LMFDB - Embedded newform 855.2.be.d.334.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(64,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("855.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.be (of order $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 $ x^12 - 6x^10 + 29x^8 - 40x^6 + 43x^4 - 7*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.6
Root			$0.352587 + 0.203566i$ of defining polynomial
Character	$\chi$	$=$	855.334
Dual form			855.2.be.d.64.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.12713 + 1.22810i) q^{2} +(2.01647 + 3.49262i) q^{4} +(1.45193 - 1.70056i) q^{5} +4.50527i q^{7} +4.99330i q^{8} +O(q^{10})$	\(q+(2.12713 + 1.22810i) q^{2} +(2.01647 + 3.49262i) q^{4} +(1.45193 - 1.70056i) q^{5} +4.50527i q^{7} +4.99330i q^{8} +(5.17691 - 1.83419i) q^{10} -2.19869 q^{11} +(3.25495 - 1.87925i) q^{13} +(-5.53293 + 9.58332i) q^{14} +(-2.09935 + 3.63617i) q^{16} +(0.576674 + 0.332943i) q^{17} +(-3.79804 + 2.13891i) q^{19} +(8.86718 + 1.64194i) q^{20} +(-4.67691 - 2.70022i) q^{22} +(-0.422643 + 0.244013i) q^{23} +(-0.783783 - 4.93819i) q^{25} +9.23163 q^{26} +(-15.7352 + 9.08474i) q^{28} +(-1.79804 - 3.11429i) q^{29} +6.83424 q^{31} +(-0.282531 + 0.163119i) q^{32} +(0.817776 + 1.41643i) q^{34} +(7.66147 + 6.54135i) q^{35} -3.01171i q^{37} +(-10.7057 - 0.114636i) q^{38} +(8.49139 + 7.24994i) q^{40} +(0.0362063 - 0.0627112i) q^{41} +(0.364199 + 0.210271i) q^{43} +(-4.43359 - 7.67920i) q^{44} -1.19869 q^{46} +(-4.34986 + 2.51139i) q^{47} -13.2975 q^{49} +(4.39738 - 11.4668i) q^{50} +(13.1270 + 7.57888i) q^{52} +(2.26725 - 1.30900i) q^{53} +(-3.19235 + 3.73900i) q^{55} -22.4962 q^{56} -8.83269i q^{58} +(-6.26783 + 10.8562i) q^{59} +(-3.53293 - 6.11922i) q^{61} +(14.5374 + 8.39315i) q^{62} +7.59607 q^{64} +(1.53020 - 8.26377i) q^{65} +(4.95944 - 2.86334i) q^{67} +2.68548i q^{68} +(8.26353 + 23.3234i) q^{70} +(3.48626 - 6.03838i) q^{71} +(-2.56139 - 1.47882i) q^{73} +(3.69869 - 6.40632i) q^{74} +(-15.1290 - 8.95208i) q^{76} -9.90571i q^{77} +(5.66849 - 9.81811i) q^{79} +(3.13541 + 8.84953i) q^{80} +(0.154031 - 0.0889301i) q^{82} -15.6999i q^{83} +(1.40348 - 0.497256i) q^{85} +(0.516467 + 0.894547i) q^{86} -10.9787i q^{88} +(0.668486 + 1.15785i) q^{89} +(8.46652 + 14.6644i) q^{91} +(-1.70449 - 0.984089i) q^{92} -12.3370 q^{94} +(-1.87716 + 9.56432i) q^{95} +(-3.79871 - 2.19319i) q^{97} +(-28.2856 - 16.3307i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{4} + 2 q^{5}+O(q^{10}) $ 12 * q + 2 * q^4 + 2 * q^5	$ 12 q + 2 q^{4} + 2 q^{5} + 6 q^{10} - 4 q^{11} - 22 q^{14} - 14 q^{16} - 12 q^{19} + 40 q^{20} - 6 q^{25} + 44 q^{26} + 12 q^{29} + 60 q^{31} + 10 q^{34} + 10 q^{40} + 12 q^{41} - 20 q^{44} + 8 q^{46} - 4 q^{49} + 8 q^{50} - 18 q^{55} - 92 q^{56} - 20 q^{59} + 2 q^{61} + 24 q^{64} + 40 q^{65} + 46 q^{70} - 2 q^{71} + 22 q^{74} - 70 q^{76} + 24 q^{79} + 22 q^{80} + 2 q^{85} - 16 q^{86} - 36 q^{89} + 24 q^{91} - 60 q^{94} - 46 q^{95}+O(q^{100}) $ 12 * q + 2 * q^4 + 2 * q^5 + 6 * q^10 - 4 * q^11 - 22 * q^14 - 14 * q^16 - 12 * q^19 + 40 * q^20 - 6 * q^25 + 44 * q^26 + 12 * q^29 + 60 * q^31 + 10 * q^34 + 10 * q^40 + 12 * q^41 - 20 * q^44 + 8 * q^46 - 4 * q^49 + 8 * q^50 - 18 * q^55 - 92 * q^56 - 20 * q^59 + 2 * q^61 + 24 * q^64 + 40 * q^65 + 46 * q^70 - 2 * q^71 + 22 * q^74 - 70 * q^76 + 24 * q^79 + 22 * q^80 + 2 * q^85 - 16 * q^86 - 36 * q^89 + 24 * q^91 - 60 * q^94 - 46 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.12713	+	1.22810i	1.50411	+	0.868399i	0.999989	+	0.00476685i	$0.00151734\pi$
$2$	2.12713	+	1.22810i	1.50411	+	0.868399i	0.504123	+	0.863632i	$0.331816\pi$
$3$		0			0
$3$		0			0
$4$	2.01647	+	3.49262i	1.00823	+	1.74631i
$5$	1.45193	−	1.70056i	0.649324	−	0.760512i
$5$	1.45193	−	1.70056i	0.649324	−	0.760512i
$6$		0			0
$7$			4.50527i			1.70283i	0.524490	+	0.851417i	$0.324256\pi$
$7$			4.50527i			1.70283i	−0.524490	+	0.851417i	$0.675744\pi$
$8$			4.99330i			1.76540i
$9$		0			0
$10$	5.17691	−	1.83419i	1.63708	−	0.580022i
$11$	−2.19869			−0.662930			−0.331465	−	0.943467i	$-0.607543\pi$
$11$	−2.19869			−0.662930			−0.331465	+	0.943467i	$0.607543\pi$
$12$		0			0
$13$	3.25495	−	1.87925i	0.902761	−	0.521209i	0.0246661	−	0.999696i	$-0.492148\pi$
$13$	3.25495	−	1.87925i	0.902761	−	0.521209i	0.878095	+	0.478486i	$0.158814\pi$
$14$	−5.53293	+	9.58332i	−1.47874	+	2.56125i
$15$		0			0
$16$	−2.09935	+	3.63617i	−0.524836	+	0.909043i
$17$	0.576674	+	0.332943i	0.139864	+	0.0807506i	0.568299	−	0.822822i	$-0.307602\pi$
$17$	0.576674	+	0.332943i	0.139864	+	0.0807506i	−0.428435	+	0.903573i	$0.640935\pi$
$18$		0			0
$19$	−3.79804	+	2.13891i	−0.871329	+	0.490699i
$19$	−3.79804	+	2.13891i	−0.871329	+	0.490699i
$20$	8.86718	+	1.64194i	1.98276	+	0.367149i
$21$		0			0
$22$	−4.67691	−	2.70022i	−0.997121	−	0.575688i
$23$	−0.422643	+	0.244013i	−0.0881272	+	0.0508802i	−0.543416	−	0.839464i	$-0.682869\pi$
$23$	−0.422643	+	0.244013i	−0.0881272	+	0.0508802i	0.455289	+	0.890344i	$0.349536\pi$
$24$		0			0
$25$	−0.783783	−	4.93819i	−0.156757	−	0.987637i
$26$	9.23163			1.81047
$27$		0			0
$28$	−15.7352	+	9.08474i	−2.97368	+	1.71685i
$29$	−1.79804	−	3.11429i	−0.333887	−	0.578309i	0.649383	−	0.760461i	$-0.275027\pi$
$29$	−1.79804	−	3.11429i	−0.333887	−	0.578309i	−0.983270	+	0.182152i	$0.941694\pi$
$30$		0			0
$31$	6.83424			1.22747			0.613733	−	0.789514i	$-0.289667\pi$
$31$	6.83424			1.22747			0.613733	+	0.789514i	$0.289667\pi$
$32$	−0.282531	+	0.163119i	−0.0499449	+	0.0288357i
$33$		0			0
$34$	0.817776	+	1.41643i	0.140247	+	0.242916i
$35$	7.66147	+	6.54135i	1.29503	+	1.10569i
$36$		0			0
$37$		−	3.01171i		−	0.495123i	−0.968872	−	0.247561i	$-0.920371\pi$
$37$		−	3.01171i		−	0.495123i	0.968872	−	0.247561i	$-0.0796292\pi$
$38$	−10.7057	−	0.114636i	−1.73670	−	0.0185964i
$39$		0			0
$40$	8.49139	+	7.24994i	1.34261	+	1.14632i
$41$	0.0362063	−	0.0627112i	0.00565448	−	0.00979384i	−0.863184	−	0.504889i	$-0.831533\pi$
$41$	0.0362063	−	0.0627112i	0.00565448	−	0.00979384i	0.868839	+	0.495095i	$0.164867\pi$
$42$		0			0
$43$	0.364199	+	0.210271i	0.0555399	+	0.0320660i	0.527513	−	0.849547i	$-0.323125\pi$
$43$	0.364199	+	0.210271i	0.0555399	+	0.0320660i	−0.471973	+	0.881613i	$0.656458\pi$
$44$	−4.43359	−	7.67920i	−0.668389	−	1.15768i
$45$		0			0
$46$	−1.19869			−0.176737
$47$	−4.34986	+	2.51139i	−0.634492	+	0.366324i	−0.782490	−	0.622664i	$-0.786050\pi$
$47$	−4.34986	+	2.51139i	−0.634492	+	0.366324i	0.147998	+	0.988988i	$0.452717\pi$
$48$		0			0
$49$	−13.2975			−1.89964
$50$	4.39738	−	11.4668i	0.621884	−	1.62164i
$51$		0			0
$52$	13.1270	+	7.57888i	1.82039	+	1.05100i
$53$	2.26725	−	1.30900i	0.311430	−	0.179804i	−0.336136	−	0.941813i	$-0.609120\pi$
$53$	2.26725	−	1.30900i	0.311430	−	0.179804i	0.647566	+	0.762009i	$0.275787\pi$
$54$		0			0
$55$	−3.19235	+	3.73900i	−0.430457	+	0.504166i
$56$	−22.4962			−3.00618
$57$		0			0
$58$		−	8.83269i		−	1.15979i
$59$	−6.26783	+	10.8562i	−0.816002	+	1.41336i	0.0926038	+	0.995703i	$0.470481\pi$
$59$	−6.26783	+	10.8562i	−0.816002	+	1.41336i	−0.908606	+	0.417654i	$0.862852\pi$
$60$		0			0
$61$	−3.53293	−	6.11922i	−0.452346	−	0.783486i	0.546185	−	0.837664i	$-0.316079\pi$
$61$	−3.53293	−	6.11922i	−0.452346	−	0.783486i	−0.998531	+	0.0541782i	$0.982746\pi$
$62$	14.5374	+	8.39315i	1.84625	+	1.06593i
$63$		0			0
$64$	7.59607			0.949509
$65$	1.53020	−	8.26377i	0.189799	−	1.02499i
$66$		0			0
$67$	4.95944	−	2.86334i	0.605892	−	0.349812i	−0.165464	−	0.986216i	$-0.552912\pi$
$67$	4.95944	−	2.86334i	0.605892	−	0.349812i	0.771356	+	0.636404i	$0.219579\pi$
$68$			2.68548i			0.325662i
$69$		0			0
$70$	8.26353	+	23.3234i	0.987681	+	2.78768i
$71$	3.48626	−	6.03838i	0.413743	−	0.716624i	−0.581552	−	0.813509i	$-0.697554\pi$
$71$	3.48626	−	6.03838i	0.413743	−	0.716624i	0.995296	+	0.0968847i	$0.0308878\pi$
$72$		0			0
$73$	−2.56139	−	1.47882i	−0.299788	−	0.173083i	0.342560	−	0.939496i	$-0.388706\pi$
$73$	−2.56139	−	1.47882i	−0.299788	−	0.173083i	−0.642348	+	0.766413i	$0.722039\pi$
$74$	3.69869	−	6.40632i	0.429964	−	0.744720i
$75$		0			0
$76$	−15.1290	−	8.95208i	−1.73542	−	1.02687i
$77$		−	9.90571i		−	1.12886i
$78$		0			0
$79$	5.66849	−	9.81811i	0.637755	−	1.10462i	−0.348170	−	0.937431i	$-0.613197\pi$
$79$	5.66849	−	9.81811i	0.637755	−	1.10462i	0.985924	−	0.167192i	$-0.0534699\pi$
$80$	3.13541	+	8.84953i	0.350549	+	0.989408i
$81$		0			0
$82$	0.154031	−	0.0889301i	0.0170099	−	0.00982068i
$83$		−	15.6999i		−	1.72328i	−0.507517	−	0.861642i	$-0.669436\pi$
$83$		−	15.6999i		−	1.72328i	0.507517	−	0.861642i	$-0.330564\pi$
$84$		0			0
$85$	1.40348	−	0.497256i	0.152229	−	0.0539350i
$86$	0.516467	+	0.894547i	0.0556921	+	0.0964615i
$87$		0			0
$88$		−	10.9787i		−	1.17034i
$89$	0.668486	+	1.15785i	0.0708594	+	0.122732i	0.899278	−	0.437377i	$-0.144092\pi$
$89$	0.668486	+	1.15785i	0.0708594	+	0.122732i	−0.828419	+	0.560109i	$0.810759\pi$
$90$		0			0
$91$	8.46652	+	14.6644i	0.887533	+	1.53725i
$92$	−1.70449	−	0.984089i	−0.177706	−	0.102598i
$93$		0			0
$94$	−12.3370			−1.27246
$95$	−1.87716	+	9.56432i	−0.192593	+	0.981279i
$96$		0			0
$97$	−3.79871	−	2.19319i	−0.385701	−	0.222685i	0.294595	−	0.955622i	$-0.404815\pi$
$97$	−3.79871	−	2.19319i	−0.385701	−	0.222685i	−0.680296	+	0.732938i	$0.738149\pi$
$98$	−28.2856	−	16.3307i	−2.85727	−	1.64965i
$99$		0			0
$100$	15.6668	−	12.6952i	1.56668	−	1.26952i
$101$	−5.28430	−	9.15267i	−0.525807	−	0.910725i	−0.999548	−	0.0300608i	$-0.990430\pi$
$101$	−5.28430	−	9.15267i	−0.525807	−	0.910725i	0.473741	−	0.880664i	$-0.342903\pi$
$102$		0			0
$103$		−	5.75615i		−	0.567171i	−0.958947	−	0.283585i	$-0.908476\pi$
$103$		−	5.75615i		−	0.567171i	0.958947	−	0.283585i	$-0.0915239\pi$
$104$	9.38364	+	16.2529i	0.920142	+	1.59373i
$105$		0			0
$106$	6.43032			0.624568
$107$			1.30229i			0.125897i	0.998017	+	0.0629486i	$0.0200504\pi$
$107$			1.30229i			0.125897i	−0.998017	+	0.0629486i	$0.979950\pi$
$108$		0			0
$109$	−6.01647	+	10.4208i	−0.576273	+	0.998134i	0.419629	+	0.907696i	$0.362160\pi$
$109$	−6.01647	+	10.4208i	−0.576273	+	0.998134i	−0.995902	+	0.0904385i	$0.971173\pi$
$110$	−11.3824	+	4.03282i	−1.08527	+	0.384514i
$111$		0			0
$112$	−16.3820	−	9.45813i	−1.54795	−	0.893709i
$113$			7.74626i			0.728707i	0.931261	+	0.364353i	$0.118710\pi$
$113$			7.74626i			0.728707i	−0.931261	+	0.364353i	$0.881290\pi$
$114$		0			0
$115$	−0.198691	+	1.07302i	−0.0185281	+	0.100060i
$116$	7.25136	−	12.5597i	0.673272	−	1.16614i
$117$		0			0
$118$	−26.6650	+	15.3951i	−2.45472	+	1.41723i
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	−6.16576			−0.560523
$122$		−	17.3552i		−	1.57127i
$123$		0			0
$124$	13.7810	+	23.8694i	1.23757	+	2.14354i
$125$	−9.53566	−	5.83705i	−0.852896	−	0.522081i
$126$		0			0
$127$	−3.40898	+	1.96818i	−0.302498	+	0.174647i	−0.643565	−	0.765392i	$-0.722545\pi$
$127$	−3.40898	+	1.96818i	−0.302498	+	0.174647i	0.341066	+	0.940039i	$0.389212\pi$
$128$	16.7229	+	9.65499i	1.47811	+	0.853389i
$129$		0			0
$130$	13.4037	−	15.6989i	1.17558	−	1.37688i
$131$	−8.16248	+	14.1378i	−0.713160	+	1.23523i	0.250505	+	0.968115i	$0.419403\pi$
$131$	−8.16248	+	14.1378i	−0.713160	+	1.23523i	−0.963665	+	0.267114i	$0.913930\pi$
$132$		0			0
$133$	−9.63635	−	17.1112i	−0.835578	−	1.48373i
$134$	14.0659			1.21511
$135$		0			0
$136$	−1.66248	+	2.87951i	−0.142557	+	0.246916i
$137$	14.2293	−	8.21529i	1.21569	−	0.701879i	0.251697	−	0.967806i	$-0.419011\pi$
$137$	14.2293	−	8.21529i	1.21569	−	0.701879i	0.963993	+	0.265927i	$0.0856780\pi$
$138$		0			0
$139$	−1.33424	−	2.31098i	−0.113169	−	0.196015i	0.803877	−	0.594795i	$-0.202767\pi$
$139$	−1.33424	−	2.31098i	−0.113169	−	0.196015i	−0.917046	+	0.398781i	$0.869433\pi$
$140$	−7.39738	+	39.9491i	−0.625193	+	3.37631i
$141$		0			0
$142$	14.8315	−	8.56297i	1.24463	−	0.718588i
$143$	−7.15663	+	4.13188i	−0.598468	+	0.345526i
$144$		0			0
$145$	−7.90666	−	1.46408i	−0.656612	−	0.121585i
$146$	−3.63228	−	6.29129i	−0.300610	−	0.520671i
$147$		0			0
$148$	10.5188	−	6.07302i	0.864639	−	0.499199i
$149$	8.98299	−	15.5590i	0.735915	−	1.27464i	−0.218405	−	0.975858i	$-0.570085\pi$
$149$	8.98299	−	15.5590i	0.735915	−	1.27464i	0.954321	−	0.298784i	$-0.0965812\pi$
$150$		0			0
$151$	−12.7344			−1.03631			−0.518154	−	0.855288i	$-0.673380\pi$
$151$	−12.7344			−1.03631			−0.518154	+	0.855288i	$0.673380\pi$
$152$	−10.6802	−	18.9647i	−0.866278	−	1.53824i
$153$		0			0
$154$	12.1652	−	21.0708i	0.980301	−	1.69793i
$155$	9.92286	−	11.6220i	0.797023	−	0.933503i
$156$		0			0
$157$	17.3674	+	10.0270i	1.38607	+	0.800245i	0.992869	−	0.119209i	$-0.0380358\pi$
$157$	17.3674	+	10.0270i	1.38607	+	0.800245i	0.393197	+	0.919454i	$0.371369\pi$
$158$	24.1153	−	13.9230i	1.91851	−	1.10765i
$159$		0			0
$160$	−0.132822	+	0.717298i	−0.0105005	+	0.0567074i
$161$	−1.09935	−	1.90412i	−0.0866406	−	0.150066i
$162$		0			0
$163$			14.2331i			1.11482i	0.830236	+	0.557412i	$0.188206\pi$
$163$			14.2331i			1.11482i	−0.830236	+	0.557412i	$0.811794\pi$
$164$	0.292035			0.0228041
$165$		0			0
$166$	19.2810	−	33.3957i	1.49650	−	2.59201i
$167$	−4.86386	+	2.80815i	−0.376376	+	0.217301i	−0.676241	−	0.736681i	$-0.736392\pi$
$167$	−4.86386	+	2.80815i	−0.376376	+	0.217301i	0.299864	+	0.953982i	$0.403059\pi$
$168$		0			0
$169$	0.563139	−	0.975386i	0.0433184	−	0.0750297i
$170$	3.59607	+	0.665886i	0.275806	+	0.0510711i
$171$		0			0
$172$			1.69601i			0.129320i
$173$	9.25824	+	5.34524i	0.703891	+	0.406391i	0.808795	−	0.588091i	$-0.200120\pi$
$173$	9.25824	+	5.34524i	0.703891	+	0.406391i	−0.104904	+	0.994482i	$0.533454\pi$
$174$		0			0
$175$	22.2479	−	3.53116i	1.68178	−	0.266930i
$176$	4.61581	−	7.99482i	0.347930	−	0.602632i
$177$		0			0
$178$			3.28388i			0.246137i
$179$	7.68942			0.574734			0.287367	−	0.957821i	$-0.407220\pi$
$179$	7.68942			0.574734			0.287367	+	0.957821i	$0.407220\pi$
$180$		0			0
$181$	3.06314	+	5.30551i	0.227681	+	0.394356i	0.957121	−	0.289690i	$-0.0935522\pi$
$181$	3.06314	+	5.30551i	0.227681	+	0.394356i	−0.729439	+	0.684046i	$0.760219\pi$
$182$			41.5910i			3.08293i
$183$		0			0
$184$	−1.21843	−	2.11038i	−0.0898239	−	0.155580i
$185$	−5.12159	−	4.37281i	−0.376547	−	0.321495i
$186$		0			0
$187$	−1.26793	−	0.732039i	−0.0927201	−	0.0535320i
$188$	−17.5427	−	10.1283i	−1.27943	−	0.738680i
$189$		0			0
$190$	−15.7389	+	18.0392i	−1.14182	+	1.30870i
$191$	−5.85517			−0.423666			−0.211833	−	0.977306i	$-0.567943\pi$
$191$	−5.85517			−0.423666			−0.211833	+	0.977306i	$0.567943\pi$
$192$		0			0
$193$	2.24402	+	1.29559i	0.161528	+	0.0932584i	0.578585	−	0.815622i	$-0.303605\pi$
$193$	2.24402	+	1.29559i	0.161528	+	0.0932584i	−0.417057	+	0.908880i	$0.636938\pi$
$194$	−5.38692	−	9.33041i	−0.386758	−	0.669885i
$195$		0			0
$196$	−26.8140	−	46.4431i	−1.91528	−	3.31737i
$197$			19.8628i			1.41517i	0.706629	+	0.707584i	$0.250215\pi$
$197$			19.8628i			1.41517i	−0.706629	+	0.707584i	$0.749785\pi$
$198$		0			0
$199$	−6.38092	−	11.0521i	−0.452331	−	0.783460i	0.546199	−	0.837655i	$-0.316074\pi$
$199$	−6.38092	−	11.0521i	−0.452331	−	0.783460i	−0.998530	+	0.0541948i	$0.982741\pi$
$200$	24.6578	−	3.91366i	1.74357	−	0.276738i
$201$		0			0
$202$		−	25.9586i		−	1.82644i
$203$	14.0307	−	8.10065i	0.984765	−	0.568554i
$204$		0			0
$205$	−0.0540748	−	0.152623i	−0.00377675	−	0.0106597i
$206$	7.06914	−	12.2441i	0.492530	−	0.853088i
$207$		0			0
$208$			15.7808i			1.09420i
$209$	8.35071	−	4.70279i	0.577631	−	0.325299i
$210$		0			0
$211$	−6.92759	+	11.9989i	−0.476915	+	0.826041i	−0.999650	−	0.0264545i	$-0.991578\pi$
$211$	−6.92759	+	11.9989i	−0.476915	+	0.826041i	0.522735	+	0.852495i	$0.324912\pi$
$212$	9.14366	+	5.27909i	0.627989	+	0.362570i
$213$		0			0
$214$	−1.59935	+	2.77015i	−0.109329	+	0.189363i
$215$	0.886370	−	0.314043i	0.0604499	−	0.0214175i
$216$		0			0
$217$			30.7901i			2.09017i
$218$	−25.5957	+	14.7777i	−1.73356	+	1.00087i
$219$		0			0
$220$	−19.4962	−	3.61012i	−1.31443	−	0.243394i
$221$	2.50273			0.168352
$222$		0			0
$223$	−18.7893	−	10.8480i	−1.25823	−	0.726437i	−0.285496	−	0.958380i	$-0.592158\pi$
$223$	−18.7893	−	10.8480i	−1.25823	−	0.726437i	−0.972729	+	0.231943i	$0.925492\pi$
$224$	−0.734898	−	1.27288i	−0.0491024	−	0.0850479i
$225$		0			0
$226$	−9.51320	+	16.4773i	−0.632808	+	1.09606i
$227$			8.19628i			0.544006i	0.962296	+	0.272003i	$0.0876861\pi$
$227$			8.19628i			0.544006i	−0.962296	+	0.272003i	$0.912314\pi$
$228$		0			0
$229$	16.6619			1.10105			0.550526	−	0.834818i	$-0.314427\pi$
$229$	16.6619			1.10105			0.550526	+	0.834818i	$0.314427\pi$
$230$	−1.74042	+	2.03844i	−0.114760	+	0.134411i
$231$		0			0
$232$	15.5506	−	8.97814i	1.02095	−	0.589444i
$233$	10.5772	+	6.10677i	0.692937	+	0.400068i	0.804711	−	0.593666i	$-0.202320\pi$
$233$	10.5772	+	6.10677i	0.692937	+	0.400068i	−0.111774	+	0.993734i	$0.535653\pi$
$234$		0			0
$235$	−2.04494	+	11.0435i	−0.133397	+	0.720402i
$236$	−50.5555			−3.29088
$237$		0			0
$238$	−6.38140	+	3.68430i	−0.413645	+	0.238818i
$239$	2.03948			0.131923			0.0659614	−	0.997822i	$-0.478989\pi$
$239$	2.03948			0.131923			0.0659614	+	0.997822i	$0.478989\pi$
$240$		0			0
$241$	−8.76183	−	15.1759i	−0.564399	−	0.977568i	−0.997105	−	0.0760330i	$-0.975775\pi$
$241$	−8.76183	−	15.1759i	−0.564399	−	0.977568i	0.432706	−	0.901535i	$-0.357559\pi$
$242$	−13.1154	−	7.57218i	−0.843089	−	0.486758i
$243$		0			0
$244$	14.2481	−	24.6784i	0.912141	−	1.57987i
$245$	−19.3071	+	22.6131i	−1.23348	+	1.44470i
$246$		0			0
$247$	−8.34289	+	14.0995i	−0.530846	+	0.897129i
$248$			34.1254i			2.16697i
$249$		0			0
$250$	−13.1152	−	24.1269i	−0.829475	−	1.52592i
$251$	−1.66903	−	2.89084i	−0.105348	−	0.182468i	0.808532	−	0.588452i	$-0.200262\pi$
$251$	−1.66903	−	2.89084i	−0.105348	−	0.182468i	−0.913880	+	0.405984i	$0.866929\pi$
$252$		0			0
$253$	0.929261	−	0.536509i	0.0584222	−	0.0337301i
$254$	−9.66849			−0.606655
$255$		0			0
$256$	16.1185	+	27.9181i	1.00741	+	1.74488i
$257$	−23.8889	+	13.7922i	−1.49015	+	0.860337i	−0.999937	−	0.0112676i	$-0.996413\pi$
$257$	−23.8889	+	13.7922i	−1.49015	+	0.860337i	−0.490210	+	0.871604i	$0.663080\pi$
$258$		0			0
$259$	13.5686			0.843112
$260$	31.9478	−	11.3192i	1.98132	−	0.701986i
$261$		0			0
$262$	−34.7254	+	20.0487i	−2.14534	+	1.23861i
$263$	−11.8006	−	6.81310i	−0.727658	−	0.420114i	0.0899066	−	0.995950i	$-0.471343\pi$
$263$	−11.8006	−	6.81310i	−0.727658	−	0.420114i	−0.817565	+	0.575837i	$0.804676\pi$
$264$		0			0
$265$	1.06587	−	5.75615i	0.0654758	−	0.353598i
$266$	0.516467	−	48.2322i	0.0316666	−	2.95731i
$267$		0			0
$268$	20.0011	+	11.5476i	1.22176	+	0.705385i
$269$	1.80404	−	3.12469i	0.109994	−	0.190515i	−0.805773	−	0.592224i	$-0.798250\pi$
$269$	1.80404	−	3.12469i	0.109994	−	0.190515i	0.915768	+	0.401708i	$0.131583\pi$
$270$		0			0
$271$	−5.28157	+	9.14795i	−0.320833	+	0.555698i	−0.980660	−	0.195719i	$-0.937296\pi$
$271$	−5.28157	+	9.14795i	−0.320833	+	0.555698i	0.659828	+	0.751417i	$0.270629\pi$
$272$	−2.42128	+	1.39793i	−0.146812	+	0.0847617i
$273$		0			0
$274$	40.3568			2.43804
$275$	1.72330	+	10.8575i	0.103919	+	0.654735i
$276$		0			0
$277$			6.73487i			0.404659i	0.979317	+	0.202330i	$0.0648512\pi$
$277$			6.73487i			0.404659i	−0.979317	+	0.202330i	$0.935149\pi$
$278$		−	6.55434i		−	0.393103i
$279$		0			0
$280$	−32.6629	+	38.2560i	−1.95198	+	2.28624i
$281$	11.7152	+	20.2912i	0.698868	+	1.21047i	0.968859	+	0.247612i	$0.0796457\pi$
$281$	11.7152	+	20.2912i	0.698868	+	1.21047i	−0.269992	+	0.962863i	$0.587021\pi$
$282$		0			0
$283$	12.7160	+	7.34157i	0.755886	+	0.436411i	0.827817	−	0.560999i	$-0.189583\pi$
$283$	12.7160	+	7.34157i	0.755886	+	0.436411i	−0.0719306	+	0.997410i	$0.522916\pi$
$284$	28.1197			1.66860
$285$		0			0
$286$	−20.2975			−1.20022
$287$	0.282531	+	0.163119i	0.0166773	+	0.00962863i
$288$		0			0
$289$	−8.27830	−	14.3384i	−0.486959	−	0.843437i
$290$	−15.0205	−	12.8245i	−0.882033	−	0.753079i
$291$		0			0
$292$		−	11.9280i		−	0.698031i
$293$			18.1855i			1.06241i	0.847243	+	0.531206i	$0.178261\pi$
$293$			18.1855i			1.06241i	−0.847243	+	0.531206i	$0.821739\pi$
$294$		0			0
$295$	9.36111	+	26.4213i	0.545025	+	1.53831i
$296$	15.0384			0.874089
$297$		0			0
$298$	38.2161	−	22.0641i	2.21380	−	1.27814i
$299$	−0.917122	+	1.58850i	−0.0530385	+	0.0918654i
$300$		0			0
$301$	−0.947326	+	1.64082i	−0.0546030	+	0.0945752i
$302$	−27.0877	−	15.6391i	−1.55872	−	0.899928i
$303$		0			0
$304$	0.195962	−	18.3006i	0.0112392	−	1.04961i
$305$	−15.5357	−	2.87674i	−0.889570	−	0.164722i
$306$		0			0
$307$	25.4439	+	14.6901i	1.45216	+	0.838406i	0.998604	−	0.0528200i	$-0.0168209\pi$
$307$	25.4439	+	14.6901i	1.45216	+	0.838406i	0.453559	+	0.891226i	$0.350154\pi$
$308$	34.5969	−	19.9745i	1.97134	−	1.13815i
$309$		0			0
$310$	35.3803	−	12.5353i	2.00946	−	0.711958i
$311$	0.193232			0.0109572			0.00547859	−	0.999985i	$-0.498256\pi$
$311$	0.193232			0.0109572			0.00547859	+	0.999985i	$0.498256\pi$
$312$		0			0
$313$	−18.4251	+	10.6377i	−1.04145	+	0.601281i	−0.920243	−	0.391346i	$-0.872009\pi$
$313$	−18.4251	+	10.6377i	−1.04145	+	0.601281i	−0.121206	+	0.992627i	$0.538676\pi$
$314$	24.6285	+	42.6578i	1.38986	+	2.40732i
$315$		0			0
$316$	45.7213			2.57202
$317$	16.6018	−	9.58506i	0.932451	−	0.538351i	0.0448649	−	0.998993i	$-0.485714\pi$
$317$	16.6018	−	9.58506i	0.932451	−	0.538351i	0.887586	+	0.460642i	$0.152381\pi$
$318$		0			0
$319$	3.95333	+	6.84736i	0.221344	+	0.383379i
$320$	11.0290	−	12.9176i	0.616539	−	0.722113i
$321$		0			0
$322$		−	5.40043i		−	0.300954i
$323$	−2.90236	−	0.0310783i	−0.161492	−	0.00172924i
$324$		0			0
$325$	−11.8312	−	14.6006i	−0.656280	−	0.809897i
$326$	−17.4797	+	30.2758i	−0.968112	+	1.67682i
$327$		0			0
$328$	0.313136	+	0.180789i	0.0172900	+	0.00998240i
$329$	−11.3145	−	19.5973i	−0.623789	−	1.08043i
$330$		0			0
$331$	−20.6070			−1.13266			−0.566331	−	0.824178i	$-0.691638\pi$
$331$	−20.6070			−1.13266			−0.566331	+	0.824178i	$0.691638\pi$
$332$	54.8337	−	31.6583i	3.00939	−	1.73747i
$333$		0			0
$334$	−13.7948			−0.754816
$335$	2.33151	−	12.5912i	0.127384	−	0.687930i
$336$		0			0
$337$	−8.83982	−	5.10368i	−0.481536	−	0.278015i	0.239520	−	0.970891i	$-0.423010\pi$
$337$	−8.83982	−	5.10368i	−0.481536	−	0.278015i	−0.721056	+	0.692876i	$0.756343\pi$
$338$	2.39575	−	1.38318i	0.130311	−	0.0752353i
$339$		0			0
$340$	4.56680	+	3.89913i	0.247670	+	0.211460i
$341$	−15.0264			−0.813725
$342$		0			0
$343$		−	28.3719i		−	1.53194i
$344$	−1.04994	+	1.81856i	−0.0566092	+	0.0980500i
$345$		0			0
$346$	13.1290	+	22.7401i	0.705820	+	1.22252i
$347$	−4.71213	−	2.72055i	−0.252960	−	0.146047i	0.368159	−	0.929763i	$-0.379988\pi$
$347$	−4.71213	−	2.72055i	−0.252960	−	0.146047i	−0.621119	+	0.783716i	$0.713322\pi$
$348$		0			0
$349$	1.55114			0.0830304			0.0415152	−	0.999138i	$-0.486781\pi$
$349$	1.55114			0.0830304			0.0415152	+	0.999138i	$0.486781\pi$
$350$	51.6609	+	19.8114i	2.76139	+	1.05896i
$351$		0			0
$352$	0.621199	−	0.358649i	0.0331100	−	0.0191161i
$353$			32.9335i			1.75287i	0.481517	+	0.876437i	$0.340086\pi$
$353$			32.9335i			1.75287i	−0.481517	+	0.876437i	$0.659914\pi$
$354$		0			0
$355$	−5.20679	−	14.6959i	−0.276348	−	0.779978i
$356$	−2.69596	+	4.66954i	−0.142886	+	0.247485i
$357$		0			0
$358$	16.3564	+	9.44339i	0.864464	+	0.499098i
$359$	1.74864	−	3.02873i	0.0922894	−	0.159850i	−0.816185	−	0.577791i	$-0.803915\pi$
$359$	1.74864	−	3.02873i	0.0922894	−	0.159850i	0.908474	+	0.417941i	$0.137248\pi$
$360$		0			0
$361$	9.85017	−	16.2473i	0.518430	−	0.855120i
$362$			15.0474i			0.790873i
$363$		0			0
$364$	−34.1449	+	59.1408i	−1.78968	+	3.09982i
$365$	−6.23378	+	2.20864i	−0.326291	+	0.115606i
$366$		0			0
$367$	−16.8909	+	9.75196i	−0.881697	+	0.509048i	−0.871218	−	0.490897i	$-0.836669\pi$
$367$	−16.8909	+	9.75196i	−0.881697	+	0.509048i	−0.0104794	+	0.999945i	$0.503336\pi$
$368$		−	2.04907i		−	0.106815i
$369$		0			0
$370$	−5.52406	−	15.5914i	−0.287182	−	0.810557i
$371$	5.89738	+	10.2146i	0.306177	+	0.530314i
$372$		0			0
$373$			23.5158i			1.21760i	0.793322	+	0.608802i	$0.208350\pi$
$373$			23.5158i			1.21760i	−0.793322	+	0.608802i	$0.791650\pi$
$374$	−1.79804	−	3.11429i	−0.0929743	−	0.161036i
$375$		0			0
$376$	−12.5401	−	21.7201i	−0.646708	−	1.12013i
$377$	−11.7050	−	6.75791i	−0.602841	−	0.348050i
$378$		0			0
$379$	7.05148			0.362210			0.181105	−	0.983464i	$-0.442033\pi$
$379$	7.05148			0.362210			0.181105	+	0.983464i	$0.442033\pi$
$380$	−37.1898	+	12.7299i	−1.90780	+	0.653031i
$381$		0			0
$382$	−12.4547	−	7.19075i	−0.637240	−	0.367911i
$383$	2.67090	+	1.54204i	0.136476	+	0.0787947i	0.566684	−	0.823935i	$-0.308226\pi$
$383$	2.67090	+	1.54204i	0.136476	+	0.0787947i	−0.430207	+	0.902730i	$0.641560\pi$
$384$		0			0
$385$	−16.8452	−	14.3824i	−0.858511	−	0.732996i
$386$	3.18222	+	5.51177i	0.161971	+	0.280542i
$387$		0			0
$388$		−	17.6900i		−	0.898072i
$389$	−4.69542	−	8.13270i	−0.238067	−	0.412345i	0.722092	−	0.691797i	$-0.243181\pi$
$389$	−4.69542	−	8.13270i	−0.238067	−	0.412345i	−0.960160	+	0.279452i	$0.909847\pi$
$390$		0			0
$391$	−0.324970			−0.0164344
$392$		−	66.3984i		−	3.35362i
$393$		0			0
$394$	−24.3936	+	42.2509i	−1.22893	+	2.12857i
$395$	−8.46598	−	23.8948i	−0.425970	−	1.20228i
$396$		0			0
$397$	−23.1744	−	13.3797i	−1.16309	−	0.671510i	−0.211047	−	0.977476i	$-0.567687\pi$
$397$	−23.1744	−	13.3797i	−1.16309	−	0.671510i	−0.952042	+	0.305966i	$0.901021\pi$
$398$		−	31.3456i		−	1.57122i
$399$		0			0
$400$	19.6015	+	7.51699i	0.980077	+	0.375849i
$401$	−12.5851	+	21.7980i	−0.628468	+	1.08854i	0.359391	+	0.933187i	$0.382984\pi$
$401$	−12.5851	+	21.7980i	−0.628468	+	1.08854i	−0.987859	+	0.155352i	$0.950349\pi$
$402$		0			0
$403$	22.2451	−	12.8432i	1.10811	−	0.639767i
$404$	21.3112	−	36.9121i	1.06027	−	1.83645i
$405$		0			0
$406$	39.7937			1.97493
$407$			6.62183i			0.328232i
$408$		0			0
$409$	−14.1608	−	24.5271i	−0.700204	−	1.21279i	−0.968395	−	0.249423i	$-0.919759\pi$
$409$	−14.1608	−	24.5271i	−0.700204	−	1.21279i	0.268191	−	0.963366i	$-0.413574\pi$
$410$	0.0724126	−	0.391060i	0.00357621	−	0.0193131i
$411$		0			0
$412$	20.1041	−	11.6071i	0.990457	−	0.571840i
$413$	−48.9102	−	28.2383i	−2.40671	−	1.38952i
$414$		0			0
$415$	−26.6985	−	22.7951i	−1.31058	−	1.11897i
$416$	−0.613083	+	1.06189i	−0.0300589	+	0.0520635i
$417$		0			0
$418$	23.5386	+	0.252049i	1.15131	+	0.0123281i
$419$	13.0449			0.637287			0.318643	−	0.947875i	$-0.396773\pi$
$419$	13.0449			0.637287			0.318643	+	0.947875i	$0.396773\pi$
$420$		0			0
$421$	−1.66248	+	2.87951i	−0.0810246	+	0.140339i	−0.903690	−	0.428187i	$-0.859153\pi$
$421$	−1.66248	+	2.87951i	−0.0810246	+	0.140339i	0.822666	+	0.568525i	$0.192486\pi$
$422$	−29.4718	+	17.0156i	−1.43467	+	0.828305i
$423$		0			0
$424$	6.53621	+	11.3210i	0.317426	+	0.549798i
$425$	1.19215	−	3.10868i	0.0578276	−	0.150793i
$426$		0			0
$427$	27.5688	−	15.9168i	1.33415	−	0.770270i
$428$	−4.54841	+	2.62603i	−0.219856	+	0.126934i
$429$		0			0
$430$	2.27110	+	0.420541i	0.109522	+	0.0202803i
$431$	0.0242034	+	0.0419216i	0.00116584	+	0.00201929i	0.866608	−	0.498990i	$-0.166296\pi$
$431$	0.0242034	+	0.0419216i	0.00116584	+	0.00201929i	−0.865442	+	0.501009i	$0.832962\pi$
$432$		0			0
$433$	−8.28676	+	4.78436i	−0.398236	+	0.229922i	−0.685723	−	0.727863i	$-0.740514\pi$
$433$	−8.28676	+	4.78436i	−0.398236	+	0.229922i	0.287486	+	0.957785i	$0.407180\pi$
$434$	−37.8134	+	65.4948i	−1.81510	+	3.14385i
$435$		0			0
$436$	−48.5280			−2.32407
$437$	1.08329	−	1.83076i	0.0518209	−	0.0875773i
$438$		0			0
$439$	−11.1257	+	19.2703i	−0.531002	+	0.919723i	0.468343	+	0.883547i	$0.344851\pi$
$439$	−11.1257	+	19.2703i	−0.531002	+	0.919723i	−0.999345	+	0.0361764i	$0.988482\pi$
$440$	−18.6699	−	15.9404i	−0.890054	−	0.759927i
$441$		0			0
$442$	5.32364	+	3.07361i	0.253220	+	0.146197i
$443$	−17.4207	+	10.0579i	−0.827684	+	0.477863i	−0.853059	−	0.521815i	$-0.825255\pi$
$443$	−17.4207	+	10.0579i	−0.827684	+	0.477863i	0.0253753	+	0.999678i	$0.491922\pi$
$444$		0			0
$445$	2.93959	+	0.544325i	0.139350	+	0.0258035i
$446$	−26.6449	−	46.1504i	−1.26167	−	2.18528i
$447$		0			0
$448$			34.2224i			1.61686i
$449$	−12.4973			−0.589783			−0.294891	−	0.955531i	$-0.595283\pi$
$449$	−12.4973			−0.589783			−0.294891	+	0.955531i	$0.595283\pi$
$450$		0			0
$451$	−0.0796065	+	0.137883i	−0.00374852	+	0.00649263i
$452$	−27.0548	+	15.6201i	−1.27255	+	0.734707i
$453$		0			0
$454$	−10.0659	+	17.4346i	−0.472415	+	0.818246i
$455$	37.2305	+	6.89399i	1.74539	+	0.323195i
$456$		0			0
$457$			28.3179i			1.32465i	0.749215	+	0.662327i	$0.230431\pi$
$457$			28.3179i			1.32465i	−0.749215	+	0.662327i	$0.769569\pi$
$458$	35.4422	+	20.4626i	1.65610	+	0.956153i
$459$		0			0
$460$	−4.14830	+	1.46975i	−0.193416	+	0.0685276i
$461$	2.65976	−	4.60683i	0.123877	−	0.214562i	−0.797416	−	0.603430i	$-0.793800\pi$
$461$	2.65976	−	4.60683i	0.123877	−	0.214562i	0.921293	+	0.388868i	$0.127134\pi$
$462$		0			0
$463$		−	17.9327i		−	0.833401i	−0.909044	−	0.416701i	$-0.863186\pi$
$463$		−	17.9327i		−	0.833401i	0.909044	−	0.416701i	$-0.136814\pi$
$464$	15.0988			0.700944
$465$		0			0
$466$	14.9995	+	25.9798i	0.694836	+	1.20349i
$467$			28.7791i			1.33174i	0.746069	+	0.665868i	$0.231939\pi$
$467$			28.7791i			1.33174i	−0.746069	+	0.665868i	$0.768061\pi$
$468$		0			0
$469$	12.9001	+	22.3436i	0.595672	+	1.03173i
$470$	−17.9125	+	20.9797i	−0.826240	+	0.967722i
$471$		0			0
$472$	−54.2083	−	31.2972i	−2.49514	−	1.44057i
$473$	−0.800762	−	0.462320i	−0.0368191	−	0.0212575i
$474$		0			0
$475$	13.5392	+	17.0790i	0.621219	+	0.783637i
$476$	−12.0988			−0.554548
$477$		0			0
$478$	4.33824	+	2.50469i	0.198427	+	0.114562i
$479$	4.02574	+	6.97279i	0.183941	+	0.318595i	0.943219	−	0.332171i	$-0.107781\pi$
$479$	4.02574	+	6.97279i	0.183941	+	0.318595i	−0.759278	+	0.650766i	$0.774448\pi$
$480$		0			0
$481$	−5.65976	−	9.80298i	−0.258063	−	0.446978i
$482$		−	43.0417i		−	1.96049i
$483$		0			0
$484$	−12.4330	−	21.5347i	−0.565138	−	0.978849i
$485$	−9.24512	+	3.27556i	−0.419799	+	0.148736i
$486$		0			0
$487$		−	1.09761i		−	0.0497376i	−0.999691	−	0.0248688i	$-0.992083\pi$
$487$		−	1.09761i		−	0.0497376i	0.999691	−	0.0248688i	$-0.00791680\pi$
$488$	30.5551	−	17.6410i	1.38316	−	0.798571i
$489$		0			0
$490$	−68.8400	+	24.3901i	−3.10987	+	1.10183i
$491$	6.55267	−	11.3496i	0.295718	−	0.512199i	−0.679434	−	0.733737i	$-0.737774\pi$
$491$	6.55267	−	11.3496i	0.295718	−	0.512199i	0.975152	+	0.221538i	$0.0711078\pi$
$492$		0			0
$493$		−	2.39458i		−	0.107846i
$494$	−35.0621	+	19.7456i	−1.57752	+	0.888395i
$495$		0			0
$496$	−14.3474	+	24.8505i	−0.644219	+	1.11582i
$497$	27.2046	+	15.7066i	1.22029	+	0.704536i
$498$		0			0
$499$	12.0703	−	20.9064i	0.540342	−	0.935900i	−0.458542	−	0.888673i	$-0.651628\pi$
$499$	12.0703	−	20.9064i	0.540342	−	0.935900i	0.998884	−	0.0472275i	$-0.0150386\pi$
$500$	1.15825	−	45.0747i	0.0517987	−	2.01580i
$501$		0			0
$502$		−	8.19895i		−	0.365937i
$503$	16.4214	−	9.48090i	0.732194	−	0.422733i	−0.0870300	−	0.996206i	$-0.527738\pi$
$503$	16.4214	−	9.48090i	0.732194	−	0.422733i	0.819224	+	0.573473i	$0.194404\pi$
$504$		0			0
$505$	−23.2371	−	4.30282i	−1.03404	−	0.191473i
$506$	2.63555			0.117165
$507$		0			0
$508$	−13.7482	−	7.93753i	−0.609978	−	0.352171i
$509$	−10.9803	−	19.0184i	−0.486692	−	0.842974i	0.513191	−	0.858274i	$-0.328463\pi$
$509$	−10.9803	−	19.0184i	−0.486692	−	0.842974i	−0.999883	+	0.0152997i	$0.995130\pi$
$510$		0			0
$511$	6.66248	−	11.5398i	0.294731	−	0.510489i
$512$			40.5609i			1.79255i
$513$		0			0
$514$	−67.7531			−2.98846
$515$	−9.78866	−	8.35755i	−0.431340	−	0.368277i
$516$		0			0
$517$	9.56399	−	5.52177i	0.420624	−	0.242847i
$518$	28.8622	+	16.6636i	1.26813	+	0.732157i
$519$		0			0
$520$	41.2635	+	7.64077i	1.80952	+	0.335070i
$521$	−6.56968			−0.287823			−0.143912	−	0.989591i	$-0.545968\pi$
$521$	−6.56968			−0.287823			−0.143912	+	0.989591i	$0.545968\pi$
$522$		0			0
$523$	3.63538	−	2.09889i	0.158964	−	0.0917779i	−0.418408	−	0.908259i	$-0.637412\pi$
$523$	3.63538	−	2.09889i	0.158964	−	0.0917779i	0.577372	+	0.816481i	$0.304078\pi$
$524$	−65.8375			−2.87613
$525$		0			0
$526$	−16.7344	−	28.9848i	−0.729653	−	1.26380i
$527$	3.94113	+	2.27541i	0.171678	+	0.0991186i
$528$		0			0
$529$	−11.3809	+	19.7123i	−0.494822	+	0.857058i
$530$	9.33639	−	10.9351i	0.405547	−	0.474991i
$531$		0			0
$532$	40.3316	−	68.1603i	1.74860	−	2.95513i
$533$		−	0.272162i		−	0.0117887i
$534$		0			0
$535$	2.21462	+	1.89084i	0.0957463	+	0.0817481i
$536$	14.2975	+	24.7640i	0.617558	+	1.06964i
$537$		0			0
$538$	7.67486	−	4.43108i	0.330887	−	0.191038i
$539$	29.2371			1.25933
$540$		0			0
$541$	2.31505	+	4.00978i	0.0995316	+	0.172394i	0.911491	−	0.411320i	$-0.134932\pi$
$541$	2.31505	+	4.00978i	0.0995316	+	0.172394i	−0.811959	+	0.583714i	$0.801599\pi$
$542$	−22.4692	+	12.9726i	−0.965136	+	0.557221i
$543$		0			0
$544$	−0.217238			−0.00931400
$545$	8.98570	+	25.3617i	0.384905	+	1.08638i
$546$		0			0
$547$	32.9435	−	19.0199i	1.40856	−	0.813233i	0.413312	−	0.910590i	$-0.364372\pi$
$547$	32.9435	−	19.0199i	1.40856	−	0.813233i	0.995250	+	0.0973563i	$0.0310386\pi$
$548$	57.3858	+	33.1317i	2.45140	+	1.41532i
$549$		0			0
$550$	−9.66849	+	25.2118i	−0.412266	+	1.07504i
$551$	13.4902	+	7.98236i	0.574701	+	0.340060i
$552$		0			0
$553$	44.2333	+	25.5381i	1.88099	+	1.08599i
$554$	−8.27110	+	14.3260i	−0.351406	+	0.608652i
$555$		0			0
$556$	5.38092	−	9.32002i	0.228202	−	0.395257i
$557$	31.5498	−	18.2153i	1.33681	−	0.771807i	0.350476	−	0.936572i	$-0.386020\pi$
$557$	31.5498	−	18.2153i	1.33681	−	0.771807i	0.986333	+	0.164765i	$0.0526866\pi$
$558$		0			0
$559$	1.58060			0.0668523
$560$	−39.8696	+	14.1259i	−1.68480	+	0.596927i
$561$		0			0
$562$			57.5496i			2.42758i
$563$		−	20.6856i		−	0.871795i	−0.899996	−	0.435897i	$-0.856431\pi$
$563$		−	20.6856i		−	0.871795i	0.899996	−	0.435897i	$-0.143569\pi$
$564$		0			0
$565$	13.1730	+	11.2470i	0.554190	+	0.473167i
$566$	18.0324	+	31.2330i	0.757958	+	1.31282i
$567$		0			0
$568$	30.1515	+	17.4080i	1.26513	+	0.730422i
$569$	−27.1132			−1.13664			−0.568322	−	0.822806i	$-0.692407\pi$
$569$	−27.1132			−1.13664			−0.568322	+	0.822806i	$0.692407\pi$
$570$		0			0
$571$	46.4687			1.94466			0.972328	−	0.233622i	$-0.0750578\pi$
$571$	46.4687			1.94466			0.972328	+	0.233622i	$0.0750578\pi$
$572$	−28.8622	−	16.6636i	−1.20679	−	0.696741i
$573$		0			0
$574$	0.400654	+	0.693954i	0.0167230	+	0.0289651i
$575$	1.53624	+	1.89584i	0.0640657	+	0.0790618i
$576$		0			0
$577$		−	18.0398i		−	0.751008i	−0.926821	−	0.375504i	$-0.877470\pi$
$577$		−	18.0398i		−	0.751008i	0.926821	−	0.375504i	$-0.122530\pi$
$578$		−	40.6664i		−	1.69150i
$579$		0			0
$580$	−10.8300	−	30.5672i	−0.449693	−	1.26924i
$581$	70.7322			2.93447
$582$		0			0
$583$	−4.98497	+	2.87808i	−0.206457	+	0.119198i
$584$	7.38419	−	12.7898i	0.305560	−	0.529245i
$585$		0			0
$586$	−22.3337	+	38.6831i	−0.922597	+	1.59798i
$587$	−22.5458	−	13.0168i	−0.930565	−	0.537262i	−0.0435750	−	0.999050i	$-0.513875\pi$
$587$	−22.5458	−	13.0168i	−0.930565	−	0.537262i	−0.886990	+	0.461788i	$0.847208\pi$
$588$		0			0
$589$	−25.9567	+	14.6178i	−1.06953	+	0.602316i
$590$	−12.5357	+	67.6980i	−0.516085	+	2.78708i
$591$		0			0
$592$	10.9511	+	6.32263i	0.450088	+	0.259858i
$593$	15.7236	−	9.07803i	0.645691	−	0.372790i	−0.141112	−	0.989994i	$-0.545068\pi$
$593$	15.7236	−	9.07803i	0.645691	−	0.372790i	0.786804	+	0.617203i	$0.211734\pi$
$594$		0			0
$595$	2.24028	+	6.32307i	0.0918424	+	0.259220i
$596$	72.4556			2.96790
$597$		0			0
$598$	−3.90168	+	2.25264i	−0.159552	+	0.0921172i
$599$	−20.0357	−	34.7028i	−0.818635	−	1.41792i	−0.906688	−	0.421802i	$-0.861398\pi$
$599$	−20.0357	−	34.7028i	−0.818635	−	1.41792i	0.0880531	−	0.996116i	$-0.471935\pi$
$600$		0			0
$601$	15.0473			0.613793			0.306897	−	0.951743i	$-0.400709\pi$
$601$	15.0473			0.613793			0.306897	+	0.951743i	$0.400709\pi$
$602$	−4.03018	+	2.32683i	−0.164258	+	0.0948344i
$603$		0			0
$604$	−25.6784	−	44.4763i	−1.04484	−	1.80972i
$605$	−8.95226	+	10.4852i	−0.363961	+	0.426285i
$606$		0			0
$607$			29.3860i			1.19274i	0.802709	+	0.596370i	$0.203391\pi$
$607$			29.3860i			1.19274i	−0.802709	+	0.596370i	$0.796609\pi$
$608$	0.724166	−	1.22384i	0.0293688	−	0.0496333i
$609$		0			0
$610$	−29.5135	−	25.1986i	−1.19497	−	1.02026i
$611$	−9.43905	+	16.3489i	−0.381863	+	0.661406i
$612$		0			0
$613$	30.0578	+	17.3539i	1.21402	+	0.700917i	0.963633	−	0.267229i	$-0.0861079\pi$
$613$	30.0578	+	17.3539i	1.21402	+	0.700917i	0.250390	+	0.968145i	$0.419441\pi$
$614$	36.0818	+	62.4955i	1.45614	+	2.52211i
$615$		0			0
$616$	49.4622			1.99289
$617$	9.29031	−	5.36376i	0.374014	−	0.215937i	−0.301197	−	0.953562i	$-0.597386\pi$
$617$	9.29031	−	5.36376i	0.374014	−	0.215937i	0.675210	+	0.737625i	$0.264053\pi$
$618$		0			0
$619$	36.1437			1.45274			0.726370	−	0.687304i	$-0.241206\pi$
$619$	36.1437			1.45274			0.726370	+	0.687304i	$0.241206\pi$
$620$	60.6004	+	11.2214i	2.43377	+	0.450663i
$621$		0			0
$622$	0.411031	+	0.237309i	0.0164808	+	0.00951521i
$623$	−5.21644	+	3.01171i	−0.208992	+	0.120662i
$624$		0			0
$625$	−23.7714	+	7.74093i	−0.950855	+	0.309637i
$626$	−52.2569			−2.08861
$627$		0			0
$628$			80.8768i			3.22734i
$629$	1.00273	−	1.73678i	0.0399814	−	0.0692499i
$630$		0			0
$631$	15.7882	+	27.3460i	0.628519	+	1.08863i	0.987849	+	0.155417i	$0.0496720\pi$
$631$	15.7882	+	27.3460i	0.628519	+	1.08863i	−0.359330	+	0.933211i	$0.616995\pi$
$632$	49.0248	+	28.3045i	1.95010	+	1.12589i
$633$		0			0
$634$	47.0857			1.87001
$635$	−1.60262	+	8.65483i	−0.0635979	+	0.343456i
$636$		0			0
$637$	−43.2827	+	24.9893i	−1.71492	+	0.990111i
$638$			19.4204i			0.768859i
$639$		0			0
$640$	40.6994	−	14.4199i	1.60879	−	0.569996i
$641$	9.91331	−	17.1704i	0.391552	−	0.678188i	−0.601102	−	0.799172i	$-0.705272\pi$
$641$	9.91331	−	17.1704i	0.391552	−	0.678188i	0.992654	+	0.120984i	$0.0386049\pi$
$642$		0			0
$643$	−11.6540	−	6.72843i	−0.459588	−	0.265343i	0.252283	−	0.967654i	$-0.418819\pi$
$643$	−11.6540	−	6.72843i	−0.459588	−	0.265343i	−0.711871	+	0.702310i	$0.752152\pi$
$644$	4.43359	−	7.67920i	0.174708	−	0.302603i
$645$		0			0
$646$	−6.13555	−	3.63051i	−0.241400	−	0.142840i
$647$			4.19511i			0.164927i	0.996594	+	0.0824634i	$0.0262787\pi$
$647$			4.19511i			0.164927i	−0.996594	+	0.0824634i	$0.973721\pi$
$648$		0			0
$649$	13.7810	−	23.8694i	0.540953	−	0.936957i
$650$	−7.23559	−	45.5875i	−0.283803	−	1.78809i
$651$		0			0
$652$	−49.7109	+	28.7006i	−1.94683	+	1.12400i
$653$			12.1680i			0.476170i	0.971244	+	0.238085i	$0.0765196\pi$
$653$			12.1680i			0.476170i	−0.971244	+	0.238085i	$0.923480\pi$
$654$		0			0
$655$	12.1908	+	34.4080i	0.476334	+	1.34443i
$656$	0.152019	+	0.263305i	0.00593535	+	0.0102803i
$657$		0			0
$658$		−	55.5814i		−	2.16679i
$659$	−4.12236	−	7.14013i	−0.160584	−	0.278140i	0.774494	−	0.632581i	$-0.218004\pi$
$659$	−4.12236	−	7.14013i	−0.160584	−	0.278140i	−0.935078	+	0.354441i	$0.884671\pi$
$660$		0			0
$661$	−10.5599	−	18.2902i	−0.410731	−	0.711407i	0.584239	−	0.811582i	$-0.301393\pi$
$661$	−10.5599	−	18.2902i	−0.410731	−	0.711407i	−0.994970	+	0.100175i	$0.968060\pi$
$662$	−43.8338	−	25.3075i	−1.70365	−	0.983603i
$663$		0			0
$664$	78.3941			3.04228
$665$	−43.0899	−	8.45714i	−1.67095	−	0.327954i
$666$		0			0
$667$	1.51986	+	0.877489i	0.0588490	+	0.0339765i
$668$	−19.6156	−	11.3251i	−0.758951	−	0.438180i
$669$		0			0
$670$	20.4227	−	23.9198i	0.788998	−	0.924103i
$671$	7.76783	+	13.4543i	0.299874	+	0.519397i
$672$		0			0
$673$		−	30.2802i		−	1.16722i	−0.812036	−	0.583608i	$-0.801641\pi$
$673$		−	30.2802i		−	1.16722i	0.812036	−	0.583608i	$-0.198359\pi$
$674$	−12.5357	−	21.7124i	−0.482856	−	0.836331i
$675$		0			0
$676$	4.54221			0.174700
$677$			49.9003i			1.91783i	0.283701	+	0.958913i	$0.408438\pi$
$677$			49.9003i			1.91783i	−0.283701	+	0.958913i	$0.591562\pi$
$678$		0			0
$679$	9.88092	−	17.1142i	0.379195	−	0.656785i
$680$	2.48295	+	7.00800i	0.0952168	+	0.268745i
$681$		0			0
$682$	−31.9632	−	18.4539i	−1.22393	−	0.706638i
$683$		−	3.11357i		−	0.119137i	−0.998224	−	0.0595687i	$-0.981027\pi$
$683$		−	3.11357i		−	0.119137i	0.998224	−	0.0595687i	$-0.0189725\pi$
$684$		0			0
$685$	6.68942	−	36.1258i	0.255590	−	1.38029i
$686$	34.8436	−	60.3509i	1.33034	−	2.30421i
$687$		0			0
$688$	−1.52916	+	0.882861i	−0.0582987	+	0.0336588i
$689$	4.91985	−	8.52143i	0.187431	−	0.324641i
$690$		0			0
$691$	−30.2831			−1.15202			−0.576012	−	0.817441i	$-0.695392\pi$
$691$	−30.2831			−1.15202			−0.576012	+	0.817441i	$0.695392\pi$
$692$			43.1140i			1.63895i
$693$		0			0
$694$	−6.68222	−	11.5740i	−0.253654	−	0.439341i
$695$	−5.86718	−	1.08643i	−0.222555	−	0.0412105i
$696$		0			0
$697$	0.0417585	−	0.0241093i	0.00158172	−	0.000913204i
$698$	3.29948	+	1.90495i	0.124887	+	0.0721035i
$699$		0			0
$700$	57.1951	+	70.5830i	2.16177	+	2.66779i
$701$	22.2849	−	38.5987i	0.841691	−	1.45785i	−0.0467733	−	0.998906i	$-0.514894\pi$
$701$	22.2849	−	38.5987i	0.841691	−	1.45785i	0.888464	−	0.458946i	$-0.151773\pi$
$702$		0			0
$703$	6.44177	+	11.4386i	0.242956	+	0.431415i
$704$	−16.7014			−0.629458
$705$		0			0
$706$	−40.4457	+	70.0540i	−1.52219	+	2.63652i
$707$	41.2353	−	23.8072i	1.55081	−	0.895363i
$708$		0			0
$709$	4.67176	+	8.09172i	0.175452	+	0.303891i	0.940317	−	0.340299i	$-0.110528\pi$
$709$	4.67176	+	8.09172i	0.175452	+	0.303891i	−0.764866	+	0.644190i	$0.777195\pi$
$710$	6.97252	−	37.6546i	0.261674	−	1.41315i
$711$		0			0
$712$	−5.78150	+	3.33795i	−0.216671	+	0.125095i
$713$	−2.88844	+	1.66764i	−0.108173	+	0.0624538i
$714$		0			0
$715$	−3.36445	+	18.1695i	−0.125823	+	0.679500i
$716$	15.5055	+	26.8562i	0.579466	+	1.00366i
$717$		0			0
$718$	7.43916	−	4.29500i	0.277627	−	0.160288i
$719$	−12.6987	+	21.9948i	−0.473581	+	0.820267i	−0.999543	−	0.0302417i	$-0.990372\pi$
$719$	−12.6987	+	21.9948i	−0.473581	+	0.820267i	0.525961	+	0.850508i	$0.323706\pi$
$720$		0			0
$721$	25.9330			0.965797
$722$	40.9059	−	22.4631i	1.52236	−	0.835992i
$723$		0			0
$724$	−12.3534	+	21.3968i	−0.459112	+	0.795205i
$725$	−13.9697	+	11.3200i	−0.518821	+	0.420413i
$726$		0			0
$727$	−27.2259	−	15.7189i	−1.00975	−	0.582980i	−0.0986328	−	0.995124i	$-0.531447\pi$
$727$	−27.2259	−	15.7189i	−1.00975	−	0.582980i	−0.911119	+	0.412143i	$0.864780\pi$
$728$	−73.2240	+	42.2759i	−2.71386	+	1.56685i
$729$		0			0
$730$	−15.9725	−	2.95764i	−0.591170	−	0.109467i
$731$	0.140016	+	0.242515i	0.00517869	+	0.00896975i
$732$		0			0
$733$		−	25.3946i		−	0.937971i	−0.883206	−	0.468985i	$-0.844620\pi$
$733$		−	25.3946i		−	0.937971i	0.883206	−	0.468985i	$-0.155380\pi$
$734$	−47.9056			−1.76823
$735$		0			0
$736$	0.0796065	−	0.137883i	0.00293434	−	0.00508242i
$737$	−10.9043	+	6.29559i	−0.401664	+	0.231901i
$738$		0			0
$739$	17.7541	−	30.7510i	0.653095	−	1.13119i	−0.329273	−	0.944235i	$-0.606804\pi$
$739$	17.7541	−	30.7510i	0.653095	−	1.13119i	0.982368	−	0.186959i	$-0.0598631\pi$
$740$	4.94505	−	26.7054i	0.181784	−	0.981710i
$741$		0			0
$742$			28.9703i			1.06353i
$743$	14.8176	+	8.55493i	0.543604	+	0.313850i	0.746538	−	0.665342i	$-0.231714\pi$
$743$	14.8176	+	8.55493i	0.543604	+	0.313850i	−0.202934	+	0.979192i	$0.565048\pi$
$744$		0			0
$745$	−13.4163	−	37.8667i	−0.491533	−	1.38733i
$746$	−28.8798	+	50.0213i	−1.05737	+	1.83141i
$747$		0			0
$748$		−	5.90453i		−	0.215891i
$749$	−5.86718			−0.214382
$750$		0			0
$751$	3.72562	+	6.45297i	0.135950	+	0.235472i	0.925960	−	0.377622i	$-0.123258\pi$
$751$	3.72562	+	6.45297i	0.135950	+	0.235472i	−0.790010	+	0.613094i	$0.789925\pi$
$752$		−	21.0891i		−	0.769041i
$753$		0			0
$754$	−16.5988	−	28.7500i	−0.604493	−	1.04701i
$755$	−18.4894	+	21.6555i	−0.672899	+	0.788124i
$756$		0			0
$757$	46.5640	+	26.8838i	1.69240	+	0.977107i	0.952574	+	0.304306i	$0.0984245\pi$
$757$	46.5640	+	26.8838i	1.69240	+	0.977107i	0.739824	+	0.672801i	$0.234909\pi$
$758$	14.9994	+	8.65994i	0.544804	+	0.314543i
$759$		0			0
$760$	−47.7575	−	9.37325i	−1.73235	−	0.340003i
$761$	−23.3939			−0.848029			−0.424014	−	0.905655i	$-0.639379\pi$
$761$	−23.3939			−0.848029			−0.424014	+	0.905655i	$0.639379\pi$
$762$		0			0
$763$	−46.9487	−	27.1058i	−1.69966	−	0.981297i
$764$	−11.8068	−	20.4499i	−0.427154	−	0.739852i
$765$		0			0
$766$	3.78757	+	6.56027i	0.136851	+	0.237032i
$767$			47.1152i			1.70123i
$768$		0			0
$769$	−6.62236	−	11.4703i	−0.238808	−	0.413628i	0.721564	−	0.692347i	$-0.243423\pi$
$769$	−6.62236	−	11.4703i	−0.238808	−	0.413628i	−0.960373	+	0.278719i	$0.910090\pi$
$770$	−18.1690	−	51.2810i	−0.654764	−	1.84804i
$771$		0			0
$772$			10.4500i			0.376105i
$773$	15.4198	−	8.90262i	0.554611	−	0.320205i	−0.196369	−	0.980530i	$-0.562915\pi$
$773$	15.4198	−	8.90262i	0.554611	−	0.320205i	0.750980	+	0.660325i	$0.229582\pi$
$774$		0			0
$775$	−5.35656	−	33.7488i	−0.192413	−	1.21229i
$776$	10.9512	−	18.9681i	0.393127	−	0.680916i
$777$		0			0
$778$		−	23.0658i		−	0.826949i
$779$	−0.00337965	+	0.315621i	−0.000121088	+	0.0113083i
$780$		0			0
$781$	−7.66521	+	13.2765i	−0.274283	+	0.475072i
$782$	−0.691255	−	0.399096i	−0.0247192	−	0.0142716i
$783$		0			0
$784$	27.9160	−	48.3520i	0.997001	−	1.72686i
$785$	42.2678	−	14.9756i	1.50860	−	0.534501i
$786$		0			0
$787$			43.5779i			1.55339i	0.629880	+	0.776693i	$0.283104\pi$
$787$			43.5779i			1.55339i	−0.629880	+	0.776693i	$0.716896\pi$
$788$	−69.3734	+	40.0527i	−2.47132	+	1.42682i
$789$		0			0
$790$	11.3370	−	61.2246i	0.403351	−	2.17827i
$791$	−34.8990			−1.24087
$792$		0			0
$793$	−22.9991	−	13.2785i	−0.816721	−	0.471534i
$794$	−32.8634	−	56.9210i	−1.16628	−	2.02005i
$795$		0			0
$796$	25.7338	−	44.5723i	0.912111	−	1.57982i
$797$		−	16.1311i		−	0.571395i	−0.958320	−	0.285697i	$-0.907775\pi$
$797$		−	16.1311i		−	0.571395i	0.958320	−	0.285697i	$-0.0922252\pi$
$798$		0			0
$799$	−3.34460			−0.118323
$800$	1.02696	+	1.26734i	0.0363084	+	0.0448073i
$801$		0			0
$802$	−53.5403	+	30.9115i	−1.89057	+	1.09152i
$803$	5.63170	+	3.25147i	0.198739	+	0.114742i
$804$		0			0
$805$	−4.83424	−	0.895159i	−0.170385	−	0.0315502i
$806$	63.0912			2.22229
$807$		0			0
$808$	45.7021	−	26.3861i	1.60779	−	0.928259i
$809$	28.7134			1.00951			0.504755	−	0.863263i	$-0.331583\pi$
$809$	28.7134			1.00951			0.504755	+	0.863263i	$0.331583\pi$
$810$		0			0
$811$	−10.7711	−	18.6561i	−0.378225	−	0.655104i	0.612579	−	0.790409i	$-0.290132\pi$
$811$	−10.7711	−	18.6561i	−0.378225	−	0.655104i	−0.990804	+	0.135305i	$0.956799\pi$
$812$	56.5850	+	32.6694i	1.98575	+	1.14647i
$813$		0			0
$814$	−8.13228	+	14.0855i	−0.285036	+	0.493697i
$815$	24.2042	+	20.6655i	0.847837	+	0.723882i
$816$		0			0
$817$	−1.83299	−	0.0196275i	−0.0641282	−	0.000686680i
$818$		−	69.5634i		−	2.43223i
$819$		0			0
$820$	0.424016	−	0.496623i	0.0148073	−	0.0173428i
$821$	16.6602	+	28.8563i	0.581445	+	1.00709i	0.995308	+	0.0967536i	$0.0308459\pi$
$821$	16.6602	+	28.8563i	0.581445	+	1.00709i	−0.413863	+	0.910339i	$0.635821\pi$
$822$		0			0
$823$	32.2499	−	18.6195i	1.12416	−	0.649035i	0.181701	−	0.983354i	$-0.441840\pi$
$823$	32.2499	−	18.6195i	1.12416	−	0.649035i	0.942460	+	0.334319i	$0.108506\pi$
$824$	28.7422			1.00128
$825$		0			0
$826$	−69.3590	−	120.133i	−2.41331	−	4.17997i
$827$	25.1591	−	14.5256i	0.874868	−	0.505105i	0.00590503	−	0.999983i	$-0.498120\pi$
$827$	25.1591	−	14.5256i	0.874868	−	0.505105i	0.868963	+	0.494877i	$0.164787\pi$
$828$		0			0
$829$	−34.5380			−1.19956			−0.599778	−	0.800166i	$-0.704744\pi$
$829$	−34.5380			−1.19956			−0.599778	+	0.800166i	$0.704744\pi$
$830$	−28.7965	−	81.2768i	−0.999543	−	2.82116i
$831$		0			0
$832$	24.7249	−	14.2749i	0.857180	−	0.494893i
$833$	−7.66832	−	4.42731i	−0.265692	−	0.153397i
$834$		0			0
$835$	−2.28658	+	12.3485i	−0.0791302	+	0.427338i
$836$	33.2640	+	19.6829i	1.15046	+	0.680746i
$837$		0			0
$838$	27.7483	+	16.0205i	0.958550	+	0.553419i
$839$	22.3622	−	38.7324i	0.772028	−	1.33719i	−0.164422	−	0.986390i	$-0.552576\pi$
$839$	22.3622	−	38.7324i	0.772028	−	1.33719i	0.936450	−	0.350801i	$-0.114091\pi$
$840$		0			0
$841$	8.03413	−	13.9155i	0.277039	−	0.479845i
$842$	−7.07266	+	4.08340i	−0.243740	+	0.140723i
$843$		0			0
$844$	−55.8770			−1.92337
$845$	−0.841058	−	2.37384i	−0.0289333	−	0.0816627i
$846$		0			0
$847$		−	27.7784i		−	0.954478i
$848$			10.9921i			0.377471i
$849$		0			0
$850$	6.35363	−	5.14850i	0.217928	−	0.176592i
$851$	0.734898	+	1.27288i	0.0251920	+	0.0436338i
$852$		0			0
$853$	−14.0818	−	8.13013i	−0.482152	−	0.278370i	0.239161	−	0.970980i	$-0.423128\pi$
$853$	−14.0818	−	8.13013i	−0.482152	−	0.278370i	−0.721313	+	0.692610i	$0.756461\pi$
$854$	78.1900			2.67561
$855$		0			0
$856$	−6.50273			−0.222259
$857$	−14.4089	−	8.31896i	−0.492197	−	0.284170i	0.233288	−	0.972408i	$-0.425051\pi$
$857$	−14.4089	−	8.31896i	−0.492197	−	0.284170i	−0.725485	+	0.688237i	$0.758385\pi$
$858$		0			0
$859$	20.1362	+	34.8769i	0.687038	+	1.18999i	0.972792	+	0.231682i	$0.0744229\pi$
$859$	20.1362	+	34.8769i	0.687038	+	1.18999i	−0.285753	+	0.958303i	$0.592244\pi$
$860$	2.88417	+	2.46250i	0.0983493	+	0.0839705i
$861$		0			0
$862$			0.118897i			0.00404965i
$863$		−	32.9634i		−	1.12209i	−0.827786	−	0.561044i	$-0.810400\pi$
$863$		−	32.9634i		−	1.12209i	0.827786	−	0.561044i	$-0.189600\pi$
$864$		0			0
$865$	22.5322	−	7.98322i	0.766119	−	0.271437i
$866$	−23.5027			−0.798655
$867$		0			0
$868$	−107.538	+	62.0873i	−3.65009	+	2.10738i
$869$	−12.4633	+	21.5870i	−0.422787	+	0.732288i
$870$		0			0
$871$	10.7618	−	18.6400i	0.364651	−	0.631594i
$872$	−52.0343	−	30.0420i	−1.76210	−	1.01735i
$873$		0			0
$874$	4.55267	−	2.56389i	0.153996	−	0.0867248i
$875$	26.2975	−	42.9608i	0.889018	−	1.45234i
$876$		0			0
$877$	−0.184636	−	0.106600i	−0.00623472	−	0.00359962i	0.496879	−	0.867820i	$-0.334479\pi$
$877$	−0.184636	−	0.106600i	−0.00623472	−	0.00359962i	−0.503114	+	0.864220i	$0.667812\pi$
$878$	−47.3319	+	27.3271i	−1.59737	+	0.922244i
$879$		0			0
$880$	−6.89380	−	19.4574i	−0.232390	−	0.655909i
$881$	−51.8661			−1.74741			−0.873707	−	0.486453i	$-0.838290\pi$
$881$	−51.8661			−1.74741			−0.873707	+	0.486453i	$0.838290\pi$
$882$		0			0
$883$	−36.0657	+	20.8225i	−1.21371	+	0.700734i	−0.963565	−	0.267475i	$-0.913811\pi$
$883$	−36.0657	+	20.8225i	−1.21371	+	0.700734i	−0.250142	+	0.968209i	$0.580477\pi$
$884$	5.04667	+	8.74109i	0.169738	+	0.293995i
$885$		0			0
$886$	−49.4083			−1.65990
$887$	−3.54486	+	2.04663i	−0.119025	+	0.0687190i	−0.558330	−	0.829619i	$-0.688558\pi$
$887$	−3.54486	+	2.04663i	−0.119025	+	0.0687190i	0.439306	+	0.898338i	$0.355225\pi$
$888$		0			0
$889$	−8.86718	−	15.3584i	−0.297396	−	0.515104i
$890$	5.58442	+	4.76797i	0.187190	+	0.159823i
$891$		0			0
$892$		−	87.4987i		−	2.92967i
$893$	11.1493	−	18.8423i	0.373097	−	0.630533i
$894$		0			0
$895$	11.1645	−	13.0763i	0.373189	−	0.437092i
$896$	−43.4984	+	75.3414i	−1.45318	+	2.51698i
$897$		0			0
$898$	−26.5834	−	15.3479i	−0.887099	−	0.512167i
$899$	−12.2882	−	21.2838i	−0.409835	−	0.709855i
$900$		0			0
$901$	1.74328			0.0580772
$902$	−0.338668	+	0.195530i	−0.0112764	+	0.00651043i
$903$		0			0
$904$	−38.6794			−1.28646
$905$	13.4698	+	2.49421i	0.447751	+	0.0829102i
$906$		0			0
$907$	−7.28090	−	4.20363i	−0.241758	−	0.139579i	0.374226	−	0.927337i	$-0.377908\pi$
$907$	−7.28090	−	4.20363i	−0.241758	−	0.139579i	−0.615985	+	0.787758i	$0.711242\pi$
$908$	−28.6265	+	16.5275i	−0.950005	+	0.548486i
$909$		0			0
$910$	70.7278	+	60.3873i	2.34461	+	2.00182i
$911$	−8.87918			−0.294180			−0.147090	−	0.989123i	$-0.546991\pi$
$911$	−8.87918			−0.294180			−0.147090	+	0.989123i	$0.546991\pi$
$912$		0			0
$913$			34.5192i			1.14242i
$914$	−34.7772	+	60.2359i	−1.15033	+	1.99243i
$915$		0			0
$916$	33.5983	+	58.1939i	1.11012	+	1.92278i
$917$	−63.6948	−	36.7742i	−2.10339	−	1.21439i
$918$		0			0
$919$	45.9834			1.51685			0.758427	−	0.651758i	$-0.225968\pi$
$919$	45.9834			1.51685			0.758427	+	0.651758i	$0.225968\pi$
$920$	−5.35790	−	0.992125i	−0.176645	−	0.0327094i
$921$		0			0
$922$	11.3153	−	6.53290i	0.372650	−	0.215150i
$923$		−	26.2062i		−	0.862587i
$924$		0			0
$925$	−14.8724	+	2.36053i	−0.489002	+	0.0776138i
$926$	22.0231	−	38.1452i	0.723725	−	1.25353i
$927$		0			0
$928$	1.01600	+	0.586589i	0.0333519	+	0.0192557i
$929$	11.0889	−	19.2065i	0.363814	−	0.630145i	−0.624771	−	0.780808i	$-0.714808\pi$
$929$	11.0889	−	19.2065i	0.363814	−	0.630145i	0.988585	+	0.150663i	$0.0481409\pi$
$930$		0			0
$931$	50.5044	−	28.4421i	1.65521	−	0.932152i
$932$			49.2564i			1.61345i
$933$		0			0
$934$	−35.3436	+	61.2170i	−1.15648	+	2.00308i
$935$	−3.08582	+	1.09331i	−0.100917	+	0.0357552i
$936$		0			0
$937$	29.7284	−	17.1637i	0.971186	−	0.560714i	0.0715882	−	0.997434i	$-0.477193\pi$
$937$	29.7284	−	17.1637i	0.971186	−	0.560714i	0.899598	+	0.436720i	$0.143860\pi$
$938$			63.3706i			2.06912i
$939$		0			0
$940$	−42.6945	+	15.1268i	−1.39254	+	0.493380i
$941$	16.8606	+	29.2035i	0.549641	+	0.952006i	0.998299	+	0.0583025i	$0.0185688\pi$
$941$	16.8606	+	29.2035i	0.549641	+	0.952006i	−0.448658	+	0.893704i	$0.648098\pi$
$942$		0			0
$943$			0.0353393i			0.00115080i
$944$	−26.3167	−	45.5818i	−0.856535	−	1.48356i
$945$		0			0
$946$	−1.13555	−	1.96683i	−0.0369200	−	0.0639473i
$947$	−19.1794	−	11.0732i	−0.623248	−	0.359832i	0.154885	−	0.987933i	$-0.450499\pi$
$947$	−19.1794	−	11.0732i	−0.623248	−	0.359832i	−0.778132	+	0.628100i	$0.783833\pi$
$948$		0			0
$949$	−11.1163			−0.360849
$950$	7.82487	+	52.9567i	0.253872	+	1.71814i
$951$		0			0
$952$	−12.9730	−	7.48995i	−0.420457	−	0.242751i
$953$	32.2999	+	18.6484i	1.04630	+	0.604079i	0.921610	−	0.388117i	$-0.126874\pi$
$953$	32.2999	+	18.6484i	1.04630	+	0.604079i	0.124686	+	0.992196i	$0.460208\pi$
$954$		0			0
$955$	−8.50132	+	9.95705i	−0.275096	+	0.322203i
$956$	4.11254	+	7.12313i	0.133009	+	0.230378i
$957$		0			0
$958$			19.7761i			0.638936i
$959$	37.0121	+	64.1069i	1.19518	+	2.07012i
$960$		0			0
$961$	15.7069			0.506674
$962$		−	27.8030i		−	0.896405i
$963$		0			0
$964$	35.3359	−	61.2036i	1.13809	−	1.97123i
$965$	5.46139	−	1.93498i	0.175808	−	0.0622892i
$966$		0			0
$967$	16.1718	+	9.33679i	0.520050	+	0.300251i	0.736955	−	0.675942i	$-0.236263\pi$
$967$	16.1718	+	9.33679i	0.520050	+	0.300251i	−0.216905	+	0.976193i	$0.569596\pi$
$968$		−	30.7875i		−	0.989547i
$969$		0			0
$970$	−23.6883	−	4.38638i	−0.760587	−	0.140838i
$971$	14.2903	−	24.7515i	0.458598	−	0.794314i	−0.540290	−	0.841479i	$-0.681685\pi$
$971$	14.2903	−	24.7515i	0.458598	−	0.794314i	0.998887	+	0.0471649i	$0.0150186\pi$
$972$		0			0
$973$	10.4116	−	6.01113i	0.333780	−	0.192708i
$974$	1.34798	−	2.33477i	0.0431921	−	0.0748109i
$975$		0			0
$976$	29.6674			0.949630
$977$		−	58.1909i		−	1.86169i	−0.365411	−	0.930846i	$-0.619072\pi$
$977$		−	58.1909i		−	1.86169i	0.365411	−	0.930846i	$-0.380928\pi$
$978$		0			0
$979$	−1.46980	−	2.54576i	−0.0469749	−	0.0813628i
$980$	−117.911	−	21.8337i	−3.76654	−	0.697451i
$981$		0			0
$982$	27.8768	−	16.0947i	0.889586	−	0.513602i
$983$	−41.6320	−	24.0363i	−1.32786	−	0.766638i	−0.342888	−	0.939376i	$-0.611405\pi$
$983$	−41.6320	−	24.0363i	−1.32786	−	0.766638i	−0.984968	+	0.172738i	$0.944738\pi$
$984$		0			0
$985$	33.7779	+	28.8395i	1.07625	+	0.918902i
$986$	2.94078	−	5.09359i	0.0936536	−	0.162213i
$987$		0			0
$988$	−66.0674	−	0.707444i	−2.10188	−	0.0225068i
$989$	−0.205235			−0.00652609
$990$		0			0
$991$	−19.1976	+	33.2512i	−0.609832	+	1.05626i	0.381436	+	0.924395i	$0.375430\pi$
$991$	−19.1976	+	33.2512i	−0.609832	+	1.05626i	−0.991268	+	0.131865i	$0.957904\pi$
$992$	−1.93089	+	1.11480i	−0.0613057	+	0.0353949i
$993$		0			0
$994$	38.5785	+	66.8200i	1.22364	+	2.11940i
$995$	−28.0593	−	5.19576i	−0.889540	−	0.164717i
$996$		0			0
$997$	32.7546	−	18.9109i	1.03735	−	0.598914i	0.118268	−	0.992982i	$-0.462266\pi$
$997$	32.7546	−	18.9109i	1.03735	−	0.598914i	0.919081	+	0.394068i	$0.128933\pi$
$998$	51.3504	−	29.6472i	1.62547	−	0.938465i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.be.d.334.6		12
3.2	odd	2		95.2.i.b.49.1	✓	12
5.4	even	2	inner	855.2.be.d.334.1		12
15.2	even	4		475.2.e.g.201.6		12
15.8	even	4		475.2.e.g.201.1		12
15.14	odd	2		95.2.i.b.49.6	yes	12
19.7	even	3	inner	855.2.be.d.64.1		12
57.8	even	6		1805.2.b.g.1084.1		6
57.11	odd	6		1805.2.b.f.1084.6		6
57.26	odd	6		95.2.i.b.64.6	yes	12
95.64	even	6	inner	855.2.be.d.64.6		12
285.8	odd	12		9025.2.a.bt.1.1		6
285.68	even	12		9025.2.a.bu.1.6		6
285.83	even	12		475.2.e.g.26.1		12
285.122	odd	12		9025.2.a.bt.1.6		6
285.179	even	6		1805.2.b.g.1084.6		6
285.182	even	12		9025.2.a.bu.1.1		6
285.197	even	12		475.2.e.g.26.6		12
285.239	odd	6		1805.2.b.f.1084.1		6
285.254	odd	6		95.2.i.b.64.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.b.49.1	✓	12	3.2	odd	2
95.2.i.b.49.6	yes	12	15.14	odd	2
95.2.i.b.64.1	yes	12	285.254	odd	6
95.2.i.b.64.6	yes	12	57.26	odd	6
475.2.e.g.26.1		12	285.83	even	12
475.2.e.g.26.6		12	285.197	even	12
475.2.e.g.201.1		12	15.8	even	4
475.2.e.g.201.6		12	15.2	even	4
855.2.be.d.64.1		12	19.7	even	3	inner
855.2.be.d.64.6		12	95.64	even	6	inner
855.2.be.d.334.1		12	5.4	even	2	inner
855.2.be.d.334.6		12	1.1	even	1	trivial
1805.2.b.f.1084.1		6	285.239	odd	6
1805.2.b.f.1084.6		6	57.11	odd	6
1805.2.b.g.1084.1		6	57.8	even	6
1805.2.b.g.1084.6		6	285.179	even	6
9025.2.a.bt.1.1		6	285.8	odd	12
9025.2.a.bt.1.6		6	285.122	odd	12
9025.2.a.bu.1.1		6	285.182	even	12
9025.2.a.bu.1.6		6	285.68	even	12

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.12713 + 1.22810i) q^{2} +(2.01647 + 3.49262i) q^{4} +(1.45193 - 1.70056i) q^{5} +4.50527i q^{7} +4.99330i q^{8} +O(q^{10})\)	\(q+(2.12713 + 1.22810i) q^{2} +(2.01647 + 3.49262i) q^{4} +(1.45193 - 1.70056i) q^{5} +4.50527i q^{7} +4.99330i q^{8} +(5.17691 - 1.83419i) q^{10} -2.19869 q^{11} +(3.25495 - 1.87925i) q^{13} +(-5.53293 + 9.58332i) q^{14} +(-2.09935 + 3.63617i) q^{16} +(0.576674 + 0.332943i) q^{17} +(-3.79804 + 2.13891i) q^{19} +(8.86718 + 1.64194i) q^{20} +(-4.67691 - 2.70022i) q^{22} +(-0.422643 + 0.244013i) q^{23} +(-0.783783 - 4.93819i) q^{25} +9.23163 q^{26} +(-15.7352 + 9.08474i) q^{28} +(-1.79804 - 3.11429i) q^{29} +6.83424 q^{31} +(-0.282531 + 0.163119i) q^{32} +(0.817776 + 1.41643i) q^{34} +(7.66147 + 6.54135i) q^{35} -3.01171i q^{37} +(-10.7057 - 0.114636i) q^{38} +(8.49139 + 7.24994i) q^{40} +(0.0362063 - 0.0627112i) q^{41} +(0.364199 + 0.210271i) q^{43} +(-4.43359 - 7.67920i) q^{44} -1.19869 q^{46} +(-4.34986 + 2.51139i) q^{47} -13.2975 q^{49} +(4.39738 - 11.4668i) q^{50} +(13.1270 + 7.57888i) q^{52} +(2.26725 - 1.30900i) q^{53} +(-3.19235 + 3.73900i) q^{55} -22.4962 q^{56} -8.83269i q^{58} +(-6.26783 + 10.8562i) q^{59} +(-3.53293 - 6.11922i) q^{61} +(14.5374 + 8.39315i) q^{62} +7.59607 q^{64} +(1.53020 - 8.26377i) q^{65} +(4.95944 - 2.86334i) q^{67} +2.68548i q^{68} +(8.26353 + 23.3234i) q^{70} +(3.48626 - 6.03838i) q^{71} +(-2.56139 - 1.47882i) q^{73} +(3.69869 - 6.40632i) q^{74} +(-15.1290 - 8.95208i) q^{76} -9.90571i q^{77} +(5.66849 - 9.81811i) q^{79} +(3.13541 + 8.84953i) q^{80} +(0.154031 - 0.0889301i) q^{82} -15.6999i q^{83} +(1.40348 - 0.497256i) q^{85} +(0.516467 + 0.894547i) q^{86} -10.9787i q^{88} +(0.668486 + 1.15785i) q^{89} +(8.46652 + 14.6644i) q^{91} +(-1.70449 - 0.984089i) q^{92} -12.3370 q^{94} +(-1.87716 + 9.56432i) q^{95} +(-3.79871 - 2.19319i) q^{97} +(-28.2856 - 16.3307i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) 12 * q + 2 * q^4 + 2 * q^5	\( 12 q + 2 q^{4} + 2 q^{5} + 6 q^{10} - 4 q^{11} - 22 q^{14} - 14 q^{16} - 12 q^{19} + 40 q^{20} - 6 q^{25} + 44 q^{26} + 12 q^{29} + 60 q^{31} + 10 q^{34} + 10 q^{40} + 12 q^{41} - 20 q^{44} + 8 q^{46} - 4 q^{49} + 8 q^{50} - 18 q^{55} - 92 q^{56} - 20 q^{59} + 2 q^{61} + 24 q^{64} + 40 q^{65} + 46 q^{70} - 2 q^{71} + 22 q^{74} - 70 q^{76} + 24 q^{79} + 22 q^{80} + 2 q^{85} - 16 q^{86} - 36 q^{89} + 24 q^{91} - 60 q^{94} - 46 q^{95}+O(q^{100}) \) 12 * q + 2 * q^4 + 2 * q^5 + 6 * q^10 - 4 * q^11 - 22 * q^14 - 14 * q^16 - 12 * q^19 + 40 * q^20 - 6 * q^25 + 44 * q^26 + 12 * q^29 + 60 * q^31 + 10 * q^34 + 10 * q^40 + 12 * q^41 - 20 * q^44 + 8 * q^46 - 4 * q^49 + 8 * q^50 - 18 * q^55 - 92 * q^56 - 20 * q^59 + 2 * q^61 + 24 * q^64 + 40 * q^65 + 46 * q^70 - 2 * q^71 + 22 * q^74 - 70 * q^76 + 24 * q^79 + 22 * q^80 + 2 * q^85 - 16 * q^86 - 36 * q^89 + 24 * q^91 - 60 * q^94 - 46 * q^95

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