LMFDB - Embedded newform 441.2.bb.d.46.2

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			46.2
Character	$\chi$	$=$	441.46
Dual form			441.2.bb.d.163.2

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$1$

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	−0.942447	−	0.334356i	$-0.891481\pi$
$2$	−0.0341744	+	0.0870750i	−0.0241650	+	0.0615713i	0.918282	+	0.395927i	$0.129577\pi$
$3$		0			0
$3$		0			0
$4$	1.45969	+	1.35439i	0.729845	+	0.677197i
$5$	2.09852	+	1.43075i	0.938486	+	0.639849i	0.932900	−	0.360136i	$-0.117270\pi$
$5$	2.09852	+	1.43075i	0.938486	+	0.639849i	0.00558567	+	0.999984i	$0.498222\pi$
$6$		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	0.764348	−	0.644804i	$-0.223061\pi$
$11$	5.58784	−	0.842231i	1.68480	−	0.253942i	0.920449	+	0.390862i	$0.127823\pi$
$12$		0			0
$13$	−2.04987	−	2.57046i	−0.568533	−	0.712918i	0.411577	−	0.911375i	$-0.364978\pi$
$13$	−2.04987	−	2.57046i	−0.568533	−	0.712918i	−0.980110	+	0.198457i	$0.936407\pi$
$14$	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	−0.111339	−	0.993782i	$-0.535514\pi$
$17$	−3.14655	−	0.970581i	−0.763150	−	0.235401i	−0.651810	+	0.758382i	$0.725990\pi$
$18$		0			0
$19$	1.63713	+	2.83559i	0.375583	+	0.650529i	0.990414	−	0.138130i	$-0.0441091\pi$
$19$	1.63713	+	2.83559i	0.375583	+	0.650529i	−0.614831	+	0.788659i	$0.710776\pi$
$20$	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	−0.635559	−	0.772052i	$-0.719230\pi$
$23$	−3.48067	+	1.07365i	−0.725770	+	0.223870i	−0.0902111	+	0.995923i	$0.528754\pi$
$24$		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	0.996413	−	0.0846210i	$-0.0269680\pi$
$29$	0.333666	+	1.46189i	0.0619602	+	0.271466i	−0.934453	+	0.356087i	$0.884111\pi$
$30$		0			0
$31$	−3.45509	+	5.98439i	−0.620553	+	1.07483i	0.368830	+	0.929497i	$0.379758\pi$
$31$	−3.45509	+	5.98439i	−0.620553	+	1.07483i	−0.989383	+	0.145332i	$0.953575\pi$
$32$	−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	−0.438312	−	0.898823i	$-0.644423\pi$
$37$	2.58665	−	2.40006i	0.425243	−	0.394568i	0.863555	+	0.504255i	$0.168233\pi$
$38$	−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	−0.544774	−	0.838583i	$-0.683385\pi$
$41$	−1.46507	+	0.705541i	−0.228805	+	0.110187i	0.315969	+	0.948770i	$0.397670\pi$
$42$		0			0
$43$	−1.89663	−	0.913369i	−0.289233	−	0.139287i	0.283641	−	0.958930i	$-0.408458\pi$
$43$	−1.89663	−	0.913369i	−0.289233	−	0.139287i	−0.572875	+	0.819643i	$0.694172\pi$
$44$	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	−0.723233	−	0.690604i	$-0.757345\pi$
$47$	1.89671	−	4.83275i	0.276664	−	0.704928i	0.999897	−	0.0143247i	$-0.00455985\pi$
$48$		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	0.838179	−	0.545394i	$-0.183620\pi$
$53$	2.59862	+	2.41116i	0.356947	+	0.331199i	−0.481232	+	0.876593i	$0.659811\pi$
$54$		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	−0.770648	−	0.637260i	$-0.780068\pi$
$59$	−3.52556	+	2.40369i	−0.458989	+	0.312933i	0.311660	+	0.950194i	$0.399115\pi$
$60$		0			0
$61$	7.78410	−	7.22259i	0.996652	−	0.924758i	−0.000512856	−	1.00000i	$-0.500163\pi$
$61$	7.78410	−	7.22259i	0.996652	−	0.924758i	0.997165	+	0.0752415i	$0.0239728\pi$
$62$	−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	−0.845287	−	0.534313i	$-0.820570\pi$
$67$	0.328115	−	0.568312i	0.0400856	−	0.0694303i	0.885372	+	0.464883i	$0.153904\pi$
$68$	−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	−0.986882	−	0.161445i	$-0.948385\pi$
$71$	−0.233268	+	1.02201i	−0.0276838	+	0.121291i	0.959198	+	0.282735i	$0.0912418\pi$
$72$		0			0
$73$	−1.98838	−	5.06632i	−0.232723	−	0.592968i	0.766035	−	0.642799i	$-0.222227\pi$
$73$	−1.98838	−	5.06632i	−0.232723	−	0.592968i	−0.998758	+	0.0498311i	$0.984132\pi$
$74$	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	0.502353	−	0.864663i	$-0.332468\pi$
$79$	−4.42315	−	7.66113i	−0.497644	−	0.861944i	−0.999996	+	0.00271872i	$0.999135\pi$
$80$	−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	0.141308	+	0.989966i	$0.454869\pi$
$83$	−7.79198	+	9.77083i	−0.855281	+	1.07249i	−0.996589	+	0.0825228i	$0.973702\pi$
$84$		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	−0.857835	−	0.513925i	$-0.828191\pi$
$89$	−17.2551	−	2.60079i	−1.82904	−	0.275684i	−0.971206	+	0.238242i	$0.923429\pi$
$90$		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	−0.824130	−	0.566400i	$-0.808336\pi$
$101$	0.755878	−	10.0865i	0.0752127	−	1.00364i	0.899343	−	0.437244i	$-0.144045\pi$
$102$		0			0
$103$	−6.92198	−	4.71932i	−0.682043	−	0.465009i	0.172078	−	0.985083i	$-0.444952\pi$
$103$	−6.92198	−	4.71932i	−0.682043	−	0.465009i	−0.854121	+	0.520074i	$0.825904\pi$
$104$	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	0.622996	−	0.782225i	$-0.285915\pi$
$107$	10.2174	+	1.54002i	0.987750	+	0.148879i	0.364754	+	0.931104i	$0.381153\pi$
$108$		0			0
$109$	8.47138	−	1.27685i	0.811411	−	0.122300i	0.269785	−	0.962920i	$-0.413047\pi$
$109$	8.47138	−	1.27685i	0.811411	−	0.122300i	0.541625	+	0.840620i	$0.317809\pi$
$110$	−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	−0.876924	−	0.480629i	$-0.840408\pi$
$113$	−2.26646	+	2.84205i	−0.213211	+	0.267358i	0.663713	+	0.747987i	$0.268980\pi$
$114$		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	0.848190	+	0.529692i	$0.177692\pi$
$127$	3.53659	+	15.4948i	0.313822	+	1.37494i	−0.534368	+	0.845252i	$0.679450\pi$
$128$	−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	−0.991950	−	0.126633i	$-0.959583\pi$
$131$	−0.342826	−	4.57470i	−0.0299529	−	0.399693i	0.961997	−	0.273061i	$-0.0880360\pi$
$132$		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	−0.142044	−	0.989860i	$-0.545368\pi$
$137$	8.51512	−	5.80551i	0.727496	−	0.495998i	0.869540	+	0.493862i	$0.164415\pi$
$138$		0			0
$139$	3.87696	−	1.86705i	0.328840	−	0.158361i	−0.262178	−	0.965020i	$-0.584441\pi$
$139$	3.87696	−	1.86705i	0.328840	−	0.158361i	0.591018	+	0.806659i	$0.298726\pi$
$140$	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	−0.262879	−	0.964829i	$-0.584672\pi$
$149$	7.15396	−	18.2280i	0.586075	−	1.49330i	0.848954	−	0.528466i	$-0.177233\pi$
$150$		0			0
$151$	−4.50881	−	4.18356i	−0.366922	−	0.340453i	0.475066	−	0.879950i	$-0.342424\pi$
$151$	−4.50881	−	4.18356i	−0.366922	−	0.340453i	−0.841988	+	0.539497i	$0.818615\pi$
$152$	−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	−0.362319	−	0.932054i	$-0.618015\pi$
$157$	4.67286	−	3.18590i	0.372935	−	0.254263i	0.735254	+	0.677791i	$0.237063\pi$
$158$	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	0.947243	+	0.320518i	$0.103857\pi$
$163$	0.744970	+	9.94094i	0.0583506	+	0.778635i	−0.888892	+	0.458117i	$0.848524\pi$
$164$	−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	0.723872	+	0.689935i	$0.242361\pi$
$167$	4.79486	+	21.0076i	0.371037	+	1.62562i	−0.352835	+	0.935686i	$0.614782\pi$
$168$		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	0.0550658	−	0.998483i	$-0.482463\pi$
$173$	8.72078	−	2.69000i	0.663029	−	0.204517i	0.607963	+	0.793965i	$0.291987\pi$
$174$		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	0.462388	−	0.886678i	$-0.346993\pi$
$179$	4.61508	+	1.42356i	0.344948	+	0.106402i	−0.117440	+	0.993080i	$0.537469\pi$
$180$		0			0
$181$	−6.22935	+	7.81136i	−0.463024	+	0.580614i	−0.957447	−	0.288608i	$-0.906808\pi$
$181$	−6.22935	+	7.81136i	−0.463024	+	0.580614i	0.494424	+	0.869221i	$0.335379\pi$
$182$	−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	0.603997	−	0.796987i	$-0.293574\pi$
$191$	1.14387	+	0.779879i	0.0827677	+	0.0564301i	−0.521229	+	0.853417i	$0.674526\pi$
$192$		0			0
$193$	−1.62094	+	21.6300i	−0.116678	+	1.55696i	0.564865	+	0.825183i	$0.308928\pi$
$193$	−1.62094	+	21.6300i	−0.116678	+	1.55696i	−0.681543	+	0.731778i	$0.738691\pi$
$194$	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	−0.997778	−	0.0666287i	$-0.978776\pi$
$199$	−0.0171235	+	0.228498i	−0.00121386	+	0.0161978i	0.996564	+	0.0828265i	$0.0263947\pi$
$200$	−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	−0.404797	−	0.914406i	$-0.632658\pi$
$211$	8.37791	−	10.5056i	0.576759	−	0.723233i	0.981556	+	0.191173i	$0.0612293\pi$
$212$	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	−0.957015	−	0.290038i	$-0.906332\pi$
$223$	0.463950	−	2.03270i	0.0310684	−	0.136119i	0.988084	+	0.153918i	$0.0491893\pi$
$224$	−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	−0.828071	−	0.560624i	$-0.810562\pi$
$227$	1.07694	−	1.86531i	0.0714788	−	0.123805i	0.899550	+	0.436819i	$0.143895\pi$
$228$		0			0
$229$	−0.312139	−	4.16521i	−0.0206268	−	0.275245i	−0.997975	−	0.0636075i	$-0.979739\pi$
$229$	−0.312139	−	4.16521i	−0.0206268	−	0.275245i	0.977348	−	0.211637i	$-0.0678796\pi$
$230$	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	−0.617574	−	0.786513i	$-0.711884\pi$
$233$	1.84071	−	1.70792i	0.120589	−	0.111890i	0.738162	+	0.674623i	$0.235694\pi$
$234$		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	0.319622	−	0.947545i	$-0.396444\pi$
$239$	−3.43076	−	1.65217i	−0.221918	−	0.106870i	−0.541540	+	0.840675i	$0.682158\pi$
$240$		0			0
$241$	−4.12223	−	3.82487i	−0.265536	−	0.246381i	0.536156	−	0.844119i	$-0.319876\pi$
$241$	−4.12223	−	3.82487i	−0.265536	−	0.246381i	−0.801692	+	0.597738i	$0.796066\pi$
$242$	−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	0.265967	−	0.963982i	$-0.414309\pi$
$251$	−5.09948	−	2.45578i	−0.321876	−	0.155007i	−0.587843	+	0.808975i	$0.700023\pi$
$252$		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	0.153224	−	0.988192i	$-0.451034\pi$
$257$	18.4375	−	17.1075i	1.15010	−	1.06714i	0.996879	−	0.0789477i	$-0.0251560\pi$
$258$		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	0.204475	+	0.978872i	$0.434451\pi$
$263$	−12.0898	+	20.9402i	−0.745490	+	1.29123i	−0.949965	+	0.312356i	$0.898882\pi$
$264$		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	0.838559	+	0.544812i	$0.183399\pi$
$269$	9.74917	+	24.8405i	0.594418	+	1.51455i	−0.244141	+	0.969740i	$0.578506\pi$
$270$		0			0
$271$	19.5180	−	6.02049i	1.18563	−	0.365719i	0.361638	−	0.932319i	$-0.382218\pi$
$271$	19.5180	−	6.02049i	1.18563	−	0.365719i	0.823993	+	0.566600i	$0.191741\pi$
$272$	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	0.726263	−	0.687417i	$-0.241255\pi$
$277$	15.6296	+	4.82111i	0.939095	+	0.289672i	0.212831	+	0.977089i	$0.431732\pi$
$278$	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	0.957818	−	0.287376i	$-0.0927830\pi$
$281$	7.78664	+	9.76414i	0.464512	+	0.582480i	−0.493306	+	0.869856i	$0.664212\pi$
$282$		0			0
$283$	−4.34306	+	0.654611i	−0.258168	+	0.0389126i	−0.276851	−	0.960913i	$-0.589291\pi$
$283$	−4.34306	+	0.654611i	−0.258168	+	0.0389126i	0.0186828	+	0.999825i	$0.494053\pi$
$284$	−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	0.823377	−	0.567495i	$-0.192087\pi$
$307$	1.52247	+	1.90912i	0.0868919	+	0.108959i	−0.736485	+	0.676454i	$0.763516\pi$
$308$	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	0.428955	−	0.903326i	$-0.358882\pi$
$311$	4.84107	+	1.49327i	0.274512	+	0.0846757i	−0.154443	+	0.988002i	$0.549358\pi$
$312$		0			0
$313$	9.04913	+	15.6735i	0.511487	+	0.885921i	0.999911	+	0.0133151i	$0.00423846\pi$
$313$	9.04913	+	15.6735i	0.511487	+	0.885921i	−0.488424	+	0.872606i	$0.662428\pi$
$314$	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	0.652112	−	0.758122i	$-0.273883\pi$
$317$	28.8073	−	8.88587i	1.61798	−	0.499080i	0.965866	+	0.259042i	$0.0834069\pi$
$318$		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	−0.990298	−	0.138957i	$-0.955625\pi$
$331$	−16.8423	+	15.6274i	−0.925736	+	0.858957i	0.0645629	+	0.997914i	$0.479435\pi$
$332$	−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	−0.0833113	−	0.996524i	$-0.526550\pi$
$337$	−16.7856	−	8.08351i	−0.914369	−	0.440337i	−0.831057	+	0.556187i	$0.812264\pi$
$338$	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	−0.997366	−	0.0725302i	$-0.976893\pi$
$347$	−21.3146	−	19.7770i	−1.14423	−	1.06169i	−0.146861	−	0.989157i	$-0.546917\pi$
$348$		0			0
$349$	−14.8838	−	7.16767i	−0.796713	−	0.383677i	−0.00918667	−	0.999958i	$-0.502924\pi$
$349$	−14.8838	−	7.16767i	−0.796713	−	0.383677i	−0.787526	+	0.616281i	$0.788639\pi$
$350$	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	−0.849549	−	0.527510i	$-0.823126\pi$
$353$	−12.5671	+	8.56809i	−0.668878	+	0.456033i	0.180671	+	0.983544i	$0.442173\pi$
$354$		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	0.973890	+	0.227021i	$0.0728986\pi$
$359$	0.847196	+	11.3050i	0.0447133	+	0.596657i	−0.929177	+	0.369636i	$0.879482\pi$
$360$		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	0.775740	−	0.631053i	$-0.217377\pi$
$367$	−4.25564	−	10.8432i	−0.222143	−	0.566010i	−0.997882	+	0.0650428i	$0.979282\pi$
$368$	−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	0.971785	−	0.235867i	$-0.0757929\pi$
$373$	5.43910	+	9.42080i	0.281626	+	0.487791i	−0.690159	+	0.723657i	$0.742460\pi$
$374$	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	0.991360	−	0.131167i	$-0.0418725\pi$
$379$	12.5156	+	15.6941i	0.642883	+	0.806150i	−0.348477	+	0.937317i	$0.613301\pi$
$380$	−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	0.308022	−	0.951379i	$-0.400333\pi$
$383$	6.30041	+	0.949634i	0.321936	+	0.0485240i	0.0139137	+	0.999903i	$0.495571\pi$
$384$		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	0.980846	+	0.194786i	$0.0624012\pi$
$389$	−0.356516	+	4.75738i	−0.0180761	+	0.241209i	−0.998922	+	0.0464228i	$0.985218\pi$
$390$		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	0.932467	−	0.361254i	$-0.117651\pi$
$397$	18.6667	+	12.7267i	0.936854	+	0.638736i	0.00438652	+	0.999990i	$0.498604\pi$
$398$	−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	−0.934065	−	0.357104i	$-0.883764\pi$
$401$	−38.6861	−	5.83099i	−1.93189	−	0.291185i	−0.997825	+	0.0659187i	$0.979002\pi$
$402$		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	0.839516	−	0.543336i	$-0.182839\pi$
$409$	24.8162	+	7.65480i	1.22708	+	0.378505i	0.387568	+	0.921841i	$0.373315\pi$
$410$	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	0.0270924	+	0.999633i	$0.491375\pi$
$419$	−8.82320	+	38.6570i	−0.431041	+	1.88852i	−0.458134	+	0.888883i	$0.651482\pi$
$420$		0			0
$421$	4.12186	+	18.0591i	0.200887	+	0.880145i	0.970398	+	0.241511i	$0.0776430\pi$
$421$	4.12186	+	18.0591i	0.200887	+	0.880145i	−0.769511	+	0.638634i	$0.779500\pi$
$422$	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	−0.0812429	−	0.996694i	$-0.525889\pi$
$431$	16.9587	−	11.5623i	0.816872	−	0.556934i	0.898115	+	0.439760i	$0.144937\pi$
$432$		0			0
$433$	−11.0650	+	5.32862i	−0.531750	+	0.256077i	−0.680436	−	0.732807i	$-0.738210\pi$
$433$	−11.0650	+	5.32862i	−0.531750	+	0.256077i	0.148687	+	0.988884i	$0.452495\pi$
$434$	−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	0.515826	+	0.856693i	$0.327485\pi$
$439$	−9.32379	+	23.7566i	−0.445000	+	1.13384i	−0.960827	+	0.277149i	$0.910610\pi$
$440$	−5.35847			−0.255455
$441$		0			0
$442$	−1.01268			−0.0481682
$443$	−15.0627	+	38.3791i	−0.715651	+	1.82345i	−0.169982	+	0.985447i	$0.554371\pi$
$443$	−15.0627	+	38.3791i	−0.715651	+	1.82345i	−0.545668	+	0.838001i	$0.683724\pi$
$444$		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	−0.631147	−	0.775663i	$-0.717415\pi$
$449$	−8.86197	+	4.26770i	−0.418222	+	0.201405i	0.212925	+	0.977069i	$0.431701\pi$
$450$		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	−0.955050	−	0.296443i	$-0.904199\pi$
$457$	−1.17255	−	15.6466i	−0.0548497	−	0.731919i	0.900201	−	0.435475i	$-0.143420\pi$
$458$	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	−0.856221	−	0.516609i	$-0.827194\pi$
$461$	−6.63324	−	29.0621i	−0.308941	−	1.35356i	0.547280	−	0.836949i	$-0.315663\pi$
$462$		0			0
$463$	4.24774	−	18.6106i	0.197409	−	0.864907i	−0.775062	−	0.631885i	$-0.782281\pi$
$463$	4.24774	−	18.6106i	0.197409	−	0.864907i	0.972471	−	0.233022i	$-0.0748614\pi$
$464$	−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	−0.0629983	−	0.998014i	$-0.520066\pi$
$467$	9.66302	−	2.98065i	0.447151	−	0.137928i	0.510149	+	0.860086i	$0.329590\pi$
$468$		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	−0.0434537	−	0.999055i	$-0.513836\pi$
$479$	4.58513	−	0.691097i	0.209500	−	0.0315770i	0.252954	+	0.967478i	$0.418598\pi$
$480$		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	0.819485	+	0.573101i	$0.194260\pi$
$487$	−1.68298	+	22.4579i	−0.0762633	+	1.01766i	−0.895748	+	0.444562i	$0.853359\pi$
$488$	−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	0.541044	−	0.840994i	$-0.318029\pi$
$499$	18.0977	+	2.72779i	0.810163	+	0.122112i	0.269119	+	0.963107i	$0.413267\pi$
$500$	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	0.934302	−	0.356482i	$-0.116024\pi$
$503$	8.49686	+	10.6547i	0.378856	+	0.475071i	−0.555446	+	0.831553i	$0.687452\pi$
$504$		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	0.940992	+	0.338429i	$0.109896\pi$
$509$	17.2272	+	29.8385i	0.763584	+	1.32257i	−0.177408	+	0.984137i	$0.556771\pi$
$510$		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	−0.540277	−	0.841487i	$-0.681681\pi$
$521$	10.4680	−	18.1311i	0.458611	−	0.794337i	0.998888	+	0.0471503i	$0.0150140\pi$
$522$		0			0
$523$	0.281796	+	3.76030i	0.0123221	+	0.164426i	0.999970	+	0.00773753i	$0.00246296\pi$
$523$	0.281796	+	3.76030i	0.0123221	+	0.164426i	−0.987648	+	0.156689i	$0.949918\pi$
$524$	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	−0.895102	−	0.445861i	$-0.852898\pi$
$541$	1.49596	−	3.81165i	0.0643164	−	0.163875i	0.959419	+	0.281985i	$0.0909929\pi$
$542$	−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	0.200657	−	0.979662i	$-0.435692\pi$
$547$	25.5326	−	12.2958i	1.09169	−	0.525733i	0.891038	+	0.453929i	$0.149978\pi$
$548$	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	−0.779639	−	0.626229i	$-0.784598\pi$
$557$	3.59938	−	6.23430i	0.152510	−	0.264156i	0.932150	+	0.362073i	$0.117931\pi$
$558$		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	0.944753	+	0.327784i	$0.106302\pi$
$563$	11.2742	+	28.7261i	0.475150	+	1.21066i	−0.469603	+	0.882878i	$0.655603\pi$
$564$		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	0.538869	−	0.842389i	$-0.318852\pi$
$569$	−10.9750	−	19.0093i	−0.460096	−	0.796909i	−0.998965	+	0.0454799i	$0.985518\pi$
$570$		0			0
$571$	−27.7739	−	8.56711i	−1.16230	−	0.358523i	−0.347172	−	0.937801i	$-0.612858\pi$
$571$	−27.7739	−	8.56711i	−1.16230	−	0.358523i	−0.815129	+	0.579279i	$0.803334\pi$
$572$	−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	0.00542264	−	0.999985i	$-0.498274\pi$
$577$	7.33488	−	1.10556i	0.305355	−	0.0460249i	0.299933	+	0.953960i	$0.403036\pi$
$578$	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	0.959264	−	0.282512i	$-0.0911678\pi$
$593$	25.4898	+	17.3786i	1.04674	+	0.713654i	0.0874752	+	0.996167i	$0.472120\pi$
$594$		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	0.438298	−	0.898830i	$-0.355581\pi$
$599$	27.4618	−	4.13920i	1.12206	−	0.169123i	0.683761	+	0.729706i	$0.260343\pi$
$600$		0			0
$601$	11.9118	+	14.9370i	0.485893	+	0.609291i	0.962983	−	0.269564i	$-0.0868795\pi$
$601$	11.9118	+	14.9370i	0.485893	+	0.609291i	−0.477089	+	0.878855i	$0.658308\pi$
$602$	−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	0.590860	−	0.806774i	$-0.298789\pi$
$607$	−9.93520	−	17.2083i	−0.403257	−	0.698462i	−0.994117	+	0.108312i	$0.965455\pi$
$608$	−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	−0.785408	−	0.618978i	$-0.787547\pi$
$613$	−15.6148	−	39.7858i	−0.630675	−	1.60693i	0.154733	−	0.987956i	$-0.450548\pi$
$614$	−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	−0.981137	−	0.193314i	$-0.938076\pi$
$617$	−4.49691	−	19.7023i	−0.181039	−	0.793183i	0.800098	−	0.599869i	$-0.204781\pi$
$618$		0			0
$619$	7.86487	−	13.6224i	0.316116	−	0.547529i	−0.663558	−	0.748125i	$-0.730954\pi$
$619$	7.86487	−	13.6224i	0.316116	−	0.547529i	0.979674	+	0.200596i	$0.0642878\pi$
$620$	−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	0.187608	−	0.982244i	$-0.439927\pi$
$631$	−11.6397	−	5.60540i	−0.463370	−	0.223147i	−0.650978	+	0.759097i	$0.725641\pi$
$632$	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	−0.0156275	−	0.999878i	$-0.504975\pi$
$641$	−25.6693	−	23.8177i	−1.01388	−	0.940741i	−0.998250	+	0.0591371i	$0.981165\pi$
$642$		0			0
$643$	23.8937	+	11.5066i	0.942274	+	0.453775i	0.840971	−	0.541081i	$-0.181985\pi$
$643$	23.8937	+	11.5066i	0.942274	+	0.453775i	0.101303	+	0.994856i	$0.467699\pi$
$644$	−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	0.165790	−	0.986161i	$-0.446983\pi$
$647$	29.1080	−	19.8455i	1.14435	−	0.780206i	0.978561	+	0.205955i	$0.0660301\pi$
$648$		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	0.974879	+	0.222734i	$0.0714981\pi$
$653$	1.12655	+	15.0328i	0.0440854	+	0.588278i	−0.930794	+	0.365544i	$0.880883\pi$
$654$		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	−0.949631	−	0.313371i	$-0.898542\pi$
$659$	1.07622	−	4.71525i	0.0419238	−	0.183680i	0.991554	+	0.129691i	$0.0413987\pi$
$660$		0			0
$661$	4.13895	+	10.5459i	0.160986	+	0.410186i	0.988492	−	0.151270i	$-0.0483364\pi$
$661$	4.13895	+	10.5459i	0.160986	+	0.410186i	−0.827506	+	0.561457i	$0.810241\pi$
$662$	−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	0.922468	−	0.386072i	$-0.126169\pi$
$673$	8.84130	+	11.0866i	0.340807	+	0.427359i	−0.581661	+	0.813431i	$0.697597\pi$
$674$	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	−0.546891	−	0.837204i	$-0.684189\pi$
$677$	−34.2479	−	5.16205i	−1.31626	−	0.198394i	−0.769364	+	0.638810i	$0.779427\pi$
$678$		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	0.729234	+	0.684264i	$0.239877\pi$
$683$	−2.45242	+	32.7253i	−0.0938394	+	1.25220i	−0.823073	+	0.567935i	$0.807742\pi$
$684$		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	0.923905	+	0.382622i	$0.124979\pi$
$691$	42.5221	+	28.9911i	1.61762	+	1.10287i	0.693713	+	0.720251i	$0.255973\pi$
$692$	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	−0.899380	−	0.437168i	$-0.855982\pi$
$701$	−7.22918	+	9.06511i	−0.273042	+	0.342384i	0.626338	+	0.779552i	$0.284553\pi$
$702$		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	−0.652646	−	0.757663i	$-0.726341\pi$
$709$	−20.3719	+	6.28389i	−0.765081	+	0.235996i	−0.112435	+	0.993659i	$0.535865\pi$
$710$	−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	0.969867	+	0.243635i	$0.0783401\pi$
$719$	1.26414	+	16.8688i	0.0471446	+	0.629101i	−0.922722	+	0.385465i	$0.874041\pi$
$720$		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	−0.511602	−	0.859223i	$-0.670948\pi$
$727$	−4.28205	+	2.06213i	−0.158812	+	0.0764800i	0.352789	+	0.935703i	$0.385233\pi$
$728$	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	−0.766679	−	0.642031i	$-0.778092\pi$
$733$	6.28193	−	16.0061i	0.232028	−	0.591198i	0.998707	+	0.0508324i	$0.0161874\pi$
$734$	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	0.634799	−	0.772677i	$-0.281083\pi$
$739$	−2.39982	−	2.22671i	−0.0882788	−	0.0819107i	−0.723078	+	0.690766i	$0.757273\pi$
$740$	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	−0.0840857	−	0.996459i	$-0.526797\pi$
$743$	17.5147	−	8.43461i	0.642550	−	0.309436i	0.726636	+	0.687023i	$0.241083\pi$
$744$		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	−0.937100	−	0.349062i	$-0.886500\pi$
$751$	−1.71255	−	22.8523i	−0.0624917	−	0.833893i	0.874608	−	0.484831i	$-0.161119\pi$
$752$	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	0.441245	+	0.897386i	$0.354537\pi$
$757$	−9.51048	+	41.6681i	−0.345664	+	1.51445i	−0.786910	+	0.617068i	$0.788320\pi$
$758$	−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	−0.307967	−	0.951397i	$-0.599649\pi$
$761$	−0.730491	+	0.225327i	−0.0264803	+	0.00816809i	0.281487	+	0.959565i	$0.409172\pi$
$762$		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	−0.891333	−	0.453348i	$-0.850229\pi$
$769$	−6.96075	+	8.72851i	−0.251011	+	0.314758i	0.640322	+	0.768106i	$0.278801\pi$
$770$	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	0.328564	−	0.944482i	$-0.393435\pi$
$773$	25.6042	−	3.85922i	0.920921	−	0.138806i	0.592357	+	0.805675i	$0.298197\pi$
$774$		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	−0.976692	−	0.214648i	$-0.931140\pi$
$787$	0.591445	−	7.89229i	0.0210827	−	0.281330i	0.997774	−	0.0666820i	$-0.0212413\pi$
$788$	−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	0.479728	−	0.877417i	$-0.340735\pi$
$797$	−13.6199	−	17.0788i	−0.482440	−	0.604961i	−0.962168	+	0.272456i	$0.912164\pi$
$798$		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	0.938799	−	0.344466i	$-0.111940\pi$
$809$	0.464021	+	1.18231i	0.0163141	+	0.0415677i	−0.922485	+	0.386034i	$0.873845\pi$
$810$		0			0
$811$	1.33915	−	5.86720i	0.0470239	−	0.206025i	−0.945958	−	0.324288i	$-0.894875\pi$
$811$	1.33915	−	5.86720i	0.0470239	−	0.206025i	0.992982	+	0.118263i	$0.0377325\pi$
$812$	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	−0.889784	−	0.456382i	$-0.849145\pi$
$821$	−14.3601	+	13.3242i	−0.501171	+	0.465019i	0.388612	+	0.921401i	$0.372955\pi$
$822$		0			0
$823$	3.54830	−	2.41919i	0.123686	−	0.0843277i	−0.499897	−	0.866085i	$-0.666629\pi$
$823$	3.54830	−	2.41919i	0.123686	−	0.0843277i	0.623583	+	0.781757i	$0.285676\pi$
$824$	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	0.644361	−	0.764722i	$-0.277124\pi$
$827$	12.8900	+	6.20750i	0.448230	+	0.215856i	−0.196131	+	0.980578i	$0.562838\pi$
$828$		0			0
$829$	−8.28997	−	7.69197i	−0.287922	−	0.267153i	0.522966	−	0.852353i	$-0.324825\pi$
$829$	−8.28997	−	7.69197i	−0.287922	−	0.267153i	−0.810889	+	0.585200i	$0.801016\pi$
$830$	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	−0.120481	−	0.992716i	$-0.538444\pi$
$839$	−28.1468	−	13.5548i	−0.971735	−	0.467963i	−0.851255	+	0.524753i	$0.824158\pi$
$840$		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	−0.999814	−	0.0192797i	$-0.993863\pi$
$853$	−3.13610	−	13.7401i	−0.107378	−	0.470453i	0.892436	−	0.451173i	$-0.148994\pi$
$854$	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	−0.885097	−	0.465407i	$-0.845908\pi$
$857$	−16.1839	−	41.2360i	−0.552832	−	1.40859i	0.332264	−	0.943186i	$-0.392187\pi$
$858$		0			0
$859$	37.3909	−	11.5336i	1.27576	−	0.393520i	0.418412	−	0.908257i	$-0.362587\pi$
$859$	37.3909	−	11.5336i	1.27576	−	0.393520i	0.857348	+	0.514737i	$0.172111\pi$
$860$	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	0.518684	−	0.854966i	$-0.326422\pi$
$863$	−14.1326	−	24.4784i	−0.481081	−	0.833256i	−0.999764	+	0.0217102i	$0.993089\pi$
$864$		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	0.0160226	−	0.999872i	$-0.494900\pi$
$877$	−26.9157	−	18.3508i	−0.908878	−	0.619662i	−0.924901	+	0.380209i	$0.875852\pi$
$878$	−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	0.999803	−	0.0198706i	$-0.00632542\pi$
$887$	40.1044	+	27.3427i	1.34657	+	0.918079i	0.346772	+	0.937949i	$0.387278\pi$
$888$		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	0.941808	+	0.336152i	$0.109126\pi$
$907$	14.4576	+	36.8373i	0.480055	+	1.22316i	−0.461752	+	0.887009i	$0.652779\pi$
$908$	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	−0.961630	−	0.274351i	$-0.911537\pi$
$911$	−6.46720	−	28.3346i	−0.214268	−	0.938769i	0.747362	−	0.664417i	$-0.231320\pi$
$912$		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	−0.247726	−	0.968830i	$-0.579683\pi$
$919$	21.2169	−	19.6864i	0.699882	−	0.649396i	0.947608	+	0.319434i	$0.103493\pi$
$920$	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	0.658136	+	0.752899i	$0.271345\pi$
$929$	−10.2537	+	26.1260i	−0.336413	+	0.857167i	−0.994549	+	0.104268i	$0.966750\pi$
$930$		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	−0.0296786	−	0.999559i	$-0.509448\pi$
$937$	−25.3966	−	12.2303i	−0.829670	−	0.399548i	−0.799991	+	0.600011i	$0.795163\pi$
$938$	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	0.0312849	−	0.999511i	$-0.490040\pi$
$941$	29.8515	−	20.3524i	0.973133	−	0.663471i	0.941848	+	0.336040i	$0.109088\pi$
$942$		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	−0.880068	−	0.474848i	$-0.842503\pi$
$947$	−2.48039	−	33.0986i	−0.0806020	−	1.07556i	0.799466	−	0.600711i	$-0.205116\pi$
$948$		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	0.498127	+	0.867104i	$0.334021\pi$
$953$	−10.0914	+	44.2133i	−0.326892	+	1.43221i	−0.825020	+	0.565104i	$0.808836\pi$
$954$		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	−0.915745	−	0.401759i	$-0.868399\pi$
$967$	−34.3201	−	43.0360i	−1.10366	−	1.38394i	−0.187914	−	0.982186i	$-0.560173\pi$
$968$	−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	0.335201	−	0.942147i	$-0.391196\pi$
$971$	11.7728	+	1.77446i	0.377806	+	0.0569451i	0.0426058	+	0.999092i	$0.486434\pi$
$972$		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	0.724125	+	0.689669i	$0.242244\pi$
$977$	−2.96010	+	39.4998i	−0.0947019	+	1.26371i	−0.818827	+	0.574041i	$0.805375\pi$
$978$		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	−0.808779	−	0.588112i	$-0.799871\pi$
$983$	2.46497	−	32.8927i	0.0786202	−	1.04911i	0.887399	−	0.461001i	$-0.152510\pi$
$984$		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	−0.522558	−	0.852604i	$-0.675022\pi$
$991$	−24.2583	+	3.65636i	−0.770591	+	0.116148i	−0.248033	+	0.968752i	$0.579784\pi$
$992$	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	−0.155848	−	0.987781i	$-0.549811\pi$
$997$	−26.5565	−	8.19159i	−0.841052	−	0.259430i	−0.685204	+	0.728351i	$0.740287\pi$
$998$	−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.46.2		48
3.2	odd	2		49.2.g.a.46.3	yes	48
12.11	even	2		784.2.bg.c.193.3		48
21.2	odd	6		343.2.g.i.79.2		48
21.5	even	6		343.2.g.h.79.2		48
21.11	odd	6		343.2.e.d.50.4		48
21.17	even	6		343.2.e.c.50.4		48
21.20	even	2		343.2.g.g.214.3		48
49.16	even	21	inner	441.2.bb.d.163.2		48
147.53	odd	42		2401.2.a.h.1.12		24
147.59	even	42		343.2.e.c.295.4		48
147.65	odd	42		49.2.g.a.16.3	✓	48
147.92	odd	14		343.2.g.i.165.2		48
147.104	even	14		343.2.g.h.165.2		48
147.131	even	42		343.2.g.g.226.3		48
147.137	odd	42		343.2.e.d.295.4		48
147.143	even	42		2401.2.a.i.1.12		24
588.359	even	42		784.2.bg.c.65.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.16.3	✓	48	147.65	odd	42
49.2.g.a.46.3	yes	48	3.2	odd	2
343.2.e.c.50.4		48	21.17	even	6
343.2.e.c.295.4		48	147.59	even	42
343.2.e.d.50.4		48	21.11	odd	6
343.2.e.d.295.4		48	147.137	odd	42
343.2.g.g.214.3		48	21.20	even	2
343.2.g.g.226.3		48	147.131	even	42
343.2.g.h.79.2		48	21.5	even	6
343.2.g.h.165.2		48	147.104	even	14
343.2.g.i.79.2		48	21.2	odd	6
343.2.g.i.165.2		48	147.92	odd	14
441.2.bb.d.46.2		48	1.1	even	1	trivial
441.2.bb.d.163.2		48	49.16	even	21	inner
784.2.bg.c.65.3		48	588.359	even	42
784.2.bg.c.193.3		48	12.11	even	2
2401.2.a.h.1.12		24	147.53	odd	42
2401.2.a.i.1.12		24	147.143	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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