LMFDB - Embedded newform 387.2.h.d.208.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(208,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("387.208");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.h (of order $3$, degree $2$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			208.1
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	387.208
Dual form			387.2.h.d.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.381966 q^{2} -1.85410 q^{4} +(0.618034 + 1.07047i) q^{5} +(2.11803 - 3.66854i) q^{7} -1.47214 q^{8} +O(q^{10})$	\(q+0.381966 q^{2} -1.85410 q^{4} +(0.618034 + 1.07047i) q^{5} +(2.11803 - 3.66854i) q^{7} -1.47214 q^{8} +(0.236068 + 0.408882i) q^{10} +3.61803 q^{11} +(-0.690983 + 1.19682i) q^{13} +(0.809017 - 1.40126i) q^{14} +3.14590 q^{16} +(3.04508 - 5.27424i) q^{17} +(0.618034 + 1.07047i) q^{19} +(-1.14590 - 1.98475i) q^{20} +1.38197 q^{22} +(2.19098 + 3.79489i) q^{23} +(1.73607 - 3.00696i) q^{25} +(-0.263932 + 0.457144i) q^{26} +(-3.92705 + 6.80185i) q^{28} +(1.50000 - 2.59808i) q^{29} +4.14590 q^{32} +(1.16312 - 2.01458i) q^{34} +5.23607 q^{35} +(2.42705 + 4.20378i) q^{37} +(0.236068 + 0.408882i) q^{38} +(-0.909830 - 1.57587i) q^{40} -9.47214 q^{41} +(-6.50000 - 0.866025i) q^{43} -6.70820 q^{44} +(0.836881 + 1.44952i) q^{46} -1.14590 q^{47} +(-5.47214 - 9.47802i) q^{49} +(0.663119 - 1.14856i) q^{50} +(1.28115 - 2.21902i) q^{52} +(-0.690983 - 1.19682i) q^{53} +(2.23607 + 3.87298i) q^{55} +(-3.11803 + 5.40059i) q^{56} +(0.572949 - 0.992377i) q^{58} -5.09017 q^{59} +(-1.42705 + 2.47172i) q^{61} -4.70820 q^{64} -1.70820 q^{65} +(1.92705 + 3.33775i) q^{67} +(-5.64590 + 9.77898i) q^{68} +2.00000 q^{70} +(-5.39919 + 9.35167i) q^{71} +(-0.927051 + 1.60570i) q^{73} +(0.927051 + 1.60570i) q^{74} +(-1.14590 - 1.98475i) q^{76} +(7.66312 - 13.2729i) q^{77} +(0.690983 - 1.19682i) q^{79} +(1.94427 + 3.36758i) q^{80} -3.61803 q^{82} +(8.01722 + 13.8862i) q^{83} +7.52786 q^{85} +(-2.48278 - 0.330792i) q^{86} -5.32624 q^{88} +(-0.927051 - 1.60570i) q^{89} +(2.92705 + 5.06980i) q^{91} +(-4.06231 - 7.03612i) q^{92} -0.437694 q^{94} +(-0.763932 + 1.32317i) q^{95} -9.23607 q^{97} +(-2.09017 - 3.62028i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8	$ 4 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8} - 8 q^{10} + 10 q^{11} - 5 q^{13} + q^{14} + 26 q^{16} + q^{17} - 2 q^{19} - 18 q^{20} + 10 q^{22} + 11 q^{23} - 2 q^{25} - 10 q^{26} - 9 q^{28} + 6 q^{29} + 30 q^{32} - 11 q^{34} + 12 q^{35} + 3 q^{37} - 8 q^{38} - 26 q^{40} - 20 q^{41} - 26 q^{43} + 19 q^{46} - 18 q^{47} - 4 q^{49} - 13 q^{50} - 15 q^{52} - 5 q^{53} - 8 q^{56} + 9 q^{58} + 2 q^{59} + q^{61} + 8 q^{64} + 20 q^{65} + q^{67} - 36 q^{68} + 8 q^{70} + 3 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{76} + 15 q^{77} + 5 q^{79} - 28 q^{80} - 10 q^{82} + 3 q^{83} + 48 q^{85} - 39 q^{86} + 10 q^{88} + 3 q^{89} + 5 q^{91} + 24 q^{92} - 42 q^{94} - 12 q^{95} - 28 q^{97} + 14 q^{98}+O(q^{100}) $ 4 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8 - 8 * q^10 + 10 * q^11 - 5 * q^13 + q^14 + 26 * q^16 + q^17 - 2 * q^19 - 18 * q^20 + 10 * q^22 + 11 * q^23 - 2 * q^25 - 10 * q^26 - 9 * q^28 + 6 * q^29 + 30 * q^32 - 11 * q^34 + 12 * q^35 + 3 * q^37 - 8 * q^38 - 26 * q^40 - 20 * q^41 - 26 * q^43 + 19 * q^46 - 18 * q^47 - 4 * q^49 - 13 * q^50 - 15 * q^52 - 5 * q^53 - 8 * q^56 + 9 * q^58 + 2 * q^59 + q^61 + 8 * q^64 + 20 * q^65 + q^67 - 36 * q^68 + 8 * q^70 + 3 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^76 + 15 * q^77 + 5 * q^79 - 28 * q^80 - 10 * q^82 + 3 * q^83 + 48 * q^85 - 39 * q^86 + 10 * q^88 + 3 * q^89 + 5 * q^91 + 24 * q^92 - 42 * q^94 - 12 * q^95 - 28 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.381966			0.270091			0.135045	−	0.990839i	$-0.456882\pi$
$2$	0.381966			0.270091			0.135045	+	0.990839i	$0.456882\pi$
$3$		0			0
$3$		0			0
$4$	−1.85410			−0.927051
$5$	0.618034	+	1.07047i	0.276393	+	0.478727i	0.970486	−	0.241159i	$-0.0775275\pi$
$5$	0.618034	+	1.07047i	0.276393	+	0.478727i	−0.694092	+	0.719886i	$0.744194\pi$
$6$		0			0
$7$	2.11803	−	3.66854i	0.800542	−	1.38658i	−0.118718	−	0.992928i	$-0.537879\pi$
$7$	2.11803	−	3.66854i	0.800542	−	1.38658i	0.919260	−	0.393651i	$-0.128788\pi$
$8$	−1.47214			−0.520479
$9$		0			0
$10$	0.236068	+	0.408882i	0.0746512	+	0.129300i
$11$	3.61803			1.09088			0.545439	−	0.838150i	$-0.316363\pi$
$11$	3.61803			1.09088			0.545439	+	0.838150i	$0.316363\pi$
$12$		0			0
$13$	−0.690983	+	1.19682i	−0.191644	+	0.331937i	−0.945795	−	0.324763i	$-0.894715\pi$
$13$	−0.690983	+	1.19682i	−0.191644	+	0.331937i	0.754151	+	0.656701i	$0.228049\pi$
$14$	0.809017	−	1.40126i	0.216219	−	0.374502i
$15$		0			0
$16$	3.14590			0.786475
$17$	3.04508	−	5.27424i	0.738542	−	1.27919i	−0.214610	−	0.976700i	$-0.568848\pi$
$17$	3.04508	−	5.27424i	0.738542	−	1.27919i	0.953152	−	0.302492i	$-0.0978185\pi$
$18$		0			0
$19$	0.618034	+	1.07047i	0.141787	+	0.245582i	0.928170	−	0.372158i	$-0.121382\pi$
$19$	0.618034	+	1.07047i	0.141787	+	0.245582i	−0.786383	+	0.617740i	$0.788049\pi$
$20$	−1.14590	−	1.98475i	−0.256231	−	0.443804i
$21$		0			0
$22$	1.38197			0.294636
$23$	2.19098	+	3.79489i	0.456852	+	0.791290i	0.998793	−	0.0491264i	$-0.0156437\pi$
$23$	2.19098	+	3.79489i	0.456852	+	0.791290i	−0.541941	+	0.840417i	$0.682310\pi$
$24$		0			0
$25$	1.73607	−	3.00696i	0.347214	−	0.601392i
$26$	−0.263932	+	0.457144i	−0.0517613	+	0.0896533i
$27$		0			0
$28$	−3.92705	+	6.80185i	−0.742143	+	1.28543i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	4.14590			0.732898
$33$		0			0
$34$	1.16312	−	2.01458i	0.199473	−	0.345498i
$35$	5.23607			0.885057
$36$		0			0
$37$	2.42705	+	4.20378i	0.399005	+	0.691096i	0.993603	−	0.112926i	$-0.0360224\pi$
$37$	2.42705	+	4.20378i	0.399005	+	0.691096i	−0.594599	+	0.804023i	$0.702689\pi$
$38$	0.236068	+	0.408882i	0.0382953	+	0.0663294i
$39$		0			0
$40$	−0.909830	−	1.57587i	−0.143857	−	0.249167i
$41$	−9.47214			−1.47930			−0.739650	−	0.672992i	$-0.765009\pi$
$41$	−9.47214			−1.47930			−0.739650	+	0.672992i	$0.765009\pi$
$42$		0			0
$43$	−6.50000	−	0.866025i	−0.991241	−	0.132068i
$43$	−6.50000	−	0.866025i	−0.991241	−	0.132068i
$44$	−6.70820			−1.01130
$45$		0			0
$46$	0.836881	+	1.44952i	0.123391	+	0.213720i
$47$	−1.14590			−0.167146			−0.0835732	−	0.996502i	$-0.526633\pi$
$47$	−1.14590			−0.167146			−0.0835732	+	0.996502i	$0.526633\pi$
$48$		0			0
$49$	−5.47214	−	9.47802i	−0.781734	−	1.35400i
$50$	0.663119	−	1.14856i	0.0937792	−	0.162430i
$51$		0			0
$52$	1.28115	−	2.21902i	0.177664	−	0.307723i
$53$	−0.690983	−	1.19682i	−0.0949138	−	0.164396i	0.814659	−	0.579941i	$-0.196924\pi$
$53$	−0.690983	−	1.19682i	−0.0949138	−	0.164396i	−0.909573	+	0.415545i	$0.863591\pi$
$54$		0			0
$55$	2.23607	+	3.87298i	0.301511	+	0.522233i
$56$	−3.11803	+	5.40059i	−0.416665	+	0.721685i
$57$		0			0
$58$	0.572949	−	0.992377i	0.0752319	−	0.130305i
$59$	−5.09017			−0.662684			−0.331342	−	0.943511i	$-0.607501\pi$
$59$	−5.09017			−0.662684			−0.331342	+	0.943511i	$0.607501\pi$
$60$		0			0
$61$	−1.42705	+	2.47172i	−0.182715	+	0.316472i	−0.942804	−	0.333347i	$-0.891822\pi$
$61$	−1.42705	+	2.47172i	−0.182715	+	0.316472i	0.760089	+	0.649819i	$0.225155\pi$
$62$		0			0
$63$		0			0
$64$	−4.70820			−0.588525
$65$	−1.70820			−0.211877
$66$		0			0
$67$	1.92705	+	3.33775i	0.235427	+	0.407771i	0.959397	−	0.282061i	$-0.0910179\pi$
$67$	1.92705	+	3.33775i	0.235427	+	0.407771i	−0.723970	+	0.689832i	$0.757685\pi$
$68$	−5.64590	+	9.77898i	−0.684666	+	1.18588i
$69$		0			0
$70$	2.00000			0.239046
$71$	−5.39919	+	9.35167i	−0.640766	+	1.10984i	0.344497	+	0.938788i	$0.388050\pi$
$71$	−5.39919	+	9.35167i	−0.640766	+	1.10984i	−0.985262	+	0.171051i	$0.945284\pi$
$72$		0			0
$73$	−0.927051	+	1.60570i	−0.108503	+	0.187933i	−0.915164	−	0.403082i	$-0.867939\pi$
$73$	−0.927051	+	1.60570i	−0.108503	+	0.187933i	0.806661	+	0.591015i	$0.201272\pi$
$74$	0.927051	+	1.60570i	0.107767	+	0.186659i
$75$		0			0
$76$	−1.14590	−	1.98475i	−0.131444	−	0.227667i
$77$	7.66312	−	13.2729i	0.873293	−	1.51259i
$78$		0			0
$79$	0.690983	−	1.19682i	0.0777417	−	0.134653i	−0.824534	−	0.565813i	$-0.808562\pi$
$79$	0.690983	−	1.19682i	0.0777417	−	0.134653i	0.902275	+	0.431161i	$0.141896\pi$
$80$	1.94427	+	3.36758i	0.217376	+	0.376507i
$81$		0			0
$82$	−3.61803			−0.399545
$83$	8.01722	+	13.8862i	0.880004	+	1.52421i	0.851335	+	0.524623i	$0.175794\pi$
$83$	8.01722	+	13.8862i	0.880004	+	1.52421i	0.0286698	+	0.999589i	$0.490873\pi$
$84$		0			0
$85$	7.52786			0.816511
$86$	−2.48278	−	0.330792i	−0.267725	−	0.0356702i
$87$		0			0
$88$	−5.32624			−0.567779
$89$	−0.927051	−	1.60570i	−0.0982672	−	0.170204i	0.812700	−	0.582682i	$-0.197997\pi$
$89$	−0.927051	−	1.60570i	−0.0982672	−	0.170204i	−0.910968	+	0.412478i	$0.864663\pi$
$90$		0			0
$91$	2.92705	+	5.06980i	0.306838	+	0.531460i
$92$	−4.06231	−	7.03612i	−0.423525	−	0.733566i
$93$		0			0
$94$	−0.437694			−0.0451447
$95$	−0.763932	+	1.32317i	−0.0783778	+	0.135754i
$96$		0			0
$97$	−9.23607			−0.937781			−0.468890	−	0.883256i	$-0.655346\pi$
$97$	−9.23607			−0.937781			−0.468890	+	0.883256i	$0.655346\pi$
$98$	−2.09017	−	3.62028i	−0.211139	−	0.365704i
$99$		0			0
$100$	−3.21885	+	5.57521i	−0.321885	+	0.557521i
$101$	1.88197	−	3.25966i	0.187263	−	0.324348i	−0.757074	−	0.653329i	$-0.773372\pi$
$101$	1.88197	−	3.25966i	0.187263	−	0.324348i	0.944337	+	0.328981i	$0.106705\pi$
$102$		0			0
$103$	8.20820	−	14.2170i	0.808778	−	1.40085i	−0.104932	−	0.994479i	$-0.533463\pi$
$103$	8.20820	−	14.2170i	0.808778	−	1.40085i	0.913710	−	0.406366i	$-0.133204\pi$
$104$	1.01722	−	1.76188i	0.0997467	−	0.172766i
$105$		0			0
$106$	−0.263932	−	0.457144i	−0.0256353	−	0.0444017i
$107$	−7.52786			−0.727746			−0.363873	−	0.931449i	$-0.618546\pi$
$107$	−7.52786			−0.727746			−0.363873	+	0.931449i	$0.618546\pi$
$108$		0			0
$109$	6.92705	+	11.9980i	0.663491	+	1.14920i	0.979692	+	0.200508i	$0.0642593\pi$
$109$	6.92705	+	11.9980i	0.663491	+	1.14920i	−0.316201	+	0.948692i	$0.602407\pi$
$110$	0.854102	+	1.47935i	0.0814354	+	0.141050i
$111$		0			0
$112$	6.66312	−	11.5409i	0.629606	−	1.09051i
$113$	15.6180			1.46922			0.734611	−	0.678489i	$-0.237365\pi$
$113$	15.6180			1.46922			0.734611	+	0.678489i	$0.237365\pi$
$114$		0			0
$115$	−2.70820	+	4.69075i	−0.252541	+	0.437414i
$116$	−2.78115	+	4.81710i	−0.258224	+	0.447256i
$117$		0			0
$118$	−1.94427			−0.178985
$119$	−12.8992	−	22.3420i	−1.18247	−	2.04809i
$120$		0			0
$121$	2.09017			0.190015
$122$	−0.545085	+	0.944115i	−0.0493497	+	0.0854761i
$123$		0			0
$124$		0			0
$125$	10.4721			0.936656
$126$		0			0
$127$	−14.6525			−1.30020			−0.650098	−	0.759850i	$-0.725272\pi$
$127$	−14.6525			−1.30020			−0.650098	+	0.759850i	$0.725272\pi$
$128$	−10.0902			−0.891853
$129$		0			0
$130$	−0.652476			−0.0572259
$131$	−9.94427			−0.868835			−0.434418	−	0.900712i	$-0.643046\pi$
$131$	−9.94427			−0.868835			−0.434418	+	0.900712i	$0.643046\pi$
$132$		0			0
$133$	5.23607			0.454025
$134$	0.736068	+	1.27491i	0.0635866	+	0.110135i
$135$		0			0
$136$	−4.48278	+	7.76440i	−0.384395	+	0.665792i
$137$	−3.70820			−0.316813			−0.158407	−	0.987374i	$-0.550636\pi$
$137$	−3.70820			−0.316813			−0.158407	+	0.987374i	$0.550636\pi$
$138$		0			0
$139$	2.64590	+	4.58283i	0.224422	+	0.388711i	0.956146	−	0.292891i	$-0.0946172\pi$
$139$	2.64590	+	4.58283i	0.224422	+	0.388711i	−0.731724	+	0.681601i	$0.761284\pi$
$140$	−9.70820			−0.820493
$141$		0			0
$142$	−2.06231	+	3.57202i	−0.173065	+	0.299757i
$143$	−2.50000	+	4.33013i	−0.209061	+	0.362103i
$144$		0			0
$145$	3.70820			0.307950
$146$	−0.354102	+	0.613323i	−0.0293057	+	0.0507589i
$147$		0			0
$148$	−4.50000	−	7.79423i	−0.369898	−	0.640682i
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$		0			0
$151$	−8.85410			−0.720537			−0.360268	−	0.932849i	$-0.617315\pi$
$151$	−8.85410			−0.720537			−0.360268	+	0.932849i	$0.617315\pi$
$152$	−0.909830	−	1.57587i	−0.0737970	−	0.127820i
$153$		0			0
$154$	2.92705	−	5.06980i	0.235868	−	0.408536i
$155$		0			0
$156$		0			0
$157$	2.57295	−	4.45648i	0.205344	−	0.355666i	−0.744898	−	0.667178i	$-0.767502\pi$
$157$	2.57295	−	4.45648i	0.205344	−	0.355666i	0.950242	+	0.311512i	$0.100835\pi$
$158$	0.263932	−	0.457144i	0.0209973	−	0.0363684i
$159$		0			0
$160$	2.56231	+	4.43804i	0.202568	+	0.350858i
$161$	18.5623			1.46291
$162$		0			0
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	0.450110	+	0.892973i	$0.351385\pi$
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	−0.998392	+	0.0566798i	$0.981949\pi$
$164$	17.5623			1.37139
$165$		0			0
$166$	3.06231	+	5.30407i	0.237681	+	0.411676i
$167$	7.11803	+	12.3288i	0.550810	+	0.954031i	0.998216	+	0.0597001i	$0.0190144\pi$
$167$	7.11803	+	12.3288i	0.550810	+	0.954031i	−0.447406	+	0.894331i	$0.647652\pi$
$168$		0			0
$169$	5.54508	+	9.60437i	0.426545	+	0.738798i
$170$	2.87539			0.220532
$171$		0			0
$172$	12.0517	+	1.60570i	0.918931	+	0.122433i
$173$	3.76393			0.286166			0.143083	−	0.989711i	$-0.454298\pi$
$173$	3.76393			0.286166			0.143083	+	0.989711i	$0.454298\pi$
$174$		0			0
$175$	−7.35410	−	12.7377i	−0.555918	−	0.962878i
$176$	11.3820			0.857948
$177$		0			0
$178$	−0.354102	−	0.613323i	−0.0265411	−	0.0459705i
$179$	4.82624	−	8.35929i	0.360730	−	0.624803i	−0.627351	−	0.778736i	$-0.715861\pi$
$179$	4.82624	−	8.35929i	0.360730	−	0.624803i	0.988081	+	0.153934i	$0.0491943\pi$
$180$		0			0
$181$	9.69098	−	16.7853i	0.720325	−	1.24764i	−0.240544	−	0.970638i	$-0.577326\pi$
$181$	9.69098	−	16.7853i	0.720325	−	1.24764i	0.960869	−	0.277002i	$-0.0893407\pi$
$182$	1.11803	+	1.93649i	0.0828742	+	0.143542i
$183$		0			0
$184$	−3.22542	−	5.58660i	−0.237781	−	0.411850i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$	11.0172	−	19.0824i	0.805659	−	1.39544i
$188$	2.12461			0.154953
$189$		0			0
$190$	−0.291796	+	0.505406i	−0.0211691	+	0.0366660i
$191$	−7.26393	−	12.5815i	−0.525600	−	0.910365i	−0.999555	−	0.0298167i	$-0.990508\pi$
$191$	−7.26393	−	12.5815i	−0.525600	−	0.910365i	0.473956	−	0.880549i	$-0.342826\pi$
$192$		0			0
$193$	2.70820			0.194941			0.0974704	−	0.995238i	$-0.468925\pi$
$193$	2.70820			0.194941			0.0974704	+	0.995238i	$0.468925\pi$
$194$	−3.52786			−0.253286
$195$		0			0
$196$	10.1459	+	17.5732i	0.724707	+	1.25523i
$197$	−1.47214	+	2.54981i	−0.104885	+	0.181667i	−0.913691	−	0.406409i	$-0.866781\pi$
$197$	−1.47214	+	2.54981i	−0.104885	+	0.181667i	0.808806	+	0.588076i	$0.200114\pi$
$198$		0			0
$199$	1.94427			0.137826			0.0689129	−	0.997623i	$-0.478047\pi$
$199$	1.94427			0.137826			0.0689129	+	0.997623i	$0.478047\pi$
$200$	−2.55573	+	4.42665i	−0.180717	+	0.313011i
$201$		0			0
$202$	0.718847	−	1.24508i	0.0505779	−	0.0876035i
$203$	−6.35410	−	11.0056i	−0.445971	−	0.772444i
$204$		0			0
$205$	−5.85410	−	10.1396i	−0.408868	−	0.708181i
$206$	3.13525	−	5.43042i	0.218444	−	0.378355i
$207$		0			0
$208$	−2.17376	+	3.76507i	−0.150723	+	0.261060i
$209$	2.23607	+	3.87298i	0.154672	+	0.267900i
$210$		0			0
$211$	−9.23607			−0.635837			−0.317919	−	0.948118i	$-0.602984\pi$
$211$	−9.23607			−0.635837			−0.317919	+	0.948118i	$0.602984\pi$
$212$	1.28115	+	2.21902i	0.0879899	+	0.152403i
$213$		0			0
$214$	−2.87539			−0.196557
$215$	−3.09017	−	7.49326i	−0.210748	−	0.511036i
$216$		0			0
$217$		0			0
$218$	2.64590	+	4.58283i	0.179203	+	0.310388i
$219$		0			0
$220$	−4.14590	−	7.18091i	−0.279516	−	0.484137i
$221$	4.20820	+	7.28882i	0.283074	+	0.490299i
$222$		0			0
$223$	2.76393			0.185087			0.0925433	−	0.995709i	$-0.470500\pi$
$223$	2.76393			0.185087			0.0925433	+	0.995709i	$0.470500\pi$
$224$	8.78115	−	15.2094i	0.586715	−	1.01622i
$225$		0			0
$226$	5.96556			0.396823
$227$	−0.736068	−	1.27491i	−0.0488545	−	0.0846186i	0.840564	−	0.541712i	$-0.182224\pi$
$227$	−0.736068	−	1.27491i	−0.0488545	−	0.0846186i	−0.889419	+	0.457094i	$0.848890\pi$
$228$		0			0
$229$	1.14590	−	1.98475i	0.0757231	−	0.131156i	−0.825677	−	0.564143i	$-0.809207\pi$
$229$	1.14590	−	1.98475i	0.0757231	−	0.131156i	0.901400	+	0.432986i	$0.142540\pi$
$230$	−1.03444	+	1.79171i	−0.0682091	+	0.118142i
$231$		0			0
$232$	−2.20820	+	3.82472i	−0.144976	+	0.251105i
$233$	9.01722	−	15.6183i	0.590738	−	1.02319i	−0.403395	−	0.915026i	$-0.632170\pi$
$233$	9.01722	−	15.6183i	0.590738	−	1.02319i	0.994133	−	0.108162i	$-0.0344966\pi$
$234$		0			0
$235$	−0.708204	−	1.22665i	−0.0461981	−	0.0800175i
$236$	9.43769			0.614342
$237$		0			0
$238$	−4.92705	−	8.53390i	−0.319373	−	0.553171i
$239$	−4.14590	−	7.18091i	−0.268176	−	0.464494i	0.700215	−	0.713932i	$-0.253087\pi$
$239$	−4.14590	−	7.18091i	−0.268176	−	0.464494i	−0.968391	+	0.249438i	$0.919754\pi$
$240$		0			0
$241$	−2.13525	+	3.69837i	−0.137544	+	0.238233i	−0.926566	−	0.376131i	$-0.877254\pi$
$241$	−2.13525	+	3.69837i	−0.137544	+	0.238233i	0.789022	+	0.614364i	$0.210587\pi$
$242$	0.798374			0.0513214
$243$		0			0
$244$	2.64590	−	4.58283i	0.169386	−	0.293386i
$245$	6.76393	−	11.7155i	0.432132	−	0.748474i
$246$		0			0
$247$	−1.70820			−0.108690
$248$		0			0
$249$		0			0
$250$	4.00000			0.252982
$251$	−14.5902	+	25.2709i	−0.920923	+	1.59509i	−0.122934	+	0.992415i	$0.539230\pi$
$251$	−14.5902	+	25.2709i	−0.920923	+	1.59509i	−0.797990	+	0.602671i	$0.794103\pi$
$252$		0			0
$253$	7.92705	+	13.7301i	0.498369	+	0.863201i
$254$	−5.59675			−0.351171
$255$		0			0
$256$	5.56231			0.347644
$257$	−3.43769			−0.214437			−0.107219	−	0.994235i	$-0.534195\pi$
$257$	−3.43769			−0.214437			−0.107219	+	0.994235i	$0.534195\pi$
$258$		0			0
$259$	20.5623			1.27768
$260$	3.16718			0.196420
$261$		0			0
$262$	−3.79837			−0.234664
$263$	13.7533	+	23.8214i	0.848064	+	1.46889i	0.882933	+	0.469498i	$0.155565\pi$
$263$	13.7533	+	23.8214i	0.848064	+	1.46889i	−0.0348693	+	0.999392i	$0.511101\pi$
$264$		0			0
$265$	0.854102	−	1.47935i	0.0524671	−	0.0908756i
$266$	2.00000			0.122628
$267$		0			0
$268$	−3.57295	−	6.18853i	−0.218253	−	0.378025i
$269$	−11.5623			−0.704966			−0.352483	−	0.935818i	$-0.614663\pi$
$269$	−11.5623			−0.704966			−0.352483	+	0.935818i	$0.614663\pi$
$270$		0			0
$271$	−6.92705	+	11.9980i	−0.420788	+	0.728827i	−0.996017	−	0.0891660i	$-0.971580\pi$
$271$	−6.92705	+	11.9980i	−0.420788	+	0.728827i	0.575228	+	0.817993i	$0.304913\pi$
$272$	9.57953	−	16.5922i	0.580844	−	1.00605i
$273$		0			0
$274$	−1.41641			−0.0855683
$275$	6.28115	−	10.8793i	0.378768	−	0.656045i
$276$		0			0
$277$	6.23607	+	10.8012i	0.374689	+	0.648980i	0.990280	−	0.139085i	$-0.0444161\pi$
$277$	6.23607	+	10.8012i	0.374689	+	0.648980i	−0.615591	+	0.788065i	$0.711083\pi$
$278$	1.01064	+	1.75049i	0.0606143	+	0.104987i
$279$		0			0
$280$	−7.70820			−0.460653
$281$	3.73607	+	6.47106i	0.222875	+	0.386031i	0.955680	−	0.294408i	$-0.0951224\pi$
$281$	3.73607	+	6.47106i	0.222875	+	0.386031i	−0.732805	+	0.680439i	$0.761789\pi$
$282$		0			0
$283$	−5.38197	+	9.32184i	−0.319925	+	0.554126i	−0.980472	−	0.196659i	$-0.936991\pi$
$283$	−5.38197	+	9.32184i	−0.319925	+	0.554126i	0.660547	+	0.750784i	$0.270324\pi$
$284$	10.0106	−	17.3389i	0.594022	−	1.02888i
$285$		0			0
$286$	−0.954915	+	1.65396i	−0.0564653	+	0.0978008i
$287$	−20.0623	+	34.7489i	−1.18424	+	2.05116i
$288$		0			0
$289$	−10.0451	−	17.3986i	−0.590887	−	1.02345i
$290$	1.41641			0.0831743
$291$		0			0
$292$	1.71885	−	2.97713i	0.100588	−	0.174223i
$293$	12.0902			0.706315			0.353158	−	0.935564i	$-0.385108\pi$
$293$	12.0902			0.706315			0.353158	+	0.935564i	$0.385108\pi$
$294$		0			0
$295$	−3.14590	−	5.44886i	−0.183161	−	0.317245i
$296$	−3.57295	−	6.18853i	−0.207673	−	0.359701i
$297$		0			0
$298$	1.71885	+	2.97713i	0.0995701	+	0.172461i
$299$	−6.05573			−0.350212
$300$		0			0
$301$	−16.9443	+	22.0113i	−0.976652	+	1.26871i
$302$	−3.38197			−0.194610
$303$		0			0
$304$	1.94427	+	3.36758i	0.111512	+	0.193144i
$305$	−3.52786			−0.202005
$306$		0			0
$307$	11.6074	+	20.1046i	0.662469	+	1.14743i	0.979965	+	0.199170i	$0.0638246\pi$
$307$	11.6074	+	20.1046i	0.662469	+	1.14743i	−0.317496	+	0.948260i	$0.602842\pi$
$308$	−14.2082	+	24.6093i	−0.809588	+	1.40225i
$309$		0			0
$310$		0			0
$311$	−14.9164	−	25.8360i	−0.845832	−	1.46502i	−0.884897	−	0.465787i	$-0.845771\pi$
$311$	−14.9164	−	25.8360i	−0.845832	−	1.46502i	0.0390649	−	0.999237i	$-0.487562\pi$
$312$		0			0
$313$	−6.56231	−	11.3662i	−0.370923	−	0.642458i	0.618784	−	0.785561i	$-0.287625\pi$
$313$	−6.56231	−	11.3662i	−0.370923	−	0.642458i	−0.989708	+	0.143103i	$0.954292\pi$
$314$	0.982779	−	1.70222i	0.0554614	−	0.0960620i
$315$		0			0
$316$	−1.28115	+	2.21902i	−0.0720705	+	0.124830i
$317$	−33.3050			−1.87059			−0.935296	−	0.353866i	$-0.884867\pi$
$317$	−33.3050			−1.87059			−0.935296	+	0.353866i	$0.884867\pi$
$318$		0			0
$319$	5.42705	−	9.39993i	0.303857	−	0.526295i
$320$	−2.90983	−	5.03997i	−0.162664	−	0.281743i
$321$		0			0
$322$	7.09017			0.395120
$323$	7.52786			0.418862
$324$		0			0
$325$	2.39919	+	4.15551i	0.133083	+	0.230506i
$326$	−2.67376	+	4.63109i	−0.148086	+	0.256492i
$327$		0			0
$328$	13.9443			0.769944
$329$	−2.42705	+	4.20378i	−0.133808	+	0.231762i
$330$		0			0
$331$	2.73607	−	4.73901i	0.150388	−	0.260479i	−0.780982	−	0.624553i	$-0.785281\pi$
$331$	2.73607	−	4.73901i	0.150388	−	0.260479i	0.931370	+	0.364074i	$0.118614\pi$
$332$	−14.8647	−	25.7465i	−0.815809	−	1.41302i
$333$		0			0
$334$	2.71885	+	4.70918i	0.148769	+	0.257675i
$335$	−2.38197	+	4.12569i	−0.130141	+	0.225410i
$336$		0			0
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	0.178863	+	0.983874i	$0.442758\pi$
$337$	−14.0000	+	24.2487i	−0.762629	+	1.32091i	−0.941491	+	0.337037i	$0.890575\pi$
$338$	2.11803	+	3.66854i	0.115206	+	0.199542i
$339$		0			0
$340$	−13.9574			−0.756948
$341$		0			0
$342$		0			0
$343$	−16.7082			−0.902158
$344$	9.56888	+	1.27491i	0.515920	+	0.0687384i
$345$		0			0
$346$	1.43769			0.0772909
$347$	5.04508	+	8.73834i	0.270834	+	0.469099i	0.969076	−	0.246764i	$-0.0793671\pi$
$347$	5.04508	+	8.73834i	0.270834	+	0.469099i	−0.698241	+	0.715862i	$0.746034\pi$
$348$		0			0
$349$	−10.3541	−	17.9338i	−0.554242	−	0.959976i	−0.997962	−	0.0638103i	$-0.979675\pi$
$349$	−10.3541	−	17.9338i	−0.554242	−	0.959976i	0.443720	−	0.896166i	$-0.353659\pi$
$350$	−2.80902	−	4.86536i	−0.150148	−	0.260064i
$351$		0			0
$352$	15.0000			0.799503
$353$	−8.61803	+	14.9269i	−0.458692	+	0.794477i	−0.998892	−	0.0470591i	$-0.985015\pi$
$353$	−8.61803	+	14.9269i	−0.458692	+	0.794477i	0.540200	+	0.841536i	$0.318348\pi$
$354$		0			0
$355$	−13.3475			−0.708413
$356$	1.71885	+	2.97713i	0.0910987	+	0.157788i
$357$		0			0
$358$	1.84346	−	3.19296i	0.0974298	−	0.168753i
$359$	−2.67376	+	4.63109i	−0.141116	+	0.244420i	−0.927917	−	0.372787i	$-0.878402\pi$
$359$	−2.67376	+	4.63109i	−0.141116	+	0.244420i	0.786801	+	0.617206i	$0.211736\pi$
$360$		0			0
$361$	8.73607	−	15.1313i	0.459793	−	0.796385i
$362$	3.70163	−	6.41140i	0.194553	−	0.336976i
$363$		0			0
$364$	−5.42705	−	9.39993i	−0.284455	−	0.492690i
$365$	−2.29180			−0.119958
$366$		0			0
$367$	−9.59017	−	16.6107i	−0.500603	−	0.867069i	−1.00000		0.000696189i	$-0.999778\pi$
$367$	−9.59017	−	16.6107i	−0.500603	−	0.867069i	0.499397	−	0.866373i	$-0.333555\pi$
$368$	6.89261	+	11.9383i	0.359302	+	0.622329i
$369$		0			0
$370$	−1.14590	+	1.98475i	−0.0595724	+	0.103182i
$371$	−5.85410			−0.303930
$372$		0			0
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$	4.20820	−	7.28882i	0.217601	−	0.376896i
$375$		0			0
$376$	1.68692			0.0869961
$377$	2.07295	+	3.59045i	0.106762	+	0.184918i
$378$		0			0
$379$	−27.3607			−1.40542			−0.702712	−	0.711475i	$-0.748028\pi$
$379$	−27.3607			−1.40542			−0.702712	+	0.711475i	$0.748028\pi$
$380$	1.41641	−	2.45329i	0.0726602	−	0.125851i
$381$		0			0
$382$	−2.77458	−	4.80571i	−0.141960	−	0.245881i
$383$	−38.1246			−1.94808			−0.974038	−	0.226383i	$-0.927310\pi$
$383$	−38.1246			−1.94808			−0.974038	+	0.226383i	$0.927310\pi$
$384$		0			0
$385$	18.9443			0.965489
$386$	1.03444			0.0526517
$387$		0			0
$388$	17.1246			0.869370
$389$	35.0689			1.77806			0.889031	−	0.457846i	$-0.151379\pi$
$389$	35.0689			1.77806			0.889031	+	0.457846i	$0.151379\pi$
$390$		0			0
$391$	26.6869			1.34962
$392$	8.05573	+	13.9529i	0.406876	+	0.704729i
$393$		0			0
$394$	−0.562306	+	0.973942i	−0.0283286	+	0.0490665i
$395$	1.70820			0.0859491
$396$		0			0
$397$	−16.2082	−	28.0734i	−0.813466	−	1.40897i	−0.910424	−	0.413677i	$-0.864244\pi$
$397$	−16.2082	−	28.0734i	−0.813466	−	1.40897i	0.0969574	−	0.995289i	$-0.469089\pi$
$398$	0.742646			0.0372255
$399$		0			0
$400$	5.46149	−	9.45958i	0.273075	−	0.472979i
$401$	−12.7082	+	22.0113i	−0.634617	+	1.09919i	0.351979	+	0.936008i	$0.385509\pi$
$401$	−12.7082	+	22.0113i	−0.634617	+	1.09919i	−0.986596	+	0.163182i	$0.947824\pi$
$402$		0			0
$403$		0			0
$404$	−3.48936	+	6.04374i	−0.173602	+	0.300687i
$405$		0			0
$406$	−2.42705	−	4.20378i	−0.120453	−	0.208630i
$407$	8.78115	+	15.2094i	0.435266	+	0.753902i
$408$		0			0
$409$	8.90983			0.440563			0.220281	−	0.975436i	$-0.429302\pi$
$409$	8.90983			0.440563			0.220281	+	0.975436i	$0.429302\pi$
$410$	−2.23607	−	3.87298i	−0.110432	−	0.191273i
$411$		0			0
$412$	−15.2188	+	26.3598i	−0.749779	+	1.29865i
$413$	−10.7812	+	18.6735i	−0.530506	+	0.918863i
$414$		0			0
$415$	−9.90983	+	17.1643i	−0.486454	+	0.842564i
$416$	−2.86475	+	4.96188i	−0.140456	+	0.243276i
$417$		0			0
$418$	0.854102	+	1.47935i	0.0417755	+	0.0723573i
$419$	10.2361			0.500065			0.250032	−	0.968237i	$-0.419559\pi$
$419$	10.2361			0.500065			0.250032	+	0.968237i	$0.419559\pi$
$420$		0			0
$421$	3.82624	−	6.62724i	0.186479	−	0.322992i	−0.757595	−	0.652725i	$-0.773626\pi$
$421$	3.82624	−	6.62724i	0.186479	−	0.322992i	0.944074	+	0.329734i	$0.106959\pi$
$422$	−3.52786			−0.171734
$423$		0			0
$424$	1.01722	+	1.76188i	0.0494006	+	0.0855644i
$425$	−10.5729	−	18.3129i	−0.512863	−	0.888305i
$426$		0			0
$427$	6.04508	+	10.4704i	0.292542	+	0.506698i
$428$	13.9574			0.674658
$429$		0			0
$430$	−1.18034	−	2.86217i	−0.0569210	−	0.138026i
$431$	24.7984			1.19450			0.597248	−	0.802057i	$-0.296261\pi$
$431$	24.7984			1.19450			0.597248	+	0.802057i	$0.296261\pi$
$432$		0			0
$433$	17.3541	+	30.0582i	0.833985	+	1.44450i	0.894854	+	0.446359i	$0.147279\pi$
$433$	17.3541	+	30.0582i	0.833985	+	1.44450i	−0.0608693	+	0.998146i	$0.519387\pi$
$434$		0			0
$435$		0			0
$436$	−12.8435	−	22.2455i	−0.615090	−	1.06537i
$437$	−2.70820	+	4.69075i	−0.129551	+	0.224389i
$438$		0			0
$439$	−0.572949	+	0.992377i	−0.0273454	+	0.0473636i	−0.879374	−	0.476131i	$-0.842039\pi$
$439$	−0.572949	+	0.992377i	−0.0273454	+	0.0473636i	0.852029	+	0.523495i	$0.175372\pi$
$440$	−3.29180	−	5.70156i	−0.156930	−	0.271811i
$441$		0			0
$442$	1.60739	+	2.78408i	0.0764558	+	0.132425i
$443$	1.23607	−	2.14093i	0.0587274	−	0.101719i	−0.835167	−	0.549996i	$-0.814629\pi$
$443$	1.23607	−	2.14093i	0.0587274	−	0.101719i	0.893894	+	0.448278i	$0.147962\pi$
$444$		0			0
$445$	1.14590	−	1.98475i	0.0543208	−	0.0940863i
$446$	1.05573			0.0499902
$447$		0			0
$448$	−9.97214	+	17.2722i	−0.471139	+	0.816037i
$449$	−16.4164	−	28.4341i	−0.774738	−	1.34189i	−0.934942	−	0.354802i	$-0.884548\pi$
$449$	−16.4164	−	28.4341i	−0.774738	−	1.34189i	0.160203	−	0.987084i	$-0.448785\pi$
$450$		0			0
$451$	−34.2705			−1.61374
$452$	−28.9574			−1.36204
$453$		0			0
$454$	−0.281153	−	0.486971i	−0.0131952	−	0.0228547i
$455$	−3.61803	+	6.26662i	−0.169616	+	0.293784i
$456$		0			0
$457$	−15.7082			−0.734799			−0.367399	−	0.930063i	$-0.619752\pi$
$457$	−15.7082			−0.734799			−0.367399	+	0.930063i	$0.619752\pi$
$458$	0.437694	−	0.758108i	0.0204521	−	0.0354241i
$459$		0			0
$460$	5.02129	−	8.69712i	0.234119	−	0.405505i
$461$	−15.7984	−	27.3636i	−0.735804	−	1.27445i	−0.954370	−	0.298627i	$-0.903471\pi$
$461$	−15.7984	−	27.3636i	−0.735804	−	1.27445i	0.218566	−	0.975822i	$-0.429862\pi$
$462$		0			0
$463$	14.9164	+	25.8360i	0.693224	+	1.20070i	0.970776	+	0.239989i	$0.0771438\pi$
$463$	14.9164	+	25.8360i	0.693224	+	1.20070i	−0.277551	+	0.960711i	$0.589523\pi$
$464$	4.71885	−	8.17328i	0.219067	−	0.379435i
$465$		0			0
$466$	3.44427	−	5.96565i	0.159553	−	0.276354i
$467$	−7.52786	−	13.0386i	−0.348348	−	0.603356i	0.637608	−	0.770361i	$-0.279924\pi$
$467$	−7.52786	−	13.0386i	−0.348348	−	0.603356i	−0.985956	+	0.167004i	$0.946591\pi$
$468$		0			0
$469$	16.3262			0.753876
$470$	−0.270510	−	0.468537i	−0.0124777	−	0.0216120i
$471$		0			0
$472$	7.49342			0.344913
$473$	−23.5172	−	3.13331i	−1.08132	−	0.144070i
$474$		0			0
$475$	4.29180			0.196921
$476$	23.9164	+	41.4244i	1.09621	+	1.89869i
$477$		0			0
$478$	−1.58359	−	2.74286i	−0.0724318	−	0.125456i
$479$	−6.90983	−	11.9682i	−0.315718	−	0.546840i	0.663872	−	0.747846i	$-0.268912\pi$
$479$	−6.90983	−	11.9682i	−0.315718	−	0.546840i	−0.979590	+	0.201007i	$0.935579\pi$
$480$		0			0
$481$	−6.70820			−0.305868
$482$	−0.815595	+	1.41265i	−0.0371493	+	0.0643445i
$483$		0			0
$484$	−3.87539			−0.176154
$485$	−5.70820	−	9.88690i	−0.259196	−	0.448941i
$486$		0			0
$487$	−0.663119	+	1.14856i	−0.0300488	+	0.0520460i	−0.880659	−	0.473751i	$-0.842900\pi$
$487$	−0.663119	+	1.14856i	−0.0300488	+	0.0520460i	0.850610	+	0.525797i	$0.176233\pi$
$488$	2.10081	−	3.63871i	0.0950993	−	0.164717i
$489$		0			0
$490$	2.58359	−	4.47491i	0.116715	−	0.202156i
$491$	10.8262	−	18.7516i	0.488581	−	0.846248i	−0.511332	−	0.859383i	$-0.670848\pi$
$491$	10.8262	−	18.7516i	0.488581	−	0.846248i	0.999914	+	0.0131354i	$0.00418125\pi$
$492$		0			0
$493$	−9.13525	−	15.8227i	−0.411431	−	0.712620i
$494$	−0.652476			−0.0293563
$495$		0			0
$496$		0			0
$497$	22.8713	+	39.6143i	1.02592	+	1.77694i
$498$		0			0
$499$	−6.92705	+	11.9980i	−0.310097	+	0.537104i	−0.978383	−	0.206800i	$-0.933695\pi$
$499$	−6.92705	+	11.9980i	−0.310097	+	0.537104i	0.668286	+	0.743905i	$0.267028\pi$
$500$	−19.4164			−0.868328
$501$		0			0
$502$	−5.57295	+	9.65263i	−0.248733	+	0.430818i
$503$	−6.73607	+	11.6672i	−0.300346	+	0.520215i	−0.976214	−	0.216807i	$-0.930436\pi$
$503$	−6.73607	+	11.6672i	−0.300346	+	0.520215i	0.675868	+	0.737023i	$0.263769\pi$
$504$		0			0
$505$	4.65248			0.207032
$506$	3.02786	+	5.24441i	0.134605	+	0.233143i
$507$		0			0
$508$	27.1672			1.20535
$509$	9.35410	−	16.2018i	0.414613	−	0.718131i	−0.580774	−	0.814064i	$-0.697250\pi$
$509$	9.35410	−	16.2018i	0.414613	−	0.718131i	0.995388	+	0.0959332i	$0.0305835\pi$
$510$		0			0
$511$	3.92705	+	6.80185i	0.173723	+	0.300896i
$512$	22.3050			0.985749
$513$		0			0
$514$	−1.31308			−0.0579176
$515$	20.2918			0.894163
$516$		0			0
$517$	−4.14590			−0.182336
$518$	7.85410			0.345089
$519$		0			0
$520$	2.51471			0.110277
$521$	−11.0172	−	19.0824i	−0.482673	−	0.836015i	0.517129	−	0.855908i	$-0.327001\pi$
$521$	−11.0172	−	19.0824i	−0.482673	−	0.836015i	−0.999802	+	0.0198930i	$0.993667\pi$
$522$		0			0
$523$	−17.9164	+	31.0321i	−0.783430	+	1.35694i	0.146503	+	0.989210i	$0.453198\pi$
$523$	−17.9164	+	31.0321i	−0.783430	+	1.35694i	−0.929933	+	0.367730i	$0.880135\pi$
$524$	18.4377			0.805454
$525$		0			0
$526$	5.25329	+	9.09896i	0.229054	+	0.396734i
$527$		0			0
$528$		0			0
$529$	1.89919	−	3.28949i	0.0825733	−	0.143021i
$530$	0.326238	−	0.565061i	0.0141709	−	0.0245447i
$531$		0			0
$532$	−9.70820			−0.420904
$533$	6.54508	−	11.3364i	0.283499	−	0.491035i
$534$		0			0
$535$	−4.65248	−	8.05832i	−0.201144	−	0.348392i
$536$	−2.83688	−	4.91362i	−0.122535	−	0.212236i
$537$		0			0
$538$	−4.41641			−0.190405
$539$	−19.7984	−	34.2918i	−0.852776	−	1.47705i
$540$		0			0
$541$	18.9721	−	32.8607i	0.815676	−	1.41279i	−0.0931658	−	0.995651i	$-0.529699\pi$
$541$	18.9721	−	32.8607i	0.815676	−	1.41279i	0.908842	−	0.417141i	$-0.136968\pi$
$542$	−2.64590	+	4.58283i	−0.113651	+	0.196849i
$543$		0			0
$544$	12.6246	−	21.8665i	0.541276	−	0.937517i
$545$	−8.56231	+	14.8303i	−0.366769	+	0.635262i
$546$		0			0
$547$	−10.5000	−	18.1865i	−0.448948	−	0.777600i	0.549370	−	0.835579i	$-0.314868\pi$
$547$	−10.5000	−	18.1865i	−0.448948	−	0.777600i	−0.998318	+	0.0579790i	$0.981534\pi$
$548$	6.87539			0.293702
$549$		0			0
$550$	2.39919	−	4.15551i	0.102302	−	0.177192i
$551$	3.70820			0.157975
$552$		0			0
$553$	−2.92705	−	5.06980i	−0.124471	−	0.215590i
$554$	2.38197	+	4.12569i	0.101200	+	0.175284i
$555$		0			0
$556$	−4.90576	−	8.49703i	−0.208051	−	0.360354i
$557$	38.5623			1.63394			0.816969	−	0.576682i	$-0.195653\pi$
$557$	38.5623			1.63394			0.816969	+	0.576682i	$0.195653\pi$
$558$		0			0
$559$	5.52786	−	7.18091i	0.233804	−	0.303720i
$560$	16.4721			0.696075
$561$		0			0
$562$	1.42705	+	2.47172i	0.0601965	+	0.104263i
$563$	1.32624			0.0558943			0.0279471	−	0.999609i	$-0.491103\pi$
$563$	1.32624			0.0558943			0.0279471	+	0.999609i	$0.491103\pi$
$564$		0			0
$565$	9.65248	+	16.7186i	0.406083	+	0.703356i
$566$	−2.05573	+	3.56063i	−0.0864087	+	0.149664i
$567$		0			0
$568$	7.94834	−	13.7669i	0.333505	−	0.577647i
$569$	−12.9721	−	22.4684i	−0.543820	−	0.941924i	−0.998680	−	0.0513613i	$-0.983644\pi$
$569$	−12.9721	−	22.4684i	−0.543820	−	0.941924i	0.454860	−	0.890563i	$-0.349689\pi$
$570$		0			0
$571$	21.5902	+	37.3953i	0.903520	+	1.56494i	0.822891	+	0.568199i	$0.192360\pi$
$571$	21.5902	+	37.3953i	0.903520	+	1.56494i	0.0806295	+	0.996744i	$0.474307\pi$
$572$	4.63525	−	8.02850i	0.193810	−	0.335688i
$573$		0			0
$574$	−7.66312	+	13.2729i	−0.319852	+	0.554001i
$575$	15.2148			0.634500
$576$		0			0
$577$	14.1074	−	24.4347i	0.587298	−	1.01723i	−0.407286	−	0.913301i	$-0.633525\pi$
$577$	14.1074	−	24.4347i	0.587298	−	1.01723i	0.994585	−	0.103930i	$-0.0331418\pi$
$578$	−3.83688	−	6.64567i	−0.159593	−	0.276424i
$579$		0			0
$580$	−6.87539			−0.285485
$581$	67.9230			2.81792
$582$		0			0
$583$	−2.50000	−	4.33013i	−0.103539	−	0.179336i
$584$	1.36475	−	2.36381i	0.0564736	−	0.0978151i
$585$		0			0
$586$	4.61803			0.190769
$587$	7.87132	−	13.6335i	0.324884	−	0.562716i	−0.656605	−	0.754235i	$-0.728008\pi$
$587$	7.87132	−	13.6335i	0.324884	−	0.562716i	0.981489	+	0.191519i	$0.0613413\pi$
$588$		0			0
$589$		0			0
$590$	−1.20163	−	2.08128i	−0.0494702	−	0.0856848i
$591$		0			0
$592$	7.63525	+	13.2246i	0.313807	+	0.543530i
$593$	−15.2361	+	26.3896i	−0.625670	+	1.08369i	0.362741	+	0.931890i	$0.381841\pi$
$593$	−15.2361	+	26.3896i	−0.625670	+	1.08369i	−0.988411	+	0.151803i	$0.951492\pi$
$594$		0			0
$595$	15.9443	−	27.6163i	0.653651	−	1.13216i
$596$	−8.34346	−	14.4513i	−0.341761	−	0.591948i
$597$		0			0
$598$	−2.31308			−0.0945890
$599$	18.1180	+	31.3814i	0.740283	+	1.28221i	0.952366	+	0.304956i	$0.0986417\pi$
$599$	18.1180	+	31.3814i	0.740283	+	1.28221i	−0.212084	+	0.977252i	$0.568025\pi$
$600$		0			0
$601$	29.4164			1.19992			0.599960	−	0.800030i	$-0.295183\pi$
$601$	29.4164			1.19992			0.599960	+	0.800030i	$0.295183\pi$
$602$	−6.47214	+	8.40755i	−0.263785	+	0.342666i
$603$		0			0
$604$	16.4164			0.667974
$605$	1.29180	+	2.23746i	0.0525190	+	0.0909655i
$606$		0			0
$607$	11.9271	+	20.6583i	0.484104	+	0.838493i	0.999833	−	0.0182588i	$-0.00581228\pi$
$607$	11.9271	+	20.6583i	0.484104	+	0.838493i	−0.515729	+	0.856752i	$0.672479\pi$
$608$	2.56231	+	4.43804i	0.103915	+	0.179986i
$609$		0			0
$610$	−1.34752			−0.0545597
$611$	0.791796	−	1.37143i	0.0320326	−	0.0554822i
$612$		0			0
$613$	5.20163			0.210092			0.105046	−	0.994467i	$-0.466501\pi$
$613$	5.20163			0.210092			0.105046	+	0.994467i	$0.466501\pi$
$614$	4.43363	+	7.67927i	0.178927	+	0.309910i
$615$		0			0
$616$	−11.2812	+	19.5395i	−0.454531	+	0.787270i
$617$	4.85410	−	8.40755i	0.195419	−	0.338475i	−0.751619	−	0.659598i	$-0.770727\pi$
$617$	4.85410	−	8.40755i	0.195419	−	0.338475i	0.947038	+	0.321122i	$0.104060\pi$
$618$		0			0
$619$	15.1353	−	26.2150i	0.608337	−	1.05367i	−0.383177	−	0.923675i	$-0.625170\pi$
$619$	15.1353	−	26.2150i	0.608337	−	1.05367i	0.991514	−	0.129996i	$-0.0414965\pi$
$620$		0			0
$621$		0			0
$622$	−5.69756	−	9.86846i	−0.228451	−	0.395689i
$623$	−7.85410			−0.314668
$624$		0			0
$625$	−2.20820	−	3.82472i	−0.0883282	−	0.152989i
$626$	−2.50658	−	4.34152i	−0.100183	−	0.173522i
$627$		0			0
$628$	−4.77051	+	8.26277i	−0.190364	+	0.329720i
$629$	29.5623			1.17873
$630$		0			0
$631$	13.5451	−	23.4608i	0.539221	−	0.933959i	−0.459725	−	0.888061i	$-0.652052\pi$
$631$	13.5451	−	23.4608i	0.539221	−	0.933959i	0.998946	−	0.0458973i	$-0.0146147\pi$
$632$	−1.01722	+	1.76188i	−0.0404629	+	0.0700838i
$633$		0			0
$634$	−12.7214			−0.505230
$635$	−9.05573	−	15.6850i	−0.359366	−	0.622439i
$636$		0			0
$637$	15.1246			0.599259
$638$	2.07295	−	3.59045i	0.0820688	−	0.142147i
$639$		0			0
$640$	−6.23607	−	10.8012i	−0.246502	−	0.426954i
$641$	−10.8197			−0.427351			−0.213675	−	0.976905i	$-0.568543\pi$
$641$	−10.8197			−0.427351			−0.213675	+	0.976905i	$0.568543\pi$
$642$		0			0
$643$	9.43769			0.372186			0.186093	−	0.982532i	$-0.440417\pi$
$643$	9.43769			0.372186			0.186093	+	0.982532i	$0.440417\pi$
$644$	−34.4164			−1.35620
$645$		0			0
$646$	2.87539			0.113131
$647$	21.6738			0.852084			0.426042	−	0.904703i	$-0.359908\pi$
$647$	21.6738			0.852084			0.426042	+	0.904703i	$0.359908\pi$
$648$		0			0
$649$	−18.4164			−0.722907
$650$	0.916408	+	1.58726i	0.0359445	+	0.0622577i
$651$		0			0
$652$	12.9787	−	22.4798i	0.508286	−	0.880377i
$653$	32.8885			1.28703			0.643514	−	0.765434i	$-0.277476\pi$
$653$	32.8885			1.28703			0.643514	+	0.765434i	$0.277476\pi$
$654$		0			0
$655$	−6.14590	−	10.6450i	−0.240140	−	0.415935i
$656$	−29.7984			−1.16343
$657$		0			0
$658$	−0.927051	+	1.60570i	−0.0361402	+	0.0625967i
$659$	−14.6803	+	25.4271i	−0.571865	+	0.990499i	0.424510	+	0.905423i	$0.360447\pi$
$659$	−14.6803	+	25.4271i	−0.571865	+	0.990499i	−0.996375	+	0.0850756i	$0.972887\pi$
$660$		0			0
$661$	−43.3951			−1.68787			−0.843937	−	0.536442i	$-0.819768\pi$
$661$	−43.3951			−1.68787			−0.843937	+	0.536442i	$0.819768\pi$
$662$	1.04508	−	1.81014i	0.0406184	−	0.0703531i
$663$		0			0
$664$	−11.8024	−	20.4424i	−0.458023	−	0.793320i
$665$	3.23607	+	5.60503i	0.125489	+	0.217354i
$666$		0			0
$667$	13.1459			0.509011
$668$	−13.1976	−	22.8588i	−0.510629	−	0.884435i
$669$		0			0
$670$	−0.909830	+	1.57587i	−0.0351498	+	0.0608812i
$671$	−5.16312	+	8.94278i	−0.199320	+	0.345232i
$672$		0			0
$673$	−6.91641	+	11.9796i	−0.266608	+	0.461778i	−0.967984	−	0.251013i	$-0.919236\pi$
$673$	−6.91641	+	11.9796i	−0.266608	+	0.461778i	0.701376	+	0.712792i	$0.252570\pi$
$674$	−5.34752	+	9.26218i	−0.205979	+	0.356766i
$675$		0			0
$676$	−10.2812	−	17.8075i	−0.395429	−	0.684903i
$677$	31.7639			1.22079			0.610394	−	0.792098i	$-0.291011\pi$
$677$	31.7639			1.22079			0.610394	+	0.792098i	$0.291011\pi$
$678$		0			0
$679$	−19.5623	+	33.8829i	−0.750732	+	1.30031i
$680$	−11.0820			−0.424977
$681$		0			0
$682$		0			0
$683$	−5.56231	−	9.63420i	−0.212836	−	0.368642i	0.739765	−	0.672865i	$-0.234937\pi$
$683$	−5.56231	−	9.63420i	−0.212836	−	0.368642i	−0.952601	+	0.304223i	$0.901603\pi$
$684$		0			0
$685$	−2.29180	−	3.96951i	−0.0875650	−	0.151667i
$686$	−6.38197			−0.243665
$687$		0			0
$688$	−20.4483	−	2.72443i	−0.779586	−	0.103868i
$689$	1.90983			0.0727587
$690$		0			0
$691$	−7.86475	−	13.6221i	−0.299189	−	0.518211i	0.676762	−	0.736202i	$-0.263383\pi$
$691$	−7.86475	−	13.6221i	−0.299189	−	0.518211i	−0.975951	+	0.217992i	$0.930049\pi$
$692$	−6.97871			−0.265291
$693$		0			0
$694$	1.92705	+	3.33775i	0.0731499	+	0.126699i
$695$	−3.27051	+	5.66469i	−0.124058	+	0.214874i
$696$		0			0
$697$	−28.8435	+	49.9583i	−1.09252	+	1.89231i
$698$	−3.95492	−	6.85011i	−0.149696	−	0.259281i
$699$		0			0
$700$	13.6353	+	23.6170i	0.515364	+	0.892637i
$701$	−7.25329	+	12.5631i	−0.273953	+	0.474500i	−0.969870	−	0.243621i	$-0.921665\pi$
$701$	−7.25329	+	12.5631i	−0.273953	+	0.474500i	0.695917	+	0.718122i	$0.254998\pi$
$702$		0			0
$703$	−3.00000	+	5.19615i	−0.113147	+	0.195977i
$704$	−17.0344			−0.642010
$705$		0			0
$706$	−3.29180	+	5.70156i	−0.123888	+	0.214581i
$707$	−7.97214	−	13.8081i	−0.299823	−	0.519309i
$708$		0			0
$709$	28.8885			1.08493			0.542466	−	0.840078i	$-0.317491\pi$
$709$	28.8885			1.08493			0.542466	+	0.840078i	$0.317491\pi$
$710$	−5.09830			−0.191336
$711$		0			0
$712$	1.36475	+	2.36381i	0.0511460	+	0.0885874i
$713$		0			0
$714$		0			0
$715$	−6.18034			−0.231132
$716$	−8.94834	+	15.4990i	−0.334415	+	0.579224i
$717$		0			0
$718$	−1.02129	+	1.76892i	−0.0381141	+	0.0660155i
$719$	−5.39919	−	9.35167i	−0.201356	−	0.348758i	0.747610	−	0.664138i	$-0.231201\pi$
$719$	−5.39919	−	9.35167i	−0.201356	−	0.348758i	−0.948965	+	0.315380i	$0.897868\pi$
$720$		0			0
$721$	−34.7705	−	60.2243i	−1.29492	−	2.24287i
$722$	3.33688	−	5.77965i	0.124186	−	0.215096i
$723$		0			0
$724$	−17.9681	+	31.1216i	−0.667778	+	1.15663i
$725$	−5.20820	−	9.02087i	−0.193428	−	0.335027i
$726$		0			0
$727$	−17.9787			−0.666794			−0.333397	−	0.942787i	$-0.608195\pi$
$727$	−17.9787			−0.666794			−0.333397	+	0.942787i	$0.608195\pi$
$728$	−4.30902	−	7.46344i	−0.159703	−	0.276613i
$729$		0			0
$730$	−0.875388			−0.0323996
$731$	−24.3607	+	31.6455i	−0.901012	+	1.17045i
$732$		0			0
$733$	24.5410			0.906443			0.453222	−	0.891398i	$-0.350275\pi$
$733$	24.5410			0.906443			0.453222	+	0.891398i	$0.350275\pi$
$734$	−3.66312	−	6.34471i	−0.135208	−	0.234187i
$735$		0			0
$736$	9.08359	+	15.7332i	0.334826	+	0.579935i
$737$	6.97214	+	12.0761i	0.256822	+	0.444829i
$738$		0			0
$739$	49.5410			1.82240			0.911198	−	0.411969i	$-0.135159\pi$
$739$	49.5410			1.82240			0.911198	+	0.411969i	$0.135159\pi$
$740$	5.56231	−	9.63420i	0.204474	−	0.354160i
$741$		0			0
$742$	−2.23607			−0.0820886
$743$	16.6803	+	28.8912i	0.611942	+	1.05992i	0.990913	+	0.134506i	$0.0429449\pi$
$743$	16.6803	+	28.8912i	0.611942	+	1.05992i	−0.378970	+	0.925409i	$0.623722\pi$
$744$		0			0
$745$	−5.56231	+	9.63420i	−0.203787	+	0.352970i
$746$	−1.14590	+	1.98475i	−0.0419543	+	0.0726670i
$747$		0			0
$748$	−20.4271	+	35.3807i	−0.746887	+	1.29365i
$749$	−15.9443	+	27.6163i	−0.582591	+	1.00908i
$750$		0			0
$751$	18.9894	+	32.8905i	0.692931	+	1.20019i	0.970873	+	0.239595i	$0.0770145\pi$
$751$	18.9894	+	32.8905i	0.692931	+	1.20019i	−0.277942	+	0.960598i	$0.589652\pi$
$752$	−3.60488			−0.131456
$753$		0			0
$754$	0.791796	+	1.37143i	0.0288355	+	0.0499446i
$755$	−5.47214	−	9.47802i	−0.199151	−	0.344940i
$756$		0			0
$757$	15.4894	−	26.8284i	0.562970	−	0.975093i	−0.434265	−	0.900785i	$-0.642992\pi$
$757$	15.4894	−	26.8284i	0.562970	−	0.975093i	0.997235	−	0.0743080i	$-0.0236748\pi$
$758$	−10.4508			−0.379592
$759$		0			0
$760$	1.12461	−	1.94788i	0.0407940	−	0.0706572i
$761$	0.545085	−	0.944115i	0.0197593	−	0.0342241i	−0.855977	−	0.517014i	$-0.827043\pi$
$761$	0.545085	−	0.944115i	0.0197593	−	0.0342241i	0.875736	+	0.482790i	$0.160377\pi$
$762$		0			0
$763$	58.6869			2.12461
$764$	13.4681	+	23.3274i	0.487258	+	0.843955i
$765$		0			0
$766$	−14.5623			−0.526157
$767$	3.51722	−	6.09201i	0.126999	−	0.219970i
$768$		0			0
$769$	−9.94427	−	17.2240i	−0.358600	−	0.621113i	0.629128	−	0.777302i	$-0.283412\pi$
$769$	−9.94427	−	17.2240i	−0.358600	−	0.621113i	−0.987727	+	0.156189i	$0.950079\pi$
$770$	7.23607			0.260770
$771$		0			0
$772$	−5.02129			−0.180720
$773$	−15.5967			−0.560976			−0.280488	−	0.959858i	$-0.590496\pi$
$773$	−15.5967			−0.560976			−0.280488	+	0.959858i	$0.590496\pi$
$774$		0			0
$775$		0			0
$776$	13.5967			0.488095
$777$		0			0
$778$	13.3951			0.480238
$779$	−5.85410	−	10.1396i	−0.209745	−	0.363289i
$780$		0			0
$781$	−19.5344	+	33.8346i	−0.698997	+	1.21070i
$782$	10.1935			0.364519
$783$		0			0
$784$	−17.2148	−	29.8169i	−0.614814	−	1.06489i
$785$	6.36068			0.227022
$786$		0			0
$787$	−5.22542	+	9.05070i	−0.186266	+	0.322623i	−0.944002	−	0.329938i	$-0.892972\pi$
$787$	−5.22542	+	9.05070i	−0.186266	+	0.322623i	0.757736	+	0.652561i	$0.226305\pi$
$788$	2.72949	−	4.72762i	0.0972341	−	0.168414i
$789$		0			0
$790$	0.652476			0.0232140
$791$	33.0795	−	57.2954i	1.17617	−	2.03719i
$792$		0			0
$793$	−1.97214	−	3.41584i	−0.0700326	−	0.121300i
$794$	−6.19098	−	10.7231i	−0.219710	−	0.380548i
$795$		0			0
$796$	−3.60488			−0.127772
$797$	−4.11803	−	7.13264i	−0.145868	−	0.252651i	0.783828	−	0.620978i	$-0.213264\pi$
$797$	−4.11803	−	7.13264i	−0.145868	−	0.252651i	−0.929697	+	0.368326i	$0.879931\pi$
$798$		0			0
$799$	−3.48936	+	6.04374i	−0.123445	+	0.213812i
$800$	7.19756	−	12.4665i	0.254472	−	0.440759i
$801$		0			0
$802$	−4.85410	+	8.40755i	−0.171404	+	0.296881i
$803$	−3.35410	+	5.80948i	−0.118364	+	0.205012i
$804$		0			0
$805$	11.4721	+	19.8703i	0.404340	+	0.700337i
$806$		0			0
$807$		0			0
$808$	−2.77051	+	4.79866i	−0.0974662	+	0.168816i
$809$	−4.74265			−0.166743			−0.0833713	−	0.996519i	$-0.526569\pi$
$809$	−4.74265			−0.166743			−0.0833713	+	0.996519i	$0.526569\pi$
$810$		0			0
$811$	−23.6976	−	41.0454i	−0.832134	−	1.44130i	−0.896343	−	0.443362i	$-0.853786\pi$
$811$	−23.6976	−	41.0454i	−0.832134	−	1.44130i	0.0642089	−	0.997936i	$-0.479548\pi$
$812$	11.7812	+	20.4056i	0.413437	+	0.716095i
$813$		0			0
$814$	3.35410	+	5.80948i	0.117561	+	0.203622i
$815$	−17.3050			−0.606166
$816$		0			0
$817$	−3.09017	−	7.49326i	−0.108111	−	0.262156i
$818$	3.40325			0.118992
$819$		0			0
$820$	10.8541	+	18.7999i	0.379042	+	0.656519i
$821$	−0.326238			−0.0113858			−0.00569289	−	0.999984i	$-0.501812\pi$
$821$	−0.326238			−0.0113858			−0.00569289	+	0.999984i	$0.501812\pi$
$822$		0			0
$823$	−26.0066	−	45.0447i	−0.906532	−	1.57016i	−0.818847	−	0.574012i	$-0.805386\pi$
$823$	−26.0066	−	45.0447i	−0.906532	−	1.57016i	−0.0876853	−	0.996148i	$-0.527947\pi$
$824$	−12.0836	+	20.9294i	−0.420952	+	0.729110i
$825$		0			0
$826$	−4.11803	+	7.13264i	−0.143285	+	0.248176i
$827$	4.59017	+	7.95041i	0.159616	+	0.276463i	0.934730	−	0.355358i	$-0.115641\pi$
$827$	4.59017	+	7.95041i	0.159616	+	0.276463i	−0.775114	+	0.631821i	$0.782308\pi$
$828$		0			0
$829$	−14.0795	−	24.3865i	−0.489002	−	0.846977i	0.510918	−	0.859630i	$-0.329306\pi$
$829$	−14.0795	−	24.3865i	−0.489002	−	0.846977i	−0.999920	+	0.0126530i	$0.995972\pi$
$830$	−3.78522	+	6.55619i	−0.131387	+	0.227569i
$831$		0			0
$832$	3.25329	−	5.63486i	0.112787	−	0.195354i
$833$	−66.6525			−2.30937
$834$		0			0
$835$	−8.79837	+	15.2392i	−0.304480	+	0.527375i
$836$	−4.14590	−	7.18091i	−0.143389	−	0.248357i
$837$		0			0
$838$	3.90983			0.135063
$839$	−25.8885			−0.893772			−0.446886	−	0.894591i	$-0.647467\pi$
$839$	−25.8885			−0.893772			−0.446886	+	0.894591i	$0.647467\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	1.46149	−	2.53138i	0.0503664	−	0.0872371i
$843$		0			0
$844$	17.1246			0.589453
$845$	−6.85410	+	11.8717i	−0.235788	+	0.408397i
$846$		0			0
$847$	4.42705	−	7.66788i	0.152115	−	0.263471i
$848$	−2.17376	−	3.76507i	−0.0746473	−	0.129293i
$849$		0			0
$850$	−4.03851	−	6.99490i	−0.138520	−	0.239923i
$851$	−10.6353	+	18.4208i	−0.364572	+	0.631457i
$852$		0			0
$853$	−5.62868	+	9.74915i	−0.192722	+	0.333805i	−0.946151	−	0.323724i	$-0.895065\pi$
$853$	−5.62868	+	9.74915i	−0.192722	+	0.333805i	0.753429	+	0.657529i	$0.228398\pi$
$854$	2.30902	+	3.99933i	0.0790129	+	0.136854i
$855$		0			0
$856$	11.0820			0.378776
$857$	−18.0902	−	31.3331i	−0.617948	−	1.07032i	−0.989860	−	0.142050i	$-0.954631\pi$
$857$	−18.0902	−	31.3331i	−0.617948	−	1.07032i	0.371911	−	0.928268i	$-0.378703\pi$
$858$		0			0
$859$	−49.4164			−1.68607			−0.843033	−	0.537862i	$-0.819232\pi$
$859$	−49.4164			−1.68607			−0.843033	+	0.537862i	$0.819232\pi$
$860$	5.72949	+	13.8933i	0.195374	+	0.473757i
$861$		0			0
$862$	9.47214			0.322622
$863$	4.75329	+	8.23294i	0.161804	+	0.280252i	0.935516	−	0.353285i	$-0.114935\pi$
$863$	4.75329	+	8.23294i	0.161804	+	0.280252i	−0.773712	+	0.633538i	$0.781602\pi$
$864$		0			0
$865$	2.32624	+	4.02916i	0.0790945	+	0.136996i
$866$	6.62868	+	11.4812i	0.225252	+	0.390147i
$867$		0			0
$868$		0			0
$869$	2.50000	−	4.33013i	0.0848067	−	0.146889i
$870$		0			0
$871$	−5.32624			−0.180473
$872$	−10.1976	−	17.6627i	−0.345333	−	0.598134i
$873$		0			0
$874$	−1.03444	+	1.79171i	−0.0349905	+	0.0606054i
$875$	22.1803	−	38.4175i	0.749832	−	1.29875i
$876$		0			0
$877$	3.82624	−	6.62724i	0.129203	−	0.223786i	−0.794165	−	0.607702i	$-0.792091\pi$
$877$	3.82624	−	6.62724i	0.129203	−	0.223786i	0.923368	+	0.383916i	$0.125425\pi$
$878$	−0.218847	+	0.379054i	−0.00738573	+	0.0127925i
$879$		0			0
$880$	7.03444	+	12.1840i	0.237131	+	0.410723i
$881$	−33.7639			−1.13754			−0.568768	−	0.822498i	$-0.692580\pi$
$881$	−33.7639			−1.13754			−0.568768	+	0.822498i	$0.692580\pi$
$882$		0			0
$883$	−6.56231	−	11.3662i	−0.220839	−	0.382505i	0.734224	−	0.678907i	$-0.237546\pi$
$883$	−6.56231	−	11.3662i	−0.220839	−	0.382505i	−0.955063	+	0.296403i	$0.904213\pi$
$884$	−7.80244	−	13.5142i	−0.262424	−	0.454532i
$885$		0			0
$886$	0.472136	−	0.817763i	0.0158617	−	0.0274733i
$887$	52.9574			1.77814			0.889068	−	0.457775i	$-0.151353\pi$
$887$	52.9574			1.77814			0.889068	+	0.457775i	$0.151353\pi$
$888$		0			0
$889$	−31.0344	+	53.7532i	−1.04086	+	1.80283i
$890$	0.437694	−	0.758108i	0.0146715	−	0.0254119i
$891$		0			0
$892$	−5.12461			−0.171585
$893$	−0.708204	−	1.22665i	−0.0236991	−	0.0410481i
$894$		0			0
$895$	11.9311			0.398813
$896$	−21.3713	+	37.0162i	−0.713966	+	1.23663i
$897$		0			0
$898$	−6.27051	−	10.8608i	−0.209250	−	0.362431i
$899$		0			0
$900$		0			0
$901$	−8.41641			−0.280391
$902$	−13.0902			−0.435855
$903$		0			0
$904$	−22.9919			−0.764698
$905$	23.9574			0.796372
$906$		0			0
$907$	−21.7082			−0.720809			−0.360405	−	0.932796i	$-0.617361\pi$
$907$	−21.7082			−0.720809			−0.360405	+	0.932796i	$0.617361\pi$
$908$	1.36475	+	2.36381i	0.0452907	+	0.0784457i
$909$		0			0
$910$	−1.38197	+	2.39364i	−0.0458117	+	0.0793482i
$911$	42.9787			1.42395			0.711974	−	0.702206i	$-0.247801\pi$
$911$	42.9787			1.42395			0.711974	+	0.702206i	$0.247801\pi$
$912$		0			0
$913$	29.0066	+	50.2409i	0.959978	+	1.66273i
$914$	−6.00000			−0.198462
$915$		0			0
$916$	−2.12461	+	3.67994i	−0.0701991	+	0.121588i
$917$	−21.0623	+	36.4810i	−0.695539	+	1.20471i
$918$		0			0
$919$	29.3951			0.969656			0.484828	−	0.874610i	$-0.338882\pi$
$919$	29.3951			0.969656			0.484828	+	0.874610i	$0.338882\pi$
$920$	3.98684	−	6.90542i	0.131442	−	0.227665i
$921$		0			0
$922$	−6.03444	−	10.4520i	−0.198734	−	0.344217i
$923$	−7.46149	−	12.9237i	−0.245598	−	0.425388i
$924$		0			0
$925$	16.8541			0.554159
$926$	5.69756	+	9.86846i	0.187233	+	0.324298i
$927$		0			0
$928$	6.21885	−	10.7714i	0.204144	−	0.353587i
$929$	17.6180	−	30.5153i	0.578029	−	1.00118i	−0.417676	−	0.908596i	$-0.637155\pi$
$929$	17.6180	−	30.5153i	0.578029	−	1.00118i	0.995705	−	0.0925796i	$-0.0295113\pi$
$930$		0			0
$931$	6.76393	−	11.7155i	0.221679	−	0.383959i
$932$	−16.7188	+	28.9579i	−0.547644	+	0.948547i
$933$		0			0
$934$	−2.87539	−	4.98032i	−0.0940856	−	0.162961i
$935$	27.2361			0.890715
$936$		0			0
$937$	27.6631	−	47.9139i	0.903715	−	1.56528i	0.0810814	−	0.996707i	$-0.474163\pi$
$937$	27.6631	−	47.9139i	0.903715	−	1.56528i	0.822633	−	0.568572i	$-0.192504\pi$
$938$	6.23607			0.203615
$939$		0			0
$940$	1.31308	+	2.27433i	0.0428280	+	0.0741803i
$941$	−13.1180	−	22.7211i	−0.427636	−	0.740687i	0.569027	−	0.822319i	$-0.307320\pi$
$941$	−13.1180	−	22.7211i	−0.427636	−	0.740687i	−0.996663	+	0.0816322i	$0.973987\pi$
$942$		0			0
$943$	−20.7533	−	35.9458i	−0.675820	−	1.17055i
$944$	−16.0132			−0.521184
$945$		0			0
$946$	−8.98278	−	1.19682i	−0.292055	−	0.0389119i
$947$	−25.3607			−0.824111			−0.412056	−	0.911159i	$-0.635189\pi$
$947$	−25.3607			−0.824111			−0.412056	+	0.911159i	$0.635189\pi$
$948$		0			0
$949$	−1.28115	−	2.21902i	−0.0415880	−	0.0720325i
$950$	1.63932			0.0531866
$951$		0			0
$952$	18.9894	+	32.8905i	0.615449	+	1.06599i
$953$	−19.4443	+	33.6785i	−0.629862	+	1.09095i	0.357717	+	0.933830i	$0.383555\pi$
$953$	−19.4443	+	33.6785i	−0.629862	+	1.09095i	−0.987579	+	0.157123i	$0.949778\pi$
$954$		0			0
$955$	8.97871	−	15.5516i	0.290544	−	0.503238i
$956$	7.68692	+	13.3141i	0.248613	+	0.430610i
$957$		0			0
$958$	−2.63932	−	4.57144i	−0.0852726	−	0.147696i
$959$	−7.85410	+	13.6037i	−0.253622	+	0.439287i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−2.56231			−0.0826121
$963$		0			0
$964$	3.95898	−	6.85716i	0.127510	−	0.220854i
$965$	1.67376	+	2.89904i	0.0538803	+	0.0933234i
$966$		0			0
$967$	38.1033			1.22532			0.612660	−	0.790346i	$-0.290099\pi$
$967$	38.1033			1.22532			0.612660	+	0.790346i	$0.290099\pi$
$968$	−3.07701			−0.0988990
$969$		0			0
$970$	−2.18034	−	3.77646i	−0.0700065	−	0.121255i
$971$	−8.68034	+	15.0348i	−0.278565	+	0.482489i	−0.971028	−	0.238964i	$-0.923192\pi$
$971$	−8.68034	+	15.0348i	−0.278565	+	0.482489i	0.692463	+	0.721453i	$0.256526\pi$
$972$		0			0
$973$	22.4164			0.718637
$974$	−0.253289	+	0.438709i	−0.00811590	+	0.0140572i
$975$		0			0
$976$	−4.48936	+	7.77579i	−0.143701	+	0.248897i
$977$	20.6180	+	35.7115i	0.659629	+	1.14251i	0.980712	+	0.195460i	$0.0626201\pi$
$977$	20.6180	+	35.7115i	0.659629	+	1.14251i	−0.321082	+	0.947051i	$0.604047\pi$
$978$		0			0
$979$	−3.35410	−	5.80948i	−0.107198	−	0.185672i
$980$	−12.5410	+	21.7217i	−0.400608	+	0.693874i
$981$		0			0
$982$	4.13525	−	7.16247i	0.131961	−	0.228564i
$983$	−5.23607	−	9.06914i	−0.167005	−	0.289261i	0.770361	−	0.637608i	$-0.220076\pi$
$983$	−5.23607	−	9.06914i	−0.167005	−	0.289261i	−0.937365	+	0.348348i	$0.886743\pi$
$984$		0			0
$985$	−3.63932			−0.115958
$986$	−3.48936	−	6.04374i	−0.111124	−	0.192472i
$987$		0			0
$988$	3.16718			0.100762
$989$	−10.9549	−	26.5643i	−0.348346	−	0.844694i
$990$		0			0
$991$	−10.8197			−0.343698			−0.171849	−	0.985123i	$-0.554974\pi$
$991$	−10.8197			−0.343698			−0.171849	+	0.985123i	$0.554974\pi$
$992$		0			0
$993$		0			0
$994$	8.73607	+	15.1313i	0.277091	+	0.479936i
$995$	1.20163	+	2.08128i	0.0380941	+	0.0659809i
$996$		0			0
$997$	−19.4508			−0.616015			−0.308007	−	0.951384i	$-0.599662\pi$
$997$	−19.4508			−0.616015			−0.308007	+	0.951384i	$0.599662\pi$
$998$	−2.64590	+	4.58283i	−0.0837544	+	0.145067i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.h.d.208.1		4
3.2	odd	2		43.2.c.b.36.2	yes	4
12.11	even	2		688.2.i.e.337.1		4
43.6	even	3	inner	387.2.h.d.307.1		4
129.50	even	6		1849.2.a.h.1.1		2
129.92	odd	6		43.2.c.b.6.2	✓	4
129.122	odd	6		1849.2.a.e.1.2		2
516.479	even	6		688.2.i.e.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.c.b.6.2	✓	4	129.92	odd	6
43.2.c.b.36.2	yes	4	3.2	odd	2
387.2.h.d.208.1		4	1.1	even	1	trivial
387.2.h.d.307.1		4	43.6	even	3	inner
688.2.i.e.49.1		4	516.479	even	6
688.2.i.e.337.1		4	12.11	even	2
1849.2.a.e.1.2		2	129.122	odd	6
1849.2.a.h.1.1		2	129.50	even	6

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.381966 q^{2} -1.85410 q^{4} +(0.618034 + 1.07047i) q^{5} +(2.11803 - 3.66854i) q^{7} -1.47214 q^{8} +O(q^{10})\)	\(q+0.381966 q^{2} -1.85410 q^{4} +(0.618034 + 1.07047i) q^{5} +(2.11803 - 3.66854i) q^{7} -1.47214 q^{8} +(0.236068 + 0.408882i) q^{10} +3.61803 q^{11} +(-0.690983 + 1.19682i) q^{13} +(0.809017 - 1.40126i) q^{14} +3.14590 q^{16} +(3.04508 - 5.27424i) q^{17} +(0.618034 + 1.07047i) q^{19} +(-1.14590 - 1.98475i) q^{20} +1.38197 q^{22} +(2.19098 + 3.79489i) q^{23} +(1.73607 - 3.00696i) q^{25} +(-0.263932 + 0.457144i) q^{26} +(-3.92705 + 6.80185i) q^{28} +(1.50000 - 2.59808i) q^{29} +4.14590 q^{32} +(1.16312 - 2.01458i) q^{34} +5.23607 q^{35} +(2.42705 + 4.20378i) q^{37} +(0.236068 + 0.408882i) q^{38} +(-0.909830 - 1.57587i) q^{40} -9.47214 q^{41} +(-6.50000 - 0.866025i) q^{43} -6.70820 q^{44} +(0.836881 + 1.44952i) q^{46} -1.14590 q^{47} +(-5.47214 - 9.47802i) q^{49} +(0.663119 - 1.14856i) q^{50} +(1.28115 - 2.21902i) q^{52} +(-0.690983 - 1.19682i) q^{53} +(2.23607 + 3.87298i) q^{55} +(-3.11803 + 5.40059i) q^{56} +(0.572949 - 0.992377i) q^{58} -5.09017 q^{59} +(-1.42705 + 2.47172i) q^{61} -4.70820 q^{64} -1.70820 q^{65} +(1.92705 + 3.33775i) q^{67} +(-5.64590 + 9.77898i) q^{68} +2.00000 q^{70} +(-5.39919 + 9.35167i) q^{71} +(-0.927051 + 1.60570i) q^{73} +(0.927051 + 1.60570i) q^{74} +(-1.14590 - 1.98475i) q^{76} +(7.66312 - 13.2729i) q^{77} +(0.690983 - 1.19682i) q^{79} +(1.94427 + 3.36758i) q^{80} -3.61803 q^{82} +(8.01722 + 13.8862i) q^{83} +7.52786 q^{85} +(-2.48278 - 0.330792i) q^{86} -5.32624 q^{88} +(-0.927051 - 1.60570i) q^{89} +(2.92705 + 5.06980i) q^{91} +(-4.06231 - 7.03612i) q^{92} -0.437694 q^{94} +(-0.763932 + 1.32317i) q^{95} -9.23607 q^{97} +(-2.09017 - 3.62028i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8	\( 4 q + 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} + 12 q^{8} - 8 q^{10} + 10 q^{11} - 5 q^{13} + q^{14} + 26 q^{16} + q^{17} - 2 q^{19} - 18 q^{20} + 10 q^{22} + 11 q^{23} - 2 q^{25} - 10 q^{26} - 9 q^{28} + 6 q^{29} + 30 q^{32} - 11 q^{34} + 12 q^{35} + 3 q^{37} - 8 q^{38} - 26 q^{40} - 20 q^{41} - 26 q^{43} + 19 q^{46} - 18 q^{47} - 4 q^{49} - 13 q^{50} - 15 q^{52} - 5 q^{53} - 8 q^{56} + 9 q^{58} + 2 q^{59} + q^{61} + 8 q^{64} + 20 q^{65} + q^{67} - 36 q^{68} + 8 q^{70} + 3 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{76} + 15 q^{77} + 5 q^{79} - 28 q^{80} - 10 q^{82} + 3 q^{83} + 48 q^{85} - 39 q^{86} + 10 q^{88} + 3 q^{89} + 5 q^{91} + 24 q^{92} - 42 q^{94} - 12 q^{95} - 28 q^{97} + 14 q^{98}+O(q^{100}) \) 4 * q + 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 + 12 * q^8 - 8 * q^10 + 10 * q^11 - 5 * q^13 + q^14 + 26 * q^16 + q^17 - 2 * q^19 - 18 * q^20 + 10 * q^22 + 11 * q^23 - 2 * q^25 - 10 * q^26 - 9 * q^28 + 6 * q^29 + 30 * q^32 - 11 * q^34 + 12 * q^35 + 3 * q^37 - 8 * q^38 - 26 * q^40 - 20 * q^41 - 26 * q^43 + 19 * q^46 - 18 * q^47 - 4 * q^49 - 13 * q^50 - 15 * q^52 - 5 * q^53 - 8 * q^56 + 9 * q^58 + 2 * q^59 + q^61 + 8 * q^64 + 20 * q^65 + q^67 - 36 * q^68 + 8 * q^70 + 3 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^76 + 15 * q^77 + 5 * q^79 - 28 * q^80 - 10 * q^82 + 3 * q^83 + 48 * q^85 - 39 * q^86 + 10 * q^88 + 3 * q^89 + 5 * q^91 + 24 * q^92 - 42 * q^94 - 12 * q^95 - 28 * q^97 + 14 * q^98

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