LMFDB - Embedded newform 690.2.w.a.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	690.37
Dual form			690.2.w.a.373.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.11884 - 0.714499i) q^{5} +(0.841254 + 0.540641i) q^{6} +(0.271075 + 0.726780i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.11884 - 0.714499i) q^{5} +(0.841254 + 0.540641i) q^{6} +(0.271075 + 0.726780i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-2.20209 - 0.388352i) q^{10} +(-1.66072 + 5.65588i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(3.64999 + 1.36138i) q^{13} +(0.110392 - 0.767791i) q^{14} +(-2.16442 + 0.561523i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-3.47850 + 0.756701i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-3.10501 + 1.99547i) q^{19} +(1.74661 + 1.39620i) q^{20} +(-0.218536 - 0.744266i) q^{21} +(4.16815 - 4.16815i) q^{22} +(0.782098 - 4.73163i) q^{23} +1.00000i q^{24} +(3.97898 - 3.02782i) q^{25} +(-2.55108 - 2.94411i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(-0.464852 + 0.620969i) q^{28} +(-4.42134 + 6.87974i) q^{29} +(2.16877 + 0.544457i) q^{30} +(-0.455780 + 0.525998i) q^{31} +(0.800541 - 0.599278i) q^{32} +(2.05997 - 5.52300i) q^{33} +(3.41565 + 1.00293i) q^{34} +(1.09365 + 1.34625i) q^{35} +(0.415415 + 0.909632i) q^{36} +(3.93943 + 5.26246i) q^{37} +(3.68153 - 0.263308i) q^{38} +(-3.54357 - 1.61829i) q^{39} +(-0.863835 - 2.06247i) q^{40} +(0.0215894 + 0.150158i) q^{41} +(-0.164884 + 0.757960i) q^{42} +(-0.836505 + 11.6959i) q^{43} +(-5.65588 + 1.66072i) q^{44} +(2.19896 - 0.405684i) q^{45} +(-2.95406 + 3.77803i) q^{46} +(-0.875308 - 0.875308i) q^{47} +(0.479249 - 0.877679i) q^{48} +(4.83552 - 4.19000i) q^{49} +(-4.94335 + 0.750534i) q^{50} +(3.52362 - 0.506620i) q^{51} +(0.828071 + 3.80658i) q^{52} +(8.51077 - 3.17435i) q^{53} +(0.755750 + 0.654861i) q^{54} +(0.522329 + 13.1705i) q^{55} +(0.705590 - 0.322232i) q^{56} +(3.23946 - 1.76888i) q^{57} +(7.17763 - 3.91928i) q^{58} +(-11.6922 + 5.33967i) q^{59} +(-1.64255 - 1.51724i) q^{60} +(9.88231 + 8.56307i) q^{61} +(0.652113 - 0.243225i) q^{62} +(0.164884 + 0.757960i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(8.70645 + 0.276624i) q^{65} +(-4.45489 + 3.86018i) q^{66} +(6.73221 - 12.3291i) q^{67} +(-2.51720 - 2.51720i) q^{68} +(-1.11766 + 4.66378i) q^{69} +(-0.314684 - 1.70570i) q^{70} +(7.40082 - 2.17308i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(-0.107206 + 0.492818i) q^{73} +(-0.935524 - 6.50671i) q^{74} +(-4.18485 + 2.73625i) q^{75} +(-3.35739 - 1.53327i) q^{76} +(-4.56076 + 0.326192i) q^{77} +(2.33455 + 3.11860i) q^{78} +(6.48309 + 14.1960i) q^{79} +(-0.230267 + 2.22418i) q^{80} +(0.959493 + 0.281733i) q^{81} +(0.0530144 - 0.142137i) q^{82} +(2.80499 - 2.09979i) q^{83} +(0.507967 - 0.586225i) q^{84} +(-6.82972 + 4.08871i) q^{85} +(6.33941 - 9.86432i) q^{86} +(4.90087 - 6.54680i) q^{87} +(5.75995 + 1.25300i) q^{88} +(0.988512 + 1.14080i) q^{89} +(-2.12440 - 0.697788i) q^{90} +3.02177i q^{91} +(4.40333 - 1.90017i) q^{92} +(0.492143 - 0.492143i) q^{93} +(0.348749 + 1.18773i) q^{94} +(-5.15327 + 6.44662i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-3.94307 - 2.95174i) q^{97} +(-6.25209 + 1.36006i) q^{98} +(-2.44873 + 5.36197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{21}{22}\right)$

Coefficient data

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

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

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

$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$3$	−0.997452	−	0.0713392i	−0.575879	−	0.0411877i
$3$	−0.997452	−	0.0713392i	−0.575879	−	0.0411877i
$4$	0.540641	+	0.841254i	0.270320	+	0.420627i
$5$	2.11884	−	0.714499i	0.947575	−	0.319534i
$5$	2.11884	−	0.714499i	0.947575	−	0.319534i
$6$	0.841254	+	0.540641i	0.343440	+	0.220716i
$7$	0.271075	+	0.726780i	0.102457	+	0.274697i	0.978056	−	0.208341i	$-0.0668062\pi$
$7$	0.271075	+	0.726780i	0.102457	+	0.274697i	−0.875600	+	0.483037i	$0.839534\pi$
$8$	−0.0713392	−	0.997452i	−0.0252222	−	0.352653i
$9$	0.989821	+	0.142315i	0.329940	+	0.0474383i
$10$	−2.20209	−	0.388352i	−0.696361	−	0.122808i
$11$	−1.66072	+	5.65588i	−0.500725	+	1.70531i	0.189641	+	0.981853i	$0.439268\pi$
$11$	−1.66072	+	5.65588i	−0.500725	+	1.70531i	−0.690366	+	0.723460i	$0.742551\pi$
$12$	−0.479249	−	0.877679i	−0.138347	−	0.253364i
$13$	3.64999	+	1.36138i	1.01233	+	0.377578i	0.800244	−	0.599674i	$-0.204703\pi$
$13$	3.64999	+	1.36138i	1.01233	+	0.377578i	0.212081	+	0.977252i	$0.431976\pi$
$14$	0.110392	−	0.767791i	0.0295034	−	0.205201i
$15$	−2.16442	+	0.561523i	−0.558850	+	0.144985i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	−3.47850	+	0.756701i	−0.843660	+	0.183527i	−0.613568	−	0.789642i	$-0.710266\pi$
$17$	−3.47850	+	0.756701i	−0.843660	+	0.183527i	−0.230092	+	0.973169i	$0.573903\pi$
$18$	−0.800541	−	0.599278i	−0.188689	−	0.141251i
$19$	−3.10501	+	1.99547i	−0.712339	+	0.457792i	−0.845964	−	0.533240i	$-0.820974\pi$
$19$	−3.10501	+	1.99547i	−0.712339	+	0.457792i	0.133626	+	0.991032i	$0.457338\pi$
$20$	1.74661	+	1.39620i	0.390553	+	0.312199i
$21$	−0.218536	−	0.744266i	−0.0476885	−	0.162412i
$22$	4.16815	−	4.16815i	0.888653	−	0.888653i
$23$	0.782098	−	4.73163i	0.163079	−	0.986613i
$23$	0.782098	−	4.73163i	0.163079	−	0.986613i
$24$			1.00000i			0.204124i
$25$	3.97898	−	3.02782i	0.795796	−	0.605565i
$26$	−2.55108	−	2.94411i	−0.500308	−	0.577387i
$27$	−0.977147	−	0.212565i	−0.188052	−	0.0409082i
$28$	−0.464852	+	0.620969i	−0.0878487	+	0.117352i
$29$	−4.42134	+	6.87974i	−0.821023	+	1.27754i	0.136922	+	0.990582i	$0.456279\pi$
$29$	−4.42134	+	6.87974i	−0.821023	+	1.27754i	−0.957944	+	0.286954i	$0.907357\pi$
$30$	2.16877	+	0.544457i	0.395962	+	0.0994038i
$31$	−0.455780	+	0.525998i	−0.0818605	+	0.0944721i	−0.795202	−	0.606344i	$-0.792635\pi$
$31$	−0.455780	+	0.525998i	−0.0818605	+	0.0944721i	0.713342	+	0.700816i	$0.247181\pi$
$32$	0.800541	−	0.599278i	0.141517	−	0.105938i
$33$	2.05997	−	5.52300i	0.358595	−	0.961431i
$34$	3.41565	+	1.00293i	0.585780	+	0.172000i
$35$	1.09365	+	1.34625i	0.184860	+	0.227557i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	3.93943	+	5.26246i	0.647638	+	0.865142i	0.997427	−	0.0716858i	$-0.0228379\pi$
$37$	3.93943	+	5.26246i	0.647638	+	0.865142i	−0.349790	+	0.936828i	$0.613747\pi$
$38$	3.68153	−	0.263308i	0.597223	−	0.0427142i
$39$	−3.54357	−	1.61829i	−0.567426	−	0.259135i
$40$	−0.863835	−	2.06247i	−0.136584	−	0.326105i
$41$	0.0215894	+	0.150158i	0.00337170	+	0.0234507i	0.991438	−	0.130580i	$-0.0416838\pi$
$41$	0.0215894	+	0.150158i	0.00337170	+	0.0234507i	−0.988066	+	0.154030i	$0.950775\pi$
$42$	−0.164884	+	0.757960i	−0.0254422	+	0.116956i
$43$	−0.836505	+	11.6959i	−0.127566	+	1.78360i	0.382985	+	0.923755i	$0.374896\pi$
$43$	−0.836505	+	11.6959i	−0.127566	+	1.78360i	−0.510551	+	0.859848i	$0.670558\pi$
$44$	−5.65588	+	1.66072i	−0.852657	+	0.250363i
$45$	2.19896	−	0.405684i	0.327801	−	0.0604758i
$46$	−2.95406	+	3.77803i	−0.435552	+	0.557040i
$47$	−0.875308	−	0.875308i	−0.127677	−	0.127677i	0.640381	−	0.768058i	$-0.278777\pi$
$47$	−0.875308	−	0.875308i	−0.127677	−	0.127677i	−0.768058	+	0.640381i	$0.778777\pi$
$48$	0.479249	−	0.877679i	0.0691736	−	0.126682i
$49$	4.83552	−	4.19000i	0.690789	−	0.598572i
$50$	−4.94335	+	0.750534i	−0.699095	+	0.106142i
$51$	3.52362	−	0.506620i	0.493405	−	0.0709409i
$52$	0.828071	+	3.80658i	0.114833	+	0.527878i
$53$	8.51077	−	3.17435i	1.16904	−	0.436031i	0.311402	−	0.950278i	$-0.399201\pi$
$53$	8.51077	−	3.17435i	1.16904	−	0.436031i	0.857642	+	0.514247i	$0.171929\pi$
$54$	0.755750	+	0.654861i	0.102844	+	0.0891153i
$55$	0.522329	+	13.1705i	0.0704308	+	1.77591i
$56$	0.705590	−	0.322232i	0.0942884	−	0.0430601i
$57$	3.23946	−	1.76888i	0.429076	−	0.234293i
$58$	7.17763	−	3.91928i	0.942469	−	0.514627i
$59$	−11.6922	+	5.33967i	−1.52220	+	0.695166i	−0.988599	−	0.150571i	$-0.951889\pi$
$59$	−11.6922	+	5.33967i	−1.52220	+	0.695166i	−0.533601	+	0.845736i	$0.679162\pi$
$60$	−1.64255	−	1.51724i	−0.212053	−	0.195875i
$61$	9.88231	+	8.56307i	1.26530	+	1.09639i	0.990876	+	0.134779i	$0.0430326\pi$
$61$	9.88231	+	8.56307i	1.26530	+	1.09639i	0.274424	+	0.961609i	$0.411513\pi$
$62$	0.652113	−	0.243225i	0.0828184	−	0.0308897i
$63$	0.164884	+	0.757960i	0.0207734	+	0.0954940i
$64$	−0.989821	+	0.142315i	−0.123728	+	0.0177894i
$65$	8.70645	+	0.276624i	1.07990	+	0.0343110i
$66$	−4.45489	+	3.86018i	−0.548359	+	0.475155i
$67$	6.73221	−	12.3291i	0.822470	−	1.50624i	−0.0394640	−	0.999221i	$-0.512565\pi$
$67$	6.73221	−	12.3291i	0.822470	−	1.50624i	0.861934	−	0.507020i	$-0.169253\pi$
$68$	−2.51720	−	2.51720i	−0.305255	−	0.305255i
$69$	−1.11766	+	4.66378i	−0.134550	+	0.561453i
$70$	−0.314684	−	1.70570i	−0.0376119	−	0.203871i
$71$	7.40082	−	2.17308i	0.878316	−	0.257897i	0.188667	−	0.982041i	$-0.439583\pi$
$71$	7.40082	−	2.17308i	0.878316	−	0.257897i	0.689648	+	0.724144i	$0.257765\pi$
$72$	0.0713392	−	0.997452i	0.00840740	−	0.117551i
$73$	−0.107206	+	0.492818i	−0.0125475	+	0.0576800i	−0.982995	−	0.183633i	$-0.941214\pi$
$73$	−0.107206	+	0.492818i	−0.0125475	+	0.0576800i	0.970447	+	0.241313i	$0.0775779\pi$
$74$	−0.935524	−	6.50671i	−0.108752	−	0.756390i
$75$	−4.18485	+	2.73625i	−0.483224	+	0.315955i
$76$	−3.35739	−	1.53327i	−0.385119	−	0.175878i
$77$	−4.56076	+	0.326192i	−0.519747	+	0.0371730i
$78$	2.33455	+	3.11860i	0.264336	+	0.353111i
$79$	6.48309	+	14.1960i	0.729404	+	1.59717i	0.800237	+	0.599684i	$0.204707\pi$
$79$	6.48309	+	14.1960i	0.729404	+	1.59717i	−0.0708326	+	0.997488i	$0.522566\pi$
$80$	−0.230267	+	2.22418i	−0.0257446	+	0.248671i
$81$	0.959493	+	0.281733i	0.106610	+	0.0313036i
$82$	0.0530144	−	0.142137i	0.00585446	−	0.0156964i
$83$	2.80499	−	2.09979i	0.307888	−	0.230482i	−0.434149	−	0.900841i	$-0.642951\pi$
$83$	2.80499	−	2.09979i	0.307888	−	0.230482i	0.742037	+	0.670359i	$0.233860\pi$
$84$	0.507967	−	0.586225i	0.0554237	−	0.0639624i
$85$	−6.82972	+	4.08871i	−0.740788	+	0.443483i
$86$	6.33941	−	9.86432i	0.683596	−	1.06370i
$87$	4.90087	−	6.54680i	0.525429	−	0.701890i
$88$	5.75995	+	1.25300i	0.614013	+	0.133570i
$89$	0.988512	+	1.14080i	0.104782	+	0.120925i	0.805718	−	0.592299i	$-0.201780\pi$
$89$	0.988512	+	1.14080i	0.104782	+	0.120925i	−0.700936	+	0.713224i	$0.747234\pi$
$90$	−2.12440	−	0.697788i	−0.223932	−	0.0735533i
$91$			3.02177i			0.316768i
$92$	4.40333	−	1.90017i	0.459079	−	0.198106i
$93$	0.492143	−	0.492143i	0.0510328	−	0.0510328i
$94$	0.348749	+	1.18773i	0.0359707	+	0.122505i
$95$	−5.15327	+	6.44662i	−0.528714	+	0.661409i
$96$	−0.841254	+	0.540641i	−0.0858601	+	0.0551789i
$97$	−3.94307	−	2.95174i	−0.400358	−	0.299704i	0.380061	−	0.924962i	$-0.375903\pi$
$97$	−3.94307	−	2.95174i	−0.400358	−	0.299704i	−0.780419	+	0.625257i	$0.784994\pi$
$98$	−6.25209	+	1.36006i	−0.631556	+	0.137387i
$99$	−2.44873	+	5.36197i	−0.246107	+	0.538898i
$100$	4.69837	+	1.71037i	0.469837	+	0.171037i
$101$	1.46023	−	10.1561i	0.145298	−	1.01057i	−0.778488	−	0.627660i	$-0.784013\pi$
$101$	1.46023	−	10.1561i	0.145298	−	1.01057i	0.923786	−	0.382910i	$-0.125078\pi$
$102$	−3.33540	−	1.24404i	−0.330254	−	0.123178i
$103$	7.76239	+	14.2158i	0.764851	+	1.40072i	0.911402	+	0.411516i	$0.135001\pi$
$103$	7.76239	+	14.2158i	0.764851	+	1.40072i	−0.146552	+	0.989203i	$0.546817\pi$
$104$	1.09752	−	3.73781i	0.107621	−	0.366522i
$105$	−0.994821	−	1.42084i	−0.0970846	−	0.138660i
$106$	−8.99103	−	1.29271i	−0.873286	−	0.125560i
$107$	−1.07578	−	15.0414i	−0.104000	−	1.45411i	−0.734863	−	0.678216i	$-0.762753\pi$
$107$	−1.07578	−	15.0414i	−0.104000	−	1.45411i	0.630863	−	0.775895i	$-0.282701\pi$
$108$	−0.349464	−	0.936950i	−0.0336272	−	0.0901580i
$109$	−10.2489	−	6.58658i	−0.981668	−	0.630880i	−0.0517554	−	0.998660i	$-0.516482\pi$
$109$	−10.2489	−	6.58658i	−0.981668	−	0.630880i	−0.929913	+	0.367780i	$0.880118\pi$
$110$	5.85351	−	11.8098i	0.558111	−	1.12602i
$111$	−3.55397	−	5.53008i	−0.337328	−	0.524892i
$112$	−0.773710	−	0.0553369i	−0.0731088	−	0.00522884i
$113$	−10.2436	−	5.59343i	−0.963636	−	0.526185i	−0.0812413	−	0.996694i	$-0.525888\pi$
$113$	−10.2436	−	5.59343i	−0.963636	−	0.526185i	−0.882395	+	0.470509i	$0.844070\pi$
$114$	−3.69094			−0.345688
$115$	−1.72360	−	10.5844i	−0.160727	−	0.986999i
$116$	−8.17797			−0.759305
$117$	3.41909	+	1.86697i	0.316095	+	0.172601i
$118$	12.8211	+	0.916981i	1.18027	+	0.0844149i
$119$	−1.49289	−	2.32298i	−0.136853	−	0.212947i
$120$	0.714499	+	2.11884i	0.0652246	+	0.193423i
$121$	−19.9773	−	12.8386i	−1.81611	−	1.16715i
$122$	−4.56965	−	12.2517i	−0.413717	−	1.10922i
$123$	−0.0108223	−	0.151315i	−0.000975813	−	0.0136436i
$124$	−0.688911	−	0.0990505i	−0.0618660	−	0.00889499i
$125$	6.26745	−	9.25846i	0.560578	−	0.828102i
$126$	0.218536	−	0.744266i	0.0194688	−	0.0663045i
$127$	−2.45876	−	4.50288i	−0.218180	−	0.399566i	0.745549	−	0.666451i	$-0.232187\pi$
$127$	−2.45876	−	4.50288i	−0.218180	−	0.399566i	−0.963728	+	0.266885i	$0.914006\pi$
$128$	0.936950	+	0.349464i	0.0828154	+	0.0308886i
$129$	1.66875	−	11.6064i	0.146925	−	1.02189i
$130$	−7.50890	−	4.41535i	−0.658574	−	0.387252i
$131$	−4.19911	+	9.19477i	−0.366878	+	0.803351i	0.632702	+	0.774395i	$0.281946\pi$
$131$	−4.19911	+	9.19477i	−0.366878	+	0.803351i	−0.999581	+	0.0289562i	$0.990782\pi$
$132$	5.75995	−	1.25300i	0.501339	−	0.109060i
$133$	−2.29196	−	1.71574i	−0.198738	−	0.148773i
$134$	−11.8174	+	7.59460i	−1.02087	+	0.656074i
$135$	−2.22230	+	0.247779i	−0.191265	+	0.0213254i
$136$	1.00293	+	3.41565i	0.0860002	+	0.292890i
$137$	−10.2686	+	10.2686i	−0.877307	+	0.877307i	−0.993255	−	0.115948i	$-0.963009\pi$
$137$	−10.2686	+	10.2686i	−0.877307	+	0.877307i	0.115948	+	0.993255i	$0.463009\pi$
$138$	3.21606	−	3.55767i	0.273769	−	0.302849i
$139$			8.45001i			0.716721i	0.933583	+	0.358360i	$0.116664\pi$
$139$			8.45001i			0.716721i	−0.933583	+	0.358360i	$0.883336\pi$
$140$	−0.541265	+	1.64787i	−0.0457453	+	0.139271i
$141$	0.810634	+	0.935521i	0.0682677	+	0.0787851i
$142$	−7.53699	−	1.63957i	−0.632490	−	0.137590i
$143$	−13.7614	+	18.3831i	−1.15079	+	1.53727i
$144$	−0.540641	+	0.841254i	−0.0450534	+	0.0701045i
$145$	−4.45255	+	17.7361i	−0.369764	+	1.47291i
$146$	0.330275	−	0.381158i	0.0273338	−	0.0315448i
$147$	−5.12211	+	3.83436i	−0.422465	+	0.316253i
$148$	−2.29725	+	6.15915i	−0.188832	+	0.506279i
$149$	18.8481	+	5.53431i	1.54410	+	0.453389i	0.939331	−	0.343012i	$-0.111447\pi$
$149$	18.8481	+	5.53431i	1.54410	+	0.453389i	0.604769	+	0.796401i	$0.293265\pi$
$150$	4.98430	−	0.395967i	0.406966	−	0.0323306i
$151$	−3.70797	−	8.11933i	−0.301751	−	0.660742i	0.696642	−	0.717419i	$-0.254677\pi$
$151$	−3.70797	−	8.11933i	−0.301751	−	0.660742i	−0.998393	+	0.0566772i	$0.981949\pi$
$152$	2.21189	+	2.95475i	0.179408	+	0.239662i
$153$	−3.55078	+	0.253957i	−0.287064	+	0.0205312i
$154$	4.15921	+	1.89945i	0.335159	+	0.153062i
$155$	−0.589900	+	1.44016i	−0.0473819	+	0.115677i
$156$	−0.554403	−	3.85596i	−0.0443878	−	0.308724i
$157$	3.82423	−	17.5797i	0.305207	−	1.40301i	−0.527620	−	0.849480i	$-0.676916\pi$
$157$	3.82423	−	17.5797i	0.305207	−	1.40301i	0.832827	−	0.553533i	$-0.186721\pi$
$158$	1.11334	−	15.5665i	0.0885726	−	1.23841i
$159$	−8.71554	+	2.55911i	−0.691187	+	0.202951i
$160$	1.26804	−	1.84176i	0.100247	−	0.145604i
$161$	3.65086	−	0.714212i	0.287728	−	0.0562878i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	5.51798	−	10.1054i	0.432202	−	0.791518i	−0.567286	−	0.823521i	$-0.692007\pi$
$163$	5.51798	−	10.1054i	0.432202	−	0.791518i	0.999488	+	0.0320025i	$0.0101885\pi$
$164$	−0.114649	+	0.0993436i	−0.00895255	+	0.00775743i
$165$	0.418575	−	13.1742i	0.0325860	−	1.02561i
$166$	−3.46821	+	0.498653i	−0.269185	+	0.0387030i
$167$	−0.335639	−	1.54291i	−0.0259726	−	0.119394i	0.962335	−	0.271865i	$-0.0876405\pi$
$167$	−0.335639	−	1.54291i	−0.0259726	−	0.119394i	−0.988308	+	0.152471i	$0.951277\pi$
$168$	−0.726780	+	0.271075i	−0.0560723	+	0.0209139i
$169$	1.64434	+	1.42483i	0.126488	+	0.109602i
$170$	7.95382	−	0.315440i	0.610030	−	0.0241932i
$171$	−3.35739	+	1.53327i	−0.256746	+	0.117252i
$172$	−10.2914	+	5.61955i	−0.784714	+	0.428487i
$173$	−12.0382	+	6.57333i	−0.915244	+	0.499761i	−0.866571	−	0.499054i	$-0.833681\pi$
$173$	−12.0382	+	6.57333i	−0.915244	+	0.499761i	−0.0486731	+	0.998815i	$0.515499\pi$
$174$	−7.43894	+	3.39725i	−0.563945	+	0.257545i
$175$	3.27916	+	2.07108i	0.247881	+	0.156559i
$176$	−4.45489	−	3.86018i	−0.335800	−	0.290972i
$177$	12.0434	−	4.49195i	0.905236	−	0.337635i
$178$	−0.320867	−	1.47500i	−0.0240500	−	0.110556i
$179$	−2.65863	+	0.382254i	−0.198716	+	0.0285710i	−0.240954	−	0.970537i	$-0.577460\pi$
$179$	−2.65863	+	0.382254i	−0.198716	+	0.0285710i	0.0422382	+	0.999108i	$0.486551\pi$
$180$	1.53013	+	1.63055i	0.114049	+	0.121534i
$181$	15.1217	−	13.1030i	1.12399	−	0.973941i	0.124156	−	0.992263i	$-0.460378\pi$
$181$	15.1217	−	13.1030i	1.12399	−	0.973941i	0.999832	+	0.0183213i	$0.00583218\pi$
$182$	1.44818	−	2.65215i	0.107346	−	0.196590i
$183$	−9.24624	−	9.24624i	−0.683502	−	0.683502i
$184$	−4.77537	−	0.442555i	−0.352045	−	0.0326256i
$185$	12.1070	+	8.33559i	0.890127	+	0.612845i
$186$	−0.667803	+	0.196085i	−0.0489657	+	0.0143776i
$187$	1.49699	−	20.9306i	0.109471	−	1.53060i
$188$	0.263129	−	1.20958i	0.0191906	−	0.0882179i
$189$	−0.110392	−	0.767791i	−0.00802982	−	0.0558486i
$190$	7.61245	−	3.18836i	0.552265	−	0.231308i
$191$	−4.93363	−	2.25311i	−0.356985	−	0.163030i	0.228846	−	0.973463i	$-0.426505\pi$
$191$	−4.93363	−	2.25311i	−0.356985	−	0.163030i	−0.585831	+	0.810433i	$0.699232\pi$
$192$	0.997452	−	0.0713392i	0.0719849	−	0.00514846i
$193$	−9.20060	−	12.2906i	−0.662273	−	0.884694i	0.336093	−	0.941829i	$-0.390894\pi$
$193$	−9.20060	−	12.2906i	−0.662273	−	0.884694i	−0.998366	+	0.0571350i	$0.981803\pi$
$194$	2.04613	+	4.48039i	0.146903	+	0.321674i
$195$	−8.66454	−	0.897031i	−0.620480	−	0.0642377i
$196$	6.13913	+	1.80261i	0.438510	+	0.128758i
$197$	−4.91167	+	13.1687i	−0.349942	+	0.938232i	0.636081	+	0.771623i	$0.280555\pi$
$197$	−4.91167	+	13.1687i	−0.349942	+	0.938232i	−0.986023	+	0.166609i	$0.946718\pi$
$198$	4.71892	−	3.53254i	0.335359	−	0.251047i
$199$	−0.953648	+	1.10057i	−0.0676023	+	0.0780172i	−0.788543	−	0.614979i	$-0.789164\pi$
$199$	−0.953648	+	1.10057i	−0.0676023	+	0.0780172i	0.720941	+	0.692996i	$0.243710\pi$
$200$	−3.30397	−	3.75284i	−0.233626	−	0.265366i
$201$	−7.59460	+	11.8174i	−0.535682	+	0.833538i
$202$	−6.14891	+	8.21399i	−0.432636	+	0.577934i
$203$	−6.19857	−	1.34842i	−0.435054	−	0.0946403i
$204$	2.33121	+	2.69036i	0.163217	+	0.188363i
$205$	0.153032	+	0.302735i	0.0106882	+	0.0211439i
$206$		−	16.1970i		−	1.12850i
$207$	1.44752	−	4.57216i	0.100610	−	0.317787i
$208$	−2.75461	+	2.75461i	−0.190998	+	0.190998i
$209$	−6.12960	−	20.8755i	−0.423993	−	1.44399i
$210$	0.192199	+	1.72381i	0.0132630	+	0.118954i
$211$	6.60190	−	4.24278i	0.454493	−	0.292085i	−0.293295	−	0.956022i	$-0.594752\pi$
$211$	6.60190	−	4.24278i	0.454493	−	0.292085i	0.747789	+	0.663937i	$0.231116\pi$
$212$	7.27170	+	5.44353i	0.499423	+	0.373863i
$213$	−7.53699	+	1.63957i	−0.516426	+	0.112342i
$214$	−6.26440	+	13.7171i	−0.428226	+	0.937683i
$215$	6.58427	+	25.3794i	0.449043	+	1.73086i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	−0.505835	−	0.188667i	−0.0343383	−	0.0128075i
$218$	5.83865	+	10.6927i	0.395443	+	0.724200i
$219$	0.142090	−	0.483915i	0.00960156	−	0.0326999i
$220$	−10.7973	+	7.55992i	−0.727957	+	0.509690i
$221$	−13.7266	−	1.97359i	−0.923354	−	0.132758i
$222$	0.468957	+	6.55687i	0.0314743	+	0.440069i
$223$	0.0782052	+	0.209676i	0.00523701	+	0.0140410i	0.939542	−	0.342434i	$-0.111251\pi$
$223$	0.0782052	+	0.209676i	0.00523701	+	0.0140410i	−0.934305	+	0.356475i	$0.883979\pi$
$224$	0.652549	+	0.419368i	0.0436003	+	0.0280202i
$225$	4.36938	−	2.43074i	0.291292	−	0.162049i
$226$	6.30994	+	9.81847i	0.419731	+	0.653115i
$227$	−0.593085	−	0.0424182i	−0.0393644	−	0.00281540i	0.0516431	−	0.998666i	$-0.483554\pi$
$227$	−0.593085	−	0.0424182i	−0.0393644	−	0.00281540i	−0.0910075	+	0.995850i	$0.529009\pi$
$228$	3.23946	+	1.76888i	0.214538	+	0.117147i
$229$	0.358862			0.0237143			0.0118571	−	0.999930i	$-0.496226\pi$
$229$	0.358862			0.0237143			0.0118571	+	0.999930i	$0.496226\pi$
$230$	−3.55978	+	10.1157i	−0.234725	+	0.667011i
$231$	4.57241			0.300842
$232$	7.17763	+	3.91928i	0.471234	+	0.257313i
$233$	16.4286	+	1.17500i	1.07628	+	0.0769767i	0.598204	−	0.801344i	$-0.295881\pi$
$233$	16.4286	+	1.17500i	1.07628	+	0.0769767i	0.478072	+	0.878321i	$0.341336\pi$
$234$	−2.10613	−	3.27720i	−0.137682	−	0.214237i
$235$	−2.48005	−	1.22923i	−0.161780	−	0.0801862i
$236$	−10.8133	−	6.94930i	−0.703887	−	0.452361i
$237$	−5.45384	−	14.6223i	−0.354265	−	0.949821i
$238$	0.196991	+	2.75429i	0.0127690	+	0.178534i
$239$	18.4280	+	2.64954i	1.19201	+	0.171385i	0.709627	−	0.704577i	$-0.248863\pi$
$239$	18.4280	+	2.64954i	1.19201	+	0.171385i	0.482380	+	0.875962i	$0.339773\pi$
$240$	0.388352	−	2.20209i	0.0250680	−	0.142144i
$241$	−0.249155	+	0.848545i	−0.0160495	+	0.0546596i	−0.967128	−	0.254288i	$-0.918159\pi$
$241$	−0.249155	+	0.848545i	−0.0160495	+	0.0546596i	0.951079	+	0.308948i	$0.0999769\pi$
$242$	11.3807	+	20.8423i	0.731581	+	1.33979i
$243$	−0.936950	−	0.349464i	−0.0601054	−	0.0224181i
$244$	−1.86093	+	12.9431i	−0.119134	+	0.828595i
$245$	7.25195	−	12.3329i	0.463310	−	0.787922i
$246$	−0.0630192	+	0.137993i	−0.00401796	+	0.00879810i
$247$	−14.0498	+	3.05636i	−0.893971	+	0.194471i
$248$	0.557173	+	0.417094i	0.0353805	+	0.0264855i
$249$	−2.94764	+	1.89433i	−0.186799	+	0.120049i
$250$	−9.93792	+	5.12228i	−0.628529	+	0.323962i
$251$	−0.916603	−	3.12166i	−0.0578555	−	0.197038i	0.925494	−	0.378762i	$-0.123650\pi$
$251$	−0.916603	−	3.12166i	−0.0578555	−	0.197038i	−0.983349	+	0.181725i	$0.941832\pi$
$252$	−0.548493	+	0.548493i	−0.0345518	+	0.0345518i
$253$	25.4627	+	12.2814i	1.60083	+	0.772122i
$254$			5.13045i			0.321913i
$255$	7.10401	−	3.59107i	0.444870	−	0.224881i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−10.0141	−	2.17844i	−0.624663	−	0.135887i	−0.110917	−	0.993830i	$-0.535379\pi$
$257$	−10.0141	−	2.17844i	−0.624663	−	0.135887i	−0.513746	+	0.857943i	$0.671742\pi$
$258$	−7.02697	+	9.38694i	−0.437480	+	0.584405i
$259$	−2.75677	+	4.28961i	−0.171297	+	0.266544i
$260$	4.47435	+	7.47389i	0.277488	+	0.463511i
$261$	−5.35543	+	6.18049i	−0.331493	+	0.382563i
$262$	8.09206	−	6.05764i	0.499929	−	0.374242i
$263$	3.79624	−	10.1781i	0.234086	−	0.627610i	−0.765794	−	0.643086i	$-0.777654\pi$
$263$	3.79624	−	10.1781i	0.234086	−	0.627610i	0.999880	+	0.0154761i	$0.00492641\pi$
$264$	−5.65588	−	1.66072i	−0.348096	−	0.102210i
$265$	15.7649	−	12.8069i	0.968430	−	0.786721i
$266$	1.18934	+	2.60429i	0.0729229	+	0.159679i
$267$	−0.904610	−	1.20842i	−0.0553612	−	0.0739539i
$268$	14.0116	−	1.00213i	0.855896	−	0.0612149i
$269$	0.155333	+	0.0709382i	0.00947083	+	0.00432518i	0.420145	−	0.907457i	$-0.361979\pi$
$269$	0.155333	+	0.0709382i	0.00947083	+	0.00432518i	−0.410674	+	0.911782i	$0.634707\pi$
$270$	2.06921	+	0.847564i	0.125928	+	0.0515811i
$271$	−3.24048	−	22.5380i	−0.196845	−	1.36909i	−0.813368	−	0.581750i	$-0.802368\pi$
$271$	−3.24048	−	22.5380i	−0.196845	−	1.36909i	0.616523	−	0.787337i	$-0.288541\pi$
$272$	0.756701	−	3.47850i	0.0458817	−	0.210915i
$273$	0.215571	−	3.01407i	0.0130469	−	0.182420i
$274$	13.9338	−	4.09132i	0.841770	−	0.247166i
$275$	10.5171	+	27.5330i	0.634202	+	1.66030i
$276$	−4.52767	+	1.58120i	−0.272534	+	0.0951769i
$277$	−0.179460	−	0.179460i	−0.0107827	−	0.0107827i	0.701695	−	0.712478i	$-0.252427\pi$
$277$	−0.179460	−	0.179460i	−0.0107827	−	0.0107827i	−0.712478	+	0.701695i	$0.752427\pi$
$278$	4.04966	−	7.41640i	0.242882	−	0.444806i
$279$	−0.525998	+	0.455780i	−0.0314907	+	0.0272868i
$280$	1.26480	−	1.18690i	0.0755861	−	0.0709310i
$281$	−0.142098	+	0.0204307i	−0.00847688	+	0.00121879i	−0.146552	−	0.989203i	$-0.546818\pi$
$281$	−0.142098	+	0.0204307i	−0.00847688	+	0.00121879i	0.138075	+	0.990422i	$0.455908\pi$
$282$	−0.263129	−	1.20958i	−0.0156691	−	0.0720296i
$283$	−30.2609	+	11.2867i	−1.79883	+	0.670928i	−0.801488	+	0.598010i	$0.795958\pi$
$283$	−30.2609	+	11.2867i	−1.79883	+	0.670928i	−0.997338	+	0.0729171i	$0.976769\pi$
$284$	5.82929	+	5.05111i	0.345905	+	0.299728i
$285$	5.60003	−	6.06256i	0.331717	−	0.359115i
$286$	20.8881	−	9.53930i	1.23514	−	0.564070i
$287$	−0.103279	+	0.0563947i	−0.00609638	+	0.00332888i
$288$	0.877679	−	0.479249i	0.0517177	−	0.0282400i
$289$	−3.93639	+	1.79769i	−0.231553	+	0.105747i
$290$	12.4079	−	13.4327i	0.728619	−	0.788798i
$291$	3.72245	+	3.22552i	0.218214	+	0.189083i
$292$	−0.472545	+	0.176250i	−0.0276536	+	0.0103143i
$293$	1.08344	+	4.98049i	0.0632952	+	0.290963i	0.997904	−	0.0647144i	$-0.0206136\pi$
$293$	1.08344	+	4.98049i	0.0632952	+	0.290963i	−0.934609	+	0.355678i	$0.884250\pi$
$294$	6.33318	−	0.910574i	0.369359	−	0.0531058i
$295$	−20.9588	+	19.6680i	−1.22027	+	1.14512i
$296$	4.96801	−	4.30481i	0.288760	−	0.250212i
$297$	2.82501	−	5.17362i	0.163924	−	0.300204i
$298$	−13.8903	−	13.8903i	−0.804644	−	0.804644i
$299$	9.29618	−	16.2057i	0.537612	−	0.937198i
$300$	−4.56438	−	2.04119i	−0.263525	−	0.117848i
$301$	−8.72707	+	2.56250i	−0.503020	+	0.147700i
$302$	−0.636770	+	8.90321i	−0.0366420	+	0.512322i
$303$	−2.18103	+	10.0261i	−0.125297	+	0.575982i
$304$	−0.525275	−	3.65337i	−0.0301266	−	0.209535i
$305$	27.0573	+	11.0829i	1.54930	+	0.634604i
$306$	3.23815	+	1.47882i	0.185113	+	0.0845383i
$307$	12.4573	−	0.890962i	0.710974	−	0.0508499i	0.288833	−	0.957380i	$-0.406733\pi$
$307$	12.4573	−	0.890962i	0.710974	−	0.0508499i	0.422142	+	0.906530i	$0.361278\pi$
$308$	−2.74014	−	3.66040i	−0.156134	−	0.208571i
$309$	−6.72847	−	14.7333i	−0.382769	−	0.838148i
$310$	1.20794	−	0.981290i	0.0686063	−	0.0557335i
$311$	5.80163	+	1.70351i	0.328980	+	0.0965974i	0.442052	−	0.896989i	$-0.354251\pi$
$311$	5.80163	+	1.70351i	0.328980	+	0.0965974i	−0.113071	+	0.993587i	$0.536069\pi$
$312$	−1.36138	+	3.64999i	−0.0770727	+	0.206640i
$313$	−4.96472	+	3.71654i	−0.280622	+	0.210071i	−0.730312	−	0.683113i	$-0.760625\pi$
$313$	−4.96472	+	3.71654i	−0.280622	+	0.210071i	0.449690	+	0.893185i	$0.351535\pi$
$314$	−11.7815	+	13.5966i	−0.664869	+	0.767299i
$315$	0.890925	+	1.48819i	0.0501980	+	0.0838499i
$316$	−8.43740	+	13.1288i	−0.474641	+	0.738555i
$317$	8.02425	−	10.7191i	0.450687	−	0.602047i	−0.516446	−	0.856320i	$-0.672745\pi$
$317$	8.02425	−	10.7191i	0.450687	−	0.602047i	0.967133	+	0.254273i	$0.0818361\pi$
$318$	8.87590	+	1.93083i	0.497736	+	0.108276i
$319$	−31.5684	−	36.4319i	−1.76749	−	2.03980i
$320$	−1.99559	+	1.00877i	−0.111557	+	0.0563919i
$321$			15.0799i			0.841676i
$322$	−3.54657	−	1.12282i	−0.197642	−	0.0625724i
$323$	9.29080	−	9.29080i	0.516954	−	0.516954i
$324$	0.281733	+	0.959493i	0.0156518	+	0.0533052i
$325$	18.6452	−	5.63463i	1.03425	−	0.312553i
$326$	−9.68603	+	6.22483i	−0.536460	+	0.344762i
$327$	9.75292	+	7.30095i	0.539338	+	0.403743i
$328$	0.148235	−	0.0322465i	0.00818491	−	0.00178052i
$329$	0.398882	−	0.873429i	0.0219911	−	0.0481537i
$330$	−6.68110	+	11.3621i	−0.367783	+	0.625465i
$331$	1.61451	−	11.2292i	0.0887416	−	0.617212i	−0.896113	−	0.443827i	$-0.853621\pi$
$331$	1.61451	−	11.2292i	0.0887416	−	0.617212i	0.984854	−	0.173385i	$-0.0554704\pi$
$332$	3.28295	+	1.22448i	0.180175	+	0.0672019i
$333$	3.15040	+	5.76953i	0.172641	+	0.316168i
$334$	−0.444854	+	1.51503i	−0.0243413	+	0.0828990i
$335$	5.45533	−	30.9336i	0.298057	−	1.69008i
$336$	0.767791	+	0.110392i	0.0418865	+	0.00602236i
$337$	−1.68486	−	23.5574i	−0.0917803	−	1.28326i	−0.809581	−	0.587008i	$-0.800306\pi$
$337$	−1.68486	−	23.5574i	−0.0917803	−	1.28326i	0.717801	−	0.696248i	$-0.245149\pi$
$338$	−0.760355	−	2.03859i	−0.0413579	−	0.110885i
$339$	9.81847	+	6.30994i	0.533266	+	0.342709i
$340$	−7.13207	−	3.53500i	−0.386791	−	0.191712i
$341$	−2.21806	−	3.45137i	−0.120115	−	0.186902i
$342$	3.68153	+	0.263308i	0.199074	+	0.0142381i
$343$	9.12162	+	4.98078i	0.492521	+	0.268937i
$344$	11.7257			0.632209
$345$	0.964132	+	10.6804i	0.0519071	+	0.575012i
$346$	13.7159			0.737371
$347$	11.4087	+	6.22962i	0.612451	+	0.334424i	0.755358	−	0.655313i	$-0.227463\pi$
$347$	11.4087	+	6.22962i	0.612451	+	0.334424i	−0.142907	+	0.989736i	$0.545645\pi$
$348$	8.15713	+	0.583409i	0.437268	+	0.0312740i
$349$	7.40403	+	11.5209i	0.396329	+	0.616699i	0.980870	−	0.194665i	$-0.0623619\pi$
$349$	7.40403	+	11.5209i	0.396329	+	0.616699i	−0.584541	+	0.811364i	$0.698726\pi$
$350$	−1.88549	−	3.38927i	−0.100784	−	0.181164i
$351$	−3.27720	−	2.10613i	−0.174924	−	0.112417i
$352$	2.05997	+	5.52300i	0.109797	+	0.294377i
$353$	1.53683	+	21.4877i	0.0817971	+	1.14367i	0.858158	+	0.513385i	$0.171609\pi$
$353$	1.53683	+	21.4877i	0.0817971	+	1.14367i	−0.776361	+	0.630288i	$0.782937\pi$
$354$	−12.7230	−	1.82929i	−0.676219	−	0.0972256i
$355$	14.1285	−	9.89229i	0.749863	−	0.525028i
$356$	−0.425275	+	1.44835i	−0.0225395	+	0.0767626i
$357$	1.32336	+	2.42356i	0.0700399	+	0.128268i
$358$	2.51662	+	0.938652i	0.133008	+	0.0496093i
$359$	3.24093	−	22.5412i	0.171050	−	1.18968i	−0.705622	−	0.708588i	$-0.749333\pi$
$359$	3.24093	−	22.5412i	0.171050	−	1.18968i	0.876672	−	0.481088i	$-0.159758\pi$
$360$	−0.561523	−	2.16442i	−0.0295948	−	0.114075i
$361$	−2.23369	+	4.89109i	−0.117562	+	0.257426i
$362$	−19.5516	+	4.25320i	−1.02761	+	0.223543i
$363$	19.0105	+	14.2311i	0.997790	+	0.746937i
$364$	−2.54208	+	1.63369i	−0.133241	+	0.0856288i
$365$	0.124966	+	1.12080i	0.00654101	+	0.0586655i
$366$	3.68398	+	12.5465i	0.192565	+	0.655815i
$367$	−17.0929	+	17.0929i	−0.892242	+	0.892242i	−0.994734	−	0.102492i	$-0.967318\pi$
$367$	−17.0929	+	17.0929i	−0.892242	+	0.892242i	0.102492	+	0.994734i	$0.467318\pi$
$368$	3.97915	+	2.67701i	0.207427	+	0.139549i
$369$			0.151702i			0.00789728i
$370$	−6.63127	−	13.1183i	−0.344743	−	0.681986i
$371$	4.61411	+	5.32497i	0.239553	+	0.276458i
$372$	0.680090	+	0.147944i	0.0352610	+	0.00767056i
$373$	3.32475	−	4.44134i	0.172149	−	0.229964i	−0.706166	−	0.708046i	$-0.749577\pi$
$373$	3.32475	−	4.44134i	0.172149	−	0.229964i	0.878315	+	0.478082i	$0.158668\pi$
$374$	−11.3449	+	17.6530i	−0.586629	+	0.912813i
$375$	−6.91198	+	8.78775i	−0.356933	+	0.453798i
$376$	−0.810634	+	0.935521i	−0.0418052	+	0.0482458i
$377$	−25.5038	+	19.0919i	−1.31351	+	0.983282i
$378$	−0.271075	+	0.726780i	−0.0139426	+	0.0373815i
$379$	12.7300	+	3.73787i	0.653897	+	0.192001i	0.591820	−	0.806070i	$-0.298410\pi$
$379$	12.7300	+	3.73787i	0.653897	+	0.192001i	0.0620764	+	0.998071i	$0.480228\pi$
$380$	−8.20930	−	0.849901i	−0.421128	−	0.0435990i
$381$	2.13126	+	4.66682i	0.109188	+	0.239088i
$382$	3.25034	+	4.34195i	0.166302	+	0.222154i
$383$	−6.43509	+	0.460246i	−0.328817	+	0.0235175i	−0.234772	−	0.972050i	$-0.575434\pi$
$383$	−6.43509	+	0.460246i	−0.328817	+	0.0235175i	−0.0940453	+	0.995568i	$0.529980\pi$
$384$	−0.909632	−	0.415415i	−0.0464195	−	0.0211991i
$385$	−9.43046	+	3.94981i	−0.480621	+	0.201301i
$386$	2.18493	+	15.1965i	0.111210	+	0.773484i
$387$	−2.49248	+	11.4578i	−0.126700	+	0.582431i
$388$	0.351381	−	4.91295i	0.0178387	−	0.249417i
$389$	−21.1877	+	6.22126i	−1.07426	+	0.315430i	−0.770579	−	0.637344i	$-0.780033\pi$
$389$	−21.1877	+	6.22126i	−1.07426	+	0.315430i	−0.303678	+	0.952775i	$0.598215\pi$
$390$	7.17478	+	4.93978i	0.363309	+	0.250135i
$391$	0.859901	+	17.0508i	0.0434871	+	0.862295i
$392$	−4.52429	−	4.52429i	−0.228511	−	0.228511i
$393$	4.84436	−	8.87179i	0.244366	−	0.447522i
$394$	10.6220	−	9.20398i	0.535127	−	0.463690i
$395$	23.8797	+	25.4469i	1.20152	+	1.28037i
$396$	−5.83466	+	0.838898i	−0.293203	+	0.0421562i
$397$	3.48642	+	16.0268i	0.174979	+	0.804363i	0.978032	+	0.208456i	$0.0668438\pi$
$397$	3.48642	+	16.0268i	0.174979	+	0.804363i	−0.803053	+	0.595907i	$0.796793\pi$
$398$	1.36444	−	0.508911i	0.0683934	−	0.0255094i
$399$	2.16372	+	1.87487i	0.108321	+	0.0938610i
$400$	1.10128	+	4.87721i	0.0550638	+	0.243861i
$401$	22.6478	−	10.3429i	1.13098	−	0.516501i	0.240103	−	0.970747i	$-0.422819\pi$
$401$	22.6478	−	10.3429i	1.13098	−	0.516501i	0.890876	+	0.454247i	$0.150092\pi$
$402$	12.3291	−	6.73221i	0.614920	−	0.335772i
$403$	−2.37967	+	1.29940i	−0.118540	+	0.0647277i
$404$	9.33332	−	4.26238i	0.464350	−	0.212061i
$405$	2.23431	−	0.0886105i	0.111024	−	0.00440309i
$406$	4.79413	+	4.15414i	0.237929	+	0.206166i
$407$	−36.3061	+	13.5415i	−1.79963	+	0.671226i
$408$	−0.756701	−	3.47850i	−0.0374623	−	0.172211i
$409$	5.08236	−	0.730732i	0.251306	−	0.0361324i	−0.0155103	−	0.999880i	$-0.504937\pi$
$409$	5.08236	−	0.730732i	0.251306	−	0.0361324i	0.266817	+	0.963747i	$0.414028\pi$
$410$	0.0107722	−	0.339045i	0.000532002	−	0.0167442i
$411$	10.9750	−	9.50989i	0.541357	−	0.469088i
$412$	−7.76239	+	14.2158i	−0.382425	+	0.700360i
$413$	−7.05023	−	7.05023i	−0.346919	−	0.346919i
$414$	−3.46166	+	3.31917i	−0.170131	+	0.163128i
$415$	4.44304	−	6.45329i	0.218100	−	0.316780i
$416$	3.73781	−	1.09752i	0.183261	−	0.0538103i
$417$	0.602817	−	8.42848i	0.0295201	−	0.412745i
$418$	−4.62474	+	21.2596i	−0.226204	+	1.03984i
$419$	3.22085	+	22.4015i	0.157349	+	1.09439i	0.903493	+	0.428602i	$0.140994\pi$
$419$	3.22085	+	22.4015i	0.157349	+	1.09439i	−0.746144	+	0.665784i	$0.768097\pi$
$420$	0.657444	−	1.60506i	0.0320800	−	0.0783189i
$421$	−0.0852494	−	0.0389321i	−0.00415480	−	0.00189743i	0.413337	−	0.910578i	$-0.364363\pi$
$421$	−0.0852494	−	0.0389321i	−0.00415480	−	0.00189743i	−0.417491	+	0.908681i	$0.637091\pi$
$422$	−7.82769	+	0.559848i	−0.381046	+	0.0272530i
$423$	−0.741829	−	0.990967i	−0.0360690	−	0.0481825i
$424$	−3.77342	−	8.26263i	−0.183253	−	0.401269i
$425$	−11.5497	+	13.5432i	−0.560244	+	0.656940i
$426$	7.40082	+	2.17308i	0.358571	+	0.105286i
$427$	−3.54462	+	9.50349i	−0.171536	+	0.459906i
$428$	12.0720	−	9.03702i	0.583525	−	0.436821i
$429$	15.0378	−	17.3545i	0.726030	−	0.837883i
$430$	6.38416	−	25.4304i	0.307872	−	1.22636i
$431$	−0.836111	+	1.30101i	−0.0402740	+	0.0626676i	−0.860807	−	0.508932i	$-0.830041\pi$
$431$	−0.836111	+	1.30101i	−0.0402740	+	0.0626676i	0.820533	+	0.571599i	$0.193677\pi$
$432$	0.599278	−	0.800541i	0.0288328	−	0.0385161i
$433$	−3.53880	−	0.769818i	−0.170064	−	0.0369951i	0.126727	−	0.991938i	$-0.459553\pi$
$433$	−3.53880	−	0.769818i	−0.170064	−	0.0369951i	−0.296791	+	0.954943i	$0.595916\pi$
$434$	0.353543	+	0.408010i	0.0169706	+	0.0195851i
$435$	5.70649	−	17.3733i	0.273605	−	0.832986i
$436$		−	12.1829i		−	0.583456i
$437$	7.01340	+	16.2524i	0.335496	+	0.777459i
$438$	−0.356625	+	0.356625i	−0.0170402	+	0.0170402i
$439$	−0.567656	−	1.93326i	−0.0270928	−	0.0922695i	0.944837	−	0.327541i	$-0.106220\pi$
$439$	−0.567656	−	1.93326i	−0.0270928	−	0.0922695i	−0.971930	+	0.235272i	$0.924402\pi$
$440$	13.0997	−	1.46057i	0.624503	−	0.0696300i
$441$	5.38260	−	3.45919i	0.256314	−	0.164723i
$442$	11.1017	+	8.31066i	0.528056	+	0.395298i
$443$	−5.41278	+	1.17748i	−0.257169	+	0.0559437i	−0.339301	−	0.940678i	$-0.610191\pi$
$443$	−5.41278	+	1.17748i	−0.257169	+	0.0559437i	0.0821323	+	0.996621i	$0.473827\pi$
$444$	2.73078	−	5.97958i	0.129597	−	0.283778i
$445$	2.90960	+	1.71089i	0.137928	+	0.0811040i
$446$	0.0318481	−	0.221508i	0.00150805	−	0.0104887i
$447$	−18.4053	−	6.86482i	−0.870541	−	0.324695i
$448$	−0.371747	−	0.680804i	−0.0175634	−	0.0321650i
$449$	−3.06691	+	10.4450i	−0.144737	+	0.492928i	−0.999667	−	0.0258155i	$-0.991782\pi$
$449$	−3.06691	+	10.4450i	−0.144737	+	0.492928i	0.854930	+	0.518743i	$0.173600\pi$
$450$	−4.99984	+	0.0393825i	−0.235695	+	0.00185651i
$451$	−0.885129	−	0.127262i	−0.0416791	−	0.00599255i
$452$	−0.832616	−	11.6415i	−0.0391630	−	0.547570i
$453$	3.11930	+	8.36317i	0.146558	+	0.392936i
$454$	0.500209	+	0.321465i	0.0234760	+	0.0150871i
$455$	2.15906	+	6.40266i	0.101218	+	0.300161i
$456$	−1.99547	−	3.10501i	−0.0934465	−	0.145406i
$457$	15.0313	+	1.07506i	0.703132	+	0.0502890i	0.418327	−	0.908296i	$-0.362617\pi$
$457$	15.0313	+	1.07506i	0.703132	+	0.0502890i	0.284805	+	0.958585i	$0.408071\pi$
$458$	−0.314966	−	0.171984i	−0.0147174	−	0.00803630i
$459$	3.55985			0.166160
$460$	7.97230	−	7.17234i	0.371710	−	0.334412i
$461$	−20.1085			−0.936547			−0.468274	−	0.883584i	$-0.655124\pi$
$461$	−20.1085			−0.936547			−0.468274	+	0.883584i	$0.655124\pi$
$462$	−4.01311	−	2.19132i	−0.186707	−	0.101950i
$463$	−15.4499	−	1.10500i	−0.718017	−	0.0513536i	−0.292451	−	0.956281i	$-0.594471\pi$
$463$	−15.4499	−	1.10500i	−0.718017	−	0.0513536i	−0.425567	+	0.904927i	$0.639925\pi$
$464$	−4.42134	−	6.87974i	−0.205256	−	0.319384i
$465$	0.691137	−	1.39441i	0.0320507	−	0.0646642i
$466$	−13.8559	−	8.90468i	−0.641864	−	0.412501i
$467$	−4.71479	−	12.6409i	−0.218175	−	0.584949i	0.781044	−	0.624476i	$-0.214688\pi$
$467$	−4.71479	−	12.6409i	−0.218175	−	0.584949i	−0.999218	+	0.0395273i	$0.987415\pi$
$468$	0.277910	+	3.88568i	0.0128464	+	0.179616i
$469$	10.7855	+	1.55072i	0.498027	+	0.0716055i
$470$	1.58758	+	2.26743i	0.0732294	+	0.104589i
$471$	−5.06861	+	17.2621i	−0.233549	+	0.795395i
$472$	6.16018	+	11.2815i	0.283545	+	0.519274i
$473$	−64.7612	−	24.1547i	−2.97773	−	1.11063i
$474$	−2.22101	+	15.4474i	−0.102014	+	0.709524i
$475$	−6.31285	+	17.3414i	−0.289654	+	0.795676i
$476$	1.14710	−	2.51179i	0.0525771	−	0.115128i
$477$	8.87590	−	1.93083i	0.406399	−	0.0884068i
$478$	−14.9041	−	11.1570i	−0.681696	−	0.510311i
$479$	23.0458	−	14.8106i	1.05299	−	0.676714i	0.104822	−	0.994491i	$-0.466573\pi$
$479$	23.0458	−	14.8106i	1.05299	−	0.676714i	0.948166	+	0.317777i	$0.102936\pi$
$480$	−1.39620	+	1.74661i	−0.0637273	+	0.0797214i
$481$	7.21468	+	24.5710i	0.328961	+	1.12034i
$482$	0.625343	−	0.625343i	0.0284836	−	0.0284836i
$483$	−3.69251	+	0.451943i	−0.168015	+	0.0205641i
$484$		−	23.7470i		−	1.07941i
$485$	−10.4638	−	3.43696i	−0.475135	−	0.156064i
$486$	0.654861	+	0.755750i	0.0297051	+	0.0342815i
$487$	1.49402	+	0.325004i	0.0677005	+	0.0147274i	0.246288	−	0.969197i	$-0.420789\pi$
$487$	1.49402	+	0.325004i	0.0677005	+	0.0147274i	−0.178587	+	0.983924i	$0.557153\pi$
$488$	7.83625	−	10.4680i	0.354731	−	0.473864i
$489$	−6.22483	+	9.68603i	−0.281497	+	0.438018i
$490$	−12.2754	+	7.34886i	−0.554547	+	0.331988i
$491$	11.0808	−	12.7879i	0.500069	−	0.577111i	−0.448459	−	0.893803i	$-0.648027\pi$
$491$	11.0808	−	12.7879i	0.500069	−	0.577111i	0.948528	+	0.316693i	$0.102572\pi$
$492$	0.121444	−	0.0909115i	0.00547510	−	0.00409861i
$493$	10.1737	−	27.2768i	0.458201	−	1.22849i
$494$	13.7960	+	4.05088i	0.620712	+	0.182257i
$495$	−1.35735	+	13.1108i	−0.0610082	+	0.589286i
$496$	−0.289127	−	0.633100i	−0.0129822	−	0.0284270i
$497$	3.58552	+	4.78970i	0.160833	+	0.214847i
$498$	3.49494	−	0.249963i	0.156612	−	0.0112011i
$499$	−11.8295	−	5.40235i	−0.529561	−	0.241843i	0.132646	−	0.991164i	$-0.457653\pi$
$499$	−11.8295	−	5.40235i	−0.529561	−	0.241843i	−0.662207	+	0.749321i	$0.730380\pi$
$500$	11.1772	+	0.267018i	0.499857	+	0.0119414i
$501$	0.224714	+	1.56292i	0.0100395	+	0.0698262i
$502$	−0.691571	+	3.17910i	−0.0308663	+	0.141890i
$503$	2.05131	−	28.6811i	0.0914634	−	1.27883i	−0.719815	−	0.694166i	$-0.755773\pi$
$503$	2.05131	−	28.6811i	0.0914634	−	1.27883i	0.811279	−	0.584660i	$-0.198772\pi$
$504$	0.744266	−	0.218536i	0.0331522	−	0.00973438i
$505$	−4.16254	−	22.5625i	−0.185231	−	1.00402i
$506$	−16.4623	−	22.9821i	−0.731837	−	1.02168i
$507$	−1.53851	−	1.53851i	−0.0683274	−	0.0683274i
$508$	2.45876	−	4.50288i	0.109090	−	0.199783i
$509$	25.7347	−	22.2992i	1.14067	−	0.988396i	0.140671	−	0.990056i	$-0.455074\pi$
$509$	25.7347	−	22.2992i	1.14067	−	0.988396i	0.999999	+	0.00166013i	$0.000528435\pi$
$510$	−7.95605	−	0.252782i	−0.352300	−	0.0111934i
$511$	−0.387231	+	0.0556754i	−0.0171301	+	0.00246294i
$512$	0.212565	+	0.977147i	0.00939415	+	0.0431842i
$513$	3.45822	−	1.28985i	0.152684	−	0.0569483i
$514$	7.74516	+	6.71122i	0.341624	+	0.296019i
$515$	26.6044	+	24.5747i	1.17233	+	1.08289i
$516$	10.6661	−	4.87105i	0.469549	−	0.214436i
$517$	6.40428	−	3.49700i	0.281660	−	0.153798i
$518$	4.47535	−	2.44373i	0.196636	−	0.107371i
$519$	12.4764	−	5.69779i	0.547654	−	0.250105i
$520$	−0.345192	−	8.70401i	−0.0151377	−	0.381696i
$521$	33.1732	+	28.7448i	1.45334	+	1.25933i	0.906573	+	0.422049i	$0.138689\pi$
$521$	33.1732	+	28.7448i	1.45334	+	1.25933i	0.546772	+	0.837282i	$0.315856\pi$
$522$	7.66234	−	2.85791i	0.335372	−	0.125087i
$523$	−4.58828	−	21.0920i	−0.200631	−	0.922287i	−0.961804	−	0.273738i	$-0.911740\pi$
$523$	−4.58828	−	21.0920i	−0.200631	−	0.922287i	0.761173	−	0.648549i	$-0.224624\pi$
$524$	−10.0053	+	1.43855i	−0.437086	+	0.0628434i
$525$	−3.12306	−	2.29973i	−0.136301	−	0.100369i
$526$	−8.20974	+	7.11378i	−0.357962	+	0.310176i
$527$	1.18741	−	2.17457i	0.0517242	−	0.0947259i
$528$	4.16815	+	4.16815i	0.181396	+	0.181396i
$529$	−21.7766	−	7.40120i	−0.946811	−	0.321791i
$530$	−19.9742	+	3.68503i	−0.867624	+	0.160067i
$531$	−12.3331	+	3.62134i	−0.535213	+	0.157153i
$532$	0.204245	−	2.85571i	0.00885513	−	0.123811i
$533$	−0.125620	+	0.577466i	−0.00544120	+	0.0250128i
$534$	0.214824	+	1.49414i	0.00929635	+	0.0646576i
$535$	−13.0265	−	31.1018i	−0.563185	−	1.34465i
$536$	−12.7780	−	5.83551i	−0.551924	−	0.252055i
$537$	2.67913	−	0.191615i	0.115613	−	0.00826881i
$538$	−0.102336	−	0.136704i	−0.00441200	−	0.00589374i
$539$	15.6677	+	34.3076i	0.674857	+	1.47773i
$540$	−1.40991	−	1.73556i	−0.0606728	−	0.0746864i
$541$	−32.8758	−	9.65320i	−1.41344	−	0.415023i	−0.516163	−	0.856491i	$-0.672640\pi$
$541$	−32.8758	−	9.65320i	−1.41344	−	0.415023i	−0.897277	+	0.441467i	$0.854458\pi$
$542$	−7.95722	+	21.3341i	−0.341792	+	0.916379i
$543$	−16.0179	+	11.9909i	−0.687396	+	0.514578i
$544$	−2.33121	+	2.69036i	−0.0999497	+	0.115348i
$545$	−26.4219	−	6.63307i	−1.13179	−	0.284130i
$546$	−1.63369	+	2.54208i	−0.0699156	+	0.108791i
$547$	11.4158	−	15.2497i	0.488104	−	0.652031i	−0.487098	−	0.873348i	$-0.661944\pi$
$547$	11.4158	−	15.2497i	0.488104	−	0.652031i	0.975202	+	0.221316i	$0.0710353\pi$
$548$	−14.1901	−	3.08688i	−0.606173	−	0.131865i
$549$	8.56307	+	9.88231i	0.365463	+	0.421767i
$550$	3.96457	−	29.2054i	0.169050	−	1.24532i
$551$		−	30.1843i		−	1.28590i
$552$	4.73163	+	0.782098i	0.201392	+	0.0332883i
$553$	−8.55995	+	8.55995i	−0.364006	+	0.364006i
$554$	0.0715024	+	0.243515i	0.00303785	+	0.0103460i
$555$	−11.4815	−	9.17806i	−0.487364	−	0.389587i
$556$	−7.10860	+	4.56842i	−0.301472	+	0.193744i
$557$	29.1644	+	21.8322i	1.23573	+	0.925059i	0.998919	−	0.0464950i	$-0.0148052\pi$
$557$	29.1644	+	21.8322i	1.23573	+	0.925059i	0.236816	+	0.971554i	$0.423896\pi$
$558$	0.680090	−	0.147944i	0.0287905	−	0.00626299i
$559$	−18.9757	+	41.5510i	−0.802587	+	1.75742i
$560$	−1.67891	+	0.435566i	−0.0709468	+	0.0184060i
$561$	−2.98635	+	20.7705i	−0.126084	+	0.876932i
$562$	0.134508	+	0.0501689i	0.00567388	+	0.00211625i
$563$	−2.29063	−	4.19497i	−0.0965383	−	0.176797i	0.824947	−	0.565210i	$-0.191205\pi$
$563$	−2.29063	−	4.19497i	−0.0965383	−	0.176797i	−0.921485	+	0.388414i	$0.873023\pi$
$564$	−0.348749	+	1.18773i	−0.0146850	+	0.0500124i
$565$	−25.7011	−	4.53254i	−1.08125	−	0.190685i
$566$	31.9686	+	4.59638i	1.34374	+	0.193200i
$567$	0.0553369	+	0.773710i	0.00232393	+	0.0324928i
$568$	−2.69551	−	7.22694i	−0.113101	−	0.303236i
$569$	13.9007	+	8.93343i	0.582747	+	0.374509i	0.798550	−	0.601928i	$-0.205601\pi$
$569$	13.9007	+	8.93343i	0.582747	+	0.374509i	−0.215803	+	0.976437i	$0.569237\pi$
$570$	−7.82051	+	2.63717i	−0.327565	+	0.110459i
$571$	3.88753	+	6.04912i	0.162688	+	0.253148i	0.913021	−	0.407913i	$-0.133743\pi$
$571$	3.88753	+	6.04912i	0.162688	+	0.253148i	−0.750333	+	0.661060i	$0.770107\pi$
$572$	−22.9048	−	1.63818i	−0.957697	−	0.0684959i
$573$	4.76033	+	2.59934i	0.198866	+	0.108589i
$574$	0.117673			0.00491158
$575$	−11.2146	−	21.1951i	−0.467680	−	0.883898i
$576$	−1.00000			−0.0416667
$577$	12.5969	+	6.87840i	0.524414	+	0.286352i	0.719569	−	0.694421i	$-0.244339\pi$
$577$	12.5969	+	6.87840i	0.524414	+	0.286352i	−0.195155	+	0.980772i	$0.562521\pi$
$578$	4.31643	+	0.308717i	0.179540	+	0.0128409i
$579$	8.30036	+	12.9156i	0.344951	+	0.536754i
$580$	−17.3278	+	5.84315i	−0.719498	+	0.242624i
$581$	2.28645	+	1.46941i	0.0948578	+	0.0609614i
$582$	−1.72129	−	4.61495i	−0.0713496	−	0.191296i
$583$	3.81979	+	53.4076i	0.158199	+	2.21192i
$584$	0.499211	+	0.0717757i	0.0206575	+	0.00297010i
$585$	8.57847	+	1.51287i	0.354676	+	0.0625493i
$586$	1.43598	−	4.89051i	0.0593199	−	0.202025i
$587$	−8.88271	−	16.2675i	−0.366629	−	0.671431i	0.627621	−	0.778519i	$-0.284029\pi$
$587$	−8.88271	−	16.2675i	−0.366629	−	0.671431i	−0.994249	+	0.107089i	$0.965847\pi$
$588$	−5.99489	−	2.23598i	−0.247225	−	0.0922103i
$589$	0.365589	−	2.54273i	0.0150638	−	0.104771i
$590$	27.8210	−	7.21771i	1.14537	−	0.297148i
$591$	5.83861	−	12.7848i	0.240168	−	0.525895i
$592$	−6.42339	+	1.39732i	−0.264000	+	0.0574297i
$593$	−21.0093	−	15.7274i	−0.862749	−	0.645846i	0.0734565	−	0.997298i	$-0.476597\pi$
$593$	−21.0093	−	15.7274i	−0.862749	−	0.645846i	−0.936206	+	0.351452i	$0.885688\pi$
$594$	−4.95890	+	3.18689i	−0.203466	+	0.130760i
$595$	−4.82296	−	3.85536i	−0.197722	−	0.158054i
$596$	5.53431	+	18.8481i	0.226694	+	0.772050i
$597$	1.02973	−	1.02973i	0.0421441	−	0.0421441i
$598$	−15.9256	+	9.76820i	−0.651247	+	0.399451i
$599$		−	31.8778i		−	1.30249i	−0.758867	−	0.651245i	$-0.774247\pi$
$599$		−	31.8778i		−	1.30249i	0.758867	−	0.651245i	$-0.225753\pi$
$600$	3.02782	+	3.97898i	0.123610	+	0.162441i
$601$	−8.96436	−	10.3454i	−0.365664	−	0.421998i	0.542866	−	0.839820i	$-0.317339\pi$
$601$	−8.96436	−	10.3454i	−0.365664	−	0.421998i	−0.908529	+	0.417821i	$0.862794\pi$
$602$	8.88764	+	1.93339i	0.362233	+	0.0787990i
$603$	8.41830	−	11.2455i	0.342820	−	0.457953i
$604$	4.82573	−	7.50899i	0.196356	−	0.305536i
$605$	−51.5018	−	12.9292i	−2.09385	−	0.525648i
$606$	6.71923	−	7.75440i	0.272950	−	0.315001i
$607$	13.2885	−	9.94765i	0.539364	−	0.403763i	−0.294568	−	0.955631i	$-0.595176\pi$
$607$	13.2885	−	9.94765i	0.539364	−	0.403763i	0.833932	+	0.551868i	$0.186085\pi$
$608$	−1.28985	+	3.45822i	−0.0523103	+	0.140249i
$609$	6.08658	+	1.78718i	0.246641	+	0.0724203i
$610$	−18.4362	−	22.6944i	−0.746460	−	0.918870i
$611$	−2.00324	−	4.38649i	−0.0810425	−	0.177458i
$612$	−2.13334	−	2.84981i	−0.0862351	−	0.115197i
$613$	42.3009	−	3.02542i	1.70852	−	0.122195i	0.817429	−	0.576029i	$-0.195398\pi$
$613$	42.3009	−	3.02542i	1.70852	−	0.122195i	0.891087	+	0.453833i	$0.149944\pi$
$614$	−11.3605	−	5.18816i	−0.458472	−	0.209377i
$615$	−0.131045	−	0.312881i	−0.00528426	−	0.0126166i
$616$	0.650722	+	4.52587i	0.0262183	+	0.182352i
$617$	1.09836	−	5.04907i	0.0442182	−	0.203268i	−0.949738	−	0.313046i	$-0.898650\pi$
$617$	1.09836	−	5.04907i	0.0442182	−	0.203268i	0.993956	+	0.109778i	$0.0350141\pi$
$618$	−1.15548	+	16.1557i	−0.0464802	+	0.649878i
$619$	−28.5794	+	8.39167i	−1.14870	+	0.337290i	−0.800033	−	0.599956i	$-0.795185\pi$
$619$	−28.5794	+	8.39167i	−1.14870	+	0.337290i	−0.348670	+	0.937245i	$0.613367\pi$
$620$	−1.53046	+	0.282354i	−0.0614650	+	0.0113396i
$621$	−1.77001	+	4.45725i	−0.0710279	+	0.178863i
$622$	−4.27557	−	4.27557i	−0.171435	−	0.171435i
$623$	−0.561152	+	1.02767i	−0.0224821	+	0.0411729i
$624$	2.94411	−	2.55108i	0.117859	−	0.102125i
$625$	6.66458	−	24.0953i	0.266583	−	0.963812i
$626$	6.13858	−	0.882594i	0.245347	−	0.0352755i
$627$	4.62474	+	21.2596i	0.184694	+	0.849026i
$628$	16.8565	−	6.28716i	0.672649	−	0.250885i
$629$	−17.6854	−	15.3245i	−0.705163	−	0.611027i
$630$	−0.0687340	−	1.73313i	−0.00273843	−	0.0690494i
$631$	3.31772	−	1.51515i	0.132076	−	0.0603173i	−0.348281	−	0.937390i	$-0.613234\pi$
$631$	3.31772	−	1.51515i	0.132076	−	0.0603173i	0.480357	+	0.877073i	$0.340507\pi$
$632$	13.6973	−	7.47930i	0.544850	−	0.297510i
$633$	−6.88775	+	3.76100i	−0.273764	+	0.149486i
$634$	−12.1799	+	5.56236i	−0.483724	+	0.220909i
$635$	−8.42703	−	7.78412i	−0.334417	−	0.308903i
$636$	−6.86484	−	5.94842i	−0.272209	−	0.235870i
$637$	23.3538	−	8.71051i	0.925310	−	0.345123i
$638$	10.2470	+	47.1047i	0.405682	+	1.86489i
$639$	7.63475	−	1.09771i	0.302026	−	0.0434248i
$640$	2.23494	+	0.0710092i	0.0883438	+	0.00280689i
$641$	3.76074	−	3.25870i	0.148540	−	0.128711i	−0.577421	−	0.816447i	$-0.695941\pi$
$641$	3.76074	−	3.25870i	0.148540	−	0.128711i	0.725961	+	0.687736i	$0.241395\pi$
$642$	7.22701	−	13.2353i	0.285227	−	0.522355i
$643$	−31.9392	−	31.9392i	−1.25956	−	1.25956i	−0.951304	−	0.308254i	$-0.900255\pi$
$643$	−31.9392	−	31.9392i	−1.25956	−	1.25956i	−0.308254	−	0.951304i	$-0.599745\pi$
$644$	2.57464	+	2.68517i	0.101455	+	0.105810i
$645$	−4.75695	−	25.7844i	−0.187305	−	1.01526i
$646$	−12.6070	+	3.70173i	−0.496014	+	0.145643i
$647$	−1.73282	+	24.2280i	−0.0681243	+	0.952502i	0.842348	+	0.538933i	$0.181173\pi$
$647$	−1.73282	+	24.2280i	−0.0681243	+	0.952502i	−0.910473	+	0.413569i	$0.864282\pi$
$648$	0.212565	−	0.977147i	0.00835035	−	0.0383860i
$649$	−10.7830	−	74.9976i	−0.423271	−	2.94392i
$650$	−19.0649	−	3.99032i	−0.747788	−	0.156513i
$651$	0.491087	+	0.224272i	0.0192472	+	0.00878991i
$652$	11.4845	−	0.821386i	0.449767	−	0.0321679i
$653$	10.8204	+	14.4544i	0.423436	+	0.565645i	0.960636	−	0.277810i	$-0.0896087\pi$
$653$	10.8204	+	14.4544i	0.423436	+	0.565645i	−0.537199	+	0.843455i	$0.680518\pi$
$654$	−5.06096	−	11.0820i	−0.197899	−	0.433339i
$655$	−2.32759	+	22.4825i	−0.0909466	+	0.878465i
$656$	−0.145557	−	0.0427393i	−0.00568304	−	0.00166869i
$657$	−0.176250	+	0.472545i	−0.00687618	+	0.0184357i
$658$	−0.768680	+	0.575427i	−0.0299663	+	0.0224325i
$659$	28.8820	−	33.3316i	1.12508	−	1.29841i	0.175647	−	0.984453i	$-0.443798\pi$
$659$	28.8820	−	33.3316i	1.12508	−	1.29841i	0.949436	−	0.313962i	$-0.101656\pi$
$660$	11.3092	−	6.77039i	0.440208	−	0.263537i
$661$	21.1067	−	32.8427i	0.820956	−	1.27743i	−0.137016	−	0.990569i	$-0.543751\pi$
$661$	21.1067	−	32.8427i	0.820956	−	1.27743i	0.957972	−	0.286863i	$-0.0926125\pi$
$662$	−6.79860	+	9.08186i	−0.264235	+	0.352977i
$663$	13.5509	+	2.94781i	0.526272	+	0.114483i
$664$	−2.29455	−	2.64805i	−0.0890457	−	0.102764i
$665$	−6.08219	−	1.99777i	−0.235857	−	0.0774704i
$666$		−	6.57362i		−	0.254723i
$667$	29.0945	+	26.3008i	1.12654	+	1.01837i
$668$	1.11652	−	1.11652i	0.0431994	−	0.0431994i
$669$	−0.0630478	−	0.214721i	−0.00243757	−	0.00830160i
$670$	−19.6129	+	24.5353i	−0.757714	+	0.947882i
$671$	−64.8434	+	41.6723i	−2.50325	+	1.60874i
$672$	−0.620969	−	0.464852i	−0.0239544	−	0.0179320i
$673$	−20.1841	+	4.39079i	−0.778042	+	0.169253i	−0.584014	−	0.811744i	$-0.698519\pi$
$673$	−20.1841	+	4.39079i	−0.778042	+	0.169253i	−0.194027	+	0.980996i	$0.562155\pi$
$674$	−9.81111	+	21.4833i	−0.377910	+	0.827507i
$675$	−4.53166	+	2.11283i	−0.174424	+	0.0813230i
$676$	−0.309645	+	2.15363i	−0.0119094	+	0.0828319i
$677$	−26.6235	−	9.93007i	−1.02323	−	0.381644i	−0.218847	−	0.975759i	$-0.570229\pi$
$677$	−26.6235	−	9.93007i	−1.02323	−	0.381644i	−0.804380	+	0.594116i	$0.797502\pi$
$678$	−5.59343	−	10.2436i	−0.214814	−	0.393403i
$679$	1.07640	−	3.66588i	0.0413085	−	0.140684i
$680$	4.56552	+	6.52064i	0.175080	+	0.250055i
$681$	0.588547	+	0.0846203i	0.0225532	+	0.00324266i
$682$	0.292680	+	4.09220i	0.0112073	+	0.156699i
$683$	−13.2463	−	35.5146i	−0.506854	−	1.35893i	−0.898565	−	0.438841i	$-0.855389\pi$
$683$	−13.2463	−	35.5146i	−0.506854	−	1.35893i	0.391711	−	0.920088i	$-0.371883\pi$
$684$	−3.10501	−	1.99547i	−0.118723	−	0.0762987i
$685$	−14.4206	+	29.0945i	−0.550985	+	1.11164i
$686$	−5.61882	−	8.74306i	−0.214528	−	0.333811i
$687$	−0.357948	−	0.0256009i	−0.0136566	−	0.000976737i
$688$	−10.2914	−	5.61955i	−0.392357	−	0.214243i
$689$	35.3857			1.34809
$690$	4.27236	−	9.83600i	0.162646	−	0.374450i
$691$	18.6399			0.709094			0.354547	−	0.935038i	$-0.384635\pi$
$691$	18.6399			0.709094			0.354547	+	0.935038i	$0.384635\pi$
$692$	−12.0382	−	6.57333i	−0.457622	−	0.249881i
$693$	−4.56076	−	0.326192i	−0.173249	−	0.0123910i
$694$	−7.02764	−	10.9352i	−0.266765	−	0.415095i
$695$	6.03753	+	17.9042i	0.229017	+	0.679146i
$696$	−6.87974	−	4.42134i	−0.260776	−	0.167591i
$697$	−0.188723	−	0.505987i	−0.00714840	−	0.0191656i
$698$	−0.976984	−	13.6600i	−0.0369794	−	0.517039i
$699$	−16.3029	−	2.34401i	−0.616634	−	0.0886586i
$700$	0.0305485	+	3.87831i	0.00115462	+	0.146586i
$701$	−7.96685	+	27.1326i	−0.300904	+	1.02478i	0.660770	+	0.750588i	$0.270230\pi$
$701$	−7.96685	+	27.1326i	−0.300904	+	1.02478i	−0.961674	+	0.274196i	$0.911588\pi$
$702$	1.86697	+	3.41909i	0.0704641	+	0.129045i
$703$	−22.7330	−	8.47898i	−0.857393	−	0.319791i
$704$	0.838898	−	5.83466i	0.0316171	−	0.219902i
$705$	2.38603	+	1.40302i	0.0898632	+	0.0528409i
$706$	8.94910	−	19.5958i	0.336804	−	0.737498i
$707$	7.77708	−	1.69180i	0.292487	−	0.0636267i
$708$	10.2900	+	7.70300i	0.386722	+	0.289497i
$709$	16.0724	−	10.3291i	0.603613	−	0.387919i	−0.202844	−	0.979211i	$-0.565018\pi$
$709$	16.0724	−	10.3291i	0.603613	−	0.387919i	0.806457	+	0.591292i	$0.201382\pi$
$710$	−17.1412	+	1.91118i	−0.643296	+	0.0717254i
$711$	4.39680	+	14.9741i	0.164893	+	0.561573i
$712$	1.06738	−	1.06738i	0.0400017	−	0.0400017i
$713$	2.13236	+	2.56796i	0.0798576	+	0.0961710i
$714$		−	2.76133i		−	0.103340i
$715$	−16.0235	+	48.7833i	−0.599246	+	1.82439i
$716$	−1.75894	−	2.02992i	−0.0657346	−	0.0758618i
$717$	−18.1920	−	3.95743i	−0.679393	−	0.147793i
$718$	−13.6473	+	18.2307i	−0.509313	+	0.680363i
$719$	−8.17149	+	12.7151i	−0.304745	+	0.474193i	−0.959524	−	0.281628i	$-0.909126\pi$
$719$	−8.17149	+	12.7151i	−0.304745	+	0.474193i	0.654778	+	0.755821i	$0.272762\pi$
$720$	−0.544457	+	2.16877i	−0.0202907	+	0.0808253i
$721$	−8.22753	+	9.49508i	−0.306409	+	0.353615i
$722$	4.30451	−	3.22232i	0.160197	−	0.119922i
$723$	0.309055	−	0.828609i	0.0114939	−	0.0308163i
$724$	19.1984	+	5.63716i	0.713503	+	0.209503i
$725$	3.23820	+	40.7614i	0.120264	+	1.51384i
$726$	−9.86487	−	21.6010i	−0.366119	−	0.801690i
$727$	−24.8952	−	33.2561i	−0.923313	−	1.23340i	−0.972094	−	0.234592i	$-0.924624\pi$
$727$	−24.8952	−	33.2561i	−0.923313	−	1.23340i	0.0487807	−	0.998810i	$-0.484466\pi$
$728$	3.01407	−	0.215571i	0.111709	−	0.00798959i
$729$	0.909632	+	0.415415i	0.0336901	+	0.0153857i
$730$	0.427464	−	1.04359i	0.0158211	−	0.0386252i
$731$	−5.94049	−	41.3170i	−0.219717	−	1.52816i
$732$	2.77954	−	12.7773i	0.102735	−	0.472264i
$733$	0.00668141	−	0.0934183i	0.000246783	−	0.00345048i	−0.997327	−	0.0730643i	$-0.976722\pi$
$733$	0.00668141	−	0.0934183i	0.000246783	−	0.00345048i	0.997574	+	0.0696138i	$0.0221767\pi$
$734$	23.1938	−	6.81032i	0.856100	−	0.251374i
$735$	−8.11329	+	11.7842i	−0.299263	+	0.434665i
$736$	−2.20946	−	4.25656i	−0.0814417	−	0.156899i
$737$	58.5518	+	58.5518i	2.15678	+	2.15678i
$738$	0.0727030	−	0.133146i	0.00267623	−	0.00490115i
$739$	−4.45183	+	3.85753i	−0.163763	+	0.141902i	−0.732887	−	0.680350i	$-0.761828\pi$
$739$	−4.45183	+	3.85753i	−0.163763	+	0.141902i	0.569124	+	0.822252i	$0.307282\pi$
$740$	−0.466788	+	14.6917i	−0.0171595	+	0.540076i
$741$	14.2321	−	2.04627i	0.522829	−	0.0751714i
$742$	−1.49772	−	6.88492i	−0.0549831	−	0.252753i
$743$	29.9011	−	11.1525i	1.09696	−	0.409147i	0.265154	−	0.964206i	$-0.414577\pi$
$743$	29.9011	−	11.1525i	1.09696	−	0.409147i	0.831811	+	0.555059i	$0.187304\pi$
$744$	−0.525998	−	0.455780i	−0.0192840	−	0.0167097i
$745$	43.8905	−	1.74065i	1.60802	−	0.0637726i
$746$	−5.04657	+	2.30469i	−0.184768	+	0.0843807i
$747$	3.07527	−	1.67923i	0.112518	−	0.0614397i
$748$	18.4173	−	10.0566i	0.673404	−	0.367706i
$749$	10.6402	−	4.85921i	0.388784	−	0.177552i
$750$	10.2780	−	4.40027i	0.375300	−	0.160675i
$751$	27.2940	+	23.6504i	0.995971	+	0.863014i	0.990575	−	0.136971i	$-0.0437369\pi$
$751$	27.2940	+	23.6504i	0.995971	+	0.863014i	0.00539620	+	0.999985i	$0.498282\pi$
$752$	1.15982	−	0.432592i	0.0422944	−	0.0157750i
$753$	0.691571	+	3.17910i	0.0252022	+	0.115853i
$754$	31.5339	−	4.53389i	1.14840	−	0.165115i
$755$	−13.6579	−	14.5542i	−0.497061	−	0.529683i
$756$	0.586225	−	0.507967i	0.0213208	−	0.0184746i
$757$	−3.90241	+	7.14673i	−0.141836	+	0.259752i	−0.938934	−	0.344097i	$-0.888185\pi$
$757$	−3.90241	+	7.14673i	−0.141836	+	0.259752i	0.797099	+	0.603849i	$0.206367\pi$
$758$	−9.38149	−	9.38149i	−0.340751	−	0.340751i
$759$	−24.5217	−	14.0666i	−0.890081	−	0.510584i
$760$	6.79782	+	4.68024i	0.246583	+	0.169770i
$761$	−20.3172	+	5.96568i	−0.736499	+	0.216256i	−0.628406	−	0.777885i	$-0.716292\pi$
$761$	−20.3172	+	5.96568i	−0.736499	+	0.216256i	−0.108093	+	0.994141i	$0.534474\pi$
$762$	0.366002	−	5.11737i	0.0132588	−	0.185383i
$763$	2.00877	−	9.23416i	0.0727223	−	0.334299i
$764$	−0.771883	−	5.36856i	−0.0279257	−	0.194228i
$765$	−7.34209	+	3.07513i	−0.265454	+	0.111181i
$766$	5.86851	+	2.68006i	0.212038	+	0.0968345i
$767$	−49.9459	+	3.57220i	−1.80344	+	0.128985i
$768$	0.599278	+	0.800541i	0.0216246	+	0.0288870i
$769$	−9.11070	−	19.9496i	−0.328540	−	0.719403i	0.671221	−	0.741257i	$-0.265770\pi$
$769$	−9.11070	−	19.9496i	−0.328540	−	0.719403i	−0.999761	+	0.0218547i	$0.993043\pi$
$770$	10.1699	+	1.05288i	0.366496	+	0.0379430i
$771$	9.83318	+	2.88728i	0.354133	+	0.103983i
$772$	5.36526	−	14.3848i	0.193100	−	0.517721i
$773$	−16.7379	+	12.5298i	−0.602020	+	0.450667i	−0.856311	−	0.516461i	$-0.827249\pi$
$773$	−16.7379	+	12.5298i	−0.602020	+	0.450667i	0.254290	+	0.967128i	$0.418158\pi$
$774$	7.67873	−	8.86172i	0.276006	−	0.318528i
$775$	−0.220911	+	3.47296i	−0.00793535	+	0.124752i
$776$	−2.66293	+	4.14360i	−0.0955935	+	0.148746i
$777$	3.05576	−	4.08202i	0.109625	−	0.146442i
$778$	21.5775	+	4.69390i	0.773591	+	0.168284i
$779$	−0.366671	−	0.423161i	−0.0131373	−	0.0151613i
$780$	−3.92977	−	7.77404i	−0.140708	−	0.278355i
$781$			45.4670i			1.62694i
$782$	7.41685	−	15.3772i	0.265226	−	0.549888i
$783$	5.78269	−	5.78269i	0.206657	−	0.206657i
$784$	1.80261	+	6.13913i	0.0643790	+	0.219255i
$785$	−4.45775	−	39.9810i	−0.159104	−	1.42698i
$786$	−8.50359	+	5.46492i	−0.303313	+	0.194927i
$787$	5.84079	+	4.37236i	0.208202	+	0.155858i	0.698290	−	0.715815i	$-0.253945\pi$
$787$	5.84079	+	4.37236i	0.208202	+	0.155858i	−0.490088	+	0.871673i	$0.663036\pi$
$788$	−13.7337	+	2.98758i	−0.489242	+	0.106428i
$789$	−4.51267	+	9.88137i	−0.160655	+	0.351786i
$790$	−8.76328	−	33.7785i	−0.311784	−	1.20178i
$791$	1.28841	−	8.96107i	0.0458105	−	0.318619i
$792$	5.52300	+	2.05997i	0.196251	+	0.0731979i
$793$	24.4128	+	44.7086i	0.866923	+	1.58765i
$794$	4.62088	−	15.7373i	0.163989	−	0.558495i
$795$	−16.6384	+	11.6496i	−0.590102	+	0.413169i
$796$	−1.44144	−	0.207248i	−0.0510904	−	0.00734569i
$797$	0.963146	+	13.4665i	0.0341164	+	0.477009i	0.985576	+	0.169235i	$0.0541297\pi$
$797$	0.963146	+	13.4665i	0.0341164	+	0.477009i	−0.951459	+	0.307774i	$0.900416\pi$
$798$	−1.00052	−	2.68250i	−0.0354180	−	0.0949593i
$799$	3.70710	+	2.38241i	0.131148	+	0.0842836i
$800$	1.37083	−	4.80841i	0.0484662	−	0.170003i
$801$	0.816097	+	1.26987i	0.0288354	+	0.0448687i
$802$	−24.8344	−	1.77619i	−0.876932	−	0.0627194i
$803$	−2.60928	−	1.42478i	−0.0920796	−	0.0502793i
$804$	−14.0474			−0.495414
$805$	7.22529	−	4.12184i	0.254658	−	0.145276i
$806$	2.71133			0.0955024
$807$	−0.149877	−	0.0818388i	−0.00527591	−	0.00288086i
$808$	−10.2344	−	0.731979i	−0.360045	−	0.0257509i
$809$	12.2478	+	19.0580i	0.430611	+	0.670044i	0.986971	−	0.160897i	$-0.0514388\pi$
$809$	12.2478	+	19.0580i	0.430611	+	0.670044i	−0.556360	+	0.830941i	$0.687802\pi$
$810$	−2.00347	−	0.993020i	−0.0703949	−	0.0348912i
$811$	40.9462	+	26.3145i	1.43782	+	0.924028i	0.999685	+	0.0251166i	$0.00799570\pi$
$811$	40.9462	+	26.3145i	1.43782	+	0.924028i	0.438131	+	0.898911i	$0.355641\pi$
$812$	−2.21684	−	5.94358i	−0.0777958	−	0.208579i
$813$	1.62438	+	22.7118i	0.0569694	+	0.796536i
$814$	38.3549	+	5.51460i	1.34434	+	0.193286i
$815$	4.47141	−	25.3544i	0.156627	−	0.888126i
$816$	−1.00293	+	3.41565i	−0.0351094	+	0.119572i
$817$	−20.7414	−	37.9850i	−0.725649	−	1.32893i
$818$	−4.81088	−	1.79437i	−0.168208	−	0.0627385i
$819$	−0.430043	+	2.99102i	−0.0150269	+	0.104515i
$820$	−0.171941	+	0.292410i	−0.00600445	+	0.0102114i
$821$	14.1816	−	31.0534i	0.494942	−	1.08377i	−0.483138	−	0.875544i	$-0.660503\pi$
$821$	14.1816	−	31.0534i	0.494942	−	1.08377i	0.978080	−	0.208228i	$-0.0667697\pi$
$822$	−14.1901	+	3.08688i	−0.494938	+	0.107667i
$823$	13.2111	+	9.88972i	0.460511	+	0.344734i	0.804209	−	0.594346i	$-0.202589\pi$
$823$	13.2111	+	9.88972i	0.460511	+	0.344734i	−0.343699	+	0.939080i	$0.611680\pi$
$824$	13.6258	−	8.75675i	0.474676	−	0.305056i
$825$	−8.52607	−	28.2131i	−0.296840	−	0.982256i
$826$	2.80902	+	9.56666i	0.0977385	+	0.332867i
$827$	−15.7934	+	15.7934i	−0.549192	+	0.549192i	−0.926207	−	0.377015i	$-0.876950\pi$
$827$	−15.7934	+	15.7934i	−0.549192	+	0.549192i	0.377015	+	0.926207i	$0.376950\pi$
$828$	4.62894	−	1.25417i	0.160867	−	0.0435854i
$829$			36.4542i			1.26611i	0.774108	+	0.633053i	$0.218198\pi$
$829$			36.4542i			1.26611i	−0.774108	+	0.633053i	$0.781802\pi$
$830$	−6.99229	+	3.53460i	−0.242706	+	0.122688i
$831$	0.166201	+	0.191806i	0.00576544	+	0.00665367i
$832$	−3.80658	−	0.828071i	−0.131970	−	0.0287082i
$833$	−13.6498	+	18.2340i	−0.472936	+	0.631769i
$834$	−4.56842	+	7.10860i	−0.158191	+	0.246151i
$835$	−1.81357	−	3.02937i	−0.0627613	−	0.104836i
$836$	14.2477	−	16.4427i	0.492766	−	0.568683i
$837$	0.557173	−	0.417094i	0.0192587	−	0.0144169i
$838$	7.90903	−	21.2049i	0.273213	−	0.732512i
$839$	24.4642	+	7.18333i	0.844597	+	0.247996i	0.675276	−	0.737565i	$-0.264024\pi$
$839$	24.4642	+	7.18333i	0.844597	+	0.247996i	0.169321	+	0.985561i	$0.445843\pi$
$840$	−1.34625	+	1.09365i	−0.0464500	+	0.0377344i
$841$	−15.7356	−	34.4561i	−0.542605	−	1.18814i
$842$	0.0561634	+	0.0750256i	0.00193552	+	0.00258555i
$843$	0.143194	−	0.0102414i	0.00493186	−	0.000352733i
$844$	7.13851	+	3.26005i	0.245718	+	0.112215i
$845$	4.50214	+	1.84411i	0.154878	+	0.0634392i
$846$	0.176168	+	1.22527i	0.00605676	+	0.0421257i
$847$	3.91550	−	17.9993i	0.134538	−	0.618463i
$848$	−0.648008	+	9.06034i	−0.0222527	+	0.311133i
$849$	30.9890	−	9.09920i	1.06354	−	0.312284i
$850$	16.6275	−	6.35137i	0.570318	−	0.217850i
$851$	27.9810	−	14.5241i	0.959177	−	0.497881i
$852$	−5.45410	−	5.45410i	−0.186854	−	0.186854i
$853$	2.39310	−	4.38263i	0.0819380	−	0.150058i	−0.833497	−	0.552524i	$-0.813665\pi$
$853$	2.39310	−	4.38263i	0.0819380	−	0.150058i	0.915435	+	0.402465i	$0.131847\pi$
$854$	7.66557	−	6.64226i	0.262311	−	0.227293i
$855$	−6.01826	+	5.64761i	−0.205820	+	0.193144i
$856$	−14.9264	+	2.14609i	−0.510173	+	0.0733518i
$857$	0.672070	+	3.08946i	0.0229575	+	0.105534i	0.987200	−	0.159488i	$-0.0509844\pi$
$857$	0.672070	+	3.08946i	0.0229575	+	0.105534i	−0.964242	+	0.265022i	$0.914621\pi$
$858$	−21.5155	+	8.02485i	−0.734525	+	0.273964i
$859$	32.1182	+	27.8306i	1.09586	+	0.949567i	0.998954	−	0.0457263i	$-0.0145602\pi$
$859$	32.1182	+	27.8306i	1.09586	+	0.949567i	0.0969051	+	0.995294i	$0.469106\pi$
$860$	−17.7908	+	19.2602i	−0.606660	+	0.656766i
$861$	0.107039	−	0.0488832i	0.00364789	−	0.00166593i
$862$	1.35735	−	0.741167i	0.0462314	−	0.0252443i
$863$	14.6225	−	7.98452i	0.497757	−	0.271796i	−0.210699	−	0.977551i	$-0.567574\pi$
$863$	14.6225	−	7.98452i	0.497757	−	0.271796i	0.708456	+	0.705755i	$0.249392\pi$
$864$	−0.909632	+	0.415415i	−0.0309463	+	0.0141327i
$865$	−20.8103	+	22.5291i	−0.707572	+	0.766013i
$866$	2.73699	+	2.37162i	0.0930068	+	0.0805909i
$867$	4.05461	−	1.51229i	0.137702	−	0.0513601i
$868$	−0.114759	−	0.527537i	−0.00389516	−	0.0179058i
$869$	−91.0574	+	13.0921i	−3.08891	+	0.444118i
$870$	−13.3346	+	12.5134i	−0.452085	+	0.424242i
$871$	41.3571	−	35.8361i	1.40133	−	1.21426i
$872$	−5.83865	+	10.6927i	−0.197722	+	0.362100i
$873$	−3.48286	−	3.48286i	−0.117877	−	0.117877i
$874$	1.63344	−	17.6256i	0.0552520	−	0.596194i
$875$	8.42781	+	2.04532i	0.284912	+	0.0691445i
$876$	0.483915	−	0.142090i	0.0163500	−	0.00480078i
$877$	−2.91302	+	40.7293i	−0.0983656	+	1.37533i	0.673332	+	0.739341i	$0.264863\pi$
$877$	−2.91302	+	40.7293i	−0.0983656	+	1.37533i	−0.771697	+	0.635990i	$0.780592\pi$
$878$	−0.428293	+	1.96883i	−0.0144542	+	0.0664448i
$879$	−0.725375	−	5.04509i	−0.0244663	−	0.170167i
$880$	−12.1973	−	4.99610i	−0.411171	−	0.168418i
$881$	30.3191	+	13.8463i	1.02148	+	0.466492i	0.854490	−	0.519467i	$-0.173870\pi$
$881$	30.3191	+	13.8463i	1.02148	+	0.466492i	0.166985	+	0.985959i	$0.446597\pi$
$882$	−6.38201	+	0.456450i	−0.214893	+	0.0153695i
$883$	21.6961	+	28.9827i	0.730133	+	0.975344i	0.999923	+	0.0124247i	$0.00395501\pi$
$883$	21.6961	+	28.9827i	0.730133	+	0.975344i	−0.269789	+	0.962919i	$0.586954\pi$
$884$	−5.76089	−	12.6146i	−0.193760	−	0.424274i
$885$	22.3085	−	18.1227i	0.749893	−	0.609188i
$886$	5.31499	+	1.56062i	0.178561	+	0.0524301i
$887$	8.24706	−	22.1112i	0.276909	−	0.742422i	−0.721823	−	0.692078i	$-0.756696\pi$
$887$	8.24706	−	22.1112i	0.276909	−	0.742422i	0.998732	−	0.0503440i	$-0.0160318\pi$
$888$	−5.26246	+	3.93943i	−0.176596	+	0.132198i
$889$	2.60610	−	3.00759i	0.0874057	−	0.100871i
$890$	−1.73376	−	2.89604i	−0.0581156	−	0.0970754i
$891$	−3.18689	+	4.95890i	−0.106765	+	0.166130i
$892$	−0.134110	+	0.179150i	−0.00449033	+	0.00599838i
$893$	4.46449	+	0.971191i	0.149398	+	0.0324997i
$894$	12.8640	+	14.8458i	0.430236	+	0.496519i
$895$	−5.36011	+	2.70953i	−0.179169	+	0.0905696i
$896$			0.775687i			0.0259139i
$897$	−10.4286	+	15.5012i	−0.348201	+	0.517570i
$898$	7.69750	−	7.69750i	0.256869	−	0.256869i
$899$	−1.60357	−	5.46127i	−0.0534821	−	0.182143i
$900$	4.40713	+	2.36161i	0.146904	+	0.0787202i
$901$	−27.2027	+	17.4821i	−0.906252	+	0.582413i
$902$	0.715869	+	0.535893i	0.0238358	+	0.0178433i
$903$	8.88764	−	1.93339i	0.295762	−	0.0643391i
$904$	−4.84840	+	10.6165i	−0.161256	+	0.353100i
$905$	22.6784	−	38.5677i	0.753856	−	1.28203i
$906$	1.27030	−	8.83510i	0.0422027	−	0.293526i
$907$	0.554797	+	0.206928i	0.0184217	+	0.00687094i	0.358658	−	0.933469i	$-0.383234\pi$
$907$	0.554797	+	0.206928i	0.0184217	+	0.00687094i	−0.340236	+	0.940340i	$0.610507\pi$
$908$	−0.284961	−	0.521868i	−0.00945677	−	0.0173188i
$909$	2.89073	−	9.84492i	0.0958794	−	0.326535i
$910$	1.17351	−	6.65420i	0.0389015	−	0.220585i
$911$	31.6222	+	4.54659i	1.04769	+	0.150635i	0.644596	−	0.764523i	$-0.277026\pi$
$911$	31.6222	+	4.54659i	1.04769	+	0.150635i	0.403094	+	0.915158i	$0.367935\pi$
$912$	0.263308	+	3.68153i	0.00871901	+	0.121908i
$913$	7.21787	+	19.3519i	0.238877	+	0.640453i
$914$	−12.6774	−	8.14727i	−0.419331	−	0.269488i
$915$	−26.1978	−	12.9849i	−0.866071	−	0.429267i
$916$	0.194016	+	0.301894i	0.00641045	+	0.00997486i
$917$	−7.82085	−	0.559358i	−0.258267	−	0.0184716i
$918$	−3.12441	−	1.70606i	−0.103121	−	0.0563082i
$919$	−8.30582			−0.273984			−0.136992	−	0.990572i	$-0.543743\pi$
$919$	−8.30582			−0.273984			−0.136992	+	0.990572i	$0.543743\pi$
$920$	−10.4345	+	2.47429i	−0.344014	+	0.0815751i
$921$	−12.4891			−0.411530
$922$	17.6488	+	9.63699i	0.581233	+	0.317377i
$923$	29.9713	+	2.14359i	0.986517	+	0.0705571i
$924$	2.47203	+	3.84656i	0.0813239	+	0.126542i
$925$	31.6087	+	9.01133i	1.03929	+	0.296291i
$926$	13.0305	+	8.37418i	0.428208	+	0.275193i
$927$	5.66026	+	15.1758i	0.185907	+	0.498437i
$928$	0.583409	+	8.15713i	0.0191514	+	0.267771i
$929$	−5.60739	−	0.806221i	−0.183972	−	0.0264512i	0.0497127	−	0.998764i	$-0.484169\pi$
$929$	−5.60739	−	0.806221i	−0.183972	−	0.0264512i	−0.233685	+	0.972312i	$0.575079\pi$
$930$	−1.27487	+	0.892617i	−0.0418045	+	0.0292701i
$931$	−6.65332	+	22.6591i	−0.218054	+	0.742623i
$932$	7.89352	+	14.4559i	0.258561	+	0.473519i
$933$	−5.66532	−	2.11306i	−0.185474	−	0.0691784i
$934$	−1.92004	+	13.3542i	−0.0628256	+	0.436962i
$935$	−11.7831	−	45.4183i	−0.385347	−	1.48534i
$936$	1.61829	−	3.54357i	0.0528956	−	0.115825i
$937$	−33.0997	+	7.20041i	−1.08132	+	0.235227i	−0.717723	−	0.696329i	$-0.754816\pi$
$937$	−33.0997	+	7.20041i	−1.08132	+	0.235227i	−0.363598	+	0.931556i	$0.618452\pi$
$938$	−8.72301	−	6.52996i	−0.284816	−	0.213211i
$939$	5.21720	−	3.35289i	0.170257	−	0.109418i
$940$	−0.306718	−	2.75092i	−0.0100040	−	0.0897251i
$941$	−4.42364	−	15.0655i	−0.144206	−	0.491122i	0.855435	−	0.517911i	$-0.173290\pi$
$941$	−4.42364	−	15.0655i	−0.144206	−	0.491122i	−0.999641	+	0.0267887i	$0.991472\pi$
$942$	12.7215	−	12.7215i	0.414487	−	0.414487i
$943$	0.727376	+	0.0152850i	0.0236866	+	0.000497747i
$944$		−	12.8538i		−	0.418356i
$945$	−0.782489	−	1.54795i	−0.0254544	−	0.0503549i
$946$	45.2635	+	52.2368i	1.47164	+	1.69837i
$947$	53.3466	+	11.6048i	1.73353	+	0.377107i	0.964906	−	0.262594i	$-0.0845779\pi$
$947$	53.3466	+	11.6048i	1.73353	+	0.377107i	0.768624	+	0.639700i	$0.220942\pi$
$948$	9.35250	−	12.4935i	0.303755	−	0.405769i
$949$	−1.06221	+	1.65283i	−0.0344809	+	0.0536533i
$950$	13.8515	−	12.1947i	0.449402	−	0.395649i
$951$	−8.76850	+	10.1194i	−0.284338	+	0.328144i
$952$	−2.21056	+	1.65480i	−0.0716446	+	0.0536325i
$953$	1.17209	−	3.14249i	0.0379676	−	0.101795i	−0.916582	−	0.399846i	$-0.869064\pi$
$953$	1.17209	−	3.14249i	0.0379676	−	0.101795i	0.954550	+	0.298051i	$0.0963364\pi$
$954$	−8.71554	−	2.55911i	−0.282176	−	0.0828544i
$955$	−12.0634	−	1.24892i	−0.390364	−	0.0404140i
$956$	7.73398	+	16.9351i	0.250135	+	0.547719i
$957$	28.8890	+	38.5911i	0.933848	+	1.24747i
$958$	−27.3247	+	1.95430i	−0.882823	+	0.0631407i
$959$	−10.2466	−	4.67946i	−0.330879	−	0.151108i
$960$	2.06247	−	0.863835i	0.0665660	−	0.0278802i
$961$	4.34282	+	30.2050i	0.140091	+	0.974354i
$962$	5.44343	−	25.0230i	0.175503	−	0.806775i
$963$	1.07578	−	15.0414i	0.0346667	−	0.484704i
$964$	−0.848545	+	0.249155i	−0.0273298	+	0.00802475i
$965$	−28.2762	−	19.4679i	−0.910243	−	0.626695i
$966$	3.45743	+	1.37297i	0.111241	+	0.0441746i
$967$	−29.4286	−	29.4286i	−0.946361	−	0.946361i	0.0522719	−	0.998633i	$-0.483354\pi$
$967$	−29.4286	−	29.4286i	−0.946361	−	0.946361i	−0.998633	+	0.0522719i	$0.983354\pi$
$968$	−11.3807	+	20.8423i	−0.365791	+	0.669895i
$969$	−9.92993	+	8.60433i	−0.318995	+	0.276411i
$970$	7.53666	+	8.03129i	0.241988	+	0.257869i
$971$	33.3860	−	4.80018i	1.07141	−	0.154045i	0.416032	−	0.909350i	$-0.363420\pi$
$971$	33.3860	−	4.80018i	1.07141	−	0.154045i	0.655374	+	0.755305i	$0.272511\pi$
$972$	−0.212565	−	0.977147i	−0.00681803	−	0.0313420i
$973$	−6.14130	+	2.29058i	−0.196881	+	0.0734328i
$974$	−1.15551	−	1.00126i	−0.0370250	−	0.0320824i
$975$	−18.9997	+	4.29014i	−0.608478	+	0.137394i
$976$	−11.8945	+	5.43203i	−0.380734	+	0.173875i
$977$	5.87086	−	3.20573i	0.187826	−	0.102561i	−0.382585	−	0.923920i	$-0.624966\pi$
$977$	5.87086	−	3.20573i	0.187826	−	0.102561i	0.570410	+	0.821360i	$0.306784\pi$
$978$	10.1054	−	5.51798i	0.323136	−	0.176446i
$979$	−8.09389	+	3.69636i	−0.258682	+	0.118136i
$980$	14.2958	−	0.566958i	0.456663	−	0.0181108i
$981$	−9.20723	−	7.97811i	−0.293964	−	0.254721i
$982$	−15.8540	+	5.91323i	−0.505921	+	0.188699i
$983$	−2.10335	−	9.66896i	−0.0670865	−	0.308392i	0.931361	−	0.364098i	$-0.118623\pi$
$983$	−2.10335	−	9.66896i	−0.0670865	−	0.308392i	−0.998447	+	0.0557061i	$0.982259\pi$
$984$	−0.150158	+	0.0215894i	−0.00478685	+	0.000688246i
$985$	−0.998025	+	31.4118i	−0.0317997	+	1.00086i
$986$	−22.0016	+	19.0645i	−0.700675	+	0.607138i
$987$	−0.460175	+	0.842748i	−0.0146475	+	0.0268250i
$988$	−10.1671	−	10.1671i	−0.323458	−	0.323458i
$989$	54.6863	+	13.1053i	1.73892	+	0.416726i
$990$	7.47464	−	10.8566i	0.237560	−	0.345044i
$991$	−45.6319	+	13.3987i	−1.44954	+	0.425625i	−0.909391	−	0.415942i	$-0.863452\pi$
$991$	−45.6319	+	13.3987i	−1.44954	+	0.425625i	−0.540154	+	0.841566i	$0.681634\pi$
$992$	−0.0496517	+	0.694222i	−0.00157644	+	0.0220416i
$993$	−2.41148	+	11.0854i	−0.0765260	+	0.351784i
$994$	−0.851480	−	5.92217i	−0.0270073	−	0.187840i
$995$	−1.23427	+	3.01331i	−0.0391291	+	0.0955284i
$996$	−3.18723	−	1.45556i	−0.100991	−	0.0461212i
$997$	18.9383	−	1.35450i	0.599783	−	0.0428974i	0.231853	−	0.972751i	$-0.425521\pi$
$997$	18.9383	−	1.35450i	0.599783	−	0.0428974i	0.367930	+	0.929853i	$0.380067\pi$
$998$	7.79344	+	10.4108i	0.246697	+	0.329548i
$999$	−2.73078	−	5.97958i	−0.0863981	−	0.189185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.37.5	✓	240
5.3	odd	4	inner	690.2.w.a.313.6	yes	240
23.5	odd	22	inner	690.2.w.a.97.6	yes	240
115.28	even	44	inner	690.2.w.a.373.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.37.5	✓	240	1.1	even	1	trivial
690.2.w.a.97.6	yes	240	23.5	odd	22	inner
690.2.w.a.313.6	yes	240	5.3	odd	4	inner
690.2.w.a.373.5	yes	240	115.28	even	44	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.11884 - 0.714499i) q^{5} +(0.841254 + 0.540641i) q^{6} +(0.271075 + 0.726780i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(2.11884 - 0.714499i) q^{5} +(0.841254 + 0.540641i) q^{6} +(0.271075 + 0.726780i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-2.20209 - 0.388352i) q^{10} +(-1.66072 + 5.65588i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(3.64999 + 1.36138i) q^{13} +(0.110392 - 0.767791i) q^{14} +(-2.16442 + 0.561523i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-3.47850 + 0.756701i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(-3.10501 + 1.99547i) q^{19} +(1.74661 + 1.39620i) q^{20} +(-0.218536 - 0.744266i) q^{21} +(4.16815 - 4.16815i) q^{22} +(0.782098 - 4.73163i) q^{23} +1.00000i q^{24} +(3.97898 - 3.02782i) q^{25} +(-2.55108 - 2.94411i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(-0.464852 + 0.620969i) q^{28} +(-4.42134 + 6.87974i) q^{29} +(2.16877 + 0.544457i) q^{30} +(-0.455780 + 0.525998i) q^{31} +(0.800541 - 0.599278i) q^{32} +(2.05997 - 5.52300i) q^{33} +(3.41565 + 1.00293i) q^{34} +(1.09365 + 1.34625i) q^{35} +(0.415415 + 0.909632i) q^{36} +(3.93943 + 5.26246i) q^{37} +(3.68153 - 0.263308i) q^{38} +(-3.54357 - 1.61829i) q^{39} +(-0.863835 - 2.06247i) q^{40} +(0.0215894 + 0.150158i) q^{41} +(-0.164884 + 0.757960i) q^{42} +(-0.836505 + 11.6959i) q^{43} +(-5.65588 + 1.66072i) q^{44} +(2.19896 - 0.405684i) q^{45} +(-2.95406 + 3.77803i) q^{46} +(-0.875308 - 0.875308i) q^{47} +(0.479249 - 0.877679i) q^{48} +(4.83552 - 4.19000i) q^{49} +(-4.94335 + 0.750534i) q^{50} +(3.52362 - 0.506620i) q^{51} +(0.828071 + 3.80658i) q^{52} +(8.51077 - 3.17435i) q^{53} +(0.755750 + 0.654861i) q^{54} +(0.522329 + 13.1705i) q^{55} +(0.705590 - 0.322232i) q^{56} +(3.23946 - 1.76888i) q^{57} +(7.17763 - 3.91928i) q^{58} +(-11.6922 + 5.33967i) q^{59} +(-1.64255 - 1.51724i) q^{60} +(9.88231 + 8.56307i) q^{61} +(0.652113 - 0.243225i) q^{62} +(0.164884 + 0.757960i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(8.70645 + 0.276624i) q^{65} +(-4.45489 + 3.86018i) q^{66} +(6.73221 - 12.3291i) q^{67} +(-2.51720 - 2.51720i) q^{68} +(-1.11766 + 4.66378i) q^{69} +(-0.314684 - 1.70570i) q^{70} +(7.40082 - 2.17308i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(-0.107206 + 0.492818i) q^{73} +(-0.935524 - 6.50671i) q^{74} +(-4.18485 + 2.73625i) q^{75} +(-3.35739 - 1.53327i) q^{76} +(-4.56076 + 0.326192i) q^{77} +(2.33455 + 3.11860i) q^{78} +(6.48309 + 14.1960i) q^{79} +(-0.230267 + 2.22418i) q^{80} +(0.959493 + 0.281733i) q^{81} +(0.0530144 - 0.142137i) q^{82} +(2.80499 - 2.09979i) q^{83} +(0.507967 - 0.586225i) q^{84} +(-6.82972 + 4.08871i) q^{85} +(6.33941 - 9.86432i) q^{86} +(4.90087 - 6.54680i) q^{87} +(5.75995 + 1.25300i) q^{88} +(0.988512 + 1.14080i) q^{89} +(-2.12440 - 0.697788i) q^{90} +3.02177i q^{91} +(4.40333 - 1.90017i) q^{92} +(0.492143 - 0.492143i) q^{93} +(0.348749 + 1.18773i) q^{94} +(-5.15327 + 6.44662i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-3.94307 - 2.95174i) q^{97} +(-6.25209 + 1.36006i) q^{98} +(-2.44873 + 5.36197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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