8.18323	+	20.8359i	−0.325511	+	0.828807i
$633$	0.891938	+	1.16240i	0.0354513	+	0.0462011i
$634$	−20.0950	+	3.21963i	−0.798075	+	0.127868i
$635$	8.92749	+	4.40255i	0.354277	+	0.174710i
$636$	−6.18966	−	4.22148i	−0.245436	−	0.167393i
$637$	−30.5419	+	33.9696i	−1.21011	+	1.34592i
$638$	8.01893	+	15.1755i	0.317473	+	0.600803i
$639$	−17.9955	+	10.3897i	−0.711890	+	0.411010i
$640$	15.2587	−	5.17013i	0.603152	−	0.204367i
$641$	4.61643	−	7.99589i	0.182338	−	0.315818i	−0.760338	−	0.649527i	$-0.774967\pi$
$641$	4.61643	−	7.99589i	0.182338	−	0.315818i	0.942676	+	0.333709i	$0.108300\pi$
$642$	10.9572	−	17.4352i	0.432447	−	0.688114i
$643$	0.903511	+	4.54225i	0.0356310	+	0.179129i	0.994503	−	0.104711i	$-0.0333916\pi$
$643$	0.903511	+	4.54225i	0.0356310	+	0.179129i	−0.958872	+	0.283840i	$0.908392\pi$
$644$	22.1378	+	6.30576i	0.872353	+	0.248482i
$645$	−0.523481	+	0.349779i	−0.0206120	+	0.0137725i
$646$	−36.3144	−	13.8652i	−1.42877	−	0.545521i
$647$	−31.1980	+	23.9391i	−1.22652	+	0.941141i	−0.999464	−	0.0327404i	$-0.989577\pi$
$647$	−31.1980	+	23.9391i	−1.22652	+	0.941141i	−0.227055	+	0.973882i	$0.572910\pi$
$648$	10.5372	−	1.58566i	0.413941	−	0.0622904i
$649$	11.1811	−	14.5715i	0.438898	−	0.571983i
$650$	−24.1296	−	13.0454i	−0.946442	−	0.511684i
$651$	−10.8961	+	8.25433i	−0.427052	+	0.323513i
$652$	13.3647	+	5.68534i	0.523404	+	0.222655i
$653$	2.65261	−	40.4710i	0.103805	−	1.58375i	−0.555266	−	0.831673i	$-0.687384\pi$
$653$	2.65261	−	40.4710i	0.103805	−	1.58375i	0.659071	−	0.752081i	$-0.270950\pi$
$654$	−0.673343	+	1.46750i	−0.0263298	+	0.0573837i
$655$	−4.02375	−	15.0168i	−0.157221	−	0.586756i
$656$	2.71815	−	9.42363i	0.106126	−	0.367931i
$657$	0.0818996	+	0.0818996i	0.00319521	+	0.00319521i
$658$	−2.26847	+	1.82053i	−0.0884341	+	0.0709716i
$659$	−33.2438	−	22.2128i	−1.29499	−	0.865287i	−0.298960	−	0.954266i	$-0.596640\pi$
$659$	−33.2438	−	22.2128i	−1.29499	−	0.865287i	−0.996034	+	0.0889785i	$0.971640\pi$
$660$	−6.01021	−	10.6424i	−0.233947	−	0.414256i
$661$	14.3607	−	16.3753i	0.558567	−	0.636924i	−0.401778	−	0.915737i	$-0.631608\pi$
$661$	14.3607	−	16.3753i	0.558567	−	0.636924i	0.960345	+	0.278813i	$0.0899410\pi$
$662$	−16.7171	−	3.98179i	−0.649730	−	0.154757i
$663$	13.5690	−	17.6834i	0.526975	−	0.686768i
$664$	19.9313	+	16.8386i	0.773485	+	0.653466i
$665$	19.8432	+	13.4370i	0.769485	+	0.521065i
$666$	24.8210	+	2.56388i	0.961796	+	0.0993482i
$667$	−8.72120	−	4.30082i	−0.337686	−	0.166529i
$668$	−29.8490	+	1.67151i	−1.15489	+	0.0646728i
$669$	−3.81128	+	11.2277i	−0.147353	+	0.434086i
$670$	−4.87730	−	21.3767i	−0.188427	−	0.825854i
$671$			54.1321i			2.08975i
$672$	−0.741034	+	11.8067i	−0.0285860	+	0.455455i
$673$		−	13.0027i		−	0.501216i	−0.968089	−	0.250608i	$-0.919369\pi$
$673$		−	13.0027i		−	0.501216i	0.968089	−	0.250608i	$-0.0806306\pi$
$674$	−42.0356	+	9.59083i	−1.61915	+	0.369425i
$675$	4.05916	−	11.9579i	0.156237	−	0.460259i
$676$	39.4369	−	44.1157i	1.51680	−	1.69676i
$677$	−7.51851	−	3.70772i	−0.288960	−	0.142499i	0.292032	−	0.956408i	$-0.405669\pi$
$677$	−7.51851	−	3.70772i	−0.288960	−	0.142499i	−0.580992	+	0.813909i	$0.697335\pi$
$678$	0.154708	−	1.49774i	0.00594153	−	0.0575203i
$679$	1.94850	−	27.1545i	0.0747764	−	1.04209i
$680$	−16.5813	−	5.28929i	−0.635862	−	0.202835i
$681$	1.44231	−	1.87965i	0.0552693	−	0.0720283i
$682$	−11.6291	+	48.8238i	−0.445303	+	1.86956i
$683$	−2.85282	+	3.25302i	−0.109160	+	0.124473i	−0.803840	−	0.594846i	$-0.797213\pi$
$683$	−2.85282	+	3.25302i	−0.109160	+	0.124473i	0.694679	+	0.719320i	$0.255546\pi$
$684$	8.09784	−	29.1114i	0.309629	−	1.11310i
$685$	0.536405	+	0.358414i	0.0204950	+	0.0136943i
$686$	−18.3450	+	18.6939i	−0.700414	+	0.713736i
$687$	7.28561	+	7.28561i	0.277963	+	0.277963i
$688$	1.70991	−	1.44296i	0.0651899	−	0.0550124i
$689$	8.00481	+	29.8744i	0.304959	+	1.13812i
$690$	6.29352	+	2.88770i	0.239590	+	0.109933i
$691$	−1.88713	+	28.7920i	−0.0717897	+	1.09530i	0.798253	+	0.602323i	$0.205758\pi$
$691$	−1.88713	+	28.7920i	−0.0717897	+	1.09530i	−0.870042	+	0.492977i	$0.835909\pi$
$692$	−15.6551	+	6.31084i	−0.595119	+	0.239902i
$693$	−33.8547	+	4.24426i	−1.28603	+	0.161226i
$694$	−13.9610	+	25.8231i	−0.529953	+	0.980233i
$695$	−0.216379	+	0.281990i	−0.00820771	+	0.0106965i
$696$	1.20412	−	4.85029i	0.0456421	−	0.183850i
$697$	−8.40587	+	6.45005i	−0.318395	+	0.244313i
$698$	7.21605	−	18.8995i	0.273132	−	0.715358i
$699$	5.85613	−	3.91294i	0.221499	−	0.148001i
$700$	−13.4953	−	8.07649i	−0.510075	−	0.305263i
$701$	−3.80970	−	19.1526i	−0.143890	−	0.723385i	−0.983602	−	0.180353i	$-0.942276\pi$
$701$	−3.80970	−	19.1526i	−0.143890	−	0.723385i	0.839712	−	0.543032i	$-0.182724\pi$
$702$	33.1993	+	20.8642i	1.25303	+	0.787467i
$703$	23.6257	−	40.9209i	0.891060	−	1.54336i
$704$	25.4479	+	35.1996i	0.959105	+	1.32663i
$705$	−0.757757	+	0.437491i	−0.0285388	+	0.0164769i
$706$	43.0093	−	22.7267i	1.61868	−	0.855331i
$707$	0.374255	+	0.00231418i	0.0140753	+	8.70336e-5i
$708$	−5.25476	+	0.993388i	−0.197486	+	0.0373338i
$709$	30.4100	+	14.9965i	1.14207	+	0.563207i	0.912091	−	0.409988i	$-0.134467\pi$
$709$	30.4100	+	14.9965i	1.14207	+	0.563207i	0.229980	+	0.973195i	$0.426134\pi$
$710$	2.78719	+	17.3960i	0.104601	+	0.652860i
$711$	11.4438	+	14.9138i	0.429176	+	0.559312i
$712$	12.4397	−	0.229677i	0.466199	−	0.00860750i
$713$	−10.8814	−	26.2700i	−0.407511	−	0.983818i
$714$	8.21505	−	9.78973i	0.307441	−	0.366371i
$715$	−9.84315	+	49.4849i	−0.368113	+	1.85063i
$716$	−21.7700	+	27.8194i	−0.813584	+	1.03966i
$717$	0.823400	+	1.66969i	0.0307504	+	0.0623557i
$718$	17.0203	−	37.0945i	0.635193	−	1.38435i
$719$	−6.22433	+	23.2295i	−0.232128	+	0.866314i	0.747294	+	0.664493i	$0.231353\pi$
$719$	−6.22433	+	23.2295i	−0.232128	+	0.866314i	−0.979422	+	0.201821i	$0.935314\pi$
$720$	2.89132	−	13.2168i	0.107753	−	0.492561i
$721$	0.719688	+	12.1290i	0.0268026	+	0.451709i
$722$	−23.3679	−	19.3642i	−0.869662	−	0.720660i
$723$	−0.850797	+	12.9807i	−0.0316415	+	0.482756i
$724$	44.7905	−	11.5462i	1.66463	−	0.429112i
$725$	4.99522	+	4.38069i	0.185518	+	0.162695i
$726$	14.1914	−	15.0084i	0.526694	−	0.557013i
$727$	14.8595	+	35.8740i	0.551108	+	1.33049i	0.916647	+	0.399697i	$0.130885\pi$
$727$	14.8595	+	35.8740i	0.551108	+	1.33049i	−0.365539	+	0.930796i	$0.619115\pi$
$728$	34.1049	−	34.9529i	1.26401	−	1.29544i
$729$	−0.431038	+	1.04062i	−0.0159644	+	0.0385414i
$730$	0.0896397	−	0.0401026i	0.00331771	−	0.00148426i
$731$	−2.41188	+	0.158083i	−0.0892066	+	0.00584691i
$732$	10.5044	−	11.7507i	0.388254	−	0.434317i
$733$	14.0101	−	12.2866i	0.517476	−	0.453814i	−0.360334	−	0.932823i	$-0.617337\pi$
$733$	14.0101	−	12.2866i	0.517476	−	0.453814i	0.877810	+	0.479009i	$0.159004\pi$
$734$	−2.85832	+	9.26382i	−0.105502	+	0.341934i
$735$	−6.30964	+	4.71874i	−0.232735	+	0.174053i
$736$	−23.3716	−	7.70097i	−0.861490	−	0.283862i
$737$	51.1935	−	29.5566i	1.88574	−	1.08873i
$738$	−5.60164	−	6.03809i	−0.206199	−	0.222265i
$739$	21.4840	+	7.29283i	0.790301	+	0.268271i	0.687265	−	0.726407i	$-0.258811\pi$
$739$	21.4840	+	7.29283i	0.790301	+	0.268271i	0.103036	+	0.994678i	$0.467144\pi$
$740$	9.53732	−	18.8849i	0.350599	−	0.694223i
$741$	27.2806	−	18.2283i	1.00218	−	0.669633i
$742$	3.83761	+	17.3128i	0.140883	+	0.635572i
$743$	−1.98455	−	0.822029i	−0.0728062	−	0.0301573i	0.345983	−	0.938241i	$-0.387545\pi$
$743$	−1.98455	−	0.822029i	−0.0728062	−	0.0301573i	−0.418789	+	0.908083i	$0.637545\pi$
$744$	11.9987	−	8.34172i	0.439894	−	0.305822i
$745$	2.92208	−	22.1954i	0.107057	−	0.813177i
$746$	4.73391	−	19.8749i	0.173321	−	0.727671i
$747$	20.7485	−	7.04318i	0.759149	−	0.257697i
$748$	0.446194	−	46.9207i	0.0163145	−	1.71559i
$749$	−47.1559	+	12.3234i	−1.72304	+	0.450287i
$750$	−9.77119	−	8.09706i	−0.356793	−	0.295663i
$751$	−2.09845	+	7.83151i	−0.0765735	+	0.285776i	−0.993585	−	0.113084i	$-0.963927\pi$
$751$	−2.09845	+	7.83151i	−0.0765735	+	0.285776i	0.917012	+	0.398860i	$0.130594\pi$
$752$	2.50247	−	1.84568i	0.0912557	−	0.0673049i
$753$	5.93851	−	1.59122i	0.216412	−	0.0579873i
$754$	−16.8260	+	11.9367i	−0.612769	+	0.434709i
$755$	−17.9410	−	11.9878i	−0.652939	−	0.436280i
$756$	18.4948	+	12.7822i	0.672651	+	0.464882i
$757$	−47.6130	−	9.47082i	−1.73052	−	0.344223i	−0.773404	−	0.633913i	$-0.781448\pi$
$757$	−47.6130	−	9.47082i	−1.73052	−	0.344223i	−0.957120	+	0.289691i	$0.906448\pi$
$758$	0.880453	+	31.4699i	0.0319795	+	1.14304i
$759$	−2.43671	+	18.5087i	−0.0884470	+	0.671821i
$760$	−20.6096	−	15.2182i	−0.747589	−	0.552021i
$761$	42.3132	−	5.57063i	1.53385	−	0.201935i	0.684205	−	0.729289i	$-0.260149\pi$
$761$	42.3132	−	5.57063i	1.53385	−	0.201935i	0.849646	+	0.527354i	$0.176816\pi$
$762$	6.06365	−	4.92824i	0.219663	−	0.178531i
$763$	3.53963	−	1.44059i	0.128143	−	0.0521527i
$764$	18.0531	+	12.3126i	0.653137	+	0.445454i
$765$	−10.9887	+	9.63683i	−0.397297	+	0.348420i
$766$	−0.380843	+	10.1566i	−0.0137604	+	0.366973i
$767$	19.1186	+	11.0381i	0.690331	+	0.398563i
$768$	1.30644	−	12.5791i	0.0471421	−	0.453910i
$769$			24.9556i			0.899923i	0.893048	+	0.449961i	$0.148562\pi$
$769$			24.9556i			0.899923i	−0.893048	+	0.449961i	$0.851438\pi$
$770$	−6.87673	+	28.0993i	−0.247820	+	1.01263i
$771$	18.8198	−	3.74350i	0.677779	−	0.134819i
$772$	−41.4555	−	3.11330i	−1.49202	−	0.112050i
$773$	−10.5250	+	0.689845i	−0.378558	+	0.0248120i	−0.253495	−	0.967337i	$-0.581580\pi$
$773$	−10.5250	+	0.689845i	−0.378558	+	0.0248120i	−0.125063	+	0.992149i	$0.539913\pi$
$774$	−0.297247	−	1.85524i	−0.0106843	−	0.0666852i
$775$	2.53586	+	19.2618i	0.0910908	+	0.691904i
$776$	−3.26552	+	28.9202i	−0.117225	+	1.03818i
$777$	10.1706	+	11.7430i	0.364867	+	0.421277i
$778$	2.23682	−	4.13735i	0.0801937	−	0.148331i
$779$	−14.7687	+	5.01328i	−0.529142	+	0.179620i
$780$	11.7393	−	8.83180i	0.420334	−	0.316229i
$781$	−42.5999	+	21.0079i	−1.52434	+	0.751723i
$782$	15.3815	+	21.6818i	0.550040	+	0.775340i
$783$	−6.71571	−	6.71571i	−0.240000	−	0.240000i
$784$	20.4105	−	19.1679i	0.728948	−	0.684570i
$785$	11.5625	−	11.5625i	0.412683	−	0.412683i
$786$	−12.0313	−	2.04518i	−0.429142	−	0.0729493i
$787$	−14.5965	−	29.5988i	−0.520310	−	1.05508i	−0.985469	−	0.169857i	$-0.945669\pi$
$787$	−14.5965	−	29.5988i	−0.520310	−	1.05508i	0.465159	−	0.885227i	$-0.345997\pi$
$788$	−35.5627	−	20.9856i	−1.26687	−	0.747579i
$789$	−6.50737	−	19.1701i	−0.231669	−	0.682474i
$790$	15.2739	−	4.55409i	0.543420	−	0.162027i
$791$	−2.69390	+	2.33317i	−0.0957839	+	0.0829581i
$792$	36.3472	−	3.05710i	1.29154	−	0.108629i
$793$	−64.5073	+	8.49255i	−2.29072	+	0.301579i
$794$	−29.8115	−	21.5779i	−1.05797	−	0.765770i
$795$	0.348890	+	5.32303i	0.0123738	+	0.188788i
$796$	0.0591632	+	0.0298788i	0.00209698	+	0.00105903i
$797$	3.82128	+	19.2109i	0.135357	+	0.680485i	0.987556	+	0.157267i	$0.0502684\pi$
$797$	3.82128	+	19.2109i	0.135357	+	0.680485i	−0.852199	+	0.523217i	$0.824732\pi$
$798$	16.0829	−	9.75868i	0.569328	−	0.345453i
$799$	−3.35917			−0.118839
$800$	14.0629	+	9.21549i	0.497197	+	0.325817i
$801$	5.22415	−	9.04850i	0.184586	−	0.319713i
$802$	−19.0578	−	20.5427i	−0.672955	−	0.725389i
$803$	0.174564	+	0.199052i	0.00616023	+	0.00702440i
$804$	−16.8483	−	3.51821i	−0.594193	−	0.124078i
$805$	−6.17811	−	15.1801i	−0.217750	−	0.535028i
$806$	−60.0061	−	6.19829i	−2.11362	−	0.218325i
$807$	0.475076	+	3.60856i	0.0167235	+	0.127027i
$808$	−0.399661	−	0.0187934i	−0.0140600	−	0.000661151i
$809$	−19.3068	−	2.54179i	−0.678793	−	0.0893647i	−0.216756	−	0.976226i	$-0.569548\pi$
$809$	−19.3068	−	2.54179i	−0.678793	−	0.0893647i	−0.462036	+	0.886861i	$0.652881\pi$
$810$	−5.51275	−	5.21268i	−0.193698	−	0.183155i
$811$	3.42025	−	17.1948i	0.120101	−	0.603790i	−0.873115	−	0.487513i	$-0.837904\pi$
$811$	3.42025	−	17.1948i	0.120101	−	0.603790i	0.993217	−	0.116277i	$-0.0370960\pi$
$812$	−9.93693	+	6.41641i	−0.348718	+	0.225172i
$813$	−0.396779	+	0.593821i	−0.0139156	+	0.0208262i
$814$	56.2320	+	9.55881i	1.97093	+	0.335036i
$815$	−2.67643	−	9.98859i	−0.0937514	−	0.349885i
$816$	−9.20189	+	10.0987i	−0.322130	+	0.353525i
$817$	−3.43667	−	0.920853i	−0.120234	−	0.0322166i
$818$	1.27526	−	0.119483i	0.0445885	−	0.00417762i
$819$	−10.3691	−	39.6776i	−0.362324	−	1.38645i
$820$	−6.47674	+	2.61088i	−0.226178	+	0.0911759i
$821$	2.42918	+	7.15614i	0.0847791	+	0.249751i	0.981050	−	0.193757i	$-0.0620672\pi$
$821$	2.42918	+	7.15614i	0.0847791	+	0.249751i	−0.896271	+	0.443508i	$0.853734\pi$
$822$	0.431318	−	0.265376i	0.0150440	−	0.00925603i
$823$	3.17969	+	0.418615i	0.110837	+	0.0145920i	0.185741	−	0.982599i	$-0.440532\pi$
$823$	3.17969	+	0.418615i	0.110837	+	0.0145920i	−0.0749035	+	0.997191i	$0.523865\pi$
$824$	−0.239782	−	12.9871i	−0.00835321	−	0.452426i
$825$	4.88123	−	11.7843i	0.169943	−	0.410278i
$826$	10.6751	+	6.80125i	0.371435	+	0.236646i
$827$	2.84490	+	4.25769i	0.0989267	+	0.148054i	0.877631	−	0.479337i	$-0.159123\pi$
$827$	2.84490	+	4.25769i	0.0989267	+	0.148054i	−0.778704	+	0.627391i	$0.784123\pi$
$828$	−15.6655	+	13.4769i	−0.544414	+	0.468355i
$829$	13.7836	−	40.6052i	0.478724	−	1.41028i	−0.392664	−	0.919682i	$-0.628447\pi$
$829$	13.7836	−	40.6052i	0.478724	−	1.41028i	0.871388	−	0.490594i	$-0.163220\pi$
$830$	0.696118	−	18.5646i	0.0241626	−	0.644386i
$831$	9.13751	+	15.8266i	0.316977	+	0.549020i
$832$	−37.9537	+	35.8477i	−1.31581	+	1.24280i
$833$	−30.0361	+	3.57704i	−1.04069	+	0.123937i
$834$	0.130356	+	0.246694i	0.00451387	+	0.00854230i
$835$	14.0347	+	16.0035i	0.485692	+	0.553825i
$836$	22.8229	−	65.1907i	0.789345	−	2.25467i
$837$	−1.81637	−	27.7124i	−0.0627828	−	0.957881i
$838$	−19.5300	−	7.45679i	−0.674654	−	0.257591i
$839$	37.6742	+	15.6052i	1.30066	+	0.538750i	0.922145	−	0.386845i	$-0.126435\pi$
$839$	37.6742	+	15.6052i	1.30066	+	0.538750i	0.378514	+	0.925596i	$0.376435\pi$
$840$	6.94546	−	4.76518i	0.239641	−	0.164414i
$841$	−22.1760	+	9.18559i	−0.764689	+	0.316745i
$842$	−0.505351	−	18.0627i	−0.0174155	−	0.622482i
$843$	−16.8199	+	19.1794i	−0.579306	+	0.660572i
$844$	−0.518829	+	3.67082i	−0.0178588	+	0.126355i
$845$	−42.0412	−	2.75553i	−1.44626	−	0.0947930i
$846$	−0.243589	−	2.59987i	−0.00837476	−	0.0893853i
$847$	−48.8029	+	2.89577i	−1.67689	+	0.0994999i
$848$	−3.34414	−	18.6601i	−0.114838	−	0.640790i
$849$	−15.4618	−	4.14299i	−0.530649	−	0.142187i
$850$	−6.31718	−	17.0295i	−0.216677	−	0.584107i
$851$	−28.9821	+	14.2924i	−0.993495	+	0.489938i
$852$	13.3239	+	3.70629i	0.456471	+	0.126975i
$853$	−8.24824	−	1.64068i	−0.282414	−	0.0561757i	0.0518506	−	0.998655i	$-0.483488\pi$
$853$	−8.24824	−	1.64068i	−0.282414	−	0.0561757i	−0.334265	+	0.942479i	$0.608488\pi$
$854$	−37.1632	+	3.25025i	−1.27170	+	0.111221i
$855$	−19.8767	+	8.23318i	−0.679767	+	0.281569i
$856$	50.9072	−	11.1068i	1.73997	−	0.379622i
$857$	17.8312	−	13.6824i	0.609103	−	0.467381i	−0.257569	−	0.966260i	$-0.582921\pi$
$857$	17.8312	−	13.6824i	0.609103	−	0.467381i	0.866672	+	0.498879i	$0.166255\pi$
$858$	32.0836	+	23.2225i	1.09532	+	0.792802i
$859$	13.3717	−	27.1152i	0.456238	−	0.925160i	−0.540256	−	0.841501i	$-0.681673\pi$
$859$	13.3717	−	27.1152i	0.456238	−	0.925160i	0.996494	−	0.0836590i	$-0.0266606\pi$
$860$	−1.55940	−	0.325628i	−0.0531750	−	0.0111038i
$861$	0.0317060	−	5.12758i	0.00108054	−	0.174748i
$862$	15.5097	+	4.78547i	0.528264	+	0.162994i
$863$	20.9562	+	36.2971i	0.713356	+	1.23557i	0.963590	+	0.267384i	$0.0861591\pi$
$863$	20.9562	+	36.2971i	0.713356	+	1.23557i	−0.250234	+	0.968185i	$0.580508\pi$
$864$	−19.1979	−	14.4599i	−0.653127	−	0.491936i
$865$	10.4080	+	6.00904i	0.353882	+	0.204314i
$866$	8.13195	−	1.85538i	0.276335	−	0.0630485i
$867$	1.29675	−	0.257939i	0.0440398	−	0.00876006i
$868$	−34.2172	−	5.05222i	−1.16141	−	0.171483i
$869$	23.8730	+	35.7284i	0.809835	+	1.21200i
$870$	−3.24802	+	1.45309i	−0.110118	+	0.0492643i
$871$	43.2531	+	56.3685i	1.46558	+	1.90998i
$872$	−3.84370	+	1.38440i	−0.130164	+	0.0468818i
$873$	19.3901	+	14.8786i	0.656256	+	0.503563i
$874$	11.1810	+	37.4997i	0.378202	+	1.26845i
$875$	3.73625	+	29.8025i	0.126308	+	1.00751i
$876$	0.000733028	−	0.0770834i	2.47667e−5	−	0.00260441i
$877$	−30.4949	−	1.99874i	−1.02974	−	0.0674928i	−0.458846	−	0.888516i	$-0.651737\pi$
$877$	−30.4949	−	1.99874i	−1.02974	−	0.0674928i	−0.570895	+	0.821023i	$0.693404\pi$
$878$	12.1362	+	32.7162i	0.409578	+	1.10412i
$879$	−19.2325	+	5.15332i	−0.648694	+	0.173817i
$880$	8.57085	−	29.7145i	0.288923	−	1.00168i
$881$	−10.6954	+	10.6954i	−0.360336	+	0.360336i	−0.863937	−	0.503601i	$-0.832008\pi$
$881$	−10.6954	+	10.6954i	−0.360336	+	0.360336i	0.503601	+	0.863937i	$0.332008\pi$
$882$	−4.94655	−	22.9874i	−0.166559	−	0.774026i
$883$	4.48030	−	6.70525i	0.150774	−	0.225649i	−0.748392	−	0.663256i	$-0.769174\pi$
$883$	4.48030	−	6.70525i	0.150774	−	0.225649i	0.899166	+	0.437607i	$0.144174\pi$
$884$	55.9838	−	6.82948i	1.88294	−	0.229700i
$885$	2.86276	+	2.51057i	0.0962306	+	0.0843920i
$886$	−4.98071	+	3.06446i	−0.167330	+	0.102953i
$887$	−25.9116	−	19.8827i	−0.870026	−	0.667594i	0.0740744	−	0.997253i	$-0.476400\pi$
$887$	−25.9116	−	19.8827i	−0.870026	−	0.667594i	−0.944100	+	0.329658i	$0.893066\pi$
$888$	−10.3516	−	12.9869i	−0.347377	−	0.435811i
$889$	−18.4468	−	1.32367i	−0.618686	−	0.0443944i
$890$	−5.58723	−	6.87446i	−0.187284	−	0.230432i
$891$	9.04690	−	18.3453i	0.303083	−	0.614591i
$892$	−27.0324	+	13.0128i	−0.905112	+	0.435701i
$893$	−4.68227	−	1.58942i	−0.156686	−	0.0531878i
$894$	−14.8792	−	9.35084i	−0.497633	−	0.312739i
$895$	25.1515			0.840721
$896$	−22.6375	+	19.5842i	−0.756267	+	0.654263i
$897$	−22.4384			−0.749197
$898$	−2.79780	−	1.75829i	−0.0933639	−	0.0586748i
$899$	13.8362	+	4.69675i	0.461462	+	0.156645i
$900$	12.7221	−	6.12414i	0.424070	−	0.204138i
$901$	−9.05791	+	18.3676i	−0.301763	+	0.611914i
$902$	−11.8743	−	14.6100i	−0.395371	−	0.486459i
$903$	0.655878	−	0.968572i	0.0218263	−	0.0322321i
$904$	2.97925	−	2.37471i	0.0990884	−	0.0789816i
$905$	−26.1279	−	20.0486i	−0.868521	−	0.666440i
$906$	−14.4262	+	8.87594i	−0.479277	+	0.294883i
$907$	32.5839	+	28.5753i	1.08193	+	0.948827i	0.998861	−	0.0477169i	$-0.0151945\pi$
$907$	32.5839	+	28.5753i	1.08193	+	0.948827i	0.0830688	+	0.996544i	$0.473528\pi$
$908$	5.95076	−	0.725935i	0.197483	−	0.0240910i
$909$	−0.186669	+	0.279370i	−0.00619141	+	0.00926610i
$910$	−34.5638	−	3.78639i	−1.14578	−	0.125518i
$911$	5.38031	−	5.38031i	0.178258	−	0.178258i	−0.612338	−	0.790596i	$-0.709771\pi$
$911$	5.38031	−	5.38031i	0.178258	−	0.178258i	0.790596	+	0.612338i	$0.209771\pi$
$912$	−17.6046	+	9.72239i	−0.582946	+	0.321941i
$913$	48.3791	−	12.9632i	1.60112	−	0.429018i
$914$	−6.24288	−	16.8292i	−0.206496	−	0.556661i
$915$	−11.1981	−	0.733962i	−0.370198	−	0.0242640i
$916$	−0.247908	+	26.0694i	−0.00819112	+	0.861359i
$917$	17.4420	+	23.0243i	0.575987	+	0.760329i
$918$	7.41880	+	24.8818i	0.244857	+	0.821221i
$919$	−15.6365	−	11.9983i	−0.515800	−	0.395787i	0.317799	−	0.948158i	$-0.397056\pi$
$919$	−15.6365	−	11.9983i	−0.515800	−	0.395787i	−0.833598	+	0.552371i	$0.813723\pi$
$920$	5.93716	+	16.4841i	0.195742	+	0.543465i
$921$	6.88348	+	8.97073i	0.226818	+	0.295596i
$922$	−9.65108	+	4.31766i	−0.317842	+	0.142195i
$923$	−31.7177	−	47.4689i	−1.04400	−	1.56246i
$924$	17.7968	+	14.1051i	0.585470	+	0.464023i
$925$	21.6550	−	4.30744i	0.712011	−	0.141628i
$926$	14.2096	−	3.24206i	0.466957	−	0.106541i
$927$	−9.44663	−	5.45401i	−0.310268	−	0.179133i
$928$	10.8940	−	6.42036i	0.357613	−	0.210759i
$929$	21.2835	+	36.8641i	0.698289	+	1.20947i	0.969059	+	0.246829i	$0.0793885\pi$
$929$	21.2835	+	36.8641i	0.698289	+	1.20947i	−0.270770	+	0.962644i	$0.587278\pi$
$930$	−9.94232	−	3.06767i	−0.326021	−	0.100593i
$931$	−43.5592	−	9.22587i	−1.42760	−	0.302366i
$932$	17.4448	+	3.64277i	0.571424	+	0.119323i
$933$	0.182705	−	0.370490i	0.00598150	−	0.0121293i
$934$	18.0834	+	13.0889i	0.591706	+	0.428283i
$935$	−26.5053	+	20.3382i	−0.866815	+	0.665131i
$936$	9.34540	+	42.8341i	0.305464	+	1.40008i
$937$	−3.94434	+	1.63380i	−0.128856	+	0.0533739i	−0.446180	−	0.894943i	$-0.647216\pi$
$937$	−3.94434	+	1.63380i	−0.128856	+	0.0533739i	0.317324	+	0.948317i	$0.397216\pi$
$938$	23.3653	+	33.3712i	0.762903	+	1.08961i
$939$	0.692395	+	0.137726i	0.0225955	+	0.00449451i
$940$	−2.13297	−	0.593324i	−0.0695700	−	0.0193521i
$941$	17.0937	−	8.42966i	0.557238	−	0.274799i	−0.141787	−	0.989897i	$-0.545285\pi$
$941$	17.0937	−	8.42966i	0.557238	−	0.274799i	0.699024	+	0.715098i	$0.253618\pi$
$942$	−4.46431	−	12.0346i	−0.145455	−	0.392110i
$943$	10.3027	+	2.76061i	0.335503	+	0.0898977i
$944$	−11.1061	−	7.73034i	−0.361472	−	0.251601i
$945$	−0.948140	−	15.9792i	−0.0308430	−	0.519802i
$946$	−0.400643	−	4.27613i	−0.0130260	−	0.139029i
$947$	32.9329	+	2.15854i	1.07018	+	0.0701431i	0.590293	−	0.807189i	$-0.299012\pi$
$947$	32.9329	+	2.15854i	1.07018	+	0.0701431i	0.479884	+	0.877332i	$0.340679\pi$
$948$	1.75095	−	12.3883i	0.0568682	−	0.402353i
$949$	−0.209817	+	0.239250i	−0.00681095	+	0.00776640i
$950$	−0.747732	−	26.7261i	−0.0242596	−	0.867109i
$951$	10.5088	−	4.35288i	0.340770	−	0.141152i
$952$	32.2392	−	2.51093i	1.04488	−	0.0813798i
$953$	−39.5069	−	16.3643i	−1.27975	−	0.530091i	−0.363838	−	0.931462i	$-0.618534\pi$
$953$	−39.5069	−	16.3643i	−1.27975	−	0.530091i	−0.915916	+	0.401371i	$0.868534\pi$
$954$	−14.8727	−	5.67855i	−0.481520	−	0.183850i
$955$	−1.01759	−	15.5254i	−0.0329284	−	0.502391i
$956$	−1.55652	+	4.44600i	−0.0503414	+	0.143794i
$957$	−6.32519	−	7.21250i	−0.204464	−	0.233147i
$958$	3.67029	+	6.94587i	0.118582	+	0.224411i
$959$	−1.17413	−	0.241105i	−0.0379145	−	0.00778568i
$960$	−7.62664	+	4.78706i	−0.246149	+	0.154502i
$961$	5.86321	+	10.1554i	0.189136	+	0.327593i
$962$	−2.56890	+	68.5094i	−0.0828248	+	2.20883i
$963$	14.0649	−	41.4340i	0.453236	−	1.33519i
$964$	−24.9523	+	21.4663i	−0.803659	+	0.691382i
$965$	16.4446	+	24.6111i	0.529371	+	0.792260i
$966$	−12.8530	−	0.561557i	−0.413539	−	0.0180678i
$967$	−5.06306	+	12.2233i	−0.162817	+	0.393075i	−0.984141	−	0.177386i	$-0.943236\pi$
$967$	−5.06306	+	12.2233i	−0.162817	+	0.393075i	0.821324	+	0.570462i	$0.193236\pi$
$968$	52.2554	−	0.964799i	1.67955	−	0.0310098i
$969$	21.5399	+	2.83578i	0.691960	+	0.0910983i
$970$	17.6491	−	10.8589i	0.566678	−	0.348658i
$971$	−1.46096	−	4.30385i	−0.0468844	−	0.138117i	0.920966	−	0.389642i	$-0.127401\pi$
$971$	−1.46096	−	4.30385i	−0.0468844	−	0.138117i	−0.967851	+	0.251525i	$0.919068\pi$
$972$	−29.1672	+	11.7578i	−0.935540	+	0.377131i
$973$	0.174864	−	0.636825i	0.00560589	−	0.0204157i
$974$	−45.6959	+	4.28138i	−1.46419	+	0.137184i
$975$	14.8088	+	3.96800i	0.474261	+	0.127078i
$976$	39.8378	−	1.85105i	1.27518	−	0.0592508i
$977$	8.58095	+	32.0245i	0.274529	+	1.02456i	0.956156	+	0.292856i	$0.0946058\pi$
$977$	8.58095	+	32.0245i	0.274529	+	1.02456i	−0.681628	+	0.731699i	$0.738728\pi$
$978$	−8.00273	−	1.36037i	−0.255899	−	0.0435000i
$979$	13.2687	−	19.8581i	0.424071	−	0.634667i
$980$	−19.7039	−	3.03391i	−0.629417	−	0.0969147i
$981$	−0.669318	+	3.36489i	−0.0213697	+	0.107433i
$982$	−17.1948	−	16.2588i	−0.548708	−	0.518841i
$983$	−11.3995	−	1.50077i	−0.363588	−	0.0478672i	−0.0534807	−	0.998569i	$-0.517032\pi$
$983$	−11.3995	−	1.50077i	−0.363588	−	0.0478672i	−0.310107	+	0.950702i	$0.600365\pi$
$984$	−0.257485	+	5.47567i	−0.00820831	+	0.174558i
$985$	3.83755	+	29.1491i	0.122275	+	0.928767i
$986$	−13.5883	−	1.40359i	−0.432738	−	0.0446995i
$987$	0.997611	−	1.28360i	0.0317543	−	0.0408574i
$988$	81.2661	+	16.9697i	2.58542	+	0.539879i
$989$	1.60432	+	1.82938i	0.0510145	+	0.0581709i
$990$	−17.6630	−	19.0392i	−0.561367	−	0.605107i
$991$	−5.80618	+	10.0566i	−0.184439	+	0.319458i	−0.943387	−	0.331693i	$-0.892380\pi$
$991$	−5.80618	+	10.0566i	−0.184439	+	0.319458i	0.758948	+	0.651151i	$0.225714\pi$
$992$	36.3289	+	6.88879i	1.15344	+	0.218719i
$993$	9.60482			0.304800
$994$	−16.9804	−	27.9847i	−0.538585	−	0.887619i
$995$	−0.00920660	−	0.0462847i	−0.000291869	−	0.00146732i
$996$	−13.0174	−	6.57408i	−0.412471	−	0.208308i
$997$	1.86519	+	28.4572i	0.0590710	+	0.901249i	0.919850	+	0.392270i	$0.128310\pi$
$997$	1.86519	+	28.4572i	0.0590710	+	0.901249i	−0.860779	+	0.508979i	$0.830023\pi$
$998$	48.1019	+	34.8167i	1.52264	+	1.10210i
$999$	−31.2917	+	4.11963i	−0.990026	+	0.130339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.bm.a.171.11	yes	992
7.5	odd	6	inner	448.2.bm.a.299.32	yes	992
64.3	odd	16	inner	448.2.bm.a.3.32	✓	992
448.131	even	48	inner	448.2.bm.a.131.11	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.2.bm.a.3.32	✓	992	64.3	odd	16	inner
448.2.bm.a.131.11	yes	992	448.131	even	48	inner
448.2.bm.a.171.11	yes	992	1.1	even	1	trivial
448.2.bm.a.299.32	yes	992	7.5	odd	6	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.bm (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19739 - 0.752502i) q^{2} +(0.748476 + 0.254073i) q^{3} +(0.867480 + 1.80208i) q^{4} +(0.629821 - 1.27715i) q^{5} +(-0.705026 - 0.867454i) q^{6} +(-0.189362 + 2.63897i) q^{7} +(0.317355 - 2.81057i) q^{8} +(-1.88440 - 1.44595i) q^{9} +O(q^{10})\)	\(q+(-1.19739 - 0.752502i) q^{2} +(0.748476 + 0.254073i) q^{3} +(0.867480 + 1.80208i) q^{4} +(0.629821 - 1.27715i) q^{5} +(-0.705026 - 0.867454i) q^{6} +(-0.189362 + 2.63897i) q^{7} +(0.317355 - 2.81057i) q^{8} +(-1.88440 - 1.44595i) q^{9} +(-1.71520 + 1.05530i) q^{10} +(-4.08203 - 3.57984i) q^{11} +(0.191429 + 1.56921i) q^{12} +(3.62556 - 5.42604i) q^{13} +(2.21257 - 3.01737i) q^{14} +(0.795896 - 0.795896i) q^{15} +(-2.49496 + 3.12653i) q^{16} +(4.17395 - 1.11841i) q^{17} +(1.16828 + 3.14938i) q^{18} +(6.34717 + 0.416015i) q^{19} +(2.84788 + 0.0270820i) q^{20} +(-0.812223 + 1.92709i) q^{21} +(2.19394 + 7.35820i) q^{22} +(-3.45114 - 2.64815i) q^{23} +(0.951622 - 2.02301i) q^{24} +(1.80937 + 2.35801i) q^{25} +(-8.42431 + 3.76883i) q^{26} +(-2.36046 - 3.53267i) q^{27} +(-4.91988 + 1.94801i) q^{28} +(2.19242 - 0.436100i) q^{29} +(-1.55191 + 0.354083i) q^{30} +(5.66081 + 3.26827i) q^{31} +(5.34015 - 1.86621i) q^{32} +(-2.14576 - 3.71656i) q^{33} +(-5.83945 - 1.80174i) q^{34} +(3.25109 + 1.90392i) q^{35} +(0.971032 - 4.65016i) q^{36} +(3.28556 - 6.66246i) q^{37} +(-7.28698 - 5.27439i) q^{38} +(4.09226 - 3.14010i) q^{39} +(-3.38964 - 2.17546i) q^{40} +(-2.26531 + 0.938322i) q^{41} +(2.42269 - 1.69628i) q^{42} +(-0.548601 - 0.109124i) q^{43} +(2.91007 - 10.4616i) q^{44} +(-3.03353 + 1.49597i) q^{45} +(2.13961 + 5.76786i) q^{46} +(-0.750882 - 0.201198i) q^{47} +(-2.66178 + 1.70623i) q^{48} +(-6.92828 - 0.999438i) q^{49} +(-0.392106 - 4.18501i) q^{50} +(3.40826 + 0.223389i) q^{51} +(12.9232 + 1.82656i) q^{52} +(-3.12487 + 3.56323i) q^{53} +(0.168040 + 6.00623i) q^{54} +(-7.14295 + 2.95871i) q^{55} +(7.35690 + 1.36970i) q^{56} +(4.64500 + 1.92402i) q^{57} +(-2.95335 - 1.12762i) q^{58} +(0.221252 + 3.37565i) q^{59} +(2.12469 + 0.743841i) q^{60} +(-6.57381 - 7.49599i) q^{61} +(-4.31881 - 8.17317i) q^{62} +(4.17264 - 4.69905i) q^{63} +(-7.79857 - 1.78389i) q^{64} +(-4.64641 - 8.04782i) q^{65} +(-0.227414 + 6.06485i) q^{66} +(-3.49972 + 10.3098i) q^{67} +(5.63628 + 6.55158i) q^{68} +(-1.91027 - 2.85892i) q^{69} +(-2.46012 - 4.72619i) q^{70} +(3.34785 - 8.08243i) q^{71} +(-4.66196 + 4.83735i) q^{72} +(-0.0483459 - 0.00636486i) q^{73} +(-8.94762 + 5.50517i) q^{74} +(0.755159 + 2.22463i) q^{75} +(4.75635 + 11.7990i) q^{76} +(10.2201 - 10.0944i) q^{77} +(-7.26295 + 0.680487i) q^{78} +(-7.64470 - 2.04839i) q^{79} +(2.42168 + 5.15559i) q^{80} +(0.975079 + 3.63904i) q^{81} +(3.41855 + 0.581115i) q^{82} +(-5.12511 + 7.67026i) q^{83} +(-4.17735 + 0.208025i) q^{84} +(1.20047 - 6.03516i) q^{85} +(0.574774 + 0.543487i) q^{86} +(1.75177 + 0.230625i) q^{87} +(-11.3568 + 10.3367i) q^{88} +(0.574166 + 4.36123i) q^{89} +(4.75803 + 0.491479i) q^{90} +(13.6326 + 10.5952i) q^{91} +(1.77838 - 8.51643i) q^{92} +(3.40660 + 3.88448i) q^{93} +(0.747696 + 0.805953i) q^{94} +(4.52889 - 7.84428i) q^{95} +(4.47113 - 0.0400257i) q^{96} -10.2898 q^{97} +(7.54377 + 6.41027i) q^{98} +(2.51589 + 12.6482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 8 q^{2} - 24 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{7} - 32 q^{8} - 8 q^{9}+O(q^{10}) \) 992 * q - 8 * q^2 - 24 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^7 - 32 * q^8 - 8 * q^9	\( 992 q - 8 q^{2} - 24 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{7} - 32 q^{8} - 8 q^{9} - 24 q^{10} - 8 q^{11} - 24 q^{12} - 16 q^{14} - 32 q^{15} - 8 q^{16} - 24 q^{17} - 8 q^{18} - 24 q^{19} - 16 q^{21} - 48 q^{22} - 8 q^{23} - 24 q^{24} - 8 q^{25} - 24 q^{26} - 56 q^{28} - 32 q^{29} + 72 q^{30} - 48 q^{31} - 8 q^{32} - 16 q^{35} - 192 q^{36} - 8 q^{37} - 24 q^{38} - 8 q^{39} - 24 q^{40} - 56 q^{42} - 32 q^{43} - 24 q^{45} - 8 q^{46} - 24 q^{47} - 16 q^{49} - 80 q^{50} - 8 q^{51} + 120 q^{52} - 8 q^{53} - 24 q^{54} - 16 q^{56} - 32 q^{57} - 8 q^{58} - 216 q^{59} + 88 q^{60} - 24 q^{61} - 224 q^{64} - 16 q^{65} + 264 q^{66} - 88 q^{67} - 24 q^{68} - 16 q^{70} + 96 q^{71} - 8 q^{72} - 24 q^{73} + 48 q^{74} - 24 q^{75} - 16 q^{77} - 128 q^{78} - 8 q^{79} + 48 q^{80} - 8 q^{81} - 264 q^{82} + 96 q^{84} - 32 q^{85} - 8 q^{86} - 24 q^{87} - 8 q^{88} - 24 q^{89} - 16 q^{91} - 32 q^{92} - 56 q^{93} - 24 q^{94} - 16 q^{95} - 432 q^{96} + 120 q^{98} + 16 q^{99}+O(q^{100}) \) 992 * q - 8 * q^2 - 24 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^7 - 32 * q^8 - 8 * q^9 - 24 * q^10 - 8 * q^11 - 24 * q^12 - 16 * q^14 - 32 * q^15 - 8 * q^16 - 24 * q^17 - 8 * q^18 - 24 * q^19 - 16 * q^21 - 48 * q^22 - 8 * q^23 - 24 * q^24 - 8 * q^25 - 24 * q^26 - 56 * q^28 - 32 * q^29 + 72 * q^30 - 48 * q^31 - 8 * q^32 - 16 * q^35 - 192 * q^36 - 8 * q^37 - 24 * q^38 - 8 * q^39 - 24 * q^40 - 56 * q^42 - 32 * q^43 - 24 * q^45 - 8 * q^46 - 24 * q^47 - 16 * q^49 - 80 * q^50 - 8 * q^51 + 120 * q^52 - 8 * q^53 - 24 * q^54 - 16 * q^56 - 32 * q^57 - 8 * q^58 - 216 * q^59 + 88 * q^60 - 24 * q^61 - 224 * q^64 - 16 * q^65 + 264 * q^66 - 88 * q^67 - 24 * q^68 - 16 * q^70 + 96 * q^71 - 8 * q^72 - 24 * q^73 + 48 * q^74 - 24 * q^75 - 16 * q^77 - 128 * q^78 - 8 * q^79 + 48 * q^80 - 8 * q^81 - 264 * q^82 + 96 * q^84 - 32 * q^85 - 8 * q^86 - 24 * q^87 - 8 * q^88 - 24 * q^89 - 16 * q^91 - 32 * q^92 - 56 * q^93 - 24 * q^94 - 16 * q^95 - 432 * q^96 + 120 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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