LMFDB - Embedded newform 696.2.l.b.347.92

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [696,2,Mod(347,696)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(696, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("696.347");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 696 = 2^{3} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	696.l (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:	$5.55758798068$
Analytic rank:	$0$
Dimension:	$104$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			347.92
Character	$\chi$	$=$	696.347
Dual form			696.2.l.b.347.89

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30342 + 0.548731i) q^{2} +(-1.37036 + 1.05930i) q^{3} +(1.39779 + 1.43045i) q^{4} +1.96366 q^{5} +(-2.36742 + 0.628752i) q^{6} -2.07610i q^{7} +(1.03697 + 2.63148i) q^{8} +(0.755764 - 2.90324i) q^{9} +O(q^{10})$	\(q+(1.30342 + 0.548731i) q^{2} +(-1.37036 + 1.05930i) q^{3} +(1.39779 + 1.43045i) q^{4} +1.96366 q^{5} +(-2.36742 + 0.628752i) q^{6} -2.07610i q^{7} +(1.03697 + 2.63148i) q^{8} +(0.755764 - 2.90324i) q^{9} +(2.55947 + 1.07752i) q^{10} +4.32719 q^{11} +(-3.43075 - 0.479550i) q^{12} -2.09729i q^{13} +(1.13922 - 2.70602i) q^{14} +(-2.69092 + 2.08011i) q^{15} +(-0.0923716 + 3.99893i) q^{16} +4.93860 q^{17} +(2.57817 - 3.36942i) q^{18} +6.72758i q^{19} +(2.74479 + 2.80892i) q^{20} +(2.19921 + 2.84500i) q^{21} +(5.64014 + 2.37446i) q^{22} -1.88085 q^{23} +(-4.20855 - 2.50761i) q^{24} -1.14403 q^{25} +(1.15084 - 2.73364i) q^{26} +(2.03974 + 4.77907i) q^{27} +(2.96975 - 2.90195i) q^{28} +(-0.219453 - 5.38069i) q^{29} +(-4.64881 + 1.23466i) q^{30} -8.14094 q^{31} +(-2.31474 + 5.16159i) q^{32} +(-5.92981 + 4.58380i) q^{33} +(6.43705 + 2.70996i) q^{34} -4.07675i q^{35} +(5.20934 - 2.97704i) q^{36} -9.56194 q^{37} +(-3.69163 + 8.76884i) q^{38} +(2.22166 + 2.87403i) q^{39} +(2.03626 + 5.16734i) q^{40} -5.31532 q^{41} +(1.30535 + 4.91499i) q^{42} -5.06216i q^{43} +(6.04850 + 6.18983i) q^{44} +(1.48407 - 5.70099i) q^{45} +(-2.45154 - 1.03208i) q^{46} +6.70159i q^{47} +(-4.10949 - 5.57782i) q^{48} +2.68982 q^{49} +(-1.49115 - 0.627765i) q^{50} +(-6.76765 + 5.23146i) q^{51} +(3.00006 - 2.93156i) q^{52} +13.7107 q^{53} +(0.0362091 + 7.34838i) q^{54} +8.49715 q^{55} +(5.46321 - 2.15285i) q^{56} +(-7.12653 - 9.21919i) q^{57} +(2.66651 - 7.13370i) q^{58} +7.04044i q^{59} +(-6.73683 - 0.941674i) q^{60} +11.7831 q^{61} +(-10.6110 - 4.46718i) q^{62} +(-6.02742 - 1.56904i) q^{63} +(-5.84939 + 5.45753i) q^{64} -4.11836i q^{65} +(-10.2443 + 2.72073i) q^{66} -1.72208 q^{67} +(6.90311 + 7.06441i) q^{68} +(2.57744 - 1.99239i) q^{69} +(2.23704 - 5.31371i) q^{70} -2.62273 q^{71} +(8.42353 - 1.02179i) q^{72} -9.08611i q^{73} +(-12.4632 - 5.24693i) q^{74} +(1.56773 - 1.21187i) q^{75} +(-9.62346 + 9.40374i) q^{76} -8.98368i q^{77} +(1.31867 + 4.96515i) q^{78} -9.00744 q^{79} +(-0.181387 + 7.85255i) q^{80} +(-7.85764 - 4.38834i) q^{81} +(-6.92808 - 2.91668i) q^{82} -13.3661i q^{83} +(-0.995592 + 7.12257i) q^{84} +9.69773 q^{85} +(2.77776 - 6.59810i) q^{86} +(6.00050 + 7.14101i) q^{87} +(4.48717 + 11.3869i) q^{88} +5.04147 q^{89} +(5.06266 - 6.61641i) q^{90} -4.35417 q^{91} +(-2.62904 - 2.69047i) q^{92} +(11.1560 - 8.62370i) q^{93} +(-3.67737 + 8.73496i) q^{94} +13.2107i q^{95} +(-2.29566 - 9.52523i) q^{96} +9.01124i q^{97} +(3.50596 + 1.47599i) q^{98} +(3.27034 - 12.5629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 4 q^{4} - 12 q^{6} - 40 q^{9}+O(q^{10}) $ 104 * q - 4 * q^4 - 12 * q^6 - 40 * q^9	$ 104 q - 4 q^{4} - 12 q^{6} - 40 q^{9} + 12 q^{16} - 16 q^{22} - 12 q^{24} + 152 q^{25} - 44 q^{28} - 16 q^{30} - 16 q^{33} + 20 q^{34} - 16 q^{36} - 24 q^{42} - 16 q^{49} - 16 q^{51} + 104 q^{52} + 16 q^{54} + 8 q^{57} + 24 q^{58} - 4 q^{64} - 72 q^{67} - 76 q^{78} - 128 q^{81} + 4 q^{82} - 48 q^{88} + 120 q^{91} + 172 q^{94} - 12 q^{96}+O(q^{100}) $ 104 * q - 4 * q^4 - 12 * q^6 - 40 * q^9 + 12 * q^16 - 16 * q^22 - 12 * q^24 + 152 * q^25 - 44 * q^28 - 16 * q^30 - 16 * q^33 + 20 * q^34 - 16 * q^36 - 24 * q^42 - 16 * q^49 - 16 * q^51 + 104 * q^52 + 16 * q^54 + 8 * q^57 + 24 * q^58 - 4 * q^64 - 72 * q^67 - 76 * q^78 - 128 * q^81 + 4 * q^82 - 48 * q^88 + 120 * q^91 + 172 * q^94 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/696\mathbb{Z}\right)^\times$.

$n$	$175$	$233$	$349$	$553$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	1.30342	+	0.548731i	0.921655	+	0.388011i
$2$	1.30342	+	0.548731i	0.921655	+	0.388011i
$3$	−1.37036	+	1.05930i	−0.791177	+	0.611587i
$3$	−1.37036	+	1.05930i	−0.791177	+	0.611587i
$4$	1.39779	+	1.43045i	0.698895	+	0.715225i
$5$	1.96366			0.878177			0.439088	−	0.898444i	$-0.355302\pi$
$5$	1.96366			0.878177			0.439088	+	0.898444i	$0.355302\pi$
$6$	−2.36742	+	0.628752i	−0.966495	+	0.256687i
$7$		−	2.07610i		−	0.784691i	−0.919818	−	0.392346i	$-0.871664\pi$
$7$		−	2.07610i		−	0.784691i	0.919818	−	0.392346i	$-0.128336\pi$
$8$	1.03697	+	2.63148i	0.366624	+	0.930369i
$9$	0.755764	−	2.90324i	0.251921	−	0.967748i
$10$	2.55947	+	1.07752i	0.809375	+	0.340742i
$11$	4.32719			1.30470			0.652349	−	0.757919i	$-0.273784\pi$
$11$	4.32719			1.30470			0.652349	+	0.757919i	$0.273784\pi$
$12$	−3.43075	−	0.479550i	−0.990372	−	0.138434i
$13$		−	2.09729i		−	0.581682i	−0.956771	−	0.290841i	$-0.906065\pi$
$13$		−	2.09729i		−	0.581682i	0.956771	−	0.290841i	$-0.0939351\pi$
$14$	1.13922	−	2.70602i	0.304469	−	0.723214i
$15$	−2.69092	+	2.08011i	−0.694793	+	0.537082i
$16$	−0.0923716	+	3.99893i	−0.0230929	+	0.999733i
$17$	4.93860			1.19779			0.598893	−	0.800829i	$-0.295608\pi$
$17$	4.93860			1.19779			0.598893	+	0.800829i	$0.295608\pi$
$18$	2.57817	−	3.36942i	0.607682	−	0.794181i
$19$			6.72758i			1.54341i	0.635979	+	0.771706i	$0.280596\pi$
$19$			6.72758i			1.54341i	−0.635979	+	0.771706i	$0.719404\pi$
$20$	2.74479	+	2.80892i	0.613753	+	0.628094i
$21$	2.19921	+	2.84500i	0.479907	+	0.620829i
$22$	5.64014	+	2.37446i	1.20248	+	0.506238i
$23$	−1.88085			−0.392185			−0.196093	−	0.980585i	$-0.562825\pi$
$23$	−1.88085			−0.392185			−0.196093	+	0.980585i	$0.562825\pi$
$24$	−4.20855	−	2.50761i	−0.859067	−	0.511864i
$25$	−1.14403			−0.228806
$26$	1.15084	−	2.73364i	0.225699	−	0.536110i
$27$	2.03974	+	4.77907i	0.392548	+	0.919732i
$28$	2.96975	−	2.90195i	0.561230	−	0.548416i
$29$	−0.219453	−	5.38069i	−0.0407514	−	0.999169i
$29$	−0.219453	−	5.38069i	−0.0407514	−	0.999169i
$30$	−4.64881	+	1.23466i	−0.848753	+	0.225416i
$31$	−8.14094			−1.46216			−0.731078	−	0.682294i	$-0.760982\pi$
$31$	−8.14094			−1.46216			−0.731078	+	0.682294i	$0.760982\pi$
$32$	−2.31474	+	5.16159i	−0.409191	+	0.912449i
$33$	−5.92981	+	4.58380i	−1.03225	+	0.797937i
$34$	6.43705	+	2.70996i	1.10394	+	0.464754i
$35$		−	4.07675i		−	0.689097i
$36$	5.20934	−	2.97704i	0.868224	−	0.496173i
$37$	−9.56194			−1.57197			−0.785987	−	0.618243i	$-0.787845\pi$
$37$	−9.56194			−1.57197			−0.785987	+	0.618243i	$0.787845\pi$
$38$	−3.69163	+	8.76884i	−0.598861	+	1.42249i
$39$	2.22166	+	2.87403i	0.355750	+	0.460213i
$40$	2.03626	+	5.16734i	0.321961	+	0.817028i
$41$	−5.31532			−0.830114			−0.415057	−	0.909795i	$-0.636238\pi$
$41$	−5.31532			−0.830114			−0.415057	+	0.909795i	$0.636238\pi$
$42$	1.30535	+	4.91499i	0.201420	+	0.758400i
$43$		−	5.06216i		−	0.771971i	−0.922505	−	0.385986i	$-0.873861\pi$
$43$		−	5.06216i		−	0.771971i	0.922505	−	0.385986i	$-0.126139\pi$
$44$	6.04850	+	6.18983i	0.911846	+	0.933152i
$45$	1.48407	−	5.70099i	0.221232	−	0.849853i
$46$	−2.45154	−	1.03208i	−0.361459	−	0.152172i
$47$			6.70159i			0.977528i	0.872416	+	0.488764i	$0.162552\pi$
$47$			6.70159i			0.977528i	−0.872416	+	0.488764i	$0.837448\pi$
$48$	−4.10949	−	5.57782i	−0.593154	−	0.805089i
$49$	2.68982			0.384260
$50$	−1.49115	−	0.627765i	−0.210880	−	0.0887793i
$51$	−6.76765	+	5.23146i	−0.947660	+	0.732550i
$52$	3.00006	−	2.93156i	0.416034	−	0.406535i
$53$	13.7107			1.88331			0.941654	−	0.336582i	$-0.109271\pi$
$53$	13.7107			1.88331			0.941654	+	0.336582i	$0.109271\pi$
$54$	0.0362091	+	7.34838i	0.00492743	+	0.999988i
$55$	8.49715			1.14576
$56$	5.46321	−	2.15285i	0.730052	−	0.287687i
$57$	−7.12653	−	9.21919i	−0.943932	−	1.22111i
$58$	2.66651	−	7.13370i	0.350130	−	0.936701i
$59$			7.04044i			0.916587i	0.888801	+	0.458293i	$0.151539\pi$
$59$			7.04044i			0.916587i	−0.888801	+	0.458293i	$0.848461\pi$
$60$	−6.73683	−	0.941674i	−0.869721	−	0.121570i
$61$	11.7831			1.50867			0.754336	−	0.656489i	$-0.227959\pi$
$61$	11.7831			1.50867			0.754336	+	0.656489i	$0.227959\pi$
$62$	−10.6110	−	4.46718i	−1.34760	−	0.567333i
$63$	−6.02742	−	1.56904i	−0.759383	−	0.197681i
$64$	−5.84939	+	5.45753i	−0.731174	+	0.682192i
$65$		−	4.11836i		−	0.510820i
$66$	−10.2443	+	2.72073i	−1.26098	+	0.334899i
$67$	−1.72208			−0.210385			−0.105193	−	0.994452i	$-0.533546\pi$
$67$	−1.72208			−0.210385			−0.105193	+	0.994452i	$0.533546\pi$
$68$	6.90311	+	7.06441i	0.837126	+	0.856686i
$69$	2.57744	−	1.99239i	0.310288	−	0.239856i
$70$	2.23704	−	5.31371i	0.267377	−	0.635110i
$71$	−2.62273			−0.311260			−0.155630	−	0.987815i	$-0.549741\pi$
$71$	−2.62273			−0.311260			−0.155630	+	0.987815i	$0.549741\pi$
$72$	8.42353	−	1.02179i	0.992723	−	0.120420i
$73$		−	9.08611i		−	1.06345i	−0.846917	−	0.531724i	$-0.821544\pi$
$73$		−	9.08611i		−	1.06345i	0.846917	−	0.531724i	$-0.178456\pi$
$74$	−12.4632	−	5.24693i	−1.44882	−	0.609944i
$75$	1.56773	−	1.21187i	0.181026	−	0.139935i
$76$	−9.62346	+	9.40374i	−1.10389	+	1.07868i
$77$		−	8.98368i		−	1.02378i
$78$	1.31867	+	4.96515i	0.149310	+	0.562193i
$79$	−9.00744			−1.01342			−0.506708	−	0.862118i	$-0.669138\pi$
$79$	−9.00744			−1.01342			−0.506708	+	0.862118i	$0.669138\pi$
$80$	−0.181387	+	7.85255i	−0.0202796	+	0.877942i
$81$	−7.85764	−	4.38834i	−0.873071	−	0.487593i
$82$	−6.92808	−	2.91668i	−0.765078	−	0.322094i
$83$		−	13.3661i		−	1.46712i	−0.679626	−	0.733559i	$-0.737858\pi$
$83$		−	13.3661i		−	1.46712i	0.679626	−	0.733559i	$-0.262142\pi$
$84$	−0.995592	+	7.12257i	−0.108628	+	0.777136i
$85$	9.69773			1.05187
$86$	2.77776	−	6.59810i	0.299534	−	0.711491i
$87$	6.00050	+	7.14101i	0.643321	+	0.765597i
$88$	4.48717	+	11.3869i	0.478334	+	1.21385i
$89$	5.04147			0.534395			0.267198	−	0.963642i	$-0.413902\pi$
$89$	5.04147			0.534395			0.267198	+	0.963642i	$0.413902\pi$
$90$	5.06266	−	6.61641i	0.533652	−	0.697431i
$91$	−4.35417			−0.456441
$92$	−2.62904	−	2.69047i	−0.274096	−	0.280501i
$93$	11.1560	−	8.62370i	1.15682	−	0.894236i
$94$	−3.67737	+	8.73496i	−0.379292	+	0.900943i
$95$			13.2107i			1.35539i
$96$	−2.29566	−	9.52523i	−0.234299	−	0.972165i
$97$			9.01124i			0.914952i	0.889222	+	0.457476i	$0.151247\pi$
$97$			9.01124i			0.914952i	−0.889222	+	0.457476i	$0.848753\pi$
$98$	3.50596	+	1.47599i	0.354155	+	0.149097i
$99$	3.27034	−	12.5629i	0.328681	−	1.26262i
$100$	−1.59911	−	1.63648i	−0.159911	−	0.163648i
$101$		−	13.3504i		−	1.32841i	−0.747549	−	0.664207i	$-0.768769\pi$
$101$		−	13.3504i		−	1.32841i	0.747549	−	0.664207i	$-0.231231\pi$
$102$	−11.6917	+	3.10515i	−1.15765	+	0.307456i
$103$		−	3.69126i		−	0.363710i	−0.983325	−	0.181855i	$-0.941790\pi$
$103$		−	3.69126i		−	0.363710i	0.983325	−	0.181855i	$-0.0582102\pi$
$104$	5.51897	−	2.17482i	0.541179	−	0.213259i
$105$	4.31851	+	5.58661i	0.421443	+	0.545198i
$106$	17.8707	+	7.52348i	1.73576	+	0.730745i
$107$		−	3.25638i		−	0.314806i	−0.987534	−	0.157403i	$-0.949688\pi$
$107$		−	3.25638i		−	0.314806i	0.987534	−	0.157403i	$-0.0503122\pi$
$108$	−3.98509	+	9.59787i	−0.383465	+	0.923555i
$109$			9.06882i			0.868635i	0.900760	+	0.434318i	$0.143010\pi$
$109$			9.06882i			0.868635i	−0.900760	+	0.434318i	$0.856990\pi$
$110$	11.0753	+	4.66265i	1.05599	+	0.444566i
$111$	13.1033	−	10.1290i	1.24371	−	0.961399i
$112$	8.30217	+	0.191772i	0.784482	+	0.0181208i
$113$	−20.8820			−1.96441			−0.982207	−	0.187801i	$-0.939864\pi$
$113$	−20.8820			−1.96441			−0.982207	+	0.187801i	$0.939864\pi$
$114$	−4.22998	−	15.9270i	−0.396174	−	1.49170i
$115$	−3.69336			−0.344408
$116$	7.39006	−	7.83499i	0.686150	−	0.727460i
$117$	−6.08893	−	1.58505i	−0.562922	−	0.146538i
$118$	−3.86331	+	9.17662i	−0.355646	+	0.844777i
$119$		−	10.2530i		−	0.939891i
$120$	−8.26417	−	4.92410i	−0.754412	−	0.449507i
$121$	7.72461			0.702237
$122$	15.3583	+	6.46575i	1.39047	+	0.585382i
$123$	7.28390	−	5.63053i	0.656767	−	0.507687i
$124$	−11.3793	−	11.6452i	−1.02189	−	1.04577i
$125$	−12.0648			−1.07911
$126$	−6.99525	−	5.35254i	−0.623187	−	0.476842i
$127$	−7.89886			−0.700911			−0.350455	−	0.936579i	$-0.613973\pi$
$127$	−7.89886			−0.700911			−0.350455	+	0.936579i	$0.613973\pi$
$128$	−10.6189	+	3.90370i	−0.938587	+	0.345041i
$129$	5.36234	+	6.93697i	0.472128	+	0.610766i
$130$	2.25987	−	5.36794i	0.198204	−	0.470799i
$131$	0.760056			0.0664064			0.0332032	−	0.999449i	$-0.489429\pi$
$131$	0.760056			0.0664064			0.0332032	+	0.999449i	$0.489429\pi$
$132$	−14.8455	−	2.07510i	−1.29214	−	0.180615i
$133$	13.9671			1.21110
$134$	−2.24458	−	0.944956i	−0.193902	−	0.0816318i
$135$	4.00536	+	9.38447i	0.344726	+	0.807687i
$136$	5.12117	+	12.9958i	0.439137	+	1.11438i
$137$	−9.11021			−0.778338			−0.389169	−	0.921166i	$-0.627238\pi$
$137$	−9.11021			−0.778338			−0.389169	+	0.921166i	$0.627238\pi$
$138$	4.45277	−	1.18259i	0.379045	−	0.100669i
$139$	−5.62933			−0.477473			−0.238737	−	0.971084i	$-0.576733\pi$
$139$	−5.62933			−0.477473			−0.238737	+	0.971084i	$0.576733\pi$
$140$	5.83159	−	5.69844i	0.492859	−	0.481606i
$141$	−7.09900	−	9.18358i	−0.597844	−	0.773397i
$142$	−3.41850	−	1.43917i	−0.286875	−	0.120773i
$143$		−	9.07536i		−	0.758920i
$144$	11.5401	+	3.29043i	0.961672	+	0.274202i
$145$	−0.430932	−	10.5659i	−0.0357869	−	0.877447i
$146$	4.98583	−	11.8430i	0.412630	−	0.980132i
$147$	−3.68602	+	2.84933i	−0.304018	+	0.235009i
$148$	−13.3656	−	13.6779i	−1.09864	−	1.12431i
$149$	−4.52749			−0.370906			−0.185453	−	0.982653i	$-0.559375\pi$
$149$	−4.52749			−0.370906			−0.185453	+	0.982653i	$0.559375\pi$
$150$	2.70840	−	0.719311i	0.221140	−	0.0587315i
$151$		−	18.7745i		−	1.52785i	−0.645308	−	0.763923i	$-0.723271\pi$
$151$		−	18.7745i		−	1.52785i	0.645308	−	0.763923i	$-0.276729\pi$
$152$	−17.7035	+	6.97629i	−1.43594	+	0.565852i
$153$	3.73241	−	14.3379i	0.301748	−	1.15915i
$154$	4.92962	−	11.7095i	0.397240	−	0.943576i
$155$	−15.9861			−1.28403
$156$	−1.00575	+	7.19526i	−0.0805247	+	0.576082i
$157$	6.23944			0.497961			0.248981	−	0.968508i	$-0.419904\pi$
$157$	6.23944			0.497961			0.248981	+	0.968508i	$0.419904\pi$
$158$	−11.7405	−	4.94266i	−0.934020	−	0.393217i
$159$	−18.7886	+	14.5237i	−1.49003	+	1.15181i
$160$	−4.54536	+	10.1356i	−0.359342	+	0.801291i
$161$			3.90484i			0.307744i
$162$	−7.83376	−	10.0316i	−0.615479	−	0.788154i
$163$		−	17.4983i		−	1.37057i	−0.728275	−	0.685285i	$-0.759678\pi$
$163$		−	17.4983i		−	1.37057i	0.728275	−	0.685285i	$-0.240322\pi$
$164$	−7.42970	−	7.60330i	−0.580162	−	0.593718i
$165$	−11.6441	+	9.00103i	−0.906495	+	0.700730i
$166$	7.33438	−	17.4216i	0.569258	−	1.35218i
$167$	16.5928			1.28399			0.641993	−	0.766711i	$-0.278108\pi$
$167$	16.5928			1.28399			0.641993	+	0.766711i	$0.278108\pi$
$168$	−5.20604	+	8.73736i	−0.401655	+	0.674102i
$169$	8.60140			0.661646
$170$	12.6402	+	5.32144i	0.969458	+	0.408136i
$171$	19.5318	+	5.08446i	1.49363	+	0.388819i
$172$	7.24116	−	7.07583i	0.552133	−	0.539527i
$173$	1.89421			0.144014			0.0720069	−	0.997404i	$-0.477060\pi$
$173$	1.89421			0.144014			0.0720069	+	0.997404i	$0.477060\pi$
$174$	3.90266	+	12.6004i	0.295860	+	0.955231i
$175$			2.37512i			0.179542i
$176$	−0.399710	+	17.3042i	−0.0301293	+	1.30435i
$177$	−7.45794	−	9.64792i	−0.560573	−	0.725182i
$178$	6.57114	+	2.76641i	0.492528	+	0.207351i
$179$			2.40985i			0.180121i	0.995936	+	0.0900603i	$0.0287060\pi$
$179$			2.40985i			0.180121i	−0.995936	+	0.0900603i	$0.971294\pi$
$180$	10.2294	−	5.84590i	0.762454	−	0.435728i
$181$			23.2465i			1.72790i	0.503577	+	0.863950i	$0.332017\pi$
$181$			23.2465i			1.72790i	−0.503577	+	0.863950i	$0.667983\pi$
$182$	−5.67529	−	2.38927i	−0.420681	−	0.177104i
$183$	−16.1471	+	12.4818i	−1.19363	+	0.922685i
$184$	−1.95039	−	4.94943i	−0.143785	−	0.364877i
$185$	−18.7764			−1.38047
$186$	19.2730	−	5.11863i	1.41317	−	0.375316i
$187$	21.3703			1.56275
$188$	−9.58629	+	9.36741i	−0.699152	+	0.683189i
$189$	9.92180	−	4.23470i	0.721705	−	0.308029i
$190$	−7.24911	+	17.2190i	−0.525906	+	1.24920i
$191$			1.00718i			0.0728769i	0.999336	+	0.0364384i	$0.0116013\pi$
$191$			1.00718i			0.0728769i	−0.999336	+	0.0364384i	$0.988399\pi$
$192$	2.23459	−	13.6750i	0.161268	−	0.986911i
$193$		−	7.26070i		−	0.522637i	−0.965253	−	0.261318i	$-0.915843\pi$
$193$		−	7.26070i		−	0.522637i	0.965253	−	0.261318i	$-0.0841572\pi$
$194$	−4.94474	+	11.7454i	−0.355012	+	0.843270i
$195$	4.36258	+	5.64363i	0.312411	+	0.404149i
$196$	3.75980	+	3.84765i	0.268557	+	0.274832i
$197$	−8.52791			−0.607589			−0.303794	−	0.952738i	$-0.598254\pi$
$197$	−8.52791			−0.607589			−0.303794	+	0.952738i	$0.598254\pi$
$198$	11.1563	−	14.5801i	0.792841	−	1.03617i
$199$		−	2.01449i		−	0.142803i	−0.997448	−	0.0714017i	$-0.977253\pi$
$199$		−	2.01449i		−	0.142803i	0.997448	−	0.0714017i	$-0.0227472\pi$
$200$	−1.18632	−	3.01049i	−0.0838858	−	0.212874i
$201$	2.35986	−	1.82420i	0.166452	−	0.128669i
$202$	7.32577	−	17.4011i	0.515440	−	1.22434i
$203$	−11.1708	+	0.455606i	−0.784039	+	0.0319773i
$204$	−16.9431	−	2.36830i	−1.18625	−	0.165814i
$205$	−10.4375			−0.728987
$206$	2.02551	−	4.81124i	0.141124	−	0.335215i
$207$	−1.42148	+	5.46058i	−0.0987999	+	0.379536i
$208$	8.38690	+	0.193730i	0.581527	+	0.0134327i
$209$			29.1115i			2.01369i
$210$	2.56327	+	9.65138i	0.176882	+	0.666009i
$211$			20.6650i			1.42263i	0.702871	+	0.711317i	$0.251901\pi$
$211$			20.6650i			1.42263i	−0.702871	+	0.711317i	$0.748099\pi$
$212$	19.1647	+	19.6124i	1.31623	+	1.34699i
$213$	3.59408	−	2.77826i	0.246262	−	0.190363i
$214$	1.78688	−	4.24442i	0.122148	−	0.290143i
$215$		−	9.94036i		−	0.677927i
$216$	−10.4609	+	10.3233i	−0.711772	+	0.702410i
$217$			16.9014i			1.14734i
$218$	−4.97634	+	11.8204i	−0.337040	+	0.800582i
$219$	9.62492	+	12.4512i	0.650392	+	0.841376i
$220$	11.8772	+	12.1547i	0.800762	+	0.819472i
$221$		−	10.3576i		−	0.696730i
$222$	22.6371	−	6.01209i	1.51930	−	0.403505i
$223$			1.54064i			0.103169i	0.998669	+	0.0515844i	$0.0164271\pi$
$223$			1.54064i			0.103169i	−0.998669	+	0.0515844i	$0.983573\pi$
$224$	10.7160	+	4.80562i	0.715990	+	0.321089i
$225$	−0.864617	+	3.32140i	−0.0576411	+	0.221426i
$226$	−27.2180	−	11.4586i	−1.81051	−	0.762215i
$227$			8.60601i			0.571201i	0.958349	+	0.285600i	$0.0921930\pi$
$227$			8.60601i			0.571201i	−0.958349	+	0.285600i	$0.907807\pi$
$228$	3.22621	−	23.0806i	0.213661	−	1.52855i
$229$	−6.21209			−0.410507			−0.205253	−	0.978709i	$-0.565802\pi$
$229$	−6.21209			−0.410507			−0.205253	+	0.978709i	$0.565802\pi$
$230$	−4.81399	−	2.02666i	−0.317425	−	0.133634i
$231$	9.51641	+	12.3109i	0.626134	+	0.809995i
$232$	13.9316	−	6.15710i	0.914656	−	0.404233i
$233$		−	20.5496i		−	1.34625i	−0.739529	−	0.673125i	$-0.764952\pi$
$233$		−	20.5496i		−	1.34625i	0.739529	−	0.673125i	$-0.235048\pi$
$234$	−7.06664	−	5.40717i	−0.461961	−	0.353478i
$235$			13.1597i			0.858442i
$236$	−10.0710	+	9.84105i	−0.655566	+	0.640598i
$237$	12.3434	−	9.54159i	0.801792	−	0.619793i
$238$	5.62614	−	13.3639i	0.364688	−	0.866255i
$239$	−3.72056			−0.240663			−0.120331	−	0.992734i	$-0.538396\pi$
$239$	−3.72056			−0.240663			−0.120331	+	0.992734i	$0.538396\pi$
$240$	−8.06965	−	10.9530i	−0.520894	−	0.707010i
$241$	−12.8782			−0.829556			−0.414778	−	0.909923i	$-0.636141\pi$
$241$	−12.8782			−0.829556			−0.414778	+	0.909923i	$0.636141\pi$
$242$	10.0684	+	4.23873i	0.647220	+	0.272476i
$243$	15.4164	−	2.31001i	0.988959	−	0.148187i
$244$	16.4703	+	16.8551i	1.05440	+	1.07904i
$245$	5.28190			0.337448
$246$	12.5836	−	3.34202i	0.802301	−	0.213079i
$247$	14.1097			0.897776
$248$	−8.44190	−	21.4227i	−0.536061	−	1.36034i
$249$	14.1587	+	18.3163i	0.897270	+	1.16075i
$250$	−15.7255	−	6.62033i	−0.994565	−	0.418706i
$251$	6.14205			0.387683			0.193842	−	0.981033i	$-0.437905\pi$
$251$	6.14205			0.387683			0.193842	+	0.981033i	$0.437905\pi$
$252$	−6.18062	−	10.8151i	−0.389343	−	0.681287i
$253$	−8.13882			−0.511683
$254$	−10.2955	−	4.33435i	−0.645998	−	0.271961i
$255$	−13.2894	+	10.2728i	−0.832213	+	0.643309i
$256$	−15.9829	−	0.738776i	−0.998933	−	0.0461735i
$257$		−	0.622954i		−	0.0388588i	−0.999811	−	0.0194294i	$-0.993815\pi$
$257$		−	0.622954i		−	0.0388588i	0.999811	−	0.0194294i	$-0.00618496\pi$
$258$	3.18284	+	11.9842i	0.198155	+	0.746106i
$259$			19.8515i			1.23351i
$260$	5.89111	−	5.75660i	0.365351	−	0.357009i
$261$	−15.7873	−	3.42941i	−0.977210	−	0.212275i
$262$	0.990669	+	0.417066i	0.0612037	+	0.0257664i
$263$			1.27900i			0.0788667i	0.999222	+	0.0394333i	$0.0125553\pi$
$263$			1.27900i			0.0788667i	−0.999222	+	0.0394333i	$0.987445\pi$
$264$	−18.2112	−	10.8509i	−1.12082	−	0.667828i
$265$	26.9232			1.65388
$266$	18.2050	+	7.66418i	1.11622	+	0.469921i
$267$	−6.90863	+	5.34044i	−0.422801	+	0.326829i
$268$	−2.40710	−	2.46334i	−0.147037	−	0.150473i
$269$			27.0208i			1.64749i	0.566960	+	0.823745i	$0.308119\pi$
$269$			27.0208i			1.64749i	−0.566960	+	0.823745i	$0.691881\pi$
$270$	0.0711024	+	14.4297i	0.00432715	+	0.878166i
$271$	−5.00662			−0.304131			−0.152065	−	0.988370i	$-0.548592\pi$
$271$	−5.00662			−0.304131			−0.152065	+	0.988370i	$0.548592\pi$
$272$	−0.456186	+	19.7491i	−0.0276603	+	1.19747i
$273$	5.96677	−	4.61237i	0.361125	−	0.279154i
$274$	−11.8744	−	4.99905i	−0.717359	−	0.302004i
$275$	−4.95044			−0.298523
$276$	6.45274	+	0.901963i	0.388409	+	0.0542918i
$277$			12.9186i			0.776200i	0.921617	+	0.388100i	$0.126869\pi$
$277$			12.9186i			0.776200i	−0.921617	+	0.388100i	$0.873131\pi$
$278$	−7.33736	−	3.08899i	−0.440066	−	0.185265i
$279$	−6.15263	+	23.6351i	−0.368348	+	1.41500i
$280$	10.7279	−	4.22747i	0.641115	−	0.252640i
$281$			4.75037i			0.283383i	0.989911	+	0.141692i	$0.0452542\pi$
$281$			4.75037i			0.283383i	−0.989911	+	0.141692i	$0.954746\pi$
$282$	−4.21364	−	15.8655i	−0.250919	−	0.944775i
$283$	−1.05572			−0.0627559			−0.0313779	−	0.999508i	$-0.509990\pi$
$283$	−1.05572			−0.0627559			−0.0313779	+	0.999508i	$0.509990\pi$
$284$	−3.66602	−	3.75168i	−0.217538	−	0.222621i
$285$	−13.9941	−	18.1034i	−0.828939	−	1.07235i
$286$	4.97993	−	11.8290i	0.294469	−	0.699462i
$287$			11.0351i			0.651383i
$288$	13.2360	+	10.6212i	0.779936	+	0.625859i
$289$	7.38972			0.434690
$290$	5.23613	−	14.0082i	0.307476	−	0.822589i
$291$	−9.54561	−	12.3486i	−0.559573	−	0.723889i
$292$	12.9972	−	12.7005i	0.760605	−	0.743238i
$293$		−	19.2849i		−	1.12664i	−0.826240	−	0.563319i	$-0.809524\pi$
$293$		−	19.2849i		−	1.12664i	0.826240	−	0.563319i	$-0.190476\pi$
$294$	−6.36793	+	1.69123i	−0.371385	+	0.0986345i
$295$			13.8250i			0.804925i
$296$	−9.91544	−	25.1621i	−0.576323	−	1.46252i
$297$	8.82635	+	20.6799i	0.512157	+	1.19997i
$298$	−5.90120	−	2.48437i	−0.341847	−	0.143916i
$299$			3.94469i			0.228127i
$300$	3.92488	+	0.548619i	0.226603	+	0.0316746i
$301$	−10.5095			−0.605759
$302$	10.3021	−	24.4710i	0.592821	−	1.40815i
$303$	14.1421	+	18.2948i	0.812442	+	1.05101i
$304$	−26.9031	−	0.621437i	−1.54300	−	0.0356419i
$305$	23.1380			1.32488
$306$	12.7326	−	16.6402i	0.727872	−	0.951258i
$307$		−	21.8596i		−	1.24759i	−0.781588	−	0.623795i	$-0.785590\pi$
$307$		−	21.8596i		−	1.24759i	0.781588	−	0.623795i	$-0.214410\pi$
$308$	12.8507	−	12.5573i	0.732236	−	0.715518i
$309$	3.91015	+	5.05834i	0.222441	+	0.287759i
$310$	−20.8365	−	8.77204i	−1.18343	−	0.498218i
$311$			6.18026i			0.350450i	0.984528	+	0.175225i	$0.0560653\pi$
$311$			6.18026i			0.350450i	−0.984528	+	0.175225i	$0.943935\pi$
$312$	−5.25917	+	8.82653i	−0.297742	+	0.499704i
$313$	−6.80564			−0.384677			−0.192339	−	0.981329i	$-0.561607\pi$
$313$	−6.80564			−0.384677			−0.192339	+	0.981329i	$0.561607\pi$
$314$	8.13259	+	3.42377i	0.458948	+	0.193215i
$315$	−11.8358	−	3.08107i	−0.666872	−	0.173598i
$316$	−12.5905	−	12.8847i	−0.708271	−	0.724821i
$317$		−	15.0701i		−	0.846421i	−0.906031	−	0.423211i	$-0.860903\pi$
$317$		−	15.0701i		−	0.846421i	0.906031	−	0.423211i	$-0.139097\pi$
$318$	−32.4589	+	8.62062i	−1.82021	+	0.483421i
$319$	−0.949616	−	23.2833i	−0.0531683	−	1.30361i
$320$	−11.4862	+	10.7168i	−0.642099	+	0.599085i
$321$	3.44949	+	4.46241i	0.192532	+	0.249067i
$322$	−2.14270	+	5.08963i	−0.119408	+	0.283634i
$323$			33.2248i			1.84868i
$324$	−4.70603	−	17.3739i	−0.261446	−	0.965218i
$325$			2.39936i			0.133092i
$326$	9.60183	−	22.8075i	0.531796	−	1.26319i
$327$	−9.60661	−	12.4275i	−0.531247	−	0.687244i
$328$	−5.51183	−	13.9872i	−0.304340	−	0.772313i
$329$	13.9132			0.767057
$330$	−20.1163	+	5.34260i	−1.10737	+	0.294100i
$331$			3.20058i			0.175920i	0.996124	+	0.0879598i	$0.0280347\pi$
$331$			3.20058i			0.175920i	−0.996124	+	0.0879598i	$0.971965\pi$
$332$	19.1195	−	18.6829i	1.04932	−	1.02536i
$333$	−7.22658	+	27.7606i	−0.396014	+	1.52127i
$334$	21.6273	+	9.10495i	1.18339	+	0.498201i
$335$	−3.38157			−0.184755
$336$	−11.5801	+	8.53170i	−0.631746	+	0.465442i
$337$			2.17304i			0.118373i	0.998247	+	0.0591864i	$0.0188506\pi$
$337$			2.17304i			0.118373i	−0.998247	+	0.0591864i	$0.981149\pi$
$338$	11.2112	+	4.71985i	0.609809	+	0.256726i
$339$	28.6158	−	22.1203i	1.55420	−	1.20141i
$340$	13.5554	+	13.8721i	0.735144	+	0.752321i
$341$	−35.2274			−1.90767
$342$	22.6681	+	17.3449i	1.22575	+	0.937903i
$343$		−	20.1170i		−	1.08622i
$344$	13.3210	−	5.24930i	0.718218	−	0.283023i
$345$	5.06123	−	3.91238i	0.272487	−	0.210636i
$346$	2.46894	+	1.03941i	0.132731	+	0.0558790i
$347$		−	10.4049i		−	0.558567i	−0.960209	−	0.279283i	$-0.909903\pi$
$347$		−	10.4049i		−	0.558567i	0.960209	−	0.279283i	$-0.0900969\pi$
$348$	−1.82742	+	18.5650i	−0.0979601	+	0.995190i
$349$			28.9456i			1.54942i	0.632316	+	0.774711i	$0.282105\pi$
$349$			28.9456i			1.54942i	−0.632316	+	0.774711i	$0.717895\pi$
$350$	−1.30330	+	3.09577i	−0.0696643	+	0.165476i
$351$	10.0231	−	4.27791i	0.534992	−	0.228338i
$352$	−10.0163	+	22.3352i	−0.533871	+	1.19047i
$353$		−	9.11546i		−	0.485167i	−0.970131	−	0.242584i	$-0.922005\pi$
$353$		−	9.11546i		−	0.485167i	0.970131	−	0.242584i	$-0.0779949\pi$
$354$	−4.42669	−	16.6677i	−0.235276	−	0.885876i
$355$	−5.15015			−0.273342
$356$	7.04692	+	7.21157i	0.373486	+	0.382213i
$357$	10.8610	+	14.0503i	0.574826	+	0.743620i
$358$	−1.32236	+	3.14104i	−0.0698888	+	0.166009i
$359$		−	12.2766i		−	0.647932i	−0.946069	−	0.323966i	$-0.894984\pi$
$359$		−	12.2766i		−	0.647932i	0.946069	−	0.323966i	$-0.105016\pi$
$360$	16.5410	−	2.00646i	0.871786	−	0.105750i
$361$	−26.2603			−1.38212
$362$	−12.7561	+	30.2999i	−0.670445	+	1.59253i
$363$	−10.5855	+	8.18268i	−0.555594	+	0.429479i
$364$	−6.08621	−	6.22842i	−0.319004	−	0.326458i
$365$		−	17.8421i		−	0.933896i
$366$	−27.8955	+	7.40865i	−1.45812	+	0.387256i
$367$	8.04220			0.419799			0.209900	−	0.977723i	$-0.432686\pi$
$367$	8.04220			0.419799			0.209900	+	0.977723i	$0.432686\pi$
$368$	0.173738	−	7.52141i	0.00905670	−	0.392081i
$369$	−4.01713	+	15.4317i	−0.209124	+	0.803341i
$370$	−24.4735	−	10.3032i	−1.27232	−	0.535638i
$371$		−	28.4647i		−	1.47781i
$372$	27.9295	+	3.90398i	1.44808	+	0.202412i
$373$		−	4.77531i		−	0.247256i	−0.992329	−	0.123628i	$-0.960547\pi$
$373$		−	4.77531i		−	0.247256i	0.992329	−	0.123628i	$-0.0394530\pi$
$374$	27.8543	+	11.7265i	1.44031	+	0.606364i
$375$	16.5331	−	12.7803i	0.853766	−	0.659969i
$376$	−17.6351	+	6.94935i	−0.909462	+	0.358385i
$377$	−11.2848	+	0.460255i	−0.581199	+	0.0237044i
$378$	15.2560	−	0.0751736i	0.784682	−	0.00386651i
$379$		−	17.8655i		−	0.917688i	−0.888517	−	0.458844i	$-0.848264\pi$
$379$		−	17.8655i		−	0.917688i	0.888517	−	0.458844i	$-0.151736\pi$
$380$	−18.8972	+	18.4658i	−0.969407	+	0.947274i
$381$	10.8243	−	8.36727i	0.554544	−	0.428668i
$382$	−0.552670	+	1.31277i	−0.0282771	+	0.0671673i
$383$	16.1041			0.822880			0.411440	−	0.911437i	$-0.365026\pi$
$383$	16.1041			0.822880			0.411440	+	0.911437i	$0.365026\pi$
$384$	10.4165	−	16.5981i	0.531566	−	0.847017i
$385$		−	17.6409i		−	0.899064i
$386$	3.98417	−	9.46372i	0.202789	−	0.481691i
$387$	−14.6967	−	3.82580i	−0.747074	−	0.194476i
$388$	−12.8901	+	12.5958i	−0.654397	+	0.639455i
$389$			13.5780i			0.688432i	0.938891	+	0.344216i	$0.111855\pi$
$389$			13.5780i			0.688432i	−0.938891	+	0.344216i	$0.888145\pi$
$390$	2.58943	+	9.74988i	0.131121	+	0.493704i
$391$	−9.28878			−0.469754
$392$	2.78926	+	7.07821i	0.140879	+	0.357504i
$393$	−1.04155	+	0.805127i	−0.0525392	+	0.0406133i
$394$	−11.1154	−	4.67953i	−0.559987	−	0.235751i
$395$	−17.6876			−0.889959
$396$	22.5418	−	12.8822i	1.13277	−	0.647356i
$397$			12.2193i			0.613271i	0.951827	+	0.306635i	$0.0992032\pi$
$397$			12.2193i			0.613271i	−0.951827	+	0.306635i	$0.900797\pi$
$398$	1.10541	−	2.62572i	0.0554093	−	0.131615i
$399$	−19.1399	+	14.7954i	−0.958196	+	0.740695i
$400$	0.105676	−	4.57490i	0.00528380	−	0.228745i
$401$		−	18.9027i		−	0.943958i	−0.881610	−	0.471979i	$-0.843540\pi$
$401$		−	18.9027i		−	0.943958i	0.881610	−	0.471979i	$-0.156460\pi$
$402$	4.07687	−	1.08276i	0.203336	−	0.0540031i
$403$			17.0739i			0.850510i
$404$	19.0971	−	18.6610i	0.950115	−	0.928421i
$405$	−15.4298	−	8.61721i	−0.766711	−	0.428193i
$406$	−14.8103	−	5.53594i	−0.735021	−	0.274744i
$407$	−41.3764			−2.05095
$408$	−20.7843	−	12.3841i	−1.02898	−	0.613103i
$409$		−	10.2779i		−	0.508210i	−0.967177	−	0.254105i	$-0.918219\pi$
$409$		−	10.2779i		−	0.508210i	0.967177	−	0.254105i	$-0.0817809\pi$
$410$	−13.6044	−	5.72738i	−0.671874	−	0.282855i
$411$	12.4843	−	9.65045i	0.615803	−	0.476022i
$412$	5.28016	−	5.15960i	0.260135	−	0.254195i
$413$	14.6166			0.719238
$414$	−4.84917	+	6.33739i	−0.238324	+	0.311466i
$415$		−	26.2465i		−	1.28839i
$416$	10.8253	+	4.85466i	0.530755	+	0.238019i
$417$	7.71420	−	5.96315i	0.377766	−	0.292017i
$418$	−15.9744	+	37.9445i	−0.781333	+	1.85592i
$419$			31.6772i			1.54753i	0.633472	+	0.773765i	$0.281629\pi$
$419$			31.6772i			1.54753i	−0.633472	+	0.773765i	$0.718371\pi$
$420$	−1.95501	+	13.9863i	−0.0953946	+	0.682462i
$421$	7.12287			0.347147			0.173574	−	0.984821i	$-0.444469\pi$
$421$	7.12287			0.347147			0.173574	+	0.984821i	$0.444469\pi$
$422$	−11.3395	+	26.9351i	−0.551998	+	1.31118i
$423$	19.4563	+	5.06482i	0.946000	+	0.246260i
$424$	14.2176	+	36.0794i	0.690466	+	1.75217i
$425$	−5.64990			−0.274060
$426$	6.20909	−	1.64904i	0.300831	−	0.0798965i
$427$		−	24.4629i		−	1.18384i
$428$	4.65809	−	4.55174i	0.225157	−	0.220016i
$429$	9.61353	+	12.4365i	0.464146	+	0.600440i
$430$	5.45458	−	12.9564i	0.263043	−	0.624815i
$431$	5.38353			0.259315			0.129658	−	0.991559i	$-0.458612\pi$
$431$	5.38353			0.259315			0.129658	+	0.991559i	$0.458612\pi$
$432$	−19.2996	+	7.71533i	−0.928551	+	0.371204i
$433$			34.8684i			1.67567i	0.545926	+	0.837834i	$0.316178\pi$
$433$			34.8684i			1.67567i	−0.545926	+	0.837834i	$0.683822\pi$
$434$	−9.27431	+	22.0295i	−0.445181	+	1.05745i
$435$	11.7830	+	14.0225i	0.564949	+	0.672329i
$436$	−12.9725	+	12.6763i	−0.621270	+	0.607084i
$437$		−	12.6536i		−	0.605304i
$438$	5.71291	+	21.5106i	0.272973	+	1.02782i
$439$			10.9877i			0.524413i	0.965012	+	0.262207i	$0.0844502\pi$
$439$			10.9877i			0.524413i	−0.965012	+	0.262207i	$0.915550\pi$
$440$	8.81128	+	22.3601i	0.420061	+	1.06598i
$441$	2.03287	−	7.80920i	0.0968033	−	0.371867i
$442$	5.68356	−	13.5003i	0.270339	−	0.642145i
$443$	24.7425			1.17555			0.587776	−	0.809024i	$-0.300004\pi$
$443$	24.7425			1.17555			0.587776	+	0.809024i	$0.300004\pi$
$444$	32.8046	+	4.58543i	1.55684	+	0.217615i
$445$	9.89975			0.469293
$446$	−0.845395	+	2.00809i	−0.0400306	+	0.0950860i
$447$	6.20428	−	4.79597i	0.293452	−	0.226842i
$448$	11.3304	+	12.1439i	0.535310	+	0.573745i
$449$	16.6966			0.787962			0.393981	−	0.919118i	$-0.371098\pi$
$449$	16.6966			0.787962			0.393981	+	0.919118i	$0.371098\pi$
$450$	−2.94951	+	3.85472i	−0.139041	+	0.181713i
$451$	−23.0004			−1.08305
$452$	−29.1886	−	29.8707i	−1.37292	−	1.40500i
$453$	19.8878	+	25.7278i	0.934411	+	1.20880i
$454$	−4.72238	+	11.2172i	−0.221632	+	0.526450i
$455$	−8.55012			−0.400836
$456$	16.8701	−	28.3134i	0.790017	−	1.32589i
$457$	24.6038			1.15092			0.575459	−	0.817831i	$-0.304823\pi$
$457$	24.6038			1.15092			0.575459	+	0.817831i	$0.304823\pi$
$458$	−8.09694	−	3.40877i	−0.378345	−	0.159281i
$459$	10.0734	+	23.6019i	0.470188	+	1.10164i
$460$	−5.16254	−	5.28317i	−0.240705	−	0.246329i
$461$			37.8537i			1.76302i	0.472161	+	0.881512i	$0.343474\pi$
$461$			37.8537i			1.76302i	−0.472161	+	0.881512i	$0.656526\pi$
$462$	5.64850	+	21.2681i	0.262792	+	0.989483i
$463$			24.3762i			1.13286i	0.824110	+	0.566429i	$0.191676\pi$
$463$			24.3762i			1.13286i	−0.824110	+	0.566429i	$0.808324\pi$
$464$	21.5373	−	0.380555i	0.999844	−	0.0176668i
$465$	21.9066	−	16.9340i	1.01590	−	0.785297i
$466$	11.2762	−	26.7847i	0.522360	−	1.24078i
$467$	30.1355			1.39450			0.697252	−	0.716826i	$-0.254406\pi$
$467$	30.1355			1.39450			0.697252	+	0.716826i	$0.254406\pi$
$468$	−6.24370	−	10.9255i	−0.288615	−	0.505030i
$469$			3.57520i			0.165087i
$470$	−7.22111	+	17.1525i	−0.333085	+	0.791187i
$471$	−8.55027	+	6.60944i	−0.393976	+	0.304547i
$472$	−18.5268	+	7.30072i	−0.852764	+	0.336043i
$473$		−	21.9049i		−	1.00719i
$474$	21.3244	−	5.66345i	0.979462	−	0.260131i
$475$		−	7.69655i		−	0.353142i
$476$	14.6664	−	14.3315i	0.672234	−	0.656885i
$477$	10.3621	−	39.8055i	0.474446	−	1.82257i
$478$	−4.84944	−	2.04158i	−0.221808	−	0.0933799i
$479$		−	11.4675i		−	0.523962i	−0.965073	−	0.261981i	$-0.915624\pi$
$479$		−	11.4675i		−	0.523962i	0.965073	−	0.261981i	$-0.0843757\pi$
$480$	−4.50789	−	18.7043i	−0.205756	−	0.853732i
$481$			20.0541i			0.914389i
$482$	−16.7856	−	7.06665i	−0.764564	−	0.321877i
$483$	−4.13640	−	5.35103i	−0.188213	−	0.243480i
$484$	10.7974	+	11.0497i	0.490790	+	0.502257i
$485$			17.6950i			0.803490i
$486$	21.3615	+	5.44852i	0.968977	+	0.247150i
$487$			2.01108i			0.0911307i	0.998961	+	0.0455653i	$0.0145089\pi$
$487$			2.01108i			0.0911307i	−0.998961	+	0.0455653i	$0.985491\pi$
$488$	12.2187	+	31.0070i	0.553115	+	1.40362i
$489$	18.5359	+	23.9789i	0.838223	+	1.08436i
$490$	6.88451	+	2.89834i	0.311011	+	0.130934i
$491$	−9.94480			−0.448802			−0.224401	−	0.974497i	$-0.572043\pi$
$491$	−9.94480			−0.448802			−0.224401	+	0.974497i	$0.572043\pi$
$492$	18.2355	+	2.54896i	0.822121	+	0.114916i
$493$	−1.08379	−	26.5731i	−0.0488114	−	1.19679i
$494$	18.3908	+	7.74240i	0.827439	+	0.348347i
$495$	6.42184	−	24.6693i	0.288640	−	1.10880i
$496$	0.751992	−	32.5551i	0.0337654	−	1.46177i
$497$			5.44504i			0.244243i
$498$	8.40394	+	31.6431i	0.376590	+	1.41796i
$499$	4.16291			0.186358			0.0931788	−	0.995649i	$-0.470297\pi$
$499$	4.16291			0.186358			0.0931788	+	0.995649i	$0.470297\pi$
$500$	−16.8640	−	17.2581i	−0.754183	−	0.771805i
$501$	−22.7380	+	17.5767i	−1.01586	+	0.785270i
$502$	8.00565	+	3.37033i	0.357310	+	0.150425i
$503$		−	9.71293i		−	0.433078i	−0.976274	−	0.216539i	$-0.930523\pi$
$503$		−	9.71293i		−	0.433078i	0.976274	−	0.216539i	$-0.0694769\pi$
$504$	−2.12135	−	17.4881i	−0.0944922	−	0.778981i
$505$		−	26.2157i		−	1.16658i
$506$	−10.6083	−	4.46602i	−0.471595	−	0.198539i
$507$	−11.7870	+	9.11146i	−0.523479	+	0.404654i
$508$	−11.0409	−	11.2989i	−0.489863	−	0.501309i
$509$	39.9855			1.77233			0.886163	−	0.463374i	$-0.153361\pi$
$509$	39.9855			1.77233			0.886163	+	0.463374i	$0.153361\pi$
$510$	−22.9586	+	6.09747i	−1.01662	+	0.270000i
$511$	−18.8636			−0.834479
$512$	−20.4270	−	9.73326i	−0.902756	−	0.430153i
$513$	−32.1515	+	13.7225i	−1.41953	+	0.605863i
$514$	0.341834	−	0.811968i	0.0150776	−	0.0358144i
$515$		−	7.24838i		−	0.319402i
$516$	−2.42756	+	17.3670i	−0.106867	+	0.764539i
$517$			28.9991i			1.27538i
$518$	−10.8931	+	25.8748i	−0.478617	+	1.13687i
$519$	−2.59574	+	2.00653i	−0.113940	+	0.0880771i
$520$	10.8374	−	4.27061i	0.475251	−	0.187279i
$521$			16.7131i			0.732212i	0.930573	+	0.366106i	$0.119309\pi$
$521$			16.7131i			0.732212i	−0.930573	+	0.366106i	$0.880691\pi$
$522$	−18.6956	−	13.1329i	−0.818285	−	0.574813i
$523$	−21.9455			−0.959612			−0.479806	−	0.877375i	$-0.659293\pi$
$523$	−21.9455			−0.959612			−0.479806	+	0.877375i	$0.659293\pi$
$524$	1.06240	+	1.08722i	0.0464111	+	0.0474955i
$525$	−2.51596	−	3.25476i	−0.109806	−	0.142049i
$526$	−0.701828	+	1.66707i	−0.0306012	+	0.0726878i
$527$	−40.2048			−1.75135
$528$	−17.7826	−	24.1363i	−0.773887	−	1.05040i
$529$	−19.4624			−0.846191
$530$	35.0921	+	14.7736i	1.52430	+	0.641723i
$531$	20.4401	+	5.32091i	0.887025	+	0.230908i
$532$	19.5231	+	19.9792i	0.846433	+	0.866210i
$533$			11.1477i			0.482863i
$534$	−11.9353	+	3.16984i	−0.516490	+	0.137172i
$535$		−	6.39443i		−	0.276456i
$536$	−1.78574	−	4.53161i	−0.0771322	−	0.195736i
$537$	−2.55275	−	3.30236i	−0.110160	−	0.142507i
$538$	−14.8272	+	35.2194i	−0.639245	+	1.51842i
$539$	11.6394			0.501343
$540$	−7.82537	+	18.8470i	−0.336750	+	0.811045i
$541$	−3.70442			−0.159265			−0.0796327	−	0.996824i	$-0.525375\pi$
$541$	−3.70442			−0.159265			−0.0796327	+	0.996824i	$0.525375\pi$
$542$	−6.52572	−	2.74729i	−0.280304	−	0.118006i
$543$	−24.6251	−	31.8561i	−1.05676	−	1.36707i
$544$	−11.4315	+	25.4910i	−0.490124	+	1.09292i
$545$			17.8081i			0.762815i
$546$	10.3081	−	2.73769i	0.441148	−	0.117162i
$547$	26.5790			1.13644			0.568219	−	0.822878i	$-0.307633\pi$
$547$	26.5790			1.13644			0.568219	+	0.822878i	$0.307633\pi$
$548$	−12.7342	−	13.0317i	−0.543976	−	0.556686i
$549$	8.90525	−	34.2092i	0.380067	−	1.46001i
$550$	−6.45249	−	2.71646i	−0.275135	−	0.115830i
$551$	36.1990	−	1.47639i	1.54213	−	0.0628962i
$552$	7.91567	+	4.71645i	0.336913	+	0.200745i
$553$			18.7003i			0.795219i
$554$	−7.08881	+	16.8383i	−0.301175	+	0.715389i
$555$	25.7304	−	19.8899i	1.09220	−	0.844278i
$556$	−7.86861	−	8.05247i	−0.333703	−	0.341501i
$557$	39.1813			1.66016			0.830082	−	0.557641i	$-0.188293\pi$
$557$	39.1813			1.66016			0.830082	+	0.557641i	$0.188293\pi$
$558$	−20.9888	+	27.4303i	−0.888525	+	1.16122i
$559$	−10.6168			−0.449042
$560$	16.3027	+	0.376576i	0.688913	+	0.0159133i
$561$	−29.2849	+	22.6375i	−1.23641	+	0.955757i
$562$	−2.60667	+	6.19171i	−0.109956	+	0.261182i
$563$	−9.03341			−0.380713			−0.190356	−	0.981715i	$-0.560964\pi$
$563$	−9.03341			−0.380713			−0.190356	+	0.981715i	$0.560964\pi$
$564$	3.21375	−	22.9915i	0.135323	−	0.968116i
$565$	−41.0052			−1.72510
$566$	−1.37604	−	0.579305i	−0.0578392	−	0.0243500i
$567$	−9.11061	+	16.3132i	−0.382610	+	0.685091i
$568$	−2.71969	−	6.90166i	−0.114116	−	0.289587i
$569$	5.48409			0.229905			0.114952	−	0.993371i	$-0.463328\pi$
$569$	5.48409			0.229905			0.114952	+	0.993371i	$0.463328\pi$
$570$	−8.30625	−	31.2752i	−0.347911	−	1.30998i
$571$	−43.5754			−1.82357			−0.911787	−	0.410664i	$-0.865297\pi$
$571$	−43.5754			−1.82357			−0.911787	+	0.410664i	$0.865297\pi$
$572$	12.9818	−	12.6854i	0.542798	−	0.530405i
$573$	−1.06690	−	1.38020i	−0.0445706	−	0.0576585i
$574$	−6.05532	+	14.3834i	−0.252744	+	0.600350i
$575$	2.15175			0.0897343
$576$	11.4238	+	21.1068i	0.475991	+	0.879450i
$577$		−	36.7415i		−	1.52957i	−0.644287	−	0.764784i	$-0.722846\pi$
$577$		−	36.7415i		−	1.52957i	0.644287	−	0.764784i	$-0.277154\pi$
$578$	9.63189	+	4.05497i	0.400634	+	0.168664i
$579$	7.69127	+	9.94976i	0.319638	+	0.413498i
$580$	14.5116	−	15.3853i	0.602561	−	0.638839i
$581$	−27.7493			−1.15123
$582$	−5.66583	−	21.3334i	−0.234856	−	0.884297i
$583$	59.3288			2.45715
$584$	23.9099	−	9.42202i	0.989400	−	0.389886i
$585$	−11.9566	−	3.11251i	−0.494345	−	0.128686i
$586$	10.5822	−	25.1363i	0.437148	−	1.03837i
$587$			31.1727i			1.28664i	0.765599	+	0.643318i	$0.222443\pi$
$587$			31.1727i			1.28664i	−0.765599	+	0.643318i	$0.777557\pi$
$588$	−9.22809	−	1.28990i	−0.380560	−	0.0531947i
$589$		−	54.7688i		−	2.25671i
$590$	−7.58623	+	18.0198i	−0.312320	+	0.741863i
$591$	11.6863	−	9.03362i	0.480710	−	0.371594i
$592$	0.883252	−	38.2376i	0.0363014	−	1.57155i
$593$		−	1.04978i		−	0.0431095i	−0.999768	−	0.0215548i	$-0.993138\pi$
$593$		−	1.04978i		−	0.0431095i	0.999768	−	0.0215548i	$-0.00686162\pi$
$594$	0.156684	+	31.7979i	0.00642881	+	1.30468i
$595$		−	20.1334i		−	0.825391i
$596$	−6.32847	−	6.47634i	−0.259224	−	0.265281i
$597$	2.13395	+	2.76057i	0.0873367	+	0.112983i
$598$	−2.16457	+	5.14157i	−0.0885159	+	0.210254i
$599$		−	13.3246i		−	0.544429i	−0.962237	−	0.272215i	$-0.912244\pi$
$599$		−	13.3246i		−	0.544429i	0.962237	−	0.272215i	$-0.0877561\pi$
$600$	4.81471	+	2.86878i	0.196560	+	0.117118i
$601$		−	0.0187465i		−	0.000764687i	−1.00000		0.000382344i	$-0.999878\pi$
$601$		−	0.0187465i		−	0.000764687i	1.00000		0.000382344i	$-0.000121704\pi$
$602$	−13.6983	−	5.76690i	−0.558301	−	0.235041i
$603$	−1.30148	+	4.99960i	−0.0530005	+	0.203600i
$604$	26.8559	−	26.2428i	1.09275	−	1.06780i
$605$	15.1685			0.616688
$606$	8.39409	+	31.6060i	0.340987	+	1.28391i
$607$	36.3818			1.47669			0.738345	−	0.674423i	$-0.235608\pi$
$607$	36.3818			1.47669			0.738345	+	0.674423i	$0.235608\pi$
$608$	−34.7250	−	15.5726i	−1.40828	−	0.631551i
$609$	14.8254	−	12.4576i	0.600757	−	0.504808i
$610$	30.1585	+	12.6966i	1.22108	+	0.514068i
$611$	14.0551			0.568610
$612$	25.7268	−	14.7024i	1.03995	−	0.594309i
$613$		−	22.5092i		−	0.909136i	−0.890712	−	0.454568i	$-0.849794\pi$
$613$		−	22.5092i		−	0.909136i	0.890712	−	0.454568i	$-0.150206\pi$
$614$	11.9950	−	28.4921i	0.484079	−	1.14985i
$615$	14.3031	−	11.0565i	0.576757	−	0.445839i
$616$	23.6404	−	9.31580i	0.952498	−	0.375344i
$617$	−18.8536			−0.759016			−0.379508	−	0.925188i	$-0.623907\pi$
$617$	−18.8536			−0.759016			−0.379508	+	0.925188i	$0.623907\pi$
$618$	2.32088	+	8.73875i	0.0933597	+	0.351524i
$619$		−	10.7359i		−	0.431513i	−0.976447	−	0.215757i	$-0.930778\pi$
$619$		−	10.7359i		−	0.431513i	0.976447	−	0.215757i	$-0.0692217\pi$
$620$	−22.3451	−	22.8672i	−0.897402	−	0.918371i
$621$	−3.83645	−	8.98873i	−0.153951	−	0.360705i
$622$	−3.39130	+	8.05545i	−0.135979	+	0.322994i
$623$		−	10.4666i		−	0.419335i
$624$	−11.6983	+	8.61877i	−0.468306	+	0.345027i
$625$	−17.9710			−0.718842
$626$	−8.87058	−	3.73446i	−0.354540	−	0.149259i
$627$	−30.8379	−	39.8932i	−1.23155	−	1.59318i
$628$	8.72142	+	8.92520i	0.348022	+	0.356154i
$629$	−47.2226			−1.88289
$630$	−13.7363	−	10.5106i	−0.547268	−	0.418752i
$631$		−	26.0984i		−	1.03896i	−0.854483	−	0.519480i	$-0.826126\pi$
$631$		−	26.0984i		−	1.03896i	0.854483	−	0.519480i	$-0.173874\pi$
$632$	−9.34044	−	23.7029i	−0.371543	−	0.942851i
$633$	−21.8904	−	28.3184i	−0.870066	−	1.12556i
$634$	8.26943	−	19.6426i	0.328421	−	0.780108i
$635$	−15.5107			−0.615523
$636$	−47.0379	−	6.57496i	−1.86517	−	0.260714i
$637$		−	5.64132i		−	0.223517i
$638$	11.5385	−	30.8689i	0.456814	−	1.22211i
$639$	−1.98216	+	7.61441i	−0.0784132	+	0.301221i
$640$	−20.8519	+	7.66554i	−0.824245	+	0.303007i
$641$	5.91097			0.233469			0.116735	−	0.993163i	$-0.462757\pi$
$641$	5.91097			0.233469			0.116735	+	0.993163i	$0.462757\pi$
$642$	2.04746	+	7.70922i	0.0808067	+	0.304259i
$643$	−41.3587			−1.63103			−0.815514	−	0.578737i	$-0.803546\pi$
$643$	−41.3587			−1.63103			−0.815514	+	0.578737i	$0.803546\pi$
$644$	−5.58567	+	5.45814i	−0.220106	+	0.215081i
$645$	10.5298	+	13.6219i	0.414612	+	0.536360i
$646$	−18.2315	+	43.3057i	−0.717307	+	1.70384i
$647$	26.9548			1.05970			0.529850	−	0.848091i	$-0.322248\pi$
$647$	26.9548			1.05970			0.529850	+	0.848091i	$0.322248\pi$
$648$	3.39969	−	25.2278i	0.133552	−	0.991042i
$649$			30.4653i			1.19587i
$650$	−1.31660	+	3.12736i	−0.0516413	+	0.122665i
$651$	−17.9036	−	23.1609i	−0.701699	−	0.907749i
$652$	25.0304	−	24.4589i	0.980265	−	0.957883i
$653$			37.4648i			1.46611i	0.680170	+	0.733055i	$0.261906\pi$
$653$			37.4648i			1.46611i	−0.680170	+	0.733055i	$0.738094\pi$
$654$	−5.70204	−	21.4697i	−0.222967	−	0.839531i
$655$	1.49249			0.0583165
$656$	0.490985	−	21.2556i	0.0191697	−	0.829893i
$657$	−26.3792	−	6.86696i	−1.02915	−	0.267906i
$658$	18.1346	+	7.63458i	0.706962	+	0.297627i
$659$	−32.6896			−1.27341			−0.636703	−	0.771109i	$-0.719702\pi$
$659$	−32.6896			−1.27341			−0.636703	+	0.771109i	$0.719702\pi$
$660$	−29.1516	−	4.07481i	−1.13472	−	0.158612i
$661$			21.4743i			0.835255i	0.908618	+	0.417628i	$0.137138\pi$
$661$			21.4743i			0.835255i	−0.908618	+	0.417628i	$0.862862\pi$
$662$	−1.75626	+	4.17169i	−0.0682588	+	0.162137i
$663$	10.9719	+	14.1937i	0.426112	+	0.551237i
$664$	35.1726	−	13.8602i	1.36496	−	0.537880i
$665$	27.4267			1.06356
$666$	−24.6524	+	32.2182i	−0.955259	+	1.24843i
$667$	0.412759	+	10.1203i	0.0159821	+	0.391859i
$668$	23.1932	+	23.7351i	0.897370	+	0.918338i
$669$	−1.63200	−	2.11123i	−0.0630967	−	0.0816247i
$670$	−4.40760	−	1.85557i	−0.170280	−	0.0716871i
$671$	50.9878			1.96836
$672$	−19.7753	+	4.76600i	−0.762849	+	0.183853i
$673$	46.7441			1.80185			0.900926	−	0.433973i	$-0.142889\pi$
$673$	46.7441			1.80185			0.900926	+	0.433973i	$0.142889\pi$
$674$	−1.19241	+	2.83237i	−0.0459300	+	0.109099i
$675$	−2.33352	−	5.46739i	−0.0898173	−	0.210440i
$676$	12.0229	+	12.3039i	0.462421	+	0.473225i
$677$			35.4077i			1.36083i	0.732828	+	0.680414i	$0.238200\pi$
$677$			35.4077i			1.36083i	−0.732828	+	0.680414i	$0.761800\pi$
$678$	49.4365	−	13.1296i	1.89860	−	0.504239i
$679$	18.7082			0.717955
$680$	10.0563	+	25.5194i	0.385640	+	0.978625i
$681$	−9.11635	−	11.7933i	−0.349339	−	0.451921i
$682$	−45.9160	−	19.3304i	−1.75821	−	0.740198i
$683$		−	20.1991i		−	0.772898i	−0.922311	−	0.386449i	$-0.873701\pi$
$683$		−	20.1991i		−	0.772898i	0.922311	−	0.386449i	$-0.126299\pi$
$684$	20.0283	+	35.0463i	0.765800	+	1.34003i
$685$	−17.8894			−0.683518
$686$	11.0388	−	26.2208i	0.421464	−	1.00112i
$687$	8.51279	−	6.58047i	0.324783	−	0.251061i
$688$	20.2432	+	0.467599i	0.771766	+	0.0178271i
$689$		−	28.7552i		−	1.09549i
$690$	8.74374	−	2.32221i	0.332868	−	0.0884050i
$691$	−0.237432			−0.00903233			−0.00451616	−	0.999990i	$-0.501438\pi$
$691$	−0.237432			−0.00903233			−0.00451616	+	0.999990i	$0.501438\pi$
$692$	2.64770	+	2.70957i	0.100651	+	0.103002i
$693$	−26.0818	−	6.78954i	−0.990765	−	0.257913i
$694$	5.70951	−	13.5620i	0.216730	−	0.514806i
$695$	−11.0541			−0.419306
$696$	−12.5691	+	23.1952i	−0.476430	+	0.879212i
$697$	−26.2502			−0.994298
$698$	−15.8833	+	37.7281i	−0.601193	+	1.42803i
$699$	21.7682	+	28.1603i	0.823349	+	1.06512i
$700$	−3.39749	+	3.31991i	−0.128413	+	0.125481i
$701$	41.5222			1.56827			0.784136	−	0.620589i	$-0.213107\pi$
$701$	41.5222			1.56827			0.784136	+	0.620589i	$0.213107\pi$
$702$	15.4116	−	0.0759408i	0.581675	−	0.00286620i
$703$		−	64.3287i		−	2.42620i
$704$	−25.3114	+	23.6158i	−0.953961	+	0.890054i
$705$	−13.9400	−	18.0335i	−0.525012	−	0.679179i
$706$	5.00193	−	11.8812i	0.188250	−	0.447156i
$707$	−27.7167			−1.04239
$708$	3.37624	−	24.1540i	0.126887	−	0.907762i
$709$			29.4416i			1.10570i	0.833280	+	0.552852i	$0.186460\pi$
$709$			29.4416i			1.10570i	−0.833280	+	0.552852i	$0.813540\pi$
$710$	−6.71279	−	2.82605i	−0.251926	−	0.106060i
$711$	−6.80751	+	26.1508i	−0.255301	+	0.980732i
$712$	5.22785	+	13.2665i	0.195922	+	0.497185i
$713$	15.3119			0.573436
$714$	6.44660	+	24.2732i	0.241258	+	0.908400i
$715$		−	17.8209i		−	0.666465i
$716$	−3.44717	+	3.36846i	−0.128827	+	0.125885i
$717$	5.09850	−	3.94119i	0.190407	−	0.147186i
$718$	6.73652	−	16.0015i	0.251405	−	0.597169i
$719$	−42.1831			−1.57316			−0.786582	−	0.617486i	$-0.788151\pi$
$719$	−42.1831			−1.57316			−0.786582	+	0.617486i	$0.788151\pi$
$720$	22.6608	+	6.46129i	0.844518	+	0.240798i
$721$	−7.66341			−0.285400
$722$	−34.2281	−	14.4098i	−1.27384	−	0.536279i
$723$	17.6477	−	13.6419i	0.656326	−	0.507346i
$724$	−33.2530	+	32.4937i	−1.23584	+	1.20762i
$725$	0.251061	+	6.15567i	0.00932416	+	0.228616i
$726$	−18.2874	+	4.85686i	−0.678708	+	0.180255i
$727$	−6.89099			−0.255573			−0.127786	−	0.991802i	$-0.540787\pi$
$727$	−6.89099			−0.255573			−0.127786	+	0.991802i	$0.540787\pi$
$728$	−4.51514	−	11.4579i	−0.167342	−	0.424658i
$729$	−18.6789	+	19.4961i	−0.691812	+	0.722077i
$730$	9.79048	−	23.2556i	0.362362	−	0.860729i
$731$		−	24.9999i		−	0.924656i
$732$	−40.4249	−	5.65058i	−1.49415	−	0.208852i
$733$	−7.86962			−0.290671			−0.145335	−	0.989382i	$-0.546426\pi$
$733$	−7.86962			−0.290671			−0.145335	+	0.989382i	$0.546426\pi$
$734$	10.4823	+	4.41300i	0.386910	+	0.162887i
$735$	−7.23809	+	5.59512i	−0.266981	+	0.206379i
$736$	4.35368	−	9.70820i	0.160479	−	0.357849i
$737$	−7.45175			−0.274489
$738$	−13.7038	+	17.9096i	−0.504445	+	0.659261i
$739$			47.3048i			1.74013i	0.492934	+	0.870067i	$0.335924\pi$
$739$			47.3048i			1.74013i	−0.492934	+	0.870067i	$0.664076\pi$
$740$	−26.2455	−	26.8587i	−0.964803	−	0.987347i
$741$	−19.3353	+	14.9464i	−0.710299	+	0.549068i
$742$	15.6195	−	37.1014i	0.573409	−	1.36203i
$743$		−	18.1882i		−	0.667260i	−0.942704	−	0.333630i	$-0.891726\pi$
$743$		−	18.1882i		−	0.667260i	0.942704	−	0.333630i	$-0.108274\pi$
$744$	34.2615	+	20.4143i	1.25609	+	0.748424i
$745$	−8.89045			−0.325721
$746$	2.62036	−	6.22422i	0.0959382	−	0.227885i
$747$	−38.8050	−	10.1016i	−1.41980	−	0.369598i
$748$	29.8711	+	30.5691i	1.09220	+	1.11772i
$749$	−6.76057			−0.247026
$750$	28.5624	−	7.58577i	1.04295	−	0.276993i
$751$	−25.1488			−0.917691			−0.458846	−	0.888516i	$-0.651737\pi$
$751$	−25.1488			−0.917691			−0.458846	+	0.888516i	$0.651737\pi$
$752$	−26.7992	−	0.619037i	−0.977267	−	0.0225740i
$753$	−8.41682	+	6.50628i	−0.306726	+	0.237102i
$754$	−14.9614	−	5.59244i	−0.544862	−	0.203665i
$755$		−	36.8667i		−	1.34172i
$756$	19.9261	+	8.27343i	0.724706	+	0.300902i
$757$	−35.9086			−1.30512			−0.652561	−	0.757736i	$-0.726305\pi$
$757$	−35.9086			−1.30512			−0.652561	+	0.757736i	$0.726305\pi$
$758$	9.80334	−	23.2862i	0.356073	−	0.845792i
$759$	11.1531	−	8.62146i	0.404832	−	0.312939i
$760$	−34.7637	+	13.6991i	−1.26101	+	0.496918i
$761$		−	1.16063i		−	0.0420728i	−0.999779	−	0.0210364i	$-0.993303\pi$
$761$		−	1.16063i		−	0.0420728i	0.999779	−	0.0210364i	$-0.00669659\pi$
$762$	18.6999	−	4.96642i	0.677426	−	0.179915i
$763$	18.8278			0.681610
$764$	−1.44072	+	1.40782i	−0.0521233	+	0.0509333i
$765$	7.32920	−	28.1549i	0.264988	−	1.01794i
$766$	20.9903	+	8.83680i	0.758411	+	0.319287i
$767$	14.7658			0.533162
$768$	22.6849	−	15.9183i	0.818572	−	0.574404i
$769$			44.0832i			1.58968i	0.606817	+	0.794841i	$0.292446\pi$
$769$			44.0832i			1.58968i	−0.606817	+	0.794841i	$0.707554\pi$
$770$	9.68011	−	22.9934i	0.348847	−	0.828626i
$771$	0.659895	+	0.853670i	0.0237655	+	0.0307442i
$772$	10.3861	−	10.1489i	0.373803	−	0.365268i
$773$			37.6792i			1.35523i	0.735418	+	0.677614i	$0.236986\pi$
$773$			37.6792i			1.35523i	−0.735418	+	0.677614i	$0.763014\pi$
$774$	−17.0565	−	13.0511i	−0.613085	−	0.469113i
$775$	9.31348			0.334550
$776$	−23.7129	+	9.34438i	−0.851244	+	0.335444i
$777$	−21.0287	−	27.2037i	−0.754402	−	0.975927i
$778$	−7.45067	+	17.6978i	−0.267119	+	0.634496i
$779$		−	35.7593i		−	1.28121i
$780$	−1.97496	+	14.1291i	−0.0707149	+	0.505901i
$781$	−11.3490			−0.406101
$782$	−12.1071	−	5.09704i	−0.432951	−	0.182270i
$783$	25.2670	−	12.0240i	0.902971	−	0.429702i
$784$	−0.248463	+	10.7564i	−0.00887368	+	0.384158i
$785$	12.2522			0.437298
$786$	−1.79937	+	0.477887i	−0.0641814	+	0.0170456i
$787$	−40.0972			−1.42931			−0.714655	−	0.699478i	$-0.753416\pi$
$787$	−40.0972			−1.42931			−0.714655	+	0.699478i	$0.753416\pi$
$788$	−11.9202	−	12.1987i	−0.424640	−	0.434562i
$789$	−1.35485	−	1.75269i	−0.0482339	−	0.0623975i
$790$	−23.0543	−	9.70572i	−0.820234	−	0.345314i
$791$			43.3531i			1.54146i
$792$	36.4503	−	4.42150i	1.29520	−	0.157111i
$793$		−	24.7125i		−	0.877568i
$794$	−6.70512	+	15.9269i	−0.237956	+	0.565224i
$795$	−36.8944	+	28.5197i	−1.30851	+	1.01149i
$796$	2.88163	−	2.81583i	0.102136	−	0.0998045i
$797$		−	20.8449i		−	0.738364i	−0.929357	−	0.369182i	$-0.879638\pi$
$797$		−	20.8449i		−	0.738364i	0.929357	−	0.369182i	$-0.120362\pi$
$798$	−33.0660	+	8.78185i	−1.17052	+	0.310874i
$799$			33.0964i			1.17087i
$800$	2.64813	−	5.90501i	0.0936255	−	0.208774i
$801$	3.81017	−	14.6366i	0.134626	−	0.517160i
$802$	10.3725	−	24.6382i	0.366266	−	0.870003i
$803$		−	39.3174i		−	1.38748i
$804$	5.90801	+	0.825821i	0.208359	+	0.0291245i
$805$			7.66778i			0.270254i
$806$	−9.36896	+	22.2544i	−0.330007	+	0.783876i
$807$	−28.6232	−	37.0282i	−1.00758	−	1.30346i
$808$	35.1313	−	13.8440i	1.23592	−	0.487029i
$809$	16.1878			0.569133			0.284567	−	0.958656i	$-0.408150\pi$
$809$	16.1878			0.569133			0.284567	+	0.958656i	$0.408150\pi$
$810$	−15.3829	−	19.6986i	−0.540499	−	0.692138i
$811$	−8.92823			−0.313513			−0.156756	−	0.987637i	$-0.550104\pi$
$811$	−8.92823			−0.313513			−0.156756	+	0.987637i	$0.550104\pi$
$812$	−16.2662	−	15.3425i	−0.570832	−	0.538416i
$813$	6.86087	−	5.30352i	0.240621	−	0.186003i
$814$	−53.9307	−	22.7045i	−1.89027	−	0.795792i
$815$		−	34.3607i		−	1.20360i
$816$	−20.2951	−	27.5466i	−0.710471	−	0.964324i
$817$	34.0560			1.19147
$818$	5.63981	−	13.3964i	0.197191	−	0.468394i
$819$	−3.29073	+	12.6412i	−0.114987	+	0.441720i
$820$	−14.5894	−	14.9303i	−0.509485	−	0.521389i
$821$	5.47330			0.191019			0.0955097	−	0.995428i	$-0.469552\pi$
$821$	5.47330			0.191019			0.0955097	+	0.995428i	$0.469552\pi$
$822$	21.5677	−	5.72806i	0.752259	−	0.199789i
$823$	16.0731			0.560274			0.280137	−	0.959960i	$-0.409620\pi$
$823$	16.0731			0.560274			0.280137	+	0.959960i	$0.409620\pi$
$824$	9.71347	−	3.82772i	0.338385	−	0.133345i
$825$	6.78388	−	5.24400i	0.236184	−	0.182573i
$826$	19.0516	+	8.02060i	0.662889	+	0.279072i
$827$	36.6105			1.27307			0.636536	−	0.771247i	$-0.280366\pi$
$827$	36.6105			1.27307			0.636536	+	0.771247i	$0.280366\pi$
$828$	−9.79801	+	5.59938i	−0.340504	+	0.194592i
$829$	44.2971			1.53850			0.769251	−	0.638947i	$-0.220630\pi$
$829$	44.2971			1.53850			0.769251	+	0.638947i	$0.220630\pi$
$830$	14.4022	−	34.2101i	0.499909	−	1.18745i
$831$	−13.6846	−	17.7030i	−0.474715	−	0.614112i
$832$	11.4460	+	12.2678i	0.396819	+	0.425311i
$833$	13.2839			0.460261
$834$	13.3270	−	3.53945i	0.461475	−	0.122561i
$835$	32.5826			1.12757
$836$	−41.6426	+	40.6918i	−1.44024	+	1.40735i
$837$	−16.6054	−	38.9061i	−0.573966	−	1.34479i
$838$	−17.3822	+	41.2885i	−0.600459	+	1.42629i
$839$		−	24.2758i		−	0.838094i	−0.907964	−	0.419047i	$-0.862364\pi$
$839$		−	24.2758i		−	0.838094i	0.907964	−	0.419047i	$-0.137636\pi$
$840$	−10.2229	+	17.1572i	−0.352724	+	0.591980i
$841$	−28.9037	+	2.36162i	−0.996679	+	0.0814351i
$842$	9.28406	+	3.90854i	0.319950	+	0.134697i
$843$	−5.03207	−	6.50971i	−0.173314	−	0.224206i
$844$	−29.5602	+	28.8853i	−1.01750	+	0.994272i
$845$	16.8902			0.581042
$846$	22.5805	+	17.2779i	0.776334	+	0.594026i
$847$		−	16.0370i		−	0.551039i
$848$	−1.26648	+	54.8281i	−0.0434911	+	1.88281i
$849$	1.44671	−	1.11832i	0.0496510	−	0.0383807i
$850$	−7.36417	−	3.10027i	−0.252589	−	0.106339i
$851$	17.9846			0.616505
$852$	8.99791	+	1.25773i	0.308263	+	0.0430890i
$853$	−17.7494			−0.607727			−0.303863	−	0.952716i	$-0.598277\pi$
$853$	−17.7494			−0.607727			−0.303863	+	0.952716i	$0.598277\pi$
$854$	13.4235	−	31.8853i	0.459344	−	1.09109i
$855$	38.3539	+	9.98417i	1.31167	+	0.341451i
$856$	8.56911	−	3.37677i	0.292886	−	0.115416i
$857$			0.647482i			0.0221176i	0.999939	+	0.0110588i	$0.00352019\pi$
$857$			0.647482i			0.0221176i	−0.999939	+	0.0110588i	$0.996480\pi$
$858$	5.70615	+	21.4852i	0.194805	+	0.733492i
$859$		−	36.6021i		−	1.24885i	−0.781085	−	0.624424i	$-0.785334\pi$
$859$		−	36.6021i		−	1.24885i	0.781085	−	0.624424i	$-0.214666\pi$
$860$	14.2192	−	13.8945i	0.484870	−	0.473800i
$861$	−11.6895	−	15.1221i	−0.398378	−	0.515359i
$862$	7.01698	+	2.95411i	0.238999	+	0.100617i
$863$	13.0617			0.444627			0.222313	−	0.974975i	$-0.428639\pi$
$863$	13.0617			0.444627			0.222313	+	0.974975i	$0.428639\pi$
$864$	−29.3890	−	0.533984i	−0.999835	−	0.0181665i
$865$	3.71958			0.126470
$866$	−19.1334	+	45.4480i	−0.650178	+	1.54439i
$867$	−10.1266	+	7.82794i	−0.343916	+	0.265851i
$868$	−24.1766	+	23.6246i	−0.820606	+	0.801870i
$869$	−38.9770			−1.32220
$870$	7.66350	+	24.7429i	0.259817	+	0.838862i
$871$			3.61168i			0.122377i
$872$	−23.8644	+	9.40409i	−0.808152	+	0.318463i
$873$	26.1618	+	6.81037i	0.885443	+	0.230496i
$874$	6.94342	−	16.4929i	0.234865	−	0.557881i
$875$			25.0477i			0.846767i
$876$	−4.35724	+	31.1722i	−0.147218	+	1.05321i
$877$		−	18.2462i		−	0.616132i	−0.951365	−	0.308066i	$-0.900318\pi$
$877$		−	18.2462i		−	0.616132i	0.951365	−	0.308066i	$-0.0996817\pi$
$878$	−6.02928	+	14.3215i	−0.203478	+	0.483328i
$879$	20.4285	+	26.4273i	0.689037	+	0.891369i
$880$	−0.784895	+	33.9795i	−0.0264588	+	1.14545i
$881$	30.7299			1.03532			0.517658	−	0.855588i	$-0.326804\pi$
$881$	30.7299			1.03532			0.517658	+	0.855588i	$0.326804\pi$
$882$	6.93483	−	9.06314i	0.233508	−	0.305172i
$883$	46.7068			1.57181			0.785905	−	0.618347i	$-0.212197\pi$
$883$	46.7068			1.57181			0.785905	+	0.618347i	$0.212197\pi$
$884$	14.8161	−	14.4778i	0.498319	−	0.486941i
$885$	−14.6449	−	18.9453i	−0.492282	−	0.636838i
$886$	32.2498	+	13.5770i	1.08345	+	0.456127i
$887$		−	54.4701i		−	1.82893i	−0.404668	−	0.914464i	$-0.632613\pi$
$887$		−	54.4701i		−	1.82893i	0.404668	−	0.914464i	$-0.367387\pi$
$888$	40.2419	+	23.9776i	1.35043	+	0.804636i
$889$			16.3988i			0.549998i
$890$	12.9035	+	5.43230i	0.432526	+	0.182091i
$891$	−34.0015	−	18.9892i	−1.13909	−	0.636161i
$892$	−2.20380	+	2.15349i	−0.0737888	+	0.0721041i
$893$	−45.0855			−1.50873
$894$	10.7185	−	2.84667i	0.358479	−	0.0952068i
$895$			4.73213i			0.158178i
$896$	8.10446	+	22.0459i	0.270751	+	0.736501i
$897$	−4.17861	−	5.40564i	−0.139520	−	0.180489i
$898$	21.7627	+	9.16195i	0.726229	+	0.305738i
$899$	1.78655	+	43.8039i	0.0595849	+	1.46094i
$900$	−5.95964	+	3.40582i	−0.198655	+	0.113527i
$901$	67.7115			2.25580
$902$	−29.9791	−	12.6210i	−0.998196	−	0.420235i
$903$	14.4018	−	11.1327i	0.479263	−	0.370475i
$904$	−21.6540	−	54.9506i	−0.720202	−	1.82763i
$905$			45.6483i			1.51740i
$906$	11.8045	+	44.4470i	0.392178	+	1.47665i
$907$			9.46685i			0.314341i	0.987571	+	0.157171i	$0.0502373\pi$
$907$			9.46685i			0.314341i	−0.987571	+	0.157171i	$0.949763\pi$
$908$	−12.3105	+	12.0294i	−0.408537	+	0.399209i
$909$	−38.7594	−	10.0898i	−1.28557	−	0.334656i
$910$	−11.1444	−	4.69171i	−0.369432	−	0.155529i
$911$			46.0659i			1.52623i	0.646262	+	0.763116i	$0.276331\pi$
$911$			46.0659i			1.52623i	−0.646262	+	0.763116i	$0.723669\pi$
$912$	37.5252	−	27.6469i	1.24258	−	0.915481i
$913$		−	57.8376i		−	1.91414i
$914$	32.0690	+	13.5009i	1.06075	+	0.446569i
$915$	−31.7074	+	24.5101i	−1.04821	+	0.810280i
$916$	−8.68319	−	8.88608i	−0.286901	−	0.293604i
$917$		−	1.57795i		−	0.0521085i
$918$	0.178822	+	36.2907i	0.00590200	+	1.19777i
$919$			43.2586i			1.42697i	0.700670	+	0.713485i	$0.252884\pi$
$919$			43.2586i			1.42697i	−0.700670	+	0.713485i	$0.747116\pi$
$920$	−3.82990	−	9.71901i	−0.126268	−	0.320426i
$921$	23.1558	+	29.9554i	0.763011	+	0.987065i
$922$	−20.7715	+	49.3392i	−0.684073	+	1.62490i
$923$			5.50060i			0.181055i
$924$	−4.30812	+	30.8207i	−0.141727	+	1.01393i
$925$	10.9392			0.359677
$926$	−13.3760	+	31.7724i	−0.439562	+	1.04410i
$927$	−10.7166	−	2.78972i	−0.351980	−	0.0916264i
$928$	28.2809	+	11.3222i	0.928366	+	0.371668i
$929$			13.2344i			0.434208i	0.976149	+	0.217104i	$0.0696610\pi$
$929$			13.2344i			0.434208i	−0.976149	+	0.217104i	$0.930339\pi$
$930$	37.8457	−	10.0513i	1.24101	−	0.329594i
$931$			18.0960i			0.593072i
$932$	29.3952	−	28.7240i	0.962871	−	0.940886i
$933$	−6.54675	−	8.46917i	−0.214331	−	0.277268i
$934$	39.2791	+	16.5363i	1.28525	+	0.541083i
$935$	41.9640			1.37237
$936$	−2.14299	−	17.6666i	−0.0700460	−	0.577449i
$937$	10.8006			0.352841			0.176420	−	0.984315i	$-0.443548\pi$
$937$	10.8006			0.352841			0.176420	+	0.984315i	$0.443548\pi$
$938$	−1.96182	+	4.65997i	−0.0640557	+	0.152153i
$939$	9.32616	−	7.20921i	0.304348	−	0.235264i
$940$	−18.8242	+	18.3944i	−0.613979	+	0.599960i
$941$	−34.1094			−1.11193			−0.555967	−	0.831204i	$-0.687652\pi$
$941$	−34.1094			−1.11193			−0.555967	+	0.831204i	$0.687652\pi$
$942$	−14.7714	+	3.92306i	−0.481277	+	0.127820i
$943$	9.99735			0.325558
$944$	−28.1542	−	0.650337i	−0.916343	−	0.0211667i
$945$	19.4831	−	8.31551i	0.633784	−	0.270504i
$946$	12.0199	−	28.5512i	0.390801	−	0.928281i
$947$	−24.3264			−0.790503			−0.395251	−	0.918573i	$-0.629343\pi$
$947$	−24.3264			−0.790503			−0.395251	+	0.918573i	$0.629343\pi$
$948$	30.9023	+	4.31952i	1.00366	+	0.140291i
$949$	−19.0562			−0.618589
$950$	4.22334	−	10.0318i	0.137023	−	0.325475i
$951$	15.9638	+	20.6514i	0.517661	+	0.669669i
$952$	26.9806	−	10.6321i	0.874446	−	0.344587i
$953$			15.4131i			0.499280i	0.968339	+	0.249640i	$0.0803123\pi$
$953$			15.4131i			0.499280i	−0.968339	+	0.249640i	$0.919688\pi$
$954$	35.3486	−	46.1971i	1.14445	−	1.49569i
$955$			1.97776i			0.0639988i
$956$	−5.20055	−	5.32207i	−0.168198	−	0.172128i
$957$	25.9653	+	30.9005i	0.839340	+	0.998872i
$958$	6.29255	−	14.9469i	0.203303	−	0.482912i
$959$			18.9137i			0.610755i
$960$	4.38798	−	26.8532i	0.141622	−	0.866682i
$961$	35.2749			1.13790
$962$	−11.0043	+	26.1389i	−0.354793	+	0.842751i
$963$	−9.45407	−	2.46106i	−0.304653	−	0.0793065i
$964$	−18.0010	−	18.4216i	−0.579772	−	0.593319i
$965$		−	14.2576i		−	0.458967i
$966$	−2.45517	−	9.24438i	−0.0789939	−	0.297433i
$967$	−58.7655			−1.88977			−0.944885	−	0.327401i	$-0.893827\pi$
$967$	−58.7655			−1.88977			−0.944885	+	0.327401i	$0.893827\pi$
$968$	8.01018	+	20.3272i	0.257457	+	0.653340i
$969$	−35.1950	−	45.5299i	−1.13063	−	1.46263i
$970$	−9.70981	+	23.0640i	−0.311763	+	0.740540i
$971$	22.1575			0.711069			0.355535	−	0.934663i	$-0.384299\pi$
$971$	22.1575			0.711069			0.355535	+	0.934663i	$0.384299\pi$
$972$	24.8532	+	18.8234i	0.797165	+	0.603761i
$973$			11.6870i			0.374669i
$974$	−1.10354	+	2.62127i	−0.0353597	+	0.0839910i
$975$	−2.54164	−	3.28798i	−0.0813976	−	0.105300i
$976$	−1.08842	+	47.1198i	−0.0348396	+	1.50827i
$977$		−	46.5956i		−	1.49072i	−0.666660	−	0.745362i	$-0.732277\pi$
$977$		−	46.5956i		−	1.49072i	0.666660	−	0.745362i	$-0.267723\pi$
$978$	11.0021	+	41.4257i	0.351807	+	1.32465i
$979$	21.8154			0.697224
$980$	7.38298	+	7.55549i	0.235841	+	0.241351i
$981$	26.3290	+	6.85389i	0.840620	+	0.218828i
$982$	−12.9622	−	5.45702i	−0.413641	−	0.174140i
$983$			3.49122i			0.111352i	0.998449	+	0.0556762i	$0.0177315\pi$
$983$			3.49122i			0.111352i	−0.998449	+	0.0556762i	$0.982269\pi$
$984$	22.3698	+	13.3288i	0.713123	+	0.424905i
$985$	−16.7459			−0.533570
$986$	13.1688	−	35.2305i	0.419381	−	1.12197i
$987$	−19.0660	+	14.7382i	−0.606878	+	0.469123i
$988$	19.7223	+	20.1831i	0.627450	+	0.642111i
$989$			9.52118i			0.302756i
$990$	21.9071	−	28.6305i	0.696254	−	0.909937i
$991$		−	29.3482i		−	0.932276i	−0.884712	−	0.466138i	$-0.845645\pi$
$991$		−	29.3482i		−	0.932276i	0.884712	−	0.466138i	$-0.154355\pi$
$992$	18.8441	−	42.0202i	0.598302	−	1.33414i
$993$	−3.39037	−	4.38594i	−0.107590	−	0.139184i
$994$	−2.98786	+	7.09715i	−0.0947691	+	0.225108i
$995$		−	3.95578i		−	0.125407i
$996$	−6.40970	+	45.8556i	−0.203099	+	1.45299i
$997$	52.5786			1.66518			0.832591	−	0.553888i	$-0.186856\pi$
$997$	52.5786			1.66518			0.832591	+	0.553888i	$0.186856\pi$
$998$	5.42601	+	2.28432i	0.171757	+	0.0723088i
$999$	−19.5039	−	45.6971i	−0.617075	−	1.44579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	696.2.l.b.347.92	yes	104
3.2	odd	2	inner	696.2.l.b.347.14	yes	104
8.3	odd	2	inner	696.2.l.b.347.90	yes	104
24.11	even	2	inner	696.2.l.b.347.16	yes	104
29.28	even	2	inner	696.2.l.b.347.13	✓	104
87.86	odd	2	inner	696.2.l.b.347.91	yes	104
232.115	odd	2	inner	696.2.l.b.347.15	yes	104
696.347	even	2	inner	696.2.l.b.347.89	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
696.2.l.b.347.13	✓	104	29.28	even	2	inner
696.2.l.b.347.14	yes	104	3.2	odd	2	inner
696.2.l.b.347.15	yes	104	232.115	odd	2	inner
696.2.l.b.347.16	yes	104	24.11	even	2	inner
696.2.l.b.347.89	yes	104	696.347	even	2	inner
696.2.l.b.347.90	yes	104	8.3	odd	2	inner
696.2.l.b.347.91	yes	104	87.86	odd	2	inner
696.2.l.b.347.92	yes	104	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	696.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30342 + 0.548731i) q^{2} +(-1.37036 + 1.05930i) q^{3} +(1.39779 + 1.43045i) q^{4} +1.96366 q^{5} +(-2.36742 + 0.628752i) q^{6} -2.07610i q^{7} +(1.03697 + 2.63148i) q^{8} +(0.755764 - 2.90324i) q^{9} +O(q^{10})\)	\(q+(1.30342 + 0.548731i) q^{2} +(-1.37036 + 1.05930i) q^{3} +(1.39779 + 1.43045i) q^{4} +1.96366 q^{5} +(-2.36742 + 0.628752i) q^{6} -2.07610i q^{7} +(1.03697 + 2.63148i) q^{8} +(0.755764 - 2.90324i) q^{9} +(2.55947 + 1.07752i) q^{10} +4.32719 q^{11} +(-3.43075 - 0.479550i) q^{12} -2.09729i q^{13} +(1.13922 - 2.70602i) q^{14} +(-2.69092 + 2.08011i) q^{15} +(-0.0923716 + 3.99893i) q^{16} +4.93860 q^{17} +(2.57817 - 3.36942i) q^{18} +6.72758i q^{19} +(2.74479 + 2.80892i) q^{20} +(2.19921 + 2.84500i) q^{21} +(5.64014 + 2.37446i) q^{22} -1.88085 q^{23} +(-4.20855 - 2.50761i) q^{24} -1.14403 q^{25} +(1.15084 - 2.73364i) q^{26} +(2.03974 + 4.77907i) q^{27} +(2.96975 - 2.90195i) q^{28} +(-0.219453 - 5.38069i) q^{29} +(-4.64881 + 1.23466i) q^{30} -8.14094 q^{31} +(-2.31474 + 5.16159i) q^{32} +(-5.92981 + 4.58380i) q^{33} +(6.43705 + 2.70996i) q^{34} -4.07675i q^{35} +(5.20934 - 2.97704i) q^{36} -9.56194 q^{37} +(-3.69163 + 8.76884i) q^{38} +(2.22166 + 2.87403i) q^{39} +(2.03626 + 5.16734i) q^{40} -5.31532 q^{41} +(1.30535 + 4.91499i) q^{42} -5.06216i q^{43} +(6.04850 + 6.18983i) q^{44} +(1.48407 - 5.70099i) q^{45} +(-2.45154 - 1.03208i) q^{46} +6.70159i q^{47} +(-4.10949 - 5.57782i) q^{48} +2.68982 q^{49} +(-1.49115 - 0.627765i) q^{50} +(-6.76765 + 5.23146i) q^{51} +(3.00006 - 2.93156i) q^{52} +13.7107 q^{53} +(0.0362091 + 7.34838i) q^{54} +8.49715 q^{55} +(5.46321 - 2.15285i) q^{56} +(-7.12653 - 9.21919i) q^{57} +(2.66651 - 7.13370i) q^{58} +7.04044i q^{59} +(-6.73683 - 0.941674i) q^{60} +11.7831 q^{61} +(-10.6110 - 4.46718i) q^{62} +(-6.02742 - 1.56904i) q^{63} +(-5.84939 + 5.45753i) q^{64} -4.11836i q^{65} +(-10.2443 + 2.72073i) q^{66} -1.72208 q^{67} +(6.90311 + 7.06441i) q^{68} +(2.57744 - 1.99239i) q^{69} +(2.23704 - 5.31371i) q^{70} -2.62273 q^{71} +(8.42353 - 1.02179i) q^{72} -9.08611i q^{73} +(-12.4632 - 5.24693i) q^{74} +(1.56773 - 1.21187i) q^{75} +(-9.62346 + 9.40374i) q^{76} -8.98368i q^{77} +(1.31867 + 4.96515i) q^{78} -9.00744 q^{79} +(-0.181387 + 7.85255i) q^{80} +(-7.85764 - 4.38834i) q^{81} +(-6.92808 - 2.91668i) q^{82} -13.3661i q^{83} +(-0.995592 + 7.12257i) q^{84} +9.69773 q^{85} +(2.77776 - 6.59810i) q^{86} +(6.00050 + 7.14101i) q^{87} +(4.48717 + 11.3869i) q^{88} +5.04147 q^{89} +(5.06266 - 6.61641i) q^{90} -4.35417 q^{91} +(-2.62904 - 2.69047i) q^{92} +(11.1560 - 8.62370i) q^{93} +(-3.67737 + 8.73496i) q^{94} +13.2107i q^{95} +(-2.29566 - 9.52523i) q^{96} +9.01124i q^{97} +(3.50596 + 1.47599i) q^{98} +(3.27034 - 12.5629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 4 q^{4} - 12 q^{6} - 40 q^{9}+O(q^{10}) \) 104 * q - 4 * q^4 - 12 * q^6 - 40 * q^9	\( 104 q - 4 q^{4} - 12 q^{6} - 40 q^{9} + 12 q^{16} - 16 q^{22} - 12 q^{24} + 152 q^{25} - 44 q^{28} - 16 q^{30} - 16 q^{33} + 20 q^{34} - 16 q^{36} - 24 q^{42} - 16 q^{49} - 16 q^{51} + 104 q^{52} + 16 q^{54} + 8 q^{57} + 24 q^{58} - 4 q^{64} - 72 q^{67} - 76 q^{78} - 128 q^{81} + 4 q^{82} - 48 q^{88} + 120 q^{91} + 172 q^{94} - 12 q^{96}+O(q^{100}) \) 104 * q - 4 * q^4 - 12 * q^6 - 40 * q^9 + 12 * q^16 - 16 * q^22 - 12 * q^24 + 152 * q^25 - 44 * q^28 - 16 * q^30 - 16 * q^33 + 20 * q^34 - 16 * q^36 - 24 * q^42 - 16 * q^49 - 16 * q^51 + 104 * q^52 + 16 * q^54 + 8 * q^57 + 24 * q^58 - 4 * q^64 - 72 * q^67 - 76 * q^78 - 128 * q^81 + 4 * q^82 - 48 * q^88 + 120 * q^91 + 172 * q^94 - 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more