LMFDB - Embedded newform 315.2.bf.c.289.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(109,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bf (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 26x^{12} - 96x^{10} - 781x^{8} - 2400x^{6} + 16250x^{4} + 125000x^{2} + 390625 $ x^16 + 8x^14 + 26x^12 - 96x^10 - 781x^8 - 2400x^6 + 16250x^4 + 125000*x^2 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.6
Root			$-0.717291 - 2.11790i$ of defining polynomial
Character	$\chi$	$=$	315.289
Dual form			315.2.bf.c.109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.515448 + 0.297594i) q^{2} +(-0.822876 - 1.42526i) q^{4} +(2.19280 - 0.437757i) q^{5} +(-1.68480 - 2.03996i) q^{7} -2.16991i q^{8} +O(q^{10})$	\(q+(0.515448 + 0.297594i) q^{2} +(-0.822876 - 1.42526i) q^{4} +(2.19280 - 0.437757i) q^{5} +(-1.68480 - 2.03996i) q^{7} -2.16991i q^{8} +(1.26055 + 0.426923i) q^{10} +(-2.68967 - 4.65864i) q^{11} +4.07992i q^{13} +(-0.261348 - 1.55288i) q^{14} +(-1.00000 + 1.73205i) q^{16} +(4.27384 - 2.46750i) q^{17} +(-0.322876 + 0.559237i) q^{19} +(-2.42832 - 2.76510i) q^{20} -3.20172i q^{22} +(5.30473 + 3.06269i) q^{23} +(4.61674 - 1.91983i) q^{25} +(-1.21416 + 2.10299i) q^{26} +(-1.52110 + 4.07992i) q^{28} +2.42832 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-4.78929 + 2.76510i) q^{32} +2.93725 q^{34} +(-4.58744 - 3.73569i) q^{35} +(-0.760548 - 0.439102i) q^{37} +(-0.332851 + 0.192172i) q^{38} +(-0.949892 - 4.75817i) q^{40} +11.2814 q^{41} +10.7945i q^{43} +(-4.42652 + 7.66697i) q^{44} +(1.82288 + 3.15731i) q^{46} +(-1.87919 - 1.08495i) q^{47} +(-1.32288 + 6.87386i) q^{49} +(2.95102 + 0.384343i) q^{50} +(5.81496 - 3.35727i) q^{52} +(-6.85108 + 3.95547i) q^{53} +(-7.93725 - 9.03805i) q^{55} +(-4.42652 + 3.65587i) q^{56} +(1.25167 + 0.722653i) q^{58} +(4.16518 + 7.21430i) q^{59} +(-0.177124 + 0.306788i) q^{61} -2.97594i q^{62} +0.708497 q^{64} +(1.78601 + 8.94645i) q^{65} +(-2.01222 + 1.16176i) q^{67} +(-7.03367 - 4.06089i) q^{68} +(-1.25287 - 3.29075i) q^{70} -2.42832 q^{71} +(-7.82718 + 4.51902i) q^{73} +(-0.261348 - 0.452669i) q^{74} +1.06275 q^{76} +(-4.97188 + 13.3357i) q^{77} +(2.96863 - 5.14181i) q^{79} +(-1.43458 + 4.23580i) q^{80} +(5.81496 + 3.35727i) q^{82} -11.6556i q^{83} +(8.29150 - 7.28164i) q^{85} +(-3.21236 + 5.56398i) q^{86} +(-10.1088 + 5.83633i) q^{88} +(2.68967 - 4.65864i) q^{89} +(8.32288 - 6.87386i) q^{91} -10.0808i q^{92} +(-0.645751 - 1.11847i) q^{94} +(-0.463192 + 1.36764i) q^{95} -6.71453i q^{97} +(-2.72749 + 3.14944i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 8 q^{10} - 16 q^{16} + 16 q^{19} - 16 q^{25} - 40 q^{31} - 80 q^{34} + 8 q^{40} + 8 q^{46} - 24 q^{61} + 96 q^{64} - 56 q^{70} + 144 q^{76} - 16 q^{79} + 48 q^{85} + 112 q^{91} + 32 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^10 - 16 * q^16 + 16 * q^19 - 16 * q^25 - 40 * q^31 - 80 * q^34 + 8 * q^40 + 8 * q^46 - 24 * q^61 + 96 * q^64 - 56 * q^70 + 144 * q^76 - 16 * q^79 + 48 * q^85 + 112 * q^91 + 32 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.515448	+	0.297594i	0.364477	+	0.210431i	0.671043	−	0.741419i	$-0.265847\pi$
$2$	0.515448	+	0.297594i	0.364477	+	0.210431i	−0.306566	+	0.951849i	$0.599180\pi$
$3$		0			0
$3$		0			0
$4$	−0.822876	−	1.42526i	−0.411438	−	0.712631i
$5$	2.19280	−	0.437757i	0.980650	−	0.195771i
$5$	2.19280	−	0.437757i	0.980650	−	0.195771i
$6$		0			0
$7$	−1.68480	−	2.03996i	−0.636796	−	0.771033i
$7$	−1.68480	−	2.03996i	−0.636796	−	0.771033i
$8$		−	2.16991i		−	0.767178i
$9$		0			0
$10$	1.26055	+	0.426923i	0.398620	+	0.135005i
$11$	−2.68967	−	4.65864i	−0.810965	−	1.40463i	−0.912189	−	0.409770i	$-0.865609\pi$
$11$	−2.68967	−	4.65864i	−0.810965	−	1.40463i	0.101224	−	0.994864i	$-0.467724\pi$
$12$		0			0
$13$			4.07992i			1.13157i	0.824554	+	0.565783i	$0.191426\pi$
$13$			4.07992i			1.13157i	−0.824554	+	0.565783i	$0.808574\pi$
$14$	−0.261348	−	1.55288i	−0.0698483	−	0.415025i
$15$		0			0
$16$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$17$	4.27384	−	2.46750i	1.03656	−	0.598457i	0.117701	−	0.993049i	$-0.462447\pi$
$17$	4.27384	−	2.46750i	1.03656	−	0.598457i	0.918856	+	0.394592i	$0.129114\pi$
$18$		0			0
$19$	−0.322876	+	0.559237i	−0.0740728	+	0.128298i	−0.900683	−	0.434478i	$-0.856933\pi$
$19$	−0.322876	+	0.559237i	−0.0740728	+	0.128298i	0.826610	+	0.562775i	$0.190266\pi$
$20$	−2.42832	−	2.76510i	−0.542989	−	0.618294i
$21$		0			0
$22$		−	3.20172i		−	0.682608i
$23$	5.30473	+	3.06269i	1.10611	+	0.638615i	0.937820	−	0.347122i	$-0.112841\pi$
$23$	5.30473	+	3.06269i	1.10611	+	0.638615i	0.168293	+	0.985737i	$0.446174\pi$
$24$		0			0
$25$	4.61674	−	1.91983i	0.923348	−	0.383965i
$26$	−1.21416	+	2.10299i	−0.238116	+	0.412430i
$27$		0			0
$28$	−1.52110	+	4.07992i	−0.287460	+	0.771033i
$29$	2.42832			0.450928			0.225464	−	0.974252i	$-0.427610\pi$
$29$	2.42832			0.450928			0.225464	+	0.974252i	$0.427610\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	−4.78929	+	2.76510i	−0.846634	+	0.488804i
$33$		0			0
$34$	2.93725			0.503735
$35$	−4.58744	−	3.73569i	−0.775419	−	0.631447i
$36$		0			0
$37$	−0.760548	−	0.439102i	−0.125033	−	0.0721880i	0.436179	−	0.899860i	$-0.356331\pi$
$37$	−0.760548	−	0.439102i	−0.125033	−	0.0721880i	−0.561212	+	0.827672i	$0.689665\pi$
$38$	−0.332851	+	0.192172i	−0.0539956	+	0.0311744i
$39$		0			0
$40$	−0.949892	−	4.75817i	−0.150191	−	0.752333i
$41$	11.2814			1.76185			0.880927	−	0.473252i	$-0.156920\pi$
$41$	11.2814			1.76185			0.880927	+	0.473252i	$0.156920\pi$
$42$		0			0
$43$			10.7945i			1.64614i	0.567941	+	0.823069i	$0.307740\pi$
$43$			10.7945i			1.64614i	−0.567941	+	0.823069i	$0.692260\pi$
$44$	−4.42652	+	7.66697i	−0.667324	+	1.15584i
$45$		0			0
$46$	1.82288	+	3.15731i	0.268768	+	0.465520i
$47$	−1.87919	−	1.08495i	−0.274109	−	0.158257i	0.356645	−	0.934240i	$-0.383921\pi$
$47$	−1.87919	−	1.08495i	−0.274109	−	0.158257i	−0.630753	+	0.775983i	$0.717254\pi$
$48$		0			0
$49$	−1.32288	+	6.87386i	−0.188982	+	0.981981i
$50$	2.95102	+	0.384343i	0.417337	+	0.0543544i
$51$		0			0
$52$	5.81496	−	3.35727i	0.806390	−	0.465569i
$53$	−6.85108	+	3.95547i	−0.941068	+	0.543326i	−0.890295	−	0.455384i	$-0.849502\pi$
$53$	−6.85108	+	3.95547i	−0.941068	+	0.543326i	−0.0507729	+	0.998710i	$0.516168\pi$
$54$		0			0
$55$	−7.93725	−	9.03805i	−1.07026	−	1.21869i
$56$	−4.42652	+	3.65587i	−0.591519	+	0.488536i
$57$		0			0
$58$	1.25167	+	0.722653i	0.164353	+	0.0948890i
$59$	4.16518	+	7.21430i	0.542260	+	0.939221i	0.998774	+	0.0495053i	$0.0157645\pi$
$59$	4.16518	+	7.21430i	0.542260	+	0.939221i	−0.456514	+	0.889716i	$0.650902\pi$
$60$		0			0
$61$	−0.177124	+	0.306788i	−0.0226784	+	0.0392802i	−0.877142	−	0.480231i	$-0.840553\pi$
$61$	−0.177124	+	0.306788i	−0.0226784	+	0.0392802i	0.854463	+	0.519512i	$0.173886\pi$
$62$		−	2.97594i		−	0.377945i
$63$		0			0
$64$	0.708497			0.0885622
$65$	1.78601	+	8.94645i	0.221528	+	1.10967i
$66$		0			0
$67$	−2.01222	+	1.16176i	−0.245832	+	0.141931i	−0.617854	−	0.786293i	$-0.711998\pi$
$67$	−2.01222	+	1.16176i	−0.245832	+	0.141931i	0.372022	+	0.928224i	$0.378664\pi$
$68$	−7.03367	−	4.06089i	−0.852958	−	0.492456i
$69$		0			0
$70$	−1.25287	−	3.29075i	−0.149746	−	0.393320i
$71$	−2.42832			−0.288189			−0.144094	−	0.989564i	$-0.546027\pi$
$71$	−2.42832			−0.288189			−0.144094	+	0.989564i	$0.546027\pi$
$72$		0			0
$73$	−7.82718	+	4.51902i	−0.916102	+	0.528912i	−0.882389	−	0.470520i	$-0.844066\pi$
$73$	−7.82718	+	4.51902i	−0.916102	+	0.528912i	−0.0337124	+	0.999432i	$0.510733\pi$
$74$	−0.261348	−	0.452669i	−0.0303811	−	0.0526217i
$75$		0			0
$76$	1.06275			0.121905
$77$	−4.97188	+	13.3357i	−0.566599	+	1.51975i
$78$		0			0
$79$	2.96863	−	5.14181i	0.333997	−	0.578499i	−0.649295	−	0.760537i	$-0.724936\pi$
$79$	2.96863	−	5.14181i	0.333997	−	0.578499i	0.983292	+	0.182038i	$0.0582693\pi$
$80$	−1.43458	+	4.23580i	−0.160391	+	0.473576i
$81$		0			0
$82$	5.81496	+	3.35727i	0.642155	+	0.370748i
$83$		−	11.6556i		−	1.27936i	−0.768639	−	0.639682i	$-0.779066\pi$
$83$		−	11.6556i		−	1.27936i	0.768639	−	0.639682i	$-0.220934\pi$
$84$		0			0
$85$	8.29150	−	7.28164i	0.899340	−	0.789804i
$86$	−3.21236	+	5.56398i	−0.346398	+	0.599979i
$87$		0			0
$88$	−10.1088	+	5.83633i	−1.07760	+	0.622155i
$89$	2.68967	−	4.65864i	0.285104	−	0.493815i	−0.687530	−	0.726156i	$-0.741305\pi$
$89$	2.68967	−	4.65864i	0.285104	−	0.493815i	0.972634	+	0.232341i	$0.0746385\pi$
$90$		0			0
$91$	8.32288	−	6.87386i	0.872474	−	0.720577i
$92$		−	10.0808i		−	1.05100i
$93$		0			0
$94$	−0.645751	−	1.11847i	−0.0666042	−	0.115362i
$95$	−0.463192	+	1.36764i	−0.0475225	+	0.140316i
$96$		0			0
$97$		−	6.71453i		−	0.681758i	−0.940107	−	0.340879i	$-0.889275\pi$
$97$		−	6.71453i		−	0.681758i	0.940107	−	0.340879i	$-0.110725\pi$
$98$	−2.72749	+	3.14944i	−0.275518	+	0.318141i
$99$		0			0
$100$	−6.53526	−	5.00029i	−0.653526	−	0.500029i
$101$	1.73686	+	3.00832i	0.172824	+	0.299339i	0.939406	−	0.342807i	$-0.111378\pi$
$101$	1.73686	+	3.00832i	0.172824	+	0.299339i	−0.766582	+	0.642146i	$0.778044\pi$
$102$		0			0
$103$	6.30608	+	3.64082i	0.621357	+	0.358740i	0.777397	−	0.629010i	$-0.216540\pi$
$103$	6.30608	+	3.64082i	0.621357	+	0.358740i	−0.156040	+	0.987751i	$0.549873\pi$
$104$	8.85305			0.868113
$105$		0			0
$106$	−4.70850			−0.457330
$107$	4.45643	+	2.57292i	0.430820	+	0.248734i	0.699696	−	0.714441i	$-0.253319\pi$
$107$	4.45643	+	2.57292i	0.430820	+	0.248734i	−0.268876	+	0.963175i	$0.586652\pi$
$108$		0			0
$109$	−6.61438	−	11.4564i	−0.633543	−	1.09733i	−0.986822	−	0.161810i	$-0.948267\pi$
$109$	−6.61438	−	11.4564i	−0.633543	−	1.09733i	0.353279	−	0.935518i	$-0.385067\pi$
$110$	−1.40157	−	7.02072i	−0.133635	−	0.669399i
$111$		0			0
$112$	5.21812	−	0.878205i	0.493066	−	0.0829825i
$113$			15.8219i			1.48840i	0.667958	+	0.744199i	$0.267169\pi$
$113$			15.8219i			1.48840i	−0.667958	+	0.744199i	$0.732831\pi$
$114$		0			0
$115$	12.9729	+	4.39368i	1.20973	+	0.409713i
$116$	−1.99820	−	3.46099i	−0.185529	−	0.321345i
$117$		0			0
$118$			4.95813i			0.456432i
$119$	−12.2342	−	4.56120i	−1.12151	−	0.418125i
$120$		0			0
$121$	−8.96863	+	15.5341i	−0.815330	+	1.41219i
$122$	−0.182597	+	0.105422i	−0.0165315	+	0.00954448i
$123$		0			0
$124$	−4.11438	+	7.12631i	−0.369482	+	0.639962i
$125$	9.28316	−	6.23080i	0.830311	−	0.557300i
$126$		0			0
$127$			4.07992i			0.362034i	0.983480	+	0.181017i	$0.0579390\pi$
$127$			4.07992i			0.362034i	−0.983480	+	0.181017i	$0.942061\pi$
$128$	9.94376	+	5.74103i	0.878913	+	0.507441i
$129$		0			0
$130$	−1.74181	+	5.14293i	−0.152767	+	0.451065i
$131$	3.90383	−	6.76163i	0.341079	−	0.590766i	−0.643554	−	0.765400i	$-0.722541\pi$
$131$	3.90383	−	6.76163i	0.341079	−	0.590766i	0.984633	+	0.174634i	$0.0558743\pi$
$132$		0			0
$133$	1.68480	−	0.283551i	0.146091	−	0.0245870i
$134$	−1.38293			−0.119467
$135$		0			0
$136$	−5.35425	−	9.27383i	−0.459123	−	0.795224i
$137$	3.42554	−	1.97774i	0.292663	−	0.168969i	−0.346479	−	0.938058i	$-0.612623\pi$
$137$	3.42554	−	1.97774i	0.292663	−	0.168969i	0.639142	+	0.769088i	$0.279289\pi$
$138$		0			0
$139$	7.22876			0.613135			0.306568	−	0.951849i	$-0.400819\pi$
$139$	7.22876			0.613135			0.306568	+	0.951849i	$0.400819\pi$
$140$	−1.54944	+	9.61232i	−0.130952	+	0.812389i
$141$		0			0
$142$	−1.25167	−	0.722653i	−0.105038	−	0.0606437i
$143$	19.0069	−	10.9736i	1.58944	−	0.917661i
$144$		0			0
$145$	5.32482	−	1.06301i	0.442202	−	0.0882785i
$146$	−5.37934			−0.445197
$147$		0			0
$148$			1.44531i			0.118803i
$149$	1.47551	−	2.55566i	0.120878	−	0.209367i	−0.799236	−	0.601017i	$-0.794762\pi$
$149$	1.47551	−	2.55566i	0.120878	−	0.209367i	0.920114	+	0.391650i	$0.128096\pi$
$150$		0			0
$151$	4.46863	+	7.73989i	0.363652	+	0.629863i	0.988559	−	0.150836i	$-0.0481965\pi$
$151$	4.46863	+	7.73989i	0.363652	+	0.629863i	−0.624907	+	0.780699i	$0.714863\pi$
$152$	1.21349	+	0.700610i	0.0984272	+	0.0568270i
$153$		0			0
$154$	−6.53137	+	5.39426i	−0.526313	+	0.434682i
$155$	−7.37754	−	8.40071i	−0.592578	−	0.674761i
$156$		0			0
$157$	−10.1088	+	5.83633i	−0.806772	+	0.465790i	−0.845834	−	0.533447i	$-0.820896\pi$
$157$	−10.1088	+	5.83633i	−0.806772	+	0.465790i	0.0390619	+	0.999237i	$0.487563\pi$
$158$	3.06034	−	1.76689i	0.243468	−	0.140566i
$159$		0			0
$160$	−9.29150	+	8.15984i	−0.734558	+	0.645092i
$161$	−2.68967	−	15.9815i	−0.211976	−	1.25952i
$162$		0			0
$163$	1.52110	+	0.878205i	0.119141	+	0.0687863i	0.558386	−	0.829581i	$-0.311421\pi$
$163$	1.52110	+	0.878205i	0.119141	+	0.0687863i	−0.439245	+	0.898367i	$0.644754\pi$
$164$	−9.28316	−	16.0789i	−0.724893	−	1.25555i
$165$		0			0
$166$	3.46863	−	6.00784i	0.269218	−	0.466299i
$167$		−	12.6351i		−	0.977733i	−0.872359	−	0.488867i	$-0.837410\pi$
$167$		−	12.6351i		−	0.977733i	0.872359	−	0.488867i	$-0.162590\pi$
$168$		0			0
$169$	−3.64575			−0.280442
$170$	6.44081	−	1.28580i	0.493987	−	0.0986166i
$171$		0			0
$172$	15.3849	−	8.88249i	1.17309	−	0.677284i
$173$	−8.06457	−	4.65608i	−0.613138	−	0.353995i	0.161055	−	0.986945i	$-0.448510\pi$
$173$	−8.06457	−	4.65608i	−0.613138	−	0.353995i	−0.774193	+	0.632950i	$0.781844\pi$
$174$		0			0
$175$	−11.6947	−	6.18343i	−0.884033	−	0.467424i
$176$	10.7587			0.810965
$177$		0			0
$178$	2.77277	−	1.60086i	0.207828	−	0.119989i
$179$	−8.33035	−	14.4286i	−0.622640	−	1.07844i	−0.988992	−	0.147968i	$-0.952727\pi$
$179$	−8.33035	−	14.4286i	−0.622640	−	1.07844i	0.366352	−	0.930476i	$-0.380606\pi$
$180$		0			0
$181$	12.6458			0.939951			0.469976	−	0.882679i	$-0.344263\pi$
$181$	12.6458			0.939951			0.469976	+	0.882679i	$0.344263\pi$
$182$	6.33563	−	1.06628i	0.469628	−	0.0790380i
$183$		0			0
$184$	6.64575	−	11.5108i	0.489931	−	0.848586i
$185$	−1.85995	−	0.629928i	−0.136746	−	0.0463133i
$186$		0			0
$187$	−22.9904	−	13.2735i	−1.68123	−	0.970656i
$188$			3.57113i			0.260451i
$189$		0			0
$190$	−0.645751	+	0.567102i	−0.0468477	+	0.0411419i
$191$	−5.37934	+	9.31728i	−0.389235	+	0.674175i	−0.992347	−	0.123482i	$-0.960594\pi$
$191$	−5.37934	+	9.31728i	−0.389235	+	0.674175i	0.603112	+	0.797657i	$0.293927\pi$
$192$		0			0
$193$	10.8694	−	6.27543i	0.782394	−	0.451715i	−0.0548839	−	0.998493i	$-0.517479\pi$
$193$	10.8694	−	6.27543i	0.782394	−	0.451715i	0.837278	+	0.546777i	$0.184146\pi$
$194$	1.99820	−	3.46099i	0.143463	−	0.248485i
$195$		0			0
$196$	10.8856	−	3.77089i	0.777544	−	0.269349i
$197$			5.91453i			0.421393i	0.977552	+	0.210697i	$0.0675732\pi$
$197$			5.91453i			0.421393i	−0.977552	+	0.210697i	$0.932427\pi$
$198$		0			0
$199$	8.82288	+	15.2817i	0.625437	+	1.08329i	0.988456	+	0.151507i	$0.0484126\pi$
$199$	8.82288	+	15.2817i	0.625437	+	1.08329i	−0.363019	+	0.931782i	$0.618254\pi$
$200$	−4.16584	−	10.0179i	−0.294570	−	0.708372i
$201$		0			0
$202$			2.06751i			0.145470i
$203$	−4.09124	−	4.95368i	−0.287149	−	0.347680i
$204$		0			0
$205$	24.7378	−	4.93850i	1.72776	−	0.344919i
$206$	2.16697	+	3.75330i	0.150980	+	0.261505i
$207$		0			0
$208$	−7.06663	−	4.07992i	−0.489983	−	0.282892i
$209$	3.47371			0.240282
$210$		0			0
$211$	−14.9373			−1.02832			−0.514161	−	0.857693i	$-0.671897\pi$
$211$	−14.9373			−1.02832			−0.514161	+	0.857693i	$0.671897\pi$
$212$	11.2752	+	6.50972i	0.774382	+	0.447090i
$213$		0			0
$214$	1.53137	+	2.65242i	0.104683	+	0.181315i
$215$	4.72535	+	23.6701i	0.322266	+	1.61429i
$216$		0			0
$217$	−4.62128	+	12.3953i	−0.313713	+	0.841449i
$218$		−	7.87360i		−	0.533267i
$219$		0			0
$220$	−6.35021	+	18.7499i	−0.428131	+	1.26412i
$221$	10.0672	+	17.4369i	0.677194	+	1.17293i
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$	13.7097	+	5.11131i	0.916017	+	0.341514i
$225$		0			0
$226$	−4.70850	+	8.15536i	−0.313205	+	0.542486i
$227$	−3.06034	+	1.76689i	−0.203122	+	0.117273i	−0.598111	−	0.801413i	$-0.704082\pi$
$227$	−3.06034	+	1.76689i	−0.203122	+	0.117273i	0.394989	+	0.918686i	$0.370748\pi$
$228$		0			0
$229$	−1.14575	+	1.98450i	−0.0757134	+	0.131139i	−0.901396	−	0.432995i	$-0.857457\pi$
$229$	−1.14575	+	1.98450i	−0.0757134	+	0.131139i	0.825683	+	0.564135i	$0.190790\pi$
$230$	5.37934	+	6.12538i	0.354703	+	0.403895i
$231$		0			0
$232$		−	5.26923i		−	0.345942i
$233$	−6.66848	−	3.85005i	−0.436867	−	0.252225i	0.265401	−	0.964138i	$-0.414496\pi$
$233$	−6.66848	−	3.85005i	−0.436867	−	0.252225i	−0.702268	+	0.711913i	$0.747829\pi$
$234$		0			0
$235$	−4.59564	−	1.55646i	−0.299787	−	0.101532i
$236$	6.85484	−	11.8729i	0.446212	−	0.772862i
$237$		0			0
$238$	−4.94870	−	5.99188i	−0.320776	−	0.388396i
$239$	−8.85305			−0.572656			−0.286328	−	0.958132i	$-0.592435\pi$
$239$	−8.85305			−0.572656			−0.286328	+	0.958132i	$0.592435\pi$
$240$		0			0
$241$	−14.1144	−	24.4468i	−0.909187	−	1.57476i	−0.815196	−	0.579185i	$-0.803371\pi$
$241$	−14.1144	−	24.4468i	−0.909187	−	1.57476i	−0.0939910	−	0.995573i	$-0.529962\pi$
$242$	−9.24572	+	5.33802i	−0.594337	+	0.343141i
$243$		0			0
$244$	0.583005			0.0373231
$245$	0.108279	+	15.6521i	0.00691772	+	0.999976i
$246$		0			0
$247$	−2.28164	−	1.31731i	−0.145177	−	0.0838182i
$248$	−9.39597	+	5.42477i	−0.596645	+	0.344473i
$249$		0			0
$250$	6.63924	−	0.449039i	0.419902	−	0.0283997i
$251$	−16.1380			−1.01862			−0.509311	−	0.860583i	$-0.670100\pi$
$251$	−16.1380			−1.01862			−0.509311	+	0.860583i	$0.670100\pi$
$252$		0			0
$253$		−	32.9505i		−	2.07158i
$254$	−1.21416	+	2.10299i	−0.0761832	+	0.131953i
$255$		0			0
$256$	2.70850	+	4.69126i	0.169281	+	0.293203i
$257$	1.36375	+	0.787360i	0.0850682	+	0.0491141i	0.541931	−	0.840423i	$-0.317694\pi$
$257$	1.36375	+	0.787360i	0.0850682	+	0.0491141i	−0.456862	+	0.889537i	$0.651027\pi$
$258$		0			0
$259$	0.385622	+	2.29129i	0.0239614	+	0.142374i
$260$	11.2814	−	9.90735i	0.699641	−	0.614428i
$261$		0			0
$262$	4.02444	−	2.32351i	0.248631	−	0.143547i
$263$	−12.4887	+	7.21033i	−0.770084	+	0.444608i	−0.832905	−	0.553417i	$-0.813324\pi$
$263$	−12.4887	+	7.21033i	−0.770084	+	0.444608i	0.0628207	+	0.998025i	$0.479990\pi$
$264$		0			0
$265$	−13.2915	+	11.6727i	−0.816491	+	0.717046i
$266$	0.952811	+	0.355232i	0.0584206	+	0.0217806i
$267$		0			0
$268$	3.31161	+	1.91196i	0.202289	+	0.116792i
$269$	12.2342	+	21.1902i	0.745931	+	1.29199i	0.949758	+	0.312984i	$0.101329\pi$
$269$	12.2342	+	21.1902i	0.745931	+	1.29199i	−0.203827	+	0.979007i	$0.565338\pi$
$270$		0			0
$271$	−11.1144	+	19.2507i	−0.675150	+	1.16939i	0.301275	+	0.953537i	$0.402588\pi$
$271$	−11.1144	+	19.2507i	−0.675150	+	1.16939i	−0.976425	+	0.215857i	$0.930745\pi$
$272$			9.87000i			0.598457i
$273$		0			0
$274$	2.35425			0.142225
$275$	−21.3613	−	16.3440i	−1.28813	−	0.985582i
$276$		0			0
$277$	−14.8938	+	8.59894i	−0.894882	+	0.516660i	−0.875536	−	0.483152i	$-0.839492\pi$
$277$	−14.8938	+	8.59894i	−0.894882	+	0.516660i	−0.0193459	+	0.999813i	$0.506158\pi$
$278$	3.72605	+	2.15123i	0.223473	+	0.129022i
$279$		0			0
$280$	−8.10610	+	9.95432i	−0.484432	+	0.594885i
$281$	−3.99641			−0.238406			−0.119203	−	0.992870i	$-0.538034\pi$
$281$	−3.99641			−0.238406			−0.119203	+	0.992870i	$0.538034\pi$
$282$		0			0
$283$	20.4393	−	11.8007i	1.21499	−	0.701476i	0.251150	−	0.967948i	$-0.419191\pi$
$283$	20.4393	−	11.8007i	1.21499	−	0.701476i	0.963843	+	0.266472i	$0.0858579\pi$
$284$	1.99820	+	3.46099i	0.118572	+	0.205372i
$285$		0			0
$286$	13.0627			0.772416
$287$	−19.0069	−	23.0135i	−1.12194	−	1.35845i
$288$		0			0
$289$	3.67712	−	6.36897i	0.216301	−	0.374645i
$290$	3.06101	+	1.03671i	0.179749	+	0.0608774i
$291$		0			0
$292$	12.8816	+	7.43719i	0.753838	+	0.435228i
$293$			15.1894i			0.887371i	0.896182	+	0.443686i	$0.146329\pi$
$293$			15.1894i			0.887371i	−0.896182	+	0.443686i	$0.853671\pi$
$294$		0			0
$295$	12.2915	+	13.9962i	0.715639	+	0.814889i
$296$	−0.952811	+	1.65032i	−0.0553810	+	0.0959228i
$297$		0			0
$298$	1.52110	−	0.878205i	0.0881147	−	0.0508730i
$299$	−12.4955	+	21.6429i	−0.722635	+	1.25164i
$300$		0			0
$301$	22.0203	−	18.1865i	1.26923	−	1.04825i
$302$			5.31935i			0.306094i
$303$		0			0
$304$	−0.645751	−	1.11847i	−0.0370364	−	0.0641489i
$305$	−0.254099	+	0.750263i	−0.0145497	+	0.0429599i
$306$		0			0
$307$			20.3996i			1.16427i	0.813093	+	0.582133i	$0.197782\pi$
$307$			20.3996i			1.16427i	−0.813093	+	0.582133i	$0.802218\pi$
$308$	23.0981	−	3.88739i	1.31614	−	0.221505i
$309$		0			0
$310$	−1.30274	−	6.52564i	−0.0739905	−	0.370631i
$311$	1.73686	+	3.00832i	0.0984881	+	0.170586i	0.911059	−	0.412276i	$-0.135266\pi$
$311$	1.73686	+	3.00832i	0.0984881	+	0.170586i	−0.812571	+	0.582862i	$0.801933\pi$
$312$		0			0
$313$	−7.82718	−	4.51902i	−0.442418	−	0.255430i	0.262205	−	0.965012i	$-0.415550\pi$
$313$	−7.82718	−	4.51902i	−0.442418	−	0.255430i	−0.704623	+	0.709582i	$0.748884\pi$
$314$	−6.94743			−0.392066
$315$		0			0
$316$	−9.77124			−0.549675
$317$	−15.2485	−	8.80372i	−0.856441	−	0.494466i	0.00637790	−	0.999980i	$-0.497970\pi$
$317$	−15.2485	−	8.80372i	−0.856441	−	0.494466i	−0.862819	+	0.505513i	$0.831303\pi$
$318$		0			0
$319$	−6.53137	−	11.3127i	−0.365687	−	0.633388i
$320$	1.55359	−	0.310150i	0.0868485	−	0.0173379i
$321$		0			0
$322$	3.36961	−	9.03805i	0.187781	−	0.503671i
$323$			3.18678i			0.177317i
$324$		0			0
$325$	7.83274	+	18.8359i	0.434482	+	1.04483i
$326$	0.522697	+	0.905337i	0.0289495	+	0.0501420i
$327$		0			0
$328$		−	24.4795i		−	1.35166i
$329$	0.952811	+	5.66142i	0.0525302	+	0.312124i
$330$		0			0
$331$	−8.79150	+	15.2273i	−0.483225	+	0.836970i	−0.999814	−	0.0192633i	$-0.993868\pi$
$331$	−8.79150	+	15.2273i	−0.483225	+	0.836970i	0.516590	+	0.856233i	$0.327201\pi$
$332$	−16.6122	+	9.59108i	−0.911715	+	0.526379i
$333$		0			0
$334$	3.76013	−	6.51274i	0.205745	−	0.356361i
$335$	−3.90383	+	3.42836i	−0.213289	+	0.187311i
$336$		0			0
$337$			12.2398i			0.666742i	0.942796	+	0.333371i	$0.108186\pi$
$337$			12.2398i			0.666742i	−0.942796	+	0.333371i	$0.891814\pi$
$338$	−1.87919	−	1.08495i	−0.102215	−	0.0590137i
$339$		0			0
$340$	−17.2011	−	5.82569i	−0.932862	−	0.315942i
$341$	−13.4483	+	23.2932i	−0.728268	+	1.26140i
$342$		0			0
$343$	16.2512	−	8.88249i	0.877482	−	0.479610i
$344$	23.4230			1.26288
$345$		0			0
$346$	−2.77124	−	4.79993i	−0.148983	−	0.258046i
$347$	16.7948	−	9.69651i	0.901594	−	0.520536i	0.0238772	−	0.999715i	$-0.492399\pi$
$347$	16.7948	−	9.69651i	0.901594	−	0.520536i	0.877717	+	0.479179i	$0.159066\pi$
$348$		0			0
$349$	−25.8745			−1.38503			−0.692515	−	0.721403i	$-0.743498\pi$
$349$	−25.8745			−1.38503			−0.692515	+	0.721403i	$0.743498\pi$
$350$	−4.18784	−	6.66750i	−0.223849	−	0.356393i
$351$		0			0
$352$	25.7632	+	14.8744i	1.37318	+	0.792807i
$353$	−1.36375	+	0.787360i	−0.0725849	+	0.0419069i	−0.535853	−	0.844311i	$-0.680010\pi$
$353$	−1.36375	+	0.787360i	−0.0725849	+	0.0419069i	0.463268	+	0.886218i	$0.346677\pi$
$354$		0			0
$355$	−5.32482	+	1.06301i	−0.282612	+	0.0564189i
$356$	−8.85305			−0.469211
$357$		0			0
$358$		−	9.91625i		−	0.524090i
$359$	9.54451	−	16.5316i	0.503740	−	0.872503i	−0.496251	−	0.868179i	$-0.665290\pi$
$359$	9.54451	−	16.5316i	0.503740	−	0.872503i	0.999991	−	0.00432406i	$-0.00137640\pi$
$360$		0			0
$361$	9.29150	+	16.0934i	0.489026	+	0.847019i
$362$	6.51823	+	3.76330i	0.342590	+	0.197795i
$363$		0			0
$364$	−16.6458	−	6.20595i	−0.872474	−	0.325280i
$365$	−15.1852	+	13.3357i	−0.794829	+	0.698023i
$366$		0			0
$367$	−16.1455	+	9.32160i	−0.842787	+	0.486583i	−0.858211	−	0.513298i	$-0.828424\pi$
$367$	−16.1455	+	9.32160i	−0.842787	+	0.486583i	0.0154235	+	0.999881i	$0.495090\pi$
$368$	−10.6095	+	6.12538i	−0.553057	+	0.319307i
$369$		0			0
$370$	−0.771243	−	0.878205i	−0.0400950	−	0.0456557i
$371$	19.6117	+	7.31173i	1.01819	+	0.379606i
$372$		0			0
$373$	−20.7088	−	11.9562i	−1.07226	−	0.619069i	−0.143461	−	0.989656i	$-0.545823\pi$
$373$	−20.7088	−	11.9562i	−1.07226	−	0.619069i	−0.928798	+	0.370587i	$0.879157\pi$
$374$	−7.90024	−	13.6836i	−0.408512	−	0.707563i
$375$		0			0
$376$	−2.35425	+	4.07768i	−0.121411	+	0.210290i
$377$			9.90735i			0.510255i
$378$		0			0
$379$	2.29150			0.117707			0.0588533	−	0.998267i	$-0.481256\pi$
$379$	2.29150			0.117707			0.0588533	+	0.998267i	$0.481256\pi$
$380$	2.33039	−	0.465224i	0.119546	−	0.0238655i
$381$		0			0
$382$	−5.54553	+	3.20172i	−0.283734	+	0.163814i
$383$	−12.3061	−	7.10491i	−0.628811	−	0.363044i	0.151481	−	0.988460i	$-0.451596\pi$
$383$	−12.3061	−	7.10491i	−0.628811	−	0.363044i	−0.780291	+	0.625416i	$0.784929\pi$
$384$		0			0
$385$	−5.06454	+	31.4190i	−0.258113	+	1.60126i
$386$	7.47012			0.380219
$387$		0			0
$388$	−9.56997	+	5.52523i	−0.485842	+	0.280501i
$389$	15.4465	+	26.7542i	0.783171	+	1.35649i	0.930086	+	0.367343i	$0.119732\pi$
$389$	15.4465	+	26.7542i	0.783171	+	1.35649i	−0.146915	+	0.989149i	$0.546934\pi$
$390$		0			0
$391$	30.2288			1.52873
$392$	14.9156	+	2.87052i	0.753354	+	0.144983i
$393$		0			0
$394$	−1.76013	+	3.04863i	−0.0886740	+	0.153588i
$395$	4.25874	−	12.5745i	0.214280	−	0.632692i
$396$		0			0
$397$	27.5060	+	15.8806i	1.38049	+	0.797023i	0.992217	−	0.124523i	$-0.0397400\pi$
$397$	27.5060	+	15.8806i	1.38049	+	0.797023i	0.388268	+	0.921546i	$0.373073\pi$
$398$			10.5025i			0.526445i
$399$		0			0
$400$	−1.29150	+	9.91625i	−0.0645751	+	0.495813i
$401$	19.6117	−	33.9685i	0.979363	−	1.69631i	0.314648	−	0.949208i	$-0.398114\pi$
$401$	19.6117	−	33.9685i	0.979363	−	1.69631i	0.664715	−	0.747097i	$-0.268553\pi$
$402$		0			0
$403$	17.6666	−	10.1998i	0.880035	−	0.508088i
$404$	2.85843	−	4.95095i	0.142212	−	0.246319i
$405$		0			0
$406$	−0.634637	−	3.77089i	−0.0314965	−	0.187146i
$407$			4.72416i			0.234168i
$408$		0			0
$409$	12.7915	+	22.1555i	0.632499	+	1.09552i	0.987039	+	0.160480i	$0.0513041\pi$
$409$	12.7915	+	22.1555i	0.632499	+	1.09552i	−0.354540	+	0.935041i	$0.615363\pi$
$410$	14.2207	+	4.81628i	0.702310	+	0.237859i
$411$		0			0
$412$		−	11.9838i		−	0.590398i
$413$	7.69938	−	20.6515i	0.378862	−	1.01619i
$414$		0			0
$415$	−5.10230	−	25.5583i	−0.250462	−	1.25461i
$416$	−11.2814	−	19.5399i	−0.553115	−	0.958023i
$417$		0			0
$418$	1.79052	+	1.03376i	0.0875771	+	0.0505627i
$419$	−17.7061			−0.864999			−0.432500	−	0.901634i	$-0.642368\pi$
$419$	−17.7061			−0.864999			−0.432500	+	0.901634i	$0.642368\pi$
$420$		0			0
$421$	−9.22876			−0.449782			−0.224891	−	0.974384i	$-0.572203\pi$
$421$	−9.22876			−0.449782			−0.224891	+	0.974384i	$0.572203\pi$
$422$	−7.69938	−	4.44524i	−0.374800	−	0.216391i
$423$		0			0
$424$	8.58301	+	14.8662i	0.416828	+	0.721967i
$425$	14.9940	−	19.5968i	0.727317	−	0.950586i
$426$		0			0
$427$	0.924256	−	0.155551i	0.0447279	−	0.00752766i
$428$		−	8.46878i		−	0.409354i
$429$		0			0
$430$	−4.60840	+	13.6069i	−0.222237	+	0.656184i
$431$	−10.3286	−	17.8896i	−0.497509	−	0.861711i	0.502487	−	0.864585i	$-0.332419\pi$
$431$	−10.3286	−	17.8896i	−0.497509	−	0.861711i	−0.999996	+	0.00287387i	$0.999085\pi$
$432$		0			0
$433$		−	33.8287i		−	1.62570i	−0.582472	−	0.812851i	$-0.697914\pi$
$433$		−	33.8287i		−	1.62570i	0.582472	−	0.812851i	$-0.302086\pi$
$434$	−6.07080	+	5.01387i	−0.291408	+	0.240674i
$435$		0			0
$436$	−10.8856	+	18.8544i	−0.521327	+	0.902964i
$437$	−3.42554	+	1.97774i	−0.163866	+	0.0946079i
$438$		0			0
$439$	15.1144	−	26.1789i	0.721370	−	1.24945i	−0.239081	−	0.971000i	$-0.576846\pi$
$439$	15.1144	−	26.1789i	0.721370	−	1.24945i	0.960451	−	0.278450i	$-0.0898206\pi$
$440$	−19.6117	+	17.2231i	−0.934952	+	0.821079i
$441$		0			0
$442$			11.9838i			0.570009i
$443$	−14.5505	−	8.40071i	−0.691313	−	0.399130i	0.112791	−	0.993619i	$-0.464021\pi$
$443$	−14.5505	−	8.40071i	−0.691313	−	0.399130i	−0.804104	+	0.594489i	$0.797354\pi$
$444$		0			0
$445$	3.85855	−	11.3929i	0.182913	−	0.540075i
$446$		0			0
$447$		0			0
$448$	−1.19368	−	1.44531i	−0.0563960	−	0.0682843i
$449$	−22.5627			−1.06480			−0.532401	−	0.846492i	$-0.678710\pi$
$449$	−22.5627			−1.06480			−0.532401	+	0.846492i	$0.678710\pi$
$450$		0			0
$451$	−30.3431	−	52.5559i	−1.42880	−	2.47476i
$452$	22.5503	−	13.0194i	1.06068	−	0.612383i
$453$		0			0
$454$	−2.10326			−0.0987111
$455$	15.2413	−	18.7164i	0.714524	−	0.877438i
$456$		0			0
$457$	−27.7754	−	16.0361i	−1.29928	−	0.750139i	−0.318999	−	0.947755i	$-0.603347\pi$
$457$	−27.7754	−	16.0361i	−1.29928	−	0.750139i	−0.980279	+	0.197617i	$0.936680\pi$
$458$	−1.18115	+	0.681937i	−0.0551915	+	0.0318648i
$459$		0			0
$460$	−4.41296	−	22.1053i	−0.205755	−	1.03066i
$461$	16.1380			0.751622			0.375811	−	0.926696i	$-0.377364\pi$
$461$	16.1380			0.751622			0.375811	+	0.926696i	$0.377364\pi$
$462$		0			0
$463$			17.5090i			0.813712i	0.913492	+	0.406856i	$0.133375\pi$
$463$			17.5090i			0.813712i	−0.913492	+	0.406856i	$0.866625\pi$
$464$	−2.42832	+	4.20597i	−0.112732	+	0.195257i
$465$		0			0
$466$	−2.29150	−	3.96900i	−0.106152	−	0.183860i
$467$	35.5868	+	20.5460i	1.64676	+	0.950757i	0.978348	+	0.206966i	$0.0663591\pi$
$467$	35.5868	+	20.5460i	1.64676	+	0.950757i	0.668412	+	0.743791i	$0.266974\pi$
$468$		0			0
$469$	5.76013	+	2.14752i	0.265978	+	0.0991632i
$470$	−1.90562	−	2.16991i	−0.0878998	−	0.100090i
$471$		0			0
$472$	15.6544	−	9.03805i	0.720550	−	0.416010i
$473$	50.2875	−	29.0335i	2.31222	−	1.33496i
$474$		0			0
$475$	−0.416995	+	3.20172i	−0.0191330	+	0.146905i
$476$	3.56630	+	21.1902i	0.163461	+	0.971252i
$477$		0			0
$478$	−4.56329	−	2.63461i	−0.208720	−	0.120504i
$479$	−6.33215	−	10.9676i	−0.289323	−	0.501122i	0.684325	−	0.729177i	$-0.260097\pi$
$479$	−6.33215	−	10.9676i	−0.289323	−	0.501122i	−0.973648	+	0.228055i	$0.926764\pi$
$480$		0			0
$481$	1.79150	−	3.10297i	0.0816855	−	0.141483i
$482$		−	16.8014i		−	0.765284i
$483$		0			0
$484$	29.5203			1.34183
$485$	−2.93933	−	14.7236i	−0.133468	−	0.668565i
$486$		0			0
$487$	−20.7088	+	11.9562i	−0.938404	+	0.541788i	−0.889460	−	0.457014i	$-0.848919\pi$
$487$	−20.7088	+	11.9562i	−0.938404	+	0.541788i	−0.0489441	+	0.998802i	$0.515586\pi$
$488$	0.665702	+	0.384343i	0.0301349	+	0.0173984i
$489$		0			0
$490$	−4.60216	+	8.10007i	−0.207904	+	0.365924i
$491$	−36.2724			−1.63695			−0.818476	−	0.574541i	$-0.805181\pi$
$491$	−36.2724			−1.63695			−0.818476	+	0.574541i	$0.805181\pi$
$492$		0			0
$493$	10.3782	−	5.99188i	0.467413	−	0.269861i
$494$	−0.784045	−	1.35801i	−0.0352759	−	0.0610996i
$495$		0			0
$496$	10.0000			0.449013
$497$	4.09124	+	4.95368i	0.183517	+	0.222203i
$498$		0			0
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$	−16.5194	−	8.10377i	−0.738771	−	0.362412i
$501$		0			0
$502$	−8.31830	−	4.80257i	−0.371264	−	0.214349i
$503$			15.8219i			0.705463i	0.935725	+	0.352731i	$0.114747\pi$
$503$			15.8219i			0.705463i	−0.935725	+	0.352731i	$0.885253\pi$
$504$		0			0
$505$	5.12549	+	5.83633i	0.228081	+	0.259713i
$506$	9.80586	−	16.9842i	0.435924	−	0.755042i
$507$		0			0
$508$	5.81496	−	3.35727i	0.257997	−	0.148955i
$509$	10.7587	−	18.6346i	0.476870	−	0.825963i	−0.522779	−	0.852468i	$-0.675105\pi$
$509$	10.7587	−	18.6346i	0.476870	−	0.825963i	0.999649	+	0.0265057i	$0.00843801\pi$
$510$		0			0
$511$	22.4059	+	8.35347i	0.991178	+	0.369536i
$512$		−	19.7400i		−	0.872393i
$513$		0			0
$514$	0.468627	+	0.811686i	0.0206702	+	0.0358019i
$515$	15.4218	+	5.22305i	0.679564	+	0.230155i
$516$		0			0
$517$			11.6727i			0.513363i
$518$	−0.483106	+	1.29580i	−0.0212264	+	0.0569341i
$519$		0			0
$520$	19.4130	−	3.87548i	0.851315	−	0.169951i
$521$	−8.33035	−	14.4286i	−0.364959	−	0.632128i	0.623810	−	0.781576i	$-0.285584\pi$
$521$	−8.33035	−	14.4286i	−0.364959	−	0.632128i	−0.988770	+	0.149448i	$0.952250\pi$
$522$		0			0
$523$	−2.01222	−	1.16176i	−0.0879882	−	0.0508000i	0.455360	−	0.890307i	$-0.349510\pi$
$523$	−2.01222	−	1.16176i	−0.0879882	−	0.0508000i	−0.543349	+	0.839507i	$0.682844\pi$
$524$	−12.8495			−0.561331
$525$		0			0
$526$	−8.58301			−0.374237
$527$	−21.3692	−	12.3375i	−0.930856	−	0.537430i
$528$		0			0
$529$	7.26013	+	12.5749i	0.315658	+	0.546735i
$530$	−10.3248	+	2.06118i	−0.448480	+	0.0895318i
$531$		0			0
$532$	−1.79052	−	2.16796i	−0.0776288	−	0.0939930i
$533$			46.0271i			1.99365i
$534$		0			0
$535$	10.8984	+	3.69107i	0.471178	+	0.159579i
$536$	2.52090	+	4.36633i	0.108886	+	0.188597i
$537$		0			0
$538$			14.5633i			0.627867i
$539$	35.5810	−	12.3256i	1.53258	−	0.530901i
$540$		0			0
$541$	−14.7915	+	25.6196i	−0.635936	+	1.10147i	0.350380	+	0.936608i	$0.386053\pi$
$541$	−14.7915	+	25.6196i	−0.635936	+	1.10147i	−0.986316	+	0.164866i	$0.947281\pi$
$542$	−11.4578	+	6.61514i	−0.492153	+	0.284145i
$543$		0			0
$544$	−13.6458	+	23.6351i	−0.585057	+	1.01335i
$545$	−19.5191	−	22.2262i	−0.836108	−	0.952065i
$546$		0			0
$547$		−	32.6394i		−	1.39556i	−0.716313	−	0.697779i	$-0.754172\pi$
$547$		−	32.6394i		−	1.39556i	0.716313	−	0.697779i	$-0.245828\pi$
$548$	−5.63758	−	3.25486i	−0.240826	−	0.139041i
$549$		0			0
$550$	−6.14674	−	14.7815i	−0.262098	−	0.630285i
$551$	−0.784045	+	1.35801i	−0.0334015	+	0.0578530i
$552$		0			0
$553$	−15.4906	+	2.60706i	−0.658729	+	0.110864i
$554$	−10.2360			−0.434885
$555$		0			0
$556$	−5.94837	−	10.3029i	−0.252267	−	0.436939i
$557$	1.57869	−	0.911455i	0.0668911	−	0.0386196i	−0.466181	−	0.884689i	$-0.654371\pi$
$557$	1.57869	−	0.911455i	0.0668911	−	0.0386196i	0.533073	+	0.846070i	$0.321037\pi$
$558$		0			0
$559$	−44.0405			−1.86272
$560$	11.0578	−	4.20999i	0.467279	−	0.177905i
$561$		0			0
$562$	−2.05994	−	1.18931i	−0.0868934	−	0.0501679i
$563$	7.51678	−	4.33981i	0.316794	−	0.182901i	−0.333168	−	0.942867i	$-0.608118\pi$
$563$	7.51678	−	4.33981i	0.316794	−	0.182901i	0.649963	+	0.759966i	$0.274784\pi$
$564$		0			0
$565$	6.92614	+	34.6942i	0.291385	+	1.45960i
$566$	14.0472			0.590449
$567$		0			0
$568$			5.26923i			0.221092i
$569$	11.5427	−	19.9926i	0.483896	−	0.838132i	−0.515933	−	0.856629i	$-0.672555\pi$
$569$	11.5427	−	19.9926i	0.483896	−	0.838132i	0.999829	+	0.0184967i	$0.00588801\pi$
$570$		0			0
$571$	−2.26013	−	3.91466i	−0.0945835	−	0.163823i	0.814851	−	0.579670i	$-0.196819\pi$
$571$	−2.26013	−	3.91466i	−0.0945835	−	0.163823i	−0.909435	+	0.415847i	$0.863485\pi$
$572$	−31.2806	−	18.0599i	−1.30791	−	0.755121i
$573$		0			0
$574$	−2.94837	−	17.5186i	−0.123062	−	0.731213i
$575$	30.3704	+	3.95547i	1.26653	+	0.164955i
$576$		0			0
$577$	19.1877	−	11.0780i	0.798793	−	0.461183i	−0.0442559	−	0.999020i	$-0.514092\pi$
$577$	19.1877	−	11.0780i	0.798793	−	0.461183i	0.843049	+	0.537837i	$0.180758\pi$
$578$	3.79073	−	2.18858i	0.157674	−	0.0910329i
$579$		0			0
$580$	−5.89674	−	6.71453i	−0.244849	−	0.278806i
$581$	−23.7769	+	19.6373i	−0.986432	+	0.814694i
$582$		0			0
$583$	36.8542	+	21.2778i	1.52635	+	0.881237i
$584$	9.80586	+	16.9842i	0.405769	+	0.702813i
$585$		0			0
$586$	−4.52026	+	7.82932i	−0.186730	+	0.323426i
$587$			44.2789i			1.82758i	0.406182	+	0.913792i	$0.366860\pi$
$587$			44.2789i			1.82758i	−0.406182	+	0.913792i	$0.633140\pi$
$588$		0			0
$589$	3.22876			0.133039
$590$	2.17045	+	10.8722i	0.0893561	+	0.447600i
$591$		0			0
$592$	1.52110	−	0.878205i	0.0625166	−	0.0360940i
$593$	21.9170	+	12.6538i	0.900022	+	0.519628i	0.877207	−	0.480112i	$-0.159404\pi$
$593$	21.9170	+	12.6538i	0.900022	+	0.519628i	0.0228149	+	0.999740i	$0.492737\pi$
$594$		0			0
$595$	−28.8238	−	4.64621i	−1.18166	−	0.190476i
$596$	−4.85664			−0.198936
$597$		0			0
$598$	−12.8816	+	7.43719i	−0.526767	+	0.304129i
$599$	12.2342	+	21.1902i	0.499875	+	0.865809i	1.00000		0.000144290i	$-4.59290e-5\pi$
$599$	12.2342	+	21.1902i	0.499875	+	0.865809i	−0.500125	+	0.865953i	$0.666713\pi$
$600$		0			0
$601$	23.1033			0.942402			0.471201	−	0.882026i	$-0.343821\pi$
$601$	23.1033			0.942402			0.471201	+	0.882026i	$0.343821\pi$
$602$	16.7625	−	2.82111i	0.683188	−	0.114980i
$603$		0			0
$604$	7.35425	−	12.7379i	0.299240	−	0.518299i
$605$	−12.8662	+	37.9893i	−0.523087	+	1.54448i
$606$		0			0
$607$	−16.1455	−	9.32160i	−0.655325	−	0.378352i	0.135169	−	0.990823i	$-0.456842\pi$
$607$	−16.1455	−	9.32160i	−0.655325	−	0.378352i	−0.790493	+	0.612471i	$0.790176\pi$
$608$		−	3.57113i		−	0.144828i
$609$		0			0
$610$	−0.354249	+	0.311103i	−0.0143431	+	0.0125962i
$611$	4.42652	−	7.66697i	0.179078	−	0.310172i
$612$		0			0
$613$	−25.4938	+	14.7188i	−1.02968	+	0.594488i	−0.916894	−	0.399131i	$-0.869312\pi$
$613$	−25.4938	+	14.7188i	−1.02968	+	0.594488i	−0.112789	+	0.993619i	$0.535978\pi$
$614$	−6.07080	+	10.5149i	−0.244997	+	0.424348i
$615$		0			0
$616$	28.9373	+	10.7885i	1.16592	+	0.434682i
$617$			13.8628i			0.558096i	0.960277	+	0.279048i	$0.0900189\pi$
$617$			13.8628i			0.558096i	−0.960277	+	0.279048i	$0.909981\pi$
$618$		0			0
$619$	6.50000	+	11.2583i	0.261257	+	0.452510i	0.966576	−	0.256379i	$-0.0825296\pi$
$619$	6.50000	+	11.2583i	0.261257	+	0.452510i	−0.705319	+	0.708890i	$0.749196\pi$
$620$	−5.90241	+	17.4277i	−0.237047	+	0.699912i
$621$		0			0
$622$			2.06751i			0.0828997i
$623$	−14.0350	+	2.36208i	−0.562301	+	0.0946347i
$624$		0			0
$625$	17.6285	−	17.7267i	0.705142	−	0.709067i
$626$	−2.68967	−	4.65864i	−0.107501	−	0.186197i
$627$		0			0
$628$	16.6366	+	9.60515i	0.663873	+	0.383287i
$629$	−4.33394			−0.172806
$630$		0			0
$631$	3.16601			0.126037			0.0630184	−	0.998012i	$-0.479927\pi$
$631$	3.16601			0.126037			0.0630184	+	0.998012i	$0.479927\pi$
$632$	−11.1573	−	6.44165i	−0.443812	−	0.256235i
$633$		0			0
$634$	−5.23987	−	9.07572i	−0.208102	−	0.360443i
$635$	1.78601	+	8.94645i	0.0708758	+	0.355029i
$636$		0			0
$637$	−28.0448	−	5.39723i	−1.11118	−	0.213846i
$638$		−	7.77479i		−	0.307807i
$639$		0			0
$640$	24.3179	+	8.23599i	0.961248	+	0.325556i
$641$	11.0200	+	19.0872i	0.435265	+	0.753900i	0.997317	−	0.0732011i	$-0.0233215\pi$
$641$	11.0200	+	19.0872i	0.435265	+	0.753900i	−0.562053	+	0.827102i	$0.689988\pi$
$642$		0			0
$643$			39.0979i			1.54187i	0.636913	+	0.770935i	$0.280211\pi$
$643$			39.0979i			1.54187i	−0.636913	+	0.770935i	$0.719789\pi$
$644$	−20.5645	+	16.9842i	−0.810356	+	0.669273i
$645$		0			0
$646$	−0.948368	+	1.64262i	−0.0373130	+	0.0646281i
$647$	21.1866	−	12.2321i	0.832931	−	0.480893i	−0.0219243	−	0.999760i	$-0.506979\pi$
$647$	21.1866	−	12.2321i	0.832931	−	0.480893i	0.854855	+	0.518867i	$0.173646\pi$
$648$		0			0
$649$	22.4059	−	38.8081i	0.879508	−	1.52335i
$650$	−1.56809	+	12.0399i	−0.0615056	+	0.472244i
$651$		0			0
$652$		−	2.89061i		−	0.113205i
$653$	−24.8271	−	14.3339i	−0.971558	−	0.560929i	−0.0718473	−	0.997416i	$-0.522889\pi$
$653$	−24.8271	−	14.3339i	−0.971558	−	0.560929i	−0.899711	+	0.436486i	$0.856223\pi$
$654$		0			0
$655$	5.60036	−	16.5358i	0.218824	−	0.646108i
$656$	−11.2814	+	19.5399i	−0.440463	+	0.762905i
$657$		0			0
$658$	−1.19368	+	3.20172i	−0.0465344	+	0.124816i
$659$	17.7061			0.689732			0.344866	−	0.938652i	$-0.387924\pi$
$659$	17.7061			0.689732			0.344866	+	0.938652i	$0.387924\pi$
$660$		0			0
$661$	−9.32288	−	16.1477i	−0.362618	−	0.628073i	0.625773	−	0.780005i	$-0.284784\pi$
$661$	−9.32288	−	16.1477i	−0.362618	−	0.628073i	−0.988391	+	0.151933i	$0.951450\pi$
$662$	−9.06312	+	5.23260i	−0.352248	+	0.203371i
$663$		0			0
$664$	−25.2915			−0.981501
$665$	3.57031	−	1.35930i	0.138451	−	0.0527116i
$666$		0			0
$667$	12.8816	+	7.43719i	0.498777	+	0.287969i
$668$	−18.0083	+	10.3971i	−0.696763	+	0.402277i
$669$		0			0
$670$	−3.03248	+	0.605385i	−0.117155	+	0.0233881i
$671$	1.90562			0.0735657
$672$		0			0
$673$			12.2398i			0.471808i	0.971776	+	0.235904i	$0.0758051\pi$
$673$			12.2398i			0.471808i	−0.971776	+	0.235904i	$0.924195\pi$
$674$	−3.64248	+	6.30896i	−0.140303	+	0.243012i
$675$		0			0
$676$	3.00000	+	5.19615i	0.115385	+	0.199852i
$677$	−26.2232	−	15.1399i	−1.00784	−	0.581875i	−0.0972799	−	0.995257i	$-0.531014\pi$
$677$	−26.2232	−	15.1399i	−1.00784	−	0.581875i	−0.910558	+	0.413382i	$0.864348\pi$
$678$		0			0
$679$	−13.6974	+	11.3127i	−0.525657	+	0.434140i
$680$	−15.8005	−	17.9918i	−0.605921	−	0.689954i
$681$		0			0
$682$	−13.8638	+	8.00429i	−0.530874	+	0.306500i
$683$	−29.7990	+	17.2044i	−1.14023	+	0.658309i	−0.946486	−	0.322744i	$-0.895395\pi$
$683$	−29.7990	+	17.2044i	−1.14023	+	0.658309i	−0.193739	+	0.981053i	$0.562061\pi$
$684$		0			0
$685$	6.64575	−	5.83633i	0.253921	−	0.222995i
$686$	11.0200	+	0.257794i	0.420746	+	0.00984264i
$687$		0			0
$688$	−18.6965	−	10.7945i	−0.712799	−	0.411535i
$689$	−16.1380	−	27.9518i	−0.614809	−	1.06488i
$690$		0			0
$691$	−7.14575	+	12.3768i	−0.271837	+	0.470836i	−0.969332	−	0.245754i	$-0.920965\pi$
$691$	−7.14575	+	12.3768i	−0.271837	+	0.470836i	0.697495	+	0.716590i	$0.254298\pi$
$692$			15.3255i			0.582588i
$693$		0			0
$694$	11.5425			0.438147
$695$	15.8512	−	3.16444i	0.601271	−	0.120034i
$696$		0			0
$697$	48.2147	−	27.8368i	1.82626	−	1.05439i
$698$	−13.3370	−	7.70010i	−0.504811	−	0.291453i
$699$		0			0
$700$	0.810238	+	21.7562i	0.0306241	+	0.822306i
$701$	25.8513			0.976390			0.488195	−	0.872735i	$-0.337656\pi$
$701$	25.8513			0.976390			0.488195	+	0.872735i	$0.337656\pi$
$702$		0			0
$703$	0.491125	−	0.283551i	0.0185231	−	0.0106943i
$704$	−1.90562	−	3.30064i	−0.0718209	−	0.124397i
$705$		0			0
$706$	−0.937254			−0.0352740
$707$	3.21060	−	8.61155i	0.120747	−	0.323871i
$708$		0			0
$709$	−3.17712	+	5.50294i	−0.119319	+	0.206667i	−0.919498	−	0.393094i	$-0.871405\pi$
$709$	−3.17712	+	5.50294i	−0.119319	+	0.206667i	0.800179	+	0.599762i	$0.204738\pi$
$710$	−3.06101	−	1.03671i	−0.114878	−	0.0389069i
$711$		0			0
$712$	−10.1088	−	5.83633i	−0.378844	−	0.218726i
$713$		−	30.6269i		−	1.14699i
$714$		0			0
$715$	36.8745	−	32.3834i	1.37903	−	1.21107i
$716$	−13.7097	+	23.7459i	−0.512355	+	0.887425i
$717$		0			0
$718$	9.83940	−	5.68078i	0.367203	−	0.212005i
$719$	−9.80586	+	16.9842i	−0.365697	+	0.633406i	−0.988888	−	0.148664i	$-0.952503\pi$
$719$	−9.80586	+	16.9842i	−0.365697	+	0.633406i	0.623191	+	0.782070i	$0.285836\pi$
$720$		0			0
$721$	−3.19738	−	18.9982i	−0.119077	−	0.707531i
$722$			11.0604i			0.411625i
$723$		0			0
$724$	−10.4059	−	18.0235i	−0.386732	−	0.669839i
$725$	11.2109	−	4.66195i	0.416363	−	0.173140i
$726$		0			0
$727$		−	40.5432i		−	1.50366i	−0.659355	−	0.751832i	$-0.729170\pi$
$727$		−	40.5432i		−	1.50366i	0.659355	−	0.751832i	$-0.270830\pi$
$728$	−14.9156	−	18.0599i	−0.552811	−	0.669343i
$729$		0			0
$730$	−11.7958	+	2.35484i	−0.436582	+	0.0871566i
$731$	26.6353	+	46.1337i	0.985143	+	1.70632i
$732$		0			0
$733$	−9.07885	−	5.24168i	−0.335335	−	0.193606i	0.322872	−	0.946443i	$-0.395352\pi$
$733$	−9.07885	−	5.24168i	−0.335335	−	0.193606i	−0.658207	+	0.752837i	$0.728685\pi$
$734$	−11.0962			−0.409568
$735$		0			0
$736$	−33.8745			−1.24863
$737$	10.8244	+	6.24947i	0.398722	+	0.230202i
$738$		0			0
$739$	5.96863	+	10.3380i	0.219559	+	0.380288i	0.954673	−	0.297655i	$-0.0962047\pi$
$739$	5.96863	+	10.3380i	0.219559	+	0.380288i	−0.735114	+	0.677944i	$0.762871\pi$
$740$	0.632693	+	3.16927i	0.0232582	+	0.116505i
$741$		0			0
$742$	7.93289	+	9.60515i	0.291226	+	0.352616i
$743$		−	10.6760i		−	0.391666i	−0.980637	−	0.195833i	$-0.937259\pi$
$743$		−	10.6760i		−	0.391666i	0.980637	−	0.195833i	$-0.0627410\pi$
$744$		0			0
$745$	2.11674	−	6.24995i	0.0775513	−	0.228981i
$746$	−7.11619	−	12.3256i	−0.260542	−	0.451273i
$747$		0			0
$748$			43.6898i			1.59746i
$749$	−2.25955	−	13.4258i	−0.0825623	−	0.490569i
$750$		0			0
$751$	−13.7288	+	23.7789i	−0.500969	+	0.867705i	0.499030	+	0.866585i	$0.333690\pi$
$751$	−13.7288	+	23.7789i	−0.500969	+	0.867705i	−0.999999	+	0.00111978i	$0.999644\pi$
$752$	3.75839	−	2.16991i	0.137054	−	0.0791284i
$753$		0			0
$754$	−2.94837	+	5.10672i	−0.107373	+	0.185976i
$755$	13.1870	+	15.0159i	0.479924	+	0.546483i
$756$		0			0
$757$			40.7992i			1.48287i	0.671023	+	0.741436i	$0.265855\pi$
$757$			40.7992i			1.48287i	−0.671023	+	0.741436i	$0.734145\pi$
$758$	1.18115	+	0.681937i	0.0429013	+	0.0247691i
$759$		0			0
$760$	2.96764	+	1.00508i	0.107648	+	0.0364582i
$761$	2.25955	−	3.91366i	0.0819087	−	0.141870i	−0.822161	−	0.569255i	$-0.807232\pi$
$761$	2.25955	−	3.91366i	0.0819087	−	0.141870i	0.904070	+	0.427385i	$0.140565\pi$
$762$		0			0
$763$	−12.2268	+	32.7949i	−0.442638	+	1.18726i
$764$	17.7061			0.640584
$765$		0			0
$766$	−4.22876	−	7.32442i	−0.152791	−	0.264642i
$767$	−29.4338	+	16.9936i	−1.06279	+	0.613603i
$768$		0			0
$769$	24.6458			0.888749			0.444374	−	0.895841i	$-0.353426\pi$
$769$	24.6458			0.888749			0.444374	+	0.895841i	$0.353426\pi$
$770$	−11.9606	+	14.6877i	−0.431031	+	0.529307i
$771$		0			0
$772$	−17.8883	−	10.3278i	−0.643813	−	0.371706i
$773$	−16.5799	+	9.57241i	−0.596338	+	0.344296i	−0.767599	−	0.640930i	$-0.778549\pi$
$773$	−16.5799	+	9.57241i	−0.596338	+	0.344296i	0.171262	+	0.985226i	$0.445216\pi$
$774$		0			0
$775$	−19.8549	−	15.1915i	−0.713210	−	0.545695i
$776$	−14.5699			−0.523030
$777$		0			0
$778$			18.3872i			0.659213i
$779$	−3.64248	+	6.30896i	−0.130505	+	0.226042i
$780$		0			0
$781$	6.53137	+	11.3127i	0.233711	+	0.404799i
$782$	15.5813	+	8.99590i	0.557188	+	0.321693i
$783$		0			0
$784$	−10.5830	−	9.16515i	−0.377964	−	0.327327i
$785$	−19.6117	+	17.2231i	−0.699972	+	0.614719i
$786$		0			0
$787$	−12.6122	+	7.28164i	−0.449575	+	0.259562i	−0.707651	−	0.706562i	$-0.750245\pi$
$787$	−12.6122	+	7.28164i	−0.449575	+	0.259562i	0.258076	+	0.966125i	$0.416912\pi$
$788$	8.42976	−	4.86693i	0.300298	−	0.173377i
$789$		0			0
$790$	5.93725	−	5.21412i	0.211238	−	0.185510i
$791$	32.2760	−	26.6568i	1.14760	−	0.947805i
$792$		0			0
$793$	−1.25167	−	0.722653i	−0.0444482	−	0.0256622i
$794$	9.45193	+	16.3712i	0.335436	+	0.580993i
$795$		0			0
$796$	14.5203	−	25.1498i	0.514657	−	0.891412i
$797$		−	3.53378i		−	0.125173i	−0.998040	−	0.0625865i	$-0.980065\pi$
$797$		−	3.53378i		−	0.125173i	0.998040	−	0.0625865i	$-0.0199349\pi$
$798$		0			0
$799$	−10.7085			−0.378839
$800$	−16.8024	+	21.9603i	−0.594054	+	0.776414i
$801$		0			0
$802$	20.2176	−	11.6727i	0.713910	−	0.412176i
$803$	42.1050	+	24.3093i	1.48585	+	0.857858i
$804$		0			0
$805$	−12.8939	−	33.8667i	−0.454450	−	1.19365i
$806$	12.1416			0.427670
$807$		0			0
$808$	6.52778	−	3.76882i	0.229647	−	0.132587i
$809$	−22.4702	−	38.9194i	−0.790009	−	1.36833i	−0.925961	−	0.377620i	$-0.876743\pi$
$809$	−22.4702	−	38.9194i	−0.790009	−	1.36833i	0.135952	−	0.990715i	$-0.456591\pi$
$810$		0			0
$811$	40.2288			1.41262			0.706311	−	0.707901i	$-0.250358\pi$
$811$	40.2288			1.41262			0.706311	+	0.707901i	$0.250358\pi$
$812$	−3.69370	+	9.90735i	−0.129624	+	0.347680i
$813$		0			0
$814$	−1.40588	+	2.43506i	−0.0492761	+	0.0853487i
$815$	3.71990	+	1.25986i	0.130302	+	0.0441309i
$816$		0			0
$817$	−6.03666	−	3.48527i	−0.211196	−	0.121934i
$818$			15.2267i			0.532389i
$819$		0			0
$820$	−27.3948	−	31.1941i	−0.956667	−	1.08934i
$821$	−8.59170	+	14.8813i	−0.299852	+	0.519360i	−0.976102	−	0.217313i	$-0.930271\pi$
$821$	−8.59170	+	14.8813i	−0.299852	+	0.519360i	0.676250	+	0.736673i	$0.263604\pi$
$822$		0			0
$823$	−41.6870	+	24.0680i	−1.45312	+	0.838957i	−0.998657	−	0.0518109i	$-0.983501\pi$
$823$	−41.6870	+	24.0680i	−1.45312	+	0.838957i	−0.454459	+	0.890768i	$0.650167\pi$
$824$	7.90024	−	13.6836i	0.275218	−	0.476691i
$825$		0			0
$826$	10.1144	−	8.35347i	0.351924	−	0.290654i
$827$		−	31.0112i		−	1.07837i	−0.842189	−	0.539183i	$-0.818733\pi$
$827$		−	31.0112i		−	1.07837i	0.842189	−	0.539183i	$-0.181267\pi$
$828$		0			0
$829$	15.5516	+	26.9362i	0.540131	+	0.935533i	0.998896	+	0.0469761i	$0.0149585\pi$
$829$	15.5516	+	26.9362i	0.540131	+	0.935533i	−0.458766	+	0.888557i	$0.651708\pi$
$830$	4.97603	−	14.6924i	0.172721	−	0.509981i
$831$		0			0
$832$			2.89061i			0.100214i
$833$	11.3075	+	32.6420i	0.391782	+	1.13098i
$834$		0			0
$835$	−5.53110	−	27.7062i	−0.191412	−	0.958814i
$836$	−2.85843	−	4.95095i	−0.0988610	−	0.171232i
$837$		0			0
$838$	−9.12657	−	5.26923i	−0.315272	−	0.182022i
$839$	42.6972			1.47407			0.737035	−	0.675855i	$-0.236225\pi$
$839$	42.6972			1.47407			0.737035	+	0.675855i	$0.236225\pi$
$840$		0			0
$841$	−23.1033			−0.796664
$842$	−4.75694	−	2.74642i	−0.163935	−	0.0946480i
$843$		0			0
$844$	12.2915	+	21.2895i	0.423091	+	0.732815i
$845$	−7.99440	+	1.59595i	−0.275016	+	0.0549024i
$846$		0			0
$847$	46.7994	−	7.87629i	1.60804	−	0.270633i
$848$		−	15.8219i		−	0.543326i
$849$		0			0
$850$	13.5605	−	5.63902i	0.465122	−	0.193417i
$851$	−2.68967	−	4.65864i	−0.0922006	−	0.159696i
$852$		0			0
$853$		−	2.63461i		−	0.0902075i	−0.998982	−	0.0451037i	$-0.985638\pi$
$853$		−	2.63461i		−	0.0902075i	0.998982	−	0.0451037i	$-0.0143618\pi$
$854$	0.522697	+	0.194874i	0.0178863	+	0.00666846i
$855$		0			0
$856$	5.58301	−	9.67005i	0.190823	−	0.330515i
$857$	41.4393	−	23.9250i	1.41554	−	0.817262i	0.419637	−	0.907692i	$-0.362157\pi$
$857$	41.4393	−	23.9250i	1.41554	−	0.817262i	0.995903	+	0.0904296i	$0.0288240\pi$
$858$		0			0
$859$	8.53137	−	14.7768i	0.291087	−	0.504177i	−0.682980	−	0.730437i	$-0.739317\pi$
$859$	8.53137	−	14.7768i	0.291087	−	0.504177i	0.974067	+	0.226260i	$0.0726499\pi$
$860$	29.8477	−	26.2124i	1.01780	−	0.893835i
$861$		0			0
$862$		−	12.2949i		−	0.418765i
$863$	38.1317	+	22.0153i	1.29802	+	0.749411i	0.980061	−	0.198695i	$-0.0636702\pi$
$863$	38.1317	+	22.0153i	1.29802	+	0.749411i	0.317956	+	0.948105i	$0.397003\pi$
$864$		0			0
$865$	−19.7222	−	6.67953i	−0.670575	−	0.227111i
$866$	10.0672	−	17.4369i	0.342098	−	0.592531i
$867$		0			0
$868$	21.4693	−	3.61327i	0.728716	−	0.122642i
$869$	−31.9385			−1.08344
$870$		0			0
$871$	−4.73987	−	8.20970i	−0.160604	−	0.278175i
$872$	−24.8594	+	14.3526i	−0.841846	+	0.486040i
$873$		0			0
$874$	−2.35425			−0.0796336
$875$	−28.3509	−	8.43961i	−0.958435	−	0.285311i
$876$		0			0
$877$	27.2843	+	15.7526i	0.921324	+	0.531927i	0.884057	−	0.467379i	$-0.154801\pi$
$877$	27.2843	+	15.7526i	0.921324	+	0.531927i	0.0372670	+	0.999305i	$0.488135\pi$
$878$	15.5813	−	8.99590i	0.525845	−	0.303597i
$879$		0			0
$880$	23.5916	−	4.70968i	0.795273	−	0.158763i
$881$	−45.9857			−1.54930			−0.774649	−	0.632392i	$-0.782073\pi$
$881$	−45.9857			−1.54930			−0.774649	+	0.632392i	$0.782073\pi$
$882$		0			0
$883$			21.8449i			0.735140i	0.929996	+	0.367570i	$0.119810\pi$
$883$			21.8449i			0.735140i	−0.929996	+	0.367570i	$0.880190\pi$
$884$	16.5681	−	28.6968i	0.557246	−	0.965179i
$885$		0			0
$886$	−5.00000	−	8.66025i	−0.167978	−	0.290947i
$887$	−0.0323423	−	0.0186729i	−0.00108595	−	0.000626973i	0.499457	−	0.866339i	$-0.333533\pi$
$887$	−0.0323423	−	0.0186729i	−0.00108595	−	0.000626973i	−0.500543	+	0.865712i	$0.666866\pi$
$888$		0			0
$889$	8.32288	−	6.87386i	0.279140	−	0.230542i
$890$	5.37934	−	4.72416i	0.180316	−	0.158354i
$891$		0			0
$892$		0			0
$893$	1.21349	−	0.700610i	0.0406080	−	0.0234450i
$894$		0			0
$895$	−24.5830	−	27.9923i	−0.821719	−	0.935681i
$896$	−5.04180	−	29.9574i	−0.168435	−	1.00081i
$897$		0			0
$898$	−11.6299	−	6.71453i	−0.388095	−	0.224067i
$899$	−6.07080	−	10.5149i	−0.202472	−	0.350693i
$900$		0			0
$901$	−19.5203	+	33.8101i	−0.650314	+	1.12638i
$902$		−	36.1197i		−	1.20266i
$903$		0			0
$904$	34.3320			1.14187
$905$	27.7296	−	5.53576i	0.921763	−	0.184015i
$906$		0			0
$907$	−0.760548	+	0.439102i	−0.0252536	+	0.0145802i	−0.512574	−	0.858643i	$-0.671308\pi$
$907$	−0.760548	+	0.439102i	−0.0252536	+	0.0145802i	0.487320	+	0.873223i	$0.337975\pi$
$908$	5.03657	+	2.90786i	0.167144	+	0.0965008i
$909$		0			0
$910$	13.4260	−	5.11160i	0.445067	−	0.169448i
$911$	1.56809			0.0519532			0.0259766	−	0.999663i	$-0.491730\pi$
$911$	1.56809			0.0519532			0.0259766	+	0.999663i	$0.491730\pi$
$912$		0			0
$913$	−54.2991	+	31.3496i	−1.79704	+	1.03752i
$914$	−9.54451	−	16.5316i	−0.315704	−	0.546816i
$915$		0			0
$916$	3.77124			0.124605
$917$	−20.3706	+	3.42836i	−0.672698	+	0.113214i
$918$		0			0
$919$	−4.43725	+	7.68555i	−0.146372	+	0.253523i	−0.929884	−	0.367853i	$-0.880093\pi$
$919$	−4.43725	+	7.68555i	−0.146372	+	0.253523i	0.783512	+	0.621376i	$0.213426\pi$
$920$	9.53388	−	28.1501i	0.314323	−	0.928080i
$921$		0			0
$922$	8.31830	+	4.80257i	0.273949	+	0.158164i
$923$		−	9.90735i		−	0.326104i
$924$		0			0
$925$	−4.35425	−	0.567102i	−0.143167	−	0.0186462i
$926$	−5.21057	+	9.02497i	−0.171230	+	0.296579i
$927$		0			0
$928$	−11.6299	+	6.71453i	−0.381771	+	0.220415i
$929$	6.68608	−	11.5806i	0.219363	−	0.379948i	−0.735250	−	0.677796i	$-0.762935\pi$
$929$	6.68608	−	11.5806i	0.219363	−	0.379948i	0.954613	+	0.297848i	$0.0962687\pi$
$930$		0			0
$931$	−3.41699	−	2.95920i	−0.111987	−	0.0969840i
$932$			12.6724i			0.415100i
$933$		0			0
$934$	12.2288	+	21.1808i	0.400137	+	0.693058i
$935$	−56.2239	−	19.0420i	−1.83872	−	0.622739i
$936$		0			0
$937$		−	0.255999i		−	0.00836312i	−0.999991	−	0.00418156i	$-0.998669\pi$
$937$		−	0.255999i		−	0.00836312i	0.999991	−	0.00418156i	$-0.00133104\pi$
$938$	2.32996	+	2.82111i	0.0760758	+	0.0921126i
$939$		0			0
$940$	1.56329	+	7.83077i	0.0509887	+	0.255411i
$941$	−15.9692	−	27.6595i	−0.520582	−	0.901675i	−0.999714	−	0.0239319i	$-0.992382\pi$
$941$	−15.9692	−	27.6595i	−0.520582	−	0.901675i	0.479131	−	0.877743i	$-0.340952\pi$
$942$		0			0
$943$	59.8447	+	34.5513i	1.94881	+	1.12515i
$944$	−16.6607			−0.542260
$945$		0			0
$946$	34.5608			1.12367
$947$	25.3102	+	14.6128i	0.822470	+	0.474853i	0.851268	−	0.524732i	$-0.175834\pi$
$947$	25.3102	+	14.6128i	0.822470	+	0.474853i	−0.0287974	+	0.999585i	$0.509168\pi$
$948$		0			0
$949$	−18.4373	−	31.9343i	−0.598499	−	1.03663i
$950$	−1.16775	+	1.52622i	−0.0378868	+	0.0495172i
$951$		0			0
$952$	−9.89739	+	26.5470i	−0.320776	+	0.860394i
$953$		−	57.6827i		−	1.86852i	−0.356587	−	0.934262i	$-0.616060\pi$
$953$		−	57.6827i		−	1.86852i	0.356587	−	0.934262i	$-0.383940\pi$
$954$		0			0
$955$	−7.71710	+	22.7858i	−0.249720	+	0.737330i
$956$	7.28496	+	12.6179i	0.235612	+	0.408093i
$957$		0			0
$958$		−	7.53764i		−	0.243530i
$959$	−9.80586	−	3.65587i	−0.316648	−	0.118054i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	1.84685	−	1.06628i	0.0595449	−	0.0343783i
$963$		0			0
$964$	−23.2288	+	40.2334i	−0.748148	+	1.29583i
$965$	21.0872	−	18.5189i	0.678822	−	0.596145i
$966$		0			0
$967$		−	24.2235i		−	0.778976i	−0.921032	−	0.389488i	$-0.872652\pi$
$967$		−	24.2235i		−	0.778976i	0.921032	−	0.389488i	$-0.127348\pi$
$968$	33.7076	+	19.4611i	1.08340	+	0.625503i
$969$		0			0
$970$	2.86659	−	8.46399i	0.0920406	−	0.271762i
$971$	11.1888	−	19.3795i	0.359065	−	0.621919i	−0.628740	−	0.777616i	$-0.716429\pi$
$971$	11.1888	−	19.3795i	0.359065	−	0.621919i	0.987805	+	0.155697i	$0.0497622\pi$
$972$		0			0
$973$	−12.1790	−	14.7464i	−0.390442	−	0.472747i
$974$	−14.2324			−0.456035
$975$		0			0
$976$	−0.354249	−	0.613577i	−0.0113392	−	0.0196401i
$977$	50.1696	−	28.9654i	1.60507	−	0.926686i	0.614615	−	0.788827i	$-0.289311\pi$
$977$	50.1696	−	28.9654i	1.60507	−	0.926686i	0.990452	−	0.137859i	$-0.0440221\pi$
$978$		0			0
$979$	−28.9373			−0.924839
$980$	22.2193	−	13.0341i	0.709768	−	0.416358i
$981$		0			0
$982$	−18.6965	−	10.7945i	−0.596631	−	0.344465i
$983$	−5.85252	+	3.37896i	−0.186667	+	0.107772i	−0.590421	−	0.807095i	$-0.701038\pi$
$983$	−5.85252	+	3.37896i	−0.186667	+	0.107772i	0.403755	+	0.914867i	$0.367705\pi$
$984$		0			0
$985$	2.58913	+	12.9694i	0.0824965	+	0.413239i
$986$	7.13259			0.227148
$987$		0			0
$988$			4.33592i			0.137944i
$989$	−33.0601	+	57.2617i	−1.05125	+	1.82082i
$990$		0			0
$991$	8.19738	+	14.1983i	0.260398	+	0.451023i	0.966348	−	0.257239i	$-0.0828127\pi$
$991$	8.19738	+	14.1983i	0.260398	+	0.451023i	−0.705949	+	0.708262i	$0.749479\pi$
$992$	23.9464	+	13.8255i	0.760300	+	0.438959i
$993$		0			0
$994$	0.634637	+	3.77089i	0.0201295	+	0.119605i
$995$	26.0365	+	29.6474i	0.825411	+	0.939885i
$996$		0			0
$997$	27.5060	−	15.8806i	0.871123	−	0.502943i	0.00340163	−	0.999994i	$-0.498917\pi$
$997$	27.5060	−	15.8806i	0.871123	−	0.502943i	0.867721	+	0.497051i	$0.165584\pi$
$998$	−2.57724	+	1.48797i	−0.0815811	+	0.0471009i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bf.c.289.6	yes	16
3.2	odd	2	inner	315.2.bf.c.289.3	yes	16
5.4	even	2	inner	315.2.bf.c.289.4	yes	16
7.2	even	3		2205.2.d.p.1324.3		8
7.4	even	3	inner	315.2.bf.c.109.4	yes	16
7.5	odd	6		2205.2.d.r.1324.4		8
15.14	odd	2	inner	315.2.bf.c.289.5	yes	16
21.2	odd	6		2205.2.d.p.1324.6		8
21.5	even	6		2205.2.d.r.1324.5		8
21.11	odd	6	inner	315.2.bf.c.109.5	yes	16
35.4	even	6	inner	315.2.bf.c.109.6	yes	16
35.9	even	6		2205.2.d.p.1324.5		8
35.19	odd	6		2205.2.d.r.1324.6		8
105.44	odd	6		2205.2.d.p.1324.4		8
105.74	odd	6	inner	315.2.bf.c.109.3	✓	16
105.89	even	6		2205.2.d.r.1324.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bf.c.109.3	✓	16	105.74	odd	6	inner
315.2.bf.c.109.4	yes	16	7.4	even	3	inner
315.2.bf.c.109.5	yes	16	21.11	odd	6	inner
315.2.bf.c.109.6	yes	16	35.4	even	6	inner
315.2.bf.c.289.3	yes	16	3.2	odd	2	inner
315.2.bf.c.289.4	yes	16	5.4	even	2	inner
315.2.bf.c.289.5	yes	16	15.14	odd	2	inner
315.2.bf.c.289.6	yes	16	1.1	even	1	trivial
2205.2.d.p.1324.3		8	7.2	even	3
2205.2.d.p.1324.4		8	105.44	odd	6
2205.2.d.p.1324.5		8	35.9	even	6
2205.2.d.p.1324.6		8	21.2	odd	6
2205.2.d.r.1324.3		8	105.89	even	6
2205.2.d.r.1324.4		8	7.5	odd	6
2205.2.d.r.1324.5		8	21.5	even	6
2205.2.d.r.1324.6		8	35.19	odd	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.515448 + 0.297594i) q^{2} +(-0.822876 - 1.42526i) q^{4} +(2.19280 - 0.437757i) q^{5} +(-1.68480 - 2.03996i) q^{7} -2.16991i q^{8} +O(q^{10})\)	\(q+(0.515448 + 0.297594i) q^{2} +(-0.822876 - 1.42526i) q^{4} +(2.19280 - 0.437757i) q^{5} +(-1.68480 - 2.03996i) q^{7} -2.16991i q^{8} +(1.26055 + 0.426923i) q^{10} +(-2.68967 - 4.65864i) q^{11} +4.07992i q^{13} +(-0.261348 - 1.55288i) q^{14} +(-1.00000 + 1.73205i) q^{16} +(4.27384 - 2.46750i) q^{17} +(-0.322876 + 0.559237i) q^{19} +(-2.42832 - 2.76510i) q^{20} -3.20172i q^{22} +(5.30473 + 3.06269i) q^{23} +(4.61674 - 1.91983i) q^{25} +(-1.21416 + 2.10299i) q^{26} +(-1.52110 + 4.07992i) q^{28} +2.42832 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-4.78929 + 2.76510i) q^{32} +2.93725 q^{34} +(-4.58744 - 3.73569i) q^{35} +(-0.760548 - 0.439102i) q^{37} +(-0.332851 + 0.192172i) q^{38} +(-0.949892 - 4.75817i) q^{40} +11.2814 q^{41} +10.7945i q^{43} +(-4.42652 + 7.66697i) q^{44} +(1.82288 + 3.15731i) q^{46} +(-1.87919 - 1.08495i) q^{47} +(-1.32288 + 6.87386i) q^{49} +(2.95102 + 0.384343i) q^{50} +(5.81496 - 3.35727i) q^{52} +(-6.85108 + 3.95547i) q^{53} +(-7.93725 - 9.03805i) q^{55} +(-4.42652 + 3.65587i) q^{56} +(1.25167 + 0.722653i) q^{58} +(4.16518 + 7.21430i) q^{59} +(-0.177124 + 0.306788i) q^{61} -2.97594i q^{62} +0.708497 q^{64} +(1.78601 + 8.94645i) q^{65} +(-2.01222 + 1.16176i) q^{67} +(-7.03367 - 4.06089i) q^{68} +(-1.25287 - 3.29075i) q^{70} -2.42832 q^{71} +(-7.82718 + 4.51902i) q^{73} +(-0.261348 - 0.452669i) q^{74} +1.06275 q^{76} +(-4.97188 + 13.3357i) q^{77} +(2.96863 - 5.14181i) q^{79} +(-1.43458 + 4.23580i) q^{80} +(5.81496 + 3.35727i) q^{82} -11.6556i q^{83} +(8.29150 - 7.28164i) q^{85} +(-3.21236 + 5.56398i) q^{86} +(-10.1088 + 5.83633i) q^{88} +(2.68967 - 4.65864i) q^{89} +(8.32288 - 6.87386i) q^{91} -10.0808i q^{92} +(-0.645751 - 1.11847i) q^{94} +(-0.463192 + 1.36764i) q^{95} -6.71453i q^{97} +(-2.72749 + 3.14944i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 8 q^{10} - 16 q^{16} + 16 q^{19} - 16 q^{25} - 40 q^{31} - 80 q^{34} + 8 q^{40} + 8 q^{46} - 24 q^{61} + 96 q^{64} - 56 q^{70} + 144 q^{76} - 16 q^{79} + 48 q^{85} + 112 q^{91} + 32 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^10 - 16 * q^16 + 16 * q^19 - 16 * q^25 - 40 * q^31 - 80 * q^34 + 8 * q^40 + 8 * q^46 - 24 * q^61 + 96 * q^64 - 56 * q^70 + 144 * q^76 - 16 * q^79 + 48 * q^85 + 112 * q^91 + 32 * q^94

Introduction

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