LMFDB - Embedded newform 147.2.m.a.25.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [147,2,Mod(4,147)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("147.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.m (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	147.25
Dual form			147.2.m.a.100.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.24916 - 0.693774i) q^{2} +(-0.365341 - 0.930874i) q^{3} +(2.92492 - 1.99418i) q^{4} +(-0.982858 - 0.148142i) q^{5} +(-1.46753 - 1.84022i) q^{6} +(-2.07146 + 1.64592i) q^{7} +(2.26005 - 2.83402i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(-2.31338 + 0.348686i) q^{10} +(3.21592 + 2.98394i) q^{11} +(-2.92492 - 1.99418i) q^{12} +(-0.00383811 + 0.0168159i) q^{13} +(-3.51714 + 5.13907i) q^{14} +(0.221177 + 0.969039i) q^{15} +(0.530409 - 1.35146i) q^{16} +(0.149951 - 2.00095i) q^{17} +(-1.17686 + 2.03839i) q^{18} +(-0.178003 - 0.308310i) q^{19} +(-3.17020 + 1.52669i) q^{20} +(2.28893 + 1.32694i) q^{21} +(9.30331 + 4.48024i) q^{22} +(-0.512321 - 6.83645i) q^{23} +(-3.46380 - 1.06844i) q^{24} +(-3.83380 - 1.18257i) q^{25} +(0.00303388 + 0.0404844i) q^{26} +(0.900969 + 0.433884i) q^{27} +(-2.77659 + 8.94505i) q^{28} +(2.89389 - 1.39362i) q^{29} +(1.16976 + 2.02608i) q^{30} +(-2.52299 + 4.36995i) q^{31} +(-0.286403 + 3.82178i) q^{32} +(1.60276 - 4.08378i) q^{33} +(-1.05095 - 4.60450i) q^{34} +(2.27978 - 1.31084i) q^{35} +(-0.787734 + 3.45129i) q^{36} +(-9.67885 - 6.59893i) q^{37} +(-0.614254 - 0.569944i) q^{38} +(0.0170557 - 0.00257073i) q^{39} +(-2.64115 + 2.45063i) q^{40} +(-6.39800 + 8.02284i) q^{41} +(6.06878 + 1.39651i) q^{42} +(2.58159 + 3.23721i) q^{43} +(15.3568 + 2.31467i) q^{44} +(0.821248 - 0.559917i) q^{45} +(-5.89525 - 15.0208i) q^{46} +(9.52767 - 2.93890i) q^{47} -1.45182 q^{48} +(1.58188 - 6.81892i) q^{49} -9.44327 q^{50} +(-1.91742 + 0.591446i) q^{51} +(0.0223077 + 0.0568390i) q^{52} +(4.57690 - 3.12048i) q^{53} +(2.32744 + 0.350805i) q^{54} +(-2.71875 - 3.40920i) q^{55} +(-0.0170352 + 9.59042i) q^{56} +(-0.221966 + 0.278336i) q^{57} +(5.54195 - 5.14218i) q^{58} +(10.9381 - 1.64865i) q^{59} +(2.57936 + 2.39330i) q^{60} +(-11.3038 - 7.70678i) q^{61} +(-2.64286 + 11.5791i) q^{62} +(0.398975 - 2.61550i) q^{63} +(2.65341 + 11.6253i) q^{64} +(0.00626346 - 0.0159590i) q^{65} +(0.771655 - 10.2970i) q^{66} +(-3.48108 + 6.02941i) q^{67} +(-3.55166 - 6.15166i) q^{68} +(-6.17670 + 2.97454i) q^{69} +(4.21816 - 4.52993i) q^{70} +(3.82385 + 1.84147i) q^{71} +(0.270885 + 3.61471i) q^{72} +(11.2807 + 3.47963i) q^{73} +(-26.3475 - 8.12711i) q^{74} +(0.299820 + 4.00083i) q^{75} +(-1.13547 - 0.546813i) q^{76} +(-11.5730 - 0.887951i) q^{77} +(0.0365774 - 0.0176148i) q^{78} +(0.240066 + 0.415807i) q^{79} +(-0.721524 + 1.24972i) q^{80} +(0.0747301 - 0.997204i) q^{81} +(-8.82410 + 22.4834i) q^{82} +(-0.429851 - 1.88330i) q^{83} +(9.34111 - 0.683336i) q^{84} +(-0.443806 + 1.94444i) q^{85} +(8.05230 + 5.48997i) q^{86} +(-2.35454 - 2.18470i) q^{87} +(15.7247 - 2.37012i) q^{88} +(6.29680 - 5.84258i) q^{89} +(1.45866 - 1.82910i) q^{90} +(-0.0197271 - 0.0411506i) q^{91} +(-15.1316 - 18.9744i) q^{92} +(4.98963 + 0.752065i) q^{93} +(19.3903 - 13.2201i) q^{94} +(0.129278 + 0.329394i) q^{95} +(3.66223 - 1.12965i) q^{96} +12.4244 q^{97} +(-1.17289 - 16.4343i) q^{98} -4.38704 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 4 q^{3} + 3 q^{4} - 2 q^{6} + 6 q^{8} + 4 q^{9} + 30 q^{10} - 9 q^{11} - 3 q^{12} - 42 q^{14} - 7 q^{15} + 29 q^{16} - 5 q^{17} + 6 q^{18} - 26 q^{19} - 5 q^{20} + 7 q^{21} + q^{22} - 4 q^{23}+ \cdots - 24 q^{99}+O(q^{100}) $ 48 * q - q^2 - 4 * q^3 + 3 * q^4 - 2 * q^6 + 6 * q^8 + 4 * q^9 + 30 * q^10 - 9 * q^11 - 3 * q^12 - 42 * q^14 - 7 * q^15 + 29 * q^16 - 5 * q^17 + 6 * q^18 - 26 * q^19 - 5 * q^20 + 7 * q^21 + q^22 - 4 * q^23 - 18 * q^24 - 56 * q^25 - 62 * q^26 + 8 * q^27 + 7 * q^28 + 12 * q^29 + 12 * q^30 - 36 * q^31 - 14 * q^32 + 16 * q^33 - 76 * q^34 + 7 * q^35 - 6 * q^36 - 20 * q^37 - 60 * q^38 + 14 * q^39 + 28 * q^40 + 41 * q^41 + 28 * q^42 + 12 * q^43 + 44 * q^44 + 14 * q^45 + 16 * q^46 + 13 * q^47 - 12 * q^48 - 84 * q^49 - 12 * q^50 - 2 * q^51 + 92 * q^52 + 14 * q^53 + q^54 - 38 * q^55 + 105 * q^56 + 18 * q^57 + 3 * q^58 + 57 * q^59 + 36 * q^60 + 11 * q^61 - 16 * q^62 - 7 * q^63 - 110 * q^64 + 21 * q^65 + 11 * q^66 + 34 * q^67 + 22 * q^68 - 8 * q^69 + 6 * q^71 - 24 * q^72 - 69 * q^73 - 90 * q^74 - 42 * q^75 - 49 * q^76 + 2 * q^78 + 34 * q^79 + 55 * q^80 + 4 * q^81 + 91 * q^82 + 28 * q^83 + 28 * q^84 - 44 * q^85 - 26 * q^86 - 29 * q^87 + 45 * q^88 + 11 * q^89 + 24 * q^90 + 84 * q^92 + q^93 + 90 * q^94 + 150 * q^95 - 35 * q^96 + 124 * q^97 + 119 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{8}{21}\right)$

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 $

$2$	2.24916	−	0.693774i	1.59040	−	0.490572i	0.631750	−	0.775172i	$-0.282337\pi$
$2$	2.24916	−	0.693774i	1.59040	−	0.490572i	0.958646	+	0.284600i	$0.0918608\pi$
$3$	−0.365341	−	0.930874i	−0.210930	−	0.537440i
$3$	−0.365341	−	0.930874i	−0.210930	−	0.537440i
$4$	2.92492	−	1.99418i	1.46246	−	0.997089i
$5$	−0.982858	−	0.148142i	−0.439547	−	0.0662511i	−0.0744592	−	0.997224i	$-0.523723\pi$
$5$	−0.982858	−	0.148142i	−0.439547	−	0.0662511i	−0.365088	+	0.930973i	$0.618961\pi$
$6$	−1.46753	−	1.84022i	−0.599115	−	0.751267i
$7$	−2.07146	+	1.64592i	−0.782938	+	0.622100i
$7$	−2.07146	+	1.64592i	−0.782938	+	0.622100i
$8$	2.26005	−	2.83402i	0.799050	−	1.00198i
$9$	−0.733052	+	0.680173i	−0.244351	+	0.226724i
$10$	−2.31338	+	0.348686i	−0.731555	+	0.110264i
$11$	3.21592	+	2.98394i	0.969638	+	0.899692i	0.994989	−	0.0999863i	$-0.0318799\pi$
$11$	3.21592	+	2.98394i	0.969638	+	0.899692i	−0.0253511	+	0.999679i	$0.508070\pi$
$12$	−2.92492	−	1.99418i	−0.844352	−	0.575669i
$13$	−0.00383811	+	0.0168159i	−0.00106450	+	0.00466388i	−0.975457	−	0.220188i	$-0.929333\pi$
$13$	−0.00383811	+	0.0168159i	−0.00106450	+	0.00466388i	0.974393	+	0.224852i	$0.0721899\pi$
$14$	−3.51714	+	5.13907i	−0.939996	+	1.37347i
$15$	0.221177	+	0.969039i	0.0571076	+	0.250205i
$16$	0.530409	−	1.35146i	0.132602	−	0.337865i
$17$	0.149951	−	2.00095i	0.0363684	−	0.485303i	−0.949047	−	0.315135i	$-0.897950\pi$
$17$	0.149951	−	2.00095i	0.0363684	−	0.485303i	0.985415	−	0.170167i	$-0.0544309\pi$
$18$	−1.17686	+	2.03839i	−0.277390	+	0.480453i
$19$	−0.178003	−	0.308310i	−0.0408366	−	0.0707311i	0.844885	−	0.534948i	$-0.179669\pi$
$19$	−0.178003	−	0.308310i	−0.0408366	−	0.0707311i	−0.885721	+	0.464217i	$0.846336\pi$
$20$	−3.17020	+	1.52669i	−0.708879	+	0.341378i
$21$	2.28893	+	1.32694i	0.499486	+	0.289563i
$22$	9.30331	+	4.48024i	1.98347	+	0.955190i
$23$	−0.512321	−	6.83645i	−0.106826	−	1.42550i	−0.750840	−	0.660485i	$-0.770351\pi$
$23$	−0.512321	−	6.83645i	−0.106826	−	1.42550i	0.644013	−	0.765014i	$-0.277268\pi$
$24$	−3.46380	−	1.06844i	−0.707046	−	0.218095i
$25$	−3.83380	−	1.18257i	−0.766760	−	0.236514i
$26$	0.00303388	+	0.0404844i	0.000594994	+	0.00793964i
$27$	0.900969	+	0.433884i	0.173392	+	0.0835010i
$28$	−2.77659	+	8.94505i	−0.524727	+	1.69046i
$29$	2.89389	−	1.39362i	0.537381	−	0.258789i	−0.145450	−	0.989366i	$-0.546463\pi$
$29$	2.89389	−	1.39362i	0.537381	−	0.258789i	0.682831	+	0.730577i	$0.260749\pi$
$30$	1.16976	+	2.02608i	0.213567	+	0.369909i
$31$	−2.52299	+	4.36995i	−0.453143	+	0.784867i	−0.998579	−	0.0532856i	$-0.983031\pi$
$31$	−2.52299	+	4.36995i	−0.453143	+	0.784867i	0.545436	+	0.838152i	$0.316364\pi$
$32$	−0.286403	+	3.82178i	−0.0506294	+	0.675602i
$33$	1.60276	−	4.08378i	0.279005	−	0.710894i
$34$	−1.05095	−	4.60450i	−0.180236	−	0.789665i
$35$	2.27978	−	1.31084i	0.385353	−	0.221572i
$36$	−0.787734	+	3.45129i	−0.131289	+	0.575214i
$37$	−9.67885	−	6.59893i	−1.59119	−	1.08486i	−0.947586	−	0.319502i	$-0.896484\pi$
$37$	−9.67885	−	6.59893i	−1.59119	−	1.08486i	−0.643608	−	0.765356i	$-0.722563\pi$
$38$	−0.614254	−	0.569944i	−0.0996451	−	0.0924572i
$39$	0.0170557	−	0.00257073i	0.00273109	−	0.000411646i
$40$	−2.64115	+	2.45063i	−0.417602	+	0.387478i
$41$	−6.39800	+	8.02284i	−0.999200	+	1.25296i	−0.0318559	+	0.999492i	$0.510142\pi$
$41$	−6.39800	+	8.02284i	−0.999200	+	1.25296i	−0.967345	+	0.253465i	$0.918430\pi$
$42$	6.06878	+	1.39651i	0.936433	+	0.215485i
$43$	2.58159	+	3.23721i	0.393689	+	0.493670i	0.938689	−	0.344766i	$-0.112042\pi$
$43$	2.58159	+	3.23721i	0.393689	+	0.493670i	−0.545000	+	0.838436i	$0.683470\pi$
$44$	15.3568	+	2.31467i	2.31513	+	0.348950i
$45$	0.821248	−	0.559917i	0.122424	−	0.0834675i
$46$	−5.89525	−	15.0208i	−0.869207	−	2.21470i
$47$	9.52767	−	2.93890i	1.38975	−	0.428682i	0.492544	−	0.870287i	$-0.336067\pi$
$47$	9.52767	−	2.93890i	1.38975	−	0.428682i	0.897209	+	0.441605i	$0.145591\pi$
$48$	−1.45182			−0.209552
$49$	1.58188	−	6.81892i	0.225983	−	0.974131i
$50$	−9.44327			−1.33548
$51$	−1.91742	+	0.591446i	−0.268492	+	0.0828189i
$52$	0.0223077	+	0.0568390i	0.00309352	+	0.00788215i
$53$	4.57690	−	3.12048i	0.628685	−	0.428630i	−0.206616	−	0.978422i	$-0.566245\pi$
$53$	4.57690	−	3.12048i	0.628685	−	0.428630i	0.835302	+	0.549792i	$0.185293\pi$
$54$	2.32744	+	0.350805i	0.316725	+	0.0477385i
$55$	−2.71875	−	3.40920i	−0.366596	−	0.459697i
$56$	−0.0170352	+	9.59042i	−0.00227642	+	1.28157i
$57$	−0.221966	+	0.278336i	−0.0294001	+	0.0368665i
$58$	5.54195	−	5.14218i	0.727694	−	0.675202i
$59$	10.9381	−	1.64865i	1.42402	−	0.214636i	0.608585	−	0.793489i	$-0.291737\pi$
$59$	10.9381	−	1.64865i	1.42402	−	0.214636i	0.815432	+	0.578853i	$0.196499\pi$
$60$	2.57936	+	2.39330i	0.332994	+	0.308973i
$61$	−11.3038	−	7.70678i	−1.44730	−	0.986752i	−0.995513	−	0.0946251i	$-0.969835\pi$
$61$	−11.3038	−	7.70678i	−1.44730	−	0.986752i	−0.451786	−	0.892126i	$-0.649213\pi$
$62$	−2.64286	+	11.5791i	−0.335643	+	1.47055i
$63$	0.398975	−	2.61550i	0.0502662	−	0.329522i
$64$	2.65341	+	11.6253i	0.331676	+	1.45317i
$65$	0.00626346	−	0.0159590i	0.000776886	−	0.00197947i
$66$	0.771655	−	10.2970i	0.0949842	−	1.26748i
$67$	−3.48108	+	6.02941i	−0.425282	+	0.736610i	−0.996447	−	0.0842256i	$-0.973158\pi$
$67$	−3.48108	+	6.02941i	−0.425282	+	0.736610i	0.571165	+	0.820835i	$0.306492\pi$
$68$	−3.55166	−	6.15166i	−0.430703	−	0.745999i
$69$	−6.17670	+	2.97454i	−0.743588	+	0.358093i
$70$	4.21816	−	4.52993i	0.504167	−	0.541431i
$71$	3.82385	+	1.84147i	0.453808	+	0.218542i	0.646802	−	0.762658i	$-0.276106\pi$
$71$	3.82385	+	1.84147i	0.453808	+	0.218542i	−0.192995	+	0.981200i	$0.561820\pi$
$72$	0.270885	+	3.61471i	0.0319241	+	0.425998i
$73$	11.2807	+	3.47963i	1.32030	+	0.407260i	0.873261	−	0.487252i	$-0.162001\pi$
$73$	11.2807	+	3.47963i	1.32030	+	0.407260i	0.447044	+	0.894512i	$0.352477\pi$
$74$	−26.3475	−	8.12711i	−3.06283	−	0.944758i
$75$	0.299820	+	4.00083i	0.0346203	+	0.461976i
$76$	−1.13547	−	0.546813i	−0.130247	−	0.0627237i
$77$	−11.5730	−	0.887951i	−1.31886	−	0.101191i
$78$	0.0365774	−	0.0176148i	0.00414158	−	0.00199448i
$79$	0.240066	+	0.415807i	0.0270096	+	0.0467820i	0.879214	−	0.476427i	$-0.158068\pi$
$79$	0.240066	+	0.415807i	0.0270096	+	0.0467820i	−0.852205	+	0.523209i	$0.824735\pi$
$80$	−0.721524	+	1.24972i	−0.0806689	+	0.139723i
$81$	0.0747301	−	0.997204i	0.00830334	−	0.110800i
$82$	−8.82410	+	22.4834i	−0.974458	+	2.48288i
$83$	−0.429851	−	1.88330i	−0.0471823	−	0.206719i	0.945842	−	0.324626i	$-0.105239\pi$
$83$	−0.429851	−	1.88330i	−0.0471823	−	0.206719i	−0.993025	+	0.117907i	$0.962381\pi$
$84$	9.34111	−	0.683336i	1.01920	−	0.0745581i
$85$	−0.443806	+	1.94444i	−0.0481375	+	0.210904i
$86$	8.05230	+	5.48997i	0.868302	+	0.591998i
$87$	−2.35454	−	2.18470i	−0.252433	−	0.234224i
$88$	15.7247	−	2.37012i	1.67626	−	0.252655i
$89$	6.29680	−	5.84258i	0.667460	−	0.619312i	−0.271867	−	0.962335i	$-0.587641\pi$
$89$	6.29680	−	5.84258i	0.667460	−	0.619312i	0.939327	+	0.343023i	$0.111451\pi$
$90$	1.45866	−	1.82910i	0.153756	−	0.192804i
$91$	−0.0197271	−	0.0411506i	−0.00206796	−	0.00431376i
$92$	−15.1316	−	18.9744i	−1.57758	−	1.97822i
$93$	4.98963	+	0.752065i	0.517400	+	0.0779855i
$94$	19.3903	−	13.2201i	1.99996	−	1.36355i
$95$	0.129278	+	0.329394i	0.0132636	+	0.0337951i
$96$	3.66223	−	1.12965i	0.373775	−	0.115294i
$97$	12.4244			1.26151			0.630754	−	0.775983i	$-0.282746\pi$
$97$	12.4244			1.26151			0.630754	+	0.775983i	$0.282746\pi$
$98$	−1.17289	−	16.4343i	−0.118479	−	1.66012i
$99$	−4.38704			−0.440914
$100$	−13.5718	+	4.18635i	−1.35718	+	0.418635i
$101$	0.455493	+	1.16058i	0.0453233	+	0.115482i	0.951743	−	0.306897i	$-0.0992906\pi$
$101$	0.455493	+	1.16058i	0.0453233	+	0.115482i	−0.906420	+	0.422378i	$0.861195\pi$
$102$	−3.90225	+	2.66051i	−0.386381	+	0.263430i
$103$	2.99443	+	0.451338i	0.295050	+	0.0444717i	0.294899	−	0.955528i	$-0.404714\pi$
$103$	2.99443	+	0.451338i	0.295050	+	0.0444717i	0.000150958		1.00000i	$0.499952\pi$
$104$	0.0389821	+	0.0488821i	0.00382251	+	0.00479328i
$105$	−2.05312	−	1.64328i	−0.200364	−	0.160368i
$106$	8.12927	−	10.1938i	0.789585	−	0.990108i
$107$	−2.73582	+	2.53847i	−0.264482	+	0.245403i	−0.801255	−	0.598324i	$-0.795834\pi$
$107$	−2.73582	+	2.53847i	−0.264482	+	0.245403i	0.536773	+	0.843727i	$0.319643\pi$
$108$	3.50050	−	0.527616i	0.336836	−	0.0507699i
$109$	1.83300	+	1.70078i	0.175570	+	0.162905i	0.763063	−	0.646324i	$-0.223695\pi$
$109$	1.83300	+	1.70078i	0.175570	+	0.162905i	−0.587493	+	0.809229i	$0.699885\pi$
$110$	−8.48012	−	5.78165i	−0.808548	−	0.551258i
$111$	−2.60669	+	11.4206i	−0.247416	+	1.08400i
$112$	1.12568	+	3.67251i	0.106367	+	0.347019i
$113$	−1.50750	−	6.60481i	−0.141814	−	0.621328i	−0.995013	−	0.0997429i	$-0.968198\pi$
$113$	−1.50750	−	6.60481i	−0.141814	−	0.621328i	0.853199	−	0.521585i	$-0.174659\pi$
$114$	−0.306134	+	0.780017i	−0.0286721	+	0.0730553i
$115$	−0.509227	+	6.79516i	−0.0474856	+	0.633652i
$116$	5.68526	−	9.84716i	0.527863	−	0.914286i
$117$	−0.00862416	−	0.0149375i	−0.000797304	−	0.00138097i
$118$	23.4577	−	11.2966i	2.15946	−	1.03994i
$119$	2.98280	+	4.39170i	0.273433	+	0.402587i
$120$	3.24614	+	1.56326i	0.296331	+	0.142706i
$121$	0.616230	+	8.22302i	0.0560209	+	0.747547i
$122$	−30.7707	−	9.49151i	−2.78585	−	0.859321i
$123$	9.80571	+	3.02466i	0.884151	+	0.272724i
$124$	1.33490	+	17.8131i	0.119878	+	1.59966i
$125$	8.07053	+	3.88656i	0.721850	+	0.347625i
$126$	−0.917204	−	6.15947i	−0.0817110	−	0.548729i
$127$	7.34145	−	3.53546i	0.651449	−	0.313721i	−0.0788122	−	0.996889i	$-0.525113\pi$
$127$	7.34145	−	3.53546i	0.651449	−	0.313721i	0.730261	+	0.683168i	$0.239398\pi$
$128$	10.2008	+	17.6683i	0.901632	+	1.56167i
$129$	2.07028	−	3.58582i	0.182278	−	0.315714i
$130$	0.00301556	−	0.0402398i	0.000264482	−	0.00352927i
$131$	−5.44096	+	13.8633i	−0.475379	+	1.21125i	0.469239	+	0.883071i	$0.344528\pi$
$131$	−5.44096	+	13.8633i	−0.475379	+	1.21125i	−0.944617	+	0.328174i	$0.893567\pi$
$132$	−3.45582	−	15.1409i	−0.300790	−	1.31785i
$133$	0.876179	+	0.345672i	0.0759744	+	0.0299736i
$134$	−3.64646	+	15.9762i	−0.315006	+	1.38013i
$135$	−0.821248	−	0.559917i	−0.0706818	−	0.0481900i
$136$	−5.33184	−	4.94723i	−0.457202	−	0.424221i
$137$	−17.4682	+	2.63291i	−1.49241	+	0.224945i	−0.844000	−	0.536344i	$-0.819805\pi$
$137$	−17.4682	+	2.63291i	−1.49241	+	0.224945i	−0.648413	+	0.761289i	$0.724567\pi$
$138$	−11.8287	+	10.9755i	−1.00693	+	0.934293i
$139$	−12.4178	+	15.5715i	−1.05327	+	1.32075i	−0.108108	+	0.994139i	$0.534479\pi$
$139$	−12.4178	+	15.5715i	−1.05327	+	1.32075i	−0.945158	+	0.326614i	$0.894092\pi$
$140$	4.05413	−	8.38038i	0.342637	−	0.708271i
$141$	−6.21659	−	7.79536i	−0.523531	−	0.656488i
$142$	9.87802	+	1.48887i	0.828945	+	0.124943i
$143$	−0.0625207	+	0.0426259i	−0.00522824	+	0.00356455i
$144$	0.530409	+	1.35146i	0.0442007	+	0.112622i
$145$	−3.05073	+	0.941026i	−0.253350	+	0.0781480i
$146$	27.7862			2.29960
$147$	−6.92548	+	1.01870i	−0.571204	+	0.0840209i
$148$	−41.4693			−3.40876
$149$	−18.2025	+	5.61472i	−1.49121	+	0.459976i	−0.929956	−	0.367671i	$-0.880155\pi$
$149$	−18.2025	+	5.61472i	−1.49121	+	0.459976i	−0.561249	+	0.827647i	$0.689679\pi$
$150$	3.45001	+	8.79049i	0.281692	+	0.717741i
$151$	5.43875	−	3.70808i	0.442600	−	0.301759i	−0.321438	−	0.946930i	$-0.604166\pi$
$151$	5.43875	−	3.70808i	0.442600	−	0.301759i	0.764038	+	0.645171i	$0.223214\pi$
$152$	−1.27605	−	0.192334i	−0.103501	−	0.0156003i
$153$	1.25107	+	1.56880i	0.101143	+	0.126830i
$154$	−26.6455	+	6.03190i	−2.14716	+	0.486064i
$155$	3.12712	−	3.92128i	0.251176	−	0.314965i
$156$	0.0447600	−	0.0415312i	0.00358367	−	0.00332516i
$157$	−17.9382	+	2.70374i	−1.43162	+	0.215782i	−0.818636	−	0.574312i	$-0.805270\pi$
$157$	−17.9382	+	2.70374i	−1.43162	+	0.215782i	−0.612985	+	0.790094i	$0.710032\pi$
$158$	0.828424	+	0.768665i	0.0659059	+	0.0611517i
$159$	−4.57690	−	3.12048i	−0.362972	−	0.247470i
$160$	0.847660	−	3.71384i	0.0670134	−	0.293605i
$161$	12.3135	+	13.3182i	0.970441	+	1.04962i
$162$	−0.523754	−	2.29472i	−0.0411500	−	0.180290i
$163$	−3.41833	+	8.70977i	−0.267744	+	0.682202i	0.732255	+	0.681031i	$0.238468\pi$
$163$	−3.41833	+	8.70977i	−0.267744	+	0.682202i	−0.999999	+	0.00117098i	$0.999627\pi$
$164$	−2.71468	+	36.2249i	−0.211981	+	2.82869i
$165$	−2.18027	+	3.77633i	−0.169734	+	0.293987i
$166$	−2.27339	−	3.93762i	−0.176449	−	0.305619i
$167$	−4.77897	+	2.30143i	−0.369808	+	0.178090i	−0.609552	−	0.792746i	$-0.708651\pi$
$167$	−4.77897	+	2.30143i	−0.369808	+	0.178090i	0.239744	+	0.970836i	$0.422936\pi$
$168$	8.93370	−	3.48792i	0.689250	−	0.269099i
$169$	11.7123	+	5.64036i	0.900948	+	0.433874i
$170$	0.350812	+	4.68126i	0.0269060	+	0.359036i
$171$	0.340189	+	0.104934i	0.0260149	+	0.00802454i
$172$	14.0065	+	4.32044i	1.06799	+	0.329430i
$173$	−1.34974	−	18.0110i	−0.102619	−	1.36935i	−0.776315	−	0.630345i	$-0.782914\pi$
$173$	−1.34974	−	18.0110i	−0.102619	−	1.36935i	0.673697	−	0.739008i	$-0.264705\pi$
$174$	−6.81143	−	3.28021i	−0.516373	−	0.248672i
$175$	9.88798	−	3.86049i	0.747461	−	0.291826i
$176$	5.73843	−	2.76348i	0.432551	−	0.208305i
$177$	−5.53082	−	9.57965i	−0.415722	−	0.720051i
$178$	10.1091	−	17.5095i	0.757708	−	1.31239i
$179$	0.485682	−	6.48097i	0.0363016	−	0.484411i	−0.949192	−	0.314698i	$-0.898097\pi$
$179$	0.485682	−	6.48097i	0.0363016	−	0.484411i	0.985494	−	0.169713i	$-0.0542841\pi$
$180$	1.28551	−	3.27543i	0.0958163	−	0.244136i
$181$	−0.428051	−	1.87541i	−0.0318168	−	0.139398i	0.956525	−	0.291651i	$-0.0942045\pi$
$181$	−0.428051	−	1.87541i	−0.0318168	−	0.139398i	−0.988342	+	0.152252i	$0.951347\pi$
$182$	−0.0729187	−	0.0788682i	−0.00540509	−	0.00584610i
$183$	−3.04431	+	13.3380i	−0.225042	+	0.985972i
$184$	−20.5325	−	13.9988i	−1.51368	−	1.03201i
$185$	8.53536	+	7.91965i	0.627532	+	0.582264i
$186$	11.7442	−	1.77016i	0.861129	−	0.129794i
$187$	6.45296	−	5.98747i	0.471887	−	0.437848i
$188$	22.0070	−	27.5959i	1.60503	−	2.01264i
$189$	−2.58046	+	0.584152i	−0.187701	+	0.0424908i
$190$	0.519292	+	0.651171i	0.0376734	+	0.0472409i
$191$	4.61872	+	0.696160i	0.334199	+	0.0503724i	0.313998	−	0.949424i	$-0.398331\pi$
$191$	4.61872	+	0.696160i	0.334199	+	0.0503724i	0.0202006	+	0.999796i	$0.493570\pi$
$192$	9.85233	−	6.71720i	0.711030	−	0.484772i
$193$	−0.0593246	−	0.151157i	−0.00427028	−	0.0108805i	0.928723	−	0.370775i	$-0.120908\pi$
$193$	−0.0593246	−	0.151157i	−0.00427028	−	0.0108805i	−0.932993	+	0.359895i	$0.882813\pi$
$194$	27.9445	−	8.61974i	2.00630	−	0.618861i
$195$	−0.0171441			−0.00122772
$196$	−8.97126	−	23.0993i	−0.640804	−	1.64995i
$197$	5.26305			0.374977			0.187488	−	0.982267i	$-0.439965\pi$
$197$	5.26305			0.374977			0.187488	+	0.982267i	$0.439965\pi$
$198$	−9.86714	+	3.04361i	−0.701227	+	0.216300i
$199$	5.45072	+	13.8882i	0.386391	+	0.984509i	0.983266	+	0.182175i	$0.0583137\pi$
$199$	5.45072	+	13.8882i	0.386391	+	0.984509i	−0.596875	+	0.802334i	$0.703591\pi$
$200$	−12.0160	+	8.19239i	−0.849661	+	0.579289i
$201$	6.88440	+	1.03766i	0.485588	+	0.0731907i
$202$	1.82966	+	2.29432i	0.128734	+	0.161428i
$203$	−3.70077	+	7.64994i	−0.259743	+	0.536921i
$204$	−4.42885	+	5.55361i	−0.310082	+	0.388830i
$205$	7.47685	−	6.93750i	0.522206	−	0.484536i
$206$	7.04809	−	1.06233i	0.491064	−	0.0740159i
$207$	5.02553	+	4.66301i	0.349298	+	0.324101i
$208$	0.0206902	+	0.0141063i	0.00143461	+	0.000978099i
$209$	0.347535	−	1.52265i	0.0240395	−	0.105324i
$210$	−5.75787	−	2.27161i	−0.397330	−	0.156756i
$211$	−0.734828	−	3.21949i	−0.0505876	−	0.221639i	0.943315	−	0.331898i	$-0.107689\pi$
$211$	−0.734828	−	3.21949i	−0.0505876	−	0.221639i	−0.993903	+	0.110259i	$0.964832\pi$
$212$	7.16428	−	18.2543i	0.492045	−	1.25371i
$213$	0.317166	−	4.23229i	0.0217319	−	0.289991i
$214$	−4.39217	+	7.60747i	−0.300243	+	0.520036i
$215$	−2.05777	−	3.56416i	−0.140339	−	0.243074i
$216$	3.26587	−	1.57276i	0.222214	−	0.107013i
$217$	−1.96633	−	13.2048i	−0.133483	−	0.896402i
$218$	5.30267	+	2.55363i	0.359142	+	0.172954i
$219$	−0.882201	−	11.7722i	−0.0596136	−	0.795488i
$220$	−14.7507	−	4.54998i	−0.994491	−	0.306760i
$221$	0.0330723	+	0.0102014i	0.00222468	+	0.000686224i
$222$	2.06049	+	27.4953i	0.138291	+	1.84536i
$223$	−12.4405	−	5.99104i	−0.833079	−	0.401190i	−0.0318102	−	0.999494i	$-0.510127\pi$
$223$	−12.4405	−	5.99104i	−0.833079	−	0.401190i	−0.801269	+	0.598304i	$0.795842\pi$
$224$	−5.69709	−	8.38807i	−0.380653	−	0.560451i
$225$	3.61473	−	1.74076i	0.240982	−	0.116051i
$226$	−7.97286	−	13.8094i	−0.530347	−	0.918588i
$227$	−4.95599	+	8.58403i	−0.328941	+	0.569742i	−0.982302	−	0.187304i	$-0.940025\pi$
$227$	−4.95599	+	8.58403i	−0.328941	+	0.569742i	0.653361	+	0.757046i	$0.273358\pi$
$228$	−0.0941804	+	1.25675i	−0.00623725	+	0.0832303i
$229$	7.46424	−	19.0186i	0.493251	−	1.25678i	−0.440143	−	0.897928i	$-0.645072\pi$
$229$	7.46424	−	19.0186i	0.493251	−	1.25678i	0.933394	−	0.358854i	$-0.116833\pi$
$230$	3.56897	+	15.6367i	0.235331	+	1.03105i
$231$	3.40152	+	11.0974i	0.223803	+	0.730155i
$232$	2.59079	−	11.3510i	0.170094	−	0.745229i
$233$	−11.8038	−	8.04770i	−0.773294	−	0.527223i	0.111187	−	0.993799i	$-0.464535\pi$
$233$	−11.8038	−	8.04770i	−0.773294	−	0.527223i	−0.884481	+	0.466577i	$0.845487\pi$
$234$	−0.0297604	−	0.0276136i	−0.00194550	−	0.00180516i
$235$	−9.79972	+	1.47707i	−0.639263	+	0.0963534i
$236$	28.7053	−	26.6346i	1.86856	−	1.73377i
$237$	0.299358	−	0.375383i	0.0194454	−	0.0243838i
$238$	9.75564	+	7.80825i	0.632364	+	0.506134i
$239$	1.15092	+	1.44321i	0.0744469	+	0.0933535i	0.817660	−	0.575701i	$-0.195271\pi$
$239$	1.15092	+	1.44321i	0.0744469	+	0.0933535i	−0.743213	+	0.669054i	$0.766699\pi$
$240$	1.42693	+	0.215075i	0.0921080	+	0.0138831i
$241$	−3.11018	+	2.12049i	−0.200345	+	0.136593i	−0.659337	−	0.751848i	$-0.729163\pi$
$241$	−3.11018	+	2.12049i	−0.200345	+	0.136593i	0.458992	+	0.888440i	$0.348211\pi$
$242$	7.09092	+	18.0674i	0.455822	+	1.16141i
$243$	−0.955573	+	0.294755i	−0.0613000	+	0.0189086i
$244$	−48.4313			−3.10050
$245$	−2.56493	+	6.46768i	−0.163867	+	0.413205i
$246$	24.1530			1.53994
$247$	0.00586769	−	0.00180994i	0.000373352	−	0.000115164i
$248$	6.68242	+	17.0265i	0.424334	+	1.08119i
$249$	−1.59607	+	1.08818i	−0.101147	+	0.0689609i
$250$	20.8483	+	3.14238i	1.31856	+	0.198741i
$251$	−7.35006	−	9.21668i	−0.463932	−	0.581752i	0.493742	−	0.869608i	$-0.335629\pi$
$251$	−7.35006	−	9.21668i	−0.463932	−	0.581752i	−0.957673	+	0.287857i	$0.907057\pi$
$252$	−4.04879	−	8.44575i	−0.255050	−	0.532032i
$253$	18.7520	−	23.5143i	1.17893	−	1.47833i
$254$	14.0593	−	13.0451i	0.882159	−	0.818524i
$255$	1.97217	−	0.297257i	0.123502	−	0.0186149i
$256$	17.7188	+	16.4406i	1.10742	+	1.02754i
$257$	16.4532	+	11.2176i	1.02632	+	0.699735i	0.954661	−	0.297694i	$-0.0962176\pi$
$257$	16.4532	+	11.2176i	1.02632	+	0.699735i	0.0716610	+	0.997429i	$0.477170\pi$
$258$	2.16863	−	9.50139i	0.135013	−	0.591531i
$259$	30.9107	−	2.26123i	1.92070	−	0.140506i
$260$	−0.0135050	−	0.0591693i	−0.000837545	−	0.00366953i
$261$	−1.17346	+	2.98994i	−0.0726357	+	0.185073i
$262$	−2.61956	+	34.9557i	−0.161837	+	2.15957i
$263$	12.5442	−	21.7272i	0.773509	−	1.33976i	−0.162120	−	0.986771i	$-0.551833\pi$
$263$	12.5442	−	21.7272i	0.773509	−	1.33976i	0.935629	−	0.352986i	$-0.114834\pi$
$264$	−7.95116	−	13.7718i	−0.489360	−	0.847597i
$265$	−4.96071	+	2.38895i	−0.304734	+	0.146752i
$266$	2.21049	+	0.169602i	0.135534	+	0.0103990i
$267$	−7.73918	−	3.72699i	−0.473630	−	0.228088i
$268$	1.84182	+	24.5774i	0.112507	+	1.50131i
$269$	−15.7600	−	4.86132i	−0.960905	−	0.296400i	−0.225663	−	0.974205i	$-0.572455\pi$
$269$	−15.7600	−	4.86132i	−0.960905	−	0.296400i	−0.735241	+	0.677805i	$0.762931\pi$
$270$	−2.23557	−	0.689583i	−0.136053	−	0.0419667i
$271$	0.457879	+	6.10998i	0.0278142	+	0.371155i	0.993691	+	0.112153i	$0.0357746\pi$
$271$	0.457879	+	6.10998i	0.0278142	+	0.371155i	−0.965877	+	0.259002i	$0.916606\pi$
$272$	−2.62467	−	1.26398i	−0.159144	−	0.0766399i
$273$	−0.0310989	+	0.0333975i	−0.00188219	+	0.00202131i
$274$	−37.4622	+	18.0409i	−2.26318	+	1.08989i
$275$	−8.80049	−	15.2429i	−0.530690	−	0.919181i
$276$	−12.1346	+	21.0177i	−0.730417	+	1.26512i
$277$	−2.08589	+	27.8342i	−0.125329	+	1.67240i	0.480648	+	0.876913i	$0.340401\pi$
$277$	−2.08589	+	27.8342i	−0.125329	+	1.67240i	−0.605977	+	0.795482i	$0.707218\pi$
$278$	−17.1266	+	43.6378i	−1.02718	+	2.61722i
$279$	−1.12284	−	4.91947i	−0.0672225	−	0.294521i
$280$	1.43749	−	9.42350i	0.0859063	−	0.563162i
$281$	−1.28818	+	5.64389i	−0.0768464	+	0.336686i	−0.998707	−	0.0508354i	$-0.983812\pi$
$281$	−1.28818	+	5.64389i	−0.0768464	+	0.336686i	0.921861	+	0.387522i	$0.126669\pi$
$282$	−19.3903	−	13.2201i	−1.15468	−	0.787245i
$283$	−18.6556	−	17.3098i	−1.10896	−	1.02896i	−0.999388	−	0.0349835i	$-0.988862\pi$
$283$	−18.6556	−	17.3098i	−1.10896	−	1.02896i	−0.109570	−	0.993979i	$-0.534947\pi$
$284$	14.8567	−	2.23928i	0.881582	−	0.132877i
$285$	0.259394	−	0.240683i	0.0153652	−	0.0142568i
$286$	−0.111046	+	0.139248i	−0.00656630	+	0.00823389i
$287$	0.0482251	−	27.1496i	0.00284664	−	1.60259i
$288$	−2.38953	−	2.99637i	−0.140804	−	0.176563i
$289$	12.8288	+	1.93363i	0.754635	+	0.113743i
$290$	−6.20873	+	4.23304i	−0.364589	+	0.248573i
$291$	−4.53915	−	11.5656i	−0.266090	−	0.677985i
$292$	39.9341	−	12.3180i	2.33697	−	0.720859i
$293$	5.59675			0.326966			0.163483	−	0.986546i	$-0.447727\pi$
$293$	5.59675			0.326966			0.163483	+	0.986546i	$0.447727\pi$
$294$	−14.8698	+	7.09593i	−0.867222	+	0.413843i
$295$	−10.9948			−0.640143
$296$	−40.5762	+	12.5161i	−2.35844	+	0.727484i
$297$	1.60276	+	4.08378i	0.0930018	+	0.236965i
$298$	−37.0449	+	25.2568i	−2.14596	+	1.46309i
$299$	0.116927	+	0.0176240i	0.00676208	+	0.00101922i
$300$	8.85531	+	11.1042i	0.511261	+	0.641102i
$301$	−10.6759	−	2.45665i	−0.615346	−	0.141599i
$302$	9.66006	−	12.1133i	0.555874	−	0.697044i
$303$	0.913941	−	0.848013i	0.0525045	−	0.0487171i
$304$	−0.511083	+	0.0770333i	−0.0293126	+	0.00441816i
$305$	9.96830	+	9.24923i	0.570783	+	0.529609i
$306$	3.90225	+	2.66051i	0.223077	+	0.152091i
$307$	7.00991	−	30.7124i	0.400077	−	1.75285i	−0.227001	−	0.973895i	$-0.572892\pi$
$307$	7.00991	−	30.7124i	0.400077	−	1.75285i	0.627078	−	0.778957i	$-0.284251\pi$
$308$	−35.6208	+	20.4814i	−2.02968	+	1.16704i
$309$	−0.673851	−	2.95233i	−0.0383340	−	0.167952i
$310$	4.31290	−	10.9891i	0.244956	−	0.624139i
$311$	−0.216425	+	2.88799i	−0.0122724	+	0.163763i	0.987700	+	0.156359i	$0.0499758\pi$
$311$	−0.216425	+	2.88799i	−0.0122724	+	0.163763i	−0.999973	+	0.00740384i	$0.997643\pi$
$312$	0.0312613	−	0.0541461i	0.00176982	−	0.00306542i
$313$	−11.1490	−	19.3106i	−0.630178	−	1.09150i	−0.987515	−	0.157524i	$-0.949649\pi$
$313$	−11.1490	−	19.3106i	−0.630178	−	1.09150i	0.357337	−	0.933975i	$-0.383685\pi$
$314$	−38.4700	+	18.5262i	−2.17099	+	1.04549i
$315$	−0.779601	+	2.51156i	−0.0439255	+	0.141510i
$316$	1.53137	+	0.737468i	0.0861462	+	0.0414858i
$317$	−0.267380	−	3.56794i	−0.0150176	−	0.200396i	−0.999666	−	0.0258459i	$-0.991772\pi$
$317$	−0.267380	−	3.56794i	−0.0150176	−	0.200396i	0.984648	−	0.174550i	$-0.0558470\pi$
$318$	−12.4591	−	3.84312i	−0.698671	−	0.215511i
$319$	13.4650	+	4.15340i	0.753896	+	0.232546i
$320$	−0.885722	−	11.8191i	−0.0495134	−	0.660710i
$321$	3.36250	+	1.61930i	0.187677	+	0.0903803i
$322$	36.9349	+	21.4119i	2.05830	+	1.19324i
$323$	−0.643606	+	0.309944i	−0.0358112	+	0.0172458i
$324$	−1.77002	−	3.06577i	−0.0983345	−	0.170320i
$325$	0.0346005	−	0.0599299i	0.00191929	−	0.00332431i
$326$	−1.64577	+	21.9612i	−0.0911505	+	1.21632i
$327$	0.913539	−	2.32766i	0.0505188	−	0.128720i
$328$	8.27705	+	36.2641i	0.457024	+	2.00235i
$329$	−14.8990	+	21.7696i	−0.821407	+	1.20020i
$330$	−2.28385	+	10.0062i	−0.125722	+	0.550823i
$331$	4.78132	+	3.25985i	0.262805	+	0.179178i	0.687553	−	0.726134i	$-0.258685\pi$
$331$	4.78132	+	3.25985i	0.262805	+	0.179178i	−0.424748	+	0.905312i	$0.639637\pi$
$332$	−5.01292	−	4.65131i	−0.275119	−	0.255274i
$333$	11.5835	−	1.74593i	0.634773	−	0.0956766i
$334$	−9.15199	+	8.49181i	−0.500775	+	0.464651i
$335$	4.31462	−	5.41036i	0.235733	−	0.295599i
$336$	3.00738	−	2.38958i	0.164066	−	0.130362i
$337$	13.0314	+	16.3408i	0.709863	+	0.890141i	0.997717	−	0.0675339i	$-0.0215131\pi$
$337$	13.0314	+	16.3408i	0.709863	+	0.890141i	−0.287854	+	0.957674i	$0.592942\pi$
$338$	30.2560	+	4.56036i	1.64571	+	0.248051i
$339$	−5.59749	+	3.81630i	−0.304014	+	0.207273i
$340$	2.57946	+	6.57236i	0.139891	+	0.356436i
$341$	−21.1534	+	6.52497i	−1.14552	+	0.353347i
$342$	0.837941			0.0453106
$343$	7.94661	+	16.7288i	0.429077	+	0.903268i
$344$	15.0089			0.809223
$345$	6.51147	−	2.00852i	0.350566	−	0.108135i
$346$	−15.5314	−	39.5733i	−0.834971	−	2.12747i
$347$	8.95112	−	6.10277i	0.480521	−	0.327614i	−0.298717	−	0.954342i	$-0.596559\pi$
$347$	8.95112	−	6.10277i	0.480521	−	0.327614i	0.779238	+	0.626728i	$0.215606\pi$
$348$	−11.2435	−	1.69469i	−0.602716	−	0.0908448i
$349$	−8.36176	−	10.4853i	−0.447595	−	0.561266i	0.505932	−	0.862573i	$-0.331149\pi$
$349$	−8.36176	−	10.4853i	−0.447595	−	0.561266i	−0.953527	+	0.301307i	$0.902577\pi$
$350$	19.5613	−	15.5429i	1.04560	−	0.830802i
$351$	−0.0107542	+	0.0134853i	−0.000574014	+	0.000719791i
$352$	−12.3250	+	11.4360i	−0.656927	+	0.609539i
$353$	20.6354	−	3.11028i	1.09831	−	0.165544i	0.425210	−	0.905095i	$-0.360200\pi$
$353$	20.6354	−	3.11028i	1.09831	−	0.165544i	0.673100	+	0.739551i	$0.264962\pi$
$354$	−19.0858	−	17.7090i	−1.01440	−	0.941225i
$355$	−3.48550	−	2.37638i	−0.184991	−	0.126125i
$356$	6.76651	−	29.6460i	0.358624	−	1.57124i
$357$	2.99838	−	4.38108i	0.158691	−	0.231871i
$358$	−3.40395	−	14.9137i	−0.179905	−	0.788214i
$359$	−0.908275	+	2.31425i	−0.0479369	+	0.122141i	−0.952837	−	0.303483i	$-0.901850\pi$
$359$	−0.908275	+	2.31425i	−0.0479369	+	0.122141i	0.904900	+	0.425625i	$0.139946\pi$
$360$	0.269249	−	3.59287i	0.0141907	−	0.189361i
$361$	9.43663	−	16.3447i	0.496665	−	0.860249i
$362$	−2.26387	−	3.92114i	−0.118986	−	0.206090i
$363$	7.42946	−	3.57784i	0.389946	−	0.187788i
$364$	−0.139762	−	0.0810229i	−0.00732552	−	0.00424676i
$365$	−10.5718	−	5.09113i	−0.553355	−	0.266482i
$366$	2.40641	+	32.1113i	0.125785	+	1.67849i
$367$	6.39029	+	1.97114i	0.333570	+	0.102893i	0.457016	−	0.889458i	$-0.348918\pi$
$367$	6.39029	+	1.97114i	0.333570	+	0.102893i	−0.123446	+	0.992351i	$0.539394\pi$
$368$	−9.51093	−	2.93373i	−0.495792	−	0.152931i
$369$	−0.766850	−	10.2329i	−0.0399206	−	0.532704i
$370$	24.6918	+	11.8910i	1.28367	+	0.618182i
$371$	−4.34479	+	13.9972i	−0.225570	+	0.726696i
$372$	16.0940	−	7.75047i	0.834436	−	0.401843i
$373$	18.6519	+	32.3061i	0.965761	+	1.67275i	0.707557	+	0.706656i	$0.249797\pi$
$373$	18.6519	+	32.3061i	0.965761	+	1.67275i	0.258204	+	0.966090i	$0.416869\pi$
$374$	10.3598	−	17.9437i	0.535692	−	0.927846i
$375$	0.669403	−	8.93256i	0.0345678	−	0.461275i
$376$	13.2042	−	33.6437i	0.680953	−	1.73504i
$377$	0.0123279	+	0.0540121i	0.000634920	+	0.00278177i
$378$	−5.39859	+	3.10411i	−0.277674	+	0.159658i
$379$	−1.75528	+	7.69038i	−0.0901626	+	0.395028i	−0.999792	−	0.0203923i	$-0.993508\pi$
$379$	−1.75528	+	7.69038i	−0.0901626	+	0.395028i	0.909629	+	0.415421i	$0.136366\pi$
$380$	1.03500	+	0.705650i	0.0530943	+	0.0361991i
$381$	−5.97320	−	5.54232i	−0.306016	−	0.283942i
$382$	10.8712	−	1.63857i	0.556220	−	0.0838367i
$383$	−12.7244	+	11.8065i	−0.650185	+	0.603284i	−0.934721	−	0.355382i	$-0.884351\pi$
$383$	−12.7244	+	11.8065i	−0.650185	+	0.603284i	0.284536	+	0.958665i	$0.408160\pi$
$384$	12.7202	−	15.9506i	0.649124	−	0.813976i
$385$	11.2431	+	2.58717i	0.572999	+	0.131855i
$386$	−0.238299	−	0.298818i	−0.0121291	−	0.0152094i
$387$	−4.09430	−	0.617117i	−0.208125	−	0.0313698i
$388$	36.3404	−	24.7765i	1.84491	−	1.25784i
$389$	−3.27199	−	8.33689i	−0.165896	−	0.422697i	0.823616	−	0.567148i	$-0.191953\pi$
$389$	−3.27199	−	8.33689i	−0.165896	−	0.422697i	−0.989512	+	0.144452i	$0.953858\pi$
$390$	−0.0385599	+	0.0118942i	−0.00195256	+	0.000602284i
$391$	−13.7563			−0.695684
$392$	−15.7498	−	19.8942i	−0.795485	−	1.00481i
$393$	14.8928			0.751243
$394$	11.8374	−	3.65136i	0.596361	−	0.183953i
$395$	−0.174353	−	0.444243i	−0.00877264	−	0.0223523i
$396$	−12.8317	+	8.74853i	−0.644819	+	0.439630i
$397$	−20.0460	−	3.02144i	−1.00608	−	0.151642i	−0.374724	−	0.927136i	$-0.622262\pi$
$397$	−20.0460	−	3.02144i	−1.00608	−	0.151642i	−0.631354	+	0.775495i	$0.717501\pi$
$398$	21.8948	+	27.4552i	1.09749	+	1.37621i
$399$	0.00167307	−	0.941900i	8.37583e−5	−	0.0471540i
$400$	−3.63168	+	4.55398i	−0.181584	+	0.227699i
$401$	−11.7873	+	10.9371i	−0.588632	+	0.546170i	−0.917260	−	0.398289i	$-0.869604\pi$
$401$	−11.7873	+	10.9371i	−0.588632	+	0.546170i	0.328628	+	0.944459i	$0.393414\pi$
$402$	16.2040	−	2.44236i	0.808183	−	0.121814i
$403$	−0.0638010	−	0.0591987i	−0.00317816	−	0.00294890i
$404$	3.64668	+	2.48626i	0.181429	+	0.123696i
$405$	−0.221177	+	0.969039i	−0.0109904	+	0.0481519i
$406$	−3.01630	+	19.7734i	−0.149696	+	0.981340i
$407$	−11.4356	−	50.1028i	−0.566843	−	2.48350i
$408$	−2.65730	+	6.77070i	−0.131556	+	0.335200i
$409$	−0.573863	+	7.65766i	−0.0283757	+	0.378647i	0.964879	+	0.262694i	$0.0846111\pi$
$409$	−0.573863	+	7.65766i	−0.0283757	+	0.378647i	−0.993255	+	0.115953i	$0.963008\pi$
$410$	12.0036	−	20.7908i	0.592814	−	1.02678i
$411$	8.83278	+	15.2988i	0.435689	+	0.754635i
$412$	9.65853	−	4.65130i	0.475842	−	0.229153i
$413$	−19.9442	+	21.4183i	−0.981392	+	1.05393i
$414$	14.5383	+	7.00127i	0.714518	+	0.344094i
$415$	0.143487	+	1.91470i	0.00704348	+	0.0939887i
$416$	−0.0631674	−	0.0194846i	−0.00309704	−	0.000955309i
$417$	19.0318	+	5.87053i	0.931991	+	0.287481i
$418$	−0.274713	−	3.66580i	−0.0134367	−	0.179300i
$419$	−14.6563	−	7.05810i	−0.716007	−	0.344811i	0.0401568	−	0.999193i	$-0.487214\pi$
$419$	−14.6563	−	7.05810i	−0.716007	−	0.344811i	−0.756164	+	0.654383i	$0.772929\pi$
$420$	−9.28222	−	0.712188i	−0.452926	−	0.0347512i
$421$	−21.8730	+	10.5335i	−1.06602	+	0.513370i	−0.882823	−	0.469706i	$-0.844360\pi$
$421$	−21.8730	+	10.5335i	−1.06602	+	0.513370i	−0.183200	+	0.983076i	$0.558646\pi$
$422$	−3.88635	−	6.73135i	−0.189184	−	0.327677i
$423$	−4.98532	+	8.63483i	−0.242395	+	0.419840i
$424$	1.50055	−	20.0235i	0.0728732	−	0.972425i
$425$	−2.94115	+	7.49393i	−0.142667	+	0.363509i
$426$	−2.22289	−	9.73913i	−0.107700	−	0.471862i
$427$	36.1000	−	2.64085i	1.74700	−	0.127800i
$428$	−2.93990	+	12.8805i	−0.142105	+	0.622604i
$429$	0.0625207	+	0.0426259i	0.00301853	+	0.00205800i
$430$	−7.10098	−	6.58874i	−0.342439	−	0.317737i
$431$	−0.458634	+	0.0691279i	−0.0220916	+	0.00332977i	−0.160079	−	0.987104i	$-0.551175\pi$
$431$	−0.458634	+	0.0691279i	−0.0220916	+	0.00332977i	0.137987	+	0.990434i	$0.455937\pi$
$432$	1.06426	−	0.987488i	0.0512042	−	0.0475105i
$433$	3.73958	−	4.68928i	0.179713	−	0.225352i	−0.683813	−	0.729657i	$-0.739680\pi$
$433$	3.73958	−	4.68928i	0.179713	−	0.225352i	0.863526	+	0.504305i	$0.168251\pi$
$434$	−13.5837	−	28.3356i	−0.652041	−	1.36015i
$435$	1.99053	+	2.49605i	0.0954388	+	0.119677i
$436$	8.75304	+	1.31931i	0.419195	+	0.0631834i
$437$	−2.01655	+	1.37486i	−0.0964647	+	0.0657685i
$438$	−10.1514	−	25.8654i	−0.485054	−	1.23590i
$439$	−26.2140	+	8.08594i	−1.25112	+	0.385921i	−0.848378	−	0.529391i	$-0.822421\pi$
$439$	−26.2140	+	8.08594i	−1.25112	+	0.385921i	−0.402746	+	0.915312i	$0.631944\pi$
$440$	−15.8063			−0.753534
$441$	3.47844	+	6.07457i	0.165640	+	0.289265i
$442$	0.0814623			0.00387477
$443$	21.2713	−	6.56133i	1.01063	−	0.311738i	0.255144	−	0.966903i	$-0.417877\pi$
$443$	21.2713	−	6.56133i	1.01063	−	0.311738i	0.755486	+	0.655165i	$0.227401\pi$
$444$	15.1504	+	38.6027i	0.719008	+	1.83200i
$445$	−7.05439	+	4.80960i	−0.334410	+	0.227997i
$446$	−32.1372	−	4.84390i	−1.52174	−	0.229365i
$447$	11.8767	+	14.8929i	0.561749	+	0.704411i
$448$	−24.6308	−	19.7141i	−1.16370	−	0.931404i
$449$	−7.67300	+	9.62163i	−0.362111	+	0.454073i	−0.929197	−	0.369586i	$-0.879500\pi$
$449$	−7.67300	+	9.62163i	−0.362111	+	0.454073i	0.567085	+	0.823659i	$0.308071\pi$
$450$	6.92241	−	6.42305i	0.326325	−	0.302786i
$451$	−44.5152	+	6.70959i	−2.09614	+	0.315942i
$452$	−17.5805	−	16.3123i	−0.826917	−	0.767267i
$453$	−5.43875	−	3.70808i	−0.255535	−	0.174221i
$454$	−5.19145	+	22.7452i	−0.243647	+	1.06749i
$455$	0.0132928	+	0.0433676i	0.000623177	+	0.00203311i
$456$	0.287155	+	1.25811i	0.0134473	+	0.0589164i
$457$	−1.02222	+	2.60456i	−0.0478172	+	0.121836i	−0.952787	−	0.303640i	$-0.901798\pi$
$457$	−1.02222	+	2.60456i	−0.0478172	+	0.121836i	0.904970	+	0.425476i	$0.139893\pi$
$458$	3.59368	−	47.9543i	0.167921	−	2.24076i
$459$	1.00328	−	1.73774i	0.0468292	−	0.0811106i
$460$	12.0613	+	20.8908i	0.562361	+	0.974038i
$461$	7.93737	−	3.82243i	0.369680	−	0.178029i	−0.239815	−	0.970819i	$-0.577087\pi$
$461$	7.93737	−	3.82243i	0.369680	−	0.178029i	0.609495	+	0.792790i	$0.291372\pi$
$462$	15.3496	+	22.5999i	0.714130	+	1.05144i
$463$	−30.1465	−	14.5178i	−1.40103	−	0.674700i	−0.427658	−	0.903940i	$-0.640661\pi$
$463$	−30.1465	−	14.5178i	−1.40103	−	0.674700i	−0.973370	+	0.229241i	$0.926376\pi$
$464$	−0.348481	−	4.65016i	−0.0161778	−	0.215878i
$465$	−4.79268	−	1.47835i	−0.222255	−	0.0685567i
$466$	−32.1320	−	9.91140i	−1.48848	−	0.459137i
$467$	3.05427	+	40.7564i	0.141335	+	1.88598i	0.394986	+	0.918687i	$0.370749\pi$
$467$	3.05427	+	40.7564i	0.141335	+	1.88598i	−0.253651	+	0.967296i	$0.581631\pi$
$468$	−0.0550130	−	0.0264929i	−0.00254298	−	0.00122463i
$469$	−2.71302	−	18.2193i	−0.125276	−	0.841287i
$470$	−21.0164	+	10.1210i	−0.969413	+	0.466845i
$471$	9.07039	+	15.7104i	0.417942	+	0.723896i
$472$	20.0483	−	34.7248i	0.922800	−	1.59834i
$473$	−1.35745	+	18.1139i	−0.0624157	+	0.832880i
$474$	0.412873	−	1.05198i	0.0189639	−	0.0483192i
$475$	0.317829	+	1.39250i	0.0145830	+	0.0638922i
$476$	17.4823	+	6.89715i	0.801299	+	0.316130i
$477$	−1.23264	+	5.40055i	−0.0564388	+	0.247274i
$478$	3.58987	+	2.44753i	0.164197	+	0.111947i
$479$	18.9653	+	17.5973i	0.866548	+	0.804039i	0.981923	−	0.189283i	$-0.0606162\pi$
$479$	18.9653	+	17.5973i	0.866548	+	0.804039i	−0.115374	+	0.993322i	$0.536807\pi$
$480$	−3.76680	+	0.567754i	−0.171930	+	0.0259143i
$481$	0.148115	−	0.137431i	0.00675348	−	0.00626631i
$482$	−5.52416	+	6.92708i	−0.251619	+	0.315520i
$483$	7.89892	−	16.3280i	0.359413	−	0.742950i
$484$	18.2006	+	22.8228i	0.827299	+	1.03740i
$485$	−12.2114	−	1.84058i	−0.554493	−	0.0835763i
$486$	−1.94474	+	1.32590i	−0.0882153	+	0.0601442i
$487$	−7.49639	−	19.1005i	−0.339694	−	0.865526i	−0.994008	−	0.109304i	$-0.965138\pi$
$487$	−7.49639	−	19.1005i	−0.339694	−	0.865526i	0.654314	−	0.756223i	$-0.272957\pi$
$488$	−47.3883	+	14.6173i	−2.14517	+	0.661696i
$489$	9.35655			0.423118
$490$	−1.28183	+	16.3263i	−0.0579072	+	0.737549i
$491$	25.4140			1.14692			0.573459	−	0.819234i	$-0.305601\pi$
$491$	25.4140			1.14692			0.573459	+	0.819234i	$0.305601\pi$
$492$	34.7126	−	10.7074i	1.56497	−	0.482728i
$493$	−2.35463	−	5.99951i	−0.106047	−	0.270204i
$494$	0.0119417	−	0.00814171i	0.000537282	−	0.000366313i
$495$	4.31183	+	0.649904i	0.193802	+	0.0292110i
$496$	4.56760	+	5.72759i	0.205091	+	0.257176i
$497$	−10.9519	+	2.47923i	−0.491258	+	0.111209i
$498$	−2.83487	+	3.55481i	−0.127034	+	0.159295i
$499$	5.29357	−	4.91172i	0.236973	−	0.219879i	−0.552743	−	0.833352i	$-0.686419\pi$
$499$	5.29357	−	4.91172i	0.236973	−	0.219879i	0.789715	+	0.613473i	$0.210228\pi$
$500$	31.3561	−	4.72618i	1.40229	−	0.211361i
$501$	3.88829	+	3.60781i	0.173716	+	0.161185i
$502$	−22.9257	−	15.6305i	−1.02323	−	0.697624i
$503$	2.69104	−	11.7902i	0.119988	−	0.525700i	−0.878832	−	0.477131i	$-0.841677\pi$
$503$	2.69104	−	11.7902i	0.119988	−	0.525700i	0.998820	−	0.0485691i	$-0.0154661\pi$
$504$	−6.51066	−	7.04186i	−0.290008	−	0.313670i
$505$	−0.275755	−	1.20816i	−0.0122709	−	0.0537624i
$506$	25.8626	−	65.8970i	1.14974	−	2.92948i
$507$	0.971469	−	12.9634i	0.0431445	−	0.575723i
$508$	14.4228	−	24.9811i	0.639910	−	1.10836i
$509$	18.3510	+	31.7848i	0.813392	+	1.40884i	0.910477	+	0.413560i	$0.135715\pi$
$509$	18.3510	+	31.7848i	0.813392	+	1.40884i	−0.0970849	+	0.995276i	$0.530952\pi$
$510$	4.22949	−	2.03682i	0.187285	−	0.0901918i
$511$	−29.0947	+	11.3592i	−1.28707	+	0.502502i
$512$	14.4960	+	6.98090i	0.640638	+	0.308515i
$513$	−0.0266043	−	0.355010i	−0.00117461	−	0.0156741i
$514$	44.7884	+	13.8154i	1.97553	+	0.609370i
$515$	−2.87624	−	0.887203i	−0.126742	−	0.0390948i
$516$	−1.09537	−	14.6167i	−0.0482211	−	0.643466i
$517$	39.4098	+	18.9787i	1.73324	+	0.834684i
$518$	67.9542	−	26.5309i	2.98574	−	1.16570i
$519$	−16.2729	+	7.83660i	−0.714300	+	0.343989i
$520$	−0.0310724	−	0.0538190i	−0.00136262	−	0.00236012i
$521$	7.40909	−	12.8329i	0.324598	−	0.562221i	−0.656833	−	0.754036i	$-0.728104\pi$
$521$	7.40909	−	12.8329i	0.324598	−	0.562221i	0.981431	+	0.191816i	$0.0614376\pi$
$522$	−0.564968	+	7.53897i	−0.0247280	+	0.329972i
$523$	4.04898	−	10.3166i	0.177050	−	0.451115i	−0.814608	−	0.580011i	$-0.803048\pi$
$523$	4.04898	−	10.3166i	0.177050	−	0.451115i	0.991658	+	0.128896i	$0.0411434\pi$
$524$	11.7316	+	51.3994i	0.512496	+	2.24539i
$525$	−7.20611	−	7.79406i	−0.314501	−	0.340161i
$526$	13.1402	−	57.5708i	0.572938	−	2.51021i
$527$	8.36575	+	5.70367i	0.364418	+	0.248456i
$528$	−4.66894	−	4.33214i	−0.203190	−	0.188532i
$529$	−23.7315	+	3.57695i	−1.03180	+	0.155519i
$530$	−9.50005	+	8.81475i	−0.412656	+	0.382888i
$531$	−6.89681	+	8.64833i	−0.299296	+	0.375306i
$532$	3.25209	−	0.736192i	0.140996	−	0.0319180i
$533$	−0.110355	−	0.138381i	−0.00478000	−	0.00599393i
$534$	−19.9924	−	3.01336i	−0.865154	−	0.130401i
$535$	3.06498	−	2.08967i	0.132511	−	0.0903441i
$536$	9.22002	+	23.4922i	0.398244	+	1.01471i
$537$	−6.21041	+	1.91566i	−0.267999	+	0.0826667i
$538$	−38.8194			−1.67363
$539$	25.4345	−	17.2089i	1.09554	−	0.741239i
$540$	−3.51866			−0.151419
$541$	3.05469	−	0.942248i	0.131331	−	0.0405104i	−0.228393	−	0.973569i	$-0.573347\pi$
$541$	3.05469	−	0.942248i	0.131331	−	0.0405104i	0.359724	+	0.933059i	$0.382871\pi$
$542$	5.26879	+	13.4246i	0.226314	+	0.576638i
$543$	−1.58939	+	1.08363i	−0.0682072	+	0.0465029i
$544$	7.60427	+	1.14616i	0.326030	+	0.0491412i
$545$	−1.54962	−	1.94317i	−0.0663786	−	0.0832362i
$546$	−0.0467761	+	0.0966919i	−0.00200183	+	0.00413803i
$547$	−10.2680	+	12.8756i	−0.439027	+	0.550522i	−0.951286	−	0.308309i	$-0.900237\pi$
$547$	−10.2680	+	12.8756i	−0.439027	+	0.550522i	0.512260	+	0.858831i	$0.328808\pi$
$548$	−45.8427	+	42.5358i	−1.95830	+	1.81704i
$549$	13.5282	−	2.03905i	0.577369	−	0.0870244i
$550$	−30.3688	−	28.1782i	−1.29493	−	1.20152i
$551$	−0.944787	−	0.644145i	−0.0402493	−	0.0274415i
$552$	−5.52977	+	24.2275i	−0.235363	+	1.03119i
$553$	−1.18167	−	0.466197i	−0.0502499	−	0.0198247i
$554$	14.6192	+	64.0507i	0.621109	+	2.72125i
$555$	4.25388	−	10.8387i	0.180567	−	0.460078i
$556$	−5.26890	+	70.3086i	−0.223451	+	2.98175i
$557$	8.30543	−	14.3854i	0.351912	−	0.609530i	−0.634672	−	0.772782i	$-0.718865\pi$
$557$	8.30543	−	14.3854i	0.351912	−	0.609530i	0.986585	+	0.163251i	$0.0521981\pi$
$558$	−5.93844	−	10.2857i	−0.251394	−	0.435428i
$559$	−0.0643450	+	0.0309869i	−0.00272150	+	0.00131061i
$560$	−0.562329	−	3.77631i	−0.0237627	−	0.159578i
$561$	−7.93112	−	3.81942i	−0.334852	−	0.161256i
$562$	1.01826	+	13.5877i	0.0429527	+	0.573163i
$563$	−4.43221	−	1.36716i	−0.186795	−	0.0576187i	0.199946	−	0.979807i	$-0.435923\pi$
$563$	−4.43221	−	1.36716i	−0.186795	−	0.0576187i	−0.386742	+	0.922188i	$0.626399\pi$
$564$	−33.7284	−	10.4038i	−1.42022	−	0.438080i
$565$	0.503213	+	6.71491i	0.0211703	+	0.282499i
$566$	−53.9684	−	25.9898i	−2.26846	−	1.09243i
$567$	1.48652	+	2.18867i	0.0624279	+	0.0919153i
$568$	13.8609	−	6.67504i	0.581589	−	0.280078i
$569$	−0.117839	−	0.204103i	−0.00494007	−	0.00855645i	0.863545	−	0.504272i	$-0.168239\pi$
$569$	−0.117839	−	0.204103i	−0.00494007	−	0.00855645i	−0.868485	+	0.495716i	$0.834906\pi$
$570$	0.416440	−	0.721294i	0.0174427	−	0.0302117i
$571$	−0.387445	+	5.17010i	−0.0162141	+	0.216362i	0.983211	+	0.182470i	$0.0584092\pi$
$571$	−0.387445	+	5.17010i	−0.0162141	+	0.216362i	−0.999426	+	0.0338919i	$0.989210\pi$
$572$	−0.0978645	+	0.249355i	−0.00409192	+	0.0104260i
$573$	−1.03937	−	4.55378i	−0.0434203	−	0.190237i
$574$	−18.7272	−	61.0973i	−0.781659	−	2.55015i
$575$	−6.12045	+	26.8155i	−0.255240	+	1.11828i
$576$	−9.85233	−	6.71720i	−0.410514	−	0.279883i
$577$	2.16795	+	2.01156i	0.0902529	+	0.0837425i	0.724009	−	0.689790i	$-0.242297\pi$
$577$	2.16795	+	2.01156i	0.0902529	+	0.0837425i	−0.633756	+	0.773533i	$0.718488\pi$
$578$	30.1955	−	4.55124i	1.25597	−	0.189307i
$579$	−0.119034	+	0.110447i	−0.00494689	+	0.00459004i
$580$	−7.04658	+	8.83613i	−0.292593	+	0.366900i
$581$	3.99018	+	3.19368i	0.165541	+	0.132496i
$582$	−18.2332	−	22.8637i	−0.755789	−	0.947729i
$583$	24.0303	+	3.62198i	0.995233	+	0.150007i
$584$	35.3563	−	24.1055i	1.46305	−	0.997494i
$585$	0.00626346	+	0.0159590i	0.000258962	+	0.000659825i
$586$	12.5880	−	3.88288i	0.520005	−	0.160400i
$587$	18.3860			0.758871			0.379435	−	0.925218i	$-0.376118\pi$
$587$	18.3860			0.758871			0.379435	+	0.925218i	$0.376118\pi$
$588$	−18.2250	+	16.7902i	−0.751587	+	0.692418i
$589$	1.79640			0.0740193
$590$	−24.7291	+	7.62792i	−1.01808	+	0.314036i
$591$	−1.92281	−	4.89923i	−0.0790937	−	0.201527i
$592$	−14.0519	+	9.58045i	−0.577531	+	0.393754i
$593$	12.6432	+	1.90566i	0.519194	+	0.0782559i	0.403411	−	0.915019i	$-0.367824\pi$
$593$	12.6432	+	1.90566i	0.519194	+	0.0782559i	0.115782	+	0.993275i	$0.463062\pi$
$594$	6.43809	+	8.07311i	0.264158	+	0.331244i
$595$	−2.28107	−	4.75830i	−0.0935148	−	0.195071i
$596$	−42.0441	+	52.7216i	−1.72219	+	2.15956i
$597$	10.9368	−	10.1479i	0.447613	−	0.415325i
$598$	0.275215	−	0.0414820i	0.0112544	−	0.00169633i
$599$	−23.2147	−	21.5401i	−0.948526	−	0.880103i	0.0443793	−	0.999015i	$-0.485869\pi$
$599$	−23.2147	−	21.5401i	−0.948526	−	0.880103i	−0.992905	+	0.118912i	$0.962059\pi$
$600$	12.0160	+	8.19239i	0.490552	+	0.334453i
$601$	−5.75775	+	25.2263i	−0.234864	+	1.02900i	0.710682	+	0.703514i	$0.248387\pi$
$601$	−5.75775	+	25.2263i	−0.234864	+	1.02900i	−0.945545	+	0.325491i	$0.894471\pi$
$602$	−25.7161	+	1.88122i	−1.04811	+	0.0766730i
$603$	−1.54923	−	6.78761i	−0.0630894	−	0.276413i
$604$	8.51336	−	21.6917i	0.346404	−	0.882622i
$605$	0.612508	−	8.17335i	0.0249020	−	0.332294i
$606$	1.46727	−	2.54139i	0.0596038	−	0.103237i
$607$	−2.18386	−	3.78256i	−0.0886402	−	0.153529i	0.818296	−	0.574796i	$-0.194919\pi$
$607$	−2.18386	−	3.78256i	−0.0886402	−	0.153529i	−0.906937	+	0.421267i	$0.861585\pi$
$608$	1.22927	−	0.591987i	0.0498537	−	0.0240083i
$609$	8.47317	+	0.650114i	0.343350	+	0.0263439i
$610$	28.8372	+	13.8872i	1.16758	+	0.562278i
$611$	0.0128518	+	0.171496i	0.000519930	+	0.00693798i
$612$	6.78775	+	2.09374i	0.274378	+	0.0846345i
$613$	−6.50100	−	2.00529i	−0.262573	−	0.0809930i	0.160674	−	0.987008i	$-0.448633\pi$
$613$	−6.50100	−	2.00529i	−0.262573	−	0.0809930i	−0.423246	+	0.906015i	$0.639110\pi$
$614$	−5.54107	−	73.9405i	−0.223620	−	2.98400i
$615$	−9.18954	−	4.42545i	−0.370558	−	0.178451i
$616$	−28.6720	+	30.7912i	−1.15523	+	1.24061i
$617$	34.1847	−	16.4625i	1.37623	−	0.662755i	0.408034	−	0.912967i	$-0.366214\pi$
$617$	34.1847	−	16.4625i	1.37623	−	0.662755i	0.968191	+	0.250211i	$0.0805000\pi$
$618$	−3.56385	−	6.17277i	−0.143359	−	0.248305i
$619$	5.00528	−	8.66939i	0.201179	−	0.348452i	−0.747730	−	0.664003i	$-0.768856\pi$
$619$	5.00528	−	8.66939i	0.201179	−	0.348452i	0.948909	+	0.315551i	$0.102189\pi$
$620$	1.32684	−	17.7055i	0.0532872	−	0.711068i
$621$	2.50464	−	6.38172i	0.100508	−	0.256090i
$622$	1.51684	+	6.64571i	0.0608198	+	0.266469i
$623$	−3.42714	+	22.4667i	−0.137305	+	0.900109i
$624$	0.00557225	−	0.0244136i	0.000223068	−	0.000977326i
$625$	9.21812	+	6.28481i	0.368725	+	0.251392i
$626$	−38.4730	−	35.6978i	−1.53769	−	1.42677i
$627$	−1.54436	+	0.232775i	−0.0616760	+	0.00929616i
$628$	−47.0760	+	43.6801i	−1.87854	+	1.74303i
$629$	−14.6555	+	18.3774i	−0.584354	+	0.732756i
$630$	−0.0109947	+	6.18976i	−0.000438039	+	0.246606i
$631$	27.9507	+	35.0491i	1.11270	+	1.39528i	0.909277	+	0.416192i	$0.136636\pi$
$631$	27.9507	+	35.0491i	1.11270	+	1.39528i	0.203424	+	0.979091i	$0.434793\pi$
$632$	1.72097	+	0.259394i	0.0684565	+	0.0103182i
$633$	−2.72848	+	1.86024i	−0.108447	+	0.0739381i
$634$	−3.07673	−	7.83937i	−0.122192	−	0.311341i
$635$	−7.73935	+	2.38727i	−0.307127	+	0.0947361i
$636$	−19.6099			−0.777581
$637$	0.108595	+	0.0527725i	0.00430268	+	0.00209092i
$638$	33.1665			1.31307
$639$	−4.05560	+	1.25099i	−0.160437	+	0.0494883i
$640$	−7.40852	−	18.8766i	−0.292847	−	0.746163i
$641$	−6.48813	+	4.42353i	−0.256266	+	0.174719i	−0.684638	−	0.728883i	$-0.740040\pi$
$641$	−6.48813	+	4.42353i	−0.256266	+	0.174719i	0.428372	+	0.903602i	$0.359087\pi$
$642$	8.68623	+	1.30924i	0.342818	+	0.0516715i
$643$	−10.7356	−	13.4620i	−0.423371	−	0.530891i	0.523705	−	0.851900i	$-0.324549\pi$
$643$	−10.7356	−	13.4620i	−0.423371	−	0.530891i	−0.947076	+	0.321009i	$0.895978\pi$
$644$	62.5749	+	14.3993i	2.46580	+	0.567412i
$645$	−2.56600	+	3.21766i	−0.101036	+	0.126695i
$646$	−1.23254	+	1.14363i	−0.0484937	+	0.0449955i
$647$	−22.6750	+	3.41771i	−0.891446	+	0.134364i	−0.578765	−	0.815494i	$-0.696465\pi$
$647$	−22.6750	+	3.41771i	−0.891446	+	0.134364i	−0.312681	+	0.949858i	$0.601227\pi$
$648$	−2.65720	−	2.46552i	−0.104385	−	0.0968548i
$649$	40.0955	+	27.3367i	1.57389	+	1.07306i
$650$	0.0362443	−	0.158797i	0.00142162	−	0.00622852i
$651$	−11.5736	+	6.65467i	−0.453607	+	0.260817i
$652$	7.37047	+	32.2921i	0.288650	+	1.26466i
$653$	−11.0092	+	28.0509i	−0.430822	+	1.09772i	0.536440	+	0.843939i	$0.319769\pi$
$653$	−11.0092	+	28.0509i	−0.430822	+	1.09772i	−0.967262	+	0.253779i	$0.918326\pi$
$654$	0.439826	−	5.86907i	0.0171985	−	0.229499i
$655$	7.40143	−	12.8197i	0.289198	−	0.500905i
$656$	7.44899	+	12.9020i	0.290834	+	0.503740i
$657$	−10.6361	+	5.12207i	−0.414953	+	0.199831i
$658$	−18.4070	+	59.2999i	−0.717580	+	2.31175i
$659$	−31.5242	−	15.1812i	−1.22801	−	0.591377i	−0.296477	−	0.955040i	$-0.595812\pi$
$659$	−31.5242	−	15.1812i	−1.22801	−	0.591377i	−0.931531	+	0.363663i	$0.881526\pi$
$660$	1.15357	+	15.3933i	0.0449026	+	0.599184i
$661$	11.2852	+	3.48101i	0.438942	+	0.135396i	0.506347	−	0.862330i	$-0.330996\pi$
$661$	11.2852	+	3.48101i	0.438942	+	0.135396i	−0.0674047	+	0.997726i	$0.521472\pi$
$662$	13.0156	+	4.01477i	0.505864	+	0.156038i
$663$	−0.00258640	−	0.0345131i	−0.000100447	−	0.00134038i
$664$	−6.30879	−	3.03816i	−0.244829	−	0.117903i
$665$	−0.809951	−	0.469546i	−0.0314086	−	0.0182082i
$666$	24.8419	−	11.9632i	0.962604	−	0.463565i
$667$	−11.0100	−	19.0699i	−0.426310	−	0.738391i
$668$	−9.38865	+	16.2616i	−0.363258	+	0.629181i
$669$	−1.03187	+	13.7693i	−0.0398944	+	0.532353i
$670$	5.95070	−	15.1621i	0.229896	−	0.585764i
$671$	−13.3555	−	58.5142i	−0.515583	−	2.25892i
$672$	−5.72685	+	8.36777i	−0.220918	+	0.322794i
$673$	11.1693	−	48.9358i	0.430544	−	1.88634i	−0.0315450	−	0.999502i	$-0.510043\pi$
$673$	11.1693	−	48.9358i	0.430544	−	1.88634i	0.462089	−	0.886834i	$-0.347100\pi$
$674$	40.6464	+	27.7123i	1.56564	+	1.06744i
$675$	−2.94104	−	2.72888i	−0.113201	−	0.105035i
$676$	45.5055	−	6.85885i	1.75021	−	0.263802i
$677$	11.5899	−	10.7538i	0.445435	−	0.413303i	−0.425303	−	0.905051i	$-0.639832\pi$
$677$	11.5899	−	10.7538i	0.445435	−	0.413303i	0.870738	+	0.491748i	$0.163642\pi$
$678$	−9.94200	+	12.4669i	−0.381820	+	0.478787i
$679$	−25.7367	+	20.4496i	−0.987682	+	0.784784i
$680$	4.50755	+	5.65229i	0.172857	+	0.216756i
$681$	9.80128	+	1.47731i	0.375586	+	0.0566105i
$682$	−43.0506	+	29.3514i	−1.64849	+	1.12392i
$683$	−9.36098	−	23.8514i	−0.358188	−	0.912648i	−0.990447	−	0.137891i	$-0.955968\pi$
$683$	−9.36098	−	23.8514i	−0.358188	−	0.912648i	0.632260	−	0.774757i	$-0.282128\pi$
$684$	1.20428	−	0.371472i	0.0460470	−	0.0142036i
$685$	17.5588			0.670889
$686$	29.4792	+	32.1125i	1.12552	+	1.22606i
$687$	−20.4309			−0.779486
$688$	5.74426	−	1.77187i	0.218998	−	0.0675519i
$689$	0.0349069	+	0.0889413i	0.00132985	+	0.00338839i
$690$	13.2519	−	9.03498i	0.504491	−	0.343956i
$691$	−9.05624	−	1.36501i	−0.344516	−	0.0519274i	−0.0254945	−	0.999675i	$-0.508116\pi$
$691$	−9.05624	−	1.36501i	−0.344516	−	0.0519274i	−0.319021	+	0.947748i	$0.603354\pi$
$692$	−39.8651	−	49.9892i	−1.51544	−	1.90030i
$693$	9.08756	−	7.22072i	0.345208	−	0.274292i
$694$	15.8986	−	19.9362i	0.603501	−	0.756767i
$695$	14.5117	−	13.4649i	0.550461	−	0.510754i
$696$	−11.5129	+	1.73528i	−0.436394	+	0.0657758i
$697$	15.0940	+	14.0051i	0.571725	+	0.530483i
$698$	−26.0814	−	17.7820i	−0.987195	−	0.673058i
$699$	−3.17898	+	13.9280i	−0.120240	+	0.526806i
$700$	21.2231	−	31.0100i	0.802156	−	1.17207i
$701$	4.72038	+	20.6813i	0.178286	+	0.781123i	0.982421	+	0.186677i	$0.0597716\pi$
$701$	4.72038	+	20.6813i	0.178286	+	0.781123i	−0.804135	+	0.594446i	$0.797371\pi$
$702$	−0.0148321	+	0.0377915i	−0.000559801	+	0.00142635i
$703$	−0.311652	+	4.15871i	−0.0117542	+	0.156849i
$704$	−26.1562	+	45.3038i	−0.985798	+	1.70745i
$705$	4.95521	+	8.58267i	0.186624	+	0.323242i
$706$	44.2544	−	21.3118i	1.66554	−	0.802080i
$707$	−2.85376	−	1.65438i	−0.107327	−	0.0622195i
$708$	−35.2807	−	16.9903i	−1.32593	−	0.638535i
$709$	−1.05733	−	14.1090i	−0.0397087	−	0.529876i	−0.981220	−	0.192893i	$-0.938213\pi$
$709$	−1.05733	−	14.1090i	−0.0397087	−	0.529876i	0.941511	−	0.336982i	$-0.109406\pi$
$710$	−9.48812	−	2.92670i	−0.356083	−	0.109837i
$711$	−0.458802	−	0.141522i	−0.0172064	−	0.00530748i
$712$	−2.32686	−	31.0498i	−0.0872028	−	1.16364i
$713$	31.1676	+	15.0095i	1.16723	+	0.562110i
$714$	3.70436	−	11.9339i	0.138632	−	0.446617i
$715$	0.0677636	−	0.0326332i	0.00253422	−	0.00122041i
$716$	−11.5036	−	19.9249i	−0.429911	−	0.744627i
$717$	0.922967	−	1.59863i	0.0344689	−	0.0597018i
$718$	−0.437291	+	5.83525i	−0.0163196	+	0.217769i
$719$	18.1884	−	46.3434i	0.678315	−	1.72832i	−0.00689962	−	0.999976i	$-0.502196\pi$
$719$	18.1884	−	46.3434i	0.678315	−	1.72832i	0.685214	−	0.728341i	$-0.259709\pi$
$720$	−0.321109	−	1.40687i	−0.0119670	−	0.0524309i
$721$	−6.94571	+	3.99368i	−0.258672	+	0.148732i
$722$	9.88495	−	43.3088i	0.367880	−	1.61179i
$723$	3.11018	+	2.12049i	0.115669	+	0.0788618i
$724$	−4.99192	−	4.63183i	−0.185523	−	0.172141i
$725$	−12.7426	+	1.92064i	−0.473250	+	0.0713309i
$726$	14.2278	−	13.2015i	0.528044	−	0.489954i
$727$	−3.31554	+	4.15755i	−0.122966	+	0.154195i	−0.839504	−	0.543353i	$-0.817154\pi$
$727$	−3.31554	+	4.15755i	−0.122966	+	0.154195i	0.716538	+	0.697548i	$0.245726\pi$
$728$	−0.161206	−	0.0370956i	−0.00597469	−	0.00137485i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	−27.3098	−	4.11630i	−1.01078	−	0.152351i
$731$	6.86463	−	4.68022i	0.253897	−	0.173104i
$732$	17.6939	+	45.0834i	0.653987	+	1.66633i
$733$	−36.1916	+	11.1636i	−1.33677	+	0.412338i	−0.879037	−	0.476754i	$-0.841813\pi$
$733$	−36.1916	+	11.1636i	−1.33677	+	0.412338i	−0.457729	+	0.889092i	$0.651337\pi$
$734$	15.7403			0.580986
$735$	6.95767	+	0.0247175i	0.256638	+	0.000911719i
$736$	26.2742			0.968479
$737$	−29.1863	+	9.00278i	−1.07509	+	0.331622i
$738$	−8.82410	−	22.4834i	−0.324819	−	0.827626i
$739$	34.5927	−	23.5849i	1.27251	−	0.867584i	0.276875	−	0.960906i	$-0.410701\pi$
$739$	34.5927	−	23.5849i	1.27251	−	0.867584i	0.995636	+	0.0933223i	$0.0297487\pi$
$740$	40.7584	+	6.14335i	1.49831	+	0.225834i
$741$	−0.00382854	−	0.00480084i	−0.000140645	−	0.000176363i
$742$	−0.0612745	+	34.4962i	−0.00224946	+	1.26639i
$743$	−10.9103	+	13.6810i	−0.400259	+	0.501909i	−0.940590	−	0.339543i	$-0.889727\pi$
$743$	−10.9103	+	13.6810i	−0.400259	+	0.501909i	0.540331	+	0.841452i	$0.318299\pi$
$744$	13.4082	−	12.4410i	0.491568	−	0.456109i
$745$	18.7222	−	2.82192i	0.685929	−	0.103387i
$746$	64.3643	+	59.7214i	2.35655	+	2.18655i
$747$	1.59607	+	1.08818i	0.0583973	+	0.0398146i
$748$	6.93432	−	30.3812i	0.253544	−	1.11085i
$749$	1.48901	−	9.76128i	0.0544074	−	0.356670i
$750$	−4.69158	−	20.5552i	−0.171312	−	0.750569i
$751$	8.47774	−	21.6009i	0.309357	−	0.788229i	−0.688648	−	0.725096i	$-0.741796\pi$
$751$	8.47774	−	21.6009i	0.309357	−	0.788229i	0.998005	−	0.0631331i	$-0.0201093\pi$
$752$	1.08176	−	14.4351i	0.0394477	−	0.526393i
$753$	−5.89429	+	10.2092i	−0.214800	+	0.372044i
$754$	0.0651996	+	0.112929i	0.00237443	+	0.00411264i
$755$	−5.89484	+	2.83881i	−0.214535	+	0.103315i
$756$	−6.38273	+	6.85449i	−0.232138	+	0.249295i
$757$	−17.7338	−	8.54016i	−0.644547	−	0.310397i	0.0829038	−	0.996558i	$-0.473581\pi$
$757$	−17.7338	−	8.54016i	−0.644547	−	0.310397i	−0.727450	+	0.686160i	$0.759295\pi$
$758$	1.38748	+	18.5147i	0.0503956	+	0.672483i
$759$	−28.7397	−	8.86501i	−1.04318	−	0.321780i
$760$	1.22568	+	0.378073i	0.0444602	+	0.0137142i
$761$	−2.59517	−	34.6301i	−0.0940748	−	1.25534i	−0.821922	−	0.569601i	$-0.807098\pi$
$761$	−2.59517	−	34.6301i	−0.0940748	−	1.25534i	0.727847	−	0.685740i	$-0.240521\pi$
$762$	−17.2798	−	8.32151i	−0.625981	−	0.301457i
$763$	−6.59634	−	0.506112i	−0.238804	−	0.0183225i
$764$	14.8977	−	7.17433i	0.538978	−	0.259558i
$765$	−0.997222	−	1.72724i	−0.0360547	−	0.0624485i
$766$	−20.4281	+	35.3825i	−0.738098	+	1.27842i
$767$	−0.0142581	+	0.190261i	−0.000514830	+	0.00686993i
$768$	8.83074	−	22.5004i	0.318652	−	0.811912i
$769$	−4.56216	−	19.9881i	−0.164516	−	0.720791i	−0.988127	−	0.153636i	$-0.950902\pi$
$769$	−4.56216	−	19.9881i	−0.164516	−	0.720791i	0.823612	−	0.567154i	$-0.191956\pi$
$770$	27.0824	−	1.98117i	0.975980	−	0.0713965i
$771$	4.43114	−	19.4141i	0.159584	−	0.699182i
$772$	−0.474953	−	0.323817i	−0.0170939	−	0.0116544i
$773$	−34.5058	−	32.0167i	−1.24109	−	1.15156i	−0.982638	−	0.185535i	$-0.940598\pi$
$773$	−34.5058	−	32.0167i	−1.24109	−	1.15156i	−0.258449	−	0.966025i	$-0.583211\pi$
$774$	−9.63688	+	1.45253i	−0.346391	+	0.0522100i
$775$	14.8404	−	13.7699i	0.533084	−	0.494630i
$776$	28.0798	−	35.2110i	1.00801	−	1.26400i
$777$	−13.3979	−	27.9478i	−0.480645	−	1.00262i
$778$	−13.1431	−	16.4810i	−0.471204	−	0.590871i
$779$	3.61238	+	0.544479i	0.129427	+	0.0195080i
$780$	−0.0501452	+	0.0341884i	−0.00179549	+	0.00122414i
$781$	6.80238	+	17.3322i	0.243408	+	0.620194i
$782$	−30.9400	+	9.54373i	−1.10641	+	0.341283i
$783$	3.21197			0.114786
$784$	−8.37645	−	5.75466i	−0.299159	−	0.205524i
$785$	18.0312			0.643561
$786$	33.4963	−	10.3323i	1.19477	−	0.368539i
$787$	7.59737	+	19.3578i	0.270817	+	0.690030i	0.999984	+	0.00569425i	$0.00181255\pi$
$787$	7.59737	+	19.3578i	0.270817	+	0.690030i	−0.729167	+	0.684336i	$0.760092\pi$
$788$	15.3940	−	10.4954i	0.548388	−	0.373885i
$789$	−24.8082	−	3.73923i	−0.883195	−	0.133120i
$790$	−0.700352	−	0.878213i	−0.0249174	−	0.0312454i
$791$	13.9937	+	11.2004i	0.497560	+	0.398239i
$792$	−9.91494	+	12.4329i	−0.352312	+	0.441785i
$793$	0.172981	−	0.160503i	0.00614275	−	0.00569964i
$794$	−47.1828	+	7.11166i	−1.67445	+	0.252383i
$795$	4.03617	+	3.74502i	0.143148	+	0.132822i
$796$	43.6385	+	29.7522i	1.54673	+	1.05454i
$797$	−2.53045	+	11.0866i	−0.0896330	+	0.392708i	−0.999767	−	0.0216072i	$-0.993122\pi$
$797$	−2.53045	+	11.0866i	−0.0896330	+	0.392708i	0.910134	+	0.414315i	$0.135979\pi$
$798$	−0.649703	−	2.11965i	−0.0229992	−	0.0750346i
$799$	−4.45192	−	19.5051i	−0.157498	−	0.690042i
$800$	5.61754	−	14.3133i	0.198610	−	0.506050i
$801$	−0.641920	+	8.56583i	−0.0226811	+	0.302659i
$802$	−18.9238	+	32.7769i	−0.668222	+	1.15739i
$803$	25.8948	+	44.8512i	0.913809	+	1.58276i
$804$	22.2056	−	10.6937i	0.783131	−	0.377136i
$805$	−10.1295	−	14.9140i	−0.357016	−	0.525651i
$806$	−0.184569	−	0.0888839i	−0.00650118	−	0.00313080i
$807$	1.23250	+	16.4466i	0.0433862	+	0.578948i
$808$	4.31854	+	1.33209i	0.151926	+	0.0468629i
$809$	43.2131	+	13.3295i	1.51929	+	0.468639i	0.938461	−	0.345386i	$-0.112252\pi$
$809$	43.2131	+	13.3295i	1.51929	+	0.468639i	0.580830	+	0.814025i	$0.302728\pi$
$810$	0.174832	+	2.33297i	0.00614297	+	0.0819722i
$811$	19.9771	+	9.62047i	0.701492	+	0.337821i	0.750401	−	0.660983i	$-0.229860\pi$
$811$	19.9771	+	9.62047i	0.701492	+	0.337821i	−0.0489096	+	0.998803i	$0.515575\pi$
$812$	4.43088	+	29.7555i	0.155493	+	1.04421i
$813$	5.52033	−	2.65845i	0.193607	−	0.0932360i
$814$	−60.4806	−	104.755i	−2.11984	−	3.67168i
$815$	4.65002	−	8.05406i	0.162883	−	0.282122i
$816$	−0.217701	+	2.90502i	−0.00762107	+	0.101696i
$817$	0.538534	−	1.37216i	0.0188409	−	0.0480059i
$818$	4.02198	+	17.6214i	0.140625	+	0.616119i
$819$	0.0424505	+	0.0167477i	0.00148334	+	0.000585212i
$820$	8.03458	−	35.2018i	0.280580	−	1.22930i
$821$	0.318345	+	0.217044i	0.0111103	+	0.00757488i	0.568862	−	0.822433i	$-0.307384\pi$
$821$	0.318345	+	0.217044i	0.0111103	+	0.00757488i	−0.557752	+	0.830008i	$0.688336\pi$
$822$	30.4803	+	28.2815i	1.06312	+	0.986432i
$823$	−4.31815	+	0.650856i	−0.150521	+	0.0226874i	−0.223870	−	0.974619i	$-0.571869\pi$
$823$	−4.31815	+	0.650856i	−0.150521	+	0.0226874i	0.0733494	+	0.997306i	$0.476631\pi$
$824$	8.04668	−	7.46623i	0.280320	−	0.260098i
$825$	−10.9740	+	13.7610i	−0.382067	+	0.479097i
$826$	−29.9983	+	62.0101i	−1.04377	+	2.15761i
$827$	15.2781	+	19.1582i	0.531273	+	0.666196i	0.972960	−	0.230974i	$-0.0741912\pi$
$827$	15.2781	+	19.1582i	0.531273	+	0.666196i	−0.441687	+	0.897169i	$0.645620\pi$
$828$	23.9981	+	3.61714i	0.833993	+	0.125704i
$829$	45.6653	−	31.1341i	1.58602	−	1.08133i	0.634866	−	0.772622i	$-0.281055\pi$
$829$	45.6653	−	31.1341i	1.58602	−	1.08133i	0.951156	−	0.308710i	$-0.0998972\pi$
$830$	1.65109	+	4.20691i	0.0573102	+	0.146024i
$831$	26.6722	−	8.22728i	0.925248	−	0.285401i
$832$	−0.205674			−0.00713048
$833$	−13.4071	−	4.18777i	−0.464530	−	0.145098i
$834$	46.8784			1.62327
$835$	5.03798	−	1.55401i	0.174347	−	0.0537788i
$836$	−2.01992	−	5.14668i	−0.0698605	−	0.178002i
$837$	−4.16919	+	2.84251i	−0.144108	+	0.0982514i
$838$	−37.8611	−	5.70664i	−1.30789	−	0.197133i
$839$	−21.7576	−	27.2832i	−0.751157	−	0.941921i	0.248486	−	0.968636i	$-0.420067\pi$
$839$	−21.7576	−	27.2832i	−0.751157	−	0.941921i	−0.999643	+	0.0267142i	$0.991496\pi$
$840$	−9.29726	+	2.10467i	−0.320786	+	0.0726181i
$841$	−11.6488	+	14.6071i	−0.401683	+	0.503695i
$842$	−41.8880	+	38.8664i	−1.44355	+	1.33942i
$843$	5.72437	−	0.862811i	0.197158	−	0.0297168i
$844$	−8.56955	−	7.95138i	−0.294976	−	0.273698i
$845$	−10.6760	−	7.27876i	−0.367265	−	0.250397i
$846$	−5.22216	+	22.8798i	−0.179542	+	0.786623i
$847$	−14.8109	−	16.0194i	−0.508910	−	0.550432i
$848$	−1.78957	−	7.84062i	−0.0614541	−	0.269248i
$849$	−9.29762	+	23.6900i	−0.319094	+	0.813037i
$850$	−1.41603	+	18.8956i	−0.0485693	+	0.648112i
$851$	−40.1546	+	69.5498i	−1.37648	+	2.38414i
$852$	−7.51224	−	13.0116i	−0.257365	−	0.445770i
$853$	−7.73120	+	3.72315i	−0.264711	+	0.127478i	−0.561532	−	0.827455i	$-0.689788\pi$
$853$	−7.73120	+	3.72315i	−0.264711	+	0.127478i	0.296821	+	0.954933i	$0.404074\pi$
$854$	79.3626	−	30.9850i	2.71573	−	1.06028i
$855$	−0.318812	−	0.153532i	−0.0109032	−	0.00525068i
$856$	1.01097	+	13.4904i	0.0345542	+	0.461094i
$857$	9.92447	+	3.06129i	0.339013	+	0.104572i	0.459587	−	0.888133i	$-0.347997\pi$
$857$	9.92447	+	3.06129i	0.339013	+	0.104572i	−0.120574	+	0.992704i	$0.538474\pi$
$858$	0.170192	+	0.0524972i	0.00581025	+	0.00179222i
$859$	2.23764	+	29.8593i	0.0763474	+	1.01879i	0.895457	+	0.445148i	$0.146849\pi$
$859$	2.23764	+	29.8593i	0.0763474	+	1.01879i	−0.819110	+	0.573637i	$0.805532\pi$
$860$	−13.1264	−	6.32133i	−0.447606	−	0.215556i
$861$	−25.2905	+	9.87397i	−0.861897	+	0.336504i
$862$	−0.983581	+	0.473668i	−0.0335009	+	0.0161332i
$863$	14.6824	+	25.4307i	0.499795	+	0.865670i	1.00000		0.000236754i	$-7.53612e-5\pi$
$863$	14.6824	+	25.4307i	0.499795	+	0.865670i	−0.500205	+	0.865907i	$0.666742\pi$
$864$	−1.91625	+	3.31904i	−0.0651922	+	0.112916i
$865$	−1.34159	+	17.9022i	−0.0456153	+	0.608694i
$866$	5.15760	−	13.1414i	0.175263	−	0.446562i
$867$	−2.88692	−	12.6484i	−0.0980449	−	0.429563i
$868$	−32.0841	−	34.7019i	−1.08901	−	1.17786i
$869$	−0.468709	+	2.05355i	−0.0158999	+	0.0696619i
$870$	6.20873	+	4.23304i	0.210496	+	0.143513i
$871$	−0.0880290	−	0.0816790i	−0.00298275	−	0.00276759i
$872$	8.96272	−	1.35091i	0.303516	−	0.0457477i
$873$	−9.10774	+	8.45075i	−0.308250	+	0.286015i
$874$	−3.58170	+	4.49131i	−0.121153	+	0.151921i
$875$	−23.1147	+	5.23261i	−0.781421	+	0.176894i
$876$	−26.0561	−	32.6733i	−0.880355	−	1.10393i
$877$	−34.5025	−	5.20042i	−1.16507	−	0.175606i	−0.462100	−	0.886828i	$-0.652904\pi$
$877$	−34.5025	−	5.20042i	−1.16507	−	0.175606i	−0.702967	+	0.711222i	$0.748142\pi$
$878$	−53.3496	+	36.3731i	−1.80046	+	1.22753i
$879$	−2.04472	−	5.20987i	−0.0689668	−	0.175725i
$880$	−6.04945	+	1.86601i	−0.203927	+	0.0629031i
$881$	39.1959			1.32054			0.660272	−	0.751027i	$-0.270441\pi$
$881$	39.1959			1.32054			0.660272	+	0.751027i	$0.270441\pi$
$882$	12.0380	+	11.2494i	0.405339	+	0.378788i
$883$	−27.6657			−0.931024			−0.465512	−	0.885042i	$-0.654130\pi$
$883$	−27.6657			−0.931024			−0.465512	+	0.885042i	$0.654130\pi$
$884$	0.117077	−	0.0361136i	0.00393774	−	0.00121463i
$885$	4.01686	+	10.2348i	0.135025	+	0.344038i
$886$	43.2905	−	29.5149i	1.45437	−	0.991574i
$887$	2.46598	+	0.371686i	0.0827994	+	0.0124800i	0.190311	−	0.981724i	$-0.439050\pi$
$887$	2.46598	+	0.371686i	0.0827994	+	0.0124800i	−0.107512	+	0.994204i	$0.534288\pi$
$888$	26.4751	+	33.1987i	0.888445	+	1.11407i
$889$	−9.38843	+	19.4070i	−0.314878	+	0.650890i
$890$	−12.5297	+	15.7117i	−0.419996	+	0.526658i
$891$	3.21592	−	2.98394i	0.107738	−	0.0999658i
$892$	−48.3348	+	7.28529i	−1.61837	+	0.243930i
$893$	−2.60204	−	2.41434i	−0.0870740	−	0.0807929i
$894$	37.0449	+	25.2568i	1.23897	+	0.844714i
$895$	−1.43746	+	6.29793i	−0.0480490	+	0.210516i
$896$	−50.2112	−	19.8094i	−1.67744	−	0.661787i
$897$	−0.0263127	−	0.115283i	−0.000878554	−	0.00384920i
$898$	−10.5826	+	26.9639i	−0.353145	+	0.899798i
$899$	−1.21119	+	16.1622i	−0.0403955	+	0.539041i
$900$	7.10141	−	12.3000i	0.236714	−	0.410000i
$901$	−5.55762	−	9.62609i	−0.185151	−	0.320691i
$902$	−95.4669	+	45.9744i	−3.17870	+	1.53078i
$903$	1.61349	+	10.8354i	0.0536937	+	0.360579i
$904$	−22.1252	−	10.6549i	−0.735873	−	0.354378i
$905$	0.142886	+	1.90668i	0.00474968	+	0.0633801i
$906$	−14.8052	−	4.56680i	−0.491870	−	0.151722i
$907$	−36.2296	−	11.1753i	−1.20298	−	0.371071i	−0.372456	−	0.928050i	$-0.621484\pi$
$907$	−36.2296	−	11.1753i	−1.20298	−	0.371071i	−0.830527	+	0.556978i	$0.811961\pi$
$908$	2.62219	+	34.9908i	0.0870206	+	1.16121i
$909$	−1.12329	−	0.540950i	−0.0372573	−	0.0179422i
$910$	0.0599850	+	0.0883185i	0.00198848	+	0.00292773i
$911$	15.3453	−	7.38993i	0.508414	−	0.244839i	−0.162048	−	0.986783i	$-0.551810\pi$
$911$	15.3453	−	7.38993i	0.508414	−	0.244839i	0.670462	+	0.741944i	$0.266096\pi$
$912$	0.258428	+	0.447610i	0.00855740	+	0.0148218i
$913$	4.23729	−	7.33920i	0.140234	−	0.242892i
$914$	−0.492148	+	6.56726i	−0.0162788	+	0.217226i
$915$	4.96803	−	12.6583i	0.164238	−	0.418472i
$916$	−16.0941	−	70.5128i	−0.531764	−	2.32981i
$917$	−11.5473	−	37.6727i	−0.381324	−	1.24406i
$918$	1.05095	−	4.60450i	0.0346864	−	0.151971i
$919$	−6.03762	−	4.11638i	−0.199163	−	0.135787i	0.459632	−	0.888109i	$-0.347981\pi$
$919$	−6.03762	−	4.11638i	−0.199163	−	0.135787i	−0.658795	+	0.752322i	$0.728934\pi$
$920$	18.1067	+	16.8006i	0.596961	+	0.553899i
$921$	−31.1504	+	4.69517i	−1.02644	+	0.154711i
$922$	15.2005	−	14.1040i	0.500602	−	0.464491i
$923$	−0.0456423	+	0.0572336i	−0.00150233	+	0.00188387i
$924$	32.0793	+	25.6758i	1.05533	+	0.844671i
$925$	29.3031	+	36.7449i	0.963480	+	1.20817i
$926$	−77.8764	−	11.7380i	−2.55918	−	0.385734i
$927$	−2.50206	+	1.70588i	−0.0821786	+	0.0560284i
$928$	4.49731	+	11.4589i	0.147631	+	0.376158i
$929$	−10.1458	+	3.12955i	−0.332871	+	0.102677i	−0.456685	−	0.889628i	$-0.650964\pi$
$929$	−10.1458	+	3.12955i	−0.332871	+	0.102677i	0.123814	+	0.992305i	$0.460487\pi$
$930$	−11.8051			−0.387106
$931$	−2.38392	+	0.726077i	−0.0781298	+	0.0237962i
$932$	−50.5738			−1.65660
$933$	2.76743	−	0.853638i	0.0906015	−	0.0279469i
$934$	35.1453	+	89.5488i	1.14999	+	2.93013i
$935$	−7.22934	+	4.92888i	−0.236425	+	0.161192i
$936$	−0.0618242	−	0.00931850i	−0.00202079	−	0.000304585i
$937$	−16.2061	−	20.3218i	−0.529431	−	0.663886i	0.443150	−	0.896447i	$-0.353861\pi$
$937$	−16.2061	−	20.3218i	−0.529431	−	0.663886i	−0.972582	+	0.232561i	$0.925289\pi$
$938$	−18.7421	−	39.0958i	−0.611950	−	1.27652i
$939$	−13.9026	+	17.4332i	−0.453693	+	0.568913i
$940$	−25.7179	+	23.8627i	−0.838824	+	0.778315i
$941$	38.2277	−	5.76190i	1.24619	−	0.187832i	0.507364	−	0.861732i	$-0.330620\pi$
$941$	38.2277	−	5.76190i	1.24619	−	0.187832i	0.738823	+	0.673900i	$0.235382\pi$
$942$	31.3002	+	29.0424i	1.01982	+	0.946251i
$943$	58.1256	+	39.6294i	1.89283	+	1.29051i
$944$	3.57357	−	15.6568i	0.116310	−	0.509587i
$945$	2.62276	−	0.191865i	0.0853184	−	0.00624135i
$946$	9.51386	+	41.6829i	0.309322	+	1.35523i
$947$	7.35886	−	18.7501i	0.239131	−	0.609295i	−0.760046	−	0.649870i	$-0.774823\pi$
$947$	7.35886	−	18.7501i	0.239131	−	0.609295i	0.999177	+	0.0405742i	$0.0129187\pi$
$948$	0.127018	−	1.69494i	0.00412536	−	0.0550491i
$949$	−0.101810	+	0.176339i	−0.00330488	+	0.00572422i
$950$	1.68093	+	2.91145i	0.0545365	+	0.0944600i
$951$	−3.22362	+	1.55241i	−0.104533	+	0.0503404i
$952$	19.1874	+	1.47218i	0.621869	+	0.0477136i
$953$	0.463686	+	0.223300i	0.0150203	+	0.00723338i	0.441379	−	0.897321i	$-0.354490\pi$
$953$	0.463686	+	0.223300i	0.0150203	+	0.00723338i	−0.426359	+	0.904554i	$0.640204\pi$
$954$	0.974356	+	13.0019i	0.0315460	+	0.420951i
$955$	−4.43641	−	1.36845i	−0.143559	−	0.0442821i
$956$	6.24437	+	1.92613i	0.201957	+	0.0622956i
$957$	−1.05302	−	14.0516i	−0.0340394	−	0.454225i
$958$	54.8646	+	26.4214i	1.77259	+	0.853637i
$959$	31.8512	−	34.2053i	1.02853	−	1.10455i
$960$	−10.6785	+	5.14251i	−0.344648	+	0.165974i
$961$	2.76901	+	4.79606i	0.0893229	+	0.154712i
$962$	0.237789	−	0.411863i	0.00766663	−	0.0132790i
$963$	0.278900	−	3.72166i	0.00898743	−	0.119929i
$964$	−4.86841	+	12.4045i	−0.156801	+	0.399523i
$965$	0.0359150	+	0.157354i	0.00115615	+	0.00506540i
$966$	6.43798	−	42.2044i	0.207138	−	1.35790i
$967$	−11.2256	+	49.1824i	−0.360990	+	1.58160i	0.389697	+	0.920943i	$0.372580\pi$
$967$	−11.2256	+	49.1824i	−0.360990	+	1.58160i	−0.750687	+	0.660658i	$0.770278\pi$
$968$	24.6969	+	16.8381i	0.793789	+	0.541196i
$969$	0.523654	+	0.485880i	0.0168222	+	0.0156087i
$970$	−28.7424	+	4.33222i	−0.922863	+	0.139099i
$971$	−25.4043	+	23.5717i	−0.815261	+	0.756452i	−0.972945	−	0.231038i	$-0.925788\pi$
$971$	−25.4043	+	23.5717i	−0.815261	+	0.756452i	0.157683	+	0.987490i	$0.449597\pi$
$972$	−2.20718	+	2.76772i	−0.0707954	+	0.0887746i
$973$	0.0935995	−	52.6944i	0.00300066	−	1.68930i
$974$	−30.1120	−	37.7593i	−0.964851	−	1.20989i
$975$	−0.0684281	−	0.0103139i	−0.00219145	−	0.000330309i
$976$	−16.4110	+	11.1888i	−0.525304	+	0.358146i
$977$	−21.6039	−	55.0460i	−0.691172	−	1.76108i	−0.647544	−	0.762028i	$-0.724204\pi$
$977$	−21.6039	−	55.0460i	−0.691172	−	1.76108i	−0.0436280	−	0.999048i	$-0.513892\pi$
$978$	21.0444	−	6.49133i	0.672925	−	0.207570i
$979$	37.6840			1.20438
$980$	5.39549	+	24.0324i	0.172352	+	0.767687i
$981$	−2.50051			−0.0798351
$982$	57.1602	−	17.6316i	1.82406	−	0.562646i
$983$	0.654461	+	1.66754i	0.0208741	+	0.0531863i	0.940931	−	0.338599i	$-0.109953\pi$
$983$	0.654461	+	1.66754i	0.0208741	+	0.0531863i	−0.920057	+	0.391785i	$0.871858\pi$
$984$	30.7334	−	20.9537i	0.979744	−	0.667978i
$985$	−5.17283	−	0.779678i	−0.164820	−	0.0248426i
$986$	−9.45825	−	11.8603i	−0.301212	−	0.377708i
$987$	25.7080	+	5.91574i	0.818293	+	0.188300i
$988$	0.0135532	−	0.0169952i	0.000431184	−	0.000540688i
$989$	20.8084	−	19.3074i	0.661670	−	0.613940i
$990$	10.1489	−	1.52970i	0.322553	−	0.0486170i
$991$	13.3751	+	12.4102i	0.424873	+	0.394224i	0.863422	−	0.504483i	$-0.168317\pi$
$991$	13.3751	+	12.4102i	0.424873	+	0.394224i	−0.438549	+	0.898707i	$0.644507\pi$
$992$	−15.9784	−	10.8939i	−0.507315	−	0.345882i
$993$	1.28770	−	5.64176i	0.0408638	−	0.179036i
$994$	−22.9125	+	13.1743i	−0.726739	+	0.417864i
$995$	−3.29986	−	14.4576i	−0.104612	−	0.458337i
$996$	−2.49835	+	6.36570i	−0.0791634	+	0.201705i
$997$	1.77504	−	23.6862i	0.0562160	−	0.750150i	−0.895869	−	0.444318i	$-0.853446\pi$
$997$	1.77504	−	23.6862i	0.0562160	−	0.750150i	0.952085	−	0.305833i	$-0.0989348\pi$
$998$	8.49847	−	14.7198i	0.269014	−	0.465946i
$999$	−5.85718	−	10.1449i	−0.185313	−	0.320971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.m.a.25.4	✓	48
3.2	odd	2		441.2.bb.c.172.1		48
49.2	even	21	inner	147.2.m.a.100.4	yes	48
49.10	odd	42		7203.2.a.k.1.24		24
49.39	even	21		7203.2.a.i.1.24		24
147.2	odd	42		441.2.bb.c.100.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.25.4	✓	48	1.1	even	1	trivial
147.2.m.a.100.4	yes	48	49.2	even	21	inner
441.2.bb.c.100.1		48	147.2	odd	42
441.2.bb.c.172.1		48	3.2	odd	2
7203.2.a.i.1.24		24	49.39	even	21
7203.2.a.k.1.24		24	49.10	odd	42

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24916 - 0.693774i) q^{2} +(-0.365341 - 0.930874i) q^{3} +(2.92492 - 1.99418i) q^{4} +(-0.982858 - 0.148142i) q^{5} +(-1.46753 - 1.84022i) q^{6} +(-2.07146 + 1.64592i) q^{7} +(2.26005 - 2.83402i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(-2.31338 + 0.348686i) q^{10} +(3.21592 + 2.98394i) q^{11} +(-2.92492 - 1.99418i) q^{12} +(-0.00383811 + 0.0168159i) q^{13} +(-3.51714 + 5.13907i) q^{14} +(0.221177 + 0.969039i) q^{15} +(0.530409 - 1.35146i) q^{16} +(0.149951 - 2.00095i) q^{17} +(-1.17686 + 2.03839i) q^{18} +(-0.178003 - 0.308310i) q^{19} +(-3.17020 + 1.52669i) q^{20} +(2.28893 + 1.32694i) q^{21} +(9.30331 + 4.48024i) q^{22} +(-0.512321 - 6.83645i) q^{23} +(-3.46380 - 1.06844i) q^{24} +(-3.83380 - 1.18257i) q^{25} +(0.00303388 + 0.0404844i) q^{26} +(0.900969 + 0.433884i) q^{27} +(-2.77659 + 8.94505i) q^{28} +(2.89389 - 1.39362i) q^{29} +(1.16976 + 2.02608i) q^{30} +(-2.52299 + 4.36995i) q^{31} +(-0.286403 + 3.82178i) q^{32} +(1.60276 - 4.08378i) q^{33} +(-1.05095 - 4.60450i) q^{34} +(2.27978 - 1.31084i) q^{35} +(-0.787734 + 3.45129i) q^{36} +(-9.67885 - 6.59893i) q^{37} +(-0.614254 - 0.569944i) q^{38} +(0.0170557 - 0.00257073i) q^{39} +(-2.64115 + 2.45063i) q^{40} +(-6.39800 + 8.02284i) q^{41} +(6.06878 + 1.39651i) q^{42} +(2.58159 + 3.23721i) q^{43} +(15.3568 + 2.31467i) q^{44} +(0.821248 - 0.559917i) q^{45} +(-5.89525 - 15.0208i) q^{46} +(9.52767 - 2.93890i) q^{47} -1.45182 q^{48} +(1.58188 - 6.81892i) q^{49} -9.44327 q^{50} +(-1.91742 + 0.591446i) q^{51} +(0.0223077 + 0.0568390i) q^{52} +(4.57690 - 3.12048i) q^{53} +(2.32744 + 0.350805i) q^{54} +(-2.71875 - 3.40920i) q^{55} +(-0.0170352 + 9.59042i) q^{56} +(-0.221966 + 0.278336i) q^{57} +(5.54195 - 5.14218i) q^{58} +(10.9381 - 1.64865i) q^{59} +(2.57936 + 2.39330i) q^{60} +(-11.3038 - 7.70678i) q^{61} +(-2.64286 + 11.5791i) q^{62} +(0.398975 - 2.61550i) q^{63} +(2.65341 + 11.6253i) q^{64} +(0.00626346 - 0.0159590i) q^{65} +(0.771655 - 10.2970i) q^{66} +(-3.48108 + 6.02941i) q^{67} +(-3.55166 - 6.15166i) q^{68} +(-6.17670 + 2.97454i) q^{69} +(4.21816 - 4.52993i) q^{70} +(3.82385 + 1.84147i) q^{71} +(0.270885 + 3.61471i) q^{72} +(11.2807 + 3.47963i) q^{73} +(-26.3475 - 8.12711i) q^{74} +(0.299820 + 4.00083i) q^{75} +(-1.13547 - 0.546813i) q^{76} +(-11.5730 - 0.887951i) q^{77} +(0.0365774 - 0.0176148i) q^{78} +(0.240066 + 0.415807i) q^{79} +(-0.721524 + 1.24972i) q^{80} +(0.0747301 - 0.997204i) q^{81} +(-8.82410 + 22.4834i) q^{82} +(-0.429851 - 1.88330i) q^{83} +(9.34111 - 0.683336i) q^{84} +(-0.443806 + 1.94444i) q^{85} +(8.05230 + 5.48997i) q^{86} +(-2.35454 - 2.18470i) q^{87} +(15.7247 - 2.37012i) q^{88} +(6.29680 - 5.84258i) q^{89} +(1.45866 - 1.82910i) q^{90} +(-0.0197271 - 0.0411506i) q^{91} +(-15.1316 - 18.9744i) q^{92} +(4.98963 + 0.752065i) q^{93} +(19.3903 - 13.2201i) q^{94} +(0.129278 + 0.329394i) q^{95} +(3.66223 - 1.12965i) q^{96} +12.4244 q^{97} +(-1.17289 - 16.4343i) q^{98} -4.38704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 4 q^{3} + 3 q^{4} - 2 q^{6} + 6 q^{8} + 4 q^{9} + 30 q^{10} - 9 q^{11} - 3 q^{12} - 42 q^{14} - 7 q^{15} + 29 q^{16} - 5 q^{17} + 6 q^{18} - 26 q^{19} - 5 q^{20} + 7 q^{21} + q^{22} - 4 q^{23}+ \cdots - 24 q^{99}+O(q^{100}) \) 48 * q - q^2 - 4 * q^3 + 3 * q^4 - 2 * q^6 + 6 * q^8 + 4 * q^9 + 30 * q^10 - 9 * q^11 - 3 * q^12 - 42 * q^14 - 7 * q^15 + 29 * q^16 - 5 * q^17 + 6 * q^18 - 26 * q^19 - 5 * q^20 + 7 * q^21 + q^22 - 4 * q^23 - 18 * q^24 - 56 * q^25 - 62 * q^26 + 8 * q^27 + 7 * q^28 + 12 * q^29 + 12 * q^30 - 36 * q^31 - 14 * q^32 + 16 * q^33 - 76 * q^34 + 7 * q^35 - 6 * q^36 - 20 * q^37 - 60 * q^38 + 14 * q^39 + 28 * q^40 + 41 * q^41 + 28 * q^42 + 12 * q^43 + 44 * q^44 + 14 * q^45 + 16 * q^46 + 13 * q^47 - 12 * q^48 - 84 * q^49 - 12 * q^50 - 2 * q^51 + 92 * q^52 + 14 * q^53 + q^54 - 38 * q^55 + 105 * q^56 + 18 * q^57 + 3 * q^58 + 57 * q^59 + 36 * q^60 + 11 * q^61 - 16 * q^62 - 7 * q^63 - 110 * q^64 + 21 * q^65 + 11 * q^66 + 34 * q^67 + 22 * q^68 - 8 * q^69 + 6 * q^71 - 24 * q^72 - 69 * q^73 - 90 * q^74 - 42 * q^75 - 49 * q^76 + 2 * q^78 + 34 * q^79 + 55 * q^80 + 4 * q^81 + 91 * q^82 + 28 * q^83 + 28 * q^84 - 44 * q^85 - 26 * q^86 - 29 * q^87 + 45 * q^88 + 11 * q^89 + 24 * q^90 + 84 * q^92 + q^93 + 90 * q^94 + 150 * q^95 - 35 * q^96 + 124 * q^97 + 119 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more