LMFDB - Embedded newform 819.2.n.d.172.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.4
Root			$-0.437442 - 0.757672i$ of defining polynomial
Character	$\chi$	$=$	819.172
Dual form			819.2.n.d.100.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.134063 + 0.232203i) q^{2} +(0.964054 + 1.66979i) q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.773854 - 2.53005i) q^{7} -1.05323 q^{8} +0.686871 q^{10} -3.94600 q^{11} +(-3.15374 - 1.74755i) q^{13} +(0.483741 + 0.518876i) q^{14} +(-1.78691 + 3.09502i) q^{16} +(0.392550 + 0.679916i) q^{17} -7.49527 q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} +(-3.97759 + 6.88938i) q^{23} +(-0.781294 + 1.35324i) q^{25} +(0.828585 - 0.498028i) q^{26} +(4.97069 - 1.14693i) q^{28} +(1.17586 + 2.03666i) q^{29} +(1.27718 - 2.21215i) q^{31} +(-1.53234 - 2.65409i) q^{32} -0.210505 q^{34} +(-6.60424 + 1.52385i) q^{35} +(-3.37858 + 5.85187i) q^{37} +(1.00484 - 1.74043i) q^{38} +(1.34905 + 2.33663i) q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} +(-3.80416 - 6.58900i) q^{44} +(-1.06649 - 1.84722i) q^{46} +(0.658276 + 1.14017i) q^{47} +(-5.80230 - 3.91578i) q^{49} +(-0.209485 - 0.362838i) q^{50} +(-0.122340 - 6.95082i) q^{52} +(4.63977 - 8.03632i) q^{53} +(5.05434 + 8.75438i) q^{55} +(-0.815042 + 2.66471i) q^{56} -0.630558 q^{58} +(-4.48335 - 7.76540i) q^{59} +9.44547 q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(0.162546 + 9.23511i) q^{65} -1.35256 q^{67} +(-0.756879 + 1.31095i) q^{68} +(0.531538 - 1.73782i) q^{70} +(6.15808 - 10.6661i) q^{71} +(-0.384295 + 0.665619i) q^{73} +(-0.905882 - 1.56903i) q^{74} +(-7.22585 - 12.5155i) q^{76} +(-3.05363 + 9.98358i) q^{77} +(-3.09642 - 5.36316i) q^{79} +9.15525 q^{80} +0.653548 q^{82} +1.07292 q^{83} +(1.00562 - 1.74178i) q^{85} +(0.301568 + 0.522332i) q^{86} +4.15603 q^{88} +(3.83149 - 6.63634i) q^{89} +(-6.86191 + 6.62678i) q^{91} -15.3384 q^{92} -0.353001 q^{94} +(9.60052 + 16.6286i) q^{95} +(1.18601 - 2.05423i) q^{97} +(1.68713 - 0.822354i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29}+ \cdots - 62 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.134063	+	0.232203i	−0.0947966	+	0.164193i	−0.909524	−	0.415652i	$-0.863553\pi$
$2$	−0.134063	+	0.232203i	−0.0947966	+	0.164193i	0.814727	+	0.579845i	$0.196887\pi$
$3$		0			0
$3$		0			0
$4$	0.964054	+	1.66979i	0.482027	+	0.834896i
$5$	−1.28088	−	2.21854i	−0.572826	−	0.992163i	−0.996274	−	0.0862431i	$-0.972514\pi$
$5$	−1.28088	−	2.21854i	−0.572826	−	0.992163i	0.423448	−	0.905920i	$-0.360820\pi$
$6$		0			0
$7$	0.773854	−	2.53005i	0.292489	−	0.956269i
$7$	0.773854	−	2.53005i	0.292489	−	0.956269i
$8$	−1.05323			−0.372371
$9$		0			0
$10$	0.686871			0.217208
$11$	−3.94600			−1.18976			−0.594882	−	0.803813i	$-0.702801\pi$
$11$	−3.94600			−1.18976			−0.594882	+	0.803813i	$0.702801\pi$
$12$		0			0
$13$	−3.15374	−	1.74755i	−0.874690	−	0.484682i
$13$	−3.15374	−	1.74755i	−0.874690	−	0.484682i
$14$	0.483741	+	0.518876i	0.129285	+	0.138676i
$15$		0			0
$16$	−1.78691	+	3.09502i	−0.446728	+	0.773755i
$17$	0.392550	+	0.679916i	0.0952073	+	0.164904i	0.909695	−	0.415277i	$-0.136315\pi$
$17$	0.392550	+	0.679916i	0.0952073	+	0.164904i	−0.814488	+	0.580181i	$0.802982\pi$
$18$		0			0
$19$	−7.49527			−1.71953			−0.859767	−	0.510687i	$-0.829391\pi$
$19$	−7.49527			−1.71953			−0.859767	+	0.510687i	$0.829391\pi$
$20$	2.46967	−	4.27760i	0.552235	−	0.956500i
$21$		0			0
$22$	0.529011	−	0.916274i	0.112786	−	0.195350i
$23$	−3.97759	+	6.88938i	−0.829384	+	1.43654i	0.0691375	+	0.997607i	$0.477975\pi$
$23$	−3.97759	+	6.88938i	−0.829384	+	1.43654i	−0.898522	+	0.438929i	$0.855358\pi$
$24$		0			0
$25$	−0.781294	+	1.35324i	−0.156259	+	0.270648i
$26$	0.828585	−	0.498028i	0.162499	−	0.0976714i
$27$		0			0
$28$	4.97069	−	1.14693i	0.939372	−	0.216750i
$29$	1.17586	+	2.03666i	0.218353	+	0.378198i	0.954304	−	0.298836i	$-0.0965984\pi$
$29$	1.17586	+	2.03666i	0.218353	+	0.378198i	−0.735952	+	0.677034i	$0.763265\pi$
$30$		0			0
$31$	1.27718	−	2.21215i	0.229389	−	0.397313i	−0.728238	−	0.685324i	$-0.759661\pi$
$31$	1.27718	−	2.21215i	0.229389	−	0.397313i	0.957627	+	0.288011i	$0.0929939\pi$
$32$	−1.53234	−	2.65409i	−0.270882	−	0.469182i
$33$		0			0
$34$	−0.210505			−0.0361013
$35$	−6.60424	+	1.52385i	−1.11632	+	0.257578i
$36$		0			0
$37$	−3.37858	+	5.85187i	−0.555435	+	0.962041i	0.442435	+	0.896801i	$0.354115\pi$
$37$	−3.37858	+	5.85187i	−0.555435	+	0.962041i	−0.997870	+	0.0652406i	$0.979219\pi$
$38$	1.00484	−	1.74043i	0.163006	−	0.282334i
$39$		0			0
$40$	1.34905	+	2.33663i	0.213304	+	0.369453i
$41$	−1.21874	−	2.11091i	−0.190335	−	0.329669i	0.755027	−	0.655694i	$-0.227624\pi$
$41$	−1.21874	−	2.11091i	−0.190335	−	0.329669i	−0.945361	+	0.326025i	$0.894291\pi$
$42$		0			0
$43$	1.12473	−	1.94809i	0.171520	−	0.297081i	−0.767432	−	0.641131i	$-0.778466\pi$
$43$	1.12473	−	1.94809i	0.171520	−	0.297081i	0.938951	+	0.344050i	$0.111799\pi$
$44$	−3.80416	−	6.58900i	−0.573499	−	0.993329i
$45$		0			0
$46$	−1.06649	−	1.84722i	−0.157246	−	0.272357i
$47$	0.658276	+	1.14017i	0.0960195	+	0.166311i	0.910034	−	0.414534i	$-0.136056\pi$
$47$	0.658276	+	1.14017i	0.0960195	+	0.166311i	−0.814014	+	0.580845i	$0.802722\pi$
$48$		0			0
$49$	−5.80230	−	3.91578i	−0.828900	−	0.559397i
$50$	−0.209485	−	0.362838i	−0.0296256	−	0.0513130i
$51$		0			0
$52$	−0.122340	−	6.95082i	−0.0169655	−	0.963905i
$53$	4.63977	−	8.03632i	0.637321	−	1.10387i	−0.348697	−	0.937236i	$-0.613376\pi$
$53$	4.63977	−	8.03632i	0.637321	−	1.10387i	0.986018	−	0.166637i	$-0.0532909\pi$
$54$		0			0
$55$	5.05434	+	8.75438i	0.681528	+	1.18044i
$56$	−0.815042	+	2.66471i	−0.108915	+	0.356087i
$57$		0			0
$58$	−0.630558			−0.0827963
$59$	−4.48335	−	7.76540i	−0.583683	−	1.01097i	−0.995038	−	0.0994935i	$-0.968278\pi$
$59$	−4.48335	−	7.76540i	−0.583683	−	1.01097i	0.411355	−	0.911475i	$-0.365056\pi$
$60$		0			0
$61$	9.44547			1.20937			0.604684	−	0.796465i	$-0.293299\pi$
$61$	9.44547			1.20937			0.604684	+	0.796465i	$0.293299\pi$
$62$	0.342445	+	0.593132i	0.0434906	+	0.0753279i
$63$		0			0
$64$	−6.32592			−0.790741
$65$	0.162546	+	9.23511i	0.0201613	+	1.14547i
$66$		0			0
$67$	−1.35256			−0.165242			−0.0826209	−	0.996581i	$-0.526329\pi$
$67$	−1.35256			−0.165242			−0.0826209	+	0.996581i	$0.526329\pi$
$68$	−0.756879	+	1.31095i	−0.0917851	+	0.158976i
$69$		0			0
$70$	0.531538	−	1.73782i	0.0635309	−	0.207709i
$71$	6.15808	−	10.6661i	0.730829	−	1.26583i	−0.225700	−	0.974197i	$-0.572467\pi$
$71$	6.15808	−	10.6661i	0.730829	−	1.26583i	0.956529	−	0.291637i	$-0.0941998\pi$
$72$		0			0
$73$	−0.384295	+	0.665619i	−0.0449783	+	0.0779048i	−0.887638	−	0.460542i	$-0.847655\pi$
$73$	−0.384295	+	0.665619i	−0.0449783	+	0.0779048i	0.842660	+	0.538446i	$0.180989\pi$
$74$	−0.905882	−	1.56903i	−0.105307	−	0.182396i
$75$		0			0
$76$	−7.22585	−	12.5155i	−0.828862	−	1.43563i
$77$	−3.05363	+	9.98358i	−0.347993	+	1.13773i
$78$		0			0
$79$	−3.09642	−	5.36316i	−0.348375	−	0.603402i	0.637586	−	0.770379i	$-0.279933\pi$
$79$	−3.09642	−	5.36316i	−0.348375	−	0.603402i	−0.985961	+	0.166976i	$0.946600\pi$
$80$	9.15525			1.02359
$81$		0			0
$82$	0.653548			0.0721723
$83$	1.07292			0.117768			0.0588841	−	0.998265i	$-0.481246\pi$
$83$	1.07292			0.117768			0.0588841	+	0.998265i	$0.481246\pi$
$84$		0			0
$85$	1.00562	−	1.74178i	0.109074	−	0.188922i
$86$	0.301568	+	0.522332i	0.0325190	+	0.0563245i
$87$		0			0
$88$	4.15603			0.443034
$89$	3.83149	−	6.63634i	0.406138	−	0.703451i	−0.588316	−	0.808631i	$-0.700209\pi$
$89$	3.83149	−	6.63634i	0.406138	−	0.703451i	0.994453	+	0.105180i	$0.0335420\pi$
$90$		0			0
$91$	−6.86191	+	6.62678i	−0.719324	+	0.694675i
$92$	−15.3384			−1.59914
$93$		0			0
$94$	−0.353001			−0.0364093
$95$	9.60052	+	16.6286i	0.984993	+	1.70606i
$96$		0			0
$97$	1.18601	−	2.05423i	0.120421	−	0.208575i	−0.799513	−	0.600649i	$-0.794909\pi$
$97$	1.18601	−	2.05423i	0.120421	−	0.208575i	0.919934	+	0.392074i	$0.128242\pi$
$98$	1.68713	−	0.822354i	0.170426	−	0.0830703i
$99$		0			0
$100$	−3.01284			−0.301284
$101$	0.797330			0.0793373			0.0396686	−	0.999213i	$-0.487370\pi$
$101$	0.797330			0.0793373			0.0396686	+	0.999213i	$0.487370\pi$
$102$		0			0
$103$	−1.08309	−	1.87597i	−0.106720	−	0.184844i	0.807720	−	0.589567i	$-0.200701\pi$
$103$	−1.08309	−	1.87597i	−0.106720	−	0.184844i	−0.914440	+	0.404722i	$0.867368\pi$
$104$	3.32160	+	1.84056i	0.325710	+	0.180482i
$105$		0			0
$106$	1.24404	+	2.15474i	0.120832	+	0.209287i
$107$	−5.76311	+	9.98201i	−0.557141	+	0.964997i	0.440592	+	0.897707i	$0.354768\pi$
$107$	−5.76311	+	9.98201i	−0.557141	+	0.964997i	−0.997733	+	0.0672896i	$0.978565\pi$
$108$		0			0
$109$	−4.03912	+	6.99595i	−0.386877	+	0.670091i	−0.992028	−	0.126020i	$-0.959780\pi$
$109$	−4.03912	+	6.99595i	−0.386877	+	0.670091i	0.605151	+	0.796111i	$0.293113\pi$
$110$	−2.71039			−0.258426
$111$		0			0
$112$	6.44775	+	6.91607i	0.609255	+	0.653507i
$113$	4.02067	−	6.96401i	0.378233	−	0.655119i	−0.612572	−	0.790415i	$-0.709865\pi$
$113$	4.02067	−	6.96401i	0.378233	−	0.655119i	0.990805	+	0.135296i	$0.0431984\pi$
$114$		0			0
$115$	20.3792			1.90037
$116$	−2.26719	+	3.92690i	−0.210504	+	0.364603i
$117$		0			0
$118$	2.40420			0.221325
$119$	2.02400	−	0.467015i	0.185540	−	0.0428112i
$120$		0			0
$121$	4.57093			0.415539
$122$	−1.26628	+	2.19327i	−0.114644	+	0.198569i
$123$		0			0
$124$	4.92510			0.442287
$125$	−8.80581			−0.787615
$126$		0			0
$127$	−0.894023	−	1.54849i	−0.0793317	−	0.137406i	0.823630	−	0.567127i	$-0.191945\pi$
$127$	−0.894023	−	1.54849i	−0.0793317	−	0.137406i	−0.902962	+	0.429721i	$0.858612\pi$
$128$	3.91275	−	6.77709i	0.345842	−	0.599015i
$129$		0			0
$130$	−2.16621	−	1.20034i	−0.189989	−	0.105277i
$131$	−3.19545	−	5.53469i	−0.279188	−	0.483568i	0.691995	−	0.721902i	$-0.256732\pi$
$131$	−3.19545	−	5.53469i	−0.279188	−	0.483568i	−0.971183	+	0.238334i	$0.923399\pi$
$132$		0			0
$133$	−5.80024	+	18.9634i	−0.502945	+	1.64434i
$134$	0.181328	−	0.314069i	0.0156644	−	0.0271315i
$135$		0			0
$136$	−0.413443	−	0.716105i	−0.0354525	−	0.0614055i
$137$	5.01827	+	8.69190i	0.428740	+	0.742599i	0.996762	−	0.0804144i	$-0.0256244\pi$
$137$	5.01827	+	8.69190i	0.428740	+	0.742599i	−0.568022	+	0.823014i	$0.692291\pi$
$138$		0			0
$139$	2.77278	−	4.80260i	0.235184	−	0.407351i	−0.724142	−	0.689651i	$-0.757764\pi$
$139$	2.77278	−	4.80260i	0.235184	−	0.407351i	0.959326	+	0.282300i	$0.0910972\pi$
$140$	−8.91137	−	9.55862i	−0.753148	−	0.807851i
$141$		0			0
$142$	1.65114	+	2.85985i	0.138560	+	0.239993i
$143$	12.4447	+	6.89582i	1.04068	+	0.576658i
$144$		0			0
$145$	3.01228	−	5.21742i	0.250156	−	0.433283i
$146$	−0.103039	−	0.178469i	−0.00852759	−	0.0147702i
$147$		0			0
$148$	−13.0285			−1.07094
$149$	−18.4651			−1.51272			−0.756359	−	0.654157i	$-0.773024\pi$
$149$	−18.4651			−1.51272			−0.756359	+	0.654157i	$0.773024\pi$
$150$		0			0
$151$	−0.803678	+	1.39201i	−0.0654024	+	0.113280i	−0.896872	−	0.442289i	$-0.854166\pi$
$151$	−0.803678	+	1.39201i	−0.0654024	+	0.113280i	0.831470	+	0.555570i	$0.187500\pi$
$152$	7.89421			0.640305
$153$		0			0
$154$	−1.90884	−	2.04749i	−0.153819	−	0.164991i
$155$	−6.54366			−0.525600
$156$		0			0
$157$	0.822967	−	1.42542i	0.0656799	−	0.113761i	−0.831315	−	0.555801i	$-0.812412\pi$
$157$	0.822967	−	1.42542i	0.0656799	−	0.113761i	0.896995	+	0.442040i	$0.145745\pi$
$158$	1.66046			0.132099
$159$		0			0
$160$	−3.92548	+	6.79913i	−0.310337	+	0.537519i
$161$	14.3524	+	15.3949i	1.13113	+	1.21329i
$162$		0			0
$163$	−6.54819			−0.512894			−0.256447	−	0.966558i	$-0.582552\pi$
$163$	−6.54819			−0.512894			−0.256447	+	0.966558i	$0.582552\pi$
$164$	2.34986	−	4.07007i	0.183493	−	0.317819i
$165$		0			0
$166$	−0.143838	+	0.249135i	−0.0111640	+	0.0193367i
$167$	4.77440	+	8.26950i	0.369454	+	0.639913i	0.989480	−	0.144668i	$-0.0462114\pi$
$167$	4.77440	+	8.26950i	0.369454	+	0.639913i	−0.620026	+	0.784581i	$0.712878\pi$
$168$		0			0
$169$	6.89216	+	11.0226i	0.530166	+	0.847894i
$170$	0.269631	+	0.467015i	0.0206798	+	0.0358184i
$171$		0			0
$172$	4.33720			0.330709
$173$	−11.1316			−0.846322			−0.423161	−	0.906054i	$-0.639080\pi$
$173$	−11.1316			−0.846322			−0.423161	+	0.906054i	$0.639080\pi$
$174$		0			0
$175$	2.81916	+	3.02392i	0.213108	+	0.228587i
$176$	7.05115	−	12.2130i	0.531501	−	0.920586i
$177$		0			0
$178$	1.02732	+	1.77937i	0.0770009	+	0.133369i
$179$	12.6435			0.945017			0.472508	−	0.881326i	$-0.343349\pi$
$179$	12.6435			0.945017			0.472508	+	0.881326i	$0.343349\pi$
$180$		0			0
$181$	14.9158			1.10868			0.554341	−	0.832289i	$-0.312970\pi$
$181$	14.9158			1.10868			0.554341	+	0.832289i	$0.312970\pi$
$182$	−0.618833	−	2.48176i	−0.0458709	−	0.183960i
$183$		0			0
$184$	4.18930	−	7.25607i	0.308839	−	0.534925i
$185$	17.3102			1.27267
$186$		0			0
$187$	−1.54900	−	2.68295i	−0.113274	−	0.196197i
$188$	−1.26923	+	2.19837i	−0.0925680	+	0.160332i
$189$		0			0
$190$	−5.14829			−0.373496
$191$	14.1306			1.02245			0.511226	−	0.859447i	$-0.329192\pi$
$191$	14.1306			1.02245			0.511226	+	0.859447i	$0.329192\pi$
$192$		0			0
$193$	3.89454			0.280335			0.140167	−	0.990128i	$-0.455236\pi$
$193$	3.89454			0.280335			0.140167	+	0.990128i	$0.455236\pi$
$194$	0.317999	+	0.550790i	0.0228310	+	0.0395444i
$195$		0			0
$196$	0.944795	−	13.4637i	0.0674853	−	0.961689i
$197$	−5.85445	−	10.1402i	−0.417112	−	0.722459i	0.578536	−	0.815657i	$-0.303624\pi$
$197$	−5.85445	−	10.1402i	−0.417112	−	0.722459i	−0.995648	+	0.0931979i	$0.970291\pi$
$198$		0			0
$199$	−1.74842	−	3.02835i	−0.123942	−	0.214674i	0.797377	−	0.603482i	$-0.206220\pi$
$199$	−1.74842	−	3.02835i	−0.123942	−	0.214674i	−0.921319	+	0.388808i	$0.872887\pi$
$200$	0.822878	−	1.42527i	0.0581863	−	0.100782i
$201$		0			0
$202$	−0.106892	+	0.185143i	−0.00752090	+	0.0130266i
$203$	6.06279	−	1.39892i	0.425524	−	0.0981850i
$204$		0			0
$205$	−3.12210	+	5.40764i	−0.218057	+	0.377686i
$206$	0.580807			0.0404667
$207$		0			0
$208$	11.0441	−	6.63818i	0.765774	−	0.460275i
$209$	29.5764			2.04584
$210$		0			0
$211$	−9.50258	−	16.4589i	−0.654184	−	1.13308i	−0.982098	−	0.188373i	$-0.939679\pi$
$211$	−9.50258	−	16.4589i	−0.654184	−	1.13308i	0.327913	−	0.944708i	$-0.393655\pi$
$212$	17.8920			1.22882
$213$		0			0
$214$	−1.54524	−	2.67643i	−0.105630	−	0.182957i
$215$	−5.76256			−0.393004
$216$		0			0
$217$	−4.60849	−	4.94321i	−0.312844	−	0.335567i
$218$	−1.08299	−	1.87579i	−0.0733492	−	0.127045i
$219$		0			0
$220$	−9.74533	+	16.8794i	−0.657030	+	1.13801i
$221$	−0.0498153	−	2.83028i	−0.00335094	−	0.190385i
$222$		0			0
$223$	5.98311	+	10.3630i	0.400658	+	0.693961i	0.993805	−	0.111133i	$-0.0354481\pi$
$223$	5.98311	+	10.3630i	0.400658	+	0.693961i	−0.593147	+	0.805094i	$0.702115\pi$
$224$	−7.90079	+	1.82302i	−0.527894	+	0.121806i
$225$		0			0
$226$	1.07804	+	1.86723i	0.0717104	+	0.124206i
$227$	7.69209	+	13.3231i	0.510542	+	0.884284i	0.999925	+	0.0122157i	$0.00388847\pi$
$227$	7.69209	+	13.3231i	0.510542	+	0.884284i	−0.489384	+	0.872069i	$0.662778\pi$
$228$		0			0
$229$	−4.33084	−	7.50123i	−0.286190	−	0.495695i	0.686707	−	0.726934i	$-0.259055\pi$
$229$	−4.33084	−	7.50123i	−0.286190	−	0.495695i	−0.972897	+	0.231239i	$0.925722\pi$
$230$	−2.73209	+	4.73212i	−0.180149	+	0.312027i
$231$		0			0
$232$	−1.23845	−	2.14506i	−0.0813082	−	0.140830i
$233$	10.1253	+	17.5376i	0.663333	+	1.14893i	0.979734	+	0.200301i	$0.0641919\pi$
$233$	10.1253	+	17.5376i	0.663333	+	1.14893i	−0.316402	+	0.948625i	$0.602475\pi$
$234$		0			0
$235$	1.68634	−	2.92083i	0.110005	−	0.190534i
$236$	8.64440	−	14.9725i	0.562702	−	0.974629i
$237$		0			0
$238$	−0.162900	+	0.532588i	−0.0105592	+	0.0345226i
$239$	−16.5526			−1.07070			−0.535350	−	0.844630i	$-0.679820\pi$
$239$	−16.5526			−1.07070			−0.535350	+	0.844630i	$0.679820\pi$
$240$		0			0
$241$	8.20038	+	14.2035i	0.528233	+	0.914926i	0.999458	+	0.0329132i	$0.0104785\pi$
$241$	8.20038	+	14.2035i	0.528233	+	0.914926i	−0.471225	+	0.882013i	$0.656188\pi$
$242$	−0.612791	+	1.06138i	−0.0393917	+	0.0682284i
$243$		0			0
$244$	9.10595	+	15.7720i	0.582949	+	1.00970i
$245$	−1.25529	+	17.8883i	−0.0801974	+	1.14284i
$246$		0			0
$247$	23.6381	+	13.0983i	1.50406	+	0.833427i
$248$	−1.34516	+	2.32989i	−0.0854178	+	0.147948i
$249$		0			0
$250$	1.18053	−	2.04474i	0.0746632	−	0.129321i
$251$	−10.2154	+	17.6935i	−0.644788	+	1.11681i	0.339563	+	0.940583i	$0.389721\pi$
$251$	−10.2154	+	17.6935i	−0.644788	+	1.11681i	−0.984350	+	0.176222i	$0.943612\pi$
$252$		0			0
$253$	15.6956	−	27.1855i	0.986772	−	1.70914i
$254$	0.479420			0.0300815
$255$		0			0
$256$	−5.27682	−	9.13972i	−0.329801	−	0.571232i
$257$	6.88895	−	11.9320i	0.429721	−	0.744299i	−0.567127	−	0.823630i	$-0.691945\pi$
$257$	6.88895	−	11.9320i	0.429721	−	0.744299i	0.996848	+	0.0793315i	$0.0252786\pi$
$258$		0			0
$259$	12.1910	+	13.0765i	0.757511	+	0.812532i
$260$	−15.2640	+	9.17456i	−0.946633	+	0.568982i
$261$		0			0
$262$	1.71356			0.105864
$263$	−25.9173			−1.59813			−0.799065	−	0.601244i	$-0.794672\pi$
$263$	−25.9173			−1.59813			−0.799065	+	0.601244i	$0.794672\pi$
$264$		0			0
$265$	−23.7719			−1.46030
$266$	−3.62577	−	3.88912i	−0.222310	−	0.238457i
$267$		0			0
$268$	−1.30394	−	2.25850i	−0.0796510	−	0.137960i
$269$	−15.0333	−	26.0384i	−0.916596	−	1.58759i	−0.804547	−	0.593889i	$-0.797592\pi$
$269$	−15.0333	−	26.0384i	−0.916596	−	1.58759i	−0.112050	−	0.993703i	$-0.535742\pi$
$270$		0			0
$271$	−7.22527	+	12.5145i	−0.438904	+	0.760204i	−0.997605	−	0.0691651i	$-0.977966\pi$
$271$	−7.22527	+	12.5145i	−0.438904	+	0.760204i	0.558701	+	0.829369i	$0.311300\pi$
$272$	−2.80581			−0.170127
$273$		0			0
$274$	−2.69105			−0.162572
$275$	3.08299	−	5.33989i	0.185911	−	0.322008i
$276$		0			0
$277$	7.66274	+	13.2723i	0.460409	+	0.797452i	0.998981	−	0.0451272i	$-0.0143693\pi$
$277$	7.66274	+	13.2723i	0.460409	+	0.797452i	−0.538572	+	0.842580i	$0.681036\pi$
$278$	0.743453	+	1.28770i	0.0445894	+	0.0772310i
$279$		0			0
$280$	6.95575	−	1.60496i	0.415686	−	0.0959148i
$281$	−5.29279			−0.315741			−0.157871	−	0.987460i	$-0.550463\pi$
$281$	−5.29279			−0.315741			−0.157871	+	0.987460i	$0.550463\pi$
$282$		0			0
$283$	−30.7845			−1.82995			−0.914975	−	0.403511i	$-0.867790\pi$
$283$	−30.7845			−1.82995			−0.914975	+	0.403511i	$0.867790\pi$
$284$	23.7469			1.40912
$285$		0			0
$286$	−3.26960	+	1.96522i	−0.193335	+	0.116206i
$287$	−6.28384	+	1.44992i	−0.370923	+	0.0855864i
$288$		0			0
$289$	8.19181	−	14.1886i	0.481871	−	0.834625i
$290$	0.807667	+	1.39892i	0.0474279	+	0.0821474i
$291$		0			0
$292$	−1.48193			−0.0867231
$293$	−8.75864	+	15.1704i	−0.511685	+	0.886265i	0.488223	+	0.872719i	$0.337645\pi$
$293$	−8.75864	+	15.1704i	−0.511685	+	0.886265i	−0.999908	+	0.0135461i	$0.995688\pi$
$294$		0			0
$295$	−11.4853	+	19.8930i	−0.668697	+	1.15822i
$296$	3.55840	−	6.16333i	0.206828	−	0.358237i
$297$		0			0
$298$	2.47548	−	4.28765i	0.143400	−	0.248377i
$299$	24.5838	−	14.7763i	1.42172	−	0.854536i
$300$		0			0
$301$	−4.05839	−	4.35316i	−0.233921	−	0.250912i
$302$	−0.215486	−	0.373233i	−0.0123998	−	0.0214772i
$303$		0			0
$304$	13.3934	−	23.1980i	0.768163	−	1.33050i
$305$	−12.0985	−	20.9552i	−0.692757	−	1.19989i
$306$		0			0
$307$	−8.63573			−0.492867			−0.246434	−	0.969160i	$-0.579259\pi$
$307$	−8.63573			−0.492867			−0.246434	+	0.969160i	$0.579259\pi$
$308$	−19.6144	+	4.52579i	−1.11763	+	0.257881i
$309$		0			0
$310$	0.877260	−	1.51946i	0.0498250	−	0.0862995i
$311$	−8.21130	+	14.2224i	−0.465620	+	0.806478i	−0.999229	−	0.0392535i	$-0.987502\pi$
$311$	−8.21130	+	14.2224i	−0.465620	+	0.806478i	0.533609	+	0.845731i	$0.320835\pi$
$312$		0			0
$313$	−5.02308	−	8.70024i	−0.283921	−	0.491766i	0.688426	−	0.725307i	$-0.258302\pi$
$313$	−5.02308	−	8.70024i	−0.283921	−	0.491766i	−0.972347	+	0.233541i	$0.924969\pi$
$314$	0.220658	+	0.382191i	0.0124525	+	0.0215683i
$315$		0			0
$316$	5.97024	−	10.3408i	0.335852	−	0.581713i
$317$	5.07249	+	8.78581i	0.284899	+	0.493460i	0.972585	−	0.232549i	$-0.0747064\pi$
$317$	5.07249	+	8.78581i	0.284899	+	0.493460i	−0.687685	+	0.726009i	$0.741373\pi$
$318$		0			0
$319$	−4.63996	−	8.03665i	−0.259788	−	0.449966i
$320$	8.10273	+	14.0343i	0.452957	+	0.784544i
$321$		0			0
$322$	−5.49886	+	1.26880i	−0.306440	+	0.0707075i
$323$	−2.94227	−	5.09616i	−0.163712	−	0.283558i
$324$		0			0
$325$	4.82885	−	2.90242i	0.267856	−	0.160998i
$326$	0.877867	−	1.52051i	0.0486206	−	0.0842133i
$327$		0			0
$328$	1.28360	+	2.22327i	0.0708751	+	0.122759i
$329$	3.39409	−	0.783149i	0.187122	−	0.0431764i
$330$		0			0
$331$	2.31916			0.127473			0.0637363	−	0.997967i	$-0.479698\pi$
$331$	2.31916			0.127473			0.0637363	+	0.997967i	$0.479698\pi$
$332$	1.03435	+	1.79155i	0.0567675	+	0.0983242i
$333$		0			0
$334$	−2.56027			−0.140092
$335$	1.73247	+	3.00072i	0.0946547	+	0.163947i
$336$		0			0
$337$	−15.9998			−0.871565			−0.435783	−	0.900052i	$-0.643528\pi$
$337$	−15.9998			−0.871565			−0.435783	+	0.900052i	$0.643528\pi$
$338$	−3.48347	+	0.122662i	−0.189476	+	0.00667193i
$339$		0			0
$340$	3.87788			0.210307
$341$	−5.03977	+	8.72913i	−0.272919	+	0.472709i
$342$		0			0
$343$	−14.3972	+	11.6499i	−0.777378	+	0.629034i
$344$	−1.18459	+	2.05178i	−0.0638690	+	0.110624i
$345$		0			0
$346$	1.49234	−	2.58480i	0.0802285	−	0.138960i
$347$	−11.4104	−	19.7634i	−0.612543	−	1.06096i	−0.990810	−	0.135259i	$-0.956813\pi$
$347$	−11.4104	−	19.7634i	−0.612543	−	1.06096i	0.378267	−	0.925696i	$-0.376520\pi$
$348$		0			0
$349$	11.3511	+	19.6607i	0.607612	+	1.05241i	0.991633	+	0.129090i	$0.0412056\pi$
$349$	11.3511	+	19.6607i	0.607612	+	1.05241i	−0.384021	+	0.923324i	$0.625461\pi$
$350$	−1.08011	+	0.249223i	−0.0577342	+	0.0133215i
$351$		0			0
$352$	6.04662	+	10.4731i	0.322286	+	0.558216i
$353$	27.2644			1.45114			0.725568	−	0.688150i	$-0.241577\pi$
$353$	27.2644			1.45114			0.725568	+	0.688150i	$0.241577\pi$
$354$		0			0
$355$	−31.5510			−1.67455
$356$	14.7751			0.783077
$357$		0			0
$358$	−1.69502	+	2.93585i	−0.0895844	+	0.155165i
$359$	−7.21309	−	12.4934i	−0.380692	−	0.659378i	0.610469	−	0.792040i	$-0.290981\pi$
$359$	−7.21309	−	12.4934i	−0.380692	−	0.659378i	−0.991161	+	0.132662i	$0.957648\pi$
$360$		0			0
$361$	37.1791			1.95679
$362$	−1.99965	+	3.46350i	−0.105099	+	0.182037i
$363$		0			0
$364$	−17.6806	−	5.06939i	−0.926715	−	0.265708i
$365$	1.96894			0.103059
$366$		0			0
$367$	−11.3917			−0.594643			−0.297322	−	0.954777i	$-0.596093\pi$
$367$	−11.3917			−0.594643			−0.297322	+	0.954777i	$0.596093\pi$
$368$	−14.2152	−	24.6214i	−0.741018	−	1.28348i
$369$		0			0
$370$	−2.32065	+	4.01948i	−0.120645	+	0.208963i
$371$	−16.7418	−	17.9578i	−0.869190	−	0.932321i
$372$		0			0
$373$	−30.9629			−1.60320			−0.801599	−	0.597862i	$-0.796017\pi$
$373$	−30.9629			−1.60320			−0.801599	+	0.597862i	$0.796017\pi$
$374$	0.830653			0.0429521
$375$		0			0
$376$	−0.693313	−	1.20085i	−0.0357549	−	0.0619293i
$377$	−0.149219	−	8.47796i	−0.00768518	−	0.436637i
$378$		0			0
$379$	−5.29330	−	9.16826i	−0.271898	−	0.470942i	0.697450	−	0.716634i	$-0.254318\pi$
$379$	−5.29330	−	9.16826i	−0.271898	−	0.470942i	−0.969348	+	0.245692i	$0.920985\pi$
$380$	−18.5109	+	32.0617i	−0.949587	+	1.64473i
$381$		0			0
$382$	−1.89438	+	3.28116i	−0.0969249	+	0.167879i
$383$	−30.7517			−1.57134			−0.785668	−	0.618648i	$-0.787681\pi$
$383$	−30.7517			−1.57134			−0.785668	+	0.618648i	$0.787681\pi$
$384$		0			0
$385$	26.0603	−	6.01313i	1.32816	−	0.306458i
$386$	−0.522112	+	0.904324i	−0.0265748	+	0.0460289i
$387$		0			0
$388$	4.57351			0.232185
$389$	−8.18978	+	14.1851i	−0.415239	+	0.719214i	−0.995453	−	0.0952492i	$-0.969635\pi$
$389$	−8.18978	+	14.1851i	−0.415239	+	0.719214i	0.580215	+	0.814463i	$0.302969\pi$
$390$		0			0
$391$	−6.24561			−0.315854
$392$	6.11113	+	4.12419i	0.308659	+	0.208303i
$393$		0			0
$394$	3.13945			0.158163
$395$	−7.93227	+	13.7391i	−0.399116	+	0.691289i
$396$		0			0
$397$	−15.8827			−0.797127			−0.398564	−	0.917141i	$-0.630491\pi$
$397$	−15.8827			−0.797127			−0.398564	+	0.917141i	$0.630491\pi$
$398$	0.937591			0.0469972
$399$		0			0
$400$	−2.79221	−	4.83624i	−0.139610	−	0.241812i
$401$	3.31787	−	5.74671i	0.165686	−	0.286977i	−0.771212	−	0.636578i	$-0.780349\pi$
$401$	3.31787	−	5.74671i	0.165686	−	0.286977i	0.936899	+	0.349601i	$0.113683\pi$
$402$		0			0
$403$	−7.89373	+	4.74460i	−0.393215	+	0.236345i
$404$	0.768670	+	1.33137i	0.0382427	+	0.0662384i
$405$		0			0
$406$	−0.487959	+	1.59534i	−0.0242170	+	0.0791755i
$407$	13.3319	−	23.0915i	0.660836	−	1.14460i
$408$		0			0
$409$	−2.93617	−	5.08560i	−0.145184	−	0.251467i	0.784257	−	0.620436i	$-0.213044\pi$
$409$	−2.93617	−	5.08560i	−0.145184	−	0.251467i	−0.929442	+	0.368969i	$0.879711\pi$
$410$	−0.837115	−	1.44992i	−0.0413421	−	0.0716067i
$411$		0			0
$412$	2.08831	−	3.61707i	0.102884	−	0.178200i
$413$	−23.1163	+	5.33383i	−1.13748	+	0.262460i
$414$		0			0
$415$	−1.37428	−	2.38032i	−0.0674607	−	0.116845i
$416$	0.194457	+	11.0482i	0.00953403	+	0.541680i
$417$		0			0
$418$	−3.96508	+	6.86773i	−0.193939	+	0.335911i
$419$	−15.0712	−	26.1040i	−0.736274	−	1.27526i	−0.954162	−	0.299290i	$-0.903250\pi$
$419$	−15.0712	−	26.1040i	−0.736274	−	1.27526i	0.217888	−	0.975974i	$-0.430083\pi$
$420$		0			0
$421$	40.0580			1.95231			0.976153	−	0.217083i	$-0.0696543\pi$
$421$	40.0580			1.95231			0.976153	+	0.217083i	$0.0696543\pi$
$422$	5.09576			0.248058
$423$		0			0
$424$	−4.88672	+	8.46405i	−0.237320	+	0.411051i
$425$	−1.22679			−0.0595079
$426$		0			0
$427$	7.30941	−	23.8975i	0.353727	−	1.15648i
$428$	−22.2238			−1.07423
$429$		0			0
$430$	0.772544	−	1.33809i	0.0372554	−	0.0645282i
$431$	3.91587			0.188621			0.0943104	−	0.995543i	$-0.469935\pi$
$431$	3.91587			0.188621			0.0943104	+	0.995543i	$0.469935\pi$
$432$		0			0
$433$	20.3963	−	35.3274i	0.980182	−	1.69772i	0.318532	−	0.947912i	$-0.396810\pi$
$433$	20.3963	−	35.3274i	0.980182	−	1.69772i	0.661650	−	0.749813i	$-0.269856\pi$
$434$	1.76566	−	0.407405i	0.0847542	−	0.0195561i
$435$		0			0
$436$	−15.5757			−0.745941
$437$	29.8131	−	51.6378i	1.42615	−	2.47017i
$438$		0			0
$439$	12.7811	−	22.1376i	0.610010	−	1.05657i	−0.381228	−	0.924481i	$-0.624499\pi$
$439$	12.7811	−	22.1376i	0.610010	−	1.05657i	0.991238	−	0.132087i	$-0.0421680\pi$
$440$	−5.32336	−	9.22033i	−0.253781	−	0.439562i
$441$		0			0
$442$	0.663878	+	0.367867i	0.0315775	+	0.0174977i
$443$	−13.7282	−	23.7779i	−0.652247	−	1.12972i	−0.982576	−	0.185859i	$-0.940493\pi$
$443$	−13.7282	−	23.7779i	−0.652247	−	1.12972i	0.330330	−	0.943866i	$-0.392840\pi$
$444$		0			0
$445$	−19.6307			−0.930584
$446$	−3.20844			−0.151924
$447$		0			0
$448$	−4.89534	+	16.0049i	−0.231283	+	0.756161i
$449$	−7.40181	+	12.8203i	−0.349313	+	0.605028i	−0.986128	−	0.165989i	$-0.946918\pi$
$449$	−7.40181	+	12.8203i	−0.349313	+	0.605028i	0.636815	+	0.771017i	$0.280252\pi$
$450$		0			0
$451$	4.80913	+	8.32966i	0.226453	+	0.392229i
$452$	15.5046			0.729275
$453$		0			0
$454$	−4.12489			−0.193590
$455$	23.4911	+	6.73537i	1.10128	+	0.315759i
$456$		0			0
$457$	0.325975	−	0.564606i	0.0152485	−	0.0264112i	−0.858300	−	0.513147i	$-0.828479\pi$
$457$	0.325975	−	0.564606i	0.0152485	−	0.0264112i	0.873549	+	0.486736i	$0.161813\pi$
$458$	2.32241			0.108519
$459$		0			0
$460$	19.6467	+	34.0290i	0.916031	+	1.58661i
$461$	6.24774	−	10.8214i	0.290986	−	0.504003i	−0.683057	−	0.730365i	$-0.739350\pi$
$461$	6.24774	−	10.8214i	0.290986	−	0.504003i	0.974043	+	0.226362i	$0.0726833\pi$
$462$		0			0
$463$	−0.309503			−0.0143838			−0.00719190	−	0.999974i	$-0.502289\pi$
$463$	−0.309503			−0.0143838			−0.00719190	+	0.999974i	$0.502289\pi$
$464$	−8.40466			−0.390176
$465$		0			0
$466$	−5.42972			−0.251527
$467$	12.2387	+	21.1980i	0.566338	+	0.980926i	0.996924	+	0.0783762i	$0.0249735\pi$
$467$	12.2387	+	21.1980i	0.566338	+	0.980926i	−0.430586	+	0.902549i	$0.641693\pi$
$468$		0			0
$469$	−1.04668	+	3.42205i	−0.0483314	+	0.158016i
$470$	0.452151	+	0.783149i	0.0208562	+	0.0361240i
$471$		0			0
$472$	4.72198	+	8.17871i	0.217347	+	0.376456i
$473$	−4.43818	+	7.68716i	−0.204068	+	0.353456i
$474$		0			0
$475$	5.85601	−	10.1429i	0.268692	−	0.465389i
$476$	2.73106	+	2.92943i	0.125178	+	0.134270i
$477$		0			0
$478$	2.21909	−	3.84357i	0.101499	−	0.175801i
$479$	−8.13850			−0.371858			−0.185929	−	0.982563i	$-0.559529\pi$
$479$	−8.13850			−0.371858			−0.185929	+	0.982563i	$0.559529\pi$
$480$		0			0
$481$	20.8816	−	12.5511i	0.952118	−	0.572279i
$482$	−4.39746			−0.200299
$483$		0			0
$484$	4.40662	+	7.63250i	0.200301	+	0.346932i
$485$	−6.07653			−0.275921
$486$		0			0
$487$	−2.30480	−	3.99203i	−0.104440	−	0.180896i	0.809069	−	0.587714i	$-0.199972\pi$
$487$	−2.30480	−	3.99203i	−0.104440	−	0.180896i	−0.913509	+	0.406817i	$0.866638\pi$
$488$	−9.94821			−0.450334
$489$		0			0
$490$	−3.98543	−	2.68963i	−0.180044	−	0.121505i
$491$	6.50947	+	11.2747i	0.293768	+	0.508822i	0.974698	−	0.223527i	$-0.0717572\pi$
$491$	6.50947	+	11.2747i	0.293768	+	0.508822i	−0.680929	+	0.732349i	$0.738424\pi$
$492$		0			0
$493$	−0.923171	+	1.59898i	−0.0415775	+	0.0720144i
$494$	−6.21047	+	3.73286i	−0.279422	+	0.167949i
$495$		0			0
$496$	4.56443	+	7.90582i	0.204949	+	0.354982i
$497$	−22.2203	−	23.8342i	−0.996718	−	1.06911i
$498$		0			0
$499$	16.1603	+	27.9905i	0.723436	+	1.25303i	0.959614	+	0.281319i	$0.0907717\pi$
$499$	16.1603	+	27.9905i	0.723436	+	1.25303i	−0.236178	+	0.971710i	$0.575895\pi$
$500$	−8.48928	−	14.7039i	−0.379652	−	0.657577i
$501$		0			0
$502$	−2.73900	−	4.74408i	−0.122247	−	0.211739i
$503$	−15.9126	+	27.5615i	−0.709509	+	1.22891i	0.255531	+	0.966801i	$0.417750\pi$
$503$	−15.9126	+	27.5615i	−0.709509	+	1.22891i	−0.965039	+	0.262105i	$0.915583\pi$
$504$		0			0
$505$	−1.02128	−	1.76891i	−0.0454465	−	0.0787156i
$506$	4.20838	+	7.28912i	0.187085	+	0.324041i
$507$		0			0
$508$	1.72377	−	2.98566i	0.0764801	−	0.132467i
$509$	1.12788	−	1.95354i	0.0499922	−	0.0865891i	−0.839946	−	0.542669i	$-0.817414\pi$
$509$	1.12788	−	1.95354i	0.0499922	−	0.0865891i	0.889939	+	0.456080i	$0.150747\pi$
$510$		0			0
$511$	1.38666	+	1.48738i	0.0613422	+	0.0657977i
$512$	18.4807			0.816739
$513$		0			0
$514$	1.84710	+	3.19927i	0.0814722	+	0.141114i
$515$	−2.77461	+	4.80576i	−0.122264	+	0.211767i
$516$		0			0
$517$	−2.59756	−	4.49911i	−0.114241	−	0.197870i
$518$	−4.67075	+	1.07772i	−0.205221	+	0.0473525i
$519$		0			0
$520$	−0.171197	−	9.72665i	−0.00750749	−	0.426542i
$521$	5.38562	−	9.32817i	0.235948	−	0.408675i	−0.723600	−	0.690220i	$-0.757514\pi$
$521$	5.38562	−	9.32817i	0.235948	−	0.408675i	0.959548	+	0.281546i	$0.0908471\pi$
$522$		0			0
$523$	−3.70397	+	6.41546i	−0.161963	+	0.280528i	−0.935573	−	0.353134i	$-0.885116\pi$
$523$	−3.70397	+	6.41546i	−0.161963	+	0.280528i	0.773610	+	0.633663i	$0.218449\pi$
$524$	6.16118	−	10.6715i	0.269152	−	0.466186i
$525$		0			0
$526$	3.47454	−	6.01809i	0.151497	−	0.262401i
$527$	2.00543			0.0873580
$528$		0			0
$529$	−20.1424	−	34.8877i	−0.875757	−	1.51686i
$530$	3.18692	−	5.51991i	0.138431	−	0.239770i
$531$		0			0
$532$	−37.2567	+	8.59656i	−1.61528	+	0.372708i
$533$	0.154660	+	8.78707i	0.00669906	+	0.380610i
$534$		0			0
$535$	29.5274			1.27658
$536$	1.42455			0.0615313
$537$		0			0
$538$	8.06161			0.347561
$539$	22.8959	+	15.4517i	0.986196	+	0.665550i
$540$		0			0
$541$	−16.2741	−	28.1875i	−0.699676	−	1.21188i	−0.968579	−	0.248708i	$-0.919994\pi$
$541$	−16.2741	−	28.1875i	−0.699676	−	1.21188i	0.268902	−	0.963168i	$-0.413339\pi$
$542$	−1.93728	−	3.35546i	−0.0832132	−	0.144129i
$543$		0			0
$544$	1.20304	−	2.08373i	0.0515799	−	0.0893391i
$545$	20.6944			0.886453
$546$		0			0
$547$	−13.4997			−0.577206			−0.288603	−	0.957449i	$-0.593191\pi$
$547$	−13.4997			−0.577206			−0.288603	+	0.957449i	$0.593191\pi$
$548$	−9.67577	+	16.7589i	−0.413329	+	0.715906i
$549$		0			0
$550$	0.826627	+	1.43176i	0.0352475	+	0.0610504i
$551$	−8.81342	−	15.2653i	−0.375464	−	0.650323i
$552$		0			0
$553$	−15.9652	+	3.68380i	−0.678911	+	0.156651i
$554$	−4.10915			−0.174581
$555$		0			0
$556$	10.6925			0.453461
$557$	29.7703			1.26141			0.630703	−	0.776024i	$-0.282767\pi$
$557$	29.7703			1.26141			0.630703	+	0.776024i	$0.282767\pi$
$558$		0			0
$559$	−6.95148	+	4.17825i	−0.294016	+	0.176721i
$560$	7.08483	−	23.1632i	0.299389	−	0.978826i
$561$		0			0
$562$	0.709566	−	1.22900i	0.0299312	−	0.0518424i
$563$	7.06629	+	12.2392i	0.297809	+	0.515819i	0.975634	−	0.219403i	$-0.0704110\pi$
$563$	7.06629	+	12.2392i	0.297809	+	0.515819i	−0.677826	+	0.735223i	$0.737078\pi$
$564$		0			0
$565$	−20.6000			−0.866647
$566$	4.12705	−	7.14826i	0.173473	−	0.300464i
$567$		0			0
$568$	−6.48584	+	11.2338i	−0.272140	+	0.471360i
$569$	−12.1270	+	21.0046i	−0.508391	+	0.880558i	0.491562	+	0.870842i	$0.336426\pi$
$569$	−12.1270	+	21.0046i	−0.508391	+	0.880558i	−0.999953	+	0.00971585i	$0.996907\pi$
$570$		0			0
$571$	−0.604159	+	1.04643i	−0.0252832	+	0.0437919i	−0.878390	−	0.477944i	$-0.841382\pi$
$571$	−0.604159	+	1.04643i	−0.0252832	+	0.0437919i	0.853107	+	0.521736i	$0.174715\pi$
$572$	0.482755	+	27.4279i	0.0201850	+	1.14682i
$573$		0			0
$574$	0.505750	−	1.65351i	0.0211096	−	0.0690161i
$575$	−6.21533	−	10.7653i	−0.259197	−	0.448943i
$576$		0			0
$577$	7.30518	−	12.6529i	0.304119	−	0.526749i	−0.672946	−	0.739692i	$-0.734971\pi$
$577$	7.30518	−	12.6529i	0.304119	−	0.526749i	0.977065	+	0.212943i	$0.0683047\pi$
$578$	2.19643	+	3.80433i	0.0913595	+	0.158239i
$579$		0			0
$580$	11.6160			0.482328
$581$	0.830283	−	2.71454i	0.0344459	−	0.112618i
$582$		0			0
$583$	−18.3085	+	31.7113i	−0.758262	+	1.31335i
$584$	0.404749	−	0.701046i	0.0167486	−	0.0290095i
$585$		0			0
$586$	−2.34841	−	4.06757i	−0.0970120	−	0.168030i
$587$	10.7548	+	18.6278i	0.443897	+	0.768852i	0.997975	−	0.0636132i	$-0.0202624\pi$
$587$	10.7548	+	18.6278i	0.443897	+	0.768852i	−0.554078	+	0.832465i	$0.686929\pi$
$588$		0			0
$589$	−9.57284	+	16.5806i	−0.394442	+	0.683193i
$590$	−3.07949	−	5.33383i	−0.126780	−	0.219590i
$591$		0			0
$592$	−12.0744	−	20.9135i	−0.496256	−	0.859541i
$593$	−1.32429	−	2.29373i	−0.0543820	−	0.0941923i	0.837553	−	0.546356i	$-0.183986\pi$
$593$	−1.32429	−	2.29373i	−0.0543820	−	0.0941923i	−0.891935	+	0.452164i	$0.850652\pi$
$594$		0			0
$595$	−3.62859	−	3.89214i	−0.148758	−	0.159562i
$596$	−17.8013	−	30.8328i	−0.729171	−	1.26296i
$597$		0			0
$598$	0.135340	+	7.68939i	0.00553445	+	0.314443i
$599$	−20.1250	+	34.8576i	−0.822287	+	1.42424i	0.0816889	+	0.996658i	$0.473969\pi$
$599$	−20.1250	+	34.8576i	−0.822287	+	1.42424i	−0.903975	+	0.427584i	$0.859365\pi$
$600$		0			0
$601$	−19.1725	−	33.2077i	−0.782061	−	1.35457i	−0.930739	−	0.365683i	$-0.880835\pi$
$601$	−19.1725	−	33.2077i	−0.782061	−	1.35457i	0.148679	−	0.988886i	$-0.452498\pi$
$602$	1.55490	−	0.358775i	0.0633728	−	0.0146226i
$603$		0			0
$604$	−3.09916			−0.126103
$605$	−5.85480	−	10.1408i	−0.238031	−	0.412283i
$606$		0			0
$607$	42.5547			1.72724			0.863620	−	0.504143i	$-0.168192\pi$
$607$	42.5547			1.72724			0.863620	+	0.504143i	$0.168192\pi$
$608$	11.4853	+	19.8931i	0.465791	+	0.806773i
$609$		0			0
$610$	6.48782			0.262684
$611$	−0.0835364	−	4.74616i	−0.00337952	−	0.192009i
$612$		0			0
$613$	15.2652			0.616556			0.308278	−	0.951296i	$-0.400247\pi$
$613$	15.2652			0.616556			0.308278	+	0.951296i	$0.400247\pi$
$614$	1.15773	−	2.00524i	0.0467221	−	0.0809251i
$615$		0			0
$616$	3.21616	−	10.5150i	0.129583	−	0.423660i
$617$	6.99061	−	12.1081i	0.281431	−	0.487453i	−0.690306	−	0.723517i	$-0.742524\pi$
$617$	6.99061	−	12.1081i	0.281431	−	0.487453i	0.971737	+	0.236064i	$0.0758575\pi$
$618$		0			0
$619$	4.25792	−	7.37494i	0.171140	−	0.296424i	−0.767678	−	0.640835i	$-0.778588\pi$
$619$	4.25792	−	7.37494i	0.171140	−	0.296424i	0.938819	+	0.344411i	$0.111921\pi$
$620$	−6.30845	−	10.9265i	−0.253353	−	0.438821i
$621$		0			0
$622$	−2.20166	−	3.81338i	−0.0882784	−	0.152903i
$623$	−13.8253	−	14.8294i	−0.553897	−	0.594129i
$624$		0			0
$625$	15.1856	+	26.3023i	0.607425	+	1.05209i
$626$	2.69363			0.107659
$627$		0			0
$628$	3.17354			0.126638
$629$	−5.30504			−0.211526
$630$		0			0
$631$	−18.4146	+	31.8950i	−0.733074	+	1.26972i	0.222490	+	0.974935i	$0.428582\pi$
$631$	−18.4146	+	31.8950i	−0.733074	+	1.26972i	−0.955563	+	0.294786i	$0.904752\pi$
$632$	3.26123	+	5.64861i	0.129725	+	0.224690i
$633$		0			0
$634$	−2.72013			−0.108030
$635$	−2.29027	+	3.96686i	−0.0908865	+	0.157420i
$636$		0			0
$637$	11.4560	+	22.4891i	0.453901	+	0.891052i
$638$	2.48818			0.0985081
$639$		0			0
$640$	−20.0470			−0.792428
$641$	12.9374	+	22.4082i	0.510996	+	0.885070i	0.999919	+	0.0127435i	$0.00405649\pi$
$641$	12.9374	+	22.4082i	0.510996	+	0.885070i	−0.488923	+	0.872327i	$0.662610\pi$
$642$		0			0
$643$	−20.2626	+	35.0958i	−0.799078	+	1.38404i	0.121139	+	0.992636i	$0.461345\pi$
$643$	−20.2626	+	35.0958i	−0.799078	+	1.38404i	−0.920217	+	0.391408i	$0.871988\pi$
$644$	−11.8697	+	38.8070i	−0.467732	+	1.52921i
$645$		0			0
$646$	1.57779			0.0620774
$647$	−1.78400			−0.0701364			−0.0350682	−	0.999385i	$-0.511165\pi$
$647$	−1.78400			−0.0701364			−0.0350682	+	0.999385i	$0.511165\pi$
$648$		0			0
$649$	17.6913	+	30.6423i	0.694445	+	1.20281i
$650$	0.0265840	+	1.51038i	0.00104271	+	0.0592420i
$651$		0			0
$652$	−6.31281	−	10.9341i	−0.247229	−	0.428213i
$653$	6.20210	−	10.7424i	0.242707	−	0.420381i	−0.718778	−	0.695240i	$-0.755298\pi$
$653$	6.20210	−	10.7424i	0.242707	−	0.420381i	0.961484	+	0.274860i	$0.0886313\pi$
$654$		0			0
$655$	−8.18597	+	14.1785i	−0.319852	+	0.554000i
$656$	8.71109			0.340111
$657$		0			0
$658$	−0.273171	+	0.893110i	−0.0106493	+	0.0348171i
$659$	−0.564336	+	0.977458i	−0.0219834	+	0.0380764i	−0.876808	−	0.480841i	$-0.840331\pi$
$659$	−0.564336	+	0.977458i	−0.0219834	+	0.0380764i	0.854824	+	0.518917i	$0.173665\pi$
$660$		0			0
$661$	−28.9254			−1.12507			−0.562534	−	0.826774i	$-0.690174\pi$
$661$	−28.9254			−1.12507			−0.562534	+	0.826774i	$0.690174\pi$
$662$	−0.310913	+	0.538517i	−0.0120840	+	0.0209301i
$663$		0			0
$664$	−1.13003			−0.0438535
$665$	49.5006	−	11.4217i	1.91955	−	0.442915i
$666$		0			0
$667$	−18.7084			−0.724393
$668$	−9.20556	+	15.9445i	−0.356174	+	0.616911i
$669$		0			0
$670$	−0.929036			−0.0358918
$671$	−37.2718			−1.43886
$672$		0			0
$673$	3.54980	+	6.14843i	0.136835	+	0.237005i	0.926297	−	0.376795i	$-0.122974\pi$
$673$	3.54980	+	6.14843i	0.136835	+	0.237005i	−0.789462	+	0.613799i	$0.789640\pi$
$674$	2.14498	−	3.71521i	0.0826214	−	0.143104i
$675$		0			0
$676$	−11.7610	+	22.1349i	−0.452348	+	0.851341i
$677$	−25.2010	−	43.6494i	−0.968552	−	1.67758i	−0.699752	−	0.714386i	$-0.746706\pi$
$677$	−25.2010	−	43.6494i	−0.968552	−	1.67758i	−0.268800	−	0.963196i	$-0.586627\pi$
$678$		0			0
$679$	−4.27950	−	4.59033i	−0.164232	−	0.176161i
$680$	−1.05914	+	1.83449i	−0.0406162	+	0.0703493i
$681$		0			0
$682$	−1.35129	−	2.34050i	−0.0517435	−	0.0896224i
$683$	13.7641	+	23.8401i	0.526669	+	0.912217i	0.999517	+	0.0310735i	$0.00989259\pi$
$683$	13.7641	+	23.8401i	0.526669	+	0.912217i	−0.472848	+	0.881144i	$0.656774\pi$
$684$		0			0
$685$	12.8556	−	22.2665i	0.491186	−	0.850760i
$686$	−0.775007	−	4.90490i	−0.0295899	−	0.187270i
$687$		0			0
$688$	4.01958	+	6.96212i	0.153245	+	0.265428i
$689$	−28.6765	+	17.2362i	−1.09249	+	0.656649i
$690$		0			0
$691$	12.1669	−	21.0737i	0.462851	−	0.801682i	−0.536251	−	0.844059i	$-0.680160\pi$
$691$	12.1669	−	21.0737i	0.462851	−	0.801682i	0.999102	+	0.0423772i	$0.0134931\pi$
$692$	−10.7315	−	18.5875i	−0.407950	−	0.706591i
$693$		0			0
$694$	6.11884			0.232268
$695$	−14.2064			−0.538879
$696$		0			0
$697$	0.956829	−	1.65728i	0.0362425	−	0.0627738i
$698$	−6.08704			−0.230398
$699$		0			0
$700$	−2.33150	+	7.62263i	−0.0881223	+	0.288108i
$701$	20.5588			0.776495			0.388248	−	0.921555i	$-0.373081\pi$
$701$	20.5588			0.776495			0.388248	+	0.921555i	$0.373081\pi$
$702$		0			0
$703$	25.3234	−	43.8613i	0.955088	−	1.65426i
$704$	24.9621			0.940795
$705$		0			0
$706$	−3.65513	+	6.33088i	−0.137563	+	0.238266i
$707$	0.617017	−	2.01728i	0.0232053	−	0.0758678i
$708$		0			0
$709$	40.9089			1.53637			0.768183	−	0.640230i	$-0.221161\pi$
$709$	40.9089			1.53637			0.768183	+	0.640230i	$0.221161\pi$
$710$	4.22981	−	7.32624i	0.158742	−	0.274949i
$711$		0			0
$712$	−4.03543	+	6.98956i	−0.151234	+	0.261945i
$713$	10.1602	+	17.5980i	0.380503	+	0.659051i
$714$		0			0
$715$	−0.641405	−	36.4418i	−0.0239872	−	1.36284i
$716$	12.1890	+	21.1119i	0.455524	+	0.788990i
$717$		0			0
$718$	3.86802			0.144353
$719$	1.19947			0.0447326			0.0223663	−	0.999750i	$-0.492880\pi$
$719$	1.19947			0.0447326			0.0223663	+	0.999750i	$0.492880\pi$
$720$		0			0
$721$	−5.58444	+	1.28855i	−0.207975	+	0.0479880i
$722$	−4.98433	+	8.63311i	−0.185497	+	0.321291i
$723$		0			0
$724$	14.3796	+	24.9063i	0.534415	+	0.925634i
$725$	−3.67478			−0.136478
$726$		0			0
$727$	−2.06230			−0.0764865			−0.0382433	−	0.999268i	$-0.512176\pi$
$727$	−2.06230			−0.0764865			−0.0382433	+	0.999268i	$0.512176\pi$
$728$	7.22714	−	6.97949i	0.267856	−	0.258677i
$729$		0			0
$730$	−0.263961	+	0.457194i	−0.00976964	+	0.0169215i
$731$	1.76605			0.0653197
$732$		0			0
$733$	−15.0310	−	26.0345i	−0.555184	−	0.961606i	−0.997889	−	0.0649392i	$-0.979315\pi$
$733$	−15.0310	−	26.0345i	−0.555184	−	0.961606i	0.442706	−	0.896667i	$-0.354019\pi$
$734$	1.52720	−	2.64520i	0.0563702	−	0.0976360i
$735$		0			0
$736$	24.3801			0.898662
$737$	5.33721			0.196599
$738$		0			0
$739$	44.2548			1.62794			0.813969	−	0.580908i	$-0.197303\pi$
$739$	44.2548			1.62794			0.813969	+	0.580908i	$0.197303\pi$
$740$	16.6880	+	28.9044i	0.613461	+	1.06255i
$741$		0			0
$742$	6.41430	−	1.48003i	0.235476	−	0.0543335i
$743$	−4.31326	−	7.47078i	−0.158238	−	0.274076i	0.775995	−	0.630739i	$-0.217248\pi$
$743$	−4.31326	−	7.47078i	−0.158238	−	0.274076i	−0.934233	+	0.356662i	$0.883915\pi$
$744$		0			0
$745$	23.6515	+	40.9656i	0.866524	+	1.50086i
$746$	4.15097	−	7.18969i	0.151978	−	0.263233i
$747$		0			0
$748$	2.98665	−	5.17302i	0.109203	−	0.189144i
$749$	20.7952	+	22.3056i	0.759839	+	0.815028i
$750$		0			0
$751$	−2.86105	+	4.95549i	−0.104401	+	0.180828i	−0.913493	−	0.406853i	$-0.866626\pi$
$751$	−2.86105	+	4.95549i	−0.104401	+	0.180828i	0.809092	+	0.587682i	$0.199959\pi$
$752$	−4.70512			−0.171578
$753$		0			0
$754$	1.98862	+	1.10193i	0.0724211	+	0.0401299i
$755$	4.11765			0.149857
$756$		0			0
$757$	17.3611	+	30.0703i	0.631000	+	1.09292i	0.987348	+	0.158571i	$0.0506887\pi$
$757$	17.3611	+	30.0703i	0.631000	+	1.09292i	−0.356347	+	0.934354i	$0.615978\pi$
$758$	2.83853			0.103100
$759$		0			0
$760$	−10.1115	−	17.5137i	−0.366783	−	0.635287i
$761$	53.1735			1.92754			0.963768	−	0.266741i	$-0.0859467\pi$
$761$	53.1735			1.92754			0.963768	+	0.266741i	$0.0859467\pi$
$762$		0			0
$763$	14.5744	+	15.6330i	0.527630	+	0.565953i
$764$	13.6226	+	23.5951i	0.492849	+	0.853640i
$765$		0			0
$766$	4.12265	−	7.14063i	0.148957	−	0.258002i
$767$	0.568946	+	32.3249i	0.0205434	+	1.16719i
$768$		0			0
$769$	−2.45578	−	4.25354i	−0.0885578	−	0.153387i	0.818344	−	0.574729i	$-0.194892\pi$
$769$	−2.45578	−	4.25354i	−0.0885578	−	0.153387i	−0.906902	+	0.421342i	$0.861559\pi$
$770$	−2.09745	+	6.85743i	−0.0755868	+	0.247125i
$771$		0			0
$772$	3.75455	+	6.50306i	0.135129	+	0.234050i
$773$	−11.4903	−	19.9018i	−0.413279	−	0.715819i	0.581967	−	0.813212i	$-0.302283\pi$
$773$	−11.4903	−	19.9018i	−0.413279	−	0.715819i	−0.995246	+	0.0973926i	$0.968950\pi$
$774$		0			0
$775$	1.99571	+	3.45667i	0.0716881	+	0.124167i
$776$	−1.24913	+	2.16356i	−0.0448413	+	0.0776674i
$777$		0			0
$778$	−2.19589	−	3.80339i	−0.0787264	−	0.136358i
$779$	9.13476	+	15.8219i	0.327287	+	0.566877i
$780$		0			0
$781$	−24.2998	+	42.0885i	−0.869515	+	1.50604i
$782$	0.837302	−	1.45025i	0.0299419	−	0.0518608i
$783$		0			0
$784$	22.4876	−	10.9611i	0.803129	−	0.391468i
$785$	−4.21648			−0.150493
$786$		0			0
$787$	1.59387	+	2.76067i	0.0568154	+	0.0984071i	0.893034	−	0.449989i	$-0.148572\pi$
$787$	1.59387	+	2.76067i	0.0568154	+	0.0984071i	−0.836219	+	0.548396i	$0.815239\pi$
$788$	11.2880	−	19.5514i	0.402119	−	0.696490i
$789$		0			0
$790$	−2.12684	−	3.68380i	−0.0756696	−	0.131064i
$791$	−14.5079	−	15.5616i	−0.515841	−	0.553308i
$792$		0			0
$793$	−29.7886	−	16.5064i	−1.05782	−	0.586159i
$794$	2.12927	−	3.68800i	0.0755650	−	0.130882i
$795$		0			0
$796$	3.37114	−	5.83899i	0.119487	−	0.206958i
$797$	27.3255	−	47.3291i	0.967918	−	1.67648i	0.266355	−	0.963875i	$-0.414180\pi$
$797$	27.3255	−	47.3291i	0.967918	−	1.67648i	0.701562	−	0.712608i	$-0.252486\pi$
$798$		0			0
$799$	−0.516813	+	0.895146i	−0.0182835	+	0.0316680i
$800$	4.78884			0.169311
$801$		0			0
$802$	0.889604	+	1.54084i	0.0314130	+	0.0544089i
$803$	1.51643	−	2.62653i	0.0535136	−	0.0926883i
$804$		0			0
$805$	15.7705	−	51.5604i	0.555838	−	1.81727i
$806$	−0.0434569	−	2.46902i	−0.00153070	−	0.0869677i
$807$		0			0
$808$	−0.839768			−0.0295429
$809$	20.2995			0.713694			0.356847	−	0.934163i	$-0.383852\pi$
$809$	20.2995			0.713694			0.356847	+	0.934163i	$0.383852\pi$
$810$		0			0
$811$	2.43587			0.0855350			0.0427675	−	0.999085i	$-0.486383\pi$
$811$	2.43587			0.0855350			0.0427675	+	0.999085i	$0.486383\pi$
$812$	8.18076	+	8.77496i	0.287089	+	0.307941i
$813$		0			0
$814$	3.57461	+	6.19141i	0.125290	+	0.217009i
$815$	8.38742	+	14.5274i	0.293799	+	0.508874i
$816$		0			0
$817$	−8.43015	+	14.6015i	−0.294934	+	0.510840i
$818$	1.57452			0.0550519
$819$		0			0
$820$	−12.0395			−0.420438
$821$	22.6762	−	39.2763i	0.791405	−	1.37075i	−0.133692	−	0.991023i	$-0.542683\pi$
$821$	22.6762	−	39.2763i	0.791405	−	1.37075i	0.925097	−	0.379731i	$-0.123983\pi$
$822$		0			0
$823$	1.37871	+	2.38800i	0.0480588	+	0.0832403i	0.889054	−	0.457802i	$-0.151363\pi$
$823$	1.37871	+	2.38800i	0.0480588	+	0.0832403i	−0.840995	+	0.541042i	$0.818030\pi$
$824$	1.14074	+	1.97581i	0.0397394	+	0.0688307i
$825$		0			0
$826$	1.86050	−	6.08275i	0.0647351	−	0.211646i
$827$	8.64504			0.300618			0.150309	−	0.988639i	$-0.451973\pi$
$827$	8.64504			0.300618			0.150309	+	0.988639i	$0.451973\pi$
$828$		0			0
$829$	−29.5741			−1.02715			−0.513576	−	0.858044i	$-0.671680\pi$
$829$	−29.5741			−1.02715			−0.513576	+	0.858044i	$0.671680\pi$
$830$	0.736958			0.0255802
$831$		0			0
$832$	19.9503	+	11.0548i	0.691653	+	0.383258i
$833$	0.384708	−	5.48222i	0.0133293	−	0.189948i
$834$		0			0
$835$	12.2308	−	21.1844i	0.423266	−	0.733117i
$836$	28.5132	+	49.3863i	0.986150	+	1.70806i
$837$		0			0
$838$	8.08191			0.279185
$839$	12.6236	−	21.8648i	0.435817	−	0.754857i	−0.561545	−	0.827446i	$-0.689793\pi$
$839$	12.6236	−	21.8648i	0.435817	−	0.754857i	0.997362	+	0.0725895i	$0.0231263\pi$
$840$		0			0
$841$	11.7347	−	20.3251i	0.404644	−	0.700865i
$842$	−5.37028	+	9.30159i	−0.185072	+	0.320554i
$843$		0			0
$844$	18.3220	−	31.7346i	0.630669	−	1.09235i
$845$	15.6262	−	29.4092i	0.537556	−	1.01171i
$846$		0			0
$847$	3.53723	−	11.5647i	0.121541	−	0.397367i
$848$	16.5817	+	28.7204i	0.569418	+	0.986261i
$849$		0			0
$850$	0.164466	−	0.284864i	0.00564115	−	0.00977076i
$851$	−26.8772	−	46.5526i	−0.921338	−	1.59580i
$852$		0			0
$853$	−35.1368			−1.20306			−0.601531	−	0.798850i	$-0.705442\pi$
$853$	−35.1368			−1.20306			−0.601531	+	0.798850i	$0.705442\pi$
$854$	4.56916	+	4.90103i	0.156353	+	0.167710i
$855$		0			0
$856$	6.06986	−	10.5133i	0.207463	−	0.359337i
$857$	−0.671345	+	1.16280i	−0.0229327	+	0.0397206i	−0.877264	−	0.480008i	$-0.840634\pi$
$857$	−0.671345	+	1.16280i	−0.0229327	+	0.0397206i	0.854331	+	0.519729i	$0.173967\pi$
$858$		0			0
$859$	−2.38386	−	4.12897i	−0.0813363	−	0.140879i	0.822488	−	0.568783i	$-0.192585\pi$
$859$	−2.38386	−	4.12897i	−0.0813363	−	0.140879i	−0.903824	+	0.427904i	$0.859252\pi$
$860$	−5.55542	−	9.62228i	−0.189438	−	0.328117i
$861$		0			0
$862$	−0.524972	+	0.909278i	−0.0178806	+	0.0309701i
$863$	−13.3052	−	23.0453i	−0.452915	−	0.784472i	0.545650	−	0.838013i	$-0.316283\pi$
$863$	−13.3052	−	23.0453i	−0.452915	−	0.784472i	−0.998566	+	0.0535407i	$0.982949\pi$
$864$		0			0
$865$	14.2583	+	24.6960i	0.484795	+	0.839690i
$866$	5.46875	+	9.47216i	0.185836	+	0.321877i
$867$		0			0
$868$	3.81130	−	12.4607i	0.129364	−	0.422945i
$869$	12.2185	+	21.1630i	0.414484	+	0.717907i
$870$		0			0
$871$	4.26563	+	2.36366i	0.144535	+	0.0800897i
$872$	4.25410	−	7.36831i	0.144062	−	0.249523i
$873$		0			0
$874$	7.99364	+	13.8454i	0.270389	+	0.468328i
$875$	−6.81441	+	22.2791i	−0.230369	+	0.753172i
$876$		0			0
$877$	8.03696			0.271389			0.135695	−	0.990751i	$-0.456673\pi$
$877$	8.03696			0.271389			0.135695	+	0.990751i	$0.456673\pi$
$878$	3.42694	+	5.93564i	0.115654	+	0.200318i
$879$		0			0
$880$	−36.1266			−1.21783
$881$	−27.3349	−	47.3454i	−0.920935	−	1.59511i	−0.797971	−	0.602695i	$-0.794093\pi$
$881$	−27.3349	−	47.3454i	−0.920935	−	1.59511i	−0.122964	−	0.992411i	$-0.539240\pi$
$882$		0			0
$883$	−8.45085			−0.284394			−0.142197	−	0.989838i	$-0.545417\pi$
$883$	−8.45085			−0.284394			−0.142197	+	0.989838i	$0.545417\pi$
$884$	4.67795	−	2.81172i	0.157337	−	0.0945685i
$885$		0			0
$886$	7.36176			0.247323
$887$	−5.17784	+	8.96829i	−0.173855	+	0.301126i	−0.939764	−	0.341823i	$-0.888956\pi$
$887$	−5.17784	+	8.96829i	−0.173855	+	0.301126i	0.765909	+	0.642948i	$0.222289\pi$
$888$		0			0
$889$	−4.60961	+	1.06361i	−0.154601	+	0.0356725i
$890$	2.63174	−	4.55831i	0.0882162	−	0.152795i
$891$		0			0
$892$	−11.5361	+	19.9811i	−0.386256	+	0.669016i
$893$	−4.93396	−	8.54587i	−0.165109	−	0.285977i
$894$		0			0
$895$	−16.1947	−	28.0501i	−0.541330	−	0.937611i
$896$	−14.1185	−	15.1439i	−0.471665	−	0.505923i
$897$		0			0
$898$	−1.98461	−	3.43745i	−0.0662274	−	0.114709i
$899$	6.00718			0.200351
$900$		0			0
$901$	7.28536			0.242711
$902$	−2.57890			−0.0858680
$903$		0			0
$904$	−4.23468	+	7.33467i	−0.140843	+	0.243948i
$905$	−19.1053	−	33.0914i	−0.635082	−	1.09999i
$906$		0			0
$907$	18.4804			0.613631			0.306815	−	0.951769i	$-0.400737\pi$
$907$	18.4804			0.613631			0.306815	+	0.951769i	$0.400737\pi$
$908$	−14.8312	+	25.6884i	−0.492190	+	0.852498i
$909$		0			0
$910$	−4.71325	+	4.55174i	−0.156243	+	0.150889i
$911$	26.6282			0.882230			0.441115	−	0.897451i	$-0.354583\pi$
$911$	26.6282			0.882230			0.441115	+	0.897451i	$0.354583\pi$
$912$		0			0
$913$	−4.23374			−0.140116
$914$	0.0874022	+	0.151385i	0.00289101	+	0.00500737i
$915$		0			0
$916$	8.35033	−	14.4632i	0.275903	−	0.477877i
$917$	−16.4758	+	3.80162i	−0.544080	+	0.125540i
$918$		0			0
$919$	−11.1493			−0.367783			−0.183891	−	0.982947i	$-0.558869\pi$
$919$	−11.1493			−0.367783			−0.183891	+	0.982947i	$0.558869\pi$
$920$	−21.4639			−0.707644
$921$		0			0
$922$	1.67518	+	2.90149i	0.0551690	+	0.0955555i
$923$	−38.0605	+	22.8766i	−1.25278	+	0.752993i
$924$		0			0
$925$	−5.27933	−	9.14406i	−0.173583	−	0.300655i
$926$	0.0414927	−	0.0718675i	0.00136354	−	0.00236171i
$927$		0			0
$928$	3.60365	−	6.24170i	0.118296	−	0.204894i
$929$	−7.74510			−0.254108			−0.127054	−	0.991896i	$-0.540552\pi$
$929$	−7.74510			−0.254108			−0.127054	+	0.991896i	$0.540552\pi$
$930$		0			0
$931$	43.4898	+	29.3498i	1.42532	+	0.961901i
$932$	−19.5227	+	33.8144i	−0.639489	+	1.10763i
$933$		0			0
$934$	−6.56299			−0.214748
$935$	−3.96817	+	6.87306i	−0.129773	+	0.224773i
$936$		0			0
$937$	36.4239			1.18992			0.594959	−	0.803756i	$-0.297168\pi$
$937$	36.4239			1.18992			0.594959	+	0.803756i	$0.297168\pi$
$938$	−0.654289	−	0.701812i	−0.0213633	−	0.0229150i
$939$		0			0
$940$	6.50291			0.212101
$941$	−9.89466	+	17.1381i	−0.322557	+	0.558685i	−0.981015	−	0.193933i	$-0.937876\pi$
$941$	−9.89466	+	17.1381i	−0.322557	+	0.558685i	0.658458	+	0.752617i	$0.271209\pi$
$942$		0			0
$943$	19.3905			0.631442
$944$	32.0454			1.04299
$945$		0			0
$946$	−1.18999	−	2.06112i	−0.0386899	−	0.0670129i
$947$	4.97398	−	8.61519i	0.161633	−	0.279956i	−0.773822	−	0.633403i	$-0.781657\pi$
$947$	4.97398	−	8.61519i	0.161633	−	0.279956i	0.935454	+	0.353448i	$0.114991\pi$
$948$		0			0
$949$	2.37517	−	1.42762i	0.0771012	−	0.0463424i
$950$	1.57014	+	2.71957i	0.0509422	+	0.0882345i
$951$		0			0
$952$	−2.13173	+	0.491872i	−0.0690896	+	0.0159417i
$953$	0.0105567	−	0.0182847i	0.000341965	−	0.000592300i	−0.865854	−	0.500296i	$-0.833224\pi$
$953$	0.0105567	−	0.0182847i	0.000341965	−	0.000592300i	0.866196	+	0.499704i	$0.166558\pi$
$954$		0			0
$955$	−18.0995	−	31.3493i	−0.585686	−	1.01444i
$956$	−15.9576	−	27.6394i	−0.516106	−	0.893922i
$957$		0			0
$958$	1.09107	−	1.88979i	0.0352508	−	0.0610562i
$959$	25.8743	−	5.97022i	0.835526	−	0.192788i
$960$		0			0
$961$	12.2376	+	21.1962i	0.394761	+	0.683747i
$962$	0.114958	+	6.53140i	0.00370640	+	0.210581i
$963$		0			0
$964$	−15.8112	+	27.3858i	−0.509245	+	0.882039i
$965$	−4.98842	−	8.64020i	−0.160583	−	0.278138i
$966$		0			0
$967$	−19.8102			−0.637053			−0.318526	−	0.947914i	$-0.603188\pi$
$967$	−19.8102			−0.637053			−0.318526	+	0.947914i	$0.603188\pi$
$968$	−4.81422			−0.154735
$969$		0			0
$970$	0.814635	−	1.41099i	0.0261563	−	0.0453041i
$971$	3.61774			0.116099			0.0580493	−	0.998314i	$-0.481512\pi$
$971$	3.61774			0.116099			0.0580493	+	0.998314i	$0.481512\pi$
$972$		0			0
$973$	−10.0051	−	10.7318i	−0.320749	−	0.344045i
$974$	1.23595			0.0396024
$975$		0			0
$976$	−16.8782	+	29.2339i	−0.540258	+	0.935755i
$977$	−2.16169			−0.0691586			−0.0345793	−	0.999402i	$-0.511009\pi$
$977$	−2.16169			−0.0691586			−0.0345793	+	0.999402i	$0.511009\pi$
$978$		0			0
$979$	−15.1191	+	26.1870i	−0.483208	+	0.836941i
$980$	−31.0799	+	15.1492i	−0.992810	+	0.483924i
$981$		0			0
$982$	−3.49071			−0.111393
$983$	−15.0545	+	26.0752i	−0.480165	+	0.831671i	−0.999741	−	0.0227535i	$-0.992757\pi$
$983$	−15.0545	+	26.0752i	−0.480165	+	0.831671i	0.519576	+	0.854424i	$0.326090\pi$
$984$		0			0
$985$	−14.9977	+	25.9767i	−0.477865	+	0.827687i
$986$	−0.247525	−	0.428727i	−0.00788281	−	0.0136534i
$987$		0			0
$988$	0.916973	+	52.0983i	0.0291728	+	1.65747i
$989$	8.94742	+	15.4974i	0.284511	+	0.492788i
$990$		0			0
$991$	−27.1460			−0.862323			−0.431161	−	0.902275i	$-0.641896\pi$
$991$	−27.1460			−0.862323			−0.431161	+	0.902275i	$0.641896\pi$
$992$	−7.82832			−0.248549
$993$		0			0
$994$	8.51330	−	1.96435i	0.270026	−	0.0623054i
$995$	−4.47902	+	7.75790i	−0.141995	+	0.245942i
$996$		0			0
$997$	−25.4005	−	43.9949i	−0.804441	−	1.39333i	−0.916668	−	0.399650i	$-0.869132\pi$
$997$	−25.4005	−	43.9949i	−0.804441	−	1.39333i	0.112227	−	0.993683i	$-0.464202\pi$
$998$	−8.66599			−0.274317
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.d.172.4		12
3.2	odd	2		91.2.g.b.81.3	yes	12
7.2	even	3		819.2.s.d.289.3		12
13.9	even	3		819.2.s.d.802.3		12
21.2	odd	6		91.2.h.b.16.4	yes	12
21.5	even	6		637.2.h.l.471.4		12
21.11	odd	6		637.2.f.k.393.3		12
21.17	even	6		637.2.f.j.393.3		12
21.20	even	2		637.2.g.l.263.3		12
39.23	odd	6		1183.2.e.g.508.4		12
39.29	odd	6		1183.2.e.h.508.3		12
39.35	odd	6		91.2.h.b.74.4	yes	12
91.9	even	3	inner	819.2.n.d.100.4		12
273.23	odd	6		1183.2.e.g.170.4		12
273.74	odd	6		637.2.f.k.295.3		12
273.101	even	6		8281.2.a.cf.1.3		6
273.107	odd	6		1183.2.e.h.170.3		12
273.152	even	6		637.2.g.l.373.3		12
273.179	odd	6		8281.2.a.ce.1.3		6
273.185	even	6		8281.2.a.ca.1.4		6
273.191	odd	6		91.2.g.b.9.3	✓	12
273.230	even	6		637.2.h.l.165.4		12
273.263	odd	6		8281.2.a.bz.1.4		6
273.269	even	6		637.2.f.j.295.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.3	✓	12	273.191	odd	6
91.2.g.b.81.3	yes	12	3.2	odd	2
91.2.h.b.16.4	yes	12	21.2	odd	6
91.2.h.b.74.4	yes	12	39.35	odd	6
637.2.f.j.295.3		12	273.269	even	6
637.2.f.j.393.3		12	21.17	even	6
637.2.f.k.295.3		12	273.74	odd	6
637.2.f.k.393.3		12	21.11	odd	6
637.2.g.l.263.3		12	21.20	even	2
637.2.g.l.373.3		12	273.152	even	6
637.2.h.l.165.4		12	273.230	even	6
637.2.h.l.471.4		12	21.5	even	6
819.2.n.d.100.4		12	91.9	even	3	inner
819.2.n.d.172.4		12	1.1	even	1	trivial
819.2.s.d.289.3		12	7.2	even	3
819.2.s.d.802.3		12	13.9	even	3
1183.2.e.g.170.4		12	273.23	odd	6
1183.2.e.g.508.4		12	39.23	odd	6
1183.2.e.h.170.3		12	273.107	odd	6
1183.2.e.h.508.3		12	39.29	odd	6
8281.2.a.bz.1.4		6	273.263	odd	6
8281.2.a.ca.1.4		6	273.185	even	6
8281.2.a.ce.1.3		6	273.179	odd	6
8281.2.a.cf.1.3		6	273.101	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.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.134063 + 0.232203i) q^{2} +(0.964054 + 1.66979i) q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.773854 - 2.53005i) q^{7} -1.05323 q^{8} +0.686871 q^{10} -3.94600 q^{11} +(-3.15374 - 1.74755i) q^{13} +(0.483741 + 0.518876i) q^{14} +(-1.78691 + 3.09502i) q^{16} +(0.392550 + 0.679916i) q^{17} -7.49527 q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} +(-3.97759 + 6.88938i) q^{23} +(-0.781294 + 1.35324i) q^{25} +(0.828585 - 0.498028i) q^{26} +(4.97069 - 1.14693i) q^{28} +(1.17586 + 2.03666i) q^{29} +(1.27718 - 2.21215i) q^{31} +(-1.53234 - 2.65409i) q^{32} -0.210505 q^{34} +(-6.60424 + 1.52385i) q^{35} +(-3.37858 + 5.85187i) q^{37} +(1.00484 - 1.74043i) q^{38} +(1.34905 + 2.33663i) q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} +(-3.80416 - 6.58900i) q^{44} +(-1.06649 - 1.84722i) q^{46} +(0.658276 + 1.14017i) q^{47} +(-5.80230 - 3.91578i) q^{49} +(-0.209485 - 0.362838i) q^{50} +(-0.122340 - 6.95082i) q^{52} +(4.63977 - 8.03632i) q^{53} +(5.05434 + 8.75438i) q^{55} +(-0.815042 + 2.66471i) q^{56} -0.630558 q^{58} +(-4.48335 - 7.76540i) q^{59} +9.44547 q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(0.162546 + 9.23511i) q^{65} -1.35256 q^{67} +(-0.756879 + 1.31095i) q^{68} +(0.531538 - 1.73782i) q^{70} +(6.15808 - 10.6661i) q^{71} +(-0.384295 + 0.665619i) q^{73} +(-0.905882 - 1.56903i) q^{74} +(-7.22585 - 12.5155i) q^{76} +(-3.05363 + 9.98358i) q^{77} +(-3.09642 - 5.36316i) q^{79} +9.15525 q^{80} +0.653548 q^{82} +1.07292 q^{83} +(1.00562 - 1.74178i) q^{85} +(0.301568 + 0.522332i) q^{86} +4.15603 q^{88} +(3.83149 - 6.63634i) q^{89} +(-6.86191 + 6.62678i) q^{91} -15.3384 q^{92} -0.353001 q^{94} +(9.60052 + 16.6286i) q^{95} +(1.18601 - 2.05423i) q^{97} +(1.68713 - 0.822354i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 4 q^{4} - q^{5} + 9 q^{7} + 6 q^{8} - 8 q^{10} + 8 q^{11} - 2 q^{13} + 2 q^{14} + 8 q^{16} - 5 q^{17} + 2 q^{19} + q^{20} - 5 q^{22} + q^{23} + 7 q^{25} - 5 q^{26} - 7 q^{28} - 3 q^{29}+ \cdots - 62 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 4 * q^4 - q^5 + 9 * q^7 + 6 * q^8 - 8 * q^10 + 8 * q^11 - 2 * q^13 + 2 * q^14 + 8 * q^16 - 5 * q^17 + 2 * q^19 + q^20 - 5 * q^22 + q^23 + 7 * q^25 - 5 * q^26 - 7 * q^28 - 3 * q^29 + 16 * q^31 - 8 * q^32 + 32 * q^34 - 8 * q^35 - 13 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 + 16 * q^46 + q^47 - 3 * q^49 - 6 * q^50 - 25 * q^52 + 2 * q^53 + 9 * q^55 + 18 * q^56 + 16 * q^58 - 13 * q^59 + 10 * q^61 - 5 * q^62 - 30 * q^64 - 19 * q^65 + 22 * q^67 - 29 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 + 3 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 - 14 * q^80 - 2 * q^82 + 54 * q^83 - q^85 + 7 * q^86 - 4 * q^89 - 20 * q^91 - 54 * q^92 - 90 * q^94 + 6 * q^95 - 35 * q^97 - 62 * q^98

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