LMFDB - Embedded newform 925.2.bb.e.576.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(151,925)] 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("925.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			576.12
Character	$\chi$	$=$	925.576
Dual form			925.2.bb.e.326.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.454714 - 1.24932i) q^{2} +(-1.95762 + 0.712514i) q^{3} +(0.178063 + 0.149413i) q^{4} +2.76967i q^{6} +(0.362791 - 2.05749i) q^{7} +(2.57038 - 1.48401i) q^{8} +(1.02645 - 0.861296i) q^{9} +(1.09872 + 1.90303i) q^{11} +(-0.455038 - 0.165620i) q^{12} +(0.0916955 - 0.109278i) q^{13} +(-2.40549 - 1.38881i) q^{14} +(-0.604483 - 3.42819i) q^{16} +(-1.41689 - 1.68858i) q^{17} +(-0.609289 - 1.67401i) q^{18} +(1.39535 + 3.83370i) q^{19} +(0.755786 + 4.28627i) q^{21} +(2.87709 - 0.507309i) q^{22} +(2.41756 + 1.39578i) q^{23} +(-3.97445 + 4.73656i) q^{24} +(-0.0948281 - 0.164247i) q^{26} +(1.72916 - 2.99500i) q^{27} +(0.372015 - 0.312158i) q^{28} +(2.08912 - 1.20615i) q^{29} -7.10743i q^{31} +(1.28810 + 0.227127i) q^{32} +(-3.50681 - 2.94256i) q^{33} +(-2.75385 + 1.00232i) q^{34} +0.311462 q^{36} +(5.77175 + 1.92013i) q^{37} +5.42399 q^{38} +(-0.101642 + 0.279260i) q^{39} +(3.30254 + 2.77116i) q^{41} +(5.69858 + 1.00481i) q^{42} +0.637427i q^{43} +(-0.0886964 + 0.503022i) q^{44} +(2.84307 - 2.38562i) q^{46} +(2.51859 - 4.36233i) q^{47} +(3.62598 + 6.28039i) q^{48} +(2.47619 + 0.901260i) q^{49} +(3.97686 + 2.29604i) q^{51} +(0.0326552 - 0.00575799i) q^{52} +(-2.11651 - 12.0033i) q^{53} +(-2.95542 - 3.52214i) q^{54} +(-2.12083 - 5.82693i) q^{56} +(-5.46313 - 6.51071i) q^{57} +(-0.556915 - 3.15842i) q^{58} +(13.3122 - 2.34730i) q^{59} +(6.93152 - 8.26066i) q^{61} +(-8.87943 - 3.23185i) q^{62} +(-1.39972 - 2.42439i) q^{63} +(4.35055 - 7.53537i) q^{64} +(-5.27078 + 3.04309i) q^{66} +(-0.555953 + 3.15297i) q^{67} -0.512375i q^{68} +(-5.72717 - 1.00985i) q^{69} +(-7.56215 + 2.75240i) q^{71} +(1.36020 - 3.73713i) q^{72} -1.78846 q^{73} +(5.02334 - 6.33763i) q^{74} +(-0.324343 + 0.891124i) q^{76} +(4.31408 - 1.57020i) q^{77} +(0.302665 + 0.253966i) q^{78} +(15.4992 + 2.73292i) q^{79} +(-1.94909 + 11.0539i) q^{81} +(4.96377 - 2.86583i) q^{82} +(-2.54512 + 2.13561i) q^{83} +(-0.505846 + 0.876151i) q^{84} +(0.796348 + 0.289847i) q^{86} +(-3.23029 + 3.84971i) q^{87} +(5.64825 + 3.26102i) q^{88} +(-18.4072 + 3.24569i) q^{89} +(-0.191573 - 0.228308i) q^{91} +(0.221931 + 0.609751i) q^{92} +(5.06414 + 13.9136i) q^{93} +(-4.30469 - 5.13013i) q^{94} +(-2.68343 + 0.473162i) q^{96} +(-8.28814 - 4.78516i) q^{97} +(2.25192 - 2.68373i) q^{98} +(2.76686 + 1.00705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

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 $

$2$	0.454714	−	1.24932i	0.321531	−	0.883400i	−0.668646	−	0.743581i	$-0.733126\pi$
$2$	0.454714	−	1.24932i	0.321531	−	0.883400i	0.990177	−	0.139819i	$-0.0446520\pi$
$3$	−1.95762	+	0.712514i	−1.13023	+	0.411370i	−0.838376	−	0.545092i	$-0.816495\pi$
$3$	−1.95762	+	0.712514i	−1.13023	+	0.411370i	−0.291855	+	0.956463i	$0.594272\pi$
$4$	0.178063	+	0.149413i	0.0890315	+	0.0747063i
$5$		0			0
$5$		0			0
$6$			2.76967i			1.13071i
$7$	0.362791	−	2.05749i	0.137122	−	0.777659i	−0.836236	−	0.548370i	$-0.815249\pi$
$7$	0.362791	−	2.05749i	0.137122	−	0.777659i	0.973358	−	0.229289i	$-0.0736402\pi$
$8$	2.57038	−	1.48401i	0.908768	−	0.524677i
$9$	1.02645	−	0.861296i	0.342151	−	0.287099i
$10$		0			0
$11$	1.09872	+	1.90303i	0.331276	+	0.573786i	0.982762	−	0.184874i	$-0.0591876\pi$
$11$	1.09872	+	1.90303i	0.331276	+	0.573786i	−0.651487	+	0.758660i	$0.725854\pi$
$12$	−0.455038	−	0.165620i	−0.131358	−	0.0478104i
$13$	0.0916955	−	0.109278i	0.0254318	−	0.0303084i	−0.753179	−	0.657816i	$-0.771480\pi$
$13$	0.0916955	−	0.109278i	0.0254318	−	0.0303084i	0.778610	+	0.627508i	$0.215925\pi$
$14$	−2.40549	−	1.38881i	−0.642895	−	0.371175i
$15$		0			0
$16$	−0.604483	−	3.42819i	−0.151121	−	0.857049i
$17$	−1.41689	−	1.68858i	−0.343645	−	0.409541i	0.566346	−	0.824168i	$-0.308357\pi$
$17$	−1.41689	−	1.68858i	−0.343645	−	0.409541i	−0.909992	+	0.414627i	$0.863912\pi$
$18$	−0.609289	−	1.67401i	−0.143611	−	0.394567i
$19$	1.39535	+	3.83370i	0.320116	+	0.879511i	0.990502	+	0.137499i	$0.0439063\pi$
$19$	1.39535	+	3.83370i	0.320116	+	0.879511i	−0.670386	+	0.742013i	$0.733871\pi$
$20$		0			0
$21$	0.755786	+	4.28627i	0.164926	+	0.935342i
$22$	2.87709	−	0.507309i	0.613398	−	0.108159i
$23$	2.41756	+	1.39578i	0.504096	+	0.291040i	0.730404	−	0.683016i	$-0.239332\pi$
$23$	2.41756	+	1.39578i	0.504096	+	0.291040i	−0.226307	+	0.974056i	$0.572665\pi$
$24$	−3.97445	+	4.73656i	−0.811280	+	0.966846i
$25$		0			0
$26$	−0.0948281	−	0.164247i	−0.0185973	−	0.0322115i
$27$	1.72916	−	2.99500i	0.332778	−	0.576388i
$28$	0.372015	−	0.312158i	0.0703043	−	0.0589923i
$29$	2.08912	−	1.20615i	0.387940	−	0.223977i	−0.293327	−	0.956012i	$-0.594763\pi$
$29$	2.08912	−	1.20615i	0.387940	−	0.223977i	0.681267	+	0.732035i	$0.261429\pi$
$30$		0			0
$31$		−	7.10743i		−	1.27653i	−0.769816	−	0.638266i	$-0.779652\pi$
$31$		−	7.10743i		−	1.27653i	0.769816	−	0.638266i	$-0.220348\pi$
$32$	1.28810	+	0.227127i	0.227706	+	0.0401507i
$33$	−3.50681	−	2.94256i	−0.610457	−	0.512234i
$34$	−2.75385	+	1.00232i	−0.472281	+	0.171896i
$35$		0			0
$36$	0.311462			0.0519103
$37$	5.77175	+	1.92013i	0.948870	+	0.315667i
$37$	5.77175	+	1.92013i	0.948870	+	0.315667i
$38$	5.42399			0.879888
$39$	−0.101642	+	0.279260i	−0.0162758	+	0.0447173i
$40$		0			0
$41$	3.30254	+	2.77116i	0.515770	+	0.432783i	0.863154	−	0.504940i	$-0.168486\pi$
$41$	3.30254	+	2.77116i	0.515770	+	0.432783i	−0.347384	+	0.937723i	$0.612930\pi$
$42$	5.69858	+	1.00481i	0.879310	+	0.155046i
$43$			0.637427i			0.0972067i	0.998818	+	0.0486034i	$0.0154770\pi$
$43$			0.637427i			0.0972067i	−0.998818	+	0.0486034i	$0.984523\pi$
$44$	−0.0886964	+	0.503022i	−0.0133715	+	0.0758335i
$45$		0			0
$46$	2.84307	−	2.38562i	0.419187	−	0.351740i
$47$	2.51859	−	4.36233i	0.367374	−	0.636311i	−0.621780	−	0.783192i	$-0.713590\pi$
$47$	2.51859	−	4.36233i	0.367374	−	0.636311i	0.989154	+	0.146881i	$0.0469235\pi$
$48$	3.62598	+	6.28039i	0.523366	+	0.906496i
$49$	2.47619	+	0.901260i	0.353742	+	0.128751i
$50$		0			0
$51$	3.97686	+	2.29604i	0.556871	+	0.321510i
$52$	0.0326552	−	0.00575799i	0.00452846	−	0.000798489i
$53$	−2.11651	−	12.0033i	−0.290725	−	1.64879i	−0.684086	−	0.729401i	$-0.739799\pi$
$53$	−2.11651	−	12.0033i	−0.290725	−	1.64879i	0.393360	−	0.919384i	$-0.371312\pi$
$54$	−2.95542	−	3.52214i	−0.402182	−	0.479302i
$55$		0			0
$56$	−2.12083	−	5.82693i	−0.283408	−	0.778656i
$57$	−5.46313	−	6.51071i	−0.723610	−	0.862364i
$58$	−0.556915	−	3.15842i	−0.0731266	−	0.414721i
$59$	13.3122	−	2.34730i	1.73310	−	0.305592i	0.784046	−	0.620703i	$-0.213153\pi$
$59$	13.3122	−	2.34730i	1.73310	−	0.305592i	0.949055	+	0.315111i	$0.102042\pi$
$60$		0			0
$61$	6.93152	−	8.26066i	0.887490	−	1.05767i	−0.110474	−	0.993879i	$-0.535237\pi$
$61$	6.93152	−	8.26066i	0.887490	−	1.05767i	0.997963	−	0.0637899i	$-0.0203188\pi$
$62$	−8.87943	−	3.23185i	−1.12769	−	0.410445i
$63$	−1.39972	−	2.42439i	−0.176348	−	0.305444i
$64$	4.35055	−	7.53537i	0.543819	−	0.941921i
$65$		0			0
$66$	−5.27078	+	3.04309i	−0.648788	+	0.374578i
$67$	−0.555953	+	3.15297i	−0.0679205	+	0.385196i	0.931831	+	0.362893i	$0.118211\pi$
$67$	−0.555953	+	3.15297i	−0.0679205	+	0.385196i	−0.999751	+	0.0223030i	$0.992900\pi$
$68$		−	0.512375i		−	0.0621345i
$69$	−5.72717	−	1.00985i	−0.689470	−	0.121572i
$70$		0			0
$71$	−7.56215	+	2.75240i	−0.897462	+	0.326649i	−0.749235	−	0.662304i	$-0.769579\pi$
$71$	−7.56215	+	2.75240i	−0.897462	+	0.326649i	−0.148227	+	0.988953i	$0.547357\pi$
$72$	1.36020	−	3.73713i	0.160302	−	0.440425i
$73$	−1.78846			−0.209323			−0.104662	−	0.994508i	$-0.533376\pi$
$73$	−1.78846			−0.209323			−0.104662	+	0.994508i	$0.533376\pi$
$74$	5.02334	−	6.33763i	0.583951	−	0.736735i
$75$		0			0
$76$	−0.324343	+	0.891124i	−0.0372047	+	0.102219i
$77$	4.31408	−	1.57020i	0.491635	−	0.178941i
$78$	0.302665	+	0.253966i	0.0342701	+	0.0287560i
$79$	15.4992	+	2.73292i	1.74379	+	0.307478i	0.952631	−	0.304129i	$-0.0983653\pi$
$79$	15.4992	+	2.73292i	1.74379	+	0.307478i	0.791162	+	0.611606i	$0.209476\pi$
$80$		0			0
$81$	−1.94909	+	11.0539i	−0.216566	+	1.22821i
$82$	4.96377	−	2.86583i	0.548156	−	0.316478i
$83$	−2.54512	+	2.13561i	−0.279363	+	0.234413i	−0.771693	−	0.635995i	$-0.780590\pi$
$83$	−2.54512	+	2.13561i	−0.279363	+	0.234413i	0.492330	+	0.870409i	$0.336145\pi$
$84$	−0.505846	+	0.876151i	−0.0551923	+	0.0955959i
$85$		0			0
$86$	0.796348	+	0.289847i	0.0858724	+	0.0312550i
$87$	−3.23029	+	3.84971i	−0.346324	+	0.412732i
$88$	5.64825	+	3.26102i	0.602105	+	0.347626i
$89$	−18.4072	+	3.24569i	−1.95116	+	0.344043i	−0.951869	+	0.306505i	$0.900840\pi$
$89$	−18.4072	+	3.24569i	−1.95116	+	0.344043i	−0.999295	+	0.0375378i	$0.988049\pi$
$90$		0			0
$91$	−0.191573	−	0.228308i	−0.0200823	−	0.0239332i
$92$	0.221931	+	0.609751i	0.0231379	+	0.0635709i
$93$	5.06414	+	13.9136i	0.525127	+	1.44278i
$94$	−4.30469	−	5.13013i	−0.443995	−	0.529132i
$95$		0			0
$96$	−2.68343	+	0.473162i	−0.273877	+	0.0482919i
$97$	−8.28814	−	4.78516i	−0.841533	−	0.485859i	0.0162519	−	0.999868i	$-0.494827\pi$
$97$	−8.28814	−	4.78516i	−0.841533	−	0.485859i	−0.857785	+	0.514009i	$0.828160\pi$
$98$	2.25192	−	2.68373i	0.227478	−	0.271098i
$99$	2.76686	+	1.00705i	0.278080	+	0.101213i
$100$		0			0
$101$	0.914760	−	1.58441i	0.0910220	−	0.157655i	−0.816919	−	0.576752i	$-0.804320\pi$
$101$	0.914760	−	1.58441i	0.0910220	−	0.157655i	0.907941	+	0.419097i	$0.137653\pi$
$102$	4.67681	−	3.92431i	0.463073	−	0.388565i
$103$	−11.0853	+	6.40012i	−1.09227	+	0.630623i	−0.934180	−	0.356802i	$-0.883867\pi$
$103$	−11.0853	+	6.40012i	−1.09227	+	0.630623i	−0.158090	+	0.987425i	$0.550534\pi$
$104$	0.0735221	−	0.416965i	0.00720944	−	0.0408868i
$105$		0			0
$106$	−15.9584	−	2.81389i	−1.55001	−	0.273309i
$107$	5.67934	+	4.76553i	0.549042	+	0.460701i	0.874617	−	0.484815i	$-0.161113\pi$
$107$	5.67934	+	4.76553i	0.549042	+	0.460701i	−0.325574	+	0.945517i	$0.605558\pi$
$108$	0.755391	−	0.274940i	0.0726875	−	0.0264561i
$109$	2.87069	−	7.88717i	0.274963	−	0.755454i	−0.722951	−	0.690899i	$-0.757215\pi$
$109$	2.87069	−	7.88717i	0.274963	−	0.755454i	0.997914	−	0.0645550i	$-0.0205628\pi$
$110$		0			0
$111$	−12.6670	+	0.353584i	−1.20230	+	0.0335607i
$112$	−7.27278			−0.687213
$113$	−4.25150	+	11.6809i	−0.399947	+	1.09885i	0.562363	+	0.826891i	$0.309893\pi$
$113$	−4.25150	+	11.6809i	−0.399947	+	1.09885i	−0.962310	+	0.271955i	$0.912330\pi$
$114$	−10.6181	+	3.86467i	−0.994476	+	0.361960i
$115$		0			0
$116$	0.552209	+	0.0973694i	0.0512714	+	0.00904052i
$117$		−	0.191146i		−	0.0176715i
$118$	3.12072	−	17.6985i	0.287286	−	1.62928i
$119$	−3.98827	+	2.30263i	−0.365604	+	0.211082i
$120$		0			0
$121$	3.08564	−	5.34449i	0.280513	−	0.485862i
$122$	−7.16832	−	12.4159i	−0.648989	−	1.12408i
$123$	−8.43960	−	3.07176i	−0.760973	−	0.276972i
$124$	1.06194	−	1.26557i	0.0953650	−	0.113652i
$125$		0			0
$126$	−3.66530	+	0.646291i	−0.326531	+	0.0575762i
$127$	3.57911	+	20.2981i	0.317594	+	1.80117i	0.557289	+	0.830318i	$0.311841\pi$
$127$	3.57911	+	20.2981i	0.317594	+	1.80117i	−0.239695	+	0.970848i	$0.577047\pi$
$128$	−5.75431	−	6.85772i	−0.508614	−	0.606143i
$129$	−0.454176	−	1.24784i	−0.0399879	−	0.109866i
$130$		0			0
$131$	0.580925	+	0.692320i	0.0507557	+	0.0604883i	0.790825	−	0.612042i	$-0.209652\pi$
$131$	0.580925	+	0.692320i	0.0507557	+	0.0604883i	−0.740069	+	0.672531i	$0.765207\pi$
$132$	−0.184777	−	1.04792i	−0.0160828	−	0.0912099i
$133$	8.39403	−	1.48009i	0.727855	−	0.128340i
$134$	3.68625	+	2.12826i	0.318444	+	0.183853i
$135$		0			0
$136$	−6.14781	−	2.23762i	−0.527171	−	0.191874i
$137$	1.29879	+	2.24956i	0.110963	+	0.192193i	0.916159	−	0.400816i	$-0.131273\pi$
$137$	1.29879	+	2.24956i	0.110963	+	0.192193i	−0.805196	+	0.593009i	$0.797940\pi$
$138$	−3.86585	+	6.69585i	−0.329083	+	0.569989i
$139$	−12.1476	+	10.1930i	−1.03035	+	0.864563i	−0.990892	−	0.134658i	$-0.957006\pi$
$139$	−12.1476	+	10.1930i	−1.03035	+	0.864563i	−0.0394541	+	0.999221i	$0.512562\pi$
$140$		0			0
$141$	−1.82222	+	10.3343i	−0.153458	+	0.870305i
$142$			10.6991i			0.897846i
$143$	0.308708	+	0.0544336i	0.0258155	+	0.00455196i
$144$	−3.57316	−	2.99824i	−0.297764	−	0.249853i
$145$		0			0
$146$	−0.813238	+	2.23435i	−0.0673040	+	0.184916i
$147$	−5.48960			−0.452774
$148$	0.740845	+	1.20428i	0.0608971	+	0.0989909i
$149$	−19.1935			−1.57240			−0.786198	−	0.617975i	$-0.787953\pi$
$149$	−19.1935			−1.57240			−0.786198	+	0.617975i	$0.787953\pi$
$150$		0			0
$151$	11.2417	−	4.09164i	0.914836	−	0.332973i	0.158654	−	0.987334i	$-0.449285\pi$
$151$	11.2417	−	4.09164i	0.914836	−	0.332973i	0.756182	+	0.654361i	$0.227062\pi$
$152$	9.27585	+	7.78336i	0.752371	+	0.631314i
$153$	−2.90873	−	0.512888i	−0.235157	−	0.0414646i
$154$		−	6.10364i		−	0.491846i
$155$		0			0
$156$	−0.0598237	+	0.0345392i	−0.00478973	+	0.00276535i
$157$	0.0632556	−	0.0530778i	0.00504835	−	0.00423607i	−0.640260	−	0.768158i	$-0.721173\pi$
$157$	0.0632556	−	0.0530778i	0.00504835	−	0.00423607i	0.645308	+	0.763922i	$0.276729\pi$
$158$	10.4620	−	18.1207i	0.832310	−	1.44160i
$159$	12.6959	+	21.9899i	1.00685	+	1.74391i
$160$		0			0
$161$	3.74887	−	4.46774i	0.295453	−	0.352107i
$162$	12.9235	+	7.46137i	1.01536	+	0.586221i
$163$	22.2419	−	3.92185i	1.74212	−	0.307183i	0.790046	−	0.613047i	$-0.210057\pi$
$163$	22.2419	−	3.92185i	1.74212	−	0.307183i	0.952075	+	0.305864i	$0.0989454\pi$
$164$	0.174014	+	0.986883i	0.0135882	+	0.0770626i
$165$		0			0
$166$	1.51075	+	4.15075i	0.117257	+	0.322160i
$167$	3.23359	+	8.88421i	0.250223	+	0.687481i	0.999677	+	0.0254245i	$0.00809375\pi$
$167$	3.23359	+	8.88421i	0.250223	+	0.687481i	−0.749454	+	0.662056i	$0.769684\pi$
$168$	8.30354	+	9.89577i	0.640632	+	0.763475i
$169$	2.25389	+	12.7825i	0.173376	+	0.983266i
$170$		0			0
$171$	4.73422	+	2.73330i	0.362035	+	0.209021i
$172$	−0.0952397	+	0.113502i	−0.00726196	+	0.00865446i
$173$	−19.9871	−	7.27472i	−1.51959	−	0.553086i	−0.558546	−	0.829474i	$-0.688641\pi$
$173$	−19.9871	−	7.27472i	−1.51959	−	0.553086i	−0.961046	+	0.276387i	$0.910863\pi$
$174$	3.34065	+	5.78617i	0.253254	+	0.438649i
$175$		0			0
$176$	5.85981	−	4.91697i	0.441700	−	0.370630i
$177$	−24.3877	+	14.0802i	−1.83309	+	1.05834i
$178$	−4.31513	+	24.4723i	−0.323433	+	1.83428i
$179$		−	9.99260i		−	0.746882i	−0.927654	−	0.373441i	$-0.878178\pi$
$179$		−	9.99260i		−	0.746882i	0.927654	−	0.373441i	$-0.121822\pi$
$180$		0			0
$181$	−9.05557	−	7.59852i	−0.673095	−	0.564794i	0.240885	−	0.970554i	$-0.422562\pi$
$181$	−9.05557	−	7.59852i	−0.673095	−	0.564794i	−0.913980	+	0.405760i	$0.867007\pi$
$182$	−0.372340	+	0.135521i	−0.0275997	+	0.0100455i
$183$	−7.68341	+	21.1100i	−0.567974	+	1.56050i
$184$	8.28541			0.610809
$185$		0			0
$186$	19.6852			1.44339
$187$	1.65667	−	4.55166i	0.121148	−	0.332850i
$188$	1.10026	−	0.400460i	0.0802444	−	0.0292066i
$189$	−5.53486	−	4.64430i	−0.402602	−	0.337823i
$190$		0			0
$191$		−	18.9524i		−	1.37135i	−0.727909	−	0.685674i	$-0.759507\pi$
$191$		−	18.9524i		−	1.37135i	0.727909	−	0.685674i	$-0.240493\pi$
$192$	−3.14765	+	17.8512i	−0.227162	+	1.28830i
$193$	−12.1967	+	7.04176i	−0.877937	+	0.506877i	−0.869978	−	0.493091i	$-0.835867\pi$
$193$	−12.1967	+	7.04176i	−0.877937	+	0.506877i	−0.00795950	+	0.999968i	$0.502534\pi$
$194$	−9.74691	+	8.17863i	−0.699787	+	0.587191i
$195$		0			0
$196$	0.306259	+	0.530456i	0.0218756	+	0.0378897i
$197$	−13.3080	−	4.84371i	−0.948154	−	0.345100i	−0.178773	−	0.983890i	$-0.557213\pi$
$197$	−13.3080	−	4.84371i	−0.948154	−	0.345100i	−0.769381	+	0.638790i	$0.779435\pi$
$198$	2.51626	−	2.99876i	0.178823	−	0.213112i
$199$	8.71697	+	5.03275i	0.617930	+	0.356762i	0.776063	−	0.630656i	$-0.217214\pi$
$199$	8.71697	+	5.03275i	0.617930	+	0.356762i	−0.158133	+	0.987418i	$0.550547\pi$
$200$		0			0
$201$	−1.15819	−	6.56842i	−0.0816924	−	0.463301i
$202$	−1.56348	−	1.86328i	−0.110006	−	0.131100i
$203$	−1.72374	−	4.73593i	−0.120983	−	0.332397i
$204$	0.365074	+	1.00303i	0.0255603	+	0.0702264i
$205$		0			0
$206$	2.95512	+	16.7593i	0.205893	+	1.16768i
$207$	3.68369	−	0.649534i	0.256034	−	0.0451457i
$208$	−0.430056	−	0.248293i	−0.0298190	−	0.0172160i
$209$	−5.76257	+	6.86756i	−0.398605	+	0.475039i
$210$		0			0
$211$	6.02963	+	10.4436i	0.415097	+	0.718969i	0.995439	−	0.0954044i	$-0.0304144\pi$
$211$	6.02963	+	10.4436i	0.415097	+	0.718969i	−0.580342	+	0.814373i	$0.697081\pi$
$212$	1.41658	−	2.45359i	0.0972910	−	0.168513i
$213$	12.8427	−	10.7763i	0.879965	−	0.738378i
$214$	8.53613	−	4.92834i	0.583518	−	0.336894i
$215$		0			0
$216$		−	10.2644i		−	0.698403i
$217$	−14.6235	−	2.57851i	−0.992706	−	0.175041i
$218$	−8.54822	−	7.17281i	−0.578959	−	0.485804i
$219$	3.50112	−	1.27430i	0.236584	−	0.0861094i
$220$		0			0
$221$	−0.314448			−0.0211520
$222$	−5.31812	+	15.9859i	−0.356929	+	1.07290i
$223$	1.11069			0.0743776			0.0371888	−	0.999308i	$-0.488160\pi$
$223$	1.11069			0.0743776			0.0371888	+	0.999308i	$0.488160\pi$
$224$	0.934622	−	2.56785i	0.0624471	−	0.171572i
$225$		0			0
$226$	12.6599	+	10.6229i	0.842125	+	0.706627i
$227$	−9.58318	−	1.68977i	−0.636058	−	0.112154i	−0.153685	−	0.988120i	$-0.549114\pi$
$227$	−9.58318	−	1.68977i	−0.636058	−	0.112154i	−0.482373	+	0.875966i	$0.660225\pi$
$228$		−	1.97558i		−	0.130836i
$229$	2.60606	−	14.7797i	0.172213	−	0.976669i	−0.769098	−	0.639130i	$-0.779294\pi$
$229$	2.60606	−	14.7797i	0.172213	−	0.976669i	0.941312	−	0.337539i	$-0.109594\pi$
$230$		0			0
$231$	−7.32653	+	6.14769i	−0.482050	+	0.404488i
$232$	3.57989	−	6.20055i	0.235031	−	0.407086i
$233$	11.1145	+	19.2509i	0.728134	+	1.26117i	0.957671	+	0.287866i	$0.0929456\pi$
$233$	11.1145	+	19.2509i	0.728134	+	1.26117i	−0.229537	+	0.973300i	$0.573721\pi$
$234$	−0.238802	−	0.0869168i	−0.0156110	−	0.00568193i
$235$		0			0
$236$	2.72113	+	1.57104i	0.177130	+	0.102266i
$237$	−32.2887	+	5.69337i	−2.09738	+	0.369824i
$238$	1.06319	+	6.02965i	0.0689164	+	0.390844i
$239$	−3.56934	−	4.25378i	−0.230882	−	0.275154i	0.638148	−	0.769913i	$-0.279701\pi$
$239$	−3.56934	−	4.25378i	−0.230882	−	0.275154i	−0.869030	+	0.494759i	$0.835256\pi$
$240$		0			0
$241$	4.93122	+	13.5484i	0.317648	+	0.872731i	0.991054	+	0.133458i	$0.0426082\pi$
$241$	4.93122	+	13.5484i	0.317648	+	0.872731i	−0.673406	+	0.739272i	$0.735170\pi$
$242$	−5.27387	−	6.28515i	−0.339017	−	0.404025i
$243$	−2.25886	−	12.8106i	−0.144906	−	0.821801i
$244$	2.46849	−	0.435262i	0.158029	−	0.0278648i
$245$		0			0
$246$	−7.67520	+	9.14695i	−0.489353	+	0.583188i
$247$	0.546889	+	0.199051i	0.0347977	+	0.0126653i
$248$	−10.5475	−	18.2688i	−0.669767	−	1.16007i
$249$	3.46071	−	5.99413i	0.219314	−	0.379863i
$250$		0			0
$251$	−0.243065	+	0.140333i	−0.0153421	+	0.00885777i	−0.507651	−	0.861563i	$-0.669486\pi$
$251$	−0.243065	+	0.140333i	−0.0153421	+	0.00885777i	0.492309	+	0.870420i	$0.336153\pi$
$252$	0.112996	−	0.640830i	0.00711806	−	0.0403685i
$253$			6.13427i			0.385658i
$254$	26.9862	+	4.75840i	1.69327	+	0.298569i
$255$		0			0
$256$	5.16869	−	1.88125i	0.323043	−	0.117578i
$257$	2.19011	−	6.01727i	0.136615	−	0.375347i	−0.852454	−	0.522803i	$-0.824886\pi$
$257$	2.19011	−	6.01727i	0.136615	−	0.375347i	0.989069	+	0.147456i	$0.0471086\pi$
$258$	−1.76546			−0.109913
$259$	6.04459	−	11.1787i	0.375592	−	0.694612i
$260$		0			0
$261$	1.10553	−	3.03741i	0.0684304	−	0.188011i
$262$	1.12908	−	0.410952i	0.0697548	−	0.0253887i
$263$	−17.4300	−	14.6255i	−1.07478	−	0.901850i	−0.0793057	−	0.996850i	$-0.525270\pi$
$263$	−17.4300	−	14.6255i	−1.07478	−	0.901850i	−0.995477	+	0.0950004i	$0.969715\pi$
$264$	−13.3806	−	2.35937i	−0.823521	−	0.145209i
$265$		0			0
$266$	1.96778	−	11.1598i	0.120652	−	0.684252i
$267$	33.7217	−	19.4692i	2.06374	−	1.19150i
$268$	−0.570088	+	0.478360i	−0.0348237	+	0.0292205i
$269$	−6.24891	+	10.8234i	−0.381003	+	0.659916i	−0.991206	−	0.132329i	$-0.957754\pi$
$269$	−6.24891	+	10.8234i	−0.381003	+	0.659916i	0.610203	+	0.792245i	$0.291088\pi$
$270$		0			0
$271$	9.15858	+	3.33345i	0.556344	+	0.202493i	0.604863	−	0.796329i	$-0.293228\pi$
$271$	9.15858	+	3.33345i	0.556344	+	0.202493i	−0.0485187	+	0.998822i	$0.515450\pi$
$272$	−4.93230	+	5.87808i	−0.299064	+	0.356411i
$273$	0.537700	+	0.310441i	0.0325431	+	0.0187887i
$274$	3.40099	−	0.599687i	0.205462	−	0.0362284i
$275$		0			0
$276$	−0.868912	−	1.03553i	−0.0523024	−	0.0623316i
$277$	7.47266	+	20.5310i	0.448988	+	1.23359i	0.933429	+	0.358761i	$0.116801\pi$
$277$	7.47266	+	20.5310i	0.448988	+	1.23359i	−0.484441	+	0.874824i	$0.660977\pi$
$278$	7.21066	+	19.8111i	0.432466	+	1.18819i
$279$	−6.12160	−	7.29544i	−0.366491	−	0.436767i
$280$		0			0
$281$	−19.9371	+	3.51546i	−1.18935	+	0.209715i	−0.733090	−	0.680132i	$-0.761923\pi$
$281$	−19.9371	+	3.51546i	−1.18935	+	0.209715i	−0.456260	+	0.889846i	$0.650811\pi$
$282$	12.0822	+	6.97567i	0.719485	+	0.415395i
$283$	−16.1985	+	19.3047i	−0.962903	+	1.14754i	0.0261013	+	0.999659i	$0.491691\pi$
$283$	−16.1985	+	19.3047i	−0.962903	+	1.14754i	−0.989005	+	0.147884i	$0.952754\pi$
$284$	−1.75778	−	0.639781i	−0.104305	−	0.0379640i
$285$		0			0
$286$	0.208379	−	0.360922i	0.0123217	−	0.0213418i
$287$	6.89977	−	5.78960i	0.407281	−	0.341749i
$288$	1.51780	−	0.876300i	0.0894370	−	0.0516365i
$289$	2.10829	−	11.9567i	0.124017	−	0.703334i
$290$		0			0
$291$	19.6345	+	3.46209i	1.15099	+	0.202951i
$292$	−0.318459	−	0.267219i	−0.0186364	−	0.0156378i
$293$	−7.46503	+	2.71705i	−0.436112	+	0.158732i	−0.550740	−	0.834677i	$-0.685654\pi$
$293$	−7.46503	+	2.71705i	−0.436112	+	0.158732i	0.114628	+	0.993408i	$0.463432\pi$
$294$	−2.49620	+	6.85824i	−0.145581	+	0.399981i
$295$		0			0
$296$	17.6851	−	3.62989i	1.02793	−	0.210983i
$297$	7.59944			0.440965
$298$	−8.72757	+	23.9788i	−0.505574	+	1.38905i
$299$	0.374208	−	0.136201i	0.0216410	−	0.00787669i
$300$		0			0
$301$	1.31150	+	0.231253i	0.0755937	+	0.0133292i
$302$		−	15.9050i		−	0.915228i
$303$	−0.661834	+	3.75345i	−0.0380214	+	0.215630i
$304$	12.2992	−	7.10095i	0.705408	−	0.407267i
$305$		0			0
$306$	−1.96340	+	3.40071i	−0.112240	+	0.194406i
$307$	8.25618	+	14.3001i	0.471205	+	0.816151i	0.999457	−	0.0329361i	$-0.0104858\pi$
$307$	8.25618	+	14.3001i	0.471205	+	0.816151i	−0.528252	+	0.849087i	$0.677152\pi$
$308$	1.00279	+	0.364984i	0.0571391	+	0.0207969i
$309$	17.1407	−	20.4274i	0.975098	−	1.16208i
$310$		0			0
$311$	−21.6718	+	3.82132i	−1.22889	+	0.216687i	−0.750150	−	0.661268i	$-0.770019\pi$
$311$	−21.6718	+	3.82132i	−1.22889	+	0.216687i	−0.478743	+	0.877955i	$0.658907\pi$
$312$	0.153165	+	0.868643i	0.00867127	+	0.0491772i
$313$	−3.34370	−	3.98487i	−0.188997	−	0.225238i	0.663222	−	0.748422i	$-0.269188\pi$
$313$	−3.34370	−	3.98487i	−0.188997	−	0.225238i	−0.852220	+	0.523184i	$0.824744\pi$
$314$	−0.0375477	−	0.103161i	−0.00211894	−	0.00582174i
$315$		0			0
$316$	2.35150	+	2.80241i	0.132282	+	0.157648i
$317$	−0.936949	−	5.31370i	−0.0526243	−	0.298447i	0.947124	−	0.320867i	$-0.103974\pi$
$317$	−0.936949	−	5.31370i	−0.0526243	−	0.298447i	−0.999749	+	0.0224194i	$0.992863\pi$
$318$	33.2453	−	5.86205i	1.86430	−	0.328727i
$319$	4.59070	+	2.65044i	0.257030	+	0.148396i
$320$		0			0
$321$	−14.5135	−	5.28247i	−0.810063	−	0.294839i
$322$	−3.87695	−	6.71507i	−0.216054	−	0.374216i
$323$	4.49645	−	7.78809i	0.250189	−	0.433341i
$324$	−1.99865	+	1.67706i	−0.111036	+	0.0931703i
$325$		0			0
$326$	5.21408	−	29.5705i	0.288781	−	1.63776i
$327$			17.4855i			0.966948i
$328$	12.6012	+	2.22194i	0.695786	+	0.122686i
$329$	−8.06173	−	6.76460i	−0.444458	−	0.372944i
$330$		0			0
$331$	−0.834469	+	2.29269i	−0.0458666	+	0.126017i	−0.960511	−	0.278242i	$-0.910248\pi$
$331$	−0.834469	+	2.29269i	−0.0458666	+	0.126017i	0.914645	+	0.404259i	$0.132471\pi$
$332$	−0.772279			−0.0423843
$333$	7.57823	−	3.00027i	0.415284	−	0.164414i
$334$	12.5695			0.687775
$335$		0			0
$336$	14.2373	−	5.18196i	0.776710	−	0.282699i
$337$	−13.5936	−	11.4063i	−0.740488	−	0.621343i	0.192481	−	0.981301i	$-0.438347\pi$
$337$	−13.5936	−	11.4063i	−0.740488	−	0.621343i	−0.932969	+	0.359958i	$0.882791\pi$
$338$	16.9942	+	2.99654i	0.924363	+	0.162990i
$339$		−	25.8960i		−	1.40648i
$340$		0			0
$341$	13.5257	−	7.80906i	0.732457	−	0.422884i
$342$	5.56747	−	4.67166i	0.301054	−	0.252615i
$343$	10.0650	−	17.4331i	0.543458	−	0.941297i
$344$	0.945949	+	1.63843i	0.0510021	+	0.0883383i
$345$		0			0
$346$	−18.1768	+	21.6623i	−0.977193	+	1.16457i
$347$	10.2882	+	5.93991i	0.552301	+	0.318871i	0.750049	−	0.661382i	$-0.230030\pi$
$347$	10.2882	+	5.93991i	0.552301	+	0.318871i	−0.197749	+	0.980253i	$0.563363\pi$
$348$	−1.15039	+	0.202845i	−0.0616674	+	0.0108736i
$349$	−4.87443	−	27.6443i	−0.260922	−	1.47976i	−0.780401	−	0.625280i	$-0.784985\pi$
$349$	−4.87443	−	27.6443i	−0.260922	−	1.47976i	0.519479	−	0.854483i	$-0.326126\pi$
$350$		0			0
$351$	−0.168732	−	0.463588i	−0.00900626	−	0.0247445i
$352$	0.983027	+	2.70084i	0.0523955	+	0.143955i
$353$	−13.9243	−	16.5944i	−0.741117	−	0.883228i	0.255382	−	0.966840i	$-0.417799\pi$
$353$	−13.9243	−	16.5944i	−0.741117	−	0.883228i	−0.996498	+	0.0836120i	$0.973354\pi$
$354$	6.50125	+	36.8704i	0.345537	+	1.95964i
$355$		0			0
$356$	−3.76260	−	2.17234i	−0.199417	−	0.115134i
$357$	6.16685	−	7.34937i	0.326384	−	0.388970i
$358$	−12.4839	−	4.54377i	−0.659795	−	0.240146i
$359$	13.0696	+	22.6372i	0.689786	+	1.19474i	0.971907	+	0.235366i	$0.0756288\pi$
$359$	13.0696	+	22.6372i	0.689786	+	1.19474i	−0.282121	+	0.959379i	$0.591038\pi$
$360$		0			0
$361$	1.80459	−	1.51423i	0.0949784	−	0.0796963i
$362$	−13.6106	+	7.85811i	−0.715360	+	0.413013i
$363$	−2.23248	+	12.6610i	−0.117175	+	0.664531i
$364$		−	0.0692767i		−	0.00363109i
$365$		0			0
$366$	22.8793	+	19.1980i	1.19592	+	1.00350i
$367$	10.6051	−	3.85993i	0.553580	−	0.201487i	−0.0500565	−	0.998746i	$-0.515940\pi$
$367$	10.6051	−	3.85993i	0.553580	−	0.201487i	0.603636	+	0.797260i	$0.293718\pi$
$368$	3.32363	−	9.13159i	0.173256	−	0.476017i
$369$	5.77669			0.300723
$370$		0			0
$371$	−25.4646			−1.32206
$372$	−1.17713	+	3.23415i	−0.0610316	+	0.167683i
$373$	−10.2653	+	3.73627i	−0.531519	+	0.193457i	−0.593816	−	0.804601i	$-0.702379\pi$
$373$	−10.2653	+	3.73627i	−0.531519	+	0.193457i	0.0622977	+	0.998058i	$0.480157\pi$
$374$	−4.93315	−	4.13940i	−0.255087	−	0.214043i
$375$		0			0
$376$		−	14.9505i		−	0.771012i
$377$	0.0597562	−	0.338894i	0.00307760	−	0.0174540i
$378$	−8.31897	+	4.80296i	−0.427882	+	0.247038i
$379$	−19.4059	+	16.2835i	−0.996813	+	0.836425i	−0.986540	−	0.163522i	$-0.947715\pi$
$379$	−19.4059	+	16.2835i	−0.996813	+	0.836425i	−0.0102730	+	0.999947i	$0.503270\pi$
$380$		0			0
$381$	−21.4692	−	37.1858i	−1.09990	−	1.90508i
$382$	−23.6776	−	8.61792i	−1.21145	−	0.440931i
$383$	11.0543	−	13.1740i	0.564850	−	0.673162i	−0.405715	−	0.913999i	$-0.632978\pi$
$383$	11.0543	−	13.1740i	0.564850	−	0.673162i	0.970565	+	0.240837i	$0.0774220\pi$
$384$	16.1510	+	9.32476i	0.824200	+	0.475852i
$385$		0			0
$386$	3.25138	+	18.4395i	0.165491	+	0.938546i
$387$	0.549013	+	0.654289i	0.0279079	+	0.0332594i
$388$	−0.760848	−	2.09041i	−0.0386262	−	0.106125i
$389$	5.33010	+	14.6443i	0.270247	+	0.742497i	0.998371	+	0.0570519i	$0.0181700\pi$
$389$	5.33010	+	14.6443i	0.270247	+	0.742497i	−0.728124	+	0.685445i	$0.759608\pi$
$390$		0			0
$391$	−1.06852	−	6.05991i	−0.0540376	−	0.306463i
$392$	7.70224	−	1.35811i	0.389022	−	0.0685951i
$393$	−1.63052	−	0.941379i	−0.0822487	−	0.0474863i
$394$	−12.1026	+	14.4234i	−0.609722	+	0.726639i
$395$		0			0
$396$	0.342209	+	0.592723i	0.0171966	+	0.0297854i
$397$	1.10014	−	1.90550i	0.0552144	−	0.0956341i	−0.837097	−	0.547054i	$-0.815749\pi$
$397$	1.10014	−	1.90550i	0.0552144	−	0.0956341i	0.892311	+	0.451420i	$0.149082\pi$
$398$	10.2512	−	8.60179i	0.513847	−	0.431169i
$399$	−15.3777	+	8.87832i	−0.769848	+	0.444472i
$400$		0			0
$401$			21.3109i			1.06422i	0.846677	+	0.532108i	$0.178600\pi$
$401$			21.3109i			1.06422i	−0.846677	+	0.532108i	$0.821400\pi$
$402$	−8.73268	−	1.53981i	−0.435546	−	0.0767986i
$403$	−0.776689	−	0.651719i	−0.0386896	−	0.0324645i
$404$	0.399616	−	0.145448i	0.0198816	−	0.00723632i
$405$		0			0
$406$	−6.70047			−0.332539
$407$	2.68746	+	13.0935i	0.133212	+	0.649022i
$408$	13.6294			0.674756
$409$	−4.65509	+	12.7898i	−0.230179	+	0.632413i	−0.999983	−	0.00586827i	$-0.998132\pi$
$409$	−4.65509	+	12.7898i	−0.230179	+	0.632413i	0.769803	+	0.638281i	$0.220354\pi$
$410$		0			0
$411$	−4.14537	−	3.47838i	−0.204476	−	0.171576i
$412$	−2.93015	−	0.516664i	−0.144358	−	0.0254542i
$413$		−	28.2413i		−	1.38966i
$414$	0.863552	−	4.89745i	0.0424413	−	0.240696i
$415$		0			0
$416$	0.142933	−	0.119935i	0.00700786	−	0.00588030i
$417$	16.5177	−	28.6094i	0.808873	−	1.40101i
$418$	5.95943	+	10.3220i	0.291485	+	0.504867i
$419$	−16.0684	−	5.84843i	−0.784994	−	0.285714i	−0.0817404	−	0.996654i	$-0.526048\pi$
$419$	−16.0684	−	5.84843i	−0.784994	−	0.285714i	−0.703253	+	0.710939i	$0.748270\pi$
$420$		0			0
$421$	8.59287	+	4.96110i	0.418791	+	0.241789i	0.694560	−	0.719435i	$-0.255599\pi$
$421$	8.59287	+	4.96110i	0.418791	+	0.241789i	−0.275769	+	0.961224i	$0.588932\pi$
$422$	15.7891	−	2.78405i	0.768603	−	0.135525i
$423$	−1.17204	−	6.64698i	−0.0569866	−	0.323187i
$424$	−23.2533	−	27.7123i	−1.12928	−	1.34583i
$425$		0			0
$426$	−7.62324	−	20.9447i	−0.369347	−	1.01477i
$427$	−14.4815	−	17.2584i	−0.700811	−	0.835194i
$428$	0.299250	+	1.69713i	0.0144648	+	0.0820339i
$429$	−0.643117	+	0.113399i	−0.0310500	+	0.00547495i
$430$		0			0
$431$	−5.07276	+	6.04548i	−0.244346	+	0.291201i	−0.874253	−	0.485470i	$-0.838649\pi$
$431$	−5.07276	+	6.04548i	−0.244346	+	0.291201i	0.629907	+	0.776671i	$0.283093\pi$
$432$	−11.3127	−	4.11748i	−0.544282	−	0.198102i
$433$	2.04140	+	3.53581i	0.0981036	+	0.169920i	0.910900	−	0.412628i	$-0.135389\pi$
$433$	2.04140	+	3.53581i	0.0981036	+	0.169920i	−0.812796	+	0.582548i	$0.802056\pi$
$434$	−9.87088	+	17.0969i	−0.473817	+	0.820676i
$435$		0			0
$436$	1.68961	−	0.975496i	0.0809175	−	0.0467178i
$437$	−1.97765	+	11.2158i	−0.0946038	+	0.536525i
$438$		−	4.95345i		−	0.236685i
$439$	−22.3347	−	3.93820i	−1.06598	−	0.187960i	−0.386969	−	0.922093i	$-0.626478\pi$
$439$	−22.3347	−	3.93820i	−1.06598	−	0.187960i	−0.679006	+	0.734132i	$0.737589\pi$
$440$		0			0
$441$	3.31795	−	1.20763i	0.157997	−	0.0575064i
$442$	−0.142984	+	0.392844i	−0.00680104	+	0.0186857i
$443$	4.29550			0.204085			0.102043	−	0.994780i	$-0.467462\pi$
$443$	4.29550			0.204085			0.102043	+	0.994780i	$0.467462\pi$
$444$	−2.30835	−	1.82965i	−0.109550	−	0.0868313i
$445$		0			0
$446$	0.505048	−	1.38761i	0.0239147	−	0.0657051i
$447$	37.5736	−	13.6757i	1.77717	−	0.646837i
$448$	−13.9256	−	11.6850i	−0.657924	−	0.552064i
$449$	−13.3603	−	2.35578i	−0.630512	−	0.111176i	−0.150746	−	0.988573i	$-0.548168\pi$
$449$	−13.3603	−	2.35578i	−0.630512	−	0.111176i	−0.479767	+	0.877396i	$0.659279\pi$
$450$		0			0
$451$	−1.64505	+	9.32957i	−0.0774626	+	0.439312i
$452$	−2.50231	+	1.44471i	−0.117699	+	0.0679534i
$453$	−19.0916	+	16.0197i	−0.897001	+	0.752673i
$454$	−6.46866	+	11.2041i	−0.303589	+	0.525832i
$455$		0			0
$456$	−23.7043	−	8.62766i	−1.11006	−	0.404027i
$457$	15.4454	−	18.4071i	0.722504	−	0.861047i	−0.272368	−	0.962193i	$-0.587807\pi$
$457$	15.4454	−	18.4071i	0.722504	−	0.861047i	0.994872	+	0.101147i	$0.0322511\pi$
$458$	−17.2795	−	9.97632i	−0.807418	−	0.466163i
$459$	−7.50732	+	1.32374i	−0.350412	+	0.0617870i
$460$		0			0
$461$	−10.2581	−	12.2251i	−0.477766	−	0.569379i	0.472296	−	0.881440i	$-0.343425\pi$
$461$	−10.2581	−	12.2251i	−0.477766	−	0.569379i	−0.950062	+	0.312061i	$0.898981\pi$
$462$	4.34893	+	11.9486i	0.202331	+	0.555899i
$463$	10.7194	+	29.4514i	0.498175	+	1.36872i	0.893037	+	0.449984i	$0.148570\pi$
$463$	10.7194	+	29.4514i	0.498175	+	1.36872i	−0.394862	+	0.918741i	$0.629207\pi$
$464$	−5.39776	−	6.43280i	−0.250585	−	0.298635i
$465$		0			0
$466$	29.1043	−	5.13188i	1.34823	−	0.237730i
$467$	−32.5560	−	18.7962i	−1.50651	−	0.869786i	−0.999971	−	0.00757047i	$-0.997590\pi$
$467$	−32.5560	−	18.7962i	−1.50651	−	0.869786i	−0.506542	−	0.862215i	$-0.669076\pi$
$468$	0.0285597	−	0.0340361i	0.00132017	−	0.00157332i
$469$	6.28551	+	2.28774i	0.290238	+	0.105638i
$470$		0			0
$471$	−0.0860116	+	0.148976i	−0.00396321	+	0.00686447i
$472$	30.7340	−	25.7889i	1.41465	−	1.18703i
$473$	−1.21305	+	0.700352i	−0.0557759	+	0.0322022i
$474$	−7.56930	+	42.9276i	−0.347669	+	1.97173i
$475$		0			0
$476$	−1.05421	−	0.185885i	−0.0483195	−	0.00852003i
$477$	−12.5109	−	10.4979i	−0.572836	−	0.480667i
$478$	−6.93734	+	2.52499i	−0.317307	+	0.115490i
$479$	6.18829	−	17.0022i	0.282750	−	0.776850i	−0.714281	−	0.699859i	$-0.753246\pi$
$479$	6.18829	−	17.0022i	0.282750	−	0.776850i	0.997032	−	0.0769916i	$-0.0245315\pi$
$480$		0			0
$481$	0.739072	−	0.454661i	0.0336988	−	0.0207308i
$482$	19.1686			0.873104
$483$	−4.15553	+	11.4172i	−0.189083	+	0.519502i
$484$	1.34797	−	0.490622i	0.0612715	−	0.0223010i
$485$		0			0
$486$	−17.0316	−	3.00314i	−0.772571	−	0.136225i
$487$			4.82913i			0.218829i	0.993996	+	0.109414i	$0.0348975\pi$
$487$			4.82913i			0.218829i	−0.993996	+	0.109414i	$0.965102\pi$
$488$	5.55774	−	31.5195i	0.251587	−	1.42682i
$489$	−40.7468	+	23.5252i	−1.84263	+	1.06384i
$490$		0			0
$491$	−17.3191	+	29.9976i	−0.781601	+	1.35377i	0.149408	+	0.988776i	$0.452263\pi$
$491$	−17.3191	+	29.9976i	−0.781601	+	1.35377i	−0.931009	+	0.364997i	$0.881070\pi$
$492$	−1.04382	−	1.80795i	−0.0470591	−	0.0815087i
$493$	−4.99673	−	1.81866i	−0.225041	−	0.0819084i
$494$	0.497356	−	0.592725i	0.0223771	−	0.0266680i
$495$		0			0
$496$	−24.3656	+	4.29632i	−1.09405	+	0.192911i
$497$	2.91955	+	16.5576i	0.130960	+	0.742710i
$498$	−5.91493	−	7.04914i	−0.265054	−	0.315880i
$499$	6.97162	+	19.1544i	0.312092	+	0.857467i	0.992234	+	0.124386i	$0.0396961\pi$
$499$	6.97162	+	19.1544i	0.312092	+	0.857467i	−0.680141	+	0.733081i	$0.738082\pi$
$500$		0			0
$501$	−12.6602	−	15.0879i	−0.565618	−	0.674078i
$502$	0.0647959	+	0.367476i	0.00289198	+	0.0164013i
$503$	6.19494	−	1.09234i	0.276219	−	0.0487048i	−0.0338227	−	0.999428i	$-0.510768\pi$
$503$	6.19494	−	1.09234i	0.276219	−	0.0487048i	0.310042	+	0.950723i	$0.399657\pi$
$504$	−7.19564	−	4.15441i	−0.320519	−	0.185052i
$505$		0			0
$506$	7.66364	+	2.78934i	0.340690	+	0.124001i
$507$	−13.5199	−	23.4172i	−0.600442	−	1.04000i
$508$	−2.39549	+	4.14911i	−0.106283	+	0.184087i
$509$	20.1589	−	16.9153i	0.893526	−	0.749757i	−0.0753881	−	0.997154i	$-0.524020\pi$
$509$	20.1589	−	16.9153i	0.893526	−	0.749757i	0.968914	+	0.247397i	$0.0795751\pi$
$510$		0			0
$511$	−0.648838	+	3.67974i	−0.0287029	+	0.162782i
$512$		−	25.2170i		−	1.11444i
$513$	13.8947	+	2.45001i	0.613467	+	0.108171i
$514$	−6.52159	−	5.47227i	−0.287655	−	0.241371i
$515$		0			0
$516$	0.105571	−	0.290053i	0.00464750	−	0.0127689i
$517$	11.0689			0.486809
$518$	−11.2172	−	12.6347i	−0.492856	−	0.555138i
$519$	44.3104			1.94501
$520$		0			0
$521$	−10.5656	+	3.84556i	−0.462887	+	0.168477i	−0.562928	−	0.826506i	$-0.690325\pi$
$521$	−10.5656	+	3.84556i	−0.462887	+	0.168477i	0.100040	+	0.994983i	$0.468103\pi$
$522$	−3.29198	−	2.76230i	−0.144086	−	0.120903i
$523$	22.4946	+	3.96641i	0.983621	+	0.173439i	0.642255	−	0.766491i	$-0.277999\pi$
$523$	22.4946	+	3.96641i	0.983621	+	0.173439i	0.341367	+	0.939930i	$0.389110\pi$
$524$			0.210074i			0.00917713i
$525$		0			0
$526$	−26.1976	+	15.1252i	−1.14227	+	0.659490i
$527$	−12.0015	+	10.0704i	−0.522792	+	0.438674i
$528$	−7.96786	+	13.8007i	−0.346757	+	0.600600i
$529$	−7.60360	−	13.1698i	−0.330591	−	0.572601i
$530$		0			0
$531$	11.6426	−	13.8751i	0.505247	−	0.602130i
$532$	1.71581	+	0.990625i	0.0743899	+	0.0429490i
$533$	0.605656	−	0.106794i	0.0262339	−	0.00462574i
$534$	−8.98951	−	50.9820i	−0.389014	−	2.20621i
$535$		0			0
$536$	3.25002	+	8.92937i	0.140380	+	0.385690i
$537$	7.11987	+	19.5617i	0.307245	+	0.844149i
$538$	10.6804	+	12.7284i	0.460465	+	0.548761i
$539$	1.00551	+	5.70251i	0.0433102	+	0.245624i
$540$		0			0
$541$	−0.0544889	−	0.0314592i	−0.00234266	−	0.00135254i	0.498828	−	0.866701i	$-0.333764\pi$
$541$	−0.0544889	−	0.0314592i	−0.00234266	−	0.00135254i	−0.501171	+	0.865348i	$0.667097\pi$
$542$	8.32907	−	9.92620i	0.357764	−	0.426367i
$543$	23.1414	+	8.42277i	0.993092	+	0.361456i
$544$	−1.44157	−	2.49687i	−0.0618068	−	0.107052i
$545$		0			0
$546$	0.632338	−	0.530595i	0.0270616	−	0.0227074i
$547$	−2.77677	+	1.60317i	−0.118726	+	0.0685464i	−0.558187	−	0.829715i	$-0.688503\pi$
$547$	−2.77677	+	1.60317i	−0.118726	+	0.0685464i	0.439461	+	0.898262i	$0.355169\pi$
$548$	−0.104847	+	0.594620i	−0.00447886	+	0.0254009i
$549$		−	14.4493i		−	0.616679i
$550$		0			0
$551$	7.53909	+	6.32605i	0.321176	+	0.269499i
$552$	−16.2197	+	5.90347i	−0.690354	+	0.251268i
$553$	11.2459	−	30.8979i	0.478226	−	1.31391i
$554$	29.0476			1.23411
$555$		0			0
$556$	−3.68601			−0.156322
$557$	5.13642	−	14.1122i	0.217637	−	0.597953i	−0.782044	−	0.623224i	$-0.785823\pi$
$557$	5.13642	−	14.1122i	0.217637	−	0.597953i	0.999681	+	0.0252709i	$0.00804485\pi$
$558$	−11.8979	+	4.33048i	−0.503678	+	0.183324i
$559$	0.0696570	+	0.0584492i	0.00294618	+	0.00247214i
$560$		0			0
$561$			10.0908i			0.426034i
$562$	−4.67378	+	26.5063i	−0.197151	+	1.11810i
$563$	29.3696	−	16.9565i	1.23778	−	0.714633i	0.269141	−	0.963101i	$-0.413260\pi$
$563$	29.3696	−	16.9565i	1.23778	−	0.714633i	0.968640	+	0.248468i	$0.0799269\pi$
$564$	−1.86854	+	1.56789i	−0.0786799	+	0.0660203i
$565$		0			0
$566$	16.7519	+	29.0152i	0.704136	+	1.21960i
$567$	22.0361	+	8.02049i	0.925430	+	0.336829i
$568$	−15.3530	+	18.2970i	−0.644199	+	0.767726i
$569$	21.1609	+	12.2173i	0.887111	+	0.512174i	0.872997	−	0.487726i	$-0.162174\pi$
$569$	21.1609	+	12.2173i	0.887111	+	0.512174i	0.0141148	+	0.999900i	$0.495507\pi$
$570$		0			0
$571$	−1.40560	−	7.97157i	−0.0588227	−	0.333600i	0.941168	−	0.337939i	$-0.109730\pi$
$571$	−1.40560	−	7.97157i	−0.0588227	−	0.333600i	−0.999991	+	0.00433936i	$0.998619\pi$
$572$	0.0468365	+	0.0558175i	0.00195833	+	0.00233385i
$573$	13.5039	+	37.1016i	0.564132	+	1.54994i
$574$	−4.09561	−	11.2526i	−0.170948	−	0.469675i
$575$		0			0
$576$	−2.02455	−	11.4818i	−0.0843564	−	0.478409i
$577$	13.2954	−	2.34435i	0.553497	−	0.0975964i	0.110098	−	0.993921i	$-0.464884\pi$
$577$	13.2954	−	2.34435i	0.553497	−	0.0975964i	0.443399	+	0.896324i	$0.353772\pi$
$578$	−13.9790	−	8.07078i	−0.581450	−	0.335700i
$579$	18.8591	−	22.4754i	0.783757	−	0.934045i
$580$		0			0
$581$	3.47065	+	6.01134i	0.143987	+	0.249392i
$582$	13.2533	−	22.9554i	0.549368	−	0.951533i
$583$	20.5173	−	17.2161i	0.849741	−	0.713017i
$584$	−4.59703	+	2.65410i	−0.190226	+	0.109827i
$585$		0			0
$586$			10.5617i			0.436298i
$587$	12.2159	+	2.15400i	0.504205	+	0.0889050i	0.419965	−	0.907540i	$-0.362042\pi$
$587$	12.2159	+	2.15400i	0.504205	+	0.0889050i	0.0842405	+	0.996445i	$0.473154\pi$
$588$	−0.977495	−	0.820215i	−0.0403112	−	0.0338251i
$589$	27.2478	−	9.91737i	1.12272	−	0.408638i
$590$		0			0
$591$	29.5031			1.21360
$592$	3.09364	−	20.9474i	0.127148	−	0.860932i
$593$	−7.59807			−0.312015			−0.156008	−	0.987756i	$-0.549862\pi$
$593$	−7.59807			−0.312015			−0.156008	+	0.987756i	$0.549862\pi$
$594$	3.45557	−	9.49411i	0.141784	−	0.389548i
$595$		0			0
$596$	−3.41766	−	2.86776i	−0.139993	−	0.117468i
$597$	−20.6504	−	3.64122i	−0.845164	−	0.149025i
$598$		−	0.529437i		−	0.0216503i
$599$	0.841380	−	4.77171i	0.0343779	−	0.194967i	−0.962782	−	0.270279i	$-0.912884\pi$
$599$	0.841380	−	4.77171i	0.0343779	−	0.194967i	0.997160	+	0.0753120i	$0.0239953\pi$
$600$		0			0
$601$	1.41912	−	1.19078i	0.0578870	−	0.0485729i	−0.613385	−	0.789784i	$-0.710193\pi$
$601$	1.41912	−	1.19078i	0.0578870	−	0.0485729i	0.671272	+	0.741211i	$0.265748\pi$
$602$	0.885266	−	1.53333i	0.0360807	−	0.0624937i
$603$	2.14498	+	3.71521i	0.0873502	+	0.151295i
$604$	2.61308	+	0.951082i	0.106325	+	0.0386990i
$605$		0			0
$606$	4.38830	+	2.53358i	0.178262	+	0.102920i
$607$	1.87362	−	0.330369i	0.0760478	−	0.0134093i	−0.135495	−	0.990778i	$-0.543262\pi$
$607$	1.87362	−	0.330369i	0.0760478	−	0.0134093i	0.211543	+	0.977369i	$0.432151\pi$
$608$	0.926617	+	5.25511i	0.0375793	+	0.213123i
$609$	6.74883	+	8.04294i	0.273476	+	0.325916i
$610$		0			0
$611$	−0.245765	−	0.675234i	−0.00994259	−	0.0273170i
$612$	−0.441306	−	0.525928i	−0.0178387	−	0.0212594i
$613$	−4.26097	−	24.1651i	−0.172099	−	0.976021i	−0.941440	−	0.337182i	$-0.890526\pi$
$613$	−4.26097	−	24.1651i	−0.172099	−	0.976021i	0.769341	−	0.638839i	$-0.220585\pi$
$614$	21.6196	−	3.81211i	0.872495	−	0.153844i
$615$		0			0
$616$	8.75865	−	10.4382i	0.352896	−	0.420565i
$617$	−26.8031	−	9.75554i	−1.07905	−	0.392743i	−0.259498	−	0.965744i	$-0.583557\pi$
$617$	−26.8031	−	9.75554i	−1.07905	−	0.392743i	−0.819555	+	0.573000i	$0.805779\pi$
$618$	−17.7262	−	30.7027i	−0.713054	−	1.23505i
$619$	−9.57288	+	16.5807i	−0.384767	+	0.666435i	−0.991737	−	0.128289i	$-0.959051\pi$
$619$	−9.57288	+	16.5807i	−0.384767	+	0.666435i	0.606970	+	0.794725i	$0.292385\pi$
$620$		0			0
$621$	8.36071	−	4.82706i	0.335504	−	0.193703i
$622$	−5.08042	+	28.8125i	−0.203706	+	1.15528i
$623$			39.0503i			1.56452i
$624$	1.01880	+	0.179641i	0.0407845	+	0.00719141i
$625$		0			0
$626$	−6.49879	+	2.36537i	−0.259744	+	0.0945390i
$627$	6.38766	−	17.5500i	0.255099	−	0.700878i
$628$	0.0191940			0.000765924
$629$	−4.93563	−	12.4667i	−0.196797	−	0.497078i
$630$		0			0
$631$	5.02154	−	13.7966i	0.199905	−	0.549233i	−0.798718	−	0.601706i	$-0.794488\pi$
$631$	5.02154	−	13.7966i	0.199905	−	0.549233i	0.998622	+	0.0524726i	$0.0167102\pi$
$632$	43.8945	−	15.9763i	1.74603	−	0.635503i
$633$	−19.2449	−	16.1484i	−0.764917	−	0.641842i
$634$	−7.06454	−	1.24567i	−0.280569	−	0.0494718i
$635$		0			0
$636$	−1.02490	+	5.81251i	−0.0406400	+	0.230481i
$637$	0.325544	−	0.187953i	0.0128985	−	0.00744697i
$638$	5.39870	−	4.53004i	0.213736	−	0.179346i
$639$	−5.39156	+	9.33846i	−0.213287	+	0.369424i
$640$		0			0
$641$	24.9108	+	9.06678i	0.983916	+	0.358116i	0.783361	−	0.621566i	$-0.213503\pi$
$641$	24.9108	+	9.06678i	0.983916	+	0.358116i	0.200555	+	0.979683i	$0.435726\pi$
$642$	−13.1990	+	15.7299i	−0.520921	+	0.620810i
$643$	11.5181	+	6.64999i	0.454230	+	0.262250i	0.709615	−	0.704590i	$-0.248869\pi$
$643$	11.5181	+	6.64999i	0.454230	+	0.262250i	−0.255385	+	0.966839i	$0.582202\pi$
$644$	1.33507	−	0.235409i	0.0526092	−	0.00927643i
$645$		0			0
$646$	−7.68518	−	9.15884i	−0.302369	−	0.360350i
$647$	10.1382	+	27.8545i	0.398574	+	1.09507i	0.962979	+	0.269576i	$0.0868836\pi$
$647$	10.1382	+	27.8545i	0.398574	+	1.09507i	−0.564405	+	0.825498i	$0.690894\pi$
$648$	11.3941	+	31.3051i	0.447604	+	1.22978i
$649$	19.0933	+	22.7545i	0.749479	+	0.893194i
$650$		0			0
$651$	30.4644	−	5.37169i	1.19399	−	0.210533i
$652$	4.54644	+	2.62489i	0.178052	+	0.102799i
$653$	−13.4223	+	15.9960i	−0.525253	+	0.625972i	−0.961815	−	0.273702i	$-0.911752\pi$
$653$	−13.4223	+	15.9960i	−0.525253	+	0.625972i	0.436561	+	0.899675i	$0.356196\pi$
$654$	21.8449	+	7.95088i	0.854202	+	0.310904i
$655$		0			0
$656$	7.50375	−	12.9969i	0.292972	−	0.507443i
$657$	−1.83577	+	1.54039i	−0.0716202	+	0.0600965i
$658$	−12.1169	+	6.99569i	−0.472366	+	0.272721i
$659$	3.22331	−	18.2803i	0.125562	−	0.712099i	−0.855410	−	0.517952i	$-0.826695\pi$
$659$	3.22331	−	18.2803i	0.125562	−	0.712099i	0.980972	−	0.194148i	$-0.0621942\pi$
$660$		0			0
$661$	19.6481	+	3.46449i	0.764222	+	0.134753i	0.542155	−	0.840278i	$-0.317608\pi$
$661$	19.6481	+	3.46449i	0.764222	+	0.134753i	0.222067	+	0.975031i	$0.428720\pi$
$662$	2.48484	+	2.08503i	0.0965762	+	0.0810371i
$663$	0.615568	−	0.224048i	0.0239067	−	0.00870132i
$664$	−3.37266	+	9.26631i	−0.130885	+	0.359603i
$665$		0			0
$666$	−0.302358	−	10.8319i	−0.0117162	−	0.419726i
$667$	6.73409			0.260745
$668$	−0.751631	+	2.06509i	−0.0290815	+	0.0799007i
$669$	−2.17431	+	0.791385i	−0.0840638	+	0.0305967i
$670$		0			0
$671$	23.3361	+	4.11478i	0.900880	+	0.158849i
$672$			5.69280i			0.219605i
$673$	0.914124	−	5.18426i	0.0352369	−	0.199838i	−0.962107	−	0.272671i	$-0.912093\pi$
$673$	0.914124	−	5.18426i	0.0352369	−	0.199838i	0.997344	+	0.0728329i	$0.0232040\pi$
$674$	−20.4313	+	11.7960i	−0.786984	+	0.454366i
$675$		0			0
$676$	−1.50853	+	2.61284i	−0.0580202	+	0.100494i
$677$	−9.17542	−	15.8923i	−0.352640	−	0.610791i	0.634071	−	0.773275i	$-0.281383\pi$
$677$	−9.17542	−	15.8923i	−0.352640	−	0.610791i	−0.986711	+	0.162484i	$0.948049\pi$
$678$	−32.3522	−	11.7753i	−1.24248	−	0.452226i
$679$	−12.8523	+	15.3168i	−0.493226	+	0.587804i
$680$		0			0
$681$	19.9642	−	3.52022i	0.765029	−	0.134895i
$682$	−3.60566	−	20.4487i	−0.138068	−	0.783023i
$683$	−1.40769	−	1.67762i	−0.0538636	−	0.0641922i	0.738440	−	0.674319i	$-0.235563\pi$
$683$	−1.40769	−	1.67762i	−0.0538636	−	0.0641922i	−0.792304	+	0.610127i	$0.791118\pi$
$684$	0.434599	+	1.19405i	0.0166173	+	0.0456557i
$685$		0			0
$686$	−17.2027	−	20.5014i	−0.656803	−	0.782748i
$687$	5.42907	+	30.7898i	0.207132	+	1.17470i
$688$	2.18522	−	0.385314i	0.0833109	−	0.0146900i
$689$	−1.50578	−	0.869363i	−0.0573657	−	0.0331201i
$690$		0			0
$691$	21.0301	+	7.65434i	0.800023	+	0.291185i	0.709496	−	0.704709i	$-0.248923\pi$
$691$	21.0301	+	7.65434i	0.800023	+	0.291185i	0.0905272	+	0.995894i	$0.471145\pi$
$692$	−2.47203	−	4.28169i	−0.0939726	−	0.162765i
$693$	3.07580	−	5.32744i	0.116840	−	0.202373i
$694$	12.0990	−	10.1523i	0.459272	−	0.385375i
$695$		0			0
$696$	−2.59007	+	14.6890i	−0.0981764	+	0.556786i
$697$		−	9.50302i		−	0.359953i
$698$	−36.7529	−	6.48052i	−1.39112	−	0.245291i
$699$	−35.4744	−	29.7666i	−1.34177	−	1.12587i
$700$		0			0
$701$	16.5034	−	45.3428i	0.623326	−	1.71257i	−0.0753692	−	0.997156i	$-0.524014\pi$
$701$	16.5034	−	45.3428i	0.623326	−	1.71257i	0.698695	−	0.715419i	$-0.253764\pi$
$702$	−0.655893			−0.0247551
$703$	0.692441	+	24.8064i	0.0261159	+	0.935592i
$704$	19.1201			0.720616
$705$		0			0
$706$	−27.0632	+	9.85019i	−1.01854	+	0.370717i
$707$	−2.92804	−	2.45692i	−0.110120	−	0.0924020i
$708$	−6.44631	−	1.13666i	−0.242267	−	0.0427183i
$709$			35.8242i			1.34540i	0.739913	+	0.672702i	$0.234867\pi$
$709$			35.8242i			1.34540i	−0.739913	+	0.672702i	$0.765133\pi$
$710$		0			0
$711$	18.2630	−	10.5442i	0.684917	−	0.395437i
$712$	−42.4970	+	35.6592i	−1.59264	+	1.33639i
$713$	9.92040	−	17.1826i	0.371522	−	0.643495i
$714$	−6.37753	−	11.0462i	−0.238673	−	0.413394i
$715$		0			0
$716$	1.49302	−	1.77931i	0.0557968	−	0.0664961i
$717$	10.0183	+	5.78406i	0.374140	+	0.216010i
$718$	34.2239	−	6.03460i	1.27722	−	0.225209i
$719$	0.902323	+	5.11733i	0.0336510	+	0.190844i	0.996999	−	0.0774090i	$-0.0246647\pi$
$719$	0.902323	+	5.11733i	0.0336510	+	0.190844i	−0.963348	+	0.268253i	$0.913554\pi$
$720$		0			0
$721$	9.14653	+	25.1299i	0.340635	+	0.935886i
$722$	−1.07118	−	2.94304i	−0.0398652	−	0.109529i
$723$	−19.3069	−	23.0090i	−0.718031	−	0.855716i
$724$	−0.477147	−	2.70603i	−0.0177330	−	0.100569i
$725$		0			0
$726$	14.8025	+	8.54621i	0.549371	+	0.317180i
$727$	−10.7663	+	12.8308i	−0.399302	+	0.475869i	−0.927807	−	0.373061i	$-0.878308\pi$
$727$	−10.7663	+	12.8308i	−0.399302	+	0.475869i	0.528505	+	0.848930i	$0.322753\pi$
$728$	−0.831228	−	0.302542i	−0.0308074	−	0.0112130i
$729$	−3.28685	−	5.69300i	−0.121735	−	0.210852i
$730$		0			0
$731$	1.07635	−	0.903162i	0.0398101	−	0.0334046i
$732$	−4.52223	+	2.61091i	−0.167147	+	0.0965021i
$733$	3.75680	−	21.3058i	0.138760	−	0.786949i	−0.833407	−	0.552660i	$-0.813613\pi$
$733$	3.75680	−	21.3058i	0.138760	−	0.786949i	0.972167	−	0.234289i	$-0.0752762\pi$
$734$		−	15.0042i		−	0.553817i
$735$		0			0
$736$	2.79704	+	2.34699i	0.103100	+	0.0865113i
$737$	−6.61104	+	2.40622i	−0.243521	+	0.0886343i
$738$	2.62674	−	7.21691i	0.0966917	−	0.265658i
$739$	−1.79050			−0.0658646			−0.0329323	−	0.999458i	$-0.510485\pi$
$739$	−1.79050			−0.0658646			−0.0329323	+	0.999458i	$0.510485\pi$
$740$		0			0
$741$	−1.21243			−0.0445395
$742$	−11.5791	+	31.8134i	−0.425083	+	1.16791i
$743$	32.4307	−	11.8038i	1.18977	−	0.433040i	0.330126	−	0.943937i	$-0.392909\pi$
$743$	32.4307	−	11.8038i	1.18977	−	0.433040i	0.859642	+	0.510897i	$0.170687\pi$
$744$	33.6648	+	28.2481i	1.23421	+	1.03563i
$745$		0			0
$746$			14.5236i			0.531746i
$747$	−0.773053	+	4.38420i	−0.0282845	+	0.160410i
$748$	0.975066	−	0.562955i	0.0356520	−	0.0205837i
$749$	11.8655	−	9.95630i	0.433554	−	0.363795i
$750$		0			0
$751$	−5.48231	−	9.49563i	−0.200052	−	0.346501i	0.748493	−	0.663143i	$-0.230778\pi$
$751$	−5.48231	−	9.49563i	−0.200052	−	0.346501i	−0.948545	+	0.316642i	$0.897444\pi$
$752$	−16.4774	−	5.99727i	−0.600867	−	0.218698i
$753$	0.375838	−	0.447906i	0.0136963	−	0.0163226i
$754$	−0.396214	−	0.228754i	−0.0144293	−	0.00833075i
$755$		0			0
$756$	−0.291637	−	1.65396i	−0.0106067	−	0.0601538i
$757$	19.8187	+	23.6190i	0.720323	+	0.858447i	0.994662	−	0.103186i	$-0.0329036\pi$
$757$	19.8187	+	23.6190i	0.720323	+	0.858447i	−0.274339	+	0.961633i	$0.588459\pi$
$758$	11.5191	+	31.6484i	0.418391	+	1.14952i
$759$	−4.37075	−	12.0085i	−0.158648	−	0.435883i
$760$		0			0
$761$	2.55661	+	14.4993i	0.0926772	+	0.525598i	0.995434	+	0.0954479i	$0.0304283\pi$
$761$	2.55661	+	14.4993i	0.0926772	+	0.525598i	−0.902757	+	0.430150i	$0.858461\pi$
$762$	−56.2191	+	9.91295i	−2.03660	+	0.359108i
$763$	−15.1863	−	8.76783i	−0.549782	−	0.317417i
$764$	2.83173	−	3.37473i	0.102448	−	0.122093i
$765$		0			0
$766$	−11.4320	−	19.8008i	−0.413054	−	0.715431i
$767$	0.964160	−	1.66997i	0.0348138	−	0.0602992i
$768$	−8.77789	+	7.36553i	−0.316745	+	0.265781i
$769$	−23.3973	+	13.5084i	−0.843728	+	0.487127i	−0.858530	−	0.512764i	$-0.828622\pi$
$769$	−23.3973	+	13.5084i	−0.843728	+	0.487127i	0.0148015	+	0.999890i	$0.495288\pi$
$770$		0			0
$771$			13.3400i			0.480428i
$772$	−3.22391	−	0.568462i	−0.116031	−	0.0204594i
$773$	16.3941	+	13.7563i	0.589654	+	0.494778i	0.888101	−	0.459648i	$-0.152024\pi$
$773$	16.3941	+	13.7563i	0.589654	+	0.494778i	−0.298447	+	0.954426i	$0.596469\pi$
$774$	1.06706	−	0.388377i	0.0383546	−	0.0139599i
$775$		0			0
$776$	−28.4049			−1.01968
$777$	−3.86798	+	26.1905i	−0.138763	+	0.939579i
$778$	20.7191			0.742814
$779$	−6.01559	+	16.5277i	−0.215531	+	0.592166i
$780$		0			0
$781$	−13.5466	−	11.3669i	−0.484734	−	0.406740i
$782$	−8.05661	−	1.42060i	−0.288104	−	0.0508005i
$783$		−	8.34254i		−	0.298138i
$784$	1.59288	−	9.03367i	0.0568885	−	0.322631i
$785$		0			0
$786$	−1.91750	+	1.60897i	−0.0683949	+	0.0573901i
$787$	5.56426	−	9.63758i	0.198344	−	0.343543i	−0.749647	−	0.661838i	$-0.769777\pi$
$787$	5.56426	−	9.63758i	0.198344	−	0.343543i	0.947992	+	0.318295i	$0.103110\pi$
$788$	−1.64595	−	2.85087i	−0.0586345	−	0.101558i
$789$	44.5423	+	16.2121i	1.58575	+	0.577165i
$790$		0			0
$791$	22.4909	+	12.9852i	0.799686	+	0.461699i
$792$	8.60636	−	1.51753i	0.305814	−	0.0539232i
$793$	−0.267123	−	1.51493i	−0.00948582	−	0.0537968i
$794$	−1.88032	−	2.24088i	−0.0667300	−	0.0795257i
$795$		0			0
$796$	0.800215	+	2.19857i	0.0283629	+	0.0779263i
$797$	−14.3465	−	17.0974i	−0.508177	−	0.605622i	0.449566	−	0.893247i	$-0.351579\pi$
$797$	−14.3465	−	17.0974i	−0.508177	−	0.605622i	−0.957743	+	0.287625i	$0.907134\pi$
$798$	4.09938	+	23.2487i	0.145116	+	0.822995i
$799$	−10.9347	+	1.92808i	−0.386842	+	0.0682106i
$800$		0			0
$801$	−16.0987	+	19.1856i	−0.568818	+	0.677891i
$802$	26.6240	+	9.69036i	0.940127	+	0.342178i
$803$	−1.96501	−	3.40350i	−0.0693438	−	0.120107i
$804$	0.775175	−	1.34264i	0.0273383	−	0.0473513i
$805$		0			0
$806$	−1.16737	+	0.673984i	−0.0411190	+	0.0237401i
$807$	4.52112	−	25.6405i	0.159151	−	0.902590i
$808$		−	5.43005i		−	0.191029i
$809$	45.1641	+	7.96366i	1.58789	+	0.279987i	0.896683	−	0.442673i	$-0.145970\pi$
$809$	45.1641	+	7.96366i	1.58789	+	0.279987i	0.691203	+	0.722660i	$0.257081\pi$
$810$		0			0
$811$	19.3106	−	7.02847i	0.678086	−	0.246803i	0.0200603	−	0.999799i	$-0.493614\pi$
$811$	19.3106	−	7.02847i	0.678086	−	0.246803i	0.658025	+	0.752996i	$0.271392\pi$
$812$	0.400674	−	1.10084i	0.0140609	−	0.0386320i
$813$	−20.3041			−0.712097
$814$	17.5800	+	2.59632i	0.616177	+	0.0910009i
$815$		0			0
$816$	5.46733	−	15.0214i	0.191395	−	0.525853i
$817$	−2.44370	+	0.889436i	−0.0854944	+	0.0311174i
$818$	13.8617	+	11.6314i	0.484664	+	0.406681i
$819$	−0.393282	−	0.0693462i	−0.0137424	−	0.00242315i
$820$		0			0
$821$	7.67867	−	43.5479i	0.267987	−	1.51983i	−0.492404	−	0.870367i	$-0.663882\pi$
$821$	7.67867	−	43.5479i	0.267987	−	1.51983i	0.760392	−	0.649465i	$-0.225007\pi$
$822$	−6.23056	+	3.59721i	−0.217316	+	0.125467i
$823$	10.1418	−	8.50996i	0.353520	−	0.296639i	−0.448682	−	0.893692i	$-0.648106\pi$
$823$	10.1418	−	8.50996i	0.353520	−	0.296639i	0.802202	+	0.597053i	$0.203662\pi$
$824$	−18.9957	+	32.9015i	−0.661747	+	1.14618i
$825$		0			0
$826$	−35.2823	−	12.8417i	−1.22763	−	0.446821i
$827$	−34.8089	+	41.4837i	−1.21042	+	1.44253i	−0.347138	+	0.937814i	$0.612847\pi$
$827$	−34.8089	+	41.4837i	−1.21042	+	1.44253i	−0.863287	+	0.504714i	$0.831598\pi$
$828$	0.752978	+	0.434732i	0.0261678	+	0.0151080i
$829$	−47.4160	+	8.36072i	−1.64683	+	0.290380i	−0.918668	−	0.395031i	$-0.870734\pi$
$829$	−47.4160	+	8.36072i	−1.64683	+	0.290380i	−0.728157	+	0.685410i	$0.759623\pi$
$830$		0			0
$831$	−29.2572	−	34.8674i	−1.01492	−	1.20954i
$832$	−0.424528	−	1.16638i	−0.0147179	−	0.0404370i
$833$	−1.98663	−	5.45823i	−0.0688328	−	0.189117i
$834$	−28.2314	−	33.6449i	−0.977573	−	1.16503i
$835$		0			0
$836$	−2.05220	+	0.361858i	−0.0709768	+	0.0125151i
$837$	−21.2867	−	12.2899i	−0.735777	−	0.424801i
$838$	−14.6131	+	17.4152i	−0.504800	+	0.601597i
$839$	−44.9348	−	16.3549i	−1.55132	−	0.564635i	−0.582595	−	0.812762i	$-0.697963\pi$
$839$	−44.9348	−	16.3549i	−1.55132	−	0.564635i	−0.968728	+	0.248127i	$0.920185\pi$
$840$		0			0
$841$	−11.5904	+	20.0751i	−0.399669	+	0.692246i
$842$	10.1053	−	8.47933i	0.348251	−	0.292217i
$843$	36.5245	−	21.0874i	1.25797	−	0.726289i
$844$	−0.486755	+	2.76053i	−0.0167548	+	0.0950212i
$845$		0			0
$846$	−8.83712	−	1.55822i	−0.303826	−	0.0535728i
$847$	−9.87679	−	8.28761i	−0.339371	−	0.284766i
$848$	−39.8704	+	14.5116i	−1.36915	+	0.498332i
$849$	17.9557	−	49.3328i	0.616237	−	1.69310i
$850$		0			0
$851$	11.2735	+	12.6981i	0.386450	+	0.435286i
$852$	3.89692			0.133506
$853$	−14.0194	+	38.5181i	−0.480016	+	1.31883i	0.429464	+	0.903084i	$0.358703\pi$
$853$	−14.0194	+	38.5181i	−0.480016	+	1.31883i	−0.909479	+	0.415749i	$0.863520\pi$
$854$	−28.1462	+	10.2444i	−0.963143	+	0.350555i
$855$		0			0
$856$	21.6702	+	3.82104i	0.740672	+	0.130600i
$857$			25.8675i			0.883618i	0.897109	+	0.441809i	$0.145663\pi$
$857$			25.8675i			0.883618i	−0.897109	+	0.441809i	$0.854337\pi$
$858$	−0.150763	+	0.855020i	−0.00514697	+	0.0291899i
$859$	−22.6747	+	13.0913i	−0.773652	+	0.446668i	−0.834176	−	0.551499i	$-0.814056\pi$
$859$	−22.6747	+	13.0913i	−0.773652	+	0.446668i	0.0605241	+	0.998167i	$0.480723\pi$
$860$		0			0
$861$	−9.38194	+	16.2500i	−0.319736	+	0.553798i
$862$	5.24606	+	9.08645i	0.178682	+	0.309486i
$863$	−1.71410	−	0.623881i	−0.0583486	−	0.0212371i	0.312681	−	0.949858i	$-0.398773\pi$
$863$	−1.71410	−	0.623881i	−0.0583486	−	0.0212371i	−0.371030	+	0.928621i	$0.620995\pi$
$864$	2.90758	−	3.46511i	0.0989178	−	0.117886i
$865$		0			0
$866$	5.34560	−	0.942574i	0.181651	−	0.0320300i
$867$	4.39209	+	24.9088i	0.149163	+	0.845946i
$868$	−2.21864	−	2.64407i	−0.0753055	−	0.0897456i
$869$	11.8284	+	32.4982i	0.401250	+	1.10242i
$870$		0			0
$871$	0.293573	+	0.349867i	0.00994734	+	0.0118548i
$872$	−4.32586	−	24.5332i	−0.146492	−	0.830799i
$873$	−12.6288	+	2.22680i	−0.427421	+	0.0753658i
$874$	13.1128	+	7.57069i	0.443548	+	0.256083i
$875$		0			0
$876$	0.813817	+	0.296205i	0.0274963	+	0.0100078i
$877$	−28.2870	−	48.9945i	−0.955184	−	1.65443i	−0.733946	−	0.679208i	$-0.762323\pi$
$877$	−28.2870	−	48.9945i	−0.955184	−	1.65443i	−0.221239	−	0.975220i	$-0.571010\pi$
$878$	−15.0759	+	26.1123i	−0.508789	+	0.881248i
$879$	12.6777	−	10.6379i	0.427609	−	0.358807i
$880$		0			0
$881$	−7.41720	+	42.0650i	−0.249892	+	1.41721i	0.558960	+	0.829195i	$0.311201\pi$
$881$	−7.41720	+	42.0650i	−0.249892	+	1.41721i	−0.808852	+	0.588013i	$0.799911\pi$
$882$		−	4.69429i		−	0.158065i
$883$	−24.7822	−	4.36976i	−0.833986	−	0.147054i	−0.259680	−	0.965695i	$-0.583617\pi$
$883$	−24.7822	−	4.36976i	−0.833986	−	0.147054i	−0.574306	+	0.818641i	$0.694728\pi$
$884$	−0.0559915	−	0.0469825i	−0.00188320	−	0.00158019i
$885$		0			0
$886$	1.95322	−	5.36643i	0.0656198	−	0.180289i
$887$	39.2137			1.31667			0.658333	−	0.752727i	$-0.271262\pi$
$887$	39.2137			1.31667			0.658333	+	0.752727i	$0.271262\pi$
$888$	−32.0343	+	19.7068i	−1.07500	+	0.661317i
$889$	43.0617			1.44424
$890$		0			0
$891$	−23.1774	+	8.43587i	−0.776471	+	0.282612i
$892$	0.197774	+	0.165952i	0.00662195	+	0.00555648i
$893$	20.2382	+	3.56854i	0.677245	+	0.119417i
$894$		−	53.1598i		−	1.77793i
$895$		0			0
$896$	−16.1973	+	9.35153i	−0.541115	+	0.312413i
$897$	−0.635511	+	0.533257i	−0.0212191	+	0.0178049i
$898$	−9.01824	+	15.6201i	−0.300943	+	0.521248i
$899$	−8.57265	−	14.8483i	−0.285914	−	0.495217i
$900$		0			0
$901$	−17.2697	+	20.5813i	−0.575339	+	0.685662i
$902$	10.9076	+	6.29748i	0.363182	+	0.209683i
$903$	−2.73219	+	0.481758i	−0.0909215	+	0.0160319i
$904$	6.40660	+	36.3336i	0.213080	+	1.20844i
$905$		0			0
$906$	11.3325	+	31.1358i	0.376497	+	1.03442i
$907$	14.1364	+	38.8394i	0.469391	+	1.28964i	0.918237	+	0.396031i	$0.129613\pi$
$907$	14.1364	+	38.8394i	0.469391	+	1.28964i	−0.448847	+	0.893609i	$0.648165\pi$
$908$	−1.45394	−	1.73273i	−0.0482506	−	0.0575028i
$909$	−0.425689	−	2.41420i	−0.0141192	−	0.0800740i
$910$		0			0
$911$	−37.9514	−	21.9112i	−1.25739	−	0.725952i	−0.284820	−	0.958581i	$-0.591934\pi$
$911$	−37.9514	−	21.9112i	−1.25739	−	0.725952i	−0.972565	+	0.232629i	$0.925267\pi$
$912$	−19.0176	+	22.6643i	−0.629736	+	0.750490i
$913$	−6.86050	−	2.49702i	−0.227049	−	0.0826392i
$914$	−15.9730	−	27.6661i	−0.528341	−	0.915113i
$915$		0			0
$916$	2.67232	−	2.24234i	0.0882958	−	0.0740890i
$917$	1.63520	−	0.944081i	0.0539990	−	0.0311763i
$918$	−1.75991	+	9.98094i	−0.0580857	+	0.329420i
$919$			6.58051i			0.217071i	0.994093	+	0.108535i	$0.0346161\pi$
$919$			6.58051i			0.217071i	−0.994093	+	0.108535i	$0.965384\pi$
$920$		0			0
$921$	−26.3515	−	22.1115i	−0.868311	−	0.728599i
$922$	−19.9375	+	7.25665i	−0.656606	+	0.238985i
$923$	−0.392638	+	1.07876i	−0.0129238	+	0.0355079i
$924$	−2.22313			−0.0731355
$925$		0			0
$926$	41.6684			1.36931
$927$	−5.86617	+	16.1172i	−0.192670	+	0.529358i
$928$	2.96494	−	1.07915i	0.0973289	−	0.0354248i
$929$	29.3245	+	24.6062i	0.962106	+	0.807303i	0.981294	−	0.192513i	$-0.0616638\pi$
$929$	29.3245	+	24.6062i	0.962106	+	0.807303i	−0.0191883	+	0.999816i	$0.506108\pi$
$930$		0			0
$931$			10.7506i			0.352335i
$932$	−0.897242	+	5.08851i	−0.0293901	+	0.166680i
$933$	39.7023	−	22.9221i	1.29979	−	0.750436i
$934$	−38.2861	+	32.1259i	−1.25276	+	1.05119i
$935$		0			0
$936$	−0.283663	−	0.491319i	−0.00927182	−	0.0160593i
$937$	26.4954	+	9.64352i	0.865565	+	0.315040i	0.736370	−	0.676579i	$-0.236538\pi$
$937$	26.4954	+	9.64352i	0.865565	+	0.315040i	0.129195	+	0.991619i	$0.458761\pi$
$938$	5.71621	−	6.81232i	0.186641	−	0.222430i
$939$	9.38496	+	5.41841i	0.306267	+	0.176823i
$940$		0			0
$941$	4.01276	+	22.7575i	0.130812	+	0.741873i	0.977685	+	0.210077i	$0.0673715\pi$
$941$	4.01276	+	22.7575i	0.130812	+	0.741873i	−0.846873	+	0.531796i	$0.821517\pi$
$942$	0.147008	+	0.175197i	0.00478978	+	0.00570824i
$943$	4.11616	+	11.3091i	0.134041	+	0.368274i
$944$	−16.0940	−	44.2179i	−0.523815	−	1.43917i
$945$		0			0
$946$	0.323373	+	1.83394i	0.0105137	+	0.0596264i
$947$	35.6167	−	6.28019i	1.15739	−	0.204079i	0.438189	−	0.898883i	$-0.355620\pi$
$947$	35.6167	−	6.28019i	1.15739	−	0.204079i	0.719199	+	0.694804i	$0.244509\pi$
$948$	−6.60008	−	3.81056i	−0.214361	−	0.123761i
$949$	−0.163994	+	0.195440i	−0.00532346	+	0.00634426i
$950$		0			0
$951$	5.62028	+	9.73460i	0.182250	+	0.315666i
$952$	−6.83426	+	11.8373i	−0.221500	+	0.383649i
$953$	−2.54903	+	2.13889i	−0.0825712	+	0.0692855i	−0.683139	−	0.730288i	$-0.739386\pi$
$953$	−2.54903	+	2.13889i	−0.0825712	+	0.0692855i	0.600568	+	0.799574i	$0.294941\pi$
$954$	−18.8041	+	10.8566i	−0.608806	+	0.351494i
$955$		0			0
$956$		−	1.29075i		−	0.0417457i
$957$	−10.8753	−	1.91761i	−0.351549	−	0.0619875i
$958$	−18.4272	−	15.4623i	−0.595356	−	0.499563i
$959$	5.09965	−	1.85612i	0.164676	−	0.0599373i
$960$		0			0
$961$	−19.5156			−0.629534
$962$	−0.231949	−	1.13008i	−0.00747834	−	0.0364351i
$963$	9.93411			0.320122
$964$	−1.14624	+	3.14926i	−0.0369178	+	0.101431i
$965$		0			0
$966$	12.3742	+	10.3832i	0.398132	+	0.334072i
$967$	−8.67808	−	1.53018i	−0.279068	−	0.0492073i	0.0323622	−	0.999476i	$-0.489697\pi$
$967$	−8.67808	−	1.53018i	−0.279068	−	0.0492073i	−0.311430	+	0.950269i	$0.600808\pi$
$968$		−	18.3165i		−	0.588715i
$969$	−3.25321	+	18.4499i	−0.104508	+	0.592695i
$970$		0			0
$971$	19.8224	−	16.6330i	0.636132	−	0.533778i	−0.266695	−	0.963781i	$-0.585932\pi$
$971$	19.8224	−	16.6330i	0.636132	−	0.533778i	0.902828	+	0.430003i	$0.141487\pi$
$972$	1.51185	−	2.61860i	0.0484926	−	0.0839916i
$973$	16.5651	+	28.6915i	0.531052	+	0.919809i
$974$	6.03311	+	2.19587i	0.193313	+	0.0703603i
$975$		0			0
$976$	−32.5091	−	18.7692i	−1.04059	−	0.600786i
$977$	−28.4487	+	5.01628i	−0.910156	+	0.160485i	−0.609074	−	0.793113i	$-0.708459\pi$
$977$	−28.4487	+	5.01628i	−0.910156	+	0.160485i	−0.301082	+	0.953598i	$0.597348\pi$
$978$	10.8622	+	61.6028i	0.347336	+	1.96984i
$979$	−26.4010	−	31.4635i	−0.843780	−	1.00558i
$980$		0			0
$981$	−3.84656	−	10.5683i	−0.122811	−	0.337421i
$982$	29.6012	+	35.2774i	0.944613	+	1.12575i
$983$	3.68171	+	20.8800i	0.117428	+	0.665969i	0.985519	+	0.169564i	$0.0542358\pi$
$983$	3.68171	+	20.8800i	0.117428	+	0.665969i	−0.868091	+	0.496405i	$0.834653\pi$
$984$	−26.2515	+	4.62885i	−0.836868	+	0.147562i
$985$		0			0
$986$	−4.54416	+	5.41552i	−0.144716	+	0.172465i
$987$	20.6016	+	7.49839i	0.655758	+	0.238676i
$988$	0.0676399	+	0.117156i	0.00215191	+	0.00372722i
$989$	−0.889707	+	1.54102i	−0.0282910	+	0.0490015i
$990$		0			0
$991$	−32.8374	+	18.9587i	−1.04311	+	0.602242i	−0.920714	−	0.390238i	$-0.872393\pi$
$991$	−32.8374	+	18.9587i	−1.04311	+	0.602242i	−0.122401	+	0.992481i	$0.539059\pi$
$992$	1.61429	−	9.15507i	0.0512536	−	0.290674i
$993$		−	5.08277i		−	0.161297i
$994$	22.0132	+	3.88153i	0.698218	+	0.123115i
$995$		0			0
$996$	1.51183	−	0.550259i	0.0479040	−	0.0174356i
$997$	−3.57007	+	9.80869i	−0.113065	+	0.310644i	−0.983300	−	0.181993i	$-0.941745\pi$
$997$	−3.57007	+	9.80869i	−0.113065	+	0.310644i	0.870234	+	0.492638i	$0.163967\pi$
$998$	27.0999			0.857834
$999$	15.7311	−	13.9662i	0.497709	−	0.441870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.e.576.12		96
5.2	odd	4		185.2.v.a.169.12	yes	96
5.3	odd	4		185.2.v.a.169.5	yes	96
5.4	even	2	inner	925.2.bb.e.576.5		96
37.30	even	18	inner	925.2.bb.e.326.12		96
185.67	odd	36		185.2.v.a.104.5	✓	96
185.104	even	18	inner	925.2.bb.e.326.5		96
185.178	odd	36		185.2.v.a.104.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.5	✓	96	185.67	odd	36
185.2.v.a.104.12	yes	96	185.178	odd	36
185.2.v.a.169.5	yes	96	5.3	odd	4
185.2.v.a.169.12	yes	96	5.2	odd	4
925.2.bb.e.326.5		96	185.104	even	18	inner
925.2.bb.e.326.12		96	37.30	even	18	inner
925.2.bb.e.576.5		96	5.4	even	2	inner
925.2.bb.e.576.12		96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.454714 - 1.24932i) q^{2} +(-1.95762 + 0.712514i) q^{3} +(0.178063 + 0.149413i) q^{4} +2.76967i q^{6} +(0.362791 - 2.05749i) q^{7} +(2.57038 - 1.48401i) q^{8} +(1.02645 - 0.861296i) q^{9} +(1.09872 + 1.90303i) q^{11} +(-0.455038 - 0.165620i) q^{12} +(0.0916955 - 0.109278i) q^{13} +(-2.40549 - 1.38881i) q^{14} +(-0.604483 - 3.42819i) q^{16} +(-1.41689 - 1.68858i) q^{17} +(-0.609289 - 1.67401i) q^{18} +(1.39535 + 3.83370i) q^{19} +(0.755786 + 4.28627i) q^{21} +(2.87709 - 0.507309i) q^{22} +(2.41756 + 1.39578i) q^{23} +(-3.97445 + 4.73656i) q^{24} +(-0.0948281 - 0.164247i) q^{26} +(1.72916 - 2.99500i) q^{27} +(0.372015 - 0.312158i) q^{28} +(2.08912 - 1.20615i) q^{29} -7.10743i q^{31} +(1.28810 + 0.227127i) q^{32} +(-3.50681 - 2.94256i) q^{33} +(-2.75385 + 1.00232i) q^{34} +0.311462 q^{36} +(5.77175 + 1.92013i) q^{37} +5.42399 q^{38} +(-0.101642 + 0.279260i) q^{39} +(3.30254 + 2.77116i) q^{41} +(5.69858 + 1.00481i) q^{42} +0.637427i q^{43} +(-0.0886964 + 0.503022i) q^{44} +(2.84307 - 2.38562i) q^{46} +(2.51859 - 4.36233i) q^{47} +(3.62598 + 6.28039i) q^{48} +(2.47619 + 0.901260i) q^{49} +(3.97686 + 2.29604i) q^{51} +(0.0326552 - 0.00575799i) q^{52} +(-2.11651 - 12.0033i) q^{53} +(-2.95542 - 3.52214i) q^{54} +(-2.12083 - 5.82693i) q^{56} +(-5.46313 - 6.51071i) q^{57} +(-0.556915 - 3.15842i) q^{58} +(13.3122 - 2.34730i) q^{59} +(6.93152 - 8.26066i) q^{61} +(-8.87943 - 3.23185i) q^{62} +(-1.39972 - 2.42439i) q^{63} +(4.35055 - 7.53537i) q^{64} +(-5.27078 + 3.04309i) q^{66} +(-0.555953 + 3.15297i) q^{67} -0.512375i q^{68} +(-5.72717 - 1.00985i) q^{69} +(-7.56215 + 2.75240i) q^{71} +(1.36020 - 3.73713i) q^{72} -1.78846 q^{73} +(5.02334 - 6.33763i) q^{74} +(-0.324343 + 0.891124i) q^{76} +(4.31408 - 1.57020i) q^{77} +(0.302665 + 0.253966i) q^{78} +(15.4992 + 2.73292i) q^{79} +(-1.94909 + 11.0539i) q^{81} +(4.96377 - 2.86583i) q^{82} +(-2.54512 + 2.13561i) q^{83} +(-0.505846 + 0.876151i) q^{84} +(0.796348 + 0.289847i) q^{86} +(-3.23029 + 3.84971i) q^{87} +(5.64825 + 3.26102i) q^{88} +(-18.4072 + 3.24569i) q^{89} +(-0.191573 - 0.228308i) q^{91} +(0.221931 + 0.609751i) q^{92} +(5.06414 + 13.9136i) q^{93} +(-4.30469 - 5.13013i) q^{94} +(-2.68343 + 0.473162i) q^{96} +(-8.28814 - 4.78516i) q^{97} +(2.25192 - 2.68373i) q^{98} +(2.76686 + 1.00705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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