LMFDB - Embedded newform 819.2.s.d.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.217953 - 0.377506i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.d.802.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.85816 q^{2} +1.45276 q^{4} +(-0.0986811 + 0.170921i) q^{5} +(1.03826 - 2.43352i) q^{7} +1.01686 q^{8} +(0.183365 - 0.317598i) q^{10} +(-2.09137 + 3.62236i) q^{11} +(-2.72221 + 2.36423i) q^{13} +(-1.92926 + 4.52187i) q^{14} -4.79501 q^{16} -0.841305 q^{17} +(-0.675876 - 1.17065i) q^{19} +(-0.143360 + 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} +4.11519 q^{23} +(2.48052 + 4.29639i) q^{25} +(5.05830 - 4.39312i) q^{26} +(1.50835 - 3.53532i) q^{28} +(-4.11931 - 7.13485i) q^{29} +(0.640350 + 1.10912i) q^{31} +6.87618 q^{32} +1.56328 q^{34} +(0.313482 + 0.417603i) q^{35} +3.04485 q^{37} +(1.25589 + 2.17526i) q^{38} +(-0.100344 + 0.173802i) q^{40} +(2.69848 + 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} +(-3.03826 + 5.26242i) q^{44} -7.64669 q^{46} +(-5.83204 + 10.1014i) q^{47} +(-4.84403 - 5.05326i) q^{49} +(-4.60921 - 7.98339i) q^{50} +(-3.95472 + 3.43466i) q^{52} +(2.32398 + 4.02525i) q^{53} +(-0.412757 - 0.714916i) q^{55} +(1.05576 - 2.47454i) q^{56} +(7.65434 + 13.2577i) q^{58} -6.05811 q^{59} +(5.68285 + 9.84298i) q^{61} +(-1.18987 - 2.06092i) q^{62} -3.18704 q^{64} +(-0.135465 - 0.698587i) q^{65} +(-6.69851 + 11.6022i) q^{67} -1.22222 q^{68} +(-0.582500 - 0.775973i) q^{70} +(-2.98520 + 5.17051i) q^{71} +(-1.94273 - 3.36491i) q^{73} -5.65782 q^{74} +(-0.981887 - 1.70068i) q^{76} +(6.64368 + 8.85034i) q^{77} +(5.36669 - 9.29537i) q^{79} +(0.473177 - 0.819566i) q^{80} +(-5.01421 - 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 - 0.143797i) q^{85} +(4.94994 - 8.57354i) q^{86} +(-2.12662 + 3.68341i) q^{88} +11.9841 q^{89} +(2.92702 + 9.07924i) q^{91} +5.97840 q^{92} +(10.8369 - 18.7700i) q^{94} +0.266785 q^{95} +(-9.73637 + 16.8639i) q^{97} +(9.00098 + 9.38977i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29}+ \cdots - 20 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^13 + 2 * q^14 - 16 * q^16 + 10 * q^17 - q^19 + q^20 - 5 * q^22 - 2 * q^23 + 7 * q^25 + 16 * q^26 - q^28 - 3 * q^29 + 16 * q^31 + 16 * q^32 + 32 * q^34 - 20 * q^35 + 26 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 - 32 * q^46 + q^47 - 3 * q^49 - 6 * q^50 + 41 * q^52 + 2 * q^53 + 9 * q^55 - 9 * q^56 - 8 * q^58 + 26 * q^59 - 5 * q^61 - 5 * q^62 - 30 * q^64 + 5 * q^65 - 11 * q^67 + 58 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 - 6 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 + 7 * q^80 + q^82 + 54 * q^83 - q^85 + 7 * q^86 + 8 * q^89 - 23 * q^91 - 54 * q^92 + 45 * q^94 - 12 * q^95 - 35 * q^97 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.85816			−1.31392			−0.656959	−	0.753926i	$-0.728158\pi$
$2$	−1.85816			−1.31392			−0.656959	+	0.753926i	$0.728158\pi$
$3$		0			0
$3$		0			0
$4$	1.45276			0.726381
$5$	−0.0986811	+	0.170921i	−0.0441315	+	0.0764381i	−0.887247	−	0.461294i	$-0.847385\pi$
$5$	−0.0986811	+	0.170921i	−0.0441315	+	0.0764381i	0.843116	+	0.537732i	$0.180719\pi$
$6$		0			0
$7$	1.03826	−	2.43352i	0.392426	−	0.919784i
$7$	1.03826	−	2.43352i	0.392426	−	0.919784i
$8$	1.01686			0.359513
$9$		0			0
$10$	0.183365	−	0.317598i	0.0579852	−	0.100433i
$11$	−2.09137	+	3.62236i	−0.630571	+	1.09218i	0.356864	+	0.934156i	$0.383846\pi$
$11$	−2.09137	+	3.62236i	−0.630571	+	1.09218i	−0.987435	+	0.158025i	$0.949487\pi$
$12$		0			0
$13$	−2.72221	+	2.36423i	−0.755005	+	0.655719i
$13$	−2.72221	+	2.36423i	−0.755005	+	0.655719i
$14$	−1.92926	+	4.52187i	−0.515616	+	1.20852i
$15$		0			0
$16$	−4.79501			−1.19875
$17$	−0.841305			−0.204047			−0.102023	−	0.994782i	$-0.532532\pi$
$17$	−0.841305			−0.204047			−0.102023	+	0.994782i	$0.532532\pi$
$18$		0			0
$19$	−0.675876	−	1.17065i	−0.155057	−	0.268566i	0.778023	−	0.628236i	$-0.216223\pi$
$19$	−0.675876	−	1.17065i	−0.155057	−	0.268566i	−0.933080	+	0.359670i	$0.882889\pi$
$20$	−0.143360	+	0.248307i	−0.0320563	+	0.0555232i
$21$		0			0
$22$	3.88610	−	6.73092i	0.828519	−	1.43504i
$23$	4.11519			0.858077			0.429038	−	0.903286i	$-0.358853\pi$
$23$	4.11519			0.858077			0.429038	+	0.903286i	$0.358853\pi$
$24$		0			0
$25$	2.48052	+	4.29639i	0.496105	+	0.859279i
$26$	5.05830	−	4.39312i	0.992015	−	0.861561i
$27$		0			0
$28$	1.50835	−	3.53532i	0.285051	−	0.668113i
$29$	−4.11931	−	7.13485i	−0.764936	−	1.32491i	−0.940280	−	0.340401i	$-0.889437\pi$
$29$	−4.11931	−	7.13485i	−0.764936	−	1.32491i	0.175344	−	0.984507i	$-0.443896\pi$
$30$		0			0
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	0.917784	−	0.397080i	$-0.129977\pi$
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	−0.802774	+	0.596284i	$0.796643\pi$
$32$	6.87618			1.21555
$33$		0			0
$34$	1.56328			0.268100
$35$	0.313482	+	0.417603i	0.0529881	+	0.0705878i
$36$		0			0
$37$	3.04485			0.500570			0.250285	−	0.968172i	$-0.419476\pi$
$37$	3.04485			0.500570			0.250285	+	0.968172i	$0.419476\pi$
$38$	1.25589	+	2.17526i	0.203732	+	0.352874i
$39$		0			0
$40$	−0.100344	+	0.173802i	−0.0158659	+	0.0274805i
$41$	2.69848	+	4.67390i	0.421431	+	0.729941i	0.996080	−	0.0884599i	$-0.0281945\pi$
$41$	2.69848	+	4.67390i	0.421431	+	0.729941i	−0.574648	+	0.818400i	$0.694861\pi$
$42$		0			0
$43$	−2.66389	+	4.61399i	−0.406239	+	0.703627i	−0.994465	−	0.105070i	$-0.966493\pi$
$43$	−2.66389	+	4.61399i	−0.406239	+	0.703627i	0.588226	+	0.808697i	$0.299827\pi$
$44$	−3.03826	+	5.26242i	−0.458035	+	0.793340i
$45$		0			0
$46$	−7.64669			−1.12744
$47$	−5.83204	+	10.1014i	−0.850690	+	1.47344i	0.0298969	+	0.999553i	$0.490482\pi$
$47$	−5.83204	+	10.1014i	−0.850690	+	1.47344i	−0.880587	+	0.473885i	$0.842851\pi$
$48$		0			0
$49$	−4.84403	−	5.05326i	−0.692004	−	0.721894i
$50$	−4.60921	−	7.98339i	−0.651841	−	1.12902i
$51$		0			0
$52$	−3.95472	+	3.43466i	−0.548422	+	0.476302i
$53$	2.32398	+	4.02525i	0.319223	+	0.552911i	0.980326	−	0.197384i	$-0.0632446\pi$
$53$	2.32398	+	4.02525i	0.319223	+	0.552911i	−0.661103	+	0.750295i	$0.729911\pi$
$54$		0			0
$55$	−0.412757	−	0.714916i	−0.0556562	−	0.0963993i
$56$	1.05576	−	2.47454i	0.141082	−	0.330674i
$57$		0			0
$58$	7.65434	+	13.2577i	1.00506	+	1.74082i
$59$	−6.05811			−0.788698			−0.394349	−	0.918961i	$-0.629030\pi$
$59$	−6.05811			−0.788698			−0.394349	+	0.918961i	$0.629030\pi$
$60$		0			0
$61$	5.68285	+	9.84298i	0.727614	+	1.26026i	0.957889	+	0.287139i	$0.0927042\pi$
$61$	5.68285	+	9.84298i	0.727614	+	1.26026i	−0.230275	+	0.973126i	$0.573962\pi$
$62$	−1.18987	−	2.06092i	−0.151114	−	0.261737i
$63$		0			0
$64$	−3.18704			−0.398380
$65$	−0.135465	−	0.698587i	−0.0168023	−	0.0866490i
$66$		0			0
$67$	−6.69851	+	11.6022i	−0.818354	+	1.41743i	0.0885411	+	0.996073i	$0.471780\pi$
$67$	−6.69851	+	11.6022i	−0.818354	+	1.41743i	−0.906895	+	0.421357i	$0.861554\pi$
$68$	−1.22222			−0.148216
$69$		0			0
$70$	−0.582500	−	0.775973i	−0.0696221	−	0.0927465i
$71$	−2.98520	+	5.17051i	−0.354278	+	0.613627i	−0.986994	−	0.160757i	$-0.948607\pi$
$71$	−2.98520	+	5.17051i	−0.354278	+	0.613627i	0.632716	+	0.774384i	$0.281940\pi$
$72$		0			0
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	0.729651	−	0.683820i	$-0.239683\pi$
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	−0.957031	+	0.289986i	$0.906349\pi$
$74$	−5.65782			−0.657708
$75$		0			0
$76$	−0.981887	−	1.70068i	−0.112630	−	0.195081i
$77$	6.64368	+	8.85034i	0.757118	+	1.00859i
$78$		0			0
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	−0.388441	−	0.921474i	$-0.626986\pi$
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	0.992240	−	0.124337i	$-0.0396805\pi$
$80$	0.473177	−	0.819566i	0.0529028	−	0.0916303i
$81$		0			0
$82$	−5.01421	−	8.68486i	−0.553726	−	0.959082i
$83$	−3.07390			−0.337404			−0.168702	−	0.985667i	$-0.553958\pi$
$83$	−3.07390			−0.337404			−0.168702	+	0.985667i	$0.553958\pi$
$84$		0			0
$85$	0.0830210	−	0.143797i	0.00900489	−	0.0155969i
$86$	4.94994	−	8.57354i	0.533765	−	0.924509i
$87$		0			0
$88$	−2.12662	+	3.68341i	−0.226698	+	0.392653i
$89$	11.9841			1.27032			0.635159	−	0.772382i	$-0.280935\pi$
$89$	11.9841			1.27032			0.635159	+	0.772382i	$0.280935\pi$
$90$		0			0
$91$	2.92702	+	9.07924i	0.306836	+	0.951763i
$92$	5.97840			0.623291
$93$		0			0
$94$	10.8369	−	18.7700i	1.11774	−	1.93598i
$95$	0.266785			0.0273715
$96$		0			0
$97$	−9.73637	+	16.8639i	−0.988578	+	1.71227i	−0.363771	+	0.931488i	$0.618511\pi$
$97$	−9.73637	+	16.8639i	−0.988578	+	1.71227i	−0.624807	+	0.780779i	$0.714822\pi$
$98$	9.00098	+	9.38977i	0.909236	+	0.948510i
$99$		0			0
$100$	3.60361	+	6.24164i	0.360361	+	0.624164i
$101$	−8.46697	+	14.6652i	−0.842495	+	1.45924i	0.0452843	+	0.998974i	$0.485581\pi$
$101$	−8.46697	+	14.6652i	−0.842495	+	1.45924i	−0.887779	+	0.460270i	$0.847753\pi$
$102$		0			0
$103$	3.61712	−	6.26504i	0.356406	−	0.617313i	−0.630952	−	0.775822i	$-0.717335\pi$
$103$	3.61712	−	6.26504i	0.356406	−	0.617313i	0.987357	+	0.158509i	$0.0506688\pi$
$104$	−2.76809	+	2.40408i	−0.271434	+	0.235739i
$105$		0			0
$106$	−4.31833	−	7.47957i	−0.419434	−	0.726480i
$107$	9.85249			0.952477			0.476238	−	0.879316i	$-0.342000\pi$
$107$	9.85249			0.952477			0.476238	+	0.879316i	$0.342000\pi$
$108$		0			0
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	0.980179	+	0.198115i	$0.0634821\pi$
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	−0.318516	+	0.947917i	$0.603185\pi$
$110$	0.766969	+	1.32843i	0.0731277	+	0.126661i
$111$		0			0
$112$	−4.97847	+	11.6687i	−0.470421	+	1.10259i
$113$	−2.13432	+	3.69675i	−0.200780	+	0.347761i	−0.948780	−	0.315938i	$-0.897681\pi$
$113$	−2.13432	+	3.69675i	−0.200780	+	0.347761i	0.748000	+	0.663699i	$0.231014\pi$
$114$		0			0
$115$	−0.406092	+	0.703371i	−0.0378682	+	0.0655897i
$116$	−5.98437	−	10.3652i	−0.555635	−	0.962388i
$117$		0			0
$118$	11.2569			1.03629
$119$	−0.873495	+	2.04733i	−0.0800732	+	0.187679i
$120$		0			0
$121$	−3.24765	−	5.62509i	−0.295240	−	0.511372i
$122$	−10.5596	−	18.2898i	−0.956026	−	1.65589i
$123$		0			0
$124$	0.930276	+	1.61129i	0.0835412	+	0.144698i
$125$	−1.96593			−0.175839
$126$		0			0
$127$	1.09512	+	1.89680i	0.0971761	+	0.168314i	0.910515	−	0.413477i	$-0.135686\pi$
$127$	1.09512	+	1.89680i	0.0971761	+	0.168314i	−0.813339	+	0.581791i	$0.802352\pi$
$128$	−7.83033			−0.692110
$129$		0			0
$130$	0.251715	+	1.29809i	0.0220769	+	0.113850i
$131$	1.13806	−	1.97117i	0.0994326	−	0.172222i	−0.812017	−	0.583633i	$-0.801631\pi$
$131$	1.13806	−	1.97117i	0.0994326	−	0.172222i	0.911450	+	0.411411i	$0.134964\pi$
$132$		0			0
$133$	−3.55054	+	0.429314i	−0.307871	+	0.0372262i
$134$	12.4469	−	21.5587i	1.07525	−	1.86239i
$135$		0			0
$136$	−0.855486			−0.0733573
$137$	−13.4480			−1.14894			−0.574469	−	0.818526i	$-0.694791\pi$
$137$	−13.4480			−1.14894			−0.574469	+	0.818526i	$0.694791\pi$
$138$		0			0
$139$	−2.02270	+	3.50342i	−0.171563	+	0.297156i	−0.938966	−	0.344009i	$-0.888215\pi$
$139$	−2.02270	+	3.50342i	−0.171563	+	0.297156i	0.767403	+	0.641165i	$0.221548\pi$
$140$	0.455415	+	0.606678i	0.0384896	+	0.0512736i
$141$		0			0
$142$	5.54698	−	9.60765i	0.465492	−	0.806256i
$143$	−2.87093	−	14.8053i	−0.240079	−	1.23808i
$144$		0			0
$145$	1.62599			0.135031
$146$	3.60991	+	6.25255i	0.298758	+	0.517465i
$147$		0			0
$148$	4.42344			0.363605
$149$	7.67596	+	13.2952i	0.628840	+	1.08918i	0.987785	+	0.155823i	$0.0498031\pi$
$149$	7.67596	+	13.2952i	0.628840	+	1.08918i	−0.358945	+	0.933359i	$0.616864\pi$
$150$		0			0
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	0.714203	−	0.699939i	$-0.246789\pi$
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	−0.963266	+	0.268548i	$0.913456\pi$
$152$	−0.687268	−	1.19038i	−0.0557448	−	0.0965528i
$153$		0			0
$154$	−12.3450	−	16.4454i	−0.994791	−	1.32520i
$155$	−0.252762			−0.0203023
$156$		0			0
$157$	−2.26834	−	3.92888i	−0.181033	−	0.313559i	0.761199	−	0.648518i	$-0.224611\pi$
$157$	−2.26834	−	3.92888i	−0.181033	−	0.313559i	−0.942233	+	0.334959i	$0.891278\pi$
$158$	−9.97217	+	17.2723i	−0.793343	+	1.37411i
$159$		0			0
$160$	−0.678549	+	1.17528i	−0.0536440	+	0.0929142i
$161$	4.27265	−	10.0144i	0.336732	−	0.789245i
$162$		0			0
$163$	−0.911271	−	1.57837i	−0.0713762	−	0.123627i	0.828128	−	0.560538i	$-0.189406\pi$
$163$	−0.911271	−	1.57837i	−0.0713762	−	0.123627i	−0.899505	+	0.436911i	$0.856072\pi$
$164$	3.92025	+	6.79007i	0.306120	+	0.530215i
$165$		0			0
$166$	5.71180			0.443322
$167$	−5.35397	−	9.27336i	−0.414303	−	0.717594i	0.581052	−	0.813866i	$-0.302641\pi$
$167$	−5.35397	−	9.27336i	−0.414303	−	0.717594i	−0.995355	+	0.0962726i	$0.969308\pi$
$168$		0			0
$169$	1.82086	−	12.8718i	0.140066	−	0.990142i
$170$	−0.154266	+	0.267197i	−0.0118317	+	0.0204931i
$171$		0			0
$172$	−3.87000	+	6.70303i	−0.295085	+	0.511102i
$173$	−6.74634	−	11.6850i	−0.512915	−	0.888395i	−0.999888	−	0.0149778i	$-0.995232\pi$
$173$	−6.74634	−	11.6850i	−0.512915	−	0.888395i	0.486973	−	0.873417i	$-0.338101\pi$
$174$		0			0
$175$	13.0308	−	1.57562i	0.985035	−	0.119106i
$176$	10.0281	−	17.3692i	0.755898	−	1.30925i
$177$		0			0
$178$	−22.2685			−1.66909
$179$	5.23458	−	9.06657i	0.391251	−	0.677667i	−0.601364	−	0.798975i	$-0.705376\pi$
$179$	5.23458	−	9.06657i	0.391251	−	0.677667i	0.992615	+	0.121309i	$0.0387090\pi$
$180$		0			0
$181$	12.5209			0.930674			0.465337	−	0.885133i	$-0.345933\pi$
$181$	12.5209			0.930674			0.465337	+	0.885133i	$0.345933\pi$
$182$	−5.43888	−	16.8707i	−0.403157	−	1.25054i
$183$		0			0
$184$	4.18455			0.308489
$185$	−0.300469	+	0.520428i	−0.0220909	+	0.0382626i
$186$		0			0
$187$	1.75948	−	3.04751i	0.128666	−	0.222856i
$188$	−8.47256	+	14.6749i	−0.617925	+	1.07028i
$189$		0			0
$190$	−0.495729			−0.0359640
$191$	6.55685	+	11.3568i	0.474437	+	0.821749i	0.999572	−	0.0292704i	$-0.00931840\pi$
$191$	6.55685	+	11.3568i	0.474437	+	0.821749i	−0.525135	+	0.851019i	$0.675985\pi$
$192$		0			0
$193$	−0.520786	+	0.902028i	−0.0374870	+	0.0649294i	−0.884160	−	0.467184i	$-0.845269\pi$
$193$	−0.520786	+	0.902028i	−0.0374870	+	0.0649294i	0.846673	+	0.532113i	$0.178602\pi$
$194$	18.0917	−	31.3358i	1.29891	−	2.24978i
$195$		0			0
$196$	−7.03722	−	7.34118i	−0.502658	−	0.524370i
$197$	0.739167	+	1.28027i	0.0526635	+	0.0912158i	0.891155	−	0.453698i	$-0.149896\pi$
$197$	0.739167	+	1.28027i	0.0526635	+	0.0912158i	−0.838492	+	0.544914i	$0.816562\pi$
$198$		0			0
$199$	14.0999			0.999512			0.499756	−	0.866166i	$-0.333423\pi$
$199$	14.0999			0.999512			0.499756	+	0.866166i	$0.333423\pi$
$200$	2.52233	+	4.36881i	0.178356	+	0.308922i
$201$		0			0
$202$	15.7330	−	27.2503i	1.10697	−	1.91733i
$203$	−21.6397	+	2.61657i	−1.51881	+	0.183647i
$204$		0			0
$205$	−1.06516			−0.0743937
$206$	−6.72120	+	11.6415i	−0.468288	+	0.811099i
$207$		0			0
$208$	13.0530	−	11.3365i	0.905064	−	0.786044i
$209$	5.65402			0.391097
$210$		0			0
$211$	−13.2346	−	22.9230i	−0.911108	−	1.57809i	−0.812501	−	0.582959i	$-0.801895\pi$
$211$	−13.2346	−	22.9230i	−0.911108	−	1.57809i	−0.0986067	−	0.995126i	$-0.531439\pi$
$212$	3.37619	+	5.84774i	0.231878	+	0.401624i
$213$		0			0
$214$	−18.3075			−1.25148
$215$	−0.525751	−	0.910628i	−0.0358559	−	0.0621043i
$216$		0			0
$217$	3.36391	−	0.406748i	0.228357	−	0.0276118i
$218$	−12.8361	−	22.2328i	−0.869370	−	1.50579i
$219$		0			0
$220$	−0.599638	−	1.03860i	−0.0404276	−	0.0700227i
$221$	2.29021	−	1.98904i	0.154056	−	0.133797i
$222$		0			0
$223$	0.364024	+	0.630508i	0.0243769	+	0.0422219i	0.877956	−	0.478740i	$-0.158907\pi$
$223$	0.364024	+	0.630508i	0.0243769	+	0.0422219i	−0.853580	+	0.520962i	$0.825573\pi$
$224$	7.13928	−	16.7333i	0.477013	−	1.11804i
$225$		0			0
$226$	3.96591	−	6.86916i	0.263808	−	0.456929i
$227$	2.85195			0.189291			0.0946454	−	0.995511i	$-0.469828\pi$
$227$	2.85195			0.189291			0.0946454	+	0.995511i	$0.469828\pi$
$228$		0			0
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	−0.913679	−	0.406436i	$-0.866772\pi$
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	0.808823	+	0.588052i	$0.200105\pi$
$230$	0.754584	−	1.30698i	0.0497558	−	0.0861795i
$231$		0			0
$232$	−4.18874	−	7.25511i	−0.275004	−	0.476321i
$233$	6.70354	−	11.6109i	0.439163	−	0.760653i	−0.558462	−	0.829530i	$-0.688608\pi$
$233$	6.70354	−	11.6109i	0.439163	−	0.760653i	0.997625	+	0.0688769i	$0.0219416\pi$
$234$		0			0
$235$	−1.15102	−	1.99363i	−0.0750845	−	0.130050i
$236$	−8.80099			−0.572896
$237$		0			0
$238$	1.62309	−	3.80427i	0.105210	−	0.246594i
$239$	15.5538			1.00609			0.503046	−	0.864259i	$-0.332212\pi$
$239$	15.5538			1.00609			0.503046	+	0.864259i	$0.332212\pi$
$240$		0			0
$241$	−7.57574			−0.487996			−0.243998	−	0.969776i	$-0.578459\pi$
$241$	−7.57574			−0.487996			−0.243998	+	0.969776i	$0.578459\pi$
$242$	6.03465	+	10.4523i	0.387922	+	0.671900i
$243$		0			0
$244$	8.25583	+	14.2995i	0.528525	+	0.915433i
$245$	1.34172	−	0.329283i	0.0857194	−	0.0210371i
$246$		0			0
$247$	4.60756	+	1.58883i	0.293172	+	0.101095i
$248$	0.651143	+	1.12781i	0.0413476	+	0.0716162i
$249$		0			0
$250$	3.65302			0.231038
$251$	0.637382	−	1.10398i	0.0402312	−	0.0696825i	−0.845209	−	0.534436i	$-0.820524\pi$
$251$	0.637382	−	1.10398i	0.0402312	−	0.0696825i	0.885440	+	0.464754i	$0.153857\pi$
$252$		0			0
$253$	−8.60638	+	14.9067i	−0.541079	+	0.937176i
$254$	−2.03491	−	3.52456i	−0.127682	−	0.221151i
$255$		0			0
$256$	20.9241			1.30776
$257$	8.48019			0.528980			0.264490	−	0.964388i	$-0.414796\pi$
$257$	8.48019			0.528980			0.264490	+	0.964388i	$0.414796\pi$
$258$		0			0
$259$	3.16135	−	7.40970i	0.196437	−	0.460416i
$260$	−0.196798	−	1.01488i	−0.0122049	−	0.0629402i
$261$		0			0
$262$	−2.11470	+	3.66276i	−0.130646	+	0.226286i
$263$	6.39415	−	11.0750i	0.394280	−	0.682913i	−0.598729	−	0.800952i	$-0.704327\pi$
$263$	6.39415	−	11.0750i	0.394280	−	0.682913i	0.993009	+	0.118038i	$0.0376606\pi$
$264$		0			0
$265$	−0.917333			−0.0563513
$266$	6.59747	−	0.797735i	0.404517	−	0.0489122i
$267$		0			0
$268$	−9.73135	+	16.8552i	−0.594437	+	1.02959i
$269$	4.71172			0.287278			0.143639	−	0.989630i	$-0.454120\pi$
$269$	4.71172			0.287278			0.143639	+	0.989630i	$0.454120\pi$
$270$		0			0
$271$	−18.0112			−1.09410			−0.547052	−	0.837098i	$-0.684250\pi$
$271$	−18.0112			−1.09410			−0.547052	+	0.837098i	$0.684250\pi$
$272$	4.03407			0.244601
$273$		0			0
$274$	24.9885			1.50961
$275$	−20.7508			−1.25132
$276$		0			0
$277$	−26.1209			−1.56945			−0.784725	−	0.619844i	$-0.787196\pi$
$277$	−26.1209			−1.56945			−0.784725	+	0.619844i	$0.787196\pi$
$278$	3.75850	−	6.50991i	0.225420	−	0.390439i
$279$		0			0
$280$	0.318766	+	0.424642i	0.0190499	+	0.0253772i
$281$	3.66197			0.218455			0.109227	−	0.994017i	$-0.465162\pi$
$281$	3.66197			0.218455			0.109227	+	0.994017i	$0.465162\pi$
$282$		0			0
$283$	−3.82263	+	6.62099i	−0.227232	+	0.393577i	−0.956987	−	0.290132i	$-0.906301\pi$
$283$	−3.82263	+	6.62099i	−0.227232	+	0.393577i	0.729755	+	0.683709i	$0.239634\pi$
$284$	−4.33678	+	7.51153i	−0.257341	+	0.445727i
$285$		0			0
$286$	5.33465	+	27.5106i	0.315445	+	1.62674i
$287$	14.1757	−	1.71406i	0.836768	−	0.101178i
$288$		0			0
$289$	−16.2922			−0.958365
$290$	−3.02135			−0.177420
$291$		0			0
$292$	−2.82233	−	4.88842i	−0.165164	−	0.286073i
$293$	−8.57670	+	14.8553i	−0.501056	+	0.867855i	0.498943	+	0.866635i	$0.333722\pi$
$293$	−8.57670	+	14.8553i	−0.501056	+	0.867855i	−0.999999	+	0.00122001i	$0.999612\pi$
$294$		0			0
$295$	0.597821	−	1.03546i	0.0348065	−	0.0602866i
$296$	3.09617			0.179961
$297$		0			0
$298$	−14.2632	−	24.7045i	−0.826244	−	1.43110i
$299$	−11.2024	+	9.72925i	−0.647852	+	0.562657i
$300$		0			0
$301$	8.46242	+	11.2732i	0.487766	+	0.649774i
$302$	5.68698	+	9.85014i	0.327249	+	0.566812i
$303$		0			0
$304$	3.24083	+	5.61328i	0.185874	+	0.321944i
$305$	−2.24316			−0.128443
$306$		0			0
$307$	−28.0696			−1.60201			−0.801007	−	0.598655i	$-0.795702\pi$
$307$	−28.0696			−1.60201			−0.801007	+	0.598655i	$0.795702\pi$
$308$	9.65169	+	12.8574i	0.549956	+	0.732621i
$309$		0			0
$310$	0.469672			0.0266756
$311$	−11.7670	−	20.3811i	−0.667248	−	1.15571i	−0.978671	−	0.205436i	$-0.934139\pi$
$311$	−11.7670	−	20.3811i	−0.667248	−	1.15571i	0.311423	−	0.950271i	$-0.399194\pi$
$312$		0			0
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	−0.814820	−	0.579714i	$-0.803164\pi$
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	0.909457	+	0.415798i	$0.136498\pi$
$314$	4.21494	+	7.30050i	0.237863	+	0.411991i
$315$		0			0
$316$	7.79652	−	13.5040i	0.438588	−	0.759658i
$317$	−3.63917	+	6.30323i	−0.204396	+	0.354025i	−0.949940	−	0.312432i	$-0.898856\pi$
$317$	−3.63917	+	6.30323i	−0.204396	+	0.354025i	0.745544	+	0.666456i	$0.232190\pi$
$318$		0			0
$319$	34.4600			1.92939
$320$	0.314501	−	0.544732i	0.0175811	−	0.0304514i
$321$		0			0
$322$	−7.93926	+	18.6084i	−0.442438	+	1.03700i
$323$	0.568618	+	0.984875i	0.0316388	+	0.0547999i
$324$		0			0
$325$	−16.9102	−	5.83116i	−0.938007	−	0.323455i
$326$	1.69329	+	2.93286i	0.0937826	+	0.162436i
$327$		0			0
$328$	2.74396	+	4.75268i	0.151510	+	0.262423i
$329$	18.5267	+	24.6802i	1.02141	+	1.36067i
$330$		0			0
$331$	7.16168	+	12.4044i	0.393642	+	0.681807i	0.992927	−	0.118728i	$-0.0378818\pi$
$331$	7.16168	+	12.4044i	0.393642	+	0.681807i	−0.599285	+	0.800536i	$0.704548\pi$
$332$	−4.46564			−0.245084
$333$		0			0
$334$	9.94855	+	17.2314i	0.544360	+	0.942860i
$335$	−1.32203	−	2.28983i	−0.0722304	−	0.125107i
$336$		0			0
$337$	17.1802			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$338$	−3.38344	+	23.9180i	−0.184035	+	1.30097i
$339$		0			0
$340$	0.120610	−	0.208902i	0.00654098	−	0.0113293i
$341$	−5.35683			−0.290089
$342$		0			0
$343$	−17.3266	+	6.54142i	−0.935547	+	0.353203i
$344$	−2.70879	+	4.69176i	−0.146048	+	0.252963i
$345$		0			0
$346$	12.5358	+	21.7126i	0.673928	+	1.16728i
$347$	7.70278			0.413507			0.206753	−	0.978393i	$-0.433710\pi$
$347$	7.70278			0.413507			0.206753	+	0.978393i	$0.433710\pi$
$348$		0			0
$349$	−11.1850	−	19.3730i	−0.598721	−	1.03702i	−0.993010	−	0.118029i	$-0.962343\pi$
$349$	−11.1850	−	19.3730i	−0.598721	−	1.03702i	0.394289	−	0.918986i	$-0.370991\pi$
$350$	−24.2133	+	2.92776i	−1.29426	+	0.156495i
$351$		0			0
$352$	−14.3806	+	24.9080i	−0.766490	+	1.32760i
$353$	−11.1311	+	19.2797i	−0.592451	+	1.02616i	0.401450	+	0.915881i	$0.368506\pi$
$353$	−11.1311	+	19.2797i	−0.592451	+	1.02616i	−0.993901	+	0.110275i	$0.964827\pi$
$354$		0			0
$355$	−0.589165	−	1.02046i	−0.0312697	−	0.0541606i
$356$	17.4101			0.922735
$357$		0			0
$358$	−9.72670	+	16.8471i	−0.514072	+	0.890399i
$359$	−1.37921	+	2.38887i	−0.0727920	+	0.126079i	−0.900124	−	0.435634i	$-0.856524\pi$
$359$	−1.37921	+	2.38887i	−0.0727920	+	0.126079i	0.827332	+	0.561713i	$0.189858\pi$
$360$		0			0
$361$	8.58638	−	14.8721i	0.451915	−	0.782740i
$362$	−23.2659			−1.22283
$363$		0			0
$364$	4.25227	+	13.1900i	0.222880	+	0.691342i
$365$	0.766844			0.0401385
$366$		0			0
$367$	7.07485	−	12.2540i	0.369304	−	0.639654i	−0.620153	−	0.784481i	$-0.712929\pi$
$367$	7.07485	−	12.2540i	0.369304	−	0.639654i	0.989457	+	0.144827i	$0.0462626\pi$
$368$	−19.7324			−1.02862
$369$		0			0
$370$	0.558320	−	0.967039i	0.0290257	−	0.0502740i
$371$	12.2084	−	1.47619i	0.633830	−	0.0766397i
$372$		0			0
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	0.923890	−	0.382657i	$-0.124991\pi$
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	−0.793336	+	0.608784i	$0.791658\pi$
$374$	−3.26940	+	5.66276i	−0.169056	+	0.292814i
$375$		0			0
$376$	−5.93034	+	10.2716i	−0.305834	+	0.529720i
$377$	28.0820	+	9.68358i	1.44630	+	0.498730i
$378$		0			0
$379$	3.02982	+	5.24780i	0.155631	+	0.269561i	0.933289	−	0.359127i	$-0.116925\pi$
$379$	3.02982	+	5.24780i	0.155631	+	0.269561i	−0.777657	+	0.628688i	$0.783592\pi$
$380$	0.387575			0.0198822
$381$		0			0
$382$	−12.1837	−	21.1028i	−0.623371	−	1.07971i
$383$	−2.27052	−	3.93266i	−0.116018	−	0.200950i	0.802168	−	0.597098i	$-0.203680\pi$
$383$	−2.27052	−	3.93266i	−0.116018	−	0.200950i	−0.918186	+	0.396149i	$0.870346\pi$
$384$		0			0
$385$	−2.16831	+	0.262182i	−0.110507	+	0.0133620i
$386$	0.967705	−	1.67611i	0.0492549	−	0.0853120i
$387$		0			0
$388$	−14.1446	+	24.4992i	−0.718085	+	1.24376i
$389$	2.25383	+	3.90374i	0.114273	+	0.197927i	0.917489	−	0.397761i	$-0.130213\pi$
$389$	2.25383	+	3.90374i	0.114273	+	0.197927i	−0.803216	+	0.595688i	$0.796879\pi$
$390$		0			0
$391$	−3.46213			−0.175088
$392$	−4.92567	−	5.13843i	−0.248784	−	0.259530i
$393$		0			0
$394$	−1.37349	−	2.37896i	−0.0691955	−	0.119850i
$395$	1.05918	+	1.83456i	0.0532932	+	0.0923065i
$396$		0			0
$397$	−2.00174	−	3.46712i	−0.100465	−	0.174010i	0.811412	−	0.584475i	$-0.198700\pi$
$397$	−2.00174	−	3.46712i	−0.100465	−	0.174010i	−0.911876	+	0.410465i	$0.865366\pi$
$398$	−26.1998			−1.31328
$399$		0			0
$400$	−11.8941	−	20.6012i	−0.594706	−	1.03006i
$401$	−12.6135			−0.629887			−0.314944	−	0.949110i	$-0.601986\pi$
$401$	−12.6135			−0.629887			−0.314944	+	0.949110i	$0.601986\pi$
$402$		0			0
$403$	−4.36537	−	1.50532i	−0.217455	−	0.0749853i
$404$	−12.3005	+	21.3051i	−0.611972	+	1.05997i
$405$		0			0
$406$	40.2101	−	4.86201i	1.99559	−	0.241297i
$407$	−6.36790	+	11.0295i	−0.315645	+	0.546713i
$408$		0			0
$409$	20.6952			1.02331			0.511657	−	0.859190i	$-0.329032\pi$
$409$	20.6952			1.02331			0.511657	+	0.859190i	$0.329032\pi$
$410$	1.97923			0.0977472
$411$		0			0
$412$	5.25482	−	9.10162i	0.258886	−	0.448404i
$413$	−6.28990	+	14.7425i	−0.309506	+	0.725432i
$414$		0			0
$415$	0.303336	−	0.525393i	0.0148902	−	0.0257905i
$416$	−18.7184	+	16.2569i	−0.917746	+	0.797058i
$417$		0			0
$418$	−10.5061			−0.513869
$419$	−10.9088	−	18.8945i	−0.532928	−	0.923058i	−0.999261	−	0.0384484i	$-0.987758\pi$
$419$	−10.9088	−	18.8945i	−0.532928	−	0.923058i	0.466333	−	0.884609i	$-0.345575\pi$
$420$		0			0
$421$	9.42727			0.459457			0.229728	−	0.973255i	$-0.426216\pi$
$421$	9.42727			0.459457			0.229728	+	0.973255i	$0.426216\pi$
$422$	24.5920	+	42.5947i	1.19712	+	2.07348i
$423$		0			0
$424$	2.36315	+	4.09310i	0.114765	+	0.198779i
$425$	−2.08688	−	3.61458i	−0.101228	−	0.175333i
$426$		0			0
$427$	29.8534	−	3.60973i	1.44471	−	0.174687i
$428$	14.3133			0.691861
$429$		0			0
$430$	0.976930	+	1.69209i	0.0471118	+	0.0816000i
$431$	10.2138	−	17.6908i	0.491980	−	0.852134i	−0.507977	−	0.861370i	$-0.669607\pi$
$431$	10.2138	−	17.6908i	0.491980	−	0.852134i	0.999957	+	0.00923613i	$0.00293999\pi$
$432$		0			0
$433$	−13.1743	+	22.8186i	−0.633117	+	1.09659i	0.353794	+	0.935323i	$0.384891\pi$
$433$	−13.1743	+	22.8186i	−0.633117	+	1.09659i	−0.986911	+	0.161267i	$0.948442\pi$
$434$	−6.25069	+	0.755803i	−0.300043	+	0.0362797i
$435$		0			0
$436$	10.0356	+	17.3822i	0.480619	+	0.832457i
$437$	−2.78136	−	4.81745i	−0.133050	−	0.230450i
$438$		0			0
$439$	25.1310			1.19944			0.599720	−	0.800210i	$-0.295279\pi$
$439$	25.1310			1.19944			0.599720	+	0.800210i	$0.295279\pi$
$440$	−0.419714	−	0.726967i	−0.0200091	−	0.0346568i
$441$		0			0
$442$	−4.25558	+	3.69595i	−0.202417	+	0.175799i
$443$	9.25995	−	16.0387i	0.439953	−	0.762022i	−0.557732	−	0.830021i	$-0.688328\pi$
$443$	9.25995	−	16.0387i	0.439953	−	0.762022i	0.997685	+	0.0679994i	$0.0216616\pi$
$444$		0			0
$445$	−1.18261	+	2.04834i	−0.0560611	+	0.0971006i
$446$	−0.676415	−	1.17159i	−0.0320292	−	0.0554762i
$447$		0			0
$448$	−3.30898	+	7.75573i	−0.156335	+	0.366424i
$449$	5.82155	−	10.0832i	0.274736	−	0.475856i	−0.695333	−	0.718688i	$-0.744743\pi$
$449$	5.82155	−	10.0832i	0.274736	−	0.475856i	0.970068	+	0.242832i	$0.0780763\pi$
$450$		0			0
$451$	−22.5740			−1.06297
$452$	−3.10066	+	5.37050i	−0.145843	+	0.252607i
$453$		0			0
$454$	−5.29939			−0.248713
$455$	−1.84067	−	0.395660i	−0.0862920	−	0.0185488i
$456$		0			0
$457$	20.5184			0.959812			0.479906	−	0.877320i	$-0.340671\pi$
$457$	20.5184			0.959812			0.479906	+	0.877320i	$0.340671\pi$
$458$	2.94845	−	5.10687i	0.137772	−	0.238629i
$459$		0			0
$460$	−0.589955	+	1.02183i	−0.0275068	+	0.0476431i
$461$	1.02038	−	1.76734i	0.0475236	−	0.0823134i	−0.841285	−	0.540592i	$-0.818200\pi$
$461$	1.02038	−	1.76734i	0.0475236	−	0.0823134i	0.888809	+	0.458278i	$0.151534\pi$
$462$		0			0
$463$	3.03155			0.140888			0.0704441	−	0.997516i	$-0.477558\pi$
$463$	3.03155			0.140888			0.0704441	+	0.997516i	$0.477558\pi$
$464$	19.7521	+	34.2116i	0.916968	+	1.58824i
$465$		0			0
$466$	−12.4563	+	21.5749i	−0.577025	+	0.999436i
$467$	−6.46371	+	11.1955i	−0.299105	+	0.518065i	−0.975931	−	0.218078i	$-0.930021\pi$
$467$	−6.46371	+	11.1955i	−0.299105	+	0.518065i	0.676827	+	0.736142i	$0.263355\pi$
$468$		0			0
$469$	21.2793	+	28.3470i	0.982585	+	1.30894i
$470$	2.13879	+	3.70449i	0.0986549	+	0.170875i
$471$		0			0
$472$	−6.16022			−0.283547
$473$	−11.1423	−	19.2991i	−0.512326	−	0.887374i
$474$		0			0
$475$	3.35305	−	5.80766i	0.153849	−	0.266474i
$476$	−1.26898	+	2.97429i	−0.0581637	+	0.136326i
$477$		0			0
$478$	−28.9015			−1.32192
$479$	18.2911	−	31.6810i	0.835740	−	1.44754i	−0.0576873	−	0.998335i	$-0.518373\pi$
$479$	18.2911	−	31.6810i	0.835740	−	1.44754i	0.893427	−	0.449209i	$-0.148294\pi$
$480$		0			0
$481$	−8.28872	+	7.19872i	−0.377933	+	0.328233i
$482$	14.0769			0.641187
$483$		0			0
$484$	−4.71806	−	8.17191i	−0.214457	−	0.371451i
$485$	−1.92159	−	3.32829i	−0.0872550	−	0.151130i
$486$		0			0
$487$	36.7496			1.66528			0.832642	−	0.553812i	$-0.186827\pi$
$487$	36.7496			1.66528			0.832642	+	0.553812i	$0.186827\pi$
$488$	5.77864	+	10.0089i	0.261587	+	0.453081i
$489$		0			0
$490$	−2.49313	+	0.611861i	−0.112628	+	0.0276411i
$491$	−4.09899	−	7.09965i	−0.184985	−	0.320403i	0.758587	−	0.651572i	$-0.225890\pi$
$491$	−4.09899	−	7.09965i	−0.184985	−	0.320403i	−0.943571	+	0.331169i	$0.892557\pi$
$492$		0			0
$493$	3.46560	+	6.00259i	0.156083	+	0.270343i
$494$	−8.56159	−	2.95231i	−0.385204	−	0.132831i
$495$		0			0
$496$	−3.07048	−	5.31823i	−0.137869	−	0.238795i
$497$	9.48313	+	12.6329i	0.425376	+	0.566662i
$498$		0			0
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.267211	−	0.963638i	$-0.413898\pi$
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.700929	−	0.713231i	$-0.252769\pi$
$500$	−2.85604			−0.127726
$501$		0			0
$502$	−1.18436	+	2.05137i	−0.0528605	+	0.0915571i
$503$	0.00909609	−	0.0157549i	0.000405575	−	0.000702476i	−0.865823	−	0.500351i	$-0.833204\pi$
$503$	0.00909609	−	0.0157549i	0.000405575	−	0.000702476i	0.866228	+	0.499649i	$0.166538\pi$
$504$		0			0
$505$	−1.67106	−	2.89436i	−0.0743612	−	0.128797i
$506$	15.9920	−	27.6990i	0.710933	−	1.23137i
$507$		0			0
$508$	1.59095	+	2.75560i	0.0705869	+	0.122260i
$509$	−43.1006			−1.91040			−0.955200	−	0.295960i	$-0.904361\pi$
$509$	−43.1006			−1.91040			−0.955200	+	0.295960i	$0.904361\pi$
$510$		0			0
$511$	−10.2056	+	1.23402i	−0.451471	+	0.0545897i
$512$	−23.2197			−1.02617
$513$		0			0
$514$	−15.7576			−0.695036
$515$	0.713884	+	1.23648i	0.0314575	+	0.0544859i
$516$		0			0
$517$	−24.3939	−	42.2514i	−1.07284	−	1.85822i
$518$	−5.87430	+	13.7684i	−0.258102	+	0.604949i
$519$		0			0
$520$	−0.137748	−	0.710362i	−0.00604065	−	0.0311514i
$521$	10.4770	+	18.1467i	0.459006	+	0.795022i	0.998909	−	0.0467056i	$-0.0148723\pi$
$521$	10.4770	+	18.1467i	0.459006	+	0.795022i	−0.539903	+	0.841727i	$0.681539\pi$
$522$		0			0
$523$	−34.7403			−1.51909			−0.759543	−	0.650457i	$-0.774577\pi$
$523$	−34.7403			−1.51909			−0.759543	+	0.650457i	$0.774577\pi$
$524$	1.65333	−	2.86365i	0.0722260	−	0.125099i
$525$		0			0
$526$	−11.8814	+	20.5791i	−0.518052	+	0.897292i
$527$	−0.538730	−	0.933107i	−0.0234674	−	0.0406468i
$528$		0			0
$529$	−6.06520			−0.263704
$530$	1.70455			0.0740410
$531$		0			0
$532$	−5.15809	+	0.623691i	−0.223631	+	0.0270404i
$533$	−18.3960	−	6.34352i	−0.796819	−	0.274769i
$534$		0			0
$535$	−0.972255	+	1.68400i	−0.0420343	+	0.0728055i
$536$	−6.81142	+	11.7977i	−0.294209	+	0.509584i
$537$		0			0
$538$	−8.75513			−0.377460
$539$	28.4353	−	6.97856i	1.22480	−	0.300588i
$540$		0			0
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	−0.828393	−	0.560148i	$-0.810744\pi$
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	0.899299	+	0.437335i	$0.144078\pi$
$542$	33.4678			1.43756
$543$		0			0
$544$	−5.78497			−0.248029
$545$	−2.72674			−0.116801
$546$		0			0
$547$	21.9417			0.938161			0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417			0.938161			0.469080	+	0.883155i	$0.344585\pi$
$548$	−19.5367			−0.834567
$549$		0			0
$550$	38.5583			1.64413
$551$	−5.56828	+	9.64455i	−0.237217	+	0.410871i
$552$		0			0
$553$	−17.0484	−	22.7110i	−0.724973	−	0.965768i
$554$	48.5368			2.06213
$555$		0			0
$556$	−2.93850	+	5.08963i	−0.124620	+	0.215848i
$557$	−7.14329	+	12.3725i	−0.302671	+	0.524241i	−0.976740	−	0.214427i	$-0.931212\pi$
$557$	−7.14329	+	12.3725i	−0.302671	+	0.524241i	0.674069	+	0.738668i	$0.264545\pi$
$558$		0			0
$559$	−3.65686	−	18.8583i	−0.154669	−	0.797621i
$560$	−1.50315	−	2.00241i	−0.0635196	−	0.0846172i
$561$		0			0
$562$	−6.80453			−0.287032
$563$	−6.78784			−0.286073			−0.143037	−	0.989717i	$-0.545687\pi$
$563$	−6.78784			−0.286073			−0.143037	+	0.989717i	$0.545687\pi$
$564$		0			0
$565$	−0.421234	−	0.729599i	−0.0177215	−	0.0306945i
$566$	7.10307	−	12.3029i	0.298564	−	0.517128i
$567$		0			0
$568$	−3.03552	+	5.25767i	−0.127367	+	0.220607i
$569$	17.3212			0.726143			0.363072	−	0.931761i	$-0.381728\pi$
$569$	17.3212			0.726143			0.363072	+	0.931761i	$0.381728\pi$
$570$		0			0
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	0.969440	−	0.245328i	$-0.0788957\pi$
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	−0.697180	+	0.716896i	$0.745562\pi$
$572$	−4.17078	−	21.5086i	−0.174389	−	0.899318i
$573$		0			0
$574$	−26.3408	+	3.18501i	−1.09944	+	0.132940i
$575$	10.2078	+	17.6805i	0.425696	+	0.737327i
$576$		0			0
$577$	0.365767	+	0.633528i	0.0152271	+	0.0263741i	0.873539	−	0.486755i	$-0.161820\pi$
$577$	0.365767	+	0.633528i	0.0152271	+	0.0263741i	−0.858311	+	0.513129i	$0.828486\pi$
$578$	30.2735			1.25921
$579$		0			0
$580$	2.36218			0.0980842
$581$	−3.19151	+	7.48039i	−0.132406	+	0.310339i
$582$		0			0
$583$	−19.4412			−0.805173
$584$	−1.97548	−	3.42163i	−0.0817459	−	0.141588i
$585$		0			0
$586$	15.9369	−	27.6035i	0.658347	−	1.14029i
$587$	−4.26142	−	7.38099i	−0.175888	−	0.304646i	0.764581	−	0.644528i	$-0.222946\pi$
$587$	−4.26142	−	7.38099i	−0.175888	−	0.304646i	−0.940468	+	0.339882i	$0.889613\pi$
$588$		0			0
$589$	0.865594	−	1.49925i	0.0356662	−	0.0617756i
$590$	−1.11085	+	1.92404i	−0.0457329	+	0.0792117i
$591$		0			0
$592$	−14.6001			−0.600059
$593$	−15.6547	+	27.1147i	−0.642860	+	1.11347i	0.341932	+	0.939725i	$0.388919\pi$
$593$	−15.6547	+	27.1147i	−0.642860	+	1.11347i	−0.984791	+	0.173741i	$0.944415\pi$
$594$		0			0
$595$	−0.263734	−	0.351332i	−0.0108120	−	0.0144032i
$596$	11.1514	+	19.3147i	0.456777	+	0.791161i
$597$		0			0
$598$	20.8159	−	18.0785i	0.851225	−	0.739285i
$599$	−0.375116	−	0.649720i	−0.0153268	−	0.0265468i	0.858260	−	0.513215i	$-0.171546\pi$
$599$	−0.375116	−	0.649720i	−0.0153268	−	0.0265468i	−0.873587	+	0.486668i	$0.838212\pi$
$600$		0			0
$601$	4.77652	+	8.27318i	0.194838	+	0.337470i	0.946848	−	0.321683i	$-0.104248\pi$
$601$	4.77652	+	8.27318i	0.194838	+	0.337470i	−0.752009	+	0.659153i	$0.770915\pi$
$602$	−15.7245	−	20.9473i	−0.640884	−	0.853750i
$603$		0			0
$604$	−4.44624	−	7.70111i	−0.180915	−	0.313354i
$605$	1.28193			0.0521177
$606$		0			0
$607$	−11.1197	−	19.2599i	−0.451336	−	0.781737i	0.547133	−	0.837045i	$-0.315719\pi$
$607$	−11.1197	−	19.2599i	−0.451336	−	0.781737i	−0.998469	+	0.0553087i	$0.982386\pi$
$608$	−4.64745	−	8.04961i	−0.188479	−	0.326455i
$609$		0			0
$610$	4.16815			0.168764
$611$	−8.00594	−	41.2863i	−0.323886	−	1.67027i
$612$		0			0
$613$	4.13993	−	7.17057i	0.167210	−	0.289617i	−0.770228	−	0.637769i	$-0.779857\pi$
$613$	4.13993	−	7.17057i	0.167210	−	0.289617i	0.937438	+	0.348152i	$0.113191\pi$
$614$	52.1578			2.10492
$615$		0			0
$616$	6.75567	+	8.99952i	0.272194	+	0.362601i
$617$	10.1656	−	17.6073i	0.409252	−	0.708845i	−0.585554	−	0.810633i	$-0.699123\pi$
$617$	10.1656	−	17.6073i	0.409252	−	0.708845i	0.994806	+	0.101789i	$0.0324565\pi$
$618$		0			0
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	0.807354	−	0.590067i	$-0.200899\pi$
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	−0.914690	+	0.404156i	$0.867565\pi$
$620$	−0.367203			−0.0147472
$621$		0			0
$622$	21.8651	+	37.8714i	0.876709	+	1.51850i
$623$	12.4427	−	29.1636i	0.498506	−	1.16842i
$624$		0			0
$625$	−12.2086	+	21.1459i	−0.488345	+	0.845838i
$626$	−3.11112	+	5.38862i	−0.124345	+	0.215372i
$627$		0			0
$628$	−3.29536	−	5.70773i	−0.131499	−	0.227763i
$629$	−2.56165			−0.102140
$630$		0			0
$631$	−3.23331	+	5.60026i	−0.128716	+	0.222943i	−0.923179	−	0.384369i	$-0.874419\pi$
$631$	−3.23331	+	5.60026i	−0.128716	+	0.222943i	0.794463	+	0.607312i	$0.207752\pi$
$632$	5.45714	−	9.45205i	0.217074	−	0.375982i
$633$		0			0
$634$	6.76217	−	11.7124i	0.268560	−	0.465160i
$635$	−0.432271			−0.0171541
$636$		0			0
$637$	25.1335	+	2.30365i	0.995826	+	0.0912741i
$638$	−64.0322			−2.53506
$639$		0			0
$640$	0.772706	−	1.33837i	0.0305439	−	0.0529035i
$641$	−23.3289			−0.921434			−0.460717	−	0.887547i	$-0.652408\pi$
$641$	−23.3289			−0.921434			−0.460717	+	0.887547i	$0.652408\pi$
$642$		0			0
$643$	1.79439	−	3.10797i	0.0707637	−	0.122566i	−0.828472	−	0.560030i	$-0.810790\pi$
$643$	1.79439	−	3.10797i	0.0707637	−	0.122566i	0.899236	+	0.437463i	$0.144123\pi$
$644$	6.20714	−	14.5485i	0.244596	−	0.573293i
$645$		0			0
$646$	−1.05658	−	1.83006i	−0.0415707	−	0.0720026i
$647$	−19.8262	+	34.3400i	−0.779448	+	1.35004i	0.152812	+	0.988255i	$0.451167\pi$
$647$	−19.8262	+	34.3400i	−0.779448	+	1.35004i	−0.932260	+	0.361788i	$0.882166\pi$
$648$		0			0
$649$	12.6697	−	21.9446i	0.497331	−	0.861402i
$650$	31.4218	+	10.8352i	1.23246	+	0.424993i
$651$		0			0
$652$	−1.32386	−	2.29299i	−0.0518464	−	0.0898005i
$653$	−18.1355			−0.709699			−0.354849	−	0.934923i	$-0.615468\pi$
$653$	−18.1355			−0.709699			−0.354849	+	0.934923i	$0.615468\pi$
$654$		0			0
$655$	0.224610	+	0.389035i	0.00877623	+	0.0152009i
$656$	−12.9392	−	22.4114i	−0.505192	−	0.875017i
$657$		0			0
$658$	−34.4256	−	45.8599i	−1.34205	−	1.78780i
$659$	6.74052	−	11.6749i	0.262573	−	0.454791i	−0.704352	−	0.709851i	$-0.748762\pi$
$659$	6.74052	−	11.6749i	0.262573	−	0.454791i	0.966925	+	0.255061i	$0.0820955\pi$
$660$		0			0
$661$	−5.15611	+	8.93064i	−0.200549	+	0.347362i	−0.948706	−	0.316161i	$-0.897606\pi$
$661$	−5.15611	+	8.93064i	−0.200549	+	0.347362i	0.748156	+	0.663523i	$0.230939\pi$
$662$	−13.3076	−	23.0494i	−0.517213	−	0.895839i
$663$		0			0
$664$	−3.12571			−0.121301
$665$	0.276992	−	0.649226i	0.0107413	−	0.0251759i
$666$		0			0
$667$	−16.9517	−	29.3613i	−0.656374	−	1.13687i
$668$	−7.77805	−	13.4720i	−0.300942	−	0.521247i
$669$		0			0
$670$	2.45655	+	4.25487i	0.0949049	+	0.164380i
$671$	−47.5397			−1.83525
$672$		0			0
$673$	4.61528	+	7.99390i	0.177906	+	0.308142i	0.941163	−	0.337953i	$-0.109734\pi$
$673$	4.61528	+	7.99390i	0.177906	+	0.308142i	−0.763257	+	0.646095i	$0.776401\pi$
$674$	−31.9237			−1.22965
$675$		0			0
$676$	2.64527	−	18.6997i	0.101741	−	0.719221i
$677$	−10.5467	+	18.2674i	−0.405343	+	0.702075i	−0.994361	−	0.106045i	$-0.966181\pi$
$677$	−10.5467	+	18.2674i	−0.405343	+	0.702075i	0.589018	+	0.808120i	$0.299515\pi$
$678$		0			0
$679$	30.9297	+	41.2027i	1.18697	+	1.58122i
$680$	0.0844203	−	0.146220i	0.00323737	−	0.00560729i
$681$		0			0
$682$	9.95385			0.381153
$683$	38.2212			1.46249			0.731246	−	0.682113i	$-0.238939\pi$
$683$	38.2212			1.46249			0.731246	+	0.682113i	$0.238939\pi$
$684$		0			0
$685$	1.32706	−	2.29854i	0.0507044	−	0.0878226i
$686$	32.1955	−	12.1550i	1.22923	−	0.464081i
$687$		0			0
$688$	12.7734	−	22.1241i	0.486980	−	0.843474i
$689$	−15.8430	−	5.46317i	−0.603570	−	0.208130i
$690$		0			0
$691$	−26.2322			−0.997920			−0.498960	−	0.866625i	$-0.666285\pi$
$691$	−26.2322			−0.997920			−0.498960	+	0.866625i	$0.666285\pi$
$692$	−9.80084	−	16.9755i	−0.372572	−	0.645313i
$693$		0			0
$694$	−14.3130			−0.543314
$695$	−0.399204	−	0.691442i	−0.0151427	−	0.0262279i
$696$		0			0
$697$	−2.27024	−	3.93218i	−0.0859916	−	0.148942i
$698$	20.7836	+	35.9982i	0.786670	+	1.36255i
$699$		0			0
$700$	18.9306	−	2.28900i	0.715511	−	0.0865161i
$701$	46.7346			1.76514			0.882570	−	0.470180i	$-0.155811\pi$
$701$	46.7346			1.76514			0.882570	+	0.470180i	$0.155811\pi$
$702$		0			0
$703$	−2.05794	−	3.56446i	−0.0776167	−	0.134436i
$704$	6.66528	−	11.5446i	0.251207	−	0.435104i
$705$		0			0
$706$	20.6835	−	35.8248i	0.778433	−	1.34828i
$707$	26.8972	+	35.8309i	1.01157	+	1.34756i
$708$		0			0
$709$	23.7232	+	41.0898i	0.890944	+	1.54316i	0.838745	+	0.544524i	$0.183290\pi$
$709$	23.7232	+	41.0898i	0.890944	+	1.54316i	0.0521988	+	0.998637i	$0.483377\pi$
$710$	1.09476	+	1.89619i	0.0410858	+	0.0711626i
$711$		0			0
$712$	12.1861			0.456695
$713$	2.63516	+	4.56423i	0.0986876	+	0.170932i
$714$		0			0
$715$	2.81384	+	0.970301i	0.105232	+	0.0362872i
$716$	7.60461	−	13.1716i	0.284197	−	0.492244i
$717$		0			0
$718$	2.56280	−	4.43890i	0.0956428	−	0.165658i
$719$	−24.6190	−	42.6413i	−0.918133	−	1.59025i	−0.802249	−	0.596990i	$-0.796363\pi$
$719$	−24.6190	−	42.6413i	−0.918133	−	1.59025i	−0.115884	−	0.993263i	$-0.536970\pi$
$720$		0			0
$721$	−11.4906	−	15.3071i	−0.427931	−	0.570066i
$722$	−15.9549	+	27.6347i	−0.593779	+	1.02846i
$723$		0			0
$724$	18.1900			0.676024
$725$	20.4361	−	35.3963i	0.758977	−	1.31459i
$726$		0			0
$727$	−32.0495			−1.18865			−0.594325	−	0.804225i	$-0.702581\pi$
$727$	−32.0495			−1.18865			−0.594325	+	0.804225i	$0.702581\pi$
$728$	2.97636	+	9.23227i	0.110311	+	0.342171i
$729$		0			0
$730$	−1.42492			−0.0527387
$731$	2.24114	−	3.88178i	0.0828917	−	0.143573i
$732$		0			0
$733$	−14.1005	+	24.4228i	−0.520813	+	0.902075i	0.478894	+	0.877873i	$0.341038\pi$
$733$	−14.1005	+	24.4228i	−0.520813	+	0.902075i	−0.999707	+	0.0242025i	$0.992295\pi$
$734$	−13.1462	+	22.7699i	−0.485236	+	0.840453i
$735$		0			0
$736$	28.2968			1.04303
$737$	−28.0181	−	48.5288i	−1.03206	−	1.78758i
$738$		0			0
$739$	21.2685	−	36.8381i	0.782375	−	1.35511i	−0.148180	−	0.988960i	$-0.547342\pi$
$739$	21.2685	−	36.8381i	0.782375	−	1.35511i	0.930555	−	0.366153i	$-0.119325\pi$
$740$	−0.436510	+	0.756058i	−0.0160464	+	0.0277932i
$741$		0			0
$742$	−22.6852	+	2.74299i	−0.832801	+	0.100698i
$743$	7.95711	+	13.7821i	0.291918	+	0.505617i	0.974263	−	0.225413i	$-0.0723732\pi$
$743$	7.95711	+	13.7821i	0.291918	+	0.505617i	−0.682345	+	0.731030i	$0.739040\pi$
$744$		0			0
$745$	−3.02989			−0.111007
$746$	−4.68521	−	8.11502i	−0.171538	−	0.297112i
$747$		0			0
$748$	2.55611	−	4.42731i	0.0934605	−	0.161878i
$749$	10.2295	−	23.9762i	0.373777	−	0.876072i
$750$		0			0
$751$	18.1996			0.664114			0.332057	−	0.943259i	$-0.392257\pi$
$751$	18.1996			0.664114			0.332057	+	0.943259i	$0.392257\pi$
$752$	27.9646	−	48.4362i	1.01977	−	1.76629i
$753$		0			0
$754$	−52.1809	−	17.9937i	−1.90032	−	0.655290i
$755$	1.20807			0.0439662
$756$		0			0
$757$	22.4502	+	38.8849i	0.815967	+	1.41330i	0.908632	+	0.417598i	$0.137128\pi$
$757$	22.4502	+	38.8849i	0.815967	+	1.41330i	−0.0926649	+	0.995697i	$0.529539\pi$
$758$	−5.62989	−	9.75126i	−0.204487	−	0.354182i
$759$		0			0
$760$	0.271282			0.00984042
$761$	−13.2444	−	22.9399i	−0.480108	−	0.831572i	0.519631	−	0.854391i	$-0.326069\pi$
$761$	−13.2444	−	22.9399i	−0.480108	−	0.831572i	−0.999740	+	0.0228184i	$0.992736\pi$
$762$		0			0
$763$	36.2892	−	4.38791i	1.31376	−	0.158853i
$764$	9.52554	+	16.4987i	0.344622	+	0.596903i
$765$		0			0
$766$	4.21900	+	7.30752i	0.152439	+	0.264031i
$767$	16.4914	−	14.3227i	0.595471	−	0.517164i
$768$		0			0
$769$	−6.98127	−	12.0919i	−0.251751	−	0.436045i	0.712257	−	0.701919i	$-0.247673\pi$
$769$	−6.98127	−	12.0919i	−0.251751	−	0.436045i	−0.964008	+	0.265873i	$0.914340\pi$
$770$	4.02907	−	0.487176i	0.145198	−	0.0175566i
$771$		0			0
$772$	−0.756579	+	1.31043i	−0.0272299	+	0.0471635i
$773$	−12.8113			−0.460790			−0.230395	−	0.973097i	$-0.574002\pi$
$773$	−12.8113			−0.460790			−0.230395	+	0.973097i	$0.574002\pi$
$774$		0			0
$775$	−3.17681	+	5.50239i	−0.114114	+	0.197652i
$776$	−9.90048	+	17.1481i	−0.355406	+	0.615582i
$777$		0			0
$778$	−4.18797	−	7.25378i	−0.150146	−	0.260061i
$779$	3.64767	−	6.31795i	0.130691	−	0.226364i
$780$		0			0
$781$	−12.4863	−	21.6269i	−0.446795	−	0.773871i
$782$	6.43320			0.230051
$783$		0			0
$784$	23.2271	+	24.2304i	0.829540	+	0.865372i
$785$	0.895370			0.0319571
$786$		0			0
$787$	−27.3199			−0.973848			−0.486924	−	0.873444i	$-0.661881\pi$
$787$	−27.3199			−0.973848			−0.486924	+	0.873444i	$0.661881\pi$
$788$	1.07383	+	1.85993i	0.0382537	+	0.0662574i
$789$		0			0
$790$	−1.96813	−	3.40890i	−0.0700229	−	0.121283i
$791$	6.78013	+	9.03210i	0.241074	+	0.321145i
$792$		0			0
$793$	−38.7410	−	13.3591i	−1.37573	−	0.474396i
$794$	3.71956	+	6.44247i	0.132002	+	0.228635i
$795$		0			0
$796$	20.4837			0.726027
$797$	−14.7002	+	25.4614i	−0.520707	+	0.901891i	0.479003	+	0.877813i	$0.340998\pi$
$797$	−14.7002	+	25.4614i	−0.520707	+	0.901891i	−0.999710	+	0.0240775i	$0.992335\pi$
$798$		0			0
$799$	4.90652	−	8.49835i	0.173580	−	0.300650i
$800$	17.0565	+	29.5428i	0.603040	+	1.04450i
$801$		0			0
$802$	23.4379			0.827621
$803$	16.2519			0.573517
$804$		0			0
$805$	1.29004	+	1.71852i	0.0454679	+	0.0605697i
$806$	8.11157	+	2.79713i	0.285718	+	0.0985246i
$807$		0			0
$808$	−8.60968	+	14.9124i	−0.302888	+	0.524617i
$809$	−3.00617	+	5.20683i	−0.105691	+	0.183063i	−0.914020	−	0.405668i	$-0.867039\pi$
$809$	−3.00617	+	5.20683i	−0.105691	+	0.183063i	0.808329	+	0.588731i	$0.200372\pi$
$810$		0			0
$811$	8.44807			0.296652			0.148326	−	0.988939i	$-0.452612\pi$
$811$	8.44807			0.296652			0.148326	+	0.988939i	$0.452612\pi$
$812$	−31.4374	+	3.80125i	−1.10323	+	0.133398i
$813$		0			0
$814$	11.8326	−	20.4946i	0.414732	−	0.718337i
$815$	0.359701			0.0125998
$816$		0			0
$817$	7.20184			0.251960
$818$	−38.4551			−1.34455
$819$		0			0
$820$	−1.54742			−0.0540382
$821$	34.2635			1.19581			0.597903	−	0.801569i	$-0.296001\pi$
$821$	34.2635			1.19581			0.597903	+	0.801569i	$0.296001\pi$
$822$		0			0
$823$	−6.23732			−0.217419			−0.108710	−	0.994074i	$-0.534672\pi$
$823$	−6.23732			−0.217419			−0.108710	+	0.994074i	$0.534672\pi$
$824$	3.67809	−	6.37064i	0.128132	−	0.221932i
$825$		0			0
$826$	11.6876	−	27.3940i	0.406665	−	0.953158i
$827$	−19.5232			−0.678889			−0.339445	−	0.940626i	$-0.610239\pi$
$827$	−19.5232			−0.678889			−0.339445	+	0.940626i	$0.610239\pi$
$828$		0			0
$829$	−16.3383	+	28.2988i	−0.567453	+	0.982857i	0.429364	+	0.903131i	$0.358738\pi$
$829$	−16.3383	+	28.2988i	−0.567453	+	0.982857i	−0.996817	+	0.0797254i	$0.974596\pi$
$830$	−0.563647	+	0.976265i	−0.0195645	+	0.0338866i
$831$		0			0
$832$	8.67580	−	7.53489i	0.300779	−	0.261225i
$833$	4.07530	+	4.25133i	0.141201	+	0.147300i
$834$		0			0
$835$	2.11334			0.0731353
$836$	8.21395			0.284085
$837$		0			0
$838$	20.2702	+	35.1091i	0.700223	+	1.21282i
$839$	12.3713	−	21.4278i	0.427106	−	0.739769i	−0.569508	−	0.821985i	$-0.692866\pi$
$839$	12.3713	−	21.4278i	0.427106	−	0.739769i	0.996615	+	0.0822161i	$0.0261998\pi$
$840$		0			0
$841$	−19.4374	+	33.6665i	−0.670255	+	1.16092i
$842$	−17.5174			−0.603689
$843$		0			0
$844$	−19.2267	−	33.3017i	−0.661812	−	1.14629i
$845$	2.02038	+	1.58143i	0.0695032	+	0.0544029i
$846$		0			0
$847$	−17.0607	+	2.06289i	−0.586211	+	0.0708818i
$848$	−11.1435	−	19.3011i	−0.382670	−	0.662803i
$849$		0			0
$850$	3.87776	+	6.71647i	0.133006	+	0.230373i
$851$	12.5301			0.429528
$852$		0			0
$853$	18.2245			0.623994			0.311997	−	0.950083i	$-0.399002\pi$
$853$	18.2245			0.623994			0.311997	+	0.950083i	$0.399002\pi$
$854$	−55.4724	+	6.70745i	−1.89823	+	0.229524i
$855$		0			0
$856$	10.0186			0.342427
$857$	1.27340	+	2.20559i	0.0434984	+	0.0753414i	0.886955	−	0.461856i	$-0.152816\pi$
$857$	1.27340	+	2.20559i	0.0434984	+	0.0753414i	−0.843457	+	0.537197i	$0.819483\pi$
$858$		0			0
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.124104	+	0.992269i	$0.539606\pi$
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.797278	+	0.603612i	$0.793728\pi$
$860$	−0.763792	−	1.32293i	−0.0260451	−	0.0451114i
$861$		0			0
$862$	−18.9788	+	32.8723i	−0.646421	+	1.11963i
$863$	0.621545	−	1.07655i	0.0211576	−	0.0366461i	−0.855253	−	0.518211i	$-0.826598\pi$
$863$	0.621545	−	1.07655i	0.0211576	−	0.0366461i	0.876410	+	0.481565i	$0.159931\pi$
$864$		0			0
$865$	2.66295			0.0905429
$866$	24.4800	−	42.4006i	0.831864	−	1.44083i
$867$		0			0
$868$	4.88696	−	0.590908i	0.165874	−	0.0200567i
$869$	22.4474	+	38.8801i	0.761477	+	1.31892i
$870$		0			0
$871$	−9.19540	−	47.4203i	−0.311574	−	1.60678i
$872$	7.02440	+	12.1666i	0.237876	+	0.412013i
$873$		0			0
$874$	5.16821	+	8.95161i	0.174817	+	0.302793i
$875$	−2.04116	+	4.78414i	−0.0690036	+	0.161733i
$876$		0			0
$877$	−0.401330	−	0.695125i	−0.0135520	−	0.0234727i	0.859170	−	0.511690i	$-0.170981\pi$
$877$	−0.401330	−	0.695125i	−0.0135520	−	0.0234727i	−0.872722	+	0.488218i	$0.837647\pi$
$878$	−46.6975			−1.57597
$879$		0			0
$880$	1.97917	+	3.42803i	0.0667179	+	0.115559i
$881$	−18.5318	−	32.0980i	−0.624352	−	1.08141i	−0.988666	−	0.150133i	$-0.952030\pi$
$881$	−18.5318	−	32.0980i	−0.624352	−	1.08141i	0.364314	−	0.931276i	$-0.381304\pi$
$882$		0			0
$883$	−22.8671			−0.769539			−0.384770	−	0.923013i	$-0.625719\pi$
$883$	−22.8671			−0.769539			−0.384770	+	0.923013i	$0.625719\pi$
$884$	3.32713	−	2.88960i	0.111904	−	0.0971877i
$885$		0			0
$886$	−17.2065	+	29.8025i	−0.578063	+	1.00123i
$887$	49.2573			1.65390			0.826950	−	0.562276i	$-0.190074\pi$
$887$	49.2573			1.65390			0.826950	+	0.562276i	$0.190074\pi$
$888$		0			0
$889$	5.75292	−	0.695616i	0.192947	−	0.0233302i
$890$	2.19748	−	3.80614i	0.0736597	−	0.127582i
$891$		0			0
$892$	0.528840	+	0.915978i	0.0177069	+	0.0306692i
$893$	15.7669			0.527620
$894$		0			0
$895$	1.03311	+	1.78940i	0.0345330	+	0.0598130i
$896$	−8.12993	+	19.0552i	−0.271602	+	0.636591i
$897$		0			0
$898$	−10.8174	+	18.7362i	−0.360980	+	0.625236i
$899$	5.27559	−	9.13760i	0.175951	−	0.304756i
$900$		0			0
$901$	−1.95518	−	3.38647i	−0.0651365	−	0.112820i
$902$	41.9462			1.39666
$903$		0			0
$904$	−2.17029	+	3.75906i	−0.0721829	+	0.125024i
$905$	−1.23558	+	2.14009i	−0.0410721	+	0.0711390i
$906$		0			0
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	−0.821488	−	0.570226i	$-0.806855\pi$
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	0.904574	+	0.426316i	$0.140189\pi$
$908$	4.14321			0.137497
$909$		0			0
$910$	3.42026	+	0.735200i	0.113381	+	0.0243716i
$911$	−49.0582			−1.62537			−0.812685	−	0.582703i	$-0.801995\pi$
$911$	−49.0582			−1.62537			−0.812685	+	0.582703i	$0.801995\pi$
$912$		0			0
$913$	6.42866	−	11.1348i	0.212757	−	0.368507i
$914$	−38.1266			−1.26111
$915$		0			0
$916$	−2.30518	+	3.99270i	−0.0761654	+	0.131922i
$917$	−3.61529	−	4.81608i	−0.119387	−	0.159041i
$918$		0			0
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	0.511611	−	0.859217i	$-0.329049\pi$
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	−0.999909	+	0.0134590i	$0.995716\pi$
$920$	−0.412937	+	0.715227i	−0.0136141	+	0.0235803i
$921$		0			0
$922$	−1.89602	+	3.28401i	−0.0624422	+	0.108153i
$923$	−4.09794	−	21.1329i	−0.134885	−	0.695598i
$924$		0			0
$925$	7.55282	+	13.0819i	0.248335	+	0.430129i
$926$	−5.63311			−0.185116
$927$		0			0
$928$	−28.3251	−	49.0605i	−0.929817	−	1.61049i
$929$	8.41525	+	14.5756i	0.276095	+	0.478211i	0.970411	−	0.241460i	$-0.0776261\pi$
$929$	8.41525	+	14.5756i	0.276095	+	0.478211i	−0.694316	+	0.719671i	$0.744293\pi$
$930$		0			0
$931$	−2.64164	+	9.08604i	−0.0865764	+	0.297783i
$932$	9.73865	−	16.8678i	0.319000	−	0.552524i
$933$		0			0
$934$	12.0106	−	20.8030i	0.392999	−	0.680695i
$935$	0.347255	+	0.601463i	0.0113565	+	0.0196699i
$936$		0			0
$937$	44.0131			1.43784			0.718922	−	0.695091i	$-0.244636\pi$
$937$	44.0131			1.43784			0.718922	+	0.695091i	$0.244636\pi$
$938$	−39.5403	−	52.6734i	−1.29104	−	1.71985i
$939$		0			0
$940$	−1.67216	−	2.89627i	−0.0545400	−	0.0944660i
$941$	26.5338	+	45.9578i	0.864976	+	1.49818i	0.867071	+	0.498184i	$0.166000\pi$
$941$	26.5338	+	45.9578i	0.864976	+	1.49818i	−0.00209573	+	0.999998i	$0.500667\pi$
$942$		0			0
$943$	11.1048	+	19.2340i	0.361620	+	0.626345i
$944$	29.0487			0.945453
$945$		0			0
$946$	20.7043	+	35.8609i	0.673154	+	1.16594i
$947$	27.8817			0.906034			0.453017	−	0.891502i	$-0.350348\pi$
$947$	27.8817			0.906034			0.453017	+	0.891502i	$0.350348\pi$
$948$		0			0
$949$	13.2439	+	4.56694i	0.429917	+	0.148249i
$950$	−6.23051	+	10.7916i	−0.202145	+	0.350125i
$951$		0			0
$952$	−0.888219	+	2.08184i	−0.0287873	+	0.0674729i
$953$	−18.1784	+	31.4859i	−0.588856	+	1.01993i	0.405527	+	0.914083i	$0.367088\pi$
$953$	−18.1784	+	31.4859i	−0.588856	+	1.01993i	−0.994383	+	0.105845i	$0.966245\pi$
$954$		0			0
$955$	−2.58815			−0.0837505
$956$	22.5960			0.730807
$957$		0			0
$958$	−33.9877	+	58.8685i	−1.09809	+	1.90195i
$959$	−13.9625	+	32.7259i	−0.450873	+	1.05677i
$960$		0			0
$961$	14.6799	−	25.4263i	0.473545	−	0.820205i
$962$	15.4018	−	13.3764i	0.496573	−	0.431272i
$963$		0			0
$964$	−11.0057			−0.354471
$965$	−0.102784	−	0.178026i	−0.00330872	−	0.00573087i
$966$		0			0
$967$	−15.2681			−0.490988			−0.245494	−	0.969398i	$-0.578950\pi$
$967$	−15.2681			−0.490988			−0.245494	+	0.969398i	$0.578950\pi$
$968$	−3.30239	−	5.71990i	−0.106143	−	0.183845i
$969$		0			0
$970$	3.57063	+	6.18450i	0.114646	+	0.198572i
$971$	−18.4460	−	31.9494i	−0.591961	−	1.02531i	−0.993968	−	0.109669i	$-0.965021\pi$
$971$	−18.4460	−	31.9494i	−0.591961	−	1.02531i	0.402008	−	0.915636i	$-0.368313\pi$
$972$		0			0
$973$	6.42554	+	8.55974i	0.205993	+	0.274413i
$974$	−68.2867			−2.18805
$975$		0			0
$976$	−27.2493	−	47.1972i	−0.872229	−	1.51074i
$977$	−0.221957	+	0.384441i	−0.00710104	+	0.0122994i	−0.869554	−	0.493838i	$-0.835594\pi$
$977$	−0.221957	+	0.384441i	−0.00710104	+	0.0122994i	0.862453	+	0.506137i	$0.168927\pi$
$978$		0			0
$979$	−25.0633	+	43.4109i	−0.801026	+	1.38742i
$980$	1.94920	−	0.478370i	0.0622649	−	0.0152810i
$981$		0			0
$982$	7.61658	+	13.1923i	0.243055	+	0.420983i
$983$	22.7802	+	39.4564i	0.726575	+	1.25846i	0.958323	+	0.285688i	$0.0922222\pi$
$983$	22.7802	+	39.4564i	0.726575	+	1.25846i	−0.231748	+	0.972776i	$0.574444\pi$
$984$		0			0
$985$	−0.291767			−0.00929648
$986$	−6.43964	−	11.1538i	−0.205080	−	0.355209i
$987$		0			0
$988$	6.69369	+	2.30820i	0.212955	+	0.0734336i
$989$	−10.9624	+	18.9875i	−0.348585	+	0.603766i
$990$		0			0
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	0.0277842	+	0.999614i	$0.491155\pi$
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	−0.879583	+	0.475745i	$0.842178\pi$
$992$	4.40316	+	7.62650i	0.139801	+	0.242142i
$993$		0			0
$994$	−17.6212	−	23.4739i	−0.558910	−	0.744548i
$995$	−1.39139	+	2.40996i	−0.0441100	+	0.0764008i
$996$		0			0
$997$	29.0852			0.921139			0.460569	−	0.887624i	$-0.347645\pi$
$997$	29.0852			0.921139			0.460569	+	0.887624i	$0.347645\pi$
$998$	−40.1857	+	69.6038i	−1.27206	+	2.20327i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.d.289.1		12
3.2	odd	2		91.2.h.b.16.6	yes	12
7.4	even	3		819.2.n.d.172.6		12
13.9	even	3		819.2.n.d.100.6		12
21.2	odd	6		637.2.f.k.393.1		12
21.5	even	6		637.2.f.j.393.1		12
21.11	odd	6		91.2.g.b.81.1	yes	12
21.17	even	6		637.2.g.l.263.1		12
21.20	even	2		637.2.h.l.471.6		12
39.23	odd	6		1183.2.e.g.170.6		12
39.29	odd	6		1183.2.e.h.170.1		12
39.35	odd	6		91.2.g.b.9.1	✓	12
91.74	even	3	inner	819.2.s.d.802.1		12
273.23	odd	6		8281.2.a.ce.1.1		6
273.68	even	6		8281.2.a.ca.1.6		6
273.74	odd	6		91.2.h.b.74.6	yes	12
273.107	odd	6		8281.2.a.bz.1.6		6
273.152	even	6		637.2.f.j.295.1		12
273.179	odd	6		1183.2.e.g.508.6		12
273.191	odd	6		637.2.f.k.295.1		12
273.230	even	6		637.2.g.l.373.1		12
273.257	even	6		8281.2.a.cf.1.1		6
273.263	odd	6		1183.2.e.h.508.1		12
273.269	even	6		637.2.h.l.165.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	39.35	odd	6
91.2.g.b.81.1	yes	12	21.11	odd	6
91.2.h.b.16.6	yes	12	3.2	odd	2
91.2.h.b.74.6	yes	12	273.74	odd	6
637.2.f.j.295.1		12	273.152	even	6
637.2.f.j.393.1		12	21.5	even	6
637.2.f.k.295.1		12	273.191	odd	6
637.2.f.k.393.1		12	21.2	odd	6
637.2.g.l.263.1		12	21.17	even	6
637.2.g.l.373.1		12	273.230	even	6
637.2.h.l.165.6		12	273.269	even	6
637.2.h.l.471.6		12	21.20	even	2
819.2.n.d.100.6		12	13.9	even	3
819.2.n.d.172.6		12	7.4	even	3
819.2.s.d.289.1		12	1.1	even	1	trivial
819.2.s.d.802.1		12	91.74	even	3	inner
1183.2.e.g.170.6		12	39.23	odd	6
1183.2.e.g.508.6		12	273.179	odd	6
1183.2.e.h.170.1		12	39.29	odd	6
1183.2.e.h.508.1		12	273.263	odd	6
8281.2.a.bz.1.6		6	273.107	odd	6
8281.2.a.ca.1.6		6	273.68	even	6
8281.2.a.ce.1.1		6	273.23	odd	6
8281.2.a.cf.1.1		6	273.257	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.85816 q^{2} +1.45276 q^{4} +(-0.0986811 + 0.170921i) q^{5} +(1.03826 - 2.43352i) q^{7} +1.01686 q^{8} +(0.183365 - 0.317598i) q^{10} +(-2.09137 + 3.62236i) q^{11} +(-2.72221 + 2.36423i) q^{13} +(-1.92926 + 4.52187i) q^{14} -4.79501 q^{16} -0.841305 q^{17} +(-0.675876 - 1.17065i) q^{19} +(-0.143360 + 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} +4.11519 q^{23} +(2.48052 + 4.29639i) q^{25} +(5.05830 - 4.39312i) q^{26} +(1.50835 - 3.53532i) q^{28} +(-4.11931 - 7.13485i) q^{29} +(0.640350 + 1.10912i) q^{31} +6.87618 q^{32} +1.56328 q^{34} +(0.313482 + 0.417603i) q^{35} +3.04485 q^{37} +(1.25589 + 2.17526i) q^{38} +(-0.100344 + 0.173802i) q^{40} +(2.69848 + 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} +(-3.03826 + 5.26242i) q^{44} -7.64669 q^{46} +(-5.83204 + 10.1014i) q^{47} +(-4.84403 - 5.05326i) q^{49} +(-4.60921 - 7.98339i) q^{50} +(-3.95472 + 3.43466i) q^{52} +(2.32398 + 4.02525i) q^{53} +(-0.412757 - 0.714916i) q^{55} +(1.05576 - 2.47454i) q^{56} +(7.65434 + 13.2577i) q^{58} -6.05811 q^{59} +(5.68285 + 9.84298i) q^{61} +(-1.18987 - 2.06092i) q^{62} -3.18704 q^{64} +(-0.135465 - 0.698587i) q^{65} +(-6.69851 + 11.6022i) q^{67} -1.22222 q^{68} +(-0.582500 - 0.775973i) q^{70} +(-2.98520 + 5.17051i) q^{71} +(-1.94273 - 3.36491i) q^{73} -5.65782 q^{74} +(-0.981887 - 1.70068i) q^{76} +(6.64368 + 8.85034i) q^{77} +(5.36669 - 9.29537i) q^{79} +(0.473177 - 0.819566i) q^{80} +(-5.01421 - 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 - 0.143797i) q^{85} +(4.94994 - 8.57354i) q^{86} +(-2.12662 + 3.68341i) q^{88} +11.9841 q^{89} +(2.92702 + 9.07924i) q^{91} +5.97840 q^{92} +(10.8369 - 18.7700i) q^{94} +0.266785 q^{95} +(-9.73637 + 16.8639i) q^{97} +(9.00098 + 9.38977i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29}+ \cdots - 20 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^13 + 2 * q^14 - 16 * q^16 + 10 * q^17 - q^19 + q^20 - 5 * q^22 - 2 * q^23 + 7 * q^25 + 16 * q^26 - q^28 - 3 * q^29 + 16 * q^31 + 16 * q^32 + 32 * q^34 - 20 * q^35 + 26 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 - 32 * q^46 + q^47 - 3 * q^49 - 6 * q^50 + 41 * q^52 + 2 * q^53 + 9 * q^55 - 9 * q^56 - 8 * q^58 + 26 * q^59 - 5 * q^61 - 5 * q^62 - 30 * q^64 + 5 * q^65 - 11 * q^67 + 58 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 - 6 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 + 7 * q^80 + q^82 + 54 * q^83 - q^85 + 7 * q^86 + 8 * q^89 - 23 * q^91 - 54 * q^92 + 45 * q^94 - 12 * q^95 - 35 * q^97 - 20 * q^98

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