LMFDB - Embedded newform 608.2.s.c.559.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [608,2,Mod(335,608)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(608, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 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("608.335"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.1
Character	$\chi$	$=$	608.559
Dual form			608.2.s.c.335.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.07624 - 1.19872i) q^{3} +(-0.418341 - 0.241529i) q^{5} +1.56686i q^{7} +(1.37385 + 2.37958i) q^{9} -1.24363 q^{11} +(1.80015 + 3.11796i) q^{13} +(0.579050 + 1.00294i) q^{15} +(-1.35570 + 2.34815i) q^{17} +(4.25703 - 0.936862i) q^{19} +(1.87822 - 3.25318i) q^{21} +(5.52533 - 3.19005i) q^{23} +(-2.38333 - 4.12804i) q^{25} +0.604878i q^{27} +(-0.695157 - 1.20405i) q^{29} +4.86016 q^{31} +(2.58207 + 1.49076i) q^{33} +(0.378442 - 0.655481i) q^{35} +10.9720 q^{37} -8.63150i q^{39} +(1.10008 + 0.635132i) q^{41} +(-4.78175 + 8.28223i) q^{43} -1.32730i q^{45} +(7.26763 - 4.19597i) q^{47} +4.54495 q^{49} +(5.62954 - 3.25022i) q^{51} +(1.50024 + 2.59849i) q^{53} +(0.520259 + 0.300372i) q^{55} +(-9.96165 - 3.15782i) q^{57} +(-4.43723 - 2.56184i) q^{59} +(9.42313 - 5.44044i) q^{61} +(-3.72846 + 2.15263i) q^{63} -1.73916i q^{65} +(3.22460 - 1.86172i) q^{67} -15.2959 q^{69} +(-6.62670 + 11.4778i) q^{71} +(-0.494526 + 0.856544i) q^{73} +11.4277i q^{75} -1.94859i q^{77} +(-5.81311 + 10.0686i) q^{79} +(4.84663 - 8.39460i) q^{81} +12.1949 q^{83} +(1.13429 - 0.654884i) q^{85} +3.33319i q^{87} +(-11.1625 + 6.44469i) q^{89} +(-4.88540 + 2.82059i) q^{91} +(-10.0909 - 5.82596i) q^{93} +(-2.00717 - 0.636268i) q^{95} +(2.42717 + 1.40133i) q^{97} +(-1.70855 - 2.95930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81}+ \cdots + 28 q^{99}+O(q^{100}) $ 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.07624	−	1.19872i	−1.19872	−	0.692080i	−0.238449	−	0.971155i	$-0.576639\pi$
$3$	−2.07624	−	1.19872i	−1.19872	−	0.692080i	−0.960269	+	0.279075i	$0.909972\pi$
$4$		0			0
$5$	−0.418341	−	0.241529i	−0.187088	−	0.108015i	0.403531	−	0.914966i	$-0.367783\pi$
$5$	−0.418341	−	0.241529i	−0.187088	−	0.108015i	−0.590618	+	0.806951i	$0.701116\pi$
$6$		0			0
$7$			1.56686i			0.592217i	0.955154	+	0.296109i	$0.0956891\pi$
$7$			1.56686i			0.592217i	−0.955154	+	0.296109i	$0.904311\pi$
$8$		0			0
$9$	1.37385	+	2.37958i	0.457950	+	0.793192i
$10$		0			0
$11$	−1.24363			−0.374967			−0.187484	−	0.982268i	$-0.560033\pi$
$11$	−1.24363			−0.374967			−0.187484	+	0.982268i	$0.560033\pi$
$12$		0			0
$13$	1.80015	+	3.11796i	0.499273	+	0.864766i	1.00000		0.000839577i	$-0.000267246\pi$
$13$	1.80015	+	3.11796i	0.499273	+	0.864766i	−0.500727	+	0.865605i	$0.666934\pi$
$14$		0			0
$15$	0.579050	+	1.00294i	0.149510	+	0.258959i
$16$		0			0
$17$	−1.35570	+	2.34815i	−0.328807	+	0.569510i	−0.982275	−	0.187444i	$-0.939980\pi$
$17$	−1.35570	+	2.34815i	−0.328807	+	0.569510i	0.653469	+	0.756954i	$0.273313\pi$
$18$		0			0
$19$	4.25703	−	0.936862i	0.976629	−	0.214931i
$19$	4.25703	−	0.936862i	0.976629	−	0.214931i
$20$		0			0
$21$	1.87822	−	3.25318i	0.409862	−	0.709901i
$22$		0			0
$23$	5.52533	−	3.19005i	1.15211	−	0.665171i	0.202710	−	0.979239i	$-0.435025\pi$
$23$	5.52533	−	3.19005i	1.15211	−	0.665171i	0.949401	+	0.314068i	$0.101692\pi$
$24$		0			0
$25$	−2.38333	−	4.12804i	−0.476665	−	0.825609i
$26$		0			0
$27$			0.604878i			0.116409i
$28$		0			0
$29$	−0.695157	−	1.20405i	−0.129087	−	0.223586i	0.794236	−	0.607610i	$-0.207871\pi$
$29$	−0.695157	−	1.20405i	−0.129087	−	0.223586i	−0.923323	+	0.384024i	$0.874538\pi$
$30$		0			0
$31$	4.86016			0.872910			0.436455	−	0.899726i	$-0.356234\pi$
$31$	4.86016			0.872910			0.436455	+	0.899726i	$0.356234\pi$
$32$		0			0
$33$	2.58207	+	1.49076i	0.449480	+	0.259507i
$34$		0			0
$35$	0.378442	−	0.655481i	0.0639684	−	0.110797i
$36$		0			0
$37$	10.9720			1.80379			0.901894	−	0.431957i	$-0.142177\pi$
$37$	10.9720			1.80379			0.901894	+	0.431957i	$0.142177\pi$
$38$		0			0
$39$		−	8.63150i		−	1.38215i
$40$		0			0
$41$	1.10008	+	0.635132i	0.171804	+	0.0991909i	0.583436	−	0.812159i	$-0.301708\pi$
$41$	1.10008	+	0.635132i	0.171804	+	0.0991909i	−0.411632	+	0.911350i	$0.635041\pi$
$42$		0			0
$43$	−4.78175	+	8.28223i	−0.729210	+	1.26303i	0.228008	+	0.973659i	$0.426779\pi$
$43$	−4.78175	+	8.28223i	−0.729210	+	1.26303i	−0.957218	+	0.289369i	$0.906554\pi$
$44$		0			0
$45$		−	1.32730i		−	0.197862i
$46$		0			0
$47$	7.26763	−	4.19597i	1.06009	−	0.612045i	0.134635	−	0.990895i	$-0.457014\pi$
$47$	7.26763	−	4.19597i	1.06009	−	0.612045i	0.925458	+	0.378850i	$0.123680\pi$
$48$		0			0
$49$	4.54495			0.649279
$50$		0			0
$51$	5.62954	−	3.25022i	0.788293	−	0.455121i
$52$		0			0
$53$	1.50024	+	2.59849i	0.206074	+	0.356930i	0.950474	−	0.310803i	$-0.100598\pi$
$53$	1.50024	+	2.59849i	0.206074	+	0.356930i	−0.744400	+	0.667733i	$0.767265\pi$
$54$		0			0
$55$	0.520259	+	0.300372i	0.0701517	+	0.0405021i
$56$		0			0
$57$	−9.96165	−	3.15782i	−1.31945	−	0.418264i
$58$		0			0
$59$	−4.43723	−	2.56184i	−0.577678	−	0.333523i	0.182532	−	0.983200i	$-0.441571\pi$
$59$	−4.43723	−	2.56184i	−0.577678	−	0.333523i	−0.760210	+	0.649677i	$0.774904\pi$
$60$		0			0
$61$	9.42313	−	5.44044i	1.20651	−	0.696578i	0.244513	−	0.969646i	$-0.421372\pi$
$61$	9.42313	−	5.44044i	1.20651	−	0.696578i	0.961995	+	0.273068i	$0.0880385\pi$
$62$		0			0
$63$	−3.72846	+	2.15263i	−0.469742	+	0.271206i
$64$		0			0
$65$		−	1.73916i		−	0.215716i
$66$		0			0
$67$	3.22460	−	1.86172i	0.393947	−	0.227446i	−0.289922	−	0.957050i	$-0.593629\pi$
$67$	3.22460	−	1.86172i	0.393947	−	0.227446i	0.683869	+	0.729605i	$0.260296\pi$
$68$		0			0
$69$	−15.2959			−1.84141
$70$		0			0
$71$	−6.62670	+	11.4778i	−0.786444	+	1.36216i	0.141688	+	0.989911i	$0.454747\pi$
$71$	−6.62670	+	11.4778i	−0.786444	+	1.36216i	−0.928132	+	0.372250i	$0.878586\pi$
$72$		0			0
$73$	−0.494526	+	0.856544i	−0.0578799	+	0.100251i	−0.893514	−	0.449036i	$-0.851767\pi$
$73$	−0.494526	+	0.856544i	−0.0578799	+	0.100251i	0.835634	+	0.549287i	$0.185101\pi$
$74$		0			0
$75$			11.4277i			1.31956i
$76$		0			0
$77$		−	1.94859i		−	0.222062i
$78$		0			0
$79$	−5.81311	+	10.0686i	−0.654026	+	1.13281i	0.328111	+	0.944639i	$0.393588\pi$
$79$	−5.81311	+	10.0686i	−0.654026	+	1.13281i	−0.982137	+	0.188168i	$0.939745\pi$
$80$		0			0
$81$	4.84663	−	8.39460i	0.538514	−	0.932733i
$82$		0			0
$83$	12.1949			1.33856			0.669280	−	0.743010i	$-0.266603\pi$
$83$	12.1949			1.33856			0.669280	+	0.743010i	$0.266603\pi$
$84$		0			0
$85$	1.13429	−	0.654884i	0.123031	−	0.0710322i
$86$		0			0
$87$			3.33319i			0.357355i
$88$		0			0
$89$	−11.1625	+	6.44469i	−1.18323	+	0.683136i	−0.956759	−	0.290883i	$-0.906051\pi$
$89$	−11.1625	+	6.44469i	−1.18323	+	0.683136i	−0.226467	+	0.974019i	$0.572718\pi$
$90$		0			0
$91$	−4.88540	+	2.82059i	−0.512129	+	0.295678i
$92$		0			0
$93$	−10.0909	−	5.82596i	−1.04637	−	0.604124i
$94$		0			0
$95$	−2.00717	−	0.636268i	−0.205931	−	0.0652798i
$96$		0			0
$97$	2.42717	+	1.40133i	0.246442	+	0.142283i	0.618134	−	0.786073i	$-0.287889\pi$
$97$	2.42717	+	1.40133i	0.246442	+	0.142283i	−0.371692	+	0.928356i	$0.621222\pi$
$98$		0			0
$99$	−1.70855	−	2.95930i	−0.171716	−	0.297421i
$100$		0			0
$101$	−0.655955	+	0.378716i	−0.0652700	+	0.0376837i	−0.532280	−	0.846568i	$-0.678665\pi$
$101$	−0.655955	+	0.378716i	−0.0652700	+	0.0376837i	0.467010	+	0.884252i	$0.345331\pi$
$102$		0			0
$103$	−4.06152			−0.400193			−0.200097	−	0.979776i	$-0.564126\pi$
$103$	−4.06152			−0.400193			−0.200097	+	0.979776i	$0.564126\pi$
$104$		0			0
$105$	−1.57147	+	0.907291i	−0.153360	+	0.0885425i
$106$		0			0
$107$		−	4.15320i		−	0.401505i	−0.979642	−	0.200753i	$-0.935661\pi$
$107$		−	4.15320i		−	0.401505i	0.979642	−	0.200753i	$-0.0643388\pi$
$108$		0			0
$109$	−9.07011	+	15.7099i	−0.868759	+	1.50473i	−0.00549325	+	0.999985i	$0.501749\pi$
$109$	−9.07011	+	15.7099i	−0.868759	+	1.50473i	−0.863266	+	0.504750i	$0.831585\pi$
$110$		0			0
$111$	−22.7805	−	13.1523i	−2.16223	−	1.24837i
$112$		0			0
$113$		−	7.00334i		−	0.658819i	−0.944187	−	0.329409i	$-0.893150\pi$
$113$		−	7.00334i		−	0.658819i	0.944187	−	0.329409i	$-0.106850\pi$
$114$		0			0
$115$	−3.08196			−0.287394
$116$		0			0
$117$	−4.94628	+	8.56720i	−0.457284	+	0.792038i
$118$		0			0
$119$	−3.67922	−	2.12420i	−0.337274	−	0.194725i
$120$		0			0
$121$	−9.45340			−0.859400
$122$		0			0
$123$	−1.52269	−	2.63737i	−0.137296	−	0.237804i
$124$		0			0
$125$			4.71786i			0.421978i
$126$		0			0
$127$	7.61514	+	13.1898i	0.675734	+	1.17041i	0.976254	+	0.216630i	$0.0695065\pi$
$127$	7.61514	+	13.1898i	0.675734	+	1.17041i	−0.300520	+	0.953776i	$0.597160\pi$
$128$		0			0
$129$	19.8561	−	11.4639i	1.74823	−	1.00934i
$130$		0			0
$131$	4.14342	−	7.17662i	0.362012	−	0.627024i	−0.626279	−	0.779599i	$-0.715423\pi$
$131$	4.14342	−	7.17662i	0.362012	−	0.627024i	0.988292	+	0.152575i	$0.0487564\pi$
$132$		0			0
$133$	1.46793	+	6.67017i	0.127286	+	0.578377i
$134$		0			0
$135$	0.146096	−	0.253045i	0.0125739	−	0.0217787i
$136$		0			0
$137$	8.90976	+	15.4322i	0.761212	+	1.31846i	0.942226	+	0.334978i	$0.108729\pi$
$137$	8.90976	+	15.4322i	0.761212	+	1.31846i	−0.181013	+	0.983481i	$0.557938\pi$
$138$		0			0
$139$	−4.16150	−	7.20793i	−0.352974	−	0.611368i	0.633795	−	0.773501i	$-0.281496\pi$
$139$	−4.16150	−	7.20793i	−0.352974	−	0.611368i	−0.986769	+	0.162132i	$0.948163\pi$
$140$		0			0
$141$	−20.1191			−1.69434
$142$		0			0
$143$	−2.23872	−	3.87757i	−0.187211	−	0.324259i
$144$		0			0
$145$			0.671602i			0.0557735i
$146$		0			0
$147$	−9.43641	−	5.44811i	−0.778302	−	0.449353i
$148$		0			0
$149$	−16.0928	−	9.29117i	−1.31837	−	0.761162i	−0.334905	−	0.942252i	$-0.608704\pi$
$149$	−16.0928	−	9.29117i	−1.31837	−	0.761162i	−0.983467	+	0.181090i	$0.942037\pi$
$150$		0			0
$151$	4.56745			0.371694			0.185847	−	0.982579i	$-0.440497\pi$
$151$	4.56745			0.371694			0.185847	+	0.982579i	$0.440497\pi$
$152$		0			0
$153$	−7.45013			−0.602308
$154$		0			0
$155$	−2.03320	−	1.17387i	−0.163311	−	0.0942875i
$156$		0			0
$157$	16.0994	+	9.29499i	1.28487	+	0.741821i	0.977735	−	0.209844i	$-0.0672957\pi$
$157$	16.0994	+	9.29499i	1.28487	+	0.741821i	0.307137	+	0.951665i	$0.400629\pi$
$158$		0			0
$159$		−	7.19346i		−	0.570479i
$160$		0			0
$161$	4.99836	+	8.65741i	0.393926	+	0.682300i
$162$		0			0
$163$	−13.2618			−1.03874			−0.519370	−	0.854549i	$-0.673833\pi$
$163$	−13.2618			−1.03874			−0.519370	+	0.854549i	$0.673833\pi$
$164$		0			0
$165$	−0.720122	−	1.24729i	−0.0560614	−	0.0971012i
$166$		0			0
$167$	5.01139	+	8.67998i	0.387793	+	0.671677i	0.992152	−	0.125035i	$-0.0399042\pi$
$167$	5.01139	+	8.67998i	0.387793	+	0.671677i	−0.604359	+	0.796712i	$0.706571\pi$
$168$		0			0
$169$	0.0188953	−	0.0327276i	0.00145348	−	0.00251751i
$170$		0			0
$171$	8.07785	+	8.84281i	0.617729	+	0.676227i
$172$		0			0
$173$	7.75097	−	13.4251i	0.589296	−	1.02069i	−0.405029	−	0.914304i	$-0.632739\pi$
$173$	7.75097	−	13.4251i	0.589296	−	1.02069i	0.994325	−	0.106386i	$-0.0339280\pi$
$174$		0			0
$175$	6.46807	−	3.73434i	0.488940	−	0.282290i
$176$		0			0
$177$	6.14184	+	10.6380i	0.461649	+	0.799599i
$178$		0			0
$179$		−	2.86093i		−	0.213836i	−0.994268	−	0.106918i	$-0.965902\pi$
$179$		−	2.86093i		−	0.213836i	0.994268	−	0.106918i	$-0.0340982\pi$
$180$		0			0
$181$	−0.305140	−	0.528519i	−0.0226809	−	0.0392845i	0.854462	−	0.519514i	$-0.173887\pi$
$181$	−0.305140	−	0.528519i	−0.0226809	−	0.0392845i	−0.877143	+	0.480229i	$0.840554\pi$
$182$		0			0
$183$	−26.0862			−1.92835
$184$		0			0
$185$	−4.59004	−	2.65006i	−0.337466	−	0.194836i
$186$		0			0
$187$	1.68599	−	2.92022i	0.123292	−	0.213548i
$188$		0			0
$189$	−0.947760			−0.0689394
$190$		0			0
$191$		−	21.9035i		−	1.58488i	−0.609947	−	0.792442i	$-0.708809\pi$
$191$		−	21.9035i		−	1.58488i	0.609947	−	0.792442i	$-0.291191\pi$
$192$		0			0
$193$	4.60435	+	2.65832i	0.331428	+	0.191350i	0.656475	−	0.754348i	$-0.272047\pi$
$193$	4.60435	+	2.65832i	0.331428	+	0.191350i	−0.325047	+	0.945698i	$0.605380\pi$
$194$		0			0
$195$	−2.08476	+	3.61091i	−0.149293	+	0.258583i
$196$		0			0
$197$		−	0.913518i		−	0.0650855i	−0.999470	−	0.0325427i	$-0.989639\pi$
$197$		−	0.913518i		−	0.0650855i	0.999470	−	0.0325427i	$-0.0103605\pi$
$198$		0			0
$199$	17.3763	−	10.0322i	1.23177	−	0.711164i	0.264373	−	0.964421i	$-0.414835\pi$
$199$	17.3763	−	10.0322i	1.23177	−	0.711164i	0.967399	+	0.253257i	$0.0815017\pi$
$200$		0			0
$201$	−8.92672			−0.629642
$202$		0			0
$203$	1.88657	−	1.08921i	0.132411	−	0.0764478i
$204$		0			0
$205$	−0.306806	−	0.531403i	−0.0214282	−	0.0371148i
$206$		0			0
$207$	15.1819	+	8.76529i	1.05522	+	0.609230i
$208$		0			0
$209$	−5.29415	+	1.16511i	−0.366204	+	0.0805921i
$210$		0			0
$211$	21.5716	+	12.4544i	1.48505	+	0.857394i	0.999855	−	0.0170124i	$-0.00541549\pi$
$211$	21.5716	+	12.4544i	1.48505	+	0.857394i	0.485194	+	0.874406i	$0.338749\pi$
$212$		0			0
$213$	27.5172	−	15.8871i	1.88545	−	1.08856i
$214$		0			0
$215$	4.00080	−	2.30986i	0.272852	−	0.157531i
$216$		0			0
$217$			7.61519i			0.516953i
$218$		0			0
$219$	2.05351	−	1.18559i	0.138763	−	0.0801151i
$220$		0			0
$221$	−9.76191			−0.656657
$222$		0			0
$223$	−1.75003	+	3.03114i	−0.117191	+	0.202980i	−0.918653	−	0.395065i	$-0.870722\pi$
$223$	−1.75003	+	3.03114i	−0.117191	+	0.202980i	0.801463	+	0.598045i	$0.204056\pi$
$224$		0			0
$225$	6.54866	−	11.3426i	0.436578	−	0.756175i
$226$		0			0
$227$		−	5.29383i		−	0.351364i	−0.984447	−	0.175682i	$-0.943787\pi$
$227$		−	5.29383i		−	0.351364i	0.984447	−	0.175682i	$-0.0562130\pi$
$228$		0			0
$229$			1.20868i			0.0798721i	0.999202	+	0.0399360i	$0.0127154\pi$
$229$			1.20868i			0.0798721i	−0.999202	+	0.0399360i	$0.987285\pi$
$230$		0			0
$231$	−2.33581	+	4.04573i	−0.153685	+	0.266190i
$232$		0			0
$233$	5.58944	−	9.68119i	0.366176	−	0.634236i	−0.622788	−	0.782391i	$-0.714000\pi$
$233$	5.58944	−	9.68119i	0.366176	−	0.634236i	0.988964	+	0.148155i	$0.0473334\pi$
$234$		0			0
$235$	−4.05380			−0.264440
$236$		0			0
$237$	24.1388	−	13.9366i	1.56799	−	0.905277i
$238$		0			0
$239$			20.3237i			1.31463i	0.753615	+	0.657317i	$0.228309\pi$
$239$			20.3237i			1.31463i	−0.753615	+	0.657317i	$0.771691\pi$
$240$		0			0
$241$	5.48096	−	3.16443i	0.353060	−	0.203839i	−0.312972	−	0.949762i	$-0.601325\pi$
$241$	5.48096	−	3.16443i	0.353060	−	0.203839i	0.666032	+	0.745923i	$0.267991\pi$
$242$		0			0
$243$	−18.5540	+	10.7122i	−1.19024	+	0.687185i
$244$		0			0
$245$	−1.90134	−	1.09774i	−0.121472	−	0.0701319i
$246$		0			0
$247$	10.5844	+	11.5867i	0.673469	+	0.737246i
$248$		0			0
$249$	−25.3195	−	14.6182i	−1.60456	−	0.926391i
$250$		0			0
$251$	−12.1536	−	21.0507i	−0.767131	−	1.32871i	−0.939113	−	0.343609i	$-0.888350\pi$
$251$	−12.1536	−	21.0507i	−0.767131	−	1.32871i	0.171982	−	0.985100i	$-0.444983\pi$
$252$		0			0
$253$	−6.87144	+	3.96723i	−0.432004	+	0.249417i
$254$		0			0
$255$	−3.14009			−0.196640
$256$		0			0
$257$	7.08286	−	4.08929i	0.441817	−	0.255083i	−0.262551	−	0.964918i	$-0.584564\pi$
$257$	7.08286	−	4.08929i	0.441817	−	0.255083i	0.704368	+	0.709835i	$0.251231\pi$
$258$		0			0
$259$			17.1916i			1.06823i
$260$		0			0
$261$	1.91008	−	3.30836i	0.118231	−	0.204782i
$262$		0			0
$263$	−19.0322	−	10.9882i	−1.17358	−	0.677564i	−0.219056	−	0.975712i	$-0.570298\pi$
$263$	−19.0322	−	10.9882i	−1.17358	−	0.677564i	−0.954520	+	0.298148i	$0.903631\pi$
$264$		0			0
$265$		−	1.44941i		−	0.0890364i
$266$		0			0
$267$	30.9015			1.89114
$268$		0			0
$269$	1.94226	−	3.36410i	0.118422	−	0.205113i	−0.800721	−	0.599038i	$-0.795550\pi$
$269$	1.94226	−	3.36410i	0.118422	−	0.205113i	0.919142	+	0.393925i	$0.128883\pi$
$270$		0			0
$271$	1.81233	+	1.04635i	0.110091	+	0.0635611i	0.554035	−	0.832494i	$-0.313088\pi$
$271$	1.81233	+	1.04635i	0.110091	+	0.0635611i	−0.443943	+	0.896055i	$0.646421\pi$
$272$		0			0
$273$	13.5244			0.818531
$274$		0			0
$275$	2.96397	+	5.13374i	0.178734	+	0.309576i
$276$		0			0
$277$			27.8262i			1.67191i	0.548797	+	0.835956i	$0.315086\pi$
$277$			27.8262i			1.67191i	−0.548797	+	0.835956i	$0.684914\pi$
$278$		0			0
$279$	6.67712	+	11.5651i	0.399749	+	0.692385i
$280$		0			0
$281$	−20.0761	+	11.5910i	−1.19764	+	0.691458i	−0.960029	−	0.279902i	$-0.909698\pi$
$281$	−20.0761	+	11.5910i	−1.19764	+	0.691458i	−0.237612	+	0.971360i	$0.576365\pi$
$282$		0			0
$283$	−1.40718	+	2.43730i	−0.0836480	+	0.144883i	−0.904814	−	0.425806i	$-0.859990\pi$
$283$	−1.40718	+	2.43730i	−0.0836480	+	0.144883i	0.821166	+	0.570689i	$0.193324\pi$
$284$		0			0
$285$	3.40466	+	3.72707i	0.201674	+	0.220773i
$286$		0			0
$287$	−0.995162	+	1.72367i	−0.0587426	+	0.101745i
$288$		0			0
$289$	4.82413	+	8.35564i	0.283772	+	0.491508i
$290$		0			0
$291$	−3.35959	−	5.81899i	−0.196943	−	0.341115i
$292$		0			0
$293$	−8.65633			−0.505708			−0.252854	−	0.967504i	$-0.581369\pi$
$293$	−8.65633			−0.505708			−0.252854	+	0.967504i	$0.581369\pi$
$294$		0			0
$295$	1.23752	+	2.14344i	0.0720510	+	0.124796i
$296$		0			0
$297$		−	0.752242i		−	0.0436495i
$298$		0			0
$299$	19.8929	+	11.4852i	1.15043	+	0.664204i
$300$		0			0
$301$	−12.9771	−	7.49233i	−0.747987	−	0.431851i
$302$		0			0
$303$	1.81589			0.104320
$304$		0			0
$305$	−5.25610			−0.300964
$306$		0			0
$307$	−8.98393	−	5.18688i	−0.512740	−	0.296031i	0.221219	−	0.975224i	$-0.428996\pi$
$307$	−8.98393	−	5.18688i	−0.512740	−	0.296031i	−0.733959	+	0.679194i	$0.762330\pi$
$308$		0			0
$309$	8.43268	+	4.86861i	0.479719	+	0.276966i
$310$		0			0
$311$		−	20.7808i		−	1.17837i	−0.807997	−	0.589186i	$-0.799449\pi$
$311$		−	20.7808i		−	1.17837i	0.807997	−	0.589186i	$-0.200551\pi$
$312$		0			0
$313$	−11.9901	−	20.7674i	−0.677720	−	1.17384i	−0.975666	−	0.219262i	$-0.929635\pi$
$313$	−11.9901	−	20.7674i	−0.677720	−	1.17384i	0.297946	−	0.954583i	$-0.403698\pi$
$314$		0			0
$315$	2.07969			0.117177
$316$		0			0
$317$	9.45498	+	16.3765i	0.531045	+	0.919797i	0.999344	+	0.0362265i	$0.0115338\pi$
$317$	9.45498	+	16.3765i	0.531045	+	0.919797i	−0.468299	+	0.883570i	$0.655133\pi$
$318$		0			0
$319$	0.864515	+	1.49738i	0.0484035	+	0.0838374i
$320$		0			0
$321$	−4.97852	+	8.62305i	−0.277874	+	0.481292i
$322$		0			0
$323$	−3.57138	+	11.2662i	−0.198717	+	0.626871i
$324$		0			0
$325$	8.58071	−	14.8622i	0.475972	−	0.824408i
$326$		0			0
$327$	37.6635	−	21.7450i	2.08279	−	1.20250i
$328$		0			0
$329$	6.57450	+	11.3874i	0.362464	+	0.627806i
$330$		0			0
$331$		−	15.9594i		−	0.877208i	−0.898680	−	0.438604i	$-0.855473\pi$
$331$		−	15.9594i		−	0.877208i	0.898680	−	0.438604i	$-0.144527\pi$
$332$		0			0
$333$	15.0739	+	26.1087i	0.826044	+	1.43075i
$334$		0			0
$335$	−1.79864			−0.0982702
$336$		0			0
$337$	−21.3485	−	12.3256i	−1.16293	−	0.671418i	−0.210925	−	0.977502i	$-0.567648\pi$
$337$	−21.3485	−	12.3256i	−1.16293	−	0.671418i	−0.952004	+	0.306085i	$0.900981\pi$
$338$		0			0
$339$	−8.39503	+	14.5406i	−0.455955	+	0.789738i
$340$		0			0
$341$	−6.04422			−0.327313
$342$		0			0
$343$			18.0893i			0.976731i
$344$		0			0
$345$	6.39889	+	3.69440i	0.344504	+	0.198900i
$346$		0			0
$347$	−4.57443	+	7.92314i	−0.245568	+	0.425336i	−0.962291	−	0.272022i	$-0.912308\pi$
$347$	−4.57443	+	7.92314i	−0.245568	+	0.425336i	0.716723	+	0.697358i	$0.245641\pi$
$348$		0			0
$349$		−	17.8070i		−	0.953189i	−0.879123	−	0.476595i	$-0.841871\pi$
$349$		−	17.8070i		−	0.953189i	0.879123	−	0.476595i	$-0.158129\pi$
$350$		0			0
$351$	−1.88599	+	1.08887i	−0.100666	+	0.0581198i
$352$		0			0
$353$	23.3856			1.24469			0.622344	−	0.782744i	$-0.286181\pi$
$353$	23.3856			1.24469			0.622344	+	0.782744i	$0.286181\pi$
$354$		0			0
$355$	5.54443	−	3.20108i	0.294268	−	0.169896i
$356$		0			0
$357$	5.09263	+	8.82070i	0.269531	+	0.466841i
$358$		0			0
$359$	−11.4051	−	6.58476i	−0.601940	−	0.347530i	0.167864	−	0.985810i	$-0.446313\pi$
$359$	−11.4051	−	6.58476i	−0.601940	−	0.347530i	−0.769805	+	0.638280i	$0.779646\pi$
$360$		0			0
$361$	17.2446	−	7.97650i	0.907609	−	0.419816i
$362$		0			0
$363$	19.6275	+	11.3320i	1.03018	+	0.594773i
$364$		0			0
$365$	0.413761	−	0.238885i	0.0216572	−	0.0125038i
$366$		0			0
$367$	13.2710	−	7.66199i	0.692738	−	0.399953i	−0.111899	−	0.993720i	$-0.535693\pi$
$367$	13.2710	−	7.66199i	0.692738	−	0.399953i	0.804637	+	0.593767i	$0.202360\pi$
$368$		0			0
$369$			3.49030i			0.181698i
$370$		0			0
$371$	−4.07147	+	2.35067i	−0.211380	+	0.122041i
$372$		0			0
$373$	−8.33115			−0.431370			−0.215685	−	0.976463i	$-0.569199\pi$
$373$	−8.33115			−0.431370			−0.215685	+	0.976463i	$0.569199\pi$
$374$		0			0
$375$	5.65539	−	9.79541i	0.292043	−	0.505833i
$376$		0			0
$377$	2.50278	−	4.33494i	0.128900	−	0.223261i
$378$		0			0
$379$		−	10.4481i		−	0.536682i	−0.963324	−	0.268341i	$-0.913525\pi$
$379$		−	10.4481i		−	0.536682i	0.963324	−	0.268341i	$-0.0864754\pi$
$380$		0			0
$381$		−	36.5136i		−	1.87065i
$382$		0			0
$383$	−4.22512	+	7.31812i	−0.215893	+	0.373938i	−0.953549	−	0.301239i	$-0.902600\pi$
$383$	−4.22512	+	7.31812i	−0.215893	+	0.373938i	0.737655	+	0.675178i	$0.235933\pi$
$384$		0			0
$385$	−0.470640	+	0.815173i	−0.0239861	+	0.0415451i
$386$		0			0
$387$	−26.2776			−1.33577
$388$		0			0
$389$	5.29150	−	3.05505i	0.268290	−	0.154897i	−0.359820	−	0.933022i	$-0.617162\pi$
$389$	5.29150	−	3.05505i	0.268290	−	0.154897i	0.628110	+	0.778124i	$0.283829\pi$
$390$		0			0
$391$			17.2991i			0.874851i
$392$		0			0
$393$	−17.2055	+	9.93359i	−0.867902	+	0.501083i
$394$		0			0
$395$	4.86372	−	2.80807i	0.244720	−	0.141289i
$396$		0			0
$397$	19.5160	+	11.2676i	0.979481	+	0.565504i	0.902113	−	0.431499i	$-0.142015\pi$
$397$	19.5160	+	11.2676i	0.979481	+	0.565504i	0.0773678	+	0.997003i	$0.475348\pi$
$398$		0			0
$399$	4.94787	−	15.6085i	0.247703	−	0.781403i
$400$		0			0
$401$	−1.59335	−	0.919919i	−0.0795679	−	0.0459386i	0.459688	−	0.888080i	$-0.347961\pi$
$401$	−1.59335	−	0.919919i	−0.0795679	−	0.0459386i	−0.539256	+	0.842142i	$0.681295\pi$
$402$		0			0
$403$	8.74903	+	15.1538i	0.435820	+	0.754863i
$404$		0			0
$405$	−4.05508	+	2.34120i	−0.201499	+	0.116335i
$406$		0			0
$407$	−13.6451			−0.676361
$408$		0			0
$409$	−31.6805	+	18.2907i	−1.56650	+	0.904418i	−0.569925	+	0.821696i	$0.693028\pi$
$409$	−31.6805	+	18.2907i	−1.56650	+	0.904418i	−0.996573	+	0.0827216i	$0.973639\pi$
$410$		0			0
$411$		−	42.7212i		−	2.10728i
$412$		0			0
$413$	4.01404	−	6.95252i	0.197518	−	0.342111i
$414$		0			0
$415$	−5.10161	−	2.94542i	−0.250428	−	0.144585i
$416$		0			0
$417$			19.9539i			0.977144i
$418$		0			0
$419$	−4.03779			−0.197259			−0.0986294	−	0.995124i	$-0.531446\pi$
$419$	−4.03779			−0.197259			−0.0986294	+	0.995124i	$0.531446\pi$
$420$		0			0
$421$	−3.23520	+	5.60354i	−0.157674	+	0.273100i	−0.934030	−	0.357196i	$-0.883733\pi$
$421$	−3.23520	+	5.60354i	−0.157674	+	0.273100i	0.776355	+	0.630295i	$0.217066\pi$
$422$		0			0
$423$	19.9693	+	11.5293i	0.970939	+	0.560572i
$424$		0			0
$425$	12.9244			0.626923
$426$		0			0
$427$	8.52441	+	14.7647i	0.412525	+	0.714515i
$428$		0			0
$429$			10.7344i			0.518260i
$430$		0			0
$431$	−3.17434	−	5.49811i	−0.152902	−	0.264835i	0.779391	−	0.626538i	$-0.215529\pi$
$431$	−3.17434	−	5.49811i	−0.152902	−	0.264835i	−0.932293	+	0.361703i	$0.882195\pi$
$432$		0			0
$433$	20.1286	−	11.6213i	0.967320	−	0.558482i	0.0689019	−	0.997623i	$-0.478050\pi$
$433$	20.1286	−	11.6213i	0.967320	−	0.558482i	0.898418	+	0.439141i	$0.144717\pi$
$434$		0			0
$435$	0.805062	−	1.39441i	0.0385997	−	0.0668567i
$436$		0			0
$437$	20.5328	−	18.7566i	0.982219	−	0.897250i
$438$		0			0
$439$	5.22682	−	9.05312i	0.249462	−	0.432082i	−0.713914	−	0.700233i	$-0.753079\pi$
$439$	5.22682	−	9.05312i	0.249462	−	0.432082i	0.963377	+	0.268151i	$0.0864127\pi$
$440$		0			0
$441$	6.24408	+	10.8151i	0.297337	+	0.515003i
$442$		0			0
$443$	−7.15226	−	12.3881i	−0.339814	−	0.588575i	0.644584	−	0.764534i	$-0.277031\pi$
$443$	−7.15226	−	12.3881i	−0.339814	−	0.588575i	−0.984398	+	0.175959i	$0.943697\pi$
$444$		0			0
$445$	6.22632			0.295156
$446$		0			0
$447$	22.2750	+	38.5814i	1.05357	+	1.82484i
$448$		0			0
$449$		−	35.1956i		−	1.66098i	−0.557030	−	0.830492i	$-0.688059\pi$
$449$		−	35.1956i		−	1.66098i	0.557030	−	0.830492i	$-0.311941\pi$
$450$		0			0
$451$	−1.36809	−	0.789866i	−0.0644208	−	0.0371933i
$452$		0			0
$453$	−9.48312	−	5.47508i	−0.445556	−	0.257242i
$454$		0			0
$455$	2.72502			0.127751
$456$		0			0
$457$	5.76335			0.269598			0.134799	−	0.990873i	$-0.456961\pi$
$457$	5.76335			0.269598			0.134799	+	0.990873i	$0.456961\pi$
$458$		0			0
$459$	−1.42035	−	0.820037i	−0.0662960	−	0.0382760i
$460$		0			0
$461$	−23.7050	−	13.6861i	−1.10405	−	0.637424i	−0.166769	−	0.985996i	$-0.553333\pi$
$461$	−23.7050	−	13.6861i	−1.10405	−	0.637424i	−0.937282	+	0.348572i	$0.886667\pi$
$462$		0			0
$463$		−	9.63243i		−	0.447657i	−0.974629	−	0.223828i	$-0.928144\pi$
$463$		−	9.63243i		−	0.447657i	0.974629	−	0.223828i	$-0.0718555\pi$
$464$		0			0
$465$	2.81428	+	4.87447i	0.130509	+	0.226048i
$466$		0			0
$467$	−14.1545			−0.654992			−0.327496	−	0.944853i	$-0.606205\pi$
$467$	−14.1545			−0.654992			−0.327496	+	0.944853i	$0.606205\pi$
$468$		0			0
$469$	2.91706	+	5.05249i	0.134697	+	0.233302i
$470$		0			0
$471$	−22.2841	−	38.5973i	−1.02680	−	1.77847i
$472$		0			0
$473$	5.94671	−	10.3000i	0.273430	−	0.473594i
$474$		0			0
$475$	−14.0133	−	15.3404i	−0.642974	−	0.703864i
$476$		0			0
$477$	−4.12221	+	7.13987i	−0.188743	+	0.326912i
$478$		0			0
$479$	20.5947	−	11.8903i	0.940995	−	0.543284i	0.0507227	−	0.998713i	$-0.483848\pi$
$479$	20.5947	−	11.8903i	0.940995	−	0.543284i	0.890272	+	0.455429i	$0.150514\pi$
$480$		0			0
$481$	19.7513	+	34.2103i	0.900582	+	1.55985i
$482$		0			0
$483$		−	23.9665i		−	1.09051i
$484$		0			0
$485$	−0.676923	−	1.17246i	−0.0307375	−	0.0532389i
$486$		0			0
$487$	−7.31176			−0.331327			−0.165664	−	0.986182i	$-0.552977\pi$
$487$	−7.31176			−0.331327			−0.165664	+	0.986182i	$0.552977\pi$
$488$		0			0
$489$	27.5346	+	15.8971i	1.24516	+	0.718892i
$490$		0			0
$491$	−7.42662	+	12.8633i	−0.335159	+	0.580512i	−0.983515	−	0.180825i	$-0.942123\pi$
$491$	−7.42662	+	12.8633i	−0.335159	+	0.580512i	0.648357	+	0.761337i	$0.275457\pi$
$492$		0			0
$493$	3.76971			0.169779
$494$		0			0
$495$			1.65066i			0.0741917i
$496$		0			0
$497$	−17.9841	−	10.3831i	−0.806696	−	0.465746i
$498$		0			0
$499$	1.07280	−	1.85814i	0.0480251	−	0.0831819i	−0.841014	−	0.541014i	$-0.818041\pi$
$499$	1.07280	−	1.85814i	0.0480251	−	0.0831819i	0.889039	+	0.457832i	$0.151374\pi$
$500$		0			0
$501$		−	24.0290i		−	1.07353i
$502$		0			0
$503$	−17.1288	+	9.88932i	−0.763736	+	0.440943i	−0.830635	−	0.556817i	$-0.812023\pi$
$503$	−17.1288	+	9.88932i	−0.763736	+	0.440943i	0.0668997	+	0.997760i	$0.478689\pi$
$504$		0			0
$505$	0.365884			0.0162816
$506$		0			0
$507$	−0.0784624	+	0.0453003i	−0.00348464	+	0.00201186i
$508$		0			0
$509$	−7.29492	−	12.6352i	−0.323342	−	0.560044i	0.657834	−	0.753163i	$-0.271473\pi$
$509$	−7.29492	−	12.6352i	−0.323342	−	0.560044i	−0.981175	+	0.193119i	$0.938140\pi$
$510$		0			0
$511$	−1.34208	−	0.774853i	−0.0593703	−	0.0342775i
$512$		0			0
$513$	0.566688	+	2.57498i	0.0250199	+	0.113688i
$514$		0			0
$515$	1.69910	+	0.980974i	0.0748712	+	0.0432269i
$516$		0			0
$517$	−9.03822	+	5.21822i	−0.397500	+	0.229497i
$518$		0			0
$519$	−32.1858	+	18.5825i	−1.41280	+	0.815679i
$520$		0			0
$521$			27.1524i			1.18957i	0.803885	+	0.594784i	$0.202763\pi$
$521$			27.1524i			1.18957i	−0.803885	+	0.594784i	$0.797237\pi$
$522$		0			0
$523$	−1.66719	+	0.962550i	−0.0729009	+	0.0420894i	−0.536007	−	0.844213i	$-0.680068\pi$
$523$	−1.66719	+	0.962550i	−0.0729009	+	0.0420894i	0.463106	+	0.886303i	$0.346735\pi$
$524$		0			0
$525$	−17.9057			−0.781468
$526$		0			0
$527$	−6.58894	+	11.4124i	−0.287019	+	0.497131i
$528$		0			0
$529$	8.85283	−	15.3336i	0.384906	−	0.666676i
$530$		0			0
$531$		−	14.0783i		−	0.610947i
$532$		0			0
$533$			4.57334i			0.198093i
$534$		0			0
$535$	−1.00312	+	1.73745i	−0.0433686	+	0.0751167i
$536$		0			0
$537$	−3.42944	+	5.93997i	−0.147991	+	0.256329i
$538$		0			0
$539$	−5.65222			−0.243458
$540$		0			0
$541$	−30.5146	+	17.6176i	−1.31193	+	0.757441i	−0.982415	−	0.186711i	$-0.940217\pi$
$541$	−30.5146	+	17.6176i	−1.31193	+	0.757441i	−0.329511	+	0.944152i	$0.606884\pi$
$542$		0			0
$543$			1.46311i			0.0627880i
$544$		0			0
$545$	7.58879	−	4.38139i	0.325068	−	0.187678i
$546$		0			0
$547$	7.93165	−	4.57934i	0.339133	−	0.195798i	−0.320756	−	0.947162i	$-0.603937\pi$
$547$	7.93165	−	4.57934i	0.339133	−	0.195798i	0.659888	+	0.751364i	$0.270604\pi$
$548$		0			0
$549$	25.8919	+	14.9487i	1.10504	+	0.637995i
$550$		0			0
$551$	−4.08733	−	4.47439i	−0.174126	−	0.190616i
$552$		0			0
$553$	−15.7761	−	9.10833i	−0.670868	−	0.387326i
$554$		0			0
$555$	6.35335	+	11.0043i	0.269685	+	0.467108i
$556$		0			0
$557$	−26.0361	+	15.0319i	−1.10318	+	0.636924i	−0.937056	−	0.349180i	$-0.886460\pi$
$557$	−26.0361	+	15.0319i	−1.10318	+	0.636924i	−0.166129	+	0.986104i	$0.553127\pi$
$558$		0			0
$559$	−34.4315			−1.45630
$560$		0			0
$561$	−7.00104	+	4.04205i	−0.295584	+	0.170656i
$562$		0			0
$563$			35.3632i			1.49038i	0.666851	+	0.745191i	$0.267642\pi$
$563$			35.3632i			1.49038i	−0.666851	+	0.745191i	$0.732358\pi$
$564$		0			0
$565$	−1.69151	+	2.92978i	−0.0711624	+	0.123257i
$566$		0			0
$567$	13.1532	+	7.59398i	0.552381	+	0.318917i
$568$		0			0
$569$		−	24.5320i		−	1.02844i	−0.857660	−	0.514218i	$-0.828082\pi$
$569$		−	24.5320i		−	1.02844i	0.857660	−	0.514218i	$-0.171918\pi$
$570$		0			0
$571$	−16.3080			−0.682467			−0.341233	−	0.939979i	$-0.610845\pi$
$571$	−16.3080			−0.682467			−0.341233	+	0.939979i	$0.610845\pi$
$572$		0			0
$573$	−26.2562	+	45.4770i	−1.09687	+	1.89983i
$574$		0			0
$575$	−26.3373	−	15.2059i	−1.09834	−	0.634128i
$576$		0			0
$577$	−13.0747			−0.544305			−0.272153	−	0.962254i	$-0.587736\pi$
$577$	−13.0747			−0.544305			−0.272153	+	0.962254i	$0.587736\pi$
$578$		0			0
$579$	−6.37315	−	11.0386i	−0.264859	−	0.458750i
$580$		0			0
$581$			19.1076i			0.792719i
$582$		0			0
$583$	−1.86574	−	3.23155i	−0.0772710	−	0.133837i
$584$		0			0
$585$	4.13846	−	2.38934i	0.171104	−	0.0987870i
$586$		0			0
$587$	−8.90580	+	15.4253i	−0.367582	+	0.636671i	−0.989187	−	0.146660i	$-0.953148\pi$
$587$	−8.90580	+	15.4253i	−0.367582	+	0.636671i	0.621605	+	0.783331i	$0.286481\pi$
$588$		0			0
$589$	20.6898	−	4.55330i	0.852510	−	0.187615i
$590$		0			0
$591$	−1.09505	+	1.89668i	−0.0450443	+	0.0780191i
$592$		0			0
$593$	−14.1110	−	24.4410i	−0.579471	−	1.00367i	−0.995540	−	0.0943399i	$-0.969926\pi$
$593$	−14.1110	−	24.4410i	−0.579471	−	1.00367i	0.416069	−	0.909333i	$-0.363407\pi$
$594$		0			0
$595$	1.02611	+	1.77728i	0.0420665	+	0.0728613i
$596$		0			0
$597$	−48.1031			−1.96873
$598$		0			0
$599$	18.3746	+	31.8258i	0.750766	+	1.30037i	0.947452	+	0.319899i	$0.103649\pi$
$599$	18.3746	+	31.8258i	0.750766	+	1.30037i	−0.196685	+	0.980467i	$0.563018\pi$
$600$		0			0
$601$			13.0119i			0.530767i	0.964143	+	0.265384i	$0.0854986\pi$
$601$			13.0119i			0.530767i	−0.964143	+	0.265384i	$0.914501\pi$
$602$		0			0
$603$	8.86022	+	5.11545i	0.360816	+	0.208317i
$604$		0			0
$605$	3.95474	+	2.28327i	0.160783	+	0.0928281i
$606$		0			0
$607$	−28.9061			−1.17326			−0.586631	−	0.809854i	$-0.699546\pi$
$607$	−28.9061			−1.17326			−0.586631	+	0.809854i	$0.699546\pi$
$608$		0			0
$609$	−5.22264			−0.211632
$610$		0			0
$611$	26.1657	+	15.1068i	1.05855	+	0.611155i
$612$		0			0
$613$	−25.3842	−	14.6556i	−1.02526	−	0.591934i	−0.109636	−	0.993972i	$-0.534969\pi$
$613$	−25.3842	−	14.6556i	−1.02526	−	0.591934i	−0.915623	+	0.402038i	$0.868302\pi$
$614$		0			0
$615$			1.47109i			0.0593202i
$616$		0			0
$617$	−2.44550	−	4.23572i	−0.0984519	−	0.170524i	0.812592	−	0.582833i	$-0.198056\pi$
$617$	−2.44550	−	4.23572i	−0.0984519	−	0.170524i	−0.911044	+	0.412309i	$0.864722\pi$
$618$		0			0
$619$	31.8807			1.28139			0.640696	−	0.767795i	$-0.278646\pi$
$619$	31.8807			1.28139			0.640696	+	0.767795i	$0.278646\pi$
$620$		0			0
$621$	1.92959	+	3.34215i	0.0774319	+	0.134116i
$622$		0			0
$623$	−10.0979	−	17.4901i	−0.404565	−	0.700727i
$624$		0			0
$625$	−10.7771	+	18.6665i	−0.431085	+	0.746662i
$626$		0			0
$627$	12.3886	+	3.92715i	0.494751	+	0.156835i
$628$		0			0
$629$	−14.8748	+	25.7639i	−0.593098	+	1.02728i
$630$		0			0
$631$	−7.83877	+	4.52572i	−0.312057	+	0.180166i	−0.647846	−	0.761771i	$-0.724330\pi$
$631$	−7.83877	+	4.52572i	−0.312057	+	0.180166i	0.335790	+	0.941937i	$0.390997\pi$
$632$		0			0
$633$	−29.8585	−	51.7165i	−1.18677	−	2.05555i
$634$		0			0
$635$		−	7.35711i		−	0.291958i
$636$		0			0
$637$	8.18161	+	14.1710i	0.324167	+	0.561474i
$638$		0			0
$639$	−36.4163			−1.44061
$640$		0			0
$641$	−33.2407	−	19.1916i	−1.31293	−	0.758021i	−0.330350	−	0.943859i	$-0.607167\pi$
$641$	−33.2407	−	19.1916i	−1.31293	−	0.758021i	−0.982580	+	0.185838i	$0.940500\pi$
$642$		0			0
$643$	14.9780	−	25.9427i	0.590677	−	1.02308i	−0.403465	−	0.914995i	$-0.632194\pi$
$643$	14.9780	−	25.9427i	0.590677	−	1.02308i	0.994141	−	0.108087i	$-0.0344724\pi$
$644$		0			0
$645$	−11.0755			−0.436097
$646$		0			0
$647$			14.7012i			0.577963i	0.957335	+	0.288982i	$0.0933167\pi$
$647$			14.7012i			0.577963i	−0.957335	+	0.288982i	$0.906683\pi$
$648$		0			0
$649$	5.51826	+	3.18597i	0.216610	+	0.125060i
$650$		0			0
$651$	9.12846	−	15.8110i	0.357773	−	0.619680i
$652$		0			0
$653$		−	12.1042i		−	0.473673i	−0.971550	−	0.236836i	$-0.923889\pi$
$653$		−	12.1042i		−	0.473673i	0.971550	−	0.236836i	$-0.0761105\pi$
$654$		0			0
$655$	−3.46672	+	2.00151i	−0.135456	+	0.0782056i
$656$		0			0
$657$	−2.71762			−0.106024
$658$		0			0
$659$	8.35717	−	4.82502i	0.325549	−	0.187956i	−0.328314	−	0.944569i	$-0.606480\pi$
$659$	8.35717	−	4.82502i	0.325549	−	0.187956i	0.653863	+	0.756613i	$0.273147\pi$
$660$		0			0
$661$	−18.5479	−	32.1258i	−0.721428	−	1.24955i	−0.960427	−	0.278530i	$-0.910153\pi$
$661$	−18.5479	−	32.1258i	−0.721428	−	1.24955i	0.238999	−	0.971020i	$-0.423181\pi$
$662$		0			0
$663$	20.2681	+	11.7018i	0.787146	+	0.454459i
$664$		0			0
$665$	0.996943	−	3.14495i	0.0386598	−	0.121956i
$666$		0			0
$667$	−7.68194	−	4.43517i	−0.297446	−	0.171730i
$668$		0			0
$669$	7.26697	−	4.19559i	0.280957	−	0.162211i
$670$		0			0
$671$	−11.7188	+	6.76588i	−0.452401	+	0.261194i
$672$		0			0
$673$		−	10.8787i		−	0.419342i	−0.977772	−	0.209671i	$-0.932761\pi$
$673$		−	10.8787i		−	0.419342i	0.977772	−	0.209671i	$-0.0672392\pi$
$674$		0			0
$675$	2.49697	−	1.44162i	0.0961082	−	0.0554881i
$676$		0			0
$677$	37.4698			1.44008			0.720040	−	0.693932i	$-0.244123\pi$
$677$	37.4698			1.44008			0.720040	+	0.693932i	$0.244123\pi$
$678$		0			0
$679$	−2.19568	+	3.80304i	−0.0842626	+	0.145947i
$680$		0			0
$681$	−6.34580	+	10.9913i	−0.243172	+	0.421186i
$682$		0			0
$683$			51.9840i			1.98911i	0.104201	+	0.994556i	$0.466771\pi$
$683$			51.9840i			1.98911i	−0.104201	+	0.994556i	$0.533229\pi$
$684$		0			0
$685$		−	8.60787i		−	0.328890i
$686$		0			0
$687$	1.44887	−	2.50952i	0.0552779	−	0.0957441i
$688$		0			0
$689$	−5.40133	+	9.35537i	−0.205774	+	0.356411i
$690$		0			0
$691$	7.12137			0.270910			0.135455	−	0.990784i	$-0.456750\pi$
$691$	7.12137			0.270910			0.135455	+	0.990784i	$0.456750\pi$
$692$		0			0
$693$	4.63681	−	2.67706i	0.176138	−	0.101693i
$694$		0			0
$695$			4.02049i			0.152506i
$696$		0			0
$697$	−2.98277	+	1.72210i	−0.112980	+	0.0652293i
$698$		0			0
$699$	−23.2100	+	13.4003i	−0.877884	+	0.506847i
$700$		0			0
$701$	6.27811	+	3.62467i	0.237121	+	0.136902i	0.613853	−	0.789421i	$-0.289619\pi$
$701$	6.27811	+	3.62467i	0.237121	+	0.136902i	−0.376732	+	0.926322i	$0.622952\pi$
$702$		0			0
$703$	46.7082	−	10.2793i	1.76163	−	0.387690i
$704$		0			0
$705$	8.41665	+	4.85936i	0.316990	+	0.183014i
$706$		0			0
$707$	−0.593395	−	1.02779i	−0.0223169	−	0.0386540i
$708$		0			0
$709$	16.8968	−	9.75535i	0.634571	−	0.366370i	−0.147949	−	0.988995i	$-0.547267\pi$
$709$	16.8968	−	9.75535i	0.634571	−	0.366370i	0.782520	+	0.622625i	$0.213934\pi$
$710$		0			0
$711$	−31.9454			−1.19804
$712$		0			0
$713$	26.8540	−	15.5041i	1.00569	−	0.580635i
$714$		0			0
$715$			2.16286i			0.0808864i
$716$		0			0
$717$	24.3624	−	42.1970i	0.909831	−	1.57587i
$718$		0			0
$719$	37.0563	+	21.3944i	1.38197	+	0.797878i	0.992392	−	0.123117i	$-0.0392891\pi$
$719$	37.0563	+	21.3944i	1.38197	+	0.797878i	0.389573	+	0.920995i	$0.372622\pi$
$720$		0			0
$721$		−	6.36383i		−	0.237001i
$722$		0			0
$723$	−15.1731			−0.564292
$724$		0			0
$725$	−3.31357	+	5.73928i	−0.123063	+	0.213151i
$726$		0			0
$727$	−21.7487	−	12.5566i	−0.806614	−	0.465699i	0.0391646	−	0.999233i	$-0.487530\pi$
$727$	−21.7487	−	12.5566i	−0.806614	−	0.465699i	−0.845779	+	0.533534i	$0.820864\pi$
$728$		0			0
$729$	22.2837			0.825320
$730$		0			0
$731$	−12.9653	−	22.4565i	−0.479538	−	0.830585i
$732$		0			0
$733$		−	0.990917i		−	0.0366004i	−0.999833	−	0.0183002i	$-0.994175\pi$
$733$		−	0.990917i		−	0.0366004i	0.999833	−	0.0183002i	$-0.00582545\pi$
$734$		0			0
$735$	2.63176	+	4.55833i	0.0970738	+	0.168137i
$736$		0			0
$737$	−4.01019	+	2.31529i	−0.147717	+	0.0852846i
$738$		0			0
$739$	8.15940	−	14.1325i	0.300149	−	0.519872i	−0.676021	−	0.736882i	$-0.736297\pi$
$739$	8.15940	−	14.1325i	0.300149	−	0.519872i	0.976169	+	0.217010i	$0.0696304\pi$
$740$		0			0
$741$	−8.08653	−	36.7446i	−0.297066	−	1.34984i
$742$		0			0
$743$	21.4854	−	37.2138i	0.788223	−	1.36524i	−0.138832	−	0.990316i	$-0.544335\pi$
$743$	21.4854	−	37.2138i	0.788223	−	1.36524i	0.927055	−	0.374926i	$-0.122332\pi$
$744$		0			0
$745$	4.48817	+	7.77374i	0.164434	+	0.284808i
$746$		0			0
$747$	16.7539	+	29.0186i	0.612993	+	1.06174i
$748$		0			0
$749$	6.50749			0.237778
$750$		0			0
$751$	10.3838	+	17.9853i	0.378910	+	0.656292i	0.990904	−	0.134571i	$-0.0429656\pi$
$751$	10.3838	+	17.9853i	0.378910	+	0.656292i	−0.611994	+	0.790863i	$0.709632\pi$
$752$		0			0
$753$			58.2751i			2.12366i
$754$		0			0
$755$	−1.91075	−	1.10317i	−0.0695393	−	0.0401485i
$756$		0			0
$757$	10.7348	+	6.19774i	0.390163	+	0.225261i	0.682231	−	0.731137i	$-0.261010\pi$
$757$	10.7348	+	6.19774i	0.390163	+	0.225261i	−0.292068	+	0.956398i	$0.594343\pi$
$758$		0			0
$759$	19.0223			0.690467
$760$		0			0
$761$	46.1918			1.67445			0.837226	−	0.546858i	$-0.184176\pi$
$761$	46.1918			1.67445			0.837226	+	0.546858i	$0.184176\pi$
$762$		0			0
$763$	−24.6152	−	14.2116i	−0.891130	−	0.514494i
$764$		0			0
$765$	3.11669	+	1.79942i	0.112684	+	0.0650583i
$766$		0			0
$767$		−	18.4468i		−	0.666075i
$768$		0			0
$769$	7.84569	+	13.5891i	0.282923	+	0.490037i	0.972103	−	0.234553i	$-0.0753627\pi$
$769$	7.84569	+	13.5891i	0.282923	+	0.490037i	−0.689181	+	0.724590i	$0.742029\pi$
$770$		0			0
$771$	−19.6076			−0.706151
$772$		0			0
$773$	2.97659	+	5.15560i	0.107060	+	0.185434i	0.914578	−	0.404409i	$-0.132523\pi$
$773$	2.97659	+	5.15560i	0.107060	+	0.185434i	−0.807518	+	0.589843i	$0.799190\pi$
$774$		0			0
$775$	−11.5833	−	20.0629i	−0.416086	−	0.720682i
$776$		0			0
$777$	20.6079	−	35.6939i	0.739304	−	1.28051i
$778$		0			0
$779$	5.27810	+	1.67315i	0.189108	+	0.0599468i
$780$		0			0
$781$	8.24113	−	14.2741i	0.294891	−	0.510766i
$782$		0			0
$783$	0.728302	−	0.420485i	0.0260274	−	0.0150269i
$784$		0			0
$785$	−4.49002	−	7.77694i	−0.160256	−	0.277571i
$786$		0			0
$787$			5.02671i			0.179183i	0.995979	+	0.0895915i	$0.0285561\pi$
$787$			5.02671i			0.179183i	−0.995979	+	0.0895915i	$0.971444\pi$
$788$		0			0
$789$	26.3436	+	45.6285i	0.937857	+	1.62442i
$790$		0			0
$791$	10.9733			0.390164
$792$		0			0
$793$	33.9261	+	19.5873i	1.20475	+	0.695564i
$794$		0			0
$795$	−1.73743	+	3.00932i	−0.0616203	+	0.106729i
$796$		0			0
$797$	−23.2783			−0.824558			−0.412279	−	0.911058i	$-0.635267\pi$
$797$	−23.2783			−0.824558			−0.412279	+	0.911058i	$0.635267\pi$
$798$		0			0
$799$			22.7540i			0.804978i
$800$		0			0
$801$	−30.6713	−	17.7081i	−1.08372	−	0.625684i
$802$		0			0
$803$	0.615005	−	1.06522i	0.0217031	−	0.0375908i
$804$		0			0
$805$		−	4.82900i		−	0.170200i
$806$		0			0
$807$	−8.06521	+	4.65645i	−0.283909	+	0.163915i
$808$		0			0
$809$	−38.1510			−1.34132			−0.670659	−	0.741766i	$-0.733989\pi$
$809$	−38.1510			−1.34132			−0.670659	+	0.741766i	$0.733989\pi$
$810$		0			0
$811$	−43.8993	+	25.3453i	−1.54151	+	0.889993i	−0.542770	+	0.839881i	$0.682625\pi$
$811$	−43.8993	+	25.3453i	−1.54151	+	0.889993i	−0.998744	+	0.0501122i	$0.984042\pi$
$812$		0			0
$813$	−2.50855	−	4.34494i	−0.0879788	−	0.152384i
$814$		0			0
$815$	5.54793	+	3.20310i	0.194336	+	0.112200i
$816$		0			0
$817$	−12.5967	+	39.7375i	−0.440704	+	1.39024i
$818$		0			0
$819$	−13.4236	−	7.75012i	−0.469059	−	0.270811i
$820$		0			0
$821$	17.8048	−	10.2796i	0.621391	−	0.358760i	−0.156019	−	0.987754i	$-0.549866\pi$
$821$	17.8048	−	10.2796i	0.621391	−	0.358760i	0.777410	+	0.628994i	$0.216533\pi$
$822$		0			0
$823$	16.8787	−	9.74491i	0.588354	−	0.339686i	−0.176093	−	0.984374i	$-0.556346\pi$
$823$	16.8787	−	9.74491i	0.588354	−	0.339686i	0.764446	+	0.644687i	$0.223012\pi$
$824$		0			0
$825$		−	14.2118i		−	0.494793i
$826$		0			0
$827$	−12.7206	+	7.34424i	−0.442338	+	0.255384i	−0.704589	−	0.709616i	$-0.748869\pi$
$827$	−12.7206	+	7.34424i	−0.442338	+	0.255384i	0.262251	+	0.965000i	$0.415535\pi$
$828$		0			0
$829$	35.2405			1.22395			0.611976	−	0.790876i	$-0.290375\pi$
$829$	35.2405			1.22395			0.611976	+	0.790876i	$0.290375\pi$
$830$		0			0
$831$	33.3557	−	57.7738i	1.15710	−	2.00415i
$832$		0			0
$833$	−6.16161	+	10.6722i	−0.213487	+	0.369771i
$834$		0			0
$835$		−	4.84158i		−	0.167550i
$836$		0			0
$837$			2.93981i			0.101615i
$838$		0			0
$839$	3.11351	−	5.39276i	0.107490	−	0.186179i	−0.807263	−	0.590192i	$-0.799052\pi$
$839$	3.11351	−	5.39276i	0.107490	−	0.186179i	0.914753	+	0.404014i	$0.132385\pi$
$840$		0			0
$841$	13.5335	−	23.4407i	0.466673	−	0.808301i
$842$		0			0
$843$	55.5771			1.91418
$844$		0			0
$845$	−0.0158093	+	0.00912753i	−0.000543858	+	0.000313997i
$846$		0			0
$847$		−	14.8121i		−	0.508951i
$848$		0			0
$849$	5.84328	−	3.37362i	0.200541	−	0.115782i
$850$		0			0
$851$	60.6240	−	35.0013i	2.07816	−	1.19983i
$852$		0			0
$853$	28.3047	+	16.3417i	0.969134	+	0.559530i	0.898972	−	0.438006i	$-0.144315\pi$
$853$	28.3047	+	16.3417i	0.969134	+	0.559530i	0.0701616	+	0.997536i	$0.477649\pi$
$854$		0			0
$855$	−1.24350	−	5.65034i	−0.0425266	−	0.193238i
$856$		0			0
$857$	45.5110	+	26.2758i	1.55463	+	0.897564i	0.997755	+	0.0669647i	$0.0213315\pi$
$857$	45.5110	+	26.2758i	1.55463	+	0.897564i	0.556871	+	0.830599i	$0.312002\pi$
$858$		0			0
$859$	−12.3600	−	21.4082i	−0.421718	−	0.730437i	0.574390	−	0.818582i	$-0.305239\pi$
$859$	−12.3600	−	21.4082i	−0.421718	−	0.730437i	−0.996108	+	0.0881450i	$0.971906\pi$
$860$		0			0
$861$	4.13239	−	2.38584i	0.140832	−	0.0813091i
$862$		0			0
$863$	25.0075			0.851266			0.425633	−	0.904896i	$-0.360051\pi$
$863$	25.0075			0.851266			0.425633	+	0.904896i	$0.360051\pi$
$864$		0			0
$865$	−6.48509	+	3.74417i	−0.220500	+	0.127306i
$866$		0			0
$867$		−	23.1311i		−	0.785572i
$868$		0			0
$869$	7.22934	−	12.5216i	0.245238	−	0.424765i
$870$		0			0
$871$	11.6095	+	6.70277i	0.393374	+	0.227115i
$872$		0			0
$873$			7.70085i			0.260634i
$874$		0			0
$875$	−7.39223			−0.249903
$876$		0			0
$877$	1.76754	−	3.06146i	0.0596855	−	0.103378i	−0.834639	−	0.550798i	$-0.814324\pi$
$877$	1.76754	−	3.06146i	0.0596855	−	0.103378i	0.894324	+	0.447419i	$0.147657\pi$
$878$		0			0
$879$	17.9726	+	10.3765i	0.606202	+	0.349991i
$880$		0			0
$881$	−5.22599			−0.176068			−0.0880341	−	0.996117i	$-0.528058\pi$
$881$	−5.22599			−0.176068			−0.0880341	+	0.996117i	$0.528058\pi$
$882$		0			0
$883$	2.22587	+	3.85532i	0.0749066	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$883$	2.22587	+	3.85532i	0.0749066	+	0.129742i	−0.826139	+	0.563466i	$0.809467\pi$
$884$		0			0
$885$		−	5.93373i		−	0.199460i
$886$		0			0
$887$	23.1207	+	40.0463i	0.776318	+	1.34462i	0.934051	+	0.357141i	$0.116248\pi$
$887$	23.1207	+	40.0463i	0.776318	+	1.34462i	−0.157732	+	0.987482i	$0.550418\pi$
$888$		0			0
$889$	−20.6666	+	11.9318i	−0.693134	+	0.400181i
$890$		0			0
$891$	−6.02739	+	10.4397i	−0.201925	+	0.349744i
$892$		0			0
$893$	27.0075	−	24.6711i	0.903771	−	0.825588i
$894$		0			0
$895$	−0.690997	+	1.19684i	−0.0230975	+	0.0400060i
$896$		0			0
$897$	−27.5349	−	47.6919i	−0.919364	−	1.59239i
$898$		0			0
$899$	−3.37857	−	5.85186i	−0.112682	−	0.195170i
$900$		0			0
$901$	−8.13553			−0.271034
$902$		0			0
$903$	17.9624	+	31.1118i	0.597751	+	1.03533i
$904$		0			0
$905$			0.294801i			0.00979952i
$906$		0			0
$907$	−1.48781	−	0.858985i	−0.0494018	−	0.0285221i	0.475096	−	0.879934i	$-0.342413\pi$
$907$	−1.48781	−	0.858985i	−0.0494018	−	0.0285221i	−0.524497	+	0.851412i	$0.675747\pi$
$908$		0			0
$909$	−1.80237	−	1.04060i	−0.0597807	−	0.0345144i
$910$		0			0
$911$	0.307661			0.0101933			0.00509664	−	0.999987i	$-0.498378\pi$
$911$	0.307661			0.0101933			0.00509664	+	0.999987i	$0.498378\pi$
$912$		0			0
$913$	−15.1659			−0.501916
$914$		0			0
$915$	10.9129	+	6.30058i	0.360770	+	0.208291i
$916$		0			0
$917$	11.2448	+	6.49216i	0.371334	+	0.214390i
$918$		0			0
$919$		−	28.6229i		−	0.944183i	−0.881550	−	0.472091i	$-0.843499\pi$
$919$		−	28.6229i		−	0.944183i	0.881550	−	0.472091i	$-0.156501\pi$
$920$		0			0
$921$	12.4352	+	21.5384i	0.409754	+	0.709714i
$922$		0			0
$923$	−47.7163			−1.57060
$924$		0			0
$925$	−26.1499	−	45.2930i	−0.859803	−	1.48922i
$926$		0			0
$927$	−5.57991	−	9.66469i	−0.183268	−	0.317430i
$928$		0			0
$929$	−30.2173	+	52.3378i	−0.991396	+	1.71715i	−0.382337	+	0.924023i	$0.624881\pi$
$929$	−30.2173	+	52.3378i	−0.991396	+	1.71715i	−0.609059	+	0.793125i	$0.708453\pi$
$930$		0			0
$931$	19.3480	−	4.25799i	0.634105	−	0.139550i
$932$		0			0
$933$	−24.9103	+	43.1460i	−0.815528	+	1.41254i
$934$		0			0
$935$	−1.41064	+	0.814431i	−0.0461327	+	0.0266347i
$936$		0			0
$937$	−10.5175	−	18.2168i	−0.343592	−	0.595118i	0.641505	−	0.767119i	$-0.278310\pi$
$937$	−10.5175	−	18.2168i	−0.343592	−	0.595118i	−0.985097	+	0.172000i	$0.944977\pi$
$938$		0			0
$939$			57.4909i			1.87614i
$940$		0			0
$941$	17.6157	+	30.5113i	0.574256	+	0.994641i	0.996122	+	0.0879826i	$0.0280420\pi$
$941$	17.6157	+	30.5113i	0.574256	+	0.994641i	−0.421866	+	0.906658i	$0.638625\pi$
$942$		0			0
$943$	8.10441			0.263916
$944$		0			0
$945$	0.396486	+	0.228912i	0.0128977	+	0.00744649i
$946$		0			0
$947$	8.10653	−	14.0409i	0.263427	−	0.456268i	−0.703724	−	0.710474i	$-0.748481\pi$
$947$	8.10653	−	14.0409i	0.263427	−	0.456268i	0.967150	+	0.254205i	$0.0818139\pi$
$948$		0			0
$949$	−3.56089			−0.115591
$950$		0			0
$951$		−	45.3354i		−	1.47010i
$952$		0			0
$953$	32.1131	+	18.5405i	1.04024	+	0.600585i	0.919902	−	0.392148i	$-0.128268\pi$
$953$	32.1131	+	18.5405i	1.04024	+	0.600585i	0.120341	+	0.992733i	$0.461601\pi$
$954$		0			0
$955$	−5.29034	+	9.16314i	−0.171191	+	0.296512i
$956$		0			0
$957$		−	4.14524i		−	0.133996i
$958$		0			0
$959$	−24.1800	+	13.9603i	−0.780814	+	0.450803i
$960$		0			0
$961$	−7.37886			−0.238028
$962$		0			0
$963$	9.88286	−	5.70587i	0.318471	−	0.183869i
$964$		0			0
$965$	−1.28412	−	2.22417i	−0.0413374	−	0.0715985i
$966$		0			0
$967$	−0.859439	−	0.496197i	−0.0276377	−	0.0159566i	0.486117	−	0.873893i	$-0.338413\pi$
$967$	−0.859439	−	0.496197i	−0.0276377	−	0.0159566i	−0.513755	+	0.857937i	$0.671746\pi$
$968$		0			0
$969$	20.9201	−	19.1104i	0.672050	−	0.613913i
$970$		0			0
$971$	−31.4894	−	18.1804i	−1.01054	−	0.583437i	−0.0991922	−	0.995068i	$-0.531626\pi$
$971$	−31.4894	−	18.1804i	−1.01054	−	0.583437i	−0.911351	+	0.411631i	$0.864959\pi$
$972$		0			0
$973$	11.2938	−	6.52049i	0.362063	−	0.209037i
$974$		0			0
$975$	−35.6312	+	20.5717i	−1.14111	+	0.658822i
$976$		0			0
$977$		−	39.6271i		−	1.26778i	−0.773421	−	0.633892i	$-0.781456\pi$
$977$		−	39.6271i		−	1.26778i	0.773421	−	0.633892i	$-0.218544\pi$
$978$		0			0
$979$	13.8820	−	8.01478i	0.443671	−	0.256154i
$980$		0			0
$981$	−49.8438			−1.59139
$982$		0			0
$983$	21.5716	−	37.3631i	0.688027	−	1.19170i	−0.284448	−	0.958691i	$-0.591810\pi$
$983$	21.5716	−	37.3631i	0.688027	−	1.19170i	0.972475	−	0.233007i	$-0.0748564\pi$
$984$		0			0
$985$	−0.220641	+	0.382162i	−0.00703021	+	0.0121767i
$986$		0			0
$987$		−	31.5239i		−	1.00342i
$988$		0			0
$989$			61.0161i			1.94020i
$990$		0			0
$991$	4.38682	−	7.59820i	0.139352	−	0.241365i	−0.787899	−	0.615804i	$-0.788831\pi$
$991$	4.38682	−	7.59820i	0.139352	−	0.241365i	0.927252	+	0.374439i	$0.122165\pi$
$992$		0			0
$993$	−19.1308	+	33.1356i	−0.607098	+	1.05153i
$994$		0			0
$995$	−9.69227			−0.307266
$996$		0			0
$997$	−15.8403	+	9.14540i	−0.501667	+	0.289638i	−0.729402	−	0.684085i	$-0.760202\pi$
$997$	−15.8403	+	9.14540i	−0.501667	+	0.289638i	0.227734	+	0.973723i	$0.426868\pi$
$998$		0			0
$999$			6.63673i			0.209977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.s.c.559.1		28
4.3	odd	2		152.2.o.c.27.10	yes	28
8.3	odd	2	inner	608.2.s.c.559.2		28
8.5	even	2		152.2.o.c.27.4	✓	28
19.12	odd	6	inner	608.2.s.c.335.2		28
76.31	even	6		152.2.o.c.107.4	yes	28
152.69	odd	6		152.2.o.c.107.10	yes	28
152.107	even	6	inner	608.2.s.c.335.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.4	✓	28	8.5	even	2
152.2.o.c.27.10	yes	28	4.3	odd	2
152.2.o.c.107.4	yes	28	76.31	even	6
152.2.o.c.107.10	yes	28	152.69	odd	6
608.2.s.c.335.1		28	152.107	even	6	inner
608.2.s.c.335.2		28	19.12	odd	6	inner
608.2.s.c.559.1		28	1.1	even	1	trivial
608.2.s.c.559.2		28	8.3	odd	2	inner

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:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.07624 - 1.19872i) q^{3} +(-0.418341 - 0.241529i) q^{5} +1.56686i q^{7} +(1.37385 + 2.37958i) q^{9} -1.24363 q^{11} +(1.80015 + 3.11796i) q^{13} +(0.579050 + 1.00294i) q^{15} +(-1.35570 + 2.34815i) q^{17} +(4.25703 - 0.936862i) q^{19} +(1.87822 - 3.25318i) q^{21} +(5.52533 - 3.19005i) q^{23} +(-2.38333 - 4.12804i) q^{25} +0.604878i q^{27} +(-0.695157 - 1.20405i) q^{29} +4.86016 q^{31} +(2.58207 + 1.49076i) q^{33} +(0.378442 - 0.655481i) q^{35} +10.9720 q^{37} -8.63150i q^{39} +(1.10008 + 0.635132i) q^{41} +(-4.78175 + 8.28223i) q^{43} -1.32730i q^{45} +(7.26763 - 4.19597i) q^{47} +4.54495 q^{49} +(5.62954 - 3.25022i) q^{51} +(1.50024 + 2.59849i) q^{53} +(0.520259 + 0.300372i) q^{55} +(-9.96165 - 3.15782i) q^{57} +(-4.43723 - 2.56184i) q^{59} +(9.42313 - 5.44044i) q^{61} +(-3.72846 + 2.15263i) q^{63} -1.73916i q^{65} +(3.22460 - 1.86172i) q^{67} -15.2959 q^{69} +(-6.62670 + 11.4778i) q^{71} +(-0.494526 + 0.856544i) q^{73} +11.4277i q^{75} -1.94859i q^{77} +(-5.81311 + 10.0686i) q^{79} +(4.84663 - 8.39460i) q^{81} +12.1949 q^{83} +(1.13429 - 0.654884i) q^{85} +3.33319i q^{87} +(-11.1625 + 6.44469i) q^{89} +(-4.88540 + 2.82059i) q^{91} +(-10.0909 - 5.82596i) q^{93} +(-2.00717 - 0.636268i) q^{95} +(2.42717 + 1.40133i) q^{97} +(-1.70855 - 2.95930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81}+ \cdots + 28 q^{99}+O(q^{100}) \) 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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