LMFDB - Embedded newform 603.2.u.b.442.1

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			442.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	603.442
Dual form			603.2.u.b.397.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.898983 - 1.03748i) q^{2} +(0.0164316 - 0.114284i) q^{4} +(0.297176 + 0.0872586i) q^{5} +(-1.28820 - 1.48666i) q^{7} +(-2.44306 + 1.57006i) q^{8} +O(q^{10})$	\(q+(-0.898983 - 1.03748i) q^{2} +(0.0164316 - 0.114284i) q^{4} +(0.297176 + 0.0872586i) q^{5} +(-1.28820 - 1.48666i) q^{7} +(-2.44306 + 1.57006i) q^{8} +(-0.176627 - 0.386758i) q^{10} +(-1.41329 - 0.414980i) q^{11} +(-2.40499 - 1.54559i) q^{13} +(-0.384315 + 2.67297i) q^{14} +(3.60362 + 1.05812i) q^{16} +(0.675178 + 4.69597i) q^{17} +(-3.31797 + 3.82914i) q^{19} +(0.0148554 - 0.0325288i) q^{20} +(0.839992 + 1.83933i) q^{22} +(2.31117 - 5.06076i) q^{23} +(-4.12557 - 2.65134i) q^{25} +(0.558521 + 3.88460i) q^{26} +(-0.191070 + 0.122793i) q^{28} -7.60574 q^{29} +(-1.07602 + 0.691518i) q^{31} +(0.270978 + 0.593359i) q^{32} +(4.26501 - 4.92208i) q^{34} +(-0.253098 - 0.554206i) q^{35} +0.658623 q^{37} +6.95546 q^{38} +(-0.863019 + 0.253405i) q^{40} +(-1.14528 - 7.96561i) q^{41} +(1.74029 + 12.1040i) q^{43} +(-0.0706485 + 0.154699i) q^{44} +(-7.32815 + 2.15174i) q^{46} +(-4.10185 + 8.98180i) q^{47} +(0.445499 - 3.09851i) q^{49} +(0.958098 + 6.66372i) q^{50} +(-0.216155 + 0.249457i) q^{52} +(-0.309775 + 2.15453i) q^{53} +(-0.383785 - 0.246644i) q^{55} +(5.48130 + 1.60946i) q^{56} +(6.83743 + 7.89082i) q^{58} +(-3.02904 + 1.94665i) q^{59} +(8.20409 - 2.40894i) q^{61} +(1.68476 + 0.494691i) q^{62} +(3.49238 - 7.64725i) q^{64} +(-0.579838 - 0.669169i) q^{65} +(-7.89015 - 2.17842i) q^{67} +0.547770 q^{68} +(-0.347449 + 0.760807i) q^{70} +(-0.381067 + 2.65038i) q^{71} +(-10.6431 + 3.12509i) q^{73} +(-0.592092 - 0.683310i) q^{74} +(0.383092 + 0.442111i) q^{76} +(1.20367 + 2.63567i) q^{77} +(-0.548906 - 0.352760i) q^{79} +(0.978577 + 0.628893i) q^{80} +(-7.23459 + 8.34916i) q^{82} +(-6.61500 - 1.94234i) q^{83} +(-0.209117 + 1.45444i) q^{85} +(10.9932 - 12.6868i) q^{86} +(4.10430 - 1.20513i) q^{88} +(-3.05330 - 6.68579i) q^{89} +(0.800334 + 5.56645i) q^{91} +(-0.540390 - 0.347287i) q^{92} +(13.0060 - 3.81889i) q^{94} +(-1.32014 + 0.848406i) q^{95} +7.97669 q^{97} +(-3.61514 + 2.32331i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8}+O(q^{10}) $ 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8	$ 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8} - 15 q^{10} - 15 q^{11} - 18 q^{13} - 6 q^{16} + 26 q^{17} - q^{19} - 25 q^{20} - 9 q^{22} + 6 q^{23} - 4 q^{25} - 24 q^{26} + 11 q^{28} - 28 q^{29} - 10 q^{31} + 4 q^{32} + 64 q^{34} - 22 q^{37} + 6 q^{38} - 18 q^{40} - 9 q^{41} + 21 q^{43} - 48 q^{44} - 25 q^{46} + 22 q^{47} + 7 q^{49} + 35 q^{50} - 62 q^{52} - 20 q^{53} - 23 q^{55} + 11 q^{56} - 8 q^{58} + 17 q^{59} + 13 q^{61} - 50 q^{62} + 10 q^{64} - 10 q^{65} + 23 q^{67} + 114 q^{68} + 11 q^{70} - q^{71} - 18 q^{73} - 22 q^{74} + 21 q^{76} + 22 q^{77} + 5 q^{79} - 18 q^{80} - 12 q^{82} + 12 q^{83} + 23 q^{85} + 61 q^{86} - 2 q^{88} - 51 q^{89} - 11 q^{91} - 38 q^{92} + 11 q^{94} - 3 q^{95} - 10 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8 - 15 * q^10 - 15 * q^11 - 18 * q^13 - 6 * q^16 + 26 * q^17 - q^19 - 25 * q^20 - 9 * q^22 + 6 * q^23 - 4 * q^25 - 24 * q^26 + 11 * q^28 - 28 * q^29 - 10 * q^31 + 4 * q^32 + 64 * q^34 - 22 * q^37 + 6 * q^38 - 18 * q^40 - 9 * q^41 + 21 * q^43 - 48 * q^44 - 25 * q^46 + 22 * q^47 + 7 * q^49 + 35 * q^50 - 62 * q^52 - 20 * q^53 - 23 * q^55 + 11 * q^56 - 8 * q^58 + 17 * q^59 + 13 * q^61 - 50 * q^62 + 10 * q^64 - 10 * q^65 + 23 * q^67 + 114 * q^68 + 11 * q^70 - q^71 - 18 * q^73 - 22 * q^74 + 21 * q^76 + 22 * q^77 + 5 * q^79 - 18 * q^80 - 12 * q^82 + 12 * q^83 + 23 * q^85 + 61 * q^86 - 2 * q^88 - 51 * q^89 - 11 * q^91 - 38 * q^92 + 11 * q^94 - 3 * q^95 - 10 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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 $

$2$	−0.898983	−	1.03748i	−0.635677	−	0.733611i	0.342927	−	0.939362i	$-0.388582\pi$
$2$	−0.898983	−	1.03748i	−0.635677	−	0.733611i	−0.978604	+	0.205751i	$0.934036\pi$
$3$		0			0
$3$		0			0
$4$	0.0164316	−	0.114284i	0.00821581	−	0.0571422i
$5$	0.297176	+	0.0872586i	0.132901	+	0.0390232i	0.347507	−	0.937678i	$-0.387028\pi$
$5$	0.297176	+	0.0872586i	0.132901	+	0.0390232i	−0.214606	+	0.976701i	$0.568847\pi$
$6$		0			0
$7$	−1.28820	−	1.48666i	−0.486894	−	0.561906i	0.458139	−	0.888881i	$-0.348516\pi$
$7$	−1.28820	−	1.48666i	−0.486894	−	0.561906i	−0.945033	+	0.326975i	$0.893971\pi$
$8$	−2.44306	+	1.57006i	−0.863753	+	0.555100i
$9$		0			0
$10$	−0.176627	−	0.386758i	−0.0558542	−	0.122304i
$11$	−1.41329	−	0.414980i	−0.426124	−	0.125121i	0.0616369	−	0.998099i	$-0.480368\pi$
$11$	−1.41329	−	0.414980i	−0.426124	−	0.125121i	−0.487761	+	0.872977i	$0.662186\pi$
$12$		0			0
$13$	−2.40499	−	1.54559i	−0.667025	−	0.428671i	0.162827	−	0.986655i	$-0.447939\pi$
$13$	−2.40499	−	1.54559i	−0.667025	−	0.428671i	−0.829852	+	0.557984i	$0.811575\pi$
$14$	−0.384315	+	2.67297i	−0.102713	+	0.714381i
$15$		0			0
$16$	3.60362	+	1.05812i	0.900904	+	0.264529i
$17$	0.675178	+	4.69597i	0.163755	+	1.13894i	0.891477	+	0.453067i	$0.149670\pi$
$17$	0.675178	+	4.69597i	0.163755	+	1.13894i	−0.727722	+	0.685872i	$0.759421\pi$
$18$		0			0
$19$	−3.31797	+	3.82914i	−0.761194	+	0.878465i	−0.995603	−	0.0936730i	$-0.970139\pi$
$19$	−3.31797	+	3.82914i	−0.761194	+	0.878465i	0.234409	+	0.972138i	$0.424685\pi$
$20$	0.0148554	−	0.0325288i	0.00332177	−	0.00727365i
$21$		0			0
$22$	0.839992	+	1.83933i	0.179087	+	0.392146i
$23$	2.31117	−	5.06076i	0.481912	−	1.05524i	−0.500021	−	0.866013i	$-0.666674\pi$
$23$	2.31117	−	5.06076i	0.481912	−	1.05524i	0.981933	−	0.189227i	$-0.0605983\pi$
$24$		0			0
$25$	−4.12557	−	2.65134i	−0.825114	−	0.530268i
$26$	0.558521	+	3.88460i	0.109535	+	0.761833i
$27$		0			0
$28$	−0.191070	+	0.122793i	−0.0361088	+	0.0232057i
$29$	−7.60574			−1.41235			−0.706175	−	0.708037i	$-0.749581\pi$
$29$	−7.60574			−1.41235			−0.706175	+	0.708037i	$0.749581\pi$
$30$		0			0
$31$	−1.07602	+	0.691518i	−0.193259	+	0.124200i	−0.633692	−	0.773585i	$-0.718461\pi$
$31$	−1.07602	+	0.691518i	−0.193259	+	0.124200i	0.440433	+	0.897786i	$0.354825\pi$
$32$	0.270978	+	0.593359i	0.0479026	+	0.104892i
$33$		0			0
$34$	4.26501	−	4.92208i	0.731443	−	0.844130i
$35$	−0.253098	−	0.554206i	−0.0427813	−	0.0936780i
$36$		0			0
$37$	0.658623			0.108277			0.0541385	−	0.998533i	$-0.482759\pi$
$37$	0.658623			0.108277			0.0541385	+	0.998533i	$0.482759\pi$
$38$	6.95546			1.12833
$39$		0			0
$40$	−0.863019	+	0.253405i	−0.136455	+	0.0400669i
$41$	−1.14528	−	7.96561i	−0.178863	−	1.24402i	−0.859399	−	0.511305i	$-0.829162\pi$
$41$	−1.14528	−	7.96561i	−0.178863	−	1.24402i	0.680536	−	0.732714i	$-0.261747\pi$
$42$		0			0
$43$	1.74029	+	12.1040i	0.265392	+	1.84584i	0.490418	+	0.871487i	$0.336844\pi$
$43$	1.74029	+	12.1040i	0.265392	+	1.84584i	−0.225026	+	0.974353i	$0.572247\pi$
$44$	−0.0706485	+	0.154699i	−0.0106507	+	0.0233217i
$45$		0			0
$46$	−7.32815	+	2.15174i	−1.08048	+	0.317257i
$47$	−4.10185	+	8.98180i	−0.598317	+	1.31013i	0.331968	+	0.943291i	$0.392288\pi$
$47$	−4.10185	+	8.98180i	−0.598317	+	1.31013i	−0.930284	+	0.366840i	$0.880440\pi$
$48$		0			0
$49$	0.445499	−	3.09851i	0.0636426	−	0.442644i
$50$	0.958098	+	6.66372i	0.135495	+	0.942392i
$51$		0			0
$52$	−0.216155	+	0.249457i	−0.0299754	+	0.0345934i
$53$	−0.309775	+	2.15453i	−0.0425508	+	0.295948i	0.957423	+	0.288689i	$0.0932195\pi$
$53$	−0.309775	+	2.15453i	−0.0425508	+	0.295948i	−0.999974	+	0.00725820i	$0.997690\pi$
$54$		0			0
$55$	−0.383785	−	0.246644i	−0.0517496	−	0.0332575i
$56$	5.48130	+	1.60946i	0.732470	+	0.215073i
$57$		0			0
$58$	6.83743	+	7.89082i	0.897799	+	1.03612i
$59$	−3.02904	+	1.94665i	−0.394348	+	0.253432i	−0.722755	−	0.691104i	$-0.757124\pi$
$59$	−3.02904	+	1.94665i	−0.394348	+	0.253432i	0.328407	+	0.944536i	$0.393488\pi$
$60$		0			0
$61$	8.20409	−	2.40894i	1.05043	−	0.308433i	0.289437	−	0.957197i	$-0.406532\pi$
$61$	8.20409	−	2.40894i	1.05043	−	0.308433i	0.760990	+	0.648764i	$0.224714\pi$
$62$	1.68476	+	0.494691i	0.213965	+	0.0628258i
$63$		0			0
$64$	3.49238	−	7.64725i	0.436548	−	0.955907i
$65$	−0.579838	−	0.669169i	−0.0719201	−	0.0830002i
$66$		0			0
$67$	−7.89015	−	2.17842i	−0.963935	−	0.266137i
$67$	−7.89015	−	2.17842i	−0.963935	−	0.266137i
$68$	0.547770			0.0664269
$69$		0			0
$70$	−0.347449	+	0.760807i	−0.0415281	+	0.0909338i
$71$	−0.381067	+	2.65038i	−0.0452243	+	0.314542i	0.954635	+	0.297778i	$0.0962455\pi$
$71$	−0.381067	+	2.65038i	−0.0452243	+	0.314542i	−0.999859	+	0.0167641i	$0.994664\pi$
$72$		0			0
$73$	−10.6431	+	3.12509i	−1.24568	+	0.365764i	−0.837146	−	0.546980i	$-0.815778\pi$
$73$	−10.6431	+	3.12509i	−1.24568	+	0.365764i	−0.408532	+	0.912744i	$0.633959\pi$
$74$	−0.592092	−	0.683310i	−0.0688292	−	0.0794332i
$75$		0			0
$76$	0.383092	+	0.442111i	0.0439436	+	0.0507137i
$77$	1.20367	+	2.63567i	0.137171	+	0.300362i
$78$		0			0
$79$	−0.548906	−	0.352760i	−0.0617567	−	0.0396886i	0.509398	−	0.860531i	$-0.329868\pi$
$79$	−0.548906	−	0.352760i	−0.0617567	−	0.0396886i	−0.571155	+	0.820842i	$0.693504\pi$
$80$	0.978577	+	0.628893i	0.109408	+	0.0703124i
$81$		0			0
$82$	−7.23459	+	8.34916i	−0.798927	+	0.922010i
$83$	−6.61500	−	1.94234i	−0.726091	−	0.213199i	−0.102259	−	0.994758i	$-0.532607\pi$
$83$	−6.61500	−	1.94234i	−0.726091	−	0.213199i	−0.623832	+	0.781558i	$0.714425\pi$
$84$		0			0
$85$	−0.209117	+	1.45444i	−0.0226819	+	0.157756i
$86$	10.9932	−	12.6868i	1.18542	−	1.36805i
$87$		0			0
$88$	4.10430	−	1.20513i	0.437520	−	0.128468i
$89$	−3.05330	−	6.68579i	−0.323649	−	0.708692i	0.675952	−	0.736946i	$-0.263733\pi$
$89$	−3.05330	−	6.68579i	−0.323649	−	0.708692i	−0.999601	+	0.0282535i	$0.991005\pi$
$90$		0			0
$91$	0.800334	+	5.56645i	0.0838978	+	0.583522i
$92$	−0.540390	−	0.347287i	−0.0563395	−	0.0362072i
$93$		0			0
$94$	13.0060	−	3.81889i	1.34146	−	0.393889i
$95$	−1.32014	+	0.848406i	−0.135444	+	0.0870446i
$96$		0			0
$97$	7.97669			0.809910			0.404955	−	0.914337i	$-0.367287\pi$
$97$	7.97669			0.809910			0.404955	+	0.914337i	$0.367287\pi$
$98$	−3.61514	+	2.32331i	−0.365185	+	0.234690i
$99$		0			0
$100$	−0.370797	+	0.427923i	−0.0370797	+	0.0427923i
$101$	11.1969	−	12.9219i	1.11413	−	1.28577i	0.159756	−	0.987156i	$-0.448929\pi$
$101$	11.1969	−	12.9219i	1.11413	−	1.28577i	0.954373	−	0.298617i	$-0.0965254\pi$
$102$		0			0
$103$	4.47425	−	2.87543i	0.440861	−	0.283324i	−0.301321	−	0.953523i	$-0.597427\pi$
$103$	4.47425	−	2.87543i	0.440861	−	0.283324i	0.742182	+	0.670199i	$0.233791\pi$
$104$	8.30222			0.814099
$105$		0			0
$106$	2.51377	−	1.61550i	0.244159	−	0.156911i
$107$	−13.1526	+	3.86195i	−1.27151	+	0.373349i	−0.846767	−	0.531965i	$-0.821454\pi$
$107$	−13.1526	+	3.86195i	−1.27151	+	0.373349i	−0.424743	+	0.905314i	$0.639636\pi$
$108$		0			0
$109$	9.09669	+	5.84609i	0.871305	+	0.559954i	0.898152	−	0.439686i	$-0.144910\pi$
$109$	9.09669	+	5.84609i	0.871305	+	0.559954i	−0.0268468	+	0.999640i	$0.508547\pi$
$110$	0.0891281	+	0.619899i	0.00849803	+	0.0591051i
$111$		0			0
$112$	−3.06912	−	6.72043i	−0.290004	−	0.635021i
$113$	1.71672	−	0.504073i	0.161495	−	0.0474192i	−0.199986	−	0.979799i	$-0.564090\pi$
$113$	1.71672	−	0.504073i	0.161495	−	0.0474192i	0.361481	+	0.932380i	$0.382271\pi$
$114$		0			0
$115$	1.12842	−	1.30226i	0.105226	−	0.121437i
$116$	−0.124975	+	0.869218i	−0.0116036	+	0.0807049i
$117$		0			0
$118$	4.74267	+	1.39257i	0.436598	+	0.128197i
$119$	6.11155	−	7.05311i	0.560245	−	0.646557i
$120$		0			0
$121$	−7.42860	−	4.77407i	−0.675327	−	0.434007i
$122$	−9.87457	−	6.34600i	−0.894002	−	0.574540i
$123$		0			0
$124$	0.0613489	+	0.134335i	0.00550930	+	0.0120637i
$125$	−2.00879	−	2.31826i	−0.179671	−	0.207352i
$126$		0			0
$127$	−11.5047	−	13.2771i	−1.02088	−	1.17816i	−0.983878	−	0.178841i	$-0.942765\pi$
$127$	−11.5047	−	13.2771i	−1.02088	−	1.17816i	−0.0370000	−	0.999315i	$-0.511780\pi$
$128$	−9.82172	+	2.88392i	−0.868125	+	0.254905i
$129$		0			0
$130$	−0.172986	+	1.20314i	−0.0151719	+	0.105523i
$131$	6.50513	−	14.2442i	0.568355	−	1.24452i	−0.379313	−	0.925268i	$-0.623840\pi$
$131$	6.50513	−	14.2442i	0.568355	−	1.24452i	0.947668	−	0.319256i	$-0.103433\pi$
$132$		0			0
$133$	9.96685			0.864236
$134$	4.83304	+	10.1443i	0.417511	+	0.876330i
$135$		0			0
$136$	−9.02245	−	10.4125i	−0.773669	−	0.892861i
$137$	7.93600	−	17.3774i	0.678018	−	1.48465i	−0.186711	−	0.982415i	$-0.559783\pi$
$137$	7.93600	−	17.3774i	0.678018	−	1.48465i	0.864729	−	0.502238i	$-0.167490\pi$
$138$		0			0
$139$	−8.42455	−	2.47367i	−0.714561	−	0.209814i	−0.0958083	−	0.995400i	$-0.530544\pi$
$139$	−8.42455	−	2.47367i	−0.714561	−	0.209814i	−0.618753	+	0.785586i	$0.712362\pi$
$140$	−0.0674960	+	0.0198186i	−0.00570445	+	0.00167498i
$141$		0			0
$142$	3.09229	−	1.98730i	0.259499	−	0.166770i
$143$	2.75757	+	3.18240i	0.230599	+	0.266126i
$144$		0			0
$145$	−2.26024	−	0.663666i	−0.187703	−	0.0551145i
$146$	12.8102	+	8.23260i	1.06018	+	0.681335i
$147$		0			0
$148$	0.0108223	−	0.0752704i	0.000889584	−	0.00618719i
$149$	−2.26300	+	2.61164i	−0.185392	+	0.213954i	−0.840836	−	0.541290i	$-0.817936\pi$
$149$	−2.26300	+	2.61164i	−0.185392	+	0.213954i	0.655444	+	0.755244i	$0.272482\pi$
$150$		0			0
$151$	−3.05669	−	21.2598i	−0.248750	−	1.73010i	−0.605456	−	0.795879i	$-0.707009\pi$
$151$	−3.05669	−	21.2598i	−0.248750	−	1.73010i	0.356706	−	0.934217i	$-0.383900\pi$
$152$	2.09402	−	14.5642i	0.169848	−	1.18132i
$153$		0			0
$154$	1.65238	−	3.61821i	0.133153	−	0.291563i
$155$	−0.380108	+	0.111610i	−0.0305310	+	0.00896472i
$156$		0			0
$157$	4.71569	−	10.3259i	0.376353	−	0.824098i	−0.622777	−	0.782399i	$-0.713996\pi$
$157$	4.71569	−	10.3259i	0.376353	−	0.824098i	0.999130	−	0.0416991i	$-0.0132771\pi$
$158$	0.127475	+	0.886605i	0.0101413	+	0.0705345i
$159$		0			0
$160$	0.0287523	+	0.199977i	0.00227307	+	0.0158096i
$161$	−10.5009	+	3.08334i	−0.827586	+	0.243001i
$162$		0			0
$163$	−0.815436			−0.0638699			−0.0319349	−	0.999490i	$-0.510167\pi$
$163$	−0.815436			−0.0638699			−0.0319349	+	0.999490i	$0.510167\pi$
$164$	−0.929164			−0.0725556
$165$		0			0
$166$	3.93163	+	8.60908i	0.305154	+	0.668194i
$167$	3.83962	−	4.43116i	0.297119	−	0.342893i	−0.587487	−	0.809234i	$-0.699883\pi$
$167$	3.83962	−	4.43116i	0.297119	−	0.342893i	0.884605	+	0.466341i	$0.154428\pi$
$168$		0			0
$169$	−2.00527	−	4.39093i	−0.154252	−	0.337764i
$170$	1.69695	−	1.09056i	0.130150	−	0.0836424i
$171$		0			0
$172$	1.41189			0.107656
$173$	−12.6857	+	8.15258i	−0.964473	+	0.619829i	−0.925232	−	0.379401i	$-0.876130\pi$
$173$	−12.6857	+	8.15258i	−0.964473	+	0.619829i	−0.0392402	+	0.999230i	$0.512494\pi$
$174$		0			0
$175$	1.37291	+	9.54879i	0.103782	+	0.721821i
$176$	−4.65387	−	2.99086i	−0.350798	−	0.225444i
$177$		0			0
$178$	−4.19152	+	9.17816i	−0.314168	+	0.687932i
$179$	3.79980	+	8.32041i	0.284011	+	0.621897i	0.996840	−	0.0794413i	$-0.0253136\pi$
$179$	3.79980	+	8.32041i	0.284011	+	0.621897i	−0.712829	+	0.701338i	$0.752586\pi$
$180$		0			0
$181$	3.54479	−	7.76200i	0.263482	−	0.576945i	−0.730937	−	0.682445i	$-0.760917\pi$
$181$	3.54479	−	7.76200i	0.263482	−	0.576945i	0.994419	+	0.105499i	$0.0336441\pi$
$182$	5.05560	−	5.83448i	0.374746	−	0.432480i
$183$		0			0
$184$	2.29936	+	15.9924i	0.169511	+	1.17898i
$185$	0.195727	+	0.0574706i	0.0143901	+	0.00422532i
$186$		0			0
$187$	0.994509	−	6.91696i	0.0727257	−	0.505818i
$188$	0.959081	+	0.616364i	0.0699481	+	0.0449529i
$189$		0			0
$190$	2.06699	+	0.606924i	0.149956	+	0.0440309i
$191$	3.20128	+	7.00982i	0.231636	+	0.507213i	0.989382	−	0.145337i	$-0.0464267\pi$
$191$	3.20128	+	7.00982i	0.231636	+	0.507213i	−0.757746	+	0.652550i	$0.773699\pi$
$192$		0			0
$193$	−19.6250	+	12.6122i	−1.41264	+	0.907848i	−0.999995	−	0.00304370i	$-0.999031\pi$
$193$	−19.6250	+	12.6122i	−1.41264	+	0.907848i	−0.412644	+	0.910892i	$0.635395\pi$
$194$	−7.17091	−	8.27567i	−0.514841	−	0.594158i
$195$		0			0
$196$	−0.346791	−	0.101827i	−0.0247708	−	0.00727337i
$197$	0.945050	−	6.57297i	0.0673320	−	0.468304i	−0.928061	−	0.372428i	$-0.878525\pi$
$197$	0.945050	−	6.57297i	0.0673320	−	0.468304i	0.995393	−	0.0958767i	$-0.0305655\pi$
$198$		0			0
$199$	0.265938	+	0.306909i	0.0188519	+	0.0217562i	0.765097	−	0.643915i	$-0.222691\pi$
$199$	0.265938	+	0.306909i	0.0188519	+	0.0217562i	−0.746245	+	0.665671i	$0.768145\pi$
$200$	14.2418			1.00705
$201$		0			0
$202$	−23.4720			−1.65148
$203$	9.79772	+	11.3072i	0.687665	+	0.793608i
$204$		0			0
$205$	0.354718	−	2.46712i	0.0247746	−	0.172311i
$206$	−7.00548	−	2.05699i	−0.488095	−	0.143318i
$207$		0			0
$208$	−7.03125	−	8.11449i	−0.487529	−	0.562639i
$209$	6.27828	−	4.03480i	0.434278	−	0.279093i
$210$		0			0
$211$	0.997056	+	2.18325i	0.0686402	+	0.150301i	0.940842	−	0.338844i	$-0.110036\pi$
$211$	0.997056	+	2.18325i	0.0686402	+	0.150301i	−0.872202	+	0.489145i	$0.837309\pi$
$212$	0.241139	+	0.0708049i	0.0165615	+	0.00486290i
$213$		0			0
$214$	15.8307	+	10.1738i	1.08216	+	0.695464i
$215$	−0.539005	+	3.74886i	−0.0367599	+	0.255670i
$216$		0			0
$217$	2.41419	+	0.708869i	0.163886	+	0.0481212i
$218$	−2.11256	−	14.6932i	−0.143081	−	0.995148i
$219$		0			0
$220$	−0.0344938	+	0.0398080i	−0.00232557	+	0.00268385i
$221$	5.63426	−	12.3373i	0.379001	−	0.829897i
$222$		0			0
$223$	4.11436	+	9.00920i	0.275518	+	0.603300i	0.995918	−	0.0902580i	$-0.0287692\pi$
$223$	4.11436	+	9.00920i	0.275518	+	0.603300i	−0.720400	+	0.693558i	$0.756042\pi$
$224$	0.533050	−	1.16722i	0.0356159	−	0.0779880i
$225$		0			0
$226$	−2.06627	−	1.32791i	−0.137446	−	0.0883312i
$227$	1.78475	+	12.4132i	0.118458	+	0.823895i	0.959254	+	0.282544i	$0.0911782\pi$
$227$	1.78475	+	12.4132i	0.118458	+	0.823895i	−0.840796	+	0.541352i	$0.817913\pi$
$228$		0			0
$229$	3.43471	−	2.20736i	0.226972	−	0.145866i	−0.422213	−	0.906497i	$-0.638746\pi$
$229$	3.43471	−	2.20736i	0.226972	−	0.145866i	0.649185	+	0.760631i	$0.275110\pi$
$230$	−2.36550			−0.155977
$231$		0			0
$232$	18.5813	−	11.9415i	1.21992	−	0.783996i
$233$	2.76172	+	6.04733i	0.180926	+	0.396173i	0.978265	−	0.207359i	$-0.0664867\pi$
$233$	2.76172	+	6.04733i	0.180926	+	0.396173i	−0.797339	+	0.603532i	$0.793759\pi$
$234$		0			0
$235$	−2.00271	+	2.31125i	−0.130642	+	0.150769i
$236$	0.172699	+	0.378159i	0.0112418	+	0.0246161i
$237$		0			0
$238$	−12.8117			−0.830457
$239$	−9.76989			−0.631962			−0.315981	−	0.948766i	$-0.602334\pi$
$239$	−9.76989			−0.631962			−0.315981	+	0.948766i	$0.602334\pi$
$240$		0			0
$241$	21.8958	−	6.42918i	1.41043	−	0.414140i	0.514179	−	0.857683i	$-0.328097\pi$
$241$	21.8958	−	6.42918i	1.41043	−	0.414140i	0.896253	+	0.443543i	$0.146279\pi$
$242$	1.72517	+	11.9989i	0.110898	+	0.771315i
$243$		0			0
$244$	−0.140498	−	0.977183i	−0.00899445	−	0.0625577i
$245$	0.402763	−	0.881928i	0.0257316	−	0.0563443i
$246$		0			0
$247$	13.8980	−	4.08082i	0.884308	−	0.259656i
$248$	1.54306	−	3.37884i	0.0979847	−	0.214557i
$249$		0			0
$250$	−0.599291	+	4.16816i	−0.0379025	+	0.263618i
$251$	0.00841847	+	0.0585517i	0.000531369	+	0.00369575i	0.990085	−	0.140467i	$-0.0448603\pi$
$251$	0.00841847	+	0.0585517i	0.000531369	+	0.00369575i	−0.989554	+	0.144162i	$0.953951\pi$
$252$		0			0
$253$	−5.36647	+	6.19324i	−0.337387	+	0.389366i
$254$	−3.43226	+	23.8719i	−0.215359	+	1.49785i
$255$		0			0
$256$	−2.32322	−	1.49304i	−0.145201	−	0.0933153i
$257$	−8.95774	−	2.63023i	−0.558768	−	0.164069i	−0.00985941	−	0.999951i	$-0.503138\pi$
$257$	−8.95774	−	2.63023i	−0.558768	−	0.164069i	−0.548909	+	0.835882i	$0.684957\pi$
$258$		0			0
$259$	−0.848439	−	0.979151i	−0.0527194	−	0.0608415i
$260$	−0.0860033	+	0.0552710i	−0.00533370	+	0.00342776i
$261$		0			0
$262$	−20.6261	+	6.05638i	−1.27429	+	0.374165i
$263$	−16.9296	−	4.97099i	−1.04393	−	0.306524i	−0.285565	−	0.958359i	$-0.592181\pi$
$263$	−16.9296	−	4.97099i	−1.04393	−	0.306524i	−0.758361	+	0.651835i	$0.773999\pi$
$264$		0			0
$265$	−0.280059	+	0.613243i	−0.0172039	+	0.0376712i
$266$	−8.96003	−	10.3404i	−0.549375	−	0.634012i
$267$		0			0
$268$	−0.378608	+	0.865927i	−0.0231272	+	0.0528949i
$269$	−4.28594			−0.261319			−0.130659	−	0.991427i	$-0.541709\pi$
$269$	−4.28594			−0.261319			−0.130659	+	0.991427i	$0.541709\pi$
$270$		0			0
$271$	−8.48281	+	18.5748i	−0.515294	+	1.12834i	0.455896	+	0.890033i	$0.349319\pi$
$271$	−8.48281	+	18.5748i	−0.515294	+	1.12834i	−0.971191	+	0.238304i	$0.923409\pi$
$272$	−2.53580	+	17.6369i	−0.153755	+	1.06939i
$273$		0			0
$274$	−25.1631	+	7.38855i	−1.52016	+	0.446359i
$275$	4.73038	+	5.45915i	0.285253	+	0.329199i
$276$		0			0
$277$	19.0951	+	22.0369i	1.14731	+	1.32407i	0.938167	+	0.346182i	$0.112522\pi$
$277$	19.0951	+	22.0369i	1.14731	+	1.32407i	0.209143	+	0.977885i	$0.432933\pi$
$278$	5.00714	+	10.9641i	0.300308	+	0.657584i
$279$		0			0
$280$	1.48847	+	0.956582i	0.0889531	+	0.0571667i
$281$	1.64009	+	1.05402i	0.0978397	+	0.0628778i	0.588646	−	0.808391i	$-0.299661\pi$
$281$	1.64009	+	1.05402i	0.0978397	+	0.0628778i	−0.490806	+	0.871269i	$0.663298\pi$
$282$		0			0
$283$	13.8328	−	15.9638i	0.822272	−	0.948952i	−0.177107	−	0.984192i	$-0.556674\pi$
$283$	13.8328	−	15.9638i	0.822272	−	0.948952i	0.999379	+	0.0352394i	$0.0112194\pi$
$284$	0.296636	+	0.0871001i	0.0176021	+	0.00516844i
$285$		0			0
$286$	0.822678	−	5.72185i	0.0486460	−	0.338340i
$287$	−10.3668	+	11.9640i	−0.611934	+	0.706210i
$288$		0			0
$289$	−5.28486	+	1.55177i	−0.310874	+	0.0912808i
$290$	1.34338	+	2.94158i	0.0788858	+	0.172736i
$291$		0			0
$292$	0.182266	+	1.26769i	0.0106663	+	0.0741859i
$293$	22.8771	+	14.7022i	1.33650	+	0.858914i	0.996667	−	0.0815730i	$-0.0259944\pi$
$293$	22.8771	+	14.7022i	1.33650	+	0.858914i	0.339829	+	0.940487i	$0.389631\pi$
$294$		0			0
$295$	−1.07002	+	0.314186i	−0.0622989	+	0.0182926i
$296$	−1.60906	+	1.03408i	−0.0935246	+	0.0601046i
$297$		0			0
$298$	4.74393			0.274808
$299$	−13.3802	+	8.59895i	−0.773798	+	0.497290i
$300$		0			0
$301$	15.7527	−	18.1796i	0.907970	−	1.04785i
$302$	−19.3087	+	22.2834i	−1.11109	+	1.28227i
$303$		0			0
$304$	−16.0084	+	10.2880i	−0.918143	+	0.590054i
$305$	2.64826			0.151639
$306$		0			0
$307$	−18.9009	+	12.1469i	−1.07873	+	0.693259i	−0.954264	−	0.298965i	$-0.903359\pi$
$307$	−18.9009	+	12.1469i	−1.07873	+	0.693259i	−0.124467	+	0.992224i	$0.539722\pi$
$308$	0.320994	−	0.0942524i	0.0182903	−	0.00537053i
$309$		0			0
$310$	0.457504	+	0.294020i	0.0259845	+	0.0166992i
$311$	1.42786	+	9.93096i	0.0809663	+	0.563133i	0.989412	+	0.145131i	$0.0463604\pi$
$311$	1.42786	+	9.93096i	0.0809663	+	0.563133i	−0.908446	+	0.418002i	$0.862731\pi$
$312$		0			0
$313$	5.45925	+	11.9541i	0.308575	+	0.675685i	0.998854	−	0.0478579i	$-0.0152395\pi$
$313$	5.45925	+	11.9541i	0.308575	+	0.675685i	−0.690279	+	0.723543i	$0.742512\pi$
$314$	−14.9523	+	4.39039i	−0.843806	+	0.247764i
$315$		0			0
$316$	−0.0493344	+	0.0569350i	−0.00277528	+	0.00320284i
$317$	2.24632	−	15.6235i	0.126166	−	0.877502i	−0.824185	−	0.566321i	$-0.808366\pi$
$317$	2.24632	−	15.6235i	0.126166	−	0.877502i	0.950351	−	0.311181i	$-0.100725\pi$
$318$		0			0
$319$	10.7491	+	3.15623i	0.601836	+	0.176715i
$320$	1.70514	−	1.96784i	0.0953202	−	0.110005i
$321$		0			0
$322$	12.6390	+	8.12261i	0.704346	+	0.452656i
$323$	−20.2217	−	12.9957i	−1.12517	−	0.723101i
$324$		0			0
$325$	5.82406	+	12.7529i	0.323061	+	0.707404i
$326$	0.733063	+	0.846000i	0.0406006	+	0.0468556i
$327$		0			0
$328$	15.3045	+	17.6623i	0.845048	+	0.975238i
$329$	18.6369	−	5.47229i	1.02749	−	0.301697i
$330$		0			0
$331$	3.18994	−	22.1865i	0.175335	−	1.21948i	−0.692052	−	0.721848i	$-0.743293\pi$
$331$	3.18994	−	22.1865i	0.175335	−	1.21948i	0.867387	−	0.497635i	$-0.165798\pi$
$332$	−0.330675	+	0.724076i	−0.0181481	+	0.0397389i
$333$		0			0
$334$	−8.04900			−0.440422
$335$	−2.15467	−	1.33586i	−0.117722	−	0.0729857i
$336$		0			0
$337$	5.34982	+	6.17402i	0.291423	+	0.336321i	0.882515	−	0.470284i	$-0.155848\pi$
$337$	5.34982	+	6.17402i	0.291423	+	0.336321i	−0.591092	+	0.806604i	$0.701303\pi$
$338$	−2.75281	+	6.02781i	−0.149733	+	0.327870i
$339$		0			0
$340$	0.162784	+	0.0477977i	0.00882820	+	0.00259219i
$341$	1.80770	−	0.530789i	0.0978925	−	0.0287438i
$342$		0			0
$343$	−16.7644	+	10.7738i	−0.905190	+	0.581730i
$344$	−23.2556	−	26.8384i	−1.25386	−	1.44703i
$345$		0			0
$346$	19.8623	+	5.83211i	1.06781	+	0.313536i
$347$	17.3406	+	11.1441i	0.930892	+	0.598248i	0.915798	−	0.401638i	$-0.131559\pi$
$347$	17.3406	+	11.1441i	0.930892	+	0.598248i	0.0150935	+	0.999886i	$0.495195\pi$
$348$		0			0
$349$	−2.66789	+	18.5556i	−0.142809	+	0.993259i	0.784811	+	0.619735i	$0.212760\pi$
$349$	−2.66789	+	18.5556i	−0.142809	+	0.993259i	−0.927620	+	0.373524i	$0.878149\pi$
$350$	8.67248	−	10.0086i	0.463563	−	0.534981i
$351$		0			0
$352$	−0.136739	−	0.951040i	−0.00728821	−	0.0506906i
$353$	−2.81503	+	19.5790i	−0.149829	+	1.04208i	0.766668	+	0.642044i	$0.221913\pi$
$353$	−2.81503	+	19.5790i	−0.149829	+	1.04208i	−0.916497	+	0.400041i	$0.868996\pi$
$354$		0			0
$355$	−0.344512	+	0.754376i	−0.0182848	+	0.0400381i
$356$	−0.814253	+	0.239086i	−0.0431553	+	0.0126715i
$357$		0			0
$358$	5.21632	−	11.4221i	0.275691	−	0.603679i
$359$	−1.18423	−	8.23652i	−0.0625014	−	0.434707i	−0.996913	−	0.0785121i	$-0.974983\pi$
$359$	−1.18423	−	8.23652i	−0.0625014	−	0.434707i	0.934412	−	0.356195i	$-0.115926\pi$
$360$		0			0
$361$	−0.949416	−	6.60334i	−0.0499693	−	0.347544i
$362$	−11.2396	+	3.30026i	−0.590743	+	0.173458i
$363$		0			0
$364$	0.649309			0.0340331
$365$	−3.43555			−0.179825
$366$		0			0
$367$	0.358924	+	0.785933i	0.0187357	+	0.0410254i	0.918769	−	0.394797i	$-0.129185\pi$
$367$	0.358924	+	0.785933i	0.0187357	+	0.0410254i	−0.900033	+	0.435822i	$0.856458\pi$
$368$	13.6834	−	15.7915i	0.713299	−	0.823190i
$369$		0			0
$370$	−0.116330	−	0.254728i	−0.00604773	−	0.0132427i
$371$	3.60211	−	2.31494i	0.187012	−	0.120186i
$372$		0			0
$373$	−28.9962			−1.50137			−0.750683	−	0.660663i	$-0.770275\pi$
$373$	−28.9962			−1.50137			−0.750683	+	0.660663i	$0.770275\pi$
$374$	−8.07027	+	5.18645i	−0.417304	+	0.268185i
$375$		0			0
$376$	−4.08090	−	28.3833i	−0.210456	−	1.46375i
$377$	18.2917	+	11.7554i	0.942072	+	0.605433i
$378$		0			0
$379$	−7.82043	+	17.1243i	−0.401708	+	0.879618i	0.595386	+	0.803440i	$0.296999\pi$
$379$	−7.82043	+	17.1243i	−0.401708	+	0.879618i	−0.997094	+	0.0761785i	$0.975728\pi$
$380$	0.0752675	+	0.164813i	0.00386114	+	0.00845472i
$381$		0			0
$382$	4.39467	−	9.62298i	0.224851	−	0.492354i
$383$	−23.2068	+	26.7821i	−1.18581	+	1.36850i	−0.272037	+	0.962287i	$0.587697\pi$
$383$	−23.2068	+	26.7821i	−1.18581	+	1.36850i	−0.913777	+	0.406215i	$0.866848\pi$
$384$		0			0
$385$	0.127716	+	0.888286i	0.00650903	+	0.0452713i
$386$	30.7275	+	9.02242i	1.56399	+	0.459229i
$387$		0			0
$388$	0.131070	−	0.911611i	0.00665407	−	0.0462801i
$389$	−3.25735	−	2.09337i	−0.165154	−	0.106138i	0.455453	−	0.890260i	$-0.349477\pi$
$389$	−3.25735	−	2.09337i	−0.165154	−	0.106138i	−0.620607	+	0.784122i	$0.713114\pi$
$390$		0			0
$391$	25.3256	+	7.43627i	1.28077	+	0.376068i
$392$	3.77647	+	8.26931i	0.190740	+	0.417663i
$393$		0			0
$394$	−7.66892	+	4.92852i	−0.386355	+	0.248295i
$395$	−0.132340	−	0.152728i	−0.00665875	−	0.00768460i
$396$		0			0
$397$	−18.4816	−	5.42669i	−0.927566	−	0.272358i	−0.217148	−	0.976139i	$-0.569676\pi$
$397$	−18.4816	−	5.42669i	−0.927566	−	0.272358i	−0.710417	+	0.703781i	$0.751494\pi$
$398$	0.0793387	−	0.551813i	0.00397689	−	0.0276599i
$399$		0			0
$400$	−12.0615	−	13.9198i	−0.603077	−	0.695988i
$401$	−13.3667			−0.667500			−0.333750	−	0.942662i	$-0.608314\pi$
$401$	−13.3667			−0.667500			−0.333750	+	0.942662i	$0.608314\pi$
$402$		0			0
$403$	3.65663			0.182150
$404$	−1.29279	−	1.49195i	−0.0643185	−	0.0742275i
$405$		0			0
$406$	2.92300	−	20.3299i	0.145066	−	1.00896i
$407$	−0.930828	−	0.273316i	−0.0461394	−	0.0135478i
$408$		0			0
$409$	−14.4840	−	16.7155i	−0.716189	−	0.826527i	0.274654	−	0.961543i	$-0.411437\pi$
$409$	−14.4840	−	16.7155i	−0.716189	−	0.826527i	−0.990843	+	0.135017i	$0.956891\pi$
$410$	−2.87848	+	1.84989i	−0.142158	+	0.0913594i
$411$		0			0
$412$	−0.255097	−	0.558585i	−0.0125677	−	0.0275195i
$413$	6.79602	+	1.99549i	0.334410	+	0.0981917i
$414$		0			0
$415$	−1.79633	−	1.15443i	−0.0881784	−	0.0566688i
$416$	0.265392	−	1.84584i	0.0130119	−	0.0905000i
$417$		0			0
$418$	−9.83011	−	2.88638i	−0.480806	−	0.141177i
$419$	−1.54310	−	10.7325i	−0.0753853	−	0.524316i	−0.992166	−	0.124926i	$-0.960131\pi$
$419$	−1.54310	−	10.7325i	−0.0753853	−	0.524316i	0.916781	−	0.399391i	$-0.130778\pi$
$420$		0			0
$421$	−7.48552	+	8.63875i	−0.364822	+	0.421027i	−0.908249	−	0.418429i	$-0.862581\pi$
$421$	−7.48552	+	8.63875i	−0.364822	+	0.421027i	0.543428	+	0.839456i	$0.317126\pi$
$422$	1.36874	−	2.99713i	0.0666294	−	0.145898i
$423$		0			0
$424$	−2.62594	−	5.75002i	−0.127527	−	0.279245i
$425$	9.66512	−	21.1637i	0.468827	−	1.02659i
$426$		0			0
$427$	−14.1498	−	9.09352i	−0.684757	−	0.440066i
$428$	0.225243	+	1.56660i	0.0108875	+	0.0757243i
$429$		0			0
$430$	4.37394	−	2.81096i	0.210930	−	0.135556i
$431$	19.9947			0.963112			0.481556	−	0.876415i	$-0.340072\pi$
$431$	19.9947			0.963112			0.481556	+	0.876415i	$0.340072\pi$
$432$		0			0
$433$	33.7267	−	21.6749i	1.62080	−	1.04163i	0.665331	−	0.746548i	$-0.268290\pi$
$433$	33.7267	−	21.6749i	1.62080	−	1.04163i	0.955473	−	0.295079i	$-0.0953461\pi$
$434$	−1.43487	−	3.14194i	−0.0688762	−	0.150818i
$435$		0			0
$436$	0.817590	−	0.943550i	0.0391555	−	0.0451878i
$437$	11.7100	+	25.6412i	0.560163	+	1.22659i
$438$		0			0
$439$	−7.24472			−0.345772			−0.172886	−	0.984942i	$-0.555309\pi$
$439$	−7.24472			−0.345772			−0.172886	+	0.984942i	$0.555309\pi$
$440$	1.32486			0.0631601
$441$		0			0
$442$	−17.8648	+	5.24559i	−0.849744	+	0.249507i
$443$	−3.97613	−	27.6546i	−0.188912	−	1.31391i	−0.834832	−	0.550505i	$-0.814435\pi$
$443$	−3.97613	−	27.6546i	−0.188912	−	1.31391i	0.645920	−	0.763405i	$-0.276474\pi$
$444$		0			0
$445$	−0.323973	−	2.25328i	−0.0153578	−	0.106816i
$446$	5.64814	−	12.3677i	0.267447	−	0.585627i
$447$		0			0
$448$	−15.8678	+	4.65920i	−0.749682	+	0.220127i
$449$	15.6715	−	34.3158i	0.739583	−	1.61946i	−0.0446564	−	0.999002i	$-0.514219\pi$
$449$	15.6715	−	34.3158i	0.739583	−	1.61946i	0.784239	−	0.620458i	$-0.213053\pi$
$450$		0			0
$451$	−1.68695	+	11.7330i	−0.0794354	+	0.552486i
$452$	−0.0293993	−	0.204477i	−0.00138283	−	0.00961778i
$453$		0			0
$454$	11.2740	−	13.0109i	0.529117	−	0.610634i
$455$	−0.247881	+	1.72405i	−0.0116208	+	0.0808246i
$456$		0			0
$457$	−5.47150	−	3.51632i	−0.255946	−	0.164486i	0.406376	−	0.913706i	$-0.366792\pi$
$457$	−5.47150	−	3.51632i	−0.255946	−	0.164486i	−0.662322	+	0.749220i	$0.730429\pi$
$458$	−5.37784	−	1.57908i	−0.251290	−	0.0737854i
$459$		0			0
$460$	−0.130287	−	0.150359i	−0.00607465	−	0.00701052i
$461$	−7.27332	+	4.67428i	−0.338752	+	0.217703i	−0.698946	−	0.715175i	$-0.746347\pi$
$461$	−7.27332	+	4.67428i	−0.338752	+	0.217703i	0.360193	+	0.932878i	$0.382711\pi$
$462$		0			0
$463$	−10.7360	+	3.15238i	−0.498945	+	0.146503i	−0.521515	−	0.853242i	$-0.674633\pi$
$463$	−10.7360	+	3.15238i	−0.498945	+	0.146503i	0.0225708	+	0.999745i	$0.492815\pi$
$464$	−27.4082	−	8.04776i	−1.27239	−	0.373608i
$465$		0			0
$466$	3.79125	−	8.30168i	0.175626	−	0.384568i
$467$	−12.3091	−	14.2055i	−0.569597	−	0.657350i	0.395738	−	0.918363i	$-0.370489\pi$
$467$	−12.3091	−	14.2055i	−0.569597	−	0.657350i	−0.965335	+	0.261013i	$0.915943\pi$
$468$		0			0
$469$	6.92551	+	14.5362i	0.319791	+	0.671221i
$470$	4.19828			0.193652
$471$		0			0
$472$	4.34378	−	9.51156i	0.199939	−	0.437805i
$473$	2.56337	−	17.8287i	0.117864	−	0.819763i
$474$		0			0
$475$	23.8409	−	7.00031i	1.09389	−	0.321196i
$476$	−0.705638	−	0.814350i	−0.0323429	−	0.0373257i
$477$		0			0
$478$	8.78297	+	10.1361i	0.401724	+	0.463614i
$479$	12.6555	+	27.7116i	0.578243	+	1.26617i	0.942291	+	0.334795i	$0.108667\pi$
$479$	12.6555	+	27.7116i	0.578243	+	1.26617i	−0.364048	+	0.931380i	$0.618606\pi$
$480$		0			0
$481$	−1.58398	−	1.01796i	−0.0722234	−	0.0464152i
$482$	−26.3541	−	16.9368i	−1.20040	−	0.771448i
$483$		0			0
$484$	−0.667666	+	0.770528i	−0.0303485	+	0.0350240i
$485$	2.37048	+	0.696035i	0.107638	+	0.0316053i
$486$		0			0
$487$	−1.07331	+	7.46504i	−0.0486363	+	0.338273i	0.950946	+	0.309358i	$0.100114\pi$
$487$	−1.07331	+	7.46504i	−0.0486363	+	0.338273i	−0.999582	+	0.0289148i	$0.990795\pi$
$488$	−16.2609	+	18.7661i	−0.736097	+	0.849502i
$489$		0			0
$490$	−1.27706	+	0.374979i	−0.0576918	+	0.0169398i
$491$	2.86495	+	6.27337i	0.129293	+	0.283113i	0.963197	−	0.268797i	$-0.0866262\pi$
$491$	2.86495	+	6.27337i	0.129293	+	0.283113i	−0.833903	+	0.551911i	$0.813899\pi$
$492$		0			0
$493$	−5.13523	−	35.7163i	−0.231279	−	1.60858i
$494$	−16.7278	−	10.7503i	−0.752621	−	0.483680i
$495$		0			0
$496$	−4.60928	+	1.35341i	−0.206963	+	0.0607697i
$497$	4.43111	−	2.84770i	0.198762	−	0.127737i
$498$		0			0
$499$	−20.5980			−0.922092			−0.461046	−	0.887376i	$-0.652526\pi$
$499$	−20.5980			−0.922092			−0.461046	+	0.887376i	$0.652526\pi$
$500$	−0.297949	+	0.191480i	−0.0133247	+	0.00856327i
$501$		0			0
$502$	0.0531783	−	0.0613711i	0.00237346	−	0.00273912i
$503$	20.4803	−	23.6355i	0.913172	−	1.05386i	−0.0851745	−	0.996366i	$-0.527145\pi$
$503$	20.4803	−	23.6355i	0.913172	−	1.05386i	0.998346	−	0.0574901i	$-0.0183098\pi$
$504$		0			0
$505$	4.45498	−	2.86304i	0.198244	−	0.127404i
$506$	11.2497			0.500112
$507$		0			0
$508$	−1.70641	+	1.09664i	−0.0757098	+	0.0486557i
$509$	6.70679	−	1.96929i	0.297273	−	0.0872873i	−0.129695	−	0.991554i	$-0.541400\pi$
$509$	6.70679	−	1.96929i	0.297273	−	0.0872873i	0.426968	+	0.904267i	$0.359582\pi$
$510$		0			0
$511$	18.3564	+	11.7969i	0.812038	+	0.521865i
$512$	3.45310	+	24.0169i	0.152607	+	1.06141i
$513$		0			0
$514$	5.32404	+	11.6580i	0.234833	+	0.514213i
$515$	1.58054	−	0.464090i	0.0696471	−	0.0204502i
$516$		0			0
$517$	9.52439	−	10.9917i	0.418882	−	0.483416i
$518$	−0.253119	+	1.76048i	−0.0111214	+	0.0773511i
$519$		0			0
$520$	2.46722	+	0.724440i	0.108195	+	0.0317688i
$521$	−1.92613	+	2.22288i	−0.0843854	+	0.0973860i	−0.796372	−	0.604807i	$-0.793250\pi$
$521$	−1.92613	+	2.22288i	−0.0843854	+	0.0973860i	0.711987	+	0.702193i	$0.247796\pi$
$522$		0			0
$523$	5.86196	+	3.76725i	0.256325	+	0.164730i	0.662493	−	0.749068i	$-0.269499\pi$
$523$	5.86196	+	3.76725i	0.256325	+	0.164730i	−0.406167	+	0.913799i	$0.633135\pi$
$524$	−1.52101	−	0.977491i	−0.0664454	−	0.0427019i
$525$		0			0
$526$	10.0621	+	22.0330i	0.438730	+	0.960686i
$527$	−3.97385	−	4.58607i	−0.173104	−	0.199772i
$528$		0			0
$529$	−5.20795	−	6.01030i	−0.226433	−	0.261317i
$530$	0.887997	−	0.260740i	0.0385721	−	0.0113258i
$531$		0			0
$532$	0.163772	−	1.13906i	0.00710040	−	0.0493844i
$533$	−9.55721	+	20.9274i	−0.413969	+	0.906465i
$534$		0			0
$535$	−4.24562			−0.183554
$536$	22.6964	−	7.06599i	0.980334	−	0.305204i
$537$		0			0
$538$	3.85299	+	4.44659i	0.166114	+	0.191706i
$539$	−1.91544	+	4.19423i	−0.0825038	+	0.180658i
$540$		0			0
$541$	13.1987	+	3.87550i	0.567458	+	0.166621i	0.552862	−	0.833273i	$-0.313536\pi$
$541$	13.1987	+	3.87550i	0.567458	+	0.166621i	0.0145960	+	0.999893i	$0.495354\pi$
$542$	26.8969	−	7.89764i	1.15532	−	0.339233i
$543$		0			0
$544$	−2.60343	+	1.67313i	−0.111621	+	0.0717347i
$545$	2.19319	+	2.53108i	0.0939460	+	0.108419i
$546$		0			0
$547$	−25.0032	−	7.34161i	−1.06906	−	0.313905i	−0.300566	−	0.953761i	$-0.597176\pi$
$547$	−25.0032	−	7.34161i	−1.06906	−	0.313905i	−0.768495	+	0.639856i	$0.778994\pi$
$548$	−1.85557	−	1.19250i	−0.0792659	−	0.0509411i
$549$		0			0
$550$	1.41124	−	9.81537i	0.0601754	−	0.418529i
$551$	25.2356	−	29.1234i	1.07507	−	1.24070i
$552$		0			0
$553$	0.182665	+	1.27046i	0.00776771	+	0.0540256i
$554$	5.69672	−	39.6216i	0.242030	−	1.68336i
$555$		0			0
$556$	−0.421131	+	0.922149i	−0.0178599	+	0.0391078i
$557$	19.4318	−	5.70570i	0.823353	−	0.241758i	0.157194	−	0.987568i	$-0.449755\pi$
$557$	19.4318	−	5.70570i	0.823353	−	0.241758i	0.666159	+	0.745810i	$0.267937\pi$
$558$		0			0
$559$	14.5225	−	31.7998i	0.614235	−	1.34499i
$560$	−0.325651	−	2.26495i	−0.0137613	−	0.0957118i
$561$		0			0
$562$	−0.380885	−	2.64912i	−0.0160667	−	0.111746i
$563$	5.97610	−	1.75474i	0.251863	−	0.0739536i	−0.153364	−	0.988170i	$-0.549011\pi$
$563$	5.97610	−	1.75474i	0.251863	−	0.0739536i	0.405227	+	0.914216i	$0.367193\pi$
$564$		0			0
$565$	0.554151			0.0233133
$566$	−28.9976			−1.21886
$567$		0			0
$568$	−3.23028	−	7.07333i	−0.135540	−	0.296791i
$569$	−14.9253	+	17.2247i	−0.625701	+	0.722098i	−0.976779	−	0.214249i	$-0.931270\pi$
$569$	−14.9253	+	17.2247i	−0.625701	+	0.722098i	0.351078	+	0.936346i	$0.385815\pi$
$570$		0			0
$571$	12.1334	+	26.5685i	0.507768	+	1.11186i	0.973866	+	0.227123i	$0.0729321\pi$
$571$	12.1334	+	26.5685i	0.507768	+	1.11186i	−0.466098	+	0.884733i	$0.654341\pi$
$572$	0.409010	−	0.262855i	0.0171016	−	0.0109905i
$573$		0			0
$574$	21.7320			0.907076
$575$	−22.9527	+	14.7508i	−0.957193	+	0.615151i
$576$		0			0
$577$	−3.46388	−	24.0918i	−0.144203	−	1.00296i	−0.925487	−	0.378779i	$-0.876344\pi$
$577$	−3.46388	−	24.0918i	−0.144203	−	1.00296i	0.781284	−	0.624176i	$-0.214565\pi$
$578$	6.36094	+	4.08793i	0.264580	+	0.170035i
$579$		0			0
$580$	−0.112986	+	0.247405i	−0.00469150	+	0.0102729i
$581$	5.63385	+	12.3364i	0.233731	+	0.511800i
$582$		0			0
$583$	1.33189	−	2.91643i	0.0551612	−	0.120786i
$584$	21.0951	−	24.3451i	0.872922	−	1.00741i
$585$		0			0
$586$	−5.31285	−	36.9517i	−0.219472	−	1.52646i
$587$	−4.07949	−	1.19784i	−0.168378	−	0.0494404i	0.196457	−	0.980512i	$-0.437056\pi$
$587$	−4.07949	−	1.19784i	−0.168378	−	0.0494404i	−0.364835	+	0.931072i	$0.618875\pi$
$588$		0			0
$589$	0.922291	−	6.41467i	0.0380023	−	0.264312i
$590$	1.28789	+	0.827678i	0.0530217	+	0.0340749i
$591$		0			0
$592$	2.37343	+	0.696901i	0.0975472	+	0.0286424i
$593$	−9.41372	−	20.6132i	−0.386575	−	0.846482i	−0.998457	−	0.0555324i	$-0.982314\pi$
$593$	−9.41372	−	20.6132i	−0.386575	−	0.846482i	0.611882	−	0.790949i	$-0.290413\pi$
$594$		0			0
$595$	2.43165	−	1.56273i	0.0996879	−	0.0640655i
$596$	0.261285	+	0.301539i	0.0107027	+	0.0123515i
$597$		0			0
$598$	20.9498	+	6.15143i	0.856703	+	0.251551i
$599$	−5.11405	+	35.5690i	−0.208954	+	1.45331i	0.567624	+	0.823288i	$0.307863\pi$
$599$	−5.11405	+	35.5690i	−0.208954	+	1.45331i	−0.776578	+	0.630021i	$0.783046\pi$
$600$		0			0
$601$	1.64760	+	1.90143i	0.0672070	+	0.0775610i	0.788357	−	0.615218i	$-0.210932\pi$
$601$	1.64760	+	1.90143i	0.0672070	+	0.0775610i	−0.721150	+	0.692778i	$0.756386\pi$
$602$	−33.0224			−1.34589
$603$		0			0
$604$	−2.47989			−0.100905
$605$	−1.79102	−	2.06695i	−0.0728153	−	0.0840334i
$606$		0			0
$607$	−2.71899	+	18.9110i	−0.110360	+	0.767574i	0.857209	+	0.514969i	$0.172196\pi$
$607$	−2.71899	+	18.9110i	−0.110360	+	0.767574i	−0.967569	+	0.252605i	$0.918713\pi$
$608$	−3.17115	−	0.931134i	−0.128607	−	0.0377625i
$609$		0			0
$610$	−2.38074	−	2.74752i	−0.0963933	−	0.111244i
$611$	23.7471	−	15.2614i	0.960707	−	0.617409i
$612$		0			0
$613$	15.4889	+	33.9160i	0.625592	+	1.36986i	0.911381	+	0.411563i	$0.135017\pi$
$613$	15.4889	+	33.9160i	0.625592	+	1.36986i	−0.285789	+	0.958293i	$0.592256\pi$
$614$	29.5938	+	8.68951i	1.19431	+	0.350680i
$615$		0			0
$616$	−7.07879	−	4.54926i	−0.285213	−	0.183295i
$617$	−1.32170	+	9.19262i	−0.0532096	+	0.370081i	0.945767	+	0.324846i	$0.105313\pi$
$617$	−1.32170	+	9.19262i	−0.0532096	+	0.370081i	−0.998976	+	0.0452345i	$0.985596\pi$
$618$		0			0
$619$	29.2504	+	8.58869i	1.17567	+	0.345209i	0.810504	−	0.585733i	$-0.199193\pi$
$619$	29.2504	+	8.58869i	1.17567	+	0.345209i	0.365168	+	0.930942i	$0.381011\pi$
$620$	0.00650948	+	0.0452744i	0.000261427	+	0.00181826i
$621$		0			0
$622$	9.01957	−	10.4091i	0.361652	−	0.417369i
$623$	−6.00625	+	13.1519i	−0.240636	+	0.526918i
$624$		0			0
$625$	9.79145	+	21.4403i	0.391658	+	0.857612i
$626$	7.49438	−	16.4104i	0.299536	−	0.655892i
$627$		0			0
$628$	−1.10261	−	0.708602i	−0.0439988	−	0.0282763i
$629$	0.444688	+	3.09287i	0.0177309	+	0.123321i
$630$		0			0
$631$	−16.4752	+	10.5880i	−0.655868	+	0.421501i	−0.825806	−	0.563954i	$-0.809280\pi$
$631$	−16.4752	+	10.5880i	−0.655868	+	0.421501i	0.169938	+	0.985455i	$0.445643\pi$
$632$	1.89486			0.0753737
$633$		0			0
$634$	−18.2285	+	11.7147i	−0.723945	+	0.465252i
$635$	−2.26037	−	4.94953i	−0.0897002	−	0.196416i
$636$		0			0
$637$	−5.86046	+	6.76333i	−0.232200	+	0.267973i
$638$	−6.38876	−	13.9894i	−0.252933	−	0.553847i
$639$		0			0
$640$	−3.17042			−0.125322
$641$	13.4789			0.532383			0.266192	−	0.963920i	$-0.414235\pi$
$641$	13.4789			0.532383			0.266192	+	0.963920i	$0.414235\pi$
$642$		0			0
$643$	4.97394	−	1.46048i	0.196153	−	0.0575958i	−0.182180	−	0.983265i	$-0.558315\pi$
$643$	4.97394	−	1.46048i	0.196153	−	0.0575958i	0.378333	+	0.925669i	$0.376497\pi$
$644$	0.179831	+	1.25075i	0.00708634	+	0.0492866i
$645$		0			0
$646$	4.69618	+	32.6626i	0.184769	+	1.28509i
$647$	4.39629	−	9.62653i	0.172836	−	0.378458i	−0.803314	−	0.595556i	$-0.796932\pi$
$647$	4.39629	−	9.62653i	0.172836	−	0.378458i	0.976150	+	0.217098i	$0.0696591\pi$
$648$		0			0
$649$	5.08874	−	1.49419i	0.199751	−	0.0586521i
$650$	7.99518	−	17.5070i	0.313597	−	0.686681i
$651$		0			0
$652$	−0.0133989	+	0.0931917i	−0.000524743	+	0.00364967i
$653$	5.54152	+	38.5421i	0.216856	+	1.50827i	0.749543	+	0.661956i	$0.230273\pi$
$653$	5.54152	+	38.5421i	0.216856	+	1.50827i	−0.532686	+	0.846313i	$0.678818\pi$
$654$		0			0
$655$	3.17610	−	3.66541i	0.124100	−	0.143219i
$656$	4.30139	−	29.9168i	0.167941	−	1.16806i
$657$		0			0
$658$	−22.4317	−	14.4160i	−0.874478	−	0.561993i
$659$	−8.51341	−	2.49976i	−0.331635	−	0.0973770i	0.111676	−	0.993745i	$-0.464378\pi$
$659$	−8.51341	−	2.49976i	−0.331635	−	0.0973770i	−0.443311	+	0.896368i	$0.646196\pi$
$660$		0			0
$661$	−23.3406	−	26.9365i	−0.907845	−	1.04771i	−0.998655	−	0.0518407i	$-0.983491\pi$
$661$	−23.3406	−	26.9365i	−0.907845	−	1.04771i	0.0908104	−	0.995868i	$-0.471054\pi$
$662$	−25.8858	+	16.6358i	−1.00608	+	0.646570i
$663$		0			0
$664$	19.2104	−	5.64070i	0.745510	−	0.218901i
$665$	2.96190	+	0.869694i	0.114858	+	0.0337253i
$666$		0			0
$667$	−17.5782	+	38.4908i	−0.680629	+	1.49037i
$668$	−0.443321	−	0.511620i	−0.0171526	−	0.0197952i
$669$		0			0
$670$	0.551087	+	3.43635i	0.0212903	+	0.132758i
$671$	−12.5944			−0.486203
$672$		0			0
$673$	3.52499	−	7.71864i	0.135878	−	0.297532i	−0.829445	−	0.558588i	$-0.811343\pi$
$673$	3.52499	−	7.71864i	0.135878	−	0.297532i	0.965324	+	0.261056i	$0.0840707\pi$
$674$	1.59604	−	11.1007i	0.0614771	−	0.427583i
$675$		0			0
$676$	−0.534766	+	0.157021i	−0.0205679	+	0.00603928i
$677$	−26.3439	−	30.4024i	−1.01248	−	1.16846i	−0.985647	−	0.168820i	$-0.946004\pi$
$677$	−26.3439	−	30.4024i	−1.01248	−	1.16846i	−0.0268297	−	0.999640i	$-0.508541\pi$
$678$		0			0
$679$	−10.2756	−	11.8586i	−0.394340	−	0.455093i
$680$	−1.77268	−	3.88162i	−0.0679790	−	0.148853i
$681$		0			0
$682$	−2.17578	−	1.39829i	−0.0833148	−	0.0535432i
$683$	0.0225549	+	0.0144951i	0.000863038	+	0.000554641i	0.541072	−	0.840976i	$-0.318019\pi$
$683$	0.0225549	+	0.0144951i	0.000863038	+	0.000554641i	−0.540209	+	0.841531i	$0.681655\pi$
$684$		0			0
$685$	3.87471	−	4.47166i	0.148045	−	0.170853i
$686$	26.2485	+	7.70726i	1.00217	+	0.294264i
$687$		0			0
$688$	−6.53609	+	45.4595i	−0.249186	+	1.73313i
$689$	4.07504	−	4.70284i	0.155246	−	0.179164i
$690$		0			0
$691$	−27.5473	+	8.08863i	−1.04795	+	0.307706i	−0.759989	−	0.649936i	$-0.774796\pi$
$691$	−27.5473	+	8.08863i	−1.04795	+	0.307706i	−0.287961	+	0.957642i	$0.592977\pi$
$692$	0.723267	+	1.58373i	0.0274945	+	0.0602045i
$693$		0			0
$694$	−4.02708	−	28.0089i	−0.152866	−	1.06320i
$695$	−2.28772	−	1.47023i	−0.0867782	−	0.0557690i
$696$		0			0
$697$	36.6330	−	10.7564i	1.38757	−	0.407428i
$698$	21.6495	−	13.9133i	0.819446	−	0.526626i
$699$		0			0
$700$	1.11384			0.0420991
$701$	24.5335	−	15.7667i	0.926618	−	0.595501i	0.0120472	−	0.999927i	$-0.496165\pi$
$701$	24.5335	−	15.7667i	0.926618	−	0.595501i	0.914571	+	0.404426i	$0.132529\pi$
$702$		0			0
$703$	−2.18529	+	2.52196i	−0.0824199	+	0.0951176i
$704$	−8.10922	+	9.35854i	−0.305628	+	0.352713i
$705$		0			0
$706$	22.8435	−	14.6806i	0.859727	−	0.552513i
$707$	−33.6343			−1.26495
$708$		0			0
$709$	−39.0717	+	25.1098i	−1.46737	+	0.943019i	−0.469163	+	0.883112i	$0.655444\pi$
$709$	−39.0717	+	25.1098i	−1.46737	+	0.943019i	−0.998204	+	0.0599076i	$0.980919\pi$
$710$	1.09236	−	0.320747i	0.0409956	−	0.0120374i
$711$		0			0
$712$	17.9565	+	11.5399i	0.672948	+	0.432477i
$713$	1.01273	+	7.04370i	0.0379271	+	0.263789i
$714$		0			0
$715$	0.541789	+	1.18635i	0.0202618	+	0.0443671i
$716$	1.01333	−	0.297541i	0.0378700	−	0.0111196i
$717$		0			0
$718$	−7.48063	+	8.63311i	−0.279175	+	0.322185i
$719$	−7.25759	+	50.4777i	−0.270662	+	1.88250i	0.170930	+	0.985283i	$0.445323\pi$
$719$	−7.25759	+	50.4777i	−0.270662	+	1.88250i	−0.441593	+	0.897216i	$0.645586\pi$
$720$		0			0
$721$	−10.0385	−	2.94758i	−0.373854	−	0.109773i
$722$	−5.99733	+	6.92129i	−0.223198	+	0.257584i
$723$		0			0
$724$	−0.828830	−	0.532657i	−0.0308032	−	0.0197960i
$725$	31.3780	+	20.1654i	1.16535	+	0.748925i
$726$		0			0
$727$	10.6098	+	23.2323i	0.393497	+	0.861638i	0.997888	+	0.0649506i	$0.0206890\pi$
$727$	10.6098	+	23.2323i	0.393497	+	0.861638i	−0.604392	+	0.796687i	$0.706584\pi$
$728$	−10.6949	−	12.3426i	−0.396380	−	0.457447i
$729$		0			0
$730$	3.08851	+	3.56433i	0.114311	+	0.131922i
$731$	−55.6649	+	16.3447i	−2.05884	+	0.604530i
$732$		0			0
$733$	−1.70863	+	11.8838i	−0.0631097	+	0.438937i	0.933629	+	0.358241i	$0.116623\pi$
$733$	−1.70863	+	11.8838i	−0.0631097	+	0.438937i	−0.996739	+	0.0806962i	$0.974286\pi$
$734$	0.492725	−	1.07892i	0.0181868	−	0.0398236i
$735$		0			0
$736$	3.62912			0.133771
$737$	10.2471	+	6.35301i	0.377456	+	0.234016i
$738$		0			0
$739$	30.7174	+	35.4498i	1.12996	+	1.30404i	0.947114	+	0.320899i	$0.103985\pi$
$739$	30.7174	+	35.4498i	1.12996	+	1.30404i	0.182844	+	0.983142i	$0.441470\pi$
$740$	0.00978411	−	0.0214242i	0.000359671	−	0.000787569i
$741$		0			0
$742$	−5.63994	−	1.65604i	−0.207049	−	0.0607950i
$743$	−33.8468	+	9.93833i	−1.24172	+	0.364602i	−0.835661	−	0.549245i	$-0.814915\pi$
$743$	−33.8468	+	9.93833i	−1.24172	+	0.364602i	−0.406059	+	0.913847i	$0.633097\pi$
$744$		0			0
$745$	−0.900396	+	0.578649i	−0.0329879	+	0.0212001i
$746$	26.0671	+	30.0830i	0.954384	+	1.10142i
$747$		0			0
$748$	−0.774160	−	0.227314i	−0.0283061	−	0.00831142i
$749$	22.6846	+	14.5785i	0.828878	+	0.532687i
$750$		0			0
$751$	6.66291	−	46.3416i	0.243133	−	1.69103i	−0.393072	−	0.919508i	$-0.628588\pi$
$751$	6.66291	−	46.3416i	0.243133	−	1.69103i	0.636205	−	0.771520i	$-0.280503\pi$
$752$	−24.2853	+	28.0267i	−0.885594	+	1.02203i
$753$		0			0
$754$	−4.24796	−	29.5452i	−0.154702	−	1.07597i
$755$	0.946724	−	6.58461i	0.0344548	−	0.239638i
$756$		0			0
$757$	4.33128	−	9.48417i	0.157423	−	0.344708i	−0.814443	−	0.580244i	$-0.802957\pi$
$757$	4.33128	−	9.48417i	0.157423	−	0.344708i	0.971866	+	0.235536i	$0.0756845\pi$
$758$	24.7966	−	7.28095i	0.900654	−	0.264456i
$759$		0			0
$760$	1.89315	−	4.14541i	0.0686717	−	0.150370i
$761$	−4.64673	−	32.3187i	−0.168444	−	1.17155i	−0.882102	−	0.471059i	$-0.843872\pi$
$761$	−4.64673	−	32.3187i	−0.168444	−	1.17155i	0.713658	−	0.700495i	$-0.247037\pi$
$762$		0			0
$763$	−3.02720	−	21.0546i	−0.109592	−	0.762229i
$764$	0.853715	−	0.250673i	0.0308863	−	0.00906905i
$765$		0			0
$766$	48.6485			1.75774
$767$	10.2935			0.371678
$768$		0			0
$769$	−7.67250	−	16.8004i	−0.276677	−	0.605839i	0.719373	−	0.694624i	$-0.244429\pi$
$769$	−7.67250	−	16.8004i	−0.276677	−	0.605839i	−0.996051	+	0.0887844i	$0.971702\pi$
$770$	0.806766	−	0.931058i	0.0290738	−	0.0335530i
$771$		0			0
$772$	1.11891	+	2.45007i	0.0402705	+	0.0881801i
$773$	45.7556	−	29.4054i	1.64572	−	1.05764i	0.710416	−	0.703782i	$-0.248507\pi$
$773$	45.7556	−	29.4054i	1.64572	−	1.05764i	0.935300	−	0.353856i	$-0.115130\pi$
$774$		0			0
$775$	6.27265			0.225320
$776$	−19.4875	+	12.5239i	−0.699562	+	0.449581i
$777$		0			0
$778$	0.756468	+	5.26135i	0.0271207	+	0.188628i
$779$	34.3014	+	22.0442i	1.22898	+	0.789815i
$780$		0			0
$781$	1.63841	−	3.58762i	0.0586270	−	0.128375i
$782$	−15.0523	−	32.9599i	−0.538269	−	1.17864i
$783$		0			0
$784$	4.88399	−	10.6945i	0.174428	−	0.381945i
$785$	2.30241	−	2.65713i	0.0821767	−	0.0948369i
$786$		0			0
$787$	5.04115	+	35.0620i	0.179698	+	1.24982i	0.857463	+	0.514546i	$0.172039\pi$
$787$	5.04115	+	35.0620i	0.179698	+	1.24982i	−0.677766	+	0.735278i	$0.737052\pi$
$788$	−0.735659	−	0.216009i	−0.0262068	−	0.00769501i
$789$		0			0
$790$	−0.0394816	+	0.274601i	−0.00140469	+	0.00976986i
$791$	−2.96086	−	1.90283i	−0.105276	−	0.0676569i
$792$		0			0
$793$	−23.4540	−	6.88672i	−0.832876	−	0.244555i
$794$	10.9846	+	24.0528i	0.389828	+	0.853604i
$795$		0			0
$796$	0.0394448	−	0.0253496i	0.00139808	−	0.000898493i
$797$	−7.40313	−	8.54367i	−0.262232	−	0.302632i	0.609330	−	0.792917i	$-0.291438\pi$
$797$	−7.40313	−	8.54367i	−0.262232	−	0.302632i	−0.871563	+	0.490284i	$0.836893\pi$
$798$		0			0
$799$	−44.9477	−	13.1978i	−1.59014	−	0.466906i
$800$	0.455259	−	3.16640i	0.0160958	−	0.111949i
$801$		0			0
$802$	12.0164	+	13.8677i	0.424315	+	0.489685i
$803$	16.3386			0.576578
$804$		0			0
$805$	−3.38966			−0.119470
$806$	−3.28725	−	3.79369i	−0.115788	−	0.133627i
$807$		0			0
$808$	−7.06651	+	49.1487i	−0.248599	+	1.72904i
$809$	−40.9297	−	12.0180i	−1.43901	−	0.422532i	−0.533118	−	0.846041i	$-0.678980\pi$
$809$	−40.9297	−	12.0180i	−1.43901	−	0.422532i	−0.905892	+	0.423509i	$0.860798\pi$
$810$		0			0
$811$	−18.9554	−	21.8757i	−0.665615	−	0.768160i	0.318069	−	0.948068i	$-0.396966\pi$
$811$	−18.9554	−	21.8757i	−0.665615	−	0.768160i	−0.983684	+	0.179907i	$0.942420\pi$
$812$	1.45323	−	0.933932i	0.0509982	−	0.0327746i
$813$		0			0
$814$	0.553238	+	1.21142i	0.0193910	+	0.0424604i
$815$	−0.242328	−	0.0711538i	−0.00848837	−	0.00249241i
$816$		0			0
$817$	−52.1221	−	33.4968i	−1.82352	−	1.17191i
$818$	−4.32109	+	30.0539i	−0.151083	+	1.05081i
$819$		0			0
$820$	−0.276125	−	0.0810776i	−0.00964270	−	0.00283135i
$821$	3.12602	+	21.7419i	0.109099	+	0.758798i	0.968772	+	0.247954i	$0.0797581\pi$
$821$	3.12602	+	21.7419i	0.109099	+	0.758798i	−0.859673	+	0.510845i	$0.829333\pi$
$822$		0			0
$823$	22.6799	−	26.1740i	0.790573	−	0.912369i	−0.207252	−	0.978287i	$-0.566452\pi$
$823$	22.6799	−	26.1740i	0.790573	−	0.912369i	0.997825	+	0.0659181i	$0.0209976\pi$
$824$	−6.41628	+	14.0497i	−0.223522	+	0.489444i
$825$		0			0
$826$	−4.03922	−	8.84466i	−0.140543	−	0.307745i
$827$	−8.13947	+	17.8229i	−0.283037	+	0.619765i	−0.996740	−	0.0806842i	$-0.974289\pi$
$827$	−8.13947	+	17.8229i	−0.283037	+	0.619765i	0.713703	+	0.700449i	$0.247017\pi$
$828$		0			0
$829$	−0.315550	−	0.202792i	−0.0109595	−	0.00704324i	0.535150	−	0.844757i	$-0.320255\pi$
$829$	−0.315550	−	0.202792i	−0.0109595	−	0.00704324i	−0.546109	+	0.837714i	$0.683892\pi$
$830$	0.417169	+	2.90148i	0.0144802	+	0.100712i
$831$		0			0
$832$	−20.2187	+	12.9938i	−0.700957	+	0.450478i
$833$	14.8513			0.514567
$834$		0			0
$835$	1.52770	−	0.981791i	0.0528681	−	0.0339763i
$836$	−0.357953	−	0.783808i	−0.0123801	−	0.0271086i
$837$		0			0
$838$	−9.74754	+	11.2493i	−0.336723	+	0.388599i
$839$	5.35944	+	11.7355i	0.185028	+	0.405156i	0.979302	−	0.202405i	$-0.0648756\pi$
$839$	5.35944	+	11.7355i	0.185028	+	0.405156i	−0.794274	+	0.607560i	$0.792148\pi$
$840$		0			0
$841$	28.8472			0.994733
$842$	15.6919			0.540779
$843$		0			0
$844$	0.265895	−	0.0780737i	0.00915247	−	0.00268741i
$845$	−0.212771	−	1.47986i	−0.00731955	−	0.0509086i
$846$		0			0
$847$	2.47209	+	17.1938i	0.0849421	+	0.590786i
$848$	−3.39605	+	7.43632i	−0.116621	+	0.255364i
$849$		0			0
$850$	−30.6457	+	8.99839i	−1.05114	+	0.308642i
$851$	1.52219	−	3.33313i	0.0521800	−	0.114258i
$852$		0			0
$853$	3.77858	−	26.2806i	0.129376	−	0.899831i	−0.816971	−	0.576679i	$-0.804348\pi$
$853$	3.77858	−	26.2806i	0.129376	−	0.899831i	0.946347	−	0.323152i	$-0.104743\pi$
$854$	3.28607	+	22.8551i	0.112447	+	0.782085i
$855$		0			0
$856$	26.0691	−	30.0854i	0.891024	−	1.02830i
$857$	1.42418	−	9.90541i	0.0486492	−	0.338362i	−0.950931	−	0.309402i	$-0.899871\pi$
$857$	1.42418	−	9.90541i	0.0486492	−	0.338362i	0.999581	−	0.0289606i	$-0.00921974\pi$
$858$		0			0
$859$	−27.0197	−	17.3645i	−0.921900	−	0.592469i	−0.00869145	−	0.999962i	$-0.502767\pi$
$859$	−27.0197	−	17.3645i	−0.921900	−	0.592469i	−0.913208	+	0.407493i	$0.866403\pi$
$860$	0.419580	+	0.123200i	0.0143076	+	0.00420108i
$861$		0			0
$862$	−17.9749	−	20.7442i	−0.612229	−	0.706549i
$863$	−8.79690	+	5.65342i	−0.299450	+	0.192445i	−0.681734	−	0.731600i	$-0.738774\pi$
$863$	−8.79690	+	5.65342i	−0.299450	+	0.192445i	0.382284	+	0.924045i	$0.375138\pi$
$864$		0			0
$865$	−4.48125	+	1.31581i	−0.152367	+	0.0447390i
$866$	−52.8071	−	15.5056i	−1.79446	−	0.526900i
$867$		0			0
$868$	0.120682	−	0.264256i	0.00409621	−	0.00896944i
$869$	0.629376	+	0.726338i	0.0213501	+	0.0246393i
$870$		0			0
$871$	15.6088	+	17.4341i	0.528884	+	0.590731i
$872$	−31.4025			−1.06342
$873$		0			0
$874$	16.0753	−	35.1999i	0.543754	−	1.19065i
$875$	−0.858756	+	5.97278i	−0.0290313	+	0.201917i
$876$		0			0
$877$	−35.3220	+	10.3715i	−1.19274	+	0.350219i	−0.817072	−	0.576536i	$-0.804404\pi$
$877$	−35.3220	+	10.3715i	−1.19274	+	0.350219i	−0.375666	+	0.926755i	$0.622586\pi$
$878$	6.51289	+	7.51627i	0.219799	+	0.253662i
$879$		0			0
$880$	−1.12204	−	1.29490i	−0.0378239	−	0.0436511i
$881$	−8.14228	−	17.8291i	−0.274320	−	0.600678i	0.721459	−	0.692457i	$-0.243472\pi$
$881$	−8.14228	−	17.8291i	−0.274320	−	0.600678i	−0.995779	+	0.0917793i	$0.970745\pi$
$882$		0			0
$883$	29.2191	+	18.7780i	0.983300	+	0.631929i	0.930352	−	0.366669i	$-0.119502\pi$
$883$	29.2191	+	18.7780i	0.983300	+	0.631929i	0.0529486	+	0.998597i	$0.483138\pi$
$884$	−1.31738	−	0.846631i	−0.0443084	−	0.0284753i
$885$		0			0
$886$	−25.1167	+	28.9862i	−0.843812	+	0.973811i
$887$	−0.996981	−	0.292740i	−0.0334753	−	0.00982925i	0.264952	−	0.964262i	$-0.414644\pi$
$887$	−0.996981	−	0.292740i	−0.0334753	−	0.00982925i	−0.298427	+	0.954432i	$0.596462\pi$
$888$		0			0
$889$	−4.91826	+	34.2073i	−0.164953	+	1.14727i
$890$	−2.04649	+	2.36178i	−0.0685986	+	0.0791670i
$891$		0			0
$892$	1.09722	−	0.322172i	0.0367375	−	0.0107871i
$893$	−20.7828	−	45.5079i	−0.695469	−	1.52286i
$894$		0			0
$895$	0.403181	+	2.80419i	0.0134769	+	0.0937337i
$896$	16.9398	+	10.8865i	0.565918	+	0.363693i
$897$		0			0
$898$	−49.6904	+	14.5904i	−1.65819	+	0.486888i
$899$	8.18394	−	5.25950i	0.272950	−	0.175414i
$900$		0			0
$901$	−10.3268			−0.344034
$902$	13.6893	−	8.79760i	0.455805	−	0.292928i
$903$		0			0
$904$	−3.40262	+	3.92683i	−0.113169	+	0.130604i
$905$	1.73073	−	1.99736i	0.0575313	−	0.0663946i
$906$		0			0
$907$	3.03289	−	1.94912i	0.100705	−	0.0647194i	−0.489319	−	0.872105i	$-0.662755\pi$
$907$	3.03289	−	1.94912i	0.100705	−	0.0647194i	0.590024	+	0.807386i	$0.299118\pi$
$908$	1.44797			0.0480525
$909$		0			0
$910$	2.01151	−	1.29272i	0.0666809	−	0.0428532i
$911$	−9.94951	+	2.92144i	−0.329642	+	0.0967917i	−0.442366	−	0.896835i	$-0.645861\pi$
$911$	−9.94951	+	2.92144i	−0.329642	+	0.0967917i	0.112724	+	0.993626i	$0.464043\pi$
$912$		0			0
$913$	8.54290	+	5.49019i	0.282729	+	0.181699i
$914$	1.27067	+	8.83769i	0.0420300	+	0.292325i
$915$		0			0
$916$	−0.195829	−	0.428805i	−0.00647036	−	0.0141681i
$917$	−29.5563	+	8.67851i	−0.976035	+	0.286590i
$918$		0			0
$919$	14.8924	−	17.1868i	0.491256	−	0.566940i	−0.454945	−	0.890520i	$-0.650341\pi$
$919$	14.8924	−	17.1868i	0.491256	−	0.566940i	0.946201	+	0.323580i	$0.104886\pi$
$920$	−0.712162	+	4.95319i	−0.0234793	+	0.163302i
$921$		0			0
$922$	11.3881	+	3.34384i	0.375046	+	0.110123i
$923$	5.01287	−	5.78516i	0.165001	−	0.190421i
$924$		0			0
$925$	−2.71720	−	1.74624i	−0.0893409	−	0.0574159i
$926$	12.9220	+	8.30448i	0.424644	+	0.272902i
$927$		0			0
$928$	−2.06099	−	4.51293i	−0.0676552	−	0.148144i
$929$	−26.3158	−	30.3701i	−0.863394	−	0.996410i	−0.999983	−	0.00578220i	$-0.998159\pi$
$929$	−26.3158	−	30.3701i	−0.863394	−	0.996410i	0.136589	−	0.990628i	$-0.456386\pi$
$930$		0			0
$931$	10.3865	+	11.9866i	0.340403	+	0.392846i
$932$	0.736495	−	0.216254i	0.0241247	−	0.00708365i
$933$		0			0
$934$	−3.67223	+	25.5409i	−0.120159	+	0.835725i
$935$	0.899108	−	1.96877i	0.0294040	−	0.0643857i
$936$		0			0
$937$	40.5245			1.32388			0.661939	−	0.749558i	$-0.269734\pi$
$937$	40.5245			1.32388			0.661939	+	0.749558i	$0.269734\pi$
$938$	8.85517	−	20.2529i	0.289131	−	0.661282i
$939$		0			0
$940$	0.231232	+	0.266856i	0.00754197	+	0.00870389i
$941$	11.0668	−	24.2330i	0.360769	−	0.789974i	−0.639015	−	0.769194i	$-0.720658\pi$
$941$	11.0668	−	24.2330i	0.360769	−	0.789974i	0.999784	−	0.0207795i	$-0.00661481\pi$
$942$		0			0
$943$	−42.9589	−	12.6139i	−1.39894	−	0.410765i
$944$	−12.9753	+	3.80989i	−0.422309	+	0.124001i
$945$		0			0
$946$	−20.8013	+	13.3682i	−0.676310	+	0.434638i
$947$	14.7211	+	16.9890i	0.478370	+	0.552069i	0.942721	−	0.333583i	$-0.108258\pi$
$947$	14.7211	+	16.9890i	0.478370	+	0.552069i	−0.464351	+	0.885651i	$0.653712\pi$
$948$		0			0
$949$	30.4266	+	8.93407i	0.987691	+	0.290012i
$950$	−28.6952	−	18.4413i	−0.930997	−	0.598315i
$951$		0			0
$952$	−3.85710	+	26.8267i	−0.125009	+	0.869458i
$953$	−29.3456	+	33.8666i	−0.950597	+	1.09705i	0.0445853	+	0.999006i	$0.485803\pi$
$953$	−29.3456	+	33.8666i	−0.950597	+	1.09705i	−0.995182	+	0.0980419i	$0.968742\pi$
$954$		0			0
$955$	0.339674	+	2.36249i	0.0109916	+	0.0764482i
$956$	−0.160535	+	1.11655i	−0.00519208	+	0.0361117i
$957$		0			0
$958$	17.3732	−	38.0421i	0.561304	−	1.22908i
$959$	−36.0575	+	10.5874i	−1.16436	+	0.341886i
$960$		0			0
$961$	−12.1982	+	26.7104i	−0.393492	+	0.861626i
$962$	0.367855	+	2.55849i	0.0118601	+	0.0824890i
$963$		0			0
$964$	−0.374972	−	2.60799i	−0.0120771	−	0.0839977i
$965$	−6.93260	+	2.03560i	−0.223168	+	0.0655281i
$966$		0			0
$967$	22.2880			0.716733			0.358367	−	0.933581i	$-0.383334\pi$
$967$	22.2880			0.716733			0.358367	+	0.933581i	$0.383334\pi$
$968$	25.6441			0.824233
$969$		0			0
$970$	−1.40890	−	3.08505i	−0.0452369	−	0.0990550i
$971$	2.95958	−	3.41554i	0.0949774	−	0.109610i	−0.706271	−	0.707941i	$-0.749624\pi$
$971$	2.95958	−	3.41554i	0.0949774	−	0.109610i	0.801249	+	0.598332i	$0.204169\pi$
$972$		0			0
$973$	7.17500	+	15.7111i	0.230020	+	0.503673i
$974$	8.70973	−	5.59740i	0.279078	−	0.179352i
$975$		0			0
$976$	32.1133			1.02792
$977$	−4.37138	+	2.80931i	−0.139853	+	0.0898779i	−0.608696	−	0.793403i	$-0.708307\pi$
$977$	−4.37138	+	2.80931i	−0.139853	+	0.0898779i	0.468843	+	0.883281i	$0.344671\pi$
$978$		0			0
$979$	1.54073	+	10.7160i	0.0492421	+	0.342486i
$980$	−0.0941726	−	0.0605211i	−0.00300823	−	0.00193327i
$981$		0			0
$982$	3.93296	−	8.61199i	0.125506	−	0.274820i
$983$	−14.0097	−	30.6770i	−0.446840	−	0.978444i	−0.990292	−	0.139004i	$-0.955610\pi$
$983$	−14.0097	−	30.6770i	−0.446840	−	0.978444i	0.543451	−	0.839441i	$-0.317117\pi$
$984$		0			0
$985$	0.854394	−	1.87086i	0.0272232	−	0.0596106i
$986$	−32.4385	+	37.4361i	−1.03305	+	1.19221i
$987$		0			0
$988$	−0.238008	−	1.65538i	−0.00757203	−	0.0526646i
$989$	65.2774	+	19.1672i	2.07570	+	0.609481i
$990$		0			0
$991$	4.78719	−	33.2957i	0.152070	−	1.05767i	−0.760672	−	0.649136i	$-0.775130\pi$
$991$	4.78719	−	33.2957i	0.152070	−	1.05767i	0.912742	−	0.408536i	$-0.133960\pi$
$992$	−0.701896	−	0.451081i	−0.0222852	−	0.0143218i
$993$		0			0
$994$	−6.93793	−	2.03716i	−0.220058	−	0.0646148i
$995$	0.0522499	+	0.114411i	0.00165643	+	0.00362708i
$996$		0			0
$997$	30.5713	−	19.6470i	0.968204	−	0.622227i	0.0419469	−	0.999120i	$-0.486644\pi$
$997$	30.5713	−	19.6470i	0.968204	−	0.622227i	0.926257	+	0.376893i	$0.123008\pi$
$998$	18.5172	+	21.3700i	0.586153	+	0.676457i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.u.b.442.1		10
3.2	odd	2		67.2.e.a.40.1	✓	10
67.62	even	11	inner	603.2.u.b.397.1		10
201.14	odd	22		4489.2.a.f.1.3		5
201.53	even	22		4489.2.a.k.1.3		5
201.62	odd	22		67.2.e.a.62.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.a.40.1	✓	10	3.2	odd	2
67.2.e.a.62.1	yes	10	201.62	odd	22
603.2.u.b.397.1		10	67.62	even	11	inner
603.2.u.b.442.1		10	1.1	even	1	trivial
4489.2.a.f.1.3		5	201.14	odd	22
4489.2.a.k.1.3		5	201.53	even	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)

\(f(q)\)	\(=\)	\(q+(-0.898983 - 1.03748i) q^{2} +(0.0164316 - 0.114284i) q^{4} +(0.297176 + 0.0872586i) q^{5} +(-1.28820 - 1.48666i) q^{7} +(-2.44306 + 1.57006i) q^{8} +O(q^{10})\)	\(q+(-0.898983 - 1.03748i) q^{2} +(0.0164316 - 0.114284i) q^{4} +(0.297176 + 0.0872586i) q^{5} +(-1.28820 - 1.48666i) q^{7} +(-2.44306 + 1.57006i) q^{8} +(-0.176627 - 0.386758i) q^{10} +(-1.41329 - 0.414980i) q^{11} +(-2.40499 - 1.54559i) q^{13} +(-0.384315 + 2.67297i) q^{14} +(3.60362 + 1.05812i) q^{16} +(0.675178 + 4.69597i) q^{17} +(-3.31797 + 3.82914i) q^{19} +(0.0148554 - 0.0325288i) q^{20} +(0.839992 + 1.83933i) q^{22} +(2.31117 - 5.06076i) q^{23} +(-4.12557 - 2.65134i) q^{25} +(0.558521 + 3.88460i) q^{26} +(-0.191070 + 0.122793i) q^{28} -7.60574 q^{29} +(-1.07602 + 0.691518i) q^{31} +(0.270978 + 0.593359i) q^{32} +(4.26501 - 4.92208i) q^{34} +(-0.253098 - 0.554206i) q^{35} +0.658623 q^{37} +6.95546 q^{38} +(-0.863019 + 0.253405i) q^{40} +(-1.14528 - 7.96561i) q^{41} +(1.74029 + 12.1040i) q^{43} +(-0.0706485 + 0.154699i) q^{44} +(-7.32815 + 2.15174i) q^{46} +(-4.10185 + 8.98180i) q^{47} +(0.445499 - 3.09851i) q^{49} +(0.958098 + 6.66372i) q^{50} +(-0.216155 + 0.249457i) q^{52} +(-0.309775 + 2.15453i) q^{53} +(-0.383785 - 0.246644i) q^{55} +(5.48130 + 1.60946i) q^{56} +(6.83743 + 7.89082i) q^{58} +(-3.02904 + 1.94665i) q^{59} +(8.20409 - 2.40894i) q^{61} +(1.68476 + 0.494691i) q^{62} +(3.49238 - 7.64725i) q^{64} +(-0.579838 - 0.669169i) q^{65} +(-7.89015 - 2.17842i) q^{67} +0.547770 q^{68} +(-0.347449 + 0.760807i) q^{70} +(-0.381067 + 2.65038i) q^{71} +(-10.6431 + 3.12509i) q^{73} +(-0.592092 - 0.683310i) q^{74} +(0.383092 + 0.442111i) q^{76} +(1.20367 + 2.63567i) q^{77} +(-0.548906 - 0.352760i) q^{79} +(0.978577 + 0.628893i) q^{80} +(-7.23459 + 8.34916i) q^{82} +(-6.61500 - 1.94234i) q^{83} +(-0.209117 + 1.45444i) q^{85} +(10.9932 - 12.6868i) q^{86} +(4.10430 - 1.20513i) q^{88} +(-3.05330 - 6.68579i) q^{89} +(0.800334 + 5.56645i) q^{91} +(-0.540390 - 0.347287i) q^{92} +(13.0060 - 3.81889i) q^{94} +(-1.32014 + 0.848406i) q^{95} +7.97669 q^{97} +(-3.61514 + 2.32331i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8}+O(q^{10}) \) 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8	\( 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8} - 15 q^{10} - 15 q^{11} - 18 q^{13} - 6 q^{16} + 26 q^{17} - q^{19} - 25 q^{20} - 9 q^{22} + 6 q^{23} - 4 q^{25} - 24 q^{26} + 11 q^{28} - 28 q^{29} - 10 q^{31} + 4 q^{32} + 64 q^{34} - 22 q^{37} + 6 q^{38} - 18 q^{40} - 9 q^{41} + 21 q^{43} - 48 q^{44} - 25 q^{46} + 22 q^{47} + 7 q^{49} + 35 q^{50} - 62 q^{52} - 20 q^{53} - 23 q^{55} + 11 q^{56} - 8 q^{58} + 17 q^{59} + 13 q^{61} - 50 q^{62} + 10 q^{64} - 10 q^{65} + 23 q^{67} + 114 q^{68} + 11 q^{70} - q^{71} - 18 q^{73} - 22 q^{74} + 21 q^{76} + 22 q^{77} + 5 q^{79} - 18 q^{80} - 12 q^{82} + 12 q^{83} + 23 q^{85} + 61 q^{86} - 2 q^{88} - 51 q^{89} - 11 q^{91} - 38 q^{92} + 11 q^{94} - 3 q^{95} - 10 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8 - 15 * q^10 - 15 * q^11 - 18 * q^13 - 6 * q^16 + 26 * q^17 - q^19 - 25 * q^20 - 9 * q^22 + 6 * q^23 - 4 * q^25 - 24 * q^26 + 11 * q^28 - 28 * q^29 - 10 * q^31 + 4 * q^32 + 64 * q^34 - 22 * q^37 + 6 * q^38 - 18 * q^40 - 9 * q^41 + 21 * q^43 - 48 * q^44 - 25 * q^46 + 22 * q^47 + 7 * q^49 + 35 * q^50 - 62 * q^52 - 20 * q^53 - 23 * q^55 + 11 * q^56 - 8 * q^58 + 17 * q^59 + 13 * q^61 - 50 * q^62 + 10 * q^64 - 10 * q^65 + 23 * q^67 + 114 * q^68 + 11 * q^70 - q^71 - 18 * q^73 - 22 * q^74 + 21 * q^76 + 22 * q^77 + 5 * q^79 - 18 * q^80 - 12 * q^82 + 12 * q^83 + 23 * q^85 + 61 * q^86 - 2 * q^88 - 51 * q^89 - 11 * q^91 - 38 * q^92 + 11 * q^94 - 3 * q^95 - 10 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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