LMFDB - Embedded newform 441.2.bb.d.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			163.2
Character	$\chi$	$=$	441.163
Dual form			441.2.bb.d.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0341744 - 0.0870750i) q^{2} +(1.45969 - 1.35439i) q^{4} +(2.09852 - 1.43075i) q^{5} +(-0.301609 + 2.62850i) q^{7} +(-0.336373 - 0.161989i) q^{8} +O(q^{10})$	\(q+(-0.0341744 - 0.0870750i) q^{2} +(1.45969 - 1.35439i) q^{4} +(2.09852 - 1.43075i) q^{5} +(-0.301609 + 2.62850i) q^{7} +(-0.336373 - 0.161989i) q^{8} +(-0.196298 - 0.133834i) q^{10} +(5.58784 + 0.842231i) q^{11} +(-2.04987 + 2.57046i) q^{13} +(0.239184 - 0.0635650i) q^{14} +(0.295003 - 3.93654i) q^{16} +(-3.14655 + 0.970581i) q^{17} +(1.63713 - 2.83559i) q^{19} +(1.12539 - 4.93066i) q^{20} +(-0.117624 - 0.515344i) q^{22} +(-3.48067 - 1.07365i) q^{23} +(0.530039 - 1.35052i) q^{25} +(0.293876 + 0.0906489i) q^{26} +(3.11977 + 4.24530i) q^{28} +(0.333666 - 1.46189i) q^{29} +(-3.45509 - 5.98439i) q^{31} +(-1.06637 + 0.328933i) q^{32} +(0.192045 + 0.240817i) q^{34} +(3.12779 + 5.94749i) q^{35} +(2.58665 + 2.40006i) q^{37} +(-0.302857 - 0.0456484i) q^{38} +(-0.937650 + 0.141328i) q^{40} +(-1.46507 - 0.705541i) q^{41} +(-1.89663 + 0.913369i) q^{43} +(9.29723 - 6.33874i) q^{44} +(0.0254623 + 0.339771i) q^{46} +(1.89671 + 4.83275i) q^{47} +(-6.81806 - 1.58556i) q^{49} -0.135710 q^{50} +(0.489237 + 6.52841i) q^{52} +(2.59862 - 2.41116i) q^{53} +(12.9312 - 6.22734i) q^{55} +(0.527242 - 0.835301i) q^{56} +(-0.138697 + 0.0209052i) q^{58} +(-3.52556 - 2.40369i) q^{59} +(7.78410 + 7.22259i) q^{61} +(-0.403016 + 0.505366i) q^{62} +(-4.85746 - 6.09107i) q^{64} +(-0.624023 + 8.32701i) q^{65} +(0.328115 + 0.568312i) q^{67} +(-3.27843 + 5.67841i) q^{68} +(0.410987 - 0.475604i) q^{70} +(-0.233268 - 1.02201i) q^{71} +(-1.98838 + 5.06632i) q^{73} +(0.120588 - 0.307254i) q^{74} +(-1.45081 - 6.35640i) q^{76} +(-3.89915 + 14.4336i) q^{77} +(-4.42315 + 7.66113i) q^{79} +(-5.01311 - 8.68297i) q^{80} +(-0.0113670 + 0.151682i) q^{82} +(-7.79198 - 9.77083i) q^{83} +(-5.21443 + 6.53869i) q^{85} +(0.144348 + 0.133935i) q^{86} +(-1.74317 - 1.18847i) q^{88} +(-17.2551 + 2.60079i) q^{89} +(-6.13821 - 6.16338i) q^{91} +(-6.53484 + 3.14701i) q^{92} +(0.355992 - 0.330313i) q^{94} +(-0.621463 - 8.29285i) q^{95} -16.4625 q^{97} +(0.0949408 + 0.647869i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{10}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0341744	−	0.0870750i	−0.0241650	−	0.0615713i	0.918282	−	0.395927i	$-0.129577\pi$
$2$	−0.0341744	−	0.0870750i	−0.0241650	−	0.0615713i	−0.942447	+	0.334356i	$0.891481\pi$
$3$		0			0
$3$		0			0
$4$	1.45969	−	1.35439i	0.729845	−	0.677197i
$5$	2.09852	−	1.43075i	0.938486	−	0.639849i	0.00558567	−	0.999984i	$-0.498222\pi$
$5$	2.09852	−	1.43075i	0.938486	−	0.639849i	0.932900	+	0.360136i	$0.117270\pi$
$6$		0			0
$7$	−0.301609	+	2.62850i	−0.113997	+	0.993481i
$7$	−0.301609	+	2.62850i	−0.113997	+	0.993481i
$8$	−0.336373	−	0.161989i	−0.118926	−	0.0572717i
$9$		0			0
$10$	−0.196298	−	0.133834i	−0.0620748	−	0.0423219i
$11$	5.58784	+	0.842231i	1.68480	+	0.253942i	0.920449	−	0.390862i	$-0.127823\pi$
$11$	5.58784	+	0.842231i	1.68480	+	0.253942i	0.764348	+	0.644804i	$0.223061\pi$
$12$		0			0
$13$	−2.04987	+	2.57046i	−0.568533	+	0.712918i	−0.980110	−	0.198457i	$-0.936407\pi$
$13$	−2.04987	+	2.57046i	−0.568533	+	0.712918i	0.411577	+	0.911375i	$0.364978\pi$
$14$	0.239184	−	0.0635650i	0.0639247	−	0.0169885i
$15$		0			0
$16$	0.295003	−	3.93654i	0.0737507	−	0.984135i
$17$	−3.14655	+	0.970581i	−0.763150	+	0.235401i	−0.651810	−	0.758382i	$-0.725990\pi$
$17$	−3.14655	+	0.970581i	−0.763150	+	0.235401i	−0.111339	+	0.993782i	$0.535514\pi$
$18$		0			0
$19$	1.63713	−	2.83559i	0.375583	−	0.650529i	−0.614831	−	0.788659i	$-0.710776\pi$
$19$	1.63713	−	2.83559i	0.375583	−	0.650529i	0.990414	+	0.138130i	$0.0441091\pi$
$20$	1.12539	−	4.93066i	0.251645	−	1.10253i
$21$		0			0
$22$	−0.117624	−	0.515344i	−0.0250775	−	0.109872i
$23$	−3.48067	−	1.07365i	−0.725770	−	0.223870i	−0.0902111	−	0.995923i	$-0.528754\pi$
$23$	−3.48067	−	1.07365i	−0.725770	−	0.223870i	−0.635559	+	0.772052i	$0.719230\pi$
$24$		0			0
$25$	0.530039	−	1.35052i	0.106008	−	0.270104i
$26$	0.293876	+	0.0906489i	0.0576339	+	0.0177777i
$27$		0			0
$28$	3.11977	+	4.24530i	0.589582	+	0.802286i
$29$	0.333666	−	1.46189i	0.0619602	−	0.271466i	−0.934453	−	0.356087i	$-0.884111\pi$
$29$	0.333666	−	1.46189i	0.0619602	−	0.271466i	0.996413	+	0.0846210i	$0.0269680\pi$
$30$		0			0
$31$	−3.45509	−	5.98439i	−0.620553	−	1.07483i	−0.989383	−	0.145332i	$-0.953575\pi$
$31$	−3.45509	−	5.98439i	−0.620553	−	1.07483i	0.368830	−	0.929497i	$-0.379758\pi$
$32$	−1.06637	+	0.328933i	−0.188510	+	0.0581477i
$33$		0			0
$34$	0.192045	+	0.240817i	0.0329354	+	0.0412997i
$35$	3.12779	+	5.94749i	0.528693	+	1.00531i
$36$		0			0
$37$	2.58665	+	2.40006i	0.425243	+	0.394568i	0.863555	−	0.504255i	$-0.168233\pi$
$37$	2.58665	+	2.40006i	0.425243	+	0.394568i	−0.438312	+	0.898823i	$0.644423\pi$
$38$	−0.302857	−	0.0456484i	−0.0491299	−	0.00740514i
$39$		0			0
$40$	−0.937650	+	0.141328i	−0.148256	+	0.0223459i
$41$	−1.46507	−	0.705541i	−0.228805	−	0.110187i	0.315969	−	0.948770i	$-0.397670\pi$
$41$	−1.46507	−	0.705541i	−0.228805	−	0.110187i	−0.544774	+	0.838583i	$0.683385\pi$
$42$		0			0
$43$	−1.89663	+	0.913369i	−0.289233	+	0.139287i	−0.572875	−	0.819643i	$-0.694172\pi$
$43$	−1.89663	+	0.913369i	−0.289233	+	0.139287i	0.283641	+	0.958930i	$0.408458\pi$
$44$	9.29723	−	6.33874i	1.40161	−	0.955601i
$45$		0			0
$46$	0.0254623	+	0.339771i	0.00375421	+	0.0500965i
$47$	1.89671	+	4.83275i	0.276664	+	0.704928i	0.999897	+	0.0143247i	$0.00455985\pi$
$47$	1.89671	+	4.83275i	0.276664	+	0.704928i	−0.723233	+	0.690604i	$0.757345\pi$
$48$		0			0
$49$	−6.81806	−	1.58556i	−0.974009	−	0.226509i
$50$	−0.135710			−0.0191923
$51$		0			0
$52$	0.489237	+	6.52841i	0.0678450	+	0.905328i
$53$	2.59862	−	2.41116i	0.356947	−	0.331199i	−0.481232	−	0.876593i	$-0.659811\pi$
$53$	2.59862	−	2.41116i	0.356947	−	0.331199i	0.838179	+	0.545394i	$0.183620\pi$
$54$		0			0
$55$	12.9312	−	6.22734i	1.74364	−	0.839694i
$56$	0.527242	−	0.835301i	0.0704556	−	0.111622i
$57$		0			0
$58$	−0.138697	+	0.0209052i	−0.0182118	+	0.00274498i
$59$	−3.52556	−	2.40369i	−0.458989	−	0.312933i	0.311660	−	0.950194i	$-0.399115\pi$
$59$	−3.52556	−	2.40369i	−0.458989	−	0.312933i	−0.770648	+	0.637260i	$0.780068\pi$
$60$		0			0
$61$	7.78410	+	7.22259i	0.996652	+	0.924758i	0.997165	−	0.0752415i	$-0.0239728\pi$
$61$	7.78410	+	7.22259i	0.996652	+	0.924758i	−0.000512856		1.00000i	$0.500163\pi$
$62$	−0.403016	+	0.505366i	−0.0511830	+	0.0641815i
$63$		0			0
$64$	−4.85746	−	6.09107i	−0.607183	−	0.761383i
$65$	−0.624023	+	8.32701i	−0.0774005	+	1.03284i
$66$		0			0
$67$	0.328115	+	0.568312i	0.0400856	+	0.0694303i	0.885372	−	0.464883i	$-0.153904\pi$
$67$	0.328115	+	0.568312i	0.0400856	+	0.0694303i	−0.845287	+	0.534313i	$0.820570\pi$
$68$	−3.27843	+	5.67841i	−0.397568	+	0.688609i
$69$		0			0
$70$	0.410987	−	0.475604i	0.0491224	−	0.0568456i
$71$	−0.233268	−	1.02201i	−0.0276838	−	0.121291i	0.959198	−	0.282735i	$-0.0912418\pi$
$71$	−0.233268	−	1.02201i	−0.0276838	−	0.121291i	−0.986882	+	0.161445i	$0.948385\pi$
$72$		0			0
$73$	−1.98838	+	5.06632i	−0.232723	+	0.592968i	−0.998758	−	0.0498311i	$-0.984132\pi$
$73$	−1.98838	+	5.06632i	−0.232723	+	0.592968i	0.766035	+	0.642799i	$0.222227\pi$
$74$	0.120588	−	0.307254i	0.0140181	−	0.0357175i
$75$		0			0
$76$	−1.45081	−	6.35640i	−0.166419	−	0.729129i
$77$	−3.89915	+	14.4336i	−0.444349	+	1.64487i
$78$		0			0
$79$	−4.42315	+	7.66113i	−0.497644	+	0.861944i	−0.999996	−	0.00271872i	$-0.999135\pi$
$79$	−4.42315	+	7.66113i	−0.497644	+	0.861944i	0.502353	+	0.864663i	$0.332468\pi$
$80$	−5.01311	−	8.68297i	−0.560483	−	0.970785i
$81$		0			0
$82$	−0.0113670	+	0.151682i	−0.00125528	+	0.0167505i
$83$	−7.79198	−	9.77083i	−0.855281	−	1.07249i	−0.996589	−	0.0825228i	$-0.973702\pi$
$83$	−7.79198	−	9.77083i	−0.855281	−	1.07249i	0.141308	−	0.989966i	$-0.454869\pi$
$84$		0			0
$85$	−5.21443	+	6.53869i	−0.565584	+	0.709220i
$86$	0.144348	+	0.133935i	0.0155654	+	0.0144426i
$87$		0			0
$88$	−1.74317	−	1.18847i	−0.185822	−	0.126692i
$89$	−17.2551	+	2.60079i	−1.82904	+	0.275684i	−0.971206	−	0.238242i	$-0.923429\pi$
$89$	−17.2551	+	2.60079i	−1.82904	+	0.275684i	−0.857835	+	0.513925i	$0.828191\pi$
$90$		0			0
$91$	−6.13821	−	6.16338i	−0.643459	−	0.646098i
$92$	−6.53484	+	3.14701i	−0.681304	+	0.328099i
$93$		0			0
$94$	0.355992	−	0.330313i	0.0367178	−	0.0340692i
$95$	−0.621463	−	8.29285i	−0.0637608	−	0.850828i
$96$		0			0
$97$	−16.4625			−1.67151			−0.835757	−	0.549099i	$-0.814971\pi$
$97$	−16.4625			−1.67151			−0.835757	+	0.549099i	$0.814971\pi$
$98$	0.0949408	+	0.647869i	0.00959047	+	0.0654446i
$99$		0			0
$100$	−1.05544	−	2.68922i	−0.105544	−	0.268922i
$101$	0.755878	+	10.0865i	0.0752127	+	1.00364i	0.899343	+	0.437244i	$0.144045\pi$
$101$	0.755878	+	10.0865i	0.0752127	+	1.00364i	−0.824130	+	0.566400i	$0.808336\pi$
$102$		0			0
$103$	−6.92198	+	4.71932i	−0.682043	+	0.465009i	−0.854121	−	0.520074i	$-0.825904\pi$
$103$	−6.92198	+	4.71932i	−0.682043	+	0.465009i	0.172078	+	0.985083i	$0.444952\pi$
$104$	1.10591	−	0.532578i	0.108443	−	0.0522236i
$105$		0			0
$106$	−0.298758	−	0.143874i	−0.0290180	−	0.0139743i
$107$	10.2174	−	1.54002i	0.987750	−	0.148879i	0.364754	−	0.931104i	$-0.381153\pi$
$107$	10.2174	−	1.54002i	0.987750	−	0.148879i	0.622996	+	0.782225i	$0.285915\pi$
$108$		0			0
$109$	8.47138	+	1.27685i	0.811411	+	0.122300i	0.541625	−	0.840620i	$-0.317809\pi$
$109$	8.47138	+	1.27685i	0.811411	+	0.122300i	0.269785	+	0.962920i	$0.413047\pi$
$110$	−0.984162	−	0.913169i	−0.0938362	−	0.0870672i
$111$		0			0
$112$	10.2582	+	1.96271i	0.969312	+	0.185459i
$113$	−2.26646	−	2.84205i	−0.213211	−	0.267358i	0.663713	−	0.747987i	$-0.268980\pi$
$113$	−2.26646	−	2.84205i	−0.213211	−	0.267358i	−0.876924	+	0.480629i	$0.840408\pi$
$114$		0			0
$115$	−8.84036	+	2.72689i	−0.824368	+	0.254284i
$116$	−1.49292	−	2.58582i	−0.138614	−	0.240087i
$117$		0			0
$118$	−0.0888171	+	0.389133i	−0.00817627	+	0.0358226i
$119$	−1.60215	−	8.56345i	−0.146869	−	0.785010i
$120$		0			0
$121$	20.0033	+	6.17020i	1.81848	+	0.560927i
$122$	0.362890	−	0.924629i	0.0328545	−	0.0837120i
$123$		0			0
$124$	−13.1486	−	4.05580i	−1.18078	−	0.364222i
$125$	2.00589	+	8.78839i	0.179412	+	0.786057i
$126$		0			0
$127$	3.53659	−	15.4948i	0.313822	−	1.37494i	−0.534368	−	0.845252i	$-0.679450\pi$
$127$	3.53659	−	15.4948i	0.313822	−	1.37494i	0.848190	−	0.529692i	$-0.177692\pi$
$128$	−1.48033	+	2.56401i	−0.130844	+	0.226629i
$129$		0			0
$130$	0.746400	−	0.230234i	0.0654636	−	0.0201929i
$131$	−0.342826	+	4.57470i	−0.0299529	+	0.399693i	0.961997	+	0.273061i	$0.0880360\pi$
$131$	−0.342826	+	4.57470i	−0.0299529	+	0.399693i	−0.991950	+	0.126633i	$0.959583\pi$
$132$		0			0
$133$	6.95959	+	5.15844i	0.603473	+	0.447293i
$134$	0.0382726	−	0.0479924i	0.00330625	−	0.00414591i
$135$		0			0
$136$	1.21564	+	0.183228i	0.104240	+	0.0157117i
$137$	8.51512	+	5.80551i	0.727496	+	0.495998i	0.869540	−	0.493862i	$-0.164415\pi$
$137$	8.51512	+	5.80551i	0.727496	+	0.495998i	−0.142044	+	0.989860i	$0.545368\pi$
$138$		0			0
$139$	3.87696	+	1.86705i	0.328840	+	0.158361i	0.591018	−	0.806659i	$-0.298726\pi$
$139$	3.87696	+	1.86705i	0.328840	+	0.158361i	−0.262178	+	0.965020i	$0.584441\pi$
$140$	12.6208	+	4.44523i	1.06666	+	0.375690i
$141$		0			0
$142$	−0.0810200	+	0.0552385i	−0.00679905	+	0.00463551i
$143$	−13.6193	+	12.6369i	−1.13890	+	1.05675i
$144$		0			0
$145$	−1.39138	−	3.54519i	−0.115548	−	0.294412i
$146$	0.509102			0.0421336
$147$		0			0
$148$	7.02634			0.577561
$149$	7.15396	+	18.2280i	0.586075	+	1.49330i	0.848954	+	0.528466i	$0.177233\pi$
$149$	7.15396	+	18.2280i	0.586075	+	1.49330i	−0.262879	+	0.964829i	$0.584672\pi$
$150$		0			0
$151$	−4.50881	+	4.18356i	−0.366922	+	0.340453i	−0.841988	−	0.539497i	$-0.818615\pi$
$151$	−4.50881	+	4.18356i	−0.366922	+	0.340453i	0.475066	+	0.879950i	$0.342424\pi$
$152$	−1.01002	+	0.688620i	−0.0819235	+	0.0558545i
$153$		0			0
$154$	1.39006	−	0.153743i	0.112014	−	0.0123889i
$155$	−15.8127	−	7.61500i	−1.27011	−	0.611652i
$156$		0			0
$157$	4.67286	+	3.18590i	0.372935	+	0.254263i	0.735254	−	0.677791i	$-0.237063\pi$
$157$	4.67286	+	3.18590i	0.372935	+	0.254263i	−0.362319	+	0.932054i	$0.618015\pi$
$158$	0.818252	+	0.123332i	0.0650966	+	0.00981174i
$159$		0			0
$160$	−1.76719	+	2.21598i	−0.139708	+	0.175189i
$161$	3.87188	−	8.82514i	0.305147	−	0.695518i
$162$		0			0
$163$	0.744970	−	9.94094i	0.0583506	−	0.778635i	−0.888892	−	0.458117i	$-0.848524\pi$
$163$	0.744970	−	9.94094i	0.0583506	−	0.778635i	0.947243	−	0.320518i	$-0.103857\pi$
$164$	−3.09413	+	0.954412i	−0.241611	+	0.0745270i
$165$		0			0
$166$	−0.584509	+	1.01240i	−0.0453667	+	0.0785775i
$167$	4.79486	−	21.0076i	0.371037	−	1.62562i	−0.352835	−	0.935686i	$-0.614782\pi$
$167$	4.79486	−	21.0076i	0.371037	−	1.62562i	0.723872	−	0.689935i	$-0.242361\pi$
$168$		0			0
$169$	0.487485	+	2.13581i	0.0374989	+	0.164293i
$170$	0.747557	+	0.230591i	0.0573350	+	0.0176855i
$171$		0			0
$172$	−1.53143	+	3.90202i	−0.116770	+	0.297526i
$173$	8.72078	+	2.69000i	0.663029	+	0.204517i	0.607963	−	0.793965i	$-0.291987\pi$
$173$	8.72078	+	2.69000i	0.663029	+	0.204517i	0.0550658	+	0.998483i	$0.482463\pi$
$174$		0			0
$175$	3.38998	+	1.80054i	0.256258	+	0.136108i
$176$	4.96390	−	21.7483i	0.374168	−	1.63934i
$177$		0			0
$178$	0.816149	+	1.41361i	0.0611729	+	0.105955i
$179$	4.61508	−	1.42356i	0.344948	−	0.106402i	−0.117440	−	0.993080i	$-0.537469\pi$
$179$	4.61508	−	1.42356i	0.344948	−	0.106402i	0.462388	+	0.886678i	$0.346993\pi$
$180$		0			0
$181$	−6.22935	−	7.81136i	−0.463024	−	0.580614i	0.494424	−	0.869221i	$-0.335379\pi$
$181$	−6.22935	−	7.81136i	−0.463024	−	0.580614i	−0.957447	+	0.288608i	$0.906808\pi$
$182$	−0.326907	+	0.745115i	−0.0242319	+	0.0552316i
$183$		0			0
$184$	0.996887	+	0.924976i	0.0734915	+	0.0681901i
$185$	8.86201	+	1.33573i	0.651548	+	0.0982051i
$186$		0			0
$187$	−18.3999	+	2.77333i	−1.34553	+	0.202806i
$188$	9.31405	+	4.48541i	0.679297	+	0.327132i
$189$		0			0
$190$	−0.700862	+	0.337517i	−0.0508459	+	0.0244861i
$191$	1.14387	−	0.779879i	0.0827677	−	0.0564301i	−0.521229	−	0.853417i	$-0.674526\pi$
$191$	1.14387	−	0.779879i	0.0827677	−	0.0564301i	0.603997	+	0.796987i	$0.293574\pi$
$192$		0			0
$193$	−1.62094	−	21.6300i	−0.116678	−	1.55696i	−0.681543	−	0.731778i	$-0.738691\pi$
$193$	−1.62094	−	21.6300i	−0.116678	−	1.55696i	0.564865	−	0.825183i	$-0.308928\pi$
$194$	0.562597	+	1.43347i	0.0403921	+	0.102917i
$195$		0			0
$196$	−12.0997	+	6.91992i	−0.864266	+	0.494280i
$197$	−11.4909			−0.818692			−0.409346	−	0.912379i	$-0.634243\pi$
$197$	−11.4909			−0.818692			−0.409346	+	0.912379i	$0.634243\pi$
$198$		0			0
$199$	−0.0171235	−	0.228498i	−0.00121386	−	0.0161978i	0.996564	−	0.0828265i	$-0.0263947\pi$
$199$	−0.0171235	−	0.228498i	−0.00121386	−	0.0161978i	−0.997778	+	0.0666287i	$0.978776\pi$
$200$	−0.397060	+	0.368418i	−0.0280764	+	0.0260511i
$201$		0			0
$202$	0.852450	−	0.410518i	0.0599782	−	0.0288840i
$203$	3.74194	+	1.31796i	0.262633	+	0.0925027i
$204$		0			0
$205$	−4.08392	+	0.615552i	−0.285234	+	0.0429920i
$206$	0.647490	+	0.441451i	0.0451128	+	0.0307574i
$207$		0			0
$208$	9.51400	+	8.82770i	0.659677	+	0.612091i
$209$	11.5362	−	14.4660i	0.797978	−	1.00063i
$210$		0			0
$211$	8.37791	+	10.5056i	0.576759	+	0.723233i	0.981556	−	0.191173i	$-0.0612293\pi$
$211$	8.37791	+	10.5056i	0.576759	+	0.723233i	−0.404797	+	0.914406i	$0.632658\pi$
$212$	0.527507	−	7.03910i	0.0362294	−	0.483447i
$213$		0			0
$214$	−0.483270	−	0.837048i	−0.0330357	−	0.0572194i
$215$	−2.67331	+	4.63032i	−0.182318	+	0.315785i
$216$		0			0
$217$	16.7721	−	7.27678i	1.13856	−	0.493980i
$218$	−0.178322	−	0.781281i	−0.0120775	−	0.0529150i
$219$		0			0
$220$	10.4413	−	26.6039i	0.703950	−	1.79364i
$221$	3.95519	−	10.0777i	0.266055	−	0.677896i
$222$		0			0
$223$	0.463950	+	2.03270i	0.0310684	+	0.136119i	0.988084	−	0.153918i	$-0.0491893\pi$
$223$	0.463950	+	2.03270i	0.0310684	+	0.136119i	−0.957015	+	0.290038i	$0.906332\pi$
$224$	−0.542974	−	2.90218i	−0.0362790	−	0.193910i
$225$		0			0
$226$	−0.170017	+	0.294478i	−0.0113094	+	0.0195884i
$227$	1.07694	+	1.86531i	0.0714788	+	0.123805i	0.899550	−	0.436819i	$-0.143895\pi$
$227$	1.07694	+	1.86531i	0.0714788	+	0.123805i	−0.828071	+	0.560624i	$0.810562\pi$
$228$		0			0
$229$	−0.312139	+	4.16521i	−0.0206268	+	0.275245i	0.977348	+	0.211637i	$0.0678796\pi$
$229$	−0.312139	+	4.16521i	−0.0206268	+	0.275245i	−0.997975	+	0.0636075i	$0.979739\pi$
$230$	0.539559	+	0.676585i	0.0355774	+	0.0446127i
$231$		0			0
$232$	−0.349046	+	0.437690i	−0.0229160	+	0.0287357i
$233$	1.84071	+	1.70792i	0.120589	+	0.111890i	0.738162	−	0.674623i	$-0.235694\pi$
$233$	1.84071	+	1.70792i	0.120589	+	0.111890i	−0.617574	+	0.786513i	$0.711884\pi$
$234$		0			0
$235$	10.8947	+	7.42789i	0.710693	+	0.484542i
$236$	−8.40176	+	1.26636i	−0.546908	+	0.0824331i
$237$		0			0
$238$	−0.690910	+	0.432158i	−0.0447850	+	0.0280127i
$239$	−3.43076	+	1.65217i	−0.221918	+	0.106870i	−0.541540	−	0.840675i	$-0.682158\pi$
$239$	−3.43076	+	1.65217i	−0.221918	+	0.106870i	0.319622	+	0.947545i	$0.396444\pi$
$240$		0			0
$241$	−4.12223	+	3.82487i	−0.265536	+	0.246381i	−0.801692	−	0.597738i	$-0.796066\pi$
$241$	−4.12223	+	3.82487i	−0.265536	+	0.246381i	0.536156	+	0.844119i	$0.319876\pi$
$242$	−0.146331	−	1.95265i	−0.00940651	−	0.125521i
$243$		0			0
$244$	21.1446			1.35365
$245$	−16.5764	+	6.42759i	−1.05902	+	0.410643i
$246$		0			0
$247$	3.93287	+	10.0208i	0.250242	+	0.637607i
$248$	0.192796	+	2.57268i	0.0122425	+	0.163365i
$249$		0			0
$250$	0.696699	−	0.475001i	0.0440631	−	0.0300417i
$251$	−5.09948	+	2.45578i	−0.321876	+	0.155007i	−0.587843	−	0.808975i	$-0.700023\pi$
$251$	−5.09948	+	2.45578i	−0.321876	+	0.155007i	0.265967	+	0.963982i	$0.414309\pi$
$252$		0			0
$253$	−18.5452	−	8.93089i	−1.16593	−	0.561480i
$254$	−1.47007	+	0.221578i	−0.0922407	+	0.0139030i
$255$		0			0
$256$	−15.1336	−	2.28103i	−0.945853	−	0.142564i
$257$	18.4375	+	17.1075i	1.15010	+	1.06714i	0.996879	+	0.0789477i	$0.0251560\pi$
$257$	18.4375	+	17.1075i	1.15010	+	1.06714i	0.153224	+	0.988192i	$0.451034\pi$
$258$		0			0
$259$	−7.08873	+	6.07514i	−0.440472	+	0.377491i
$260$	10.3672	+	13.0000i	0.642945	+	0.806227i
$261$		0			0
$262$	0.410058	−	0.126486i	0.0253335	−	0.00781434i
$263$	−12.0898	−	20.9402i	−0.745490	−	1.29123i	−0.949965	−	0.312356i	$-0.898882\pi$
$263$	−12.0898	−	20.9402i	−0.745490	−	1.29123i	0.204475	−	0.978872i	$-0.434451\pi$
$264$		0			0
$265$	2.00348	−	8.77782i	0.123073	−	0.539217i
$266$	0.211331	−	0.782293i	0.0129576	−	0.0479655i
$267$		0			0
$268$	1.24866	+	0.385162i	0.0762743	+	0.0235275i
$269$	9.74917	−	24.8405i	0.594418	−	1.51455i	−0.244141	−	0.969740i	$-0.578506\pi$
$269$	9.74917	−	24.8405i	0.594418	−	1.51455i	0.838559	−	0.544812i	$-0.183399\pi$
$270$		0			0
$271$	19.5180	+	6.02049i	1.18563	+	0.365719i	0.823993	−	0.566600i	$-0.191741\pi$
$271$	19.5180	+	6.02049i	1.18563	+	0.365719i	0.361638	+	0.932319i	$0.382218\pi$
$272$	2.89249	+	12.6728i	0.175383	+	0.768403i
$273$		0			0
$274$	0.214516	−	0.939855i	0.0129594	−	0.0567787i
$275$	4.09922	−	7.10006i	0.247193	−	0.428150i
$276$		0			0
$277$	15.6296	−	4.82111i	0.939095	−	0.289672i	0.212831	−	0.977089i	$-0.431732\pi$
$277$	15.6296	−	4.82111i	0.939095	−	0.289672i	0.726263	+	0.687417i	$0.241255\pi$
$278$	0.0300802	−	0.401392i	0.00180409	−	0.0240739i
$279$		0			0
$280$	−0.0886777	−	2.50724i	−0.00529951	−	0.149836i
$281$	7.78664	−	9.76414i	0.464512	−	0.582480i	−0.493306	−	0.869856i	$-0.664212\pi$
$281$	7.78664	−	9.76414i	0.464512	−	0.582480i	0.957818	+	0.287376i	$0.0927830\pi$
$282$		0			0
$283$	−4.34306	−	0.654611i	−0.258168	−	0.0389126i	0.0186828	−	0.999825i	$-0.494053\pi$
$283$	−4.34306	−	0.654611i	−0.258168	−	0.0389126i	−0.276851	+	0.960913i	$0.589291\pi$
$284$	−1.72471	−	1.17588i	−0.102342	−	0.0697759i
$285$		0			0
$286$	1.56579	+	0.754043i	0.0925869	+	0.0445875i
$287$	2.29639	−	3.63814i	0.135552	−	0.214753i
$288$		0			0
$289$	−5.08733	+	3.46848i	−0.299254	+	0.204028i
$290$	−0.261147	+	0.242309i	−0.0153351	+	0.0142289i
$291$		0			0
$292$	3.95937	+	10.0883i	0.231705	+	0.590374i
$293$	−7.63542			−0.446066			−0.223033	−	0.974811i	$-0.571596\pi$
$293$	−7.63542			−0.446066			−0.223033	+	0.974811i	$0.571596\pi$
$294$		0			0
$295$	−10.8375			−0.630984
$296$	−0.481297	−	1.22633i	−0.0279748	−	0.0712787i
$297$		0			0
$298$	1.34272	−	1.24586i	0.0777817	−	0.0721709i
$299$	9.89470	−	6.74610i	0.572226	−	0.390137i
$300$		0			0
$301$	−1.82875	−	5.26078i	−0.105408	−	0.303226i
$302$	0.518370	+	0.249634i	0.0298288	+	0.0143648i
$303$		0			0
$304$	−10.6795	−	7.28113i	−0.612509	−	0.417601i
$305$	26.6688	+	4.01967i	1.52705	+	0.230166i
$306$		0			0
$307$	1.52247	−	1.90912i	0.0868919	−	0.108959i	−0.736485	−	0.676454i	$-0.763516\pi$
$307$	1.52247	−	1.90912i	0.0868919	−	0.108959i	0.823377	+	0.567495i	$0.192087\pi$
$308$	13.8573	+	26.3496i	0.789592	+	1.50141i
$309$		0			0
$310$	−0.122686	+	1.63713i	−0.00696810	+	0.0929828i
$311$	4.84107	−	1.49327i	0.274512	−	0.0846757i	−0.154443	−	0.988002i	$-0.549358\pi$
$311$	4.84107	−	1.49327i	0.274512	−	0.0846757i	0.428955	+	0.903326i	$0.358882\pi$
$312$		0			0
$313$	9.04913	−	15.6735i	0.511487	−	0.885921i	−0.488424	−	0.872606i	$-0.662428\pi$
$313$	9.04913	−	15.6735i	0.511487	−	0.885921i	0.999911	−	0.0133151i	$-0.00423846\pi$
$314$	0.117720	−	0.515766i	0.00664334	−	0.0291064i
$315$		0			0
$316$	3.91975	+	17.1736i	0.220503	+	0.966088i
$317$	28.8073	+	8.88587i	1.61798	+	0.499080i	0.965866	−	0.259042i	$-0.0834069\pi$
$317$	28.8073	+	8.88587i	1.61798	+	0.499080i	0.652112	+	0.758122i	$0.273883\pi$
$318$		0			0
$319$	3.09572	−	7.88776i	0.173327	−	0.441630i
$320$	−18.9082	−	5.83242i	−1.05700	−	0.326042i
$321$		0			0
$322$	−0.900769	−	0.0355501i	−0.0501979	−	0.00198113i
$323$	−2.39913	+	10.5113i	−0.133491	+	0.584864i
$324$		0			0
$325$	2.38494	+	4.13084i	0.132293	+	0.229138i
$326$	−0.891067	+	0.274858i	−0.0493516	+	0.0152230i
$327$		0			0
$328$	0.378521	+	0.474650i	0.0209003	+	0.0262082i
$329$	−13.2750	+	3.52792i	−0.731872	+	0.194500i
$330$		0			0
$331$	−16.8423	−	15.6274i	−0.925736	−	0.858957i	0.0645629	−	0.997914i	$-0.479435\pi$
$331$	−16.8423	−	15.6274i	−0.925736	−	0.858957i	−0.990298	+	0.138957i	$0.955625\pi$
$332$	−24.6074	−	3.70897i	−1.35051	−	0.203556i
$333$		0			0
$334$	−1.99310	+	0.300412i	−0.109058	+	0.0164378i
$335$	1.50166	+	0.723163i	0.0820447	+	0.0395106i
$336$		0			0
$337$	−16.7856	+	8.08351i	−0.914369	+	0.440337i	−0.831057	−	0.556187i	$-0.812264\pi$
$337$	−16.7856	+	8.08351i	−0.914369	+	0.440337i	−0.0833113	+	0.996524i	$0.526550\pi$
$338$	0.169316	−	0.115438i	0.00920960	−	0.00627900i
$339$		0			0
$340$	1.24451	+	16.6068i	0.0674931	+	0.900633i
$341$	−14.2663	−	36.3498i	−0.772561	−	1.96845i
$342$		0			0
$343$	6.22404	−	17.4431i	0.336066	−	0.941838i
$344$	0.785932			0.0423746
$345$		0			0
$346$	−0.0637955	−	0.851292i	−0.00342967	−	0.0457657i
$347$	−21.3146	+	19.7770i	−1.14423	+	1.06169i	−0.146861	+	0.989157i	$0.546917\pi$
$347$	−21.3146	+	19.7770i	−1.14423	+	1.06169i	−0.997366	+	0.0725302i	$0.976893\pi$
$348$		0			0
$349$	−14.8838	+	7.16767i	−0.796713	+	0.383677i	−0.787526	−	0.616281i	$-0.788639\pi$
$349$	−14.8838	+	7.16767i	−0.796713	+	0.383677i	−0.00918667	+	0.999958i	$0.502924\pi$
$350$	0.0409314	−	0.356715i	0.00218788	−	0.0190672i
$351$		0			0
$352$	−6.23577	+	0.939891i	−0.332368	+	0.0500964i
$353$	−12.5671	−	8.56809i	−0.668878	−	0.456033i	0.180671	−	0.983544i	$-0.442173\pi$
$353$	−12.5671	−	8.56809i	−0.668878	−	0.456033i	−0.849549	+	0.527510i	$0.823126\pi$
$354$		0			0
$355$	−1.95176	−	1.81096i	−0.103588	−	0.0961160i
$356$	−21.6646	+	27.1666i	−1.14822	+	1.43983i
$357$		0			0
$358$	−0.281675	−	0.353209i	−0.0148870	−	0.0186677i
$359$	0.847196	−	11.3050i	0.0447133	−	0.596657i	−0.929177	−	0.369636i	$-0.879482\pi$
$359$	0.847196	−	11.3050i	0.0447133	−	0.596657i	0.973890	−	0.227021i	$-0.0728986\pi$
$360$		0			0
$361$	4.13962	+	7.17003i	0.217875	+	0.377370i
$362$	−0.467290	+	0.809369i	−0.0245602	+	0.0425395i
$363$		0			0
$364$	−17.3075	−	0.683066i	−0.907161	−	0.0358024i
$365$	3.07595	+	13.4766i	0.161003	+	0.705399i
$366$		0			0
$367$	−4.25564	+	10.8432i	−0.222143	+	0.566010i	−0.997882	−	0.0650428i	$-0.979282\pi$
$367$	−4.25564	+	10.8432i	−0.222143	+	0.566010i	0.775740	+	0.631053i	$0.217377\pi$
$368$	−5.25325	+	13.3851i	−0.273845	+	0.697745i
$369$		0			0
$370$	−0.186545	−	0.817308i	−0.00969802	−	0.0424898i
$371$	5.55399	+	7.55770i	0.288349	+	0.392376i
$372$		0			0
$373$	5.43910	−	9.42080i	0.281626	−	0.487791i	−0.690159	−	0.723657i	$-0.742460\pi$
$373$	5.43910	−	9.42080i	0.281626	−	0.487791i	0.971785	+	0.235867i	$0.0757929\pi$
$374$	0.870293	+	1.50739i	0.0450018	+	0.0779454i
$375$		0			0
$376$	0.144847	−	1.93285i	0.00746993	−	0.0996793i
$377$	3.07375	+	3.85436i	0.158306	+	0.198510i
$378$		0			0
$379$	12.5156	−	15.6941i	0.642883	−	0.806150i	−0.348477	−	0.937317i	$-0.613301\pi$
$379$	12.5156	−	15.6941i	0.642883	−	0.806150i	0.991360	+	0.131167i	$0.0418725\pi$
$380$	−12.1389	−	11.2633i	−0.622714	−	0.577794i
$381$		0			0
$382$	−0.106999	−	0.0729508i	−0.00547456	−	0.00373249i
$383$	6.30041	−	0.949634i	0.321936	−	0.0485240i	0.0139137	−	0.999903i	$-0.495571\pi$
$383$	6.30041	−	0.949634i	0.321936	−	0.0485240i	0.308022	+	0.951379i	$0.400333\pi$
$384$		0			0
$385$	12.4684	+	35.8679i	0.635449	+	1.82800i
$386$	−1.82804	+	0.880336i	−0.0930446	+	0.0448079i
$387$		0			0
$388$	−24.0302	+	22.2967i	−1.21995	+	1.13194i
$389$	−0.356516	−	4.75738i	−0.0180761	−	0.241209i	−0.998922	−	0.0464228i	$-0.985218\pi$
$389$	−0.356516	−	4.75738i	−0.0180761	−	0.241209i	0.980846	−	0.194786i	$-0.0624012\pi$
$390$		0			0
$391$	11.9942			0.606571
$392$	2.03657	+	1.63779i	0.102862	+	0.0827209i
$393$		0			0
$394$	0.392695	+	1.00057i	0.0197837	+	0.0504080i
$395$	1.67905	+	22.4054i	0.0844824	+	1.12734i
$396$		0			0
$397$	18.6667	−	12.7267i	0.936854	−	0.638736i	0.00438652	−	0.999990i	$-0.498604\pi$
$397$	18.6667	−	12.7267i	0.936854	−	0.638736i	0.932467	+	0.361254i	$0.117651\pi$
$398$	−0.0193113	+	0.00929981i	−0.000967986	+	0.000466158i
$399$		0			0
$400$	−5.16000	−	2.48493i	−0.258000	−	0.124246i
$401$	−38.6861	+	5.83099i	−1.93189	+	0.291185i	−0.997825	−	0.0659187i	$-0.979002\pi$
$401$	−38.6861	+	5.83099i	−1.93189	+	0.291185i	−0.934065	+	0.357104i	$0.883764\pi$
$402$		0			0
$403$	22.4652	+	3.38608i	1.11907	+	0.168673i
$404$	14.7644	+	13.6994i	0.734558	+	0.681570i
$405$		0			0
$406$	−0.0131172	−	0.370870i	−0.000650994	−	0.0184060i
$407$	12.4324	+	15.5897i	0.616251	+	0.772754i
$408$		0			0
$409$	24.8162	−	7.65480i	1.22708	−	0.378505i	0.387568	−	0.921841i	$-0.373315\pi$
$409$	24.8162	−	7.65480i	1.22708	−	0.378505i	0.839516	+	0.543336i	$0.182839\pi$
$410$	0.193165	+	0.334572i	0.00953974	+	0.0165233i
$411$		0			0
$412$	−3.71211	+	16.2638i	−0.182883	+	0.801262i
$413$	7.38144	−	8.54198i	0.363217	−	0.420323i
$414$		0			0
$415$	−30.3312	−	9.35593i	−1.48890	−	0.459265i
$416$	1.34043	−	3.41535i	0.0657197	−	0.167451i
$417$		0			0
$418$	−1.65387	−	0.510152i	−0.0808935	−	0.0249523i
$419$	−8.82320	−	38.6570i	−0.431041	−	1.88852i	−0.458134	−	0.888883i	$-0.651482\pi$
$419$	−8.82320	−	38.6570i	−0.431041	−	1.88852i	0.0270924	−	0.999633i	$-0.491375\pi$
$420$		0			0
$421$	4.12186	−	18.0591i	0.200887	−	0.880145i	−0.769511	−	0.638634i	$-0.779500\pi$
$421$	4.12186	−	18.0591i	0.200887	−	0.880145i	0.970398	−	0.241511i	$-0.0776430\pi$
$422$	0.628462	−	1.08853i	0.0305931	−	0.0529887i
$423$		0			0
$424$	−1.26469	+	0.390104i	−0.0614186	+	0.0189451i
$425$	−0.357006	+	4.76392i	−0.0173173	+	0.231084i
$426$		0			0
$427$	−21.3324	+	18.2822i	−1.03235	+	0.884735i
$428$	12.8284	−	16.0863i	0.620084	−	0.777560i
$429$		0			0
$430$	0.494544	+	0.0745405i	0.0238490	+	0.00359466i
$431$	16.9587	+	11.5623i	0.816872	+	0.556934i	0.898115	−	0.439760i	$-0.144937\pi$
$431$	16.9587	+	11.5623i	0.816872	+	0.556934i	−0.0812429	+	0.996694i	$0.525889\pi$
$432$		0			0
$433$	−11.0650	−	5.32862i	−0.531750	−	0.256077i	0.148687	−	0.988884i	$-0.452495\pi$
$433$	−11.0650	−	5.32862i	−0.531750	−	0.256077i	−0.680436	+	0.732807i	$0.738210\pi$
$434$	−1.20680	−	1.21175i	−0.0579284	−	0.0581659i
$435$		0			0
$436$	14.0949	−	9.60977i	0.675025	−	0.460225i
$437$	−8.74273	+	8.11206i	−0.418221	+	0.388053i
$438$		0			0
$439$	−9.32379	−	23.7566i	−0.445000	−	1.13384i	−0.960827	−	0.277149i	$-0.910610\pi$
$439$	−9.32379	−	23.7566i	−0.445000	−	1.13384i	0.515826	−	0.856693i	$-0.327485\pi$
$440$	−5.35847			−0.255455
$441$		0			0
$442$	−1.01268			−0.0481682
$443$	−15.0627	−	38.3791i	−0.715651	−	1.82345i	−0.545668	−	0.838001i	$-0.683724\pi$
$443$	−15.0627	−	38.3791i	−0.715651	−	1.82345i	−0.169982	−	0.985447i	$-0.554371\pi$
$444$		0			0
$445$	−32.4891	+	30.1455i	−1.54013	+	1.42903i
$446$	0.161142	−	0.109865i	0.00763029	−	0.00520224i
$447$		0			0
$448$	17.4754	−	10.9307i	0.825637	−	0.516429i
$449$	−8.86197	−	4.26770i	−0.418222	−	0.201405i	0.212925	−	0.977069i	$-0.431701\pi$
$449$	−8.86197	−	4.26770i	−0.418222	−	0.201405i	−0.631147	+	0.775663i	$0.717415\pi$
$450$		0			0
$451$	−7.59235	−	5.17638i	−0.357510	−	0.243746i
$452$	−7.15759	−	1.07883i	−0.336665	−	0.0507440i
$453$		0			0
$454$	0.125618	−	0.157520i	0.00589555	−	0.00739279i
$455$	−21.6994	−	4.15175i	−1.01728	−	0.194637i
$456$		0			0
$457$	−1.17255	+	15.6466i	−0.0548497	+	0.731919i	0.900201	+	0.435475i	$0.143420\pi$
$457$	−1.17255	+	15.6466i	−0.0548497	+	0.731919i	−0.955050	+	0.296443i	$0.904199\pi$
$458$	0.373353	−	0.115164i	0.0174456	−	0.00538127i
$459$		0			0
$460$	−9.21090	+	15.9537i	−0.429460	+	0.743847i
$461$	−6.63324	+	29.0621i	−0.308941	+	1.35356i	0.547280	+	0.836949i	$0.315663\pi$
$461$	−6.63324	+	29.0621i	−0.308941	+	1.35356i	−0.856221	+	0.516609i	$0.827194\pi$
$462$		0			0
$463$	4.24774	+	18.6106i	0.197409	+	0.864907i	0.972471	+	0.233022i	$0.0748614\pi$
$463$	4.24774	+	18.6106i	0.197409	+	0.864907i	−0.775062	+	0.631885i	$0.782281\pi$
$464$	−5.65634	−	1.74475i	−0.262589	−	0.0809980i
$465$		0			0
$466$	0.0858126	−	0.218647i	0.00397519	−	0.0101286i
$467$	9.66302	+	2.98065i	0.447151	+	0.137928i	0.510149	−	0.860086i	$-0.329590\pi$
$467$	9.66302	+	2.98065i	0.447151	+	0.137928i	−0.0629983	+	0.998014i	$0.520066\pi$
$468$		0			0
$469$	−1.59277	+	0.691044i	−0.0735474	+	0.0319094i
$470$	0.274463	−	1.20250i	0.0126600	−	0.0554673i
$471$		0			0
$472$	0.796534	+	1.37964i	0.0366635	+	0.0635030i
$473$	−11.3673	+	3.50636i	−0.522671	+	0.161223i
$474$		0			0
$475$	−2.96177	−	3.71395i	−0.135896	−	0.170408i
$476$	−13.9369	−	10.3300i	−0.638798	−	0.473476i
$477$		0			0
$478$	0.261107	+	0.242272i	0.0119428	+	0.0110813i
$479$	4.58513	+	0.691097i	0.209500	+	0.0315770i	0.252954	−	0.967478i	$-0.418598\pi$
$479$	4.58513	+	0.691097i	0.209500	+	0.0315770i	−0.0434537	+	0.999055i	$0.513836\pi$
$480$		0			0
$481$	−11.4716	+	1.72906i	−0.523059	+	0.0788385i
$482$	0.473925	+	0.228230i	0.0215867	+	0.0103956i
$483$		0			0
$484$	37.5555	−	18.0858i	1.70707	−	0.822081i
$485$	−34.5469	+	23.5537i	−1.56869	+	1.06952i
$486$		0			0
$487$	−1.68298	−	22.4579i	−0.0762633	−	1.01766i	−0.895748	−	0.444562i	$-0.853359\pi$
$487$	−1.68298	−	22.4579i	−0.0762633	−	1.01766i	0.819485	−	0.573101i	$-0.194260\pi$
$488$	−1.44839	−	3.69043i	−0.0655653	−	0.167058i
$489$		0			0
$490$	1.12617	+	1.22373i	0.0508752	+	0.0552824i
$491$	−0.710899			−0.0320824			−0.0160412	−	0.999871i	$-0.505106\pi$
$491$	−0.710899			−0.0320824			−0.0160412	+	0.999871i	$0.505106\pi$
$492$		0			0
$493$	0.368984	+	4.92375i	0.0166182	+	0.221754i
$494$	0.738157	−	0.684909i	0.0332112	−	0.0308155i
$495$		0			0
$496$	−24.5771	+	11.8357i	−1.10354	+	0.531438i
$497$	2.75672	−	0.304897i	0.123656	−	0.0136765i
$498$		0			0
$499$	18.0977	−	2.72779i	0.810163	−	0.122112i	0.269119	−	0.963107i	$-0.413267\pi$
$499$	18.0977	−	2.72779i	0.810163	−	0.122112i	0.541044	+	0.840994i	$0.318029\pi$
$500$	14.8309	+	10.1115i	0.663259	+	0.452202i
$501$		0			0
$502$	0.388109	+	0.360112i	0.0173221	+	0.0160726i
$503$	8.49686	−	10.6547i	0.378856	−	0.475071i	−0.555446	−	0.831553i	$-0.687452\pi$
$503$	8.49686	−	10.6547i	0.378856	−	0.475071i	0.934302	+	0.356482i	$0.116024\pi$
$504$		0			0
$505$	16.0174	+	20.0852i	0.712766	+	0.893781i
$506$	−0.143886	+	1.92003i	−0.00639653	+	0.0853558i
$507$		0			0
$508$	−15.8238	−	27.4076i	−0.702067	−	1.21601i
$509$	17.2272	−	29.8385i	0.763584	−	1.32257i	−0.177408	−	0.984137i	$-0.556771\pi$
$509$	17.2272	−	29.8385i	0.763584	−	1.32257i	0.940992	−	0.338429i	$-0.109896\pi$
$510$		0			0
$511$	−12.7171	−	6.75452i	−0.562572	−	0.298802i
$512$	1.63618	+	7.16859i	0.0723097	+	0.316810i
$513$		0			0
$514$	0.859547	−	2.19009i	0.0379130	−	0.0966008i
$515$	−7.77374	+	19.8072i	−0.342552	+	0.872808i
$516$		0			0
$517$	6.52824	+	28.6021i	0.287112	+	1.25792i
$518$	0.771247	+	0.409637i	0.0338866	+	0.0179984i
$519$		0			0
$520$	1.55879	−	2.69990i	0.0683573	−	0.118398i
$521$	10.4680	+	18.1311i	0.458611	+	0.794337i	0.998888	−	0.0471503i	$-0.0150140\pi$
$521$	10.4680	+	18.1311i	0.458611	+	0.794337i	−0.540277	+	0.841487i	$0.681681\pi$
$522$		0			0
$523$	0.281796	−	3.76030i	0.0123221	−	0.164426i	−0.987648	−	0.156689i	$-0.949918\pi$
$523$	0.281796	−	3.76030i	0.0123221	−	0.164426i	0.999970	−	0.00773753i	$-0.00246296\pi$
$524$	5.69552	+	7.14196i	0.248810	+	0.311998i
$525$		0			0
$526$	−1.41020	+	1.76834i	−0.0614879	+	0.0771033i
$527$	16.6800	+	15.4767i	0.726590	+	0.674177i
$528$		0			0
$529$	−8.04113	−	5.48235i	−0.349614	−	0.238363i
$530$	−0.832797	+	0.125524i	−0.0361744	+	0.00545241i
$531$		0			0
$532$	17.1454	−	1.89630i	0.743347	−	0.0822152i
$533$	4.81678	−	2.31964i	0.208638	−	0.100475i
$534$		0			0
$535$	19.2379	−	17.8502i	0.831729	−	0.771732i
$536$	−0.0183089	−	0.244316i	−0.000790826	−	0.0105528i
$537$		0			0
$538$	−2.49616			−0.107617
$539$	−36.7628	−	14.6022i	−1.58349	−	0.628963i
$540$		0			0
$541$	1.49596	+	3.81165i	0.0643164	+	0.163875i	0.959419	−	0.281985i	$-0.0909929\pi$
$541$	1.49596	+	3.81165i	0.0643164	+	0.163875i	−0.895102	+	0.445861i	$0.852898\pi$
$542$	−0.142780	−	1.90527i	−0.00613295	−	0.0818385i
$543$		0			0
$544$	3.03614	−	2.07001i	0.130174	−	0.0887508i
$545$	19.6042	−	9.44088i	0.839751	−	0.404403i
$546$		0			0
$547$	25.5326	+	12.2958i	1.09169	+	0.525733i	0.891038	−	0.453929i	$-0.149978\pi$
$547$	25.5326	+	12.2958i	1.09169	+	0.525733i	0.200657	+	0.979662i	$0.435692\pi$
$548$	20.2924	−	3.05858i	0.866848	−	0.130656i
$549$		0			0
$550$	−0.758327	−	0.114299i	−0.0323352	−	0.00487374i
$551$	−3.59906	−	3.33944i	−0.153325	−	0.142265i
$552$		0			0
$553$	−18.8032	−	13.9369i	−0.799595	−	0.592659i
$554$	−0.953933	−	1.19619i	−0.0405287	−	0.0508214i
$555$		0			0
$556$	8.18788	−	2.52563i	0.347244	−	0.107110i
$557$	3.59938	+	6.23430i	0.152510	+	0.264156i	0.932150	−	0.362073i	$-0.117931\pi$
$557$	3.59938	+	6.23430i	0.152510	+	0.264156i	−0.779639	+	0.626229i	$0.784598\pi$
$558$		0			0
$559$	1.54007	−	6.74751i	0.0651382	−	0.285389i
$560$	24.3352	−	10.5581i	1.02835	−	0.446162i
$561$		0			0
$562$	−1.11632	−	0.344338i	−0.0470890	−	0.0145250i
$563$	11.2742	−	28.7261i	0.475150	−	1.21066i	−0.469603	−	0.882878i	$-0.655603\pi$
$563$	11.2742	−	28.7261i	0.475150	−	1.21066i	0.944753	−	0.327784i	$-0.106302\pi$
$564$		0			0
$565$	−8.82246	−	2.72137i	−0.371164	−	0.114489i
$566$	0.0914214	+	0.400543i	0.00384273	+	0.0168361i
$567$		0			0
$568$	−0.0870896	+	0.381565i	−0.00365420	+	0.0160101i
$569$	−10.9750	+	19.0093i	−0.460096	+	0.796909i	−0.998965	−	0.0454799i	$-0.985518\pi$
$569$	−10.9750	+	19.0093i	−0.460096	+	0.796909i	0.538869	+	0.842389i	$0.318852\pi$
$570$		0			0
$571$	−27.7739	+	8.56711i	−1.16230	+	0.358523i	−0.815129	−	0.579279i	$-0.803334\pi$
$571$	−27.7739	+	8.56711i	−1.16230	+	0.358523i	−0.347172	+	0.937801i	$0.612858\pi$
$572$	−2.76466	+	36.8918i	−0.115596	+	1.54252i
$573$		0			0
$574$	−0.395270	−	0.0756270i	−0.0164982	−	0.00315661i
$575$	−3.29487	+	4.13164i	−0.137406	+	0.172301i
$576$		0			0
$577$	7.33488	+	1.10556i	0.305355	+	0.0460249i	0.299933	−	0.953960i	$-0.403036\pi$
$577$	7.33488	+	1.10556i	0.305355	+	0.0460249i	0.00542264	+	0.999985i	$0.498274\pi$
$578$	0.475875	+	0.324446i	0.0197938	+	0.0134952i
$579$		0			0
$580$	−6.83257	−	3.29039i	−0.283707	−	0.136626i
$581$	28.0328	−	17.5343i	1.16300	−	0.727445i
$582$		0			0
$583$	16.5514	−	11.2846i	0.685489	−	0.467359i
$584$	1.48953	−	1.38208i	0.0616371	−	0.0571908i
$585$		0			0
$586$	0.260936	+	0.664854i	0.0107792	+	0.0274649i
$587$	−28.4715			−1.17515			−0.587573	−	0.809171i	$-0.699916\pi$
$587$	−28.4715			−1.17515			−0.587573	+	0.809171i	$0.699916\pi$
$588$		0			0
$589$	−22.6257			−0.932277
$590$	0.370366	+	0.943677i	0.0152477	+	0.0388506i
$591$		0			0
$592$	10.2110	−	9.47443i	0.419670	−	0.389397i
$593$	25.4898	−	17.3786i	1.04674	−	0.713654i	0.0874752	−	0.996167i	$-0.472120\pi$
$593$	25.4898	−	17.3786i	1.04674	−	0.713654i	0.959264	+	0.282512i	$0.0911678\pi$
$594$		0			0
$595$	−15.6143	−	15.6783i	−0.640122	−	0.642747i
$596$	35.1304	+	16.9179i	1.43900	+	0.692985i
$597$		0			0
$598$	−0.925562	−	0.631038i	−0.0378491	−	0.0258051i
$599$	27.4618	+	4.13920i	1.12206	+	0.169123i	0.683761	−	0.729706i	$-0.260343\pi$
$599$	27.4618	+	4.13920i	1.12206	+	0.169123i	0.438298	+	0.898830i	$0.355581\pi$
$600$		0			0
$601$	11.9118	−	14.9370i	0.485893	−	0.609291i	−0.477089	−	0.878855i	$-0.658308\pi$
$601$	11.9118	−	14.9370i	0.485893	−	0.609291i	0.962983	+	0.269564i	$0.0868795\pi$
$602$	−0.395586	+	0.339023i	−0.0161229	+	0.0138175i
$603$		0			0
$604$	−0.915268	+	12.2134i	−0.0372417	+	0.496956i
$605$	50.8053	−	15.6714i	2.06553	−	0.637131i
$606$		0			0
$607$	−9.93520	+	17.2083i	−0.403257	+	0.698462i	−0.994117	−	0.108312i	$-0.965455\pi$
$607$	−9.93520	+	17.2083i	−0.403257	+	0.698462i	0.590860	+	0.806774i	$0.298789\pi$
$608$	−0.813074	+	3.56231i	−0.0329745	+	0.144471i
$609$		0			0
$610$	−0.561377	−	2.45955i	−0.0227295	−	0.0995844i
$611$	−16.3104	−	5.03110i	−0.659849	−	0.203536i
$612$		0			0
$613$	−15.6148	+	39.7858i	−0.630675	+	1.60693i	0.154733	+	0.987956i	$0.450548\pi$
$613$	−15.6148	+	39.7858i	−0.630675	+	1.60693i	−0.785408	+	0.618978i	$0.787547\pi$
$614$	−0.218266	−	0.0673261i	−0.00880850	−	0.00271706i
$615$		0			0
$616$	3.64966	−	4.22347i	0.147049	−	0.170169i
$617$	−4.49691	+	19.7023i	−0.181039	+	0.793183i	0.800098	+	0.599869i	$0.204781\pi$
$617$	−4.49691	+	19.7023i	−0.181039	+	0.793183i	−0.981137	+	0.193314i	$0.938076\pi$
$618$		0			0
$619$	7.86487	+	13.6224i	0.316116	+	0.547529i	0.979674	−	0.200596i	$-0.0642878\pi$
$619$	7.86487	+	13.6224i	0.316116	+	0.547529i	−0.663558	+	0.748125i	$0.730954\pi$
$620$	−33.3954	+	10.3011i	−1.34119	+	0.413702i
$621$		0			0
$622$	−0.295468	−	0.370505i	−0.0118472	−	0.0148559i
$623$	−1.63189	−	46.1396i	−0.0653805	−	1.84854i
$624$		0			0
$625$	22.1009	+	20.5067i	0.884037	+	0.820266i
$626$	−1.67402	−	0.252318i	−0.0669074	−	0.0100847i
$627$		0			0
$628$	11.1359	−	1.67847i	0.444371	−	0.0669781i
$629$	−10.4685	−	5.04135i	−0.417406	−	0.201012i
$630$		0			0
$631$	−11.6397	+	5.60540i	−0.463370	+	0.223147i	−0.650978	−	0.759097i	$-0.725641\pi$
$631$	−11.6397	+	5.60540i	−0.463370	+	0.223147i	0.187608	+	0.982244i	$0.439927\pi$
$632$	2.72885	−	1.86050i	0.108548	−	0.0740066i
$633$		0			0
$634$	−0.210735	−	2.81207i	−0.00836936	−	0.111681i
$635$	−14.7475	−	37.5761i	−0.585239	−	1.49116i
$636$		0			0
$637$	18.0518	−	14.2754i	0.715238	−	0.565611i
$638$	−0.792622			−0.0313802
$639$		0			0
$640$	0.561942	+	7.49860i	0.0222127	+	0.296408i
$641$	−25.6693	+	23.8177i	−1.01388	+	0.940741i	−0.998250	−	0.0591371i	$-0.981165\pi$
$641$	−25.6693	+	23.8177i	−1.01388	+	0.940741i	−0.0156275	+	0.999878i	$0.504975\pi$
$642$		0			0
$643$	23.8937	−	11.5066i	0.942274	−	0.453775i	0.101303	−	0.994856i	$-0.467699\pi$
$643$	23.8937	−	11.5066i	0.942274	−	0.453775i	0.840971	+	0.541081i	$0.181985\pi$
$644$	−6.30097	−	18.1260i	−0.248293	−	0.714265i
$645$		0			0
$646$	0.997260	−	0.150313i	0.0392367	−	0.00591397i
$647$	29.1080	+	19.8455i	1.14435	+	0.780206i	0.978561	−	0.205955i	$-0.0660301\pi$
$647$	29.1080	+	19.8455i	1.14435	+	0.780206i	0.165790	+	0.986161i	$0.446983\pi$
$648$		0			0
$649$	−17.6758	−	16.4008i	−0.693836	−	0.643786i
$650$	0.278189	−	0.348838i	0.0109115	−	0.0136825i
$651$		0			0
$652$	−12.3765	−	15.5197i	−0.484702	−	0.607797i
$653$	1.12655	−	15.0328i	0.0440854	−	0.588278i	−0.930794	−	0.365544i	$-0.880883\pi$
$653$	1.12655	−	15.0328i	0.0440854	−	0.588278i	0.974879	−	0.222734i	$-0.0714981\pi$
$654$		0			0
$655$	5.82580	+	10.0906i	0.227633	+	0.394272i
$656$	−3.20959	+	5.55917i	−0.125313	+	0.217049i
$657$		0			0
$658$	0.760858	+	1.03535i	0.0296613	+	0.0403622i
$659$	1.07622	+	4.71525i	0.0419238	+	0.183680i	0.991554	−	0.129691i	$-0.0413987\pi$
$659$	1.07622	+	4.71525i	0.0419238	+	0.183680i	−0.949631	+	0.313371i	$0.898542\pi$
$660$		0			0
$661$	4.13895	−	10.5459i	0.160986	−	0.410186i	−0.827506	−	0.561457i	$-0.810241\pi$
$661$	4.13895	−	10.5459i	0.160986	−	0.410186i	0.988492	+	0.151270i	$0.0483364\pi$
$662$	−0.785177	+	2.00060i	−0.0305168	+	0.0777555i
$663$		0			0
$664$	1.03825	+	4.54886i	0.0402918	+	0.176530i
$665$	21.9852	+	0.867678i	0.852551	+	0.0336471i
$666$		0			0
$667$	−2.73093	+	4.73011i	−0.105742	+	0.183151i
$668$	−21.4536	−	37.1588i	−0.830066	−	1.43772i
$669$		0			0
$670$	0.0116510	−	0.155471i	0.000450116	−	0.00600638i
$671$	37.4132	+	46.9147i	1.44432	+	1.81112i
$672$		0			0
$673$	8.84130	−	11.0866i	0.340807	−	0.427359i	−0.581661	−	0.813431i	$-0.697597\pi$
$673$	8.84130	−	11.0866i	0.340807	−	0.427359i	0.922468	+	0.386072i	$0.126169\pi$
$674$	1.27751	+	1.18536i	0.0492078	+	0.0456582i
$675$		0			0
$676$	3.60431	+	2.45738i	0.138627	+	0.0945145i
$677$	−34.2479	+	5.16205i	−1.31626	+	0.198394i	−0.769364	−	0.638810i	$-0.779427\pi$
$677$	−34.2479	+	5.16205i	−1.31626	+	0.198394i	−0.546891	+	0.837204i	$0.684189\pi$
$678$		0			0
$679$	4.96524	−	43.2718i	0.190548	−	1.66062i
$680$	2.81319	−	1.35476i	0.107881	−	0.0519527i
$681$		0			0
$682$	−2.67762	+	2.48447i	−0.102531	+	0.0951353i
$683$	−2.45242	−	32.7253i	−0.0938394	−	1.25220i	−0.823073	−	0.567935i	$-0.807742\pi$
$683$	−2.45242	−	32.7253i	−0.0938394	−	1.25220i	0.729234	−	0.684264i	$-0.239877\pi$
$684$		0			0
$685$	26.1753			1.00011
$686$	−1.73156	+	0.0541494i	−0.0661113	+	0.00206743i
$687$		0			0
$688$	3.03600	+	7.73561i	0.115746	+	0.294917i
$689$	0.870965	+	11.6222i	0.0331811	+	0.442771i
$690$		0			0
$691$	42.5221	−	28.9911i	1.61762	−	1.10287i	0.693713	−	0.720251i	$-0.255973\pi$
$691$	42.5221	−	28.9911i	1.61762	−	1.10287i	0.923905	−	0.382622i	$-0.124979\pi$
$692$	16.3730	−	7.88480i	0.622406	−	0.299735i
$693$		0			0
$694$	2.45050	+	1.18010i	0.0930197	+	0.0447959i
$695$	10.8071	−	1.62892i	0.409938	−	0.0617883i
$696$		0			0
$697$	5.29470	+	0.798047i	0.200551	+	0.0302282i
$698$	1.13277	+	1.05106i	0.0428760	+	0.0397832i
$699$		0			0
$700$	7.38695	−	1.96314i	0.279201	−	0.0741996i
$701$	−7.22918	−	9.06511i	−0.273042	−	0.342384i	0.626338	−	0.779552i	$-0.284553\pi$
$701$	−7.22918	−	9.06511i	−0.273042	−	0.342384i	−0.899380	+	0.437168i	$0.855982\pi$
$702$		0			0
$703$	11.0403	−	3.40547i	0.416392	−	0.128440i
$704$	−22.0126	−	38.1270i	−0.829633	−	1.43697i
$705$		0			0
$706$	−0.316594	+	1.38709i	−0.0119152	+	0.0522038i
$707$	−26.7404	−	1.05535i	−1.00568	−	0.0396904i
$708$		0			0
$709$	−20.3719	−	6.28389i	−0.765081	−	0.235996i	−0.112435	−	0.993659i	$-0.535865\pi$
$709$	−20.3719	−	6.28389i	−0.765081	−	0.235996i	−0.652646	+	0.757663i	$0.726341\pi$
$710$	−0.0909897	+	0.231838i	−0.00341478	+	0.00870072i
$711$		0			0
$712$	6.22547	+	1.92030i	0.233309	+	0.0719664i
$713$	5.60092	+	24.5393i	0.209756	+	0.919002i
$714$		0			0
$715$	−10.5002	+	46.0044i	−0.392685	+	1.72047i
$716$	4.80852	−	8.32860i	0.179703	−	0.311255i
$717$		0			0
$718$	−1.01334	+	0.312574i	−0.0378175	+	0.0116651i
$719$	1.26414	−	16.8688i	0.0471446	−	0.629101i	−0.922722	−	0.385465i	$-0.874041\pi$
$719$	1.26414	−	16.8688i	0.0471446	−	0.629101i	0.969867	−	0.243635i	$-0.0783401\pi$
$720$		0			0
$721$	−10.3170	−	19.6178i	−0.384226	−	0.730606i
$722$	0.482861	−	0.605489i	0.0179702	−	0.0225340i
$723$		0			0
$724$	−19.6726	−	2.96516i	−0.731125	−	0.110199i
$725$	−1.79745	−	1.22548i	−0.0667556	−	0.0455132i
$726$		0			0
$727$	−4.28205	−	2.06213i	−0.158812	−	0.0764800i	0.352789	−	0.935703i	$-0.385233\pi$
$727$	−4.28205	−	2.06213i	−0.158812	−	0.0764800i	−0.511602	+	0.859223i	$0.670948\pi$
$728$	1.06633	+	3.06752i	0.0395209	+	0.113690i
$729$		0			0
$730$	1.06836	−	0.728395i	0.0395417	−	0.0269591i
$731$	5.08134	−	4.71479i	0.187940	−	0.174383i
$732$		0			0
$733$	6.28193	+	16.0061i	0.232028	+	0.591198i	0.998707	−	0.0508324i	$-0.0161874\pi$
$733$	6.28193	+	16.0061i	0.232028	+	0.591198i	−0.766679	+	0.642031i	$0.778092\pi$
$734$	1.08961			0.0402181
$735$		0			0
$736$	4.06486			0.149833
$737$	1.35480	+	3.45198i	0.0499049	+	0.127155i
$738$		0			0
$739$	−2.39982	+	2.22671i	−0.0882788	+	0.0819107i	−0.723078	−	0.690766i	$-0.757273\pi$
$739$	−2.39982	+	2.22671i	−0.0882788	+	0.0819107i	0.634799	+	0.772677i	$0.281083\pi$
$740$	14.7449	−	10.0529i	0.542033	−	0.369552i
$741$		0			0
$742$	0.468283	−	0.741894i	0.0171912	−	0.0272358i
$743$	17.5147	+	8.43461i	0.642550	+	0.309436i	0.726636	−	0.687023i	$-0.241083\pi$
$743$	17.5147	+	8.43461i	0.642550	+	0.309436i	−0.0840857	+	0.996459i	$0.526797\pi$
$744$		0			0
$745$	41.0923	+	28.0163i	1.50551	+	1.02644i
$746$	−1.00620	−	0.151660i	−0.0368394	−	0.00555265i
$747$		0			0
$748$	−23.1019	+	28.9689i	−0.844689	+	1.05921i
$749$	0.966302	+	27.3209i	0.0353079	+	0.998283i
$750$		0			0
$751$	−1.71255	+	22.8523i	−0.0624917	+	0.833893i	0.874608	+	0.484831i	$0.161119\pi$
$751$	−1.71255	+	22.8523i	−0.0624917	+	0.833893i	−0.937100	+	0.349062i	$0.886500\pi$
$752$	19.5838	−	6.04081i	0.714149	−	0.220286i
$753$		0			0
$754$	0.230575	−	0.399367i	0.00839704	−	0.0145441i
$755$	−3.47620	+	15.2302i	−0.126512	+	0.554285i
$756$		0			0
$757$	−9.51048	−	41.6681i	−0.345664	−	1.51445i	−0.786910	−	0.617068i	$-0.788320\pi$
$757$	−9.51048	−	41.6681i	−0.345664	−	1.51445i	0.441245	−	0.897386i	$-0.354537\pi$
$758$	−1.79428	−	0.553461i	−0.0651710	−	0.0201026i
$759$		0			0
$760$	−1.13431	+	2.89016i	−0.0411456	+	0.104837i
$761$	−0.730491	−	0.225327i	−0.0264803	−	0.00816809i	0.281487	−	0.959565i	$-0.409172\pi$
$761$	−0.730491	−	0.225327i	−0.0264803	−	0.00816809i	−0.307967	+	0.951397i	$0.599649\pi$
$762$		0			0
$763$	−5.91126	+	21.8819i	−0.214002	+	0.792179i
$764$	0.613435	−	2.68764i	0.0221933	−	0.0972353i
$765$		0			0
$766$	−0.298002	−	0.516155i	−0.0107673	−	0.0186494i
$767$	13.4055	−	4.13506i	0.484046	−	0.149308i
$768$		0			0
$769$	−6.96075	−	8.72851i	−0.251011	−	0.314758i	0.640322	−	0.768106i	$-0.278801\pi$
$769$	−6.96075	−	8.72851i	−0.251011	−	0.314758i	−0.891333	+	0.453348i	$0.850229\pi$
$770$	2.69710	−	2.31145i	0.0971967	−	0.0832990i
$771$		0			0
$772$	−31.6616	−	29.3777i	−1.13953	−	1.05733i
$773$	25.6042	+	3.85922i	0.920921	+	0.138806i	0.592357	−	0.805675i	$-0.298197\pi$
$773$	25.6042	+	3.85922i	0.920921	+	0.138806i	0.328564	+	0.944482i	$0.393435\pi$
$774$		0			0
$775$	−9.91337	+	1.49420i	−0.356099	+	0.0536732i
$776$	5.53755	+	2.66674i	0.198786	+	0.0957305i
$777$		0			0
$778$	−0.402065	+	0.193624i	−0.0144147	+	0.00694177i
$779$	−4.39913	+	2.99928i	−0.157615	+	0.107460i
$780$		0			0
$781$	−0.442691	−	5.90731i	−0.0158407	−	0.211380i
$782$	−0.409894	−	1.04439i	−0.0146578	−	0.0373474i
$783$		0			0
$784$	−8.25296	+	26.3718i	−0.294749	+	0.941851i
$785$	14.3643			0.512684
$786$		0			0
$787$	0.591445	+	7.89229i	0.0210827	+	0.281330i	0.997774	+	0.0666820i	$0.0212413\pi$
$787$	0.591445	+	7.89229i	0.0210827	+	0.281330i	−0.976692	+	0.214648i	$0.931140\pi$
$788$	−16.7731	+	15.5632i	−0.597518	+	0.554416i
$789$		0			0
$790$	1.89357	−	0.911896i	0.0673703	−	0.0324438i
$791$	8.15393	−	5.10021i	0.289920	−	0.181343i
$792$		0			0
$793$	−34.5218	+	5.20333i	−1.22591	+	0.184776i
$794$	−1.74610	−	1.19047i	−0.0619669	−	0.0422483i
$795$		0			0
$796$	−0.334471	−	0.310344i	−0.0118550	−	0.0109998i
$797$	−13.6199	+	17.0788i	−0.482440	+	0.604961i	−0.962168	−	0.272456i	$-0.912164\pi$
$797$	−13.6199	+	17.0788i	−0.482440	+	0.604961i	0.479728	+	0.877417i	$0.340735\pi$
$798$		0			0
$799$	−10.6587	−	13.3655i	−0.377077	−	0.472839i
$800$	−0.120991	+	1.61451i	−0.00427766	+	0.0570814i
$801$		0			0
$802$	1.82981	+	3.16932i	0.0646127	+	0.111913i
$803$	−15.3778	+	26.6351i	−0.542670	+	0.939932i
$804$		0			0
$805$	−4.50131	−	24.0594i	−0.158650	−	0.847982i
$806$	−0.472891	−	2.07187i	−0.0166569	−	0.0729786i
$807$		0			0
$808$	1.37964	−	3.51527i	0.0485357	−	0.123667i
$809$	0.464021	−	1.18231i	0.0163141	−	0.0415677i	−0.922485	−	0.386034i	$-0.873845\pi$
$809$	0.464021	−	1.18231i	0.0163141	−	0.0415677i	0.938799	+	0.344466i	$0.111940\pi$
$810$		0			0
$811$	1.33915	+	5.86720i	0.0470239	+	0.206025i	0.992982	−	0.118263i	$-0.0377325\pi$
$811$	1.33915	+	5.86720i	0.0470239	+	0.206025i	−0.945958	+	0.324288i	$0.894875\pi$
$812$	7.24711	−	3.14425i	0.254324	−	0.110341i
$813$		0			0
$814$	0.932606	−	1.61532i	0.0326878	−	0.0566170i
$815$	−12.6596	−	21.9271i	−0.443447	−	0.768073i
$816$		0			0
$817$	−0.515088	+	6.87337i	−0.0180206	+	0.240469i
$818$	−1.51462	−	1.89928i	−0.0529575	−	0.0664066i
$819$		0			0
$820$	−5.12756	+	6.42976i	−0.179062	+	0.224537i
$821$	−14.3601	−	13.3242i	−0.501171	−	0.465019i	0.388612	−	0.921401i	$-0.372955\pi$
$821$	−14.3601	−	13.3242i	−0.501171	−	0.465019i	−0.889784	+	0.456382i	$0.849145\pi$
$822$		0			0
$823$	3.54830	+	2.41919i	0.123686	+	0.0843277i	0.623583	−	0.781757i	$-0.285676\pi$
$823$	3.54830	+	2.41919i	0.123686	+	0.0843277i	−0.499897	+	0.866085i	$0.666629\pi$
$824$	3.09285	−	0.466172i	0.107744	−	0.0162399i
$825$		0			0
$826$	−0.996049	−	0.350822i	−0.0346570	−	0.0122067i
$827$	12.8900	−	6.20750i	0.448230	−	0.215856i	−0.196131	−	0.980578i	$-0.562838\pi$
$827$	12.8900	−	6.20750i	0.448230	−	0.215856i	0.644361	+	0.764722i	$0.277124\pi$
$828$		0			0
$829$	−8.28997	+	7.69197i	−0.287922	+	0.267153i	−0.810889	−	0.585200i	$-0.801016\pi$
$829$	−8.28997	+	7.69197i	−0.287922	+	0.267153i	0.522966	+	0.852353i	$0.324825\pi$
$830$	0.221883	+	2.96082i	0.00770167	+	0.102772i
$831$		0			0
$832$	25.6140			0.888007
$833$	22.9923	−	1.62845i	0.796635	−	0.0564224i
$834$		0			0
$835$	−19.9945	−	50.9451i	−0.691938	−	1.76303i
$836$	−2.75332	−	36.7405i	−0.0952255	−	1.27070i
$837$		0			0
$838$	−3.06453	+	2.08936i	−0.105862	+	0.0721757i
$839$	−28.1468	+	13.5548i	−0.971735	+	0.467963i	−0.851255	−	0.524753i	$-0.824158\pi$
$839$	−28.1468	+	13.5548i	−0.971735	+	0.467963i	−0.120481	+	0.992716i	$0.538444\pi$
$840$		0			0
$841$	24.1023	+	11.6071i	0.831114	+	0.400244i
$842$	−1.71336	+	0.258247i	−0.0590461	+	0.00889977i
$843$		0			0
$844$	26.4578	+	3.98788i	0.910716	+	0.137268i
$845$	4.07880	+	3.78457i	0.140315	+	0.130193i
$846$		0			0
$847$	−22.2516	+	50.7178i	−0.764573	+	1.74268i
$848$	−8.72504	−	10.9408i	−0.299619	−	0.375710i
$849$		0			0
$850$	0.427019	−	0.131718i	0.0146466	−	0.00451788i
$851$	−6.42647	−	11.1310i	−0.220297	−	0.381565i
$852$		0			0
$853$	−3.13610	+	13.7401i	−0.107378	+	0.470453i	0.892436	+	0.451173i	$0.148994\pi$
$853$	−3.13610	+	13.7401i	−0.107378	+	0.470453i	−0.999814	+	0.0192797i	$0.993863\pi$
$854$	2.32094	+	1.23273i	0.0794210	+	0.0421833i
$855$		0			0
$856$	−3.68632	−	1.13708i	−0.125996	−	0.0388645i
$857$	−16.1839	+	41.2360i	−0.552832	+	1.40859i	0.332264	+	0.943186i	$0.392187\pi$
$857$	−16.1839	+	41.2360i	−0.552832	+	1.40859i	−0.885097	+	0.465407i	$0.845908\pi$
$858$		0			0
$859$	37.3909	+	11.5336i	1.27576	+	0.393520i	0.857348	−	0.514737i	$-0.172111\pi$
$859$	37.3909	+	11.5336i	1.27576	+	0.393520i	0.418412	+	0.908257i	$0.362587\pi$
$860$	2.36906	+	10.3795i	0.0807844	+	0.353939i
$861$		0			0
$862$	0.427229	−	1.87181i	0.0145515	−	0.0637542i
$863$	−14.1326	+	24.4784i	−0.481081	+	0.833256i	−0.999764	−	0.0217102i	$-0.993089\pi$
$863$	−14.1326	+	24.4784i	−0.481081	+	0.833256i	0.518684	+	0.854966i	$0.326422\pi$
$864$		0			0
$865$	22.1494	−	6.83219i	0.753103	−	0.232301i
$866$	−0.0858499	+	1.14559i	−0.00291730	+	0.0389287i
$867$		0			0
$868$	14.6264	−	33.3379i	0.496453	−	1.13156i
$869$	−31.1683	+	39.0838i	−1.05731	+	1.32583i
$870$		0			0
$871$	−2.13342	−	0.321561i	−0.0722881	−	0.0108957i
$872$	−2.64271	−	1.80177i	−0.0894934	−	0.0610156i
$873$		0			0
$874$	1.00514	+	0.484048i	0.0339992	+	0.0163732i
$875$	−23.7053	+	2.62184i	−0.801385	+	0.0886344i
$876$		0			0
$877$	−26.9157	+	18.3508i	−0.908878	+	0.619662i	−0.924901	−	0.380209i	$-0.875852\pi$
$877$	−26.9157	+	18.3508i	−0.908878	+	0.619662i	0.0160226	+	0.999872i	$0.494900\pi$
$878$	−1.74998	+	1.62374i	−0.0590588	+	0.0547986i
$879$		0			0
$880$	−20.6994	−	52.7412i	−0.697777	−	1.77791i
$881$	17.4328			0.587327			0.293664	−	0.955909i	$-0.405125\pi$
$881$	17.4328			0.587327			0.293664	+	0.955909i	$0.405125\pi$
$882$		0			0
$883$	9.99745			0.336441			0.168220	−	0.985749i	$-0.446198\pi$
$883$	9.99745			0.336441			0.168220	+	0.985749i	$0.446198\pi$
$884$	−7.87576	−	20.0671i	−0.264891	−	0.674930i
$885$		0			0
$886$	−2.82711	+	2.62317i	−0.0949785	+	0.0881272i
$887$	40.1044	−	27.3427i	1.34657	−	0.918079i	0.346772	−	0.937949i	$-0.387278\pi$
$887$	40.1044	−	27.3427i	1.34657	−	0.918079i	0.999803	+	0.0198706i	$0.00632542\pi$
$888$		0			0
$889$	39.6616	+	13.9693i	1.33021	+	0.468516i
$890$	3.73522	+	1.79879i	0.125205	+	0.0602955i
$891$		0			0
$892$	3.43029	+	2.33874i	0.114855	+	0.0783066i
$893$	16.8089	+	2.53353i	0.562487	+	0.0847812i
$894$		0			0
$895$	7.64807	−	9.59038i	0.255647	−	0.320571i
$896$	−6.29303	−	4.66439i	−0.210235	−	0.155826i
$897$		0			0
$898$	−0.0687573	+	0.917502i	−0.00229446	+	0.0306175i
$899$	−9.90135	+	3.05416i	−0.330229	+	0.101862i
$900$		0			0
$901$	−5.83644	+	10.1090i	−0.194440	+	0.336780i
$902$	−0.191269	+	0.838004i	−0.00636856	+	0.0279025i
$903$		0			0
$904$	0.301996	+	1.32313i	0.0100442	+	0.0440067i
$905$	−24.2485	−	7.47966i	−0.806046	−	0.248632i
$906$		0			0
$907$	14.4576	−	36.8373i	0.480055	−	1.22316i	−0.461752	−	0.887009i	$-0.652779\pi$
$907$	14.4576	−	36.8373i	0.480055	−	1.22316i	0.941808	−	0.336152i	$-0.109126\pi$
$908$	4.09836	+	1.26418i	0.136009	+	0.0419531i
$909$		0			0
$910$	0.380050	+	2.03136i	0.0125985	+	0.0673388i
$911$	−6.46720	+	28.3346i	−0.214268	+	0.938769i	0.747362	+	0.664417i	$0.231320\pi$
$911$	−6.46720	+	28.3346i	−0.214268	+	0.938769i	−0.961630	+	0.274351i	$0.911537\pi$
$912$		0			0
$913$	−35.3110	−	61.1605i	−1.16862	−	2.02412i
$914$	1.40250	−	0.432615i	0.0463907	−	0.0143096i
$915$		0			0
$916$	5.18571	+	6.50268i	0.171341	+	0.214854i
$917$	−11.9212	−	2.28089i	−0.393673	−	0.0753216i
$918$		0			0
$919$	21.2169	+	19.6864i	0.699882	+	0.649396i	0.947608	−	0.319434i	$-0.103493\pi$
$919$	21.2169	+	19.6864i	0.699882	+	0.649396i	−0.247726	+	0.968830i	$0.579683\pi$
$920$	3.41539	+	0.514787i	0.112602	+	0.0169720i
$921$		0			0
$922$	2.75727	−	0.415592i	0.0908060	−	0.0136868i
$923$	3.10521	+	1.49539i	0.102209	+	0.0492214i
$924$		0			0
$925$	4.61236	−	2.22119i	0.151653	−	0.0730324i
$926$	1.47535	−	1.00588i	0.0484831	−	0.0330552i
$927$		0			0
$928$	0.125050	+	1.66867i	0.00410496	+	0.0547769i
$929$	−10.2537	−	26.1260i	−0.336413	−	0.857167i	−0.994549	−	0.104268i	$-0.966750\pi$
$929$	−10.2537	−	26.1260i	−0.336413	−	0.857167i	0.658136	−	0.752899i	$-0.271345\pi$
$930$		0			0
$931$	−15.6580	+	16.7375i	−0.513172	+	0.548548i
$932$	5.00006			0.163782
$933$		0			0
$934$	−0.0706883	−	0.943270i	−0.00231299	−	0.0308647i
$935$	−34.6445	+	32.1454i	−1.13300	+	1.05127i
$936$		0			0
$937$	−25.3966	+	12.2303i	−0.829670	+	0.399548i	−0.799991	−	0.600011i	$-0.795163\pi$
$937$	−25.3966	+	12.2303i	−0.829670	+	0.399548i	−0.0296786	+	0.999559i	$0.509448\pi$
$938$	0.114605	+	0.115075i	0.00374198	+	0.00375732i
$939$		0			0
$940$	25.9632	−	3.91332i	0.846826	−	0.127638i
$941$	29.8515	+	20.3524i	0.973133	+	0.663471i	0.941848	−	0.336040i	$-0.109088\pi$
$941$	29.8515	+	20.3524i	0.973133	+	0.663471i	0.0312849	+	0.999511i	$0.490040\pi$
$942$		0			0
$943$	4.34193	+	4.02872i	0.141393	+	0.131193i
$944$	−10.5023	+	13.1694i	−0.341819	+	0.428628i
$945$		0			0
$946$	0.693789	+	0.869983i	0.0225570	+	0.0282856i
$947$	−2.48039	+	33.0986i	−0.0806020	+	1.07556i	0.799466	+	0.600711i	$0.205116\pi$
$947$	−2.48039	+	33.0986i	−0.0806020	+	1.07556i	−0.880068	+	0.474848i	$0.842503\pi$
$948$		0			0
$949$	−8.94684	−	15.4964i	−0.290427	−	0.503034i
$950$	−0.222175	+	0.384819i	−0.00720831	+	0.0124852i
$951$		0			0
$952$	−0.848263	+	3.14005i	−0.0274923	+	0.101769i
$953$	−10.0914	−	44.2133i	−0.326892	−	1.43221i	−0.825020	−	0.565104i	$-0.808836\pi$
$953$	−10.0914	−	44.2133i	−0.326892	−	1.43221i	0.498127	−	0.867104i	$-0.334021\pi$
$954$		0			0
$955$	1.28463	−	3.27318i	0.0415696	−	0.105918i
$956$	−2.77016	+	7.05826i	−0.0895934	+	0.228280i
$957$		0			0
$958$	−0.0965169	−	0.422868i	−0.00311832	−	0.0136622i
$959$	−17.8280	+	20.6310i	−0.575698	+	0.666211i
$960$		0			0
$961$	−8.37532	+	14.5065i	−0.270172	+	0.467951i
$962$	0.542593	+	0.939799i	0.0174939	+	0.0303003i
$963$		0			0
$964$	−0.836794	+	11.1662i	−0.0269513	+	0.359640i
$965$	−34.3486	−	43.0718i	−1.10572	−	1.38653i
$966$		0			0
$967$	−34.3201	+	43.0360i	−1.10366	+	1.38394i	−0.187914	+	0.982186i	$0.560173\pi$
$967$	−34.3201	+	43.0360i	−1.10366	+	1.38394i	−0.915745	+	0.401759i	$0.868399\pi$
$968$	−5.72908	−	5.31580i	−0.184139	−	0.170856i
$969$		0			0
$970$	3.23155	+	2.20324i	0.103759	+	0.0707417i
$971$	11.7728	−	1.77446i	0.377806	−	0.0569451i	0.0426058	−	0.999092i	$-0.486434\pi$
$971$	11.7728	−	1.77446i	0.377806	−	0.0569451i	0.335201	+	0.942147i	$0.391196\pi$
$972$		0			0
$973$	−6.07687	+	9.62750i	−0.194815	+	0.308643i
$974$	−1.89800	+	0.914031i	−0.0608160	+	0.0292874i
$975$		0			0
$976$	30.7284	−	28.5117i	0.983591	−	0.912639i
$977$	−2.96010	−	39.4998i	−0.0947019	−	1.26371i	−0.818827	−	0.574041i	$-0.805375\pi$
$977$	−2.96010	−	39.4998i	−0.0947019	−	1.26371i	0.724125	−	0.689669i	$-0.242244\pi$
$978$		0			0
$979$	−98.6094			−3.15157
$980$	−15.4909	+	31.8332i	−0.494837	+	1.01687i
$981$		0			0
$982$	0.0242946	+	0.0619016i	0.000775271	+	0.00197536i
$983$	2.46497	+	32.8927i	0.0786202	+	1.04911i	0.887399	+	0.461001i	$0.152510\pi$
$983$	2.46497	+	32.8927i	0.0786202	+	1.04911i	−0.808779	+	0.588112i	$0.799871\pi$
$984$		0			0
$985$	−24.1138	+	16.4405i	−0.768331	+	0.523839i
$986$	0.416126	−	0.200395i	0.0132521	−	0.00638189i
$987$		0			0
$988$	19.3129	+	9.30058i	0.614424	+	0.295891i
$989$	7.58218	−	1.14283i	0.241099	−	0.0363399i
$990$		0			0
$991$	−24.2583	−	3.65636i	−0.770591	−	0.116148i	−0.248033	−	0.968752i	$-0.579784\pi$
$991$	−24.2583	−	3.65636i	−0.770591	−	0.116148i	−0.522558	+	0.852604i	$0.675022\pi$
$992$	5.65289	+	5.24511i	0.179479	+	0.166533i
$993$		0			0
$994$	−0.120758	−	0.229622i	−0.00383022	−	0.00728316i
$995$	−0.362856	−	0.455007i	−0.0115033	−	0.0144247i
$996$		0			0
$997$	−26.5565	+	8.19159i	−0.841052	+	0.259430i	−0.685204	−	0.728351i	$-0.740287\pi$
$997$	−26.5565	+	8.19159i	−0.841052	+	0.259430i	−0.155848	+	0.987781i	$0.549811\pi$
$998$	−0.856000	−	1.48264i	−0.0270962	−	0.0469320i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.163.2		48
3.2	odd	2		49.2.g.a.16.3	✓	48
12.11	even	2		784.2.bg.c.65.3		48
21.2	odd	6		343.2.e.d.295.4		48
21.5	even	6		343.2.e.c.295.4		48
21.11	odd	6		343.2.g.i.165.2		48
21.17	even	6		343.2.g.h.165.2		48
21.20	even	2		343.2.g.g.226.3		48
49.46	even	21	inner	441.2.bb.d.46.2		48
147.5	even	42		343.2.e.c.50.4		48
147.8	odd	14		343.2.g.i.79.2		48
147.41	even	14		343.2.g.h.79.2		48
147.44	odd	42		343.2.e.d.50.4		48
147.86	odd	42		2401.2.a.h.1.12		24
147.95	odd	42		49.2.g.a.46.3	yes	48
147.101	even	42		343.2.g.g.214.3		48
147.110	even	42		2401.2.a.i.1.12		24
588.95	even	42		784.2.bg.c.193.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.16.3	✓	48	3.2	odd	2
49.2.g.a.46.3	yes	48	147.95	odd	42
343.2.e.c.50.4		48	147.5	even	42
343.2.e.c.295.4		48	21.5	even	6
343.2.e.d.50.4		48	147.44	odd	42
343.2.e.d.295.4		48	21.2	odd	6
343.2.g.g.214.3		48	147.101	even	42
343.2.g.g.226.3		48	21.20	even	2
343.2.g.h.79.2		48	147.41	even	14
343.2.g.h.165.2		48	21.17	even	6
343.2.g.i.79.2		48	147.8	odd	14
343.2.g.i.165.2		48	21.11	odd	6
441.2.bb.d.46.2		48	49.46	even	21	inner
441.2.bb.d.163.2		48	1.1	even	1	trivial
784.2.bg.c.65.3		48	12.11	even	2
784.2.bg.c.193.3		48	588.95	even	42
2401.2.a.h.1.12		24	147.86	odd	42
2401.2.a.i.1.12		24	147.110	even	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0341744 - 0.0870750i) q^{2} +(1.45969 - 1.35439i) q^{4} +(2.09852 - 1.43075i) q^{5} +(-0.301609 + 2.62850i) q^{7} +(-0.336373 - 0.161989i) q^{8} +O(q^{10})\)	\(q+(-0.0341744 - 0.0870750i) q^{2} +(1.45969 - 1.35439i) q^{4} +(2.09852 - 1.43075i) q^{5} +(-0.301609 + 2.62850i) q^{7} +(-0.336373 - 0.161989i) q^{8} +(-0.196298 - 0.133834i) q^{10} +(5.58784 + 0.842231i) q^{11} +(-2.04987 + 2.57046i) q^{13} +(0.239184 - 0.0635650i) q^{14} +(0.295003 - 3.93654i) q^{16} +(-3.14655 + 0.970581i) q^{17} +(1.63713 - 2.83559i) q^{19} +(1.12539 - 4.93066i) q^{20} +(-0.117624 - 0.515344i) q^{22} +(-3.48067 - 1.07365i) q^{23} +(0.530039 - 1.35052i) q^{25} +(0.293876 + 0.0906489i) q^{26} +(3.11977 + 4.24530i) q^{28} +(0.333666 - 1.46189i) q^{29} +(-3.45509 - 5.98439i) q^{31} +(-1.06637 + 0.328933i) q^{32} +(0.192045 + 0.240817i) q^{34} +(3.12779 + 5.94749i) q^{35} +(2.58665 + 2.40006i) q^{37} +(-0.302857 - 0.0456484i) q^{38} +(-0.937650 + 0.141328i) q^{40} +(-1.46507 - 0.705541i) q^{41} +(-1.89663 + 0.913369i) q^{43} +(9.29723 - 6.33874i) q^{44} +(0.0254623 + 0.339771i) q^{46} +(1.89671 + 4.83275i) q^{47} +(-6.81806 - 1.58556i) q^{49} -0.135710 q^{50} +(0.489237 + 6.52841i) q^{52} +(2.59862 - 2.41116i) q^{53} +(12.9312 - 6.22734i) q^{55} +(0.527242 - 0.835301i) q^{56} +(-0.138697 + 0.0209052i) q^{58} +(-3.52556 - 2.40369i) q^{59} +(7.78410 + 7.22259i) q^{61} +(-0.403016 + 0.505366i) q^{62} +(-4.85746 - 6.09107i) q^{64} +(-0.624023 + 8.32701i) q^{65} +(0.328115 + 0.568312i) q^{67} +(-3.27843 + 5.67841i) q^{68} +(0.410987 - 0.475604i) q^{70} +(-0.233268 - 1.02201i) q^{71} +(-1.98838 + 5.06632i) q^{73} +(0.120588 - 0.307254i) q^{74} +(-1.45081 - 6.35640i) q^{76} +(-3.89915 + 14.4336i) q^{77} +(-4.42315 + 7.66113i) q^{79} +(-5.01311 - 8.68297i) q^{80} +(-0.0113670 + 0.151682i) q^{82} +(-7.79198 - 9.77083i) q^{83} +(-5.21443 + 6.53869i) q^{85} +(0.144348 + 0.133935i) q^{86} +(-1.74317 - 1.18847i) q^{88} +(-17.2551 + 2.60079i) q^{89} +(-6.13821 - 6.16338i) q^{91} +(-6.53484 + 3.14701i) q^{92} +(0.355992 - 0.330313i) q^{94} +(-0.621463 - 8.29285i) q^{95} -16.4625 q^{97} +(0.0949408 + 0.647869i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

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