LMFDB - Embedded newform 216.2.v.b.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03887 - 0.959554i) q^{2} +(0.130423 - 1.72713i) q^{3} +(0.158512 + 1.99371i) q^{4} +(0.588722 + 0.214277i) q^{5} +(-1.79277 + 1.66912i) q^{6} +(-4.57427 - 0.806567i) q^{7} +(1.74840 - 2.22331i) q^{8} +(-2.96598 - 0.450516i) q^{9} +O(q^{10})$	\(q+(-1.03887 - 0.959554i) q^{2} +(0.130423 - 1.72713i) q^{3} +(0.158512 + 1.99371i) q^{4} +(0.588722 + 0.214277i) q^{5} +(-1.79277 + 1.66912i) q^{6} +(-4.57427 - 0.806567i) q^{7} +(1.74840 - 2.22331i) q^{8} +(-2.96598 - 0.450516i) q^{9} +(-0.405997 - 0.787518i) q^{10} +(-1.37081 - 3.76628i) q^{11} +(3.46407 - 0.0137460i) q^{12} +(-0.583330 - 0.695185i) q^{13} +(3.97814 + 5.22718i) q^{14} +(0.446868 - 0.988855i) q^{15} +(-3.94975 + 0.632053i) q^{16} +(2.52763 - 1.45933i) q^{17} +(2.64898 + 3.31405i) q^{18} +(-2.50619 + 4.34085i) q^{19} +(-0.333887 + 1.20771i) q^{20} +(-1.98964 + 7.79518i) q^{21} +(-2.18985 + 5.22805i) q^{22} +(-0.819150 - 4.64563i) q^{23} +(-3.61192 - 3.30969i) q^{24} +(-3.52954 - 2.96164i) q^{25} +(-0.0610627 + 1.28195i) q^{26} +(-1.16493 + 5.06389i) q^{27} +(0.882983 - 9.24761i) q^{28} +(6.21586 + 5.21572i) q^{29} +(-1.41310 + 0.598500i) q^{30} +(4.29253 - 0.756889i) q^{31} +(4.70977 + 3.13337i) q^{32} +(-6.68365 + 1.87637i) q^{33} +(-4.02619 - 0.909343i) q^{34} +(-2.52015 - 1.45501i) q^{35} +(0.428054 - 5.98471i) q^{36} +(3.72940 - 2.15317i) q^{37} +(6.76889 - 2.10476i) q^{38} +(-1.27676 + 0.916820i) q^{39} +(1.50573 - 0.934270i) q^{40} +(-5.41092 - 6.44848i) q^{41} +(9.54688 - 6.18903i) q^{42} +(5.48086 - 1.99487i) q^{43} +(7.29157 - 3.33000i) q^{44} +(-1.64960 - 0.900771i) q^{45} +(-3.60674 + 5.61224i) q^{46} +(1.38464 - 7.85268i) q^{47} +(0.576503 + 6.90418i) q^{48} +(13.6955 + 4.98477i) q^{49} +(0.824893 + 6.46355i) q^{50} +(-2.19079 - 4.55589i) q^{51} +(1.29353 - 1.27318i) q^{52} -3.06833 q^{53} +(6.06929 - 4.14291i) q^{54} -2.51103i q^{55} +(-9.79089 + 8.75982i) q^{56} +(7.17036 + 4.89467i) q^{57} +(-1.45271 - 11.3829i) q^{58} +(-0.537968 + 1.47805i) q^{59} +(2.04232 + 0.734180i) q^{60} +(-3.32732 - 0.586696i) q^{61} +(-5.18567 - 3.33260i) q^{62} +(13.2038 + 4.45304i) q^{63} +(-1.88621 - 7.77446i) q^{64} +(-0.194457 - 0.534265i) q^{65} +(8.74394 + 4.46402i) q^{66} +(9.02325 - 7.57140i) q^{67} +(3.31014 + 4.80804i) q^{68} +(-8.13046 + 0.808885i) q^{69} +(1.22195 + 3.92978i) q^{70} +(-3.19304 - 5.53051i) q^{71} +(-6.18735 + 5.80661i) q^{72} +(-2.18272 + 3.78059i) q^{73} +(-5.94045 - 1.34169i) q^{74} +(-5.57548 + 5.70973i) q^{75} +(-9.05165 - 4.30854i) q^{76} +(3.23271 + 18.3336i) q^{77} +(2.20613 + 0.272659i) q^{78} +(-5.52630 + 6.58598i) q^{79} +(-2.46074 - 0.474238i) q^{80} +(8.59407 + 2.67244i) q^{81} +(-0.566412 + 11.8912i) q^{82} +(6.42426 - 7.65613i) q^{83} +(-15.8567 - 2.73113i) q^{84} +(1.80077 - 0.317525i) q^{85} +(-7.60810 - 3.18677i) q^{86} +(9.81894 - 10.0554i) q^{87} +(-10.7703 - 3.53721i) q^{88} +(-1.88520 - 1.08842i) q^{89} +(0.849389 + 2.51867i) q^{90} +(2.10759 + 3.65046i) q^{91} +(9.13219 - 2.36954i) q^{92} +(-0.747404 - 7.51249i) q^{93} +(-8.97354 + 6.82930i) q^{94} +(-2.40560 + 2.01853i) q^{95} +(6.02602 - 7.72574i) q^{96} +(-0.312612 + 0.113782i) q^{97} +(-9.44477 - 18.3202i) q^{98} +(2.36904 + 11.7883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.03887	−	0.959554i	−0.734594	−	0.678507i
$2$	−1.03887	−	0.959554i	−0.734594	−	0.678507i
$3$	0.130423	−	1.72713i	0.0752997	−	0.997161i
$3$	0.130423	−	1.72713i	0.0752997	−	0.997161i
$4$	0.158512	+	1.99371i	0.0792560	+	0.996854i
$5$	0.588722	+	0.214277i	0.263285	+	0.0958277i	0.470290	−	0.882512i	$-0.344149\pi$
$5$	0.588722	+	0.214277i	0.263285	+	0.0958277i	−0.207005	+	0.978340i	$0.566372\pi$
$6$	−1.79277	+	1.66912i	−0.731896	+	0.681417i
$7$	−4.57427	−	0.806567i	−1.72891	−	0.304854i	−0.781271	−	0.624192i	$-0.785428\pi$
$7$	−4.57427	−	0.806567i	−1.72891	−	0.304854i	−0.947641	+	0.319339i	$0.896539\pi$
$8$	1.74840	−	2.22331i	0.618152	−	0.786059i
$9$	−2.96598	−	0.450516i	−0.988660	−	0.150172i
$10$	−0.405997	−	0.787518i	−0.128387	−	0.249035i
$11$	−1.37081	−	3.76628i	−0.413316	−	1.13558i	−0.955416	−	0.295262i	$-0.904593\pi$
$11$	−1.37081	−	3.76628i	−0.413316	−	1.13558i	0.542100	−	0.840314i	$-0.317629\pi$
$12$	3.46407	−	0.0137460i	0.999992	−	0.00396811i
$13$	−0.583330	−	0.695185i	−0.161787	−	0.192810i	0.679061	−	0.734082i	$-0.262387\pi$
$13$	−0.583330	−	0.695185i	−0.161787	−	0.192810i	−0.840847	+	0.541272i	$0.817943\pi$
$14$	3.97814	+	5.22718i	1.06320	+	1.39702i
$15$	0.446868	−	0.988855i	0.115381	−	0.255321i
$16$	−3.94975	+	0.632053i	−0.987437	+	0.158013i
$17$	2.52763	−	1.45933i	0.613041	−	0.353939i	−0.161114	−	0.986936i	$-0.551509\pi$
$17$	2.52763	−	1.45933i	0.613041	−	0.353939i	0.774155	+	0.632997i	$0.218175\pi$
$18$	2.64898	+	3.31405i	0.624371	+	0.781128i
$19$	−2.50619	+	4.34085i	−0.574959	+	0.995859i	0.421087	+	0.907020i	$0.361649\pi$
$19$	−2.50619	+	4.34085i	−0.574959	+	0.995859i	−0.996046	+	0.0888386i	$0.971684\pi$
$20$	−0.333887	+	1.20771i	−0.0746594	+	0.270051i
$21$	−1.98964	+	7.79518i	−0.434175	+	1.70105i
$22$	−2.18985	+	5.22805i	−0.466877	+	1.11462i
$23$	−0.819150	−	4.64563i	−0.170805	−	0.968681i	−0.942876	−	0.333145i	$-0.891890\pi$
$23$	−0.819150	−	4.64563i	−0.170805	−	0.968681i	0.772071	−	0.635536i	$-0.219221\pi$
$24$	−3.61192	−	3.30969i	−0.737280	−	0.675587i
$25$	−3.52954	−	2.96164i	−0.705909	−	0.592328i
$26$	−0.0610627	+	1.28195i	−0.0119754	+	0.251410i
$27$	−1.16493	+	5.06389i	−0.224191	+	0.974545i
$28$	0.882983	−	9.24761i	0.166868	−	1.74763i
$29$	6.21586	+	5.21572i	1.15426	+	0.968535i	0.999811	−	0.0194661i	$-0.00619664\pi$
$29$	6.21586	+	5.21572i	1.15426	+	0.968535i	0.154445	+	0.988001i	$0.450641\pi$
$30$	−1.41310	+	0.598500i	−0.257995	+	0.109271i
$31$	4.29253	−	0.756889i	0.770961	−	0.135941i	0.225688	−	0.974200i	$-0.427537\pi$
$31$	4.29253	−	0.756889i	0.770961	−	0.135941i	0.545273	+	0.838258i	$0.316426\pi$
$32$	4.70977	+	3.13337i	0.832578	+	0.553907i
$33$	−6.68365	+	1.87637i	−1.16347	+	0.326634i
$34$	−4.02619	−	0.909343i	−0.690486	−	0.155951i
$35$	−2.52015	−	1.45501i	−0.425982	−	0.245941i
$36$	0.428054	−	5.98471i	0.0713423	−	0.997452i
$37$	3.72940	−	2.15317i	0.613109	−	0.353979i	−0.161072	−	0.986943i	$-0.551495\pi$
$37$	3.72940	−	2.15317i	0.613109	−	0.353979i	0.774181	+	0.632964i	$0.218162\pi$
$38$	6.76889	−	2.10476i	1.09806	−	0.341438i
$39$	−1.27676	+	0.916820i	−0.204445	+	0.146809i
$40$	1.50573	−	0.934270i	0.238076	−	0.147721i
$41$	−5.41092	−	6.44848i	−0.845043	−	1.00708i	−0.999817	−	0.0191334i	$-0.993909\pi$
$41$	−5.41092	−	6.44848i	−0.845043	−	1.00708i	0.154774	−	0.987950i	$-0.450535\pi$
$42$	9.54688	−	6.18903i	1.47312	−	0.954988i
$43$	5.48086	−	1.99487i	0.835823	−	0.304215i	0.111577	−	0.993756i	$-0.464410\pi$
$43$	5.48086	−	1.99487i	0.835823	−	0.304215i	0.724247	+	0.689541i	$0.242188\pi$
$44$	7.29157	−	3.33000i	1.09925	−	0.502017i
$45$	−1.64960	−	0.900771i	−0.245908	−	0.134279i
$46$	−3.60674	+	5.61224i	−0.531785	+	0.827480i
$47$	1.38464	−	7.85268i	0.201971	−	1.14543i	−0.700166	−	0.713980i	$-0.746891\pi$
$47$	1.38464	−	7.85268i	0.201971	−	1.14543i	0.902136	−	0.431451i	$-0.141998\pi$
$48$	0.576503	+	6.90418i	0.0832110	+	0.996532i
$49$	13.6955	+	4.98477i	1.95651	+	0.712110i
$50$	0.824893	+	6.46355i	0.116657	+	0.914084i
$51$	−2.19079	−	4.55589i	−0.306773	−	0.637952i
$52$	1.29353	−	1.27318i	0.179381	−	0.176559i
$53$	−3.06833			−0.421467			−0.210734	−	0.977544i	$-0.567585\pi$
$53$	−3.06833			−0.421467			−0.210734	+	0.977544i	$0.567585\pi$
$54$	6.06929	−	4.14291i	0.825925	−	0.563779i
$55$		−	2.51103i		−	0.338587i
$56$	−9.79089	+	8.75982i	−1.30836	+	1.17058i
$57$	7.17036	+	4.89467i	0.949737	+	0.648315i
$58$	−1.45271	−	11.3829i	−0.190751	−	1.49465i
$59$	−0.537968	+	1.47805i	−0.0700375	+	0.192426i	−0.969773	−	0.244010i	$-0.921537\pi$
$59$	−0.537968	+	1.47805i	−0.0700375	+	0.192426i	0.899735	+	0.436436i	$0.143759\pi$
$60$	2.04232	+	0.734180i	0.263663	+	0.0947822i
$61$	−3.32732	−	0.586696i	−0.426020	−	0.0751188i	−0.0434723	−	0.999055i	$-0.513842\pi$
$61$	−3.32732	−	0.586696i	−0.426020	−	0.0751188i	−0.382547	+	0.923936i	$0.624953\pi$
$62$	−5.18567	−	3.33260i	−0.658580	−	0.423241i
$63$	13.2038	+	4.45304i	1.66352	+	0.561031i
$64$	−1.88621	−	7.77446i	−0.235777	−	0.971807i
$65$	−0.194457	−	0.534265i	−0.0241194	−	0.0662675i
$66$	8.74394	+	4.46402i	1.07630	+	0.549483i
$67$	9.02325	−	7.57140i	1.10237	−	0.924994i	0.104783	−	0.994495i	$-0.466585\pi$
$67$	9.02325	−	7.57140i	1.10237	−	0.924994i	0.997582	+	0.0695008i	$0.0221406\pi$
$68$	3.31014	+	4.80804i	0.401413	+	0.583060i
$69$	−8.13046	+	0.808885i	−0.978793	+	0.0973783i
$70$	1.22195	+	3.92978i	0.146051	+	0.469699i
$71$	−3.19304	−	5.53051i	−0.378944	−	0.656350i	0.611965	−	0.790885i	$-0.290379\pi$
$71$	−3.19304	−	5.53051i	−0.378944	−	0.656350i	−0.990909	+	0.134535i	$0.957046\pi$
$72$	−6.18735	+	5.80661i	−0.729186	+	0.684316i
$73$	−2.18272	+	3.78059i	−0.255469	+	0.442485i	−0.965023	−	0.262166i	$-0.915563\pi$
$73$	−2.18272	+	3.78059i	−0.255469	+	0.442485i	0.709554	+	0.704651i	$0.248896\pi$
$74$	−5.94045	−	1.34169i	−0.690563	−	0.155968i
$75$	−5.57548	+	5.70973i	−0.643801	+	0.659302i
$76$	−9.05165	−	4.30854i	−1.03830	−	0.494223i
$77$	3.23271	+	18.3336i	0.368402	+	2.08931i
$78$	2.20613	+	0.272659i	0.249795	+	0.0308725i
$79$	−5.52630	+	6.58598i	−0.621757	+	0.740981i	−0.981371	−	0.192120i	$-0.938464\pi$
$79$	−5.52630	+	6.58598i	−0.621757	+	0.740981i	0.359615	+	0.933101i	$0.382908\pi$
$80$	−2.46074	−	0.474238i	−0.275119	−	0.0530214i
$81$	8.59407	+	2.67244i	0.954897	+	0.296938i
$82$	−0.566412	+	11.8912i	−0.0625498	+	1.31317i
$83$	6.42426	−	7.65613i	0.705154	−	0.840370i	−0.287945	−	0.957647i	$-0.592972\pi$
$83$	6.42426	−	7.65613i	0.705154	−	0.840370i	0.993099	+	0.117277i	$0.0374166\pi$
$84$	−15.8567	−	2.73113i	−1.73011	−	0.297991i
$85$	1.80077	−	0.317525i	0.195321	−	0.0344404i
$86$	−7.60810	−	3.18677i	−0.820403	−	0.343638i
$87$	9.81894	−	10.0554i	1.05270	−	1.07805i
$88$	−10.7703	−	3.53721i	−1.14812	−	0.377068i
$89$	−1.88520	−	1.08842i	−0.199830	−	0.115372i	0.396746	−	0.917928i	$-0.370139\pi$
$89$	−1.88520	−	1.08842i	−0.199830	−	0.115372i	−0.596576	+	0.802556i	$0.703473\pi$
$90$	0.849389	+	2.51867i	0.0895334	+	0.265491i
$91$	2.10759	+	3.65046i	0.220936	+	0.382672i
$92$	9.13219	−	2.36954i	0.952097	−	0.247041i
$93$	−0.747404	−	7.51249i	−0.0775022	−	0.779009i
$94$	−8.97354	+	6.82930i	−0.925550	+	0.704389i
$95$	−2.40560	+	2.01853i	−0.246809	+	0.207097i
$96$	6.02602	−	7.72574i	0.615028	−	0.788505i
$97$	−0.312612	+	0.113782i	−0.0317410	+	0.0115528i	−0.357842	−	0.933782i	$-0.616487\pi$
$97$	−0.312612	+	0.113782i	−0.0317410	+	0.0115528i	0.326101	+	0.945335i	$0.394265\pi$
$98$	−9.44477	−	18.3202i	−0.954066	−	1.85062i
$99$	2.36904	+	11.7883i	0.238097	+	1.18477i
$100$	5.34517	−	7.50634i	0.534517	−	0.750634i
$101$	1.17640	−	6.67170i	0.117056	−	0.663859i	−0.868655	−	0.495417i	$-0.835015\pi$
$101$	1.17640	−	6.67170i	0.117056	−	0.663859i	0.985712	−	0.168442i	$-0.0538736\pi$
$102$	−2.09566	+	6.83517i	−0.207502	+	0.676783i
$103$	−4.03772	+	11.0936i	−0.397849	+	1.09308i	0.565481	+	0.824761i	$0.308690\pi$
$103$	−4.03772	+	11.0936i	−0.397849	+	1.09308i	−0.963330	+	0.268319i	$0.913532\pi$
$104$	−2.56550	+	0.0814625i	−0.251568	+	0.00798805i
$105$	−2.84167	+	4.16286i	−0.277319	+	0.406254i
$106$	3.18760	+	2.94423i	0.309607	+	0.285969i
$107$			11.7674i			1.13759i	0.822478	+	0.568797i	$0.192591\pi$
$107$			11.7674i			1.13759i	−0.822478	+	0.568797i	$0.807409\pi$
$108$	−10.2806	−	1.51985i	−0.989248	−	0.146248i
$109$		−	4.09964i		−	0.392674i	−0.980536	−	0.196337i	$-0.937095\pi$
$109$		−	4.09964i		−	0.392674i	0.980536	−	0.196337i	$-0.0629047\pi$
$110$	−2.40947	+	2.60864i	−0.229734	+	0.248724i
$111$	−3.23241	−	6.72199i	−0.306807	−	0.638023i
$112$	18.5770	+	0.294554i	1.75536	+	0.0278328i
$113$	0.0392698	−	0.107893i	0.00369419	−	0.0101497i	−0.937832	−	0.347090i	$-0.887170\pi$
$113$	0.0392698	−	0.107893i	0.00369419	−	0.0101497i	0.941526	+	0.336940i	$0.109392\pi$
$114$	−2.75239	−	11.9653i	−0.257785	−	1.12065i
$115$	0.513202	−	2.91051i	0.0478563	−	0.271407i
$116$	−9.41334	+	13.2194i	−0.874007	+	1.22739i
$117$	1.41695	+	2.32470i	0.130997	+	0.214919i
$118$	1.97715	−	1.01930i	0.182012	−	0.0938343i
$119$	−12.7391	+	4.63666i	−1.16779	+	0.425042i
$120$	−1.41723	−	2.72244i	−0.129375	−	0.248524i
$121$	−3.87924	+	3.25507i	−0.352658	+	0.295916i
$122$	2.89369	+	3.80225i	0.261983	+	0.344239i
$123$	−11.8431	+	8.50435i	−1.06786	+	0.766811i
$124$	2.18943	+	8.43808i	0.196617	+	0.757762i
$125$	−3.00957	−	5.21273i	−0.269184	−	0.466241i
$126$	−9.44415	−	17.2959i	−0.841352	−	1.54084i
$127$	−10.7644	−	6.21480i	−0.955182	−	0.551475i	−0.0604953	−	0.998168i	$-0.519268\pi$
$127$	−10.7644	−	6.21480i	−0.955182	−	0.551475i	−0.894687	+	0.446694i	$0.852601\pi$
$128$	−5.50048	+	9.88659i	−0.486178	+	0.873860i
$129$	−2.73058	−	9.72636i	−0.240414	−	0.856358i
$130$	−0.310641	+	0.741625i	−0.0272450	+	0.0650448i
$131$	0.499778	−	0.0881243i	0.0436658	−	0.00769945i	−0.151773	−	0.988415i	$-0.548498\pi$
$131$	0.499778	−	0.0881243i	0.0436658	−	0.00769945i	0.195438	+	0.980716i	$0.437387\pi$
$132$	−4.80037	−	13.0278i	−0.417819	−	1.13393i
$133$	14.9652	−	17.8348i	1.29765	−	1.54647i
$134$	−16.6392	−	0.792571i	−1.43741	−	0.0684677i
$135$	−1.77090	+	2.73160i	−0.152415	+	0.235099i
$136$	1.17476	−	8.17119i	0.100735	−	0.700674i
$137$	5.79017	−	6.90045i	0.494687	−	0.589545i	−0.459716	−	0.888066i	$-0.652049\pi$
$137$	5.79017	−	6.90045i	0.494687	−	0.589545i	0.954403	+	0.298521i	$0.0964932\pi$
$138$	9.22268	+	6.96129i	0.785087	+	0.592584i
$139$	3.21820	+	18.2513i	0.272965	+	1.54806i	0.745354	+	0.666669i	$0.232280\pi$
$139$	3.21820	+	18.2513i	0.272965	+	1.54806i	−0.472389	+	0.881390i	$0.656608\pi$
$140$	2.50139	−	5.25507i	0.211406	−	0.444135i
$141$	−13.3820	−	3.41563i	−1.12697	−	0.287648i
$142$	−1.98966	+	8.80938i	−0.166968	+	0.739267i
$143$	−1.81863	+	3.14995i	−0.152081	+	0.263412i
$144$	11.9996	−	0.0952340i	0.999969	−	0.00793617i
$145$	2.54180	+	4.40253i	0.211085	+	0.365610i
$146$	5.89525	−	1.83311i	0.487895	−	0.151709i
$147$	10.3956	−	23.0039i	0.857413	−	1.89733i
$148$	4.88394	+	7.09402i	0.401458	+	0.583125i
$149$	−9.83276	+	8.25067i	−0.805531	+	0.675921i	−0.949537	−	0.313656i	$-0.898446\pi$
$149$	−9.83276	+	8.25067i	−0.805531	+	0.675921i	0.144006	+	0.989577i	$0.454002\pi$
$150$	11.2710	−	0.581705i	0.920273	−	0.0474960i
$151$	8.03472	+	22.0752i	0.653856	+	1.79645i	0.602989	+	0.797749i	$0.293976\pi$
$151$	8.03472	+	22.0752i	0.653856	+	1.79645i	0.0508665	+	0.998705i	$0.483802\pi$
$152$	5.26924	+	13.1616i	0.427391	+	1.06754i
$153$	−8.15435	+	3.18960i	−0.659240	+	0.257864i
$154$	14.2337	−	22.1483i	1.14699	−	1.78476i
$155$	2.68929	+	0.474195i	0.216009	+	0.0380882i
$156$	−2.03025	−	2.40016i	−0.162550	−	0.192166i
$157$	1.30901	−	3.59647i	0.104470	−	0.287029i	−0.876434	−	0.481522i	$-0.840084\pi$
$157$	1.30901	−	3.59647i	0.104470	−	0.287029i	0.980904	+	0.194493i	$0.0623062\pi$
$158$	12.0607	−	1.53922i	0.959500	−	0.122454i
$159$	−0.400180	+	5.29941i	−0.0317364	+	0.420271i
$160$	2.10134	+	2.85388i	0.166125	+	0.225619i
$161$			21.9111i			1.72683i
$162$	−6.36379	−	11.0228i	−0.499987	−	0.866033i
$163$	−9.80547			−0.768023			−0.384012	−	0.923328i	$-0.625458\pi$
$163$	−9.80547			−0.768023			−0.384012	+	0.923328i	$0.625458\pi$
$164$	11.9987	−	11.8100i	0.936941	−	0.922202i
$165$	−4.33688	−	0.327496i	−0.337625	−	0.0254955i
$166$	−14.0205	+	1.78932i	−1.08820	+	0.138878i
$167$	5.51424	+	2.00702i	0.426705	+	0.155308i	0.546440	−	0.837498i	$-0.315982\pi$
$167$	5.51424	+	2.00702i	0.426705	+	0.155308i	−0.119736	+	0.992806i	$0.538205\pi$
$168$	13.8524	+	18.0527i	1.06874	+	1.39279i
$169$	2.11442	−	11.9915i	0.162647	−	0.922420i
$170$	−2.17546	−	1.39807i	−0.166850	−	0.107227i
$171$	9.38893	−	11.7458i	0.717989	−	0.898223i
$172$	4.84597	+	10.6110i	0.369502	+	0.809083i
$173$	16.3275	−	5.94273i	1.24136	−	0.451817i	0.363885	−	0.931444i	$-0.381450\pi$
$173$	16.3275	−	5.94273i	1.24136	−	0.451817i	0.877473	+	0.479627i	$0.159228\pi$
$174$	−19.8493	+	1.02444i	−1.50477	+	0.0776623i
$175$	13.7563	+	16.3941i	1.03988	+	1.23928i
$176$	7.79486	+	14.0094i	0.587560	+	1.05600i
$177$	2.48263	+	1.12191i	0.186606	+	0.0843283i
$178$	0.914081	+	2.93967i	0.0685133	+	0.220338i
$179$	2.25513	−	1.30200i	0.168556	−	0.0973161i	−0.413349	−	0.910573i	$-0.635641\pi$
$179$	2.25513	−	1.30200i	0.168556	−	0.0973161i	0.581905	+	0.813257i	$0.302308\pi$
$180$	1.53439	−	3.43161i	0.114367	−	0.255777i
$181$	16.9999	+	9.81488i	1.26359	+	0.729535i	0.973767	−	0.227546i	$-0.0730701\pi$
$181$	16.9999	+	9.81488i	1.26359	+	0.729535i	0.289823	+	0.957080i	$0.406403\pi$
$182$	1.31329	−	5.81471i	0.0973477	−	0.431015i
$183$	−1.44726	+	5.67021i	−0.106985	+	0.419154i
$184$	−11.7609	−	6.30119i	−0.867024	−	0.464530i
$185$	2.65695	−	0.468492i	0.195343	−	0.0344442i
$186$	−6.43218	+	8.52169i	−0.471630	+	0.624841i
$187$	−8.96115	−	7.51930i	−0.655304	−	0.549866i
$188$	15.8754	+	1.51582i	1.15784	+	0.110553i
$189$	9.41308	−	22.2240i	0.684701	−	1.61656i
$190$	4.43600	+	0.211299i	0.321821	+	0.0153293i
$191$	−11.2413	−	9.43260i	−0.813394	−	0.682519i	0.138021	−	0.990429i	$-0.455926\pi$
$191$	−11.2413	−	9.43260i	−0.813394	−	0.682519i	−0.951415	+	0.307910i	$0.900370\pi$
$192$	−13.6735	+	2.24377i	−0.986802	+	0.161930i
$193$	−3.08198	−	17.4788i	−0.221846	−	1.25815i	−0.868624	−	0.495472i	$-0.834995\pi$
$193$	−3.08198	−	17.4788i	−0.221846	−	1.25815i	0.646778	−	0.762678i	$-0.276116\pi$
$194$	0.433944	+	0.181764i	0.0311554	+	0.0130499i
$195$	−0.948109	+	0.266172i	−0.0678955	+	0.0190610i
$196$	−7.76727	+	28.0951i	−0.554805	+	2.00679i
$197$	0.959735	−	1.66231i	0.0683783	−	0.118435i	−0.829809	−	0.558047i	$-0.811551\pi$
$197$	0.959735	−	1.66231i	0.0683783	−	0.118435i	0.898188	+	0.439612i	$0.144884\pi$
$198$	8.85037	−	14.5197i	0.628968	−	1.03187i
$199$	14.5078	−	8.37608i	1.02843	−	0.593765i	0.111896	−	0.993720i	$-0.464308\pi$
$199$	14.5078	−	8.37608i	1.02843	−	0.593765i	0.916535	+	0.399955i	$0.130974\pi$
$200$	−12.7557	+	2.66915i	−0.901963	+	0.188737i
$201$	−11.9000	−	16.5718i	−0.839360	−	1.16889i
$202$	−7.62399	+	5.80223i	−0.536422	+	0.408243i
$203$	−24.2262	−	28.8716i	−1.70034	−	2.02639i
$204$	8.73584	−	5.08997i	0.611631	−	0.356369i
$205$	−1.80376	−	4.95580i	−0.125980	−	0.346128i
$206$	14.8395	−	7.65037i	1.03392	−	0.533027i
$207$	0.336653	+	14.1479i	0.0233990	+	0.983347i
$208$	2.74340	+	2.37711i	0.190221	+	0.164823i
$209$	19.7844	+	3.48852i	1.36851	+	0.241306i
$210$	6.94663	−	1.59794i	0.479363	−	0.110268i
$211$	−6.38063	−	2.32236i	−0.439261	−	0.159878i	0.112917	−	0.993604i	$-0.463981\pi$
$211$	−6.38063	−	2.32236i	−0.439261	−	0.159878i	−0.552177	+	0.833727i	$0.686203\pi$
$212$	−0.486367	−	6.11735i	−0.0334038	−	0.420141i
$213$	−9.96837	+	4.79350i	−0.683021	+	0.328445i
$214$	11.2914	−	12.2248i	0.771866	−	0.835670i
$215$	3.65416			0.249212
$216$	9.22182	+	11.4437i	0.627465	+	0.778644i
$217$	−20.2457			−1.37437
$218$	−3.93382	+	4.25900i	−0.266432	+	0.288456i
$219$	6.24491	+	4.26293i	0.421992	+	0.288062i
$220$	5.00626	−	0.398028i	0.337522	−	0.0268350i
$221$	−2.48895	−	0.905902i	−0.167425	−	0.0609376i
$222$	−3.09205	+	10.0850i	−0.207525	+	0.676858i
$223$	−27.4675	−	4.84327i	−1.83936	−	0.324329i	−0.857582	−	0.514348i	$-0.828034\pi$
$223$	−27.4675	−	4.84327i	−1.83936	−	0.324329i	−0.981780	+	0.190019i	$0.939145\pi$
$224$	−19.0165	−	18.1316i	−1.27059	−	1.21147i
$225$	9.13429	+	10.3743i	0.608953	+	0.691618i
$226$	−0.144325	+	0.0744054i	−0.00960037	+	0.00494937i
$227$	7.70763	+	21.1766i	0.511574	+	1.40554i	0.879597	+	0.475720i	$0.157813\pi$
$227$	7.70763	+	21.1766i	0.511574	+	1.40554i	−0.368023	+	0.929817i	$0.619965\pi$
$228$	−8.62196	+	15.0715i	−0.571003	+	0.998133i
$229$	−11.0943	−	13.2216i	−0.733130	−	0.873710i	0.262706	−	0.964876i	$-0.415385\pi$
$229$	−11.0943	−	13.2216i	−0.733130	−	0.873710i	−0.995836	+	0.0911658i	$0.970941\pi$
$230$	−3.32595	+	2.53121i	−0.219306	+	0.166903i
$231$	32.0862	−	3.19220i	2.11112	−	0.210031i
$232$	22.4640	−	4.70062i	1.47483	−	0.308611i
$233$	−12.5406	+	7.24033i	−0.821564	+	0.474330i	−0.850955	−	0.525238i	$-0.823976\pi$
$233$	−12.5406	+	7.24033i	−0.821564	+	0.474330i	0.0293918	+	0.999568i	$0.490643\pi$
$234$	0.758647	−	3.77471i	0.0495943	−	0.246761i
$235$	2.49782	−	4.32635i	0.162940	−	0.282220i
$236$	−3.03208	−	0.838262i	−0.197372	−	0.0545662i
$237$	10.6541	+	10.4036i	0.692059	+	0.675787i
$238$	17.6834	+	7.40697i	1.14625	+	0.480123i
$239$	−3.39066	−	19.2294i	−0.219324	−	1.24385i	−0.873244	−	0.487283i	$-0.837988\pi$
$239$	−3.39066	−	19.2294i	−0.219324	−	1.24385i	0.653920	−	0.756563i	$-0.273123\pi$
$240$	−1.14001	+	4.18817i	−0.0735872	+	0.270345i
$241$	1.60322	+	1.34526i	0.103272	+	0.0866558i	0.692962	−	0.720974i	$-0.256305\pi$
$241$	1.60322	+	1.34526i	0.103272	+	0.0866558i	−0.589689	+	0.807630i	$0.700750\pi$
$242$	7.15345	+	0.340739i	0.459841	+	0.0219036i
$243$	5.73653	−	14.4946i	0.367998	−	0.929826i
$244$	0.642281	−	6.72670i	0.0411178	−	0.430633i
$245$	6.99475	+	5.86929i	0.446878	+	0.374975i
$246$	20.4638	+	2.52916i	1.30473	+	0.161253i
$247$	4.47963	−	0.789880i	0.285032	−	0.0502588i
$248$	5.82225	−	10.8670i	0.369713	−	0.690053i
$249$	−12.3853	−	12.0941i	−0.784886	−	0.766431i
$250$	−1.87534	+	8.30321i	−0.118607	+	0.525141i
$251$	7.71685	+	4.45533i	0.487083	+	0.281218i	0.723364	−	0.690467i	$-0.242595\pi$
$251$	7.71685	+	4.45533i	0.487083	+	0.281218i	−0.236280	+	0.971685i	$0.575928\pi$
$252$	−6.78510	+	27.0304i	−0.427421	+	1.70276i
$253$	−16.3738	+	9.45345i	−1.02942	+	0.594333i
$254$	5.21935	+	16.7854i	0.327491	+	1.05321i
$255$	−0.313546	−	3.15159i	−0.0196350	−	0.197360i
$256$	15.2010	−	4.99290i	0.950064	−	0.312056i
$257$	−7.13593	−	8.50427i	−0.445127	−	0.530482i	0.496096	−	0.868268i	$-0.334766\pi$
$257$	−7.13593	−	8.50427i	−0.445127	−	0.530482i	−0.941223	+	0.337786i	$0.890322\pi$
$258$	−6.49624	+	12.7246i	−0.404438	+	0.792198i
$259$	−18.7959	+	6.84116i	−1.16792	+	0.425089i
$260$	1.03435	−	0.472377i	0.0641474	−	0.0292956i
$261$	−16.0863	−	18.2701i	−0.995719	−	1.13089i
$262$	−0.603765	−	0.388014i	−0.0373007	−	0.0239716i
$263$	−3.30401	+	18.7379i	−0.203734	+	1.15543i	0.695686	+	0.718346i	$0.255100\pi$
$263$	−3.30401	+	18.7379i	−0.203734	+	1.15543i	−0.899420	+	0.437085i	$0.856011\pi$
$264$	−7.51393	+	18.1405i	−0.462451	+	1.11647i
$265$	−1.80639	−	0.657473i	−0.110966	−	0.0403883i
$266$	−32.6604	+	4.16819i	−2.00254	+	0.255568i
$267$	−2.12572	+	3.11403i	−0.130092	+	0.190575i
$268$	16.5255	+	16.7896i	1.00945	+	1.02559i
$269$	−2.37780			−0.144977			−0.0724886	−	0.997369i	$-0.523094\pi$
$269$	−2.37780			−0.144977			−0.0724886	+	0.997369i	$0.523094\pi$
$270$	4.46086	−	1.13852i	0.271479	−	0.0692878i
$271$			18.7598i			1.13957i	0.821792	+	0.569787i	$0.192974\pi$
$271$			18.7598i			1.13957i	−0.821792	+	0.569787i	$0.807026\pi$
$272$	−9.06113	+	7.36158i	−0.549412	+	0.446361i
$273$	6.57971	−	3.16399i	0.398222	−	0.191494i
$274$	−12.6366	+	1.61271i	−0.763405	+	0.0974274i
$275$	−6.31601	+	17.3531i	−0.380870	+	1.04643i
$276$	−2.90146	−	16.0816i	−0.174647	−	0.967996i
$277$	−4.07892	−	0.719224i	−0.245079	−	0.0432140i	0.0497594	−	0.998761i	$-0.484155\pi$
$277$	−4.07892	−	0.719224i	−0.245079	−	0.0432140i	−0.294838	+	0.955547i	$0.595266\pi$
$278$	14.1698	−	22.0489i	0.849851	−	1.32240i
$279$	−13.0725	+	0.311065i	−0.782633	+	0.0186230i
$280$	−7.64115	+	3.05913i	−0.456646	+	0.182818i
$281$	−5.40819	−	14.8589i	−0.322625	−	0.886406i	−0.989922	−	0.141614i	$-0.954771\pi$
$281$	−5.40819	−	14.8589i	−0.322625	−	0.886406i	0.667297	−	0.744792i	$-0.267451\pi$
$282$	10.6248	+	16.3892i	0.632695	+	0.975962i
$283$	6.74592	−	5.66050i	0.401003	−	0.336482i	−0.419878	−	0.907581i	$-0.637927\pi$
$283$	6.74592	−	5.66050i	0.401003	−	0.336482i	0.820881	+	0.571099i	$0.193483\pi$
$284$	10.5201	−	7.24264i	0.624252	−	0.429772i
$285$	3.17253	+	4.41805i	0.187925	+	0.261703i
$286$	4.91187	−	1.52733i	0.290445	−	0.0903129i
$287$	19.5499	+	33.8614i	1.15399	+	1.99877i
$288$	−12.5575	−	11.4154i	−0.739955	−	0.672656i
$289$	−4.24072	+	7.34514i	−0.249454	+	0.432067i
$290$	1.58386	−	7.01266i	0.0930073	−	0.411798i
$291$	0.155744	+	0.554763i	0.00912988	+	0.0325208i
$292$	−7.88338	−	3.75245i	−0.461340	−	0.219595i
$293$	−1.65024	−	9.35900i	−0.0964083	−	0.546759i	−0.994307	−	0.106556i	$-0.966018\pi$
$293$	−1.65024	−	9.35900i	−0.0964083	−	0.546759i	0.897898	−	0.440203i	$-0.145093\pi$
$294$	−32.8732	+	13.9230i	−1.91720	+	0.812006i
$295$	−0.633427	+	0.754889i	−0.0368796	+	0.0439514i
$296$	1.73331	−	12.0562i	0.100746	−	0.700752i
$297$	20.6689	−	2.55418i	1.19933	−	0.148209i
$298$	18.1319	+	0.863676i	1.05036	+	0.0500314i
$299$	−2.75174	+	3.27940i	−0.159137	+	0.189652i
$300$	−12.2673	−	10.2108i	−0.708254	−	0.589522i
$301$	−26.6799	+	4.70439i	−1.53781	+	0.271157i
$302$	12.8353	−	30.6431i	0.738589	−	1.76331i
$303$	−11.3695	−	2.90194i	−0.653160	−	0.166712i
$304$	7.15517	−	18.7293i	0.410377	−	1.07420i
$305$	−1.83315	−	1.05837i	−0.104966	−	0.0606021i
$306$	11.5319	+	4.51095i	0.659236	+	0.257874i
$307$	−7.38935	−	12.7987i	−0.421733	−	0.730462i	0.574376	−	0.818591i	$-0.305245\pi$
$307$	−7.38935	−	12.7987i	−0.421733	−	0.730462i	−0.996109	+	0.0881289i	$0.971911\pi$
$308$	−36.0395	+	9.35119i	−2.05354	+	0.532833i
$309$	18.6334	+	8.42054i	1.06002	+	0.479028i
$310$	−2.33882	−	3.07315i	−0.132836	−	0.174543i
$311$	22.8823	−	19.2005i	1.29753	−	1.08876i	0.306969	−	0.951720i	$-0.400685\pi$
$311$	22.8823	−	19.2005i	1.29753	−	1.08876i	0.990565	−	0.137041i	$-0.0437591\pi$
$312$	−0.193904	+	4.44159i	−0.0109777	+	0.251456i
$313$	4.41539	−	1.60707i	0.249572	−	0.0908369i	−0.214205	−	0.976789i	$-0.568716\pi$
$313$	4.41539	−	1.60707i	0.249572	−	0.0908369i	0.463777	+	0.885952i	$0.346494\pi$
$314$	−4.81090	+	2.48021i	−0.271495	+	0.139966i
$315$	6.81920	+	5.45088i	0.384218	+	0.307123i
$316$	−14.0065	−	9.97387i	−0.787928	−	0.561074i
$317$	−1.83138	+	10.3863i	−0.102861	+	0.583352i	0.889193	+	0.457533i	$0.151267\pi$
$317$	−1.83138	+	10.3863i	−0.102861	+	0.583352i	−0.992053	+	0.125819i	$0.959844\pi$
$318$	5.50081	−	5.12142i	0.308470	−	0.287195i
$319$	11.1231	−	30.5604i	0.622773	−	1.71106i
$320$	0.555435	−	4.98117i	0.0310498	−	0.278456i
$321$	20.3238	+	1.53474i	1.13437	+	0.0856606i
$322$	21.0249	−	22.7628i	1.17167	−	1.26852i
$323$			14.6294i			0.814003i
$324$	−3.96581	+	17.5577i	−0.220323	+	0.975427i
$325$			4.18130i			0.231937i
$326$	10.1866	+	9.40888i	0.564185	+	0.521109i
$327$	−7.08062	−	0.534687i	−0.391559	−	0.0295683i
$328$	−23.7974	+	0.755639i	−1.31399	+	0.0417232i
$329$	−12.6674	+	34.8035i	−0.698378	+	1.91878i
$330$	4.19121	+	4.50170i	0.230719	+	0.247810i
$331$	2.08554	−	11.8277i	0.114632	−	0.650108i	−0.872300	−	0.488971i	$-0.837373\pi$
$331$	2.08554	−	11.8277i	0.114632	−	0.650108i	0.986932	−	0.161138i	$-0.0515163\pi$
$332$	16.2824	+	11.5945i	0.893614	+	0.636331i
$333$	−12.0313	+	4.70610i	−0.659314	+	0.257893i
$334$	−3.80275	−	7.37625i	−0.208077	−	0.403610i
$335$	6.93457	−	2.52398i	0.378876	−	0.137900i
$336$	2.93160	−	32.0466i	0.159932	−	1.74828i
$337$	−8.14386	+	6.83351i	−0.443624	+	0.372245i	−0.837064	−	0.547106i	$-0.815730\pi$
$337$	−8.14386	+	6.83351i	−0.443624	+	0.372245i	0.393439	+	0.919351i	$0.371285\pi$
$338$	−13.7031	+	10.4287i	−0.745348	+	0.567246i
$339$	−0.181224	−	0.0818958i	−0.00984271	−	0.00444797i
$340$	0.918496	+	3.53989i	0.0498125	+	0.191977i
$341$	−8.73492	−	15.1293i	−0.473022	−	0.819298i
$342$	−21.0246	+	3.19319i	−1.13688	+	0.172668i
$343$	−30.4687	−	17.5911i	−1.64516	−	0.949832i
$344$	5.14751	−	15.6735i	0.277535	−	0.845057i
$345$	−4.95991	−	1.26597i	−0.267033	−	0.0681573i
$346$	−22.6646	−	9.49339i	−1.21845	−	0.510368i
$347$	13.6704	−	2.41047i	0.733868	−	0.129401i	0.205789	−	0.978596i	$-0.434024\pi$
$347$	13.6704	−	2.41047i	0.733868	−	0.129401i	0.528078	+	0.849196i	$0.322913\pi$
$348$	21.6039	+	17.9822i	1.15809	+	0.963947i
$349$	13.0999	−	15.6119i	0.701223	−	0.835685i	−0.291441	−	0.956589i	$-0.594135\pi$
$349$	13.0999	−	15.6119i	0.701223	−	0.835685i	0.992664	+	0.120904i	$0.0385792\pi$
$350$	1.44001	−	30.2314i	0.0769715	−	1.61593i
$351$	4.19988	−	2.14407i	0.224173	−	0.114442i
$352$	5.34494	−	22.0336i	0.284886	−	1.17439i
$353$	−2.23673	+	2.66563i	−0.119049	+	0.141877i	−0.822277	−	0.569087i	$-0.807297\pi$
$353$	−2.23673	+	2.66563i	−0.119049	+	0.141877i	0.703228	+	0.710964i	$0.251741\pi$
$354$	−1.50260	−	3.54775i	−0.0798624	−	0.188561i
$355$	−0.694751	−	3.94013i	−0.0368735	−	0.209120i
$356$	1.87116	−	3.93106i	0.0991714	−	0.208346i
$357$	6.34665	+	22.6069i	0.335901	+	1.19648i
$358$	−3.59213	−	0.811307i	−0.189850	−	0.0428789i
$359$	0.993822	−	1.72135i	0.0524519	−	0.0908494i	−0.838607	−	0.544736i	$-0.816630\pi$
$359$	0.993822	−	1.72135i	0.0524519	−	0.0908494i	0.891059	+	0.453887i	$0.149963\pi$
$360$	−4.88685	+	2.09267i	−0.257560	+	0.110294i
$361$	−3.06198	−	5.30350i	−0.161157	−	0.279132i
$362$	−8.24279	−	26.5087i	−0.433232	−	1.39327i
$363$	5.11600	+	7.12450i	0.268520	+	0.373940i
$364$	−6.94387	+	4.78057i	−0.363958	+	0.250570i
$365$	−2.09511	+	1.75801i	−0.109663	+	0.0920184i
$366$	6.94439	−	4.50190i	0.362989	−	0.235318i
$367$	−1.09533	−	3.00938i	−0.0571755	−	0.157089i	0.907817	−	0.419368i	$-0.137748\pi$
$367$	−1.09533	−	3.00938i	−0.0571755	−	0.157089i	−0.964992	+	0.262279i	$0.915526\pi$
$368$	6.17173	+	17.8313i	0.321723	+	0.929522i
$369$	13.1435	+	21.5638i	0.684225	+	1.12256i
$370$	−3.20978	−	2.06279i	−0.166868	−	0.107239i
$371$	14.0354	+	2.47481i	0.728679	+	0.128486i
$372$	14.8592	−	2.68092i	0.770416	−	0.138999i
$373$	0.734328	−	2.01755i	0.0380221	−	0.104465i	−0.919229	−	0.393724i	$-0.871187\pi$
$373$	0.734328	−	2.01755i	0.0380221	−	0.104465i	0.957251	+	0.289259i	$0.0934089\pi$
$374$	2.09432	+	16.4103i	0.108295	+	0.848556i
$375$	−9.39560	+	4.51807i	−0.485187	+	0.233312i
$376$	−15.0380	−	16.8081i	−0.775528	−	0.866811i
$377$		−	7.36366i		−	0.379248i
$378$	−31.1041	+	14.0555i	−1.59982	+	0.722938i
$379$	10.2488			0.526447			0.263223	−	0.964735i	$-0.415214\pi$
$379$	10.2488			0.526447			0.263223	+	0.964735i	$0.415214\pi$
$380$	−4.40568	−	4.47609i	−0.226007	−	0.229619i
$381$	−12.1377	+	17.7809i	−0.621834	+	0.910945i
$382$	2.62722	+	20.5859i	0.134420	+	1.05327i
$383$	−20.9591	−	7.62848i	−1.07096	−	0.389797i	−0.254423	−	0.967093i	$-0.581886\pi$
$383$	−20.9591	−	7.62848i	−1.07096	−	0.389797i	−0.816535	+	0.577296i	$0.804108\pi$
$384$	16.3581	+	10.7895i	0.834770	+	0.550599i
$385$	−2.02531	+	11.4861i	−0.103219	+	0.585387i
$386$	−13.5701	+	21.1156i	−0.690697	+	1.07475i
$387$	−17.1548	+	3.44753i	−0.872030	+	0.175248i
$388$	−0.276400	−	0.605222i	−0.0140321	−	0.0307255i
$389$	8.94456	−	3.25555i	0.453507	−	0.165063i	−0.105160	−	0.994455i	$-0.533535\pi$
$389$	8.94456	−	3.25555i	0.453507	−	0.165063i	0.558667	+	0.829392i	$0.311313\pi$
$390$	1.24037	+	0.633243i	0.0628086	+	0.0320655i
$391$	−8.85001	−	10.5470i	−0.447564	−	0.533387i
$392$	35.0279	−	21.7341i	1.76918	−	1.09774i
$393$	−0.0870199	−	0.874676i	−0.00438957	−	0.0441216i
$394$	−2.59212	+	0.806010i	−0.130589	+	0.0406062i
$395$	−4.66468	+	2.69315i	−0.234706	+	0.135507i
$396$	−23.1269	+	6.59175i	−1.16217	+	0.331248i
$397$	31.4195	+	18.1401i	1.57690	+	0.910424i	0.995289	+	0.0969571i	$0.0309110\pi$
$397$	31.4195	+	18.1401i	1.57690	+	0.910424i	0.581612	+	0.813467i	$0.302422\pi$
$398$	−23.1091	−	5.21934i	−1.15835	−	0.261622i
$399$	−28.8513	−	28.1729i	−1.44437	−	1.41041i
$400$	15.8127	+	9.46687i	0.790636	+	0.473343i
$401$	32.5501	−	5.73946i	1.62547	−	0.286615i	0.714673	−	0.699459i	$-0.246576\pi$
$401$	32.5501	−	5.73946i	1.62547	−	0.286615i	0.910802	+	0.412844i	$0.135465\pi$
$402$	−3.53901	+	28.6347i	−0.176510	+	1.42817i
$403$	−3.03014	−	2.54259i	−0.150942	−	0.126655i
$404$	13.4879	+	1.28786i	0.671048	+	0.0640732i
$405$	4.48688	+	3.41484i	0.222955	+	0.169685i
$406$	−2.53598	+	53.2403i	−0.125859	+	2.64227i
$407$	−13.2217	−	11.0944i	−0.655377	−	0.549927i
$408$	−13.9595	−	3.09469i	−0.691099	−	0.153210i
$409$	3.81109	+	21.6138i	0.188446	+	1.06873i	0.921447	+	0.388504i	$0.127008\pi$
$409$	3.81109	+	21.6138i	0.188446	+	1.06873i	−0.733001	+	0.680228i	$0.761881\pi$
$410$	−2.88148	+	6.87925i	−0.142306	+	0.339742i
$411$	−11.1628	−	10.9004i	−0.550622	−	0.537675i
$412$	−22.7573	−	6.29158i	−1.12117	−	0.309964i
$413$	3.65296	−	6.32711i	0.179750	−	0.311337i
$414$	13.2259	−	15.0209i	0.650019	−	0.738237i
$415$	5.42264	−	3.13076i	0.266187	−	0.153683i
$416$	−0.569076	−	5.10196i	−0.0279012	−	0.250144i
$417$	31.9422	−	3.17787i	1.56422	−	0.155621i
$418$	−17.2060	−	22.6083i	−0.841574	−	1.10581i
$419$	10.2635	+	12.2316i	0.501405	+	0.597551i	0.956080	−	0.293106i	$-0.0946890\pi$
$419$	10.2635	+	12.2316i	0.501405	+	0.597551i	−0.454675	+	0.890658i	$0.650245\pi$
$420$	−8.74997	−	5.00561i	−0.426955	−	0.244249i
$421$	9.89676	+	27.1911i	0.482338	+	1.32521i	0.907483	+	0.420088i	$0.138001\pi$
$421$	9.89676	+	27.1911i	0.482338	+	1.32521i	−0.425145	+	0.905125i	$0.639777\pi$
$422$	4.40023	+	8.53519i	0.214200	+	0.415487i
$423$	−7.64457	+	22.6671i	−0.371692	+	1.10211i
$424$	−5.36466	+	6.82184i	−0.260531	+	0.331298i
$425$	−13.2434	−	2.33517i	−0.642399	−	0.113272i
$426$	14.9555	+	4.58535i	0.724595	+	0.222161i
$427$	14.7468	+	5.36741i	0.713650	+	0.259747i
$428$	−23.4607	+	1.86527i	−1.13402	+	0.0901612i
$429$	5.20320	+	3.55184i	0.251213	+	0.171484i
$430$	−3.79621	−	3.50636i	−0.183069	−	0.169092i
$431$	30.7042			1.47897			0.739484	−	0.673174i	$-0.235070\pi$
$431$	30.7042			1.47897			0.739484	+	0.673174i	$0.235070\pi$
$432$	1.40054	−	20.7374i	0.0673837	−	0.997727i
$433$	24.3318			1.16931			0.584657	−	0.811281i	$-0.301229\pi$
$433$	24.3318			1.16931			0.584657	+	0.811281i	$0.301229\pi$
$434$	21.0327	+	19.4268i	1.00960	+	0.932517i
$435$	7.93526	−	3.81584i	0.380467	−	0.182955i
$436$	8.17348	−	0.649842i	0.391439	−	0.0311218i
$437$	22.2189	+	8.08703i	1.06288	+	0.386855i
$438$	−2.39715	−	10.4210i	−0.114540	−	0.497933i
$439$	15.6481	+	2.75919i	0.746844	+	0.131689i	0.534102	−	0.845420i	$-0.320650\pi$
$439$	15.6481	+	2.75919i	0.746844	+	0.131689i	0.212741	+	0.977109i	$0.431761\pi$
$440$	−5.58279	−	4.39027i	−0.266149	−	0.209298i
$441$	−38.3750	−	20.9548i	−1.82738	−	0.997847i
$442$	1.71644	+	3.32940i	0.0816425	+	0.158363i
$443$	−7.27214	−	19.9800i	−0.345510	−	0.949280i	−0.983766	−	0.179456i	$-0.942566\pi$
$443$	−7.27214	−	19.9800i	−0.345510	−	0.949280i	0.638256	−	0.769824i	$-0.279656\pi$
$444$	12.8893	−	7.51000i	0.611699	−	0.356409i
$445$	−0.876633	−	1.04473i	−0.0415564	−	0.0495250i
$446$	23.8879	+	31.3881i	1.13112	+	1.48627i
$447$	12.9676	+	18.0586i	0.613346	+	0.854141i
$448$	2.35742	+	37.0838i	0.111378	+	1.75205i
$449$	10.3738	−	5.98931i	0.489569	−	0.282653i	−0.234827	−	0.972037i	$-0.575452\pi$
$449$	10.3738	−	5.98931i	0.489569	−	0.282653i	0.724396	+	0.689384i	$0.242119\pi$
$450$	0.465316	−	19.5424i	0.0219352	−	0.921237i
$451$	−16.8694	+	29.2187i	−0.794350	+	1.37585i
$452$	0.221331	+	0.0611902i	0.0104106	+	0.00287814i
$453$	39.1747	−	10.9979i	1.84059	−	0.516727i
$454$	12.3128	−	29.3956i	0.577868	−	1.37961i
$455$	0.458576	+	2.60072i	0.0214984	+	0.121923i
$456$	23.4190	−	7.38410i	1.09670	−	0.345792i
$457$	−19.6891	−	16.5211i	−0.921015	−	0.772823i	0.0531674	−	0.998586i	$-0.483068\pi$
$457$	−19.6891	−	16.5211i	−0.921015	−	0.772823i	−0.974182	+	0.225762i	$0.927513\pi$
$458$	−1.16134	+	24.3811i	−0.0542660	+	1.13926i
$459$	4.44535	+	14.4997i	0.207491	+	0.676786i
$460$	5.88406	+	0.561824i	0.274346	+	0.0261952i
$461$	−19.7573	−	16.5784i	−0.920190	−	0.772131i	0.0538400	−	0.998550i	$-0.482854\pi$
$461$	−19.7573	−	16.5784i	−0.920190	−	0.772131i	−0.974030	+	0.226418i	$0.927298\pi$
$462$	−36.3966	−	27.4722i	−1.69332	−	1.27812i
$463$	23.8682	−	4.20861i	1.10925	−	0.195591i	0.411133	−	0.911575i	$-0.365133\pi$
$463$	23.8682	−	4.20861i	1.10925	−	0.195591i	0.698116	+	0.715985i	$0.254022\pi$
$464$	−27.8477	−	16.6720i	−1.29280	−	0.773980i
$465$	1.16974	−	4.58292i	0.0542455	−	0.212528i
$466$	19.9756	+	4.51162i	0.925352	+	0.208997i
$467$	1.80364	+	1.04133i	0.0834624	+	0.0481870i	0.541150	−	0.840926i	$-0.317989\pi$
$467$	1.80364	+	1.04133i	0.0834624	+	0.0481870i	−0.457688	+	0.889113i	$0.651322\pi$
$468$	−4.41018	+	3.19348i	−0.203861	+	0.147619i
$469$	−47.3816	+	27.3558i	−2.18788	+	1.26317i
$470$	−6.74629	+	2.09773i	−0.311183	+	0.0967613i
$471$	−6.04085	−	2.72989i	−0.278348	−	0.125787i
$472$	2.34559	+	3.78030i	0.107965	+	0.174002i
$473$	−15.0265	−	17.9079i	−0.690918	−	0.823404i
$474$	−1.08544	−	21.0312i	−0.0498558	−	0.965996i
$475$	21.7017	−	7.89878i	0.995744	−	0.362421i
$476$	−11.2634	−	24.6631i	−0.516259	−	1.13043i
$477$	9.10060	+	1.38233i	0.416688	+	0.0632925i
$478$	−14.9292	+	23.2304i	−0.682845	+	1.06253i
$479$	−2.00257	+	11.3572i	−0.0914999	+	0.518922i	0.904264	+	0.426974i	$0.140420\pi$
$479$	−2.00257	+	11.3572i	−0.0914999	+	0.518922i	−0.995764	+	0.0919478i	$0.970691\pi$
$480$	5.20310	−	3.25708i	0.237488	−	0.148665i
$481$	−3.67232	−	1.33661i	−0.167443	−	0.0609444i
$482$	−0.374690	−	2.93593i	−0.0170667	−	0.133728i
$483$	37.8434	+	2.85771i	1.72193	+	0.130030i
$484$	−7.10457	−	7.21811i	−0.322935	−	0.328096i
$485$	−0.208423			−0.00946398
$486$	−19.8678	+	9.55349i	−0.901223	+	0.433355i
$487$		−	29.2353i		−	1.32478i	−0.749160	−	0.662389i	$-0.769542\pi$
$487$		−	29.2353i		−	1.32478i	0.749160	−	0.662389i	$-0.230458\pi$
$488$	−7.12189	+	6.37188i	−0.322393	+	0.288442i
$489$	−1.27886	+	16.9353i	−0.0578320	+	0.765843i
$490$	−1.63475	−	12.8093i	−0.0738504	−	0.578664i
$491$	−1.76088	+	4.83798i	−0.0794674	+	0.218335i	−0.973064	−	0.230537i	$-0.925952\pi$
$491$	−1.76088	+	4.83798i	−0.0794674	+	0.218335i	0.893596	+	0.448872i	$0.148174\pi$
$492$	−18.8325	−	22.2636i	−0.849033	−	1.00372i
$493$	23.3228	+	4.11245i	1.05041	+	0.185215i
$494$	−5.41170	−	3.47786i	−0.243484	−	0.156476i
$495$	−1.13126	+	7.44765i	−0.0508462	+	0.334747i
$496$	−16.4760	+	5.70263i	−0.739795	+	0.256056i
$497$	10.1451	+	27.8734i	0.455070	+	1.25029i
$498$	1.26181	+	24.4486i	0.0565430	+	1.09557i
$499$	−19.4599	+	16.3288i	−0.871144	+	0.730977i	−0.964339	−	0.264671i	$-0.914737\pi$
$499$	−19.4599	+	16.3288i	−0.871144	+	0.730977i	0.0931946	+	0.995648i	$0.470292\pi$
$500$	9.91561	−	6.82649i	0.443440	−	0.305290i
$501$	4.18557	−	9.26207i	0.186998	−	0.413799i
$502$	−3.74170	−	12.0333i	−0.167000	−	0.537070i
$503$	3.28486	+	5.68954i	0.146465	+	0.253684i	0.929918	−	0.367766i	$-0.119877\pi$
$503$	3.28486	+	5.68954i	0.146465	+	0.253684i	−0.783454	+	0.621450i	$0.786544\pi$
$504$	32.9860	−	21.5705i	1.46931	−	0.960826i
$505$	2.12217	−	3.67570i	0.0944352	−	0.163567i
$506$	26.0814	+	5.89067i	1.15946	+	0.261872i
$507$	−20.4351	−	5.21584i	−0.907554	−	0.231644i
$508$	10.6842	−	22.4461i	0.474036	−	0.995885i
$509$	−0.0426035	−	0.241616i	−0.00188837	−	0.0107095i	0.983849	−	0.179000i	$-0.0572863\pi$
$509$	−0.0426035	−	0.241616i	−0.00188837	−	0.0107095i	−0.985737	+	0.168291i	$0.946175\pi$
$510$	−2.69839	+	3.57496i	−0.119487	+	0.158302i
$511$	13.0337	−	15.5329i	0.576576	−	0.687136i
$512$	−20.5829	−	9.39921i	−0.909643	−	0.415390i
$513$	−19.0620	−	17.7479i	−0.841609	−	0.783587i
$514$	−0.746986	+	15.6822i	−0.0329481	+	0.691711i
$515$	−4.75419	+	5.66583i	−0.209495	+	0.249666i
$516$	18.9587	−	6.98572i	0.834610	−	0.307529i
$517$	−31.4735	+	5.54962i	−1.38420	+	0.244072i
$518$	26.0910	+	10.9286i	1.14637	+	0.480176i
$519$	−8.13440	−	28.9749i	−0.357061	−	1.27185i
$520$	−1.52783	−	0.501771i	−0.0669996	−	0.0220041i
$521$	29.9500	+	17.2916i	1.31213	+	0.757560i	0.982449	−	0.186532i	$-0.0597248\pi$
$521$	29.9500	+	17.2916i	1.31213	+	0.757560i	0.329683	+	0.944092i	$0.393058\pi$
$522$	−0.819465	+	34.4160i	−0.0358670	+	1.50635i
$523$	12.9546	+	22.4380i	0.566466	+	0.981147i	0.996912	+	0.0785309i	$0.0250229\pi$
$523$	12.9546	+	22.4380i	0.566466	+	0.981147i	−0.430446	+	0.902616i	$0.641644\pi$
$524$	0.254915	+	0.982442i	0.0111360	+	0.0429182i
$525$	30.1090	−	21.6208i	1.31407	−	0.943610i
$526$	21.4125	−	16.2960i	0.933630	−	0.710538i
$527$	9.74539	−	8.17735i	0.424516	−	0.356211i
$528$	25.2128	−	11.6356i	1.09725	−	0.506375i
$529$	0.702032	−	0.255519i	0.0305231	−	0.0111095i
$530$	1.24573	+	2.41636i	0.0541111	+	0.104960i
$531$	2.26149	−	4.14152i	0.0981402	−	0.179727i
$532$	37.9296	+	27.0092i	1.64445	+	1.17100i
$533$	−1.32654	+	7.52318i	−0.0574588	+	0.325865i
$534$	5.19643	−	1.19534i	0.224871	−	0.0517274i
$535$	−2.52148	+	6.92771i	−0.109013	+	0.299511i
$536$	−1.05735	−	33.2993i	−0.0456707	−	1.43831i
$537$	−1.95461	−	4.06472i	−0.0843475	−	0.175406i
$538$	2.47023	+	2.28163i	0.106499	+	0.0983681i
$539$		−	58.4144i		−	2.51609i
$540$	−5.72673	−	3.09766i	−0.246439	−	0.133302i
$541$			12.5921i			0.541376i	0.962667	+	0.270688i	$0.0872512\pi$
$541$			12.5921i			0.541376i	−0.962667	+	0.270688i	$0.912749\pi$
$542$	18.0010	−	19.4890i	0.773210	−	0.837124i
$543$	19.1688	−	28.0810i	0.822611	−	1.20507i
$544$	16.4772	+	1.04691i	0.706454	+	0.0448857i
$545$	0.878460	−	2.41355i	0.0376291	−	0.103385i
$546$	−9.87150	−	3.02660i	−0.422461	−	0.129527i
$547$	−3.19463	+	18.1176i	−0.136592	+	0.774654i	0.837145	+	0.546981i	$0.184223\pi$
$547$	−3.19463	+	18.1176i	−0.136592	+	0.774654i	−0.973738	+	0.227673i	$0.926888\pi$
$548$	14.6753	+	10.4501i	0.626898	+	0.446406i
$549$	9.60445	+	3.23914i	0.409908	+	0.138243i
$550$	23.2128	−	11.9671i	0.989796	−	0.510279i
$551$	−38.2188	+	13.9105i	−1.62817	+	0.592607i
$552$	−12.4169	+	19.4908i	−0.528498	+	0.829583i
$553$	30.5908	−	25.6687i	1.30085	−	1.09155i
$554$	3.54734	+	4.66113i	0.150712	+	0.198032i
$555$	−0.462621	−	4.65001i	−0.0196372	−	0.197382i
$556$	−35.8777	+	9.30922i	−1.52156	+	0.394799i
$557$	−8.10237	−	14.0337i	−0.343308	−	0.594628i	0.641737	−	0.766925i	$-0.278214\pi$
$557$	−8.10237	−	14.0337i	−0.343308	−	0.594628i	−0.985045	+	0.172298i	$0.944881\pi$
$558$	13.8792	+	12.2207i	0.587553	+	0.517342i
$559$	−4.58395	−	2.64655i	−0.193881	−	0.111937i
$560$	10.8736	+	4.15404i	0.459493	+	0.175540i
$561$	−14.1556	+	14.4964i	−0.597649	+	0.612039i
$562$	−8.63947	+	20.6259i	−0.364434	+	0.870052i
$563$	18.5122	−	3.26419i	0.780194	−	0.137569i	0.230653	−	0.973036i	$-0.425914\pi$
$563$	18.5122	−	3.26419i	0.780194	−	0.137569i	0.549541	+	0.835467i	$0.314803\pi$
$564$	4.68855	−	27.2213i	0.197424	−	1.14622i
$565$	0.0462380	−	0.0551042i	0.00194525	−	0.00231825i
$566$	−12.4397	−	0.592539i	−0.522880	−	0.0249063i
$567$	−37.1561	−	19.1562i	−1.56041	−	0.804483i
$568$	−17.8787	−	2.57041i	−0.750175	−	0.107852i
$569$	−11.3736	+	13.5546i	−0.476807	+	0.568237i	−0.949811	−	0.312823i	$-0.898725\pi$
$569$	−11.3736	+	13.5546i	−0.476807	+	0.568237i	0.473004	+	0.881060i	$0.343170\pi$
$570$	0.943498	−	7.63401i	0.0395188	−	0.319753i
$571$	−6.91365	−	39.2093i	−0.289327	−	1.64086i	−0.689405	−	0.724376i	$-0.742128\pi$
$571$	−6.91365	−	39.2093i	−0.289327	−	1.64086i	0.400078	−	0.916481i	$-0.368983\pi$
$572$	−6.56836	−	3.12651i	−0.274637	−	0.130726i
$573$	−17.7575	+	18.1851i	−0.741830	+	0.759692i
$574$	12.1820	−	53.9368i	0.508466	−	2.25128i
$575$	−10.8675	+	18.8230i	−0.453204	+	0.784973i
$576$	2.09195	+	23.9087i	0.0871647	+	0.996194i
$577$	1.07337	+	1.85913i	0.0446850	+	0.0773967i	0.887503	−	0.460802i	$-0.152438\pi$
$577$	1.07337	+	1.85913i	0.0446850	+	0.0773967i	−0.842818	+	0.538199i	$0.819105\pi$
$578$	11.4536	−	3.56147i	0.476408	−	0.148137i
$579$	−30.5901	+	3.04336i	−1.27128	+	0.126478i
$580$	−8.37445	+	5.76546i	−0.347730	+	0.239398i
$581$	−35.5615	+	29.8396i	−1.47534	+	1.23796i
$582$	0.370527	−	0.725773i	0.0153588	−	0.0300842i
$583$	4.20611	+	11.5562i	0.174199	+	0.478608i
$584$	4.58915	+	11.4628i	0.189901	+	0.474336i
$585$	0.336060	+	1.67223i	0.0138944	+	0.0691380i
$586$	−7.26607	+	11.3063i	−0.300159	+	0.467059i
$587$	−34.2197	−	6.03386i	−1.41240	−	0.249044i	−0.585171	−	0.810910i	$-0.698973\pi$
$587$	−34.2197	−	6.03386i	−1.41240	−	0.249044i	−0.827228	+	0.561866i	$0.810084\pi$
$588$	47.5109	+	17.0794i	1.95932	+	0.704341i
$589$	−7.47236	+	20.5301i	−0.307893	+	0.845930i
$590$	1.38241	−	0.176426i	0.0569128	−	0.00726334i
$591$	−2.74586	−	1.87439i	−0.112950	−	0.0771022i
$592$	−13.3693	+	10.8616i	−0.549473	+	0.446411i
$593$		−	41.3775i		−	1.69917i	−0.527450	−	0.849586i	$-0.676852\pi$
$593$		−	41.3775i		−	1.69917i	0.527450	−	0.849586i	$-0.323148\pi$
$594$	−23.9232	−	17.1795i	−0.981582	−	0.704882i
$595$	−8.49333			−0.348193
$596$	−18.0080	−	18.2958i	−0.737638	−	0.749426i
$597$	−12.5745	−	26.1493i	−0.514638	−	1.07022i
$598$	6.00547	−	0.766431i	0.245582	−	0.0313417i
$599$	31.9356	+	11.6236i	1.30485	+	0.474928i	0.898575	−	0.438821i	$-0.144604\pi$
$599$	31.9356	+	11.6236i	1.30485	+	0.474928i	0.406280	+	0.913749i	$0.366826\pi$
$600$	2.94634	+	22.3789i	0.120284	+	0.913614i
$601$	−0.244918	+	1.38900i	−0.00999041	+	0.0566584i	−0.989395	−	0.145247i	$-0.953602\pi$
$601$	−0.244918	+	1.38900i	−0.00999041	+	0.0566584i	0.979405	+	0.201906i	$0.0647134\pi$
$602$	32.2312	+	20.7136i	1.31364	+	0.844222i
$603$	−30.1738	+	18.3915i	−1.22877	+	0.748960i
$604$	−42.7379	+	19.5181i	−1.73898	+	0.794179i
$605$	−2.98128	+	1.08510i	−0.121206	+	0.0441155i
$606$	9.02687	+	13.9244i	0.366692	+	0.565640i
$607$	−0.276419	−	0.329424i	−0.0112195	−	0.0133709i	0.760406	−	0.649449i	$-0.225000\pi$
$607$	−0.276419	−	0.329424i	−0.0112195	−	0.0133709i	−0.771625	+	0.636078i	$0.780556\pi$
$608$	−25.4051	+	12.5916i	−1.03031	+	0.510656i
$609$	−53.0248	+	38.0763i	−2.14867	+	1.54293i
$610$	0.888847	+	2.85852i	0.0359884	+	0.115738i
$611$	−6.26677	+	3.61812i	−0.253526	+	0.146374i
$612$	−7.65170	−	15.7518i	−0.309302	−	0.636729i
$613$	11.9125	+	6.87769i	0.481142	+	0.277787i	0.720892	−	0.693047i	$-0.243732\pi$
$613$	11.9125	+	6.87769i	0.481142	+	0.277787i	−0.239750	+	0.970835i	$0.577066\pi$
$614$	−4.60448	+	20.3867i	−0.185822	+	0.822742i
$615$	−8.79458	+	2.46899i	−0.354632	+	0.0995593i
$616$	46.4134	+	24.8671i	1.87005	+	1.00193i
$617$	−16.8375	+	2.96891i	−0.677854	+	0.119524i	−0.501967	−	0.864887i	$-0.667390\pi$
$617$	−16.8375	+	2.96891i	−0.677854	+	0.119524i	−0.175886	+	0.984410i	$0.556279\pi$
$618$	−11.2778	−	26.6277i	−0.453660	−	1.07112i
$619$	20.7852	+	17.4409i	0.835429	+	0.701008i	0.956531	−	0.291632i	$-0.0941982\pi$
$619$	20.7852	+	17.4409i	0.835429	+	0.701008i	−0.121101	+	0.992640i	$0.538643\pi$
$620$	−0.519121	+	5.43683i	−0.0208484	+	0.218348i
$621$	24.4792	+	1.26377i	0.982317	+	0.0507132i
$622$	−42.1957	−	2.00990i	−1.69189	−	0.0805896i
$623$	7.74551	+	6.49925i	0.310317	+	0.260387i
$624$	4.46339	−	4.42819i	0.178679	−	0.177269i
$625$	3.34558	+	18.9737i	0.133823	+	0.758949i
$626$	−6.12909	−	2.56726i	−0.244968	−	0.102608i
$627$	8.60547	−	33.7153i	0.343669	−	1.34646i
$628$	7.37780	+	2.03970i	0.294406	+	0.0813927i
$629$	6.28436	−	10.8848i	0.250574	−	0.434006i
$630$	−1.85386	−	12.2062i	−0.0738594	−	0.486305i
$631$	36.5260	−	21.0883i	1.45408	−	0.839512i	0.455369	−	0.890303i	$-0.349507\pi$
$631$	36.5260	−	21.0883i	1.45408	−	0.839512i	0.998709	+	0.0507908i	$0.0161742\pi$
$632$	4.98052	+	23.8016i	0.198114	+	0.946776i
$633$	−4.84320	+	10.7173i	−0.192500	+	0.425975i
$634$	11.8688	−	9.03271i	0.471369	−	0.358735i
$635$	−5.00552	−	5.96535i	−0.198638	−	0.236728i
$636$	−10.6289	+	0.0421771i	−0.421464	+	0.00167243i
$637$	−4.52368	−	12.4287i	−0.179235	−	0.492443i
$638$	−40.8799	+	21.0752i	−1.61845	+	0.834375i
$639$	6.97891	+	17.8419i	0.276081	+	0.705814i
$640$	−5.35673	+	4.64183i	−0.211743	+	0.183484i
$641$	−27.2082	−	4.79753i	−1.07466	−	0.189491i	−0.391806	−	0.920048i	$-0.628150\pi$
$641$	−27.2082	−	4.79753i	−1.07466	−	0.189491i	−0.682852	+	0.730557i	$0.739261\pi$
$642$	−19.6412	−	21.0962i	−0.775176	−	0.832601i
$643$	−6.31128	−	2.29712i	−0.248892	−	0.0905894i	0.214561	−	0.976711i	$-0.431168\pi$
$643$	−6.31128	−	2.29712i	−0.248892	−	0.0905894i	−0.463454	+	0.886121i	$0.653390\pi$
$644$	−43.6843	+	3.47317i	−1.72140	+	0.136862i
$645$	0.476586	−	6.31122i	0.0187656	−	0.248504i
$646$	14.0377	−	15.1981i	0.552307	−	0.597961i
$647$	−3.89370			−0.153077			−0.0765386	−	0.997067i	$-0.524387\pi$
$647$	−3.89370			−0.153077			−0.0765386	+	0.997067i	$0.524387\pi$
$648$	20.9675	−	14.4348i	0.823682	−	0.567052i
$649$	6.30422			0.247462
$650$	4.01218	−	4.34384i	0.157371	−	0.170379i
$651$	−2.64050	+	34.9670i	−0.103489	+	1.37046i
$652$	−1.55428	−	19.5492i	−0.0608705	−	0.765607i
$653$	−46.1107	−	16.7829i	−1.80445	−	0.656767i	−0.997840	−	0.0656846i	$-0.979077\pi$
$653$	−46.1107	−	16.7829i	−1.80445	−	0.656767i	−0.806611	−	0.591082i	$-0.798701\pi$
$654$	6.84280	+	7.34971i	0.267575	+	0.287396i
$655$	0.313113	+	0.0552103i	0.0122343	+	0.00215724i
$656$	25.4475	+	22.0499i	0.993560	+	0.860903i
$657$	8.17713	−	10.2298i	0.319020	−	0.399103i
$658$	46.5557	−	24.0013i	1.81493	−	0.935668i
$659$	−6.99121	−	19.2082i	−0.272339	−	0.748245i	−0.998176	−	0.0603781i	$-0.980769\pi$
$659$	−6.99121	−	19.2082i	−0.272339	−	0.748245i	0.725837	−	0.687867i	$-0.241453\pi$
$660$	−0.0345164	−	8.69838i	−0.00134355	−	0.338584i
$661$	−1.63166	−	1.94453i	−0.0634642	−	0.0756336i	0.733378	−	0.679821i	$-0.237942\pi$
$661$	−1.63166	−	1.94453i	−0.0634642	−	0.0756336i	−0.796843	+	0.604187i	$0.793498\pi$
$662$	−13.5159	+	10.2863i	−0.525311	+	0.399787i
$663$	−1.88923	+	4.18059i	−0.0733716	+	0.162361i
$664$	−5.78980	−	27.6691i	−0.224688	−	1.07377i
$665$	12.6319	−	7.29305i	0.489845	−	0.282812i
$666$	17.0148	+	6.65569i	0.659310	+	0.257903i
$667$	19.1386	−	33.1490i	0.741050	−	1.28354i
$668$	−3.12734	+	11.3119i	−0.121000	+	0.437671i
$669$	−11.9474	+	46.8084i	−0.461912	+	1.80972i
$670$	−9.62602	−	4.03200i	−0.371886	−	0.155770i
$671$	2.35147	+	13.3359i	0.0907776	+	0.514825i
$672$	−33.7960	+	30.4792i	−1.30371	+	1.17576i
$673$	16.2031	+	13.5960i	0.624582	+	0.524087i	0.899240	−	0.437455i	$-0.144120\pi$
$673$	16.2031	+	13.5960i	0.624582	+	0.524087i	−0.274658	+	0.961542i	$0.588565\pi$
$674$	15.0176	+	0.715329i	0.578454	+	0.0275534i
$675$	19.1091	−	14.4231i	0.735509	−	0.555145i
$676$	24.2426	+	2.31474i	0.932409	+	0.0890286i
$677$	9.66175	+	8.10717i	0.371331	+	0.311584i	0.809288	−	0.587412i	$-0.199853\pi$
$677$	9.66175	+	8.10717i	0.371331	+	0.311584i	−0.437957	+	0.898996i	$0.644298\pi$
$678$	0.109685	+	0.258973i	0.00421241	+	0.00994580i
$679$	1.52175	−	0.268325i	0.0583992	−	0.0102974i
$680$	2.44251	−	4.55884i	0.0936660	−	0.174823i
$681$	37.5800	−	10.5502i	1.44007	−	0.404285i
$682$	−5.44293	+	24.0991i	−0.208421	+	0.922800i
$683$	−18.7608	−	10.8315i	−0.717860	−	0.414457i	0.0961043	−	0.995371i	$-0.469362\pi$
$683$	−18.7608	−	10.8315i	−0.717860	−	0.414457i	−0.813965	+	0.580914i	$0.802695\pi$
$684$	24.9059	+	16.8569i	0.952303	+	0.644541i
$685$	4.88741	−	2.82175i	0.186738	−	0.107813i
$686$	14.7735	+	47.5114i	0.564054	+	1.81399i
$687$	−24.2825	+	17.4369i	−0.926434	+	0.665258i
$688$	−20.3872	+	11.3434i	−0.777253	+	0.432464i
$689$	1.78985	+	2.13306i	0.0681877	+	0.0812630i
$690$	3.93795	+	6.07448i	0.149915	+	0.231251i
$691$	19.0830	−	6.94564i	0.725951	−	0.264225i	0.0475010	−	0.998871i	$-0.484874\pi$
$691$	19.0830	−	6.94564i	0.725951	−	0.264225i	0.678450	+	0.734647i	$0.262652\pi$
$692$	14.4362	+	31.6103i	0.548781	+	1.20164i
$693$	−1.32857	−	55.8336i	−0.0504684	−	2.12094i
$694$	−16.5148	−	10.6134i	−0.626894	−	0.402878i
$695$	−2.01622	+	11.4346i	−0.0764796	+	0.433738i
$696$	−5.18878	−	39.4113i	−0.196680	−	1.49388i
$697$	−23.0873	−	8.40307i	−0.874492	−	0.318289i
$698$	−28.5896	+	3.64867i	−1.08213	+	0.138104i
$699$	10.8694	+	22.6036i	0.411120	+	0.854948i
$700$	−30.5046	+	30.0248i	−1.15297	+	1.13483i
$701$	−38.5604			−1.45640			−0.728202	−	0.685362i	$-0.759644\pi$
$701$	−38.5604			−1.45640			−0.728202	+	0.685362i	$0.759644\pi$
$702$	−6.42049	−	1.80259i	−0.242326	−	0.0680345i
$703$			21.5850i			0.814093i
$704$	−26.6951	+	17.7613i	−1.00611	+	0.669406i
$705$	−7.14641	−	4.87833i	−0.269150	−	0.183728i
$706$	4.88149	−	0.622987i	0.183717	−	0.0234464i
$707$	−10.7623	+	29.5693i	−0.404760	+	1.11207i
$708$	−1.84324	+	5.12749i	−0.0692733	+	0.192703i
$709$	−12.2287	−	2.15625i	−0.459258	−	0.0809796i	−0.0607673	−	0.998152i	$-0.519355\pi$
$709$	−12.2287	−	2.15625i	−0.459258	−	0.0809796i	−0.398491	+	0.917172i	$0.630466\pi$
$710$	−3.05901	+	4.75994i	−0.114803	+	0.178637i
$711$	19.3580	−	17.0442i	0.725981	−	0.639208i
$712$	−5.71596	+	2.28839i	−0.214215	+	0.0857609i
$713$	−7.03246	−	19.3215i	−0.263368	−	0.723596i
$714$	15.0992	−	29.5756i	0.565072	−	1.10684i
$715$	−1.74563	+	1.46476i	−0.0652828	+	0.0547788i
$716$	2.95327	+	4.28969i	0.110369	+	0.160313i
$717$	−33.6540	+	3.34817i	−1.25683	+	0.125040i
$718$	−2.68418	+	0.834637i	−0.100173	+	0.0311484i
$719$	3.49686	+	6.05674i	0.130411	+	0.225878i	0.923835	−	0.382791i	$-0.125037\pi$
$719$	3.49686	+	6.05674i	0.130411	+	0.225878i	−0.793424	+	0.608669i	$0.791704\pi$
$720$	7.08485	+	2.51518i	0.264037	+	0.0937353i
$721$	27.4173	−	47.4882i	1.02107	−	1.76855i
$722$	−1.90799	+	8.44780i	−0.0710081	+	0.314395i
$723$	2.53254	−	2.59352i	0.0941862	−	0.0964540i
$724$	−16.8733	+	35.4486i	−0.627092	+	1.31744i
$725$	−6.49205	−	36.8182i	−0.241109	−	1.36739i
$726$	1.52148	−	12.3105i	0.0564673	−	0.456887i
$727$	−8.35207	+	9.95361i	−0.309761	+	0.369159i	−0.898355	−	0.439270i	$-0.855237\pi$
$727$	−8.35207	+	9.95361i	−0.309761	+	0.369159i	0.588594	+	0.808429i	$0.299682\pi$
$728$	11.8010	+	1.69662i	0.437375	+	0.0628809i
$729$	−24.2859	−	11.7982i	−0.899476	−	0.436969i
$730$	3.86346	+	0.184028i	0.142993	+	0.00681117i
$731$	10.9424	−	13.0407i	0.404720	−	0.482327i
$732$	−11.5341	−	1.98662i	−0.426314	−	0.0734277i
$733$	47.3767	−	8.35378i	1.74990	−	0.308554i	0.795247	−	0.606285i	$-0.207341\pi$
$733$	47.3767	−	8.35378i	1.74990	−	0.308554i	0.954650	+	0.297731i	$0.0962300\pi$
$734$	−1.74976	+	4.17739i	−0.0645849	+	0.154190i
$735$	11.0493	−	11.3154i	0.407560	−	0.417374i
$736$	10.6985	−	24.4466i	0.394352	−	0.901113i
$737$	−40.8852	−	23.6051i	−1.50603	−	0.869505i
$738$	7.03715	−	35.0139i	0.259041	−	1.28888i
$739$	−8.56966	−	14.8431i	−0.315240	−	0.546012i	0.664249	−	0.747512i	$-0.268752\pi$
$739$	−8.56966	−	14.8431i	−0.315240	−	0.546012i	−0.979488	+	0.201500i	$0.935418\pi$
$740$	1.35520	+	5.22293i	0.0498180	+	0.191999i
$741$	−0.779981	−	7.83994i	−0.0286533	−	0.288007i
$742$	−12.2062	−	16.0387i	−0.448105	−	0.588799i
$743$	−2.86000	+	2.39983i	−0.104923	+	0.0880412i	−0.693740	−	0.720225i	$-0.744038\pi$
$743$	−2.86000	+	2.39983i	−0.104923	+	0.0880412i	0.588817	+	0.808267i	$0.299594\pi$
$744$	−18.0093	−	11.4731i	−0.660255	−	0.420625i
$745$	−7.55669	+	2.75041i	−0.276856	+	0.100767i
$746$	−2.69882	+	1.39135i	−0.0988109	+	0.0509409i
$747$	−22.5034	+	19.8137i	−0.823357	+	0.724945i
$748$	13.5708	−	19.0578i	0.496199	−	0.696823i
$749$	9.49118	−	53.8271i	0.346800	−	1.96680i
$750$	14.0962	+	4.32188i	0.514719	+	0.157813i
$751$	−3.19769	+	8.78557i	−0.116685	+	0.320590i	−0.984263	−	0.176712i	$-0.943454\pi$
$751$	−3.19769	+	8.78557i	−0.116685	+	0.320590i	0.867577	+	0.497302i	$0.165676\pi$
$752$	−0.505664	+	31.8913i	−0.0184397	+	1.16296i
$753$	8.70140	−	12.7470i	0.317097	−	0.464525i
$754$	−7.06583	+	7.64990i	−0.257322	+	0.278593i
$755$			14.7178i			0.535636i
$756$	45.8002	+	15.2442i	1.66574	+	0.554425i
$757$		−	15.4500i		−	0.561539i	−0.959775	−	0.280770i	$-0.909410\pi$
$757$		−	15.4500i		−	0.561539i	0.959775	−	0.280770i	$-0.0905897\pi$
$758$	−10.6472	−	9.83430i	−0.386724	−	0.357198i
$759$	14.1918	+	29.5128i	0.515131	+	1.07125i
$760$	0.281890	+	8.87758i	0.0102252	+	0.322024i
$761$	4.45855	−	12.2498i	0.161622	−	0.444053i	−0.832275	−	0.554363i	$-0.812962\pi$
$761$	4.45855	−	12.2498i	0.161622	−	0.444053i	0.993897	+	0.110309i	$0.0351842\pi$
$762$	29.6713	−	6.82532i	1.07488	−	0.247255i
$763$	−3.30663	+	18.7529i	−0.119708	+	0.678899i
$764$	17.0240	−	23.9071i	0.615906	−	0.864929i
$765$	−5.48411	+	0.130496i	−0.198278	+	0.00471809i
$766$	14.4539	+	28.0364i	0.522239	+	1.01300i
$767$	1.34133	−	0.488206i	0.0484328	−	0.0176281i
$768$	−6.64085	−	26.9054i	−0.239631	−	0.970864i
$769$	−7.85539	+	6.59146i	−0.283273	+	0.237694i	−0.773341	−	0.633990i	$-0.781416\pi$
$769$	−7.85539	+	6.59146i	−0.283273	+	0.237694i	0.490069	+	0.871684i	$0.336972\pi$
$770$	13.1256	−	9.98921i	0.473013	−	0.359986i
$771$	−15.6187	+	11.2156i	−0.562494	+	0.403918i
$772$	34.3591	−	8.91517i	1.23661	−	0.320864i
$773$	11.5460	+	19.9983i	0.415281	+	0.719288i	0.995458	−	0.0952026i	$-0.0303499\pi$
$773$	11.5460	+	19.9983i	0.415281	+	0.719288i	−0.580177	+	0.814491i	$0.697017\pi$
$774$	21.1298	+	12.8795i	0.759494	+	0.462942i
$775$	−17.3923	−	10.0415i	−0.624750	−	0.360700i
$776$	−0.293599	+	0.893969i	−0.0105396	+	0.0320916i
$777$	9.36417	+	33.3553i	0.335938	+	1.19662i
$778$	−12.4161	−	5.20068i	−0.445140	−	0.186454i
$779$	41.5527	−	7.32686i	1.48878	−	0.262512i
$780$	−0.680957	−	1.84806i	−0.0243822	−	0.0661712i
$781$	−16.4524	+	19.6072i	−0.588712	+	0.701600i
$782$	−0.926416	+	19.4491i	−0.0331286	+	0.695498i
$783$	−33.6529	+	25.4004i	−1.20266	+	0.907737i
$784$	−57.2446	−	11.0323i	−2.04445	−	0.394010i
$785$	1.54128	−	1.83683i	0.0550107	−	0.0655593i
$786$	−0.748896	+	0.992177i	−0.0267122	+	0.0353898i
$787$	−2.55103	−	14.4676i	−0.0909343	−	0.515714i	−0.995918	−	0.0902670i	$-0.971228\pi$
$787$	−2.55103	−	14.4676i	−0.0909343	−	0.515714i	0.904983	−	0.425447i	$-0.139883\pi$
$788$	3.46629	+	1.64994i	0.123481	+	0.0587765i
$789$	31.9320	+	8.15032i	1.13681	+	0.290159i
$790$	7.43024	+	1.67817i	0.264356	+	0.0597066i
$791$	−0.266653	+	0.461857i	−0.00948110	+	0.0164217i
$792$	30.3510	+	15.3435i	1.07848	+	0.545207i
$793$	1.53306	+	2.65534i	0.0544406	+	0.0942939i
$794$	−15.2345	−	48.9939i	−0.540652	−	1.73873i
$795$	−1.37114	+	3.03413i	−0.0486293	+	0.107610i
$796$	18.9991	+	27.5966i	0.673406	+	0.978136i
$797$	37.4213	−	31.4002i	1.32553	−	1.11225i	0.340431	−	0.940269i	$-0.389427\pi$
$797$	37.4213	−	31.4002i	1.32553	−	1.11225i	0.985100	−	0.171983i	$-0.0550174\pi$
$798$	2.93936	+	56.9524i	0.104052	+	2.01609i
$799$	−7.95979	−	21.8693i	−0.281597	−	0.773681i
$800$	−7.34343	−	25.0080i	−0.259629	−	0.884167i
$801$	5.10110	+	4.07754i	0.180239	+	0.144073i
$802$	−39.3227	−	25.2710i	−1.38853	−	0.892350i
$803$	17.2309	+	3.03827i	0.608064	+	0.107218i
$804$	31.1531	−	26.3519i	1.09869	−	0.929361i
$805$	−4.69505	+	12.8995i	−0.165479	+	0.454649i
$806$	0.708177	+	5.54901i	0.0249445	+	0.195455i
$807$	−0.310120	+	4.10678i	−0.0109167	+	0.144566i
$808$	−12.7764	−	14.2803i	−0.449474	−	0.502379i
$809$		−	22.9120i		−	0.805542i	−0.915301	−	0.402771i	$-0.868047\pi$
$809$		−	22.9120i		−	0.805542i	0.915301	−	0.402771i	$-0.131953\pi$
$810$	−1.38457	−	7.85298i	−0.0486488	−	0.275926i
$811$	28.0030			0.983320			0.491660	−	0.870787i	$-0.336390\pi$
$811$	28.0030			0.983320			0.491660	+	0.870787i	$0.336390\pi$
$812$	53.7215	−	52.8764i	1.88525	−	1.85560i
$813$	32.4006	+	2.44670i	1.13634	+	0.0858097i
$814$	3.09006	+	24.2126i	0.108307	+	0.848651i
$815$	−5.77270	−	2.10109i	−0.202209	−	0.0735980i
$816$	11.5326	+	16.6099i	0.403723	+	0.581463i
$817$	−5.07665	+	28.7911i	−0.177610	+	1.00727i
$818$	16.7803	−	26.1109i	0.586711	−	0.912946i
$819$	−4.60649	−	11.7767i	−0.160964	−	0.411511i
$820$	9.59450	−	4.38173i	0.335055	−	0.153017i
$821$	−4.83141	+	1.75849i	−0.168617	+	0.0613717i	−0.424950	−	0.905217i	$-0.639708\pi$
$821$	−4.83141	+	1.75849i	−0.168617	+	0.0613717i	0.256332	+	0.966589i	$0.417486\pi$
$822$	1.13726	+	22.0354i	0.0396667	+	0.768574i
$823$	13.1233	+	15.6398i	0.457450	+	0.545168i	0.944632	−	0.328133i	$-0.106419\pi$
$823$	13.1233	+	15.6398i	0.457450	+	0.545168i	−0.487181	+	0.873301i	$0.661975\pi$
$824$	17.6049	+	28.3730i	0.613294	+	0.988422i
$825$	29.1474	+	13.1718i	1.01478	+	0.458585i
$826$	−9.86617	+	3.06785i	−0.343288	+	0.106744i
$827$	−7.13738	+	4.12077i	−0.248191	+	0.143293i	−0.618936	−	0.785442i	$-0.712436\pi$
$827$	−7.13738	+	4.12077i	−0.248191	+	0.143293i	0.370745	+	0.928735i	$0.379103\pi$
$828$	−28.1534	+	2.91380i	−0.978399	+	0.101261i
$829$	11.9497	+	6.89919i	0.415032	+	0.239619i	0.692949	−	0.720986i	$-0.256311\pi$
$829$	11.9497	+	6.89919i	0.415032	+	0.239619i	−0.277918	+	0.960605i	$0.589644\pi$
$830$	−8.63756	−	1.95085i	−0.299814	−	0.0677151i
$831$	−1.77418	+	6.95104i	−0.0615456	+	0.241129i
$832$	−4.30441	+	5.84634i	−0.149228	+	0.202685i
$833$	41.8917	−	7.38664i	1.45146	−	0.255932i
$834$	−36.2332	−	27.3489i	−1.25465	−	0.947015i
$835$	2.81630	+	2.36315i	0.0974620	+	0.0817803i
$836$	−3.81903	+	39.9972i	−0.132084	+	1.38333i
$837$	−1.16771	+	22.6186i	−0.0403620	+	0.781813i
$838$	1.07438	−	22.5554i	0.0371138	−	0.779164i
$839$	39.2115	+	32.9024i	1.35373	+	1.13592i	0.977863	+	0.209244i	$0.0671003\pi$
$839$	39.2115	+	32.9024i	1.35373	+	1.13592i	0.375869	+	0.926673i	$0.377344\pi$
$840$	4.28695	+	13.5963i	0.147914	+	0.469115i
$841$	6.39731	+	36.2809i	0.220597	+	1.25107i
$842$	15.8099	−	37.7446i	0.544844	−	1.30076i
$843$	−26.3686	+	7.40272i	−0.908183	+	0.254963i
$844$	3.61870	−	13.0892i	0.124561	−	0.450550i
$845$	3.81430	−	6.60656i	0.131216	−	0.227273i
$846$	29.6920	−	16.2128i	1.02083	−	0.557409i
$847$	20.3701	−	11.7607i	0.699926	−	0.404102i
$848$	12.1191	−	1.93935i	0.416172	−	0.0665974i
$849$	−8.89662	−	12.3894i	−0.305331	−	0.425202i
$850$	11.5175	+	15.1337i	0.395046	+	0.519081i
$851$	−13.0578	−	15.5616i	−0.447614	−	0.533446i
$852$	−11.1369	−	19.1142i	−0.381545	−	0.654841i
$853$	−15.2286	−	41.8402i	−0.521417	−	1.43258i	−0.868943	−	0.494912i	$-0.835200\pi$
$853$	−15.2286	−	41.8402i	−0.521417	−	1.43258i	0.347526	−	0.937670i	$-0.387022\pi$
$854$	−10.1698	−	19.7265i	−0.348002	−	0.675025i
$855$	8.04433	−	4.90317i	0.275110	−	0.167685i
$856$	26.1625	+	20.5740i	0.894216	+	0.703206i
$857$	−2.44277	−	0.430726i	−0.0834434	−	0.0147133i	0.131771	−	0.991280i	$-0.457934\pi$
$857$	−2.44277	−	0.430726i	−0.0834434	−	0.0147133i	−0.215214	+	0.976567i	$0.569045\pi$
$858$	−1.99728	−	8.68265i	−0.0681860	−	0.296421i
$859$	22.1180	+	8.05028i	0.754655	+	0.274672i	0.690563	−	0.723272i	$-0.257363\pi$
$859$	22.1180	+	8.05028i	0.754655	+	0.274672i	0.0640917	+	0.997944i	$0.479585\pi$
$860$	0.579228	+	7.28533i	0.0197515	+	0.248428i
$861$	61.0328	−	29.3489i	2.07999	−	1.00021i
$862$	−31.8977	−	29.4623i	−1.08644	−	1.00349i
$863$	−24.1686			−0.822708			−0.411354	−	0.911476i	$-0.634944\pi$
$863$	−24.1686			−0.822708			−0.411354	+	0.911476i	$0.634944\pi$
$864$	−21.3536	+	20.1996i	−0.726465	+	0.687204i
$865$	10.8858			0.370127
$866$	−25.2777	−	23.3477i	−0.858970	−	0.793387i
$867$	12.1330	+	8.28227i	0.412057	+	0.281280i
$868$	−3.20918	−	40.3640i	−0.108927	−	1.37004i
$869$	32.3802	+	11.7854i	1.09842	+	0.399793i
$870$	−11.9052	−	3.65014i	−0.403625	−	0.123751i
$871$	−10.5271	−	1.85620i	−0.356696	−	0.0628951i
$872$	−9.11477	−	7.16780i	−0.308665	−	0.242732i
$873$	0.978462	−	0.196637i	0.0331159	−	0.00665516i
$874$	−15.3227	−	29.7217i	−0.518298	−	1.00535i
$875$	9.56217	+	26.2719i	0.323260	+	0.888151i
$876$	−7.50915	+	13.1263i	−0.253711	+	0.443495i
$877$	−12.5608	−	14.9694i	−0.424148	−	0.505480i	0.511077	−	0.859535i	$-0.329247\pi$
$877$	−12.5608	−	14.9694i	−0.424148	−	0.505480i	−0.935224	+	0.354056i	$0.884802\pi$
$878$	−13.6088	−	17.8817i	−0.459275	−	0.603477i
$879$	−16.3795	+	1.62956i	−0.552466	+	0.0549638i
$880$	1.58710	+	9.91792i	0.0535012	+	0.334333i
$881$	−39.3096	+	22.6954i	−1.32437	+	0.764627i	−0.984423	−	0.175817i	$-0.943743\pi$
$881$	−39.3096	+	22.6954i	−1.32437	+	0.764627i	−0.339950	+	0.940444i	$0.610410\pi$
$882$	19.7595	+	58.5922i	0.665336	+	1.97290i
$883$	21.0724	−	36.4984i	0.709142	−	1.22827i	−0.256034	−	0.966668i	$-0.582416\pi$
$883$	21.0724	−	36.4984i	0.709142	−	1.22827i	0.965176	−	0.261602i	$-0.0842509\pi$
$884$	1.41158	−	5.10583i	0.0474765	−	0.171728i
$885$	1.22118	+	1.19247i	0.0410495	+	0.0400844i
$886$	−11.6171	+	27.7347i	−0.390284	+	0.931766i
$887$	−1.04275	−	5.91374i	−0.0350122	−	0.198564i	0.962284	−	0.272045i	$-0.0877001\pi$
$887$	−1.04275	−	5.91374i	−0.0350122	−	0.198564i	−0.997297	+	0.0734815i	$0.976589\pi$
$888$	−20.5966	−	4.56606i	−0.691176	−	0.153227i
$889$	44.2264	+	37.1104i	1.48331	+	1.24464i
$890$	−0.0917655	+	1.92652i	−0.00307599	+	0.0645770i
$891$	−1.71571	−	36.0311i	−0.0574785	−	1.20709i
$892$	5.30213	−	55.5300i	0.177528	−	1.85928i
$893$	30.6171	+	25.6908i	1.02456	+	0.859711i
$894$	3.85651	−	31.2036i	0.128981	−	1.04361i
$895$	1.60663	−	0.283293i	0.0537039	−	0.00946944i
$896$	33.1349	−	40.7874i	1.10696	−	1.36261i
$897$	5.30507	+	5.18033i	0.177131	+	0.172966i
$898$	−16.5241	−	3.73208i	−0.551416	−	0.124541i
$899$	30.6295	+	17.6839i	1.02155	+	0.589792i
$900$	−19.2354	+	19.8556i	−0.641179	+	0.661852i
$901$	−7.75560	+	4.47770i	−0.258377	+	0.149174i
$902$	45.5621	−	14.1674i	1.51705	−	0.471722i
$903$	4.64544	+	46.6934i	0.154590	+	1.55386i
$904$	−0.171220	−	0.275948i	−0.00569469	−	0.00917790i
$905$	7.90510	+	9.42093i	0.262774	+	0.313162i
$906$	−51.2506	−	26.1648i	−1.70269	−	0.869269i
$907$	−24.0330	+	8.74731i	−0.798004	+	0.290450i	−0.708659	−	0.705551i	$-0.750699\pi$
$907$	−24.0330	+	8.74731i	−0.798004	+	0.290450i	−0.0893447	+	0.996001i	$0.528477\pi$
$908$	−40.9981	+	18.7235i	−1.36057	+	0.621362i
$909$	−6.49489	+	19.2581i	−0.215422	+	0.638752i
$910$	2.01913	−	3.14184i	0.0669334	−	0.104151i
$911$	4.86428	−	27.5867i	0.161161	−	0.913988i	−0.791774	−	0.610814i	$-0.790842\pi$
$911$	4.86428	−	27.5867i	0.161161	−	0.913988i	0.952935	−	0.303175i	$-0.0980465\pi$
$912$	−31.4148	−	14.8007i	−1.04025	−	0.490099i
$913$	−37.6416	−	13.7004i	−1.24575	−	0.453418i
$914$	4.60155	+	36.0560i	0.152206	+	1.19263i
$915$	−2.06703	+	3.02806i	−0.0683340	+	0.100105i
$916$	24.6015	−	24.2145i	0.812857	−	0.800070i
$917$	−2.35720			−0.0778414
$918$	9.29505	−	19.3288i	0.306782	−	0.637947i
$919$			49.4765i			1.63208i	0.577996	+	0.816040i	$0.303835\pi$
$919$			49.4765i			1.63208i	−0.577996	+	0.816040i	$0.696165\pi$
$920$	−5.57369	−	6.22974i	−0.183759	−	0.205388i
$921$	−23.0689	+	11.0932i	−0.760145	+	0.365532i
$922$	4.61750	+	36.1810i	0.152069	+	1.19156i
$923$	−1.98213	+	5.44586i	−0.0652427	+	0.179253i
$924$	11.4504	+	63.4646i	0.376690	+	2.08783i
$925$	−19.5400	−	3.44542i	−0.642470	−	0.113285i
$926$	−28.8344	−	18.5306i	−0.947557	−	0.608954i
$927$	16.9736	−	31.0842i	0.557487	−	1.02094i
$928$	12.9325	+	44.0415i	0.424529	+	1.44573i
$929$	6.23688	+	17.1357i	0.204625	+	0.562203i	0.998975	−	0.0452568i	$-0.0144106\pi$
$929$	6.23688	+	17.1357i	0.204625	+	0.562203i	−0.794350	+	0.607460i	$0.792188\pi$
$930$	−5.61277	+	3.63864i	−0.184050	+	0.119316i
$931$	−55.9618	+	46.9575i	−1.83407	+	1.53897i
$932$	−16.4230	−	23.8547i	−0.537952	−	0.781386i
$933$	−30.1774	−	42.0249i	−0.987965	−	1.37583i
$934$	−0.874536	−	2.81250i	−0.0286157	−	0.0920277i
$935$	−3.66441	−	6.34695i	−0.119839	−	0.207567i
$936$	7.64594	+	0.914184i	0.249915	+	0.0298810i
$937$	−11.2761	+	19.5307i	−0.368373	+	0.638041i	−0.989311	−	0.145819i	$-0.953418\pi$
$937$	−11.2761	+	19.5307i	−0.368373	+	0.638041i	0.620938	+	0.783859i	$0.286752\pi$
$938$	75.4728	+	17.0460i	2.46427	+	0.556573i
$939$	−2.19975	−	7.83556i	−0.0717863	−	0.255704i
$940$	9.02142	+	4.29415i	0.294246	+	0.140060i
$941$	10.3351	+	58.6135i	0.336916	+	1.91075i	0.407434	+	0.913235i	$0.366424\pi$
$941$	10.3351	+	58.6135i	0.336916	+	1.91075i	−0.0705179	+	0.997511i	$0.522465\pi$
$942$	3.65620	+	8.63254i	0.119125	+	0.281263i
$943$	−25.5249	+	30.4194i	−0.831206	+	0.990592i
$944$	1.19063	−	6.17797i	0.0387516	−	0.201076i
$945$	10.3038	−	11.0667i	0.335182	−	0.360001i
$946$	−1.57296	+	33.0227i	−0.0511415	+	1.07366i
$947$	−33.2910	+	39.6746i	−1.08181	+	1.28925i	−0.127045	+	0.991897i	$0.540549\pi$
$947$	−33.2910	+	39.6746i	−1.08181	+	1.28925i	−0.954767	+	0.297356i	$0.903895\pi$
$948$	−19.0530	+	22.8903i	−0.618812	+	0.743442i
$949$	3.90146	−	0.687933i	0.126647	−	0.0223312i
$950$	−30.1246	−	12.6182i	−0.977372	−	0.409387i
$951$	17.6996	+	4.51765i	0.573950	+	0.146495i
$952$	−11.9643	+	36.4297i	−0.387765	+	1.18069i
$953$	19.9155	+	11.4982i	0.645125	+	0.372463i	0.786586	−	0.617481i	$-0.211847\pi$
$953$	19.9155	+	11.4982i	0.645125	+	0.372463i	−0.141461	+	0.989944i	$0.545180\pi$
$954$	−8.12794	−	10.1686i	−0.263152	−	0.329220i
$955$	−4.59683	−	7.96194i	−0.148750	−	0.257642i
$956$	37.8004	−	9.80808i	1.22255	−	0.317216i
$957$	−51.3312	−	23.1968i	−1.65930	−	0.749847i
$958$	12.9782	−	9.87706i	0.419307	−	0.319113i
$959$	−32.0515	+	26.8944i	−1.03500	+	0.868464i
$960$	−8.53070	−	1.60897i	−0.275327	−	0.0519293i
$961$	−11.2775	+	4.10469i	−0.363791	+	0.132409i
$962$	2.53252	+	4.91236i	0.0816516	+	0.158381i
$963$	5.30139	−	34.9018i	0.170835	−	1.12469i
$964$	−2.42793	+	3.40959i	−0.0781983	+	0.109816i
$965$	1.93088	−	10.9505i	0.0621571	−	0.352511i
$966$	−36.5723	−	39.2815i	−1.17669	−	1.26386i
$967$	5.56318	−	15.2847i	0.178900	−	0.491523i	−0.817536	−	0.575877i	$-0.804661\pi$
$967$	5.56318	−	15.2847i	0.178900	−	0.491523i	0.996436	+	0.0843543i	$0.0268828\pi$
$968$	0.454573	+	14.3159i	0.0146105	+	0.460131i
$969$	25.2670	+	1.90801i	0.811692	+	0.0612942i
$970$	0.216524	+	0.199993i	0.00695218	+	0.00642138i
$971$		−	38.0842i		−	1.22218i	−0.791561	−	0.611090i	$-0.790731\pi$
$971$		−	38.0842i		−	1.22218i	0.791561	−	0.611090i	$-0.209269\pi$
$972$	29.8072	+	9.13940i	0.956068	+	0.293146i
$973$		−	86.0823i		−	2.75967i
$974$	−28.0529	+	30.3718i	−0.898872	+	0.973174i
$975$	7.22166	+	0.545337i	0.231278	+	0.0174648i
$976$	13.5129	+	0.214259i	0.432537	+	0.00685825i
$977$	−10.6918	+	29.3754i	−0.342060	+	0.939803i	0.642736	+	0.766088i	$0.277799\pi$
$977$	−10.6918	+	29.3754i	−0.342060	+	0.939803i	−0.984796	+	0.173715i	$0.944423\pi$
$978$	17.5790	−	16.3665i	0.562113	−	0.523344i
$979$	−1.51503	+	8.59219i	−0.0484207	+	0.274608i
$980$	−10.5929	+	14.8758i	−0.338378	+	0.475191i
$981$	−1.84695	+	12.1594i	−0.0589686	+	0.388221i
$982$	6.47163	−	3.33638i	0.206518	−	0.106468i
$983$	52.5891	−	19.1409i	1.67733	−	0.610498i	0.684390	−	0.729116i	$-0.260068\pi$
$983$	52.5891	−	19.1409i	1.67733	−	0.610498i	0.992940	+	0.118617i	$0.0378462\pi$
$984$	−1.79864	+	41.1998i	−0.0573385	+	1.31340i
$985$	0.921212	−	0.772989i	0.0293523	−	0.0246295i
$986$	−20.2833	−	26.6518i	−0.645953	−	0.848767i
$987$	58.4581	+	26.4175i	1.86074	+	0.840879i
$988$	2.28486	+	8.80587i	0.0726912	+	0.280152i
$989$	−13.7571	−	23.8280i	−0.437450	−	0.757685i
$990$	8.32166	−	6.65166i	0.264480	−	0.211404i
$991$	−33.9036	−	19.5742i	−1.07698	−	0.621796i	−0.146901	−	0.989151i	$-0.546930\pi$
$991$	−33.9036	−	19.5742i	−1.07698	−	0.621796i	−0.930081	+	0.367355i	$0.880263\pi$
$992$	22.5885	+	9.88533i	0.717184	+	0.313859i
$993$	−20.1560	−	5.14461i	−0.639631	−	0.163259i
$994$	16.2066	−	38.6917i	0.514042	−	1.22723i
$995$	10.3359	−	1.82249i	0.327669	−	0.0577769i
$996$	22.1489	−	26.6097i	0.701814	−	0.843161i
$997$	−9.08868	+	10.8315i	−0.287841	+	0.343036i	−0.890517	−	0.454950i	$-0.849657\pi$
$997$	−9.08868	+	10.8315i	−0.287841	+	0.343036i	0.602675	+	0.797986i	$0.294101\pi$
$998$	35.8847	+	1.70929i	1.13591	+	0.0541066i
$999$	6.55890	+	21.3935i	0.207514	+	0.676861i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.9	✓	192
3.2	odd	2		648.2.v.b.35.24		192
4.3	odd	2		864.2.bh.b.335.14		192
8.3	odd	2	inner	216.2.v.b.11.26	yes	192
8.5	even	2		864.2.bh.b.335.13		192
24.11	even	2		648.2.v.b.35.7		192
27.5	odd	18	inner	216.2.v.b.59.26	yes	192
27.22	even	9		648.2.v.b.611.7		192
108.59	even	18		864.2.bh.b.815.13		192
216.5	odd	18		864.2.bh.b.815.14		192
216.59	even	18	inner	216.2.v.b.59.9	yes	192
216.211	odd	18		648.2.v.b.611.24		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.9	✓	192	1.1	even	1	trivial
216.2.v.b.11.26	yes	192	8.3	odd	2	inner
216.2.v.b.59.9	yes	192	216.59	even	18	inner
216.2.v.b.59.26	yes	192	27.5	odd	18	inner
648.2.v.b.35.7		192	24.11	even	2
648.2.v.b.35.24		192	3.2	odd	2
648.2.v.b.611.7		192	27.22	even	9
648.2.v.b.611.24		192	216.211	odd	18
864.2.bh.b.335.13		192	8.5	even	2
864.2.bh.b.335.14		192	4.3	odd	2
864.2.bh.b.815.13		192	108.59	even	18
864.2.bh.b.815.14		192	216.5	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03887 - 0.959554i) q^{2} +(0.130423 - 1.72713i) q^{3} +(0.158512 + 1.99371i) q^{4} +(0.588722 + 0.214277i) q^{5} +(-1.79277 + 1.66912i) q^{6} +(-4.57427 - 0.806567i) q^{7} +(1.74840 - 2.22331i) q^{8} +(-2.96598 - 0.450516i) q^{9} +O(q^{10})\)	\(q+(-1.03887 - 0.959554i) q^{2} +(0.130423 - 1.72713i) q^{3} +(0.158512 + 1.99371i) q^{4} +(0.588722 + 0.214277i) q^{5} +(-1.79277 + 1.66912i) q^{6} +(-4.57427 - 0.806567i) q^{7} +(1.74840 - 2.22331i) q^{8} +(-2.96598 - 0.450516i) q^{9} +(-0.405997 - 0.787518i) q^{10} +(-1.37081 - 3.76628i) q^{11} +(3.46407 - 0.0137460i) q^{12} +(-0.583330 - 0.695185i) q^{13} +(3.97814 + 5.22718i) q^{14} +(0.446868 - 0.988855i) q^{15} +(-3.94975 + 0.632053i) q^{16} +(2.52763 - 1.45933i) q^{17} +(2.64898 + 3.31405i) q^{18} +(-2.50619 + 4.34085i) q^{19} +(-0.333887 + 1.20771i) q^{20} +(-1.98964 + 7.79518i) q^{21} +(-2.18985 + 5.22805i) q^{22} +(-0.819150 - 4.64563i) q^{23} +(-3.61192 - 3.30969i) q^{24} +(-3.52954 - 2.96164i) q^{25} +(-0.0610627 + 1.28195i) q^{26} +(-1.16493 + 5.06389i) q^{27} +(0.882983 - 9.24761i) q^{28} +(6.21586 + 5.21572i) q^{29} +(-1.41310 + 0.598500i) q^{30} +(4.29253 - 0.756889i) q^{31} +(4.70977 + 3.13337i) q^{32} +(-6.68365 + 1.87637i) q^{33} +(-4.02619 - 0.909343i) q^{34} +(-2.52015 - 1.45501i) q^{35} +(0.428054 - 5.98471i) q^{36} +(3.72940 - 2.15317i) q^{37} +(6.76889 - 2.10476i) q^{38} +(-1.27676 + 0.916820i) q^{39} +(1.50573 - 0.934270i) q^{40} +(-5.41092 - 6.44848i) q^{41} +(9.54688 - 6.18903i) q^{42} +(5.48086 - 1.99487i) q^{43} +(7.29157 - 3.33000i) q^{44} +(-1.64960 - 0.900771i) q^{45} +(-3.60674 + 5.61224i) q^{46} +(1.38464 - 7.85268i) q^{47} +(0.576503 + 6.90418i) q^{48} +(13.6955 + 4.98477i) q^{49} +(0.824893 + 6.46355i) q^{50} +(-2.19079 - 4.55589i) q^{51} +(1.29353 - 1.27318i) q^{52} -3.06833 q^{53} +(6.06929 - 4.14291i) q^{54} -2.51103i q^{55} +(-9.79089 + 8.75982i) q^{56} +(7.17036 + 4.89467i) q^{57} +(-1.45271 - 11.3829i) q^{58} +(-0.537968 + 1.47805i) q^{59} +(2.04232 + 0.734180i) q^{60} +(-3.32732 - 0.586696i) q^{61} +(-5.18567 - 3.33260i) q^{62} +(13.2038 + 4.45304i) q^{63} +(-1.88621 - 7.77446i) q^{64} +(-0.194457 - 0.534265i) q^{65} +(8.74394 + 4.46402i) q^{66} +(9.02325 - 7.57140i) q^{67} +(3.31014 + 4.80804i) q^{68} +(-8.13046 + 0.808885i) q^{69} +(1.22195 + 3.92978i) q^{70} +(-3.19304 - 5.53051i) q^{71} +(-6.18735 + 5.80661i) q^{72} +(-2.18272 + 3.78059i) q^{73} +(-5.94045 - 1.34169i) q^{74} +(-5.57548 + 5.70973i) q^{75} +(-9.05165 - 4.30854i) q^{76} +(3.23271 + 18.3336i) q^{77} +(2.20613 + 0.272659i) q^{78} +(-5.52630 + 6.58598i) q^{79} +(-2.46074 - 0.474238i) q^{80} +(8.59407 + 2.67244i) q^{81} +(-0.566412 + 11.8912i) q^{82} +(6.42426 - 7.65613i) q^{83} +(-15.8567 - 2.73113i) q^{84} +(1.80077 - 0.317525i) q^{85} +(-7.60810 - 3.18677i) q^{86} +(9.81894 - 10.0554i) q^{87} +(-10.7703 - 3.53721i) q^{88} +(-1.88520 - 1.08842i) q^{89} +(0.849389 + 2.51867i) q^{90} +(2.10759 + 3.65046i) q^{91} +(9.13219 - 2.36954i) q^{92} +(-0.747404 - 7.51249i) q^{93} +(-8.97354 + 6.82930i) q^{94} +(-2.40560 + 2.01853i) q^{95} +(6.02602 - 7.72574i) q^{96} +(-0.312612 + 0.113782i) q^{97} +(-9.44477 - 18.3202i) q^{98} +(2.36904 + 11.7883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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