LMFDB - Embedded newform 450.2.h.e.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.2
Root			$-0.983224 - 0.644389i$ of defining polynomial
Character	$\chi$	$=$	450.181
Dual form			450.2.h.e.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.15743 + 0.587785i) q^{5} -0.833366 q^{7} +(0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.15743 + 0.587785i) q^{5} -0.833366 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.107666 - 2.23347i) q^{10} +(-0.257524 - 0.792578i) q^{11} +(1.41027 - 4.34038i) q^{13} +(0.257524 + 0.792578i) q^{14} +(0.309017 - 0.951057i) q^{16} +(4.41027 + 3.20425i) q^{17} +(7.00116 + 5.08664i) q^{19} +(-2.09089 + 0.792578i) q^{20} +(-0.674207 + 0.489840i) q^{22} +(-1.09089 - 3.35741i) q^{23} +(4.30902 + 2.53621i) q^{25} -4.56375 q^{26} +(0.674207 - 0.489840i) q^{28} +(2.64518 - 1.92183i) q^{29} +(-4.85599 - 3.52808i) q^{31} -1.00000 q^{32} +(1.68458 - 5.18459i) q^{34} +(-1.79793 - 0.489840i) q^{35} +(2.26042 - 6.95685i) q^{37} +(2.67421 - 8.23036i) q^{38} +(1.39991 + 1.74363i) q^{40} +(-0.576909 + 1.77554i) q^{41} -1.63877 q^{43} +(0.674207 + 0.489840i) q^{44} +(-2.85599 + 2.07500i) q^{46} +(-0.674207 + 0.489840i) q^{47} -6.30550 q^{49} +(1.08052 - 4.88185i) q^{50} +(1.41027 + 4.34038i) q^{52} +(5.19972 - 3.77782i) q^{53} +(-0.0897250 - 1.86130i) q^{55} +(-0.674207 - 0.489840i) q^{56} +(-2.64518 - 1.92183i) q^{58} +(-4.18178 + 12.8702i) q^{59} +(1.81832 + 5.59621i) q^{61} +(-1.85482 + 5.70855i) q^{62} +(0.309017 + 0.951057i) q^{64} +(5.59378 - 8.53513i) q^{65} +(-1.21345 - 0.881621i) q^{67} -5.45140 q^{68} +(0.0897250 + 1.86130i) q^{70} +(-1.91027 + 1.38790i) q^{71} +(-1.02903 - 3.16703i) q^{73} -7.31486 q^{74} -8.65392 q^{76} +(0.214612 + 0.660507i) q^{77} +(-4.18178 + 3.03824i) q^{79} +(1.22570 - 1.87020i) q^{80} +1.86692 q^{82} +(-9.97971 - 7.25068i) q^{83} +(7.63145 + 9.50525i) q^{85} +(0.506408 + 1.55856i) q^{86} +(0.257524 - 0.792578i) q^{88} +(2.16491 + 6.66290i) q^{89} +(-1.17527 + 3.61712i) q^{91} +(2.85599 + 2.07500i) q^{92} +(0.674207 + 0.489840i) q^{94} +(12.1147 + 15.0893i) q^{95} +(-8.97214 + 6.51864i) q^{97} +(1.94851 + 5.99689i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8} - q^{11} - 13 q^{13} + q^{14} - 2 q^{16} + 11 q^{17} + 20 q^{19} - 5 q^{20} + q^{22} + 3 q^{23} + 30 q^{25} - 22 q^{26} - q^{28} + 15 q^{29} - 9 q^{31} - 8 q^{32} - q^{34} + 15 q^{35} - 6 q^{37} + 15 q^{38} - 5 q^{40} + 9 q^{41} + 12 q^{43} - q^{44} + 7 q^{46} + q^{47} - 4 q^{49} + 5 q^{50} - 13 q^{52} - 7 q^{53} - 25 q^{55} + q^{56} - 15 q^{58} - 10 q^{59} + 6 q^{61} - 21 q^{62} - 2 q^{64} + 10 q^{65} - 11 q^{67} - 24 q^{68} + 25 q^{70} + 9 q^{71} - 8 q^{73} - 24 q^{74} - 10 q^{76} - 33 q^{77} - 10 q^{79} + 26 q^{82} - 27 q^{83} + 5 q^{85} + 23 q^{86} + q^{88} + 15 q^{89} + q^{91} - 7 q^{92} - q^{94} + 30 q^{95} - 36 q^{97} + 19 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8 - q^11 - 13 * q^13 + q^14 - 2 * q^16 + 11 * q^17 + 20 * q^19 - 5 * q^20 + q^22 + 3 * q^23 + 30 * q^25 - 22 * q^26 - q^28 + 15 * q^29 - 9 * q^31 - 8 * q^32 - q^34 + 15 * q^35 - 6 * q^37 + 15 * q^38 - 5 * q^40 + 9 * q^41 + 12 * q^43 - q^44 + 7 * q^46 + q^47 - 4 * q^49 + 5 * q^50 - 13 * q^52 - 7 * q^53 - 25 * q^55 + q^56 - 15 * q^58 - 10 * q^59 + 6 * q^61 - 21 * q^62 - 2 * q^64 + 10 * q^65 - 11 * q^67 - 24 * q^68 + 25 * q^70 + 9 * q^71 - 8 * q^73 - 24 * q^74 - 10 * q^76 - 33 * q^77 - 10 * q^79 + 26 * q^82 - 27 * q^83 + 5 * q^85 + 23 * q^86 + q^88 + 15 * q^89 + q^91 - 7 * q^92 - q^94 + 30 * q^95 - 36 * q^97 + 19 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	2.15743	+	0.587785i	0.964832	+	0.262866i
$5$	2.15743	+	0.587785i	0.964832	+	0.262866i
$6$		0			0
$7$	−0.833366			−0.314983			−0.157491	−	0.987520i	$-0.550341\pi$
$7$	−0.833366			−0.314983			−0.157491	+	0.987520i	$0.550341\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$		0			0
$10$	−0.107666	−	2.23347i	−0.0340469	−	0.706287i
$11$	−0.257524	−	0.792578i	−0.0776465	−	0.238971i	0.904698	−	0.426054i	$-0.140097\pi$
$11$	−0.257524	−	0.792578i	−0.0776465	−	0.238971i	−0.982344	+	0.187083i	$0.940097\pi$
$12$		0			0
$13$	1.41027	−	4.34038i	0.391140	−	1.20380i	−0.540787	−	0.841159i	$-0.681874\pi$
$13$	1.41027	−	4.34038i	0.391140	−	1.20380i	0.931927	−	0.362645i	$-0.118126\pi$
$14$	0.257524	+	0.792578i	0.0688262	+	0.211825i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	4.41027	+	3.20425i	1.06965	+	0.777145i	0.975849	−	0.218446i	$-0.0700987\pi$
$17$	4.41027	+	3.20425i	1.06965	+	0.777145i	0.0937997	+	0.995591i	$0.470099\pi$
$18$		0			0
$19$	7.00116	+	5.08664i	1.60618	+	1.16696i	0.874116	+	0.485718i	$0.161442\pi$
$19$	7.00116	+	5.08664i	1.60618	+	1.16696i	0.732062	+	0.681238i	$0.238558\pi$
$20$	−2.09089	+	0.792578i	−0.467537	+	0.177226i
$21$		0			0
$22$	−0.674207	+	0.489840i	−0.143741	+	0.104434i
$23$	−1.09089	−	3.35741i	−0.227466	−	0.700069i	−0.998032	−	0.0627085i	$-0.980026\pi$
$23$	−1.09089	−	3.35741i	−0.227466	−	0.700069i	0.770566	−	0.637361i	$-0.219974\pi$
$24$		0			0
$25$	4.30902	+	2.53621i	0.861803	+	0.507242i
$26$	−4.56375			−0.895024
$27$		0			0
$28$	0.674207	−	0.489840i	0.127413	−	0.0925711i
$29$	2.64518	−	1.92183i	0.491197	−	0.356876i	−0.314447	−	0.949275i	$-0.601819\pi$
$29$	2.64518	−	1.92183i	0.491197	−	0.356876i	0.805645	+	0.592399i	$0.201819\pi$
$30$		0			0
$31$	−4.85599	−	3.52808i	−0.872161	−	0.633662i	0.0590050	−	0.998258i	$-0.481207\pi$
$31$	−4.85599	−	3.52808i	−0.872161	−	0.633662i	−0.931166	+	0.364596i	$0.881207\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.68458	−	5.18459i	0.288902	−	0.889150i
$35$	−1.79793	−	0.489840i	−0.303905	−	0.0827981i
$36$		0			0
$37$	2.26042	−	6.95685i	0.371610	−	1.14370i	−0.574127	−	0.818766i	$-0.694658\pi$
$37$	2.26042	−	6.95685i	0.371610	−	1.14370i	0.945737	−	0.324932i	$-0.105342\pi$
$38$	2.67421	−	8.23036i	0.433814	−	1.33514i
$39$		0			0
$40$	1.39991	+	1.74363i	0.221345	+	0.275693i
$41$	−0.576909	+	1.77554i	−0.0900981	+	0.277293i	−0.985945	−	0.167069i	$-0.946570\pi$
$41$	−0.576909	+	1.77554i	−0.0900981	+	0.277293i	0.895847	+	0.444362i	$0.146570\pi$
$42$		0			0
$43$	−1.63877			−0.249910			−0.124955	−	0.992162i	$-0.539879\pi$
$43$	−1.63877			−0.249910			−0.124955	+	0.992162i	$0.539879\pi$
$44$	0.674207	+	0.489840i	0.101641	+	0.0738462i
$45$		0			0
$46$	−2.85599	+	2.07500i	−0.421092	+	0.305941i
$47$	−0.674207	+	0.489840i	−0.0983432	+	0.0714505i	−0.635870	−	0.771796i	$-0.719359\pi$
$47$	−0.674207	+	0.489840i	−0.0983432	+	0.0714505i	0.537527	+	0.843247i	$0.319359\pi$
$48$		0			0
$49$	−6.30550			−0.900786
$50$	1.08052	−	4.88185i	0.152809	−	0.690398i
$51$		0			0
$52$	1.41027	+	4.34038i	0.195570	+	0.601902i
$53$	5.19972	−	3.77782i	0.714237	−	0.518923i	−0.170301	−	0.985392i	$-0.554474\pi$
$53$	5.19972	−	3.77782i	0.714237	−	0.518923i	0.884538	+	0.466469i	$0.154474\pi$
$54$		0			0
$55$	−0.0897250	−	1.86130i	−0.0120985	−	0.250978i
$56$	−0.674207	−	0.489840i	−0.0900947	−	0.0654576i
$57$		0			0
$58$	−2.64518	−	1.92183i	−0.347329	−	0.252349i
$59$	−4.18178	+	12.8702i	−0.544421	+	1.67556i	0.177940	+	0.984041i	$0.443057\pi$
$59$	−4.18178	+	12.8702i	−0.544421	+	1.67556i	−0.722362	+	0.691515i	$0.756943\pi$
$60$		0			0
$61$	1.81832	+	5.59621i	0.232812	+	0.716521i	0.997404	+	0.0720066i	$0.0229403\pi$
$61$	1.81832	+	5.59621i	0.232812	+	0.716521i	−0.764592	+	0.644514i	$0.777060\pi$
$62$	−1.85482	+	5.70855i	−0.235563	+	0.724987i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	5.59378	−	8.53513i	0.693823	−	1.05865i
$66$		0			0
$67$	−1.21345	−	0.881621i	−0.148246	−	0.107707i	0.511190	−	0.859468i	$-0.329205\pi$
$67$	−1.21345	−	0.881621i	−0.148246	−	0.107707i	−0.659436	+	0.751761i	$0.729205\pi$
$68$	−5.45140			−0.661079
$69$		0			0
$70$	0.0897250	+	1.86130i	0.0107242	+	0.222468i
$71$	−1.91027	+	1.38790i	−0.226708	+	0.164713i	−0.695341	−	0.718680i	$-0.744747\pi$
$71$	−1.91027	+	1.38790i	−0.226708	+	0.164713i	0.468633	+	0.883393i	$0.344747\pi$
$72$		0			0
$73$	−1.02903	−	3.16703i	−0.120439	−	0.370672i	0.872604	−	0.488429i	$-0.162430\pi$
$73$	−1.02903	−	3.16703i	−0.120439	−	0.370672i	−0.993043	+	0.117756i	$0.962430\pi$
$74$	−7.31486			−0.850335
$75$		0			0
$76$	−8.65392			−0.992672
$77$	0.214612	+	0.660507i	0.0244573	+	0.0752718i
$78$		0			0
$79$	−4.18178	+	3.03824i	−0.470487	+	0.341829i	−0.797631	−	0.603146i	$-0.793914\pi$
$79$	−4.18178	+	3.03824i	−0.470487	+	0.341829i	0.327144	+	0.944974i	$0.393914\pi$
$80$	1.22570	−	1.87020i	0.137037	−	0.209095i
$81$		0			0
$82$	1.86692			0.206167
$83$	−9.97971	−	7.25068i	−1.09542	−	0.795866i	−0.115110	−	0.993353i	$-0.536722\pi$
$83$	−9.97971	−	7.25068i	−1.09542	−	0.795866i	−0.980306	+	0.197487i	$0.936722\pi$
$84$		0			0
$85$	7.63145	+	9.50525i	0.827747	+	1.03099i
$86$	0.506408	+	1.55856i	0.0546074	+	0.168064i
$87$		0			0
$88$	0.257524	−	0.792578i	0.0274522	−	0.0844891i
$89$	2.16491	+	6.66290i	0.229480	+	0.706266i	0.997806	+	0.0662073i	$0.0210899\pi$
$89$	2.16491	+	6.66290i	0.229480	+	0.706266i	−0.768326	+	0.640058i	$0.778910\pi$
$90$		0			0
$91$	−1.17527	+	3.61712i	−0.123202	+	0.379178i
$92$	2.85599	+	2.07500i	0.297757	+	0.216333i
$93$		0			0
$94$	0.674207	+	0.489840i	0.0695391	+	0.0505231i
$95$	12.1147	+	15.0893i	1.24294	+	1.54813i
$96$		0			0
$97$	−8.97214	+	6.51864i	−0.910982	+	0.661867i	−0.941263	−	0.337674i	$-0.890360\pi$
$97$	−8.97214	+	6.51864i	−0.910982	+	0.661867i	0.0302807	+	0.999541i	$0.490360\pi$
$98$	1.94851	+	5.99689i	0.196829	+	0.605777i
$99$		0			0
$100$	−4.97682	+	0.480938i	−0.497682	+	0.0480938i
$101$	−12.7085			−1.26454			−0.632272	−	0.774746i	$-0.717878\pi$
$101$	−12.7085			−1.26454			−0.632272	+	0.774746i	$0.717878\pi$
$102$		0			0
$103$	−5.67537	+	4.12340i	−0.559211	+	0.406291i	−0.831170	−	0.556018i	$-0.812328\pi$
$103$	−5.67537	+	4.12340i	−0.559211	+	0.406291i	0.271959	+	0.962309i	$0.412328\pi$
$104$	3.69215	−	2.68250i	0.362045	−	0.263041i
$105$		0			0
$106$	−5.19972	−	3.77782i	−0.505042	−	0.366934i
$107$	10.7700			1.04118			0.520589	−	0.853807i	$-0.325712\pi$
$107$	10.7700			1.04118			0.520589	+	0.853807i	$0.325712\pi$
$108$		0			0
$109$	−3.28655	+	10.1150i	−0.314795	+	0.968838i	0.661044	+	0.750347i	$0.270114\pi$
$109$	−3.28655	+	10.1150i	−0.314795	+	0.968838i	−0.975839	+	0.218491i	$0.929886\pi$
$110$	−1.74248	+	0.660507i	−0.166139	+	0.0629769i
$111$		0			0
$112$	−0.257524	+	0.792578i	−0.0243337	+	0.0748916i
$113$	−0.538232	+	1.65651i	−0.0506326	+	0.155831i	−0.973176	−	0.230063i	$-0.926107\pi$
$113$	−0.538232	+	1.65651i	−0.0506326	+	0.155831i	0.922543	+	0.385894i	$0.126107\pi$
$114$		0			0
$115$	−0.380081	−	7.88460i	−0.0354428	−	0.735242i
$116$	−1.01037	+	3.10959i	−0.0938103	+	0.288718i
$117$		0			0
$118$	13.5325			1.24577
$119$	−3.67537	−	2.67031i	−0.336921	−	0.244787i
$120$		0			0
$121$	8.33733	−	6.05742i	0.757939	−	0.550675i
$122$	4.76042	−	3.45865i	0.430988	−	0.313131i
$123$		0			0
$124$	6.00233			0.539025
$125$	7.80566	+	8.00448i	0.698159	+	0.715942i
$126$		0			0
$127$	1.75112	+	5.38938i	0.155386	+	0.478230i	0.998200	−	0.0599756i	$-0.0191023\pi$
$127$	1.75112	+	5.38938i	0.155386	+	0.478230i	−0.842813	+	0.538206i	$0.819102\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$		0			0
$130$	−9.84597	−	2.68250i	−0.863548	−	0.235271i
$131$	−13.3281	−	9.68345i	−1.16448	−	0.846047i	−0.174145	−	0.984720i	$-0.555716\pi$
$131$	−13.3281	−	9.68345i	−1.16448	−	0.846047i	−0.990338	+	0.138673i	$0.955716\pi$
$132$		0			0
$133$	−5.83453	−	4.23903i	−0.505918	−	0.367571i
$134$	−0.463496	+	1.42649i	−0.0400399	+	0.123230i
$135$		0			0
$136$	1.68458	+	5.18459i	0.144451	+	0.444575i
$137$	0.894062	−	2.75164i	0.0763849	−	0.235088i	−0.905572	−	0.424192i	$-0.860558\pi$
$137$	0.894062	−	2.75164i	0.0763849	−	0.235088i	0.981957	+	0.189104i	$0.0605582\pi$
$138$		0			0
$139$	1.54184	+	4.74531i	0.130778	+	0.402492i	0.994909	−	0.100774i	$-0.0321318\pi$
$139$	1.54184	+	4.74531i	0.130778	+	0.402492i	−0.864132	+	0.503266i	$0.832132\pi$
$140$	1.74248	−	0.660507i	0.147266	−	0.0558230i
$141$		0			0
$142$	1.91027	+	1.38790i	0.160307	+	0.116470i
$143$	−3.80327			−0.318045
$144$		0			0
$145$	6.83642	−	2.59143i	0.567733	−	0.215206i
$146$	−2.69403	+	1.95733i	−0.222960	+	0.161990i
$147$		0			0
$148$	2.26042	+	6.95685i	0.185805	+	0.571849i
$149$	−2.00579			−0.164320			−0.0821602	−	0.996619i	$-0.526182\pi$
$149$	−2.00579			−0.164320			−0.0821602	+	0.996619i	$0.526182\pi$
$150$		0			0
$151$	−1.96971			−0.160293			−0.0801463	−	0.996783i	$-0.525539\pi$
$151$	−1.96971			−0.160293			−0.0801463	+	0.996783i	$0.525539\pi$
$152$	2.67421	+	8.23036i	0.216907	+	0.667571i
$153$		0			0
$154$	0.561861	−	0.408216i	0.0452760	−	0.0328950i
$155$	−8.40270	−	10.4659i	−0.674921	−	0.840639i
$156$		0			0
$157$	7.78467			0.621284			0.310642	−	0.950527i	$-0.399456\pi$
$157$	7.78467			0.621284			0.310642	+	0.950527i	$0.399456\pi$
$158$	4.18178	+	3.03824i	0.332685	+	0.241709i
$159$		0			0
$160$	−2.15743	−	0.587785i	−0.170560	−	0.0464685i
$161$	0.909110	+	2.79795i	0.0716479	+	0.220510i
$162$		0			0
$163$	4.35589	−	13.4060i	0.341180	−	1.05004i	−0.622418	−	0.782685i	$-0.713849\pi$
$163$	4.35589	−	13.4060i	0.341180	−	1.05004i	0.963597	−	0.267358i	$-0.0861505\pi$
$164$	−0.576909	−	1.77554i	−0.0450490	−	0.138647i
$165$		0			0
$166$	−3.81191	+	11.7319i	−0.295862	+	0.910568i
$167$	−6.59846	−	4.79406i	−0.510604	−	0.370976i	0.302448	−	0.953166i	$-0.402196\pi$
$167$	−6.59846	−	4.79406i	−0.510604	−	0.370976i	−0.813053	+	0.582190i	$0.802196\pi$
$168$		0			0
$169$	−6.33280	−	4.60105i	−0.487139	−	0.353927i
$170$	6.68178	−	10.1952i	0.512469	−	0.781938i
$171$		0			0
$172$	1.32579	−	0.963245i	0.101091	−	0.0734467i
$173$	0.773580	+	2.38084i	0.0588142	+	0.181012i	0.976147	−	0.217109i	$-0.0696626\pi$
$173$	0.773580	+	2.38084i	0.0588142	+	0.181012i	−0.917333	+	0.398120i	$0.869663\pi$
$174$		0			0
$175$	−3.59099	−	2.11359i	−0.271453	−	0.159773i
$176$	−0.833366			−0.0628173
$177$		0			0
$178$	5.66780	−	4.11790i	0.424820	−	0.308649i
$179$	−16.2067	+	11.7749i	−1.21135	+	0.880096i	−0.995352	−	0.0962986i	$-0.969300\pi$
$179$	−16.2067	+	11.7749i	−1.21135	+	0.880096i	−0.215995	+	0.976394i	$0.569300\pi$
$180$		0			0
$181$	−6.37367	−	4.63074i	−0.473751	−	0.344201i	0.325150	−	0.945662i	$-0.394585\pi$
$181$	−6.37367	−	4.63074i	−0.473751	−	0.344201i	−0.798902	+	0.601462i	$0.794585\pi$
$182$	3.80327			0.281917
$183$		0			0
$184$	1.09089	−	3.35741i	0.0804215	−	0.247512i
$185$	8.96583	−	13.6803i	0.659181	−	1.00579i
$186$		0			0
$187$	1.40387	−	4.32066i	0.102661	−	0.315958i
$188$	0.257524	−	0.792578i	0.0187819	−	0.0578047i
$189$		0			0
$190$	10.6071	−	16.1846i	0.769520	−	1.17415i
$191$	1.63013	−	5.01702i	0.117952	−	0.363019i	−0.874599	−	0.484847i	$-0.838875\pi$
$191$	1.63013	−	5.01702i	0.117952	−	0.363019i	0.992551	+	0.121827i	$0.0388755\pi$
$192$		0			0
$193$	−13.4461			−0.967873			−0.483937	−	0.875103i	$-0.660793\pi$
$193$	−13.4461			−0.967873			−0.483937	+	0.875103i	$0.660793\pi$
$194$	8.97214	+	6.51864i	0.644162	+	0.468011i
$195$		0			0
$196$	5.10126	−	3.70628i	0.364376	−	0.264734i
$197$	−4.39991	+	3.19672i	−0.313480	+	0.227757i	−0.733388	−	0.679810i	$-0.762062\pi$
$197$	−4.39991	+	3.19672i	−0.313480	+	0.227757i	0.419908	+	0.907567i	$0.362062\pi$
$198$		0			0
$199$	−17.4090			−1.23409			−0.617045	−	0.786927i	$-0.711671\pi$
$199$	−17.4090			−1.23409			−0.617045	+	0.786927i	$0.711671\pi$
$200$	1.99532	+	4.58462i	0.141090	+	0.324181i
$201$		0			0
$202$	3.92715	+	12.0865i	0.276313	+	0.850404i
$203$	−2.20440	+	1.60159i	−0.154719	+	0.112410i
$204$		0			0
$205$	−2.28828	+	3.49152i	−0.159820	+	0.243858i
$206$	5.67537	+	4.12340i	0.395422	+	0.287291i
$207$		0			0
$208$	−3.69215	−	2.68250i	−0.256004	−	0.185998i
$209$	2.22859	−	6.85890i	0.154155	−	0.474440i
$210$		0			0
$211$	−0.0834142	−	0.256723i	−0.00574247	−	0.0176735i	0.948144	−	0.317840i	$-0.102958\pi$
$211$	−0.0834142	−	0.256723i	−0.00574247	−	0.0176735i	−0.953887	+	0.300167i	$0.902958\pi$
$212$	−1.98612	+	6.11264i	−0.136407	+	0.419818i
$213$		0			0
$214$	−3.32812	−	10.2429i	−0.227506	−	0.700191i
$215$	−3.53553	−	0.963245i	−0.241121	−	0.0656928i
$216$		0			0
$217$	4.04681	+	2.94018i	0.274716	+	0.199593i
$218$	10.6355			0.720328
$219$		0			0
$220$	1.16663	+	1.45309i	0.0786545	+	0.0979670i
$221$	20.1274	−	14.6234i	1.35391	−	0.983676i
$222$		0			0
$223$	7.16032	+	22.0372i	0.479491	+	1.47572i	0.839804	+	0.542889i	$0.182670\pi$
$223$	7.16032	+	22.0372i	0.479491	+	1.47572i	−0.360313	+	0.932831i	$0.617330\pi$
$224$	0.833366			0.0556816
$225$		0			0
$226$	1.74176			0.115860
$227$	0.0780741	+	0.240287i	0.00518196	+	0.0159484i	0.953614	−	0.301032i	$-0.0973311\pi$
$227$	0.0780741	+	0.240287i	0.00518196	+	0.0159484i	−0.948432	+	0.316980i	$0.897331\pi$
$228$		0			0
$229$	17.0625	−	12.3966i	1.12752	−	0.819191i	0.142187	−	0.989840i	$-0.454586\pi$
$229$	17.0625	−	12.3966i	1.12752	−	0.819191i	0.985332	+	0.170649i	$0.0545864\pi$
$230$	−7.38125	+	2.79795i	−0.486705	+	0.184492i
$231$		0			0
$232$	3.26962			0.214661
$233$	−11.8178	−	8.58610i	−0.774207	−	0.562494i	0.129028	−	0.991641i	$-0.458814\pi$
$233$	−11.8178	−	8.58610i	−0.774207	−	0.562494i	−0.903235	+	0.429147i	$0.858814\pi$
$234$		0			0
$235$	−1.74248	+	0.660507i	−0.113667	+	0.0430867i
$236$	−4.18178	−	12.8702i	−0.272211	−	0.837778i
$237$		0			0
$238$	−1.40387	+	4.32066i	−0.0909992	+	0.280067i
$239$	−1.79793	−	5.53346i	−0.116298	−	0.357930i	0.875917	−	0.482461i	$-0.160257\pi$
$239$	−1.79793	−	5.53346i	−0.116298	−	0.357930i	−0.992216	+	0.124532i	$0.960257\pi$
$240$		0			0
$241$	4.24254	−	13.0572i	0.273286	−	0.841087i	−0.716382	−	0.697708i	$-0.754203\pi$
$241$	4.24254	−	13.0572i	0.273286	−	0.841087i	0.989668	−	0.143379i	$-0.0457968\pi$
$242$	−8.33733	−	6.05742i	−0.535944	−	0.389386i
$243$		0			0
$244$	−4.76042	−	3.45865i	−0.304754	−	0.221417i
$245$	−13.6037	−	3.70628i	−0.869108	−	0.236786i
$246$		0			0
$247$	31.9515	−	23.2141i	2.03303	−	1.47708i
$248$	−1.85482	−	5.70855i	−0.117781	−	0.362494i
$249$		0			0
$250$	5.20063	−	9.89714i	0.328917	−	0.625950i
$251$	15.8938			1.00320			0.501602	−	0.865098i	$-0.332744\pi$
$251$	15.8938			1.00320			0.501602	+	0.865098i	$0.332744\pi$
$252$		0			0
$253$	−2.38008	+	1.72923i	−0.149634	+	0.108716i
$254$	4.58448	−	3.33082i	0.287656	−	0.208994i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	2.31253			0.144252			0.0721259	−	0.997396i	$-0.477022\pi$
$257$	2.31253			0.144252			0.0721259	+	0.997396i	$0.477022\pi$
$258$		0			0
$259$	−1.88375	+	5.79760i	−0.117051	+	0.360245i
$260$	0.491360	+	10.1930i	0.0304728	+	0.632144i
$261$		0			0
$262$	−5.09089	+	15.6681i	−0.314516	+	0.967981i
$263$	6.63129	−	20.4090i	0.408903	−	1.25847i	−0.508689	−	0.860951i	$-0.669870\pi$
$263$	6.63129	−	20.4090i	0.408903	−	1.25847i	0.917592	−	0.397524i	$-0.130130\pi$
$264$		0			0
$265$	13.4386	−	5.09406i	0.825526	−	0.312926i
$266$	−2.22859	+	6.85890i	−0.136644	+	0.420546i
$267$		0			0
$268$	1.49990			0.0916212
$269$	17.3020	+	12.5706i	1.05492	+	0.766445i	0.973142	−	0.230206i	$-0.0739399\pi$
$269$	17.3020	+	12.5706i	1.05492	+	0.766445i	0.0817787	+	0.996651i	$0.473940\pi$
$270$		0			0
$271$	21.1400	−	15.3591i	1.28417	−	0.933001i	0.284495	−	0.958677i	$-0.408174\pi$
$271$	21.1400	−	15.3591i	1.28417	−	0.933001i	0.999670	+	0.0256766i	$0.00817402\pi$
$272$	4.41027	−	3.20425i	0.267412	−	0.194286i
$273$		0			0
$274$	−2.89324			−0.174787
$275$	0.900470	−	4.06837i	0.0543004	−	0.245332i
$276$		0			0
$277$	−5.76220	−	17.7342i	−0.346217	−	1.06555i	−0.960929	−	0.276795i	$-0.910728\pi$
$277$	−5.76220	−	17.7342i	−0.346217	−	1.06555i	0.614712	−	0.788752i	$-0.289272\pi$
$278$	4.03660	−	2.93276i	0.242099	−	0.175895i
$279$		0			0
$280$	−1.16663	−	1.45309i	−0.0697197	−	0.0868384i
$281$	11.9886	+	8.71023i	0.715180	+	0.519609i	0.884841	−	0.465894i	$-0.154267\pi$
$281$	11.9886	+	8.71023i	0.715180	+	0.519609i	−0.169661	+	0.985503i	$0.554267\pi$
$282$		0			0
$283$	−12.7663	−	9.27523i	−0.758875	−	0.551355i	0.139690	−	0.990195i	$-0.455389\pi$
$283$	−12.7663	−	9.27523i	−0.758875	−	0.551355i	−0.898565	+	0.438840i	$0.855389\pi$
$284$	0.729660	−	2.24566i	0.0432974	−	0.133256i
$285$		0			0
$286$	1.17527	+	3.61712i	0.0694955	+	0.213885i
$287$	0.480776	−	1.47968i	0.0283793	−	0.0873426i
$288$		0			0
$289$	3.93000	+	12.0953i	0.231177	+	0.711489i
$290$	−4.57716	−	5.70102i	−0.268780	−	0.334776i
$291$		0			0
$292$	2.69403	+	1.95733i	0.157656	+	0.114544i
$293$	−18.4003			−1.07496			−0.537479	−	0.843277i	$-0.680623\pi$
$293$	−18.4003			−1.07496			−0.537479	+	0.843277i	$0.680623\pi$
$294$		0			0
$295$	−16.5868	+	25.3086i	−0.965722	+	1.47352i
$296$	5.91785	−	4.29957i	0.343968	−	0.249907i
$297$		0			0
$298$	0.619822	+	1.90761i	0.0359053	+	0.110505i
$299$	−16.1109			−0.931718
$300$		0			0
$301$	1.36569			0.0787173
$302$	0.608674	+	1.87330i	0.0350252	+	0.107797i
$303$		0			0
$304$	7.00116	−	5.08664i	0.401544	−	0.291739i
$305$	0.633527	+	13.1422i	0.0362757	+	0.752521i
$306$		0			0
$307$	−34.1179			−1.94721			−0.973606	−	0.228237i	$-0.926704\pi$
$307$	−34.1179			−1.94721			−0.973606	+	0.228237i	$0.926704\pi$
$308$	−0.561861	−	0.408216i	−0.0320150	−	0.0232603i
$309$		0			0
$310$	−7.35705	+	11.2256i	−0.417853	+	0.637570i
$311$	4.02893	+	12.3998i	0.228460	+	0.703127i	0.997922	+	0.0644345i	$0.0205243\pi$
$311$	4.02893	+	12.3998i	0.228460	+	0.703127i	−0.769462	+	0.638692i	$0.779476\pi$
$312$		0			0
$313$	1.07619	−	3.31217i	0.0608298	−	0.187215i	−0.916024	−	0.401124i	$-0.868620\pi$
$313$	1.07619	−	3.31217i	0.0608298	−	0.187215i	0.976854	+	0.213909i	$0.0686196\pi$
$314$	−2.40559	−	7.40366i	−0.135756	−	0.417813i
$315$		0			0
$316$	1.59730	−	4.91598i	0.0898550	−	0.276545i
$317$	3.89975	+	2.83333i	0.219032	+	0.159136i	0.691891	−	0.722002i	$-0.256778\pi$
$317$	3.89975	+	2.83333i	0.219032	+	0.159136i	−0.472859	+	0.881138i	$0.656778\pi$
$318$		0			0
$319$	−2.20440	−	1.60159i	−0.123423	−	0.0896719i
$320$	0.107666	+	2.23347i	0.00601870	+	0.124855i
$321$		0			0
$322$	2.38008	−	1.72923i	0.132637	−	0.0963662i
$323$	14.5782	+	44.8670i	0.811151	+	2.49647i
$324$		0			0
$325$	17.0850	−	15.1260i	0.947707	−	0.839040i
$326$	−14.0960			−0.780703
$327$		0			0
$328$	−1.51037	+	1.09735i	−0.0833961	+	0.0605908i
$329$	0.561861	−	0.408216i	0.0309764	−	0.0225057i
$330$		0			0
$331$	−6.92796	−	5.03346i	−0.380795	−	0.276664i	0.380878	−	0.924625i	$-0.375622\pi$
$331$	−6.92796	−	5.03346i	−0.380795	−	0.276664i	−0.761673	+	0.647961i	$0.775622\pi$
$332$	12.3356			0.677004
$333$		0			0
$334$	−2.52039	+	7.75696i	−0.137910	+	0.424442i
$335$	−2.09972	−	2.61528i	−0.114720	−	0.142888i
$336$		0			0
$337$	−4.53365	+	13.9531i	−0.246964	+	0.760076i	0.748344	+	0.663311i	$0.230849\pi$
$337$	−4.53365	+	13.9531i	−0.246964	+	0.760076i	−0.995307	+	0.0967646i	$0.969151\pi$
$338$	−2.41892	+	7.44466i	−0.131572	+	0.404936i
$339$		0			0
$340$	−11.7610	−	3.20425i	−0.637831	−	0.173775i
$341$	−1.54574	+	4.75731i	−0.0837068	+	0.257623i
$342$		0			0
$343$	11.0883			0.598715
$344$	−1.32579	−	0.963245i	−0.0714820	−	0.0519347i
$345$		0			0
$346$	2.02526	−	1.47144i	0.108879	−	0.0791049i
$347$	−18.5970	+	13.5115i	−0.998340	+	0.725337i	−0.961732	−	0.273993i	$-0.911656\pi$
$347$	−18.5970	+	13.5115i	−0.998340	+	0.725337i	−0.0366088	+	0.999330i	$0.511656\pi$
$348$		0			0
$349$	3.55023			0.190040			0.0950198	−	0.995475i	$-0.469709\pi$
$349$	3.55023			0.190040			0.0950198	+	0.995475i	$0.469709\pi$
$350$	−0.900470	+	4.06837i	−0.0481321	+	0.217463i
$351$		0			0
$352$	0.257524	+	0.792578i	0.0137261	+	0.0422445i
$353$	−4.56375	+	3.31576i	−0.242904	+	0.176480i	−0.702576	−	0.711609i	$-0.747967\pi$
$353$	−4.56375	+	3.31576i	−0.242904	+	0.176480i	0.459672	+	0.888089i	$0.347967\pi$
$354$		0			0
$355$	−4.93707	+	1.87146i	−0.262033	+	0.0993267i
$356$	−5.66780	−	4.11790i	−0.300393	−	0.218248i
$357$		0			0
$358$	16.2067	+	11.7749i	0.856552	+	0.622322i
$359$	5.22442	−	16.0791i	0.275734	−	0.848623i	−0.713290	−	0.700869i	$-0.752796\pi$
$359$	5.22442	−	16.0791i	0.275734	−	0.848623i	0.989024	−	0.147754i	$-0.0472043\pi$
$360$		0			0
$361$	17.2710	+	53.1548i	0.909002	+	2.79762i
$362$	−2.43453	+	7.49270i	−0.127956	+	0.393808i
$363$		0			0
$364$	−1.17527	−	3.61712i	−0.0616011	−	0.189589i
$365$	−0.358528	−	7.43749i	−0.0187662	−	0.389296i
$366$		0			0
$367$	10.2044	+	7.41393i	0.532665	+	0.387004i	0.821354	−	0.570419i	$-0.193219\pi$
$367$	10.2044	+	7.41393i	0.532665	+	0.387004i	−0.288688	+	0.957423i	$0.593219\pi$
$368$	−3.53019			−0.184024
$369$		0			0
$370$	−15.7813	−	4.29957i	−0.820431	−	0.223524i
$371$	−4.33327	+	3.14830i	−0.224972	+	0.163452i
$372$		0			0
$373$	4.09435	+	12.6011i	0.211997	+	0.652460i	0.999353	+	0.0359616i	$0.0114494\pi$
$373$	4.09435	+	12.6011i	0.211997	+	0.652460i	−0.787356	+	0.616499i	$0.788551\pi$
$374$	−4.54301			−0.234913
$375$		0			0
$376$	−0.833366			−0.0429776
$377$	−4.61106	−	14.1914i	−0.237482	−	0.730894i
$378$		0			0
$379$	−18.0702	+	13.1288i	−0.928203	+	0.674379i	−0.945552	−	0.325470i	$-0.894477\pi$
$379$	−18.0702	+	13.1288i	−0.928203	+	0.674379i	0.0173488	+	0.999849i	$0.494477\pi$
$380$	−18.6702	−	5.08664i	−0.957762	−	0.260939i
$381$		0			0
$382$	−5.27521			−0.269903
$383$	19.7019	+	14.3143i	1.00672	+	0.731425i	0.963519	−	0.267642i	$-0.0862443\pi$
$383$	19.7019	+	14.3143i	1.00672	+	0.731425i	0.0432012	+	0.999066i	$0.486244\pi$
$384$		0			0
$385$	0.0747738	+	1.55114i	0.00381082	+	0.0790536i
$386$	4.15508	+	12.7880i	0.211488	+	0.650893i
$387$		0			0
$388$	3.42705	−	10.5474i	0.173982	−	0.535462i
$389$	−9.30500	−	28.6378i	−0.471782	−	1.45200i	−0.850249	−	0.526381i	$-0.823548\pi$
$389$	−9.30500	−	28.6378i	−0.471782	−	1.45200i	0.378467	−	0.925615i	$-0.376452\pi$
$390$		0			0
$391$	5.94688	−	18.3026i	0.300746	−	0.925602i
$392$	−5.10126	−	3.70628i	−0.257652	−	0.187195i
$393$		0			0
$394$	4.39991	+	3.19672i	0.221664	+	0.161048i
$395$	−10.8077	+	4.09681i	−0.543796	+	0.206133i
$396$		0			0
$397$	−28.6152	+	20.7902i	−1.43616	+	1.04343i	−0.447328	+	0.894370i	$0.647624\pi$
$397$	−28.6152	+	20.7902i	−1.43616	+	1.04343i	−0.988828	+	0.149059i	$0.952376\pi$
$398$	5.37968	+	16.5569i	0.269659	+	0.829924i
$399$		0			0
$400$	3.74364	−	3.31439i	0.187182	−	0.165719i
$401$	5.66794			0.283043			0.141522	−	0.989935i	$-0.454801\pi$
$401$	5.66794			0.283043			0.141522	+	0.989935i	$0.454801\pi$
$402$		0			0
$403$	−22.1615	+	16.1013i	−1.10394	+	0.802061i
$404$	10.2814	−	7.46988i	0.511519	−	0.371640i
$405$		0			0
$406$	2.20440	+	1.60159i	0.109403	+	0.0794856i
$407$	−6.09595			−0.302165
$408$		0			0
$409$	5.98493	−	18.4197i	0.295936	−	0.910797i	−0.686970	−	0.726686i	$-0.741060\pi$
$409$	5.98493	−	18.4197i	0.295936	−	0.910797i	0.982906	−	0.184111i	$-0.0589405\pi$
$410$	4.02775	+	1.09735i	0.198916	+	0.0541941i
$411$		0			0
$412$	2.16780	−	6.67180i	0.106800	−	0.328696i
$413$	3.48495	−	10.7256i	0.171483	−	0.527771i
$414$		0			0
$415$	−17.2687	−	21.5088i	−0.847687	−	1.05582i
$416$	−1.41027	+	4.34038i	−0.0691444	+	0.212805i
$417$		0			0
$418$	−7.21188			−0.352744
$419$	18.5906	+	13.5068i	0.908209	+	0.659853i	0.940561	−	0.339624i	$-0.110300\pi$
$419$	18.5906	+	13.5068i	0.908209	+	0.659853i	−0.0323520	+	0.999477i	$0.510300\pi$
$420$		0			0
$421$	8.19306	−	5.95261i	0.399305	−	0.290112i	−0.369953	−	0.929051i	$-0.620626\pi$
$421$	8.19306	−	5.95261i	0.399305	−	0.290112i	0.769258	+	0.638938i	$0.220626\pi$
$422$	−0.218381	+	0.158663i	−0.0106306	+	0.00772361i
$423$		0			0
$424$	6.42721			0.312133
$425$	10.8773	+	24.9926i	0.527626	+	1.21232i
$426$		0			0
$427$	−1.51532	−	4.66369i	−0.0733316	−	0.225692i
$428$	−8.71314	+	6.33047i	−0.421165	+	0.305995i
$429$		0			0
$430$	0.176440	+	3.66015i	0.00850867	+	0.176508i
$431$	−23.0589	−	16.7533i	−1.11071	−	0.806978i	−0.127935	−	0.991783i	$-0.540835\pi$
$431$	−23.0589	−	16.7533i	−1.11071	−	0.806978i	−0.982775	+	0.184804i	$0.940835\pi$
$432$		0			0
$433$	−12.8550	−	9.33971i	−0.617772	−	0.448838i	0.234370	−	0.972147i	$-0.424697\pi$
$433$	−12.8550	−	9.33971i	−0.617772	−	0.448838i	−0.852143	+	0.523309i	$0.824697\pi$
$434$	1.54574	−	4.75731i	0.0741981	−	0.228358i
$435$		0			0
$436$	−3.28655	−	10.1150i	−0.157397	−	0.484419i
$437$	9.44047	−	29.0548i	0.451599	−	1.38988i
$438$		0			0
$439$	0.910550	+	2.80238i	0.0434582	+	0.133751i	0.970431	−	0.241377i	$-0.0775990\pi$
$439$	0.910550	+	2.80238i	0.0434582	+	0.133751i	−0.926973	+	0.375127i	$0.877599\pi$
$440$	1.02146	−	1.55856i	0.0486960	−	0.0743016i
$441$		0			0
$442$	−20.1274	−	14.6234i	−0.957362	−	0.695564i
$443$	5.27327			0.250541			0.125270	−	0.992123i	$-0.460020\pi$
$443$	5.27327			0.250541			0.125270	+	0.992123i	$0.460020\pi$
$444$		0			0
$445$	0.754284	+	15.6472i	0.0357565	+	0.741750i
$446$	18.7460	−	13.6197i	0.887647	−	0.644914i
$447$		0			0
$448$	−0.257524	−	0.792578i	−0.0121669	−	0.0374458i
$449$	6.81659			0.321695			0.160847	−	0.986979i	$-0.448577\pi$
$449$	6.81659			0.321695			0.160847	+	0.986979i	$0.448577\pi$
$450$		0			0
$451$	1.55583			0.0732609
$452$	−0.538232	−	1.65651i	−0.0253163	−	0.0779156i
$453$		0			0
$454$	0.204401	−	0.148506i	0.00959300	−	0.00696972i
$455$	−4.66167	+	7.11289i	−0.218542	+	0.333457i
$456$		0			0
$457$	4.17712			0.195397			0.0976987	−	0.995216i	$-0.468852\pi$
$457$	4.17712			0.195397			0.0976987	+	0.995216i	$0.468852\pi$
$458$	−17.0625	−	12.3966i	−0.797277	−	0.579255i
$459$		0			0
$460$	4.94194	+	6.15537i	0.230419	+	0.286995i
$461$	11.5678	+	35.6020i	0.538766	+	1.65815i	0.735367	+	0.677669i	$0.237010\pi$
$461$	11.5678	+	35.6020i	0.538766	+	1.65815i	−0.196601	+	0.980484i	$0.562990\pi$
$462$		0			0
$463$	−4.28879	+	13.1995i	−0.199317	+	0.613434i	0.800582	+	0.599223i	$0.204524\pi$
$463$	−4.28879	+	13.1995i	−0.199317	+	0.613434i	−0.999899	+	0.0142111i	$0.995476\pi$
$464$	−1.01037	−	3.10959i	−0.0469052	−	0.144359i
$465$		0			0
$466$	−4.51398	+	13.8926i	−0.209106	+	0.643562i
$467$	11.2134	+	8.14705i	0.518896	+	0.377000i	0.816188	−	0.577786i	$-0.196083\pi$
$467$	11.2134	+	8.14705i	0.518896	+	0.377000i	−0.297292	+	0.954787i	$0.596083\pi$
$468$		0			0
$469$	1.01125	+	0.734713i	0.0466950	+	0.0339259i
$470$	1.16663	+	1.45309i	0.0538128	+	0.0670258i
$471$		0			0
$472$	−10.9480	+	7.95422i	−0.503924	+	0.366123i
$473$	0.422023	+	1.29885i	0.0194046	+	0.0597213i
$474$		0			0
$475$	17.2673	+	39.6749i	0.792279	+	1.82041i
$476$	4.54301			0.208228
$477$		0			0
$478$	−4.70704	+	3.41986i	−0.215295	+	0.156421i
$479$	23.2976	−	16.9267i	1.06450	−	0.773401i	0.0895806	−	0.995980i	$-0.471447\pi$
$479$	23.2976	−	16.9267i	1.06450	−	0.773401i	0.974915	+	0.222578i	$0.0714473\pi$
$480$		0			0
$481$	−27.0076	−	19.6221i	−1.23144	−	0.894692i
$482$	−13.7291			−0.625345
$483$		0			0
$484$	−3.18458	+	9.80111i	−0.144753	+	0.445505i
$485$	−23.1883	+	8.78982i	−1.05293	+	0.399125i
$486$		0			0
$487$	12.0366	−	37.0449i	0.545430	−	1.67866i	−0.174534	−	0.984651i	$-0.555842\pi$
$487$	12.0366	−	37.0449i	0.545430	−	1.67866i	0.719964	−	0.694011i	$-0.244158\pi$
$488$	−1.81832	+	5.59621i	−0.0823114	+	0.253328i
$489$		0			0
$490$	0.678887	+	14.0832i	0.0306690	+	0.636213i
$491$	7.26403	−	22.3564i	0.327821	−	1.00893i	−0.642330	−	0.766428i	$-0.722032\pi$
$491$	7.26403	−	22.3564i	0.327821	−	1.00893i	0.970151	−	0.242501i	$-0.0779679\pi$
$492$		0			0
$493$	17.8240			0.802753
$494$	−31.9515	−	23.2141i	−1.43757	−	1.04445i
$495$		0			0
$496$	−4.85599	+	3.52808i	−0.218040	+	0.158416i
$497$	1.59196	−	1.15662i	0.0714091	−	0.0518817i
$498$		0			0
$499$	28.2651			1.26532			0.632660	−	0.774430i	$-0.281963\pi$
$499$	28.2651			1.26532			0.632660	+	0.774430i	$0.281963\pi$
$500$	−11.0198	−	1.88771i	−0.492822	−	0.0844209i
$501$		0			0
$502$	−4.91144	−	15.1159i	−0.219208	−	0.674654i
$503$	5.58565	−	4.05821i	0.249052	−	0.180947i	−0.456255	−	0.889849i	$-0.650809\pi$
$503$	5.58565	−	4.05821i	0.249052	−	0.180947i	0.705306	+	0.708903i	$0.250809\pi$
$504$		0			0
$505$	−27.4178	−	7.46988i	−1.22007	−	0.332405i
$506$	2.38008	+	1.72923i	0.105808	+	0.0768737i
$507$		0			0
$508$	−4.58448	−	3.33082i	−0.203403	−	0.147781i
$509$	−10.3641	+	31.8975i	−0.459382	+	1.41383i	0.406531	+	0.913637i	$0.366738\pi$
$509$	−10.3641	+	31.8975i	−0.459382	+	1.41383i	−0.865913	+	0.500195i	$0.833262\pi$
$510$		0			0
$511$	0.857557	+	2.63929i	0.0379361	+	0.116755i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	−0.714612	−	2.19935i	−0.0315202	−	0.0970091i
$515$	−14.6679	+	5.56005i	−0.646345	+	0.245005i
$516$		0			0
$517$	0.561861	+	0.408216i	0.0247106	+	0.0179533i
$518$	6.09595			0.267841
$519$		0			0
$520$	9.54229	−	3.61712i	0.418457	−	0.158621i
$521$	0.997861	−	0.724989i	0.0437171	−	0.0317623i	−0.565712	−	0.824603i	$-0.691399\pi$
$521$	0.997861	−	0.724989i	0.0437171	−	0.0317623i	0.609429	+	0.792840i	$0.291399\pi$
$522$		0			0
$523$	7.11681	+	21.9033i	0.311196	+	0.957764i	0.977292	+	0.211898i	$0.0679643\pi$
$523$	7.11681	+	21.9033i	0.311196	+	0.957764i	−0.666095	+	0.745867i	$0.732036\pi$
$524$	16.4745			0.719690
$525$		0			0
$526$	−21.4593			−0.935671
$527$	−10.1114	−	31.1196i	−0.440458	−	1.35559i
$528$		0			0
$529$	8.52520	−	6.19392i	0.370661	−	0.269301i
$530$	−8.99749	−	11.2067i	−0.390826	−	0.486788i
$531$		0			0
$532$	7.21188			0.312674
$533$	6.89294	+	5.00801i	0.298566	+	0.216921i
$534$		0			0
$535$	23.2356	+	6.33047i	1.00456	+	0.273690i
$536$	−0.463496	−	1.42649i	−0.0200200	−	0.0616151i
$537$		0			0
$538$	6.60877	−	20.3397i	0.284924	−	0.876907i
$539$	1.62382	+	4.99760i	0.0699428	+	0.215262i
$540$		0			0
$541$	−8.27238	+	25.4598i	−0.355657	+	1.09460i	0.599970	+	0.800023i	$0.295179\pi$
$541$	−8.27238	+	25.4598i	−0.355657	+	1.09460i	−0.955627	+	0.294578i	$0.904821\pi$
$542$	−21.1400	−	15.3591i	−0.908042	−	0.659731i
$543$		0			0
$544$	−4.41027	−	3.20425i	−0.189089	−	0.137381i
$545$	−13.0359	+	19.8906i	−0.558398	+	0.852018i
$546$		0			0
$547$	−5.19947	+	3.77763i	−0.222313	+	0.161520i	−0.693367	−	0.720584i	$-0.743874\pi$
$547$	−5.19947	+	3.77763i	−0.222313	+	0.161520i	0.471054	+	0.882104i	$0.343874\pi$
$548$	0.894062	+	2.75164i	0.0381924	+	0.117544i
$549$		0			0
$550$	−4.14751	+	0.400797i	−0.176850	+	0.0170900i
$551$	28.2950			1.20541
$552$		0			0
$553$	3.48495	−	2.53197i	0.148195	−	0.107670i
$554$	−15.0856	+	10.9604i	−0.640928	+	0.465661i
$555$		0			0
$556$	−4.03660	−	2.93276i	−0.171190	−	0.124377i
$557$	−44.0843			−1.86791			−0.933957	−	0.357386i	$-0.883668\pi$
$557$	−44.0843			−1.86791			−0.933957	+	0.357386i	$0.883668\pi$
$558$		0			0
$559$	−2.31112	+	7.11289i	−0.0977498	+	0.300843i
$560$	−1.02146	+	1.55856i	−0.0431644	+	0.0658613i
$561$		0			0
$562$	4.57924	−	14.0934i	0.193164	−	0.594496i
$563$	−6.20440	+	19.0952i	−0.261484	+	0.804766i	0.730998	+	0.682379i	$0.239055\pi$
$563$	−6.20440	+	19.0952i	−0.261484	+	0.804766i	−0.992483	+	0.122387i	$0.960945\pi$
$564$		0			0
$565$	−2.13487	+	3.25744i	−0.0898147	+	0.137041i
$566$	−4.87628	+	15.0076i	−0.204965	+	0.630818i
$567$		0			0
$568$	−2.36123			−0.0990750
$569$	−24.2170	−	17.5947i	−1.01523	−	0.737609i	−0.0499312	−	0.998753i	$-0.515900\pi$
$569$	−24.2170	−	17.5947i	−1.01523	−	0.737609i	−0.965300	+	0.261144i	$0.915900\pi$
$570$		0			0
$571$	11.5201	−	8.36985i	0.482102	−	0.350267i	−0.320037	−	0.947405i	$-0.603695\pi$
$571$	11.5201	−	8.36985i	0.482102	−	0.350267i	0.802139	+	0.597138i	$0.203695\pi$
$572$	3.07691	−	2.23551i	0.128652	−	0.0934712i
$573$		0			0
$574$	−1.55583			−0.0649389
$575$	3.81445	−	17.2339i	0.159074	−	0.718703i
$576$		0			0
$577$	−5.62687	−	17.3177i	−0.234250	−	0.720946i	−0.997220	−	0.0745128i	$-0.976260\pi$
$577$	−5.62687	−	17.3177i	−0.234250	−	0.720946i	0.762970	−	0.646433i	$-0.223740\pi$
$578$	10.2889	−	7.47531i	0.427961	−	0.310932i
$579$		0			0
$580$	−4.00757	+	6.11485i	−0.166405	+	0.253905i
$581$	8.31675	+	6.04247i	0.345037	+	0.250684i
$582$		0			0
$583$	−4.33327	−	3.14830i	−0.179466	−	0.130389i
$584$	1.02903	−	3.16703i	0.0425815	−	0.131052i
$585$		0			0
$586$	5.68601	+	17.4998i	0.234887	+	0.722908i
$587$	−1.59586	+	4.91155i	−0.0658681	+	0.202721i	−0.978574	−	0.205896i	$-0.933989\pi$
$587$	−1.59586	+	4.91155i	−0.0658681	+	0.202721i	0.912706	+	0.408618i	$0.133989\pi$
$588$		0			0
$589$	−16.0515	−	49.4014i	−0.661389	−	2.03555i
$590$	29.1955	+	7.95422i	1.20196	+	0.327470i
$591$		0			0
$592$	−5.91785	−	4.29957i	−0.243222	−	0.176711i
$593$	35.6286			1.46309			0.731546	−	0.681793i	$-0.238799\pi$
$593$	35.6286			1.46309			0.731546	+	0.681793i	$0.238799\pi$
$594$		0			0
$595$	−6.35979	−	7.92135i	−0.260726	−	0.324744i
$596$	1.62271	−	1.17897i	0.0664690	−	0.0482925i
$597$		0			0
$598$	4.97854	+	15.3224i	0.203588	+	0.626579i
$599$	31.8284			1.30047			0.650236	−	0.759733i	$-0.274670\pi$
$599$	31.8284			1.30047			0.650236	+	0.759733i	$0.274670\pi$
$600$		0			0
$601$	−12.6378			−0.515508			−0.257754	−	0.966211i	$-0.582982\pi$
$601$	−12.6378			−0.515508			−0.257754	+	0.966211i	$0.582982\pi$
$602$	−0.422023	−	1.29885i	−0.0172004	−	0.0529373i
$603$		0			0
$604$	1.59353	−	1.15777i	0.0648397	−	0.0471088i
$605$	21.5477	−	8.16791i	0.876037	−	0.332073i
$606$		0			0
$607$	34.9481			1.41850			0.709250	−	0.704957i	$-0.249034\pi$
$607$	34.9481			1.41850			0.709250	+	0.704957i	$0.249034\pi$
$608$	−7.00116	−	5.08664i	−0.283935	−	0.206291i
$609$		0			0
$610$	12.3032	−	4.66369i	0.498142	−	0.188827i
$611$	1.17527	+	3.61712i	0.0475465	+	0.146333i
$612$		0			0
$613$	2.20106	−	6.77418i	0.0889001	−	0.273606i	−0.896716	−	0.442607i	$-0.854054\pi$
$613$	2.20106	−	6.77418i	0.0889001	−	0.273606i	0.985616	+	0.169000i	$0.0540538\pi$
$614$	10.5430	+	32.4480i	0.425481	+	1.30950i
$615$		0			0
$616$	−0.214612	+	0.660507i	−0.00864696	+	0.0266126i
$617$	−13.0147	−	9.45572i	−0.523951	−	0.380673i	0.294139	−	0.955763i	$-0.404967\pi$
$617$	−13.0147	−	9.45572i	−0.523951	−	0.380673i	−0.818090	+	0.575090i	$0.804967\pi$
$618$		0			0
$619$	0.607103	+	0.441086i	0.0244015	+	0.0177287i	0.599919	−	0.800061i	$-0.295199\pi$
$619$	0.607103	+	0.441086i	0.0244015	+	0.0177287i	−0.575518	+	0.817789i	$0.695199\pi$
$620$	12.9496	+	3.52808i	0.520069	+	0.141691i
$621$		0			0
$622$	10.5479	−	7.66348i	0.422931	−	0.307278i
$623$	−1.80416	−	5.55263i	−0.0722821	−	0.222461i
$624$		0			0
$625$	12.1353	+	21.8572i	0.485410	+	0.874287i
$626$	−3.48262			−0.139194
$627$		0			0
$628$	−6.29793	+	4.57571i	−0.251315	+	0.182591i
$629$	32.2606	−	23.4387i	1.28631	−	0.934561i
$630$		0			0
$631$	12.4391	+	9.03753i	0.495192	+	0.359778i	0.807178	−	0.590309i	$-0.200994\pi$
$631$	12.4391	+	9.03753i	0.495192	+	0.359778i	−0.311985	+	0.950087i	$0.600994\pi$
$632$	−5.16896			−0.205610
$633$		0			0
$634$	1.48957	−	4.58443i	0.0591585	−	0.182071i
$635$	0.610113	+	12.6565i	0.0242116	+	0.502258i
$636$		0			0
$637$	−8.89249	+	27.3683i	−0.352333	+	1.08437i
$638$	−0.842006	+	2.59143i	−0.0333353	+	0.102596i
$639$		0			0
$640$	2.09089	−	0.792578i	0.0826497	−	0.0313294i
$641$	−2.92140	+	8.99114i	−0.115388	+	0.355129i	−0.992028	−	0.126019i	$-0.959780\pi$
$641$	−2.92140	+	8.99114i	−0.115388	+	0.355129i	0.876639	+	0.481148i	$0.159780\pi$
$642$		0			0
$643$	32.8334			1.29482			0.647411	−	0.762141i	$-0.275852\pi$
$643$	32.8334			1.29482			0.647411	+	0.762141i	$0.275852\pi$
$644$	−2.38008	−	1.72923i	−0.0937883	−	0.0681412i
$645$		0			0
$646$	38.1661	−	27.7293i	1.50163	−	1.09100i
$647$	14.4556	−	10.5026i	0.568309	−	0.412901i	−0.266182	−	0.963923i	$-0.585762\pi$
$647$	14.4556	−	10.5026i	0.568309	−	0.412901i	0.834490	+	0.551022i	$0.185762\pi$
$648$		0			0
$649$	11.2775			0.442682
$650$	−19.6653	−	11.5746i	−0.771335	−	0.453994i
$651$		0			0
$652$	4.35589	+	13.4060i	0.170590	+	0.525021i
$653$	−25.8596	+	18.7881i	−1.01196	+	0.735235i	−0.964620	−	0.263644i	$-0.915076\pi$
$653$	−25.8596	+	18.7881i	−1.01196	+	0.735235i	−0.0473435	+	0.998879i	$0.515076\pi$
$654$		0			0
$655$	−23.0627	−	28.7254i	−0.901135	−	1.12240i
$656$	1.51037	+	1.09735i	0.0589700	+	0.0428442i
$657$		0			0
$658$	−0.561861	−	0.408216i	−0.0219036	−	0.0159139i
$659$	3.52244	−	10.8410i	0.137215	−	0.422304i	−0.858713	−	0.512457i	$-0.828736\pi$
$659$	3.52244	−	10.8410i	0.137215	−	0.422304i	0.995928	+	0.0901527i	$0.0287355\pi$
$660$		0			0
$661$	2.26642	+	6.97531i	0.0881533	+	0.271308i	0.985409	−	0.170203i	$-0.0544425\pi$
$661$	2.26642	+	6.97531i	0.0881533	+	0.271308i	−0.897256	+	0.441511i	$0.854442\pi$
$662$	−2.64625	+	8.14431i	−0.102849	+	0.316537i
$663$		0			0
$664$	−3.81191	−	11.7319i	−0.147931	−	0.455284i
$665$	−10.0960	−	12.5749i	−0.391504	−	0.487633i
$666$		0			0
$667$	−9.33799	−	6.78445i	−0.361568	−	0.262695i
$668$	8.15615			0.315571
$669$		0			0
$670$	−1.83843	+	2.80512i	−0.0710248	+	0.108371i
$671$	3.96717	−	2.88232i	0.153151	−	0.111271i
$672$		0			0
$673$	−10.1243	−	31.1595i	−0.390264	−	1.20111i	−0.932589	−	0.360940i	$-0.882456\pi$
$673$	−10.1243	−	31.1595i	−0.390264	−	1.20111i	0.542325	−	0.840169i	$-0.317544\pi$
$674$	14.6712			0.565113
$675$		0			0
$676$	7.82777			0.301068
$677$	10.0686	+	30.9879i	0.386967	+	1.19096i	0.935043	+	0.354534i	$0.115360\pi$
$677$	10.0686	+	30.9879i	0.386967	+	1.19096i	−0.548076	+	0.836428i	$0.684640\pi$
$678$		0			0
$679$	7.47707	−	5.43241i	0.286944	−	0.208477i
$680$	0.586930	+	12.1756i	0.0225077	+	0.466911i
$681$		0			0
$682$	5.00214			0.191542
$683$	−3.51875	−	2.55652i	−0.134641	−	0.0978227i	0.518426	−	0.855123i	$-0.326518\pi$
$683$	−3.51875	−	2.55652i	−0.134641	−	0.0978227i	−0.653067	+	0.757300i	$0.726518\pi$
$684$		0			0
$685$	3.54625	−	5.41096i	0.135495	−	0.206742i
$686$	−3.42649	−	10.5456i	−0.130824	−	0.402635i
$687$		0			0
$688$	−0.506408	+	1.55856i	−0.0193066	+	0.0594197i
$689$	−9.06413	−	27.8965i	−0.345316	−	1.06277i
$690$		0			0
$691$	−6.26053	+	19.2679i	−0.238162	+	0.732987i	0.758524	+	0.651645i	$0.225921\pi$
$691$	−6.26053	+	19.2679i	−0.238162	+	0.732987i	−0.996686	+	0.0813423i	$0.974079\pi$
$692$	−2.02526	−	1.47144i	−0.0769888	−	0.0559356i
$693$		0			0
$694$	18.5970	+	13.5115i	0.705933	+	0.512891i
$695$	0.537200	+	11.1440i	0.0203772	+	0.422714i
$696$		0			0
$697$	−8.23362	+	5.98208i	−0.311871	+	0.226587i
$698$	−1.09708	−	3.37647i	−0.0415252	−	0.127801i
$699$		0			0
$700$	4.14751	−	0.400797i	0.156761	−	0.0151487i
$701$	−12.5964			−0.475758			−0.237879	−	0.971295i	$-0.576452\pi$
$701$	−12.5964			−0.475758			−0.237879	+	0.971295i	$0.576452\pi$
$702$		0			0
$703$	51.2126	−	37.2081i	1.93152	−	1.40333i
$704$	0.674207	−	0.489840i	0.0254101	−	0.0184615i
$705$		0			0
$706$	4.56375	+	3.31576i	0.171759	+	0.124790i
$707$	10.5908			0.398310
$708$		0			0
$709$	9.10924	−	28.0354i	0.342105	−	1.05289i	−0.621011	−	0.783802i	$-0.713278\pi$
$709$	9.10924	−	28.0354i	0.342105	−	1.05289i	0.963116	−	0.269088i	$-0.0867222\pi$
$710$	3.30550	+	4.11712i	0.124053	+	0.154513i
$711$		0			0
$712$	−2.16491	+	6.66290i	−0.0811333	+	0.249703i
$713$	−6.54788	+	20.1523i	−0.245220	+	0.754710i
$714$		0			0
$715$	−8.20529	−	2.23551i	−0.306860	−	0.0836032i
$716$	6.19042	−	19.0522i	0.231347	−	0.712012i
$717$		0			0
$718$	−16.9066			−0.630948
$719$	−24.3987	−	17.7267i	−0.909919	−	0.661095i	0.0310756	−	0.999517i	$-0.490107\pi$
$719$	−24.3987	−	17.7267i	−0.909919	−	0.661095i	−0.940994	+	0.338422i	$0.890107\pi$
$720$		0			0
$721$	4.72966	−	3.43630i	0.176142	−	0.127974i
$722$	45.2162	−	32.8515i	1.68277	−	1.22261i
$723$		0			0
$724$	7.87829			0.292794
$725$	16.2723	−	1.57248i	0.604338	−	0.0584006i
$726$		0			0
$727$	1.83783	+	5.65626i	0.0681614	+	0.209779i	0.979336	−	0.202242i	$-0.0648229\pi$
$727$	1.83783	+	5.65626i	0.0681614	+	0.209779i	−0.911174	+	0.412021i	$0.864823\pi$
$728$	−3.07691	+	2.23551i	−0.114038	+	0.0828533i
$729$		0			0
$730$	−6.96268	+	2.63929i	−0.257700	+	0.0976845i
$731$	−7.22743	−	5.25103i	−0.267316	−	0.194216i
$732$		0			0
$733$	−8.23281	−	5.98148i	−0.304086	−	0.220931i	0.425269	−	0.905067i	$-0.360180\pi$
$733$	−8.23281	−	5.98148i	−0.304086	−	0.220931i	−0.729355	+	0.684136i	$0.760180\pi$
$734$	3.89773	−	11.9960i	0.143868	−	0.442780i
$735$		0			0
$736$	1.09089	+	3.35741i	0.0402107	+	0.123756i
$737$	−0.386261	+	1.18879i	−0.0142281	+	0.0437896i
$738$		0			0
$739$	11.2234	+	34.5422i	0.412861	+	1.27066i	0.914150	+	0.405376i	$0.132859\pi$
$739$	11.2234	+	34.5422i	0.412861	+	1.27066i	−0.501289	+	0.865280i	$0.667141\pi$
$740$	0.787561	+	16.3376i	0.0289513	+	0.600581i
$741$		0			0
$742$	4.33327	+	3.14830i	0.159079	+	0.115578i
$743$	−2.84832			−0.104495			−0.0522473	−	0.998634i	$-0.516638\pi$
$743$	−2.84832			−0.104495			−0.0522473	+	0.998634i	$0.516638\pi$
$744$		0			0
$745$	−4.32734	−	1.17897i	−0.158542	−	0.0431941i
$746$	10.7191	−	7.78791i	0.392455	−	0.285136i
$747$		0			0
$748$	1.40387	+	4.32066i	0.0513305	+	0.157979i
$749$	−8.97537			−0.327953
$750$		0			0
$751$	−31.5502			−1.15128			−0.575641	−	0.817702i	$-0.695248\pi$
$751$	−31.5502			−1.15128			−0.575641	+	0.817702i	$0.695248\pi$
$752$	0.257524	+	0.792578i	0.00939094	+	0.0289023i
$753$		0			0
$754$	−12.0719	+	8.77076i	−0.439633	+	0.319412i
$755$	−4.24951	−	1.15777i	−0.154656	−	0.0421354i
$756$		0			0
$757$	−45.6446			−1.65898			−0.829491	−	0.558520i	$-0.811369\pi$
$757$	−45.6446			−1.65898			−0.829491	+	0.558520i	$0.811369\pi$
$758$	18.0702	+	13.1288i	0.656339	+	0.476858i
$759$		0			0
$760$	0.931731	+	19.3283i	0.0337974	+	0.701111i
$761$	−2.80550	−	8.63445i	−0.101699	−	0.312998i	0.887242	−	0.461304i	$-0.152618\pi$
$761$	−2.80550	−	8.63445i	−0.101699	−	0.312998i	−0.988942	+	0.148305i	$0.952618\pi$
$762$		0			0
$763$	2.73890	−	8.42947i	0.0991549	−	0.305167i
$764$	1.63013	+	5.01702i	0.0589760	+	0.181510i
$765$		0			0
$766$	7.52545	−	23.1610i	0.271906	−	0.836840i
$767$	49.9641	+	36.3010i	1.80410	+	1.31075i
$768$		0			0
$769$	20.5964	+	14.9641i	0.742724	+	0.539621i	0.893563	−	0.448938i	$-0.148198\pi$
$769$	20.5964	+	14.9641i	0.742724	+	0.539621i	−0.150839	+	0.988558i	$0.548198\pi$
$770$	1.45212	−	0.550444i	0.0523308	−	0.0198366i
$771$		0			0
$772$	10.8781	−	7.90343i	0.391513	−	0.284451i
$773$	−5.30034	−	16.3128i	−0.190640	−	0.586729i	0.809360	−	0.587313i	$-0.199814\pi$
$773$	−5.30034	−	16.3128i	−0.190640	−	0.586729i	−1.00000		0.000583568i	$0.999814\pi$
$774$		0			0
$775$	−11.9766	−	27.5184i	−0.430211	−	0.988489i
$776$	−11.0902			−0.398114
$777$		0			0
$778$	−24.3608	+	17.6992i	−0.873377	+	0.634546i
$779$	−13.0706	+	9.49635i	−0.468303	+	0.340242i
$780$		0			0
$781$	1.59196	+	1.15662i	0.0569647	+	0.0413873i
$782$	−19.2445			−0.688182
$783$		0			0
$784$	−1.94851	+	5.99689i	−0.0695895	+	0.214175i
$785$	16.7949	+	4.57571i	0.599435	+	0.163314i
$786$		0			0
$787$	3.48351	−	10.7211i	0.124174	−	0.382168i	−0.869576	−	0.493799i	$-0.835608\pi$
$787$	3.48351	−	10.7211i	0.124174	−	0.382168i	0.993750	+	0.111632i	$0.0356077\pi$
$788$	1.68061	−	5.17240i	0.0598694	−	0.184259i
$789$		0			0
$790$	7.23607	+	9.01278i	0.257448	+	0.320660i
$791$	0.448544	−	1.38048i	0.0159484	−	0.0490841i
$792$		0			0
$793$	26.8540			0.953613
$794$	28.6152	+	20.7902i	1.01552	+	0.737816i
$795$		0			0
$796$	14.0842	−	10.2328i	0.499200	−	0.362690i
$797$	−21.5775	+	15.6770i	−0.764315	+	0.555307i	−0.900231	−	0.435413i	$-0.856602\pi$
$797$	−21.5775	+	15.6770i	−0.764315	+	0.555307i	0.135916	+	0.990720i	$0.456602\pi$
$798$		0			0
$799$	−4.54301			−0.160720
$800$	−4.30902	−	2.53621i	−0.152347	−	0.0896686i
$801$		0			0
$802$	−1.75149	−	5.39053i	−0.0618472	−	0.190346i
$803$	−2.24511	+	1.63117i	−0.0792284	+	0.0575628i
$804$		0			0
$805$	0.316747	+	6.57075i	0.0111639	+	0.231589i
$806$	22.1615	+	16.1013i	0.780605	+	0.567143i
$807$		0			0
$808$	−10.2814	−	7.46988i	−0.361699	−	0.262789i
$809$	−3.39121	+	10.4371i	−0.119229	+	0.366948i	−0.992805	−	0.119738i	$-0.961794\pi$
$809$	−3.39121	+	10.4371i	−0.119229	+	0.366948i	0.873577	+	0.486686i	$0.161794\pi$
$810$		0			0
$811$	−3.04882	−	9.38329i	−0.107058	−	0.329492i	0.883150	−	0.469091i	$-0.155419\pi$
$811$	−3.04882	−	9.38329i	−0.107058	−	0.329492i	−0.990208	+	0.139599i	$0.955419\pi$
$812$	0.842006	−	2.59143i	0.0295486	−	0.0909413i
$813$		0			0
$814$	1.88375	+	5.79760i	0.0660255	+	0.203206i
$815$	17.2774	−	26.3623i	0.605201	−	0.923431i
$816$		0			0
$817$	−11.4733	−	8.33584i	−0.401400	−	0.291634i
$818$	−19.3676			−0.677174
$819$		0			0
$820$	−0.201003	−	4.16971i	−0.00701934	−	0.145613i
$821$	−1.85904	+	1.35067i	−0.0648808	+	0.0471387i	−0.619753	−	0.784797i	$-0.712767\pi$
$821$	−1.85904	+	1.35067i	−0.0648808	+	0.0471387i	0.554872	+	0.831936i	$0.312767\pi$
$822$		0			0
$823$	0.248884	+	0.765985i	0.00867554	+	0.0267006i	0.955301	−	0.295636i	$-0.0955316\pi$
$823$	0.248884	+	0.765985i	0.00867554	+	0.0267006i	−0.946625	+	0.322337i	$0.895532\pi$
$824$	−7.01515			−0.244384
$825$		0			0
$826$	−11.2775			−0.392396
$827$	−11.2650	−	34.6701i	−0.391722	−	1.20560i	−0.931485	−	0.363780i	$-0.881486\pi$
$827$	−11.2650	−	34.6701i	−0.391722	−	1.20560i	0.539762	−	0.841817i	$-0.318514\pi$
$828$		0			0
$829$	−23.9231	+	17.3811i	−0.830883	+	0.603672i	−0.919809	−	0.392367i	$-0.871656\pi$
$829$	−23.9231	+	17.3811i	−0.830883	+	0.603672i	0.0889263	+	0.996038i	$0.471656\pi$
$830$	−15.1197	+	23.0701i	−0.524814	+	0.800774i
$831$		0			0
$832$	4.56375			0.158219
$833$	−27.8090	−	20.2044i	−0.963525	−	0.700042i
$834$		0			0
$835$	−11.4178	−	14.2213i	−0.395131	−	0.492150i
$836$	2.22859	+	6.85890i	0.0770775	+	0.237220i
$837$		0			0
$838$	7.10097	−	21.8545i	0.245299	−	0.754953i
$839$	13.4507	+	41.3969i	0.464369	+	1.42918i	0.859774	+	0.510674i	$0.170604\pi$
$839$	13.4507	+	41.3969i	0.464369	+	1.42918i	−0.395405	+	0.918507i	$0.629396\pi$
$840$		0			0
$841$	−5.65797	+	17.4135i	−0.195103	+	0.600464i
$842$	−8.19306	−	5.95261i	−0.282351	−	0.205140i
$843$		0			0
$844$	0.218381	+	0.158663i	0.00751699	+	0.00546141i
$845$	−10.9582	−	13.6488i	−0.376972	−	0.469532i
$846$		0			0
$847$	−6.94804	+	5.04805i	−0.238738	+	0.173453i
$848$	−1.98612	−	6.11264i	−0.0682035	−	0.209909i
$849$		0			0
$850$	20.4081	−	18.0680i	0.699991	−	0.619729i
$851$	−25.8229			−0.885197
$852$		0			0
$853$	−40.9415	+	29.7458i	−1.40181	+	1.01848i	−0.407361	+	0.913267i	$0.633551\pi$
$853$	−40.9415	+	29.7458i	−1.40181	+	1.01848i	−0.994450	+	0.105208i	$0.966449\pi$
$854$	−3.96717	+	2.88232i	−0.135754	+	0.0986308i
$855$		0			0
$856$	8.71314	+	6.33047i	0.297809	+	0.216371i
$857$	−34.1589			−1.16684			−0.583422	−	0.812169i	$-0.698287\pi$
$857$	−34.1589			−1.16684			−0.583422	+	0.812169i	$0.698287\pi$
$858$		0			0
$859$	3.39523	−	10.4494i	0.115844	−	0.356530i	−0.876278	−	0.481805i	$-0.839981\pi$
$859$	3.39523	−	10.4494i	0.115844	−	0.356530i	0.992122	+	0.125275i	$0.0399813\pi$
$860$	3.42649	−	1.29885i	0.116842	−	0.0442905i
$861$		0			0
$862$	−8.80773	+	27.1074i	−0.299993	+	0.923282i
$863$	14.3100	−	44.0415i	0.487117	−	1.49919i	−0.341774	−	0.939782i	$-0.611028\pi$
$863$	14.3100	−	44.0415i	0.487117	−	1.49919i	0.828891	−	0.559410i	$-0.188972\pi$
$864$		0			0
$865$	0.269526	+	5.59119i	0.00916417	+	0.190106i
$866$	−4.91018	+	15.1120i	−0.166855	+	0.513526i
$867$		0			0
$868$	−5.00214			−0.169784
$869$	3.48495	+	2.53197i	0.118219	+	0.0858911i
$870$		0			0
$871$	−5.53786	+	4.02349i	−0.187643	+	0.136331i
$872$	−8.60431	+	6.25140i	−0.291379	+	0.211699i
$873$		0			0
$874$	−30.5500			−1.03337
$875$	−6.50497	−	6.67066i	−0.219908	−	0.225509i
$876$		0			0
$877$	6.48231	+	19.9505i	0.218892	+	0.673681i	0.998854	+	0.0478541i	$0.0152383\pi$
$877$	6.48231	+	19.9505i	0.218892	+	0.673681i	−0.779962	+	0.625827i	$0.784762\pi$
$878$	2.38385	−	1.73197i	0.0804511	−	0.0584511i
$879$		0			0
$880$	−1.79793	−	0.489840i	−0.0606082	−	0.0165125i
$881$	−41.1491	−	29.8966i	−1.38635	−	1.00724i	−0.996255	−	0.0864666i	$-0.972442\pi$
$881$	−41.1491	−	29.8966i	−1.38635	−	1.00724i	−0.390094	−	0.920775i	$-0.627558\pi$
$882$		0			0
$883$	39.7141	+	28.8540i	1.33649	+	0.971014i	0.999565	+	0.0294804i	$0.00938527\pi$
$883$	39.7141	+	28.8540i	1.33649	+	0.971014i	0.336920	+	0.941533i	$0.390615\pi$
$884$	−7.68797	+	23.6611i	−0.258574	+	0.795810i
$885$		0			0
$886$	−1.62953	−	5.01518i	−0.0547451	−	0.168488i
$887$	11.4242	−	35.1599i	0.383586	−	1.18056i	−0.553915	−	0.832573i	$-0.686867\pi$
$887$	11.4242	−	35.1599i	0.383586	−	1.18056i	0.937501	−	0.347982i	$-0.113133\pi$
$888$		0			0
$889$	−1.45932	−	4.49133i	−0.0489440	−	0.150634i
$890$	14.6483	−	5.55263i	0.491013	−	0.186125i
$891$		0			0
$892$	−18.7460	−	13.6197i	−0.627662	−	0.456023i
$893$	−7.21188			−0.241336
$894$		0			0
$895$	−41.8860	+	15.8774i	−1.40009	+	0.530723i
$896$	−0.674207	+	0.489840i	−0.0225237	+	0.0163644i
$897$		0			0
$898$	−2.10644	−	6.48297i	−0.0702929	−	0.216339i
$899$	−19.6253			−0.654542
$900$		0			0
$901$	35.0373			1.16726
$902$	−0.480776	−	1.47968i	−0.0160081	−	0.0492679i
$903$		0			0
$904$	−1.40911	+	1.02378i	−0.0468663	+	0.0340504i
$905$	−11.0289	−	13.7369i	−0.366612	−	0.456629i
$906$		0			0
$907$	44.9718			1.49326			0.746632	−	0.665237i	$-0.231670\pi$
$907$	44.9718			1.49326			0.746632	+	0.665237i	$0.231670\pi$
$908$	−0.204401	−	0.148506i	−0.00678327	−	0.00492834i
$909$		0			0
$910$	8.20529	+	2.23551i	0.272003	+	0.0741063i
$911$	8.32785	+	25.6305i	0.275914	+	0.849176i	0.988976	+	0.148075i	$0.0473077\pi$
$911$	8.32785	+	25.6305i	0.275914	+	0.849176i	−0.713062	+	0.701101i	$0.752692\pi$
$912$		0			0
$913$	−3.17671	+	9.77692i	−0.105134	+	0.323569i
$914$	−1.29080	−	3.97268i	−0.0426959	−	0.131404i
$915$		0			0
$916$	−6.51728	+	20.0581i	−0.215337	+	0.662739i
$917$	11.1072	+	8.06985i	0.366792	+	0.266490i
$918$		0			0
$919$	−25.8087	−	18.7511i	−0.851350	−	0.618542i	0.0741679	−	0.997246i	$-0.476370\pi$
$919$	−25.8087	−	18.7511i	−0.851350	−	0.618542i	−0.925518	+	0.378704i	$0.876370\pi$
$920$	4.32696	−	6.60218i	0.142656	−	0.217667i
$921$		0			0
$922$	30.2849	−	22.0033i	0.997380	−	0.724639i
$923$	3.32998	+	10.2486i	0.109608	+	0.337338i
$924$		0			0
$925$	27.3842	−	24.2443i	0.900387	−	0.797147i
$926$	13.8788			0.456086
$927$		0			0
$928$	−2.64518	+	1.92183i	−0.0868322	+	0.0630873i
$929$	−5.06070	+	3.67681i	−0.166036	+	0.120632i	−0.667700	−	0.744430i	$-0.732721\pi$
$929$	−5.06070	+	3.67681i	−0.166036	+	0.120632i	0.501664	+	0.865062i	$0.332721\pi$
$930$		0			0
$931$	−44.1459	−	32.0738i	−1.44682	−	1.05118i
$932$	14.6075			0.478486
$933$		0			0
$934$	4.28316	−	13.1822i	0.140149	−	0.431335i
$935$	5.56837	−	8.49635i	0.182105	−	0.277860i
$936$		0			0
$937$	−9.55466	+	29.4062i	−0.312137	+	0.960660i	0.664780	+	0.747040i	$0.268525\pi$
$937$	−9.55466	+	29.4062i	−0.312137	+	0.960660i	−0.976917	+	0.213620i	$0.931475\pi$
$938$	0.386261	−	1.18879i	0.0126119	−	0.0388154i
$939$		0			0
$940$	1.02146	−	1.55856i	0.0333162	−	0.0508347i
$941$	7.92136	−	24.3794i	0.258229	−	0.794747i	−0.734947	−	0.678124i	$-0.762793\pi$
$941$	7.92136	−	24.3794i	0.258229	−	0.794747i	0.993176	−	0.116623i	$-0.0372069\pi$
$942$		0			0
$943$	6.59058			0.214619
$944$	10.9480	+	7.95422i	0.356328	+	0.258888i
$945$		0			0
$946$	1.10487	−	0.802735i	0.0359224	−	0.0260992i
$947$	−36.5775	+	26.5751i	−1.18861	+	0.863575i	−0.993117	−	0.117130i	$-0.962630\pi$
$947$	−36.5775	+	26.5751i	−1.18861	+	0.863575i	−0.195492	+	0.980705i	$0.562630\pi$
$948$		0			0
$949$	−15.1973			−0.493325
$950$	32.3972	−	28.6824i	1.05110	−	0.930580i
$951$		0			0
$952$	−1.40387	−	4.32066i	−0.0454996	−	0.140033i
$953$	−16.6690	+	12.1107i	−0.539961	+	0.392304i	−0.824070	−	0.566487i	$-0.808302\pi$
$953$	−16.6690	+	12.1107i	−0.539961	+	0.392304i	0.284110	+	0.958792i	$0.408302\pi$
$954$		0			0
$955$	6.46583	−	9.86572i	0.209229	−	0.319247i
$956$	4.70704	+	3.41986i	0.152237	+	0.110606i
$957$		0			0
$958$	−23.2976	−	16.9267i	−0.752712	−	0.546877i
$959$	−0.745080	+	2.29312i	−0.0240599	+	0.0740488i
$960$		0			0
$961$	1.55373	+	4.78188i	0.0501202	+	0.154254i
$962$	−10.3160	+	31.7493i	−0.332600	+	1.02364i
$963$		0			0
$964$	4.24254	+	13.0572i	0.136643	+	0.420544i
$965$	−29.0091	−	7.90343i	−0.933835	−	0.254421i
$966$		0			0
$967$	41.3373	+	30.0333i	1.32932	+	0.965806i	0.999765	+	0.0216692i	$0.00689807\pi$
$967$	41.3373	+	30.0333i	1.32932	+	0.965806i	0.329553	+	0.944137i	$0.393102\pi$
$968$	10.3055			0.331231
$969$		0			0
$970$	15.5252	+	19.3372i	0.498484	+	0.620880i
$971$	11.8229	−	8.58982i	0.379414	−	0.275661i	−0.381690	−	0.924291i	$-0.624658\pi$
$971$	11.8229	−	8.58982i	0.379414	−	0.275661i	0.761104	+	0.648630i	$0.224658\pi$
$972$		0			0
$973$	−1.28492	−	3.95458i	−0.0411927	−	0.126778i
$974$	−38.9513			−1.24808
$975$		0			0
$976$	5.88420			0.188349
$977$	16.1479	+	49.6981i	0.516616	+	1.58998i	0.780322	+	0.625379i	$0.215055\pi$
$977$	16.1479	+	49.6981i	0.516616	+	1.58998i	−0.263705	+	0.964603i	$0.584945\pi$
$978$		0			0
$979$	4.72335	−	3.43171i	0.150959	−	0.109678i
$980$	13.1841	−	4.99760i	0.421151	−	0.159643i
$981$		0			0
$982$	−23.5069			−0.750135
$983$	23.9541	+	17.4037i	0.764016	+	0.555090i	0.900140	−	0.435602i	$-0.143464\pi$
$983$	23.9541	+	17.4037i	0.764016	+	0.555090i	−0.136123	+	0.990692i	$0.543464\pi$
$984$		0			0
$985$	−11.3715	+	4.31050i	−0.362325	+	0.137344i
$986$	−5.50792	−	16.9516i	−0.175408	−	0.539850i
$987$		0			0
$988$	−12.2044	+	37.5613i	−0.388274	+	1.19498i
$989$	1.78772	+	5.50203i	0.0568461	+	0.174954i
$990$		0			0
$991$	4.59673	−	14.1473i	0.146020	−	0.449403i	−0.851121	−	0.524970i	$-0.824077\pi$
$991$	4.59673	−	14.1473i	0.146020	−	0.449403i	0.997141	+	0.0755666i	$0.0240765\pi$
$992$	4.85599	+	3.52808i	0.154178	+	0.112017i
$993$		0			0
$994$	−1.59196	−	1.15662i	−0.0504938	−	0.0366859i
$995$	−37.5587	−	10.2328i	−1.19069	−	0.324400i
$996$		0			0
$997$	24.8971	−	18.0888i	0.788500	−	0.572879i	−0.119018	−	0.992892i	$-0.537974\pi$
$997$	24.8971	−	18.0888i	0.788500	−	0.572879i	0.907518	+	0.420013i	$0.137974\pi$
$998$	−8.73440	−	26.8817i	−0.276483	−	0.850926i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.e.181.2		8
3.2	odd	2		50.2.d.b.31.2	yes	8
12.11	even	2		400.2.u.d.81.1		8
15.2	even	4		250.2.e.c.99.1		16
15.8	even	4		250.2.e.c.99.4		16
15.14	odd	2		250.2.d.d.151.1		8
25.21	even	5	inner	450.2.h.e.271.2		8
75.2	even	20		1250.2.b.e.1249.7		8
75.11	odd	10		1250.2.a.l.1.2		4
75.14	odd	10		1250.2.a.f.1.3		4
75.23	even	20		1250.2.b.e.1249.2		8
75.29	odd	10		250.2.d.d.101.1		8
75.47	even	20		250.2.e.c.149.4		16
75.53	even	20		250.2.e.c.149.1		16
75.71	odd	10		50.2.d.b.21.2	✓	8
300.11	even	10		10000.2.a.t.1.3		4
300.71	even	10		400.2.u.d.321.1		8
300.239	even	10		10000.2.a.x.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.21.2	✓	8	75.71	odd	10
50.2.d.b.31.2	yes	8	3.2	odd	2
250.2.d.d.101.1		8	75.29	odd	10
250.2.d.d.151.1		8	15.14	odd	2
250.2.e.c.99.1		16	15.2	even	4
250.2.e.c.99.4		16	15.8	even	4
250.2.e.c.149.1		16	75.53	even	20
250.2.e.c.149.4		16	75.47	even	20
400.2.u.d.81.1		8	12.11	even	2
400.2.u.d.321.1		8	300.71	even	10
450.2.h.e.181.2		8	1.1	even	1	trivial
450.2.h.e.271.2		8	25.21	even	5	inner
1250.2.a.f.1.3		4	75.14	odd	10
1250.2.a.l.1.2		4	75.11	odd	10
1250.2.b.e.1249.2		8	75.23	even	20
1250.2.b.e.1249.7		8	75.2	even	20
10000.2.a.t.1.3		4	300.11	even	10
10000.2.a.x.1.2		4	300.239	even	10

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.15743 + 0.587785i) q^{5} -0.833366 q^{7} +(0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.15743 + 0.587785i) q^{5} -0.833366 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.107666 - 2.23347i) q^{10} +(-0.257524 - 0.792578i) q^{11} +(1.41027 - 4.34038i) q^{13} +(0.257524 + 0.792578i) q^{14} +(0.309017 - 0.951057i) q^{16} +(4.41027 + 3.20425i) q^{17} +(7.00116 + 5.08664i) q^{19} +(-2.09089 + 0.792578i) q^{20} +(-0.674207 + 0.489840i) q^{22} +(-1.09089 - 3.35741i) q^{23} +(4.30902 + 2.53621i) q^{25} -4.56375 q^{26} +(0.674207 - 0.489840i) q^{28} +(2.64518 - 1.92183i) q^{29} +(-4.85599 - 3.52808i) q^{31} -1.00000 q^{32} +(1.68458 - 5.18459i) q^{34} +(-1.79793 - 0.489840i) q^{35} +(2.26042 - 6.95685i) q^{37} +(2.67421 - 8.23036i) q^{38} +(1.39991 + 1.74363i) q^{40} +(-0.576909 + 1.77554i) q^{41} -1.63877 q^{43} +(0.674207 + 0.489840i) q^{44} +(-2.85599 + 2.07500i) q^{46} +(-0.674207 + 0.489840i) q^{47} -6.30550 q^{49} +(1.08052 - 4.88185i) q^{50} +(1.41027 + 4.34038i) q^{52} +(5.19972 - 3.77782i) q^{53} +(-0.0897250 - 1.86130i) q^{55} +(-0.674207 - 0.489840i) q^{56} +(-2.64518 - 1.92183i) q^{58} +(-4.18178 + 12.8702i) q^{59} +(1.81832 + 5.59621i) q^{61} +(-1.85482 + 5.70855i) q^{62} +(0.309017 + 0.951057i) q^{64} +(5.59378 - 8.53513i) q^{65} +(-1.21345 - 0.881621i) q^{67} -5.45140 q^{68} +(0.0897250 + 1.86130i) q^{70} +(-1.91027 + 1.38790i) q^{71} +(-1.02903 - 3.16703i) q^{73} -7.31486 q^{74} -8.65392 q^{76} +(0.214612 + 0.660507i) q^{77} +(-4.18178 + 3.03824i) q^{79} +(1.22570 - 1.87020i) q^{80} +1.86692 q^{82} +(-9.97971 - 7.25068i) q^{83} +(7.63145 + 9.50525i) q^{85} +(0.506408 + 1.55856i) q^{86} +(0.257524 - 0.792578i) q^{88} +(2.16491 + 6.66290i) q^{89} +(-1.17527 + 3.61712i) q^{91} +(2.85599 + 2.07500i) q^{92} +(0.674207 + 0.489840i) q^{94} +(12.1147 + 15.0893i) q^{95} +(-8.97214 + 6.51864i) q^{97} +(1.94851 + 5.99689i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8} - q^{11} - 13 q^{13} + q^{14} - 2 q^{16} + 11 q^{17} + 20 q^{19} - 5 q^{20} + q^{22} + 3 q^{23} + 30 q^{25} - 22 q^{26} - q^{28} + 15 q^{29} - 9 q^{31} - 8 q^{32} - q^{34} + 15 q^{35} - 6 q^{37} + 15 q^{38} - 5 q^{40} + 9 q^{41} + 12 q^{43} - q^{44} + 7 q^{46} + q^{47} - 4 q^{49} + 5 q^{50} - 13 q^{52} - 7 q^{53} - 25 q^{55} + q^{56} - 15 q^{58} - 10 q^{59} + 6 q^{61} - 21 q^{62} - 2 q^{64} + 10 q^{65} - 11 q^{67} - 24 q^{68} + 25 q^{70} + 9 q^{71} - 8 q^{73} - 24 q^{74} - 10 q^{76} - 33 q^{77} - 10 q^{79} + 26 q^{82} - 27 q^{83} + 5 q^{85} + 23 q^{86} + q^{88} + 15 q^{89} + q^{91} - 7 q^{92} - q^{94} + 30 q^{95} - 36 q^{97} + 19 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8 - q^11 - 13 * q^13 + q^14 - 2 * q^16 + 11 * q^17 + 20 * q^19 - 5 * q^20 + q^22 + 3 * q^23 + 30 * q^25 - 22 * q^26 - q^28 + 15 * q^29 - 9 * q^31 - 8 * q^32 - q^34 + 15 * q^35 - 6 * q^37 + 15 * q^38 - 5 * q^40 + 9 * q^41 + 12 * q^43 - q^44 + 7 * q^46 + q^47 - 4 * q^49 + 5 * q^50 - 13 * q^52 - 7 * q^53 - 25 * q^55 + q^56 - 15 * q^58 - 10 * q^59 + 6 * q^61 - 21 * q^62 - 2 * q^64 + 10 * q^65 - 11 * q^67 - 24 * q^68 + 25 * q^70 + 9 * q^71 - 8 * q^73 - 24 * q^74 - 10 * q^76 - 33 * q^77 - 10 * q^79 + 26 * q^82 - 27 * q^83 + 5 * q^85 + 23 * q^86 + q^88 + 15 * q^89 + q^91 - 7 * q^92 - q^94 + 30 * q^95 - 36 * q^97 + 19 * q^98

Introduction

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