LMFDB - Embedded newform 925.2.bc.e.49.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(49,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14]))

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

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

chi := DirichletCharacter("925.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bc (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.20
Character	$\chi$	$=$	925.49
Dual form			925.2.bc.e.774.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04160 + 1.24133i) q^{2} +(-0.916161 + 1.09184i) q^{3} +(-0.108678 + 0.616341i) q^{4} -2.30961 q^{6} +(-1.01845 - 2.79817i) q^{7} +(1.92841 - 1.11337i) q^{8} +(0.168185 + 0.953823i) q^{9} +O(q^{10})$	\(q+(1.04160 + 1.24133i) q^{2} +(-0.916161 + 1.09184i) q^{3} +(-0.108678 + 0.616341i) q^{4} -2.30961 q^{6} +(-1.01845 - 2.79817i) q^{7} +(1.92841 - 1.11337i) q^{8} +(0.168185 + 0.953823i) q^{9} +(1.28658 + 2.22843i) q^{11} +(-0.573379 - 0.683326i) q^{12} +(4.71774 + 0.831864i) q^{13} +(2.41264 - 4.17882i) q^{14} +(4.56692 + 1.66222i) q^{16} +(-3.07296 + 0.541846i) q^{17} +(-1.00883 + 1.20228i) q^{18} +(0.591780 + 0.496563i) q^{19} +(3.98822 + 1.45159i) q^{21} +(-1.42611 + 3.91821i) q^{22} +(1.82372 + 1.05293i) q^{23} +(-0.551117 + 3.12554i) q^{24} +(3.88139 + 6.72276i) q^{26} +(-4.89853 - 2.82817i) q^{27} +(1.83531 - 0.323615i) q^{28} +(3.18174 + 5.51093i) q^{29} +9.39971 q^{31} +(1.17036 + 3.21555i) q^{32} +(-3.61180 - 0.636857i) q^{33} +(-3.87342 - 3.25018i) q^{34} -0.606159 q^{36} +(-5.54118 + 2.50905i) q^{37} +1.25182i q^{38} +(-5.23047 + 4.38888i) q^{39} +(-0.812712 + 4.60912i) q^{41} +(2.35223 + 6.46269i) q^{42} +3.55740i q^{43} +(-1.51329 + 0.550794i) q^{44} +(0.592560 + 3.36058i) q^{46} +(3.67619 + 2.12245i) q^{47} +(-5.99891 + 3.46347i) q^{48} +(-1.43021 + 1.20009i) q^{49} +(2.22372 - 3.85159i) q^{51} +(-1.02542 + 2.81733i) q^{52} +(1.89374 - 5.20300i) q^{53} +(-1.59162 - 9.02654i) q^{54} +(-5.07939 - 4.26212i) q^{56} +(-1.08433 + 0.191197i) q^{57} +(-3.52680 + 9.68981i) q^{58} +(-3.25692 - 1.18542i) q^{59} +(-1.15054 + 6.52502i) q^{61} +(9.79077 + 11.6682i) q^{62} +(2.49767 - 1.44203i) q^{63} +(2.08749 - 3.61565i) q^{64} +(-2.97151 - 5.14680i) q^{66} +(-4.27336 - 11.7410i) q^{67} -1.95288i q^{68} +(-2.82045 + 1.02656i) q^{69} +(-4.65562 - 3.90653i) q^{71} +(1.38629 + 1.65211i) q^{72} -6.74732i q^{73} +(-8.88628 - 4.26502i) q^{74} +(-0.370365 + 0.310773i) q^{76} +(4.92519 - 5.86962i) q^{77} +(-10.8961 - 1.92128i) q^{78} +(12.7155 - 4.62808i) q^{79} +(4.84536 - 1.76357i) q^{81} +(-6.56798 + 3.79203i) q^{82} +(-12.9084 + 2.27610i) q^{83} +(-1.32811 + 2.30035i) q^{84} +(-4.41592 + 3.70540i) q^{86} +(-8.93203 - 1.57496i) q^{87} +(4.96212 + 2.86488i) q^{88} +(-11.9729 - 4.35777i) q^{89} +(-2.47708 - 14.0482i) q^{91} +(-0.847159 + 1.00960i) q^{92} +(-8.61165 + 10.2630i) q^{93} +(1.19446 + 6.77413i) q^{94} +(-4.58310 - 1.66811i) q^{96} +(4.82854 + 2.78776i) q^{97} +(-2.97942 - 0.525352i) q^{98} +(-1.90914 + 1.60196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{4}+O(q^{10}) $ 156 * q - 6 * q^4	$ 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) $ 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	1.04160	+	1.24133i	0.736525	+	0.877756i	0.996124	−	0.0879603i	$-0.0280349\pi$
$2$	1.04160	+	1.24133i	0.736525	+	0.877756i	−0.259599	+	0.965716i	$0.583590\pi$
$3$	−0.916161	+	1.09184i	−0.528946	+	0.630373i	−0.962672	−	0.270672i	$-0.912754\pi$
$3$	−0.916161	+	1.09184i	−0.528946	+	0.630373i	0.433726	+	0.901045i	$0.357199\pi$
$4$	−0.108678	+	0.616341i	−0.0543388	+	0.308171i
$5$		0			0
$5$		0			0
$6$	−2.30961			−0.942896
$7$	−1.01845	−	2.79817i	−0.384938	−	1.05761i	−0.969250	−	0.246080i	$-0.920857\pi$
$7$	−1.01845	−	2.79817i	−0.384938	−	1.05761i	0.584311	−	0.811530i	$-0.301365\pi$
$8$	1.92841	−	1.11337i	0.681797	−	0.393635i
$9$	0.168185	+	0.953823i	0.0560616	+	0.317941i
$10$		0			0
$11$	1.28658	+	2.22843i	0.387919	+	0.671896i	0.992169	−	0.124899i	$-0.0398607\pi$
$11$	1.28658	+	2.22843i	0.387919	+	0.671896i	−0.604250	+	0.796794i	$0.706527\pi$
$12$	−0.573379	−	0.683326i	−0.165520	−	0.197259i
$13$	4.71774	+	0.831864i	1.30846	+	0.230718i	0.784024	−	0.620730i	$-0.213164\pi$
$13$	4.71774	+	0.831864i	1.30846	+	0.230718i	0.524440	+	0.851447i	$0.324275\pi$
$14$	2.41264	−	4.17882i	0.644806	−	1.11684i
$15$		0			0
$16$	4.56692	+	1.66222i	1.14173	+	0.415555i
$17$	−3.07296	+	0.541846i	−0.745302	+	0.131417i	−0.533387	−	0.845871i	$-0.679081\pi$
$17$	−3.07296	+	0.541846i	−0.745302	+	0.131417i	−0.211915	+	0.977288i	$0.567970\pi$
$18$	−1.00883	+	1.20228i	−0.237784	+	0.283380i
$19$	0.591780	+	0.496563i	0.135764	+	0.113919i	0.708141	−	0.706071i	$-0.249534\pi$
$19$	0.591780	+	0.496563i	0.135764	+	0.113919i	−0.572377	+	0.819991i	$0.693979\pi$
$20$		0			0
$21$	3.98822	+	1.45159i	0.870300	+	0.316763i
$22$	−1.42611	+	3.91821i	−0.304048	+	0.835366i
$23$	1.82372	+	1.05293i	0.380272	+	0.219550i	0.677937	−	0.735120i	$-0.262874\pi$
$23$	1.82372	+	1.05293i	0.380272	+	0.219550i	−0.297665	+	0.954670i	$0.596208\pi$
$24$	−0.551117	+	3.12554i	−0.112496	+	0.637998i
$25$		0			0
$26$	3.88139	+	6.72276i	0.761203	+	1.31844i
$27$	−4.89853	−	2.82817i	−0.942722	−	0.544281i
$28$	1.83531	−	0.323615i	0.346841	−	0.0611575i
$29$	3.18174	+	5.51093i	0.590834	+	1.02335i	0.994120	+	0.108281i	$0.0345346\pi$
$29$	3.18174	+	5.51093i	0.590834	+	1.02335i	−0.403286	+	0.915074i	$0.632132\pi$
$30$		0			0
$31$	9.39971			1.68824			0.844119	−	0.536156i	$-0.180124\pi$
$31$	9.39971			1.68824			0.844119	+	0.536156i	$0.180124\pi$
$32$	1.17036	+	3.21555i	0.206893	+	0.568434i
$33$	−3.61180	−	0.636857i	−0.628733	−	0.110863i
$34$	−3.87342	−	3.25018i	−0.664286	−	0.557402i
$35$		0			0
$36$	−0.606159			−0.101026
$37$	−5.54118	+	2.50905i	−0.910964	+	0.412485i
$37$	−5.54118	+	2.50905i	−0.910964	+	0.412485i
$38$			1.25182i			0.203072i
$39$	−5.23047	+	4.38888i	−0.837545	+	0.702784i
$40$		0			0
$41$	−0.812712	+	4.60912i	−0.126924	+	0.719823i	0.853222	+	0.521548i	$0.174645\pi$
$41$	−0.812712	+	4.60912i	−0.126924	+	0.719823i	−0.980146	+	0.198275i	$0.936466\pi$
$42$	2.35223	+	6.46269i	0.362957	+	0.997215i
$43$			3.55740i			0.542498i	0.962509	+	0.271249i	$0.0874367\pi$
$43$			3.55740i			0.542498i	−0.962509	+	0.271249i	$0.912563\pi$
$44$	−1.51329	+	0.550794i	−0.228138	+	0.0830353i
$45$		0			0
$46$	0.592560	+	3.36058i	0.0873683	+	0.495490i
$47$	3.67619	+	2.12245i	0.536227	+	0.309591i	0.743548	−	0.668682i	$-0.233141\pi$
$47$	3.67619	+	2.12245i	0.536227	+	0.309591i	−0.207321	+	0.978273i	$0.566475\pi$
$48$	−5.99891	+	3.46347i	−0.865868	+	0.499909i
$49$	−1.43021	+	1.20009i	−0.204316	+	0.171441i
$50$		0			0
$51$	2.22372	−	3.85159i	0.311383	−	0.539331i
$52$	−1.02542	+	2.81733i	−0.142201	+	0.390693i
$53$	1.89374	−	5.20300i	0.260125	−	0.714687i	−0.739033	−	0.673669i	$-0.764717\pi$
$53$	1.89374	−	5.20300i	0.260125	−	0.714687i	0.999158	−	0.0410187i	$-0.0130603\pi$
$54$	−1.59162	−	9.02654i	−0.216592	−	1.22836i
$55$		0			0
$56$	−5.07939	−	4.26212i	−0.678762	−	0.569549i
$57$	−1.08433	+	0.191197i	−0.143623	+	0.0253247i
$58$	−3.52680	+	9.68981i	−0.463092	+	1.27233i
$59$	−3.25692	−	1.18542i	−0.424015	−	0.154329i	0.121195	−	0.992629i	$-0.461328\pi$
$59$	−3.25692	−	1.18542i	−0.424015	−	0.154329i	−0.545209	+	0.838300i	$0.683550\pi$
$60$		0			0
$61$	−1.15054	+	6.52502i	−0.147311	+	0.835443i	0.818171	+	0.574975i	$0.194988\pi$
$61$	−1.15054	+	6.52502i	−0.147311	+	0.835443i	−0.965482	+	0.260468i	$0.916123\pi$
$62$	9.79077	+	11.6682i	1.24343	+	1.48186i
$63$	2.49767	−	1.44203i	0.314677	−	0.181679i
$64$	2.08749	−	3.61565i	0.260937	−	0.451956i
$65$		0			0
$66$	−2.97151	−	5.14680i	−0.365767	−	0.633527i
$67$	−4.27336	−	11.7410i	−0.522074	−	1.43439i	−0.868207	−	0.496202i	$-0.834727\pi$
$67$	−4.27336	−	11.7410i	−0.522074	−	1.43439i	0.346133	−	0.938186i	$-0.387495\pi$
$68$		−	1.95288i		−	0.236821i
$69$	−2.82045	+	1.02656i	−0.339542	+	0.123583i
$70$		0			0
$71$	−4.65562	−	3.90653i	−0.552520	−	0.463619i	0.323273	−	0.946306i	$-0.395217\pi$
$71$	−4.65562	−	3.90653i	−0.552520	−	0.463619i	−0.875793	+	0.482686i	$0.839661\pi$
$72$	1.38629	+	1.65211i	0.163376	+	0.194703i
$73$		−	6.74732i		−	0.789714i	−0.918743	−	0.394857i	$-0.870794\pi$
$73$		−	6.74732i		−	0.789714i	0.918743	−	0.394857i	$-0.129206\pi$
$74$	−8.88628	−	4.26502i	−1.03301	−	0.495799i
$75$		0			0
$76$	−0.370365	+	0.310773i	−0.0424838	+	0.0356482i
$77$	4.92519	−	5.86962i	0.561278	−	0.668905i
$78$	−10.8961	−	1.92128i	−1.23375	−	0.217543i
$79$	12.7155	−	4.62808i	1.43061	−	0.520700i	0.493504	−	0.869744i	$-0.335716\pi$
$79$	12.7155	−	4.62808i	1.43061	−	0.520700i	0.937106	+	0.349044i	$0.113494\pi$
$80$		0			0
$81$	4.84536	−	1.76357i	0.538373	−	0.195952i
$82$	−6.56798	+	3.79203i	−0.725312	+	0.418759i
$83$	−12.9084	+	2.27610i	−1.41688	+	0.249834i	−0.829061	−	0.559158i	$-0.811125\pi$
$83$	−12.9084	+	2.27610i	−1.41688	+	0.249834i	−0.587820	+	0.808992i	$0.700014\pi$
$84$	−1.32811	+	2.30035i	−0.144908	+	0.250988i
$85$		0			0
$86$	−4.41592	+	3.70540i	−0.476181	+	0.399563i
$87$	−8.93203	−	1.57496i	−0.957615	−	0.168853i
$88$	4.96212	+	2.86488i	0.528964	+	0.305397i
$89$	−11.9729	−	4.35777i	−1.26912	−	0.461923i	−0.382302	−	0.924037i	$-0.624869\pi$
$89$	−11.9729	−	4.35777i	−1.26912	−	0.461923i	−0.886820	+	0.462115i	$0.847091\pi$
$90$		0			0
$91$	−2.47708	−	14.0482i	−0.259669	−	1.47266i
$92$	−0.847159	+	1.00960i	−0.0883224	+	0.105259i
$93$	−8.61165	+	10.2630i	−0.892986	+	1.06422i
$94$	1.19446	+	6.77413i	0.123199	+	0.698698i
$95$		0			0
$96$	−4.58310	−	1.66811i	−0.467761	−	0.170251i
$97$	4.82854	+	2.78776i	0.490264	+	0.283054i	0.724684	−	0.689081i	$-0.241986\pi$
$97$	4.82854	+	2.78776i	0.490264	+	0.283054i	−0.234420	+	0.972135i	$0.575319\pi$
$98$	−2.97942	−	0.525352i	−0.300967	−	0.0530686i
$99$	−1.90914	+	1.60196i	−0.191876	+	0.161003i
$100$		0			0
$101$	−5.01199	+	8.68103i	−0.498712	+	0.863794i	−0.999999	−	0.00148673i	$-0.999527\pi$
$101$	−5.01199	+	8.68103i	−0.498712	+	0.863794i	0.501287	+	0.865281i	$0.332860\pi$
$102$	7.09735	−	1.25145i	0.702742	−	0.123912i
$103$	2.68276	−	1.54889i	0.264340	−	0.152617i	−0.361973	−	0.932189i	$-0.617897\pi$
$103$	2.68276	−	1.54889i	0.264340	−	0.152617i	0.626313	+	0.779572i	$0.284563\pi$
$104$	10.0239	−	3.64840i	0.982925	−	0.357756i
$105$		0			0
$106$	8.43119	−	3.06870i	0.818910	−	0.298059i
$107$	17.7647	+	3.13240i	1.71738	+	0.302821i	0.943712	−	0.330768i	$-0.107308\pi$
$107$	17.7647	+	3.13240i	1.71738	+	0.302821i	0.773670	+	0.633589i	$0.218419\pi$
$108$	2.27548	−	2.71181i	0.218958	−	0.260944i
$109$	0.893433	−	0.749679i	0.0855754	−	0.0718063i	−0.598996	−	0.800752i	$-0.704434\pi$
$109$	0.893433	−	0.749679i	0.0855754	−	0.0718063i	0.684572	+	0.728945i	$0.259989\pi$
$110$		0			0
$111$	2.33714	−	8.34877i	0.221831	−	0.792430i
$112$		−	14.4719i		−	1.36747i
$113$	4.11041	+	4.89859i	0.386675	+	0.460821i	0.923909	−	0.382612i	$-0.124975\pi$
$113$	4.11041	+	4.89859i	0.386675	+	0.460821i	−0.537234	+	0.843433i	$0.680531\pi$
$114$	−1.36678	−	1.14687i	−0.128011	−	0.107414i
$115$		0			0
$116$	−3.74240	+	1.36212i	−0.347473	+	0.126470i
$117$			4.63979i			0.428949i
$118$	−1.92091	−	5.27766i	−0.176834	−	0.485848i
$119$	4.64584	+	8.04682i	0.425883	+	0.737651i
$120$		0			0
$121$	2.18941	−	3.79218i	0.199038	−	0.344743i
$122$	−9.29813	+	5.36828i	−0.841813	+	0.486021i
$123$	−4.28784	−	5.11004i	−0.386621	−	0.460757i
$124$	−1.02154	+	5.79343i	−0.0917368	+	0.520265i
$125$		0			0
$126$	4.39163	+	1.59842i	0.391238	+	0.142399i
$127$	5.63420	−	15.4798i	0.499954	−	1.37361i	−0.391364	−	0.920236i	$-0.627997\pi$
$127$	5.63420	−	15.4798i	0.499954	−	1.37361i	0.891319	−	0.453377i	$-0.149781\pi$
$128$	13.4024	−	2.36321i	1.18462	−	0.208880i
$129$	−3.88410	−	3.25915i	−0.341976	−	0.286952i
$130$		0			0
$131$	0.380497	+	2.15790i	0.0332442	+	0.188537i	0.996908	−	0.0785823i	$-0.0250393\pi$
$131$	0.380497	+	2.15790i	0.0332442	+	0.188537i	−0.963663	+	0.267119i	$0.913928\pi$
$132$	0.785043	−	2.15689i	0.0683292	−	0.187733i
$133$	0.786768	−	2.16163i	0.0682214	−	0.187437i
$134$	10.1233	−	17.5341i	0.874522	−	1.51472i
$135$		0			0
$136$	−5.32266	+	4.46624i	−0.456414	+	0.382977i
$137$	−12.9863	+	7.49766i	−1.10950	+	0.640568i	−0.938699	−	0.344738i	$-0.887968\pi$
$137$	−12.9863	+	7.49766i	−1.10950	+	0.640568i	−0.170797	+	0.985306i	$0.554634\pi$
$138$	−4.21209	−	2.43185i	−0.358557	−	0.207013i
$139$	−2.00456	−	11.3684i	−0.170024	−	0.964256i	−0.943732	−	0.330712i	$-0.892711\pi$
$139$	−2.00456	−	11.3684i	−0.170024	−	0.964256i	0.773707	−	0.633543i	$-0.218400\pi$
$140$		0			0
$141$	−5.68535	+	2.06930i	−0.478793	+	0.174266i
$142$		−	9.84823i		−	0.826445i
$143$	4.21601	+	11.5834i	0.352560	+	0.968651i
$144$	−0.817380	+	4.63559i	−0.0681150	+	0.386299i
$145$		0			0
$146$	8.37568	−	7.02803i	0.693176	−	0.581644i
$147$		−	2.66103i		−	0.219478i
$148$	−0.944228	−	3.68794i	−0.0776151	−	0.303146i
$149$	3.27724			0.268482			0.134241	−	0.990949i	$-0.457140\pi$
$149$	3.27724			0.268482			0.134241	+	0.990949i	$0.457140\pi$
$150$		0			0
$151$	12.0644	+	10.1232i	0.981785	+	0.823815i	0.984358	−	0.176182i	$-0.0563746\pi$
$151$	12.0644	+	10.1232i	0.981785	+	0.823815i	−0.00257308	+	0.999997i	$0.500819\pi$
$152$	1.69405	+	0.298707i	0.137406	+	0.0242284i
$153$	−1.03365	−	2.83993i	−0.0835657	−	0.229595i
$154$	12.4163			1.00053
$155$		0			0
$156$	−2.13662	−	3.70073i	−0.171066	−	0.296295i
$157$	−5.13675	+	0.905748i	−0.409957	+	0.0722865i	−0.374824	−	0.927096i	$-0.622297\pi$
$157$	−5.13675	+	0.905748i	−0.409957	+	0.0722865i	−0.0351336	+	0.999383i	$0.511186\pi$
$158$	18.9895	+	10.9636i	1.51073	+	0.872219i
$159$	3.94587	+	6.83445i	0.312928	+	0.542007i
$160$		0			0
$161$	1.08890	−	6.17543i	0.0858170	−	0.486692i
$162$	7.23612	+	4.17777i	0.568523	+	0.328237i
$163$	−5.44512	+	14.9603i	−0.426494	+	1.17178i	0.521431	+	0.853293i	$0.325398\pi$
$163$	−5.44512	+	14.9603i	−0.426494	+	1.17178i	−0.947926	+	0.318491i	$0.896824\pi$
$164$	−2.75247	−	1.00182i	−0.214932	−	0.0782287i
$165$		0			0
$166$	−16.2708	−	13.6529i	−1.26286	−	1.05967i
$167$	2.79338	−	3.32902i	0.216158	−	0.257607i	−0.647059	−	0.762440i	$-0.724001\pi$
$167$	2.79338	−	3.32902i	0.216158	−	0.257607i	0.863217	+	0.504832i	$0.168446\pi$
$168$	9.30708	−	1.64109i	0.718057	−	0.126613i
$169$	9.34902	+	3.40277i	0.719156	+	0.261751i
$170$		0			0
$171$	−0.374105	+	0.647968i	−0.0286085	+	0.0495514i
$172$	−2.19257	−	0.386610i	−0.167182	−	0.0294787i
$173$	−9.77503	−	11.6494i	−0.743182	−	0.885690i	0.253479	−	0.967341i	$-0.418425\pi$
$173$	−9.77503	−	11.6494i	−0.743182	−	0.885690i	−0.996661	+	0.0816513i	$0.973981\pi$
$174$	−7.34859	−	12.7281i	−0.557095	−	0.964917i
$175$		0			0
$176$	2.17158	+	12.3156i	0.163689	+	0.928325i
$177$	4.27815	−	2.46999i	0.321565	−	0.185656i
$178$	−7.06154	−	19.4014i	−0.529285	−	1.45420i
$179$	−8.22680			−0.614900			−0.307450	−	0.951564i	$-0.599476\pi$
$179$	−8.22680			−0.614900			−0.307450	+	0.951564i	$0.599476\pi$
$180$		0			0
$181$	2.81930	−	15.9891i	0.209557	−	1.18846i	−0.680548	−	0.732703i	$-0.738258\pi$
$181$	2.81930	−	15.9891i	0.209557	−	1.18846i	0.890105	−	0.455755i	$-0.150631\pi$
$182$	14.8584	−	17.7076i	1.10138	−	1.31257i
$183$	−6.07019	−	7.23417i	−0.448721	−	0.534765i
$184$	4.68918			0.345691
$185$		0			0
$186$	−21.7097			−1.59183
$187$	−5.16108	−	6.15073i	−0.377415	−	0.449786i
$188$	−1.70767	+	2.03512i	−0.124545	+	0.148427i
$189$	−2.92478	+	16.5873i	−0.212747	+	1.20655i
$190$		0			0
$191$	−22.9771			−1.66257			−0.831283	−	0.555850i	$-0.812393\pi$
$191$	−22.9771			−1.66257			−0.831283	+	0.555850i	$0.812393\pi$
$192$	2.03522	+	5.59172i	0.146879	+	0.403548i
$193$	−2.78749	+	1.60936i	−0.200648	+	0.115844i	−0.596958	−	0.802273i	$-0.703624\pi$
$193$	−2.78749	+	1.60936i	−0.200648	+	0.115844i	0.396310	+	0.918117i	$0.370291\pi$
$194$	1.56888	+	8.89757i	0.112639	+	0.638808i
$195$		0			0
$196$	−0.584232	−	1.01192i	−0.0417309	−	0.0722800i
$197$	−1.16169	−	1.38445i	−0.0827671	−	0.0986379i	0.723072	−	0.690773i	$-0.242730\pi$
$197$	−1.16169	−	1.38445i	−0.0827671	−	0.0986379i	−0.805839	+	0.592135i	$0.798285\pi$
$198$	−3.97714	−	0.701276i	−0.282643	−	0.0498375i
$199$	−5.41270	+	9.37507i	−0.383696	+	0.664581i	−0.991587	−	0.129439i	$-0.958682\pi$
$199$	−5.41270	+	9.37507i	−0.383696	+	0.664581i	0.607891	+	0.794020i	$0.292016\pi$
$200$		0			0
$201$	16.7343	+	6.09080i	1.18035	+	0.429612i
$202$	−15.9966	+	2.82063i	−1.12551	+	0.198459i
$203$	12.1801	−	14.5157i	0.854875	−	1.01880i
$204$	2.13223	+	1.78915i	0.149286	+	0.125266i
$205$		0			0
$206$	4.71706	+	1.71687i	0.328653	+	0.119620i
$207$	−0.697583	+	1.91659i	−0.0484854	+	0.133212i
$208$	20.1628	+	11.6410i	1.39804	+	0.807156i
$209$	−0.345179	+	1.95761i	−0.0238765	+	0.135411i
$210$		0			0
$211$	−3.50895	−	6.07768i	−0.241566	−	0.418405i	0.719594	−	0.694395i	$-0.244328\pi$
$211$	−3.50895	−	6.07768i	−0.241566	−	0.418405i	−0.961161	+	0.275990i	$0.910994\pi$
$212$	3.00102	+	1.73264i	0.206111	+	0.118998i
$213$	8.53059	−	1.50417i	0.584506	−	0.103064i
$214$	14.6155	+	25.3147i	0.999092	+	1.73048i
$215$		0			0
$216$	−12.5952			−0.856993
$217$	−9.57314	−	26.3020i	−0.649867	−	1.78550i
$218$	1.86121	+	0.328181i	0.126057	+	0.0222272i
$219$	7.36698	+	6.18163i	0.497815	+	0.417716i
$220$		0			0
$221$	−14.9482			−1.00552
$222$	12.7980	−	5.79493i	0.858944	−	0.388930i
$223$		−	26.3947i		−	1.76752i	−0.467940	−	0.883760i	$-0.655004\pi$
$223$		−	26.3947i		−	1.76752i	0.467940	−	0.883760i	$-0.344996\pi$
$224$	7.80570	−	6.54976i	0.521540	−	0.437624i
$225$		0			0
$226$	−1.79938	+	10.2048i	−0.119693	+	0.678812i
$227$	−3.22906	−	8.87177i	−0.214320	−	0.588840i	0.785218	−	0.619219i	$-0.212551\pi$
$227$	−3.22906	−	8.87177i	−0.214320	−	0.588840i	−0.999538	+	0.0303792i	$0.990329\pi$
$228$		−	0.689098i		−	0.0456366i
$229$	−16.4174	+	5.97543i	−1.08489	+	0.394868i	−0.821725	−	0.569884i	$-0.806988\pi$
$229$	−16.4174	+	5.97543i	−1.08489	+	0.394868i	−0.263164	+	0.964751i	$0.584766\pi$
$230$		0			0
$231$	1.89640	+	10.7550i	0.124774	+	0.707629i
$232$	12.2714	+	7.08490i	0.805657	+	0.465147i
$233$	2.81355	−	1.62441i	0.184322	−	0.106418i	−0.405000	−	0.914317i	$-0.632728\pi$
$233$	2.81355	−	1.62441i	0.184322	−	0.106418i	0.589322	+	0.807898i	$0.299395\pi$
$234$	−5.75954	+	4.83283i	−0.376513	+	0.315932i
$235$		0			0
$236$	1.08458	−	1.87854i	0.0706000	−	0.122283i
$237$	−6.59637	+	18.1234i	−0.428480	+	1.17724i
$238$	−5.14968	+	14.1486i	−0.333804	+	0.917120i
$239$	−1.18172	−	6.70184i	−0.0764388	−	0.433506i	−0.998878	−	0.0473631i	$-0.984918\pi$
$239$	−1.18172	−	6.70184i	−0.0764388	−	0.433506i	0.922439	−	0.386143i	$-0.126193\pi$
$240$		0			0
$241$	−12.7007	−	10.6571i	−0.818122	−	0.686486i	0.134409	−	0.990926i	$-0.457086\pi$
$241$	−12.7007	−	10.6571i	−0.818122	−	0.686486i	−0.952532	+	0.304440i	$0.901531\pi$
$242$	6.98786	−	1.23215i	0.449197	−	0.0792055i
$243$	3.29014	−	9.03958i	0.211063	−	0.579890i
$244$	−3.89660	−	1.41825i	−0.249454	−	0.0907939i
$245$		0			0
$246$	1.87705	−	10.6453i	0.119676	−	0.678718i
$247$	2.37879	+	2.83493i	0.151359	+	0.180382i
$248$	18.1265	−	10.4653i	1.15103	−	0.664550i
$249$	9.34104	−	16.1792i	0.591965	−	1.02531i
$250$		0			0
$251$	−11.6361	−	20.1543i	−0.734462	−	1.27213i	−0.954959	−	0.296737i	$-0.904101\pi$
$251$	−11.6361	−	20.1543i	−0.734462	−	1.27213i	0.220497	−	0.975388i	$-0.429232\pi$
$252$	0.617343	+	1.69614i	0.0388890	+	0.106847i
$253$			5.41870i			0.340671i
$254$	25.0843	−	9.12992i	1.57393	−	0.572862i
$255$		0			0
$256$	10.4971	+	8.80811i	0.656068	+	0.550507i
$257$	−5.73476	−	6.83442i	−0.357724	−	0.426319i	0.556928	−	0.830561i	$-0.311980\pi$
$257$	−5.73476	−	6.83442i	−0.357724	−	0.426319i	−0.914652	+	0.404242i	$0.867536\pi$
$258$		−	8.21622i		−	0.511519i
$259$	12.6642	+	12.9498i	0.786913	+	0.804663i
$260$		0			0
$261$	−4.72134	+	3.96167i	−0.292243	+	0.245221i
$262$	−2.28236	+	2.72000i	−0.141004	+	0.168042i
$263$	8.85877	+	1.56204i	0.546255	+	0.0963195i	0.439964	−	0.898016i	$-0.354991\pi$
$263$	8.85877	+	1.56204i	0.546255	+	0.0963195i	0.106291	+	0.994335i	$0.466102\pi$
$264$	−7.67409	+	2.79314i	−0.472308	+	0.171906i
$265$		0			0
$266$	3.50280	−	1.27492i	0.214771	−	0.0781701i
$267$	15.7271	−	9.08002i	0.962481	−	0.555688i
$268$	7.70086	−	1.35787i	0.470405	−	0.0829451i
$269$	−1.95221	+	3.38133i	−0.119029	+	0.206164i	−0.919383	−	0.393364i	$-0.871311\pi$
$269$	−1.95221	+	3.38133i	−0.119029	+	0.206164i	0.800354	+	0.599527i	$0.204645\pi$
$270$		0			0
$271$	12.2833	−	10.3069i	0.746158	−	0.626101i	−0.188326	−	0.982107i	$-0.560306\pi$
$271$	12.2833	−	10.3069i	0.746158	−	0.626101i	0.934484	+	0.356006i	$0.115862\pi$
$272$	−14.9346	−	2.63338i	−0.905544	−	0.159672i
$273$	17.6078	+	10.1659i	1.06567	+	0.615267i
$274$	−22.8337	−	8.31079i	−1.37943	−	0.502073i
$275$		0			0
$276$	−0.326191	−	1.84992i	−0.0196344	−	0.111352i
$277$	−15.7006	+	18.7112i	−0.943357	+	1.12425i	0.0487447	+	0.998811i	$0.484478\pi$
$277$	−15.7006	+	18.7112i	−0.943357	+	1.12425i	−0.992102	+	0.125438i	$0.959967\pi$
$278$	12.0240	−	14.3297i	0.721154	−	0.859438i
$279$	1.58089	+	8.96566i	0.0946453	+	0.536760i
$280$		0			0
$281$	25.5631	+	9.30420i	1.52497	+	0.555042i	0.962383	−	0.271698i	$-0.0875852\pi$
$281$	25.5631	+	9.30420i	1.52497	+	0.555042i	0.562584	+	0.826740i	$0.309807\pi$
$282$	−8.49057	−	4.90203i	−0.505606	−	0.291912i
$283$	−8.45722	−	1.49124i	−0.502730	−	0.0886448i	−0.0834685	−	0.996510i	$-0.526600\pi$
$283$	−8.45722	−	1.49124i	−0.502730	−	0.0886448i	−0.419261	+	0.907866i	$0.637711\pi$
$284$	2.91371	−	2.44490i	0.172897	−	0.145078i
$285$		0			0
$286$	−9.98745	+	17.2988i	−0.590570	+	1.02290i
$287$	13.7248	−	2.42005i	0.810150	−	0.142851i
$288$	−2.87023	+	1.65713i	−0.169130	+	0.0976471i
$289$	−6.82529	+	2.48420i	−0.401488	+	0.146130i
$290$		0			0
$291$	−7.46750	+	2.71795i	−0.437753	+	0.159329i
$292$	4.15865	+	0.733283i	0.243367	+	0.0429121i
$293$	14.9859	−	17.8595i	0.875484	−	1.04336i	−0.123216	−	0.992380i	$-0.539321\pi$
$293$	14.9859	−	17.8595i	0.875484	−	1.04336i	0.998700	−	0.0509810i	$-0.0162348\pi$
$294$	3.30323	−	2.77174i	0.192648	−	0.161651i
$295$		0			0
$296$	−7.89218	+	11.0079i	−0.458724	+	0.639819i
$297$		−	14.5547i		−	0.844548i
$298$	3.41359	+	4.06816i	0.197744	+	0.235662i
$299$	7.72794	+	6.48451i	0.446918	+	0.375009i
$300$		0			0
$301$	9.95421	−	3.62304i	0.573751	−	0.208828i
$302$			25.5203i			1.46853i
$303$	−4.88648	−	13.4255i	−0.280721	−	0.771275i
$304$	1.87721	+	3.25143i	0.107666	+	0.186482i
$305$		0			0
$306$	2.44865	−	4.24119i	0.139980	−	0.242453i
$307$	−24.2923	+	14.0252i	−1.38644	+	0.800459i	−0.992912	−	0.118855i	$-0.962078\pi$
$307$	−24.2923	+	14.0252i	−1.38644	+	0.800459i	−0.393525	+	0.919314i	$0.628744\pi$
$308$	3.08243	+	3.67350i	0.175638	+	0.209317i
$309$	−0.766700	+	4.34817i	−0.0436160	+	0.247359i
$310$		0			0
$311$	18.7419	+	6.82148i	1.06275	+	0.386811i	0.813462	−	0.581618i	$-0.197580\pi$
$311$	18.7419	+	6.82148i	1.06275	+	0.386811i	0.249292	+	0.968428i	$0.419802\pi$
$312$	−5.20005	+	14.2870i	−0.294395	+	0.808843i
$313$	−19.1129	+	3.37011i	−1.08032	+	0.190490i	−0.685358	−	0.728206i	$-0.740354\pi$
$313$	−19.1129	+	3.37011i	−1.08032	+	0.190490i	−0.394965	+	0.918696i	$0.629243\pi$
$314$	−6.47479	−	5.43300i	−0.365394	−	0.306602i
$315$		0			0
$316$	1.47058	+	8.34008i	0.0827267	+	0.469166i
$317$	−10.1386	+	27.8557i	−0.569442	+	1.56453i	0.235936	+	0.971769i	$0.424185\pi$
$317$	−10.1386	+	27.8557i	−0.569442	+	1.56453i	−0.805378	+	0.592761i	$0.798038\pi$
$318$	−4.37380	+	12.0169i	−0.245271	+	0.673876i
$319$	−8.18714	+	14.1805i	−0.458392	+	0.793958i
$320$		0			0
$321$	−19.6954	+	16.5264i	−1.09929	+	0.922416i
$322$	8.79998	−	5.08067i	0.490404	−	0.283135i
$323$	−2.08758	−	1.20526i	−0.116156	−	0.0670627i
$324$	0.560377	+	3.17805i	0.0311320	+	0.176559i
$325$		0			0
$326$	−24.2424	+	8.82353i	−1.34266	+	0.488690i
$327$			1.66231i			0.0919260i
$328$	3.56441	+	9.79313i	0.196811	+	0.540735i
$329$	2.19496	−	12.4482i	0.121012	−	0.686292i
$330$		0			0
$331$	−5.99544	+	5.03077i	−0.329539	+	0.276516i	−0.792512	−	0.609856i	$-0.791227\pi$
$331$	−5.99544	+	5.03077i	−0.329539	+	0.276516i	0.462973	+	0.886372i	$0.346783\pi$
$332$		−	8.20334i		−	0.450217i
$333$	−3.32513	−	4.86332i	−0.182216	−	0.266508i
$334$	7.04202			0.385322
$335$		0			0
$336$	15.8010	+	13.2586i	0.862014	+	0.723316i
$337$	21.3381	+	3.76248i	1.16236	+	0.204955i	0.721366	−	0.692555i	$-0.243515\pi$
$337$	21.3381	+	3.76248i	1.16236	+	0.204955i	0.440994	+	0.897510i	$0.354626\pi$
$338$	5.51400	+	15.1496i	0.299922	+	0.824030i
$339$	−9.11427			−0.495019
$340$		0			0
$341$	12.0935	+	20.9465i	0.654899	+	1.13432i
$342$	−1.19401	+	0.210537i	−0.0645649	+	0.0113845i
$343$	−13.2370	−	7.64239i	−0.714731	−	0.412650i
$344$	3.96070	+	6.86013i	0.213547	+	0.369873i
$345$		0			0
$346$	4.27913	−	24.2682i	0.230048	−	1.30466i
$347$	23.5219	+	13.5804i	1.26272	+	0.729034i	0.973601	−	0.228258i	$-0.0733031\pi$
$347$	23.5219	+	13.5804i	1.26272	+	0.729034i	0.289123	+	0.957292i	$0.406636\pi$
$348$	1.94142	−	5.33402i	0.104071	−	0.285933i
$349$	−26.6938	−	9.71575i	−1.42889	−	0.520072i	−0.492275	−	0.870440i	$-0.663834\pi$
$349$	−26.6938	−	9.71575i	−1.42889	−	0.520072i	−0.936612	+	0.350368i	$0.886057\pi$
$350$		0			0
$351$	−20.7573	−	17.4174i	−1.10794	−	0.929675i
$352$	−5.65984	+	6.74514i	−0.301671	+	0.359517i
$353$	−31.2636	+	5.51261i	−1.66399	+	0.293407i	−0.924904	−	0.380201i	$-0.875855\pi$
$353$	−31.2636	+	5.51261i	−1.66399	+	0.293407i	−0.739089	+	0.673608i	$0.764744\pi$
$354$	7.52222	+	2.73786i	0.399802	+	0.145516i
$355$		0			0
$356$	3.98706	−	6.90579i	0.211314	−	0.366006i
$357$	−13.0422	−	2.29969i	−0.690265	−	0.121712i
$358$	−8.56906	−	10.2122i	−0.452889	−	0.539732i
$359$	−8.60823	−	14.9099i	−0.454325	−	0.786914i	0.544324	−	0.838875i	$-0.316786\pi$
$359$	−8.60823	−	14.9099i	−0.454325	−	0.786914i	−0.998649	+	0.0519610i	$0.983453\pi$
$360$		0			0
$361$	−3.19569	−	18.1236i	−0.168194	−	0.953876i
$362$	22.7844	−	13.1546i	1.19752	−	0.691389i
$363$	2.13459	+	5.86473i	0.112037	+	0.307819i
$364$	8.92772			0.467940
$365$		0			0
$366$	2.65729	−	15.0703i	0.138899	−	0.787735i
$367$	17.8279	−	21.2465i	0.930611	−	1.10906i	−0.0632031	−	0.998001i	$-0.520132\pi$
$367$	17.8279	−	21.2465i	0.930611	−	1.10906i	0.993814	−	0.111058i	$-0.0354240\pi$
$368$	6.57858	+	7.84005i	0.342932	+	0.408691i
$369$	−4.53297			−0.235977
$370$		0			0
$371$	−16.4876			−0.855992
$372$	−5.38959	−	6.42307i	−0.279437	−	0.333021i
$373$	−23.2355	+	27.6909i	−1.20309	+	1.43378i	−0.331559	+	0.943434i	$0.607575\pi$
$373$	−23.2355	+	27.6909i	−1.20309	+	1.43378i	−0.871527	+	0.490348i	$0.836870\pi$
$374$	2.25932	−	12.8132i	0.116827	−	0.662557i
$375$		0			0
$376$	9.45227			0.487464
$377$	10.4263	+	28.6459i	0.536979	+	1.47534i
$378$	−23.6368	+	13.6467i	−1.21575	+	0.701912i
$379$	−2.08098	−	11.8018i	−0.106893	−	0.606218i	−0.990447	−	0.137890i	$-0.955968\pi$
$379$	−2.08098	−	11.8018i	−0.106893	−	0.606218i	0.883555	−	0.468328i	$-0.155143\pi$
$380$		0			0
$381$	11.7396	+	20.3337i	0.601440	+	1.04172i
$382$	−23.9330	−	28.5223i	−1.22452	−	1.45933i
$383$	−7.51044	−	1.32429i	−0.383766	−	0.0676683i	−0.0215628	−	0.999767i	$-0.506864\pi$
$383$	−7.51044	−	1.32429i	−0.383766	−	0.0676683i	−0.362203	+	0.932099i	$0.617975\pi$
$384$	−9.69854	+	16.7984i	−0.494927	+	0.857238i
$385$		0			0
$386$	−4.90121	−	1.78389i	−0.249465	−	0.0907979i
$387$	−3.39313	+	0.598300i	−0.172483	+	0.0304133i
$388$	−2.24297	+	2.67306i	−0.113869	+	0.135704i
$389$	−26.1796	−	21.9673i	−1.32736	−	1.11378i	−0.984688	−	0.174328i	$-0.944225\pi$
$389$	−26.1796	−	21.9673i	−1.32736	−	1.11378i	−0.342668	−	0.939456i	$-0.611331\pi$
$390$		0			0
$391$	−6.17474	−	2.24742i	−0.312270	−	0.113657i
$392$	−1.42189	+	3.90661i	−0.0718164	+	0.197314i
$393$	−2.70468	−	1.56155i	−0.136433	−	0.0787696i
$394$	0.508544	−	2.88409i	0.0256201	−	0.145299i
$395$		0			0
$396$	−0.779873	−	1.35078i	−0.0391901	−	0.0678792i
$397$	−6.01226	−	3.47118i	−0.301747	−	0.174214i	0.341481	−	0.939889i	$-0.389072\pi$
$397$	−6.01226	−	3.47118i	−0.301747	−	0.174214i	−0.643227	+	0.765675i	$0.722405\pi$
$398$	−17.2755	+	3.04613i	−0.865942	+	0.152689i
$399$	1.63934	+	2.83942i	0.0820697	+	0.142149i
$400$		0			0
$401$	26.6564			1.33115			0.665577	−	0.746329i	$-0.268185\pi$
$401$	26.6564			1.33115			0.665577	+	0.746329i	$0.268185\pi$
$402$	9.86982	+	27.1171i	0.492262	+	1.35248i
$403$	44.3453	+	7.81928i	2.20900	+	0.389506i
$404$	−4.80578	−	4.03253i	−0.239097	−	0.200626i
$405$		0			0
$406$	30.7056			1.52389
$407$	−12.7204	−	9.12001i	−0.630527	−	0.452062i
$408$		−	9.90328i		−	0.490285i
$409$	15.2045	−	12.7581i	0.751813	−	0.630846i	−0.184169	−	0.982895i	$-0.558959\pi$
$409$	15.2045	−	12.7581i	0.751813	−	0.630846i	0.935982	+	0.352048i	$0.114515\pi$
$410$		0			0
$411$	3.71133	−	21.0480i	0.183067	−	1.03822i
$412$	0.663090	+	1.82182i	0.0326681	+	0.0897549i
$413$			10.3207i			0.507849i
$414$	−3.10574	+	1.13040i	−0.152639	+	0.0555559i
$415$		0			0
$416$	2.84657	+	16.1437i	0.139564	+	0.791510i
$417$	14.2490	+	8.22664i	0.697775	+	0.402860i
$418$	−2.78958	+	1.61057i	−0.136443	+	0.0787754i
$419$	12.0480	−	10.1094i	0.588582	−	0.493879i	−0.299171	−	0.954200i	$-0.596710\pi$
$419$	12.0480	−	10.1094i	0.588582	−	0.493879i	0.887753	+	0.460321i	$0.152266\pi$
$420$		0			0
$421$	11.8135	−	20.4616i	0.575756	−	0.997239i	−0.420203	−	0.907430i	$-0.638041\pi$
$421$	11.8135	−	20.4616i	0.575756	−	0.997239i	0.995959	−	0.0898085i	$-0.0286255\pi$
$422$	3.88950	−	10.6863i	0.189338	−	0.520202i
$423$	−1.40616	+	3.86340i	−0.0683699	+	0.187845i
$424$	−2.14096	−	12.1420i	−0.103974	−	0.589666i
$425$		0			0
$426$	10.7527	+	9.02256i	0.520969	+	0.437145i
$427$	19.4299	−	3.42601i	0.940278	−	0.165796i
$428$	−3.86126	+	10.6087i	−0.186641	+	0.512792i
$429$	−16.5097	−	6.00905i	−0.797097	−	0.290120i
$430$		0			0
$431$	−3.38953	+	19.2230i	−0.163268	+	0.925938i	0.787565	+	0.616232i	$0.211342\pi$
$431$	−3.38953	+	19.2230i	−0.163268	+	0.925938i	−0.950832	+	0.309706i	$0.899769\pi$
$432$	−17.6701	−	21.0584i	−0.850154	−	1.01317i
$433$	−16.3977	+	9.46720i	−0.788022	+	0.454965i	−0.839266	−	0.543722i	$-0.817015\pi$
$433$	−16.3977	+	9.46720i	−0.788022	+	0.454965i	0.0512438	+	0.998686i	$0.483681\pi$
$434$	22.6782	−	39.2797i	1.08859	−	1.88549i
$435$		0			0
$436$	0.364962	+	0.632133i	0.0174785	+	0.0302737i
$437$	0.556398	+	1.52869i	0.0266161	+	0.0731272i
$438$			15.5837i			0.744618i
$439$	−6.10044	+	2.22038i	−0.291158	+	0.105973i	−0.483470	−	0.875361i	$-0.660624\pi$
$439$	−6.10044	+	2.22038i	−0.291158	+	0.105973i	0.192312	+	0.981334i	$0.438402\pi$
$440$		0			0
$441$	−1.38521	−	1.16233i	−0.0659624	−	0.0553491i
$442$	−15.5700	−	18.5557i	−0.740592	−	0.882603i
$443$			27.0518i			1.28527i	0.766172	+	0.642636i	$0.222159\pi$
$443$			27.0518i			1.28527i	−0.766172	+	0.642636i	$0.777841\pi$
$444$	4.89170	+	2.34780i	0.232150	+	0.111422i
$445$		0			0
$446$	32.7647	−	27.4928i	1.55145	−	1.30182i
$447$	−3.00248	+	3.57822i	−0.142013	+	0.169244i
$448$	−12.2432	−	2.15881i	−0.578437	−	0.101994i
$449$	20.4266	−	7.43467i	0.963991	−	0.350864i	0.188395	−	0.982093i	$-0.439672\pi$
$449$	20.4266	−	7.43467i	0.963991	−	0.350864i	0.775596	+	0.631229i	$0.217449\pi$
$450$		0			0
$451$	−11.3167	+	4.11894i	−0.532882	+	0.193953i
$452$	−3.46592	+	2.00105i	−0.163023	+	0.0941213i
$453$	−22.1058	+	3.89785i	−1.03862	+	0.183137i
$454$	7.64943	−	13.2492i	0.359006	−	0.621816i
$455$		0			0
$456$	−1.87817	+	1.57597i	−0.0879532	+	0.0738015i
$457$	−5.60320	−	0.987995i	−0.262106	−	0.0462164i	0.0410505	−	0.999157i	$-0.486930\pi$
$457$	−5.60320	−	0.987995i	−0.262106	−	0.0462164i	−0.303157	+	0.952941i	$0.598041\pi$
$458$	−24.5179	−	14.1554i	−1.14565	−	0.661439i
$459$	16.5854	+	6.03659i	0.774140	+	0.281764i
$460$		0			0
$461$	−4.53759	−	25.7340i	−0.211337	−	1.19855i	−0.887151	−	0.461478i	$-0.847319\pi$
$461$	−4.53759	−	25.7340i	−0.211337	−	1.19855i	0.675815	−	0.737072i	$-0.263792\pi$
$462$	−11.3753	+	13.5566i	−0.529227	+	0.630708i
$463$	9.09288	−	10.8365i	0.422582	−	0.503614i	−0.512185	−	0.858875i	$-0.671164\pi$
$463$	9.09288	−	10.8365i	0.422582	−	0.503614i	0.934767	+	0.355261i	$0.115608\pi$
$464$	5.37034	+	30.4567i	0.249312	+	1.41392i
$465$		0			0
$466$	4.94704	+	1.80058i	0.229167	+	0.0834100i
$467$	−7.84420	−	4.52885i	−0.362986	−	0.209570i	0.307404	−	0.951579i	$-0.400540\pi$
$467$	−7.84420	−	4.52885i	−0.362986	−	0.209570i	−0.670390	+	0.742009i	$0.733873\pi$
$468$	−2.85970	−	0.504242i	−0.132190	−	0.0233086i
$469$	−28.5010	+	23.9152i	−1.31606	+	1.10430i
$470$		0			0
$471$	3.71716	−	6.43831i	0.171278	−	0.296662i
$472$	−7.60049	+	1.34017i	−0.349841	+	0.0616864i
$473$	−7.92740	+	4.57688i	−0.364502	+	0.210445i
$474$	−29.3680	+	10.6891i	−1.34892	+	0.490965i
$475$		0			0
$476$	−5.46449	+	1.98891i	−0.250464	+	0.0911616i
$477$	5.28124	+	0.931226i	0.241812	+	0.0426379i
$478$	7.08835	−	8.44757i	0.324214	−	0.386383i
$479$	−11.3596	+	9.53185i	−0.519034	+	0.435521i	−0.864295	−	0.502986i	$-0.832235\pi$
$479$	−11.3596	+	9.53185i	−0.519034	+	0.435521i	0.345261	+	0.938507i	$0.387790\pi$
$480$		0			0
$481$	−28.2290	+	7.22752i	−1.28713	+	0.329547i
$482$		−	26.8663i		−	1.22373i
$483$	5.74497	+	6.84659i	0.261405	+	0.311531i
$484$	2.09933	+	1.76155i	0.0954243	+	0.0800705i
$485$		0			0
$486$	14.6482	−	5.33150i	0.664454	−	0.241842i
$487$			17.1816i			0.778575i	0.921116	+	0.389287i	$0.127279\pi$
$487$			17.1816i			0.778575i	−0.921116	+	0.389287i	$0.872721\pi$
$488$	5.04604	+	13.8639i	0.228424	+	0.627589i
$489$	−11.3457	−	19.6513i	−0.513069	−	0.888661i
$490$		0			0
$491$	6.10718	−	10.5779i	0.275613	−	0.477376i	−0.694677	−	0.719322i	$-0.744453\pi$
$491$	6.10718	−	10.5779i	0.275613	−	0.477376i	0.970290	+	0.241946i	$0.0777858\pi$
$492$	3.61552	−	2.08742i	0.163000	−	0.0941083i
$493$	−12.7634	−	15.2109i	−0.574836	−	0.685063i
$494$	−1.04134	+	5.90575i	−0.0468522	+	0.265712i
$495$		0			0
$496$	42.9277	+	15.6244i	1.92751	+	0.701556i
$497$	−6.18961	+	17.0058i	−0.277642	+	0.762815i
$498$	29.8134	−	5.25691i	1.33597	−	0.235568i
$499$	22.3440	+	18.7489i	1.00026	+	0.839315i	0.987020	−	0.160598i	$-0.0513422\pi$
$499$	22.3440	+	18.7489i	1.00026	+	0.839315i	0.0132363	+	0.999912i	$0.495787\pi$
$500$		0			0
$501$	1.07557	+	6.09984i	0.0480528	+	0.272521i
$502$	12.8980	−	35.4370i	0.575666	−	1.58163i
$503$	2.79848	−	7.68875i	0.124778	−	0.342825i	−0.861537	−	0.507694i	$-0.830498\pi$
$503$	2.79848	−	7.68875i	0.124778	−	0.342825i	0.986315	+	0.164869i	$0.0527203\pi$
$504$	3.21103	−	5.56167i	0.143031	−	0.247736i
$505$		0			0
$506$	−6.72642	+	5.64413i	−0.299026	+	0.250912i
$507$	−12.2805	+	7.09014i	−0.545395	+	0.314884i
$508$	8.92855	+	5.15490i	0.396140	+	0.228712i
$509$	2.27238	+	12.8873i	0.100721	+	0.571220i	0.992843	+	0.119425i	$0.0381051\pi$
$509$	2.27238	+	12.8873i	0.100721	+	0.571220i	−0.892122	+	0.451795i	$0.850784\pi$
$510$		0			0
$511$	−18.8802	+	6.87182i	−0.835209	+	0.303991i
$512$		−	5.01340i		−	0.221563i
$513$	−1.49449	−	4.10608i	−0.0659834	−	0.181288i
$514$	2.51046	−	14.2375i	0.110731	−	0.627989i
$515$		0			0
$516$	2.43086	−	2.03974i	0.107013	−	0.0897944i
$517$			10.9228i			0.480385i
$518$	−2.88403	+	29.2091i	−0.126717	+	1.28337i
$519$	21.6748			0.951418
$520$		0			0
$521$	20.0904	+	16.8578i	0.880175	+	0.738554i	0.966215	−	0.257737i	$-0.0829770\pi$
$521$	20.0904	+	16.8578i	0.880175	+	0.738554i	−0.0860404	+	0.996292i	$0.527421\pi$
$522$	−9.83552	−	1.73427i	−0.430489	−	0.0759069i
$523$	−3.69170	−	10.1429i	−0.161427	−	0.443516i	0.832438	−	0.554118i	$-0.186944\pi$
$523$	−3.69170	−	10.1429i	−0.161427	−	0.443516i	−0.993865	+	0.110602i	$0.964722\pi$
$524$	−1.37136			−0.0599080
$525$		0			0
$526$	7.28831	+	12.6237i	0.317785	+	0.550420i
$527$	−28.8849	+	5.09319i	−1.25825	+	0.221863i
$528$	−15.4362	−	8.91208i	−0.671773	−	0.387849i
$529$	−9.28270	−	16.0781i	−0.403596	−	0.699048i
$530$		0			0
$531$	0.582918	−	3.30589i	0.0252965	−	0.143464i
$532$	1.24680	+	0.719838i	0.0540555	+	0.0312089i
$533$	−7.66832	+	21.0685i	−0.332152	+	0.912579i
$534$	27.6527	+	10.0648i	1.19665	+	0.435545i
$535$		0			0
$536$	−21.3128	−	17.8836i	−0.920574	−	0.772454i
$537$	7.53708	−	8.98234i	0.325249	−	0.387616i
$538$	−6.23080	+	1.09866i	−0.268629	+	0.0473665i
$539$	−4.51439	−	1.64310i	−0.194448	−	0.0707734i
$540$		0			0
$541$	−18.7525	+	32.4803i	−0.806233	+	1.39644i	0.109222	+	0.994017i	$0.465164\pi$
$541$	−18.7525	+	32.4803i	−0.806233	+	1.39644i	−0.915455	+	0.402420i	$0.868169\pi$
$542$	25.5887	+	4.51198i	1.09913	+	0.193806i
$543$	14.8745	+	17.7268i	0.638327	+	0.760729i
$544$	−5.33881	−	9.24709i	−0.228900	−	0.396466i
$545$		0			0
$546$	5.72111	+	32.4460i	0.244841	+	1.38856i
$547$	24.6997	−	14.2604i	1.05608	−	0.609730i	0.131737	−	0.991285i	$-0.457944\pi$
$547$	24.6997	−	14.2604i	1.05608	−	0.609730i	0.924346	+	0.381554i	$0.124611\pi$
$548$	−3.20979	−	8.81884i	−0.137116	−	0.376722i
$549$	−6.41722			−0.273880
$550$		0			0
$551$	−0.853633	+	4.84120i	−0.0363660	+	0.206242i
$552$	−4.29604	+	5.11982i	−0.182852	+	0.217914i
$553$	−25.9003	−	30.8668i	−1.10139	−	1.31259i
$554$	−39.5807			−1.68162
$555$		0			0
$556$	7.22467			0.306394
$557$	19.2194	+	22.9048i	0.814353	+	0.970508i	0.999927	−	0.0121226i	$-0.00385884\pi$
$557$	19.2194	+	22.9048i	0.814353	+	0.970508i	−0.185574	+	0.982630i	$0.559414\pi$
$558$	−9.48273	+	11.3011i	−0.401436	+	0.478413i
$559$	−2.95927	+	16.7829i	−0.125164	+	0.709840i
$560$		0			0
$561$	11.4440			0.483165
$562$	15.0770	+	41.4236i	0.635984	+	1.74735i
$563$	24.5205	−	14.1569i	1.03341	−	0.596642i	0.115453	−	0.993313i	$-0.463168\pi$
$563$	24.5205	−	14.1569i	1.03341	−	0.596642i	0.917961	+	0.396671i	$0.129835\pi$
$564$	−0.657524	−	3.72900i	−0.0276867	−	0.157019i
$565$		0			0
$566$	−6.95795	−	12.0515i	−0.292464	−	0.506563i
$567$	−9.86952	−	11.7620i	−0.414481	−	0.493959i
$568$	−13.3274	−	2.34997i	−0.559203	−	0.0986026i
$569$	6.62094	−	11.4678i	0.277564	−	0.480755i	−0.693215	−	0.720731i	$-0.743806\pi$
$569$	6.62094	−	11.4678i	0.277564	−	0.480755i	0.970779	+	0.239976i	$0.0771395\pi$
$570$		0			0
$571$	−16.8077	−	6.11751i	−0.703382	−	0.256010i	−0.0345276	−	0.999404i	$-0.510993\pi$
$571$	−16.8077	−	6.11751i	−0.703382	−	0.256010i	−0.668854	+	0.743394i	$0.733215\pi$
$572$	−7.59750	+	1.33964i	−0.317668	+	0.0560134i
$573$	21.0507	−	25.0873i	0.879407	−	1.04804i
$574$	17.2999	+	14.5163i	0.722084	+	0.605900i
$575$		0			0
$576$	3.79977	+	1.38300i	0.158324	+	0.0576252i
$577$	−16.0520	+	44.1025i	−0.668254	+	1.83601i	−0.133412	+	0.991061i	$0.542593\pi$
$577$	−16.0520	+	44.1025i	−0.668254	+	1.83601i	−0.534842	+	0.844952i	$0.679629\pi$
$578$	−10.1930	−	5.88491i	−0.423972	−	0.244780i
$579$	0.796631	−	4.51792i	0.0331069	−	0.187758i
$580$		0			0
$581$	19.5155	+	33.8018i	0.809639	+	1.40234i
$582$	−11.1521	−	6.43864i	−0.462268	−	0.266890i
$583$	14.0310	−	2.47404i	0.581103	−	0.102464i
$584$	−7.51226	−	13.0116i	−0.310859	−	0.538424i
$585$		0			0
$586$	37.7789			1.56063
$587$	15.3230	+	42.0996i	0.632448	+	1.73764i	0.674241	+	0.738511i	$0.264471\pi$
$587$	15.3230	+	42.0996i	0.632448	+	1.73764i	−0.0417926	+	0.999126i	$0.513307\pi$
$588$	1.64010	+	0.289194i	0.0676367	+	0.0119262i
$589$	5.56256	+	4.66754i	0.229201	+	0.192323i
$590$		0			0
$591$	2.57589			0.105958
$592$	−29.4767	+	2.24795i	−1.21149	+	0.0923901i
$593$			18.6865i			0.767361i	0.923466	+	0.383681i	$0.125344\pi$
$593$			18.6865i			0.767361i	−0.923466	+	0.383681i	$0.874656\pi$
$594$	18.0672	−	15.1602i	0.741307	−	0.622030i
$595$		0			0
$596$	−0.356163	+	2.01990i	−0.0145890	+	0.0827384i
$597$	−5.27716	−	14.4989i	−0.215980	−	0.593399i
$598$			16.3472i			0.668488i
$599$	−26.3197	+	9.57960i	−1.07540	+	0.391412i	−0.818192	−	0.574945i	$-0.805023\pi$
$599$	−26.3197	+	9.57960i	−1.07540	+	0.391412i	−0.257204	+	0.966357i	$0.582801\pi$
$600$		0			0
$601$	3.11064	+	17.6413i	0.126886	+	0.719604i	0.980170	+	0.198158i	$0.0634960\pi$
$601$	3.11064	+	17.6413i	0.126886	+	0.719604i	−0.853284	+	0.521446i	$0.825393\pi$
$602$	14.8657	+	8.58274i	0.605882	+	0.349806i
$603$	10.4801	−	6.05069i	0.426783	−	0.246403i
$604$	−7.55048	+	6.33561i	−0.307225	+	0.257792i
$605$		0			0
$606$	11.5758	−	20.0498i	0.470233	−	0.814468i
$607$	6.20576	−	17.0502i	0.251884	−	0.692046i	−0.747723	−	0.664011i	$-0.768853\pi$
$607$	6.20576	−	17.0502i	0.251884	−	0.692046i	0.999607	−	0.0280348i	$-0.00892492\pi$
$608$	−0.904123	+	2.48406i	−0.0366670	+	0.100742i
$609$	4.68984	+	26.5974i	0.190042	+	1.07778i
$610$		0			0
$611$	15.5777	+	13.0712i	0.630206	+	0.528806i
$612$	1.86270	−	0.328445i	0.0752953	−	0.0132766i
$613$	−2.46152	+	6.76296i	−0.0994197	+	0.273153i	−0.979424	−	0.201812i	$-0.935317\pi$
$613$	−2.46152	+	6.76296i	−0.0994197	+	0.273153i	0.880005	+	0.474965i	$0.157539\pi$
$614$	−42.7129	−	15.5462i	−1.72375	−	0.627395i
$615$		0			0
$616$	2.96275	−	16.8026i	0.119373	−	0.676996i
$617$	−10.5615	−	12.5867i	−0.425189	−	0.506720i	0.510339	−	0.859973i	$-0.329520\pi$
$617$	−10.5615	−	12.5867i	−0.425189	−	0.506720i	−0.935528	+	0.353253i	$0.885075\pi$
$618$	−6.19613	+	3.57734i	−0.249245	+	0.143902i
$619$	20.2224	−	35.0263i	0.812808	−	1.40783i	−0.0980830	−	0.995178i	$-0.531271\pi$
$619$	20.2224	−	35.0263i	0.812808	−	1.40783i	0.910891	−	0.412647i	$-0.135396\pi$
$620$		0			0
$621$	−5.95569	−	10.3156i	−0.238994	−	0.413949i
$622$	11.0539	+	30.3702i	0.443219	+	1.21773i
$623$			37.9403i			1.52005i
$624$	−31.1824	+	11.3495i	−1.24830	+	0.454342i
$625$		0			0
$626$	−24.0915	−	20.2151i	−0.962889	−	0.807959i
$627$	−1.82115	−	2.17036i	−0.0727298	−	0.0866759i
$628$		−	3.26443i		−	0.130265i
$629$	15.6683	−	10.7127i	0.624736	−	0.427142i
$630$		0			0
$631$	21.9104	−	18.3850i	0.872241	−	0.731897i	−0.0923279	−	0.995729i	$-0.529431\pi$
$631$	21.9104	−	18.3850i	0.872241	−	0.731897i	0.964569	+	0.263832i	$0.0849863\pi$
$632$	19.3680	−	23.0819i	0.770419	−	0.918150i
$633$	9.85061	+	1.73693i	0.391527	+	0.0690367i
$634$	−45.1386	+	16.4291i	−1.79268	+	0.652484i
$635$		0			0
$636$	−4.64118	+	1.68925i	−0.184035	+	0.0669832i
$637$	−7.74566	+	4.47196i	−0.306894	+	0.177185i
$638$	−26.1305	+	4.60752i	−1.03452	+	0.182413i
$639$	2.94313	−	5.09765i	0.116429	−	0.201660i
$640$		0			0
$641$	5.15320	−	4.32405i	0.203539	−	0.170790i	−0.535320	−	0.844649i	$-0.679809\pi$
$641$	5.15320	−	4.32405i	0.203539	−	0.170790i	0.738860	+	0.673859i	$0.235365\pi$
$642$	−41.0297	−	7.23464i	−1.61931	−	0.285528i
$643$	13.6801	+	7.89822i	0.539492	+	0.311476i	0.744873	−	0.667206i	$-0.232510\pi$
$643$	13.6801	+	7.89822i	0.539492	+	0.311476i	−0.205381	+	0.978682i	$0.565843\pi$
$644$	3.68784	+	1.34226i	0.145321	+	0.0528926i
$645$		0			0
$646$	−0.678293	−	3.84679i	−0.0266871	−	0.151350i
$647$	−20.8545	+	24.8535i	−0.819876	+	0.977090i	−0.999978	−	0.00655762i	$-0.997913\pi$
$647$	−20.8545	+	24.8535i	−0.819876	+	0.977090i	0.180102	+	0.983648i	$0.442357\pi$
$648$	7.38035	−	8.79555i	0.289927	−	0.345522i
$649$	−1.54867	−	8.78294i	−0.0607906	−	0.344761i
$650$		0			0
$651$	37.4881	+	13.6445i	1.46927	+	0.534772i
$652$	−8.62891	−	4.98190i	−0.337934	−	0.195106i
$653$	43.3574	+	7.64508i	1.69671	+	0.299175i	0.936542	−	0.350555i	$-0.114007\pi$
$653$	43.3574	+	7.64508i	1.69671	+	0.299175i	0.760165	+	0.649731i	$0.225118\pi$
$654$	−2.06349	+	1.73147i	−0.0806886	+	0.0677058i
$655$		0			0
$656$	−11.3730	+	19.6985i	−0.444040	+	0.769099i
$657$	6.43575	−	1.13480i	0.251083	−	0.0442726i
$658$	17.7387	−	10.2414i	0.691525	−	0.399252i
$659$	1.74097	−	0.633661i	0.0678186	−	0.0246839i	−0.307888	−	0.951423i	$-0.599622\pi$
$659$	1.74097	−	0.633661i	0.0678186	−	0.0246839i	0.375707	+	0.926739i	$0.377400\pi$
$660$		0			0
$661$	−34.3429	+	12.4998i	−1.33578	+	0.486185i	−0.908482	−	0.417924i	$-0.862758\pi$
$661$	−34.3429	+	12.4998i	−1.33578	+	0.486185i	−0.427301	+	0.904110i	$0.640535\pi$
$662$	−12.4897	−	2.20228i	−0.485428	−	0.0855940i
$663$	13.6949	−	16.3210i	0.531867	−	0.633854i
$664$	−22.3586	+	18.7611i	−0.867681	+	0.728071i
$665$		0			0
$666$	2.57354	−	9.19326i	0.0997228	−	0.356231i
$667$			13.4005i			0.518871i
$668$	1.74824	+	2.08347i	0.0676413	+	0.0806117i
$669$	28.8188	+	24.1818i	1.11420	+	0.934923i
$670$		0			0
$671$	−16.0208	+	5.83108i	−0.618475	+	0.225106i
$672$			14.5232i			0.560244i
$673$	−1.38809	−	3.81374i	−0.0535069	−	0.147009i	0.910060	−	0.414477i	$-0.136035\pi$
$673$	−1.38809	−	3.81374i	−0.0535069	−	0.147009i	−0.963567	+	0.267468i	$0.913813\pi$
$674$	17.5553	+	30.4067i	0.676206	+	1.17122i
$675$		0			0
$676$	−3.11330	+	5.39239i	−0.119742	+	0.207399i
$677$	16.5359	−	9.54701i	0.635527	−	0.366921i	−0.147363	−	0.989083i	$-0.547078\pi$
$677$	16.5359	−	9.54701i	0.635527	−	0.366921i	0.782889	+	0.622161i	$0.213745\pi$
$678$	−9.49345	−	11.3139i	−0.364594	−	0.434506i
$679$	2.88299	−	16.3503i	0.110639	−	0.627466i
$680$		0			0
$681$	12.6449	+	4.60236i	0.484553	+	0.176363i
$682$	−13.4050	+	36.8301i	−0.513306	+	1.41030i
$683$	7.66667	−	1.35184i	0.293357	−	0.0517268i	−0.0250328	−	0.999687i	$-0.507969\pi$
$683$	7.66667	−	1.35184i	0.293357	−	0.0517268i	0.318390	+	0.947960i	$0.396858\pi$
$684$	−0.358713	−	0.300996i	−0.0137157	−	0.0115089i
$685$		0			0
$686$	−4.30095	−	24.3919i	−0.164211	−	0.931287i
$687$	8.51674	−	23.3996i	0.324934	−	0.892749i
$688$	−5.91319	+	16.2463i	−0.225438	+	0.619386i
$689$	13.2623	−	22.9711i	0.505255	−	0.875128i
$690$		0			0
$691$	−36.4188	+	30.5590i	−1.38544	+	1.16252i	−0.418285	+	0.908316i	$0.637369\pi$
$691$	−36.4188	+	30.5590i	−1.38544	+	1.16252i	−0.967151	+	0.254203i	$0.918187\pi$
$692$	8.24235	−	4.75872i	0.313327	−	0.180900i
$693$	6.42692	+	3.71059i	0.244139	+	0.140954i
$694$	7.64271	+	43.3440i	0.290113	+	1.64531i
$695$		0			0
$696$	−18.9782	+	6.90748i	−0.719365	+	0.261827i
$697$		−	14.6040i		−	0.553166i
$698$	−15.7439	−	43.2559i	−0.595914	−	1.63726i
$699$	−0.804080	+	4.56016i	−0.0304131	+	0.172481i
$700$		0			0
$701$	−22.8581	+	19.1802i	−0.863337	+	0.724426i	−0.962684	−	0.270627i	$-0.912769\pi$
$701$	−22.8581	+	19.1802i	−0.863337	+	0.724426i	0.0993471	+	0.995053i	$0.468325\pi$
$702$		−	43.9088i		−	1.65723i
$703$	−4.52506	−	1.26674i	−0.170666	−	0.0477759i
$704$	10.7429			0.404889
$705$		0			0
$706$	−39.4073	−	33.0666i	−1.48311	−	1.24448i
$707$	29.3955	+	5.18321i	1.10553	+	0.194935i
$708$	1.05742	+	2.90523i	0.0397402	+	0.109185i
$709$	39.6550			1.48927			0.744637	−	0.667469i	$-0.232622\pi$
$709$	39.6550			1.48927			0.744637	+	0.667469i	$0.232622\pi$
$710$		0			0
$711$	6.55293	+	11.3500i	0.245754	+	0.425659i
$712$	−27.9404	+	4.92665i	−1.04711	+	0.184634i
$713$	17.1424	+	9.89719i	0.641989	+	0.370653i
$714$	−10.7301	−	18.5851i	−0.401563	−	0.695528i
$715$		0			0
$716$	0.894069	−	5.07052i	0.0334129	−	0.189494i
$717$	8.39997	+	4.84973i	0.313703	+	0.181116i
$718$	9.54180	−	26.2159i	0.356097	−	0.978368i
$719$	−24.9744	−	9.08994i	−0.931388	−	0.338997i	−0.168628	−	0.985680i	$-0.553934\pi$
$719$	−24.9744	−	9.08994i	−0.931388	−	0.338997i	−0.762759	+	0.646682i	$0.776156\pi$
$720$		0			0
$721$	−7.06632	−	5.92935i	−0.263164	−	0.220820i
$722$	19.1689	−	22.8446i	0.713391	−	0.850186i
$723$	23.2717	−	4.10343i	0.865485	−	0.152608i
$724$	9.54833	+	3.47531i	0.354861	+	0.129159i
$725$		0			0
$726$	−5.05670	+	8.75846i	−0.187672	+	0.325057i
$727$	5.27659	+	0.930405i	0.195698	+	0.0345068i	0.270638	−	0.962681i	$-0.412765\pi$
$727$	5.27659	+	0.930405i	0.195698	+	0.0345068i	−0.0749400	+	0.997188i	$0.523877\pi$
$728$	−20.4177	−	24.3329i	−0.756731	−	0.901837i
$729$	14.5899	+	25.2705i	0.540368	+	0.935946i
$730$		0			0
$731$	−1.92756	−	10.9317i	−0.0712934	−	0.404325i
$732$	5.11841	−	2.95512i	0.189182	−	0.109224i
$733$	−5.30946	−	14.5876i	−0.196109	−	0.538806i	0.802192	−	0.597066i	$-0.203667\pi$
$733$	−5.30946	−	14.5876i	−0.196109	−	0.538806i	−0.998301	+	0.0582602i	$0.981445\pi$
$734$	44.9437			1.65890
$735$		0			0
$736$	−1.25132	+	7.09657i	−0.0461241	+	0.261583i
$737$	20.6658	−	24.6286i	0.761236	−	0.907206i
$738$	−4.72156	−	5.62693i	−0.173803	−	0.207130i
$739$	25.0339			0.920886			0.460443	−	0.887689i	$-0.347691\pi$
$739$	25.0339			0.920886			0.460443	+	0.887689i	$0.347691\pi$
$740$		0			0
$741$	−5.27464			−0.193769
$742$	−17.1735	−	20.4666i	−0.630460	−	0.751352i
$743$	14.3581	−	17.1113i	0.526748	−	0.627754i	−0.435414	−	0.900230i	$-0.643398\pi$
$743$	14.3581	−	17.1113i	0.526748	−	0.627754i	0.962163	+	0.272476i	$0.0878425\pi$
$744$	−5.18034	+	29.3792i	−0.189920	+	1.07709i
$745$		0			0
$746$	−58.5758			−2.14461
$747$	−4.34199	−	11.9295i	−0.158865	−	0.436479i
$748$	4.35184	−	2.51254i	0.159119	−	0.0918675i
$749$	−9.32752	−	52.8990i	−0.340820	−	1.93289i
$750$		0			0
$751$	−2.86061	−	4.95473i	−0.104385	−	0.180800i	0.809102	−	0.587669i	$-0.199954\pi$
$751$	−2.86061	−	4.95473i	−0.104385	−	0.180800i	−0.913487	+	0.406868i	$0.866621\pi$
$752$	13.2609	+	15.8037i	0.483574	+	0.576301i
$753$	32.6657	+	5.75984i	1.19040	+	0.209900i
$754$	−24.6991	+	42.7801i	−0.899489	+	1.55796i
$755$		0			0
$756$	−9.90556	−	3.60533i	−0.360262	−	0.131125i
$757$	31.8709	−	5.61970i	1.15837	−	0.204251i	0.438741	−	0.898613i	$-0.355424\pi$
$757$	31.8709	−	5.61970i	1.15837	−	0.204251i	0.719626	+	0.694362i	$0.244313\pi$
$758$	12.4824	−	14.8760i	0.453383	−	0.540320i
$759$	−5.91634	−	4.96440i	−0.214750	−	0.180196i
$760$		0			0
$761$	47.4438	+	17.2681i	1.71983	+	0.625969i	0.997825	−	0.0659145i	$-0.0209965\pi$
$761$	47.4438	+	17.2681i	1.71983	+	0.625969i	0.722009	+	0.691883i	$0.243219\pi$
$762$	−13.0128	+	35.7524i	−0.471405	+	1.29517i
$763$	−3.00765	−	1.73647i	−0.108884	−	0.0628643i
$764$	2.49710	−	14.1617i	0.0903418	−	0.512354i
$765$		0			0
$766$	−6.17901	−	10.7024i	−0.223257	−	0.386692i
$767$	−14.3792	−	8.30182i	−0.519202	−	0.299761i
$768$	−19.2341	+	3.39148i	−0.694049	+	0.122380i
$769$	16.4220	+	28.4438i	0.592194	+	1.02571i	0.993936	+	0.109957i	$0.0350714\pi$
$769$	16.4220	+	28.4438i	0.592194	+	1.02571i	−0.401742	+	0.915753i	$0.631595\pi$
$770$		0			0
$771$	12.7160			0.457957
$772$	−0.688976	−	1.89295i	−0.0247968	−	0.0681286i
$773$	47.1481	+	8.31348i	1.69580	+	0.299015i	0.936224	−	0.351405i	$-0.114296\pi$
$773$	47.1481	+	8.31348i	1.69580	+	0.299015i	0.759575	+	0.650420i	$0.225407\pi$
$774$	−4.27699	−	3.58882i	−0.153733	−	0.128997i
$775$		0			0
$776$	12.4152			0.445680
$777$	−25.7415	+	1.96310i	−0.923473	+	0.0704257i
$778$		−	55.3788i		−	1.98542i
$779$	−2.76966	+	2.32402i	−0.0992335	+	0.0832668i
$780$		0			0
$781$	2.71557	−	15.4008i	0.0971707	−	0.551082i
$782$	−3.64183	−	10.0058i	−0.130232	−	0.357808i
$783$		−	35.9939i		−	1.28632i
$784$	−8.52646	+	3.10338i	−0.304516	+	0.110835i
$785$		0			0
$786$	−0.878801	−	4.98393i	−0.0313458	−	0.177771i
$787$	30.2108	+	17.4422i	1.07690	+	0.621749i	0.930059	−	0.367411i	$-0.119756\pi$
$787$	30.2108	+	17.4422i	1.07690	+	0.621749i	0.146842	+	0.989160i	$0.453089\pi$
$788$	0.979543	−	0.565540i	0.0348948	−	0.0201465i
$789$	−9.82155	+	8.24126i	−0.349657	+	0.293397i
$790$		0			0
$791$	9.52085	−	16.4906i	0.338523	−	0.586338i
$792$	−1.89804	+	5.21482i	−0.0674438	+	0.185300i
$793$	−10.8559	+	29.8262i	−0.385503	+	1.05916i
$794$	−1.95350	−	11.0788i	−0.0693270	−	0.393173i
$795$		0			0
$796$	−5.19000	−	4.35493i	−0.183955	−	0.154356i
$797$	−17.3061	+	3.05152i	−0.613012	+	0.108091i	−0.471530	−	0.881850i	$-0.656298\pi$
$797$	−17.3061	+	3.05152i	−0.613012	+	0.108091i	−0.141482	+	0.989941i	$0.545187\pi$
$798$	−1.81713	+	4.99252i	−0.0643257	+	0.176733i
$799$	−12.4468	−	4.53027i	−0.440337	−	0.160269i
$800$		0			0
$801$	2.14289	−	12.1529i	0.0757152	−	0.429402i
$802$	27.7653	+	33.0895i	0.980429	+	1.16843i
$803$	15.0359	−	8.68098i	0.530605	−	0.306345i
$804$	−5.57266	+	9.65213i	−0.196532	+	0.340404i
$805$		0			0
$806$	36.4839	+	63.1920i	1.28509	+	2.22584i
$807$	−1.90333	−	5.22935i	−0.0670003	−	0.184082i
$808$			22.3208i			0.785243i
$809$	23.2123	−	8.44858i	0.816101	−	0.297036i	0.0999592	−	0.994992i	$-0.468129\pi$
$809$	23.2123	−	8.44858i	0.816101	−	0.297036i	0.716141	+	0.697955i	$0.245907\pi$
$810$		0			0
$811$	−18.4508	−	15.4821i	−0.647897	−	0.543650i	0.258535	−	0.966002i	$-0.416760\pi$
$811$	−18.4508	−	15.4821i	−0.647897	−	0.543650i	−0.906432	+	0.422352i	$0.861205\pi$
$812$	7.62290	+	9.08462i	0.267511	+	0.318808i
$813$			22.8542i			0.801532i
$814$	−1.92864	−	25.2897i	−0.0675988	−	0.886404i
$815$		0			0
$816$	16.5577	−	13.8936i	0.579637	−	0.486373i
$817$	−1.76647	+	2.10520i	−0.0618010	+	0.0736516i
$818$	31.6741	+	5.58500i	1.10746	+	0.195275i
$819$	12.9829	−	4.72540i	0.453661	−	0.165119i
$820$		0			0
$821$	−19.4653	+	7.08477i	−0.679342	+	0.247260i	−0.658565	−	0.752524i	$-0.728836\pi$
$821$	−19.4653	+	7.08477i	−0.679342	+	0.247260i	−0.0207771	+	0.999784i	$0.506614\pi$
$822$	29.9934	−	17.3167i	1.04614	−	0.603989i
$823$	−23.4772	+	4.13966i	−0.818363	+	0.144299i	−0.567131	−	0.823628i	$-0.691947\pi$
$823$	−23.4772	+	4.13966i	−0.818363	+	0.144299i	−0.251232	+	0.967927i	$0.580836\pi$
$824$	3.44898	−	5.97380i	0.120151	−	0.208107i
$825$		0			0
$826$	−12.8115	+	10.7501i	−0.445767	+	0.374043i
$827$	−22.5822	−	3.98186i	−0.785262	−	0.138463i	−0.233380	−	0.972386i	$-0.574979\pi$
$827$	−22.5822	−	3.98186i	−0.785262	−	0.138463i	−0.551881	+	0.833923i	$0.686090\pi$
$828$	−1.10546	−	0.638240i	−0.0384175	−	0.0221804i
$829$	−13.9455	−	5.07575i	−0.484348	−	0.176288i	0.0882930	−	0.996095i	$-0.471859\pi$
$829$	−13.9455	−	5.07575i	−0.484348	−	0.176288i	−0.572641	+	0.819806i	$0.694081\pi$
$830$		0			0
$831$	−6.04537	−	34.2850i	−0.209712	−	1.18933i
$832$	12.8560	−	15.3212i	0.445701	−	0.531165i
$833$	3.74471	−	4.46277i	0.129747	−	0.154626i
$834$	4.62975	+	26.2566i	0.160315	+	0.909193i
$835$		0			0
$836$	−1.16904	−	0.425496i	−0.0404321	−	0.0147161i
$837$	−46.0447	−	26.5839i	−1.59154	−	0.918875i
$838$	25.0984	+	4.42553i	0.867010	+	0.152877i
$839$	9.50523	−	7.97583i	0.328157	−	0.275356i	−0.463791	−	0.885944i	$-0.653511\pi$
$839$	9.50523	−	7.97583i	0.328157	−	0.275356i	0.791948	+	0.610588i	$0.209067\pi$
$840$		0			0
$841$	−5.74693	+	9.95397i	−0.198170	+	0.343240i
$842$	37.7047	−	6.64836i	1.29939	−	0.229118i
$843$	−33.5786	+	19.3866i	−1.15651	+	0.667710i
$844$	4.12727	−	1.50220i	0.142067	−	0.0517080i
$845$		0			0
$846$	−6.26043	+	2.27861i	−0.215238	+	0.0783403i
$847$	−12.8410	−	2.26421i	−0.441221	−	0.0777992i
$848$	17.2971	−	20.6139i	0.593985	−	0.707883i
$849$	9.37637	−	7.86771i	0.321796	−	0.270019i
$850$		0			0
$851$	−12.7474	−	1.25865i	−0.436975	−	0.0431458i
$852$			5.42122i			0.185728i
$853$	13.5771	+	16.1806i	0.464872	+	0.554013i	0.946643	−	0.322284i	$-0.104451\pi$
$853$	13.5771	+	16.1806i	0.464872	+	0.554013i	−0.481771	+	0.876297i	$0.660006\pi$
$854$	24.4911	+	20.5504i	0.838067	+	0.703221i
$855$		0			0
$856$	37.7453	−	13.7381i	1.29011	−	0.469560i
$857$		−	48.6366i		−	1.66139i	−0.556725	−	0.830697i	$-0.687942\pi$
$857$		−	48.6366i		−	1.66139i	0.556725	−	0.830697i	$-0.312058\pi$
$858$	−9.73734	−	26.7531i	−0.332427	−	0.913337i
$859$	−4.97136	−	8.61065i	−0.169621	−	0.293792i	0.768666	−	0.639651i	$-0.220921\pi$
$859$	−4.97136	−	8.61065i	−0.169621	−	0.293792i	−0.938287	+	0.345859i	$0.887588\pi$
$860$		0			0
$861$	−9.93183	+	17.2024i	−0.338476	+	0.586257i
$862$	−27.3927	+	15.8152i	−0.932999	+	0.538667i
$863$	−3.82028	−	4.55283i	−0.130044	−	0.154980i	0.697093	−	0.716981i	$-0.254476\pi$
$863$	−3.82028	−	4.55283i	−0.130044	−	0.154980i	−0.827137	+	0.562000i	$0.810032\pi$
$864$	3.36105	−	19.0614i	0.114345	−	0.648483i
$865$		0			0
$866$	−28.8318	−	10.4939i	−0.979746	−	0.356598i
$867$	3.54072	−	9.72804i	0.120249	−	0.330382i
$868$	17.2514	−	3.04189i	0.585550	−	0.103248i
$869$	26.6729	+	22.3812i	0.904817	+	0.759231i
$870$		0			0
$871$	−10.3937	−	58.9456i	−0.352177	−	1.99730i
$872$	0.888237	−	2.44041i	0.0300795	−	0.0826428i
$873$	−1.84694	+	5.07443i	−0.0625095	+	0.171744i
$874$	−1.31807	+	2.28297i	−0.0445844	+	0.0772225i
$875$		0			0
$876$	−4.61062	+	3.86877i	−0.155778	+	0.130714i
$877$	0.432245	−	0.249557i	0.0145959	−	0.00842694i	−0.492684	−	0.870208i	$-0.663984\pi$
$877$	0.432245	−	0.249557i	0.0145959	−	0.00842694i	0.507280	+	0.861781i	$0.330651\pi$
$878$	−9.11047	−	5.25993i	−0.307463	−	0.177514i
$879$	5.77017	+	32.7243i	0.194623	+	1.10376i
$880$		0			0
$881$	−28.8674	+	10.5069i	−0.972567	+	0.353986i	−0.778946	−	0.627091i	$-0.784245\pi$
$881$	−28.8674	+	10.5069i	−0.972567	+	0.353986i	−0.193621	+	0.981076i	$0.562023\pi$
$882$		−	2.93020i		−	0.0986649i
$883$	−6.25471	−	17.1847i	−0.210488	−	0.578310i	0.788854	−	0.614580i	$-0.210675\pi$
$883$	−6.25471	−	17.1847i	−0.210488	−	0.578310i	−0.999342	+	0.0362700i	$0.988452\pi$
$884$	1.62453	−	9.21317i	0.0546388	−	0.309872i
$885$		0			0
$886$	−33.5804	+	28.1773i	−1.12815	+	0.946634i
$887$		−	22.6424i		−	0.760256i	−0.924934	−	0.380128i	$-0.875880\pi$
$887$		−	22.6424i		−	0.760256i	0.924934	−	0.380128i	$-0.124120\pi$
$888$	−4.78829	−	18.7020i	−0.160685	−	0.627597i
$889$	−49.0534			−1.64520
$890$		0			0
$891$	10.1639	+	8.52854i	0.340504	+	0.285717i
$892$	16.2682	+	2.86851i	0.544698	+	0.0960450i
$893$	1.12157	+	3.08148i	0.0375318	+	0.103118i
$894$	−7.56917			−0.253151
$895$		0			0
$896$	−20.2624	−	35.0955i	−0.676919	−	1.17246i
$897$	−14.1601	+	2.49680i	−0.472791	+	0.0833658i
$898$	30.5053	+	17.6123i	1.01798	+	0.587729i
$899$	29.9074	+	51.8012i	0.997468	+	1.72767i
$900$		0			0
$901$	−3.00016	+	17.0147i	−0.0999497	+	0.566843i
$902$	−16.9005	−	9.75750i	−0.562725	−	0.324889i
$903$	−5.16389	+	14.1877i	−0.171844	+	0.472136i
$904$	13.3805	+	4.87011i	0.445029	+	0.161977i
$905$		0			0
$906$	−27.8640	−	23.3807i	−0.925720	−	0.776772i
$907$	8.46179	−	10.0844i	0.280969	−	0.334846i	−0.607040	−	0.794671i	$-0.707643\pi$
$907$	8.46179	−	10.0844i	0.280969	−	0.334846i	0.888010	+	0.459825i	$0.152088\pi$
$908$	5.81896	−	1.02604i	0.193109	−	0.0340504i
$909$	−9.12311	−	3.32054i	−0.302594	−	0.110135i
$910$		0			0
$911$	27.0477	−	46.8480i	0.896130	−	1.55214i	0.0637306	−	0.997967i	$-0.479700\pi$
$911$	27.0477	−	46.8480i	0.896130	−	1.55214i	0.832400	−	0.554176i	$-0.186967\pi$
$912$	−5.26987	−	0.929220i	−0.174503	−	0.0307695i
$913$	−21.6798	−	25.8370i	−0.717498	−	0.855080i
$914$	−4.60988	−	7.98454i	−0.152481	−	0.264105i
$915$		0			0
$916$	−1.89871	−	10.7681i	−0.0627350	−	0.355788i
$917$	5.65067	−	3.26242i	0.186602	−	0.107734i
$918$	9.78198	+	26.8758i	0.322854	+	0.887033i
$919$	−30.4634			−1.00489			−0.502447	−	0.864608i	$-0.667567\pi$
$919$	−30.4634			−1.00489			−0.502447	+	0.864608i	$0.667567\pi$
$920$		0			0
$921$	6.94246	−	39.3726i	0.228762	−	1.29737i
$922$	27.2181	−	32.4372i	0.896380	−	1.06826i
$923$	−18.7143	−	22.3028i	−0.615988	−	0.734105i
$924$	−6.83487			−0.224851
$925$		0			0
$926$	22.9229			0.753292
$927$	1.92857	+	2.29838i	0.0633425	+	0.0754886i
$928$	−13.9969	+	16.6808i	−0.459470	+	0.547575i
$929$	4.34718	−	24.6541i	0.142626	−	0.808874i	−0.826616	−	0.562766i	$-0.809737\pi$
$929$	4.34718	−	24.6541i	0.142626	−	0.808874i	0.969242	−	0.246108i	$-0.0791517\pi$
$930$		0			0
$931$	−1.44229			−0.0472691
$932$	0.695419	+	1.91065i	0.0227792	+	0.0625853i
$933$	−24.6185	+	14.2135i	−0.805975	+	0.465330i
$934$	−2.54873	−	14.4546i	−0.0833969	−	0.472967i
$935$		0			0
$936$	5.16580	+	8.94743i	0.168850	+	0.292456i
$937$	6.79311	+	8.09571i	0.221921	+	0.264475i	0.865505	−	0.500900i	$-0.166998\pi$
$937$	6.79311	+	8.09571i	0.221921	+	0.264475i	−0.643584	+	0.765376i	$0.722553\pi$
$938$	−59.3735	−	10.4692i	−1.93862	−	0.341830i
$939$	13.8308	−	23.9557i	0.451353	−	0.781766i
$940$		0			0
$941$	31.3663	+	11.4164i	1.02251	+	0.372163i	0.798225	−	0.602360i	$-0.205773\pi$
$941$	31.3663	+	11.4164i	1.02251	+	0.372163i	0.224286	+	0.974523i	$0.427995\pi$
$942$	11.8639	−	2.09193i	0.386547	−	0.0681587i
$943$	−6.33521	+	7.55001i	−0.206303	+	0.245862i
$944$	−12.9036	−	10.8274i	−0.419978	−	0.352403i
$945$		0			0
$946$	−13.9386	−	5.07325i	−0.453185	−	0.164946i
$947$	8.82082	−	24.2350i	0.286638	−	0.787532i	−0.709893	−	0.704310i	$-0.751257\pi$
$947$	8.82082	−	24.2350i	0.286638	−	0.787532i	0.996531	−	0.0832221i	$-0.0265211\pi$
$948$	−10.4533	−	6.03522i	−0.339508	−	0.196015i
$949$	5.61285	−	31.8321i	0.182201	−	1.03331i
$950$		0			0
$951$	−21.1253	−	36.5900i	−0.685034	−	1.18651i
$952$	17.9182	+	10.3451i	0.580731	+	0.335285i
$953$	−54.3219	+	9.57842i	−1.75966	+	0.310276i	−0.957843	−	0.287294i	$-0.907244\pi$
$953$	−54.3219	+	9.57842i	−1.75966	+	0.310276i	−0.801817	+	0.597569i	$0.796133\pi$
$954$	4.34500	+	7.52576i	0.140675	+	0.243655i
$955$		0			0
$956$	4.25905			0.137747
$957$	−7.98212	−	21.9307i	−0.258025	−	0.708918i
$958$	−23.6644	−	4.17268i	−0.764563	−	0.134813i
$959$	34.2057	+	28.7020i	1.10456	+	0.926835i
$960$		0			0
$961$	57.3545			1.85015
$962$	−38.3752	−	27.5134i	−1.23727	−	0.887069i
$963$			17.4712i			0.563003i
$964$	7.94871	−	6.66976i	0.256011	−	0.214819i
$965$		0			0
$966$	−2.51493	+	14.2629i	−0.0809165	+	0.458900i
$967$	−0.287990	−	0.791247i	−0.00926115	−	0.0254448i	0.934976	−	0.354711i	$-0.115421\pi$
$967$	−0.287990	−	0.791247i	−0.00926115	−	0.0254448i	−0.944237	+	0.329266i	$0.893199\pi$
$968$		−	9.75050i		−	0.313393i
$969$	3.22851	−	1.17508i	0.103715	−	0.0377491i
$970$		0			0
$971$	4.88572	+	27.7083i	0.156790	+	0.889201i	0.957131	+	0.289656i	$0.0935408\pi$
$971$	4.88572	+	27.7083i	0.156790	+	0.889201i	−0.800341	+	0.599545i	$0.795348\pi$
$972$	5.21390	+	3.01025i	0.167236	+	0.0965538i
$973$	−29.7692	+	17.1873i	−0.954357	+	0.550998i
$974$	−21.3282	+	17.8965i	−0.683399	+	0.573440i
$975$		0			0
$976$	−16.1004	+	27.8868i	−0.515362	+	0.892633i
$977$	−6.12481	+	16.8278i	−0.195950	+	0.538368i	−0.998287	−	0.0585028i	$-0.981367\pi$
$977$	−6.12481	+	16.8278i	−0.195950	+	0.538368i	0.802337	+	0.596871i	$0.203590\pi$
$978$	12.5761	−	34.5526i	0.402140	−	1.10487i
$979$	−5.69312	−	32.2873i	−0.181953	−	1.03191i
$980$		0			0
$981$	0.865324	+	0.726093i	0.0276277	+	0.0231824i
$982$	19.4920	−	3.43697i	0.622015	−	0.109678i
$983$	−2.91385	+	8.00573i	−0.0929373	+	0.255343i	−0.977448	−	0.211177i	$-0.932270\pi$
$983$	−2.91385	+	8.00573i	−0.0929373	+	0.255343i	0.884511	+	0.466520i	$0.154493\pi$
$984$	−13.9581	−	5.08033i	−0.444967	−	0.161955i
$985$		0			0
$986$	5.58734	−	31.6874i	0.177937	−	1.00913i
$987$	11.5805	+	13.8011i	0.368611	+	0.439294i
$988$	−2.00581	+	1.15805i	−0.0638132	+	0.0368426i
$989$	−3.74567	+	6.48770i	−0.119106	+	0.206297i
$990$		0			0
$991$	−8.03390	−	13.9151i	−0.255205	−	0.442029i	0.709746	−	0.704458i	$-0.248810\pi$
$991$	−8.03390	−	13.9151i	−0.255205	−	0.442029i	−0.964951	+	0.262429i	$0.915476\pi$
$992$	11.0011	+	30.2252i	0.349285	+	0.959652i
$993$		−	11.1551i		−	0.353995i
$994$	−27.5570	+	10.0299i	−0.874056	+	0.318130i
$995$		0			0
$996$	8.95672	+	7.51558i	0.283805	+	0.238140i
$997$	−0.125712	−	0.149817i	−0.00398133	−	0.00474476i	0.764050	−	0.645157i	$-0.223208\pi$
$997$	−0.125712	−	0.149817i	−0.00398133	−	0.00474476i	−0.768031	+	0.640412i	$0.778764\pi$
$998$			47.2653i			1.49616i
$999$	34.2396	+	3.38073i	1.08329	+	0.106962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bc.e.49.20		156
5.2	odd	4		925.2.p.f.826.3	yes	78
5.3	odd	4		925.2.p.e.826.11	yes	78
5.4	even	2	inner	925.2.bc.e.49.7		156
37.34	even	9	inner	925.2.bc.e.774.7		156
185.34	even	18	inner	925.2.bc.e.774.20		156
185.108	odd	36		925.2.p.e.626.11	✓	78
185.182	odd	36		925.2.p.f.626.3	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.p.e.626.11	✓	78	185.108	odd	36
925.2.p.e.826.11	yes	78	5.3	odd	4
925.2.p.f.626.3	yes	78	185.182	odd	36
925.2.p.f.826.3	yes	78	5.2	odd	4
925.2.bc.e.49.7		156	5.4	even	2	inner
925.2.bc.e.49.20		156	1.1	even	1	trivial
925.2.bc.e.774.7		156	37.34	even	9	inner
925.2.bc.e.774.20		156	185.34	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.04160 + 1.24133i) q^{2} +(-0.916161 + 1.09184i) q^{3} +(-0.108678 + 0.616341i) q^{4} -2.30961 q^{6} +(-1.01845 - 2.79817i) q^{7} +(1.92841 - 1.11337i) q^{8} +(0.168185 + 0.953823i) q^{9} +O(q^{10})\)	\(q+(1.04160 + 1.24133i) q^{2} +(-0.916161 + 1.09184i) q^{3} +(-0.108678 + 0.616341i) q^{4} -2.30961 q^{6} +(-1.01845 - 2.79817i) q^{7} +(1.92841 - 1.11337i) q^{8} +(0.168185 + 0.953823i) q^{9} +(1.28658 + 2.22843i) q^{11} +(-0.573379 - 0.683326i) q^{12} +(4.71774 + 0.831864i) q^{13} +(2.41264 - 4.17882i) q^{14} +(4.56692 + 1.66222i) q^{16} +(-3.07296 + 0.541846i) q^{17} +(-1.00883 + 1.20228i) q^{18} +(0.591780 + 0.496563i) q^{19} +(3.98822 + 1.45159i) q^{21} +(-1.42611 + 3.91821i) q^{22} +(1.82372 + 1.05293i) q^{23} +(-0.551117 + 3.12554i) q^{24} +(3.88139 + 6.72276i) q^{26} +(-4.89853 - 2.82817i) q^{27} +(1.83531 - 0.323615i) q^{28} +(3.18174 + 5.51093i) q^{29} +9.39971 q^{31} +(1.17036 + 3.21555i) q^{32} +(-3.61180 - 0.636857i) q^{33} +(-3.87342 - 3.25018i) q^{34} -0.606159 q^{36} +(-5.54118 + 2.50905i) q^{37} +1.25182i q^{38} +(-5.23047 + 4.38888i) q^{39} +(-0.812712 + 4.60912i) q^{41} +(2.35223 + 6.46269i) q^{42} +3.55740i q^{43} +(-1.51329 + 0.550794i) q^{44} +(0.592560 + 3.36058i) q^{46} +(3.67619 + 2.12245i) q^{47} +(-5.99891 + 3.46347i) q^{48} +(-1.43021 + 1.20009i) q^{49} +(2.22372 - 3.85159i) q^{51} +(-1.02542 + 2.81733i) q^{52} +(1.89374 - 5.20300i) q^{53} +(-1.59162 - 9.02654i) q^{54} +(-5.07939 - 4.26212i) q^{56} +(-1.08433 + 0.191197i) q^{57} +(-3.52680 + 9.68981i) q^{58} +(-3.25692 - 1.18542i) q^{59} +(-1.15054 + 6.52502i) q^{61} +(9.79077 + 11.6682i) q^{62} +(2.49767 - 1.44203i) q^{63} +(2.08749 - 3.61565i) q^{64} +(-2.97151 - 5.14680i) q^{66} +(-4.27336 - 11.7410i) q^{67} -1.95288i q^{68} +(-2.82045 + 1.02656i) q^{69} +(-4.65562 - 3.90653i) q^{71} +(1.38629 + 1.65211i) q^{72} -6.74732i q^{73} +(-8.88628 - 4.26502i) q^{74} +(-0.370365 + 0.310773i) q^{76} +(4.92519 - 5.86962i) q^{77} +(-10.8961 - 1.92128i) q^{78} +(12.7155 - 4.62808i) q^{79} +(4.84536 - 1.76357i) q^{81} +(-6.56798 + 3.79203i) q^{82} +(-12.9084 + 2.27610i) q^{83} +(-1.32811 + 2.30035i) q^{84} +(-4.41592 + 3.70540i) q^{86} +(-8.93203 - 1.57496i) q^{87} +(4.96212 + 2.86488i) q^{88} +(-11.9729 - 4.35777i) q^{89} +(-2.47708 - 14.0482i) q^{91} +(-0.847159 + 1.00960i) q^{92} +(-8.61165 + 10.2630i) q^{93} +(1.19446 + 6.77413i) q^{94} +(-4.58310 - 1.66811i) q^{96} +(4.82854 + 2.78776i) q^{97} +(-2.97942 - 0.525352i) q^{98} +(-1.90914 + 1.60196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{4}+O(q^{10}) \) 156 * q - 6 * q^4	\( 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) \) 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Introduction

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