LMFDB - Embedded newform 936.2.dg.e.829.17

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			829.17
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.e.901.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.751196 + 1.19821i) q^{2} +(-0.871409 + 1.80018i) q^{4} +1.88587 q^{5} +(3.80954 + 2.19944i) q^{7} +(-2.81159 + 0.308157i) q^{8} +(1.41666 + 2.25966i) q^{10} +(-0.0662772 - 0.114795i) q^{11} +(3.59512 - 0.274112i) q^{13} +(0.226324 + 6.21684i) q^{14} +(-2.48129 - 3.13739i) q^{16} +(-1.14806 + 1.98850i) q^{17} +(2.18964 - 3.79257i) q^{19} +(-1.64336 + 3.39490i) q^{20} +(0.0877618 - 0.165648i) q^{22} +(-1.97584 - 3.42225i) q^{23} -1.44351 q^{25} +(3.02908 + 4.10179i) q^{26} +(-7.27906 + 4.94125i) q^{28} +(2.20762 - 1.27457i) q^{29} -1.06736i q^{31} +(1.89531 - 5.32990i) q^{32} +(-3.24505 + 0.118136i) q^{34} +(7.18429 + 4.14785i) q^{35} +(5.28540 + 9.15458i) q^{37} +(6.18914 - 0.225315i) q^{38} +(-5.30228 + 0.581142i) q^{40} +(-7.14559 + 4.12551i) q^{41} +(-8.32354 - 4.80560i) q^{43} +(0.264407 - 0.0192770i) q^{44} +(2.61633 - 4.93825i) q^{46} +10.1114i q^{47} +(6.17508 + 10.6956i) q^{49} +(-1.08436 - 1.72962i) q^{50} +(-2.63937 + 6.71072i) q^{52} -8.28514i q^{53} +(-0.124990 - 0.216489i) q^{55} +(-11.3886 - 5.00999i) q^{56} +(3.18555 + 1.68774i) q^{58} +(1.65394 - 2.86472i) q^{59} +(-6.40470 - 3.69775i) q^{61} +(1.27892 - 0.801795i) q^{62} +(7.81008 - 1.73282i) q^{64} +(6.77991 - 0.516938i) q^{65} +(-0.540655 - 0.936442i) q^{67} +(-2.57922 - 3.79951i) q^{68} +(0.426816 + 11.7241i) q^{70} +(-6.45016 - 3.72400i) q^{71} +6.14363i q^{73} +(-6.99873 + 13.2099i) q^{74} +(4.91923 + 7.24662i) q^{76} -0.583091i q^{77} -15.9309 q^{79} +(-4.67938 - 5.91669i) q^{80} +(-10.3110 - 5.46284i) q^{82} +0.144468 q^{83} +(-2.16509 + 3.75004i) q^{85} +(-0.494498 - 13.5833i) q^{86} +(0.221719 + 0.302334i) q^{88} +(14.2114 - 8.20498i) q^{89} +(14.2986 + 6.86301i) q^{91} +(7.88243 - 0.574680i) q^{92} +(-12.1156 + 7.59567i) q^{94} +(4.12937 - 7.15228i) q^{95} +(6.11866 + 3.53261i) q^{97} +(-8.17682 + 15.4335i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.751196	+	1.19821i	0.531176	+	0.847262i
$2$	0.751196	+	1.19821i	0.531176	+	0.847262i
$3$		0			0
$3$		0			0
$4$	−0.871409	+	1.80018i	−0.435705	+	0.900090i
$5$	1.88587			0.843385			0.421693	−	0.906739i	$-0.361436\pi$
$5$	1.88587			0.843385			0.421693	+	0.906739i	$0.361436\pi$
$6$		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
$10$	1.41666	+	2.25966i	0.447986	+	0.714568i
$11$	−0.0662772	−	0.114795i	−0.0199833	−	0.0346121i	0.855861	−	0.517206i	$-0.173028\pi$
$11$	−0.0662772	−	0.114795i	−0.0199833	−	0.0346121i	−0.875844	+	0.482594i	$0.839695\pi$
$12$		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
$16$	−2.48129	−	3.13739i	−0.620323	−	0.784347i
$17$	−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	$-0.665807\pi$
$19$	2.18964	−	3.79257i	0.502338	−	0.870075i	0.999996	−	0.00270169i	$-0.000859974\pi$
$20$	−1.64336	+	3.39490i	−0.367467	+	0.759122i
$21$		0			0
$22$	0.0877618	−	0.165648i	0.0187109	−	0.0353162i
$23$	−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
$26$	3.02908	+	4.10179i	0.594051	+	0.804427i
$27$		0			0
$28$	−7.27906	+	4.94125i	−1.37561	+	0.933808i
$29$	2.20762	−	1.27457i	0.409944	−	0.236682i	−0.280821	−	0.959760i	$-0.590607\pi$
$29$	2.20762	−	1.27457i	0.409944	−	0.236682i	0.690766	+	0.723078i	$0.257274\pi$
$30$		0			0
$31$		−	1.06736i		−	0.191703i	−0.995396	−	0.0958516i	$-0.969443\pi$
$31$		−	1.06736i		−	0.191703i	0.995396	−	0.0958516i	$-0.0305574\pi$
$32$	1.89531	−	5.32990i	0.335046	−	0.942202i
$33$		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	$0.168515\pi$
$37$	5.28540	+	9.15458i	0.868914	+	1.50500i	0.00580626	+	0.999983i	$0.498152\pi$
$38$	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	−0.294467	−	0.955662i	$-0.595142\pi$
$43$	−8.32354	−	4.80560i	−1.26933	−	0.732847i	−0.974861	+	0.222815i	$0.928475\pi$
$44$	0.264407	−	0.0192770i	0.0398608	−	0.00290611i
$45$		0			0
$46$	2.61633	−	4.93825i	0.385757	−	0.728105i
$47$			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
$50$	−1.08436	−	1.72962i	−0.153351	−	0.244606i
$51$		0			0
$52$	−2.63937	+	6.71072i	−0.366015	+	0.930609i
$53$		−	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
$56$	−11.3886	−	5.00999i	−1.52187	−	0.669488i
$57$		0			0
$58$	3.18555	+	1.68774i	0.418284	+	0.221611i
$59$	1.65394	−	2.86472i	0.215325	−	0.372954i	−0.738048	−	0.674748i	$-0.764252\pi$
$59$	1.65394	−	2.86472i	0.215325	−	0.372954i	0.953373	+	0.301794i	$0.0975855\pi$
$60$		0			0
$61$	−6.40470	−	3.69775i	−0.820038	−	0.473449i	0.0303918	−	0.999538i	$-0.490325\pi$
$61$	−6.40470	−	3.69775i	−0.820038	−	0.473449i	−0.850429	+	0.526089i	$0.823658\pi$
$62$	1.27892	−	0.801795i	0.162423	−	0.101828i
$63$		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	$-0.187707\pi$
$67$	−0.540655	−	0.936442i	−0.0660515	−	0.114405i	−0.897160	+	0.441706i	$0.854373\pi$
$68$	−2.57922	−	3.79951i	−0.312777	−	0.460758i
$69$		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	$0.882938\pi$
$74$	−6.99873	+	13.2099i	−0.813585	+	1.53562i
$75$		0			0
$76$	4.91923	+	7.24662i	0.564274	+	0.831245i
$77$		−	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	$0.853670\pi$
$80$	−4.67938	−	5.91669i	−0.523171	−	0.661506i
$81$		0			0
$82$	−10.3110	−	5.46284i	−1.13865	−	0.603270i
$83$	0.144468			0.0158574			0.00792871	−	0.999969i	$-0.497476\pi$
$83$	0.144468			0.0158574			0.00792871	+	0.999969i	$0.497476\pi$
$84$		0			0
$85$	−2.16509	+	3.75004i	−0.234837	+	0.406749i
$86$	−0.494498	−	13.5833i	−0.0533231	−	1.46472i
$87$		0			0
$88$	0.221719	+	0.302334i	0.0236353	+	0.0322289i
$89$	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
$94$	−12.1156	+	7.59567i	−1.24963	+	0.783434i
$95$	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	$0.549893\pi$
$98$	−8.17682	+	15.4335i	−0.825983	+	1.55902i
$99$		0			0
$100$	1.25789	−	2.59857i	0.125789	−	0.259857i
$101$	9.34844	−	5.39732i	0.930204	−	0.537054i	0.0433280	−	0.999061i	$-0.486204\pi$
$101$	9.34844	−	5.39732i	0.930204	−	0.537054i	0.886876	+	0.462007i	$0.152871\pi$
$102$		0			0
$103$	−10.9719			−1.08110			−0.540548	−	0.841313i	$-0.681783\pi$
$103$	−10.9719			−1.08110			−0.540548	+	0.841313i	$0.681783\pi$
$104$	−10.0235	+	1.87855i	−0.982887	+	0.184207i
$105$		0			0
$106$	9.92733	−	6.22376i	0.964227	−	0.604505i
$107$	3.34576	−	1.93168i	0.323447	−	0.186742i	−0.329481	−	0.944162i	$-0.606874\pi$
$107$	3.34576	−	1.93168i	0.323447	−	0.186742i	0.652928	+	0.757420i	$0.273540\pi$
$108$		0			0
$109$	1.14546			0.109716			0.0548578	−	0.998494i	$-0.482529\pi$
$109$	1.14546			0.109716			0.0548578	+	0.998494i	$0.482529\pi$
$110$	0.165507	−	0.312390i	0.0157805	−	0.0297852i
$111$		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
$124$	1.92144	+	0.930106i	0.172550	+	0.0835260i
$125$	−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	$-0.393939\pi$
$128$	7.94318	+	8.05642i	0.702085	+	0.712094i
$129$		0			0
$130$	5.71244	+	7.73543i	0.501014	+	0.678442i
$131$			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
$134$	0.715915	−	1.35127i	0.0618456	−	0.116732i
$135$		0			0
$136$	2.61511	−	5.94463i	0.224243	−	0.509747i
$137$	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	0.314444	−	0.949276i	$-0.398182\pi$
$139$	−4.13153	−	2.38534i	−0.350432	−	0.202322i	−0.664875	+	0.746954i	$0.731515\pi$
$140$	−13.7273	+	9.31854i	−1.16017	+	0.787560i
$141$		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
$146$	−7.36135	+	4.61507i	−0.609230	+	0.381946i
$147$		0			0
$148$	−21.0856	+	1.53728i	−1.73323	+	0.126363i
$149$	3.97531	−	6.88544i	0.325670	−	0.564077i	−0.655978	−	0.754780i	$-0.727743\pi$
$149$	3.97531	−	6.88544i	0.325670	−	0.564077i	0.981648	+	0.190703i	$0.0610768\pi$
$150$		0			0
$151$		−	13.5552i		−	1.10311i	−0.834139	−	0.551554i	$-0.814035\pi$
$151$		−	13.5552i		−	1.10311i	0.834139	−	0.551554i	$-0.185965\pi$
$152$	−4.98767	+	11.3379i	−0.404553	+	0.919625i
$153$		0			0
$154$	0.698665	−	0.438016i	0.0563000	−	0.0352963i
$155$		−	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	$-0.000823140\pi$
$158$	−11.9672	−	19.0885i	−0.952060	−	1.51860i
$159$		0			0
$160$	3.57430	−	10.0515i	0.282573	−	0.794639i
$161$		−	17.3830i		−	1.36997i
$162$		0			0
$163$	5.26292	−	9.11565i	0.412224	−	0.713993i	−0.582909	−	0.812538i	$-0.698085\pi$
$163$	5.26292	−	9.11565i	0.412224	−	0.713993i	0.995133	+	0.0985448i	$0.0314188\pi$
$164$	−1.19992	−	16.4583i	−0.0936980	−	1.28518i
$165$		0			0
$166$	0.108524	+	0.173103i	0.00842308	+	0.0134354i
$167$	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
$172$	15.9041	−	10.7962i	1.21268	−	0.823204i
$173$	−7.41252	−	4.27962i	−0.563564	−	0.325374i	0.191011	−	0.981588i	$-0.438823\pi$
$173$	−7.41252	−	4.27962i	−0.563564	−	0.325374i	−0.754575	+	0.656214i	$0.772157\pi$
$174$		0			0
$175$	−5.49910	−	3.17491i	−0.415693	−	0.240000i
$176$	−0.195705	+	0.492778i	−0.0147518	+	0.0371445i
$177$		0			0
$178$	20.5068	+	10.8647i	1.53705	+	0.814346i
$179$	14.8169	−	8.55453i	1.10747	−	0.639396i	0.169294	−	0.985566i	$-0.445851\pi$
$179$	14.8169	−	8.55453i	1.10747	−	0.639396i	0.938172	+	0.346170i	$0.112518\pi$
$180$		0			0
$181$		−	11.8391i		−	0.879992i	−0.898000	−	0.439996i	$-0.854980\pi$
$181$		−	11.8391i		−	0.879992i	0.898000	−	0.439996i	$-0.145020\pi$
$182$	2.51777	+	22.2882i	0.186629	+	1.65211i
$183$		0			0
$184$	6.60983	+	9.01310i	0.487283	+	0.664455i
$185$	9.96755	+	17.2643i	0.732829	+	1.26930i
$186$		0			0
$187$	0.304361			0.0222571
$188$	−18.2024	−	8.81121i	−1.32755	−	0.642623i
$189$		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	$0.130192\pi$
$197$	11.2731	+	19.5256i	0.803178	+	1.39114i	−0.114337	+	0.993442i	$0.536474\pi$
$198$		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
$202$	13.4896	+	7.14693i	0.949127	+	0.502856i
$203$	11.2134			0.787024
$204$		0			0
$205$	−13.4756	+	7.78016i	−0.941179	+	0.543390i
$206$	−8.24207	−	13.1467i	−0.574252	−	0.915972i
$207$		0			0
$208$	−9.78052	−	10.5991i	−0.678157	−	0.734917i
$209$	−0.580493			−0.0401535
$210$		0			0
$211$	8.91704	−	5.14826i	0.613875	−	0.354421i	−0.160606	−	0.987019i	$-0.551345\pi$
$211$	8.91704	−	5.14826i	0.613875	−	0.354421i	0.774480	+	0.632598i	$0.218011\pi$
$212$	14.9147	+	7.21975i	1.02435	+	0.495854i
$213$		0			0
$214$	4.82788	+	2.55785i	0.330027	+	0.174851i
$215$	−15.6971	−	9.06271i	−1.07053	−	0.618072i
$216$		0			0
$217$	2.34759	−	4.06615i	0.159365	−	0.276028i
$218$	0.860468	+	1.37251i	0.0582783	+	0.0929578i
$219$		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	$0.308221\pi$
$224$	18.9431	−	16.1359i	1.26569	−	1.07812i
$225$		0			0
$226$	−13.8190	+	0.503080i	−0.919227	+	0.0334644i
$227$	−13.6449	+	23.6336i	−0.905643	+	1.56862i	−0.0855919	+	0.996330i	$0.527278\pi$
$227$	−13.6449	+	23.6336i	−0.905643	+	1.56862i	−0.820051	+	0.572290i	$0.806055\pi$
$228$		0			0
$229$	−14.1611			−0.935794			−0.467897	−	0.883783i	$-0.654988\pi$
$229$	−14.1611			−0.935794			−0.467897	+	0.883783i	$0.654988\pi$
$230$	4.93405	−	9.31288i	0.325342	−	0.614073i
$231$		0			0
$232$	−5.81415	+	4.26386i	−0.381718	+	0.279936i
$233$	−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
$236$	3.71574	+	5.47374i	0.241874	+	0.356310i
$237$		0			0
$238$	−12.6220	−	6.68726i	−0.818164	−	0.433471i
$239$		−	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
$244$	12.2377	−	8.30735i	0.783441	−	0.531823i
$245$	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
$250$	−9.12823	−	14.5601i	−0.577320	−	0.920865i
$251$	−26.7083	−	15.4201i	−1.68581	−	0.973305i	−0.957664	−	0.287887i	$-0.907047\pi$
$251$	−26.7083	−	15.4201i	−1.68581	−	0.973305i	−0.728150	−	0.685418i	$-0.759619\pi$
$252$		0			0
$253$	−0.261906	+	0.453634i	−0.0164659	+	0.0285197i
$254$	9.77218	−	18.4447i	0.613161	−	1.15732i
$255$		0			0
$256$	−3.68639	+	15.5695i	−0.230399	+	0.973096i
$257$	−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
$260$	−4.97750	+	12.6555i	−0.308691	+	0.784862i
$261$		0			0
$262$	−1.47596	+	0.925330i	−0.0911854	+	0.0571671i
$263$	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
$266$	24.0734	+	12.7543i	1.47603	+	0.782016i
$267$		0			0
$268$	2.15689	−	0.157252i	0.131753	−	0.00960567i
$269$	0.118107	+	0.0681891i	0.00720111	+	0.00415756i	0.503596	−	0.863939i	$-0.332010\pi$
$269$	0.118107	+	0.0681891i	0.00720111	+	0.00415756i	−0.496395	+	0.868097i	$0.665343\pi$
$270$		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	0.786174	−	0.618006i	$-0.212059\pi$
$277$	10.7192	+	6.18871i	0.644051	+	0.371843i	−0.142122	+	0.989849i	$0.545393\pi$
$278$	−0.245452	−	6.74229i	−0.0147213	−	0.404376i
$279$		0			0
$280$	−21.4775	−	9.44818i	−1.28352	−	0.564637i
$281$		−	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	−0.372517	−	0.928025i	$-0.621505\pi$
$283$	4.12015	−	2.37877i	0.244917	−	0.141403i	0.617435	+	0.786622i	$0.288172\pi$
$284$	12.3246	−	8.36631i	0.731330	−	0.496449i
$285$		0			0
$286$	0.270108	−	0.619579i	0.0159718	−	0.0366365i
$287$	−36.2952			−2.14244
$288$		0			0
$289$	5.86392	+	10.1566i	0.344936	+	0.597447i
$290$	6.00753	+	3.18285i	0.352774	+	0.186903i
$291$		0			0
$292$	−11.0596	−	5.35362i	−0.647216	−	0.313297i
$293$	−0.923728	+	1.59994i	−0.0539647	+	0.0934697i	−0.891746	−	0.452537i	$-0.850519\pi$
$293$	−0.923728	+	1.59994i	−0.0539647	+	0.0934697i	0.837781	+	0.546006i	$0.183853\pi$
$294$		0			0
$295$	3.11912	−	5.40247i	0.181602	−	0.314544i
$296$	−17.6814	−	24.1102i	−1.02771	−	1.40138i
$297$		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
$302$	16.2420	−	10.1826i	0.934621	−	0.585944i
$303$		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	$-0.363989\pi$
$307$	14.5220			0.828815			0.414408	+	0.910091i	$0.363989\pi$
$308$	1.04967	+	0.508111i	0.0598104	+	0.0289523i
$309$		0			0
$310$	2.41187	−	1.51208i	0.136985	−	0.0858803i
$311$	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	$0.814615\pi$
$314$	0.0776489	−	0.0486806i	0.00438198	−	0.00274721i
$315$		0			0
$316$	13.8823	−	28.6784i	0.780941	−	1.61329i
$317$	−14.3523			−0.806105			−0.403052	−	0.915177i	$-0.632051\pi$
$317$	−14.3523			−0.806105			−0.403052	+	0.915177i	$0.632051\pi$
$318$		0			0
$319$	−0.292629	−	0.168950i	−0.0163841	−	0.00945936i
$320$	14.7288	−	3.26787i	0.823363	−	0.182679i
$321$		0			0
$322$	20.8284	−	13.0580i	1.16072	−	0.727694i
$323$	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
$328$	18.8192	−	13.8012i	1.03911	−	0.762044i
$329$	−22.2395	+	38.5200i	−1.22610	+	2.12368i
$330$		0			0
$331$	−11.0998	+	19.2255i	−0.610102	+	1.05673i	0.381120	+	0.924525i	$0.375538\pi$
$331$	−11.0998	+	19.2255i	−0.610102	+	1.05673i	−0.991223	+	0.132203i	$0.957795\pi$
$332$	−0.125891	+	0.260068i	−0.00690916	+	0.0142731i
$333$		0			0
$334$	18.0090	+	9.54134i	0.985408	+	0.522079i
$335$	−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	$0.346839\pi$
$338$	12.0142	+	13.9161i	0.653489	+	0.756936i
$339$		0			0
$340$	−4.86407	−	7.16537i	−0.263791	−	0.388597i
$341$	−0.122528	+	0.0707415i	−0.00663525	+	0.00383086i
$342$		0			0
$343$			23.5348i			1.27076i
$344$	24.8832	+	10.9464i	1.34161	+	0.590191i
$345$		0			0
$346$	−0.440375	−	12.0966i	−0.0236747	−	0.650317i
$347$	−10.8759	−	6.27918i	−0.583846	−	0.337084i	0.178814	−	0.983883i	$-0.442774\pi$
$347$	−10.8759	−	6.27918i	−0.583846	−	0.337084i	−0.762660	+	0.646799i	$0.776107\pi$
$348$		0			0
$349$	14.8271	+	25.6812i	0.793674	+	1.37468i	0.923678	+	0.383170i	$0.125168\pi$
$349$	14.8271	+	25.6812i	0.793674	+	1.37468i	−0.130004	+	0.991513i	$0.541499\pi$
$350$	−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
$358$	21.3805	+	11.3276i	1.12999	+	0.598682i
$359$		−	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
$362$	14.1857	−	8.89347i	0.745584	−	0.467430i
$363$		0			0
$364$	−24.8146	+	19.7596i	−1.30064	+	1.03569i
$365$			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	$0.876341\pi$
$368$	−5.83430	+	14.6906i	−0.304134	+	0.765799i
$369$		0			0
$370$	−13.1987	+	24.9121i	−0.686166	+	1.29512i
$371$	18.2227	−	31.5626i	0.946074	−	1.63865i
$372$		0			0
$373$	−4.57477	−	2.64124i	−0.236873	−	0.136758i	0.376866	−	0.926268i	$-0.377002\pi$
$373$	−4.57477	−	2.64124i	−0.236873	−	0.136758i	−0.613738	+	0.789509i	$0.710335\pi$
$374$	0.228635	+	0.364688i	0.0118224	+	0.0188576i
$375$		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	$-0.784772\pi$
$379$	−18.1432	−	31.4249i	−0.931951	−	1.61419i	−0.151970	−	0.988385i	$-0.548562\pi$
$380$	9.27701	+	13.6662i	0.475901	+	0.701060i
$381$		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
$386$	−17.5642	−	9.30567i	−0.893993	−	0.473646i
$387$		0			0
$388$	−11.6912	+	7.93633i	−0.593530	+	0.402906i
$389$		−	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
$392$	−20.6577	−	28.1686i	−1.04337	−	1.42273i
$393$		0			0
$394$	−14.9275	+	28.1752i	−0.752035	+	1.41944i
$395$	−30.0435			−1.51165
$396$		0			0
$397$	−10.5034	+	18.1925i	−0.527152	+	0.913055i	0.472347	+	0.881413i	$0.343407\pi$
$397$	−10.5034	+	18.1925i	−0.527152	+	0.913055i	−0.999499	+	0.0316419i	$0.989926\pi$
$398$	−18.3664	+	0.668626i	−0.920623	+	0.0335152i
$399$		0			0
$400$	3.58176	+	4.52884i	0.179088	+	0.226442i
$401$	−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
$406$	8.42343	+	13.4359i	0.418048	+	0.666815i
$407$	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	$0.538584\pi$
$410$	−19.4451	−	10.3022i	−0.960325	−	0.508789i
$411$		0			0
$412$	9.56105	−	19.7515i	0.471039	−	0.973084i
$413$	12.6016	−	7.27551i	0.620082	−	0.358004i
$414$		0			0
$415$	0.272448			0.0133739
$416$	5.35287	−	19.6811i	0.262446	−	0.964947i
$417$		0			0
$418$	−0.436064	−	0.695551i	−0.0213286	−	0.0340205i
$419$	−19.4162	+	11.2100i	−0.948544	+	0.547642i	−0.892628	−	0.450793i	$-0.851141\pi$
$419$	−19.4162	+	11.2100i	−0.948544	+	0.547642i	−0.0559155	+	0.998436i	$0.517808\pi$
$420$		0			0
$421$	1.50715			0.0734541			0.0367270	−	0.999325i	$-0.488307\pi$
$421$	1.50715			0.0734541			0.0367270	+	0.999325i	$0.488307\pi$
$422$	12.8671	+	6.81713i	0.626362	+	0.331853i
$423$		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
$436$	−0.998169	+	2.06204i	−0.0478036	+	0.0987539i
$437$	−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	$0.734478\pi$
$440$	0.418133	+	0.570161i	0.0199337	+	0.0271814i
$441$		0			0
$442$	−11.6340	+	1.31422i	−0.553371	+	0.0625111i
$443$			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
$446$	2.94147	+	1.55842i	0.139283	+	0.0737933i
$447$		0			0
$448$	33.5641	+	10.5766i	1.58575	+	0.499695i
$449$	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
$452$	−10.9836	−	16.1802i	−0.516624	−	0.761050i
$453$		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	$0.434662\pi$
$458$	−10.6378	−	16.9680i	−0.497071	−	0.792862i
$459$		0			0
$460$	14.8652	−	1.08377i	0.693094	−	0.0505310i
$461$	−17.4992	+	30.3095i	−0.815019	+	1.41165i	0.0942954	+	0.995544i	$0.469940\pi$
$461$	−17.4992	+	30.3095i	−0.815019	+	1.41165i	−0.909314	+	0.416110i	$0.863393\pi$
$462$		0			0
$463$			18.2272i			0.847092i	0.905875	+	0.423546i	$0.139215\pi$
$463$			18.2272i			0.847092i	−0.905875	+	0.423546i	$0.860785\pi$
$464$	−9.47656	−	3.76358i	−0.439938	−	0.174720i
$465$		0			0
$466$	−9.27138	−	14.7885i	−0.429488	−	0.685063i
$467$			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
$470$	−22.8484	+	14.3244i	−1.05392	+	0.660737i
$471$		0			0
$472$	−3.76743	+	8.56408i	−0.173410	+	0.394194i
$473$			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
$478$	20.8513	−	13.0723i	0.953716	−	0.597915i
$479$	−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
$484$	12.3365	+	18.1732i	0.560751	+	0.826055i
$485$	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	$0.895600\pi$
$488$	19.1469	+	8.42292i	0.866738	+	0.381288i
$489$		0			0
$490$	−15.4204	+	29.1055i	−0.696622	+	1.31485i
$491$	−15.9306	+	9.19753i	−0.718938	+	0.415079i	−0.814362	−	0.580358i	$-0.802913\pi$
$491$	−15.9306	+	9.19753i	−0.718938	+	0.415079i	0.0954238	+	0.995437i	$0.469579\pi$
$492$		0			0
$493$			5.85313i			0.263612i
$494$	22.1889	−	2.50655i	0.998326	−	0.112775i
$495$		0			0
$496$	−3.34871	+	2.64843i	−0.150362	+	0.118918i
$497$	−16.3814	−	28.3735i	−0.734808	−	1.27273i
$498$		0			0
$499$	−3.03922			−0.136054			−0.0680270	−	0.997683i	$-0.521670\pi$
$499$	−3.03922			−0.136054			−0.0680270	+	0.997683i	$0.521670\pi$
$500$	10.5890	−	21.8750i	0.473555	−	0.978282i
$501$		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	$-0.983210\pi$
$509$	−12.2950	−	21.2955i	−0.544965	−	0.943906i	0.453645	−	0.891183i	$-0.350124\pi$
$510$		0			0
$511$	−13.5125	+	23.4044i	−0.597760	+	1.03535i
$512$	−21.4248	+	7.27871i	−0.946850	+	0.321677i
$513$		0			0
$514$	12.9485	−	24.4399i	0.571135	−	1.07800i
$515$	−20.6916			−0.911781
$516$		0			0
$517$	1.16075	−	0.670158i	0.0510496	−	0.0294735i
$518$	−55.7163	+	34.9304i	−2.44804	+	1.53475i
$519$		0			0
$520$	−18.9030	+	3.54269i	−0.828953	+	0.155357i
$521$	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	$-0.509231\pi$
$523$	18.8023	−	10.8555i	0.822167	−	0.474678i	0.851163	+	0.524901i	$0.175898\pi$
$524$	−2.21748	−	1.07341i	−0.0968709	−	0.0468921i
$525$		0			0
$526$	−20.9325	+	39.5095i	−0.912700	+	1.72269i
$527$	2.12244	+	1.22539i	0.0924549	+	0.0533789i
$528$		0			0
$529$	3.69213	−	6.39496i	0.160527	−	0.278042i
$530$	18.7216	−	11.7372i	0.813215	−	0.509831i
$531$		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
$536$	1.80867	+	2.46628i	0.0781227	+	0.106527i
$537$		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	$-0.751222\pi$
$541$	−33.0198			−1.41963			−0.709816	+	0.704387i	$0.751222\pi$
$542$	18.9139	+	10.0208i	0.812423	+	0.430429i
$543$		0			0
$544$	8.42256	+	9.88786i	0.361114	+	0.423939i
$545$	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	$0.785464\pi$
$548$	−30.0929	+	20.4280i	−1.28550	+	0.872639i
$549$		0			0
$550$	−0.126685	+	0.239114i	−0.00540185	+	0.0101958i
$551$		−	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
$556$	7.89429	−	5.35888i	0.334792	−	0.227267i
$557$	−5.03804	−	8.72614i	−0.213469	−	0.369739i	0.739329	−	0.673344i	$-0.235143\pi$
$557$	−5.03804	−	8.72614i	−0.213469	−	0.369739i	−0.952798	+	0.303606i	$0.901809\pi$
$558$		0			0
$559$	−31.2414	−	14.9951i	−1.32137	−	0.634225i
$560$	−4.81290	−	32.8319i	−0.203382	−	1.38740i
$561$		0			0
$562$	1.30720	−	0.819525i	0.0551409	−	0.0345696i
$563$	20.2190	+	11.6734i	0.852128	+	0.491977i	0.861368	−	0.507981i	$-0.169608\pi$
$563$	20.2190	+	11.6734i	0.852128	+	0.491977i	−0.00923997	+	0.999957i	$0.502941\pi$
$564$		0			0
$565$	−9.22000	+	15.9695i	−0.387888	+	0.671842i
$566$	5.94530	+	3.14988i	0.249899	+	0.132399i
$567$		0			0
$568$	19.2828	+	8.48271i	0.809088	+	0.355926i
$569$	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	$-0.963713\pi$
$571$		−	5.43630i		−	0.227502i	0.993509	−	0.113751i	$-0.0362866\pi$
$572$	0.945290	−	0.141780i	0.0395245	−	0.00592812i
$573$		0			0
$574$	−27.2648	−	43.4893i	−1.13801	−	1.81521i
$575$	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	$-0.0291443\pi$
$578$	−7.76478	+	14.6558i	−0.322972	+	0.609601i
$579$		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	$0.0593248\pi$
$587$	15.7922	+	27.3529i	0.651813	+	1.12897i	−0.330869	+	0.943677i	$0.607342\pi$
$588$		0			0
$589$	−4.04803	−	2.33713i	−0.166796	−	0.0962998i
$590$	8.81636	−	0.320959i	0.362964	−	0.0132137i
$591$		0			0
$592$	15.6068	−	39.2975i	0.641437	−	1.61512i
$593$		−	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
$596$	8.93090	+	13.1563i	0.365824	+	0.538903i
$597$		0			0
$598$	8.05238	−	18.4707i	0.329286	−	0.755325i
$599$	−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	$0.790444\pi$
$602$	27.9918	−	52.8337i	1.14086	−	2.15334i
$603$		0			0
$604$	24.4018	+	11.8121i	0.992896	+	0.480629i
$605$	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	$0.198719\pi$
$608$	−16.0640	−	18.8586i	−0.651479	−	0.764819i
$609$		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	$-0.248012\pi$
$613$	−6.25855	−	10.8401i	−0.252780	−	0.437828i	−0.964290	+	0.264848i	$0.914678\pi$
$614$	10.9089	+	17.4004i	0.440247	+	0.702223i
$615$		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	$-0.516434\pi$
$619$	−2.56782			−0.103209			−0.0516047	+	0.998668i	$0.516434\pi$
$620$	3.62357	+	1.75406i	0.145526	+	0.0704446i
$621$		0			0
$622$	11.7233	+	18.6994i	0.470061	+	0.749779i
$623$	72.1855			2.89205
$624$		0			0
$625$	−15.6988			−0.627950
$626$	−22.1981	−	35.4075i	−0.887216	−	1.41517i
$627$		0			0
$628$	0.116659	+	0.0564709i	0.00465520	+	0.00225344i
$629$	−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
$634$	−10.7814	−	17.1970i	−0.428183	−	0.682982i
$635$	−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
$640$	14.9798	+	15.1933i	0.592128	+	0.600569i
$641$	−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	−0.654281	−	0.756251i	$-0.727029\pi$
$643$	8.31198	−	14.3968i	0.327792	−	0.567753i	0.982073	+	0.188498i	$0.0603620\pi$
$644$	31.2924	+	15.1477i	1.23309	+	0.596902i
$645$		0			0
$646$	−6.65746	+	12.5658i	−0.261934	+	0.494393i
$647$	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
$650$	−4.37250	−	5.92096i	−0.171503	−	0.232239i
$651$		0			0
$652$	11.8236	+	17.4177i	0.463050	+	0.682129i
$653$	13.0481	−	7.53330i	0.510610	−	0.294801i	−0.222475	−	0.974938i	$-0.571413\pi$
$653$	13.0481	−	7.53330i	0.510610	−	0.294801i	0.733084	+	0.680138i	$0.238080\pi$
$654$		0			0
$655$			2.32303i			0.0907682i
$656$	30.6736	+	12.1819i	1.19760	+	0.475623i
$657$		0			0
$658$	−62.8612	+	2.28846i	−2.45059	+	0.0892134i
$659$	42.5147	+	24.5459i	1.65614	+	0.956171i	0.974473	+	0.224506i	$0.0720769\pi$
$659$	42.5147	+	24.5459i	1.65614	+	0.956171i	0.681664	+	0.731665i	$0.261256\pi$
$660$		0			0
$661$	3.87600	+	6.71343i	0.150759	+	0.261122i	0.931507	−	0.363724i	$-0.118495\pi$
$661$	3.87600	+	6.71343i	0.150759	+	0.261122i	−0.780748	+	0.624846i	$0.785162\pi$
$662$	−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
$670$	1.35012	−	2.54831i	0.0521597	−	0.0984499i
$671$			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	$0.887641\pi$
$674$	12.7646	+	20.3604i	0.491674	+	0.784254i
$675$		0			0
$676$	−7.64935	+	24.8493i	−0.294206	+	0.955742i
$677$		−	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
$680$	4.93174	−	11.2108i	0.189124	−	0.429913i
$681$		0			0
$682$	−0.176805	−	0.0936732i	−0.00677023	−	0.00358693i
$683$	1.34924	−	2.33695i	0.0516273	−	0.0894211i	−0.839057	−	0.544044i	$-0.816893\pi$
$683$	1.34924	−	2.33695i	0.0516273	−	0.0894211i	0.890684	+	0.454623i	$0.150226\pi$
$684$		0			0
$685$	29.7011	+	17.1479i	1.13482	+	0.655189i
$686$	−28.1996	+	17.6792i	−1.07666	+	0.674996i
$687$		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	$-0.142263\pi$
$691$	2.01331	+	3.48715i	0.0765898	+	0.132657i	−0.825187	+	0.564860i	$0.808930\pi$
$692$	14.1634	−	9.61457i	0.538413	−	0.365491i
$693$		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
$698$	−19.6334	+	37.0575i	−0.743136	+	1.40265i
$699$		0			0
$700$	10.5074	−	7.13272i	0.397141	−	0.269592i
$701$		−	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
$704$	−0.716550	−	0.781715i	−0.0270060	−	0.0294620i
$705$		0			0
$706$	40.4766	+	21.4449i	1.52336	+	0.807090i
$707$	47.4844			1.78583
$708$		0			0
$709$	−1.66790	+	2.88889i	−0.0626393	+	0.108494i	−0.895644	−	0.444771i	$-0.853285\pi$
$709$	−1.66790	+	2.88889i	−0.0626393	+	0.108494i	0.833005	+	0.553265i	$0.186618\pi$
$710$	−0.722667	−	19.8508i	−0.0271212	−	0.744988i
$711$		0			0
$712$	−37.4283	+	27.4484i	−1.40269	+	1.02867i
$713$	−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
$718$	3.55784	−	2.23053i	0.132777	−	0.0832425i
$719$	−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
$722$	0.117914	−	0.222559i	0.00438831	−	0.00828280i
$723$		0			0
$724$	21.3125	+	10.3167i	0.792072	+	0.383417i
$725$	−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	$0.238649\pi$
$728$	−42.3168	−	14.8897i	−1.56837	−	0.551851i
$729$		0			0
$730$	−13.8825	+	8.70340i	−0.513815	+	0.322127i
$731$	19.1118	−	11.0342i	0.706877	−	0.408116i
$732$		0			0
$733$	23.7942			0.878860			0.439430	−	0.898277i	$-0.355180\pi$
$733$	23.7942			0.878860			0.439430	+	0.898277i	$0.355180\pi$
$734$	3.41704	−	6.44955i	0.126125	−	0.238057i
$735$		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	$-0.148686\pi$
$739$	1.53475	+	2.65827i	0.0564568	+	0.0977861i	−0.836416	+	0.548096i	$0.815353\pi$
$740$	−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
$748$	−0.265223	+	0.547904i	−0.00969751	+	0.0200333i
$749$	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	$0.801233\pi$
$752$	31.7235	−	25.0894i	1.15684	−	0.914917i
$753$		0			0
$754$	11.9151	+	5.19441i	0.433921	+	0.189169i
$755$		−	25.5633i		−	0.930345i
$756$		0			0
$757$	−18.7724	+	10.8383i	−0.682296	+	0.393924i	−0.800720	−	0.599039i	$-0.795549\pi$
$757$	−18.7724	+	10.8383i	−0.682296	+	0.393924i	0.118424	+	0.992963i	$0.462216\pi$
$758$	24.0245	−	45.3455i	0.872609	−	1.64702i
$759$		0			0
$760$	−9.40607	+	21.3818i	−0.341194	+	0.775598i
$761$	−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
$764$	7.99100	+	11.7717i	0.289104	+	0.425886i
$765$		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	$0.323296\pi$
$770$	1.31759	−	0.826039i	0.0474826	−	0.0297684i
$771$		0			0
$772$	−2.04400	−	28.0359i	−0.0735652	−	1.00904i
$773$	3.35588	−	5.81256i	0.120703	−	0.209063i	−0.799342	−	0.600876i	$-0.794819\pi$
$773$	3.35588	−	5.81256i	0.120703	−	0.209063i	0.920045	+	0.391813i	$0.128152\pi$
$774$		0			0
$775$			1.54074i			0.0553449i
$776$	−18.2918	−	8.04674i	−0.656636	−	0.288861i
$777$		0			0
$778$	17.8427	−	11.1862i	0.639691	−	0.401043i
$779$			36.1335i			1.29462i
$780$		0			0
$781$			0.987265i			0.0353271i
$782$	6.81599	+	10.8720i	0.243739	+	0.388781i
$783$		0			0
$784$	18.2339	−	45.9124i	0.651212	−	1.63973i
$785$		−	0.122212i		−	0.00436193i
$786$		0			0
$787$	25.3707	−	43.9434i	0.904369	−	1.56641i	0.0826068	−	0.996582i	$-0.473675\pi$
$787$	25.3707	−	43.9434i	0.904369	−	1.56641i	0.821762	−	0.569831i	$-0.192991\pi$
$788$	−44.9732	+	3.27883i	−1.60210	+	0.116804i
$789$		0			0
$790$	−22.5686	−	35.9984i	−0.802953	−	1.28077i
$791$	−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
$796$	−14.5979	−	21.5045i	−0.517409	−	0.762206i
$797$	8.65924	+	4.99942i	0.306726	+	0.177088i	0.645461	−	0.763794i	$-0.276665\pi$
$797$	8.65924	+	4.99942i	0.306726	+	0.177088i	−0.338734	+	0.940882i	$0.609999\pi$
$798$		0			0
$799$	−20.1066	−	11.6085i	−0.711320	−	0.410681i
$800$	−2.73589	+	7.69374i	−0.0967284	+	0.272015i
$801$		0			0
$802$	−19.8584	−	10.5212i	−0.701223	−	0.371515i
$803$	0.705260	−	0.407182i	0.0248881	−	0.0143691i
$804$		0			0
$805$		−	32.7819i		−	1.15541i
$806$	4.37808	−	3.23311i	0.154211	−	0.113882i
$807$		0			0
$808$	−24.6207	+	18.0558i	−0.866155	+	0.635202i
$809$	−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	$-0.663644\pi$
$811$	−28.0084			−0.983508			−0.491754	+	0.870734i	$0.663644\pi$
$812$	−9.77143	+	20.1861i	−0.342910	+	0.708392i
$813$		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	$-0.302165\pi$
$821$	−11.8321	−	20.4937i	−0.412942	−	0.715236i	−0.995210	+	0.0977607i	$0.968832\pi$
$822$		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
$826$	18.1838	+	9.63396i	0.632696	+	0.335208i
$827$	32.9357			1.14529			0.572643	−	0.819805i	$-0.305918\pi$
$827$	32.9357			1.14529			0.572643	+	0.819805i	$0.305918\pi$
$828$		0			0
$829$	7.25966	−	4.19137i	0.252138	−	0.145572i	−0.368605	−	0.929586i	$-0.620164\pi$
$829$	7.25966	−	4.19137i	0.252138	−	0.145572i	0.620743	+	0.784014i	$0.286831\pi$
$830$	0.204661	+	0.326449i	0.00710390	+	0.0113312i
$831$		0			0
$832$	27.6032	−	8.37053i	0.956967	−	0.290196i
$833$	−28.3575			−0.982528
$834$		0			0
$835$	23.5364	−	13.5887i	0.814509	−	0.470257i
$836$	0.505847	−	1.04499i	0.0174951	−	0.0361418i
$837$		0			0
$838$	−28.0172	−	14.8438i	−0.967840	−	0.512771i
$839$	−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
$842$	1.13217	+	1.80588i	0.0390170	+	0.0622348i
$843$		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
$848$	−25.9937	+	20.5578i	−0.892627	+	0.705959i
$849$		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	$-0.634499\pi$
$853$	−23.9537			−0.820160			−0.410080	+	0.912049i	$0.634499\pi$
$854$	21.5388	−	40.6539i	0.737043	−	1.39115i
$855$		0			0
$856$	−8.81165	+	6.46210i	−0.301176	+	0.220870i
$857$	−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	$-0.201529\pi$
$860$	29.9931	−	20.3602i	1.02276	−	0.694278i
$861$		0			0
$862$	−28.9868	−	15.3575i	−0.987293	−	0.523077i
$863$			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
$868$	5.27408	+	7.76936i	0.179014	+	0.263709i
$869$	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
$874$	−12.9998	−	20.7356i	−0.439725	−	0.701392i
$875$	−46.2920	−	26.7267i	−1.56496	−	0.903528i
$876$		0			0
$877$	22.9591	−	39.7663i	0.775274	−	1.34281i	−0.159367	−	0.987219i	$-0.550945\pi$
$877$	22.9591	−	39.7663i	0.775274	−	1.34281i	0.934641	−	0.355594i	$-0.115721\pi$
$878$	−8.47855	+	16.0030i	−0.286137	+	0.540076i
$879$		0			0
$880$	−0.369073	+	0.929314i	−0.0124414	+	0.0313272i
$881$	−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	$0.318785\pi$
$883$			50.0570i			1.68455i	−0.539046	+	0.842276i	$0.681215\pi$
$884$	−10.3141	−	12.9527i	−0.346901	−	0.435646i
$885$		0			0
$886$	−7.26359	+	4.55378i	−0.244025	+	0.152987i
$887$	−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
$890$	38.6732	+	20.4894i	1.29633	+	0.686807i
$891$		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
$904$	11.1364	−	25.3151i	0.370391	−	0.841967i
$905$		−	22.3269i		−	0.742172i
$906$		0			0
$907$	−19.4736	+	11.2431i	−0.646610	+	0.373321i	−0.787156	−	0.616754i	$-0.788447\pi$
$907$	−19.4736	+	11.2431i	−0.646610	+	0.373321i	0.140546	+	0.990074i	$0.455114\pi$
$908$	−30.6545	−	45.1578i	−1.01731	−	1.49862i
$909$		0			0
$910$	4.74818	+	42.0326i	0.157400	+	1.39337i
$911$	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
$914$	−16.7225	−	8.85974i	−0.553131	−	0.293054i
$915$		0			0
$916$	12.3401	−	25.4926i	0.407730	−	0.842298i
$917$	−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	$0.232303\pi$
$920$	12.4653	+	16.9975i	0.410968	+	0.560391i
$921$		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
$926$	−21.8401	+	13.6922i	−0.717709	+	0.449955i
$927$		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
$932$	10.7551	−	22.2181i	0.352294	−	0.727778i
$933$		0			0
$934$	−13.7730	+	8.63476i	−0.450667	+	0.282538i
$935$	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	$0.489394\pi$
$938$	5.69935	−	3.57310i	0.186090	−	0.116666i
$939$		0			0
$940$	−34.3273	−	16.6168i	−1.11963	−	0.541979i
$941$	35.2677			1.14969			0.574847	−	0.818261i	$-0.305062\pi$
$941$	35.2677			1.14969			0.574847	+	0.818261i	$0.305062\pi$
$942$		0			0
$943$	28.2370	+	16.3027i	0.919525	+	0.530888i
$944$	−13.0916	+	1.91913i	−0.426097	+	0.0624624i
$945$		0			0
$946$	−1.52652	+	0.957027i	−0.0496316	+	0.0311156i
$947$	12.6695	+	21.9442i	0.411702	+	0.713089i	0.995076	−	0.0991144i	$-0.0316010\pi$
$947$	12.6695	+	21.9442i	0.411702	+	0.713089i	−0.583374	+	0.812204i	$0.698268\pi$
$948$		0			0
$949$	1.68404	+	22.0871i	0.0546662	+	0.716976i
$950$	−8.93406	+	0.325244i	−0.289859	+	0.0105523i
$951$		0			0
$952$	23.0372	−	16.8945i	0.746640	−	0.547555i
$953$	−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
$956$	31.3268	+	15.1643i	1.01318	+	0.490449i
$957$		0			0
$958$	−5.41252	−	2.86760i	−0.174870	−	0.0926481i
$959$	39.9984	+	69.2793i	1.29162	+	2.23715i
$960$		0			0
$961$	29.8607			0.963250
$962$	−21.5403	+	49.4095i	−0.694486	+	1.59303i
$963$		0			0
$964$	−23.9112	+	16.2317i	−0.770128	+	0.522787i
$965$	−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	$-0.129435\pi$
$968$	−12.5081	+	28.4334i	−0.402027	+	0.913883i
$969$		0			0
$970$	0.685526	+	18.8306i	0.0220109	+	0.604614i
$971$	−16.8251	−	9.71399i	−0.539944	−	0.311737i	0.205112	−	0.978738i	$-0.434244\pi$
$971$	−16.8251	−	9.71399i	−0.539944	−	0.311737i	−0.745056	+	0.667002i	$0.767577\pi$
$972$		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
$982$	−22.9876	−	12.1790i	−0.733563	−	0.388649i
$983$			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
$986$	−7.01327	+	4.39685i	−0.223348	+	0.140024i
$987$		0			0
$988$	19.6716	+	24.7040i	0.625837	+	0.785940i
$989$			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	$0.796519\pi$
$992$	−5.68891	−	2.02297i	−0.180623	−	0.0642295i
$993$		0			0
$994$	21.6917	−	40.9424i	0.688019	−	1.29862i
$995$	−12.2540	+	21.2245i	−0.388477	+	0.672862i
$996$		0			0
$997$	17.0286	+	9.83147i	0.539301	+	0.311366i	0.744796	−	0.667293i	$-0.232547\pi$
$997$	17.0286	+	9.83147i	0.539301	+	0.311366i	−0.205494	+	0.978658i	$0.565880\pi$
$998$	−2.28305	−	3.64162i	−0.0722686	−	0.115273i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.751196 + 1.19821i) q^{2} +(-0.871409 + 1.80018i) q^{4} +1.88587 q^{5} +(3.80954 + 2.19944i) q^{7} +(-2.81159 + 0.308157i) q^{8} +(1.41666 + 2.25966i) q^{10} +(-0.0662772 - 0.114795i) q^{11} +(3.59512 - 0.274112i) q^{13} +(0.226324 + 6.21684i) q^{14} +(-2.48129 - 3.13739i) q^{16} +(-1.14806 + 1.98850i) q^{17} +(2.18964 - 3.79257i) q^{19} +(-1.64336 + 3.39490i) q^{20} +(0.0877618 - 0.165648i) q^{22} +(-1.97584 - 3.42225i) q^{23} -1.44351 q^{25} +(3.02908 + 4.10179i) q^{26} +(-7.27906 + 4.94125i) q^{28} +(2.20762 - 1.27457i) q^{29} -1.06736i q^{31} +(1.89531 - 5.32990i) q^{32} +(-3.24505 + 0.118136i) q^{34} +(7.18429 + 4.14785i) q^{35} +(5.28540 + 9.15458i) q^{37} +(6.18914 - 0.225315i) q^{38} +(-5.30228 + 0.581142i) q^{40} +(-7.14559 + 4.12551i) q^{41} +(-8.32354 - 4.80560i) q^{43} +(0.264407 - 0.0192770i) q^{44} +(2.61633 - 4.93825i) q^{46} +10.1114i q^{47} +(6.17508 + 10.6956i) q^{49} +(-1.08436 - 1.72962i) q^{50} +(-2.63937 + 6.71072i) q^{52} -8.28514i q^{53} +(-0.124990 - 0.216489i) q^{55} +(-11.3886 - 5.00999i) q^{56} +(3.18555 + 1.68774i) q^{58} +(1.65394 - 2.86472i) q^{59} +(-6.40470 - 3.69775i) q^{61} +(1.27892 - 0.801795i) q^{62} +(7.81008 - 1.73282i) q^{64} +(6.77991 - 0.516938i) q^{65} +(-0.540655 - 0.936442i) q^{67} +(-2.57922 - 3.79951i) q^{68} +(0.426816 + 11.7241i) q^{70} +(-6.45016 - 3.72400i) q^{71} +6.14363i q^{73} +(-6.99873 + 13.2099i) q^{74} +(4.91923 + 7.24662i) q^{76} -0.583091i q^{77} -15.9309 q^{79} +(-4.67938 - 5.91669i) q^{80} +(-10.3110 - 5.46284i) q^{82} +0.144468 q^{83} +(-2.16509 + 3.75004i) q^{85} +(-0.494498 - 13.5833i) q^{86} +(0.221719 + 0.302334i) q^{88} +(14.2114 - 8.20498i) q^{89} +(14.2986 + 6.86301i) q^{91} +(7.88243 - 0.574680i) q^{92} +(-12.1156 + 7.59567i) q^{94} +(4.12937 - 7.15228i) q^{95} +(6.11866 + 3.53261i) q^{97} +(-8.17682 + 15.4335i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 12 q^{7} - 4 q^{10} + 36 q^{14} - 2 q^{16} - 12 q^{17} - 54 q^{20} - 14 q^{22} - 20 q^{23} + 48 q^{25} + 42 q^{26} + 6 q^{28} + 28 q^{38} - 8 q^{40} + 12 q^{41} - 30 q^{46} + 16 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) \) 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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