LMFDB - Embedded newform 675.2.u.e.49.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.13
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.177808 + 0.211903i) q^{2} +(-1.66326 + 0.483303i) q^{3} +(0.334009 - 1.89426i) q^{4} +(-0.398153 - 0.266514i) q^{6} +(-1.66379 + 0.293371i) q^{7} +(0.939908 - 0.542656i) q^{8} +(2.53284 - 1.60771i) q^{9} +(-4.65944 - 1.69590i) q^{11} +(0.359958 + 3.31206i) q^{12} +(-2.40892 + 2.87084i) q^{13} +(-0.358001 - 0.300398i) q^{14} +(-3.33285 - 1.21306i) q^{16} +(5.46979 + 3.15798i) q^{17} +(0.791037 + 0.250852i) q^{18} +(3.42671 + 5.93524i) q^{19} +(2.62552 - 1.29206i) q^{21} +(-0.469119 - 1.28889i) q^{22} +(-6.37131 - 1.12343i) q^{23} +(-1.30104 + 1.35684i) q^{24} -1.03667 q^{26} +(-3.43574 + 3.89816i) q^{27} +3.24964i q^{28} +(0.115261 - 0.0967151i) q^{29} +(-1.06440 + 6.03653i) q^{31} +(-1.07795 - 2.96165i) q^{32} +(8.56948 + 0.568791i) q^{33} +(0.303384 + 1.72058i) q^{34} +(-2.19943 - 5.33484i) q^{36} +(-2.13979 - 1.23541i) q^{37} +(-0.648400 + 1.78146i) q^{38} +(2.61917 - 5.93918i) q^{39} +(-3.02499 - 2.53826i) q^{41} +(0.740630 + 0.326617i) q^{42} +(-2.39437 + 6.57849i) q^{43} +(-4.76877 + 8.25975i) q^{44} +(-0.894809 - 1.54985i) q^{46} +(-6.10414 + 1.07632i) q^{47} +(6.12965 + 0.406850i) q^{48} +(-3.89572 + 1.41793i) q^{49} +(-10.6239 - 2.60897i) q^{51} +(4.63352 + 5.52201i) q^{52} +0.373453i q^{53} +(-1.43693 - 0.0349210i) q^{54} +(-1.40461 + 1.17861i) q^{56} +(-8.56802 - 8.21568i) q^{57} +(0.0409885 + 0.00722737i) q^{58} +(-0.342887 + 0.124801i) q^{59} +(1.07271 + 6.08365i) q^{61} +(-1.46842 + 0.847791i) q^{62} +(-3.74245 + 3.41795i) q^{63} +(-3.11083 + 5.38811i) q^{64} +(1.40319 + 1.91703i) q^{66} +(-0.398928 + 0.475424i) q^{67} +(7.80900 - 9.30640i) q^{68} +(11.1401 - 1.21071i) q^{69} +(-3.39814 + 5.88576i) q^{71} +(1.50820 - 2.88556i) q^{72} +(-3.94359 + 2.27683i) q^{73} +(-0.118685 - 0.673094i) q^{74} +(12.3874 - 4.50866i) q^{76} +(8.24986 + 1.45467i) q^{77} +(1.72424 - 0.501023i) q^{78} +(12.4889 - 10.4794i) q^{79} +(3.83053 - 8.14414i) q^{81} -1.09233i q^{82} +(-7.18726 - 8.56544i) q^{83} +(-1.57056 - 5.40498i) q^{84} +(-1.81974 + 0.662331i) q^{86} +(-0.144965 + 0.216568i) q^{87} +(-5.29974 + 0.934487i) q^{88} +(-4.58274 - 7.93753i) q^{89} +(3.16572 - 5.48319i) q^{91} +(-4.25615 + 11.6937i) q^{92} +(-1.14710 - 10.5547i) q^{93} +(-1.31344 - 1.10211i) q^{94} +(3.22429 + 4.40501i) q^{96} +(4.70945 - 12.9391i) q^{97} +(-0.993152 - 0.573397i) q^{98} +(-14.5281 + 3.19561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.177808	+	0.211903i	0.125729	+	0.149838i	0.825237	−	0.564787i	$-0.191042\pi$
$2$	0.177808	+	0.211903i	0.125729	+	0.149838i	−0.699508	+	0.714625i	$0.746597\pi$
$3$	−1.66326	+	0.483303i	−0.960281	+	0.279035i
$3$	−1.66326	+	0.483303i	−0.960281	+	0.279035i
$4$	0.334009	−	1.89426i	0.167005	−	0.947130i
$5$		0			0
$5$		0			0
$6$	−0.398153	−	0.266514i	−0.162545	−	0.108804i
$7$	−1.66379	+	0.293371i	−0.628853	+	0.110884i	−0.478986	−	0.877822i	$-0.658996\pi$
$7$	−1.66379	+	0.293371i	−0.628853	+	0.110884i	−0.149867	+	0.988706i	$0.547885\pi$
$8$	0.939908	−	0.542656i	0.332308	−	0.191858i
$9$	2.53284	−	1.60771i	0.844279	−	0.535904i
$10$		0			0
$11$	−4.65944	−	1.69590i	−1.40488	−	0.511333i	−0.475254	−	0.879849i	$-0.657644\pi$
$11$	−4.65944	−	1.69590i	−1.40488	−	0.511333i	−0.929621	+	0.368516i	$0.879866\pi$
$12$	0.359958	+	3.31206i	0.103911	+	0.956111i
$13$	−2.40892	+	2.87084i	−0.668115	+	0.796229i	−0.988526	−	0.151050i	$-0.951735\pi$
$13$	−2.40892	+	2.87084i	−0.668115	+	0.796229i	0.320411	+	0.947279i	$0.396179\pi$
$14$	−0.358001	−	0.300398i	−0.0956798	−	0.0802849i
$15$		0			0
$16$	−3.33285	−	1.21306i	−0.833212	−	0.303264i
$17$	5.46979	+	3.15798i	1.32662	+	0.765923i	0.984775	−	0.173834i	$-0.0556155\pi$
$17$	5.46979	+	3.15798i	1.32662	+	0.765923i	0.341843	+	0.939757i	$0.388949\pi$
$18$	0.791037	+	0.250852i	0.186449	+	0.0591265i
$19$	3.42671	+	5.93524i	0.786142	+	1.36164i	0.928314	+	0.371796i	$0.121258\pi$
$19$	3.42671	+	5.93524i	0.786142	+	1.36164i	−0.142172	+	0.989842i	$0.545409\pi$
$20$		0			0
$21$	2.62552	−	1.29206i	0.572935	−	0.281952i
$22$	−0.469119	−	1.28889i	−0.100017	−	0.274793i
$23$	−6.37131	−	1.12343i	−1.32851	−	0.234252i	−0.536055	−	0.844183i	$-0.680086\pi$
$23$	−6.37131	−	1.12343i	−1.32851	−	0.234252i	−0.792454	+	0.609931i	$0.791197\pi$
$24$	−1.30104	+	1.35684i	−0.265574	+	0.276963i
$25$		0			0
$26$	−1.03667			−0.203307
$27$	−3.43574	+	3.89816i	−0.661209	+	0.750202i
$28$			3.24964i			0.614124i
$29$	0.115261	−	0.0967151i	0.0214034	−	0.0179596i	−0.632023	−	0.774949i	$-0.717775\pi$
$29$	0.115261	−	0.0967151i	0.0214034	−	0.0179596i	0.653427	+	0.756990i	$0.273331\pi$
$30$		0			0
$31$	−1.06440	+	6.03653i	−0.191172	+	1.08419i	0.726593	+	0.687068i	$0.241103\pi$
$31$	−1.06440	+	6.03653i	−0.191172	+	1.08419i	−0.917765	+	0.397124i	$0.870008\pi$
$32$	−1.07795	−	2.96165i	−0.190557	−	0.523551i
$33$	8.56948	+	0.568791i	1.49175	+	0.0990138i
$34$	0.303384	+	1.72058i	0.0520300	+	0.295077i
$35$		0			0
$36$	−2.19943	−	5.33484i	−0.366572	−	0.889140i
$37$	−2.13979	−	1.23541i	−0.351780	−	0.203100i	0.313689	−	0.949526i	$-0.398435\pi$
$37$	−2.13979	−	1.23541i	−0.351780	−	0.203100i	−0.665469	+	0.746426i	$0.731768\pi$
$38$	−0.648400	+	1.78146i	−0.105184	+	0.288992i
$39$	2.61917	−	5.93918i	0.419403	−	0.951031i
$40$		0			0
$41$	−3.02499	−	2.53826i	−0.472423	−	0.396410i	0.375254	−	0.926922i	$-0.377555\pi$
$41$	−3.02499	−	2.53826i	−0.472423	−	0.396410i	−0.847678	+	0.530512i	$0.822000\pi$
$42$	0.740630	+	0.326617i	0.114282	+	0.0503980i
$43$	−2.39437	+	6.57849i	−0.365139	+	1.00321i	0.612047	+	0.790822i	$0.290346\pi$
$43$	−2.39437	+	6.57849i	−0.365139	+	1.00321i	−0.977185	+	0.212388i	$0.931876\pi$
$44$	−4.76877	+	8.25975i	−0.718919	+	1.24520i
$45$		0			0
$46$	−0.894809	−	1.54985i	−0.131932	−	0.228514i
$47$	−6.10414	+	1.07632i	−0.890380	+	0.156998i	−0.600082	−	0.799938i	$-0.704865\pi$
$47$	−6.10414	+	1.07632i	−0.890380	+	0.156998i	−0.290298	+	0.956936i	$0.593754\pi$
$48$	6.12965	+	0.406850i	0.884739	+	0.0587238i
$49$	−3.89572	+	1.41793i	−0.556531	+	0.202561i
$50$		0			0
$51$	−10.6239	−	2.60897i	−1.48765	−	0.365329i
$52$	4.63352	+	5.52201i	0.642554	+	0.765766i
$53$			0.373453i			0.0512977i	0.999671	+	0.0256488i	$0.00816518\pi$
$53$			0.373453i			0.0512977i	−0.999671	+	0.0256488i	$0.991835\pi$
$54$	−1.43693	−	0.0349210i	−0.195542	−	0.00475215i
$55$		0			0
$56$	−1.40461	+	1.17861i	−0.187699	+	0.157498i
$57$	−8.56802	−	8.21568i	−1.13486	−	1.08819i
$58$	0.0409885	+	0.00722737i	0.00538205	+	0.000949001i
$59$	−0.342887	+	0.124801i	−0.0446401	+	0.0162477i	−0.364244	−	0.931304i	$-0.618672\pi$
$59$	−0.342887	+	0.124801i	−0.0446401	+	0.0162477i	0.319604	+	0.947551i	$0.396450\pi$
$60$		0			0
$61$	1.07271	+	6.08365i	0.137347	+	0.778931i	0.973197	+	0.229974i	$0.0738640\pi$
$61$	1.07271	+	6.08365i	0.137347	+	0.778931i	−0.835850	+	0.548958i	$0.815025\pi$
$62$	−1.46842	+	0.847791i	−0.186489	+	0.107670i
$63$	−3.74245	+	3.41795i	−0.471505	+	0.430622i
$64$	−3.11083	+	5.38811i	−0.388854	+	0.673514i
$65$		0			0
$66$	1.40319	+	1.91703i	0.172721	+	0.235971i
$67$	−0.398928	+	0.475424i	−0.0487369	+	0.0580823i	−0.789862	−	0.613284i	$-0.789848\pi$
$67$	−0.398928	+	0.475424i	−0.0487369	+	0.0580823i	0.741125	+	0.671367i	$0.234292\pi$
$68$	7.80900	−	9.30640i	0.946980	−	1.12857i
$69$	11.1401	−	1.21071i	1.34111	−	0.145753i
$70$		0			0
$71$	−3.39814	+	5.88576i	−0.403285	+	0.698511i	−0.994120	−	0.108282i	$-0.965465\pi$
$71$	−3.39814	+	5.88576i	−0.403285	+	0.698511i	0.590835	+	0.806793i	$0.298799\pi$
$72$	1.50820	−	2.88556i	0.177743	−	0.340067i
$73$	−3.94359	+	2.27683i	−0.461563	+	0.266483i	−0.712701	−	0.701468i	$-0.752528\pi$
$73$	−3.94359	+	2.27683i	−0.461563	+	0.266483i	0.251138	+	0.967951i	$0.419195\pi$
$74$	−0.118685	−	0.673094i	−0.0137968	−	0.0782456i
$75$		0			0
$76$	12.3874	−	4.50866i	1.42094	−	0.517179i
$77$	8.24986	+	1.45467i	0.940159	+	0.165775i
$78$	1.72424	−	0.501023i	0.195232	−	0.0567297i
$79$	12.4889	−	10.4794i	1.40511	−	1.17903i	0.446338	−	0.894864i	$-0.352728\pi$
$79$	12.4889	−	10.4794i	1.40511	−	1.17903i	0.958775	−	0.284166i	$-0.0917166\pi$
$80$		0			0
$81$	3.83053	−	8.14414i	0.425614	−	0.904905i
$82$		−	1.09233i		−	0.120627i
$83$	−7.18726	−	8.56544i	−0.788904	−	0.940179i	0.210395	−	0.977616i	$-0.432525\pi$
$83$	−7.18726	−	8.56544i	−0.788904	−	0.940179i	−0.999299	+	0.0374374i	$0.988081\pi$
$84$	−1.57056	−	5.40498i	−0.171362	−	0.589731i
$85$		0			0
$86$	−1.81974	+	0.662331i	−0.196228	+	0.0714210i
$87$	−0.144965	+	0.216568i	−0.0155419	+	0.0232185i
$88$	−5.29974	+	0.934487i	−0.564954	+	0.0996167i
$89$	−4.58274	−	7.93753i	−0.485769	−	0.841377i	0.514097	−	0.857732i	$-0.328127\pi$
$89$	−4.58274	−	7.93753i	−0.485769	−	0.841377i	−0.999866	+	0.0163553i	$0.994794\pi$
$90$		0			0
$91$	3.16572	−	5.48319i	0.331858	−	0.574794i
$92$	−4.25615	+	11.6937i	−0.443734	+	1.21915i
$93$	−1.14710	−	10.5547i	−0.118948	−	1.09447i
$94$	−1.31344	−	1.10211i	−0.135471	−	0.113674i
$95$		0			0
$96$	3.22429	+	4.40501i	0.329077	+	0.449584i
$97$	4.70945	−	12.9391i	0.478172	−	1.31377i	−0.432871	−	0.901456i	$-0.642499\pi$
$97$	4.70945	−	12.9391i	0.478172	−	1.31377i	0.911043	−	0.412312i	$-0.135279\pi$
$98$	−0.993152	−	0.573397i	−0.100324	−	0.0579218i
$99$	−14.5281	+	3.19561i	−1.46013	+	0.321171i
$100$		0			0
$101$	1.98385	+	11.2510i	0.197400	+	1.11951i	0.908959	+	0.416886i	$0.136879\pi$
$101$	1.98385	+	11.2510i	0.197400	+	1.11951i	−0.711558	+	0.702627i	$0.752010\pi$
$102$	−1.33617	−	2.71514i	−0.132300	−	0.268838i
$103$	3.13998	+	8.62703i	0.309392	+	0.850046i	0.992775	+	0.119987i	$0.0382853\pi$
$103$	3.13998	+	8.62703i	0.309392	+	0.850046i	−0.683384	+	0.730059i	$0.739492\pi$
$104$	−0.706286	+	4.00555i	−0.0692571	+	0.392776i
$105$		0			0
$106$	−0.0791358	+	0.0664028i	−0.00768635	+	0.00644961i
$107$		−	1.09015i		−	0.105389i	−0.998611	−	0.0526946i	$-0.983219\pi$
$107$		−	1.09015i		−	0.105389i	0.998611	−	0.0526946i	$-0.0167810\pi$
$108$	6.23656	+	7.81021i	0.600113	+	0.751538i
$109$	0.574982			0.0550733			0.0275366	−	0.999621i	$-0.491234\pi$
$109$	0.574982			0.0550733			0.0275366	+	0.999621i	$0.491234\pi$
$110$		0			0
$111$	4.15610	+	1.02063i	0.394480	+	0.0968744i
$112$	5.90104	+	1.04051i	0.557595	+	0.0983191i
$113$	−6.02550	−	16.5549i	−0.566832	−	1.55736i	−0.809421	−	0.587228i	$-0.800219\pi$
$113$	−6.02550	−	16.5549i	−0.566832	−	1.55736i	0.242590	−	0.970129i	$-0.422003\pi$
$114$	0.217468	−	3.27640i	0.0203678	−	0.306863i
$115$		0			0
$116$	−0.144705	−	0.250637i	−0.0134356	−	0.0232711i
$117$	−1.48592	+	11.1442i	−0.137374	+	1.03028i
$118$	−0.0874136	−	0.0504683i	−0.00804708	−	0.00464598i
$119$	−10.0270	−	3.64954i	−0.919177	−	0.334553i
$120$		0			0
$121$	10.4079	+	8.73323i	0.946169	+	0.793930i
$122$	−1.09841	+	1.30903i	−0.0994451	+	0.118514i
$123$	6.25807	+	2.75980i	0.564272	+	0.248843i
$124$	11.0792	+	4.03251i	0.994944	+	0.362130i
$125$		0			0
$126$	−1.38971	−	0.185298i	−0.123805	−	0.0165077i
$127$	6.89096	−	3.97850i	0.611474	−	0.353035i	−0.162068	−	0.986780i	$-0.551816\pi$
$127$	6.89096	−	3.97850i	0.611474	−	0.353035i	0.773542	+	0.633745i	$0.218483\pi$
$128$	−7.90257	+	1.39344i	−0.698496	+	0.123164i
$129$	0.803054	−	12.0989i	0.0707050	−	1.06525i
$130$		0			0
$131$	1.46844	−	8.32796i	0.128298	−	0.727617i	−0.850995	−	0.525173i	$-0.824001\pi$
$131$	1.46844	−	8.32796i	0.128298	−	0.727617i	0.979294	−	0.202444i	$-0.0648883\pi$
$132$	3.93972	−	16.0428i	0.342909	−	1.39635i
$133$	−7.44256	−	8.86970i	−0.645352	−	0.769100i
$134$	−0.171676			−0.0148306
$135$		0			0
$136$	6.85480			0.587794
$137$	0.254931	+	0.303815i	0.0217802	+	0.0259567i	0.776825	−	0.629717i	$-0.216829\pi$
$137$	0.254931	+	0.303815i	0.0217802	+	0.0259567i	−0.755044	+	0.655674i	$0.772385\pi$
$138$	2.23734	+	2.14534i	0.190455	+	0.182624i
$139$	0.813377	−	4.61289i	0.0689897	−	0.391260i	−0.930687	−	0.365818i	$-0.880789\pi$
$139$	0.813377	−	4.61289i	0.0689897	−	0.391260i	0.999676	−	0.0254426i	$-0.00809950\pi$
$140$		0			0
$141$	9.63255	−	4.74035i	0.811207	−	0.399209i
$142$	−1.85143	+	0.326456i	−0.155368	+	0.0273956i
$143$	16.0929	−	9.29124i	1.34576	−	0.776973i
$144$	−10.3918	+	2.28578i	−0.865984	+	0.190482i
$145$		0			0
$146$	−1.18367	−	0.430821i	−0.0979612	−	0.0356550i
$147$	5.79429	−	4.24118i	0.477905	−	0.349807i
$148$	−3.05490	+	3.64069i	−0.251111	+	0.299263i
$149$	17.6585	+	14.8172i	1.44664	+	1.21387i	0.934987	+	0.354682i	$0.115411\pi$
$149$	17.6585	+	14.8172i	1.44664	+	1.21387i	0.511653	+	0.859192i	$0.329033\pi$
$150$		0			0
$151$	−4.86203	−	1.76963i	−0.395666	−	0.144011i	0.136522	−	0.990637i	$-0.456408\pi$
$151$	−4.86203	−	1.76963i	−0.395666	−	0.144011i	−0.532188	+	0.846626i	$0.678630\pi$
$152$	6.44159	+	3.71906i	0.522482	+	0.301655i
$153$	18.9312	−	0.795184i	1.53050	−	0.0642868i
$154$	1.15864	+	2.00682i	0.0933659	+	0.161714i
$155$		0			0
$156$	−10.3755	−	6.94513i	−0.830707	−	0.556055i
$157$	4.73812	+	13.0179i	0.378143	+	1.03894i	0.972125	+	0.234462i	$0.0753328\pi$
$157$	4.73812	+	13.0179i	0.378143	+	1.03894i	−0.593982	+	0.804478i	$0.702445\pi$
$158$	4.44125	+	0.783113i	0.353327	+	0.0623011i
$159$	−0.180491	−	0.621147i	−0.0143138	−	0.0492602i
$160$		0			0
$161$	10.9301			0.861412
$162$	2.40687	−	0.636392i	0.189101	−	0.0499997i
$163$		−	2.98083i		−	0.233477i	−0.993163	−	0.116738i	$-0.962756\pi$
$163$		−	2.98083i		−	0.233477i	0.993163	−	0.116738i	$-0.0372439\pi$
$164$	−5.81850	+	4.88231i	−0.454349	+	0.381244i
$165$		0			0
$166$	0.537093	−	3.04600i	0.0416865	−	0.236416i
$167$	−6.41805	−	17.6335i	−0.496644	−	1.36452i	−0.894499	−	0.447070i	$-0.852468\pi$
$167$	−6.41805	−	17.6335i	−0.496644	−	1.36452i	0.397855	−	0.917448i	$-0.369755\pi$
$168$	1.76660	−	2.63918i	0.136296	−	0.203617i
$169$	−0.181402	−	1.02878i	−0.0139540	−	0.0791371i
$170$		0			0
$171$	18.2215	+	9.52383i	1.39343	+	0.728306i
$172$	11.6616	+	6.73284i	0.889190	+	0.513374i
$173$	−2.87196	+	7.89065i	−0.218351	+	0.599915i	−0.999708	−	0.0241697i	$-0.992306\pi$
$173$	−2.87196	+	7.89065i	−0.218351	+	0.599915i	0.781357	+	0.624085i	$0.214528\pi$
$174$	−0.0716673	+	0.00778887i	−0.00543308	+	0.000590473i
$175$		0			0
$176$	13.4720	+	11.3043i	1.01549	+	0.852097i
$177$	0.509992	−	0.373294i	0.0383334	−	0.0280585i
$178$	0.867141	−	2.38245i	0.0649950	−	0.178572i
$179$	−11.7123	+	20.2863i	−0.875420	+	1.51627i	−0.0191052	+	0.999817i	$0.506082\pi$
$179$	−11.7123	+	20.2863i	−0.875420	+	1.51627i	−0.856315	+	0.516454i	$0.827252\pi$
$180$		0			0
$181$	4.02049	+	6.96369i	0.298841	+	0.517607i	0.975871	−	0.218348i	$-0.0700667\pi$
$181$	4.02049	+	6.96369i	0.298841	+	0.517607i	−0.677030	+	0.735955i	$0.736733\pi$
$182$	1.72479	−	0.304128i	0.127850	−	0.0225434i
$183$	−4.72444	−	9.60022i	−0.349240	−	0.709668i
$184$	−6.59808	+	2.40151i	−0.486417	+	0.177041i
$185$		0			0
$186$	2.03261	−	2.11978i	0.149038	−	0.155430i
$187$	−20.1305	−	23.9906i	−1.47209	−	1.75437i
$188$			11.9223i			0.869525i
$189$	4.57275	−	7.49367i	0.332618	−	0.545084i
$190$		0			0
$191$	2.02875	−	1.70232i	0.146795	−	0.123176i	−0.566433	−	0.824108i	$-0.691677\pi$
$191$	2.02875	−	1.70232i	0.146795	−	0.123176i	0.713228	+	0.700932i	$0.247232\pi$
$192$	2.57001	−	10.4653i	0.185475	−	0.755267i
$193$	−13.5598	−	2.39096i	−0.976055	−	0.172105i	−0.337201	−	0.941433i	$-0.609480\pi$
$193$	−13.5598	−	2.39096i	−0.976055	−	0.172105i	−0.638854	+	0.769328i	$0.720591\pi$
$194$	3.57921	−	1.30273i	0.256973	−	0.0935304i
$195$		0			0
$196$	1.38471	+	7.85310i	0.0989081	+	0.560936i
$197$	9.42236	−	5.44000i	0.671315	−	0.387584i	−0.125260	−	0.992124i	$-0.539976\pi$
$197$	9.42236	−	5.44000i	0.671315	−	0.387584i	0.796575	+	0.604540i	$0.206643\pi$
$198$	−3.26037	−	2.51035i	−0.231705	−	0.178403i
$199$	−9.58456	+	16.6009i	−0.679431	+	1.17681i	0.295721	+	0.955274i	$0.404440\pi$
$199$	−9.58456	+	16.6009i	−0.679431	+	1.17681i	−0.975152	+	0.221535i	$0.928893\pi$
$200$		0			0
$201$	0.433746	−	0.983555i	0.0305941	−	0.0693747i
$202$	−2.03137	+	2.42089i	−0.142927	+	0.170334i
$203$	−0.163396	+	0.194728i	−0.0114682	+	0.0136672i
$204$	−8.49055	+	19.2530i	−0.594457	+	1.34798i
$205$		0			0
$206$	−1.26978	+	2.19932i	−0.0884698	+	0.153234i
$207$	−17.9436	+	7.39775i	−1.24717	+	0.514179i
$208$	11.5111	−	6.64592i	0.798150	−	0.460812i
$209$	−5.90101	−	33.4663i	−0.408181	−	2.31491i
$210$		0			0
$211$	−14.2097	+	5.17190i	−0.978235	+	0.356048i	−0.781154	−	0.624339i	$-0.785369\pi$
$211$	−14.2097	+	5.17190i	−0.978235	+	0.356048i	−0.197081	+	0.980387i	$0.563146\pi$
$212$	0.707417	+	0.124737i	0.0485856	+	0.00856695i
$213$	2.80738	−	11.4319i	0.192358	−	0.783297i
$214$	0.231007	−	0.193838i	0.0157913	−	0.0132505i
$215$		0			0
$216$	−1.11392	+	5.52834i	−0.0757928	+	0.376156i
$217$		−	10.3558i		−	0.702996i
$218$	0.102236	+	0.121840i	0.00692431	+	0.00825207i
$219$	5.45880	−	5.69291i	0.368872	−	0.384691i
$220$		0			0
$221$	−22.2424	+	8.09556i	−1.49618	+	0.544566i
$222$	0.522711	+	1.06217i	0.0350821	+	0.0712880i
$223$	4.59088	−	0.809497i	0.307428	−	0.0542079i	−0.0178057	−	0.999841i	$-0.505668\pi$
$223$	4.59088	−	0.809497i	0.307428	−	0.0542079i	0.325234	+	0.945634i	$0.394557\pi$
$224$	2.66235	+	4.61133i	0.177886	+	0.308107i
$225$		0			0
$226$	2.43666	−	4.22042i	0.162084	−	0.280738i
$227$	−0.0682374	+	0.187481i	−0.00452908	+	0.0124435i	−0.941937	−	0.335791i	$-0.890996\pi$
$227$	−0.0682374	+	0.187481i	−0.00452908	+	0.0124435i	0.937407	+	0.348234i	$0.113219\pi$
$228$	−18.4244	+	13.4859i	−1.22019	+	0.893128i
$229$	−13.3044	−	11.1637i	−0.879179	−	0.737719i	0.0868311	−	0.996223i	$-0.472326\pi$
$229$	−13.3044	−	11.1637i	−0.879179	−	0.737719i	−0.966010	+	0.258504i	$0.916770\pi$
$230$		0			0
$231$	−14.4247	+	1.56769i	−0.949074	+	0.103146i
$232$	0.0558513	−	0.153450i	0.00366682	−	0.0100745i
$233$	−13.6919	−	7.90504i	−0.896988	−	0.517876i	−0.0207662	−	0.999784i	$-0.506611\pi$
$233$	−13.6919	−	7.90504i	−0.896988	−	0.517876i	−0.876222	+	0.481908i	$0.839944\pi$
$234$	−2.62571	+	1.66666i	−0.171648	+	0.108953i
$235$		0			0
$236$	0.121877	+	0.691202i	0.00793355	+	0.0449934i
$237$	−15.7075	+	23.4659i	−1.02031	+	1.52428i
$238$	−1.00954	−	2.77368i	−0.0654385	−	0.179791i
$239$	5.21235	−	29.5607i	0.337159	−	1.91212i	−0.0676249	−	0.997711i	$-0.521542\pi$
$239$	5.21235	−	29.5607i	0.337159	−	1.91212i	0.404784	−	0.914412i	$-0.367347\pi$
$240$		0			0
$241$	−2.74958	+	2.30717i	−0.177116	+	0.148618i	−0.727036	−	0.686600i	$-0.759103\pi$
$241$	−2.74958	+	2.30717i	−0.177116	+	0.148618i	0.549920	+	0.835217i	$0.314658\pi$
$242$			3.75829i			0.241592i
$243$	−2.43506	+	15.3971i	−0.156209	+	0.987724i
$244$	11.8823			0.760686
$245$		0			0
$246$	0.527925	+	1.81682i	0.0336592	+	0.115836i
$247$	−25.2938	−	4.45999i	−1.60941	−	0.283782i
$248$	2.27532	+	6.25139i	0.144483	+	0.396964i
$249$	16.0939	+	10.7729i	1.01991	+	0.682704i
$250$		0			0
$251$	−12.8233	−	22.2107i	−0.809401	−	1.40192i	−0.913279	−	0.407334i	$-0.866458\pi$
$251$	−12.8233	−	22.2107i	−0.809401	−	1.40192i	0.103878	−	0.994590i	$-0.466875\pi$
$252$	5.22448	+	8.23080i	0.329111	+	0.518492i
$253$	27.7815	+	16.0397i	1.74661	+	1.00841i
$254$	2.06832	+	0.752808i	0.129778	+	0.0472354i
$255$		0			0
$256$	7.83172	+	6.57159i	0.489483	+	0.410725i
$257$	−5.38768	+	6.42079i	−0.336075	+	0.400518i	−0.907443	−	0.420176i	$-0.861968\pi$
$257$	−5.38768	+	6.42079i	−0.336075	+	0.400518i	0.571368	+	0.820694i	$0.306413\pi$
$258$	2.70659	−	1.98111i	0.168505	−	0.123339i
$259$	3.92260	+	1.42771i	0.243738	+	0.0887135i
$260$		0			0
$261$	0.136446	−	0.430270i	0.00844581	−	0.0266330i
$262$	2.02582	−	1.16961i	0.125156	−	0.0722586i
$263$	−5.01183	+	0.883720i	−0.309043	+	0.0544925i	−0.326019	−	0.945363i	$-0.605707\pi$
$263$	−5.01183	+	0.883720i	−0.309043	+	0.0544925i	0.0169761	+	0.999856i	$0.494596\pi$
$264$	8.36318	−	4.11567i	0.514718	−	0.253302i
$265$		0			0
$266$	0.556171	−	3.15420i	0.0341010	−	0.193397i
$267$	11.4585	+	10.9873i	0.701248	+	0.672411i
$268$	0.767331	+	0.914470i	0.0468722	+	0.0558601i
$269$	−28.2625			−1.72320			−0.861599	−	0.507590i	$-0.830536\pi$
$269$	−28.2625			−1.72320			−0.861599	+	0.507590i	$0.830536\pi$
$270$		0			0
$271$	−17.2893			−1.05025			−0.525125	−	0.851025i	$-0.675982\pi$
$271$	−17.2893			−1.05025			−0.525125	+	0.851025i	$0.675982\pi$
$272$	−14.3992	−	17.1602i	−0.873077	−	1.04049i
$273$	−2.61536	+	10.6499i	−0.158289	+	0.644564i
$274$	−0.0190506	+	0.108041i	−0.00115089	+	0.00652702i
$275$		0			0
$276$	1.42748	−	21.5066i	0.0859241	−	1.29454i
$277$	4.07733	−	0.718943i	0.244983	−	0.0431971i	−0.0498083	−	0.998759i	$-0.515861\pi$
$277$	4.07733	−	0.718943i	0.244983	−	0.0431971i	0.294791	+	0.955562i	$0.404750\pi$
$278$	1.12211	−	0.647851i	0.0672997	−	0.0388555i
$279$	7.00904	+	17.0008i	0.419620	+	1.01781i
$280$		0			0
$281$	18.0380	+	6.56528i	1.07605	+	0.391652i	0.818438	−	0.574595i	$-0.194840\pi$
$281$	18.0380	+	6.56528i	1.07605	+	0.391652i	0.257617	+	0.966247i	$0.417063\pi$
$282$	2.71724	+	1.19830i	0.161809	+	0.0713575i
$283$	−6.13548	+	7.31199i	−0.364717	+	0.434652i	−0.916929	−	0.399051i	$-0.869339\pi$
$283$	−6.13548	+	7.31199i	−0.364717	+	0.434652i	0.552212	+	0.833704i	$0.313784\pi$
$284$	10.0141	+	8.40286i	0.594230	+	0.498618i
$285$		0			0
$286$	4.83029	+	1.75808i	0.285621	+	0.103957i
$287$	5.77759	+	3.33570i	0.341041	+	0.196900i
$288$	−7.49176	−	5.76835i	−0.441456	−	0.339903i
$289$	11.4457	+	19.8246i	0.673277	+	1.16615i
$290$		0			0
$291$	−1.57951	+	23.7971i	−0.0925927	+	1.39501i
$292$	2.99572	+	8.23067i	0.175311	+	0.481664i
$293$	−6.25900	−	1.10363i	−0.365655	−	0.0644748i	−0.0121977	−	0.999926i	$-0.503883\pi$
$293$	−6.25900	−	1.10363i	−0.365655	−	0.0644748i	−0.353457	+	0.935451i	$0.614994\pi$
$294$	1.92899	+	0.473712i	0.112501	+	0.0276274i
$295$		0			0
$296$	−2.68161			−0.155866
$297$	22.6195	−	12.3366i	1.31252	−	0.715842i
$298$			6.37651i			0.369381i
$299$	18.5732	−	15.5848i	1.07412	−	0.901290i
$300$		0			0
$301$	2.05380	−	11.6477i	0.118379	−	0.671360i
$302$	−0.489516	−	1.34493i	−0.0281685	−	0.0773922i
$303$	−8.73727	−	17.7544i	−0.501943	−	1.01997i
$304$	−4.22093	−	23.9381i	−0.242087	−	1.37294i
$305$		0			0
$306$	3.53462	+	3.87019i	0.202061	+	0.221244i
$307$	7.43535	+	4.29280i	0.424358	+	0.245003i	0.696940	−	0.717129i	$-0.254544\pi$
$307$	7.43535	+	4.29280i	0.424358	+	0.245003i	−0.272582	+	0.962133i	$0.587878\pi$
$308$	5.51106	−	15.1415i	0.314022	−	0.862767i
$309$	−9.39206	−	12.8314i	−0.534295	−	0.729952i
$310$		0			0
$311$	−8.78608	−	7.37239i	−0.498213	−	0.418050i	0.358746	−	0.933435i	$-0.383204\pi$
$311$	−8.78608	−	7.37239i	−0.498213	−	0.418050i	−0.856959	+	0.515385i	$0.827649\pi$
$312$	−0.761158	−	7.00360i	−0.0430921	−	0.396501i
$313$	8.53424	−	23.4476i	0.482384	−	1.32534i	−0.425060	−	0.905165i	$-0.639747\pi$
$313$	8.53424	−	23.4476i	0.482384	−	1.32534i	0.907444	−	0.420173i	$-0.138031\pi$
$314$	−1.91605	+	3.31870i	−0.108129	+	0.187285i
$315$		0			0
$316$	−15.6794	−	27.1575i	−0.882034	−	1.52773i
$317$	−0.624658	+	0.110144i	−0.0350843	+	0.00618630i	−0.191163	−	0.981558i	$-0.561226\pi$
$317$	−0.624658	+	0.110144i	−0.0350843	+	0.00618630i	0.156078	+	0.987745i	$0.450115\pi$
$318$	0.0995304	−	0.148691i	0.00558139	−	0.00833820i
$319$	−0.701069	+	0.255168i	−0.0392524	+	0.0142867i
$320$		0			0
$321$	0.526875	+	1.81321i	0.0294073	+	0.101203i
$322$	1.94346	+	2.31612i	0.108305	+	0.129072i
$323$			43.2860i			2.40850i
$324$	−14.1477	−	9.97623i	−0.785983	−	0.554235i
$325$		0			0
$326$	0.631648	−	0.530015i	0.0349837	−	0.0293548i
$327$	−0.956342	+	0.277890i	−0.0528858	+	0.0153674i
$328$	−4.22062	−	0.744208i	−0.233045	−	0.0410920i
$329$	9.84024	−	3.58155i	0.542510	−	0.197457i
$330$		0			0
$331$	−3.50296	−	19.8662i	−0.192540	−	1.09195i	−0.915879	−	0.401455i	$-0.868505\pi$
$331$	−3.50296	−	19.8662i	−0.192540	−	1.09195i	0.723339	−	0.690493i	$-0.242606\pi$
$332$	−18.6258	+	10.7536i	−1.02222	+	0.590180i
$333$	−7.40593	+	0.311078i	−0.405843	+	0.0170470i
$334$	2.59540	−	4.49537i	0.142014	−	0.245976i
$335$		0			0
$336$	−10.3178	+	1.12135i	−0.562883	+	0.0611746i
$337$	−19.5507	+	23.2996i	−1.06499	+	1.26921i	−0.103428	+	0.994637i	$0.532981\pi$
$337$	−19.5507	+	23.2996i	−1.06499	+	1.26921i	−0.961566	+	0.274574i	$0.911463\pi$
$338$	0.185747	−	0.221365i	0.0101033	−	0.0120407i
$339$	18.0230	+	24.6229i	0.978875	+	1.33733i
$340$		0			0
$341$	15.1969	−	26.3217i	0.822956	−	1.42540i
$342$	1.22179	+	5.55460i	0.0660668	+	0.300358i
$343$	16.3075	−	9.41512i	0.880520	−	0.508369i
$344$	1.31937	+	7.48250i	0.0711355	+	0.403429i
$345$		0			0
$346$	−2.18271	+	0.794442i	−0.117343	+	0.0427094i
$347$	36.3972	+	6.41781i	1.95391	+	0.344526i	0.998841	+	0.0481276i	$0.0153254\pi$
$347$	36.3972	+	6.41781i	1.95391	+	0.344526i	0.955064	+	0.296399i	$0.0957857\pi$
$348$	0.361816	+	0.346937i	0.0193954	+	0.0185978i
$349$	−5.58600	+	4.68721i	−0.299012	+	0.250901i	−0.779933	−	0.625863i	$-0.784747\pi$
$349$	−5.58600	+	4.68721i	−0.299012	+	0.250901i	0.480921	+	0.876764i	$0.340302\pi$
$350$		0			0
$351$	−2.91457	−	19.2539i	−0.155568	−	1.02769i
$352$			15.6278i			0.832962i
$353$	7.31939	+	8.72291i	0.389572	+	0.464273i	0.924811	−	0.380427i	$-0.124223\pi$
$353$	7.31939	+	8.72291i	0.389572	+	0.464273i	−0.535239	+	0.844700i	$0.679779\pi$
$354$	0.169783	+	0.0416944i	0.00902385	+	0.00221603i
$355$		0			0
$356$	−16.5664	+	6.02968i	−0.878018	+	0.319573i
$357$	18.4414	+	1.22403i	0.976020	+	0.0647824i
$358$	−6.38128	+	1.12519i	−0.337261	+	0.0594682i
$359$	12.4562	+	21.5748i	0.657414	+	1.13867i	0.981283	+	0.192573i	$0.0616831\pi$
$359$	12.4562	+	21.5748i	0.657414	+	1.13867i	−0.323869	+	0.946102i	$0.604984\pi$
$360$		0			0
$361$	−13.9847	+	24.2223i	−0.736039	+	1.27486i
$362$	−0.760754	+	2.09015i	−0.0399843	+	0.109856i
$363$	−21.5317	−	9.49544i	−1.13012	−	0.498381i
$364$	−9.32920	−	7.82813i	−0.488983	−	0.410305i
$365$		0			0
$366$	1.19427	−	2.70812i	0.0624257	−	0.141555i
$367$	−9.83014	+	27.0081i	−0.513129	+	1.40981i	0.364830	+	0.931074i	$0.381127\pi$
$367$	−9.83014	+	27.0081i	−0.513129	+	1.40981i	−0.877959	+	0.478736i	$0.841095\pi$
$368$	19.8718	+	11.4730i	1.03589	+	0.598071i
$369$	−11.7426	−	1.56571i	−0.611295	−	0.0815074i
$370$		0			0
$371$	−0.109560	−	0.621347i	−0.00568808	−	0.0322587i
$372$	−20.3765	−	1.35247i	−1.05647	−	0.0701224i
$373$	6.34227	+	17.4252i	0.328390	+	0.902245i	0.988520	+	0.151093i	$0.0482793\pi$
$373$	6.34227	+	17.4252i	0.328390	+	0.902245i	−0.660129	+	0.751152i	$0.729499\pi$
$374$	1.50432	−	8.53145i	0.0777868	−	0.441151i
$375$		0			0
$376$	−5.15326	+	4.32410i	−0.265759	+	0.222998i
$377$			0.563875i			0.0290410i
$378$	2.40100	−	0.363454i	0.123494	−	0.0186940i
$379$	−23.8701			−1.22613			−0.613063	−	0.790034i	$-0.710063\pi$
$379$	−23.8701			−1.22613			−0.613063	+	0.790034i	$0.710063\pi$
$380$		0			0
$381$	−9.53861	+	9.94768i	−0.488678	+	0.509635i
$382$	0.721455	+	0.127212i	0.0369129	+	0.00650873i
$383$	10.4525	+	28.7180i	0.534097	+	1.46742i	0.854154	+	0.520021i	$0.174076\pi$
$383$	10.4525	+	28.7180i	0.534097	+	1.46742i	−0.320057	+	0.947398i	$0.603702\pi$
$384$	12.4705	−	6.13698i	0.636385	−	0.313176i
$385$		0			0
$386$	−1.90439	−	3.29849i	−0.0969307	−	0.167889i
$387$	4.51175	+	20.5117i	0.229345	+	1.04267i
$388$	−22.9370	−	13.2427i	−1.16445	−	0.672296i
$389$	−7.60180	−	2.76683i	−0.385427	−	0.140284i	0.142037	−	0.989861i	$-0.454635\pi$
$389$	−7.60180	−	2.76683i	−0.385427	−	0.140284i	−0.527464	+	0.849578i	$0.676857\pi$
$390$		0			0
$391$	−31.3019	−	26.2654i	−1.58301	−	1.32830i
$392$	−2.89217	+	3.44676i	−0.146077	+	0.174088i
$393$	1.58253	+	14.5612i	0.0798279	+	0.734516i
$394$	2.82812	+	1.02935i	0.142479	+	0.0518580i
$395$		0			0
$396$	1.20078	+	28.5874i	0.0603416	+	1.43657i
$397$	16.9021	−	9.75843i	0.848292	−	0.489762i	−0.0117821	−	0.999931i	$-0.503750\pi$
$397$	16.9021	−	9.75843i	0.848292	−	0.489762i	0.860074	+	0.510169i	$0.170417\pi$
$398$	−5.22200	+	0.920780i	−0.261755	+	0.0461545i
$399$	16.6656	+	11.1556i	0.834325	+	0.558477i
$400$		0			0
$401$	2.44572	−	13.8704i	0.122134	−	0.692654i	−0.860835	−	0.508883i	$-0.830058\pi$
$401$	2.44572	−	13.8704i	0.122134	−	0.692654i	0.982969	−	0.183771i	$-0.0588305\pi$
$402$	0.285542	−	0.0829717i	0.0142415	−	0.00413825i
$403$	−14.7659	−	17.5973i	−0.735540	−	0.876582i
$404$	21.9749			1.09329
$405$		0			0
$406$	−0.0703165			−0.00348975
$407$	7.87512	+	9.38520i	0.390355	+	0.465207i
$408$	−11.4013	+	3.31294i	−0.564448	+	0.164015i
$409$	−0.282399	+	1.60156i	−0.0139637	+	0.0791923i	−0.990993	−	0.133912i	$-0.957246\pi$
$409$	−0.282399	+	1.60156i	−0.0139637	+	0.0791923i	0.977030	+	0.213104i	$0.0683573\pi$
$410$		0			0
$411$	−0.570850	−	0.382113i	−0.0281580	−	0.0188482i
$412$	17.3906	−	3.06643i	0.856774	−	0.151072i
$413$	0.533879	−	0.308235i	0.0262705	−	0.0151673i
$414$	−4.75812	−	2.48693i	−0.233849	−	0.122226i
$415$		0			0
$416$	11.0991	+	4.03976i	0.544181	+	0.198066i
$417$	0.876569	+	8.06552i	0.0429257	+	0.394970i
$418$	6.04236	−	7.20101i	0.295542	−	0.352213i
$419$	24.5436	+	20.5945i	1.19903	+	1.00611i	0.999657	+	0.0261853i	$0.00833601\pi$
$419$	24.5436	+	20.5945i	1.19903	+	1.00611i	0.199376	+	0.979923i	$0.436108\pi$
$420$		0			0
$421$	−3.21532	−	1.17028i	−0.156705	−	0.0570360i	0.262477	−	0.964938i	$-0.415461\pi$
$421$	−3.21532	−	1.17028i	−0.156705	−	0.0570360i	−0.419182	+	0.907902i	$0.637683\pi$
$422$	−3.62254	−	2.09147i	−0.176342	−	0.101811i
$423$	−13.7304	+	12.5398i	−0.667593	+	0.609708i
$424$	0.202657	+	0.351011i	0.00984187	+	0.0170466i
$425$		0			0
$426$	2.92162	−	1.43778i	0.141553	−	0.0696607i
$427$	−3.56953	−	9.80721i	−0.172742	−	0.474604i
$428$	−2.06504	−	0.364121i	−0.0998173	−	0.0176005i
$429$	−22.2761	+	23.2315i	−1.07550	+	1.12163i
$430$		0			0
$431$	33.8955			1.63269			0.816344	−	0.577565i	$-0.195997\pi$
$431$	33.8955			1.63269			0.816344	+	0.577565i	$0.195997\pi$
$432$	16.1795	−	8.82423i	0.778437	−	0.424556i
$433$		−	17.6676i		−	0.849049i	−0.905417	−	0.424524i	$-0.860441\pi$
$433$		−	17.6676i		−	0.849049i	0.905417	−	0.424524i	$-0.139559\pi$
$434$	2.19442	−	1.84134i	0.105336	−	0.0883870i
$435$		0			0
$436$	0.192049	−	1.08916i	0.00919748	−	0.0521615i
$437$	−15.1648	−	41.6649i	−0.725430	−	1.99310i
$438$	2.17696	+	0.144494i	0.104019	+	0.00690418i
$439$	−1.25144	−	7.09728i	−0.0597281	−	0.338735i	0.940270	−	0.340428i	$-0.110572\pi$
$439$	−1.25144	−	7.09728i	−0.0597281	−	0.338735i	−0.999999	+	0.00169354i	$0.999461\pi$
$440$		0			0
$441$	−7.58761	+	9.85457i	−0.361315	+	0.469265i
$442$	−5.67034	−	3.27377i	−0.269711	−	0.155718i
$443$	−11.8604	+	32.5861i	−0.563504	+	1.54821i	0.250959	+	0.967998i	$0.419254\pi$
$443$	−11.8604	+	32.5861i	−0.563504	+	1.54821i	−0.814463	+	0.580216i	$0.802968\pi$
$444$	3.32152	−	7.53183i	0.157632	−	0.357445i
$445$		0			0
$446$	0.987830	+	0.828888i	0.0467751	+	0.0392490i
$447$	−36.5318	−	16.1104i	−1.72789	−	0.761998i
$448$	3.59505	−	9.87731i	0.169850	−	0.466659i
$449$	4.87046	−	8.43589i	0.229851	−	0.398114i	−0.727913	−	0.685670i	$-0.759509\pi$
$449$	4.87046	−	8.43589i	0.229851	−	0.398114i	0.957764	+	0.287556i	$0.0928427\pi$
$450$		0			0
$451$	9.79011	+	16.9570i	0.460998	+	0.798473i
$452$	−33.3719	+	5.88437i	−1.56968	+	0.276777i
$453$	8.94206	+	0.593521i	0.420135	+	0.0278861i
$454$	−0.0518609	+	0.0188758i	−0.00243395	+	0.000885886i
$455$		0			0
$456$	−12.5114	−	3.07250i	−0.585902	−	0.143883i
$457$	−20.3177	−	24.2137i	−0.950421	−	1.13267i	−0.991050	−	0.133493i	$-0.957381\pi$
$457$	−20.3177	−	24.2137i	−0.950421	−	1.13267i	0.0406289	−	0.999174i	$-0.487064\pi$
$458$		−	4.80424i		−	0.224487i
$459$	−31.1031	+	10.4721i	−1.45177	+	0.488796i
$460$		0			0
$461$	−13.9469	+	11.7028i	−0.649572	+	0.545056i	−0.906941	−	0.421258i	$-0.861589\pi$
$461$	−13.9469	+	11.7028i	−0.649572	+	0.545056i	0.257369	+	0.966313i	$0.417144\pi$
$462$	−2.89702	−	2.77789i	−0.134781	−	0.129239i
$463$	27.8450	+	4.90983i	1.29407	+	0.228179i	0.777943	−	0.628334i	$-0.216263\pi$
$463$	27.8450	+	4.90983i	1.29407	+	0.228179i	0.516125	+	0.856513i	$0.327374\pi$
$464$	−0.501467	+	0.182519i	−0.0232800	+	0.00847324i
$465$		0			0
$466$	−0.759430	−	4.30694i	−0.0351799	−	0.199515i
$467$	12.1683	−	7.02539i	0.563083	−	0.325096i	−0.191299	−	0.981532i	$-0.561270\pi$
$467$	12.1683	−	7.02539i	0.563083	−	0.325096i	0.754382	+	0.656435i	$0.227937\pi$
$468$	20.6138	+	6.53700i	0.952871	+	0.302173i
$469$	0.524257	−	0.908040i	0.0242080	−	0.0419294i
$470$		0			0
$471$	−14.1723	−	19.3621i	−0.653024	−	0.892159i
$472$	−0.254559	+	0.303371i	−0.0117170	+	0.0139638i
$473$	22.3129	−	26.5915i	1.02595	−	1.22268i
$474$	−7.76542	+	0.843953i	−0.356678	+	0.0387641i
$475$		0			0
$476$	−10.2623	+	17.7748i	−0.470372	+	0.814708i
$477$	0.600404	+	0.945895i	0.0274906	+	0.0433096i
$478$	7.19080	−	4.15161i	0.328900	−	0.189890i
$479$	−1.21657	−	6.89953i	−0.0555867	−	0.315248i	0.944318	−	0.329033i	$-0.106723\pi$
$479$	−1.21657	−	6.89953i	−0.0555867	−	0.315248i	−0.999905	+	0.0137857i	$0.995612\pi$
$480$		0			0
$481$	8.70127	−	3.16700i	0.396744	−	0.144403i
$482$	−0.977792	−	0.172411i	−0.0445372	−	0.00785311i
$483$	−18.1795	+	5.28254i	−0.827198	+	0.240364i
$484$	20.0193	−	16.7982i	0.909969	−	0.763555i
$485$		0			0
$486$	−3.69566	+	2.22173i	−0.167639	+	0.100780i
$487$			20.2826i			0.919093i	0.888154	+	0.459547i	$0.151988\pi$
$487$			20.2826i			0.919093i	−0.888154	+	0.459547i	$0.848012\pi$
$488$	4.30958	+	5.13596i	0.195086	+	0.232494i
$489$	1.44064	+	4.95789i	0.0651482	+	0.224203i
$490$		0			0
$491$	4.72637	−	1.72026i	0.213298	−	0.0776342i	−0.233161	−	0.972438i	$-0.574907\pi$
$491$	4.72637	−	1.72026i	0.213298	−	0.0776342i	0.446459	+	0.894804i	$0.352685\pi$
$492$	7.31803	−	10.9326i	0.329922	−	0.492881i
$493$	0.935876	−	0.165020i	0.0421497	−	0.00743213i
$494$	−3.55236	−	6.15286i	−0.159828	−	0.276830i
$495$		0			0
$496$	10.8701	−	18.8277i	0.488084	−	0.845387i
$497$	3.92709	−	10.7896i	0.176154	−	0.483979i
$498$	0.578820	+	5.32586i	0.0259375	+	0.238658i
$499$	−18.3084	−	15.3625i	−0.819595	−	0.687722i	0.133282	−	0.991078i	$-0.457448\pi$
$499$	−18.3084	−	15.3625i	−0.819595	−	0.687722i	−0.952877	+	0.303356i	$0.901893\pi$
$500$		0			0
$501$	19.1972	+	26.2271i	0.857666	+	1.17174i
$502$	2.42642	−	6.66653i	0.108296	−	0.297542i
$503$	6.99778	+	4.04017i	0.312015	+	0.180142i	0.647828	−	0.761787i	$-0.275678\pi$
$503$	6.99778	+	4.04017i	0.312015	+	0.180142i	−0.335813	+	0.941929i	$0.609011\pi$
$504$	−1.66279	+	5.24343i	−0.0740664	+	0.233561i
$505$		0			0
$506$	1.54092	+	8.73897i	0.0685020	+	0.388494i
$507$	0.798931	+	1.62346i	0.0354818	+	0.0721002i
$508$	−5.23467	−	14.3821i	−0.232251	−	0.638104i
$509$	−2.73491	+	15.5104i	−0.121223	+	0.687487i	0.862257	+	0.506470i	$0.169050\pi$
$509$	−2.73491	+	15.5104i	−0.121223	+	0.687487i	−0.983480	+	0.181017i	$0.942061\pi$
$510$		0			0
$511$	5.89335	−	4.94511i	0.260707	−	0.218759i
$512$			18.8770i			0.834254i
$513$	−34.9098	−	7.03408i	−1.54131	−	0.310562i
$514$	−2.31856			−0.102267
$515$		0			0
$516$	−22.6503	−	5.56234i	−0.997122	−	0.244868i
$517$	30.2672	+	5.33693i	1.33115	+	0.234718i
$518$	0.394933	+	1.08507i	0.0173523	+	0.0476752i
$519$	0.963233	−	14.5122i	0.0422813	−	0.637015i
$520$		0			0
$521$	6.71663	+	11.6335i	0.294261	+	0.509675i	0.974813	−	0.223025i	$-0.0715932\pi$
$521$	6.71663	+	11.6335i	0.294261	+	0.509675i	−0.680552	+	0.732700i	$0.738260\pi$
$522$	0.115437	−	0.0475919i	0.00505253	−	0.00208304i
$523$	15.6709	+	9.04762i	0.685242	+	0.395625i	0.801827	−	0.597556i	$-0.203861\pi$
$523$	15.6709	+	9.04762i	0.685242	+	0.395625i	−0.116585	+	0.993181i	$0.537195\pi$
$524$	−15.2848	−	5.56323i	−0.667721	−	0.243031i
$525$		0			0
$526$	−1.07841	−	0.904889i	−0.0470207	−	0.0394551i
$527$	−24.8853	+	29.6572i	−1.08402	+	1.29189i
$528$	−27.8708	−	12.2910i	−1.21292	−	0.534896i
$529$	17.7185	+	6.44901i	0.770370	+	0.280392i
$530$		0			0
$531$	−0.667833	+	0.867363i	−0.0289815	+	0.0376404i
$532$	−19.2874	+	11.1356i	−0.836214	+	0.482789i
$533$	14.5739	−	2.56978i	0.631267	−	0.111309i
$534$	−0.290832	+	4.38172i	−0.0125855	+	0.189615i
$535$		0			0
$536$	−0.116964	+	0.663337i	−0.00505208	+	0.0286518i
$537$	9.67614	−	39.4020i	0.417556	−	1.70032i
$538$	−5.02530	−	5.98892i	−0.216656	−	0.258201i
$539$	20.5565			0.885433
$540$		0			0
$541$	10.6112			0.456211			0.228106	−	0.973636i	$-0.426747\pi$
$541$	10.6112			0.456211			0.228106	+	0.973636i	$0.426747\pi$
$542$	−3.07417	−	3.66366i	−0.132047	−	0.157368i
$543$	−10.0527	−	9.63929i	−0.431402	−	0.413661i
$544$	3.45667	−	19.6038i	0.148204	−	0.840505i
$545$		0			0
$546$	−2.72179	+	1.33944i	−0.116482	+	0.0573227i
$547$	−16.5817	+	2.92380i	−0.708983	+	0.125013i	−0.516500	−	0.856287i	$-0.672765\pi$
$547$	−16.5817	+	2.92380i	−0.708983	+	0.125013i	−0.192483	+	0.981300i	$0.561654\pi$
$548$	0.660654	−	0.381429i	0.0282217	−	0.0162938i
$549$	12.4978	+	13.6843i	0.533391	+	0.584031i
$550$		0			0
$551$	0.968993	+	0.352685i	0.0412805	+	0.0150249i
$552$	9.81364	−	7.18319i	0.417696	−	0.305737i
$553$	−17.7046	+	21.0995i	−0.752875	+	0.897241i
$554$	0.877326	+	0.736164i	0.0372740	+	0.0312766i
$555$		0			0
$556$	−8.46634	−	3.08149i	−0.359053	−	0.130684i
$557$	−3.98565	−	2.30112i	−0.168877	−	0.0975015i	0.413179	−	0.910650i	$-0.364418\pi$
$557$	−3.98565	−	2.30112i	−0.168877	−	0.0975015i	−0.582056	+	0.813148i	$0.697752\pi$
$558$	−2.35626	+	4.50811i	−0.0997484	+	0.190844i
$559$	−13.1179	−	22.7209i	−0.554830	−	0.960994i
$560$		0			0
$561$	45.0770	+	30.1734i	1.90315	+	1.27392i
$562$	1.81609	+	4.98966i	0.0766070	+	0.210476i
$563$	−10.5736	−	1.86442i	−0.445626	−	0.0785758i	−0.0536674	−	0.998559i	$-0.517091\pi$
$563$	−10.5736	−	1.86442i	−0.445626	−	0.0785758i	−0.391958	+	0.919983i	$0.628202\pi$
$564$	−5.76209	−	19.8299i	−0.242628	−	0.834988i
$565$		0			0
$566$	−2.64037			−0.110983
$567$	−3.98393	+	14.6739i	−0.167310	+	0.616246i
$568$			7.37610i			0.309494i
$569$	−10.4618	+	8.77850i	−0.438582	+	0.368014i	−0.835178	−	0.549979i	$-0.814636\pi$
$569$	−10.4618	+	8.77850i	−0.438582	+	0.368014i	0.396597	+	0.917993i	$0.370191\pi$
$570$		0			0
$571$	−2.92720	+	16.6010i	−0.122499	+	0.694729i	0.860262	+	0.509852i	$0.170300\pi$
$571$	−2.92720	+	16.6010i	−0.122499	+	0.694729i	−0.982762	+	0.184877i	$0.940811\pi$
$572$	−12.2248	−	33.5875i	−0.511147	−	1.40436i
$573$	−2.55159	+	3.81190i	−0.106594	+	0.159244i
$574$	0.320457	+	1.81740i	0.0133756	+	0.0758569i
$575$		0			0
$576$	0.783310	+	18.6485i	0.0326379	+	0.777022i
$577$	13.3591	+	7.71289i	0.556147	+	0.321092i	0.751598	−	0.659622i	$-0.229284\pi$
$577$	13.3591	+	7.71289i	0.556147	+	0.321092i	−0.195450	+	0.980714i	$0.562617\pi$
$578$	−2.16575	+	5.95034i	−0.0900832	+	0.247502i
$579$	23.7090	−	2.57671i	0.985311	−	0.107085i
$580$		0			0
$581$	14.4709	+	12.1426i	0.600355	+	0.503758i
$582$	−5.32354	+	3.89661i	−0.220668	+	0.161520i
$583$	0.633338	−	1.74008i	0.0262302	−	0.0720668i
$584$	−2.47108	+	4.28003i	−0.102254	+	0.177109i
$585$		0			0
$586$	−0.879036	−	1.52254i	−0.0363126	−	0.0628953i
$587$	11.6775	−	2.05906i	0.481983	−	0.0849866i	0.0726229	−	0.997359i	$-0.476863\pi$
$587$	11.6775	−	2.05906i	0.481983	−	0.0849866i	0.409360	+	0.912373i	$0.365752\pi$
$588$	−6.09856	−	12.3925i	−0.251500	−	0.511057i
$589$	−39.4757	+	14.3680i	−1.62657	+	0.592022i
$590$		0			0
$591$	−13.0426	+	13.6020i	−0.536502	+	0.559510i
$592$	5.63298	+	6.71313i	0.231514	+	0.275908i
$593$		−	34.8582i		−	1.43146i	−0.698379	−	0.715728i	$-0.746095\pi$
$593$		−	34.8582i		−	1.43146i	0.698379	−	0.715728i	$-0.253905\pi$
$594$	6.63609	+	2.59961i	0.272282	+	0.106663i
$595$		0			0
$596$	33.9658	−	28.5007i	1.39129	−	1.16743i
$597$	7.91829	−	32.2439i	0.324074	−	1.31965i
$598$	6.60492	+	1.16462i	0.270095	+	0.0476251i
$599$	−11.2279	+	4.08662i	−0.458759	+	0.166975i	−0.561054	−	0.827779i	$-0.689604\pi$
$599$	−11.2279	+	4.08662i	−0.458759	+	0.166975i	0.102294	+	0.994754i	$0.467382\pi$
$600$		0			0
$601$	3.39336	+	19.2447i	0.138418	+	0.785007i	0.972418	+	0.233243i	$0.0749338\pi$
$601$	3.39336	+	19.2447i	0.138418	+	0.785007i	−0.834001	+	0.551764i	$0.813955\pi$
$602$	2.83336	−	1.63584i	0.115479	−	0.0666718i
$603$	−0.246075	+	1.84553i	−0.0100210	+	0.0751560i
$604$	−4.97611	+	8.61887i	−0.202475	+	0.350697i
$605$		0			0
$606$	2.20867	−	5.00833i	0.0897209	−	0.203450i
$607$	6.56061	−	7.81863i	0.266287	−	0.317348i	−0.616287	−	0.787521i	$-0.711364\pi$
$607$	6.56061	−	7.81863i	0.266287	−	0.317348i	0.882574	+	0.470173i	$0.155808\pi$
$608$	13.8843	−	16.5467i	0.563082	−	0.671055i
$609$	0.177657	−	0.402852i	0.00719902	−	0.0163244i
$610$		0			0
$611$	11.6144	−	20.1168i	0.469870	−	0.813839i
$612$	4.81691	−	36.1262i	0.194712	−	1.46032i
$613$	12.7859	−	7.38192i	0.516416	−	0.298153i	−0.219051	−	0.975713i	$-0.570296\pi$
$613$	12.7859	−	7.38192i	0.516416	−	0.298153i	0.735467	+	0.677560i	$0.236963\pi$
$614$	0.412406	+	2.33887i	0.0166433	+	0.0943890i
$615$		0			0
$616$	8.54350	−	3.10958i	0.344228	−	0.125289i
$617$	32.1559	+	5.66996i	1.29455	+	0.228264i	0.778147	−	0.628082i	$-0.216160\pi$
$617$	32.1559	+	5.66996i	1.29455	+	0.228264i	0.516402	+	0.856346i	$0.327271\pi$
$618$	1.04903	−	4.27173i	0.0421982	−	0.171834i
$619$	−11.2792	+	9.46438i	−0.453350	+	0.380406i	−0.840677	−	0.541537i	$-0.817843\pi$
$619$	−11.2792	+	9.46438i	−0.453350	+	0.380406i	0.387327	+	0.921942i	$0.373398\pi$
$620$		0			0
$621$	26.2695	−	20.9766i	1.05416	−	0.841760i
$622$		−	3.17267i		−	0.127212i
$623$	9.95335	+	11.8619i	0.398773	+	0.475239i
$624$	−15.9339	+	16.6172i	−0.637865	+	0.665220i
$625$		0			0
$626$	6.48608	−	2.36074i	0.259236	−	0.0943541i
$627$	25.9892	+	52.8110i	1.03791	+	2.10907i
$628$	26.2418	−	4.62714i	1.04716	−	0.184643i
$629$	−7.80281	−	13.5149i	−0.311118	−	0.538873i
$630$		0			0
$631$	12.9621	−	22.4511i	0.516014	−	0.893762i	−0.483813	−	0.875171i	$-0.660749\pi$
$631$	12.9621	−	22.4511i	0.516014	−	0.893762i	0.999827	−	0.0185911i	$-0.00591806\pi$
$632$	6.05170	−	16.6269i	0.240724	−	0.661383i
$633$	21.1347	−	15.4698i	0.840031	−	0.614868i
$634$	−0.134409	−	0.112782i	−0.00533806	−	0.00447916i
$635$		0			0
$636$	−1.23690	+	0.134427i	−0.0490463	+	0.00533040i
$637$	5.31385	−	14.5997i	0.210542	−	0.578460i
$638$	−0.178727	−	0.103188i	−0.00707585	−	0.00408525i
$639$	0.855657	+	20.3709i	0.0338493	+	0.805860i
$640$		0			0
$641$	−3.45147	−	19.5742i	−0.136325	−	0.773136i	−0.973928	−	0.226857i	$-0.927155\pi$
$641$	−3.45147	−	19.5742i	−0.136325	−	0.773136i	0.837603	−	0.546279i	$-0.183956\pi$
$642$	−0.290541	+	0.434048i	−0.0114668	+	0.0171305i
$643$	−11.3450	−	31.1702i	−0.447404	−	1.22923i	−0.934525	−	0.355897i	$-0.884175\pi$
$643$	−11.3450	−	31.1702i	−0.447404	−	1.22923i	0.487121	−	0.873334i	$-0.338047\pi$
$644$	3.65075	−	20.7044i	0.143860	−	0.815869i
$645$		0			0
$646$	−9.17244	+	7.69659i	−0.360885	+	0.302818i
$647$		−	18.8740i		−	0.742014i	−0.928630	−	0.371007i	$-0.879013\pi$
$647$		−	18.8740i		−	0.742014i	0.928630	−	0.371007i	$-0.120987\pi$
$648$	−0.819127	−	9.73341i	−0.0321783	−	0.382364i
$649$	1.80931			0.0710217
$650$		0			0
$651$	5.00497	+	17.2243i	0.196160	+	0.675074i
$652$	−5.64647	−	0.995625i	−0.221133	−	0.0389917i
$653$	9.37817	+	25.7663i	0.366996	+	1.00831i	0.976498	+	0.215528i	$0.0691474\pi$
$653$	9.37817	+	25.7663i	0.366996	+	1.00831i	−0.609502	+	0.792785i	$0.708630\pi$
$654$	−0.228931	−	0.153241i	−0.00895190	−	0.00599218i
$655$		0			0
$656$	7.00276	+	12.1291i	0.273412	+	0.473563i
$657$	−6.32798	+	12.1070i	−0.246878	+	0.472339i
$658$	2.50861	+	1.44835i	0.0977959	+	0.0564625i
$659$	4.90832	+	1.78648i	0.191201	+	0.0695915i	0.435846	−	0.900021i	$-0.356449\pi$
$659$	4.90832	+	1.78648i	0.191201	+	0.0695915i	−0.244645	+	0.969613i	$0.578671\pi$
$660$		0			0
$661$	17.4652	+	14.6551i	0.679319	+	0.570017i	0.915807	−	0.401618i	$-0.131552\pi$
$661$	17.4652	+	14.6551i	0.679319	+	0.570017i	−0.236488	+	0.971634i	$0.575996\pi$
$662$	3.58687	−	4.27466i	0.139408	−	0.166139i
$663$	33.0821	−	24.2148i	1.28480	−	0.940424i
$664$	−11.4035	−	4.15052i	−0.442540	−	0.161071i
$665$		0			0
$666$	−1.38275	−	1.51403i	−0.0535805	−	0.0586674i
$667$	−0.843014	+	0.486714i	−0.0326416	+	0.0188456i
$668$	−35.5460	+	6.26772i	−1.37532	+	0.242505i
$669$	−7.24458	+	3.56519i	−0.280092	+	0.137838i
$670$		0			0
$671$	5.31901	−	30.1656i	0.205338	−	1.16453i
$672$	−6.65684	−	6.38309i	−0.256793	−	0.246233i
$673$	11.1986	+	13.3460i	0.431675	+	0.514450i	0.937405	−	0.348242i	$-0.113221\pi$
$673$	11.1986	+	13.3460i	0.431675	+	0.514450i	−0.505730	+	0.862692i	$0.668777\pi$
$674$	−8.41353			−0.324077
$675$		0			0
$676$	−2.00937			−0.0772835
$677$	20.6209	+	24.5750i	0.792526	+	0.944495i	0.999426	−	0.0338665i	$-0.0107821\pi$
$677$	20.6209	+	24.5750i	0.792526	+	0.944495i	−0.206901	+	0.978362i	$0.566338\pi$
$678$	−2.01305	+	8.19728i	−0.0773107	+	0.314815i
$679$	−4.03958	+	22.9096i	−0.155025	+	0.879189i
$680$		0			0
$681$	0.0228863	−	0.344808i	0.000877005	−	0.0132131i
$682$	8.27978	−	1.45995i	0.317049	−	0.0559043i
$683$	−18.3599	+	10.6001i	−0.702520	+	0.405600i	−0.808285	−	0.588791i	$-0.799604\pi$
$683$	−18.3599	+	10.6001i	−0.702520	+	0.405600i	0.105765	+	0.994391i	$0.466271\pi$
$684$	24.1267	−	31.3351i	0.922509	−	1.19813i
$685$		0			0
$686$	4.89469	+	1.78152i	0.186880	+	0.0680188i
$687$	27.5241	+	12.1381i	1.05011	+	0.463096i
$688$	15.9602	−	19.0206i	0.608476	−	0.725153i
$689$	−1.07212	−	0.899619i	−0.0408447	−	0.0342728i
$690$		0			0
$691$	−10.2500	−	3.73069i	−0.389928	−	0.141922i	0.139614	−	0.990206i	$-0.455414\pi$
$691$	−10.2500	−	3.73069i	−0.389928	−	0.141922i	−0.529542	+	0.848284i	$0.677636\pi$
$692$	13.9877	+	8.07579i	0.531732	+	0.306995i
$693$	23.2342	−	9.57895i	0.882596	−	0.363874i
$694$	5.11176	+	8.85382i	0.194040	+	0.336086i
$695$		0			0
$696$	−0.0187321	+	0.282220i	−0.000710038	+	0.0106975i
$697$	−8.53023	−	23.4366i	−0.323106	−	0.887725i
$698$	−1.98647	−	0.350268i	−0.0751889	−	0.0132578i
$699$	26.5937	+	6.53075i	1.00587	+	0.247016i
$700$		0			0
$701$	−16.5817			−0.626282			−0.313141	−	0.949707i	$-0.601381\pi$
$701$	−16.5817			−0.626282			−0.313141	+	0.949707i	$0.601381\pi$
$702$	3.56172	−	4.04109i	0.134428	−	0.152521i
$703$		−	16.9336i		−	0.638662i
$704$	23.6324	−	19.8300i	0.890681	−	0.747370i
$705$		0			0
$706$	−0.546967	+	3.10200i	−0.0205854	+	0.116745i
$707$	−6.60142	−	18.1372i	−0.248272	−	0.682121i
$708$	−0.536773	−	1.09074i	−0.0201732	−	0.0409926i
$709$	0.653972	+	3.70886i	0.0245604	+	0.139289i	0.994622	−	0.103569i	$-0.0330262\pi$
$709$	0.653972	+	3.70886i	0.0245604	+	0.139289i	−0.970062	+	0.242858i	$0.921915\pi$
$710$		0			0
$711$	14.7845	−	46.6213i	0.554461	−	1.74844i
$712$	−8.61470	−	4.97370i	−0.322850	−	0.186397i
$713$	13.5633	−	37.2648i	0.507948	−	1.39558i
$714$	3.01964	+	4.12542i	0.113007	+	0.154390i
$715$		0			0
$716$	34.5156	+	28.9620i	1.28991	+	1.08236i
$717$	5.61730	+	51.6861i	0.209782	+	1.93025i
$718$	−2.35695	+	6.47568i	−0.0879608	+	0.241670i
$719$	−0.0341167	+	0.0590919i	−0.00127234	+	0.00220375i	−0.866661	−	0.498898i	$-0.833738\pi$
$719$	−0.0341167	+	0.0590919i	−0.00127234	+	0.00220375i	0.865389	+	0.501101i	$0.167072\pi$
$720$		0			0
$721$	−7.75519	−	13.4324i	−0.288818	−	0.500248i
$722$	−7.61937	+	1.34350i	−0.283564	+	0.0499999i
$723$	3.45819	−	5.16629i	0.128611	−	0.192136i
$724$	14.5339	−	5.28992i	0.540149	−	0.196598i
$725$		0			0
$726$	−1.81639	−	6.25100i	−0.0674127	−	0.231996i
$727$	28.1700	+	33.5717i	1.04477	+	1.24511i	0.968760	+	0.247998i	$0.0797727\pi$
$727$	28.1700	+	33.5717i	1.04477	+	1.24511i	0.0760072	+	0.997107i	$0.475783\pi$
$728$		−	6.87159i		−	0.254678i
$729$	−3.39133	−	26.7862i	−0.125605	−	0.992080i
$730$		0			0
$731$	−33.8715	+	28.4215i	−1.25278	+	1.05121i
$732$	−19.7633	+	5.74275i	−0.730473	+	0.212258i
$733$	−5.07348	−	0.894591i	−0.187393	−	0.0330425i	0.0791639	−	0.996862i	$-0.474775\pi$
$733$	−5.07348	−	0.894591i	−0.187393	−	0.0330425i	−0.266557	+	0.963819i	$0.585886\pi$
$734$	−7.47097	+	2.71921i	−0.275759	+	0.100368i
$735$		0			0
$736$	3.54075	+	20.0806i	0.130514	+	0.740181i
$737$	2.66506	−	1.53867i	0.0981686	−	0.0566777i
$738$	−1.75615	−	2.76669i	−0.0646447	−	0.101843i
$739$	0.515367	−	0.892642i	0.0189581	−	0.0328364i	−0.856391	−	0.516328i	$-0.827298\pi$
$739$	0.515367	−	0.892642i	0.0189581	−	0.0328364i	0.875349	+	0.483492i	$0.160632\pi$
$740$		0			0
$741$	44.2256	−	4.80648i	1.62467	−	0.176571i
$742$	0.112185	−	0.133696i	0.00411843	−	0.00490815i
$743$	−27.2972	+	32.5316i	−1.00144	+	1.19347i	−0.0203733	+	0.999792i	$0.506485\pi$
$743$	−27.2972	+	32.5316i	−1.00144	+	1.19347i	−0.981066	+	0.193676i	$0.937959\pi$
$744$	−6.80575	−	9.29799i	−0.249511	−	0.340881i
$745$		0			0
$746$	−2.56476	+	4.44229i	−0.0939025	+	0.162644i
$747$	−31.9749	−	10.1398i	−1.16990	−	0.370997i
$748$	−52.1683	+	30.1194i	−1.90746	+	1.10127i
$749$	0.319820	+	1.81379i	0.0116860	+	0.0662744i
$750$		0			0
$751$	2.32349	−	0.845681i	0.0847853	−	0.0308593i	−0.299279	−	0.954166i	$-0.596746\pi$
$751$	2.32349	−	0.845681i	0.0847853	−	0.0308593i	0.384065	+	0.923306i	$0.374524\pi$
$752$	21.6498	+	3.81745i	0.789487	+	0.139208i
$753$	32.0629	+	30.7444i	1.16844	+	1.12039i
$754$	−0.119487	+	0.100261i	−0.00435145	+	0.00365130i
$755$		0			0
$756$	−12.6676	−	11.1649i	−0.460717	−	0.406064i
$757$		−	52.6699i		−	1.91432i	−0.289559	−	0.957160i	$-0.593509\pi$
$757$		−	52.6699i		−	1.91432i	0.289559	−	0.957160i	$-0.406491\pi$
$758$	−4.24430	−	5.05816i	−0.154160	−	0.183721i
$759$	−53.9598	−	13.2512i	−1.95862	−	0.480987i
$760$		0			0
$761$	−28.1597	+	10.2493i	−1.02079	+	0.371537i	−0.797567	−	0.603231i	$-0.793880\pi$
$761$	−28.1597	+	10.2493i	−1.02079	+	0.371537i	−0.223222	+	0.974768i	$0.571658\pi$
$762$	−3.80398	−	0.252486i	−0.137804	−	0.00914660i
$763$	−0.956649	+	0.168683i	−0.0346330	+	0.00610673i
$764$	−2.54702	−	4.41157i	−0.0921480	−	0.159605i
$765$		0			0
$766$	−4.22689	+	7.32119i	−0.152724	+	0.264525i
$767$	0.467705	−	1.28501i	0.0168879	−	0.0463990i
$768$	−16.2022	−	7.14515i	−0.584647	−	0.257828i
$769$	33.0529	+	27.7347i	1.19192	+	1.00014i	0.999824	+	0.0187613i	$0.00597225\pi$
$769$	33.0529	+	27.7347i	1.19192	+	1.00014i	0.192094	+	0.981377i	$0.438472\pi$
$770$		0			0
$771$	5.85791	−	13.2833i	0.210967	−	0.478386i
$772$	−9.05819	+	24.8872i	−0.326011	+	0.895709i
$773$	33.7376	+	19.4784i	1.21346	+	0.700590i	0.963511	−	0.267669i	$-0.0862535\pi$
$773$	33.7376	+	19.4784i	1.21346	+	0.700590i	0.249947	+	0.968260i	$0.419587\pi$
$774$	−3.54427	+	4.60319i	−0.127396	+	0.165458i
$775$		0			0
$776$	−2.59504	−	14.7172i	−0.0931565	−	0.528316i
$777$	−7.21430	−	0.478843i	−0.258812	−	0.0171784i
$778$	−0.765360	−	2.10281i	−0.0274395	−	0.0753894i
$779$	4.69945	−	26.6519i	0.168375	−	0.954905i
$780$		0			0
$781$	25.8151	−	21.6614i	0.923737	−	0.775108i
$782$		−	11.3032i		−	0.404200i
$783$	−0.0189946	+	0.781593i	−0.000678813	+	0.0279319i
$784$	14.7039			0.525138
$785$		0			0
$786$	−2.80418	+	2.92444i	−0.100022	+	0.104311i
$787$	−10.3244	−	1.82048i	−0.368027	−	0.0648930i	−0.0134234	−	0.999910i	$-0.504273\pi$
$787$	−10.3244	−	1.82048i	−0.368027	−	0.0648930i	−0.354603	+	0.935017i	$0.615384\pi$
$788$	−7.15762	−	19.6654i	−0.254980	−	0.700551i
$789$	7.90884	−	3.89208i	0.281562	−	0.138562i
$790$		0			0
$791$	14.8819	+	25.7762i	0.529140	+	0.916497i
$792$	−11.9210	+	10.8874i	−0.423594	+	0.386865i
$793$	−20.0493	−	11.5755i	−0.711971	−	0.411056i
$794$	5.07317	+	1.84648i	0.180040	+	0.0655292i
$795$		0			0
$796$	28.2452	+	23.7005i	1.00112	+	0.840042i
$797$	−18.6906	+	22.2746i	−0.662055	+	0.789007i	−0.987679	−	0.156493i	$-0.949981\pi$
$797$	−18.6906	+	22.2746i	−0.662055	+	0.789007i	0.325624	+	0.945499i	$0.394426\pi$
$798$	0.599380	+	5.51504i	0.0212178	+	0.195230i
$799$	−36.7873	−	13.3895i	−1.30144	−	0.473686i
$800$		0			0
$801$	−24.3686	−	12.7368i	−0.861022	−	0.450031i
$802$	3.37405	−	1.94801i	0.119142	−	0.0687865i
$803$	22.2362	−	3.92085i	0.784699	−	0.138364i
$804$	−1.71823	−	1.15014i	−0.0605974	−	0.0405624i
$805$		0			0
$806$	1.10343	−	6.25786i	0.0388667	−	0.220424i
$807$	47.0078	−	13.6594i	1.65475	−	0.480832i
$808$	7.97005	+	9.49834i	0.280385	+	0.334150i
$809$	−37.5077			−1.31870			−0.659350	−	0.751836i	$-0.729169\pi$
$809$	−37.5077			−1.31870			−0.659350	+	0.751836i	$0.729169\pi$
$810$		0			0
$811$	−9.23252			−0.324198			−0.162099	−	0.986775i	$-0.551826\pi$
$811$	−9.23252			−0.324198			−0.162099	+	0.986775i	$0.551826\pi$
$812$	0.314289	+	0.374555i	0.0110294	+	0.0131443i
$813$	28.7565	−	8.35597i	1.00854	−	0.293057i
$814$	−0.588495	+	3.33752i	−0.0206268	+	0.116980i
$815$		0			0
$816$	32.2431	+	21.5827i	1.12873	+	0.755546i
$817$	−47.2498	+	8.33141i	−1.65306	+	0.291479i
$818$	−0.389589	+	0.224929i	−0.0136217	+	0.00786447i
$819$	−0.797132	−	18.9776i	−0.0278540	−	0.663130i
$820$		0			0
$821$	−26.4820	−	9.63866i	−0.924228	−	0.336392i	−0.164309	−	0.986409i	$-0.552539\pi$
$821$	−26.4820	−	9.63866i	−0.924228	−	0.336392i	−0.759919	+	0.650017i	$0.774762\pi$
$822$	−0.0205307	−	0.188908i	−0.000716089	−	0.00658891i
$823$	14.1420	−	16.8538i	0.492959	−	0.587485i	−0.461009	−	0.887396i	$-0.652512\pi$
$823$	14.1420	−	16.8538i	0.492959	−	0.587485i	0.953967	+	0.299910i	$0.0969567\pi$
$824$	7.63281	+	6.40468i	0.265901	+	0.223118i
$825$		0			0
$826$	0.160244	+	0.0583240i	0.00557560	+	0.00202935i
$827$	−7.12323	−	4.11260i	−0.247699	−	0.143009i	0.371011	−	0.928628i	$-0.379011\pi$
$827$	−7.12323	−	4.11260i	−0.247699	−	0.143009i	−0.618710	+	0.785619i	$0.712344\pi$
$828$	8.01992	+	36.4608i	0.278712	+	1.26710i
$829$	−5.60468	−	9.70759i	−0.194659	−	0.337159i	0.752130	−	0.659015i	$-0.229027\pi$
$829$	−5.60468	−	9.70759i	−0.194659	−	0.337159i	−0.946789	+	0.321856i	$0.895693\pi$
$830$		0			0
$831$	−6.43417	+	3.16637i	−0.223199	+	0.109840i
$832$	−7.97468	−	21.9103i	−0.276472	−	0.759601i
$833$	−25.7865	−	4.54686i	−0.893451	−	0.157539i
$834$	−1.55325	+	1.61986i	−0.0537846	+	0.0560912i
$835$		0			0
$836$	−65.3648			−2.26069
$837$	−19.8743	−	24.8892i	−0.686958	−	0.860296i
$838$			8.86273i			0.306158i
$839$	−6.85960	+	5.75589i	−0.236820	+	0.198715i	−0.753472	−	0.657480i	$-0.771622\pi$
$839$	−6.85960	+	5.75589i	−0.236820	+	0.198715i	0.516652	+	0.856195i	$0.327178\pi$
$840$		0			0
$841$	−5.03187	+	28.5371i	−0.173513	+	0.984039i
$842$	−0.323723	−	0.889421i	−0.0111562	−	0.0306515i
$843$	−33.1748	−	2.20194i	−1.14260	−	0.0758390i
$844$	5.05076	+	28.6443i	0.173854	+	0.985977i
$845$		0			0
$846$	−5.09860	−	0.679825i	−0.175293	−	0.0233729i
$847$	−19.8786	−	11.4769i	−0.683035	−	0.394351i
$848$	0.453020	−	1.24466i	0.0155568	−	0.0427419i
$849$	6.67097	−	15.1270i	0.228947	−	0.519157i
$850$		0			0
$851$	12.2454	+	10.2751i	0.419766	+	0.352226i
$852$	−20.7172	−	9.13624i	−0.709760	−	0.313003i
$853$	−17.3097	+	47.5581i	−0.592674	+	1.62836i	0.172847	+	0.984949i	$0.444703\pi$
$853$	−17.3097	+	47.5581i	−0.592674	+	1.62836i	−0.765522	+	0.643410i	$0.777519\pi$
$854$	1.44349	−	2.50019i	0.0493951	−	0.0855548i
$855$		0			0
$856$	−0.591579	−	1.02465i	−0.0202198	−	0.0350217i
$857$	26.4841	−	4.66987i	0.904681	−	0.159520i	0.298094	−	0.954537i	$-0.403649\pi$
$857$	26.4841	−	4.66987i	0.904681	−	0.159520i	0.606587	+	0.795017i	$0.292538\pi$
$858$	−8.88369	−	0.589646i	−0.303284	−	0.0201302i
$859$	51.3051	−	18.6735i	1.75051	−	0.637133i	0.750782	−	0.660550i	$-0.229677\pi$
$859$	51.3051	−	18.6735i	1.75051	−	0.637133i	0.999726	+	0.0234172i	$0.00745462\pi$
$860$		0			0
$861$	−11.2218	−	2.75579i	−0.382437	−	0.0939170i
$862$	6.02689	+	7.18256i	0.205277	+	0.244639i
$863$		−	36.0299i		−	1.22647i	−0.789900	−	0.613235i	$-0.789868\pi$
$863$		−	36.0299i		−	1.22647i	0.789900	−	0.613235i	$-0.210132\pi$
$864$	15.2486	+	5.97344i	0.518767	+	0.203221i
$865$		0			0
$866$	3.74381	−	3.14143i	0.127220	−	0.106750i
$867$	−28.6184	−	27.4416i	−0.971932	−	0.931964i
$868$	−19.6165	−	3.45892i	−0.665828	−	0.117403i
$869$	−75.9635	+	27.6485i	−2.57689	+	0.937910i
$870$		0			0
$871$	−0.403881	−	2.29052i	−0.0136850	−	0.0776114i
$872$	0.540430	−	0.312018i	0.0183013	−	0.0105662i
$873$	−8.87409	−	40.3441i	−0.300342	−	1.36544i
$874$	6.13251	−	10.6218i	0.207435	−	0.359288i
$875$		0			0
$876$	−8.96055	−	12.2419i	−0.302749	−	0.413614i
$877$	4.95158	−	5.90106i	0.167203	−	0.199265i	−0.675936	−	0.736960i	$-0.736261\pi$
$877$	4.95158	−	5.90106i	0.167203	−	0.199265i	0.843139	+	0.537695i	$0.180705\pi$
$878$	1.28142	−	1.52714i	0.0432458	−	0.0515384i
$879$	10.9437	−	1.18937i	0.369122	−	0.0401165i
$880$		0			0
$881$	−8.21595	+	14.2305i	−0.276803	+	0.479436i	−0.970588	−	0.240745i	$-0.922608\pi$
$881$	−8.21595	+	14.2305i	−0.276803	+	0.479436i	0.693786	+	0.720181i	$0.255941\pi$
$882$	−3.43735	+	0.144382i	−0.115742	+	0.00486159i
$883$	1.57404	−	0.908772i	0.0529706	−	0.0305826i	−0.473281	−	0.880912i	$-0.656930\pi$
$883$	1.57404	−	0.908772i	0.0529706	−	0.0305826i	0.526251	+	0.850329i	$0.323597\pi$
$884$	7.90594	+	44.8368i	0.265906	+	1.50803i
$885$		0			0
$886$	−9.01397	+	3.28082i	−0.302830	+	0.110221i
$887$	−19.1288	−	3.37292i	−0.642281	−	0.113251i	−0.156985	−	0.987601i	$-0.550177\pi$
$887$	−19.1288	−	3.37292i	−0.642281	−	0.113251i	−0.485297	+	0.874350i	$0.661288\pi$
$888$	4.46021	−	1.29603i	0.149675	−	0.0434919i
$889$	−10.2979	+	8.64099i	−0.345382	+	0.289810i
$890$		0			0
$891$	−31.6598	+	31.4510i	−1.06064	+	1.05365i
$892$		−	8.96671i		−	0.300228i
$893$	−27.3054	−	32.5413i	−0.913740	−	1.08895i
$894$	−3.08178	−	10.6058i	−0.103070	−	0.354710i
$895$		0			0
$896$	12.7394	−	4.63677i	0.425594	−	0.154904i
$897$	−23.3598	+	34.8979i	−0.779961	+	1.16521i
$898$	2.65360	−	0.467901i	0.0885516	−	0.0156140i
$899$	0.461140	+	0.798718i	0.0153799	+	0.0266387i
$900$		0			0
$901$	−1.17936	+	2.04271i	−0.0392901	+	0.0680524i
$902$	−1.85248	+	5.08964i	−0.0616807	+	0.169466i
$903$	2.21336	+	20.3656i	0.0736559	+	0.677726i
$904$	−14.6471	−	12.2903i	−0.487154	−	0.408771i
$905$		0			0
$906$	1.46420	+	2.00038i	0.0486448	+	0.0664583i
$907$	11.8456	−	32.5455i	0.393327	−	1.08066i	−0.572146	−	0.820152i	$-0.693889\pi$
$907$	11.8456	−	32.5455i	0.393327	−	1.08066i	0.965473	−	0.260505i	$-0.0838889\pi$
$908$	0.332345	+	0.191880i	0.0110293	+	0.00636775i
$909$	23.1131	+	25.3074i	0.766613	+	0.839394i
$910$		0			0
$911$	−3.90409	−	22.1412i	−0.129348	−	0.733570i	−0.978630	−	0.205630i	$-0.934076\pi$
$911$	−3.90409	−	22.1412i	−0.129348	−	0.733570i	0.849282	−	0.527940i	$-0.177035\pi$
$912$	18.5898	+	37.7751i	0.615570	+	1.25086i
$913$	18.9625	+	52.0990i	0.627567	+	1.72423i
$914$	1.51831	−	8.61076i	0.0502212	−	0.284819i
$915$		0			0
$916$	−25.5908	+	21.4732i	−0.845542	+	0.709494i
$917$			14.2868i			0.471791i
$918$	−7.74945	−	4.72883i	−0.255770	−	0.156075i
$919$	21.3527			0.704360			0.352180	−	0.935932i	$-0.385440\pi$
$919$	21.3527			0.704360			0.352180	+	0.935932i	$0.385440\pi$
$920$		0			0
$921$	−14.4416	−	3.54650i	−0.475867	−	0.116861i
$922$	−4.95974	−	0.874535i	−0.163340	−	0.0288013i
$923$	−8.71122	−	23.9339i	−0.286733	−	0.787793i
$924$	−1.84837	+	27.8477i	−0.0608068	+	0.916122i
$925$		0			0
$926$	3.91066	+	6.77345i	0.128512	+	0.222589i
$927$	21.8228	+	16.8027i	0.716756	+	0.551872i
$928$	−0.410682	−	0.237108i	−0.0134813	−	0.00778344i
$929$	41.3431	+	15.0476i	1.35642	+	0.493697i	0.914946	−	0.403576i	$-0.132233\pi$
$929$	41.3431	+	15.0476i	1.35642	+	0.493697i	0.441476	+	0.897273i	$0.354455\pi$
$930$		0			0
$931$	−21.7652	−	18.2632i	−0.713327	−	0.598553i
$932$	−19.5474	+	23.2957i	−0.640297	+	0.763076i
$933$	18.1766	+	8.01584i	0.595075	+	0.262427i
$934$	3.65233	+	1.32934i	0.119508	+	0.0434973i
$935$		0			0
$936$	4.65086	+	11.2809i	0.152018	+	0.368728i
$937$	−1.83833	+	1.06136i	−0.0600555	+	0.0346731i	−0.529727	−	0.848168i	$-0.677706\pi$
$937$	−1.83833	+	1.06136i	−0.0600555	+	0.0346731i	0.469672	+	0.882841i	$0.344372\pi$
$938$	0.285634	−	0.0503649i	0.00932627	−	0.00164447i
$939$	−2.86232	+	43.1240i	−0.0934082	+	1.40730i
$940$		0			0
$941$	9.63291	−	54.6309i	0.314024	−	1.78092i	−0.263617	−	0.964627i	$-0.584916\pi$
$941$	9.63291	−	54.6309i	0.314024	−	1.78092i	0.577641	−	0.816291i	$-0.303973\pi$
$942$	1.58295	−	6.44589i	0.0515753	−	0.210018i
$943$	16.4215	+	19.5704i	0.534759	+	0.637301i
$944$	1.29418			0.0421220
$945$		0			0
$946$	9.60222			0.312195
$947$	−5.80959	−	6.92360i	−0.188786	−	0.224987i	0.663346	−	0.748312i	$-0.269136\pi$
$947$	−5.80959	−	6.92360i	−0.188786	−	0.224987i	−0.852133	+	0.523326i	$0.824691\pi$
$948$	39.2041	+	37.5919i	1.27329	+	1.22093i
$949$	2.96338	−	16.8062i	0.0961953	−	0.545551i
$950$		0			0
$951$	0.985732	−	0.485096i	0.0319646	−	0.0157303i
$952$	−11.4049	+	2.01100i	−0.369636	+	0.0651769i
$953$	−14.1093	+	8.14599i	−0.457044	+	0.263874i	−0.710801	−	0.703394i	$-0.751667\pi$
$953$	−14.1093	+	8.14599i	−0.457044	+	0.263874i	0.253757	+	0.967268i	$0.418334\pi$
$954$	−0.0936815	+	0.295415i	−0.00303305	+	0.00956442i
$955$		0			0
$956$	−54.2547	−	19.7471i	−1.75472	−	0.638666i
$957$	1.04273	−	0.763239i	0.0337068	−	0.0246720i
$958$	1.24572	−	1.48459i	0.0402472	−	0.0479648i
$959$	−0.513282	−	0.430695i	−0.0165747	−	0.0139079i
$960$		0			0
$961$	−6.17624	−	2.24797i	−0.199233	−	0.0725150i
$962$	2.21825	+	1.28071i	0.0715193	+	0.0412917i
$963$	−1.75265	−	2.76118i	−0.0564785	−	0.0889779i
$964$	3.45199	+	5.97902i	0.111181	+	0.192571i
$965$		0			0
$966$	−4.35185	−	2.91302i	−0.140019	−	0.0937250i
$967$	16.3693	+	44.9743i	0.526402	+	1.44628i	0.863279	+	0.504728i	$0.168407\pi$
$967$	16.3693	+	44.9743i	0.526402	+	1.44628i	−0.336877	+	0.941549i	$0.609371\pi$
$968$	14.5216	+	2.56054i	0.466741	+	0.0822990i
$969$	−20.9202	−	71.9957i	−0.672055	−	2.31284i
$970$		0			0
$971$	17.2383			0.553202			0.276601	−	0.960985i	$-0.410792\pi$
$971$	17.2383			0.553202			0.276601	+	0.960985i	$0.410792\pi$
$972$	28.3528	+	9.75540i	0.909415	+	0.312905i
$973$			7.91350i			0.253695i
$974$	−4.29795	+	3.60641i	−0.137715	+	0.115557i
$975$		0			0
$976$	3.80463	−	21.5771i	0.121783	−	0.690667i
$977$	4.78345	+	13.1424i	0.153036	+	0.420463i	0.992392	−	0.123119i	$-0.0392898\pi$
$977$	4.78345	+	13.1424i	0.153036	+	0.420463i	−0.839356	+	0.543582i	$0.817068\pi$
$978$	−0.794434	+	1.18683i	−0.0254032	+	0.0379506i
$979$	7.89175	+	44.7563i	0.252221	+	1.43042i
$980$		0			0
$981$	1.45634	−	0.924405i	0.0464972	−	0.0295140i
$982$	1.20491	+	0.695657i	0.0384503	+	0.0221993i
$983$	−6.61856	+	18.1844i	−0.211099	+	0.579991i	−0.999376	−	0.0353306i	$-0.988752\pi$
$983$	−6.61856	+	18.1844i	−0.211099	+	0.579991i	0.788276	+	0.615322i	$0.210974\pi$
$984$	7.37964	−	0.802026i	0.235254	−	0.0255677i
$985$		0			0
$986$	0.201374	+	0.168973i	0.00641306	+	0.00538120i
$987$	−14.6359	+	10.7129i	−0.465864	+	0.340994i
$988$	−16.8967	+	46.4234i	−0.537557	+	1.47693i
$989$	22.6458	−	39.2236i	0.720094	−	1.24724i
$990$		0			0
$991$	8.67263	+	15.0214i	0.275495	+	0.477172i	0.970260	−	0.242065i	$-0.0778249\pi$
$991$	8.67263	+	15.0214i	0.275495	+	0.477172i	−0.694765	+	0.719237i	$0.744492\pi$
$992$	19.0255	−	3.35470i	0.604059	−	0.106512i
$993$	15.4277	+	31.3497i	0.489584	+	0.994851i
$994$	2.98461	−	1.08631i	0.0946661	−	0.0344557i
$995$		0			0
$996$	25.7822	−	26.8879i	0.816939	−	0.851974i
$997$	11.5520	+	13.7671i	0.365855	+	0.436009i	0.917297	−	0.398204i	$-0.130366\pi$
$997$	11.5520	+	13.7671i	0.365855	+	0.436009i	−0.551442	+	0.834214i	$0.685922\pi$
$998$		−	6.61118i		−	0.209273i
$999$	12.1676	−	4.09671i	0.384966	−	0.129614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.e.49.13		132
5.2	odd	4		675.2.l.g.76.5	yes	66
5.3	odd	4		675.2.l.f.76.7	✓	66
5.4	even	2	inner	675.2.u.e.49.10		132
27.16	even	9	inner	675.2.u.e.124.10		132
135.43	odd	36		675.2.l.f.151.7	yes	66
135.97	odd	36		675.2.l.g.151.5	yes	66
135.124	even	18	inner	675.2.u.e.124.13		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.7	✓	66	5.3	odd	4
675.2.l.f.151.7	yes	66	135.43	odd	36
675.2.l.g.76.5	yes	66	5.2	odd	4
675.2.l.g.151.5	yes	66	135.97	odd	36
675.2.u.e.49.10		132	5.4	even	2	inner
675.2.u.e.49.13		132	1.1	even	1	trivial
675.2.u.e.124.10		132	27.16	even	9	inner
675.2.u.e.124.13		132	135.124	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.177808 + 0.211903i) q^{2} +(-1.66326 + 0.483303i) q^{3} +(0.334009 - 1.89426i) q^{4} +(-0.398153 - 0.266514i) q^{6} +(-1.66379 + 0.293371i) q^{7} +(0.939908 - 0.542656i) q^{8} +(2.53284 - 1.60771i) q^{9} +(-4.65944 - 1.69590i) q^{11} +(0.359958 + 3.31206i) q^{12} +(-2.40892 + 2.87084i) q^{13} +(-0.358001 - 0.300398i) q^{14} +(-3.33285 - 1.21306i) q^{16} +(5.46979 + 3.15798i) q^{17} +(0.791037 + 0.250852i) q^{18} +(3.42671 + 5.93524i) q^{19} +(2.62552 - 1.29206i) q^{21} +(-0.469119 - 1.28889i) q^{22} +(-6.37131 - 1.12343i) q^{23} +(-1.30104 + 1.35684i) q^{24} -1.03667 q^{26} +(-3.43574 + 3.89816i) q^{27} +3.24964i q^{28} +(0.115261 - 0.0967151i) q^{29} +(-1.06440 + 6.03653i) q^{31} +(-1.07795 - 2.96165i) q^{32} +(8.56948 + 0.568791i) q^{33} +(0.303384 + 1.72058i) q^{34} +(-2.19943 - 5.33484i) q^{36} +(-2.13979 - 1.23541i) q^{37} +(-0.648400 + 1.78146i) q^{38} +(2.61917 - 5.93918i) q^{39} +(-3.02499 - 2.53826i) q^{41} +(0.740630 + 0.326617i) q^{42} +(-2.39437 + 6.57849i) q^{43} +(-4.76877 + 8.25975i) q^{44} +(-0.894809 - 1.54985i) q^{46} +(-6.10414 + 1.07632i) q^{47} +(6.12965 + 0.406850i) q^{48} +(-3.89572 + 1.41793i) q^{49} +(-10.6239 - 2.60897i) q^{51} +(4.63352 + 5.52201i) q^{52} +0.373453i q^{53} +(-1.43693 - 0.0349210i) q^{54} +(-1.40461 + 1.17861i) q^{56} +(-8.56802 - 8.21568i) q^{57} +(0.0409885 + 0.00722737i) q^{58} +(-0.342887 + 0.124801i) q^{59} +(1.07271 + 6.08365i) q^{61} +(-1.46842 + 0.847791i) q^{62} +(-3.74245 + 3.41795i) q^{63} +(-3.11083 + 5.38811i) q^{64} +(1.40319 + 1.91703i) q^{66} +(-0.398928 + 0.475424i) q^{67} +(7.80900 - 9.30640i) q^{68} +(11.1401 - 1.21071i) q^{69} +(-3.39814 + 5.88576i) q^{71} +(1.50820 - 2.88556i) q^{72} +(-3.94359 + 2.27683i) q^{73} +(-0.118685 - 0.673094i) q^{74} +(12.3874 - 4.50866i) q^{76} +(8.24986 + 1.45467i) q^{77} +(1.72424 - 0.501023i) q^{78} +(12.4889 - 10.4794i) q^{79} +(3.83053 - 8.14414i) q^{81} -1.09233i q^{82} +(-7.18726 - 8.56544i) q^{83} +(-1.57056 - 5.40498i) q^{84} +(-1.81974 + 0.662331i) q^{86} +(-0.144965 + 0.216568i) q^{87} +(-5.29974 + 0.934487i) q^{88} +(-4.58274 - 7.93753i) q^{89} +(3.16572 - 5.48319i) q^{91} +(-4.25615 + 11.6937i) q^{92} +(-1.14710 - 10.5547i) q^{93} +(-1.31344 - 1.10211i) q^{94} +(3.22429 + 4.40501i) q^{96} +(4.70945 - 12.9391i) q^{97} +(-0.993152 - 0.573397i) q^{98} +(-14.5281 + 3.19561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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