LMFDB - Embedded newform 936.2.dg.e.829.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(829,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.829"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0] 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.9
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.e.901.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.662081 - 1.24966i) q^{2} +(-1.12330 + 1.65475i) q^{4} -1.88587 q^{5} +(3.80954 + 2.19944i) q^{7} +(2.81159 + 0.308157i) q^{8} +(1.24860 + 2.35669i) q^{10} +(0.0662772 + 0.114795i) q^{11} +(-3.59512 + 0.274112i) q^{13} +(0.226324 - 6.21684i) q^{14} +(-1.47641 - 3.71755i) q^{16} +(-1.14806 + 1.98850i) q^{17} +(-2.18964 + 3.79257i) q^{19} +(2.11839 - 3.12064i) q^{20} +(0.0995743 - 0.158828i) q^{22} +(-1.97584 - 3.42225i) q^{23} -1.44351 q^{25} +(2.72281 + 4.31119i) q^{26} +(-7.91878 + 3.83323i) q^{28} +(-2.20762 + 1.27457i) q^{29} -1.06736i q^{31} +(-3.66817 + 4.30633i) q^{32} +(3.24505 + 0.118136i) q^{34} +(-7.18429 - 4.14785i) q^{35} +(-5.28540 - 9.15458i) q^{37} +(6.18914 + 0.225315i) q^{38} +(-5.30228 - 0.581142i) q^{40} +(-7.14559 + 4.12551i) q^{41} +(8.32354 + 4.80560i) q^{43} +(-0.264407 - 0.0192770i) q^{44} +(-2.96848 + 4.73493i) q^{46} +10.1114i q^{47} +(6.17508 + 10.6956i) q^{49} +(0.955719 + 1.80389i) q^{50} +(3.58479 - 6.25694i) q^{52} +8.28514i q^{53} +(-0.124990 - 0.216489i) q^{55} +(10.0331 + 7.35786i) q^{56} +(3.05440 + 1.91490i) q^{58} +(-1.65394 + 2.86472i) q^{59} +(6.40470 + 3.69775i) q^{61} +(-1.33383 + 0.706678i) q^{62} +(7.81008 + 1.73282i) q^{64} +(6.77991 - 0.516938i) q^{65} +(0.540655 + 0.936442i) q^{67} +(-2.00086 - 4.13343i) q^{68} +(-0.426816 + 11.7241i) q^{70} +(-6.45016 - 3.72400i) q^{71} +6.14363i q^{73} +(-7.94074 + 12.6660i) q^{74} +(-3.81615 - 7.88349i) q^{76} +0.583091i q^{77} -15.9309 q^{79} +(2.78431 + 7.01081i) q^{80} +(9.88644 + 6.19813i) q^{82} -0.144468 q^{83} +(2.16509 - 3.75004i) q^{85} +(0.494498 - 13.5833i) q^{86} +(0.150969 + 0.343181i) q^{88} +(14.2114 - 8.20498i) q^{89} +(-14.2986 - 6.86301i) q^{91} +(7.88243 + 0.574680i) q^{92} +(12.6359 - 6.69460i) q^{94} +(4.12937 - 7.15228i) q^{95} +(6.11866 + 3.53261i) q^{97} +(9.27740 - 14.7981i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} - 12 q^{7} - 4 q^{10} + 36 q^{14} - 2 q^{16} - 12 q^{17} - 54 q^{20} - 14 q^{22} - 20 q^{23} + 48 q^{25} + 42 q^{26} + 6 q^{28} + 28 q^{38} - 8 q^{40} + 12 q^{41} - 30 q^{46} + 16 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) $ 48 * q - 2 * q^4 - 12 * q^7 - 4 * q^10 + 36 * q^14 - 2 * q^16 - 12 * q^17 - 54 * q^20 - 14 * q^22 - 20 * q^23 + 48 * q^25 + 42 * q^26 + 6 * q^28 + 28 * q^38 - 8 * q^40 + 12 * q^41 - 30 * q^46 + 16 * q^49 + 84 * q^50 - 28 * q^52 - 68 * q^55 - 18 * q^56 - 24 * q^58 - 24 * q^62 - 68 * q^64 - 12 * q^65 - 4 * q^68 + 12 * q^71 - 54 * q^74 - 54 * q^76 - 192 * q^79 - 78 * q^80 - 6 * q^82 - 10 * q^88 + 48 * q^89 + 12 * q^92 + 54 * q^94 + 20 * q^95 + 144 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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 $

$2$	−0.662081	−	1.24966i	−0.468162	−	0.883643i
$2$	−0.662081	−	1.24966i	−0.468162	−	0.883643i
$3$		0			0
$3$		0			0
$4$	−1.12330	+	1.65475i	−0.561648	+	0.827376i
$5$	−1.88587			−0.843385			−0.421693	−	0.906739i	$-0.638564\pi$
$5$	−1.88587			−0.843385			−0.421693	+	0.906739i	$0.638564\pi$
$6$		0			0
$7$	3.80954	+	2.19944i	1.43987	+	0.831311i	0.997840	−	0.0656885i	$-0.0209244\pi$
$7$	3.80954	+	2.19944i	1.43987	+	0.831311i	0.442032	+	0.896999i	$0.354258\pi$
$8$	2.81159	+	0.308157i	0.994047	+	0.108950i
$9$		0			0
$10$	1.24860	+	2.35669i	0.394841	+	0.745251i
$11$	0.0662772	+	0.114795i	0.0199833	+	0.0346121i	0.875844	−	0.482594i	$-0.160305\pi$
$11$	0.0662772	+	0.114795i	0.0199833	+	0.0346121i	−0.855861	+	0.517206i	$0.826972\pi$
$12$		0			0
$13$	−3.59512	+	0.274112i	−0.997106	+	0.0760249i
$13$	−3.59512	+	0.274112i	−0.997106	+	0.0760249i
$14$	0.226324	−	6.21684i	0.0604875	−	1.66152i
$15$		0			0
$16$	−1.47641	−	3.71755i	−0.369103	−	0.929389i
$17$	−1.14806	+	1.98850i	−0.278446	+	0.482282i	−0.970999	−	0.239085i	$-0.923152\pi$
$17$	−1.14806	+	1.98850i	−0.278446	+	0.482282i	0.692553	+	0.721367i	$0.256486\pi$
$18$		0			0
$19$	−2.18964	+	3.79257i	−0.502338	+	0.870075i	0.497658	+	0.867373i	$0.334193\pi$
$19$	−2.18964	+	3.79257i	−0.502338	+	0.870075i	−0.999996	+	0.00270169i	$0.999140\pi$
$20$	2.11839	−	3.12064i	0.473686	−	0.697797i
$21$		0			0
$22$	0.0995743	−	0.158828i	0.0212293	−	0.0338622i
$23$	−1.97584	−	3.42225i	−0.411991	−	0.713589i	0.583117	−	0.812388i	$-0.301833\pi$
$23$	−1.97584	−	3.42225i	−0.411991	−	0.713589i	−0.995107	+	0.0987997i	$0.968500\pi$
$24$		0			0
$25$	−1.44351			−0.288701
$26$	2.72281	+	4.31119i	0.533986	+	0.845493i
$27$		0			0
$28$	−7.91878	+	3.83323i	−1.49651	+	0.724412i
$29$	−2.20762	+	1.27457i	−0.409944	+	0.236682i	−0.690766	−	0.723078i	$-0.742726\pi$
$29$	−2.20762	+	1.27457i	−0.409944	+	0.236682i	0.280821	+	0.959760i	$0.409393\pi$
$30$		0			0
$31$		−	1.06736i		−	0.191703i	−0.995396	−	0.0958516i	$-0.969443\pi$
$31$		−	1.06736i		−	0.191703i	0.995396	−	0.0958516i	$-0.0305574\pi$
$32$	−3.66817	+	4.30633i	−0.648447	+	0.761260i
$33$		0			0
$34$	3.24505	+	0.118136i	0.556522	+	0.0202601i
$35$	−7.18429	−	4.14785i	−1.21437	−	0.701115i
$36$		0			0
$37$	−5.28540	−	9.15458i	−0.868914	−	1.50500i	−0.863108	−	0.505020i	$-0.831485\pi$
$37$	−5.28540	−	9.15458i	−0.868914	−	1.50500i	−0.00580626	−	0.999983i	$-0.501848\pi$
$38$	6.18914	+	0.225315i	1.00401	+	0.0365509i
$39$		0			0
$40$	−5.30228	−	0.581142i	−0.838365	−	0.0918867i
$41$	−7.14559	+	4.12551i	−1.11595	+	0.644296i	−0.940365	−	0.340168i	$-0.889516\pi$
$41$	−7.14559	+	4.12551i	−1.11595	+	0.644296i	−0.175589	+	0.984464i	$0.556183\pi$
$42$		0			0
$43$	8.32354	+	4.80560i	1.26933	+	0.732847i	0.974861	−	0.222815i	$-0.0715247\pi$
$43$	8.32354	+	4.80560i	1.26933	+	0.732847i	0.294467	+	0.955662i	$0.404858\pi$
$44$	−0.264407	−	0.0192770i	−0.0398608	−	0.00290611i
$45$		0			0
$46$	−2.96848	+	4.73493i	−0.437679	+	0.698128i
$47$			10.1114i			1.47491i	0.675399	+	0.737453i	$0.263972\pi$
$47$			10.1114i			1.47491i	−0.675399	+	0.737453i	$0.736028\pi$
$48$		0			0
$49$	6.17508	+	10.6956i	0.882155	+	1.52794i
$50$	0.955719	+	1.80389i	0.135159	+	0.255109i
$51$		0			0
$52$	3.58479	−	6.25694i	0.497121	−	0.867681i
$53$			8.28514i			1.13805i	0.822320	+	0.569026i	$0.192680\pi$
$53$			8.28514i			1.13805i	−0.822320	+	0.569026i	$0.807320\pi$
$54$		0			0
$55$	−0.124990	−	0.216489i	−0.0168536	−	0.0291914i
$56$	10.0331	+	7.35786i	1.34073	+	0.983236i
$57$		0			0
$58$	3.05440	+	1.91490i	0.401062	+	0.251439i
$59$	−1.65394	+	2.86472i	−0.215325	+	0.372954i	−0.953373	−	0.301794i	$-0.902415\pi$
$59$	−1.65394	+	2.86472i	−0.215325	+	0.372954i	0.738048	+	0.674748i	$0.235748\pi$
$60$		0			0
$61$	6.40470	+	3.69775i	0.820038	+	0.473449i	0.850429	−	0.526089i	$-0.176342\pi$
$61$	6.40470	+	3.69775i	0.820038	+	0.473449i	−0.0303918	+	0.999538i	$0.509675\pi$
$62$	−1.33383	+	0.706678i	−0.169397	+	0.0897482i
$63$		0			0
$64$	7.81008	+	1.73282i	0.976260	+	0.216603i
$65$	6.77991	−	0.516938i	0.840944	−	0.0641183i
$66$		0			0
$67$	0.540655	+	0.936442i	0.0660515	+	0.114405i	0.897160	−	0.441706i	$-0.145627\pi$
$67$	0.540655	+	0.936442i	0.0660515	+	0.114405i	−0.831108	+	0.556110i	$0.812293\pi$
$68$	−2.00086	−	4.13343i	−0.242640	−	0.501252i
$69$		0			0
$70$	−0.426816	+	11.7241i	−0.0510143	+	1.40130i
$71$	−6.45016	−	3.72400i	−0.765493	−	0.441958i	0.0657714	−	0.997835i	$-0.479049\pi$
$71$	−6.45016	−	3.72400i	−0.765493	−	0.441958i	−0.831265	+	0.555877i	$0.812383\pi$
$72$		0			0
$73$			6.14363i			0.719057i	0.933134	+	0.359529i	$0.117062\pi$
$73$			6.14363i			0.719057i	−0.933134	+	0.359529i	$0.882938\pi$
$74$	−7.94074	+	12.6660i	−0.923092	+	1.47239i
$75$		0			0
$76$	−3.81615	−	7.88349i	−0.437742	−	0.904298i
$77$			0.583091i			0.0664494i
$78$		0			0
$79$	−15.9309			−1.79236			−0.896182	−	0.443688i	$-0.853670\pi$
$79$	−15.9309			−1.79236			−0.896182	+	0.443688i	$0.853670\pi$
$80$	2.78431	+	7.01081i	0.311296	+	0.783833i
$81$		0			0
$82$	9.88644	+	6.19813i	1.09177	+	0.684469i
$83$	−0.144468			−0.0158574			−0.00792871	−	0.999969i	$-0.502524\pi$
$83$	−0.144468			−0.0158574			−0.00792871	+	0.999969i	$0.502524\pi$
$84$		0			0
$85$	2.16509	−	3.75004i	0.234837	−	0.406749i
$86$	0.494498	−	13.5833i	0.0533231	−	1.46472i
$87$		0			0
$88$	0.150969	+	0.343181i	0.0160934	+	0.0365833i
$89$	14.2114	−	8.20498i	1.50641	−	0.869726i	0.506437	−	0.862277i	$-0.330962\pi$
$89$	14.2114	−	8.20498i	1.50641	−	0.869726i	0.999972	−	0.00744871i	$-0.00237102\pi$
$90$		0			0
$91$	−14.2986	−	6.86301i	−1.49891	−	0.719439i
$92$	7.88243	+	0.574680i	0.821800	+	0.0599145i
$93$		0			0
$94$	12.6359	−	6.69460i	1.30329	−	0.690495i
$95$	4.12937	−	7.15228i	0.423664	−	0.733808i
$96$		0			0
$97$	6.11866	+	3.53261i	0.621256	+	0.358682i	0.777358	−	0.629059i	$-0.216560\pi$
$97$	6.11866	+	3.53261i	0.621256	+	0.358682i	−0.156102	+	0.987741i	$0.549893\pi$
$98$	9.27740	−	14.7981i	0.937159	−	1.49483i
$99$		0			0
$100$	1.62149	−	2.38865i	0.162149	−	0.238865i
$101$	−9.34844	+	5.39732i	−0.930204	+	0.537054i	−0.886876	−	0.462007i	$-0.847129\pi$
$101$	−9.34844	+	5.39732i	−0.930204	+	0.537054i	−0.0433280	+	0.999061i	$0.513796\pi$
$102$		0			0
$103$	−10.9719			−1.08110			−0.540548	−	0.841313i	$-0.681783\pi$
$103$	−10.9719			−1.08110			−0.540548	+	0.841313i	$0.681783\pi$
$104$	−10.1925	−	0.337169i	−0.999453	−	0.0330622i
$105$		0			0
$106$	10.3536	−	5.48544i	1.00563	−	0.532793i
$107$	−3.34576	+	1.93168i	−0.323447	+	0.186742i	−0.652928	−	0.757420i	$-0.726460\pi$
$107$	−3.34576	+	1.93168i	−0.323447	+	0.186742i	0.329481	+	0.944162i	$0.393126\pi$
$108$		0			0
$109$	−1.14546			−0.109716			−0.0548578	−	0.998494i	$-0.517471\pi$
$109$	−1.14546			−0.109716			−0.0548578	+	0.998494i	$0.517471\pi$
$110$	−0.187784	+	0.299528i	−0.0179045	+	0.0285589i
$111$		0			0
$112$	2.55209	−	17.4095i	0.241150	−	1.64504i
$113$	−4.88900	+	8.46799i	−0.459918	+	0.796601i	−0.998956	−	0.0456800i	$-0.985455\pi$
$113$	−4.88900	+	8.46799i	−0.459918	+	0.796601i	0.539038	+	0.842281i	$0.318788\pi$
$114$		0			0
$115$	3.72617	+	6.45391i	0.347467	+	0.601830i
$116$	0.370713	−	5.08478i	0.0344199	−	0.472110i
$117$		0			0
$118$	4.67497	+	0.170192i	0.430365	+	0.0156674i
$119$	−8.74717	+	5.05018i	−0.801852	+	0.462949i
$120$		0			0
$121$	5.49121	−	9.51106i	0.499201	−	0.864642i
$122$	0.380501	−	10.4519i	0.0344489	−	0.946271i
$123$		0			0
$124$	1.76621	+	1.19896i	0.158611	+	0.107670i
$125$	12.1516			1.08687
$126$		0			0
$127$	−7.37989	−	12.7824i	−0.654860	−	1.13425i	−0.981929	−	0.189250i	$-0.939394\pi$
$127$	−7.37989	−	12.7824i	−0.654860	−	1.13425i	0.327069	−	0.945000i	$-0.393939\pi$
$128$	−3.00547	−	10.9072i	−0.265649	−	0.964070i
$129$		0			0
$130$	−5.13485	−	8.13032i	−0.450356	−	0.713076i
$131$		−	1.23181i		−	0.107624i	−0.998551	−	0.0538118i	$-0.982863\pi$
$131$		−	1.23181i		−	0.107624i	0.998551	−	0.0538118i	$-0.0171371\pi$
$132$		0			0
$133$	−16.6831	+	9.63197i	−1.44660	+	0.835198i
$134$	0.812275	−	1.29563i	0.0701699	−	0.111926i
$135$		0			0
$136$	−3.84064	+	5.23706i	−0.329332	+	0.449074i
$137$	15.7493	+	9.09286i	1.34555	+	0.776856i	0.987616	−	0.156890i	$-0.0501467\pi$
$137$	15.7493	+	9.09286i	1.34555	+	0.776856i	0.357938	+	0.933745i	$0.383480\pi$
$138$		0			0
$139$	4.13153	+	2.38534i	0.350432	+	0.202322i	0.664875	−	0.746954i	$-0.268485\pi$
$139$	4.13153	+	2.38534i	0.350432	+	0.202322i	−0.314444	+	0.949276i	$0.601818\pi$
$140$	14.9338	−	7.22896i	1.26213	−	0.610958i
$141$		0			0
$142$	−0.383202	+	10.5261i	−0.0321576	+	0.883330i
$143$	−0.269741	−	0.394536i	−0.0225569	−	0.0329927i
$144$		0			0
$145$	4.16327	−	2.40367i	0.345741	−	0.199614i
$146$	7.67744	−	4.06758i	0.635390	−	0.336635i
$147$		0			0
$148$	21.0856	+	1.53728i	1.73323	+	0.126363i
$149$	−3.97531	+	6.88544i	−0.325670	+	0.564077i	−0.981648	−	0.190703i	$-0.938923\pi$
$149$	−3.97531	+	6.88544i	−0.325670	+	0.564077i	0.655978	+	0.754780i	$0.272257\pi$
$150$		0			0
$151$		−	13.5552i		−	1.10311i	−0.834139	−	0.551554i	$-0.814035\pi$
$151$		−	13.5552i		−	1.10311i	0.834139	−	0.551554i	$-0.185965\pi$
$152$	−7.32508	+	9.98839i	−0.594142	+	0.810166i
$153$		0			0
$154$	0.728665	−	0.386054i	0.0587175	−	0.0311091i
$155$			2.01290i			0.161680i
$156$		0			0
$157$			0.0648041i			0.00517193i	0.999997	+	0.00258597i	$0.000823140\pi$
$157$			0.0648041i			0.00517193i	−0.999997	+	0.00258597i	$0.999177\pi$
$158$	10.5475	+	19.9082i	0.839117	+	1.58381i
$159$		0			0
$160$	6.91768	−	8.12117i	0.546891	−	0.642035i
$161$		−	17.3830i		−	1.36997i
$162$		0			0
$163$	−5.26292	+	9.11565i	−0.412224	+	0.713993i	−0.995133	−	0.0985448i	$-0.968581\pi$
$163$	−5.26292	+	9.11565i	−0.412224	+	0.713993i	0.582909	+	0.812538i	$0.301915\pi$
$164$	1.19992	−	16.4583i	0.0936980	−	1.28518i
$165$		0			0
$166$	0.0956496	+	0.180536i	0.00742385	+	0.0140123i
$167$	12.4804	−	7.20556i	0.965762	−	0.557583i	0.0678204	−	0.997698i	$-0.478396\pi$
$167$	12.4804	−	7.20556i	0.965762	−	0.557583i	0.897942	+	0.440115i	$0.145062\pi$
$168$		0			0
$169$	12.8497	−	1.97093i	0.988440	−	0.151610i
$170$	−6.11974	−	0.222789i	−0.469363	−	0.0170871i
$171$		0			0
$172$	−17.3019	+	8.37528i	−1.31926	+	0.638609i
$173$	7.41252	+	4.27962i	0.563564	+	0.325374i	0.754575	−	0.656214i	$-0.227843\pi$
$173$	7.41252	+	4.27962i	0.563564	+	0.325374i	−0.191011	+	0.981588i	$0.561177\pi$
$174$		0			0
$175$	−5.49910	−	3.17491i	−0.415693	−	0.240000i
$176$	0.328906	−	0.415874i	0.0247922	−	0.0313477i
$177$		0			0
$178$	−19.6626	−	12.3271i	−1.47377	−	0.923954i
$179$	−14.8169	+	8.55453i	−1.10747	+	0.639396i	−0.938172	−	0.346170i	$-0.887482\pi$
$179$	−14.8169	+	8.55453i	−1.10747	+	0.639396i	−0.169294	+	0.985566i	$0.554149\pi$
$180$		0			0
$181$			11.8391i			0.879992i	0.898000	+	0.439996i	$0.145020\pi$
$181$			11.8391i			0.879992i	−0.898000	+	0.439996i	$0.854980\pi$
$182$	0.890449	+	22.4123i	0.0660045	+	1.66131i
$183$		0			0
$184$	−4.50066	−	10.2308i	−0.331793	−	0.754227i
$185$	9.96755	+	17.2643i	0.732829	+	1.26930i
$186$		0			0
$187$	−0.304361			−0.0222571
$188$	−16.7319	−	11.3581i	−1.22030	−	0.828378i
$189$		0			0
$190$	−11.6719	−	0.424914i	−0.846768	−	0.0308265i
$191$	3.55694	−	6.16081i	0.257371	−	0.445780i	−0.708166	−	0.706046i	$-0.750477\pi$
$191$	3.55694	−	6.16081i	0.257371	−	0.445780i	0.965537	+	0.260266i	$0.0838103\pi$
$192$		0			0
$193$	−12.1721	+	7.02758i	−0.876169	+	0.505857i	−0.869393	−	0.494120i	$-0.835490\pi$
$193$	−12.1721	+	7.02758i	−0.876169	+	0.505857i	−0.00677591	+	0.999977i	$0.502157\pi$
$194$	0.363507	−	9.98511i	0.0260983	−	0.716889i
$195$		0			0
$196$	−24.6350	−	1.79605i	−1.75964	−	0.128289i
$197$	−11.2731	−	19.5256i	−0.803178	−	1.39114i	−0.917514	−	0.397702i	$-0.869808\pi$
$197$	−11.2731	−	19.5256i	−0.803178	−	1.39114i	0.114337	−	0.993442i	$-0.463526\pi$
$198$		0			0
$199$	−6.49779	+	11.2545i	−0.460616	+	0.797811i	−0.998992	−	0.0448942i	$-0.985705\pi$
$199$	−6.49779	+	11.2545i	−0.460616	+	0.797811i	0.538375	+	0.842705i	$0.319038\pi$
$200$	−4.05855	−	0.444826i	−0.286983	−	0.0314540i
$201$		0			0
$202$	12.9342	+	8.10889i	0.910050	+	0.570540i
$203$	−11.2134			−0.787024
$204$		0			0
$205$	13.4756	−	7.78016i	0.941179	−	0.543390i
$206$	7.26431	+	13.7112i	0.506129	+	0.955303i
$207$		0			0
$208$	6.32689	+	12.9603i	0.438691	+	0.898638i
$209$	−0.580493			−0.0401535
$210$		0			0
$211$	−8.91704	+	5.14826i	−0.613875	+	0.354421i	−0.774480	−	0.632598i	$-0.781989\pi$
$211$	−8.91704	+	5.14826i	−0.613875	+	0.354421i	0.160606	+	0.987019i	$0.448655\pi$
$212$	−13.7099	−	9.30667i	−0.941597	−	0.639184i
$213$		0			0
$214$	4.62910	+	2.90214i	0.316439	+	0.198386i
$215$	−15.6971	−	9.06271i	−1.07053	−	0.618072i
$216$		0			0
$217$	2.34759	−	4.06615i	0.159365	−	0.276028i
$218$	0.758391	+	1.43144i	0.0513647	+	0.0969494i
$219$		0			0
$220$	0.498636	+	0.0363538i	0.0336180	+	0.00245097i
$221$	3.58234	−	7.46358i	0.240974	−	0.502055i
$222$		0			0
$223$	2.03847	−	1.17691i	0.136506	−	0.0788117i	−0.430192	−	0.902737i	$-0.641554\pi$
$223$	2.03847	−	1.17691i	0.136506	−	0.0788117i	0.566698	+	0.823926i	$0.308221\pi$
$224$	−23.4456	+	8.33724i	−1.56652	+	0.557055i
$225$		0			0
$226$	13.8190	+	0.503080i	0.919227	+	0.0334644i
$227$	13.6449	−	23.6336i	0.905643	−	1.56862i	0.0855919	−	0.996330i	$-0.472722\pi$
$227$	13.6449	−	23.6336i	0.905643	−	1.56862i	0.820051	−	0.572290i	$-0.193945\pi$
$228$		0			0
$229$	14.1611			0.935794			0.467897	−	0.883783i	$-0.345012\pi$
$229$	14.1611			0.935794			0.467897	+	0.883783i	$0.345012\pi$
$230$	5.59816	−	8.92945i	0.369132	−	0.588791i
$231$		0			0
$232$	−6.59969	+	2.90327i	−0.433291	+	0.190609i
$233$	−12.3422			−0.808562			−0.404281	−	0.914635i	$-0.632478\pi$
$233$	−12.3422			−0.808562			−0.404281	+	0.914635i	$0.632478\pi$
$234$		0			0
$235$		−	19.0688i		−	1.24391i
$236$	−2.88253	−	5.95479i	−0.187636	−	0.387624i
$237$		0			0
$238$	12.1023	+	7.58735i	0.784479	+	0.491815i
$239$		−	17.4020i		−	1.12564i	−0.826578	−	0.562822i	$-0.809715\pi$
$239$		−	17.4020i		−	1.12564i	0.826578	−	0.562822i	$-0.190285\pi$
$240$		0			0
$241$	12.5141	+	7.22501i	0.806103	+	0.465404i	0.845601	−	0.533816i	$-0.179242\pi$
$241$	12.5141	+	7.22501i	0.806103	+	0.465404i	−0.0394975	+	0.999220i	$0.512576\pi$
$242$	−15.5212	−	0.565049i	−0.997742	−	0.0363227i
$243$		0			0
$244$	−13.3132	+	6.44452i	−0.852293	+	0.412568i
$245$	−11.6454	−	20.1704i	−0.743996	−	1.28864i
$246$		0			0
$247$	6.83242	−	14.2349i	0.434737	−	0.905747i
$248$	0.328913	−	3.00097i	0.0208860	−	0.190562i
$249$		0			0
$250$	−8.04535	−	15.1854i	−0.508832	−	0.960406i
$251$	26.7083	+	15.4201i	1.68581	+	0.973305i	0.957664	+	0.287887i	$0.0929528\pi$
$251$	26.7083	+	15.4201i	1.68581	+	0.973305i	0.728150	+	0.685418i	$0.240381\pi$
$252$		0			0
$253$	0.261906	−	0.453634i	0.0164659	−	0.0285197i
$254$	−11.0875	+	17.6853i	−0.695691	+	1.10968i
$255$		0			0
$256$	−11.6404	+	10.9773i	−0.727526	+	0.686080i
$257$	−9.77864	−	16.9371i	−0.609975	−	1.05651i	−0.991244	−	0.132044i	$-0.957846\pi$
$257$	−9.77864	−	16.9371i	−0.609975	−	1.05651i	0.381269	−	0.924464i	$-0.375487\pi$
$258$		0			0
$259$		−	46.4997i		−	2.88935i
$260$	−6.76044	+	11.7997i	−0.419265	+	0.731789i
$261$		0			0
$262$	−1.53934	+	0.815558i	−0.0951008	+	0.0503853i
$263$	15.8081	+	27.3804i	0.974769	+	1.68835i	0.680695	+	0.732567i	$0.261678\pi$
$263$	15.8081	+	27.3804i	0.974769	+	1.68835i	0.294074	+	0.955783i	$0.404989\pi$
$264$		0			0
$265$		−	15.6247i		−	0.959816i
$266$	23.0822	+	14.4710i	1.41526	+	0.887274i
$267$		0			0
$268$	−2.15689	−	0.157252i	−0.131753	−	0.00960567i
$269$	−0.118107	−	0.0681891i	−0.00720111	−	0.00415756i	0.496395	−	0.868097i	$-0.334657\pi$
$269$	−0.118107	−	0.0681891i	−0.00720111	−	0.00415756i	−0.503596	+	0.863939i	$0.667990\pi$
$270$		0			0
$271$	13.1075	−	7.56763i	0.796226	−	0.459701i	−0.0459241	−	0.998945i	$-0.514623\pi$
$271$	13.1075	−	7.56763i	0.796226	−	0.459701i	0.842150	+	0.539244i	$0.181290\pi$
$272$	9.08736	+	1.33214i	0.551002	+	0.0807726i
$273$		0			0
$274$	0.935660	−	25.7015i	0.0565253	−	1.55268i
$275$	−0.0956715	−	0.165708i	−0.00576921	−	0.00999256i
$276$		0			0
$277$	−10.7192	−	6.18871i	−0.644051	−	0.371843i	0.142122	−	0.989849i	$-0.454607\pi$
$277$	−10.7192	−	6.18871i	−0.644051	−	0.371843i	−0.786174	+	0.618006i	$0.787941\pi$
$278$	0.245452	−	6.74229i	0.0147213	−	0.404376i
$279$		0			0
$280$	−18.9211	−	13.8760i	−1.13075	−	0.829247i
$281$		−	1.09096i		−	0.0650813i	−0.999470	−	0.0325406i	$-0.989640\pi$
$281$		−	1.09096i		−	0.0650813i	0.999470	−	0.0325406i	$-0.0103598\pi$
$282$		0			0
$283$	−4.12015	+	2.37877i	−0.244917	+	0.141403i	−0.617435	−	0.786622i	$-0.711828\pi$
$283$	−4.12015	+	2.37877i	−0.244917	+	0.141403i	0.372517	+	0.928025i	$0.378495\pi$
$284$	13.4077	−	6.49026i	0.795603	−	0.385126i
$285$		0			0
$286$	−0.314445	+	0.598299i	−0.0185935	+	0.0353782i
$287$	−36.2952			−2.14244
$288$		0			0
$289$	5.86392	+	10.1566i	0.344936	+	0.597447i
$290$	−5.76019	−	3.61125i	−0.338250	−	0.212060i
$291$		0			0
$292$	−10.1662	−	6.90111i	−0.594931	−	0.403857i
$293$	0.923728	−	1.59994i	0.0539647	−	0.0934697i	−0.837781	−	0.546006i	$-0.816147\pi$
$293$	0.923728	−	1.59994i	0.0539647	−	0.0934697i	0.891746	+	0.452537i	$0.149481\pi$
$294$		0			0
$295$	3.11912	−	5.40247i	0.181602	−	0.314544i
$296$	−12.0393	−	27.3676i	−0.699772	−	1.59071i
$297$		0			0
$298$	11.2364	+	0.409061i	0.650909	+	0.0236963i
$299$	8.04144	+	11.7618i	0.465049	+	0.680202i
$300$		0			0
$301$	21.1393	+	36.6143i	1.21845	+	2.11041i
$302$	−16.9394	+	8.97466i	−0.974753	+	0.516434i
$303$		0			0
$304$	17.3319	+	2.54072i	0.994052	+	0.145720i
$305$	−12.0784	−	6.97347i	−0.691608	−	0.399300i
$306$		0			0
$307$	−14.5220			−0.828815			−0.414408	−	0.910091i	$-0.636011\pi$
$307$	−14.5220			−0.828815			−0.414408	+	0.910091i	$0.636011\pi$
$308$	−0.964871	−	0.654984i	−0.0549786	−	0.0373212i
$309$		0			0
$310$	2.51543	−	1.33270i	0.142867	−	0.0756923i
$311$	15.6062			0.884944			0.442472	−	0.896782i	$-0.354102\pi$
$311$	15.6062			0.884944			0.442472	+	0.896782i	$0.354102\pi$
$312$		0			0
$313$	−29.5504			−1.67029			−0.835143	−	0.550032i	$-0.814615\pi$
$313$	−29.5504			−1.67029			−0.835143	+	0.550032i	$0.814615\pi$
$314$	0.0809831	−	0.0429056i	0.00457014	−	0.00242130i
$315$		0			0
$316$	17.8951	−	26.3616i	1.00668	−	1.48296i
$317$	14.3523			0.806105			0.403052	−	0.915177i	$-0.367949\pi$
$317$	14.3523			0.806105			0.403052	+	0.915177i	$0.367949\pi$
$318$		0			0
$319$	−0.292629	−	0.168950i	−0.0163841	−	0.00945936i
$320$	−14.7288	−	3.26787i	−0.823363	−	0.182679i
$321$		0			0
$322$	−21.7228	+	11.5089i	−1.21056	+	0.641368i
$323$	−5.02768	−	8.70819i	−0.279747	−	0.484537i
$324$		0			0
$325$	5.18957	−	0.395682i	0.287866	−	0.0219485i
$326$	14.8759	+	0.541557i	0.823902	+	0.0299941i
$327$		0			0
$328$	−21.3618	+	9.39728i	−1.17951	+	0.518878i
$329$	−22.2395	+	38.5200i	−1.22610	+	2.12368i
$330$		0			0
$331$	11.0998	−	19.2255i	0.610102	−	1.05673i	−0.381120	−	0.924525i	$-0.624462\pi$
$331$	11.0998	−	19.2255i	0.610102	−	1.05673i	0.991223	−	0.132203i	$-0.0422050\pi$
$332$	0.162280	−	0.239059i	0.00890630	−	0.0131201i
$333$		0			0
$334$	−17.2675	−	10.8256i	−0.944837	−	0.592349i
$335$	−1.01960	−	1.76600i	−0.0557069	−	0.0964871i
$336$		0			0
$337$	16.9924			0.925633			0.462817	−	0.886454i	$-0.346839\pi$
$337$	16.9924			0.925633			0.462817	+	0.886454i	$0.346839\pi$
$338$	−10.9706	−	14.7529i	−0.596719	−	0.802450i
$339$		0			0
$340$	3.77336	+	7.79510i	0.204639	+	0.422748i
$341$	0.122528	−	0.0707415i	0.00663525	−	0.00383086i
$342$		0			0
$343$			23.5348i			1.27076i
$344$	21.9215	+	16.0763i	1.18193	+	0.866777i
$345$		0			0
$346$	0.440375	−	12.0966i	0.0236747	−	0.650317i
$347$	10.8759	+	6.27918i	0.583846	+	0.337084i	0.762660	−	0.646799i	$-0.223893\pi$
$347$	10.8759	+	6.27918i	0.583846	+	0.337084i	−0.178814	+	0.983883i	$0.557226\pi$
$348$		0			0
$349$	−14.8271	−	25.6812i	−0.793674	−	1.37468i	−0.923678	−	0.383170i	$-0.874832\pi$
$349$	−14.8271	−	25.6812i	−0.793674	−	1.37468i	0.130004	−	0.991513i	$-0.458501\pi$
$350$	−0.326700	+	8.97405i	−0.0174628	+	0.479683i
$351$		0			0
$352$	−0.737463	−	0.135678i	−0.0393069	−	0.00723164i
$353$	28.0507	−	16.1951i	1.49299	−	0.861977i	0.493020	−	0.870018i	$-0.335893\pi$
$353$	28.0507	−	16.1951i	1.49299	−	0.861977i	0.999968	+	0.00804129i	$0.00255965\pi$
$354$		0			0
$355$	12.1641	+	7.02297i	0.645606	+	0.372741i
$356$	−2.38645	+	32.7330i	−0.126482	+	1.73485i
$357$		0			0
$358$	20.5002	+	12.8523i	1.08347	+	0.679263i
$359$		−	2.96930i		−	0.156714i	−0.996925	−	0.0783568i	$-0.975033\pi$
$359$		−	2.96930i		−	0.156714i	0.996925	−	0.0783568i	$-0.0249673\pi$
$360$		0			0
$361$	−0.0890480	−	0.154236i	−0.00468674	−	0.00811767i
$362$	14.7948	−	7.83844i	0.777598	−	0.411979i
$363$		0			0
$364$	27.4182	−	15.9515i	1.43710	−	0.836087i
$365$		−	11.5861i		−	0.606442i
$366$		0			0
$367$	−2.58053	−	4.46960i	−0.134702	−	0.233311i	0.790781	−	0.612099i	$-0.209674\pi$
$367$	−2.58053	−	4.46960i	−0.134702	−	0.233311i	−0.925484	+	0.378787i	$0.876341\pi$
$368$	−9.80526	+	12.3979i	−0.511134	+	0.646287i
$369$		0			0
$370$	14.9752	−	23.8864i	0.778522	−	1.24180i
$371$	−18.2227	+	31.5626i	−0.946074	+	1.63865i
$372$		0			0
$373$	4.57477	+	2.64124i	0.236873	+	0.136758i	0.613738	−	0.789509i	$-0.289665\pi$
$373$	4.57477	+	2.64124i	0.236873	+	0.136758i	−0.376866	+	0.926268i	$0.622998\pi$
$374$	0.201512	+	0.380347i	0.0104199	+	0.0196673i
$375$		0			0
$376$	−3.11591	+	28.4292i	−0.160691	+	1.46613i
$377$	7.58727	−	5.18736i	0.390764	−	0.267163i
$378$		0			0
$379$	18.1432	+	31.4249i	0.931951	+	1.61419i	0.779982	+	0.625802i	$0.215228\pi$
$379$	18.1432	+	31.4249i	0.931951	+	1.61419i	0.151970	+	0.988385i	$0.451438\pi$
$380$	7.19674	+	14.8672i	0.369185	+	0.762672i
$381$		0			0
$382$	−10.0539	−	0.366011i	−0.514402	−	0.0187268i
$383$	−8.44275	−	4.87443i	−0.431405	−	0.249072i	0.268540	−	0.963268i	$-0.413459\pi$
$383$	−8.44275	−	4.87443i	−0.431405	−	0.249072i	−0.699945	+	0.714197i	$0.746792\pi$
$384$		0			0
$385$		−	1.09963i		−	0.0560424i
$386$	16.8410	+	10.5582i	0.857186	+	0.537398i
$387$		0			0
$388$	−12.7187	+	6.15670i	−0.645692	+	0.312559i
$389$			14.8911i			0.755010i	0.926008	+	0.377505i	$0.123218\pi$
$389$			14.8911i			0.755010i	−0.926008	+	0.377505i	$0.876782\pi$
$390$		0			0
$391$	9.07352			0.458868
$392$	14.0659	+	31.9744i	0.710435	+	1.61495i
$393$		0			0
$394$	−16.9367	+	27.0151i	−0.853257	+	1.36100i
$395$	30.0435			1.51165
$396$		0			0
$397$	10.5034	−	18.1925i	0.527152	−	0.913055i	−0.472347	−	0.881413i	$-0.656593\pi$
$397$	10.5034	−	18.1925i	0.527152	−	0.913055i	0.999499	−	0.0316419i	$-0.0100736\pi$
$398$	18.3664	+	0.668626i	0.920623	+	0.0335152i
$399$		0			0
$400$	2.13121	+	5.36631i	0.106560	+	0.268316i
$401$	−13.7620	+	7.94551i	−0.687243	+	0.396780i	−0.802578	−	0.596547i	$-0.796539\pi$
$401$	−13.7620	+	7.94551i	−0.687243	+	0.396780i	0.115335	+	0.993327i	$0.463206\pi$
$402$		0			0
$403$	0.292575	+	3.83728i	0.0145742	+	0.191148i
$404$	1.56983	−	21.5321i	0.0781020	−	1.07126i
$405$		0			0
$406$	7.42416	+	14.0129i	0.368455	+	0.695448i
$407$	0.700602	−	1.21348i	0.0347276	−	0.0601499i
$408$		0			0
$409$	13.7176	+	7.91987i	0.678292	+	0.391612i	0.799211	−	0.601050i	$-0.205251\pi$
$409$	13.7176	+	7.91987i	0.678292	+	0.391612i	−0.120919	+	0.992662i	$0.538584\pi$
$410$	−18.6445	−	11.6888i	−0.920787	−	0.577271i
$411$		0			0
$412$	12.3247	−	18.1558i	0.607196	−	0.894474i
$413$	−12.6016	+	7.27551i	−0.620082	+	0.358004i
$414$		0			0
$415$	0.272448			0.0133739
$416$	12.0071	−	16.4873i	0.588696	−	0.808355i
$417$		0			0
$418$	0.384333	+	0.725418i	0.0187984	+	0.0354813i
$419$	19.4162	−	11.2100i	0.948544	−	0.547642i	0.0559155	−	0.998436i	$-0.482192\pi$
$419$	19.4162	−	11.2100i	0.948544	−	0.547642i	0.892628	+	0.450793i	$0.148859\pi$
$420$		0			0
$421$	−1.50715			−0.0734541			−0.0367270	−	0.999325i	$-0.511693\pi$
$421$	−1.50715			−0.0734541			−0.0367270	+	0.999325i	$0.511693\pi$
$422$	12.3374	+	7.73470i	0.600574	+	0.376519i
$423$		0			0
$424$	−2.55312	+	23.2944i	−0.123991	+	1.13128i
$425$	1.65723	−	2.87041i	0.0803876	−	0.139235i
$426$		0			0
$427$	16.2660	+	28.1735i	0.787166	+	1.36341i
$428$	0.561836	−	7.70625i	0.0271573	−	0.372496i
$429$		0			0
$430$	−0.932558	+	25.6163i	−0.0449719	+	1.23533i
$431$	−20.0881	+	11.5979i	−0.967609	+	0.558649i	−0.898507	−	0.438960i	$-0.855347\pi$
$431$	−20.0881	+	11.5979i	−0.967609	+	0.558649i	−0.0691026	+	0.997610i	$0.522014\pi$
$432$		0			0
$433$	−7.02656	+	12.1704i	−0.337675	+	0.584870i	−0.983995	−	0.178197i	$-0.942974\pi$
$433$	−7.02656	+	12.1704i	−0.337675	+	0.584870i	0.646320	+	0.763066i	$0.276307\pi$
$434$	−6.63560	−	0.241568i	−0.318519	−	0.0115956i
$435$		0			0
$436$	1.28670	−	1.89546i	0.0616216	−	0.0907761i
$437$	17.3055			0.827834
$438$		0			0
$439$	6.40295	+	11.0902i	0.305596	+	0.529308i	0.977394	−	0.211426i	$-0.0678109\pi$
$439$	6.40295	+	11.0902i	0.305596	+	0.529308i	−0.671798	+	0.740735i	$0.734478\pi$
$440$	−0.284708	−	0.647194i	−0.0135729	−	0.0308538i
$441$		0			0
$442$	−11.6987	+	0.464795i	−0.556452	+	0.0221080i
$443$		−	6.06204i		−	0.288016i	−0.989577	−	0.144008i	$-0.954001\pi$
$443$		−	6.06204i		−	0.288016i	0.989577	−	0.144008i	$-0.0459992\pi$
$444$		0			0
$445$	−26.8009	+	15.4735i	−1.27048	+	0.733514i
$446$	−2.82037	−	1.76818i	−0.133548	−	0.0837257i
$447$		0			0
$448$	25.9416	+	23.7791i	1.22563	+	1.12346i
$449$	6.72376	+	3.88197i	0.317314	+	0.183201i	0.650195	−	0.759768i	$-0.274687\pi$
$449$	6.72376	+	3.88197i	0.317314	+	0.183201i	−0.332881	+	0.942969i	$0.608021\pi$
$450$		0			0
$451$	−0.947179	−	0.546854i	−0.0446009	−	0.0257503i
$452$	−8.52063	−	17.6021i	−0.400777	−	0.827935i
$453$		0			0
$454$	−38.5680	−	1.40407i	−1.81009	−	0.0658961i
$455$	26.9653	+	12.9427i	1.26415	+	0.606764i
$456$		0			0
$457$	−11.5888	+	6.69082i	−0.542103	+	0.312983i	−0.745931	−	0.666023i	$-0.767995\pi$
$457$	−11.5888	+	6.69082i	−0.542103	+	0.312983i	0.203828	+	0.979007i	$0.434662\pi$
$458$	−9.37582	−	17.6966i	−0.438103	−	0.826907i
$459$		0			0
$460$	−14.8652	−	1.08377i	−0.693094	−	0.0505310i
$461$	17.4992	−	30.3095i	0.815019	−	1.41165i	−0.0942954	−	0.995544i	$-0.530060\pi$
$461$	17.4992	−	30.3095i	0.815019	−	1.41165i	0.909314	−	0.416110i	$-0.136607\pi$
$462$		0			0
$463$			18.2272i			0.847092i	0.905875	+	0.423546i	$0.139215\pi$
$463$			18.2272i			0.847092i	−0.905875	+	0.423546i	$0.860785\pi$
$464$	7.99763	+	6.32515i	0.371281	+	0.293638i
$465$		0			0
$466$	8.17152	+	15.4235i	0.378538	+	0.714480i
$467$		−	11.4947i		−	0.531910i	−0.963985	−	0.265955i	$-0.914313\pi$
$467$		−	11.4947i		−	0.531910i	0.963985	−	0.265955i	$-0.0856873\pi$
$468$		0			0
$469$			4.75655i			0.219637i
$470$	−23.8295	+	12.6251i	−1.09917	+	0.582353i
$471$		0			0
$472$	−5.53300	+	7.54473i	−0.254677	+	0.347275i
$473$			1.27401i			0.0585788i
$474$		0			0
$475$	3.16076	−	5.47460i	0.145026	−	0.251192i
$476$	1.46886	−	20.1473i	0.0673253	−	0.923448i
$477$		0			0
$478$	−21.7466	+	11.5216i	−0.994668	+	0.526984i
$479$	−3.75092	+	2.16560i	−0.171384	+	0.0989487i	−0.583238	−	0.812301i	$-0.698215\pi$
$479$	−3.75092	+	2.16560i	−0.171384	+	0.0989487i	0.411854	+	0.911250i	$0.364881\pi$
$480$		0			0
$481$	21.5110	+	31.4630i	0.980817	+	1.43459i
$482$	0.743457	−	20.4219i	0.0338635	−	0.930192i
$483$		0			0
$484$	9.57019	+	19.7703i	0.435009	+	0.898652i
$485$	−11.5390	−	6.66203i	−0.523958	−	0.302507i
$486$		0			0
$487$	−25.1811	−	14.5383i	−1.14107	−	0.658795i	−0.194372	−	0.980928i	$-0.562267\pi$
$487$	−25.1811	−	14.5383i	−1.14107	−	0.658795i	−0.946694	+	0.322133i	$0.895600\pi$
$488$	16.8679	+	12.3702i	0.763574	+	0.559974i
$489$		0			0
$490$	−17.4959	+	27.9072i	−0.790386	+	1.26072i
$491$	15.9306	−	9.19753i	0.718938	−	0.415079i	−0.0954238	−	0.995437i	$-0.530421\pi$
$491$	15.9306	−	9.19753i	0.718938	−	0.415079i	0.814362	+	0.580358i	$0.197087\pi$
$492$		0			0
$493$		−	5.85313i		−	0.263612i
$494$	−22.3124	+	0.886481i	−1.00388	+	0.0398847i
$495$		0			0
$496$	−3.96796	+	1.57586i	−0.178167	+	0.0707582i
$497$	−16.3814	−	28.3735i	−0.734808	−	1.27273i
$498$		0			0
$499$	3.03922			0.136054			0.0680270	−	0.997683i	$-0.478330\pi$
$499$	3.03922			0.136054			0.0680270	+	0.997683i	$0.478330\pi$
$500$	−13.6498	+	20.1079i	−0.610439	+	0.899252i
$501$		0			0
$502$	1.58673	−	43.5856i	0.0708193	−	1.94532i
$503$	0.148336	−	0.256925i	0.00661396	−	0.0114557i	−0.862699	−	0.505717i	$-0.831228\pi$
$503$	0.148336	−	0.256925i	0.00661396	−	0.0114557i	0.869313	+	0.494261i	$0.164561\pi$
$504$		0			0
$505$	17.6299	−	10.1786i	0.784520	−	0.452943i
$506$	−0.740291	−	0.0269502i	−0.0329100	−	0.00119808i
$507$		0			0
$508$	29.4414	+	2.14647i	1.30625	+	0.0952342i
$509$	12.2950	+	21.2955i	0.544965	+	0.943906i	0.998609	+	0.0527236i	$0.0167902\pi$
$509$	12.2950	+	21.2955i	0.544965	+	0.943906i	−0.453645	+	0.891183i	$0.649876\pi$
$510$		0			0
$511$	−13.5125	+	23.4044i	−0.597760	+	1.03535i
$512$	21.4248	+	7.27871i	0.946850	+	0.321677i
$513$		0			0
$514$	−14.6914	+	23.4337i	−0.648008	+	1.03362i
$515$	20.6916			0.911781
$516$		0			0
$517$	−1.16075	+	0.670158i	−0.0510496	+	0.0294735i
$518$	−58.1088	+	30.7866i	−2.55315	+	1.35268i
$519$		0			0
$520$	19.2216	+	0.635857i	0.842924	+	0.0278842i
$521$	27.3639			1.19883			0.599417	−	0.800437i	$-0.295399\pi$
$521$	27.3639			1.19883			0.599417	+	0.800437i	$0.295399\pi$
$522$		0			0
$523$	−18.8023	+	10.8555i	−0.822167	+	0.474678i	−0.851163	−	0.524901i	$-0.824102\pi$
$523$	−18.8023	+	10.8555i	−0.822167	+	0.474678i	0.0289964	+	0.999580i	$0.490769\pi$
$524$	2.03834	+	1.38369i	0.0890452	+	0.0604466i
$525$		0			0
$526$	23.7500	−	37.8828i	1.03555	−	1.65177i
$527$	2.12244	+	1.22539i	0.0924549	+	0.0533789i
$528$		0			0
$529$	3.69213	−	6.39496i	0.160527	−	0.278042i
$530$	−19.5255	+	10.3448i	−0.848134	+	0.449350i
$531$		0			0
$532$	2.80150	−	38.4259i	0.121460	−	1.66597i
$533$	24.5584	−	16.7904i	1.06374	−	0.727272i
$534$		0			0
$535$	6.30966	−	3.64288i	0.272790	−	0.157496i
$536$	1.23153	+	2.79950i	0.0531940	+	0.120920i
$537$		0			0
$538$	−0.00701669	+	0.192740i	−0.000302511	+	0.00830962i
$539$	−0.818534	+	1.41774i	−0.0352568	+	0.0610665i
$540$		0			0
$541$	33.0198			1.41963			0.709816	−	0.704387i	$-0.248778\pi$
$541$	33.0198			1.41963			0.709816	+	0.704387i	$0.248778\pi$
$542$	−18.1352	−	11.3696i	−0.778974	−	0.488364i
$543$		0			0
$544$	−4.35186	−	12.2381i	−0.186584	−	0.524704i
$545$	2.16019			0.0925325
$546$		0			0
$547$		−	29.1932i		−	1.24821i	−0.781340	−	0.624105i	$-0.785464\pi$
$547$		−	29.1932i		−	1.24821i	0.781340	−	0.624105i	$-0.214536\pi$
$548$	−32.7376	+	15.8472i	−1.39848	+	0.676960i
$549$		0			0
$550$	−0.143736	+	0.229269i	−0.00612893	+	0.00977606i
$551$		−	11.1634i		−	0.475576i
$552$		0			0
$553$	−60.6894	−	35.0390i	−2.58077	−	1.49001i
$554$	−0.636821	+	17.4927i	−0.0270559	+	0.743194i
$555$		0			0
$556$	−8.58807	+	4.15721i	−0.364215	+	0.176305i
$557$	5.03804	+	8.72614i	0.213469	+	0.369739i	0.952798	−	0.303606i	$-0.0981905\pi$
$557$	5.03804	+	8.72614i	0.213469	+	0.369739i	−0.739329	+	0.673344i	$0.764857\pi$
$558$		0			0
$559$	−31.2414	−	14.9951i	−1.32137	−	0.634225i
$560$	−4.81290	+	32.8319i	−0.203382	+	1.38740i
$561$		0			0
$562$	−1.36333	+	0.722305i	−0.0575086	+	0.0304686i
$563$	−20.2190	−	11.6734i	−0.852128	−	0.491977i	0.00923997	−	0.999957i	$-0.497059\pi$
$563$	−20.2190	−	11.6734i	−0.852128	−	0.491977i	−0.861368	+	0.507981i	$0.830392\pi$
$564$		0			0
$565$	9.22000	−	15.9695i	0.387888	−	0.671842i
$566$	5.70052	+	3.57384i	0.239611	+	0.150220i
$567$		0			0
$568$	−16.9876	−	12.4580i	−0.712785	−	0.522727i
$569$	21.2506	+	36.8071i	0.890870	+	1.54303i	0.838834	+	0.544388i	$0.183238\pi$
$569$	21.2506	+	36.8071i	0.890870	+	1.54303i	0.0520365	+	0.998645i	$0.483429\pi$
$570$		0			0
$571$			5.43630i			0.227502i	0.993509	+	0.113751i	$0.0362866\pi$
$571$			5.43630i			0.227502i	−0.993509	+	0.113751i	$0.963713\pi$
$572$	0.955858	−	0.00317407i	0.0399664	−	0.000132714i
$573$		0			0
$574$	24.0304	+	45.3567i	1.00301	+	1.89315i
$575$	2.85213	+	4.94004i	0.118942	+	0.206014i
$576$		0			0
$577$		−	4.39252i		−	0.182863i	−0.995811	−	0.0914316i	$-0.970856\pi$
$577$		−	4.39252i		−	0.182863i	0.995811	−	0.0914316i	$-0.0291443\pi$
$578$	8.80990	−	14.0524i	0.366443	−	0.584502i
$579$		0			0
$580$	−0.699116	+	9.58922i	−0.0290292	+	0.398171i
$581$	−0.550357	−	0.317749i	−0.0228327	−	0.0131825i
$582$		0			0
$583$	−0.951096	+	0.549116i	−0.0393904	+	0.0227420i
$584$	−1.89320	+	17.2734i	−0.0783412	+	0.714777i
$585$		0			0
$586$	−2.61097	−	0.0950520i	−0.107858	−	0.00392656i
$587$	−15.7922	−	27.3529i	−0.651813	−	1.12897i	−0.982683	−	0.185297i	$-0.940675\pi$
$587$	−15.7922	−	27.3529i	−0.651813	−	1.12897i	0.330869	−	0.943677i	$-0.392658\pi$
$588$		0			0
$589$	4.04803	+	2.33713i	0.166796	+	0.0962998i
$590$	−8.81636	−	0.320959i	−0.362964	−	0.0132137i
$591$		0			0
$592$	−26.2292	+	33.1647i	−1.07801	+	1.36306i
$593$		−	8.50710i		−	0.349345i	−0.984627	−	0.174672i	$-0.944113\pi$
$593$		−	8.50710i		−	0.349345i	0.984627	−	0.174672i	$-0.0558866\pi$
$594$		0			0
$595$	16.4960	−	9.52397i	0.676270	−	0.390445i
$596$	−6.92825	−	14.3125i	−0.283792	−	0.586265i
$597$		0			0
$598$	9.37414	−	17.8363i	0.383337	−	0.729382i
$599$	−26.3372			−1.07611			−0.538055	−	0.842910i	$-0.680841\pi$
$599$	−26.3372			−1.07611			−0.538055	+	0.842910i	$0.680841\pi$
$600$		0			0
$601$	3.29321	+	5.70401i	0.134333	+	0.232672i	0.925342	−	0.379132i	$-0.123777\pi$
$601$	3.29321	+	5.70401i	0.134333	+	0.232672i	−0.791009	+	0.611804i	$0.790444\pi$
$602$	31.7594	−	50.6585i	1.29442	−	2.06469i
$603$		0			0
$604$	22.4305	+	15.2265i	0.912685	+	0.619559i
$605$	−10.3557	+	17.9366i	−0.421019	+	0.729226i
$606$		0			0
$607$	−2.47666	+	4.28970i	−0.100524	+	0.174113i	−0.911901	−	0.410411i	$-0.865385\pi$
$607$	−2.47666	+	4.28970i	−0.100524	+	0.174113i	0.811376	+	0.584524i	$0.198719\pi$
$608$	−8.30009	−	23.3411i	−0.336613	−	0.946607i
$609$		0			0
$610$	−0.717574	+	19.7109i	−0.0290537	+	0.798071i
$611$	−2.77166	−	36.3518i	−0.112130	−	1.47064i
$612$		0			0
$613$	6.25855	+	10.8401i	0.252780	+	0.437828i	0.964290	−	0.264848i	$-0.0853217\pi$
$613$	6.25855	+	10.8401i	0.252780	+	0.437828i	−0.711510	+	0.702676i	$0.751988\pi$
$614$	9.61476	+	18.1476i	0.388020	+	0.732376i
$615$		0			0
$616$	−0.179683	+	1.63941i	−0.00723965	+	0.0660538i
$617$	−22.7830	−	13.1538i	−0.917210	−	0.529551i	−0.0344658	−	0.999406i	$-0.510973\pi$
$617$	−22.7830	−	13.1538i	−0.917210	−	0.529551i	−0.882744	+	0.469855i	$0.844306\pi$
$618$		0			0
$619$	2.56782			0.103209			0.0516047	−	0.998668i	$-0.483566\pi$
$619$	2.56782			0.103209			0.0516047	+	0.998668i	$0.483566\pi$
$620$	−3.33084	−	2.26108i	−0.133770	−	0.0908071i
$621$		0			0
$622$	−10.3325	−	19.5024i	−0.414297	−	0.781974i
$623$	72.1855			2.89205
$624$		0			0
$625$	−15.6988			−0.627950
$626$	19.5648	+	36.9279i	0.781965	+	1.47594i
$627$		0			0
$628$	−0.107235	−	0.0727942i	−0.00427913	−	0.00290481i
$629$	24.2718			0.967781
$630$		0			0
$631$	32.2263	+	18.6058i	1.28291	+	0.740687i	0.977379	−	0.211496i	$-0.0678337\pi$
$631$	32.2263	+	18.6058i	1.28291	+	0.740687i	0.305528	+	0.952183i	$0.401167\pi$
$632$	−44.7911	−	4.90920i	−1.78169	−	0.195278i
$633$		0			0
$634$	−9.50238	−	17.9355i	−0.377388	−	0.712309i
$635$	13.9175	+	24.1058i	0.552299	+	0.956610i
$636$		0			0
$637$	−25.1319	−	36.7591i	−0.995763	−	1.45645i
$638$	−0.0173850	+	0.477545i	−0.000688279	+	0.0189062i
$639$		0			0
$640$	5.66792	+	20.5695i	0.224044	+	0.813082i
$641$	−23.2163	+	40.2117i	−0.916987	+	1.58827i	−0.113021	+	0.993593i	$0.536053\pi$
$641$	−23.2163	+	40.2117i	−0.916987	+	1.58827i	−0.803966	+	0.594675i	$0.797281\pi$
$642$		0			0
$643$	−8.31198	+	14.3968i	−0.327792	+	0.567753i	−0.982073	−	0.188498i	$-0.939638\pi$
$643$	−8.31198	+	14.3968i	−0.327792	+	0.567753i	0.654281	+	0.756251i	$0.272971\pi$
$644$	28.7645	+	19.5262i	1.13348	+	0.769440i
$645$		0			0
$646$	−7.55354	+	12.0484i	−0.297190	+	0.474039i
$647$	14.5656	+	25.2283i	0.572632	+	0.991828i	0.996294	+	0.0860076i	$0.0274109\pi$
$647$	14.5656	+	25.2283i	0.572632	+	0.991828i	−0.423662	+	0.905820i	$0.639256\pi$
$648$		0			0
$649$	−0.438475			−0.0172117
$650$	−3.93039	−	6.22323i	−0.154163	−	0.244095i
$651$		0			0
$652$	−9.17232	−	18.9484i	−0.359216	−	0.742077i
$653$	−13.0481	+	7.53330i	−0.510610	+	0.294801i	−0.733084	−	0.680138i	$-0.761920\pi$
$653$	−13.0481	+	7.53330i	−0.510610	+	0.294801i	0.222475	+	0.974938i	$0.428587\pi$
$654$		0			0
$655$			2.32303i			0.0907682i
$656$	25.8866	+	20.4732i	1.01070	+	0.799343i
$657$		0			0
$658$	62.8612	+	2.28846i	2.45059	+	0.0892134i
$659$	−42.5147	−	24.5459i	−1.65614	−	0.956171i	−0.974473	−	0.224506i	$-0.927923\pi$
$659$	−42.5147	−	24.5459i	−1.65614	−	0.956171i	−0.681664	−	0.731665i	$-0.738744\pi$
$660$		0			0
$661$	−3.87600	−	6.71343i	−0.150759	−	0.261122i	0.780748	−	0.624846i	$-0.214838\pi$
$661$	−3.87600	−	6.71343i	−0.150759	−	0.261122i	−0.931507	+	0.363724i	$0.881505\pi$
$662$	−31.3743	−	1.14218i	−1.21940	−	0.0443920i
$663$		0			0
$664$	−0.406185	−	0.0445188i	−0.0157630	−	0.00172766i
$665$	31.4620	−	18.1646i	1.22005	−	0.704393i
$666$		0			0
$667$	8.72379	+	5.03668i	0.337787	+	0.195021i
$668$	−2.09576	+	28.7459i	−0.0810876	+	1.11221i
$669$		0			0
$670$	−1.53184	+	2.44339i	−0.0591803	+	0.0943966i
$671$			0.980307i			0.0378443i
$672$		0			0
$673$	−4.40466	−	7.62909i	−0.169787	−	0.294080i	0.768558	−	0.639780i	$-0.220975\pi$
$673$	−4.40466	−	7.62909i	−0.169787	−	0.294080i	−0.938345	+	0.345700i	$0.887641\pi$
$674$	−11.2503	−	21.2347i	−0.433347	−	0.817929i
$675$		0			0
$676$	−11.1727	+	23.4770i	−0.429717	+	0.902963i
$677$			33.6470i			1.29316i	0.762846	+	0.646580i	$0.223802\pi$
$677$			33.6470i			1.29316i	−0.762846	+	0.646580i	$0.776198\pi$
$678$		0			0
$679$	15.5395	+	26.9153i	0.596353	+	1.03291i
$680$	7.24294	−	9.87640i	0.277754	−	0.378743i
$681$		0			0
$682$	−0.169526	−	0.106281i	−0.00649149	−	0.00406972i
$683$	−1.34924	+	2.33695i	−0.0516273	+	0.0894211i	−0.890684	−	0.454623i	$-0.849774\pi$
$683$	−1.34924	+	2.33695i	−0.0516273	+	0.0894211i	0.839057	+	0.544044i	$0.183107\pi$
$684$		0			0
$685$	−29.7011	−	17.1479i	−1.13482	−	0.655189i
$686$	29.4104	−	15.5819i	1.12290	−	0.594921i
$687$		0			0
$688$	5.57610	−	38.0382i	0.212587	−	1.45019i
$689$	−2.27105	−	29.7860i	−0.0865202	−	1.13476i
$690$		0			0
$691$	−2.01331	−	3.48715i	−0.0765898	−	0.132657i	0.825187	−	0.564860i	$-0.191070\pi$
$691$	−2.01331	−	3.48715i	−0.0765898	−	0.132657i	−0.901777	+	0.432203i	$0.857737\pi$
$692$	−15.4082	+	7.45861i	−0.585731	+	0.283534i
$693$		0			0
$694$	0.646130	−	17.7484i	0.0245268	−	0.673721i
$695$	−7.79151	−	4.49843i	−0.295549	−	0.170635i
$696$		0			0
$697$		−	18.9453i		−	0.717605i
$698$	−22.2760	+	35.5318i	−0.843161	+	1.34490i
$699$		0			0
$700$	11.4308	−	5.53329i	0.432044	−	0.209139i
$701$			26.9620i			1.01834i	0.860666	+	0.509171i	$0.170048\pi$
$701$			26.9620i			1.01834i	−0.860666	+	0.509171i	$0.829952\pi$
$702$		0			0
$703$	46.2925			1.74595
$704$	0.318710	+	1.01141i	0.0120118	+	0.0381189i
$705$		0			0
$706$	−38.8102	−	24.3313i	−1.46064	−	0.915722i
$707$	−47.4844			−1.78583
$708$		0			0
$709$	1.66790	−	2.88889i	0.0626393	−	0.108494i	−0.833005	−	0.553265i	$-0.813382\pi$
$709$	1.66790	−	2.88889i	0.0626393	−	0.108494i	0.895644	+	0.444771i	$0.146715\pi$
$710$	0.722667	−	19.8508i	0.0271212	−	0.744988i
$711$		0			0
$712$	42.4852	−	18.6897i	1.59220	−	0.700425i
$713$	−3.65277	+	2.10893i	−0.136797	+	0.0789799i
$714$		0			0
$715$	0.508695	+	0.744041i	0.0190241	+	0.0278256i
$716$	2.48812	−	34.1276i	0.0929854	−	1.27541i
$717$		0			0
$718$	−3.71061	+	1.96592i	−0.138479	+	0.0733674i
$719$	−3.27398	+	5.67070i	−0.122099	+	0.211481i	−0.920595	−	0.390518i	$-0.872296\pi$
$719$	−3.27398	+	5.67070i	−0.122099	+	0.211481i	0.798496	+	0.602000i	$0.205629\pi$
$720$		0			0
$721$	−41.7981	−	24.1321i	−1.55664	−	0.898727i
$722$	−0.133785	+	0.213396i	−0.00497896	+	0.00794179i
$723$		0			0
$724$	−19.5908	−	13.2988i	−0.728085	−	0.494246i
$725$	3.18671	−	1.83985i	0.118351	−	0.0683303i
$726$		0			0
$727$	39.4666			1.46374			0.731868	−	0.681447i	$-0.238649\pi$
$727$	39.4666			1.46374			0.731868	+	0.681447i	$0.238649\pi$
$728$	−38.0871	−	23.7022i	−1.41160	−	0.878462i
$729$		0			0
$730$	−14.4786	+	7.67092i	−0.535878	+	0.283913i
$731$	−19.1118	+	11.0342i	−0.706877	+	0.408116i
$732$		0			0
$733$	−23.7942			−0.878860			−0.439430	−	0.898277i	$-0.644820\pi$
$733$	−23.7942			−0.878860			−0.439430	+	0.898277i	$0.644820\pi$
$734$	−3.87696	+	6.18402i	−0.143101	+	0.228256i
$735$		0			0
$736$	21.9851	+	4.04479i	0.810380	+	0.149093i
$737$	−0.0716661	+	0.124129i	−0.00263986	+	0.00457236i
$738$		0			0
$739$	−1.53475	−	2.65827i	−0.0564568	−	0.0977861i	0.836416	−	0.548096i	$-0.184647\pi$
$739$	−1.53475	−	2.65827i	−0.0564568	−	0.0977861i	−0.892873	+	0.450309i	$0.851314\pi$
$740$	−39.7647	−	2.89910i	−1.46178	−	0.106573i
$741$		0			0
$742$	51.5074	+	1.87512i	1.89090	+	0.0688379i
$743$	32.7810	−	18.9261i	1.20262	−	0.694332i	0.241482	−	0.970405i	$-0.422366\pi$
$743$	32.7810	−	18.9261i	1.20262	−	0.694332i	0.961137	+	0.276073i	$0.0890331\pi$
$744$		0			0
$745$	7.49691	−	12.9850i	0.274665	−	0.475734i
$746$	0.271785	−	7.46562i	0.00995076	−	0.273336i
$747$		0			0
$748$	0.341887	−	0.503642i	0.0125006	−	0.0184150i
$749$	−16.9944			−0.620963
$750$		0			0
$751$	2.75896	+	4.77866i	0.100676	+	0.174376i	0.911963	−	0.410272i	$-0.134566\pi$
$751$	2.75896	+	4.77866i	0.100676	+	0.174376i	−0.811287	+	0.584647i	$0.801233\pi$
$752$	37.5898	−	14.9286i	1.37076	−	0.544392i
$753$		0			0
$754$	−11.5058	−	6.04705i	−0.419017	−	0.220221i
$755$			25.5633i			0.930345i
$756$		0			0
$757$	18.7724	−	10.8383i	0.682296	−	0.393924i	−0.118424	−	0.992963i	$-0.537784\pi$
$757$	18.7724	−	10.8383i	0.682296	−	0.393924i	0.800720	+	0.599039i	$0.204451\pi$
$758$	27.2581	−	43.4786i	0.990060	−	1.57921i
$759$		0			0
$760$	13.8141	−	18.8368i	0.501091	−	0.683282i
$761$	−16.0378	−	9.25942i	−0.581369	−	0.335654i	0.180308	−	0.983610i	$-0.442291\pi$
$761$	−16.0378	−	9.25942i	−0.581369	−	0.335654i	−0.761677	+	0.647957i	$0.775624\pi$
$762$		0			0
$763$	−4.36370	−	2.51938i	−0.157976	−	0.0912078i
$764$	6.19911	+	12.8063i	0.224276	+	0.463315i
$765$		0			0
$766$	−0.501581	+	13.7778i	−0.0181229	+	0.497813i
$767$	5.16087	−	10.7524i	0.186348	−	0.388245i
$768$		0			0
$769$	1.51439	−	0.874333i	0.0546103	−	0.0315293i	−0.472446	−	0.881359i	$-0.656629\pi$
$769$	1.51439	−	0.874333i	0.0546103	−	0.0315293i	0.527057	+	0.849830i	$0.323296\pi$
$770$	−1.37417	+	0.728046i	−0.0495215	+	0.0262370i
$771$		0			0
$772$	2.04400	−	28.0359i	0.0735652	−	1.00904i
$773$	−3.35588	+	5.81256i	−0.120703	+	0.209063i	−0.920045	−	0.391813i	$-0.871848\pi$
$773$	−3.35588	+	5.81256i	−0.120703	+	0.209063i	0.799342	+	0.600876i	$0.205181\pi$
$774$		0			0
$775$			1.54074i			0.0553449i
$776$	16.1146	+	11.8178i	0.578479	+	0.424233i
$777$		0			0
$778$	18.6088	−	9.85914i	0.667159	−	0.353467i
$779$		−	36.1335i		−	1.29462i
$780$		0			0
$781$		−	0.987265i		−	0.0353271i
$782$	−6.00741	−	11.3388i	−0.214825	−	0.405475i
$783$		0			0
$784$	30.6444	−	38.7473i	1.09444	−	1.38383i
$785$		−	0.122212i		−	0.00436193i
$786$		0			0
$787$	−25.3707	+	43.9434i	−0.904369	+	1.56641i	−0.0826068	+	0.996582i	$0.526325\pi$
$787$	−25.3707	+	43.9434i	−0.904369	+	1.56641i	−0.821762	+	0.569831i	$0.807009\pi$
$788$	44.9732	+	3.27883i	1.60210	+	0.116804i
$789$		0			0
$790$	−19.8912	−	37.5441i	−0.707699	−	1.33576i
$791$	−37.2497	+	21.5061i	−1.32445	+	0.764670i
$792$		0			0
$793$	−24.0392	−	11.5383i	−0.853658	−	0.409735i
$794$	−29.6885	−	1.08081i	−1.05361	−	0.0383565i
$795$		0			0
$796$	−11.3245	−	23.3944i	−0.401385	−	0.829192i
$797$	−8.65924	−	4.99942i	−0.306726	−	0.177088i	0.338734	−	0.940882i	$-0.390001\pi$
$797$	−8.65924	−	4.99942i	−0.306726	−	0.177088i	−0.645461	+	0.763794i	$0.723335\pi$
$798$		0			0
$799$	−20.1066	−	11.6085i	−0.711320	−	0.410681i
$800$	5.29503	−	6.21622i	0.187208	−	0.219777i
$801$		0			0
$802$	19.0408	+	11.9373i	0.672353	+	0.421520i
$803$	−0.705260	+	0.407182i	−0.0248881	+	0.0143691i
$804$		0			0
$805$			32.7819i			1.15541i
$806$	4.60158	−	2.90621i	0.162084	−	0.102367i
$807$		0			0
$808$	−27.9472	+	12.2943i	−0.983179	+	0.432511i
$809$	−1.54330	−	2.67308i	−0.0542596	−	0.0939804i	0.837620	−	0.546254i	$-0.183947\pi$
$809$	−1.54330	−	2.67308i	−0.0542596	−	0.0939804i	−0.891879	+	0.452273i	$0.850613\pi$
$810$		0			0
$811$	28.0084			0.983508			0.491754	−	0.870734i	$-0.336356\pi$
$811$	28.0084			0.983508			0.491754	+	0.870734i	$0.336356\pi$
$812$	12.5959	−	18.5553i	0.442030	−	0.651165i
$813$		0			0
$814$	−1.98029	−	0.0720923i	−0.0694092	−	0.00252683i
$815$	9.92517	−	17.1909i	0.347664	−	0.602171i
$816$		0			0
$817$	−36.4511	+	21.0451i	−1.27526	+	0.736273i
$818$	0.814958	−	22.3859i	0.0284943	−	0.782706i
$819$		0			0
$820$	−2.26289	+	31.0382i	−0.0790235	+	1.08390i
$821$	11.8321	+	20.4937i	0.412942	+	0.715236i	0.995210	−	0.0977607i	$-0.0311680\pi$
$821$	11.8321	+	20.4937i	0.412942	+	0.715236i	−0.582268	+	0.812997i	$0.697835\pi$
$822$		0			0
$823$	−7.69409	+	13.3266i	−0.268199	+	0.464535i	−0.968397	−	0.249414i	$-0.919762\pi$
$823$	−7.69409	+	13.3266i	−0.268199	+	0.464535i	0.700198	+	0.713949i	$0.253095\pi$
$824$	−30.8486	−	3.38107i	−1.07466	−	0.117785i
$825$		0			0
$826$	17.4352	+	10.9307i	0.606647	+	0.380326i
$827$	−32.9357			−1.14529			−0.572643	−	0.819805i	$-0.694082\pi$
$827$	−32.9357			−1.14529			−0.572643	+	0.819805i	$0.694082\pi$
$828$		0			0
$829$	−7.25966	+	4.19137i	−0.252138	+	0.145572i	−0.620743	−	0.784014i	$-0.713169\pi$
$829$	−7.25966	+	4.19137i	−0.252138	+	0.145572i	0.368605	+	0.929586i	$0.379836\pi$
$830$	−0.180382	−	0.340467i	−0.00626117	−	0.0118178i
$831$		0			0
$832$	−28.5531	−	4.08886i	−0.989902	−	0.141756i
$833$	−28.3575			−0.982528
$834$		0			0
$835$	−23.5364	+	13.5887i	−0.814509	+	0.470257i
$836$	0.652065	−	0.960571i	0.0225521	−	0.0332221i
$837$		0			0
$838$	−26.8637	−	16.8417i	−0.927992	−	0.581788i
$839$	−24.9098	−	14.3817i	−0.859983	−	0.496512i	0.00402335	−	0.999992i	$-0.498719\pi$
$839$	−24.9098	−	14.3817i	−0.859983	−	0.496512i	−0.864007	+	0.503480i	$0.832053\pi$
$840$		0			0
$841$	−11.2509	+	19.4872i	−0.387964	+	0.671973i
$842$	0.997857	+	1.88343i	0.0343884	+	0.0649072i
$843$		0			0
$844$	1.49739	−	20.5385i	0.0515423	−	0.706965i
$845$	−24.2329	+	3.71691i	−0.833636	+	0.127865i
$846$		0			0
$847$	41.8381	−	24.1552i	1.43757	−	0.829983i
$848$	30.8005	−	12.2323i	1.05769	−	0.420058i
$849$		0			0
$850$	−4.68426	−	0.170530i	−0.160669	−	0.00584913i
$851$	−20.8862	+	36.1759i	−0.715969	+	1.24009i
$852$		0			0
$853$	23.9537			0.820160			0.410080	−	0.912049i	$-0.365501\pi$
$853$	23.9537			0.820160			0.410080	+	0.912049i	$0.365501\pi$
$854$	24.4379	−	38.9801i	0.836247	−	1.33387i
$855$		0			0
$856$	−10.0022	+	4.40006i	−0.341867	+	0.150391i
$857$	−35.6876			−1.21907			−0.609533	−	0.792761i	$-0.708643\pi$
$857$	−35.6876			−1.21907			−0.609533	+	0.792761i	$0.708643\pi$
$858$		0			0
$859$			34.6818i			1.18333i	0.806185	+	0.591664i	$0.201529\pi$
$859$			34.6818i			1.18333i	−0.806185	+	0.591664i	$0.798471\pi$
$860$	32.6290	−	15.7947i	1.11264	−	0.538594i
$861$		0			0
$862$	27.7933	+	17.4245i	0.946645	+	0.593482i
$863$			23.4077i			0.796807i	0.917210	+	0.398404i	$0.130436\pi$
$863$			23.4077i			0.796807i	−0.917210	+	0.398404i	$0.869564\pi$
$864$		0			0
$865$	−13.9790	−	8.07080i	−0.475301	−	0.274415i
$866$	19.8609	+	0.723036i	0.674902	+	0.0245698i
$867$		0			0
$868$	4.09143	+	8.45217i	0.138872	+	0.286885i
$869$	−1.05585	−	1.82879i	−0.0358174	−	0.0620375i
$870$		0			0
$871$	−2.20041	−	3.21842i	−0.0745579	−	0.109052i
$872$	−3.22058	−	0.352983i	−0.109063	−	0.0119535i
$873$		0			0
$874$	−11.4576	−	21.6260i	−0.387561	−	0.731509i
$875$	46.2920	+	26.7267i	1.56496	+	0.903528i
$876$		0			0
$877$	−22.9591	+	39.7663i	−0.775274	+	1.34281i	0.159367	+	0.987219i	$0.449055\pi$
$877$	−22.9591	+	39.7663i	−0.775274	+	1.34281i	−0.934641	+	0.355594i	$0.884279\pi$
$878$	9.61975	−	15.3442i	0.324651	−	0.517840i
$879$		0			0
$880$	−0.620273	+	0.784283i	−0.0209094	+	0.0264382i
$881$	−3.74833	−	6.49229i	−0.126284	−	0.218731i	0.795950	−	0.605362i	$-0.206972\pi$
$881$	−3.74833	−	6.49229i	−0.126284	−	0.218731i	−0.922234	+	0.386632i	$0.873638\pi$
$882$		0			0
$883$		−	50.0570i		−	1.68455i	−0.539046	−	0.842276i	$-0.681215\pi$
$883$		−	50.0570i		−	1.68455i	0.539046	−	0.842276i	$-0.318785\pi$
$884$	8.32635	+	14.3117i	0.280045	+	0.481354i
$885$		0			0
$886$	−7.57549	+	4.01357i	−0.254503	+	0.134838i
$887$	−11.5973	−	20.0872i	−0.389400	−	0.674461i	0.602969	−	0.797765i	$-0.293984\pi$
$887$	−11.5973	−	20.0872i	−0.389400	−	0.674461i	−0.992369	+	0.123304i	$0.960651\pi$
$888$		0			0
$889$		−	64.9266i		−	2.17757i
$890$	37.0810	+	23.2472i	1.24296	+	0.779249i
$891$		0			0
$892$	−0.342309	+	4.69518i	−0.0114613	+	0.157206i
$893$	−38.3483	−	22.1404i	−1.28328	−	0.740901i
$894$		0			0
$895$	27.9427	−	16.1327i	0.934021	−	0.539257i
$896$	12.5403	−	48.1618i	0.418941	−	1.60897i
$897$		0			0
$898$	0.399456	−	10.9726i	0.0133300	−	0.366160i
$899$	1.36042	+	2.35632i	0.0453726	+	0.0785877i
$900$		0			0
$901$	−16.4750	−	9.51184i	−0.548861	−	0.316885i
$902$	−0.0562715	+	1.54571i	−0.00187364	+	0.0514666i
$903$		0			0
$904$	−16.3553	+	22.3019i	−0.543970	+	0.741751i
$905$		−	22.3269i		−	0.742172i
$906$		0			0
$907$	19.4736	−	11.2431i	0.646610	−	0.373321i	−0.140546	−	0.990074i	$-0.544886\pi$
$907$	19.4736	−	11.2431i	0.646610	−	0.373321i	0.787156	+	0.616754i	$0.211553\pi$
$908$	23.7806	+	49.1265i	0.789186	+	1.63032i
$909$		0			0
$910$	−1.67927	−	42.2666i	−0.0556672	−	1.40112i
$911$	3.74738			0.124156			0.0620781	−	0.998071i	$-0.480227\pi$
$911$	3.74738			0.124156			0.0620781	+	0.998071i	$0.480227\pi$
$912$		0			0
$913$	−0.00957493	−	0.0165843i	−0.000316884	−	0.000548859i
$914$	16.0340	+	10.0522i	0.530358	+	0.332498i
$915$		0			0
$916$	−15.9071	+	23.4332i	−0.525587	+	0.774253i
$917$	2.70929	−	4.69263i	0.0894687	−	0.154964i
$918$		0			0
$919$	−6.20682	+	10.7505i	−0.204744	+	0.354627i	−0.950051	−	0.312094i	$-0.898970\pi$
$919$	−6.20682	+	10.7505i	−0.204744	+	0.354627i	0.745307	+	0.666721i	$0.232303\pi$
$920$	8.48764	+	19.2940i	0.279829	+	0.636104i
$921$		0			0
$922$	−49.4624	−	1.80068i	−1.62896	−	0.0593021i
$923$	24.2099	+	11.6202i	0.796877	+	0.382482i
$924$		0			0
$925$	7.62950	+	13.2147i	0.250857	+	0.434496i
$926$	22.7778	−	12.0679i	0.748527	−	0.396577i
$927$		0			0
$928$	2.60920	−	14.1821i	0.0856513	−	0.465550i
$929$	−35.0237	−	20.2210i	−1.14909	−	0.663428i	−0.200426	−	0.979709i	$-0.564233\pi$
$929$	−35.0237	−	20.2210i	−1.14909	−	0.663428i	−0.948666	+	0.316280i	$0.897566\pi$
$930$		0			0
$931$	−54.0849			−1.77256
$932$	13.8639	−	20.4232i	0.454127	−	0.668985i
$933$		0			0
$934$	−14.3644	+	7.61041i	−0.470019	+	0.249020i
$935$	0.573984			0.0187713
$936$		0			0
$937$	2.03951			0.0666277			0.0333139	−	0.999445i	$-0.489394\pi$
$937$	2.03951			0.0666277			0.0333139	+	0.999445i	$0.489394\pi$
$938$	5.94407	−	3.14923i	0.194081	−	0.102826i
$939$		0			0
$940$	31.5542	+	21.4199i	1.02918	+	0.698642i
$941$	−35.2677			−1.14969			−0.574847	−	0.818261i	$-0.694938\pi$
$941$	−35.2677			−1.14969			−0.574847	+	0.818261i	$0.694938\pi$
$942$		0			0
$943$	28.2370	+	16.3027i	0.919525	+	0.530888i
$944$	13.0916	+	1.91913i	0.426097	+	0.0624624i
$945$		0			0
$946$	1.59207	−	0.843495i	0.0517627	−	0.0274244i
$947$	−12.6695	−	21.9442i	−0.411702	−	0.713089i	0.583374	−	0.812204i	$-0.301732\pi$
$947$	−12.6695	−	21.9442i	−0.411702	−	0.713089i	−0.995076	+	0.0991144i	$0.968399\pi$
$948$		0			0
$949$	−1.68404	−	22.0871i	−0.0546662	−	0.716976i
$950$	−8.93406	−	0.325244i	−0.289859	−	0.0105523i
$951$		0			0
$952$	−26.1497	+	11.5035i	−0.847517	+	0.372832i
$953$	−16.5824	+	28.7215i	−0.537155	+	0.930380i	0.461901	+	0.886932i	$0.347168\pi$
$953$	−16.5824	+	28.7215i	−0.537155	+	0.930380i	−0.999056	+	0.0434482i	$0.986166\pi$
$954$		0			0
$955$	−6.70792	+	11.6185i	−0.217063	+	0.375965i
$956$	28.7961	+	19.5477i	0.931332	+	0.632216i
$957$		0			0
$958$	5.18968	+	3.25358i	0.167671	+	0.105118i
$959$	39.9984	+	69.2793i	1.29162	+	2.23715i
$960$		0			0
$961$	29.8607			0.963250
$962$	25.0760	−	47.7125i	0.808482	−	1.53831i
$963$		0			0
$964$	−26.0126	+	12.5919i	−0.837811	+	0.405557i
$965$	22.9550	−	13.2531i	0.738948	−	0.426632i
$966$		0			0
$967$		−	24.5985i		−	0.791035i	−0.918459	−	0.395517i	$-0.870565\pi$
$967$		−	24.5985i		−	0.791035i	0.918459	−	0.395517i	$-0.129435\pi$
$968$	18.3699	−	25.0491i	0.590432	−	0.805107i
$969$		0			0
$970$	−0.685526	+	18.8306i	−0.0220109	+	0.604614i
$971$	16.8251	+	9.71399i	0.539944	+	0.311737i	0.745056	−	0.667002i	$-0.232423\pi$
$971$	16.8251	+	9.71399i	0.539944	+	0.311737i	−0.205112	+	0.978738i	$0.565756\pi$
$972$		0			0
$973$	10.4928	+	18.1741i	0.336384	+	0.582635i
$974$	−1.49600	+	41.0934i	−0.0479350	+	1.31672i
$975$		0			0
$976$	4.29064	−	29.2692i	0.137340	−	0.936885i
$977$	10.4801	−	6.05071i	0.335290	−	0.193580i	−0.322898	−	0.946434i	$-0.604657\pi$
$977$	10.4801	−	6.05071i	0.335290	−	0.193580i	0.658187	+	0.752854i	$0.271324\pi$
$978$		0			0
$979$	1.88379	+	1.08761i	0.0602061	+	0.0347600i
$980$	46.4582	+	3.38711i	1.48405	+	0.108197i
$981$		0			0
$982$	−22.0411	−	13.8183i	−0.703361	−	0.440960i
$983$			26.8688i			0.856983i	0.903546	+	0.428492i	$0.140955\pi$
$983$			26.8688i			0.856983i	−0.903546	+	0.428492i	$0.859045\pi$
$984$		0			0
$985$	21.2596	+	36.8228i	0.677388	+	1.17327i
$986$	−7.31442	+	3.87525i	−0.232938	+	0.123413i
$987$		0			0
$988$	15.8804	+	27.2960i	0.505224	+	0.868402i
$989$		−	37.9803i		−	1.20770i
$990$		0			0
$991$	3.63276	+	6.29212i	0.115398	+	0.199876i	0.917939	−	0.396722i	$-0.129852\pi$
$991$	3.63276	+	6.29212i	0.115398	+	0.199876i	−0.802541	+	0.596598i	$0.796519\pi$
$992$	4.59640	+	3.91525i	0.145936	+	0.124309i
$993$		0			0
$994$	−24.6113	+	39.2568i	−0.780625	+	1.24515i
$995$	12.2540	−	21.2245i	0.388477	−	0.672862i
$996$		0			0
$997$	−17.0286	−	9.83147i	−0.539301	−	0.311366i	0.205494	−	0.978658i	$-0.434120\pi$
$997$	−17.0286	−	9.83147i	−0.539301	−	0.311366i	−0.744796	+	0.667293i	$0.767453\pi$
$998$	−2.01221	−	3.79798i	−0.0636954	−	0.120223i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.e.829.9		48
3.2	odd	2		312.2.bk.b.205.16	yes	48
8.5	even	2	inner	936.2.dg.e.829.17		48
12.11	even	2		1248.2.ca.b.49.15		48
13.4	even	6	inner	936.2.dg.e.901.17		48
24.5	odd	2		312.2.bk.b.205.8	✓	48
24.11	even	2		1248.2.ca.b.49.10		48
39.17	odd	6		312.2.bk.b.277.8	yes	48
104.69	even	6	inner	936.2.dg.e.901.9		48
156.95	even	6		1248.2.ca.b.433.10		48
312.173	odd	6		312.2.bk.b.277.16	yes	48
312.251	even	6		1248.2.ca.b.433.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.8	✓	48	24.5	odd	2
312.2.bk.b.205.16	yes	48	3.2	odd	2
312.2.bk.b.277.8	yes	48	39.17	odd	6
312.2.bk.b.277.16	yes	48	312.173	odd	6
936.2.dg.e.829.9		48	1.1	even	1	trivial
936.2.dg.e.829.17		48	8.5	even	2	inner
936.2.dg.e.901.9		48	104.69	even	6	inner
936.2.dg.e.901.17		48	13.4	even	6	inner
1248.2.ca.b.49.10		48	24.11	even	2
1248.2.ca.b.49.15		48	12.11	even	2
1248.2.ca.b.433.10		48	156.95	even	6
1248.2.ca.b.433.15		48	312.251	even	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.662081 - 1.24966i) q^{2} +(-1.12330 + 1.65475i) q^{4} -1.88587 q^{5} +(3.80954 + 2.19944i) q^{7} +(2.81159 + 0.308157i) q^{8} +(1.24860 + 2.35669i) q^{10} +(0.0662772 + 0.114795i) q^{11} +(-3.59512 + 0.274112i) q^{13} +(0.226324 - 6.21684i) q^{14} +(-1.47641 - 3.71755i) q^{16} +(-1.14806 + 1.98850i) q^{17} +(-2.18964 + 3.79257i) q^{19} +(2.11839 - 3.12064i) q^{20} +(0.0995743 - 0.158828i) q^{22} +(-1.97584 - 3.42225i) q^{23} -1.44351 q^{25} +(2.72281 + 4.31119i) q^{26} +(-7.91878 + 3.83323i) q^{28} +(-2.20762 + 1.27457i) q^{29} -1.06736i q^{31} +(-3.66817 + 4.30633i) q^{32} +(3.24505 + 0.118136i) q^{34} +(-7.18429 - 4.14785i) q^{35} +(-5.28540 - 9.15458i) q^{37} +(6.18914 + 0.225315i) q^{38} +(-5.30228 - 0.581142i) q^{40} +(-7.14559 + 4.12551i) q^{41} +(8.32354 + 4.80560i) q^{43} +(-0.264407 - 0.0192770i) q^{44} +(-2.96848 + 4.73493i) q^{46} +10.1114i q^{47} +(6.17508 + 10.6956i) q^{49} +(0.955719 + 1.80389i) q^{50} +(3.58479 - 6.25694i) q^{52} +8.28514i q^{53} +(-0.124990 - 0.216489i) q^{55} +(10.0331 + 7.35786i) q^{56} +(3.05440 + 1.91490i) q^{58} +(-1.65394 + 2.86472i) q^{59} +(6.40470 + 3.69775i) q^{61} +(-1.33383 + 0.706678i) q^{62} +(7.81008 + 1.73282i) q^{64} +(6.77991 - 0.516938i) q^{65} +(0.540655 + 0.936442i) q^{67} +(-2.00086 - 4.13343i) q^{68} +(-0.426816 + 11.7241i) q^{70} +(-6.45016 - 3.72400i) q^{71} +6.14363i q^{73} +(-7.94074 + 12.6660i) q^{74} +(-3.81615 - 7.88349i) q^{76} +0.583091i q^{77} -15.9309 q^{79} +(2.78431 + 7.01081i) q^{80} +(9.88644 + 6.19813i) q^{82} -0.144468 q^{83} +(2.16509 - 3.75004i) q^{85} +(0.494498 - 13.5833i) q^{86} +(0.150969 + 0.343181i) q^{88} +(14.2114 - 8.20498i) q^{89} +(-14.2986 - 6.86301i) q^{91} +(7.88243 + 0.574680i) q^{92} +(12.6359 - 6.69460i) q^{94} +(4.12937 - 7.15228i) q^{95} +(6.11866 + 3.53261i) q^{97} +(9.27740 - 14.7981i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 12 q^{7} - 4 q^{10} + 36 q^{14} - 2 q^{16} - 12 q^{17} - 54 q^{20} - 14 q^{22} - 20 q^{23} + 48 q^{25} + 42 q^{26} + 6 q^{28} + 28 q^{38} - 8 q^{40} + 12 q^{41} - 30 q^{46} + 16 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) \) 48 * q - 2 * q^4 - 12 * q^7 - 4 * q^10 + 36 * q^14 - 2 * q^16 - 12 * q^17 - 54 * q^20 - 14 * q^22 - 20 * q^23 + 48 * q^25 + 42 * q^26 + 6 * q^28 + 28 * q^38 - 8 * q^40 + 12 * q^41 - 30 * q^46 + 16 * q^49 + 84 * q^50 - 28 * q^52 - 68 * q^55 - 18 * q^56 - 24 * q^58 - 24 * q^62 - 68 * q^64 - 12 * q^65 - 4 * q^68 + 12 * q^71 - 54 * q^74 - 54 * q^76 - 192 * q^79 - 78 * q^80 - 6 * q^82 - 10 * q^88 + 48 * q^89 + 12 * q^92 + 54 * q^94 + 20 * q^95 + 144 * q^97 - 24 * q^98

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