LMFDB - Embedded newform 414.2.p.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	414.11
Dual form			414.2.p.a.113.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998867 + 0.0475819i) q^{2} +(1.72839 - 0.112570i) q^{3} +(0.995472 - 0.0950560i) q^{4} +(1.63439 + 1.55839i) q^{5} +(-1.72107 + 0.194682i) q^{6} +(0.163264 + 0.847095i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.97466 - 0.389129i) q^{9} +O(q^{10})$	\(q+(-0.998867 + 0.0475819i) q^{2} +(1.72839 - 0.112570i) q^{3} +(0.995472 - 0.0950560i) q^{4} +(1.63439 + 1.55839i) q^{5} +(-1.72107 + 0.194682i) q^{6} +(0.163264 + 0.847095i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.97466 - 0.389129i) q^{9} +(-1.70669 - 1.47886i) q^{10} +(-2.48769 + 1.28249i) q^{11} +(1.70986 - 0.276354i) q^{12} +(3.57694 + 0.689399i) q^{13} +(-0.203386 - 0.838367i) q^{14} +(3.00030 + 2.50952i) q^{15} +(0.981929 - 0.189251i) q^{16} +(1.44298 + 3.15968i) q^{17} +(-2.95277 + 0.530228i) q^{18} +(-5.57008 - 2.54377i) q^{19} +(1.77513 + 1.39598i) q^{20} +(0.377541 + 1.44573i) q^{21} +(2.42385 - 1.39941i) q^{22} +(-4.78906 + 0.254799i) q^{23} +(-1.69478 + 0.357399i) q^{24} +(0.00474997 + 0.0997142i) q^{25} +(-3.60569 - 0.518420i) q^{26} +(5.09756 - 1.00742i) q^{27} +(0.243046 + 0.827740i) q^{28} +(0.0583106 - 0.610656i) q^{29} +(-3.11631 - 2.36392i) q^{30} +(6.01349 - 4.72906i) q^{31} +(-0.971812 + 0.235759i) q^{32} +(-4.15533 + 2.49669i) q^{33} +(-1.59168 - 3.08744i) q^{34} +(-1.05327 + 1.63892i) q^{35} +(2.92420 - 0.670126i) q^{36} +(0.337597 - 1.14975i) q^{37} +(5.68481 + 2.27585i) q^{38} +(6.25995 + 0.788893i) q^{39} +(-1.83954 - 1.30993i) q^{40} +(-0.286729 + 0.300713i) q^{41} +(-0.445904 - 1.42613i) q^{42} +(-2.06536 + 2.62632i) q^{43} +(-2.35452 + 1.51316i) q^{44} +(5.46818 + 3.99969i) q^{45} +(4.77151 - 0.482383i) q^{46} +(5.42675 + 3.13313i) q^{47} +(1.67585 - 0.437635i) q^{48} +(5.80766 - 2.32504i) q^{49} +(-0.00948918 - 0.0993752i) q^{50} +(2.84971 + 5.29871i) q^{51} +(3.62627 + 0.346267i) q^{52} +(-4.86824 - 5.61825i) q^{53} +(-5.04385 + 1.24883i) q^{54} +(-6.06450 - 1.78070i) q^{55} +(-0.282156 - 0.815237i) q^{56} +(-9.91361 - 3.76960i) q^{57} +(-0.0291883 + 0.612739i) q^{58} +(-2.17007 + 11.2594i) q^{59} +(3.22526 + 2.21296i) q^{60} +(3.41431 - 8.52853i) q^{61} +(-5.78166 + 5.00983i) q^{62} +(0.815284 + 2.45628i) q^{63} +(0.959493 - 0.281733i) q^{64} +(4.77178 + 6.70102i) q^{65} +(4.03183 - 2.69158i) q^{66} +(2.35624 - 4.57047i) q^{67} +(1.73679 + 3.00820i) q^{68} +(-8.24867 + 0.979495i) q^{69} +(0.974091 - 1.68718i) q^{70} +(-3.69376 - 5.74760i) q^{71} +(-2.88900 + 0.808506i) q^{72} +(0.594917 - 1.30269i) q^{73} +(-0.282507 + 1.16451i) q^{74} +(0.0194346 + 0.171810i) q^{75} +(-5.78666 - 2.00278i) q^{76} +(-1.49255 - 1.89793i) q^{77} +(-6.29039 - 0.490139i) q^{78} +(-7.85292 + 2.71792i) q^{79} +(1.89979 + 1.22092i) q^{80} +(8.69716 - 2.31505i) q^{81} +(0.272096 - 0.314016i) q^{82} +(5.46082 - 5.20688i) q^{83} +(0.513257 + 1.40330i) q^{84} +(-2.56562 + 7.41287i) q^{85} +(1.93806 - 2.72162i) q^{86} +(0.0320419 - 1.06202i) q^{87} +(2.27985 - 1.62348i) q^{88} +(-0.401181 + 2.79027i) q^{89} +(-5.65229 - 3.73497i) q^{90} +3.14256i q^{91} +(-4.74315 + 0.708874i) q^{92} +(9.86129 - 8.85059i) q^{93} +(-5.56968 - 2.87137i) q^{94} +(-5.13951 - 12.8379i) q^{95} +(-1.65313 + 0.516880i) q^{96} +(2.09941 + 0.509311i) q^{97} +(-5.69045 + 2.59874i) q^{98} +(-6.90097 + 4.78301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.998867	+	0.0475819i	−0.706306	+	0.0336455i
$2$	−0.998867	+	0.0475819i	−0.706306	+	0.0336455i
$3$	1.72839	−	0.112570i	0.997886	−	0.0649923i
$3$	1.72839	−	0.112570i	0.997886	−	0.0649923i
$4$	0.995472	−	0.0950560i	0.497736	−	0.0475280i
$5$	1.63439	+	1.55839i	0.730923	+	0.696934i	0.961096	−	0.276216i	$-0.0890805\pi$
$5$	1.63439	+	1.55839i	0.730923	+	0.696934i	−0.230172	+	0.973150i	$0.573929\pi$
$6$	−1.72107	+	0.194682i	−0.702626	+	0.0794788i
$7$	0.163264	+	0.847095i	0.0617080	+	0.320172i	0.999645	−	0.0266334i	$-0.00847867\pi$
$7$	0.163264	+	0.847095i	0.0617080	+	0.320172i	−0.937937	+	0.346805i	$0.887267\pi$
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	2.97466	−	0.389129i	0.991552	−	0.129710i
$10$	−1.70669	−	1.47886i	−0.539704	−	0.467656i
$11$	−2.48769	+	1.28249i	−0.750067	+	0.386687i	−0.790473	−	0.612497i	$-0.790165\pi$
$11$	−2.48769	+	1.28249i	−0.750067	+	0.386687i	0.0404057	+	0.999183i	$0.487135\pi$
$12$	1.70986	−	0.276354i	0.493595	−	0.0797765i
$13$	3.57694	+	0.689399i	0.992065	+	0.191205i	0.659361	−	0.751827i	$-0.270827\pi$
$13$	3.57694	+	0.689399i	0.992065	+	0.191205i	0.332704	+	0.943031i	$0.392039\pi$
$14$	−0.203386	−	0.838367i	−0.0543571	−	0.224063i
$15$	3.00030	+	2.50952i	0.774673	+	0.647956i
$16$	0.981929	−	0.189251i	0.245482	−	0.0473128i
$17$	1.44298	+	3.15968i	0.349973	+	0.766334i	0.999979	+	0.00640519i	$0.00203885\pi$
$17$	1.44298	+	3.15968i	0.349973	+	0.766334i	−0.650007	+	0.759929i	$0.725234\pi$
$18$	−2.95277	+	0.530228i	−0.695975	+	0.124976i
$19$	−5.57008	−	2.54377i	−1.27786	−	0.583581i	−0.343250	−	0.939244i	$-0.611528\pi$
$19$	−5.57008	−	2.54377i	−1.27786	−	0.583581i	−0.934614	+	0.355663i	$0.884255\pi$
$20$	1.77513	+	1.39598i	0.396931	+	0.312150i
$21$	0.377541	+	1.44573i	0.0823862	+	0.315484i
$22$	2.42385	−	1.39941i	0.516767	−	0.298355i
$23$	−4.78906	+	0.254799i	−0.998588	+	0.0531292i
$23$	−4.78906	+	0.254799i	−0.998588	+	0.0531292i
$24$	−1.69478	+	0.357399i	−0.345945	+	0.0729539i
$25$	0.00474997	+	0.0997142i	0.000949994	+	0.0199428i
$26$	−3.60569	−	0.518420i	−0.707134	−	0.101671i
$27$	5.09756	−	1.00742i	0.981026	−	0.193879i
$28$	0.243046	+	0.827740i	0.0459314	+	0.156428i
$29$	0.0583106	−	0.610656i	0.0108280	−	0.113396i	−0.988442	−	0.151600i	$-0.951558\pi$
$29$	0.0583106	−	0.610656i	0.0108280	−	0.113396i	0.999270	+	0.0382038i	$0.0121636\pi$
$30$	−3.11631	−	2.36392i	−0.568957	−	0.431591i
$31$	6.01349	−	4.72906i	1.08005	−	0.849364i	0.0908435	−	0.995865i	$-0.471044\pi$
$31$	6.01349	−	4.72906i	1.08005	−	0.849364i	0.989210	+	0.146501i	$0.0468013\pi$
$32$	−0.971812	+	0.235759i	−0.171794	+	0.0416767i
$33$	−4.15533	+	2.49669i	−0.723350	+	0.434618i
$34$	−1.59168	−	3.08744i	−0.272972	−	0.529491i
$35$	−1.05327	+	1.63892i	−0.178035	+	0.277027i
$36$	2.92420	−	0.670126i	0.487366	−	0.111688i
$37$	0.337597	−	1.14975i	0.0555005	−	0.189017i	−0.927077	−	0.374871i	$-0.877687\pi$
$37$	0.337597	−	1.14975i	0.0555005	−	0.189017i	0.982577	+	0.185854i	$0.0595051\pi$
$38$	5.68481	+	2.27585i	0.922198	+	0.369192i
$39$	6.25995	+	0.788893i	1.00239	+	0.126324i
$40$	−1.83954	−	1.30993i	−0.290857	−	0.207118i
$41$	−0.286729	+	0.300713i	−0.0447796	+	0.0469635i	−0.745743	−	0.666234i	$-0.767905\pi$
$41$	−0.286729	+	0.300713i	−0.0447796	+	0.0469635i	0.700963	+	0.713197i	$0.252754\pi$
$42$	−0.445904	−	1.42613i	−0.0688045	−	0.220056i
$43$	−2.06536	+	2.62632i	−0.314965	+	0.400510i	−0.917599	−	0.397507i	$-0.869875\pi$
$43$	−2.06536	+	2.62632i	−0.314965	+	0.400510i	0.602634	+	0.798017i	$0.294118\pi$
$44$	−2.35452	+	1.51316i	−0.354957	+	0.228117i
$45$	5.46818	+	3.99969i	0.815147	+	0.596238i
$46$	4.77151	−	0.482383i	0.703521	−	0.0711235i
$47$	5.42675	+	3.13313i	0.791573	+	0.457015i	0.840516	−	0.541787i	$-0.182252\pi$
$47$	5.42675	+	3.13313i	0.791573	+	0.457015i	−0.0489433	+	0.998802i	$0.515585\pi$
$48$	1.67585	−	0.437635i	0.241888	−	0.0631672i
$49$	5.80766	−	2.32504i	0.829666	−	0.332148i
$50$	−0.00948918	−	0.0993752i	−0.00134197	−	0.0140538i
$51$	2.84971	+	5.29871i	0.399039	+	0.741968i
$52$	3.62627	+	0.346267i	0.502874	+	0.0480186i
$53$	−4.86824	−	5.61825i	−0.668705	−	0.771726i	0.315468	−	0.948936i	$-0.397838\pi$
$53$	−4.86824	−	5.61825i	−0.668705	−	0.771726i	−0.984173	+	0.177210i	$0.943293\pi$
$54$	−5.04385	+	1.24883i	−0.686381	+	0.169945i
$55$	−6.06450	−	1.78070i	−0.817737	−	0.240109i
$56$	−0.282156	−	0.815237i	−0.0377047	−	0.108941i
$57$	−9.91361	−	3.76960i	−1.31309	−	0.499296i
$58$	−0.0291883	+	0.612739i	−0.00383262	+	0.0804566i
$59$	−2.17007	+	11.2594i	−0.282519	+	1.46585i	0.512198	+	0.858868i	$0.328832\pi$
$59$	−2.17007	+	11.2594i	−0.282519	+	1.46585i	−0.794717	+	0.606981i	$0.792381\pi$
$60$	3.22526	+	2.21296i	0.416379	+	0.285692i
$61$	3.41431	−	8.52853i	0.437158	−	1.09197i	−0.532267	−	0.846577i	$-0.678660\pi$
$61$	3.41431	−	8.52853i	0.437158	−	1.09197i	0.969424	−	0.245390i	$-0.0789161\pi$
$62$	−5.78166	+	5.00983i	−0.734271	+	0.636250i
$63$	0.815284	+	2.45628i	0.102716	+	0.309463i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	4.77178	+	6.70102i	0.591866	+	0.831159i
$66$	4.03183	−	2.69158i	0.496283	−	0.331310i
$67$	2.35624	−	4.57047i	0.287860	−	0.558371i	−0.699920	−	0.714221i	$-0.746781\pi$
$67$	2.35624	−	4.57047i	0.287860	−	0.558371i	0.987781	+	0.155850i	$0.0498115\pi$
$68$	1.73679	+	3.00820i	0.210616	+	0.364798i
$69$	−8.24867	+	0.979495i	−0.993023	+	0.117917i
$70$	0.974091	−	1.68718i	0.116426	−	0.201656i
$71$	−3.69376	−	5.74760i	−0.438368	−	0.682114i	0.549833	−	0.835275i	$-0.314691\pi$
$71$	−3.69376	−	5.74760i	−0.438368	−	0.682114i	−0.988201	+	0.153160i	$0.951055\pi$
$72$	−2.88900	+	0.808506i	−0.340472	+	0.0952833i
$73$	0.594917	−	1.30269i	0.0696298	−	0.152468i	−0.871617	−	0.490188i	$-0.836928\pi$
$73$	0.594917	−	1.30269i	0.0696298	−	0.152468i	0.941247	+	0.337720i	$0.109656\pi$
$74$	−0.282507	+	1.16451i	−0.0328408	+	0.135371i
$75$	0.0194346	+	0.171810i	0.00224412	+	0.0198389i
$76$	−5.78666	−	2.00278i	−0.663775	−	0.229735i
$77$	−1.49255	−	1.89793i	−0.170091	−	0.216289i
$78$	−6.29039	−	0.490139i	−0.712247	−	0.0554973i
$79$	−7.85292	+	2.71792i	−0.883523	+	0.305790i	−0.730892	−	0.682493i	$-0.760896\pi$
$79$	−7.85292	+	2.71792i	−0.883523	+	0.305790i	−0.152631	+	0.988283i	$0.548775\pi$
$80$	1.89979	+	1.22092i	0.212403	+	0.136503i
$81$	8.69716	−	2.31505i	0.966351	−	0.257228i
$82$	0.272096	−	0.314016i	0.0300480	−	0.0346772i
$83$	5.46082	−	5.20688i	0.599403	−	0.571530i	−0.328429	−	0.944529i	$-0.606519\pi$
$83$	5.46082	−	5.20688i	0.599403	−	0.571530i	0.927832	+	0.372999i	$0.121671\pi$
$84$	0.513257	+	1.40330i	0.0560009	+	0.153112i
$85$	−2.56562	+	7.41287i	−0.278281	+	0.804039i
$86$	1.93806	−	2.72162i	0.208986	−	0.293480i
$87$	0.0320419	−	1.06202i	0.00343525	−	0.113860i
$88$	2.27985	−	1.62348i	0.243033	−	0.173063i
$89$	−0.401181	+	2.79027i	−0.0425251	+	0.295769i	0.957449	+	0.288602i	$0.0931904\pi$
$89$	−0.401181	+	2.79027i	−0.0425251	+	0.295769i	−0.999974	+	0.00716675i	$0.997719\pi$
$90$	−5.65229	−	3.73497i	−0.595804	−	0.393701i
$91$			3.14256i			0.329430i
$92$	−4.74315	+	0.708874i	−0.494508	+	0.0739052i
$93$	9.86129	−	8.85059i	1.02257	−	0.917763i
$94$	−5.56968	−	2.87137i	−0.574469	−	0.296159i
$95$	−5.13951	−	12.8379i	−0.527303	−	1.31714i
$96$	−1.65313	+	0.516880i	−0.168722	+	0.0527538i
$97$	2.09941	+	0.509311i	0.213163	+	0.0517127i	0.340918	−	0.940093i	$-0.389262\pi$
$97$	2.09941	+	0.509311i	0.213163	+	0.0517127i	−0.127755	+	0.991806i	$0.540777\pi$
$98$	−5.69045	+	2.59874i	−0.574823	+	0.262513i
$99$	−6.90097	+	4.78301i	−0.693574	+	0.480711i
$100$	0.0142069	+	0.0988111i	0.00142069	+	0.00988111i
$101$	−11.3573	−	11.9112i	−1.13010	−	1.18521i	−0.980511	−	0.196463i	$-0.937054\pi$
$101$	−11.3573	−	11.9112i	−1.13010	−	1.18521i	−0.149586	−	0.988749i	$-0.547794\pi$
$102$	−3.09860	−	5.15712i	−0.306807	−	0.510631i
$103$	−11.6828	−	0.556521i	−1.15114	−	0.0548357i	−0.536683	−	0.843784i	$-0.680323\pi$
$103$	−11.6828	−	0.556521i	−1.15114	−	0.0548357i	−0.614459	+	0.788948i	$0.710626\pi$
$104$	−3.63864	−	0.173330i	−0.356798	−	0.0169964i
$105$	−1.63596	+	2.95125i	−0.159654	+	0.288012i
$106$	5.13006	+	5.38025i	0.498275	+	0.522576i
$107$	−2.93412	−	20.4073i	−0.283652	−	1.97284i	−0.223789	−	0.974638i	$-0.571843\pi$
$107$	−2.93412	−	20.4073i	−0.283652	−	1.97284i	−0.0598629	−	0.998207i	$-0.519066\pi$
$108$	4.97871	−	1.48742i	0.479077	−	0.143127i
$109$	−18.4931	+	8.44550i	−1.77131	+	0.808932i	−0.790912	+	0.611930i	$0.790393\pi$
$109$	−18.4931	+	8.44550i	−1.77131	+	0.808932i	−0.980403	+	0.197002i	$0.936879\pi$
$110$	6.14236	+	1.49012i	0.585651	+	0.142077i
$111$	0.454071	−	2.02522i	0.0430985	−	0.192225i
$112$	0.320627	+	0.800889i	0.0302964	+	0.0756769i
$113$	−4.01609	−	2.07044i	−0.377802	−	0.194770i	0.258858	−	0.965915i	$-0.416654\pi$
$113$	−4.01609	−	2.07044i	−0.377802	−	0.194770i	−0.636659	+	0.771145i	$0.719684\pi$
$114$	10.0818	+	3.29362i	0.944242	+	0.308476i
$115$	−8.22428	−	7.04679i	−0.766918	−	0.657116i
$116$		−	0.613434i		−	0.0569559i
$117$	10.9084	+	0.658832i	1.00848	+	0.0609091i
$118$	1.63187	−	11.3499i	0.150226	−	1.04484i
$119$	−2.44096	+	1.73820i	−0.223762	+	0.159340i
$120$	−3.32690	−	2.05699i	−0.303703	−	0.187777i
$121$	−1.83680	+	2.57943i	−0.166982	+	0.234494i
$122$	−3.00464	+	8.68133i	−0.272027	+	0.785971i
$123$	−0.461728	+	0.552026i	−0.0416327	+	0.0497745i
$124$	5.53673	−	5.27926i	0.497213	−	0.474092i
$125$	7.24666	−	8.36310i	0.648161	−	0.748018i
$126$	−0.931235	−	2.41471i	−0.0829610	−	0.215119i
$127$	−13.5105	−	8.68265i	−1.19886	−	0.770461i	−0.220102	−	0.975477i	$-0.570639\pi$
$127$	−13.5105	−	8.68265i	−1.19886	−	0.770461i	−0.978759	+	0.205016i	$0.934275\pi$
$128$	−0.945001	+	0.327068i	−0.0835271	+	0.0289090i
$129$	−3.27410	+	4.77180i	−0.288269	+	0.420133i
$130$	−5.08522	−	6.46638i	−0.446003	−	0.567139i
$131$	−6.72763	−	2.32846i	−0.587796	−	0.203438i	0.0169504	−	0.999856i	$-0.494604\pi$
$131$	−6.72763	−	2.32846i	−0.587796	−	0.203438i	−0.604746	+	0.796418i	$0.706725\pi$
$132$	−3.89919	+	2.88037i	−0.339381	+	0.250704i
$133$	1.24542	−	5.13369i	0.107992	−	0.445147i
$134$	−2.13610	+	4.67740i	−0.184531	+	0.404066i
$135$	9.90138	+	6.29746i	0.852175	+	0.541999i
$136$	−1.87796	−	2.92216i	−0.161033	−	0.250573i
$137$	0.268657	−	0.465328i	0.0229529	−	0.0397556i	−0.854321	−	0.519746i	$-0.826027\pi$
$137$	0.268657	−	0.465328i	0.0229529	−	0.0397556i	0.877274	+	0.479990i	$0.159360\pi$
$138$	8.19272	−	1.37087i	0.697411	−	0.116696i
$139$	10.2225	+	17.7059i	0.867062	+	1.50179i	0.864986	+	0.501797i	$0.167327\pi$
$139$	10.2225	+	17.7059i	0.867062	+	1.50179i	0.00207602	+	0.999998i	$0.499339\pi$
$140$	−0.892709	+	1.73161i	−0.0754477	+	0.146348i
$141$	9.73223	+	4.80439i	0.819601	+	0.404602i
$142$	3.96305	+	5.56533i	0.332572	+	0.467032i
$143$	−9.78248	+	2.87239i	−0.818052	+	0.240202i
$144$	2.84726	−	0.945054i	0.237271	−	0.0787545i
$145$	1.04694	−	0.907182i	0.0869439	−	0.0753373i
$146$	−0.532259	+	1.32952i	−0.0440501	+	0.110032i
$147$	9.77617	−	4.67234i	0.806325	−	0.385368i
$148$	0.226777	−	1.17663i	0.0186410	−	0.0967186i
$149$	−0.488561	+	10.2562i	−0.0400245	+	0.840217i	0.886213	+	0.463277i	$0.153327\pi$
$149$	−0.488561	+	10.2562i	−0.0400245	+	0.840217i	−0.926238	+	0.376940i	$0.876976\pi$
$150$	−0.0275876	−	0.170691i	−0.00225252	−	0.0139368i
$151$	3.29094	+	9.50855i	0.267813	+	0.773795i	0.996076	+	0.0884975i	$0.0282065\pi$
$151$	3.29094	+	9.50855i	0.267813	+	0.773795i	−0.728263	+	0.685297i	$0.759672\pi$
$152$	5.87540	+	1.72517i	0.476558	+	0.139930i
$153$	5.52188	+	8.83744i	0.446417	+	0.714465i
$154$	1.58116	+	1.82476i	0.127414	+	0.147043i
$155$	17.1981	+	1.64222i	1.38139	+	0.131906i
$156$	6.30659	+	0.190275i	0.504931	+	0.0152342i
$157$	0.809772	+	8.48032i	0.0646268	+	0.676803i	0.968502	+	0.249006i	$0.0801040\pi$
$157$	0.809772	+	8.48032i	0.0646268	+	0.676803i	−0.903875	+	0.427797i	$0.859290\pi$
$158$	7.71471	−	3.08850i	0.613749	−	0.245708i
$159$	−9.04666	−	9.16251i	−0.717447	−	0.726634i
$160$	−1.95573	−	1.12914i	−0.154614	−	0.0892663i
$161$	−0.997720	−	4.01519i	−0.0786313	−	0.316441i
$162$	−8.57715	+	2.72626i	−0.673885	+	0.214195i
$163$	7.76037	−	4.98729i	0.607839	−	0.390635i	−0.200207	−	0.979754i	$-0.564161\pi$
$163$	7.76037	−	4.98729i	0.607839	−	0.390635i	0.808046	+	0.589119i	$0.200525\pi$
$164$	−0.256846	+	0.326607i	−0.0200563	+	0.0255037i
$165$	−10.6823	−	2.39506i	−0.831613	−	0.186455i
$166$	−5.20688	+	5.46082i	−0.404133	+	0.423842i
$167$	4.48779	+	3.19574i	0.347276	+	0.247294i	0.740363	−	0.672207i	$-0.234654\pi$
$167$	4.48779	+	3.19574i	0.347276	+	0.247294i	−0.393087	+	0.919501i	$0.628593\pi$
$168$	−0.579447	−	1.37729i	−0.0447053	−	0.106260i
$169$	0.250443	+	0.100262i	0.0192649	+	0.00771249i
$170$	2.21000	−	7.52655i	0.169499	−	0.577260i
$171$	−17.5589	−	5.39936i	−1.34276	−	0.412899i
$172$	−1.80636	+	2.81075i	−0.137734	+	0.214318i
$173$	−2.34391	−	4.54655i	−0.178204	−	0.345668i	0.782768	−	0.622314i	$-0.213807\pi$
$173$	−2.34391	−	4.54655i	−0.178204	−	0.345668i	−0.960972	+	0.276646i	$0.910777\pi$
$174$	0.0185271	+	1.06234i	0.00140454	+	0.0805355i
$175$	−0.0836918	+	0.0203034i	−0.00632651	+	0.00153479i
$176$	−2.20002	+	1.73012i	−0.165833	+	0.130412i
$177$	−2.48326	+	19.7049i	−0.186653	+	1.48111i
$178$	0.267960	−	2.80620i	0.0200844	−	0.210334i
$179$	−3.32893	−	11.3373i	−0.248816	−	0.847388i	−0.985285	−	0.170918i	$-0.945327\pi$
$179$	−3.32893	−	11.3373i	−0.248816	−	0.847388i	0.736470	−	0.676471i	$-0.236491\pi$
$180$	5.82361	+	3.46179i	0.434066	+	0.258027i
$181$	17.1344	+	2.46355i	1.27359	+	0.183114i	0.745747	−	0.666230i	$-0.232093\pi$
$181$	17.1344	+	2.46355i	1.27359	+	0.183114i	0.527840	+	0.849344i	$0.323002\pi$
$182$	−0.149529	−	3.13900i	−0.0110838	−	0.232678i
$183$	4.94120	−	15.1250i	0.365264	−	1.11807i
$184$	4.70405	−	0.933759i	0.346787	−	0.0688377i
$185$	2.34352	−	1.35303i	0.172299	−	0.0994771i
$186$	−9.42900	+	9.30978i	−0.691367	+	0.682626i
$187$	−7.64194	−	6.00969i	−0.558834	−	0.439472i
$188$	5.70000	+	2.60310i	0.415715	+	0.189851i
$189$	1.68563	+	4.15364i	0.122612	+	0.302133i
$190$	5.74454	+	12.5788i	0.416753	+	0.912562i
$191$	−0.839337	+	0.161769i	−0.0607323	+	0.0117052i	−0.219527	−	0.975606i	$-0.570451\pi$
$191$	−0.839337	+	0.161769i	−0.0607323	+	0.0117052i	0.158795	+	0.987312i	$0.449239\pi$
$192$	1.62666	−	0.594953i	0.117394	−	0.0429371i
$193$	4.58950	+	18.9182i	0.330359	+	1.36176i	0.858592	+	0.512660i	$0.171340\pi$
$193$	4.58950	+	18.9182i	0.330359	+	1.36176i	−0.528233	+	0.849100i	$0.677145\pi$
$194$	−2.12127	−	0.408840i	−0.152298	−	0.0293530i
$195$	9.00182	+	11.0448i	0.644633	+	0.790935i
$196$	5.56036	−	2.86656i	0.397168	−	0.204754i
$197$	6.74210	+	5.84207i	0.480355	+	0.416230i	0.861089	−	0.508455i	$-0.169783\pi$
$197$	6.74210	+	5.84207i	0.480355	+	0.416230i	−0.380734	+	0.924685i	$0.624329\pi$
$198$	6.66557	−	5.10596i	0.473702	−	0.362865i
$199$	−2.42043	+	0.348005i	−0.171579	+	0.0246694i	−0.227569	−	0.973762i	$-0.573078\pi$
$199$	−2.42043	+	0.348005i	−0.171579	+	0.0246694i	0.0559896	+	0.998431i	$0.482169\pi$
$200$	−0.0188924	−	0.0980232i	−0.00133590	−	0.00693129i
$201$	3.55800	−	8.16478i	0.250962	−	0.575899i
$202$	11.9112	+	11.3573i	0.838072	+	0.799100i
$203$	0.526803	−	0.0503036i	0.0369743	−	0.00353062i
$204$	3.34048	+	5.00384i	0.233880	+	0.350339i
$205$	−0.937257	+	0.0446471i	−0.0654609	+	0.00311829i
$206$	11.6961			0.814903
$207$	−14.1467	+	2.62150i	−0.983260	+	0.182207i
$208$	3.64277			0.252581
$209$	17.1190	−	0.815479i	1.18415	−	0.0564079i
$210$	1.49368	−	3.02575i	0.103074	−	0.208797i
$211$	−17.8739	+	1.70675i	−1.23049	+	0.117497i	−0.689972	−	0.723836i	$-0.742377\pi$
$211$	−17.8739	+	1.70675i	−1.23049	+	0.117497i	−0.540516	+	0.841333i	$0.681771\pi$
$212$	−5.38025	−	5.13006i	−0.369517	−	0.352334i
$213$	−7.03125	−	9.51828i	−0.481774	−	0.652182i
$214$	3.90181	+	20.2445i	0.266723	+	1.38389i
$215$	−7.46845	+	1.07380i	−0.509344	+	0.0732326i
$216$	−4.90230	+	1.72263i	−0.333559	+	0.117210i
$217$	4.98775	+	4.32191i	0.338590	+	0.293390i
$218$	18.0703	−	9.31587i	1.22387	−	0.630950i
$219$	0.881605	−	2.31852i	0.0595733	−	0.156671i
$220$	−6.20630	−	1.19617i	−0.418429	−	0.0806456i
$221$	2.98316	+	12.2968i	0.200669	+	0.827169i
$222$	−0.357193	+	2.04453i	−0.0239732	+	0.137220i
$223$	6.63120	−	1.27806i	0.444058	−	0.0855851i	0.0376792	−	0.999290i	$-0.488004\pi$
$223$	6.63120	−	1.27806i	0.444058	−	0.0855851i	0.406379	+	0.913705i	$0.366791\pi$
$224$	−0.358372	−	0.784725i	−0.0239447	−	0.0524317i
$225$	0.0529312	+	0.294767i	0.00352875	+	0.0196511i
$226$	4.11005	+	1.87700i	0.273397	+	0.124856i
$227$	7.14325	+	5.61751i	0.474114	+	0.372847i	0.826435	−	0.563032i	$-0.190365\pi$
$227$	7.14325	+	5.61751i	0.474114	+	0.372847i	−0.352321	+	0.935879i	$0.614608\pi$
$228$	−10.2270	−	2.81018i	−0.677303	−	0.186109i
$229$	9.05041	−	5.22526i	0.598068	−	0.345295i	−0.170213	−	0.985407i	$-0.554446\pi$
$229$	9.05041	−	5.22526i	0.598068	−	0.345295i	0.768281	+	0.640113i	$0.221112\pi$
$230$	8.55027	+	6.64748i	0.563788	+	0.438322i
$231$	−2.79335	−	3.11234i	−0.183789	−	0.204777i
$232$	0.0291883	+	0.612739i	0.00191631	+	0.0402283i
$233$	25.6643	+	3.68996i	1.68132	+	0.241737i	0.915789	−	0.401660i	$-0.131567\pi$
$233$	25.6643	+	3.68996i	1.68132	+	0.241737i	0.765532	+	0.643397i	$0.222476\pi$
$234$	−10.9274	−	0.139042i	−0.714348	−	0.00908947i
$235$	3.98679	+	13.5778i	0.260070	+	0.885716i
$236$	−1.08997	+	11.4147i	−0.0709510	+	0.743033i
$237$	−13.2670	+	5.58163i	−0.861781	+	0.362566i
$238$	2.35549	−	1.85237i	0.152683	−	0.120072i
$239$	−15.2106	+	3.69005i	−0.983890	+	0.238689i	−0.695265	−	0.718753i	$-0.744713\pi$
$239$	−15.2106	+	3.69005i	−0.983890	+	0.238689i	−0.288625	+	0.957442i	$0.593198\pi$
$240$	3.42101	+	1.89636i	0.220825	+	0.122410i
$241$	−0.730810	−	1.41757i	−0.0470756	−	0.0913139i	0.864124	−	0.503279i	$-0.167873\pi$
$241$	−0.730810	−	1.41757i	−0.0470756	−	0.0913139i	−0.911200	+	0.411965i	$0.864843\pi$
$242$	1.71199	−	2.66391i	0.110051	−	0.171243i
$243$	14.7715	−	4.98035i	0.947590	−	0.319489i
$244$	2.58816	−	8.81447i	0.165690	−	0.564288i
$245$	13.1153	+	5.25058i	0.837907	+	0.335447i
$246$	0.434939	−	0.573371i	0.0277307	−	0.0365568i
$247$	−18.1702	−	12.9389i	−1.15614	−	0.823283i
$248$	−5.27926	+	5.53673i	−0.335234	+	0.351583i
$249$	8.85229	−	9.61424i	0.560991	−	0.609278i
$250$	−6.84052	+	8.69843i	−0.432633	+	0.550137i
$251$	14.7985	−	9.51044i	0.934075	−	0.600293i	0.0173660	−	0.999849i	$-0.494472\pi$
$251$	14.7985	−	9.51044i	0.934075	−	0.600293i	0.916709	+	0.399556i	$0.130836\pi$
$252$	1.04508	+	2.36766i	0.0658336	+	0.149149i
$253$	11.5869	−	6.77580i	0.728464	−	0.425991i
$254$	13.9083	+	8.02996i	0.872685	+	0.503845i
$255$	−3.59992	+	13.1011i	−0.225436	+	0.820425i
$256$	0.928368	−	0.371662i	0.0580230	−	0.0232289i
$257$	0.745700	+	7.80932i	0.0465155	+	0.487132i	0.988473	+	0.151399i	$0.0483779\pi$
$257$	0.745700	+	7.80932i	0.0465155	+	0.487132i	−0.941957	+	0.335733i	$0.891016\pi$
$258$	3.04334	−	4.92218i	0.189470	−	0.306442i
$259$	1.02906	+	0.0982636i	0.0639429	+	0.00610580i
$260$	5.38714	+	6.21709i	0.334096	+	0.385568i
$261$	−0.0641701	−	1.83918i	−0.00397203	−	0.113842i
$262$	6.83080	+	2.00570i	0.422008	+	0.123913i
$263$	−8.58327	−	24.7997i	−0.529267	−	1.52922i	−0.819971	−	0.572404i	$-0.806011\pi$
$263$	−8.58327	−	24.7997i	−0.529267	−	1.52922i	0.290704	−	0.956813i	$-0.406110\pi$
$264$	3.75772	−	3.06264i	0.231272	−	0.188493i
$265$	0.798809	−	16.7691i	0.0490705	−	1.03012i
$266$	−0.999738	+	5.18713i	−0.0612979	+	0.318044i
$267$	−0.379296	+	4.86784i	−0.0232125	+	0.297907i
$268$	1.91112	−	4.77375i	0.116740	−	0.291603i
$269$	−3.59793	+	3.11762i	−0.219370	+	0.190085i	−0.757612	−	0.652705i	$-0.773634\pi$
$269$	−3.59793	+	3.11762i	−0.219370	+	0.190085i	0.538242	+	0.842790i	$0.319089\pi$
$270$	−10.1898	−	5.81921i	−0.620132	−	0.354146i
$271$	−16.0692	+	4.71833i	−0.976132	+	0.286618i	−0.730627	−	0.682777i	$-0.760772\pi$
$271$	−16.0692	+	4.71833i	−0.976132	+	0.286618i	−0.245505	+	0.969395i	$0.578954\pi$
$272$	2.01487	+	2.82949i	0.122170	+	0.171563i
$273$	0.353758	+	5.43157i	0.0214104	+	0.328733i
$274$	−0.246212	+	0.477584i	−0.0148742	+	0.0288519i
$275$	−0.139699	−	0.241966i	−0.00842419	−	0.0145911i
$276$	−8.11821	+	1.75915i	−0.488659	+	0.105888i
$277$	4.88674	−	8.46407i	0.293615	−	0.508557i	−0.681046	−	0.732240i	$-0.738475\pi$
$277$	4.88674	−	8.46407i	0.293615	−	0.508557i	0.974662	+	0.223683i	$0.0718082\pi$
$278$	−11.0534	−	17.1994i	−0.662939	−	1.03155i
$279$	16.0478	−	16.4073i	0.960759	−	0.982282i
$280$	0.809304	−	1.77213i	0.0483652	−	0.105905i
$281$	−5.82113	+	23.9950i	−0.347259	+	1.43142i	0.483770	+	0.875195i	$0.339267\pi$
$281$	−5.82113	+	23.9950i	−0.347259	+	1.43142i	−0.831030	+	0.556228i	$0.812248\pi$
$282$	−9.94981	−	4.33587i	−0.592502	−	0.258197i
$283$	14.1044	+	4.88159i	0.838422	+	0.290181i	0.712336	−	0.701839i	$-0.247637\pi$
$283$	14.1044	+	4.88159i	0.838422	+	0.290181i	0.126086	+	0.992019i	$0.459758\pi$
$284$	−4.22338	−	5.37046i	−0.250611	−	0.318678i
$285$	−10.3282	−	21.6103i	−0.611792	−	1.28008i
$286$	9.63472	−	3.33461i	0.569713	−	0.197180i
$287$	−0.301545	−	0.193791i	−0.0177996	−	0.0114391i
$288$	−2.79906	+	1.07946i	−0.164936	+	0.0636079i
$289$	3.23126	−	3.72908i	0.190074	−	0.219357i
$290$	−1.00259	+	0.955970i	−0.0588742	+	0.0561365i
$291$	3.68593	+	0.643957i	0.216073	+	0.0377495i
$292$	0.468395	−	1.35334i	0.0274108	−	0.0791982i
$293$	−5.63357	+	7.91124i	−0.329117	+	0.462180i	−0.945667	−	0.325135i	$-0.894590\pi$
$293$	−5.63357	+	7.91124i	−0.329117	+	0.462180i	0.616551	+	0.787315i	$0.288530\pi$
$294$	−9.54278	+	5.13221i	−0.556546	+	0.299317i
$295$	−21.0933	+	15.0205i	−1.22810	+	0.874525i
$296$	−0.170534	+	1.18609i	−0.00991209	+	0.0689401i
$297$	−11.3891	+	9.04375i	−0.660865	+	0.524772i
$298$		−	10.2678i		−	0.594797i
$299$	−17.3058	−	2.39017i	−1.00082	−	0.138227i
$300$	0.0356782	+	0.169185i	0.00205988	+	0.00976789i
$301$	−2.56194	−	1.32077i	−0.147668	−	0.0761280i
$302$	−3.73965	−	9.34119i	−0.215193	−	0.537525i
$303$	−20.9707	−	19.3088i	−1.20474	−	1.10926i
$304$	−5.95083	−	1.44366i	−0.341304	−	0.0827994i
$305$	18.8711	−	8.61815i	1.08056	−	0.493474i
$306$	−5.93612	−	8.56469i	−0.339346	−	0.489611i
$307$	4.61240	+	32.0800i	0.263244	+	1.83090i	0.508049	+	0.861328i	$0.330367\pi$
$307$	4.61240	+	32.0800i	0.263244	+	1.83090i	−0.244805	+	0.969572i	$0.578724\pi$
$308$	−1.66620	−	1.74746i	−0.0949403	−	0.0995705i
$309$	−20.2551	+	0.353248i	−1.15227	+	0.0200956i
$310$	−17.2568	−	0.822042i	−0.980120	−	0.0466889i
$311$	30.1905	+	1.43815i	1.71194	+	0.0815500i	0.880497	−	0.474053i	$-0.157209\pi$
$311$	30.1905	+	1.43815i	1.71194	+	0.0815500i	0.831448	+	0.555603i	$0.187512\pi$
$312$	−6.30850	+	0.110020i	−0.357149	+	0.00622866i
$313$	−15.3093	−	16.0559i	−0.865332	−	0.907534i	0.131148	−	0.991363i	$-0.458134\pi$
$313$	−15.3093	−	16.0559i	−0.865332	−	0.907534i	−0.996480	+	0.0838284i	$0.973285\pi$
$314$	−1.21236	−	8.43218i	−0.0684177	−	0.475855i
$315$	−2.49536	+	5.28507i	−0.140597	+	0.297780i
$316$	−7.55901	+	3.45208i	−0.425228	+	0.194195i
$317$	−26.0147	−	6.31110i	−1.46113	−	0.354467i	−0.575097	−	0.818085i	$-0.695036\pi$
$317$	−26.0147	−	6.31110i	−1.46113	−	0.354467i	−0.886035	+	0.463618i	$0.846551\pi$
$318$	9.47239	+	8.72167i	0.531185	+	0.489087i
$319$	0.638104	+	1.59391i	0.0357270	+	0.0892417i
$320$	2.00724	+	1.03480i	0.112208	+	0.0578473i
$321$	−7.36854	−	34.9414i	−0.411272	−	1.95024i
$322$	1.18764	+	3.96316i	0.0661846	+	0.220859i
$323$		−	21.2702i		−	1.18351i
$324$	8.43772	−	3.13129i	0.468762	−	0.173960i
$325$	−0.0517524	+	0.359946i	−0.00287071	+	0.0199662i
$326$	−7.51428	+	5.35089i	−0.416177	+	0.296359i
$327$	−31.0125	+	16.6789i	−1.71500	+	0.922344i
$328$	0.241015	−	0.338458i	0.0133078	−	0.0186882i
$329$	−1.76807	+	5.10850i	−0.0974767	+	0.281641i
$330$	10.7841	+	1.88406i	0.593647	+	0.103714i
$331$	−10.2190	+	9.74378i	−0.561686	+	0.535566i	−0.916847	−	0.399239i	$-0.869274\pi$
$331$	−10.2190	+	9.74378i	−0.561686	+	0.535566i	0.355161	+	0.934805i	$0.384426\pi$
$332$	4.94115	−	5.70239i	0.271181	−	0.312959i
$333$	0.556833	−	3.55147i	0.0305143	−	0.194620i
$334$	−4.63477	−	2.97858i	−0.253603	−	0.162981i
$335$	10.9736	−	3.79800i	0.599552	−	0.207507i
$336$	0.644325	+	1.34815i	0.0351508	+	0.0735478i
$337$	14.1631	+	18.0099i	0.771515	+	0.981061i	0.999972	+	0.00750700i	$0.00238957\pi$
$337$	14.1631	+	18.0099i	0.771515	+	0.981061i	−0.228457	+	0.973554i	$0.573368\pi$
$338$	−0.254930	−	0.0882323i	−0.0138664	−	0.00479920i
$339$	−7.17443	−	3.12643i	−0.389662	−	0.169804i
$340$	−1.84936	+	7.62319i	−0.100296	+	0.413425i
$341$	−8.89471	+	19.4767i	−0.481676	+	1.05472i
$342$	17.7959	+	4.55776i	0.962295	+	0.246455i
$343$	6.18253	+	9.62020i	0.333825	+	0.519442i
$344$	1.67057	−	2.89352i	0.0900713	−	0.156008i
$345$	−15.0080	−	11.2538i	−0.808004	−	0.605883i
$346$	2.55759	+	4.42987i	0.137497	+	0.238152i
$347$	3.83219	−	7.43342i	0.205723	−	0.399047i	−0.763290	−	0.646056i	$-0.776417\pi$
$347$	3.83219	−	7.43342i	0.205723	−	0.399047i	0.969013	+	0.247009i	$0.0794477\pi$
$348$	−0.0690542	−	1.06025i	−0.00370169	−	0.0568355i
$349$	8.18843	+	11.4990i	0.438317	+	0.615529i	0.973356	−	0.229297i	$-0.0736428\pi$
$349$	8.18843	+	11.4990i	0.438317	+	0.615529i	−0.535040	+	0.844827i	$0.679703\pi$
$350$	0.0826309	−	0.0242626i	0.00441681	−	0.00129689i
$351$	18.9282	−	0.0892423i	1.01031	−	0.00476340i
$352$	2.11521	−	1.83284i	0.112741	−	0.0976906i
$353$	9.32322	−	23.2883i	0.496225	−	1.23951i	−0.443097	−	0.896473i	$-0.646120\pi$
$353$	9.32322	−	23.2883i	0.496225	−	1.23951i	0.939322	−	0.343036i	$-0.111455\pi$
$354$	1.54285	−	19.8007i	0.0820014	−	1.05240i
$355$	2.91995	−	15.1502i	0.154975	−	0.804087i
$356$	−0.134132	+	2.81577i	−0.00710898	+	0.149236i
$357$	−4.02326	+	3.27906i	−0.212933	+	0.173546i
$358$	3.86461	+	11.1660i	0.204251	+	0.590144i
$359$	−11.1734	−	3.28080i	−0.589709	−	0.173154i	−0.0267543	−	0.999642i	$-0.508517\pi$
$359$	−11.1734	−	3.28080i	−0.589709	−	0.173154i	−0.562954	+	0.826488i	$0.690335\pi$
$360$	−5.98173	−	3.18077i	−0.315265	−	0.167642i
$361$	12.1127	+	13.9788i	0.637508	+	0.735724i
$362$	−17.2322	−	1.64547i	−0.905703	−	0.0864841i
$363$	−2.88435	+	4.66503i	−0.151389	+	0.244851i
$364$	0.298719	+	3.12833i	0.0156571	+	0.163969i
$365$	3.00243	−	1.20199i	0.157154	−	0.0629150i
$366$	−4.21593	+	15.3430i	−0.220370	+	0.801989i
$367$	7.01698	+	4.05125i	0.366283	+	0.211474i	0.671834	−	0.740702i	$-0.265507\pi$
$367$	7.01698	+	4.05125i	0.366283	+	0.211474i	−0.305550	+	0.952176i	$0.598840\pi$
$368$	−4.65429	+	1.15653i	−0.242622	+	0.0602883i
$369$	−0.735905	+	1.00609i	−0.0383097	+	0.0523751i
$370$	−2.27649	+	1.46301i	−0.118349	+	0.0760583i
$371$	3.96438	−	5.04112i	0.205820	−	0.261722i
$372$	8.97534	−	9.74789i	0.465350	−	0.505404i
$373$	16.5085	−	17.3136i	0.854777	−	0.896465i	−0.140836	−	0.990033i	$-0.544979\pi$
$373$	16.5085	−	17.3136i	0.854777	−	0.896465i	0.995613	+	0.0935684i	$0.0298274\pi$
$374$	7.91924	+	5.63927i	0.409494	+	0.291600i
$375$	11.5836	−	15.2704i	0.598176	−	0.788562i
$376$	−5.81740	−	2.32894i	−0.300010	−	0.120106i
$377$	0.629559	−	2.14408i	0.0324239	−	0.110426i
$378$	−1.88136	−	4.06873i	−0.0967667	−	0.209273i
$379$	−19.3303	+	30.0786i	−0.992932	+	1.54503i	−0.163411	+	0.986558i	$0.552250\pi$
$379$	−19.3303	+	30.0786i	−0.992932	+	1.54503i	−0.829522	+	0.558475i	$0.811387\pi$
$380$	−6.33656	−	12.2912i	−0.325059	−	0.630526i
$381$	−24.3288	−	13.4861i	−1.24640	−	0.690915i
$382$	0.830689	−	0.201523i	0.0425017	−	0.0103108i
$383$	−9.50460	+	7.47450i	−0.485662	+	0.381929i	−0.830754	−	0.556640i	$-0.812090\pi$
$383$	−9.50460	+	7.47450i	−0.485662	+	0.381929i	0.345091	+	0.938569i	$0.387848\pi$
$384$	−1.59651	+	0.671679i	−0.0814716	+	0.0342765i
$385$	0.518304	−	5.42793i	0.0264152	−	0.276633i
$386$	−5.48446	−	18.6784i	−0.279152	−	0.950703i
$387$	−5.12176	+	8.61609i	−0.260354	+	0.437980i
$388$	2.13832	+	0.307443i	0.108557	+	0.0156081i
$389$	1.46925	+	30.8434i	0.0744941	+	1.56382i	0.658817	+	0.752303i	$0.271057\pi$
$389$	1.46925	+	30.8434i	0.0744941	+	1.56382i	−0.584323	+	0.811521i	$0.698640\pi$
$390$	−9.51715	−	10.6040i	−0.481920	−	0.536953i
$391$	−7.71557	−	14.7642i	−0.390193	−	0.746658i
$392$	−5.41766	+	3.12789i	−0.273633	+	0.157982i
$393$	−11.8901	−	3.26715i	−0.599775	−	0.164806i
$394$	−7.01244	−	5.51465i	−0.353282	−	0.277824i
$395$	−17.0704	−	7.79577i	−0.858903	−	0.392248i
$396$	−6.41507	+	5.41734i	−0.322369	+	0.272231i
$397$	−14.4232	−	31.5824i	−0.723880	−	1.58508i	−0.808385	−	0.588654i	$-0.799658\pi$
$397$	−14.4232	−	31.5824i	−0.723880	−	1.58508i	0.0845048	−	0.996423i	$-0.473069\pi$
$398$	2.40112	−	0.462779i	0.120358	−	0.0231970i
$399$	1.57467	−	9.01321i	0.0788321	−	0.451225i
$400$	0.0235352	+	0.0970132i	0.00117676	+	0.00485066i
$401$	16.8650	+	3.25046i	0.842196	+	0.162320i	0.592063	−	0.805891i	$-0.298314\pi$
$401$	16.8650	+	3.25046i	0.842196	+	0.162320i	0.250133	+	0.968211i	$0.419526\pi$
$402$	−3.16547	+	8.32483i	−0.157879	+	0.415205i
$403$	24.7701	−	12.7699i	1.23389	−	0.636112i
$404$	−12.4381	−	10.7777i	−0.618821	−	0.536211i
$405$	17.8223	+	9.76987i	0.885599	+	0.485469i
$406$	−0.523813	+	0.0753130i	−0.0259964	+	0.00373772i
$407$	0.634710	+	3.29319i	0.0314614	+	0.163237i
$408$	−3.57479	−	4.83922i	−0.176978	−	0.239577i
$409$	−2.08873	−	1.99160i	−0.103281	−	0.0984784i	0.636679	−	0.771129i	$-0.280307\pi$
$409$	−2.08873	−	1.99160i	−0.103281	−	0.0984784i	−0.739961	+	0.672650i	$0.765156\pi$
$410$	0.934071	−	0.0891930i	0.0461305	−	0.00440493i
$411$	0.411962	−	0.834510i	0.0203206	−	0.0411634i
$412$	−11.6828	+	0.556521i	−0.575571	+	0.0274178i
$413$	−9.89207			−0.486757
$414$	14.0059	−	3.29166i	0.688352	−	0.161776i
$415$	17.0395			0.836436
$416$	−3.63864	+	0.173330i	−0.178399	+	0.00849820i
$417$	19.6616	+	29.4519i	0.962833	+	1.44227i
$418$	−17.0608	+	1.62911i	−0.834472	+	0.0796824i
$419$	9.07643	+	8.65436i	0.443413	+	0.422793i	0.878609	−	0.477543i	$-0.158472\pi$
$419$	9.07643	+	8.65436i	0.443413	+	0.422793i	−0.435196	+	0.900336i	$0.643321\pi$
$420$	−1.34802	+	3.09339i	−0.0657767	+	0.150942i
$421$	−3.20229	−	16.6150i	−0.156070	−	0.809768i	−0.972604	−	0.232470i	$-0.925319\pi$
$421$	−3.20229	−	16.6150i	−0.156070	−	0.809768i	0.816534	−	0.577298i	$-0.195893\pi$
$422$	17.7724	−	2.55529i	0.865148	−	0.124390i
$423$	17.3619	+	7.20829i	0.844165	+	0.350479i
$424$	5.61825	+	4.86824i	0.272846	+	0.236423i
$425$	−0.308210	+	0.158893i	−0.0149504	+	0.00770746i
$426$	7.47619	+	9.17294i	0.362223	+	0.444430i
$427$	7.78191	+	1.49984i	0.376593	+	0.0725823i
$428$	−4.86067	−	20.0359i	−0.234949	−	0.968474i
$429$	−16.5846	+	6.06583i	−0.800711	+	0.292861i
$430$	7.40889	−	1.42795i	0.357289	−	0.0688617i
$431$	5.86511	+	12.8428i	0.282512	+	0.618616i	0.996685	−	0.0813536i	$-0.0259243\pi$
$431$	5.86511	+	12.8428i	0.282512	+	0.618616i	−0.714173	+	0.699969i	$0.753197\pi$
$432$	4.81478	−	1.95394i	0.231651	−	0.0940088i
$433$	31.3666	+	14.3247i	1.50738	+	0.688399i	0.986278	−	0.165093i	$-0.0527923\pi$
$433$	31.3666	+	14.3247i	1.50738	+	0.688399i	0.521106	+	0.853492i	$0.325520\pi$
$434$	−5.18774	−	4.07968i	−0.249020	−	0.195831i
$435$	1.70740	−	1.68582i	0.0818638	−	0.0808287i
$436$	−17.6065	+	10.1651i	−0.843200	+	0.486822i
$437$	27.3236	+	10.7630i	1.30706	+	0.514865i
$438$	−0.770287	+	2.35784i	−0.0368057	+	0.112662i
$439$	−0.662547	−	13.9086i	−0.0316216	−	0.663820i	−0.957921	−	0.287032i	$-0.907332\pi$
$439$	−0.662547	−	13.9086i	−0.0316216	−	0.663820i	0.926299	−	0.376788i	$-0.122972\pi$
$440$	6.25619	+	0.899504i	0.298252	+	0.0428822i
$441$	16.3711	−	9.17612i	0.779574	−	0.436958i
$442$	−3.56488	−	12.1409i	−0.169564	−	0.577483i
$443$	0.751839	−	7.87362i	0.0357210	−	0.374087i	−0.959881	−	0.280406i	$-0.909531\pi$
$443$	0.751839	−	7.87362i	0.0357210	−	0.374087i	0.995602	−	0.0936803i	$-0.0298632\pi$
$444$	0.259506	−	2.05921i	0.0123156	−	0.0977257i
$445$	−5.00403	+	3.93521i	−0.237214	+	0.186547i
$446$	−6.56287	+	1.59214i	−0.310761	+	0.0753898i
$447$	0.310111	+	17.7816i	0.0146678	+	0.841042i
$448$	0.395305	+	0.766784i	0.0186764	+	0.0362272i
$449$	−17.1296	+	26.6542i	−0.808396	+	1.25789i	0.154493	+	0.987994i	$0.450625\pi$
$449$	−17.1296	+	26.6542i	−0.808396	+	1.25789i	−0.962890	+	0.269895i	$0.913011\pi$
$450$	−0.0668968	−	0.291915i	−0.00315355	−	0.0137610i
$451$	0.327631	−	1.11581i	0.0154276	−	0.0525415i
$452$	−4.19471	−	1.67931i	−0.197303	−	0.0789880i
$453$	6.75840	+	16.0640i	0.317537	+	0.754753i
$454$	−7.40245	−	5.27126i	−0.347414	−	0.247392i
$455$	−4.89734	+	5.13618i	−0.229591	+	0.240788i
$456$	10.3492	+	2.32038i	0.484645	+	0.108662i
$457$	−18.7382	+	23.8276i	−0.876536	+	1.11461i	0.116072	+	0.993241i	$0.462970\pi$
$457$	−18.7382	+	23.8276i	−0.876536	+	1.11461i	−0.992608	+	0.121365i	$0.961273\pi$
$458$	−8.79153	+	5.64997i	−0.410801	+	0.264006i
$459$	10.5388	+	14.6529i	0.491908	+	0.683941i
$460$	−8.85688	−	6.23311i	−0.412954	−	0.290620i
$461$	−3.16870	−	1.82945i	−0.147581	−	0.0852059i	0.424391	−	0.905479i	$-0.360488\pi$
$461$	−3.16870	−	1.82945i	−0.147581	−	0.0852059i	−0.571972	+	0.820273i	$0.693821\pi$
$462$	2.93827	+	2.97590i	0.136701	+	0.138451i
$463$	34.5046	−	13.8136i	1.60357	−	0.641971i	0.614429	−	0.788972i	$-0.289386\pi$
$463$	34.5046	−	13.8136i	1.60357	−	0.641971i	0.989136	+	0.147001i	$0.0469621\pi$
$464$	−0.0583106	−	0.610656i	−0.00270700	−	0.0283490i
$465$	29.9099	+	0.902407i	1.38704	+	0.0418481i
$466$	−25.8108	−	2.46463i	−1.19566	−	0.114172i
$467$	0.719187	+	0.829986i	0.0332800	+	0.0384072i	0.772146	−	0.635446i	$-0.219184\pi$
$467$	0.719187	+	0.829986i	0.0332800	+	0.0384072i	−0.738866	+	0.673853i	$0.764638\pi$
$468$	10.9217	−	0.381063i	0.504854	−	0.0176146i
$469$	4.25631	+	1.24976i	0.196538	+	0.0577087i
$470$	−4.62833	−	13.3727i	−0.213489	−	0.616836i
$471$	2.35423	+	14.5661i	0.108477	+	0.671172i
$472$	0.545603	−	11.4536i	0.0251134	−	0.527196i
$473$	1.76974	−	9.18229i	0.0813728	−	0.422202i
$474$	12.9863	−	6.20658i	0.596482	−	0.285078i
$475$	0.227192	−	0.567499i	0.0104243	−	0.0260386i
$476$	−2.26468	+	1.96236i	−0.103801	+	0.0899444i
$477$	−16.6676	−	14.8180i	−0.763156	−	0.678469i
$478$	15.0178	−	4.40961i	0.686897	−	0.201691i
$479$	20.4984	+	28.7859i	0.936594	+	1.31526i	0.948979	+	0.315339i	$0.102118\pi$
$479$	20.4984	+	28.7859i	0.936594	+	1.31526i	−0.0123848	+	0.999923i	$0.503942\pi$
$480$	−3.50736	−	1.73144i	−0.160089	−	0.0790289i
$481$	2.00020	−	3.87984i	0.0912012	−	0.176906i
$482$	0.797433	+	1.38119i	0.0363221	+	0.0629117i
$483$	−2.17644	−	6.82749i	−0.0990313	−	0.310661i
$484$	−1.58330	+	2.74235i	−0.0719681	+	0.124652i
$485$	2.63756	+	4.10412i	0.119765	+	0.186358i
$486$	−14.5178	+	5.67756i	−0.658539	+	0.257539i
$487$	−2.46408	+	5.39558i	−0.111658	+	0.244497i	−0.957209	−	0.289398i	$-0.906545\pi$
$487$	−2.46408	+	5.39558i	−0.111658	+	0.244497i	0.845551	+	0.533895i	$0.179272\pi$
$488$	−2.16582	+	8.92763i	−0.0980421	+	0.404135i
$489$	12.8515	−	9.49356i	0.581166	−	0.429314i
$490$	−13.3503	−	4.62058i	−0.603105	−	0.208737i
$491$	−23.0390	−	29.2965i	−1.03974	−	1.32213i	−0.945158	−	0.326614i	$-0.894092\pi$
$491$	−23.0390	−	29.2965i	−1.03974	−	1.32213i	−0.0945781	−	0.995517i	$-0.530150\pi$
$492$	−0.407164	+	0.593417i	−0.0183564	+	0.0267533i
$493$	2.01362	−	0.696919i	0.0906887	−	0.0313877i
$494$	18.7652	+	12.0597i	0.844288	+	0.542591i
$495$	−18.7327	−	2.93709i	−0.841973	−	0.132012i
$496$	5.00983	−	5.78166i	0.224948	−	0.259604i
$497$	4.26570	−	4.06734i	0.191343	−	0.182445i
$498$	−8.38480	+	10.0246i	−0.375732	+	0.449211i
$499$	−11.3840	+	32.8920i	−0.509619	+	1.47245i	0.337643	+	0.941274i	$0.390370\pi$
$499$	−11.3840	+	32.8920i	−0.509619	+	1.47245i	−0.847263	+	0.531174i	$0.821751\pi$
$500$	6.41889	−	9.01407i	0.287061	−	0.403121i
$501$	8.11639	+	5.01829i	0.362614	+	0.224201i
$502$	−14.3292	+	10.2038i	−0.639545	+	0.455418i
$503$	−2.54384	+	17.6928i	−0.113424	+	0.788882i	0.851122	+	0.524968i	$0.175923\pi$
$503$	−2.54384	+	17.6928i	−0.113424	+	0.788882i	−0.964546	+	0.263914i	$0.914986\pi$
$504$	−1.15655	−	2.31526i	−0.0515169	−	0.103130i
$505$		−	37.1668i		−	1.65390i
$506$	−11.2514	+	7.31946i	−0.500186	+	0.325389i
$507$	0.444150	+	0.145100i	0.0197254	+	0.00644412i
$508$	−14.2746	−	7.35908i	−0.633334	−	0.326507i
$509$	−2.74136	−	6.84759i	−0.121509	−	0.303514i	0.855126	−	0.518420i	$-0.173480\pi$
$509$	−2.74136	−	6.84759i	−0.121509	−	0.303514i	−0.976635	+	0.214906i	$0.931055\pi$
$510$	2.97247	−	13.2576i	0.131623	−	0.587056i
$511$	1.20063	+	0.291269i	0.0531126	+	0.0128850i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	−30.9565	−	7.35559i	−1.36676	−	0.324757i
$514$	−1.11644	−	7.76499i	−0.0492440	−	0.342499i
$515$	−18.2270	−	19.1160i	−0.803180	−	0.842350i
$516$	−2.80569	+	5.06141i	−0.123514	+	0.222816i
$517$	−17.5183	−	0.834500i	−0.770454	−	0.0367013i
$518$	−1.03257	−	0.0491875i	−0.0453687	−	0.00216118i
$519$	−4.56299	−	7.59436i	−0.200293	−	0.333355i
$520$	−5.67686	−	5.95372i	−0.248947	−	0.261088i
$521$	3.07629	+	21.3961i	0.134775	+	0.937380i	0.939211	+	0.343341i	$0.111559\pi$
$521$	3.07629	+	21.3961i	0.134775	+	0.937380i	−0.804436	+	0.594039i	$0.797532\pi$
$522$	0.151609	+	1.83405i	0.00663576	+	0.0802740i
$523$	−6.64144	+	3.03304i	−0.290410	+	0.132626i	−0.555293	−	0.831655i	$-0.687394\pi$
$523$	−6.64144	+	3.03304i	−0.290410	+	0.132626i	0.264883	+	0.964280i	$0.414667\pi$
$524$	−6.91850	−	1.67841i	−0.302236	−	0.0733217i
$525$	−0.142366	+	0.0445134i	−0.00621338	+	0.00194272i
$526$	9.75357	+	24.3632i	0.425276	+	1.06229i
$527$	23.6196	+	12.1767i	1.02889	+	0.530428i
$528$	−3.60774	+	3.23797i	−0.157007	+	0.140915i
$529$	22.8702	−	2.44049i	0.994355	−	0.106108i
$530$			16.7881i			0.729228i
$531$	−2.07385	+	34.3373i	−0.0899976	+	1.49011i
$532$	0.751792	−	5.22883i	0.0325943	−	0.226698i
$533$	−1.23292	+	0.877962i	−0.0534039	+	0.0380287i
$534$	0.147245	−	4.88037i	0.00637191	−	0.211194i
$535$	27.0070	−	37.9260i	1.16761	−	1.63968i
$536$	−1.68181	+	4.85927i	−0.0726432	+	0.209889i
$537$	−7.02992	−	19.2205i	−0.303363	−	0.829426i
$538$	3.44551	−	3.28529i	0.148547	−	0.141639i
$539$	−11.4658	+	13.2323i	−0.493868	+	0.569954i
$540$	10.4552	+	5.32776i	0.449918	+	0.229270i
$541$	−23.8172	−	15.3064i	−1.02398	−	0.658072i	−0.0830051	−	0.996549i	$-0.526452\pi$
$541$	−23.8172	−	15.3064i	−1.02398	−	0.658072i	−0.940975	+	0.338477i	$0.890088\pi$
$542$	15.8265	−	5.47759i	0.679804	−	0.235283i
$543$	29.8922	+	2.32916i	1.28280	+	0.0999537i
$544$	−2.14722	−	2.73041i	−0.0920614	−	0.117066i
$545$	−43.3864	−	15.0162i	−1.85847	−	0.643222i
$546$	−0.611801	−	5.40858i	−0.0261827	−	0.231466i
$547$	4.80264	−	19.7968i	0.205346	−	0.846448i	−0.772141	−	0.635452i	$-0.780814\pi$
$547$	4.80264	−	19.7968i	0.205346	−	0.846448i	0.977487	−	0.210997i	$-0.0676709\pi$
$548$	0.223208	−	0.488758i	0.00953499	−	0.0208787i
$549$	6.83770	−	26.6981i	0.291826	−	1.13945i
$550$	0.151054	+	0.235045i	0.00644098	+	0.0100224i
$551$	−1.87816	+	3.25307i	−0.0800124	+	0.138586i
$552$	8.02532	−	2.14343i	0.341580	−	0.0912306i
$553$	−3.58444	−	6.20843i	−0.152426	−	0.264009i
$554$	−4.47846	+	8.68701i	−0.190272	+	0.369076i
$555$	3.89821	−	2.60238i	0.165470	−	0.110465i
$556$	11.8593	+	16.6540i	0.502945	+	0.706287i
$557$	−24.6862	+	7.24851i	−1.04599	+	0.307129i	−0.759195	−	0.650864i	$-0.774407\pi$
$557$	−24.6862	+	7.24851i	−1.04599	+	0.307129i	−0.286792	+	0.957993i	$0.592589\pi$
$558$	−15.2490	+	17.1523i	−0.645540	+	0.726117i
$559$	−9.19825	+	7.97033i	−0.389045	+	0.337109i
$560$	−0.724066	+	1.80863i	−0.0305974	+	0.0764286i
$561$	−13.8848	−	9.52683i	−0.586215	−	0.402223i
$562$	4.67281	−	24.2448i	0.197110	−	1.02271i
$563$	1.89286	−	39.7361i	0.0797746	−	1.67468i	−0.504724	−	0.863281i	$-0.668406\pi$
$563$	1.89286	−	39.7361i	0.0797746	−	1.67468i	0.584499	−	0.811395i	$-0.301291\pi$
$564$	10.1448	+	3.85752i	0.427175	+	0.162431i
$565$	−3.33732	−	9.64255i	−0.140402	−	0.405665i
$566$	−14.3207	−	4.20495i	−0.601946	−	0.176747i
$567$	3.38100	+	6.98935i	0.141989	+	0.293525i
$568$	4.47413	+	5.16342i	0.187730	+	0.216652i
$569$	5.00813	+	0.478218i	0.209952	+	0.0200479i	0.199502	−	0.979897i	$-0.436068\pi$
$569$	5.00813	+	0.478218i	0.209952	+	0.0200479i	0.0104498	+	0.999945i	$0.496674\pi$
$570$	11.3448	+	21.0944i	0.475181	+	0.883547i
$571$	0.736778	+	7.71589i	0.0308332	+	0.322900i	0.997709	+	0.0676524i	$0.0215509\pi$
$571$	0.736778	+	7.71589i	0.0308332	+	0.322900i	−0.966876	+	0.255247i	$0.917843\pi$
$572$	−9.46514	+	3.78927i	−0.395757	+	0.158437i
$573$	−1.43249	+	0.374084i	−0.0598431	+	0.0156276i
$574$	0.310424	+	0.179224i	0.0129569	+	0.00748065i
$575$	−0.0481549	−	0.476327i	−0.00200820	−	0.0198642i
$576$	2.74453	−	1.21142i	0.114355	−	0.0504760i
$577$	15.9587	−	10.2560i	0.664370	−	0.426964i	−0.164522	−	0.986373i	$-0.552608\pi$
$577$	15.9587	−	10.2560i	0.664370	−	0.426964i	0.828892	+	0.559409i	$0.188972\pi$
$578$	−3.05017	+	3.87860i	−0.126870	+	0.161329i
$579$	10.0621	+	32.1813i	0.418165	+	1.33741i
$580$	0.955970	−	1.00259i	0.0396945	−	0.0416304i
$581$	5.30228	+	3.77574i	0.219976	+	0.156644i
$582$	−3.71239	−	0.467845i	−0.153884	−	0.0193928i
$583$	19.3161	+	7.73299i	0.799990	+	0.320268i
$584$	−0.403470	+	1.37409i	−0.0166957	+	0.0568604i
$585$	16.8020	+	18.0764i	0.694675	+	0.747367i
$586$	5.25076	−	8.17034i	0.216907	−	0.337514i
$587$	−4.87659	−	9.45927i	−0.201278	−	0.390426i	0.766494	−	0.642251i	$-0.221999\pi$
$587$	−4.87659	−	9.45927i	−0.201278	−	0.390426i	−0.967773	+	0.251826i	$0.918969\pi$
$588$	9.28777	−	5.58046i	0.383021	−	0.230134i
$589$	−45.5252	+	11.0443i	−1.87583	+	0.455072i
$590$	20.3547	−	16.0071i	0.837990	−	0.659002i
$591$	12.3106	+	9.33840i	0.506391	+	0.384131i
$592$	0.113904	−	1.19286i	0.00468144	−	0.0490263i
$593$	8.39953	+	28.6062i	0.344927	+	1.17471i	0.931172	+	0.364580i	$0.118788\pi$
$593$	8.39953	+	28.6062i	0.344927	+	1.17471i	−0.586245	+	0.810134i	$0.699394\pi$
$594$	10.9459	−	9.57542i	0.449117	−	0.392884i
$595$	−6.69828	−	0.963067i	−0.274603	−	0.0394819i
$596$	0.488561	+	10.2562i	0.0200122	+	0.420108i
$597$	−4.14426	+	0.873954i	−0.169613	+	0.0357686i
$598$	17.4000	+	1.56402i	0.711537	+	0.0639575i
$599$	5.87474	−	3.39178i	0.240036	−	0.138585i	−0.375158	−	0.926961i	$-0.622411\pi$
$599$	5.87474	−	3.39178i	0.240036	−	0.138585i	0.615193	+	0.788376i	$0.289078\pi$
$600$	−0.0436879	−	0.167296i	−0.00178355	−	0.00682981i
$601$	5.84609	+	4.59742i	0.238467	+	0.187532i	0.730240	−	0.683191i	$-0.239408\pi$
$601$	5.84609	+	4.59742i	0.238467	+	0.187532i	−0.491773	+	0.870724i	$0.663651\pi$
$602$	2.62188	+	1.19737i	0.106860	+	0.0488013i
$603$	5.23050	−	14.5124i	0.213002	−	0.590992i
$604$	4.17988	+	9.15267i	0.170077	+	0.372417i
$605$	−7.02183	+	1.35335i	−0.285478	+	0.0550213i
$606$	21.8657	+	18.2891i	0.888235	+	0.742942i
$607$	−0.190444	−	0.785019i	−0.00772987	−	0.0318629i	0.967816	−	0.251659i	$-0.0809760\pi$
$607$	−0.190444	−	0.785019i	−0.00772987	−	0.0318629i	−0.975546	+	0.219796i	$0.929461\pi$
$608$	6.01278	+	1.15887i	0.243851	+	0.0469983i
$609$	0.904858	−	0.146246i	0.0366667	−	0.00592620i
$610$	−18.4397	+	9.50632i	−0.746601	+	0.384899i
$611$	17.2512	+	14.9482i	0.697908	+	0.604740i
$612$	6.33693	+	8.27254i	0.256155	+	0.334398i
$613$	−43.3562	+	6.23368i	−1.75114	+	0.251776i	−0.941946	−	0.335765i	$-0.891005\pi$
$613$	−43.3562	+	6.23368i	−1.75114	+	0.251776i	−0.809195	+	0.587541i	$0.800096\pi$
$614$	−6.13361	−	31.8242i	−0.247532	−	1.28432i
$615$	−1.61492	+	0.182674i	−0.0651198	+	0.00736614i
$616$	1.74746	+	1.66620i	0.0704070	+	0.0671329i
$617$	0.563361	−	0.0537944i	0.0226800	−	0.00216568i	−0.0837099	−	0.996490i	$-0.526677\pi$
$617$	0.563361	−	0.0537944i	0.0226800	−	0.00216568i	0.106390	+	0.994324i	$0.466071\pi$
$618$	20.2153	−	1.31662i	0.813180	−	0.0529624i
$619$	4.05998	−	0.193401i	0.163184	−	0.00777342i	0.0341692	−	0.999416i	$-0.489121\pi$
$619$	4.05998	−	0.193401i	0.163184	−	0.00777342i	0.129015	+	0.991643i	$0.458818\pi$
$620$	17.2764			0.693835
$621$	−24.1558	+	6.12346i	−0.969339	+	0.245726i
$622$	−30.2247			−1.21190
$623$	−2.42912	+	0.115713i	−0.0973208	+	0.00463596i
$624$	6.29612	−	0.410066i	0.252047	−	0.0164158i
$625$	25.3738	−	2.42290i	1.01495	−	0.0969160i
$626$	16.0559	+	15.3093i	0.641724	+	0.611882i
$627$	29.4965	−	3.33655i	1.17798	−	0.133249i
$628$	1.61221	+	8.36494i	0.0643342	+	0.333798i
$629$	4.11998	−	0.592363i	0.164274	−	0.0236191i
$630$	2.24106	−	5.39781i	0.0892859	−	0.215054i
$631$	30.0884	+	26.0718i	1.19780	+	1.03790i	0.998317	+	0.0579994i	$0.0184721\pi$
$631$	30.0884	+	26.0718i	1.19780	+	1.03790i	0.199484	+	0.979901i	$0.436073\pi$
$632$	7.38619	−	3.80785i	0.293807	−	0.151468i
$633$	−30.7009	+	4.96199i	−1.22025	+	0.197221i
$634$	26.2856	+	5.06613i	1.04393	+	0.201202i
$635$	−8.55046	−	35.2455i	−0.339315	−	1.39867i
$636$	−9.87665	−	8.26108i	−0.391635	−	0.327573i
$637$	22.3765	−	4.31272i	0.886590	−	0.170876i
$638$	−0.713223	−	1.56174i	−0.0282368	−	0.0618299i
$639$	−13.2242	−	15.6598i	−0.523142	−	0.619491i
$640$	−2.05420	−	0.938123i	−0.0811995	−	0.0370826i
$641$	−2.52412	−	1.98499i	−0.0996968	−	0.0784024i	0.567066	−	0.823672i	$-0.308078\pi$
$641$	−2.52412	−	1.98499i	−0.0996968	−	0.0784024i	−0.666763	+	0.745270i	$0.732321\pi$
$642$	9.02278	+	34.5512i	0.356101	+	1.36363i
$643$	21.5662	−	12.4512i	0.850487	−	0.491029i	−0.0103279	−	0.999947i	$-0.503288\pi$
$643$	21.5662	−	12.4512i	0.850487	−	0.491029i	0.860815	+	0.508918i	$0.169954\pi$
$644$	−1.37487	−	3.90217i	−0.0541775	−	0.153767i
$645$	−12.7875	+	2.69667i	−0.503507	+	0.106181i
$646$	1.01208	+	21.2461i	0.0398197	+	0.835918i
$647$	33.0440	+	4.75101i	1.29909	+	0.186782i	0.756933	−	0.653492i	$-0.226697\pi$
$647$	33.0440	+	4.75101i	1.29909	+	0.186782i	0.542162	+	0.840274i	$0.317606\pi$
$648$	−8.27917	+	3.52922i	−0.325236	+	0.138641i
$649$	−9.04164	−	30.7930i	−0.354916	−	1.20873i
$650$	0.0345669	−	0.362001i	0.00135583	−	0.0141988i
$651$	9.10728	+	6.90846i	0.356942	+	0.270764i
$652$	7.25116	−	5.70238i	0.283977	−	0.223322i
$653$	−43.2475	+	10.4917i	−1.69240	+	0.410573i	−0.962132	−	0.272583i	$-0.912122\pi$
$653$	−43.2475	+	10.4917i	−1.69240	+	0.410573i	−0.730273	+	0.683156i	$0.760607\pi$
$654$	30.1838	−	18.1356i	1.18028	−	0.709159i
$655$	−7.36695	−	14.2899i	−0.287851	−	0.558352i
$656$	−0.224637	+	0.349543i	−0.00877062	+	0.0136473i
$657$	1.26276	−	4.10655i	0.0492650	−	0.160212i
$658$	1.52299	−	5.18684i	0.0593725	−	0.202204i
$659$	41.4741	+	16.6037i	1.61560	+	0.646789i	0.990964	−	0.134126i	$-0.0428227\pi$
$659$	41.4741	+	16.6037i	1.61560	+	0.646789i	0.624637	+	0.780915i	$0.285247\pi$
$660$	−10.8616	−	1.36880i	−0.422786	−	0.0532804i
$661$	−3.02206	−	2.15200i	−0.117544	−	0.0837030i	0.519773	−	0.854304i	$-0.326017\pi$
$661$	−3.02206	−	2.15200i	−0.117544	−	0.0837030i	−0.637317	+	0.770601i	$0.719956\pi$
$662$	9.74378	−	10.2190i	0.378703	−	0.397172i
$663$	6.54030	+	20.9178i	0.254004	+	0.812378i
$664$	−4.66422	+	5.93104i	−0.181007	+	0.230169i
$665$	10.0358	−	6.44962i	0.389172	−	0.250106i
$666$	−0.387217	+	3.57395i	−0.0150043	+	0.138488i
$667$	−0.123658	+	2.93932i	−0.00478807	+	0.113811i
$668$	4.77124	+	2.75468i	0.184605	+	0.106582i
$669$	11.3174	−	2.95546i	0.437557	−	0.114265i
$670$	−10.7805	+	4.31584i	−0.416485	+	0.166736i
$671$	2.44405	+	25.5952i	0.0943513	+	0.988092i
$672$	−0.707743	−	1.31597i	−0.0273018	−	0.0507646i
$673$	−16.7988	−	1.60409i	−0.647548	−	0.0618333i	−0.233886	−	0.972264i	$-0.575144\pi$
$673$	−16.7988	−	1.60409i	−0.647548	−	0.0618333i	−0.413662	+	0.910431i	$0.635750\pi$
$674$	−15.0040	−	17.3156i	−0.577934	−	0.666971i
$675$	0.124668	+	0.503513i	0.00479846	+	0.0193802i
$676$	0.258840	+	0.0760023i	0.00995538	+	0.00292316i
$677$	−0.862762	−	2.49279i	−0.0331586	−	0.0958056i	0.927207	−	0.374550i	$-0.122203\pi$
$677$	−0.862762	−	2.49279i	−0.0331586	−	0.0958056i	−0.960365	+	0.278745i	$0.910082\pi$
$678$	7.31507	+	2.78152i	0.280933	+	0.106823i
$679$	−0.0886766	+	1.86155i	−0.00340309	+	0.0714397i
$680$	1.48454	−	7.70255i	0.0569297	−	0.295379i
$681$	12.9787	+	8.90513i	0.497344	+	0.341245i
$682$	7.95790	−	19.8779i	0.304724	−	0.761163i
$683$	16.1495	−	13.9936i	0.617942	−	0.535450i	−0.288663	−	0.957431i	$-0.593211\pi$
$683$	16.1495	−	13.9936i	0.617942	−	0.535450i	0.906605	+	0.421981i	$0.138665\pi$
$684$	−17.9927	−	3.70583i	−0.687966	−	0.141696i
$685$	1.16425	−	0.341856i	0.0444839	−	0.0130616i
$686$	−6.63327	−	9.31512i	−0.253259	−	0.355653i
$687$	15.0544	−	10.0501i	0.574362	−	0.383434i
$688$	−1.53100	+	2.96973i	−0.0583689	+	0.113220i
$689$	−13.5402	−	23.4523i	−0.515840	−	0.893462i
$690$	15.5265	+	10.5269i	0.591083	+	0.400753i
$691$	−16.4775	+	28.5398i	−0.626833	+	1.08571i	0.361350	+	0.932430i	$0.382316\pi$
$691$	−16.4775	+	28.5398i	−0.626833	+	1.08571i	−0.988183	+	0.153277i	$0.951017\pi$
$692$	−2.76547	−	4.30316i	−0.105128	−	0.163582i
$693$	−5.17835	−	5.06488i	−0.196709	−	0.192399i
$694$	−3.47416	+	7.60734i	−0.131877	+	0.288771i
$695$	−10.8851	+	44.8691i	−0.412896	+	1.70198i
$696$	0.119425	+	1.05577i	0.00452678	+	0.0400187i
$697$	−1.36390	−	0.472050i	−0.0516613	−	0.0178802i
$698$	−8.72630	−	11.0964i	−0.330295	−	0.420005i
$699$	44.7732	+	3.48867i	1.69348	+	0.131954i
$700$	−0.0813829	+	0.0281669i	−0.00307598	+	0.00106461i
$701$	−24.0959	−	15.4855i	−0.910091	−	0.584880i	−0.000324105	−	1.00000i	$-0.500103\pi$
$701$	−24.0959	−	15.4855i	−0.910091	−	0.584880i	−0.909767	+	0.415120i	$0.863740\pi$
$702$	−18.9025	+	0.989780i	−0.713428	+	0.0373568i
$703$	−4.80514	+	5.54542i	−0.181229	+	0.209150i
$704$	−2.02560	+	1.93141i	−0.0763428	+	0.0727927i
$705$	8.41918	+	23.0189i	0.317085	+	0.866941i
$706$	−8.20456	+	23.7055i	−0.308783	+	0.892169i
$707$	8.23570	−	11.5654i	0.309735	−	0.434962i
$708$	−0.598943	+	19.8517i	−0.0225096	+	0.746073i
$709$	13.6131	−	9.69384i	0.511251	−	0.364060i	−0.295130	−	0.955457i	$-0.595363\pi$
$709$	13.6131	−	9.69384i	0.511251	−	0.364060i	0.806380	+	0.591397i	$0.201423\pi$
$710$	−2.19577	+	15.2719i	−0.0824059	+	0.573146i
$711$	−22.3021	+	11.1407i	−0.836395	+	0.417809i
$712$		−	2.81897i		−	0.105645i
$713$	−27.5940	+	24.1800i	−1.03340	+	0.905547i
$714$	3.86267	−	3.46678i	0.144557	−	0.129741i
$715$	−20.4647	−	10.5503i	−0.765338	−	0.394559i
$716$	−4.39153	−	10.9695i	−0.164119	−	0.409950i
$717$	−25.8744	+	8.09009i	−0.966297	+	0.302130i
$718$	11.3168	+	2.74544i	0.422341	+	0.102459i
$719$	−38.8464	+	17.7406i	−1.44873	+	0.661611i	−0.975634	−	0.219402i	$-0.929589\pi$
$719$	−38.8464	+	17.7406i	−1.44873	+	0.661611i	−0.473092	+	0.881013i	$0.656862\pi$
$720$	6.12630	+	2.89255i	0.228314	+	0.107799i
$721$	−1.43596	−	9.98731i	−0.0534779	−	0.371947i
$722$	−12.7641	−	13.3866i	−0.475030	−	0.498197i
$723$	−1.42270	−	2.36785i	−0.0529108	−	0.0880613i
$724$	17.2909	+	0.823669i	0.642613	+	0.0306114i
$725$	0.0611680	+	0.00291379i	0.00227172	+	0.000108216i
$726$	2.65911	−	4.79699i	0.0986888	−	0.178033i
$727$	−16.0860	−	16.8705i	−0.596595	−	0.625691i	0.354327	−	0.935122i	$-0.384710\pi$
$727$	−16.0860	−	16.8705i	−0.596595	−	0.625691i	−0.950922	+	0.309430i	$0.899862\pi$
$728$	−0.447233	−	3.11057i	−0.0165756	−	0.115286i
$729$	24.9702	−	10.2708i	0.924822	−	0.380400i
$730$	−2.94183	+	1.34349i	−0.108882	+	0.0497248i
$731$	−11.2786	−	2.73615i	−0.417153	−	0.101200i
$732$	3.48110	−	15.5262i	0.128665	−	0.573864i
$733$	15.0368	+	37.5601i	0.555397	+	1.38732i	0.894712	+	0.446643i	$0.147381\pi$
$733$	15.0368	+	37.5601i	0.555397	+	1.38732i	−0.339315	+	0.940673i	$0.610195\pi$
$734$	−7.20180	−	3.71278i	−0.265823	−	0.137041i
$735$	23.2594	+	7.59866i	0.857937	+	0.280281i
$736$	4.59399	−	1.37668i	0.169337	−	0.0507451i
$737$			14.3918i			0.530128i
$738$	0.687199	−	1.03997i	0.0252962	−	0.0382818i
$739$	1.69918	−	11.8180i	0.0625053	−	0.434734i	−0.934407	−	0.356208i	$-0.884070\pi$
$739$	1.69918	−	11.8180i	0.0625053	−	0.434734i	0.996912	−	0.0785260i	$-0.0250214\pi$
$740$	2.20430	−	1.56967i	0.0810316	−	0.0577024i
$741$	−32.8616	−	20.3181i	−1.20720	−	0.746403i
$742$	−3.72003	+	5.22404i	−0.136566	+	0.191781i
$743$	12.3832	−	35.7788i	0.454294	−	1.31260i	−0.452778	−	0.891623i	$-0.649567\pi$
$743$	12.3832	−	35.7788i	0.454294	−	1.31260i	0.907073	−	0.420974i	$-0.138312\pi$
$744$	−8.50135	+	10.1639i	−0.311675	+	0.372627i
$745$	−16.7816	+	16.0012i	−0.614830	+	0.586240i
$746$	−15.6660	+	18.0795i	−0.573572	+	0.661938i
$747$	14.2179	−	17.6137i	0.520206	−	0.644450i
$748$	−8.17860	−	5.25607i	−0.299039	−	0.192181i
$749$	16.8078	−	5.81725i	0.614145	−	0.212558i
$750$	−10.8439	+	15.8043i	−0.395963	+	0.577092i
$751$	−30.8653	−	39.2485i	−1.12629	−	1.43220i	−0.887310	−	0.461173i	$-0.847429\pi$
$751$	−30.8653	−	39.2485i	−1.12629	−	1.43220i	−0.238982	−	0.971024i	$-0.576814\pi$
$752$	5.92163	+	2.04950i	0.215940	+	0.0747374i
$753$	24.5070	−	18.1036i	0.893086	−	0.659732i
$754$	−0.526826	+	2.17161i	−0.0191859	+	0.0790853i
$755$	−9.43935	+	20.6693i	−0.343533	+	0.752232i
$756$	2.07283	+	3.97460i	0.0753880	+	0.144555i
$757$	−0.624073	−	0.971077i	−0.0226823	−	0.0352944i	0.829727	−	0.558169i	$-0.188496\pi$
$757$	−0.624073	−	0.971077i	−0.0226823	−	0.0352944i	−0.852410	+	0.522875i	$0.824860\pi$
$758$	17.8772	−	30.9643i	0.649330	−	1.12467i
$759$	19.2640	−	13.0156i	0.699237	−	0.472435i
$760$	6.91422	+	11.9758i	0.250805	+	0.434407i
$761$	−16.7207	+	32.4336i	−0.606124	+	1.17572i	0.363609	+	0.931552i	$0.381544\pi$
$761$	−16.7207	+	32.4336i	−0.606124	+	1.17572i	−0.969734	+	0.244165i	$0.921486\pi$
$762$	24.9429	+	12.3132i	0.903586	+	0.446062i
$763$	−10.1734	−	14.2865i	−0.368302	−	0.517207i
$764$	−0.820159	+	0.240820i	−0.0296723	+	0.00871258i
$765$	−4.74727	+	23.0491i	−0.171638	+	0.833342i
$766$	9.13819	−	7.91828i	0.330176	−	0.286099i
$767$	−15.5244	+	38.7781i	−0.560554	+	1.40020i
$768$	1.56274	−	0.746884i	0.0563906	−	0.0269508i
$769$	0.513359	−	2.66356i	0.0185122	−	0.0960505i	−0.971497	−	0.237050i	$-0.923819\pi$
$769$	0.513359	−	2.66356i	0.0185122	−	0.0960505i	0.990010	+	0.141000i	$0.0450316\pi$
$770$	−0.259446	+	5.44644i	−0.00934978	+	0.196276i
$771$	2.16795	+	13.4136i	0.0780769	+	0.483079i
$772$	6.36700	+	18.3962i	0.229153	+	0.662095i
$773$	0.466603	+	0.137007i	0.0167826	+	0.00492780i	0.290113	−	0.956992i	$-0.406307\pi$
$773$	0.466603	+	0.137007i	0.0167826	+	0.00492780i	−0.273331	+	0.961920i	$0.588125\pi$
$774$	4.70599	−	8.85003i	0.169153	−	0.318108i
$775$	0.500118	+	0.577167i	0.0179648	+	0.0207324i
$776$	−2.15052	−	0.205350i	−0.0771993	−	0.00737164i
$777$	1.78968	+	0.0539962i	0.0642045	+	0.00193710i
$778$	−2.93518	−	30.7386i	−0.105231	−	1.10203i
$779$	2.36205	−	0.945622i	0.0846292	−	0.0338804i
$780$	10.0109	+	10.1391i	0.358449	+	0.363039i
$781$	16.5602	+	9.56103i	0.592570	+	0.342121i
$782$	8.40934	+	14.3804i	0.300718	+	0.514240i
$783$	−0.317947	−	3.17160i	−0.0113625	−	0.113344i
$784$	5.26269	−	3.38213i	0.187953	−	0.120790i
$785$	−11.8922	+	15.1221i	−0.424450	+	0.539732i
$786$	12.0321	+	2.69770i	0.429170	+	0.0962236i
$787$	20.1796	−	21.1638i	0.719326	−	0.754407i	−0.258001	−	0.966145i	$-0.583064\pi$
$787$	20.1796	−	21.1638i	0.719326	−	0.754407i	0.977327	+	0.211738i	$0.0679123\pi$
$788$	7.26690	+	5.17473i	0.258872	+	0.184342i
$789$	−17.6269	−	41.8974i	−0.627536	−	1.49159i
$790$	17.4220	+	6.97470i	0.619846	+	0.248149i
$791$	1.09817	−	3.74003i	0.0390465	−	0.132980i
$792$	6.15004	−	5.71644i	0.218532	−	0.203125i
$793$	18.0923	−	28.1522i	0.642478	−	0.999715i
$794$	15.9096	+	30.8604i	0.564612	+	1.09519i
$795$	−0.507039	−	29.0734i	−0.0179828	−	1.03113i
$796$	−2.37639	+	0.576505i	−0.0842287	+	0.0204337i
$797$	5.02512	−	3.95180i	0.177999	−	0.139980i	−0.525185	−	0.850988i	$-0.676004\pi$
$797$	5.02512	−	3.95180i	0.177999	−	0.139980i	0.703183	+	0.711009i	$0.251761\pi$
$798$	−1.14402	+	9.07793i	−0.0404979	+	0.321355i
$799$	−2.06902	+	21.6678i	−0.0731968	+	0.766551i
$800$	−0.0281246	−	0.0957835i	−0.000994354	−	0.00338646i
$801$	−0.107598	+	8.45622i	−0.00380179	+	0.298786i
$802$	−17.0005	−	2.44431i	−0.600309	−	0.0863115i
$803$	0.190718	+	4.00366i	0.00673029	+	0.141286i
$804$	2.76578	−	8.46602i	0.0975414	−	0.298574i
$805$	4.62656	−	8.11723i	0.163065	−	0.286095i
$806$	−24.1344	+	13.9340i	−0.850098	+	0.490805i
$807$	−5.86767	+	5.79348i	−0.206552	+	0.203940i
$808$	12.9369	+	10.1737i	0.455118	+	0.357909i
$809$	−10.2768	−	4.69327i	−0.361314	−	0.165007i	0.226483	−	0.974015i	$-0.427277\pi$
$809$	−10.2768	−	4.69327i	−0.361314	−	0.165007i	−0.587797	+	0.809009i	$0.700005\pi$
$810$	−18.2670	−	8.91078i	−0.641838	−	0.313093i
$811$	5.68645	+	12.4516i	0.199678	+	0.437234i	0.982810	−	0.184622i	$-0.0591061\pi$
$811$	5.68645	+	12.4516i	0.199678	+	0.437234i	−0.783131	+	0.621856i	$0.786379\pi$
$812$	0.519636	−	0.100152i	0.0182357	−	0.00351464i
$813$	−27.2426	+	9.96402i	−0.955440	+	0.349453i
$814$	−0.790687	−	3.25926i	−0.0277136	−	0.114237i
$815$	20.4557	+	3.94250i	0.716530	+	0.138100i
$816$	3.80100	+	4.66365i	0.133061	+	0.163260i
$817$	18.1850	−	9.37500i	0.636212	−	0.327990i
$818$	2.18113	+	1.88996i	0.0762615	+	0.0660809i
$819$	1.22286	+	9.34804i	0.0427302	+	0.326647i
$820$	−0.928769	+	0.133537i	−0.0324340	+	0.00466331i
$821$	−10.4670	−	54.3080i	−0.365301	−	1.89536i	−0.439717	−	0.898137i	$-0.644921\pi$
$821$	−10.4670	−	54.3080i	−0.365301	−	1.89536i	0.0744151	−	0.997227i	$-0.476291\pi$
$822$	−0.371788	+	0.853167i	−0.0129676	+	0.0297576i
$823$	11.1765	+	10.6567i	0.389587	+	0.371470i	0.859407	−	0.511292i	$-0.170833\pi$
$823$	11.1765	+	10.6567i	0.389587	+	0.371470i	−0.469820	+	0.882762i	$0.655681\pi$
$824$	11.6431	−	1.11178i	0.405607	−	0.0387307i
$825$	−0.268693	−	0.402486i	−0.00935469	−	0.0140128i
$826$	9.88086	−	0.470683i	0.343799	−	0.0163772i
$827$	−36.3685			−1.26466			−0.632328	−	0.774701i	$-0.717901\pi$
$827$	−36.3685			−1.26466			−0.632328	+	0.774701i	$0.717901\pi$
$828$	−13.8334	+	3.95435i	−0.480744	+	0.137423i
$829$	−40.7138			−1.41405			−0.707024	−	0.707190i	$-0.749963\pi$
$829$	−40.7138			−1.41405			−0.707024	+	0.707190i	$0.749963\pi$
$830$	−17.0202	+	0.810772i	−0.590780	+	0.0281423i
$831$	7.49338	−	15.1793i	0.259942	−	0.526564i
$832$	3.62627	−	0.346267i	0.125718	−	0.0120047i
$833$	15.7267	+	14.9954i	0.544897	+	0.519558i
$834$	−21.0407	−	28.4830i	−0.728581	−	0.986287i
$835$	2.35460	+	12.2168i	0.0814844	+	0.422781i
$836$	16.9640	−	2.43905i	0.586712	−	0.0843564i
$837$	25.8899	−	30.1648i	0.894887	−	1.04265i
$838$	−9.47794	−	8.21268i	−0.327410	−	0.283702i
$839$	−8.13668	+	4.19475i	−0.280909	+	0.144819i	−0.592924	−	0.805258i	$-0.702027\pi$
$839$	−8.13668	+	4.19475i	−0.280909	+	0.144819i	0.312015	+	0.950077i	$0.398996\pi$
$840$	1.19930	−	3.15403i	0.0413799	−	0.108824i
$841$	28.1064	+	5.41707i	0.969187	+	0.186796i
$842$	3.98924	+	16.4439i	0.137478	+	0.566693i
$843$	−7.36006	+	42.1280i	−0.253494	+	1.45097i
$844$	−17.6307	+	3.39804i	−0.606874	+	0.116965i
$845$	0.253075	+	0.554157i	0.00870605	+	0.0190636i
$846$	−17.6852	−	6.37401i	−0.608030	−	0.219143i
$847$	−2.48491	−	1.13482i	−0.0853824	−	0.0389928i
$848$	−5.84353	−	4.59540i	−0.200668	−	0.157807i
$849$	24.9275	+	6.84956i	0.855509	+	0.235076i
$850$	0.300301	−	0.173379i	0.0103002	−	0.00594684i
$851$	−1.32382	+	5.59223i	−0.0453798	+	0.191699i
$852$	−7.90419	−	8.80682i	−0.270793	−	0.301717i
$853$	−1.57722	−	33.1099i	−0.0540030	−	1.13366i	−0.849460	−	0.527653i	$-0.823072\pi$
$853$	−1.57722	−	33.1099i	−0.0540030	−	1.13366i	0.795457	−	0.606010i	$-0.207231\pi$
$854$	−7.84446	−	1.12786i	−0.268432	−	0.0385947i
$855$	−20.2839	−	36.1884i	−0.693694	−	1.23762i
$856$	5.80851	+	19.7820i	0.198531	+	0.676134i
$857$	1.66132	−	17.3981i	0.0567495	−	0.594308i	−0.921711	−	0.387876i	$-0.873209\pi$
$857$	1.66132	−	17.3981i	0.0567495	−	0.594308i	0.978461	−	0.206432i	$-0.0661851\pi$
$858$	16.2772	−	6.84808i	0.555693	−	0.233790i
$859$	−40.6107	+	31.9366i	−1.38562	+	1.08966i	−0.400784	+	0.916172i	$0.631262\pi$
$859$	−40.6107	+	31.9366i	−1.38562	+	1.08966i	−0.984835	+	0.173491i	$0.944495\pi$
$860$	−7.33256	+	1.77886i	−0.250038	+	0.0606586i
$861$	−0.543002	−	0.301002i	−0.0185055	−	0.0102581i
$862$	−6.46955	−	12.5492i	−0.220354	−	0.427427i
$863$	23.8033	−	37.0387i	0.810274	−	1.26081i	−0.151905	−	0.988395i	$-0.548541\pi$
$863$	23.8033	−	37.0387i	0.810274	−	1.26081i	0.962179	−	0.272416i	$-0.0878228\pi$
$864$	−4.71636	+	2.18082i	−0.160454	+	0.0741930i
$865$	3.25443	−	11.0836i	0.110654	−	0.376853i
$866$	−32.0127	−	12.8160i	−1.08784	−	0.435504i
$867$	5.16510	−	6.80904i	0.175416	−	0.231247i
$868$	5.37598	+	3.82822i	0.182473	+	0.129938i
$869$	16.0499	−	16.8327i	0.544457	−	0.571010i
$870$	−1.62526	+	1.76515i	−0.0551013	+	0.0598442i
$871$	11.5790	−	14.7239i	0.392339	−	0.498900i
$872$	17.1029	−	10.9914i	0.579178	−	0.372215i
$873$	6.44321	+	0.698084i	0.218070	+	0.0236266i
$874$	−27.8048	−	9.45071i	−0.940510	−	0.319675i
$875$	8.26745	+	4.77322i	0.279491	+	0.161364i
$876$	0.657224	−	2.39182i	0.0222055	−	0.0808122i
$877$	−7.73752	+	3.09763i	−0.261277	+	0.104600i	−0.498603	−	0.866830i	$-0.666153\pi$
$877$	−7.73752	+	3.09763i	−0.261277	+	0.104600i	0.237326	+	0.971430i	$0.423729\pi$
$878$	1.32359	+	13.8613i	0.0446691	+	0.467796i
$879$	−8.84643	+	14.3079i	−0.298383	+	0.482593i
$880$	−6.29190	−	0.600804i	−0.212100	−	0.0202531i
$881$	20.0047	+	23.0866i	0.673974	+	0.777807i	0.984993	−	0.172596i	$-0.0552156\pi$
$881$	20.0047	+	23.0866i	0.673974	+	0.777807i	−0.311019	+	0.950404i	$0.600670\pi$
$882$	−15.9159	+	9.94469i	−0.535916	+	0.334855i
$883$	42.3114	+	12.4238i	1.42389	+	0.418093i	0.900819	−	0.434194i	$-0.142967\pi$
$883$	42.3114	+	12.4238i	1.42389	+	0.418093i	0.523074	+	0.852287i	$0.324785\pi$
$884$	4.13853	+	11.9575i	0.139194	+	0.402174i
$885$	−34.7666	+	28.3357i	−1.16867	+	0.952493i
$886$	−0.376346	+	7.90047i	−0.0126436	+	0.265422i
$887$	−0.761803	+	3.95261i	−0.0255788	+	0.132716i	−0.992473	−	0.122461i	$-0.960921\pi$
$887$	−0.761803	+	3.95261i	−0.0255788	+	0.132716i	0.966895	+	0.255176i	$0.0821336\pi$
$888$	−0.161231	+	2.06922i	−0.00541056	+	0.0694386i
$889$	5.14925	−	12.8622i	0.172700	−	0.431385i
$890$	4.81111	−	4.16885i	0.161269	−	0.139740i
$891$	−18.6668	+	16.9132i	−0.625362	+	0.566613i
$892$	6.47968	−	1.90261i	0.216956	−	0.0637040i
$893$	−22.2574	−	31.2562i	−0.744817	−	1.04595i
$894$	−1.15584	−	17.7467i	−0.0386572	−	0.593539i
$895$	12.2271	−	23.7174i	0.408709	−	0.792784i
$896$	−0.431342	−	0.747107i	−0.0144101	−	0.0249591i
$897$	−30.1803	−	2.18303i	−1.00769	−	0.0728892i
$898$	15.8419	−	27.4391i	0.528653	−	0.915653i
$899$	−2.53718	−	3.94793i	−0.0846196	−	0.131671i
$900$	0.0807109	+	0.288401i	0.00269036	+	0.00961336i
$901$	10.7271	−	23.4891i	0.357371	−	0.782534i
$902$	−0.274168	+	1.13014i	−0.00912879	+	0.0376294i
$903$	−4.57671	−	1.99441i	−0.152303	−	0.0663698i
$904$	4.26986	+	1.47781i	0.142014	+	0.0491514i
$905$	24.1651	+	30.7284i	0.803276	+	1.02145i
$906$	−7.51510	−	15.7242i	−0.249673	−	0.522403i
$907$	−26.4252	+	9.14584i	−0.877433	+	0.303683i	−0.728402	−	0.685150i	$-0.759737\pi$
$907$	−26.4252	+	9.14584i	−0.877433	+	0.303683i	−0.149031	+	0.988832i	$0.547616\pi$
$908$	7.64488	+	4.91307i	0.253704	+	0.163046i
$909$	−38.4192	−	31.0124i	−1.27428	−	1.02861i
$910$	4.64740	−	5.36339i	0.154060	−	0.177795i
$911$	−4.79957	+	4.57638i	−0.159017	+	0.151622i	−0.765411	−	0.643542i	$-0.777464\pi$
$911$	−4.79957	+	4.57638i	−0.159017	+	0.151622i	0.606394	+	0.795165i	$0.292616\pi$
$912$	−10.4479	−	1.82531i	−0.345963	−	0.0604422i
$913$	−6.90705	+	19.9566i	−0.228590	+	0.660467i
$914$	17.5832	−	24.6922i	0.581601	−	0.816744i
$915$	31.6465	−	17.0198i	1.04620	−	0.562659i
$916$	8.51274	−	6.06189i	0.281269	−	0.200291i
$917$	0.874042	−	6.07909i	0.0288634	−	0.200749i
$918$	−11.2241	−	14.1349i	−0.370449	−	0.466521i
$919$		−	20.9881i		−	0.692333i	−0.938173	−	0.346167i	$-0.887483\pi$
$919$		−	20.9881i		−	0.692333i	0.938173	−	0.346167i	$-0.112517\pi$
$920$	9.14343	+	5.80462i	0.301450	+	0.191373i
$921$	11.5833	+	54.9274i	0.381682	+	1.80992i
$922$	3.25216	+	1.67660i	0.107104	+	0.0552160i
$923$	−9.24996	−	23.1053i	−0.304466	−	0.760520i
$924$	−3.07655	−	2.83272i	−0.101211	−	0.0931896i
$925$	0.116250	+	0.0282019i	0.00382227	+	0.000927272i
$926$	−33.8083	+	15.4397i	−1.11101	+	0.507380i
$927$	−34.9689	+	2.89066i	−1.14853	+	0.0949419i
$928$	0.0873007	+	0.607190i	0.00286579	+	0.0199320i
$929$	3.54912	+	3.72221i	0.116443	+	0.122122i	0.779375	−	0.626558i	$-0.215537\pi$
$929$	3.54912	+	3.72221i	0.116443	+	0.122122i	−0.662932	+	0.748679i	$0.730688\pi$
$930$	−29.9190	+	0.521786i	−0.981082	+	0.0171101i
$931$	−38.2635	−	1.82271i	−1.25404	−	0.0597371i
$932$	25.8988	+	1.23371i	0.848343	+	0.0404116i
$933$	52.3428	−	0.912857i	1.71363	−	0.0298856i
$934$	−0.757865	−	0.794826i	−0.0247981	−	0.0260075i
$935$	−3.12450	−	21.7313i	−0.102182	−	0.710691i
$936$	−10.8912	+	0.900305i	−0.355989	+	0.0294274i
$937$	−12.1124	+	5.53154i	−0.395694	+	0.180707i	−0.603317	−	0.797502i	$-0.706155\pi$
$937$	−12.1124	+	5.53154i	−0.395694	+	0.180707i	0.207623	+	0.978209i	$0.433427\pi$
$938$	−4.31095	−	1.04583i	−0.140758	−	0.0341474i
$939$	−28.2678	−	26.0275i	−0.922486	−	0.849376i
$940$	5.25939	+	13.1373i	0.171542	+	0.428492i
$941$	−9.38116	−	4.83632i	−0.305817	−	0.157660i	0.298486	−	0.954414i	$-0.403518\pi$
$941$	−9.38116	−	4.83632i	−0.305817	−	0.157660i	−0.604304	+	0.796754i	$0.706549\pi$
$942$	−3.04465	−	14.4376i	−0.0992000	−	0.470403i
$943$	1.29654	−	1.51319i	0.0422212	−	0.0492763i
$944$			11.4666i			0.373206i
$945$	−3.71801	+	9.41555i	−0.120947	+	0.306288i
$946$	−1.33083	+	9.25610i	−0.0432689	+	0.300942i
$947$	−41.1820	+	29.3255i	−1.33823	+	0.952952i	−0.338305	+	0.941037i	$0.609853\pi$
$947$	−41.1820	+	29.3255i	−1.33823	+	0.952952i	−0.999929	+	0.0119153i	$0.996207\pi$
$948$	−12.6763	+	6.81746i	−0.411707	+	0.221421i
$949$	3.02605	−	4.24950i	0.0982299	−	0.137945i
$950$	−0.199932	+	0.577666i	−0.00648666	+	0.0187420i
$951$	−45.6740	−	7.97957i	−1.48108	−	0.258755i
$952$	2.16874	−	2.06789i	0.0702893	−	0.0670207i
$953$	−1.76337	+	2.03504i	−0.0571211	+	0.0659213i	−0.783591	−	0.621277i	$-0.786614\pi$
$953$	−1.76337	+	2.03504i	−0.0571211	+	0.0659213i	0.726470	+	0.687198i	$0.241160\pi$
$954$	17.3538	+	14.0081i	0.561849	+	0.453530i
$955$	−1.62391	−	1.04362i	−0.0525484	−	0.0337708i
$956$	−14.7909	+	5.11919i	−0.478373	+	0.165567i
$957$	1.28232	+	2.68306i	0.0414515	+	0.0867310i
$958$	−21.8448	−	27.7780i	−0.705775	−	0.897465i
$959$	0.438039	+	0.151607i	0.0141450	+	0.00489564i
$960$	3.58578	+	1.56259i	0.115730	+	0.0504323i
$961$	6.48950	−	26.7501i	0.209339	−	0.862906i
$962$	−1.81332	+	3.97062i	−0.0584638	+	0.128018i
$963$	−16.6691	−	59.5628i	−0.537153	−	1.91939i
$964$	−0.862250	−	1.34169i	−0.0277712	−	0.0432128i
$965$	−21.9809	+	38.0720i	−0.707589	+	1.22558i
$966$	2.49884	+	6.71620i	0.0803988	+	0.216090i
$967$	0.208585	+	0.361281i	0.00670765	+	0.0116180i	0.869360	−	0.494180i	$-0.164532\pi$
$967$	0.208585	+	0.361281i	0.00670765	+	0.0116180i	−0.862652	+	0.505798i	$0.831198\pi$
$968$	1.45102	−	2.81458i	0.0466375	−	0.0904641i
$969$	−2.39439	−	36.7632i	−0.0769188	−	1.18101i
$970$	−2.82985	−	3.97397i	−0.0908610	−	0.127596i
$971$	8.00179	−	2.34954i	0.256790	−	0.0754003i	−0.150804	−	0.988564i	$-0.548186\pi$
$971$	8.00179	−	2.34954i	0.256790	−	0.0754003i	0.407594	+	0.913163i	$0.366368\pi$
$972$	14.2312	−	6.36191i	0.456465	−	0.204058i
$973$	−13.3296	+	11.5502i	−0.427327	+	0.370281i
$974$	2.20456	−	5.50672i	0.0706385	−	0.176447i
$975$	−0.0489292	+	0.627953i	−0.00156699	+	0.0201106i
$976$	1.73857	−	9.02057i	0.0556504	−	0.288742i
$977$	2.25138	−	47.2624i	0.0720282	−	1.51206i	−0.616792	−	0.787126i	$-0.711568\pi$
$977$	2.25138	−	47.2624i	0.0720282	−	1.51206i	0.688821	−	0.724932i	$-0.258129\pi$
$978$	−12.3852	+	10.0943i	−0.396037	+	0.322780i
$979$	−2.58050	−	7.45586i	−0.0824730	−	0.238290i
$980$	13.5550	+	3.98012i	0.433000	+	0.127140i
$981$	−51.7241	+	32.3187i	−1.65142	+	1.03186i
$982$	24.4069	+	28.1671i	0.778855	+	0.898847i
$983$	5.66866	+	0.541292i	0.180802	+	0.0172645i	0.185064	−	0.982726i	$-0.440751\pi$
$983$	5.66866	+	0.541292i	0.180802	+	0.0172645i	−0.00426211	+	0.999991i	$0.501357\pi$
$984$	0.378467	−	0.612118i	0.0120651	−	0.0195136i
$985$	1.91503	+	20.0551i	0.0610178	+	0.639008i
$986$	−1.97817	+	0.791941i	−0.0629979	+	0.0252205i
$987$	−2.48085	+	9.02850i	−0.0789662	+	0.287380i
$988$	−19.3178	−	11.1531i	−0.614581	−	0.354829i
$989$	9.22195	−	13.1038i	0.293241	−	0.416678i
$990$	18.8513	+	2.04242i	0.599132	+	0.0649125i
$991$	−13.4130	+	8.61998i	−0.426076	+	0.273823i	−0.736056	−	0.676920i	$-0.763314\pi$
$991$	−13.4130	+	8.61998i	−0.426076	+	0.273823i	0.309980	+	0.950743i	$0.399678\pi$
$992$	−4.72906	+	6.01349i	−0.150148	+	0.190928i
$993$	−16.5655	+	17.9914i	−0.525691	+	0.570939i
$994$	−4.06734	+	4.26570i	−0.129008	+	0.135300i
$995$	−4.49826	−	3.20319i	−0.142604	−	0.101548i
$996$	7.89831	−	10.4122i	0.250268	−	0.329922i
$997$	−3.42507	−	1.37119i	−0.108473	−	0.0434261i	0.316791	−	0.948495i	$-0.397395\pi$
$997$	−3.42507	−	1.37119i	−0.108473	−	0.0434261i	−0.425264	+	0.905069i	$0.639819\pi$
$998$	9.80607	−	33.3964i	0.310406	−	1.05715i
$999$	0.562635	−	6.20101i	0.0178010	−	0.196191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.11.12	✓	480
9.5	odd	6	inner	414.2.p.a.149.2	yes	480
23.21	odd	22	inner	414.2.p.a.389.2	yes	480
207.113	even	66	inner	414.2.p.a.113.12	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.11.12	✓	480	1.1	even	1	trivial
414.2.p.a.113.12	yes	480	207.113	even	66	inner
414.2.p.a.149.2	yes	480	9.5	odd	6	inner
414.2.p.a.389.2	yes	480	23.21	odd	22	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.998867 + 0.0475819i) q^{2} +(1.72839 - 0.112570i) q^{3} +(0.995472 - 0.0950560i) q^{4} +(1.63439 + 1.55839i) q^{5} +(-1.72107 + 0.194682i) q^{6} +(0.163264 + 0.847095i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.97466 - 0.389129i) q^{9} +O(q^{10})\)	\(q+(-0.998867 + 0.0475819i) q^{2} +(1.72839 - 0.112570i) q^{3} +(0.995472 - 0.0950560i) q^{4} +(1.63439 + 1.55839i) q^{5} +(-1.72107 + 0.194682i) q^{6} +(0.163264 + 0.847095i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(2.97466 - 0.389129i) q^{9} +(-1.70669 - 1.47886i) q^{10} +(-2.48769 + 1.28249i) q^{11} +(1.70986 - 0.276354i) q^{12} +(3.57694 + 0.689399i) q^{13} +(-0.203386 - 0.838367i) q^{14} +(3.00030 + 2.50952i) q^{15} +(0.981929 - 0.189251i) q^{16} +(1.44298 + 3.15968i) q^{17} +(-2.95277 + 0.530228i) q^{18} +(-5.57008 - 2.54377i) q^{19} +(1.77513 + 1.39598i) q^{20} +(0.377541 + 1.44573i) q^{21} +(2.42385 - 1.39941i) q^{22} +(-4.78906 + 0.254799i) q^{23} +(-1.69478 + 0.357399i) q^{24} +(0.00474997 + 0.0997142i) q^{25} +(-3.60569 - 0.518420i) q^{26} +(5.09756 - 1.00742i) q^{27} +(0.243046 + 0.827740i) q^{28} +(0.0583106 - 0.610656i) q^{29} +(-3.11631 - 2.36392i) q^{30} +(6.01349 - 4.72906i) q^{31} +(-0.971812 + 0.235759i) q^{32} +(-4.15533 + 2.49669i) q^{33} +(-1.59168 - 3.08744i) q^{34} +(-1.05327 + 1.63892i) q^{35} +(2.92420 - 0.670126i) q^{36} +(0.337597 - 1.14975i) q^{37} +(5.68481 + 2.27585i) q^{38} +(6.25995 + 0.788893i) q^{39} +(-1.83954 - 1.30993i) q^{40} +(-0.286729 + 0.300713i) q^{41} +(-0.445904 - 1.42613i) q^{42} +(-2.06536 + 2.62632i) q^{43} +(-2.35452 + 1.51316i) q^{44} +(5.46818 + 3.99969i) q^{45} +(4.77151 - 0.482383i) q^{46} +(5.42675 + 3.13313i) q^{47} +(1.67585 - 0.437635i) q^{48} +(5.80766 - 2.32504i) q^{49} +(-0.00948918 - 0.0993752i) q^{50} +(2.84971 + 5.29871i) q^{51} +(3.62627 + 0.346267i) q^{52} +(-4.86824 - 5.61825i) q^{53} +(-5.04385 + 1.24883i) q^{54} +(-6.06450 - 1.78070i) q^{55} +(-0.282156 - 0.815237i) q^{56} +(-9.91361 - 3.76960i) q^{57} +(-0.0291883 + 0.612739i) q^{58} +(-2.17007 + 11.2594i) q^{59} +(3.22526 + 2.21296i) q^{60} +(3.41431 - 8.52853i) q^{61} +(-5.78166 + 5.00983i) q^{62} +(0.815284 + 2.45628i) q^{63} +(0.959493 - 0.281733i) q^{64} +(4.77178 + 6.70102i) q^{65} +(4.03183 - 2.69158i) q^{66} +(2.35624 - 4.57047i) q^{67} +(1.73679 + 3.00820i) q^{68} +(-8.24867 + 0.979495i) q^{69} +(0.974091 - 1.68718i) q^{70} +(-3.69376 - 5.74760i) q^{71} +(-2.88900 + 0.808506i) q^{72} +(0.594917 - 1.30269i) q^{73} +(-0.282507 + 1.16451i) q^{74} +(0.0194346 + 0.171810i) q^{75} +(-5.78666 - 2.00278i) q^{76} +(-1.49255 - 1.89793i) q^{77} +(-6.29039 - 0.490139i) q^{78} +(-7.85292 + 2.71792i) q^{79} +(1.89979 + 1.22092i) q^{80} +(8.69716 - 2.31505i) q^{81} +(0.272096 - 0.314016i) q^{82} +(5.46082 - 5.20688i) q^{83} +(0.513257 + 1.40330i) q^{84} +(-2.56562 + 7.41287i) q^{85} +(1.93806 - 2.72162i) q^{86} +(0.0320419 - 1.06202i) q^{87} +(2.27985 - 1.62348i) q^{88} +(-0.401181 + 2.79027i) q^{89} +(-5.65229 - 3.73497i) q^{90} +3.14256i q^{91} +(-4.74315 + 0.708874i) q^{92} +(9.86129 - 8.85059i) q^{93} +(-5.56968 - 2.87137i) q^{94} +(-5.13951 - 12.8379i) q^{95} +(-1.65313 + 0.516880i) q^{96} +(2.09941 + 0.509311i) q^{97} +(-5.69045 + 2.59874i) q^{98} +(-6.90097 + 4.78301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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