LMFDB - Embedded newform 315.2.bf.c.289.4

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			289.4
Root			$2.19280 - 0.437757i$ of defining polynomial
Character	$\chi$	$=$	315.289
Dual form			315.2.bf.c.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.515448 - 0.297594i) q^{2} +(-0.822876 - 1.42526i) q^{4} +(-0.717291 - 2.11790i) q^{5} +(1.68480 + 2.03996i) q^{7} +2.16991i q^{8} +O(q^{10})$	\(q+(-0.515448 - 0.297594i) q^{2} +(-0.822876 - 1.42526i) q^{4} +(-0.717291 - 2.11790i) q^{5} +(1.68480 + 2.03996i) q^{7} +2.16991i q^{8} +(-0.260548 + 1.30513i) q^{10} +(-2.68967 - 4.65864i) q^{11} -4.07992i q^{13} +(-0.261348 - 1.55288i) q^{14} +(-1.00000 + 1.73205i) q^{16} +(-4.27384 + 2.46750i) q^{17} +(-0.322876 + 0.559237i) q^{19} +(-2.42832 + 2.76510i) q^{20} +3.20172i q^{22} +(-5.30473 - 3.06269i) q^{23} +(-3.97099 + 3.03830i) q^{25} +(-1.21416 + 2.10299i) q^{26} +(1.52110 - 4.07992i) q^{28} +2.42832 q^{29} +(-2.50000 - 4.33013i) q^{31} +(4.78929 - 2.76510i) q^{32} +2.93725 q^{34} +(3.11193 - 5.03149i) q^{35} +(0.760548 + 0.439102i) q^{37} +(0.332851 - 0.192172i) q^{38} +(4.59564 - 1.55646i) q^{40} +11.2814 q^{41} -10.7945i q^{43} +(-4.42652 + 7.66697i) q^{44} +(1.82288 + 3.15731i) q^{46} +(1.87919 + 1.08495i) q^{47} +(-1.32288 + 6.87386i) q^{49} +(2.95102 - 0.384343i) q^{50} +(-5.81496 + 3.35727i) q^{52} +(6.85108 - 3.95547i) q^{53} +(-7.93725 + 9.03805i) q^{55} +(-4.42652 + 3.65587i) q^{56} +(-1.25167 - 0.722653i) q^{58} +(4.16518 + 7.21430i) q^{59} +(-0.177124 + 0.306788i) q^{61} +2.97594i q^{62} +0.708497 q^{64} +(-8.64086 + 2.92649i) q^{65} +(2.01222 - 1.16176i) q^{67} +(7.03367 + 4.06089i) q^{68} +(-3.10138 + 1.66738i) q^{70} -2.42832 q^{71} +(7.82718 - 4.51902i) q^{73} +(-0.261348 - 0.452669i) q^{74} +1.06275 q^{76} +(4.97188 - 13.3357i) q^{77} +(2.96863 - 5.14181i) q^{79} +(4.38560 + 0.875514i) q^{80} +(-5.81496 - 3.35727i) q^{82} +11.6556i q^{83} +(8.29150 + 7.28164i) q^{85} +(-3.21236 + 5.56398i) q^{86} +(10.1088 - 5.83633i) q^{88} +(2.68967 - 4.65864i) q^{89} +(8.32288 - 6.87386i) q^{91} +10.0808i q^{92} +(-0.645751 - 1.11847i) q^{94} +(1.41600 + 0.282682i) q^{95} +6.71453i q^{97} +(2.72749 - 3.14944i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.306566	−	0.951849i	$-0.400820\pi$
$2$	−0.515448	−	0.297594i	−0.364477	−	0.210431i	−0.671043	+	0.741419i	$0.734153\pi$
$3$		0			0
$3$		0			0
$4$	−0.822876	−	1.42526i	−0.411438	−	0.712631i
$5$	−0.717291	−	2.11790i	−0.320782	−	0.947153i
$5$	−0.717291	−	2.11790i	−0.320782	−	0.947153i
$6$		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
$10$	−0.260548	+	1.30513i	−0.0823924	+	0.412718i
$11$	−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	$-0.808574\pi$
$13$		−	4.07992i		−	1.13157i	0.824554	−	0.565783i	$-0.191426\pi$
$14$	−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	−0.918856	−	0.394592i	$-0.870886\pi$
$17$	−4.27384	+	2.46750i	−1.03656	+	0.598457i	−0.117701	+	0.993049i	$0.537553\pi$
$18$		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	−0.168293	−	0.985737i	$-0.553826\pi$
$23$	−5.30473	−	3.06269i	−1.10611	−	0.638615i	−0.937820	+	0.347122i	$0.887159\pi$
$24$		0			0
$25$	−3.97099	+	3.03830i	−0.794197	+	0.607660i
$26$	−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
$35$	3.11193	−	5.03149i	0.526013	−	0.850477i
$36$		0			0
$37$	0.760548	+	0.439102i	0.125033	+	0.0721880i	0.561212	−	0.827672i	$-0.310335\pi$
$37$	0.760548	+	0.439102i	0.125033	+	0.0721880i	−0.436179	+	0.899860i	$0.643669\pi$
$38$	0.332851	−	0.192172i	0.0539956	−	0.0311744i
$39$		0			0
$40$	4.59564	−	1.55646i	0.726635	−	0.246097i
$41$	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	$-0.692260\pi$
$43$		−	10.7945i		−	1.64614i	0.567941	−	0.823069i	$-0.307740\pi$
$44$	−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	0.630753	−	0.775983i	$-0.282746\pi$
$47$	1.87919	+	1.08495i	0.274109	+	0.158257i	−0.356645	+	0.934240i	$0.616079\pi$
$48$		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	0.0507729	−	0.998710i	$-0.483832\pi$
$53$	6.85108	−	3.95547i	0.941068	−	0.543326i	0.890295	+	0.455384i	$0.150498\pi$
$54$		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
$65$	−8.64086	+	2.92649i	−1.07177	+	0.362987i
$66$		0			0
$67$	2.01222	−	1.16176i	0.245832	−	0.141931i	−0.372022	−	0.928224i	$-0.621336\pi$
$67$	2.01222	−	1.16176i	0.245832	−	0.141931i	0.617854	+	0.786293i	$0.288002\pi$
$68$	7.03367	+	4.06089i	0.852958	+	0.492456i
$69$		0			0
$70$	−3.10138	+	1.66738i	−0.370686	+	0.199290i
$71$	−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	0.0337124	−	0.999432i	$-0.489267\pi$
$73$	7.82718	−	4.51902i	0.916102	−	0.528912i	0.882389	+	0.470520i	$0.155934\pi$
$74$	−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	$0.0582693\pi$
$80$	4.38560	+	0.875514i	0.490325	+	0.0978854i
$81$		0			0
$82$	−5.81496	−	3.35727i	−0.642155	−	0.370748i
$83$			11.6556i			1.27936i	0.768639	+	0.639682i	$0.220934\pi$
$83$			11.6556i			1.27936i	−0.768639	+	0.639682i	$0.779066\pi$
$84$		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
$95$	1.41600	+	0.282682i	0.145279	+	0.0290026i
$96$		0			0
$97$			6.71453i			0.681758i	0.940107	+	0.340879i	$0.110725\pi$
$97$			6.71453i			0.681758i	−0.940107	+	0.340879i	$0.889275\pi$
$98$	2.72749	−	3.14944i	0.275518	−	0.318141i
$99$		0			0
$100$	7.59800	+	3.15956i	0.759800	+	0.315956i
$101$	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	0.156040	−	0.987751i	$-0.450127\pi$
$103$	−6.30608	−	3.64082i	−0.621357	−	0.358740i	−0.777397	+	0.629010i	$0.783460\pi$
$104$	8.85305			0.868113
$105$		0			0
$106$	−4.70850			−0.457330
$107$	−4.45643	−	2.57292i	−0.430820	−	0.248734i	0.268876	−	0.963175i	$-0.413348\pi$
$107$	−4.45643	−	2.57292i	−0.430820	−	0.248734i	−0.699696	+	0.714441i	$0.746681\pi$
$108$		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	$-0.385067\pi$
$110$	6.78091	−	2.29656i	0.646534	−	0.218969i
$111$		0			0
$112$	−5.21812	+	0.878205i	−0.493066	+	0.0829825i
$113$		−	15.8219i		−	1.48840i	−0.667958	−	0.744199i	$-0.732831\pi$
$113$		−	15.8219i		−	1.48840i	0.667958	−	0.744199i	$-0.267169\pi$
$114$		0			0
$115$	−2.68143	+	13.4317i	−0.250044	+	1.25251i
$116$	−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	$-0.942061\pi$
$127$		−	4.07992i		−	0.362034i	0.983480	−	0.181017i	$-0.0579390\pi$
$128$	−9.94376	−	5.74103i	−0.878913	−	0.507441i
$129$		0			0
$130$	5.32482	+	1.06301i	0.467017	+	0.0932324i
$131$	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	−0.639142	−	0.769088i	$-0.720711\pi$
$137$	−3.42554	+	1.97774i	−0.292663	+	0.168969i	0.346479	+	0.938058i	$0.387377\pi$
$138$		0			0
$139$	7.22876			0.613135			0.306568	−	0.951849i	$-0.400819\pi$
$139$	7.22876			0.613135			0.306568	+	0.951849i	$0.400819\pi$
$140$	−9.73192	−	0.295034i	−0.822498	−	0.0249349i
$141$		0			0
$142$	1.25167	+	0.722653i	0.105038	+	0.0606437i
$143$	−19.0069	+	10.9736i	−1.58944	+	0.917661i
$144$		0			0
$145$	−1.74181	−	5.14293i	−0.144650	−	0.427097i
$146$	−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	−0.0390619	−	0.999237i	$-0.512437\pi$
$157$	10.1088	−	5.83633i	0.806772	−	0.465790i	0.845834	+	0.533447i	$0.179104\pi$
$158$	−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	0.439245	−	0.898367i	$-0.355246\pi$
$163$	−1.52110	−	0.878205i	−0.119141	−	0.0687863i	−0.558386	+	0.829581i	$0.688579\pi$
$164$	−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	$0.162590\pi$
$167$			12.6351i			0.977733i	−0.872359	+	0.488867i	$0.837410\pi$
$168$		0			0
$169$	−3.64575			−0.280442
$170$	−2.10687	−	6.22081i	−0.161589	−	0.477114i
$171$		0			0
$172$	−15.3849	+	8.88249i	−1.17309	+	0.677284i
$173$	8.06457	+	4.65608i	0.613138	+	0.353995i	0.774193	−	0.632950i	$-0.218156\pi$
$173$	8.06457	+	4.65608i	0.613138	+	0.353995i	−0.161055	+	0.986945i	$0.551490\pi$
$174$		0			0
$175$	−12.8883	−	2.98172i	−0.974267	−	0.225397i
$176$	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
$185$	0.384440	−	1.92573i	0.0282646	−	0.141582i
$186$		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	−0.837278	−	0.546777i	$-0.815854\pi$
$193$	−10.8694	+	6.27543i	−0.782394	+	0.451715i	0.0548839	+	0.998493i	$0.482521\pi$
$194$	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	$-0.932427\pi$
$197$		−	5.91453i		−	0.421393i	0.977552	−	0.210697i	$-0.0675732\pi$
$198$		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	$0.618254\pi$
$200$	−6.59283	−	8.61667i	−0.466183	−	0.609291i
$201$		0			0
$202$		−	2.06751i		−	0.145470i
$203$	4.09124	+	4.95368i	0.287149	+	0.347680i
$204$		0			0
$205$	−8.09203	−	23.8928i	−0.565172	−	1.66874i
$206$	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
$215$	−22.8616	+	7.74277i	−1.55915	+	0.528052i
$216$		0			0
$217$	4.62128	−	12.3953i	0.313713	−	0.841449i
$218$			7.87360i			0.533267i
$219$		0			0
$220$	19.4130	+	3.87548i	1.30882	+	0.261285i
$221$	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	−0.394989	−	0.918686i	$-0.629252\pi$
$227$	3.06034	−	1.76689i	0.203122	−	0.117273i	0.598111	+	0.801413i	$0.295918\pi$
$228$		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	0.702268	−	0.711913i	$-0.252171\pi$
$233$	6.66848	+	3.85005i	0.436867	+	0.252225i	−0.265401	+	0.964138i	$0.585504\pi$
$234$		0			0
$235$	0.949892	−	4.75817i	0.0619641	−	0.310389i
$236$	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
$245$	15.5070	−	2.12885i	0.990708	−	0.136007i
$246$		0			0
$247$	2.28164	+	1.31731i	0.145177	+	0.0838182i
$248$	9.39597	−	5.42477i	0.596645	−	0.344473i
$249$		0			0
$250$	−2.93074	−	5.97427i	−0.185356	−	0.377846i
$251$	−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	0.456862	−	0.889537i	$-0.348973\pi$
$257$	−1.36375	−	0.787360i	−0.0850682	−	0.0491141i	−0.541931	+	0.840423i	$0.682306\pi$
$258$		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	−0.0628207	−	0.998025i	$-0.520010\pi$
$263$	12.4887	−	7.21033i	0.770084	−	0.444608i	0.832905	+	0.553417i	$0.186676\pi$
$264$		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
$275$	24.8350	+	10.3274i	1.49761	+	0.622765i
$276$		0			0
$277$	14.8938	−	8.59894i	0.894882	−	0.516660i	0.0193459	−	0.999813i	$-0.493842\pi$
$277$	14.8938	−	8.59894i	0.894882	−	0.516660i	0.875536	+	0.483152i	$0.160508\pi$
$278$	−3.72605	−	2.15123i	−0.223473	−	0.129022i
$279$		0			0
$280$	10.9179	+	6.75261i	0.652467	+	0.403545i
$281$	−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	−0.963843	−	0.266472i	$-0.914142\pi$
$283$	−20.4393	+	11.8007i	−1.21499	+	0.701476i	−0.251150	+	0.967948i	$0.580809\pi$
$284$	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
$290$	−0.632693	+	3.16927i	−0.0371530	+	0.186106i
$291$		0			0
$292$	−12.8816	−	7.43719i	−0.753838	−	0.435228i
$293$		−	15.1894i		−	0.887371i	−0.896182	−	0.443686i	$-0.853671\pi$
$293$		−	15.1894i		−	0.887371i	0.896182	−	0.443686i	$-0.146329\pi$
$294$		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
$305$	0.776796	+	0.155075i	0.0444792	+	0.00887956i
$306$		0			0
$307$		−	20.3996i		−	1.16427i	−0.813093	−	0.582133i	$-0.802218\pi$
$307$		−	20.3996i		−	1.16427i	0.813093	−	0.582133i	$-0.197782\pi$
$308$	−23.0981	+	3.88739i	−1.31614	+	0.221505i
$309$		0			0
$310$	6.30274	−	2.13462i	0.357971	−	0.121238i
$311$	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	0.704623	−	0.709582i	$-0.251116\pi$
$313$	7.82718	+	4.51902i	0.442418	+	0.255430i	−0.262205	+	0.965012i	$0.584450\pi$
$314$	−6.94743			−0.392066
$315$		0			0
$316$	−9.77124			−0.549675
$317$	15.2485	+	8.80372i	0.856441	+	0.494466i	0.862819	−	0.505513i	$-0.168697\pi$
$317$	15.2485	+	8.80372i	0.856441	+	0.494466i	−0.00637790	+	0.999980i	$0.502030\pi$
$318$		0			0
$319$	−6.53137	−	11.3127i	−0.365687	−	0.633388i
$320$	−0.508199	−	1.50053i	−0.0284092	−	0.0838819i
$321$		0			0
$322$	−3.36961	+	9.03805i	−0.187781	+	0.503671i
$323$		−	3.18678i		−	0.177317i
$324$		0			0
$325$	12.3960	+	16.2013i	0.687608	+	0.898687i
$326$	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	$-0.891814\pi$
$337$		−	12.2398i		−	0.666742i	0.942796	−	0.333371i	$-0.108186\pi$
$338$	1.87919	+	1.08495i	0.102215	+	0.0590137i
$339$		0			0
$340$	3.55537	−	17.8094i	0.192817	−	0.965853i
$341$	−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	−0.877717	−	0.479179i	$-0.840934\pi$
$347$	−16.7948	+	9.69651i	−0.901594	+	0.520536i	−0.0238772	+	0.999715i	$0.507601\pi$
$348$		0			0
$349$	−25.8745			−1.38503			−0.692515	−	0.721403i	$-0.743498\pi$
$349$	−25.8745			−1.38503			−0.692515	+	0.721403i	$0.743498\pi$
$350$	5.75593	+	5.37241i	0.307667	+	0.287168i
$351$		0			0
$352$	−25.7632	−	14.8744i	−1.37318	−	0.792807i
$353$	1.36375	−	0.787360i	0.0725849	−	0.0419069i	−0.463268	−	0.886218i	$-0.653323\pi$
$353$	1.36375	−	0.787360i	0.0725849	−	0.0419069i	0.535853	+	0.844311i	$0.319990\pi$
$354$		0			0
$355$	1.74181	+	5.14293i	0.0924458	+	0.272959i
$356$	−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	−0.0154235	−	0.999881i	$-0.504910\pi$
$367$	16.1455	−	9.32160i	0.842787	−	0.486583i	0.858211	+	0.513298i	$0.171576\pi$
$368$	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	0.928798	−	0.370587i	$-0.120843\pi$
$373$	20.7088	+	11.9562i	1.07226	+	0.619069i	0.143461	+	0.989656i	$0.454177\pi$
$374$	−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	$0.481256\pi$
$380$	−0.762298	−	2.25079i	−0.0391051	−	0.115463i
$381$		0			0
$382$	5.54553	−	3.20172i	0.283734	−	0.163814i
$383$	12.3061	+	7.10491i	0.628811	+	0.363044i	0.780291	−	0.625416i	$-0.215071\pi$
$383$	12.3061	+	7.10491i	0.628811	+	0.363044i	−0.151481	+	0.988460i	$0.548404\pi$
$384$		0			0
$385$	−31.8100	−	0.964353i	−1.62119	−	0.0491480i
$386$	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
$395$	−13.0192	−	2.59907i	−0.655067	−	0.130774i
$396$		0			0
$397$	−27.5060	−	15.8806i	−1.38049	−	0.797023i	−0.388268	−	0.921546i	$-0.626927\pi$
$397$	−27.5060	−	15.8806i	−1.38049	−	0.797023i	−0.992217	+	0.124523i	$0.960260\pi$
$398$		−	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	$0.615363\pi$
$410$	−2.93933	+	14.7236i	−0.145163	+	0.727148i
$411$		0			0
$412$			11.9838i			0.590398i
$413$	−7.69938	+	20.6515i	−0.378862	+	1.01619i
$414$		0			0
$415$	24.6853	−	8.36044i	1.21175	−	0.410398i
$416$	−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
$425$	9.47434	−	22.7836i	0.459573	−	1.10517i
$426$		0			0
$427$	−0.924256	+	0.155551i	−0.0447279	+	0.00752766i
$428$			8.46878i			0.409354i
$429$		0			0
$430$	14.0881	+	2.81247i	0.679391	+	0.135629i
$431$	−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	$0.302086\pi$
$433$			33.8287i			1.62570i	−0.582472	+	0.812851i	$0.697914\pi$
$434$	−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	0.804104	−	0.594489i	$-0.202646\pi$
$443$	14.5505	+	8.40071i	0.691313	+	0.399130i	−0.112791	+	0.993619i	$0.535979\pi$
$444$		0			0
$445$	−11.7958	−	2.35484i	−0.559175	−	0.111630i
$446$		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
$455$	−20.5281	−	12.6964i	−0.962371	−	0.595218i
$456$		0			0
$457$	27.7754	+	16.0361i	1.29928	+	0.750139i	0.980279	−	0.197617i	$-0.0633201\pi$
$457$	27.7754	+	16.0361i	1.29928	+	0.750139i	0.318999	+	0.947755i	$0.396653\pi$
$458$	1.18115	−	0.681937i	0.0551915	−	0.0318648i
$459$		0			0
$460$	21.3502	−	7.23090i	0.995459	−	0.337143i
$461$	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	$-0.866625\pi$
$463$		−	17.5090i		−	0.813712i	0.913492	−	0.406856i	$-0.133375\pi$
$464$	−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	$-0.933641\pi$
$467$	−35.5868	−	20.5460i	−1.64676	−	0.950757i	−0.668412	−	0.743791i	$-0.733026\pi$
$468$		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
$485$	14.2207	−	4.81628i	0.645729	−	0.218696i
$486$		0			0
$487$	20.7088	−	11.9562i	0.938404	−	0.541788i	0.0489441	−	0.998802i	$-0.484414\pi$
$487$	20.7088	−	11.9562i	0.938404	−	0.541788i	0.889460	+	0.457014i	$0.151081\pi$
$488$	−0.665702	−	0.384343i	−0.0301349	−	0.0173984i
$489$		0			0
$490$	−8.62660	−	3.51749i	−0.389710	−	0.158904i
$491$	−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	$0.202365\pi$
$500$	1.24164	−	18.3581i	0.0555277	−	0.821000i
$501$		0			0
$502$	8.31830	+	4.80257i	0.371264	+	0.214349i
$503$		−	15.8219i		−	0.705463i	−0.935725	−	0.352731i	$-0.885253\pi$
$503$		−	15.8219i		−	0.705463i	0.935725	−	0.352731i	$-0.114747\pi$
$504$		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
$515$	−3.18759	+	15.9672i	−0.140462	+	0.703597i
$516$		0			0
$517$		−	11.6727i		−	0.513363i
$518$	0.483106	−	1.29580i	0.0212264	−	0.0569341i
$519$		0			0
$520$	−6.35021	−	18.7499i	−0.278475	−	0.822236i
$521$	−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	0.543349	−	0.839507i	$-0.317156\pi$
$523$	2.01222	+	1.16176i	0.0879882	+	0.0508000i	−0.455360	+	0.890307i	$0.650490\pi$
$524$	−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
$530$	3.37736	+	9.97212i	0.146703	+	0.433161i
$531$		0			0
$532$	1.79052	+	2.16796i	0.0776288	+	0.0939930i
$533$		−	46.0271i		−	1.99365i
$534$		0			0
$535$	−2.25263	+	11.2838i	−0.0973897	+	0.487842i
$536$	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	$0.245828\pi$
$547$			32.6394i			1.39556i	−0.716313	+	0.697779i	$0.754172\pi$
$548$	5.63758	+	3.25486i	0.240826	+	0.139041i
$549$		0			0
$550$	−9.72777	−	12.7140i	−0.414794	−	0.542126i
$551$	−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	−0.533073	−	0.846070i	$-0.678963\pi$
$557$	−1.57869	+	0.911455i	−0.0668911	+	0.0386196i	0.466181	+	0.884689i	$0.345629\pi$
$558$		0			0
$559$	−44.0405			−1.86272
$560$	5.60286	+	10.4215i	0.236764	+	0.440389i
$561$		0			0
$562$	2.05994	+	1.18931i	0.0868934	+	0.0501679i
$563$	−7.51678	+	4.33981i	−0.316794	+	0.182901i	−0.649963	−	0.759966i	$-0.725216\pi$
$563$	−7.51678	+	4.33981i	−0.316794	+	0.182901i	0.333168	+	0.942867i	$0.391882\pi$
$564$		0			0
$565$	−33.5091	+	11.3489i	−1.40974	+	0.477452i
$566$	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	−0.843049	−	0.537837i	$-0.819242\pi$
$577$	−19.1877	+	11.0780i	−0.798793	+	0.461183i	0.0442559	+	0.999020i	$0.485908\pi$
$578$	−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	$-0.633140\pi$
$587$		−	44.2789i		−	1.82758i	0.406182	−	0.913792i	$-0.366860\pi$
$588$		0			0
$589$	3.22876			0.133039
$590$	−10.5008	+	3.55642i	−0.432311	+	0.146415i
$591$		0			0
$592$	−1.52110	+	0.878205i	−0.0625166	+	0.0360940i
$593$	−21.9170	−	12.6538i	−0.900022	−	0.519628i	−0.0228149	−	0.999740i	$-0.507263\pi$
$593$	−21.9170	−	12.6538i	−0.900022	−	0.519628i	−0.877207	+	0.480112i	$0.840596\pi$
$594$		0			0
$595$	−0.884698	+	29.1825i	−0.0362691	+	1.19636i
$596$	−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
$605$	39.3328	+	7.85215i	1.59911	+	0.319235i
$606$		0			0
$607$	16.1455	+	9.32160i	0.655325	+	0.378352i	0.790493	−	0.612471i	$-0.209824\pi$
$607$	16.1455	+	9.32160i	0.655325	+	0.378352i	−0.135169	+	0.990823i	$0.543158\pi$
$608$			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	0.112789	−	0.993619i	$-0.464022\pi$
$613$	25.4938	−	14.7188i	1.02968	−	0.594488i	0.916894	+	0.399131i	$0.130688\pi$
$614$	−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	$-0.909981\pi$
$617$		−	13.8628i		−	0.558096i	0.960277	−	0.279048i	$-0.0900189\pi$
$618$		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	$0.749196\pi$
$620$	18.0440	+	3.60219i	0.724665	+	0.144668i
$621$		0			0
$622$		−	2.06751i		−	0.0828997i
$623$	14.0350	−	2.36208i	0.562301	−	0.0946347i
$624$		0			0
$625$	6.53747	−	24.1301i	0.261499	−	0.965204i
$626$	−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
$635$	−8.64086	+	2.92649i	−0.342902	+	0.116134i
$636$		0			0
$637$	28.0448	+	5.39723i	1.11118	+	0.213846i
$638$			7.77479i			0.307807i
$639$		0			0
$640$	−5.02635	+	25.1779i	−0.198684	+	0.995243i
$641$	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	$-0.719789\pi$
$643$		−	39.0979i		−	1.54187i	0.636913	−	0.770935i	$-0.280211\pi$
$644$	−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	−0.854855	−	0.518867i	$-0.826354\pi$
$647$	−21.1866	+	12.2321i	−0.832931	+	0.480893i	0.0219243	+	0.999760i	$0.493021\pi$
$648$		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	0.899711	−	0.436486i	$-0.143777\pi$
$653$	24.8271	+	14.3339i	0.971558	+	0.560929i	0.0718473	+	0.997416i	$0.477111\pi$
$654$		0			0
$655$	−17.1206	−	3.41785i	−0.668958	−	0.133547i
$656$	−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
$665$	1.80903	+	3.36485i	0.0701510	+	0.130483i
$666$		0			0
$667$	−12.8816	−	7.43719i	−0.498777	−	0.287969i
$668$	18.0083	−	10.3971i	0.696763	−	0.402277i
$669$		0			0
$670$	0.991961	+	2.92890i	0.0383228	+	0.113153i
$671$	1.90562			0.0735657
$672$		0			0
$673$		−	12.2398i		−	0.471808i	−0.971776	−	0.235904i	$-0.924195\pi$
$673$		−	12.2398i		−	0.471808i	0.971776	−	0.235904i	$-0.0758051\pi$
$674$	−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	0.910558	−	0.413382i	$-0.135652\pi$
$677$	26.2232	+	15.1399i	1.00784	+	0.581875i	0.0972799	+	0.995257i	$0.468986\pi$
$678$		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	0.193739	−	0.981053i	$-0.437939\pi$
$683$	29.7990	−	17.2044i	1.14023	−	0.658309i	0.946486	+	0.322744i	$0.104605\pi$
$684$		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
$695$	−5.18512	−	15.3098i	−0.196683	−	0.580733i
$696$		0			0
$697$	−48.2147	+	27.8368i	−1.82626	+	1.05439i
$698$	13.3370	+	7.70010i	0.504811	+	0.291453i
$699$		0			0
$700$	6.35577	+	20.8229i	0.240226	+	0.787030i
$701$	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	$0.204738\pi$
$710$	0.632693	−	3.16927i	0.0237445	−	0.118940i
$711$		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
$725$	−9.64282	+	7.37796i	−0.358126	+	0.274011i
$726$		0			0
$727$			40.5432i			1.50366i	0.659355	+	0.751832i	$0.270830\pi$
$727$			40.5432i			1.50366i	−0.659355	+	0.751832i	$0.729170\pi$
$728$	14.9156	+	18.0599i	0.552811	+	0.669343i
$729$		0			0
$730$	3.85855	+	11.3929i	0.142811	+	0.421670i
$731$	26.6353	+	46.1337i	0.985143	+	1.70632i
$732$		0			0
$733$	9.07885	+	5.24168i	0.335335	+	0.193606i	0.658207	−	0.752837i	$-0.271315\pi$
$733$	9.07885	+	5.24168i	0.335335	+	0.193606i	−0.322872	+	0.946443i	$0.604648\pi$
$734$	−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	$0.762871\pi$
$740$	−3.06101	+	1.03671i	−0.112525	+	0.0381101i
$741$		0			0
$742$	−7.93289	−	9.60515i	−0.291226	−	0.352616i
$743$			10.6760i			0.391666i	0.980637	+	0.195833i	$0.0627410\pi$
$743$			10.6760i			0.391666i	−0.980637	+	0.195833i	$0.937259\pi$
$744$		0			0
$745$	−6.47099	−	1.29183i	−0.237079	−	0.0473289i
$746$	−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	$-0.734145\pi$
$757$		−	40.7992i		−	1.48287i	0.671023	−	0.741436i	$-0.265855\pi$
$758$	−1.18115	−	0.681937i	−0.0429013	−	0.0247691i
$759$		0			0
$760$	−0.613394	+	3.07260i	−0.0222501	+	0.111455i
$761$	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	$0.353426\pi$
$770$	16.1094	+	9.96353i	0.580542	+	0.359061i
$771$		0			0
$772$	17.8883	+	10.3278i	0.643813	+	0.371706i
$773$	16.5799	−	9.57241i	0.596338	−	0.344296i	−0.171262	−	0.985226i	$-0.554784\pi$
$773$	16.5799	−	9.57241i	0.596338	−	0.344296i	0.767599	+	0.640930i	$0.221451\pi$
$774$		0			0
$775$	23.0837	+	9.59913i	0.829191	+	0.344811i
$776$	−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	−0.258076	−	0.966125i	$-0.583088\pi$
$787$	12.6122	−	7.28164i	0.449575	−	0.259562i	0.707651	+	0.706562i	$0.249755\pi$
$788$	−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	$0.0199349\pi$
$797$			3.53378i			0.125173i	−0.998040	+	0.0625865i	$0.980065\pi$
$798$		0			0
$799$	−10.7085			−0.378839
$800$	−10.6170	+	25.5314i	−0.375368	+	0.902673i
$801$		0			0
$802$	−20.2176	+	11.6727i	−0.713910	+	0.412176i
$803$	−42.1050	−	24.3093i	−1.48585	−	0.857858i
$804$		0			0
$805$	−31.9179	+	17.1598i	−1.12496	+	0.604804i
$806$	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
$815$	−0.768880	+	3.85145i	−0.0269327	+	0.134911i
$816$		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	0.454459	−	0.890768i	$-0.349833\pi$
$823$	41.6870	−	24.0680i	1.45312	−	0.838957i	0.998657	+	0.0518109i	$0.0164993\pi$
$824$	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	$0.181267\pi$
$827$			31.0112i			1.07837i	−0.842189	+	0.539183i	$0.818733\pi$
$828$		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	$0.651708\pi$
$830$	−15.2120	−	3.03683i	−0.528016	−	0.105410i
$831$		0			0
$832$		−	2.89061i		−	0.100214i
$833$	−11.3075	−	32.6420i	−0.391782	−	1.13098i
$834$		0			0
$835$	26.7599	−	9.06305i	0.926063	−	0.313640i
$836$	−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
$845$	2.61507	+	7.72133i	0.0899610	+	0.265622i
$846$		0			0
$847$	−46.7994	+	7.87629i	−1.60804	+	0.270633i
$848$			15.8219i			0.543326i
$849$		0			0
$850$	−11.6638	+	8.92426i	−0.400065	+	0.306100i
$851$	−2.68967	−	4.65864i	−0.0922006	−	0.159696i
$852$		0			0
$853$			2.63461i			0.0902075i	0.998982	+	0.0451037i	$0.0143618\pi$
$853$			2.63461i			0.0902075i	−0.998982	+	0.0451037i	$0.985638\pi$
$854$	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	−0.995903	−	0.0904296i	$-0.971176\pi$
$857$	−41.4393	+	23.9250i	−1.41554	+	0.817262i	−0.419637	+	0.907692i	$0.637843\pi$
$858$		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	−0.317956	−	0.948105i	$-0.602997\pi$
$863$	−38.1317	−	22.0153i	−1.29802	−	0.749411i	−0.980061	+	0.198695i	$0.936330\pi$
$864$		0			0
$865$	4.07646	−	20.4197i	0.138604	−	0.694291i
$866$	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
$875$	2.92972	+	29.4350i	0.0990426	+	0.995083i
$876$		0			0
$877$	−27.2843	−	15.7526i	−0.921324	−	0.531927i	−0.0372670	−	0.999305i	$-0.511865\pi$
$877$	−27.2843	−	15.7526i	−0.921324	−	0.531927i	−0.884057	+	0.467379i	$0.845199\pi$
$878$	−15.5813	+	8.99590i	−0.525845	+	0.303597i
$879$		0			0
$880$	−7.71710	−	22.7858i	−0.260143	−	0.768108i
$881$	−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	$-0.880190\pi$
$883$		−	21.8449i		−	0.735140i	0.929996	−	0.367570i	$-0.119810\pi$
$884$	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	0.500543	−	0.865712i	$-0.333134\pi$
$887$	0.0323423	+	0.0186729i	0.00108595	+	0.000626973i	−0.499457	+	0.866339i	$0.666467\pi$
$888$		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
$905$	−9.07069	−	26.7824i	−0.301520	−	0.890278i
$906$		0			0
$907$	0.760548	−	0.439102i	0.0252536	−	0.0145802i	−0.487320	−	0.873223i	$-0.662025\pi$
$907$	0.760548	−	0.439102i	0.0252536	−	0.0145802i	0.512574	+	0.858643i	$0.328692\pi$
$908$	−5.03657	−	2.90786i	−0.167144	−	0.0965008i
$909$		0			0
$910$	6.80277	+	12.6534i	0.225509	+	0.419456i
$911$	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	$0.213426\pi$
$920$	−29.1456	−	5.81845i	−0.960902	−	0.191828i
$921$		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
$935$	11.6211	−	58.2123i	0.380052	−	1.90375i
$936$		0			0
$937$			0.255999i			0.00836312i	0.999991	+	0.00418156i	$0.00133104\pi$
$937$			0.255999i			0.00836312i	−0.999991	+	0.00418156i	$0.998669\pi$
$938$	−2.32996	−	2.82111i	−0.0760758	−	0.0921126i
$939$		0			0
$940$	−7.56329	+	2.56154i	−0.246687	+	0.0835482i
$941$	−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	0.0287974	−	0.999585i	$-0.490832\pi$
$947$	−25.3102	−	14.6128i	−0.822470	−	0.474853i	−0.851268	+	0.524732i	$0.824166\pi$
$948$		0			0
$949$	−18.4373	−	31.9343i	−0.598499	−	1.03663i
$950$	−0.737872	+	1.77441i	−0.0239397	+	0.0575696i
$951$		0			0
$952$	9.89739	−	26.5470i	0.320776	−	0.860394i
$953$			57.6827i			1.86852i	0.356587	+	0.934262i	$0.383940\pi$
$953$			57.6827i			1.86852i	−0.356587	+	0.934262i	$0.616060\pi$
$954$		0			0
$955$	23.5916	+	4.70968i	0.763407	+	0.152402i
$956$	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	$0.127348\pi$
$967$			24.2235i			0.778976i	−0.921032	+	0.389488i	$0.872652\pi$
$968$	−33.7076	−	19.4611i	−1.08340	−	0.625503i
$969$		0			0
$970$	−8.76333	−	1.74946i	−0.281373	−	0.0561716i
$971$	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	$0.710689\pi$
$977$	−50.1696	+	28.9654i	−1.60507	+	0.926686i	−0.990452	+	0.137859i	$0.955978\pi$
$978$		0			0
$979$	−28.9373			−0.924839
$980$	−15.7945	−	20.3498i	−0.504538	−	0.650051i
$981$		0			0
$982$	18.6965	+	10.7945i	0.596631	+	0.344465i
$983$	5.85252	−	3.37896i	0.186667	−	0.107772i	−0.403755	−	0.914867i	$-0.632295\pi$
$983$	5.85252	−	3.37896i	0.186667	−	0.107772i	0.590421	+	0.807095i	$0.298962\pi$
$984$		0			0
$985$	−12.5264	+	4.24244i	−0.399124	+	0.135175i
$986$	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	−0.867721	−	0.497051i	$-0.834416\pi$
$997$	−27.5060	+	15.8806i	−0.871123	+	0.502943i	−0.00340163	+	0.999994i	$0.501083\pi$
$998$	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.289.4	yes	16
3.2	odd	2	inner	315.2.bf.c.289.5	yes	16
5.4	even	2	inner	315.2.bf.c.289.6	yes	16
7.2	even	3		2205.2.d.p.1324.5		8
7.4	even	3	inner	315.2.bf.c.109.6	yes	16
7.5	odd	6		2205.2.d.r.1324.6		8
15.14	odd	2	inner	315.2.bf.c.289.3	yes	16
21.2	odd	6		2205.2.d.p.1324.4		8
21.5	even	6		2205.2.d.r.1324.3		8
21.11	odd	6	inner	315.2.bf.c.109.3	✓	16
35.4	even	6	inner	315.2.bf.c.109.4	yes	16
35.9	even	6		2205.2.d.p.1324.3		8
35.19	odd	6		2205.2.d.r.1324.4		8
105.44	odd	6		2205.2.d.p.1324.6		8
105.74	odd	6	inner	315.2.bf.c.109.5	yes	16
105.89	even	6		2205.2.d.r.1324.5		8

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

\(f(q)\)	\(=\)	\(q+(-0.515448 - 0.297594i) q^{2} +(-0.822876 - 1.42526i) q^{4} +(-0.717291 - 2.11790i) q^{5} +(1.68480 + 2.03996i) q^{7} +2.16991i q^{8} +O(q^{10})\)	\(q+(-0.515448 - 0.297594i) q^{2} +(-0.822876 - 1.42526i) q^{4} +(-0.717291 - 2.11790i) q^{5} +(1.68480 + 2.03996i) q^{7} +2.16991i q^{8} +(-0.260548 + 1.30513i) q^{10} +(-2.68967 - 4.65864i) q^{11} -4.07992i q^{13} +(-0.261348 - 1.55288i) q^{14} +(-1.00000 + 1.73205i) q^{16} +(-4.27384 + 2.46750i) q^{17} +(-0.322876 + 0.559237i) q^{19} +(-2.42832 + 2.76510i) q^{20} +3.20172i q^{22} +(-5.30473 - 3.06269i) q^{23} +(-3.97099 + 3.03830i) q^{25} +(-1.21416 + 2.10299i) q^{26} +(1.52110 - 4.07992i) q^{28} +2.42832 q^{29} +(-2.50000 - 4.33013i) q^{31} +(4.78929 - 2.76510i) q^{32} +2.93725 q^{34} +(3.11193 - 5.03149i) q^{35} +(0.760548 + 0.439102i) q^{37} +(0.332851 - 0.192172i) q^{38} +(4.59564 - 1.55646i) q^{40} +11.2814 q^{41} -10.7945i q^{43} +(-4.42652 + 7.66697i) q^{44} +(1.82288 + 3.15731i) q^{46} +(1.87919 + 1.08495i) q^{47} +(-1.32288 + 6.87386i) q^{49} +(2.95102 - 0.384343i) q^{50} +(-5.81496 + 3.35727i) q^{52} +(6.85108 - 3.95547i) q^{53} +(-7.93725 + 9.03805i) q^{55} +(-4.42652 + 3.65587i) q^{56} +(-1.25167 - 0.722653i) q^{58} +(4.16518 + 7.21430i) q^{59} +(-0.177124 + 0.306788i) q^{61} +2.97594i q^{62} +0.708497 q^{64} +(-8.64086 + 2.92649i) q^{65} +(2.01222 - 1.16176i) q^{67} +(7.03367 + 4.06089i) q^{68} +(-3.10138 + 1.66738i) q^{70} -2.42832 q^{71} +(7.82718 - 4.51902i) q^{73} +(-0.261348 - 0.452669i) q^{74} +1.06275 q^{76} +(4.97188 - 13.3357i) q^{77} +(2.96863 - 5.14181i) q^{79} +(4.38560 + 0.875514i) q^{80} +(-5.81496 - 3.35727i) q^{82} +11.6556i q^{83} +(8.29150 + 7.28164i) q^{85} +(-3.21236 + 5.56398i) q^{86} +(10.1088 - 5.83633i) q^{88} +(2.68967 - 4.65864i) q^{89} +(8.32288 - 6.87386i) q^{91} +10.0808i q^{92} +(-0.645751 - 1.11847i) q^{94} +(1.41600 + 0.282682i) q^{95} +6.71453i q^{97} +(2.72749 - 3.14944i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 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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