LMFDB - Embedded newform 256.2.m.a.101.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			101.9
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02903 - 0.970104i) q^{2} +(-0.536541 + 0.134397i) q^{3} +(0.117798 + 1.99653i) q^{4} +(-0.358840 - 0.169719i) q^{5} +(0.682495 + 0.382203i) q^{6} +(-0.583623 - 1.92395i) q^{7} +(1.81562 - 2.16876i) q^{8} +(-2.37595 + 1.26997i) q^{9} +O(q^{10})$	\(q+(-1.02903 - 0.970104i) q^{2} +(-0.536541 + 0.134397i) q^{3} +(0.117798 + 1.99653i) q^{4} +(-0.358840 - 0.169719i) q^{5} +(0.682495 + 0.382203i) q^{6} +(-0.583623 - 1.92395i) q^{7} +(1.81562 - 2.16876i) q^{8} +(-2.37595 + 1.26997i) q^{9} +(0.204612 + 0.522757i) q^{10} +(-2.29041 + 0.339750i) q^{11} +(-0.331530 - 1.05539i) q^{12} +(2.35307 - 6.57638i) q^{13} +(-1.26586 + 2.54597i) q^{14} +(0.215342 + 0.0428342i) q^{15} +(-3.97225 + 0.470375i) q^{16} +(-1.16989 + 0.232706i) q^{17} +(3.67692 + 0.998080i) q^{18} +(-4.07952 - 3.69746i) q^{19} +(0.296577 - 0.736426i) q^{20} +(0.571710 + 0.953840i) q^{21} +(2.68649 + 1.87232i) q^{22} +(-7.07624 + 0.696949i) q^{23} +(-0.682682 + 1.40764i) q^{24} +(-3.07200 - 3.74325i) q^{25} +(-8.80114 + 4.48456i) q^{26} +(2.33362 - 2.11507i) q^{27} +(3.77246 - 1.39186i) q^{28} +(5.71274 + 7.70274i) q^{29} +(-0.180039 - 0.252982i) q^{30} +(-3.32277 - 1.37634i) q^{31} +(4.54387 + 3.36946i) q^{32} +(1.18324 - 0.490114i) q^{33} +(1.42960 + 0.895455i) q^{34} +(-0.117102 + 0.789440i) q^{35} +(-2.81542 - 4.59405i) q^{36} +(-0.378780 + 7.71025i) q^{37} +(0.611022 + 7.76235i) q^{38} +(-0.378674 + 3.84474i) q^{39} +(-1.01960 + 0.470093i) q^{40} +(1.61305 - 1.96550i) q^{41} +(0.337018 - 1.53615i) q^{42} +(1.95464 - 7.80335i) q^{43} +(-0.948128 - 4.53285i) q^{44} +(1.06812 - 0.0524735i) q^{45} +(7.95776 + 6.14750i) q^{46} +(-0.481663 - 0.321837i) q^{47} +(2.06806 - 0.786233i) q^{48} +(2.45933 - 1.64327i) q^{49} +(-0.470159 + 6.83207i) q^{50} +(0.596421 - 0.282086i) q^{51} +(13.4071 + 3.92327i) q^{52} +(4.92981 - 6.64707i) q^{53} +(-4.45319 - 0.0873861i) q^{54} +(0.879553 + 0.266809i) q^{55} +(-5.23222 - 2.22742i) q^{56} +(2.68576 + 1.43557i) q^{57} +(1.59388 - 13.4683i) q^{58} +(-3.76238 - 10.5151i) q^{59} +(-0.0601527 + 0.434982i) q^{60} +(5.14482 - 8.58362i) q^{61} +(2.08404 + 4.63972i) q^{62} +(3.83002 + 3.83002i) q^{63} +(-1.40704 - 7.87529i) q^{64} +(-1.96051 + 1.96051i) q^{65} +(-1.69305 - 0.643524i) q^{66} +(7.89313 + 4.73096i) q^{67} +(-0.602415 - 2.30831i) q^{68} +(3.70303 - 1.32496i) q^{69} +(0.886340 - 0.698755i) q^{70} +(-6.36138 + 11.9013i) q^{71} +(-1.55956 + 7.45865i) q^{72} +(-2.79775 + 9.22295i) q^{73} +(7.86952 - 7.56661i) q^{74} +(2.15134 + 1.59554i) q^{75} +(6.90153 - 8.58044i) q^{76} +(1.99040 + 4.20834i) q^{77} +(4.11947 - 3.58900i) q^{78} +(6.11995 + 9.15915i) q^{79} +(1.50523 + 0.505375i) q^{80} +(3.52240 - 5.27164i) q^{81} +(-3.56661 + 0.457736i) q^{82} +(0.438739 + 8.93074i) q^{83} +(-1.83702 + 1.25380i) q^{84} +(0.459298 + 0.115048i) q^{85} +(-9.58143 + 6.13367i) q^{86} +(-4.10034 - 3.36507i) q^{87} +(-3.42168 + 5.58421i) q^{88} +(-3.54632 - 0.349282i) q^{89} +(-1.15003 - 0.982193i) q^{90} +(-14.0259 - 0.689049i) q^{91} +(-2.22505 - 14.0458i) q^{92} +(1.96778 + 0.291892i) q^{93} +(0.183430 + 0.798442i) q^{94} +(0.836367 + 2.01917i) q^{95} +(-2.89082 - 1.19718i) q^{96} +(-4.20299 + 10.1469i) q^{97} +(-4.12487 - 0.694832i) q^{98} +(5.01043 - 3.71599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.02903	−	0.970104i	−0.727633	−	0.685967i
$2$	−1.02903	−	0.970104i	−0.727633	−	0.685967i
$3$	−0.536541	+	0.134397i	−0.309772	+	0.0775939i	−0.394749	−	0.918789i	$-0.629168\pi$
$3$	−0.536541	+	0.134397i	−0.309772	+	0.0775939i	0.0849766	+	0.996383i	$0.472918\pi$
$4$	0.117798	+	1.99653i	0.0588992	+	0.998264i
$5$	−0.358840	−	0.169719i	−0.160478	−	0.0759004i	0.345629	−	0.938371i	$-0.387666\pi$
$5$	−0.358840	−	0.169719i	−0.160478	−	0.0759004i	−0.506107	+	0.862471i	$0.668916\pi$
$6$	0.682495	+	0.382203i	0.278627	+	0.156034i
$7$	−0.583623	−	1.92395i	−0.220589	−	0.727184i	−0.995470	−	0.0950767i	$-0.969690\pi$
$7$	−0.583623	−	1.92395i	−0.220589	−	0.727184i	0.774881	−	0.632107i	$-0.217810\pi$
$8$	1.81562	−	2.16876i	0.641919	−	0.766773i
$9$	−2.37595	+	1.26997i	−0.791983	+	0.423324i
$10$	0.204612	+	0.522757i	0.0647039	+	0.165310i
$11$	−2.29041	+	0.339750i	−0.690585	+	0.102439i	−0.482793	−	0.875734i	$-0.660378\pi$
$11$	−2.29041	+	0.339750i	−0.690585	+	0.102439i	−0.207792	+	0.978173i	$0.566628\pi$
$12$	−0.331530	−	1.05539i	−0.0957046	−	0.304664i
$13$	2.35307	−	6.57638i	0.652623	−	1.82396i	0.0922207	−	0.995739i	$-0.470603\pi$
$13$	2.35307	−	6.57638i	0.652623	−	1.82396i	0.560402	−	0.828221i	$-0.310647\pi$
$14$	−1.26586	+	2.54597i	−0.338316	+	0.680439i
$15$	0.215342	+	0.0428342i	0.0556011	+	0.0110597i
$16$	−3.97225	+	0.470375i	−0.993062	+	0.117594i
$17$	−1.16989	+	0.232706i	−0.283740	+	0.0564395i	−0.334909	−	0.942251i	$-0.608706\pi$
$17$	−1.16989	+	0.232706i	−0.283740	+	0.0564395i	0.0511683	+	0.998690i	$0.483706\pi$
$18$	3.67692	+	0.998080i	0.866659	+	0.235250i
$19$	−4.07952	−	3.69746i	−0.935907	−	0.848256i	0.0527257	−	0.998609i	$-0.483209\pi$
$19$	−4.07952	−	3.69746i	−0.935907	−	0.848256i	−0.988632	+	0.150353i	$0.951959\pi$
$20$	0.296577	−	0.736426i	0.0663167	−	0.164670i
$21$	0.571710	+	0.953840i	0.124757	+	0.208145i
$22$	2.68649	+	1.87232i	0.572762	+	0.399181i
$23$	−7.07624	+	0.696949i	−1.47550	+	0.145324i	−0.803533	−	0.595260i	$-0.797049\pi$
$23$	−7.07624	+	0.696949i	−1.47550	+	0.145324i	−0.671964	+	0.740584i	$0.734549\pi$
$24$	−0.682682	+	1.40764i	−0.139352	+	0.287334i
$25$	−3.07200	−	3.74325i	−0.614401	−	0.748650i
$26$	−8.80114	+	4.48456i	−1.72605	+	0.879495i
$27$	2.33362	−	2.11507i	0.449104	−	0.407045i
$28$	3.77246	−	1.39186i	0.712929	−	0.263036i
$29$	5.71274	+	7.70274i	1.06083	+	1.43036i	0.896007	+	0.444039i	$0.146455\pi$
$29$	5.71274	+	7.70274i	1.06083	+	1.43036i	0.164822	+	0.986323i	$0.447295\pi$
$30$	−0.180039	−	0.252982i	−0.0328706	−	0.0461879i
$31$	−3.32277	−	1.37634i	−0.596787	−	0.247197i	0.0637805	−	0.997964i	$-0.479684\pi$
$31$	−3.32277	−	1.37634i	−0.596787	−	0.247197i	−0.660567	+	0.750767i	$0.729684\pi$
$32$	4.54387	+	3.36946i	0.803250	+	0.595642i
$33$	1.18324	−	0.490114i	0.205976	−	0.0853179i
$34$	1.42960	+	0.895455i	0.245175	+	0.153569i
$35$	−0.117102	+	0.789440i	−0.0197939	+	0.133440i
$36$	−2.81542	−	4.59405i	−0.469236	−	0.765675i
$37$	−0.378780	+	7.71025i	−0.0622711	+	1.26756i	0.740821	+	0.671703i	$0.234437\pi$
$37$	−0.378780	+	7.71025i	−0.0622711	+	1.26756i	−0.803092	+	0.595855i	$0.796813\pi$
$38$	0.611022	+	7.76235i	0.0991208	+	1.25922i
$39$	−0.378674	+	3.84474i	−0.0606364	+	0.615652i
$40$	−1.01960	+	0.470093i	−0.161212	+	0.0743282i
$41$	1.61305	−	1.96550i	0.251916	−	0.306960i	−0.631663	−	0.775243i	$-0.717627\pi$
$41$	1.61305	−	1.96550i	0.251916	−	0.306960i	0.883579	+	0.468283i	$0.155127\pi$
$42$	0.337018	−	1.53615i	0.0520030	−	0.237033i
$43$	1.95464	−	7.80335i	0.298079	−	1.19000i	−0.617078	−	0.786902i	$-0.711684\pi$
$43$	1.95464	−	7.80335i	0.298079	−	1.19000i	0.915157	−	0.403097i	$-0.132066\pi$
$44$	−0.948128	−	4.53285i	−0.142936	−	0.683353i
$45$	1.06812	−	0.0524735i	0.159226	−	0.00782229i
$46$	7.95776	+	6.14750i	1.17331	+	0.906400i
$47$	−0.481663	−	0.321837i	−0.0702577	−	0.0469447i	0.519945	−	0.854200i	$-0.325952\pi$
$47$	−0.481663	−	0.321837i	−0.0702577	−	0.0469447i	−0.590203	+	0.807255i	$0.700952\pi$
$48$	2.06806	−	0.786233i	0.298499	−	0.113483i
$49$	2.45933	−	1.64327i	0.351333	−	0.234753i
$50$	−0.470159	+	6.83207i	−0.0664905	+	0.966201i
$51$	0.596421	−	0.282086i	0.0835156	−	0.0394999i
$52$	13.4071	+	3.92327i	1.85923	+	0.544060i
$53$	4.92981	−	6.64707i	0.677161	−	0.913046i	−0.322274	−	0.946646i	$-0.604447\pi$
$53$	4.92981	−	6.64707i	0.677161	−	0.913046i	0.999435	+	0.0336004i	$0.0106974\pi$
$54$	−4.45319	−	0.0873861i	−0.606002	−	0.0118917i
$55$	0.879553	+	0.266809i	0.118599	+	0.0359766i
$56$	−5.23222	−	2.22742i	−0.699184	−	0.297652i
$57$	2.68576	+	1.43557i	0.355738	+	0.190146i
$58$	1.59388	−	13.4683i	0.209287	−	1.76847i
$59$	−3.76238	−	10.5151i	−0.489820	−	1.36895i	−0.891436	−	0.453146i	$-0.850302\pi$
$59$	−3.76238	−	10.5151i	−0.489820	−	1.36895i	0.401617	−	0.915808i	$-0.368448\pi$
$60$	−0.0601527	+	0.434982i	−0.00776568	+	0.0561560i
$61$	5.14482	−	8.58362i	0.658727	−	1.09902i	−0.329224	−	0.944252i	$-0.606787\pi$
$61$	5.14482	−	8.58362i	0.658727	−	1.09902i	0.987951	−	0.154768i	$-0.0494630\pi$
$62$	2.08404	+	4.63972i	0.264673	+	0.589245i
$63$	3.83002	+	3.83002i	0.482537	+	0.482537i
$64$	−1.40704	−	7.87529i	−0.175880	−	0.984412i
$65$	−1.96051	+	1.96051i	−0.243171	+	0.243171i
$66$	−1.69305	−	0.643524i	−0.208400	−	0.0792123i
$67$	7.89313	+	4.73096i	0.964300	+	0.577979i	0.907340	−	0.420397i	$-0.138109\pi$
$67$	7.89313	+	4.73096i	0.964300	+	0.577979i	0.0569597	+	0.998376i	$0.481859\pi$
$68$	−0.602415	−	2.30831i	−0.0730536	−	0.279924i
$69$	3.70303	−	1.32496i	0.445792	−	0.159507i
$70$	0.886340	−	0.698755i	0.105938	−	0.0835172i
$71$	−6.36138	+	11.9013i	−0.754957	+	1.41242i	0.150773	+	0.988568i	$0.451824\pi$
$71$	−6.36138	+	11.9013i	−0.754957	+	1.41242i	−0.905729	+	0.423856i	$0.860676\pi$
$72$	−1.55956	+	7.45865i	−0.183796	+	0.879010i
$73$	−2.79775	+	9.22295i	−0.327452	+	1.07947i	0.626479	+	0.779439i	$0.284496\pi$
$73$	−2.79775	+	9.22295i	−0.327452	+	1.07947i	−0.953931	+	0.300027i	$0.903004\pi$
$74$	7.86952	−	7.56661i	0.914813	−	0.879601i
$75$	2.15134	+	1.59554i	0.248415	+	0.184237i
$76$	6.90153	−	8.58044i	0.791660	−	0.984244i
$77$	1.99040	+	4.20834i	0.226827	+	0.479585i
$78$	4.11947	−	3.58900i	0.466438	−	0.406374i
$79$	6.11995	+	9.15915i	0.688548	+	1.03049i	0.996859	+	0.0791995i	$0.0252364\pi$
$79$	6.11995	+	9.15915i	0.688548	+	1.03049i	−0.308311	+	0.951286i	$0.599764\pi$
$80$	1.50523	+	0.505375i	0.168290	+	0.0565026i
$81$	3.52240	−	5.27164i	0.391377	−	0.585738i
$82$	−3.56661	+	0.457736i	−0.393867	+	0.0505485i
$83$	0.438739	+	8.93074i	0.0481579	+	0.980277i	0.894341	+	0.447385i	$0.147645\pi$
$83$	0.438739	+	8.93074i	0.0481579	+	0.980277i	−0.846184	+	0.532892i	$0.821105\pi$
$84$	−1.83702	+	1.25380i	−0.200436	+	0.136800i
$85$	0.459298	+	0.115048i	0.0498179	+	0.0124787i
$86$	−9.58143	+	6.13367i	−1.03319	+	0.661410i
$87$	−4.10034	−	3.36507i	−0.439603	−	0.360773i
$88$	−3.42168	+	5.58421i	−0.364752	+	0.595279i
$89$	−3.54632	−	0.349282i	−0.375909	−	0.0370238i	−0.0917013	−	0.995787i	$-0.529230\pi$
$89$	−3.54632	−	0.349282i	−0.375909	−	0.0370238i	−0.284208	+	0.958763i	$0.591730\pi$
$90$	−1.15003	−	0.982193i	−0.121224	−	0.103532i
$91$	−14.0259	−	0.689049i	−1.47031	−	0.0722319i
$92$	−2.22505	−	14.0458i	−0.231977	−	1.46438i
$93$	1.96778	+	0.291892i	0.204049	+	0.0302678i
$94$	0.183430	+	0.798442i	0.0189193	+	0.0823530i
$95$	0.836367	+	2.01917i	0.0858094	+	0.207162i
$96$	−2.89082	−	1.19718i	−0.295043	−	0.122186i
$97$	−4.20299	+	10.1469i	−0.426749	+	1.03026i	0.553563	+	0.832808i	$0.313268\pi$
$97$	−4.20299	+	10.1469i	−0.426749	+	1.03026i	−0.980312	+	0.197456i	$0.936732\pi$
$98$	−4.12487	−	0.694832i	−0.416674	−	0.0701886i
$99$	5.01043	−	3.71599i	0.503567	−	0.373471i
$100$	7.11162	−	6.57429i	0.711162	−	0.657429i
$101$	−2.99269	−	3.30193i	−0.297784	−	0.328554i	0.573619	−	0.819122i	$-0.305539\pi$
$101$	−2.99269	−	3.30193i	−0.297784	−	0.328554i	−0.871403	+	0.490568i	$0.836789\pi$
$102$	−0.887386	−	0.288315i	−0.0878643	−	0.0285475i
$103$	6.21458	−	5.10017i	0.612340	−	0.502535i	−0.276341	−	0.961060i	$-0.589122\pi$
$103$	6.21458	−	5.10017i	0.612340	−	0.502535i	0.888682	+	0.458525i	$0.151622\pi$
$104$	−9.99031	−	17.0434i	−0.979631	−	1.67125i
$105$	−0.0432678	−	0.439306i	−0.00422251	−	0.0428718i
$106$	−11.5213	+	2.05761i	−1.11904	+	0.199852i
$107$	0.183330	−	0.109884i	0.0177232	−	0.0106229i	−0.505214	−	0.862994i	$-0.668586\pi$
$107$	0.183330	−	0.109884i	0.0177232	−	0.0106229i	0.522937	+	0.852371i	$0.324836\pi$
$108$	4.49768	+	4.40998i	0.432790	+	0.424350i
$109$	0.741799	−	0.818449i	0.0710515	−	0.0783932i	−0.704388	−	0.709815i	$-0.748778\pi$
$109$	0.741799	−	0.818449i	0.0710515	−	0.0783932i	0.775439	+	0.631422i	$0.217528\pi$
$110$	−0.646252	−	1.12781i	−0.0616177	−	0.107533i
$111$	−0.833001	−	4.18778i	−0.0790649	−	0.397486i
$112$	3.22327	+	7.36787i	0.304571	+	0.696198i
$113$	0.869878	−	4.37317i	0.0818312	−	0.411393i	−0.918057	−	0.396448i	$-0.870243\pi$
$113$	0.869878	−	4.37317i	0.0818312	−	0.411393i	0.999888	−	0.0149452i	$-0.00475738\pi$
$114$	−1.37107	−	4.08271i	−0.128413	−	0.382380i
$115$	2.65752	+	0.950876i	0.247815	+	0.0886697i
$116$	−14.7058	+	12.3130i	−1.36540	+	1.14323i
$117$	2.76105	+	18.6135i	0.255259	+	1.72082i
$118$	−6.32918	+	14.4703i	−0.582648	+	1.33210i
$119$	1.13049	+	2.11500i	0.103632	+	0.193882i
$120$	0.483877	−	0.389255i	0.0441717	−	0.0355339i
$121$	−5.39579	+	1.63679i	−0.490526	+	0.148800i
$122$	−13.6212	+	3.84178i	−1.23320	+	0.347818i
$123$	−0.601310	+	1.27136i	−0.0542183	+	0.114635i
$124$	2.35648	−	6.79613i	0.211618	−	0.610311i
$125$	0.949315	+	3.78988i	0.0849093	+	0.338977i
$126$	−0.225683	−	7.65671i	−0.0201054	−	0.682114i
$127$		−	9.73884i		−	0.864182i	−0.901830	−	0.432091i	$-0.857776\pi$
$127$		−	9.73884i		−	0.864182i	0.901830	−	0.432091i	$-0.142224\pi$
$128$	−6.19196	+	9.46887i	−0.547297	+	0.836938i
$129$			4.44952i			0.391758i
$130$	3.91931	−	0.115522i	0.343746	−	0.0101320i
$131$	−2.00069	−	7.98719i	−0.174801	−	0.697844i	−0.992505	−	0.122205i	$-0.961003\pi$
$131$	−2.00069	−	7.98719i	−0.174801	−	0.697844i	0.817704	−	0.575639i	$-0.195247\pi$
$132$	1.11791	+	2.30464i	0.0973015	+	0.200593i
$133$	−4.73282	+	10.0067i	−0.410388	+	0.867692i
$134$	−3.53273	−	12.5255i	−0.305182	−	1.08203i
$135$	−1.19636	+	0.362912i	−0.102966	+	0.0312345i
$136$	−1.61940	+	2.95972i	−0.138862	+	0.253794i
$137$	−5.75294	−	10.7630i	−0.491507	−	0.919545i	−0.998345	−	0.0575036i	$-0.981686\pi$
$137$	−5.75294	−	10.7630i	−0.491507	−	0.919545i	0.506838	−	0.862041i	$-0.330814\pi$
$138$	−5.09587	−	2.22889i	−0.433790	−	0.189736i
$139$	−1.14646	−	7.72879i	−0.0972413	−	0.655548i	−0.981913	−	0.189333i	$-0.939367\pi$
$139$	−1.14646	−	7.72879i	−0.0972413	−	0.655548i	0.884672	−	0.466215i	$-0.154383\pi$
$140$	−1.58993	−	0.140803i	−0.134374	−	0.0119001i
$141$	0.301686	+	0.107945i	0.0254065	+	0.00909060i
$142$	18.0915	−	6.07558i	1.51821	−	0.509851i
$143$	−3.15516	+	15.8621i	−0.263848	+	1.32645i
$144$	8.84050	−	6.16223i	0.736708	−	0.513519i
$145$	−0.742660	−	3.73361i	−0.0616746	−	0.310059i
$146$	11.8262	−	6.77657i	0.978742	−	0.560833i
$147$	−1.09868	+	1.21221i	−0.0906178	+	0.0999814i
$148$	−15.4384	+	0.152009i	−1.26902	+	0.0124951i
$149$	−3.56999	+	2.13977i	−0.292465	+	0.175297i	−0.652808	−	0.757523i	$-0.726409\pi$
$149$	−3.56999	+	2.13977i	−0.292465	+	0.175297i	0.360344	+	0.932820i	$0.382659\pi$
$150$	−0.665948	−	3.72888i	−0.0543744	−	0.304462i
$151$	0.348498	+	3.53836i	0.0283604	+	0.287948i	0.998895	+	0.0469878i	$0.0149622\pi$
$151$	0.348498	+	3.53836i	0.0283604	+	0.287948i	−0.970535	+	0.240960i	$0.922538\pi$
$152$	−15.4258	+	2.13431i	−1.25120	+	0.173116i
$153$	2.48407	−	2.03863i	0.200825	−	0.164813i
$154$	2.03435	−	6.26140i	0.163933	−	0.504558i
$155$	0.958752	+	1.05782i	0.0770088	+	0.0849661i
$156$	−7.72075	−	0.303129i	−0.618154	−	0.0242698i
$157$	4.54034	−	3.36734i	0.362358	−	0.268743i	−0.399167	−	0.916878i	$-0.630701\pi$
$157$	4.54034	−	3.36734i	0.362358	−	0.268743i	0.761526	+	0.648135i	$0.224451\pi$
$158$	2.58772	−	15.3620i	0.205868	−	1.22214i
$159$	−1.75170	+	4.22898i	−0.138919	+	0.335380i
$160$	−1.05866	−	1.98028i	−0.0836944	−	0.156554i
$161$	5.47075	+	13.2076i	0.431155	+	1.04090i
$162$	−8.73868	+	2.00758i	−0.686576	+	0.157730i
$163$	−3.90883	−	0.579821i	−0.306163	−	0.0454151i	−0.00811895	−	0.999967i	$-0.502584\pi$
$163$	−3.90883	−	0.579821i	−0.306163	−	0.0454151i	−0.298044	+	0.954552i	$0.596334\pi$
$164$	4.11420	+	2.98896i	0.321265	+	0.233399i
$165$	−0.507775	−	0.0249454i	−0.0395302	−	0.00194199i
$166$	8.21227	−	9.61561i	0.637396	−	0.746316i
$167$	4.58689	+	0.451769i	0.354944	+	0.0349590i	0.273918	−	0.961753i	$-0.411680\pi$
$167$	4.58689	+	0.451769i	0.354944	+	0.0349590i	0.0810262	+	0.996712i	$0.474180\pi$
$168$	3.10666	+	0.491911i	0.239684	+	0.0379517i
$169$	−27.6627	−	22.7022i	−2.12790	−	1.74632i
$170$	−0.361022	−	0.563955i	−0.0276891	−	0.0432534i
$171$	14.3884	+	3.60411i	1.10031	+	0.275613i
$172$	15.8099	+	2.98327i	1.20549	+	0.227472i
$173$	−1.05638	−	21.5031i	−0.0803150	−	1.63485i	−0.614100	−	0.789228i	$-0.710481\pi$
$173$	−1.05638	−	21.5031i	−0.0803150	−	1.63485i	0.533785	−	0.845620i	$-0.320769\pi$
$174$	0.954908	+	7.44051i	0.0723914	+	0.564063i
$175$	−5.40892	+	8.09502i	−0.408876	+	0.611926i
$176$	8.93827	−	2.42693i	0.673747	−	0.182936i
$177$	3.43187	+	5.13616i	0.257955	+	0.386057i
$178$	3.31042	+	3.79972i	0.248127	+	0.284801i
$179$	5.52514	+	11.6819i	0.412968	+	0.873148i	0.998065	+	0.0621845i	$0.0198067\pi$
$179$	5.52514	+	11.6819i	0.412968	+	0.873148i	−0.585096	+	0.810964i	$0.698943\pi$
$180$	0.230588	+	2.12636i	0.0171870	+	0.158489i
$181$	5.06066	+	3.75324i	0.376156	+	0.278976i	0.767216	−	0.641389i	$-0.221642\pi$
$181$	5.06066	+	3.75324i	0.376156	+	0.278976i	−0.391060	+	0.920365i	$0.627892\pi$
$182$	13.7646	+	14.3156i	1.02030	+	1.06115i
$183$	−1.60680	+	5.29691i	−0.118778	+	0.391559i
$184$	−11.3363	+	16.6121i	−0.835720	+	1.22466i
$185$	1.44449	−	2.70246i	0.106201	−	0.198689i
$186$	−1.74173	−	2.20931i	−0.127710	−	0.161995i
$187$	2.60047	−	0.930464i	0.190165	−	0.0680422i
$188$	0.585817	−	0.999565i	0.0427251	−	0.0729007i
$189$	−5.43123	−	3.25535i	−0.395063	−	0.236792i
$190$	1.09816	−	2.88914i	0.0796687	−	0.209600i
$191$	11.0339	−	11.0339i	0.798387	−	0.798387i	−0.184454	−	0.982841i	$-0.559052\pi$
$191$	11.0339	−	11.0339i	0.798387	−	0.798387i	0.982841	+	0.184454i	$0.0590517\pi$
$192$	1.81335	+	4.03632i	0.130867	+	0.291296i
$193$	−13.0177	−	13.0177i	−0.937034	−	0.937034i	0.0610982	−	0.998132i	$-0.480540\pi$
$193$	−13.0177	−	13.0177i	−0.937034	−	0.937034i	−0.998132	+	0.0610982i	$0.980540\pi$
$194$	14.1686	−	6.36413i	1.01724	−	0.456918i
$195$	0.788408	−	1.31538i	0.0564591	−	0.0941962i
$196$	3.57054	+	4.71655i	0.255039	+	0.336896i
$197$	1.58663	+	4.43433i	0.113043	+	0.315933i	0.984719	−	0.174148i	$-0.0557171\pi$
$197$	1.58663	+	4.43433i	0.113043	+	0.315933i	−0.871677	+	0.490081i	$0.836967\pi$
$198$	−8.76077	−	1.03678i	−0.622600	−	0.0736806i
$199$	2.63343	+	1.40760i	0.186679	+	0.0997819i	0.562089	−	0.827077i	$-0.309998\pi$
$199$	2.63343	+	1.40760i	0.186679	+	0.0997819i	−0.375410	+	0.926859i	$0.622498\pi$
$200$	−13.6958	−	0.133879i	−0.968440	−	0.00946664i
$201$	−4.87082	−	1.47755i	−0.343561	−	0.104218i
$202$	−0.123646	+	6.30100i	−0.00869971	+	0.443337i
$203$	11.4856	−	15.4865i	0.806129	−	1.08694i
$204$	0.633450	+	1.15754i	0.0443504	+	0.0810441i
$205$	−0.912408	+	0.431537i	−0.0637254	+	0.0301398i
$206$	−11.3427	−	0.780562i	−0.790281	−	0.0543843i
$207$	15.9277	−	10.6425i	1.10705	−	0.739707i
$208$	−6.25359	+	27.2298i	−0.433609	+	1.88805i
$209$	10.6000	+	7.08269i	0.733217	+	0.489920i
$210$	−0.381648	+	0.494032i	−0.0263362	+	0.0340915i
$211$	−12.1890	+	0.598807i	−0.839125	+	0.0412236i	−0.464091	−	0.885787i	$-0.653619\pi$
$211$	−12.1890	+	0.598807i	−0.839125	+	0.0412236i	−0.375034	+	0.927011i	$0.622369\pi$
$212$	13.8518	+	9.05948i	0.951345	+	0.622208i
$213$	1.81365	−	7.24049i	0.124269	−	0.496110i
$214$	−0.295250	−	0.0647755i	−0.0201829	−	0.00442796i
$215$	−2.02577	+	2.46841i	−0.138157	+	0.168344i
$216$	−0.350110	−	8.90121i	−0.0238219	−	0.605651i
$217$	−0.708753	+	7.19609i	−0.0481133	+	0.488503i
$218$	−1.55731	+	0.122585i	−0.105475	+	0.00830254i
$219$	0.261576	−	5.32451i	0.0176757	−	0.359797i
$220$	−0.429082	+	1.78748i	−0.0289287	+	0.120512i
$221$	−1.22247	+	8.24122i	−0.0822322	+	0.554365i
$222$	−3.20540	+	5.11744i	−0.215132	+	0.343460i
$223$	25.1460	−	10.4158i	1.68390	−	0.697494i	0.684400	−	0.729107i	$-0.260064\pi$
$223$	25.1460	−	10.4158i	1.68390	−	0.697494i	0.999500	+	0.0316130i	$0.0100644\pi$
$224$	3.83076	−	10.7087i	0.255953	−	0.715502i
$225$	12.0527	+	4.99241i	0.803516	+	0.332827i
$226$	−5.13756	+	3.65625i	−0.341745	+	0.243210i
$227$	2.55868	+	3.44998i	0.169825	+	0.228983i	0.879918	−	0.475125i	$-0.157597\pi$
$227$	2.55868	+	3.44998i	0.169825	+	0.228983i	−0.710093	+	0.704108i	$0.751347\pi$
$228$	−2.54977	+	5.53130i	−0.168863	+	0.366319i
$229$	−6.23285	+	5.64912i	−0.411878	+	0.373305i	−0.851038	−	0.525104i	$-0.824026\pi$
$229$	−6.23285	+	5.64912i	−0.411878	+	0.373305i	0.439160	+	0.898409i	$0.355276\pi$
$230$	−1.81222	−	3.55655i	−0.119494	−	0.234512i
$231$	−1.63352	−	1.99045i	−0.107478	−	0.130962i
$232$	27.0776	+	1.59569i	1.77773	+	0.104762i
$233$	4.02376	−	0.396306i	0.263606	−	0.0259629i	0.0346491	−	0.999400i	$-0.488969\pi$
$233$	4.02376	−	0.396306i	0.263606	−	0.0259629i	0.228956	+	0.973437i	$0.426469\pi$
$234$	15.2158	−	21.8323i	0.994688	−	1.42722i
$235$	0.118218	+	0.197235i	0.00771169	+	0.0128662i
$236$	20.5506	−	8.75035i	1.33773	−	0.569599i
$237$	−4.51457	−	4.09176i	−0.293253	−	0.265789i
$238$	0.888461	−	3.27308i	0.0575903	−	0.212163i
$239$	−4.01118	+	0.797874i	−0.259462	+	0.0516102i	−0.323107	−	0.946362i	$-0.604727\pi$
$239$	−4.01118	+	0.797874i	−0.259462	+	0.0516102i	0.0636452	+	0.997973i	$0.479727\pi$
$240$	−0.875540	−	0.0688564i	−0.0565159	−	0.00444466i
$241$	−5.38977	−	1.07209i	−0.347185	−	0.0690595i	0.0184175	−	0.999830i	$-0.494137\pi$
$241$	−5.38977	−	1.07209i	−0.347185	−	0.0690595i	−0.365603	+	0.930771i	$0.619137\pi$
$242$	7.14028	+	3.55017i	0.458995	+	0.228213i
$243$	−4.36451	+	12.1980i	−0.279983	+	0.782501i
$244$	17.7435	+	9.26065i	1.13591	+	0.592852i
$245$	−1.16140	+	0.172277i	−0.0741991	+	0.0110064i
$246$	1.85212	−	0.724936i	0.118087	−	0.0462202i
$247$	−33.9153	+	18.1281i	−2.15798	+	1.15346i
$248$	−9.01783	+	4.70739i	−0.572633	+	0.298919i
$249$	−1.43566	−	4.73275i	−0.0909815	−	0.299926i
$250$	2.69970	−	4.82083i	0.170744	−	0.304896i
$251$	−27.5685	−	13.0389i	−1.74011	−	0.823009i	−0.986102	−	0.166140i	$-0.946870\pi$
$251$	−27.5685	−	13.0389i	−1.74011	−	0.823009i	−0.754005	−	0.656869i	$-0.771880\pi$
$252$	−7.19556	+	8.09790i	−0.453278	+	0.510120i
$253$	15.9707	−	4.00045i	1.00407	−	0.251506i
$254$	−9.44768	+	10.0215i	−0.592800	+	0.628808i
$255$	−0.261895			−0.0164005
$256$	15.5575	−	3.73689i	0.972343	−	0.233556i
$257$	6.00033			0.374290			0.187145	−	0.982332i	$-0.440077\pi$
$257$	6.00033			0.374290			0.187145	+	0.982332i	$0.440077\pi$
$258$	4.31649	−	4.57868i	0.268733	−	0.285056i
$259$	15.0552	−	3.77113i	0.935483	−	0.234326i
$260$	−4.14515	−	3.68326i	−0.257071	−	0.228426i
$261$	−23.3554	−	11.0463i	−1.44567	−	0.683749i
$262$	−5.68964	+	10.1599i	−0.351507	+	0.627682i
$263$	−5.14281	−	16.9536i	−0.317119	−	1.04540i	−0.960132	−	0.279547i	$-0.909816\pi$
$263$	−5.14281	−	16.9536i	−0.317119	−	1.04540i	0.643012	−	0.765856i	$-0.277684\pi$
$264$	1.08537	−	3.45602i	0.0668002	−	0.212704i
$265$	−2.89714	+	1.54855i	−0.177970	+	0.0951270i
$266$	14.5778	−	5.70586i	0.893819	−	0.349849i
$267$	1.94969	−	0.289209i	0.119319	−	0.0176993i
$268$	−8.51570	+	16.3162i	−0.520179	+	0.996668i
$269$	1.09499	−	3.06029i	0.0667626	−	0.186589i	−0.903529	−	0.428526i	$-0.859033\pi$
$269$	1.09499	−	3.06029i	0.0667626	−	0.186589i	0.970292	+	0.241938i	$0.0777829\pi$
$270$	1.58315	+	0.787146i	0.0963474	+	0.0479042i
$271$	25.4773	+	5.06774i	1.54763	+	0.307843i	0.893685	−	0.448696i	$-0.148111\pi$
$271$	25.4773	+	5.06774i	1.54763	+	0.307843i	0.653949	+	0.756539i	$0.273111\pi$
$272$	4.53764	−	1.47465i	0.275135	−	0.0894140i
$273$	7.61809	−	1.51533i	0.461068	−	0.0917120i
$274$	−4.52128	+	16.6564i	−0.273141	+	1.00625i
$275$	8.30793	+	7.52987i	0.500987	+	0.454068i
$276$	3.08154	+	7.23712i	0.185487	+	0.435623i
$277$	−3.41542	−	5.69829i	−0.205213	−	0.342377i	0.737865	−	0.674948i	$-0.235834\pi$
$277$	−3.41542	−	5.69829i	−0.205213	−	0.342377i	−0.943078	+	0.332571i	$0.892084\pi$
$278$	−6.31799	+	9.06533i	−0.378928	+	0.543702i
$279$	9.64264	−	0.949717i	0.577290	−	0.0568581i
$280$	1.49949	+	1.68729i	0.0896119	+	0.100835i
$281$	0.876801	+	1.06838i	0.0523055	+	0.0637345i	0.798506	−	0.601987i	$-0.205624\pi$
$281$	0.876801	+	1.06838i	0.0523055	+	0.0637345i	−0.746201	+	0.665721i	$0.768124\pi$
$282$	−0.205725	−	0.403745i	−0.0122508	−	0.0240426i
$283$	19.6091	−	17.7726i	1.16564	−	1.05647i	0.168140	−	0.985763i	$-0.446224\pi$
$283$	19.6091	−	17.7726i	1.16564	−	1.05647i	0.997497	−	0.0707091i	$-0.0225262\pi$
$284$	−24.5106	−	11.2987i	−1.45444	−	0.670456i
$285$	−0.720115	−	0.970962i	−0.0426559	−	0.0575148i
$286$	18.6346	−	13.2617i	1.10189	−	0.784180i
$287$	−4.72294	−	1.95631i	−0.278786	−	0.115477i
$288$	−15.0751	−	2.23509i	−0.888310	−	0.131704i
$289$	−14.3915	+	5.96114i	−0.846556	+	0.350655i
$290$	−2.85777	+	4.56244i	−0.167814	+	0.267916i
$291$	0.891368	−	6.00911i	0.0522529	−	0.352260i
$292$	−18.7435	−	4.49934i	−1.09688	−	0.263304i
$293$	0.540437	−	11.0008i	0.0315726	−	0.642676i	−0.929906	−	0.367797i	$-0.880112\pi$
$293$	0.540437	−	11.0008i	0.0315726	−	0.642676i	0.961479	−	0.274879i	$-0.0886378\pi$
$294$	2.30654	−	0.181562i	0.134520	−	0.0105889i
$295$	−0.434524	+	4.41179i	−0.0252989	+	0.256865i
$296$	16.0340	+	14.8204i	0.931955	+	0.861417i
$297$	−4.62634	+	5.63722i	−0.268448	+	0.327105i
$298$	5.74941	+	1.26138i	0.333055	+	0.0730695i
$299$	−12.0675	+	48.1760i	−0.697879	+	2.78609i
$300$	−2.93212	+	4.48316i	−0.169286	+	0.258835i
$301$	−16.1540	+	0.793595i	−0.931101	+	0.0457421i
$302$	3.07396	−	3.97915i	0.176886	−	0.228974i
$303$	2.04947	+	1.36941i	0.117739	+	0.0786707i
$304$	17.9441	+	12.7683i	1.02916	+	0.732314i
$305$	−3.30297	+	2.20697i	−0.189127	+	0.126371i
$306$	−4.53386	−	0.312004i	−0.259184	−	0.0178361i
$307$	5.37006	−	2.53985i	0.306486	−	0.144957i	−0.268124	−	0.963384i	$-0.586404\pi$
$307$	5.37006	−	2.53985i	0.306486	−	0.144957i	0.574610	+	0.818427i	$0.305154\pi$
$308$	−8.16761	+	4.46962i	−0.465393	+	0.254680i
$309$	−2.64893	+	3.57167i	−0.150692	+	0.203185i
$310$	0.0396118	−	2.01861i	0.00224980	−	0.114650i
$311$	0.258481	+	0.0784094i	0.0146571	+	0.00444619i	0.297605	−	0.954689i	$-0.403812\pi$
$311$	0.258481	+	0.0784094i	0.0146571	+	0.00444619i	−0.282948	+	0.959135i	$0.591312\pi$
$312$	7.65080	+	7.80185i	0.433141	+	0.441693i
$313$	−3.36486	−	1.79856i	−0.190193	−	0.101660i	0.373552	−	0.927609i	$-0.378140\pi$
$313$	−3.36486	−	1.79856i	−0.190193	−	0.101660i	−0.563745	+	0.825949i	$0.690640\pi$
$314$	−7.93880	−	0.939505i	−0.448013	−	0.0530193i
$315$	−0.724337	−	2.02439i	−0.0408118	−	0.114061i
$316$	−17.5656	+	13.2976i	−0.988141	+	0.748048i
$317$	−1.62975	+	2.71908i	−0.0915360	+	0.152719i	−0.900091	−	0.435702i	$-0.856500\pi$
$317$	−1.62975	+	2.71908i	−0.0915360	+	0.152719i	0.808555	+	0.588421i	$0.200250\pi$
$318$	5.90510	−	2.65241i	0.331142	−	0.148740i
$319$	−15.7015	−	15.7015i	−0.879117	−	0.879117i
$320$	−0.831681	+	3.06477i	−0.0464924	+	0.171326i
$321$	−0.0835961	+	0.0835961i	−0.00466588	+	0.00466588i
$322$	7.18314	−	18.8981i	0.400301	−	1.05315i
$323$	5.63302	+	3.37630i	0.313430	+	0.187863i
$324$	10.9399	+	6.41157i	0.607773	+	0.356198i
$325$	−31.8456	+	11.3946i	−1.76648	+	0.632056i
$326$	3.45981	+	4.38862i	0.191621	+	0.243063i
$327$	−0.288009	+	0.538827i	−0.0159269	+	0.0297972i
$328$	−1.33402	−	7.06693i	−0.0736592	−	0.390206i
$329$	−0.338087	+	1.11452i	−0.0186394	+	0.0614457i
$330$	0.498315	+	0.518264i	0.0274313	+	0.0285295i
$331$	−1.46779	−	1.08859i	−0.0806772	−	0.0598343i	0.554609	−	0.832111i	$-0.312868\pi$
$331$	−1.46779	−	1.08859i	−0.0806772	−	0.0598343i	−0.635286	+	0.772277i	$0.719118\pi$
$332$	−17.7788	+	1.92798i	−0.975738	+	0.105812i
$333$	−8.89184	−	18.8002i	−0.487270	−	1.03025i
$334$	−4.28178	−	4.91464i	−0.234289	−	0.268917i
$335$	−2.02944	−	3.03727i	−0.110880	−	0.165944i
$336$	−2.71964	−	3.51997i	−0.148368	−	0.192030i
$337$	5.72332	−	8.56556i	0.311769	−	0.466596i	−0.642184	−	0.766550i	$-0.721972\pi$
$337$	5.72332	−	8.56556i	0.311769	−	0.466596i	0.953953	+	0.299955i	$0.0969715\pi$
$338$	6.44222	+	50.1969i	0.350411	+	2.73035i
$339$	0.121014	+	2.46330i	0.00657258	+	0.133788i
$340$	−0.175592	+	0.930554i	−0.00952283	+	0.0504664i
$341$	8.07812	+	2.02346i	0.437455	+	0.109577i
$342$	−11.3097	−	17.6670i	−0.611560	−	0.955321i
$343$	−15.4760	−	12.7008i	−0.835623	−	0.685778i
$344$	−13.3747	−	18.4071i	−0.721116	−	0.992442i
$345$	−1.55366	−	0.153023i	−0.0836465	−	0.00823846i
$346$	−19.7732	+	23.1521i	−1.06301	+	1.24466i
$347$	17.7490	+	0.871955i	0.952819	+	0.0468090i	0.519535	−	0.854449i	$-0.326105\pi$
$347$	17.7490	+	0.871955i	0.952819	+	0.0468090i	0.433283	+	0.901258i	$0.357355\pi$
$348$	6.23543	−	8.58285i	0.334254	−	0.460089i
$349$	−4.47332	−	0.663554i	−0.239451	−	0.0355192i	0.0259262	−	0.999664i	$-0.491747\pi$
$349$	−4.47332	−	0.663554i	−0.239451	−	0.0355192i	−0.265377	+	0.964145i	$0.585497\pi$
$350$	13.4189	−	3.08279i	0.717272	−	0.164782i
$351$	−8.41832	−	20.3236i	−0.449337	−	1.08479i
$352$	−11.5521	−	6.17367i	−0.615729	−	0.329058i
$353$	1.53113	−	3.69647i	0.0814937	−	0.196743i	−0.877881	−	0.478880i	$-0.841043\pi$
$353$	1.53113	−	3.69647i	0.0814937	−	0.196743i	0.959374	+	0.282136i	$0.0910431\pi$
$354$	1.45111	−	8.61452i	0.0771257	−	0.457856i
$355$	4.30259	−	3.19102i	0.228358	−	0.169362i
$356$	0.279600	−	7.12147i	0.0148188	−	0.377437i
$357$	−0.890803	−	0.982850i	−0.0471463	−	0.0520179i
$358$	5.64715	−	17.3810i	0.298461	−	0.918614i
$359$	9.20234	−	7.55216i	0.485681	−	0.398588i	−0.359436	−	0.933170i	$-0.617031\pi$
$359$	9.20234	−	7.55216i	0.485681	−	0.398588i	0.845117	+	0.534582i	$0.179531\pi$
$360$	1.82550	−	2.41177i	0.0962125	−	0.127112i
$361$	1.10894	+	11.2593i	0.0583653	+	0.592593i
$362$	−1.56653	−	8.77155i	−0.0823350	−	0.461023i
$363$	2.67508	−	1.60338i	0.140406	−	0.0841558i
$364$	−0.276524	−	28.0843i	−0.0144938	−	1.47202i
$365$	2.56925	−	2.83473i	0.134481	−	0.148377i
$366$	6.79200	−	3.89191i	0.355024	−	0.203433i
$367$	4.24702	+	21.3512i	0.221693	+	1.11452i	0.917939	+	0.396721i	$0.129852\pi$
$367$	4.24702	+	21.3512i	0.221693	+	1.11452i	−0.696247	+	0.717803i	$0.745148\pi$
$368$	27.7807	−	6.09694i	1.44817	−	0.317825i
$369$	−1.33639	+	6.71846i	−0.0695695	+	0.349749i
$370$	−4.10809	+	1.37960i	−0.213569	+	0.0717219i
$371$	−15.6658	−	5.60530i	−0.813326	−	0.291013i
$372$	−0.350970	+	3.96311i	−0.0181970	+	0.205478i
$373$	−3.49133	−	23.5367i	−0.180774	−	1.21868i	−0.869601	−	0.493756i	$-0.835624\pi$
$373$	−3.49133	−	23.5367i	−0.180774	−	1.21868i	0.688826	−	0.724926i	$-0.258126\pi$
$374$	−3.57861	−	1.56525i	−0.185045	−	0.0809373i
$375$	−1.01869	−	1.90584i	−0.0526051	−	0.0984173i
$376$	−1.57250	+	0.460277i	−0.0810957	+	0.0237370i
$377$	64.0986	−	19.4441i	3.30124	−	1.00142i
$378$	2.43086	+	8.61870i	0.125030	+	0.443298i
$379$	−1.49102	+	3.15250i	−0.0765886	+	0.161933i	−0.938650	−	0.344870i	$-0.887923\pi$
$379$	−1.49102	+	3.15250i	−0.0765886	+	0.161933i	0.862062	+	0.506803i	$0.169173\pi$
$380$	−3.93280	+	1.90768i	−0.201748	+	0.0978621i
$381$	1.30887	+	5.22529i	0.0670553	+	0.267700i
$382$	−22.0583	+	0.650172i	−1.12860	+	0.0332657i
$383$		−	6.91471i		−	0.353325i	−0.984271	−	0.176663i	$-0.943470\pi$
$383$		−	6.91471i		−	0.353325i	0.984271	−	0.176663i	$-0.0565301\pi$
$384$	2.04966	−	5.91262i	0.104596	−	0.301727i
$385$		−	1.84793i		−	0.0941792i
$386$	0.767064	+	26.0241i	0.0390425	+	1.32459i
$387$	5.26591	+	21.0227i	0.267681	+	1.06864i
$388$	−20.7537	−	7.19610i	−1.05361	−	0.365327i
$389$	−9.47720	+	20.0379i	−0.480513	+	1.01596i	0.507509	+	0.861647i	$0.330567\pi$
$389$	−9.47720	+	20.0379i	−0.480513	+	1.01596i	−0.988022	+	0.154313i	$0.950683\pi$
$390$	−2.08735	+	0.588725i	−0.105697	+	0.0298112i
$391$	8.11625	−	2.46204i	0.410456	−	0.124511i
$392$	0.901349	−	8.31726i	0.0455250	−	0.420085i
$393$	2.14690	+	4.01657i	0.108297	+	0.202609i
$394$	2.66908	−	6.10225i	0.134466	−	0.307427i
$395$	−0.641603	−	4.32534i	−0.0322826	−	0.217631i
$396$	8.00929	+	9.56572i	0.402482	+	0.480696i
$397$	8.80876	+	3.15182i	0.442099	+	0.158185i	0.548523	−	0.836135i	$-0.315190\pi$
$397$	8.80876	+	3.15182i	0.442099	+	0.158185i	−0.106424	+	0.994321i	$0.533940\pi$
$398$	−1.34436	−	4.00316i	−0.0673866	−	0.200660i
$399$	1.19449	−	6.00509i	0.0597991	−	0.300631i
$400$	13.9635	+	13.4241i	0.698175	+	0.671206i
$401$	−4.85333	−	24.3993i	−0.242364	−	1.21844i	−0.889809	−	0.456332i	$-0.849163\pi$
$401$	−4.85333	−	24.3993i	−0.242364	−	1.21844i	0.647446	−	0.762111i	$-0.275837\pi$
$402$	3.57884	+	6.24564i	0.178496	+	0.311504i
$403$	−16.8700	+	18.6132i	−0.840355	+	0.927188i
$404$	6.23985	−	6.36395i	0.310444	−	0.316619i
$405$	−2.15867	+	1.29386i	−0.107265	+	0.0642923i
$406$	−26.8425	+	4.79385i	−1.33217	+	0.237915i
$407$	−1.75200	−	17.7883i	−0.0868433	−	0.881735i
$408$	0.471097	−	1.80565i	0.0233228	−	0.0893932i
$409$	−13.8349	+	11.3540i	−0.684094	+	0.561422i	−0.910955	−	0.412506i	$-0.864654\pi$
$409$	−13.8349	+	11.3540i	−0.684094	+	0.561422i	0.226861	+	0.973927i	$0.427154\pi$
$410$	1.35753	+	0.441067i	0.0670436	+	0.0217827i
$411$	4.53320	+	5.00162i	0.223606	+	0.246712i
$412$	10.9147	+	11.8068i	0.537729	+	0.581678i
$413$	−18.0348	+	13.3755i	−0.887432	+	0.658165i
$414$	−26.7144	−	4.50003i	−1.31294	−	0.221164i
$415$	1.35828	−	3.27917i	0.0666751	−	0.160968i
$416$	32.8509	−	21.9536i	1.61065	−	1.07637i
$417$	1.65385	+	3.99274i	0.0809892	+	0.195525i
$418$	−4.03675	−	17.5714i	−0.197444	−	0.859445i
$419$	−9.74090	−	1.44493i	−0.475874	−	0.0705893i	−0.0955147	−	0.995428i	$-0.530450\pi$
$419$	−9.74090	−	1.44493i	−0.475874	−	0.0705893i	−0.380359	+	0.924839i	$0.624200\pi$
$420$	0.871989	−	0.138135i	0.0425487	−	0.00674029i
$421$	28.5971	+	1.40489i	1.39374	+	0.0684699i	0.732020	−	0.681283i	$-0.238578\pi$
$421$	28.5971	+	1.40489i	1.39374	+	0.0684699i	0.661718	+	0.749753i	$0.269828\pi$
$422$	13.1237	+	11.2084i	0.638853	+	0.545616i
$423$	1.55313	+	0.152970i	0.0755157	+	0.00743765i
$424$	−5.46525	−	22.7601i	−0.265416	−	1.10533i
$425$	4.46499	+	3.66432i	0.216584	+	0.177746i
$426$	−8.89032	+	5.69124i	−0.430737	+	0.275742i
$427$	−19.5171	−	4.88877i	−0.944497	−	0.236584i
$428$	0.240982	+	0.353079i	0.0116483	+	0.0170667i
$429$	−0.438934	−	8.93470i	−0.0211919	−	0.431371i
$430$	4.47920	−	0.574856i	0.216006	−	0.0277220i
$431$	12.9102	−	19.3214i	0.621860	−	0.930680i	−0.378128	−	0.925753i	$-0.623432\pi$
$431$	12.9102	−	19.3214i	0.621860	−	0.930680i	0.999988	−	0.00492617i	$-0.00156805\pi$
$432$	−8.27482	+	9.49924i	−0.398123	+	0.457032i
$433$	−3.52001	−	5.26807i	−0.169161	−	0.253167i	0.737197	−	0.675678i	$-0.236149\pi$
$433$	−3.52001	−	5.26807i	−0.169161	−	0.253167i	−0.906358	+	0.422511i	$0.861149\pi$
$434$	7.71028	−	6.71742i	0.370105	−	0.322446i
$435$	0.900252	+	1.90342i	0.0431638	+	0.0912622i
$436$	1.72144	+	1.38461i	0.0824420	+	0.0663108i
$437$	31.4446	+	23.3209i	1.50420	+	1.11559i
$438$	−5.43449	+	5.22531i	−0.259670	+	0.249675i
$439$	1.55799	−	5.13602i	0.0743590	−	0.245129i	−0.911879	−	0.410458i	$-0.865369\pi$
$439$	1.55799	−	5.13602i	0.0743590	−	0.245129i	0.986238	+	0.165330i	$0.0528688\pi$
$440$	2.17558	−	1.42311i	0.103717	−	0.0678443i
$441$	−3.75634	+	7.02761i	−0.178873	+	0.334648i
$442$	9.25280	−	7.29453i	0.440111	−	0.346965i
$443$	−26.1802	+	9.36744i	−1.24386	+	0.445060i	−0.874863	−	0.484370i	$-0.839049\pi$
$443$	−26.1802	+	9.36744i	−1.24386	+	0.445060i	−0.368997	+	0.929430i	$0.620299\pi$
$444$	8.26289	−	2.15642i	0.392139	−	0.102339i
$445$	1.21328	+	0.727212i	0.0575150	+	0.0344732i
$446$	−35.9803	−	13.6760i	−1.70372	−	0.647580i
$447$	1.62787	−	1.62787i	0.0769955	−	0.0769955i
$448$	−14.3305	+	7.30328i	−0.677051	+	0.345047i
$449$	15.7937	+	15.7937i	0.745353	+	0.745353i	0.973603	−	0.228250i	$-0.0733004\pi$
$449$	15.7937	+	15.7937i	0.745353	+	0.745353i	−0.228250	+	0.973603i	$0.573300\pi$
$450$	−7.55946	−	16.8297i	−0.356356	−	0.793362i
$451$	−3.02676	+	5.04985i	−0.142525	+	0.237788i
$452$	8.83363	+	1.22158i	0.415499	+	0.0574584i
$453$	−0.662527	−	1.85164i	−0.0311282	−	0.0869976i
$454$	0.713884	−	6.03231i	0.0335042	−	0.283110i
$455$	4.91611	+	2.62771i	0.230471	+	0.123189i
$456$	7.98973	−	3.21832i	0.374153	−	0.150712i
$457$	−12.5377	−	3.80327i	−0.586489	−	0.177910i	−0.0169257	−	0.999857i	$-0.505388\pi$
$457$	−12.5377	−	3.80327i	−0.586489	−	0.177910i	−0.569564	+	0.821947i	$0.692888\pi$
$458$	11.8940	+	0.233399i	0.555771	+	0.0109060i
$459$	−2.23789	+	3.01744i	−0.104456	+	0.140842i
$460$	−1.58540	+	5.41783i	−0.0739196	+	0.252607i
$461$	−7.57043	+	3.58054i	−0.352590	+	0.166763i	−0.595641	−	0.803251i	$-0.703102\pi$
$461$	−7.57043	+	3.58054i	−0.352590	+	0.166763i	0.243051	+	0.970014i	$0.421852\pi$
$462$	−0.250004	+	3.63291i	−0.0116312	+	0.169018i
$463$	−25.6971	+	17.1703i	−1.19425	+	0.797970i	−0.983736	−	0.179622i	$-0.942513\pi$
$463$	−25.6971	+	17.1703i	−1.19425	+	0.797970i	−0.210510	+	0.977592i	$0.567513\pi$
$464$	−26.3156	−	27.9100i	−1.22167	−	1.29569i
$465$	−0.656578	−	0.438711i	−0.0304481	−	0.0203447i
$466$	−4.52502	−	3.49566i	−0.209618	−	0.161933i
$467$	−36.5997	+	1.79803i	−1.69363	+	0.0832028i	−0.872834	−	0.488017i	$-0.837720\pi$
$467$	−36.5997	+	1.79803i	−1.69363	+	0.0832028i	−0.820797	+	0.571220i	$0.806470\pi$
$468$	−36.8371	+	7.70514i	−1.70279	+	0.356170i
$469$	4.49551	−	17.9471i	0.207583	−	0.828719i
$470$	0.0696885	−	0.317644i	0.00321449	−	0.0146518i
$471$	−1.98352	+	2.41692i	−0.0913957	+	0.111366i
$472$	−29.6359	−	10.9318i	−1.36410	−	0.503177i
$473$	−1.82573	+	18.5370i	−0.0839472	+	0.852331i
$474$	0.676181	+	8.59014i	0.0310580	+	0.394558i
$475$	−1.30821	+	26.6293i	−0.0600249	+	1.22184i
$476$	−4.08948	+	2.50620i	−0.187441	+	0.114871i
$477$	−3.27138	+	22.0538i	−0.149786	+	1.00978i
$478$	4.90164	+	3.07023i	0.224196	+	0.140429i
$479$	−36.9481	+	15.3044i	−1.68820	+	0.699276i	−0.999664	−	0.0259260i	$-0.991747\pi$
$479$	−36.9481	+	15.3044i	−1.68820	+	0.699276i	−0.688537	+	0.725202i	$0.741747\pi$
$480$	0.834157	+	0.920219i	0.0380739	+	0.0420021i
$481$	49.8142	+	20.6337i	2.27133	+	0.940817i
$482$	4.50618	+	6.33184i	0.205251	+	0.288408i
$483$	−4.71033	−	6.35115i	−0.214328	−	0.288987i
$484$	−3.90352	−	10.5800i	−0.177433	−	0.480911i
$485$	3.23032	−	2.92779i	0.146681	−	0.132944i
$486$	16.3245	−	8.31805i	0.740495	−	0.377314i
$487$	18.2208	+	22.2021i	0.825662	+	1.00607i	0.999772	+	0.0213456i	$0.00679504\pi$
$487$	18.2208	+	22.2021i	0.825662	+	1.00607i	−0.174110	+	0.984726i	$0.555705\pi$
$488$	−9.27476	−	26.7425i	−0.419849	−	1.21058i
$489$	2.17518	−	0.214236i	0.0983649	−	0.00968810i
$490$	1.36224	+	0.949400i	0.0615397	+	0.0428895i
$491$	11.8922	+	19.8410i	0.536688	+	0.895410i	0.999958	+	0.00919290i	$0.00292623\pi$
$491$	11.8922	+	19.8410i	0.536688	+	0.895410i	−0.463269	+	0.886218i	$0.653324\pi$
$492$	−2.60914	−	1.05077i	−0.117629	−	0.0473723i
$493$	−8.47576	−	7.68198i	−0.381729	−	0.345979i
$494$	52.4860	+	14.2470i	2.36145	+	0.641004i
$495$	−2.42861	+	0.483081i	−0.109158	+	0.0217129i
$496$	13.8463	+	3.90420i	0.621715	+	0.175304i
$497$	26.6101	+	5.29308i	1.19363	+	0.237427i
$498$	−3.11392	+	6.26288i	−0.139538	+	0.280646i
$499$	4.23913	−	11.8476i	0.189770	−	0.530371i	−0.808543	−	0.588437i	$-0.799743\pi$
$499$	4.23913	−	11.8476i	0.189770	−	0.530371i	0.998313	+	0.0580662i	$0.0184935\pi$
$500$	−7.45477	+	2.34178i	−0.333387	+	0.104727i
$501$	−2.52177	+	0.374070i	−0.112665	+	0.0167122i
$502$	15.7196	+	40.1617i	0.701602	+	1.79250i
$503$	9.12436	−	4.87707i	0.406835	−	0.217458i	−0.255268	−	0.966870i	$-0.582164\pi$
$503$	9.12436	−	4.87707i	0.406835	−	0.217458i	0.662104	+	0.749412i	$0.269664\pi$
$504$	15.2602	−	1.35253i	0.679745	−	0.0602465i
$505$	0.513499	+	1.69278i	0.0228504	+	0.0753276i
$506$	−20.3152	−	11.3767i	−0.903119	−	0.505754i
$507$	17.8933	+	8.46289i	0.794669	+	0.375850i
$508$	19.4439	−	1.14722i	0.862682	−	0.0508996i
$509$	32.0873	−	8.03745i	1.42225	−	0.356254i	0.545865	−	0.837873i	$-0.316201\pi$
$509$	32.0873	−	8.03745i	1.42225	−	0.356254i	0.876380	+	0.481620i	$0.159951\pi$
$510$	0.269497	+	0.254065i	0.0119335	+	0.0112502i
$511$	19.3773			0.857202
$512$	−19.6343	−	11.2470i	−0.867721	−	0.497052i
$513$	−17.3404			−0.765598
$514$	−6.17451	−	5.82094i	−0.272346	−	0.256751i
$515$	−3.09563	+	0.775415i	−0.136410	+	0.0341689i
$516$	−8.88358	+	0.524146i	−0.391078	+	0.0230742i
$517$	1.21255	+	0.573493i	0.0533279	+	0.0252222i
$518$	−19.1506	−	10.7245i	−0.841429	−	0.471207i
$519$	3.45673	+	11.3953i	0.151734	+	0.500199i
$520$	0.692332	+	7.81141i	0.0303608	+	0.342553i
$521$	−8.19773	+	4.38178i	−0.359149	+	0.191969i	−0.641096	−	0.767461i	$-0.721520\pi$
$521$	−8.19773	+	4.38178i	−0.359149	+	0.191969i	0.281947	+	0.959430i	$0.409020\pi$
$522$	13.3174	+	34.0241i	0.582885	+	1.48920i
$523$	2.27436	−	0.337369i	0.0994508	−	0.0147521i	−0.0968196	−	0.995302i	$-0.530867\pi$
$523$	2.27436	−	0.337369i	0.0994508	−	0.0147521i	0.196270	+	0.980550i	$0.437117\pi$
$524$	15.7110	−	4.93531i	0.686337	−	0.215600i
$525$	1.81417	−	5.07025i	0.0791767	−	0.221284i
$526$	−11.1546	+	22.4348i	−0.486365	+	0.978203i
$527$	4.20756	+	0.836936i	0.183284	+	0.0364575i
$528$	−4.46958	+	2.50342i	−0.194514	+	0.108947i
$529$	27.0294	−	5.37647i	1.17519	−	0.233760i
$530$	4.48350	+	1.21702i	0.194751	+	0.0528640i
$531$	22.2931	+	20.2053i	0.967440	+	0.876836i
$532$	−20.5362	−	8.27044i	−0.890357	−	0.358569i
$533$	−9.13029	−	15.2330i	−0.395477	−	0.659813i
$534$	−2.28685	−	1.59380i	−0.0989616	−	0.0689703i
$535$	−0.0844353	+	0.00831616i	−0.00365046	+	0.000359539i
$536$	24.5913	−	8.52868i	1.06218	−	0.368383i
$537$	−4.53448	−	5.52528i	−0.195677	−	0.238433i
$538$	−4.09557	+	2.08687i	−0.176572	+	0.0899713i
$539$	−5.07458	+	4.59933i	−0.218578	+	0.198107i
$540$	−0.865493	−	2.34582i	−0.0372449	−	0.100948i
$541$	1.11966	+	1.50968i	0.0481378	+	0.0649063i	0.826621	−	0.562760i	$-0.190260\pi$
$541$	1.11966	+	1.50968i	0.0481378	+	0.0649063i	−0.778483	+	0.627666i	$0.784010\pi$
$542$	−21.3006	−	29.9304i	−0.914938	−	1.28562i
$543$	−3.21968	−	1.33363i	−0.138170	−	0.0572317i
$544$	−6.09993	−	2.88452i	−0.261532	−	0.123673i
$545$	−0.405093	+	0.167795i	−0.0173523	+	0.00718755i
$546$	−9.30925	−	5.83101i	−0.398399	−	0.249544i
$547$	5.13833	−	34.6398i	0.219699	−	1.48109i	−0.545942	−	0.837823i	$-0.683828\pi$
$547$	5.13833	−	34.6398i	0.219699	−	1.48109i	0.765641	−	0.643268i	$-0.222422\pi$
$548$	20.8109	−	12.7538i	0.888999	−	0.544814i
$549$	−1.32289	+	26.9280i	−0.0564595	+	1.14926i
$550$	−1.24434	−	15.8080i	−0.0530589	−	0.674055i
$551$	5.17534	−	52.5461i	0.220477	−	2.23854i
$552$	3.84976	−	10.4366i	0.163857	−	0.444212i
$553$	14.0500	−	17.1200i	0.597466	−	0.728014i
$554$	−2.01336	+	9.17701i	−0.0855396	+	0.389894i
$555$	−0.411830	+	1.64412i	−0.0174812	+	0.0697889i
$556$	15.2957	−	3.19937i	0.648682	−	0.135684i
$557$	−16.9831	+	0.834324i	−0.719595	+	0.0353514i	−0.405571	−	0.914064i	$-0.632927\pi$
$557$	−16.9831	+	0.834324i	−0.719595	+	0.0353514i	−0.314024	+	0.949415i	$0.601677\pi$
$558$	−10.8439	−	8.37707i	−0.459058	−	0.354630i
$559$	−46.7184	−	31.2162i	−1.97598	−	1.32031i
$560$	0.0938264	−	3.19093i	0.00396489	−	0.134842i
$561$	−1.27021	+	0.848727i	−0.0536283	+	0.0358333i
$562$	0.134191	−	1.94999i	0.00566051	−	0.0822552i
$563$	31.1004	−	14.7094i	1.31073	−	0.619928i	0.360872	−	0.932616i	$-0.382479\pi$
$563$	31.1004	−	14.7094i	1.31073	−	0.619928i	0.949856	+	0.312688i	$0.101229\pi$
$564$	−0.179977	+	0.615040i	−0.00757839	+	0.0258978i
$565$	−1.05436	+	1.42163i	−0.0443571	+	0.0598086i
$566$	−37.4195	−	0.734293i	−1.57286	−	0.0308647i
$567$	−12.1981	−	3.70025i	−0.512272	−	0.155396i
$568$	14.2612	+	35.4046i	0.598388	+	1.48554i
$569$	27.0441	+	14.4554i	1.13375	+	0.606001i	0.927991	−	0.372602i	$-0.121534\pi$
$569$	27.0441	+	14.4554i	1.13375	+	0.606001i	0.205758	+	0.978603i	$0.434034\pi$
$570$	−0.200916	+	1.69773i	−0.00841543	+	0.0711102i
$571$	−8.05737	−	22.5189i	−0.337191	−	0.942385i	−0.983754	−	0.179524i	$-0.942544\pi$
$571$	−8.05737	−	22.5189i	−0.337191	−	0.942385i	0.646563	−	0.762861i	$-0.276206\pi$
$572$	−32.0407	−	4.43084i	−1.33969	−	0.185263i
$573$	−4.43724	+	7.40308i	−0.185368	+	0.309268i
$574$	2.96222	+	6.59483i	0.123641	+	0.275263i
$575$	24.3471	+	24.3471i	1.01534	+	1.01534i
$576$	13.3445	+	16.9244i	0.556019	+	0.705183i
$577$	−29.6869	+	29.6869i	−1.23588	+	1.23588i	−0.274211	+	0.961670i	$0.588417\pi$
$577$	−29.6869	+	29.6869i	−1.23588	+	1.23588i	−0.961670	+	0.274211i	$0.911583\pi$
$578$	20.5921	+	7.82702i	0.856520	+	0.325561i
$579$	8.73406	+	5.23500i	0.362975	+	0.217559i
$580$	7.36677	−	1.92256i	0.305888	−	0.0798298i
$581$	16.9262	−	6.05630i	0.702218	−	0.251258i
$582$	−6.74670	+	5.31883i	−0.279660	+	0.220472i
$583$	−9.03294	+	16.8994i	−0.374106	+	0.699903i
$584$	14.9227	+	22.8130i	0.617506	+	0.944010i
$585$	2.16828	−	7.14785i	0.0896472	−	0.295527i
$586$	−11.2281	+	10.7959i	−0.463828	+	0.445974i
$587$	24.1198	+	17.8884i	0.995529	+	0.738335i	0.965283	−	0.261208i	$-0.0841208\pi$
$587$	24.1198	+	17.8884i	0.995529	+	0.738335i	0.0302463	+	0.999542i	$0.490371\pi$
$588$	−2.54963	−	2.05075i	−0.105145	−	0.0845717i
$589$	8.46636	+	17.9006i	0.348850	+	0.737582i
$590$	4.72703	−	4.11833i	0.194609	−	0.169549i
$591$	−1.44725	−	2.16597i	−0.0595320	−	0.0890959i
$592$	−2.12210	−	30.8052i	−0.0872179	−	1.26609i
$593$	−1.64357	+	2.45978i	−0.0674934	+	0.101011i	−0.863681	−	0.504039i	$-0.831847\pi$
$593$	−1.64357	+	2.45978i	−0.0674934	+	0.101011i	0.796188	+	0.605050i	$0.206847\pi$
$594$	10.2293	−	1.31282i	0.419714	−	0.0538658i
$595$	−0.0467103	−	0.950810i	−0.00191494	−	0.0389794i
$596$	−4.69264	−	6.87552i	−0.192218	−	0.281632i
$597$	−1.60212	−	0.401310i	−0.0655704	−	0.0164245i
$598$	59.1534	−	37.8678i	2.41896	−	1.54853i
$599$	−21.0891	−	17.3074i	−0.861677	−	0.707160i	0.0958837	−	0.995393i	$-0.469432\pi$
$599$	−21.0891	−	17.3074i	−0.861677	−	0.707160i	−0.957560	+	0.288233i	$0.906932\pi$
$600$	7.36636	−	1.76884i	0.300730	−	0.0722125i
$601$	42.8662	+	4.22195i	1.74855	+	0.172217i	0.921100	−	0.389327i	$-0.127292\pi$
$601$	42.8662	+	4.22195i	1.74855	+	0.172217i	0.827447	+	0.561544i	$0.189792\pi$
$602$	17.3928	+	14.8544i	0.708877	+	0.605421i
$603$	−24.7619	−	1.21647i	−1.00838	−	0.0495386i
$604$	−7.02338	+	1.11260i	−0.285777	+	0.0452710i
$605$	2.21402	+	0.328419i	0.0900126	+	0.0133521i
$606$	−0.780492	−	3.39736i	−0.0317053	−	0.138008i
$607$	10.9377	+	26.4060i	0.443948	+	1.07179i	0.974551	+	0.224165i	$0.0719654\pi$
$607$	10.9377	+	26.4060i	0.443948	+	1.07179i	−0.530603	+	0.847620i	$0.678035\pi$
$608$	−6.07835	−	30.5466i	−0.246510	−	1.23883i
$609$	−4.08115	+	9.85277i	−0.165377	+	0.399255i
$610$	5.53984	+	0.933183i	0.224301	+	0.0377835i
$611$	−3.24990	+	2.41029i	−0.131477	+	0.0975100i
$612$	4.36280	+	4.71938i	0.176356	+	0.190769i
$613$	4.02050	+	4.43593i	0.162386	+	0.179166i	0.816709	−	0.577050i	$-0.195796\pi$
$613$	4.02050	+	4.43593i	0.162386	+	0.179166i	−0.654323	+	0.756215i	$0.727046\pi$
$614$	−7.98986	−	2.59594i	−0.322445	−	0.104764i
$615$	0.431548	−	0.354162i	0.0174017	−	0.0142812i
$616$	12.7407	+	3.32406i	0.513337	+	0.133930i
$617$	−3.30377	−	33.5437i	−0.133005	−	1.35042i	−0.797587	−	0.603205i	$-0.793890\pi$
$617$	−3.30377	−	33.5437i	−0.133005	−	1.35042i	0.664582	−	0.747216i	$-0.268610\pi$
$618$	6.19072	−	1.10561i	0.249027	−	0.0444743i
$619$	5.61436	−	3.36512i	0.225660	−	0.135255i	−0.396805	−	0.917903i	$-0.629881\pi$
$619$	5.61436	−	3.36512i	0.225660	−	0.135255i	0.622465	+	0.782647i	$0.286131\pi$
$620$	−1.99903	+	2.03878i	−0.0802829	+	0.0818795i
$621$	−15.0391	+	16.5931i	−0.603499	+	0.665859i
$622$	−0.189919	−	0.331439i	−0.00761507	−	0.0132895i
$623$	1.39771	+	7.02678i	0.0559982	+	0.281522i
$624$	−0.304285	−	15.4504i	−0.0121812	−	0.618511i
$625$	−4.42100	+	22.2258i	−0.176840	+	0.889034i
$626$	1.71775	+	5.11503i	0.0686552	+	0.204438i
$627$	−6.63923	−	2.37555i	−0.265145	−	0.0948705i
$628$	7.25784	+	8.66824i	0.289619	+	0.345900i
$629$	−1.35109	−	9.10831i	−0.0538715	−	0.363172i
$630$	−1.21850	+	2.78583i	−0.0485463	+	0.110990i
$631$	11.8445	+	22.1596i	0.471523	+	0.882158i	0.999460	+	0.0328739i	$0.0104660\pi$
$631$	11.8445	+	22.1596i	0.471523	+	0.882158i	−0.527936	+	0.849284i	$0.677034\pi$
$632$	30.9755	+	3.35684i	1.23214	+	0.133528i
$633$	6.45943	−	1.95945i	0.256739	−	0.0778810i
$634$	4.31485	−	1.21698i	0.171364	−	0.0483324i
$635$	−1.65286	+	3.49468i	−0.0655918	+	0.138682i
$636$	−8.64963	−	2.99915i	−0.342980	−	0.118924i
$637$	−5.01981	−	20.0402i	−0.198892	−	0.794022i
$638$	0.925209	+	31.3894i	0.0366294	+	1.24272i
$639$		−	36.3557i		−	1.43821i
$640$	3.82897	−	2.34692i	0.151353	−	0.0927701i
$641$		−	25.6529i		−	1.01323i	−0.862173	−	0.506615i	$-0.830897\pi$
$641$		−	25.6529i		−	1.01323i	0.862173	−	0.506615i	$-0.169103\pi$
$642$	0.167120	−	0.00492588i	0.00659568	−	0.000194409i
$643$	−0.372177	−	1.48581i	−0.0146772	−	0.0585947i	0.962250	−	0.272167i	$-0.0877402\pi$
$643$	−0.372177	−	1.48581i	−0.0146772	−	0.0585947i	−0.976927	+	0.213572i	$0.931490\pi$
$644$	−25.7248	+	12.4783i	−1.01370	+	0.491715i
$645$	0.755165	−	1.59666i	0.0297346	−	0.0628686i
$646$	−2.52118	−	8.93893i	−0.0991943	−	0.351697i
$647$	13.6359	−	4.13640i	0.536082	−	0.162619i	−0.0106239	−	0.999944i	$-0.503382\pi$
$647$	13.6359	−	4.13640i	0.536082	−	0.162619i	0.546705	+	0.837325i	$0.315882\pi$
$648$	−5.03758	−	17.2105i	−0.197895	−	0.676093i
$649$	12.1899	+	22.8057i	0.478496	+	0.895203i
$650$	43.8240	+	19.1683i	1.71892	+	0.751841i
$651$	−0.586855	−	3.95626i	−0.0230007	−	0.155058i
$652$	0.697174	−	7.87240i	0.0273034	−	0.308307i
$653$	31.6744	+	11.3333i	1.23952	+	0.443506i	0.873373	−	0.487053i	$-0.161928\pi$
$653$	31.6744	+	11.3333i	1.23952	+	0.443506i	0.366143	+	0.930558i	$0.380678\pi$
$654$	0.819088	−	0.275070i	0.0320289	−	0.0107561i
$655$	−0.637648	+	3.20567i	−0.0249150	+	0.125256i
$656$	−5.48290	+	8.56621i	−0.214071	+	0.334454i
$657$	−5.06557	−	25.4663i	−0.197627	−	0.993536i
$658$	1.42911	−	0.818897i	0.0557123	−	0.0319239i
$659$	−28.5086	+	31.4544i	−1.11054	+	1.22529i	−0.138525	+	0.990359i	$0.544236\pi$
$659$	−28.5086	+	31.4544i	−1.11054	+	1.22529i	−0.972012	+	0.234930i	$0.924514\pi$
$660$	−0.0100109	−	1.01672i	−0.000389674	−	0.0395760i
$661$	−1.31771	+	0.789803i	−0.0512528	+	0.0307198i	−0.539500	−	0.841986i	$-0.681387\pi$
$661$	−1.31771	+	0.789803i	−0.0512528	+	0.0307198i	0.488247	+	0.872706i	$0.337637\pi$
$662$	0.454356	+	2.54410i	0.0176590	+	0.0988793i
$663$	−0.451687	−	4.58605i	−0.0175421	−	0.178108i
$664$	20.1652	+	15.2633i	0.782563	+	0.592332i
$665$	3.39665	−	2.78756i	0.131716	−	0.108097i
$666$	−9.08820	+	27.9719i	−0.352161	+	1.08389i
$667$	−45.7931	−	50.5249i	−1.77312	−	1.95633i
$668$	−0.361642	+	9.21108i	−0.0139923	+	0.356387i
$669$	−12.0920	+	8.96805i	−0.467504	+	0.346725i
$670$	−0.858116	+	5.09420i	−0.0331519	+	0.196806i
$671$	−8.86747	+	21.4080i	−0.342325	+	0.826446i
$672$	−0.616154	+	6.26048i	−0.0237687	+	0.241503i
$673$	−6.99987	−	16.8992i	−0.269825	−	0.651415i	0.729650	−	0.683821i	$-0.239683\pi$
$673$	−6.99987	−	16.8992i	−0.269825	−	0.651415i	−0.999475	+	0.0324057i	$0.989683\pi$
$674$	−14.1989	+	3.26199i	−0.546923	+	0.125647i
$675$	−15.0861	−	2.23781i	−0.580664	−	0.0861334i
$676$	42.0669	−	57.9036i	1.61796	−	2.22706i
$677$	−14.1737	−	0.696310i	−0.544740	−	0.0267614i	−0.225162	−	0.974321i	$-0.572291\pi$
$677$	−14.1737	−	0.696310i	−0.544740	−	0.0267614i	−0.319578	+	0.947560i	$0.603541\pi$
$678$	2.26513	−	2.65220i	0.0869916	−	0.101857i
$679$	21.9751	+	2.16436i	0.843327	+	0.0830604i
$680$	1.08342	−	0.787224i	0.0415474	−	0.0301887i
$681$	−1.83650	−	1.50718i	−0.0703749	−	0.0577552i
$682$	−6.34964	−	9.91881i	−0.243140	−	0.379811i
$683$	26.6078	+	6.66492i	1.01812	+	0.255026i	0.715893	−	0.698210i	$-0.246020\pi$
$683$	26.6078	+	6.66492i	1.01812	+	0.255026i	0.302228	+	0.953236i	$0.402270\pi$
$684$	−5.50077	+	29.1514i	−0.210327	+	1.11463i
$685$	0.237704	+	4.83857i	0.00908219	+	0.184872i
$686$	3.60412	+	28.0828i	0.137606	+	1.07220i
$687$	2.58496	−	3.86866i	0.0986223	−	0.147599i
$688$	−4.09380	+	31.9162i	−0.156075	+	1.21680i
$689$	−32.1135	−	48.0613i	−1.22343	−	1.83099i
$690$	1.45032	+	1.66468i	0.0552126	+	0.0633733i
$691$	−3.46656	−	7.32943i	−0.131874	−	0.278825i	0.827237	−	0.561852i	$-0.189911\pi$
$691$	−3.46656	−	7.32943i	−0.131874	−	0.278825i	−0.959112	+	0.283028i	$0.908661\pi$
$692$	42.8071	−	4.64212i	1.62728	−	0.176467i
$693$	−10.0736	−	7.47106i	−0.382663	−	0.283802i
$694$	−17.4184	−	18.1157i	−0.661193	−	0.687662i
$695$	−0.900325	+	2.96797i	−0.0341513	+	0.112582i
$696$	−14.7427	+	2.78298i	−0.558820	+	0.105489i
$697$	−1.42971	+	2.67479i	−0.0541540	+	0.101315i
$698$	3.95945	+	5.02240i	0.149868	+	0.190100i
$699$	−2.10565	+	0.753415i	−0.0796432	+	0.0284968i
$700$	−16.7991	−	9.84548i	−0.634946	−	0.372124i
$701$	−29.4243	−	17.6363i	−1.11134	−	0.666112i	−0.164039	−	0.986454i	$-0.552452\pi$
$701$	−29.4243	−	17.6363i	−1.11134	−	0.666112i	−0.947302	+	0.320342i	$0.896202\pi$
$702$	−11.0533	+	29.0802i	−0.417181	+	1.09756i
$703$	30.0536	−	30.0536i	1.13349	−	1.13349i
$704$	5.89834	+	17.5596i	0.222302	+	0.661803i
$705$	−0.0899366	−	0.0899366i	−0.00338721	−	0.00338721i
$706$	−5.16153	+	2.31842i	−0.194257	+	0.0872548i
$707$	−4.60613	+	7.68486i	−0.173231	+	0.289019i
$708$	−9.85021	+	7.45685i	−0.370194	+	0.280246i
$709$	−1.49123	−	4.16772i	−0.0560044	−	0.156522i	0.910284	−	0.413985i	$-0.135863\pi$
$709$	−1.49123	−	4.16772i	−0.0560044	−	0.156522i	−0.966288	+	0.257463i	$0.917113\pi$
$710$	−7.52310	−	0.890309i	−0.282337	−	0.0334127i
$711$	−26.1726	−	13.9895i	−0.981548	−	0.524648i
$712$	−7.19628	+	7.05695i	−0.269692	+	0.264470i
$713$	24.4719	+	7.42348i	0.916481	+	0.278012i
$714$	−0.0368044	+	1.87555i	−0.00137737	+	0.0701908i
$715$	3.82428	−	5.15645i	0.143020	−	0.192840i
$716$	−22.6724	+	12.4072i	−0.847309	+	0.463679i
$717$	2.04493	−	0.967182i	0.0763695	−	0.0361201i
$718$	−16.7958	−	1.15583i	−0.626815	−	0.0431352i
$719$	−34.4976	+	23.0506i	−1.28654	+	0.859641i	−0.995284	−	0.0970035i	$-0.969074\pi$
$719$	−34.4976	+	23.0506i	−1.28654	+	0.859641i	−0.291259	+	0.956644i	$0.594074\pi$
$720$	−4.21817	+	0.710856i	−0.157202	+	0.0264921i
$721$	−13.4394	−	8.97994i	−0.500510	−	0.334430i
$722$	9.78152	−	12.6619i	0.364031	−	0.471227i
$723$	3.03592	−	0.149145i	0.112907	−	0.00554677i
$724$	−6.89731	+	10.5459i	−0.256337	+	0.391934i
$725$	11.2837	−	45.0471i	0.419066	−	1.67301i
$726$	−4.30819	−	0.945182i	−0.159892	−	0.0350790i
$727$	18.6156	−	22.6832i	0.690416	−	0.841274i	−0.303336	−	0.952884i	$-0.598101\pi$
$727$	18.6156	−	22.6832i	0.690416	−	0.841274i	0.993752	+	0.111609i	$0.0356006\pi$
$728$	−26.9601	+	29.1678i	−0.999208	+	1.08103i
$729$	−1.16196	+	11.7975i	−0.0430354	+	0.436946i
$730$	−5.39382	+	0.424580i	−0.199634	+	0.0157144i
$731$	−0.470828	+	9.58393i	−0.0174142	+	0.354474i
$732$	−10.7647	−	2.58406i	−0.397875	−	0.0955095i
$733$	−3.72086	+	25.0840i	−0.137433	+	0.926499i	0.805280	+	0.592895i	$0.202015\pi$
$733$	−3.72086	+	25.0840i	−0.137433	+	0.926499i	−0.942713	+	0.333604i	$0.891735\pi$
$734$	16.3426	−	26.0910i	0.603215	−	0.963038i
$735$	0.599986	−	0.248522i	0.0221308	−	0.00916688i
$736$	−34.5018	−	20.6763i	−1.27175	−	0.762137i
$737$	−19.6859	−	8.15415i	−0.725138	−	0.300362i
$738$	7.89278	−	5.61706i	0.290537	−	0.206767i
$739$	−0.0184970	−	0.0249404i	−0.000680424	−	0.000917446i	0.802867	−	0.596158i	$-0.203307\pi$
$739$	−0.0184970	−	0.0249404i	−0.000680424	−	0.000917446i	−0.803548	+	0.595240i	$0.797057\pi$
$740$	5.56569	+	2.56563i	0.204599	+	0.0943144i
$741$	15.7606	−	14.2846i	0.578981	−	0.524757i
$742$	10.6828	+	20.9654i	0.392178	+	0.769665i
$743$	9.32457	+	11.3620i	0.342085	+	0.416832i	0.915427	−	0.402484i	$-0.131853\pi$
$743$	9.32457	+	11.3620i	0.342085	+	0.416832i	−0.573342	+	0.819316i	$0.694353\pi$
$744$	4.20578	−	3.73767i	0.154192	−	0.137030i
$745$	1.64421	−	0.161941i	0.0602392	−	0.00593305i
$746$	−19.2403	+	27.6068i	−0.704438	+	1.01076i
$747$	−12.3842	−	20.6618i	−0.453115	−	0.755976i
$748$	2.16403	+	5.08231i	0.0791247	+	0.185828i
$749$	−0.318406	−	0.288586i	−0.0116343	−	0.0105447i
$750$	−0.800599	+	2.94940i	−0.0292338	+	0.107697i
$751$	11.8074	−	2.34863i	0.430856	−	0.0857027i	0.0251022	−	0.999685i	$-0.492009\pi$
$751$	11.8074	−	2.34863i	0.430856	−	0.0857027i	0.405754	+	0.913982i	$0.367009\pi$
$752$	2.06467	+	1.05185i	0.0752906	+	0.0383571i
$753$	16.5440	+	3.29081i	0.602898	+	0.119924i
$754$	−84.8220	−	42.1737i	−3.08904	−	1.53588i
$755$	0.475470	−	1.32885i	0.0173041	−	0.0483618i
$756$	5.85961	−	11.2271i	0.213112	−	0.408324i
$757$	−13.1489	+	1.95046i	−0.477906	+	0.0708907i	−0.381338	−	0.924436i	$-0.624537\pi$
$757$	−13.1489	+	1.95046i	−0.477906	+	0.0708907i	−0.0965682	+	0.995326i	$0.530787\pi$
$758$	4.59255	−	1.79757i	0.166809	−	0.0652905i
$759$	−8.03130	+	4.29282i	−0.291518	+	0.155819i
$760$	5.89762	+	1.85216i	0.213929	+	0.0671851i
$761$	11.6225	+	38.3143i	0.421316	+	1.38889i	0.869049	+	0.494726i	$0.164732\pi$
$761$	11.6225	+	38.3143i	0.421316	+	1.38889i	−0.447733	+	0.894168i	$0.647768\pi$
$762$	3.72221	−	6.64671i	0.134842	−	0.240785i
$763$	−2.00758	−	0.949517i	−0.0726794	−	0.0343748i
$764$	23.3293	+	20.7298i	0.844025	+	0.749977i
$765$	−1.23738	+	0.309947i	−0.0447375	+	0.0112062i
$766$	−6.70798	+	7.11543i	−0.242369	+	0.257091i
$767$	−78.0046			−2.81658
$768$	−7.84501	+	4.09587i	−0.283083	+	0.147797i
$769$	−7.17777			−0.258837			−0.129419	−	0.991590i	$-0.541311\pi$
$769$	−7.17777			−0.258837			−0.129419	+	0.991590i	$0.541311\pi$
$770$	−1.79268	+	1.90157i	−0.0646038	+	0.0685279i
$771$	−3.21943	+	0.806424i	−0.115945	+	0.0290427i
$772$	24.4567	−	27.5236i	0.880216	−	0.990597i
$773$	−33.9567	−	16.0603i	−1.22134	−	0.577650i	−0.295418	−	0.955368i	$-0.595459\pi$
$773$	−33.9567	−	16.0603i	−1.22134	−	0.577650i	−0.925921	+	0.377718i	$0.876709\pi$
$774$	14.9754	−	26.7414i	0.538280	−	0.961201i
$775$	5.05559	+	16.6661i	0.181602	+	0.598663i
$776$	14.3752	+	27.5382i	0.516040	+	0.988565i
$777$	−7.57090	+	4.04673i	−0.271605	+	0.145176i
$778$	29.1911	−	11.4257i	1.04655	−	0.409630i
$779$	−13.8478	+	2.05413i	−0.496151	+	0.0735970i
$780$	2.71906	+	1.41913i	0.0973581	+	0.0508130i
$781$	10.5267	−	29.4202i	0.376675	−	1.05274i
$782$	−10.7403	−	5.34010i	−0.384072	−	0.190961i
$783$	29.6231	+	5.89241i	1.05864	+	0.210577i
$784$	−8.99612	+	7.68429i	−0.321290	+	0.274439i
$785$	−2.20075	+	0.437757i	−0.0785483	+	0.0156242i
$786$	1.68727	−	6.21589i	0.0601828	−	0.221713i
$787$	−8.83550	−	8.00803i	−0.314952	−	0.285455i	0.498741	−	0.866751i	$-0.333796\pi$
$787$	−8.83550	−	8.00803i	−0.314952	−	0.285455i	−0.813692	+	0.581296i	$0.802546\pi$
$788$	−8.66637	+	3.69011i	−0.308727	+	0.131455i
$789$	5.03784	+	8.40513i	0.179352	+	0.299230i
$790$	−3.53580	+	5.07332i	−0.125798	+	0.180500i
$791$	−8.92143	+	0.878684i	−0.317210	+	0.0312424i
$792$	1.03795	−	17.6132i	0.0368821	−	0.625859i
$793$	−44.3430	−	54.0321i	−1.57467	−	1.91874i
$794$	−6.00686	−	11.7887i	−0.213176	−	0.418366i
$795$	1.34632	−	1.22023i	0.0477489	−	0.0432771i
$796$	−2.50009	+	5.42353i	−0.0886135	+	0.192232i
$797$	7.11761	+	9.59698i	0.252119	+	0.339943i	0.911077	−	0.412237i	$-0.135252\pi$
$797$	7.11761	+	9.59698i	0.252119	+	0.339943i	−0.658958	+	0.752180i	$0.729002\pi$
$798$	−7.05472	+	5.02063i	−0.249734	+	0.177728i
$799$	0.638386	+	0.264428i	0.0225845	+	0.00935480i
$800$	−1.34605	−	27.3598i	−0.0475901	−	0.967316i
$801$	8.86945	−	3.67385i	0.313387	−	0.129809i
$802$	−18.6757	+	29.8158i	−0.659460	+	1.05283i
$803$	3.27450	−	22.0749i	0.115555	−	0.779006i
$804$	2.37619	−	9.89878i	0.0838017	−	0.349103i
$805$	0.278445	−	5.66788i	0.00981390	−	0.199767i
$806$	35.4164	−	2.78784i	1.24749	−	0.0981974i
$807$	−0.176214	+	1.78913i	−0.00620303	+	0.0629804i
$808$	−12.5947	+	0.495384i	−0.443079	+	0.0174276i
$809$	0.593298	−	0.722935i	0.0208592	−	0.0254171i	−0.762476	−	0.647016i	$-0.776017\pi$
$809$	0.593298	−	0.722935i	0.0208592	−	0.0254171i	0.783336	+	0.621599i	$0.213517\pi$
$810$	3.47651	+	0.762718i	0.122152	+	0.0267992i
$811$	−12.9078	+	51.5307i	−0.453253	+	1.80949i	0.123230	+	0.992378i	$0.460675\pi$
$811$	−12.9078	+	51.5307i	−0.453253	+	1.80949i	−0.576483	+	0.817109i	$0.695575\pi$
$812$	32.2722	+	21.1070i	1.13253	+	0.740710i
$813$	−14.3507	+	0.705004i	−0.503301	+	0.0247256i
$814$	−15.4537	+	20.0043i	−0.541651	+	0.701151i
$815$	1.30424	+	0.871464i	0.0456855	+	0.0305261i
$816$	−2.23644	+	1.40106i	−0.0782912	+	0.0490468i
$817$	−36.8266	+	24.6067i	−1.28840	+	0.860881i
$818$	25.2512	+	1.73769i	0.882886	+	0.0607571i
$819$	34.1999	−	16.1754i	1.19504	−	0.565213i
$820$	−0.969056	−	1.77081i	−0.0338409	−	0.0618395i
$821$	2.97610	−	4.01281i	0.103867	−	0.140048i	−0.748216	−	0.663455i	$-0.769089\pi$
$821$	2.97610	−	4.01281i	0.103867	−	0.140048i	0.852083	+	0.523407i	$0.175339\pi$
$822$	0.187294	−	9.54448i	0.00653262	−	0.332902i
$823$	20.5166	+	6.22365i	0.715164	+	0.216943i	0.626839	−	0.779149i	$-0.284348\pi$
$823$	20.5166	+	6.22365i	0.715164	+	0.216943i	0.0883255	+	0.996092i	$0.471848\pi$
$824$	0.222266	−	22.7379i	0.00774302	−	0.792112i
$825$	−5.46954	−	2.92353i	−0.190425	−	0.101784i
$826$	31.5339	+	3.73183i	1.09720	+	0.129847i
$827$	0.369171	+	1.03176i	0.0128373	+	0.0358779i	0.947792	−	0.318890i	$-0.103310\pi$
$827$	0.369171	+	1.03176i	0.0128373	+	0.0358779i	−0.934954	+	0.354768i	$0.884560\pi$
$828$	23.1244	+	30.5464i	0.803628	+	1.06156i
$829$	−11.3964	+	19.0137i	−0.395813	+	0.660373i	−0.989534	−	0.144297i	$-0.953908\pi$
$829$	−11.3964	+	19.0137i	−0.395813	+	0.660373i	0.593722	+	0.804670i	$0.297658\pi$
$830$	−4.57884	+	2.05669i	−0.158934	+	0.0713887i
$831$	2.59835	+	2.59835i	0.0901356	+	0.0901356i
$832$	−55.1018	−	9.27784i	−1.91031	−	0.321651i
$833$	−2.49475	+	2.49475i	−0.0864380	+	0.0864380i
$834$	2.17151	−	5.71304i	0.0751934	−	0.197826i
$835$	−1.56929	−	0.940594i	−0.0543074	−	0.0325506i
$836$	−12.8921	+	21.9975i	−0.445884	+	0.760800i
$837$	−10.6651	+	3.81604i	−0.368640	+	0.131901i
$838$	8.62193	+	10.9366i	0.297840	+	0.377797i
$839$	−3.98949	+	7.46381i	−0.137733	+	0.257679i	−0.941326	−	0.337500i	$-0.890419\pi$
$839$	−3.98949	+	7.46381i	−0.137733	+	0.257679i	0.803593	+	0.595179i	$0.202919\pi$
$840$	−1.03131	−	0.703775i	−0.0355835	−	0.0242825i
$841$	−18.2785	+	60.2562i	−0.630294	+	2.07780i
$842$	−28.0643	−	29.1878i	−0.967161	−	1.00588i
$843$	−0.614027	−	0.455394i	−0.0211482	−	0.0156846i
$844$	−2.63138	−	24.2651i	−0.0905758	−	0.835240i
$845$	6.07349	+	12.8413i	0.208934	+	0.441755i
$846$	−1.44982	−	1.66411i	−0.0498457	−	0.0572132i
$847$	6.29821	+	9.42594i	0.216409	+	0.323879i
$848$	−16.4558	+	28.7227i	−0.565094	+	0.986341i
$849$	−8.13249	+	12.1711i	−0.279106	+	0.417712i
$850$	−1.03983	−	8.10219i	−0.0356658	−	0.277903i
$851$	−2.69331	−	54.8236i	−0.0923255	−	1.87933i
$852$	14.6695	+	2.76808i	0.502568	+	0.0948329i
$853$	23.6786	+	5.93118i	0.810740	+	0.203080i	0.626117	−	0.779729i	$-0.284643\pi$
$853$	23.6786	+	5.93118i	0.810740	+	0.203080i	0.184624	+	0.982809i	$0.440893\pi$
$854$	15.3410	+	23.9643i	0.524958	+	0.820040i
$855$	−4.55145	−	3.73528i	−0.155656	−	0.127744i
$856$	0.0945461	−	0.597106i	0.00323152	−	0.0204087i
$857$	−38.1420	−	3.75666i	−1.30291	−	0.128325i	−0.577355	−	0.816493i	$-0.695915\pi$
$857$	−38.1420	−	3.75666i	−1.30291	−	0.128325i	−0.725551	+	0.688168i	$0.758415\pi$
$858$	−8.21591	+	9.61987i	−0.280487	+	0.328417i
$859$	49.0597	+	2.41015i	1.67389	+	0.0822332i	0.863725	−	0.503963i	$-0.168125\pi$
$859$	49.0597	+	2.41015i	1.67389	+	0.0822332i	0.810169	+	0.586196i	$0.199375\pi$
$860$	−5.16689	−	3.75374i	−0.176189	−	0.128001i
$861$	2.79697	+	0.414892i	0.0953206	+	0.0141395i
$862$	−32.0287	+	7.35809i	−1.09090	+	0.250618i
$863$	−8.55809	−	20.6611i	−0.291321	−	0.703311i	0.708677	−	0.705533i	$-0.249292\pi$
$863$	−8.55809	−	20.6611i	−0.291321	−	0.703311i	−0.999998	+	0.00222274i	$0.999292\pi$
$864$	17.7303	−	1.74755i	0.603196	−	0.0594529i
$865$	−3.27040	+	7.89545i	−0.111197	+	0.268453i
$866$	−1.48838	+	8.83577i	−0.0505773	+	0.300252i
$867$	6.92046	−	5.13256i	0.235031	−	0.174311i
$868$	−14.4507	−	0.567358i	−0.490488	−	0.0192574i
$869$	−17.1290	−	18.8990i	−0.581063	−	0.641104i
$870$	0.920133	−	2.83201i	0.0311954	−	0.0960143i
$871$	49.6857	−	40.7760i	1.68353	−	1.38164i
$872$	−0.428194	−	3.09478i	−0.0145005	−	0.104802i
$873$	−2.90020	−	29.4462i	−0.0981570	−	0.996605i
$874$	−9.73370	−	54.5024i	−0.329247	−	1.84357i
$875$	6.73748	−	4.03829i	0.227769	−	0.136519i
$876$	10.6613	−	0.104974i	0.360213	−	0.00354674i
$877$	13.2095	−	14.5745i	0.446054	−	0.492144i	−0.475870	−	0.879516i	$-0.657867\pi$
$877$	13.2095	−	14.5745i	0.446054	−	0.492144i	0.921924	+	0.387371i	$0.126617\pi$
$878$	−6.58569	+	3.77369i	−0.222256	+	0.127356i
$879$	1.18851	+	5.97504i	0.0400874	+	0.201533i
$880$	−3.61930	−	0.646113i	−0.122007	−	0.0217805i
$881$	2.21046	−	11.1127i	0.0744723	−	0.374397i	−0.925518	−	0.378702i	$-0.876370\pi$
$881$	2.21046	−	11.1127i	0.0744723	−	0.374397i	0.999991	+	0.00430510i	$0.00137036\pi$
$882$	10.6829	−	3.58758i	0.359712	−	0.120800i
$883$	13.7519	+	4.92052i	0.462789	+	0.165589i	0.557952	−	0.829873i	$-0.311587\pi$
$883$	13.7519	+	4.92052i	0.462789	+	0.165589i	−0.0951631	+	0.995462i	$0.530337\pi$
$884$	−16.5978	−	1.46989i	−0.558246	−	0.0494379i
$885$	−0.359790	−	2.42551i	−0.0120942	−	0.0815326i
$886$	36.0276	+	15.7582i	1.21037	+	0.529406i
$887$	10.5211	+	19.6836i	0.353264	+	0.660910i	0.994302	−	0.106599i	$-0.0339960\pi$
$887$	10.5211	+	19.6836i	0.353264	+	0.660910i	−0.641038	+	0.767509i	$0.721496\pi$
$888$	−10.5947	−	5.79684i	−0.355535	−	0.194529i
$889$	−18.7370	+	5.68381i	−0.628419	+	0.190629i
$890$	−0.543028	−	1.92533i	−0.0182024	−	0.0645372i
$891$	−6.27670	+	13.2710i	−0.210277	+	0.444594i
$892$	23.7576	+	48.9777i	0.795464	+	1.63989i
$893$	0.774974	+	3.09387i	0.0259335	+	0.103532i
$894$	−3.25432	+	0.0959217i	−0.108841	+	0.00320810i
$895$		−	5.12966i		−	0.171466i
$896$	21.8314	+	6.38676i	0.729335	+	0.213367i
$897$		−	27.4702i		−	0.917205i
$898$	−0.930642	−	31.5738i	−0.0310559	−	1.05363i
$899$	−8.38056	−	33.4571i	−0.279507	−	1.11586i
$900$	−8.54769	+	24.6517i	−0.284923	+	0.821725i
$901$	−4.22053	+	8.92355i	−0.140606	+	0.297287i
$902$	8.01350	−	2.26016i	0.266820	−	0.0752552i
$903$	8.56063	−	2.59684i	0.284880	−	0.0864174i
$904$	−7.90499	−	9.82658i	−0.262916	−	0.326827i
$905$	−1.17897	−	2.20570i	−0.0391903	−	0.0733199i
$906$	−1.11452	+	2.54811i	−0.0370275	+	0.0846552i
$907$	−0.0656425	−	0.442526i	−0.00217962	−	0.0146938i	0.988059	−	0.154073i	$-0.0492392\pi$
$907$	−0.0656425	−	0.442526i	−0.00217962	−	0.0146938i	−0.990239	+	0.139380i	$0.955489\pi$
$908$	−6.58657	+	5.51487i	−0.218583	+	0.183017i
$909$	11.3038	+	4.04458i	0.374925	+	0.134150i
$910$	−2.50966	−	7.47313i	−0.0831944	−	0.247732i
$911$	−0.745013	+	3.74543i	−0.0246834	+	0.124092i	−0.991162	−	0.132654i	$-0.957650\pi$
$911$	−0.745013	+	3.74543i	−0.0246834	+	0.124092i	0.966479	+	0.256745i	$0.0826502\pi$
$912$	−11.3438	−	4.43912i	−0.375629	−	0.146994i
$913$	−4.03912	−	20.3060i	−0.133675	−	0.672031i
$914$	9.21209	+	16.0766i	0.304709	+	0.531765i
$915$	1.47557	−	1.62804i	0.0487808	−	0.0538213i
$916$	−12.0129	−	11.7786i	−0.396916	−	0.389176i
$917$	−14.1993	+	8.51072i	−0.468902	+	0.281049i
$918$	5.23008	−	0.934051i	0.172619	−	0.0308283i
$919$	4.22755	+	42.9230i	0.139454	+	1.41590i	0.769155	+	0.639063i	$0.220678\pi$
$919$	4.22755	+	42.9230i	0.139454	+	1.41590i	−0.629701	+	0.776838i	$0.716822\pi$
$920$	6.88727	−	4.03709i	0.227067	−	0.133099i
$921$	−2.53991	+	2.08445i	−0.0836930	+	0.0686851i
$922$	11.2637	+	3.65961i	0.370950	+	0.120523i
$923$	63.2987	+	69.8394i	2.08350	+	2.29879i
$924$	3.78156	−	3.49584i	0.124404	−	0.115005i
$925$	30.0250	−	22.2681i	0.987216	−	0.732169i
$926$	43.1000	+	7.26017i	1.41635	+	0.238584i
$927$	−8.28845	+	20.0101i	−0.272228	+	0.657217i
$928$	0.00385532	+	54.2491i	0.000126557	+	1.78081i
$929$	−19.4081	−	46.8552i	−0.636758	−	1.53727i	−0.830975	−	0.556310i	$-0.812217\pi$
$929$	−19.4081	−	46.8552i	−0.636758	−	1.53727i	0.194217	−	0.980959i	$-0.437783\pi$
$930$	0.250042	+	1.08839i	0.00819919	+	0.0356899i
$931$	−16.1088	−	2.38952i	−0.527946	−	0.0783134i
$932$	1.26523	+	7.98687i	0.0414440	+	0.261619i
$933$	−0.149224	−	0.00733090i	−0.00488537	−	0.000240003i
$934$	39.4064	+	33.6553i	1.28942	+	1.10123i
$935$	−1.09107	−	0.107461i	−0.0356818	−	0.00351435i
$936$	45.3812	+	27.8070i	1.48333	+	0.908899i
$937$	−3.26854	−	2.68242i	−0.106778	−	0.0876308i	0.579489	−	0.814980i	$-0.303252\pi$
$937$	−3.26854	−	2.68242i	−0.106778	−	0.0876308i	−0.686268	+	0.727349i	$0.740752\pi$
$938$	−22.0365	+	14.1069i	−0.719518	+	0.460608i
$939$	2.04711	+	0.512774i	0.0668048	+	0.0167337i
$940$	−0.379859	+	0.259260i	−0.0123896	+	0.00845611i
$941$	0.875375	+	17.8187i	0.0285364	+	0.580872i	0.969904	+	0.243489i	$0.0782918\pi$
$941$	0.875375	+	17.8187i	0.0285364	+	0.580872i	−0.941367	+	0.337383i	$0.890458\pi$
$942$	4.38576	−	0.562865i	0.142896	−	0.0183391i
$943$	−10.0445	+	15.0326i	−0.327092	+	0.489528i
$944$	19.8911	+	39.9990i	0.647402	+	1.30186i
$945$	1.39645	+	2.08993i	0.0454264	+	0.0679854i
$946$	19.8615	−	17.3039i	0.645753	−	0.562599i
$947$	−10.3271	−	21.8349i	−0.335587	−	0.709538i	0.663673	−	0.748023i	$-0.268997\pi$
$947$	−10.3271	−	21.8349i	−0.335587	−	0.709538i	−0.999259	+	0.0384850i	$0.987747\pi$
$948$	7.63751	−	9.49546i	0.248055	−	0.308398i
$949$	54.0703	+	40.1013i	1.75520	+	1.30174i
$950$	27.1794	−	26.1332i	0.881815	−	0.847873i
$951$	0.508995	−	1.67793i	0.0165053	−	0.0544106i
$952$	6.63946	+	1.38827i	0.215186	+	0.0449942i
$953$	0.0928324	−	0.173677i	0.00300714	−	0.00562596i	−0.880413	−	0.474207i	$-0.842735\pi$
$953$	0.0928324	−	0.173677i	0.00300714	−	0.00562596i	0.883420	+	0.468581i	$0.155235\pi$
$954$	24.7608	−	19.5204i	0.801662	−	0.631997i
$955$	−5.83207	+	2.08675i	−0.188721	+	0.0675256i
$956$	−2.06549	−	7.91445i	−0.0668027	−	0.255972i
$957$	10.5348	+	6.31429i	0.340540	+	0.204112i
$958$	52.8675	+	20.0948i	1.70807	+	0.649234i
$959$	−17.3499	+	17.3499i	−0.560257	+	0.560257i
$960$	0.0343365	−	1.75615i	0.00110821	−	0.0566795i
$961$	−12.7738	−	12.7738i	−0.412059	−	0.412059i
$962$	−31.2434	−	69.5577i	−1.00733	−	2.24263i
$963$	−0.296033	+	0.493902i	−0.00953954	+	0.0159158i
$964$	1.50555	−	10.8871i	0.0484906	−	0.350650i
$965$	2.46192	+	6.88061i	0.0792520	+	0.221495i
$966$	−1.31421	+	11.1050i	−0.0422839	+	0.357298i
$967$	−9.23943	−	4.93858i	−0.297120	−	0.158814i	0.316101	−	0.948726i	$-0.397626\pi$
$967$	−9.23943	−	4.93858i	−0.297120	−	0.158814i	−0.613221	+	0.789912i	$0.710126\pi$
$968$	−6.24689	+	14.6740i	−0.200783	+	0.471639i
$969$	−3.47611	−	1.05447i	−0.111669	−	0.0338744i
$970$	−6.16435	−	0.120965i	−0.197925	−	0.00388394i
$971$	22.8911	−	30.8651i	0.734610	−	0.990507i	−0.265045	−	0.964236i	$-0.585387\pi$
$971$	22.8911	−	30.8651i	0.734610	−	0.990507i	0.999655	−	0.0262707i	$-0.00836319\pi$
$972$	−24.8678	−	7.27696i	−0.797634	−	0.233409i
$973$	−14.2007	+	6.71643i	−0.455253	+	0.215319i
$974$	2.78862	−	40.5226i	0.0893532	−	1.29843i
$975$	15.5551	−	10.3936i	0.498163	−	0.332862i
$976$	−16.3990	+	36.5163i	−0.524919	+	1.16886i
$977$	37.7779	+	25.2424i	1.20862	+	0.807576i	0.985905	−	0.167307i	$-0.0535070\pi$
$977$	37.7779	+	25.2424i	1.20862	+	0.807576i	0.222718	+	0.974883i	$0.428507\pi$
$978$	−2.44615	−	1.88969i	−0.0782192	−	0.0604257i
$979$	8.24120	−	0.404864i	0.263390	−	0.0129395i
$980$	−0.480768	−	2.29847i	−0.0153576	−	0.0734220i
$981$	−0.723070	+	2.88666i	−0.0230859	+	0.0921639i
$982$	7.01036	−	31.9536i	0.223710	−	1.01968i
$983$	20.6988	−	25.2215i	0.660189	−	0.804442i	−0.330029	−	0.943971i	$-0.607059\pi$
$983$	20.6988	−	25.2215i	0.660189	−	0.804442i	0.990218	+	0.139528i	$0.0445587\pi$
$984$	1.66553	+	3.61241i	0.0530952	+	0.115159i
$985$	0.183243	−	1.86050i	0.00583860	−	0.0592803i
$986$	1.26948	+	16.1273i	0.0404285	+	0.513599i
$987$	0.0316095	−	0.643426i	0.00100614	−	0.0204805i
$988$	−40.1884	−	65.5774i	−1.27856	−	2.08629i
$989$	−8.39294	+	56.5806i	−0.266880	+	1.79916i
$990$	2.96775	+	1.85890i	0.0943213	+	0.0590798i
$991$	−26.2579	+	10.8764i	−0.834108	+	0.345499i	−0.758528	−	0.651641i	$-0.774081\pi$
$991$	−26.2579	+	10.8764i	−0.834108	+	0.345499i	−0.0755804	+	0.997140i	$0.524081\pi$
$992$	−10.4607	−	17.4498i	−0.332128	−	0.554033i
$993$	0.933835	+	0.386807i	0.0296343	+	0.0122749i
$994$	−22.2477	−	31.2613i	−0.705655	−	0.991548i
$995$	−0.706084	−	0.952044i	−0.0223844	−	0.0301818i
$996$	9.27995	−	3.42385i	0.294046	−	0.108489i
$997$	40.1276	−	36.3696i	1.27085	−	1.15184i	0.290014	−	0.957022i	$-0.406340\pi$
$997$	40.1276	−	36.3696i	1.27085	−	1.15184i	0.980840	−	0.194813i	$-0.0624100\pi$
$998$	−15.8556	+	8.07910i	−0.501900	+	0.255740i
$999$	15.4238	+	18.7939i	0.487986	+	0.594613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.9	✓	992
256.109	even	64	inner	256.2.m.a.109.9	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.9	✓	992	1.1	even	1	trivial
256.2.m.a.109.9	yes	992	256.109	even	64	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02903 - 0.970104i) q^{2} +(-0.536541 + 0.134397i) q^{3} +(0.117798 + 1.99653i) q^{4} +(-0.358840 - 0.169719i) q^{5} +(0.682495 + 0.382203i) q^{6} +(-0.583623 - 1.92395i) q^{7} +(1.81562 - 2.16876i) q^{8} +(-2.37595 + 1.26997i) q^{9} +O(q^{10})\)	\(q+(-1.02903 - 0.970104i) q^{2} +(-0.536541 + 0.134397i) q^{3} +(0.117798 + 1.99653i) q^{4} +(-0.358840 - 0.169719i) q^{5} +(0.682495 + 0.382203i) q^{6} +(-0.583623 - 1.92395i) q^{7} +(1.81562 - 2.16876i) q^{8} +(-2.37595 + 1.26997i) q^{9} +(0.204612 + 0.522757i) q^{10} +(-2.29041 + 0.339750i) q^{11} +(-0.331530 - 1.05539i) q^{12} +(2.35307 - 6.57638i) q^{13} +(-1.26586 + 2.54597i) q^{14} +(0.215342 + 0.0428342i) q^{15} +(-3.97225 + 0.470375i) q^{16} +(-1.16989 + 0.232706i) q^{17} +(3.67692 + 0.998080i) q^{18} +(-4.07952 - 3.69746i) q^{19} +(0.296577 - 0.736426i) q^{20} +(0.571710 + 0.953840i) q^{21} +(2.68649 + 1.87232i) q^{22} +(-7.07624 + 0.696949i) q^{23} +(-0.682682 + 1.40764i) q^{24} +(-3.07200 - 3.74325i) q^{25} +(-8.80114 + 4.48456i) q^{26} +(2.33362 - 2.11507i) q^{27} +(3.77246 - 1.39186i) q^{28} +(5.71274 + 7.70274i) q^{29} +(-0.180039 - 0.252982i) q^{30} +(-3.32277 - 1.37634i) q^{31} +(4.54387 + 3.36946i) q^{32} +(1.18324 - 0.490114i) q^{33} +(1.42960 + 0.895455i) q^{34} +(-0.117102 + 0.789440i) q^{35} +(-2.81542 - 4.59405i) q^{36} +(-0.378780 + 7.71025i) q^{37} +(0.611022 + 7.76235i) q^{38} +(-0.378674 + 3.84474i) q^{39} +(-1.01960 + 0.470093i) q^{40} +(1.61305 - 1.96550i) q^{41} +(0.337018 - 1.53615i) q^{42} +(1.95464 - 7.80335i) q^{43} +(-0.948128 - 4.53285i) q^{44} +(1.06812 - 0.0524735i) q^{45} +(7.95776 + 6.14750i) q^{46} +(-0.481663 - 0.321837i) q^{47} +(2.06806 - 0.786233i) q^{48} +(2.45933 - 1.64327i) q^{49} +(-0.470159 + 6.83207i) q^{50} +(0.596421 - 0.282086i) q^{51} +(13.4071 + 3.92327i) q^{52} +(4.92981 - 6.64707i) q^{53} +(-4.45319 - 0.0873861i) q^{54} +(0.879553 + 0.266809i) q^{55} +(-5.23222 - 2.22742i) q^{56} +(2.68576 + 1.43557i) q^{57} +(1.59388 - 13.4683i) q^{58} +(-3.76238 - 10.5151i) q^{59} +(-0.0601527 + 0.434982i) q^{60} +(5.14482 - 8.58362i) q^{61} +(2.08404 + 4.63972i) q^{62} +(3.83002 + 3.83002i) q^{63} +(-1.40704 - 7.87529i) q^{64} +(-1.96051 + 1.96051i) q^{65} +(-1.69305 - 0.643524i) q^{66} +(7.89313 + 4.73096i) q^{67} +(-0.602415 - 2.30831i) q^{68} +(3.70303 - 1.32496i) q^{69} +(0.886340 - 0.698755i) q^{70} +(-6.36138 + 11.9013i) q^{71} +(-1.55956 + 7.45865i) q^{72} +(-2.79775 + 9.22295i) q^{73} +(7.86952 - 7.56661i) q^{74} +(2.15134 + 1.59554i) q^{75} +(6.90153 - 8.58044i) q^{76} +(1.99040 + 4.20834i) q^{77} +(4.11947 - 3.58900i) q^{78} +(6.11995 + 9.15915i) q^{79} +(1.50523 + 0.505375i) q^{80} +(3.52240 - 5.27164i) q^{81} +(-3.56661 + 0.457736i) q^{82} +(0.438739 + 8.93074i) q^{83} +(-1.83702 + 1.25380i) q^{84} +(0.459298 + 0.115048i) q^{85} +(-9.58143 + 6.13367i) q^{86} +(-4.10034 - 3.36507i) q^{87} +(-3.42168 + 5.58421i) q^{88} +(-3.54632 - 0.349282i) q^{89} +(-1.15003 - 0.982193i) q^{90} +(-14.0259 - 0.689049i) q^{91} +(-2.22505 - 14.0458i) q^{92} +(1.96778 + 0.291892i) q^{93} +(0.183430 + 0.798442i) q^{94} +(0.836367 + 2.01917i) q^{95} +(-2.89082 - 1.19718i) q^{96} +(-4.20299 + 10.1469i) q^{97} +(-4.12487 - 0.694832i) q^{98} +(5.01043 - 3.71599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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