LMFDB - Embedded newform 775.2.ck.c.49.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.9
Character	$\chi$	$=$	775.49
Dual form			775.2.ck.c.174.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04097 + 1.43277i) q^{2} +(0.449533 + 1.00967i) q^{3} +(-0.351182 + 1.08083i) q^{4} +(-0.978673 + 1.69511i) q^{6} +(1.31785 - 1.18660i) q^{7} +(1.45450 - 0.472596i) q^{8} +(1.19004 - 1.32168i) q^{9} +(5.80707 - 1.23433i) q^{11} +(-1.24914 + 0.131290i) q^{12} +(-5.32437 - 0.559613i) q^{13} +(3.07197 + 0.652967i) q^{14} +(4.03002 + 2.92798i) q^{16} +(-1.16563 + 5.48385i) q^{17} +(3.13246 + 0.329234i) q^{18} +(-0.236861 - 2.25358i) q^{19} +(1.79049 + 0.797178i) q^{21} +(7.81349 + 7.03529i) q^{22} +(2.37325 - 0.771116i) q^{23} +(1.13101 + 1.25611i) q^{24} +(-4.74070 - 8.21114i) q^{26} +(5.02280 + 1.63201i) q^{27} +(0.819703 + 1.84108i) q^{28} +(-6.80728 + 4.94578i) q^{29} +(-1.13585 - 5.45067i) q^{31} +5.76333i q^{32} +(3.85673 + 5.30834i) q^{33} +(-9.07049 + 4.03844i) q^{34} +(1.01058 + 1.75038i) q^{36} +(-9.97386 - 5.75841i) q^{37} +(2.98230 - 2.68528i) q^{38} +(-1.82846 - 5.62741i) q^{39} +(-0.000912316 - 0.000406189i) q^{41} +(0.721672 + 3.39520i) q^{42} +(-0.903210 + 0.0949312i) q^{43} +(-0.705239 + 6.70990i) q^{44} +(3.57531 + 2.59762i) q^{46} +(-6.53766 + 8.99832i) q^{47} +(-1.14466 + 5.38521i) q^{48} +(-0.402983 + 3.83413i) q^{49} +(-6.06086 + 1.28828i) q^{51} +(2.47467 - 5.55819i) q^{52} +(3.29826 + 2.96977i) q^{53} +(2.89028 + 8.89538i) q^{54} +(1.35603 - 2.34872i) q^{56} +(2.16889 - 1.25221i) q^{57} +(-14.1723 - 4.60487i) q^{58} +(3.45105 - 1.53651i) q^{59} -10.8733 q^{61} +(6.62719 - 7.30139i) q^{62} -3.15388i q^{63} +(-0.197490 + 0.143485i) q^{64} +(-3.59089 + 11.0516i) q^{66} +(6.83038 - 3.94352i) q^{67} +(-5.51774 - 3.18567i) q^{68} +(1.84543 + 2.04955i) q^{69} +(-0.0413227 + 0.0458935i) q^{71} +(1.10630 - 2.48479i) q^{72} +(0.731122 + 3.43966i) q^{73} +(-2.13199 - 20.2846i) q^{74} +(2.51891 + 0.535412i) q^{76} +(6.18820 - 8.51733i) q^{77} +(6.15942 - 8.47771i) q^{78} +(-4.17103 - 0.886580i) q^{79} +(0.0524211 + 0.498753i) q^{81} +(-0.000367716 - 0.00172997i) q^{82} +(-1.05722 + 2.37455i) q^{83} +(-1.49040 + 1.65525i) q^{84} +(-1.07623 - 1.19527i) q^{86} +(-8.05369 - 4.64980i) q^{87} +(7.86304 - 4.53973i) q^{88} +(2.12519 - 6.54066i) q^{89} +(-7.68077 + 5.58040i) q^{91} +2.83588i q^{92} +(4.99277 - 3.59709i) q^{93} -19.6980 q^{94} +(-5.81905 + 2.59081i) q^{96} +(4.59184 + 1.49198i) q^{97} +(-5.91292 + 3.41382i) q^{98} +(5.27927 - 9.14396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{13}{15}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.04097	+	1.43277i	0.736076	+	1.01312i	0.998835	+	0.0482603i	$0.0153677\pi$
$2$	1.04097	+	1.43277i	0.736076	+	1.01312i	−0.262759	+	0.964862i	$0.584632\pi$
$3$	0.449533	+	1.00967i	0.259538	+	0.582932i	0.995571	−	0.0940138i	$-0.0299698\pi$
$3$	0.449533	+	1.00967i	0.259538	+	0.582932i	−0.736033	+	0.676946i	$0.763303\pi$
$4$	−0.351182	+	1.08083i	−0.175591	+	0.540413i
$5$		0			0
$5$		0			0
$6$	−0.978673	+	1.69511i	−0.399541	+	0.692026i
$7$	1.31785	−	1.18660i	0.498101	−	0.448493i	−0.381385	−	0.924416i	$-0.624553\pi$
$7$	1.31785	−	1.18660i	0.498101	−	0.448493i	0.879487	+	0.475924i	$0.157886\pi$
$8$	1.45450	−	0.472596i	0.514243	−	0.167088i
$9$	1.19004	−	1.32168i	0.396681	−	0.440559i
$10$		0			0
$11$	5.80707	−	1.23433i	1.75090	−	0.372164i	0.782708	−	0.622389i	$-0.213838\pi$
$11$	5.80707	−	1.23433i	1.75090	−	0.372164i	0.968188	+	0.250224i	$0.0805044\pi$
$12$	−1.24914	+	0.131290i	−0.360597	+	0.0379002i
$13$	−5.32437	−	0.559613i	−1.47671	−	0.155209i	−0.668330	−	0.743865i	$-0.732991\pi$
$13$	−5.32437	−	0.559613i	−1.47671	−	0.155209i	−0.808384	+	0.588656i	$0.799657\pi$
$14$	3.07197	+	0.652967i	0.821018	+	0.174513i
$15$		0			0
$16$	4.03002	+	2.92798i	1.00751	+	0.731996i
$17$	−1.16563	+	5.48385i	−0.282706	+	1.33003i	0.575953	+	0.817483i	$0.304631\pi$
$17$	−1.16563	+	5.48385i	−0.282706	+	1.33003i	−0.858659	+	0.512547i	$0.828702\pi$
$18$	3.13246	+	0.329234i	0.738327	+	0.0776013i
$19$	−0.236861	−	2.25358i	−0.0543397	−	0.517008i	−0.987508	−	0.157568i	$-0.949635\pi$
$19$	−0.236861	−	2.25358i	−0.0543397	−	0.517008i	0.933168	−	0.359439i	$-0.117032\pi$
$20$		0			0
$21$	1.79049	+	0.797178i	0.390717	+	0.173958i
$22$	7.81349	+	7.03529i	1.66584	+	1.49993i
$23$	2.37325	−	0.771116i	0.494857	−	0.160789i	−0.0509474	−	0.998701i	$-0.516224\pi$
$23$	2.37325	−	0.771116i	0.494857	−	0.160789i	0.545805	+	0.837912i	$0.316224\pi$
$24$	1.13101	+	1.25611i	0.230867	+	0.256403i
$25$		0			0
$26$	−4.74070	−	8.21114i	−0.929728	−	1.61034i
$27$	5.02280	+	1.63201i	0.966637	+	0.314080i
$28$	0.819703	+	1.84108i	0.154909	+	0.347932i
$29$	−6.80728	+	4.94578i	−1.26408	+	0.918408i	−0.998950	−	0.0458051i	$-0.985415\pi$
$29$	−6.80728	+	4.94578i	−1.26408	+	0.918408i	−0.265129	+	0.964213i	$0.585415\pi$
$30$		0			0
$31$	−1.13585	−	5.45067i	−0.204004	−	0.978970i
$31$	−1.13585	−	5.45067i	−0.204004	−	0.978970i
$32$			5.76333i			1.01882i
$33$	3.85673	+	5.30834i	0.671371	+	0.924063i
$34$	−9.07049	+	4.03844i	−1.55558	+	0.692587i
$35$		0			0
$36$	1.01058	+	1.75038i	0.168430	+	0.291730i
$37$	−9.97386	−	5.75841i	−1.63969	−	0.946676i	−0.980939	−	0.194317i	$-0.937751\pi$
$37$	−9.97386	−	5.75841i	−1.63969	−	0.946676i	−0.658753	−	0.752359i	$-0.728916\pi$
$38$	2.98230	−	2.68528i	0.483794	−	0.435610i
$39$	−1.82846	−	5.62741i	−0.292787	−	0.901106i
$40$		0			0
$41$	−0.000912316	0	0.000406189i	−0.000142480	0	6.34361e-5i	0.406665	−	0.913577i	$-0.366691\pi$
$41$	−0.000912316	0	0.000406189i	−0.000142480	0	6.34361e-5i	−0.406808	+	0.913514i	$0.633358\pi$
$42$	0.721672	+	3.39520i	0.111356	+	0.523891i
$43$	−0.903210	+	0.0949312i	−0.137738	+	0.0144769i	−0.173147	−	0.984896i	$-0.555393\pi$
$43$	−0.903210	+	0.0949312i	−0.137738	+	0.0144769i	0.0354084	+	0.999373i	$0.488727\pi$
$44$	−0.705239	+	6.70990i	−0.106319	+	1.01156i
$45$		0			0
$46$	3.57531	+	2.59762i	0.527151	+	0.382998i
$47$	−6.53766	+	8.99832i	−0.953616	+	1.31254i	−0.00371323	+	0.999993i	$0.501182\pi$
$47$	−6.53766	+	8.99832i	−0.953616	+	1.31254i	−0.949903	+	0.312546i	$0.898818\pi$
$48$	−1.14466	+	5.38521i	−0.165218	+	0.777288i
$49$	−0.402983	+	3.83413i	−0.0575690	+	0.547732i
$50$		0			0
$51$	−6.06086	+	1.28828i	−0.848690	+	0.180395i
$52$	2.47467	−	5.55819i	0.343174	−	0.770782i
$53$	3.29826	+	2.96977i	0.453051	+	0.407929i	0.863812	−	0.503814i	$-0.168070\pi$
$53$	3.29826	+	2.96977i	0.453051	+	0.407929i	−0.410761	+	0.911743i	$0.634737\pi$
$54$	2.89028	+	8.89538i	0.393318	+	1.21051i
$55$		0			0
$56$	1.35603	−	2.34872i	0.181208	−	0.313861i
$57$	2.16889	−	1.25221i	0.287277	−	0.165860i
$58$	−14.1723	−	4.60487i	−1.86092	−	0.604649i
$59$	3.45105	−	1.53651i	0.449289	−	0.200036i	−0.169603	−	0.985512i	$-0.554249\pi$
$59$	3.45105	−	1.53651i	0.449289	−	0.200036i	0.618892	+	0.785476i	$0.287582\pi$
$60$		0			0
$61$	−10.8733			−1.39219			−0.696093	−	0.717952i	$-0.745080\pi$
$61$	−10.8733			−1.39219			−0.696093	+	0.717952i	$0.745080\pi$
$62$	6.62719	−	7.30139i	0.841653	−	0.927278i
$63$		−	3.15388i		−	0.397351i
$64$	−0.197490	+	0.143485i	−0.0246863	+	0.0179356i
$65$		0			0
$66$	−3.59089	+	11.0516i	−0.442008	+	1.36036i
$67$	6.83038	−	3.94352i	0.834464	−	0.481778i	−0.0209149	−	0.999781i	$-0.506658\pi$
$67$	6.83038	−	3.94352i	0.834464	−	0.481778i	0.855379	+	0.518003i	$0.173325\pi$
$68$	−5.51774	−	3.18567i	−0.669125	−	0.386319i
$69$	1.84543	+	2.04955i	0.222163	+	0.246737i
$70$		0			0
$71$	−0.0413227	+	0.0458935i	−0.00490411	+	0.00544656i	−0.745592	−	0.666403i	$-0.767833\pi$
$71$	−0.0413227	+	0.0458935i	−0.00490411	+	0.00544656i	0.740688	+	0.671849i	$0.234500\pi$
$72$	1.10630	−	2.48479i	0.130379	−	0.292835i
$73$	0.731122	+	3.43966i	0.0855714	+	0.402582i	0.999998	−	0.00217085i	$-0.000691004\pi$
$73$	0.731122	+	3.43966i	0.0855714	+	0.402582i	−0.914426	+	0.404753i	$0.867358\pi$
$74$	−2.13199	−	20.2846i	−0.247839	−	2.35803i
$75$		0			0
$76$	2.51891	+	0.535412i	0.288939	+	0.0614160i
$77$	6.18820	−	8.51733i	0.705211	−	0.970639i
$78$	6.15942	−	8.47771i	0.697417	−	0.959912i
$79$	−4.17103	−	0.886580i	−0.469278	−	0.0997480i	−0.0327976	−	0.999462i	$-0.510442\pi$
$79$	−4.17103	−	0.886580i	−0.469278	−	0.0997480i	−0.436480	+	0.899714i	$0.643775\pi$
$80$		0			0
$81$	0.0524211	+	0.498753i	0.00582456	+	0.0554170i
$82$	−0.000367716	−	0.00172997i	−4.06075e−5	−	0.000191043i
$83$	−1.05722	+	2.37455i	−0.116045	+	0.260641i	−0.962225	−	0.272257i	$-0.912230\pi$
$83$	−1.05722	+	2.37455i	−0.116045	+	0.260641i	0.846180	+	0.532897i	$0.178897\pi$
$84$	−1.49040	+	1.65525i	−0.162616	+	0.180603i
$85$		0			0
$86$	−1.07623	−	1.19527i	−0.116053	−	0.128890i
$87$	−8.05369	−	4.64980i	−0.863446	−	0.498511i
$88$	7.86304	−	4.53973i	0.838203	−	0.483937i
$89$	2.12519	−	6.54066i	0.225269	−	0.693308i	−0.772995	−	0.634413i	$-0.781242\pi$
$89$	2.12519	−	6.54066i	0.225269	−	0.693308i	0.998264	−	0.0588956i	$-0.0187579\pi$
$90$		0			0
$91$	−7.68077	+	5.58040i	−0.805163	+	0.584985i
$92$			2.83588i			0.295660i
$93$	4.99277	−	3.59709i	0.517726	−	0.373001i
$94$	−19.6980			−2.03170
$95$		0			0
$96$	−5.81905	+	2.59081i	−0.593905	+	0.264423i
$97$	4.59184	+	1.49198i	0.466231	+	0.151487i	0.532706	−	0.846301i	$-0.321175\pi$
$97$	4.59184	+	1.49198i	0.466231	+	0.151487i	−0.0664751	+	0.997788i	$0.521175\pi$
$98$	−5.91292	+	3.41382i	−0.597295	+	0.344848i
$99$	5.27927	−	9.14396i	0.530587	−	0.919003i
$100$		0			0
$101$	−0.784682	−	2.41500i	−0.0780788	−	0.240302i	0.904397	−	0.426692i	$-0.140321\pi$
$101$	−0.784682	−	2.41500i	−0.0780788	−	0.240302i	−0.982476	+	0.186390i	$0.940321\pi$
$102$	−8.15497	−	7.34277i	−0.807462	−	0.727042i
$103$	−1.38038	+	3.10039i	−0.136013	+	0.305490i	−0.968692	−	0.248266i	$-0.920139\pi$
$103$	−1.38038	+	3.10039i	−0.136013	+	0.305490i	0.832679	+	0.553756i	$0.186806\pi$
$104$	−8.00876	+	1.70232i	−0.785324	+	0.166926i
$105$		0			0
$106$	−0.821610	+	7.81709i	−0.0798018	+	0.759263i
$107$	−0.845812	+	3.97923i	−0.0817678	+	0.384687i	−0.999934	−	0.0115088i	$-0.996337\pi$
$107$	−0.845812	+	3.97923i	−0.0817678	+	0.384687i	0.918166	+	0.396196i	$0.129670\pi$
$108$	−3.52783	+	4.85564i	−0.339465	+	0.467234i
$109$	9.56853	+	6.95194i	0.916499	+	0.665875i	0.942650	−	0.333783i	$-0.108325\pi$
$109$	9.56853	+	6.95194i	0.916499	+	0.665875i	−0.0261514	+	0.999658i	$0.508325\pi$
$110$		0			0
$111$	1.33050	−	12.6589i	0.126286	−	1.20153i
$112$	8.78532	−	0.923374i	0.830135	−	0.0872507i
$113$	0.0792398	+	0.372794i	0.00745425	+	0.0350695i	0.981718	−	0.190344i	$-0.0609602\pi$
$113$	0.0792398	+	0.372794i	0.00745425	+	0.0350695i	−0.974263	+	0.225413i	$0.927627\pi$
$114$	4.05188	+	1.80402i	0.379494	+	0.168962i
$115$		0			0
$116$	−2.95493	−	9.09435i	−0.274359	−	0.844390i
$117$	−7.07585	+	6.37112i	−0.654163	+	0.589011i
$118$	5.79390	+	3.34511i	0.533372	+	0.307942i
$119$	4.97101	+	8.61004i	0.455692	+	0.789281i
$120$		0			0
$121$	22.1494	−	9.86157i	2.01359	−	0.896506i
$122$	−11.3188	−	15.5790i	−1.02475	−	1.41045i
$123$		−	0.00110373i		−	9.95201e-5i
$124$	6.29012	+	0.686524i	0.564870	+	0.0616517i
$125$		0			0
$126$	4.51878	−	3.28309i	0.402565	−	0.292481i
$127$	0.866326	+	1.94580i	0.0768740	+	0.172662i	0.947894	−	0.318585i	$-0.103208\pi$
$127$	0.866326	+	1.94580i	0.0768740	+	0.172662i	−0.871020	+	0.491247i	$0.836541\pi$
$128$	10.5513	+	3.42834i	0.932616	+	0.303025i
$129$	−0.501872	−	0.869268i	−0.0441874	−	0.0765348i
$130$		0			0
$131$	−1.83623	−	2.03934i	−0.160432	−	0.178178i	0.657569	−	0.753394i	$-0.271585\pi$
$131$	−1.83623	−	2.03934i	−0.160432	−	0.178178i	−0.818002	+	0.575216i	$0.804918\pi$
$132$	−7.09180	+	2.30427i	−0.617262	+	0.200561i
$133$	−2.98625	−	2.68883i	−0.258941	−	0.233151i
$134$	12.7604	+	5.68128i	1.10233	+	0.490788i
$135$		0			0
$136$	0.896238	+	8.52714i	0.0768518	+	0.731196i
$137$	−6.38748	−	0.671351i	−0.545719	−	0.0573574i	−0.172342	−	0.985037i	$-0.555134\pi$
$137$	−6.38748	−	0.671351i	−0.545719	−	0.0573574i	−0.373377	+	0.927680i	$0.621800\pi$
$138$	−1.01551	+	4.77760i	−0.0864459	+	0.406696i
$139$	−8.70730	−	6.32622i	−0.738544	−	0.536583i	0.153711	−	0.988116i	$-0.450877\pi$
$139$	−8.70730	−	6.32622i	−0.738544	−	0.536583i	−0.892255	+	0.451533i	$0.850877\pi$
$140$		0			0
$141$	−12.0242	−	2.55582i	−1.01262	−	0.215239i
$142$	−0.108771	−	0.0114323i	−0.00912783	−	0.000959373i
$143$	−31.6097	+	3.32231i	−2.64334	+	0.277826i
$144$	8.66574	−	1.84196i	0.722145	−	0.153497i
$145$		0			0
$146$	−4.16717	+	4.62811i	−0.344877	+	0.383025i
$147$	−4.05235	+	1.31669i	−0.334232	+	0.108599i
$148$	9.72648	−	8.75776i	0.799511	−	0.719883i
$149$	6.00653	−	10.4036i	0.492074	−	0.852297i	−0.507884	−	0.861425i	$-0.669572\pi$
$149$	6.00653	−	10.4036i	0.492074	−	0.852297i	0.999958	+	0.00912829i	$0.00290566\pi$
$150$		0			0
$151$	−4.88874	+	15.0460i	−0.397840	+	1.22443i	0.528887	+	0.848692i	$0.322609\pi$
$151$	−4.88874	+	15.0460i	−0.397840	+	1.22443i	−0.926727	+	0.375734i	$0.877391\pi$
$152$	−1.40955	−	3.16590i	−0.114330	−	0.256788i
$153$	5.86073	+	8.06660i	0.473812	+	0.652146i
$154$	18.6451			1.50246
$155$		0			0
$156$	6.72437			0.538381
$157$	−11.0944	−	15.2702i	−0.885431	−	1.21869i	−0.974887	−	0.222700i	$-0.928513\pi$
$157$	−11.0944	−	15.2702i	−0.885431	−	1.21869i	0.0894560	−	0.995991i	$-0.471487\pi$
$158$	−3.07165	−	6.89903i	−0.244367	−	0.548858i
$159$	−1.51580	+	4.66516i	−0.120211	+	0.369971i
$160$		0			0
$161$	2.21259	−	3.83232i	0.174376	−	0.302029i
$162$	−0.660030	+	0.594294i	−0.0518569	+	0.0466921i
$163$	14.0692	−	4.57135i	1.10198	−	0.358056i	0.299117	−	0.954216i	$-0.403308\pi$
$163$	14.0692	−	4.57135i	1.10198	−	0.358056i	0.802865	+	0.596161i	$0.203308\pi$
$164$	0.000759409	0	0.000843409i	5.92998e−5	0	6.58591e-5i
$165$		0			0
$166$	−4.50271	+	0.957081i	−0.349478	+	0.0742839i
$167$	10.1319	−	1.06491i	0.784033	−	0.0824052i	0.295951	−	0.955203i	$-0.404363\pi$
$167$	10.1319	−	1.06491i	0.784033	−	0.0824052i	0.488082	+	0.872798i	$0.337697\pi$
$168$	2.98101	+	0.313317i	0.229990	+	0.0241729i
$169$	15.3198	+	3.25632i	1.17845	+	0.250486i
$170$		0			0
$171$	−3.26038	−	2.36881i	−0.249328	−	0.181147i
$172$	0.214587	−	1.00955i	0.0163621	−	0.0769776i
$173$	−15.1833	−	1.59583i	−1.15437	−	0.121329i	−0.492061	−	0.870561i	$-0.663756\pi$
$173$	−15.1833	−	1.59583i	−1.15437	−	0.121329i	−0.662308	+	0.749232i	$0.730423\pi$
$174$	−1.72154	−	16.3794i	−0.130510	−	1.24172i
$175$		0			0
$176$	27.0167	+	12.0286i	2.03646	+	0.906691i
$177$	3.10272	+	2.79371i	0.233215	+	0.209988i
$178$	11.5835	−	3.76371i	0.868221	−	0.282102i
$179$	−9.75887	−	10.8383i	−0.729412	−	0.810094i	0.258352	−	0.966051i	$-0.416821\pi$
$179$	−9.75887	−	10.8383i	−0.729412	−	0.810094i	−0.987764	+	0.155957i	$0.950154\pi$
$180$		0			0
$181$	−1.24860	−	2.16265i	−0.0928081	−	0.160748i	0.815884	−	0.578216i	$-0.196251\pi$
$181$	−1.24860	−	2.16265i	−0.0928081	−	0.160748i	−0.908692	+	0.417468i	$0.862918\pi$
$182$	−15.9909	−	5.19575i	−1.18532	−	0.385135i
$183$	−4.88792	−	10.9784i	−0.361325	−	0.811550i
$184$	3.08747	−	2.24318i	0.227611	−	0.165369i
$185$		0			0
$186$	10.3511	+	3.40904i	0.758981	+	0.249963i
$187$			33.2839i			2.43396i
$188$	−7.42971	−	10.2261i	−0.541867	−	0.745817i
$189$	8.55584	−	3.80931i	0.622346	−	0.277086i
$190$		0			0
$191$	−10.3990	−	18.0116i	−0.752445	−	1.30327i	−0.946635	−	0.322308i	$-0.895541\pi$
$191$	−10.3990	−	18.0116i	−0.752445	−	1.30327i	0.194190	−	0.980964i	$-0.437792\pi$
$192$	−0.233651	−	0.134898i	−0.0168623	−	0.00973545i
$193$	−2.88096	+	2.59402i	−0.207376	+	0.186722i	−0.766273	−	0.642515i	$-0.777891\pi$
$193$	−2.88096	+	2.59402i	−0.207376	+	0.186722i	0.558898	+	0.829237i	$0.311224\pi$
$194$	2.64230	+	8.13215i	0.189706	+	0.583855i
$195$		0			0
$196$	−4.00251	−	1.78203i	−0.285893	−	0.127288i
$197$	−1.49971	−	7.05559i	−0.106850	−	0.502690i	−0.998728	−	0.0504146i	$-0.983946\pi$
$197$	−1.49971	−	7.05559i	−0.106850	−	0.502690i	0.891878	−	0.452275i	$-0.149388\pi$
$198$	18.5968	−	1.95460i	1.32161	−	0.138907i
$199$	−1.31261	+	12.4887i	−0.0930487	+	0.885299i	0.844057	+	0.536253i	$0.180161\pi$
$199$	−1.31261	+	12.4887i	−0.0930487	+	0.885299i	−0.937106	+	0.349046i	$0.886506\pi$
$200$		0			0
$201$	7.05213	+	5.12367i	0.497419	+	0.361396i
$202$	2.64332	−	3.63821i	0.185983	−	0.255984i
$203$	−3.10233	+	14.5953i	−0.217741	+	1.02439i
$204$	0.736061	−	7.00316i	0.0515346	−	0.490319i
$205$		0			0
$206$	−5.87908	+	1.24964i	−0.409615	+	0.0870663i
$207$	1.80510	−	4.05433i	0.125463	−	0.281795i
$208$	−19.8188	−	17.8449i	−1.37419	−	1.23732i
$209$	−4.15714	−	12.7943i	−0.287555	−	0.885003i
$210$		0			0
$211$	−3.50746	+	6.07510i	−0.241463	+	0.418227i	−0.961131	−	0.276092i	$-0.910961\pi$
$211$	−3.50746	+	6.07510i	−0.241463	+	0.418227i	0.719668	+	0.694318i	$0.244294\pi$
$212$	−4.36810	+	2.52192i	−0.300002	+	0.173206i
$213$	−0.0649132	−	0.0210916i	−0.00444778	−	0.00144517i
$214$	−6.58179	+	2.93040i	−0.449922	+	0.200318i
$215$		0			0
$216$	8.07694			0.549566
$217$	−7.96465	−	5.83539i	−0.540675	−	0.396132i
$218$			20.9463i			1.41866i
$219$	−3.14425	+	2.28443i	−0.212469	+	0.154368i
$220$		0			0
$221$	9.27507	−	28.5457i	0.623909	−	1.92019i
$222$	19.5223	−	11.2712i	1.31025	−	0.756473i
$223$	−12.3675	−	7.14038i	−0.828190	−	0.478155i	0.0250429	−	0.999686i	$-0.492028\pi$
$223$	−12.3675	−	7.14038i	−0.828190	−	0.478155i	−0.853232	+	0.521531i	$0.825361\pi$
$224$	6.83877	+	7.59522i	0.456935	+	0.507477i
$225$		0			0
$226$	−0.451642	+	0.501599i	−0.0300428	+	0.0333659i
$227$	0.158932	−	0.356968i	0.0105487	−	0.0236928i	−0.908194	−	0.418549i	$-0.862539\pi$
$227$	0.158932	−	0.356968i	0.0105487	−	0.0236928i	0.918743	+	0.394856i	$0.129206\pi$
$228$	0.591747	+	2.78395i	0.0391894	+	0.184372i
$229$	1.30739	+	12.4390i	0.0863950	+	0.821994i	0.948822	+	0.315812i	$0.102277\pi$
$229$	1.30739	+	12.4390i	0.0863950	+	0.821994i	−0.862427	+	0.506182i	$0.831056\pi$
$230$		0			0
$231$	11.3815	+	2.41921i	0.748846	+	0.159172i
$232$	−7.56383	+	10.4107i	−0.496590	+	0.683498i
$233$	−0.0672991	+	0.0926292i	−0.00440891	+	0.00606834i	−0.811216	−	0.584747i	$-0.801194\pi$
$233$	−0.0672991	+	0.0926292i	−0.00440891	+	0.00606834i	0.806807	+	0.590815i	$0.201194\pi$
$234$	−16.4941	−	3.50593i	−1.07825	−	0.229190i
$235$		0			0
$236$	0.448751	+	4.26958i	0.0292112	+	0.277926i
$237$	−0.979865	−	4.60990i	−0.0636491	−	0.299445i
$238$	−7.16155	+	16.0851i	−0.464214	+	1.04264i
$239$	11.0072	−	12.2247i	0.711995	−	0.790751i	−0.273242	−	0.961945i	$-0.588096\pi$
$239$	11.0072	−	12.2247i	0.711995	−	0.790751i	0.985237	+	0.171194i	$0.0547626\pi$
$240$		0			0
$241$	1.20643	+	1.33988i	0.0777130	+	0.0863090i	0.780747	−	0.624847i	$-0.214839\pi$
$241$	1.20643	+	1.33988i	0.0777130	+	0.0863090i	−0.703034	+	0.711156i	$0.748172\pi$
$242$	37.1862	+	21.4695i	2.39042	+	1.38011i
$243$	13.2412	−	7.64479i	0.849421	−	0.490413i
$244$	3.81851	−	11.7522i	0.244455	−	0.752355i
$245$		0			0
$246$	0.00158139	−	0.00114895i	0.000100826	−	7.32544e-5i
$247$			12.1315i			0.771906i
$248$	−4.22805	−	7.39121i	−0.268482	−	0.469342i
$249$	−2.87276			−0.182054
$250$		0			0
$251$	12.9739	−	5.77637i	0.818907	−	0.364601i	0.0458588	−	0.998948i	$-0.485398\pi$
$251$	12.9739	−	5.77637i	0.818907	−	0.364601i	0.773049	+	0.634347i	$0.218731\pi$
$252$	3.40879	+	1.10758i	0.214734	+	0.0697713i
$253$	12.8298	−	7.40730i	0.806604	−	0.465693i
$254$	−1.88607	+	3.26676i	−0.118342	+	0.204975i
$255$		0			0
$256$	6.22247	+	19.1508i	0.388904	+	1.19692i
$257$	−12.6635	−	11.4023i	−0.789927	−	0.711253i	0.171839	−	0.985125i	$-0.445029\pi$
$257$	−12.6635	−	11.4023i	−0.789927	−	0.711253i	−0.961766	+	0.273872i	$0.911696\pi$
$258$	0.723028	−	1.62395i	0.0450138	−	0.101103i
$259$	−19.9770	+	4.24624i	−1.24131	+	0.263849i
$260$		0			0
$261$	−1.56423	+	14.8827i	−0.0968237	+	0.921216i
$262$	1.01045	−	4.75379i	0.0624258	−	0.293690i
$263$	−2.54309	+	3.50027i	−0.156814	+	0.215836i	−0.880194	−	0.474614i	$-0.842588\pi$
$263$	−2.54309	+	3.50027i	−0.156814	+	0.215836i	0.723380	+	0.690450i	$0.242588\pi$
$264$	8.11831	+	5.89830i	0.499648	+	0.363015i
$265$		0			0
$266$	0.743886	−	7.07760i	0.0456106	−	0.433956i
$267$	7.55923	−	0.794507i	0.462618	−	0.0486231i
$268$	1.86356	+	8.76735i	0.113835	+	0.535551i
$269$	27.6116	+	12.2935i	1.68351	+	0.749546i	0.999804	+	0.0197870i	$0.00629880\pi$
$269$	27.6116	+	12.2935i	1.68351	+	0.749546i	0.683704	+	0.729759i	$0.260368\pi$
$270$		0			0
$271$	5.85583	+	18.0224i	0.355716	+	1.09478i	0.955593	+	0.294690i	$0.0952164\pi$
$271$	5.85583	+	18.0224i	0.355716	+	1.09478i	−0.599876	+	0.800093i	$0.704784\pi$
$272$	−20.7541	+	18.6871i	−1.25840	+	1.13307i
$273$	−9.08711	−	5.24645i	−0.549977	−	0.317529i
$274$	−5.68727	−	9.85065i	−0.343581	−	0.595099i
$275$		0			0
$276$	−2.86329	+	1.27482i	−0.172350	+	0.0767351i
$277$	−3.13043	−	4.30867i	−0.188090	−	0.258883i	0.704550	−	0.709654i	$-0.251149\pi$
$277$	−3.13043	−	4.30867i	−0.188090	−	0.258883i	−0.892639	+	0.450771i	$0.851149\pi$
$278$		−	19.0610i		−	1.14320i
$279$	−8.55573	−	4.98531i	−0.512218	−	0.298463i
$280$		0			0
$281$	−21.2629	+	15.4484i	−1.26844	+	0.921576i	−0.999139	−	0.0414799i	$-0.986793\pi$
$281$	−21.2629	+	15.4484i	−1.26844	+	0.921576i	−0.269301	+	0.963056i	$0.586793\pi$
$282$	−8.85492	−	19.8885i	−0.527303	−	1.18434i
$283$	−19.0755	−	6.19800i	−1.13392	−	0.368433i	−0.318856	−	0.947803i	$-0.603299\pi$
$283$	−19.0755	−	6.19800i	−1.13392	−	0.368433i	−0.815064	+	0.579370i	$0.803299\pi$
$284$	−0.0350912	−	0.0607797i	−0.00208228	−	0.00360661i
$285$		0			0
$286$	−37.6648	−	41.8310i	−2.22717	−	2.47352i
$287$	−0.00168428		0.000547256i	−9.94200e−5		3.23035e-5i
$288$	7.61726	+	6.85861i	0.448851	+	0.404148i
$289$	−13.1837	−	5.86975i	−0.775510	−	0.345279i
$290$		0			0
$291$	0.557780	+	5.30693i	0.0326977	+	0.311098i
$292$	−3.97443	−	0.417730i	−0.232586	−	0.0244458i
$293$	0.236573	−	1.11299i	0.0138208	−	0.0650216i	−0.970697	−	0.240308i	$-0.922752\pi$
$293$	0.236573	−	1.11299i	0.0138208	−	0.0650216i	0.984518	+	0.175286i	$0.0560850\pi$
$294$	−6.10488	−	4.43546i	−0.356044	−	0.258681i
$295$		0			0
$296$	−17.2284	−	3.66200i	−1.00138	−	0.212850i
$297$	31.1821	+	3.27737i	1.80937	+	0.190173i
$298$	21.1586	−	2.22386i	1.22568	−	0.128825i
$299$	−13.0676	+	2.77760i	−0.755718	+	0.160633i
$300$		0			0
$301$	−1.07765	+	1.19685i	−0.0621149	+	0.0689855i
$302$	−26.6465	+	8.65797i	−1.53333	+	0.498210i
$303$	2.08561	−	1.87789i	0.119815	−	0.107882i
$304$	5.64390	−	9.77552i	0.323700	−	0.560665i
$305$		0			0
$306$	−5.45675	+	16.7942i	−0.311942	+	0.960058i
$307$	0.211399	+	0.474811i	0.0120652	+	0.0270989i	0.919478	−	0.393142i	$-0.128612\pi$
$307$	0.211399	+	0.474811i	0.0120652	+	0.0270989i	−0.907412	+	0.420241i	$0.861945\pi$
$308$	7.03257	+	9.67950i	0.400718	+	0.551541i
$309$	−3.75089			−0.213381
$310$		0			0
$311$	28.6664			1.62552			0.812761	−	0.582598i	$-0.197964\pi$
$311$	28.6664			1.62552			0.812761	+	0.582598i	$0.197964\pi$
$312$	−5.31898	−	7.32094i	−0.301128	−	0.414467i
$313$	−7.06589	−	15.8703i	−0.399388	−	0.897040i	−0.995555	−	0.0941796i	$-0.969977\pi$
$313$	−7.06589	−	15.8703i	−0.399388	−	0.897040i	0.596167	−	0.802860i	$-0.296689\pi$
$314$	10.3297	−	31.7915i	0.582938	−	1.79410i
$315$		0			0
$316$	2.42303	−	4.19681i	0.136306	−	0.236089i
$317$	16.5270	−	14.8810i	0.928249	−	0.835799i	−0.0584609	−	0.998290i	$-0.518619\pi$
$317$	16.5270	−	14.8810i	0.928249	−	0.835799i	0.986710	+	0.162490i	$0.0519526\pi$
$318$	−8.26201	+	2.68449i	−0.463310	+	0.150539i
$319$	−33.4256	+	37.1229i	−1.87147	+	2.07848i
$320$		0			0
$321$	−4.39793	+	0.934808i	−0.245468	+	0.0521759i
$322$	7.79407	−	0.819190i	0.434346	−	0.0456517i
$323$	12.6344	+	1.32793i	0.702998	+	0.0738880i
$324$	−0.557475	−	0.118495i	−0.0309708	−	0.00658305i
$325$		0			0
$326$	21.1953	+	15.3993i	1.17390	+	0.852886i
$327$	−2.71778	+	12.7862i	−0.150294	+	0.707076i
$328$	−0.00151893		0.000159646i	−8.38687e−5		8.81495e-6i
$329$	2.06173	+	19.6160i	0.113667	+	1.08147i
$330$		0			0
$331$	−3.43899	−	1.53114i	−0.189024	−	0.0841590i	0.310042	−	0.950723i	$-0.399657\pi$
$331$	−3.43899	−	1.53114i	−0.189024	−	0.0841590i	−0.499066	+	0.866564i	$0.666324\pi$
$332$	−2.19520	−	1.97657i	−0.120477	−	0.108478i
$333$	−19.4801	+	6.32946i	−1.06750	+	0.346852i
$334$	12.0728	+	13.4082i	0.660594	+	0.733664i
$335$		0			0
$336$	4.88159	+	8.45517i	0.266313	+	0.461267i
$337$	−16.5129	−	5.36535i	−0.899512	−	0.292269i	−0.177477	−	0.984125i	$-0.556793\pi$
$337$	−16.5129	−	5.36535i	−0.899512	−	0.292269i	−0.722036	+	0.691856i	$0.756793\pi$
$338$	11.2819	+	25.3395i	0.613652	+	1.37829i
$339$	−0.340777	+	0.247589i	−0.0185085	+	0.0134472i
$340$		0			0
$341$	−13.3239	−	30.2504i	−0.721528	−	1.63815i
$342$		−	7.13724i		−	0.385938i
$343$	11.3149	+	15.5737i	0.610949	+	0.840899i
$344$	−1.26886	+	0.564931i	−0.0684121	+	0.0304590i
$345$		0			0
$346$	−13.5189	−	23.4155i	−0.726782	−	1.25882i
$347$	17.0165	+	9.82450i	0.913495	+	0.527407i	0.881554	−	0.472083i	$-0.156498\pi$
$347$	17.0165	+	9.82450i	0.913495	+	0.527407i	0.0319411	+	0.999490i	$0.489831\pi$
$348$	7.85394	−	7.07172i	0.421015	−	0.379084i
$349$	8.82193	+	27.1511i	0.472227	+	1.45337i	0.849661	+	0.527329i	$0.176807\pi$
$349$	8.82193	+	27.1511i	0.472227	+	1.45337i	−0.377434	+	0.926037i	$0.623193\pi$
$350$		0			0
$351$	−25.8299	−	11.5002i	−1.37870	−	0.613836i
$352$	7.11385	+	33.4681i	0.379170	+	1.78385i
$353$	−4.68678	+	0.492601i	−0.249452	+	0.0262185i	−0.228429	−	0.973561i	$-0.573359\pi$
$353$	−4.68678	+	0.492601i	−0.249452	+	0.0262185i	−0.0210229	+	0.999779i	$0.506692\pi$
$354$	−0.772900	+	7.35365i	−0.0410792	+	0.390842i
$355$		0			0
$356$	6.32299	+	4.59392i	0.335118	+	0.243477i
$357$	−6.45865	+	8.88957i	−0.341828	+	0.470486i
$358$	5.37015	−	25.2646i	0.283821	−	1.33527i
$359$	−1.09276	+	10.3969i	−0.0576738	+	0.548730i	0.927091	+	0.374837i	$0.122301\pi$
$359$	−1.09276	+	10.3969i	−0.0576738	+	0.548730i	−0.984765	+	0.173893i	$0.944365\pi$
$360$		0			0
$361$	13.5623	−	2.88275i	0.713803	−	0.151724i
$362$	1.79882	−	4.04021i	0.0945438	−	0.212349i
$363$	19.9138	+	17.9305i	1.04520	+	0.941106i
$364$	−3.33410	−	10.2613i	−0.174754	−	0.537839i
$365$		0			0
$366$	10.6414	−	18.4315i	0.556236	−	0.963429i
$367$	−0.523260	+	0.302104i	−0.0273139	+	0.0157697i	−0.513595	−	0.858033i	$-0.671687\pi$
$367$	−0.523260	+	0.302104i	−0.0273139	+	0.0157697i	0.486281	+	0.873803i	$0.338353\pi$
$368$	11.8221	+	3.84122i	0.616268	+	0.200238i
$369$	−0.00162254		0.000722403i	−8.44663e−5		3.76068e-5i
$370$		0			0
$371$	7.87055			0.408619
$372$	2.13446	+	6.65955i	0.110666	+	0.345282i
$373$			10.8545i			0.562027i	0.959704	+	0.281014i	$0.0906706\pi$
$373$			10.8545i			0.562027i	−0.959704	+	0.281014i	$0.909329\pi$
$374$	−47.6881	+	34.6475i	−2.46589	+	1.79158i
$375$		0			0
$376$	−5.25646	+	16.1777i	−0.271081	+	0.834302i
$377$	39.0122	−	22.5237i	2.00923	−	1.16003i
$378$	14.3642	+	8.29319i	0.738816	+	0.426556i
$379$	−8.60177	−	9.55324i	−0.441843	−	0.490717i	0.480551	−	0.876967i	$-0.340437\pi$
$379$	−8.60177	−	9.55324i	−0.441843	−	0.490717i	−0.922394	+	0.386250i	$0.873770\pi$
$380$		0			0
$381$	−1.57517	+	1.74940i	−0.0806984	+	0.0896247i
$382$	14.9814	−	33.6489i	0.766517	−	1.72163i
$383$	−3.46497	−	16.3014i	−0.177051	−	0.832962i	−0.973577	−	0.228357i	$-0.926665\pi$
$383$	−3.46497	−	16.3014i	−0.177051	−	0.832962i	0.796526	−	0.604604i	$-0.206669\pi$
$384$	1.28169	+	12.1945i	0.0654062	+	0.622299i
$385$		0			0
$386$	−6.71563	−	1.42745i	−0.341816	−	0.0726553i
$387$	−0.949390	+	1.30672i	−0.0482602	+	0.0664245i
$388$	−3.22514	+	4.43902i	−0.163732	+	0.225357i
$389$	20.9614	+	4.45547i	1.06278	+	0.225901i	0.705946	−	0.708265i	$-0.250522\pi$
$389$	20.9614	+	4.45547i	1.06278	+	0.225901i	0.356837	+	0.934167i	$0.383855\pi$
$390$		0			0
$391$	1.46236	+	13.9134i	0.0739546	+	0.703631i
$392$	1.22585	+	5.76719i	0.0619149	+	0.291287i
$393$	1.23361	−	2.77074i	0.0622275	−	0.139765i
$394$	8.54789	−	9.49340i	0.430637	−	0.478270i
$395$		0			0
$396$	8.02905	+	8.91717i	0.403475	+	0.448105i
$397$	9.52912	+	5.50164i	0.478253	+	0.276120i	0.719688	−	0.694297i	$-0.244285\pi$
$397$	9.52912	+	5.50164i	0.478253	+	0.276120i	−0.241435	+	0.970417i	$0.577618\pi$
$398$	−19.2598	+	11.1197i	−0.965407	+	0.557378i
$399$	1.37241	−	4.22384i	0.0687064	−	0.211457i
$400$		0			0
$401$	−29.4214	+	21.3759i	−1.46924	+	1.06746i	−0.488401	+	0.872619i	$0.662420\pi$
$401$	−29.4214	+	21.3759i	−1.46924	+	1.06746i	−0.980834	+	0.194843i	$0.937580\pi$
$402$			15.4377i			0.769961i
$403$	2.99739	+	29.6570i	0.149311	+	1.47732i
$404$	2.88577			0.143572
$405$		0			0
$406$	−24.1412	+	10.7483i	−1.19811	+	0.533431i
$407$	−65.0266	−	21.1284i	−3.22325	−	1.04730i
$408$	−8.20669	+	4.73813i	−0.406292	+	0.234573i
$409$	13.7039	−	23.7358i	0.677612	−	1.17366i	−0.298086	−	0.954539i	$-0.596348\pi$
$409$	13.7039	−	23.7358i	0.677612	−	1.17366i	0.975698	−	0.219119i	$-0.0703183\pi$
$410$		0			0
$411$	−2.19354	−	6.75103i	−0.108199	−	0.333004i
$412$	−2.86621	−	2.58075i	−0.141208	−	0.127144i
$413$	2.72476	−	6.11991i	0.134077	−	0.301141i
$414$	7.68798	−	1.63413i	0.377844	−	0.0803132i
$415$		0			0
$416$	3.22524	−	30.6861i	0.158130	−	1.50451i
$417$	2.47317	−	11.6353i	0.121111	−	0.569785i
$418$	14.0039	−	19.2747i	0.684954	−	0.942758i
$419$	−7.42067	−	5.39143i	−0.362524	−	0.263389i	0.391580	−	0.920144i	$-0.371929\pi$
$419$	−7.42067	−	5.39143i	−0.362524	−	0.263389i	−0.754104	+	0.656755i	$0.771929\pi$
$420$		0			0
$421$	2.01849	−	19.2047i	0.0983753	−	0.935979i	−0.828343	−	0.560222i	$-0.810716\pi$
$421$	2.01849	−	19.2047i	0.0983753	−	0.935979i	0.926718	−	0.375757i	$-0.122617\pi$
$422$	−12.3554	+	1.29860i	−0.601450	+	0.0632150i
$423$	4.11277	+	19.3490i	0.199970	+	0.940783i
$424$	6.20083	+	2.76079i	0.301139	+	0.134076i
$425$		0			0
$426$	−0.0373532	−	0.114961i	−0.00180977	−	0.00556990i
$427$	−14.3294	+	12.9023i	−0.693450	+	0.624385i
$428$	−4.00383	−	2.31161i	−0.193532	−	0.111736i
$429$	−17.5640	−	30.4218i	−0.848000	−	1.46878i
$430$		0			0
$431$	−25.2827	+	11.2566i	−1.21782	+	0.542210i	−0.912122	−	0.409918i	$-0.865557\pi$
$431$	−25.2827	+	11.2566i	−1.21782	+	0.542210i	−0.305701	+	0.952128i	$0.598891\pi$
$432$	15.4635	+	21.2837i	0.743988	+	1.02401i
$433$			25.4725i			1.22413i	0.790808	+	0.612065i	$0.209661\pi$
$433$			25.4725i			1.22413i	−0.790808	+	0.612065i	$0.790339\pi$
$434$	0.0698255	−	17.4860i	0.00335173	−	0.839354i
$435$		0			0
$436$	−10.8741	+	7.90052i	−0.520777	+	0.378366i
$437$	−2.29991	−	5.16568i	−0.110019	−	0.247108i
$438$	−6.54613	−	2.12697i	−0.312786	−	0.101630i
$439$	−1.62684	−	2.81776i	−0.0776447	−	0.134485i	0.824589	−	0.565733i	$-0.191407\pi$
$439$	−1.62684	−	2.81776i	−0.0776447	−	0.134485i	−0.902233	+	0.431248i	$0.858073\pi$
$440$		0			0
$441$	4.58791	+	5.09539i	0.218472	+	0.242637i
$442$	50.5546	−	16.4262i	2.40464	−	0.781313i
$443$	−25.8230	−	23.2512i	−1.22689	−	1.10470i	−0.991132	−	0.132885i	$-0.957576\pi$
$443$	−25.8230	−	23.2512i	−1.22689	−	1.10470i	−0.235758	−	0.971812i	$-0.575757\pi$
$444$	13.2148	+	5.88361i	0.627147	+	0.279224i
$445$		0			0
$446$	−2.64366	−	25.1527i	−0.125181	−	1.19102i
$447$	13.2043	+	1.38783i	0.624543	+	0.0656421i
$448$	−0.0900037	+	0.423434i	−0.00425228	+	0.0200054i
$449$	−3.63361	−	2.63997i	−0.171481	−	0.124588i	0.498735	−	0.866755i	$-0.333798\pi$
$449$	−3.63361	−	2.63997i	−0.171481	−	0.124588i	−0.670215	+	0.742167i	$0.733798\pi$
$450$		0			0
$451$	−0.00579925	−	0.00123267i	−0.000273076	−	5.80441e-5i
$452$	−0.430753	−	0.0452740i	−0.0202609	−	0.00212951i
$453$	−17.3891	+	1.82767i	−0.817012	+	0.0858714i
$454$	0.676897	−	0.143879i	0.0317683	−	0.00675257i
$455$		0			0
$456$	2.56287	−	2.84635i	0.120017	−	0.133293i
$457$	7.90953	−	2.56996i	0.369992	−	0.120218i	−0.118118	−	0.993000i	$-0.537686\pi$
$457$	7.90953	−	2.56996i	0.369992	−	0.120218i	0.488111	+	0.872782i	$0.337686\pi$
$458$	−16.4613	+	14.8218i	−0.769187	+	0.692579i
$459$	−14.8044	+	25.6420i	−0.691010	+	1.19686i
$460$		0			0
$461$	−3.13623	+	9.65232i	−0.146069	+	0.449553i	−0.997147	−	0.0754857i	$-0.975949\pi$
$461$	−3.13623	+	9.65232i	−0.146069	+	0.449553i	0.851078	+	0.525039i	$0.175949\pi$
$462$	8.38159	+	18.8254i	0.389947	+	0.875835i
$463$	13.3302	+	18.3475i	0.619509	+	0.852681i	0.997317	−	0.0732033i	$-0.0233222\pi$
$463$	13.3302	+	18.3475i	0.619509	+	0.852681i	−0.377808	+	0.925884i	$0.623322\pi$
$464$	−41.9146			−1.94584
$465$		0			0
$466$	−0.202773			−0.00939326
$467$	5.85650	+	8.06078i	0.271007	+	0.373009i	0.922729	−	0.385449i	$-0.125953\pi$
$467$	5.85650	+	8.06078i	0.271007	+	0.373009i	−0.651723	+	0.758457i	$0.725953\pi$
$468$	−4.40117	−	9.88519i	−0.203444	−	0.456943i
$469$	4.32205	−	13.3019i	0.199574	−	0.614225i
$470$		0			0
$471$	10.4305	−	18.0661i	0.480611	−	0.832443i
$472$	4.29341	−	3.86580i	0.197620	−	0.177938i
$473$	−5.12782	+	1.66613i	−0.235778	+	0.0766088i
$474$	5.58492	−	6.20269i	0.256524	−	0.284899i
$475$		0			0
$476$	−11.0517	+	2.34911i	−0.506553	+	0.107671i
$477$	7.85015	−	0.825084i	0.359434	−	0.0377780i
$478$	28.9733	+	3.04522i	1.32521	+	0.139285i
$479$	6.30668	+	1.34053i	0.288159	+	0.0612502i	0.349723	−	0.936853i	$-0.386276\pi$
$479$	6.30668	+	1.34053i	0.288159	+	0.0612502i	−0.0615641	+	0.998103i	$0.519609\pi$
$480$		0			0
$481$	49.8820	+	36.2414i	2.27442	+	1.65246i
$482$	−0.663879	+	3.12331i	−0.0302389	+	0.142263i
$483$	4.86400	+	0.511227i	0.221320	+	0.0232616i
$484$	2.88016	+	27.4029i	0.130916	+	1.24559i
$485$		0			0
$486$	24.7369	+	11.0136i	1.12209	+	0.499585i
$487$	14.5741	+	13.1226i	0.660417	+	0.594642i	0.929655	−	0.368431i	$-0.120105\pi$
$487$	14.5741	+	13.1226i	0.660417	+	0.594642i	−0.269238	+	0.963074i	$0.586772\pi$
$488$	−15.8152	+	5.13868i	−0.715922	+	0.232617i
$489$	10.9401	+	12.1502i	0.494728	+	0.549452i
$490$		0			0
$491$	0.200752	+	0.347712i	0.00905980	+	0.0156920i	0.870520	−	0.492133i	$-0.163783\pi$
$491$	0.200752	+	0.347712i	0.00905980	+	0.0156920i	−0.861460	+	0.507825i	$0.830449\pi$
$492$	0.00119294		0.000387610i	5.37820e−5		1.74748e-5i
$493$	−19.1872	−	43.0950i	−0.864146	−	1.94090i
$494$	−17.3816	+	12.6285i	−0.782035	+	0.568182i
$495$		0			0
$496$	11.3820	−	25.2921i	0.511067	−	1.13565i
$497$			0.109514i			0.00491239i
$498$	−2.99045	−	4.11601i	−0.134005	−	0.184443i
$499$	15.8020	−	7.03551i	0.707395	−	0.314953i	−0.0213170	−	0.999773i	$-0.506786\pi$
$499$	15.8020	−	7.03551i	0.707395	−	0.314953i	0.728712	+	0.684820i	$0.240119\pi$
$500$		0			0
$501$	5.62985	+	9.75118i	0.251523	+	0.435651i
$502$	21.7817	+	12.5757i	0.972163	+	0.561279i
$503$	21.2832	−	19.1635i	0.948971	−	0.854457i	−0.0405016	−	0.999179i	$-0.512896\pi$
$503$	21.2832	−	19.1635i	0.948971	−	0.854457i	0.989472	+	0.144722i	$0.0462289\pi$
$504$	−1.49051	−	4.58732i	−0.0663926	−	0.204335i
$505$		0			0
$506$	23.9684	+	10.6714i	1.06553	+	0.474402i
$507$	3.59895	+	16.9317i	0.159835	+	0.751964i
$508$	−2.40731	+	0.253019i	−0.106807	+	0.0112259i
$509$	−1.76708	+	16.8127i	−0.0783246	+	0.745209i	0.882922	+	0.469519i	$0.155573\pi$
$509$	−1.76708	+	16.8127i	−0.0783246	+	0.745209i	−0.961247	+	0.275689i	$0.911094\pi$
$510$		0			0
$511$	5.04501	+	3.66541i	0.223178	+	0.162148i
$512$	−7.91911	+	10.8997i	−0.349978	+	0.481704i
$513$	2.48816	−	11.7059i	0.109855	−	0.516826i
$514$	3.15452	−	30.0133i	0.139140	−	1.32383i
$515$		0			0
$516$	1.11578	−	0.237165i	0.0491193	−	0.0104406i
$517$	−26.8577	+	60.3234i	−1.18120	+	2.65302i
$518$	−26.8793	−	24.2022i	−1.18101	−	1.06339i
$519$	−5.21415	−	16.0475i	−0.228876	−	0.704408i
$520$		0			0
$521$	−15.6859	+	27.1688i	−0.687213	+	1.19029i	0.285522	+	0.958372i	$0.407833\pi$
$521$	−15.6859	+	27.1688i	−0.687213	+	1.19029i	−0.972736	+	0.231917i	$0.925500\pi$
$522$	−22.9518	+	13.2512i	−1.00457	+	0.579991i
$523$	5.24628	+	1.70462i	0.229404	+	0.0745378i	0.421463	−	0.906846i	$-0.361517\pi$
$523$	5.24628	+	1.70462i	0.229404	+	0.0745378i	−0.192060	+	0.981383i	$0.561517\pi$
$524$	2.84903	−	1.26847i	0.124460	−	0.0554133i
$525$		0			0
$526$	−7.66236			−0.334095
$527$	31.2147	+	0.124647i	1.35973	+	0.00542972i
$528$			32.6852i			1.42244i
$529$	−13.5697	+	9.85895i	−0.589986	+	0.428650i
$530$		0			0
$531$	2.07613	−	6.38968i	0.0900965	−	0.277289i
$532$	3.95488	−	2.28335i	0.171466	−	0.0989958i
$533$	0.00463019	+	0.00267324i	0.000200556	+	0.000115791i
$534$	9.00727	+	10.0036i	0.389783	+	0.432898i
$535$		0			0
$536$	8.07110	−	8.96386i	0.348618	−	0.387180i
$537$	6.55617	−	14.7254i	0.282920	−	0.635448i
$538$	11.1291	+	52.3582i	0.479809	+	2.25732i
$539$	2.39243	+	22.7624i	0.103049	+	0.980448i
$540$		0			0
$541$	8.12757	+	1.72757i	0.349431	+	0.0742740i	0.379284	−	0.925280i	$-0.376170\pi$
$541$	8.12757	+	1.72757i	0.349431	+	0.0742740i	−0.0298524	+	0.999554i	$0.509504\pi$
$542$	−19.7262	+	27.1508i	−0.847314	+	1.16623i
$543$	1.62227	−	2.23286i	0.0696181	−	0.0958211i
$544$	−31.6053	−	6.71791i	−1.35506	−	0.288028i
$545$		0			0
$546$	−1.94245	−	18.4811i	−0.0831290	−	0.790920i
$547$	−6.64903	−	31.2812i	−0.284292	−	1.33749i	−0.855977	−	0.517015i	$-0.827043\pi$
$547$	−6.64903	−	31.2812i	−0.284292	−	1.33749i	0.571685	−	0.820473i	$-0.306290\pi$
$548$	2.96878	−	6.66799i	0.126820	−	0.284842i
$549$	−12.9397	+	14.3710i	−0.552253	+	0.613339i
$550$		0			0
$551$	12.7581	+	14.1693i	0.543514	+	0.603633i
$552$	3.65278	+	2.10894i	0.155473	+	0.0897623i
$553$	−6.54882	+	3.78096i	−0.278484	+	0.160783i
$554$	2.91466	−	8.97039i	0.123832	−	0.381115i
$555$		0			0
$556$	9.89540	−	7.18943i	0.419658	−	0.304900i
$557$			11.2710i			0.477569i	0.971073	+	0.238785i	$0.0767490\pi$
$557$			11.2710i			0.477569i	−0.971073	+	0.238785i	$0.923251\pi$
$558$	−1.76344	−	17.4480i	−0.0746524	−	0.738631i
$559$	4.86215			0.205647
$560$		0			0
$561$	−33.6056	+	14.9622i	−1.41883	+	0.631705i
$562$	−44.2681	−	14.3836i	−1.86734	−	0.606735i
$563$	9.43878	−	5.44948i	0.397797	−	0.229668i	−0.287736	−	0.957710i	$-0.592903\pi$
$563$	9.43878	−	5.44948i	0.397797	−	0.229668i	0.685533	+	0.728042i	$0.259569\pi$
$564$	6.98509	−	12.0985i	0.294125	−	0.509440i
$565$		0			0
$566$	−10.9767	−	33.7827i	−0.461384	−	1.41999i
$567$	0.660903	+	0.595080i	0.0277553	+	0.0249910i
$568$	−0.0384148	+	0.0862811i	−0.00161185	+	0.00362027i
$569$	12.2494	−	2.60369i	0.513521	−	0.109152i	0.0561398	−	0.998423i	$-0.482121\pi$
$569$	12.2494	−	2.60369i	0.513521	−	0.109152i	0.457381	+	0.889271i	$0.348787\pi$
$570$		0			0
$571$	−3.87060	+	36.8263i	−0.161980	+	1.54113i	0.547739	+	0.836649i	$0.315489\pi$
$571$	−3.87060	+	36.8263i	−0.161980	+	1.54113i	−0.709719	+	0.704485i	$0.751178\pi$
$572$	7.50991	−	35.3313i	0.314005	−	1.47728i
$573$	13.5110	−	18.5963i	0.564431	−	0.776873i
$574$	−0.00253738	−	0.00184351i	−0.000105908	−	7.69467e-5i
$575$		0			0
$576$	−0.0453810	+	0.431772i	−0.00189088	+	0.0179905i
$577$	−14.7464	+	1.54991i	−0.613900	+	0.0645235i	−0.406375	−	0.913706i	$-0.633207\pi$
$577$	−14.7464	+	1.54991i	−0.613900	+	0.0645235i	−0.207525	+	0.978230i	$0.566541\pi$
$578$	−5.31379	−	24.9994i	−0.221024	−	1.03984i
$579$	−3.91419	−	1.74271i	−0.162668	−	0.0724245i
$580$		0			0
$581$	1.42438	+	4.38380i	0.0590933	+	0.181871i
$582$	−7.02298	+	6.32352i	−0.291112	+	0.262118i
$583$	22.8189	+	13.1745i	0.945063	+	0.545632i
$584$	2.68899	+	4.65746i	0.111271	+	0.192727i
$585$		0			0
$586$	1.84092	−	0.819632i	0.0760479	−	0.0338587i
$587$	−9.20098	−	12.6641i	−0.379765	−	0.522702i	0.575757	−	0.817621i	$-0.304707\pi$
$587$	−9.20098	−	12.6641i	−0.379765	−	0.522702i	−0.955522	+	0.294919i	$0.904707\pi$
$588$		−	4.84228i		−	0.199692i
$589$	−12.0145	+	3.85078i	−0.495049	+	0.158669i
$590$		0			0
$591$	6.44963	−	4.68593i	0.265303	−	0.192754i
$592$	−23.3343	−	52.4098i	−0.959036	−	2.15403i
$593$	44.2373	+	14.3736i	1.81661	+	0.590251i	0.999913	+	0.0131789i	$0.00419510\pi$
$593$	44.2373	+	14.3736i	1.81661	+	0.590251i	0.816693	+	0.577072i	$0.195805\pi$
$594$	27.7639	+	48.0885i	1.13917	+	1.97309i
$595$		0			0
$596$	9.13511	+	10.1456i	0.374189	+	0.415579i
$597$	−13.1995	+	4.28877i	−0.540219	+	0.175528i
$598$	−17.5826	−	15.8315i	−0.719007	−	0.647397i
$599$	−5.10491	−	2.27285i	−0.208581	−	0.0928662i	0.299787	−	0.954006i	$-0.403084\pi$
$599$	−5.10491	−	2.27285i	−0.208581	−	0.0928662i	−0.508368	+	0.861140i	$0.669751\pi$
$600$		0			0
$601$	−0.682667	−	6.49514i	−0.0278466	−	0.264942i	−0.999583	−	0.0288741i	$-0.990808\pi$
$601$	−0.682667	−	6.49514i	−0.0278466	−	0.264942i	0.971736	−	0.236068i	$-0.0758589\pi$
$602$	−2.83662	−	0.298141i	−0.115612	−	0.0121513i
$603$	2.91638	−	13.7205i	0.118764	−	0.558742i
$604$	−14.5453	−	10.5678i	−0.591839	−	0.429996i
$605$		0			0
$606$	4.86165	+	1.03337i	0.197491	+	0.0419780i
$607$	−10.6654	−	1.12098i	−0.432896	−	0.0454992i	−0.114425	−	0.993432i	$-0.536503\pi$
$607$	−10.6654	−	1.12098i	−0.432896	−	0.0454992i	−0.318471	+	0.947933i	$0.603169\pi$
$608$	12.9882	−	1.36511i	0.526739	−	0.0553625i
$609$	−16.1310	+	3.42876i	−0.653662	+	0.138940i
$610$		0			0
$611$	39.8445	−	44.2518i	1.61194	−	1.79024i
$612$	−10.7768	+	3.50159i	−0.435625	+	0.141543i
$613$	33.3503	−	30.0288i	1.34701	−	1.21285i	0.390689	−	0.920523i	$-0.372237\pi$
$613$	33.3503	−	30.0288i	1.34701	−	1.21285i	0.956318	−	0.292328i	$-0.0944298\pi$
$614$	−0.460235	+	0.797150i	−0.0185736	+	0.0321704i
$615$		0			0
$616$	4.97549	−	15.3130i	0.200468	−	0.616977i
$617$	6.26687	+	14.0756i	0.252295	+	0.566663i	0.994645	−	0.103349i	$-0.0329558\pi$
$617$	6.26687	+	14.0756i	0.252295	+	0.566663i	−0.742351	+	0.670012i	$0.766289\pi$
$618$	−3.90456	−	5.37416i	−0.157064	−	0.216180i
$619$	44.9616			1.80716			0.903579	−	0.428421i	$-0.140930\pi$
$619$	44.9616			1.80716			0.903579	+	0.428421i	$0.140930\pi$
$620$		0			0
$621$	13.1788			0.528848
$622$	29.8408	+	41.0724i	1.19651	+	1.64685i
$623$	−4.96046	−	11.1414i	−0.198736	−	0.446369i
$624$	9.10823	−	28.0323i	0.364621	−	1.12219i
$625$		0			0
$626$	15.3831	−	26.6442i	0.614831	−	1.06492i
$627$	11.0493	−	9.94881i	0.441265	−	0.397317i
$628$	20.4005	−	6.62854i	0.814070	−	0.264508i
$629$	43.2041	−	47.9830i	1.72266	−	1.91321i
$630$		0			0
$631$	12.5183	−	2.66085i	0.498347	−	0.105927i	0.0481207	−	0.998842i	$-0.484677\pi$
$631$	12.5183	−	2.66085i	0.498347	−	0.105927i	0.450226	+	0.892915i	$0.351343\pi$
$632$	−6.48576	+	0.681681i	−0.257990	+	0.0271158i
$633$	−7.71055	−	0.810411i	−0.306467	−	0.0322110i
$634$	38.5251	+	8.18877i	1.53003	+	0.325218i
$635$		0			0
$636$	−4.50991	−	3.27664i	−0.178829	−	0.129927i
$637$	4.29126	−	20.1888i	0.170026	−	0.799909i
$638$	−87.9836	−	9.24745i	−3.48330	−	0.366110i
$639$	0.0114806	+	0.109231i	0.000454165	+	0.00432109i
$640$		0			0
$641$	22.1203	+	9.84859i	0.873699	+	0.388996i	0.794068	−	0.607828i	$-0.207959\pi$
$641$	22.1203	+	9.84859i	0.873699	+	0.388996i	0.0796310	+	0.996824i	$0.474626\pi$
$642$	−5.91747	−	5.32811i	−0.233544	−	0.210284i
$643$	3.23064	−	1.04970i	0.127404	−	0.0413960i	−0.244621	−	0.969619i	$-0.578664\pi$
$643$	3.23064	−	1.04970i	0.127404	−	0.0413960i	0.372025	+	0.928223i	$0.378664\pi$
$644$	3.36505	+	3.73727i	0.132601	+	0.147269i
$645$		0			0
$646$	11.2494	+	19.4846i	0.442602	+	0.766610i
$647$	−5.62269	−	1.82692i	−0.221051	−	0.0718238i	0.196398	−	0.980524i	$-0.437076\pi$
$647$	−5.62269	−	1.82692i	−0.221051	−	0.0718238i	−0.417449	+	0.908701i	$0.637076\pi$
$648$	0.311955	+	0.700662i	0.0122548	+	0.0275246i
$649$	18.1439	−	13.1823i	0.712211	−	0.517452i
$650$		0			0
$651$	2.31143	−	10.6649i	0.0905922	−	0.417988i
$652$			16.8117i			0.658397i
$653$	13.6118	+	18.7351i	0.532671	+	0.733159i	0.987535	−	0.157402i	$-0.0503118\pi$
$653$	13.6118	+	18.7351i	0.532671	+	0.733159i	−0.454863	+	0.890561i	$0.650312\pi$
$654$	−21.1488	+	9.41604i	−0.826982	+	0.368196i
$655$		0			0
$656$	−0.00248734	−	0.00430820i	−9.71142e−5	−	0.000168207i
$657$	5.41618	+	3.12703i	0.211305	+	0.121997i
$658$	−25.9591	+	23.3737i	−1.01199	+	0.911201i
$659$	4.86468	+	14.9719i	0.189501	+	0.583224i	0.999997	−	0.00252045i	$-0.000802286\pi$
$659$	4.86468	+	14.9719i	0.189501	+	0.583224i	−0.810496	+	0.585744i	$0.800802\pi$
$660$		0			0
$661$	−12.1194	−	5.39589i	−0.471389	−	0.209876i	0.157272	−	0.987555i	$-0.449730\pi$
$661$	−12.1194	−	5.39589i	−0.471389	−	0.209876i	−0.628661	+	0.777679i	$0.716397\pi$
$662$	−1.38611	−	6.52116i	−0.0538729	−	0.253452i
$663$	32.9912	−	3.46751i	1.28127	−	0.134667i
$664$	−0.415521	+	3.95342i	−0.0161253	+	0.153422i
$665$		0			0
$666$	−29.3468	−	21.3217i	−1.13717	−	0.826199i
$667$	−12.3416	+	16.9868i	−0.477869	+	0.657731i
$668$	−2.40717	+	11.3248i	−0.0931362	+	0.438171i
$669$	1.64981	−	15.6969i	0.0637854	−	0.606878i
$670$		0			0
$671$	−63.1421	+	13.4213i	−2.43757	+	0.518122i
$672$	−4.59440	+	10.3192i	−0.177233	+	0.398071i
$673$	−0.899983	−	0.810348i	−0.0346918	−	0.0312366i	0.651602	−	0.758561i	$-0.274097\pi$
$673$	−0.899983	−	0.810348i	−0.0346918	−	0.0312366i	−0.686294	+	0.727324i	$0.740764\pi$
$674$	−9.50205	−	29.2443i	−0.366005	−	1.12645i
$675$		0			0
$676$	−8.89955	+	15.4145i	−0.342290	+	0.592864i
$677$	−0.421602	+	0.243412i	−0.0162035	+	0.00935507i	−0.508080	−	0.861310i	$-0.669645\pi$
$677$	−0.421602	+	0.243412i	−0.0162035	+	0.00935507i	0.491876	+	0.870665i	$0.336311\pi$
$678$	−0.709477	−	0.230523i	−0.0272473	−	0.00885318i
$679$	7.82175	−	3.48247i	0.300171	−	0.133645i
$680$		0			0
$681$	0.431864			0.0165491
$682$	29.4722	−	50.5798i	1.12855	−	1.93680i
$683$		−	46.6720i		−	1.78586i	−0.450200	−	0.892928i	$-0.648647\pi$
$683$		−	46.6720i		−	1.78586i	0.450200	−	0.892928i	$-0.351353\pi$
$684$	3.70526	−	2.69203i	0.141674	−	0.102932i
$685$		0			0
$686$	−10.5350	+	32.4234i	−0.402228	+	1.23793i
$687$	−11.9716	+	6.91179i	−0.456744	+	0.263701i
$688$	−3.91791	−	2.26201i	−0.149369	−	0.0862383i
$689$	−15.8992	−	17.6579i	−0.605713	−	0.672712i
$690$		0			0
$691$	4.57766	−	5.08401i	0.174142	−	0.193405i	−0.649755	−	0.760144i	$-0.725129\pi$
$691$	4.57766	−	5.08401i	0.174142	−	0.193405i	0.823897	+	0.566739i	$0.191795\pi$
$692$	7.05693	−	15.8501i	0.268264	−	0.602532i
$693$	−3.89293	−	18.3148i	−0.147880	−	0.695721i
$694$	3.63742	+	34.6078i	0.138075	+	1.31369i
$695$		0			0
$696$	−13.9116	−	2.95700i	−0.527317	−	0.112085i
$697$	0.00329090	−	0.00452954i	0.000124652	−	0.000171568i
$698$	−29.7180	+	40.9033i	−1.12484	+	1.54821i
$699$	−0.123778	−	0.0263098i	−0.00468171	−	0.000995128i
$700$		0			0
$701$	−2.85433	−	27.1572i	−0.107807	−	1.02571i	−0.905990	−	0.423298i	$-0.860872\pi$
$701$	−2.85433	−	27.1572i	−0.107807	−	1.02571i	0.798184	−	0.602414i	$-0.205794\pi$
$702$	−10.4110	−	48.9797i	−0.392936	−	1.84862i
$703$	−10.6146	+	23.8409i	−0.400339	+	0.899175i
$704$	−0.969731	+	1.07700i	−0.0365481	+	0.0405908i
$705$		0			0
$706$	−5.58458	−	6.20230i	−0.210178	−	0.233427i
$707$	−3.89974	−	2.25151i	−0.146665	−	0.0846769i
$708$	−4.10913	+	2.37241i	−0.154431	+	0.0891606i
$709$	9.65169	−	29.7049i	0.362477	−	1.11559i	−0.589069	−	0.808083i	$-0.700505\pi$
$709$	9.65169	−	29.7049i	0.362477	−	1.11559i	0.951546	−	0.307507i	$-0.0994946\pi$
$710$		0			0
$711$	−6.13547	+	4.45768i	−0.230098	+	0.167176i
$712$		−	10.5177i		−	0.394169i
$713$	−6.89875	−	12.0600i	−0.258360	−	0.451649i
$714$	−19.4600			−0.728271
$715$		0			0
$716$	15.1415	−	6.74142i	0.565864	−	0.251939i
$717$	17.2910	+	5.61818i	0.645744	+	0.209815i
$718$	−16.0340	+	9.25722i	−0.598383	+	0.345476i
$719$	−5.38949	+	9.33486i	−0.200994	+	0.348132i	−0.948849	−	0.315730i	$-0.897750\pi$
$719$	−5.38949	+	9.33486i	−0.200994	+	0.348132i	0.747855	+	0.663862i	$0.231084\pi$
$720$		0			0
$721$	1.85978	+	5.72381i	0.0692618	+	0.213166i
$722$	18.2482	+	16.4308i	0.679128	+	0.611490i
$723$	−0.810500	+	1.82041i	−0.0301428	+	0.0677018i
$724$	2.77593	−	0.590043i	0.103167	−	0.0219288i
$725$		0			0
$726$	−4.96060	+	47.1970i	−0.184105	+	1.75165i
$727$	1.83921	−	8.65279i	0.0682124	−	0.320914i	−0.930791	−	0.365552i	$-0.880880\pi$
$727$	1.83921	−	8.65279i	0.0682124	−	0.320914i	0.999003	+	0.0446381i	$0.0142135\pi$
$728$	−8.53440	+	11.7466i	−0.316306	+	0.435358i
$729$	14.8882	+	10.8169i	0.551415	+	0.400626i
$730$		0			0
$731$	0.532219	−	5.06373i	0.0196848	−	0.187289i
$732$	13.5823	−	1.42756i	0.502018	−	0.0527642i
$733$	0.493635	+	2.32237i	0.0182328	+	0.0857787i	0.986323	−	0.164822i	$-0.0527051\pi$
$733$	0.493635	+	2.32237i	0.0182328	+	0.0857787i	−0.968090	+	0.250601i	$0.919372\pi$
$734$	−0.977543	−	0.435230i	−0.0360818	−	0.0160646i
$735$		0			0
$736$	4.44420	+	13.6778i	0.163815	+	0.504172i
$737$	34.7969	−	31.3312i	1.28176	−	1.15410i
$738$	−0.00272406	−	0.00157273i	−0.000100274	−	5.78932e-5i
$739$	−26.9643	−	46.7035i	−0.991897	−	1.71802i	−0.605975	−	0.795484i	$-0.707217\pi$
$739$	−26.9643	−	46.7035i	−0.991897	−	1.71802i	−0.385921	−	0.922532i	$-0.626116\pi$
$740$		0			0
$741$	−12.2487	+	5.45349i	−0.449969	+	0.200339i
$742$	8.19300	+	11.2767i	0.300774	+	0.413981i
$743$			40.3898i			1.48176i	0.671639	+	0.740879i	$0.265591\pi$
$743$			40.3898i			1.48176i	−0.671639	+	0.740879i	$0.734409\pi$
$744$	5.56202	−	7.59153i	0.203913	−	0.278319i
$745$		0			0
$746$	−15.5521	+	11.2992i	−0.569402	+	0.413695i
$747$	1.88025	+	4.22311i	0.0687948	+	0.154516i
$748$	−35.9741	−	11.6887i	−1.31534	−	0.427381i
$749$	3.60710	+	6.24768i	0.131801	+	0.228285i
$750$		0			0
$751$	31.2321	+	34.6867i	1.13967	+	1.26574i	0.959378	+	0.282125i	$0.0910392\pi$
$751$	31.2321	+	34.6867i	1.13967	+	1.26574i	0.180297	+	0.983612i	$0.442294\pi$
$752$	−52.6938	+	17.1213i	−1.92155	+	0.624348i
$753$	11.6644	+	10.5027i	0.425075	+	0.382740i
$754$	72.8817	+	32.4490i	2.65420	+	1.18172i
$755$		0			0
$756$	1.11254	+	10.5851i	0.0404628	+	0.384978i
$757$	−17.7511	−	1.86572i	−0.645176	−	0.0678107i	−0.223711	−	0.974655i	$-0.571817\pi$
$757$	−17.7511	−	1.86572i	−0.645176	−	0.0678107i	−0.421465	+	0.906845i	$0.638484\pi$
$758$	4.73342	−	22.2690i	0.171926	−	0.808846i
$759$	13.2463	+	9.62403i	0.480812	+	0.349330i
$760$		0			0
$761$	−5.47424	−	1.16359i	−0.198441	−	0.0421800i	0.107619	−	0.994192i	$-0.465677\pi$
$761$	−5.47424	−	1.16359i	−0.198441	−	0.0421800i	−0.306060	+	0.952012i	$0.599011\pi$
$762$	−4.14620	−	0.435783i	−0.150201	−	0.0157867i
$763$	20.8591	−	2.19238i	0.755149	−	0.0793694i
$764$	23.1193	−	4.91417i	0.836428	−	0.177788i
$765$		0			0
$766$	19.7492	−	21.9337i	0.713568	−	0.792498i
$767$	−19.2345	+	6.24967i	−0.694518	+	0.225663i
$768$	−16.5387	+	14.8915i	−0.596790	+	0.537352i
$769$	−0.800408	+	1.38635i	−0.0288634	+	0.0499929i	−0.880096	−	0.474795i	$-0.842522\pi$
$769$	−0.800408	+	1.38635i	−0.0288634	+	0.0499929i	0.851233	+	0.524788i	$0.175855\pi$
$770$		0			0
$771$	5.81984	−	17.9116i	0.209596	−	0.645071i
$772$	−1.79195	−	4.02479i	−0.0644937	−	0.144855i
$773$	−26.8378	−	36.9391i	−0.965289	−	1.32861i	−0.944391	−	0.328825i	$-0.893348\pi$
$773$	−26.8378	−	36.9391i	−0.965289	−	1.32861i	−0.0208979	−	0.999782i	$-0.506652\pi$
$774$	−2.86052			−0.102819
$775$		0			0
$776$	7.38393			0.265068
$777$	−13.2676	−	18.2613i	−0.475973	−	0.655121i
$778$	15.4364	+	34.6708i	0.553423	+	1.24301i
$779$	−0.000699289		0.00215219i	−2.50546e−5		7.71102e-5i
$780$		0			0
$781$	−0.183316	+	0.317513i	−0.00655956	+	0.0113615i
$782$	−18.4124	+	16.5786i	−0.658428	+	0.592851i
$783$	−42.2631	+	13.7321i	−1.51036	+	0.490746i
$784$	−12.8503	+	14.2717i	−0.458939	+	0.509703i
$785$		0			0
$786$	5.25398	−	1.11677i	0.187403	−	0.0398338i
$787$	10.2454	−	1.07683i	0.365208	−	0.0383849i	0.0798528	−	0.996807i	$-0.474555\pi$
$787$	10.2454	−	1.07683i	0.365208	−	0.0383849i	0.285356	+	0.958422i	$0.407888\pi$
$788$	8.15254	+	0.856867i	0.290422	+	0.0305246i
$789$	−4.67731	−	0.994193i	−0.166517	−	0.0353942i
$790$		0			0
$791$	0.546783	+	0.397261i	0.0194414	+	0.0141250i
$792$	3.35730	−	15.7949i	0.119296	−	0.561246i
$793$	57.8935	+	6.08485i	2.05586	+	0.216080i
$794$	2.03693	+	19.3801i	0.0722879	+	0.687774i
$795$		0			0
$796$	−13.0371	−	5.80450i	−0.462089	−	0.205735i
$797$	−15.0005	−	13.5065i	−0.531346	−	0.478426i	0.359237	−	0.933246i	$-0.383037\pi$
$797$	−15.0005	−	13.5065i	−0.531346	−	0.478426i	−0.890583	+	0.454820i	$0.849703\pi$
$798$	7.48043	−	2.43054i	0.264804	−	0.0860402i
$799$	−41.7250	−	46.3403i	−1.47612	−	1.63940i
$800$		0			0
$801$	−6.11556	−	10.5925i	−0.216083	−	0.374266i
$802$	−61.2536	−	19.9025i	−2.16294	−	0.702781i
$803$	8.49135	+	19.0719i	0.299653	+	0.673032i
$804$	−8.01438	+	5.82279i	−0.282645	+	0.205354i
$805$		0			0
$806$	−39.3715	+	35.1666i	−1.38680	+	1.23869i
$807$			33.4049i			1.17591i
$808$	−2.28264	−	3.14179i	−0.0803030	−	0.110528i
$809$	15.1137	−	6.72905i	0.531369	−	0.236581i	−0.123471	−	0.992348i	$-0.539403\pi$
$809$	15.1137	−	6.72905i	0.531369	−	0.236581i	0.654840	+	0.755767i	$0.272736\pi$
$810$		0			0
$811$	−14.8937	−	25.7967i	−0.522990	−	0.905845i	−0.999642	−	0.0267530i	$-0.991483\pi$
$811$	−14.8937	−	25.7967i	−0.522990	−	0.905845i	0.476652	−	0.879092i	$-0.341850\pi$
$812$	−14.6855	−	8.47869i	−0.515361	−	0.297544i
$813$	−15.5642	+	14.0141i	−0.545862	+	0.491496i
$814$	−37.4185	−	115.162i	−1.31152	−	4.03643i
$815$		0			0
$816$	−28.1974	−	12.5543i	−0.987108	−	0.439489i
$817$	0.427871	+	2.01297i	0.0149693	+	0.0704251i
$818$	48.2732	−	5.07372i	1.68783	−	0.177398i
$819$	−1.76495	+	16.7924i	−0.0616724	+	0.586774i
$820$		0			0
$821$	17.6206	+	12.8021i	0.614964	+	0.446798i	0.851159	−	0.524908i	$-0.175900\pi$
$821$	17.6206	+	12.8021i	0.614964	+	0.446798i	−0.236195	+	0.971706i	$0.575900\pi$
$822$	7.38927	−	10.1705i	0.257730	−	0.354735i
$823$	−2.96614	+	13.9546i	−0.103393	+	0.486426i	0.895732	+	0.444595i	$0.146652\pi$
$823$	−2.96614	+	13.9546i	−0.103393	+	0.486426i	−0.999125	+	0.0418309i	$0.986681\pi$
$824$	−0.542535	+	5.16187i	−0.0189001	+	0.179822i
$825$		0			0
$826$	11.6048	−	2.46668i	0.403783	−	0.0858267i
$827$	−3.21689	+	7.22525i	−0.111862	+	0.251246i	−0.960798	−	0.277249i	$-0.910577\pi$
$827$	−3.21689	+	7.22525i	−0.111862	+	0.251246i	0.848936	+	0.528496i	$0.177244\pi$
$828$	3.74811	+	3.37481i	0.130256	+	0.117283i
$829$	10.0290	+	30.8660i	0.348321	+	1.07202i	0.959782	+	0.280747i	$0.0905821\pi$
$829$	10.0290	+	30.8660i	0.348321	+	1.07202i	−0.611461	+	0.791275i	$0.709418\pi$
$830$		0			0
$831$	2.94309	−	5.09759i	0.102095	−	0.176833i
$832$	1.13181	−	0.653449i	0.0392383	−	0.0226543i
$833$	−20.5561	−	6.67907i	−0.712225	−	0.231416i
$834$	19.2452	−	8.56854i	0.666408	−	0.296704i
$835$		0			0
$836$	15.2884			0.528760
$837$	3.19040	−	29.2313i	0.110276	−	1.01038i
$838$		−	16.2444i		−	0.561155i
$839$	−18.9902	+	13.7972i	−0.655616	+	0.476333i	−0.865180	−	0.501462i	$-0.832796\pi$
$839$	−18.9902	+	13.7972i	−0.655616	+	0.476333i	0.209564	+	0.977795i	$0.432796\pi$
$840$		0			0
$841$	12.9168	−	39.7539i	0.445408	−	1.37083i
$842$	29.6171	−	17.0994i	1.02067	−	0.589285i
$843$	−25.1562	−	14.5239i	−0.866425	−	0.500231i
$844$	−5.33437	−	5.92442i	−0.183617	−	0.203927i
$845$		0			0
$846$	−23.4415	+	26.0344i	−0.805935	+	0.895081i
$847$	17.4880	−	39.2786i	0.600893	−	1.34963i
$848$	4.59664	+	21.6255i	0.157849	+	0.742623i
$849$	−2.31714	−	22.0461i	−0.0795240	−	0.756621i
$850$		0			0
$851$	−28.1109	−	5.97515i	−0.963628	−	0.204826i
$852$	0.0455927	−	0.0627529i	0.00156198	−	0.00214988i
$853$	23.8794	−	32.8672i	0.817616	−	1.12535i	−0.172487	−	0.985012i	$-0.555180\pi$
$853$	23.8794	−	32.8672i	0.817616	−	1.12535i	0.990103	−	0.140340i	$-0.0448196\pi$
$854$	−33.4025	−	7.09992i	−1.14301	−	0.242954i
$855$		0			0
$856$	0.650335	+	6.18752i	0.0222280	+	0.211485i
$857$	−1.46492	−	6.89190i	−0.0500407	−	0.235423i	0.946019	−	0.324112i	$-0.105066\pi$
$857$	−1.46492	−	6.89190i	−0.0500407	−	0.235423i	−0.996059	+	0.0886893i	$0.971732\pi$
$858$	25.3039	−	56.8334i	0.863859	−	1.94026i
$859$	16.5579	−	18.3894i	0.564949	−	0.627440i	−0.391205	−	0.920304i	$-0.627942\pi$
$859$	16.5579	−	18.3894i	0.564949	−	0.627440i	0.956154	+	0.292864i	$0.0946083\pi$
$860$		0			0
$861$	−0.00130969	−	0.00145456i	−4.46340e−5	−	4.95711e-5i
$862$	−42.4465	−	24.5065i	−1.44573	−	0.834695i
$863$	−10.2501	+	5.91787i	−0.348916	+	0.201447i	−0.664208	−	0.747548i	$-0.731231\pi$
$863$	−10.2501	+	5.91787i	−0.348916	+	0.201447i	0.315292	+	0.948995i	$0.397898\pi$
$864$	−9.40579	+	28.9480i	−0.319991	+	0.984832i
$865$		0			0
$866$	−36.4962	+	26.5161i	−1.24019	+	0.901053i
$867$		−	15.9498i		−	0.541683i
$868$	9.10408	−	6.55912i	0.309013	−	0.222631i
$869$	−25.3158			−0.858779
$870$		0			0
$871$	−38.5743	+	17.1744i	−1.30704	+	0.581932i
$872$	17.2029	+	5.58956i	0.582563	+	0.189286i
$873$	7.43639	−	4.29340i	0.251684	−	0.145310i
$874$	5.00710	−	8.67255i	0.169368	−	0.293353i
$875$		0			0
$876$	−1.36487	−	4.20064i	−0.0461147	−	0.141926i
$877$	−25.9404	−	23.3568i	−0.875943	−	0.788703i	0.102605	−	0.994722i	$-0.467282\pi$
$877$	−25.9404	−	23.3568i	−0.875943	−	0.788703i	−0.978548	+	0.206019i	$0.933949\pi$
$878$	2.34372	−	5.26409i	0.0790969	−	0.177654i
$879$	1.23010	−	0.261465i	0.0414902	−	0.00881901i
$880$		0			0
$881$	2.08888	−	19.8744i	0.0703762	−	0.669585i	−0.901288	−	0.433220i	$-0.857377\pi$
$881$	2.08888	−	19.8744i	0.0703762	−	0.669585i	0.971664	−	0.236365i	$-0.0759561\pi$
$882$	−2.52465	+	11.8776i	−0.0850095	+	0.399938i
$883$	−22.6995	+	31.2431i	−0.763898	+	1.05142i	0.232982	+	0.972481i	$0.425152\pi$
$883$	−22.6995	+	31.2431i	−0.763898	+	1.05142i	−0.996880	+	0.0789344i	$0.974848\pi$
$884$	27.5958	+	20.0495i	0.928146	+	0.674337i
$885$		0			0
$886$	6.43261	−	61.2022i	0.216108	−	2.05613i
$887$	42.4867	−	4.46553i	1.42656	−	0.149938i	0.640441	−	0.768007i	$-0.278752\pi$
$887$	42.4867	−	4.46553i	1.42656	−	0.149938i	0.786124	+	0.618069i	$0.212085\pi$
$888$	−4.04732	−	19.0411i	−0.135819	−	0.638978i
$889$	3.45058	+	1.53630i	0.115729	+	0.0515257i
$890$		0			0
$891$	0.920038	+	2.83159i	0.0308224	+	0.0948617i
$892$	12.0608	−	10.8596i	0.403824	−	0.363605i
$893$	21.8270	+	12.6018i	0.730412	+	0.421704i
$894$	11.7568	+	20.3635i	0.393208	+	0.681056i
$895$		0			0
$896$	17.9732	−	8.00218i	0.600442	−	0.267334i
$897$	−8.67877	−	11.9453i	−0.289776	−	0.398842i
$898$		−	7.95426i		−	0.265437i
$899$	34.6898	+	31.4866i	1.15697	+	1.05014i
$900$		0			0
$901$	−20.1303	+	14.6255i	−0.670638	+	0.487247i
$902$	−0.00427071	−	0.00959216i	−0.000142199	−	0.000319384i
$903$	−1.69287	−	0.550046i	−0.0563351	−	0.0183044i
$904$	0.291435	+	0.504780i	0.00969298	+	0.0167887i
$905$		0			0
$906$	−20.7202	−	23.0121i	−0.688381	−	0.764525i
$907$	6.21939	−	2.02080i	0.206511	−	0.0670996i	−0.203935	−	0.978985i	$-0.565373\pi$
$907$	6.21939	−	2.02080i	0.206511	−	0.0670996i	0.410446	+	0.911885i	$0.365373\pi$
$908$	0.330006	+	0.297139i	0.0109516	+	0.00986090i
$909$	−4.12566	−	1.83686i	−0.136839	−	0.0609248i
$910$		0			0
$911$	4.19052	+	39.8702i	0.138838	+	1.32096i	0.812952	+	0.582330i	$0.197859\pi$
$911$	4.19052	+	39.8702i	0.138838	+	1.32096i	−0.674114	+	0.738627i	$0.735474\pi$
$912$	12.4072	+	1.30404i	0.410842	+	0.0431812i
$913$	−3.20835	+	15.0941i	−0.106181	+	0.499542i
$914$	11.9157	+	8.65729i	0.394138	+	0.286358i
$915$		0			0
$916$	−13.9036	−	2.95529i	−0.459387	−	0.0976456i
$917$	−4.83977	−	0.508680i	−0.159823	−	0.0167981i
$918$	−52.1500	+	5.48118i	−1.72120	+	0.180906i
$919$	0.0179916	−	0.00382423i	0.000593488	−	0.000126150i	−0.207615	−	0.978211i	$-0.566570\pi$
$919$	0.0179916	−	0.00382423i	0.000593488	−	0.000126150i	0.208208	+	0.978084i	$0.433237\pi$
$920$		0			0
$921$	−0.384370	+	0.426886i	−0.0126654	+	0.0140664i
$922$	−17.0943	+	5.55427i	−0.562970	+	0.182920i
$923$	0.245700	−	0.221229i	0.00808731	−	0.00728185i
$924$	−6.61171	+	11.4518i	−0.217509	+	0.376737i
$925$		0			0
$926$	−12.4114	+	38.1983i	−0.407864	+	1.25528i
$927$	2.45499	+	5.51401i	0.0806326	+	0.181104i
$928$	−28.5042	−	39.2326i	−0.935695	−	1.28787i
$929$	−29.2558			−0.959851			−0.479925	−	0.877309i	$-0.659336\pi$
$929$	−29.2558			−0.959851			−0.479925	+	0.877309i	$0.659336\pi$
$930$		0			0
$931$	8.73598			0.286310
$932$	−0.0764819	−	0.105268i	−0.00250525	−	0.00344818i
$933$	12.8865	+	28.9435i	0.421885	+	0.947569i
$934$	−5.45282	+	16.7820i	−0.178422	+	0.549125i
$935$		0			0
$936$	−7.28086	+	12.6108i	−0.237982	+	0.412197i
$937$	7.93330	−	7.14318i	0.259170	−	0.233357i	−0.529294	−	0.848438i	$-0.677543\pi$
$937$	7.93330	−	7.14318i	0.259170	−	0.233357i	0.788464	+	0.615081i	$0.210877\pi$
$938$	23.5577	−	7.65436i	0.769186	−	0.249924i
$939$	12.8473	−	14.2684i	0.419257	−	0.465632i
$940$		0			0
$941$	20.6431	−	4.38782i	0.672945	−	0.143039i	0.141249	−	0.989974i	$-0.454888\pi$
$941$	20.6431	−	4.38782i	0.672945	−	0.143039i	0.531696	+	0.846935i	$0.321555\pi$
$942$	36.7424	−	3.86178i	1.19713	−	0.125824i
$943$	−0.00247837		0.000260488i	−8.07069e−5		8.48264e-6i
$944$	18.4067	+	3.91246i	0.599087	+	0.127340i
$945$		0			0
$946$	−7.72509	−	5.61261i	−0.251164	−	0.182482i
$947$	−9.58705	+	45.1035i	−0.311537	+	1.46567i	0.492095	+	0.870541i	$0.336231\pi$
$947$	−9.58705	+	45.1035i	−0.311537	+	1.46567i	−0.803633	+	0.595126i	$0.797102\pi$
$948$	5.32662	+	0.559850i	0.173000	+	0.0181831i
$949$	−1.96788	−	18.7232i	−0.0638802	−	0.607779i
$950$		0			0
$951$	22.4543	+	9.99729i	0.728130	+	0.324184i
$952$	11.2994	+	10.1740i	0.366216	+	0.329742i
$953$	−8.30313	+	2.69785i	−0.268965	+	0.0873920i	−0.440394	−	0.897804i	$-0.645161\pi$
$953$	−8.30313	+	2.69785i	−0.268965	+	0.0873920i	0.171430	+	0.985196i	$0.445161\pi$
$954$	9.35391	+	10.3886i	0.302844	+	0.336342i
$955$		0			0
$956$	9.34727	+	16.1899i	0.302312	+	0.523620i
$957$	−52.5077	−	17.0608i	−1.69733	−	0.551497i
$958$	4.64439	+	10.4315i	0.150053	+	0.337025i
$959$	−9.21438	+	6.69464i	−0.297548	+	0.216181i
$960$		0			0
$961$	−28.4197	+	12.3823i	−0.916765	+	0.399428i
$962$			109.196i			3.52061i
$963$	4.25271	+	5.85335i	0.137042	+	0.188621i
$964$	−1.87185	+	0.833401i	−0.0602882	+	0.0268420i
$965$		0			0
$966$	4.33080	+	7.50117i	0.139341	+	0.241346i
$967$	8.36547	+	4.82981i	0.269015	+	0.155316i	0.628440	−	0.777858i	$-0.283694\pi$
$967$	8.36547	+	4.82981i	0.269015	+	0.155316i	−0.359425	+	0.933174i	$0.617027\pi$
$968$	27.5558	−	24.8114i	0.885678	−	0.797468i
$969$	4.33882	+	13.3535i	0.139383	+	0.428977i
$970$		0			0
$971$	31.8789	+	14.1934i	1.02304	+	0.455488i	0.848519	−	0.529165i	$-0.177495\pi$
$971$	31.8789	+	14.1934i	1.02304	+	0.455488i	0.174524	+	0.984653i	$0.444161\pi$
$972$	3.61263	+	16.9961i	0.115875	+	0.545150i
$973$	−18.9816	+	1.99505i	−0.608523	+	0.0639584i
$974$	−3.63047	+	34.5416i	−0.116328	+	1.10679i
$975$		0			0
$976$	−43.8197	−	31.8369i	−1.40263	−	1.01907i
$977$	19.8325	−	27.2971i	0.634498	−	0.873312i	−0.363809	−	0.931474i	$-0.618524\pi$
$977$	19.8325	−	27.2971i	0.634498	−	0.873312i	0.998307	+	0.0581615i	$0.0185238\pi$
$978$	−6.02016	+	28.3226i	−0.192504	+	0.905658i
$979$	4.26778	−	40.6052i	0.136399	−	1.29775i
$980$		0			0
$981$	20.5752	−	4.37339i	0.656915	−	0.139631i
$982$	−0.289216	+	0.649589i	−0.00922924	+	0.0207292i
$983$	7.99315	+	7.19707i	0.254942	+	0.229551i	0.786684	−	0.617355i	$-0.211796\pi$
$983$	7.99315	+	7.19707i	0.254942	+	0.229551i	−0.531742	+	0.846906i	$0.678463\pi$
$984$	−0.000521619	−	0.00160538i	−1.66286e−5	−	5.11776e-5i
$985$		0			0
$986$	41.7721	−	72.3514i	1.33029	−	2.30414i
$987$	−18.8789	+	10.8997i	−0.600921	+	0.346942i
$988$	−13.1120	−	4.26035i	−0.417148	−	0.135540i
$989$	−2.07034	+	0.921776i	−0.0658331	+	0.0293108i
$990$		0			0
$991$	16.5667			0.526258			0.263129	−	0.964761i	$-0.415245\pi$
$991$	16.5667			0.526258			0.263129	+	0.964761i	$0.415245\pi$
$992$	31.4141	−	6.54626i	0.997397	−	0.207844i
$993$		−	4.16054i		−	0.132031i
$994$	−0.156909	+	0.114001i	−0.00497685	+	0.00361590i
$995$		0			0
$996$	1.00886	−	3.10496i	0.0319670	−	0.0983843i
$997$	35.2682	−	20.3621i	1.11695	−	0.644874i	0.176332	−	0.984331i	$-0.443577\pi$
$997$	35.2682	−	20.3621i	1.11695	−	0.644874i	0.940622	+	0.339457i	$0.110243\pi$
$998$	26.5297	+	15.3169i	0.839782	+	0.484848i
$999$	−40.6989	−	45.2007i	−1.28766	−	1.43009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.c.49.9		80
5.2	odd	4		155.2.q.a.111.1	yes	40
5.3	odd	4		775.2.bl.c.576.5		40
5.4	even	2	inner	775.2.ck.c.49.2		80
31.19	even	15	inner	775.2.ck.c.174.2		80
155.19	even	30	inner	775.2.ck.c.174.9		80
155.22	even	60		4805.2.a.y.1.16		20
155.102	odd	60		4805.2.a.x.1.16		20
155.112	odd	60		155.2.q.a.81.1	✓	40
155.143	odd	60		775.2.bl.c.701.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.a.81.1	✓	40	155.112	odd	60
155.2.q.a.111.1	yes	40	5.2	odd	4
775.2.bl.c.576.5		40	5.3	odd	4
775.2.bl.c.701.5		40	155.143	odd	60
775.2.ck.c.49.2		80	5.4	even	2	inner
775.2.ck.c.49.9		80	1.1	even	1	trivial
775.2.ck.c.174.2		80	31.19	even	15	inner
775.2.ck.c.174.9		80	155.19	even	30	inner
4805.2.a.x.1.16		20	155.102	odd	60
4805.2.a.y.1.16		20	155.22	even	60

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.04097 + 1.43277i) q^{2} +(0.449533 + 1.00967i) q^{3} +(-0.351182 + 1.08083i) q^{4} +(-0.978673 + 1.69511i) q^{6} +(1.31785 - 1.18660i) q^{7} +(1.45450 - 0.472596i) q^{8} +(1.19004 - 1.32168i) q^{9} +(5.80707 - 1.23433i) q^{11} +(-1.24914 + 0.131290i) q^{12} +(-5.32437 - 0.559613i) q^{13} +(3.07197 + 0.652967i) q^{14} +(4.03002 + 2.92798i) q^{16} +(-1.16563 + 5.48385i) q^{17} +(3.13246 + 0.329234i) q^{18} +(-0.236861 - 2.25358i) q^{19} +(1.79049 + 0.797178i) q^{21} +(7.81349 + 7.03529i) q^{22} +(2.37325 - 0.771116i) q^{23} +(1.13101 + 1.25611i) q^{24} +(-4.74070 - 8.21114i) q^{26} +(5.02280 + 1.63201i) q^{27} +(0.819703 + 1.84108i) q^{28} +(-6.80728 + 4.94578i) q^{29} +(-1.13585 - 5.45067i) q^{31} +5.76333i q^{32} +(3.85673 + 5.30834i) q^{33} +(-9.07049 + 4.03844i) q^{34} +(1.01058 + 1.75038i) q^{36} +(-9.97386 - 5.75841i) q^{37} +(2.98230 - 2.68528i) q^{38} +(-1.82846 - 5.62741i) q^{39} +(-0.000912316 - 0.000406189i) q^{41} +(0.721672 + 3.39520i) q^{42} +(-0.903210 + 0.0949312i) q^{43} +(-0.705239 + 6.70990i) q^{44} +(3.57531 + 2.59762i) q^{46} +(-6.53766 + 8.99832i) q^{47} +(-1.14466 + 5.38521i) q^{48} +(-0.402983 + 3.83413i) q^{49} +(-6.06086 + 1.28828i) q^{51} +(2.47467 - 5.55819i) q^{52} +(3.29826 + 2.96977i) q^{53} +(2.89028 + 8.89538i) q^{54} +(1.35603 - 2.34872i) q^{56} +(2.16889 - 1.25221i) q^{57} +(-14.1723 - 4.60487i) q^{58} +(3.45105 - 1.53651i) q^{59} -10.8733 q^{61} +(6.62719 - 7.30139i) q^{62} -3.15388i q^{63} +(-0.197490 + 0.143485i) q^{64} +(-3.59089 + 11.0516i) q^{66} +(6.83038 - 3.94352i) q^{67} +(-5.51774 - 3.18567i) q^{68} +(1.84543 + 2.04955i) q^{69} +(-0.0413227 + 0.0458935i) q^{71} +(1.10630 - 2.48479i) q^{72} +(0.731122 + 3.43966i) q^{73} +(-2.13199 - 20.2846i) q^{74} +(2.51891 + 0.535412i) q^{76} +(6.18820 - 8.51733i) q^{77} +(6.15942 - 8.47771i) q^{78} +(-4.17103 - 0.886580i) q^{79} +(0.0524211 + 0.498753i) q^{81} +(-0.000367716 - 0.00172997i) q^{82} +(-1.05722 + 2.37455i) q^{83} +(-1.49040 + 1.65525i) q^{84} +(-1.07623 - 1.19527i) q^{86} +(-8.05369 - 4.64980i) q^{87} +(7.86304 - 4.53973i) q^{88} +(2.12519 - 6.54066i) q^{89} +(-7.68077 + 5.58040i) q^{91} +2.83588i q^{92} +(4.99277 - 3.59709i) q^{93} -19.6980 q^{94} +(-5.81905 + 2.59081i) q^{96} +(4.59184 + 1.49198i) q^{97} +(-5.91292 + 3.41382i) q^{98} +(5.27927 - 9.14396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{6} - 4 q^{9} - 56 q^{11} + 12 q^{14} + 16 q^{16} + 26 q^{19} - 16 q^{21} + 164 q^{24} + 64 q^{26} - 84 q^{29} - 20 q^{31} - 64 q^{34} - 26 q^{36} - 74 q^{39} + 72 q^{41} + 112 q^{44}+ \cdots - 106 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^6 - 4 * q^9 - 56 * q^11 + 12 * q^14 + 16 * q^16 + 26 * q^19 - 16 * q^21 + 164 * q^24 + 64 * q^26 - 84 * q^29 - 20 * q^31 - 64 * q^34 - 26 * q^36 - 74 * q^39 + 72 * q^41 + 112 * q^44 + 36 * q^46 + 62 * q^49 - 4 * q^51 - 44 * q^54 + 18 * q^56 + 2 * q^59 - 200 * q^61 - 34 * q^64 - 80 * q^66 - 16 * q^69 - 4 * q^71 + 4 * q^74 + 4 * q^76 + 134 * q^79 - 166 * q^81 - 52 * q^84 - 10 * q^86 - 40 * q^89 + 38 * q^91 - 260 * q^94 + 92 * q^96 - 106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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