LMFDB - Embedded newform 256.2.m.a.5.13

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			5.13
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.550381 + 1.30272i) q^{2} +(0.0413256 - 0.278595i) q^{3} +(-1.39416 - 1.43398i) q^{4} +(2.13467 + 0.104869i) q^{5} +(0.340186 + 0.207169i) q^{6} +(-3.02795 - 1.61847i) q^{7} +(2.63540 - 1.02697i) q^{8} +(2.79491 + 0.847828i) q^{9} +O(q^{10})$	\(q+(-0.550381 + 1.30272i) q^{2} +(0.0413256 - 0.278595i) q^{3} +(-1.39416 - 1.43398i) q^{4} +(2.13467 + 0.104869i) q^{5} +(0.340186 + 0.207169i) q^{6} +(-3.02795 - 1.61847i) q^{7} +(2.63540 - 1.02697i) q^{8} +(2.79491 + 0.847828i) q^{9} +(-1.31149 + 2.72316i) q^{10} +(2.67414 + 4.46153i) q^{11} +(-0.457115 + 0.329146i) q^{12} +(4.03307 - 4.44981i) q^{13} +(3.77494 - 3.05379i) q^{14} +(0.117432 - 0.590373i) q^{15} +(-0.112622 + 3.99841i) q^{16} +(0.194174 + 0.976178i) q^{17} +(-2.64275 + 3.17436i) q^{18} +(-0.494765 - 1.04609i) q^{19} +(-2.82569 - 3.20728i) q^{20} +(-0.576029 + 0.776685i) q^{21} +(-7.28392 + 1.02812i) q^{22} +(3.02107 + 2.47933i) q^{23} +(-0.177198 - 0.776648i) q^{24} +(-0.430121 - 0.0423632i) q^{25} +(3.57713 + 7.70305i) q^{26} +(0.712955 - 1.50742i) q^{27} +(1.90059 + 6.59844i) q^{28} +(-1.50031 + 0.375809i) q^{29} +(0.704458 + 0.477911i) q^{30} +(2.81120 + 1.16444i) q^{31} +(-5.14683 - 2.34736i) q^{32} +(1.35347 - 0.560625i) q^{33} +(-1.37856 - 0.284315i) q^{34} +(-6.29393 - 3.77243i) q^{35} +(-2.68079 - 5.18987i) q^{36} +(0.696592 + 1.94684i) q^{37} +(1.63508 - 0.0687916i) q^{38} +(-1.07302 - 1.30748i) q^{39} +(5.73340 - 1.91586i) q^{40} +(-2.84902 + 0.280604i) q^{41} +(-0.694768 - 1.17788i) q^{42} +(-11.5576 + 1.71441i) q^{43} +(2.66958 - 10.0548i) q^{44} +(5.87730 + 2.10293i) q^{45} +(-4.89261 + 2.57104i) q^{46} +(6.68867 - 10.0103i) q^{47} +(1.10928 + 0.196613i) q^{48} +(2.66002 + 3.98099i) q^{49} +(0.291918 - 0.537011i) q^{50} +(0.279982 - 0.0137547i) q^{51} +(-12.0037 + 0.420395i) q^{52} +(-7.08805 - 1.77546i) q^{53} +(1.57135 + 1.75843i) q^{54} +(5.24052 + 9.80432i) q^{55} +(-9.64197 - 1.15572i) q^{56} +(-0.311882 + 0.0946085i) q^{57} +(0.336169 - 2.16133i) q^{58} +(-4.16807 - 4.59876i) q^{59} +(-1.01030 + 0.654679i) q^{60} +(-1.22318 - 1.64926i) q^{61} +(-3.06416 + 3.02132i) q^{62} +(-7.09066 - 7.09066i) q^{63} +(5.89068 - 5.41294i) q^{64} +(9.07591 - 9.07591i) q^{65} +(-0.0145849 + 2.07175i) q^{66} +(3.30343 - 2.44999i) q^{67} +(1.12911 - 1.63939i) q^{68} +(0.815575 - 0.739194i) q^{69} +(8.37848 - 6.12295i) q^{70} +(-0.319380 - 1.05285i) q^{71} +(8.23641 - 0.635919i) q^{72} +(10.5359 - 5.63158i) q^{73} +(-2.91958 - 0.164040i) q^{74} +(-0.0295772 + 0.118079i) q^{75} +(-0.810298 + 2.16791i) q^{76} +(-0.876290 - 17.8373i) q^{77} +(2.29386 - 0.678237i) q^{78} +(-5.87938 + 3.92847i) q^{79} +(-0.659721 + 8.52347i) q^{80} +(6.89487 + 4.60700i) q^{81} +(1.20250 - 3.86592i) q^{82} +(-3.09900 + 8.66112i) q^{83} +(1.91683 - 0.256809i) q^{84} +(0.312125 + 2.10418i) q^{85} +(4.12770 - 15.9999i) q^{86} +(0.0426969 + 0.433509i) q^{87} +(11.6293 + 9.01167i) q^{88} +(-12.5430 + 10.2938i) q^{89} +(-5.97428 + 6.49906i) q^{90} +(-19.4138 + 6.94637i) q^{91} +(-0.656545 - 7.78875i) q^{92} +(0.440580 - 0.735064i) q^{93} +(9.35931 + 14.2229i) q^{94} +(-0.946456 - 2.28495i) q^{95} +(-0.866659 + 1.33687i) q^{96} +(-5.84856 + 14.1197i) q^{97} +(-6.65014 + 1.27420i) q^{98} +(3.69138 + 14.7368i) 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 $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.550381	+	1.30272i	−0.389178	+	0.921163i
$2$	−0.550381	+	1.30272i	−0.389178	+	0.921163i
$3$	0.0413256	−	0.278595i	0.0238593	−	0.160847i	−0.973972	−	0.226668i	$-0.927217\pi$
$3$	0.0413256	−	0.278595i	0.0238593	−	0.160847i	0.997831	+	0.0658214i	$0.0209668\pi$
$4$	−1.39416	−	1.43398i	−0.697081	−	0.716992i
$5$	2.13467	+	0.104869i	0.954652	+	0.0468990i	0.520428	−	0.853906i	$-0.325773\pi$
$5$	2.13467	+	0.104869i	0.954652	+	0.0468990i	0.434224	+	0.900805i	$0.357023\pi$
$6$	0.340186	+	0.207169i	0.138880	+	0.0845763i
$7$	−3.02795	−	1.61847i	−1.14446	−	0.611724i	−0.213531	−	0.976936i	$-0.568497\pi$
$7$	−3.02795	−	1.61847i	−1.14446	−	0.611724i	−0.930924	+	0.365212i	$0.880997\pi$
$8$	2.63540	−	1.02697i	0.931755	−	0.363088i
$9$	2.79491	+	0.847828i	0.931638	+	0.282609i
$10$	−1.31149	+	2.72316i	−0.414731	+	0.861138i
$11$	2.67414	+	4.46153i	0.806283	+	1.34520i	0.935407	+	0.353574i	$0.115034\pi$
$11$	2.67414	+	4.46153i	0.806283	+	1.34520i	−0.129123	+	0.991629i	$0.541216\pi$
$12$	−0.457115	+	0.329146i	−0.131958	+	0.0950162i
$13$	4.03307	−	4.44981i	1.11857	−	1.23415i	0.149135	−	0.988817i	$-0.452351\pi$
$13$	4.03307	−	4.44981i	1.11857	−	1.23415i	0.969438	−	0.245338i	$-0.0788989\pi$
$14$	3.77494	−	3.05379i	1.00889	−	0.816160i
$15$	0.117432	−	0.590373i	0.0303209	−	0.152434i
$16$	−0.112622	+	3.99841i	−0.0281554	+	0.999604i
$17$	0.194174	+	0.976178i	0.0470941	+	0.236758i	0.997162	−	0.0752850i	$-0.0239867\pi$
$17$	0.194174	+	0.976178i	0.0470941	+	0.236758i	−0.950068	+	0.312043i	$0.898987\pi$
$18$	−2.64275	+	3.17436i	−0.622902	+	0.748205i
$19$	−0.494765	−	1.04609i	−0.113507	−	0.239990i	0.839236	−	0.543767i	$-0.183002\pi$
$19$	−0.494765	−	1.04609i	−0.113507	−	0.239990i	−0.952743	+	0.303777i	$0.901752\pi$
$20$	−2.82569	−	3.20728i	−0.631844	−	0.717170i
$21$	−0.576029	+	0.776685i	−0.125700	+	0.169487i
$22$	−7.28392	+	1.02812i	−1.55294	+	0.219195i
$23$	3.02107	+	2.47933i	0.629937	+	0.516976i	0.894312	−	0.447444i	$-0.147666\pi$
$23$	3.02107	+	2.47933i	0.629937	+	0.516976i	−0.264375	+	0.964420i	$0.585166\pi$
$24$	−0.177198	−	0.776648i	−0.0361704	−	0.158533i
$25$	−0.430121	−	0.0423632i	−0.0860242	−	0.00847264i
$26$	3.57713	+	7.70305i	0.701534	+	1.51069i
$27$	0.712955	−	1.50742i	0.137208	−	0.290103i
$28$	1.90059	+	6.59844i	0.359177	+	1.24699i
$29$	−1.50031	+	0.375809i	−0.278601	+	0.0697859i	−0.379762	−	0.925084i	$-0.623994\pi$
$29$	−1.50031	+	0.375809i	−0.278601	+	0.0697859i	0.101161	+	0.994870i	$0.467744\pi$
$30$	0.704458	+	0.477911i	0.128616	+	0.0872543i
$31$	2.81120	+	1.16444i	0.504906	+	0.209139i	0.620572	−	0.784149i	$-0.286900\pi$
$31$	2.81120	+	1.16444i	0.504906	+	0.209139i	−0.115666	+	0.993288i	$0.536900\pi$
$32$	−5.14683	−	2.34736i	−0.909840	−	0.414959i
$33$	1.35347	−	0.560625i	0.235609	−	0.0975923i
$34$	−1.37856	−	0.284315i	−0.236421	−	0.0487596i
$35$	−6.29393	−	3.77243i	−1.06387	−	0.637658i
$36$	−2.68079	−	5.18987i	−0.446799	−	0.864979i
$37$	0.696592	+	1.94684i	0.114519	+	0.320059i	0.985104	−	0.171959i	$-0.0550095\pi$
$37$	0.696592	+	1.94684i	0.114519	+	0.320059i	−0.870585	+	0.492018i	$0.836260\pi$
$38$	1.63508	−	0.0687916i	0.265244	−	0.0111595i
$39$	−1.07302	−	1.30748i	−0.171821	−	0.209365i
$40$	5.73340	−	1.91586i	0.906530	−	0.302924i
$41$	−2.84902	+	0.280604i	−0.444943	+	0.0438230i	−0.318008	−	0.948088i	$-0.603014\pi$
$41$	−2.84902	+	0.280604i	−0.444943	+	0.0438230i	−0.126935	+	0.991911i	$0.540514\pi$
$42$	−0.694768	−	1.17788i	−0.107205	−	0.181750i
$43$	−11.5576	+	1.71441i	−1.76252	+	0.261446i	−0.947905	−	0.318553i	$-0.896803\pi$
$43$	−11.5576	+	1.71441i	−1.76252	+	0.261446i	−0.814618	+	0.579998i	$0.803053\pi$
$44$	2.66958	−	10.0548i	0.402455	−	1.51581i
$45$	5.87730	+	2.10293i	0.876136	+	0.313486i
$46$	−4.89261	+	2.57104i	−0.721376	+	0.379079i
$47$	6.68867	−	10.0103i	0.975642	−	1.46015i	0.0899133	−	0.995950i	$-0.471341\pi$
$47$	6.68867	−	10.0103i	0.975642	−	1.46015i	0.885729	−	0.464202i	$-0.153659\pi$
$48$	1.10928	+	0.196613i	0.160111	+	0.0283786i
$49$	2.66002	+	3.98099i	0.380002	+	0.568713i
$50$	0.291918	−	0.537011i	0.0412834	−	0.0759449i
$51$	0.279982	−	0.0137547i	0.0392054	−	0.00192604i
$52$	−12.0037	+	0.420395i	−1.66462	+	0.0582983i
$53$	−7.08805	−	1.77546i	−0.973618	−	0.243879i	−0.276642	−	0.960973i	$-0.589222\pi$
$53$	−7.08805	−	1.77546i	−0.973618	−	0.243879i	−0.696976	+	0.717094i	$0.745472\pi$
$54$	1.57135	+	1.75843i	0.213833	+	0.239293i
$55$	5.24052	+	9.80432i	0.706631	+	1.32201i
$56$	−9.64197	−	1.15572i	−1.28846	−	0.154439i
$57$	−0.311882	+	0.0946085i	−0.0413098	+	0.0125312i
$58$	0.336169	−	2.16133i	0.0441411	−	0.283796i
$59$	−4.16807	−	4.59876i	−0.542637	−	0.598707i	0.406469	−	0.913664i	$-0.366760\pi$
$59$	−4.16807	−	4.59876i	−0.542637	−	0.598707i	−0.949106	+	0.314957i	$0.898010\pi$
$60$	−1.01030	+	0.654679i	−0.130430	+	0.0845187i
$61$	−1.22318	−	1.64926i	−0.156612	−	0.211166i	0.717932	−	0.696113i	$-0.245089\pi$
$61$	−1.22318	−	1.64926i	−0.156612	−	0.211166i	−0.874544	+	0.484947i	$0.838839\pi$
$62$	−3.06416	+	3.02132i	−0.389149	+	0.383708i
$63$	−7.09066	−	7.09066i	−0.893339	−	0.893339i
$64$	5.89068	−	5.41294i	0.736335	−	0.676618i
$65$	9.07591	−	9.07591i	1.12573	−	1.12573i
$66$	−0.0145849	+	2.07175i	−0.00179528	+	0.255015i
$67$	3.30343	−	2.44999i	0.403579	−	0.299314i	−0.374804	−	0.927104i	$-0.622290\pi$
$67$	3.30343	−	2.44999i	0.403579	−	0.299314i	0.778383	+	0.627790i	$0.216040\pi$
$68$	1.12911	−	1.63939i	0.136925	−	0.198806i
$69$	0.815575	−	0.739194i	0.0981837	−	0.0889885i
$70$	8.37848	−	6.12295i	1.00142	−	0.731833i
$71$	−0.319380	−	1.05285i	−0.0379034	−	0.124951i	0.935947	−	0.352141i	$-0.114546\pi$
$71$	−0.319380	−	1.05285i	−0.0379034	−	0.124951i	−0.973850	+	0.227190i	$0.927046\pi$
$72$	8.23641	−	0.635919i	0.970670	−	0.0749438i
$73$	10.5359	−	5.63158i	1.23314	−	0.659127i	0.279519	−	0.960140i	$-0.409825\pi$
$73$	10.5359	−	5.63158i	1.23314	−	0.659127i	0.953620	+	0.301014i	$0.0973250\pi$
$74$	−2.91958	−	0.164040i	−0.339395	−	0.0190693i
$75$	−0.0295772	+	0.118079i	−0.00341528	+	0.0136345i
$76$	−0.810298	+	2.16791i	−0.0929476	+	0.248676i
$77$	−0.876290	−	17.8373i	−0.0998625	−	2.03275i
$78$	2.29386	−	0.678237i	0.259728	−	0.0767952i
$79$	−5.87938	+	3.92847i	−0.661481	+	0.441988i	−0.840466	−	0.541864i	$-0.817719\pi$
$79$	−5.87938	+	3.92847i	−0.661481	+	0.441988i	0.178985	+	0.983852i	$0.442719\pi$
$80$	−0.659721	+	8.52347i	−0.0737591	+	0.952953i
$81$	6.89487	+	4.60700i	0.766096	+	0.511889i
$82$	1.20250	−	3.86592i	0.132794	−	0.426919i
$83$	−3.09900	+	8.66112i	−0.340159	+	0.950682i	0.642667	+	0.766146i	$0.277828\pi$
$83$	−3.09900	+	8.66112i	−0.340159	+	0.950682i	−0.982826	+	0.184536i	$0.940922\pi$
$84$	1.91683	−	0.256809i	0.209143	−	0.0280201i
$85$	0.312125	+	2.10418i	0.0338547	+	0.228230i
$86$	4.12770	−	15.9999i	0.445101	−	1.72532i
$87$	0.0426969	+	0.433509i	0.00457759	+	0.0464771i
$88$	11.6293	+	9.01167i	1.23968	+	0.960647i
$89$	−12.5430	+	10.2938i	−1.32956	+	1.09114i	−0.341038	+	0.940049i	$0.610779\pi$
$89$	−12.5430	+	10.2938i	−1.32956	+	1.09114i	−0.988520	+	0.151091i	$0.951721\pi$
$90$	−5.97428	+	6.49906i	−0.629745	+	0.685062i
$91$	−19.4138	+	6.94637i	−2.03512	+	0.728177i
$92$	−0.656545	−	7.78875i	−0.0684496	−	0.812034i
$93$	0.440580	−	0.735064i	0.0456860	−	0.0762225i
$94$	9.35931	+	14.2229i	0.965339	+	1.46698i
$95$	−0.946456	−	2.28495i	−0.0971043	−	0.234431i
$96$	−0.866659	+	1.33687i	−0.0884530	+	0.136444i
$97$	−5.84856	+	14.1197i	−0.593832	+	1.43364i	0.285944	+	0.958246i	$0.407693\pi$
$97$	−5.84856	+	14.1197i	−0.593832	+	1.43364i	−0.879775	+	0.475390i	$0.842307\pi$
$98$	−6.65014	+	1.27420i	−0.671766	+	0.128713i
$99$	3.69138	+	14.7368i	0.370997	+	1.48110i
$100$	0.538910	+	0.675848i	0.0538910	+	0.0675848i
$101$	−3.73022	−	1.76426i	−0.371171	−	0.175551i	0.232863	−	0.972510i	$-0.425191\pi$
$101$	−3.73022	−	1.76426i	−0.371171	−	0.175551i	−0.604034	+	0.796959i	$0.706441\pi$
$102$	−0.136178	+	0.372309i	−0.0134837	+	0.0368641i
$103$	−0.344740	+	3.50020i	−0.0339682	+	0.344885i	0.963147	+	0.268977i	$0.0866856\pi$
$103$	−0.344740	+	3.50020i	−0.0339682	+	0.344885i	−0.997115	+	0.0759082i	$0.975814\pi$
$104$	6.05895	−	15.8689i	0.594129	−	1.55607i
$105$	−1.31108	+	1.59756i	−0.127948	+	0.155905i
$106$	6.21406	−	8.25657i	0.603563	−	0.801949i
$107$	−11.3576	−	8.42338i	−1.09798	−	0.814319i	−0.114159	−	0.993462i	$-0.536417\pi$
$107$	−11.3576	−	8.42338i	−1.09798	−	0.814319i	−0.983823	+	0.179143i	$0.942667\pi$
$108$	−3.15559	+	1.07922i	−0.303647	+	0.103848i
$109$	−17.7493	+	8.39478i	−1.70007	+	0.804074i	−0.704537	+	0.709667i	$0.748845\pi$
$109$	−17.7493	+	8.39478i	−1.70007	+	0.804074i	−0.995534	+	0.0944070i	$0.969905\pi$
$110$	−15.6566	+	1.43082i	−1.49279	+	0.136424i
$111$	0.571167	−	0.113612i	0.0542128	−	0.0107836i
$112$	6.81233	−	11.9247i	0.643705	−	1.12678i
$113$	13.8349	+	2.75194i	1.30148	+	0.258881i	0.796704	−	0.604369i	$-0.206575\pi$
$113$	13.8349	+	2.75194i	1.30148	+	0.258881i	0.504777	+	0.863250i	$0.331575\pi$
$114$	0.0484056	−	0.458366i	0.00453360	−	0.0429299i
$115$	6.18897	+	5.60936i	0.577125	+	0.523075i
$116$	2.63058	+	1.62749i	0.244243	+	0.151108i
$117$	15.0448	−	9.01748i	1.39089	−	0.833666i
$118$	8.28492	−	2.89877i	0.762689	−	0.266853i
$119$	0.991968	−	3.27008i	0.0909335	−	0.299768i
$120$	−0.296812	−	1.67647i	−0.0270951	−	0.153040i
$121$	−7.56888	+	14.1604i	−0.688080	+	1.28731i
$122$	2.82174	−	0.685735i	0.255468	−	0.0620835i
$123$	−0.0395627	+	0.805318i	−0.00356725	+	0.0726131i
$124$	−2.24948	−	5.65463i	−0.202010	−	0.507801i
$125$	−11.4843	−	1.70353i	−1.02718	−	0.152368i
$126$	13.1397	−	5.33459i	1.17058	−	0.475243i
$127$		−	9.38639i		−	0.832907i	−0.909157	−	0.416454i	$-0.863273\pi$
$127$		−	9.38639i		−	0.832907i	0.909157	−	0.416454i	$-0.136727\pi$
$128$	3.80944	+	10.6531i	0.336710	+	0.941608i
$129$			3.29074i			0.289734i
$130$	6.82817	+	16.8186i	0.598870	+	1.47509i
$131$	−3.28585	−	0.487410i	−0.287086	−	0.0425853i	0.00163410	−	0.999999i	$-0.499480\pi$
$131$	−3.28585	−	0.487410i	−0.287086	−	0.0425853i	−0.288721	+	0.957413i	$0.593230\pi$
$132$	−2.69088	−	1.15925i	−0.234211	−	0.100900i
$133$	−0.194949	+	3.96828i	−0.0169042	+	0.344093i
$134$	1.37351	+	5.65188i	0.118653	+	0.488248i
$135$	1.68000	−	3.14307i	0.144592	−	0.270512i
$136$	1.51423	+	2.37321i	0.129844	+	0.203501i
$137$	−4.95788	+	16.3439i	−0.423580	+	1.39636i	0.442642	+	0.896699i	$0.354041\pi$
$137$	−4.95788	+	16.3439i	−0.423580	+	1.39636i	−0.866222	+	0.499659i	$0.833459\pi$
$138$	0.514087	+	1.46930i	0.0437620	+	0.125076i
$139$	9.08612	−	5.44601i	0.770675	−	0.461925i	−0.0739643	−	0.997261i	$-0.523565\pi$
$139$	9.08612	−	5.44601i	0.770675	−	0.461925i	0.844639	+	0.535336i	$0.179815\pi$
$140$	3.36514	+	14.2848i	0.284407	+	1.20728i
$141$	−2.51240	−	2.27711i	−0.211582	−	0.191767i
$142$	1.54735	+	0.163408i	0.129851	+	0.0137129i
$143$	30.6379	+	6.09427i	2.56207	+	0.509628i
$144$	−3.70473	+	11.0797i	−0.308728	+	0.923312i
$145$	−3.24208	+	0.644889i	−0.269240	+	0.0535551i
$146$	1.53760	+	16.8249i	0.127252	+	1.39244i
$147$	1.21901	−	0.576549i	0.100542	−	0.0475529i
$148$	1.82058	−	3.71312i	0.149651	−	0.305216i
$149$	11.8612	+	8.79689i	0.971710	+	0.720669i	0.960214	−	0.279264i	$-0.0900906\pi$
$149$	11.8612	+	8.79689i	0.971710	+	0.720669i	0.0114961	+	0.999934i	$0.496341\pi$
$150$	−0.137545	−	0.103519i	−0.0112305	−	0.00845229i
$151$	−4.85753	+	5.91891i	−0.395300	+	0.481674i	−0.932186	−	0.361981i	$-0.882101\pi$
$151$	−4.85753	+	5.91891i	−0.395300	+	0.481674i	0.536886	+	0.843655i	$0.319601\pi$
$152$	−2.37821	−	2.24877i	−0.192898	−	0.182399i
$153$	−0.284932	+	2.89296i	−0.0230354	+	0.233882i
$154$	23.7193	+	8.67574i	1.91136	+	0.699111i
$155$	5.87886	+	2.78049i	0.472201	+	0.223335i
$156$	−0.378941	+	3.36154i	−0.0303395	+	0.269139i
$157$	−5.19125	−	20.7246i	−0.414307	−	1.65401i	−0.714131	−	0.700012i	$-0.753178\pi$
$157$	−5.19125	−	20.7246i	−0.414307	−	1.65401i	0.299824	−	0.953995i	$-0.403072\pi$
$158$	−1.88181	−	9.82134i	−0.149709	−	0.781344i
$159$	−0.787552	+	1.90132i	−0.0624570	+	0.150784i
$160$	−10.7406	−	5.55058i	−0.849119	−	0.438812i
$161$	−5.13492	−	12.3968i	−0.404688	−	0.977004i
$162$	−9.79644	+	6.44648i	−0.769681	+	0.506483i
$163$	4.82033	−	8.04224i	0.377557	−	0.629916i	−0.609031	−	0.793147i	$-0.708441\pi$
$163$	4.82033	−	8.04224i	0.377557	−	0.629916i	0.986588	+	0.163230i	$0.0521913\pi$
$164$	4.37438	+	3.69425i	0.341582	+	0.288472i
$165$	2.94800	−	1.05481i	0.229501	−	0.0821169i
$166$	−9.57739	−	8.80404i	−0.743350	−	0.683326i
$167$	5.05886	−	4.15170i	0.391467	−	0.321268i	−0.417986	−	0.908453i	$-0.637264\pi$
$167$	5.05886	−	4.15170i	0.391467	−	0.321268i	0.809453	+	0.587185i	$0.199764\pi$
$168$	−0.720437	+	2.63844i	−0.0555829	+	0.203560i
$169$	−2.26091	−	22.9554i	−0.173916	−	1.76580i
$170$	−2.91294	−	0.751487i	−0.223413	−	0.0576364i
$171$	−0.495919	−	3.34322i	−0.0379239	−	0.255662i
$172$	18.5717	+	14.1833i	1.41608	+	1.08147i
$173$	2.82428	−	7.89333i	0.214726	−	0.600119i	−0.785088	−	0.619384i	$-0.787383\pi$
$173$	2.82428	−	7.89333i	0.214726	−	0.600119i	0.999814	+	0.0192648i	$0.00613256\pi$
$174$	−0.588241	−	0.182973i	−0.0445944	−	0.0138711i
$175$	1.23382	+	0.824411i	0.0932679	+	0.0623196i
$176$	−18.1402	+	10.1898i	−1.36737	+	0.768089i
$177$	−1.45344	+	0.971155i	−0.109247	+	0.0729965i
$178$	−6.50650	−	22.0056i	−0.487683	−	1.64939i
$179$	0.621235	+	12.6455i	0.0464333	+	0.945171i	0.903134	+	0.429358i	$0.141260\pi$
$179$	0.621235	+	12.6455i	0.0464333	+	0.945171i	−0.856701	+	0.515813i	$0.827490\pi$
$180$	−5.17834	−	11.3598i	−0.385971	−	0.846708i
$181$	−4.13898	+	16.5237i	−0.307648	+	1.22820i	0.597070	+	0.802189i	$0.296331\pi$
$181$	−4.13898	+	16.5237i	−0.307648	+	1.22820i	−0.904718	+	0.426011i	$0.859919\pi$
$182$	1.63580	−	29.1139i	0.121254	−	2.15807i
$183$	−0.510024	+	0.272613i	−0.0377020	+	0.0201522i
$184$	10.5079	+	3.43148i	0.774654	+	0.252972i
$185$	1.28283	+	4.22891i	0.0943153	+	0.310916i
$186$	0.715096	+	0.978518i	0.0524334	+	0.0717484i
$187$	−3.83600	+	3.47675i	−0.280516	+	0.254245i
$188$	−23.6797	+	4.36454i	−1.72702	+	0.318317i
$189$	−4.59850	+	3.41048i	−0.334492	+	0.248076i
$190$	3.49756	+	0.0246225i	0.253739	+	0.00178630i
$191$	6.81385	−	6.81385i	0.493033	−	0.493033i	−0.416228	−	0.909260i	$-0.636648\pi$
$191$	6.81385	−	6.81385i	0.493033	−	0.493033i	0.909260	+	0.416228i	$0.136648\pi$
$192$	−1.26458	−	1.86480i	−0.0912632	−	0.134581i
$193$	−10.0673	−	10.0673i	−0.724660	−	0.724660i	0.244891	−	0.969551i	$-0.421248\pi$
$193$	−10.0673	−	10.0673i	−0.724660	−	0.724660i	−0.969551	+	0.244891i	$0.921248\pi$
$194$	−15.1751	−	15.3902i	−1.08951	−	1.10495i
$195$	−2.15343	−	2.90357i	−0.154210	−	0.207929i
$196$	2.00019	−	9.36457i	0.142871	−	0.668898i
$197$	−5.54236	−	6.11505i	−0.394876	−	0.435679i	0.510767	−	0.859719i	$-0.329362\pi$
$197$	−5.54236	−	6.11505i	−0.394876	−	0.435679i	−0.905643	+	0.424040i	$0.860612\pi$
$198$	−21.2296	−	3.30202i	−1.50872	−	0.234664i
$199$	−0.684005	+	0.207491i	−0.0484878	+	0.0147086i	−0.314435	−	0.949279i	$-0.601815\pi$
$199$	−0.684005	+	0.207491i	−0.0484878	+	0.0147086i	0.265948	+	0.963987i	$0.414315\pi$
$200$	−1.17705	+	0.330076i	−0.0832297	+	0.0233399i
$201$	−0.546039	−	1.02157i	−0.0385146	−	0.0720557i
$202$	4.35138	−	3.88842i	0.306162	−	0.273588i
$203$	5.15110	+	1.29028i	0.361536	+	0.0905601i
$204$	−0.410065	−	0.382314i	−0.0287103	−	0.0267673i
$205$	−6.11114	+	0.300221i	−0.426820	+	0.0209683i
$206$	−4.37005	−	2.37554i	−0.304476	−	0.165512i
$207$	6.34159	+	9.49086i	0.440771	+	0.659660i
$208$	17.3380	+	16.6270i	1.20217	+	1.15288i
$209$	3.34411	−	5.00481i	0.231317	−	0.346190i
$210$	−1.35958	−	2.58723i	−0.0938196	−	0.178536i
$211$	9.35255	+	3.34639i	0.643856	+	0.230375i	0.638514	−	0.769610i	$-0.279550\pi$
$211$	9.35255	+	3.34639i	0.643856	+	0.230375i	0.00534211	+	0.999986i	$0.498300\pi$
$212$	7.33590	+	12.6394i	0.503832	+	0.868080i
$213$	−0.306518	+	0.0454676i	−0.0210023	+	0.00311539i
$214$	17.2243	−	10.1597i	1.17743	−	0.694505i
$215$	−24.8515	+	2.44766i	−1.69486	+	0.166929i
$216$	0.330855	−	4.70483i	0.0225118	−	0.320123i
$217$	−6.62755	−	8.07569i	−0.449907	−	0.548214i
$218$	−1.16720	−	27.7427i	−0.0790528	−	1.87897i
$219$	−1.13352	−	3.16799i	−0.0765964	−	0.214073i
$220$	6.75310	−	21.1836i	0.455294	−	1.42820i
$221$	5.12692	+	3.07296i	0.344874	+	0.206710i
$222$	−0.166354	+	0.806601i	−0.0111650	+	0.0541355i
$223$	−12.4915	+	5.17417i	−0.836496	+	0.346488i	−0.759471	−	0.650541i	$-0.774542\pi$
$223$	−12.4915	+	5.17417i	−0.836496	+	0.346488i	−0.0770249	+	0.997029i	$0.524542\pi$
$224$	11.7852	+	15.4377i	0.787431	+	1.03147i
$225$	−1.16623	−	0.483070i	−0.0777489	−	0.0322047i
$226$	−11.1995	+	16.5084i	−0.744979	+	1.09812i
$227$	17.7264	−	4.44022i	1.17654	−	0.294708i	0.395070	−	0.918651i	$-0.370720\pi$
$227$	17.7264	−	4.44022i	1.17654	−	0.294708i	0.781470	+	0.623943i	$0.214470\pi$
$228$	0.570482	+	0.315335i	0.0377811	+	0.0208836i
$229$	−1.30774	+	2.76498i	−0.0864177	+	0.182715i	−0.942570	−	0.334009i	$-0.891599\pi$
$229$	−1.30774	+	2.76498i	−0.0864177	+	0.182715i	0.856152	+	0.516724i	$0.172849\pi$
$230$	−10.7137	+	4.97522i	−0.706441	+	0.328056i
$231$	−5.00558	−	0.493007i	−0.329343	−	0.0324375i
$232$	−3.56798	+	2.53118i	−0.234249	+	0.166180i
$233$	2.81858	+	2.31315i	0.184651	+	0.151539i	0.722178	−	0.691707i	$-0.243141\pi$
$233$	2.81858	+	2.31315i	0.184651	+	0.151539i	−0.537527	+	0.843247i	$0.680641\pi$
$234$	3.46692	+	24.5622i	0.226639	+	1.60568i
$235$	15.3278	−	20.6672i	0.999879	−	1.34818i
$236$	−0.783578	+	12.3884i	−0.0510066	+	0.806414i
$237$	0.851483	+	1.80031i	0.0553097	+	0.116943i
$238$	3.71404	+	3.09205i	0.240746	+	0.200428i
$239$	−1.01943	−	5.12503i	−0.0659416	−	0.331511i	0.933706	−	0.358039i	$-0.116555\pi$
$239$	−1.01943	−	5.12503i	−0.0659416	−	0.331511i	−0.999648	+	0.0265287i	$0.991555\pi$
$240$	2.34733	+	0.536032i	0.151519	+	0.0346007i
$241$	2.94889	−	14.8251i	0.189955	−	0.954966i	−0.761731	−	0.647893i	$-0.775650\pi$
$241$	2.94889	−	14.8251i	0.189955	−	0.954966i	0.951686	−	0.307073i	$-0.0993496\pi$
$242$	−14.2812	−	17.6537i	−0.918033	−	1.13482i
$243$	4.92793	−	5.43713i	0.316127	−	0.348792i
$244$	−0.659709	+	4.05335i	−0.0422335	+	0.259489i
$245$	5.26076	+	8.77705i	0.336098	+	0.560745i
$246$	−1.02733	−	0.494771i	−0.0655002	−	0.0315454i
$247$	−6.65034	−	2.01736i	−0.423151	−	0.128361i
$248$	8.60447	+	0.181748i	0.546385	+	0.0115410i
$249$	2.28487	+	1.22129i	0.144798	+	0.0773961i
$250$	8.53994	−	14.0232i	0.540113	−	0.886905i
$251$	−0.0707182	−	0.00347416i	−0.00446369	−	0.000219287i	0.0468357	−	0.998903i	$-0.485086\pi$
$251$	−0.0707182	−	0.00347416i	−0.00446369	−	0.000219287i	−0.0512994	+	0.998683i	$0.516336\pi$
$252$	−0.282362	+	20.0534i	−0.0177872	+	1.26325i
$253$	−2.98284	+	20.1087i	−0.187530	+	1.26422i
$254$	12.2278	+	5.16609i	0.767243	+	0.324149i
$255$	0.599111			0.0375178
$256$	−15.9746	−	0.900617i	−0.998415	−	0.0562885i
$257$	−6.58927			−0.411027			−0.205514	−	0.978654i	$-0.565887\pi$
$257$	−6.58927			−0.411027			−0.205514	+	0.978654i	$0.565887\pi$
$258$	−4.28692	−	1.81116i	−0.266892	−	0.112758i
$259$	1.04167	−	7.02235i	0.0647260	−	0.436347i
$260$	−25.6680	−	0.361418i	−1.59186	−	0.0224142i
$261$	−4.51186	−	0.221654i	−0.279277	−	0.0137200i
$262$	2.44343	−	4.01229i	0.150956	−	0.247880i
$263$	26.1608	+	13.9832i	1.61314	+	0.862242i	0.997226	+	0.0744301i	$0.0237138\pi$
$263$	26.1608	+	13.9832i	1.61314	+	0.862242i	0.615916	+	0.787812i	$0.288786\pi$
$264$	2.99119	−	2.86744i	0.184095	−	0.176479i
$265$	−14.9444	−	4.53334i	−0.918029	−	0.278481i
$266$	−5.06226	−	2.43803i	−0.310387	−	0.149485i
$267$	2.34945	+	3.91982i	0.143784	+	0.239889i
$268$	−8.11878	−	1.32138i	−0.495933	−	0.0807163i
$269$	3.37133	−	3.71969i	0.205554	−	0.226793i	−0.629446	−	0.777044i	$-0.716718\pi$
$269$	3.37133	−	3.71969i	0.205554	−	0.226793i	0.834999	+	0.550251i	$0.185468\pi$
$270$	3.16990	+	3.91846i	0.192914	+	0.238470i
$271$	5.36365	−	26.9649i	0.325819	−	1.63800i	−0.376700	−	0.926335i	$-0.622941\pi$
$271$	5.36365	−	26.9649i	0.325819	−	1.63800i	0.702519	−	0.711665i	$-0.252059\pi$
$272$	−3.92503	+	0.666449i	−0.237990	+	0.0404094i
$273$	1.13293	+	5.69564i	0.0685683	+	0.344716i
$274$	−18.5629	−	15.4541i	−1.12142	−	0.933618i
$275$	−0.961198	−	2.03228i	−0.0579624	−	0.122551i
$276$	−2.19704	−	0.138965i	−0.132246	−	0.00836471i
$277$	−9.97011	+	13.4431i	−0.599046	+	0.807720i	−0.993814	−	0.111061i	$-0.964575\pi$
$277$	−9.97011	+	13.4431i	−0.599046	+	0.807720i	0.394768	+	0.918781i	$0.370825\pi$
$278$	2.09381	+	14.8341i	0.125578	+	0.889688i
$279$	6.86982	+	5.63791i	0.411285	+	0.337533i
$280$	−20.4612	−	3.47822i	−1.22279	−	0.207863i
$281$	−0.106823	−	0.0105212i	−0.00637255	−	0.000627642i	0.0948304	−	0.995493i	$-0.469769\pi$
$281$	−0.106823	−	0.0105212i	−0.00637255	−	0.000627642i	−0.101203	+	0.994866i	$0.532269\pi$
$282$	4.34921	−	2.01968i	0.258992	−	0.120270i
$283$	−5.50063	+	11.6301i	−0.326978	+	0.691338i	−0.998779	−	0.0493940i	$-0.984271\pi$
$283$	−5.50063	+	11.6301i	−0.326978	+	0.691338i	0.671801	+	0.740732i	$0.265521\pi$
$284$	−1.06451	+	1.92583i	−0.0631669	+	0.114277i
$285$	−0.675686	+	0.169251i	−0.0400242	+	0.0100255i
$286$	−24.8017	+	36.5585i	−1.46655	+	2.16175i
$287$	9.08083	+	3.76140i	0.536025	+	0.222029i
$288$	−12.3948	−	10.9243i	−0.730370	−	0.643721i
$289$	14.7907	−	6.12652i	0.870043	−	0.360384i
$290$	0.944265	−	4.57845i	0.0554492	−	0.268856i
$291$	3.69197	+	2.21288i	0.216427	+	0.129721i
$292$	−22.7644	−	7.25704i	−1.33219	−	0.424686i
$293$	−10.0059	−	27.9646i	−0.584550	−	1.63371i	−0.760521	−	0.649314i	$-0.775056\pi$
$293$	−10.0059	−	27.9646i	−0.584550	−	1.63371i	0.175970	−	0.984395i	$-0.443694\pi$
$294$	0.0801627	+	1.90535i	0.00467518	+	0.111122i
$295$	−8.41517	−	10.2539i	−0.489950	−	0.597006i
$296$	3.83514	+	4.41533i	0.222913	+	0.256636i
$297$	8.63193	−	0.850171i	0.500875	−	0.0493319i
$298$	−17.9881	+	10.6102i	−1.04202	+	0.614635i
$299$	23.2167	−	3.44388i	1.34266	−	0.199165i
$300$	0.210558	−	0.122208i	0.0121566	−	0.00705566i
$301$	37.7706	+	13.5145i	2.17706	+	0.778965i
$302$	−5.03720	−	9.58565i	−0.289858	−	0.551592i
$303$	−0.645668	+	0.966310i	−0.0370927	+	0.0555131i
$304$	4.23844	−	1.86046i	0.243091	−	0.106705i
$305$	−2.43811	−	3.64890i	−0.139606	−	0.208935i
$306$	−3.61190	−	1.96342i	−0.206479	−	0.112241i
$307$	−2.31819	+	0.113885i	−0.132306	+	0.00649977i	−0.115113	−	0.993352i	$-0.536723\pi$
$307$	−2.31819	+	0.113885i	−0.132306	+	0.00649977i	−0.0171930	+	0.999852i	$0.505473\pi$
$308$	−24.3567	+	26.1247i	−1.38785	+	1.48859i
$309$	0.960891	+	0.240691i	0.0546632	+	0.0136924i
$310$	−6.85781	+	6.12818i	−0.389498	+	0.348057i
$311$	12.1725	+	22.7731i	0.690238	+	1.29135i	0.945862	+	0.324569i	$0.105219\pi$
$311$	12.1725	+	22.7731i	0.690238	+	1.29135i	−0.255624	+	0.966776i	$0.582281\pi$
$312$	−4.17059	−	2.34378i	−0.236113	−	0.132690i
$313$	18.6423	−	5.65509i	1.05373	−	0.319645i	0.284538	−	0.958665i	$-0.408160\pi$
$313$	18.6423	−	5.65509i	1.05373	−	0.319645i	0.769190	+	0.639020i	$0.220660\pi$
$314$	29.8556	+	4.64369i	1.68485	+	0.262059i
$315$	−14.3926	−	15.8798i	−0.810931	−	0.894725i
$316$	13.8302	+	2.95400i	0.778008	+	0.166176i
$317$	−19.8168	−	26.7198i	−1.11302	−	1.50074i	−0.843025	−	0.537874i	$-0.819228\pi$
$317$	−19.8168	−	26.7198i	−1.11302	−	1.50074i	−0.269996	−	0.962862i	$-0.587022\pi$
$318$	−2.04344	−	2.07241i	−0.114590	−	0.116215i
$319$	−5.68872	−	5.68872i	−0.318507	−	0.318507i
$320$	13.1423	−	10.9371i	0.734676	−	0.611401i
$321$	−2.81607	+	2.81607i	−0.157178	+	0.157178i
$322$	18.9757	+	0.133587i	1.05747	+	0.00744452i
$323$	0.925103	−	0.686103i	0.0514741	−	0.0381758i
$324$	−3.00620	−	16.3100i	−0.167011	−	0.906114i
$325$	−1.92322	+	1.74310i	−0.106681	+	0.0966899i
$326$	7.82377	+	10.7058i	0.433319	+	0.592941i
$327$	1.60524	+	5.29177i	0.0887700	+	0.292635i
$328$	−7.22014	+	3.66536i	−0.398666	+	0.202386i
$329$	−36.4543	+	19.4852i	−2.00979	+	1.07426i
$330$	−0.248397	+	4.42096i	−0.0136738	+	0.243366i
$331$	1.72891	−	6.90218i	0.0950293	−	0.379378i	−0.903789	−	0.427978i	$-0.859226\pi$
$331$	1.72891	−	6.90218i	0.0950293	−	0.379378i	0.998818	+	0.0486000i	$0.0154760\pi$
$332$	16.7404	−	7.63109i	0.918750	−	0.418811i
$333$	0.296326	+	6.03185i	0.0162385	+	0.330543i
$334$	2.62421	+	8.87530i	0.143590	+	0.485635i
$335$	7.30866	−	4.88349i	0.399315	−	0.266814i
$336$	−3.04063	−	2.39067i	−0.165880	−	0.130422i
$337$	19.0749	+	12.7455i	1.03908	+	0.694289i	0.953300	−	0.302025i	$-0.0976626\pi$
$337$	19.0749	+	12.7455i	1.03908	+	0.694289i	0.0857775	+	0.996314i	$0.472663\pi$
$338$	31.1488	+	9.68886i	1.69427	+	0.527005i
$339$	1.33841	−	3.74061i	0.0726926	−	0.203162i
$340$	2.58220	−	3.38115i	0.140040	−	0.183369i
$341$	2.32237	+	15.6561i	0.125763	+	0.847826i
$342$	4.62822	+	1.19400i	0.250266	+	0.0645640i
$343$	0.744432	+	7.55834i	0.0401955	+	0.408112i
$344$	−28.6984	+	16.3875i	−1.54731	+	0.883554i
$345$	1.81850	−	1.49240i	0.0979047	−	0.0803483i
$346$	8.72838	+	8.02358i	0.469240	+	0.431350i
$347$	−26.6076	+	9.52034i	−1.42837	+	0.511078i	−0.933717	−	0.358013i	$-0.883454\pi$
$347$	−26.6076	+	9.52034i	−1.42837	+	0.511078i	−0.494652	+	0.869091i	$0.664704\pi$
$348$	0.562119	−	0.665609i	0.0301327	−	0.0356804i
$349$	5.04047	−	8.40951i	0.269810	−	0.450151i	−0.692766	−	0.721162i	$-0.743608\pi$
$349$	5.04047	−	8.40951i	0.269810	−	0.450151i	0.962576	+	0.271011i	$0.0873581\pi$
$350$	−1.75305	+	1.15358i	−0.0937043	+	0.0616615i
$351$	−3.83232	−	9.25204i	−0.204554	−	0.493837i
$352$	−3.29051	−	29.2399i	−0.175385	−	1.55849i
$353$	−2.28819	+	5.52417i	−0.121788	+	0.294022i	−0.973002	−	0.230797i	$-0.925867\pi$
$353$	−2.28819	+	5.52417i	−0.121788	+	0.294022i	0.851214	+	0.524819i	$0.175867\pi$
$354$	−0.465201	−	2.42793i	−0.0247252	−	0.129043i
$355$	−0.571357	−	2.28098i	−0.0303245	−	0.121062i
$356$	32.2482	+	3.63528i	1.70915	+	0.192669i
$357$	−0.870033	−	0.411495i	−0.0460470	−	0.0217786i
$358$	−16.8155	−	6.15055i	−0.888727	−	0.325067i
$359$	0.993618	−	10.0884i	0.0524412	−	0.532444i	−0.932695	−	0.360667i	$-0.882549\pi$
$359$	0.993618	−	10.0884i	0.0524412	−	0.532444i	0.985136	−	0.171777i	$-0.0549509\pi$
$360$	17.6487	−	0.493727i	0.930167	−	0.0260217i
$361$	11.2040	−	13.6521i	0.589682	−	0.718529i
$362$	−19.2478	−	14.4863i	−1.01164	−	0.761382i
$363$	3.63221	+	2.69383i	0.190642	+	0.141390i
$364$	37.0270	+	18.1547i	1.94074	+	0.951566i
$365$	23.0813	−	10.9166i	1.20813	−	0.571403i
$366$	−0.0744319	−	0.814459i	−0.00389062	−	0.0425725i
$367$	−20.1348	+	4.00506i	−1.05103	+	0.209062i	−0.690236	−	0.723584i	$-0.742493\pi$
$367$	−20.1348	+	4.00506i	−1.05103	+	0.209062i	−0.360791	+	0.932647i	$0.617493\pi$
$368$	−10.2536	+	11.8003i	−0.534507	+	0.615131i
$369$	−8.20068	−	1.63122i	−0.426910	−	0.0849177i
$370$	−6.21513	−	0.656346i	−0.323109	−	0.0341218i
$371$	18.5887	+	16.8478i	0.965077	+	0.874694i
$372$	−1.66831	+	0.393013i	−0.0864978	+	0.0203768i
$373$	−17.2068	+	10.3134i	−0.890935	+	0.534006i	−0.884798	−	0.465975i	$-0.845704\pi$
$373$	−17.2068	+	10.3134i	−0.890935	+	0.534006i	−0.00613711	+	0.999981i	$0.501954\pi$
$374$	−2.41797	−	6.91077i	−0.125030	−	0.357348i
$375$	−0.949188	+	3.12905i	−0.0490159	+	0.161584i
$376$	7.34707	−	33.2502i	0.378896	−	1.71475i
$377$	−4.37859	+	8.19176i	−0.225509	+	0.421897i
$378$	−1.91198	−	7.86762i	−0.0983416	−	0.404667i
$379$	−0.904828	+	18.4182i	−0.0464779	+	0.946079i	0.856435	+	0.516255i	$0.172674\pi$
$379$	−0.904828	+	18.4182i	−0.0464779	+	0.946079i	−0.902913	+	0.429824i	$0.858576\pi$
$380$	−1.95706	+	4.54279i	−0.100395	+	0.233040i
$381$	−2.61500	−	0.387898i	−0.133970	−	0.0198726i
$382$	5.12633	+	12.6267i	0.262286	+	0.646041i
$383$		−	1.21702i		−	0.0621870i	−0.999516	−	0.0310935i	$-0.990101\pi$
$383$		−	1.21702i		−	0.0621870i	0.999516	−	0.0310935i	$-0.00989897\pi$
$384$	3.12532	−	0.621044i	0.159488	−	0.0316925i
$385$		−	38.1686i		−	1.94525i
$386$	18.6557	−	7.57403i	0.949551	−	0.385508i
$387$	−33.7561	−	5.00725i	−1.71592	−	0.254533i
$388$	28.4012	−	11.2984i	1.44185	−	0.573588i
$389$	0.0283275	−	0.576619i	0.00143626	−	0.0292358i	−0.997970	−	0.0636803i	$-0.979716\pi$
$389$	0.0283275	−	0.576619i	0.00143626	−	0.0292358i	0.999407	+	0.0344445i	$0.0109662\pi$
$390$	4.96774	−	1.20725i	0.251551	−	0.0611317i
$391$	−1.83365	+	3.43052i	−0.0927319	+	0.173489i
$392$	11.0986	+	7.75977i	0.560562	+	0.391927i
$393$	−0.271580	+	0.895279i	−0.0136994	+	0.0451608i
$394$	11.0166	−	3.85454i	0.555008	−	0.194189i
$395$	−12.9625	+	7.76941i	−0.652213	+	0.390922i
$396$	15.9860	−	25.8389i	0.803325	−	1.29845i
$397$	15.5981	+	14.1373i	0.782846	+	0.709531i	0.961628	−	0.274358i	$-0.0884654\pi$
$397$	15.5981	+	14.1373i	0.782846	+	0.709531i	−0.178781	+	0.983889i	$0.557215\pi$
$398$	0.106161	−	1.00527i	0.00532135	−	0.0503894i
$399$	1.09748	+	0.218303i	0.0549429	+	0.0109288i
$400$	0.217827	−	1.71503i	0.0108913	−	0.0857515i
$401$	25.0873	−	4.99017i	1.25280	−	0.249197i	0.476281	−	0.879293i	$-0.341984\pi$
$401$	25.0873	−	4.99017i	1.25280	−	0.249197i	0.776517	+	0.630096i	$0.216984\pi$
$402$	1.63134	−	0.149086i	0.0813641	−	0.00743571i
$403$	16.5193	−	7.81304i	0.822884	−	0.389195i
$404$	2.67061	+	7.80875i	0.132868	+	0.388500i
$405$	14.2351	+	10.5575i	0.707348	+	0.524605i
$406$	−4.51594	+	6.00030i	−0.224122	+	0.297790i
$407$	−6.82312	+	8.31399i	−0.338209	+	0.412109i
$408$	0.723740	−	0.323782i	0.0358305	−	0.0160296i
$409$	−2.30112	+	23.3636i	−0.113783	+	1.15526i	0.753502	+	0.657445i	$0.228363\pi$
$409$	−2.30112	+	23.3636i	−0.113783	+	1.15526i	−0.867285	+	0.497812i	$0.834137\pi$
$410$	2.97235	−	8.12634i	0.146794	−	0.401331i
$411$	4.34845	+	2.05666i	0.214493	+	0.101448i
$412$	5.49986	−	4.38550i	0.270959	−	0.216058i
$413$	5.17774	+	20.6707i	0.254780	+	1.01714i
$414$	−15.8542	+	3.03774i	−0.779193	+	0.149297i
$415$	−7.52361	+	18.1636i	−0.369320	+	0.891617i
$416$	−31.2029	+	13.4353i	−1.52985	+	0.658721i
$417$	−1.14174	−	2.75640i	−0.0559112	−	0.134982i
$418$	4.67934	+	7.11099i	0.228874	+	0.347810i
$419$	−1.52191	+	2.53916i	−0.0743503	+	0.124046i	−0.892658	−	0.450734i	$-0.851162\pi$
$419$	−1.52191	+	2.53916i	−0.0743503	+	0.124046i	0.818308	+	0.574780i	$0.194912\pi$
$420$	4.11873	−	0.347184i	0.200973	−	0.0169408i
$421$	21.1135	−	7.55452i	1.02901	−	0.368185i	0.232360	−	0.972630i	$-0.425355\pi$
$421$	21.1135	−	7.55452i	1.02901	−	0.368185i	0.796647	+	0.604445i	$0.206605\pi$
$422$	−9.50688	+	10.3420i	−0.462788	+	0.503439i
$423$	27.1813	−	22.3071i	1.32160	−	1.08461i
$424$	−20.5032	+	2.60014i	−0.995723	+	0.126274i
$425$	−0.0421642	−	0.428100i	−0.00204526	−	0.0207659i
$426$	0.109470	−	0.424332i	0.00530383	−	0.0205589i
$427$	1.03443	+	6.97355i	0.0500595	+	0.337474i
$428$	3.75537	+	28.0302i	0.181522	+	1.35489i
$429$	2.96396	−	8.28372i	0.143101	−	0.399942i
$430$	10.4892	−	33.7217i	0.505832	−	1.62620i
$431$	−13.3950	−	8.95026i	−0.645215	−	0.431119i	0.189440	−	0.981892i	$-0.439333\pi$
$431$	−13.3950	−	8.95026i	−0.645215	−	0.431119i	−0.834655	+	0.550774i	$0.814333\pi$
$432$	5.94698	+	3.02046i	0.286124	+	0.145322i
$433$	−17.2281	+	11.5114i	−0.827927	+	0.553203i	−0.895783	−	0.444492i	$-0.853384\pi$
$433$	−17.2281	+	11.5114i	−0.827927	+	0.553203i	0.0678555	+	0.997695i	$0.478384\pi$
$434$	14.1680	−	4.18914i	0.680088	−	0.201085i
$435$	0.0456818	+	0.929875i	0.00219028	+	0.0445841i
$436$	36.7833	+	13.7485i	1.76160	+	0.658433i
$437$	1.09889	−	4.38701i	0.0525670	−	0.209859i
$438$	4.75087	+	0.266933i	0.227005	+	0.0127546i
$439$	−7.03342	+	3.75944i	−0.335687	+	0.179428i	−0.630624	−	0.776088i	$-0.717201\pi$
$439$	−7.03342	+	3.75944i	−0.335687	+	0.179428i	0.294938	+	0.955517i	$0.404701\pi$
$440$	23.8796	+	20.4565i	1.13841	+	0.975224i
$441$	4.05932	+	13.3818i	0.193301	+	0.637227i
$442$	−6.82497	+	4.98765i	−0.324631	+	0.237238i
$443$	24.4017	−	22.1164i	1.15936	−	1.05078i	0.161403	−	0.986889i	$-0.448398\pi$
$443$	24.4017	−	22.1164i	1.15936	−	1.05078i	0.997957	−	0.0638942i	$-0.0203520\pi$
$444$	−0.959218	−	0.660651i	−0.0455225	−	0.0313531i
$445$	−27.8547	+	20.6584i	−1.32044	+	0.979304i
$446$	0.134608	−	19.1208i	0.00637389	−	0.905394i
$447$	2.94094	−	2.94094i	0.139102	−	0.139102i
$448$	−26.5973	+	6.85621i	−1.25661	+	0.323925i
$449$	2.82859	+	2.82859i	0.133490	+	0.133490i	0.770694	−	0.637205i	$-0.219910\pi$
$449$	2.82859	+	2.82859i	0.133490	+	0.133490i	−0.637205	+	0.770694i	$0.719910\pi$
$450$	1.27118	−	1.25340i	0.0599239	−	0.0590861i
$451$	−8.87061	−	11.9606i	−0.417701	−	0.563204i
$452$	−15.3419	−	23.6757i	−0.721623	−	1.11361i
$453$	1.44824	+	1.59788i	0.0680441	+	0.0750751i
$454$	−3.97187	+	25.5363i	−0.186409	+	1.19848i
$455$	−42.1705	+	12.7923i	−1.97698	+	0.599711i
$456$	−0.724775	+	0.569624i	−0.0339407	+	0.0266751i
$457$	−14.9144	−	27.9030i	−0.697668	−	1.30525i	−0.942019	−	0.335559i	$-0.891075\pi$
$457$	−14.9144	−	27.9030i	−0.697668	−	1.30525i	0.244351	−	0.969687i	$-0.421425\pi$
$458$	−2.88224	−	3.22541i	−0.134678	−	0.150713i
$459$	1.60995	+	0.403270i	0.0751458	+	0.0188230i
$460$	−0.584703	−	16.6952i	−0.0272619	−	0.778420i
$461$	−1.07033	+	0.0525821i	−0.0498504	+	0.00244899i	−0.0739776	−	0.997260i	$-0.523569\pi$
$461$	−1.07033	+	0.0525821i	−0.0498504	+	0.00244899i	0.0241272	+	0.999709i	$0.492319\pi$
$462$	3.39723	−	6.24954i	0.158053	−	0.290755i
$463$	−9.86909	−	14.7701i	−0.458656	−	0.686427i	0.528001	−	0.849244i	$-0.322942\pi$
$463$	−9.86909	−	14.7701i	−0.458656	−	0.686427i	−0.986656	+	0.162817i	$0.947942\pi$
$464$	−1.33367	−	6.04119i	−0.0619141	−	0.280455i
$465$	1.01758	−	1.52291i	0.0471890	−	0.0706234i
$466$	−4.56468	+	2.39871i	−0.211455	+	0.111118i
$467$	33.9532	+	12.1487i	1.57117	+	0.562173i	0.971286	−	0.237915i	$-0.0764639\pi$
$467$	33.9532	+	12.1487i	1.57117	+	0.562173i	0.599883	+	0.800088i	$0.295214\pi$
$468$	−33.9058	−	9.00211i	−1.56729	−	0.416123i
$469$	−13.9679	+	2.07194i	−0.644976	+	0.0956731i
$470$	18.4875	+	31.3427i	0.852763	+	1.44573i
$471$	−5.98831	+	0.589797i	−0.275927	+	0.0271764i
$472$	−15.7073	−	7.83910i	−0.722988	−	0.360824i
$473$	−38.5556	−	46.9802i	−1.77279	−	2.16015i
$474$	−2.81394	+	0.118389i	−0.129248	+	0.00543779i
$475$	0.168493	+	0.470906i	0.00773099	+	0.0216067i
$476$	−6.07221	+	3.13656i	−0.278319	+	0.143764i
$477$	−18.3052	−	10.9717i	−0.838137	−	0.502360i
$478$	7.23756	+	1.49268i	0.331038	+	0.0682737i
$479$	−15.8390	+	6.56073i	−0.723702	+	0.299767i	−0.713961	−	0.700185i	$-0.753101\pi$
$479$	−15.8390	+	6.56073i	−0.723702	+	0.299767i	−0.00974107	+	0.999953i	$0.503101\pi$
$480$	−1.99022	+	2.76289i	−0.0908409	+	0.126108i
$481$	11.4725	+	4.75206i	0.523100	+	0.216675i
$482$	17.6899	+	12.0010i	0.805753	+	0.546631i
$483$	−3.66588	+	0.918255i	−0.166803	+	0.0417821i
$484$	30.8580	−	8.88821i	1.40264	−	0.404010i
$485$	−13.9655	+	29.5275i	−0.634139	+	1.34077i
$486$	4.37083	+	9.41221i	0.198265	+	0.426946i
$487$	−17.9431	−	1.76724i	−0.813079	−	0.0800813i	−0.317074	−	0.948401i	$-0.602700\pi$
$487$	−17.9431	−	1.76724i	−0.813079	−	0.0800813i	−0.496005	+	0.868319i	$0.665200\pi$
$488$	−4.91729	−	3.09030i	−0.222595	−	0.139891i
$489$	−2.04132	−	1.67527i	−0.0923117	−	0.0757582i
$490$	−14.3295	+	2.02258i	−0.647339	+	0.0913711i
$491$	7.19040	−	9.69514i	0.324498	−	0.437535i	−0.610592	−	0.791946i	$-0.709068\pi$
$491$	7.19040	−	9.69514i	0.324498	−	0.437535i	0.935090	+	0.354410i	$0.115318\pi$
$492$	1.20997	−	1.06601i	0.0545497	−	0.0480595i
$493$	−0.658178	−	1.39160i	−0.0296428	−	0.0626745i
$494$	6.28827	−	7.55322i	0.282923	−	0.339835i
$495$	6.33442	+	31.8453i	0.284711	+	1.43134i
$496$	−4.97250	+	11.1092i	−0.223272	+	0.498818i
$497$	−0.736948	+	3.70489i	−0.0330566	+	0.166187i
$498$	−2.84855	+	2.30438i	−0.127647	+	0.103262i
$499$	−6.09291	+	6.72249i	−0.272756	+	0.300940i	−0.861890	−	0.507096i	$-0.830719\pi$
$499$	−6.09291	+	6.72249i	−0.272756	+	0.300940i	0.589134	+	0.808035i	$0.299469\pi$
$500$	13.5681	+	18.8433i	0.606784	+	0.842696i
$501$	−0.947581	−	1.58094i	−0.0423348	−	0.0706313i
$502$	0.0434478	−	0.0902139i	0.00193917	−	0.00402644i
$503$	20.5386	+	6.23033i	0.915772	+	0.277796i	0.712783	−	0.701385i	$-0.247434\pi$
$503$	20.5386	+	6.23033i	0.915772	+	0.277796i	0.202989	+	0.979181i	$0.434934\pi$
$504$	−25.9686	−	11.4049i	−1.15673	−	0.508013i
$505$	−7.77776	−	4.15730i	−0.346106	−	0.184997i
$506$	−24.5543	−	14.9532i	−1.09157	−	0.664752i
$507$	−6.48868	−	0.318768i	−0.288172	−	0.0141570i
$508$	−13.4599	+	13.0862i	−0.597188	+	0.580604i
$509$	−1.12697	+	7.59744i	−0.0499522	+	0.336751i	0.949765	+	0.312964i	$0.101322\pi$
$509$	−1.12697	+	7.59744i	−0.0499522	+	0.336751i	−0.999717	+	0.0237862i	$0.992428\pi$
$510$	−0.329739	+	0.780475i	−0.0146011	+	0.0345600i
$511$	−41.0168			−1.81448
$512$	9.96538	−	20.3148i	0.440412	−	0.897796i
$513$	−1.92964			−0.0851959
$514$	3.62661	−	8.58398i	0.159963	−	0.378623i
$515$	−1.10297	+	7.43561i	−0.0486026	+	0.327652i
$516$	4.71887	−	4.58783i	0.207737	−	0.201968i
$517$	62.5477	+	3.07277i	2.75084	+	0.135140i
$518$	8.57484	+	5.22196i	0.376757	+	0.229440i
$519$	−2.08232	−	1.11303i	−0.0914039	−	0.0488564i
$520$	14.5980	−	33.2393i	0.640165	−	1.45764i
$521$	24.4945	+	7.43034i	1.07313	+	0.325529i	0.776923	−	0.629596i	$-0.216780\pi$
$521$	24.4945	+	7.43034i	1.07313	+	0.325529i	0.296203	+	0.955125i	$0.404280\pi$
$522$	2.77199	−	5.75570i	0.121327	−	0.251920i
$523$	−8.20648	−	13.6917i	−0.358844	−	0.598695i	0.624375	−	0.781125i	$-0.285354\pi$
$523$	−8.20648	−	13.6917i	−0.358844	−	0.598695i	−0.983219	+	0.182430i	$0.941604\pi$
$524$	3.88208	+	5.39139i	0.169589	+	0.235524i
$525$	0.280665	−	0.309666i	0.0122492	−	0.0135149i
$526$	−32.6146	+	26.3841i	−1.42206	+	1.15040i
$527$	−0.590836	+	2.97033i	−0.0257372	+	0.129390i
$528$	2.08918	+	5.47487i	0.0909200	+	0.238263i
$529$	−1.50728	−	7.57761i	−0.0655339	−	0.329461i
$530$	14.1308	−	16.9734i	0.613803	−	0.737275i
$531$	−7.75044	−	16.3869i	−0.336341	−	0.711132i
$532$	5.96224	−	5.25287i	0.258496	−	0.227741i
$533$	−10.2417	+	13.8093i	−0.443616	+	0.598147i
$534$	−6.39952	+	0.903283i	−0.276934	+	0.0390889i
$535$	−23.3614	−	19.1722i	−1.01000	−	0.828886i
$536$	6.18981	−	9.84924i	0.267359	−	0.425422i
$537$	3.54865	+	0.349511i	0.153135	+	0.0150825i
$538$	2.99020	+	6.43914i	0.128917	+	0.277611i
$539$	−10.6481	+	22.5135i	−0.458645	+	0.969724i
$540$	−6.84931	+	1.97285i	−0.294747	+	0.0848978i
$541$	34.4466	−	8.62843i	1.48098	−	0.370965i	0.583531	−	0.812091i	$-0.301671\pi$
$541$	34.4466	−	8.62843i	1.48098	−	0.370965i	0.897445	+	0.441126i	$0.145421\pi$
$542$	32.1757	+	21.8283i	1.38206	+	0.937605i
$543$	4.43238	+	1.83595i	0.190212	+	0.0787882i
$544$	1.29207	−	5.48002i	0.0553968	−	0.234954i
$545$	−38.7691	+	16.0587i	−1.66069	+	0.687879i
$546$	−8.04338	−	1.65887i	−0.344225	−	0.0709933i
$547$	9.50535	+	5.69729i	0.406419	+	0.243598i	0.702676	−	0.711510i	$-0.251988\pi$
$547$	9.50535	+	5.69729i	0.406419	+	0.243598i	−0.296257	+	0.955108i	$0.595738\pi$
$548$	30.3491	−	15.6766i	1.29645	−	0.669671i
$549$	−2.02038	−	5.64658i	−0.0862277	−	0.240990i
$550$	3.17652	−	0.133644i	0.135447	−	0.00569859i
$551$	1.13543	+	1.38353i	0.0483711	+	0.0589403i
$552$	1.39024	−	2.78564i	0.0591725	−	0.118565i
$553$	24.1605	−	2.37961i	1.02741	−	0.101191i
$554$	−12.0253	−	20.3871i	−0.510906	−	0.866166i
$555$	1.23117	−	0.182626i	0.0522601	−	0.00775205i
$556$	−20.4770	−	5.43673i	−0.868419	−	0.230569i
$557$	−22.7589	−	8.14326i	−0.964325	−	0.345041i	−0.192799	−	0.981238i	$-0.561756\pi$
$557$	−22.7589	−	8.14326i	−0.964325	−	0.345041i	−0.771526	+	0.636197i	$0.780506\pi$
$558$	−11.1256	+	5.84645i	−0.470986	+	0.247500i
$559$	−38.9839	+	58.3436i	−1.64885	+	2.46767i
$560$	15.7926	−	24.7409i	0.667359	−	1.04549i
$561$	0.810078	+	1.21237i	0.0342015	+	0.0511862i
$562$	0.0724997	−	0.133370i	0.00305822	−	0.00562589i
$563$	−5.55402	+	0.272851i	−0.234074	+	0.0114993i	−0.165767	−	0.986165i	$-0.553010\pi$
$563$	−5.55402	+	0.272851i	−0.234074	+	0.0114993i	−0.0683073	+	0.997664i	$0.521760\pi$
$564$	0.237359	+	6.77740i	0.00999462	+	0.285380i
$565$	29.2444	+	7.32533i	1.23032	+	0.308179i
$566$	−12.1233	−	13.5668i	−0.509582	−	0.570254i
$567$	−13.4210	−	25.1089i	−0.563628	−	1.05447i
$568$	−1.92294	−	2.44670i	−0.0806847	−	0.102661i
$569$	3.76162	−	1.14108i	0.157695	−	0.0478364i	−0.210450	−	0.977605i	$-0.567493\pi$
$569$	3.76162	−	1.14108i	0.157695	−	0.0478364i	0.368145	+	0.929768i	$0.379993\pi$
$570$	0.151398	−	0.973383i	0.00634138	−	0.0407705i
$571$	22.0139	+	24.2886i	0.921254	+	1.01645i	0.999809	+	0.0195376i	$0.00621941\pi$
$571$	22.0139	+	24.2886i	0.921254	+	1.01645i	−0.0785549	+	0.996910i	$0.525031\pi$
$572$	−33.9752	−	52.4307i	−1.42057	−	2.19224i
$573$	−1.61671	−	2.17989i	−0.0675392	−	0.0910661i
$574$	−9.89797	+	9.75959i	−0.413133	+	0.407357i
$575$	−1.19439	−	1.19439i	−0.0498096	−	0.0498096i
$576$	21.0532	−	10.1344i	0.877216	−	0.422268i
$577$	−21.8605	+	21.8605i	−0.910064	+	0.910064i	−0.996277	−	0.0862124i	$-0.972524\pi$
$577$	−21.8605	+	21.8605i	−0.910064	+	0.910064i	0.0862124	+	0.996277i	$0.472524\pi$
$578$	−0.159384	+	22.6401i	−0.00662951	+	0.941704i
$579$	−3.22073	+	2.38866i	−0.133849	+	0.0992692i
$580$	5.44474	+	3.75001i	0.226081	+	0.155711i
$581$	23.4014	−	21.2098i	0.970852	−	0.879929i
$582$	−4.91476	+	3.59168i	−0.203723	+	0.148880i
$583$	−11.0331	−	36.3714i	−0.456946	−	1.50635i
$584$	21.9830	−	25.6615i	0.909663	−	1.06188i
$585$	33.0612	−	17.6716i	1.36691	−	0.730630i
$586$	41.9371	+	2.35629i	1.73241	+	0.0973373i
$587$	−1.94366	+	7.75953i	−0.0802234	+	0.320270i	−0.996834	−	0.0795115i	$-0.974664\pi$
$587$	−1.94366	+	7.75953i	−0.0802234	+	0.320270i	0.916611	+	0.399781i	$0.130914\pi$
$588$	−2.52626	−	0.944238i	−0.104181	−	0.0389397i
$589$	−0.172774	−	3.51690i	−0.00711903	−	0.144911i
$590$	17.9895	−	5.31906i	0.740617	−	0.218982i
$591$	−1.93266	+	1.29136i	−0.0794990	+	0.0531195i
$592$	−7.86274	+	2.56600i	−0.323156	+	0.105462i
$593$	14.8950	+	9.95249i	0.611662	+	0.408700i	0.822454	−	0.568831i	$-0.192604\pi$
$593$	14.8950	+	9.95249i	0.611662	+	0.408700i	−0.210792	+	0.977531i	$0.567604\pi$
$594$	−3.64331	+	11.7129i	−0.149487	+	0.480587i
$595$	2.46045	−	6.87650i	0.100869	−	0.281909i
$596$	−3.92189	−	29.2731i	−0.160647	−	1.19907i
$597$	0.0295388	+	0.199135i	0.00120894	+	0.00815004i
$598$	−8.29163	+	32.1404i	−0.339070	+	1.31432i
$599$	0.0490533	+	0.498046i	0.00200426	+	0.0203496i	0.996135	−	0.0878372i	$-0.0279955\pi$
$599$	0.0490533	+	0.498046i	0.00200426	+	0.0203496i	−0.994131	+	0.108187i	$0.965496\pi$
$600$	0.0433152	+	0.341559i	0.00176834	+	0.0139441i
$601$	−6.18747	+	5.07792i	−0.252392	+	0.207133i	−0.752078	−	0.659074i	$-0.770949\pi$
$601$	−6.18747	+	5.07792i	−0.252392	+	0.207133i	0.499686	+	0.866206i	$0.333449\pi$
$602$	−38.3939	+	41.7664i	−1.56482	+	1.70227i
$603$	11.3100	−	4.04678i	0.460578	−	0.164798i
$604$	15.2598	−	1.28631i	0.620913	−	0.0523392i
$605$	−17.6420	+	29.4339i	−0.717250	+	1.19666i
$606$	−0.903469	−	1.37296i	−0.0367009	−	0.0557728i
$607$	−1.44093	−	3.47871i	−0.0584855	−	0.141196i	0.891935	−	0.452163i	$-0.149347\pi$
$607$	−1.44093	−	3.47871i	−0.0584855	−	0.141196i	−0.950421	+	0.310966i	$0.899347\pi$
$608$	0.0909121	+	6.54546i	0.00368697	+	0.265453i
$609$	0.572338	−	1.38175i	0.0231923	−	0.0559912i
$610$	6.09538	−	1.16790i	0.246795	−	0.0472869i
$611$	−17.5680	−	70.1355i	−0.710727	−	2.83738i
$612$	4.54570	−	3.62467i	0.183749	−	0.146519i
$613$	−37.5894	−	17.7785i	−1.51822	−	0.718065i	−0.526949	−	0.849897i	$-0.676664\pi$
$613$	−37.5894	−	17.7785i	−1.51822	−	0.718065i	−0.991272	+	0.131832i	$0.957914\pi$
$614$	1.12752	−	3.08263i	0.0455032	−	0.124405i
$615$	−0.168907	+	1.71494i	−0.00681097	+	0.0691529i
$616$	−20.6277	−	46.1085i	−0.831113	−	1.85776i
$617$	21.8878	−	26.6703i	0.881168	−	1.07371i	−0.115594	−	0.993297i	$-0.536877\pi$
$617$	21.8878	−	26.6703i	0.881168	−	1.07371i	0.996762	−	0.0804096i	$-0.0256228\pi$
$618$	−0.842409	+	1.11930i	−0.0338866	+	0.0450249i
$619$	−36.6647	−	27.1924i	−1.47368	−	1.09295i	−0.973948	−	0.226771i	$-0.927183\pi$
$619$	−36.6647	−	27.1924i	−1.47368	−	1.09295i	−0.499729	−	0.866182i	$-0.666567\pi$
$620$	−4.20890	−	12.3066i	−0.169033	−	0.494247i
$621$	5.89127	−	2.78636i	0.236409	−	0.111813i
$622$	−36.3665	+	3.32347i	−1.45816	+	0.133259i
$623$	54.6398	−	10.8685i	2.18910	−	0.435439i
$624$	5.34870	−	4.14314i	0.214119	−	0.165858i
$625$	−22.2169	−	4.41922i	−0.888677	−	0.176769i
$626$	−2.89338	+	27.3982i	−0.115643	+	1.09505i
$627$	−1.25612	−	1.13848i	−0.0501644	−	0.0454664i
$628$	−22.4814	+	36.3377i	−0.897104	+	1.45003i
$629$	−1.76521	+	1.05802i	−0.0703834	+	0.0421862i
$630$	28.6083	−	10.0096i	1.13978	−	0.398793i
$631$	−10.9463	+	36.0850i	−0.435764	+	1.43652i	0.414444	+	0.910075i	$0.363976\pi$
$631$	−10.9463	+	36.0850i	−0.435764	+	1.43652i	−0.850208	+	0.526447i	$0.823524\pi$
$632$	−11.4601	+	16.3910i	−0.455858	+	0.652000i
$633$	1.31879	−	2.46728i	0.0524171	−	0.0980655i
$634$	45.7152	−	11.1097i	1.81558	−	0.441221i
$635$	0.984345	−	20.0368i	0.0390625	−	0.795136i
$636$	3.82444	−	1.52141i	0.151649	−	0.0603279i
$637$	28.4427	+	4.21907i	1.12694	+	0.167166i
$638$	10.5418	−	4.27986i	0.417353	−	0.169441i
$639$		−	3.21341i		−	0.127121i
$640$	7.01470	+	23.1403i	0.277280	+	0.914700i
$641$		−	27.6549i		−	1.09230i	−0.837686	−	0.546152i	$-0.816092\pi$
$641$		−	27.6549i		−	1.09230i	0.837686	−	0.546152i	$-0.183908\pi$
$642$	−2.11864	−	5.21846i	−0.0836161	−	0.205956i
$643$	−21.1147	−	3.13207i	−0.832683	−	0.123517i	−0.283241	−	0.959049i	$-0.591410\pi$
$643$	−21.1147	−	3.13207i	−0.832683	−	0.123517i	−0.549442	+	0.835532i	$0.685160\pi$
$644$	−10.6179	+	24.6465i	−0.418403	+	0.971209i
$645$	−0.345098	+	7.02464i	−0.0135882	+	0.276595i
$646$	0.384642	+	1.58277i	0.0151335	+	0.0622732i
$647$	−17.3598	+	32.4779i	−0.682484	+	1.27684i	0.267204	+	0.963640i	$0.413900\pi$
$647$	−17.3598	+	32.4779i	−0.682484	+	1.27684i	−0.949688	+	0.313198i	$0.898600\pi$
$648$	22.9020	+	5.06050i	0.899675	+	0.198795i
$649$	9.37150	−	30.8937i	0.367864	−	1.21268i
$650$	−1.21227	−	3.46478i	−0.0475493	−	0.135900i
$651$	−2.52373	+	1.51267i	−0.0989128	+	0.0592861i
$652$	−18.2528	+	4.29991i	−0.714833	+	0.168397i
$653$	6.70736	+	6.07920i	0.262479	+	0.237897i	0.792180	−	0.610287i	$-0.208946\pi$
$653$	6.70736	+	6.07920i	0.262479	+	0.237897i	−0.529701	+	0.848184i	$0.677696\pi$
$654$	−7.77719	−	0.821306i	−0.304112	−	0.0321156i
$655$	−6.96309	−	1.38504i	−0.272070	−	0.0541182i
$656$	−0.801110	−	11.4232i	−0.0312781	−	0.446000i
$657$	34.2217	−	6.80711i	1.33511	−	0.265571i
$658$	−5.32007	−	58.2141i	−0.207398	−	2.26942i
$659$	−5.70494	+	2.69824i	−0.222233	+	0.105108i	−0.535429	−	0.844580i	$-0.679850\pi$
$659$	−5.70494	+	2.69824i	−0.222233	+	0.105108i	0.313196	+	0.949688i	$0.398600\pi$
$660$	−5.62257	−	2.75680i	−0.218858	−	0.107308i
$661$	−8.46132	−	6.27534i	−0.329107	−	0.244083i	0.418510	−	0.908212i	$-0.362552\pi$
$661$	−8.46132	−	6.27534i	−0.329107	−	0.244083i	−0.747618	+	0.664129i	$0.768802\pi$
$662$	8.04006	+	6.05111i	0.312486	+	0.235183i
$663$	1.06798	−	1.30134i	0.0414770	−	0.0505399i
$664$	0.727585	+	26.0081i	0.0282358	+	1.00931i
$665$	−0.832302	+	8.45050i	−0.0322753	+	0.327696i
$666$	−8.02091	−	2.93378i	−0.310804	−	0.113682i
$667$	−5.46430	−	2.58442i	−0.211579	−	0.100069i
$668$	−13.0063	−	1.46618i	−0.503231	−	0.0567283i
$669$	0.925274	+	3.69390i	0.0357732	+	0.142815i
$670$	2.33928	+	12.2089i	0.0903743	+	0.471672i
$671$	4.08729	−	9.86759i	0.157788	−	0.380934i
$672$	4.78789	−	2.64532i	0.184697	−	0.102045i
$673$	5.64658	+	13.6320i	0.217659	+	0.525476i	0.994562	−	0.104144i	$-0.0332103\pi$
$673$	5.64658	+	13.6320i	0.217659	+	0.525476i	−0.776903	+	0.629621i	$0.783210\pi$
$674$	−27.1022	+	17.8345i	−1.04394	+	0.686957i
$675$	−0.370516	+	0.618168i	−0.0142612	+	0.0237933i
$676$	−29.7656	+	35.2456i	−1.14483	+	1.35560i
$677$	−26.5105	+	9.48560i	−1.01888	+	0.364561i	−0.792757	−	0.609537i	$-0.791355\pi$
$677$	−26.5105	+	9.48560i	−1.01888	+	0.364561i	−0.226123	+	0.974099i	$0.572605\pi$
$678$	4.13634	+	3.80234i	0.158855	+	0.146028i
$679$	40.5614	−	33.2879i	1.55660	−	1.27747i
$680$	2.98350	+	5.22481i	0.114412	+	0.200362i
$681$	−0.504469	−	5.12196i	−0.0193313	−	0.196274i
$682$	−21.6737	−	5.59143i	−0.829930	−	0.214107i
$683$	0.410643	+	2.76833i	0.0157128	+	0.105927i	0.995614	−	0.0935564i	$-0.0298236\pi$
$683$	0.410643	+	2.76833i	0.0157128	+	0.105927i	−0.979901	+	0.199484i	$0.936074\pi$
$684$	−4.10273	+	5.37213i	−0.156872	+	0.205408i
$685$	−12.2974	+	34.3689i	−0.469860	+	1.31317i
$686$	−10.2561	−	3.19018i	−0.391581	−	0.121802i
$687$	0.716265	+	0.478593i	0.0273272	+	0.0182595i
$688$	−5.55329	−	46.4053i	−0.211717	−	1.76919i
$689$	−36.4871	+	24.3799i	−1.39005	+	0.928800i
$690$	0.943319	+	3.19039i	0.0359115	+	0.121456i
$691$	1.53475	+	31.2405i	0.0583845	+	1.18844i	0.831995	+	0.554783i	$0.187199\pi$
$691$	1.53475	+	31.2405i	0.0583845	+	1.18844i	−0.773611	+	0.633661i	$0.781551\pi$
$692$	−15.2564	+	6.95461i	−0.579962	+	0.264375i
$693$	12.6738	−	50.5966i	0.481438	−	1.92201i
$694$	2.24194	−	39.9020i	0.0851030	−	1.51466i
$695$	19.9670	−	10.6726i	0.757390	−	0.404833i
$696$	0.557723	+	1.09862i	0.0211405	+	0.0416432i
$697$	−0.827126	−	2.72667i	−0.0313296	−	0.103280i
$698$	8.18107	+	11.1948i	0.309658	+	0.423728i
$699$	0.760910	−	0.689649i	0.0287803	−	0.0260849i
$700$	−0.537951	−	2.91864i	−0.0203326	−	0.110314i
$701$	5.25906	−	3.90039i	0.198632	−	0.147316i	−0.491812	−	0.870702i	$-0.663665\pi$
$701$	5.25906	−	3.90039i	0.198632	−	0.147316i	0.690444	+	0.723386i	$0.257415\pi$
$702$	14.1621	+	0.0996995i	0.534512	+	0.00376291i
$703$	1.69193	−	1.69193i	0.0638123	−	0.0638123i
$704$	39.9025	+	11.8065i	1.50388	+	0.444973i
$705$	−5.12434	−	5.12434i	−0.192994	−	0.192994i
$706$	−5.93708	−	6.02126i	−0.223445	−	0.226613i
$707$	8.43950	+	11.3793i	0.317400	+	0.427964i
$708$	3.41895	+	0.730257i	0.128492	+	0.0274447i
$709$	−4.05564	−	4.47471i	−0.152313	−	0.168051i	0.660015	−	0.751252i	$-0.270550\pi$
$709$	−4.05564	−	4.47471i	−0.152313	−	0.168051i	−0.812328	+	0.583201i	$0.801800\pi$
$710$	3.28595	+	0.511091i	0.123319	+	0.0191809i
$711$	−19.7630	+	5.99505i	−0.741171	+	0.224832i
$712$	−22.4845	+	40.0096i	−0.842643	+	1.49942i
$713$	5.60581	+	10.4877i	0.209939	+	0.392769i
$714$	1.01491	−	0.906931i	0.0379821	−	0.0339410i
$715$	64.7627	+	16.2222i	2.42199	+	0.606676i
$716$	17.2674	−	18.5208i	0.645312	−	0.692153i
$717$	−1.46993	+	0.0722132i	−0.0548957	+	0.00269685i
$718$	12.5955	+	6.84685i	0.470059	+	0.255522i
$719$	21.0507	+	31.5046i	0.785060	+	1.17493i	0.980943	+	0.194298i	$0.0622428\pi$
$719$	21.0507	+	31.5046i	0.785060	+	1.17493i	−0.195883	+	0.980627i	$0.562757\pi$
$720$	−9.07030	+	23.2630i	−0.338030	+	0.866962i
$721$	6.70883	−	10.0405i	0.249850	−	0.373927i
$722$	11.6184	+	22.1094i	0.432391	+	0.822829i
$723$	−4.00832	−	1.43420i	−0.149071	−	0.0533384i
$724$	29.4652	−	17.1015i	1.09507	−	0.635574i
$725$	0.661236	−	0.0980851i	0.0245577	−	0.00364279i
$726$	−5.50841	+	3.24913i	−0.204436	+	0.120586i
$727$	49.0837	−	4.83432i	1.82041	−	0.179295i	0.870574	−	0.492037i	$-0.163747\pi$
$727$	49.0837	−	4.83432i	1.82041	−	0.179295i	0.949838	+	0.312742i	$0.101247\pi$
$728$	−44.0295	+	38.2438i	−1.63184	+	1.41741i
$729$	14.4708	+	17.6327i	0.535956	+	0.653064i
$730$	1.51784	+	36.0768i	0.0561777	+	1.33526i
$731$	−3.91776	−	10.9494i	−0.144904	−	0.404979i
$732$	1.10198	+	0.351299i	0.0407303	+	0.0129844i
$733$	17.0741	+	10.2338i	0.630646	+	0.377995i	0.793425	−	0.608668i	$-0.208296\pi$
$733$	17.0741	+	10.2338i	0.630646	+	0.377995i	−0.162779	+	0.986663i	$0.552046\pi$
$734$	5.86432	−	28.4343i	0.216456	−	1.04953i
$735$	2.66264	−	1.10290i	0.0982130	−	0.0406812i
$736$	−9.72906	−	19.8522i	−0.358618	−	0.731763i
$737$	19.7646	+	8.18675i	0.728037	+	0.301563i
$738$	6.63851	−	9.78540i	0.244367	−	0.360206i
$739$	−17.0803	+	4.27839i	−0.628308	+	0.157383i	−0.544039	−	0.839060i	$-0.683106\pi$
$739$	−17.0803	+	4.27839i	−0.628308	+	0.157383i	−0.0842692	+	0.996443i	$0.526856\pi$
$740$	4.27572	−	7.73534i	0.157179	−	0.284357i
$741$	−0.836854	+	1.76938i	−0.0307426	+	0.0649998i
$742$	−32.1788	+	14.9432i	−1.18132	+	0.548581i
$743$	36.0294	+	3.54859i	1.32179	+	0.130185i	0.734178	−	0.678957i	$-0.237568\pi$
$743$	36.0294	+	3.54859i	1.32179	+	0.130185i	0.587613	+	0.809142i	$0.300068\pi$
$744$	0.406219	−	2.38965i	0.0148927	−	0.0876088i
$745$	24.3973	+	20.0223i	0.893846	+	0.733561i
$746$	−3.96514	−	28.0919i	−0.145174	−	1.02852i
$747$	−16.0046	+	21.5797i	−0.585577	+	0.789559i
$748$	10.3336	+	0.653613i	0.377834	+	0.0238984i
$749$	20.7573	+	43.8875i	0.758453	+	1.60362i
$750$	−3.55387	−	2.95870i	−0.129769	−	0.108036i
$751$	−1.26185	−	6.34373i	−0.0460455	−	0.231486i	0.950909	−	0.309470i	$-0.100152\pi$
$751$	−1.26185	−	6.34373i	−0.0460455	−	0.231486i	−0.996955	+	0.0779840i	$0.975152\pi$
$752$	39.2720	+	27.8714i	1.43210	+	1.01637i
$753$	−0.00389035	+	0.0195581i	−0.000141772	+	0.000712738i
$754$	−8.26169	−	10.2127i	−0.300873	−	0.371923i
$755$	−10.9899	+	12.1255i	−0.399964	+	0.441292i
$756$	11.3016	+	1.83941i	0.411036	+	0.0668988i
$757$	−6.48991	−	10.8278i	−0.235880	−	0.393542i	0.716913	−	0.697163i	$-0.245554\pi$
$757$	−6.48991	−	10.8278i	−0.235880	−	0.393542i	−0.952793	+	0.303621i	$0.901804\pi$
$758$	−23.4958	−	11.3158i	−0.853405	−	0.411007i
$759$	5.47890	+	1.66201i	0.198871	+	0.0603270i
$760$	−4.84085	−	5.04977i	−0.175596	−	0.183174i
$761$	9.32027	+	4.98179i	0.337859	+	0.180590i	0.631598	−	0.775296i	$-0.282399\pi$
$761$	9.32027	+	4.98179i	0.337859	+	0.180590i	−0.293738	+	0.955886i	$0.594899\pi$
$762$	1.94457	−	3.19312i	0.0704442	−	0.115674i
$763$	67.3305	+	3.30774i	2.43753	+	0.119748i
$764$	−19.2706	−	0.271339i	−0.697184	−	0.00981671i
$765$	−0.911617	+	6.14563i	−0.0329596	+	0.222196i
$766$	1.58544	+	0.669826i	0.0572844	+	0.0242018i
$767$	−37.2737			−1.34588
$768$	−0.911068	+	4.41323i	−0.0328753	+	0.159249i
$769$	6.45504			0.232775			0.116387	−	0.993204i	$-0.462869\pi$
$769$	6.45504			0.232775			0.116387	+	0.993204i	$0.462869\pi$
$770$	49.7230	+	21.0072i	1.79189	+	0.757048i
$771$	−0.272306	+	1.83574i	−0.00980685	+	0.0661124i
$772$	−0.400897	+	28.4718i	−0.0144286	+	1.02472i
$773$	−0.275675	−	0.0135430i	−0.00991533	−	0.000487109i	0.0441094	−	0.999027i	$-0.485955\pi$
$773$	−0.275675	−	0.0135430i	−0.00991533	−	0.000487109i	−0.0540247	+	0.998540i	$0.517205\pi$
$774$	25.1018	−	41.2189i	0.902264	−	1.48158i
$775$	−1.15983	−	0.619940i	−0.0416622	−	0.0222689i
$776$	−0.912858	+	43.2173i	−0.0327697	+	1.55141i
$777$	−1.91334	−	0.580405i	−0.0686407	−	0.0208219i
$778$	0.735583	+	0.354263i	0.0263719	+	0.0127009i
$779$	1.70314	+	2.84151i	0.0610212	+	0.101808i
$780$	−1.16143	+	7.13603i	−0.0415860	+	0.255511i
$781$	3.84327	−	4.24040i	0.137523	−	0.151733i
$782$	−3.45981	−	4.27683i	−0.123722	−	0.152939i
$783$	−0.503155	+	2.52953i	−0.0179813	+	0.0903981i
$784$	−16.2172	+	10.1875i	−0.579187	+	0.363839i
$785$	−8.90821	−	44.7846i	−0.317948	−	1.59843i
$786$	−1.01683	−	0.846537i	−0.0362690	−	0.0301950i
$787$	−13.4881	−	28.5181i	−0.480798	−	1.01656i	−0.987960	−	0.154711i	$-0.950555\pi$
$787$	−13.4881	−	28.5181i	−0.480798	−	1.01656i	0.507162	−	0.861851i	$-0.330695\pi$
$788$	−1.04194	+	16.4730i	−0.0371175	+	0.586827i
$789$	4.97676	−	6.71038i	0.177177	−	0.238896i
$790$	−2.98708	−	21.1626i	−0.106275	−	0.752933i
$791$	−37.4375	−	30.7241i	−1.33112	−	1.09243i
$792$	24.8625	+	35.0465i	0.883450	+	1.24532i
$793$	−12.2720	−	1.20869i	−0.435793	−	0.0429219i
$794$	−27.0018	+	12.5391i	−0.958260	+	0.444995i
$795$	−1.88055	+	3.97609i	−0.0666963	+	0.141017i
$796$	1.25115	+	0.691576i	0.0443459	+	0.0245123i
$797$	−0.689179	+	0.172630i	−0.0244120	+	0.00611488i	−0.255167	−	0.966897i	$-0.582130\pi$
$797$	−0.689179	+	0.172630i	−0.0244120	+	0.00611488i	0.230755	+	0.973012i	$0.425880\pi$
$798$	−0.888422	+	1.30957i	−0.0314498	+	0.0463581i
$799$	11.0706	+	4.58559i	0.391650	+	0.162227i
$800$	2.11432	+	1.22769i	0.0747524	+	0.0434053i
$801$	−43.7840	+	18.1359i	−1.54703	+	0.640802i
$802$	−7.30675	+	35.4282i	−0.258010	+	1.25101i
$803$	53.3000	+	31.9468i	1.88092	+	1.12738i
$804$	−0.703644	+	2.20724i	−0.0248156	+	0.0778434i
$805$	−9.66129	−	27.0015i	−0.340516	−	0.951678i
$806$	1.08632	+	25.8202i	0.0382638	+	0.909476i
$807$	−0.896963	−	1.09295i	−0.0315746	−	0.0384737i
$808$	−11.6425	−	0.818726i	−0.409581	−	0.0288027i
$809$	33.8716	−	3.33606i	1.19086	−	0.117290i	0.516894	−	0.856050i	$-0.327088\pi$
$809$	33.8716	−	3.33606i	1.19086	−	0.117290i	0.673969	+	0.738760i	$0.264588\pi$
$810$	−21.5882	+	12.7337i	−0.758531	+	0.447418i
$811$	18.0771	−	2.68149i	0.634774	−	0.0941598i	0.178414	−	0.983955i	$-0.442903\pi$
$811$	18.0771	−	2.68149i	0.634774	−	0.0941598i	0.456359	+	0.889796i	$0.349153\pi$
$812$	−5.33122	−	9.18546i	−0.187089	−	0.322346i
$813$	−7.29062	−	2.60862i	−0.255693	−	0.0914884i
$814$	−7.07550	−	13.4645i	−0.247996	−	0.471930i
$815$	11.1332	−	16.6620i	0.389978	−	0.583644i
$816$	0.0234647	+	1.12103i	0.000821429	+	0.0392441i
$817$	7.51175	+	11.2421i	0.262803	+	0.393312i
$818$	−29.1698	−	15.8566i	−1.01990	−	0.554413i
$819$	−60.1492	+	2.95494i	−2.10178	+	0.103254i
$820$	8.95043	+	8.34472i	0.312563	+	0.291410i
$821$	3.45019	+	0.864228i	0.120412	+	0.0301618i	0.302718	−	0.953080i	$-0.402106\pi$
$821$	3.45019	+	0.864228i	0.120412	+	0.0301618i	−0.182305	+	0.983242i	$0.558356\pi$
$822$	−5.07256	+	4.53287i	−0.176926	+	0.158102i
$823$	13.6065	+	25.4560i	0.474293	+	0.887340i	0.999342	+	0.0362680i	$0.0115470\pi$
$823$	13.6065	+	25.4560i	0.474293	+	0.887340i	−0.525049	+	0.851072i	$0.675953\pi$
$824$	2.68607	+	9.57848i	0.0935736	+	0.333682i
$825$	−0.605905	+	0.183799i	−0.0210949	+	0.00639907i
$826$	−29.7779	−	4.63160i	−1.03610	−	0.161154i
$827$	−33.0781	−	36.4960i	−1.15024	−	1.26909i	−0.957689	−	0.287804i	$-0.907075\pi$
$827$	−33.0781	−	36.4960i	−1.15024	−	1.26909i	−0.192549	−	0.981287i	$-0.561675\pi$
$828$	4.76854	−	22.3255i	0.165718	−	0.775866i
$829$	10.0412	+	13.5390i	0.348745	+	0.470228i	0.942398	−	0.334493i	$-0.108565\pi$
$829$	10.0412	+	13.5390i	0.348745	+	0.470228i	−0.593653	+	0.804721i	$0.702315\pi$
$830$	−19.5213	−	19.7981i	−0.677593	−	0.687201i
$831$	3.33317	+	3.33317i	0.115626	+	0.115626i
$832$	−0.329036	−	48.0432i	−0.0114073	−	1.66560i
$833$	−3.36965	+	3.36965i	−0.116752	+	0.116752i
$834$	4.21922	+	0.0297029i	0.146099	+	0.00102853i
$835$	11.2344	−	8.33198i	0.388781	−	0.288340i
$836$	−11.8390	+	2.18212i	−0.409462	+	0.0754702i
$837$	3.75955	−	3.40746i	0.129949	−	0.117779i
$838$	−2.47018	−	3.38013i	−0.0853310	−	0.116765i
$839$	−4.50946	−	14.8657i	−0.155684	−	0.513221i	0.844051	−	0.536264i	$-0.180165\pi$
$839$	−4.50946	−	14.8657i	−0.155684	−	0.513221i	−0.999734	+	0.0230424i	$0.992665\pi$
$840$	−1.81458	+	5.55663i	−0.0626091	+	0.191722i
$841$	−23.4660	+	12.5428i	−0.809173	+	0.432512i
$842$	−1.77901	+	31.6628i	−0.0613088	+	1.09117i
$843$	−0.00734569	+	0.0293256i	−0.000252999	+	0.00101003i
$844$	−8.24029	−	18.0768i	−0.283643	−	0.622230i
$845$	−2.41897	−	49.2392i	−0.0832149	−	1.69388i
$846$	14.0999	+	47.6870i	0.484763	+	1.63951i
$847$	45.8363	−	30.6268i	1.57495	−	1.05235i
$848$	7.89731	−	28.1410i	0.271195	−	0.966366i
$849$	3.01277	+	2.01307i	0.103398	+	0.0690882i
$850$	0.580902	+	0.180690i	0.0199248	+	0.00619761i
$851$	−2.72241	+	7.60863i	−0.0933230	+	0.260820i
$852$	0.492535	+	0.376152i	0.0168740	+	0.0128868i
$853$	0.536011	+	3.61350i	0.0183527	+	0.123724i	0.996417	−	0.0845814i	$-0.0269553\pi$
$853$	0.536011	+	3.61350i	0.0183527	+	0.123724i	−0.978064	+	0.208305i	$0.933205\pi$
$854$	−9.65391	−	2.49053i	−0.330350	−	0.0852243i
$855$	−0.708021	−	7.18866i	−0.0242138	−	0.245847i
$856$	−38.5824	−	10.5351i	−1.31872	−	0.360082i
$857$	21.2119	−	17.4081i	0.724583	−	0.594650i	−0.198113	−	0.980179i	$-0.563481\pi$
$857$	21.2119	−	17.4081i	0.724583	−	0.594650i	0.922696	+	0.385529i	$0.125981\pi$
$858$	9.16006	+	8.42041i	0.312719	+	0.287468i
$859$	2.64684	−	0.947056i	0.0903092	−	0.0323131i	−0.291348	−	0.956617i	$-0.594104\pi$
$859$	2.64684	−	0.947056i	0.0903092	−	0.0323131i	0.381657	+	0.924304i	$0.375354\pi$
$860$	38.1569	+	32.2242i	1.30114	+	1.09884i
$861$	1.42318	−	2.37443i	0.0485018	−	0.0809203i
$862$	19.0320	−	12.5239i	0.648234	−	0.426566i
$863$	15.4612	+	37.3267i	0.526307	+	1.27062i	0.933927	+	0.357465i	$0.116359\pi$
$863$	15.4612	+	37.3267i	0.526307	+	1.27062i	−0.407620	+	0.913152i	$0.633641\pi$
$864$	−7.20792	+	6.08486i	−0.245218	+	0.207011i
$865$	6.85666	−	16.5534i	0.233134	−	0.562834i
$866$	−5.51418	−	28.7790i	−0.187379	−	0.977950i
$867$	−1.09558	−	4.37380i	−0.0372078	−	0.148542i
$868$	−2.34053	+	20.7626i	−0.0794429	+	0.704730i
$869$	−33.2493	−	15.7257i	−1.12790	−	0.533459i
$870$	−1.23651	−	0.452275i	−0.0419216	−	0.0153335i
$871$	2.42098	−	24.5806i	0.0820319	−	0.832883i
$872$	−38.1553	+	40.3515i	−1.29210	+	1.36647i
$873$	−28.3173	+	34.5047i	−0.958395	+	1.16781i
$874$	5.11024	+	3.84607i	0.172856	+	0.130095i
$875$	32.0166	+	23.7451i	1.08236	+	0.802732i
$876$	−2.96253	+	6.04214i	−0.100094	+	0.204145i
$877$	−11.6992	+	5.53330i	−0.395053	+	0.186846i	−0.614750	−	0.788722i	$-0.710743\pi$
$877$	−11.6992	+	5.53330i	−0.395053	+	0.186846i	0.219697	+	0.975568i	$0.429493\pi$
$878$	−1.02644	−	11.2317i	−0.0346408	−	0.379052i
$879$	−8.20428	+	1.63193i	−0.276724	+	0.0550438i
$880$	−39.7919	+	19.8496i	−1.34139	+	0.669129i
$881$	18.8559	+	3.75067i	0.635272	+	0.126363i	0.502212	−	0.864745i	$-0.332520\pi$
$881$	18.8559	+	3.75067i	0.635272	+	0.126363i	0.133060	+	0.991108i	$0.457520\pi$
$882$	−19.6669	−	2.07691i	−0.662218	−	0.0699332i
$883$	23.2743	+	21.0946i	0.783242	+	0.709889i	0.961714	−	0.274056i	$-0.0883654\pi$
$883$	23.2743	+	21.0946i	0.783242	+	0.709889i	−0.178472	+	0.983945i	$0.557115\pi$
$884$	−2.74119	−	11.6361i	−0.0921962	−	0.391365i
$885$	−3.20445	+	1.92067i	−0.107716	+	0.0645627i
$886$	15.3813	+	43.9611i	0.516745	+	1.47690i
$887$	11.8002	−	38.9000i	0.396212	−	1.30614i	−0.501349	−	0.865245i	$-0.667163\pi$
$887$	11.8002	−	38.9000i	0.396212	−	1.30614i	0.897561	−	0.440891i	$-0.145337\pi$
$888$	1.38858	−	0.885983i	0.0465976	−	0.0297317i
$889$	−15.1916	+	28.4215i	−0.509510	+	0.953226i
$890$	−11.5815	−	47.6569i	−0.388213	−	1.59746i
$891$	−2.11646	+	43.0814i	−0.0709039	+	1.44328i
$892$	24.8349	+	10.6991i	0.831535	+	0.358231i
$893$	−13.7810	−	2.04422i	−0.461164	−	0.0684073i
$894$	2.21259	+	5.44986i	0.0740000	+	0.182271i
$895$			27.0591i			0.904487i
$896$	5.70693	−	38.4224i	0.190655	−	1.28360i
$897$		−	6.61037i		−	0.220714i
$898$	−5.24167	+	2.12806i	−0.174917	+	0.0710144i
$899$	−4.65528	−	0.690545i	−0.155262	−	0.0230310i
$900$	0.933205	+	2.34584i	0.0311068	+	0.0781946i
$901$	0.356855	−	7.26395i	0.0118886	−	0.241997i
$902$	20.4636	−	4.97303i	0.681362	−	0.165584i
$903$	5.32597	−	9.96419i	0.177237	−	0.331588i
$904$	39.2867	−	6.95556i	1.30666	−	0.231338i
$905$	−10.5682	+	34.8386i	−0.351298	+	1.15807i
$906$	−2.87868	+	1.00720i	−0.0956376	+	0.0334621i
$907$	18.4649	−	11.0674i	0.613118	−	0.367489i	−0.173587	−	0.984819i	$-0.555536\pi$
$907$	18.4649	−	11.0674i	0.613118	−	0.367489i	0.786704	+	0.617330i	$0.211786\pi$
$908$	−31.0806	−	19.2289i	−1.03145	−	0.638134i
$909$	−8.92986	−	8.09355i	−0.296185	−	0.268446i
$910$	6.54504	−	61.9769i	0.216966	−	2.05452i
$911$	−4.18993	−	0.833428i	−0.138818	−	0.0276127i	0.125192	−	0.992133i	$-0.460045\pi$
$911$	−4.18993	−	0.833428i	−0.138818	−	0.0276127i	−0.264010	+	0.964520i	$0.585045\pi$
$912$	−0.343159	−	1.25769i	−0.0113631	−	0.0416463i
$913$	−46.9290	+	9.33476i	−1.55312	+	0.308935i
$914$	44.5584	−	4.07211i	1.47386	−	0.134693i
$915$	−1.11732	+	0.528453i	−0.0369374	+	0.0174701i
$916$	5.78813	−	1.97955i	0.191245	−	0.0654063i
$917$	9.16053	+	6.79391i	0.302507	+	0.224355i
$918$	−1.41143	+	1.87536i	−0.0465842	+	0.0618960i
$919$	−7.06905	+	8.61367i	−0.233187	+	0.284139i	−0.876436	−	0.481518i	$-0.840086\pi$
$919$	−7.06905	+	8.61367i	−0.233187	+	0.284139i	0.643250	+	0.765656i	$0.277586\pi$
$920$	22.0710	+	8.42703i	0.727661	+	0.277831i
$921$	−0.0640726	+	0.650540i	−0.00211126	+	0.0214360i
$922$	0.520591	−	1.42329i	0.0171447	−	0.0468734i
$923$	−5.97308	−	2.82505i	−0.196606	−	0.0929878i
$924$	6.27163	+	7.86526i	0.206322	+	0.258748i
$925$	−0.217144	−	0.866887i	−0.00713965	−	0.0285031i
$926$	24.6731	−	4.72747i	0.810809	−	0.155354i
$927$	−3.93109	+	9.49049i	−0.129114	+	0.311709i
$928$	8.60401	+	1.58755i	0.282441	+	0.0521140i
$929$	7.77882	+	18.7797i	0.255215	+	0.616143i	0.998610	−	0.0527097i	$-0.0167858\pi$
$929$	7.77882	+	18.7797i	0.255215	+	0.616143i	−0.743395	+	0.668852i	$0.766786\pi$
$930$	1.42387	+	2.16380i	0.0466907	+	0.0709538i
$931$	2.84841	−	4.75228i	0.0933528	−	0.155750i
$932$	−0.612540	−	7.26670i	−0.0200644	−	0.238029i
$933$	6.84750	−	2.45008i	0.224177	−	0.0802119i
$934$	−34.5135	+	37.5452i	−1.12932	+	1.22852i
$935$	−8.55319	+	7.01942i	−0.279719	+	0.229560i
$936$	30.3883	−	39.2151i	0.993273	−	1.28179i
$937$	5.39406	+	54.7668i	0.176216	+	1.78915i	0.524141	+	0.851632i	$0.324387\pi$
$937$	5.39406	+	54.7668i	0.176216	+	1.78915i	−0.347925	+	0.937523i	$0.613113\pi$
$938$	4.98848	−	19.3366i	0.162880	−	0.631362i
$939$	−0.805072	−	5.42736i	−0.0262725	−	0.177115i
$940$	−51.0060	+	6.83356i	−1.66363	+	0.222886i
$941$	11.6489	−	32.5565i	0.379743	−	1.06131i	−0.587888	−	0.808942i	$-0.700041\pi$
$941$	11.6489	−	32.5565i	0.379743	−	1.06131i	0.967631	−	0.252368i	$-0.0812094\pi$
$942$	2.52751	−	8.12570i	0.0823506	−	0.264750i
$943$	−9.30281	−	6.21594i	−0.302941	−	0.202419i
$944$	18.8572	−	16.1478i	0.613748	−	0.525565i
$945$	−10.1739	+	6.79800i	−0.330958	+	0.221139i
$946$	82.4223	−	24.3702i	2.67978	−	0.792345i
$947$	0.856641	+	17.4373i	0.0278371	+	0.566637i	0.971688	+	0.236266i	$0.0759238\pi$
$947$	0.856641	+	17.4373i	0.0278371	+	0.566637i	−0.943851	+	0.330371i	$0.892826\pi$
$948$	1.39451	−	3.73094i	0.0452916	−	0.121175i
$949$	17.4328	−	69.5955i	0.565891	−	2.25917i
$950$	−0.706195	−	0.0396784i	−0.0229120	−	0.00128734i
$951$	−8.26294	+	4.41663i	−0.267944	+	0.143219i
$952$	−0.744032	−	9.63669i	−0.0241142	−	0.312327i
$953$	1.98156	+	6.53234i	0.0641892	+	0.211603i	0.983168	−	0.182703i	$-0.0584848\pi$
$953$	1.98156	+	6.53234i	0.0641892	+	0.211603i	−0.918979	+	0.394307i	$0.870985\pi$
$954$	24.3679	−	17.8079i	0.788940	−	0.576553i
$955$	15.2599	−	13.8307i	0.493797	−	0.447552i
$956$	−5.92796	+	8.60697i	−0.191724	+	0.278369i
$957$	−1.81994	+	1.34976i	−0.0588302	+	0.0436315i
$958$	0.170680	−	24.2447i	0.00551443	−	0.783310i
$959$	41.4644	−	41.4644i	1.33896	−	1.33896i
$960$	−2.50390	−	4.11335i	−0.0808129	−	0.132758i
$961$	−15.3734	−	15.3734i	−0.495916	−	0.495916i
$962$	−12.5048	+	12.3300i	−0.403172	+	0.397535i
$963$	−24.6020	−	33.1719i	−0.792788	−	1.06895i
$964$	−25.3701	+	16.4399i	−0.817117	+	0.529493i
$965$	−20.4346	−	22.5461i	−0.657812	−	0.725784i
$966$	0.821399	−	5.28101i	0.0264281	−	0.169914i
$967$	30.3207	−	9.19767i	0.975047	−	0.295777i	0.237735	−	0.971330i	$-0.423595\pi$
$967$	30.3207	−	9.19767i	0.975047	−	0.295777i	0.737312	+	0.675553i	$0.236095\pi$
$968$	−5.40478	+	45.0913i	−0.173716	+	1.44929i
$969$	−0.152914	−	0.286082i	−0.00491231	−	0.00919029i
$970$	−30.7797	−	34.4444i	−0.988278	−	1.10594i
$971$	21.5745	+	5.40413i	0.692359	+	0.173427i	0.573160	−	0.819443i	$-0.305717\pi$
$971$	21.5745	+	5.40413i	0.692359	+	0.173427i	0.119199	+	0.992870i	$0.461967\pi$
$972$	−14.6671	+	0.513673i	−0.470447	+	0.0164761i
$973$	−36.3265	+	1.78461i	−1.16457	+	0.0572118i
$974$	12.1778	−	22.4022i	0.390200	−	0.717813i
$975$	0.406140	+	0.607832i	0.0130069	+	0.0194662i
$976$	6.73218	−	4.70502i	0.215492	−	0.150604i
$977$	−14.8599	+	22.2394i	−0.475409	+	0.711501i	−0.989225	−	0.146400i	$-0.953231\pi$
$977$	−14.8599	+	22.2394i	−0.475409	+	0.711501i	0.513816	+	0.857900i	$0.328231\pi$
$978$	3.30591	−	1.73723i	0.105711	−	0.0555506i
$979$	−79.4679	−	28.4341i	−2.53980	−	0.908757i
$980$	5.25179	−	19.7805i	0.167762	−	0.631864i
$981$	−56.7250	+	8.41436i	−1.81109	+	0.268650i
$982$	8.67260	+	14.7031i	0.276754	+	0.469195i
$983$	19.0250	−	1.87380i	0.606804	−	0.0597650i	0.210051	−	0.977690i	$-0.432637\pi$
$983$	19.0250	−	1.87380i	0.606804	−	0.0597650i	0.396753	+	0.917925i	$0.370137\pi$
$984$	0.722772	+	2.16297i	0.0230411	+	0.0689528i
$985$	−11.1898	−	13.6348i	−0.356537	−	0.434441i
$986$	2.17511	−	0.0915123i	0.0692697	−	0.00291434i
$987$	3.92198	+	10.9612i	0.124838	+	0.348899i
$988$	6.37879	+	12.3490i	0.202936	+	0.392874i
$989$	−39.1670	−	23.4758i	−1.24544	−	0.746487i
$990$	−44.9718	−	9.27504i	−1.42930	−	0.294780i
$991$	4.69205	−	1.94351i	0.149048	−	0.0617376i	−0.306913	−	0.951738i	$-0.599296\pi$
$991$	4.69205	−	1.94351i	0.149048	−	0.0617376i	0.455960	+	0.890000i	$0.349296\pi$
$992$	−11.7354	−	12.5921i	−0.372600	−	0.399798i
$993$	−1.85146	−	0.766901i	−0.0587544	−	0.0243369i
$994$	−4.42083	−	2.99914i	−0.140220	−	0.0951268i
$995$	−1.48188	+	0.371192i	−0.0469788	+	0.0117676i
$996$	−1.43417	−	4.97915i	−0.0454435	−	0.157770i
$997$	1.87946	−	3.97378i	0.0595230	−	0.125851i	−0.872035	−	0.489443i	$-0.837200\pi$
$997$	1.87946	−	3.97378i	0.0595230	−	0.125851i	0.931558	+	0.363593i	$0.118450\pi$
$998$	−5.40411	−	11.6373i	−0.171064	−	0.368372i
$999$	3.43134	+	0.337958i	0.108563	+	0.0106925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.13	✓	992
256.205	even	64	inner	256.2.m.a.205.13	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.13	✓	992	1.1	even	1	trivial
256.2.m.a.205.13	yes	992	256.205	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)

\(f(q)\)	\(=\)	\(q+(-0.550381 + 1.30272i) q^{2} +(0.0413256 - 0.278595i) q^{3} +(-1.39416 - 1.43398i) q^{4} +(2.13467 + 0.104869i) q^{5} +(0.340186 + 0.207169i) q^{6} +(-3.02795 - 1.61847i) q^{7} +(2.63540 - 1.02697i) q^{8} +(2.79491 + 0.847828i) q^{9} +O(q^{10})\)	\(q+(-0.550381 + 1.30272i) q^{2} +(0.0413256 - 0.278595i) q^{3} +(-1.39416 - 1.43398i) q^{4} +(2.13467 + 0.104869i) q^{5} +(0.340186 + 0.207169i) q^{6} +(-3.02795 - 1.61847i) q^{7} +(2.63540 - 1.02697i) q^{8} +(2.79491 + 0.847828i) q^{9} +(-1.31149 + 2.72316i) q^{10} +(2.67414 + 4.46153i) q^{11} +(-0.457115 + 0.329146i) q^{12} +(4.03307 - 4.44981i) q^{13} +(3.77494 - 3.05379i) q^{14} +(0.117432 - 0.590373i) q^{15} +(-0.112622 + 3.99841i) q^{16} +(0.194174 + 0.976178i) q^{17} +(-2.64275 + 3.17436i) q^{18} +(-0.494765 - 1.04609i) q^{19} +(-2.82569 - 3.20728i) q^{20} +(-0.576029 + 0.776685i) q^{21} +(-7.28392 + 1.02812i) q^{22} +(3.02107 + 2.47933i) q^{23} +(-0.177198 - 0.776648i) q^{24} +(-0.430121 - 0.0423632i) q^{25} +(3.57713 + 7.70305i) q^{26} +(0.712955 - 1.50742i) q^{27} +(1.90059 + 6.59844i) q^{28} +(-1.50031 + 0.375809i) q^{29} +(0.704458 + 0.477911i) q^{30} +(2.81120 + 1.16444i) q^{31} +(-5.14683 - 2.34736i) q^{32} +(1.35347 - 0.560625i) q^{33} +(-1.37856 - 0.284315i) q^{34} +(-6.29393 - 3.77243i) q^{35} +(-2.68079 - 5.18987i) q^{36} +(0.696592 + 1.94684i) q^{37} +(1.63508 - 0.0687916i) q^{38} +(-1.07302 - 1.30748i) q^{39} +(5.73340 - 1.91586i) q^{40} +(-2.84902 + 0.280604i) q^{41} +(-0.694768 - 1.17788i) q^{42} +(-11.5576 + 1.71441i) q^{43} +(2.66958 - 10.0548i) q^{44} +(5.87730 + 2.10293i) q^{45} +(-4.89261 + 2.57104i) q^{46} +(6.68867 - 10.0103i) q^{47} +(1.10928 + 0.196613i) q^{48} +(2.66002 + 3.98099i) q^{49} +(0.291918 - 0.537011i) q^{50} +(0.279982 - 0.0137547i) q^{51} +(-12.0037 + 0.420395i) q^{52} +(-7.08805 - 1.77546i) q^{53} +(1.57135 + 1.75843i) q^{54} +(5.24052 + 9.80432i) q^{55} +(-9.64197 - 1.15572i) q^{56} +(-0.311882 + 0.0946085i) q^{57} +(0.336169 - 2.16133i) q^{58} +(-4.16807 - 4.59876i) q^{59} +(-1.01030 + 0.654679i) q^{60} +(-1.22318 - 1.64926i) q^{61} +(-3.06416 + 3.02132i) q^{62} +(-7.09066 - 7.09066i) q^{63} +(5.89068 - 5.41294i) q^{64} +(9.07591 - 9.07591i) q^{65} +(-0.0145849 + 2.07175i) q^{66} +(3.30343 - 2.44999i) q^{67} +(1.12911 - 1.63939i) q^{68} +(0.815575 - 0.739194i) q^{69} +(8.37848 - 6.12295i) q^{70} +(-0.319380 - 1.05285i) q^{71} +(8.23641 - 0.635919i) q^{72} +(10.5359 - 5.63158i) q^{73} +(-2.91958 - 0.164040i) q^{74} +(-0.0295772 + 0.118079i) q^{75} +(-0.810298 + 2.16791i) q^{76} +(-0.876290 - 17.8373i) q^{77} +(2.29386 - 0.678237i) q^{78} +(-5.87938 + 3.92847i) q^{79} +(-0.659721 + 8.52347i) q^{80} +(6.89487 + 4.60700i) q^{81} +(1.20250 - 3.86592i) q^{82} +(-3.09900 + 8.66112i) q^{83} +(1.91683 - 0.256809i) q^{84} +(0.312125 + 2.10418i) q^{85} +(4.12770 - 15.9999i) q^{86} +(0.0426969 + 0.433509i) q^{87} +(11.6293 + 9.01167i) q^{88} +(-12.5430 + 10.2938i) q^{89} +(-5.97428 + 6.49906i) q^{90} +(-19.4138 + 6.94637i) q^{91} +(-0.656545 - 7.78875i) q^{92} +(0.440580 - 0.735064i) q^{93} +(9.35931 + 14.2229i) q^{94} +(-0.946456 - 2.28495i) q^{95} +(-0.866659 + 1.33687i) q^{96} +(-5.84856 + 14.1197i) q^{97} +(-6.65014 + 1.27420i) q^{98} +(3.69138 + 14.7368i) 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

Related objects

Downloads

Learn more