LMFDB - Embedded newform 603.2.u.a.478.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(64,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

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("603.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.u (of order $11$, degree $10$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			478.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	603.478
Dual form			603.2.u.a.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34125 - 0.861971i) q^{2} +(0.225136 + 0.492980i) q^{4} +(0.857685 - 0.989821i) q^{5} +(0.313607 + 0.201543i) q^{7} +(-0.330830 + 2.30097i) q^{8} +O(q^{10})$	\(q+(-1.34125 - 0.861971i) q^{2} +(0.225136 + 0.492980i) q^{4} +(0.857685 - 0.989821i) q^{5} +(0.313607 + 0.201543i) q^{7} +(-0.330830 + 2.30097i) q^{8} +(-2.00357 + 0.588302i) q^{10} +(0.986348 - 1.13831i) q^{11} +(0.00388573 + 0.0270259i) q^{13} +(-0.246902 - 0.540641i) q^{14} +(3.13691 - 3.62019i) q^{16} +(2.04342 - 4.47447i) q^{17} +(3.71585 - 2.38803i) q^{19} +(0.681059 + 0.199977i) q^{20} +(-2.30413 + 0.676554i) q^{22} +(-2.47773 - 0.727528i) q^{23} +(0.467452 + 3.25120i) q^{25} +(0.0180838 - 0.0395979i) q^{26} +(-0.0287523 + 0.199977i) q^{28} +1.01795 q^{29} +(-0.0140840 + 0.0979567i) q^{31} +(-2.86695 + 0.841812i) q^{32} +(-6.59761 + 4.24002i) q^{34} +(0.468468 - 0.137555i) q^{35} -3.22650 q^{37} -7.04231 q^{38} +(1.99380 + 2.30097i) q^{40} +(2.97672 - 6.51810i) q^{41} +(3.97876 - 8.71228i) q^{43} +(0.783225 + 0.229976i) q^{44} +(2.69616 + 3.11153i) q^{46} +(-11.0458 - 3.24333i) q^{47} +(-2.85018 - 6.24101i) q^{49} +(2.17547 - 4.76361i) q^{50} +(-0.0124484 + 0.00800010i) q^{52} +(4.53811 + 9.93708i) q^{53} +(-0.280744 - 1.95262i) q^{55} +(-0.567496 + 0.654925i) q^{56} +(-1.36533 - 0.877444i) q^{58} +(1.82859 - 12.7181i) q^{59} +(-7.40000 - 8.54005i) q^{61} +(0.103326 - 0.119245i) q^{62} +(-4.62139 - 1.35696i) q^{64} +(0.0300835 + 0.0193335i) q^{65} +(-4.71215 - 6.69296i) q^{67} +2.66587 q^{68} +(-0.746902 - 0.219310i) q^{70} +(5.49691 + 12.0365i) q^{71} +(3.77534 + 4.35697i) q^{73} +(4.32755 + 2.78115i) q^{74} +(2.01382 + 1.29421i) q^{76} +(0.538744 - 0.158189i) q^{77} +(0.437898 + 3.04565i) q^{79} +(-0.892858 - 6.20996i) q^{80} +(-9.61094 + 6.17658i) q^{82} +(-3.04637 + 3.51570i) q^{83} +(-2.67631 - 5.86031i) q^{85} +(-12.8463 + 8.25579i) q^{86} +(2.29290 + 2.64615i) q^{88} +(-3.19574 + 0.938355i) q^{89} +(-0.00422828 + 0.00925865i) q^{91} +(-0.199171 - 1.38527i) q^{92} +(12.0195 + 13.8713i) q^{94} +(0.823304 - 5.72620i) q^{95} +13.5676 q^{97} +(-1.55677 + 10.8276i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8}+O(q^{10}) $ 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8	$ 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28} + 24 q^{29} - q^{31} + q^{32} - 15 q^{34} + 3 q^{35} + 2 q^{37} + 36 q^{38} + 25 q^{40} + 7 q^{41} - 2 q^{43} - 41 q^{44} + 6 q^{46} - 33 q^{47} + 2 q^{49} + 4 q^{50} - 21 q^{52} - 21 q^{53} + 13 q^{55} + 17 q^{56} - 3 q^{58} + 38 q^{59} - 50 q^{61} - 4 q^{62} - 31 q^{64} + 8 q^{65} + 32 q^{67} + 30 q^{68} - 10 q^{70} + 16 q^{71} + 3 q^{73} + 8 q^{74} + 5 q^{76} - 7 q^{77} - 19 q^{79} - 9 q^{80} - 16 q^{82} - 5 q^{83} - 13 q^{85} - 19 q^{86} + 48 q^{88} - 7 q^{89} - 6 q^{91} - 45 q^{92} + 22 q^{94} - 15 q^{95} + 54 q^{97} - 47 q^{98}+O(q^{100}) $ 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$

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 $

$2$	−1.34125	−	0.861971i	−0.948409	−	0.609506i	−0.0276421	−	0.999618i	$-0.508800\pi$
$2$	−1.34125	−	0.861971i	−0.948409	−	0.609506i	−0.920767	+	0.390112i	$0.872436\pi$
$3$		0			0
$3$		0			0
$4$	0.225136	+	0.492980i	0.112568	+	0.246490i
$5$	0.857685	−	0.989821i	0.383568	−	0.442662i	−0.530829	−	0.847479i	$-0.678119\pi$
$5$	0.857685	−	0.989821i	0.383568	−	0.442662i	0.914398	+	0.404817i	$0.132665\pi$
$6$		0			0
$7$	0.313607	+	0.201543i	0.118532	+	0.0761761i	0.598564	−	0.801075i	$-0.295738\pi$
$7$	0.313607	+	0.201543i	0.118532	+	0.0761761i	−0.480031	+	0.877251i	$0.659375\pi$
$8$	−0.330830	+	2.30097i	−0.116966	+	0.813517i
$9$		0			0
$10$	−2.00357	+	0.588302i	−0.633585	+	0.186037i
$11$	0.986348	−	1.13831i	0.297395	−	0.343212i	−0.587311	−	0.809361i	$-0.699813\pi$
$11$	0.986348	−	1.13831i	0.297395	−	0.343212i	0.884706	+	0.466149i	$0.154359\pi$
$12$		0			0
$13$	0.00388573	+	0.0270259i	0.00107771	+	0.00749563i	0.990353	−	0.138566i	$-0.0442493\pi$
$13$	0.00388573	+	0.0270259i	0.00107771	+	0.00749563i	−0.989275	+	0.146062i	$0.953340\pi$
$14$	−0.246902	−	0.540641i	−0.0659874	−	0.144492i
$15$		0			0
$16$	3.13691	−	3.62019i	0.784228	−	0.905047i
$17$	2.04342	−	4.47447i	0.495602	−	1.08522i	−0.482271	−	0.876022i	$-0.660188\pi$
$17$	2.04342	−	4.47447i	0.495602	−	1.08522i	0.977874	−	0.209196i	$-0.0670846\pi$
$18$		0			0
$19$	3.71585	−	2.38803i	0.852474	−	0.547852i	−0.0398717	−	0.999205i	$-0.512695\pi$
$19$	3.71585	−	2.38803i	0.852474	−	0.547852i	0.892345	+	0.451353i	$0.149059\pi$
$20$	0.681059	+	0.199977i	0.152289	+	0.0447162i
$21$		0			0
$22$	−2.30413	+	0.676554i	−0.491242	+	0.144242i
$23$	−2.47773	−	0.727528i	−0.516643	−	0.151700i	0.0130086	−	0.999915i	$-0.495859\pi$
$23$	−2.47773	−	0.727528i	−0.516643	−	0.151700i	−0.529652	+	0.848215i	$0.677677\pi$
$24$		0			0
$25$	0.467452	+	3.25120i	0.0934903	+	0.650239i
$26$	0.0180838	−	0.0395979i	0.00354652	−	0.00776579i
$27$		0			0
$28$	−0.0287523	+	0.199977i	−0.00543368	+	0.0377921i
$29$	1.01795			0.189029			0.0945143	−	0.995524i	$-0.469870\pi$
$29$	1.01795			0.189029			0.0945143	+	0.995524i	$0.469870\pi$
$30$		0			0
$31$	−0.0140840	+	0.0979567i	−0.00252957	+	0.0175935i	−0.991047	−	0.133512i	$-0.957374\pi$
$31$	−0.0140840	+	0.0979567i	−0.00252957	+	0.0175935i	0.988518	+	0.151106i	$0.0482835\pi$
$32$	−2.86695	+	0.841812i	−0.506810	+	0.148813i
$33$		0			0
$34$	−6.59761	+	4.24002i	−1.13148	+	0.727158i
$35$	0.468468	−	0.137555i	0.0791855	−	0.0232510i
$36$		0			0
$37$	−3.22650			−0.530433			−0.265216	−	0.964189i	$-0.585443\pi$
$37$	−3.22650			−0.530433			−0.265216	+	0.964189i	$0.585443\pi$
$38$	−7.04231			−1.14241
$39$		0			0
$40$	1.99380	+	2.30097i	0.315248	+	0.363816i
$41$	2.97672	−	6.51810i	0.464885	−	1.01796i	−0.521462	−	0.853275i	$-0.674613\pi$
$41$	2.97672	−	6.51810i	0.464885	−	1.01796i	0.986347	−	0.164681i	$-0.0526596\pi$
$42$		0			0
$43$	3.97876	−	8.71228i	0.606756	−	1.32861i	−0.318015	−	0.948086i	$-0.603016\pi$
$43$	3.97876	−	8.71228i	0.606756	−	1.32861i	0.924771	−	0.380524i	$-0.124256\pi$
$44$	0.783225	+	0.229976i	0.118076	+	0.0346701i
$45$		0			0
$46$	2.69616	+	3.11153i	0.397527	+	0.458771i
$47$	−11.0458	−	3.24333i	−1.61119	−	0.473088i	−0.652558	−	0.757739i	$-0.726304\pi$
$47$	−11.0458	−	3.24333i	−1.61119	−	0.473088i	−0.958631	+	0.284651i	$0.908122\pi$
$48$		0			0
$49$	−2.85018	−	6.24101i	−0.407168	−	0.891573i
$50$	2.17547	−	4.76361i	0.307658	−	0.673676i
$51$		0			0
$52$	−0.0124484	+	0.00800010i	−0.00172628	+	0.00110941i
$53$	4.53811	+	9.93708i	0.623358	+	1.36496i	0.913052	+	0.407844i	$0.133719\pi$
$53$	4.53811	+	9.93708i	0.623358	+	1.36496i	−0.289694	+	0.957119i	$0.593553\pi$
$54$		0			0
$55$	−0.280744	−	1.95262i	−0.0378555	−	0.263291i
$56$	−0.567496	+	0.654925i	−0.0758348	+	0.0875181i
$57$		0			0
$58$	−1.36533	−	0.877444i	−0.179276	−	0.115214i
$59$	1.82859	−	12.7181i	0.238062	−	1.65576i	−0.423520	−	0.905887i	$-0.639206\pi$
$59$	1.82859	−	12.7181i	0.238062	−	1.65576i	0.661583	−	0.749872i	$-0.269885\pi$
$60$		0			0
$61$	−7.40000	−	8.54005i	−0.947473	−	1.09344i	−0.995516	−	0.0945967i	$-0.969844\pi$
$61$	−7.40000	−	8.54005i	−0.947473	−	1.09344i	0.0480428	−	0.998845i	$-0.484702\pi$
$62$	0.103326	−	0.119245i	0.0131224	−	0.0151441i
$63$		0			0
$64$	−4.62139	−	1.35696i	−0.577674	−	0.169620i
$65$	0.0300835	+	0.0193335i	0.00373140	+	0.00239803i
$66$		0			0
$67$	−4.71215	−	6.69296i	−0.575681	−	0.817675i
$67$	−4.71215	−	6.69296i	−0.575681	−	0.817675i
$68$	2.66587			0.323284
$69$		0			0
$70$	−0.746902	−	0.219310i	−0.0892719	−	0.0262126i
$71$	5.49691	+	12.0365i	0.652363	+	1.42847i	0.889471	+	0.456992i	$0.151073\pi$
$71$	5.49691	+	12.0365i	0.652363	+	1.42847i	−0.237108	+	0.971483i	$0.576200\pi$
$72$		0			0
$73$	3.77534	+	4.35697i	0.441870	+	0.509945i	0.932375	−	0.361493i	$-0.117733\pi$
$73$	3.77534	+	4.35697i	0.441870	+	0.509945i	−0.490505	+	0.871439i	$0.663188\pi$
$74$	4.32755	+	2.78115i	0.503067	+	0.323302i
$75$		0			0
$76$	2.01382	+	1.29421i	0.231001	+	0.148456i
$77$	0.538744	−	0.158189i	0.0613955	−	0.0180274i
$78$		0			0
$79$	0.437898	+	3.04565i	0.0492673	+	0.342662i	0.999514	+	0.0311643i	$0.00992150\pi$
$79$	0.437898	+	3.04565i	0.0492673	+	0.342662i	−0.950247	+	0.311498i	$0.899169\pi$
$80$	−0.892858	−	6.20996i	−0.0998245	−	0.694295i
$81$		0			0
$82$	−9.61094	+	6.17658i	−1.06135	+	0.682089i
$83$	−3.04637	+	3.51570i	−0.334382	+	0.385898i	−0.897895	−	0.440210i	$-0.854904\pi$
$83$	−3.04637	+	3.51570i	−0.334382	+	0.385898i	0.563513	+	0.826107i	$0.309450\pi$
$84$		0			0
$85$	−2.67631	−	5.86031i	−0.290287	−	0.635639i
$86$	−12.8463	+	8.25579i	−1.38525	+	0.890245i
$87$		0			0
$88$	2.29290	+	2.64615i	0.244424	+	0.282080i
$89$	−3.19574	+	0.938355i	−0.338748	+	0.0994654i	−0.446682	−	0.894693i	$-0.647395\pi$
$89$	−3.19574	+	0.938355i	−0.338748	+	0.0994654i	0.107934	+	0.994158i	$0.465576\pi$
$90$		0			0
$91$	−0.00422828	+	0.00925865i	−0.000443245	+	0.000970570i
$92$	−0.199171	−	1.38527i	−0.0207650	−	0.144424i
$93$		0			0
$94$	12.0195	+	13.8713i	1.23972	+	1.43071i
$95$	0.823304	−	5.72620i	0.0844692	−	0.587496i
$96$		0			0
$97$	13.5676			1.37758			0.688792	−	0.724959i	$-0.258141\pi$
$97$	13.5676			1.37758			0.688792	+	0.724959i	$0.258141\pi$
$98$	−1.55677	+	10.8276i	−0.157257	+	1.09375i
$99$		0			0
$100$	−1.49754	+	0.962407i	−0.149754	+	0.0962407i
$101$	8.64597	−	5.55643i	0.860306	−	0.552885i	−0.0344670	−	0.999406i	$-0.510973\pi$
$101$	8.64597	−	5.55643i	0.860306	−	0.552885i	0.894773	+	0.446520i	$0.147337\pi$
$102$		0			0
$103$	0.257775	−	1.79286i	0.0253993	−	0.176656i	−0.973173	−	0.230075i	$-0.926103\pi$
$103$	0.257775	−	1.79286i	0.0253993	−	0.176656i	0.998572	+	0.0534191i	$0.0170119\pi$
$104$	−0.0634713			−0.00622388
$105$		0			0
$106$	2.47872	−	17.2399i	0.240755	−	1.67448i
$107$	−5.26856	−	6.08024i	−0.509331	−	0.587799i	0.441597	−	0.897214i	$-0.354412\pi$
$107$	−5.26856	−	6.08024i	−0.509331	−	0.587799i	−0.950927	+	0.309415i	$0.899867\pi$
$108$		0			0
$109$	1.62205	+	11.2816i	0.155364	+	1.08058i	0.907038	+	0.421048i	$0.138338\pi$
$109$	1.62205	+	11.2816i	0.155364	+	1.08058i	−0.751674	+	0.659535i	$0.770753\pi$
$110$	−1.30655	+	2.86095i	−0.124575	+	0.272781i
$111$		0			0
$112$	1.71338	−	0.503094i	0.161899	−	0.0475379i
$113$	−5.37232	−	6.19998i	−0.505385	−	0.583245i	0.444526	−	0.895766i	$-0.353372\pi$
$113$	−5.37232	−	6.19998i	−0.505385	−	0.583245i	−0.949911	+	0.312521i	$0.898827\pi$
$114$		0			0
$115$	−2.84524	+	1.82852i	−0.265320	+	0.170511i
$116$	0.229178	+	0.501829i	0.0212786	+	0.0465937i
$117$		0			0
$118$	−13.4153	+	15.4820i	−1.23497	+	1.42524i
$119$	1.54263	−	0.991388i	0.141413	−	0.0908804i
$120$		0			0
$121$	1.24260	+	8.64250i	0.112964	+	0.785682i
$122$	2.56399	+	17.8330i	0.232133	+	1.61452i
$123$		0			0
$124$	−0.0514615	+	0.0151105i	−0.00462138	+	0.00135696i
$125$	9.12807	+	5.86625i	0.816439	+	0.524694i
$126$		0			0
$127$	2.81737	+	1.81061i	0.250001	+	0.160666i	0.659640	−	0.751582i	$-0.270709\pi$
$127$	2.81737	+	1.81061i	0.250001	+	0.160666i	−0.409639	+	0.912248i	$0.634345\pi$
$128$	8.94222	+	10.3199i	0.790388	+	0.912157i
$129$		0			0
$130$	−0.0236847	−	0.0518623i	−0.00207729	−	0.00454862i
$131$	6.42924	+	1.88779i	0.561725	+	0.164937i	0.550255	−	0.834997i	$-0.314531\pi$
$131$	6.42924	+	1.88779i	0.561725	+	0.164937i	0.0114704	+	0.999934i	$0.496349\pi$
$132$		0			0
$133$	1.64661			0.142779
$134$	0.551049	+	13.0387i	0.0476034	+	1.12637i
$135$		0			0
$136$	9.61960	+	6.18214i	0.824874	+	0.530115i
$137$	8.71057	+	2.55765i	0.744194	+	0.218515i	0.631781	−	0.775147i	$-0.282324\pi$
$137$	8.71057	+	2.55765i	0.744194	+	0.218515i	0.112412	+	0.993662i	$0.464142\pi$
$138$		0			0
$139$	−12.8733	+	14.8566i	−1.09190	+	1.26012i	−0.128598	+	0.991697i	$0.541048\pi$
$139$	−12.8733	+	14.8566i	−1.09190	+	1.26012i	−0.963301	+	0.268423i	$0.913498\pi$
$140$	0.173281	+	0.199977i	0.0146449	+	0.0169011i
$141$		0			0
$142$	3.00241	−	20.8822i	0.251957	−	1.75240i
$143$	0.0345964	+	0.0222338i	0.00289310	+	0.00185928i
$144$		0			0
$145$	0.873081	−	1.00759i	0.0725054	−	0.0836757i
$146$	−1.30810	−	9.09804i	−0.108259	−	0.752959i
$147$		0			0
$148$	−0.726402	−	1.59060i	−0.0597099	−	0.130746i
$149$	4.85049	−	3.11722i	0.397368	−	0.255373i	−0.326662	−	0.945141i	$-0.605924\pi$
$149$	4.85049	−	3.11722i	0.397368	−	0.255373i	0.724030	+	0.689768i	$0.242288\pi$
$150$		0			0
$151$	2.03646	−	4.45923i	0.165725	−	0.362887i	−0.808490	−	0.588510i	$-0.799715\pi$
$151$	2.03646	−	4.45923i	0.165725	−	0.362887i	0.974215	+	0.225623i	$0.0724419\pi$
$152$	4.26548	+	9.34010i	0.345976	+	0.757582i
$153$		0			0
$154$	−0.858947	−	0.252209i	−0.0692159	−	0.0203236i
$155$	0.0848799	+	0.0979567i	0.00681772	+	0.00786807i
$156$		0			0
$157$	3.02505	+	0.888236i	0.241426	+	0.0708889i	0.400207	−	0.916425i	$-0.368938\pi$
$157$	3.02505	+	0.888236i	0.241426	+	0.0708889i	−0.158781	+	0.987314i	$0.550756\pi$
$158$	2.03793	−	4.46244i	0.162129	−	0.355012i
$159$		0			0
$160$	−1.62570	+	3.55978i	−0.128523	+	0.281425i
$161$	−0.630406	−	0.727528i	−0.0496830	−	0.0573372i
$162$		0			0
$163$	11.6569			0.913041			0.456520	−	0.889713i	$-0.349096\pi$
$163$	11.6569			0.913041			0.456520	+	0.889713i	$0.349096\pi$
$164$	3.88346			0.303247
$165$		0			0
$166$	7.11638	−	2.08956i	0.552338	−	0.162181i
$167$	0.792212	−	0.509123i	0.0613032	−	0.0393972i	−0.509630	−	0.860394i	$-0.670218\pi$
$167$	0.792212	−	0.509123i	0.0613032	−	0.0393972i	0.570933	+	0.820996i	$0.306581\pi$
$168$		0			0
$169$	12.4727	−	3.66231i	0.959438	−	0.281716i
$170$	−1.46180	+	10.1671i	−0.112115	+	0.779778i
$171$		0			0
$172$	5.19074			0.395791
$173$	−1.11658	+	7.76600i	−0.0848922	+	0.590438i	0.902325	+	0.431057i	$0.141859\pi$
$173$	−1.11658	+	7.76600i	−0.0848922	+	0.590438i	−0.987217	+	0.159382i	$0.949050\pi$
$174$		0			0
$175$	−0.508660	+	1.11381i	−0.0384511	+	0.0841962i
$176$	−1.02680	−	7.14153i	−0.0773978	−	0.538313i
$177$		0			0
$178$	5.09513	+	1.49607i	0.381897	+	0.112135i
$179$	−4.11717	+	1.20891i	−0.307731	+	0.0903581i	−0.431952	−	0.901897i	$-0.642175\pi$
$179$	−4.11717	+	1.20891i	−0.307731	+	0.0903581i	0.124221	+	0.992255i	$0.460357\pi$
$180$		0			0
$181$	15.7443	+	4.62295i	1.17027	+	0.343621i	0.808414	−	0.588615i	$-0.200326\pi$
$181$	15.7443	+	4.62295i	1.17027	+	0.343621i	0.361852	+	0.932236i	$0.382145\pi$
$182$	0.0136519	−	0.00877354i	0.00101195	−	0.000650338i
$183$		0			0
$184$	2.49373	−	5.46051i	0.183840	−	0.402554i
$185$	−2.76732	+	3.19365i	−0.203457	+	0.234802i
$186$		0			0
$187$	−3.07779	−	6.73942i	−0.225070	−	0.492835i
$188$	−0.887907	−	6.17553i	−0.0647573	−	0.450397i
$189$		0			0
$190$	−6.04008	+	6.97063i	−0.438194	+	0.505702i
$191$	22.0245	−	6.46697i	1.59363	−	0.467933i	0.639869	−	0.768484i	$-0.278989\pi$
$191$	22.0245	−	6.46697i	1.59363	−	0.467933i	0.953766	+	0.300551i	$0.0971705\pi$
$192$		0			0
$193$	−3.37657	+	23.4846i	−0.243051	+	1.69046i	0.393583	+	0.919289i	$0.371236\pi$
$193$	−3.37657	+	23.4846i	−0.243051	+	1.69046i	−0.636633	+	0.771167i	$0.719674\pi$
$194$	−18.1976	−	11.6949i	−1.30651	−	0.839645i
$195$		0			0
$196$	2.43502	−	2.81016i	0.173930	−	0.200726i
$197$	8.16173	+	17.8717i	0.581499	+	1.27331i	0.940444	+	0.339947i	$0.110409\pi$
$197$	8.16173	+	17.8717i	0.581499	+	1.27331i	−0.358945	+	0.933359i	$0.616863\pi$
$198$		0			0
$199$	−3.62067	−	2.32686i	−0.256662	−	0.164947i	0.405982	−	0.913881i	$-0.366930\pi$
$199$	−3.62067	−	2.32686i	−0.256662	−	0.164947i	−0.662644	+	0.748934i	$0.730566\pi$
$200$	−7.63556			−0.539916
$201$		0			0
$202$	−16.3859			−1.15291
$203$	0.319236	+	0.205161i	0.0224060	+	0.0143995i
$204$		0			0
$205$	−3.89867	−	8.53689i	−0.272295	−	0.596242i
$206$	−1.89114	+	2.18249i	−0.131762	+	0.152061i
$207$		0			0
$208$	0.110028	+	0.0707107i	0.00762906	+	0.00490290i
$209$	0.946809	−	6.58520i	0.0654921	−	0.455508i
$210$		0			0
$211$	7.91165	−	2.32307i	0.544660	−	0.159927i	0.00218367	−	0.999998i	$-0.499305\pi$
$211$	7.91165	−	2.32307i	0.544660	−	0.159927i	0.542477	+	0.840071i	$0.317487\pi$
$212$	−3.87709	+	4.47440i	−0.266280	+	0.307303i
$213$		0			0
$214$	1.82548	+	12.6965i	0.124787	+	0.867914i
$215$	−5.21107	−	11.4107i	−0.355392	−	0.778200i
$216$		0			0
$217$	−0.0241593	+	0.0278814i	−0.00164004	+	0.00189271i
$218$	7.54885	−	16.5297i	0.511273	−	1.11953i
$219$		0			0
$220$	0.899396	−	0.578007i	0.0606372	−	0.0389692i
$221$	0.128867	+	0.0378386i	0.00866850	+	0.00254530i
$222$		0			0
$223$	−18.3629	+	5.39183i	−1.22967	+	0.361064i	−0.831125	−	0.556085i	$-0.812303\pi$
$223$	−18.3629	+	5.39183i	−1.22967	+	0.361064i	−0.398545	+	0.917149i	$0.630485\pi$
$224$	−1.06876	−	0.313816i	−0.0714094	−	0.0209677i
$225$		0			0
$226$	1.86143	+	12.9465i	0.123821	+	0.861191i
$227$	−9.94193	+	21.7698i	−0.659869	+	1.44491i	0.222775	+	0.974870i	$0.428489\pi$
$227$	−9.94193	+	21.7698i	−0.659869	+	1.44491i	−0.882644	+	0.470042i	$0.844239\pi$
$228$		0			0
$229$	3.47790	−	24.1893i	0.229826	−	1.59847i	−0.469011	−	0.883192i	$-0.655389\pi$
$229$	3.47790	−	24.1893i	0.229826	−	1.59847i	0.698837	−	0.715281i	$-0.253701\pi$
$230$	5.39232			0.355559
$231$		0			0
$232$	−0.336768	+	2.34228i	−0.0221099	+	0.153778i
$233$	−16.4809	+	4.83923i	−1.07970	+	0.317028i	−0.772758	−	0.634700i	$-0.781124\pi$
$233$	−16.4809	+	4.83923i	−1.07970	+	0.317028i	−0.306941	+	0.951729i	$0.599305\pi$
$234$		0			0
$235$	−12.6841	+	8.15157i	−0.827419	+	0.531750i
$236$	6.68147	−	1.96186i	0.434926	−	0.127706i
$237$		0			0
$238$	−2.92360			−0.189509
$239$	−20.6942			−1.33860			−0.669300	−	0.742992i	$-0.733406\pi$
$239$	−20.6942			−1.33860			−0.669300	+	0.742992i	$0.733406\pi$
$240$		0			0
$241$	−12.7437	−	14.7071i	−0.820896	−	0.947365i	0.178434	−	0.983952i	$-0.442897\pi$
$241$	−12.7437	−	14.7071i	−0.820896	−	0.947365i	−0.999330	+	0.0365872i	$0.988351\pi$
$242$	5.78294	−	12.6629i	0.371742	−	0.814001i
$243$		0			0
$244$	2.54407	−	5.57073i	0.162867	−	0.356629i
$245$	−8.62204	−	2.53166i	−0.550842	−	0.161742i
$246$		0			0
$247$	0.0789774	+	0.0911447i	0.00502521	+	0.00579940i
$248$	−0.220736	−	0.0648140i	−0.0140168	−	0.00411569i
$249$		0			0
$250$	−7.18651	−	15.7363i	−0.454515	−	0.995249i
$251$	5.45647	−	11.9480i	0.344410	−	0.754152i	−0.655590	−	0.755117i	$-0.727580\pi$
$251$	5.45647	−	11.9480i	0.344410	−	0.754152i	1.00000		0.000965387i	$0.000307292\pi$
$252$		0			0
$253$	−3.27206	+	2.10282i	−0.205712	+	0.132203i
$254$	−2.21811	−	4.85698i	−0.139176	−	0.304754i
$255$		0			0
$256$	−1.72743	−	12.0146i	−0.107965	−	0.750911i
$257$	5.50488	−	6.35297i	0.343385	−	0.396288i	−0.557620	−	0.830097i	$-0.688285\pi$
$257$	5.50488	−	6.35297i	0.343385	−	0.396288i	0.901005	+	0.433809i	$0.142831\pi$
$258$		0			0
$259$	−1.01185	−	0.650278i	−0.0628734	−	0.0404063i
$260$	−0.00275814	+	0.0191833i	−0.000171052	+	0.00118969i
$261$		0			0
$262$	−6.99601	−	8.07383i	−0.432215	−	0.498803i
$263$	−14.6461	+	16.9025i	−0.903117	+	1.04225i	0.0957853	+	0.995402i	$0.469464\pi$
$263$	−14.6461	+	16.9025i	−0.903117	+	1.04225i	−0.998902	+	0.0468501i	$0.985082\pi$
$264$		0			0
$265$	13.7282	+	4.03097i	0.843317	+	0.247620i
$266$	−2.20852	−	1.41933i	−0.135413	−	0.0870246i
$267$		0			0
$268$	2.23862	−	3.82982i	0.136745	−	0.233944i
$269$	9.84248			0.600107			0.300053	−	0.953922i	$-0.402995\pi$
$269$	9.84248			0.600107			0.300053	+	0.953922i	$0.402995\pi$
$270$		0			0
$271$	−12.5964	−	3.69863i	−0.765176	−	0.224676i	−0.124221	−	0.992255i	$-0.539643\pi$
$271$	−12.5964	−	3.69863i	−0.765176	−	0.224676i	−0.640955	+	0.767579i	$0.721461\pi$
$272$	−9.78838	−	21.4336i	−0.593508	−	1.29960i
$273$		0			0
$274$	−9.47845	−	10.9387i	−0.572614	−	0.660832i
$275$	4.16193	+	2.67471i	0.250974	+	0.161291i
$276$		0			0
$277$	18.6396	+	11.9789i	1.11994	+	0.719745i	0.963438	−	0.267932i	$-0.0863404\pi$
$277$	18.6396	+	11.9789i	1.11994	+	0.719745i	0.156507	+	0.987677i	$0.449977\pi$
$278$	30.0723	−	8.83003i	1.80362	−	0.529590i
$279$		0			0
$280$	0.161526	+	1.12344i	0.00965304	+	0.0671383i
$281$	−1.29347	−	8.99628i	−0.0771619	−	0.536673i	−0.991336	−	0.131351i	$-0.958068\pi$
$281$	−1.29347	−	8.99628i	−0.0771619	−	0.536673i	0.914174	−	0.405322i	$-0.132841\pi$
$282$		0			0
$283$	−9.96838	+	6.40629i	−0.592558	+	0.380814i	−0.802281	−	0.596947i	$-0.796380\pi$
$283$	−9.96838	+	6.40629i	−0.592558	+	0.380814i	0.209722	+	0.977761i	$0.432744\pi$
$284$	−4.69622	+	5.41973i	−0.278670	+	0.321602i
$285$		0			0
$286$	−0.0272377	−	0.0596422i	−0.00161060	−	0.00352672i
$287$	2.24720	−	1.44419i	0.132648	−	0.0852476i
$288$		0			0
$289$	−4.71265	−	5.43869i	−0.277215	−	0.319923i
$290$	−2.03953	+	0.598861i	−0.119766	+	0.0351664i
$291$		0			0
$292$	−1.29794	+	2.84208i	−0.0759559	+	0.166320i
$293$	2.04712	+	14.2380i	0.119594	+	0.831795i	0.958004	+	0.286755i	$0.0925766\pi$
$293$	2.04712	+	14.2380i	0.119594	+	0.831795i	−0.838410	+	0.545040i	$0.816514\pi$
$294$		0			0
$295$	−11.0203	−	12.7181i	−0.641628	−	0.740478i
$296$	1.06742	−	7.42408i	0.0620426	−	0.431516i
$297$		0			0
$298$	−9.19269			−0.532518
$299$	0.0100343	−	0.0697898i	0.000580297	−	0.00403605i
$300$		0			0
$301$	3.00367	−	1.93034i	0.173129	−	0.111263i
$302$	−6.57514	+	4.22559i	−0.378357	+	0.243155i
$303$		0			0
$304$	3.01116	−	20.9431i	0.172702	−	1.20117i
$305$	−14.8000			−0.847446
$306$		0			0
$307$	−1.37973	+	9.59622i	−0.0787452	+	0.547685i	0.911814	+	0.410603i	$0.134682\pi$
$307$	−1.37973	+	9.59622i	−0.0787452	+	0.547685i	−0.990560	+	0.137082i	$0.956227\pi$
$308$	0.199275	+	0.229976i	0.0113548	+	0.0131041i
$309$		0			0
$310$	−0.0294097	−	0.204549i	−0.00167036	−	0.0116176i
$311$	8.10162	−	17.7401i	0.459401	−	1.00595i	−0.528223	−	0.849106i	$-0.677142\pi$
$311$	8.10162	−	17.7401i	0.459401	−	1.00595i	0.987624	−	0.156841i	$-0.0501312\pi$
$312$		0			0
$313$	−11.5984	+	3.40560i	−0.655581	+	0.192496i	−0.592573	−	0.805517i	$-0.701888\pi$
$313$	−11.5984	+	3.40560i	−0.655581	+	0.192496i	−0.0630083	+	0.998013i	$0.520069\pi$
$314$	−3.29173	−	3.79886i	−0.185763	−	0.214382i
$315$		0			0
$316$	−1.40286	+	0.901561i	−0.0789168	+	0.0507168i
$317$	−2.20093	−	4.81937i	−0.123617	−	0.270683i	0.837699	−	0.546133i	$-0.183901\pi$
$317$	−2.20093	−	4.81937i	−0.123617	−	0.270683i	−0.961315	+	0.275450i	$0.911173\pi$
$318$		0			0
$319$	1.00405	−	1.15874i	0.0562162	−	0.0648769i
$320$	−5.30685	+	3.41051i	−0.296662	+	0.190653i
$321$		0			0
$322$	0.218427	+	1.51919i	0.0121724	+	0.0846612i
$323$	−3.09212	−	21.5062i	−0.172050	−	1.19664i
$324$		0			0
$325$	−0.0860500	+	0.0252666i	−0.00477320	+	0.00140154i
$326$	−15.6349	−	10.0479i	−0.865937	−	0.556504i
$327$		0			0
$328$	14.0132	+	9.00573i	0.773749	+	0.497258i
$329$	−2.81036	−	3.24333i	−0.154940	−	0.178810i
$330$		0			0
$331$	−5.06555	−	11.0920i	−0.278428	−	0.609672i	0.717819	−	0.696230i	$-0.245141\pi$
$331$	−5.06555	−	11.0920i	−0.278428	−	0.609672i	−0.996247	+	0.0865576i	$0.972413\pi$
$332$	−2.41902	−	0.710287i	−0.132761	−	0.0389821i
$333$		0			0
$334$	−1.50141			−0.0821533
$335$	−10.6664	−	1.07626i	−0.582766	−	0.0588026i
$336$		0			0
$337$	28.5704	+	18.3611i	1.55633	+	1.00019i	0.983582	+	0.180459i	$0.0577584\pi$
$337$	28.5704	+	18.3611i	1.55633	+	1.00019i	0.572746	+	0.819733i	$0.305878\pi$
$338$	−19.8859	−	5.83901i	−1.08165	−	0.317600i
$339$		0			0
$340$	2.28648	−	2.63874i	0.124002	−	0.143106i
$341$	0.0976129	+	0.112651i	0.00528604	+	0.00610041i
$342$		0			0
$343$	0.735368	−	5.11460i	0.0397062	−	0.276162i
$344$	18.7304	+	12.0373i	1.00988	+	0.649008i
$345$		0			0
$346$	8.19169	−	9.45372i	0.440388	−	0.508235i
$347$	−1.36509	−	9.49439i	−0.0732817	−	0.509686i	−0.993093	−	0.117326i	$-0.962568\pi$
$347$	−1.36509	−	9.49439i	−0.0732817	−	0.509686i	0.919812	−	0.392360i	$-0.128341\pi$
$348$		0			0
$349$	1.20183	+	2.63164i	0.0643324	+	0.140868i	0.939067	−	0.343734i	$-0.111692\pi$
$349$	1.20183	+	2.63164i	0.0643324	+	0.140868i	−0.874735	+	0.484602i	$0.838964\pi$
$350$	1.64231	−	1.05545i	0.0877854	−	0.0564163i
$351$		0			0
$352$	−1.86957	+	4.09379i	−0.0996484	+	0.218200i
$353$	−2.56280	−	5.61175i	−0.136404	−	0.298683i	0.829087	−	0.559120i	$-0.188861\pi$
$353$	−2.56280	−	5.61175i	−0.136404	−	0.298683i	−0.965491	+	0.260437i	$0.916134\pi$
$354$		0			0
$355$	16.6286	+	4.88261i	0.882557	+	0.259142i
$356$	−1.18207	−	1.36418i	−0.0626495	−	0.0723014i
$357$		0			0
$358$	6.56421	+	1.92743i	0.346929	+	0.101868i
$359$	−6.49220	+	14.2159i	−0.342645	+	0.750289i	−0.999995	−	0.00329752i	$-0.998950\pi$
$359$	−6.49220	+	14.2159i	−0.342645	+	0.750289i	0.657349	+	0.753586i	$0.271678\pi$
$360$		0			0
$361$	0.211946	−	0.464097i	0.0111550	−	0.0244261i
$362$	−17.1323	−	19.7717i	−0.900452	−	1.03918i
$363$		0			0
$364$	−0.00551627			−0.000289131
$365$	7.55068			0.395221
$366$		0			0
$367$	−13.6166	+	3.99820i	−0.710782	+	0.208704i	−0.617085	−	0.786896i	$-0.711687\pi$
$367$	−13.6166	+	3.99820i	−0.710782	+	0.208704i	−0.0936969	+	0.995601i	$0.529868\pi$
$368$	−10.4062	+	6.68767i	−0.542461	+	0.348619i
$369$		0			0
$370$	6.46451	−	1.89815i	0.336074	−	0.0986802i
$371$	−0.579566	+	4.03097i	−0.0300895	+	0.209277i
$372$		0			0
$373$	−32.6630			−1.69123			−0.845614	−	0.533795i	$-0.820765\pi$
$373$	−32.6630			−1.69123			−0.845614	+	0.533795i	$0.820765\pi$
$374$	−1.68109	+	11.6922i	−0.0869271	+	0.604591i
$375$		0			0
$376$	11.1171	−	24.3430i	0.573320	−	1.25539i
$377$	0.00395548	+	0.0275110i	0.000203718	+	0.00141689i
$378$		0			0
$379$	14.0144	+	4.11501i	0.719873	+	0.211374i	0.621094	−	0.783736i	$-0.286688\pi$
$379$	14.0144	+	4.11501i	0.719873	+	0.211374i	0.0987784	+	0.995109i	$0.468506\pi$
$380$	3.00826	−	0.883305i	0.154320	−	0.0453126i
$381$		0			0
$382$	−35.1147	−	10.3106i	−1.79663	−	0.527537i
$383$	19.0062	−	12.2146i	0.971173	−	0.624135i	0.0441047	−	0.999027i	$-0.485956\pi$
$383$	19.0062	−	12.2146i	0.971173	−	0.624135i	0.927069	+	0.374892i	$0.122320\pi$
$384$		0			0
$385$	0.305493	−	0.668937i	0.0155694	−	0.0340922i
$386$	24.7719	−	28.5882i	1.26085	−	1.45510i
$387$		0			0
$388$	3.05457	+	6.68857i	0.155072	+	0.339561i
$389$	2.85397	+	19.8498i	0.144702	+	1.00642i	0.924715	+	0.380661i	$0.124303\pi$
$389$	2.85397	+	19.8498i	0.144702	+	1.00642i	−0.780013	+	0.625764i	$0.784787\pi$
$390$		0			0
$391$	−8.31835	+	9.59989i	−0.420677	+	0.485487i
$392$	15.3033	−	4.49346i	0.772935	−	0.226954i
$393$		0			0
$394$	4.45794	−	31.0057i	0.224588	−	1.56204i
$395$	3.39022	+	2.17876i	0.170581	+	0.109626i
$396$		0			0
$397$	5.92973	−	6.84327i	0.297605	−	0.343454i	−0.587178	−	0.809458i	$-0.699761\pi$
$397$	5.92973	−	6.84327i	0.297605	−	0.343454i	0.884783	+	0.466004i	$0.154307\pi$
$398$	2.85054	+	6.24182i	0.142885	+	0.312874i
$399$		0			0
$400$	13.2363	+	8.50645i	0.661815	+	0.425323i
$401$	28.2446			1.41047			0.705234	−	0.708975i	$-0.250842\pi$
$401$	28.2446			1.41047			0.705234	+	0.708975i	$0.250842\pi$
$402$		0			0
$403$	−0.00270209			−0.000134601
$404$	4.68573	+	3.01134i	0.233124	+	0.149820i
$405$		0			0
$406$	−0.251334	−	0.550345i	−0.0124735	−	0.0273132i
$407$	−3.18245	+	3.67274i	−0.157748	+	0.182051i
$408$		0			0
$409$	−11.1094	−	7.13955i	−0.549322	−	0.353028i	0.236353	−	0.971667i	$-0.424048\pi$
$409$	−11.1094	−	7.13955i	−0.549322	−	0.353028i	−0.785675	+	0.618639i	$0.787684\pi$
$410$	−2.12945	+	14.8107i	−0.105166	+	0.731447i
$411$		0			0
$412$	0.941879	−	0.276561i	0.0464031	−	0.0136252i
$413$	3.13671	−	3.61996i	0.154347	−	0.178126i
$414$		0			0
$415$	0.867087	+	6.03072i	0.0425636	+	0.296036i
$416$	−0.0338909	−	0.0742107i	−0.00166164	−	0.00363848i
$417$		0			0
$418$	−6.94616	+	8.01630i	−0.339748	+	0.392090i
$419$	−9.85983	+	21.5900i	−0.481684	+	1.05474i	0.500313	+	0.865845i	$0.333218\pi$
$419$	−9.85983	+	21.5900i	−0.481684	+	1.05474i	−0.981997	+	0.188896i	$0.939509\pi$
$420$		0			0
$421$	−6.38398	+	4.10274i	−0.311136	+	0.199955i	−0.686884	−	0.726767i	$-0.741022\pi$
$421$	−6.38398	+	4.10274i	−0.311136	+	0.199955i	0.375748	+	0.926722i	$0.377386\pi$
$422$	−12.6139	−	3.70379i	−0.614037	−	0.180298i
$423$		0			0
$424$	−24.3663	+	7.15459i	−1.18333	+	0.347458i
$425$	15.5026	+	4.55197i	0.751985	+	0.220803i
$426$		0			0
$427$	−0.599504	−	4.16964i	−0.0290120	−	0.201783i
$428$	1.81129	−	3.96618i	0.0875521	−	0.191712i
$429$		0			0
$430$	−2.84629	+	19.7964i	−0.137260	+	0.954666i
$431$	−11.6585			−0.561572			−0.280786	−	0.959770i	$-0.590595\pi$
$431$	−11.6585			−0.561572			−0.280786	+	0.959770i	$0.590595\pi$
$432$		0			0
$433$	−3.70902	+	25.7968i	−0.178244	+	1.23972i	0.682579	+	0.730812i	$0.260858\pi$
$433$	−3.70902	+	25.7968i	−0.178244	+	1.23972i	−0.860823	+	0.508904i	$0.830051\pi$
$434$	0.0564368	−	0.0165713i	0.00270905	−	0.000795449i
$435$		0			0
$436$	−5.19643	+	3.33954i	−0.248864	+	0.159935i
$437$	−10.9442	+	3.21352i	−0.523534	+	0.153723i
$438$		0			0
$439$	39.6586			1.89280			0.946400	−	0.322996i	$-0.104690\pi$
$439$	39.6586			1.89280			0.946400	+	0.322996i	$0.104690\pi$
$440$	4.58580			0.218619
$441$		0			0
$442$	−0.140227	−	0.161830i	−0.00666991	−	0.00769749i
$443$	−4.64555	+	10.1723i	−0.220717	+	0.483302i	−0.987305	−	0.158837i	$-0.949226\pi$
$443$	−4.64555	+	10.1723i	−0.220717	+	0.483302i	0.766588	+	0.642139i	$0.221953\pi$
$444$		0			0
$445$	−1.81214	+	3.96803i	−0.0859035	+	0.188103i
$446$	29.2769	+	8.59647i	1.38630	+	0.407055i
$447$		0			0
$448$	−1.17582	−	1.35696i	−0.0555521	−	0.0641105i
$449$	−1.16155	−	0.341062i	−0.0548170	−	0.0160957i	0.254209	−	0.967149i	$-0.418185\pi$
$449$	−1.16155	−	0.341062i	−0.0548170	−	0.0160957i	−0.309026	+	0.951054i	$0.600003\pi$
$450$		0			0
$451$	−4.48352	−	9.81753i	−0.211120	−	0.462289i
$452$	1.84696	−	4.04429i	0.0868739	−	0.190227i
$453$		0			0
$454$	32.0996	−	20.6292i	1.50651	−	0.968174i
$455$	0.00553787	+	0.0121263i	0.000259620	+	0.000568487i
$456$		0			0
$457$	−0.213628	−	1.48582i	−0.00999310	−	0.0695036i	0.984215	−	0.176979i	$-0.0566324\pi$
$457$	−0.213628	−	1.48582i	−0.00999310	−	0.0695036i	−0.994208	+	0.107475i	$0.965723\pi$
$458$	−25.5152	+	29.4461i	−1.19225	+	1.37593i
$459$		0			0
$460$	−1.54199	−	0.990978i	−0.0718957	−	0.0462046i
$461$	−1.28448	+	8.93375i	−0.0598241	+	0.416086i	0.937799	+	0.347179i	$0.112860\pi$
$461$	−1.28448	+	8.93375i	−0.0598241	+	0.416086i	−0.997623	+	0.0689072i	$0.978049\pi$
$462$		0			0
$463$	3.49882	+	4.03785i	0.162604	+	0.187655i	0.831205	−	0.555967i	$-0.187652\pi$
$463$	3.49882	+	4.03785i	0.162604	+	0.187655i	−0.668601	+	0.743622i	$0.733106\pi$
$464$	3.19322	−	3.68517i	0.148241	−	0.171080i
$465$		0			0
$466$	26.2763	+	7.71543i	1.21723	+	0.357410i
$467$	−25.3558	−	16.2952i	−1.17332	−	0.754050i	−0.199178	−	0.979963i	$-0.563827\pi$
$467$	−25.3558	−	16.2952i	−1.17332	−	0.754050i	−0.974147	+	0.225913i	$0.927463\pi$
$468$		0			0
$469$	−0.128844	−	3.04866i	−0.00594948	−	0.140774i
$470$	24.0390			1.10884
$471$		0			0
$472$	28.6591	+	8.41508i	1.31914	+	0.387335i
$473$	−5.99279	−	13.1224i	−0.275549	−	0.603368i
$474$		0			0
$475$	9.50093	+	10.9647i	0.435933	+	0.503093i
$476$	0.836037	+	0.537288i	0.0383197	+	0.0246266i
$477$		0			0
$478$	27.7562	+	17.8378i	1.26954	+	0.815884i
$479$	−16.7839	+	4.92820i	−0.766877	+	0.225175i	−0.641696	−	0.766959i	$-0.721769\pi$
$479$	−16.7839	+	4.92820i	−0.766877	+	0.225175i	−0.125180	+	0.992134i	$0.539951\pi$
$480$		0			0
$481$	−0.0125373	−	0.0871988i	−0.000571652	−	0.00397592i
$482$	4.41552	+	30.7106i	0.201121	+	1.39883i
$483$		0			0
$484$	−3.98083	+	2.55832i	−0.180947	+	0.116287i
$485$	11.6368	−	13.4295i	0.528398	−	0.609803i
$486$		0			0
$487$	13.3637	+	29.2624i	0.605567	+	1.32601i	0.925565	+	0.378588i	$0.123590\pi$
$487$	13.3637	+	29.2624i	0.605567	+	1.32601i	−0.319999	+	0.947418i	$0.603683\pi$
$488$	22.0986	−	14.2019i	1.00036	−	0.642890i
$489$		0			0
$490$	9.38213	+	10.8276i	0.423841	+	0.489139i
$491$	−21.5324	+	6.32247i	−0.971742	+	0.285329i	−0.728812	−	0.684714i	$-0.759927\pi$
$491$	−21.5324	+	6.32247i	−0.971742	+	0.285329i	−0.242931	+	0.970044i	$0.578109\pi$
$492$		0			0
$493$	2.08010	−	4.55478i	0.0936830	−	0.205137i
$494$	−0.0273645	−	0.190324i	−0.00123119	−	0.00856310i
$495$		0			0
$496$	0.310441	+	0.358268i	0.0139392	+	0.0160867i
$497$	−0.702013	+	4.88261i	−0.0314896	+	0.219015i
$498$		0			0
$499$	−27.9908			−1.25304			−0.626521	−	0.779405i	$-0.715522\pi$
$499$	−27.9908			−1.25304			−0.626521	+	0.779405i	$0.715522\pi$
$500$	−0.836885	+	5.82066i	−0.0374266	+	0.260308i
$501$		0			0
$502$	−17.6174	+	11.3220i	−0.786301	+	0.505325i
$503$	−22.3368	+	14.3550i	−0.995950	+	0.640058i	−0.933720	−	0.358004i	$-0.883458\pi$
$503$	−22.3368	+	14.3550i	−0.995950	+	0.640058i	−0.0622297	+	0.998062i	$0.519821\pi$
$504$		0			0
$505$	1.91565	−	13.3236i	0.0852453	−	0.592894i
$506$	6.20123			0.275678
$507$		0			0
$508$	−0.258303	+	1.79654i	−0.0114604	+	0.0797086i
$509$	20.3331	+	23.4656i	0.901249	+	1.04010i	0.998992	+	0.0448848i	$0.0142921\pi$
$509$	20.3331	+	23.4656i	0.901249	+	1.04010i	−0.0977434	+	0.995212i	$0.531162\pi$
$510$		0			0
$511$	0.305856	+	2.12727i	0.0135303	+	0.0941050i
$512$	3.30582	−	7.23875i	0.146098	−	0.319910i
$513$		0			0
$514$	−12.8595	+	3.77590i	−0.567209	+	0.166548i
$515$	−1.55352	−	1.79286i	−0.0684564	−	0.0790029i
$516$		0			0
$517$	−14.5869	+	9.37441i	−0.641529	+	0.412286i
$518$	0.796629	+	1.74438i	0.0350019	+	0.0766434i
$519$		0			0
$520$	−0.0544384	+	0.0628253i	−0.00238728	+	0.00275507i
$521$	16.8510	−	10.8295i	0.738254	−	0.474447i	−0.116689	−	0.993168i	$-0.537228\pi$
$521$	16.8510	−	10.8295i	0.738254	−	0.474447i	0.854943	+	0.518721i	$0.173592\pi$
$522$		0			0
$523$	3.03166	+	21.0857i	0.132565	+	0.922012i	0.942194	+	0.335069i	$0.108760\pi$
$523$	3.03166	+	21.0857i	0.132565	+	0.922012i	−0.809628	+	0.586943i	$0.800331\pi$
$524$	0.516811	+	3.59450i	0.0225770	+	0.157026i
$525$		0			0
$526$	34.2136	−	10.0460i	1.49178	−	0.438027i
$527$	0.409524	+	0.263185i	0.0178392	+	0.0114645i
$528$		0			0
$529$	−13.7390	−	8.82950i	−0.597347	−	0.383891i
$530$	−14.9384	−	17.2399i	−0.648884	−	0.748852i
$531$		0			0
$532$	0.370711	+	0.811745i	0.0160724	+	0.0351936i
$533$	0.187724	+	0.0551207i	0.00813123	+	0.00238754i
$534$		0			0
$535$	−10.5371			−0.455559
$536$	16.9592	−	8.62830i	0.732527	−	0.372686i
$537$		0			0
$538$	−13.2013	−	8.48394i	−0.569147	−	0.365769i
$539$	−9.91545	−	2.91144i	−0.427089	−	0.125405i
$540$		0			0
$541$	20.2651	−	23.3871i	0.871263	−	1.00549i	−0.128642	−	0.991691i	$-0.541062\pi$
$541$	20.2651	−	23.3871i	0.871263	−	1.00549i	0.999905	−	0.0138001i	$-0.00439286\pi$
$542$	13.7068	+	15.8185i	0.588759	+	0.679464i
$543$		0			0
$544$	−2.09172	+	14.5482i	−0.0896818	+	0.623751i
$545$	12.5580	+	8.07054i	0.537926	+	0.345704i
$546$		0			0
$547$	17.8423	−	20.5911i	0.762881	−	0.880412i	−0.232869	−	0.972508i	$-0.574811\pi$
$547$	17.8423	−	20.5911i	0.762881	−	0.880412i	0.995750	+	0.0920961i	$0.0293567\pi$
$548$	0.700194	+	4.86996i	0.0299108	+	0.208034i
$549$		0			0
$550$	−3.27668	−	7.17493i	−0.139718	−	0.305940i
$551$	3.78255	−	2.43089i	0.161142	−	0.103560i
$552$		0			0
$553$	−0.476501	+	1.04339i	−0.0202629	+	0.0443695i
$554$	−14.6749	−	32.1336i	−0.623477	−	1.36523i
$555$		0			0
$556$	−10.2223	−	3.00152i	−0.433520	−	0.127293i
$557$	7.40864	+	8.55003i	0.313914	+	0.362276i	0.890678	−	0.454635i	$-0.150230\pi$
$557$	7.40864	+	8.55003i	0.313914	+	0.362276i	−0.576764	+	0.816911i	$0.695685\pi$
$558$		0			0
$559$	0.250917	+	0.0736760i	0.0106127	+	0.00311616i
$560$	0.971569	−	2.12744i	0.0410563	−	0.0899007i
$561$		0			0
$562$	−6.01966	+	13.1812i	−0.253924	+	0.556016i
$563$	12.1771	+	14.0532i	0.513205	+	0.592270i	0.951916	−	0.306358i	$-0.0991105\pi$
$563$	12.1771	+	14.0532i	0.513205	+	0.592270i	−0.438712	+	0.898628i	$0.644565\pi$
$564$		0			0
$565$	−10.7446			−0.452030
$566$	18.8922			0.794096
$567$		0			0
$568$	−29.5143	+	8.66618i	−1.23839	+	0.363625i
$569$	−17.3448	+	11.1468i	−0.727132	+	0.467300i	−0.851111	−	0.524985i	$-0.824071\pi$
$569$	−17.3448	+	11.1468i	−0.727132	+	0.467300i	0.123979	+	0.992285i	$0.460434\pi$
$570$		0			0
$571$	−12.5938	+	3.69787i	−0.527034	+	0.154751i	−0.534416	−	0.845222i	$-0.679468\pi$
$571$	−12.5938	+	3.69787i	−0.527034	+	0.154751i	0.00738182	+	0.999973i	$0.497650\pi$
$572$	−0.00317189	+	0.0220610i	−0.000132623	+	0.000922415i
$573$		0			0
$574$	−4.25891			−0.177763
$575$	1.20712	−	8.39568i	0.0503402	−	0.350124i
$576$		0			0
$577$	−0.985338	+	2.15759i	−0.0410201	+	0.0898216i	−0.929033	−	0.369998i	$-0.879359\pi$
$577$	−0.985338	+	2.15759i	−0.0410201	+	0.0898216i	0.888013	+	0.459819i	$0.152086\pi$
$578$	1.63287	+	11.3568i	0.0679183	+	0.472382i
$579$		0			0
$580$	0.693283	+	0.203566i	0.0287870	+	0.00845263i
$581$	−1.66393	+	0.488573i	−0.0690313	+	0.0202694i
$582$		0			0
$583$	15.7876	+	4.63566i	0.653856	+	0.191989i
$584$	−11.2743	+	7.24554i	−0.466533	+	0.299823i
$585$		0			0
$586$	9.52708	−	20.8614i	0.393560	−	0.861776i
$587$	−20.1146	+	23.2135i	−0.830219	+	0.958124i	−0.999624	−	0.0274227i	$-0.991270\pi$
$587$	−20.1146	+	23.2135i	−0.830219	+	0.958124i	0.169405	+	0.985547i	$0.445815\pi$
$588$		0			0
$589$	0.181589	+	0.397625i	0.00748226	+	0.0163839i
$590$	3.81838	+	26.5574i	0.157200	+	1.09335i
$591$		0			0
$592$	−10.1212	+	11.6805i	−0.415980	+	0.480066i
$593$	12.1175	−	3.55801i	0.497604	−	0.146110i	−0.0232939	−	0.999729i	$-0.507415\pi$
$593$	12.1175	−	3.55801i	0.497604	−	0.146110i	0.520898	+	0.853619i	$0.325597\pi$
$594$		0			0
$595$	0.341794	−	2.37723i	0.0140122	−	0.0974568i
$596$	2.62875	+	1.68940i	0.107678	+	0.0692003i
$597$		0			0
$598$	−0.0736153	+	0.0849566i	−0.00301035	+	0.00347413i
$599$	6.76283	+	14.8085i	0.276322	+	0.605061i	0.996010	−	0.0892365i	$-0.0284427\pi$
$599$	6.76283	+	14.8085i	0.276322	+	0.605061i	−0.719689	+	0.694297i	$0.755715\pi$
$600$		0			0
$601$	−2.94395	−	1.89196i	−0.120086	−	0.0771747i	0.479219	−	0.877695i	$-0.340920\pi$
$601$	−2.94395	−	1.89196i	−0.120086	−	0.0771747i	−0.599305	+	0.800521i	$0.704556\pi$
$602$	−5.69258			−0.232012
$603$		0			0
$604$	2.65679			0.108103
$605$	9.62030	+	6.18259i	0.391121	+	0.251358i
$606$		0			0
$607$	−16.8692	−	36.9383i	−0.684698	−	1.49928i	−0.857588	−	0.514338i	$-0.828038\pi$
$607$	−16.8692	−	36.9383i	−0.684698	−	1.49928i	0.172890	−	0.984941i	$-0.444690\pi$
$608$	−8.64287	+	9.97441i	−0.350515	+	0.404516i
$609$		0			0
$610$	19.8506	+	12.7572i	0.803725	+	0.516523i
$611$	0.0447329	−	0.311124i	0.00180970	−	0.0125867i
$612$		0			0
$613$	30.0299	−	8.81758i	1.21290	−	0.356139i	0.388127	−	0.921606i	$-0.373122\pi$
$613$	30.0299	−	8.81758i	1.21290	−	0.356139i	0.824771	+	0.565467i	$0.191304\pi$
$614$	10.1222	−	11.6817i	0.408500	−	0.471434i
$615$		0			0
$616$	0.185757	+	1.29197i	0.00748436	+	0.0520549i
$617$	−1.45703	−	3.19045i	−0.0586577	−	0.128443i	0.878033	−	0.478600i	$-0.158855\pi$
$617$	−1.45703	−	3.19045i	−0.0586577	−	0.128443i	−0.936691	+	0.350157i	$0.886128\pi$
$618$		0			0
$619$	−10.0560	+	11.6052i	−0.404183	+	0.466452i	−0.920954	−	0.389672i	$-0.872589\pi$
$619$	−10.0560	+	11.6052i	−0.404183	+	0.466452i	0.516771	+	0.856124i	$0.327134\pi$
$620$	−0.0291811	+	0.0638977i	−0.00117194	+	0.00256619i
$621$		0			0
$622$	−26.1578	+	16.8106i	−1.04883	+	0.674042i
$623$	−1.19133	−	0.349805i	−0.0477295	−	0.0140146i
$624$		0			0
$625$	−2.12234	+	0.623176i	−0.0848937	+	0.0249270i
$626$	18.4919	+	5.42972i	0.739087	+	0.217015i
$627$		0			0
$628$	0.243167	+	1.69127i	0.00970343	+	0.0674888i
$629$	−6.59309	+	14.4368i	−0.262884	+	0.575635i
$630$		0			0
$631$	6.51973	−	45.3457i	0.259546	−	1.80519i	−0.276519	−	0.961009i	$-0.589181\pi$
$631$	6.51973	−	45.3457i	0.259546	−	1.80519i	0.536065	−	0.844177i	$-0.319910\pi$
$632$	−7.15282			−0.284524
$633$		0			0
$634$	−1.20215	+	8.36114i	−0.0477435	+	0.332063i
$635$	4.20859	−	1.23575i	0.167013	−	0.0490394i
$636$		0			0
$637$	0.157594	−	0.101279i	0.00624409	−	0.00401283i
$638$	−2.34549	+	0.688698i	−0.0928588	+	0.0272658i
$639$		0			0
$640$	17.8844			0.706945
$641$	25.8154			1.01965			0.509823	−	0.860279i	$-0.329711\pi$
$641$	25.8154			1.01965			0.509823	+	0.860279i	$0.329711\pi$
$642$		0			0
$643$	−24.3209	−	28.0678i	−0.959121	−	1.10689i	−0.994205	−	0.107501i	$-0.965715\pi$
$643$	−24.3209	−	28.0678i	−0.959121	−	1.10689i	0.0350835	−	0.999384i	$-0.488830\pi$
$644$	0.216729	−	0.474571i	0.00854033	−	0.0187007i
$645$		0			0
$646$	−14.3904	+	31.5106i	−0.566182	+	1.23977i
$647$	−2.82448	−	0.829342i	−0.111042	−	0.0326048i	0.225740	−	0.974188i	$-0.427520\pi$
$647$	−2.82448	−	0.829342i	−0.111042	−	0.0326048i	−0.336781	+	0.941583i	$0.609338\pi$
$648$		0			0
$649$	−12.6735	−	14.6260i	−0.497478	−	0.574120i
$650$	0.137194	+	0.0402838i	0.00538119	+	0.00158006i
$651$		0			0
$652$	2.62440	+	5.74663i	0.102779	+	0.225055i
$653$	10.6670	−	23.3574i	0.417431	−	0.914047i	−0.577770	−	0.816199i	$-0.696077\pi$
$653$	10.6670	−	23.3574i	0.417431	−	0.914047i	0.995201	−	0.0978472i	$-0.0311957\pi$
$654$		0			0
$655$	7.38284	−	4.74466i	0.288471	−	0.185389i
$656$	−14.2591	−	31.2230i	−0.556722	−	1.21905i
$657$		0			0
$658$	0.973749	+	6.77257i	0.0379607	+	0.264022i
$659$	−0.307657	+	0.355055i	−0.0119846	+	0.0138310i	−0.761710	−	0.647918i	$-0.775640\pi$
$659$	−0.307657	+	0.355055i	−0.0119846	+	0.0138310i	0.749726	+	0.661749i	$0.230185\pi$
$660$		0			0
$661$	22.7504	+	14.6208i	0.884888	+	0.568683i	0.902273	−	0.431166i	$-0.141898\pi$
$661$	22.7504	+	14.6208i	0.884888	+	0.568683i	−0.0173847	+	0.999849i	$0.505534\pi$
$662$	−2.76681	+	19.2436i	−0.107535	+	0.747923i
$663$		0			0
$664$	−7.08169	−	8.17271i	−0.274823	−	0.317163i
$665$	1.41227	−	1.62985i	0.0547655	−	0.0632028i
$666$		0			0
$667$	−2.52221	−	0.740587i	−0.0976603	−	0.0286756i
$668$	0.429343	+	0.275922i	0.0166118	+	0.0106758i
$669$		0			0
$670$	13.3786	+	10.6376i	0.516860	+	0.410968i
$671$	−17.0202			−0.657057
$672$		0			0
$673$	−33.3729	−	9.79916i	−1.28643	−	0.377730i	−0.434161	−	0.900835i	$-0.642955\pi$
$673$	−33.3729	−	9.79916i	−1.28643	−	0.377730i	−0.852268	+	0.523105i	$0.824773\pi$
$674$	−22.4934	−	49.2537i	−0.866414	−	1.89718i
$675$		0			0
$676$	4.61351	+	5.32427i	0.177443	+	0.204780i
$677$	−18.4748	−	11.8731i	−0.710046	−	0.456319i	0.135116	−	0.990830i	$-0.456859\pi$
$677$	−18.4748	−	11.8731i	−0.710046	−	0.456319i	−0.845161	+	0.534511i	$0.820496\pi$
$678$		0			0
$679$	4.25491	+	2.73446i	0.163288	+	0.104939i
$680$	14.3698	−	4.21936i	0.551057	−	0.161805i
$681$		0			0
$682$	−0.0338215	−	0.235234i	−0.00129509	−	0.00900756i
$683$	3.42277	+	23.8059i	0.130969	+	0.910908i	0.944295	+	0.329100i	$0.106745\pi$
$683$	3.42277	+	23.8059i	0.130969	+	0.910908i	−0.813326	+	0.581808i	$0.802346\pi$
$684$		0			0
$685$	10.0025	−	6.42824i	0.382178	−	0.245611i
$686$	−5.39495	+	6.22611i	−0.205980	+	0.237714i
$687$		0			0
$688$	−19.0591	−	41.7335i	−0.726620	−	1.59108i
$689$	−0.250924	+	0.161259i	−0.00955946	+	0.00614349i
$690$		0			0
$691$	14.5456	+	16.7866i	0.553342	+	0.638590i	0.961658	−	0.274250i	$-0.0884295\pi$
$691$	14.5456	+	16.7866i	0.553342	+	0.638590i	−0.408317	+	0.912840i	$0.633884\pi$
$692$	−4.07987	+	1.19796i	−0.155093	+	0.0455395i
$693$		0			0
$694$	−6.35296	+	13.9111i	−0.241155	+	0.528056i
$695$	3.66412	+	25.4845i	0.138988	+	0.966684i
$696$		0			0
$697$	−23.0823	−	26.6384i	−0.874306	−	1.00900i
$698$	0.656439	−	4.56563i	0.0248466	−	0.172812i
$699$		0			0
$700$	−0.663604			−0.0250819
$701$	0.0938487	−	0.652732i	0.00354462	−	0.0246534i	−0.987972	−	0.154630i	$-0.950581\pi$
$701$	0.0938487	−	0.652732i	0.00354462	−	0.0246534i	0.991517	+	0.129977i	$0.0414904\pi$
$702$		0			0
$703$	−11.9892	+	7.70497i	−0.452180	+	0.290598i
$704$	−6.10294	+	3.92212i	−0.230013	+	0.147821i
$705$		0			0
$706$	−1.39980	+	9.73583i	−0.0526822	+	0.366413i
$707$	3.83130			0.144091
$708$		0			0
$709$	−7.26177	+	50.5067i	−0.272721	+	1.89682i	0.146951	+	0.989144i	$0.453054\pi$
$709$	−7.26177	+	50.5067i	−0.272721	+	1.89682i	−0.419673	+	0.907675i	$0.637855\pi$
$710$	−18.0946	−	20.8822i	−0.679077	−	0.783696i
$711$		0			0
$712$	−1.10188	−	7.66375i	−0.0412947	−	0.287211i
$713$	0.106163	−	0.232464i	0.00397582	−	0.00870584i
$714$		0			0
$715$	0.0516803	−	0.0151747i	0.00193273	−	0.000567502i
$716$	−1.52289	−	1.75751i	−0.0569131	−	0.0656813i
$717$		0			0
$718$	20.9614	−	13.4711i	0.782273	−	0.502736i
$719$	−15.3675	−	33.6502i	−0.573113	−	1.25494i	−0.945123	−	0.326714i	$-0.894059\pi$
$719$	−15.3675	−	33.6502i	−0.573113	−	1.25494i	0.372011	−	0.928228i	$-0.378669\pi$
$720$		0			0
$721$	0.442179	−	0.510302i	0.0164676	−	0.0190046i
$722$	−0.684311	+	0.439780i	−0.0254674	+	0.0163669i
$723$		0			0
$724$	1.26560	+	8.80243i	0.0470356	+	0.327140i
$725$	0.475842	+	3.30956i	0.0176723	+	0.122914i
$726$		0			0
$727$	25.6461	−	7.53038i	0.951162	−	0.279286i	0.230891	−	0.972980i	$-0.425836\pi$
$727$	25.6461	−	7.53038i	0.951162	−	0.279286i	0.720271	+	0.693693i	$0.244018\pi$
$728$	−0.0199051	−	0.0127922i	−0.000737731	−	0.000474111i
$729$		0			0
$730$	−10.1274	−	6.50847i	−0.374831	−	0.240889i
$731$	−30.8525	−	35.6057i	−1.14112	−	1.31692i
$732$		0			0
$733$	19.0202	+	41.6483i	0.702526	+	1.53832i	0.836882	+	0.547383i	$0.184376\pi$
$733$	19.0202	+	41.6483i	0.702526	+	1.53832i	−0.134356	+	0.990933i	$0.542897\pi$
$734$	21.7097	+	6.37454i	0.801319	+	0.235289i
$735$		0			0
$736$	7.71597			0.284415
$737$	−12.2665	−	1.23772i	−0.451841	−	0.0455919i
$738$		0			0
$739$	10.4897	+	6.74134i	0.385871	+	0.247984i	0.719166	−	0.694838i	$-0.244524\pi$
$739$	10.4897	+	6.74134i	0.385871	+	0.247984i	−0.333295	+	0.942823i	$0.608160\pi$
$740$	−2.19743	−	0.645224i	−0.0807792	−	0.0237189i
$741$		0			0
$742$	4.25192	−	4.90698i	0.156093	−	0.180141i
$743$	5.02900	+	5.80378i	0.184496	+	0.212920i	0.840462	−	0.541871i	$-0.182284\pi$
$743$	5.02900	+	5.80378i	0.184496	+	0.212920i	−0.655966	+	0.754791i	$0.727738\pi$
$744$		0			0
$745$	1.07470	−	7.47471i	0.0393740	−	0.273852i
$746$	43.8094	+	28.1546i	1.60398	+	1.03081i
$747$		0			0
$748$	2.62948	−	3.03458i	0.0961432	−	0.110955i
$749$	−0.426827	−	2.96865i	−0.0155959	−	0.108472i
$750$		0			0
$751$	−8.22179	−	18.0032i	−0.300017	−	0.656946i	0.698246	−	0.715858i	$-0.253964\pi$
$751$	−8.22179	−	18.0032i	−0.300017	−	0.656946i	−0.998263	+	0.0589119i	$0.981237\pi$
$752$	−46.3910	+	29.8137i	−1.69171	+	1.08719i
$753$		0			0
$754$	0.0184084	−	0.0403087i	0.000670393	−	0.00146796i
$755$	−2.66720	−	5.84035i	−0.0970693	−	0.212552i
$756$		0			0
$757$	−5.50886	−	1.61755i	−0.200223	−	0.0587907i	0.180083	−	0.983651i	$-0.442363\pi$
$757$	−5.50886	−	1.61755i	−0.200223	−	0.0587907i	−0.380306	+	0.924861i	$0.624181\pi$
$758$	−15.2499	−	17.5993i	−0.553901	−	0.639236i
$759$		0			0
$760$	12.9035	+	3.78880i	0.468058	+	0.137434i
$761$	−6.42537	+	14.0696i	−0.232920	+	0.510023i	−0.989615	−	0.143745i	$-0.954085\pi$
$761$	−6.42537	+	14.0696i	−0.232920	+	0.510023i	0.756695	+	0.653768i	$0.226813\pi$
$762$		0			0
$763$	−1.76505	+	3.86491i	−0.0638989	+	0.139919i
$764$	8.14660	+	9.40167i	0.294734	+	0.340141i
$765$		0			0
$766$	−36.0208			−1.30148
$767$	0.350824			0.0126675
$768$		0			0
$769$	−1.02190	+	0.300057i	−0.0368506	+	0.0108203i	−0.300106	−	0.953906i	$-0.597022\pi$
$769$	−1.02190	+	0.300057i	−0.0368506	+	0.0108203i	0.263255	+	0.964726i	$0.415204\pi$
$770$	−0.986348	+	0.633887i	−0.0355455	+	0.0228437i
$771$		0			0
$772$	−12.3376	+	3.62265i	−0.444040	+	0.130382i
$773$	0.737933	−	5.13244i	0.0265416	−	0.184601i	−0.972238	−	0.233995i	$-0.924820\pi$
$773$	0.737933	−	5.13244i	0.0265416	−	0.184601i	0.998779	+	0.0493943i	$0.0157291\pi$
$774$		0			0
$775$	−0.325060			−0.0116765
$776$	−4.48858	+	31.2187i	−0.161131	+	1.12069i
$777$		0			0
$778$	13.2821	−	29.0837i	0.476185	−	1.04270i
$779$	−4.50439	−	31.3287i	−0.161387	−	1.12247i
$780$		0			0
$781$	19.1231	+	5.61506i	0.684280	+	0.200923i
$782$	19.4318	−	5.70570i	0.694881	−	0.204036i
$783$		0			0
$784$	−31.5344	−	9.25933i	−1.12623	−	0.330690i
$785$	3.47374	−	2.23244i	0.123983	−	0.0796791i
$786$		0			0
$787$	11.4437	−	25.0583i	0.407925	−	0.893230i	−0.588480	−	0.808512i	$-0.700274\pi$
$787$	11.4437	−	25.0583i	0.407925	−	0.893230i	0.996405	−	0.0847188i	$-0.0269992\pi$
$788$	−6.97289	+	8.04714i	−0.248399	+	0.286668i
$789$		0			0
$790$	−2.66912	−	5.84455i	−0.0949629	−	0.207940i
$791$	−0.435233	−	3.02711i	−0.0154751	−	0.107632i
$792$		0			0
$793$	0.202048	−	0.233176i	0.00717493	−	0.00828032i
$794$	−13.8520	+	4.06731i	−0.491588	+	0.144343i
$795$		0			0
$796$	0.331952	−	2.30878i	0.0117657	−	0.0818325i
$797$	9.63108	+	6.18952i	0.341150	+	0.219244i	0.699986	−	0.714157i	$-0.253190\pi$
$797$	9.63108	+	6.18952i	0.341150	+	0.219244i	−0.358835	+	0.933401i	$0.616826\pi$
$798$		0			0
$799$	−37.0833	+	42.7964i	−1.31191	+	1.51403i
$800$	−4.07706	−	8.92751i	−0.144146	−	0.315635i
$801$		0			0
$802$	−37.8832	−	24.3460i	−1.33770	−	0.859688i
$803$	8.68337			0.306430
$804$		0			0
$805$	−1.26081			−0.0444378
$806$	0.00362419	+	0.00232912i	0.000127657	+	8.20399e-5i
$807$		0			0
$808$	9.92485	+	21.7324i	0.349155	+	0.764543i
$809$	−3.55020	+	4.09715i	−0.124818	+	0.144048i	−0.814719	−	0.579856i	$-0.803109\pi$
$809$	−3.55020	+	4.09715i	−0.124818	+	0.144048i	0.689901	+	0.723904i	$0.257654\pi$
$810$		0			0
$811$	−2.16429	−	1.39090i	−0.0759984	−	0.0488412i	0.502090	−	0.864815i	$-0.332565\pi$
$811$	−2.16429	−	1.39090i	−0.0759984	−	0.0488412i	−0.578088	+	0.815974i	$0.696201\pi$
$812$	−0.0292684	+	0.203566i	−0.00102712	+	0.00714378i
$813$		0			0
$814$	7.43427	−	2.18290i	0.260571	−	0.0765105i
$815$	9.99797	−	11.5383i	0.350214	−	0.404168i
$816$		0			0
$817$	−6.02070	−	41.8749i	−0.210638	−	1.46502i
$818$	8.74637	+	19.1519i	0.305810	+	0.669630i
$819$		0			0
$820$	3.33079	−	3.84393i	0.116316	−	0.134236i
$821$	4.84153	−	10.6015i	0.168971	−	0.369994i	−0.806136	−	0.591730i	$-0.798445\pi$
$821$	4.84153	−	10.6015i	0.168971	−	0.369994i	0.975107	+	0.221736i	$0.0711723\pi$
$822$		0			0
$823$	4.06761	−	2.61409i	0.141788	−	0.0911215i	−0.467824	−	0.883822i	$-0.654962\pi$
$823$	4.06761	−	2.61409i	0.141788	−	0.0911215i	0.609612	+	0.792700i	$0.291325\pi$
$824$	4.04005	+	1.18626i	0.140742	+	0.0413255i
$825$		0			0
$826$	−7.32742	+	2.15152i	−0.254954	+	0.0748611i
$827$	40.1731	+	11.7959i	1.39696	+	0.410183i	0.891638	−	0.452750i	$-0.149557\pi$
$827$	40.1731	+	11.7959i	1.39696	+	0.410183i	0.505318	+	0.862933i	$0.331375\pi$
$828$		0			0
$829$	5.55925	+	38.6654i	0.193081	+	1.34291i	0.823794	+	0.566890i	$0.191853\pi$
$829$	5.55925	+	38.6654i	0.193081	+	1.34291i	−0.630713	+	0.776016i	$0.717238\pi$
$830$	4.03532	−	8.83613i	0.140068	−	0.306706i
$831$		0			0
$832$	0.0187156	−	0.130170i	0.000648847	−	0.00451283i
$833$	−33.7493			−1.16934
$834$		0			0
$835$	0.175527	−	1.22082i	0.00607436	−	0.0422481i
$836$	3.45953	−	1.01581i	0.119650	−	0.0351326i
$837$		0			0
$838$	31.8345	−	20.4588i	1.09970	−	0.706737i
$839$	42.8581	−	12.5843i	1.47962	−	0.434457i	0.560411	−	0.828215i	$-0.310643\pi$
$839$	42.8581	−	12.5843i	1.47962	−	0.434457i	0.919214	+	0.393758i	$0.128825\pi$
$840$		0			0
$841$	−27.9638			−0.964268
$842$	12.0990			0.416958
$843$		0			0
$844$	2.92643	+	3.37728i	0.100732	+	0.116251i
$845$	7.07261	−	15.4869i	0.243305	−	0.532764i
$846$		0			0
$847$	−1.35215	+	2.96079i	−0.0464603	+	0.101734i
$848$	50.2098	+	14.7429i	1.72421	+	0.506274i
$849$		0			0
$850$	−16.8692	−	19.4681i	−0.578609	−	0.667751i
$851$	7.99439	+	2.34737i	0.274044	+	0.0804666i
$852$		0			0
$853$	−8.69465	−	19.0386i	−0.297699	−	0.651870i	0.700383	−	0.713767i	$-0.253012\pi$
$853$	−8.69465	−	19.0386i	−0.297699	−	0.651870i	−0.998083	+	0.0618966i	$0.980285\pi$
$854$	−2.79002	+	6.10930i	−0.0954727	+	0.209056i
$855$		0			0
$856$	15.7335	−	10.1113i	0.537759	−	0.345597i
$857$	−6.80557	−	14.9021i	−0.232474	−	0.509047i	0.757060	−	0.653345i	$-0.226635\pi$
$857$	−6.80557	−	14.9021i	−0.232474	−	0.509047i	−0.989534	+	0.144298i	$0.953908\pi$
$858$		0			0
$859$	7.05381	+	49.0603i	0.240673	+	1.67392i	0.648774	+	0.760981i	$0.275282\pi$
$859$	7.05381	+	49.0603i	0.240673	+	1.67392i	−0.408101	+	0.912937i	$0.633809\pi$
$860$	4.45202	−	5.13791i	0.151813	−	0.175201i
$861$		0			0
$862$	15.6370	+	10.0493i	0.532600	+	0.342281i
$863$	5.46358	−	38.0000i	0.185982	−	1.29354i	−0.656300	−	0.754500i	$-0.727880\pi$
$863$	5.46358	−	38.0000i	0.185982	−	1.29354i	0.842283	−	0.539036i	$-0.181211\pi$
$864$		0			0
$865$	6.72928	+	7.76600i	0.228802	+	0.264052i
$866$	27.2109	−	31.4030i	0.924663	−	1.06712i
$867$		0			0
$868$	−0.0191841	−	0.00563296i	−0.000651151	−	0.000191195i
$869$	3.89880	+	2.50560i	0.132258	+	0.0849968i
$870$		0			0
$871$	0.162573	−	0.153357i	0.00550857	−	0.00519630i
$872$	−26.4953			−0.897245
$873$		0			0
$874$	17.4489	+	5.12347i	0.590219	+	0.173304i
$875$	1.68033	+	3.67940i	0.0568054	+	0.124386i
$876$		0			0
$877$	14.4737	+	16.7036i	0.488743	+	0.564039i	0.945529	−	0.325537i	$-0.105545\pi$
$877$	14.4737	+	16.7036i	0.488743	+	0.564039i	−0.456787	+	0.889576i	$0.651000\pi$
$878$	−53.1922	−	34.1846i	−1.79515	−	1.15367i
$879$		0			0
$880$	−7.94951	−	5.10884i	−0.267978	−	0.172219i
$881$	−36.3358	+	10.6691i	−1.22418	+	0.359453i	−0.829052	−	0.559172i	$-0.811119\pi$
$881$	−36.3358	+	10.6691i	−1.22418	+	0.359453i	−0.395132	+	0.918624i	$0.629301\pi$
$882$		0			0
$883$	−3.96109	−	27.5500i	−0.133301	−	0.927131i	−0.941210	−	0.337823i	$-0.890310\pi$
$883$	−3.96109	−	27.5500i	−0.133301	−	0.927131i	0.807908	−	0.589308i	$-0.200600\pi$
$884$	0.0103589	+	0.0720475i	0.000348406	+	0.00242322i
$885$		0			0
$886$	14.9991	−	9.63934i	0.503905	−	0.323840i
$887$	−16.9271	+	19.5349i	−0.568356	+	0.655918i	−0.965060	−	0.262029i	$-0.915608\pi$
$887$	−16.9271	+	19.5349i	−0.568356	+	0.655918i	0.396704	+	0.917947i	$0.370154\pi$
$888$		0			0
$889$	0.518630	+	1.13564i	0.0173943	+	0.0380882i
$890$	5.85086	−	3.76012i	0.196121	−	0.126039i
$891$		0			0
$892$	−6.79222	−	7.83864i	−0.227420	−	0.262457i
$893$	−48.7895	+	14.3259i	−1.63268	+	0.479398i
$894$		0			0
$895$	−2.33463	+	5.11212i	−0.0780380	+	0.170879i
$896$	0.724446	+	5.03863i	0.0242020	+	0.168329i
$897$		0			0
$898$	1.26395	+	1.45867i	0.0421785	+	0.0486766i
$899$	−0.0143368	+	0.0997150i	−0.000478161	+	0.00332568i
$900$		0			0
$901$	53.7364			1.79022
$902$	−2.44890	+	17.0325i	−0.0815394	+	0.567119i
$903$		0			0
$904$	16.0433	−	10.3104i	0.533593	−	0.342919i
$905$	18.0796	−	11.6190i	0.600985	−	0.386229i
$906$		0			0
$907$	−3.47403	+	24.1624i	−0.115353	+	0.802299i	0.847213	+	0.531253i	$0.178279\pi$
$907$	−3.47403	+	24.1624i	−0.115353	+	0.802299i	−0.962566	+	0.271046i	$0.912631\pi$
$908$	−12.9704			−0.430437
$909$		0			0
$910$	0.00302479	−	0.0210379i	0.000100271	−	0.000697398i
$911$	−32.0520	−	36.9900i	−1.06193	−	1.22553i	−0.973317	−	0.229466i	$-0.926302\pi$
$911$	−32.0520	−	36.9900i	−1.06193	−	1.22553i	−0.0886131	−	0.996066i	$-0.528243\pi$
$912$		0			0
$913$	0.997160	+	6.93540i	0.0330012	+	0.229528i
$914$	−0.994202	+	2.17700i	−0.0328853	+	0.0720087i
$915$		0			0
$916$	12.7078	−	3.73136i	0.419879	−	0.123288i
$917$	1.63578	+	1.88779i	0.0540183	+	0.0623405i
$918$		0			0
$919$	39.5677	−	25.4286i	1.30522	−	0.838813i	0.311449	−	0.950263i	$-0.399186\pi$
$919$	39.5677	−	25.4286i	1.30522	−	0.838813i	0.993770	+	0.111449i	$0.0355493\pi$
$920$	−3.26609	−	7.15174i	−0.107680	−	0.235786i
$921$		0			0
$922$	9.42345	−	10.8752i	0.310345	−	0.358157i
$923$	−0.303939	+	0.195329i	−0.0100043	+	0.00642935i
$924$		0			0
$925$	−1.50823	−	10.4900i	−0.0495903	−	0.344908i
$926$	−1.21229	−	8.43167i	−0.0398383	−	0.277082i
$927$		0			0
$928$	−2.91841	+	0.856923i	−0.0958015	+	0.0281299i
$929$	43.4435	+	27.9195i	1.42534	+	0.916008i	0.999939	+	0.0110012i	$0.00350185\pi$
$929$	43.4435	+	27.9195i	1.42534	+	0.916008i	0.425397	+	0.905007i	$0.360135\pi$
$930$		0			0
$931$	−25.4945	−	16.3843i	−0.835550	−	0.536975i
$932$	−6.09609	−	7.03527i	−0.199684	−	0.230448i
$933$		0			0
$934$	19.9625	+	43.7119i	0.653195	+	1.43030i
$935$	−9.31060	−	2.73384i	−0.304489	−	0.0894061i
$936$		0			0
$937$	32.0494			1.04701			0.523505	−	0.852023i	$-0.324624\pi$
$937$	32.0494			1.04701			0.523505	+	0.852023i	$0.324624\pi$
$938$	−2.45504	+	4.20009i	−0.0801600	+	0.137138i
$939$		0			0
$940$	−6.87422	−	4.41779i	−0.224212	−	0.144092i
$941$	30.3589	+	8.91417i	0.989671	+	0.290594i	0.736211	−	0.676752i	$-0.236613\pi$
$941$	30.3589	+	8.91417i	0.989671	+	0.290594i	0.253460	+	0.967346i	$0.418431\pi$
$942$		0			0
$943$	−12.1176	+	13.9845i	−0.394603	+	0.455397i
$944$	−40.3059	−	46.5155i	−1.31184	−	1.51395i
$945$		0			0
$946$	−3.27327	+	22.7661i	−0.106423	+	0.740189i
$947$	−0.989248	−	0.635751i	−0.0321462	−	0.0206591i	0.524469	−	0.851430i	$-0.324264\pi$
$947$	−0.989248	−	0.635751i	−0.0321462	−	0.0206591i	−0.556615	+	0.830770i	$0.687900\pi$
$948$		0			0
$949$	−0.103081	+	0.118962i	−0.00334615	+	0.00386167i
$950$	−3.29194	−	22.8959i	−0.106805	−	0.742842i
$951$		0			0
$952$	1.77081	+	3.87753i	0.0573922	+	0.125671i
$953$	−7.58617	+	4.87534i	−0.245740	+	0.157928i	−0.657713	−	0.753268i	$-0.728476\pi$
$953$	−7.58617	+	4.87534i	−0.245740	+	0.157928i	0.411973	+	0.911196i	$0.364840\pi$
$954$		0			0
$955$	12.4889	−	27.3469i	0.404132	−	0.884925i
$956$	−4.65903	−	10.2019i	−0.150684	−	0.329951i
$957$		0			0
$958$	26.7594	+	7.85728i	0.864559	+	0.253857i
$959$	2.21622	+	2.55765i	0.0715654	+	0.0825909i
$960$		0			0
$961$	29.7349	+	8.73095i	0.959190	+	0.281644i
$962$	−0.0583472	+	0.127763i	−0.00188119	+	0.00411923i
$963$		0			0
$964$	4.38121	−	9.59350i	0.141109	−	0.308986i
$965$	20.3495	+	23.4846i	0.655073	+	0.755995i
$966$		0			0
$967$	−0.192065			−0.00617639			−0.00308819	−	0.999995i	$-0.500983\pi$
$967$	−0.192065			−0.00617639			−0.00308819	+	0.999995i	$0.500983\pi$
$968$	−20.2973			−0.652379
$969$		0			0
$970$	−27.1837	+	7.98185i	−0.872816	+	0.256282i
$971$	20.0757	−	12.9018i	0.644259	−	0.414040i	−0.177306	−	0.984156i	$-0.556738\pi$
$971$	20.0757	−	12.9018i	0.644259	−	0.414040i	0.821564	+	0.570116i	$0.193102\pi$
$972$		0			0
$973$	−7.03140	+	2.06461i	−0.225416	+	0.0661882i
$974$	7.29925	−	50.7674i	0.233883	−	1.62669i
$975$		0			0
$976$	−54.1297			−1.73265
$977$	2.96264	−	20.6056i	0.0947831	−	0.659231i	−0.885936	−	0.463808i	$-0.846483\pi$
$977$	2.96264	−	20.6056i	0.0947831	−	0.659231i	0.980719	−	0.195423i	$-0.0626081\pi$
$978$		0			0
$979$	−2.08398	+	4.56328i	−0.0666043	+	0.145843i
$980$	−0.693078	−	4.82046i	−0.0221396	−	0.153984i
$981$		0			0
$982$	34.3302	+	10.0802i	1.09552	+	0.321674i
$983$	−6.12305	+	1.79789i	−0.195295	+	0.0573438i	−0.377917	−	0.925839i	$-0.623360\pi$
$983$	−6.12305	+	1.79789i	−0.195295	+	0.0573438i	0.182622	+	0.983183i	$0.441541\pi$
$984$		0			0
$985$	24.6900	+	7.24964i	0.786689	+	0.230993i
$986$	−6.71603	+	4.31613i	−0.213882	+	0.137454i
$987$		0			0
$988$	−0.0271519	+	0.0594543i	−0.000863816	+	0.00189149i
$989$	−16.1967	+	18.6920i	−0.515026	+	0.594372i
$990$		0			0
$991$	−20.9672	−	45.9118i	−0.666045	−	1.45844i	−0.876780	−	0.480892i	$-0.840313\pi$
$991$	−20.9672	−	45.9118i	−0.666045	−	1.45844i	0.210734	−	0.977543i	$-0.432414\pi$
$992$	−0.0420829	−	0.292693i	−0.00133613	−	0.00929301i
$993$		0			0
$994$	5.15025	−	5.94370i	0.163356	−	0.188523i
$995$	−5.40857	+	1.58810i	−0.171463	+	0.0503461i
$996$		0			0
$997$	−4.09916	+	28.5103i	−0.129822	+	0.902929i	0.815956	+	0.578114i	$0.196211\pi$
$997$	−4.09916	+	28.5103i	−0.129822	+	0.902929i	−0.945778	+	0.324815i	$0.894698\pi$
$998$	37.5428	+	24.1273i	1.18840	+	0.763736i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.u.a.478.1		10
3.2	odd	2		67.2.e.b.9.1	✓	10
67.15	even	11	inner	603.2.u.a.82.1		10
201.89	odd	22		4489.2.a.i.1.4		5
201.149	odd	22		67.2.e.b.15.1	yes	10
201.179	even	22		4489.2.a.h.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.b.9.1	✓	10	3.2	odd	2
67.2.e.b.15.1	yes	10	201.149	odd	22
603.2.u.a.82.1		10	67.15	even	11	inner
603.2.u.a.478.1		10	1.1	even	1	trivial
4489.2.a.h.1.2		5	201.179	even	22
4489.2.a.i.1.4		5	201.89	odd	22

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34125 - 0.861971i) q^{2} +(0.225136 + 0.492980i) q^{4} +(0.857685 - 0.989821i) q^{5} +(0.313607 + 0.201543i) q^{7} +(-0.330830 + 2.30097i) q^{8} +O(q^{10})\)	\(q+(-1.34125 - 0.861971i) q^{2} +(0.225136 + 0.492980i) q^{4} +(0.857685 - 0.989821i) q^{5} +(0.313607 + 0.201543i) q^{7} +(-0.330830 + 2.30097i) q^{8} +(-2.00357 + 0.588302i) q^{10} +(0.986348 - 1.13831i) q^{11} +(0.00388573 + 0.0270259i) q^{13} +(-0.246902 - 0.540641i) q^{14} +(3.13691 - 3.62019i) q^{16} +(2.04342 - 4.47447i) q^{17} +(3.71585 - 2.38803i) q^{19} +(0.681059 + 0.199977i) q^{20} +(-2.30413 + 0.676554i) q^{22} +(-2.47773 - 0.727528i) q^{23} +(0.467452 + 3.25120i) q^{25} +(0.0180838 - 0.0395979i) q^{26} +(-0.0287523 + 0.199977i) q^{28} +1.01795 q^{29} +(-0.0140840 + 0.0979567i) q^{31} +(-2.86695 + 0.841812i) q^{32} +(-6.59761 + 4.24002i) q^{34} +(0.468468 - 0.137555i) q^{35} -3.22650 q^{37} -7.04231 q^{38} +(1.99380 + 2.30097i) q^{40} +(2.97672 - 6.51810i) q^{41} +(3.97876 - 8.71228i) q^{43} +(0.783225 + 0.229976i) q^{44} +(2.69616 + 3.11153i) q^{46} +(-11.0458 - 3.24333i) q^{47} +(-2.85018 - 6.24101i) q^{49} +(2.17547 - 4.76361i) q^{50} +(-0.0124484 + 0.00800010i) q^{52} +(4.53811 + 9.93708i) q^{53} +(-0.280744 - 1.95262i) q^{55} +(-0.567496 + 0.654925i) q^{56} +(-1.36533 - 0.877444i) q^{58} +(1.82859 - 12.7181i) q^{59} +(-7.40000 - 8.54005i) q^{61} +(0.103326 - 0.119245i) q^{62} +(-4.62139 - 1.35696i) q^{64} +(0.0300835 + 0.0193335i) q^{65} +(-4.71215 - 6.69296i) q^{67} +2.66587 q^{68} +(-0.746902 - 0.219310i) q^{70} +(5.49691 + 12.0365i) q^{71} +(3.77534 + 4.35697i) q^{73} +(4.32755 + 2.78115i) q^{74} +(2.01382 + 1.29421i) q^{76} +(0.538744 - 0.158189i) q^{77} +(0.437898 + 3.04565i) q^{79} +(-0.892858 - 6.20996i) q^{80} +(-9.61094 + 6.17658i) q^{82} +(-3.04637 + 3.51570i) q^{83} +(-2.67631 - 5.86031i) q^{85} +(-12.8463 + 8.25579i) q^{86} +(2.29290 + 2.64615i) q^{88} +(-3.19574 + 0.938355i) q^{89} +(-0.00422828 + 0.00925865i) q^{91} +(-0.199171 - 1.38527i) q^{92} +(12.0195 + 13.8713i) q^{94} +(0.823304 - 5.72620i) q^{95} +13.5676 q^{97} +(-1.55677 + 10.8276i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8}+O(q^{10}) \) 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8	\( 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28} + 24 q^{29} - q^{31} + q^{32} - 15 q^{34} + 3 q^{35} + 2 q^{37} + 36 q^{38} + 25 q^{40} + 7 q^{41} - 2 q^{43} - 41 q^{44} + 6 q^{46} - 33 q^{47} + 2 q^{49} + 4 q^{50} - 21 q^{52} - 21 q^{53} + 13 q^{55} + 17 q^{56} - 3 q^{58} + 38 q^{59} - 50 q^{61} - 4 q^{62} - 31 q^{64} + 8 q^{65} + 32 q^{67} + 30 q^{68} - 10 q^{70} + 16 q^{71} + 3 q^{73} + 8 q^{74} + 5 q^{76} - 7 q^{77} - 19 q^{79} - 9 q^{80} - 16 q^{82} - 5 q^{83} - 13 q^{85} - 19 q^{86} + 48 q^{88} - 7 q^{89} - 6 q^{91} - 45 q^{92} + 22 q^{94} - 15 q^{95} + 54 q^{97} - 47 q^{98}+O(q^{100}) \) 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Introduction

L-functions

Modular forms

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