LMFDB - Embedded newform 819.2.ct.b.316.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(127,819)]

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, 0, 5]))

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

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

chi := DirichletCharacter("819.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ct (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.1
Root			$2.45308i$ of defining polynomial
Character	$\chi$	$=$	819.316
Dual form			819.2.ct.b.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12443 - 1.22654i) q^{2} +(2.00879 + 3.47933i) q^{4} +0.0682999i q^{5} +(0.866025 - 0.500000i) q^{7} -4.94928i q^{8} +O(q^{10})$	\(q+(-2.12443 - 1.22654i) q^{2} +(2.00879 + 3.47933i) q^{4} +0.0682999i q^{5} +(0.866025 - 0.500000i) q^{7} -4.94928i q^{8} +(0.0837724 - 0.145098i) q^{10} +(-0.587365 - 0.339115i) q^{11} +(-3.24851 - 1.56434i) q^{13} -2.45308 q^{14} +(-2.05290 + 3.55573i) q^{16} +(0.467479 + 0.809698i) q^{17} +(-1.79066 + 1.03384i) q^{19} +(-0.237638 + 0.137200i) q^{20} +(0.831875 + 1.44085i) q^{22} +(-2.14974 + 3.72346i) q^{23} +4.99534 q^{25} +(4.98251 + 7.30775i) q^{26} +(3.47933 + 2.00879i) q^{28} +(4.00723 - 6.94072i) q^{29} -10.0622i q^{31} +(0.150064 - 0.0866393i) q^{32} -2.29352i q^{34} +(0.0341499 + 0.0591494i) q^{35} +(0.456821 + 0.263746i) q^{37} +5.07216 q^{38} +0.338035 q^{40} +(-4.44943 - 2.56888i) q^{41} +(-0.894286 - 1.54895i) q^{43} -2.72485i q^{44} +(9.13393 - 5.27348i) q^{46} -4.22889i q^{47} +(0.500000 - 0.866025i) q^{49} +(-10.6122 - 6.12697i) q^{50} +(-1.08274 - 14.4451i) q^{52} +3.21495 q^{53} +(0.0231615 - 0.0401169i) q^{55} +(-2.47464 - 4.28620i) q^{56} +(-17.0261 + 9.83004i) q^{58} +(7.21179 - 4.16373i) q^{59} +(-0.505267 - 0.875148i) q^{61} +(-12.3416 + 21.3763i) q^{62} +7.78654 q^{64} +(0.106844 - 0.221873i) q^{65} +(-6.32225 - 3.65015i) q^{67} +(-1.87814 + 3.25303i) q^{68} -0.167545i q^{70} +(8.58321 - 4.95552i) q^{71} -3.42254i q^{73} +(-0.646989 - 1.12062i) q^{74} +(-7.19411 - 4.15352i) q^{76} -0.678230 q^{77} -14.0484 q^{79} +(-0.242856 - 0.140213i) q^{80} +(6.30166 + 10.9148i) q^{82} -7.03411i q^{83} +(-0.0553023 + 0.0319288i) q^{85} +4.38750i q^{86} +(-1.67838 + 2.90703i) q^{88} +(-13.6436 - 7.87714i) q^{89} +(-3.59547 + 0.269500i) q^{91} -17.2735 q^{92} +(-5.18689 + 8.98395i) q^{94} +(-0.0706109 - 0.122302i) q^{95} +(-14.4370 + 8.33523i) q^{97} +(-2.12443 + 1.22654i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4}+O(q^{10}) $ 16 * q + 6 * q^4	$ 16 q + 6 q^{4} - 4 q^{10} + 12 q^{11} + 4 q^{13} - 4 q^{14} - 10 q^{16} - 10 q^{17} - 6 q^{20} - 2 q^{22} + 2 q^{23} + 12 q^{25} - 20 q^{26} - 12 q^{29} - 30 q^{32} + 2 q^{35} + 18 q^{37} + 32 q^{38} - 60 q^{40} - 18 q^{41} - 10 q^{43} + 30 q^{46} + 8 q^{49} + 24 q^{50} - 26 q^{52} - 12 q^{53} + 10 q^{55} - 12 q^{56} - 54 q^{58} + 60 q^{59} - 6 q^{61} - 16 q^{62} + 16 q^{64} + 20 q^{65} - 18 q^{67} + 20 q^{68} - 6 q^{71} - 18 q^{74} + 72 q^{76} + 16 q^{77} - 4 q^{79} - 30 q^{80} - 18 q^{82} - 24 q^{85} - 2 q^{88} - 78 q^{89} - 8 q^{91} + 20 q^{92} + 16 q^{94} + 4 q^{95} - 54 q^{97}+O(q^{100}) $ 16 * q + 6 * q^4 - 4 * q^10 + 12 * q^11 + 4 * q^13 - 4 * q^14 - 10 * q^16 - 10 * q^17 - 6 * q^20 - 2 * q^22 + 2 * q^23 + 12 * q^25 - 20 * q^26 - 12 * q^29 - 30 * q^32 + 2 * q^35 + 18 * q^37 + 32 * q^38 - 60 * q^40 - 18 * q^41 - 10 * q^43 + 30 * q^46 + 8 * q^49 + 24 * q^50 - 26 * q^52 - 12 * q^53 + 10 * q^55 - 12 * q^56 - 54 * q^58 + 60 * q^59 - 6 * q^61 - 16 * q^62 + 16 * q^64 + 20 * q^65 - 18 * q^67 + 20 * q^68 - 6 * q^71 - 18 * q^74 + 72 * q^76 + 16 * q^77 - 4 * q^79 - 30 * q^80 - 18 * q^82 - 24 * q^85 - 2 * q^88 - 78 * q^89 - 8 * q^91 + 20 * q^92 + 16 * q^94 + 4 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.12443	−	1.22654i	−1.50220	−	0.867293i	−0.999997	−	0.00254149i	$-0.999191\pi$
$2$	−2.12443	−	1.22654i	−1.50220	−	0.867293i	−0.502199	−	0.864752i	$-0.667476\pi$
$3$		0			0
$3$		0			0
$4$	2.00879	+	3.47933i	1.00440	+	1.73966i
$5$			0.0682999i			0.0305446i	0.999883	+	0.0152723i	$0.00486152\pi$
$5$			0.0682999i			0.0305446i	−0.999883	+	0.0152723i	$0.995138\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		−	4.94928i		−	1.74984i
$9$		0			0
$10$	0.0837724	−	0.145098i	0.0264912	−	0.0458840i
$11$	−0.587365	−	0.339115i	−0.177097	−	0.102247i	0.408831	−	0.912610i	$-0.365937\pi$
$11$	−0.587365	−	0.339115i	−0.177097	−	0.102247i	−0.585928	+	0.810363i	$0.699270\pi$
$12$		0			0
$13$	−3.24851	−	1.56434i	−0.900976	−	0.433869i
$13$	−3.24851	−	1.56434i	−0.900976	−	0.433869i
$14$	−2.45308			−0.655612
$15$		0			0
$16$	−2.05290	+	3.55573i	−0.513225	+	0.888932i
$17$	0.467479	+	0.809698i	0.113380	+	0.196381i	0.917131	−	0.398586i	$-0.130499\pi$
$17$	0.467479	+	0.809698i	0.113380	+	0.196381i	−0.803751	+	0.594966i	$0.797165\pi$
$18$		0			0
$19$	−1.79066	+	1.03384i	−0.410805	+	0.237178i	−0.691135	−	0.722725i	$-0.742889\pi$
$19$	−1.79066	+	1.03384i	−0.410805	+	0.237178i	0.280331	+	0.959903i	$0.409556\pi$
$20$	−0.237638	+	0.137200i	−0.0531374	+	0.0306789i
$21$		0			0
$22$	0.831875	+	1.44085i	0.177356	+	0.307190i
$23$	−2.14974	+	3.72346i	−0.448252	+	0.776395i	−0.998272	−	0.0587563i	$-0.981287\pi$
$23$	−2.14974	+	3.72346i	−0.448252	+	0.776395i	0.550021	+	0.835151i	$0.314620\pi$
$24$		0			0
$25$	4.99534			0.999067
$26$	4.98251	+	7.30775i	0.977150	+	1.43317i
$27$		0			0
$28$	3.47933	+	2.00879i	0.657531	+	0.379626i
$29$	4.00723	−	6.94072i	0.744124	−	1.28886i	−0.206479	−	0.978451i	$-0.566201\pi$
$29$	4.00723	−	6.94072i	0.744124	−	1.28886i	0.950603	−	0.310409i	$-0.100466\pi$
$30$		0			0
$31$		−	10.0622i		−	1.80722i	−0.428358	−	0.903609i	$-0.640908\pi$
$31$		−	10.0622i		−	1.80722i	0.428358	−	0.903609i	$-0.359092\pi$
$32$	0.150064	−	0.0866393i	0.0265278	−	0.0153158i
$33$		0			0
$34$		−	2.29352i		−	0.393336i
$35$	0.0341499	+	0.0591494i	0.00577239	+	0.00999808i
$36$		0			0
$37$	0.456821	+	0.263746i	0.0751010	+	0.0433596i	0.537080	−	0.843531i	$-0.319527\pi$
$37$	0.456821	+	0.263746i	0.0751010	+	0.0433596i	−0.461979	+	0.886891i	$0.652861\pi$
$38$	5.07216			0.822812
$39$		0			0
$40$	0.338035			0.0534481
$41$	−4.44943	−	2.56888i	−0.694884	−	0.401191i	0.110555	−	0.993870i	$-0.464737\pi$
$41$	−4.44943	−	2.56888i	−0.694884	−	0.401191i	−0.805439	+	0.592679i	$0.798070\pi$
$42$		0			0
$43$	−0.894286	−	1.54895i	−0.136377	−	0.236212i	0.789745	−	0.613435i	$-0.210213\pi$
$43$	−0.894286	−	1.54895i	−0.136377	−	0.236212i	−0.926123	+	0.377222i	$0.876879\pi$
$44$		−	2.72485i		−	0.410786i
$45$		0			0
$46$	9.13393	−	5.27348i	1.34672	−	0.777532i
$47$		−	4.22889i		−	0.616846i	−0.951249	−	0.308423i	$-0.900199\pi$
$47$		−	4.22889i		−	0.616846i	0.951249	−	0.308423i	$-0.0998013\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−10.6122	−	6.12697i	−1.50079	−	0.866484i
$51$		0			0
$52$	−1.08274	−	14.4451i	−0.150149	−	2.00317i
$53$	3.21495			0.441608			0.220804	−	0.975318i	$-0.429132\pi$
$53$	3.21495			0.441608			0.220804	+	0.975318i	$0.429132\pi$
$54$		0			0
$55$	0.0231615	−	0.0401169i	0.00312310	−	0.00540937i
$56$	−2.47464	−	4.28620i	−0.330688	−	0.572768i
$57$		0			0
$58$	−17.0261	+	9.83004i	−2.23564	+	1.29075i
$59$	7.21179	−	4.16373i	0.938895	−	0.542071i	0.0492814	−	0.998785i	$-0.484307\pi$
$59$	7.21179	−	4.16373i	0.938895	−	0.542071i	0.889614	+	0.456714i	$0.150974\pi$
$60$		0			0
$61$	−0.505267	−	0.875148i	−0.0646928	−	0.112051i	0.831865	−	0.554978i	$-0.187273\pi$
$61$	−0.505267	−	0.875148i	−0.0646928	−	0.112051i	−0.896558	+	0.442927i	$0.853940\pi$
$62$	−12.3416	+	21.3763i	−1.56739	+	2.71480i
$63$		0			0
$64$	7.78654			0.973317
$65$	0.106844	−	0.221873i	0.0132524	−	0.0275200i
$66$		0			0
$67$	−6.32225	−	3.65015i	−0.772385	−	0.445937i	0.0613395	−	0.998117i	$-0.480463\pi$
$67$	−6.32225	−	3.65015i	−0.772385	−	0.445937i	−0.833725	+	0.552180i	$0.813796\pi$
$68$	−1.87814	+	3.25303i	−0.227757	+	0.394487i
$69$		0			0
$70$		−	0.167545i		−	0.0200254i
$71$	8.58321	−	4.95552i	1.01864	−	0.588112i	0.104930	−	0.994480i	$-0.466538\pi$
$71$	8.58321	−	4.95552i	1.01864	−	0.588112i	0.913710	+	0.406367i	$0.133205\pi$
$72$		0			0
$73$		−	3.42254i		−	0.400578i	−0.979737	−	0.200289i	$-0.935812\pi$
$73$		−	3.42254i		−	0.400578i	0.979737	−	0.200289i	$-0.0641880\pi$
$74$	−0.646989	−	1.12062i	−0.0752109	−	0.130269i
$75$		0			0
$76$	−7.19411	−	4.15352i	−0.825221	−	0.476441i
$77$	−0.678230			−0.0772915
$78$		0			0
$79$	−14.0484			−1.58057			−0.790283	−	0.612742i	$-0.790066\pi$
$79$	−14.0484			−1.58057			−0.790283	+	0.612742i	$0.790066\pi$
$80$	−0.242856	−	0.140213i	−0.0271521	−	0.0156763i
$81$		0			0
$82$	6.30166	+	10.9148i	0.695901	+	1.20534i
$83$		−	7.03411i		−	0.772094i	−0.922479	−	0.386047i	$-0.873840\pi$
$83$		−	7.03411i		−	0.772094i	0.922479	−	0.386047i	$-0.126160\pi$
$84$		0			0
$85$	−0.0553023	+	0.0319288i	−0.00599837	+	0.00346316i
$86$			4.38750i			0.473117i
$87$		0			0
$88$	−1.67838	+	2.90703i	−0.178916	+	0.309891i
$89$	−13.6436	−	7.87714i	−1.44622	−	0.834975i	−0.447966	−	0.894051i	$-0.647851\pi$
$89$	−13.6436	−	7.87714i	−1.44622	−	0.834975i	−0.998254	+	0.0590753i	$0.981185\pi$
$90$		0			0
$91$	−3.59547	+	0.269500i	−0.376907	+	0.0282513i
$92$	−17.2735			−1.80089
$93$		0			0
$94$	−5.18689	+	8.98395i	−0.534987	+	0.926624i
$95$	−0.0706109	−	0.122302i	−0.00724452	−	0.0125479i
$96$		0			0
$97$	−14.4370	+	8.33523i	−1.46586	+	0.846314i	−0.999272	−	0.0381612i	$-0.987850\pi$
$97$	−14.4370	+	8.33523i	−1.46586	+	0.846314i	−0.466587	+	0.884475i	$0.654517\pi$
$98$	−2.12443	+	1.22654i	−0.214599	+	0.123899i
$99$		0			0
$100$	10.0346	+	17.3804i	1.00346	+	1.73804i
$101$	0.752145	−	1.30275i	0.0748412	−	0.129629i	−0.826176	−	0.563412i	$-0.809488\pi$
$101$	0.752145	−	1.30275i	0.0748412	−	0.129629i	0.901017	+	0.433783i	$0.142822\pi$
$102$		0			0
$103$	2.21721			0.218468			0.109234	−	0.994016i	$-0.465160\pi$
$103$	2.21721			0.218468			0.109234	+	0.994016i	$0.465160\pi$
$104$	−7.74235	+	16.0778i	−0.759200	+	1.57656i
$105$		0			0
$106$	−6.82993	−	3.94326i	−0.663381	−	0.383003i
$107$	−9.89298	+	17.1351i	−0.956390	+	1.65652i	−0.225236	+	0.974304i	$0.572315\pi$
$107$	−9.89298	+	17.1351i	−0.956390	+	1.65652i	−0.731154	+	0.682212i	$0.761018\pi$
$108$		0			0
$109$		−	1.71086i		−	0.163870i	−0.996638	−	0.0819352i	$-0.973890\pi$
$109$		−	1.71086i		−	0.163870i	0.996638	−	0.0819352i	$-0.0261101\pi$
$110$	−0.0984099	+	0.0568170i	−0.00938302	+	0.00541729i
$111$		0			0
$112$			4.10580i			0.387962i
$113$	−6.81962	−	11.8119i	−0.641536	−	1.11117i	−0.985090	−	0.172040i	$-0.944964\pi$
$113$	−6.81962	−	11.8119i	−0.641536	−	1.11117i	0.343554	−	0.939133i	$-0.388369\pi$
$114$		0			0
$115$	−0.254312	−	0.146827i	−0.0237147	−	0.0136917i
$116$	32.1987			2.98958
$117$		0			0
$118$	−20.4279			−1.88054
$119$	0.809698	+	0.467479i	0.0742249	+	0.0428537i
$120$		0			0
$121$	−5.27000	−	9.12791i	−0.479091	−	0.829810i
$122$			2.47892i			0.224430i
$123$		0			0
$124$	35.0096	−	20.2128i	3.14395	−	1.81516i
$125$			0.682680i			0.0610608i
$126$		0			0
$127$	−4.00220	+	6.93201i	−0.355138	+	0.615116i	−0.987141	−	0.159849i	$-0.948899\pi$
$127$	−4.00220	+	6.93201i	−0.355138	+	0.615116i	0.632004	+	0.774965i	$0.282233\pi$
$128$	−16.8421	−	9.72376i	−1.48864	−	0.859467i
$129$		0			0
$130$	−0.499118	+	0.340305i	−0.0437756	+	0.0298467i
$131$	10.2912			0.899146			0.449573	−	0.893244i	$-0.351576\pi$
$131$	10.2912			0.899146			0.449573	+	0.893244i	$0.351576\pi$
$132$		0			0
$133$	−1.03384	+	1.79066i	−0.0896449	+	0.155270i
$134$	8.95410	+	15.5090i	0.773516	+	1.33977i
$135$		0			0
$136$	4.00742	−	2.31369i	0.343634	−	0.198397i
$137$	3.13463	−	1.80978i	0.267809	−	0.154620i	−0.360082	−	0.932921i	$-0.617251\pi$
$137$	3.13463	−	1.80978i	0.267809	−	0.154620i	0.627892	+	0.778301i	$0.283918\pi$
$138$		0			0
$139$	−0.609074	−	1.05495i	−0.0516610	−	0.0894794i	0.839039	−	0.544072i	$-0.183118\pi$
$139$	−0.609074	−	1.05495i	−0.0516610	−	0.0894794i	−0.890699	+	0.454593i	$0.849785\pi$
$140$	−0.137200	+	0.237638i	−0.0115955	+	0.0200841i
$141$		0			0
$142$	−24.3125			−2.04026
$143$	1.37757	+	2.02046i	0.115198	+	0.168959i
$144$		0			0
$145$	0.474051	+	0.273693i	0.0393678	+	0.0227290i
$146$	−4.19787	+	7.27092i	−0.347418	+	0.601746i
$147$		0			0
$148$			2.11924i			0.174201i
$149$	14.3130	−	8.26363i	1.17257	−	0.676983i	0.218285	−	0.975885i	$-0.429954\pi$
$149$	14.3130	−	8.26363i	1.17257	−	0.676983i	0.954284	+	0.298902i	$0.0966203\pi$
$150$		0			0
$151$		−	20.3543i		−	1.65641i	−0.560424	−	0.828206i	$-0.689362\pi$
$151$		−	20.3543i		−	1.65641i	0.560424	−	0.828206i	$-0.310638\pi$
$152$	5.11674	+	8.86246i	0.415023	+	0.718841i
$153$		0			0
$154$	1.44085	+	0.831875i	0.116107	+	0.0670344i
$155$	0.687245			0.0552008
$156$		0			0
$157$	15.1583			1.20976			0.604881	−	0.796316i	$-0.293221\pi$
$157$	15.1583			1.20976			0.604881	+	0.796316i	$0.293221\pi$
$158$	29.8447	+	17.2309i	2.37432	+	1.37081i
$159$		0			0
$160$	0.00591746	+	0.0102493i	0.000467816	+	0.000810281i
$161$			4.29948i			0.338846i
$162$		0			0
$163$	14.5849	−	8.42058i	1.14238	−	0.659551i	0.195357	−	0.980732i	$-0.437413\pi$
$163$	14.5849	−	8.42058i	1.14238	−	0.659551i	0.947018	+	0.321182i	$0.104080\pi$
$164$		−	20.6414i		−	1.61182i
$165$		0			0
$166$	−8.62761	+	14.9435i	−0.669632	+	1.15984i
$167$	−1.43006	−	0.825643i	−0.110661	−	0.0638902i	0.443648	−	0.896201i	$-0.353684\pi$
$167$	−1.43006	−	0.825643i	−0.110661	−	0.0638902i	−0.554309	+	0.832311i	$0.687017\pi$
$168$		0			0
$169$	8.10569	+	10.1636i	0.623515	+	0.781812i
$170$	0.156647			0.0120143
$171$		0			0
$172$	3.59287	−	6.22303i	0.273954	−	0.474502i
$173$	−12.3893	−	21.4589i	−0.941943	−	1.63149i	−0.761759	−	0.647861i	$-0.775664\pi$
$173$	−12.3893	−	21.4589i	−0.941943	−	1.63149i	−0.180185	−	0.983633i	$-0.557670\pi$
$174$		0			0
$175$	4.32609	−	2.49767i	0.327021	−	0.188806i
$176$	2.41160	−	1.39234i	0.181781	−	0.104952i
$177$		0			0
$178$	19.3232	+	33.4688i	1.44834	+	2.50859i
$179$	3.15142	−	5.45842i	0.235548	−	0.407982i	−0.723884	−	0.689922i	$-0.757645\pi$
$179$	3.15142	−	5.45842i	0.235548	−	0.407982i	0.959432	+	0.281940i	$0.0909781\pi$
$180$		0			0
$181$	18.9468			1.40830			0.704152	−	0.710049i	$-0.251327\pi$
$181$	18.9468			1.40830			0.704152	+	0.710049i	$0.251327\pi$
$182$	7.96885	+	3.83744i	0.590691	+	0.284450i
$183$		0			0
$184$	18.4284	+	10.6397i	1.35856	+	0.784367i
$185$	−0.0180138	+	0.0312008i	−0.00132440	+	0.00229393i
$186$		0			0
$187$		−	0.634117i		−	0.0463712i
$188$	14.7137	−	8.49495i	1.07311	−	0.619558i
$189$		0			0
$190$			0.346428i			0.0251325i
$191$	−4.39705	−	7.61592i	−0.318159	−	0.551068i	0.661945	−	0.749553i	$-0.269731\pi$
$191$	−4.39705	−	7.61592i	−0.318159	−	0.551068i	−0.980104	+	0.198484i	$0.936398\pi$
$192$		0			0
$193$	5.36850	+	3.09951i	0.386433	+	0.223107i	0.680614	−	0.732643i	$-0.261713\pi$
$193$	5.36850	+	3.09951i	0.386433	+	0.223107i	−0.294180	+	0.955750i	$0.595047\pi$
$194$	40.8939			2.93601
$195$		0			0
$196$	4.01758			0.286970
$197$	13.1145	+	7.57168i	0.934372	+	0.539460i	0.888192	−	0.459473i	$-0.151962\pi$
$197$	13.1145	+	7.57168i	0.934372	+	0.539460i	0.0461801	+	0.998933i	$0.485295\pi$
$198$		0			0
$199$	7.51860	+	13.0226i	0.532979	+	0.923147i	0.999258	+	0.0385094i	$0.0122610\pi$
$199$	7.51860	+	13.0226i	0.532979	+	0.923147i	−0.466279	+	0.884638i	$0.654406\pi$
$200$		−	24.7233i		−	1.74820i
$201$		0			0
$202$	−3.19575	+	1.84507i	−0.224852	+	0.129819i
$203$		−	8.01446i		−	0.562505i
$204$		0			0
$205$	0.175454	−	0.303895i	0.0122542	−	0.0212250i
$206$	−4.71030	−	2.71949i	−0.328182	−	0.189476i
$207$		0			0
$208$	12.2312	−	8.33940i	0.848084	−	0.578234i
$209$	1.40236			0.0970031
$210$		0			0
$211$	−12.7371	+	22.0613i	−0.876856	+	1.51876i	−0.0220844	+	0.999756i	$0.507030\pi$
$211$	−12.7371	+	22.0613i	−0.876856	+	1.51876i	−0.854772	+	0.519004i	$0.826303\pi$
$212$	6.45817	+	11.1859i	0.443549	+	0.768249i
$213$		0			0
$214$	42.0338	−	24.2682i	2.87337	−	1.65894i
$215$	0.105793	−	0.0610796i	0.00721502	−	0.00416560i
$216$		0			0
$217$	−5.03108	−	8.71409i	−0.341532	−	0.591551i
$218$	−2.09843	+	3.63459i	−0.142124	+	0.246166i
$219$		0			0
$220$	0.186107			0.0125473
$221$	−0.251972	−	3.36161i	−0.0169494	−	0.226126i
$222$		0			0
$223$	−6.06784	−	3.50327i	−0.406333	−	0.234596i	0.282880	−	0.959155i	$-0.408710\pi$
$223$	−6.06784	−	3.50327i	−0.406333	−	0.234596i	−0.689213	+	0.724559i	$0.742043\pi$
$224$	0.0866393	−	0.150064i	0.00578883	−	0.0100266i
$225$		0			0
$226$			33.4581i			2.22560i
$227$	−24.0383	+	13.8785i	−1.59548	+	0.921151i	−0.603137	+	0.797638i	$0.706083\pi$
$227$	−24.0383	+	13.8785i	−1.59548	+	0.921151i	−0.992343	+	0.123513i	$0.960584\pi$
$228$		0			0
$229$			3.61011i			0.238563i	0.992860	+	0.119281i	$0.0380591\pi$
$229$			3.61011i			0.238563i	−0.992860	+	0.119281i	$0.961941\pi$
$230$	0.360178	+	0.623846i	0.0237494	+	0.0411352i
$231$		0			0
$232$	−34.3516	−	19.8329i	−2.25529	−	1.30209i
$233$	−15.6176			−1.02315			−0.511573	−	0.859240i	$-0.670937\pi$
$233$	−15.6176			−1.02315			−0.511573	+	0.859240i	$0.670937\pi$
$234$		0			0
$235$	0.288832			0.0188413
$236$	28.9740	+	16.7281i	1.88604	+	1.08891i
$237$		0			0
$238$	−1.14676	−	1.98625i	−0.0743335	−	0.128749i
$239$			27.9831i			1.81008i	0.425332	+	0.905038i	$0.360157\pi$
$239$			27.9831i			1.81008i	−0.425332	+	0.905038i	$0.639843\pi$
$240$		0			0
$241$	22.4935	−	12.9866i	1.44893	−	0.836541i	0.450514	−	0.892769i	$-0.351241\pi$
$241$	22.4935	−	12.9866i	1.44893	−	0.836541i	0.998418	+	0.0562280i	$0.0179074\pi$
$242$			25.8554i			1.66205i
$243$		0			0
$244$	2.02995	−	3.51598i	0.129954	−	0.225087i
$245$	0.0591494	+	0.0341499i	0.00377892	+	0.00218176i
$246$		0			0
$247$	7.43424	−	0.557238i	0.473029	−	0.0354562i
$248$	−49.8005			−3.16233
$249$		0			0
$250$	0.837333	−	1.45030i	0.0529576	−	0.0917253i
$251$	3.19262	+	5.52979i	0.201517	+	0.349037i	0.949017	−	0.315224i	$-0.102080\pi$
$251$	3.19262	+	5.52979i	0.201517	+	0.349037i	−0.747501	+	0.664261i	$0.768746\pi$
$252$		0			0
$253$	2.52536	−	1.45802i	0.158768	−	0.0916649i
$254$	17.0047	−	9.81769i	1.06697	−	0.616017i
$255$		0			0
$256$	16.0666	+	27.8282i	1.00416	+	1.73926i
$257$	6.90893	−	11.9666i	0.430967	−	0.746457i	−0.565990	−	0.824412i	$-0.691506\pi$
$257$	6.90893	−	11.9666i	0.430967	−	0.746457i	0.996957	+	0.0779556i	$0.0248392\pi$
$258$		0			0
$259$	0.527492			0.0327767
$260$	0.986597	−	0.0739510i	0.0611861	−	0.00458625i
$261$		0			0
$262$	−21.8629	−	12.6225i	−1.35069	−	0.779823i
$263$	−5.66821	+	9.81762i	−0.349517	+	0.605380i	−0.986164	−	0.165775i	$-0.946988\pi$
$263$	−5.66821	+	9.81762i	−0.349517	+	0.605380i	0.636647	+	0.771155i	$0.280321\pi$
$264$		0			0
$265$			0.219581i			0.0134887i
$266$	4.39262	−	2.53608i	0.269329	−	0.155497i
$267$		0			0
$268$		−	29.3296i		−	1.79159i
$269$	10.5001	+	18.1867i	0.640202	+	1.10886i	0.985387	+	0.170328i	$0.0544828\pi$
$269$	10.5001	+	18.1867i	0.640202	+	1.10886i	−0.345185	+	0.938535i	$0.612184\pi$
$270$		0			0
$271$	−25.3269	−	14.6225i	−1.53850	−	0.888253i	−0.998927	−	0.0463142i	$-0.985252\pi$
$271$	−25.3269	−	14.6225i	−1.53850	−	0.888253i	−0.539573	−	0.841939i	$-0.681414\pi$
$272$	−3.83875			−0.232759
$273$		0			0
$274$	−8.87904			−0.536403
$275$	−2.93408	−	1.69399i	−0.176932	−	0.102152i
$276$		0			0
$277$	8.25178	+	14.2925i	0.495801	+	0.858753i	0.999988	−	0.00484129i	$-0.00154104\pi$
$277$	8.25178	+	14.2925i	0.495801	+	0.858753i	−0.504187	+	0.863595i	$0.668208\pi$
$278$			2.98821i			0.179221i
$279$		0			0
$280$	0.292747	−	0.169018i	0.0174950	−	0.0101007i
$281$		−	1.12161i		−	0.0669094i	−0.999440	−	0.0334547i	$-0.989349\pi$
$281$		−	1.12161i		−	0.0669094i	0.999440	−	0.0334547i	$-0.0106509\pi$
$282$		0			0
$283$	5.47060	−	9.47536i	0.325194	−	0.563252i	−0.656358	−	0.754450i	$-0.727904\pi$
$283$	5.47060	−	9.47536i	0.325194	−	0.563252i	0.981552	+	0.191198i	$0.0612372\pi$
$284$	34.4838	+	19.9092i	2.04624	+	1.18139i
$285$		0			0
$286$	−0.448382	−	5.98196i	−0.0265134	−	0.353721i
$287$	−5.13776			−0.303272
$288$		0			0
$289$	8.06293	−	13.9654i	0.474290	−	0.821494i
$290$	−0.671390	−	1.16288i	−0.0394254	−	0.0682868i
$291$		0			0
$292$	11.9081	−	6.87516i	0.696870	−	0.402338i
$293$	13.4669	−	7.77514i	0.786747	−	0.454229i	−0.0520690	−	0.998643i	$-0.516582\pi$
$293$	13.4669	−	7.77514i	0.786747	−	0.454229i	0.838816	+	0.544415i	$0.183248\pi$
$294$		0			0
$295$	0.284382	+	0.492564i	0.0165574	+	0.0286782i
$296$	1.30535	−	2.26094i	0.0758721	−	0.131414i
$297$		0			0
$298$	−40.5426			−2.34857
$299$	12.8082	−	8.73279i	0.740718	−	0.505030i
$300$		0			0
$301$	−1.54895	−	0.894286i	−0.0892799	−	0.0515458i
$302$	−24.9653	+	43.2413i	−1.43659	+	2.48825i
$303$		0			0
$304$		−	8.48945i		−	0.486903i
$305$	0.0597725	−	0.0345097i	0.00342256	−	0.00197602i
$306$		0			0
$307$			0.119003i			0.00679184i	0.999994	+	0.00339592i	$0.00108096\pi$
$307$			0.119003i			0.00679184i	−0.999994	+	0.00339592i	$0.998919\pi$
$308$	−1.36242	−	2.35979i	−0.0776313	−	0.134461i
$309$		0			0
$310$	−1.46000	−	0.842932i	−0.0829224	−	0.0478753i
$311$	−31.4738			−1.78472			−0.892358	−	0.451327i	$-0.850951\pi$
$311$	−31.4738			−1.78472			−0.892358	+	0.451327i	$0.850951\pi$
$312$		0			0
$313$	14.1243			0.798355			0.399178	−	0.916874i	$-0.369296\pi$
$313$	14.1243			0.798355			0.399178	+	0.916874i	$0.369296\pi$
$314$	−32.2026	−	18.5922i	−1.81730	−	1.04922i
$315$		0			0
$316$	−28.2202	−	48.8789i	−1.58751	−	2.74965i
$317$			18.6470i			1.04732i	0.851927	+	0.523661i	$0.175434\pi$
$317$			18.6470i			1.04732i	−0.851927	+	0.523661i	$0.824566\pi$
$318$		0			0
$319$	−4.70741	+	2.71783i	−0.263564	+	0.152169i
$320$			0.531820i			0.0297296i
$321$		0			0
$322$	5.27348	−	9.13393i	0.293879	−	0.509014i
$323$	−1.67419	−	0.966593i	−0.0931544	−	0.0537827i
$324$		0			0
$325$	−16.2274	−	7.81439i	−0.900135	−	0.433465i
$326$	−41.3126			−2.28810
$327$		0			0
$328$	−12.7141	+	22.0215i	−0.702019	+	1.21593i
$329$	−2.11444	−	3.66232i	−0.116573	−	0.201910i
$330$		0			0
$331$	−19.1255	+	11.0421i	−1.05123	+	0.606930i	−0.922995	−	0.384813i	$-0.874266\pi$
$331$	−19.1255	+	11.0421i	−1.05123	+	0.606930i	−0.128240	+	0.991743i	$0.540933\pi$
$332$	24.4740	−	14.1301i	1.34318	−	0.775488i
$333$		0			0
$334$	2.02537	+	3.50804i	0.110823	+	0.191951i
$335$	0.249305	−	0.431809i	0.0136210	−	0.0235922i
$336$		0			0
$337$	32.5355			1.77232			0.886161	−	0.463377i	$-0.153362\pi$
$337$	32.5355			1.77232			0.886161	+	0.463377i	$0.153362\pi$
$338$	−4.75396	−	31.5337i	−0.258581	−	1.71520i
$339$		0			0
$340$	−0.222181	−	0.128276i	−0.0120495	−	0.00695677i
$341$	−3.41223	+	5.91016i	−0.184783	+	0.320053i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−7.66618	+	4.42607i	−0.413333	+	0.238638i
$345$		0			0
$346$			60.7839i			3.26776i
$347$	2.20612	+	3.82111i	0.118431	+	0.205128i	0.919146	−	0.393917i	$-0.128880\pi$
$347$	2.20612	+	3.82111i	0.118431	+	0.205128i	−0.800715	+	0.599045i	$0.795547\pi$
$348$		0			0
$349$	−6.16974	−	3.56210i	−0.330259	−	0.190675i	0.325697	−	0.945474i	$-0.394401\pi$
$349$	−6.16974	−	3.56210i	−0.330259	−	0.190675i	−0.655956	+	0.754799i	$0.727734\pi$
$350$	−12.2539			−0.655000
$351$		0			0
$352$	−0.117523			−0.00626399
$353$	−2.88961	−	1.66832i	−0.153799	−	0.0887957i	0.421126	−	0.907002i	$-0.361635\pi$
$353$	−2.88961	−	1.66832i	−0.153799	−	0.0887957i	−0.574924	+	0.818207i	$0.694968\pi$
$354$		0			0
$355$	0.338462	+	0.586233i	0.0179637	+	0.0311140i
$356$		−	63.2941i		−	3.35458i
$357$		0			0
$358$	−13.3899	+	7.73068i	−0.707680	+	0.408579i
$359$			24.5869i			1.29765i	0.760940	+	0.648823i	$0.224738\pi$
$359$			24.5869i			1.29765i	−0.760940	+	0.648823i	$0.775262\pi$
$360$		0			0
$361$	−7.36237	+	12.7520i	−0.387493	+	0.671158i
$362$	−40.2511	−	23.2390i	−2.11555	−	1.22141i
$363$		0			0
$364$	−8.16022	−	11.9684i	−0.427712	−	0.627316i
$365$	0.233759			0.0122355
$366$		0			0
$367$	7.53829	−	13.0567i	0.393495	−	0.681554i	−0.599412	−	0.800440i	$-0.704599\pi$
$367$	7.53829	−	13.0567i	0.393495	−	0.681554i	0.992908	+	0.118886i	$0.0379324\pi$
$368$	−8.82640	−	15.2878i	−0.460108	−	0.796931i
$369$		0			0
$370$	0.0765380	−	0.0441893i	0.00397902	−	0.00229729i
$371$	2.78423	−	1.60748i	0.144550	−	0.0834560i
$372$		0			0
$373$	12.6236	+	21.8646i	0.653623	+	1.13211i	0.982237	+	0.187644i	$0.0600852\pi$
$373$	12.6236	+	21.8646i	0.653623	+	1.13211i	−0.328614	+	0.944464i	$0.606581\pi$
$374$	−0.777769	+	1.34714i	−0.0402175	+	0.0696587i
$375$		0			0
$376$	−20.9299			−1.07938
$377$	−23.8752	+	16.2784i	−1.22963	+	0.838379i
$378$		0			0
$379$	20.8220	+	12.0216i	1.06955	+	0.617508i	0.928060	−	0.372431i	$-0.121476\pi$
$379$	20.8220	+	12.0216i	1.06955	+	0.617508i	0.141495	+	0.989939i	$0.454809\pi$
$380$	0.283685	−	0.491357i	0.0145527	−	0.0252061i
$381$		0			0
$382$			21.5726i			1.10375i
$383$	−3.93109	+	2.26962i	−0.200869	+	0.115972i	−0.597061	−	0.802196i	$-0.703665\pi$
$383$	−3.93109	+	2.26962i	−0.200869	+	0.115972i	0.396192	+	0.918168i	$0.370332\pi$
$384$		0			0
$385$		−	0.0463231i		−	0.00236084i
$386$	−7.60333	−	13.1693i	−0.386999	−	0.670302i
$387$		0			0
$388$	−58.0020	−	33.4875i	−2.94460	−	1.70007i
$389$	19.7847			1.00313			0.501563	−	0.865121i	$-0.332758\pi$
$389$	19.7847			1.00313			0.501563	+	0.865121i	$0.332758\pi$
$390$		0			0
$391$	−4.01983			−0.203292
$392$	−4.28620	−	2.47464i	−0.216486	−	0.124988i
$393$		0			0
$394$	−18.5739	−	32.1709i	−0.935740	−	1.62075i
$395$		−	0.959502i		−	0.0482778i
$396$		0			0
$397$	9.05725	−	5.22920i	0.454570	−	0.262446i	−0.255188	−	0.966891i	$-0.582137\pi$
$397$	9.05725	−	5.22920i	0.454570	−	0.262446i	0.709758	+	0.704445i	$0.248804\pi$
$398$		−	36.8874i		−	1.84900i
$399$		0			0
$400$	−10.2549	+	17.7621i	−0.512746	+	0.888103i
$401$	19.4194	+	11.2118i	0.969759	+	0.559891i	0.899163	−	0.437614i	$-0.144176\pi$
$401$	19.4194	+	11.2118i	0.969759	+	0.559891i	0.0705965	+	0.997505i	$0.477510\pi$
$402$		0			0
$403$	−15.7406	+	32.6871i	−0.784097	+	1.62826i
$404$	6.04361			0.300681
$405$		0			0
$406$	−9.83004	+	17.0261i	−0.487857	+	0.844992i
$407$	−0.178880	−	0.309830i	−0.00886678	−	0.0153577i
$408$		0			0
$409$	−21.1661	+	12.2203i	−1.04660	+	0.604253i	−0.921695	−	0.387916i	$-0.873195\pi$
$409$	−21.1661	+	12.2203i	−1.04660	+	0.604253i	−0.124902	+	0.992169i	$0.539862\pi$
$410$	−0.745479	+	0.430402i	−0.0368166	+	0.0212561i
$411$		0			0
$412$	4.45391	+	7.71440i	0.219428	+	0.380061i
$413$	4.16373	−	7.21179i	0.204884	−	0.354869i
$414$		0			0
$415$	0.480429			0.0235833
$416$	−0.623017	+	0.0466987i	−0.0305459	+	0.00228959i
$417$		0			0
$418$	−2.97921	−	1.72005i	−0.145718	−	0.0841302i
$419$	13.8981	−	24.0722i	0.678965	−	1.17600i	−0.296328	−	0.955086i	$-0.595762\pi$
$419$	13.8981	−	24.0722i	0.678965	−	1.17600i	0.975293	−	0.220916i	$-0.0709046\pi$
$420$		0			0
$421$			15.8324i			0.771626i	0.922577	+	0.385813i	$0.126079\pi$
$421$			15.8324i			0.771626i	−0.922577	+	0.385813i	$0.873921\pi$
$422$	54.1179	−	31.2450i	2.63442	−	1.52098i
$423$		0			0
$424$		−	15.9117i		−	0.772741i
$425$	2.33522	+	4.04471i	0.113275	+	0.196197i
$426$		0			0
$427$	−0.875148	−	0.505267i	−0.0423514	−	0.0244516i
$428$	−79.4917			−3.84238
$429$		0			0
$430$	−0.299666			−0.0144512
$431$	−15.7701	−	9.10489i	−0.759621	−	0.438567i	0.0695388	−	0.997579i	$-0.477847\pi$
$431$	−15.7701	−	9.10489i	−0.759621	−	0.438567i	−0.829160	+	0.559012i	$0.811181\pi$
$432$		0			0
$433$	−4.70224	−	8.14452i	−0.225975	−	0.391401i	0.730636	−	0.682767i	$-0.239224\pi$
$433$	−4.70224	−	8.14452i	−0.225975	−	0.391401i	−0.956612	+	0.291366i	$0.905890\pi$
$434$			24.6833i			1.18483i
$435$		0			0
$436$	5.95264	−	3.43676i	0.285080	−	0.164591i
$437$		−	8.88991i		−	0.425262i
$438$		0			0
$439$	−9.61695	+	16.6570i	−0.458992	+	0.794998i	−0.998908	−	0.0467214i	$-0.985123\pi$
$439$	−9.61695	+	16.6570i	−0.458992	+	0.794998i	0.539916	+	0.841719i	$0.318456\pi$
$440$	−0.198550	−	0.114633i	−0.00946550	−	0.00546491i
$441$		0			0
$442$	−3.58785	+	7.45055i	−0.170656	+	0.354386i
$443$	5.40445			0.256773			0.128387	−	0.991724i	$-0.459020\pi$
$443$	5.40445			0.256773			0.128387	+	0.991724i	$0.459020\pi$
$444$		0			0
$445$	0.538008	−	0.931857i	0.0255040	−	0.0441742i
$446$	8.59378	+	14.8849i	0.406927	+	0.704819i
$447$		0			0
$448$	6.74334	−	3.89327i	0.318593	−	0.183940i
$449$	11.7376	−	6.77669i	0.553930	−	0.319812i	−0.196775	−	0.980449i	$-0.563047\pi$
$449$	11.7376	−	6.77669i	0.553930	−	0.319812i	0.750706	+	0.660637i	$0.229714\pi$
$450$		0			0
$451$	1.74229	+	3.01774i	0.0820413	+	0.142100i
$452$	27.3984	−	47.4554i	1.28871	−	2.23211i
$453$		0			0
$454$	68.0902			3.19563
$455$	−0.0184068	−	0.245570i	−0.000862926	−	0.0115125i
$456$		0			0
$457$	−25.8274	−	14.9114i	−1.20815	−	0.697528i	−0.245798	−	0.969321i	$-0.579050\pi$
$457$	−25.8274	−	14.9114i	−1.20815	−	0.697528i	−0.962356	+	0.271793i	$0.912383\pi$
$458$	4.42794	−	7.66942i	0.206904	−	0.358368i
$459$		0			0
$460$		−	1.17978i		−	0.0550075i
$461$	1.92953	−	1.11402i	0.0898673	−	0.0518849i	−0.454393	−	0.890801i	$-0.650144\pi$
$461$	1.92953	−	1.11402i	0.0898673	−	0.0518849i	0.544260	+	0.838916i	$0.316810\pi$
$462$		0			0
$463$			21.6086i			1.00424i	0.864799	+	0.502118i	$0.167446\pi$
$463$			21.6086i			1.00424i	−0.864799	+	0.502118i	$0.832554\pi$
$464$	16.4529	+	28.4972i	0.763806	+	1.32295i
$465$		0			0
$466$	33.1785	+	19.1556i	1.53696	+	0.887367i
$467$	−24.0068			−1.11090			−0.555452	−	0.831549i	$-0.687455\pi$
$467$	−24.0068			−1.11090			−0.555452	+	0.831549i	$0.687455\pi$
$468$		0			0
$469$	−7.30030			−0.337097
$470$	−0.613603	−	0.354264i	−0.0283034	−	0.0163410i
$471$		0			0
$472$	−20.6075	−	35.6932i	−0.948536	−	1.64291i
$473$			1.21306i			0.0557767i
$474$		0			0
$475$	−8.94493	+	5.16436i	−0.410421	+	0.236957i
$476$			3.75627i			0.172168i
$477$		0			0
$478$	34.3223	−	59.4480i	1.56987	−	2.71909i
$479$	26.5801	+	15.3461i	1.21448	+	0.701179i	0.963732	−	0.266874i	$-0.0859906\pi$
$479$	26.5801	+	15.3461i	1.21448	+	0.701179i	0.250746	+	0.968053i	$0.419324\pi$
$480$		0			0
$481$	−1.07140	−	1.57141i	−0.0488518	−	0.0716499i
$482$	−63.7143			−2.90211
$483$		0			0
$484$	21.1727	−	36.6721i	0.962394	−	1.66692i
$485$	−0.569295	−	0.986048i	−0.0258504	−	0.0447741i
$486$		0			0
$487$	15.4765	−	8.93535i	0.701306	−	0.404899i	−0.106528	−	0.994310i	$-0.533973\pi$
$487$	15.4765	−	8.93535i	0.701306	−	0.404899i	0.807834	+	0.589411i	$0.200640\pi$
$488$	−4.33135	+	2.50071i	−0.196071	+	0.113202i
$489$		0			0
$490$	−0.0837724	−	0.145098i	−0.00378445	−	0.00655486i
$491$	6.78481	−	11.7516i	0.306194	−	0.530344i	−0.671332	−	0.741156i	$-0.734278\pi$
$491$	6.78481	−	11.7516i	0.306194	−	0.530344i	0.977526	+	0.210813i	$0.0676110\pi$
$492$		0			0
$493$	7.49318			0.337476
$494$	−16.4770	−	7.93457i	−0.741334	−	0.356993i
$495$		0			0
$496$	35.7783	+	20.6566i	1.60649	+	0.927510i
$497$	4.95552	−	8.58321i	0.222286	−	0.385010i
$498$		0			0
$499$		−	10.4240i		−	0.466644i	−0.972399	−	0.233322i	$-0.925040\pi$
$499$		−	10.4240i		−	0.466644i	0.972399	−	0.233322i	$-0.0749597\pi$
$500$	−2.37527	+	1.37136i	−0.106225	+	0.0613292i
$501$		0			0
$502$		−	15.6635i		−	0.699096i
$503$	2.52407	+	4.37181i	0.112543	+	0.194929i	0.916795	−	0.399359i	$-0.130767\pi$
$503$	2.52407	+	4.37181i	0.112543	+	0.194929i	−0.804252	+	0.594288i	$0.797434\pi$
$504$		0			0
$505$	0.0889779	+	0.0513714i	0.00395946	+	0.00228600i
$506$	−7.15326			−0.318001
$507$		0			0
$508$	−32.1583			−1.42679
$509$	7.78769	+	4.49623i	0.345183	+	0.199292i	0.662562	−	0.749007i	$-0.269469\pi$
$509$	7.78769	+	4.49623i	0.345183	+	0.199292i	−0.317378	+	0.948299i	$0.602803\pi$
$510$		0			0
$511$	−1.71127	−	2.96400i	−0.0757020	−	0.131120i
$512$		−	39.9301i		−	1.76468i
$513$		0			0
$514$	−29.3550	+	16.9481i	−1.29479	+	0.747549i
$515$			0.151435i			0.00667303i
$516$		0			0
$517$	−1.43408	+	2.48390i	−0.0630707	+	0.109242i
$518$	−1.12062	−	0.646989i	−0.0492371	−	0.0284271i
$519$		0			0
$520$	−1.09811	−	0.528802i	−0.0481554	−	0.0231895i
$521$	9.21666			0.403789			0.201895	−	0.979407i	$-0.435290\pi$
$521$	9.21666			0.403789			0.201895	+	0.979407i	$0.435290\pi$
$522$		0			0
$523$	−9.33282	+	16.1649i	−0.408096	+	0.706842i	−0.994676	−	0.103048i	$-0.967140\pi$
$523$	−9.33282	+	16.1649i	−0.408096	+	0.706842i	0.586581	+	0.809891i	$0.300474\pi$
$524$	20.6729	+	35.8064i	0.903098	+	1.56421i
$525$		0			0
$526$	24.0834	−	13.9045i	1.05008	−	0.606267i
$527$	8.14731	−	4.70385i	0.354902	−	0.204903i
$528$		0			0
$529$	2.25724	+	3.90965i	0.0981407	+	0.169985i
$530$	0.269324	−	0.466483i	0.0116987	−	0.0202627i
$531$		0			0
$532$	−8.30704			−0.360156
$533$	10.4354	+	15.3055i	0.452009	+	0.662953i
$534$		0			0
$535$	−1.17033	−	0.675689i	−0.0505977	−	0.0292126i
$536$	−18.0656	+	31.2906i	−0.780316	+	1.35155i
$537$		0			0
$538$		−	51.5151i		−	2.22097i
$539$	−0.587365	+	0.339115i	−0.0252996	+	0.0146067i
$540$		0			0
$541$			16.3383i			0.702437i	0.936293	+	0.351219i	$0.114233\pi$
$541$			16.3383i			0.702437i	−0.936293	+	0.351219i	$0.885767\pi$
$542$	35.8701	+	62.1288i	1.54075	+	2.66866i
$543$		0			0
$544$	0.140303	+	0.0810042i	0.00601546	+	0.00347302i
$545$	0.116851			0.00500536
$546$		0			0
$547$	5.07719			0.217085			0.108542	−	0.994092i	$-0.465382\pi$
$547$	5.07719			0.217085			0.108542	+	0.994092i	$0.465382\pi$
$548$	12.5936	+	7.27093i	0.537973	+	0.310599i
$549$		0			0
$550$	4.15550	+	7.19753i	0.177191	+	0.306904i
$551$			16.5713i			0.705960i
$552$		0			0
$553$	−12.1662	+	7.02419i	−0.517362	+	0.298699i
$554$		−	40.4845i		−	1.72002i
$555$		0			0
$556$	2.44700	−	4.23833i	0.103776	−	0.179745i
$557$	1.11171	+	0.641845i	0.0471046	+	0.0271959i	0.523367	−	0.852107i	$-0.324676\pi$
$557$	1.11171	+	0.641845i	0.0471046	+	0.0271959i	−0.476263	+	0.879303i	$0.658009\pi$
$558$		0			0
$559$	0.482021	+	6.43075i	0.0203873	+	0.271992i
$560$	−0.280426			−0.0118502
$561$		0			0
$562$	−1.37569	+	2.38277i	−0.0580301	+	0.100511i
$563$	−8.48990	−	14.7049i	−0.357807	−	0.619739i	0.629788	−	0.776767i	$-0.283142\pi$
$563$	−8.48990	−	14.7049i	−0.357807	−	0.619739i	−0.987594	+	0.157028i	$0.949809\pi$
$564$		0			0
$565$	0.806753	−	0.465779i	0.0339404	−	0.0195955i
$566$	−23.2438	+	13.4198i	−0.977009	+	0.564076i
$567$		0			0
$568$	−24.5263	−	42.4807i	−1.02910	−	1.78245i
$569$	17.9814	−	31.1447i	0.753820	−	1.30566i	−0.192138	−	0.981368i	$-0.561542\pi$
$569$	17.9814	−	31.1447i	0.753820	−	1.30566i	0.945959	−	0.324287i	$-0.105124\pi$
$570$		0			0
$571$	20.6811			0.865475			0.432738	−	0.901520i	$-0.357548\pi$
$571$	20.6811			0.865475			0.432738	+	0.901520i	$0.357548\pi$
$572$	−4.26258	+	8.85170i	−0.178228	+	0.370108i
$573$		0			0
$574$	10.9148	+	6.30166i	0.455574	+	0.263026i
$575$	−10.7387	+	18.5999i	−0.447834	+	0.775670i
$576$		0			0
$577$			3.67781i			0.153109i	0.997065	+	0.0765546i	$0.0243920\pi$
$577$			3.67781i			0.153109i	−0.997065	+	0.0765546i	$0.975608\pi$
$578$	−34.2582	+	19.7790i	−1.42495	+	0.822697i
$579$		0			0
$580$			2.19917i			0.0913156i
$581$	−3.51706	−	6.09172i	−0.145912	−	0.252727i
$582$		0			0
$583$	−1.88835	−	1.09024i	−0.0782074	−	0.0451531i
$584$	−16.9391			−0.700945
$585$		0			0
$586$	−38.1460			−1.57580
$587$	−10.4298	−	6.02163i	−0.430482	−	0.248539i	0.269070	−	0.963121i	$-0.413284\pi$
$587$	−10.4298	−	6.02163i	−0.430482	−	0.248539i	−0.699552	+	0.714582i	$0.746617\pi$
$588$		0			0
$589$	10.4026	+	18.0179i	0.428633	+	0.742414i
$590$		−	1.39522i		−	0.0574404i
$591$		0			0
$592$	−1.87562	+	1.08289i	−0.0770874	+	0.0445064i
$593$			24.4737i			1.00501i	0.864573	+	0.502507i	$0.167589\pi$
$593$			24.4737i			1.00501i	−0.864573	+	0.502507i	$0.832411\pi$
$594$		0			0
$595$	−0.0319288	+	0.0553023i	−0.00130895	+	0.00226717i
$596$	57.5038	+	33.1998i	2.35545	+	1.35992i
$597$		0			0
$598$	−37.9212	+	2.84241i	−1.55071	+	0.116235i
$599$	21.8012			0.890773			0.445387	−	0.895338i	$-0.353066\pi$
$599$	21.8012			0.890773			0.445387	+	0.895338i	$0.353066\pi$
$600$		0			0
$601$	−3.29106	+	5.70029i	−0.134245	+	0.232520i	−0.925309	−	0.379214i	$-0.876194\pi$
$601$	−3.29106	+	5.70029i	−0.134245	+	0.232520i	0.791064	+	0.611734i	$0.209528\pi$
$602$	2.19375	+	3.79969i	0.0894106	+	0.154864i
$603$		0			0
$604$	70.8194	−	40.8876i	2.88160	−	1.66369i
$605$	0.623435	−	0.359940i	0.0253462	−	0.0146337i
$606$		0			0
$607$	−22.8466	−	39.5715i	−0.927317	−	1.60616i	−0.787792	−	0.615941i	$-0.788776\pi$
$607$	−22.8466	−	39.5715i	−0.927317	−	1.60616i	−0.139524	−	0.990219i	$-0.544557\pi$
$608$	−0.179142	+	0.310282i	−0.00726515	+	0.0125836i
$609$		0			0
$610$	−0.169310			−0.00685515
$611$	−6.61541	+	13.7376i	−0.267631	+	0.555764i
$612$		0			0
$613$	−36.3690	−	20.9977i	−1.46893	−	0.848088i	−0.469538	−	0.882912i	$-0.655580\pi$
$613$	−36.3690	−	20.9977i	−1.46893	−	0.848088i	−0.999393	+	0.0348243i	$0.988913\pi$
$614$	0.145961	−	0.252812i	0.00589052	−	0.0102027i
$615$		0			0
$616$			3.35675i			0.135247i
$617$	21.1634	−	12.2187i	0.852006	−	0.491906i	−0.00932137	−	0.999957i	$-0.502967\pi$
$617$	21.1634	−	12.2187i	0.852006	−	0.491906i	0.861327	+	0.508051i	$0.169634\pi$
$618$		0			0
$619$			24.1245i			0.969644i	0.874613	+	0.484822i	$0.161116\pi$
$619$			24.1245i			0.969644i	−0.874613	+	0.484822i	$0.838884\pi$
$620$	1.38053	+	2.39115i	0.0554434	+	0.0960309i
$621$		0			0
$622$	66.8638	+	38.6038i	2.68099	+	1.54787i
$623$	−15.7543			−0.631182
$624$		0			0
$625$	24.9300			0.997202
$626$	−30.0061	−	17.3240i	−1.19929	−	0.692408i
$627$		0			0
$628$	30.4498	+	52.7406i	1.21508	+	2.10458i
$629$			0.493183i			0.0196645i
$630$		0			0
$631$	20.4155	−	11.7869i	0.812727	−	0.469228i	−0.0351753	−	0.999381i	$-0.511199\pi$
$631$	20.4155	−	11.7869i	0.812727	−	0.469228i	0.847902	+	0.530153i	$0.177866\pi$
$632$			69.5294i			2.76573i
$633$		0			0
$634$	22.8713	−	39.6142i	0.908335	−	1.57328i
$635$	−0.473455	−	0.273350i	−0.0187885	−	0.0108475i
$636$		0			0
$637$	−2.97901	+	2.03113i	−0.118033	+	0.0804762i
$638$	13.3341			0.527901
$639$		0			0
$640$	0.664132	−	1.15031i	0.0262521	−	0.0454700i
$641$	−18.4479	−	31.9527i	−0.728648	−	1.26205i	−0.957455	−	0.288583i	$-0.906816\pi$
$641$	−18.4479	−	31.9527i	−0.728648	−	1.26205i	0.228807	−	0.973472i	$-0.426518\pi$
$642$		0			0
$643$	−21.8045	+	12.5888i	−0.859886	+	0.496455i	−0.863974	−	0.503536i	$-0.832032\pi$
$643$	−21.8045	+	12.5888i	−0.859886	+	0.496455i	0.00408823	+	0.999992i	$0.498699\pi$
$644$	−14.9593	+	8.63676i	−0.589479	+	0.340336i
$645$		0			0
$646$	2.37113	+	4.10691i	0.0932907	+	0.161584i
$647$	−2.50086	+	4.33161i	−0.0983189	+	0.170293i	−0.910989	−	0.412431i	$-0.864680\pi$
$647$	−2.50086	+	4.33161i	−0.0983189	+	0.170293i	0.812670	+	0.582724i	$0.198013\pi$
$648$		0			0
$649$	−5.64794			−0.221701
$650$	24.8893	+	36.5046i	0.976239	+	1.43183i
$651$		0			0
$652$	58.5959	+	33.8304i	2.29479	+	1.32490i
$653$	−13.9272	+	24.1227i	−0.545015	+	0.943993i	0.453591	+	0.891210i	$0.350143\pi$
$653$	−13.9272	+	24.1227i	−0.545015	+	0.943993i	−0.998606	+	0.0527834i	$0.983191\pi$
$654$		0			0
$655$			0.702887i			0.0274641i
$656$	18.2685	−	10.5473i	0.713264	−	0.411803i
$657$		0			0
$658$			10.3738i			0.404412i
$659$	2.39968	+	4.15637i	0.0934783	+	0.161909i	0.908973	−	0.416856i	$-0.136868\pi$
$659$	2.39968	+	4.15637i	0.0934783	+	0.161909i	−0.815494	+	0.578765i	$0.803535\pi$
$660$		0			0
$661$	2.64475	+	1.52695i	0.102869	+	0.0593914i	0.550552	−	0.834801i	$-0.314417\pi$
$661$	2.64475	+	1.52695i	0.102869	+	0.0593914i	−0.447683	+	0.894192i	$0.647751\pi$
$662$	54.1744			2.10555
$663$		0			0
$664$	−34.8138			−1.35104
$665$	−0.122302	−	0.0706109i	−0.00474265	−	0.00273817i
$666$		0			0
$667$	17.2290	+	29.8415i	0.667110	+	1.15547i
$668$		−	6.63418i		−	0.256684i
$669$		0			0
$670$	−1.05926	+	0.611564i	−0.0409228	+	0.0236268i
$671$			0.685375i			0.0264586i
$672$		0			0
$673$	6.39498	−	11.0764i	0.246508	−	0.426965i	−0.716046	−	0.698053i	$-0.754050\pi$
$673$	6.39498	−	11.0764i	0.246508	−	0.426965i	0.962555	+	0.271088i	$0.0873834\pi$
$674$	−69.1193	−	39.9061i	−2.66238	−	1.53712i
$675$		0			0
$676$	−19.0797	+	48.6188i	−0.733834	+	1.86995i
$677$	−21.6803			−0.833240			−0.416620	−	0.909081i	$-0.636785\pi$
$677$	−21.6803			−0.833240			−0.416620	+	0.909081i	$0.636785\pi$
$678$		0			0
$679$	−8.33523	+	14.4370i	−0.319877	+	0.554043i
$680$	0.158024	+	0.273706i	0.00605996	+	0.0104962i
$681$		0			0
$682$	14.4981	−	8.37047i	0.555160	−	0.320522i
$683$	−29.4162	+	16.9835i	−1.12558	+	0.649854i	−0.942820	−	0.333303i	$-0.891837\pi$
$683$	−29.4162	+	16.9835i	−1.12558	+	0.649854i	−0.182761	+	0.983157i	$0.558503\pi$
$684$		0			0
$685$	0.123608	+	0.214095i	0.00472280	+	0.00818014i
$686$	−1.22654	+	2.12443i	−0.0468294	+	0.0811110i
$687$		0			0
$688$	7.34352			0.279969
$689$	−10.4438	−	5.02927i	−0.397878	−	0.191600i
$690$		0			0
$691$	−37.4270	−	21.6085i	−1.42379	−	0.822026i	−0.427170	−	0.904171i	$-0.640490\pi$
$691$	−37.4270	−	21.6085i	−1.42379	−	0.822026i	−0.996620	+	0.0821452i	$0.973823\pi$
$692$	49.7752	−	86.2131i	1.89217	−	3.27733i
$693$		0			0
$694$		−	10.8235i		−	0.410856i
$695$	0.0720527	−	0.0415997i	0.00273312	−	0.00157796i
$696$		0			0
$697$		−	4.80359i		−	0.181949i
$698$	8.73811	+	15.1349i	0.330742	+	0.572863i
$699$		0			0
$700$	17.3804	+	10.0346i	0.656918	+	0.379272i
$701$	−0.456718			−0.0172500			−0.00862500	−	0.999963i	$-0.502745\pi$
$701$	−0.456718			−0.0172500			−0.00862500	+	0.999963i	$0.502745\pi$
$702$		0			0
$703$	−1.09068			−0.0411358
$704$	−4.57354	−	2.64053i	−0.172372	−	0.0995188i
$705$		0			0
$706$	4.09251	+	7.08844i	0.154024	+	0.266777i
$707$		−	1.50429i		−	0.0565746i
$708$		0			0
$709$	12.8902	−	7.44219i	0.484103	−	0.279497i	−0.238022	−	0.971260i	$-0.576499\pi$
$709$	12.8902	−	7.44219i	0.484103	−	0.279497i	0.722125	+	0.691763i	$0.243166\pi$
$710$		−	1.66054i		−	0.0623191i
$711$		0			0
$712$	−38.9862	+	67.5261i	−1.46107	+	2.53065i
$713$	37.4660	+	21.6310i	1.40311	+	0.810089i
$714$		0			0
$715$	−0.137997	+	0.0940880i	−0.00516080	+	0.00351869i
$716$	25.3222			0.946335
$717$		0			0
$718$	30.1567	−	52.2330i	1.12544	−	1.94932i
$719$	−4.98743	−	8.63849i	−0.186000	−	0.322161i	0.757913	−	0.652355i	$-0.226219\pi$
$719$	−4.98743	−	8.63849i	−0.186000	−	0.322161i	−0.943913	+	0.330194i	$0.892886\pi$
$720$		0			0
$721$	1.92016	−	1.10860i	0.0715105	−	0.0412866i
$722$	31.2816	−	18.0604i	1.16418	−	0.672140i
$723$		0			0
$724$	38.0601	+	65.9221i	1.41449	+	2.44998i
$725$	20.0175	−	34.6712i	0.743430	−	1.28766i
$726$		0			0
$727$	−10.4392			−0.387169			−0.193585	−	0.981084i	$-0.562011\pi$
$727$	−10.4392			−0.387169			−0.193585	+	0.981084i	$0.562011\pi$
$728$	1.33383	+	17.7950i	0.0494352	+	0.659526i
$729$		0			0
$730$	−0.496603	−	0.286714i	−0.0183801	−	0.0106118i
$731$	0.836120	−	1.44820i	0.0309250	−	0.0535637i
$732$		0			0
$733$		−	22.7887i		−	0.841718i	−0.907126	−	0.420859i	$-0.861729\pi$
$733$		−	22.7887i		−	0.841718i	0.907126	−	0.420859i	$-0.138271\pi$
$734$	−32.0291	+	18.4920i	−1.18221	+	0.682552i
$735$		0			0
$736$			0.745008i			0.0274614i
$737$	2.47564	+	4.28794i	0.0911915	+	0.157948i
$738$		0			0
$739$	36.6152	+	21.1398i	1.34691	+	0.777640i	0.987811	−	0.155659i	$-0.0497502\pi$
$739$	36.6152	+	21.1398i	1.34691	+	0.777640i	0.359101	+	0.933299i	$0.383084\pi$
$740$	−0.144744			−0.00532089
$741$		0			0
$742$	−7.88652			−0.289523
$743$	6.04660	+	3.49101i	0.221828	+	0.128073i	0.606797	−	0.794857i	$-0.292454\pi$
$743$	6.04660	+	3.49101i	0.221828	+	0.128073i	−0.384968	+	0.922930i	$0.625788\pi$
$744$		0			0
$745$	0.564405	+	0.977578i	0.0206782	+	0.0358157i
$746$		−	61.9331i		−	2.26753i
$747$		0			0
$748$	2.20630	−	1.27381i	0.0806704	−	0.0465751i
$749$			19.7860i			0.722963i
$750$		0			0
$751$	17.7765	−	30.7898i	0.648673	−	1.12353i	−0.334767	−	0.942301i	$-0.608658\pi$
$751$	17.7765	−	30.7898i	0.648673	−	1.12353i	0.983440	−	0.181234i	$-0.0580091\pi$
$752$	15.0368	+	8.68148i	0.548334	+	0.316581i
$753$		0			0
$754$	70.6871	−	5.29840i	2.57427	−	0.192956i
$755$	1.39020			0.0505945
$756$		0			0
$757$	6.55855	−	11.3597i	0.238374	−	0.412877i	−0.721874	−	0.692025i	$-0.756719\pi$
$757$	6.55855	−	11.3597i	0.238374	−	0.412877i	0.960248	+	0.279148i	$0.0900521\pi$
$758$	−29.4899	−	51.0780i	−1.07112	−	1.85524i
$759$		0			0
$760$	−0.605305	+	0.349473i	−0.0219567	+	0.0126767i
$761$	2.84572	−	1.64298i	0.103157	−	0.0595578i	−0.447534	−	0.894267i	$-0.647698\pi$
$761$	2.84572	−	1.64298i	0.103157	−	0.0595578i	0.550691	+	0.834709i	$0.314364\pi$
$762$		0			0
$763$	−0.855429	−	1.48165i	−0.0309686	−	0.0536392i
$764$	17.6655	−	30.5976i	0.639116	−	1.10698i
$765$		0			0
$766$	11.1351			0.402327
$767$	−29.9411	+	2.24425i	−1.08111	+	0.0810353i
$768$		0			0
$769$	1.11552	+	0.644047i	0.0402267	+	0.0232249i	0.519978	−	0.854179i	$-0.325940\pi$
$769$	1.11552	+	0.644047i	0.0402267	+	0.0232249i	−0.479752	+	0.877404i	$0.659273\pi$
$770$	−0.0568170	+	0.0984099i	−0.00204754	+	0.00354645i
$771$		0			0
$772$			24.9051i			0.896352i
$773$	19.0653	−	11.0073i	0.685730	−	0.395907i	−0.116280	−	0.993216i	$-0.537097\pi$
$773$	19.0653	−	11.0073i	0.685730	−	0.395907i	0.802011	+	0.597310i	$0.203764\pi$
$774$		0			0
$775$		−	50.2639i		−	1.80553i
$776$	41.2534	+	71.4530i	1.48091	+	2.56501i
$777$		0			0
$778$	−42.0312	−	24.2667i	−1.50689	−	0.870005i
$779$	10.6232			0.380615
$780$		0			0
$781$	−6.72197			−0.240531
$782$	8.53984	+	4.93048i	0.305384	+	0.176314i
$783$		0			0
$784$	2.05290	+	3.55573i	0.0733179	+	0.126990i
$785$			1.03531i			0.0369517i
$786$		0			0
$787$	−4.41431	+	2.54860i	−0.157353	+	0.0908479i	−0.576609	−	0.817020i	$-0.695624\pi$
$787$	−4.41431	+	2.54860i	−0.157353	+	0.0908479i	0.419256	+	0.907868i	$0.362291\pi$
$788$			60.8397i			2.16732i
$789$		0			0
$790$	−1.17687	+	2.03839i	−0.0418710	+	0.0725227i
$791$	−11.8119	−	6.81962i	−0.419984	−	0.242478i
$792$		0			0
$793$	0.272339	+	3.63334i	0.00967105	+	0.129024i
$794$	−25.6553			−0.910471
$795$		0			0
$796$	−30.2066	+	52.3193i	−1.07064	+	1.85441i
$797$	20.7778	+	35.9881i	0.735986	+	1.27477i	0.954289	+	0.298884i	$0.0966144\pi$
$797$	20.7778	+	35.9881i	0.735986	+	1.27477i	−0.218303	+	0.975881i	$0.570052\pi$
$798$		0			0
$799$	3.42412	−	1.97692i	0.121137	−	0.0699383i
$800$	0.749619	−	0.432793i	0.0265030	−	0.0153015i
$801$		0			0
$802$	−27.5034	−	47.6373i	−0.971179	−	1.68213i
$803$	−1.16063	+	2.01028i	−0.0409579	+	0.0709411i
$804$		0			0
$805$	−0.293654			−0.0103499
$806$	73.5317	−	50.1348i	2.59005	−	1.76592i
$807$		0			0
$808$	−6.44769	−	3.72258i	−0.226829	−	0.130960i
$809$	11.0150	−	19.0785i	0.387266	−	0.670765i	−0.604815	−	0.796366i	$-0.706753\pi$
$809$	11.0150	−	19.0785i	0.387266	−	0.670765i	0.992081	+	0.125602i	$0.0400861\pi$
$810$		0			0
$811$		−	20.0797i		−	0.705094i	−0.935794	−	0.352547i	$-0.885316\pi$
$811$		−	20.0797i		−	0.705094i	0.935794	−	0.352547i	$-0.114684\pi$
$812$	27.8849	−	16.0994i	0.978569	−	0.564977i
$813$		0			0
$814$			0.877615i			0.0307604i
$815$	0.575124	+	0.996145i	0.0201457	+	0.0348934i
$816$		0			0
$817$	3.20272	+	1.84909i	0.112049	+	0.0646915i
$818$	59.9544			2.09626
$819$		0			0
$820$	1.40980			0.0492324
$821$	12.0072	+	6.93235i	0.419054	+	0.241941i	0.694672	−	0.719326i	$-0.255549\pi$
$821$	12.0072	+	6.93235i	0.419054	+	0.241941i	−0.275619	+	0.961267i	$0.588883\pi$
$822$		0			0
$823$	−7.39021	−	12.8002i	−0.257606	−	0.446187i	0.707994	−	0.706219i	$-0.249600\pi$
$823$	−7.39021	−	12.8002i	−0.257606	−	0.446187i	−0.965600	+	0.260031i	$0.916267\pi$
$824$		−	10.9736i		−	0.382283i
$825$		0			0
$826$	−17.6911	+	10.2139i	−0.615551	+	0.355389i
$827$			26.2554i			0.912988i	0.889726	+	0.456494i	$0.150895\pi$
$827$			26.2554i			0.912988i	−0.889726	+	0.456494i	$0.849105\pi$
$828$		0			0
$829$	7.16078	−	12.4028i	0.248704	−	0.430768i	−0.714462	−	0.699674i	$-0.753329\pi$
$829$	7.16078	−	12.4028i	0.248704	−	0.430768i	0.963167	+	0.268906i	$0.0866619\pi$
$830$	−1.02064	−	0.589265i	−0.0354268	−	0.0204537i
$831$		0			0
$832$	−25.2947	−	12.1808i	−0.876935	−	0.422293i
$833$	0.934958			0.0323944
$834$		0			0
$835$	0.0563913	−	0.0976727i	0.00195150	−	0.00338010i
$836$	2.81704	+	4.87926i	0.0974295	+	0.168753i
$837$		0			0
$838$	−59.0509	+	34.0930i	−2.03988	+	1.17772i
$839$	−29.9196	+	17.2741i	−1.03294	+	0.596368i	−0.917825	−	0.396984i	$-0.870057\pi$
$839$	−29.9196	+	17.2741i	−1.03294	+	0.596368i	−0.115114	+	0.993352i	$0.536723\pi$
$840$		0			0
$841$	−17.6158	−	30.5114i	−0.607440	−	1.05212i
$842$	19.4191	−	33.6348i	0.669226	−	1.15913i
$843$		0			0
$844$	−102.344			−3.52284
$845$	−0.694169	+	0.553618i	−0.0238802	+	0.0190450i
$846$		0			0
$847$	−9.12791	−	5.27000i	−0.313639	−	0.181079i
$848$	−6.59998	+	11.4315i	−0.226644	+	0.392559i
$849$		0			0
$850$		−	11.4569i		−	0.392969i
$851$	−1.96409	+	1.13397i	−0.0673283	+	0.0388720i
$852$		0			0
$853$		−	40.2048i		−	1.37659i	−0.725432	−	0.688294i	$-0.758360\pi$
$853$		−	40.2048i		−	1.37659i	0.725432	−	0.688294i	$-0.241640\pi$
$854$	1.23946	+	2.14680i	0.0424134	+	0.0734621i
$855$		0			0
$856$	84.8066	+	48.9631i	2.89863	+	1.67353i
$857$	24.2988			0.830031			0.415015	−	0.909814i	$-0.363776\pi$
$857$	24.2988			0.830031			0.415015	+	0.909814i	$0.363776\pi$
$858$		0			0
$859$	−38.8589			−1.32585			−0.662924	−	0.748687i	$-0.730685\pi$
$859$	−38.8589			−1.32585			−0.662924	+	0.748687i	$0.730685\pi$
$860$	0.425032	+	0.245392i	0.0144935	+	0.00836781i
$861$		0			0
$862$	22.3350	+	38.6853i	0.760733	+	1.31763i
$863$			30.0838i			1.02406i	0.858966	+	0.512032i	$0.171107\pi$
$863$			30.0838i			1.02406i	−0.858966	+	0.512032i	$0.828893\pi$
$864$		0			0
$865$	1.46564	−	0.846190i	0.0498334	−	0.0287713i
$866$			23.0699i			0.783948i
$867$		0			0
$868$	20.2128	−	35.0096i	0.686067	−	1.18830i
$869$	8.25152	+	4.76402i	0.279914	+	0.161608i
$870$		0			0
$871$	14.8278	+	21.7477i	0.502422	+	0.736893i
$872$	−8.46752			−0.286746
$873$		0			0
$874$	−10.9038	+	18.8860i	−0.368827	+	0.638827i
$875$	0.341340	+	0.591218i	0.0115394	+	0.0199868i
$876$		0			0
$877$	−12.7766	+	7.37659i	−0.431436	+	0.249090i	−0.699958	−	0.714184i	$-0.746798\pi$
$877$	−12.7766	+	7.37659i	−0.431436	+	0.249090i	0.268522	+	0.963273i	$0.413465\pi$
$878$	40.8610	−	23.5911i	1.37899	−	0.796161i
$879$		0			0
$880$	0.0950966	+	0.164712i	0.00320571	+	0.00555245i
$881$	−17.2768	+	29.9244i	−0.582072	+	1.00818i	0.413162	+	0.910658i	$0.364424\pi$
$881$	−17.2768	+	29.9244i	−0.582072	+	1.00818i	−0.995234	+	0.0975203i	$0.968909\pi$
$882$		0			0
$883$	−7.47582			−0.251581			−0.125791	−	0.992057i	$-0.540147\pi$
$883$	−7.47582			−0.251581			−0.125791	+	0.992057i	$0.540147\pi$
$884$	11.1900	−	7.62946i	0.376360	−	0.256607i
$885$		0			0
$886$	−11.4814	−	6.62877i	−0.385724	−	0.222698i
$887$	−10.1782	+	17.6292i	−0.341752	+	0.591931i	−0.984758	−	0.173930i	$-0.944353\pi$
$887$	−10.1782	+	17.6292i	−0.341752	+	0.591931i	0.643007	+	0.765861i	$0.277687\pi$
$888$		0			0
$889$			8.00439i			0.268459i
$890$	−2.28592	+	1.31977i	−0.0766241	+	0.0442389i
$891$		0			0
$892$		−	28.1493i		−	0.942509i
$893$	4.37197	+	7.57248i	0.146302	+	0.253403i
$894$		0			0
$895$	0.372810	+	0.215242i	0.0124617	+	0.00719474i
$896$	−19.4475			−0.649696
$897$		0			0
$898$	−33.2475			−1.10948
$899$	−69.8387	−	40.3214i	−2.32925	−	1.34479i
$900$		0			0
$901$	1.50292	+	2.60314i	0.0500696	+	0.0867231i
$902$		−	8.54795i		−	0.284616i
$903$		0			0
$904$	−58.4605	+	33.7522i	−1.94437	+	1.12258i
$905$			1.29406i			0.0430161i
$906$		0			0
$907$	−4.95555	+	8.58327i	−0.164546	+	0.285003i	−0.936494	−	0.350683i	$-0.885949\pi$
$907$	−4.95555	+	8.58327i	−0.164546	+	0.285003i	0.771948	+	0.635686i	$0.219283\pi$
$908$	−96.5759	−	55.7581i	−3.20499	−	1.85040i
$909$		0			0
$910$	−0.262097	+	0.544272i	−0.00868842	+	0.0180424i
$911$	11.7109			0.387998			0.193999	−	0.981002i	$-0.437854\pi$
$911$	11.7109			0.387998			0.193999	+	0.981002i	$0.437854\pi$
$912$		0			0
$913$	−2.38537	+	4.13159i	−0.0789444	+	0.136736i
$914$	36.5789	+	63.3565i	1.20992	+	2.09565i
$915$		0			0
$916$	−12.5608	+	7.25196i	−0.415019	+	0.239612i
$917$	8.91244	−	5.14560i	0.294315	−	0.169923i
$918$		0			0
$919$	10.3975	+	18.0089i	0.342981	+	0.594060i	0.984985	−	0.172641i	$-0.0552301\pi$
$919$	10.3975	+	18.0089i	0.342981	+	0.594060i	−0.642004	+	0.766701i	$0.721897\pi$
$920$	−0.726688	+	1.25866i	−0.0239582	+	0.0414968i
$921$		0			0
$922$	−5.46553			−0.179998
$923$	−35.6348	+	2.67103i	−1.17293	+	0.0879180i
$924$		0			0
$925$	2.28198	+	1.31750i	0.0750309	+	0.0433191i
$926$	26.5038	−	45.9059i	0.870968	−	1.50856i
$927$		0			0
$928$		−	1.38873i		−	0.0455875i
$929$	−44.3253	+	25.5912i	−1.45426	+	0.839620i	−0.998719	−	0.0505926i	$-0.983889\pi$
$929$	−44.3253	+	25.5912i	−1.45426	+	0.839620i	−0.455545	+	0.890213i	$0.650556\pi$
$930$		0			0
$931$			2.06767i			0.0677652i
$932$	−31.3726	−	54.3389i	−1.02764	−	1.77993i
$933$		0			0
$934$	51.0007	+	29.4453i	1.66879	+	0.963479i
$935$	0.0433101			0.00141639
$936$		0			0
$937$	46.1728			1.50840			0.754200	−	0.656645i	$-0.228025\pi$
$937$	46.1728			1.50840			0.754200	+	0.656645i	$0.228025\pi$
$938$	15.5090	+	8.95410i	0.506385	+	0.292362i
$939$		0			0
$940$	0.580204	+	1.00494i	0.0189242	+	0.0327776i
$941$		−	31.6254i		−	1.03096i	−0.856902	−	0.515480i	$-0.827614\pi$
$941$		−	31.6254i		−	1.03096i	0.856902	−	0.515480i	$-0.172386\pi$
$942$		0			0
$943$	19.1302	−	11.0448i	0.622966	−	0.359670i
$944$			34.1909i			1.11282i
$945$		0			0
$946$	1.48787	−	2.57707i	0.0483748	−	0.0837876i
$947$	−16.6498	−	9.61278i	−0.541046	−	0.312373i	0.204457	−	0.978876i	$-0.434457\pi$
$947$	−16.6498	−	9.61278i	−0.541046	−	0.312373i	−0.745503	+	0.666502i	$0.767791\pi$
$948$		0			0
$949$	−5.35400	+	11.1182i	−0.173798	+	0.360911i
$950$	25.3371			0.822045
$951$		0			0
$952$	2.31369	−	4.00742i	0.0749870	−	0.129881i
$953$	−7.22075	−	12.5067i	−0.233903	−	0.405132i	0.725050	−	0.688696i	$-0.241816\pi$
$953$	−7.22075	−	12.5067i	−0.233903	−	0.405132i	−0.958953	+	0.283564i	$0.908483\pi$
$954$		0			0
$955$	0.520166	−	0.300318i	0.0168322	−	0.00971806i
$956$	−97.3623	+	56.2122i	−3.14892	+	1.81803i
$957$		0			0
$958$	−37.6450	−	65.2031i	−1.21626	−	2.10662i
$959$	1.80978	−	3.13463i	0.0584408	−	0.101222i
$960$		0			0
$961$	−70.2471			−2.26604
$962$	0.348727	+	4.65245i	0.0112434	+	0.150001i
$963$		0			0
$964$	90.3694	+	52.1748i	2.91060	+	1.68044i
$965$	−0.211696	+	0.366668i	−0.00681473	+	0.0118035i
$966$		0			0
$967$		−	3.28457i		−	0.105625i	−0.998604	−	0.0528123i	$-0.983181\pi$
$967$		−	3.28457i		−	0.105625i	0.998604	−	0.0528123i	$-0.0168185\pi$
$968$	−45.1766	+	26.0827i	−1.45203	+	0.838331i
$969$		0			0
$970$			2.79305i			0.0896794i
$971$	−7.98604	−	13.8322i	−0.256284	−	0.443897i	0.708959	−	0.705249i	$-0.249165\pi$
$971$	−7.98604	−	13.8322i	−0.256284	−	0.443897i	−0.965244	+	0.261352i	$0.915832\pi$
$972$		0			0
$973$	−1.05495	−	0.609074i	−0.0338200	−	0.0195260i
$974$	−43.8382			−1.40467
$975$		0			0
$976$	4.14905			0.132808
$977$	18.9949	+	10.9667i	0.607702	+	0.350857i	0.772065	−	0.635543i	$-0.219224\pi$
$977$	18.9949	+	10.9667i	0.607702	+	0.350857i	−0.164364	+	0.986400i	$0.552557\pi$
$978$		0			0
$979$	5.34252	+	9.25351i	0.170748	+	0.295743i
$980$			0.274400i			0.00876540i
$981$		0			0
$982$	−28.8277	+	16.6437i	−0.919927	+	0.531120i
$983$			22.0867i			0.704456i	0.935914	+	0.352228i	$0.114576\pi$
$983$			22.0867i			0.704456i	−0.935914	+	0.352228i	$0.885424\pi$
$984$		0			0
$985$	−0.517145	+	0.895721i	−0.0164776	+	0.0285400i
$986$	−15.9187	−	9.19068i	−0.506955	−	0.292691i
$987$		0			0
$988$	16.8727	+	24.7468i	0.536791	+	0.787300i
$989$	7.68993			0.244526
$990$		0			0
$991$	−2.18229	+	3.77983i	−0.0693227	+	0.120070i	−0.898603	−	0.438762i	$-0.855417\pi$
$991$	−2.18229	+	3.77983i	−0.0693227	+	0.120070i	0.829281	+	0.558832i	$0.188750\pi$
$992$	−0.871779	−	1.50997i	−0.0276790	−	0.0479415i
$993$		0			0
$994$	−21.0553	+	12.1563i	−0.667833	+	0.385573i
$995$	−0.889442	+	0.513519i	−0.0281972	+	0.0162797i
$996$		0			0
$997$	−27.6659	−	47.9188i	−0.876189	−	1.51760i	−0.855491	−	0.517818i	$-0.826744\pi$
$997$	−27.6659	−	47.9188i	−0.876189	−	1.51760i	−0.0206985	−	0.999786i	$-0.506589\pi$
$998$	−12.7855	+	22.1451i	−0.404717	+	0.700991i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ct.b.316.1		16
3.2	odd	2		273.2.bd.a.43.8	✓	16
13.10	even	6	inner	819.2.ct.b.127.1		16
39.20	even	12		3549.2.a.bd.1.7		8
39.23	odd	6		273.2.bd.a.127.8	yes	16
39.32	even	12		3549.2.a.bb.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.8	✓	16	3.2	odd	2
273.2.bd.a.127.8	yes	16	39.23	odd	6
819.2.ct.b.127.1		16	13.10	even	6	inner
819.2.ct.b.316.1		16	1.1	even	1	trivial
3549.2.a.bb.1.2		8	39.32	even	12
3549.2.a.bd.1.7		8	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.ct (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.12443 - 1.22654i) q^{2} +(2.00879 + 3.47933i) q^{4} +0.0682999i q^{5} +(0.866025 - 0.500000i) q^{7} -4.94928i q^{8} +O(q^{10})\)	\(q+(-2.12443 - 1.22654i) q^{2} +(2.00879 + 3.47933i) q^{4} +0.0682999i q^{5} +(0.866025 - 0.500000i) q^{7} -4.94928i q^{8} +(0.0837724 - 0.145098i) q^{10} +(-0.587365 - 0.339115i) q^{11} +(-3.24851 - 1.56434i) q^{13} -2.45308 q^{14} +(-2.05290 + 3.55573i) q^{16} +(0.467479 + 0.809698i) q^{17} +(-1.79066 + 1.03384i) q^{19} +(-0.237638 + 0.137200i) q^{20} +(0.831875 + 1.44085i) q^{22} +(-2.14974 + 3.72346i) q^{23} +4.99534 q^{25} +(4.98251 + 7.30775i) q^{26} +(3.47933 + 2.00879i) q^{28} +(4.00723 - 6.94072i) q^{29} -10.0622i q^{31} +(0.150064 - 0.0866393i) q^{32} -2.29352i q^{34} +(0.0341499 + 0.0591494i) q^{35} +(0.456821 + 0.263746i) q^{37} +5.07216 q^{38} +0.338035 q^{40} +(-4.44943 - 2.56888i) q^{41} +(-0.894286 - 1.54895i) q^{43} -2.72485i q^{44} +(9.13393 - 5.27348i) q^{46} -4.22889i q^{47} +(0.500000 - 0.866025i) q^{49} +(-10.6122 - 6.12697i) q^{50} +(-1.08274 - 14.4451i) q^{52} +3.21495 q^{53} +(0.0231615 - 0.0401169i) q^{55} +(-2.47464 - 4.28620i) q^{56} +(-17.0261 + 9.83004i) q^{58} +(7.21179 - 4.16373i) q^{59} +(-0.505267 - 0.875148i) q^{61} +(-12.3416 + 21.3763i) q^{62} +7.78654 q^{64} +(0.106844 - 0.221873i) q^{65} +(-6.32225 - 3.65015i) q^{67} +(-1.87814 + 3.25303i) q^{68} -0.167545i q^{70} +(8.58321 - 4.95552i) q^{71} -3.42254i q^{73} +(-0.646989 - 1.12062i) q^{74} +(-7.19411 - 4.15352i) q^{76} -0.678230 q^{77} -14.0484 q^{79} +(-0.242856 - 0.140213i) q^{80} +(6.30166 + 10.9148i) q^{82} -7.03411i q^{83} +(-0.0553023 + 0.0319288i) q^{85} +4.38750i q^{86} +(-1.67838 + 2.90703i) q^{88} +(-13.6436 - 7.87714i) q^{89} +(-3.59547 + 0.269500i) q^{91} -17.2735 q^{92} +(-5.18689 + 8.98395i) q^{94} +(-0.0706109 - 0.122302i) q^{95} +(-14.4370 + 8.33523i) q^{97} +(-2.12443 + 1.22654i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4}+O(q^{10}) \) 16 * q + 6 * q^4	\( 16 q + 6 q^{4} - 4 q^{10} + 12 q^{11} + 4 q^{13} - 4 q^{14} - 10 q^{16} - 10 q^{17} - 6 q^{20} - 2 q^{22} + 2 q^{23} + 12 q^{25} - 20 q^{26} - 12 q^{29} - 30 q^{32} + 2 q^{35} + 18 q^{37} + 32 q^{38} - 60 q^{40} - 18 q^{41} - 10 q^{43} + 30 q^{46} + 8 q^{49} + 24 q^{50} - 26 q^{52} - 12 q^{53} + 10 q^{55} - 12 q^{56} - 54 q^{58} + 60 q^{59} - 6 q^{61} - 16 q^{62} + 16 q^{64} + 20 q^{65} - 18 q^{67} + 20 q^{68} - 6 q^{71} - 18 q^{74} + 72 q^{76} + 16 q^{77} - 4 q^{79} - 30 q^{80} - 18 q^{82} - 24 q^{85} - 2 q^{88} - 78 q^{89} - 8 q^{91} + 20 q^{92} + 16 q^{94} + 4 q^{95} - 54 q^{97}+O(q^{100}) \) 16 * q + 6 * q^4 - 4 * q^10 + 12 * q^11 + 4 * q^13 - 4 * q^14 - 10 * q^16 - 10 * q^17 - 6 * q^20 - 2 * q^22 + 2 * q^23 + 12 * q^25 - 20 * q^26 - 12 * q^29 - 30 * q^32 + 2 * q^35 + 18 * q^37 + 32 * q^38 - 60 * q^40 - 18 * q^41 - 10 * q^43 + 30 * q^46 + 8 * q^49 + 24 * q^50 - 26 * q^52 - 12 * q^53 + 10 * q^55 - 12 * q^56 - 54 * q^58 + 60 * q^59 - 6 * q^61 - 16 * q^62 + 16 * q^64 + 20 * q^65 - 18 * q^67 + 20 * q^68 - 6 * q^71 - 18 * q^74 + 72 * q^76 + 16 * q^77 - 4 * q^79 - 30 * q^80 - 18 * q^82 - 24 * q^85 - 2 * q^88 - 78 * q^89 - 8 * q^91 + 20 * q^92 + 16 * q^94 + 4 * q^95 - 54 * q^97

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