LMFDB - Embedded newform 648.2.v.b.35.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(35,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("648.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.v (of order $18$, degree $6$, not 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.26
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21873 - 0.717416i) q^{2} +(0.970628 - 1.74868i) q^{4} +(-1.70638 - 0.621073i) q^{5} +(-3.32069 - 0.585528i) q^{7} +(-0.0715925 - 2.82752i) q^{8} +O(q^{10})$	\(q+(1.21873 - 0.717416i) q^{2} +(0.970628 - 1.74868i) q^{4} +(-1.70638 - 0.621073i) q^{5} +(-3.32069 - 0.585528i) q^{7} +(-0.0715925 - 2.82752i) q^{8} +(-2.52520 + 0.467264i) q^{10} +(0.942090 + 2.58837i) q^{11} +(-3.98305 - 4.74681i) q^{13} +(-4.46711 + 1.66872i) q^{14} +(-2.11576 - 3.39464i) q^{16} +(-2.90072 + 1.67473i) q^{17} +(2.87704 - 4.98318i) q^{19} +(-2.74232 + 2.38109i) q^{20} +(3.00510 + 2.47867i) q^{22} +(-0.396921 - 2.25105i) q^{23} +(-1.30421 - 1.09436i) q^{25} +(-8.25972 - 2.92760i) q^{26} +(-4.24706 + 5.23850i) q^{28} +(7.06459 + 5.92789i) q^{29} +(1.38814 - 0.244766i) q^{31} +(-5.01392 - 2.61928i) q^{32} +(-2.33373 + 4.12208i) q^{34} +(5.30272 + 3.06153i) q^{35} +(-4.33391 + 2.50218i) q^{37} +(-0.0686647 - 8.13721i) q^{38} +(-1.63393 + 4.86930i) q^{40} +(-1.54991 - 1.84711i) q^{41} +(3.42707 - 1.24735i) q^{43} +(5.44065 + 0.864933i) q^{44} +(-2.09868 - 2.45867i) q^{46} +(0.530155 - 3.00666i) q^{47} +(4.10632 + 1.49458i) q^{49} +(-2.37460 - 0.398076i) q^{50} +(-12.1667 + 2.35769i) q^{52} -0.184564 q^{53} -5.00186i q^{55} +(-1.41786 + 9.43125i) q^{56} +(12.8626 + 2.15628i) q^{58} +(4.44089 - 12.2012i) q^{59} +(13.9331 + 2.45678i) q^{61} +(1.51617 - 1.29418i) q^{62} +(-7.98975 + 0.404858i) q^{64} +(3.84849 + 10.5736i) q^{65} +(4.70680 - 3.94947i) q^{67} +(0.113048 + 6.69798i) q^{68} +(8.65900 - 0.0730677i) q^{70} +(1.83700 + 3.18178i) q^{71} +(0.136500 - 0.236424i) q^{73} +(-3.48678 + 6.15871i) q^{74} +(-5.92145 - 9.86784i) q^{76} +(-1.61283 - 9.14681i) q^{77} +(-0.710677 + 0.846952i) q^{79} +(1.50198 + 7.10659i) q^{80} +(-3.21407 - 1.13921i) q^{82} +(-2.40520 + 2.86641i) q^{83} +(5.98987 - 1.05618i) q^{85} +(3.28182 - 3.97883i) q^{86} +(7.25123 - 2.84909i) q^{88} +(-5.59452 - 3.23000i) q^{89} +(10.4471 + 18.0949i) q^{91} +(-4.32163 - 1.49084i) q^{92} +(-1.51091 - 4.04466i) q^{94} +(-8.00425 + 6.71636i) q^{95} +(-14.5548 + 5.29750i) q^{97} +(6.07674 - 1.12444i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.21873	−	0.717416i	0.861776	−	0.507290i
$2$	1.21873	−	0.717416i	0.861776	−	0.507290i
$3$		0			0
$3$		0			0
$4$	0.970628	−	1.74868i	0.485314	−	0.874340i
$5$	−1.70638	−	0.621073i	−0.763118	−	0.277752i	−0.0690029	−	0.997616i	$-0.521982\pi$
$5$	−1.70638	−	0.621073i	−0.763118	−	0.277752i	−0.694115	+	0.719864i	$0.744204\pi$
$6$		0			0
$7$	−3.32069	−	0.585528i	−1.25510	−	0.221309i	−0.493727	−	0.869617i	$-0.664366\pi$
$7$	−3.32069	−	0.585528i	−1.25510	−	0.221309i	−0.761378	+	0.648308i	$0.775477\pi$
$8$	−0.0715925	−	2.82752i	−0.0253118	−	0.999680i
$9$		0			0
$10$	−2.52520	+	0.467264i	−0.798537	+	0.147762i
$11$	0.942090	+	2.58837i	0.284051	+	0.780423i	0.996869	+	0.0790741i	$0.0251964\pi$
$11$	0.942090	+	2.58837i	0.284051	+	0.780423i	−0.712818	+	0.701349i	$0.752581\pi$
$12$		0			0
$13$	−3.98305	−	4.74681i	−1.10470	−	1.31653i	−0.944155	−	0.329501i	$-0.893120\pi$
$13$	−3.98305	−	4.74681i	−1.10470	−	1.31653i	−0.160544	−	0.987029i	$-0.551325\pi$
$14$	−4.46711	+	1.66872i	−1.19389	+	0.445983i
$15$		0			0
$16$	−2.11576	−	3.39464i	−0.528940	−	0.848659i
$17$	−2.90072	+	1.67473i	−0.703529	+	0.406182i	−0.808660	−	0.588276i	$-0.799807\pi$
$17$	−2.90072	+	1.67473i	−0.703529	+	0.406182i	0.105132	+	0.994458i	$0.466474\pi$
$18$		0			0
$19$	2.87704	−	4.98318i	0.660038	−	1.14322i	−0.320567	−	0.947226i	$-0.603873\pi$
$19$	2.87704	−	4.98318i	0.660038	−	1.14322i	0.980605	−	0.195994i	$-0.0627933\pi$
$20$	−2.74232	+	2.38109i	−0.613202	+	0.532427i
$21$		0			0
$22$	3.00510	+	2.47867i	0.640689	+	0.528454i
$23$	−0.396921	−	2.25105i	−0.0827637	−	0.469376i	−0.997817	−	0.0660428i	$-0.978963\pi$
$23$	−0.396921	−	2.25105i	−0.0827637	−	0.469376i	0.915053	−	0.403333i	$-0.132148\pi$
$24$		0			0
$25$	−1.30421	−	1.09436i	−0.260842	−	0.218872i
$26$	−8.25972	−	2.92760i	−1.61986	−	0.574150i
$27$		0			0
$28$	−4.24706	+	5.23850i	−0.802619	+	0.989983i
$29$	7.06459	+	5.92789i	1.31186	+	1.10078i	0.987963	+	0.154690i	$0.0494377\pi$
$29$	7.06459	+	5.92789i	1.31186	+	1.10078i	0.323897	+	0.946092i	$0.395007\pi$
$30$		0			0
$31$	1.38814	−	0.244766i	0.249317	−	0.0439613i	−0.0475930	−	0.998867i	$-0.515155\pi$
$31$	1.38814	−	0.244766i	0.249317	−	0.0439613i	0.296910	+	0.954906i	$0.404044\pi$
$32$	−5.01392	−	2.61928i	−0.886344	−	0.463028i
$33$		0			0
$34$	−2.33373	+	4.12208i	−0.400232	+	0.706931i
$35$	5.30272	+	3.06153i	0.896323	+	0.517493i
$36$		0			0
$37$	−4.33391	+	2.50218i	−0.712490	+	0.411356i	−0.811982	−	0.583682i	$-0.801611\pi$
$37$	−4.33391	+	2.50218i	−0.712490	+	0.411356i	0.0994922	+	0.995038i	$0.468278\pi$
$38$	−0.0686647	−	8.13721i	−0.0111389	−	1.32003i
$39$		0			0
$40$	−1.63393	+	4.86930i	−0.258347	+	0.769904i
$41$	−1.54991	−	1.84711i	−0.242055	−	0.288470i	0.631316	−	0.775526i	$-0.282515\pi$
$41$	−1.54991	−	1.84711i	−0.242055	−	0.288470i	−0.873371	+	0.487056i	$0.838071\pi$
$42$		0			0
$43$	3.42707	−	1.24735i	0.522624	−	0.190220i	−0.0672179	−	0.997738i	$-0.521412\pi$
$43$	3.42707	−	1.24735i	0.522624	−	0.190220i	0.589842	+	0.807519i	$0.299190\pi$
$44$	5.44065	+	0.864933i	0.820209	+	0.130394i
$45$		0			0
$46$	−2.09868	−	2.45867i	−0.309433	−	0.362512i
$47$	0.530155	−	3.00666i	0.0773310	−	0.438566i	−0.921419	−	0.388572i	$-0.872969\pi$
$47$	0.530155	−	3.00666i	0.0773310	−	0.438566i	0.998750	−	0.0499942i	$-0.0159203\pi$
$48$		0			0
$49$	4.10632	+	1.49458i	0.586617	+	0.213511i
$50$	−2.37460	−	0.398076i	−0.335819	−	0.0562964i
$51$		0			0
$52$	−12.1667	+	2.35769i	−1.68722	+	0.326952i
$53$	−0.184564			−0.0253518			−0.0126759	−	0.999920i	$-0.504035\pi$
$53$	−0.184564			−0.0253518			−0.0126759	+	0.999920i	$0.504035\pi$
$54$		0			0
$55$		−	5.00186i		−	0.674450i
$56$	−1.41786	+	9.43125i	−0.189469	+	1.26030i
$57$		0			0
$58$	12.8626	+	2.15628i	1.68894	+	0.283133i
$59$	4.44089	−	12.2012i	0.578154	−	1.58847i	−0.213134	−	0.977023i	$-0.568367\pi$
$59$	4.44089	−	12.2012i	0.578154	−	1.58847i	0.791288	−	0.611443i	$-0.209411\pi$
$60$		0			0
$61$	13.9331	+	2.45678i	1.78395	+	0.314559i	0.965576	−	0.260122i	$-0.0837629\pi$
$61$	13.9331	+	2.45678i	1.78395	+	0.314559i	0.818377	+	0.574681i	$0.194874\pi$
$62$	1.51617	−	1.29418i	0.192554	−	0.164361i
$63$		0			0
$64$	−7.98975	+	0.404858i	−0.998719	+	0.0506073i
$65$	3.84849	+	10.5736i	0.477347	+	1.31150i
$66$		0			0
$67$	4.70680	−	3.94947i	0.575027	−	0.482505i	−0.308283	−	0.951295i	$-0.599754\pi$
$67$	4.70680	−	3.94947i	0.575027	−	0.482505i	0.883310	+	0.468790i	$0.155310\pi$
$68$	0.113048	+	6.69798i	0.0137091	+	0.812249i
$69$		0			0
$70$	8.65900	−	0.0730677i	1.03495	−	0.00873326i
$71$	1.83700	+	3.18178i	0.218012	+	0.377608i	0.954200	−	0.299169i	$-0.0967095\pi$
$71$	1.83700	+	3.18178i	0.218012	+	0.377608i	−0.736188	+	0.676777i	$0.763376\pi$
$72$		0			0
$73$	0.136500	−	0.236424i	0.0159761	−	0.0276713i	−0.857927	−	0.513772i	$-0.828248\pi$
$73$	0.136500	−	0.236424i	0.0159761	−	0.0276713i	0.873903	+	0.486101i	$0.161581\pi$
$74$	−3.48678	+	6.15871i	−0.405330	+	0.715936i
$75$		0			0
$76$	−5.92145	−	9.86784i	−0.679237	−	1.13192i
$77$	−1.61283	−	9.14681i	−0.183799	−	1.04238i
$78$		0			0
$79$	−0.710677	+	0.846952i	−0.0799574	+	0.0952895i	−0.804540	−	0.593898i	$-0.797588\pi$
$79$	−0.710677	+	0.846952i	−0.0799574	+	0.0952895i	0.724583	+	0.689188i	$0.242033\pi$
$80$	1.50198	+	7.10659i	0.167927	+	0.794541i
$81$		0			0
$82$	−3.21407	−	1.13921i	−0.354935	−	0.125804i
$83$	−2.40520	+	2.86641i	−0.264005	+	0.314629i	−0.881720	−	0.471773i	$-0.843614\pi$
$83$	−2.40520	+	2.86641i	−0.264005	+	0.314629i	0.617715	+	0.786402i	$0.288059\pi$
$84$		0			0
$85$	5.98987	−	1.05618i	0.649693	−	0.114558i
$86$	3.28182	−	3.97883i	0.353888	−	0.429048i
$87$		0			0
$88$	7.25123	−	2.84909i	0.772983	−	0.303714i
$89$	−5.59452	−	3.23000i	−0.593018	−	0.342379i	0.173272	−	0.984874i	$-0.444566\pi$
$89$	−5.59452	−	3.23000i	−0.593018	−	0.342379i	−0.766290	+	0.642495i	$0.777899\pi$
$90$		0			0
$91$	10.4471	+	18.0949i	1.09515	+	1.89686i
$92$	−4.32163	−	1.49084i	−0.450561	−	0.155431i
$93$		0			0
$94$	−1.51091	−	4.04466i	−0.155838	−	0.417175i
$95$	−8.00425	+	6.71636i	−0.821219	+	0.689084i
$96$		0			0
$97$	−14.5548	+	5.29750i	−1.47781	+	0.537879i	−0.950209	−	0.311612i	$-0.899131\pi$
$97$	−14.5548	+	5.29750i	−1.47781	+	0.537879i	−0.527602	+	0.849492i	$0.676909\pi$
$98$	6.07674	−	1.12444i	0.613844	−	0.113586i
$99$		0			0
$100$	−3.17959	+	1.21843i	−0.317959	+	0.121843i
$101$	1.50674	−	8.54518i	0.149927	−	0.850277i	−0.813352	−	0.581772i	$-0.802359\pi$
$101$	1.50674	−	8.54518i	0.149927	−	0.850277i	0.963278	−	0.268504i	$-0.0865294\pi$
$102$		0			0
$103$	3.88002	−	10.6603i	0.382309	−	1.05039i	−0.588072	−	0.808809i	$-0.700113\pi$
$103$	3.88002	−	10.6603i	0.382309	−	1.05039i	0.970381	−	0.241578i	$-0.0776649\pi$
$104$	−13.1366	+	11.6020i	−1.28815	+	1.13767i
$105$		0			0
$106$	−0.224934	+	0.132409i	−0.0218475	+	0.0128607i
$107$		−	1.12727i		−	0.108978i	−0.998514	−	0.0544888i	$-0.982647\pi$
$107$		−	1.12727i		−	0.108978i	0.998514	−	0.0544888i	$-0.0173529\pi$
$108$		0			0
$109$		−	10.2698i		−	0.983665i	−0.870690	−	0.491832i	$-0.836327\pi$
$109$		−	10.2698i		−	0.983665i	0.870690	−	0.491832i	$-0.163673\pi$
$110$	−3.58841	−	6.09594i	−0.342142	−	0.581225i
$111$		0			0
$112$	5.03814	+	12.5114i	0.476060	+	1.18221i
$113$	−5.40999	+	14.8638i	−0.508929	+	1.39827i	0.373414	+	0.927665i	$0.378187\pi$
$113$	−5.40999	+	14.8638i	−0.508929	+	1.39827i	−0.882343	+	0.470607i	$0.844035\pi$
$114$		0			0
$115$	−0.720766	+	4.08767i	−0.0672118	+	0.381177i
$116$	17.2231	−	6.59992i	1.59912	−	0.612787i
$117$		0			0
$118$	−3.34110	−	18.0560i	−0.307573	−	1.66219i
$119$	10.6130	−	3.86282i	0.972893	−	0.354104i
$120$		0			0
$121$	2.61436	−	2.19371i	0.237669	−	0.199428i
$122$	18.7433	−	7.00167i	1.69694	−	0.633902i
$123$		0			0
$124$	0.919348	−	2.66498i	0.0825599	−	0.239323i
$125$	6.08554	+	10.5405i	0.544307	+	0.942768i
$126$		0			0
$127$	−2.22917	−	1.28701i	−0.197806	−	0.114204i	0.397825	−	0.917461i	$-0.369765\pi$
$127$	−2.22917	−	1.28701i	−0.197806	−	0.114204i	−0.595632	+	0.803258i	$0.703098\pi$
$128$	−9.44693	+	6.22539i	−0.834999	+	0.550252i
$129$		0			0
$130$	12.2760	+	10.1255i	1.07668	+	0.888065i
$131$	17.4280	−	3.07303i	1.52269	−	0.268492i	0.651203	−	0.758904i	$-0.274265\pi$
$131$	17.4280	−	3.07303i	1.52269	−	0.268492i	0.871491	+	0.490411i	$0.163154\pi$
$132$		0			0
$133$	−12.4716	+	14.8630i	−1.08142	+	1.28879i
$134$	2.90292	−	8.19009i	0.250774	−	0.707516i
$135$		0			0
$136$	4.94301	+	8.08196i	0.423860	+	0.693022i
$137$	1.83538	−	2.18732i	0.156807	−	0.186875i	−0.681921	−	0.731426i	$-0.738855\pi$
$137$	1.83538	−	2.18732i	0.156807	−	0.186875i	0.838728	+	0.544550i	$0.183300\pi$
$138$		0			0
$139$	−0.583063	−	3.30671i	−0.0494548	−	0.280472i	0.950044	−	0.312115i	$-0.101037\pi$
$139$	−0.583063	−	3.30671i	−0.0494548	−	0.280472i	−0.999499	+	0.0316426i	$0.989926\pi$
$140$	10.5006	−	6.30115i	0.887463	−	0.532545i
$141$		0			0
$142$	4.52148	+	2.55985i	0.379434	+	0.214818i
$143$	8.53412	−	14.7815i	0.713659	−	1.23609i
$144$		0			0
$145$	−8.37324	−	14.5029i	−0.695360	−	1.20440i
$146$	−0.00325775	−	0.386065i	−0.000269614	−	0.0319510i
$147$		0			0
$148$	0.168902	+	10.0073i	0.0138837	+	0.822596i
$149$	−8.18651	+	6.86930i	−0.670665	+	0.562755i	−0.913262	−	0.407372i	$-0.866445\pi$
$149$	−8.18651	+	6.86930i	−0.670665	+	0.562755i	0.242597	+	0.970127i	$0.422001\pi$
$150$		0			0
$151$	1.16307	+	3.19552i	0.0946497	+	0.260048i	0.977978	−	0.208706i	$-0.0669253\pi$
$151$	1.16307	+	3.19552i	0.0946497	+	0.260048i	−0.883329	+	0.468754i	$0.844703\pi$
$152$	−14.2960	−	7.77813i	−1.15956	−	0.630890i
$153$		0			0
$154$	−8.52768	−	9.99046i	−0.687180	−	0.805054i
$155$	−2.52071	−	0.444469i	−0.202468	−	0.0357006i
$156$		0			0
$157$	−4.73154	+	12.9998i	−0.377618	+	1.03750i	0.594723	+	0.803931i	$0.297262\pi$
$157$	−4.73154	+	12.9998i	−0.377618	+	1.03750i	−0.972341	+	0.233567i	$0.924960\pi$
$158$	−0.258510	+	1.54206i	−0.0205659	+	0.122680i
$159$		0			0
$160$	6.92890	+	7.58350i	0.547778	+	0.599528i
$161$			7.70745i			0.607432i
$162$		0			0
$163$	15.6961			1.22941			0.614706	−	0.788757i	$-0.289275\pi$
$163$	15.6961			1.22941			0.614706	+	0.788757i	$0.289275\pi$
$164$	−4.73439	+	0.917437i	−0.369694	+	0.0716398i
$165$		0			0
$166$	−0.874895	+	5.21892i	−0.0679050	+	0.405066i
$167$	−14.4977	−	5.27671i	−1.12186	−	0.408324i	−0.286531	−	0.958071i	$-0.592502\pi$
$167$	−14.4977	−	5.27671i	−1.12186	−	0.408324i	−0.835331	+	0.549747i	$0.814724\pi$
$168$		0			0
$169$	−4.41013	+	25.0111i	−0.339241	+	1.92393i
$170$	6.54235	−	5.58443i	0.501775	−	0.428306i
$171$		0			0
$172$	1.14519	−	7.20357i	0.0873203	−	0.549267i
$173$	1.50008	−	0.545984i	0.114049	−	0.0415104i	−0.284365	−	0.958716i	$-0.591783\pi$
$173$	1.50008	−	0.545984i	0.114049	−	0.0415104i	0.398414	+	0.917206i	$0.369561\pi$
$174$		0			0
$175$	3.69010	+	4.39769i	0.278946	+	0.332434i
$176$	6.79334	−	8.67443i	0.512067	−	0.653860i
$177$		0			0
$178$	−9.13549	+	0.0770885i	−0.684734	+	0.00577802i
$179$	1.72215	−	0.994286i	0.128720	−	0.0743164i	−0.434257	−	0.900789i	$-0.642989\pi$
$179$	1.72215	−	0.994286i	0.128720	−	0.0743164i	0.562977	+	0.826472i	$0.309656\pi$
$180$		0			0
$181$	−0.664023	−	0.383374i	−0.0493565	−	0.0284960i	0.475119	−	0.879922i	$-0.342405\pi$
$181$	−0.664023	−	0.383374i	−0.0493565	−	0.0284960i	−0.524475	+	0.851426i	$0.675738\pi$
$182$	25.7138	+	14.5580i	1.90603	+	1.07911i
$183$		0			0
$184$	−6.33647	+	1.28346i	−0.467131	+	0.0946179i
$185$	8.94935	−	1.57801i	0.657969	−	0.116018i
$186$		0			0
$187$	−7.06757	−	5.93040i	−0.516832	−	0.433674i
$188$	−4.74310	−	3.84542i	−0.345926	−	0.280456i
$189$		0			0
$190$	−4.93663	+	13.9278i	−0.358141	+	1.01043i
$191$	0.104873	+	0.0879985i	0.00758831	+	0.00636735i	0.646574	−	0.762851i	$-0.276201\pi$
$191$	0.104873	+	0.0879985i	0.00758831	+	0.00636735i	−0.638986	+	0.769219i	$0.720646\pi$
$192$		0			0
$193$	−2.95183	−	16.7407i	−0.212478	−	1.20502i	−0.885230	−	0.465153i	$-0.845999\pi$
$193$	−2.95183	−	16.7407i	−0.212478	−	1.20502i	0.672753	−	0.739867i	$-0.265112\pi$
$194$	−13.9379	+	16.8981i	−1.00068	+	1.21321i
$195$		0			0
$196$	6.59924	−	5.72995i	0.471374	−	0.409282i
$197$	2.84664	−	4.93053i	0.202815	−	0.351286i	−0.746619	−	0.665251i	$-0.768324\pi$
$197$	2.84664	−	4.93053i	0.202815	−	0.351286i	0.949434	+	0.313966i	$0.101658\pi$
$198$		0			0
$199$	12.2625	−	7.07975i	0.869265	−	0.501870i	0.00216093	−	0.999998i	$-0.499312\pi$
$199$	12.2625	−	7.07975i	0.869265	−	0.501870i	0.867104	+	0.498127i	$0.165979\pi$
$200$	−3.00096	+	3.76603i	−0.212200	+	0.266298i
$201$		0			0
$202$	−4.29412	−	11.4953i	−0.302133	−	0.808804i
$203$	−19.9884	−	23.8212i	−1.40291	−	1.67192i
$204$		0			0
$205$	1.49755	+	4.11448i	0.104593	+	0.287368i
$206$	−2.91913	−	15.7756i	−0.203385	−	1.09914i
$207$		0			0
$208$	−7.68652	+	23.5641i	−0.532965	+	1.63388i
$209$	15.6087	+	2.75224i	1.07968	+	0.190377i
$210$		0			0
$211$	−9.92628	−	3.61287i	−0.683354	−	0.248720i	−0.0230668	−	0.999734i	$-0.507343\pi$
$211$	−9.92628	−	3.61287i	−0.683354	−	0.248720i	−0.660287	+	0.751014i	$0.729565\pi$
$212$	−0.179143	+	0.322743i	−0.0123036	+	0.0221661i
$213$		0			0
$214$	−0.808724	−	1.37385i	−0.0552832	−	0.0939142i
$215$	−6.62260			−0.451658
$216$		0			0
$217$	−4.75290			−0.322648
$218$	−7.36769	−	12.5161i	−0.499003	−	0.847698i
$219$		0			0
$220$	−8.74665	−	4.85495i	−0.589699	−	0.327320i
$221$	19.5034	+	7.09864i	1.31194	+	0.477507i
$222$		0			0
$223$	24.8065	+	4.37405i	1.66116	+	0.292908i	0.923882	−	0.382677i	$-0.124998\pi$
$223$	24.8065	+	4.37405i	1.66116	+	0.292908i	0.737282	+	0.675585i	$0.236109\pi$
$224$	15.1160	+	11.6336i	1.00998	+	0.777304i
$225$		0			0
$226$	4.07021	+	21.9963i	0.270746	+	1.46317i
$227$	−1.35308	−	3.71757i	−0.0898074	−	0.246744i	0.886655	−	0.462432i	$-0.153023\pi$
$227$	−1.35308	−	3.71757i	−0.0898074	−	0.246744i	−0.976462	+	0.215688i	$0.930801\pi$
$228$		0			0
$229$	−5.68658	−	6.77700i	−0.375780	−	0.447837i	0.544698	−	0.838632i	$-0.316644\pi$
$229$	−5.68658	−	6.77700i	−0.375780	−	0.447837i	−0.920477	+	0.390796i	$0.872200\pi$
$230$	2.05414	+	5.49887i	0.135446	+	0.362585i
$231$		0			0
$232$	16.2555	−	20.3997i	1.06722	−	1.33930i
$233$	−18.0759	+	10.4361i	−1.18419	+	0.683694i	−0.956981	−	0.290152i	$-0.906294\pi$
$233$	−18.0759	+	10.4361i	−1.18419	+	0.683694i	−0.227211	+	0.973845i	$0.572961\pi$
$234$		0			0
$235$	−2.77200	+	4.80124i	−0.180825	+	0.313199i
$236$	−17.0256	−	19.6086i	−1.10827	−	1.27641i
$237$		0			0
$238$	10.1632	−	12.3217i	0.658782	−	0.798697i
$239$	−1.64140	−	9.30885i	−0.106173	−	0.602139i	−0.990745	−	0.135735i	$-0.956660\pi$
$239$	−1.64140	−	9.30885i	−0.106173	−	0.602139i	0.884572	−	0.466404i	$-0.154451\pi$
$240$		0			0
$241$	−15.3652	−	12.8929i	−0.989759	−	0.830506i	−0.00422600	−	0.999991i	$-0.501345\pi$
$241$	−15.3652	−	12.8929i	−0.989759	−	0.830506i	−0.985533	+	0.169485i	$0.945790\pi$
$242$	1.61241	−	4.54913i	0.103650	−	0.292429i
$243$		0			0
$244$	17.8200	−	21.9799i	1.14081	−	1.40712i
$245$	−6.07871	−	5.10064i	−0.388354	−	0.325868i
$246$		0			0
$247$	−35.1136	+	6.19148i	−2.23423	+	0.393954i
$248$	−0.791461	−	3.90746i	−0.0502578	−	0.248124i
$249$		0			0
$250$	14.9786	+	8.48017i	0.947327	+	0.536333i
$251$	−6.86153	−	3.96150i	−0.433096	−	0.250048i	0.267569	−	0.963539i	$-0.413780\pi$
$251$	−6.86153	−	3.96150i	−0.433096	−	0.250048i	−0.700665	+	0.713491i	$0.747113\pi$
$252$		0			0
$253$	5.45261	−	3.14807i	0.342803	−	0.197917i
$254$	−3.64008	+	0.0307163i	−0.228399	+	0.00192731i
$255$		0			0
$256$	−7.04711	+	14.3645i	−0.440444	+	0.897780i
$257$	−5.39668	−	6.43152i	−0.336636	−	0.401187i	0.570997	−	0.820952i	$-0.306557\pi$
$257$	−5.39668	−	6.43152i	−0.336636	−	0.401187i	−0.907633	+	0.419765i	$0.862112\pi$
$258$		0			0
$259$	15.8567	−	5.77136i	0.985286	−	0.358615i
$260$	22.2254	+	3.53330i	1.37836	+	0.219126i
$261$		0			0
$262$	19.0355	−	16.2484i	1.17602	−	1.00383i
$263$	−5.30413	+	30.0812i	−0.327067	+	1.85489i	0.167667	+	0.985844i	$0.446377\pi$
$263$	−5.30413	+	30.0812i	−0.327067	+	1.85489i	−0.494734	+	0.869045i	$0.664734\pi$
$264$		0			0
$265$	0.314936	+	0.114627i	0.0193464	+	0.00704151i
$266$	−4.53655	+	27.0614i	−0.278154	+	1.65924i
$267$		0			0
$268$	−2.33781	−	12.0642i	−0.142805	−	0.736936i
$269$	−19.5851			−1.19412			−0.597061	−	0.802196i	$-0.703665\pi$
$269$	−19.5851			−1.19412			−0.597061	+	0.802196i	$0.703665\pi$
$270$		0			0
$271$		−	4.73913i		−	0.287882i	−0.989586	−	0.143941i	$-0.954022\pi$
$271$		−	4.73913i		−	0.287882i	0.989586	−	0.143941i	$-0.0459775\pi$
$272$	11.8223	+	6.30356i	0.716835	+	0.382210i
$273$		0			0
$274$	0.667622	−	3.98249i	0.0403325	−	0.240591i
$275$	1.60393	−	4.40677i	0.0967207	−	0.265738i
$276$		0			0
$277$	7.26043	+	1.28021i	0.436237	+	0.0769203i	0.387454	−	0.921889i	$-0.373355\pi$
$277$	7.26043	+	1.28021i	0.436237	+	0.0769203i	0.0487830	+	0.998809i	$0.484466\pi$
$278$	−3.08289	−	3.61171i	−0.184899	−	0.216616i
$279$		0			0
$280$	8.27690	−	15.2127i	0.494639	−	0.909135i
$281$	−1.34319	−	3.69038i	−0.0801279	−	0.220150i	0.893159	−	0.449740i	$-0.148483\pi$
$281$	−1.34319	−	3.69038i	−0.0801279	−	0.220150i	−0.973287	+	0.229591i	$0.926261\pi$
$282$		0			0
$283$	−13.1871	+	11.0653i	−0.783894	+	0.657765i	−0.944226	−	0.329298i	$-0.893188\pi$
$283$	−13.1871	+	11.0653i	−0.783894	+	0.657765i	0.160332	+	0.987063i	$0.448744\pi$
$284$	7.34696	−	0.124001i	0.435962	−	0.00735812i
$285$		0			0
$286$	−0.203679	−	24.1373i	−0.0120438	−	1.42727i
$287$	4.06524	+	7.04120i	0.239963	+	0.415629i
$288$		0			0
$289$	−2.89054	+	5.00656i	−0.170032	+	0.294504i
$290$	−20.6094	−	11.6681i	−1.21022	−	0.685172i
$291$		0			0
$292$	−0.280940	−	0.468174i	−0.0164408	−	0.0273978i
$293$	2.84667	+	16.1443i	0.166305	+	0.943160i	0.947709	+	0.319135i	$0.103392\pi$
$293$	2.84667	+	16.1443i	0.166305	+	0.943160i	−0.781405	+	0.624025i	$0.785496\pi$
$294$		0			0
$295$	−15.1557	+	18.0619i	−0.882400	+	1.05160i
$296$	7.38525	+	12.0751i	0.429259	+	0.701850i
$297$		0			0
$298$	−5.04904	+	14.2450i	−0.292483	+	0.825190i
$299$	−9.10435	+	10.8501i	−0.526518	+	0.627480i
$300$		0			0
$301$	−12.1106	+	2.13543i	−0.698045	+	0.123084i
$302$	3.71000	+	3.06008i	0.213486	+	0.176088i
$303$		0			0
$304$	−23.0032	+	0.776714i	−1.31932	+	0.0445476i
$305$	−22.2494	−	12.8457i	−1.27400	−	0.735542i
$306$		0			0
$307$	10.0551	+	17.4159i	0.573874	+	0.993979i	0.996163	+	0.0875176i	$0.0278934\pi$
$307$	10.0551	+	17.4159i	0.573874	+	0.993979i	−0.422289	+	0.906461i	$0.638773\pi$
$308$	−17.5603	−	6.05783i	−1.00059	−	0.345177i
$309$		0			0
$310$	−3.39095	+	1.26671i	−0.192593	+	0.0719442i
$311$	−6.22295	+	5.22168i	−0.352871	+	0.296094i	−0.801942	−	0.597402i	$-0.796200\pi$
$311$	−6.22295	+	5.22168i	−0.352871	+	0.296094i	0.449070	+	0.893496i	$0.351755\pi$
$312$		0			0
$313$	−1.01105	+	0.367994i	−0.0571482	+	0.0208002i	−0.370436	−	0.928858i	$-0.620792\pi$
$313$	−1.01105	+	0.367994i	−0.0571482	+	0.0208002i	0.313288	+	0.949658i	$0.398570\pi$
$314$	3.55978	+	19.2378i	0.200890	+	1.08565i
$315$		0			0
$316$	0.791244	+	2.06482i	0.0445109	+	0.116155i
$317$	3.11019	−	17.6387i	0.174685	−	0.990690i	−0.763821	−	0.645428i	$-0.776679\pi$
$317$	3.11019	−	17.6387i	0.174685	−	0.990690i	0.938506	−	0.345262i	$-0.112210\pi$
$318$		0			0
$319$	−8.68811	+	23.8704i	−0.486441	+	1.33648i
$320$	13.8850	+	4.27137i	0.776196	+	0.238777i
$321$		0			0
$322$	5.52945	+	9.39334i	0.308144	+	0.523470i
$323$			19.2731i			1.07238i
$324$		0			0
$325$			10.5497i			0.585194i
$326$	19.1293	−	11.2606i	1.05948	−	0.623668i
$327$		0			0
$328$	−5.11178	+	4.51464i	−0.282251	+	0.249279i
$329$	−3.52096	+	9.67376i	−0.194117	+	0.533332i
$330$		0			0
$331$	2.41836	−	13.7152i	0.132925	−	0.753857i	−0.843357	−	0.537354i	$-0.819424\pi$
$331$	2.41836	−	13.7152i	0.132925	−	0.753857i	0.976282	−	0.216503i	$-0.0694650\pi$
$332$	2.67787	+	6.98814i	0.146967	+	0.383524i
$333$		0			0
$334$	−21.4544	+	3.96994i	−1.17393	+	0.217225i
$335$	−10.4845	+	3.81605i	−0.572830	+	0.208493i
$336$		0			0
$337$	14.8078	−	12.4253i	0.806635	−	0.676847i	−0.143167	−	0.989699i	$-0.545729\pi$
$337$	14.8078	−	12.4253i	0.806635	−	0.676847i	0.949802	+	0.312852i	$0.101284\pi$
$338$	12.5686	+	33.6458i	0.683641	+	1.83009i
$339$		0			0
$340$	3.96703	−	11.4995i	0.215142	−	0.623649i
$341$	1.94130	+	3.36242i	0.105127	+	0.182085i
$342$		0			0
$343$	7.68048	+	4.43433i	0.414707	+	0.239431i
$344$	−3.77227	−	9.60083i	−0.203387	−	0.517642i
$345$		0			0
$346$	1.43650	−	1.74159i	0.0772268	−	0.0936285i
$347$	4.22476	−	0.744938i	0.226797	−	0.0399904i	−0.0590948	−	0.998252i	$-0.518821\pi$
$347$	4.22476	−	0.744938i	0.226797	−	0.0399904i	0.285892	+	0.958262i	$0.407710\pi$
$348$		0			0
$349$	6.39346	−	7.61943i	0.342234	−	0.407859i	−0.567284	−	0.823522i	$-0.692006\pi$
$349$	6.39346	−	7.61943i	0.342234	−	0.407859i	0.909519	+	0.415663i	$0.136450\pi$
$350$	7.65223	+	2.71228i	0.409029	+	0.144978i
$351$		0			0
$352$	2.05611	−	15.4455i	0.109591	−	0.823247i
$353$	11.6202	−	13.8484i	0.618481	−	0.737077i	−0.362327	−	0.932051i	$-0.618018\pi$
$353$	11.6202	−	13.8484i	0.618481	−	0.737077i	0.980808	+	0.194974i	$0.0624622\pi$
$354$		0			0
$355$	−1.15851	−	6.57025i	−0.0614874	−	0.348712i
$356$	−11.0784	+	6.64789i	−0.587156	+	0.352338i
$357$		0			0
$358$	1.38553	−	2.44727i	0.0732276	−	0.129342i
$359$	−16.4564	+	28.5033i	−0.868536	+	1.50435i	−0.00504305	+	0.999987i	$0.501605\pi$
$359$	−16.4564	+	28.5033i	−0.868536	+	1.50435i	−0.863493	+	0.504361i	$0.831728\pi$
$360$		0			0
$361$	−7.05472	−	12.2191i	−0.371301	−	0.643113i
$362$	−1.08431	+	0.00914977i	−0.0569899	+	0.000480901i
$363$		0			0
$364$	41.7824	−	0.705200i	2.18999	−	0.0369625i
$365$	−0.379757	+	0.318654i	−0.0198774	+	0.0166791i
$366$		0			0
$367$	−12.7028	−	34.9007i	−0.663082	−	1.82180i	−0.562366	−	0.826888i	$-0.690109\pi$
$367$	−12.7028	−	34.9007i	−0.663082	−	1.82180i	−0.100716	−	0.994915i	$-0.532113\pi$
$368$	−6.80170	+	6.11008i	−0.354563	+	0.318510i
$369$		0			0
$370$	9.77479	−	8.34358i	0.508167	−	0.433762i
$371$	0.612880	+	0.108067i	0.0318191	+	0.00561057i
$372$		0			0
$373$	8.37871	−	23.0203i	0.433833	−	1.19195i	−0.509608	−	0.860407i	$-0.670209\pi$
$373$	8.37871	−	23.0203i	0.433833	−	1.19195i	0.943441	−	0.331540i	$-0.107568\pi$
$374$	−12.8681	−	2.15719i	−0.665391	−	0.111546i
$375$		0			0
$376$	−8.53934	−	1.28377i	−0.440383	−	0.0662053i
$377$		−	57.1454i		−	2.94314i
$378$		0			0
$379$	−32.5154			−1.67021			−0.835103	−	0.550094i	$-0.814592\pi$
$379$	−32.5154			−1.67021			−0.835103	+	0.550094i	$0.814592\pi$
$380$	3.97562	+	20.5160i	0.203945	+	1.05245i
$381$		0			0
$382$	0.190943	+	0.0320096i	0.00976951	+	0.00163775i
$383$	21.7889	+	7.93050i	1.11336	+	0.405230i	0.832225	−	0.554439i	$-0.187067\pi$
$383$	21.7889	+	7.93050i	1.11336	+	0.405230i	0.281135	+	0.959668i	$0.409289\pi$
$384$		0			0
$385$	−2.92873	+	16.6096i	−0.149262	+	0.846506i
$386$	−15.6075	−	18.2847i	−0.794402	−	0.930669i
$387$		0			0
$388$	−4.86363	+	30.5935i	−0.246914	+	1.55315i
$389$	−9.45367	+	3.44085i	−0.479320	+	0.174458i	−0.570370	−	0.821388i	$-0.693200\pi$
$389$	−9.45367	+	3.44085i	−0.479320	+	0.174458i	0.0910496	+	0.995846i	$0.470978\pi$
$390$		0			0
$391$	4.92126	+	5.86493i	0.248879	+	0.296602i
$392$	3.93197	−	11.7177i	0.198594	−	0.591833i
$393$		0			0
$394$	−0.0679392	−	8.05124i	−0.00342273	−	0.405615i
$395$	1.73871	−	1.00384i	0.0874838	−	0.0505088i
$396$		0			0
$397$	12.5559	+	7.24913i	0.630161	+	0.363823i	0.780814	−	0.624763i	$-0.214805\pi$
$397$	12.5559	+	7.24913i	0.630161	+	0.363823i	−0.150654	+	0.988587i	$0.548138\pi$
$398$	9.86559	−	17.4256i	0.494517	−	0.873469i
$399$		0			0
$400$	−0.955564	+	6.74273i	−0.0477782	+	0.337136i
$401$	3.68121	−	0.649097i	0.183831	−	0.0324143i	−0.0809748	−	0.996716i	$-0.525803\pi$
$401$	3.68121	−	0.649097i	0.183831	−	0.0324143i	0.264806	+	0.964302i	$0.414692\pi$
$402$		0			0
$403$	−6.69088	−	5.61431i	−0.333296	−	0.279669i
$404$	−13.4803	−	10.9290i	−0.670669	−	0.543738i
$405$		0			0
$406$	−41.4503	−	14.6918i	−2.05714	−	0.729140i
$407$	−10.5595	−	8.86048i	−0.523415	−	0.439198i
$408$		0			0
$409$	4.51536	+	25.6079i	0.223270	+	1.26623i	0.865965	+	0.500105i	$0.166705\pi$
$409$	4.51536	+	25.6079i	0.223270	+	1.26623i	−0.642695	+	0.766122i	$0.722184\pi$
$410$	4.77691	+	3.94010i	0.235915	+	0.194588i
$411$		0			0
$412$	−14.8753	−	17.1321i	−0.732855	−	0.844036i
$413$	−21.8910	+	37.9163i	−1.07719	+	1.86574i
$414$		0			0
$415$	5.88444	−	3.39738i	0.288856	−	0.166771i
$416$	7.53745	+	34.2329i	0.369554	+	1.67840i
$417$		0			0
$418$	20.9974	−	7.84371i	1.02702	−	0.383649i
$419$	−8.50595	−	10.1370i	−0.415543	−	0.495225i	0.517151	−	0.855894i	$-0.326993\pi$
$419$	−8.50595	−	10.1370i	−0.415543	−	0.495225i	−0.932694	+	0.360670i	$0.882548\pi$
$420$		0			0
$421$	−1.63940	−	4.50421i	−0.0798994	−	0.219522i	0.893311	−	0.449440i	$-0.148376\pi$
$421$	−1.63940	−	4.50421i	−0.0798994	−	0.219522i	−0.973210	+	0.229918i	$0.926154\pi$
$422$	−14.6894	+	2.71814i	−0.715071	+	0.132317i
$423$		0			0
$424$	0.0132134	+	0.521858i	0.000641698	+	0.0253437i
$425$	5.61592	+	0.990237i	0.272412	+	0.0480336i
$426$		0			0
$427$	−44.8291	−	16.3165i	−2.16943	−	0.789609i
$428$	−1.97124	−	1.09416i	−0.0952834	−	0.0528884i
$429$		0			0
$430$	−8.07119	+	4.75116i	−0.389227	+	0.229121i
$431$	18.8441			0.907686			0.453843	−	0.891082i	$-0.350053\pi$
$431$	18.8441			0.907686			0.453843	+	0.891082i	$0.350053\pi$
$432$		0			0
$433$	32.5586			1.56466			0.782332	−	0.622861i	$-0.214030\pi$
$433$	32.5586			1.56466			0.782332	+	0.622861i	$0.214030\pi$
$434$	−5.79252	+	3.40980i	−0.278050	+	0.163676i
$435$		0			0
$436$	−17.9585	−	9.96812i	−0.860057	−	0.477387i
$437$	−12.3593	−	4.49843i	−0.591227	−	0.215189i
$438$		0			0
$439$	−2.24864	−	0.396495i	−0.107322	−	0.0189237i	0.119729	−	0.992807i	$-0.461797\pi$
$439$	−2.24864	−	0.396495i	−0.107322	−	0.0189237i	−0.227051	+	0.973883i	$0.572908\pi$
$440$	−14.1429	+	0.358095i	−0.674234	+	0.0170715i
$441$		0			0
$442$	28.8621	−	5.34066i	1.37283	−	0.254029i
$443$	−2.34896	−	6.45372i	−0.111603	−	0.306626i	0.871300	−	0.490750i	$-0.163277\pi$
$443$	−2.34896	−	6.45372i	−0.111603	−	0.306626i	−0.982903	+	0.184125i	$0.941055\pi$
$444$		0			0
$445$	7.54033	+	8.98621i	0.357446	+	0.425987i
$446$	33.3705	−	12.4658i	1.58014	−	0.590271i
$447$		0			0
$448$	26.7686	+	3.33381i	1.26470	+	0.157508i
$449$	8.55447	−	4.93893i	0.403710	−	0.233082i	−0.284373	−	0.958714i	$-0.591786\pi$
$449$	8.55447	−	4.93893i	0.403710	−	0.233082i	0.688084	+	0.725631i	$0.258452\pi$
$450$		0			0
$451$	3.32085	−	5.75188i	0.156373	−	0.270846i
$452$	20.7410	+	23.8876i	0.975574	+	1.12358i
$453$		0			0
$454$	−4.31609	−	3.56001i	−0.202564	−	0.167079i
$455$	−6.58850	−	37.3652i	−0.308874	−	1.75171i
$456$		0			0
$457$	21.3478	+	17.9129i	0.998607	+	0.837931i	0.986791	−	0.162000i	$-0.0517944\pi$
$457$	21.3478	+	17.9129i	0.998607	+	0.837931i	0.0118159	+	0.999930i	$0.496239\pi$
$458$	−11.7924	−	4.17972i	−0.551021	−	0.195306i
$459$		0			0
$460$	6.44843	+	5.22800i	0.300659	+	0.243757i
$461$	−23.3143	−	19.5630i	−1.08585	−	0.911140i	−0.0894610	−	0.995990i	$-0.528514\pi$
$461$	−23.3143	−	19.5630i	−1.08585	−	0.911140i	−0.996394	+	0.0848500i	$0.972959\pi$
$462$		0			0
$463$	21.1468	−	3.72876i	0.982776	−	0.173290i	0.340901	−	0.940099i	$-0.389268\pi$
$463$	21.1468	−	3.72876i	0.982776	−	0.173290i	0.641875	+	0.766809i	$0.278157\pi$
$464$	5.17606	−	36.5237i	0.240292	−	1.69557i
$465$		0			0
$466$	−14.5427	+	25.6868i	−0.673677	+	1.18992i
$467$	30.9949	+	17.8949i	1.43427	+	0.828078i	0.997443	−	0.0714659i	$-0.0227677\pi$
$467$	30.9949	+	17.8949i	1.43427	+	0.828078i	0.436830	+	0.899544i	$0.356101\pi$
$468$		0			0
$469$	−17.9424	+	10.3590i	−0.828501	+	0.478336i
$470$	0.0661577	+	7.84012i	0.00305163	+	0.361638i
$471$		0			0
$472$	−34.8172	−	11.6832i	−1.60259	−	0.537762i
$473$	6.45723	+	7.69542i	0.296904	+	0.353836i
$474$		0			0
$475$	−9.20567	+	3.35059i	−0.422385	+	0.153736i
$476$	3.54646	−	22.3081i	0.162552	−	1.02249i
$477$		0			0
$478$	−8.67875	−	10.1674i	−0.396957	−	0.465048i
$479$	4.55057	−	25.8076i	0.207921	−	1.17918i	−0.684856	−	0.728679i	$-0.740135\pi$
$479$	4.55057	−	25.8076i	0.207921	−	1.17918i	0.892777	−	0.450500i	$-0.148754\pi$
$480$		0			0
$481$	29.1396	+	10.6059i	1.32865	+	0.483589i
$482$	−27.9757	−	4.68982i	−1.27426	−	0.213615i
$483$		0			0
$484$	−1.29852	−	6.70095i	−0.0590237	−	0.304589i
$485$	28.1261			1.27714
$486$		0			0
$487$			23.1000i			1.04676i	0.852099	+	0.523380i	$0.175329\pi$
$487$			23.1000i			1.04676i	−0.852099	+	0.523380i	$0.824671\pi$
$488$	5.94910	−	39.5721i	0.269303	−	1.79134i
$489$		0			0
$490$	−11.0676	−	1.85537i	−0.499984	−	0.0838169i
$491$	−11.2556	+	30.9245i	−0.507957	+	1.39560i	0.375383	+	0.926870i	$0.377511\pi$
$491$	−11.2556	+	30.9245i	−0.507957	+	1.39560i	−0.883341	+	0.468732i	$0.844711\pi$
$492$		0			0
$493$	−30.4200	−	5.36387i	−1.37005	−	0.241577i
$494$	−38.3523	+	32.7368i	−1.72555	+	1.47290i
$495$		0			0
$496$	−3.76786	−	4.19435i	−0.169182	−	0.188332i
$497$	−4.23710	−	11.6413i	−0.190060	−	0.522185i
$498$		0			0
$499$	−6.98386	+	5.86015i	−0.312640	+	0.262336i	−0.785582	−	0.618757i	$-0.787636\pi$
$499$	−6.98386	+	5.86015i	−0.312640	+	0.262336i	0.472942	+	0.881094i	$0.343192\pi$
$500$	24.3387	−	0.410786i	1.08846	−	0.0183709i
$501$		0			0
$502$	−11.2044	+	0.0945469i	−0.500078	+	0.00421984i
$503$	−7.67973	−	13.3017i	−0.342422	−	0.593093i	0.642460	−	0.766319i	$-0.277914\pi$
$503$	−7.67973	−	13.3017i	−0.342422	−	0.593093i	−0.984882	+	0.173227i	$0.944581\pi$
$504$		0			0
$505$	−7.87826	+	13.6455i	−0.350578	+	0.607219i
$506$	4.38681	−	7.74845i	0.195018	−	0.344461i
$507$		0			0
$508$	−4.41426	+	2.64889i	−0.195851	+	0.117525i
$509$	−6.62546	−	37.5748i	−0.293668	−	1.66548i	−0.672566	−	0.740037i	$-0.734808\pi$
$509$	−6.62546	−	37.5748i	−0.293668	−	1.66548i	0.378898	−	0.925439i	$-0.376303\pi$
$510$		0			0
$511$	−0.591706	+	0.705168i	−0.0261755	+	0.0311948i
$512$	1.71675	+	22.5622i	0.0758704	+	0.997118i
$513$		0			0
$514$	−11.1912	−	3.96665i	−0.493623	−	0.174961i
$515$	−13.2416	+	15.7807i	−0.583494	+	0.695381i
$516$		0			0
$517$	8.28179	−	1.46030i	0.364233	−	0.0642241i
$518$	15.1846	−	18.4096i	0.667174	−	0.808871i
$519$		0			0
$520$	29.6217	−	11.6387i	1.29900	−	0.510390i
$521$	−3.40601	−	1.96646i	−0.149220	−	0.0861521i	0.423531	−	0.905882i	$-0.360790\pi$
$521$	−3.40601	−	1.96646i	−0.149220	−	0.0861521i	−0.572751	+	0.819729i	$0.694124\pi$
$522$		0			0
$523$	12.1806	+	21.0974i	0.532619	+	0.922523i	0.999275	+	0.0380841i	$0.0121255\pi$
$523$	12.1806	+	21.0974i	0.532619	+	0.922523i	−0.466656	+	0.884439i	$0.654541\pi$
$524$	11.5424	−	33.4588i	0.504232	−	1.46166i
$525$		0			0
$526$	15.1164	+	40.4663i	0.659108	+	1.76442i
$527$	−3.61668	+	3.03476i	−0.157545	+	0.132196i
$528$		0			0
$529$	16.7033	−	6.07949i	0.726229	−	0.264326i
$530$	0.466059	−	0.0862400i	0.0202443	−	0.00374602i
$531$		0			0
$532$	13.8854	+	36.2352i	0.602009	+	1.57100i
$533$	−2.59452	+	14.7143i	−0.112381	+	0.637345i
$534$		0			0
$535$	−0.700118	+	1.92356i	−0.0302688	+	0.0831627i
$536$	−11.5042	−	13.0258i	−0.496905	−	0.562630i
$537$		0			0
$538$	−23.8690	+	14.0506i	−1.02907	+	0.605766i
$539$			12.0367i			0.518457i
$540$		0			0
$541$			8.40412i			0.361321i	0.983546	+	0.180661i	$0.0578236\pi$
$541$			8.40412i			0.361321i	−0.983546	+	0.180661i	$0.942176\pi$
$542$	−3.39993	−	5.77574i	−0.146039	−	0.248089i
$543$		0			0
$544$	18.9306	−	0.799170i	0.811642	−	0.0342641i
$545$	−6.37827	+	17.5241i	−0.273215	+	0.750652i
$546$		0			0
$547$	5.52901	−	31.3566i	0.236403	−	1.34071i	−0.603235	−	0.797564i	$-0.706122\pi$
$547$	5.52901	−	31.3566i	0.236403	−	1.34071i	0.839638	−	0.543146i	$-0.182767\pi$
$548$	−2.04345	−	5.33257i	−0.0872919	−	0.227796i
$549$		0			0
$550$	−1.20672	−	6.52137i	−0.0514546	−	0.278072i
$551$	49.8648	−	18.1493i	2.12431	−	0.773187i
$552$		0			0
$553$	2.85585	−	2.39635i	0.121443	−	0.101903i
$554$	9.76698	−	3.64851i	0.414959	−	0.155010i
$555$		0			0
$556$	−6.34832	−	2.19000i	−0.269229	−	0.0928767i
$557$	−8.29813	−	14.3728i	−0.351603	−	0.608994i	0.634928	−	0.772572i	$-0.281030\pi$
$557$	−8.29813	−	14.3728i	−0.351603	−	0.608994i	−0.986530	+	0.163578i	$0.947697\pi$
$558$		0			0
$559$	−19.5712	−	11.2994i	−0.827772	−	0.477914i
$560$	−0.826519	−	24.4783i	−0.0349268	−	1.03440i
$561$		0			0
$562$	−4.28453	−	3.53397i	−0.180732	−	0.149072i
$563$	30.3941	−	5.35931i	1.28096	−	0.225868i	0.508573	−	0.861019i	$-0.330173\pi$
$563$	30.3941	−	5.35931i	1.28096	−	0.225868i	0.772388	+	0.635151i	$0.219062\pi$
$564$		0			0
$565$	18.4630	−	22.0034i	0.776746	−	0.925690i
$566$	−8.13318	+	22.9464i	−0.341863	+	0.964508i
$567$		0			0
$568$	8.86503	−	5.42195i	0.371969	−	0.227500i
$569$	10.3725	−	12.3615i	0.434838	−	0.518220i	−0.503473	−	0.864011i	$-0.667945\pi$
$569$	10.3725	−	12.3615i	0.434838	−	0.518220i	0.938312	+	0.345791i	$0.112389\pi$
$570$		0			0
$571$	−0.657320	−	3.72785i	−0.0275080	−	0.156006i	0.967960	−	0.251105i	$-0.0807941\pi$
$571$	−0.657320	−	3.72785i	−0.0275080	−	0.156006i	−0.995468	+	0.0950998i	$0.969683\pi$
$572$	−17.5647	−	29.2708i	−0.734417	−	1.22387i
$573$		0			0
$574$	10.0059	+	5.66489i	0.417639	+	0.236448i
$575$	−1.94579	+	3.37022i	−0.0811452	+	0.140548i
$576$		0			0
$577$	−12.2824	−	21.2738i	−0.511325	−	0.885641i	−0.999914	−	0.0131265i	$-0.995822\pi$
$577$	−12.2824	−	21.2738i	−0.511325	−	0.885641i	0.488589	−	0.872514i	$-0.337512\pi$
$578$	0.0689868	+	8.17539i	0.00286947	+	0.340051i
$579$		0			0
$580$	−33.4882	+	0.565211i	−1.39052	+	0.0234691i
$581$	9.66529	−	8.11014i	0.400984	−	0.336465i
$582$		0			0
$583$	−0.173876	−	0.477719i	−0.00720119	−	0.0197851i
$584$	−0.678266	−	0.369029i	−0.0280669	−	0.0152705i
$585$		0			0
$586$	15.0515	+	17.6334i	0.621772	+	0.728427i
$587$	−30.0373	−	5.29639i	−1.23977	−	0.218605i	−0.484955	−	0.874539i	$-0.661164\pi$
$587$	−30.0373	−	5.29639i	−1.23977	−	0.218605i	−0.754819	+	0.655934i	$0.772275\pi$
$588$		0			0
$589$	2.77401	−	7.62154i	0.114301	−	0.314040i
$590$	−5.51291	+	32.8856i	−0.226963	+	1.35388i
$591$		0			0
$592$	17.6635	+	9.41802i	0.725966	+	0.387078i
$593$			38.8450i			1.59517i	0.603206	+	0.797586i	$0.293890\pi$
$593$			38.8450i			1.59517i	−0.603206	+	0.797586i	$0.706110\pi$
$594$		0			0
$595$	−20.5090			−0.840785
$596$	4.06614	+	20.9831i	0.166556	+	0.859502i
$597$		0			0
$598$	−3.31172	+	19.7551i	−0.135426	+	0.807844i
$599$	42.6481	+	15.5226i	1.74255	+	0.634238i	0.999392	−	0.0348721i	$-0.0111024\pi$
$599$	42.6481	+	15.5226i	1.74255	+	0.634238i	0.743163	+	0.669110i	$0.233325\pi$
$600$		0			0
$601$	2.26751	−	12.8597i	0.0924935	−	0.524557i	−0.902993	−	0.429655i	$-0.858635\pi$
$601$	2.26751	−	12.8597i	0.0924935	−	0.524557i	0.995487	−	0.0949017i	$-0.0302537\pi$
$602$	−13.2276	+	11.2909i	−0.539119	+	0.460182i
$603$		0			0
$604$	6.71686	+	1.06782i	0.273305	+	0.0434489i
$605$	−5.82355	+	2.11960i	−0.236761	+	0.0861739i
$606$		0			0
$607$	0.568907	+	0.677997i	0.0230912	+	0.0275190i	0.777466	−	0.628924i	$-0.216505\pi$
$607$	0.568907	+	0.677997i	0.0230912	+	0.0275190i	−0.754375	+	0.656443i	$0.772060\pi$
$608$	−27.4776	+	17.4495i	−1.11436	+	0.707670i
$609$		0			0
$610$	−36.3318	+	0.306581i	−1.47103	+	0.0124131i
$611$	−16.3837	+	9.45912i	−0.662812	+	0.382675i
$612$		0			0
$613$	1.26069	+	0.727860i	0.0509188	+	0.0293980i	0.525243	−	0.850952i	$-0.323974\pi$
$613$	1.26069	+	0.727860i	0.0509188	+	0.0293980i	−0.474324	+	0.880350i	$0.657308\pi$
$614$	24.7489	+	14.0117i	0.998786	+	0.565466i
$615$		0			0
$616$	−25.7473	+	5.21515i	−1.03739	+	0.210124i
$617$	11.7561	−	2.07291i	0.473281	−	0.0834522i	0.0680800	−	0.997680i	$-0.478313\pi$
$617$	11.7561	−	2.07291i	0.473281	−	0.0834522i	0.405201	+	0.914228i	$0.367202\pi$
$618$		0			0
$619$	1.39092	+	1.16712i	0.0559059	+	0.0469106i	0.670312	−	0.742079i	$-0.266160\pi$
$619$	1.39092	+	1.16712i	0.0559059	+	0.0469106i	−0.614407	+	0.788990i	$0.710605\pi$
$620$	−3.22391	+	3.97650i	−0.129475	+	0.159700i
$621$		0			0
$622$	−3.83801	+	10.8283i	−0.153890	+	0.434175i
$623$	16.6864	+	14.0016i	0.668528	+	0.560961i
$624$		0			0
$625$	−2.35967	−	13.3823i	−0.0943867	−	0.535293i
$626$	−0.968203	+	1.17383i	−0.0386972	+	0.0469158i
$627$		0			0
$628$	18.1399	+	20.8919i	0.723862	+	0.833679i
$629$	8.38098	−	14.5163i	0.334171	−	0.578802i
$630$		0			0
$631$	22.9218	−	13.2339i	0.912502	−	0.526834i	0.0312670	−	0.999511i	$-0.490046\pi$
$631$	22.9218	−	13.2339i	0.912502	−	0.526834i	0.881235	+	0.472678i	$0.156712\pi$
$632$	2.44565	+	1.94882i	0.0972828	+	0.0775198i
$633$		0			0
$634$	−8.86382	−	23.7282i	−0.352027	−	0.942369i
$635$	3.00448	+	3.58061i	0.119229	+	0.142092i
$636$		0			0
$637$	−9.26118	−	25.4449i	−0.366941	−	1.00816i
$638$	6.53649	+	35.3246i	0.258782	+	1.39852i
$639$		0			0
$640$	19.9865	−	4.75567i	0.790036	−	0.187984i
$641$	29.2875	+	5.16418i	1.15679	+	0.203973i	0.718937	−	0.695075i	$-0.244629\pi$
$641$	29.2875	+	5.16418i	1.15679	+	0.203973i	0.437850	+	0.899048i	$0.355740\pi$
$642$		0			0
$643$	39.9458	+	14.5391i	1.57531	+	0.573366i	0.974177	−	0.225784i	$-0.0724944\pi$
$643$	39.9458	+	14.5391i	1.57531	+	0.573366i	0.601132	+	0.799150i	$0.294717\pi$
$644$	13.4779	+	7.48107i	0.531102	+	0.294795i
$645$		0			0
$646$	13.8268	+	23.4888i	0.544009	+	0.924154i
$647$	1.31046			0.0515196			0.0257598	−	0.999668i	$-0.491799\pi$
$647$	1.31046			0.0515196			0.0257598	+	0.999668i	$0.491799\pi$
$648$		0			0
$649$	35.7651			1.40390
$650$	7.56855	+	12.8573i	0.296863	+	0.504306i
$651$		0			0
$652$	15.2351	−	27.4474i	0.596651	−	1.07492i
$653$	45.3419	+	16.5031i	1.77436	+	0.645816i	0.999913	+	0.0131827i	$0.00419629\pi$
$653$	45.3419	+	16.5031i	1.77436	+	0.645816i	0.774452	+	0.632633i	$0.218026\pi$
$654$		0			0
$655$	−31.6475	−	5.58030i	−1.23657	−	0.218040i
$656$	−2.99103	+	9.16942i	−0.116780	+	0.358006i
$657$		0			0
$658$	2.64900	+	14.3157i	0.103269	+	0.558086i
$659$	10.2281	+	28.1016i	0.398432	+	1.09468i	0.963048	+	0.269328i	$0.0868017\pi$
$659$	10.2281	+	28.1016i	0.398432	+	1.09468i	−0.564617	+	0.825353i	$0.690976\pi$
$660$		0			0
$661$	1.72700	+	2.05816i	0.0671726	+	0.0800532i	0.798584	−	0.601883i	$-0.205583\pi$
$661$	1.72700	+	2.05816i	0.0671726	+	0.0800532i	−0.731412	+	0.681936i	$0.761138\pi$
$662$	−6.89218	−	18.4502i	−0.267872	−	0.717087i
$663$		0			0
$664$	8.27702	+	6.59554i	0.321210	+	0.255957i
$665$	30.5123	−	17.6163i	1.18322	−	0.683130i
$666$		0			0
$667$	10.5399	−	18.2556i	0.408106	−	0.706861i
$668$	−23.2991	+	20.2300i	−0.901470	+	0.782723i
$669$		0			0
$670$	−10.0401	+	12.1725i	−0.387885	+	0.470265i
$671$	6.76718	+	38.3786i	0.261244	+	1.48159i
$672$		0			0
$673$	9.16634	+	7.69147i	0.353337	+	0.296485i	0.802128	−	0.597152i	$-0.203701\pi$
$673$	9.16634	+	7.69147i	0.353337	+	0.296485i	−0.448792	+	0.893636i	$0.648145\pi$
$674$	9.13276	−	25.7665i	0.351781	−	0.992488i
$675$		0			0
$676$	39.4558	+	31.9884i	1.51753	+	1.23032i
$677$	28.8050	+	24.1702i	1.10707	+	0.928938i	0.997880	−	0.0650833i	$-0.0207313\pi$
$677$	28.8050	+	24.1702i	1.10707	+	0.928938i	0.109186	+	0.994021i	$0.465176\pi$
$678$		0			0
$679$	51.4337	−	9.06915i	1.97385	−	0.348042i
$680$	−3.41519	−	16.8609i	−0.130967	−	0.646585i
$681$		0			0
$682$	4.77818	+	2.70518i	0.182966	+	0.103587i
$683$	−3.37848	−	1.95057i	−0.129274	−	0.0746363i	0.433968	−	0.900928i	$-0.357113\pi$
$683$	−3.37848	−	1.95057i	−0.129274	−	0.0746363i	−0.563242	+	0.826292i	$0.690446\pi$
$684$		0			0
$685$	−4.49034	+	2.59250i	−0.171567	+	0.0990544i
$686$	12.5417	−	0.105832i	0.478845	−	0.00404067i
$687$		0			0
$688$	−11.4852	−	8.99457i	−0.437868	−	0.342915i
$689$	0.735126	+	0.876089i	0.0280061	+	0.0333764i
$690$		0			0
$691$	21.8838	−	7.96504i	0.832497	−	0.303004i	0.109614	−	0.993974i	$-0.465039\pi$
$691$	21.8838	−	7.96504i	0.832497	−	0.303004i	0.722883	+	0.690970i	$0.242816\pi$
$692$	0.501268	−	3.15311i	0.0190554	−	0.119863i
$693$		0			0
$694$	4.61442	−	3.93879i	0.175161	−	0.149514i
$695$	−1.05878	+	6.00465i	−0.0401619	+	0.227769i
$696$		0			0
$697$	7.58927	+	2.76227i	0.287464	+	0.104628i
$698$	2.32563	−	13.8728i	0.0880265	−	0.525095i
$699$		0			0
$700$	11.2719	−	2.18428i	0.426037	−	0.0825581i
$701$	15.2353			0.575429			0.287715	−	0.957716i	$-0.407105\pi$
$701$	15.2353			0.575429			0.287715	+	0.957716i	$0.407105\pi$
$702$		0			0
$703$			28.7955i			1.08604i
$704$	−8.57499	−	20.2990i	−0.323182	−	0.765048i
$705$		0			0
$706$	4.22687	−	25.2141i	0.159080	−	0.948944i
$707$	−10.0069	+	27.4937i	−0.376347	+	1.03401i
$708$		0			0
$709$	37.6664	+	6.64161i	1.41459	+	0.249431i	0.828126	−	0.560542i	$-0.189407\pi$
$709$	37.6664	+	6.64161i	1.41459	+	0.249431i	0.586467	+	0.809973i	$0.300518\pi$
$710$	−6.12552	−	7.17625i	−0.229887	−	0.269320i
$711$		0			0
$712$	−8.73236	+	16.0499i	−0.327259	+	0.601494i
$713$	−1.10196	−	3.02761i	−0.0412687	−	0.113385i
$714$		0			0
$715$	−23.7429	+	19.9227i	−0.887934	+	0.745065i
$716$	−0.0671163	−	3.97658i	−0.00250825	−	0.148612i
$717$		0			0
$718$	0.392756	+	46.5441i	0.0146575	+	1.73701i
$719$	−11.2648	−	19.5112i	−0.420106	−	0.727645i	0.575843	−	0.817560i	$-0.304674\pi$
$719$	−11.2648	−	19.5112i	−0.420106	−	0.727645i	−0.995949	+	0.0899151i	$0.971340\pi$
$720$		0			0
$721$	−19.1262	+	33.1276i	−0.712298	+	1.23374i
$722$	−17.3640	−	9.83072i	−0.646223	−	0.365861i
$723$		0			0
$724$	−1.31492	+	0.789050i	−0.0488686	+	0.0293248i
$725$	−2.72644	−	15.4624i	−0.101258	−	0.574260i
$726$		0			0
$727$	15.4990	−	18.4710i	0.574827	−	0.685052i	−0.397787	−	0.917478i	$-0.630222\pi$
$727$	15.4990	−	18.4710i	0.574827	−	0.685052i	0.972614	+	0.232425i	$0.0746662\pi$
$728$	50.4158	−	30.8348i	1.86853	−	1.14282i
$729$		0			0
$730$	−0.234216	+	0.660798i	−0.00866871	+	0.0244572i
$731$	−7.85201	+	9.35766i	−0.290417	+	0.346106i
$732$		0			0
$733$	−13.4649	+	2.37423i	−0.497339	+	0.0876942i	−0.416691	−	0.909048i	$-0.636810\pi$
$733$	−13.4649	+	2.37423i	−0.497339	+	0.0876942i	−0.0806481	+	0.996743i	$0.525699\pi$
$734$	−40.5197	−	33.4215i	−1.49561	−	1.23361i
$735$		0			0
$736$	−3.90600	+	12.3262i	−0.143977	+	0.454350i
$737$	14.6569	+	8.46218i	0.539895	+	0.311708i
$738$		0			0
$739$	3.92286	+	6.79458i	0.144305	+	0.249943i	0.929113	−	0.369795i	$-0.120572\pi$
$739$	3.92286	+	6.79458i	0.144305	+	0.249943i	−0.784809	+	0.619738i	$0.787239\pi$
$740$	5.92705	−	17.1812i	0.217883	−	0.631594i
$741$		0			0
$742$	0.824467	−	0.307984i	0.0302671	−	0.0113065i
$743$	−2.44427	+	2.05099i	−0.0896717	+	0.0752435i	−0.686522	−	0.727109i	$-0.740863\pi$
$743$	−2.44427	+	2.05099i	−0.0896717	+	0.0752435i	0.596850	+	0.802353i	$0.296419\pi$
$744$		0			0
$745$	18.2357	−	6.63724i	0.668103	−	0.243170i
$746$	−6.30372	−	34.0667i	−0.230796	−	1.24727i
$747$		0			0
$748$	−17.2303	+	6.60271i	−0.630004	+	0.241419i
$749$	−0.660050	+	3.74333i	−0.0241177	+	0.136778i
$750$		0			0
$751$	−7.59333	+	20.8625i	−0.277085	+	0.761284i	0.720605	+	0.693346i	$0.243864\pi$
$751$	−7.59333	+	20.8625i	−0.277085	+	0.761284i	−0.997690	+	0.0679380i	$0.978358\pi$
$752$	−11.3282	+	4.56168i	−0.413096	+	0.166348i
$753$		0			0
$754$	−40.9970	−	69.6450i	−1.49302	−	2.53632i
$755$		−	6.17514i		−	0.224736i
$756$		0			0
$757$		−	39.4292i		−	1.43308i	−0.697546	−	0.716540i	$-0.745725\pi$
$757$		−	39.4292i		−	1.43308i	0.697546	−	0.716540i	$-0.254275\pi$
$758$	−39.6277	+	23.3271i	−1.43934	+	0.847278i
$759$		0			0
$760$	19.5637	+	22.1513i	0.709650	+	0.803514i
$761$	−10.6550	+	29.2743i	−0.386243	+	1.06119i	0.582436	+	0.812877i	$0.302100\pi$
$761$	−10.6550	+	29.2743i	−0.386243	+	1.06119i	−0.968679	+	0.248317i	$0.920123\pi$
$762$		0			0
$763$	−6.01323	+	34.1027i	−0.217694	+	1.23460i
$764$	0.255673	−	0.0979746i	0.00924994	−	0.00354460i
$765$		0			0
$766$	32.2443	−	5.96651i	1.16503	−	0.215579i
$767$	−75.6053	+	27.5181i	−2.72995	+	0.993620i
$768$		0			0
$769$	4.70066	−	3.94432i	0.169510	−	0.142236i	−0.554086	−	0.832459i	$-0.686932\pi$
$769$	4.70066	−	3.94432i	0.169510	−	0.142236i	0.723596	+	0.690223i	$0.242488\pi$
$770$	8.34668	+	22.3439i	0.300794	+	0.805217i
$771$		0			0
$772$	−32.1392	−	11.0872i	−1.15672	−	0.399036i
$773$	−18.0562	−	31.2743i	−0.649437	−	1.12486i	−0.983258	−	0.182221i	$-0.941671\pi$
$773$	−18.0562	−	31.2743i	−0.649437	−	1.12486i	0.333820	−	0.942637i	$-0.391662\pi$
$774$		0			0
$775$	−2.07829	−	1.19990i	−0.0746542	−	0.0431016i
$776$	16.0208	+	40.7746i	0.575113	+	1.46372i
$777$		0			0
$778$	−9.05299	+	10.9757i	−0.324565	+	0.393498i
$779$	−13.6636	+	2.40927i	−0.489550	+	0.0863209i
$780$		0			0
$781$	−6.50500	+	7.75236i	−0.232767	+	0.277401i
$782$	10.2053	+	3.61720i	0.364941	+	0.129351i
$783$		0			0
$784$	−3.61444	−	17.1016i	−0.129087	−	0.610772i
$785$	16.1476	−	19.2440i	0.576334	−	0.686848i
$786$		0			0
$787$	−0.380802	−	2.15964i	−0.0135741	−	0.0769828i	0.977268	−	0.212007i	$-0.0679999\pi$
$787$	−0.380802	−	2.15964i	−0.0135741	−	0.0769828i	−0.990842	+	0.135024i	$0.956889\pi$
$788$	−5.85889	−	9.76358i	−0.208714	−	0.347813i
$789$		0			0
$790$	1.39885	−	2.47079i	0.0497688	−	0.0879068i
$791$	26.6681	−	46.1905i	0.948209	−	1.64235i
$792$		0			0
$793$	−43.8344	−	75.9234i	−1.55661	−	2.69612i
$794$	20.5029	−	0.173011i	0.727621	−	0.00613992i
$795$		0			0
$796$	−0.477898	−	28.3150i	−0.0169386	−	1.00360i
$797$	−33.5503	+	28.1520i	−1.18841	+	0.997197i	−0.188527	+	0.982068i	$0.560371\pi$
$797$	−33.5503	+	28.1520i	−1.18841	+	0.997197i	−0.999886	+	0.0151286i	$0.995184\pi$
$798$		0			0
$799$	3.49751	+	9.60934i	0.123733	+	0.339954i
$800$	3.67276	+	8.90313i	0.129852	+	0.314773i
$801$		0			0
$802$	4.02075	−	3.43204i	0.141977	−	0.121189i
$803$	0.740548	+	0.130579i	0.0261334	+	0.00460802i
$804$		0			0
$805$	4.78689	−	13.1519i	0.168716	−	0.463542i
$806$	−12.1822	−	2.04221i	−0.429100	−	0.0719340i
$807$		0			0
$808$	−24.2695	−	3.64858i	−0.853799	−	0.128357i
$809$			2.63212i			0.0925405i	0.998929	+	0.0462703i	$0.0147335\pi$
$809$			2.63212i			0.0925405i	−0.998929	+	0.0462703i	$0.985266\pi$
$810$		0			0
$811$	−41.8492			−1.46952			−0.734762	−	0.678324i	$-0.762706\pi$
$811$	−41.8492			−1.46952			−0.734762	+	0.678324i	$0.762706\pi$
$812$	−61.0570	+	11.8317i	−2.14268	+	0.415212i
$813$		0			0
$814$	−19.2259	−	3.22301i	−0.673867	−	0.112967i
$815$	−26.7835	−	9.74840i	−0.938186	−	0.341472i
$816$		0			0
$817$	3.64405	−	20.6664i	0.127489	−	0.723026i
$818$	23.8745	+	27.9698i	0.834753	+	0.977941i
$819$		0			0
$820$	8.64848	+	1.37490i	0.302018	+	0.0480136i
$821$	37.0662	−	13.4910i	1.29362	−	0.470839i	0.398706	−	0.917079i	$-0.369459\pi$
$821$	37.0662	−	13.4910i	1.29362	−	0.470839i	0.894913	+	0.446240i	$0.147237\pi$
$822$		0			0
$823$	−24.6788	−	29.4111i	−0.860249	−	1.02521i	−0.999390	−	0.0349324i	$-0.988878\pi$
$823$	−24.6788	−	29.4111i	−0.860249	−	1.02521i	0.139140	−	0.990273i	$-0.455566\pi$
$824$	−30.4199	−	10.2076i	−1.05973	−	0.355600i
$825$		0			0
$826$	0.522460	+	61.9149i	0.0181787	+	2.15429i
$827$	23.8283	−	13.7573i	0.828592	−	0.478388i	−0.0247780	−	0.999693i	$-0.507888\pi$
$827$	23.8283	−	13.7573i	0.828592	−	0.478388i	0.853370	+	0.521305i	$0.174555\pi$
$828$		0			0
$829$	−10.9778	−	6.33802i	−0.381274	−	0.220129i	0.297098	−	0.954847i	$-0.403981\pi$
$829$	−10.9778	−	6.33802i	−0.381274	−	0.220129i	−0.678372	+	0.734718i	$0.737314\pi$
$830$	4.73423	−	8.36210i	0.164328	−	0.290253i
$831$		0			0
$832$	33.7454	+	36.3133i	1.16991	+	1.25894i
$833$	−14.4143	+	2.54163i	−0.499426	+	0.0880623i
$834$		0			0
$835$	21.4613	+	18.0082i	0.742700	+	0.623199i
$836$	19.9631	−	24.6233i	0.690438	−	0.851615i
$837$		0			0
$838$	−17.6389	−	6.25201i	−0.609327	−	0.215972i
$839$	6.62933	+	5.56267i	0.228870	+	0.192045i	0.750010	−	0.661426i	$-0.230049\pi$
$839$	6.62933	+	5.56267i	0.228870	+	0.192045i	−0.521140	+	0.853471i	$0.674493\pi$
$840$		0			0
$841$	9.73268	+	55.1968i	0.335610	+	1.90334i
$842$	−5.22939	−	4.31331i	−0.180217	−	0.148646i
$843$		0			0
$844$	−15.9525	+	13.8511i	−0.549107	+	0.476776i
$845$	23.0591	−	39.9395i	0.793256	−	1.37396i
$846$		0			0
$847$	−9.96596	+	5.75385i	−0.342434	+	0.197705i
$848$	0.390493	+	0.626527i	0.0134096	+	0.0215150i
$849$		0			0
$850$	7.55472	−	2.82211i	0.259125	−	0.0967976i
$851$	7.35275	+	8.76267i	0.252049	+	0.300380i
$852$		0			0
$853$	8.97988	+	24.6720i	0.307465	+	0.844754i	0.993149	+	0.116854i	$0.0372811\pi$
$853$	8.97988	+	24.6720i	0.307465	+	0.844754i	−0.685684	+	0.727900i	$0.740497\pi$
$854$	−66.3405	+	12.2757i	−2.27012	+	0.420065i
$855$		0			0
$856$	−3.18739	+	0.0807042i	−0.108943	+	0.00275841i
$857$	−34.2064	−	6.03150i	−1.16847	−	0.206032i	−0.444443	−	0.895807i	$-0.646598\pi$
$857$	−34.2064	−	6.03150i	−1.16847	−	0.206032i	−0.724024	+	0.689775i	$0.757709\pi$
$858$		0			0
$859$	9.91134	+	3.60743i	0.338171	+	0.123084i	0.505523	−	0.862813i	$-0.331300\pi$
$859$	9.91134	+	3.60743i	0.338171	+	0.123084i	−0.167352	+	0.985897i	$0.553522\pi$
$860$	−6.42808	+	11.5808i	−0.219196	+	0.394902i
$861$		0			0
$862$	22.9659	−	13.5190i	0.782222	−	0.460460i
$863$	4.89855			0.166748			0.0833742	−	0.996518i	$-0.473430\pi$
$863$	4.89855			0.166748			0.0833742	+	0.996518i	$0.473430\pi$
$864$		0			0
$865$	−2.89881			−0.0985624
$866$	39.6803	−	23.3580i	1.34839	−	0.793738i
$867$		0			0
$868$	−4.61330	+	8.31129i	−0.156585	+	0.282104i
$869$	−2.86175	−	1.04159i	−0.0970781	−	0.0353335i
$870$		0			0
$871$	−37.4948	−	6.61135i	−1.27046	−	0.224017i
$872$	−29.0380	+	0.735238i	−0.983350	+	0.0248983i
$873$		0			0
$874$	−18.2900	+	3.38439i	−0.618668	+	0.114479i
$875$	−14.0365	−	38.5649i	−0.474520	−	1.30373i
$876$		0			0
$877$	−2.27420	−	2.71029i	−0.0767944	−	0.0915200i	0.726279	−	0.687400i	$-0.241248\pi$
$877$	−2.27420	−	2.71029i	−0.0767944	−	0.0915200i	−0.803074	+	0.595880i	$0.796803\pi$
$878$	−3.02494	+	1.12999i	−0.102087	+	0.0381352i
$879$		0			0
$880$	−16.9795	+	10.5827i	−0.572379	+	0.356744i
$881$	4.69517	−	2.71076i	0.158184	−	0.0913277i	−0.418818	−	0.908070i	$-0.637556\pi$
$881$	4.69517	−	2.71076i	0.158184	−	0.0913277i	0.577003	+	0.816742i	$0.304222\pi$
$882$		0			0
$883$	12.7885	−	22.1503i	0.430367	−	0.745418i	−0.566537	−	0.824036i	$-0.691717\pi$
$883$	12.7885	−	22.1503i	0.430367	−	0.745418i	0.996905	+	0.0786177i	$0.0250507\pi$
$884$	31.3438	−	27.2150i	1.05421	−	0.915339i
$885$		0			0
$886$	−7.49277	−	6.18019i	−0.251724	−	0.207628i
$887$	1.48892	+	8.44410i	0.0499931	+	0.283525i	0.999548	−	0.0300771i	$-0.00957528\pi$
$887$	1.48892	+	8.44410i	0.0499931	+	0.283525i	−0.949554	+	0.313602i	$0.898464\pi$
$888$		0			0
$889$	6.64880	+	5.57900i	0.222993	+	0.187114i
$890$	15.6365	+	5.54226i	0.524137	+	0.185777i
$891$		0			0
$892$	31.7267	−	39.1330i	1.06229	−	1.31027i
$893$	−13.4574	−	11.2921i	−0.450336	−	0.377877i
$894$		0			0
$895$	−3.55618	+	0.627050i	−0.118870	+	0.0209600i
$896$	35.0155	−	15.1412i	1.16979	−	0.505831i
$897$		0			0
$898$	6.88237	−	12.1564i	0.229668	−	0.405663i
$899$	11.2576	+	6.49956i	0.375461	+	0.216772i
$900$		0			0
$901$	0.535368	−	0.309095i	0.0178357	−	0.0102974i
$902$	−0.0792568	−	9.39245i	−0.00263896	−	0.312734i
$903$		0			0
$904$	42.4151	+	14.2327i	1.41071	+	0.473373i
$905$	0.894975	+	1.06659i	0.0297500	+	0.0354546i
$906$		0			0
$907$	−1.11817	+	0.406982i	−0.0371283	+	0.0135136i	−0.360518	−	0.932752i	$-0.617400\pi$
$907$	−1.11817	+	0.406982i	−0.0371283	+	0.0135136i	0.323389	+	0.946266i	$0.395178\pi$
$908$	−7.81418	−	1.24227i	−0.259323	−	0.0412261i
$909$		0			0
$910$	−34.8361	−	40.8116i	−1.15480	−	1.35289i
$911$	0.397752	−	2.25577i	0.0131781	−	0.0747368i	−0.977509	−	0.210892i	$-0.932363\pi$
$911$	0.397752	−	2.25577i	0.0131781	−	0.0747368i	0.990688	+	0.136155i	$0.0434744\pi$
$912$		0			0
$913$	−9.68523	−	3.52514i	−0.320534	−	0.116665i
$914$	38.8683	+	6.51585i	1.28565	+	0.215525i
$915$		0			0
$916$	−17.3704	+	3.36605i	−0.573933	+	0.111218i
$917$	−59.6725			−1.97056
$918$		0			0
$919$		−	17.5458i		−	0.578782i	−0.957211	−	0.289391i	$-0.906547\pi$
$919$		−	17.5458i		−	0.578782i	0.957211	−	0.289391i	$-0.0934528\pi$
$920$	11.6096	+	1.74534i	0.382756	+	0.0575420i
$921$		0			0
$922$	−42.4488	−	7.11607i	−1.39798	−	0.234355i
$923$	7.78645	−	21.3931i	0.256294	−	0.704162i
$924$		0			0
$925$	8.39062	+	1.47949i	0.275882	+	0.0486454i
$926$	23.0973	−	19.7154i	0.759024	−	0.647890i
$927$		0			0
$928$	−19.8944	−	48.2261i	−0.653067	−	1.58310i
$929$	−4.62384	−	12.7039i	−0.151703	−	0.416801i	0.840441	−	0.541904i	$-0.182296\pi$
$929$	−4.62384	−	12.7039i	−0.151703	−	0.416801i	−0.992144	+	0.125102i	$0.960074\pi$
$930$		0			0
$931$	19.2618	−	16.1626i	0.631279	−	0.529706i
$932$	0.704460	+	41.7386i	0.0230754	+	1.36719i
$933$		0			0
$934$	50.6127	−	0.427088i	1.65610	−	0.0139747i
$935$	8.37678	+	14.5090i	0.273950	+	0.474495i
$936$		0			0
$937$	6.96020	−	12.0554i	0.227380	−	0.393834i	−0.729651	−	0.683820i	$-0.760317\pi$
$937$	6.96020	−	12.0554i	0.227380	−	0.393834i	0.957031	+	0.289986i	$0.0936507\pi$
$938$	−14.4352	+	25.4970i	−0.471328	+	0.832508i
$939$		0			0
$940$	5.70525	+	9.50756i	0.186085	+	0.310102i
$941$	4.43143	+	25.1319i	0.144460	+	0.819276i	0.967799	+	0.251725i	$0.0809978\pi$
$941$	4.43143	+	25.1319i	0.144460	+	0.819276i	−0.823338	+	0.567551i	$0.807891\pi$
$942$		0			0
$943$	−3.54274	+	4.22208i	−0.115368	+	0.137490i
$944$	−50.8146	+	10.7397i	−1.65388	+	0.349548i
$945$		0			0
$946$	13.3905	+	4.74616i	0.435362	+	0.154311i
$947$	34.1029	−	40.6422i	1.10819	−	1.32069i	0.165812	−	0.986157i	$-0.446976\pi$
$947$	34.1029	−	40.6422i	1.10819	−	1.32069i	0.942383	−	0.334537i	$-0.108580\pi$
$948$		0			0
$949$	−1.66595	+	0.293751i	−0.0540789	+	0.00953557i
$950$	−8.81550	+	10.6878i	−0.286013	+	0.346757i
$951$		0			0
$952$	−11.6820	−	29.7320i	−0.378616	−	0.963619i
$953$	7.54701	+	4.35727i	0.244472	+	0.141146i	0.617230	−	0.786783i	$-0.288255\pi$
$953$	7.54701	+	4.35727i	0.244472	+	0.141146i	−0.372759	+	0.927928i	$0.621588\pi$
$954$		0			0
$955$	−0.124299	−	0.215293i	−0.00402223	−	0.00696671i
$956$	−17.8714	−	6.16515i	−0.578002	−	0.199395i
$957$		0			0
$958$	−12.9688	−	34.7172i	−0.419004	−	1.12166i
$959$	−7.37547	+	6.18875i	−0.238166	+	0.199845i
$960$		0			0
$961$	−27.2635	+	9.92309i	−0.879466	+	0.320100i
$962$	43.1223	−	7.97937i	1.39032	−	0.257265i
$963$		0			0
$964$	−37.4595	+	14.3546i	−1.20649	+	0.462329i
$965$	−5.36022	+	30.3993i	−0.172552	+	0.978588i
$966$		0			0
$967$	1.06732	−	2.93244i	0.0343227	−	0.0943009i	−0.921348	−	0.388740i	$-0.872911\pi$
$967$	1.06732	−	2.93244i	0.0343227	−	0.0943009i	0.955670	+	0.294439i	$0.0951327\pi$
$968$	−6.38992	−	7.23510i	−0.205380	−	0.232545i
$969$		0			0
$970$	34.2783	−	20.1781i	1.10061	−	0.647881i
$971$			0.0539562i			0.00173154i	1.00000		0.000865769i	$0.000275583\pi$
$971$			0.0539562i			0.00173154i	−1.00000		0.000865769i	$0.999724\pi$
$972$		0			0
$973$			11.3220i			0.362966i
$974$	16.5723	+	28.1528i	0.531011	+	0.902073i
$975$		0			0
$976$	−21.1393	−	52.4958i	−0.676651	−	1.68035i
$977$	8.21037	−	22.5578i	0.262673	−	0.721689i	−0.736312	−	0.676642i	$-0.763434\pi$
$977$	8.21037	−	22.5578i	0.262673	−	0.721689i	0.998985	−	0.0450461i	$-0.0143435\pi$
$978$		0			0
$979$	3.08989	−	17.5236i	0.0987533	−	0.560058i
$980$	−14.8196	+	5.67888i	−0.473393	+	0.181405i
$981$		0			0
$982$	8.46813	+	45.7636i	0.270229	+	1.46038i
$983$	−48.9235	+	17.8067i	−1.56042	+	0.567946i	−0.970832	−	0.239759i	$-0.922932\pi$
$983$	−48.9235	+	17.8067i	−1.56042	+	0.567946i	−0.589586	+	0.807705i	$0.700709\pi$
$984$		0			0
$985$	−7.91968	+	6.64540i	−0.252342	+	0.211740i
$986$	−40.9221	+	15.2867i	−1.30322	+	0.486827i
$987$		0			0
$988$	−23.2554	+	67.4121i	−0.739852	+	2.14466i
$989$	−4.16813	−	7.21941i	−0.132539	−	0.229564i
$990$		0			0
$991$	−10.0455	−	5.79977i	−0.319106	−	0.184236i	0.331888	−	0.943319i	$-0.392314\pi$
$991$	−10.0455	−	5.79977i	−0.319106	−	0.184236i	−0.650994	+	0.759083i	$0.725648\pi$
$992$	−7.60112	−	2.40868i	−0.241336	−	0.0764758i
$993$		0			0
$994$	−13.5156	−	11.1479i	−0.428688	−	0.353591i
$995$	−25.3215	+	4.46487i	−0.802747	+	0.141546i
$996$		0			0
$997$	−25.3340	+	30.1918i	−0.802334	+	0.956185i	−0.999709	−	0.0241434i	$-0.992314\pi$
$997$	−25.3340	+	30.1918i	−0.802334	+	0.956185i	0.197374	+	0.980328i	$0.436759\pi$
$998$	−4.30730	+	12.1523i	−0.136345	+	0.384674i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.35.26		192
3.2	odd	2		216.2.v.b.11.7	✓	192
8.3	odd	2	inner	648.2.v.b.35.21		192
12.11	even	2		864.2.bh.b.335.30		192
24.5	odd	2		864.2.bh.b.335.29		192
24.11	even	2		216.2.v.b.11.12	yes	192
27.5	odd	18	inner	648.2.v.b.611.21		192
27.22	even	9		216.2.v.b.59.12	yes	192
108.103	odd	18		864.2.bh.b.815.29		192
216.59	even	18	inner	648.2.v.b.611.26		192
216.157	even	18		864.2.bh.b.815.30		192
216.211	odd	18		216.2.v.b.59.7	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.7	✓	192	3.2	odd	2
216.2.v.b.11.12	yes	192	24.11	even	2
216.2.v.b.59.7	yes	192	216.211	odd	18
216.2.v.b.59.12	yes	192	27.22	even	9
648.2.v.b.35.21		192	8.3	odd	2	inner
648.2.v.b.35.26		192	1.1	even	1	trivial
648.2.v.b.611.21		192	27.5	odd	18	inner
648.2.v.b.611.26		192	216.59	even	18	inner
864.2.bh.b.335.29		192	24.5	odd	2
864.2.bh.b.335.30		192	12.11	even	2
864.2.bh.b.815.29		192	108.103	odd	18
864.2.bh.b.815.30		192	216.157	even	18

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.21873 - 0.717416i) q^{2} +(0.970628 - 1.74868i) q^{4} +(-1.70638 - 0.621073i) q^{5} +(-3.32069 - 0.585528i) q^{7} +(-0.0715925 - 2.82752i) q^{8} +O(q^{10})\)	\(q+(1.21873 - 0.717416i) q^{2} +(0.970628 - 1.74868i) q^{4} +(-1.70638 - 0.621073i) q^{5} +(-3.32069 - 0.585528i) q^{7} +(-0.0715925 - 2.82752i) q^{8} +(-2.52520 + 0.467264i) q^{10} +(0.942090 + 2.58837i) q^{11} +(-3.98305 - 4.74681i) q^{13} +(-4.46711 + 1.66872i) q^{14} +(-2.11576 - 3.39464i) q^{16} +(-2.90072 + 1.67473i) q^{17} +(2.87704 - 4.98318i) q^{19} +(-2.74232 + 2.38109i) q^{20} +(3.00510 + 2.47867i) q^{22} +(-0.396921 - 2.25105i) q^{23} +(-1.30421 - 1.09436i) q^{25} +(-8.25972 - 2.92760i) q^{26} +(-4.24706 + 5.23850i) q^{28} +(7.06459 + 5.92789i) q^{29} +(1.38814 - 0.244766i) q^{31} +(-5.01392 - 2.61928i) q^{32} +(-2.33373 + 4.12208i) q^{34} +(5.30272 + 3.06153i) q^{35} +(-4.33391 + 2.50218i) q^{37} +(-0.0686647 - 8.13721i) q^{38} +(-1.63393 + 4.86930i) q^{40} +(-1.54991 - 1.84711i) q^{41} +(3.42707 - 1.24735i) q^{43} +(5.44065 + 0.864933i) q^{44} +(-2.09868 - 2.45867i) q^{46} +(0.530155 - 3.00666i) q^{47} +(4.10632 + 1.49458i) q^{49} +(-2.37460 - 0.398076i) q^{50} +(-12.1667 + 2.35769i) q^{52} -0.184564 q^{53} -5.00186i q^{55} +(-1.41786 + 9.43125i) q^{56} +(12.8626 + 2.15628i) q^{58} +(4.44089 - 12.2012i) q^{59} +(13.9331 + 2.45678i) q^{61} +(1.51617 - 1.29418i) q^{62} +(-7.98975 + 0.404858i) q^{64} +(3.84849 + 10.5736i) q^{65} +(4.70680 - 3.94947i) q^{67} +(0.113048 + 6.69798i) q^{68} +(8.65900 - 0.0730677i) q^{70} +(1.83700 + 3.18178i) q^{71} +(0.136500 - 0.236424i) q^{73} +(-3.48678 + 6.15871i) q^{74} +(-5.92145 - 9.86784i) q^{76} +(-1.61283 - 9.14681i) q^{77} +(-0.710677 + 0.846952i) q^{79} +(1.50198 + 7.10659i) q^{80} +(-3.21407 - 1.13921i) q^{82} +(-2.40520 + 2.86641i) q^{83} +(5.98987 - 1.05618i) q^{85} +(3.28182 - 3.97883i) q^{86} +(7.25123 - 2.84909i) q^{88} +(-5.59452 - 3.23000i) q^{89} +(10.4471 + 18.0949i) q^{91} +(-4.32163 - 1.49084i) q^{92} +(-1.51091 - 4.04466i) q^{94} +(-8.00425 + 6.71636i) q^{95} +(-14.5548 + 5.29750i) q^{97} +(6.07674 - 1.12444i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Introduction

L-functions

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