LMFDB - Embedded newform 900.2.s.d.349.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(49,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.1333317747165888577536.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 3x^{14} + 5x^{12} + 15x^{10} + 45x^{8} + 60x^{6} + 80x^{4} + 192x^{2} + 256 $ x^16 + 3x^14 + 5x^12 + 15x^10 + 45x^8 + 60x^6 + 80x^4 + 192*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.4
Root			$-1.27069 + 0.620769i$ of defining polynomial
Character	$\chi$	$=$	900.349
Dual form			900.2.s.d.49.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0977414 + 1.72929i) q^{3} +(-2.94604 - 1.70089i) q^{7} +(-2.98089 - 0.338047i) q^{9} +(2.20089 - 3.81206i) q^{11} +(1.78679 - 1.03160i) q^{13} +1.40179i q^{17} +6.35717 q^{19} +(3.22929 - 4.92830i) q^{21} +(0.0933799 - 0.0539129i) q^{23} +(0.875938 - 5.12179i) q^{27} +(4.54089 - 7.86505i) q^{29} +(-1.53160 - 2.65281i) q^{31} +(6.37704 + 4.17858i) q^{33} -1.95538i q^{37} +(1.60930 + 3.19070i) q^{39} +(4.34788 + 7.53074i) q^{41} +(6.17165 + 3.56320i) q^{43} +(-6.48096 - 3.74179i) q^{47} +(2.28608 + 3.95961i) q^{49} +(-2.42410 - 0.137013i) q^{51} +13.0975i q^{53} +(-0.621359 + 10.9934i) q^{57} +(-6.58966 - 11.4136i) q^{59} +(0.862308 - 1.49356i) q^{61} +(8.20684 + 6.06608i) q^{63} +(10.7177 - 6.18787i) q^{67} +(0.0841040 + 0.166751i) q^{69} -7.50961 q^{71} -5.42037i q^{73} +(-12.9678 + 7.48698i) q^{77} +(4.71806 - 8.17193i) q^{79} +(8.77145 + 2.01536i) q^{81} +(-7.77167 - 4.48698i) q^{83} +(13.1571 + 8.62126i) q^{87} -4.01576 q^{89} -7.01858 q^{91} +(4.73718 - 2.38929i) q^{93} +(1.88017 + 1.08551i) q^{97} +(-7.84929 + 10.6193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{9} + 6 q^{11} + 16 q^{19} + 26 q^{21} + 18 q^{29} - 4 q^{31} + 34 q^{39} + 18 q^{41} + 18 q^{49} + 6 q^{51} + 30 q^{59} + 2 q^{61} - 18 q^{69} - 48 q^{71} - 14 q^{79} - 62 q^{81} - 12 q^{89}+ \cdots - 66 q^{99}+O(q^{100}) $ 16 * q - 10 * q^9 + 6 * q^11 + 16 * q^19 + 26 * q^21 + 18 * q^29 - 4 * q^31 + 34 * q^39 + 18 * q^41 + 18 * q^49 + 6 * q^51 + 30 * q^59 + 2 * q^61 - 18 * q^69 - 48 * q^71 - 14 * q^79 - 62 * q^81 - 12 * q^89 - 44 * q^91 - 66 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.0977414	+	1.72929i	−0.0564310	+	0.998406i
$3$	−0.0977414	+	1.72929i	−0.0564310	+	0.998406i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.94604	−	1.70089i	−1.11350	−	0.642878i	−0.173764	−	0.984787i	$-0.555593\pi$
$7$	−2.94604	−	1.70089i	−1.11350	−	0.642878i	−0.939733	+	0.341910i	$0.888926\pi$
$8$		0			0
$9$	−2.98089	−	0.338047i	−0.993631	−	0.112682i
$10$		0			0
$11$	2.20089	−	3.81206i	0.663595	−	1.14938i	−0.316070	−	0.948736i	$-0.602363\pi$
$11$	2.20089	−	3.81206i	0.663595	−	1.14938i	0.979664	−	0.200644i	$-0.0643033\pi$
$12$		0			0
$13$	1.78679	−	1.03160i	0.495565	−	0.286115i	−0.231315	−	0.972879i	$-0.574303\pi$
$13$	1.78679	−	1.03160i	0.495565	−	0.286115i	0.726880	+	0.686764i	$0.240969\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			1.40179i			0.339984i	0.985445	+	0.169992i	$0.0543741\pi$
$17$			1.40179i			0.339984i	−0.985445	+	0.169992i	$0.945626\pi$
$18$		0			0
$19$	6.35717			1.45843			0.729217	−	0.684283i	$-0.239885\pi$
$19$	6.35717			1.45843			0.729217	+	0.684283i	$0.239885\pi$
$20$		0			0
$21$	3.22929	−	4.92830i	0.704689	−	1.07544i
$22$		0			0
$23$	0.0933799	−	0.0539129i	0.0194711	−	0.0112416i	−0.490233	−	0.871591i	$-0.663088\pi$
$23$	0.0933799	−	0.0539129i	0.0194711	−	0.0112416i	0.509704	+	0.860350i	$0.329755\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.875938	−	5.12179i	0.168574	−	0.985689i
$28$		0			0
$29$	4.54089	−	7.86505i	0.843222	−	1.46050i	−0.0439339	−	0.999034i	$-0.513989\pi$
$29$	4.54089	−	7.86505i	0.843222	−	1.46050i	0.887156	−	0.461469i	$-0.152678\pi$
$30$		0			0
$31$	−1.53160	−	2.65281i	−0.275084	−	0.476459i	0.695073	−	0.718940i	$-0.255372\pi$
$31$	−1.53160	−	2.65281i	−0.275084	−	0.476459i	−0.970156	+	0.242481i	$0.922039\pi$
$32$		0			0
$33$	6.37704	+	4.17858i	1.11010	+	0.727398i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	1.95538i		−	0.321462i	−0.986998	−	0.160731i	$-0.948615\pi$
$37$		−	1.95538i		−	0.321462i	0.986998	−	0.160731i	$-0.0513852\pi$
$38$		0			0
$39$	1.60930	+	3.19070i	0.257694	+	0.510921i
$40$		0			0
$41$	4.34788	+	7.53074i	0.679024	+	1.17610i	0.975275	+	0.220994i	$0.0709302\pi$
$41$	4.34788	+	7.53074i	0.679024	+	1.17610i	−0.296251	+	0.955110i	$0.595736\pi$
$42$		0			0
$43$	6.17165	+	3.56320i	0.941167	+	0.543383i	0.890326	−	0.455323i	$-0.150476\pi$
$43$	6.17165	+	3.56320i	0.941167	+	0.543383i	0.0508414	+	0.998707i	$0.483810\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.48096	−	3.74179i	−0.945345	−	0.545795i	−0.0537135	−	0.998556i	$-0.517106\pi$
$47$	−6.48096	−	3.74179i	−0.945345	−	0.545795i	−0.891632	+	0.452761i	$0.850439\pi$
$48$		0			0
$49$	2.28608	+	3.95961i	0.326583	+	0.565659i
$50$		0			0
$51$	−2.42410	−	0.137013i	−0.339442	−	0.0191856i
$52$		0			0
$53$			13.0975i			1.79909i	0.436833	+	0.899543i	$0.356100\pi$
$53$			13.0975i			1.79909i	−0.436833	+	0.899543i	$0.643900\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.621359	+	10.9934i	−0.0823009	+	1.45611i
$58$		0			0
$59$	−6.58966	−	11.4136i	−0.857901	−	1.48593i	−0.873928	−	0.486056i	$-0.838435\pi$
$59$	−6.58966	−	11.4136i	−0.857901	−	1.48593i	0.0160267	−	0.999872i	$-0.494898\pi$
$60$		0			0
$61$	0.862308	−	1.49356i	0.110407	−	0.191231i	−0.805527	−	0.592559i	$-0.798118\pi$
$61$	0.862308	−	1.49356i	0.110407	−	0.191231i	0.915935	+	0.401328i	$0.131451\pi$
$62$		0			0
$63$	8.20684	+	6.06608i	1.03396	+	0.764255i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	10.7177	−	6.18787i	1.30938	−	0.755969i	0.327385	−	0.944891i	$-0.393833\pi$
$67$	10.7177	−	6.18787i	1.30938	−	0.755969i	0.981992	+	0.188922i	$0.0604994\pi$
$68$		0			0
$69$	0.0841040	+	0.166751i	0.0101249	+	0.0200744i
$70$		0			0
$71$	−7.50961			−0.891227			−0.445614	−	0.895225i	$-0.647014\pi$
$71$	−7.50961			−0.891227			−0.445614	+	0.895225i	$0.647014\pi$
$72$		0			0
$73$		−	5.42037i		−	0.634406i	−0.948358	−	0.317203i	$-0.897256\pi$
$73$		−	5.42037i		−	0.634406i	0.948358	−	0.317203i	$-0.102744\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.9678	+	7.48698i	−1.47782	+	0.853220i
$78$		0			0
$79$	4.71806	−	8.17193i	0.530824	−	0.919413i	−0.468529	−	0.883448i	$-0.655216\pi$
$79$	4.71806	−	8.17193i	0.530824	−	0.919413i	0.999353	−	0.0359656i	$-0.0114507\pi$
$80$		0			0
$81$	8.77145	+	2.01536i	0.974605	+	0.223929i
$82$		0			0
$83$	−7.77167	−	4.48698i	−0.853052	−	0.492510i	0.00862744	−	0.999963i	$-0.497254\pi$
$83$	−7.77167	−	4.48698i	−0.853052	−	0.492510i	−0.861679	+	0.507453i	$0.830587\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	13.1571	+	8.62126i	1.41059	+	0.924296i
$88$		0			0
$89$	−4.01576			−0.425670			−0.212835	−	0.977088i	$-0.568270\pi$
$89$	−4.01576			−0.425670			−0.212835	+	0.977088i	$0.568270\pi$
$90$		0			0
$91$	−7.01858			−0.735747
$92$		0			0
$93$	4.73718	−	2.38929i	0.491223	−	0.247758i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.88017	+	1.08551i	0.190902	+	0.110217i	0.592405	−	0.805641i	$-0.298179\pi$
$97$	1.88017	+	1.08551i	0.190902	+	0.110217i	−0.401503	+	0.915858i	$0.631512\pi$
$98$		0			0
$99$	−7.84929	+	10.6193i	−0.788883	+	1.06728i
$100$		0			0
$101$	−1.48698	+	2.57552i	−0.147960	+	0.256274i	−0.930473	−	0.366360i	$-0.880604\pi$
$101$	−1.48698	+	2.57552i	−0.147960	+	0.256274i	0.782513	+	0.622634i	$0.213937\pi$
$102$		0			0
$103$	5.74640	−	3.31768i	0.566209	−	0.326901i	−0.189425	−	0.981895i	$-0.560662\pi$
$103$	5.74640	−	3.31768i	0.566209	−	0.326901i	0.755634	+	0.654994i	$0.227329\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	13.7878i		−	1.33292i	−0.745541	−	0.666459i	$-0.767809\pi$
$107$		−	13.7878i		−	1.33292i	0.745541	−	0.666459i	$-0.232191\pi$
$108$		0			0
$109$	18.1347			1.73699			0.868495	−	0.495699i	$-0.165088\pi$
$109$	18.1347			1.73699			0.868495	+	0.495699i	$0.165088\pi$
$110$		0			0
$111$	3.38141	+	0.191121i	0.320950	+	0.0181404i
$112$		0			0
$113$	−0.0708250	+	0.0408909i	−0.00666266	+	0.00384669i	−0.503328	−	0.864096i	$-0.667891\pi$
$113$	−0.0708250	+	0.0408909i	−0.00666266	+	0.00384669i	0.496665	+	0.867942i	$0.334558\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.67495	+	2.47108i	−0.524649	+	0.228451i
$118$		0			0
$119$	2.38429	−	4.12972i	0.218568	−	0.378571i
$120$		0			0
$121$	−4.18787	−	7.25361i	−0.380716	−	0.659419i
$122$		0			0
$123$	−13.4478	+	6.78268i	−1.21255	+	0.611573i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	21.5811i		−	1.91501i	−0.288410	−	0.957507i	$-0.593127\pi$
$127$		−	21.5811i		−	1.91501i	0.288410	−	0.957507i	$-0.406873\pi$
$128$		0			0
$129$	−6.76504	+	10.3243i	−0.595628	+	0.909004i
$130$		0			0
$131$	5.39391	+	9.34253i	0.471268	+	0.816260i	0.999460	−	0.0328649i	$-0.0104631\pi$
$131$	5.39391	+	9.34253i	0.471268	+	0.816260i	−0.528192	+	0.849125i	$0.677130\pi$
$132$		0			0
$133$	−18.7284	−	10.8129i	−1.62396	−	0.937594i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.6997	+	6.75481i	0.999570	+	0.577102i	0.908121	−	0.418708i	$-0.137517\pi$
$137$	11.6997	+	6.75481i	0.999570	+	0.577102i	0.0914491	+	0.995810i	$0.470850\pi$
$138$		0			0
$139$	7.30499	+	12.6526i	0.619601	+	1.07318i	0.989559	+	0.144132i	$0.0460389\pi$
$139$	7.30499	+	12.6526i	0.619601	+	1.07318i	−0.369958	+	0.929049i	$0.620628\pi$
$140$		0			0
$141$	7.10409	−	10.8417i	0.598273	−	0.913039i
$142$		0			0
$143$		−	9.08178i		−	0.759457i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.07077	+	3.56628i	−0.583187	+	0.294142i
$148$		0			0
$149$	0.0669350	+	0.115935i	0.00548353	+	0.00949775i	0.868754	−	0.495244i	$-0.164921\pi$
$149$	0.0669350	+	0.115935i	0.00548353	+	0.00949775i	−0.863271	+	0.504741i	$0.831588\pi$
$150$		0			0
$151$	−3.07249	+	5.32171i	−0.250036	+	0.433075i	−0.963535	−	0.267581i	$-0.913776\pi$
$151$	−3.07249	+	5.32171i	−0.250036	+	0.433075i	0.713500	+	0.700656i	$0.247109\pi$
$152$		0			0
$153$	0.473870	−	4.17858i	0.0383101	−	0.337818i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−12.7953	+	7.38736i	−1.02117	+	0.589575i	−0.914444	−	0.404713i	$-0.867372\pi$
$157$	−12.7953	+	7.38736i	−1.02117	+	0.589575i	−0.106730	+	0.994288i	$0.534038\pi$
$158$		0			0
$159$	−22.6495	−	1.28017i	−1.79622	−	0.101524i
$160$		0			0
$161$	−0.366801			−0.0289079
$162$		0			0
$163$		−	15.9451i		−	1.24892i	−0.781058	−	0.624458i	$-0.785320\pi$
$163$		−	15.9451i		−	1.24892i	0.781058	−	0.624458i	$-0.214680\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−17.7529	+	10.2497i	−1.37376	+	0.793143i	−0.991400	−	0.130869i	$-0.958223\pi$
$167$	−17.7529	+	10.2497i	−1.37376	+	0.793143i	−0.382364	+	0.924012i	$0.624890\pi$
$168$		0			0
$169$	−4.37160	+	7.57183i	−0.336277	+	0.582448i
$170$		0			0
$171$	−18.9500	−	2.14902i	−1.44915	−	0.164340i
$172$		0			0
$173$	−19.5647	−	11.2957i	−1.48748	−	0.858796i	−0.487580	−	0.873078i	$-0.662120\pi$
$173$	−19.5647	−	11.2957i	−1.48748	−	0.858796i	−0.999898	+	0.0142821i	$0.995454\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	20.3816	−	10.2799i	1.53197	−	0.772681i
$178$		0			0
$179$	−20.5879			−1.53881			−0.769407	−	0.638759i	$-0.779448\pi$
$179$	−20.5879			−1.53881			−0.769407	+	0.638759i	$0.779448\pi$
$180$		0			0
$181$	−8.32830			−0.619038			−0.309519	−	0.950893i	$-0.600168\pi$
$181$	−8.32830			−0.619038			−0.309519	+	0.950893i	$0.600168\pi$
$182$		0			0
$183$	2.49852	+	1.63716i	0.184696	+	0.121023i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	5.34370	+	3.08519i	0.390770	+	0.225611i
$188$		0			0
$189$	−11.2922	+	13.5991i	−0.821384	+	0.989189i
$190$		0			0
$191$	4.39217	−	7.60747i	0.317807	−	0.550457i	−0.662224	−	0.749306i	$-0.730387\pi$
$191$	4.39217	−	7.60747i	0.317807	−	0.550457i	0.980030	+	0.198849i	$0.0637204\pi$
$192$		0			0
$193$	6.26202	−	3.61538i	0.450750	−	0.260241i	−0.257397	−	0.966306i	$-0.582865\pi$
$193$	6.26202	−	3.61538i	0.450750	−	0.260241i	0.708147	+	0.706065i	$0.249531\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			4.17932i			0.297764i	0.988855	+	0.148882i	$0.0475675\pi$
$197$			4.17932i			0.297764i	−0.988855	+	0.148882i	$0.952432\pi$
$198$		0			0
$199$	−15.6518			−1.10953			−0.554763	−	0.832009i	$-0.687191\pi$
$199$	−15.6518			−1.10953			−0.554763	+	0.832009i	$0.687191\pi$
$200$		0			0
$201$	9.65307	+	19.1388i	0.680875	+	1.34995i
$202$		0			0
$203$	−26.7553	+	15.4472i	−1.87785	+	1.08418i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.296581	+	0.129142i	−0.0206138	+	0.00897598i
$208$		0			0
$209$	13.9914	−	24.2339i	0.967809	−	1.67629i
$210$		0			0
$211$	12.0770	+	20.9179i	0.831412	+	1.44005i	0.896918	+	0.442196i	$0.145801\pi$
$211$	12.0770	+	20.9179i	0.831412	+	1.44005i	−0.0655057	+	0.997852i	$0.520866\pi$
$212$		0			0
$213$	0.734001	−	12.9863i	0.0502929	−	0.889807i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			10.4204i			0.707381i
$218$		0			0
$219$	9.37339	+	0.529795i	0.633395	+	0.0358002i
$220$		0			0
$221$	1.44609	+	2.50470i	0.0972743	+	0.168484i
$222$		0			0
$223$	−1.25263	−	0.723206i	−0.0838823	−	0.0484295i	0.457472	−	0.889224i	$-0.348755\pi$
$223$	−1.25263	−	0.723206i	−0.0838823	−	0.0484295i	−0.541354	+	0.840794i	$0.682088\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.7755	+	10.2627i	1.17980	+	0.681158i	0.955969	−	0.293469i	$-0.0948098\pi$
$227$	17.7755	+	10.2627i	1.17980	+	0.681158i	0.223832	+	0.974628i	$0.428143\pi$
$228$		0			0
$229$	10.4743	+	18.1420i	0.692160	+	1.19886i	0.971129	+	0.238556i	$0.0766741\pi$
$229$	10.4743	+	18.1420i	0.692160	+	1.19886i	−0.278969	+	0.960300i	$0.589993\pi$
$230$		0			0
$231$	−11.6797	−	23.1569i	−0.768466	−	1.52361i
$232$		0			0
$233$		−	9.90112i		−	0.648644i	−0.945947	−	0.324322i	$-0.894864\pi$
$233$		−	9.90112i		−	0.648644i	0.945947	−	0.324322i	$-0.105136\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	13.6705	+	8.95764i	0.887993	+	0.581861i
$238$		0			0
$239$	3.05391	+	5.28953i	0.197541	+	0.342151i	0.947731	−	0.319072i	$-0.103371\pi$
$239$	3.05391	+	5.28953i	0.197541	+	0.342151i	−0.750189	+	0.661223i	$0.770038\pi$
$240$		0			0
$241$	0.148392	−	0.257022i	0.00955875	−	0.0165562i	−0.861206	−	0.508255i	$-0.830291\pi$
$241$	0.148392	−	0.257022i	0.00955875	−	0.0165562i	0.870765	+	0.491699i	$0.163624\pi$
$242$		0			0
$243$	−4.34248	+	14.9714i	−0.278570	+	0.960416i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	11.3589	−	6.55806i	0.722749	−	0.417279i
$248$		0			0
$249$	8.51890	−	13.0009i	0.539864	−	0.823900i
$250$		0			0
$251$	−4.51643			−0.285075			−0.142537	−	0.989789i	$-0.545526\pi$
$251$	−4.51643			−0.285075			−0.142537	+	0.989789i	$0.545526\pi$
$252$		0			0
$253$		−	0.474626i		−	0.0298395i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.7764	+	6.79911i	−0.734591	+	0.424117i	−0.820100	−	0.572221i	$-0.806082\pi$
$257$	−11.7764	+	6.79911i	−0.734591	+	0.424117i	0.0855081	+	0.996337i	$0.472749\pi$
$258$		0			0
$259$	−3.32589	+	5.76061i	−0.206661	+	0.357947i
$260$		0			0
$261$	−16.1947	+	21.9099i	−1.00242	+	1.35619i
$262$		0			0
$263$	6.16921	+	3.56179i	0.380409	+	0.219630i	0.677996	−	0.735065i	$-0.262848\pi$
$263$	6.16921	+	3.56179i	0.380409	+	0.219630i	−0.297587	+	0.954695i	$0.596182\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.392506	−	6.94441i	0.0240210	−	0.424991i
$268$		0			0
$269$	−8.80358			−0.536764			−0.268382	−	0.963313i	$-0.586489\pi$
$269$	−8.80358			−0.536764			−0.268382	+	0.963313i	$0.586489\pi$
$270$		0			0
$271$	−9.95885			−0.604957			−0.302478	−	0.953156i	$-0.597814\pi$
$271$	−9.95885			−0.604957			−0.302478	+	0.953156i	$0.597814\pi$
$272$		0			0
$273$	0.686006	−	12.1372i	0.0415190	−	0.734575i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−7.73303	−	4.46467i	−0.464633	−	0.268256i	0.249358	−	0.968411i	$-0.419781\pi$
$277$	−7.73303	−	4.46467i	−0.464633	−	0.268256i	−0.713990	+	0.700156i	$0.753114\pi$
$278$		0			0
$279$	3.66877	+	8.42550i	0.219643	+	0.504421i
$280$		0			0
$281$	−16.0402	+	27.7825i	−0.956879	+	1.65736i	−0.226872	+	0.973925i	$0.572850\pi$
$281$	−16.0402	+	27.7825i	−0.956879	+	1.65736i	−0.730008	+	0.683439i	$0.760484\pi$
$282$		0			0
$283$	−5.51437	+	3.18373i	−0.327796	+	0.189253i	−0.654862	−	0.755749i	$-0.727273\pi$
$283$	−5.51437	+	3.18373i	−0.327796	+	0.189253i	0.327066	+	0.945001i	$0.393940\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	29.5811i		−	1.74612i
$288$		0			0
$289$	15.0350			0.884411
$290$		0			0
$291$	−2.06094	+	3.14525i	−0.120814	+	0.184378i
$292$		0			0
$293$	24.1631	−	13.9506i	1.41162	−	0.815000i	0.416081	−	0.909328i	$-0.363403\pi$
$293$	24.1631	−	13.9506i	1.41162	−	0.815000i	0.995541	+	0.0943273i	$0.0300700\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−17.5967	−	14.6116i	−1.02107	−	0.847854i
$298$		0			0
$299$	0.111233	−	0.192662i	0.00643278	−	0.0111419i
$300$		0			0
$301$	−12.1213	−	20.9946i	−0.698658	−	1.21011i
$302$		0			0
$303$	−4.30849	−	2.82315i	−0.247516	−	0.162186i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			12.2054i			0.696597i	0.937384	+	0.348299i	$0.113240\pi$
$307$			12.2054i			0.696597i	−0.937384	+	0.348299i	$0.886760\pi$
$308$		0			0
$309$	5.17558	+	10.2615i	0.294428	+	0.583755i
$310$		0			0
$311$	2.45123	+	4.24565i	0.138996	+	0.240749i	0.927117	−	0.374772i	$-0.122279\pi$
$311$	2.45123	+	4.24565i	0.138996	+	0.240749i	−0.788121	+	0.615521i	$0.788946\pi$
$312$		0			0
$313$	15.2322	+	8.79429i	0.860972	+	0.497083i	0.864338	−	0.502912i	$-0.167738\pi$
$313$	15.2322	+	8.79429i	0.860972	+	0.497083i	−0.00336551	+	0.999994i	$0.501071\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.9500	+	9.78608i	0.952007	+	0.549641i	0.893704	−	0.448658i	$-0.148098\pi$
$317$	16.9500	+	9.78608i	0.952007	+	0.549641i	0.0583028	+	0.998299i	$0.481431\pi$
$318$		0			0
$319$	−19.9880	−	34.6203i	−1.11912	−	1.93836i
$320$		0			0
$321$	23.8431	+	1.34764i	1.33079	+	0.0752180i
$322$		0			0
$323$			8.91140i			0.495844i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.77251	+	31.3602i	−0.0980201	+	1.73422i
$328$		0			0
$329$	12.7288	+	22.0469i	0.701759	+	1.21548i
$330$		0			0
$331$	−7.29537	+	12.6360i	−0.400990	+	0.694535i	−0.993846	−	0.110774i	$-0.964667\pi$
$331$	−7.29537	+	12.6360i	−0.400990	+	0.694535i	0.592856	+	0.805309i	$0.298000\pi$
$332$		0			0
$333$	−0.661009	+	5.82877i	−0.0362231	+	0.319415i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.58108	−	4.95429i	0.467441	−	0.269877i	−0.247727	−	0.968830i	$-0.579683\pi$
$337$	8.58108	−	4.95429i	0.467441	−	0.269877i	0.715168	+	0.698953i	$0.246350\pi$
$338$		0			0
$339$	−0.0637896	−	0.126474i	−0.00346458	−	0.00686911i
$340$		0			0
$341$	−13.4836			−0.730176
$342$		0			0
$343$			8.25897i			0.445943i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.93739	+	5.16000i	−0.479784	+	0.277004i	−0.720327	−	0.693635i	$-0.756008\pi$
$347$	−8.93739	+	5.16000i	−0.479784	+	0.277004i	0.240542	+	0.970639i	$0.422675\pi$
$348$		0			0
$349$	8.56767	−	14.8396i	0.458617	−	0.794348i	−0.540271	−	0.841491i	$-0.681678\pi$
$349$	8.56767	−	14.8396i	0.458617	−	0.794348i	0.998888	+	0.0471429i	$0.0150116\pi$
$350$		0			0
$351$	−3.71853	−	10.0552i	−0.198481	−	0.536705i
$352$		0			0
$353$	11.4845	+	6.63055i	0.611256	+	0.352909i	0.773457	−	0.633849i	$-0.218526\pi$
$353$	11.4845	+	6.63055i	0.611256	+	0.352909i	−0.162201	+	0.986758i	$0.551859\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	6.90844	+	4.52678i	0.365634	+	0.239583i
$358$		0			0
$359$	−14.2817			−0.753758			−0.376879	−	0.926263i	$-0.623003\pi$
$359$	−14.2817			−0.753758			−0.376879	+	0.926263i	$0.623003\pi$
$360$		0			0
$361$	21.4136			1.12703
$362$		0			0
$363$	12.9529	−	6.53307i	0.679852	−	0.342897i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.29749	+	4.79056i	0.433125	+	0.250065i	0.700677	−	0.713478i	$-0.252881\pi$
$367$	8.29749	+	4.79056i	0.433125	+	0.250065i	−0.267552	+	0.963543i	$0.586215\pi$
$368$		0			0
$369$	−10.4148	−	23.9181i	−0.542173	−	1.24513i
$370$		0			0
$371$	22.2775	−	38.5858i	1.15659	−	2.00328i
$372$		0			0
$373$	−20.8763	+	12.0529i	−1.08093	+	0.624076i	−0.931148	−	0.364642i	$-0.881191\pi$
$373$	−20.8763	+	12.0529i	−1.08093	+	0.624076i	−0.149784	+	0.988719i	$0.547858\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	18.7376i		−	0.965033i
$378$		0			0
$379$	−2.73973			−0.140730			−0.0703651	−	0.997521i	$-0.522416\pi$
$379$	−2.73973			−0.140730			−0.0703651	+	0.997521i	$0.522416\pi$
$380$		0			0
$381$	37.3200	+	2.10937i	1.91196	+	0.108066i
$382$		0			0
$383$	18.4924	−	10.6766i	0.944917	−	0.545548i	0.0534187	−	0.998572i	$-0.482988\pi$
$383$	18.4924	−	10.6766i	0.944917	−	0.545548i	0.891498	+	0.453024i	$0.149655\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−17.1925	−	12.7078i	−0.873944	−	0.645975i
$388$		0			0
$389$	−7.33485	+	12.7043i	−0.371892	+	0.644136i	−0.989857	−	0.142070i	$-0.954624\pi$
$389$	−7.33485	+	12.7043i	−0.371892	+	0.644136i	0.617965	+	0.786206i	$0.287957\pi$
$390$		0			0
$391$	0.0755745	+	0.130899i	0.00382197	+	0.00661984i
$392$		0			0
$393$	−16.6832	+	8.41449i	−0.841554	+	0.424455i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	6.43065i		−	0.322745i	−0.986894	−	0.161373i	$-0.948408\pi$
$397$		−	6.43065i		−	0.322745i	0.986894	−	0.161373i	$-0.0515921\pi$
$398$		0			0
$399$	20.5291	−	31.3300i	1.02774	−	1.56846i
$400$		0			0
$401$	−9.03748	−	15.6534i	−0.451310	−	0.781693i	0.547157	−	0.837030i	$-0.315710\pi$
$401$	−9.03748	−	15.6534i	−0.451310	−	0.781693i	−0.998468	+	0.0553373i	$0.982377\pi$
$402$		0			0
$403$	−5.47329	−	3.16000i	−0.272644	−	0.157411i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.45402	−	4.30358i	−0.369482	−	0.213320i
$408$		0			0
$409$	−9.39532	−	16.2732i	−0.464569	−	0.804657i	0.534613	−	0.845097i	$-0.320457\pi$
$409$	−9.39532	−	16.2732i	−0.464569	−	0.804657i	−0.999182	+	0.0404403i	$0.987124\pi$
$410$		0			0
$411$	−12.8246	+	19.5719i	−0.632589	+	0.965411i
$412$		0			0
$413$			44.8333i			2.20610i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−22.5940	+	11.3958i	−1.10643	+	0.558053i
$418$		0			0
$419$	19.8297	+	34.3461i	0.968745	+	1.67792i	0.699198	+	0.714928i	$0.253540\pi$
$419$	19.8297	+	34.3461i	0.968745	+	1.67792i	0.269547	+	0.962987i	$0.413126\pi$
$420$		0			0
$421$	18.7682	−	32.5076i	0.914708	−	1.58432i	0.107380	−	0.994218i	$-0.465754\pi$
$421$	18.7682	−	32.5076i	0.914708	−	1.58432i	0.807328	−	0.590103i	$-0.200913\pi$
$422$		0			0
$423$	18.0542	+	13.3447i	0.877823	+	0.648843i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.08078	+	2.93339i	−0.245876	+	0.141957i
$428$		0			0
$429$	15.7050	+	0.887666i	0.758247	+	0.0428569i
$430$		0			0
$431$	16.7357			0.806132			0.403066	−	0.915171i	$-0.367945\pi$
$431$	16.7357			0.806132			0.403066	+	0.915171i	$0.367945\pi$
$432$		0			0
$433$			21.0008i			1.00924i	0.863343	+	0.504618i	$0.168367\pi$
$433$			21.0008i			1.00924i	−0.863343	+	0.504618i	$0.831633\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.593631	−	0.342733i	0.0283972	−	0.0163952i
$438$		0			0
$439$	−3.01576	+	5.22345i	−0.143934	+	0.249302i	−0.928975	−	0.370143i	$-0.879309\pi$
$439$	−3.01576	+	5.22345i	−0.143934	+	0.249302i	0.785041	+	0.619444i	$0.212642\pi$
$440$		0			0
$441$	−5.47604	−	12.5760i	−0.260764	−	0.598856i
$442$		0			0
$443$	−5.47803	−	3.16274i	−0.260269	−	0.150266i	0.364188	−	0.931325i	$-0.381346\pi$
$443$	−5.47803	−	3.16274i	−0.260269	−	0.150266i	−0.624457	+	0.781059i	$0.714680\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.207027	+	0.104418i	−0.00979205	+	0.00493882i
$448$		0			0
$449$	18.6594			0.880593			0.440296	−	0.897853i	$-0.354873\pi$
$449$	18.6594			0.880593			0.440296	+	0.897853i	$0.354873\pi$
$450$		0			0
$451$	38.2769			1.80239
$452$		0			0
$453$	−8.90248	−	5.83338i	−0.418275	−	0.274076i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−23.8889	−	13.7923i	−1.11748	−	0.645176i	−0.176722	−	0.984261i	$-0.556549\pi$
$457$	−23.8889	−	13.7923i	−1.11748	−	0.645176i	−0.940756	+	0.339085i	$0.889883\pi$
$458$		0			0
$459$	7.17967	+	1.22788i	0.335118	+	0.0573125i
$460$		0			0
$461$	6.76442	−	11.7163i	0.315051	−	0.545684i	−0.664398	−	0.747379i	$-0.731312\pi$
$461$	6.76442	−	11.7163i	0.315051	−	0.545684i	0.979448	+	0.201696i	$0.0646452\pi$
$462$		0			0
$463$	23.8020	−	13.7421i	1.10617	−	0.638650i	0.168338	−	0.985729i	$-0.446160\pi$
$463$	23.8020	−	13.7421i	1.10617	−	0.638650i	0.937836	+	0.347079i	$0.112827\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	32.7515i		−	1.51556i	−0.652511	−	0.757779i	$-0.726284\pi$
$467$		−	32.7515i		−	1.51556i	0.652511	−	0.757779i	$-0.273716\pi$
$468$		0			0
$469$	−42.0997			−1.94398
$470$		0			0
$471$	−11.5243	−	22.8488i	−0.531010	−	1.05282i
$472$		0			0
$473$	27.1663	−	15.6845i	1.24911	−	0.721172i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	4.42758	−	39.0424i	0.202725	−	1.78763i
$478$		0			0
$479$	2.92783	−	5.07116i	0.133776	−	0.231707i	−0.791353	−	0.611359i	$-0.790623\pi$
$479$	2.92783	−	5.07116i	0.133776	−	0.231707i	0.925129	+	0.379652i	$0.123956\pi$
$480$		0			0
$481$	−2.01717	−	3.49384i	−0.0919750	−	0.159305i
$482$		0			0
$483$	0.0358516	−	0.634305i	0.00163131	−	0.0288619i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			16.4864i			0.747070i	0.927616	+	0.373535i	$0.121854\pi$
$487$			16.4864i			0.747070i	−0.927616	+	0.373535i	$0.878146\pi$
$488$		0			0
$489$	27.5737	+	1.55850i	1.24693	+	0.0704776i
$490$		0			0
$491$	6.85302	+	11.8698i	0.309272	+	0.535676i	0.978203	−	0.207649i	$-0.0665812\pi$
$491$	6.85302	+	11.8698i	0.309272	+	0.535676i	−0.668931	+	0.743324i	$0.733248\pi$
$492$		0			0
$493$	11.0251	+	6.36537i	0.496548	+	0.286682i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	22.1236	+	12.7731i	0.992379	+	0.572950i
$498$		0			0
$499$	2.23482	+	3.87082i	0.100044	+	0.173282i	0.911703	−	0.410851i	$-0.134768\pi$
$499$	2.23482	+	3.87082i	0.100044	+	0.173282i	−0.811658	+	0.584132i	$0.801435\pi$
$500$		0			0
$501$	−15.9895	−	31.7018i	−0.714356	−	1.41633i
$502$		0			0
$503$		−	18.1010i		−	0.807084i	−0.914961	−	0.403542i	$-0.867779\pi$
$503$		−	18.1010i		−	0.807084i	0.914961	−	0.403542i	$-0.132221\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−12.6666	−	8.29985i	−0.562544	−	0.368609i
$508$		0			0
$509$	−10.6044	−	18.3674i	−0.470033	−	0.814120i	0.529380	−	0.848385i	$-0.322425\pi$
$509$	−10.6044	−	18.3674i	−0.470033	−	0.814120i	−0.999413	+	0.0342644i	$0.989091\pi$
$510$		0			0
$511$	−9.21947	+	15.9686i	−0.407846	+	0.706409i
$512$		0			0
$513$	5.56848	−	32.5601i	0.245855	−	1.43756i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−28.5278	+	16.4705i	−1.25465	+	0.724374i
$518$		0			0
$519$	21.4458	−	32.7290i	0.941368	−	1.43665i
$520$		0			0
$521$	−28.4507			−1.24645			−0.623224	−	0.782043i	$-0.714178\pi$
$521$	−28.4507			−1.24645			−0.623224	+	0.782043i	$0.714178\pi$
$522$		0			0
$523$			26.5111i			1.15925i	0.814884	+	0.579625i	$0.196801\pi$
$523$			26.5111i			1.15925i	−0.814884	+	0.579625i	$0.803199\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.71868	−	2.14698i	0.161988	−	0.0935240i
$528$		0			0
$529$	−11.4942	+	19.9085i	−0.499747	+	0.865588i
$530$		0			0
$531$	15.7847	+	36.2504i	0.684999	+	1.57313i
$532$		0			0
$533$	15.5374	+	8.97055i	0.673001	+	0.388558i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.01229	−	35.6025i	0.0868369	−	1.53636i
$538$		0			0
$539$	20.1257			0.866876
$540$		0			0
$541$	−14.3132			−0.615372			−0.307686	−	0.951488i	$-0.599555\pi$
$541$	−14.3132			−0.615372			−0.307686	+	0.951488i	$0.599555\pi$
$542$		0			0
$543$	0.814020	−	14.4021i	0.0349329	−	0.618051i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	11.8222	+	6.82556i	0.505482	+	0.291840i	0.730974	−	0.682405i	$-0.239066\pi$
$547$	11.8222	+	6.82556i	0.505482	+	0.291840i	−0.225493	+	0.974245i	$0.572399\pi$
$548$		0			0
$549$	−3.07534	+	4.16065i	−0.131252	+	0.177572i
$550$		0			0
$551$	28.8672	−	49.9994i	1.22978	−	2.13005i
$552$		0			0
$553$	−27.7992	+	16.0499i	−1.18214	+	0.682509i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			23.4665i			0.994306i	0.867663	+	0.497153i	$0.165621\pi$
$557$			23.4665i			0.994306i	−0.867663	+	0.497153i	$0.834379\pi$
$558$		0			0
$559$	14.7032			0.621880
$560$		0			0
$561$	−5.85749	+	8.93927i	−0.247303	+	0.377416i
$562$		0			0
$563$	−0.504418	+	0.291226i	−0.0212587	+	0.0122737i	−0.510592	−	0.859823i	$-0.670574\pi$
$563$	−0.504418	+	0.291226i	−0.0212587	+	0.0122737i	0.489333	+	0.872097i	$0.337240\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−22.4131	−	20.8566i	−0.941261	−	0.875896i
$568$		0			0
$569$	−2.77994	+	4.81500i	−0.116541	+	0.201855i	−0.918395	−	0.395665i	$-0.870514\pi$
$569$	−2.77994	+	4.81500i	−0.116541	+	0.201855i	0.801854	+	0.597521i	$0.203847\pi$
$570$		0			0
$571$	11.3706	+	19.6945i	0.475845	+	0.824188i	0.999617	−	0.0276708i	$-0.00880903\pi$
$571$	11.3706	+	19.6945i	0.475845	+	0.824188i	−0.523772	+	0.851858i	$0.675476\pi$
$572$		0			0
$573$	12.7262	+	8.33891i	0.531646	+	0.348363i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			30.5522i			1.27191i	0.771728	+	0.635953i	$0.219393\pi$
$577$			30.5522i			1.27191i	−0.771728	+	0.635953i	$0.780607\pi$
$578$		0			0
$579$	5.63998	+	11.1822i	0.234390	+	0.464718i
$580$		0			0
$581$	15.2638	+	26.4376i	0.633247	+	1.09682i
$582$		0			0
$583$	49.9286	+	28.8263i	2.06783	+	1.19386i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.6353	+	10.1817i	0.727886	+	0.420245i	0.817648	−	0.575718i	$-0.195278\pi$
$587$	17.6353	+	10.1817i	0.727886	+	0.420245i	−0.0897626	+	0.995963i	$0.528611\pi$
$588$		0			0
$589$	−9.73664	−	16.8644i	−0.401191	−	0.694884i
$590$		0			0
$591$	−7.22726	−	0.408493i	−0.297290	−	0.0168032i
$592$		0			0
$593$			15.5199i			0.637326i	0.947868	+	0.318663i	$0.103234\pi$
$593$			15.5199i			0.637326i	−0.947868	+	0.318663i	$0.896766\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.52983	−	27.0665i	0.0626117	−	1.10776i
$598$		0			0
$599$	14.6288	+	25.3379i	0.597717	+	1.03528i	0.993157	+	0.116785i	$0.0372588\pi$
$599$	14.6288	+	25.3379i	0.597717	+	1.03528i	−0.395440	+	0.918492i	$0.629408\pi$
$600$		0			0
$601$	9.15254	−	15.8527i	0.373340	−	0.646644i	−0.616737	−	0.787169i	$-0.711546\pi$
$601$	9.15254	−	15.8527i	0.373340	−	0.646644i	0.990077	+	0.140526i	$0.0448792\pi$
$602$		0			0
$603$	−34.0401	+	14.8223i	−1.38622	+	0.603611i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−14.5845	+	8.42037i	−0.591967	+	0.341772i	−0.765875	−	0.642990i	$-0.777694\pi$
$607$	−14.5845	+	8.42037i	−0.591967	+	0.341772i	0.173908	+	0.984762i	$0.444360\pi$
$608$		0			0
$609$	−24.0975	−	47.7774i	−0.976481	−	1.93604i
$610$		0			0
$611$	−15.4401			−0.624640
$612$		0			0
$613$			13.5954i			0.549113i	0.961571	+	0.274556i	$0.0885310\pi$
$613$			13.5954i			0.549113i	−0.961571	+	0.274556i	$0.911469\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	25.3861	−	14.6567i	1.02201	−	0.590056i	0.107322	−	0.994224i	$-0.465772\pi$
$617$	25.3861	−	14.6567i	1.02201	−	0.590056i	0.914685	+	0.404168i	$0.132439\pi$
$618$		0			0
$619$	6.08211	−	10.5345i	0.244461	−	0.423418i	−0.717519	−	0.696539i	$-0.754722\pi$
$619$	6.08211	−	10.5345i	0.244461	−	0.423418i	0.961980	+	0.273121i	$0.0880558\pi$
$620$		0			0
$621$	−0.194336	−	0.525497i	−0.00779842	−	0.0210875i
$622$		0			0
$623$	11.8306	+	6.83038i	0.473982	+	0.273653i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	40.5399	+	26.5639i	1.61901	+	1.06086i
$628$		0			0
$629$	2.74103			0.109292
$630$		0			0
$631$	5.45471			0.217148			0.108574	−	0.994088i	$-0.465371\pi$
$631$	5.45471			0.217148			0.108574	+	0.994088i	$0.465371\pi$
$632$		0			0
$633$	−37.3536	+	18.8400i	−1.48467	+	0.748824i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	8.16948	+	4.71665i	0.323687	+	0.186881i
$638$		0			0
$639$	22.3854	+	2.53860i	0.885551	+	0.100425i
$640$		0			0
$641$	0.839996	−	1.45492i	0.0331779	−	0.0574657i	−0.848960	−	0.528458i	$-0.822771\pi$
$641$	0.839996	−	1.45492i	0.0331779	−	0.0574657i	0.882138	+	0.470992i	$0.156104\pi$
$642$		0			0
$643$	−4.92202	+	2.84173i	−0.194106	+	0.112067i	−0.593903	−	0.804537i	$-0.702414\pi$
$643$	−4.92202	+	2.84173i	−0.194106	+	0.112067i	0.399797	+	0.916603i	$0.369080\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			34.3064i			1.34872i	0.738401	+	0.674361i	$0.235581\pi$
$647$			34.3064i			1.34872i	−0.738401	+	0.674361i	$0.764419\pi$
$648$		0			0
$649$	−58.0126			−2.27719
$650$		0			0
$651$	−18.0198	−	1.01850i	−0.706253	−	0.0399182i
$652$		0			0
$653$	10.9377	−	6.31486i	0.428024	−	0.247120i	−0.270480	−	0.962725i	$-0.587183\pi$
$653$	10.9377	−	6.31486i	0.428024	−	0.247120i	0.698504	+	0.715606i	$0.253849\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.83234	+	16.1575i	−0.0714863	+	0.630366i
$658$		0			0
$659$	−3.16697	+	5.48535i	−0.123368	+	0.213679i	−0.921094	−	0.389341i	$-0.872703\pi$
$659$	−3.16697	+	5.48535i	−0.123368	+	0.213679i	0.797726	+	0.603020i	$0.206036\pi$
$660$		0			0
$661$	18.8448	+	32.6401i	0.732978	+	1.26955i	0.955605	+	0.294651i	$0.0952033\pi$
$661$	18.8448	+	32.6401i	0.732978	+	1.26955i	−0.222628	+	0.974904i	$0.571463\pi$
$662$		0			0
$663$	−4.47269	+	2.25589i	−0.173705	+	0.0876116i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	0.979251i		−	0.0379167i
$668$		0			0
$669$	1.37307	−	2.09547i	0.0530859	−	0.0810157i
$670$		0			0
$671$	−3.79570	−	6.57434i	−0.146531	−	0.253800i
$672$		0			0
$673$	−26.5477	−	15.3273i	−1.02334	−	0.590824i	−0.108268	−	0.994122i	$-0.534531\pi$
$673$	−26.5477	−	15.3273i	−1.02334	−	0.590824i	−0.915069	+	0.403298i	$0.867864\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	25.0035	+	14.4358i	0.960964	+	0.554813i	0.896470	−	0.443105i	$-0.146123\pi$
$677$	25.0035	+	14.4358i	0.960964	+	0.554813i	0.0644945	+	0.997918i	$0.479456\pi$
$678$		0			0
$679$	−3.69269	−	6.39593i	−0.141712	−	0.245453i
$680$		0			0
$681$	−19.4846	+	29.7359i	−0.746650	+	1.13948i
$682$		0			0
$683$		−	47.0352i		−	1.79975i	−0.436147	−	0.899875i	$-0.643657\pi$
$683$		−	47.0352i		−	1.79975i	0.436147	−	0.899875i	$-0.356343\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−32.3965	+	16.3399i	−1.23601	+	0.623404i
$688$		0			0
$689$	13.5114	+	23.4025i	0.514745	+	0.891564i
$690$		0			0
$691$	−0.425186	+	0.736443i	−0.0161748	+	0.0280156i	−0.874000	−	0.485927i	$-0.838482\pi$
$691$	−0.425186	+	0.736443i	−0.0161748	+	0.0280156i	0.857825	+	0.513942i	$0.171815\pi$
$692$		0			0
$693$	41.1867	−	17.9342i	1.56455	−	0.681262i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−10.5565	+	6.09480i	−0.399856	+	0.230857i
$698$		0			0
$699$	17.1219	+	0.967750i	0.647610	+	0.0366037i
$700$		0			0
$701$	−35.6821			−1.34770			−0.673848	−	0.738870i	$-0.735360\pi$
$701$	−35.6821			−1.34770			−0.673848	+	0.738870i	$0.735360\pi$
$702$		0			0
$703$		−	12.4307i		−	0.468831i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.76138	−	5.05838i	0.329506	−	0.190240i
$708$		0			0
$709$	7.69543	−	13.3289i	0.289008	−	0.500576i	−0.684565	−	0.728951i	$-0.740008\pi$
$709$	7.69543	−	13.3289i	0.289008	−	0.500576i	0.973573	+	0.228375i	$0.0733413\pi$
$710$		0			0
$711$	−16.8265	+	22.7647i	−0.631044	+	0.853743i
$712$		0			0
$713$	−0.286042	−	0.165146i	−0.0107123	−	0.00618477i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−9.44563	+	4.76410i	−0.352754	+	0.177918i
$718$		0			0
$719$	−25.5846			−0.954144			−0.477072	−	0.878864i	$-0.658302\pi$
$719$	−25.5846			−0.954144			−0.477072	+	0.878864i	$0.658302\pi$
$720$		0			0
$721$	−22.5721			−0.840630
$722$		0			0
$723$	0.429962	+	0.281734i	0.0159904	+	0.0104778i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	5.31509	+	3.06867i	0.197126	+	0.113811i	0.595314	−	0.803493i	$-0.297028\pi$
$727$	5.31509	+	3.06867i	0.197126	+	0.113811i	−0.398188	+	0.917304i	$0.630361\pi$
$728$		0			0
$729$	−25.4655	−	8.97274i	−0.943165	−	0.332324i
$730$		0			0
$731$	−4.99486	+	8.65135i	−0.184741	+	0.319982i
$732$		0			0
$733$	4.44306	−	2.56520i	0.164108	−	0.0947478i	−0.415697	−	0.909503i	$-0.636462\pi$
$733$	4.44306	−	2.56520i	0.164108	−	0.0947478i	0.579805	+	0.814756i	$0.303129\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	54.4754i		−	2.00663i
$738$		0			0
$739$	−18.8784			−0.694454			−0.347227	−	0.937781i	$-0.612877\pi$
$739$	−18.8784			−0.694454			−0.347227	+	0.937781i	$0.612877\pi$
$740$		0			0
$741$	10.2306	+	20.2838i	0.375829	+	0.745145i
$742$		0			0
$743$	19.0152	−	10.9784i	0.697600	−	0.402759i	−0.108853	−	0.994058i	$-0.534718\pi$
$743$	19.0152	−	10.9784i	0.697600	−	0.402759i	0.806453	+	0.591298i	$0.201384\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	21.6497	+	16.0024i	0.792122	+	0.585497i
$748$		0			0
$749$	−23.4516	+	40.6194i	−0.856904	+	1.48420i
$750$		0			0
$751$	1.58037	+	2.73728i	0.0576686	+	0.0998849i	0.893418	−	0.449225i	$-0.148300\pi$
$751$	1.58037	+	2.73728i	0.0576686	+	0.0998849i	−0.835750	+	0.549110i	$0.814967\pi$
$752$		0			0
$753$	0.441442	−	7.81022i	0.0160871	−	0.284620i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	39.1753i		−	1.42385i	−0.702255	−	0.711926i	$-0.747823\pi$
$757$		−	39.1753i		−	1.42385i	0.702255	−	0.711926i	$-0.252177\pi$
$758$		0			0
$759$	0.820767	+	0.0463907i	0.0297920	+	0.00168387i
$760$		0			0
$761$	−5.03916	−	8.72807i	−0.182669	−	0.316392i	0.760119	−	0.649783i	$-0.225140\pi$
$761$	−5.03916	−	8.72807i	−0.182669	−	0.316392i	−0.942789	+	0.333391i	$0.891807\pi$
$762$		0			0
$763$	−53.4255	−	30.8452i	−1.93413	−	1.11667i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−23.5486	−	13.5958i	−0.850292	−	0.490916i
$768$		0			0
$769$	10.5790	+	18.3233i	0.381487	+	0.660755i	0.991275	−	0.131810i	$-0.0420787\pi$
$769$	10.5790	+	18.3233i	0.381487	+	0.660755i	−0.609788	+	0.792565i	$0.708745\pi$
$770$		0			0
$771$	−10.6066	−	21.0294i	−0.381987	−	0.757354i
$772$		0			0
$773$			43.2543i			1.55575i	0.628420	+	0.777874i	$0.283702\pi$
$773$			43.2543i			1.55575i	−0.628420	+	0.777874i	$0.716298\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−9.63669	−	6.31448i	−0.345714	−	0.226531i
$778$		0			0
$779$	27.6402	+	47.8742i	0.990312	+	1.71527i
$780$		0			0
$781$	−16.5279	+	28.6271i	−0.591414	+	1.02436i
$782$		0			0
$783$	−36.3056	−	30.1468i	−1.29746	−	1.07736i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1.02189	−	0.589986i	0.0364263	−	0.0210307i	−0.481676	−	0.876349i	$-0.659972\pi$
$787$	1.02189	−	0.589986i	0.0364263	−	0.0210307i	0.518103	+	0.855318i	$0.326639\pi$
$788$		0			0
$789$	−6.76236	+	10.3202i	−0.240746	+	0.367409i
$790$		0			0
$791$	0.278204			0.00989180
$792$		0			0
$793$		−	3.55823i		−	0.126357i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.989706	−	0.571407i	0.0350572	−	0.0202403i	−0.482369	−	0.875968i	$-0.660224\pi$
$797$	0.989706	−	0.571407i	0.0350572	−	0.0202403i	0.517426	+	0.855728i	$0.326890\pi$
$798$		0			0
$799$	5.24519	−	9.08494i	0.185562	−	0.321402i
$800$		0			0
$801$	11.9705	+	1.35751i	0.422959	+	0.0479654i
$802$		0			0
$803$	−20.6628	−	11.9297i	−0.729173	−	0.420988i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.860474	−	15.2239i	0.0302901	−	0.535908i
$808$		0			0
$809$	11.3723			0.399828			0.199914	−	0.979813i	$-0.435934\pi$
$809$	11.3723			0.399828			0.199914	+	0.979813i	$0.435934\pi$
$810$		0			0
$811$	2.08590			0.0732459			0.0366230	−	0.999329i	$-0.488340\pi$
$811$	2.08590			0.0732459			0.0366230	+	0.999329i	$0.488340\pi$
$812$		0			0
$813$	0.973392	−	17.2217i	0.0341384	−	0.603993i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	39.2342	+	22.6519i	1.37263	+	0.792489i
$818$		0			0
$819$	20.9216	+	2.37261i	0.731061	+	0.0829056i
$820$		0			0
$821$	−7.89564	+	13.6757i	−0.275560	+	0.477284i	−0.970276	−	0.242000i	$-0.922197\pi$
$821$	−7.89564	+	13.6757i	−0.275560	+	0.477284i	0.694716	+	0.719284i	$0.255530\pi$
$822$		0			0
$823$	6.34003	−	3.66042i	0.221000	−	0.127594i	−0.385413	−	0.922744i	$-0.625941\pi$
$823$	6.34003	−	3.66042i	0.221000	−	0.127594i	0.606413	+	0.795150i	$0.292608\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			14.8401i			0.516040i	0.966140	+	0.258020i	$0.0830701\pi$
$827$			14.8401i			0.516040i	−0.966140	+	0.258020i	$0.916930\pi$
$828$		0			0
$829$	23.3346			0.810444			0.405222	−	0.914218i	$-0.367194\pi$
$829$	23.3346			0.810444			0.405222	+	0.914218i	$0.367194\pi$
$830$		0			0
$831$	8.47654	−	12.9363i	0.294048	−	0.448754i
$832$		0			0
$833$	−5.55054	+	3.20461i	−0.192315	+	0.111033i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−14.9287	+	5.52084i	−0.516012	+	0.190828i
$838$		0			0
$839$	−7.33826	+	12.7102i	−0.253345	+	0.438806i	−0.964445	−	0.264285i	$-0.914864\pi$
$839$	−7.33826	+	12.7102i	−0.253345	+	0.438806i	0.711100	+	0.703091i	$0.248197\pi$
$840$		0			0
$841$	−26.7394	−	46.3140i	−0.922048	−	1.59703i
$842$		0			0
$843$	−46.4762	−	30.4537i	−1.60072	−	1.04888i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			28.4925i			0.979014i
$848$		0			0
$849$	−4.96660	−	9.84714i	−0.170453	−	0.337953i
$850$		0			0
$851$	−0.105420	−	0.182593i	−0.00361375	−	0.00625920i
$852$		0			0
$853$	−21.2369	−	12.2611i	−0.727136	−	0.419812i	0.0902375	−	0.995920i	$-0.471237\pi$
$853$	−21.2369	−	12.2611i	−0.727136	−	0.419812i	−0.817374	+	0.576108i	$0.804571\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.83929	+	2.79396i	0.165307	+	0.0954400i	0.580371	−	0.814352i	$-0.302908\pi$
$857$	4.83929	+	2.79396i	0.165307	+	0.0954400i	−0.415064	+	0.909792i	$0.636241\pi$
$858$		0			0
$859$	−20.0309	−	34.6946i	−0.683447	−	1.18376i	−0.973922	−	0.226882i	$-0.927147\pi$
$859$	−20.0309	−	34.6946i	−0.683447	−	1.18376i	0.290476	−	0.956882i	$-0.406186\pi$
$860$		0			0
$861$	51.1543	+	2.89130i	1.74334	+	0.0985353i
$862$		0			0
$863$		−	27.2157i		−	0.926432i	−0.886246	−	0.463216i	$-0.846695\pi$
$863$		−	27.2157i		−	0.926432i	0.886246	−	0.463216i	$-0.153305\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.46954	+	25.9999i	−0.0499082	+	0.883002i
$868$		0			0
$869$	−20.7679	−	35.9711i	−0.704503	−	1.22024i
$870$		0			0
$871$	12.7668	−	22.1128i	0.432588	−	0.749264i
$872$		0			0
$873$	−5.23762	−	3.87139i	−0.177267	−	0.131027i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	20.6806	−	11.9399i	0.698334	−	0.403183i	−0.108393	−	0.994108i	$-0.534570\pi$
$877$	20.6806	−	11.9399i	0.698334	−	0.403183i	0.806727	+	0.590925i	$0.201237\pi$
$878$		0			0
$879$	21.7628	+	43.1485i	0.734042	+	1.45536i
$880$		0			0
$881$	28.3585			0.955421			0.477710	−	0.878517i	$-0.341467\pi$
$881$	28.3585			0.955421			0.477710	+	0.878517i	$0.341467\pi$
$882$		0			0
$883$			28.3449i			0.953881i	0.878936	+	0.476941i	$0.158254\pi$
$883$			28.3449i			0.953881i	−0.878936	+	0.476941i	$0.841746\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.446080	+	0.257544i	−0.0149779	+	0.00864749i	−0.507470	−	0.861669i	$-0.669419\pi$
$887$	−0.446080	+	0.257544i	−0.0149779	+	0.00864749i	0.492492	+	0.870317i	$0.336086\pi$
$888$		0			0
$889$	−36.7072	+	63.5787i	−1.23112	+	2.13236i
$890$		0			0
$891$	26.9877	−	29.0017i	0.904123	−	0.971593i
$892$		0			0
$893$	−41.2005	−	23.7871i	−1.37872	−	0.796007i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.322296	+	0.211186i	0.0107611	+	0.00705128i
$898$		0			0
$899$	−27.8193			−0.927827
$900$		0			0
$901$	−18.3600			−0.611660
$902$		0			0
$903$	37.4906	−	18.9091i	1.24761	−	0.629257i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.87426	+	1.08211i	0.0622339	+	0.0359308i	0.530794	−	0.847501i	$-0.321894\pi$
$907$	1.87426	+	1.08211i	0.0622339	+	0.0359308i	−0.468560	+	0.883432i	$0.655227\pi$
$908$		0			0
$909$	5.30317	−	7.17469i	0.175895	−	0.237969i
$910$		0			0
$911$	−19.2332	+	33.3129i	−0.637226	+	1.10371i	0.348813	+	0.937192i	$0.386585\pi$
$911$	−19.2332	+	33.3129i	−0.637226	+	1.10371i	−0.986039	+	0.166515i	$0.946749\pi$
$912$		0			0
$913$	−34.2093	+	19.7507i	−1.13216	+	0.653654i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	36.6979i		−	1.21187i
$918$		0			0
$919$	−18.6992			−0.616830			−0.308415	−	0.951252i	$-0.599799\pi$
$919$	−18.6992			−0.616830			−0.308415	+	0.951252i	$0.599799\pi$
$920$		0			0
$921$	−21.1066	−	1.19297i	−0.695487	−	0.0393097i
$922$		0			0
$923$	−13.4181	+	7.74693i	−0.441661	+	0.254993i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−18.2509	+	7.94711i	−0.599439	+	0.261017i
$928$		0			0
$929$	−1.10335	+	1.91106i	−0.0361999	+	0.0627000i	−0.883558	−	0.468322i	$-0.844859\pi$
$929$	−1.10335	+	1.91106i	−0.0361999	+	0.0627000i	0.847358	+	0.531022i	$0.178192\pi$
$930$		0			0
$931$	14.5330	+	25.1719i	0.476300	+	0.824976i
$932$		0			0
$933$	−7.58156	+	3.82391i	−0.248209	+	0.125189i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			21.3429i			0.697242i	0.937264	+	0.348621i	$0.113350\pi$
$937$			21.3429i			0.697242i	−0.937264	+	0.348621i	$0.886650\pi$
$938$		0			0
$939$	−16.6967	+	25.4813i	−0.544876	+	0.831549i
$940$		0			0
$941$	0.589661	+	1.02132i	0.0192224	+	0.0332942i	0.875477	−	0.483261i	$-0.160548\pi$
$941$	0.589661	+	1.02132i	0.0192224	+	0.0332942i	−0.856254	+	0.516555i	$0.827214\pi$
$942$		0			0
$943$	0.812008	+	0.468813i	0.0264426	+	0.0152667i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−20.5152	−	11.8445i	−0.666655	−	0.384894i	0.128153	−	0.991754i	$-0.459095\pi$
$947$	−20.5152	−	11.8445i	−0.666655	−	0.384894i	−0.794808	+	0.606861i	$0.792428\pi$
$948$		0			0
$949$	−5.59166	−	9.68504i	−0.181513	−	0.314390i
$950$		0			0
$951$	−18.5797	+	28.3550i	−0.602488	+	0.919473i
$952$		0			0
$953$		−	12.8125i		−	0.415038i	−0.978231	−	0.207519i	$-0.933461\pi$
$953$		−	12.8125i		−	0.415038i	0.978231	−	0.207519i	$-0.0665389\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	61.8222	−	31.1813i	1.99843	−	1.00795i
$958$		0			0
$959$	−22.9784	−	39.7998i	−0.742012	−	1.28520i
$960$		0			0
$961$	10.8084	−	18.7207i	0.348658	−	0.603893i
$962$		0			0
$963$	−4.66093	+	41.1000i	−0.150196	+	1.32443i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	9.46264	−	5.46326i	0.304298	−	0.175686i	−0.340074	−	0.940399i	$-0.610452\pi$
$967$	9.46264	−	5.46326i	0.304298	−	0.175686i	0.644372	+	0.764712i	$0.277119\pi$
$968$		0			0
$969$	−15.4104	−	0.871013i	−0.495054	−	0.0279810i
$970$		0			0
$971$	15.7933			0.506831			0.253415	−	0.967358i	$-0.418446\pi$
$971$	15.7933			0.506831			0.253415	+	0.967358i	$0.418446\pi$
$972$		0			0
$973$		−	49.7001i		−	1.59331i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−32.4742	+	18.7490i	−1.03894	+	0.599833i	−0.919533	−	0.393012i	$-0.871433\pi$
$977$	−32.4742	+	18.7490i	−1.03894	+	0.599833i	−0.119409	+	0.992845i	$0.538100\pi$
$978$		0			0
$979$	−8.83826	+	15.3083i	−0.282472	+	0.489256i
$980$		0			0
$981$	−54.0576	−	6.13038i	−1.72593	−	0.195728i
$982$		0			0
$983$	20.3795	+	11.7661i	0.650004	+	0.375280i	0.788458	−	0.615089i	$-0.210880\pi$
$983$	20.3795	+	11.7661i	0.650004	+	0.375280i	−0.138454	+	0.990369i	$0.544213\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−39.3696	+	19.8568i	−1.25315	+	0.632050i
$988$		0			0
$989$	0.768410			0.0244340
$990$		0			0
$991$	46.7019			1.48353			0.741767	−	0.670658i	$-0.233988\pi$
$991$	46.7019			1.48353			0.741767	+	0.670658i	$0.233988\pi$
$992$		0			0
$993$	−21.1382	−	13.8509i	−0.670800	−	0.439544i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−37.1161	−	21.4290i	−1.17548	−	0.678663i	−0.220514	−	0.975384i	$-0.570774\pi$
$997$	−37.1161	−	21.4290i	−1.17548	−	0.678663i	−0.954964	+	0.296721i	$0.904107\pi$
$998$		0			0
$999$	−10.0150	−	1.71279i	−0.316861	−	0.0541902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.s.d.349.4		16
3.2	odd	2		2700.2.s.d.2449.2		16
5.2	odd	4		900.2.i.e.601.4	yes	8
5.3	odd	4		900.2.i.d.601.1	yes	8
5.4	even	2	inner	900.2.s.d.349.5		16
9.2	odd	6		8100.2.d.s.649.7		8
9.4	even	3	inner	900.2.s.d.49.5		16
9.5	odd	6		2700.2.s.d.1549.7		16
9.7	even	3		8100.2.d.q.649.7		8
15.2	even	4		2700.2.i.d.1801.4		8
15.8	even	4		2700.2.i.e.1801.1		8
15.14	odd	2		2700.2.s.d.2449.7		16
45.2	even	12		8100.2.a.ba.1.1		4
45.4	even	6	inner	900.2.s.d.49.4		16
45.7	odd	12		8100.2.a.z.1.1		4
45.13	odd	12		900.2.i.d.301.1	✓	8
45.14	odd	6		2700.2.s.d.1549.2		16
45.22	odd	12		900.2.i.e.301.4	yes	8
45.23	even	12		2700.2.i.e.901.1		8
45.29	odd	6		8100.2.d.s.649.2		8
45.32	even	12		2700.2.i.d.901.4		8
45.34	even	6		8100.2.d.q.649.2		8
45.38	even	12		8100.2.a.y.1.4		4
45.43	odd	12		8100.2.a.x.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.i.d.301.1	✓	8	45.13	odd	12
900.2.i.d.601.1	yes	8	5.3	odd	4
900.2.i.e.301.4	yes	8	45.22	odd	12
900.2.i.e.601.4	yes	8	5.2	odd	4
900.2.s.d.49.4		16	45.4	even	6	inner
900.2.s.d.49.5		16	9.4	even	3	inner
900.2.s.d.349.4		16	1.1	even	1	trivial
900.2.s.d.349.5		16	5.4	even	2	inner
2700.2.i.d.901.4		8	45.32	even	12
2700.2.i.d.1801.4		8	15.2	even	4
2700.2.i.e.901.1		8	45.23	even	12
2700.2.i.e.1801.1		8	15.8	even	4
2700.2.s.d.1549.2		16	45.14	odd	6
2700.2.s.d.1549.7		16	9.5	odd	6
2700.2.s.d.2449.2		16	3.2	odd	2
2700.2.s.d.2449.7		16	15.14	odd	2
8100.2.a.x.1.4		4	45.43	odd	12
8100.2.a.y.1.4		4	45.38	even	12
8100.2.a.z.1.1		4	45.7	odd	12
8100.2.a.ba.1.1		4	45.2	even	12
8100.2.d.q.649.2		8	45.34	even	6
8100.2.d.q.649.7		8	9.7	even	3
8100.2.d.s.649.2		8	45.29	odd	6
8100.2.d.s.649.7		8	9.2	odd	6

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0977414 + 1.72929i) q^{3} +(-2.94604 - 1.70089i) q^{7} +(-2.98089 - 0.338047i) q^{9} +(2.20089 - 3.81206i) q^{11} +(1.78679 - 1.03160i) q^{13} +1.40179i q^{17} +6.35717 q^{19} +(3.22929 - 4.92830i) q^{21} +(0.0933799 - 0.0539129i) q^{23} +(0.875938 - 5.12179i) q^{27} +(4.54089 - 7.86505i) q^{29} +(-1.53160 - 2.65281i) q^{31} +(6.37704 + 4.17858i) q^{33} -1.95538i q^{37} +(1.60930 + 3.19070i) q^{39} +(4.34788 + 7.53074i) q^{41} +(6.17165 + 3.56320i) q^{43} +(-6.48096 - 3.74179i) q^{47} +(2.28608 + 3.95961i) q^{49} +(-2.42410 - 0.137013i) q^{51} +13.0975i q^{53} +(-0.621359 + 10.9934i) q^{57} +(-6.58966 - 11.4136i) q^{59} +(0.862308 - 1.49356i) q^{61} +(8.20684 + 6.06608i) q^{63} +(10.7177 - 6.18787i) q^{67} +(0.0841040 + 0.166751i) q^{69} -7.50961 q^{71} -5.42037i q^{73} +(-12.9678 + 7.48698i) q^{77} +(4.71806 - 8.17193i) q^{79} +(8.77145 + 2.01536i) q^{81} +(-7.77167 - 4.48698i) q^{83} +(13.1571 + 8.62126i) q^{87} -4.01576 q^{89} -7.01858 q^{91} +(4.73718 - 2.38929i) q^{93} +(1.88017 + 1.08551i) q^{97} +(-7.84929 + 10.6193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{9} + 6 q^{11} + 16 q^{19} + 26 q^{21} + 18 q^{29} - 4 q^{31} + 34 q^{39} + 18 q^{41} + 18 q^{49} + 6 q^{51} + 30 q^{59} + 2 q^{61} - 18 q^{69} - 48 q^{71} - 14 q^{79} - 62 q^{81} - 12 q^{89}+ \cdots - 66 q^{99}+O(q^{100}) \) 16 * q - 10 * q^9 + 6 * q^11 + 16 * q^19 + 26 * q^21 + 18 * q^29 - 4 * q^31 + 34 * q^39 + 18 * q^41 + 18 * q^49 + 6 * q^51 + 30 * q^59 + 2 * q^61 - 18 * q^69 - 48 * q^71 - 14 * q^79 - 62 * q^81 - 12 * q^89 - 44 * q^91 - 66 * q^99

Introduction

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