LMFDB - Embedded newform 243.2.e.b.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, not 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			136.1
Root			$0.500000 - 1.00210i$ of defining polynomial
Character	$\chi$	$=$	243.136
Dual form			243.2.e.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.807660 - 0.677707i) q^{2} +(-0.154269 - 0.874902i) q^{4} +(-1.64050 - 0.597094i) q^{5} +(0.427044 - 2.42189i) q^{7} +(-1.52266 + 2.63732i) q^{8} +O(q^{10})$	\(q+(-0.807660 - 0.677707i) q^{2} +(-0.154269 - 0.874902i) q^{4} +(-1.64050 - 0.597094i) q^{5} +(0.427044 - 2.42189i) q^{7} +(-1.52266 + 2.63732i) q^{8} +(0.920313 + 1.59403i) q^{10} +(-1.17857 + 0.428966i) q^{11} +(-3.48476 + 2.92406i) q^{13} +(-1.98623 + 1.66665i) q^{14} +(1.34747 - 0.490439i) q^{16} +(-3.32358 - 5.75662i) q^{17} +(-0.124578 + 0.215776i) q^{19} +(-0.269321 + 1.52739i) q^{20} +(1.24260 + 0.452270i) q^{22} +(-0.146212 - 0.829209i) q^{23} +(-1.49549 - 1.25487i) q^{25} +4.79615 q^{26} -2.18479 q^{28} +(0.392508 + 0.329353i) q^{29} +(-0.142392 - 0.807546i) q^{31} +(4.30264 + 1.56603i) q^{32} +(-1.21697 + 6.90180i) q^{34} +(-2.14666 + 3.71812i) q^{35} +(-1.30403 - 2.25865i) q^{37} +(0.246849 - 0.0898458i) q^{38} +(4.07265 - 3.41736i) q^{40} +(6.24542 - 5.24053i) q^{41} +(-4.06619 + 1.47997i) q^{43} +(0.557121 + 0.964962i) q^{44} +(-0.443871 + 0.768808i) q^{46} +(0.920741 - 5.22178i) q^{47} +(0.894687 + 0.325640i) q^{49} +(0.357417 + 2.02701i) q^{50} +(3.09586 + 2.59773i) q^{52} +10.4841 q^{53} +2.18959 q^{55} +(5.73704 + 4.81395i) q^{56} +(-0.0938079 - 0.532011i) q^{58} +(-2.82491 - 1.02818i) q^{59} +(0.500658 - 2.83937i) q^{61} +(-0.432275 + 0.748722i) q^{62} +(-3.84771 - 6.66442i) q^{64} +(7.46270 - 2.71620i) q^{65} +(7.72653 - 6.48333i) q^{67} +(-4.52375 + 3.79588i) q^{68} +(4.25357 - 1.54817i) q^{70} +(0.0447378 + 0.0774882i) q^{71} +(2.66057 - 4.60824i) q^{73} +(-0.477488 + 2.70797i) q^{74} +(0.208001 + 0.0757062i) q^{76} +(0.535604 + 3.03756i) q^{77} +(3.65933 + 3.07054i) q^{79} -2.50337 q^{80} -8.59571 q^{82} +(-6.15950 - 5.16844i) q^{83} +(2.01511 + 11.4282i) q^{85} +(4.28708 + 1.56037i) q^{86} +(0.663244 - 3.76144i) q^{88} +(3.35189 - 5.80564i) q^{89} +(5.59359 + 9.68839i) q^{91} +(-0.702921 + 0.255842i) q^{92} +(-4.28248 + 3.59343i) q^{94} +(0.333209 - 0.279596i) q^{95} +(-5.15946 + 1.87789i) q^{97} +(-0.501915 - 0.869342i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28} - 30 q^{29} - 15 q^{31} + 27 q^{32} - 9 q^{34} - 12 q^{35} - 3 q^{37} + 12 q^{38} - 6 q^{40} + 21 q^{41} + 12 q^{43} - 3 q^{44} - 3 q^{46} - 3 q^{47} + 21 q^{49} - 12 q^{50} + 36 q^{52} + 18 q^{53} - 12 q^{55} - 3 q^{56} + 30 q^{58} - 15 q^{59} + 21 q^{61} + 12 q^{62} + 12 q^{64} + 24 q^{65} + 21 q^{67} + 18 q^{68} + 30 q^{70} - 27 q^{71} + 6 q^{73} + 12 q^{74} + 42 q^{76} + 3 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 33 q^{83} - 9 q^{85} + 30 q^{86} - 12 q^{88} - 9 q^{89} + 6 q^{91} - 42 q^{92} - 33 q^{94} - 30 q^{95} - 42 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−0.807660	−	0.677707i	−0.571102	−	0.479211i	0.310910	−	0.950439i	$-0.399366\pi$
$2$	−0.807660	−	0.677707i	−0.571102	−	0.479211i	−0.882011	+	0.471228i	$0.843811\pi$
$3$		0			0
$3$		0			0
$4$	−0.154269	−	0.874902i	−0.0771344	−	0.437451i
$5$	−1.64050	−	0.597094i	−0.733655	−	0.267029i	−0.0519440	−	0.998650i	$-0.516542\pi$
$5$	−1.64050	−	0.597094i	−0.733655	−	0.267029i	−0.681711	+	0.731621i	$0.738764\pi$
$6$		0			0
$7$	0.427044	−	2.42189i	0.161407	−	0.915387i	−0.791284	−	0.611448i	$-0.790587\pi$
$7$	0.427044	−	2.42189i	0.161407	−	0.915387i	0.952692	−	0.303938i	$-0.0983017\pi$
$8$	−1.52266	+	2.63732i	−0.538340	+	0.932432i
$9$		0			0
$10$	0.920313	+	1.59403i	0.291029	+	0.504076i
$11$	−1.17857	+	0.428966i	−0.355354	+	0.129338i	−0.513528	−	0.858073i	$-0.671662\pi$
$11$	−1.17857	+	0.428966i	−0.355354	+	0.129338i	0.158174	+	0.987411i	$0.449439\pi$
$12$		0			0
$13$	−3.48476	+	2.92406i	−0.966498	+	0.810988i	−0.981998	−	0.188892i	$-0.939511\pi$
$13$	−3.48476	+	2.92406i	−0.966498	+	0.810988i	0.0154998	+	0.999880i	$0.495066\pi$
$14$	−1.98623	+	1.66665i	−0.530843	+	0.445431i
$15$		0			0
$16$	1.34747	−	0.490439i	0.336868	−	0.122610i
$17$	−3.32358	−	5.75662i	−0.806088	−	1.39618i	−0.915554	−	0.402194i	$-0.868248\pi$
$17$	−3.32358	−	5.75662i	−0.806088	−	1.39618i	0.109467	−	0.993990i	$-0.465086\pi$
$18$		0			0
$19$	−0.124578	+	0.215776i	−0.0285802	+	0.0495023i	−0.879962	−	0.475045i	$-0.842432\pi$
$19$	−0.124578	+	0.215776i	−0.0285802	+	0.0495023i	0.851382	+	0.524547i	$0.175765\pi$
$20$	−0.269321	+	1.52739i	−0.0602219	+	0.341536i
$21$		0			0
$22$	1.24260	+	0.452270i	0.264923	+	0.0964242i
$23$	−0.146212	−	0.829209i	−0.0304873	−	0.172902i	0.965762	−	0.259429i	$-0.0835343\pi$
$23$	−0.146212	−	0.829209i	−0.0304873	−	0.172902i	−0.996250	+	0.0865268i	$0.972423\pi$
$24$		0			0
$25$	−1.49549	−	1.25487i	−0.299099	−	0.250974i
$26$	4.79615			0.940603
$27$		0			0
$28$	−2.18479			−0.412887
$29$	0.392508	+	0.329353i	0.0728869	+	0.0611594i	0.678503	−	0.734597i	$-0.262629\pi$
$29$	0.392508	+	0.329353i	0.0728869	+	0.0611594i	−0.605616	+	0.795757i	$0.707073\pi$
$30$		0			0
$31$	−0.142392	−	0.807546i	−0.0255744	−	0.145040i	0.969347	−	0.245696i	$-0.0790167\pi$
$31$	−0.142392	−	0.807546i	−0.0255744	−	0.145040i	−0.994921	+	0.100657i	$0.967906\pi$
$32$	4.30264	+	1.56603i	0.760607	+	0.276838i
$33$		0			0
$34$	−1.21697	+	6.90180i	−0.208709	+	1.18365i
$35$	−2.14666	+	3.71812i	−0.362852	+	0.628478i
$36$		0			0
$37$	−1.30403	−	2.25865i	−0.214381	−	0.371319i	0.738700	−	0.674035i	$-0.235440\pi$
$37$	−1.30403	−	2.25865i	−0.214381	−	0.371319i	−0.953081	+	0.302715i	$0.902107\pi$
$38$	0.246849	−	0.0898458i	0.0400442	−	0.0145749i
$39$		0			0
$40$	4.07265	−	3.41736i	0.643942	−	0.540332i
$41$	6.24542	−	5.24053i	0.975370	−	0.818433i	−0.00801406	−	0.999968i	$-0.502551\pi$
$41$	6.24542	−	5.24053i	0.975370	−	0.818433i	0.983385	+	0.181535i	$0.0581065\pi$
$42$		0			0
$43$	−4.06619	+	1.47997i	−0.620087	+	0.225693i	−0.632911	−	0.774224i	$-0.718140\pi$
$43$	−4.06619	+	1.47997i	−0.620087	+	0.225693i	0.0128237	+	0.999918i	$0.495918\pi$
$44$	0.557121	+	0.964962i	0.0839891	+	0.145473i
$45$		0			0
$46$	−0.443871	+	0.768808i	−0.0654452	+	0.113354i
$47$	0.920741	−	5.22178i	0.134304	−	0.761675i	−0.841038	−	0.540976i	$-0.818055\pi$
$47$	0.920741	−	5.22178i	0.134304	−	0.761675i	0.975342	−	0.220699i	$-0.0708339\pi$
$48$		0			0
$49$	0.894687	+	0.325640i	0.127812	+	0.0465199i
$50$	0.357417	+	2.02701i	0.0505464	+	0.286663i
$51$		0			0
$52$	3.09586	+	2.59773i	0.429318	+	0.360241i
$53$	10.4841			1.44010			0.720052	−	0.693920i	$-0.244118\pi$
$53$	10.4841			1.44010			0.720052	+	0.693920i	$0.244118\pi$
$54$		0			0
$55$	2.18959			0.295244
$56$	5.73704	+	4.81395i	0.766644	+	0.643291i
$57$		0			0
$58$	−0.0938079	−	0.532011i	−0.0123176	−	0.0698565i
$59$	−2.82491	−	1.02818i	−0.367772	−	0.133858i	0.151522	−	0.988454i	$-0.451583\pi$
$59$	−2.82491	−	1.02818i	−0.367772	−	0.133858i	−0.519293	+	0.854596i	$0.673805\pi$
$60$		0			0
$61$	0.500658	−	2.83937i	0.0641026	−	0.363544i	−0.935836	−	0.352437i	$-0.885353\pi$
$61$	0.500658	−	2.83937i	0.0641026	−	0.363544i	0.999938	−	0.0111075i	$-0.00353569\pi$
$62$	−0.432275	+	0.748722i	−0.0548990	+	0.0950878i
$63$		0			0
$64$	−3.84771	−	6.66442i	−0.480963	−	0.833053i
$65$	7.46270	−	2.71620i	0.925634	−	0.336903i
$66$		0			0
$67$	7.72653	−	6.48333i	0.943945	−	0.792064i	−0.0343221	−	0.999411i	$-0.510927\pi$
$67$	7.72653	−	6.48333i	0.943945	−	0.792064i	0.978268	+	0.207347i	$0.0664828\pi$
$68$	−4.52375	+	3.79588i	−0.548586	+	0.460318i
$69$		0			0
$70$	4.25357	−	1.54817i	0.508399	−	0.185042i
$71$	0.0447378	+	0.0774882i	0.00530940	+	0.00919615i	0.868668	−	0.495395i	$-0.164977\pi$
$71$	0.0447378	+	0.0774882i	0.00530940	+	0.00919615i	−0.863358	+	0.504591i	$0.831643\pi$
$72$		0			0
$73$	2.66057	−	4.60824i	0.311396	−	0.539354i	−0.667269	−	0.744817i	$-0.732537\pi$
$73$	2.66057	−	4.60824i	0.311396	−	0.539354i	0.978665	+	0.205463i	$0.0658701\pi$
$74$	−0.477488	+	2.70797i	−0.0555069	+	0.314795i
$75$		0			0
$76$	0.208001	+	0.0757062i	0.0238594	+	0.00868410i
$77$	0.535604	+	3.03756i	0.0610377	+	0.346162i
$78$		0			0
$79$	3.65933	+	3.07054i	0.411707	+	0.345463i	0.824998	−	0.565136i	$-0.191176\pi$
$79$	3.65933	+	3.07054i	0.411707	+	0.345463i	−0.413291	+	0.910599i	$0.635621\pi$
$80$	−2.50337			−0.279885
$81$		0			0
$82$	−8.59571			−0.949238
$83$	−6.15950	−	5.16844i	−0.676093	−	0.567310i	0.238769	−	0.971077i	$-0.423256\pi$
$83$	−6.15950	−	5.16844i	−0.676093	−	0.567310i	−0.914862	+	0.403767i	$0.867701\pi$
$84$		0			0
$85$	2.01511	+	11.4282i	0.218569	+	1.23957i
$86$	4.28708	+	1.56037i	0.462288	+	0.168259i
$87$		0			0
$88$	0.663244	−	3.76144i	0.0707020	−	0.400971i
$89$	3.35189	−	5.80564i	0.355299	−	0.615396i	−0.631870	−	0.775074i	$-0.717712\pi$
$89$	3.35189	−	5.80564i	0.355299	−	0.615396i	0.987169	+	0.159678i	$0.0510457\pi$
$90$		0			0
$91$	5.59359	+	9.68839i	0.586368	+	1.01562i
$92$	−0.702921	+	0.255842i	−0.0732846	+	0.0266734i
$93$		0			0
$94$	−4.28248	+	3.59343i	−0.441704	+	0.370634i
$95$	0.333209	−	0.279596i	0.0341865	−	0.0286859i
$96$		0			0
$97$	−5.15946	+	1.87789i	−0.523863	+	0.190671i	−0.590396	−	0.807114i	$-0.701028\pi$
$97$	−5.15946	+	1.87789i	−0.523863	+	0.190671i	0.0665329	+	0.997784i	$0.478806\pi$
$98$	−0.501915	−	0.869342i	−0.0507010	−	0.0878168i
$99$		0			0
$100$	−0.867179	+	1.50200i	−0.0867179	+	0.150200i
$101$	−0.869190	+	4.92942i	−0.0864876	+	0.490496i	0.910538	+	0.413425i	$0.135668\pi$
$101$	−0.869190	+	4.92942i	−0.0864876	+	0.490496i	−0.997026	+	0.0770703i	$0.975443\pi$
$102$		0			0
$103$	−10.9184	−	3.97399i	−1.07583	−	0.391569i	−0.257473	−	0.966285i	$-0.582890\pi$
$103$	−10.9184	−	3.97399i	−1.07583	−	0.391569i	−0.818352	+	0.574717i	$0.805112\pi$
$104$	−2.40558	−	13.6427i	−0.235887	−	1.33778i
$105$		0			0
$106$	−8.46760	−	7.10516i	−0.822446	−	0.690114i
$107$	−19.4581			−1.88109			−0.940544	−	0.339673i	$-0.889684\pi$
$107$	−19.4581			−1.88109			−0.940544	+	0.339673i	$0.889684\pi$
$108$		0			0
$109$	6.31515			0.604881			0.302441	−	0.953168i	$-0.402199\pi$
$109$	6.31515			0.604881			0.302441	+	0.953168i	$0.402199\pi$
$110$	−1.76844	−	1.48390i	−0.168614	−	0.141484i
$111$		0			0
$112$	−0.612359	−	3.47286i	−0.0578625	−	0.328154i
$113$	−6.49866	−	2.36532i	−0.611342	−	0.222510i	0.0177483	−	0.999842i	$-0.494350\pi$
$113$	−6.49866	−	2.36532i	−0.611342	−	0.222510i	−0.629090	+	0.777332i	$0.716572\pi$
$114$		0			0
$115$	−0.255255	+	1.44762i	−0.0238026	+	0.134991i
$116$	0.227600	−	0.394215i	0.0211322	−	0.0366020i
$117$		0			0
$118$	1.58476	+	2.74488i	0.145889	+	0.252687i
$119$	−15.3612	+	5.59101i	−1.40816	+	0.512527i
$120$		0			0
$121$	−7.22146	+	6.05953i	−0.656497	+	0.550866i
$122$	−2.32862	+	1.95395i	−0.210824	+	0.176902i
$123$		0			0
$124$	−0.684557	+	0.249158i	−0.0614750	+	0.0223751i
$125$	6.06855	+	10.5110i	0.542788	+	0.940136i
$126$		0			0
$127$	−6.01162	+	10.4124i	−0.533445	+	0.923954i	0.465792	+	0.884894i	$0.345770\pi$
$127$	−6.01162	+	10.4124i	−0.533445	+	0.923954i	−0.999237	+	0.0390598i	$0.987564\pi$
$128$	0.181303	−	1.02822i	0.0160251	−	0.0908828i
$129$		0			0
$130$	−7.86811	−	2.86376i	−0.690079	−	0.251168i
$131$	2.44580	+	13.8708i	0.213690	+	1.21190i	0.883164	+	0.469063i	$0.155408\pi$
$131$	2.44580	+	13.8708i	0.213690	+	1.21190i	−0.669474	+	0.742835i	$0.733480\pi$
$132$		0			0
$133$	0.469383	+	0.393859i	0.0407007	+	0.0341519i
$134$	−10.6342			−0.918655
$135$		0			0
$136$	20.2427			1.73580
$137$	−1.72984	−	1.45150i	−0.147790	−	0.124010i	0.565895	−	0.824477i	$-0.308531\pi$
$137$	−1.72984	−	1.45150i	−0.147790	−	0.124010i	−0.713685	+	0.700467i	$0.752975\pi$
$138$		0			0
$139$	−1.38486	−	7.85393i	−0.117462	−	0.666162i	−0.985502	−	0.169666i	$-0.945731\pi$
$139$	−1.38486	−	7.85393i	−0.117462	−	0.666162i	0.868039	−	0.496496i	$-0.165380\pi$
$140$	3.58416	+	1.30453i	0.302917	+	0.110253i
$141$		0			0
$142$	0.0163813	−	0.0929032i	0.00137469	−	0.00779626i
$143$	2.85273	−	4.94107i	0.238557	−	0.413193i
$144$		0			0
$145$	−0.447256	−	0.774670i	−0.0371426	−	0.0643328i
$146$	−5.27187	+	1.91880i	−0.436303	+	0.158801i
$147$		0			0
$148$	−1.77492	+	1.48934i	−0.145898	+	0.122423i
$149$	0.0819196	−	0.0687387i	0.00671111	−	0.00563129i	−0.639426	−	0.768853i	$-0.720828\pi$
$149$	0.0819196	−	0.0687387i	0.00671111	−	0.00563129i	0.646137	+	0.763221i	$0.276383\pi$
$150$		0			0
$151$	19.0376	−	6.92913i	1.54926	−	0.563884i	0.581016	−	0.813892i	$-0.302655\pi$
$151$	19.0376	−	6.92913i	1.54926	−	0.563884i	0.968244	+	0.250008i	$0.0804333\pi$
$152$	−0.379379	−	0.657104i	−0.0307717	−	0.0532982i
$153$		0			0
$154$	1.62599	−	2.81630i	0.131026	−	0.226944i
$155$	−0.248586	+	1.40980i	−0.0199669	+	0.113238i
$156$		0			0
$157$	19.4985	+	7.09686i	1.55615	+	0.566391i	0.969850	−	0.243704i	$-0.0783626\pi$
$157$	19.4985	+	7.09686i	1.55615	+	0.566391i	0.586298	+	0.810096i	$0.300585\pi$
$158$	−0.874566	−	4.95991i	−0.0695767	−	0.394589i
$159$		0			0
$160$	−6.12343	−	5.13816i	−0.484099	−	0.406208i
$161$	−2.07069			−0.163193
$162$		0			0
$163$	−20.1346			−1.57706			−0.788531	−	0.614995i	$-0.789158\pi$
$163$	−20.1346			−1.57706			−0.788531	+	0.614995i	$0.789158\pi$
$164$	−5.54842	−	4.65568i	−0.433259	−	0.363548i
$165$		0			0
$166$	1.47210	+	8.34868i	0.114257	+	0.647983i
$167$	−18.6647	−	6.79341i	−1.44432	−	0.525690i	−0.503322	−	0.864099i	$-0.667889\pi$
$167$	−18.6647	−	6.79341i	−1.44432	−	0.525690i	−0.940999	+	0.338409i	$0.890111\pi$
$168$		0			0
$169$	1.33599	−	7.57678i	0.102769	−	0.582830i
$170$	6.11748	−	10.5958i	0.469189	−	0.812660i
$171$		0			0
$172$	1.92212	+	3.32920i	0.146560	+	0.253849i
$173$	17.7838	−	6.47277i	1.35208	−	0.492116i	0.438481	−	0.898740i	$-0.355517\pi$
$173$	17.7838	−	6.47277i	1.35208	−	0.492116i	0.913595	+	0.406625i	$0.133294\pi$
$174$		0			0
$175$	−3.67779	+	3.08603i	−0.278015	+	0.233282i
$176$	−1.37771	+	1.15604i	−0.103849	+	0.0871397i
$177$		0			0
$178$	−6.64170	+	2.41738i	−0.497817	+	0.181190i
$179$	5.45683	+	9.45151i	0.407863	+	0.706439i	0.994650	−	0.103302i	$-0.0329409\pi$
$179$	5.45683	+	9.45151i	0.407863	+	0.706439i	−0.586787	+	0.809741i	$0.699608\pi$
$180$		0			0
$181$	8.97393	−	15.5433i	0.667027	−	1.15532i	−0.311704	−	0.950179i	$-0.600900\pi$
$181$	8.97393	−	15.5433i	0.667027	−	1.15532i	0.978731	−	0.205146i	$-0.0657668\pi$
$182$	2.04817	−	11.6157i	0.151820	−	0.861016i
$183$		0			0
$184$	2.40952	+	0.876993i	0.177632	+	0.0646528i
$185$	0.790641	+	4.48395i	0.0581291	+	0.329666i
$186$		0			0
$187$	6.38649	+	5.35890i	0.467026	+	0.391881i
$188$	−4.71059			−0.343555
$189$		0			0
$190$	−0.458604			−0.0332706
$191$	20.6572	+	17.3334i	1.49470	+	1.25420i	0.888485	+	0.458905i	$0.151758\pi$
$191$	20.6572	+	17.3334i	1.49470	+	1.25420i	0.606217	+	0.795299i	$0.292686\pi$
$192$		0			0
$193$	−2.97890	−	16.8942i	−0.214426	−	1.21607i	−0.881900	−	0.471437i	$-0.843735\pi$
$193$	−2.97890	−	16.8942i	−0.214426	−	1.21607i	0.667474	−	0.744633i	$-0.267376\pi$
$194$	5.43974	+	1.97990i	0.390551	+	0.142149i
$195$		0			0
$196$	0.146880	−	0.833000i	0.0104915	−	0.0595000i
$197$	1.25612	−	2.17567i	0.0894951	−	0.155010i	−0.817803	−	0.575499i	$-0.804808\pi$
$197$	1.25612	−	2.17567i	0.0894951	−	0.155010i	0.907298	+	0.420489i	$0.138141\pi$
$198$		0			0
$199$	−9.26942	−	16.0551i	−0.657092	−	1.13812i	−0.981365	−	0.192153i	$-0.938453\pi$
$199$	−9.26942	−	16.0551i	−0.657092	−	1.13812i	0.324273	−	0.945964i	$-0.394880\pi$
$200$	5.58660	−	2.03336i	0.395033	−	0.143780i
$201$		0			0
$202$	4.04271	−	3.39224i	0.284444	−	0.238677i
$203$	0.965274	−	0.809961i	0.0677490	−	0.0568481i
$204$		0			0
$205$	−13.3747	+	4.86800i	−0.934131	+	0.339996i
$206$	6.12519	+	10.6091i	0.426762	+	0.739173i
$207$		0			0
$208$	−3.26154	+	5.64915i	−0.226147	+	0.391698i
$209$	0.0542642	−	0.307747i	0.00375353	−	0.0212873i
$210$		0			0
$211$	3.46857	+	1.26246i	0.238787	+	0.0869112i	0.458642	−	0.888621i	$-0.348336\pi$
$211$	3.46857	+	1.26246i	0.238787	+	0.0869112i	−0.219855	+	0.975533i	$0.570558\pi$
$212$	−1.61737	−	9.17258i	−0.111082	−	0.629975i
$213$		0			0
$214$	15.7155	+	13.1869i	1.07429	+	0.901438i
$215$	7.55427			0.515197
$216$		0			0
$217$	−2.01659			−0.136895
$218$	−5.10049	−	4.27982i	−0.345449	−	0.289866i
$219$		0			0
$220$	−0.337785	−	1.91568i	−0.0227735	−	0.129155i
$221$	28.4146	+	10.3421i	1.91137	+	0.695682i
$222$		0			0
$223$	−3.68847	+	20.9183i	−0.246998	+	1.40080i	0.568808	+	0.822470i	$0.307405\pi$
$223$	−3.68847	+	20.9183i	−0.246998	+	1.40080i	−0.815806	+	0.578326i	$0.803706\pi$
$224$	5.63017	−	9.75174i	0.376181	−	0.651565i
$225$		0			0
$226$	3.64571	+	6.31456i	0.242509	+	0.420038i
$227$	−13.4752	+	4.90459i	−0.894383	+	0.325529i	−0.748000	−	0.663699i	$-0.768986\pi$
$227$	−13.4752	+	4.90459i	−0.894383	+	0.325529i	−0.146383	+	0.989228i	$0.546763\pi$
$228$		0			0
$229$	12.9353	−	10.8540i	0.854787	−	0.717252i	−0.106051	−	0.994361i	$-0.533821\pi$
$229$	12.9353	−	10.8540i	0.854787	−	0.717252i	0.960839	+	0.277109i	$0.0893763\pi$
$230$	1.18722	−	0.996198i	0.0782832	−	0.0656874i
$231$		0			0
$232$	−1.46626	+	0.533676i	−0.0962650	+	0.0350376i
$233$	2.79972	+	4.84926i	0.183416	+	0.317686i	0.943042	−	0.332675i	$-0.107951\pi$
$233$	2.79972	+	4.84926i	0.183416	+	0.317686i	−0.759626	+	0.650361i	$0.774618\pi$
$234$		0			0
$235$	−4.62837	+	8.01658i	−0.301922	+	0.522944i
$236$	−0.463764	+	2.63013i	−0.0301884	+	0.171207i
$237$		0			0
$238$	16.1957	+	5.89474i	1.04981	+	0.382100i
$239$	0.915868	+	5.19415i	0.0592426	+	0.335981i	0.999995	−	0.00311238i	$-0.000990704\pi$
$239$	0.915868	+	5.19415i	0.0592426	+	0.335981i	−0.940753	+	0.339094i	$0.889880\pi$
$240$		0			0
$241$	−6.81969	−	5.72240i	−0.439295	−	0.368612i	0.396150	−	0.918186i	$-0.370346\pi$
$241$	−6.81969	−	5.72240i	−0.439295	−	0.368612i	−0.835446	+	0.549573i	$0.814790\pi$
$242$	9.93907			0.638907
$243$		0			0
$244$	−2.56141			−0.163977
$245$	−1.27330	−	1.06843i	−0.0813481	−	0.0682592i
$246$		0			0
$247$	−0.196816	−	1.11620i	−0.0125231	−	0.0710221i
$248$	2.34657	+	0.854081i	0.149007	+	0.0542342i
$249$		0			0
$250$	2.22208	−	12.6020i	0.140537	−	0.797024i
$251$	−3.89010	+	6.73786i	−0.245541	+	0.425290i	−0.962284	−	0.272048i	$-0.912299\pi$
$251$	−3.89010	+	6.73786i	−0.245541	+	0.425290i	0.716742	+	0.697338i	$0.245632\pi$
$252$		0			0
$253$	0.528024	+	0.914565i	0.0331966	+	0.0574982i
$254$	11.9119	−	4.33559i	0.747421	−	0.272039i
$255$		0			0
$256$	−12.6333	+	10.6006i	−0.789583	+	0.662538i
$257$	15.6553	−	13.1364i	0.976551	−	0.819424i	−0.00701430	−	0.999975i	$-0.502233\pi$
$257$	15.6553	−	13.1364i	0.976551	−	0.819424i	0.983566	+	0.180552i	$0.0577883\pi$
$258$		0			0
$259$	−6.02706	+	2.19367i	−0.374503	+	0.136308i
$260$	−3.52767	−	6.11011i	−0.218777	−	0.378933i
$261$		0			0
$262$	7.42498	−	12.8604i	0.458717	−	0.794520i
$263$	−1.95872	+	11.1084i	−0.120780	+	0.684976i	0.862946	+	0.505297i	$0.168617\pi$
$263$	−1.95872	+	11.1084i	−0.120780	+	0.684976i	−0.983725	+	0.179679i	$0.942494\pi$
$264$		0			0
$265$	−17.1992	−	6.26001i	−1.05654	−	0.384549i
$266$	−0.112181	−	0.636209i	−0.00687824	−	0.0390085i
$267$		0			0
$268$	−6.86424	−	5.75978i	−0.419300	−	0.351835i
$269$	0.307761			0.0187645			0.00938226	−	0.999956i	$-0.497013\pi$
$269$	0.307761			0.0187645			0.00938226	+	0.999956i	$0.497013\pi$
$270$		0			0
$271$	−2.22251			−0.135008			−0.0675040	−	0.997719i	$-0.521504\pi$
$271$	−2.22251			−0.135008			−0.0675040	+	0.997719i	$0.521504\pi$
$272$	−7.30171	−	6.12686i	−0.442731	−	0.371495i
$273$		0			0
$274$	0.413424	+	2.34464i	0.0249759	+	0.141645i
$275$	2.30085	+	0.837439i	0.138746	+	0.0504995i
$276$		0			0
$277$	−4.05116	+	22.9753i	−0.243411	+	1.38045i	0.580744	+	0.814087i	$0.302762\pi$
$277$	−4.05116	+	22.9753i	−0.243411	+	1.38045i	−0.824154	+	0.566365i	$0.808349\pi$
$278$	−4.20417	+	7.28184i	−0.252149	+	0.436735i
$279$		0			0
$280$	−6.53725	−	11.3228i	−0.390675	−	0.676670i
$281$	6.78971	−	2.47125i	0.405040	−	0.147422i	−0.131463	−	0.991321i	$-0.541967\pi$
$281$	6.78971	−	2.47125i	0.405040	−	0.147422i	0.536503	+	0.843899i	$0.319745\pi$
$282$		0			0
$283$	5.45446	−	4.57683i	0.324234	−	0.272065i	−0.466112	−	0.884726i	$-0.654345\pi$
$283$	5.45446	−	4.57683i	0.324234	−	0.272065i	0.790346	+	0.612661i	$0.209901\pi$
$284$	0.0608929	−	0.0510952i	0.00361333	−	0.00303194i
$285$		0			0
$286$	−5.65263	+	2.05739i	−0.334247	+	0.121656i
$287$	−10.0249	−	17.3636i	−0.591751	−	1.02494i
$288$		0			0
$289$	−13.5924	+	23.5428i	−0.799555	+	1.38487i
$290$	−0.163769	+	0.928778i	−0.00961682	+	0.0545397i
$291$		0			0
$292$	−4.44220	−	1.61683i	−0.259960	−	0.0946178i
$293$	−0.0959380	−	0.544092i	−0.00560476	−	0.0317862i	0.981877	−	0.189519i	$-0.0606927\pi$
$293$	−0.0959380	−	0.544092i	−0.00560476	−	0.0317862i	−0.987482	+	0.157732i	$0.949582\pi$
$294$		0			0
$295$	4.02035	+	3.37347i	0.234074	+	0.196411i
$296$	7.94236			0.461640
$297$		0			0
$298$	−0.112748			−0.00653131
$299$	2.93417	+	2.46206i	0.169687	+	0.142385i
$300$		0			0
$301$	1.84788	+	10.4798i	0.106510	+	0.604048i
$302$	−20.0718	−	7.30555i	−1.15500	−	0.420387i
$303$		0			0
$304$	−0.0620405	+	0.351849i	−0.00355827	+	0.0201799i
$305$	−2.51670	+	4.35906i	−0.144106	+	0.249599i
$306$		0			0
$307$	−3.36438	−	5.82728i	−0.192015	−	0.332580i	0.753903	−	0.656986i	$-0.228169\pi$
$307$	−3.36438	−	5.82728i	−0.192015	−	0.332580i	−0.945918	+	0.324406i	$0.894836\pi$
$308$	2.57494	−	0.937202i	0.146721	−	0.0534020i
$309$		0			0
$310$	1.15621	−	0.970173i	0.0656681	−	0.0551021i
$311$	−11.8151	+	9.91400i	−0.669970	+	0.562172i	−0.913057	−	0.407833i	$-0.866285\pi$
$311$	−11.8151	+	9.91400i	−0.669970	+	0.562172i	0.243087	+	0.970005i	$0.421840\pi$
$312$		0			0
$313$	22.1400	−	8.05829i	1.25143	−	0.455482i	0.370542	−	0.928816i	$-0.379172\pi$
$313$	22.1400	−	8.05829i	1.25143	−	0.455482i	0.880883	+	0.473334i	$0.156950\pi$
$314$	−10.9385	−	18.9461i	−0.617297	−	1.06919i
$315$		0			0
$316$	2.12191	−	3.67525i	0.119367	−	0.206749i
$317$	−1.25930	+	7.14187i	−0.0707296	+	0.401127i	0.928804	+	0.370573i	$0.120839\pi$
$317$	−1.25930	+	7.14187i	−0.0707296	+	0.401127i	−0.999533	+	0.0305547i	$0.990273\pi$
$318$		0			0
$319$	−0.603882	−	0.219795i	−0.0338109	−	0.0123062i
$320$	2.33289	+	13.2305i	0.130412	+	0.739605i
$321$		0			0
$322$	1.67241	+	1.40332i	0.0931998	+	0.0782039i
$323$	1.65618			0.0921525
$324$		0			0
$325$	8.88074			0.492615
$326$	16.2619	+	13.6453i	0.900663	+	0.755746i
$327$		0			0
$328$	4.31131	+	24.4507i	0.238052	+	1.35006i
$329$	−12.2534	−	4.45986i	−0.675549	−	0.245880i
$330$		0			0
$331$	5.04178	−	28.5934i	0.277121	−	1.57163i	−0.455020	−	0.890481i	$-0.650368\pi$
$331$	5.04178	−	28.5934i	0.277121	−	1.57163i	0.732142	−	0.681152i	$-0.238521\pi$
$332$	−3.57166	+	6.18629i	−0.196020	+	0.339517i
$333$		0			0
$334$	10.4708	+	18.1360i	0.572938	+	0.992357i
$335$	−16.5465	+	6.02245i	−0.904035	+	0.329042i
$336$		0			0
$337$	−0.887919	+	0.745052i	−0.0483680	+	0.0405856i	−0.666651	−	0.745370i	$-0.732273\pi$
$337$	−0.887919	+	0.745052i	−0.0483680	+	0.0405856i	0.618283	+	0.785955i	$0.287828\pi$
$338$	−6.21387	+	5.21405i	−0.337990	+	0.283607i
$339$		0			0
$340$	9.68773	−	3.52604i	0.525391	−	0.191227i
$341$	0.514230	+	0.890672i	0.0278471	+	0.0482326i
$342$		0			0
$343$	9.77810	−	16.9362i	0.527968	−	0.914467i
$344$	2.28825	−	12.9773i	0.123374	−	0.699689i
$345$		0			0
$346$	−18.7499	−	6.82440i	−1.00800	−	0.366882i
$347$	−1.02274	−	5.80023i	−0.0549034	−	0.311373i	0.944972	−	0.327151i	$-0.106089\pi$
$347$	−1.02274	−	5.80023i	−0.0549034	−	0.311373i	−0.999876	+	0.0157782i	$0.994977\pi$
$348$		0			0
$349$	−23.4354	−	19.6646i	−1.25447	−	1.05262i	−0.996249	−	0.0865352i	$-0.972420\pi$
$349$	−23.4354	−	19.6646i	−1.25447	−	1.05262i	−0.258217	−	0.966087i	$-0.583135\pi$
$350$	5.06182			0.270566
$351$		0			0
$352$	−5.74276			−0.306090
$353$	−28.3140	−	23.7582i	−1.50700	−	1.26452i	−0.869348	−	0.494200i	$-0.835461\pi$
$353$	−28.3140	−	23.7582i	−1.50700	−	1.26452i	−0.637653	−	0.770324i	$-0.720094\pi$
$354$		0			0
$355$	−0.0271248	−	0.153832i	−0.00143963	−	0.00816457i
$356$	−5.59646	−	2.03694i	−0.296612	−	0.107958i
$357$		0			0
$358$	1.99809	−	11.3317i	0.105602	−	0.598901i
$359$	−13.1880	+	22.8423i	−0.696037	+	1.20557i	0.273792	+	0.961789i	$0.411722\pi$
$359$	−13.1880	+	22.8423i	−0.696037	+	1.20557i	−0.969830	+	0.243783i	$0.921611\pi$
$360$		0			0
$361$	9.46896	+	16.4007i	0.498366	+	0.863196i
$362$	−17.7817	+	6.47201i	−0.934585	+	0.340161i
$363$		0			0
$364$	7.61347	−	6.38846i	0.399055	−	0.334846i
$365$	−7.11623	+	5.97122i	−0.372480	+	0.312548i
$366$		0			0
$367$	10.6309	−	3.86932i	0.554927	−	0.201977i	−0.0493074	−	0.998784i	$-0.515701\pi$
$367$	10.6309	−	3.86932i	0.554927	−	0.201977i	0.604234	+	0.796807i	$0.293479\pi$
$368$	−0.603693	−	1.04563i	−0.0314697	−	0.0545071i
$369$		0			0
$370$	2.40023	−	4.15733i	0.124782	−	0.216129i
$371$	4.47717	−	25.3913i	0.232443	−	1.31825i
$372$		0			0
$373$	−5.49164	−	1.99879i	−0.284346	−	0.103494i	0.195910	−	0.980622i	$-0.437234\pi$
$373$	−5.49164	−	1.99879i	−0.284346	−	0.103494i	−0.480256	+	0.877128i	$0.659456\pi$
$374$	−1.52634	−	8.65633i	−0.0789254	−	0.447608i
$375$		0			0
$376$	12.3695	+	10.3793i	0.637909	+	0.535269i
$377$	−2.33085			−0.120045
$378$		0			0
$379$	24.3265			1.24957			0.624783	−	0.780798i	$-0.285187\pi$
$379$	24.3265			1.24957			0.624783	+	0.780798i	$0.285187\pi$
$380$	−0.296023	−	0.248393i	−0.0151856	−	0.0127423i
$381$		0			0
$382$	−4.93699	−	27.9991i	−0.252598	−	1.43256i
$383$	−3.58591	−	1.30517i	−0.183232	−	0.0666909i	0.248775	−	0.968561i	$-0.419972\pi$
$383$	−3.58591	−	1.30517i	−0.183232	−	0.0666909i	−0.432007	+	0.901870i	$0.642194\pi$
$384$		0			0
$385$	0.935050	−	5.30293i	0.0476546	−	0.270262i
$386$	−9.04337	+	15.6636i	−0.460295	+	0.797255i
$387$		0			0
$388$	2.43891	+	4.22432i	0.123817	+	0.214457i
$389$	10.1880	−	3.70813i	0.516552	−	0.188010i	−0.0705716	−	0.997507i	$-0.522482\pi$
$389$	10.1880	−	3.70813i	0.516552	−	0.188010i	0.587124	+	0.809497i	$0.300260\pi$
$390$		0			0
$391$	−4.28749	+	3.59763i	−0.216828	+	0.181940i
$392$	−2.22111	+	1.86374i	−0.112183	+	0.0941329i
$393$		0			0
$394$	−2.48899	+	0.905917i	−0.125393	+	0.0456394i
$395$	−4.16974	−	7.22221i	−0.209802	−	0.363389i
$396$		0			0
$397$	5.25461	−	9.10124i	0.263721	−	0.456778i	−0.703507	−	0.710689i	$-0.748383\pi$
$397$	5.25461	−	9.10124i	0.263721	−	0.456778i	0.967228	+	0.253910i	$0.0817168\pi$
$398$	−3.39412	+	19.2490i	−0.170132	+	0.964866i
$399$		0			0
$400$	−2.63057	−	0.957449i	−0.131529	−	0.0478725i
$401$	−2.49456	−	14.1473i	−0.124572	−	0.706484i	−0.981561	−	0.191149i	$-0.938779\pi$
$401$	−2.49456	−	14.1473i	−0.124572	−	0.706484i	0.856989	−	0.515335i	$-0.172332\pi$
$402$		0			0
$403$	2.85751	+	2.39774i	0.142343	+	0.119440i
$404$	4.44685			0.221239
$405$		0			0
$406$	−1.32853			−0.0659338
$407$	2.50578	+	2.10260i	0.124207	+	0.104222i
$408$		0			0
$409$	3.07049	+	17.4136i	0.151826	+	0.861048i	0.961630	+	0.274348i	$0.0884621\pi$
$409$	3.07049	+	17.4136i	0.151826	+	0.861048i	−0.809804	+	0.586700i	$0.800427\pi$
$410$	14.1013	+	5.13245i	0.696413	+	0.253474i
$411$		0			0
$412$	−1.79248	+	10.1656i	−0.0883089	+	0.500825i
$413$	−3.69650	+	6.40252i	−0.181893	+	0.315047i
$414$		0			0
$415$	7.01864	+	12.1566i	0.344532	+	0.596746i
$416$	−19.5728	+	7.12393i	−0.959637	+	0.349279i
$417$		0			0
$418$	−0.252390	+	0.211780i	−0.0123448	+	0.0103585i
$419$	−6.99687	+	5.87107i	−0.341819	+	0.286821i	−0.797495	−	0.603325i	$-0.793842\pi$
$419$	−6.99687	+	5.87107i	−0.341819	+	0.286821i	0.455676	+	0.890146i	$0.349398\pi$
$420$		0			0
$421$	−22.7358	+	8.27515i	−1.10807	+	0.403306i	−0.830287	−	0.557337i	$-0.811823\pi$
$421$	−22.7358	+	8.27515i	−1.10807	+	0.403306i	−0.277787	+	0.960643i	$0.589601\pi$
$422$	−1.94585	−	3.37031i	−0.0947226	−	0.164064i
$423$		0			0
$424$	−15.9637	+	27.6499i	−0.775265	+	1.34280i
$425$	−2.25340	+	12.7796i	−0.109306	+	0.619904i
$426$		0			0
$427$	−6.66283	−	2.42507i	−0.322437	−	0.117357i
$428$	3.00178	+	17.0240i	0.145097	+	0.822884i
$429$		0			0
$430$	−6.10128	−	5.11958i	−0.294230	−	0.246888i
$431$	29.5332			1.42256			0.711282	−	0.702907i	$-0.248115\pi$
$431$	29.5332			1.42256			0.711282	+	0.702907i	$0.248115\pi$
$432$		0			0
$433$	0.669754			0.0321863			0.0160932	−	0.999870i	$-0.494877\pi$
$433$	0.669754			0.0321863			0.0160932	+	0.999870i	$0.494877\pi$
$434$	1.62872	+	1.36666i	0.0781810	+	0.0656017i
$435$		0			0
$436$	−0.974231	−	5.52514i	−0.0466572	−	0.264606i
$437$	0.197138	+	0.0717523i	0.00943038	+	0.00343238i
$438$		0			0
$439$	−1.10247	+	6.25242i	−0.0526180	+	0.298412i	−0.999748	−	0.0224379i	$-0.992857\pi$
$439$	−1.10247	+	6.25242i	−0.0526180	+	0.298412i	0.947130	+	0.320849i	$0.103968\pi$
$440$	−3.33399	+	5.77464i	−0.158942	+	0.275295i
$441$		0			0
$442$	−15.9404	−	27.6096i	−0.758209	−	1.31326i
$443$	14.4280	−	5.25135i	0.685494	−	0.249499i	0.0242891	−	0.999705i	$-0.492268\pi$
$443$	14.4280	−	5.25135i	0.685494	−	0.249499i	0.661204	+	0.750206i	$0.270046\pi$
$444$		0			0
$445$	−8.96529	+	7.52277i	−0.424996	+	0.356614i
$446$	17.1555	−	14.3952i	0.812338	−	0.681633i
$447$		0			0
$448$	−17.7836	+	6.47270i	−0.840196	+	0.305806i
$449$	−16.0199	−	27.7473i	−0.756027	−	1.30948i	−0.944862	−	0.327468i	$-0.893805\pi$
$449$	−16.0199	−	27.7473i	−0.756027	−	1.30948i	0.188836	−	0.982009i	$-0.439529\pi$
$450$		0			0
$451$	−5.11268	+	8.85543i	−0.240747	+	0.416986i
$452$	−1.06688	+	6.05058i	−0.0501819	+	0.284596i
$453$		0			0
$454$	14.2073	+	5.17103i	0.666781	+	0.242688i
$455$	−3.39143	−	19.2337i	−0.158992	−	0.901691i
$456$		0			0
$457$	14.6836	+	12.3210i	0.686868	+	0.576351i	0.918004	−	0.396570i	$-0.129800\pi$
$457$	14.6836	+	12.3210i	0.686868	+	0.576351i	−0.231136	+	0.972921i	$0.574244\pi$
$458$	−17.8031			−0.831886
$459$		0			0
$460$	1.30591			0.0608882
$461$	3.99898	+	3.35554i	0.186251	+	0.156283i	0.731146	−	0.682221i	$-0.238986\pi$
$461$	3.99898	+	3.35554i	0.186251	+	0.156283i	−0.544895	+	0.838504i	$0.683430\pi$
$462$		0			0
$463$	0.294749	+	1.67160i	0.0136981	+	0.0776859i	0.990890	−	0.134670i	$-0.0429975\pi$
$463$	0.294749	+	1.67160i	0.0136981	+	0.0776859i	−0.977192	+	0.212356i	$0.931886\pi$
$464$	0.690421	+	0.251293i	0.0320520	+	0.0116660i
$465$		0			0
$466$	1.02516	−	5.81395i	0.0474894	−	0.269326i
$467$	9.84136	−	17.0457i	0.455404	−	0.788783i	−0.543307	−	0.839534i	$-0.682828\pi$
$467$	9.84136	−	17.0457i	0.455404	−	0.788783i	0.998711	+	0.0507511i	$0.0161615\pi$
$468$		0			0
$469$	−12.4023	−	21.4814i	−0.572685	−	0.991920i
$470$	9.17104	−	3.33799i	0.423029	−	0.153970i
$471$		0			0
$472$	7.01300	−	5.88461i	0.322800	−	0.270861i
$473$	4.15745	−	3.48851i	0.191160	−	0.160402i
$474$		0			0
$475$	0.457076	−	0.166362i	0.0209721	−	0.00763321i
$476$	7.26134	+	12.5770i	0.332823	+	0.576467i
$477$		0			0
$478$	2.78040	−	4.81579i	0.127173	−	0.220269i
$479$	5.07980	−	28.8090i	0.232102	−	1.31632i	−0.616529	−	0.787332i	$-0.711462\pi$
$479$	5.07980	−	28.8090i	0.232102	−	1.31632i	0.848631	−	0.528985i	$-0.177427\pi$
$480$		0			0
$481$	11.1487	+	4.05778i	0.508335	+	0.185019i
$482$	1.62988	+	9.24351i	0.0742390	+	0.421030i
$483$		0			0
$484$	6.41554	+	5.38328i	0.291616	+	0.244694i
$485$	9.58538			0.435250
$486$		0			0
$487$	−20.5056			−0.929199			−0.464600	−	0.885521i	$-0.653802\pi$
$487$	−20.5056			−0.929199			−0.464600	+	0.885521i	$0.653802\pi$
$488$	6.72599	+	5.64378i	0.304471	+	0.255482i
$489$		0			0
$490$	0.304314	+	1.72585i	0.0137475	+	0.0779659i
$491$	16.4700	+	5.99458i	0.743280	+	0.270532i	0.685775	−	0.727813i	$-0.259463\pi$
$491$	16.4700	+	5.99458i	0.743280	+	0.270532i	0.0575048	+	0.998345i	$0.481686\pi$
$492$		0			0
$493$	0.591428	−	3.35415i	0.0266366	−	0.151063i
$494$	−0.597496	+	1.03489i	−0.0268826	+	0.0465620i
$495$		0			0
$496$	−0.587922	−	1.01831i	−0.0263985	−	0.0457235i
$497$	0.206772	−	0.0752590i	0.00927501	−	0.00337583i
$498$		0			0
$499$	−14.6360	+	12.2811i	−0.655199	+	0.549777i	−0.908643	−	0.417573i	$-0.862881\pi$
$499$	−14.6360	+	12.2811i	−0.655199	+	0.549777i	0.253445	+	0.967350i	$0.418436\pi$
$500$	8.25995	−	6.93092i	0.369396	−	0.309960i
$501$		0			0
$502$	7.70817	−	2.80555i	0.344033	−	0.125218i
$503$	−5.48381	−	9.49824i	−0.244511	−	0.423506i	0.717483	−	0.696576i	$-0.245294\pi$
$503$	−5.48381	−	9.49824i	−0.244511	−	0.423506i	−0.961994	+	0.273070i	$0.911961\pi$
$504$		0			0
$505$	4.36924	−	7.56774i	0.194429	−	0.336760i
$506$	0.193343	−	1.09650i	0.00859515	−	0.0487455i
$507$		0			0
$508$	10.0373	+	3.65327i	0.445332	+	0.162088i
$509$	3.45549	+	19.5970i	0.153162	+	0.868624i	0.960447	+	0.278462i	$0.0898247\pi$
$509$	3.45549	+	19.5970i	0.153162	+	0.868624i	−0.807285	+	0.590161i	$0.799064\pi$
$510$		0			0
$511$	−10.0245	−	8.41151i	−0.443456	−	0.372103i
$512$	15.2994			0.676143
$513$		0			0
$514$	−21.5468			−0.950387
$515$	15.5389	+	13.0387i	0.684725	+	0.574553i
$516$		0			0
$517$	1.15480	+	6.54922i	0.0507883	+	0.288035i
$518$	6.35448	+	2.31284i	0.279200	+	0.101620i
$519$		0			0
$520$	−4.19964	+	23.8173i	−0.184166	+	1.04446i
$521$	17.5583	−	30.4119i	0.769244	−	1.33237i	−0.168729	−	0.985662i	$-0.553966\pi$
$521$	17.5583	−	30.4119i	0.769244	−	1.33237i	0.937973	−	0.346708i	$-0.112700\pi$
$522$		0			0
$523$	7.12269	+	12.3369i	0.311453	+	0.539453i	0.978677	−	0.205404i	$-0.0658509\pi$
$523$	7.12269	+	12.3369i	0.311453	+	0.539453i	−0.667224	+	0.744857i	$0.732518\pi$
$524$	11.7583	−	4.27967i	0.513664	−	0.186958i
$525$		0			0
$526$	9.11025	−	7.64441i	0.397226	−	0.333312i
$527$	−4.17548	+	3.50364i	−0.181887	+	0.152621i
$528$		0			0
$529$	20.9467	−	7.62398i	0.910727	−	0.331478i
$530$	9.64867	+	16.7120i	0.419111	+	0.725922i
$531$		0			0
$532$	0.272177	−	0.471425i	0.0118004	−	0.0204389i
$533$	−6.44016	+	36.5240i	−0.278954	+	1.58203i
$534$		0			0
$535$	31.9211	+	11.6183i	1.38007	+	0.502304i
$536$	5.33374	+	30.2492i	0.230383	+	1.30657i
$537$		0			0
$538$	−0.248566	−	0.208572i	−0.0107164	−	0.00899217i
$539$	−1.19414			−0.0514354
$540$		0			0
$541$	−13.2368			−0.569094			−0.284547	−	0.958662i	$-0.591843\pi$
$541$	−13.2368			−0.569094			−0.284547	+	0.958662i	$0.591843\pi$
$542$	1.79503	+	1.50621i	0.0771033	+	0.0646974i
$543$		0			0
$544$	−5.28514	−	29.9735i	−0.226598	−	1.28510i
$545$	−10.3600	−	3.77074i	−0.443775	−	0.161521i
$546$		0			0
$547$	−2.83132	+	16.0572i	−0.121058	+	0.686557i	0.862513	+	0.506035i	$0.168890\pi$
$547$	−2.83132	+	16.0572i	−0.121058	+	0.686557i	−0.983571	+	0.180521i	$0.942222\pi$
$548$	−1.00306	+	1.73736i	−0.0428488	+	0.0742163i
$549$		0			0
$550$	−1.29076	−	2.23567i	−0.0550383	−	0.0953291i
$551$	−0.119964	+	0.0436635i	−0.00511065	+	0.00186013i
$552$		0			0
$553$	8.99920	−	7.55123i	0.382685	−	0.321111i
$554$	18.8425	−	15.8107i	0.800540	−	0.671733i
$555$		0			0
$556$	−6.65778	+	2.42324i	−0.282353	+	0.102768i
$557$	15.4486	+	26.7577i	0.654577	+	1.13376i	0.982000	+	0.188883i	$0.0604867\pi$
$557$	15.4486	+	26.7577i	0.654577	+	1.13376i	−0.327422	+	0.944878i	$0.606180\pi$
$558$		0			0
$559$	9.84215	−	17.0471i	0.416279	−	0.721016i
$560$	−1.06905	+	6.06287i	−0.0451755	+	0.256203i
$561$		0			0
$562$	−7.15856	−	2.60550i	−0.301965	−	0.109906i
$563$	−4.64959	−	26.3692i	−0.195957	−	1.11133i	−0.911049	−	0.412298i	$-0.864726\pi$
$563$	−4.64959	−	26.3692i	−0.195957	−	1.11133i	0.715092	−	0.699030i	$-0.246385\pi$
$564$		0			0
$565$	9.24875	+	7.76062i	0.389098	+	0.326492i
$566$	−7.50710			−0.315547
$567$		0			0
$568$	−0.272481			−0.0114331
$569$	−14.6013	−	12.2519i	−0.612118	−	0.513628i	0.283197	−	0.959062i	$-0.408605\pi$
$569$	−14.6013	−	12.2519i	−0.612118	−	0.513628i	−0.895315	+	0.445434i	$0.853050\pi$
$570$		0			0
$571$	−3.26011	−	18.4890i	−0.136431	−	0.773740i	−0.973852	−	0.227182i	$-0.927049\pi$
$571$	−3.26011	−	18.4890i	−0.136431	−	0.773740i	0.837421	−	0.546558i	$-0.184062\pi$
$572$	−4.76304	−	1.73360i	−0.199153	−	0.0724856i
$573$		0			0
$574$	−3.67075	+	20.8178i	−0.153214	+	0.868920i
$575$	−0.821889	+	1.42355i	−0.0342751	+	0.0593663i
$576$		0			0
$577$	2.42981	+	4.20856i	0.101154	+	0.175204i	0.912161	−	0.409833i	$-0.134413\pi$
$577$	2.42981	+	4.20856i	0.101154	+	0.175204i	−0.811006	+	0.585038i	$0.801080\pi$
$578$	26.9332	−	9.80287i	1.12027	−	0.407746i
$579$		0			0
$580$	−0.608763	+	0.510813i	−0.0252775	+	0.0212103i
$581$	−15.1477	+	12.7105i	−0.628434	+	0.527319i
$582$		0			0
$583$	−12.3563	+	4.49733i	−0.511746	+	0.186260i
$584$	8.10226	+	14.0335i	0.335274	+	0.580712i
$585$		0			0
$586$	−0.291249	+	0.504459i	−0.0120314	+	0.0208390i
$587$	5.69520	−	32.2991i	0.235066	−	1.33313i	−0.607409	−	0.794390i	$-0.707791\pi$
$587$	5.69520	−	32.2991i	0.235066	−	1.33313i	0.842475	−	0.538736i	$-0.181098\pi$
$588$		0			0
$589$	0.191988	+	0.0698778i	0.00791071	+	0.00287926i
$590$	−0.960847	−	5.44923i	−0.0395574	−	0.224341i
$591$		0			0
$592$	−2.86487	−	2.40391i	−0.117746	−	0.0988003i
$593$	−17.3446			−0.712258			−0.356129	−	0.934437i	$-0.615904\pi$
$593$	−17.3446			−0.712258			−0.356129	+	0.934437i	$0.615904\pi$
$594$		0			0
$595$	28.5384			1.16996
$596$	−0.0727773	−	0.0610674i	−0.00298107	−	0.00250142i
$597$		0			0
$598$	−0.701255	−	3.97702i	−0.0286765	−	0.162632i
$599$	22.9359	+	8.34800i	0.937137	+	0.341090i	0.765035	−	0.643989i	$-0.222722\pi$
$599$	22.9359	+	8.34800i	0.937137	+	0.341090i	0.172102	+	0.985079i	$0.444944\pi$
$600$		0			0
$601$	1.36666	−	7.75070i	0.0557471	−	0.316158i	−0.944164	−	0.329475i	$-0.893128\pi$
$601$	1.36666	−	7.75070i	0.0557471	−	0.316158i	0.999911	+	0.0133177i	$0.00423928\pi$
$602$	5.60981	−	9.71647i	0.228639	−	0.396014i
$603$		0			0
$604$	−8.99922	−	15.5871i	−0.366173	−	0.634230i
$605$	15.4649	−	5.62878i	0.628739	−	0.228842i
$606$		0			0
$607$	−7.84236	+	6.58052i	−0.318311	+	0.267095i	−0.787917	−	0.615781i	$-0.788841\pi$
$607$	−7.84236	+	6.58052i	−0.318311	+	0.267095i	0.469606	+	0.882876i	$0.344396\pi$
$608$	−0.873926	+	0.733311i	−0.0354424	+	0.0297397i
$609$		0			0
$610$	4.98680	−	1.81505i	0.201910	−	0.0734891i
$611$	12.0602	+	20.8889i	0.487905	+	0.845076i
$612$		0			0
$613$	−1.11753	+	1.93563i	−0.0451368	+	0.0781792i	−0.887711	−	0.460401i	$-0.847706\pi$
$613$	−1.11753	+	1.93563i	−0.0451368	+	0.0781792i	0.842574	+	0.538580i	$0.181039\pi$
$614$	−1.23191	+	6.98652i	−0.0497159	+	0.281953i
$615$		0			0
$616$	−8.82655	−	3.21260i	−0.355632	−	0.129439i
$617$	−5.89982	−	33.4595i	−0.237518	−	1.34703i	−0.837246	−	0.546826i	$-0.815836\pi$
$617$	−5.89982	−	33.4595i	−0.237518	−	1.34703i	0.599729	−	0.800203i	$-0.295275\pi$
$618$		0			0
$619$	−22.1050	−	18.5483i	−0.888473	−	0.745518i	0.0794301	−	0.996840i	$-0.474690\pi$
$619$	−22.1050	−	18.5483i	−0.888473	−	0.745518i	−0.967903	+	0.251323i	$0.919134\pi$
$620$	1.27179			0.0510763
$621$		0			0
$622$	16.2613			0.652020
$623$	−12.6292	−	10.5971i	−0.505977	−	0.424565i
$624$		0			0
$625$	−1.98439	−	11.2541i	−0.0793758	−	0.450162i
$626$	−23.3427	−	8.49606i	−0.932963	−	0.339571i
$627$		0			0
$628$	3.20105	−	18.1541i	0.127736	−	0.724427i
$629$	−8.66811	+	15.0136i	−0.345620	+	0.598632i
$630$		0			0
$631$	1.57039	+	2.71999i	0.0625162	+	0.108281i	0.895590	−	0.444881i	$-0.146754\pi$
$631$	1.57039	+	2.71999i	0.0625162	+	0.108281i	−0.833073	+	0.553163i	$0.813421\pi$
$632$	−13.6699	+	4.97544i	−0.543759	+	0.197912i
$633$		0			0
$634$	5.85718	−	4.91476i	0.232618	−	0.195190i
$635$	16.0793	−	13.4921i	0.638087	−	0.535419i
$636$		0			0
$637$	−4.06996	+	1.48134i	−0.161258	+	0.0586930i
$638$	0.338774	+	0.586774i	0.0134122	+	0.0232306i
$639$		0			0
$640$	−0.911374	+	1.57855i	−0.0360252	+	0.0623975i
$641$	5.52593	−	31.3391i	0.218261	−	1.23782i	−0.656896	−	0.753981i	$-0.728131\pi$
$641$	5.52593	−	31.3391i	0.218261	−	1.23782i	0.875157	−	0.483838i	$-0.160758\pi$
$642$		0			0
$643$	12.0723	+	4.39396i	0.476085	+	0.173281i	0.568907	−	0.822402i	$-0.307367\pi$
$643$	12.0723	+	4.39396i	0.476085	+	0.173281i	−0.0928219	+	0.995683i	$0.529589\pi$
$644$	0.319443	+	1.81165i	0.0125878	+	0.0713890i
$645$		0			0
$646$	−1.33763	−	1.12241i	−0.0526285	−	0.0441605i
$647$	−28.2444			−1.11040			−0.555200	−	0.831717i	$-0.687358\pi$
$647$	−28.2444			−1.11040			−0.555200	+	0.831717i	$0.687358\pi$
$648$		0			0
$649$	3.77042			0.148002
$650$	−7.17262	−	6.01854i	−0.281333	−	0.236067i
$651$		0			0
$652$	3.10614	+	17.6158i	0.121646	+	0.689888i
$653$	24.4231	+	8.88927i	0.955749	+	0.347864i	0.772366	−	0.635178i	$-0.219073\pi$
$653$	24.4231	+	8.88927i	0.955749	+	0.347864i	0.183383	+	0.983042i	$0.441295\pi$
$654$		0			0
$655$	4.26984	−	24.2155i	0.166837	−	0.946178i
$656$	5.84536	−	10.1245i	0.228223	−	0.395294i
$657$		0			0
$658$	6.87407	+	11.9062i	0.267979	+	0.464153i
$659$	−44.7461	+	16.2863i	−1.74306	+	0.634422i	−0.999417	−	0.0341533i	$-0.989127\pi$
$659$	−44.7461	+	16.2863i	−1.74306	+	0.634422i	−0.743644	+	0.668576i	$0.766904\pi$
$660$		0			0
$661$	−0.671444	+	0.563408i	−0.0261161	+	0.0219140i	−0.655752	−	0.754976i	$-0.727648\pi$
$661$	−0.671444	+	0.563408i	−0.0261161	+	0.0219140i	0.629636	+	0.776890i	$0.283204\pi$
$662$	−23.4500	+	19.6769i	−0.911409	+	0.764763i
$663$		0			0
$664$	23.0096	−	8.37481i	0.892946	−	0.325006i
$665$	−0.534854	−	0.926394i	−0.0207407	−	0.0359240i
$666$		0			0
$667$	0.215714	−	0.373627i	0.00835246	−	0.0144669i
$668$	−3.06418	+	17.3778i	−0.118557	+	0.672369i
$669$		0			0
$670$	17.4454	+	6.34962i	0.673976	+	0.245307i
$671$	0.627931	+	3.56118i	0.0242410	+	0.137478i
$672$		0			0
$673$	28.6037	+	24.0013i	1.10259	+	0.925183i	0.997597	−	0.0692894i	$-0.0220732\pi$
$673$	28.6037	+	24.0013i	1.10259	+	0.925183i	0.104994	+	0.994473i	$0.466518\pi$
$674$	1.22206			0.0470721
$675$		0			0
$676$	−6.83505			−0.262886
$677$	10.5095	+	8.81851i	0.403913	+	0.338923i	0.822004	−	0.569482i	$-0.192856\pi$
$677$	10.5095	+	8.81851i	0.403913	+	0.338923i	−0.418091	+	0.908405i	$0.637301\pi$
$678$		0			0
$679$	2.34472	+	13.2975i	0.0899820	+	0.510313i
$680$	−33.2082	−	12.0868i	−1.27348	−	0.463508i
$681$		0			0
$682$	0.188292	−	1.06786i	0.00721007	−	0.0408903i
$683$	24.9943	−	43.2914i	0.956381	−	1.65650i	0.225206	−	0.974311i	$-0.427694\pi$
$683$	24.9943	−	43.2914i	0.956381	−	1.65650i	0.731175	−	0.682190i	$-0.238972\pi$
$684$		0			0
$685$	1.97112	+	3.41407i	0.0753125	+	0.130445i
$686$	−19.3751	+	7.05197i	−0.739746	+	0.269245i
$687$		0			0
$688$	−4.75323	+	3.98843i	−0.181215	+	0.152058i
$689$	−36.5346	+	30.6562i	−1.39186	+	1.16791i
$690$		0			0
$691$	−22.3788	+	8.14523i	−0.851331	+	0.309859i	−0.730583	−	0.682824i	$-0.760752\pi$
$691$	−22.3788	+	8.14523i	−0.851331	+	0.309859i	−0.120748	+	0.992683i	$0.538529\pi$
$692$	−8.40653	−	14.5605i	−0.319568	−	0.553508i
$693$		0			0
$694$	−3.10483	+	5.37773i	−0.117858	+	0.204136i
$695$	−2.41767	+	13.7113i	−0.0917075	+	0.520099i
$696$		0			0
$697$	−50.9249	−	18.5351i	−1.92892	−	0.702069i
$698$	5.60096	+	31.7646i	0.211999	+	1.20231i
$699$		0			0
$700$	3.26734	+	2.74163i	0.123494	+	0.103624i
$701$	−34.4493			−1.30113			−0.650565	−	0.759450i	$-0.725468\pi$
$701$	−34.4493			−1.30113			−0.650565	+	0.759450i	$0.725468\pi$
$702$		0			0
$703$	0.649815			0.0245082
$704$	7.39362	+	6.20398i	0.278658	+	0.233821i
$705$		0			0
$706$	6.76693	+	38.3772i	0.254677	+	1.44434i
$707$	11.5673	+	4.21016i	0.435033	+	0.158339i
$708$		0			0
$709$	2.69559	−	15.2874i	0.101235	−	0.574132i	−0.891423	−	0.453173i	$-0.850292\pi$
$709$	2.69559	−	15.2874i	0.101235	−	0.574132i	0.992658	−	0.120959i	$-0.0385969\pi$
$710$	−0.0823456	+	0.142627i	−0.00309038	+	0.00535269i
$711$		0			0
$712$	10.2075	+	17.6800i	0.382543	+	0.662585i
$713$	−0.648805	+	0.236146i	−0.0242979	+	0.00884373i
$714$		0			0
$715$	−7.63019	+	6.40249i	−0.285353	+	0.239439i
$716$	7.42733	−	6.23227i	0.277572	−	0.232911i
$717$		0			0
$718$	26.1318	−	9.51121i	0.975232	−	0.354955i
$719$	6.02686	+	10.4388i	0.224764	+	0.389303i	0.956249	−	0.292555i	$-0.0945056\pi$
$719$	6.02686	+	10.4388i	0.224764	+	0.389303i	−0.731485	+	0.681858i	$0.761172\pi$
$720$		0			0
$721$	−14.2872	+	24.7461i	−0.532083	+	0.921594i
$722$	3.46718	−	19.6634i	0.129035	−	0.731795i
$723$		0			0
$724$	−14.9833	−	5.45347i	−0.556849	−	0.202676i
$725$	−0.173698	−	0.985092i	−0.00645099	−	0.0365854i
$726$		0			0
$727$	−24.2302	−	20.3315i	−0.898647	−	0.754055i	0.0712781	−	0.997456i	$-0.477292\pi$
$727$	−24.2302	−	20.3315i	−0.898647	−	0.754055i	−0.969926	+	0.243402i	$0.921737\pi$
$728$	−34.0685			−1.26266
$729$		0			0
$730$	9.79423			0.362501
$731$	22.0339	+	18.4887i	0.814955	+	0.683828i
$732$		0			0
$733$	−3.30466	−	18.7417i	−0.122060	−	0.692239i	−0.983010	−	0.183550i	$-0.941241\pi$
$733$	−3.30466	−	18.7417i	−0.122060	−	0.692239i	0.860950	−	0.508690i	$-0.169870\pi$
$734$	−11.2084	−	4.07952i	−0.413709	−	0.150578i
$735$		0			0
$736$	0.669471	−	3.79676i	0.0246770	−	0.139950i
$737$	−6.32516	+	10.9555i	−0.232990	+	0.403551i
$738$		0			0
$739$	−8.30036	−	14.3767i	−0.305334	−	0.528854i	0.672002	−	0.740550i	$-0.265435\pi$
$739$	−8.30036	−	14.3767i	−0.305334	−	0.528854i	−0.977336	+	0.211696i	$0.932101\pi$
$740$	3.80105	−	1.38347i	0.139729	−	0.0508573i
$741$		0			0
$742$	−20.8239	+	17.4733i	−0.764470	+	0.641466i
$743$	25.5120	−	21.4071i	0.935944	−	0.785350i	−0.0409308	−	0.999162i	$-0.513032\pi$
$743$	25.5120	−	21.4071i	0.935944	−	0.785350i	0.976875	+	0.213812i	$0.0685879\pi$
$744$		0			0
$745$	−0.175433	+	0.0638523i	−0.00642736	+	0.00233937i
$746$	3.08078	+	5.33606i	0.112795	+	0.195367i
$747$		0			0
$748$	3.70328	−	6.41426i	0.135405	−	0.234529i
$749$	−8.30947	+	47.1253i	−0.303621	+	1.72192i
$750$		0			0
$751$	−26.1062	−	9.50187i	−0.952627	−	0.346728i	−0.181487	−	0.983393i	$-0.558091\pi$
$751$	−26.1062	−	9.50187i	−0.952627	−	0.346728i	−0.771140	+	0.636665i	$0.780313\pi$
$752$	−1.32030	−	7.48777i	−0.0481462	−	0.273051i
$753$		0			0
$754$	1.88253	+	1.57963i	0.0685577	+	0.0575267i
$755$	−35.3686			−1.28720
$756$		0			0
$757$	−3.12036			−0.113411			−0.0567057	−	0.998391i	$-0.518060\pi$
$757$	−3.12036			−0.113411			−0.0567057	+	0.998391i	$0.518060\pi$
$758$	−19.6475	−	16.4862i	−0.713629	−	0.598806i
$759$		0			0
$760$	0.230020	+	1.30451i	0.00834369	+	0.0473194i
$761$	−41.3081	−	15.0349i	−1.49742	−	0.545016i	−0.542028	−	0.840360i	$-0.682343\pi$
$761$	−41.3081	−	15.0349i	−1.49742	−	0.545016i	−0.955391	+	0.295345i	$0.904566\pi$
$762$		0			0
$763$	2.69684	−	15.2946i	0.0976323	−	0.553700i
$764$	11.9783	−	20.7470i	0.433360	−	0.750602i
$765$		0			0
$766$	2.01168	+	3.48433i	0.0726849	+	0.125894i
$767$	12.8506	−	4.67723i	0.464008	−	0.168885i
$768$		0			0
$769$	2.84421	−	2.38658i	0.102565	−	0.0860622i	−0.590063	−	0.807357i	$-0.700897\pi$
$769$	2.84421	−	2.38658i	0.102565	−	0.0860622i	0.692628	+	0.721295i	$0.256453\pi$
$770$	−4.34904	+	3.64927i	−0.156728	+	0.131511i
$771$		0			0
$772$	−14.3212	+	5.21250i	−0.515432	+	0.187602i
$773$	−4.48452	−	7.76741i	−0.161297	−	0.279374i	0.774037	−	0.633140i	$-0.218234\pi$
$773$	−4.48452	−	7.76741i	−0.161297	−	0.279374i	−0.935334	+	0.353766i	$0.884901\pi$
$774$		0			0
$775$	−0.800417	+	1.38636i	−0.0287518	+	0.0497996i
$776$	2.90349	−	16.4665i	0.104229	−	0.591113i
$777$		0			0
$778$	−10.7415	−	3.90957i	−0.385100	−	0.140165i
$779$	0.352736	+	2.00046i	0.0126381	+	0.0716741i
$780$		0			0
$781$	−0.0859667	−	0.0721346i	−0.00307613	−	0.00258118i
$782$	5.90098			0.211018
$783$		0			0
$784$	1.36527			0.0487597
$785$	−27.7498	−	23.2849i	−0.990433	−	0.831072i
$786$		0			0
$787$	7.61472	+	43.1852i	0.271435	+	1.53939i	0.750061	+	0.661368i	$0.230024\pi$
$787$	7.61472	+	43.1852i	0.271435	+	1.53939i	−0.478626	+	0.878019i	$0.658865\pi$
$788$	−2.09728	−	0.763347i	−0.0747125	−	0.0271931i
$789$		0			0
$790$	−1.52681	+	8.65895i	−0.0543213	+	0.308072i
$791$	−8.50374	+	14.7289i	−0.302358	+	0.523699i
$792$		0			0
$793$	6.55782	+	11.3585i	0.232875	+	0.403351i
$794$	−10.4119	+	3.78962i	−0.369505	+	0.134489i
$795$		0			0
$796$	−12.6167	+	10.5866i	−0.447186	+	0.375234i
$797$	−9.20480	+	7.72375i	−0.326051	+	0.273589i	−0.791088	−	0.611702i	$-0.790485\pi$
$797$	−9.20480	+	7.72375i	−0.326051	+	0.273589i	0.465038	+	0.885291i	$0.346041\pi$
$798$		0			0
$799$	−33.1200	+	12.0547i	−1.17170	+	0.426464i
$800$	−4.46940	−	7.74124i	−0.158017	−	0.273694i
$801$		0			0
$802$	−7.57299	+	13.1168i	−0.267412	+	0.463171i
$803$	−1.15890	+	6.57245i	−0.0408967	+	0.231937i
$804$		0			0
$805$	3.39697	+	1.23640i	0.119727	+	0.0435772i
$806$	−0.682935	−	3.87312i	−0.0240554	−	0.136425i
$807$		0			0
$808$	−11.6770	−	9.79814i	−0.410794	−	0.344697i
$809$	8.02937			0.282298			0.141149	−	0.989988i	$-0.454920\pi$
$809$	8.02937			0.282298			0.141149	+	0.989988i	$0.454920\pi$
$810$		0			0
$811$	−12.8345			−0.450681			−0.225341	−	0.974280i	$-0.572349\pi$
$811$	−12.8345			−0.450681			−0.225341	+	0.974280i	$0.572349\pi$
$812$	−0.857549	−	0.719569i	−0.0300941	−	0.0252519i
$813$		0			0
$814$	−0.598872	−	3.39637i	−0.0209904	−	0.119043i
$815$	33.0308	+	12.0222i	1.15702	+	0.421121i
$816$		0			0
$817$	0.187216	−	1.06176i	0.00654986	−	0.0371461i
$818$	9.32142	−	16.1452i	0.325916	−	0.564503i
$819$		0			0
$820$	6.32233	+	10.9506i	0.220785	+	0.382411i
$821$	−27.8763	+	10.1462i	−0.972891	+	0.354103i	−0.779072	−	0.626934i	$-0.784310\pi$
$821$	−27.8763	+	10.1462i	−0.972891	+	0.354103i	−0.193819	+	0.981037i	$0.562087\pi$
$822$		0			0
$823$	37.9504	−	31.8442i	1.32287	−	1.11002i	0.337179	−	0.941440i	$-0.390527\pi$
$823$	37.9504	−	31.8442i	1.32287	−	1.11002i	0.985688	−	0.168577i	$-0.0539173\pi$
$824$	27.1057	−	22.7444i	0.944271	−	0.792338i
$825$		0			0
$826$	7.32454	−	2.66592i	0.254854	−	0.0927591i
$827$	20.4215	+	35.3711i	0.710126	+	1.22997i	0.964809	+	0.262950i	$0.0846955\pi$
$827$	20.4215	+	35.3711i	0.710126	+	1.22997i	−0.254683	+	0.967025i	$0.581971\pi$
$828$		0			0
$829$	4.72638	−	8.18633i	0.164154	−	0.284323i	−0.772201	−	0.635379i	$-0.780844\pi$
$829$	4.72638	−	8.18633i	0.164154	−	0.284323i	0.936355	+	0.351056i	$0.114177\pi$
$830$	2.56997	−	14.5750i	0.0892049	−	0.505906i
$831$		0			0
$832$	32.8955	+	11.9730i	1.14045	+	0.415088i
$833$	−1.09899	−	6.23266i	−0.0380776	−	0.215949i
$834$		0			0
$835$	26.5633	+	22.2892i	0.919259	+	0.771350i
$836$	−0.277620			−0.00960170
$837$		0			0
$838$	9.62995			0.332661
$839$	9.41230	+	7.89786i	0.324949	+	0.272664i	0.790638	−	0.612284i	$-0.209749\pi$
$839$	9.41230	+	7.89786i	0.324949	+	0.272664i	−0.465689	+	0.884948i	$0.654194\pi$
$840$		0			0
$841$	−4.99021	−	28.3009i	−0.172076	−	0.975892i
$842$	23.9709	+	8.72469i	0.826092	+	0.300673i
$843$		0			0
$844$	0.569434	−	3.22942i	0.0196007	−	0.111161i
$845$	−6.71575	+	11.6320i	−0.231029	+	0.400154i
$846$		0			0
$847$	11.5916	+	20.0772i	0.398292	+	0.689862i
$848$	14.1270	−	5.14182i	0.485125	−	0.176571i
$849$		0			0
$850$	10.4808	−	8.79446i	0.359489	−	0.301647i
$851$	−1.68223	+	1.41156i	−0.0576660	+	0.0483875i
$852$		0			0
$853$	29.0044	−	10.5567i	0.993092	−	0.361456i	0.206175	−	0.978515i	$-0.433898\pi$
$853$	29.0044	−	10.5567i	0.993092	−	0.361456i	0.786917	+	0.617059i	$0.211676\pi$
$854$	3.73781	+	6.47408i	0.127905	+	0.221538i
$855$		0			0
$856$	29.6280	−	51.3172i	1.01266	−	1.75399i
$857$	−1.93549	+	10.9767i	−0.0661150	+	0.374957i	0.933740	+	0.357951i	$0.116525\pi$
$857$	−1.93549	+	10.9767i	−0.0661150	+	0.374957i	−0.999855	+	0.0170059i	$0.994587\pi$
$858$		0			0
$859$	−3.89848	−	1.41893i	−0.133014	−	0.0484133i	0.274655	−	0.961543i	$-0.411436\pi$
$859$	−3.89848	−	1.41893i	−0.133014	−	0.0484133i	−0.407670	+	0.913129i	$0.633659\pi$
$860$	−1.16539	−	6.60925i	−0.0397394	−	0.225374i
$861$		0			0
$862$	−23.8528	−	20.0149i	−0.812429	−	0.681709i
$863$	47.2534			1.60852			0.804262	−	0.594275i	$-0.202561\pi$
$863$	47.2534			1.60852			0.804262	+	0.594275i	$0.202561\pi$
$864$		0			0
$865$	−33.0392			−1.12337
$866$	−0.540933	−	0.453897i	−0.0183817	−	0.0154240i
$867$		0			0
$868$	0.311097	+	1.76432i	0.0105593	+	0.0598849i
$869$	−5.62996	−	2.04914i	−0.190983	−	0.0695122i
$870$		0			0
$871$	−7.96745	+	45.1857i	−0.269967	+	1.53106i
$872$	−9.61579	+	16.6550i	−0.325632	+	0.564011i
$873$		0			0
$874$	−0.110593	−	0.191553i	−0.00374087	−	0.00647938i
$875$	28.0481	−	10.2087i	0.948198	−	0.345116i
$876$		0			0
$877$	26.9268	−	22.5943i	0.909253	−	0.762954i	−0.0627236	−	0.998031i	$-0.519979\pi$
$877$	26.9268	−	22.5943i	0.909253	−	0.762954i	0.971977	+	0.235077i	$0.0755342\pi$
$878$	5.12773	−	4.30267i	0.173052	−	0.145208i
$879$		0			0
$880$	2.95041	−	1.07386i	0.0994582	−	0.0361998i
$881$	−9.67981	−	16.7659i	−0.326121	−	0.564858i	0.655618	−	0.755093i	$-0.272408\pi$
$881$	−9.67981	−	16.7659i	−0.326121	−	0.564858i	−0.981739	+	0.190235i	$0.939075\pi$
$882$		0			0
$883$	6.89302	−	11.9391i	0.231969	−	0.401781i	−0.726419	−	0.687252i	$-0.758817\pi$
$883$	6.89302	−	11.9391i	0.231969	−	0.401781i	0.958387	+	0.285471i	$0.0921500\pi$
$884$	4.66481	−	26.4554i	0.156895	−	0.889793i
$885$		0			0
$886$	−15.2118	−	5.53663i	−0.511049	−	0.186007i
$887$	5.17775	+	29.3645i	0.173852	+	0.985962i	0.939461	+	0.342656i	$0.111327\pi$
$887$	5.17775	+	29.3645i	0.173852	+	0.985962i	−0.765609	+	0.643306i	$0.777562\pi$
$888$		0			0
$889$	22.6505	+	19.0060i	0.759673	+	0.637442i
$890$	12.3391			0.413609
$891$		0			0
$892$	18.8705			0.631832
$893$	1.01203	+	0.849193i	0.0338662	+	0.0284172i
$894$		0			0
$895$	−3.30851	−	18.7635i	−0.110591	−	0.627194i
$896$	−2.41281	−	0.878191i	−0.0806063	−	0.0293383i
$897$		0			0
$898$	−5.86590	+	33.2672i	−0.195748	+	1.11014i
$899$	0.210078	−	0.363866i	0.00700649	−	0.0121356i
$900$		0			0
$901$	−34.8448	−	60.3530i	−1.16085	−	2.01065i
$902$	10.1307	−	3.68727i	0.337315	−	0.122773i
$903$		0			0
$904$	16.1333	−	13.5374i	0.536586	−	0.450249i
$905$	−24.0026	+	20.1406i	−0.797873	+	0.669495i
$906$		0			0
$907$	5.85576	−	2.13132i	0.194437	−	0.0707694i	−0.242966	−	0.970035i	$-0.578120\pi$
$907$	5.85576	−	2.13132i	0.194437	−	0.0707694i	0.437403	+	0.899265i	$0.355898\pi$
$908$	6.36984	+	11.0329i	0.211391	+	0.366139i
$909$		0			0
$910$	−10.2957	+	17.8327i	−0.341300	+	0.591148i
$911$	5.49414	−	31.1588i	0.182029	−	1.03234i	−0.747685	−	0.664054i	$-0.768835\pi$
$911$	5.49414	−	31.1588i	0.182029	−	1.03234i	0.929714	−	0.368283i	$-0.120054\pi$
$912$		0			0
$913$	9.47652	+	3.44917i	0.313627	+	0.114151i
$914$	−3.50931	−	19.9023i	−0.116078	−	0.658310i
$915$		0			0
$916$	−11.4917	−	9.64268i	−0.379696	−	0.318603i
$917$	34.6380			1.14385
$918$		0			0
$919$	36.0031			1.18763			0.593816	−	0.804601i	$-0.297621\pi$
$919$	36.0031			1.18763			0.593816	+	0.804601i	$0.297621\pi$
$920$	−3.42917	−	2.87742i	−0.113057	−	0.0948657i
$921$		0			0
$922$	−0.955739	−	5.42027i	−0.0314756	−	0.178507i
$923$	−0.382481	−	0.139212i	−0.0125895	−	0.00458220i
$924$		0			0
$925$	−0.884135	+	5.01418i	−0.0290702	+	0.164865i
$926$	0.894800	−	1.54984i	0.0294049	−	0.0509309i
$927$		0			0
$928$	1.17304	+	2.03177i	0.0385070	+	0.0666961i
$929$	23.9130	−	8.70363i	0.784561	−	0.285557i	0.0814880	−	0.996674i	$-0.474033\pi$
$929$	23.9130	−	8.70363i	0.784561	−	0.285557i	0.703073	+	0.711117i	$0.251811\pi$
$930$		0			0
$931$	−0.181723	+	0.152484i	−0.00595575	+	0.00499746i
$932$	3.81072	−	3.19758i	0.124824	−	0.104740i
$933$		0			0
$934$	−19.5005	+	7.09760i	−0.638075	+	0.232240i
$935$	−7.27728	−	12.6046i	−0.237993	−	0.412215i
$936$		0			0
$937$	−14.1524	+	24.5127i	−0.462338	+	0.800794i	−0.999077	−	0.0429549i	$-0.986323\pi$
$937$	−14.1524	+	24.5127i	−0.462338	+	0.800794i	0.536739	+	0.843749i	$0.319656\pi$
$938$	−4.54127	+	25.7548i	−0.148278	+	0.840924i
$939$		0			0
$940$	7.72774	+	2.81267i	0.252051	+	0.0917391i
$941$	−1.44031	−	8.16843i	−0.0469529	−	0.266283i	0.952290	−	0.305195i	$-0.0987218\pi$
$941$	−1.44031	−	8.16843i	−0.0469529	−	0.266283i	−0.999243	+	0.0389123i	$0.987611\pi$
$942$		0			0
$943$	−5.25865	−	4.41253i	−0.171245	−	0.143692i
$944$	−4.31074			−0.140303
$945$		0			0
$946$	−5.72199			−0.186038
$947$	34.0511	+	28.5723i	1.10651	+	0.928475i	0.997846	−	0.0656031i	$-0.0208971\pi$
$947$	34.0511	+	28.5723i	1.10651	+	0.928475i	0.108668	+	0.994078i	$0.465342\pi$
$948$		0			0
$949$	4.20333	+	23.8383i	0.136446	+	0.773823i
$950$	−0.481906	−	0.175399i	−0.0156351	−	0.00569071i
$951$		0			0
$952$	8.64452	−	49.0255i	0.280170	−	1.58893i
$953$	−4.83574	+	8.37576i	−0.156645	+	0.271317i	−0.933657	−	0.358169i	$-0.883401\pi$
$953$	−4.83574	+	8.37576i	−0.156645	+	0.271317i	0.777012	+	0.629486i	$0.216735\pi$
$954$		0			0
$955$	−23.5385	−	40.7699i	−0.761688	−	1.31928i
$956$	4.40308	−	1.60259i	0.142406	−	0.0518315i
$957$		0			0
$958$	−23.6268	+	19.8252i	−0.763348	+	0.640525i
$959$	−4.25409	+	3.56961i	−0.137372	+	0.115269i
$960$		0			0
$961$	28.4986	−	10.3726i	0.919310	−	0.334602i
$962$	−6.25433	−	10.8328i	−0.201648	−	0.349264i
$963$		0			0
$964$	−3.95448	+	6.84936i	−0.127365	+	0.220603i
$965$	−5.20053	+	29.4937i	−0.167411	+	0.949434i
$966$		0			0
$967$	31.1180	+	11.3260i	1.00069	+	0.364220i	0.789850	−	0.613301i	$-0.210159\pi$
$967$	31.1180	+	11.3260i	1.00069	+	0.364220i	0.210838	+	0.977521i	$0.432381\pi$
$968$	−4.98509	−	28.2719i	−0.160227	−	0.908692i
$969$		0			0
$970$	−7.74172	−	6.49608i	−0.248572	−	0.208576i
$971$	27.4309			0.880298			0.440149	−	0.897925i	$-0.354926\pi$
$971$	27.4309			0.880298			0.440149	+	0.897925i	$0.354926\pi$
$972$		0			0
$973$	−19.6127			−0.628755
$974$	16.5616	+	13.8968i	0.530667	+	0.445283i
$975$		0			0
$976$	−0.717917	−	4.07151i	−0.0229800	−	0.130326i
$977$	34.1837	+	12.4419i	1.09363	+	0.398050i	0.824966	−	0.565182i	$-0.191194\pi$
$977$	34.1837	+	12.4419i	1.09363	+	0.398050i	0.268669	+	0.963233i	$0.413416\pi$
$978$		0			0
$979$	−1.46003	+	8.28022i	−0.0466626	+	0.264637i
$980$	−0.738337	+	1.27884i	−0.0235853	+	0.0408510i
$981$		0			0
$982$	−9.23957	−	16.0034i	−0.294847	−	0.510689i
$983$	39.5960	−	14.4118i	1.26292	−	0.459664i	0.378170	−	0.925736i	$-0.376553\pi$
$983$	39.5960	−	14.4118i	1.26292	−	0.459664i	0.884747	+	0.466072i	$0.154331\pi$
$984$		0			0
$985$	−3.35975	+	2.81917i	−0.107051	+	0.0898262i
$986$	−2.75081	+	2.30820i	−0.0876035	+	0.0735081i
$987$		0			0
$988$	−0.946203	+	0.344390i	−0.0301027	+	0.0109565i
$989$	1.82173	+	3.15533i	0.0579276	+	0.100334i
$990$		0			0
$991$	−12.7705	+	22.1191i	−0.405667	+	0.702635i	−0.994399	−	0.105693i	$-0.966294\pi$
$991$	−12.7705	+	22.1191i	−0.405667	+	0.702635i	0.588732	+	0.808328i	$0.299627\pi$
$992$	0.651981	−	3.69757i	0.0207004	−	0.117398i
$993$		0			0
$994$	−0.218005	−	0.0793475i	−0.00691471	−	0.00251675i
$995$	5.62010	+	31.8732i	0.178169	+	1.01045i
$996$		0			0
$997$	18.0272	+	15.1266i	0.570928	+	0.479066i	0.881954	−	0.471336i	$-0.156228\pi$
$997$	18.0272	+	15.1266i	0.570928	+	0.479066i	−0.311026	+	0.950402i	$0.600673\pi$
$998$	20.1439			0.637644
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.e.b.136.1		12
3.2	odd	2		243.2.e.c.136.2		12
9.2	odd	6		27.2.e.a.25.2	yes	12
9.4	even	3		243.2.e.a.55.2		12
9.5	odd	6		243.2.e.d.55.1		12
9.7	even	3		81.2.e.a.73.1		12
27.2	odd	18		729.2.c.e.244.2		12
27.4	even	9		81.2.e.a.10.1		12
27.5	odd	18		243.2.e.c.109.2		12
27.7	even	9		729.2.a.d.1.2		6
27.11	odd	18		729.2.c.e.487.2		12
27.13	even	9		243.2.e.a.190.2		12
27.14	odd	18		243.2.e.d.190.1		12
27.16	even	9		729.2.c.b.487.5		12
27.20	odd	18		729.2.a.a.1.5		6
27.22	even	9	inner	243.2.e.b.109.1		12
27.23	odd	18		27.2.e.a.13.2	✓	12
27.25	even	9		729.2.c.b.244.5		12
36.11	even	6		432.2.u.c.241.2		12
45.2	even	12		675.2.u.b.349.3		24
45.29	odd	6		675.2.l.c.376.1		12
45.38	even	12		675.2.u.b.349.2		24
108.23	even	18		432.2.u.c.337.2		12
135.23	even	36		675.2.u.b.499.3		24
135.77	even	36		675.2.u.b.499.2		24
135.104	odd	18		675.2.l.c.526.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.2	✓	12	27.23	odd	18
27.2.e.a.25.2	yes	12	9.2	odd	6
81.2.e.a.10.1		12	27.4	even	9
81.2.e.a.73.1		12	9.7	even	3
243.2.e.a.55.2		12	9.4	even	3
243.2.e.a.190.2		12	27.13	even	9
243.2.e.b.109.1		12	27.22	even	9	inner
243.2.e.b.136.1		12	1.1	even	1	trivial
243.2.e.c.109.2		12	27.5	odd	18
243.2.e.c.136.2		12	3.2	odd	2
243.2.e.d.55.1		12	9.5	odd	6
243.2.e.d.190.1		12	27.14	odd	18
432.2.u.c.241.2		12	36.11	even	6
432.2.u.c.337.2		12	108.23	even	18
675.2.l.c.376.1		12	45.29	odd	6
675.2.l.c.526.1		12	135.104	odd	18
675.2.u.b.349.2		24	45.38	even	12
675.2.u.b.349.3		24	45.2	even	12
675.2.u.b.499.2		24	135.77	even	36
675.2.u.b.499.3		24	135.23	even	36
729.2.a.a.1.5		6	27.20	odd	18
729.2.a.d.1.2		6	27.7	even	9
729.2.c.b.244.5		12	27.25	even	9
729.2.c.b.487.5		12	27.16	even	9
729.2.c.e.244.2		12	27.2	odd	18
729.2.c.e.487.2		12	27.11	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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.807660 - 0.677707i) q^{2} +(-0.154269 - 0.874902i) q^{4} +(-1.64050 - 0.597094i) q^{5} +(0.427044 - 2.42189i) q^{7} +(-1.52266 + 2.63732i) q^{8} +O(q^{10})\)	\(q+(-0.807660 - 0.677707i) q^{2} +(-0.154269 - 0.874902i) q^{4} +(-1.64050 - 0.597094i) q^{5} +(0.427044 - 2.42189i) q^{7} +(-1.52266 + 2.63732i) q^{8} +(0.920313 + 1.59403i) q^{10} +(-1.17857 + 0.428966i) q^{11} +(-3.48476 + 2.92406i) q^{13} +(-1.98623 + 1.66665i) q^{14} +(1.34747 - 0.490439i) q^{16} +(-3.32358 - 5.75662i) q^{17} +(-0.124578 + 0.215776i) q^{19} +(-0.269321 + 1.52739i) q^{20} +(1.24260 + 0.452270i) q^{22} +(-0.146212 - 0.829209i) q^{23} +(-1.49549 - 1.25487i) q^{25} +4.79615 q^{26} -2.18479 q^{28} +(0.392508 + 0.329353i) q^{29} +(-0.142392 - 0.807546i) q^{31} +(4.30264 + 1.56603i) q^{32} +(-1.21697 + 6.90180i) q^{34} +(-2.14666 + 3.71812i) q^{35} +(-1.30403 - 2.25865i) q^{37} +(0.246849 - 0.0898458i) q^{38} +(4.07265 - 3.41736i) q^{40} +(6.24542 - 5.24053i) q^{41} +(-4.06619 + 1.47997i) q^{43} +(0.557121 + 0.964962i) q^{44} +(-0.443871 + 0.768808i) q^{46} +(0.920741 - 5.22178i) q^{47} +(0.894687 + 0.325640i) q^{49} +(0.357417 + 2.02701i) q^{50} +(3.09586 + 2.59773i) q^{52} +10.4841 q^{53} +2.18959 q^{55} +(5.73704 + 4.81395i) q^{56} +(-0.0938079 - 0.532011i) q^{58} +(-2.82491 - 1.02818i) q^{59} +(0.500658 - 2.83937i) q^{61} +(-0.432275 + 0.748722i) q^{62} +(-3.84771 - 6.66442i) q^{64} +(7.46270 - 2.71620i) q^{65} +(7.72653 - 6.48333i) q^{67} +(-4.52375 + 3.79588i) q^{68} +(4.25357 - 1.54817i) q^{70} +(0.0447378 + 0.0774882i) q^{71} +(2.66057 - 4.60824i) q^{73} +(-0.477488 + 2.70797i) q^{74} +(0.208001 + 0.0757062i) q^{76} +(0.535604 + 3.03756i) q^{77} +(3.65933 + 3.07054i) q^{79} -2.50337 q^{80} -8.59571 q^{82} +(-6.15950 - 5.16844i) q^{83} +(2.01511 + 11.4282i) q^{85} +(4.28708 + 1.56037i) q^{86} +(0.663244 - 3.76144i) q^{88} +(3.35189 - 5.80564i) q^{89} +(5.59359 + 9.68839i) q^{91} +(-0.702921 + 0.255842i) q^{92} +(-4.28248 + 3.59343i) q^{94} +(0.333209 - 0.279596i) q^{95} +(-5.15946 + 1.87789i) q^{97} +(-0.501915 - 0.869342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} + 3 q^{13} - 6 q^{14} - 9 q^{16} - 9 q^{17} - 3 q^{19} + 21 q^{20} - 15 q^{22} - 24 q^{23} - 15 q^{25} + 30 q^{26} - 12 q^{28} - 30 q^{29} - 15 q^{31} + 27 q^{32} - 9 q^{34} - 12 q^{35} - 3 q^{37} + 12 q^{38} - 6 q^{40} + 21 q^{41} + 12 q^{43} - 3 q^{44} - 3 q^{46} - 3 q^{47} + 21 q^{49} - 12 q^{50} + 36 q^{52} + 18 q^{53} - 12 q^{55} - 3 q^{56} + 30 q^{58} - 15 q^{59} + 21 q^{61} + 12 q^{62} + 12 q^{64} + 24 q^{65} + 21 q^{67} + 18 q^{68} + 30 q^{70} - 27 q^{71} + 6 q^{73} + 12 q^{74} + 42 q^{76} + 3 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 33 q^{83} - 9 q^{85} + 30 q^{86} - 12 q^{88} - 9 q^{89} + 6 q^{91} - 42 q^{92} - 33 q^{94} - 30 q^{95} - 42 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^4 + 3 * q^5 + 3 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 + 3 * q^13 - 6 * q^14 - 9 * q^16 - 9 * q^17 - 3 * q^19 + 21 * q^20 - 15 * q^22 - 24 * q^23 - 15 * q^25 + 30 * q^26 - 12 * q^28 - 30 * q^29 - 15 * q^31 + 27 * q^32 - 9 * q^34 - 12 * q^35 - 3 * q^37 + 12 * q^38 - 6 * q^40 + 21 * q^41 + 12 * q^43 - 3 * q^44 - 3 * q^46 - 3 * q^47 + 21 * q^49 - 12 * q^50 + 36 * q^52 + 18 * q^53 - 12 * q^55 - 3 * q^56 + 30 * q^58 - 15 * q^59 + 21 * q^61 + 12 * q^62 + 12 * q^64 + 24 * q^65 + 21 * q^67 + 18 * q^68 + 30 * q^70 - 27 * q^71 + 6 * q^73 + 12 * q^74 + 42 * q^76 + 3 * q^77 + 21 * q^79 - 42 * q^80 - 12 * q^82 + 33 * q^83 - 9 * q^85 + 30 * q^86 - 12 * q^88 - 9 * q^89 + 6 * q^91 - 42 * q^92 - 33 * q^94 - 30 * q^95 - 42 * q^97 + 45 * q^98

Introduction

L-functions

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