LMFDB - Embedded newform 605.2.e.a.362.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 67x^{16} + 1315x^{12} + 9193x^{8} + 16040x^{4} + 16 $ x^20 + 67x^16 + 1315x^12 + 9193x^8 + 16040x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.7
Root			$0.895288 - 0.895288i$ of defining polynomial
Character	$\chi$	$=$	605.362
Dual form			605.2.e.a.483.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.895288 - 0.895288i) q^{2} +(-1.60711 + 1.60711i) q^{3} +0.396917i q^{4} +(-0.452009 - 2.18991i) q^{5} +2.87765i q^{6} +(-1.81197 + 1.81197i) q^{7} +(2.14593 + 2.14593i) q^{8} -2.16559i q^{9} +O(q^{10})$	\(q+(0.895288 - 0.895288i) q^{2} +(-1.60711 + 1.60711i) q^{3} +0.396917i q^{4} +(-0.452009 - 2.18991i) q^{5} +2.87765i q^{6} +(-1.81197 + 1.81197i) q^{7} +(2.14593 + 2.14593i) q^{8} -2.16559i q^{9} +(-2.36528 - 1.55592i) q^{10} +(-0.637889 - 0.637889i) q^{12} +(-3.52344 - 3.52344i) q^{13} +3.24447i q^{14} +(4.24584 + 2.79299i) q^{15} +3.04862 q^{16} +(-0.212794 + 0.212794i) q^{17} +(-1.93883 - 1.93883i) q^{18} -6.08244 q^{19} +(0.869212 - 0.179410i) q^{20} -5.82406i q^{21} +(-5.07364 + 5.07364i) q^{23} -6.89749 q^{24} +(-4.59138 + 1.97971i) q^{25} -6.30899 q^{26} +(-1.34098 - 1.34098i) q^{27} +(-0.719202 - 0.719202i) q^{28} -3.98426 q^{29} +(6.30178 - 1.30072i) q^{30} +7.59403 q^{31} +(-1.56247 + 1.56247i) q^{32} +0.381023i q^{34} +(4.78707 + 3.14902i) q^{35} +0.859562 q^{36} +(-4.56304 - 4.56304i) q^{37} +(-5.44554 + 5.44554i) q^{38} +11.3251 q^{39} +(3.72941 - 5.66937i) q^{40} -2.42532i q^{41} +(-5.21422 - 5.21422i) q^{42} +(-1.43561 - 1.43561i) q^{43} +(-4.74245 + 0.978869i) q^{45} +9.08474i q^{46} +(2.49745 + 2.49745i) q^{47} +(-4.89947 + 4.89947i) q^{48} +0.433531i q^{49} +(-2.33819 + 5.88302i) q^{50} -0.683965i q^{51} +(1.39851 - 1.39851i) q^{52} +(-6.21422 + 6.21422i) q^{53} -2.40113 q^{54} -7.77673 q^{56} +(9.77514 - 9.77514i) q^{57} +(-3.56706 + 3.56706i) q^{58} +1.17470i q^{59} +(-1.10859 + 1.68525i) q^{60} +0.0929527i q^{61} +(6.79885 - 6.79885i) q^{62} +(3.92399 + 3.92399i) q^{63} +8.89496i q^{64} +(-6.12337 + 9.30862i) q^{65} +(7.07364 + 7.07364i) q^{67} +(-0.0844615 - 0.0844615i) q^{68} -16.3078i q^{69} +(7.10509 - 1.46653i) q^{70} +11.2433 q^{71} +(4.64722 - 4.64722i) q^{72} +(2.80629 + 2.80629i) q^{73} -8.17047 q^{74} +(4.19722 - 10.5605i) q^{75} -2.41423i q^{76} +(10.1392 - 10.1392i) q^{78} -2.35834 q^{79} +(-1.37800 - 6.67620i) q^{80} +10.8070 q^{81} +(-2.17136 - 2.17136i) q^{82} +(-5.86965 - 5.86965i) q^{83} +2.31167 q^{84} +(0.562183 + 0.369813i) q^{85} -2.57056 q^{86} +(6.40314 - 6.40314i) q^{87} +2.55325i q^{89} +(-3.36949 + 5.12223i) q^{90} +12.7687 q^{91} +(-2.01382 - 2.01382i) q^{92} +(-12.2044 + 12.2044i) q^{93} +4.47188 q^{94} +(2.74932 + 13.3200i) q^{95} -5.02211i q^{96} +(5.32387 + 5.32387i) q^{97} +(0.388135 + 0.388135i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^3 + 4 * q^5	$ 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) $ 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.895288	−	0.895288i	0.633065	−	0.633065i	−0.315771	−	0.948835i	$-0.602263\pi$
$2$	0.895288	−	0.895288i	0.633065	−	0.633065i	0.948835	+	0.315771i	$0.102263\pi$
$3$	−1.60711	+	1.60711i	−0.927864	+	0.927864i	−0.997568	−	0.0697033i	$-0.977795\pi$
$3$	−1.60711	+	1.60711i	−0.927864	+	0.927864i	0.0697033	+	0.997568i	$0.477795\pi$
$4$			0.396917i			0.198459i
$5$	−0.452009	−	2.18991i	−0.202145	−	0.979356i
$5$	−0.452009	−	2.18991i	−0.202145	−	0.979356i
$6$			2.87765i			1.17480i
$7$	−1.81197	+	1.81197i	−0.684860	+	0.684860i	−0.961091	−	0.276231i	$-0.910915\pi$
$7$	−1.81197	+	1.81197i	−0.684860	+	0.684860i	0.276231	+	0.961091i	$0.410915\pi$
$8$	2.14593	+	2.14593i	0.758702	+	0.758702i
$9$		−	2.16559i		−	0.721865i
$10$	−2.36528	−	1.55592i	−0.747966	−	0.492025i
$11$		0			0
$11$		0			0
$12$	−0.637889	−	0.637889i	−0.184143	−	0.184143i
$13$	−3.52344	−	3.52344i	−0.977226	−	0.977226i	0.0225204	−	0.999746i	$-0.492831\pi$
$13$	−3.52344	−	3.52344i	−0.977226	−	0.977226i	−0.999746	+	0.0225204i	$0.992831\pi$
$14$			3.24447i			0.867121i
$15$	4.24584	+	2.79299i	1.09627	+	0.721147i
$16$	3.04862			0.762155
$17$	−0.212794	+	0.212794i	−0.0516100	+	0.0516100i	−0.732441	−	0.680831i	$-0.761619\pi$
$17$	−0.212794	+	0.212794i	−0.0516100	+	0.0516100i	0.680831	+	0.732441i	$0.261619\pi$
$18$	−1.93883	−	1.93883i	−0.456987	−	0.456987i
$19$	−6.08244			−1.39541			−0.697704	−	0.716386i	$-0.745795\pi$
$19$	−6.08244			−1.39541			−0.697704	+	0.716386i	$0.745795\pi$
$20$	0.869212	−	0.179410i	0.194362	−	0.0401174i
$21$		−	5.82406i		−	1.27091i
$22$		0			0
$23$	−5.07364	+	5.07364i	−1.05793	+	1.05793i	−0.0597111	+	0.998216i	$0.519018\pi$
$23$	−5.07364	+	5.07364i	−1.05793	+	1.05793i	−0.998216	+	0.0597111i	$0.980982\pi$
$24$	−6.89749			−1.40794
$25$	−4.59138	+	1.97971i	−0.918275	+	0.395943i
$26$	−6.30899			−1.23729
$27$	−1.34098	−	1.34098i	−0.258072	−	0.258072i
$28$	−0.719202	−	0.719202i	−0.135916	−	0.135916i
$29$	−3.98426			−0.739859			−0.369930	−	0.929060i	$-0.620618\pi$
$29$	−3.98426			−0.739859			−0.369930	+	0.929060i	$0.620618\pi$
$30$	6.30178	−	1.30072i	1.15054	−	0.237479i
$31$	7.59403			1.36393			0.681964	−	0.731386i	$-0.261126\pi$
$31$	7.59403			1.36393			0.681964	+	0.731386i	$0.261126\pi$
$32$	−1.56247	+	1.56247i	−0.276208	+	0.276208i
$33$		0			0
$34$			0.381023i			0.0653449i
$35$	4.78707	+	3.14902i	0.809163	+	0.532281i
$36$	0.859562			0.143260
$37$	−4.56304	−	4.56304i	−0.750159	−	0.750159i	0.224350	−	0.974509i	$-0.427974\pi$
$37$	−4.56304	−	4.56304i	−0.750159	−	0.750159i	−0.974509	+	0.224350i	$0.927974\pi$
$38$	−5.44554	+	5.44554i	−0.883383	+	0.883383i
$39$	11.3251			1.81347
$40$	3.72941	−	5.66937i	0.589671	−	0.896406i
$41$		−	2.42532i		−	0.378771i	−0.981903	−	0.189385i	$-0.939350\pi$
$41$		−	2.42532i		−	0.378771i	0.981903	−	0.189385i	$-0.0606496\pi$
$42$	−5.21422	−	5.21422i	−0.804571	−	0.804571i
$43$	−1.43561	−	1.43561i	−0.218928	−	0.218928i	0.589119	−	0.808047i	$-0.299475\pi$
$43$	−1.43561	−	1.43561i	−0.218928	−	0.218928i	−0.808047	+	0.589119i	$0.799475\pi$
$44$		0			0
$45$	−4.74245	+	0.978869i	−0.706963	+	0.145921i
$46$			9.08474i			1.33947i
$47$	2.49745	+	2.49745i	0.364291	+	0.364291i	0.865390	−	0.501099i	$-0.167071\pi$
$47$	2.49745	+	2.49745i	0.364291	+	0.364291i	−0.501099	+	0.865390i	$0.667071\pi$
$48$	−4.89947	+	4.89947i	−0.707177	+	0.707177i
$49$			0.433531i			0.0619330i
$50$	−2.33819	+	5.88302i	−0.330670	+	0.831985i
$51$		−	0.683965i		−	0.0957742i
$52$	1.39851	−	1.39851i	0.193939	−	0.193939i
$53$	−6.21422	+	6.21422i	−0.853588	+	0.853588i	−0.990573	−	0.136985i	$-0.956259\pi$
$53$	−6.21422	+	6.21422i	−0.853588	+	0.853588i	0.136985	+	0.990573i	$0.456259\pi$
$54$	−2.40113			−0.326752
$55$		0			0
$56$	−7.77673			−1.03921
$57$	9.77514	−	9.77514i	1.29475	−	1.29475i
$58$	−3.56706	+	3.56706i	−0.468379	+	0.468379i
$59$			1.17470i			0.152933i	0.997072	+	0.0764664i	$0.0243638\pi$
$59$			1.17470i			0.152933i	−0.997072	+	0.0764664i	$0.975636\pi$
$60$	−1.10859	+	1.68525i	−0.143118	+	0.217565i
$61$			0.0929527i			0.0119014i	0.999982	+	0.00595069i	$0.00189417\pi$
$61$			0.0929527i			0.0119014i	−0.999982	+	0.00595069i	$0.998106\pi$
$62$	6.79885	−	6.79885i	0.863454	−	0.863454i
$63$	3.92399	+	3.92399i	0.494377	+	0.494377i
$64$			8.89496i			1.11187i
$65$	−6.12337	+	9.30862i	−0.759511	+	1.15459i
$66$		0			0
$67$	7.07364	+	7.07364i	0.864183	+	0.864183i	0.991821	−	0.127638i	$-0.0407397\pi$
$67$	7.07364	+	7.07364i	0.864183	+	0.864183i	−0.127638	+	0.991821i	$0.540740\pi$
$68$	−0.0844615	−	0.0844615i	−0.0102425	−	0.0102425i
$69$		−	16.3078i		−	1.96323i
$70$	7.10509	−	1.46653i	0.849220	−	0.175284i
$71$	11.2433			1.33433			0.667165	−	0.744910i	$-0.267508\pi$
$71$	11.2433			1.33433			0.667165	+	0.744910i	$0.267508\pi$
$72$	4.64722	−	4.64722i	0.547680	−	0.547680i
$73$	2.80629	+	2.80629i	0.328451	+	0.328451i	0.851997	−	0.523546i	$-0.175391\pi$
$73$	2.80629	+	2.80629i	0.328451	+	0.328451i	−0.523546	+	0.851997i	$0.675391\pi$
$74$	−8.17047			−0.949798
$75$	4.19722	−	10.5605i	0.484653	−	1.21942i
$76$		−	2.41423i		−	0.276931i
$77$		0			0
$78$	10.1392	−	10.1392i	1.14804	−	1.14804i
$79$	−2.35834			−0.265334			−0.132667	−	0.991161i	$-0.542354\pi$
$79$	−2.35834			−0.265334			−0.132667	+	0.991161i	$0.542354\pi$
$80$	−1.37800	−	6.67620i	−0.154066	−	0.746421i
$81$	10.8070			1.20078
$82$	−2.17136	−	2.17136i	−0.239786	−	0.239786i
$83$	−5.86965	−	5.86965i	−0.644278	−	0.644278i	0.307327	−	0.951604i	$-0.400566\pi$
$83$	−5.86965	−	5.86965i	−0.644278	−	0.644278i	−0.951604	+	0.307327i	$0.900566\pi$
$84$	2.31167			0.252224
$85$	0.562183	+	0.369813i	0.0609773	+	0.0401119i
$86$	−2.57056			−0.277191
$87$	6.40314	−	6.40314i	0.686489	−	0.686489i
$88$		0			0
$89$			2.55325i			0.270644i	0.990802	+	0.135322i	$0.0432069\pi$
$89$			2.55325i			0.270644i	−0.990802	+	0.135322i	$0.956793\pi$
$90$	−3.36949	+	5.12223i	−0.355175	+	0.539930i
$91$	12.7687			1.33853
$92$	−2.01382	−	2.01382i	−0.209955	−	0.209955i
$93$	−12.2044	+	12.2044i	−1.26554	+	1.26554i
$94$	4.47188			0.461239
$95$	2.74932	+	13.3200i	0.282074	+	1.36660i
$96$		−	5.02211i		−	0.512567i
$97$	5.32387	+	5.32387i	0.540557	+	0.540557i	0.923692	−	0.383135i	$-0.125156\pi$
$97$	5.32387	+	5.32387i	0.540557	+	0.540557i	−0.383135	+	0.923692i	$0.625156\pi$
$98$	0.388135	+	0.388135i	0.0392076	+	0.0392076i
$99$		0			0
$100$	−0.785783	−	1.82240i	−0.0785783	−	0.182240i
$101$		−	16.0361i		−	1.59565i	−0.602887	−	0.797826i	$-0.705983\pi$
$101$		−	16.0361i		−	1.59565i	0.602887	−	0.797826i	$-0.294017\pi$
$102$	−0.612346	−	0.612346i	−0.0606313	−	0.0606313i
$103$	1.01770	−	1.01770i	0.100277	−	0.100277i	−0.655188	−	0.755465i	$-0.727411\pi$
$103$	1.01770	−	1.01770i	0.100277	−	0.100277i	0.755465	+	0.655188i	$0.227411\pi$
$104$		−	15.1221i		−	1.48285i
$105$	−12.7542	+	2.63253i	−1.24468	+	0.256909i
$106$			11.1270i			1.08075i
$107$	−7.90751	+	7.90751i	−0.764448	+	0.764448i	−0.977123	−	0.212675i	$-0.931782\pi$
$107$	−7.90751	+	7.90751i	−0.764448	+	0.764448i	0.212675	+	0.977123i	$0.431782\pi$
$108$	0.532258	−	0.532258i	0.0512166	−	0.0512166i
$109$	16.2607			1.55749			0.778746	−	0.627339i	$-0.215856\pi$
$109$	16.2607			1.55749			0.778746	+	0.627339i	$0.215856\pi$
$110$		0			0
$111$	14.6666			1.39209
$112$	−5.52401	+	5.52401i	−0.521970	+	0.521970i
$113$	−1.35809	+	1.35809i	−0.127758	+	0.127758i	−0.768094	−	0.640337i	$-0.778795\pi$
$113$	−1.35809	+	1.35809i	−0.127758	+	0.127758i	0.640337	+	0.768094i	$0.278795\pi$
$114$		−	17.5031i		−	1.63932i
$115$	13.4041	+	8.81746i	1.24994	+	0.822232i
$116$		−	1.58142i		−	0.146831i
$117$	−7.63034	+	7.63034i	−0.705425	+	0.705425i
$118$	1.05169	+	1.05169i	0.0968164	+	0.0968164i
$119$		−	0.771151i		−	0.0706913i
$120$	3.11773	+	15.1049i	0.284608	+	1.37888i
$121$		0			0
$122$	0.0832195	+	0.0832195i	0.00753434	+	0.00753434i
$123$	3.89775	+	3.89775i	0.351448	+	0.351448i
$124$			3.01420i			0.270683i
$125$	6.41073	+	9.15983i	0.573393	+	0.819280i
$126$	7.02621			0.625945
$127$	−1.78209	+	1.78209i	−0.158135	+	0.158135i	−0.781740	−	0.623605i	$-0.785667\pi$
$127$	−1.78209	+	1.78209i	−0.158135	+	0.158135i	0.623605	+	0.781740i	$0.285667\pi$
$128$	4.83862	+	4.83862i	0.427678	+	0.427678i
$129$	4.61435			0.406271
$130$	2.85172	+	13.8161i	0.250112	+	1.21175i
$131$			13.8354i			1.20880i	0.796680	+	0.604401i	$0.206588\pi$
$131$			13.8354i			1.20880i	−0.796680	+	0.604401i	$0.793412\pi$
$132$		0			0
$133$	11.0212	−	11.0212i	0.955659	−	0.955659i
$134$	12.6659			1.09417
$135$	−2.33048	+	3.54275i	−0.200576	+	0.304912i
$136$	−0.913281			−0.0783132
$137$	−1.38713	−	1.38713i	−0.118510	−	0.118510i	0.645364	−	0.763875i	$-0.276706\pi$
$137$	−1.38713	−	1.38713i	−0.118510	−	0.118510i	−0.763875	+	0.645364i	$0.776706\pi$
$138$	−14.6002	−	14.6002i	−1.24285	−	1.24285i
$139$	−8.66388			−0.734861			−0.367430	−	0.930051i	$-0.619762\pi$
$139$	−8.66388			−0.734861			−0.367430	+	0.930051i	$0.619762\pi$
$140$	−1.24990	+	1.90007i	−0.105636	+	0.160585i
$141$	−8.02735			−0.676025
$142$	10.0660	−	10.0660i	0.844717	−	0.844717i
$143$		0			0
$144$		−	6.60208i		−	0.550173i
$145$	1.80092	+	8.72516i	0.149559	+	0.724585i
$146$	5.02488			0.415862
$147$	−0.696731	−	0.696731i	−0.0574654	−	0.0574654i
$148$	1.81115	−	1.81115i	0.148876	−	0.148876i
$149$	−8.51526			−0.697598			−0.348799	−	0.937198i	$-0.613410\pi$
$149$	−8.51526			−0.697598			−0.348799	+	0.937198i	$0.613410\pi$
$150$	−5.69693	−	13.2124i	−0.465152	−	1.07879i
$151$		−	6.89254i		−	0.560907i	−0.959868	−	0.280454i	$-0.909515\pi$
$151$		−	6.89254i		−	0.560907i	0.959868	−	0.280454i	$-0.0904849\pi$
$152$	−13.0525	−	13.0525i	−1.05870	−	1.05870i
$153$	0.460825	+	0.460825i	0.0372555	+	0.0372555i
$154$		0			0
$155$	−3.43257	−	16.6302i	−0.275711	−	1.33577i
$156$			4.49513i			0.359898i
$157$	3.85613	+	3.85613i	0.307753	+	0.307753i	0.844037	−	0.536284i	$-0.180173\pi$
$157$	3.85613	+	3.85613i	0.307753	+	0.307753i	−0.536284	+	0.844037i	$0.680173\pi$
$158$	−2.11140	+	2.11140i	−0.167974	+	0.167974i
$159$		−	19.9738i		−	1.58403i
$160$	4.12791	+	2.71541i	0.326340	+	0.214672i
$161$		−	18.3866i		−	1.44906i
$162$	9.67537	−	9.67537i	0.760169	−	0.760169i
$163$	−1.58417	+	1.58417i	−0.124082	+	0.124082i	−0.766421	−	0.642339i	$-0.777964\pi$
$163$	−1.58417	+	1.58417i	−0.124082	+	0.124082i	0.642339	+	0.766421i	$0.277964\pi$
$164$	0.962651			0.0751704
$165$		0			0
$166$	−10.5101			−0.815738
$167$	−5.94876	+	5.94876i	−0.460329	+	0.460329i	−0.898763	−	0.438435i	$-0.855533\pi$
$167$	−5.94876	+	5.94876i	−0.460329	+	0.460329i	0.438435	+	0.898763i	$0.355533\pi$
$168$	12.4980	−	12.4980i	0.964245	−	0.964245i
$169$			11.8292i			0.909941i
$170$	0.834405	−	0.172226i	0.0639959	−	0.0132091i
$171$			13.1721i			1.00730i
$172$	0.569817	−	0.569817i	0.0434482	−	0.0434482i
$173$	9.76335	+	9.76335i	0.742294	+	0.742294i	0.973019	−	0.230725i	$-0.0741098\pi$
$173$	9.76335	+	9.76335i	0.742294	+	0.742294i	−0.230725	+	0.973019i	$0.574110\pi$
$174$		−	11.4653i		−	0.869184i
$175$	4.73225	−	11.9066i	0.357725	−	0.900056i
$176$		0			0
$177$	−1.88787	−	1.88787i	−0.141901	−	0.141901i
$178$	2.28589	+	2.28589i	0.171335	+	0.171335i
$179$		−	6.88939i		−	0.514937i	−0.966287	−	0.257468i	$-0.917112\pi$
$179$		−	6.88939i		−	0.514937i	0.966287	−	0.257468i	$-0.0828883\pi$
$180$	−0.388530	−	1.88236i	−0.0289593	−	0.140303i
$181$	−23.2695			−1.72961			−0.864805	−	0.502108i	$-0.832558\pi$
$181$	−23.2695			−1.72961			−0.864805	+	0.502108i	$0.832558\pi$
$182$	11.4317	−	11.4317i	0.847374	−	0.847374i
$183$	−0.149385	−	0.149385i	−0.0110429	−	0.0110429i
$184$	−21.7754			−1.60530
$185$	−7.93009	+	12.0552i	−0.583032	+	0.886313i
$186$			21.8530i			1.60234i
$187$		0			0
$188$	−0.991282	+	0.991282i	−0.0722967	+	0.0722967i
$189$	4.85963			0.353486
$190$	14.3867	+	9.46379i	1.04372	+	0.686575i
$191$	7.53352			0.545106			0.272553	−	0.962141i	$-0.412132\pi$
$191$	7.53352			0.545106			0.272553	+	0.962141i	$0.412132\pi$
$192$	−14.2952	−	14.2952i	−1.03167	−	1.03167i
$193$	−17.8684	−	17.8684i	−1.28619	−	1.28619i	−0.937081	−	0.349112i	$-0.886483\pi$
$193$	−17.8684	−	17.8684i	−1.28619	−	1.28619i	−0.349112	−	0.937081i	$-0.613517\pi$
$194$	9.53280			0.684416
$195$	−5.11905	−	24.8009i	−0.366583	−	1.77603i
$196$	−0.172076			−0.0122911
$197$	−10.3579	+	10.3579i	−0.737967	+	0.737967i	−0.972184	−	0.234217i	$-0.924747\pi$
$197$	−10.3579	+	10.3579i	−0.737967	+	0.737967i	0.234217	+	0.972184i	$0.424747\pi$
$198$		0			0
$199$			8.62950i			0.611729i	0.952075	+	0.305865i	$0.0989455\pi$
$199$			8.62950i			0.611729i	−0.952075	+	0.305865i	$0.901055\pi$
$200$	−14.1011	−	5.60445i	−0.997099	−	0.396294i
$201$	−22.7362			−1.60369
$202$	−14.3569	−	14.3569i	−1.01015	−	1.01015i
$203$	7.21936	−	7.21936i	0.506700	−	0.506700i
$204$	0.271477			0.0190072
$205$	−5.31122	+	1.09627i	−0.370952	+	0.0765665i
$206$		−	1.82227i		−	0.126964i
$207$	10.9874	+	10.9874i	0.763680	+	0.763680i
$208$	−10.7416	−	10.7416i	−0.744798	−	0.744798i
$209$		0			0
$210$	−9.06177	+	13.7755i	−0.625322	+	0.950601i
$211$			16.9115i			1.16423i	0.813105	+	0.582117i	$0.197775\pi$
$211$			16.9115i			1.16423i	−0.813105	+	0.582117i	$0.802225\pi$
$212$	−2.46653	−	2.46653i	−0.169402	−	0.169402i
$213$	−18.0691	+	18.0691i	−1.23808	+	1.23808i
$214$			14.1590i			0.967890i
$215$	−2.49494	+	3.79275i	−0.170153	+	0.258663i
$216$		−	5.75530i		−	0.391599i
$217$	−13.7602	+	13.7602i	−0.934100	+	0.934100i
$218$	14.5580	−	14.5580i	0.985993	−	0.985993i
$219$	−9.02002			−0.609517
$220$		0			0
$221$	1.49953			0.100869
$222$	13.1308	−	13.1308i	0.881284	−	0.881284i
$223$	5.32716	−	5.32716i	0.356733	−	0.356733i	−0.505874	−	0.862607i	$-0.668830\pi$
$223$	5.32716	−	5.32716i	0.356733	−	0.356733i	0.862607	+	0.505874i	$0.168830\pi$
$224$		−	5.66229i		−	0.378328i
$225$	4.28726	+	9.94306i	0.285817	+	0.662871i
$226$			2.43176i			0.161758i
$227$	−4.15249	+	4.15249i	−0.275610	+	0.275610i	−0.831354	−	0.555744i	$-0.812434\pi$
$227$	−4.15249	+	4.15249i	−0.275610	+	0.275610i	0.555744	+	0.831354i	$0.312434\pi$
$228$	3.87992	+	3.87992i	0.256954	+	0.256954i
$229$		−	23.9755i		−	1.58435i	−0.610295	−	0.792174i	$-0.708949\pi$
$229$		−	23.9755i		−	1.58435i	0.610295	−	0.792174i	$-0.291051\pi$
$230$	19.8947	−	4.10639i	1.31182	−	0.270767i
$231$		0			0
$232$	−8.54996	−	8.54996i	−0.561332	−	0.561332i
$233$	−10.1914	−	10.1914i	−0.667661	−	0.667661i	0.289513	−	0.957174i	$-0.406507\pi$
$233$	−10.1914	−	10.1914i	−0.667661	−	0.667661i	−0.957174	+	0.289513i	$0.906507\pi$
$234$			13.6627i			0.893159i
$235$	4.34031	−	6.59805i	0.283131	−	0.430410i
$236$	−0.466259			−0.0303509
$237$	3.79011	−	3.79011i	0.246194	−	0.246194i
$238$	−0.690403	−	0.690403i	−0.0447522	−	0.0447522i
$239$	15.1177			0.977885			0.488942	−	0.872316i	$-0.337383\pi$
$239$	15.1177			0.977885			0.488942	+	0.872316i	$0.337383\pi$
$240$	12.9440	+	8.51477i	0.835530	+	0.549626i
$241$		−	3.12966i		−	0.201599i	−0.994907	−	0.100800i	$-0.967860\pi$
$241$		−	3.12966i		−	0.201599i	0.994907	−	0.100800i	$-0.0321401\pi$
$242$		0			0
$243$	−13.3451	+	13.3451i	−0.856086	+	0.856086i
$244$	−0.0368945			−0.00236193
$245$	0.949392	−	0.195960i	0.0606544	−	0.0125194i
$246$	6.97922			0.444979
$247$	21.4311	+	21.4311i	1.36363	+	1.36363i
$248$	16.2963	+	16.2963i	1.03481	+	1.03481i
$249$	18.8663			1.19560
$250$	13.9401	+	2.46124i	0.881652	+	0.155662i
$251$	−6.19727			−0.391168			−0.195584	−	0.980687i	$-0.562660\pi$
$251$	−6.19727			−0.391168			−0.195584	+	0.980687i	$0.562660\pi$
$252$	−1.55750	+	1.55750i	−0.0981133	+	0.0981133i
$253$		0			0
$254$			3.19096i			0.200219i
$255$	−1.49782	+	0.309158i	−0.0937970	+	0.0193602i
$256$	−9.12601			−0.570375
$257$	−0.957737	−	0.957737i	−0.0597420	−	0.0597420i	0.676605	−	0.736347i	$-0.263451\pi$
$257$	−0.957737	−	0.957737i	−0.0597420	−	0.0597420i	−0.736347	+	0.676605i	$0.763451\pi$
$258$	4.13117	−	4.13117i	0.257196	−	0.257196i
$259$	16.5362			1.02751
$260$	−3.69475	−	2.43047i	−0.229139	−	0.150732i
$261$			8.62830i			0.534078i
$262$	12.3867	+	12.3867i	0.765250	+	0.765250i
$263$	−6.97161	−	6.97161i	−0.429888	−	0.429888i	0.458702	−	0.888590i	$-0.348314\pi$
$263$	−6.97161	−	6.97161i	−0.429888	−	0.429888i	−0.888590	+	0.458702i	$0.848314\pi$
$264$		0			0
$265$	16.4174	+	10.7997i	1.00851	+	0.663418i
$266$		−	19.7343i		−	1.20999i
$267$	−4.10335	−	4.10335i	−0.251121	−	0.251121i
$268$	−2.80765	+	2.80765i	−0.171505	+	0.171505i
$269$			13.5535i			0.826369i	0.910647	+	0.413184i	$0.135584\pi$
$269$			13.5535i			0.826369i	−0.910647	+	0.413184i	$0.864416\pi$
$270$	1.08533	+	5.25824i	0.0660511	+	0.320006i
$271$			5.38948i			0.327388i	0.986511	+	0.163694i	$0.0523409\pi$
$271$			5.38948i			0.327388i	−0.986511	+	0.163694i	$0.947659\pi$
$272$	−0.648727	+	0.648727i	−0.0393349	+	0.0393349i
$273$	−20.5207	+	20.5207i	−1.24197	+	1.24197i
$274$	−2.48376			−0.150049
$275$		0			0
$276$	6.47284			0.389619
$277$	−20.1679	+	20.1679i	−1.21177	+	1.21177i	−0.241328	+	0.970444i	$0.577583\pi$
$277$	−20.1679	+	20.1679i	−1.21177	+	1.21177i	−0.970444	+	0.241328i	$0.922417\pi$
$278$	−7.75667	+	7.75667i	−0.465214	+	0.465214i
$279$		−	16.4456i		−	0.984572i
$280$	3.51515	+	17.0303i	0.210071	+	1.01776i
$281$			11.4142i			0.680912i	0.940260	+	0.340456i	$0.110581\pi$
$281$			11.4142i			0.680912i	−0.940260	+	0.340456i	$0.889419\pi$
$282$	−7.18679	+	7.18679i	−0.427967	+	0.427967i
$283$	1.31371	+	1.31371i	0.0780921	+	0.0780921i	0.745074	−	0.666982i	$-0.232414\pi$
$283$	1.31371	+	1.31371i	0.0780921	+	0.0780921i	−0.666982	+	0.745074i	$0.732414\pi$
$284$			4.46264i			0.264809i
$285$	−25.8251	−	16.9882i	−1.52975	−	1.00629i
$286$		0			0
$287$	4.39460	+	4.39460i	0.259405	+	0.259405i
$288$	3.38367	+	3.38367i	0.199385	+	0.199385i
$289$			16.9094i			0.994673i
$290$	9.42388	+	6.19919i	0.553389	+	0.364029i
$291$	−17.1121			−1.00313
$292$	−1.11387	+	1.11387i	−0.0651840	+	0.0651840i
$293$	12.6589	+	12.6589i	0.739540	+	0.739540i	0.972489	−	0.232949i	$-0.0748374\pi$
$293$	12.6589	+	12.6589i	0.739540	+	0.739540i	−0.232949	+	0.972489i	$0.574837\pi$
$294$	−1.24755			−0.0727586
$295$	2.57248	−	0.530975i	0.149776	−	0.0309146i
$296$		−	19.5839i		−	1.13829i
$297$		0			0
$298$	−7.62362	+	7.62362i	−0.441624	+	0.441624i
$299$	35.7533			2.06767
$300$	4.19163	+	1.66595i	0.242004	+	0.0961837i
$301$	5.20255			0.299870
$302$	−6.17081	−	6.17081i	−0.355090	−	0.355090i
$303$	25.7718	+	25.7718i	1.48055	+	1.48055i
$304$	−18.5431			−1.06352
$305$	0.203558	−	0.0420155i	0.0116557	−	0.00240580i
$306$	0.825142			0.0471702
$307$	9.10688	−	9.10688i	0.519757	−	0.519757i	−0.397741	−	0.917498i	$-0.630206\pi$
$307$	9.10688	−	9.10688i	0.519757	−	0.519757i	0.917498	+	0.397741i	$0.130206\pi$
$308$		0			0
$309$			3.27111i			0.186087i
$310$	−17.9620	−	11.8157i	−1.02017	−	0.671086i
$311$	−18.8540			−1.06911			−0.534557	−	0.845133i	$-0.679521\pi$
$311$	−18.8540			−1.06911			−0.534557	+	0.845133i	$0.679521\pi$
$312$	24.3029	+	24.3029i	1.37588	+	1.37588i
$313$	6.78679	−	6.78679i	0.383612	−	0.383612i	−0.488790	−	0.872402i	$-0.662561\pi$
$313$	6.78679	−	6.78679i	0.383612	−	0.383612i	0.872402	+	0.488790i	$0.162561\pi$
$314$	6.90470			0.389655
$315$	6.81949	−	10.3669i	0.384235	−	0.584106i
$316$		−	0.936066i		−	0.0526578i
$317$	−9.33298	−	9.33298i	−0.524192	−	0.524192i	0.394642	−	0.918835i	$-0.370868\pi$
$317$	−9.33298	−	9.33298i	−0.524192	−	0.524192i	−0.918835	+	0.394642i	$0.870868\pi$
$318$	−17.8823	−	17.8823i	−1.00279	−	1.00279i
$319$		0			0
$320$	19.4791	−	4.02060i	1.08892	−	0.224759i
$321$		−	25.4165i		−	1.41861i
$322$	−16.4613	−	16.4613i	−0.917351	−	0.917351i
$323$	1.29430	−	1.29430i	0.0720170	−	0.0720170i
$324$			4.28948i			0.238304i
$325$	23.1528	+	9.20203i	1.28429	+	0.510437i
$326$			2.83658i			0.157104i
$327$	−26.1327	+	26.1327i	−1.44514	+	1.44514i
$328$	5.20457	−	5.20457i	0.287374	−	0.287374i
$329$	−9.05061			−0.498976
$330$		0			0
$331$	−12.7005			−0.698084			−0.349042	−	0.937107i	$-0.613493\pi$
$331$	−12.7005			−0.698084			−0.349042	+	0.937107i	$0.613493\pi$
$332$	2.32977	−	2.32977i	0.127862	−	0.127862i
$333$	−9.88169	+	9.88169i	−0.541513	+	0.541513i
$334$			10.6517i			0.582835i
$335$	12.2933	−	18.6880i	0.671652	−	1.02103i
$336$		−	17.7554i		−	0.968635i
$337$	11.0394	−	11.0394i	0.601356	−	0.601356i	−0.339316	−	0.940672i	$-0.610196\pi$
$337$	11.0394	−	11.0394i	0.601356	−	0.601356i	0.940672	+	0.339316i	$0.110196\pi$
$338$	10.5906	+	10.5906i	0.576052	+	0.576052i
$339$		−	4.36518i		−	0.237084i
$340$	−0.146785	+	0.223140i	−0.00796055	+	0.0121015i
$341$		0			0
$342$	11.7928	+	11.7928i	0.637683	+	0.637683i
$343$	−13.4693	−	13.4693i	−0.727276	−	0.727276i
$344$		−	6.16143i		−	0.332202i
$345$	−35.7125	+	7.37126i	−1.92270	+	0.396855i
$346$	17.4820			0.939840
$347$	−1.68836	+	1.68836i	−0.0906360	+	0.0906360i	−0.750971	−	0.660335i	$-0.770414\pi$
$347$	−1.68836	+	1.68836i	−0.0906360	+	0.0906360i	0.660335	+	0.750971i	$0.270414\pi$
$348$	2.54152	+	2.54152i	0.136240	+	0.136240i
$349$	35.3076			1.88997			0.944987	−	0.327107i	$-0.106074\pi$
$349$	35.3076			1.88997			0.944987	+	0.327107i	$0.106074\pi$
$350$	−6.42313	−	14.8966i	−0.343331	−	0.796256i
$351$			9.44972i			0.504389i
$352$		0			0
$353$	−0.0520523	+	0.0520523i	−0.00277046	+	0.00277046i	−0.708491	−	0.705720i	$-0.750624\pi$
$353$	−0.0520523	+	0.0520523i	−0.00277046	+	0.00277046i	0.705720	+	0.708491i	$0.250624\pi$
$354$	−3.38038			−0.179665
$355$	−5.08206	−	24.6217i	−0.269728	−	1.30678i
$356$	−1.01343			−0.0537116
$357$	1.23932	+	1.23932i	0.0655920	+	0.0655920i
$358$	−6.16799	−	6.16799i	−0.325988	−	0.325988i
$359$	−16.2236			−0.856250			−0.428125	−	0.903719i	$-0.640826\pi$
$359$	−16.2236			−0.856250			−0.428125	+	0.903719i	$0.640826\pi$
$360$	−12.2776	−	8.07639i	−0.647084	−	0.425663i
$361$	17.9961			0.947163
$362$	−20.8329	+	20.8329i	−1.09495	+	1.09495i
$363$		0			0
$364$			5.06813i			0.265642i
$365$	4.87704	−	7.41398i	0.255276	−	0.388065i
$366$	−0.267485			−0.0139817
$367$	−9.29959	−	9.29959i	−0.485435	−	0.485435i	0.421427	−	0.906862i	$-0.361529\pi$
$367$	−9.29959	−	9.29959i	−0.485435	−	0.485435i	−0.906862	+	0.421427i	$0.861529\pi$
$368$	−15.4676	+	15.4676i	−0.806305	+	0.806305i
$369$	−5.25226			−0.273421
$370$	3.69313	+	17.8926i	0.191997	+	0.930190i
$371$		−	22.5199i		−	1.16918i
$372$	−4.84415	−	4.84415i	−0.251157	−	0.251157i
$373$	18.8004	+	18.8004i	0.973446	+	0.973446i	0.999656	−	0.0262108i	$-0.00834413\pi$
$373$	18.8004	+	18.8004i	0.973446	+	0.973446i	−0.0262108	+	0.999656i	$0.508344\pi$
$374$		0			0
$375$	−25.0236	−	4.41810i	−1.29221	−	0.228150i
$376$			10.7187i			0.552776i
$377$	14.0383	+	14.0383i	0.723010	+	0.723010i
$378$	4.35077	−	4.35077i	0.223779	−	0.223779i
$379$		−	13.5195i		−	0.694448i	−0.937782	−	0.347224i	$-0.887124\pi$
$379$		−	13.5195i		−	0.694448i	0.937782	−	0.347224i	$-0.112876\pi$
$380$	−5.28693	+	1.09125i	−0.271214	+	0.0559801i
$381$		−	5.72801i		−	0.293455i
$382$	6.74467	−	6.74467i	0.345087	−	0.345087i
$383$	12.9136	−	12.9136i	0.659855	−	0.659855i	−0.295490	−	0.955346i	$-0.595483\pi$
$383$	12.9136	−	12.9136i	0.659855	−	0.659855i	0.955346	+	0.295490i	$0.0954830\pi$
$384$	−15.5524			−0.793654
$385$		0			0
$386$	−31.9947			−1.62849
$387$	−3.10894	+	3.10894i	−0.158036	+	0.158036i
$388$	−2.11314	+	2.11314i	−0.107278	+	0.107278i
$389$		−	17.6678i		−	0.895793i	−0.894085	−	0.447896i	$-0.852173\pi$
$389$		−	17.6678i		−	0.895793i	0.894085	−	0.447896i	$-0.147827\pi$
$390$	−26.7870	−	17.6209i	−1.35641	−	0.892270i
$391$		−	2.15928i		−	0.109199i
$392$	−0.930328	+	0.930328i	−0.0469886	+	0.0469886i
$393$	−22.2349	−	22.2349i	−1.12160	−	1.12160i
$394$			18.5465i			0.934362i
$395$	1.06599	+	5.16454i	0.0536359	+	0.259856i
$396$		0			0
$397$	−11.7203	−	11.7203i	−0.588223	−	0.588223i	0.348927	−	0.937150i	$-0.386546\pi$
$397$	−11.7203	−	11.7203i	−0.588223	−	0.588223i	−0.937150	+	0.348927i	$0.886546\pi$
$398$	7.72589	+	7.72589i	0.387264	+	0.387264i
$399$			35.4245i			1.77344i
$400$	−13.9974	+	6.03540i	−0.699868	+	0.301770i
$401$	−21.8570			−1.09149			−0.545744	−	0.837952i	$-0.683753\pi$
$401$	−21.8570			−1.09149			−0.545744	+	0.837952i	$0.683753\pi$
$402$	−20.3555	+	20.3555i	−1.01524	+	1.01524i
$403$	−26.7571	−	26.7571i	−1.33287	−	1.33287i
$404$	6.36501			0.316671
$405$	−4.88485	−	23.6663i	−0.242730	−	1.17599i
$406$		−	12.9268i		−	0.641548i
$407$		0			0
$408$	1.46774	−	1.46774i	0.0726641	−	0.0726641i
$409$	−20.1955			−0.998602			−0.499301	−	0.866429i	$-0.666410\pi$
$409$	−20.1955			−0.998602			−0.499301	+	0.866429i	$0.666410\pi$
$410$	−3.77360	+	5.73655i	−0.186365	+	0.283308i
$411$	4.45853			0.219923
$412$	0.403943	+	0.403943i	0.0199009	+	0.0199009i
$413$	−2.12852	−	2.12852i	−0.104738	−	0.104738i
$414$	19.6739			0.966918
$415$	−10.2008	+	15.5071i	−0.500740	+	0.761214i
$416$	11.0105			0.539835
$417$	13.9238	−	13.9238i	0.681851	−	0.681851i
$418$		0			0
$419$			11.1391i			0.544179i	0.962272	+	0.272090i	$0.0877148\pi$
$419$			11.1391i			0.544179i	−0.962272	+	0.272090i	$0.912285\pi$
$420$	−1.04490	−	5.06234i	−0.0509857	−	0.247017i
$421$	29.9049			1.45748			0.728738	−	0.684793i	$-0.240107\pi$
$421$	29.9049			1.45748			0.728738	+	0.684793i	$0.240107\pi$
$422$	15.1406	+	15.1406i	0.737035	+	0.737035i
$423$	5.40847	−	5.40847i	0.262969	−	0.262969i
$424$	−26.6706			−1.29524
$425$	0.555745	−	1.39829i	0.0269576	−	0.0678268i
$426$			32.3542i			1.56757i
$427$	−0.168428	−	0.168428i	−0.00815078	−	0.00815078i
$428$	−3.13863	−	3.13863i	−0.151711	−	0.151711i
$429$		0			0
$430$	1.16192	+	5.62929i	0.0560327	+	0.271469i
$431$			38.0839i			1.83444i	0.398386	+	0.917218i	$0.369570\pi$
$431$			38.0839i			1.83444i	−0.398386	+	0.917218i	$0.630430\pi$
$432$	−4.08814	−	4.08814i	−0.196691	−	0.196691i
$433$	−2.71048	+	2.71048i	−0.130257	+	0.130257i	−0.769230	−	0.638972i	$-0.779360\pi$
$433$	−2.71048	+	2.71048i	−0.130257	+	0.130257i	0.638972	+	0.769230i	$0.279360\pi$
$434$			24.6386i			1.18269i
$435$	−16.9166	−	11.1280i	−0.811087	−	0.533547i
$436$			6.45415i			0.309098i
$437$	30.8601	−	30.8601i	1.47624	−	1.47624i
$438$	−8.07552	+	8.07552i	−0.385863	+	0.385863i
$439$	17.8832			0.853518			0.426759	−	0.904365i	$-0.359655\pi$
$439$	17.8832			0.853518			0.426759	+	0.904365i	$0.359655\pi$
$440$		0			0
$441$	0.938852			0.0447072
$442$	1.34251	−	1.34251i	0.0638568	−	0.0638568i
$443$	−1.27317	+	1.27317i	−0.0604903	+	0.0604903i	−0.736705	−	0.676215i	$-0.763619\pi$
$443$	−1.27317	+	1.27317i	−0.0604903	+	0.0604903i	0.676215	+	0.736705i	$0.263619\pi$
$444$			5.82143i			0.276273i
$445$	5.59138	−	1.15409i	0.265057	−	0.0547092i
$446$		−	9.53870i		−	0.451670i
$447$	13.6850	−	13.6850i	0.647276	−	0.647276i
$448$	−16.1174	−	16.1174i	−0.761476	−	0.761476i
$449$			14.4932i			0.683974i	0.939705	+	0.341987i	$0.111100\pi$
$449$			14.4932i			0.683974i	−0.939705	+	0.341987i	$0.888900\pi$
$450$	12.7402	+	5.06357i	0.600581	+	0.238699i
$451$		0			0
$452$	−0.539048	−	0.539048i	−0.0253547	−	0.0253547i
$453$	11.0771	+	11.0771i	0.520446	+	0.520446i
$454$			7.43534i			0.348958i
$455$	−5.77158	−	27.9623i	−0.270576	−	1.31089i
$456$	41.9536			1.96466
$457$	27.2363	−	27.2363i	1.27406	−	1.27406i	0.330121	−	0.943939i	$-0.392910\pi$
$457$	27.2363	−	27.2363i	1.27406	−	1.27406i	0.943939	−	0.330121i	$-0.107090\pi$
$458$	−21.4650	−	21.4650i	−1.00299	−	1.00299i
$459$	0.570704			0.0266382
$460$	−3.49980	+	5.32033i	−0.163179	+	0.248062i
$461$		−	19.2825i		−	0.898077i	−0.893512	−	0.449038i	$-0.851767\pi$
$461$		−	19.2825i		−	0.898077i	0.893512	−	0.449038i	$-0.148233\pi$
$462$		0			0
$463$	13.7252	−	13.7252i	0.637863	−	0.637863i	−0.312165	−	0.950028i	$-0.601054\pi$
$463$	13.7252	−	13.7252i	0.637863	−	0.637863i	0.950028	+	0.312165i	$0.101054\pi$
$464$	−12.1465			−0.563888
$465$	32.2431	+	21.2100i	1.49524	+	0.983592i
$466$	−18.2485			−0.845344
$467$	−25.7033	−	25.7033i	−1.18941	−	1.18941i	−0.977232	−	0.212174i	$-0.931946\pi$
$467$	−25.7033	−	25.7033i	−1.18941	−	1.18941i	−0.212174	−	0.977232i	$-0.568054\pi$
$468$	−3.02861	−	3.02861i	−0.139998	−	0.139998i
$469$	−25.6344			−1.18369
$470$	−2.02133	−	9.79299i	−0.0932370	−	0.451717i
$471$	−12.3944			−0.571106
$472$	−2.52083	+	2.52083i	−0.116030	+	0.116030i
$473$		0			0
$474$		−	6.78648i		−	0.311713i
$475$	27.9268	−	12.0415i	1.28137	−	0.552502i
$476$	0.306083			0.0140293
$477$	13.4575	+	13.4575i	0.616176	+	0.616176i
$478$	13.5347	−	13.5347i	0.619064	−	0.619064i
$479$	−8.51668			−0.389137			−0.194569	−	0.980889i	$-0.562331\pi$
$479$	−8.51668			−0.389137			−0.194569	+	0.980889i	$0.562331\pi$
$480$	−10.9980	+	2.27004i	−0.501986	+	0.103613i
$481$			32.1552i			1.46615i
$482$	−2.80195	−	2.80195i	−0.127625	−	0.127625i
$483$	29.5492	+	29.5492i	1.34454	+	1.34454i
$484$		0			0
$485$	9.25234	−	14.0652i	0.420127	−	0.638669i
$486$			23.8953i			1.08391i
$487$	−3.08581	−	3.08581i	−0.139831	−	0.139831i	0.633726	−	0.773557i	$-0.281525\pi$
$487$	−3.08581	−	3.08581i	−0.139831	−	0.139831i	−0.773557	+	0.633726i	$0.781525\pi$
$488$	−0.199470	+	0.199470i	−0.00902959	+	0.00902959i
$489$		−	5.09187i		−	0.230262i
$490$	0.674539	−	1.02542i	0.0304726	−	0.0463238i
$491$		−	17.4116i		−	0.785776i	−0.919586	−	0.392888i	$-0.871476\pi$
$491$		−	17.4116i		−	0.785776i	0.919586	−	0.392888i	$-0.128524\pi$
$492$	−1.54708	+	1.54708i	−0.0697479	+	0.0697479i
$493$	0.847826	−	0.847826i	0.0381841	−	0.0381841i
$494$	38.3740			1.72653
$495$		0			0
$496$	23.1513			1.03953
$497$	−20.3724	+	20.3724i	−0.913829	+	0.913829i
$498$	16.8908	−	16.8908i	0.756895	−	0.756895i
$499$		−	7.90395i		−	0.353829i	−0.984226	−	0.176915i	$-0.943388\pi$
$499$		−	7.90395i		−	0.353829i	0.984226	−	0.176915i	$-0.0566117\pi$
$500$	−3.63570	+	2.54453i	−0.162593	+	0.113795i
$501$		−	19.1206i		−	0.854245i
$502$	−5.54834	+	5.54834i	−0.247635	+	0.247635i
$503$	−26.6750	−	26.6750i	−1.18938	−	1.18938i	−0.977239	−	0.212140i	$-0.931957\pi$
$503$	−26.6750	−	26.6750i	−1.18938	−	1.18938i	−0.212140	−	0.977239i	$-0.568043\pi$
$504$			16.8412i			0.750169i
$505$	−35.1176	+	7.24847i	−1.56271	+	0.322553i
$506$		0			0
$507$	−19.0109	−	19.0109i	−0.844302	−	0.844302i
$508$	−0.707341	−	0.707341i	−0.0313832	−	0.0313832i
$509$		−	41.0367i		−	1.81892i	−0.415793	−	0.909459i	$-0.636496\pi$
$509$		−	41.0367i		−	1.81892i	0.415793	−	0.909459i	$-0.363504\pi$
$510$	−1.06419	+	1.61777i	−0.0471233	+	0.0716358i
$511$	−10.1698			−0.449887
$512$	−17.8476	+	17.8476i	−0.788762	+	0.788762i
$513$	8.15643	+	8.15643i	0.360115	+	0.360115i
$514$	−1.71490			−0.0756411
$515$	−2.68868	−	1.76866i	−0.118477	−	0.0779364i
$516$			1.83152i			0.0806280i
$517$		0			0
$518$	14.8046	−	14.8046i	0.650479	−	0.650479i
$519$	−31.3815			−1.37750
$520$	−33.1160	+	6.83534i	−1.45223	+	0.299749i
$521$	−35.5162			−1.55599			−0.777996	−	0.628269i	$-0.783764\pi$
$521$	−35.5162			−1.55599			−0.777996	+	0.628269i	$0.783764\pi$
$522$	7.72482	+	7.72482i	0.338106	+	0.338106i
$523$	23.8121	+	23.8121i	1.04123	+	1.04123i	0.999113	+	0.0421189i	$0.0134108\pi$
$523$	23.8121	+	23.8121i	1.04123	+	1.04123i	0.0421189	+	0.999113i	$0.486589\pi$
$524$	−5.49150			−0.239897
$525$	11.5300	+	26.7405i	0.503210	+	1.16705i
$526$	−12.4832			−0.544293
$527$	−1.61596	+	1.61596i	−0.0703923	+	0.0703923i
$528$		0			0
$529$		−	28.4836i		−	1.23842i
$530$	24.3672	−	5.02952i	1.05844	−	0.218468i
$531$	2.54392			0.110397
$532$	4.37451	+	4.37451i	0.189659	+	0.189659i
$533$	−8.54546	+	8.54546i	−0.370145	+	0.370145i
$534$	−7.34736			−0.317951
$535$	20.8910	+	13.7424i	0.903195	+	0.594137i
$536$			30.3591i			1.31131i
$537$	11.0720	+	11.0720i	0.477792	+	0.477792i
$538$	12.1343	+	12.1343i	0.523145	+	0.523145i
$539$		0			0
$540$	−1.40618	−	0.925009i	−0.0605124	−	0.0398061i
$541$			12.8744i			0.553515i	0.960940	+	0.276758i	$0.0892599\pi$
$541$			12.8744i			0.553515i	−0.960940	+	0.276758i	$0.910740\pi$
$542$	4.82514	+	4.82514i	0.207258	+	0.207258i
$543$	37.3966	−	37.3966i	1.60484	−	1.60484i
$544$		−	0.664967i		−	0.0285102i
$545$	−7.34998	−	35.6094i	−0.314839	−	1.52534i
$546$			36.7439i			1.57250i
$547$	15.3187	−	15.3187i	0.654980	−	0.654980i	−0.299208	−	0.954188i	$-0.596722\pi$
$547$	15.3187	−	15.3187i	0.654980	−	0.654980i	0.954188	+	0.299208i	$0.0967224\pi$
$548$	0.550575	−	0.550575i	0.0235194	−	0.0235194i
$549$	0.201298			0.00859119
$550$		0			0
$551$	24.2340			1.03241
$552$	34.9954	−	34.9954i	1.48950	−	1.48950i
$553$	4.27324	−	4.27324i	0.181717	−	0.181717i
$554$			36.1122i			1.53426i
$555$	−6.62944	−	32.1185i	−0.281404	−	1.36335i
$556$		−	3.43884i		−	0.145839i
$557$	−12.5950	+	12.5950i	−0.533666	+	0.533666i	−0.921661	−	0.387995i	$-0.873168\pi$
$557$	−12.5950	+	12.5950i	−0.533666	+	0.533666i	0.387995	+	0.921661i	$0.373168\pi$
$558$	−14.7235	−	14.7235i	−0.623297	−	0.623297i
$559$			10.1165i			0.427884i
$560$	14.5940	+	9.60016i	0.616708	+	0.405681i
$561$		0			0
$562$	10.2190	+	10.2190i	0.431061	+	0.431061i
$563$	−19.8779	−	19.8779i	−0.837752	−	0.837752i	0.150811	−	0.988563i	$-0.451812\pi$
$563$	−19.8779	−	19.8779i	−0.837752	−	0.837752i	−0.988563	+	0.150811i	$0.951812\pi$
$564$		−	3.18619i		−	0.134163i
$565$	3.58795	+	2.36021i	0.150946	+	0.0992948i
$566$	2.35230			0.0988747
$567$	−19.5819	+	19.5819i	−0.822364	+	0.822364i
$568$	24.1273	+	24.1273i	1.01236	+	1.01236i
$569$	−26.1664			−1.09695			−0.548476	−	0.836167i	$-0.684792\pi$
$569$	−26.1664			−1.09695			−0.548476	+	0.836167i	$0.684792\pi$
$570$	−38.3302	+	7.91158i	−1.60548	+	0.331380i
$571$			27.6158i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$571$			27.6158i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$572$		0			0
$573$	−12.1072	+	12.1072i	−0.505785	+	0.505785i
$574$	7.86887			0.328440
$575$	13.2506	−	33.3393i	0.552589	−	1.39035i
$576$	19.2629			0.802620
$577$	20.9132	+	20.9132i	0.870629	+	0.870629i	0.992541	−	0.121912i	$-0.0389024\pi$
$577$	20.9132	+	20.9132i	0.870629	+	0.870629i	−0.121912	+	0.992541i	$0.538902\pi$
$578$	15.1388	+	15.1388i	0.629692	+	0.629692i
$579$	57.4328			2.38683
$580$	−3.46317	+	0.714818i	−0.143800	+	0.0296812i
$581$	21.2712			0.882480
$582$	−15.3203	+	15.3203i	−0.635045	+	0.635045i
$583$		0			0
$584$			12.0442i			0.498393i
$585$	20.1587	+	13.2607i	0.833460	+	0.548264i
$586$	22.6667			0.936353
$587$	5.11085	+	5.11085i	0.210947	+	0.210947i	0.804670	−	0.593723i	$-0.202342\pi$
$587$	5.11085	+	5.11085i	0.210947	+	0.210947i	−0.593723	+	0.804670i	$0.702342\pi$
$588$	0.276545	−	0.276545i	0.0114045	−	0.0114045i
$589$	−46.1902			−1.90324
$590$	1.82774	−	2.77849i	0.0752467	−	0.114389i
$591$		−	33.2924i		−	1.36947i
$592$	−13.9110	−	13.9110i	−0.571738	−	0.571738i
$593$	−7.89832	−	7.89832i	−0.324345	−	0.324345i	0.526086	−	0.850431i	$-0.323659\pi$
$593$	−7.89832	−	7.89832i	−0.324345	−	0.324345i	−0.850431	+	0.526086i	$0.823659\pi$
$594$		0			0
$595$	−1.68875	+	0.348567i	−0.0692319	+	0.0142899i
$596$		−	3.37986i		−	0.138444i
$597$	−13.8685	−	13.8685i	−0.567602	−	0.567602i
$598$	32.0095	−	32.0095i	1.30897	−	1.30897i
$599$			16.3481i			0.667964i	0.942579	+	0.333982i	$0.108392\pi$
$599$			16.3481i			0.667964i	−0.942579	+	0.333982i	$0.891608\pi$
$600$	31.6690	−	13.6551i	1.29288	−	0.557466i
$601$			32.5519i			1.32782i	0.747813	+	0.663909i	$0.231104\pi$
$601$			32.5519i			1.32782i	−0.747813	+	0.663909i	$0.768896\pi$
$602$	4.65778	−	4.65778i	0.189837	−	0.189837i
$603$	15.3186	−	15.3186i	0.623823	−	0.623823i
$604$	2.73577			0.111317
$605$		0			0
$606$	46.1463			1.87457
$607$	14.9647	−	14.9647i	0.607399	−	0.607399i	−0.334867	−	0.942266i	$-0.608691\pi$
$607$	14.9647	−	14.9647i	0.607399	−	0.607399i	0.942266	+	0.334867i	$0.108691\pi$
$608$	9.50362	−	9.50362i	0.385423	−	0.385423i
$609$			23.2046i			0.940298i
$610$	0.144627	−	0.219859i	0.00585577	−	0.00890182i
$611$		−	17.5992i		−	0.711989i
$612$	−0.182909	+	0.182909i	−0.00739367	+	0.00739367i
$613$	21.1838	+	21.1838i	0.855607	+	0.855607i	0.990817	−	0.135210i	$-0.0431710\pi$
$613$	21.1838	+	21.1838i	0.855607	+	0.855607i	−0.135210	+	0.990817i	$0.543171\pi$
$614$		−	16.3066i		−	0.658079i
$615$	6.77388	−	10.2975i	0.273149	−	0.415236i
$616$		0			0
$617$	16.8977	+	16.8977i	0.680276	+	0.680276i	0.960062	−	0.279786i	$-0.0902636\pi$
$617$	16.8977	+	16.8977i	0.680276	+	0.680276i	−0.279786	+	0.960062i	$0.590264\pi$
$618$	2.92859	+	2.92859i	0.117805	+	0.117805i
$619$		−	6.97674i		−	0.280419i	−0.990122	−	0.140209i	$-0.955222\pi$
$619$		−	6.97674i		−	0.280419i	0.990122	−	0.140209i	$-0.0447776\pi$
$620$	6.60082	−	1.36245i	0.265095	−	0.0547172i
$621$	13.6073			0.546042
$622$	−16.8798	+	16.8798i	−0.676818	+	0.676818i
$623$	−4.62641	−	4.62641i	−0.185353	−	0.185353i
$624$	34.5259			1.38214
$625$	17.1615	−	18.1792i	0.686458	−	0.727169i
$626$		−	12.1523i		−	0.485702i
$627$		0			0
$628$	−1.53057	+	1.53057i	−0.0610762	+	0.0610762i
$629$	1.94197			0.0774314
$630$	−3.17591	−	15.3867i	−0.126531	−	0.613022i
$631$	17.3689			0.691445			0.345723	−	0.938337i	$-0.387634\pi$
$631$	17.3689			0.691445			0.345723	+	0.938337i	$0.387634\pi$
$632$	−5.06084	−	5.06084i	−0.201309	−	0.201309i
$633$	−27.1786	−	27.1786i	−1.08025	−	1.08025i
$634$	−16.7114			−0.663695
$635$	4.70812	+	3.09708i	0.186836	+	0.122904i
$636$	7.92796			0.314364
$637$	1.52752	−	1.52752i	0.0605225	−	0.0605225i
$638$		0			0
$639$		−	24.3483i		−	0.963206i
$640$	8.40902	−	12.7832i	0.332396	−	0.505301i
$641$	−27.8829			−1.10131			−0.550653	−	0.834734i	$-0.685621\pi$
$641$	−27.8829			−1.10131			−0.550653	+	0.834734i	$0.685621\pi$
$642$	−22.7551	−	22.7551i	−0.898070	−	0.898070i
$643$	−11.8044	+	11.8044i	−0.465519	+	0.465519i	−0.900459	−	0.434940i	$-0.856770\pi$
$643$	−11.8044	+	11.8044i	−0.465519	+	0.465519i	0.434940	+	0.900459i	$0.356770\pi$
$644$	7.29795			0.287579
$645$	−2.08573	−	10.1050i	−0.0821255	−	0.397884i
$646$		−	2.31755i		−	0.0911828i
$647$	14.0447	+	14.0447i	0.552153	+	0.552153i	0.927062	−	0.374908i	$-0.122326\pi$
$647$	14.0447	+	14.0447i	0.552153	+	0.552153i	−0.374908	+	0.927062i	$0.622326\pi$
$648$	23.1911	+	23.1911i	0.911031	+	0.911031i
$649$		0			0
$650$	28.9669	−	12.4900i	1.13618	−	0.489898i
$651$		−	44.2281i		−	1.73344i
$652$	−0.628785	−	0.628785i	−0.0246251	−	0.0246251i
$653$	26.2218	−	26.2218i	1.02614	−	1.02614i	0.0264889	−	0.999649i	$-0.491567\pi$
$653$	26.2218	−	26.2218i	1.02614	−	1.02614i	0.999649	−	0.0264889i	$-0.00843267\pi$
$654$			46.7926i			1.82974i
$655$	30.2982	−	6.25372i	1.18385	−	0.244353i
$656$		−	7.39388i		−	0.288682i
$657$	6.07729	−	6.07729i	0.237098	−	0.237098i
$658$	−8.10291	+	8.10291i	−0.315884	+	0.315884i
$659$	−25.1740			−0.980641			−0.490320	−	0.871542i	$-0.663120\pi$
$659$	−25.1740			−0.980641			−0.490320	+	0.871542i	$0.663120\pi$
$660$		0			0
$661$	−25.7739			−1.00249			−0.501244	−	0.865306i	$-0.667124\pi$
$661$	−25.7739			−1.00249			−0.501244	+	0.865306i	$0.667124\pi$
$662$	−11.3706	+	11.3706i	−0.441932	+	0.441932i
$663$	−2.40991	+	2.40991i	−0.0935931	+	0.0935931i
$664$		−	25.1917i		−	0.977629i
$665$	−29.1171	−	19.1537i	−1.12911	−	0.742749i
$666$			17.6939i			0.685626i
$667$	20.2147	−	20.2147i	0.782717	−	0.782717i
$668$	−2.36116	−	2.36116i	−0.0913562	−	0.0913562i
$669$			17.1227i			0.662000i
$670$	−5.72510	−	27.7371i	−0.221180	−	1.07158i
$671$		0			0
$672$	9.09992	+	9.09992i	0.351037	+	0.351037i
$673$	15.9996	+	15.9996i	0.616740	+	0.616740i	0.944694	−	0.327954i	$-0.106359\pi$
$673$	15.9996	+	15.9996i	0.616740	+	0.616740i	−0.327954	+	0.944694i	$0.606359\pi$
$674$		−	19.7670i		−	0.761395i
$675$	8.81170	+	3.50218i	0.339162	+	0.134799i
$676$	−4.69523			−0.180586
$677$	19.8094	−	19.8094i	0.761336	−	0.761336i	−0.215228	−	0.976564i	$-0.569050\pi$
$677$	19.8094	−	19.8094i	0.761336	−	0.761336i	0.976564	+	0.215228i	$0.0690495\pi$
$678$	−3.90809	−	3.90809i	−0.150089	−	0.150089i
$679$	−19.2934			−0.740413
$680$	0.412811	+	2.00000i	0.0158306	+	0.0766965i
$681$		−	13.3470i		−	0.511458i
$682$		0			0
$683$	−27.8670	+	27.8670i	−1.06630	+	1.06630i	−0.0686610	+	0.997640i	$0.521873\pi$
$683$	−27.8670	+	27.8670i	−1.06630	+	1.06630i	−0.997640	+	0.0686610i	$0.978127\pi$
$684$	−5.22824			−0.199907
$685$	−2.41068	+	3.66467i	−0.0921075	+	0.140020i
$686$	−24.1179			−0.920825
$687$	38.5313	+	38.5313i	1.47006	+	1.47006i
$688$	−4.37662	−	4.37662i	−0.166857	−	0.166857i
$689$	43.7908			1.66830
$690$	−25.3736	+	38.5724i	−0.965955	+	1.46843i
$691$	−46.7547			−1.77863			−0.889317	−	0.457291i	$-0.848820\pi$
$691$	−46.7547			−1.77863			−0.889317	+	0.457291i	$0.848820\pi$
$692$	−3.87524	+	3.87524i	−0.147315	+	0.147315i
$693$		0			0
$694$			3.02314i			0.114757i
$695$	3.91615	+	18.9731i	0.148548	+	0.719690i
$696$	27.4814			1.04168
$697$	0.516092	+	0.516092i	0.0195484	+	0.0195484i
$698$	31.6105	−	31.6105i	1.19648	−	1.19648i
$699$	32.7574			1.23900
$700$	4.72594	+	1.87831i	0.178624	+	0.0709935i
$701$		−	22.9748i		−	0.867748i	−0.900974	−	0.433874i	$-0.857146\pi$
$701$		−	22.9748i		−	0.867748i	0.900974	−	0.433874i	$-0.142854\pi$
$702$	8.46022	+	8.46022i	0.319310	+	0.319310i
$703$	27.7544	+	27.7544i	1.04678	+	1.04678i
$704$		0			0
$705$	3.62844	+	17.5791i	0.136655	+	0.662069i
$706$			0.0932036i			0.00350776i
$707$	29.0569	+	29.0569i	1.09280	+	1.09280i
$708$	0.749328	−	0.749328i	0.0281615	−	0.0281615i
$709$			10.9351i			0.410675i	0.978691	+	0.205338i	$0.0658292\pi$
$709$			10.9351i			0.410675i	−0.978691	+	0.205338i	$0.934171\pi$
$710$	−26.5934	−	17.4936i	−0.998033	−	0.656523i
$711$			5.10721i			0.191535i
$712$	−5.47910	+	5.47910i	−0.205338	+	0.205338i
$713$	−38.5294	+	38.5294i	−1.44294	+	1.44294i
$714$	2.21910			0.0830479
$715$		0			0
$716$	2.73452			0.102194
$717$	−24.2958	+	24.2958i	−0.907345	+	0.907345i
$718$	−14.5248	+	14.5248i	−0.542062	+	0.542062i
$719$			45.7653i			1.70676i	0.521291	+	0.853379i	$0.325451\pi$
$719$			45.7653i			1.70676i	−0.521291	+	0.853379i	$0.674549\pi$
$720$	−14.4579	+	2.98420i	−0.538815	+	0.111215i
$721$			3.68809i			0.137352i
$722$	16.1117	−	16.1117i	0.599615	−	0.599615i
$723$	5.02971	+	5.02971i	0.187057	+	0.187057i
$724$		−	9.23608i		−	0.343256i
$725$	18.2932	−	7.88770i	0.679394	−	0.292942i
$726$		0			0
$727$	−36.0611	−	36.0611i	−1.33743	−	1.33743i	−0.898539	−	0.438893i	$-0.855371\pi$
$727$	−36.0611	−	36.0611i	−1.33743	−	1.33743i	−0.438893	−	0.898539i	$-0.644629\pi$
$728$	27.4008	+	27.4008i	1.01554	+	1.01554i
$729$		−	10.4730i		−	0.387887i
$730$	−2.27129	−	11.0040i	−0.0840642	−	0.407277i
$731$	0.610976			0.0225978
$732$	0.0592935	−	0.0592935i	0.00219155	−	0.00219155i
$733$	2.80629	+	2.80629i	0.103653	+	0.103653i	0.757031	−	0.653379i	$-0.226649\pi$
$733$	2.80629	+	2.80629i	0.103653	+	0.103653i	−0.653379	+	0.757031i	$0.726649\pi$
$734$	−16.6516			−0.614623
$735$	−1.21085	+	1.84070i	−0.0446627	+	0.0678954i
$736$		−	15.8548i		−	0.584416i
$737$		0			0
$738$	−4.70228	+	4.70228i	−0.173093	+	0.173093i
$739$	−1.57253			−0.0578465			−0.0289232	−	0.999582i	$-0.509208\pi$
$739$	−1.57253			−0.0578465			−0.0289232	+	0.999582i	$0.509208\pi$
$740$	−4.78490	−	3.14759i	−0.175897	−	0.115708i
$741$	−68.8842			−2.53053
$742$	−20.1618	−	20.1618i	−0.740165	−	0.740165i
$743$	30.1633	+	30.1633i	1.10658	+	1.10658i	0.993596	+	0.112988i	$0.0360423\pi$
$743$	30.1633	+	30.1633i	1.10658	+	1.10658i	0.112988	+	0.993596i	$0.463958\pi$
$744$	−52.3797			−1.92033
$745$	3.84898	+	18.6476i	0.141016	+	0.683196i
$746$	33.6635			1.23251
$747$	−12.7113	+	12.7113i	−0.465081	+	0.465081i
$748$		0			0
$749$		−	28.6563i		−	1.04708i
$750$	−26.3588	+	18.4479i	−0.962487	+	0.673620i
$751$	39.3563			1.43613			0.718066	−	0.695975i	$-0.245028\pi$
$751$	39.3563			1.43613			0.718066	+	0.695975i	$0.245028\pi$
$752$	7.61379	+	7.61379i	0.277646	+	0.277646i
$753$	9.95968	−	9.95968i	0.362951	−	0.362951i
$754$	25.1367			0.915423
$755$	−15.0940	+	3.11549i	−0.549328	+	0.113384i
$756$			1.92887i			0.0701524i
$757$	10.8518	+	10.8518i	0.394417	+	0.394417i	0.876258	−	0.481842i	$-0.160032\pi$
$757$	10.8518	+	10.8518i	0.394417	+	0.394417i	−0.481842	+	0.876258i	$0.660032\pi$
$758$	−12.1038	−	12.1038i	−0.439631	−	0.439631i
$759$		0			0
$760$	−22.6839	+	34.4836i	−0.822832	+	1.25085i
$761$		−	3.99343i		−	0.144762i	−0.997377	−	0.0723808i	$-0.976940\pi$
$761$		−	3.99343i		−	0.144762i	0.997377	−	0.0723808i	$-0.0230597\pi$
$762$	−5.12822	−	5.12822i	−0.185776	−	0.185776i
$763$	−29.4639	+	29.4639i	−1.06666	+	1.06666i
$764$			2.99018i			0.108181i
$765$	0.800866	−	1.21746i	0.0289554	−	0.0440173i
$766$		−	23.1228i		−	0.835462i
$767$	4.13898	−	4.13898i	0.149450	−	0.149450i
$768$	14.6665	−	14.6665i	0.529231	−	0.529231i
$769$	−43.6566			−1.57430			−0.787148	−	0.616764i	$-0.788443\pi$
$769$	−43.6566			−1.57430			−0.787148	+	0.616764i	$0.788443\pi$
$770$		0			0
$771$	3.07838			0.110865
$772$	7.09226	−	7.09226i	0.255256	−	0.255256i
$773$	−3.55842	+	3.55842i	−0.127987	+	0.127987i	−0.768199	−	0.640211i	$-0.778847\pi$
$773$	−3.55842	+	3.55842i	−0.127987	+	0.127987i	0.640211	+	0.768199i	$0.278847\pi$
$774$			5.56680i			0.200094i
$775$	−34.8670	+	15.0340i	−1.25246	+	0.540038i
$776$			22.8493i			0.820244i
$777$	−26.5754	+	26.5754i	−0.953388	+	0.953388i
$778$	−15.8178	−	15.8178i	−0.567095	−	0.567095i
$779$			14.7519i			0.528540i
$780$	9.84390	−	2.03184i	0.352468	−	0.0727515i
$781$		0			0
$782$	−1.93317	−	1.93317i	−0.0691302	−	0.0691302i
$783$	5.34281	+	5.34281i	0.190937	+	0.190937i
$784$			1.32167i			0.0472026i
$785$	6.70156	−	10.1876i	0.239189	−	0.363610i
$786$	−39.8134			−1.42010
$787$	−29.9760	+	29.9760i	−1.06853	+	1.06853i	−0.0710579	+	0.997472i	$0.522638\pi$
$787$	−29.9760	+	29.9760i	−1.06853	+	1.06853i	−0.997472	+	0.0710579i	$0.977362\pi$
$788$	−4.11122	−	4.11122i	−0.146456	−	0.146456i
$789$	22.4083			0.797755
$790$	5.57813	+	3.66939i	0.198461	+	0.130551i
$791$		−	4.92162i		−	0.174993i
$792$		0			0
$793$	0.327513	−	0.327513i	0.0116303	−	0.0116303i
$794$	−20.9860			−0.744766
$795$	−43.7408	+	9.02836i	−1.55133	+	0.320203i
$796$	−3.42520			−0.121403
$797$	32.2937	+	32.2937i	1.14390	+	1.14390i	0.987730	+	0.156170i	$0.0499149\pi$
$797$	32.2937	+	32.2937i	1.14390	+	1.14390i	0.156170	+	0.987730i	$0.450085\pi$
$798$	31.7152	+	31.7152i	1.12270	+	1.12270i
$799$	−1.06288			−0.0376021
$800$	4.08064	−	10.2671i	0.144272	−	0.362998i
$801$	5.52930			0.195368
$802$	−19.5683	+	19.5683i	−0.690982	+	0.690982i
$803$		0			0
$804$		−	9.02440i		−	0.318266i
$805$	−40.2648	+	8.31089i	−1.41915	+	0.292920i
$806$	−47.9106			−1.68758
$807$	−21.7819	−	21.7819i	−0.766758	−	0.766758i
$808$	34.4124	−	34.4124i	1.21062	−	1.21062i
$809$	−31.8280			−1.11901			−0.559507	−	0.828825i	$-0.689010\pi$
$809$	−31.8280			−1.11901			−0.559507	+	0.828825i	$0.689010\pi$
$810$	−25.5615	−	16.8148i	−0.898139	−	0.590811i
$811$		−	31.7003i		−	1.11315i	−0.830798	−	0.556574i	$-0.812116\pi$
$811$		−	31.7003i		−	1.11315i	0.830798	−	0.556574i	$-0.187884\pi$
$812$	2.86549	+	2.86549i	0.100559	+	0.100559i
$813$	−8.66148	−	8.66148i	−0.303772	−	0.303772i
$814$		0			0
$815$	4.18524	+	2.75312i	0.146603	+	0.0964377i
$816$		−	2.08515i		−	0.0729948i
$817$	8.73199	+	8.73199i	0.305494	+	0.305494i
$818$	−18.0808	+	18.0808i	−0.632179	+	0.632179i
$819$		−	27.6519i		−	0.966235i
$820$	−0.435127	−	2.10811i	−0.0151953	−	0.0736185i
$821$		−	31.0257i		−	1.08280i	−0.840764	−	0.541402i	$-0.817894\pi$
$821$		−	31.0257i		−	1.08280i	0.840764	−	0.541402i	$-0.182106\pi$
$822$	3.99167	−	3.99167i	0.139225	−	0.139225i
$823$	28.4141	−	28.4141i	0.990453	−	0.990453i	−0.00950231	−	0.999955i	$-0.503025\pi$
$823$	28.4141	−	28.4141i	0.990453	−	0.990453i	0.999955	+	0.00950231i	$0.00302472\pi$
$824$	4.36783			0.152161
$825$		0			0
$826$	−3.81128			−0.132611
$827$	1.98953	−	1.98953i	0.0691826	−	0.0691826i	−0.671669	−	0.740851i	$-0.734422\pi$
$827$	1.98953	−	1.98953i	0.0691826	−	0.0691826i	0.740851	+	0.671669i	$0.234422\pi$
$828$	−4.36111	+	4.36111i	−0.151559	+	0.151559i
$829$			27.9016i			0.969062i	0.874774	+	0.484531i	$0.161010\pi$
$829$			27.9016i			0.969062i	−0.874774	+	0.484531i	$0.838990\pi$
$830$	4.75064	+	23.0160i	0.164897	+	0.798898i
$831$		−	64.8240i		−	2.24872i
$832$	31.3409	−	31.3409i	1.08655	−	1.08655i
$833$	−0.0922526	−	0.0922526i	−0.00319636	−	0.00319636i
$834$		−	24.9316i		−	0.863311i
$835$	15.7161	+	10.3383i	0.543878	+	0.357772i
$836$		0			0
$837$	−10.1834	−	10.1834i	−0.351991	−	0.351991i
$838$	9.97269	+	9.97269i	0.344501	+	0.344501i
$839$			43.1638i			1.49018i	0.666964	+	0.745090i	$0.267594\pi$
$839$			43.1638i			1.49018i	−0.666964	+	0.745090i	$0.732406\pi$
$840$	−33.0188	−	21.7203i	−1.13926	−	0.749422i
$841$	−13.1256			−0.452609
$842$	26.7735	−	26.7735i	0.922676	−	0.922676i
$843$	−18.3438	−	18.3438i	−0.631794	−	0.631794i
$844$	−6.71246			−0.231052
$845$	25.9049	−	5.34692i	0.891156	−	0.183940i
$846$		−	9.68428i		−	0.332952i
$847$		0			0
$848$	−18.9448	+	18.9448i	−0.650567	+	0.650567i
$849$	−4.22256			−0.144918
$850$	−0.754317	−	1.74942i	−0.0258729	−	0.0600046i
$851$	46.3024			1.58723
$852$	−7.17195	−	7.17195i	−0.245707	−	0.245707i
$853$	4.64124	+	4.64124i	0.158913	+	0.158913i	0.782085	−	0.623172i	$-0.214156\pi$
$853$	4.64124	+	4.64124i	0.158913	+	0.158913i	−0.623172	+	0.782085i	$0.714156\pi$
$854$	−0.301582			−0.0103199
$855$	28.8457	−	5.95391i	0.986501	−	0.203619i
$856$	−33.9380			−1.15998
$857$	16.3855	−	16.3855i	0.559717	−	0.559717i	−0.369510	−	0.929227i	$-0.620474\pi$
$857$	16.3855	−	16.3855i	0.559717	−	0.559717i	0.929227	+	0.369510i	$0.120474\pi$
$858$		0			0
$859$			44.6723i			1.52420i	0.647461	+	0.762099i	$0.275831\pi$
$859$			44.6723i			1.52420i	−0.647461	+	0.762099i	$0.724169\pi$
$860$	−1.50541	−	0.990283i	−0.0513340	−	0.0337684i
$861$	−14.1252			−0.481386
$862$	34.0960	+	34.0960i	1.16132	+	1.16132i
$863$	−8.43404	+	8.43404i	−0.287098	+	0.287098i	−0.835932	−	0.548834i	$-0.815072\pi$
$863$	−8.43404	+	8.43404i	−0.287098	+	0.287098i	0.548834	+	0.835932i	$0.315072\pi$
$864$	4.19048			0.142563
$865$	16.9677	−	25.7939i	0.576919	−	0.877020i
$866$			4.85331i			0.164922i
$867$	−27.1753	−	27.1753i	−0.922922	−	0.922922i
$868$	−5.46164	−	5.46164i	−0.185380	−	0.185380i
$869$		0			0
$870$	−25.1080	+	5.18243i	−0.851240	+	0.175701i
$871$		−	49.8471i		−	1.68900i
$872$	34.8943	+	34.8943i	1.18167	+	1.18167i
$873$	11.5294	−	11.5294i	0.390210	−	0.390210i
$874$		−	55.2574i		−	1.86911i
$875$	−28.2134	−	4.98128i	−0.953787	−	0.168398i
$876$		−	3.58020i		−	0.120964i
$877$	11.2634	−	11.2634i	0.380337	−	0.380337i	−0.490886	−	0.871224i	$-0.663327\pi$
$877$	11.2634	−	11.2634i	0.380337	−	0.380337i	0.871224	+	0.490886i	$0.163327\pi$
$878$	16.0106	−	16.0106i	0.540332	−	0.540332i
$879$	−40.6884			−1.37239
$880$		0			0
$881$	−35.9869			−1.21243			−0.606214	−	0.795301i	$-0.707313\pi$
$881$	−35.9869			−1.21243			−0.606214	+	0.795301i	$0.707313\pi$
$882$	0.840543	−	0.840543i	0.0283026	−	0.0283026i
$883$	−11.4964	+	11.4964i	−0.386886	+	0.386886i	−0.873575	−	0.486689i	$-0.838204\pi$
$883$	−11.4964	+	11.4964i	−0.386886	+	0.386886i	0.486689	+	0.873575i	$0.338204\pi$
$884$			0.595190i			0.0200184i
$885$	−3.28092	+	4.98759i	−0.110287	+	0.167656i
$886$			2.27971i			0.0765885i
$887$	−22.0357	+	22.0357i	−0.739886	+	0.739886i	−0.972556	−	0.232670i	$-0.925254\pi$
$887$	−22.0357	+	22.0357i	−0.739886	+	0.739886i	0.232670	+	0.972556i	$0.425254\pi$
$888$	31.4735	+	31.4735i	1.05618	+	1.05618i
$889$		−	6.45817i		−	0.216600i
$890$	3.97265	−	6.03914i	0.133163	−	0.202432i
$891$		0			0
$892$	2.11444	+	2.11444i	0.0707968	+	0.0707968i
$893$	−15.1906	−	15.1906i	−0.508334	−	0.508334i
$894$		−	24.5040i		−	0.819535i
$895$	−15.0871	+	3.11407i	−0.504306	+	0.104092i
$896$	−17.5349			−0.585799
$897$	−57.4594	+	57.4594i	−1.91851	+	1.91851i
$898$	12.9756	+	12.9756i	0.433000	+	0.433000i
$899$	−30.2566			−1.00911
$900$	−3.94657	+	1.70169i	−0.131552	+	0.0567229i
$901$		−	2.64469i		−	0.0881074i
$902$		0			0
$903$	−8.36106	+	8.36106i	−0.278239	+	0.278239i
$904$	−5.82872			−0.193860
$905$	10.5180	+	50.9581i	0.349631	+	1.69390i
$906$	19.8343			0.658952
$907$	−24.4871	−	24.4871i	−0.813081	−	0.813081i	0.172013	−	0.985095i	$-0.444973\pi$
$907$	−24.4871	−	24.4871i	−0.813081	−	0.813081i	−0.985095	+	0.172013i	$0.944973\pi$
$908$	−1.64819	−	1.64819i	−0.0546972	−	0.0546972i
$909$	−34.7277			−1.15185
$910$	−30.2016	−	19.8671i	−1.00117	−	0.658588i
$911$	−30.6831			−1.01658			−0.508288	−	0.861187i	$-0.669722\pi$
$911$	−30.6831			−1.01658			−0.508288	+	0.861187i	$0.669722\pi$
$912$	29.8007	−	29.8007i	0.986800	−	0.986800i
$913$		0			0
$914$		−	48.7687i		−	1.61312i
$915$	−0.259616	+	0.394663i	−0.00858264	+	0.0130471i
$916$	9.51631			0.314428
$917$	−25.0693	−	25.0693i	−0.827861	−	0.827861i
$918$	0.510944	−	0.510944i	0.0168637	−	0.0168637i
$919$	−26.7907			−0.883742			−0.441871	−	0.897079i	$-0.645685\pi$
$919$	−26.7907			−0.883742			−0.441871	+	0.897079i	$0.645685\pi$
$920$	9.84267	+	47.6860i	0.324503	+	1.57216i
$921$			29.2715i			0.964528i
$922$	−17.2634	−	17.2634i	−0.568541	−	0.568541i
$923$	−39.6149	−	39.6149i	−1.30394	−	1.30394i
$924$		0			0
$925$	29.9841	+	11.9171i	0.985872	+	0.391832i
$926$		−	24.5760i		−	0.807617i
$927$	−2.20393	−	2.20393i	−0.0723865	−	0.0723865i
$928$	6.22529	−	6.22529i	0.204355	−	0.204355i
$929$		−	25.4532i		−	0.835094i	−0.908655	−	0.417547i	$-0.862890\pi$
$929$		−	25.4532i		−	0.835094i	0.908655	−	0.417547i	$-0.137110\pi$
$930$	47.8559	−	9.87774i	1.56926	−	0.323904i
$931$		−	2.63693i		−	0.0864218i
$932$	4.04514	−	4.04514i	0.132503	−	0.132503i
$933$	30.3005	−	30.3005i	0.991993	−	0.991993i
$934$	−46.0237			−1.50594
$935$		0			0
$936$	−32.7484			−1.07041
$937$	27.9630	−	27.9630i	0.913513	−	0.913513i	−0.0830341	−	0.996547i	$-0.526461\pi$
$937$	27.9630	−	27.9630i	0.913513	−	0.913513i	0.996547	+	0.0830341i	$0.0264610\pi$
$938$	−22.9502	+	22.9502i	−0.749351	+	0.749351i
$939$			21.8142i			0.711880i
$940$	2.61888	+	1.72275i	0.0854185	+	0.0561898i
$941$			41.0094i			1.33687i	0.743772	+	0.668433i	$0.233035\pi$
$941$			41.0094i			1.33687i	−0.743772	+	0.668433i	$0.766965\pi$
$942$	−11.0966	+	11.0966i	−0.361547	+	0.361547i
$943$	12.3052	+	12.3052i	0.400712	+	0.400712i
$944$			3.58121i			0.116559i
$945$	−2.19660	−	10.6421i	−0.0714553	−	0.346188i
$946$		0			0
$947$	42.9022	+	42.9022i	1.39413	+	1.39413i	0.815799	+	0.578336i	$0.196298\pi$
$947$	42.9022	+	42.9022i	1.39413	+	1.39413i	0.578336	+	0.815799i	$0.303702\pi$
$948$	1.50436	+	1.50436i	0.0488593	+	0.0488593i
$949$		−	19.7756i		−	0.641942i
$950$	14.2219	−	35.7831i	0.461419	−	1.16096i
$951$	29.9982			0.972759
$952$	1.65484	−	1.65484i	0.0536336	−	0.0536336i
$953$	3.22534	+	3.22534i	0.104479	+	0.104479i	0.757414	−	0.652935i	$-0.226463\pi$
$953$	3.22534	+	3.22534i	0.104479	+	0.104479i	−0.652935	+	0.757414i	$0.726463\pi$
$954$	24.0966			0.780158
$955$	−3.40522	−	16.4977i	−0.110190	−	0.533853i
$956$			6.00049i			0.194070i
$957$		0			0
$958$	−7.62489	+	7.62489i	−0.246349	+	0.246349i
$959$	5.02687			0.162326
$960$	−24.8435	+	37.7666i	−0.801822	+	1.21891i
$961$	26.6693			0.860299
$962$	28.7882	+	28.7882i	0.928167	+	0.928167i
$963$	17.1245	+	17.1245i	0.551828	+	0.551828i
$964$	1.24222			0.0400091
$965$	−31.0534	+	47.2067i	−0.999643	+	1.51964i
$966$	52.9101			1.70235
$967$	27.0023	−	27.0023i	0.868336	−	0.868336i	−0.123952	−	0.992288i	$-0.539557\pi$
$967$	27.0023	−	27.0023i	0.868336	−	0.868336i	0.992288	+	0.123952i	$0.0395569\pi$
$968$		0			0
$969$			4.16018i			0.133644i
$970$	−4.30891	−	20.8759i	−0.138351	−	0.670286i
$971$	−39.6545			−1.27257			−0.636287	−	0.771452i	$-0.719531\pi$
$971$	−39.6545			−1.27257			−0.636287	+	0.771452i	$0.719531\pi$
$972$	−5.29688	−	5.29688i	−0.169898	−	0.169898i
$973$	15.6987	−	15.6987i	0.503277	−	0.503277i
$974$	−5.52537			−0.177044
$975$	−51.9978	+	22.4205i	−1.66526	+	0.718029i
$976$			0.283378i			0.00907070i
$977$	−4.49528	−	4.49528i	−0.143817	−	0.143817i	0.631533	−	0.775349i	$-0.282426\pi$
$977$	−4.49528	−	4.49528i	−0.143817	−	0.143817i	−0.775349	+	0.631533i	$0.782426\pi$
$978$	−4.55869	−	4.55869i	−0.145771	−	0.145771i
$979$		0			0
$980$	0.0777799	+	0.376830i	0.00248459	+	0.0120374i
$981$		−	35.2141i		−	1.12430i
$982$	−15.5884	−	15.5884i	−0.497447	−	0.497447i
$983$	0.848538	−	0.848538i	0.0270642	−	0.0270642i	−0.693445	−	0.720509i	$-0.743908\pi$
$983$	0.848538	−	0.848538i	0.0270642	−	0.0270642i	0.720509	+	0.693445i	$0.243908\pi$
$984$			16.7286i			0.533289i
$985$	27.3646	+	18.0009i	0.871908	+	0.573556i
$986$		−	1.51810i		−	0.0483461i
$987$	14.5453	−	14.5453i	0.462983	−	0.462983i
$988$	−8.50638	+	8.50638i	−0.270624	+	0.270624i
$989$	14.5675			0.463220
$990$		0			0
$991$	9.57879			0.304280			0.152140	−	0.988359i	$-0.451383\pi$
$991$	9.57879			0.304280			0.152140	+	0.988359i	$0.451383\pi$
$992$	−11.8654	+	11.8654i	−0.376728	+	0.376728i
$993$	20.4111	−	20.4111i	0.647727	−	0.647727i
$994$			36.4784i			1.15703i
$995$	18.8978	−	3.90061i	0.599100	−	0.123658i
$996$			7.48837i			0.237278i
$997$	−11.9246	+	11.9246i	−0.377657	+	0.377657i	−0.870256	−	0.492599i	$-0.836047\pi$
$997$	−11.9246	+	11.9246i	−0.377657	+	0.377657i	0.492599	+	0.870256i	$0.336047\pi$
$998$	−7.07631	−	7.07631i	−0.223997	−	0.223997i
$999$			12.2379i			0.387189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.a.362.7	yes	20
5.3	odd	4	inner	605.2.e.a.483.4	yes	20
11.2	odd	10		605.2.m.f.282.7		80
11.3	even	5		605.2.m.f.112.4		80
11.4	even	5		605.2.m.f.457.7		80
11.5	even	5		605.2.m.f.602.4		80
11.6	odd	10		605.2.m.f.602.7		80
11.7	odd	10		605.2.m.f.457.4		80
11.8	odd	10		605.2.m.f.112.7		80
11.9	even	5		605.2.m.f.282.4		80
11.10	odd	2	inner	605.2.e.a.362.4	✓	20
55.3	odd	20		605.2.m.f.233.4		80
55.8	even	20		605.2.m.f.233.7		80
55.13	even	20		605.2.m.f.403.4		80
55.18	even	20		605.2.m.f.578.4		80
55.28	even	20		605.2.m.f.118.4		80
55.38	odd	20		605.2.m.f.118.7		80
55.43	even	4	inner	605.2.e.a.483.7	yes	20
55.48	odd	20		605.2.m.f.578.7		80
55.53	odd	20		605.2.m.f.403.7		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.4	✓	20	11.10	odd	2	inner
605.2.e.a.362.7	yes	20	1.1	even	1	trivial
605.2.e.a.483.4	yes	20	5.3	odd	4	inner
605.2.e.a.483.7	yes	20	55.43	even	4	inner
605.2.m.f.112.4		80	11.3	even	5
605.2.m.f.112.7		80	11.8	odd	10
605.2.m.f.118.4		80	55.28	even	20
605.2.m.f.118.7		80	55.38	odd	20
605.2.m.f.233.4		80	55.3	odd	20
605.2.m.f.233.7		80	55.8	even	20
605.2.m.f.282.4		80	11.9	even	5
605.2.m.f.282.7		80	11.2	odd	10
605.2.m.f.403.4		80	55.13	even	20
605.2.m.f.403.7		80	55.53	odd	20
605.2.m.f.457.4		80	11.7	odd	10
605.2.m.f.457.7		80	11.4	even	5
605.2.m.f.578.4		80	55.18	even	20
605.2.m.f.578.7		80	55.48	odd	20
605.2.m.f.602.4		80	11.5	even	5
605.2.m.f.602.7		80	11.6	odd	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.895288 - 0.895288i) q^{2} +(-1.60711 + 1.60711i) q^{3} +0.396917i q^{4} +(-0.452009 - 2.18991i) q^{5} +2.87765i q^{6} +(-1.81197 + 1.81197i) q^{7} +(2.14593 + 2.14593i) q^{8} -2.16559i q^{9} +O(q^{10})\)	\(q+(0.895288 - 0.895288i) q^{2} +(-1.60711 + 1.60711i) q^{3} +0.396917i q^{4} +(-0.452009 - 2.18991i) q^{5} +2.87765i q^{6} +(-1.81197 + 1.81197i) q^{7} +(2.14593 + 2.14593i) q^{8} -2.16559i q^{9} +(-2.36528 - 1.55592i) q^{10} +(-0.637889 - 0.637889i) q^{12} +(-3.52344 - 3.52344i) q^{13} +3.24447i q^{14} +(4.24584 + 2.79299i) q^{15} +3.04862 q^{16} +(-0.212794 + 0.212794i) q^{17} +(-1.93883 - 1.93883i) q^{18} -6.08244 q^{19} +(0.869212 - 0.179410i) q^{20} -5.82406i q^{21} +(-5.07364 + 5.07364i) q^{23} -6.89749 q^{24} +(-4.59138 + 1.97971i) q^{25} -6.30899 q^{26} +(-1.34098 - 1.34098i) q^{27} +(-0.719202 - 0.719202i) q^{28} -3.98426 q^{29} +(6.30178 - 1.30072i) q^{30} +7.59403 q^{31} +(-1.56247 + 1.56247i) q^{32} +0.381023i q^{34} +(4.78707 + 3.14902i) q^{35} +0.859562 q^{36} +(-4.56304 - 4.56304i) q^{37} +(-5.44554 + 5.44554i) q^{38} +11.3251 q^{39} +(3.72941 - 5.66937i) q^{40} -2.42532i q^{41} +(-5.21422 - 5.21422i) q^{42} +(-1.43561 - 1.43561i) q^{43} +(-4.74245 + 0.978869i) q^{45} +9.08474i q^{46} +(2.49745 + 2.49745i) q^{47} +(-4.89947 + 4.89947i) q^{48} +0.433531i q^{49} +(-2.33819 + 5.88302i) q^{50} -0.683965i q^{51} +(1.39851 - 1.39851i) q^{52} +(-6.21422 + 6.21422i) q^{53} -2.40113 q^{54} -7.77673 q^{56} +(9.77514 - 9.77514i) q^{57} +(-3.56706 + 3.56706i) q^{58} +1.17470i q^{59} +(-1.10859 + 1.68525i) q^{60} +0.0929527i q^{61} +(6.79885 - 6.79885i) q^{62} +(3.92399 + 3.92399i) q^{63} +8.89496i q^{64} +(-6.12337 + 9.30862i) q^{65} +(7.07364 + 7.07364i) q^{67} +(-0.0844615 - 0.0844615i) q^{68} -16.3078i q^{69} +(7.10509 - 1.46653i) q^{70} +11.2433 q^{71} +(4.64722 - 4.64722i) q^{72} +(2.80629 + 2.80629i) q^{73} -8.17047 q^{74} +(4.19722 - 10.5605i) q^{75} -2.41423i q^{76} +(10.1392 - 10.1392i) q^{78} -2.35834 q^{79} +(-1.37800 - 6.67620i) q^{80} +10.8070 q^{81} +(-2.17136 - 2.17136i) q^{82} +(-5.86965 - 5.86965i) q^{83} +2.31167 q^{84} +(0.562183 + 0.369813i) q^{85} -2.57056 q^{86} +(6.40314 - 6.40314i) q^{87} +2.55325i q^{89} +(-3.36949 + 5.12223i) q^{90} +12.7687 q^{91} +(-2.01382 - 2.01382i) q^{92} +(-12.2044 + 12.2044i) q^{93} +4.47188 q^{94} +(2.74932 + 13.3200i) q^{95} -5.02211i q^{96} +(5.32387 + 5.32387i) q^{97} +(0.388135 + 0.388135i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^3 + 4 * q^5	\( 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) \) 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

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