LMFDB - Embedded newform 855.2.bs.b.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.1
Root			$1.01081 - 1.75077i$ of defining polynomial
Character	$\chi$	$=$	855.271
Dual form			855.2.bs.b.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89970 + 0.691434i) q^{2} +(1.59869 - 1.34146i) q^{4} +(0.766044 + 0.642788i) q^{5} +(-1.54609 - 2.67790i) q^{7} +(-0.0878797 + 0.152212i) q^{8} +O(q^{10})$	\(q+(-1.89970 + 0.691434i) q^{2} +(1.59869 - 1.34146i) q^{4} +(0.766044 + 0.642788i) q^{5} +(-1.54609 - 2.67790i) q^{7} +(-0.0878797 + 0.152212i) q^{8} +(-1.89970 - 0.691434i) q^{10} +(0.481594 - 0.834145i) q^{11} +(-0.513859 - 2.91424i) q^{13} +(4.78870 + 4.01819i) q^{14} +(-0.663086 + 3.76055i) q^{16} +(0.0366124 - 0.0133258i) q^{17} +(-4.31788 + 0.596607i) q^{19} +2.08694 q^{20} +(-0.338127 + 1.91762i) q^{22} +(-2.97348 + 2.49504i) q^{23} +(0.173648 + 0.984808i) q^{25} +(2.99118 + 5.18088i) q^{26} +(-6.06401 - 2.20712i) q^{28} +(-8.76529 - 3.19030i) q^{29} +(4.68894 + 8.12148i) q^{31} +(-1.40155 - 7.94857i) q^{32} +(-0.0603386 + 0.0506301i) q^{34} +(0.536951 - 3.04520i) q^{35} -1.11739 q^{37} +(7.79016 - 4.11890i) q^{38} +(-0.165160 + 0.0601132i) q^{40} +(-2.09674 + 11.8912i) q^{41} +(-3.79459 - 3.18404i) q^{43} +(-0.349053 - 1.97958i) q^{44} +(3.92356 - 6.79580i) q^{46} +(7.53217 + 2.74148i) q^{47} +(-1.28078 + 2.21837i) q^{49} +(-1.01081 - 1.75077i) q^{50} +(-4.73083 - 3.96964i) q^{52} +(-4.64208 + 3.89517i) q^{53} +(0.905101 - 0.329430i) q^{55} +0.543479 q^{56} +18.8573 q^{58} +(2.60732 - 0.948987i) q^{59} +(-7.68360 + 6.44731i) q^{61} +(-14.5230 - 12.1863i) q^{62} +(4.33987 + 7.51688i) q^{64} +(1.47960 - 2.56274i) q^{65} +(-8.78501 - 3.19748i) q^{67} +(0.0406557 - 0.0704178i) q^{68} +(1.08551 + 6.15623i) q^{70} +(-9.64404 - 8.09231i) q^{71} +(0.155782 - 0.883486i) q^{73} +(2.12271 - 0.772603i) q^{74} +(-6.10262 + 6.74604i) q^{76} -2.97835 q^{77} +(1.54415 - 8.75731i) q^{79} +(-2.92519 + 2.45452i) q^{80} +(-4.23882 - 24.0395i) q^{82} +(-4.80224 - 8.31772i) q^{83} +(0.0366124 + 0.0133258i) q^{85} +(9.41012 + 3.42500i) q^{86} +(0.0846446 + 0.146609i) q^{88} +(1.51886 + 8.61386i) q^{89} +(-7.00958 + 5.88173i) q^{91} +(-1.40667 + 7.97760i) q^{92} -16.2044 q^{94} +(-3.69118 - 2.31845i) q^{95} +(-7.31855 + 2.66374i) q^{97} +(0.899233 - 5.09981i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.89970	+	0.691434i	−1.34329	+	0.488918i	−0.910847	−	0.412743i	$-0.864571\pi$
$2$	−1.89970	+	0.691434i	−1.34329	+	0.488918i	−0.432443	+	0.901661i	$0.642348\pi$
$3$		0			0
$3$		0			0
$4$	1.59869	−	1.34146i	0.799344	−	0.670730i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$6$		0			0
$7$	−1.54609	−	2.67790i	−0.584366	−	1.01215i	−0.994954	−	0.100331i	$-0.968010\pi$
$7$	−1.54609	−	2.67790i	−0.584366	−	1.01215i	0.410588	−	0.911821i	$-0.365324\pi$
$8$	−0.0878797	+	0.152212i	−0.0310701	+	0.0538151i
$9$		0			0
$10$	−1.89970	−	0.691434i	−0.600738	−	0.218651i
$11$	0.481594	−	0.834145i	0.145206	−	0.251504i	−0.784244	−	0.620453i	$-0.786949\pi$
$11$	0.481594	−	0.834145i	0.145206	−	0.251504i	0.929450	+	0.368949i	$0.120282\pi$
$12$		0			0
$13$	−0.513859	−	2.91424i	−0.142519	−	0.808264i	−0.969326	−	0.245779i	$-0.920956\pi$
$13$	−0.513859	−	2.91424i	−0.142519	−	0.808264i	0.826807	−	0.562486i	$-0.190155\pi$
$14$	4.78870	+	4.01819i	1.27983	+	1.07391i
$15$		0			0
$16$	−0.663086	+	3.76055i	−0.165772	+	0.940137i
$17$	0.0366124	−	0.0133258i	0.00887980	−	0.00323198i	−0.337576	−	0.941298i	$-0.609607\pi$
$17$	0.0366124	−	0.0133258i	0.00887980	−	0.00323198i	0.346456	+	0.938066i	$0.387385\pi$
$18$		0			0
$19$	−4.31788	+	0.596607i	−0.990589	+	0.136871i
$19$	−4.31788	+	0.596607i	−0.990589	+	0.136871i
$20$	2.08694			0.466654
$21$		0			0
$22$	−0.338127	+	1.91762i	−0.0720890	+	0.408837i
$23$	−2.97348	+	2.49504i	−0.620013	+	0.520253i	−0.897808	−	0.440388i	$-0.854841\pi$
$23$	−2.97348	+	2.49504i	−0.620013	+	0.520253i	0.277795	+	0.960641i	$0.410397\pi$
$24$		0			0
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	2.99118	+	5.18088i	0.586619	+	1.01605i
$27$		0			0
$28$	−6.06401	−	2.20712i	−1.14599	−	0.417106i
$29$	−8.76529	−	3.19030i	−1.62767	−	0.592425i	−0.642851	−	0.765991i	$-0.722249\pi$
$29$	−8.76529	−	3.19030i	−1.62767	−	0.592425i	−0.984822	+	0.173566i	$0.944471\pi$
$30$		0			0
$31$	4.68894	+	8.12148i	0.842158	+	1.45866i	0.888067	+	0.459715i	$0.152048\pi$
$31$	4.68894	+	8.12148i	0.842158	+	1.45866i	−0.0459085	+	0.998946i	$0.514618\pi$
$32$	−1.40155	−	7.94857i	−0.247761	−	1.40512i
$33$		0			0
$34$	−0.0603386	+	0.0506301i	−0.0103480	+	0.00868299i
$35$	0.536951	−	3.04520i	0.0907612	−	0.514733i
$36$		0			0
$37$	−1.11739			−0.183698			−0.0918491	−	0.995773i	$-0.529278\pi$
$37$	−1.11739			−0.183698			−0.0918491	+	0.995773i	$0.529278\pi$
$38$	7.79016	−	4.11890i	1.26373	−	0.668174i
$39$		0			0
$40$	−0.165160	+	0.0601132i	−0.0261140	+	0.00950473i
$41$	−2.09674	+	11.8912i	−0.327456	+	1.85710i	0.164362	+	0.986400i	$0.447443\pi$
$41$	−2.09674	+	11.8912i	−0.327456	+	1.85710i	−0.491818	+	0.870698i	$0.663668\pi$
$42$		0			0
$43$	−3.79459	−	3.18404i	−0.578669	−	0.485561i	0.305841	−	0.952083i	$-0.401062\pi$
$43$	−3.79459	−	3.18404i	−0.578669	−	0.485561i	−0.884510	+	0.466522i	$0.845507\pi$
$44$	−0.349053	−	1.97958i	−0.0526217	−	0.298432i
$45$		0			0
$46$	3.92356	−	6.79580i	0.578497	−	1.00199i
$47$	7.53217	+	2.74148i	1.09868	+	0.399887i	0.826829	−	0.562453i	$-0.190142\pi$
$47$	7.53217	+	2.74148i	1.09868	+	0.399887i	0.271850	+	0.962340i	$0.412364\pi$
$48$		0			0
$49$	−1.28078	+	2.21837i	−0.182968	+	0.316910i
$50$	−1.01081	−	1.75077i	−0.142950	−	0.247597i
$51$		0			0
$52$	−4.73083	−	3.96964i	−0.656048	−	0.550490i
$53$	−4.64208	+	3.89517i	−0.637639	+	0.535043i	−0.903292	−	0.429026i	$-0.858857\pi$
$53$	−4.64208	+	3.89517i	−0.637639	+	0.535043i	0.265653	+	0.964069i	$0.414412\pi$
$54$		0			0
$55$	0.905101	−	0.329430i	0.122044	−	0.0444203i
$56$	0.543479			0.0726254
$57$		0			0
$58$	18.8573			2.47609
$59$	2.60732	−	0.948987i	0.339444	−	0.123548i	−0.166673	−	0.986012i	$-0.553302\pi$
$59$	2.60732	−	0.948987i	0.339444	−	0.123548i	0.506117	+	0.862465i	$0.331080\pi$
$60$		0			0
$61$	−7.68360	+	6.44731i	−0.983784	+	0.825493i	−0.984656	−	0.174507i	$-0.944167\pi$
$61$	−7.68360	+	6.44731i	−0.983784	+	0.825493i	0.000871917		1.00000i	$0.499722\pi$
$62$	−14.5230	−	12.1863i	−1.84443	−	1.54766i
$63$		0			0
$64$	4.33987	+	7.51688i	0.542484	+	0.939610i
$65$	1.47960	−	2.56274i	0.183522	−	0.317869i
$66$		0			0
$67$	−8.78501	−	3.19748i	−1.07326	−	0.390635i	−0.255865	−	0.966713i	$-0.582360\pi$
$67$	−8.78501	−	3.19748i	−1.07326	−	0.390635i	−0.817395	+	0.576078i	$0.804582\pi$
$68$	0.0406557	−	0.0704178i	0.00493023	−	0.00853941i
$69$		0			0
$70$	1.08551	+	6.15623i	0.129743	+	0.735810i
$71$	−9.64404	−	8.09231i	−1.14454	−	0.960381i	−0.144959	−	0.989438i	$-0.546305\pi$
$71$	−9.64404	−	8.09231i	−1.14454	−	0.960381i	−0.999578	+	0.0290571i	$0.990750\pi$
$72$		0			0
$73$	0.155782	−	0.883486i	0.0182330	−	0.103404i	−0.974333	−	0.225111i	$-0.927726\pi$
$73$	0.155782	−	0.883486i	0.0182330	−	0.103404i	0.992566	+	0.121707i	$0.0388367\pi$
$74$	2.12271	−	0.772603i	0.246760	−	0.0898133i
$75$		0			0
$76$	−6.10262	+	6.74604i	−0.700018	+	0.773824i
$77$	−2.97835			−0.339414
$78$		0			0
$79$	1.54415	−	8.75731i	0.173731	−	0.985275i	−0.765868	−	0.642997i	$-0.777691\pi$
$79$	1.54415	−	8.75731i	0.173731	−	0.985275i	0.939599	−	0.342277i	$-0.111198\pi$
$80$	−2.92519	+	2.45452i	−0.327046	+	0.274424i
$81$		0			0
$82$	−4.23882	−	24.0395i	−0.468099	−	2.65472i
$83$	−4.80224	−	8.31772i	−0.527114	−	0.912988i	−0.999501	−	0.0315966i	$-0.989941\pi$
$83$	−4.80224	−	8.31772i	−0.527114	−	0.912988i	0.472387	−	0.881391i	$-0.343393\pi$
$84$		0			0
$85$	0.0366124	+	0.0133258i	0.00397117	+	0.00144539i
$86$	9.41012	+	3.42500i	1.01472	+	0.369328i
$87$		0			0
$88$	0.0846446	+	0.146609i	0.00902315	+	0.0156285i
$89$	1.51886	+	8.61386i	0.160998	+	0.913068i	0.953095	+	0.302672i	$0.0978786\pi$
$89$	1.51886	+	8.61386i	0.160998	+	0.913068i	−0.792096	+	0.610396i	$0.791010\pi$
$90$		0			0
$91$	−7.00958	+	5.88173i	−0.734803	+	0.616573i
$92$	−1.40667	+	7.97760i	−0.146655	+	0.831722i
$93$		0			0
$94$	−16.2044			−1.67136
$95$	−3.69118	−	2.31845i	−0.378707	−	0.237868i
$96$		0			0
$97$	−7.31855	+	2.66374i	−0.743087	+	0.270461i	−0.685694	−	0.727890i	$-0.740501\pi$
$97$	−7.31855	+	2.66374i	−0.743087	+	0.270461i	−0.0573929	+	0.998352i	$0.518279\pi$
$98$	0.899233	−	5.09981i	0.0908363	−	0.515158i
$99$		0			0
$100$	1.59869	+	1.34146i	0.159869	+	0.134146i
$101$	0.528521	+	2.99739i	0.0525898	+	0.298251i	0.999746	−	0.0225200i	$-0.00716895\pi$
$101$	0.528521	+	2.99739i	0.0525898	+	0.298251i	−0.947157	+	0.320771i	$0.896058\pi$
$102$		0			0
$103$	0.164287	−	0.284553i	0.0161876	−	0.0280378i	−0.857818	−	0.513953i	$-0.828180\pi$
$103$	0.164287	−	0.284553i	0.0161876	−	0.0280378i	0.874006	+	0.485916i	$0.161514\pi$
$104$	0.488740	+	0.177887i	0.0479249	+	0.0174432i
$105$		0			0
$106$	6.12531	−	10.6093i	0.594943	−	1.03047i
$107$	−6.39366	−	11.0741i	−0.618099	−	1.07058i	−0.989832	−	0.142239i	$-0.954570\pi$
$107$	−6.39366	−	11.0741i	−0.618099	−	1.07058i	0.371734	−	0.928339i	$-0.378763\pi$
$108$		0			0
$109$	−11.6754	−	9.79682i	−1.11830	−	0.938366i	−0.119783	−	0.992800i	$-0.538220\pi$
$109$	−11.6754	−	9.79682i	−1.11830	−	0.938366i	−0.998517	+	0.0544346i	$0.982664\pi$
$110$	−1.49164	+	1.25163i	−0.142222	+	0.119339i
$111$		0			0
$112$	11.0956	−	4.03846i	1.04843	−	0.381598i
$113$	−2.56380			−0.241182			−0.120591	−	0.992702i	$-0.538479\pi$
$113$	−2.56380			−0.241182			−0.120591	+	0.992702i	$0.538479\pi$
$114$		0			0
$115$	−3.88160			−0.361961
$116$	−18.2926	+	6.65797i	−1.69843	+	0.618177i
$117$		0			0
$118$	−4.29697	+	3.60558i	−0.395568	+	0.331921i
$119$	−0.0922912	−	0.0774415i	−0.00846032	−	0.00709905i
$120$		0			0
$121$	5.03613	+	8.72284i	0.457830	+	0.792986i
$122$	10.1386	−	17.5606i	0.917910	−	1.58987i
$123$		0			0
$124$	18.3908	+	6.69370i	1.65154	+	0.601112i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$		0			0
$127$	−2.68740	−	15.2410i	−0.238468	−	1.35242i	−0.835186	−	0.549968i	$-0.814640\pi$
$127$	−2.68740	−	15.2410i	−0.238468	−	1.35242i	0.596718	−	0.802451i	$-0.296471\pi$
$128$	−1.07610	−	0.902953i	−0.0951145	−	0.0798105i
$129$		0			0
$130$	−1.03883	+	5.89148i	−0.0911111	+	0.516717i
$131$	0.791413	−	0.288051i	0.0691461	−	0.0251671i	−0.307216	−	0.951640i	$-0.599397\pi$
$131$	0.791413	−	0.288051i	0.0691461	−	0.0251671i	0.376362	+	0.926473i	$0.377175\pi$
$132$		0			0
$133$	8.27347	+	10.6404i	0.717401	+	0.922644i
$134$	18.8997			1.63269
$135$		0			0
$136$	−0.00118913	+	0.00674391i	−0.000101967	+	0.000578285i
$137$	3.88675	−	3.26137i	0.332068	−	0.278638i	−0.461474	−	0.887154i	$-0.652679\pi$
$137$	3.88675	−	3.26137i	0.332068	−	0.278638i	0.793542	+	0.608516i	$0.208235\pi$
$138$		0			0
$139$	0.474127	+	2.68891i	0.0402150	+	0.228070i	0.998291	−	0.0584449i	$-0.0186142\pi$
$139$	0.474127	+	2.68891i	0.0402150	+	0.228070i	−0.958076	+	0.286515i	$0.907503\pi$
$140$	−3.22659	−	5.58862i	−0.272697	−	0.472325i
$141$		0			0
$142$	23.9161	+	8.70474i	2.00699	+	0.730486i
$143$	−2.67837	−	0.974847i	−0.223977	−	0.0815208i
$144$		0			0
$145$	−4.66391	−	8.07814i	−0.387317	−	0.670853i
$146$	0.314933	+	1.78607i	0.0260640	+	0.147816i
$147$		0			0
$148$	−1.78636	+	1.49894i	−0.146838	+	0.123212i
$149$	1.15401	−	6.54471i	0.0945401	−	0.536164i	−0.900347	−	0.435172i	$-0.856687\pi$
$149$	1.15401	−	6.54471i	0.0945401	−	0.536164i	0.994887	−	0.100991i	$-0.0322014\pi$
$150$		0			0
$151$	−5.19059			−0.422404			−0.211202	−	0.977442i	$-0.567738\pi$
$151$	−5.19059			−0.422404			−0.211202	+	0.977442i	$0.567738\pi$
$152$	0.288643	−	0.709662i	0.0234120	−	0.0575612i
$153$		0			0
$154$	5.65796	−	2.05933i	0.455932	−	0.165946i
$155$	−1.62845	+	9.23540i	−0.130800	+	0.741806i
$156$		0			0
$157$	8.92275	+	7.48708i	0.712113	+	0.597534i	0.925191	−	0.379501i	$-0.123904\pi$
$157$	8.92275	+	7.48708i	0.712113	+	0.597534i	−0.213078	+	0.977035i	$0.568349\pi$
$158$	3.12168	+	17.7039i	0.248348	+	1.40845i
$159$		0			0
$160$	4.03560	−	6.98986i	0.319042	−	0.552597i
$161$	11.2787	+	4.10513i	0.888890	+	0.323529i
$162$		0			0
$163$	0.278398	−	0.482199i	0.0218058	−	0.0377688i	−0.854917	−	0.518765i	$-0.826392\pi$
$163$	0.278398	−	0.482199i	0.0218058	−	0.0377688i	0.876722	+	0.480997i	$0.159725\pi$
$164$	12.5996	+	21.8231i	0.983860	+	1.70410i
$165$		0			0
$166$	14.8740	+	12.4807i	1.15444	+	0.968693i
$167$	−16.9727	+	14.2418i	−1.31339	+	1.10206i	−0.325727	+	0.945464i	$0.605609\pi$
$167$	−16.9727	+	14.2418i	−1.31339	+	1.10206i	−0.987662	+	0.156600i	$0.949947\pi$
$168$		0			0
$169$	3.98727	−	1.45125i	0.306713	−	0.111634i
$170$	−0.0787664			−0.00604111
$171$		0			0
$172$	−10.3376			−0.788236
$173$	−10.7653	+	3.91823i	−0.818467	+	0.297898i	−0.717117	−	0.696953i	$-0.754539\pi$
$173$	−10.7653	+	3.91823i	−0.818467	+	0.297898i	−0.101350	+	0.994851i	$0.532316\pi$
$174$		0			0
$175$	2.36874	−	1.98761i	0.179060	−	0.150249i
$176$	2.81751	+	2.36417i	0.212377	+	0.178206i
$177$		0			0
$178$	−8.84129	−	15.3136i	−0.662683	−	1.14780i
$179$	2.98306	−	5.16681i	0.222964	−	0.386185i	−0.732743	−	0.680506i	$-0.761760\pi$
$179$	2.98306	−	5.16681i	0.222964	−	0.386185i	0.955707	+	0.294321i	$0.0950934\pi$
$180$		0			0
$181$	5.80527	+	2.11294i	0.431502	+	0.157054i	0.548634	−	0.836062i	$-0.315148\pi$
$181$	5.80527	+	2.11294i	0.431502	+	0.157054i	−0.117132	+	0.993116i	$0.537370\pi$
$182$	9.24926	−	16.0202i	0.685601	−	1.18750i
$183$		0			0
$184$	−0.118468	−	0.671863i	−0.00873354	−	0.0495304i
$185$	−0.855972	−	0.718246i	−0.0629323	−	0.0528065i
$186$		0			0
$187$	0.00651663	−	0.0369577i	0.000476543	−	0.00270261i
$188$	15.7192	−	5.72131i	1.14644	−	0.417270i
$189$		0			0
$190$	8.61518	+	1.85215i	0.625011	+	0.134369i
$191$	18.6639			1.35047			0.675235	−	0.737602i	$-0.264042\pi$
$191$	18.6639			1.35047			0.675235	+	0.737602i	$0.264042\pi$
$192$		0			0
$193$	−4.15136	+	23.5435i	−0.298821	+	1.69470i	0.352431	+	0.935838i	$0.385355\pi$
$193$	−4.15136	+	23.5435i	−0.298821	+	1.69470i	−0.651252	+	0.758861i	$0.725756\pi$
$194$	12.0613	−	10.1206i	0.865948	−	0.726616i
$195$		0			0
$196$	0.928289	+	5.26459i	0.0663064	+	0.376042i
$197$	−3.35076	−	5.80368i	−0.238732	−	0.413495i	0.721619	−	0.692290i	$-0.243398\pi$
$197$	−3.35076	−	5.80368i	−0.238732	−	0.413495i	−0.960351	+	0.278795i	$0.910065\pi$
$198$		0			0
$199$	−2.96836	−	1.08040i	−0.210422	−	0.0765872i	0.234659	−	0.972078i	$-0.424603\pi$
$199$	−2.96836	−	1.08040i	−0.210422	−	0.0765872i	−0.445080	+	0.895491i	$0.646825\pi$
$200$	−0.165160	−	0.0601132i	−0.0116786	−	0.00425065i
$201$		0			0
$202$	−3.07653	−	5.32870i	−0.216464	−	0.374926i
$203$	5.00858	+	28.4051i	0.351534	+	1.99365i
$204$		0			0
$205$	−9.24973	+	7.76145i	−0.646029	+	0.542083i
$206$	−0.115346	+	0.654158i	−0.00803652	+	0.0455774i
$207$		0			0
$208$	11.2999			0.783505
$209$	−1.58181	+	3.88906i	−0.109416	+	0.269012i
$210$		0			0
$211$	10.7670	−	3.91887i	0.741231	−	0.269786i	0.0563198	−	0.998413i	$-0.482063\pi$
$211$	10.7670	−	3.91887i	0.741231	−	0.269786i	0.684911	+	0.728627i	$0.259841\pi$
$212$	−2.19603	+	12.4543i	−0.150824	+	0.855367i
$213$		0			0
$214$	19.8031	+	16.6168i	1.35371	+	1.13590i
$215$	−0.860163	−	4.87822i	−0.0586626	−	0.332692i
$216$		0			0
$217$	14.4990	−	25.1130i	0.984258	−	1.70478i
$218$	28.9536	+	10.5383i	1.96099	+	0.713741i
$219$		0			0
$220$	1.00506	−	1.74081i	0.0677610	−	0.117365i
$221$	−0.0576482	−	0.0998496i	−0.00387784	−	0.00671661i
$222$		0			0
$223$	−5.75623	−	4.83005i	−0.385465	−	0.323444i	0.429378	−	0.903125i	$-0.358733\pi$
$223$	−5.75623	−	4.83005i	−0.385465	−	0.323444i	−0.814844	+	0.579681i	$0.803177\pi$
$224$	−19.1186	+	16.0424i	−1.27741	+	1.07188i
$225$		0			0
$226$	4.87044	−	1.77270i	0.323977	−	0.117918i
$227$	4.20184			0.278886			0.139443	−	0.990230i	$-0.455469\pi$
$227$	4.20184			0.278886			0.139443	+	0.990230i	$0.455469\pi$
$228$		0			0
$229$	22.5758			1.49185			0.745927	−	0.666028i	$-0.232007\pi$
$229$	22.5758			1.49185			0.745927	+	0.666028i	$0.232007\pi$
$230$	7.37388	−	2.68387i	0.486219	−	0.176969i
$231$		0			0
$232$	1.25589	−	1.05382i	0.0824534	−	0.0691867i
$233$	8.41032	+	7.05710i	0.550978	+	0.462326i	0.875272	−	0.483631i	$-0.160682\pi$
$233$	8.41032	+	7.05710i	0.550978	+	0.462326i	−0.324294	+	0.945956i	$0.605127\pi$
$234$		0			0
$235$	4.00778	+	6.94168i	0.261439	+	0.452826i
$236$	2.89527	−	5.01475i	0.188466	−	0.326432i
$237$		0			0
$238$	0.228871	+	0.0833023i	0.0148355	+	0.00539969i
$239$	−1.36280	+	2.36043i	−0.0881520	+	0.152684i	−0.906730	−	0.421712i	$-0.861429\pi$
$239$	−1.36280	+	2.36043i	−0.0881520	+	0.152684i	0.818578	+	0.574395i	$0.194763\pi$
$240$		0			0
$241$	1.93687	+	10.9846i	0.124765	+	0.707577i	0.981447	+	0.191733i	$0.0614107\pi$
$241$	1.93687	+	10.9846i	0.124765	+	0.707577i	−0.856682	+	0.515845i	$0.827478\pi$
$242$	−15.5984	−	13.0886i	−1.00270	−	0.841369i
$243$		0			0
$244$	−3.63489	+	20.6145i	−0.232700	+	1.31971i
$245$	−2.40707	+	0.876102i	−0.153782	+	0.0559721i
$246$		0			0
$247$	3.95743	+	12.2768i	0.251805	+	0.781151i
$248$	−1.64825			−0.104664
$249$		0			0
$250$	0.351050	−	1.99091i	0.0222024	−	0.125916i
$251$	20.9654	−	17.5920i	1.32332	−	1.11040i	0.337732	−	0.941242i	$-0.390340\pi$
$251$	20.9654	−	17.5920i	1.32332	−	1.11040i	0.985589	−	0.169156i	$-0.0541042\pi$
$252$		0			0
$253$	0.649220	+	3.68191i	0.0408161	+	0.231480i
$254$	15.6434	+	27.0951i	0.981553	+	1.70010i
$255$		0			0
$256$	−13.6440	−	4.96601i	−0.852749	−	0.310375i
$257$	−19.0408	−	6.93029i	−1.18773	−	0.432300i	−0.328806	−	0.944397i	$-0.606646\pi$
$257$	−19.0408	−	6.93029i	−1.18773	−	0.432300i	−0.858927	+	0.512098i	$0.828869\pi$
$258$		0			0
$259$	1.72759	+	2.99227i	0.107347	+	0.185931i
$260$	−1.07239	−	6.08184i	−0.0665070	−	0.377180i
$261$		0			0
$262$	−1.30428	+	1.09442i	−0.0805786	+	0.0676135i
$263$	−1.66049	+	9.41708i	−0.102390	+	0.580682i	0.889841	+	0.456271i	$0.150815\pi$
$263$	−1.66049	+	9.41708i	−0.102390	+	0.580682i	−0.992231	+	0.124411i	$0.960296\pi$
$264$		0			0
$265$	−6.05981			−0.372251
$266$	−23.0743	−	14.4931i	−1.41477	−	0.888629i
$267$		0			0
$268$	−18.3338	+	6.67295i	−1.11991	+	0.407615i
$269$	−0.794363	+	4.50506i	−0.0484332	+	0.274678i	−0.999401	−	0.0346123i	$-0.988980\pi$
$269$	−0.794363	+	4.50506i	−0.0484332	+	0.274678i	0.950968	+	0.309290i	$0.100091\pi$
$270$		0			0
$271$	−16.9571	−	14.2287i	−1.03007	−	0.864330i	−0.0392098	−	0.999231i	$-0.512484\pi$
$271$	−16.9571	−	14.2287i	−1.03007	−	0.864330i	−0.990859	+	0.134901i	$0.956928\pi$
$272$	0.0258352	+	0.146519i	0.00156649	+	0.00888400i
$273$		0			0
$274$	−5.12864	+	8.88306i	−0.309832	+	0.536645i
$275$	0.905101	+	0.329430i	0.0545796	+	0.0198654i
$276$		0			0
$277$	−11.7771	+	20.3985i	−0.707617	+	1.22563i	0.258122	+	0.966112i	$0.416896\pi$
$277$	−11.7771	+	20.3985i	−0.707617	+	1.22563i	−0.965739	+	0.259516i	$0.916437\pi$
$278$	−2.75990	−	4.78029i	−0.165528	−	0.286703i
$279$		0			0
$280$	0.416329	+	0.349341i	0.0248804	+	0.0208771i
$281$	−7.90783	+	6.63545i	−0.471741	+	0.395838i	−0.847429	−	0.530908i	$-0.821851\pi$
$281$	−7.90783	+	6.63545i	−0.471741	+	0.395838i	0.375688	+	0.926746i	$0.377406\pi$
$282$		0			0
$283$	29.0110	−	10.5592i	1.72453	−	0.627676i	0.726310	−	0.687367i	$-0.241234\pi$
$283$	29.0110	−	10.5592i	1.72453	−	0.627676i	0.998217	+	0.0596910i	$0.0190115\pi$
$284$	−26.2733			−1.55903
$285$		0			0
$286$	5.76214			0.340722
$287$	35.0853	−	12.7700i	2.07102	−	0.753790i
$288$		0			0
$289$	−13.0216	+	10.9264i	−0.765976	+	0.642730i
$290$	14.4455	+	12.1212i	0.848271	+	0.711784i
$291$		0			0
$292$	−0.936113	−	1.62140i	−0.0547819	−	0.0948850i
$293$	3.18052	−	5.50882i	0.185808	−	0.321828i	−0.758041	−	0.652207i	$-0.773843\pi$
$293$	3.18052	−	5.50882i	0.185808	−	0.321828i	0.943848	+	0.330379i	$0.107176\pi$
$294$		0			0
$295$	2.60732	+	0.948987i	0.151804	+	0.0552522i
$296$	0.0981961	−	0.170081i	0.00570753	−	0.00988573i
$297$		0			0
$298$	2.33297	+	13.2309i	0.135145	+	0.766446i
$299$	8.79910	+	7.38332i	0.508865	+	0.426989i
$300$		0			0
$301$	−2.65977	+	15.0843i	−0.153307	+	0.869446i
$302$	9.86055	−	3.58895i	0.567411	−	0.206521i
$303$		0			0
$304$	0.619557	−	16.6332i	0.0355340	−	0.953979i
$305$	−10.0302			−0.574329
$306$		0			0
$307$	−1.02217	+	5.79702i	−0.0583384	+	0.330854i	−0.999983	−	0.00575393i	$-0.998168\pi$
$307$	−1.02217	+	5.79702i	−0.0583384	+	0.330854i	0.941645	+	0.336608i	$0.109280\pi$
$308$	−4.76145	+	3.99533i	−0.271309	+	0.227655i
$309$		0			0
$310$	−3.29211	−	18.6705i	−0.186979	−	1.06041i
$311$	−12.6942	−	21.9871i	−0.719825	−	1.24677i	−0.961069	−	0.276308i	$-0.910889\pi$
$311$	−12.6942	−	21.9871i	−0.719825	−	1.24677i	0.241245	−	0.970464i	$-0.422444\pi$
$312$		0			0
$313$	−5.67434	−	2.06529i	−0.320733	−	0.116737i	0.176637	−	0.984276i	$-0.443478\pi$
$313$	−5.67434	−	2.06529i	−0.320733	−	0.116737i	−0.497369	+	0.867539i	$0.665701\pi$
$314$	−22.1274	−	8.05371i	−1.24872	−	0.454497i
$315$		0			0
$316$	−9.27896	−	16.0716i	−0.521982	−	0.904100i
$317$	−2.75679	−	15.6346i	−0.154837	−	0.878124i	−0.958935	−	0.283627i	$-0.908462\pi$
$317$	−2.75679	−	15.6346i	−0.154837	−	0.878124i	0.804098	−	0.594497i	$-0.202649\pi$
$318$		0			0
$319$	−6.88249	+	5.77509i	−0.385345	+	0.323343i
$320$	−1.50722	+	8.54788i	−0.0842563	+	0.477841i
$321$		0			0
$322$	−24.2647			−1.35222
$323$	−0.150137	+	0.0793824i	−0.00835387	+	0.00441695i
$324$		0			0
$325$	2.78073	−	1.01210i	0.154247	−	0.0561415i
$326$	−0.195463	+	1.10853i	−0.0108257	+	0.0613956i
$327$		0			0
$328$	−1.62573	−	1.36415i	−0.0897657	−	0.0753224i
$329$	−4.30396	−	24.4090i	−0.237285	−	1.34571i
$330$		0			0
$331$	7.08478	−	12.2712i	0.389414	−	0.674486i	−0.602956	−	0.797774i	$-0.706011\pi$
$331$	7.08478	−	12.2712i	0.389414	−	0.674486i	0.992371	+	0.123288i	$0.0393440\pi$
$332$	−18.8352	−	6.85544i	−1.03371	−	0.376241i
$333$		0			0
$334$	22.3958	−	38.7907i	1.22544	−	2.12253i
$335$	−4.67441	−	8.09631i	−0.255390	−	0.442349i
$336$		0			0
$337$	−1.64694	−	1.38195i	−0.0897147	−	0.0752796i	0.596827	−	0.802370i	$-0.296428\pi$
$337$	−1.64694	−	1.38195i	−0.0897147	−	0.0752796i	−0.686542	+	0.727090i	$0.740872\pi$
$338$	−6.57117	+	5.51387i	−0.357425	+	0.299915i
$339$		0			0
$340$	0.0764078	−	0.0278102i	0.00414380	−	0.00150822i
$341$	9.03266			0.489146
$342$		0			0
$343$	−13.7245			−0.741051
$344$	0.818115	−	0.297770i	0.0441098	−	0.0160547i
$345$		0			0
$346$	17.7415	−	14.8869i	0.953791	−	0.800326i
$347$	8.46670	+	7.10441i	0.454516	+	0.381385i	0.841109	−	0.540866i	$-0.181903\pi$
$347$	8.46670	+	7.10441i	0.454516	+	0.381385i	−0.386592	+	0.922251i	$0.626348\pi$
$348$		0			0
$349$	−17.6725	−	30.6097i	−0.945989	−	1.63850i	−0.753759	−	0.657151i	$-0.771762\pi$
$349$	−17.6725	−	30.6097i	−0.945989	−	1.63850i	−0.192229	−	0.981350i	$-0.561572\pi$
$350$	−3.12560	+	5.41370i	−0.167070	+	0.289374i
$351$		0			0
$352$	−7.30524	−	2.65889i	−0.389371	−	0.141719i
$353$	11.0952	−	19.2174i	0.590538	−	1.02284i	−0.403622	−	0.914926i	$-0.632249\pi$
$353$	11.0952	−	19.2174i	0.590538	−	1.02284i	0.994160	−	0.107916i	$-0.0344176\pi$
$354$		0			0
$355$	−2.18613	−	12.3981i	−0.116028	−	0.658025i
$356$	13.9833	+	11.7334i	0.741115	+	0.621869i
$357$		0			0
$358$	−2.09441	+	11.8780i	−0.110693	+	0.627770i
$359$	−8.93517	+	3.25214i	−0.471580	+	0.171641i	−0.566868	−	0.823809i	$-0.691845\pi$
$359$	−8.93517	+	3.25214i	−0.471580	+	0.171641i	0.0952879	+	0.995450i	$0.469623\pi$
$360$		0			0
$361$	18.2881	−	5.15215i	0.962533	−	0.271166i
$362$	−12.4892			−0.656419
$363$		0			0
$364$	−3.31603	+	18.8061i	−0.173807	+	0.985709i
$365$	0.687230	−	0.576655i	0.0359713	−	0.0301835i
$366$		0			0
$367$	−0.379110	−	2.15004i	−0.0197894	−	0.112231i	0.973313	−	0.229482i	$-0.0737031\pi$
$367$	−0.379110	−	2.15004i	−0.0197894	−	0.112231i	−0.993102	+	0.117250i	$0.962592\pi$
$368$	−7.41107	−	12.8363i	−0.386328	−	0.669141i
$369$		0			0
$370$	2.12271	+	0.772603i	0.110354	+	0.0401657i
$371$	17.6079	+	6.40877i	0.914159	+	0.332727i
$372$		0			0
$373$	6.17035	+	10.6874i	0.319488	+	0.553370i	0.980381	−	0.197110i	$-0.0631556\pi$
$373$	6.17035	+	10.6874i	0.319488	+	0.553370i	−0.660893	+	0.750480i	$0.729822\pi$
$374$	0.0131741	+	0.0747143i	0.000681219	+	0.00386338i
$375$		0			0
$376$	−1.07921	+	0.905566i	−0.0556561	+	0.0467010i
$377$	−4.79319	+	27.1835i	−0.246862	+	1.40002i
$378$		0			0
$379$	−18.5014			−0.950352			−0.475176	−	0.879891i	$-0.657616\pi$
$379$	−18.5014			−0.950352			−0.475176	+	0.879891i	$0.657616\pi$
$380$	−9.01115	+	1.24508i	−0.462262	+	0.0638714i
$381$		0			0
$382$	−35.4558	+	12.9048i	−1.81407	+	0.660269i
$383$	1.98517	−	11.2585i	0.101438	−	0.575282i	−0.891146	−	0.453717i	$-0.850098\pi$
$383$	1.98517	−	11.2585i	0.101438	−	0.575282i	0.992584	−	0.121565i	$-0.0387912\pi$
$384$		0			0
$385$	−2.28155	−	1.91444i	−0.116278	−	0.0975691i
$386$	−8.39246	−	47.5960i	−0.427165	−	2.42257i
$387$		0			0
$388$	−8.12680	+	14.0760i	−0.412576	+	0.714602i
$389$	11.7685	+	4.28337i	0.596684	+	0.217175i	0.622667	−	0.782487i	$-0.286049\pi$
$389$	11.7685	+	4.28337i	0.596684	+	0.217175i	−0.0259826	+	0.999662i	$0.508271\pi$
$390$		0			0
$391$	−0.0756176	+	0.130974i	−0.00382415	+	0.00662361i
$392$	−0.225108	−	0.389899i	−0.0113697	−	0.0196929i
$393$		0			0
$394$	10.3783	+	8.70843i	0.522851	+	0.438724i
$395$	6.81198	−	5.71593i	0.342748	−	0.287600i
$396$		0			0
$397$	−11.0417	+	4.01886i	−0.554168	+	0.201701i	−0.603898	−	0.797062i	$-0.706386\pi$
$397$	−11.0417	+	4.01886i	−0.554168	+	0.201701i	0.0497292	+	0.998763i	$0.484164\pi$
$398$	6.38602			0.320102
$399$		0			0
$400$	−3.81856			−0.190928
$401$	−13.7588	+	5.00780i	−0.687083	+	0.250078i	−0.661886	−	0.749605i	$-0.730244\pi$
$401$	−13.7588	+	5.00780i	−0.687083	+	0.250078i	−0.0251970	+	0.999683i	$0.508021\pi$
$402$		0			0
$403$	21.2585	−	17.8380i	1.05896	−	0.888573i
$404$	4.86582	+	4.08290i	0.242083	+	0.203132i
$405$		0			0
$406$	−29.1551	−	50.4980i	−1.44694	−	2.50618i
$407$	−0.538130	+	0.932068i	−0.0266741	+	0.0462009i
$408$		0			0
$409$	−11.9790	−	4.36001i	−0.592324	−	0.215588i	0.0284271	−	0.999596i	$-0.490950\pi$
$409$	−11.9790	−	4.36001i	−0.592324	−	0.215588i	−0.620751	+	0.784007i	$0.713172\pi$
$410$	12.2052	−	21.1400i	0.602771	−	1.04403i
$411$		0			0
$412$	−0.119073	−	0.675295i	−0.00586630	−	0.0332694i
$413$	−6.57244	−	5.51494i	−0.323409	−	0.271372i
$414$		0			0
$415$	1.66780	−	9.45856i	0.0818690	−	0.464302i
$416$	−22.4438	+	8.16889i	−1.10040	+	0.400513i
$417$		0			0
$418$	0.315930	−	8.48176i	0.0154527	−	0.414856i
$419$	−2.84601			−0.139037			−0.0695184	−	0.997581i	$-0.522146\pi$
$419$	−2.84601			−0.139037			−0.0695184	+	0.997581i	$0.522146\pi$
$420$		0			0
$421$	1.93626	−	10.9811i	0.0943677	−	0.535186i	−0.900572	−	0.434708i	$-0.856852\pi$
$421$	1.93626	−	10.9811i	0.0943677	−	0.535186i	0.994939	−	0.100478i	$-0.0320372\pi$
$422$	−17.7444	+	14.8893i	−0.863785	+	0.724802i
$423$		0			0
$424$	−0.184947	−	1.04889i	−0.00898182	−	0.0509384i
$425$	0.0194810	+	0.0337421i	0.000944969	+	0.00163673i
$426$		0			0
$427$	29.1448	+	10.6078i	1.41041	+	0.513349i
$428$	−25.0770	−	9.12728i	−1.21214	−	0.441184i
$429$		0			0
$430$	5.00702	+	8.67242i	0.241460	+	0.418221i
$431$	2.59366	+	14.7094i	0.124932	+	0.708525i	0.981348	+	0.192239i	$0.0615747\pi$
$431$	2.59366	+	14.7094i	0.124932	+	0.708525i	−0.856416	+	0.516286i	$0.827314\pi$
$432$		0			0
$433$	−29.6894	+	24.9123i	−1.42678	+	1.19721i	−0.479195	+	0.877708i	$0.659071\pi$
$433$	−29.6894	+	24.9123i	−1.42678	+	1.19721i	−0.947585	+	0.319503i	$0.896484\pi$
$434$	−10.1798	+	57.7323i	−0.488645	+	2.77124i
$435$		0			0
$436$	−31.8074			−1.52330
$437$	11.3506	−	12.5473i	0.542971	−	0.600218i
$438$		0			0
$439$	29.5331	−	10.7492i	1.40954	−	0.513030i	0.478544	−	0.878064i	$-0.341165\pi$
$439$	29.5331	−	10.7492i	1.40954	−	0.513030i	0.930994	+	0.365034i	$0.118943\pi$
$440$	−0.0293968	+	0.166717i	−0.00140144	+	0.00794794i
$441$		0			0
$442$	0.178554	+	0.149824i	0.00849293	+	0.00712641i
$443$	−1.84950	−	10.4890i	−0.0878722	−	0.498348i	−0.996700	−	0.0811761i	$-0.974132\pi$
$443$	−1.84950	−	10.4890i	−0.0878722	−	0.498348i	0.908828	−	0.417172i	$-0.136979\pi$
$444$		0			0
$445$	−4.37337	+	7.57490i	−0.207318	+	0.359085i
$446$	14.2748	+	5.19559i	0.675930	+	0.246018i
$447$		0			0
$448$	13.4196	−	23.2435i	0.634019	−	1.09815i
$449$	2.05200	+	3.55417i	0.0968399	+	0.167732i	0.910375	−	0.413784i	$-0.135793\pi$
$449$	2.05200	+	3.55417i	0.0968399	+	0.167732i	−0.813535	+	0.581516i	$0.802460\pi$
$450$		0			0
$451$	8.90923	+	7.47573i	0.419519	+	0.352019i
$452$	−4.09871	+	3.43923i	−0.192787	+	0.161768i
$453$		0			0
$454$	−7.98224	+	2.90530i	−0.374625	+	0.136352i
$455$	−9.15035			−0.428975
$456$		0			0
$457$	9.25947			0.433140			0.216570	−	0.976267i	$-0.430513\pi$
$457$	9.25947			0.433140			0.216570	+	0.976267i	$0.430513\pi$
$458$	−42.8873	+	15.6097i	−2.00399	+	0.729394i
$459$		0			0
$460$	−6.20547	+	5.20701i	−0.289332	+	0.242778i
$461$	−5.09121	−	4.27203i	−0.237121	−	0.198968i	0.516482	−	0.856298i	$-0.327241\pi$
$461$	−5.09121	−	4.27203i	−0.237121	−	0.198968i	−0.753603	+	0.657330i	$0.771686\pi$
$462$		0			0
$463$	−11.1474	−	19.3079i	−0.518064	−	0.897313i	−0.999780	−	0.0209853i	$-0.993320\pi$
$463$	−11.1474	−	19.3079i	−0.518064	−	0.897313i	0.481716	−	0.876327i	$-0.340014\pi$
$464$	17.8094	−	30.8469i	0.826783	−	1.43203i
$465$		0			0
$466$	−20.8566	−	7.59118i	−0.966163	−	0.351655i
$467$	−7.73697	+	13.4008i	−0.358024	+	0.620116i	−0.987631	−	0.156798i	$-0.949883\pi$
$467$	−7.73697	+	13.4008i	−0.358024	+	0.620116i	0.629606	+	0.776914i	$0.283216\pi$
$468$		0			0
$469$	5.01985	+	28.4690i	0.231795	+	1.31458i
$470$	−12.4133	−	10.4160i	−0.572583	−	0.480454i
$471$		0			0
$472$	−0.0846832	+	0.480262i	−0.00389786	+	0.0221059i
$473$	−4.48340	+	1.63182i	−0.206147	+	0.0750313i
$474$		0			0
$475$	−1.33733	−	4.14868i	−0.0613611	−	0.190354i
$476$	−0.251429			−0.0115242
$477$		0			0
$478$	0.956820	−	5.42640i	0.0437639	−	0.248198i
$479$	−24.6710	+	20.7014i	−1.12725	+	0.945872i	−0.998948	−	0.0458635i	$-0.985396\pi$
$479$	−24.6710	+	20.7014i	−1.12725	+	0.945872i	−0.128299	+	0.991736i	$0.540952\pi$
$480$		0			0
$481$	0.574182	+	3.25635i	0.0261805	+	0.148477i
$482$	−11.2746	−	19.5281i	−0.513543	−	0.889482i
$483$		0			0
$484$	19.7525	+	7.18934i	0.897843	+	0.326788i
$485$	−7.31855	−	2.66374i	−0.332318	−	0.120954i
$486$		0			0
$487$	1.82569	+	3.16219i	0.0827301	+	0.143293i	0.904422	−	0.426640i	$-0.140303\pi$
$487$	1.82569	+	3.16219i	0.0827301	+	0.143293i	−0.821692	+	0.569932i	$0.806969\pi$
$488$	−0.306125	−	1.73612i	−0.0138576	−	0.0785906i
$489$		0			0
$490$	3.96694	−	3.32866i	0.179208	−	0.150374i
$491$	−0.789859	+	4.47952i	−0.0356459	+	0.202158i	−0.997430	−	0.0716523i	$-0.977173\pi$
$491$	−0.789859	+	4.47952i	−0.0356459	+	0.202158i	0.961784	+	0.273810i	$0.0882839\pi$
$492$		0			0
$493$	−0.363431			−0.0163681
$494$	−16.0065	−	20.5858i	−0.720166	−	0.926201i
$495$		0			0
$496$	−33.6504	+	12.2477i	−1.51095	+	0.549940i
$497$	−6.75989	+	38.3372i	−0.303222	+	1.71966i
$498$		0			0
$499$	−16.7177	−	14.0278i	−0.748387	−	0.627972i	0.186689	−	0.982419i	$-0.440224\pi$
$499$	−16.7177	−	14.0278i	−0.748387	−	0.627972i	−0.935076	+	0.354448i	$0.884669\pi$
$500$	0.362393	+	2.05523i	0.0162067	+	0.0919129i
$501$		0			0
$502$	−27.6641	+	47.9157i	−1.23471	+	2.13858i
$503$	−23.2469	−	8.46117i	−1.03653	−	0.377265i	−0.232964	−	0.972485i	$-0.574842\pi$
$503$	−23.2469	−	8.46117i	−1.03653	−	0.377265i	−0.803562	+	0.595221i	$0.797065\pi$
$504$		0			0
$505$	−1.52181	+	2.63586i	−0.0677199	+	0.117294i
$506$	−3.77912	−	6.54563i	−0.168003	−	0.290989i
$507$		0			0
$508$	−24.7415	−	20.7606i	−1.09773	−	0.921101i
$509$	13.2902	−	11.1518i	0.589078	−	0.494295i	−0.298836	−	0.954305i	$-0.596598\pi$
$509$	13.2902	−	11.1518i	0.589078	−	0.494295i	0.887914	+	0.460009i	$0.152154\pi$
$510$		0			0
$511$	−2.60674	+	0.948777i	−0.115316	+	0.0419714i
$512$	32.1626			1.42140
$513$		0			0
$514$	40.9637			1.80683
$515$	0.308758	−	0.112379i	0.0136055	−	0.00495200i
$516$		0			0
$517$	5.91424	−	4.96264i	0.260108	−	0.218257i
$518$	−5.35085	−	4.48990i	−0.235103	−	0.197275i
$519$		0			0
$520$	0.260053	+	0.450425i	0.0114041	+	0.0197524i
$521$	0.228337	−	0.395492i	0.0100036	−	0.0173268i	−0.860980	−	0.508638i	$-0.830149\pi$
$521$	0.228337	−	0.395492i	0.0100036	−	0.0173268i	0.870984	+	0.491312i	$0.163482\pi$
$522$		0			0
$523$	35.5171	+	12.9272i	1.55305	+	0.565265i	0.969132	−	0.246544i	$-0.0792951\pi$
$523$	35.5171	+	12.9272i	1.55305	+	0.565265i	0.583922	+	0.811810i	$0.301517\pi$
$524$	0.878815	−	1.52215i	0.0383912	−	0.0664955i
$525$		0			0
$526$	−3.35687	−	19.0377i	−0.146366	−	0.830085i
$527$	0.279898	+	0.234863i	0.0121926	+	0.0102308i
$528$		0			0
$529$	−1.37758	+	7.81265i	−0.0598949	+	0.339681i
$530$	11.5118	−	4.18996i	0.500041	−	0.182000i
$531$		0			0
$532$	27.5004	+	5.91224i	1.19229	+	0.256328i
$533$	35.7313			1.54769
$534$		0			0
$535$	2.22050	−	12.5931i	0.0960004	−	0.544445i
$536$	1.25872	−	1.05619i	0.0543684	−	0.0456205i
$537$		0			0
$538$	−1.60590	−	9.10750i	−0.0692352	−	0.392652i
$539$	1.23363	+	2.13671i	0.0531361	+	0.0920344i
$540$		0			0
$541$	19.8556	+	7.22684i	0.853658	+	0.310706i	0.731531	−	0.681808i	$-0.238806\pi$
$541$	19.8556	+	7.22684i	0.853658	+	0.310706i	0.122127	+	0.992514i	$0.461028\pi$
$542$	42.0515	+	15.3055i	1.80627	+	0.657428i
$543$		0			0
$544$	−0.157235	−	0.272339i	−0.00674140	−	0.0116765i
$545$	−2.64660	−	15.0096i	−0.113368	−	0.642941i
$546$		0			0
$547$	−9.60806	+	8.06212i	−0.410811	+	0.344711i	−0.824655	−	0.565637i	$-0.808631\pi$
$547$	−9.60806	+	8.06212i	−0.410811	+	0.344711i	0.413843	+	0.910348i	$0.364186\pi$
$548$	1.83871	−	10.4278i	0.0785458	−	0.445455i
$549$		0			0
$550$	−1.94720			−0.0830288
$551$	39.7508	+	8.54591i	1.69344	+	0.364068i
$552$		0			0
$553$	−25.8386	+	9.40449i	−1.09877	+	0.399920i
$554$	8.26870	−	46.8941i	0.351303	−	1.99234i
$555$		0			0
$556$	4.36504	+	3.66271i	0.185119	+	0.155333i
$557$	5.56111	+	31.5386i	0.235632	+	1.33633i	0.841279	+	0.540601i	$0.181803\pi$
$557$	5.56111	+	31.5386i	0.235632	+	1.33633i	−0.605647	+	0.795733i	$0.707086\pi$
$558$		0			0
$559$	−7.32916	+	12.6945i	−0.309990	+	0.536919i
$560$	11.0956	+	4.03846i	0.468874	+	0.170656i
$561$		0			0
$562$	10.4345	−	18.0731i	0.440153	−	0.762368i
$563$	9.79034	+	16.9574i	0.412614	+	0.714668i	0.995175	−	0.0981190i	$-0.0312826\pi$
$563$	9.79034	+	16.9574i	0.412614	+	0.714668i	−0.582561	+	0.812787i	$0.697949\pi$
$564$		0			0
$565$	−1.96398	−	1.64798i	−0.0826254	−	0.0693309i
$566$	−47.8113	+	40.1184i	−2.00966	+	1.68630i
$567$		0			0
$568$	2.07926	−	0.756789i	0.0872439	−	0.0317542i
$569$	18.6525			0.781953			0.390977	−	0.920401i	$-0.372137\pi$
$569$	18.6525			0.781953			0.390977	+	0.920401i	$0.372137\pi$
$570$		0			0
$571$	−0.460181			−0.0192580			−0.00962899	−	0.999954i	$-0.503065\pi$
$571$	−0.460181			−0.0192580			−0.00962899	+	0.999954i	$0.503065\pi$
$572$	−5.58960	+	2.03445i	−0.233713	+	0.0850645i
$573$		0			0
$574$	−57.8219	+	48.5184i	−2.41344	+	2.02512i
$575$	−2.97348	−	2.49504i	−0.124003	−	0.104051i
$576$		0			0
$577$	−5.87392	−	10.1739i	−0.244534	−	0.423546i	0.717466	−	0.696593i	$-0.245302\pi$
$577$	−5.87392	−	10.1739i	−0.244534	−	0.423546i	−0.962001	+	0.273047i	$0.911968\pi$
$578$	17.1822	−	29.7605i	0.714686	−	1.23787i
$579$		0			0
$580$	−18.2926	−	6.65797i	−0.759560	−	0.276457i
$581$	−14.8494	+	25.7198i	−0.616055	+	1.06704i
$582$		0			0
$583$	1.01354	+	5.74806i	0.0419765	+	0.238060i
$584$	0.120787	+	0.101352i	0.00499821	+	0.00419399i
$585$		0			0
$586$	−2.23304	+	12.6642i	−0.0922461	+	0.523154i
$587$	−4.60486	+	1.67603i	−0.190063	+	0.0691773i	−0.435298	−	0.900286i	$-0.643357\pi$
$587$	−4.60486	+	1.67603i	−0.190063	+	0.0691773i	0.245235	+	0.969464i	$0.421135\pi$
$588$		0			0
$589$	−25.0916	−	32.2701i	−1.03388	−	1.32967i
$590$	−5.60929			−0.230931
$591$		0			0
$592$	0.740928	−	4.20201i	0.0304519	−	0.172702i
$593$	14.1700	−	11.8900i	0.581892	−	0.488265i	−0.303676	−	0.952775i	$-0.598214\pi$
$593$	14.1700	−	11.8900i	0.581892	−	0.488265i	0.885568	+	0.464510i	$0.153770\pi$
$594$		0			0
$595$	−0.0209207	−	0.118647i	−0.000857665	−	0.00486406i
$596$	−6.93456	−	12.0110i	−0.284051	−	0.491990i
$597$		0			0
$598$	−21.8207	−	7.94210i	−0.892316	−	0.324777i
$599$	−20.1336	−	7.32805i	−0.822638	−	0.299416i	−0.103804	−	0.994598i	$-0.533102\pi$
$599$	−20.1336	−	7.32805i	−0.822638	−	0.299416i	−0.718834	+	0.695182i	$0.755324\pi$
$600$		0			0
$601$	−15.0195	−	26.0146i	−0.612659	−	1.06116i	−0.990790	−	0.135404i	$-0.956767\pi$
$601$	−15.0195	−	26.0146i	−0.612659	−	1.06116i	0.378132	−	0.925752i	$-0.376567\pi$
$602$	−5.37705	−	30.4948i	−0.219152	−	1.24287i
$603$		0			0
$604$	−8.29813	+	6.96296i	−0.337646	+	0.283319i
$605$	−1.74903	+	9.91925i	−0.0711082	+	0.403275i
$606$		0			0
$607$	29.3882			1.19283			0.596415	−	0.802676i	$-0.296591\pi$
$607$	29.3882			1.19283			0.596415	+	0.802676i	$0.296591\pi$
$608$	10.7939	+	33.4848i	0.437750	+	1.35799i
$609$		0			0
$610$	19.0544	−	6.93524i	0.771491	−	0.280800i
$611$	4.11887	−	23.3593i	0.166632	−	0.945015i
$612$		0			0
$613$	−4.22183	−	3.54254i	−0.170518	−	0.143082i	0.553535	−	0.832826i	$-0.313279\pi$
$613$	−4.22183	−	3.54254i	−0.170518	−	0.143082i	−0.724053	+	0.689744i	$0.757723\pi$
$614$	−2.06644	−	11.7194i	−0.0833948	−	0.472955i
$615$		0			0
$616$	0.261736	−	0.453340i	0.0105456	−	0.0182656i
$617$	43.1381	+	15.7010i	1.73667	+	0.632098i	0.999069	−	0.0431340i	$-0.0137342\pi$
$617$	43.1381	+	15.7010i	1.73667	+	0.632098i	0.737606	+	0.675232i	$0.235956\pi$
$618$		0			0
$619$	0.239303	−	0.414484i	0.00961839	−	0.0166595i	−0.861176	−	0.508307i	$-0.830272\pi$
$619$	0.239303	−	0.414484i	0.00961839	−	0.0166595i	0.870795	+	0.491647i	$0.163605\pi$
$620$	9.78553	+	16.9490i	0.392996	+	0.680690i
$621$		0			0
$622$	39.3179	+	32.9916i	1.57650	+	1.32284i
$623$	20.7188	−	17.3851i	0.830081	−	0.696521i
$624$		0			0
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	12.2075			0.487912
$627$		0			0
$628$	24.3083			0.970008
$629$	−0.0409104	+	0.0148902i	−0.00163120	+	0.000593710i
$630$		0			0
$631$	12.9110	−	10.8336i	0.513980	−	0.431281i	−0.348547	−	0.937291i	$-0.613325\pi$
$631$	12.9110	−	10.8336i	0.513980	−	0.431281i	0.862527	+	0.506011i	$0.168880\pi$
$632$	1.19727	+	1.00463i	0.0476248	+	0.0399620i
$633$		0			0
$634$	16.0473	+	27.7948i	0.637321	+	1.10387i
$635$	7.73805	−	13.4027i	0.307075	−	0.531870i
$636$		0			0
$637$	7.12299	+	2.59256i	0.282223	+	0.102721i
$638$	9.08156	−	15.7297i	0.359543	−	0.622746i
$639$		0			0
$640$	−0.243932	−	1.38340i	−0.00964224	−	0.0546839i
$641$	−17.5433	−	14.7206i	−0.692920	−	0.581429i	0.226830	−	0.973934i	$-0.427164\pi$
$641$	−17.5433	−	14.7206i	−0.692920	−	0.581429i	−0.919750	+	0.392506i	$0.871608\pi$
$642$		0			0
$643$	−1.49019	+	8.45131i	−0.0587675	+	0.333287i	−0.999990	−	0.00450051i	$-0.998567\pi$
$643$	−1.49019	+	8.45131i	−0.0587675	+	0.333287i	0.941222	+	0.337788i	$0.109679\pi$
$644$	23.5381	−	8.56716i	0.927530	−	0.337593i
$645$		0			0
$646$	0.230328	−	0.254613i	0.00906215	−	0.0100176i
$647$	27.2647			1.07188			0.535942	−	0.844255i	$-0.319957\pi$
$647$	27.2647			1.07188			0.535942	+	0.844255i	$0.319957\pi$
$648$		0			0
$649$	0.464077	−	2.63191i	0.0182166	−	0.103312i
$650$	−4.58276	+	3.84539i	−0.179750	+	0.150829i
$651$		0			0
$652$	−0.201779	−	1.14435i	−0.00790228	−	0.0448160i
$653$	−13.1299	−	22.7417i	−0.513813	−	0.889950i	−0.999872	−	0.0160238i	$-0.994899\pi$
$653$	−13.1299	−	22.7417i	−0.513813	−	0.889950i	0.486059	−	0.873926i	$-0.338434\pi$
$654$		0			0
$655$	0.791413	+	0.288051i	0.0309231	+	0.0112551i
$656$	−43.3272	−	15.7698i	−1.69164	−	0.615708i
$657$		0			0
$658$	25.0534	+	43.3938i	0.976685	+	1.69167i
$659$	3.99590	+	22.6619i	0.155658	+	0.882781i	0.958182	+	0.286160i	$0.0923790\pi$
$659$	3.99590	+	22.6619i	0.155658	+	0.882781i	−0.802524	+	0.596620i	$0.796510\pi$
$660$		0			0
$661$	23.4408	−	19.6692i	0.911742	−	0.765042i	−0.0607080	−	0.998156i	$-0.519336\pi$
$661$	23.4408	−	19.6692i	0.911742	−	0.765042i	0.972450	+	0.233114i	$0.0748914\pi$
$662$	−4.97423	+	28.2102i	−0.193329	+	1.09642i
$663$		0			0
$664$	1.68807			0.0655100
$665$	−0.501701	+	13.4691i	−0.0194551	+	0.522311i
$666$		0			0
$667$	34.0234	−	12.3835i	1.31739	−	0.479491i
$668$	−8.02930	+	45.5364i	−0.310663	+	1.76186i
$669$		0			0
$670$	14.4780	+	12.1485i	0.559335	+	0.469338i
$671$	1.67761	+	9.51422i	0.0647636	+	0.367292i
$672$		0			0
$673$	18.9334	−	32.7936i	0.729828	−	1.26410i	−0.227128	−	0.973865i	$-0.572934\pi$
$673$	18.9334	−	32.7936i	0.729828	−	1.26410i	0.956956	−	0.290234i	$-0.0937331\pi$
$674$	4.08422	+	1.48654i	0.157318	+	0.0572592i
$675$		0			0
$676$	4.42761	−	7.66885i	0.170293	−	0.294956i
$677$	−21.8471	−	37.8403i	−0.839654	−	1.45432i	−0.890184	−	0.455600i	$-0.849425\pi$
$677$	−21.8471	−	37.8403i	−0.839654	−	1.45432i	0.0505308	−	0.998723i	$-0.483909\pi$
$678$		0			0
$679$	18.4484	+	15.4800i	0.707983	+	0.594068i
$680$	−0.00524583	+	0.00440177i	−0.000201168	+	0.000168800i
$681$		0			0
$682$	−17.1593	+	6.24549i	−0.657065	+	0.239152i
$683$	−15.0878			−0.577320			−0.288660	−	0.957432i	$-0.593210\pi$
$683$	−15.0878			−0.577320			−0.288660	+	0.957432i	$0.593210\pi$
$684$		0			0
$685$	5.07379			0.193860
$686$	26.0724	−	9.48956i	0.995447	−	0.362313i
$687$		0			0
$688$	14.4899	−	12.1584i	0.552421	−	0.463536i
$689$	13.7368	+	11.5266i	0.523331	+	0.439127i
$690$		0			0
$691$	−5.36034	−	9.28438i	−0.203917	−	0.353194i	0.745870	−	0.666091i	$-0.232034\pi$
$691$	−5.36034	−	9.28438i	−0.203917	−	0.353194i	−0.949787	+	0.312897i	$0.898701\pi$
$692$	−11.9541	+	20.7052i	−0.454428	+	0.787093i
$693$		0			0
$694$	−20.9964	−	7.64207i	−0.797013	−	0.290089i
$695$	−1.36520	+	2.36459i	−0.0517848	+	0.0896939i
$696$		0			0
$697$	0.0816935	+	0.463307i	0.00309436	+	0.0175490i
$698$	54.7371	+	45.9299i	2.07183	+	1.73847i
$699$		0			0
$700$	1.12058	−	6.35515i	0.0423541	−	0.240202i
$701$	23.0611	−	8.39354i	0.871005	−	0.317020i	0.132431	−	0.991192i	$-0.457722\pi$
$701$	23.0611	−	8.39354i	0.871005	−	0.317020i	0.738574	+	0.674172i	$0.235500\pi$
$702$		0			0
$703$	4.82476	−	0.666644i	0.181969	−	0.0251429i
$704$	8.36023			0.315088
$705$		0			0
$706$	−7.78994	+	44.1790i	−0.293178	+	1.66270i
$707$	7.20958	−	6.04956i	0.271144	−	0.227517i
$708$		0			0
$709$	−7.43295	−	42.1543i	−0.279150	−	1.58314i	−0.725462	−	0.688262i	$-0.758374\pi$
$709$	−7.43295	−	42.1543i	−0.279150	−	1.58314i	0.446312	−	0.894878i	$-0.352737\pi$
$710$	12.7255	+	22.0412i	0.477579	+	0.827191i
$711$		0			0
$712$	−1.44461	−	0.525795i	−0.0541391	−	0.0197050i
$713$	−34.2059	−	12.4499i	−1.28102	−	0.466254i
$714$		0			0
$715$	−1.42513	−	2.46840i	−0.0532969	−	0.0923129i
$716$	−2.16208	−	12.2618i	−0.0808007	−	0.458244i
$717$		0			0
$718$	14.7255	−	12.3562i	0.549551	−	0.461128i
$719$	−3.69371	+	20.9481i	−0.137752	+	0.781231i	0.835152	+	0.550020i	$0.185380\pi$
$719$	−3.69371	+	20.9481i	−0.137752	+	0.781231i	−0.972904	+	0.231211i	$0.925731\pi$
$720$		0			0
$721$	−1.01601			−0.0378381
$722$	−31.1796	+	22.4326i	−1.16038	+	0.834854i
$723$		0			0
$724$	12.1152	−	4.40959i	0.450259	−	0.163881i
$725$	1.61976	−	9.18612i	0.0601564	−	0.341164i
$726$		0			0
$727$	−8.06976	−	6.77133i	−0.299291	−	0.251135i	0.480758	−	0.876853i	$-0.340361\pi$
$727$	−8.06976	−	6.77133i	−0.299291	−	0.251135i	−0.780049	+	0.625718i	$0.784806\pi$
$728$	−0.279271	−	1.58383i	−0.0103505	−	0.0587005i
$729$		0			0
$730$	−0.906813	+	1.57065i	−0.0335626	+	0.0581322i
$731$	−0.181359	−	0.0660091i	−0.00670779	−	0.00244144i
$732$		0			0
$733$	12.5446	−	21.7279i	0.463346	−	0.802538i	−0.535779	−	0.844358i	$-0.679982\pi$
$733$	12.5446	−	21.7279i	0.463346	−	0.802538i	0.999125	+	0.0418196i	$0.0133155\pi$
$734$	2.20681	+	3.82230i	0.0814548	+	0.141084i
$735$		0			0
$736$	23.9995	+	20.1380i	0.884634	+	0.742296i
$737$	−6.89797	+	5.78809i	−0.254090	+	0.213207i
$738$		0			0
$739$	−26.7511	+	9.73660i	−0.984054	+	0.358166i	−0.783415	−	0.621499i	$-0.786524\pi$
$739$	−26.7511	+	9.73660i	−0.984054	+	0.358166i	−0.200639	+	0.979665i	$0.564302\pi$
$740$	−2.33193			−0.0857235
$741$		0			0
$742$	−37.8811			−1.39066
$743$	−9.54830	+	3.47530i	−0.350293	+	0.127496i	−0.511173	−	0.859478i	$-0.670789\pi$
$743$	−9.54830	+	3.47530i	−0.350293	+	0.127496i	0.160880	+	0.986974i	$0.448567\pi$
$744$		0			0
$745$	5.09088	−	4.27176i	0.186515	−	0.156505i
$746$	−19.1114	−	16.0364i	−0.699718	−	0.587133i
$747$		0			0
$748$	−0.0391591	−	0.0678256i	−0.00143180	−	0.00247995i
$749$	−19.7703	+	34.2432i	−0.722392	+	1.25122i
$750$		0			0
$751$	24.1407	+	8.78648i	0.880905	+	0.320623i	0.742575	−	0.669763i	$-0.233604\pi$
$751$	24.1407	+	8.78648i	0.880905	+	0.320623i	0.138330	+	0.990386i	$0.455826\pi$
$752$	−15.3040	+	26.5072i	−0.558078	+	0.966620i
$753$		0			0
$754$	−9.68999	−	54.9547i	−0.352889	−	2.00133i
$755$	−3.97622	−	3.33644i	−0.144709	−	0.121426i
$756$		0			0
$757$	−5.48348	+	31.0983i	−0.199300	+	1.13029i	0.706860	+	0.707354i	$0.250111\pi$
$757$	−5.48348	+	31.0983i	−0.199300	+	1.13029i	−0.906160	+	0.422935i	$0.861000\pi$
$758$	35.1471	−	12.7925i	1.27660	−	0.464644i
$759$		0			0
$760$	0.677275	−	0.358097i	0.0245674	−	0.0129895i
$761$	3.42183			0.124041			0.0620207	−	0.998075i	$-0.480246\pi$
$761$	3.42183			0.124041			0.0620207	+	0.998075i	$0.480246\pi$
$762$		0			0
$763$	−8.18375	+	46.4123i	−0.296272	+	1.68024i
$764$	29.8377	−	25.0368i	1.07949	−	0.905801i
$765$		0			0
$766$	4.01327	+	22.7604i	0.145005	+	0.822365i
$767$	−4.10537	−	7.11071i	−0.148236	−	0.256753i
$768$		0			0
$769$	26.7893	+	9.75052i	0.966048	+	0.351613i	0.776401	−	0.630239i	$-0.217043\pi$
$769$	26.7893	+	9.75052i	0.966048	+	0.351613i	0.189648	+	0.981852i	$0.439265\pi$
$770$	5.65796	+	2.05933i	0.203899	+	0.0742131i
$771$		0			0
$772$	24.9459	+	43.2076i	0.897824	+	1.55508i
$773$	−0.247597	−	1.40419i	−0.00890545	−	0.0505053i	0.980031	−	0.198844i	$-0.0637186\pi$
$773$	−0.247597	−	1.40419i	−0.00890545	−	0.0505053i	−0.988937	+	0.148338i	$0.952608\pi$
$774$		0			0
$775$	−7.18387	+	6.02798i	−0.258052	+	0.216532i
$776$	0.237699	−	1.34806i	0.00853291	−	0.0483925i
$777$		0			0
$778$	−25.3182			−0.907701
$779$	1.95910	−	52.5958i	0.0701920	−	1.88444i
$780$		0			0
$781$	−11.3947	+	4.14732i	−0.407733	+	0.148403i
$782$	0.0530912	−	0.301095i	0.00189854	−	0.0107671i
$783$		0			0
$784$	−7.49302	−	6.28739i	−0.267608	−	0.224550i
$785$	2.02262	+	11.4709i	0.0721906	+	0.409413i
$786$		0			0
$787$	−12.1600	+	21.0617i	−0.433456	+	0.750768i	−0.997168	−	0.0752034i	$-0.976039\pi$
$787$	−12.1600	+	21.0617i	−0.433456	+	0.750768i	0.563712	+	0.825971i	$0.309373\pi$
$788$	−13.1422	−	4.78338i	−0.468172	−	0.170401i
$789$		0			0
$790$	−8.98853	+	15.5686i	−0.319797	+	0.553905i
$791$	3.96386	+	6.86560i	0.140938	+	0.244113i
$792$		0			0
$793$	22.7373	+	19.0788i	0.807424	+	0.677509i
$794$	18.1972	−	15.2693i	0.645794	−	0.541885i
$795$		0			0
$796$	−6.19479	+	2.25472i	−0.219569	+	0.0799164i
$797$	−33.5714			−1.18916			−0.594580	−	0.804037i	$-0.702681\pi$
$797$	−33.5714			−1.18916			−0.594580	+	0.804037i	$0.702681\pi$
$798$		0			0
$799$	0.312303			0.0110485
$800$	7.58444	−	2.76051i	0.268150	−	0.0975988i
$801$		0			0
$802$	22.6751	−	19.0266i	0.800684	−	0.671854i
$803$	−0.661932	−	0.555427i	−0.0233591	−	0.0196006i
$804$		0			0
$805$	6.00130	+	10.3945i	0.211518	+	0.366360i
$806$	−28.0509	+	48.5856i	−0.988052	+	1.71136i
$807$		0			0
$808$	−0.502685	−	0.182962i	−0.0176844	−	0.00643659i
$809$	9.12037	−	15.7970i	0.320655	−	0.555391i	−0.659968	−	0.751294i	$-0.729430\pi$
$809$	9.12037	−	15.7970i	0.320655	−	0.555391i	0.980623	+	0.195902i	$0.0627636\pi$
$810$		0			0
$811$	−6.34578	−	35.9887i	−0.222830	−	1.26373i	−0.866790	−	0.498674i	$-0.833820\pi$
$811$	−6.34578	−	35.9887i	−0.222830	−	1.26373i	0.643959	−	0.765060i	$-0.277291\pi$
$812$	46.1114	+	38.6921i	1.61819	+	1.35783i
$813$		0			0
$814$	0.377821	−	2.14273i	0.0132426	−	0.0751026i
$815$	0.523217	−	0.190435i	0.0183275	−	0.00667066i
$816$		0			0
$817$	18.2842	+	11.4844i	0.639682	+	0.401788i
$818$	25.7712			0.901069
$819$		0			0
$820$	−4.37578	+	24.8163i	−0.152809	+	0.866622i
$821$	−8.13847	+	6.82899i	−0.284035	+	0.238333i	−0.773662	−	0.633598i	$-0.781577\pi$
$821$	−8.13847	+	6.82899i	−0.284035	+	0.238333i	0.489628	+	0.871932i	$0.337133\pi$
$822$		0			0
$823$	−6.43574	−	36.4989i	−0.224336	−	1.27227i	−0.863951	−	0.503577i	$-0.832017\pi$
$823$	−6.43574	−	36.4989i	−0.224336	−	1.27227i	0.639615	−	0.768696i	$-0.279094\pi$
$824$	0.0288749	+	0.0500128i	0.00100591	+	0.00174228i
$825$		0			0
$826$	16.2989	+	5.93231i	0.567111	+	0.206411i
$827$	26.1420	+	9.51490i	0.909045	+	0.330865i	0.753871	−	0.657022i	$-0.228184\pi$
$827$	26.1420	+	9.51490i	0.909045	+	0.330865i	0.155174	+	0.987887i	$0.450406\pi$
$828$		0			0
$829$	6.90991	+	11.9683i	0.239991	+	0.415677i	0.960711	−	0.277549i	$-0.0895221\pi$
$829$	6.90991	+	11.9683i	0.239991	+	0.415677i	−0.720720	+	0.693226i	$0.756189\pi$
$830$	3.37165	+	19.1216i	0.117032	+	0.663720i
$831$		0			0
$832$	19.6759	−	16.5100i	0.682139	−	0.572383i
$833$	−0.0173307	+	0.0982871i	−0.000600472	+	0.00340545i
$834$		0			0
$835$	−22.1563			−0.766751
$836$	2.68820	+	8.33932i	0.0929732	+	0.288422i
$837$		0			0
$838$	5.40657	−	1.96783i	0.186767	−	0.0679776i
$839$	1.11616	−	6.33006i	0.0385341	−	0.218538i	−0.959460	−	0.281845i	$-0.909054\pi$
$839$	1.11616	−	6.33006i	0.0385341	−	0.218538i	0.997994	+	0.0633071i	$0.0201648\pi$
$840$		0			0
$841$	44.4370	+	37.2871i	1.53231	+	1.28576i
$842$	3.91439	+	22.1996i	0.134899	+	0.765048i
$843$		0			0
$844$	11.9561	−	20.7085i	0.411545	−	0.712817i
$845$	3.98727	+	1.45125i	0.137166	+	0.0499244i
$846$		0			0
$847$	15.5726	−	26.9726i	0.535081	−	0.926788i
$848$	−11.5699	−	20.0396i	−0.397311	−	0.688163i
$849$		0			0
$850$	−0.0603386	−	0.0506301i	−0.00206960	−	0.00173660i
$851$	3.32254	−	2.78794i	0.113895	−	0.0955695i
$852$		0			0
$853$	−24.8033	+	9.02767i	−0.849250	+	0.309102i	−0.729734	−	0.683731i	$-0.760356\pi$
$853$	−24.8033	+	9.02767i	−0.849250	+	0.309102i	−0.119515	+	0.992832i	$0.538134\pi$
$854$	−62.7009			−2.14558
$855$		0			0
$856$	2.24749			0.0768177
$857$	16.0036	−	5.82483i	0.546672	−	0.198973i	−0.0538950	−	0.998547i	$-0.517164\pi$
$857$	16.0036	−	5.82483i	0.546672	−	0.198973i	0.600567	+	0.799574i	$0.294941\pi$
$858$		0			0
$859$	18.9375	−	15.8905i	0.646140	−	0.542176i	−0.259757	−	0.965674i	$-0.583642\pi$
$859$	18.9375	−	15.8905i	0.646140	−	0.542176i	0.905897	+	0.423498i	$0.139198\pi$
$860$	−7.91907	−	6.64489i	−0.270038	−	0.226589i
$861$		0			0
$862$	−15.0977	−	26.1500i	−0.514230	−	0.890673i
$863$	−0.519450	+	0.899714i	−0.0176823	+	0.0306266i	−0.874731	−	0.484609i	$-0.838962\pi$
$863$	−0.519450	+	0.899714i	−0.0176823	+	0.0306266i	0.857049	+	0.515235i	$0.172295\pi$
$864$		0			0
$865$	−10.7653	−	3.91823i	−0.366030	−	0.133224i
$866$	39.1757	−	67.8542i	1.33124	−	2.30578i
$867$		0			0
$868$	−10.5087	−	59.5978i	−0.356688	−	2.02288i
$869$	−6.56122	−	5.50552i	−0.222574	−	0.186762i
$870$		0			0
$871$	−4.80397	+	27.2447i	−0.162776	+	0.923150i
$872$	2.51722	−	0.916195i	0.0852440	−	0.0310263i
$873$		0			0
$874$	−12.8870	+	31.6842i	−0.435910	+	1.07174i
$875$	3.09218			0.104535
$876$		0			0
$877$	3.68173	−	20.8801i	0.124323	−	0.705071i	−0.857385	−	0.514676i	$-0.827912\pi$
$877$	3.68173	−	20.8801i	0.124323	−	0.705071i	0.981708	−	0.190395i	$-0.0609768\pi$
$878$	−48.6717	+	40.8404i	−1.64259	+	1.37830i
$879$		0			0
$880$	0.638677	+	3.62212i	0.0215298	+	0.122101i
$881$	7.84097	+	13.5810i	0.264169	+	0.457554i	0.967346	−	0.253461i	$-0.0815690\pi$
$881$	7.84097	+	13.5810i	0.264169	+	0.457554i	−0.703176	+	0.711015i	$0.748236\pi$
$882$		0			0
$883$	−18.4562	−	6.71750i	−0.621100	−	0.226062i	0.0122532	−	0.999925i	$-0.496100\pi$
$883$	−18.4562	−	6.71750i	−0.621100	−	0.226062i	−0.633353	+	0.773863i	$0.718322\pi$
$884$	−0.226106	−	0.0822957i	−0.00760476	−	0.00276790i
$885$		0			0
$886$	10.7659	+	18.6472i	0.361689	+	0.626464i
$887$	−4.30310	−	24.4041i	−0.144484	−	0.819408i	−0.967780	−	0.251797i	$-0.918979\pi$
$887$	−4.30310	−	24.4041i	−0.144484	−	0.819408i	0.823296	−	0.567612i	$-0.192133\pi$
$888$		0			0
$889$	−36.6589	+	30.7605i	−1.22950	+	1.03167i
$890$	3.07055	−	17.4139i	0.102925	−	0.583717i
$891$		0			0
$892$	−15.6817			−0.525063
$893$	−34.1586	−	7.34365i	−1.14307	−	0.245746i
$894$		0			0
$895$	5.60632	−	2.04053i	0.187398	−	0.0682075i
$896$	−0.754279	+	4.27773i	−0.0251987	+	0.142909i
$897$		0			0
$898$	−6.35566	−	5.33303i	−0.212091	−	0.177966i
$899$	−15.1899	−	86.1463i	−0.506612	−	2.87314i
$900$		0			0
$901$	−0.118051	+	0.204471i	−0.00393286	+	0.00681191i
$902$	−22.0938	−	8.04150i	−0.735644	−	0.267753i
$903$		0			0
$904$	0.225306	−	0.390241i	0.00749355	−	0.0129792i
$905$	3.08892	+	5.35016i	0.102679	+	0.177845i
$906$		0			0
$907$	−16.3342	−	13.7060i	−0.542368	−	0.455100i	0.329979	−	0.943988i	$-0.392958\pi$
$907$	−16.3342	−	13.7060i	−0.542368	−	0.455100i	−0.872347	+	0.488888i	$0.837403\pi$
$908$	6.71744	−	5.63660i	0.222926	−	0.187057i
$909$		0			0
$910$	17.3829	−	6.32687i	0.576238	−	0.209734i
$911$	34.0175			1.12705			0.563524	−	0.826100i	$-0.309445\pi$
$911$	34.0175			1.12705			0.563524	+	0.826100i	$0.309445\pi$
$912$		0			0
$913$	−9.25091			−0.306160
$914$	−17.5902	+	6.40232i	−0.581833	+	0.211770i
$915$		0			0
$916$	36.0917	−	30.2846i	1.19250	−	1.00063i
$917$	−1.99497	−	1.67397i	−0.0658796	−	0.0552795i
$918$		0			0
$919$	20.8710	+	36.1496i	0.688470	+	1.19246i	0.972333	+	0.233600i	$0.0750505\pi$
$919$	20.8710	+	36.1496i	0.688470	+	1.19246i	−0.283863	+	0.958865i	$0.591616\pi$
$920$	0.341114	−	0.590826i	0.0112462	−	0.0194790i
$921$		0			0
$922$	12.6256	+	4.59534i	0.415802	+	0.151340i
$923$	−18.6272	+	32.2633i	−0.613123	+	1.06196i
$924$		0			0
$925$	−0.194033	−	1.10042i	−0.00637977	−	0.0361815i
$926$	34.5268	+	28.9715i	1.13462	+	0.952061i
$927$		0			0
$928$	−13.0734	+	74.1429i	−0.429155	+	2.43386i
$929$	−21.5234	+	7.83389i	−0.706161	+	0.257022i	−0.670039	−	0.742326i	$-0.733723\pi$
$929$	−21.5234	+	7.83389i	−0.706161	+	0.257022i	−0.0361220	+	0.999347i	$0.511500\pi$
$930$		0			0
$931$	4.20674	−	10.3428i	0.137870	−	0.338970i
$932$	22.9123			0.750517
$933$		0			0
$934$	5.43213	−	30.8071i	0.177745	−	1.00804i
$935$	0.0287480	−	0.0241224i	0.000940159	−	0.000788887i
$936$		0			0
$937$	2.02604	+	11.4902i	0.0661877	+	0.375369i	0.999852	+	0.0172191i	$0.00548128\pi$
$937$	2.02604	+	11.4902i	0.0661877	+	0.375369i	−0.933664	+	0.358150i	$0.883408\pi$
$938$	−29.2206	−	50.6116i	−0.954088	−	1.65253i
$939$		0			0
$940$	15.7192	+	5.72131i	0.512703	+	0.186609i
$941$	52.0967	+	18.9616i	1.69830	+	0.618132i	0.995630	−	0.0933820i	$-0.0297678\pi$
$941$	52.0967	+	18.9616i	1.69830	+	0.618132i	0.702672	+	0.711514i	$0.251990\pi$
$942$		0			0
$943$	−23.4345	−	40.5898i	−0.763133	−	1.32179i
$944$	1.83983	+	10.4342i	0.0598815	+	0.339605i
$945$		0			0
$946$	7.38881	−	6.19995i	0.240231	−	0.201578i
$947$	1.61575	−	9.16340i	0.0525049	−	0.297770i	−0.947236	−	0.320537i	$-0.896137\pi$
$947$	1.61575	−	9.16340i	0.0525049	−	0.297770i	0.999741	+	0.0227671i	$0.00724762\pi$
$948$		0			0
$949$	−2.65474			−0.0861765
$950$	5.40907	+	6.95657i	0.175493	+	0.225701i
$951$		0			0
$952$	0.0198980	−	0.00724229i	0.000644899	−	0.000234724i
$953$	2.99473	−	16.9840i	0.0970090	−	0.550165i	−0.897104	−	0.441819i	$-0.854333\pi$
$953$	2.99473	−	16.9840i	0.0970090	−	0.550165i	0.994113	−	0.108346i	$-0.0345555\pi$
$954$		0			0
$955$	14.2974	+	11.9969i	0.462652	+	0.388211i
$956$	0.987737	+	5.60173i	0.0319457	+	0.181173i
$957$		0			0
$958$	32.5538	−	56.3848i	1.05177	−	1.82171i
$959$	−14.7429	−	5.36598i	−0.476073	−	0.173276i
$960$		0			0
$961$	−28.4723	+	49.3154i	−0.918460	+	1.59082i
$962$	−3.34232	−	5.78908i	−0.107761	−	0.186647i
$963$		0			0
$964$	17.8318	+	14.9626i	0.574323	+	0.481914i
$965$	−18.3136	+	15.3669i	−0.589536	+	0.494679i
$966$		0			0
$967$	−3.46405	+	1.26081i	−0.111396	+	0.0405449i	−0.397117	−	0.917768i	$-0.629989\pi$
$967$	−3.46405	+	1.26081i	−0.111396	+	0.0405449i	0.285721	+	0.958313i	$0.407767\pi$
$968$	−1.77029			−0.0568994
$969$		0			0
$970$	15.7449			0.505537
$971$	−21.3740	+	7.77948i	−0.685923	+	0.249656i	−0.661389	−	0.750043i	$-0.730033\pi$
$971$	−21.3740	+	7.77948i	−0.685923	+	0.249656i	−0.0245344	+	0.999699i	$0.507810\pi$
$972$		0			0
$973$	6.46760	−	5.42696i	0.207342	−	0.173980i
$974$	−5.65472	−	4.74487i	−0.181189	−	0.152036i
$975$		0			0
$976$	−19.1505	−	33.1697i	−0.612993	−	1.06174i
$977$	−22.5088	+	38.9865i	−0.720122	+	1.24729i	0.240829	+	0.970568i	$0.422581\pi$
$977$	−22.5088	+	38.9865i	−0.720122	+	1.24729i	−0.960951	+	0.276720i	$0.910753\pi$
$978$		0			0
$979$	7.91669	+	2.88144i	0.253018	+	0.0920911i
$980$	−2.67290	+	4.62960i	−0.0853827	+	0.147887i
$981$		0			0
$982$	−1.59679	−	9.05587i	−0.0509557	−	0.288984i
$983$	−32.4157	−	27.2000i	−1.03390	−	0.867544i	−0.0425891	−	0.999093i	$-0.513561\pi$
$983$	−32.4157	−	27.2000i	−1.03390	−	0.867544i	−0.991310	+	0.131548i	$0.958005\pi$
$984$		0			0
$985$	1.16371	−	6.59971i	0.0370788	−	0.210284i
$986$	0.690411	−	0.251289i	0.0219872	−	0.00800267i
$987$		0			0
$988$	22.7955	+	14.3180i	0.725220	+	0.455515i
$989$	19.2274			0.611397
$990$		0			0
$991$	5.41069	−	30.6856i	0.171876	−	0.974759i	−0.769812	−	0.638271i	$-0.779650\pi$
$991$	5.41069	−	30.6856i	0.171876	−	0.974759i	0.941688	−	0.336488i	$-0.109239\pi$
$992$	57.9824	−	48.6530i	1.84094	−	1.54473i
$993$		0			0
$994$	−13.6659	−	77.5032i	−0.433456	−	2.45825i
$995$	−1.57943	−	2.73566i	−0.0500714	−	0.0867261i
$996$		0			0
$997$	−36.5451	−	13.3013i	−1.15740	−	0.421258i	−0.309229	−	0.950987i	$-0.600071\pi$
$997$	−36.5451	−	13.3013i	−1.15740	−	0.421258i	−0.848166	+	0.529730i	$0.822293\pi$
$998$	41.4579	+	15.0895i	1.31233	+	0.477648i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.b.271.1		18
3.2	odd	2		95.2.k.b.81.3	yes	18
15.2	even	4		475.2.u.c.24.6		36
15.8	even	4		475.2.u.c.24.1		36
15.14	odd	2		475.2.l.b.176.1		18
19.4	even	9	inner	855.2.bs.b.631.1		18
57.2	even	18		1805.2.a.u.1.9		9
57.17	odd	18		1805.2.a.t.1.1		9
57.23	odd	18		95.2.k.b.61.3	✓	18
285.23	even	36		475.2.u.c.99.6		36
285.59	even	18		9025.2.a.cd.1.1		9
285.74	odd	18		9025.2.a.ce.1.9		9
285.137	even	36		475.2.u.c.99.1		36
285.194	odd	18		475.2.l.b.251.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.3	✓	18	57.23	odd	18
95.2.k.b.81.3	yes	18	3.2	odd	2
475.2.l.b.176.1		18	15.14	odd	2
475.2.l.b.251.1		18	285.194	odd	18
475.2.u.c.24.1		36	15.8	even	4
475.2.u.c.24.6		36	15.2	even	4
475.2.u.c.99.1		36	285.137	even	36
475.2.u.c.99.6		36	285.23	even	36
855.2.bs.b.271.1		18	1.1	even	1	trivial
855.2.bs.b.631.1		18	19.4	even	9	inner
1805.2.a.t.1.1		9	57.17	odd	18
1805.2.a.u.1.9		9	57.2	even	18
9025.2.a.cd.1.1		9	285.59	even	18
9025.2.a.ce.1.9		9	285.74	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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89970 + 0.691434i) q^{2} +(1.59869 - 1.34146i) q^{4} +(0.766044 + 0.642788i) q^{5} +(-1.54609 - 2.67790i) q^{7} +(-0.0878797 + 0.152212i) q^{8} +O(q^{10})\)	\(q+(-1.89970 + 0.691434i) q^{2} +(1.59869 - 1.34146i) q^{4} +(0.766044 + 0.642788i) q^{5} +(-1.54609 - 2.67790i) q^{7} +(-0.0878797 + 0.152212i) q^{8} +(-1.89970 - 0.691434i) q^{10} +(0.481594 - 0.834145i) q^{11} +(-0.513859 - 2.91424i) q^{13} +(4.78870 + 4.01819i) q^{14} +(-0.663086 + 3.76055i) q^{16} +(0.0366124 - 0.0133258i) q^{17} +(-4.31788 + 0.596607i) q^{19} +2.08694 q^{20} +(-0.338127 + 1.91762i) q^{22} +(-2.97348 + 2.49504i) q^{23} +(0.173648 + 0.984808i) q^{25} +(2.99118 + 5.18088i) q^{26} +(-6.06401 - 2.20712i) q^{28} +(-8.76529 - 3.19030i) q^{29} +(4.68894 + 8.12148i) q^{31} +(-1.40155 - 7.94857i) q^{32} +(-0.0603386 + 0.0506301i) q^{34} +(0.536951 - 3.04520i) q^{35} -1.11739 q^{37} +(7.79016 - 4.11890i) q^{38} +(-0.165160 + 0.0601132i) q^{40} +(-2.09674 + 11.8912i) q^{41} +(-3.79459 - 3.18404i) q^{43} +(-0.349053 - 1.97958i) q^{44} +(3.92356 - 6.79580i) q^{46} +(7.53217 + 2.74148i) q^{47} +(-1.28078 + 2.21837i) q^{49} +(-1.01081 - 1.75077i) q^{50} +(-4.73083 - 3.96964i) q^{52} +(-4.64208 + 3.89517i) q^{53} +(0.905101 - 0.329430i) q^{55} +0.543479 q^{56} +18.8573 q^{58} +(2.60732 - 0.948987i) q^{59} +(-7.68360 + 6.44731i) q^{61} +(-14.5230 - 12.1863i) q^{62} +(4.33987 + 7.51688i) q^{64} +(1.47960 - 2.56274i) q^{65} +(-8.78501 - 3.19748i) q^{67} +(0.0406557 - 0.0704178i) q^{68} +(1.08551 + 6.15623i) q^{70} +(-9.64404 - 8.09231i) q^{71} +(0.155782 - 0.883486i) q^{73} +(2.12271 - 0.772603i) q^{74} +(-6.10262 + 6.74604i) q^{76} -2.97835 q^{77} +(1.54415 - 8.75731i) q^{79} +(-2.92519 + 2.45452i) q^{80} +(-4.23882 - 24.0395i) q^{82} +(-4.80224 - 8.31772i) q^{83} +(0.0366124 + 0.0133258i) q^{85} +(9.41012 + 3.42500i) q^{86} +(0.0846446 + 0.146609i) q^{88} +(1.51886 + 8.61386i) q^{89} +(-7.00958 + 5.88173i) q^{91} +(-1.40667 + 7.97760i) q^{92} -16.2044 q^{94} +(-3.69118 - 2.31845i) q^{95} +(-7.31855 + 2.66374i) q^{97} +(0.899233 - 5.09981i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

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