LMFDB - Embedded newform 369.2.u.a.226.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(46,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(20))

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

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

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

chi := DirichletCharacter("369.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.u (of order $20$, degree $8$, 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:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			226.3
Character	$\chi$	$=$	369.226
Dual form			369.2.u.a.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05153 + 0.666584i) q^{2} +(2.14642 + 1.55947i) q^{4} +(-1.72514 + 2.37446i) q^{5} +(-1.11329 + 2.18496i) q^{7} +(0.828108 + 1.13979i) q^{8} +O(q^{10})$	\(q+(2.05153 + 0.666584i) q^{2} +(2.14642 + 1.55947i) q^{4} +(-1.72514 + 2.37446i) q^{5} +(-1.11329 + 2.18496i) q^{7} +(0.828108 + 1.13979i) q^{8} +(-5.12196 + 3.72132i) q^{10} +(6.07021 + 0.961426i) q^{11} +(0.531087 - 0.270602i) q^{13} +(-3.74042 + 3.74042i) q^{14} +(-0.700597 - 2.15622i) q^{16} +(-0.0921689 + 0.581932i) q^{17} +(-1.67787 - 0.854919i) q^{19} +(-7.40577 + 2.40628i) q^{20} +(11.8124 + 6.01870i) q^{22} +(1.21857 - 3.75036i) q^{23} +(-1.11684 - 3.43727i) q^{25} +(1.26992 - 0.201136i) q^{26} +(-5.79698 + 2.95371i) q^{28} +(-0.785988 - 4.96253i) q^{29} +(4.03548 - 2.93195i) q^{31} -7.70828i q^{32} +(-0.576994 + 1.13241i) q^{34} +(-3.26751 - 6.41285i) q^{35} +(-1.87618 - 1.36313i) q^{37} +(-2.87234 - 2.87234i) q^{38} -4.13499 q^{40} +(1.29313 + 6.27119i) q^{41} +(2.50072 + 0.812532i) q^{43} +(11.5299 + 11.5299i) q^{44} +(4.99986 - 6.88172i) q^{46} +(-2.33269 - 4.57815i) q^{47} +(0.579854 + 0.798101i) q^{49} -7.79615i q^{50} +(1.56193 + 0.247386i) q^{52} +(-0.818669 - 5.16887i) q^{53} +(-12.7548 + 12.7548i) q^{55} +(-3.41233 + 0.540460i) q^{56} +(1.69546 - 10.7047i) q^{58} +(-3.23058 + 9.94272i) q^{59} +(0.968261 - 0.314607i) q^{61} +(10.2333 - 3.32501i) q^{62} +(3.73702 - 11.5014i) q^{64} +(-0.273668 + 1.72787i) q^{65} +(-3.42634 + 0.542679i) q^{67} +(-1.10534 + 1.10534i) q^{68} +(-2.42870 - 15.3342i) q^{70} +(-4.74402 - 0.751379i) q^{71} +0.596626i q^{73} +(-2.94042 - 4.04714i) q^{74} +(-2.26821 - 4.45161i) q^{76} +(-8.85861 + 12.1928i) q^{77} +(3.13817 + 3.13817i) q^{79} +(6.32847 + 2.05625i) q^{80} +(-1.52737 + 13.7275i) q^{82} -3.79458 q^{83} +(-1.22277 - 1.22277i) q^{85} +(4.58868 + 3.33387i) q^{86} +(3.93096 + 7.71494i) q^{88} +(5.50333 - 10.8009i) q^{89} +1.46167i q^{91} +(8.46413 - 6.14955i) q^{92} +(-1.73386 - 10.9472i) q^{94} +(4.92454 - 2.50918i) q^{95} +(-10.0255 + 1.58788i) q^{97} +(0.657590 + 2.02385i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	2.05153	+	0.666584i	1.45065	+	0.471346i	0.925201	−	0.379477i	$-0.123896\pi$
$2$	2.05153	+	0.666584i	1.45065	+	0.471346i	0.525452	+	0.850823i	$0.323896\pi$
$3$		0			0
$3$		0			0
$4$	2.14642	+	1.55947i	1.07321	+	0.779734i
$5$	−1.72514	+	2.37446i	−0.771508	+	1.06189i	0.224661	+	0.974437i	$0.427873\pi$
$5$	−1.72514	+	2.37446i	−0.771508	+	1.06189i	−0.996169	+	0.0874522i	$0.972127\pi$
$6$		0			0
$7$	−1.11329	+	2.18496i	−0.420786	+	0.825839i	0.579158	+	0.815216i	$0.303382\pi$
$7$	−1.11329	+	2.18496i	−0.420786	+	0.825839i	−0.999944	+	0.0106232i	$0.996618\pi$
$8$	0.828108	+	1.13979i	0.292780	+	0.402977i
$9$		0			0
$10$	−5.12196	+	3.72132i	−1.61971	+	1.17679i
$11$	6.07021	+	0.961426i	1.83024	+	0.289881i	0.973974	−	0.226660i	$-0.0727808\pi$
$11$	6.07021	+	0.961426i	1.83024	+	0.289881i	0.856262	+	0.516541i	$0.172781\pi$
$12$		0			0
$13$	0.531087	−	0.270602i	0.147297	−	0.0750516i	−0.378788	−	0.925483i	$-0.623659\pi$
$13$	0.531087	−	0.270602i	0.147297	−	0.0750516i	0.526085	+	0.850432i	$0.323659\pi$
$14$	−3.74042	+	3.74042i	−0.999670	+	0.999670i
$15$		0			0
$16$	−0.700597	−	2.15622i	−0.175149	−	0.539054i
$17$	−0.0921689	+	0.581932i	−0.0223542	+	0.141139i	−0.996341	−	0.0854651i	$-0.972762\pi$
$17$	−0.0921689	+	0.581932i	−0.0223542	+	0.141139i	0.973987	+	0.226604i	$0.0727624\pi$
$18$		0			0
$19$	−1.67787	−	0.854919i	−0.384931	−	0.196132i	0.250807	−	0.968037i	$-0.419304\pi$
$19$	−1.67787	−	0.854919i	−0.384931	−	0.196132i	−0.635738	+	0.771905i	$0.719304\pi$
$20$	−7.40577	+	2.40628i	−1.65598	+	0.538061i
$21$		0			0
$22$	11.8124	+	6.01870i	2.51840	+	1.28319i
$23$	1.21857	−	3.75036i	0.254089	−	0.782005i	−0.739919	−	0.672696i	$-0.765136\pi$
$23$	1.21857	−	3.75036i	0.254089	−	0.782005i	0.994008	−	0.109309i	$-0.0348637\pi$
$24$		0			0
$25$	−1.11684	−	3.43727i	−0.223368	−	0.687455i
$26$	1.26992	−	0.201136i	0.249052	−	0.0394460i
$27$		0			0
$28$	−5.79698	+	2.95371i	−1.09553	+	0.558199i
$29$	−0.785988	−	4.96253i	−0.145954	−	0.921519i	−0.946607	−	0.322390i	$-0.895514\pi$
$29$	−0.785988	−	4.96253i	−0.145954	−	0.921519i	0.800652	−	0.599129i	$-0.204486\pi$
$30$		0			0
$31$	4.03548	−	2.93195i	0.724794	−	0.526593i	−0.163118	−	0.986606i	$-0.552155\pi$
$31$	4.03548	−	2.93195i	0.724794	−	0.526593i	0.887912	+	0.460013i	$0.152155\pi$
$32$		−	7.70828i		−	1.36264i
$33$		0			0
$34$	−0.576994	+	1.13241i	−0.0989536	+	0.194207i
$35$	−3.26751	−	6.41285i	−0.552310	−	1.08397i
$36$		0			0
$37$	−1.87618	−	1.36313i	−0.308443	−	0.224097i	0.422785	−	0.906230i	$-0.361052\pi$
$37$	−1.87618	−	1.36313i	−0.308443	−	0.224097i	−0.731228	+	0.682133i	$0.761052\pi$
$38$	−2.87234	−	2.87234i	−0.465955	−	0.465955i
$39$		0			0
$40$	−4.13499			−0.653800
$41$	1.29313	+	6.27119i	0.201953	+	0.979395i
$41$	1.29313	+	6.27119i	0.201953	+	0.979395i
$42$		0			0
$43$	2.50072	+	0.812532i	0.381356	+	0.123910i	0.493420	−	0.869791i	$-0.335746\pi$
$43$	2.50072	+	0.812532i	0.381356	+	0.123910i	−0.112065	+	0.993701i	$0.535746\pi$
$44$	11.5299	+	11.5299i	1.73820	+	1.73820i
$45$		0			0
$46$	4.99986	−	6.88172i	0.737189	−	1.01465i
$47$	−2.33269	−	4.57815i	−0.340257	−	0.667792i	0.655950	−	0.754804i	$-0.272268\pi$
$47$	−2.33269	−	4.57815i	−0.340257	−	0.667792i	−0.996207	+	0.0870119i	$0.972268\pi$
$48$		0			0
$49$	0.579854	+	0.798101i	0.0828364	+	0.114014i
$50$		−	7.79615i		−	1.10254i
$51$		0			0
$52$	1.56193	+	0.247386i	0.216601	+	0.0343062i
$53$	−0.818669	−	5.16887i	−0.112453	−	0.710000i	−0.977912	−	0.209019i	$-0.932973\pi$
$53$	−0.818669	−	5.16887i	−0.112453	−	0.710000i	0.865459	−	0.500980i	$-0.167027\pi$
$54$		0			0
$55$	−12.7548	+	12.7548i	−1.71986	+	1.71986i
$56$	−3.41233	+	0.540460i	−0.455992	+	0.0722221i
$57$		0			0
$58$	1.69546	−	10.7047i	0.222625	−	1.40560i
$59$	−3.23058	+	9.94272i	−0.420586	+	1.29443i	0.486572	+	0.873641i	$0.338247\pi$
$59$	−3.23058	+	9.94272i	−0.420586	+	1.29443i	−0.907158	+	0.420791i	$0.861753\pi$
$60$		0			0
$61$	0.968261	−	0.314607i	0.123973	−	0.0402813i	−0.246373	−	0.969175i	$-0.579239\pi$
$61$	0.968261	−	0.314607i	0.123973	−	0.0402813i	0.370347	+	0.928894i	$0.379239\pi$
$62$	10.2333	−	3.32501i	1.29963	−	0.422276i
$63$		0			0
$64$	3.73702	−	11.5014i	0.467127	−	1.43767i
$65$	−0.273668	+	1.72787i	−0.0339443	+	0.214316i
$66$		0			0
$67$	−3.42634	+	0.542679i	−0.418594	+	0.0662988i	−0.362179	−	0.932109i	$-0.617967\pi$
$67$	−3.42634	+	0.542679i	−0.418594	+	0.0662988i	−0.0564152	+	0.998407i	$0.517967\pi$
$68$	−1.10534	+	1.10534i	−0.134042	+	0.134042i
$69$		0			0
$70$	−2.42870	−	15.3342i	−0.290286	−	1.83279i
$71$	−4.74402	−	0.751379i	−0.563012	−	0.0891723i	−0.131560	−	0.991308i	$-0.541999\pi$
$71$	−4.74402	−	0.751379i	−0.563012	−	0.0891723i	−0.431452	+	0.902136i	$0.641999\pi$
$72$		0			0
$73$			0.596626i			0.0698297i	0.999390	+	0.0349149i	$0.0111160\pi$
$73$			0.596626i			0.0698297i	−0.999390	+	0.0349149i	$0.988884\pi$
$74$	−2.94042	−	4.04714i	−0.341816	−	0.470470i
$75$		0			0
$76$	−2.26821	−	4.45161i	−0.260181	−	0.510634i
$77$	−8.85861	+	12.1928i	−1.00953	+	1.38950i
$78$		0			0
$79$	3.13817	+	3.13817i	0.353072	+	0.353072i	0.861251	−	0.508179i	$-0.169681\pi$
$79$	3.13817	+	3.13817i	0.353072	+	0.353072i	−0.508179	+	0.861251i	$0.669681\pi$
$80$	6.32847	+	2.05625i	0.707545	+	0.229895i
$81$		0			0
$82$	−1.52737	+	13.7275i	−0.168670	+	1.51595i
$83$	−3.79458			−0.416509			−0.208254	−	0.978075i	$-0.566778\pi$
$83$	−3.79458			−0.416509			−0.208254	+	0.978075i	$0.566778\pi$
$84$		0			0
$85$	−1.22277	−	1.22277i	−0.132628	−	0.132628i
$86$	4.58868	+	3.33387i	0.494811	+	0.359501i
$87$		0			0
$88$	3.93096	+	7.71494i	0.419042	+	0.822415i
$89$	5.50333	−	10.8009i	0.583352	−	1.14489i	−0.391111	−	0.920343i	$-0.627909\pi$
$89$	5.50333	−	10.8009i	0.583352	−	1.14489i	0.974463	−	0.224549i	$-0.0720908\pi$
$90$		0			0
$91$			1.46167i			0.153224i
$92$	8.46413	−	6.14955i	0.882446	−	0.641135i
$93$		0			0
$94$	−1.73386	−	10.9472i	−0.178834	−	1.12911i
$95$	4.92454	−	2.50918i	0.505247	−	0.257436i
$96$		0			0
$97$	−10.0255	+	1.58788i	−1.01793	+	0.161224i	−0.643030	−	0.765841i	$-0.722323\pi$
$97$	−10.0255	+	1.58788i	−1.01793	+	0.161224i	−0.374900	+	0.927065i	$0.622323\pi$
$98$	0.657590	+	2.02385i	0.0664266	+	0.204440i
$99$		0			0
$100$	2.96311	−	9.11951i	0.296311	−	0.911951i
$101$	−3.94458	−	2.00986i	−0.392500	−	0.199989i	0.246591	−	0.969120i	$-0.420689\pi$
$101$	−3.94458	−	2.00986i	−0.392500	−	0.199989i	−0.639091	+	0.769131i	$0.720689\pi$
$102$		0			0
$103$	0.205290	−	0.0667028i	0.0202278	−	0.00657242i	−0.298886	−	0.954289i	$-0.596615\pi$
$103$	0.205290	−	0.0667028i	0.0202278	−	0.00657242i	0.319113	+	0.947717i	$0.396615\pi$
$104$	0.748228	+	0.381241i	0.0733698	+	0.0373838i
$105$		0			0
$106$	1.76596	−	11.1498i	0.171525	−	1.08297i
$107$	4.88121	+	15.0228i	0.471885	+	1.45231i	0.850113	+	0.526600i	$0.176533\pi$
$107$	4.88121	+	15.0228i	0.471885	+	1.45231i	−0.378229	+	0.925712i	$0.623467\pi$
$108$		0			0
$109$	4.23511	−	4.23511i	0.405650	−	0.405650i	−0.474568	−	0.880219i	$-0.657396\pi$
$109$	4.23511	−	4.23511i	0.405650	−	0.405650i	0.880219	+	0.474568i	$0.157396\pi$
$110$	−34.6692	+	17.6648i	−3.30557	+	1.68427i
$111$		0			0
$112$	5.49123	+	0.869725i	0.518872	+	0.0821813i
$113$	14.7878	−	10.7440i	1.39112	−	1.01071i	0.395383	−	0.918517i	$-0.370612\pi$
$113$	14.7878	−	10.7440i	1.39112	−	1.01071i	0.995741	−	0.0921939i	$-0.0293880\pi$
$114$		0			0
$115$	6.80287	+	9.36335i	0.634371	+	0.873137i
$116$	6.05185	−	11.8774i	0.561900	−	1.10279i
$117$		0			0
$118$	−13.2553	+	18.2444i	−1.22025	+	1.67953i
$119$	−1.16889	−	0.849247i	−0.107152	−	0.0778504i
$120$		0			0
$121$	25.4614	+	8.27292i	2.31468	+	0.752084i
$122$	2.19613			0.198828
$123$		0			0
$124$	13.2341			1.18846
$125$	−3.86834	−	1.25690i	−0.345995	−	0.112421i
$126$		0			0
$127$	−14.7740	−	10.7340i	−1.31098	−	0.952485i	−0.999998	−	0.00206962i	$-0.999341\pi$
$127$	−14.7740	−	10.7340i	−1.31098	−	0.952485i	−0.310985	−	0.950415i	$-0.600659\pi$
$128$	6.27161	−	8.63214i	0.554338	−	0.762980i
$129$		0			0
$130$	−1.71321	+	3.36236i	−0.150258	+	0.294899i
$131$	7.96565	+	10.9638i	0.695962	+	0.957909i	0.999986	+	0.00524501i	$0.00166955\pi$
$131$	7.96565	+	10.9638i	0.695962	+	0.957909i	−0.304024	+	0.952664i	$0.598330\pi$
$132$		0			0
$133$	3.73594	−	2.71432i	0.323947	−	0.235361i
$134$	−7.39099	−	1.17062i	−0.638485	−	0.101126i
$135$		0			0
$136$	−0.739607	+	0.376849i	−0.0634208	+	0.0323145i
$137$	−10.5077	+	10.5077i	−0.897730	+	0.897730i	−0.995235	−	0.0975051i	$-0.968914\pi$
$137$	−10.5077	+	10.5077i	−0.897730	+	0.897730i	0.0975051	+	0.995235i	$0.468914\pi$
$138$		0			0
$139$	0.195261	+	0.600951i	0.0165618	+	0.0509720i	0.958996	−	0.283420i	$-0.0914690\pi$
$139$	0.195261	+	0.600951i	0.0165618	+	0.0509720i	−0.942434	+	0.334392i	$0.891469\pi$
$140$	2.98717	−	18.8603i	0.252462	−	1.59398i
$141$		0			0
$142$	−9.23166	−	4.70377i	−0.774704	−	0.394731i
$143$	3.48397	−	1.13201i	0.291344	−	0.0946635i
$144$		0			0
$145$	13.1393	+	6.69479i	1.09116	+	0.555972i
$146$	−0.397701	+	1.22400i	−0.0329140	+	0.101299i
$147$		0			0
$148$	−1.90133	−	5.85170i	−0.156288	−	0.481006i
$149$	12.6918	−	2.01019i	1.03975	−	0.164681i	0.386866	−	0.922136i	$-0.373557\pi$
$149$	12.6918	−	2.01019i	1.03975	−	0.164681i	0.652887	+	0.757455i	$0.273557\pi$
$150$		0			0
$151$	−12.1082	+	6.16943i	−0.985350	+	0.502061i	−0.870949	−	0.491374i	$-0.836495\pi$
$151$	−12.1082	+	6.16943i	−0.985350	+	0.502061i	−0.114401	+	0.993435i	$0.536495\pi$
$152$	−0.415029	−	2.62039i	−0.0336633	−	0.212542i
$153$		0			0
$154$	−26.3013	+	19.1090i	−2.11942	+	1.53985i
$155$			14.6401i			1.17592i
$156$		0			0
$157$	1.90025	−	3.72944i	0.151656	−	0.297642i	−0.802662	−	0.596434i	$-0.796584\pi$
$157$	1.90025	−	3.72944i	0.151656	−	0.297642i	0.954318	+	0.298792i	$0.0965837\pi$
$158$	4.34621	+	8.52992i	0.345766	+	0.678604i
$159$		0			0
$160$	18.3030	+	13.2979i	1.44698	+	1.05129i
$161$	6.83778	+	6.83778i	0.538893	+	0.538893i
$162$		0			0
$163$	−16.9510			−1.32770			−0.663851	−	0.747865i	$-0.731079\pi$
$163$	−16.9510			−1.32770			−0.663851	+	0.747865i	$0.731079\pi$
$164$	−7.00411	+	15.4772i	−0.546929	+	1.20857i
$165$		0			0
$166$	−7.78470	−	2.52940i	−0.604210	−	0.196320i
$167$	−18.1214	−	18.1214i	−1.40227	−	1.40227i	−0.792827	−	0.609446i	$-0.791392\pi$
$167$	−18.1214	−	18.1214i	−1.40227	−	1.40227i	−0.609446	−	0.792827i	$-0.708608\pi$
$168$		0			0
$169$	−7.43238	+	10.2298i	−0.571722	+	0.786907i
$170$	−1.69347	−	3.32362i	−0.129883	−	0.254910i
$171$		0			0
$172$	4.10048	+	5.64382i	0.312659	+	0.430338i
$173$			6.83171i			0.519405i	0.965689	+	0.259702i	$0.0836245\pi$
$173$			6.83171i			0.519405i	−0.965689	+	0.259702i	$0.916376\pi$
$174$		0			0
$175$	8.75369	+	1.38645i	0.661717	+	0.104806i
$176$	−2.17973	−	13.7623i	−0.164303	−	1.03737i
$177$		0			0
$178$	18.4900	−	18.4900i	1.38588	−	1.38588i
$179$	−15.4408	+	2.44559i	−1.15410	+	0.182792i	−0.704009	−	0.710191i	$-0.748609\pi$
$179$	−15.4408	+	2.44559i	−1.15410	+	0.182792i	−0.450092	+	0.892982i	$0.648609\pi$
$180$		0			0
$181$	3.13498	−	19.7935i	0.233022	−	1.47124i	−0.542573	−	0.840009i	$-0.682550\pi$
$181$	3.13498	−	19.7935i	0.233022	−	1.47124i	0.775594	−	0.631232i	$-0.217450\pi$
$182$	−0.974323	+	2.99866i	−0.0722216	+	0.222275i
$183$		0			0
$184$	5.28374	−	1.71679i	0.389522	−	0.126563i
$185$	6.47337	−	2.10333i	0.475932	−	0.154640i
$186$		0			0
$187$	−1.11897	+	3.44383i	−0.0818271	+	0.251838i
$188$	2.13255	−	13.4644i	0.155532	−	0.981992i
$189$		0			0
$190$	11.7754	−	1.86505i	0.854280	−	0.135305i
$191$	4.38486	−	4.38486i	0.317277	−	0.317277i	−0.530443	−	0.847721i	$-0.677974\pi$
$191$	4.38486	−	4.38486i	0.317277	−	0.317277i	0.847721	+	0.530443i	$0.177974\pi$
$192$		0			0
$193$	−2.21890	−	14.0096i	−0.159720	−	1.00843i	−0.929150	−	0.369702i	$-0.879460\pi$
$193$	−2.21890	−	14.0096i	−0.159720	−	1.00843i	0.769430	−	0.638731i	$-0.220540\pi$
$194$	−21.6260	−	3.42522i	−1.55266	−	0.245917i
$195$		0			0
$196$			2.61733i			0.186952i
$197$	−5.40427	−	7.43834i	−0.385038	−	0.529960i	0.571872	−	0.820343i	$-0.306217\pi$
$197$	−5.40427	−	7.43834i	−0.385038	−	0.529960i	−0.956911	+	0.290383i	$0.906217\pi$
$198$		0			0
$199$	−4.04507	−	7.93889i	−0.286747	−	0.562773i	0.702034	−	0.712143i	$-0.252275\pi$
$199$	−4.04507	−	7.93889i	−0.286747	−	0.562773i	−0.988781	+	0.149370i	$0.952275\pi$
$200$	2.99292	−	4.11940i	0.211631	−	0.291285i
$201$		0			0
$202$	−6.75269	−	6.75269i	−0.475118	−	0.475118i
$203$	11.7180	+	3.80741i	0.822442	+	0.267228i
$204$		0			0
$205$	−17.1215	−	7.74822i	−1.19582	−	0.541159i
$206$	0.465623			0.0324415
$207$		0			0
$208$	−0.955555	−	0.955555i	−0.0662558	−	0.0662558i
$209$	−9.36310	−	6.80269i	−0.647659	−	0.470552i
$210$		0			0
$211$	−1.13287	−	2.22339i	−0.0779901	−	0.153064i	0.848719	−	0.528845i	$-0.177375\pi$
$211$	−1.13287	−	2.22339i	−0.0779901	−	0.153064i	−0.926709	+	0.375781i	$0.877375\pi$
$212$	6.30348	−	12.3713i	0.432925	−	0.849663i
$213$		0			0
$214$			34.0736i			2.32922i
$215$	−6.24342	+	4.53611i	−0.425798	+	0.309360i
$216$		0			0
$217$	1.91352	+	12.0815i	0.129898	+	0.820146i
$218$	11.5115	−	5.86542i	0.779660	−	0.397256i
$219$		0			0
$220$	−47.2680	+	7.48652i	−3.18681	+	0.504741i
$221$	0.108522	+	0.333997i	0.00730000	+	0.0224671i
$222$		0			0
$223$	−7.66122	+	23.5788i	−0.513034	+	1.57895i	0.273798	+	0.961787i	$0.411720\pi$
$223$	−7.66122	+	23.5788i	−0.513034	+	1.57895i	−0.786832	+	0.617168i	$0.788280\pi$
$224$	16.8423	+	8.58159i	1.12532	+	0.573381i
$225$		0			0
$226$	37.4995	−	12.1843i	2.49443	−	0.810490i
$227$	−2.03948	−	1.03917i	−0.135365	−	0.0689721i	0.384996	−	0.922918i	$-0.374203\pi$
$227$	−2.03948	−	1.03917i	−0.135365	−	0.0689721i	−0.520361	+	0.853946i	$0.674203\pi$
$228$		0			0
$229$	−3.28848	+	20.7626i	−0.217309	+	1.37203i	0.601915	+	0.798560i	$0.294404\pi$
$229$	−3.28848	+	20.7626i	−0.217309	+	1.37203i	−0.819224	+	0.573474i	$0.805596\pi$
$230$	7.71486	+	23.7439i	0.508703	+	1.56563i
$231$		0			0
$232$	5.00538	−	5.00538i	0.328619	−	0.328619i
$233$	7.76709	−	3.95753i	0.508839	−	0.259267i	−0.180670	−	0.983544i	$-0.557826\pi$
$233$	7.76709	−	3.95753i	0.508839	−	0.259267i	0.689509	+	0.724277i	$0.257826\pi$
$234$		0			0
$235$	14.8948	+	2.35911i	0.971633	+	0.153891i
$236$	−22.4395	+	16.3033i	−1.46069	+	1.06125i
$237$		0			0
$238$	−1.83192	−	2.52142i	−0.118746	−	0.163439i
$239$	−10.4691	+	20.5467i	−0.677188	+	1.32906i	0.254950	+	0.966954i	$0.417941\pi$
$239$	−10.4691	+	20.5467i	−0.677188	+	1.32906i	−0.932138	+	0.362102i	$0.882059\pi$
$240$		0			0
$241$	3.16869	−	4.36133i	0.204113	−	0.280938i	−0.694672	−	0.719326i	$-0.744451\pi$
$241$	3.16869	−	4.36133i	0.204113	−	0.280938i	0.898786	+	0.438389i	$0.144451\pi$
$242$	46.7204	+	33.9444i	3.00330	+	2.18203i
$243$		0			0
$244$	2.56892	+	0.834692i	0.164458	+	0.0534357i
$245$	−2.89539			−0.184980
$246$		0			0
$247$	−1.12244			−0.0714191
$248$	6.68362	+	2.17164i	0.424411	+	0.137899i
$249$		0			0
$250$	−7.09820	−	5.15715i	−0.448930	−	0.326167i
$251$	6.43570	−	8.85798i	0.406218	−	0.559111i	−0.556073	−	0.831133i	$-0.687693\pi$
$251$	6.43570	−	8.85798i	0.406218	−	0.559111i	0.962291	+	0.272023i	$0.0876925\pi$
$252$		0			0
$253$	11.0026	−	21.5939i	0.691730	−	1.35760i
$254$	−23.1543	−	31.8692i	−1.45283	−	1.99965i
$255$		0			0
$256$	−0.946816	+	0.687902i	−0.0591760	+	0.0429939i
$257$	11.7305	+	1.85792i	0.731726	+	0.115894i	0.511169	−	0.859480i	$-0.329213\pi$
$257$	11.7305	+	1.85792i	0.731726	+	0.115894i	0.220557	+	0.975374i	$0.429213\pi$
$258$		0			0
$259$	5.06713	−	2.58183i	0.314856	−	0.160427i
$260$	−3.28196	+	3.28196i	−0.203539	+	0.203539i
$261$		0			0
$262$	9.03352	+	27.8023i	0.558093	+	1.71763i
$263$	1.09630	−	6.92176i	0.0676007	−	0.426814i	−0.930557	−	0.366146i	$-0.880677\pi$
$263$	1.09630	−	6.92176i	0.0676007	−	0.426814i	0.998158	−	0.0606678i	$-0.0193230\pi$
$264$		0			0
$265$	13.6856	+	6.97316i	0.840699	+	0.428358i
$266$	9.47372	−	3.07820i	0.580871	−	0.188736i
$267$		0			0
$268$	−8.20066	−	4.17845i	−0.500935	−	0.255239i
$269$	−9.10933	+	28.0356i	−0.555406	+	1.70936i	0.139463	+	0.990227i	$0.455462\pi$
$269$	−9.10933	+	28.0356i	−0.555406	+	1.70936i	−0.694869	+	0.719136i	$0.744538\pi$
$270$		0			0
$271$	−0.323450	−	0.995477i	−0.0196482	−	0.0604709i	0.940752	−	0.339096i	$-0.110121\pi$
$271$	−0.323450	−	0.995477i	−0.0196482	−	0.0604709i	−0.960400	+	0.278625i	$0.910121\pi$
$272$	1.31934	−	0.208964i	0.0799970	−	0.0126703i
$273$		0			0
$274$	−28.5611	+	14.5526i	−1.72544	+	0.879154i
$275$	−3.47475	−	21.9387i	−0.209535	−	1.32295i
$276$		0			0
$277$	19.6390	−	14.2685i	1.17999	−	0.857314i	0.187820	−	0.982203i	$-0.439858\pi$
$277$	19.6390	−	14.2685i	1.17999	−	0.857314i	0.992171	+	0.124890i	$0.0398577\pi$
$278$			1.36303i			0.0817491i
$279$		0			0
$280$	4.60346	−	9.03481i	0.275110	−	0.539933i
$281$	8.65174	+	16.9800i	0.516120	+	1.01294i	0.991122	+	0.132957i	$0.0424472\pi$
$281$	8.65174	+	16.9800i	0.516120	+	1.01294i	−0.475002	+	0.879985i	$0.657553\pi$
$282$		0			0
$283$	16.9992	+	12.3506i	1.01050	+	0.734168i	0.964313	−	0.264765i	$-0.0852944\pi$
$283$	16.9992	+	12.3506i	1.01050	+	0.734168i	0.0461826	+	0.998933i	$0.485294\pi$
$284$	−9.01092	−	9.01092i	−0.534700	−	0.534700i
$285$		0			0
$286$	7.90207			0.467259
$287$	−15.1420	−	4.15624i	−0.893801	−	0.245335i
$288$		0			0
$289$	15.8378	+	5.14602i	0.931636	+	0.302707i
$290$	22.4930	+	22.4930i	1.32083	+	1.32083i
$291$		0			0
$292$	−0.930418	+	1.28061i	−0.0544486	+	0.0749421i
$293$	−5.11758	−	10.0438i	−0.298972	−	0.586766i	0.691834	−	0.722057i	$-0.256803\pi$
$293$	−5.11758	−	10.0438i	−0.298972	−	0.586766i	−0.990806	+	0.135291i	$0.956803\pi$
$294$		0			0
$295$	−18.0353	−	24.8235i	−1.05006	−	1.44528i
$296$		−	3.26728i		−	0.189907i
$297$		0			0
$298$	27.3776	+	4.33619i	1.58594	+	0.251189i
$299$	−0.367692	−	2.32152i	−0.0212642	−	0.134257i
$300$		0			0
$301$	−4.55939	+	4.55939i	−0.262799	+	0.262799i
$302$	−28.9528	+	4.58567i	−1.66605	+	0.263876i
$303$		0			0
$304$	−0.667878	+	4.21681i	−0.0383054	+	0.241851i
$305$	−0.923368	+	2.84184i	−0.0528719	+	0.162723i
$306$		0			0
$307$	8.99276	−	2.92192i	0.513244	−	0.166763i	−0.0409331	−	0.999162i	$-0.513033\pi$
$307$	8.99276	−	2.92192i	0.513244	−	0.166763i	0.554177	+	0.832399i	$0.313033\pi$
$308$	−38.0286	+	12.3563i	−2.16688	+	0.704063i
$309$		0			0
$310$	−9.75886	+	30.0347i	−0.554266	+	1.70585i
$311$	2.64006	−	16.6687i	0.149704	−	0.945195i	−0.792431	−	0.609962i	$-0.791185\pi$
$311$	2.64006	−	16.6687i	0.149704	−	0.945195i	0.942135	−	0.335234i	$-0.108815\pi$
$312$		0			0
$313$	−24.1931	+	3.83181i	−1.36747	+	0.216587i	−0.796628	−	0.604471i	$-0.793385\pi$
$313$	−24.1931	+	3.83181i	−1.36747	+	0.216587i	−0.570846	+	0.821057i	$0.693385\pi$
$314$	6.38440	−	6.38440i	0.360293	−	0.360293i
$315$		0			0
$316$	1.84197	+	11.6297i	0.103619	+	0.654223i
$317$	9.70461	+	1.53706i	0.545065	+	0.0863299i	0.422894	−	0.906179i	$-0.361014\pi$
$317$	9.70461	+	1.53706i	0.545065	+	0.0863299i	0.122171	+	0.992509i	$0.461014\pi$
$318$		0			0
$319$		−	30.8793i		−	1.72891i
$320$	20.8626	+	28.7149i	1.16625	+	1.60521i
$321$		0			0
$322$	9.46999	+	18.5859i	0.527742	+	1.03575i
$323$	0.652152	−	0.897611i	0.0362867	−	0.0499444i
$324$		0			0
$325$	−1.52327	−	1.52327i	−0.0844959	−	0.0844959i
$326$	−34.7755	−	11.2992i	−1.92604	−	0.625807i
$327$		0			0
$328$	−6.07700	+	6.66712i	−0.335546	+	0.368130i
$329$	12.6001			0.694664
$330$		0			0
$331$	−14.3440	−	14.3440i	−0.788417	−	0.788417i	0.192818	−	0.981235i	$-0.438237\pi$
$331$	−14.3440	−	14.3440i	−0.788417	−	0.788417i	−0.981235	+	0.192818i	$0.938237\pi$
$332$	−8.14476	−	5.91752i	−0.447002	−	0.324766i
$333$		0			0
$334$	−25.0972	−	49.2560i	−1.37326	−	2.69517i
$335$	4.62236	−	9.07189i	0.252547	−	0.495651i
$336$		0			0
$337$		−	8.81241i		−	0.480043i	−0.970768	−	0.240021i	$-0.922846\pi$
$337$		−	8.81241i		−	0.480043i	0.970768	−	0.240021i	$-0.0771545\pi$
$338$	−22.0668	+	16.0325i	−1.20028	+	0.872051i
$339$		0			0
$340$	−0.717709	−	4.53144i	−0.0389233	−	0.245752i
$341$	27.3151	−	13.9177i	1.47919	−	0.753687i
$342$		0			0
$343$	−19.3437	+	3.06375i	−1.04446	+	0.165427i
$344$	1.14474	+	3.52316i	0.0617205	+	0.189956i
$345$		0			0
$346$	−4.55390	+	14.0155i	−0.244819	+	0.753477i
$347$	4.18176	+	2.13071i	0.224489	+	0.114383i	0.562618	−	0.826717i	$-0.309794\pi$
$347$	4.18176	+	2.13071i	0.224489	+	0.114383i	−0.338129	+	0.941100i	$0.609794\pi$
$348$		0			0
$349$	12.3323	−	4.00699i	0.660130	−	0.214489i	0.0402548	−	0.999189i	$-0.487183\pi$
$349$	12.3323	−	4.00699i	0.660130	−	0.214489i	0.619876	+	0.784700i	$0.287183\pi$
$350$	17.0343	+	8.67941i	0.910522	+	0.463934i
$351$		0			0
$352$	7.41094	−	46.7908i	0.395005	−	2.49396i
$353$	−6.12880	−	18.8625i	−0.326203	−	1.00395i	−0.970895	−	0.239507i	$-0.923014\pi$
$353$	−6.12880	−	18.8625i	−0.326203	−	1.00395i	0.644692	−	0.764443i	$-0.276986\pi$
$354$		0			0
$355$	9.96824	−	9.96824i	0.529059	−	0.529059i
$356$	28.6561	−	14.6010i	1.51877	−	0.773852i
$357$		0			0
$358$	−33.3075	−	5.27540i	−1.76036	−	0.278813i
$359$	1.27423	−	0.925784i	0.0672514	−	0.0488610i	−0.553652	−	0.832748i	$-0.686766\pi$
$359$	1.27423	−	0.925784i	0.0672514	−	0.0488610i	0.620903	+	0.783887i	$0.286766\pi$
$360$		0			0
$361$	−9.08355	−	12.5024i	−0.478081	−	0.658023i
$362$	19.6256	−	38.5173i	1.03150	−	2.02443i
$363$		0			0
$364$	−2.27942	+	3.13735i	−0.119474	+	0.164442i
$365$	−1.41666	−	1.02926i	−0.0741514	−	0.0538742i
$366$		0			0
$367$	−10.0426	−	3.26304i	−0.524219	−	0.170329i	0.0349400	−	0.999389i	$-0.488876\pi$
$367$	−10.0426	−	3.26304i	−0.524219	−	0.170329i	−0.559159	+	0.829060i	$0.688876\pi$
$368$	−8.94032			−0.466046
$369$		0			0
$370$	14.6824			0.763301
$371$	12.2052	+	3.96572i	0.633664	+	0.205890i
$372$		0			0
$373$	28.7981	+	20.9230i	1.49111	+	1.08335i	0.973760	+	0.227579i	$0.0730811\pi$
$373$	28.7981	+	20.9230i	1.49111	+	1.08335i	0.517349	+	0.855774i	$0.326919\pi$
$374$	−4.59120	+	6.31925i	−0.237406	+	0.326761i
$375$		0			0
$376$	3.28643	−	6.44998i	0.169485	−	0.332632i
$377$	−1.76030	−	2.42285i	−0.0906601	−	0.124783i
$378$		0			0
$379$	−1.34011	+	0.973646i	−0.0688368	+	0.0500129i	−0.621671	−	0.783278i	$-0.713546\pi$
$379$	−1.34011	+	0.973646i	−0.0688368	+	0.0500129i	0.552835	+	0.833291i	$0.313546\pi$
$380$	14.4831	+	2.29390i	0.742969	+	0.117675i
$381$		0			0
$382$	11.9186	−	6.07281i	0.609807	−	0.310712i
$383$	−6.91149	+	6.91149i	−0.353161	+	0.353161i	−0.861284	−	0.508123i	$-0.830339\pi$
$383$	−6.91149	+	6.91149i	−0.353161	+	0.353161i	0.508123	+	0.861284i	$0.330339\pi$
$384$		0			0
$385$	−13.6690	−	42.0688i	−0.696635	−	2.14402i
$386$	4.78641	−	30.2202i	0.243622	−	1.53817i
$387$		0			0
$388$	−23.9951	−	12.2261i	−1.21817	−	0.620687i
$389$	15.4034	−	5.00488i	0.780985	−	0.253757i	0.108724	−	0.994072i	$-0.465323\pi$
$389$	15.4034	−	5.00488i	0.780985	−	0.253757i	0.672261	+	0.740314i	$0.265323\pi$
$390$		0			0
$391$	2.07014	+	1.05479i	0.104692	+	0.0533430i
$392$	−0.429488	+	1.32183i	−0.0216924	+	0.0667624i
$393$		0			0
$394$	−6.12877	−	18.8624i	−0.308763	−	0.950274i
$395$	−12.8653	+	2.03766i	−0.647321	+	0.102526i
$396$		0			0
$397$	16.0168	−	8.16099i	0.803862	−	0.409588i	−0.00324401	−	0.999995i	$-0.501033\pi$
$397$	16.0168	−	8.16099i	0.803862	−	0.409588i	0.807106	+	0.590407i	$0.201033\pi$
$398$	−3.00665	−	18.9833i	−0.150710	−	0.951545i
$399$		0			0
$400$	−6.62905	+	4.81629i	−0.331453	+	0.240814i
$401$		−	8.90016i		−	0.444453i	−0.974995	−	0.222226i	$-0.928668\pi$
$401$		−	8.90016i		−	0.444453i	0.974995	−	0.222226i	$-0.0713324\pi$
$402$		0			0
$403$	1.34980	−	2.64913i	0.0672383	−	0.131963i
$404$	−5.33242	−	10.4655i	−0.265298	−	0.520676i
$405$		0			0
$406$	21.5019	+	15.6220i	1.06712	+	0.775309i
$407$	−10.0783	−	10.0783i	−0.499562	−	0.499562i
$408$		0			0
$409$	−31.3466			−1.54999			−0.774996	−	0.631966i	$-0.782248\pi$
$409$	−31.3466			−1.54999			−0.774996	+	0.631966i	$0.782248\pi$
$410$	−29.9605	−	27.3086i	−1.47964	−	1.34868i
$411$		0			0
$412$	0.544660	+	0.176971i	0.0268335	+	0.00871873i
$413$	−18.1279	−	18.1279i	−0.892015	−	0.892015i
$414$		0			0
$415$	6.54619	−	9.01005i	0.321340	−	0.442286i
$416$	−2.08588	−	4.09377i	−0.102269	−	0.200713i
$417$		0			0
$418$	−14.6741	−	20.1972i	−0.717736	−	0.987879i
$419$		−	7.90991i		−	0.386424i	−0.981157	−	0.193212i	$-0.938109\pi$
$419$		−	7.90991i		−	0.386424i	0.981157	−	0.193212i	$-0.0618906\pi$
$420$		0			0
$421$	16.1064	+	2.55101i	0.784979	+	0.124329i	0.536042	−	0.844191i	$-0.319919\pi$
$421$	16.1064	+	2.55101i	0.784979	+	0.124329i	0.248937	+	0.968520i	$0.419919\pi$
$422$	−0.842052	−	5.31651i	−0.0409905	−	0.258804i
$423$		0			0
$424$	5.21350	−	5.21350i	0.253190	−	0.253190i
$425$	2.10320	−	0.333114i	0.102020	−	0.0161584i
$426$		0			0
$427$	−0.390555	+	2.46587i	−0.0189003	+	0.119332i
$428$	−12.9505	+	39.8574i	−0.625984	+	1.92658i
$429$		0			0
$430$	−15.8323	+	5.14422i	−0.763500	+	0.248076i
$431$	−0.374602	+	0.121716i	−0.0180439	+	0.00586283i	−0.318025	−	0.948082i	$-0.603020\pi$
$431$	−0.374602	+	0.121716i	−0.0180439	+	0.00586283i	0.299981	+	0.953945i	$0.403020\pi$
$432$		0			0
$433$	−5.34527	+	16.4510i	−0.256877	+	0.790587i	0.736577	+	0.676354i	$0.236441\pi$
$433$	−5.34527	+	16.4510i	−0.256877	+	0.790587i	−0.993454	+	0.114233i	$0.963559\pi$
$434$	−4.12768	+	26.0611i	−0.198135	+	1.25097i
$435$		0			0
$436$	15.6949	−	2.48582i	0.751648	−	0.119049i
$437$	−5.25086	+	5.25086i	−0.251183	+	0.251183i
$438$		0			0
$439$	0.0655373	+	0.413787i	0.00312793	+	0.0197490i	0.989203	−	0.146552i	$-0.0468176\pi$
$439$	0.0655373	+	0.413787i	0.00312793	+	0.0197490i	−0.986075	+	0.166301i	$0.946818\pi$
$440$	−25.1003	−	3.97549i	−1.19661	−	0.189524i
$441$		0			0
$442$			0.757546i			0.0360328i
$443$	15.5288	+	21.3736i	0.737796	+	1.01549i	0.998742	+	0.0501355i	$0.0159653\pi$
$443$	15.5288	+	21.3736i	0.737796	+	1.01549i	−0.260947	+	0.965353i	$0.584035\pi$
$444$		0			0
$445$	16.1522	+	31.7005i	0.765688	+	1.50275i
$446$	−31.4345	+	43.2659i	−1.48847	+	2.04870i
$447$		0			0
$448$	20.9697	+	20.9697i	0.990723	+	0.990723i
$449$	−22.1252	−	7.18892i	−1.04415	−	0.339266i	−0.263783	−	0.964582i	$-0.584970\pi$
$449$	−22.1252	−	7.18892i	−1.04415	−	0.339266i	−0.780372	+	0.625316i	$0.784970\pi$
$450$		0			0
$451$	1.82028	+	39.3107i	0.0857138	+	1.85107i
$452$	48.4959			2.28105
$453$		0			0
$454$	−3.49138	−	3.49138i	−0.163858	−	0.163858i
$455$	−3.47066	−	2.52158i	−0.162707	−	0.118214i
$456$		0			0
$457$	−4.13792	−	8.12113i	−0.193564	−	0.379890i	0.773743	−	0.633500i	$-0.218382\pi$
$457$	−4.13792	−	8.12113i	−0.193564	−	0.379890i	−0.967307	+	0.253609i	$0.918382\pi$
$458$	−20.5865	+	40.4032i	−0.961942	+	1.88792i
$459$		0			0
$460$			30.7065i			1.43170i
$461$	31.8495	−	23.1400i	1.48338	−	1.07774i	0.506929	−	0.861988i	$-0.330781\pi$
$461$	31.8495	−	23.1400i	1.48338	−	1.07774i	0.976449	−	0.215749i	$-0.0692194\pi$
$462$		0			0
$463$	2.77611	+	17.5277i	0.129017	+	0.814580i	0.964310	+	0.264776i	$0.0852979\pi$
$463$	2.77611	+	17.5277i	0.129017	+	0.814580i	−0.835293	+	0.549805i	$0.814702\pi$
$464$	−10.1496	+	5.17150i	−0.471185	+	0.240081i
$465$		0			0
$466$	18.5725	−	2.94159i	0.860353	−	0.136267i
$467$	−1.24330	−	3.82647i	−0.0575329	−	0.177068i	0.918160	−	0.396209i	$-0.129674\pi$
$467$	−1.24330	−	3.82647i	−0.0575329	−	0.177068i	−0.975693	+	0.219141i	$0.929674\pi$
$468$		0			0
$469$	2.62879	−	8.09059i	0.121386	−	0.373589i
$470$	28.9847	+	14.7685i	1.33697	+	0.681218i
$471$		0			0
$472$	−14.0079	+	4.55144i	−0.644766	+	0.209497i
$473$	14.3987	+	7.33649i	0.662052	+	0.337332i
$474$		0			0
$475$	−1.06468	+	6.72212i	−0.0488508	+	0.308432i
$476$	−1.18456	−	3.64569i	−0.0542940	−	0.167100i
$477$		0			0
$478$	−35.1738	+	35.1738i	−1.60881	+	1.60881i
$479$	−16.7284	+	8.52355i	−0.764340	+	0.389451i	−0.792279	−	0.610159i	$-0.791106\pi$
$479$	−16.7284	+	8.52355i	−0.764340	+	0.389451i	0.0279388	+	0.999610i	$0.491106\pi$
$480$		0			0
$481$	−1.36528	−	0.216240i	−0.0622515	−	0.00985967i
$482$	9.40786	−	6.83521i	0.428516	−	0.311335i
$483$		0			0
$484$	41.7497	+	57.4635i	1.89771	+	2.61198i
$485$	13.5250	−	26.5443i	0.614139	−	1.20532i
$486$		0			0
$487$	3.29322	−	4.53273i	0.149230	−	0.205398i	−0.727857	−	0.685729i	$-0.759484\pi$
$487$	3.29322	−	4.53273i	0.149230	−	0.205398i	0.877087	+	0.480331i	$0.159484\pi$
$488$	1.16041	+	0.843088i	0.0525293	+	0.0381648i
$489$		0			0
$490$	−5.93999	−	1.93002i	−0.268341	−	0.0871894i
$491$	−31.8490			−1.43733			−0.718663	−	0.695358i	$-0.755246\pi$
$491$	−31.8490			−1.43733			−0.718663	+	0.695358i	$0.755246\pi$
$492$		0			0
$493$	2.96030			0.133325
$494$	−2.30272	−	0.748200i	−0.103604	−	0.0336631i
$495$		0			0
$496$	−9.14916	−	6.64726i	−0.410810	−	0.298471i
$497$	6.92323	−	9.52901i	0.310549	−	0.427434i
$498$		0			0
$499$	1.89386	−	3.71692i	0.0847810	−	0.166392i	−0.844723	−	0.535203i	$-0.820235\pi$
$499$	1.89386	−	3.71692i	0.0847810	−	0.166392i	0.929504	+	0.368811i	$0.120235\pi$
$500$	−6.34300	−	8.73039i	−0.283668	−	0.390435i
$501$		0			0
$502$	19.1076	−	13.8825i	0.852816	−	0.619607i
$503$	3.67805	+	0.582545i	0.163996	+	0.0259744i	0.237892	−	0.971292i	$-0.423543\pi$
$503$	3.67805	+	0.582545i	0.163996	+	0.0259744i	−0.0738965	+	0.997266i	$0.523543\pi$
$504$		0			0
$505$	11.5773	−	5.89893i	0.515183	−	0.262499i
$506$	36.9664	−	36.9664i	1.64336	−	1.64336i
$507$		0			0
$508$	−14.9720	−	46.0792i	−0.664277	−	2.04443i
$509$	−4.30277	+	27.1666i	−0.190717	+	1.20414i	0.687611	+	0.726079i	$0.258659\pi$
$509$	−4.30277	+	27.1666i	−0.190717	+	1.20414i	−0.878328	+	0.478059i	$0.841341\pi$
$510$		0			0
$511$	−1.30361	−	0.664220i	−0.0576681	−	0.0293834i
$512$	−22.6963	+	7.37449i	−1.00305	+	0.325909i
$513$		0			0
$514$	22.8270	+	11.6309i	1.00685	+	0.513018i
$515$	−0.195772	+	0.602524i	−0.00862674	+	0.0265504i
$516$		0			0
$517$	−9.75833	−	30.0330i	−0.429171	−	1.32085i
$518$	12.1164	−	1.91905i	0.532364	−	0.0843182i
$519$		0			0
$520$	−2.19604	+	1.11894i	−0.0963027	+	0.0490687i
$521$	0.365315	+	2.30651i	0.0160047	+	0.101050i	0.994398	−	0.105705i	$-0.0337098\pi$
$521$	0.365315	+	2.30651i	0.0160047	+	0.101050i	−0.978393	+	0.206755i	$0.933710\pi$
$522$		0			0
$523$	10.9719	−	7.97156i	0.479768	−	0.348572i	−0.321468	−	0.946921i	$-0.604176\pi$
$523$	10.9719	−	7.97156i	0.479768	−	0.348572i	0.801236	+	0.598349i	$0.204176\pi$
$524$			35.9551i			1.57070i
$525$		0			0
$526$	6.86303	−	13.4695i	0.299242	−	0.587296i
$527$	1.33425	+	2.61861i	0.0581207	+	0.114068i
$528$		0			0
$529$	6.02708	+	4.37893i	0.262047	+	0.190388i
$530$	23.4283	+	23.4283i	1.01766	+	1.01766i
$531$		0			0
$532$	12.2518			0.531182
$533$	2.38376	+	2.98062i	0.103252	+	0.129105i
$534$		0			0
$535$	−44.0918	−	14.3263i	−1.90626	−	0.619380i
$536$	−3.45592	−	3.45592i	−0.149273	−	0.149273i
$537$		0			0
$538$	−37.3762	+	51.4439i	−1.61140	+	2.21791i
$539$	2.75252	+	5.40213i	0.118559	+	0.232686i
$540$		0			0
$541$	20.2273	+	27.8405i	0.869640	+	1.19696i	0.979184	+	0.202974i	$0.0650608\pi$
$541$	20.2273	+	27.8405i	0.869640	+	1.19696i	−0.109544	+	0.993982i	$0.534939\pi$
$542$		−	2.25786i		−	0.0969835i
$543$		0			0
$544$	4.48569	+	0.710464i	0.192322	+	0.0304609i
$545$	2.74991	+	17.3623i	0.117793	+	0.743718i
$546$		0			0
$547$	−4.29151	+	4.29151i	−0.183492	+	0.183492i	−0.792875	−	0.609384i	$-0.791417\pi$
$547$	−4.29151	+	4.29151i	−0.183492	+	0.183492i	0.609384	+	0.792875i	$0.291417\pi$
$548$	−38.9402	+	6.16753i	−1.66344	+	0.263464i
$549$		0			0
$550$	7.49542	−	47.3242i	0.319606	−	2.01791i
$551$	−2.92378	+	8.99846i	−0.124557	+	0.383347i
$552$		0			0
$553$	−10.3505	+	3.36308i	−0.440148	+	0.143013i
$554$	49.8012	−	16.1814i	2.11585	−	0.687481i
$555$		0			0
$556$	−0.518051	+	1.59440i	−0.0219703	+	0.0676175i
$557$	1.52108	−	9.60372i	0.0644502	−	0.406923i	−0.934280	−	0.356541i	$-0.883956\pi$
$557$	1.52108	−	9.60372i	0.0644502	−	0.406923i	0.998730	−	0.0503819i	$-0.0160439\pi$
$558$		0			0
$559$	1.54797	−	0.245175i	0.0654722	−	0.0103698i
$560$	−11.5383	+	11.5383i	−0.487581	+	0.487581i
$561$		0			0
$562$	6.43075	+	40.6021i	0.271265	+	1.71270i
$563$	19.5048	+	3.08926i	0.822030	+	0.130197i	0.553261	−	0.833008i	$-0.313383\pi$
$563$	19.5048	+	3.08926i	0.822030	+	0.130197i	0.268769	+	0.963205i	$0.413383\pi$
$564$		0			0
$565$			53.6480i			2.25699i
$566$	26.6416	+	36.6691i	1.11983	+	1.54132i
$567$		0			0
$568$	−3.07214	−	6.02942i	−0.128904	−	0.252989i
$569$	21.8076	−	30.0155i	0.914220	−	1.25832i	−0.0514845	−	0.998674i	$-0.516395\pi$
$569$	21.8076	−	30.0155i	0.914220	−	1.25832i	0.965705	−	0.259643i	$-0.0836047\pi$
$570$		0			0
$571$	9.74733	+	9.74733i	0.407913	+	0.407913i	0.881010	−	0.473097i	$-0.156864\pi$
$571$	9.74733	+	9.74733i	0.407913	+	0.407913i	−0.473097	+	0.881010i	$0.656864\pi$
$572$	9.24341	+	3.00337i	0.386486	+	0.125577i
$573$		0			0
$574$	−28.2938	−	18.6200i	−1.18096	−	0.777186i
$575$	−14.2520			−0.594348
$576$		0			0
$577$	4.93444	+	4.93444i	0.205423	+	0.205423i	0.802319	−	0.596895i	$-0.203599\pi$
$577$	4.93444	+	4.93444i	0.205423	+	0.205423i	−0.596895	+	0.802319i	$0.703599\pi$
$578$	29.0616	+	21.1145i	1.20880	+	0.878245i
$579$		0			0
$580$	17.7621	+	34.8601i	0.737531	+	1.44749i
$581$	4.22448	−	8.29101i	0.175261	−	0.343969i
$582$		0			0
$583$		−	32.1632i		−	1.33206i
$584$	−0.680029	+	0.494070i	−0.0281398	+	0.0204448i
$585$		0			0
$586$	−3.80385	−	24.0165i	−0.157135	−	0.992114i
$587$	−0.548784	+	0.279619i	−0.0226507	+	0.0115411i	−0.465279	−	0.885164i	$-0.654046\pi$
$587$	−0.548784	+	0.279619i	−0.0226507	+	0.0115411i	0.442628	+	0.896705i	$0.354046\pi$
$588$		0			0
$589$	−9.27760	+	1.46943i	−0.382277	+	0.0605467i
$590$	−20.4531	−	62.9483i	−0.842042	−	2.59154i
$591$		0			0
$592$	−1.62475	+	5.00046i	−0.0667768	+	0.205518i
$593$	−38.3541	−	19.5424i	−1.57501	−	0.802509i	−0.575134	−	0.818059i	$-0.695050\pi$
$593$	−38.3541	−	19.5424i	−1.57501	−	0.802509i	−0.999879	+	0.0155502i	$0.995050\pi$
$594$		0			0
$595$	4.03300	−	1.31040i	0.165337	−	0.0537212i
$596$	30.3768	+	15.4778i	1.24428	+	0.633994i
$597$		0			0
$598$	0.793152	−	5.00776i	0.0324344	−	0.204783i
$599$	13.1007	+	40.3197i	0.535278	+	1.64742i	0.743047	+	0.669239i	$0.233380\pi$
$599$	13.1007	+	40.3197i	0.535278	+	1.64742i	−0.207769	+	0.978178i	$0.566620\pi$
$600$		0			0
$601$	13.3208	−	13.3208i	0.543365	−	0.543365i	−0.381148	−	0.924514i	$-0.624471\pi$
$601$	13.3208	−	13.3208i	0.543365	−	0.543365i	0.924514	+	0.381148i	$0.124471\pi$
$602$	−12.3930	+	6.31452i	−0.505099	+	0.257361i
$603$		0			0
$604$	−35.6103	−	5.64012i	−1.44896	−	0.229493i
$605$	−63.5683	+	46.1851i	−2.58442	+	1.87769i
$606$		0			0
$607$	13.4407	+	18.4996i	0.545543	+	0.750875i	0.989399	−	0.145223i	$-0.0463899\pi$
$607$	13.4407	+	18.4996i	0.545543	+	0.750875i	−0.443856	+	0.896098i	$0.646390\pi$
$608$	−6.58996	+	12.9335i	−0.267258	+	0.524523i
$609$		0			0
$610$	−3.78864	+	5.21462i	−0.153398	+	0.211134i
$611$	−2.47772	−	1.80017i	−0.100238	−	0.0728270i
$612$		0			0
$613$	−24.0488	−	7.81393i	−0.971322	−	0.315602i	−0.219973	−	0.975506i	$-0.570597\pi$
$613$	−24.0488	−	7.81393i	−0.971322	−	0.315602i	−0.751350	+	0.659904i	$0.770597\pi$
$614$	20.3967			0.823142
$615$		0			0
$616$	−21.2332			−0.855509
$617$	−16.1405	−	5.24436i	−0.649791	−	0.211130i	−0.0344691	−	0.999406i	$-0.510974\pi$
$617$	−16.1405	−	5.24436i	−0.649791	−	0.211130i	−0.615322	+	0.788276i	$0.710974\pi$
$618$		0			0
$619$	33.6865	+	24.4747i	1.35397	+	0.983720i	0.998803	+	0.0489186i	$0.0155775\pi$
$619$	33.6865	+	24.4747i	1.35397	+	0.983720i	0.355171	+	0.934801i	$0.384423\pi$
$620$	−22.8308	+	31.4239i	−0.916906	+	1.26201i
$621$		0			0
$622$	16.5273	−	32.4366i	0.662683	−	1.30059i
$623$	17.4727	+	24.0491i	0.700030	+	0.963509i
$624$		0			0
$625$	24.2775	−	17.6386i	0.971100	−	0.705545i
$626$	−52.1871	−	8.26563i	−2.08582	−	0.330361i
$627$		0			0
$628$	9.89467	−	5.04159i	0.394840	−	0.201181i
$629$	0.966173	−	0.966173i	0.0385238	−	0.0385238i
$630$		0			0
$631$	7.59021	+	23.3602i	0.302161	+	0.929957i	0.980721	+	0.195412i	$0.0626044\pi$
$631$	7.59021	+	23.3602i	0.302161	+	0.929957i	−0.678560	+	0.734545i	$0.737396\pi$
$632$	−0.978121	+	6.17561i	−0.0389076	+	0.245653i
$633$		0			0
$634$	18.8848	+	9.62227i	0.750010	+	0.382149i
$635$	50.9746	−	16.5627i	2.02287	−	0.657269i
$636$		0			0
$637$	0.523921	+	0.266951i	0.0207585	+	0.0105770i
$638$	20.5836	−	63.3499i	0.814913	−	2.50805i
$639$		0			0
$640$	9.67720	+	29.7833i	0.382525	+	1.17729i
$641$	−22.7389	+	3.60148i	−0.898131	+	0.142250i	−0.588396	−	0.808573i	$-0.700240\pi$
$641$	−22.7389	+	3.60148i	−0.898131	+	0.142250i	−0.309735	+	0.950823i	$0.600240\pi$
$642$		0			0
$643$	−21.2226	+	10.8135i	−0.836939	+	0.426442i	−0.819274	−	0.573402i	$-0.805623\pi$
$643$	−21.2226	+	10.8135i	−0.836939	+	0.426442i	−0.0176649	+	0.999844i	$0.505623\pi$
$644$	4.01347	+	25.3401i	0.158153	+	0.998539i
$645$		0			0
$646$	1.93625	−	1.40676i	0.0761805	−	0.0553484i
$647$			19.1223i			0.751777i	0.926665	+	0.375889i	$0.122662\pi$
$647$			19.1223i			0.751777i	−0.926665	+	0.375889i	$0.877338\pi$
$648$		0			0
$649$	−29.1695	+	57.2484i	−1.14500	+	2.24720i
$650$	−2.10966	−	4.14043i	−0.0827475	−	0.162401i
$651$		0			0
$652$	−36.3839	−	26.4345i	−1.42491	−	1.03525i
$653$	25.5620	+	25.5620i	1.00032	+	1.00032i	1.00000		0.000318893i	$0.000101507\pi$
$653$	25.5620	+	25.5620i	1.00032	+	1.00032i	0.000318893		1.00000i	$0.499898\pi$
$654$		0			0
$655$	−39.7749			−1.55413
$656$	12.6161	−	7.18185i	0.492575	−	0.280404i
$657$		0			0
$658$	25.8495	+	8.39900i	1.00772	+	0.327427i
$659$	14.3256	+	14.3256i	0.558044	+	0.558044i	0.928750	−	0.370706i	$-0.120884\pi$
$659$	14.3256	+	14.3256i	0.558044	+	0.558044i	−0.370706	+	0.928750i	$0.620884\pi$
$660$		0			0
$661$	−5.30607	+	7.30318i	−0.206382	+	0.284061i	−0.899643	−	0.436626i	$-0.856173\pi$
$661$	−5.30607	+	7.30318i	−0.206382	+	0.284061i	0.693261	+	0.720687i	$0.256173\pi$
$662$	−19.8657	−	38.9886i	−0.772103	−	1.51534i
$663$		0			0
$664$	−3.14232	−	4.32503i	−0.121946	−	0.167844i
$665$			13.5534i			0.525578i
$666$		0			0
$667$	−19.5691	−	3.09944i	−0.757718	−	0.120011i
$668$	−10.6364	−	67.1558i	−0.411536	−	2.59834i
$669$		0			0
$670$	15.5301	−	15.5301i	0.599980	−	0.599980i
$671$	6.18002	−	0.978818i	0.238577	−	0.0377869i
$672$		0			0
$673$	1.11504	−	7.04008i	0.0429816	−	0.271375i	−0.956833	−	0.290639i	$-0.906132\pi$
$673$	1.11504	−	7.04008i	0.0429816	−	0.271375i	0.999814	+	0.0192636i	$0.00613217\pi$
$674$	5.87421	−	18.0790i	0.226266	−	0.696376i
$675$		0			0
$676$	−31.9061	+	10.3669i	−1.22716	+	0.398727i
$677$	−14.9246	+	4.84928i	−0.573597	+	0.186373i	−0.581430	−	0.813596i	$-0.697507\pi$
$677$	−14.9246	+	4.84928i	−0.573597	+	0.186373i	0.00783293	+	0.999969i	$0.497507\pi$
$678$		0			0
$679$	7.69183	−	23.6730i	0.295185	−	0.908487i
$680$	0.381118	−	2.40628i	0.0146152	−	0.0922767i
$681$		0			0
$682$	65.3151	−	10.3449i	2.50104	−	0.396126i
$683$	−19.3845	+	19.3845i	−0.741729	+	0.741729i	−0.972911	−	0.231182i	$-0.925741\pi$
$683$	−19.3845	+	19.3845i	−0.741729	+	0.741729i	0.231182	+	0.972911i	$0.425741\pi$
$684$		0			0
$685$	−6.82276	−	43.0772i	−0.260684	−	1.64590i
$686$	−41.7266	−	6.60884i	−1.59313	−	0.252327i
$687$		0			0
$688$		−	5.96135i		−	0.227274i
$689$	−1.83349	−	2.52359i	−0.0698506	−	0.0961411i
$690$		0			0
$691$	−15.4816	−	30.3844i	−0.588948	−	1.15588i	−0.972619	−	0.232406i	$-0.925340\pi$
$691$	−15.4816	−	30.3844i	−0.588948	−	1.15588i	0.383671	−	0.923470i	$-0.374660\pi$
$692$	−10.6538	+	14.6637i	−0.404998	+	0.557431i
$693$		0			0
$694$	7.15872	+	7.15872i	0.271741	+	0.271741i
$695$	−1.76379	−	0.573089i	−0.0669042	−	0.0217385i
$696$		0			0
$697$	−3.76859	+	0.174505i	−0.142746	+	0.00660984i
$698$	27.9710			1.05872
$699$		0			0
$700$	16.6270	+	16.6270i	0.628441	+	0.628441i
$701$	21.2988	+	15.4745i	0.804445	+	0.584464i	0.912215	−	0.409712i	$-0.134371\pi$
$701$	21.2988	+	15.4745i	0.804445	+	0.584464i	−0.107769	+	0.994176i	$0.534371\pi$
$702$		0			0
$703$	1.98264	+	3.89114i	0.0747765	+	0.146757i
$704$	33.7422	−	66.2228i	1.27171	−	2.49586i
$705$		0			0
$706$		−	42.7824i		−	1.61014i
$707$	8.78296	−	6.38119i	0.330317	−	0.239989i
$708$		0			0
$709$	1.29513	+	8.17714i	0.0486397	+	0.307099i	1.00000		0.000982939i	$-0.000312879\pi$
$709$	1.29513	+	8.17714i	0.0486397	+	0.307099i	−0.951360	+	0.308082i	$0.900313\pi$
$710$	27.0948	−	13.8055i	1.01685	−	0.518111i
$711$		0			0
$712$	16.8681	−	2.67165i	0.632160	−	0.100124i
$713$	−6.07837	−	18.7073i	−0.227637	−	0.700593i
$714$		0			0
$715$	−3.32244	+	10.2254i	−0.124252	+	0.382409i
$716$	−36.9563	−	18.8302i	−1.38112	−	0.703717i
$717$		0			0
$718$	3.23124	−	1.04989i	0.120589	−	0.0391817i
$719$	−12.5280	−	6.38331i	−0.467214	−	0.238057i	0.204502	−	0.978866i	$-0.434442\pi$
$719$	−12.5280	−	6.38331i	−0.467214	−	0.238057i	−0.671716	+	0.740809i	$0.734442\pi$
$720$		0			0
$721$	−0.0828052	+	0.522811i	−0.00308383	+	0.0194705i
$722$	−10.3013	−	31.7041i	−0.383374	−	1.17990i
$723$		0			0
$724$	37.5963	−	37.5963i	1.39726	−	1.39726i
$725$	−16.1798	+	8.24400i	−0.600901	+	0.306175i
$726$		0			0
$727$	3.58748	+	0.568201i	0.133052	+	0.0210734i	0.222605	−	0.974909i	$-0.428544\pi$
$727$	3.58748	+	0.568201i	0.133052	+	0.0210734i	−0.0895531	+	0.995982i	$0.528544\pi$
$728$	−1.66600	+	1.21042i	−0.0617459	+	0.0448610i
$729$		0			0
$730$	−2.22024	−	3.05589i	−0.0821747	−	0.113104i
$731$	−0.703327	+	1.38036i	−0.0260135	+	0.0510543i
$732$		0			0
$733$	−11.2030	+	15.4196i	−0.413793	+	0.569537i	−0.964138	−	0.265400i	$-0.914496\pi$
$733$	−11.2030	+	15.4196i	−0.413793	+	0.569537i	0.550346	+	0.834937i	$0.314496\pi$
$734$	−18.4276	−	13.3885i	−0.680177	−	0.494177i
$735$		0			0
$736$	−28.9088	−	9.39305i	−1.06559	−	0.346232i
$737$	−21.3203			−0.785345
$738$		0			0
$739$	3.70903			0.136439			0.0682195	−	0.997670i	$-0.478268\pi$
$739$	3.70903			0.136439			0.0682195	+	0.997670i	$0.478268\pi$
$740$	17.1747	+	5.58039i	0.631353	+	0.205139i
$741$		0			0
$742$	22.3959	+	16.2716i	0.822181	+	0.597349i
$743$	−22.4945	+	30.9610i	−0.825243	+	1.13585i	0.163546	+	0.986536i	$0.447707\pi$
$743$	−22.4945	+	30.9610i	−0.825243	+	1.13585i	−0.988790	+	0.149314i	$0.952293\pi$
$744$		0			0
$745$	−17.1221	+	33.6040i	−0.627305	+	1.23116i
$746$	45.1333	+	62.1207i	1.65245	+	2.27440i
$747$		0			0
$748$	−7.77232	+	5.64692i	−0.284184	+	0.206472i
$749$	−38.2586	−	6.05956i	−1.39794	−	0.221412i
$750$		0			0
$751$	45.1176	−	22.9886i	1.64636	−	0.838864i	0.649446	−	0.760407i	$-0.275001\pi$
$751$	45.1176	−	22.9886i	1.64636	−	0.838864i	0.996918	−	0.0784569i	$-0.0249993\pi$
$752$	−8.23722	+	8.23722i	−0.300380	+	0.300380i
$753$		0			0
$754$	−1.99629	−	6.14394i	−0.0727005	−	0.223749i
$755$	6.23932	−	39.3935i	0.227072	−	1.43368i
$756$		0			0
$757$	−16.4699	−	8.39181i	−0.598607	−	0.305006i	0.128306	−	0.991735i	$-0.459046\pi$
$757$	−16.4699	−	8.39181i	−0.598607	−	0.305006i	−0.726914	+	0.686729i	$0.759046\pi$
$758$	−3.39830	+	1.10417i	−0.123432	+	0.0401054i
$759$		0			0
$760$	6.93799	+	3.53508i	0.251667	+	0.128231i
$761$	4.05425	−	12.4777i	0.146967	−	0.452317i	−0.850292	−	0.526311i	$-0.823575\pi$
$761$	4.05425	−	12.4777i	0.146967	−	0.452317i	0.997259	+	0.0739945i	$0.0235747\pi$
$762$		0			0
$763$	4.53864	+	13.9685i	0.164310	+	0.505694i
$764$	16.2498	−	2.57372i	0.587898	−	0.0931138i
$765$		0			0
$766$	−18.7862	+	9.57207i	−0.678775	+	0.345853i
$767$	0.974801	+	6.15465i	0.0351980	+	0.222232i
$768$		0			0
$769$	−9.65861	+	7.01739i	−0.348298	+	0.253053i	−0.748155	−	0.663524i	$-0.769060\pi$
$769$	−9.65861	+	7.01739i	−0.348298	+	0.253053i	0.399857	+	0.916578i	$0.369060\pi$
$770$		−	95.4170i		−	3.43859i
$771$		0			0
$772$	17.0848	−	33.5308i	0.614895	−	1.20680i
$773$	6.63677	+	13.0254i	0.238708	+	0.468491i	0.979018	−	0.203775i	$-0.0653211\pi$
$773$	6.63677	+	13.0254i	0.238708	+	0.468491i	−0.740310	+	0.672266i	$0.765321\pi$
$774$		0			0
$775$	−14.5849	−	10.5965i	−0.523905	−	0.380639i
$776$	−10.1120	−	10.1120i	−0.363000	−	0.363000i
$777$		0			0
$778$	34.9368			1.25255
$779$	3.19165	−	11.6278i	0.114353	−	0.416609i
$780$		0			0
$781$	−28.0748	−	9.12205i	−1.00460	−	0.326413i
$782$	3.54386	+	3.54386i	0.126728	+	0.126728i
$783$		0			0
$784$	1.31463	−	1.80944i	0.0469512	−	0.0646228i
$785$	5.57720	+	10.9459i	0.199059	+	0.390675i
$786$		0			0
$787$	−22.3369	−	30.7442i	−0.796226	−	1.09591i	−0.993305	−	0.115524i	$-0.963145\pi$
$787$	−22.3369	−	30.7442i	−0.796226	−	1.09591i	0.197078	−	0.980388i	$-0.436855\pi$
$788$		−	24.3936i		−	0.868986i
$789$		0			0
$790$	−27.7518	−	4.39545i	−0.987364	−	0.156383i
$791$	7.01202	+	44.2722i	0.249319	+	1.57414i
$792$		0			0
$793$	0.429097	−	0.429097i	0.0152377	−	0.0152377i
$794$	38.2991	−	6.06597i	1.35918	−	0.215273i
$795$		0			0
$796$	3.69802	−	23.3484i	0.131073	−	0.827560i
$797$	−3.31857	+	10.2135i	−0.117550	+	0.361781i	−0.992470	−	0.122485i	$-0.960914\pi$
$797$	−3.31857	+	10.2135i	−0.117550	+	0.361781i	0.874920	+	0.484267i	$0.160914\pi$
$798$		0			0
$799$	2.87917	−	0.935500i	0.101858	−	0.0330956i
$800$	−26.4955	+	8.60890i	−0.936756	+	0.304371i
$801$		0			0
$802$	5.93270	−	18.2590i	0.209491	−	0.644747i
$803$	−0.573611	+	3.62164i	−0.0202423	+	0.127805i
$804$		0			0
$805$	−28.0322	+	4.43986i	−0.988004	+	0.156484i
$806$	4.53503	−	4.53503i	0.159739	−	0.159739i
$807$		0			0
$808$	−0.975709	−	6.16038i	−0.0343253	−	0.216722i
$809$	−25.5063	−	4.03980i	−0.896754	−	0.142032i	−0.308991	−	0.951065i	$-0.599991\pi$
$809$	−25.5063	−	4.03980i	−0.896754	−	0.142032i	−0.587763	+	0.809033i	$0.699991\pi$
$810$		0			0
$811$			41.1472i			1.44488i	0.691436	+	0.722438i	$0.256978\pi$
$811$			41.1472i			1.44488i	−0.691436	+	0.722438i	$0.743022\pi$
$812$	19.2142	+	26.4461i	0.674288	+	0.928077i
$813$		0			0
$814$	−13.9579	−	27.3939i	−0.489225	−	0.960157i
$815$	29.2429	−	40.2493i	1.02433	−	1.40987i
$816$		0			0
$817$	−3.50124	−	3.50124i	−0.122493	−	0.122493i
$818$	−64.3087	−	20.8952i	−2.24850	−	0.730582i
$819$		0			0
$820$	−24.6669	−	43.3314i	−0.861405	−	1.51320i
$821$	21.5835			0.753268			0.376634	−	0.926362i	$-0.377081\pi$
$821$	21.5835			0.753268			0.376634	+	0.926362i	$0.377081\pi$
$822$		0			0
$823$	14.2285	+	14.2285i	0.495975	+	0.495975i	0.910182	−	0.414208i	$-0.135941\pi$
$823$	14.2285	+	14.2285i	0.495975	+	0.495975i	−0.414208	+	0.910182i	$0.635941\pi$
$824$	0.246030	+	0.178751i	0.00857085	+	0.00622709i
$825$		0			0
$826$	−25.1062	−	49.2737i	−0.873557	−	1.71445i
$827$	9.37300	−	18.3955i	0.325931	−	0.639676i	−0.668657	−	0.743571i	$-0.733131\pi$
$827$	9.37300	−	18.3955i	0.325931	−	0.639676i	0.994588	+	0.103895i	$0.0331307\pi$
$828$		0			0
$829$		−	32.8047i		−	1.13935i	−0.821868	−	0.569677i	$-0.807068\pi$
$829$		−	32.8047i		−	1.13935i	0.821868	−	0.569677i	$-0.192932\pi$
$830$	19.4357	−	14.1208i	0.674622	−	0.490142i
$831$		0			0
$832$	−1.12761	−	7.11947i	−0.0390930	−	0.246823i
$833$	−0.517885	+	0.263876i	−0.0179436	+	0.00914275i
$834$		0			0
$835$	74.2904	−	11.7664i	2.57092	−	0.407194i
$836$	−9.48859	−	29.2029i	−0.328170	−	1.01000i
$837$		0			0
$838$	5.27262	−	16.2274i	0.182140	−	0.560568i
$839$	8.20381	+	4.18005i	0.283227	+	0.144311i	0.589833	−	0.807525i	$-0.299193\pi$
$839$	8.20381	+	4.18005i	0.283227	+	0.144311i	−0.306606	+	0.951836i	$0.599193\pi$
$840$		0			0
$841$	3.57168	−	1.16051i	0.123161	−	0.0400175i
$842$	31.3424	+	15.9698i	1.08013	+	0.550354i
$843$		0			0
$844$	1.03568	−	6.53901i	0.0356495	−	0.225082i
$845$	−11.4683	−	35.2957i	−0.394521	−	1.21421i
$846$		0			0
$847$	−46.4221	+	46.4221i	−1.59508	+	1.59508i
$848$	−10.5717	+	5.38653i	−0.363032	+	0.184974i
$849$		0			0
$850$	4.53683	+	0.718563i	0.155612	+	0.0246465i
$851$	−7.39848	+	5.37531i	−0.253617	+	0.184263i
$852$		0			0
$853$	3.94397	+	5.42840i	0.135039	+	0.185865i	0.871181	−	0.490962i	$-0.163355\pi$
$853$	3.94397	+	5.42840i	0.135039	+	0.185865i	−0.736142	+	0.676827i	$0.763355\pi$
$854$	−2.44494	+	4.79847i	−0.0836642	+	0.164200i
$855$		0			0
$856$	−13.0807	+	18.0041i	−0.447090	+	0.615367i
$857$	22.0856	+	16.0461i	0.754428	+	0.548124i	0.897196	−	0.441632i	$-0.145600\pi$
$857$	22.0856	+	16.0461i	0.754428	+	0.548124i	−0.142768	+	0.989756i	$0.545600\pi$
$858$		0			0
$859$	39.2836	+	12.7640i	1.34034	+	0.435503i	0.889432	−	0.457068i	$-0.151100\pi$
$859$	39.2836	+	12.7640i	1.34034	+	0.435503i	0.450907	+	0.892571i	$0.351100\pi$
$860$	−20.4749			−0.698189
$861$		0			0
$862$	−0.849642			−0.0289389
$863$	−31.0353	−	10.0840i	−1.05646	−	0.343263i	−0.271257	−	0.962507i	$-0.587439\pi$
$863$	−31.0353	−	10.0840i	−1.05646	−	0.343263i	−0.785199	+	0.619244i	$0.787439\pi$
$864$		0			0
$865$	−16.2216	−	11.7857i	−0.551551	−	0.400725i
$866$	−21.9320	+	30.1868i	−0.745280	+	1.02579i
$867$		0			0
$868$	−14.7335	+	28.9161i	−0.500087	+	0.981476i
$869$	16.0322	+	22.0665i	0.543856	+	0.748554i
$870$		0			0
$871$	−1.67283	+	1.21539i	−0.0566818	+	0.0411818i
$872$	8.33428	+	1.32002i	0.282234	+	0.0447015i
$873$		0			0
$874$	−14.2724	+	7.27217i	−0.482773	+	0.245985i
$875$	7.05289	−	7.05289i	0.238431	−	0.238431i
$876$		0			0
$877$	−3.53001	−	10.8643i	−0.119200	−	0.366860i	0.873600	−	0.486645i	$-0.161780\pi$
$877$	−3.53001	−	10.8643i	−0.119200	−	0.366860i	−0.992800	+	0.119785i	$0.961780\pi$
$878$	−0.141371	+	0.892583i	−0.00477105	+	0.0301232i
$879$		0			0
$880$	36.4382	+	18.5662i	1.22833	+	0.625866i
$881$	−19.8386	+	6.44595i	−0.668379	+	0.217169i	−0.623500	−	0.781823i	$-0.714290\pi$
$881$	−19.8386	+	6.44595i	−0.668379	+	0.217169i	−0.0448784	+	0.998992i	$0.514290\pi$
$882$		0			0
$883$	14.2619	+	7.26681i	0.479951	+	0.244547i	0.677190	−	0.735808i	$-0.263197\pi$
$883$	14.2619	+	7.26681i	0.479951	+	0.244547i	−0.197239	+	0.980355i	$0.563197\pi$
$884$	−0.287923	+	0.886137i	−0.00968391	+	0.0298040i
$885$		0			0
$886$	17.6106	+	54.1998i	0.591639	+	1.82088i
$887$	−1.51345	+	0.239706i	−0.0508165	+	0.00804855i	−0.181791	−	0.983337i	$-0.558189\pi$
$887$	−1.51345	+	0.239706i	−0.0508165	+	0.00804855i	0.130974	+	0.991386i	$0.458189\pi$
$888$		0			0
$889$	39.9011	−	20.3307i	1.33824	−	0.681868i
$890$	12.0058	+	75.8014i	0.402434	+	2.54087i
$891$		0			0
$892$	−53.2146	+	38.6627i	−1.78176	+	1.29452i
$893$			9.67582i			0.323789i
$894$		0			0
$895$	20.8307	−	40.8825i	0.696293	−	1.36655i
$896$	11.8788	+	23.3134i	0.396841	+	0.778845i
$897$		0			0
$898$	−40.5986	−	29.4966i	−1.35479	−	0.984316i
$899$	−17.7217	−	17.7217i	−0.591053	−	0.591053i
$900$		0			0
$901$	3.08339			0.102723
$902$	−22.4695	+	81.8605i	−0.748152	+	2.72566i
$903$		0			0
$904$	24.4919	+	7.95789i	0.814587	+	0.264675i
$905$	41.5905	+	41.5905i	1.38252	+	1.38252i
$906$		0			0
$907$	−10.1296	+	13.9421i	−0.336346	+	0.462941i	−0.943370	−	0.331743i	$-0.892363\pi$
$907$	−10.1296	+	13.9421i	−0.336346	+	0.462941i	0.607023	+	0.794684i	$0.292363\pi$
$908$	−2.75704	−	5.41100i	−0.0914957	−	0.179570i
$909$		0			0
$910$	−5.43933	−	7.48660i	−0.180312	−	0.248178i
$911$		−	10.8340i		−	0.358947i	−0.983763	−	0.179474i	$-0.942561\pi$
$911$		−	10.8340i		−	0.358947i	0.983763	−	0.179474i	$-0.0574395\pi$
$912$		0			0
$913$	−23.0339	−	3.64820i	−0.762309	−	0.120738i
$914$	−3.07567	−	19.4190i	−0.101734	−	0.642325i
$915$		0			0
$916$	−39.4371	+	39.4371i	−1.30304	+	1.30304i
$917$	−32.8236	+	5.19874i	−1.08393	+	0.171678i
$918$		0			0
$919$	−8.24478	+	52.0555i	−0.271970	+	1.71715i	0.352251	+	0.935905i	$0.385416\pi$
$919$	−8.24478	+	52.0555i	−0.271970	+	1.71715i	−0.624222	+	0.781247i	$0.714584\pi$
$920$	−5.03876	+	15.5077i	−0.166123	+	0.511274i
$921$		0			0
$922$	80.7650	−	26.2421i	2.65985	−	0.864239i
$923$	−2.72281	+	0.884696i	−0.0896225	+	0.0291201i
$924$		0			0
$925$	−2.59005	+	7.97135i	−0.0851603	+	0.262096i
$926$	−5.98838	+	37.8091i	−0.196790	+	1.24249i
$927$		0			0
$928$	−38.2526	+	6.05862i	−1.25570	+	0.198884i
$929$	25.6149	−	25.6149i	0.840396	−	0.840396i	−0.148514	−	0.988910i	$-0.547449\pi$
$929$	25.6149	−	25.6149i	0.840396	−	0.840396i	0.988910	+	0.148514i	$0.0474490\pi$
$930$		0			0
$931$	−0.290610	−	1.83484i	−0.00952437	−	0.0601345i
$932$	22.8431	+	3.61799i	0.748251	+	0.118511i
$933$		0			0
$934$		−	8.67890i		−	0.283982i
$935$	−6.24685	−	8.59805i	−0.204294	−	0.281186i
$936$		0			0
$937$	−4.26783	−	8.37609i	−0.139424	−	0.273635i	0.810728	−	0.585424i	$-0.199072\pi$
$937$	−4.26783	−	8.37609i	−0.139424	−	0.273635i	−0.950151	+	0.311789i	$0.899072\pi$
$938$	10.7861	−	14.8458i	0.352179	−	0.484733i
$939$		0			0
$940$	28.2917	+	28.2917i	0.922773	+	0.922773i
$941$	15.1051	+	4.90795i	0.492413	+	0.159995i	0.544689	−	0.838638i	$-0.316648\pi$
$941$	15.1051	+	4.90795i	0.492413	+	0.159995i	−0.0522762	+	0.998633i	$0.516648\pi$
$942$		0			0
$943$	25.0950	+	2.79215i	0.817205	+	0.0909250i
$944$	23.7020			0.771434
$945$		0			0
$946$	24.6490	+	24.6490i	0.801408	+	0.801408i
$947$	30.5510	+	22.1966i	0.992775	+	0.721293i	0.960527	−	0.278186i	$-0.0897333\pi$
$947$	30.5510	+	22.1966i	0.992775	+	0.721293i	0.0322482	+	0.999480i	$0.489733\pi$
$948$		0			0
$949$	0.161448	+	0.316860i	0.00524083	+	0.0102857i
$950$	−6.66508	+	13.0810i	−0.216244	+	0.424402i
$951$		0			0
$952$		−	2.03556i		−	0.0659728i
$953$	−25.8698	+	18.7955i	−0.838006	+	0.608847i	−0.921813	−	0.387635i	$-0.873292\pi$
$953$	−25.8698	+	18.7955i	−0.838006	+	0.608847i	0.0838068	+	0.996482i	$0.473292\pi$
$954$		0			0
$955$	2.84715	+	17.9762i	0.0921315	+	0.581695i
$956$	−54.5130	+	27.7758i	−1.76308	+	0.898332i
$957$		0			0
$958$	−40.0005	+	6.33546i	−1.29236	+	0.204690i
$959$	−11.2607	−	34.6570i	−0.363628	−	1.11913i
$960$		0			0
$961$	−1.89074	+	5.81911i	−0.0609917	+	0.187713i
$962$	−2.65678	−	1.35370i	−0.0856581	−	0.0436450i
$963$		0			0
$964$	13.6027	−	4.41978i	0.438113	−	0.142352i
$965$	37.0931	+	18.8999i	1.19407	+	0.608408i
$966$		0			0
$967$	−7.26414	+	45.8640i	−0.233599	+	1.47489i	0.540243	+	0.841509i	$0.318332\pi$
$967$	−7.26414	+	45.8640i	−0.233599	+	1.47489i	−0.773842	+	0.633378i	$0.781668\pi$
$968$	11.6554	+	35.8716i	0.374619	+	1.15296i
$969$		0			0
$970$	45.4410	−	45.4410i	1.45902	−	1.45902i
$971$	45.6829	−	23.2766i	1.46603	−	0.746982i	0.474925	−	0.880027i	$-0.342475\pi$
$971$	45.6829	−	23.2766i	1.46603	−	0.746982i	0.991110	+	0.133045i	$0.0424753\pi$
$972$		0			0
$973$	−1.53044	−	0.242398i	−0.0490636	−	0.00777092i
$974$	9.77760	−	7.10384i	0.313294	−	0.227622i
$975$		0			0
$976$	−1.35672	−	1.86737i	−0.0434276	−	0.0597730i
$977$	−5.61016	+	11.0106i	−0.179485	+	0.352259i	−0.963167	−	0.268903i	$-0.913339\pi$
$977$	−5.61016	+	11.0106i	−0.179485	+	0.352259i	0.783682	+	0.621162i	$0.213339\pi$
$978$		0			0
$979$	43.7906	−	60.2726i	1.39955	−	1.92632i
$980$	−6.21473	−	4.51526i	−0.198522	−	0.144235i
$981$		0			0
$982$	−65.3394	−	21.2300i	−2.08506	−	0.677478i
$983$	33.4651			1.06737			0.533686	−	0.845683i	$-0.320806\pi$
$983$	33.4651			1.06737			0.533686	+	0.845683i	$0.320806\pi$
$984$		0			0
$985$	26.9852			0.859819
$986$	6.07315	+	1.97329i	0.193409	+	0.0628423i
$987$		0			0
$988$	−2.40923	−	1.75041i	−0.0766478	−	0.0556879i
$989$	6.09458	−	8.38847i	0.193796	−	0.266738i
$990$		0			0
$991$	3.03259	−	5.95180i	0.0963335	−	0.189065i	−0.837811	−	0.545961i	$-0.816165\pi$
$991$	3.03259	−	5.95180i	0.0963335	−	0.189065i	0.934144	+	0.356895i	$0.116165\pi$
$992$	−22.6003	−	31.1066i	−0.717560	−	0.987636i
$993$		0			0
$994$	20.5551	−	14.9342i	0.651969	−	0.473683i
$995$	25.8289	+	4.09089i	0.818830	+	0.129690i
$996$		0			0
$997$	−53.5880	+	27.3044i	−1.69715	+	0.864740i	−0.710142	+	0.704058i	$0.751369\pi$
$997$	−53.5880	+	27.3044i	−1.69715	+	0.864740i	−0.987006	+	0.160682i	$0.948631\pi$
$998$	6.36296	−	6.36296i	0.201416	−	0.201416i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.226.3		24
3.2	odd	2		41.2.g.a.21.1	yes	24
12.11	even	2		656.2.bs.d.513.1		24
41.2	even	20	inner	369.2.u.a.289.3		24
123.2	odd	20		41.2.g.a.2.1	✓	24
123.17	even	40		1681.2.a.m.1.19		24
123.65	even	40		1681.2.a.m.1.20		24
492.371	even	20		656.2.bs.d.289.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.2.1	✓	24	123.2	odd	20
41.2.g.a.21.1	yes	24	3.2	odd	2
369.2.u.a.226.3		24	1.1	even	1	trivial
369.2.u.a.289.3		24	41.2	even	20	inner
656.2.bs.d.289.1		24	492.371	even	20
656.2.bs.d.513.1		24	12.11	even	2
1681.2.a.m.1.19		24	123.17	even	40
1681.2.a.m.1.20		24	123.65	even	40

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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.05153 + 0.666584i) q^{2} +(2.14642 + 1.55947i) q^{4} +(-1.72514 + 2.37446i) q^{5} +(-1.11329 + 2.18496i) q^{7} +(0.828108 + 1.13979i) q^{8} +O(q^{10})\)	\(q+(2.05153 + 0.666584i) q^{2} +(2.14642 + 1.55947i) q^{4} +(-1.72514 + 2.37446i) q^{5} +(-1.11329 + 2.18496i) q^{7} +(0.828108 + 1.13979i) q^{8} +(-5.12196 + 3.72132i) q^{10} +(6.07021 + 0.961426i) q^{11} +(0.531087 - 0.270602i) q^{13} +(-3.74042 + 3.74042i) q^{14} +(-0.700597 - 2.15622i) q^{16} +(-0.0921689 + 0.581932i) q^{17} +(-1.67787 - 0.854919i) q^{19} +(-7.40577 + 2.40628i) q^{20} +(11.8124 + 6.01870i) q^{22} +(1.21857 - 3.75036i) q^{23} +(-1.11684 - 3.43727i) q^{25} +(1.26992 - 0.201136i) q^{26} +(-5.79698 + 2.95371i) q^{28} +(-0.785988 - 4.96253i) q^{29} +(4.03548 - 2.93195i) q^{31} -7.70828i q^{32} +(-0.576994 + 1.13241i) q^{34} +(-3.26751 - 6.41285i) q^{35} +(-1.87618 - 1.36313i) q^{37} +(-2.87234 - 2.87234i) q^{38} -4.13499 q^{40} +(1.29313 + 6.27119i) q^{41} +(2.50072 + 0.812532i) q^{43} +(11.5299 + 11.5299i) q^{44} +(4.99986 - 6.88172i) q^{46} +(-2.33269 - 4.57815i) q^{47} +(0.579854 + 0.798101i) q^{49} -7.79615i q^{50} +(1.56193 + 0.247386i) q^{52} +(-0.818669 - 5.16887i) q^{53} +(-12.7548 + 12.7548i) q^{55} +(-3.41233 + 0.540460i) q^{56} +(1.69546 - 10.7047i) q^{58} +(-3.23058 + 9.94272i) q^{59} +(0.968261 - 0.314607i) q^{61} +(10.2333 - 3.32501i) q^{62} +(3.73702 - 11.5014i) q^{64} +(-0.273668 + 1.72787i) q^{65} +(-3.42634 + 0.542679i) q^{67} +(-1.10534 + 1.10534i) q^{68} +(-2.42870 - 15.3342i) q^{70} +(-4.74402 - 0.751379i) q^{71} +0.596626i q^{73} +(-2.94042 - 4.04714i) q^{74} +(-2.26821 - 4.45161i) q^{76} +(-8.85861 + 12.1928i) q^{77} +(3.13817 + 3.13817i) q^{79} +(6.32847 + 2.05625i) q^{80} +(-1.52737 + 13.7275i) q^{82} -3.79458 q^{83} +(-1.22277 - 1.22277i) q^{85} +(4.58868 + 3.33387i) q^{86} +(3.93096 + 7.71494i) q^{88} +(5.50333 - 10.8009i) q^{89} +1.46167i q^{91} +(8.46413 - 6.14955i) q^{92} +(-1.73386 - 10.9472i) q^{94} +(4.92454 - 2.50918i) q^{95} +(-10.0255 + 1.58788i) q^{97} +(0.657590 + 2.02385i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

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