LMFDB - Embedded newform 936.2.dg.e.901.9

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			901.9
Character	$\chi$	$=$	936.901
Dual form			936.2.dg.e.829.9

$q$-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 $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

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

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	0.442032	−	0.896999i	$-0.354258\pi$
$7$	3.80954	−	2.19944i	1.43987	−	0.831311i	0.997840	+	0.0656885i	$0.0209244\pi$
$8$	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	−0.855861	−	0.517206i	$-0.826972\pi$
$11$	0.0662772	−	0.114795i	0.0199833	−	0.0346121i	0.875844	+	0.482594i	$0.160305\pi$
$12$		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	0.692553	−	0.721367i	$-0.256486\pi$
$17$	−1.14806	−	1.98850i	−0.278446	−	0.482282i	−0.970999	+	0.239085i	$0.923152\pi$
$18$		0			0
$19$	−2.18964	−	3.79257i	−0.502338	−	0.870075i	−0.999996	−	0.00270169i	$-0.999140\pi$
$19$	−2.18964	−	3.79257i	−0.502338	−	0.870075i	0.497658	−	0.867373i	$-0.334193\pi$
$20$	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	−0.995107	−	0.0987997i	$-0.968500\pi$
$23$	−1.97584	+	3.42225i	−0.411991	+	0.713589i	0.583117	+	0.812388i	$0.301833\pi$
$24$		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	0.280821	−	0.959760i	$-0.409393\pi$
$29$	−2.20762	−	1.27457i	−0.409944	−	0.236682i	−0.690766	+	0.723078i	$0.742726\pi$
$30$		0			0
$31$			1.06736i			0.191703i	0.995396	+	0.0958516i	$0.0305574\pi$
$31$			1.06736i			0.191703i	−0.995396	+	0.0958516i	$0.969443\pi$
$32$	−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	−0.00580626	+	0.999983i	$0.501848\pi$
$37$	−5.28540	+	9.15458i	−0.868914	+	1.50500i	−0.863108	+	0.505020i	$0.831485\pi$
$38$	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	−0.175589	−	0.984464i	$-0.556183\pi$
$41$	−7.14559	−	4.12551i	−1.11595	−	0.644296i	−0.940365	+	0.340168i	$0.889516\pi$
$42$		0			0
$43$	8.32354	−	4.80560i	1.26933	−	0.732847i	0.294467	−	0.955662i	$-0.404858\pi$
$43$	8.32354	−	4.80560i	1.26933	−	0.732847i	0.974861	+	0.222815i	$0.0715247\pi$
$44$	−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	$-0.736028\pi$
$47$		−	10.1114i		−	1.47491i	0.675399	−	0.737453i	$-0.263972\pi$
$48$		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	$-0.807320\pi$
$53$		−	8.28514i		−	1.13805i	0.822320	−	0.569026i	$-0.192680\pi$
$54$		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	0.738048	−	0.674748i	$-0.235748\pi$
$59$	−1.65394	−	2.86472i	−0.215325	−	0.372954i	−0.953373	+	0.301794i	$0.902415\pi$
$60$		0			0
$61$	6.40470	−	3.69775i	0.820038	−	0.473449i	−0.0303918	−	0.999538i	$-0.509675\pi$
$61$	6.40470	−	3.69775i	0.820038	−	0.473449i	0.850429	+	0.526089i	$0.176342\pi$
$62$	−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	−0.831108	−	0.556110i	$-0.812293\pi$
$67$	0.540655	−	0.936442i	0.0660515	−	0.114405i	0.897160	+	0.441706i	$0.145627\pi$
$68$	−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	−0.831265	−	0.555877i	$-0.812383\pi$
$71$	−6.45016	+	3.72400i	−0.765493	+	0.441958i	0.0657714	+	0.997835i	$0.479049\pi$
$72$		0			0
$73$		−	6.14363i		−	0.719057i	−0.933134	−	0.359529i	$-0.882938\pi$
$73$		−	6.14363i		−	0.719057i	0.933134	−	0.359529i	$-0.117062\pi$
$74$	−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	0.999972	+	0.00744871i	$0.00237102\pi$
$89$	14.2114	+	8.20498i	1.50641	+	0.869726i	0.506437	+	0.862277i	$0.330962\pi$
$90$		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	−0.156102	−	0.987741i	$-0.549893\pi$
$97$	6.11866	−	3.53261i	0.621256	−	0.358682i	0.777358	+	0.629059i	$0.216560\pi$
$98$	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	−0.0433280	−	0.999061i	$-0.513796\pi$
$101$	−9.34844	−	5.39732i	−0.930204	−	0.537054i	−0.886876	+	0.462007i	$0.847129\pi$
$102$		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	0.329481	−	0.944162i	$-0.393126\pi$
$107$	−3.34576	−	1.93168i	−0.323447	−	0.186742i	−0.652928	+	0.757420i	$0.726460\pi$
$108$		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	0.539038	−	0.842281i	$-0.318788\pi$
$113$	−4.88900	−	8.46799i	−0.459918	−	0.796601i	−0.998956	+	0.0456800i	$0.985455\pi$
$114$		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	0.327069	+	0.945000i	$0.393939\pi$
$127$	−7.37989	+	12.7824i	−0.654860	+	1.13425i	−0.981929	+	0.189250i	$0.939394\pi$
$128$	−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	$0.0171371\pi$
$131$			1.23181i			0.107624i	−0.998551	+	0.0538118i	$0.982863\pi$
$132$		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	0.357938	−	0.933745i	$-0.383480\pi$
$137$	15.7493	−	9.09286i	1.34555	−	0.776856i	0.987616	+	0.156890i	$0.0501467\pi$
$138$		0			0
$139$	4.13153	−	2.38534i	0.350432	−	0.202322i	−0.314444	−	0.949276i	$-0.601818\pi$
$139$	4.13153	−	2.38534i	0.350432	−	0.202322i	0.664875	+	0.746954i	$0.268485\pi$
$140$	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	0.655978	−	0.754780i	$-0.272257\pi$
$149$	−3.97531	−	6.88544i	−0.325670	−	0.564077i	−0.981648	+	0.190703i	$0.938923\pi$
$150$		0			0
$151$			13.5552i			1.10311i	0.834139	+	0.551554i	$0.185965\pi$
$151$			13.5552i			1.10311i	−0.834139	+	0.551554i	$0.814035\pi$
$152$	−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	$-0.999177\pi$
$157$		−	0.0648041i		−	0.00517193i	0.999997	−	0.00258597i	$-0.000823140\pi$
$158$	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	0.582909	−	0.812538i	$-0.301915\pi$
$163$	−5.26292	−	9.11565i	−0.412224	−	0.713993i	−0.995133	+	0.0985448i	$0.968581\pi$
$164$	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	0.897942	−	0.440115i	$-0.145062\pi$
$167$	12.4804	+	7.20556i	0.965762	+	0.557583i	0.0678204	+	0.997698i	$0.478396\pi$
$168$		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	−0.191011	−	0.981588i	$-0.561177\pi$
$173$	7.41252	−	4.27962i	0.563564	−	0.325374i	0.754575	+	0.656214i	$0.227843\pi$
$174$		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	−0.169294	−	0.985566i	$-0.554149\pi$
$179$	−14.8169	−	8.55453i	−1.10747	−	0.639396i	−0.938172	+	0.346170i	$0.887482\pi$
$180$		0			0
$181$		−	11.8391i		−	0.879992i	−0.898000	−	0.439996i	$-0.854980\pi$
$181$		−	11.8391i		−	0.879992i	0.898000	−	0.439996i	$-0.145020\pi$
$182$	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	0.965537	−	0.260266i	$-0.0838103\pi$
$191$	3.55694	+	6.16081i	0.257371	+	0.445780i	−0.708166	+	0.706046i	$0.750477\pi$
$192$		0			0
$193$	−12.1721	−	7.02758i	−0.876169	−	0.505857i	−0.00677591	−	0.999977i	$-0.502157\pi$
$193$	−12.1721	−	7.02758i	−0.876169	−	0.505857i	−0.869393	+	0.494120i	$0.835490\pi$
$194$	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	0.114337	+	0.993442i	$0.463526\pi$
$197$	−11.2731	+	19.5256i	−0.803178	+	1.39114i	−0.917514	+	0.397702i	$0.869808\pi$
$198$		0			0
$199$	−6.49779	−	11.2545i	−0.460616	−	0.797811i	0.538375	−	0.842705i	$-0.319038\pi$
$199$	−6.49779	−	11.2545i	−0.460616	−	0.797811i	−0.998992	+	0.0448942i	$0.985705\pi$
$200$	−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	0.160606	−	0.987019i	$-0.448655\pi$
$211$	−8.91704	−	5.14826i	−0.613875	−	0.354421i	−0.774480	+	0.632598i	$0.781989\pi$
$212$	−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	0.566698	−	0.823926i	$-0.308221\pi$
$223$	2.03847	+	1.17691i	0.136506	+	0.0788117i	−0.430192	+	0.902737i	$0.641554\pi$
$224$	−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	0.820051	+	0.572290i	$0.193945\pi$
$227$	13.6449	+	23.6336i	0.905643	+	1.56862i	0.0855919	+	0.996330i	$0.472722\pi$
$228$		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	$0.190285\pi$
$239$			17.4020i			1.12564i	−0.826578	+	0.562822i	$0.809715\pi$
$240$		0			0
$241$	12.5141	−	7.22501i	0.806103	−	0.465404i	−0.0394975	−	0.999220i	$-0.512576\pi$
$241$	12.5141	−	7.22501i	0.806103	−	0.465404i	0.845601	+	0.533816i	$0.179242\pi$
$242$	−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	0.728150	−	0.685418i	$-0.240381\pi$
$251$	26.7083	−	15.4201i	1.68581	−	0.973305i	0.957664	−	0.287887i	$-0.0929528\pi$
$252$		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	0.381269	+	0.924464i	$0.375487\pi$
$257$	−9.77864	+	16.9371i	−0.609975	+	1.05651i	−0.991244	+	0.132044i	$0.957846\pi$
$258$		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	0.294074	−	0.955783i	$-0.404989\pi$
$263$	15.8081	−	27.3804i	0.974769	−	1.68835i	0.680695	−	0.732567i	$-0.261678\pi$
$264$		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	−0.503596	−	0.863939i	$-0.667990\pi$
$269$	−0.118107	+	0.0681891i	−0.00720111	+	0.00415756i	0.496395	+	0.868097i	$0.334657\pi$
$270$		0			0
$271$	13.1075	+	7.56763i	0.796226	+	0.459701i	0.842150	−	0.539244i	$-0.181290\pi$
$271$	13.1075	+	7.56763i	0.796226	+	0.459701i	−0.0459241	+	0.998945i	$0.514623\pi$
$272$	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	−0.786174	−	0.618006i	$-0.787941\pi$
$277$	−10.7192	+	6.18871i	−0.644051	+	0.371843i	0.142122	+	0.989849i	$0.454607\pi$
$278$	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	$0.0103598\pi$
$281$			1.09096i			0.0650813i	−0.999470	+	0.0325406i	$0.989640\pi$
$282$		0			0
$283$	−4.12015	−	2.37877i	−0.244917	−	0.141403i	0.372517	−	0.928025i	$-0.378495\pi$
$283$	−4.12015	−	2.37877i	−0.244917	−	0.141403i	−0.617435	+	0.786622i	$0.711828\pi$
$284$	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	0.891746	−	0.452537i	$-0.149481\pi$
$293$	0.923728	+	1.59994i	0.0539647	+	0.0934697i	−0.837781	+	0.546006i	$0.816147\pi$
$294$		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	0.991223	+	0.132203i	$0.0422050\pi$
$331$	11.0998	+	19.2255i	0.610102	+	1.05673i	−0.381120	+	0.924525i	$0.624462\pi$
$332$	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	−0.178814	−	0.983883i	$-0.557226\pi$
$347$	10.8759	−	6.27918i	0.583846	−	0.337084i	0.762660	+	0.646799i	$0.223893\pi$
$348$		0			0
$349$	−14.8271	+	25.6812i	−0.793674	+	1.37468i	0.130004	+	0.991513i	$0.458501\pi$
$349$	−14.8271	+	25.6812i	−0.793674	+	1.37468i	−0.923678	+	0.383170i	$0.874832\pi$
$350$	−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	0.999968	−	0.00804129i	$-0.00255965\pi$
$353$	28.0507	+	16.1951i	1.49299	+	0.861977i	0.493020	+	0.870018i	$0.335893\pi$
$354$		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	$0.0249673\pi$
$359$			2.96930i			0.156714i	−0.996925	+	0.0783568i	$0.975033\pi$
$360$		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	−0.925484	−	0.378787i	$-0.876341\pi$
$367$	−2.58053	+	4.46960i	−0.134702	+	0.233311i	0.790781	+	0.612099i	$0.209674\pi$
$368$	−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	−0.376866	−	0.926268i	$-0.622998\pi$
$373$	4.57477	−	2.64124i	0.236873	−	0.136758i	0.613738	+	0.789509i	$0.289665\pi$
$374$	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	0.151970	−	0.988385i	$-0.451438\pi$
$379$	18.1432	−	31.4249i	0.931951	−	1.61419i	0.779982	−	0.625802i	$-0.215228\pi$
$380$	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	−0.699945	−	0.714197i	$-0.746792\pi$
$383$	−8.44275	+	4.87443i	−0.431405	+	0.249072i	0.268540	+	0.963268i	$0.413459\pi$
$384$		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	$-0.876782\pi$
$389$		−	14.8911i		−	0.755010i	0.926008	−	0.377505i	$-0.123218\pi$
$390$		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	0.999499	+	0.0316419i	$0.0100736\pi$
$397$	10.5034	+	18.1925i	0.527152	+	0.913055i	−0.472347	+	0.881413i	$0.656593\pi$
$398$	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	0.115335	−	0.993327i	$-0.463206\pi$
$401$	−13.7620	−	7.94551i	−0.687243	−	0.396780i	−0.802578	+	0.596547i	$0.796539\pi$
$402$		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	−0.120919	−	0.992662i	$-0.538584\pi$
$409$	13.7176	−	7.91987i	0.678292	−	0.391612i	0.799211	+	0.601050i	$0.205251\pi$
$410$	−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	0.892628	−	0.450793i	$-0.148859\pi$
$419$	19.4162	+	11.2100i	0.948544	+	0.547642i	0.0559155	+	0.998436i	$0.482192\pi$
$420$		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	−0.0691026	−	0.997610i	$-0.522014\pi$
$431$	−20.0881	−	11.5979i	−0.967609	−	0.558649i	−0.898507	+	0.438960i	$0.855347\pi$
$432$		0			0
$433$	−7.02656	−	12.1704i	−0.337675	−	0.584870i	0.646320	−	0.763066i	$-0.276307\pi$
$433$	−7.02656	−	12.1704i	−0.337675	−	0.584870i	−0.983995	+	0.178197i	$0.942974\pi$
$434$	−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	−0.671798	−	0.740735i	$-0.734478\pi$
$439$	6.40295	−	11.0902i	0.305596	−	0.529308i	0.977394	+	0.211426i	$0.0678109\pi$
$440$	−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	$0.0459992\pi$
$443$			6.06204i			0.288016i	−0.989577	+	0.144008i	$0.954001\pi$
$444$		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	−0.332881	−	0.942969i	$-0.608021\pi$
$449$	6.72376	−	3.88197i	0.317314	−	0.183201i	0.650195	+	0.759768i	$0.274687\pi$
$450$		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	0.203828	−	0.979007i	$-0.434662\pi$
$457$	−11.5888	−	6.69082i	−0.542103	−	0.312983i	−0.745931	+	0.666023i	$0.767995\pi$
$458$	−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	0.909314	+	0.416110i	$0.136607\pi$
$461$	17.4992	+	30.3095i	0.815019	+	1.41165i	−0.0942954	+	0.995544i	$0.530060\pi$
$462$		0			0
$463$		−	18.2272i		−	0.847092i	−0.905875	−	0.423546i	$-0.860785\pi$
$463$		−	18.2272i		−	0.847092i	0.905875	−	0.423546i	$-0.139215\pi$
$464$	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	$0.0856873\pi$
$467$			11.4947i			0.531910i	−0.963985	+	0.265955i	$0.914313\pi$
$468$		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	0.411854	−	0.911250i	$-0.364881\pi$
$479$	−3.75092	−	2.16560i	−0.171384	−	0.0989487i	−0.583238	+	0.812301i	$0.698215\pi$
$480$		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	−0.946694	−	0.322133i	$-0.895600\pi$
$487$	−25.1811	+	14.5383i	−1.14107	+	0.658795i	−0.194372	+	0.980928i	$0.562267\pi$
$488$	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	0.814362	−	0.580358i	$-0.197087\pi$
$491$	15.9306	+	9.19753i	0.718938	+	0.415079i	−0.0954238	+	0.995437i	$0.530421\pi$
$492$		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	0.869313	−	0.494261i	$-0.164561\pi$
$503$	0.148336	+	0.256925i	0.00661396	+	0.0114557i	−0.862699	+	0.505717i	$0.831228\pi$
$504$		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	−0.453645	−	0.891183i	$-0.649876\pi$
$509$	12.2950	−	21.2955i	0.544965	−	0.943906i	0.998609	−	0.0527236i	$-0.0167902\pi$
$510$		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	0.0289964	−	0.999580i	$-0.490769\pi$
$523$	−18.8023	−	10.8555i	−0.822167	−	0.474678i	−0.851163	+	0.524901i	$0.824102\pi$
$524$	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	$0.214536\pi$
$547$			29.1932i			1.24821i	−0.781340	+	0.624105i	$0.785464\pi$
$548$	−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	−0.739329	−	0.673344i	$-0.764857\pi$
$557$	5.03804	−	8.72614i	0.213469	−	0.369739i	0.952798	+	0.303606i	$0.0981905\pi$
$558$		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	−0.861368	−	0.507981i	$-0.830392\pi$
$563$	−20.2190	+	11.6734i	−0.852128	+	0.491977i	0.00923997	+	0.999957i	$0.497059\pi$
$564$		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	0.0520365	−	0.998645i	$-0.483429\pi$
$569$	21.2506	−	36.8071i	0.890870	−	1.54303i	0.838834	−	0.544388i	$-0.183238\pi$
$570$		0			0
$571$		−	5.43630i		−	0.227502i	−0.993509	−	0.113751i	$-0.963713\pi$
$571$		−	5.43630i		−	0.227502i	0.993509	−	0.113751i	$-0.0362866\pi$
$572$	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	$0.0291443\pi$
$577$			4.39252i			0.182863i	−0.995811	+	0.0914316i	$0.970856\pi$
$578$	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	0.330869	+	0.943677i	$0.392658\pi$
$587$	−15.7922	+	27.3529i	−0.651813	+	1.12897i	−0.982683	+	0.185297i	$0.940675\pi$
$588$		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	$0.0558866\pi$
$593$			8.50710i			0.349345i	−0.984627	+	0.174672i	$0.944113\pi$
$594$		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	−0.791009	−	0.611804i	$-0.790444\pi$
$601$	3.29321	−	5.70401i	0.134333	−	0.232672i	0.925342	+	0.379132i	$0.123777\pi$
$602$	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	0.811376	−	0.584524i	$-0.198719\pi$
$607$	−2.47666	−	4.28970i	−0.100524	−	0.174113i	−0.911901	+	0.410411i	$0.865385\pi$
$608$	−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	−0.711510	−	0.702676i	$-0.751988\pi$
$613$	6.25855	−	10.8401i	0.252780	−	0.437828i	0.964290	+	0.264848i	$0.0853217\pi$
$614$	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	−0.882744	−	0.469855i	$-0.844306\pi$
$617$	−22.7830	+	13.1538i	−0.917210	+	0.529551i	−0.0344658	+	0.999406i	$0.510973\pi$
$618$		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	0.305528	−	0.952183i	$-0.401167\pi$
$631$	32.2263	−	18.6058i	1.28291	−	0.740687i	0.977379	+	0.211496i	$0.0678337\pi$
$632$	−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	−0.803966	−	0.594675i	$-0.797281\pi$
$641$	−23.2163	−	40.2117i	−0.916987	−	1.58827i	−0.113021	−	0.993593i	$-0.536053\pi$
$642$		0			0
$643$	−8.31198	−	14.3968i	−0.327792	−	0.567753i	0.654281	−	0.756251i	$-0.272971\pi$
$643$	−8.31198	−	14.3968i	−0.327792	−	0.567753i	−0.982073	+	0.188498i	$0.939638\pi$
$644$	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	−0.423662	−	0.905820i	$-0.639256\pi$
$647$	14.5656	−	25.2283i	0.572632	−	0.991828i	0.996294	−	0.0860076i	$-0.0274109\pi$
$648$		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	0.222475	−	0.974938i	$-0.428587\pi$
$653$	−13.0481	−	7.53330i	−0.510610	−	0.294801i	−0.733084	+	0.680138i	$0.761920\pi$
$654$		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	−0.681664	+	0.731665i	$0.738744\pi$
$659$	−42.5147	+	24.5459i	−1.65614	+	0.956171i	−0.974473	+	0.224506i	$0.927923\pi$
$660$		0			0
$661$	−3.87600	+	6.71343i	−0.150759	+	0.261122i	−0.931507	−	0.363724i	$-0.881505\pi$
$661$	−3.87600	+	6.71343i	−0.150759	+	0.261122i	0.780748	+	0.624846i	$0.214838\pi$
$662$	−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	−0.938345	−	0.345700i	$-0.887641\pi$
$673$	−4.40466	+	7.62909i	−0.169787	+	0.294080i	0.768558	+	0.639780i	$0.220975\pi$
$674$	−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	$-0.776198\pi$
$677$		−	33.6470i		−	1.29316i	0.762846	−	0.646580i	$-0.223802\pi$
$678$		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	0.839057	−	0.544044i	$-0.183107\pi$
$683$	−1.34924	−	2.33695i	−0.0516273	−	0.0894211i	−0.890684	+	0.454623i	$0.849774\pi$
$684$		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	−0.901777	−	0.432203i	$-0.857737\pi$
$691$	−2.01331	+	3.48715i	−0.0765898	+	0.132657i	0.825187	+	0.564860i	$0.191070\pi$
$692$	−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	$-0.829952\pi$
$701$		−	26.9620i		−	1.01834i	0.860666	−	0.509171i	$-0.170048\pi$
$702$		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	0.895644	−	0.444771i	$-0.146715\pi$
$709$	1.66790	+	2.88889i	0.0626393	+	0.108494i	−0.833005	+	0.553265i	$0.813382\pi$
$710$	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	0.798496	−	0.602000i	$-0.205629\pi$
$719$	−3.27398	−	5.67070i	−0.122099	−	0.211481i	−0.920595	+	0.390518i	$0.872296\pi$
$720$		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	−0.892873	−	0.450309i	$-0.851314\pi$
$739$	−1.53475	+	2.65827i	−0.0564568	+	0.0977861i	0.836416	+	0.548096i	$0.184647\pi$
$740$	−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	0.961137	−	0.276073i	$-0.0890331\pi$
$743$	32.7810	+	18.9261i	1.20262	+	0.694332i	0.241482	+	0.970405i	$0.422366\pi$
$744$		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	−0.811287	−	0.584647i	$-0.801233\pi$
$751$	2.75896	−	4.77866i	0.100676	−	0.174376i	0.911963	+	0.410272i	$0.134566\pi$
$752$	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	0.800720	−	0.599039i	$-0.204451\pi$
$757$	18.7724	+	10.8383i	0.682296	+	0.393924i	−0.118424	+	0.992963i	$0.537784\pi$
$758$	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	−0.761677	−	0.647957i	$-0.775624\pi$
$761$	−16.0378	+	9.25942i	−0.581369	+	0.335654i	0.180308	+	0.983610i	$0.442291\pi$
$762$		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	0.527057	−	0.849830i	$-0.323296\pi$
$769$	1.51439	+	0.874333i	0.0546103	+	0.0315293i	−0.472446	+	0.881359i	$0.656629\pi$
$770$	−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	0.799342	−	0.600876i	$-0.205181\pi$
$773$	−3.35588	−	5.81256i	−0.120703	−	0.209063i	−0.920045	+	0.391813i	$0.871848\pi$
$774$		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	−0.821762	−	0.569831i	$-0.807009\pi$
$787$	−25.3707	−	43.9434i	−0.904369	−	1.56641i	−0.0826068	−	0.996582i	$-0.526325\pi$
$788$	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	−0.645461	−	0.763794i	$-0.723335\pi$
$797$	−8.65924	+	4.99942i	−0.306726	+	0.177088i	0.338734	+	0.940882i	$0.390001\pi$
$798$		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	−0.891879	−	0.452273i	$-0.850613\pi$
$809$	−1.54330	+	2.67308i	−0.0542596	+	0.0939804i	0.837620	+	0.546254i	$0.183947\pi$
$810$		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	−0.582268	−	0.812997i	$-0.697835\pi$
$821$	11.8321	−	20.4937i	0.412942	−	0.715236i	0.995210	+	0.0977607i	$0.0311680\pi$
$822$		0			0
$823$	−7.69409	−	13.3266i	−0.268199	−	0.464535i	0.700198	−	0.713949i	$-0.253095\pi$
$823$	−7.69409	−	13.3266i	−0.268199	−	0.464535i	−0.968397	+	0.249414i	$0.919762\pi$
$824$	−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	0.368605	−	0.929586i	$-0.379836\pi$
$829$	−7.25966	−	4.19137i	−0.252138	−	0.145572i	−0.620743	+	0.784014i	$0.713169\pi$
$830$	−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	−0.864007	−	0.503480i	$-0.832053\pi$
$839$	−24.9098	+	14.3817i	−0.859983	+	0.496512i	0.00402335	+	0.999992i	$0.498719\pi$
$840$		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	$-0.798471\pi$
$859$		−	34.6818i		−	1.18333i	0.806185	−	0.591664i	$-0.201529\pi$
$860$	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	$-0.869564\pi$
$863$		−	23.4077i		−	0.796807i	0.917210	−	0.398404i	$-0.130436\pi$
$864$		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	−0.934641	−	0.355594i	$-0.884279\pi$
$877$	−22.9591	−	39.7663i	−0.775274	−	1.34281i	0.159367	−	0.987219i	$-0.449055\pi$
$878$	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	−0.922234	−	0.386632i	$-0.873638\pi$
$881$	−3.74833	+	6.49229i	−0.126284	+	0.218731i	0.795950	+	0.605362i	$0.206972\pi$
$882$		0			0
$883$			50.0570i			1.68455i	0.539046	+	0.842276i	$0.318785\pi$
$883$			50.0570i			1.68455i	−0.539046	+	0.842276i	$0.681215\pi$
$884$	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	−0.992369	−	0.123304i	$-0.960651\pi$
$887$	−11.5973	+	20.0872i	−0.389400	+	0.674461i	0.602969	+	0.797765i	$0.293984\pi$
$888$		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	0.787156	−	0.616754i	$-0.211553\pi$
$907$	19.4736	+	11.2431i	0.646610	+	0.373321i	−0.140546	+	0.990074i	$0.544886\pi$
$908$	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	0.745307	−	0.666721i	$-0.232303\pi$
$919$	−6.20682	−	10.7505i	−0.204744	−	0.354627i	−0.950051	+	0.312094i	$0.898970\pi$
$920$	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	−0.948666	−	0.316280i	$-0.897566\pi$
$929$	−35.0237	+	20.2210i	−1.14909	+	0.663428i	−0.200426	+	0.979709i	$0.564233\pi$
$930$		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	−0.995076	−	0.0991144i	$-0.968399\pi$
$947$	−12.6695	+	21.9442i	−0.411702	+	0.713089i	0.583374	+	0.812204i	$0.301732\pi$
$948$		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	−0.999056	−	0.0434482i	$-0.986166\pi$
$953$	−16.5824	−	28.7215i	−0.537155	−	0.930380i	0.461901	−	0.886932i	$-0.347168\pi$
$954$		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	$0.129435\pi$
$967$			24.5985i			0.791035i	−0.918459	+	0.395517i	$0.870565\pi$
$968$	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	−0.205112	−	0.978738i	$-0.565756\pi$
$971$	16.8251	−	9.71399i	0.539944	−	0.311737i	0.745056	+	0.667002i	$0.232423\pi$
$972$		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	0.658187	−	0.752854i	$-0.271324\pi$
$977$	10.4801	+	6.05071i	0.335290	+	0.193580i	−0.322898	+	0.946434i	$0.604657\pi$
$978$		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	$-0.859045\pi$
$983$		−	26.8688i		−	0.856983i	0.903546	−	0.428492i	$-0.140955\pi$
$984$		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	−0.802541	−	0.596598i	$-0.796519\pi$
$991$	3.63276	−	6.29212i	0.115398	−	0.199876i	0.917939	+	0.396722i	$0.129852\pi$
$992$	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	−0.744796	−	0.667293i	$-0.767453\pi$
$997$	−17.0286	+	9.83147i	−0.539301	+	0.311366i	0.205494	+	0.978658i	$0.434120\pi$
$998$	−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.901.9		48
3.2	odd	2		312.2.bk.b.277.16	yes	48
8.5	even	2	inner	936.2.dg.e.901.17		48
12.11	even	2		1248.2.ca.b.433.15		48
13.10	even	6	inner	936.2.dg.e.829.17		48
24.5	odd	2		312.2.bk.b.277.8	yes	48
24.11	even	2		1248.2.ca.b.433.10		48
39.23	odd	6		312.2.bk.b.205.8	✓	48
104.101	even	6	inner	936.2.dg.e.829.9		48
156.23	even	6		1248.2.ca.b.49.10		48
312.101	odd	6		312.2.bk.b.205.16	yes	48
312.179	even	6		1248.2.ca.b.49.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.8	✓	48	39.23	odd	6
312.2.bk.b.205.16	yes	48	312.101	odd	6
312.2.bk.b.277.8	yes	48	24.5	odd	2
312.2.bk.b.277.16	yes	48	3.2	odd	2
936.2.dg.e.829.9		48	104.101	even	6	inner
936.2.dg.e.829.17		48	13.10	even	6	inner
936.2.dg.e.901.9		48	1.1	even	1	trivial
936.2.dg.e.901.17		48	8.5	even	2	inner
1248.2.ca.b.49.10		48	156.23	even	6
1248.2.ca.b.49.15		48	312.179	even	6
1248.2.ca.b.433.10		48	24.11	even	2
1248.2.ca.b.433.15		48	12.11	even	2

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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