LMFDB - Embedded newform 930.2.bs.a.293.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(107,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 15, 44]))

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

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

chi := DirichletCharacter("930.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			293.19
Character	$\chi$	$=$	930.293
Dual form			930.2.bs.a.857.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 + 0.453990i) q^{2} +(0.622763 - 1.61622i) q^{3} +(0.587785 - 0.809017i) q^{4} +(1.27838 - 1.83460i) q^{5} +(0.178863 + 1.72279i) q^{6} +(-0.375409 - 0.463591i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-2.22433 - 2.01304i) q^{9} +O(q^{10})$	\(q+(-0.891007 + 0.453990i) q^{2} +(0.622763 - 1.61622i) q^{3} +(0.587785 - 0.809017i) q^{4} +(1.27838 - 1.83460i) q^{5} +(0.178863 + 1.72279i) q^{6} +(-0.375409 - 0.463591i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-2.22433 - 2.01304i) q^{9} +(-0.306155 + 2.21501i) q^{10} +(-0.839446 - 1.88543i) q^{11} +(-0.941498 - 1.45382i) q^{12} +(0.837629 + 1.28984i) q^{13} +(0.544957 + 0.242631i) q^{14} +(-2.16898 - 3.20866i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.551919 - 1.43780i) q^{17} +(2.89580 + 0.783809i) q^{18} +(0.0719150 + 0.338333i) q^{19} +(-0.732808 - 2.11258i) q^{20} +(-0.983055 + 0.318035i) q^{21} +(1.60392 + 1.29883i) q^{22} +(0.617391 - 3.89805i) q^{23} +(1.49890 + 0.867928i) q^{24} +(-1.73149 - 4.69062i) q^{25} +(-1.33191 - 0.768976i) q^{26} +(-4.63875 + 2.34136i) q^{27} +(-0.595712 + 0.0312200i) q^{28} +(2.11711 - 6.51581i) q^{29} +(3.38928 + 1.87424i) q^{30} +(-3.18205 + 4.56887i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.57004 + 0.182556i) q^{33} +(1.14451 + 1.03052i) q^{34} +(-1.33042 + 0.0960782i) q^{35} +(-2.93602 + 0.616286i) q^{36} +(2.08888 + 0.559713i) q^{37} +(-0.217677 - 0.268809i) q^{38} +(2.60630 - 0.550531i) q^{39} +(1.61203 + 1.54963i) q^{40} +(-3.71846 + 3.34811i) q^{41} +(0.731524 - 0.729669i) q^{42} +(4.26508 + 2.76977i) q^{43} +(-2.01876 - 0.429100i) q^{44} +(-6.53666 + 1.50732i) q^{45} +(1.21958 + 3.75348i) q^{46} +(-1.95931 + 3.84537i) q^{47} +(-1.72956 - 0.0928433i) q^{48} +(1.38140 - 6.49896i) q^{49} +(3.67227 + 3.39329i) q^{50} +(-2.66751 - 0.00338488i) q^{51} +(1.53584 + 0.0804902i) q^{52} +(1.29507 + 1.04873i) q^{53} +(3.07020 - 4.19212i) q^{54} +(-4.53213 - 0.870246i) q^{55} +(0.516610 - 0.298265i) q^{56} +(0.591607 + 0.0944711i) q^{57} +(1.07175 + 6.76678i) q^{58} +(-2.24166 + 2.48961i) q^{59} +(-3.87076 - 0.131258i) q^{60} -8.05452 q^{61} +(0.761005 - 5.51551i) q^{62} +(-0.0981951 + 1.78689i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(3.43713 + 0.112188i) q^{65} +(3.09805 - 1.78342i) q^{66} +(1.73224 + 6.46480i) q^{67} +(-1.48761 - 0.398605i) q^{68} +(-5.91562 - 3.42540i) q^{69} +(1.14179 - 0.689603i) q^{70} +(-11.2306 + 1.18038i) q^{71} +(2.33622 - 1.88204i) q^{72} +(-0.311127 - 0.119430i) q^{73} +(-2.11531 + 0.449623i) q^{74} +(-8.65939 - 0.122674i) q^{75} +(0.315988 + 0.140687i) q^{76} +(-0.558932 + 1.09697i) q^{77} +(-2.07230 + 1.67376i) q^{78} +(6.17323 - 13.8653i) q^{79} +(-2.13985 - 0.648889i) q^{80} +(0.895313 + 8.95536i) q^{81} +(1.79316 - 4.67133i) q^{82} +(8.56129 + 0.448678i) q^{83} +(-0.320529 + 0.982245i) q^{84} +(-3.34334 - 0.825503i) q^{85} +(-5.05766 - 0.531582i) q^{86} +(-9.21252 - 7.47952i) q^{87} +(1.99353 - 0.534166i) q^{88} +(-5.96446 - 4.33343i) q^{89} +(5.13990 - 4.31062i) q^{90} +(0.283503 - 0.872532i) q^{91} +(-2.79070 - 2.79070i) q^{92} +(5.40263 + 7.98821i) q^{93} -4.31576i q^{94} +(0.712640 + 0.300583i) q^{95} +(1.58320 - 0.702480i) q^{96} +(10.0376 - 1.58980i) q^{97} +(1.71963 + 6.41776i) q^{98} +(-1.92824 + 5.88366i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) $ 1024 * q - 8 * q^3 + 24 * q^7	$ 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) $ 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	−0.891007	+	0.453990i	−0.630037	+	0.321020i
$2$	−0.891007	+	0.453990i	−0.630037	+	0.321020i
$3$	0.622763	−	1.61622i	0.359552	−	0.933125i
$3$	0.622763	−	1.61622i	0.359552	−	0.933125i
$4$	0.587785	−	0.809017i	0.293893	−	0.404508i
$5$	1.27838	−	1.83460i	0.571709	−	0.820457i
$5$	1.27838	−	1.83460i	0.571709	−	0.820457i
$6$	0.178863	+	1.72279i	0.0730204	+	0.703326i
$7$	−0.375409	−	0.463591i	−0.141891	−	0.175221i	0.701246	−	0.712919i	$-0.252627\pi$
$7$	−0.375409	−	0.463591i	−0.141891	−	0.175221i	−0.843137	+	0.537698i	$0.819294\pi$
$8$	−0.156434	+	0.987688i	−0.0553079	+	0.349201i
$9$	−2.22433	−	2.01304i	−0.741444	−	0.671014i
$10$	−0.306155	+	2.21501i	−0.0968147	+	0.700448i
$11$	−0.839446	−	1.88543i	−0.253103	−	0.568478i	0.741650	−	0.670787i	$-0.234044\pi$
$11$	−0.839446	−	1.88543i	−0.253103	−	0.568478i	−0.994753	+	0.102309i	$0.967377\pi$
$12$	−0.941498	−	1.45382i	−0.271787	−	0.419680i
$13$	0.837629	+	1.28984i	0.232316	+	0.357736i	0.935533	−	0.353240i	$-0.114920\pi$
$13$	0.837629	+	1.28984i	0.232316	+	0.357736i	−0.703216	+	0.710976i	$0.748253\pi$
$14$	0.544957	+	0.242631i	0.145646	+	0.0648458i
$15$	−2.16898	−	3.20866i	−0.560029	−	0.828473i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.551919	−	1.43780i	−0.133860	−	0.348717i	0.850224	−	0.526421i	$-0.176466\pi$
$17$	−0.551919	−	1.43780i	−0.133860	−	0.348717i	−0.984084	+	0.177704i	$0.943133\pi$
$18$	2.89580	+	0.783809i	0.682546	+	0.184745i
$19$	0.0719150	+	0.338333i	0.0164984	+	0.0776190i	0.985627	−	0.168938i	$-0.0540339\pi$
$19$	0.0719150	+	0.338333i	0.0164984	+	0.0776190i	−0.969128	+	0.246557i	$0.920701\pi$
$20$	−0.732808	−	2.11258i	−0.163861	−	0.472387i
$21$	−0.983055	+	0.318035i	−0.214520	+	0.0694010i
$22$	1.60392	+	1.29883i	0.341957	+	0.276911i
$23$	0.617391	−	3.89805i	0.128735	−	0.812800i	−0.835837	−	0.548978i	$-0.815017\pi$
$23$	0.617391	−	3.89805i	0.128735	−	0.812800i	0.964571	−	0.263822i	$-0.0849830\pi$
$24$	1.49890	+	0.867928i	0.305962	+	0.177165i
$25$	−1.73149	−	4.69062i	−0.346298	−	0.938124i
$26$	−1.33191	−	0.768976i	−0.261208	−	0.150809i
$27$	−4.63875	+	2.34136i	−0.892728	+	0.450595i
$28$	−0.595712	+	0.0312200i	−0.112579	+	0.00590002i
$29$	2.11711	−	6.51581i	0.393138	−	1.20995i	−0.537264	−	0.843414i	$-0.680542\pi$
$29$	2.11711	−	6.51581i	0.393138	−	1.20995i	0.930402	−	0.366541i	$-0.119458\pi$
$30$	3.38928	+	1.87424i	0.618795	+	0.342188i
$31$	−3.18205	+	4.56887i	−0.571513	+	0.820593i
$31$	−3.18205	+	4.56887i	−0.571513	+	0.820593i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−3.57004	+	0.182556i	−0.621464	+	0.0317789i
$34$	1.14451	+	1.03052i	0.196282	+	0.176733i
$35$	−1.33042	+	0.0960782i	−0.224882	+	0.0162402i
$36$	−2.93602	+	0.616286i	−0.489336	+	0.102714i
$37$	2.08888	+	0.559713i	0.343410	+	0.0920163i	0.426402	−	0.904534i	$-0.359781\pi$
$37$	2.08888	+	0.559713i	0.343410	+	0.0920163i	−0.0829922	+	0.996550i	$0.526448\pi$
$38$	−0.217677	−	0.268809i	−0.0353119	−	0.0436065i
$39$	2.60630	−	0.550531i	0.417342	−	0.0881555i
$40$	1.61203	+	1.54963i	0.254884	+	0.245019i
$41$	−3.71846	+	3.34811i	−0.580725	+	0.522887i	−0.906303	−	0.422628i	$-0.861108\pi$
$41$	−3.71846	+	3.34811i	−0.580725	+	0.522887i	0.325578	+	0.945515i	$0.394441\pi$
$42$	0.731524	−	0.729669i	0.112877	−	0.112590i
$43$	4.26508	+	2.76977i	0.650418	+	0.422387i	0.827234	−	0.561857i	$-0.189913\pi$
$43$	4.26508	+	2.76977i	0.650418	+	0.422387i	−0.176816	+	0.984244i	$0.556580\pi$
$44$	−2.01876	−	0.429100i	−0.304339	−	0.0646893i
$45$	−6.53666	+	1.50732i	−0.974428	+	0.224698i
$46$	1.21958	+	3.75348i	0.179817	+	0.553420i
$47$	−1.95931	+	3.84537i	−0.285795	+	0.560905i	−0.988616	−	0.150462i	$-0.951924\pi$
$47$	−1.95931	+	3.84537i	−0.285795	+	0.560905i	0.702820	+	0.711367i	$0.251924\pi$
$48$	−1.72956	−	0.0928433i	−0.249641	−	0.0134008i
$49$	1.38140	−	6.49896i	0.197342	−	0.928423i
$50$	3.67227	+	3.39329i	0.519337	+	0.479884i
$51$	−2.66751	−	0.00338488i	−0.373526	−	0.000473978i
$52$	1.53584	+	0.0804902i	0.212983	+	0.0111620i
$53$	1.29507	+	1.04873i	0.177892	+	0.144054i	0.714131	−	0.700012i	$-0.246822\pi$
$53$	1.29507	+	1.04873i	0.177892	+	0.144054i	−0.536239	+	0.844066i	$0.680156\pi$
$54$	3.07020	−	4.19212i	0.417802	−	0.570475i
$55$	−4.53213	−	0.870246i	−0.611112	−	0.117344i
$56$	0.516610	−	0.298265i	0.0690349	−	0.0398573i
$57$	0.591607	+	0.0944711i	0.0783603	+	0.0125130i
$58$	1.07175	+	6.76678i	0.140728	+	0.888521i
$59$	−2.24166	+	2.48961i	−0.291839	+	0.324120i	−0.871179	−	0.490966i	$-0.836644\pi$
$59$	−2.24166	+	2.48961i	−0.291839	+	0.324120i	0.579340	+	0.815086i	$0.303311\pi$
$60$	−3.87076	−	0.131258i	−0.499713	−	0.0169454i
$61$	−8.05452			−1.03128			−0.515638	−	0.856807i	$-0.672445\pi$
$61$	−8.05452			−1.03128			−0.515638	+	0.856807i	$0.672445\pi$
$62$	0.761005	−	5.51551i	0.0966478	−	0.700471i
$63$	−0.0981951	+	1.78689i	−0.0123714	+	0.225127i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$	3.43713	+	0.112188i	0.426324	+	0.0139152i
$66$	3.09805	−	1.78342i	0.381344	−	0.219524i
$67$	1.73224	+	6.46480i	0.211627	+	0.789801i	0.987327	+	0.158700i	$0.0507302\pi$
$67$	1.73224	+	6.46480i	0.211627	+	0.789801i	−0.775700	+	0.631101i	$0.782603\pi$
$68$	−1.48761	−	0.398605i	−0.180400	−	0.0483379i
$69$	−5.91562	−	3.42540i	−0.712157	−	0.412370i
$70$	1.14179	−	0.689603i	0.136470	−	0.0824233i
$71$	−11.2306	+	1.18038i	−1.33283	+	0.140086i	−0.744004	−	0.668176i	$-0.767075\pi$
$71$	−11.2306	+	1.18038i	−1.33283	+	0.140086i	−0.588824	+	0.808261i	$0.700409\pi$
$72$	2.33622	−	1.88204i	0.275326	−	0.221800i
$73$	−0.311127	−	0.119430i	−0.0364146	−	0.0139783i	0.340092	−	0.940392i	$-0.389542\pi$
$73$	−0.311127	−	0.119430i	−0.0364146	−	0.0139783i	−0.376507	+	0.926414i	$0.622875\pi$
$74$	−2.11531	+	0.449623i	−0.245900	+	0.0522676i
$75$	−8.65939	−	0.122674i	−0.999900	−	0.0141651i
$76$	0.315988	+	0.140687i	0.0362463	+	0.0161379i
$77$	−0.558932	+	1.09697i	−0.0636962	+	0.125011i
$78$	−2.07230	+	1.67376i	−0.234641	+	0.189516i
$79$	6.17323	−	13.8653i	0.694543	−	1.55997i	−0.128323	−	0.991732i	$-0.540959\pi$
$79$	6.17323	−	13.8653i	0.694543	−	1.55997i	0.822866	−	0.568236i	$-0.192374\pi$
$80$	−2.13985	−	0.648889i	−0.239242	−	0.0725480i
$81$	0.895313	+	8.95536i	0.0994792	+	0.995040i
$82$	1.79316	−	4.67133i	0.198021	−	0.515863i
$83$	8.56129	+	0.448678i	0.939724	+	0.0492488i	0.516043	−	0.856563i	$-0.327404\pi$
$83$	8.56129	+	0.448678i	0.939724	+	0.0492488i	0.423681	+	0.905812i	$0.360738\pi$
$84$	−0.320529	+	0.982245i	−0.0349726	+	0.107172i
$85$	−3.34334	−	0.825503i	−0.362636	−	0.0895383i
$86$	−5.05766	−	0.531582i	−0.545382	−	0.0573219i
$87$	−9.21252	−	7.47952i	−0.987685	−	0.801889i
$88$	1.99353	−	0.534166i	0.212511	−	0.0569422i
$89$	−5.96446	−	4.33343i	−0.632231	−	0.459343i	0.224941	−	0.974372i	$-0.427781\pi$
$89$	−5.96446	−	4.33343i	−0.632231	−	0.459343i	−0.857172	+	0.515030i	$0.827781\pi$
$90$	5.13990	−	4.31062i	0.541793	−	0.454379i
$91$	0.283503	−	0.872532i	0.0297192	−	0.0914662i
$92$	−2.79070	−	2.79070i	−0.290950	−	0.290950i
$93$	5.40263	+	7.98821i	0.560227	+	0.828339i
$94$		−	4.31576i		−	0.445137i
$95$	0.712640	+	0.300583i	0.0731153	+	0.0308392i
$96$	1.58320	−	0.702480i	0.161585	−	0.0716966i
$97$	10.0376	−	1.58980i	1.01917	−	0.161420i	0.375577	−	0.926791i	$-0.377445\pi$
$97$	10.0376	−	1.58980i	1.01917	−	0.161420i	0.643589	+	0.765371i	$0.277445\pi$
$98$	1.71963	+	6.41776i	0.173709	+	0.648291i
$99$	−1.92824	+	5.88366i	−0.193795	+	0.591330i
$100$	−4.81254	−	1.35627i	−0.481254	−	0.135627i
$101$	−7.82617	−	10.7718i	−0.778733	−	1.07183i	−0.995421	−	0.0955930i	$-0.969525\pi$
$101$	−7.82617	−	10.7718i	−0.778733	−	1.07183i	0.216688	−	0.976241i	$-0.430475\pi$
$102$	2.37831	−	1.20801i	0.235488	−	0.119611i
$103$	0.407489	−	7.77536i	0.0401511	−	0.766129i	−0.902162	−	0.431397i	$-0.858021\pi$
$103$	0.407489	−	7.77536i	0.0401511	−	0.766129i	0.942313	−	0.334732i	$-0.108646\pi$
$104$	−1.40499	+	0.625541i	−0.137771	+	0.0613394i
$105$	−0.673251	+	2.21008i	−0.0657025	+	0.215682i
$106$	−1.63003	−	0.346473i	−0.158322	−	0.0336524i
$107$	0.288723	+	0.752149i	0.0279119	+	0.0727130i	0.946828	−	0.321740i	$-0.104268\pi$
$107$	0.288723	+	0.752149i	0.0279119	+	0.0727130i	−0.918916	+	0.394453i	$0.870934\pi$
$108$	−0.832388	+	5.12905i	−0.0800966	+	0.493543i
$109$	16.0685	−	5.22096i	1.53908	−	0.500078i	0.587958	−	0.808891i	$-0.299932\pi$
$109$	16.0685	−	5.22096i	1.53908	−	0.500078i	0.951123	+	0.308814i	$0.0999320\pi$
$110$	4.43324	−	1.28215i	0.422693	−	0.122248i
$111$	2.20550	−	3.02752i	0.209336	−	0.287359i
$112$	−0.324894	+	0.500292i	−0.0306996	+	0.0472732i
$113$	−0.352354	+	0.917913i	−0.0331467	+	0.0863500i	−0.949155	−	0.314810i	$-0.898059\pi$
$113$	−0.352354	+	0.917913i	−0.0331467	+	0.0863500i	0.916008	+	0.401160i	$0.131393\pi$
$114$	−0.570015	+	0.184410i	−0.0533868	+	0.0172716i
$115$	−6.36209	−	6.11585i	−0.593268	−	0.570306i
$116$	−4.02699	−	5.54268i	−0.373897	−	0.514625i
$117$	0.733329	−	4.55521i	0.0677963	−	0.421129i
$118$	0.867071	−	3.23595i	0.0798204	−	0.297894i
$119$	−0.459355	+	0.795626i	−0.0421090	+	0.0729349i
$120$	3.50846	−	1.64034i	0.320277	−	0.149741i
$121$	4.51027	−	5.00916i	0.410025	−	0.455378i
$122$	7.17663	−	3.65667i	0.649741	−	0.331060i
$123$	3.09557	+	8.09492i	0.279118	+	0.729895i
$124$	1.82593	+	5.25985i	0.163973	+	0.472348i
$125$	−10.8189	−	2.81980i	−0.967672	−	0.252211i
$126$	−0.723740	−	1.63671i	−0.0644759	−	0.145810i
$127$	−0.0451642	−	0.861785i	−0.00400768	−	0.0764710i	0.995893	−	0.0905331i	$-0.0288571\pi$
$127$	−0.0451642	−	0.861785i	−0.00400768	−	0.0764710i	−0.999901	+	0.0140621i	$0.995524\pi$
$128$	0.987688	−	0.156434i	0.0873001	−	0.0138270i
$129$	7.13269	−	5.16839i	0.627999	−	0.455051i
$130$	−3.11344	+	1.46047i	−0.273067	+	0.128091i
$131$	−1.11327	−	0.117009i	−0.0972666	−	0.0102231i	0.0557701	−	0.998444i	$-0.482239\pi$
$131$	−1.11327	−	0.117009i	−0.0972666	−	0.0102231i	−0.153037	+	0.988221i	$0.548905\pi$
$132$	−1.95073	+	2.99553i	−0.169789	+	0.260727i
$133$	0.129851	−	0.160352i	0.0112595	−	0.0139043i
$134$	−4.47839	−	4.97376i	−0.386874	−	0.429667i
$135$	−1.63463	+	11.5034i	−0.140687	+	0.990054i
$136$	1.50644	−	0.320203i	0.129176	−	0.0274572i
$137$	4.22264	+	6.50230i	0.360765	+	0.555529i	0.971720	−	0.236136i	$-0.0758811\pi$
$137$	4.22264	+	6.50230i	0.360765	+	0.555529i	−0.610955	+	0.791665i	$0.709214\pi$
$138$	6.82596	+	0.366419i	0.581064	+	0.0311917i
$139$	4.39906	−	1.42934i	0.373123	−	0.121235i	−0.116452	−	0.993196i	$-0.537152\pi$
$139$	4.39906	−	1.42934i	0.373123	−	0.121235i	0.489575	+	0.871961i	$0.337152\pi$
$140$	−0.704271	+	1.13280i	−0.0595217	+	0.0957394i
$141$	4.99478	+	5.56144i	0.420636	+	0.468357i
$142$	9.47066	−	6.15032i	0.794760	−	0.516123i
$143$	1.72875	−	2.66204i	0.144565	−	0.222611i
$144$	−1.22716	+	2.73753i	−0.102263	+	0.228128i
$145$	−9.24740	−	12.2137i	−0.767955	−	1.01429i
$146$	0.331436	−	0.0348353i	0.0274298	−	0.00288299i
$147$	−9.64347	−	6.27995i	−0.795380	−	0.517962i
$148$	1.68063	−	1.36095i	0.138147	−	0.111869i
$149$	0.975371	+	1.68939i	0.0799055	+	0.138400i	0.903209	−	0.429201i	$-0.141205\pi$
$149$	0.975371	+	1.68939i	0.0799055	+	0.138400i	−0.823303	+	0.567601i	$0.807871\pi$
$150$	7.77126	−	3.82198i	0.634521	−	0.312063i
$151$	4.80404	+	3.49034i	0.390947	+	0.284040i	0.765844	−	0.643027i	$-0.222322\pi$
$151$	4.80404	+	3.49034i	0.390947	+	0.284040i	−0.374896	+	0.927067i	$0.622322\pi$
$152$	−0.345418	+	0.0181026i	−0.0280171	+	0.00146831i
$153$	−1.66670	+	4.30918i	−0.134745	+	0.348376i
$154$		−	1.23115i		−	0.0992091i
$155$	4.31416	+	11.6785i	0.346522	+	0.938042i
$156$	1.08656	−	2.43214i	0.0869942	−	0.194727i
$157$	10.1500	+	19.9204i	0.810054	+	1.58982i	0.807532	+	0.589824i	$0.200803\pi$
$157$	10.1500	+	19.9204i	0.810054	+	1.58982i	0.00252279	+	0.999997i	$0.499197\pi$
$158$	0.794327	+	15.1567i	0.0631933	+	1.20580i
$159$	2.50149	−	1.44001i	0.198381	−	0.114200i
$160$	2.20121	−	0.393305i	0.174021	−	0.0310935i
$161$	−2.03887	+	1.17714i	−0.160686	+	0.0927720i
$162$	−4.86338	−	7.57282i	−0.382103	−	0.594977i
$163$	−1.88546	−	0.298628i	−0.147681	−	0.0233903i	0.0821563	−	0.996619i	$-0.473819\pi$
$163$	−1.88546	−	0.298628i	−0.147681	−	0.0233903i	−0.229837	+	0.973229i	$0.573819\pi$
$164$	0.523027	+	4.97627i	0.0408415	+	0.388581i
$165$	−4.22895	+	6.78296i	−0.329223	+	0.528053i
$166$	−7.83186	+	3.48697i	−0.607870	+	0.270641i
$167$	−0.121465	−	0.0788804i	−0.00939926	−	0.00610395i	0.539931	−	0.841709i	$-0.318450\pi$
$167$	−0.121465	−	0.0788804i	−0.00939926	−	0.00610395i	−0.549330	+	0.835605i	$0.685117\pi$
$168$	−0.160336	−	1.02070i	−0.0123702	−	0.0787490i
$169$	4.32552	−	9.71529i	0.332733	−	0.747330i
$170$	3.35371	−	0.782317i	0.257218	−	0.0600010i
$171$	0.521117	−	0.897334i	0.0398508	−	0.0686209i
$172$	4.74774	−	1.82249i	0.362012	−	0.138963i
$173$	18.4350	−	11.9718i	1.40159	−	0.910201i	0.401603	−	0.915814i	$-0.368453\pi$
$173$	18.4350	−	11.9718i	1.40159	−	0.910201i	0.999984	+	0.00561265i	$0.00178657\pi$
$174$	11.6040	+	2.48191i	0.879700	+	0.188153i
$175$	−1.52451	+	2.56360i	−0.115242	+	0.193790i
$176$	−1.53374	+	1.38099i	−0.115610	+	0.104096i
$177$	2.62774	+	5.17345i	0.197513	+	0.388861i
$178$	7.28170	+	1.15331i	0.545787	+	0.0864441i
$179$	−0.429168	+	4.08326i	−0.0320775	+	0.305197i	0.966706	+	0.255889i	$0.0823682\pi$
$179$	−0.429168	+	4.08326i	−0.0320775	+	0.305197i	−0.998784	+	0.0493079i	$0.984298\pi$
$180$	−2.62271	+	6.17425i	−0.195485	+	0.460202i
$181$	5.53677	−	9.58997i	0.411545	−	0.712817i	−0.583514	−	0.812103i	$-0.698323\pi$
$181$	5.53677	−	9.58997i	0.411545	−	0.712817i	0.995059	+	0.0992861i	$0.0316559\pi$
$182$	0.143518	+	0.906139i	0.0106383	+	0.0671675i
$183$	−5.01605	+	13.0179i	−0.370797	+	0.962309i
$184$	3.75348	+	1.21958i	0.276710	+	0.0899086i
$185$	3.69723	−	3.11672i	0.271826	−	0.229146i
$186$	−8.44035	−	4.66481i	−0.618877	−	0.342040i
$187$	−2.24756	+	2.24756i	−0.164358	+	0.164358i
$188$	1.95931	+	3.84537i	0.142898	+	0.280452i
$189$	2.82686	+	1.27152i	0.205624	+	0.0924892i
$190$	−0.771429	+	0.0557100i	−0.0559653	+	0.00404163i
$191$	12.1969	+	7.04191i	0.882540	+	0.509535i	0.871495	−	0.490404i	$-0.163151\pi$
$191$	12.1969	+	7.04191i	0.882540	+	0.509535i	0.0110451	+	0.999939i	$0.496484\pi$
$192$	−1.09172	+	1.34467i	−0.0787883	+	0.0970433i
$193$	0.0220232	−	0.0178341i	0.00158527	−	0.00128372i	−0.628527	−	0.777787i	$-0.716342\pi$
$193$	0.0220232	−	0.0178341i	0.00158527	−	0.00128372i	0.630113	+	0.776504i	$0.283009\pi$
$194$	−8.22183	+	5.97351i	−0.590293	+	0.428873i
$195$	2.32184	−	5.48530i	0.166270	−	0.392810i
$196$	−4.44581	−	4.93757i	−0.317558	−	0.352683i
$197$	−6.31931	−	2.42576i	−0.450232	−	0.172828i	0.122677	−	0.992447i	$-0.460852\pi$
$197$	−6.31931	−	2.42576i	−0.450232	−	0.172828i	−0.572909	+	0.819619i	$0.694185\pi$
$198$	−0.953052	−	6.11778i	−0.0677305	−	0.434772i
$199$	−3.74644	+	17.6256i	−0.265578	+	1.24945i	0.619868	+	0.784706i	$0.287186\pi$
$199$	−3.74644	+	17.6256i	−0.265578	+	1.24945i	−0.885446	+	0.464741i	$0.846147\pi$
$200$	4.90374	−	0.976400i	0.346747	−	0.0690419i
$201$	11.5273	+	1.22636i	0.813074	+	0.0865008i
$202$	11.8635	+	6.04474i	0.834710	+	0.425306i
$203$	−3.81545	+	1.46461i	−0.267792	+	0.102796i
$204$	−1.57066	+	2.15607i	−0.109968	+	0.150955i
$205$	1.38884	+	11.1020i	0.0970008	+	0.775399i
$206$	3.16686	+	7.11289i	0.220646	+	0.495579i
$207$	−9.22023	+	7.42773i	−0.640850	+	0.516263i
$208$	0.967865	−	1.19521i	0.0671093	−	0.0828731i
$209$	0.577534	−	0.419603i	0.0399489	−	0.0290246i
$210$	−0.403485	−	2.27485i	−0.0278431	−	0.156979i
$211$	−10.8276	−	18.7540i	−0.745404	−	1.29108i	−0.950006	−	0.312232i	$-0.898923\pi$
$211$	−10.8276	−	18.7540i	−0.745404	−	1.29108i	0.204602	−	0.978845i	$-0.434410\pi$
$212$	1.60966	−	0.431307i	0.110552	−	0.0296223i
$213$	−5.08624	+	18.8862i	−0.348504	+	1.29406i
$214$	−0.598722	−	0.539092i	−0.0409278	−	0.0368516i
$215$	10.5338	−	4.28388i	0.718400	−	0.292158i
$216$	−1.58688	−	4.94791i	−0.107973	−	0.336663i
$217$	3.31265	−	0.240022i	0.224878	−	0.0162938i
$218$	−11.9468	+	11.9468i	−0.809143	+	0.809143i
$219$	−0.386784	+	0.428472i	−0.0261364	+	0.0289535i
$220$	−3.36796	+	3.15505i	−0.227068	+	0.212714i
$221$	1.39222	−	1.91623i	0.0936508	−	0.128899i
$222$	−0.590647	+	3.69881i	−0.0396416	+	0.248248i
$223$	−4.23832	+	15.8176i	−0.283819	+	1.05923i	0.665880	+	0.746059i	$0.268056\pi$
$223$	−4.23832	+	15.8176i	−0.283819	+	1.05923i	−0.949698	+	0.313167i	$0.898610\pi$
$224$	0.0623544	−	0.593262i	0.00416623	−	0.0396390i
$225$	−5.59101	+	13.9191i	−0.372734	+	0.927938i
$226$	−0.102774	−	0.977832i	−0.00683644	−	0.0650444i
$227$	−0.755200	+	14.4101i	−0.0501244	+	0.956430i	0.851620	+	0.524160i	$0.175621\pi$
$227$	−0.755200	+	14.4101i	−0.0501244	+	0.956430i	−0.901744	+	0.432270i	$0.857713\pi$
$228$	0.424167	−	0.423092i	0.0280911	−	0.0280199i
$229$	0.703625	+	3.31029i	0.0464968	+	0.218750i	0.995262	−	0.0972326i	$-0.0309991\pi$
$229$	0.703625	+	3.31029i	0.0464968	+	0.218750i	−0.948765	+	0.315983i	$0.897666\pi$
$230$	8.44521	+	2.56093i	0.556860	+	0.168863i
$231$	1.42485	+	1.58651i	0.0937486	+	0.104384i
$232$	6.10440	+	3.11035i	0.400773	+	0.204204i
$233$	−9.68306	−	4.93377i	−0.634358	−	0.323222i	0.107072	−	0.994251i	$-0.465852\pi$
$233$	−9.68306	−	4.93377i	−0.634358	−	0.323222i	−0.741431	+	0.671030i	$0.765852\pi$
$234$	1.41462	+	4.39164i	0.0924765	+	0.287091i
$235$	4.54996	+	8.51039i	0.296807	+	0.555157i
$236$	0.696526	+	3.27690i	0.0453400	+	0.213308i
$237$	−18.5649	−	18.6121i	−1.20592	−	1.20899i
$238$	0.0480816	−	0.917451i	0.00311667	−	0.0594695i
$239$	−0.736252	−	7.00497i	−0.0476242	−	0.453114i	−0.992185	−	0.124777i	$-0.960179\pi$
$239$	−0.736252	−	7.00497i	−0.0476242	−	0.453114i	0.944561	−	0.328337i	$-0.106488\pi$
$240$	−2.38136	+	3.05436i	−0.153716	+	0.197158i
$241$	1.10296	−	10.4940i	0.0710479	−	0.675976i	−0.899804	−	0.436295i	$-0.856290\pi$
$241$	1.10296	−	10.4940i	0.0710479	−	0.675976i	0.970852	−	0.239681i	$-0.0770429\pi$
$242$	−1.74457	+	6.51082i	−0.112145	+	0.418531i
$243$	15.0314	+	4.13004i	0.964264	+	0.264942i
$244$	−4.73433	+	6.51624i	−0.303084	+	0.417160i
$245$	−10.1570	−	10.8424i	−0.648909	−	0.692698i
$246$	−6.43319	−	5.80727i	−0.410165	−	0.370258i
$247$	−0.376156	+	0.376156i	−0.0239343	+	0.0239343i
$248$	−4.01484	−	3.85760i	−0.254942	−	0.244958i
$249$	6.05682	−	13.5575i	0.383835	−	0.859172i
$250$	10.9199	−	2.39922i	0.690634	−	0.151740i
$251$	20.0205	+	18.0265i	1.26368	+	1.13782i	0.984083	+	0.177708i	$0.0568681\pi$
$251$	20.0205	+	18.0265i	1.26368	+	1.13782i	0.279599	+	0.960117i	$0.409799\pi$
$252$	1.38791	+	1.12975i	0.0874301	+	0.0711677i
$253$	−7.86776	+	2.10816i	−0.494642	+	0.132539i
$254$	0.431484	+	0.747352i	0.0270737	+	0.0468930i
$255$	−3.41630	+	4.88948i	−0.213937	+	0.306191i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	11.0665	−	13.6660i	0.690309	−	0.852461i	−0.304679	−	0.952455i	$-0.598549\pi$
$257$	11.0665	−	13.6660i	0.690309	−	0.852461i	0.994988	+	0.0999944i	$0.0318825\pi$
$258$	−4.00888	+	7.84325i	−0.249582	+	0.488299i
$259$	−0.524705	−	1.17851i	−0.0326036	−	0.0732288i
$260$	2.11106	−	2.71476i	0.130922	−	0.168362i
$261$	−17.8258	+	10.2315i	−1.10339	+	0.633313i
$262$	1.04505	−	0.401157i	0.0645634	−	0.0247836i
$263$	24.0850	+	12.2719i	1.48515	+	0.756720i	0.993474	−	0.114059i	$-0.0363854\pi$
$263$	24.0850	+	12.2719i	1.48515	+	0.756720i	0.491673	+	0.870780i	$0.336385\pi$
$264$	0.378169	−	3.55465i	0.0232747	−	0.218773i
$265$	3.57958	−	1.03526i	0.219892	−	0.0635955i
$266$	−0.0428995	+	0.201826i	−0.00263033	+	0.0123747i
$267$	−10.7182	+	6.94117i	−0.655944	+	0.424793i
$268$	6.24832	+	2.39850i	0.381677	+	0.146512i
$269$	−6.91199	−	7.67655i	−0.421432	−	0.468047i	0.494619	−	0.869110i	$-0.335308\pi$
$269$	−6.91199	−	7.67655i	−0.421432	−	0.468047i	−0.916051	+	0.401063i	$0.868641\pi$
$270$	−3.76596	−	10.9917i	−0.229189	−	0.668934i
$271$	1.43275	−	1.04096i	0.0870336	−	0.0632336i	−0.543418	−	0.839463i	$-0.682870\pi$
$271$	1.43275	−	1.04096i	0.0870336	−	0.0632336i	0.630451	+	0.776229i	$0.282870\pi$
$272$	−1.19688	+	0.969210i	−0.0725712	+	0.0587670i
$273$	−1.23365	−	1.00158i	−0.0746638	−	0.0606186i
$274$	−6.71438	−	3.87655i	−0.405631	−	0.234191i
$275$	−7.39033	+	7.20213i	−0.445654	+	0.434305i
$276$	−6.24832	+	2.77244i	−0.376105	+	0.166881i
$277$	10.3787	+	20.3693i	0.623594	+	1.22387i	0.959429	+	0.281952i	$0.0909819\pi$
$277$	10.3787	+	20.3693i	0.623594	+	1.22387i	−0.335834	+	0.941921i	$0.609018\pi$
$278$	−3.27068	+	3.27068i	−0.196163	+	0.196163i
$279$	16.2753	−	3.75708i	0.974375	−	0.224930i
$280$	0.113228	−	1.32907i	0.00676665	−	0.0794270i
$281$	23.8394	+	7.74589i	1.42214	+	0.462081i	0.916281	−	0.400535i	$-0.131176\pi$
$281$	23.8394	+	7.74589i	1.42214	+	0.462081i	0.505858	+	0.862617i	$0.331176\pi$
$282$	−6.97522	−	2.68769i	−0.415368	−	0.160050i
$283$	2.91059	+	18.3767i	0.173017	+	1.09238i	0.909432	+	0.415853i	$0.136517\pi$
$283$	2.91059	+	18.3767i	0.173017	+	1.09238i	−0.736415	+	0.676530i	$0.763483\pi$
$284$	−5.64623	+	9.77956i	−0.335042	+	0.580310i
$285$	0.929615	−	0.964591i	0.0550656	−	0.0571374i
$286$	−0.331785	+	3.15673i	−0.0196189	+	0.186661i
$287$	2.94809	+	0.466932i	0.174021	+	0.0275621i
$288$	−0.149404	−	2.99628i	−0.00880373	−	0.176557i
$289$	10.8708	−	9.78812i	0.639460	−	0.575772i
$290$	13.7844	+	6.68427i	0.809448	+	0.392514i
$291$	3.68159	−	17.2131i	0.215818	−	1.00905i
$292$	−0.279497	+	0.181507i	−0.0163563	+	0.0106219i
$293$	10.0811	−	3.86978i	0.588945	−	0.226075i	−0.0456010	−	0.998960i	$-0.514520\pi$
$293$	10.0811	−	3.86978i	0.588945	−	0.226075i	0.634546	+	0.772885i	$0.281187\pi$
$294$	11.4434	+	1.21744i	0.667394	+	0.0710023i
$295$	1.70175	+	7.29521i	0.0990796	+	0.424744i
$296$	−0.879595	+	1.97560i	−0.0511254	+	0.114830i
$297$	8.30845	+	6.78058i	0.482105	+	0.393449i
$298$	−1.63603	−	1.06245i	−0.0947726	−	0.0615461i
$299$	5.54499	−	2.46879i	0.320675	−	0.142774i
$300$	−5.18910	+	6.93348i	−0.299593	+	0.400305i
$301$	−0.317104	−	3.01705i	−0.0182776	−	0.173900i
$302$	−5.86501	−	0.928927i	−0.337494	−	0.0534537i
$303$	−22.2834	+	5.94053i	−1.28015	+	0.341275i
$304$	0.299551	−	0.172946i	0.0171804	−	0.00991913i
$305$	−10.2967	+	14.7768i	−0.589589	+	0.846117i
$306$	−0.471287	−	4.59617i	−0.0269417	−	0.262746i
$307$	−1.58262	−	30.1981i	−0.0903248	−	1.72350i	−0.549790	−	0.835303i	$-0.685292\pi$
$307$	−1.58262	−	30.1981i	−0.0903248	−	1.72350i	0.459465	−	0.888196i	$-0.348041\pi$
$308$	0.558932	+	1.09697i	0.0318481	+	0.0625054i
$309$	−12.3129	−	5.50080i	−0.700458	−	0.312929i
$310$	−9.14589	−	8.44706i	−0.519452	−	0.479760i
$311$			21.0947i			1.19617i	0.801433	+	0.598084i	$0.204071\pi$
$311$			21.0947i			1.19617i	−0.801433	+	0.598084i	$0.795929\pi$
$312$	0.136037	+	2.66034i	0.00770160	+	0.150612i
$313$	−3.62855	+	0.190164i	−0.205098	+	0.0107487i	−0.154608	−	0.987976i	$-0.549412\pi$
$313$	−3.62855	+	0.190164i	−0.205098	+	0.0107487i	−0.0504897	+	0.998725i	$0.516078\pi$
$314$	−18.0873	−	13.1412i	−1.02073	−	0.741602i
$315$	3.15270	+	2.46448i	0.177635	+	0.138858i
$316$	−7.58873	−	13.1441i	−0.426900	−	0.739412i
$317$	9.58390	−	7.76089i	0.538285	−	0.435895i	−0.321233	−	0.947000i	$-0.604097\pi$
$317$	9.58390	−	7.76089i	0.538285	−	0.435895i	0.859518	+	0.511105i	$0.170764\pi$
$318$	−1.57510	+	2.41871i	−0.0883271	+	0.135635i
$319$	−14.0623	+	1.47801i	−0.787337	+	0.0827524i
$320$	−1.78273	+	1.34976i	−0.0996578	+	0.0754541i
$321$	1.39544	+	0.00177072i	0.0778861	+	9.88318e-5i
$322$	1.28224	−	1.97447i	0.0714563	−	0.110033i
$323$	0.446764	−	0.290132i	0.0248586	−	0.0161434i
$324$	7.77129	+	4.53950i	0.431738	+	0.252195i
$325$	4.59978	−	6.16234i	0.255150	−	0.341825i
$326$	1.81553	−	0.589903i	0.100553	−	0.0326717i
$327$	1.56862	−	29.2216i	0.0867451	−	1.61596i
$328$	−2.72520	−	4.19644i	−0.150474	−	0.231709i
$329$	2.51822	−	0.535265i	0.138834	−	0.0295101i
$330$	0.688623	−	7.96357i	0.0379074	−	0.438380i
$331$	−4.48942	−	4.98601i	−0.246761	−	0.274056i	0.607022	−	0.794685i	$-0.292364\pi$
$331$	−4.48942	−	4.98601i	−0.246761	−	0.274056i	−0.853783	+	0.520629i	$0.825697\pi$
$332$	5.39519	−	6.66250i	0.296099	−	0.365652i
$333$	−3.51963	−	5.44999i	−0.192875	−	0.298658i
$334$	0.144037	+	0.0151389i	0.00788137	+	0.000828365i
$335$	14.0748	+	5.08651i	0.768986	+	0.277906i
$336$	0.606250	+	0.836663i	0.0330737	+	0.0456437i
$337$	15.7400	−	2.49297i	0.857411	−	0.135801i	0.287775	−	0.957698i	$-0.407084\pi$
$337$	15.7400	−	2.49297i	0.857411	−	0.135801i	0.569635	+	0.821897i	$0.307084\pi$
$338$	0.556577	+	10.6201i	0.0302738	+	0.577659i
$339$	1.26412	+	1.14112i	0.0686574	+	0.0619773i
$340$	−2.63301	+	2.21960i	−0.142795	+	0.120375i
$341$	11.2854	+	2.16421i	0.611140	+	0.117198i
$342$	−0.0569375	+	1.03611i	−0.00307882	+	0.0560266i
$343$	−7.25203	+	3.69510i	−0.391573	+	0.199516i
$344$	−3.40288	+	3.77928i	−0.183471	+	0.203765i
$345$	−13.8466	+	6.47382i	−0.745478	+	0.348539i
$346$	−10.9906	+	19.0363i	−0.590859	+	1.02340i
$347$	0.270348	−	1.00895i	0.0145131	−	0.0541635i	−0.958290	−	0.285799i	$-0.907741\pi$
$347$	0.270348	−	1.00895i	0.0145131	−	0.0541635i	0.972803	+	0.231636i	$0.0744077\pi$
$348$	−11.4660	+	3.05673i	−0.614644	+	0.163858i
$349$	11.3401	+	15.6083i	0.607022	+	0.835495i	0.996328	−	0.0856139i	$-0.0272852\pi$
$349$	11.3401	+	15.6083i	0.607022	+	0.835495i	−0.389306	+	0.921108i	$0.627285\pi$
$350$	0.194499	−	2.97630i	0.0103964	−	0.159090i
$351$	−6.90552	−	4.02203i	−0.368590	−	0.214680i
$352$	0.739620	−	1.92678i	0.0394219	−	0.102698i
$353$	15.2090	−	23.4199i	0.809496	−	1.24651i	−0.156428	−	0.987689i	$-0.549998\pi$
$353$	15.2090	−	23.4199i	0.809496	−	1.24651i	0.965924	−	0.258825i	$-0.0833353\pi$
$354$	−4.69003	−	3.41661i	−0.249272	−	0.181591i
$355$	−12.1914	+	22.1126i	−0.647055	+	1.17362i
$356$	−7.01164	+	2.27822i	−0.371616	+	0.120745i
$357$	0.999838	+	1.23791i	0.0529170	+	0.0655169i
$358$	−1.47137	−	3.83305i	−0.0777643	−	0.202583i
$359$	13.2769	+	2.82210i	0.700730	+	0.148945i	0.544481	−	0.838773i	$-0.316726\pi$
$359$	13.2769	+	2.82210i	0.700730	+	0.148945i	0.156249	+	0.987718i	$0.450060\pi$
$360$	−0.466204	−	6.69198i	−0.0245711	−	0.352699i
$361$	17.2481	−	7.67933i	0.907793	−	0.404175i
$362$	−0.579545	+	11.0584i	−0.0304602	+	0.581215i
$363$	−5.28708	−	10.4091i	−0.277500	−	0.546337i
$364$	−0.539255	−	0.742220i	−0.0282646	−	0.0389029i
$365$	−0.616844	+	0.418115i	−0.0322871	+	0.0218851i
$366$	−1.44065	−	13.8762i	−0.0753041	−	0.725323i
$367$	2.13320	+	7.96123i	0.111352	+	0.415573i	0.998988	−	0.0449733i	$-0.0143203\pi$
$367$	2.13320	+	7.96123i	0.111352	+	0.415573i	−0.887636	+	0.460546i	$0.847654\pi$
$368$	−3.89805	+	0.617391i	−0.203200	+	0.0321837i
$369$	15.0110	+	0.0380958i	0.781440	+	0.00198319i
$370$	−1.87929	+	4.45553i	−0.0976997	+	0.231632i
$371$		−	0.994084i		−	0.0516103i
$372$	9.63819	+	0.324534i	0.499717	+	0.0168263i
$373$	−14.1090	−	14.1090i	−0.730538	−	0.730538i	0.240188	−	0.970726i	$-0.422791\pi$
$373$	−14.1090	−	14.1090i	−0.730538	−	0.730538i	−0.970726	+	0.240188i	$0.922791\pi$
$374$	0.982219	−	3.02296i	0.0507893	−	0.156313i
$375$	−11.2950	+	15.7297i	−0.583273	+	0.812276i
$376$	−3.49152	−	2.53674i	−0.180062	−	0.130822i
$377$	10.1777	−	2.72710i	0.524177	−	0.140453i
$378$	−3.09601	+	0.150439i	−0.159241	+	0.00773775i
$379$	−22.6519	−	2.38081i	−1.16355	−	0.122294i	−0.496997	−	0.867752i	$-0.665564\pi$
$379$	−22.6519	−	2.38081i	−1.16355	−	0.122294i	−0.666552	+	0.745459i	$0.732231\pi$
$380$	0.662057	−	0.399859i	0.0339628	−	0.0205124i
$381$	−1.42096	−	0.463692i	−0.0727980	−	0.0237557i
$382$	−14.0645	−	0.737090i	−0.719603	−	0.0377128i
$383$	5.28229	−	13.7608i	0.269912	−	0.703146i	−0.729896	−	0.683558i	$-0.760431\pi$
$383$	5.28229	−	13.7608i	0.269912	−	0.703146i	0.999808	−	0.0195873i	$-0.00623523\pi$
$384$	0.362263	−	1.69374i	0.0184867	−	0.0864335i
$385$	1.29796	+	2.42775i	0.0661503	+	0.123730i
$386$	−0.0115264	+	0.0258886i	−0.000586676	+	0.00131770i
$387$	−3.91128	−	14.7467i	−0.198821	−	0.749616i
$388$	4.61379	−	9.05507i	0.234230	−	0.459702i
$389$	−28.0126	−	12.4720i	−1.42029	−	0.632355i	−0.454283	−	0.890858i	$-0.650104\pi$
$389$	−28.0126	−	12.4720i	−1.42029	−	0.632355i	−0.966011	+	0.258502i	$0.916771\pi$
$390$	0.421499	+	5.94153i	0.0213434	+	0.300861i
$391$	−5.94536	+	1.26373i	−0.300670	+	0.0639093i
$392$	6.20285	+	2.38105i	0.313291	+	0.120261i
$393$	−0.882414	+	1.72642i	−0.0445119	+	0.0870862i
$394$	6.73182	−	0.707542i	0.339144	−	0.0356455i
$395$	−17.5455	−	29.0505i	−0.882811	−	1.46169i
$396$	3.62659	+	5.01831i	0.182243	+	0.252179i
$397$	5.19032	+	1.39074i	0.260495	+	0.0697993i	0.386703	−	0.922204i	$-0.373614\pi$
$397$	5.19032	+	1.39074i	0.260495	+	0.0697993i	−0.126208	+	0.992004i	$0.540281\pi$
$398$	−4.66376	−	17.4054i	−0.233773	−	0.872454i
$399$	−0.178298	−	0.309729i	−0.00892609	−	0.0155058i
$400$	−3.92599	+	3.09623i	−0.196299	+	0.154811i
$401$	7.99284	+	2.59703i	0.399143	+	0.129690i	0.501709	−	0.865037i	$-0.332705\pi$
$401$	7.99284	+	2.59703i	0.399143	+	0.129690i	−0.102565	+	0.994726i	$0.532705\pi$
$402$	−10.8277	+	4.14060i	−0.540035	+	0.206514i
$403$	−8.55846	−	0.277306i	−0.426327	−	0.0138136i
$404$	−13.3147			−0.662430
$405$	17.5740	+	9.80581i	0.873260	+	0.487254i
$406$	2.73467	−	3.03716i	0.135719	−	0.150732i
$407$	−0.698203	−	4.40828i	−0.0346086	−	0.218510i
$408$	0.420634	−	2.63414i	0.0208245	−	0.130409i
$409$	−3.60364	+	2.08056i	−0.178188	+	0.102877i	−0.586441	−	0.809992i	$-0.699472\pi$
$409$	−3.60364	+	2.08056i	−0.178188	+	0.102877i	0.408253	+	0.912869i	$0.366138\pi$
$410$	−6.27768	−	9.26146i	−0.310033	−	0.457391i
$411$	13.1389	−	2.77533i	0.648092	−	0.136897i
$412$	−6.05088	−	4.89991i	−0.298106	−	0.241401i
$413$	1.99570	+	0.104590i	0.0982020	+	0.00514655i
$414$	4.84317	−	10.8041i	0.238029	−	0.530990i
$415$	11.7677	−	15.1329i	0.577655	−	0.742847i
$416$	−0.319758	+	1.50434i	−0.0156774	+	0.0737565i
$417$	0.429442	−	7.99999i	0.0210298	−	0.391761i
$418$	−0.324091	+	0.636064i	−0.0158518	+	0.0311109i
$419$	0.209539	+	0.644894i	0.0102366	+	0.0315051i	0.956044	−	0.293222i	$-0.0947275\pi$
$419$	0.209539	+	0.644894i	0.0102366	+	0.0315051i	−0.945808	+	0.324727i	$0.894728\pi$
$420$	1.39227	+	1.84372i	0.0679356	+	0.0899645i
$421$	−1.32552	−	0.281747i	−0.0646017	−	0.0137315i	0.175497	−	0.984480i	$-0.443847\pi$
$421$	−1.32552	−	0.281747i	−0.0646017	−	0.0137315i	−0.240099	+	0.970748i	$0.577180\pi$
$422$	18.1616	+	11.7943i	0.884093	+	0.574137i
$423$	12.0991	−	4.60920i	0.588277	−	0.224107i
$424$	−1.23841	+	1.11507i	−0.0601425	+	0.0541525i
$425$	−5.78852	+	5.07838i	−0.280785	+	0.246338i
$426$	−4.04229	−	19.1369i	−0.195850	−	0.927184i
$427$	3.02373	+	3.73400i	0.146329	+	0.180701i
$428$	0.778208	+	0.208520i	0.0376161	+	0.0100792i
$429$	−3.22584	−	4.45185i	−0.155745	−	0.214937i
$430$	−7.44085	+	8.59921i	−0.358830	+	0.414691i
$431$	−7.87392	−	7.08971i	−0.379274	−	0.341499i	0.457341	−	0.889291i	$-0.348802\pi$
$431$	−7.87392	−	7.08971i	−0.379274	−	0.341499i	−0.836615	+	0.547792i	$0.815469\pi$
$432$	3.66022	+	3.68819i	0.176102	+	0.177448i
$433$	28.4327	+	28.4327i	1.36639	+	1.36639i	0.865530	+	0.500857i	$0.166982\pi$
$433$	28.4327	+	28.4327i	1.36639	+	1.36639i	0.500857	+	0.865530i	$0.333018\pi$
$434$	−2.84263	+	1.71777i	−0.136451	+	0.0824558i
$435$	−25.4990	+	7.33958i	−1.22258	+	0.351906i
$436$	5.22096	−	16.0685i	0.250039	−	0.769540i
$437$	1.36324	−	0.0714444i	0.0652127	−	0.00341765i
$438$	0.150105	−	0.557368i	0.00717227	−	0.0266321i
$439$	−29.7222	−	17.1601i	−1.41856	−	0.819008i	−0.422391	−	0.906414i	$-0.638809\pi$
$439$	−29.7222	−	17.1601i	−1.41856	−	0.819008i	−0.996173	+	0.0874057i	$0.972142\pi$
$440$	1.56851	−	4.34020i	0.0747759	−	0.206911i
$441$	−16.1554	+	11.6750i	−0.769304	+	0.555954i
$442$	−0.370528	+	2.33942i	−0.0176242	+	0.111275i
$443$	−17.4404	−	14.1229i	−0.828617	−	0.671001i	0.118123	−	0.992999i	$-0.462312\pi$
$443$	−17.4404	−	14.1229i	−0.828617	−	0.671001i	−0.946740	+	0.321998i	$0.895645\pi$
$444$	−1.15296	−	3.56381i	−0.0547169	−	0.169131i
$445$	−15.5749	+	5.40260i	−0.738323	+	0.256108i
$446$	−3.40468	−	16.0178i	−0.161216	−	0.758463i
$447$	3.33785	−	0.524323i	0.157875	−	0.0247996i
$448$	0.213777	+	0.556909i	0.0101000	+	0.0263115i
$449$	−6.61531	−	20.3598i	−0.312196	−	0.960839i	−0.976893	−	0.213727i	$-0.931440\pi$
$449$	−6.61531	−	20.3598i	−0.312196	−	0.960839i	0.664698	−	0.747112i	$-0.268560\pi$
$450$	−1.33750	−	14.9403i	−0.0630503	−	0.704290i
$451$	9.43407	+	4.20032i	0.444233	+	0.197785i
$452$	0.535499	+	0.824596i	0.0251878	+	0.0387857i
$453$	8.63293	−	5.59073i	0.405611	−	0.262675i
$454$	−5.86915	−	13.1823i	−0.275453	−	0.618677i
$455$	−1.23832	−	1.63554i	−0.0580534	−	0.0766753i
$456$	−0.185856	+	0.569545i	−0.00870349	+	0.0266714i
$457$	2.68070	−	16.9253i	0.125398	−	0.791730i	−0.842187	−	0.539185i	$-0.818732\pi$
$457$	2.68070	−	16.9253i	0.125398	−	0.791730i	0.967585	−	0.252545i	$-0.0812677\pi$
$458$	−2.12978	−	2.63005i	−0.0995179	−	0.122894i
$459$	5.92662	+	5.37735i	0.276631	+	0.250993i
$460$	−8.68737	+	1.55223i	−0.405051	+	0.0723733i
$461$	−12.7024	+	17.4833i	−0.591607	+	0.814278i	−0.994908	−	0.100790i	$-0.967863\pi$
$461$	−12.7024	+	17.4833i	−0.591607	+	0.814278i	0.403300	+	0.915068i	$0.367863\pi$
$462$	−1.98981	−	0.766716i	−0.0925745	−	0.0356709i
$463$	−13.6226	+	6.94105i	−0.633095	+	0.322578i	−0.740921	−	0.671592i	$-0.765611\pi$
$463$	−13.6226	+	6.94105i	−0.633095	+	0.322578i	0.107827	+	0.994170i	$0.465611\pi$
$464$	−6.85112			−0.318055
$465$	21.5618	+	0.300318i	0.999903	+	0.0139269i
$466$	10.8676			0.503430
$467$	−26.1324	+	13.3151i	−1.20926	+	0.616150i	−0.938094	−	0.346382i	$-0.887410\pi$
$467$	−26.1324	+	13.3151i	−1.20926	+	0.616150i	−0.271169	+	0.962532i	$0.587410\pi$
$468$	−3.25420	−	3.27076i	−0.150425	−	0.151191i
$469$	2.34673	−	3.22999i	0.108362	−	0.149147i
$470$	−7.91768	−	5.51718i	−0.365215	−	0.254488i
$471$	38.5168	−	3.99887i	1.77476	−	0.184258i
$472$	−2.10829	−	2.60352i	−0.0970419	−	0.119837i
$473$	1.64190	−	10.3666i	0.0754948	−	0.476655i
$474$	24.9912	+	8.15520i	1.14788	+	0.374581i
$475$	1.46247	−	0.923148i	0.0671029	−	0.0423569i
$476$	0.373673	+	0.839284i	0.0171273	+	0.0384685i
$477$	−0.769534	−	4.93975i	−0.0352345	−	0.226176i
$478$	3.83619	+	5.90722i	0.175463	+	0.270190i
$479$	24.7758	+	11.0309i	1.13203	+	0.504014i	0.885277	−	0.465063i	$-0.153968\pi$
$479$	24.7758	+	11.0309i	1.13203	+	0.504014i	0.246757	+	0.969077i	$0.420635\pi$
$480$	0.735162	−	3.80257i	0.0335554	−	0.173563i
$481$	1.02777	+	3.16314i	0.0468621	+	0.144227i
$482$	3.78142	+	9.85093i	0.172239	+	0.448697i
$483$	0.632789	+	4.02835i	0.0287929	+	0.183296i
$484$	−1.40143	−	6.59320i	−0.0637013	−	0.299691i
$485$	9.91524	−	20.4474i	0.450228	−	0.928467i
$486$	−15.2681	+	3.14422i	−0.692574	+	0.142625i
$487$	14.6080	+	11.8293i	0.661950	+	0.536036i	0.900370	−	0.435126i	$-0.143296\pi$
$487$	14.6080	+	11.8293i	0.661950	+	0.536036i	−0.238420	+	0.971162i	$0.576629\pi$
$488$	1.26000	−	7.95535i	0.0570377	−	0.360122i
$489$	−1.65684	+	2.86135i	−0.0749251	+	0.129395i
$490$	13.9723	+	5.04950i	0.631206	+	0.228113i
$491$	−9.38202	−	5.41671i	−0.423405	−	0.244453i	0.273128	−	0.961978i	$-0.411942\pi$
$491$	−9.38202	−	5.41671i	−0.423405	−	0.244453i	−0.696533	+	0.717525i	$0.745275\pi$
$492$	8.36846	+	2.25371i	0.377279	+	0.101605i
$493$	−10.5369	+	0.552215i	−0.474558	+	0.0248705i
$494$	0.164386	−	0.505929i	0.00739609	−	0.0227628i
$495$	8.32912	+	11.0591i	0.374366	+	0.497069i
$496$	5.32856	+	1.61445i	0.239259	+	0.0724910i
$497$	4.76328	+	4.76328i	0.213662	+	0.213662i
$498$	0.758317	+	14.8296i	0.0339810	+	0.664529i
$499$	3.75964	+	3.38519i	0.168304	+	0.151542i	0.748979	−	0.662594i	$-0.230544\pi$
$499$	3.75964	+	3.38519i	0.168304	+	0.151542i	−0.580674	+	0.814136i	$0.697211\pi$
$500$	−8.64046	+	7.09524i	−0.386413	+	0.317309i
$501$	−0.203132	+	0.147191i	−0.00907527	+	0.00657599i
$502$	−26.0223	−	6.97264i	−1.16143	−	0.311204i
$503$	−21.4617	−	26.5030i	−0.956931	−	1.18171i	−0.983288	−	0.182059i	$-0.941724\pi$
$503$	−21.4617	−	26.5030i	−0.956931	−	1.18171i	0.0263568	−	0.999653i	$-0.491609\pi$
$504$	−1.74953	−	0.376518i	−0.0779304	−	0.0167714i
$505$	−29.7667	+	0.587421i	−1.32460	+	0.0261399i
$506$	6.05314	−	5.45027i	0.269095	−	0.242294i
$507$	−13.0083	−	13.0413i	−0.577717	−	0.579185i
$508$	−0.723745	−	0.470006i	−0.0321110	−	0.0208531i
$509$	−32.2661	−	6.85837i	−1.43017	−	0.303992i	−0.573224	−	0.819399i	$-0.694308\pi$
$509$	−32.2661	−	6.85837i	−1.43017	−	0.303992i	−0.856946	+	0.515407i	$0.827641\pi$
$510$	0.824169	−	5.90753i	0.0364948	−	0.261590i
$511$	0.0614328	+	0.189071i	0.00271763	+	0.00836399i
$512$	0.453990	−	0.891007i	0.0200637	−	0.0393773i
$513$	−1.12576	−	1.40107i	−0.0497034	−	0.0618586i
$514$	−3.65609	+	17.2006i	−0.161263	+	0.758684i
$515$	−13.7437	−	10.6874i	−0.605621	−	0.470945i
$516$	0.0111772	−	8.80837i	0.000492048	−	0.387767i
$517$	8.89490	+	0.466162i	0.391197	+	0.0205018i
$518$	1.00255	+	0.811846i	0.0440494	+	0.0356705i
$519$	−7.86847	−	37.2506i	−0.345388	−	1.63512i
$520$	−0.648493	+	3.37727i	−0.0284383	+	0.148103i
$521$	−19.1712	+	11.0685i	−0.839907	+	0.484920i	−0.857233	−	0.514929i	$-0.827818\pi$
$521$	−19.1712	+	11.0685i	−0.839907	+	0.484920i	0.0173257	+	0.999850i	$0.494485\pi$
$522$	11.2379	−	17.2090i	0.491869	−	0.753219i
$523$	0.602829	+	3.80611i	0.0263599	+	0.166430i	0.997357	−	0.0726634i	$-0.0231499\pi$
$523$	0.602829	+	3.80611i	0.0263599	+	0.166430i	−0.970997	+	0.239093i	$0.923150\pi$
$524$	−0.749024	+	0.831876i	−0.0327213	+	0.0363407i
$525$	3.19394	+	4.06046i	0.139395	+	0.177213i
$526$	−27.0313			−1.17862
$527$	8.32534	+	2.05350i	0.362658	+	0.0894519i
$528$	1.27682	+	3.33890i	0.0555666	+	0.145307i
$529$	7.06067	+	2.29415i	0.306985	+	0.0997456i
$530$	−2.71943	+	2.54752i	−0.118125	+	0.110657i
$531$	9.99790	−	1.02517i	0.433872	−	0.0444888i
$532$	−0.0534034	−	0.199304i	−0.00231533	−	0.00864094i
$533$	−7.43320	−	1.99172i	−0.321968	−	0.0862710i
$534$	6.39878	−	11.0506i	0.276902	−	0.478206i
$535$	1.74899	+	0.431841i	0.0756153	+	0.0186701i
$536$	−6.65619	+	0.699594i	−0.287504	+	0.0302178i
$537$	6.33217	+	3.23653i	0.273253	+	0.139667i
$538$	9.64371	+	3.70187i	0.415770	+	0.159599i
$539$	−13.4129	+	2.85101i	−0.577736	+	0.122802i
$540$	8.34563	+	8.08397i	0.359139	+	0.347879i
$541$	17.2160	+	7.66506i	0.740174	+	0.329547i	0.741953	−	0.670452i	$-0.233900\pi$
$541$	17.2160	+	7.66506i	0.740174	+	0.329547i	−0.00177941	+	0.999998i	$0.500566\pi$
$542$	−0.804008	+	1.57796i	−0.0345351	+	0.0677790i
$543$	−12.0514	−	14.9209i	−0.517175	−	0.640318i
$544$	0.626411	−	1.40694i	0.0268572	−	0.0603222i
$545$	10.9632	−	36.1535i	0.469614	−	1.54865i
$546$	1.55390	+	0.332353i	0.0665007	+	0.0142234i
$547$	6.55061	−	17.0649i	0.280084	−	0.729644i	−0.719305	−	0.694694i	$-0.755540\pi$
$547$	6.55061	−	17.0649i	0.280084	−	0.729644i	0.999389	−	0.0349495i	$-0.0111270\pi$
$548$	7.74248	+	0.405766i	0.330742	+	0.0173335i
$549$	17.9159	+	16.2141i	0.764633	+	0.692001i
$550$	3.31514	−	9.77228i	0.141358	−	0.416692i
$551$	2.35677	+	0.247706i	0.100402	+	0.0105526i
$552$	4.30864	−	5.30694i	0.183388	−	0.225878i
$553$	−8.74531	+	2.34330i	−0.371888	+	0.0996472i
$554$	−18.4949	−	13.4374i	−0.785775	−	0.570899i
$555$	−2.73482	−	7.91651i	−0.116086	−	0.336037i
$556$	1.42934	−	4.39906i	0.0606176	−	0.186562i
$557$	0.907582	+	0.907582i	0.0384555	+	0.0384555i	0.726073	−	0.687618i	$-0.241343\pi$
$557$	0.907582	+	0.907582i	0.0384555	+	0.0384555i	−0.687618	+	0.726073i	$0.741343\pi$
$558$	−12.7957	+	10.7364i	−0.541685	+	0.454508i
$559$			7.82129i			0.330805i
$560$	0.502497	+	1.23561i	0.0212344	+	0.0522141i
$561$	2.23285	+	5.03224i	0.0942711	+	0.212461i
$562$	−24.7576	+	3.92122i	−1.04434	+	0.165407i
$563$	−10.2709	−	38.3317i	−0.432869	−	1.61549i	−0.746116	−	0.665816i	$-0.768083\pi$
$563$	−10.2709	−	38.3317i	−0.432869	−	1.61549i	0.313247	−	0.949672i	$-0.398583\pi$
$564$	7.43515	−	0.771928i	0.313076	−	0.0325040i
$565$	1.23356	+	1.81987i	0.0518962	+	0.0765625i
$566$	−10.9362	−	15.0524i	−0.459683	−	0.632700i
$567$	3.81551	−	3.77698i	0.160237	−	0.158618i
$568$	0.591002	−	11.2770i	0.0247979	−	0.473172i
$569$	−6.05889	+	2.69759i	−0.254002	+	0.113089i	−0.529788	−	0.848130i	$-0.677729\pi$
$569$	−6.05889	+	2.69759i	−0.254002	+	0.113089i	0.275786	+	0.961219i	$0.411062\pi$
$570$	−0.390378	+	1.28149i	−0.0163511	+	0.0536758i
$571$	16.4213	+	3.49045i	0.687208	+	0.146071i	0.538266	−	0.842775i	$-0.319080\pi$
$571$	16.4213	+	3.49045i	0.687208	+	0.146071i	0.148943	+	0.988846i	$0.452413\pi$
$572$	−1.13750	−	2.96329i	−0.0475613	−	0.123901i
$573$	18.9771	−	15.3275i	0.792779	−	0.640316i
$574$	−2.83875	+	0.922367i	−0.118487	+	0.0384989i
$575$	−19.3533	+	3.85350i	−0.807088	+	0.160702i
$576$	1.49340	+	2.60187i	0.0622251	+	0.108411i
$577$	−11.6718	+	17.9730i	−0.485904	+	0.748227i	−0.993557	−	0.113335i	$-0.963847\pi$
$577$	−11.6718	+	17.9730i	−0.485904	+	0.748227i	0.507653	+	0.861562i	$0.330513\pi$
$578$	−5.24225	+	13.6565i	−0.218049	+	0.568037i
$579$	−0.0151085	−	0.0467008i	−0.000627889	−	0.00194082i
$580$	−15.3166	+	0.302260i	−0.635987	+	0.0125507i
$581$	−3.00598	−	4.13737i	−0.124709	−	0.171647i
$582$	4.53425	+	17.0084i	0.187951	+	0.705020i
$583$	0.890157	−	3.32211i	0.0368665	−	0.137588i
$584$	0.166631	−	0.288613i	0.00689523	−	0.0119429i
$585$	−7.41949	−	7.16864i	−0.306758	−	0.296387i
$586$	−7.22550	+	8.02473i	−0.298483	+	0.331499i
$587$	37.5890	−	19.1525i	1.55146	−	0.790510i	0.552391	−	0.833585i	$-0.313715\pi$
$587$	37.5890	−	19.1525i	1.55146	−	0.790510i	0.999072	+	0.0430751i	$0.0137155\pi$
$588$	−10.7489	+	4.11047i	−0.443276	+	0.169513i
$589$	−1.77464	−	0.748024i	−0.0731227	−	0.0308218i
$590$	−4.82823	−	5.72750i	−0.198775	−	0.235798i
$591$	−7.85599	+	8.70272i	−0.323152	+	0.357982i
$592$	−0.113180	−	2.15960i	−0.00465167	−	0.0887591i
$593$	33.9942	−	5.38415i	1.39597	−	0.221101i	0.587306	−	0.809365i	$-0.300189\pi$
$593$	33.9942	−	5.38415i	1.39597	−	0.221101i	0.808669	+	0.588264i	$0.200189\pi$
$594$	−10.4812	−	2.26959i	−0.430049	−	0.0931222i
$595$	0.872424	+	1.85984i	0.0357659	+	0.0762462i
$596$	1.94006	+	0.203908i	0.0794678	+	0.00835240i
$597$	26.1537	+	17.0317i	1.07040	+	0.697059i
$598$	−3.81981	+	4.71708i	−0.156204	+	0.192896i
$599$	22.7321	+	25.2466i	0.928809	+	1.03155i	0.999420	+	0.0340435i	$0.0108385\pi$
$599$	22.7321	+	25.2466i	0.928809	+	1.03155i	−0.0706109	+	0.997504i	$0.522495\pi$
$600$	1.47579	−	8.53358i	0.0602489	−	0.348382i
$601$	23.1130	−	4.91281i	0.942797	−	0.200398i	0.289224	−	0.957261i	$-0.406603\pi$
$601$	23.1130	−	4.91281i	0.942797	−	0.200398i	0.653573	+	0.756864i	$0.273269\pi$
$602$	1.65225	+	2.54425i	0.0673408	+	0.103696i
$603$	9.16085	−	17.8669i	0.373059	−	0.727598i
$604$	5.64749	−	1.83498i	0.229793	−	0.0746643i
$605$	−3.42396	−	14.6781i	−0.139204	−	0.596751i
$606$	17.1577	−	15.4095i	0.696986	−	0.625969i
$607$	−28.0609	+	18.2229i	−1.13896	+	0.739647i	−0.969306	−	0.245858i	$-0.920930\pi$
$607$	−28.0609	+	18.2229i	−1.13896	+	0.739647i	−0.169650	+	0.985504i	$0.554264\pi$
$608$	−0.188386	+	0.290089i	−0.00764007	+	0.0117647i
$609$	−0.00898238	+	7.07871i	−0.000363984	+	0.286844i
$610$	2.46593	−	17.8408i	0.0998426	−	0.722354i
$611$	−6.60107	+	0.693801i	−0.267051	+	0.0280682i
$612$	2.50654	+	3.88126i	0.101321	+	0.156891i
$613$	3.99441	−	3.23461i	0.161333	−	0.130645i	−0.545255	−	0.838270i	$-0.683567\pi$
$613$	3.99441	−	3.23461i	0.161333	−	0.130645i	0.706587	+	0.707626i	$0.250234\pi$
$614$	15.1198	+	26.1882i	0.610185	+	1.05687i
$615$	18.8082	+	4.66926i	0.758421	+	0.188283i
$616$	−0.996023	−	0.723653i	−0.0401309	−	0.0291568i
$617$	−8.50365	+	0.445657i	−0.342344	+	0.0179415i	−0.222733	−	0.974879i	$-0.571498\pi$
$617$	−8.50365	+	0.445657i	−0.342344	+	0.0179415i	−0.119611	+	0.992821i	$0.538165\pi$
$618$	13.4682	−	0.688703i	0.541771	−	0.0277037i
$619$			28.2955i			1.13729i	0.822582	+	0.568647i	$0.192533\pi$
$619$			28.2955i			1.13729i	−0.822582	+	0.568647i	$0.807467\pi$
$620$	11.9839	+	3.37424i	0.481286	+	0.135513i
$621$	6.26283	+	19.5276i	0.251319	+	0.783617i
$622$	−9.57677	−	18.7955i	−0.383994	−	0.753630i
$623$	0.230168	+	4.39187i	0.00922150	+	0.175957i
$624$	−1.32898	−	2.30862i	−0.0532017	−	0.0924186i
$625$	−19.0039	+	16.2435i	−0.760155	+	0.649742i
$626$	3.14673	−	1.81677i	0.125769	−	0.0726126i
$627$	−0.318504	−	1.19474i	−0.0127198	−	0.0477131i
$628$	22.0819	+	3.49744i	0.881165	+	0.139563i
$629$	−0.348137	−	3.31230i	−0.0138811	−	0.132070i
$630$	−3.92793	−	0.764569i	−0.156492	−	0.0304612i
$631$	−37.2499	+	16.5847i	−1.48290	+	0.660228i	−0.979060	−	0.203572i	$-0.934745\pi$
$631$	−37.2499	+	16.5847i	−1.48290	+	0.660228i	−0.503835	+	0.863800i	$0.668078\pi$
$632$	12.7289	+	8.26624i	0.506328	+	0.328813i
$633$	−37.0536	+	5.82053i	−1.47275	+	0.231345i
$634$	−5.01595	+	11.2660i	−0.199209	+	0.447430i
$635$	−1.63876	−	1.01883i	−0.0650324	−	0.0404310i
$636$	0.305350	−	2.87017i	0.0121079	−	0.113810i
$637$	9.53969	−	3.66194i	0.377976	−	0.145091i
$638$	11.8586	−	7.70105i	0.469486	−	0.304888i
$639$	27.3568	+	19.9821i	1.08222	+	0.790481i
$640$	0.975646	−	2.01199i	0.0385658	−	0.0795310i
$641$	6.80948	−	6.13129i	0.268958	−	0.242171i	−0.523604	−	0.851962i	$-0.675413\pi$
$641$	6.80948	−	6.13129i	0.268958	−	0.242171i	0.792563	+	0.609790i	$0.208746\pi$
$642$	−1.24415	+	0.631940i	−0.0491028	+	0.0249407i
$643$	−30.6039	−	4.84718i	−1.20690	−	0.191154i	−0.479608	−	0.877483i	$-0.659221\pi$
$643$	−30.6039	−	4.84718i	−1.20690	−	0.191154i	−0.727292	+	0.686328i	$0.759221\pi$
$644$	−0.246090	+	2.34139i	−0.00969732	+	0.0922638i
$645$	−0.363623	−	19.6928i	−0.0143176	−	0.775403i
$646$	−0.266352	+	0.461336i	−0.0104795	+	0.0181510i
$647$	3.63518	+	22.9516i	0.142914	+	0.902322i	0.950082	+	0.312001i	$0.100999\pi$
$647$	3.63518	+	22.9516i	0.142914	+	0.902322i	−0.807168	+	0.590322i	$0.799001\pi$
$648$	−8.98516	−	0.516636i	−0.352970	−	0.0202954i
$649$	6.57574	+	2.13659i	0.258120	+	0.0838684i
$650$	−1.30079	+	7.57894i	−0.0510213	+	0.297271i
$651$	1.67507	−	5.50345i	0.0656512	−	0.215697i
$652$	−1.34984	+	1.34984i	−0.0528639	+	0.0528639i
$653$	9.45379	+	18.5541i	0.369955	+	0.726078i	0.998670	−	0.0515580i	$-0.0164187\pi$
$653$	9.45379	+	18.5541i	0.369955	+	0.726078i	−0.628715	+	0.777636i	$0.716419\pi$
$654$	11.8687	+	26.7488i	0.464102	+	1.04596i
$655$	−1.63784	+	1.89281i	−0.0639958	+	0.0739584i
$656$	4.33331	+	2.50184i	0.169187	+	0.0976804i
$657$	0.451631	+	0.891964i	0.0176198	+	0.0347988i
$658$	−2.00075	+	1.62017i	−0.0779972	+	0.0631609i
$659$	8.37551	−	6.08516i	0.326263	−	0.237044i	−0.412580	−	0.910921i	$-0.635372\pi$
$659$	8.37551	−	6.08516i	0.326263	−	0.237044i	0.738843	+	0.673877i	$0.235372\pi$
$660$	3.00182	+	7.40822i	0.116846	+	0.288364i
$661$	−22.9474	−	25.4857i	−0.892551	−	0.991278i	0.107445	−	0.994211i	$-0.465733\pi$
$661$	−22.9474	−	25.4857i	−0.892551	−	0.991278i	−0.999996	+	0.00293299i	$0.999066\pi$
$662$	6.26370	+	2.40441i	0.243446	+	0.0934501i
$663$	−2.23002	−	3.44349i	−0.0866068	−	0.133734i
$664$	−1.78244	+	8.38570i	−0.0691719	+	0.325428i
$665$	−0.128183	−	0.443215i	−0.00497074	−	0.0171871i
$666$	5.61026	+	3.25810i	0.217393	+	0.126249i
$667$	−24.0919	−	12.2754i	−0.932841	−	0.475306i
$668$	−0.135211	+	0.0519027i	−0.00523147	+	0.00200817i
$669$	22.9253	+	16.7007i	0.886342	+	0.645685i
$670$	−14.8499	+	1.85769i	−0.573703	+	0.0717690i
$671$	6.76134	+	15.1862i	0.261018	+	0.586257i
$672$	−0.920010	−	0.470240i	−0.0354902	−	0.0181399i
$673$	4.92499	−	6.08185i	0.189844	−	0.234438i	−0.673333	−	0.739340i	$-0.735138\pi$
$673$	4.92499	−	6.08185i	0.189844	−	0.234438i	0.863177	+	0.504901i	$0.168471\pi$
$674$	−12.8926	+	9.36704i	−0.496606	+	0.360805i
$675$	19.0144	+	17.7046i	0.731865	+	0.681450i
$676$	−5.31735	−	9.20992i	−0.204514	−	0.354228i
$677$	−36.0010	+	9.64644i	−1.38363	+	0.370743i	−0.872439	−	0.488724i	$-0.837463\pi$
$677$	−36.0010	+	9.64644i	−1.38363	+	0.370743i	−0.511192	+	0.859466i	$0.670796\pi$
$678$	−1.64440	−	0.442852i	−0.0631526	−	0.0170076i
$679$	−4.50523	−	4.05653i	−0.172895	−	0.155675i
$680$	1.33835	−	3.17304i	0.0513235	−	0.121681i
$681$	22.8195	+	10.1946i	0.874447	+	0.390659i
$682$	−11.0379	+	3.19516i	−0.422664	+	0.122349i
$683$	−27.5893	+	27.5893i	−1.05567	+	1.05567i	−0.0573177	+	0.998356i	$0.518255\pi$
$683$	−27.5893	+	27.5893i	−1.05567	+	1.05567i	−0.998356	+	0.0573177i	$0.981745\pi$
$684$	−0.419654	−	0.949032i	−0.0160459	−	0.0362872i
$685$	17.3272	+	0.565559i	0.662040	+	0.0216089i
$686$	4.78407	−	6.58471i	0.182657	−	0.251405i
$687$	5.78835	+	0.924316i	0.220840	+	0.0352649i
$688$	1.31623	−	4.91224i	0.0501808	−	0.187277i
$689$	−0.267897	+	2.54887i	−0.0102061	+	0.0971042i
$690$	9.39839	−	12.0545i	0.357791	−	0.458905i
$691$	−1.55915	−	14.8344i	−0.0593130	−	0.564325i	−0.983312	−	0.181930i	$-0.941766\pi$
$691$	−1.55915	−	14.8344i	−0.0593130	−	0.564325i	0.923999	−	0.382396i	$-0.124901\pi$
$692$	1.15041	−	21.9511i	0.0437320	−	0.834455i
$693$	3.45149	−	1.31486i	0.131111	−	0.0499475i
$694$	0.217173	+	1.02172i	0.00824379	+	0.0387840i
$695$	3.00140	−	9.89774i	0.113850	−	0.375443i
$696$	8.82859	−	7.92904i	0.334647	−	0.300549i
$697$	6.86620	+	3.49850i	0.260076	+	0.132515i
$698$	−17.1901	−	8.75882i	−0.650657	−	0.331526i
$699$	−14.0043	+	12.5774i	−0.529691	+	0.475720i
$700$	1.17791	+	2.74021i	0.0445209	+	0.103570i
$701$	7.15334	+	33.6538i	0.270178	+	1.27109i	0.878633	+	0.477498i	$0.158456\pi$
$701$	7.15334	+	33.6538i	0.270178	+	1.27109i	−0.608455	+	0.793588i	$0.708210\pi$
$702$	7.97883	+	0.448616i	0.301142	+	0.0169319i
$703$	−0.0391481	+	0.746989i	−0.00147650	+	0.0281732i
$704$	0.215732	+	2.05255i	0.00813070	+	0.0773584i
$705$	16.5882	−	2.05377i	0.624748	−	0.0773496i
$706$	−2.91896	+	27.7720i	−0.109856	+	1.04521i
$707$	−2.05570	+	7.67197i	−0.0773124	+	0.288534i
$708$	5.72996	+	0.914991i	0.215345	+	0.0343875i
$709$	−8.00773	+	11.0217i	−0.300737	+	0.413928i	−0.932464	−	0.361262i	$-0.882346\pi$
$709$	−8.00773	+	11.0217i	−0.300737	+	0.413928i	0.631728	+	0.775190i	$0.282346\pi$
$710$	0.823741	−	25.2373i	0.0309145	−	0.947138i
$711$	−41.6428	+	18.4141i	−1.56173	+	0.690582i
$712$	5.21313	−	5.21313i	0.195370	−	0.195370i
$713$	15.8451	+	15.2246i	0.593404	+	0.570165i
$714$	−1.45286	−	0.649065i	−0.0543719	−	0.0242906i
$715$	−2.67377	−	6.57464i	−0.0999933	−	0.245878i
$716$	3.05117	+	2.74728i	0.114027	+	0.102671i
$717$	−11.7801	−	3.17249i	−0.439935	−	0.118479i
$718$	−13.1111	+	3.51310i	−0.489300	+	0.131108i
$719$	14.9722	+	25.9326i	0.558368	+	0.967122i	0.997633	+	0.0687643i	$0.0219056\pi$
$719$	14.9722	+	25.9326i	0.558368	+	0.967122i	−0.439265	+	0.898358i	$0.644761\pi$
$720$	3.45349	+	5.75095i	0.128704	+	0.214325i
$721$	−3.75756	+	2.73003i	−0.139939	+	0.101672i
$722$	−11.8818	+	14.6728i	−0.442195	+	0.546065i
$723$	−16.2737	−	8.31788i	−0.605224	−	0.309345i
$724$	−4.50402	−	10.1162i	−0.167391	−	0.375965i
$725$	−34.2289	+	1.35149i	−1.27123	+	0.0501929i
$726$	9.43646	+	6.87430i	0.350220	+	0.255129i
$727$	−31.8551	+	12.2280i	−1.18144	+	0.453513i	−0.868226	−	0.496170i	$-0.834739\pi$
$727$	−31.8551	+	12.2280i	−1.18144	+	0.453513i	−0.313215	+	0.949682i	$0.601406\pi$
$728$	0.817440	+	0.416507i	0.0302963	+	0.0154368i
$729$	16.0360	−	21.7220i	0.593928	−	0.804518i
$730$	0.359792	−	0.652584i	0.0133165	−	0.0241532i
$731$	1.62840	−	7.66101i	0.0602285	−	0.283353i
$732$	7.58332	+	11.7098i	0.280287	+	0.432806i
$733$	18.4499	+	7.08226i	0.681463	+	0.261589i	0.674379	−	0.738386i	$-0.264412\pi$
$733$	18.4499	+	7.08226i	0.681463	+	0.261589i	0.00708468	+	0.999975i	$0.497745\pi$
$734$	−5.51502	−	6.12505i	−0.203563	−	0.226080i
$735$	−23.8492	+	9.66371i	−0.879691	+	0.356451i
$736$	3.19290	−	2.31978i	0.117692	−	0.0855081i
$737$	10.7348	−	8.69286i	0.395421	−	0.320206i
$738$	−13.3922	+	6.78090i	−0.492973	+	0.249608i
$739$	2.28171	+	1.31734i	0.0839339	+	0.0484593i	0.541380	−	0.840778i	$-0.317902\pi$
$739$	2.28171	+	1.31734i	0.0839339	+	0.0484593i	−0.457446	+	0.889238i	$0.651236\pi$
$740$	−0.348307	−	4.82309i	−0.0128040	−	0.177300i
$741$	0.373695	+	0.842207i	0.0137280	+	0.0309393i
$742$	0.451305	+	0.885735i	0.0165679	+	0.0325164i
$743$	−27.0117	+	27.0117i	−0.990964	+	0.990964i	−0.999960	−	0.00899564i	$-0.997137\pi$
$743$	−27.0117	+	27.0117i	−0.990964	+	0.990964i	0.00899564	+	0.999960i	$0.497137\pi$
$744$	−8.73502	+	4.08648i	−0.320242	+	0.149818i
$745$	4.34625	+	0.370271i	0.159234	+	0.0135657i
$746$	18.9766	+	6.16588i	0.694783	+	0.225749i
$747$	−18.1400	−	18.2323i	−0.663706	−	0.667084i
$748$	0.497231	+	3.13939i	0.0181806	+	0.114788i
$749$	0.240300	−	0.416212i	0.00878038	−	0.0152081i
$750$	2.92284	−	19.1431i	0.106727	−	0.699006i
$751$	−3.01392	+	28.6755i	−0.109979	+	1.04638i	0.790790	+	0.612087i	$0.209670\pi$
$751$	−3.01392	+	28.6755i	−0.109979	+	1.04638i	−0.900770	+	0.434297i	$0.856997\pi$
$752$	4.26263	+	0.675134i	0.155442	+	0.0246196i
$753$	41.6029	−	21.1313i	1.51609	−	0.770066i
$754$	−7.83029	+	7.05043i	−0.285163	+	0.256761i
$755$	12.5448	−	4.35150i	0.456550	−	0.158367i
$756$	2.69027	−	1.53960i	0.0978440	−	0.0559947i
$757$	−15.7292	+	10.2147i	−0.571689	+	0.371259i	−0.797873	−	0.602825i	$-0.794042\pi$
$757$	−15.7292	+	10.2147i	−0.571689	+	0.371259i	0.226184	+	0.974085i	$0.427375\pi$
$758$	21.2638	−	8.16242i	0.772337	−	0.296472i
$759$	−1.49250	+	14.0289i	−0.0541743	+	0.509217i
$760$	−0.408364	+	0.656845i	−0.0148129	+	0.0238263i
$761$	−19.4906	+	43.7767i	−0.706535	+	1.58690i	0.0995012	+	0.995037i	$0.468275\pi$
$761$	−19.4906	+	43.7767i	−0.706535	+	1.58690i	−0.806036	+	0.591866i	$0.798391\pi$
$762$	1.47660	−	0.231950i	0.0534914	−	0.00840265i
$763$	−8.45263	−	5.48920i	−0.306006	−	0.198723i
$764$	12.8662	−	5.72841i	0.465483	−	0.207246i
$765$	5.77493	+	8.56649i	0.208793	+	0.309722i
$766$	1.54073	+	14.6591i	0.0556690	+	0.529655i
$767$	−5.08887	−	0.805998i	−0.183748	−	0.0291029i
$768$	0.446164	+	1.67360i	0.0160996	+	0.0603908i
$769$	−22.1589	+	12.7935i	−0.799071	+	0.461344i	−0.843146	−	0.537684i	$-0.819299\pi$
$769$	−22.1589	+	12.7935i	−0.799071	+	0.461344i	0.0440751	+	0.999028i	$0.485966\pi$
$770$	−2.25867	−	1.57388i	−0.0813968	−	0.0567187i
$771$	−15.1954	−	26.3966i	−0.547250	−	0.950649i
$772$	−0.00148313	−	0.0282998i	−5.33790e−5	−	0.00101853i
$773$	9.69726	+	19.0319i	0.348786	+	0.684531i	0.997039	−	0.0768936i	$-0.0245002\pi$
$773$	9.69726	+	19.0319i	0.348786	+	0.684531i	−0.648253	+	0.761425i	$0.724500\pi$
$774$	10.1798	+	11.3637i	0.365906	+	0.408460i
$775$	26.9405	+	7.01484i	0.967732	+	0.251980i
$776$			10.1627i			0.364821i
$777$	−2.23149	+	0.114108i	−0.0800543	+	0.00409361i
$778$	30.6215	−	1.60481i	1.09784	−	0.0575351i
$779$	−1.40019	−	1.01730i	−0.0501671	−	0.0364485i
$780$	−3.07296	−	5.10259i	−0.110030	−	0.182702i
$781$	11.6530	+	20.1836i	0.416978	+	0.722227i
$782$	4.72364	−	3.82513i	0.168917	−	0.136786i
$783$	5.43510	+	35.1821i	0.194234	+	1.25731i
$784$	−6.60775	+	0.694503i	−0.235991	+	0.0248037i
$785$	49.5214	+	6.84476i	1.76749	+	0.244300i
$786$	0.00246027	−	1.93886i	8.77548e−5	−	0.0691567i
$787$	−18.1243	+	27.9090i	−0.646062	+	0.994848i	0.352201	+	0.935925i	$0.385433\pi$
$787$	−18.1243	+	27.9090i	−0.646062	+	0.994848i	−0.998263	+	0.0589235i	$0.981233\pi$
$788$	−5.67688	+	3.68661i	−0.202230	+	0.131330i
$789$	34.8334	−	31.2842i	1.24010	−	1.11375i
$790$	28.8218	+	17.9187i	1.02543	+	0.637519i
$791$	0.557813	−	0.181244i	0.0198335	−	0.00644431i
$792$	−5.50958	−	2.82491i	−0.195774	−	0.100379i
$793$	−6.74670	−	10.3890i	−0.239582	−	0.368924i
$794$	−5.25599	+	1.11720i	−0.186528	+	0.0396478i
$795$	0.556022	−	6.43011i	0.0197201	−	0.228053i
$796$	12.0573	+	13.3910i	0.427361	+	0.474632i
$797$	11.3174	−	13.9758i	0.400882	−	0.495048i	−0.536233	−	0.844070i	$-0.680153\pi$
$797$	11.3174	−	13.9758i	0.400882	−	0.495048i	0.937114	+	0.349023i	$0.113486\pi$
$798$	0.299479	+	0.195025i	0.0106014	+	0.00690380i
$799$	6.61025	+	0.694765i	0.233854	+	0.0245790i
$800$	2.09242	−	4.54112i	0.0739783	−	0.160553i
$801$	4.54355	+	21.6457i	0.160538	+	0.764813i
$802$	−8.30070	+	1.31470i	−0.293108	+	0.0464237i
$803$	0.0359969	+	0.686862i	0.00127030	+	0.0242388i
$804$	7.76773	−	8.60495i	0.273947	−	0.303473i
$805$	−0.446869	+	5.24535i	−0.0157501	+	0.184874i
$806$	7.75154	−	3.63838i	0.273036	−	0.128156i
$807$	−16.7115	+	6.39063i	−0.588273	+	0.224961i
$808$	11.8635	−	6.04474i	0.417355	−	0.212653i
$809$	−35.6719	+	39.6176i	−1.25416	+	1.39288i	−0.367781	+	0.929912i	$0.619883\pi$
$809$	−35.6719	+	39.6176i	−1.25416	+	1.39288i	−0.886374	+	0.462969i	$0.846784\pi$
$810$	−20.1103	−	0.758598i	−0.706604	−	0.0266544i
$811$	28.4716	−	49.3143i	0.999774	−	1.73166i	0.481490	−	0.876451i	$-0.340096\pi$
$811$	28.4716	−	49.3143i	0.999774	−	1.73166i	0.518284	−	0.855209i	$-0.326571\pi$
$812$	−1.05777	+	3.94764i	−0.0371204	+	0.138535i
$813$	−0.790149	−	2.96391i	−0.0277117	−	0.103949i
$814$	2.62342	+	3.61083i	0.0919508	+	0.126559i
$815$	−2.95820	+	3.07730i	−0.103621	+	0.107793i
$816$	0.821088	+	2.53800i	0.0287438	+	0.0888478i
$817$	−0.630384	+	1.64221i	−0.0220543	+	0.0574535i
$818$	2.26631	−	3.48981i	0.0792397	−	0.122018i
$819$	−2.38705	+	1.37010i	−0.0834103	+	0.0478751i
$820$	9.79807	+	5.40201i	0.342163	+	0.188646i
$821$	42.5969	−	13.8406i	1.48664	−	0.483039i	0.550552	−	0.834801i	$-0.314417\pi$
$821$	42.5969	−	13.8406i	1.48664	−	0.483039i	0.936090	+	0.351762i	$0.114417\pi$
$822$	−10.4468	+	8.43775i	−0.364375	+	0.294300i
$823$	−16.8744	−	43.9594i	−0.588206	−	1.53233i	−0.827549	−	0.561394i	$-0.810265\pi$
$823$	−16.8744	−	43.9594i	−0.588206	−	1.53233i	0.239342	−	0.970935i	$-0.423068\pi$
$824$	7.61589	+	1.61881i	0.265312	+	0.0563938i
$825$	7.03780	+	16.4296i	0.245025	+	0.572006i
$826$	−1.82567	+	0.812838i	−0.0635230	+	0.0282823i
$827$	−1.32006	+	25.1882i	−0.0459030	+	0.875881i	0.874528	+	0.484975i	$0.161171\pi$
$827$	−1.32006	+	25.1882i	−0.0459030	+	0.875881i	−0.920431	+	0.390906i	$0.872162\pi$
$828$	0.589645	+	11.8252i	0.0204916	+	0.410955i
$829$	13.0132	+	17.9111i	0.451966	+	0.622078i	0.972819	−	0.231569i	$-0.0743858\pi$
$829$	13.0132	+	17.9111i	0.451966	+	0.622078i	−0.520852	+	0.853647i	$0.674386\pi$
$830$	−3.61491	+	18.8260i	−0.125475	+	0.653459i
$831$	39.3847	−	4.08898i	1.36624	−	0.141845i
$832$	−0.398051	−	1.48555i	−0.0137999	−	0.0515021i
$833$	−10.1066	+	1.60073i	−0.350173	+	0.0554620i
$834$	3.24928	+	7.32300i	0.112513	+	0.253575i
$835$	−0.299992	+	0.122001i	−0.0103817	+	0.00422200i
$836$		−	0.713872i		−	0.0246898i
$837$	4.06337	−	28.6442i	0.140451	−	0.990088i
$838$	−0.479476	−	0.479476i	−0.0165632	−	0.0165632i
$839$	2.75095	−	8.46655i	0.0949734	−	0.292298i	−0.892273	−	0.451496i	$-0.850891\pi$
$839$	2.75095	−	8.46655i	0.0949734	−	0.292298i	0.987247	+	0.159198i	$0.0508907\pi$
$840$	−2.07755	−	1.01069i	−0.0716823	−	0.0348723i
$841$	−14.5121	−	10.5436i	−0.500416	−	0.363574i
$842$	1.30895	−	0.350733i	0.0451095	−	0.0120871i
$843$	27.3654	−	33.7059i	0.942513	−	1.16089i
$844$	−21.5366	−	2.26359i	−0.741321	−	0.0779159i
$845$	−12.2940	−	20.3554i	−0.422925	−	0.700247i
$846$	−8.68781	+	9.59969i	−0.298693	+	0.330044i
$847$	−4.01540	−	0.210438i	−0.137971	−	0.00723074i
$848$	0.597200	−	1.55576i	0.0205079	−	0.0534250i
$849$	31.5134	+	6.74020i	1.08154	+	0.231323i
$850$	2.85208	−	7.15280i	0.0978254	−	0.245339i
$851$	3.47145	−	7.79700i	0.119000	−	0.267278i
$852$	12.2897	+	15.2159i	0.421037	+	0.521288i
$853$	−7.33260	+	14.3910i	−0.251063	+	0.492740i	−0.981800	−	0.189920i	$-0.939177\pi$
$853$	−7.33260	+	14.3910i	−0.251063	+	0.492740i	0.730736	+	0.682660i	$0.239177\pi$
$854$	−4.38937	−	1.95427i	−0.150201	−	0.0668738i
$855$	−0.980061	−	2.10317i	−0.0335174	−	0.0719270i
$856$	−0.788055	+	0.167506i	−0.0269352	+	0.00572524i
$857$	8.35431	+	3.20692i	0.285378	+	0.109546i	0.496846	−	0.867839i	$-0.334491\pi$
$857$	8.35431	+	3.20692i	0.285378	+	0.109546i	−0.211469	+	0.977385i	$0.567825\pi$
$858$	4.89534	+	2.50213i	0.167124	+	0.0854213i
$859$	35.3261	−	3.71293i	1.20531	−	0.126683i	0.519506	−	0.854467i	$-0.326116\pi$
$859$	35.3261	−	3.71293i	1.20531	−	0.126683i	0.685807	+	0.727784i	$0.259449\pi$
$860$	2.72589	−	11.0400i	0.0929520	−	0.376462i
$861$	2.59063	−	4.47398i	0.0882884	−	0.152473i
$862$	10.2344	+	2.74229i	0.348584	+	0.0934029i
$863$	8.61835	+	32.1641i	0.293372	+	1.09488i	0.942502	+	0.334201i	$0.108467\pi$
$863$	8.61835	+	32.1641i	0.293372	+	1.09488i	−0.649130	+	0.760678i	$0.724867\pi$
$864$	−4.93569	−	1.62450i	−0.167915	−	0.0552666i
$865$	1.60344	−	49.1253i	0.0545187	−	1.67031i
$866$	−38.2419	−	12.4255i	−1.29951	−	0.422237i
$867$	−9.04982	−	23.6653i	−0.307348	−	0.803716i
$868$	1.75295	−	2.82108i	0.0594989	−	0.0957535i
$869$	−31.3241			−1.06260
$870$	19.3877	−	18.1159i	0.657304	−	0.614187i
$871$	−6.88755	+	7.64940i	−0.233376	+	0.259190i
$872$	2.64302	+	16.6874i	0.0895040	+	0.565106i
$873$	−25.5274	−	16.6699i	−0.863970	−	0.564191i
$874$	−1.18222	+	0.682556i	−0.0399892	+	0.0230878i
$875$	2.75427	+	6.07412i	0.0931114	+	0.205343i
$876$	0.119296	+	0.564764i	0.00403062	+	0.0190816i
$877$	−19.7094	−	15.9604i	−0.665539	−	0.538943i	0.235939	−	0.971768i	$-0.424184\pi$
$877$	−19.7094	−	15.9604i	−0.665539	−	0.538943i	−0.901478	+	0.432825i	$0.857517\pi$
$878$	34.2732	+	1.79618i	1.15667	+	0.0606182i
$879$	0.0237331	−	18.7033i	0.000800497	−	0.630845i
$880$	0.572852	+	4.57923i	0.0193108	+	0.154366i
$881$	2.00586	−	9.43682i	0.0675791	−	0.317935i	−0.931354	−	0.364115i	$-0.881372\pi$
$881$	2.00586	−	9.43682i	0.0675791	−	0.317935i	0.998933	+	0.0461803i	$0.0147049\pi$
$882$	9.09419	−	17.7369i	0.306217	−	0.597233i
$883$	25.8387	−	50.7112i	0.869540	−	1.70657i	0.178257	−	0.983984i	$-0.442954\pi$
$883$	25.8387	−	50.7112i	0.869540	−	1.70657i	0.691283	−	0.722584i	$-0.257046\pi$
$884$	−0.731933	−	2.25266i	−0.0246176	−	0.0757651i
$885$	12.8505	+	1.79279i	0.431963	+	0.0602639i
$886$	21.9512	+	4.66586i	0.737463	+	0.156753i
$887$	−34.4313	−	22.3600i	−1.15609	−	0.750775i	−0.183437	−	0.983031i	$-0.558722\pi$
$887$	−34.4313	−	22.3600i	−1.15609	−	0.750775i	−0.972654	+	0.232257i	$0.925389\pi$
$888$	2.64523	+	2.65195i	0.0887681	+	0.0889937i
$889$	−0.382560	+	0.344459i	−0.0128307	+	0.0115528i
$890$	11.4246	−	11.8846i	0.382955	−	0.398374i
$891$	16.1331	−	9.20559i	0.540479	−	0.308399i
$892$	10.3055	+	12.7262i	0.345054	+	0.426106i
$893$	−1.44192	−	0.386362i	−0.0482521	−	0.0129291i
$894$	−2.73601	+	1.98253i	−0.0915059	+	0.0663057i
$895$	6.94249	+	6.00730i	0.232062	+	0.200802i
$896$	−0.443308	−	0.399156i	−0.0148099	−	0.0133349i
$897$	−0.536891	−	10.4994i	−0.0179263	−	0.350564i
$898$	15.1374	+	15.1374i	0.505143	+	0.505143i
$899$	23.0331	+	30.4064i	0.768197	+	1.01411i
$900$	7.97445	+	12.7046i	0.265815	+	0.423488i
$901$	0.793084	−	2.44086i	0.0264215	−	0.0813169i
$902$	−10.3127	+	0.540467i	−0.343376	+	0.0179956i
$903$	−5.07369	−	1.36639i	−0.168842	−	0.0454708i
$904$	−0.851492	−	0.491609i	−0.0283202	−	0.0163507i
$905$	−10.5156	−	22.4174i	−0.349552	−	0.745179i
$906$	−5.15386	+	8.90065i	−0.171226	+	0.295704i
$907$	5.47905	−	34.5933i	0.181929	−	1.14865i	−0.712576	−	0.701595i	$-0.752472\pi$
$907$	5.47905	−	34.5933i	0.181929	−	1.14865i	0.894505	−	0.447058i	$-0.147528\pi$
$908$	11.2141	+	9.08100i	0.372153	+	0.301364i
$909$	−4.27609	+	39.7145i	−0.141829	+	1.31725i
$910$	1.84587	+	0.895092i	0.0611900	+	0.0296720i
$911$	5.93106	+	27.9035i	0.196505	+	0.924483i	0.960288	+	0.279010i	$0.0900063\pi$
$911$	5.93106	+	27.9035i	0.196505	+	0.924483i	−0.763783	+	0.645473i	$0.776660\pi$
$912$	−0.0929694	−	0.591845i	−0.00307852	−	0.0195979i
$913$	−6.34079	−	16.5183i	−0.209850	−	0.546677i
$914$	5.29539	+	16.2975i	0.175156	+	0.539074i
$915$	17.4701	+	25.8442i	0.577545	+	0.854384i
$916$	3.09166	+	1.37650i	0.102151	+	0.0454808i
$917$	0.363686	+	0.560027i	0.0120100	+	0.0184937i
$918$	−7.72192	−	2.10062i	−0.254861	−	0.0693308i
$919$	−2.79861	−	6.28578i	−0.0923176	−	0.207349i	0.861485	−	0.507783i	$-0.169535\pi$
$919$	−2.79861	−	6.28578i	−0.0923176	−	0.207349i	−0.953802	+	0.300435i	$0.902868\pi$
$920$	7.03581	−	5.32704i	0.231964	−	0.175627i
$921$	−49.7924	−	16.2484i	−1.64072	−	0.535404i
$922$	3.38063	−	21.3445i	0.111335	−	0.702943i
$923$	−10.9296	−	13.4969i	−0.359751	−	0.444256i
$924$	2.12102	−	0.220207i	0.0697764	−	0.00724429i
$925$	−0.991473	−	10.7673i	−0.0325994	−	0.354026i
$926$	8.98663	−	12.3690i	0.295319	−	0.406472i
$927$	−16.5585	+	16.4747i	−0.543853	+	0.541100i
$928$	6.10440	−	3.11035i	0.200387	−	0.102102i
$929$	−53.4603			−1.75398			−0.876988	−	0.480512i	$-0.840451\pi$
$929$	−53.4603			−1.75398			−0.876988	+	0.480512i	$0.840451\pi$
$930$	−19.3480	+	9.52125i	−0.634446	+	0.312214i
$931$	2.29816			0.0753191
$932$	−9.68306	+	4.93377i	−0.317179	+	0.161611i
$933$	34.0936	+	13.1370i	1.11617	+	0.430085i
$934$	17.2392	−	23.7277i	0.564083	−	0.776394i
$935$	1.25013	+	6.99659i	0.0408837	+	0.228813i
$936$	4.38441	+	1.43689i	0.143309	+	0.0469663i
$937$	0.652746	+	0.806074i	0.0213243	+	0.0263333i	0.787697	−	0.616063i	$-0.211274\pi$
$937$	0.652746	+	0.806074i	0.0213243	+	0.0263333i	−0.766372	+	0.642397i	$0.777940\pi$
$938$	−0.624563	+	3.94333i	−0.0203927	+	0.128754i
$939$	−1.95238	+	5.98297i	−0.0637135	+	0.195247i
$940$	9.55945	+	1.32129i	0.311795	+	0.0430958i
$941$	−5.53661	−	12.4354i	−0.180488	−	0.405384i	0.800532	−	0.599291i	$-0.204551\pi$
$941$	−5.53661	−	12.4354i	−0.180488	−	0.405384i	−0.981020	+	0.193907i	$0.937884\pi$
$942$	−32.5032	+	21.0493i	−1.05901	+	0.685822i
$943$	10.7554	+	16.5618i	0.350243	+	0.539327i
$944$	3.06047	+	1.36261i	0.0996100	+	0.0443492i
$945$	5.94652	−	3.56067i	0.193440	−	0.115829i
$946$	3.24338	+	9.98209i	0.105451	+	0.324546i
$947$	12.6838	+	33.0425i	0.412169	+	1.07374i	0.969855	+	0.243684i	$0.0783560\pi$
$947$	12.6838	+	33.0425i	0.412169	+	1.07374i	−0.557686	+	0.830052i	$0.688311\pi$
$948$	−25.9697	+	4.07942i	−0.843456	+	0.132493i
$949$	−0.106563	−	0.501340i	−0.00345919	−	0.0162742i
$950$	−0.883974	+	1.48648i	−0.0286799	+	0.0482278i
$951$	−6.57481	−	20.3229i	−0.213203	−	0.659015i
$952$	−0.713972	−	0.578163i	−0.0231400	−	0.0187384i
$953$	2.97047	−	18.7548i	0.0962231	−	0.607529i	−0.891705	−	0.452617i	$-0.850491\pi$
$953$	2.97047	−	18.7548i	0.0962231	−	0.607529i	0.987928	−	0.154912i	$-0.0495094\pi$
$954$	2.92826	+	4.05199i	0.0948059	+	0.131188i
$955$	28.5114	−	13.3742i	0.922607	−	0.432781i
$956$	−6.09990	−	3.52178i	−0.197285	−	0.113902i
$957$	−6.36869	+	23.6482i	−0.205870	+	0.764437i
$958$	−27.0833	+	1.41938i	−0.875022	+	0.0458579i
$959$	1.42919	−	4.39860i	0.0461510	−	0.142038i
$960$	1.07130	+	3.72187i	0.0345759	+	0.120123i
$961$	−10.7491	−	29.0767i	−0.346745	−	0.937959i
$962$	−2.35178	−	2.35178i	−0.0758245	−	0.0758245i
$963$	0.871892	−	2.25424i	0.0280963	−	0.0726419i
$964$	−7.84149	−	7.06051i	−0.252557	−	0.227404i
$965$	−0.00456427	−	0.0632025i	−0.000146929	−	0.00203456i
$966$	−2.39265	−	3.30201i	−0.0769824	−	0.106240i
$967$	5.39896	+	1.44665i	0.173619	+	0.0465210i	0.344581	−	0.938757i	$-0.388021\pi$
$967$	5.39896	+	1.44665i	0.173619	+	0.0465210i	−0.170962	+	0.985278i	$0.554688\pi$
$968$	4.24193	+	5.23835i	0.136341	+	0.168367i
$969$	−0.190689	−	0.902752i	−0.00612581	−	0.0290006i
$970$	0.448363	+	22.7202i	0.0143961	+	0.729500i
$971$	−9.41681	+	8.47894i	−0.302200	+	0.272102i	−0.806253	−	0.591571i	$-0.798508\pi$
$971$	−9.41681	+	8.47894i	−0.302200	+	0.272102i	0.504053	+	0.863672i	$0.331841\pi$
$972$	12.1765	−	9.73307i	0.390562	−	0.312189i
$973$	−2.31407	−	1.50278i	−0.0741858	−	0.0481768i
$974$	−18.3862	−	3.90810i	−0.589131	−	0.125224i
$975$	−7.09512	−	11.2719i	−0.227226	−	0.360991i
$976$	2.48898	+	7.66030i	0.0796704	+	0.245200i
$977$	10.8653	−	21.3243i	0.347611	−	0.682225i	−0.649320	−	0.760516i	$-0.724946\pi$
$977$	10.8653	−	21.3243i	0.347611	−	0.682225i	0.996931	+	0.0782908i	$0.0249463\pi$
$978$	0.177235	−	3.30167i	0.00566734	−	0.105576i
$979$	−3.16353	+	14.8832i	−0.101107	+	0.475670i
$980$	−14.7419	+	1.84418i	−0.470912	+	0.0589101i
$981$	−46.2517	−	20.7334i	−1.47670	−	0.661966i
$982$	10.8186	+	0.566978i	0.345235	+	0.0180930i
$983$	5.15324	+	4.17301i	0.164363	+	0.133098i	0.707973	−	0.706239i	$-0.249610\pi$
$983$	5.15324	+	4.17301i	0.164363	+	0.133098i	−0.543610	+	0.839338i	$0.682943\pi$
$984$	−8.47951	+	1.79113i	−0.270317	+	0.0570993i
$985$	−12.5288	+	8.49235i	−0.399200	+	0.270589i
$986$	9.13774	−	5.27568i	0.291005	−	0.168012i
$987$	0.703150	−	4.40334i	0.0223815	−	0.140160i
$988$	0.0832177	+	0.525416i	0.00264751	+	0.0167157i
$989$	13.4299	−	14.9155i	0.427047	−	0.474284i
$990$	−12.4420	−	6.07238i	−0.395434	−	0.192993i
$991$	31.9965			1.01640			0.508202	−	0.861238i	$-0.330310\pi$
$991$	31.9965			1.01640			0.508202	+	0.861238i	$0.330310\pi$
$992$	−5.48073	+	0.980628i	−0.174013	+	0.0311350i
$993$	−10.8543	+	4.15079i	−0.344452	+	0.131721i
$994$	−6.40660	−	2.08163i	−0.203205	−	0.0660253i
$995$	27.5465	+	29.4054i	0.873284	+	0.932215i
$996$	−7.40815	−	12.8690i	−0.234736	−	0.407769i
$997$	−13.2680	−	49.5168i	−0.420201	−	1.56821i	−0.774184	−	0.632960i	$-0.781840\pi$
$997$	−13.2680	−	49.5168i	−0.420201	−	1.56821i	0.353983	−	0.935252i	$-0.384827\pi$
$998$	−4.88671	−	1.30939i	−0.154686	−	0.0414480i
$999$	−11.0003	+	2.29445i	−0.348034	+	0.0725932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bs.a.293.19	yes	1024
3.2	odd	2	inner	930.2.bs.a.293.53	yes	1024
5.2	odd	4	inner	930.2.bs.a.107.5	✓	1024
15.2	even	4	inner	930.2.bs.a.107.59	yes	1024
31.20	even	15	inner	930.2.bs.a.113.59	yes	1024
93.20	odd	30	inner	930.2.bs.a.113.5	yes	1024
155.82	odd	60	inner	930.2.bs.a.857.53	yes	1024
465.392	even	60	inner	930.2.bs.a.857.19	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bs.a.107.5	✓	1024	5.2	odd	4	inner
930.2.bs.a.107.59	yes	1024	15.2	even	4	inner
930.2.bs.a.113.5	yes	1024	93.20	odd	30	inner
930.2.bs.a.113.59	yes	1024	31.20	even	15	inner
930.2.bs.a.293.19	yes	1024	1.1	even	1	trivial
930.2.bs.a.293.53	yes	1024	3.2	odd	2	inner
930.2.bs.a.857.19	yes	1024	465.392	even	60	inner
930.2.bs.a.857.53	yes	1024	155.82	odd	60	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 + 0.453990i) q^{2} +(0.622763 - 1.61622i) q^{3} +(0.587785 - 0.809017i) q^{4} +(1.27838 - 1.83460i) q^{5} +(0.178863 + 1.72279i) q^{6} +(-0.375409 - 0.463591i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-2.22433 - 2.01304i) q^{9} +O(q^{10})\)	\(q+(-0.891007 + 0.453990i) q^{2} +(0.622763 - 1.61622i) q^{3} +(0.587785 - 0.809017i) q^{4} +(1.27838 - 1.83460i) q^{5} +(0.178863 + 1.72279i) q^{6} +(-0.375409 - 0.463591i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-2.22433 - 2.01304i) q^{9} +(-0.306155 + 2.21501i) q^{10} +(-0.839446 - 1.88543i) q^{11} +(-0.941498 - 1.45382i) q^{12} +(0.837629 + 1.28984i) q^{13} +(0.544957 + 0.242631i) q^{14} +(-2.16898 - 3.20866i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.551919 - 1.43780i) q^{17} +(2.89580 + 0.783809i) q^{18} +(0.0719150 + 0.338333i) q^{19} +(-0.732808 - 2.11258i) q^{20} +(-0.983055 + 0.318035i) q^{21} +(1.60392 + 1.29883i) q^{22} +(0.617391 - 3.89805i) q^{23} +(1.49890 + 0.867928i) q^{24} +(-1.73149 - 4.69062i) q^{25} +(-1.33191 - 0.768976i) q^{26} +(-4.63875 + 2.34136i) q^{27} +(-0.595712 + 0.0312200i) q^{28} +(2.11711 - 6.51581i) q^{29} +(3.38928 + 1.87424i) q^{30} +(-3.18205 + 4.56887i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.57004 + 0.182556i) q^{33} +(1.14451 + 1.03052i) q^{34} +(-1.33042 + 0.0960782i) q^{35} +(-2.93602 + 0.616286i) q^{36} +(2.08888 + 0.559713i) q^{37} +(-0.217677 - 0.268809i) q^{38} +(2.60630 - 0.550531i) q^{39} +(1.61203 + 1.54963i) q^{40} +(-3.71846 + 3.34811i) q^{41} +(0.731524 - 0.729669i) q^{42} +(4.26508 + 2.76977i) q^{43} +(-2.01876 - 0.429100i) q^{44} +(-6.53666 + 1.50732i) q^{45} +(1.21958 + 3.75348i) q^{46} +(-1.95931 + 3.84537i) q^{47} +(-1.72956 - 0.0928433i) q^{48} +(1.38140 - 6.49896i) q^{49} +(3.67227 + 3.39329i) q^{50} +(-2.66751 - 0.00338488i) q^{51} +(1.53584 + 0.0804902i) q^{52} +(1.29507 + 1.04873i) q^{53} +(3.07020 - 4.19212i) q^{54} +(-4.53213 - 0.870246i) q^{55} +(0.516610 - 0.298265i) q^{56} +(0.591607 + 0.0944711i) q^{57} +(1.07175 + 6.76678i) q^{58} +(-2.24166 + 2.48961i) q^{59} +(-3.87076 - 0.131258i) q^{60} -8.05452 q^{61} +(0.761005 - 5.51551i) q^{62} +(-0.0981951 + 1.78689i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(3.43713 + 0.112188i) q^{65} +(3.09805 - 1.78342i) q^{66} +(1.73224 + 6.46480i) q^{67} +(-1.48761 - 0.398605i) q^{68} +(-5.91562 - 3.42540i) q^{69} +(1.14179 - 0.689603i) q^{70} +(-11.2306 + 1.18038i) q^{71} +(2.33622 - 1.88204i) q^{72} +(-0.311127 - 0.119430i) q^{73} +(-2.11531 + 0.449623i) q^{74} +(-8.65939 - 0.122674i) q^{75} +(0.315988 + 0.140687i) q^{76} +(-0.558932 + 1.09697i) q^{77} +(-2.07230 + 1.67376i) q^{78} +(6.17323 - 13.8653i) q^{79} +(-2.13985 - 0.648889i) q^{80} +(0.895313 + 8.95536i) q^{81} +(1.79316 - 4.67133i) q^{82} +(8.56129 + 0.448678i) q^{83} +(-0.320529 + 0.982245i) q^{84} +(-3.34334 - 0.825503i) q^{85} +(-5.05766 - 0.531582i) q^{86} +(-9.21252 - 7.47952i) q^{87} +(1.99353 - 0.534166i) q^{88} +(-5.96446 - 4.33343i) q^{89} +(5.13990 - 4.31062i) q^{90} +(0.283503 - 0.872532i) q^{91} +(-2.79070 - 2.79070i) q^{92} +(5.40263 + 7.98821i) q^{93} -4.31576i q^{94} +(0.712640 + 0.300583i) q^{95} +(1.58320 - 0.702480i) q^{96} +(10.0376 - 1.58980i) q^{97} +(1.71963 + 6.41776i) q^{98} +(-1.92824 + 5.88366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) \) 1024 * q - 8 * q^3 + 24 * q^7	\( 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) \) 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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