LMFDB - Embedded newform 744.2.o.e.557.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [744,2,Mod(557,744)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(744, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("744.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 744 = 2^{3} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	744.o (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.94086991038$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			557.10
Character	$\chi$	$=$	744.557
Dual form			744.2.o.e.557.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32933 - 0.482574i) q^{2} +(1.03404 + 1.38952i) q^{3} +(1.53424 + 1.28300i) q^{4} +3.64345 q^{5} +(-0.704034 - 2.34613i) q^{6} +2.15013 q^{7} +(-1.42038 - 2.44592i) q^{8} +(-0.861527 + 2.87363i) q^{9} +O(q^{10})$	\(q+(-1.32933 - 0.482574i) q^{2} +(1.03404 + 1.38952i) q^{3} +(1.53424 + 1.28300i) q^{4} +3.64345 q^{5} +(-0.704034 - 2.34613i) q^{6} +2.15013 q^{7} +(-1.42038 - 2.44592i) q^{8} +(-0.861527 + 2.87363i) q^{9} +(-4.84335 - 1.75824i) q^{10} +4.61614i q^{11} +(-0.196288 + 3.45854i) q^{12} +4.68225 q^{13} +(-2.85823 - 1.03760i) q^{14} +(3.76747 + 5.06264i) q^{15} +(0.707811 + 3.93688i) q^{16} -4.44040 q^{17} +(2.53200 - 3.40426i) q^{18} -3.75116i q^{19} +(5.58994 + 4.67455i) q^{20} +(2.22331 + 2.98764i) q^{21} +(2.22763 - 6.13639i) q^{22} -3.32399 q^{23} +(1.92993 - 4.50282i) q^{24} +8.27473 q^{25} +(-6.22426 - 2.25953i) q^{26} +(-4.88382 + 1.77434i) q^{27} +(3.29882 + 2.75862i) q^{28} -6.08059i q^{29} +(-2.56511 - 8.54802i) q^{30} +(-5.18040 - 2.04044i) q^{31} +(0.958921 - 5.57499i) q^{32} +(-6.41422 + 4.77327i) q^{33} +(5.90276 + 2.14282i) q^{34} +7.83388 q^{35} +(-5.00867 + 3.30351i) q^{36} -3.22943 q^{37} +(-1.81021 + 4.98653i) q^{38} +(4.84162 + 6.50607i) q^{39} +(-5.17507 - 8.91160i) q^{40} -11.5860i q^{41} +(-1.51376 - 5.04448i) q^{42} -5.31448 q^{43} +(-5.92252 + 7.08229i) q^{44} +(-3.13893 + 10.4699i) q^{45} +(4.41868 + 1.60407i) q^{46} -0.800058i q^{47} +(-4.73846 + 5.05440i) q^{48} -2.37695 q^{49} +(-10.9999 - 3.99317i) q^{50} +(-4.59154 - 6.17002i) q^{51} +(7.18371 + 6.00733i) q^{52} +2.16409i q^{53} +(7.34847 - 0.00187925i) q^{54} +16.8187i q^{55} +(-3.05399 - 5.25904i) q^{56} +(5.21231 - 3.87884i) q^{57} +(-2.93434 + 8.08312i) q^{58} +6.10935 q^{59} +(-0.715166 + 12.6010i) q^{60} +0.579481 q^{61} +(5.90181 + 5.21236i) q^{62} +(-1.85239 + 6.17868i) q^{63} +(-3.96507 + 6.94825i) q^{64} +17.0595 q^{65} +(10.8301 - 3.24992i) q^{66} +3.42370i q^{67} +(-6.81265 - 5.69704i) q^{68} +(-3.43713 - 4.61875i) q^{69} +(-10.4138 - 3.78043i) q^{70} -3.55952i q^{71} +(8.25238 - 1.97441i) q^{72} -9.15412i q^{73} +(4.29298 + 1.55844i) q^{74} +(8.55639 + 11.4979i) q^{75} +(4.81275 - 5.75519i) q^{76} +9.92530i q^{77} +(-3.29646 - 10.9852i) q^{78} +4.15979i q^{79} +(2.57887 + 14.3438i) q^{80} +(-7.51554 - 4.95143i) q^{81} +(-5.59110 + 15.4016i) q^{82} +8.33003i q^{83} +(-0.422044 + 7.43629i) q^{84} -16.1784 q^{85} +(7.06470 + 2.56463i) q^{86} +(8.44910 - 6.28757i) q^{87} +(11.2907 - 6.55666i) q^{88} +18.6422 q^{89} +(9.22521 - 12.4033i) q^{90} +10.0674 q^{91} +(-5.09981 - 4.26469i) q^{92} +(-2.52150 - 9.30817i) q^{93} +(-0.386088 + 1.06354i) q^{94} -13.6672i q^{95} +(8.73811 - 4.43231i) q^{96} +13.5913 q^{97} +(3.15976 + 1.14706i) q^{98} +(-13.2651 - 3.97693i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9}+O(q^{10}) $ 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9	$ 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9} - 52 q^{10} - 60 q^{16} - 4 q^{18} + 168 q^{25} - 20 q^{28} + 16 q^{31} + 8 q^{33} + 8 q^{39} - 64 q^{40} - 64 q^{49} + 56 q^{63} + 72 q^{64} + 4 q^{66} - 84 q^{70} - 44 q^{72} - 28 q^{76} + 56 q^{78} - 112 q^{81} - 108 q^{82} - 168 q^{87} + 104 q^{90} + 8 q^{94} + 72 q^{97}+O(q^{100}) $ 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9 - 52 * q^10 - 60 * q^16 - 4 * q^18 + 168 * q^25 - 20 * q^28 + 16 * q^31 + 8 * q^33 + 8 * q^39 - 64 * q^40 - 64 * q^49 + 56 * q^63 + 72 * q^64 + 4 * q^66 - 84 * q^70 - 44 * q^72 - 28 * q^76 + 56 * q^78 - 112 * q^81 - 108 * q^82 - 168 * q^87 + 104 * q^90 + 8 * q^94 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/744\mathbb{Z}\right)^\times$.

$n$	$313$	$373$	$497$	$559$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.32933	−	0.482574i	−0.939979	−	0.341232i
$2$	−1.32933	−	0.482574i	−0.939979	−	0.341232i
$3$	1.03404	+	1.38952i	0.597003	+	0.802239i
$3$	1.03404	+	1.38952i	0.597003	+	0.802239i
$4$	1.53424	+	1.28300i	0.767122	+	0.641501i
$5$	3.64345			1.62940			0.814700	−	0.579882i	$-0.196901\pi$
$5$	3.64345			1.62940			0.814700	+	0.579882i	$0.196901\pi$
$6$	−0.704034	−	2.34613i	−0.287421	−	0.957804i
$7$	2.15013			0.812672			0.406336	−	0.913724i	$-0.366806\pi$
$7$	2.15013			0.812672			0.406336	+	0.913724i	$0.366806\pi$
$8$	−1.42038	−	2.44592i	−0.502178	−	0.864764i
$9$	−0.861527	+	2.87363i	−0.287176	+	0.957878i
$10$	−4.84335	−	1.75824i	−1.53160	−	0.556003i
$11$			4.61614i			1.39182i	0.718129	+	0.695910i	$0.244999\pi$
$11$			4.61614i			1.39182i	−0.718129	+	0.695910i	$0.755001\pi$
$12$	−0.196288	+	3.45854i	−0.0566635	+	0.998393i
$13$	4.68225			1.29862			0.649311	−	0.760523i	$-0.275057\pi$
$13$	4.68225			1.29862			0.649311	+	0.760523i	$0.275057\pi$
$14$	−2.85823	−	1.03760i	−0.763895	−	0.277309i
$15$	3.76747	+	5.06264i	0.972756	+	1.30717i
$16$	0.707811	+	3.93688i	0.176953	+	0.984219i
$17$	−4.44040			−1.07695			−0.538477	−	0.842640i	$-0.681000\pi$
$17$	−4.44040			−1.07695			−0.538477	+	0.842640i	$0.681000\pi$
$18$	2.53200	−	3.40426i	0.596797	−	0.802392i
$19$		−	3.75116i		−	0.860575i	−0.902692	−	0.430287i	$-0.858412\pi$
$19$		−	3.75116i		−	0.860575i	0.902692	−	0.430287i	$-0.141588\pi$
$20$	5.58994	+	4.67455i	1.24995	+	1.04526i
$21$	2.22331	+	2.98764i	0.485167	+	0.651957i
$22$	2.22763	−	6.13639i	0.474933	−	1.30828i
$23$	−3.32399			−0.693100			−0.346550	−	0.938032i	$-0.612647\pi$
$23$	−3.32399			−0.693100			−0.346550	+	0.938032i	$0.612647\pi$
$24$	1.92993	−	4.50282i	0.393946	−	0.919134i
$25$	8.27473			1.65495
$26$	−6.22426	−	2.25953i	−1.22068	−	0.443131i
$27$	−4.88382	+	1.77434i	−0.939892	+	0.341472i
$28$	3.29882	+	2.75862i	0.623418	+	0.521330i
$29$		−	6.08059i		−	1.12914i	−0.825386	−	0.564569i	$-0.809042\pi$
$29$		−	6.08059i		−	1.12914i	0.825386	−	0.564569i	$-0.190958\pi$
$30$	−2.56511	−	8.54802i	−0.468324	−	1.56065i
$31$	−5.18040	−	2.04044i	−0.930428	−	0.366474i
$31$	−5.18040	−	2.04044i	−0.930428	−	0.366474i
$32$	0.958921	−	5.57499i	0.169515	−	0.985528i
$33$	−6.41422	+	4.77327i	−1.11657	+	0.830920i
$34$	5.90276	+	2.14282i	1.01231	+	0.367491i
$35$	7.83388			1.32417
$36$	−5.00867	+	3.30351i	−0.834779	+	0.550586i
$37$	−3.22943			−0.530914			−0.265457	−	0.964123i	$-0.585523\pi$
$37$	−3.22943			−0.530914			−0.265457	+	0.964123i	$0.585523\pi$
$38$	−1.81021	+	4.98653i	−0.293655	+	0.808923i
$39$	4.84162	+	6.50607i	0.775280	+	1.04181i
$40$	−5.17507	−	8.91160i	−0.818250	−	1.40905i
$41$		−	11.5860i		−	1.80943i	−0.426020	−	0.904714i	$-0.640085\pi$
$41$		−	11.5860i		−	1.80943i	0.426020	−	0.904714i	$-0.359915\pi$
$42$	−1.51376	−	5.04448i	−0.233579	−	0.778380i
$43$	−5.31448			−0.810450			−0.405225	−	0.914217i	$-0.632807\pi$
$43$	−5.31448			−0.810450			−0.405225	+	0.914217i	$0.632807\pi$
$44$	−5.92252	+	7.08229i	−0.892854	+	1.06770i
$45$	−3.13893	+	10.4699i	−0.467924	+	1.56077i
$46$	4.41868	+	1.60407i	0.651499	+	0.236507i
$47$		−	0.800058i		−	0.116701i	−0.998296	−	0.0583503i	$-0.981416\pi$
$47$		−	0.800058i		−	0.116701i	0.998296	−	0.0583503i	$-0.0185840\pi$
$48$	−4.73846	+	5.05440i	−0.683938	+	0.729540i
$49$	−2.37695			−0.339565
$50$	−10.9999	−	3.99317i	−1.55562	−	0.564720i
$51$	−4.59154	−	6.17002i	−0.642945	−	0.863975i
$52$	7.18371	+	6.00733i	0.996201	+	0.833067i
$53$			2.16409i			0.297261i	0.988893	+	0.148630i	$0.0474865\pi$
$53$			2.16409i			0.297261i	−0.988893	+	0.148630i	$0.952514\pi$
$54$	7.34847	−	0.00187925i	1.00000	−	0.000255734i
$55$			16.8187i			2.26783i
$56$	−3.05399	−	5.25904i	−0.408106	−	0.702769i
$57$	5.21231	−	3.87884i	0.690387	−	0.513765i
$58$	−2.93434	+	8.08312i	−0.385297	+	1.06137i
$59$	6.10935			0.795370			0.397685	−	0.917522i	$-0.369814\pi$
$59$	6.10935			0.795370			0.397685	+	0.917522i	$0.369814\pi$
$60$	−0.715166	+	12.6010i	−0.0923276	+	1.62678i
$61$	0.579481			0.0741950			0.0370975	−	0.999312i	$-0.488189\pi$
$61$	0.579481			0.0741950			0.0370975	+	0.999312i	$0.488189\pi$
$62$	5.90181	+	5.21236i	0.749531	+	0.661970i
$63$	−1.85239	+	6.17868i	−0.233380	+	0.778440i
$64$	−3.96507	+	6.94825i	−0.495634	+	0.868532i
$65$	17.0595			2.11597
$66$	10.8301	−	3.24992i	1.33309	−	0.400038i
$67$			3.42370i			0.418271i	0.977887	+	0.209135i	$0.0670650\pi$
$67$			3.42370i			0.418271i	−0.977887	+	0.209135i	$0.932935\pi$
$68$	−6.81265	−	5.69704i	−0.826156	−	0.690867i
$69$	−3.43713	−	4.61875i	−0.413782	−	0.556032i
$70$	−10.4138	−	3.78043i	−1.24469	−	0.451848i
$71$		−	3.55952i		−	0.422437i	−0.977439	−	0.211219i	$-0.932257\pi$
$71$		−	3.55952i		−	0.422437i	0.977439	−	0.211219i	$-0.0677432\pi$
$72$	8.25238	−	1.97441i	0.972552	−	0.232686i
$73$		−	9.15412i		−	1.07141i	−0.844406	−	0.535704i	$-0.820046\pi$
$73$		−	9.15412i		−	1.07141i	0.844406	−	0.535704i	$-0.179954\pi$
$74$	4.29298	+	1.55844i	0.499048	+	0.181165i
$75$	8.55639	+	11.4979i	0.988007	+	1.32766i
$76$	4.81275	−	5.75519i	0.552060	−	0.660166i
$77$			9.92530i			1.13109i
$78$	−3.29646	−	10.9852i	−0.373251	−	1.24383i
$79$			4.15979i			0.468013i	0.972235	+	0.234006i	$0.0751837\pi$
$79$			4.15979i			0.468013i	−0.972235	+	0.234006i	$0.924816\pi$
$80$	2.57887	+	14.3438i	0.288327	+	1.60369i
$81$	−7.51554	−	4.95143i	−0.835060	−	0.550159i
$82$	−5.59110	+	15.4016i	−0.617434	+	1.70082i
$83$			8.33003i			0.914340i	0.889379	+	0.457170i	$0.151137\pi$
$83$			8.33003i			0.914340i	−0.889379	+	0.457170i	$0.848863\pi$
$84$	−0.422044	+	7.43629i	−0.0460488	+	0.811366i
$85$	−16.1784			−1.75479
$86$	7.06470	+	2.56463i	0.761807	+	0.276551i
$87$	8.44910	−	6.28757i	0.905839	−	0.674098i
$88$	11.2907	−	6.55666i	1.20360	−	0.698942i
$89$	18.6422			1.97607			0.988034	−	0.154235i	$-0.0492913\pi$
$89$	18.6422			1.97607			0.988034	+	0.154235i	$0.0492913\pi$
$90$	9.22521	−	12.4033i	0.972422	−	1.30742i
$91$	10.0674			1.05535
$92$	−5.09981	−	4.26469i	−0.531692	−	0.444624i
$93$	−2.52150	−	9.30817i	−0.261468	−	0.965212i
$94$	−0.386088	+	1.06354i	−0.0398219	+	0.109696i
$95$		−	13.6672i		−	1.40222i
$96$	8.73811	−	4.43231i	0.891830	−	0.452371i
$97$	13.5913			1.37999			0.689994	−	0.723815i	$-0.257613\pi$
$97$	13.5913			1.37999			0.689994	+	0.723815i	$0.257613\pi$
$98$	3.15976	+	1.14706i	0.319184	+	0.115870i
$99$	−13.2651	−	3.97693i	−1.33319	−	0.399697i
$100$	12.6955	+	10.6165i	1.26955	+	1.06165i
$101$	−0.626090			−0.0622983			−0.0311492	−	0.999515i	$-0.509917\pi$
$101$	−0.626090			−0.0622983			−0.0311492	+	0.999515i	$0.509917\pi$
$102$	3.12619	+	10.4178i	0.309539	+	1.03151i
$103$	3.40402			0.335408			0.167704	−	0.985837i	$-0.446365\pi$
$103$	3.40402			0.335408			0.167704	+	0.985837i	$0.446365\pi$
$104$	−6.65055	−	11.4524i	−0.652140	−	1.12300i
$105$	8.10054	+	10.8853i	0.790532	+	1.06230i
$106$	1.04433	−	2.87679i	0.101435	−	0.279419i
$107$	−10.5743			−1.02225			−0.511126	−	0.859506i	$-0.670772\pi$
$107$	−10.5743			−1.02225			−0.511126	+	0.859506i	$0.670772\pi$
$108$	−9.76946	−	3.54368i	−0.940067	−	0.340991i
$109$			16.8287i			1.61190i	0.591984	+	0.805950i	$0.298345\pi$
$109$			16.8287i			1.61190i	−0.591984	+	0.805950i	$0.701655\pi$
$110$	8.11627	−	22.3576i	0.773856	−	2.13172i
$111$	−3.33935	−	4.48735i	−0.316957	−	0.425920i
$112$	1.52188	+	8.46479i	0.143804	+	0.799847i
$113$		−	6.04556i		−	0.568718i	−0.958718	−	0.284359i	$-0.908219\pi$
$113$		−	6.04556i		−	0.568718i	0.958718	−	0.284359i	$-0.0917808\pi$
$114$	−8.80071	+	2.64094i	−0.824262	+	0.247347i
$115$	−12.1108			−1.12934
$116$	7.80141	−	9.32912i	0.724343	−	0.866187i
$117$	−4.03388	+	13.4551i	−0.372933	+	1.24392i
$118$	−8.12135	−	2.94822i	−0.747631	−	0.271405i
$119$	−9.54742			−0.875210
$120$	7.03161	−	16.4058i	0.641896	−	1.49764i
$121$	−10.3088			−0.937163
$122$	−0.770323	−	0.279643i	−0.0697417	−	0.0253177i
$123$	16.0990	−	11.9804i	1.45159	−	1.08023i
$124$	−5.33011	−	9.77701i	−0.478658	−	0.878001i
$125$	11.9313			1.06717
$126$	5.44412	−	7.31959i	0.485000	−	0.652081i
$127$		−	5.85414i		−	0.519471i	−0.965680	−	0.259735i	$-0.916365\pi$
$127$		−	5.85414i		−	0.519471i	0.965680	−	0.259735i	$-0.0836353\pi$
$128$	8.62394	−	7.32309i	0.762256	−	0.647276i
$129$	−5.49538	−	7.38457i	−0.483841	−	0.650175i
$130$	−22.6778	−	8.23249i	−1.98897	−	0.722037i
$131$	−6.33605			−0.553584			−0.276792	−	0.960930i	$-0.589271\pi$
$131$	−6.33605			−0.553584			−0.276792	+	0.960930i	$0.589271\pi$
$132$	−15.9651	−	0.906095i	−1.38958	−	0.0788654i
$133$		−	8.06547i		−	0.699365i
$134$	1.65219	−	4.55123i	0.142727	−	0.393166i
$135$	−17.7940	+	6.46472i	−1.53146	+	0.556394i
$136$	6.30703	+	10.8609i	0.540823	+	0.931311i
$137$	−22.5416			−1.92586			−0.962928	−	0.269758i	$-0.913056\pi$
$137$	−22.5416			−1.92586			−0.962928	+	0.269758i	$0.913056\pi$
$138$	2.34020	+	7.79852i	0.199211	+	0.663854i
$139$	14.8613			1.26052			0.630259	−	0.776385i	$-0.282949\pi$
$139$	14.8613			1.26052			0.630259	+	0.776385i	$0.282949\pi$
$140$	12.0191	+	10.0509i	1.01580	+	0.849455i
$141$	1.11170	−	0.827292i	0.0936217	−	0.0696705i
$142$	−1.71773	+	4.73178i	−0.144149	+	0.397082i
$143$			21.6139i			1.80745i
$144$	−11.9229	−	1.35774i	−0.993578	−	0.113145i
$145$		−	22.1543i		−	1.83982i
$146$	−4.41754	+	12.1689i	−0.365598	+	1.00710i
$147$	−2.45786	−	3.30282i	−0.202721	−	0.272412i
$148$	−4.95473	−	4.14336i	−0.407276	−	0.340582i
$149$	16.0839			1.31764			0.658822	−	0.752299i	$-0.271055\pi$
$149$	16.0839			1.31764			0.658822	+	0.752299i	$0.271055\pi$
$150$	−5.82569	−	19.4136i	−0.475666	−	1.58511i
$151$			18.9006i			1.53811i	0.639184	+	0.769054i	$0.279272\pi$
$151$			18.9006i			1.53811i	−0.639184	+	0.769054i	$0.720728\pi$
$152$	−9.17504	+	5.32805i	−0.744194	+	0.432162i
$153$	3.82552	−	12.7601i	0.309275	−	1.03159i
$154$	4.78969	−	13.1940i	0.385964	−	1.06320i
$155$	−18.8745	−	7.43425i	−1.51604	−	0.597134i
$156$	−0.919070	+	16.1937i	−0.0735845	+	1.29654i
$157$		−	0.00334988i		−	0.000267349i	−1.00000		0.000133675i	$-0.999957\pi$
$157$		−	0.00334988i		−	0.000267349i	1.00000		0.000133675i	$-4.25499e-5\pi$
$158$	2.00741	−	5.52974i	0.159701	−	0.439922i
$159$	−3.00705	+	2.23775i	−0.238474	+	0.177465i
$160$	3.49378	−	20.3122i	0.276208	−	1.60582i
$161$	−7.14700			−0.563263
$162$	7.60121	+	10.2089i	0.597208	+	0.802087i
$163$			13.4487i			1.05338i	0.850057	+	0.526690i	$0.176567\pi$
$163$			13.4487i			1.05338i	−0.850057	+	0.526690i	$0.823433\pi$
$164$	14.8648	−	17.7757i	1.16075	−	1.38805i
$165$	−23.3699	+	17.3912i	−1.81934	+	1.35390i
$166$	4.01986	−	11.0734i	0.312002	−	0.859461i
$167$	9.15902			0.708746			0.354373	−	0.935104i	$-0.384694\pi$
$167$	9.15902			0.708746			0.354373	+	0.935104i	$0.384694\pi$
$168$	4.14960	−	9.68163i	0.320149	−	0.746954i
$169$	8.92343			0.686418
$170$	21.5064	+	7.80726i	1.64947	+	0.598790i
$171$	10.7795	+	3.23173i	0.824326	+	0.247136i
$172$	−8.15371	−	6.81849i	−0.621714	−	0.519905i
$173$	−1.45248			−0.110430			−0.0552152	−	0.998474i	$-0.517584\pi$
$173$	−1.45248			−0.110430			−0.0552152	+	0.998474i	$0.517584\pi$
$174$	−14.2659	+	4.28095i	−1.08149	+	0.324538i
$175$	17.7917			1.34493
$176$	−18.1732	+	3.26736i	−1.36986	+	0.246286i
$177$	6.31731	+	8.48906i	0.474838	+	0.638077i
$178$	−24.7817	−	8.99624i	−1.85746	−	0.674297i
$179$			5.70221i			0.426203i	0.977030	+	0.213101i	$0.0683565\pi$
$179$			5.70221i			0.426203i	−0.977030	+	0.213101i	$0.931644\pi$
$180$	−18.2488	+	12.0362i	−1.36019	+	0.897125i
$181$	−13.3581			−0.992901			−0.496450	−	0.868065i	$-0.665364\pi$
$181$	−13.3581			−0.992901			−0.496450	+	0.868065i	$0.665364\pi$
$182$	−13.3829	−	4.85828i	−0.992010	−	0.360120i
$183$	0.599206	+	0.805200i	0.0442946	+	0.0595221i
$184$	4.72131	+	8.13022i	0.348060	+	0.599368i
$185$	−11.7663			−0.865072
$186$	−1.13997	+	13.5905i	−0.0835865	+	0.996501i
$187$		−	20.4975i		−	1.49893i
$188$	1.02648	−	1.22749i	0.0748635	−	0.0895235i
$189$	−10.5008	+	3.81506i	−0.763824	+	0.277505i
$190$	−6.59542	+	18.1682i	−0.478482	+	1.31806i
$191$			12.8003i			0.926200i	0.886306	+	0.463100i	$0.153263\pi$
$191$			12.8003i			0.926200i	−0.886306	+	0.463100i	$0.846737\pi$
$192$	−13.7548	+	1.67523i	−0.992665	+	0.120899i
$193$	−6.13413			−0.441545			−0.220772	−	0.975325i	$-0.570858\pi$
$193$	−6.13413			−0.441545			−0.220772	+	0.975325i	$0.570858\pi$
$194$	−18.0674	−	6.55882i	−1.29716	−	0.470896i
$195$	17.6402	+	23.7045i	1.26324	+	1.69752i
$196$	−3.64683	−	3.04964i	−0.260488	−	0.217831i
$197$		−	21.3129i		−	1.51848i	−0.650808	−	0.759242i	$-0.725570\pi$
$197$		−	21.3129i		−	1.51848i	0.650808	−	0.759242i	$-0.274430\pi$
$198$	15.7146	+	11.6881i	1.11679	+	0.830635i
$199$			9.72286i			0.689235i	0.938743	+	0.344618i	$0.111991\pi$
$199$			9.72286i			0.689235i	−0.938743	+	0.344618i	$0.888009\pi$
$200$	−11.7532	−	20.2393i	−0.831078	−	1.43114i
$201$	−4.75729	+	3.54023i	−0.335553	+	0.249709i
$202$	0.832282	+	0.302135i	0.0585591	+	0.0212582i
$203$		−	13.0740i		−	0.917618i
$204$	0.871597	−	15.3573i	0.0610240	−	1.07522i
$205$		−	42.2130i		−	2.94828i
$206$	−4.52507	−	1.64269i	−0.315276	−	0.114452i
$207$	2.86371	−	9.55193i	0.199041	−	0.663905i
$208$	3.31414	+	18.4334i	0.229795	+	1.27813i
$209$	17.3159			1.19777
$210$	−5.51532	−	18.3793i	−0.380593	−	1.26829i
$211$		−	3.41507i		−	0.235103i	−0.993067	−	0.117552i	$-0.962495\pi$
$211$		−	3.41507i		−	0.235103i	0.993067	−	0.117552i	$-0.0375046\pi$
$212$	−2.77653	+	3.32024i	−0.190693	+	0.228035i
$213$	4.94602	−	3.68068i	0.338896	−	0.252196i
$214$	14.0567	+	5.10287i	0.960896	+	0.348825i
$215$	−19.3630			−1.32055
$216$	11.2768	+	9.42522i	0.767286	+	0.641305i
$217$	−11.1385	−	4.38721i	−0.756133	−	0.297823i
$218$	8.12111	−	22.3709i	0.550031	−	1.51515i
$219$	12.7198	−	9.46571i	0.859526	−	0.639634i
$220$	−21.5784	+	25.8040i	−1.45482	+	1.73970i
$221$	−20.7910			−1.39856
$222$	2.27363	+	7.57666i	0.152596	+	0.508512i
$223$		−	29.2134i		−	1.95628i	−0.207955	−	0.978138i	$-0.566681\pi$
$223$		−	29.2134i		−	1.95628i	0.207955	−	0.978138i	$-0.433319\pi$
$224$	2.06180	−	11.9869i	0.137760	−	0.800910i
$225$	−7.12891	+	23.7785i	−0.475260	+	1.58524i
$226$	−2.91743	+	8.03655i	−0.194065	+	0.534583i
$227$	−0.0666612			−0.00442446			−0.00221223	−	0.999998i	$-0.500704\pi$
$227$	−0.0666612			−0.00442446			−0.00221223	+	0.999998i	$0.500704\pi$
$228$	12.9735	+	0.736308i	0.859192	+	0.0487632i
$229$	0.724315			0.0478641			0.0239320	−	0.999714i	$-0.492381\pi$
$229$	0.724315			0.0478641			0.0239320	+	0.999714i	$0.492381\pi$
$230$	16.0993	+	5.84436i	1.06155	+	0.385365i
$231$	−13.7914	+	10.2631i	−0.907407	+	0.675265i
$232$	−14.8727	+	8.63672i	−0.976438	+	0.567029i
$233$		−	18.4187i		−	1.20665i	−0.797497	−	0.603323i	$-0.793843\pi$
$233$		−	18.4187i		−	1.20665i	0.797497	−	0.603323i	$-0.206157\pi$
$234$	11.8554	−	15.9396i	0.775014	−	1.04200i
$235$		−	2.91497i		−	0.190152i
$236$	9.37324	+	7.83831i	0.610146	+	0.510231i
$237$	−5.78011	+	4.30138i	−0.375458	+	0.279405i
$238$	12.6917	+	4.60734i	0.822680	+	0.298649i
$239$	23.0007			1.48779			0.743894	−	0.668297i	$-0.232976\pi$
$239$	23.0007			1.48779			0.743894	+	0.668297i	$0.232976\pi$
$240$	−17.2644	+	18.4155i	−1.11441	+	1.18871i
$241$		−	16.4934i		−	1.06243i	−0.847236	−	0.531216i	$-0.821735\pi$
$241$		−	16.4934i		−	1.06243i	0.847236	−	0.531216i	$-0.178265\pi$
$242$	13.7038	+	4.97476i	0.880914	+	0.319789i
$243$	−0.891257	−	15.5630i	−0.0571741	−	0.998364i
$244$	0.889066	+	0.743476i	0.0569166	+	0.0475962i
$245$	−8.66031			−0.553287
$246$	−27.1823	+	8.15693i	−1.73308	+	0.520067i
$247$		−	17.5639i		−	1.11756i
$248$	2.36735	+	15.5691i	0.150327	+	0.988636i
$249$	−11.5747	+	8.61358i	−0.733519	+	0.545863i
$250$	−15.8607	−	5.75775i	−1.00312	−	0.364152i
$251$		−	24.5730i		−	1.55103i	−0.631328	−	0.775516i	$-0.717490\pi$
$251$		−	24.5730i		−	1.55103i	0.631328	−	0.775516i	$-0.282510\pi$
$252$	−10.7693	+	7.10298i	−0.678401	+	0.447445i
$253$		−	15.3440i		−	0.964670i
$254$	−2.82506	+	7.78209i	−0.177260	+	0.488292i
$255$	−16.7291	−	22.4801i	−1.04761	−	1.40776i
$256$	−14.9980	+	5.57313i	−0.937376	+	0.348320i
$257$			16.6238i			1.03697i	0.855088	+	0.518483i	$0.173503\pi$
$257$			16.6238i			1.03697i	−0.855088	+	0.518483i	$0.826497\pi$
$258$	3.74157	+	12.4685i	0.232940	+	0.776253i
$259$	−6.94368			−0.431459
$260$	26.1735	+	21.8874i	1.62321	+	1.35740i
$261$	17.4734	+	5.23860i	1.08158	+	0.324261i
$262$	8.42272	+	3.05762i	0.520357	+	0.188900i
$263$	−11.5856			−0.714401			−0.357200	−	0.934028i	$-0.616269\pi$
$263$	−11.5856			−0.714401			−0.357200	+	0.934028i	$0.616269\pi$
$264$	20.7857	+	8.90885i	1.27927	+	0.548302i
$265$			7.88476i			0.484357i
$266$	−3.89219	+	10.7217i	−0.238645	+	0.657388i
$267$	19.2768	+	25.9037i	1.17972	+	1.58528i
$268$	−4.39261	+	5.25278i	−0.268321	+	0.320865i
$269$		−	15.1840i		−	0.925783i	−0.886415	−	0.462892i	$-0.846812\pi$
$269$		−	15.1840i		−	0.925783i	0.886415	−	0.462892i	$-0.153188\pi$
$270$	26.7738	−	0.00684696i	1.62940	−	0.000416693i
$271$			10.0915i			0.613018i	0.951868	+	0.306509i	$0.0991609\pi$
$271$			10.0915i			0.613018i	−0.951868	+	0.306509i	$0.900839\pi$
$272$	−3.14296	−	17.4813i	−0.190570	−	1.05996i
$273$	10.4101	+	13.9889i	0.630048	+	0.846646i
$274$	29.9652	+	10.8780i	1.81027	+	0.657163i
$275$			38.1974i			2.30339i
$276$	0.652460	−	11.4961i	0.0392735	−	0.691986i
$277$	−11.0158			−0.661876			−0.330938	−	0.943653i	$-0.607365\pi$
$277$	−11.0158			−0.661876			−0.330938	+	0.943653i	$0.607365\pi$
$278$	−19.7556	−	7.17167i	−1.18486	−	0.430128i
$279$	10.3265	−	13.1287i	0.618234	−	0.785994i
$280$	−11.1271	−	19.1611i	−0.664969	−	1.14509i
$281$			20.1673i			1.20308i	0.798844	+	0.601539i	$0.205445\pi$
$281$			20.1673i			1.20308i	−0.798844	+	0.601539i	$0.794555\pi$
$282$	−1.87704	+	0.563268i	−0.111776	+	0.0335421i
$283$		−	22.2447i		−	1.32231i	−0.750249	−	0.661155i	$-0.770066\pi$
$283$		−	22.2447i		−	1.32231i	0.750249	−	0.661155i	$-0.229934\pi$
$284$	4.56687	−	5.46117i	0.270994	−	0.324061i
$285$	18.9908	−	14.1324i	1.12492	−	0.837130i
$286$	10.4303	−	28.7321i	0.616758	−	1.69896i
$287$		−	24.9113i		−	1.47047i
$288$	15.1943	+	7.55859i	0.895335	+	0.445394i
$289$	2.71712			0.159831
$290$	−10.6911	+	29.4505i	−0.627804	+	1.72939i
$291$	14.0539	+	18.8854i	0.823857	+	1.10708i
$292$	11.7448	−	14.0447i	0.687310	−	0.821901i
$293$	34.0021			1.98643			0.993213	−	0.116307i	$-0.0371055\pi$
$293$	34.0021			1.98643			0.993213	+	0.116307i	$0.0371055\pi$
$294$	1.67346	+	5.57665i	0.0975980	+	0.325237i
$295$	22.2591			1.29598
$296$	4.58700	+	7.89892i	0.266614	+	0.459116i
$297$	−8.19061	−	22.5444i	−0.475267	−	1.30816i
$298$	−21.3808	−	7.76167i	−1.23856	−	0.449622i
$299$	−15.5637			−0.900074
$300$	−1.62423	+	28.6185i	−0.0937751	+	1.65229i
$301$	−11.4268			−0.658630
$302$	9.12093	−	25.1251i	0.524851	−	1.44579i
$303$	−0.647402	−	0.869965i	−0.0371923	−	0.0499782i
$304$	14.7679	−	2.65511i	0.846994	−	0.152281i
$305$	2.11131			0.120893
$306$	−11.2431	+	15.1163i	−0.642724	+	0.864140i
$307$			8.28732i			0.472982i	0.971634	+	0.236491i	$0.0759974\pi$
$307$			8.28732i			0.472982i	−0.971634	+	0.236491i	$0.924003\pi$
$308$	−12.7342	+	15.2278i	−0.725597	+	0.867686i
$309$	3.51989	+	4.72995i	0.200239	+	0.269077i
$310$	21.5029	+	18.9910i	1.22129	+	1.07861i
$311$			28.1321i			1.59523i	0.603169	+	0.797614i	$0.293904\pi$
$311$			28.1321i			1.59523i	−0.603169	+	0.797614i	$0.706096\pi$
$312$	9.03642	−	21.0833i	0.511586	−	1.19361i
$313$		−	17.7290i		−	1.00210i	−0.865418	−	0.501050i	$-0.832947\pi$
$313$		−	17.7290i		−	1.00210i	0.865418	−	0.501050i	$-0.167053\pi$
$314$	−0.00161656	+	0.00445309i	−9.12280e−5	+	0.000251303i
$315$	−6.74910	+	22.5117i	−0.380269	+	1.26839i
$316$	−5.33702	+	6.38213i	−0.300231	+	0.359023i
$317$	−11.4862			−0.645129			−0.322564	−	0.946548i	$-0.604545\pi$
$317$	−11.4862			−0.645129			−0.322564	+	0.946548i	$0.604545\pi$
$318$	5.07724	−	1.52359i	0.284718	−	0.0854389i
$319$	28.0689			1.57156
$320$	−14.4465	+	25.3156i	−0.807586	+	1.41519i
$321$	−10.9342	−	14.6931i	−0.610288	−	0.820091i
$322$	9.50073	+	3.44896i	0.529455	+	0.192203i
$323$			16.6566i			0.926800i
$324$	−5.17798	−	17.2392i	−0.287666	−	0.957731i
$325$	38.7443			2.14915
$326$	6.48998	−	17.8777i	0.359447	−	0.990156i
$327$	−23.3838	+	17.4016i	−1.29313	+	0.962308i
$328$	−28.3384	+	16.4565i	−1.56473	+	0.908655i
$329$		−	1.72023i		−	0.0948392i
$330$	39.4589	−	11.8409i	2.17214	−	0.651822i
$331$	0.123201			0.00677174			0.00338587	−	0.999994i	$-0.498922\pi$
$331$	0.123201			0.00677174			0.00338587	+	0.999994i	$0.498922\pi$
$332$	−10.6875	+	12.7803i	−0.586550	+	0.701410i
$333$	2.78224	−	9.28019i	0.152466	−	0.508551i
$334$	−12.1754	−	4.41991i	−0.666207	−	0.241847i
$335$			12.4741i			0.681531i
$336$	−10.1883	+	10.8676i	−0.555817	+	0.592876i
$337$			16.1581i			0.880187i	0.897952	+	0.440093i	$0.145055\pi$
$337$			16.1581i			0.880187i	−0.897952	+	0.440093i	$0.854945\pi$
$338$	−11.8622	−	4.30622i	−0.645219	−	0.234227i
$339$	8.40042	−	6.25134i	0.456248	−	0.339526i
$340$	−24.8216	−	20.7569i	−1.34614	−	1.12570i
$341$	9.41898	−	23.9135i	0.510066	−	1.29499i
$342$	−12.7699	−	9.49792i	−0.690518	−	0.513589i
$343$	−20.1616			−1.08863
$344$	7.54855	+	12.9988i	0.406991	+	0.700848i
$345$	−12.5230	−	16.8282i	−0.674217	−	0.905999i
$346$	1.93083	+	0.700932i	0.103802	+	0.0376823i
$347$			0.874538i			0.0469476i	0.999724	+	0.0234738i	$0.00747264\pi$
$347$			0.874538i			0.0469476i	−0.999724	+	0.0234738i	$0.992527\pi$
$348$	21.0300	+	1.19355i	1.12732	+	0.0639809i
$349$		−	11.6562i		−	0.623944i	−0.950091	−	0.311972i	$-0.899011\pi$
$349$		−	11.6562i		−	0.623944i	0.950091	−	0.311972i	$-0.100989\pi$
$350$	−23.6511	−	8.58583i	−1.26420	−	0.458932i
$351$	−22.8673	+	8.30790i	−1.22056	+	0.443443i
$352$	25.7349	+	4.42652i	1.37168	+	0.235934i
$353$	19.4272			1.03401			0.517003	−	0.855984i	$-0.327048\pi$
$353$	19.4272			1.03401			0.517003	+	0.855984i	$0.327048\pi$
$354$	−4.30119	−	14.3333i	−0.228606	−	0.761809i
$355$		−	12.9689i		−	0.688319i
$356$	28.6017	+	23.9180i	1.51589	+	1.26765i
$357$	−9.87240	−	13.2663i	−0.522503	−	0.702128i
$358$	2.75174	−	7.58012i	0.145434	−	0.400622i
$359$			22.9662i			1.21211i	0.795423	+	0.606055i	$0.207249\pi$
$359$			22.9662i			1.21211i	−0.795423	+	0.606055i	$0.792751\pi$
$360$	30.0671	−	7.19366i	1.58468	−	0.379139i
$361$	4.92881			0.259411
$362$	17.7574	+	6.44628i	0.933306	+	0.338809i
$363$	−10.6597	−	14.3243i	−0.559489	−	0.751829i
$364$	15.4459	+	12.9165i	0.809585	+	0.677010i
$365$		−	33.3526i		−	1.74575i
$366$	−0.407975	−	1.35954i	−0.0213252	−	0.0710643i
$367$		−	17.3585i		−	0.906106i	−0.891484	−	0.453053i	$-0.850335\pi$
$367$		−	17.3585i		−	0.906106i	0.891484	−	0.453053i	$-0.149665\pi$
$368$	−2.35276	−	13.0861i	−0.122646	−	0.682162i
$369$	33.2939	+	9.98165i	1.73321	+	0.519624i
$370$	15.6413	+	5.67809i	0.813150	+	0.295190i
$371$			4.65307i			0.241575i
$372$	8.07380	−	17.5161i	0.418607	−	0.908168i
$373$			31.2642i			1.61880i	0.587259	+	0.809399i	$0.300207\pi$
$373$			31.2642i			1.61880i	−0.587259	+	0.809399i	$0.699793\pi$
$374$	−9.89157	+	27.2480i	−0.511481	+	1.40896i
$375$	12.3374	+	16.5788i	0.637103	+	0.856125i
$376$	−1.95688	+	1.13638i	−0.100918	+	0.0586045i
$377$		−	28.4708i		−	1.46632i
$378$	15.8001	−	0.00404063i	0.812672	−	0.000207828i
$379$			25.5152i			1.31063i	0.755356	+	0.655314i	$0.227464\pi$
$379$			25.5152i			1.31063i	−0.755356	+	0.655314i	$0.772536\pi$
$380$	17.5350	−	20.9688i	0.899526	−	1.07567i
$381$	8.13444	−	6.05341i	0.416740	−	0.310125i
$382$	6.17711	−	17.0159i	0.316049	−	0.870609i
$383$	−27.8783			−1.42452			−0.712258	−	0.701918i	$-0.752327\pi$
$383$	−27.8783			−1.42452			−0.712258	+	0.701918i	$0.752327\pi$
$384$	19.0931	+	4.41077i	0.974339	+	0.225086i
$385$			36.1623i			1.84300i
$386$	8.15430	+	2.96017i	0.415043	+	0.150669i
$387$	4.57857	−	15.2719i	0.232742	−	0.776312i
$388$	20.8524	+	17.4377i	1.05862	+	0.885264i
$389$			32.8520i			1.66566i	0.553526	+	0.832832i	$0.313282\pi$
$389$			32.8520i			1.66566i	−0.553526	+	0.832832i	$0.686718\pi$
$390$	−12.0105	−	40.0239i	−0.608175	−	2.02669i
$391$	14.7598			0.746437
$392$	3.37617	+	5.81384i	0.170522	+	0.293643i
$393$	−6.55173	−	8.80407i	−0.330491	−	0.444107i
$394$	−10.2851	+	28.3320i	−0.518155	+	1.42734i
$395$			15.1560i			0.762580i
$396$	−15.2495	−	23.1208i	−0.766316	−	1.16186i
$397$			10.1715i			0.510494i	0.966876	+	0.255247i	$0.0821568\pi$
$397$			10.1715i			0.510494i	−0.966876	+	0.255247i	$0.917843\pi$
$398$	4.69200	−	12.9249i	0.235189	−	0.647867i
$399$	11.2071	−	8.34001i	0.561058	−	0.417523i
$400$	5.85694	+	32.5766i	0.292847	+	1.62883i
$401$	−7.34867			−0.366975			−0.183488	−	0.983022i	$-0.558739\pi$
$401$	−7.34867			−0.366975			−0.183488	+	0.983022i	$0.558739\pi$
$402$	8.03244	−	2.41040i	0.400622	−	0.120220i
$403$	−24.2559	−	9.55386i	−1.20827	−	0.475912i
$404$	−0.960576	−	0.803275i	−0.0477904	−	0.0399644i
$405$	−27.3825	−	18.0403i	−1.36065	−	0.896429i
$406$	−6.30920	+	17.3797i	−0.313120	+	0.862542i
$407$		−	14.9075i		−	0.738937i
$408$	−8.56967	+	19.9943i	−0.424262	+	0.989865i
$409$		−	4.62149i		−	0.228518i	−0.993451	−	0.114259i	$-0.963551\pi$
$409$		−	4.62149i		−	0.228518i	0.993451	−	0.114259i	$-0.0364493\pi$
$410$	−20.3709	+	56.1150i	−1.00605	+	2.77132i
$411$	−23.3089	−	31.3219i	−1.14974	−	1.54500i
$412$	5.22259	+	4.36736i	0.257299	+	0.215164i
$413$	13.1359			0.646375
$414$	−8.41633	+	11.3157i	−0.413640	+	0.556138i
$415$			30.3501i			1.48983i
$416$	4.48990	−	26.1035i	0.220136	−	1.27983i
$417$	15.3671	+	20.6500i	0.752532	+	1.01124i
$418$	−23.0186	−	8.35620i	−1.12587	−	0.408715i
$419$	−13.5505			−0.661985			−0.330992	−	0.943633i	$-0.607383\pi$
$419$	−13.5505			−0.661985			−0.330992	+	0.943633i	$0.607383\pi$
$420$	−1.53770	+	27.0938i	−0.0750320	+	1.32204i
$421$			0.704088i			0.0343152i	0.999853	+	0.0171576i	$0.00546170\pi$
$421$			0.704088i			0.0343152i	−0.999853	+	0.0171576i	$0.994538\pi$
$422$	−1.64803	+	4.53976i	−0.0802246	+	0.220992i
$423$	2.29907	+	0.689272i	0.111785	+	0.0335136i
$424$	5.29320	−	3.07382i	0.257060	−	0.149278i
$425$	−36.7431			−1.78230
$426$	−8.35110	+	2.50602i	−0.404612	+	0.121417i
$427$	1.24596			0.0602961
$428$	−16.2235	−	13.5668i	−0.784193	−	0.655776i
$429$	−30.0330	+	22.3496i	−1.45001	+	1.07905i
$430$	25.7399	+	9.34410i	1.24129	+	0.450613i
$431$		−	2.51153i		−	0.120976i	−0.998169	−	0.0604882i	$-0.980734\pi$
$431$		−	2.51153i		−	0.120976i	0.998169	−	0.0604882i	$-0.0192657\pi$
$432$	−10.4422	−	17.9711i	−0.502400	−	0.864636i
$433$			9.61183i			0.461915i	0.972964	+	0.230958i	$0.0741859\pi$
$433$			9.61183i			0.461915i	−0.972964	+	0.230958i	$0.925814\pi$
$434$	12.6896	+	11.2072i	0.609122	+	0.537964i
$435$	30.7839	−	22.9084i	1.47597	−	1.09838i
$436$	−21.5913	+	25.8194i	−1.03404	+	1.23652i
$437$			12.4688i			0.596464i
$438$	−21.4768	+	6.44481i	−1.02620	+	0.307945i
$439$	−3.72802			−0.177929			−0.0889644	−	0.996035i	$-0.528356\pi$
$439$	−3.72802			−0.177929			−0.0889644	+	0.996035i	$0.528356\pi$
$440$	41.1372	−	23.8889i	1.96114	−	1.13886i
$441$	2.04781	−	6.83049i	0.0975148	−	0.325262i
$442$	27.6382	+	10.0332i	1.31461	+	0.477231i
$443$	−10.6426			−0.505644			−0.252822	−	0.967513i	$-0.581359\pi$
$443$	−10.6426			−0.505644			−0.252822	+	0.967513i	$0.581359\pi$
$444$	0.633898	−	11.1691i	0.0300835	−	0.530061i
$445$	67.9219			3.21981
$446$	−14.0977	+	38.8343i	−0.667543	+	1.83886i
$447$	16.6314	+	22.3489i	0.786637	+	1.05707i
$448$	−8.52540	+	14.9396i	−0.402787	+	0.705831i
$449$	−24.2579			−1.14480			−0.572401	−	0.819974i	$-0.693988\pi$
$449$	−24.2579			−1.14480			−0.572401	+	0.819974i	$0.693988\pi$
$450$	20.9516	−	28.1693i	0.987668	−	1.32792i
$451$	53.4826			2.51840
$452$	7.75646	−	9.27536i	0.364833	−	0.436276i
$453$	−26.2627	+	19.5439i	−1.23393	+	0.918254i
$454$	0.0886148	+	0.0321690i	0.00415890	+	0.00150976i
$455$	36.6802			1.71959
$456$	−16.8908	−	7.23948i	−0.790983	−	0.339020i
$457$			28.5826i			1.33704i	0.743696	+	0.668518i	$0.233071\pi$
$457$			28.5826i			1.33704i	−0.743696	+	0.668518i	$0.766929\pi$
$458$	−0.962855	−	0.349536i	−0.0449913	−	0.0163327i
$459$	21.6861	−	7.87877i	1.01222	−	0.367750i
$460$	−18.5809	−	15.5382i	−0.866340	−	0.724471i
$461$			26.5955i			1.23868i	0.785124	+	0.619339i	$0.212599\pi$
$461$			26.5955i			1.23868i	−0.785124	+	0.619339i	$0.787401\pi$
$462$	23.2861	−	6.98775i	1.08337	−	0.325099i
$463$		−	31.0071i		−	1.44102i	−0.693444	−	0.720511i	$-0.743907\pi$
$463$		−	31.0071i		−	1.44102i	0.693444	−	0.720511i	$-0.256093\pi$
$464$	23.9386	−	4.30391i	1.11132	−	0.199804i
$465$	−9.18698	−	33.9139i	−0.426036	−	1.57272i
$466$	−8.88837	+	24.4845i	−0.411746	+	1.13422i
$467$	−22.5236			−1.04227			−0.521135	−	0.853474i	$-0.674491\pi$
$467$	−22.5236			−1.04227			−0.521135	+	0.853474i	$0.674491\pi$
$468$	−23.4518	+	15.4679i	−1.08406	+	0.715002i
$469$			7.36138i			0.339917i
$470$	−1.40669	+	3.87497i	−0.0648858	+	0.178739i
$471$	0.00465472	−	0.00346390i	0.000214478	−	0.000159608i
$472$	−8.67757	−	14.9430i	−0.399418	−	0.687807i
$473$		−	24.5324i		−	1.12800i
$474$	9.75941	−	2.92863i	0.448265	−	0.134517i
$475$		−	31.0398i		−	1.42421i
$476$	−14.6481	−	12.2494i	−0.671393	−	0.561448i
$477$	−6.21880	−	1.86442i	−0.284740	−	0.0853661i
$478$	−30.5755	−	11.0995i	−1.39849	−	0.507680i
$479$		−	27.6730i		−	1.26441i	−0.774801	−	0.632206i	$-0.782150\pi$
$479$		−	27.6730i		−	1.26441i	0.774801	−	0.632206i	$-0.217850\pi$
$480$	31.8369	−	16.1489i	1.45315	−	0.737094i
$481$	−15.1210			−0.689457
$482$	−7.95928	+	21.9252i	−0.362535	+	0.998664i
$483$	−7.39028	−	9.93089i	−0.336269	−	0.451871i
$484$	−15.8162	−	13.2262i	−0.718918	−	0.601191i
$485$	49.5193			2.24855
$486$	−6.32551	+	21.1184i	−0.286931	+	0.957951i
$487$		−	18.5115i		−	0.838837i	−0.907793	−	0.419418i	$-0.862234\pi$
$487$		−	18.5115i		−	0.838837i	0.907793	−	0.419418i	$-0.137766\pi$
$488$	−0.823081	−	1.41737i	−0.0372591	−	0.0641611i
$489$	−18.6872	+	13.9064i	−0.845064	+	0.628871i
$490$	11.5124	+	4.17924i	0.520078	+	0.188799i
$491$		−	21.3209i		−	0.962199i	−0.876666	−	0.481100i	$-0.840238\pi$
$491$		−	21.3209i		−	0.962199i	0.876666	−	0.481100i	$-0.159762\pi$
$492$	40.0706	+	2.27419i	1.80652	+	0.102529i
$493$			27.0002i			1.21603i
$494$	−8.47586	+	23.3482i	−0.381347	+	1.05048i
$495$	−48.3308	−	14.4898i	−2.17231	−	0.651267i
$496$	4.36623	−	21.8389i	0.196050	−	0.980594i
$497$		−	7.65342i		−	0.343303i
$498$	19.5434	−	5.86463i	0.875759	−	0.262800i
$499$	−5.92357			−0.265175			−0.132588	−	0.991171i	$-0.542329\pi$
$499$	−5.92357			−0.265175			−0.132588	+	0.991171i	$0.542329\pi$
$500$	18.3056	+	15.3079i	0.818649	+	0.684591i
$501$	9.47078	+	12.7266i	0.423123	+	0.568584i
$502$	−11.8583	+	32.6656i	−0.529261	+	1.45794i
$503$			4.47081i			0.199343i	0.995020	+	0.0996717i	$0.0317793\pi$
$503$			4.47081i			0.199343i	−0.995020	+	0.0996717i	$0.968221\pi$
$504$	17.7437	−	4.24523i	0.790365	−	0.189098i
$505$	−2.28113			−0.101509
$506$	−7.40463	+	20.3973i	−0.329176	+	0.906770i
$507$	9.22717	+	12.3993i	0.409793	+	0.550671i
$508$	7.51087	−	8.98168i	0.333241	−	0.398498i
$509$			0.698629i			0.0309662i	0.999880	+	0.0154831i	$0.00492862\pi$
$509$			0.698629i			0.0309662i	−0.999880	+	0.0154831i	$0.995071\pi$
$510$	11.3901	+	37.9566i	0.504363	+	1.68075i
$511$		−	19.6825i		−	0.870703i
$512$	22.6268	−	0.170881i	0.999971	−	0.00755194i
$513$	6.65583	+	18.3200i	0.293862	+	0.808847i
$514$	8.02223	−	22.0986i	0.353846	−	0.974727i
$515$	12.4024			0.546513
$516$	1.04317	−	18.3803i	0.0459230	−	0.809148i
$517$	3.69319			0.162426
$518$	9.23045	+	3.35084i	0.405563	+	0.147227i
$519$	−1.50193	−	2.01826i	−0.0659272	−	0.0885916i
$520$	−24.2309	−	41.7263i	−1.06260	−	1.82982i
$521$			22.2422i			0.974447i	0.873277	+	0.487224i	$0.161990\pi$
$521$			22.2422i			0.974447i	−0.873277	+	0.487224i	$0.838010\pi$
$522$	−20.6999	−	15.3960i	−0.906011	−	0.673867i
$523$	6.70947			0.293385			0.146692	−	0.989182i	$-0.453137\pi$
$523$	6.70947			0.293385			0.146692	+	0.989182i	$0.453137\pi$
$524$	−9.72106	−	8.12917i	−0.424666	−	0.355125i
$525$	18.3973	+	24.7219i	0.802925	+	1.07895i
$526$	15.4011	+	5.59093i	0.671522	+	0.243776i
$527$	23.0031	+	9.06038i	1.00203	+	0.394676i
$528$	−23.3318	−	21.8734i	−1.01539	−	0.951919i
$529$	−11.9511			−0.519613
$530$	3.80498	−	10.4815i	0.165278	−	0.455285i
$531$	−5.26337	+	17.5560i	−0.228411	+	0.761867i
$532$	10.3480	−	12.3744i	0.448643	−	0.536498i
$533$		−	54.2484i		−	2.34976i
$534$	−13.1247	−	43.7370i	−0.567963	−	1.89269i
$535$	−38.5268			−1.66566
$536$	8.37409	−	4.86293i	0.361706	−	0.210047i
$537$	−7.92333	+	5.89630i	−0.341917	+	0.254444i
$538$	−7.32739	+	20.1845i	−0.315906	+	0.870217i
$539$		−	10.9724i		−	0.472613i
$540$	−35.5945	−	12.9112i	−1.53174	−	0.555611i
$541$			4.44772i			0.191222i	0.995419	+	0.0956111i	$0.0304805\pi$
$541$			4.44772i			0.191222i	−0.995419	+	0.0956111i	$0.969519\pi$
$542$	4.86992	−	13.4150i	0.209181	−	0.576224i
$543$	−13.8128	−	18.5614i	−0.592764	−	0.796544i
$544$	−4.25799	+	24.7551i	−0.182560	+	1.06137i
$545$			61.3146i			2.62643i
$546$	−7.08781	−	23.6195i	−0.303330	−	1.01082i
$547$			14.4972i			0.619855i	0.950760	+	0.309927i	$0.100305\pi$
$547$			14.4972i			0.619855i	−0.950760	+	0.309927i	$0.899695\pi$
$548$	−34.5843	−	28.9209i	−1.47737	−	1.23544i
$549$	−0.499239	+	1.66522i	−0.0213070	+	0.0710697i
$550$	18.4331	−	50.7769i	0.785988	−	2.16514i
$551$	−22.8093			−0.971708
$552$	−6.41508	+	14.9673i	−0.273044	+	0.637051i
$553$			8.94407i			0.380341i
$554$	14.6437	+	5.31594i	0.622149	+	0.225853i
$555$	−12.1668	−	16.3494i	−0.516450	−	0.693995i
$556$	22.8008	+	19.0671i	0.966971	+	0.808623i
$557$			42.8552i			1.81583i	0.419153	+	0.907916i	$0.362327\pi$
$557$			42.8552i			1.81583i	−0.419153	+	0.907916i	$0.637673\pi$
$558$	−20.0630	+	12.4691i	−0.849333	+	0.527857i
$559$	−24.8837			−1.05247
$560$	5.54490	+	30.8410i	0.234315	+	1.30327i
$561$	28.4817	−	21.1952i	1.20250	−	0.894863i
$562$	9.73220	−	26.8090i	0.410528	−	1.13087i
$563$	−39.5900			−1.66852			−0.834260	−	0.551371i	$-0.814105\pi$
$563$	−39.5900			−1.66852			−0.834260	+	0.551371i	$0.814105\pi$
$564$	2.76703	+	0.157042i	0.116513	+	0.00661266i
$565$		−	22.0267i		−	0.926670i
$566$	−10.7347	+	29.5706i	−0.451214	+	1.24294i
$567$	−16.1594	−	10.6462i	−0.678630	−	0.447098i
$568$	−8.70630	+	5.05585i	−0.365308	+	0.212139i
$569$	11.8437			0.496512			0.248256	−	0.968694i	$-0.420143\pi$
$569$	11.8437			0.496512			0.248256	+	0.968694i	$0.420143\pi$
$570$	−32.0650	+	9.62215i	−1.34305	+	0.403027i
$571$	−22.4115			−0.937891			−0.468945	−	0.883227i	$-0.655366\pi$
$571$	−22.4115			−0.937891			−0.468945	+	0.883227i	$0.655366\pi$
$572$	−27.7307	+	33.1610i	−1.15948	+	1.38653i
$573$	−17.7863	+	13.2360i	−0.743034	+	0.552944i
$574$	−12.0216	+	33.1154i	−0.501771	+	1.38221i
$575$	−27.5051			−1.14704
$576$	−16.5507	−	17.3803i	−0.689613	−	0.724178i
$577$	14.3157			0.595969			0.297984	−	0.954571i	$-0.403686\pi$
$577$	14.3157			0.595969			0.297984	+	0.954571i	$0.403686\pi$
$578$	−3.61196	−	1.31121i	−0.150238	−	0.0545393i
$579$	−6.34293	−	8.52350i	−0.263603	−	0.354224i
$580$	28.4241	−	33.9902i	1.18025	−	1.41136i
$581$			17.9106i			0.743058i
$582$	−9.56875	−	31.8870i	−0.396637	−	1.32176i
$583$	−9.98976			−0.413733
$584$	−22.3903	+	13.0023i	−0.926516	+	0.538038i
$585$	−14.6973	+	49.0228i	−0.607657	+	2.02685i
$586$	−45.2001	−	16.4086i	−1.86720	−	0.677831i
$587$		−	28.3011i		−	1.16811i	−0.811714	−	0.584055i	$-0.801465\pi$
$587$		−	28.3011i		−	1.16811i	0.811714	−	0.584055i	$-0.198535\pi$
$588$	0.466568	−	8.22078i	0.0192409	−	0.339019i
$589$	−7.65403	+	19.4325i	−0.315379	+	0.800703i
$590$	−29.5898	−	10.7417i	−1.21819	−	0.442228i
$591$	29.6147	−	22.0384i	1.21819	−	0.906539i
$592$	−2.28582	−	12.7139i	−0.0939467	−	0.522536i
$593$			1.10506i			0.0453794i	0.999743	+	0.0226897i	$0.00722298\pi$
$593$			1.10506i			0.0453794i	−0.999743	+	0.0226897i	$0.992777\pi$
$594$	0.00867490	+	33.9216i	0.000355935	+	1.39182i
$595$	−34.7855			−1.42607
$596$	24.6766	+	20.6357i	1.01079	+	0.845270i
$597$	−13.5101	+	10.0538i	−0.552932	+	0.411475i
$598$	20.6894	+	7.51066i	0.846051	+	0.307134i
$599$			13.4417i			0.549213i	0.961557	+	0.274607i	$0.0885476\pi$
$599$			13.4417i			0.549213i	−0.961557	+	0.274607i	$0.911452\pi$
$600$	15.9697	−	37.2596i	0.651959	−	1.52112i
$601$		−	33.4719i		−	1.36535i	−0.730724	−	0.682673i	$-0.760817\pi$
$601$		−	33.4719i		−	1.36535i	0.730724	−	0.682673i	$-0.239183\pi$
$602$	15.1900	+	5.51428i	0.619099	+	0.224745i
$603$	−9.83845	−	2.94961i	−0.400652	−	0.120117i
$604$	−24.2495	+	28.9981i	−0.986698	+	1.17992i
$605$	−37.5596			−1.52701
$606$	0.440789	+	1.46889i	0.0179058	+	0.0596696i
$607$	−10.0827			−0.409245			−0.204623	−	0.978841i	$-0.565597\pi$
$607$	−10.0827			−0.409245			−0.204623	+	0.978841i	$0.565597\pi$
$608$	−20.9127	−	3.59706i	−0.848120	−	0.145880i
$609$	18.1666	−	13.5191i	0.736149	−	0.547821i
$610$	−2.80663	−	1.01886i	−0.113637	−	0.0412526i
$611$		−	3.74607i		−	0.151550i
$612$	22.2405	−	14.6689i	0.899018	−	0.592956i
$613$	−25.2904			−1.02147			−0.510736	−	0.859738i	$-0.670627\pi$
$613$	−25.2904			−1.02147			−0.510736	+	0.859738i	$0.670627\pi$
$614$	3.99925	−	11.0166i	0.161396	−	0.444593i
$615$	58.6557	−	43.6499i	2.36523	−	1.76013i
$616$	24.2765	−	14.0976i	0.978128	−	0.568010i
$617$			0.251995i			0.0101449i	0.999987	+	0.00507246i	$0.00161462\pi$
$617$			0.251995i			0.0101449i	−0.999987	+	0.00507246i	$0.998385\pi$
$618$	−2.39654	−	7.98627i	−0.0964031	−	0.321255i
$619$	16.3930			0.658891			0.329446	−	0.944175i	$-0.393138\pi$
$619$	16.3930			0.658891			0.329446	+	0.944175i	$0.393138\pi$
$620$	−19.4200	−	35.6220i	−0.779926	−	1.43062i
$621$	16.2338	−	5.89789i	0.651439	−	0.236674i
$622$	13.5758	−	37.3969i	0.544342	−	1.49948i
$623$	40.0831			1.60589
$624$	−22.1867	+	23.6659i	−0.888177	+	0.947396i
$625$	2.09752			0.0839007
$626$	−8.55555	+	23.5677i	−0.341948	+	0.941954i
$627$	17.9053	+	24.0608i	0.715069	+	0.960894i
$628$	0.00429790	−	0.00513953i	0.000171505	−	0.000205089i
$629$	14.3399			0.571771
$630$	19.8354	−	26.6686i	0.790260	−	1.06250i
$631$		−	15.9578i		−	0.635268i	−0.948213	−	0.317634i	$-0.897112\pi$
$631$		−	15.9578i		−	0.635268i	0.948213	−	0.317634i	$-0.102888\pi$
$632$	10.1745	−	5.90846i	0.404721	−	0.235026i
$633$	4.74531	−	3.53132i	0.188609	−	0.140357i
$634$	15.2690	+	5.54294i	0.606408	+	0.220138i
$635$		−	21.3293i		−	0.846426i
$636$	−7.48459	−	0.424785i	−0.296783	−	0.0168438i
$637$	−11.1295			−0.440966
$638$	−37.3129	−	13.5453i	−1.47723	−	0.536265i
$639$	10.2288	+	3.06662i	0.404643	+	0.121314i
$640$	31.4209	−	26.6813i	1.24202	−	1.05467i
$641$	−17.2875			−0.682815			−0.341407	−	0.939915i	$-0.610904\pi$
$641$	−17.2875			−0.682815			−0.341407	+	0.939915i	$0.610904\pi$
$642$	7.44464	+	24.8086i	0.293817	+	0.979118i
$643$	−29.5302			−1.16456			−0.582278	−	0.812989i	$-0.697839\pi$
$643$	−29.5302			−1.16456			−0.582278	+	0.812989i	$0.697839\pi$
$644$	−10.9652	−	9.16962i	−0.432091	−	0.361334i
$645$	−20.0221	−	26.9053i	−0.788371	−	1.05940i
$646$	8.03806	−	22.1422i	0.316253	−	0.871173i
$647$	22.6935			0.892174			0.446087	−	0.894990i	$-0.352817\pi$
$647$	22.6935			0.892174			0.446087	+	0.894990i	$0.352817\pi$
$648$	−1.43592	+	25.4153i	−0.0564082	+	0.998408i
$649$			28.2017i			1.10701i
$650$	−51.5041	−	18.6970i	−2.02016	−	0.733357i
$651$	−5.42155	−	20.0137i	−0.212487	−	0.784401i
$652$	−17.2547	+	20.6335i	−0.675745	+	0.808072i
$653$	−1.25449			−0.0490919			−0.0245459	−	0.999699i	$-0.507814\pi$
$653$	−1.25449			−0.0490919			−0.0245459	+	0.999699i	$0.507814\pi$
$654$	39.4824	−	11.8480i	1.54388	−	0.463293i
$655$	−23.0851			−0.902010
$656$	45.6126	−	8.20068i	1.78087	−	0.320183i
$657$	26.3056	+	7.88652i	1.02628	+	0.307683i
$658$	−0.830137	+	2.28675i	−0.0323621	+	0.0891469i
$659$	49.7382			1.93752			0.968762	−	0.247993i	$-0.0797711\pi$
$659$	49.7382			1.93752			0.968762	+	0.247993i	$0.0797711\pi$
$660$	−58.1681	−	3.30131i	−2.26419	−	0.128503i
$661$			3.84320i			0.149483i	0.997203	+	0.0747415i	$0.0238132\pi$
$661$			3.84320i			0.149483i	−0.997203	+	0.0747415i	$0.976187\pi$
$662$	−0.163775	−	0.0594536i	−0.00636529	−	0.00231073i
$663$	−21.4987	−	28.8895i	−0.834942	−	1.12198i
$664$	20.3746	−	11.8318i	0.790688	−	0.459162i
$665$		−	29.3861i		−	1.13955i
$666$	−8.17690	+	10.9938i	−0.316848	+	0.426001i
$667$			20.2118i			0.782605i
$668$	14.0522	+	11.7510i	0.543695	+	0.454662i
$669$	40.5926	−	30.2078i	1.56940	−	1.16790i
$670$	6.01966	−	16.5822i	0.232560	−	0.640625i
$671$			2.67497i			0.103266i
$672$	18.7881	−	9.53004i	0.724765	−	0.367629i
$673$		−	17.3661i		−	0.669413i	−0.942322	−	0.334707i	$-0.891363\pi$
$673$		−	17.3661i		−	0.669413i	0.942322	−	0.334707i	$-0.108637\pi$
$674$	7.79747	−	21.4794i	0.300347	−	0.827357i
$675$	−40.4123	+	14.6822i	−1.55547	+	0.565118i
$676$	13.6907	+	11.4488i	0.526566	+	0.440338i
$677$			32.0768i			1.23281i	0.787429	+	0.616406i	$0.211412\pi$
$677$			32.0768i			1.23281i	−0.787429	+	0.616406i	$0.788588\pi$
$678$	−14.1837	+	4.25628i	−0.544721	+	0.163461i
$679$	29.2230			1.12148
$680$	22.9793	+	39.5710i	0.881218	+	1.51748i
$681$	−0.0689303	−	0.0926270i	−0.00264141	−	0.00354947i
$682$	−24.0610	+	27.2436i	−0.921343	+	1.04321i
$683$	−41.0747			−1.57168			−0.785841	−	0.618429i	$-0.787769\pi$
$683$	−41.0747			−1.57168			−0.785841	+	0.618429i	$0.787769\pi$
$684$	12.3920	+	18.7883i	0.473820	+	0.718390i
$685$	−82.1291			−3.13799
$686$	26.8015	+	9.72949i	1.02329	+	0.371474i
$687$	0.748970	+	1.00645i	0.0285750	+	0.0383985i
$688$	−3.76164	−	20.9225i	−0.143411	−	0.797661i
$689$			10.1328i			0.386029i
$690$	8.52641	+	28.4135i	0.324595	+	1.08168i
$691$		−	19.3907i		−	0.737656i	−0.929498	−	0.368828i	$-0.879759\pi$
$691$		−	19.3907i		−	0.737656i	0.929498	−	0.368828i	$-0.120241\pi$
$692$	−2.22847	−	1.86354i	−0.0847136	−	0.0708412i
$693$	−28.5217	−	8.55092i	−1.08345	−	0.324822i
$694$	0.422029	−	1.16255i	0.0160200	−	0.0441298i
$695$	54.1463			2.05389
$696$	−27.3798	−	11.7351i	−1.03783	−	0.444819i
$697$			51.4464i			1.94867i
$698$	−5.62500	+	15.4950i	−0.212909	+	0.586494i
$699$	25.5931	−	19.0456i	0.968020	−	0.720371i
$700$	27.2968	+	22.8268i	1.03172	+	0.862773i
$701$	13.7072			0.517712			0.258856	−	0.965916i	$-0.416654\pi$
$701$	13.7072			0.517712			0.258856	+	0.965916i	$0.416654\pi$
$702$	34.4073	−	0.00879912i	1.29862	−	0.000332101i
$703$			12.1141i			0.456892i
$704$	−32.0741	−	18.3033i	−1.20884	−	0.689833i
$705$	4.05041	−	3.01420i	0.152547	−	0.113521i
$706$	−25.8252	−	9.37506i	−0.971944	−	0.352835i
$707$	−1.34617			−0.0506281
$708$	−1.19919	+	21.1294i	−0.0450685	+	0.794092i
$709$	21.4474			0.805473			0.402737	−	0.915316i	$-0.368059\pi$
$709$	21.4474			0.805473			0.402737	+	0.915316i	$0.368059\pi$
$710$	−6.25847	+	17.2400i	−0.234876	+	0.647006i
$711$	−11.9537	−	3.58377i	−0.448299	−	0.134402i
$712$	−26.4789	−	45.5973i	−0.992339	−	1.70883i
$713$	17.2196	+	6.78241i	0.644880	+	0.254003i
$714$	6.72171	+	22.3995i	0.251554	+	0.838280i
$715$			78.7493i			2.94506i
$716$	−7.31594	+	8.74858i	−0.273410	+	0.326950i
$717$	23.7836	+	31.9599i	0.888214	+	1.19356i
$718$	11.0829	−	30.5297i	0.413610	−	1.13936i
$719$	26.9704			1.00583			0.502913	−	0.864337i	$-0.332261\pi$
$719$	26.9704			1.00583			0.502913	+	0.864337i	$0.332261\pi$
$720$	−43.4406	−	4.94686i	−1.61894	−	0.184358i
$721$	7.31907			0.272576
$722$	−6.55202	−	2.37852i	−0.243841	−	0.0885192i
$723$	22.9179	−	17.0548i	0.852325	−	0.634275i
$724$	−20.4946	−	17.1385i	−0.761676	−	0.636947i
$725$		−	50.3153i		−	1.86866i
$726$	7.25774	+	24.1858i	0.269360	+	0.897619i
$727$	7.32145			0.271538			0.135769	−	0.990741i	$-0.456650\pi$
$727$	7.32145			0.271538			0.135769	+	0.990741i	$0.456650\pi$
$728$	−14.2995	−	24.6241i	−0.529976	−	0.912631i
$729$	20.7034	−	17.3311i	0.766794	−	0.641893i
$730$	−16.0951	+	44.3366i	−0.595706	+	1.64097i
$731$	23.5984			0.872818
$732$	−0.113745	+	2.00416i	−0.00420415	+	0.0740758i
$733$			35.0983i			1.29638i	0.761477	+	0.648192i	$0.224475\pi$
$733$			35.0983i			1.29638i	−0.761477	+	0.648192i	$0.775525\pi$
$734$	−8.37676	+	23.0752i	−0.309192	+	0.851721i
$735$	−8.95510	−	12.0337i	−0.330314	−	0.443869i
$736$	−3.18744	+	18.5312i	−0.117491	+	0.683069i
$737$	−15.8043			−0.582158
$738$	−39.4417	−	29.3357i	−1.45187	−	1.07986i
$739$	−32.1548			−1.18283			−0.591416	−	0.806366i	$-0.701431\pi$
$739$	−32.1548			−1.18283			−0.591416	+	0.806366i	$0.701431\pi$
$740$	−18.0523	−	15.0961i	−0.663616	−	0.554945i
$741$	24.4053	−	18.1617i	0.896551	−	0.667187i
$742$	2.24545	−	6.18547i	0.0824331	−	0.227076i
$743$	−15.9147			−0.583855			−0.291927	−	0.956441i	$-0.594297\pi$
$743$	−15.9147			−0.583855			−0.291927	+	0.956441i	$0.594297\pi$
$744$	−19.1856	+	19.3885i	−0.703377	+	0.710817i
$745$	58.6009			2.14697
$746$	15.0873	−	41.5605i	0.552385	−	1.52164i
$747$	−23.9375	−	7.17655i	−0.875826	−	0.262576i
$748$	26.2984	−	31.4482i	0.961563	−	1.14986i
$749$	−22.7360			−0.830756
$750$	−8.40006	−	27.9925i	−0.306727	−	1.02214i
$751$	48.1653			1.75758			0.878788	−	0.477212i	$-0.158352\pi$
$751$	48.1653			1.75758			0.878788	+	0.477212i	$0.158352\pi$
$752$	3.14973	−	0.566290i	0.114859	−	0.0206505i
$753$	34.1446	−	25.4094i	1.24430	−	0.925970i
$754$	−13.7393	+	37.8472i	−0.500356	+	1.37831i
$755$			68.8633i			2.50619i
$756$	−21.0056	−	7.61937i	−0.763965	−	0.277114i
$757$	35.6219			1.29470			0.647351	−	0.762192i	$-0.275877\pi$
$757$	35.6219			1.29470			0.647351	+	0.762192i	$0.275877\pi$
$758$	12.3130	−	33.9182i	0.447228	−	1.23196i
$759$	21.3208	−	15.8663i	0.773896	−	0.575911i
$760$	−33.4288	+	19.4125i	−1.21259	+	0.704165i
$761$	12.1749			0.441339			0.220670	−	0.975349i	$-0.429176\pi$
$761$	12.1749			0.441339			0.220670	+	0.975349i	$0.429176\pi$
$762$	−13.7346	+	4.12151i	−0.497551	+	0.149307i
$763$			36.1839i			1.30994i
$764$	−16.4229	+	19.6388i	−0.594158	+	0.710508i
$765$	13.9381	−	46.4907i	0.503933	−	1.68087i
$766$	37.0595	+	13.4534i	1.33901	+	0.486089i
$767$	28.6055			1.03288
$768$	−23.2525	−	15.0772i	−0.839052	−	0.544051i
$769$	−31.5811			−1.13884			−0.569422	−	0.822046i	$-0.692833\pi$
$769$	−31.5811			−1.13884			−0.569422	+	0.822046i	$0.692833\pi$
$770$	17.4510	−	48.0717i	0.628891	−	1.73238i
$771$	−23.0991	+	17.1897i	−0.831895	+	0.619072i
$772$	−9.41126	−	7.87011i	−0.338719	−	0.283251i
$773$			10.4729i			0.376684i	0.982103	+	0.188342i	$0.0603114\pi$
$773$			10.4729i			0.376684i	−0.982103	+	0.188342i	$0.939689\pi$
$774$	−13.4562	+	18.0919i	−0.483675	+	0.650299i
$775$	−42.8665	−	16.8841i	−1.53981	−	0.606495i
$776$	−19.3048	−	33.2433i	−0.693001	−	1.19336i
$777$	−7.18003	−	9.64837i	−0.257582	−	0.346133i
$778$	15.8535	−	43.6712i	0.568377	−	1.56569i
$779$	−43.4609			−1.55715
$780$	−3.34858	+	59.0010i	−0.119899	+	2.11257i
$781$	16.4313			0.587956
$782$	−19.6207	−	7.12272i	−0.701635	−	0.254708i
$783$	10.7890	+	29.6965i	0.385569	+	1.06127i
$784$	−1.68243	−	9.35777i	−0.0600869	−	0.334206i
$785$		−	0.0122051i		−	0.000435619i
$786$	4.46080	+	14.8652i	0.159111	+	0.530225i
$787$	−5.49800			−0.195982			−0.0979912	−	0.995187i	$-0.531242\pi$
$787$	−5.49800			−0.195982			−0.0979912	+	0.995187i	$0.531242\pi$
$788$	27.3445	−	32.6993i	0.974109	−	1.16486i
$789$	−11.9800	−	16.0985i	−0.426499	−	0.573120i
$790$	7.31389	−	20.1473i	0.260216	−	0.716810i
$791$		−	12.9987i		−	0.462181i
$792$	9.11416	+	38.0942i	0.323858	+	1.35362i
$793$	2.71327			0.0963512
$794$	4.90852	−	13.5213i	0.174197	−	0.479854i
$795$	−10.9560	+	8.15315i	−0.388570	+	0.289162i
$796$	−12.4744	+	14.9172i	−0.442145	+	0.528728i
$797$			43.5524i			1.54271i	0.636408	+	0.771353i	$0.280420\pi$
$797$			43.5524i			1.54271i	−0.636408	+	0.771353i	$0.719580\pi$
$798$	−18.9227	+	5.67837i	−0.669855	+	0.201012i
$799$			3.55258i			0.125681i
$800$	7.93481	−	46.1315i	0.280538	−	1.63100i
$801$	−16.0608	+	53.5708i	−0.567479	+	1.89283i
$802$	9.76882	+	3.54628i	0.344949	+	0.125223i
$803$	42.2567			1.49121
$804$	−11.8410	−	0.672031i	−0.417599	−	0.0237007i
$805$	−26.0397			−0.917780
$806$	27.6337	+	24.4055i	0.973356	+	0.859648i
$807$	21.0984	−	15.7008i	0.742700	−	0.552695i
$808$	0.889283	+	1.53137i	0.0312849	+	0.0538734i
$809$	39.7151			1.39631			0.698154	−	0.715948i	$-0.254005\pi$
$809$	39.7151			1.39631			0.698154	+	0.715948i	$0.254005\pi$
$810$	27.6946	+	37.1956i	0.973091	+	1.30692i
$811$		−	42.1366i		−	1.47962i	−0.672817	−	0.739809i	$-0.734916\pi$
$811$		−	42.1366i		−	1.47962i	0.672817	−	0.739809i	$-0.265084\pi$
$812$	16.7740	−	20.0588i	0.588653	−	0.703925i
$813$	−14.0224	+	10.4350i	−0.491787	+	0.365973i
$814$	−7.19397	+	19.8170i	−0.252149	+	0.694586i
$815$			48.9996i			1.71638i
$816$	21.0407	−	22.4435i	0.736570	−	0.785681i
$817$			19.9355i			0.697453i
$818$	−2.23021	+	6.14349i	−0.0779775	+	0.214802i
$819$	−8.67336	+	28.9301i	−0.303072	+	1.01090i
$820$	54.1593	−	64.7650i	1.89133	−	2.26169i
$821$		−	7.45637i		−	0.260229i	−0.991499	−	0.130115i	$-0.958465\pi$
$821$		−	7.45637i		−	0.260229i	0.991499	−	0.130115i	$-0.0415345\pi$
$822$	15.8700	+	52.8855i	0.553531	+	1.84459i
$823$			30.9791i			1.07986i	0.841709	+	0.539932i	$0.181550\pi$
$823$			30.9791i			1.07986i	−0.841709	+	0.539932i	$0.818450\pi$
$824$	−4.83498	−	8.32596i	−0.168435	−	0.290048i
$825$	−53.0760	+	39.4975i	−1.84787	+	1.37513i
$826$	−17.4619	−	6.33904i	−0.607579	−	0.220563i
$827$			0.410205i			0.0142642i	0.999975	+	0.00713212i	$0.00227024\pi$
$827$			0.410205i			0.0142642i	−0.999975	+	0.00713212i	$0.997730\pi$
$828$	16.6488	−	10.9808i	0.578585	−	0.381611i
$829$	8.86877			0.308025			0.154013	−	0.988069i	$-0.450780\pi$
$829$	8.86877			0.308025			0.154013	+	0.988069i	$0.450780\pi$
$830$	14.6462	−	40.3453i	0.508376	−	1.40041i
$831$	−11.3908	−	15.3067i	−0.395142	−	0.530983i
$832$	−18.5654	+	32.5334i	−0.643640	+	1.12789i
$833$	10.5546			0.365696
$834$	−10.4628	−	34.8665i	−0.362299	−	1.20733i
$835$	33.3704			1.15483
$836$	26.5668	+	22.2163i	0.918832	+	0.768368i
$837$	28.9206	+	0.773363i	0.999643	+	0.0267313i
$838$	18.0131	+	6.53912i	0.622252	+	0.225890i
$839$		−	2.12446i		−	0.0733445i	−0.999327	−	0.0366723i	$-0.988324\pi$
$839$		−	2.12446i		−	0.0733445i	0.999327	−	0.0366723i	$-0.0116758\pi$
$840$	15.1189	−	35.2745i	0.521650	−	1.21709i
$841$	−7.97362			−0.274952
$842$	0.339775	−	0.935967i	0.0117094	−	0.0322556i
$843$	−28.0228	+	20.8537i	−0.965156	+	0.718240i
$844$	4.38154	−	5.23955i	0.150819	−	0.180353i
$845$	32.5121			1.11845
$846$	−2.72361	−	2.02575i	−0.0936396	−	0.0696466i
$847$	−22.1652			−0.761606
$848$	−8.51976	+	1.53177i	−0.292570	+	0.0526011i
$849$	30.9094	−	23.0019i	1.06081	−	0.789423i
$850$	48.8437	+	17.7313i	1.67533	+	0.608177i
$851$	10.7346			0.367977
$852$	12.3107	+	0.698691i	0.421758	+	0.0239368i
$853$		−	14.1989i		−	0.486161i	−0.970006	−	0.243080i	$-0.921842\pi$
$853$		−	14.1989i		−	0.486161i	0.970006	−	0.243080i	$-0.0781578\pi$
$854$	−1.65629	−	0.601267i	−0.0566771	−	0.0205749i
$855$	39.2744	+	11.7746i	1.34316	+	0.402684i
$856$	15.0194	+	25.8638i	0.513353	+	0.884007i
$857$		−	22.9886i		−	0.785274i	−0.919694	−	0.392637i	$-0.871563\pi$
$857$		−	22.9886i		−	0.785274i	0.919694	−	0.392637i	$-0.128437\pi$
$858$	50.7091	−	15.2169i	1.73118	−	0.519498i
$859$	51.8987			1.77076			0.885380	−	0.464867i	$-0.153898\pi$
$859$	51.8987			1.77076			0.885380	+	0.464867i	$0.153898\pi$
$860$	−29.7076	−	24.8428i	−1.01302	−	0.847133i
$861$	34.6148	−	25.7593i	1.17967	−	0.877875i
$862$	−1.21200	+	3.33866i	−0.0412809	+	0.113715i
$863$	23.9812			0.816328			0.408164	−	0.912909i	$-0.366169\pi$
$863$	23.9812			0.816328			0.408164	+	0.912909i	$0.366169\pi$
$864$	5.20872	+	28.9287i	0.177204	+	0.984174i
$865$	−5.29206			−0.179935
$866$	4.63842	−	12.7773i	0.157620	−	0.434191i
$867$	2.80961	+	3.77549i	0.0954193	+	0.128222i
$868$	−11.4604	−	21.0218i	−0.388992	−	0.713527i
$869$	−19.2022			−0.651390
$870$	−51.9770	+	15.5974i	−1.76219	+	0.528802i
$871$			16.0306i			0.543176i
$872$	41.1617	−	23.9031i	1.39391	−	0.809461i
$873$	−11.7093	+	39.0565i	−0.396299	+	1.32186i
$874$	6.01713	−	16.5752i	0.203532	−	0.560664i
$875$	25.6539			0.867259
$876$	31.6598	+	1.79685i	1.06969	+	0.0607098i
$877$		−	8.17468i		−	0.276039i	−0.990429	−	0.138020i	$-0.955926\pi$
$877$		−	8.17468i		−	0.276039i	0.990429	−	0.138020i	$-0.0440737\pi$
$878$	4.95578	+	1.79905i	0.167249	+	0.0607149i
$879$	35.1595	+	47.2466i	1.18590	+	1.59359i
$880$	−66.2131	+	11.9044i	−2.23204	+	0.401299i
$881$	−25.6117			−0.862879			−0.431439	−	0.902142i	$-0.641994\pi$
$881$	−25.6117			−0.862879			−0.431439	+	0.902142i	$0.641994\pi$
$882$	−6.01844	+	8.09177i	−0.202651	+	0.272464i
$883$	−7.29614			−0.245535			−0.122767	−	0.992435i	$-0.539177\pi$
$883$	−7.29614			−0.245535			−0.122767	+	0.992435i	$0.539177\pi$
$884$	−31.8985	−	26.6749i	−1.07286	−	0.897175i
$885$	23.0168	+	30.9295i	0.773701	+	1.03968i
$886$	14.1475	+	5.13584i	0.475295	+	0.172542i
$887$		−	47.3727i		−	1.59062i	−0.606204	−	0.795310i	$-0.707308\pi$
$887$		−	47.3727i		−	1.59062i	0.606204	−	0.795310i	$-0.292692\pi$
$888$	−6.23257	+	14.5415i	−0.209151	+	0.487981i
$889$		−	12.5871i		−	0.422159i
$890$	−90.2907	−	32.7774i	−3.02655	−	1.09870i
$891$	22.8565	−	34.6928i	0.765722	−	1.16225i
$892$	37.4809	−	44.8206i	1.25495	−	1.50070i
$893$	−3.00115			−0.100430
$894$	−11.3236	−	37.7349i	−0.378718	−	1.26204i
$895$			20.7757i			0.694455i
$896$	18.5426	−	15.7456i	0.619464	−	0.526023i
$897$	−16.0935	−	21.6261i	−0.537347	−	0.722075i
$898$	32.2468	+	11.7063i	1.07609	+	0.390643i
$899$	−12.4071	+	31.4999i	−0.413800	+	1.05058i
$900$	−41.4454	+	27.3357i	−1.38151	+	0.911190i
$901$		−	9.60942i		−	0.320136i
$902$	−71.0961	−	25.8093i	−2.36724	−	0.859356i
$903$	−11.8158	−	15.8778i	−0.393204	−	0.528379i
$904$	−14.7870	+	8.58696i	−0.491807	+	0.285598i
$905$	−48.6696			−1.61783
$906$	44.3433	−	13.3067i	1.47321	−	0.442084i
$907$		−	58.0442i		−	1.92733i	−0.267118	−	0.963664i	$-0.586071\pi$
$907$		−	58.0442i		−	1.92733i	0.267118	−	0.963664i	$-0.413929\pi$
$908$	−0.102275	−	0.0855264i	−0.00339410	−	0.00283829i
$909$	0.539394	−	1.79915i	0.0178906	−	0.0596742i
$910$	−48.7601	−	17.7009i	−1.61638	−	0.586779i
$911$	−57.4412			−1.90311			−0.951556	−	0.307476i	$-0.900515\pi$
$911$	−57.4412			−1.90311			−0.951556	+	0.307476i	$0.900515\pi$
$912$	18.9599	+	17.7747i	0.627824	+	0.588580i
$913$	−38.4526			−1.27260
$914$	13.7932	−	37.9957i	0.456239	−	1.25679i
$915$	2.18318	+	2.93371i	0.0721736	+	0.0969854i
$916$	1.11128	+	0.929298i	0.0367176	+	0.0307049i
$917$	−13.6233			−0.449882
$918$	−32.6301	+	0.00834462i	−1.07695	+	0.000275414i
$919$	−41.7447			−1.37703			−0.688515	−	0.725222i	$-0.741737\pi$
$919$	−41.7447			−1.37703			−0.688515	+	0.725222i	$0.741737\pi$
$920$	17.2019	+	29.6221i	0.567129	+	0.976610i
$921$	−11.5154	+	8.56941i	−0.379445	+	0.282372i
$922$	12.8343	−	35.3543i	0.422676	−	1.16433i
$923$		−	16.6665i		−	0.548586i
$924$	−34.3270	−	1.94822i	−1.12928	−	0.0640917i
$925$	−26.7226			−0.878635
$926$	−14.9632	+	41.2187i	−0.491722	+	1.35453i
$927$	−2.93265	+	9.78190i	−0.0963210	+	0.321280i
$928$	−33.8992	−	5.83081i	−1.11280	−	0.191406i
$929$	14.4303			0.473443			0.236721	−	0.971578i	$-0.423927\pi$
$929$	14.4303			0.473443			0.236721	+	0.971578i	$0.423927\pi$
$930$	−4.15342	+	49.5161i	−0.136196	+	1.62370i
$931$			8.91633i			0.292221i
$932$	23.6312	−	28.2587i	0.774065	−	0.925645i
$933$	−39.0901	+	29.0897i	−1.27975	+	0.952355i
$934$	29.9414	+	10.8693i	0.979712	+	0.355655i
$935$		−	74.6817i		−	2.44235i
$936$	38.6397	−	9.24467i	1.26298	−	0.302172i
$937$	24.0895			0.786970			0.393485	−	0.919331i	$-0.371269\pi$
$937$	24.0895			0.786970			0.393485	+	0.919331i	$0.371269\pi$
$938$	3.55241	−	9.78571i	0.115990	−	0.319515i
$939$	24.6347	−	18.3324i	0.803925	−	0.598257i
$940$	3.73992	−	4.47228i	0.121983	−	0.145870i
$941$		−	22.7146i		−	0.740474i	−0.928937	−	0.370237i	$-0.879277\pi$
$941$		−	22.7146i		−	0.740474i	0.928937	−	0.370237i	$-0.120723\pi$
$942$	−0.00785925	+	0.00235843i	−0.000256068	+	7.68417e-5i
$943$			38.5117i			1.25411i
$944$	4.32426	+	24.0518i	0.140743	+	0.782819i
$945$	−38.2593	+	13.9000i	−1.24457	+	0.452166i
$946$	−11.8387	+	32.6117i	−0.384909	+	1.06030i
$947$			14.5545i			0.472957i	0.971637	+	0.236478i	$0.0759932\pi$
$947$			14.5545i			0.472957i	−0.971637	+	0.236478i	$0.924007\pi$
$948$	−14.3868	−	0.816517i	−0.467261	−	0.0265192i
$949$		−	42.8618i		−	1.39135i
$950$	−14.9790	+	41.2622i	−0.485984	+	1.33872i
$951$	−11.8772	−	15.9603i	−0.385144	−	0.517548i
$952$	13.5609	+	23.3522i	0.439512	+	0.756850i
$953$	2.15290			0.0697392			0.0348696	−	0.999392i	$-0.488898\pi$
$953$	2.15290			0.0697392			0.0348696	+	0.999392i	$0.488898\pi$
$954$	7.36713	+	5.47947i	0.238520	+	0.177404i
$955$			46.6374i			1.50915i
$956$	35.2886	+	29.5099i	1.14132	+	0.954418i
$957$	29.0243	+	39.0023i	0.938223	+	1.26076i
$958$	−13.3543	+	36.7866i	−0.431457	+	1.18852i
$959$	−48.4672			−1.56509
$960$	−50.1148	+	6.10360i	−1.61745	+	0.196993i
$961$	22.6732	+	21.1406i	0.731393	+	0.681956i
$962$	20.1008	+	7.29699i	0.648075	+	0.235264i
$963$	9.11002	−	30.3866i	0.293566	−	0.979193i
$964$	21.1610	−	25.3049i	0.681551	−	0.815015i
$965$	−22.3494			−0.719453
$966$	5.03173	+	16.7678i	0.161893	+	0.539495i
$967$		−	11.2037i		−	0.360287i	−0.983640	−	0.180144i	$-0.942344\pi$
$967$		−	11.2037i		−	0.360287i	0.983640	−	0.180144i	$-0.0576563\pi$
$968$	14.6424	+	25.2145i	0.470623	+	0.810425i
$969$	−23.1447	+	17.2236i	−0.743515	+	0.553302i
$970$	−65.8275	−	23.8967i	−2.11359	−	0.767278i
$971$	−17.0347			−0.546668			−0.273334	−	0.961919i	$-0.588126\pi$
$971$	−17.0347			−0.546668			−0.273334	+	0.961919i	$0.588126\pi$
$972$	18.5999	−	25.0209i	0.596592	−	0.802545i
$973$	31.9536			1.02439
$974$	−8.93318	+	24.6079i	−0.286238	+	0.788489i
$975$	40.0631	+	53.8360i	1.28305	+	1.72413i
$976$	0.410163	+	2.28135i	0.0131290	+	0.0730241i
$977$			35.7021i			1.14221i	0.820877	+	0.571106i	$0.193485\pi$
$977$			35.7021i			1.14221i	−0.820877	+	0.571106i	$0.806515\pi$
$978$	31.5523	−	9.46832i	1.00893	−	0.302764i
$979$			86.0551i			2.75033i
$980$	−13.2870	−	11.1112i	−0.424439	−	0.354934i
$981$	−48.3596	−	14.4984i	−1.54400	−	0.462898i
$982$	−10.2889	+	28.3426i	−0.328333	+	0.904447i
$983$	5.55921			0.177311			0.0886557	−	0.996062i	$-0.471743\pi$
$983$	5.55921			0.177311			0.0886557	+	0.996062i	$0.471743\pi$
$984$	−52.1696	−	22.3602i	−1.66311	−	0.712816i
$985$		−	77.6526i		−	2.47422i
$986$	13.0296	−	35.8923i	0.414948	−	1.14304i
$987$	2.39029	−	1.77878i	0.0760837	−	0.0566193i
$988$	22.5345	−	26.9472i	0.716917	−	0.857306i
$989$	17.6653			0.561723
$990$	57.2552	+	42.5849i	1.81969	+	1.35344i
$991$			40.5695i			1.28873i	0.764717	+	0.644366i	$0.222879\pi$
$991$			40.5695i			1.28873i	−0.764717	+	0.644366i	$0.777121\pi$
$992$	−16.3430	+	26.9241i	−0.518892	+	0.854840i
$993$	0.127395	+	0.171190i	0.00404274	+	0.00543255i
$994$	−3.69334	+	10.1739i	−0.117146	+	0.322697i
$995$			35.4248i			1.12304i
$996$	−28.8097	−	1.63509i	−0.912871	−	0.0518097i
$997$		−	55.8026i		−	1.76729i	−0.468161	−	0.883643i	$-0.655083\pi$
$997$		−	55.8026i		−	1.76729i	0.468161	−	0.883643i	$-0.344917\pi$
$998$	7.87439	+	2.85856i	0.249259	+	0.0904862i
$999$	15.7719	−	5.73010i	0.499002	−	0.181292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	744.2.o.e.557.10	yes	96
3.2	odd	2	inner	744.2.o.e.557.88	yes	96
8.5	even	2	inner	744.2.o.e.557.85	yes	96
24.5	odd	2	inner	744.2.o.e.557.11	yes	96
31.30	odd	2	inner	744.2.o.e.557.9	✓	96
93.92	even	2	inner	744.2.o.e.557.87	yes	96
248.61	odd	2	inner	744.2.o.e.557.86	yes	96
744.557	even	2	inner	744.2.o.e.557.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
744.2.o.e.557.9	✓	96	31.30	odd	2	inner
744.2.o.e.557.10	yes	96	1.1	even	1	trivial
744.2.o.e.557.11	yes	96	24.5	odd	2	inner
744.2.o.e.557.12	yes	96	744.557	even	2	inner
744.2.o.e.557.85	yes	96	8.5	even	2	inner
744.2.o.e.557.86	yes	96	248.61	odd	2	inner
744.2.o.e.557.87	yes	96	93.92	even	2	inner
744.2.o.e.557.88	yes	96	3.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 744 = 2^{3} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	744.o (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32933 - 0.482574i) q^{2} +(1.03404 + 1.38952i) q^{3} +(1.53424 + 1.28300i) q^{4} +3.64345 q^{5} +(-0.704034 - 2.34613i) q^{6} +2.15013 q^{7} +(-1.42038 - 2.44592i) q^{8} +(-0.861527 + 2.87363i) q^{9} +O(q^{10})\)	\(q+(-1.32933 - 0.482574i) q^{2} +(1.03404 + 1.38952i) q^{3} +(1.53424 + 1.28300i) q^{4} +3.64345 q^{5} +(-0.704034 - 2.34613i) q^{6} +2.15013 q^{7} +(-1.42038 - 2.44592i) q^{8} +(-0.861527 + 2.87363i) q^{9} +(-4.84335 - 1.75824i) q^{10} +4.61614i q^{11} +(-0.196288 + 3.45854i) q^{12} +4.68225 q^{13} +(-2.85823 - 1.03760i) q^{14} +(3.76747 + 5.06264i) q^{15} +(0.707811 + 3.93688i) q^{16} -4.44040 q^{17} +(2.53200 - 3.40426i) q^{18} -3.75116i q^{19} +(5.58994 + 4.67455i) q^{20} +(2.22331 + 2.98764i) q^{21} +(2.22763 - 6.13639i) q^{22} -3.32399 q^{23} +(1.92993 - 4.50282i) q^{24} +8.27473 q^{25} +(-6.22426 - 2.25953i) q^{26} +(-4.88382 + 1.77434i) q^{27} +(3.29882 + 2.75862i) q^{28} -6.08059i q^{29} +(-2.56511 - 8.54802i) q^{30} +(-5.18040 - 2.04044i) q^{31} +(0.958921 - 5.57499i) q^{32} +(-6.41422 + 4.77327i) q^{33} +(5.90276 + 2.14282i) q^{34} +7.83388 q^{35} +(-5.00867 + 3.30351i) q^{36} -3.22943 q^{37} +(-1.81021 + 4.98653i) q^{38} +(4.84162 + 6.50607i) q^{39} +(-5.17507 - 8.91160i) q^{40} -11.5860i q^{41} +(-1.51376 - 5.04448i) q^{42} -5.31448 q^{43} +(-5.92252 + 7.08229i) q^{44} +(-3.13893 + 10.4699i) q^{45} +(4.41868 + 1.60407i) q^{46} -0.800058i q^{47} +(-4.73846 + 5.05440i) q^{48} -2.37695 q^{49} +(-10.9999 - 3.99317i) q^{50} +(-4.59154 - 6.17002i) q^{51} +(7.18371 + 6.00733i) q^{52} +2.16409i q^{53} +(7.34847 - 0.00187925i) q^{54} +16.8187i q^{55} +(-3.05399 - 5.25904i) q^{56} +(5.21231 - 3.87884i) q^{57} +(-2.93434 + 8.08312i) q^{58} +6.10935 q^{59} +(-0.715166 + 12.6010i) q^{60} +0.579481 q^{61} +(5.90181 + 5.21236i) q^{62} +(-1.85239 + 6.17868i) q^{63} +(-3.96507 + 6.94825i) q^{64} +17.0595 q^{65} +(10.8301 - 3.24992i) q^{66} +3.42370i q^{67} +(-6.81265 - 5.69704i) q^{68} +(-3.43713 - 4.61875i) q^{69} +(-10.4138 - 3.78043i) q^{70} -3.55952i q^{71} +(8.25238 - 1.97441i) q^{72} -9.15412i q^{73} +(4.29298 + 1.55844i) q^{74} +(8.55639 + 11.4979i) q^{75} +(4.81275 - 5.75519i) q^{76} +9.92530i q^{77} +(-3.29646 - 10.9852i) q^{78} +4.15979i q^{79} +(2.57887 + 14.3438i) q^{80} +(-7.51554 - 4.95143i) q^{81} +(-5.59110 + 15.4016i) q^{82} +8.33003i q^{83} +(-0.422044 + 7.43629i) q^{84} -16.1784 q^{85} +(7.06470 + 2.56463i) q^{86} +(8.44910 - 6.28757i) q^{87} +(11.2907 - 6.55666i) q^{88} +18.6422 q^{89} +(9.22521 - 12.4033i) q^{90} +10.0674 q^{91} +(-5.09981 - 4.26469i) q^{92} +(-2.52150 - 9.30817i) q^{93} +(-0.386088 + 1.06354i) q^{94} -13.6672i q^{95} +(8.73811 - 4.43231i) q^{96} +13.5913 q^{97} +(3.15976 + 1.14706i) q^{98} +(-13.2651 - 3.97693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9}+O(q^{10}) \) 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9	\( 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9} - 52 q^{10} - 60 q^{16} - 4 q^{18} + 168 q^{25} - 20 q^{28} + 16 q^{31} + 8 q^{33} + 8 q^{39} - 64 q^{40} - 64 q^{49} + 56 q^{63} + 72 q^{64} + 4 q^{66} - 84 q^{70} - 44 q^{72} - 28 q^{76} + 56 q^{78} - 112 q^{81} - 108 q^{82} - 168 q^{87} + 104 q^{90} + 8 q^{94} + 72 q^{97}+O(q^{100}) \) 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9 - 52 * q^10 - 60 * q^16 - 4 * q^18 + 168 * q^25 - 20 * q^28 + 16 * q^31 + 8 * q^33 + 8 * q^39 - 64 * q^40 - 64 * q^49 + 56 * q^63 + 72 * q^64 + 4 * q^66 - 84 * q^70 - 44 * q^72 - 28 * q^76 + 56 * q^78 - 112 * q^81 - 108 * q^82 - 168 * q^87 + 104 * q^90 + 8 * q^94 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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