LMFDB - Embedded newform 639.2.z.a.35.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, 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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			35.19
Character	$\chi$	$=$	639.35
Dual form			639.2.z.a.566.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.51831 - 0.0681876i) q^{2} +(0.308680 - 0.0277817i) q^{4} +(-1.18877 - 0.386256i) q^{5} +(-0.789589 - 2.86101i) q^{7} +(-2.54540 + 0.344798i) q^{8} +O(q^{10})$	\(q+(1.51831 - 0.0681876i) q^{2} +(0.308680 - 0.0277817i) q^{4} +(-1.18877 - 0.386256i) q^{5} +(-0.789589 - 2.86101i) q^{7} +(-2.54540 + 0.344798i) q^{8} +(-1.83127 - 0.505398i) q^{10} +(-1.51770 - 2.82036i) q^{11} +(-0.301648 - 0.162324i) q^{13} +(-1.39393 - 4.29008i) q^{14} +(-4.45110 + 0.807756i) q^{16} +(0.322355 - 0.234205i) q^{17} +(2.72489 - 6.37520i) q^{19} +(-0.377682 - 0.0862034i) q^{20} +(-2.49666 - 4.17870i) q^{22} +(3.19207 - 4.00273i) q^{23} +(-2.78110 - 2.02059i) q^{25} +(-0.469065 - 0.225890i) q^{26} +(-0.323214 - 0.861202i) q^{28} +(-5.08796 + 8.51581i) q^{29} +(-0.817786 + 4.50637i) q^{31} +(-1.69460 + 0.386781i) q^{32} +(0.473467 - 0.377577i) q^{34} +(-0.166440 + 3.70608i) q^{35} +(0.537169 + 0.673589i) q^{37} +(3.70253 - 9.86537i) q^{38} +(3.15908 + 0.573289i) q^{40} +(-4.66416 + 2.24614i) q^{41} +(11.8730 - 4.45602i) q^{43} +(-0.546838 - 0.828424i) q^{44} +(4.57363 - 6.29507i) q^{46} +(-0.789263 - 0.689559i) q^{47} +(-1.55280 + 0.927754i) q^{49} +(-4.36036 - 2.87825i) q^{50} +(-0.0976224 - 0.0417258i) q^{52} +(1.21012 + 0.108913i) q^{53} +(0.714820 + 3.93898i) q^{55} +(2.99629 + 7.01017i) q^{56} +(-7.14445 + 13.2766i) q^{58} +(-6.57948 + 6.88160i) q^{59} +(3.09227 - 11.2046i) q^{61} +(-0.934377 + 6.89785i) q^{62} +(6.17499 - 1.70419i) q^{64} +(0.295892 + 0.309479i) q^{65} +(0.368931 + 4.09916i) q^{67} +(0.0929981 - 0.0812500i) q^{68} +5.63834i q^{70} +(8.06880 + 2.42787i) q^{71} +(-0.573475 - 12.7694i) q^{73} +(0.861522 + 0.986091i) q^{74} +(0.664006 - 2.04360i) q^{76} +(-6.87072 + 6.56908i) q^{77} +(-0.413720 - 3.05421i) q^{79} +(5.60335 + 0.759025i) q^{80} +(-6.92851 + 3.72839i) q^{82} +(-1.12380 - 1.07447i) q^{83} +(-0.473671 + 0.153905i) q^{85} +(17.7231 - 7.57523i) q^{86} +(4.83560 + 6.65564i) q^{88} +(-0.464993 + 5.16650i) q^{89} +(-0.226232 + 0.991187i) q^{91} +(0.874127 - 1.32425i) q^{92} +(-1.24537 - 0.993149i) q^{94} +(-5.70174 + 6.52617i) q^{95} +(-0.680317 + 1.41269i) q^{97} +(-2.29438 + 1.51450i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{29}{70}\right)$	$-1$

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 $

$2$	1.51831	−	0.0681876i	1.07361	−	0.0482159i	0.498968	−	0.866620i	$-0.333713\pi$
$2$	1.51831	−	0.0681876i	1.07361	−	0.0482159i	0.574642	+	0.818405i	$0.305141\pi$
$3$		0			0
$3$		0			0
$4$	0.308680	−	0.0277817i	0.154340	−	0.0138909i
$5$	−1.18877	−	0.386256i	−0.531636	−	0.172739i	0.0308838	−	0.999523i	$-0.490168\pi$
$5$	−1.18877	−	0.386256i	−0.531636	−	0.172739i	−0.562519	+	0.826784i	$0.690168\pi$
$6$		0			0
$7$	−0.789589	−	2.86101i	−0.298437	−	1.08136i	−0.947272	−	0.320432i	$-0.896172\pi$
$7$	−0.789589	−	2.86101i	−0.298437	−	1.08136i	0.648835	−	0.760929i	$-0.275257\pi$
$8$	−2.54540	+	0.344798i	−0.899935	+	0.121904i
$9$		0			0
$10$	−1.83127	−	0.505398i	−0.579098	−	0.159821i
$11$	−1.51770	−	2.82036i	−0.457603	−	0.850369i	−0.999948	−	0.0102132i	$-0.996749\pi$
$11$	−1.51770	−	2.82036i	−0.457603	−	0.850369i	0.542345	−	0.840156i	$-0.317537\pi$
$12$		0			0
$13$	−0.301648	−	0.162324i	−0.0836621	−	0.0450205i	0.431503	−	0.902112i	$-0.357984\pi$
$13$	−0.301648	−	0.162324i	−0.0836621	−	0.0450205i	−0.515165	+	0.857091i	$0.672269\pi$
$14$	−1.39393	−	4.29008i	−0.372543	−	1.14657i
$15$		0			0
$16$	−4.45110	+	0.807756i	−1.11278	+	0.201939i
$17$	0.322355	−	0.234205i	0.0781827	−	0.0568030i	−0.548007	−	0.836474i	$-0.684613\pi$
$17$	0.322355	−	0.234205i	0.0781827	−	0.0568030i	0.626190	+	0.779670i	$0.284613\pi$
$18$		0			0
$19$	2.72489	−	6.37520i	0.625133	−	1.46257i	−0.244885	−	0.969552i	$-0.578750\pi$
$19$	2.72489	−	6.37520i	0.625133	−	1.46257i	0.870018	−	0.493020i	$-0.164107\pi$
$20$	−0.377682	−	0.0862034i	−0.0844522	−	0.0192757i
$21$		0			0
$22$	−2.49666	−	4.17870i	−0.532289	−	0.890902i
$23$	3.19207	−	4.00273i	0.665593	−	0.834628i	−0.328346	−	0.944558i	$-0.606491\pi$
$23$	3.19207	−	4.00273i	0.665593	−	0.834628i	0.993939	+	0.109930i	$0.0350626\pi$
$24$		0			0
$25$	−2.78110	−	2.02059i	−0.556219	−	0.404117i
$26$	−0.469065	−	0.225890i	−0.0919912	−	0.0443006i
$27$		0			0
$28$	−0.323214	−	0.861202i	−0.0610818	−	0.162752i
$29$	−5.08796	+	8.51581i	−0.944810	+	1.58135i	−0.138085	+	0.990420i	$0.544095\pi$
$29$	−5.08796	+	8.51581i	−0.944810	+	1.58135i	−0.806726	+	0.590926i	$0.798763\pi$
$30$		0			0
$31$	−0.817786	+	4.50637i	−0.146879	+	0.809368i	0.823415	+	0.567439i	$0.192066\pi$
$31$	−0.817786	+	4.50637i	−0.146879	+	0.809368i	−0.970294	+	0.241929i	$0.922220\pi$
$32$	−1.69460	+	0.386781i	−0.299566	+	0.0683739i
$33$		0			0
$34$	0.473467	−	0.377577i	0.0811989	−	0.0647540i
$35$	−0.166440	+	3.70608i	−0.0281335	+	0.626442i
$36$		0			0
$37$	0.537169	+	0.673589i	0.0883100	+	0.110737i	0.824023	−	0.566556i	$-0.191724\pi$
$37$	0.537169	+	0.673589i	0.0883100	+	0.110737i	−0.735713	+	0.677293i	$0.763153\pi$
$38$	3.70253	−	9.86537i	0.600630	−	1.60037i
$39$		0			0
$40$	3.15908	+	0.573289i	0.499495	+	0.0906450i
$41$	−4.66416	+	2.24614i	−0.728420	+	0.350789i	−0.761063	−	0.648679i	$-0.775322\pi$
$41$	−4.66416	+	2.24614i	−0.728420	+	0.350789i	0.0326426	+	0.999467i	$0.489608\pi$
$42$		0			0
$43$	11.8730	−	4.45602i	1.81062	−	0.679536i	0.815744	−	0.578413i	$-0.196328\pi$
$43$	11.8730	−	4.45602i	1.81062	−	0.679536i	0.994874	−	0.101123i	$-0.0322436\pi$
$44$	−0.546838	−	0.828424i	−0.0824389	−	0.124890i
$45$		0			0
$46$	4.57363	−	6.29507i	0.674346	−	0.928157i
$47$	−0.789263	−	0.689559i	−0.115126	−	0.100582i	0.598451	−	0.801159i	$-0.295783\pi$
$47$	−0.789263	−	0.689559i	−0.115126	−	0.100582i	−0.713577	+	0.700577i	$0.752926\pi$
$48$		0			0
$49$	−1.55280	+	0.927754i	−0.221828	+	0.132536i
$50$	−4.36036	−	2.87825i	−0.616648	−	0.407046i
$51$		0			0
$52$	−0.0976224	−	0.0417258i	−0.0135378	−	0.00578633i
$53$	1.21012	+	0.108913i	0.166223	+	0.0149603i	0.172438	−	0.985020i	$-0.444836\pi$
$53$	1.21012	+	0.108913i	0.166223	+	0.0149603i	−0.00621521	+	0.999981i	$0.501978\pi$
$54$		0			0
$55$	0.714820	+	3.93898i	0.0963863	+	0.531132i
$56$	2.99629	+	7.01017i	0.400396	+	0.936774i
$57$		0			0
$58$	−7.14445	+	13.2766i	−0.938112	+	1.74330i
$59$	−6.57948	+	6.88160i	−0.856575	+	0.895908i	−0.995535	−	0.0943905i	$-0.969910\pi$
$59$	−6.57948	+	6.88160i	−0.856575	+	0.895908i	0.138960	+	0.990298i	$0.455624\pi$
$60$		0			0
$61$	3.09227	−	11.2046i	0.395925	−	1.43460i	−0.446012	−	0.895027i	$-0.647156\pi$
$61$	3.09227	−	11.2046i	0.395925	−	1.43460i	0.841937	−	0.539575i	$-0.181415\pi$
$62$	−0.934377	+	6.89785i	−0.118666	+	0.876028i
$63$		0			0
$64$	6.17499	−	1.70419i	0.771874	−	0.213024i
$65$	0.295892	+	0.309479i	0.0367009	+	0.0383862i
$66$		0			0
$67$	0.368931	+	4.09916i	0.0450721	+	0.500792i	0.986521	+	0.163636i	$0.0523223\pi$
$67$	0.368931	+	4.09916i	0.0450721	+	0.500792i	−0.941449	+	0.337156i	$0.890535\pi$
$68$	0.0929981	−	0.0812500i	0.0112777	−	0.00985301i
$69$		0			0
$70$			5.63834i			0.673911i
$71$	8.06880	+	2.42787i	0.957590	+	0.288135i
$71$	8.06880	+	2.42787i	0.957590	+	0.288135i
$72$		0			0
$73$	−0.573475	−	12.7694i	−0.0671201	−	1.49455i	−0.696561	−	0.717497i	$-0.745287\pi$
$73$	−0.573475	−	12.7694i	−0.0671201	−	1.49455i	0.629441	−	0.777048i	$-0.283284\pi$
$74$	0.861522	+	0.986091i	0.100150	+	0.114631i
$75$		0			0
$76$	0.664006	−	2.04360i	0.0761667	−	0.234417i
$77$	−6.87072	+	6.56908i	−0.782991	+	0.748616i
$78$		0			0
$79$	−0.413720	−	3.05421i	−0.0465472	−	0.343625i	−0.999215	−	0.0396123i	$-0.987388\pi$
$79$	−0.413720	−	3.05421i	−0.0465472	−	0.343625i	0.952668	−	0.304013i	$-0.0983266\pi$
$80$	5.60335	+	0.759025i	0.626474	+	0.0848616i
$81$		0			0
$82$	−6.92851	+	3.72839i	−0.765126	+	0.411732i
$83$	−1.12380	−	1.07447i	−0.123353	−	0.117938i	0.626865	−	0.779128i	$-0.284338\pi$
$83$	−1.12380	−	1.07447i	−0.123353	−	0.117938i	−0.750219	+	0.661190i	$0.770052\pi$
$84$		0			0
$85$	−0.473671	+	0.153905i	−0.0513768	+	0.0166933i
$86$	17.7231	−	7.57523i	1.91113	−	0.816858i
$87$		0			0
$88$	4.83560	+	6.65564i	0.515477	+	0.709493i
$89$	−0.464993	+	5.16650i	−0.0492892	+	0.547648i	0.932949	+	0.360009i	$0.117226\pi$
$89$	−0.464993	+	5.16650i	−0.0492892	+	0.547648i	−0.982238	+	0.187639i	$0.939917\pi$
$90$		0			0
$91$	−0.226232	+	0.991187i	−0.0237156	+	0.103905i
$92$	0.874127	−	1.32425i	0.0911341	−	0.138062i
$93$		0			0
$94$	−1.24537	−	0.993149i	−0.128450	−	0.102435i
$95$	−5.70174	+	6.52617i	−0.584986	+	0.669570i
$96$		0			0
$97$	−0.680317	+	1.41269i	−0.0690757	+	0.143437i	−0.932648	−	0.360788i	$-0.882508\pi$
$97$	−0.680317	+	1.41269i	−0.0690757	+	0.143437i	0.863572	+	0.504226i	$0.168222\pi$
$98$	−2.29438	+	1.51450i	−0.231767	+	0.152988i
$99$		0			0
$100$	−0.914605	−	0.546451i	−0.0914605	−	0.0546451i
$101$	−4.31568	−	8.96159i	−0.429426	−	0.891712i	−0.997629	−	0.0688236i	$-0.978075\pi$
$101$	−4.31568	−	8.96159i	−0.429426	−	0.891712i	0.568203	−	0.822888i	$-0.307639\pi$
$102$		0			0
$103$	2.05062	+	8.98434i	0.202053	+	0.885254i	0.969684	+	0.244361i	$0.0785783\pi$
$103$	2.05062	+	8.98434i	0.202053	+	0.885254i	−0.767631	+	0.640892i	$0.778565\pi$
$104$	0.823783	+	0.309171i	0.0807786	+	0.0303167i
$105$		0			0
$106$	1.84477	+	0.0828487i	0.179180	+	0.00804698i
$107$	−11.5119	−	0.517001i	−1.11290	−	0.0499804i	−0.519190	−	0.854659i	$-0.673766\pi$
$107$	−11.5119	−	0.517001i	−1.11290	−	0.0499804i	−0.593711	+	0.804679i	$0.702338\pi$
$108$		0			0
$109$	4.46491	+	1.67571i	0.427660	+	0.160504i	0.555918	−	0.831237i	$-0.312367\pi$
$109$	4.46491	+	1.67571i	0.427660	+	0.160504i	−0.128257	+	0.991741i	$0.540938\pi$
$110$	1.35391	+	5.93187i	0.129090	+	0.565582i
$111$		0			0
$112$	5.82554	+	12.0969i	0.550462	+	1.14305i
$113$	4.93195	+	2.94671i	0.463959	+	0.277203i	0.725797	−	0.687909i	$-0.241471\pi$
$113$	4.93195	+	2.94671i	0.463959	+	0.277203i	−0.261837	+	0.965112i	$0.584328\pi$
$114$		0			0
$115$	−5.34073	+	3.52539i	−0.498026	+	0.328744i
$116$	−1.33397	+	2.77001i	−0.123856	+	0.257189i
$117$		0			0
$118$	−9.52048	+	10.8971i	−0.876431	+	1.00316i
$119$	−0.924592	−	0.737337i	−0.0847572	−	0.0675916i
$120$		0			0
$121$	0.408867	−	0.619407i	0.0371697	−	0.0563097i
$122$	3.93103	−	17.2230i	0.355899	−	1.55929i
$123$		0			0
$124$	−0.127240	+	1.41375i	−0.0114264	+	0.126958i
$125$	6.19914	+	8.53239i	0.554468	+	0.763160i
$126$		0			0
$127$	−4.46449	+	1.90821i	−0.396159	+	0.169327i	−0.581877	−	0.813276i	$-0.697682\pi$
$127$	−4.46449	+	1.90821i	−0.396159	+	0.169327i	0.185718	+	0.982603i	$0.440539\pi$
$128$	12.5656	−	4.08281i	1.11065	−	0.360872i
$129$		0			0
$130$	0.470360	+	0.449711i	0.0412533	+	0.0394422i
$131$	18.7864	−	10.1094i	1.64137	−	0.883260i	0.648889	−	0.760883i	$-0.275234\pi$
$131$	18.7864	−	10.1094i	1.64137	−	0.883260i	0.992484	−	0.122377i	$-0.0390517\pi$
$132$		0			0
$133$	−20.3911	−	2.76216i	−1.76813	−	0.239510i
$134$	0.839666	+	6.19866i	0.0725361	+	0.535483i
$135$		0			0
$136$	−0.739770	+	0.707293i	−0.0634348	+	0.0606499i
$137$	4.53741	−	13.9647i	0.387657	−	1.19309i	−0.546878	−	0.837213i	$-0.684184\pi$
$137$	4.53741	−	13.9647i	0.387657	−	1.19309i	0.934535	−	0.355873i	$-0.115816\pi$
$138$		0			0
$139$	6.61593	+	7.57254i	0.561156	+	0.642294i	0.961739	−	0.273966i	$-0.0883355\pi$
$139$	6.61593	+	7.57254i	0.561156	+	0.642294i	−0.400584	+	0.916260i	$0.631193\pi$
$140$	0.0515844	+	1.14862i	0.00435968	+	0.0970758i
$141$		0			0
$142$	12.4165	+	3.13607i	1.04197	+	0.263173i
$143$			1.09711i			0.0917452i
$144$		0			0
$145$	9.33771	−	8.15811i	0.775455	−	0.677494i
$146$	−1.74143	−	19.3489i	−0.144122	−	1.60132i
$147$		0			0
$148$	0.184527	+	0.193000i	0.0151680	+	0.0158645i
$149$	−4.33671	+	1.19686i	−0.355277	+	0.0980503i	−0.439119	−	0.898429i	$-0.644709\pi$
$149$	−4.33671	+	1.19686i	−0.355277	+	0.0980503i	0.0838420	+	0.996479i	$0.473281\pi$
$150$		0			0
$151$	0.00845124	−	0.0623896i	0.000687752	−	0.00507719i	−0.990603	−	0.136771i	$-0.956327\pi$
$151$	0.00845124	−	0.0623896i	0.000687752	−	0.00507719i	0.991290	+	0.131694i	$0.0420417\pi$
$152$	−4.73779	+	17.1670i	−0.384285	+	1.39243i
$153$		0			0
$154$	−9.98398	+	10.4424i	−0.804532	+	0.841474i
$155$	2.71277	−	5.04118i	0.217895	−	0.404917i
$156$		0			0
$157$	3.89652	+	9.11637i	0.310976	+	0.727565i	0.999996	+	0.00282268i	$0.000898487\pi$
$157$	3.89652	+	9.11637i	0.310976	+	0.727565i	−0.689020	+	0.724743i	$0.741959\pi$
$158$	−0.836416	−	4.60903i	−0.0665417	−	0.366675i
$159$		0			0
$160$	2.16389	+	0.194754i	0.171071	+	0.0153966i
$161$	−13.9723	−	5.97205i	−1.10117	−	0.470663i
$162$		0			0
$163$	−16.5590	−	10.9305i	−1.29700	−	0.856141i	−0.301739	−	0.953391i	$-0.597567\pi$
$163$	−16.5590	−	10.9305i	−1.29700	−	0.856141i	−0.995260	+	0.0972494i	$0.968996\pi$
$164$	−1.37733	+	0.822918i	−0.107552	+	0.0642591i
$165$		0			0
$166$	−1.77955	−	1.55475i	−0.138120	−	0.120672i
$167$	10.5711	−	14.5499i	0.818019	−	1.12591i	−0.172017	−	0.985094i	$-0.555028\pi$
$167$	10.5711	−	14.5499i	0.818019	−	1.12591i	0.990036	−	0.140813i	$-0.0449716\pi$
$168$		0			0
$169$	−7.09702	−	10.7515i	−0.545924	−	0.827040i
$170$	−0.708686	+	0.265974i	−0.0543538	+	0.0203993i
$171$		0			0
$172$	3.54117	−	1.70534i	0.270012	−	0.130031i
$173$	14.7365	+	2.67428i	1.12039	+	0.203321i	0.706988	−	0.707226i	$-0.250053\pi$
$173$	14.7365	+	2.67428i	1.12039	+	0.203321i	0.413406	+	0.910547i	$0.364339\pi$
$174$		0			0
$175$	−3.58499	+	9.55218i	−0.271000	+	0.722077i
$176$	9.03359	+	11.3278i	0.680932	+	0.853862i
$177$		0			0
$178$	−0.353715	+	7.87608i	−0.0265121	+	0.590337i
$179$	2.63057	−	2.09781i	0.196618	−	0.156798i	−0.520232	−	0.854025i	$-0.674155\pi$
$179$	2.63057	−	2.09781i	0.196618	−	0.156798i	0.716850	+	0.697227i	$0.245583\pi$
$180$		0			0
$181$	16.8326	−	3.84194i	1.25116	−	0.285569i	0.454910	−	0.890538i	$-0.349672\pi$
$181$	16.8326	−	3.84194i	1.25116	−	0.285569i	0.796249	+	0.604969i	$0.206814\pi$
$182$	−0.275905	+	1.52036i	−0.0204514	+	0.112697i
$183$		0			0
$184$	−6.74497	+	11.2892i	−0.497246	+	0.832249i
$185$	−0.378395	−	1.00823i	−0.0278201	−	0.0741264i
$186$		0			0
$187$	−1.14978	−	0.553705i	−0.0840802	−	0.0404909i
$188$	−0.262787	−	0.190926i	−0.0191657	−	0.0139247i
$189$		0			0
$190$	−8.21203	+	10.2976i	−0.595763	+	0.747063i
$191$	−12.6179	−	21.1188i	−0.912999	−	1.52810i	−0.847856	−	0.530227i	$-0.822107\pi$
$191$	−12.6179	−	21.1188i	−0.912999	−	1.52810i	−0.0651432	−	0.997876i	$-0.520750\pi$
$192$		0			0
$193$	−15.0865	−	3.44340i	−1.08595	−	0.247862i	−0.358161	−	0.933660i	$-0.616596\pi$
$193$	−15.0865	−	3.44340i	−1.08595	−	0.247862i	−0.727792	+	0.685798i	$0.759453\pi$
$194$	−0.936607	+	2.19130i	−0.0672445	+	0.157326i
$195$		0			0
$196$	−0.453544	+	0.329519i	−0.0323960	+	0.0235371i
$197$	3.19233	−	0.579322i	0.227444	−	0.0412750i	−0.0636383	−	0.997973i	$-0.520270\pi$
$197$	3.19233	−	0.579322i	0.227444	−	0.0412750i	0.291082	+	0.956698i	$0.405985\pi$
$198$		0			0
$199$	1.25600	+	3.86558i	0.0890357	+	0.274024i	0.985653	−	0.168782i	$-0.0539833\pi$
$199$	1.25600	+	3.86558i	0.0890357	+	0.274024i	−0.896618	+	0.442805i	$0.853983\pi$
$200$	7.77570	+	4.18428i	0.549825	+	0.295873i
$201$		0			0
$202$	−7.16362	−	13.3122i	−0.504031	−	0.936646i
$203$	28.3812	+	7.83272i	1.99197	+	0.549749i
$204$		0			0
$205$	6.41222	−	0.868594i	0.447849	−	0.0606652i
$206$	3.72610	+	13.5012i	0.259610	+	0.940675i
$207$		0			0
$208$	1.47378	+	0.478861i	0.102188	+	0.0332030i
$209$	−22.1159	+	1.99047i	−1.52979	+	0.137684i
$210$		0			0
$211$	−25.5292	+	1.14652i	−1.75750	+	0.0789294i	−0.900090	−	0.435704i	$-0.856499\pi$
$211$	−25.5292	+	1.14652i	−1.75750	+	0.0789294i	−0.857410	+	0.514634i	$0.827928\pi$
$212$	0.376566			0.0258627
$213$		0			0
$214$	−17.5140			−1.19723
$215$	−15.8355	+	0.711172i	−1.07997	+	0.0485016i
$216$		0			0
$217$	13.5385	−	1.21849i	0.919053	−	0.0827163i
$218$	6.89339	+	2.23980i	0.466880	+	0.151698i
$219$		0			0
$220$	0.330083	+	1.19603i	0.0222542	+	0.0806361i
$221$	−0.135255	+	0.0183215i	−0.00909823	+	0.00123244i
$222$		0			0
$223$	12.7378	+	3.51541i	0.852987	+	0.235409i	0.665075	−	0.746777i	$-0.268400\pi$
$223$	12.7378	+	3.51541i	0.852987	+	0.235409i	0.187912	+	0.982186i	$0.439828\pi$
$224$	2.44462	+	4.54287i	0.163338	+	0.303533i
$225$		0			0
$226$	7.68919	+	4.13773i	0.511477	+	0.275238i
$227$	1.72904	+	5.32142i	0.114760	+	0.353195i	0.991897	−	0.127045i	$-0.0405493\pi$
$227$	1.72904	+	5.32142i	0.114760	+	0.353195i	−0.877137	+	0.480241i	$0.840549\pi$
$228$		0			0
$229$	25.6652	−	4.65755i	1.69601	−	0.307780i	0.757446	−	0.652897i	$-0.226447\pi$
$229$	25.6652	−	4.65755i	1.69601	−	0.307780i	0.938559	+	0.345118i	$0.112161\pi$
$230$	−7.86852	+	5.71682i	−0.518835	+	0.376956i
$231$		0			0
$232$	10.0147	−	23.4305i	0.657495	−	1.53829i
$233$	−13.2498	−	3.02418i	−0.868023	−	0.198121i	−0.234756	−	0.972054i	$-0.575429\pi$
$233$	−13.2498	−	3.02418i	−0.868023	−	0.198121i	−0.633267	+	0.773934i	$0.718286\pi$
$234$		0			0
$235$	0.671909	+	1.12459i	0.0438305	+	0.0733599i
$236$	−1.83977	+	2.30700i	−0.119759	+	0.150173i
$237$		0			0
$238$	−1.45410	−	1.05646i	−0.0942552	−	0.0684804i
$239$	−10.2826	−	4.95183i	−0.665125	−	0.320308i	0.0706815	−	0.997499i	$-0.477483\pi$
$239$	−10.2826	−	4.95183i	−0.665125	−	0.320308i	−0.735807	+	0.677191i	$0.763197\pi$
$240$		0			0
$241$	−2.38557	−	6.35634i	−0.153668	−	0.409448i	0.836743	−	0.547595i	$-0.184457\pi$
$241$	−2.38557	−	6.35634i	−0.153668	−	0.409448i	−0.990412	+	0.138147i	$0.955885\pi$
$242$	0.578553	−	0.968334i	0.0371908	−	0.0622469i
$243$		0			0
$244$	0.643240	−	3.54455i	0.0411793	−	0.226916i
$245$	2.20428	−	0.503112i	0.140826	−	0.0321426i
$246$		0			0
$247$	−1.85680	+	1.48075i	−0.118146	+	0.0942180i
$248$	0.527805	−	11.7525i	0.0335156	−	0.746284i
$249$		0			0
$250$	9.99405	+	12.5321i	0.632079	+	0.792602i
$251$	−3.00979	+	8.01955i	−0.189976	+	0.506190i	−0.996364	−	0.0851972i	$-0.972848\pi$
$251$	−3.00979	+	8.01955i	−0.189976	+	0.506190i	0.806388	+	0.591387i	$0.201419\pi$
$252$		0			0
$253$	−16.1337	−	2.92784i	−1.01432	−	0.184072i
$254$	−6.64838	+	3.20169i	−0.417156	+	0.200892i
$255$		0			0
$256$	6.80537	−	2.55410i	0.425336	−	0.159631i
$257$	−3.19874	−	4.84589i	−0.199532	−	0.302278i	0.721008	−	0.692927i	$-0.243679\pi$
$257$	−3.19874	−	4.84589i	−0.199532	−	0.302278i	−0.920540	+	0.390649i	$0.872251\pi$
$258$		0			0
$259$	1.50300	−	2.06871i	0.0933920	−	0.128543i
$260$	0.0999340	+	0.0873097i	0.00619764	+	0.00541472i
$261$		0			0
$262$	27.8343	−	16.6302i	1.71961	−	1.02742i
$263$	0.929098	+	0.613293i	0.0572907	+	0.0378172i	0.579218	−	0.815173i	$-0.303358\pi$
$263$	0.929098	+	0.613293i	0.0572907	+	0.0378172i	−0.521927	+	0.852990i	$0.674787\pi$
$264$		0			0
$265$	−1.39649	−	0.596889i	−0.0857858	−	0.0366666i
$266$	−31.1484	−	2.80341i	−1.90983	−	0.171888i
$267$		0			0
$268$	0.227764	+	1.25508i	0.0139129	+	0.0766662i
$269$	−4.33900	−	10.1516i	−0.264554	−	0.618954i	0.733607	−	0.679574i	$-0.237835\pi$
$269$	−4.33900	−	10.1516i	−0.264554	−	0.618954i	−0.998161	+	0.0606196i	$0.980692\pi$
$270$		0			0
$271$	3.43150	−	6.37680i	0.208449	−	0.387363i	−0.754807	−	0.655946i	$-0.772270\pi$
$271$	3.43150	−	6.37680i	0.208449	−	0.387363i	0.963256	+	0.268583i	$0.0865554\pi$
$272$	−1.24566	+	1.30285i	−0.0755290	+	0.0789972i
$273$		0			0
$274$	5.93699	−	21.5122i	0.358667	−	1.29960i
$275$	−1.47790	+	10.9103i	−0.0891209	+	0.657917i
$276$		0			0
$277$	−0.435604	+	0.120219i	−0.0261729	+	0.00722327i	−0.279099	−	0.960262i	$-0.590036\pi$
$277$	−0.435604	+	0.120219i	−0.0261729	+	0.00722327i	0.252926	+	0.967486i	$0.418607\pi$
$278$	10.5614	+	11.0464i	0.633431	+	0.662517i
$279$		0			0
$280$	−0.854191	−	9.49084i	−0.0510477	−	0.567186i
$281$	8.09167	−	7.06948i	0.482709	−	0.421730i	−0.381879	−	0.924213i	$-0.624723\pi$
$281$	8.09167	−	7.06948i	0.482709	−	0.421730i	0.864587	+	0.502483i	$0.167580\pi$
$282$		0			0
$283$			29.5811i			1.75841i	0.476442	+	0.879206i	$0.341926\pi$
$283$			29.5811i			1.75841i	−0.476442	+	0.879206i	$0.658074\pi$
$284$	2.55813	+	0.525269i	0.151797	+	0.0311690i
$285$		0			0
$286$	0.0748095	+	1.66576i	0.00442358	+	0.0984986i
$287$	10.1090	+	11.5707i	0.596716	+	0.682997i
$288$		0			0
$289$	−5.20423	+	16.0170i	−0.306131	+	0.942174i
$290$	13.6213	−	13.0233i	0.799870	−	0.764754i
$291$		0			0
$292$	−0.531776	−	3.92573i	−0.0311199	−	0.229736i
$293$	0.480696	+	0.0651148i	0.0280826	+	0.00380405i	0.148261	−	0.988948i	$-0.452632\pi$
$293$	0.480696	+	0.0651148i	0.0280826	+	0.00380405i	−0.120178	+	0.992752i	$0.538347\pi$
$294$		0			0
$295$	10.4796	−	5.63929i	0.610144	−	0.328332i
$296$	−1.59956	−	1.52934i	−0.0929726	−	0.0888909i
$297$		0			0
$298$	−6.50288	+	2.11291i	−0.376702	+	0.122398i
$299$	−1.61262	+	0.689267i	−0.0932603	+	0.0398614i
$300$		0			0
$301$	−22.1235	−	30.4504i	−1.27518	−	1.75513i
$302$	0.00857745	−	0.0953032i	0.000493577	−	0.00548408i
$303$		0			0
$304$	−6.97917	+	30.5777i	−0.400283	+	1.75375i
$305$	−8.00385	+	12.1253i	−0.458299	+	0.694294i
$306$		0			0
$307$	−2.60341	−	2.07615i	−0.148585	−	0.118492i	0.546376	−	0.837540i	$-0.316007\pi$
$307$	−2.60341	−	2.07615i	−0.148585	−	0.118492i	−0.694961	+	0.719048i	$0.744578\pi$
$308$	−1.93835	+	2.21862i	−0.110448	+	0.126418i
$309$		0			0
$310$	3.77510	−	7.83907i	0.214411	−	0.445229i
$311$	−8.72998	+	5.76261i	−0.495032	+	0.326768i	−0.773627	−	0.633641i	$-0.781560\pi$
$311$	−8.72998	+	5.76261i	−0.495032	+	0.326768i	0.278596	+	0.960409i	$0.410131\pi$
$312$		0			0
$313$	3.47742	+	2.07766i	0.196556	+	0.117437i	0.607805	−	0.794086i	$-0.292050\pi$
$313$	3.47742	+	2.07766i	0.196556	+	0.117437i	−0.411249	+	0.911523i	$0.634907\pi$
$314$	6.53777	+	13.5758i	0.368948	+	0.766128i
$315$		0			0
$316$	−0.212558	−	0.931279i	−0.0119573	−	0.0523885i
$317$	5.64679	+	2.11928i	0.317156	+	0.119030i	0.504876	−	0.863192i	$-0.331538\pi$
$317$	5.64679	+	2.11928i	0.317156	+	0.119030i	−0.187720	+	0.982223i	$0.560110\pi$
$318$		0			0
$319$	31.7396	+	1.42543i	1.77708	+	0.0798086i
$320$	−7.99891	−	0.359232i	−0.447153	−	0.0200817i
$321$		0			0
$322$	−21.6216	−	8.11471i	−1.20492	−	0.452215i
$323$	−0.614720	−	2.69326i	−0.0342039	−	0.149857i
$324$		0			0
$325$	0.510923	+	1.06094i	0.0283409	+	0.0588505i
$326$	−25.8870	−	15.4668i	−1.43375	−	0.856626i
$327$		0			0
$328$	11.0977	−	7.32553i	0.612768	−	0.404485i
$329$	−1.34964	+	2.80256i	−0.0744082	+	0.154510i
$330$		0			0
$331$	7.37881	−	8.44572i	0.405576	−	0.464219i	−0.513621	−	0.858017i	$-0.671696\pi$
$331$	7.37881	−	8.44572i	0.405576	−	0.464219i	0.919197	+	0.393798i	$0.128839\pi$
$332$	−0.376746	−	0.300445i	−0.0206766	−	0.0164891i
$333$		0			0
$334$	15.0582	−	22.8122i	0.823947	−	1.24823i
$335$	1.14475	−	5.01548i	0.0625444	−	0.274025i
$336$		0			0
$337$	0.857469	−	9.52726i	0.0467093	−	0.518983i	−0.938222	−	0.346035i	$-0.887528\pi$
$337$	0.857469	−	9.52726i	0.0467093	−	0.518983i	0.984931	−	0.172948i	$-0.0553293\pi$
$338$	−11.5086	−	15.8403i	−0.625987	−	0.861597i
$339$		0			0
$340$	−0.141937	+	0.0606668i	−0.00769761	+	0.00329012i
$341$	13.9507	−	4.53286i	0.755474	−	0.245468i
$342$		0			0
$343$	−11.1362	−	10.6473i	−0.601301	−	0.574902i
$344$	−28.6852	+	15.4361i	−1.54660	+	0.832261i
$345$		0			0
$346$	22.5570	+	3.05555i	1.21267	+	0.164267i
$347$	2.32906	+	17.1938i	0.125031	+	0.923013i	0.939438	+	0.342719i	$0.111348\pi$
$347$	2.32906	+	17.1938i	0.125031	+	0.923013i	−0.814407	+	0.580294i	$0.802938\pi$
$348$		0			0
$349$	−6.80495	+	6.50619i	−0.364260	+	0.348269i	−0.850894	−	0.525338i	$-0.823939\pi$
$349$	−6.80495	+	6.50619i	−0.364260	+	0.348269i	0.486633	+	0.873606i	$0.338225\pi$
$350$	−4.79181	+	14.7477i	−0.256133	+	0.788296i
$351$		0			0
$352$	3.66275	+	4.19236i	0.195225	+	0.223453i
$353$	0.765399	+	17.0429i	0.0407381	+	0.907104i	0.910469	+	0.413578i	$0.135721\pi$
$353$	0.765399	+	17.0429i	0.0407381	+	0.907104i	−0.869731	+	0.493526i	$0.835708\pi$
$354$		0			0
$355$	−8.65419	−	6.00280i	−0.459317	−	0.318596i
$356$			1.60771i			0.0852087i
$357$		0			0
$358$	3.85099	−	3.36451i	0.203531	−	0.177820i
$359$	−1.24737	−	13.8594i	−0.0658335	−	0.731470i	−0.959309	−	0.282358i	$-0.908883\pi$
$359$	−1.24737	−	13.8594i	−0.0658335	−	0.731470i	0.893475	−	0.449112i	$-0.148260\pi$
$360$		0			0
$361$	−20.0880	−	21.0104i	−1.05726	−	1.10581i
$362$	25.2952	−	6.98104i	1.32949	−	0.366915i
$363$		0			0
$364$	−0.0422965	+	0.312245i	−0.00221694	+	0.0163661i
$365$	−4.25053	+	15.4014i	−0.222483	+	0.806148i
$366$		0			0
$367$	−12.0040	+	12.5552i	−0.626602	+	0.655375i	−0.957548	−	0.288275i	$-0.906918\pi$
$367$	−12.0040	+	12.5552i	−0.626602	+	0.655375i	0.330945	+	0.943650i	$0.392632\pi$
$368$	−10.9750	+	20.3950i	−0.572112	+	1.06316i
$369$		0			0
$370$	−0.643270	−	1.50501i	−0.0334420	−	0.0782415i
$371$	−0.643897	−	3.54817i	−0.0334295	−	0.184212i
$372$		0			0
$373$	4.99088	+	0.449187i	0.258418	+	0.0232580i	0.218091	−	0.975929i	$-0.430017\pi$
$373$	4.99088	+	0.449187i	0.258418	+	0.0232580i	0.0403271	+	0.999187i	$0.487160\pi$
$374$	−1.78348	−	0.762297i	−0.0922217	−	0.0394174i
$375$		0			0
$376$	2.24675	+	1.48307i	0.115867	+	0.0764833i
$377$	2.91709	−	1.74288i	0.150238	−	0.0897629i
$378$		0			0
$379$	−4.69967	−	4.10597i	−0.241406	−	0.210910i	0.528730	−	0.848790i	$-0.322669\pi$
$379$	−4.69967	−	4.10597i	−0.241406	−	0.210910i	−0.770135	+	0.637880i	$0.779811\pi$
$380$	−1.57871	+	2.17290i	−0.0809859	+	0.111468i
$381$		0			0
$382$	−20.5980	−	31.2046i	−1.05388	−	1.59657i
$383$	9.76050	−	3.66318i	0.498738	−	0.187180i	−0.0893125	−	0.996004i	$-0.528467\pi$
$383$	9.76050	−	3.66318i	0.498738	−	0.187180i	0.588051	+	0.808824i	$0.299896\pi$
$384$		0			0
$385$	10.7051	−	5.15529i	0.545581	−	0.262738i
$386$	−23.1409	−	4.19946i	−1.17784	−	0.213747i
$387$		0			0
$388$	−0.170753	+	0.454971i	−0.00866869	+	0.0230976i
$389$	−17.1667	−	21.5263i	−0.870385	−	1.09143i	−0.995064	−	0.0992308i	$-0.968362\pi$
$389$	−17.1667	−	21.5263i	−0.870385	−	1.09143i	0.124680	−	0.992197i	$-0.460210\pi$
$390$		0			0
$391$	0.0915223	−	2.03790i	0.00462848	−	0.103061i
$392$	3.63261	−	2.89691i	0.183474	−	0.146316i
$393$		0			0
$394$	4.80745	−	1.09727i	0.242196	−	0.0552797i
$395$	−0.687885	+	3.79056i	−0.0346113	+	0.190724i
$396$		0			0
$397$	−10.4026	+	17.4109i	−0.522089	+	0.873831i	−0.999989	−	0.00458370i	$-0.998541\pi$
$397$	−10.4026	+	17.4109i	−0.522089	+	0.873831i	0.477900	+	0.878414i	$0.341398\pi$
$398$	2.17059	+	5.78352i	0.108802	+	0.289902i
$399$		0			0
$400$	14.0111	+	6.74738i	0.700554	+	0.337369i
$401$	−18.7747	−	13.6406i	−0.937562	−	0.681179i	0.0102703	−	0.999947i	$-0.496731\pi$
$401$	−18.7747	−	13.6406i	−0.937562	−	0.681179i	−0.947833	+	0.318768i	$0.896731\pi$
$402$		0			0
$403$	0.978174	−	1.22659i	0.0487263	−	0.0611009i
$404$	−1.58113	−	2.64637i	−0.0786643	−	0.131662i
$405$		0			0
$406$	43.6257	+	9.95729i	2.16511	+	0.494172i
$407$	1.08450	−	2.53731i	0.0537566	−	0.125770i
$408$		0			0
$409$	−9.82464	+	7.13802i	−0.485797	+	0.352952i	−0.803566	−	0.595216i	$-0.797067\pi$
$409$	−9.82464	+	7.13802i	−0.485797	+	0.352952i	0.317769	+	0.948168i	$0.397067\pi$
$410$	9.67654	−	1.75603i	0.477890	−	0.0867243i
$411$		0			0
$412$	0.882586	+	2.71632i	0.0434819	+	0.133823i
$413$	24.8834	+	13.3903i	1.22443	+	0.658895i
$414$		0			0
$415$	0.920928	+	1.71137i	0.0452066	+	0.0840079i
$416$	0.573956	+	0.158402i	0.0281405	+	0.00776629i
$417$		0			0
$418$	−33.4432	+	4.53019i	−1.63576	+	0.221579i
$419$	7.54570	+	27.3412i	0.368631	+	1.33571i	0.879439	+	0.476011i	$0.157918\pi$
$419$	7.54570	+	27.3412i	0.368631	+	1.33571i	−0.510808	+	0.859695i	$0.670654\pi$
$420$		0			0
$421$	33.0427	+	10.7362i	1.61040	+	0.523251i	0.969650	−	0.244496i	$-0.0786226\pi$
$421$	33.0427	+	10.7362i	1.61040	+	0.523251i	0.640752	+	0.767748i	$0.278623\pi$
$422$	−38.6831	+	3.48154i	−1.88306	+	0.169479i
$423$		0			0
$424$	−3.11780	+	0.140020i	−0.151414	+	0.00679999i
$425$	−1.36973			−0.0664418
$426$		0			0
$427$	−34.4981			−1.66948
$428$	−3.56787	+	0.160233i	−0.172459	+	0.00774516i
$429$		0			0
$430$	−23.9947	+	2.15957i	−1.15713	+	0.104144i
$431$	17.5836	+	5.71325i	0.846970	+	0.275197i	0.700177	−	0.713970i	$-0.253105\pi$
$431$	17.5836	+	5.71325i	0.846970	+	0.275197i	0.146794	+	0.989167i	$0.453105\pi$
$432$		0			0
$433$	−6.88168	−	24.9352i	−0.330712	−	1.19831i	−0.920497	−	0.390749i	$-0.872216\pi$
$433$	−6.88168	−	24.9352i	−0.330712	−	1.19831i	0.589785	−	0.807560i	$-0.299213\pi$
$434$	20.4726	−	2.77320i	0.982717	−	0.133118i
$435$		0			0
$436$	1.42478	+	0.393215i	0.0682347	+	0.0188316i
$437$	−16.8202	−	31.2571i	−0.804619	−	1.49523i
$438$		0			0
$439$	33.4314	+	17.9902i	1.59559	+	0.858626i	0.998401	+	0.0565291i	$0.0180034\pi$
$439$	33.4314	+	17.9902i	1.59559	+	0.858626i	0.597194	+	0.802097i	$0.296282\pi$
$440$	−3.17766	−	9.77982i	−0.151489	−	0.466235i
$441$		0			0
$442$	−0.204110	+	0.0370405i	−0.00970853	+	0.00176184i
$443$	27.1148	−	19.7001i	1.28827	−	0.935979i	0.288496	−	0.957481i	$-0.406845\pi$
$443$	27.1148	−	19.7001i	1.28827	−	0.935979i	0.999769	+	0.0215016i	$0.00684469\pi$
$444$		0			0
$445$	2.54836	−	5.96219i	0.120804	−	0.282635i
$446$	19.5797	+	4.46894i	0.927126	+	0.211610i
$447$		0			0
$448$	−9.75141	−	16.3211i	−0.460711	−	0.771100i
$449$	−12.7533	+	15.9922i	−0.601868	+	0.754718i	−0.985668	−	0.168698i	$-0.946044\pi$
$449$	−12.7533	+	15.9922i	−0.601868	+	0.754718i	0.383800	+	0.923416i	$0.374615\pi$
$450$		0			0
$451$	13.4137	+	9.74563i	0.631627	+	0.458904i
$452$	1.60426	+	0.772571i	0.0754581	+	0.0363387i
$453$		0			0
$454$	2.98807	+	7.96170i	0.140237	+	0.373661i
$455$	0.651790	−	1.09091i	0.0305564	−	0.0511428i
$456$		0			0
$457$	4.48111	−	24.6929i	0.209617	−	1.15509i	−0.691785	−	0.722104i	$-0.743175\pi$
$457$	4.48111	−	24.6929i	0.209617	−	1.15509i	0.901402	−	0.432983i	$-0.142539\pi$
$458$	38.6503	−	8.82168i	1.80601	−	0.412210i
$459$		0			0
$460$	−1.55064	+	1.23659i	−0.0722988	+	0.0576564i
$461$	1.68622	−	37.5467i	0.0785352	−	1.74872i	−0.443929	−	0.896062i	$-0.646416\pi$
$461$	1.68622	−	37.5467i	0.0785352	−	1.74872i	0.522464	−	0.852661i	$-0.325013\pi$
$462$		0			0
$463$	6.43976	+	8.07520i	0.299281	+	0.375286i	0.908620	−	0.417623i	$-0.137137\pi$
$463$	6.43976	+	8.07520i	0.299281	+	0.375286i	−0.609339	+	0.792909i	$0.708565\pi$
$464$	15.7683	−	42.0146i	0.732026	−	1.95048i
$465$		0			0
$466$	−20.3236	−	3.68818i	−0.941471	−	0.170852i
$467$	−4.95092	+	2.38424i	−0.229101	+	0.110329i	−0.544913	−	0.838492i	$-0.683437\pi$
$467$	−4.95092	+	2.38424i	−0.229101	+	0.110329i	0.315812	+	0.948822i	$0.397723\pi$
$468$		0			0
$469$	11.4364	−	4.29217i	0.528086	−	0.198194i
$470$	1.09685	+	1.66166i	0.0505940	+	0.0766466i
$471$		0			0
$472$	14.3746	−	19.7850i	0.661647	−	0.910679i
$473$	−30.5872	−	26.7232i	−1.40640	−	1.22874i
$474$		0			0
$475$	−20.4598	+	12.2242i	−0.938761	+	0.560884i
$476$	−0.305888	−	0.201915i	−0.0140203	−	0.00925474i
$477$		0			0
$478$	−15.9499	−	6.81730i	−0.729529	−	0.311816i
$479$	7.28989	+	0.656102i	0.333083	+	0.0299781i	0.254919	−	0.966962i	$-0.417951\pi$
$479$	7.28989	+	0.656102i	0.333083	+	0.0299781i	0.0781645	+	0.996940i	$0.475094\pi$
$480$		0			0
$481$	−0.0526965	−	0.290382i	−0.00240275	−	0.0132403i
$482$	−4.05547	−	9.48825i	−0.184722	−	0.432178i
$483$		0			0
$484$	0.109001	−	0.202558i	0.00495459	−	0.00920717i
$485$	1.35440	−	1.41660i	0.0615003	−	0.0643243i
$486$		0			0
$487$	−8.48678	+	30.7512i	−0.384573	+	1.39347i	0.473886	+	0.880586i	$0.342851\pi$
$487$	−8.48678	+	30.7512i	−0.384573	+	1.39347i	−0.858459	+	0.512882i	$0.828578\pi$
$488$	−4.00775	+	29.5864i	−0.181422	+	1.33931i
$489$		0			0
$490$	3.31248	−	0.914186i	0.149643	−	0.0412987i
$491$	−1.15234	−	1.20526i	−0.0520045	−	0.0543925i	0.696281	−	0.717770i	$-0.254837\pi$
$491$	−1.15234	−	1.20526i	−0.0520045	−	0.0543925i	−0.748285	+	0.663377i	$0.769123\pi$
$492$		0			0
$493$	0.354313	+	3.93674i	0.0159575	+	0.177302i
$494$	−2.71824	+	2.37486i	−0.122300	+	0.106850i
$495$		0			0
$496$		−	20.7189i		−	0.930305i
$497$	0.575120	−	25.0019i	0.0257977	−	1.12149i
$498$		0			0
$499$	0.692918	+	15.4290i	0.0310193	+	0.690698i	0.952911	+	0.303250i	$0.0980718\pi$
$499$	0.692918	+	15.4290i	0.0310193	+	0.690698i	−0.921892	+	0.387448i	$0.873357\pi$
$500$	2.15060	+	2.46156i	0.0961776	+	0.110084i
$501$		0			0
$502$	−4.02297	+	12.3814i	−0.179554	+	0.552610i
$503$	15.8220	−	15.1274i	0.705468	−	0.674496i	−0.250450	−	0.968129i	$-0.580579\pi$
$503$	15.8220	−	15.1274i	0.705468	−	0.674496i	0.955918	+	0.293633i	$0.0948644\pi$
$504$		0			0
$505$	1.66889	+	12.3203i	0.0742647	+	0.548244i
$506$	−24.6957	−	3.34526i	−1.09786	−	0.148715i
$507$		0			0
$508$	−1.32509	+	0.713059i	−0.0587912	+	0.0316369i
$509$	11.2008	+	10.7091i	0.496467	+	0.474671i	0.897263	−	0.441496i	$-0.145552\pi$
$509$	11.2008	+	10.7091i	0.496467	+	0.474671i	−0.400796	+	0.916167i	$0.631266\pi$
$510$		0			0
$511$	−36.0806	+	11.7233i	−1.59611	+	0.518608i
$512$	−14.1395	+	6.04351i	−0.624884	+	0.267088i
$513$		0			0
$514$	−5.18713	−	7.13947i	−0.228794	−	0.314908i
$515$	1.03254	−	11.4724i	0.0454990	−	0.505535i
$516$		0			0
$517$	−0.746937	+	3.27255i	−0.0328503	+	0.143926i
$518$	2.14097	−	3.24343i	0.0940688	−	0.142508i
$519$		0			0
$520$	−0.859873	−	0.685726i	−0.0377079	−	0.0300711i
$521$	12.0856	−	13.8331i	0.529479	−	0.606038i	−0.424678	−	0.905345i	$-0.639613\pi$
$521$	12.0856	−	13.8331i	0.529479	−	0.606038i	0.954157	+	0.299307i	$0.0967554\pi$
$522$		0			0
$523$	−18.5760	+	38.5734i	−0.812271	+	1.68670i	−0.0891063	+	0.996022i	$0.528401\pi$
$523$	−18.5760	+	38.5734i	−0.812271	+	1.68670i	−0.723165	+	0.690676i	$0.757313\pi$
$524$	5.51812	−	3.64248i	0.241060	−	0.159123i
$525$		0			0
$526$	1.45248	+	0.867818i	0.0633312	+	0.0378387i
$527$	0.791797	+	1.64418i	0.0344912	+	0.0716217i
$528$		0			0
$529$	−0.714563	−	3.13070i	−0.0310679	−	0.136118i
$530$	−2.16101	−	0.811042i	−0.0938684	−	0.0352294i
$531$		0			0
$532$	−6.37106	−	0.286125i	−0.276221	−	0.0124051i
$533$	1.77154	+	0.0795598i	0.0767338	+	0.00344612i
$534$		0			0
$535$	13.4854	+	5.06115i	0.583024	+	0.218813i
$536$	−2.35246	−	10.3068i	−0.101611	−	0.445186i
$537$		0			0
$538$	−7.28018	−	15.1175i	−0.313871	−	0.651760i
$539$	4.97328	+	2.97140i	0.214214	+	0.127987i
$540$		0			0
$541$	−36.0292	+	23.7827i	−1.54902	+	1.02250i	−0.569293	+	0.822134i	$0.692783\pi$
$541$	−36.0292	+	23.7827i	−1.54902	+	1.02250i	−0.979722	+	0.200362i	$0.935788\pi$
$542$	4.77528	−	9.91597i	0.205116	−	0.425928i
$543$		0			0
$544$	−0.455677	+	0.521565i	−0.0195370	+	0.0223619i
$545$	−4.66051	−	3.71663i	−0.199634	−	0.159203i
$546$		0			0
$547$	9.93866	−	15.0564i	0.424946	−	0.643766i	−0.557529	−	0.830157i	$-0.688251\pi$
$547$	9.93866	−	15.0564i	0.424946	−	0.643766i	0.982476	+	0.186391i	$0.0596792\pi$
$548$	1.01264	−	4.43668i	0.0432580	−	0.189526i
$549$		0			0
$550$	−1.49997	+	16.6661i	−0.0639591	+	0.710644i
$551$	40.4259	+	55.6415i	1.72220	+	2.37041i
$552$		0			0
$553$	−8.41145	+	3.59523i	−0.357691	+	0.152885i
$554$	−0.653187	+	0.212233i	−0.0277513	+	0.00901693i
$555$		0			0
$556$	2.25258	+	2.15369i	0.0955308	+	0.0913368i
$557$	−3.35976	+	1.80796i	−0.142358	+	0.0766059i	−0.543497	−	0.839411i	$-0.682900\pi$
$557$	−3.35976	+	1.80796i	−0.142358	+	0.0766059i	0.401139	+	0.916017i	$0.368614\pi$
$558$		0			0
$559$	−4.30479	−	0.583123i	−0.182073	−	0.0246635i
$560$	−2.25276	−	16.6306i	−0.0951967	−	0.702770i
$561$		0			0
$562$	11.8037	−	11.2854i	0.497907	−	0.476048i
$563$	4.90213	−	15.0872i	0.206600	−	0.635850i	−0.793044	−	0.609165i	$-0.791505\pi$
$563$	4.90213	−	15.0872i	0.206600	−	0.635850i	0.999644	−	0.0266852i	$-0.00849517\pi$
$564$		0			0
$565$	−4.72479	−	5.40796i	−0.198774	−	0.227515i
$566$	2.01706	+	44.9134i	0.0847834	+	1.88785i
$567$		0			0
$568$	−21.3754	−	3.39779i	−0.896893	−	0.142568i
$569$			11.3182i			0.474485i	0.971450	+	0.237242i	$0.0762436\pi$
$569$			11.3182i			0.474485i	−0.971450	+	0.237242i	$0.923756\pi$
$570$		0			0
$571$	−1.92787	+	1.68433i	−0.0806787	+	0.0704868i	−0.697333	−	0.716747i	$-0.745630\pi$
$571$	−1.92787	+	1.68433i	−0.0806787	+	0.0704868i	0.616655	+	0.787234i	$0.288487\pi$
$572$	0.0304797	+	0.338657i	0.00127442	+	0.0141600i
$573$		0			0
$574$	16.1376	+	16.8786i	0.673572	+	0.704501i
$575$	−16.9653	+	4.68213i	−0.707503	+	0.195258i
$576$		0			0
$577$	−5.31219	+	39.2162i	−0.221149	+	1.63259i	0.451247	+	0.892399i	$0.350979\pi$
$577$	−5.31219	+	39.2162i	−0.221149	+	1.63259i	−0.672396	+	0.740191i	$0.734735\pi$
$578$	−6.80950	+	24.6737i	−0.283238	+	1.02629i
$579$		0			0
$580$	2.65572	−	2.77767i	0.110273	−	0.115336i
$581$	−2.18672	+	4.06360i	−0.0907203	+	0.168587i
$582$		0			0
$583$	−1.52943	−	3.57827i	−0.0633423	−	0.148197i
$584$	5.86259	+	32.3055i	0.242596	+	1.33681i
$585$		0			0
$586$	0.734288	+	0.0660871i	0.0303332	+	0.00273004i
$587$	4.59227	+	1.96283i	0.189543	+	0.0810147i	0.485704	−	0.874124i	$-0.338563\pi$
$587$	4.59227	+	1.96283i	0.189543	+	0.0810147i	−0.296160	+	0.955138i	$0.595706\pi$
$588$		0			0
$589$	26.5007	+	17.4929i	1.09194	+	0.720783i
$590$	15.5267	−	9.27680i	0.639226	−	0.381920i
$591$		0			0
$592$	−2.93509	−	2.56431i	−0.120631	−	0.105392i
$593$	−15.6891	+	21.5942i	−0.644276	+	0.886769i	−0.998835	−	0.0482643i	$-0.984631\pi$
$593$	−15.6891	+	21.5942i	−0.644276	+	0.886769i	0.354559	+	0.935034i	$0.384631\pi$
$594$		0			0
$595$	0.814329	+	1.23366i	0.0333842	+	0.0505750i
$596$	−1.30541	+	0.489927i	−0.0534715	+	0.0200682i
$597$		0			0
$598$	−2.40147	+	1.15648i	−0.0982032	+	0.0472922i
$599$	28.0295	+	5.08660i	1.14525	+	0.207833i	0.717830	−	0.696218i	$-0.245135\pi$
$599$	28.0295	+	5.08660i	1.14525	+	0.207833i	0.427424	+	0.904051i	$0.359421\pi$
$600$		0			0
$601$	8.69344	−	23.1636i	0.354613	−	0.944863i	−0.630991	−	0.775790i	$-0.717351\pi$
$601$	8.69344	−	23.1636i	0.354613	−	0.944863i	0.985604	−	0.169072i	$-0.0540771\pi$
$602$	−35.6668	−	44.7248i	−1.45367	−	1.82285i
$603$		0			0
$604$	0.000875441	−	0.0194932i	3.56212e−5	−	0.000793167i
$605$	−0.725300	+	0.578407i	−0.0294876	+	0.0235156i
$606$		0			0
$607$	47.8759	−	10.9274i	1.94322	−	0.443528i	0.953275	−	0.302105i	$-0.0976894\pi$
$607$	47.8759	−	10.9274i	1.94322	−	0.443528i	0.989949	−	0.141423i	$-0.0451678\pi$
$608$	−2.15179	+	11.8574i	−0.0872667	+	0.480879i
$609$		0			0
$610$	−11.3256	+	18.9558i	−0.458559	+	0.767498i
$611$	0.126148	+	0.336120i	0.00510340	+	0.0135980i
$612$		0			0
$613$	29.8302	+	14.3655i	1.20483	+	0.580217i	0.925049	−	0.379847i	$-0.124023\pi$
$613$	29.8302	+	14.3655i	1.20483	+	0.580217i	0.279783	+	0.960063i	$0.409738\pi$
$614$	−4.09436	−	2.97473i	−0.165235	−	0.120050i
$615$		0			0
$616$	15.2237	−	19.0899i	0.613381	−	0.769155i
$617$	16.2297	+	27.1640i	0.653384	+	1.09358i	0.988474	+	0.151394i	$0.0483761\pi$
$617$	16.2297	+	27.1640i	0.653384	+	1.09358i	−0.335090	+	0.942186i	$0.608767\pi$
$618$		0			0
$619$	−0.879751	−	0.200797i	−0.0353602	−	0.00807073i	0.204804	−	0.978803i	$-0.434344\pi$
$619$	−0.879751	−	0.200797i	−0.0353602	−	0.00807073i	−0.240164	+	0.970732i	$0.577201\pi$
$620$	0.697327	−	1.63148i	0.0280053	−	0.0655217i
$621$		0			0
$622$	−12.8619	+	9.34473i	−0.515716	+	0.374690i
$623$	15.1486	−	2.74906i	0.606915	−	0.110139i
$624$		0			0
$625$	1.23773	+	3.80935i	0.0495093	+	0.152374i
$626$	5.42149	+	2.91743i	0.216687	+	0.116604i
$627$		0			0
$628$	1.45605	+	2.70579i	0.0581026	+	0.107973i
$629$	0.330917	+	0.0913273i	0.0131945	+	0.00364146i
$630$		0			0
$631$	17.4689	−	2.36632i	0.695425	−	0.0942017i	0.222014	−	0.975043i	$-0.428737\pi$
$631$	17.4689	−	2.36632i	0.695425	−	0.0942017i	0.473411	+	0.880842i	$0.343023\pi$
$632$	2.10617	+	7.63153i	0.0837789	+	0.303566i
$633$		0			0
$634$	8.71812	+	2.83269i	0.346241	+	0.112500i
$635$	6.04432	−	0.543999i	0.239862	−	0.0215879i
$636$		0			0
$637$	0.618995	−	0.0277991i	0.0245255	−	0.00110144i
$638$	48.2879			1.91174
$639$		0			0
$640$	−16.5146			−0.652798
$641$	−40.2092	+	1.80580i	−1.58817	+	0.0713247i	−0.821306	−	0.570488i	$-0.806754\pi$
$641$	−40.2092	+	1.80580i	−1.58817	+	0.0713247i	−0.766861	+	0.641813i	$0.778183\pi$
$642$		0			0
$643$	37.0074	−	3.33072i	1.45943	−	0.131351i	0.668706	−	0.743527i	$-0.266848\pi$
$643$	37.0074	−	3.33072i	1.45943	−	0.131351i	0.790722	+	0.612176i	$0.209705\pi$
$644$	−4.47889	−	1.45528i	−0.176493	−	0.0573460i
$645$		0			0
$646$	−1.11699	−	4.04731i	−0.0439472	−	0.159239i
$647$	42.8924	−	5.81017i	1.68627	−	0.228421i	0.772607	−	0.634885i	$-0.218952\pi$
$647$	42.8924	−	5.81017i	1.68627	−	0.228421i	0.913667	+	0.406463i	$0.133238\pi$
$648$		0			0
$649$	29.3942	+	8.11229i	1.15382	+	0.318435i
$650$	0.848085	+	1.57601i	0.0332646	+	0.0618161i
$651$		0			0
$652$	−5.41509	−	2.91399i	−0.212071	−	0.114120i
$653$	14.3058	+	44.0288i	0.559830	+	1.72298i	0.682835	+	0.730573i	$0.260747\pi$
$653$	14.3058	+	44.0288i	0.559830	+	1.72298i	−0.123005	+	0.992406i	$0.539253\pi$
$654$		0			0
$655$	−26.2375	+	4.76141i	−1.02519	+	0.186044i
$656$	18.9463	−	13.7653i	0.739730	−	0.537445i
$657$		0			0
$658$	−1.85808	+	4.34720i	−0.0724355	+	0.169471i
$659$	39.0059	+	8.90285i	1.51946	+	0.346806i	0.899180	−	0.437578i	$-0.144164\pi$
$659$	39.0059	+	8.90285i	1.51946	+	0.346806i	0.620275	+	0.784384i	$0.287021\pi$
$660$		0			0
$661$	−17.8846	−	29.9338i	−0.695631	−	1.16429i	−0.978721	−	0.205196i	$-0.934217\pi$
$661$	−17.8846	−	29.9338i	−0.695631	−	1.16429i	0.283090	−	0.959093i	$-0.408640\pi$
$662$	10.6275	−	13.3264i	0.413048	−	0.517945i
$663$		0			0
$664$	3.23100	+	2.34746i	0.125387	+	0.0910991i
$665$	23.1735	+	11.1598i	0.898629	+	0.432757i
$666$		0			0
$667$	17.8454	+	47.5488i	0.690976	+	1.84110i
$668$	2.85888	−	4.78496i	0.110613	−	0.185136i
$669$		0			0
$670$	1.39610	−	7.69313i	0.0539359	−	0.297211i
$671$	−36.2941	+	8.28389i	−1.40112	+	0.319796i
$672$		0			0
$673$	−21.5629	+	17.1958i	−0.831188	+	0.662850i	−0.943701	−	0.330800i	$-0.892681\pi$
$673$	−21.5629	+	17.1958i	−0.831188	+	0.662850i	0.112513	+	0.993650i	$0.464110\pi$
$674$	0.652267	−	14.5238i	0.0251244	−	0.559438i
$675$		0			0
$676$	−2.48940	−	3.12161i	−0.0957463	−	0.120062i
$677$	−16.1805	+	43.1127i	−0.621866	+	1.65696i	0.125139	+	0.992139i	$0.460062\pi$
$677$	−16.1805	+	43.1127i	−0.621866	+	1.65696i	−0.747005	+	0.664818i	$0.768509\pi$
$678$		0			0
$679$	4.57890	+	0.830949i	0.175722	+	0.0318889i
$680$	1.15262	−	0.555070i	0.0442008	−	0.0212860i
$681$		0			0
$682$	20.8725	−	7.83358i	0.799249	−	0.299963i
$683$	−19.3189	−	29.2668i	−0.739216	−	1.11986i	−0.988469	−	0.151426i	$-0.951614\pi$
$683$	−19.3189	−	29.2668i	−0.739216	−	1.11986i	0.249253	−	0.968438i	$-0.419815\pi$
$684$		0			0
$685$	−10.7879	+	14.8483i	−0.412184	+	0.567323i
$686$	−17.6343	−	15.4067i	−0.673282	−	0.588229i
$687$		0			0
$688$	−49.2486	+	29.4247i	−1.87759	+	1.12181i
$689$	−0.347351	−	0.229285i	−0.0132330	−	0.00873505i
$690$		0			0
$691$	37.8694	+	16.1862i	1.44062	+	0.615751i	0.964608	−	0.263687i	$-0.0849386\pi$
$691$	37.8694	+	16.1862i	1.44062	+	0.615751i	0.476013	+	0.879438i	$0.342081\pi$
$692$	4.62315	+	0.416091i	0.175746	+	0.0158174i
$693$		0			0
$694$	4.70866	+	25.9468i	0.178738	+	0.984928i
$695$	−4.93990	−	11.5575i	−0.187381	−	0.438400i
$696$		0			0
$697$	−0.977461	+	1.81643i	−0.0370240	+	0.0688021i
$698$	−9.88841	+	10.3425i	−0.374282	+	0.391468i
$699$		0			0
$700$	−0.841241	+	3.04817i	−0.0317959	+	0.115210i
$701$	−2.85805	+	21.0990i	−0.107947	+	0.796898i	0.853341	+	0.521353i	$0.174573\pi$
$701$	−2.85805	+	21.0990i	−0.107947	+	0.796898i	−0.961288	+	0.275545i	$0.911142\pi$
$702$		0			0
$703$	5.75799	−	1.58910i	0.217167	−	0.0599342i
$704$	−14.1782	−	14.8292i	−0.534361	−	0.558897i
$705$		0			0
$706$	2.32423	+	25.8243i	0.0874737	+	0.971912i
$707$	−22.2316	+	19.4232i	−0.836106	+	0.730484i
$708$		0			0
$709$			28.0891i			1.05491i	0.849583	+	0.527455i	$0.176853\pi$
$709$			28.0891i			1.05491i	−0.849583	+	0.527455i	$0.823147\pi$
$710$	−13.5491	−	8.52403i	−0.508489	−	0.319901i
$711$		0			0
$712$	−0.597804	−	13.3111i	−0.0224036	−	0.498856i
$713$	15.4274	+	17.6580i	0.577760	+	0.661299i
$714$		0			0
$715$	0.423766	−	1.30422i	0.0158480	−	0.0487750i
$716$	0.753725	−	0.720635i	0.0281680	−	0.0269314i
$717$		0			0
$718$	−2.83893	−	20.9578i	−0.105948	−	0.782140i
$719$	−4.66281	−	0.631621i	−0.173894	−	0.0235555i	0.0467688	−	0.998906i	$-0.485108\pi$
$719$	−4.66281	−	0.631621i	−0.173894	−	0.0235555i	−0.220662	+	0.975350i	$0.570822\pi$
$720$		0			0
$721$	24.0852	−	12.9608i	0.896979	−	0.482685i
$722$	−31.9325	−	30.5306i	−1.18841	−	1.13623i
$723$		0			0
$724$	5.08916	−	1.65357i	0.189137	−	0.0614544i
$725$	31.3570	−	13.4026i	1.16457	−	0.497761i
$726$		0			0
$727$	9.63731	+	13.2646i	0.357428	+	0.491957i	0.949430	−	0.313979i	$-0.101662\pi$
$727$	9.63731	+	13.2646i	0.357428	+	0.491957i	−0.592002	+	0.805937i	$0.701662\pi$
$728$	0.234092	−	2.60097i	0.00867602	−	0.0963985i
$729$		0			0
$730$	−5.40345	+	23.6740i	−0.199991	+	0.876216i
$731$	2.78371	−	4.21714i	0.102959	−	0.155977i
$732$		0			0
$733$	0.778000	+	0.620435i	0.0287361	+	0.0229163i	0.637753	−	0.770241i	$-0.279864\pi$
$733$	0.778000	+	0.620435i	0.0287361	+	0.0229163i	−0.609016	+	0.793158i	$0.708436\pi$
$734$	−17.3697	+	19.8812i	−0.641127	+	0.733829i
$735$		0			0
$736$	−3.86111	+	8.01767i	−0.142322	+	0.295535i
$737$	11.0012	−	7.26181i	0.405233	−	0.267492i
$738$		0			0
$739$	−15.5376	−	9.28328i	−0.571559	−	0.341491i	0.197864	−	0.980229i	$-0.436599\pi$
$739$	−15.5376	−	9.28328i	−0.571559	−	0.341491i	−0.769424	+	0.638739i	$0.779457\pi$
$740$	−0.144813	−	0.300708i	−0.00532344	−	0.0110542i
$741$		0			0
$742$	−1.21958	−	5.34333i	−0.0447722	−	0.196160i
$743$	−21.1639	−	7.94295i	−0.776429	−	0.291399i	−0.0684709	−	0.997653i	$-0.521812\pi$
$743$	−21.1639	−	7.94295i	−0.776429	−	0.291399i	−0.707958	+	0.706254i	$0.750383\pi$
$744$		0			0
$745$	5.61766	+	0.252289i	0.205815	+	0.00924317i
$746$	7.60835	+	0.341691i	0.278561	+	0.0125102i
$747$		0			0
$748$	−0.370297	−	0.138975i	−0.0135394	−	0.00508142i
$749$	7.61055	+	33.3440i	0.278083	+	1.21836i
$750$		0			0
$751$	−13.8380	−	28.7350i	−0.504957	−	1.04855i	−0.985198	−	0.171418i	$-0.945165\pi$
$751$	−13.8380	−	28.7350i	−0.504957	−	1.04855i	0.480241	−	0.877137i	$-0.340549\pi$
$752$	4.07009	+	2.43176i	0.148421	+	0.0886773i
$753$		0			0
$754$	4.31022	−	2.84515i	0.156969	−	0.103614i
$755$	−0.0341449	+	0.0709027i	−0.00124266	+	0.00258041i
$756$		0			0
$757$	6.44266	−	7.37421i	0.234162	−	0.268020i	−0.623971	−	0.781448i	$-0.714482\pi$
$757$	6.44266	−	7.37421i	0.234162	−	0.268020i	0.858133	+	0.513427i	$0.171624\pi$
$758$	−7.41555	−	5.91370i	−0.269345	−	0.214795i
$759$		0			0
$760$	12.2630	−	18.5777i	0.444826	−	0.673882i
$761$	3.64745	−	15.9805i	0.132220	−	0.579293i	−0.864798	−	0.502120i	$-0.832553\pi$
$761$	3.64745	−	15.9805i	0.132220	−	0.579293i	0.997018	−	0.0771731i	$-0.0245894\pi$
$762$		0			0
$763$	1.26878	−	14.0973i	0.0459328	−	0.510356i
$764$	−4.48161	−	6.16841i	−0.162139	−	0.223165i
$765$		0			0
$766$	14.5697	−	6.22740i	0.526425	−	0.225005i
$767$	3.10173	−	1.00781i	0.111997	−	0.0363900i
$768$		0			0
$769$	−39.2675	−	37.5436i	−1.41602	−	1.35386i	−0.847066	−	0.531488i	$-0.821633\pi$
$769$	−39.2675	−	37.5436i	−1.41602	−	1.35386i	−0.568956	−	0.822368i	$-0.692652\pi$
$770$	15.9021	−	8.55730i	0.573073	−	0.308384i
$771$		0			0
$772$	−4.75258	−	0.643781i	−0.171049	−	0.0231702i
$773$	−4.90505	−	36.2105i	−0.176422	−	1.30240i	−0.835151	−	0.550021i	$-0.814620\pi$
$773$	−4.90505	−	36.2105i	−0.176422	−	1.30240i	0.658729	−	0.752381i	$-0.271095\pi$
$774$		0			0
$775$	11.3798	−	10.8802i	0.408776	−	0.390830i
$776$	1.24459	−	3.83044i	0.0446780	−	0.137505i
$777$		0			0
$778$	−27.5322	−	31.5132i	−0.987078	−	1.12980i
$779$	1.61027	+	35.8555i	0.0576940	+	1.28466i
$780$		0			0
$781$	−5.39855	−	26.4416i	−0.193175	−	0.946156i
$782$		−	3.10042i		−	0.110871i
$783$		0			0
$784$	6.16227	−	5.38381i	0.220081	−	0.192279i
$785$	−1.11083	−	12.3423i	−0.0396473	−	0.440517i
$786$		0			0
$787$	8.74340	+	9.14488i	0.311669	+	0.325980i	0.860012	−	0.510273i	$-0.170456\pi$
$787$	8.74340	+	9.14488i	0.311669	+	0.325980i	−0.548344	+	0.836253i	$0.684741\pi$
$788$	0.969314	−	0.267514i	0.0345304	−	0.00952978i
$789$		0			0
$790$	−0.785957	+	5.80217i	−0.0279631	+	0.206432i
$791$	4.53634	−	16.4371i	0.161294	−	0.584435i
$792$		0			0
$793$	−2.75155	+	2.87790i	−0.0977104	+	0.102197i
$794$	−14.6071	+	27.1446i	−0.518388	+	0.963326i
$795$		0			0
$796$	0.495096	+	1.15833i	0.0175482	+	0.0410561i
$797$	6.38321	+	35.1744i	0.226105	+	1.24594i	0.874647	+	0.484761i	$0.161093\pi$
$797$	6.38321	+	35.1744i	0.226105	+	1.24594i	−0.648542	+	0.761179i	$0.724621\pi$
$798$		0			0
$799$	−0.415921	−	0.0374336i	−0.0147142	−	0.00132431i
$800$	5.49437	+	2.34841i	0.194255	+	0.0830287i
$801$		0			0
$802$	−29.4360	−	19.4305i	−1.03942	−	0.686115i
$803$	−35.1439	+	20.9975i	−1.24020	+	0.740986i
$804$		0			0
$805$	14.3032	+	12.4963i	0.504120	+	0.440436i
$806$	1.40154	−	1.92905i	0.0493670	−	0.0679479i
$807$		0			0
$808$	14.0751	+	21.3228i	0.495159	+	0.750134i
$809$	7.90104	−	2.96531i	0.277786	−	0.104255i	−0.208594	−	0.978002i	$-0.566889\pi$
$809$	7.90104	−	2.96531i	0.277786	−	0.104255i	0.486380	+	0.873748i	$0.338317\pi$
$810$		0			0
$811$	35.0505	−	16.8794i	1.23079	−	0.592717i	0.298494	−	0.954412i	$-0.403516\pi$
$811$	35.0505	−	16.8794i	1.23079	−	0.592717i	0.932297	+	0.361694i	$0.117802\pi$
$812$	8.97833	+	1.62933i	0.315078	+	0.0571782i
$813$		0			0
$814$	1.47360	−	3.92639i	0.0516496	−	0.137620i
$815$	15.4629	+	19.3899i	0.541642	+	0.679197i
$816$		0			0
$817$	3.94468	−	87.8351i	0.138007	−	3.07296i
$818$	−14.4302	+	11.5077i	−0.504539	+	0.402356i
$819$		0			0
$820$	1.95519	−	0.446260i	0.0682783	−	0.0155841i
$821$	−7.52303	+	41.4553i	−0.262556	+	1.44680i	0.535663	+	0.844432i	$0.320062\pi$
$821$	−7.52303	+	41.4553i	−0.262556	+	1.44680i	−0.798218	+	0.602368i	$0.794224\pi$
$822$		0			0
$823$	−23.0641	+	38.6028i	−0.803964	+	1.34561i	0.131187	+	0.991358i	$0.458121\pi$
$823$	−23.0641	+	38.6028i	−0.803964	+	1.34561i	−0.935150	+	0.354251i	$0.884736\pi$
$824$	−8.31743	−	22.1617i	−0.289751	−	0.772040i
$825$		0			0
$826$	38.6939	+	18.6340i	1.34633	+	0.648360i
$827$	−28.2133	−	20.4982i	−0.981073	−	0.712791i	−0.0231250	−	0.999733i	$-0.507362\pi$
$827$	−28.2133	−	20.4982i	−0.981073	−	0.712791i	−0.957948	+	0.286941i	$0.907362\pi$
$828$		0			0
$829$	−30.3509	+	38.0589i	−1.05413	+	1.32184i	−0.109398	+	0.993998i	$0.534892\pi$
$829$	−30.3509	+	38.0589i	−1.05413	+	1.32184i	−0.944733	+	0.327841i	$0.893679\pi$
$830$	1.51495	+	2.53560i	0.0525848	+	0.0880121i
$831$		0			0
$832$	−2.13930	−	0.488282i	−0.0741670	−	0.0169281i
$833$	−0.283269	+	0.662740i	−0.00981468	+	0.0229626i
$834$		0			0
$835$	−18.1867	+	13.2134i	−0.629376	+	0.457268i
$836$	−6.77144	+	1.22884i	−0.234195	+	0.0425002i
$837$		0			0
$838$	13.3211	+	40.9980i	0.460169	+	1.41625i
$839$	−13.6556	−	7.34842i	−0.471445	−	0.253696i	0.220853	−	0.975307i	$-0.429116\pi$
$839$	−13.6556	−	7.34842i	−0.471445	−	0.253696i	−0.692298	+	0.721612i	$0.743402\pi$
$840$		0			0
$841$	−32.8895	−	61.1189i	−1.13412	−	2.10755i
$842$	50.9013	+	14.0479i	1.75417	+	0.484121i
$843$		0			0
$844$	−7.84850	+	1.06315i	−0.270156	+	0.0365952i
$845$	4.28391	+	15.5224i	0.147371	+	0.533986i
$846$		0			0
$847$	−2.09497	−	0.680697i	−0.0719840	−	0.0233890i
$848$	−5.47435	+	0.492700i	−0.187990	+	0.0169194i
$849$		0			0
$850$	−2.07968	+	0.0933988i	−0.0713326	+	0.00320355i
$851$	4.41088			0.151203
$852$		0			0
$853$	−50.2676			−1.72113			−0.860566	−	0.509340i	$-0.829890\pi$
$853$	−50.2676			−1.72113			−0.860566	+	0.509340i	$0.829890\pi$
$854$	−52.3790	+	2.35234i	−1.79237	+	0.0804956i
$855$		0			0
$856$	29.4807	−	2.65331i	1.00763	−	0.0906884i
$857$	−1.46746	−	0.476805i	−0.0501273	−	0.0162874i	0.283846	−	0.958870i	$-0.408390\pi$
$857$	−1.46746	−	0.476805i	−0.0501273	−	0.0162874i	−0.333973	+	0.942583i	$0.608390\pi$
$858$		0			0
$859$	−4.22871	−	15.3224i	−0.144282	−	0.522793i	−0.999986	−	0.00532760i	$-0.998304\pi$
$859$	−4.22871	−	15.3224i	−0.144282	−	0.522793i	0.855704	−	0.517465i	$-0.173124\pi$
$860$	−4.86834	+	0.659462i	−0.166009	+	0.0224875i
$861$		0			0
$862$	27.0869	+	7.47552i	0.922585	+	0.254617i
$863$	−8.96756	−	16.6645i	−0.305259	−	0.567267i	0.681037	−	0.732249i	$-0.261529\pi$
$863$	−8.96756	−	16.6645i	−0.305259	−	0.567267i	−0.986297	+	0.164982i	$0.947243\pi$
$864$		0			0
$865$	−16.4854	−	8.87116i	−0.560519	−	0.301628i
$866$	−12.1488	−	37.3902i	−0.412834	−	1.27057i
$867$		0			0
$868$	4.14521	−	0.752245i	0.140698	−	0.0255329i
$869$	−7.98605	+	5.80220i	−0.270908	+	0.196826i
$870$		0			0
$871$	0.554104	−	1.29639i	0.0187751	−	0.0439265i
$872$	−11.9428	−	2.72586i	−0.404433	−	0.0923091i
$873$		0			0
$874$	−27.6697	−	46.3112i	−0.935941	−	1.56650i
$875$	19.5165	−	24.4729i	0.659778	−	0.827335i
$876$		0			0
$877$	20.4307	+	14.8438i	0.689895	+	0.501238i	0.876626	−	0.481173i	$-0.159789\pi$
$877$	20.4307	+	14.8438i	0.689895	+	0.501238i	−0.186731	+	0.982411i	$0.559789\pi$
$878$	51.9861	+	25.0352i	1.75445	+	0.844897i
$879$		0			0
$880$	−6.36347	−	16.9554i	−0.214513	−	0.571567i
$881$	14.3497	−	24.0173i	0.483452	−	0.809163i	−0.515405	−	0.856947i	$-0.672359\pi$
$881$	14.3497	−	24.0173i	0.483452	−	0.809163i	0.998858	+	0.0477835i	$0.0152158\pi$
$882$		0			0
$883$	−3.57831	+	19.7181i	−0.120420	+	0.663568i	0.866093	+	0.499883i	$0.166624\pi$
$883$	−3.57831	+	19.7181i	−0.120420	+	0.663568i	−0.986513	+	0.163685i	$0.947662\pi$
$884$	−0.0412415	+	0.00941310i	−0.00138710	+	0.000316597i
$885$		0			0
$886$	39.8256	−	31.7598i	1.33797	−	1.06699i
$887$	−1.31421	+	29.2632i	−0.0441269	+	0.982561i	0.847782	+	0.530345i	$0.177938\pi$
$887$	−1.31421	+	29.2632i	−0.0441269	+	0.982561i	−0.891909	+	0.452216i	$0.850634\pi$
$888$		0			0
$889$	8.98453	+	11.2662i	0.301332	+	0.377858i
$890$	3.46267	−	9.22624i	0.116069	−	0.309264i
$891$		0			0
$892$	4.02957	+	0.731260i	0.134920	+	0.0244844i
$893$	−6.54673	+	3.15274i	−0.219078	+	0.105502i
$894$		0			0
$895$	−3.93745	+	1.47775i	−0.131614	+	0.0493957i
$896$	−21.6026	−	32.7266i	−0.721693	−	1.09332i
$897$		0			0
$898$	−18.2731	+	25.1508i	−0.609782	+	0.839293i
$899$	−34.2145	−	29.8923i	−1.14112	−	0.996965i
$900$		0			0
$901$	0.415597	−	0.248308i	0.0138455	−	0.00827233i
$902$	21.0308	+	13.8823i	0.700248	+	0.462230i
$903$		0			0
$904$	−13.5698	−	5.80002i	−0.451325	−	0.192906i
$905$	−21.4941	−	1.93451i	−0.714489	−	0.0643052i
$906$		0			0
$907$	6.68711	+	36.8490i	0.222042	+	1.22355i	0.881636	+	0.471930i	$0.156442\pi$
$907$	6.68711	+	36.8490i	0.222042	+	1.22355i	−0.659594	+	0.751622i	$0.729272\pi$
$908$	0.681557	+	1.59458i	0.0226183	+	0.0529181i
$909$		0			0
$910$	0.915236	−	1.70079i	0.0303398	−	0.0563808i
$911$	26.1885	−	27.3911i	0.867665	−	0.907506i	−0.128787	−	0.991672i	$-0.541108\pi$
$911$	26.1885	−	27.3911i	0.867665	−	0.907506i	0.996452	+	0.0841660i	$0.0268226\pi$
$912$		0			0
$913$	−1.32478	+	4.80024i	−0.0438439	+	0.158865i
$914$	5.11998	−	37.7972i	0.169354	−	1.25022i
$915$		0			0
$916$	7.79295	−	2.15072i	0.257486	−	0.0710617i
$917$	−43.7566	−	45.7658i	−1.44497	−	1.51132i
$918$		0			0
$919$	−1.90935	−	21.2146i	−0.0629837	−	0.699806i	−0.963979	−	0.265978i	$-0.914305\pi$
$919$	−1.90935	−	21.2146i	−0.0629837	−	0.699806i	0.900996	−	0.433828i	$-0.142838\pi$
$920$	12.3788	−	10.8150i	0.408115	−	0.356560i
$921$		0			0
$922$		−	57.1226i		−	1.88123i
$923$	−2.03984	−	2.04212i	−0.0671420	−	0.0672171i
$924$		0			0
$925$	−0.132876	−	2.95871i	−0.00436893	−	0.0972818i
$926$	10.3282	+	11.8216i	0.339406	+	0.388481i
$927$		0			0
$928$	5.32830	−	16.3988i	0.174910	−	0.538318i
$929$	−33.8165	+	32.3319i	−1.10948	+	1.06078i	−0.111733	+	0.993738i	$0.535640\pi$
$929$	−33.8165	+	32.3319i	−1.10948	+	1.06078i	−0.997750	+	0.0670370i	$0.978645\pi$
$930$		0			0
$931$	1.68341	+	12.4274i	0.0551716	+	0.407293i
$932$	−4.17397	−	0.565402i	−0.136723	−	0.0185204i
$933$		0			0
$934$	−7.35447	+	3.95761i	−0.240646	+	0.129497i
$935$	1.15296	+	1.10234i	0.0377057	+	0.0360503i
$936$		0			0
$937$	−5.19757	+	1.68879i	−0.169797	+	0.0551705i	−0.392682	−	0.919674i	$-0.628453\pi$
$937$	−5.19757	+	1.68879i	−0.169797	+	0.0551705i	0.222885	+	0.974845i	$0.428453\pi$
$938$	17.0715	−	7.29669i	0.557403	−	0.238245i
$939$		0			0
$940$	0.238648	+	0.328471i	0.00778384	+	0.0107135i
$941$	3.55333	−	39.4808i	0.115835	−	1.28704i	−0.702246	−	0.711934i	$-0.747820\pi$
$941$	3.55333	−	39.4808i	0.115835	−	1.28704i	0.818082	−	0.575102i	$-0.195038\pi$
$942$		0			0
$943$	−5.89764	+	25.8393i	−0.192054	+	0.841442i
$944$	23.7273	−	35.9453i	0.772257	−	1.16992i
$945$		0			0
$946$	−48.2632	−	38.4886i	−1.56917	−	1.25137i
$947$	16.1382	−	18.4716i	0.524419	−	0.600246i	−0.428473	−	0.903555i	$-0.640948\pi$
$947$	16.1382	−	18.4716i	0.524419	−	0.600246i	0.952893	+	0.303308i	$0.0980912\pi$
$948$		0			0
$949$	−1.89979	+	3.94495i	−0.0616698	+	0.128059i
$950$	−30.2309	+	19.9553i	−0.980821	+	0.647434i
$951$		0			0
$952$	2.60769	+	1.55802i	0.0845157	+	0.0504958i
$953$	0.391938	+	0.813867i	0.0126961	+	0.0263637i	0.907220	−	0.420655i	$-0.138200\pi$
$953$	0.391938	+	0.813867i	0.0126961	+	0.0263637i	−0.894524	+	0.447019i	$0.852486\pi$
$954$		0			0
$955$	6.84256	+	29.9792i	0.221420	+	0.970104i
$956$	−3.31160	−	1.24286i	−0.107105	−	0.0401971i
$957$		0			0
$958$	11.1131	+	0.499089i	0.359047	+	0.0161248i
$959$	−43.5359	−	1.95520i	−1.40585	−	0.0631366i
$960$		0			0
$961$	9.38468	+	3.52213i	0.302732	+	0.113617i
$962$	−0.0998103	−	0.437298i	−0.00321801	−	0.0140990i
$963$		0			0
$964$	−0.912969	−	1.89580i	−0.0294048	−	0.0610596i
$965$	16.6044	+	9.92069i	0.534516	+	0.319358i
$966$		0			0
$967$	32.6005	−	21.5194i	1.04836	−	0.692017i	0.0955019	−	0.995429i	$-0.469554\pi$
$967$	32.6005	−	21.5194i	1.04836	−	0.692017i	0.952859	+	0.303412i	$0.0981258\pi$
$968$	−0.827160	+	1.71762i	−0.0265859	+	0.0552063i
$969$		0			0
$970$	1.95982	−	2.24319i	0.0629259	−	0.0720245i
$971$	−13.9556	−	11.1292i	−0.447856	−	0.357153i	0.373441	−	0.927654i	$-0.378178\pi$
$971$	−13.9556	−	11.1292i	−0.447856	−	0.357153i	−0.821297	+	0.570501i	$0.806749\pi$
$972$		0			0
$973$	16.4413	−	24.9074i	0.527083	−	0.798496i
$974$	−10.7888	+	47.2686i	−0.345694	+	1.51458i
$975$		0			0
$976$	−4.71344	+	52.3706i	−0.150874	+	1.67634i
$977$	−24.0116	−	33.0491i	−0.768199	−	1.05733i	−0.996488	−	0.0837415i	$-0.973313\pi$
$977$	−24.0116	−	33.0491i	−0.768199	−	1.05733i	0.228289	−	0.973593i	$-0.426687\pi$
$978$		0			0
$979$	15.2771	−	6.52974i	0.488258	−	0.208691i
$980$	0.666439	−	0.216539i	0.0212886	−	0.00691709i
$981$		0			0
$982$	−1.83180	−	1.75138i	−0.0584552	−	0.0558889i
$983$	−11.7089	+	6.30082i	−0.373455	+	0.200965i	−0.649820	−	0.760088i	$-0.725156\pi$
$983$	−11.7089	+	6.30082i	−0.373455	+	0.200965i	0.276365	+	0.961053i	$0.410870\pi$
$984$		0			0
$985$	−4.01872	−	0.544373i	−0.128047	−	0.0173452i
$986$	0.806396	+	5.95305i	0.0256809	+	0.189584i
$987$		0			0
$988$	−0.532021	+	0.508664i	−0.0169258	+	0.0161828i
$989$	20.0633	−	61.7485i	0.637976	−	1.96349i
$990$		0			0
$991$	−29.4589	−	33.7185i	−0.935794	−	1.07110i	−0.997332	−	0.0729979i	$-0.976743\pi$
$991$	−29.4589	−	33.7185i	−0.935794	−	1.07110i	0.0615379	−	0.998105i	$-0.480399\pi$
$992$	−0.357161	−	7.95280i	−0.0113399	−	0.252502i
$993$		0			0
$994$	−0.831609	−	38.0000i	−0.0263770	−	1.20529i
$995$		−	5.08044i		−	0.161061i
$996$		0			0
$997$	24.4068	−	21.3236i	0.772971	−	0.675324i	−0.178198	−	0.983995i	$-0.557027\pi$
$997$	24.4068	−	21.3236i	0.772971	−	0.675324i	0.951169	+	0.308670i	$0.0998840\pi$
$998$	2.10414	+	23.3789i	0.0666052	+	0.740045i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.35.19	yes	576
3.2	odd	2	inner	639.2.z.a.35.6	✓	576
71.69	odd	70	inner	639.2.z.a.566.6	yes	576
213.140	even	70	inner	639.2.z.a.566.19	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.35.6	✓	576	3.2	odd	2	inner
639.2.z.a.35.19	yes	576	1.1	even	1	trivial
639.2.z.a.566.6	yes	576	71.69	odd	70	inner
639.2.z.a.566.19	yes	576	213.140	even	70	inner

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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.51831 - 0.0681876i) q^{2} +(0.308680 - 0.0277817i) q^{4} +(-1.18877 - 0.386256i) q^{5} +(-0.789589 - 2.86101i) q^{7} +(-2.54540 + 0.344798i) q^{8} +O(q^{10})\)	\(q+(1.51831 - 0.0681876i) q^{2} +(0.308680 - 0.0277817i) q^{4} +(-1.18877 - 0.386256i) q^{5} +(-0.789589 - 2.86101i) q^{7} +(-2.54540 + 0.344798i) q^{8} +(-1.83127 - 0.505398i) q^{10} +(-1.51770 - 2.82036i) q^{11} +(-0.301648 - 0.162324i) q^{13} +(-1.39393 - 4.29008i) q^{14} +(-4.45110 + 0.807756i) q^{16} +(0.322355 - 0.234205i) q^{17} +(2.72489 - 6.37520i) q^{19} +(-0.377682 - 0.0862034i) q^{20} +(-2.49666 - 4.17870i) q^{22} +(3.19207 - 4.00273i) q^{23} +(-2.78110 - 2.02059i) q^{25} +(-0.469065 - 0.225890i) q^{26} +(-0.323214 - 0.861202i) q^{28} +(-5.08796 + 8.51581i) q^{29} +(-0.817786 + 4.50637i) q^{31} +(-1.69460 + 0.386781i) q^{32} +(0.473467 - 0.377577i) q^{34} +(-0.166440 + 3.70608i) q^{35} +(0.537169 + 0.673589i) q^{37} +(3.70253 - 9.86537i) q^{38} +(3.15908 + 0.573289i) q^{40} +(-4.66416 + 2.24614i) q^{41} +(11.8730 - 4.45602i) q^{43} +(-0.546838 - 0.828424i) q^{44} +(4.57363 - 6.29507i) q^{46} +(-0.789263 - 0.689559i) q^{47} +(-1.55280 + 0.927754i) q^{49} +(-4.36036 - 2.87825i) q^{50} +(-0.0976224 - 0.0417258i) q^{52} +(1.21012 + 0.108913i) q^{53} +(0.714820 + 3.93898i) q^{55} +(2.99629 + 7.01017i) q^{56} +(-7.14445 + 13.2766i) q^{58} +(-6.57948 + 6.88160i) q^{59} +(3.09227 - 11.2046i) q^{61} +(-0.934377 + 6.89785i) q^{62} +(6.17499 - 1.70419i) q^{64} +(0.295892 + 0.309479i) q^{65} +(0.368931 + 4.09916i) q^{67} +(0.0929981 - 0.0812500i) q^{68} +5.63834i q^{70} +(8.06880 + 2.42787i) q^{71} +(-0.573475 - 12.7694i) q^{73} +(0.861522 + 0.986091i) q^{74} +(0.664006 - 2.04360i) q^{76} +(-6.87072 + 6.56908i) q^{77} +(-0.413720 - 3.05421i) q^{79} +(5.60335 + 0.759025i) q^{80} +(-6.92851 + 3.72839i) q^{82} +(-1.12380 - 1.07447i) q^{83} +(-0.473671 + 0.153905i) q^{85} +(17.7231 - 7.57523i) q^{86} +(4.83560 + 6.65564i) q^{88} +(-0.464993 + 5.16650i) q^{89} +(-0.226232 + 0.991187i) q^{91} +(0.874127 - 1.32425i) q^{92} +(-1.24537 - 0.993149i) q^{94} +(-5.70174 + 6.52617i) q^{95} +(-0.680317 + 1.41269i) q^{97} +(-2.29438 + 1.51450i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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