LMFDB - Embedded newform 819.2.n.e.100.4

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.4
Root			$0.379240 + 0.656863i$ of defining polynomial
Character	$\chi$	$=$	819.100
Dual form			819.2.n.e.172.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.379240 - 0.656863i) q^{2} +(0.712354 - 1.23383i) q^{4} +(0.357869 - 0.619848i) q^{5} +(-1.32176 - 2.29193i) q^{7} -2.59757 q^{8} +O(q^{10})$	\(q+(-0.379240 - 0.656863i) q^{2} +(0.712354 - 1.23383i) q^{4} +(0.357869 - 0.619848i) q^{5} +(-1.32176 - 2.29193i) q^{7} -2.59757 q^{8} -0.542874 q^{10} -4.48772 q^{11} +(3.26504 - 1.52954i) q^{13} +(-1.00422 + 1.73741i) q^{14} +(-0.439604 - 0.761417i) q^{16} +(-1.88727 + 3.26885i) q^{17} -5.92010 q^{19} +(-0.509859 - 0.883102i) q^{20} +(1.70192 + 2.94782i) q^{22} +(-0.465673 - 0.806569i) q^{23} +(2.24386 + 3.88648i) q^{25} +(-2.24293 - 1.56463i) q^{26} +(-3.76942 - 0.00184259i) q^{28} +(1.12150 - 1.94250i) q^{29} +(0.191136 + 0.331058i) q^{31} +(-2.93100 + 5.07665i) q^{32} +2.86291 q^{34} +(-1.89367 - 0.000925671i) q^{35} +(0.328723 + 0.569365i) q^{37} +(2.24514 + 3.88870i) q^{38} +(-0.929592 + 1.61010i) q^{40} +(2.29549 - 3.97591i) q^{41} +(-2.50110 - 4.33202i) q^{43} +(-3.19684 + 5.53710i) q^{44} +(-0.353203 + 0.611766i) q^{46} +(4.18536 - 7.24926i) q^{47} +(-3.50593 + 6.05875i) q^{49} +(1.70192 - 2.94782i) q^{50} +(0.438674 - 5.11809i) q^{52} +(1.21338 + 2.10164i) q^{53} +(-1.60602 + 2.78170i) q^{55} +(3.43336 + 5.95347i) q^{56} -1.70127 q^{58} +(2.80700 - 4.86187i) q^{59} +1.99378 q^{61} +(0.144973 - 0.251101i) q^{62} +2.68780 q^{64} +(0.220379 - 2.57121i) q^{65} -14.4655 q^{67} +(2.68881 + 4.65715i) q^{68} +(0.717546 + 1.24423i) q^{70} +(-2.14741 - 3.71943i) q^{71} +(-1.34127 - 2.32315i) q^{73} +(0.249330 - 0.431852i) q^{74} +(-4.21721 + 7.30442i) q^{76} +(5.93167 + 10.2856i) q^{77} +(2.75173 - 4.76614i) q^{79} -0.629283 q^{80} -3.48217 q^{82} -11.5302 q^{83} +(1.35079 + 2.33964i) q^{85} +(-1.89703 + 3.28575i) q^{86} +11.6572 q^{88} +(-6.05088 - 10.4804i) q^{89} +(-7.82119 - 5.46159i) q^{91} -1.32689 q^{92} -6.34903 q^{94} +(-2.11862 + 3.66956i) q^{95} +(-1.79870 - 3.11544i) q^{97} +(5.30936 + 0.00519069i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.379240	−	0.656863i	−0.268163	−	0.464472i	0.700224	−	0.713923i	$-0.253083\pi$
$2$	−0.379240	−	0.656863i	−0.268163	−	0.464472i	−0.968388	+	0.249451i	$0.919750\pi$
$3$		0			0
$3$		0			0
$4$	0.712354	−	1.23383i	0.356177	−	0.616917i
$5$	0.357869	−	0.619848i	0.160044	−	0.277204i	−0.774840	−	0.632157i	$-0.782170\pi$
$5$	0.357869	−	0.619848i	0.160044	−	0.277204i	0.934884	+	0.354953i	$0.115503\pi$
$6$		0			0
$7$	−1.32176	−	2.29193i	−0.499577	−	0.866270i
$7$	−1.32176	−	2.29193i	−0.499577	−	0.866270i
$8$	−2.59757			−0.918381
$9$		0			0
$10$	−0.542874			−0.171672
$11$	−4.48772			−1.35310			−0.676549	−	0.736398i	$-0.736525\pi$
$11$	−4.48772			−1.35310			−0.676549	+	0.736398i	$0.736525\pi$
$12$		0			0
$13$	3.26504	−	1.52954i	0.905560	−	0.424217i
$13$	3.26504	−	1.52954i	0.905560	−	0.424217i
$14$	−1.00422	+	1.73741i	−0.268390	+	0.464341i
$15$		0			0
$16$	−0.439604	−	0.761417i	−0.109901	−	0.190354i
$17$	−1.88727	+	3.26885i	−0.457730	+	0.792812i	−0.998841	−	0.0481394i	$-0.984671\pi$
$17$	−1.88727	+	3.26885i	−0.457730	+	0.792812i	0.541110	+	0.840952i	$0.318004\pi$
$18$		0			0
$19$	−5.92010			−1.35816			−0.679082	−	0.734062i	$-0.737622\pi$
$19$	−5.92010			−1.35816			−0.679082	+	0.734062i	$0.737622\pi$
$20$	−0.509859	−	0.883102i	−0.114008	−	0.197468i
$21$		0			0
$22$	1.70192	+	2.94782i	0.362851	+	0.628477i
$23$	−0.465673	−	0.806569i	−0.0970995	−	0.168181i	0.813383	−	0.581728i	$-0.197623\pi$
$23$	−0.465673	−	0.806569i	−0.0970995	−	0.168181i	−0.910483	+	0.413547i	$0.864290\pi$
$24$		0			0
$25$	2.24386	+	3.88648i	0.448772	+	0.777296i
$26$	−2.24293	−	1.56463i	−0.439875	−	0.306848i
$27$		0			0
$28$	−3.76942	−	0.00184259i	−0.712354	−	0.000348216i
$29$	1.12150	−	1.94250i	0.208257	−	0.360713i	−0.742908	−	0.669393i	$-0.766554\pi$
$29$	1.12150	−	1.94250i	0.208257	−	0.360713i	0.951166	+	0.308681i	$0.0998875\pi$
$30$		0			0
$31$	0.191136	+	0.331058i	0.0343291	+	0.0594597i	0.882679	−	0.469975i	$-0.155737\pi$
$31$	0.191136	+	0.331058i	0.0343291	+	0.0594597i	−0.848350	+	0.529435i	$0.822404\pi$
$32$	−2.93100	+	5.07665i	−0.518133	+	0.897433i
$33$		0			0
$34$	2.86291			0.490986
$35$	−1.89367		0.000925671i	−0.320088		0.000156467i
$36$		0			0
$37$	0.328723	+	0.569365i	0.0540417	+	0.0936030i	0.891781	−	0.452468i	$-0.149456\pi$
$37$	0.328723	+	0.569365i	0.0540417	+	0.0936030i	−0.837739	+	0.546071i	$0.816123\pi$
$38$	2.24514	+	3.88870i	0.364210	+	0.630830i
$39$		0			0
$40$	−0.929592	+	1.61010i	−0.146981	+	0.254579i
$41$	2.29549	−	3.97591i	0.358495	−	0.620932i	−0.629214	−	0.777232i	$-0.716623\pi$
$41$	2.29549	−	3.97591i	0.358495	−	0.620932i	0.987710	+	0.156300i	$0.0499565\pi$
$42$		0			0
$43$	−2.50110	−	4.33202i	−0.381413	−	0.660627i	0.609851	−	0.792516i	$-0.291229\pi$
$43$	−2.50110	−	4.33202i	−0.381413	−	0.660627i	−0.991265	+	0.131889i	$0.957896\pi$
$44$	−3.19684	+	5.53710i	−0.481942	+	0.834749i
$45$		0			0
$46$	−0.353203	+	0.611766i	−0.0520770	+	0.0902000i
$47$	4.18536	−	7.24926i	0.610498	−	1.05741i	−0.380659	−	0.924716i	$-0.624303\pi$
$47$	4.18536	−	7.24926i	0.610498	−	1.05741i	0.991157	−	0.132698i	$-0.0423639\pi$
$48$		0			0
$49$	−3.50593	+	6.05875i	−0.500846	+	0.865536i
$50$	1.70192	−	2.94782i	0.240688	−	0.416884i
$51$		0			0
$52$	0.438674	−	5.11809i	0.0608332	−	0.709752i
$53$	1.21338	+	2.10164i	0.166671	+	0.288682i	0.937247	−	0.348665i	$-0.113365\pi$
$53$	1.21338	+	2.10164i	0.166671	+	0.288682i	−0.770577	+	0.637347i	$0.780032\pi$
$54$		0			0
$55$	−1.60602	+	2.78170i	−0.216555	+	0.375085i
$56$	3.43336	+	5.95347i	0.458802	+	0.795565i
$57$		0			0
$58$	−1.70127			−0.223388
$59$	2.80700	−	4.86187i	0.365441	−	0.632962i	−0.623406	−	0.781898i	$-0.714252\pi$
$59$	2.80700	−	4.86187i	0.365441	−	0.632962i	0.988847	+	0.148937i	$0.0475850\pi$
$60$		0			0
$61$	1.99378			0.255277			0.127639	−	0.991821i	$-0.459260\pi$
$61$	1.99378			0.255277			0.127639	+	0.991821i	$0.459260\pi$
$62$	0.144973	−	0.251101i	0.0184116	−	0.0318898i
$63$		0			0
$64$	2.68780			0.335975
$65$	0.220379	−	2.57121i	0.0273347	−	0.318919i
$66$		0			0
$67$	−14.4655			−1.76724			−0.883618	−	0.468208i	$-0.844900\pi$
$67$	−14.4655			−1.76724			−0.883618	+	0.468208i	$0.844900\pi$
$68$	2.68881	+	4.65715i	0.326066	+	0.564763i
$69$		0			0
$70$	0.717546	+	1.24423i	0.0857632	+	0.148714i
$71$	−2.14741	−	3.71943i	−0.254851	−	0.441415i	0.710004	−	0.704198i	$-0.248693\pi$
$71$	−2.14741	−	3.71943i	−0.254851	−	0.441415i	−0.964855	+	0.262783i	$0.915360\pi$
$72$		0			0
$73$	−1.34127	−	2.32315i	−0.156984	−	0.271905i	0.776796	−	0.629753i	$-0.216844\pi$
$73$	−1.34127	−	2.32315i	−0.156984	−	0.271905i	−0.933780	+	0.357848i	$0.883511\pi$
$74$	0.249330	−	0.431852i	0.0289840	−	0.0502018i
$75$		0			0
$76$	−4.21721	+	7.30442i	−0.483747	+	0.837874i
$77$	5.93167	+	10.2856i	0.675976	+	1.17215i
$78$		0			0
$79$	2.75173	−	4.76614i	0.309594	−	0.536233i	−0.668679	−	0.743551i	$-0.733140\pi$
$79$	2.75173	−	4.76614i	0.309594	−	0.536233i	0.978274	+	0.207318i	$0.0664735\pi$
$80$	−0.629283			−0.0703560
$81$		0			0
$82$	−3.48217			−0.384541
$83$	−11.5302			−1.26560			−0.632800	−	0.774316i	$-0.718094\pi$
$83$	−11.5302			−1.26560			−0.632800	+	0.774316i	$0.718094\pi$
$84$		0			0
$85$	1.35079	+	2.33964i	0.146514	+	0.253770i
$86$	−1.89703	+	3.28575i	−0.204562	+	0.354312i
$87$		0			0
$88$	11.6572			1.24266
$89$	−6.05088	−	10.4804i	−0.641392	−	1.11092i	−0.985122	−	0.171856i	$-0.945024\pi$
$89$	−6.05088	−	10.4804i	−0.641392	−	1.11092i	0.343730	−	0.939069i	$-0.388310\pi$
$90$		0			0
$91$	−7.82119	−	5.46159i	−0.819883	−	0.572531i
$92$	−1.32689			−0.138338
$93$		0			0
$94$	−6.34903			−0.654852
$95$	−2.11862	+	3.66956i	−0.217366	+	0.376489i
$96$		0			0
$97$	−1.79870	−	3.11544i	−0.182630	−	0.316325i	0.760145	−	0.649753i	$-0.225128\pi$
$97$	−1.79870	−	3.11544i	−0.182630	−	0.316325i	−0.942775	+	0.333429i	$0.891794\pi$
$98$	5.30936	+	0.00519069i	0.536326	+	0.000524339i
$99$		0			0
$100$	6.39369			0.639369
$101$	−11.9792			−1.19197			−0.595986	−	0.802995i	$-0.703239\pi$
$101$	−11.9792			−1.19197			−0.595986	+	0.802995i	$0.703239\pi$
$102$		0			0
$103$	−1.54966	+	2.68409i	−0.152692	+	0.264471i	−0.932216	−	0.361901i	$-0.882128\pi$
$103$	−1.54966	+	2.68409i	−0.152692	+	0.264471i	0.779524	+	0.626372i	$0.215461\pi$
$104$	−8.48119	+	3.97308i	−0.831649	+	0.389593i
$105$		0			0
$106$	0.920325	−	1.59405i	0.0893898	−	0.154828i
$107$	5.59313	+	9.68758i	0.540708	+	0.936534i	0.998864	+	0.0476618i	$0.0151770\pi$
$107$	5.59313	+	9.68758i	0.540708	+	0.936534i	−0.458155	+	0.888872i	$0.651490\pi$
$108$		0			0
$109$	10.1906	+	17.6506i	0.976082	+	1.69062i	0.676316	+	0.736611i	$0.263575\pi$
$109$	10.1906	+	17.6506i	0.976082	+	1.69062i	0.299766	+	0.954013i	$0.403091\pi$
$110$	2.43626			0.232289
$111$		0			0
$112$	−1.16407	+	2.01395i	−0.109994	+	0.190300i
$113$	−8.55107	−	14.8109i	−0.804417	−	1.39329i	−0.916684	−	0.399613i	$-0.869144\pi$
$113$	−8.55107	−	14.8109i	−0.804417	−	1.39329i	0.112266	−	0.993678i	$-0.464189\pi$
$114$		0			0
$115$	−0.666600			−0.0621608
$116$	−1.59781	−	2.76749i	−0.148353	−	0.256955i
$117$		0			0
$118$	−4.25811			−0.391991
$119$	9.98650	+	0.00488165i	0.915461	+	0.000447500i
$120$		0			0
$121$	9.13961			0.830874
$122$	−0.756122	−	1.30964i	−0.0684560	−	0.118569i
$123$		0			0
$124$	0.544627			0.0489089
$125$	6.79073			0.607381
$126$		0			0
$127$	9.01920	−	15.6217i	0.800325	−	1.38620i	−0.119077	−	0.992885i	$-0.537994\pi$
$127$	9.01920	−	15.6217i	0.800325	−	1.38620i	0.919402	−	0.393318i	$-0.128673\pi$
$128$	4.84269	+	8.38778i	0.428037	+	0.741382i
$129$		0			0
$130$	−1.77251	+	0.830345i	−0.155459	+	0.0728261i
$131$	9.83728	−	17.0387i	0.859487	−	1.48868i	−0.0129316	−	0.999916i	$-0.504116\pi$
$131$	9.83728	−	17.0387i	0.859487	−	1.48868i	0.872419	−	0.488759i	$-0.162550\pi$
$132$		0			0
$133$	7.82493	+	13.5685i	0.678507	+	1.17654i
$134$	5.48588	+	9.50182i	0.473908	+	0.820832i
$135$		0			0
$136$	4.90232	−	8.49107i	0.420371	−	0.728104i
$137$	9.64137	−	16.6993i	0.823718	−	1.42672i	−0.0791773	−	0.996861i	$-0.525229\pi$
$137$	9.64137	−	16.6993i	0.823718	−	1.42672i	0.902895	−	0.429861i	$-0.141437\pi$
$138$		0			0
$139$	−1.31388	−	2.27571i	−0.111442	−	0.193023i	0.804910	−	0.593397i	$-0.202214\pi$
$139$	−1.31388	−	2.27571i	−0.111442	−	0.193023i	−0.916352	+	0.400374i	$0.868880\pi$
$140$	−1.35010	+	2.33581i	−0.114105	+	0.197412i
$141$		0			0
$142$	−1.62877	+	2.82111i	−0.136683	+	0.236743i
$143$	−14.6526	+	6.86413i	−1.22531	+	0.574007i
$144$		0			0
$145$	−0.802702	−	1.39032i	−0.0666607	−	0.115460i
$146$	−1.01733	+	1.76207i	−0.0841948	+	0.145830i
$147$		0			0
$148$	0.936669			0.0769937
$149$	15.5896			1.27715			0.638573	−	0.769561i	$-0.279525\pi$
$149$	15.5896			1.27715			0.638573	+	0.769561i	$0.279525\pi$
$150$		0			0
$151$	4.61134	+	7.98707i	0.375265	+	0.649978i	0.990367	−	0.138470i	$-0.0442183\pi$
$151$	4.61134	+	7.98707i	0.375265	+	0.649978i	−0.615102	+	0.788448i	$0.710885\pi$
$152$	15.3779			1.24731
$153$		0			0
$154$	4.50668	−	7.79699i	0.363158	−	0.628299i
$155$	0.273607			0.0219767
$156$		0			0
$157$	−9.20539	−	15.9442i	−0.734670	−	1.27249i	−0.954868	−	0.297031i	$-0.904003\pi$
$157$	−9.20539	−	15.9442i	−0.734670	−	1.27249i	0.220197	−	0.975455i	$-0.429330\pi$
$158$	−4.17427			−0.332087
$159$		0			0
$160$	2.09783	+	3.63355i	0.165848	+	0.287258i
$161$	−1.23310	+	2.13338i	−0.0971817	+	0.168134i
$162$		0			0
$163$	11.1686			0.874793			0.437396	−	0.899269i	$-0.355901\pi$
$163$	11.1686			0.874793			0.437396	+	0.899269i	$0.355901\pi$
$164$	−3.27040	−	5.66451i	−0.255376	−	0.442324i
$165$		0			0
$166$	4.37270	+	7.57374i	0.339387	+	0.587836i
$167$	−7.09719	+	12.2927i	−0.549197	+	0.951237i	0.449133	+	0.893465i	$0.351733\pi$
$167$	−7.09719	+	12.2927i	−0.549197	+	0.951237i	−0.998330	+	0.0577721i	$0.981600\pi$
$168$		0			0
$169$	8.32104	−	9.98801i	0.640080	−	0.768309i
$170$	1.02455	−	1.77457i	0.0785794	−	0.136103i
$171$		0			0
$172$	−7.12666			−0.543403
$173$	−19.2725			−1.46526			−0.732630	−	0.680627i	$-0.761707\pi$
$173$	−19.2725			−1.46526			−0.732630	+	0.680627i	$0.761707\pi$
$174$		0			0
$175$	5.94172	−	10.2798i	0.449152	−	0.777076i
$176$	1.97282	+	3.41702i	0.148707	+	0.257568i
$177$		0			0
$178$	−4.58948	+	7.94921i	−0.343996	+	0.595818i
$179$	11.2324			0.839553			0.419776	−	0.907628i	$-0.362109\pi$
$179$	11.2324			0.839553			0.419776	+	0.907628i	$0.362109\pi$
$180$		0			0
$181$	2.43304			0.180846			0.0904232	−	0.995903i	$-0.471178\pi$
$181$	2.43304			0.180846			0.0904232	+	0.995903i	$0.471178\pi$
$182$	−0.621412	+	7.20871i	−0.0460621	+	0.534345i
$183$		0			0
$184$	1.20962	+	2.09512i	0.0891743	+	0.154454i
$185$	0.470560			0.0345962
$186$		0			0
$187$	8.46954	−	14.6697i	0.619354	−	1.07275i
$188$	−5.96292	−	10.3281i	−0.434890	−	0.753252i
$189$		0			0
$190$	3.21387			0.233158
$191$	13.7391			0.994124			0.497062	−	0.867715i	$-0.334412\pi$
$191$	13.7391			0.994124			0.497062	+	0.867715i	$0.334412\pi$
$192$		0			0
$193$	−13.8673			−0.998187			−0.499094	−	0.866548i	$-0.666334\pi$
$193$	−13.8673			−0.998187			−0.499094	+	0.866548i	$0.666334\pi$
$194$	−1.36428	+	2.36300i	−0.0979493	+	0.169653i
$195$		0			0
$196$	4.97803	+	8.64170i	0.355574	+	0.617265i
$197$	9.15733	−	15.8610i	0.652433	−	1.13005i	−0.330098	−	0.943947i	$-0.607082\pi$
$197$	9.15733	−	15.8610i	0.652433	−	1.13005i	0.982531	−	0.186100i	$-0.0595849\pi$
$198$		0			0
$199$	3.55862	−	6.16371i	0.252264	−	0.436933i	−0.711885	−	0.702296i	$-0.752158\pi$
$199$	3.55862	−	6.16371i	0.252264	−	0.436933i	0.964149	+	0.265363i	$0.0854916\pi$
$200$	−5.82859	−	10.0954i	−0.412143	−	0.713853i
$201$		0			0
$202$	4.54298	+	7.86867i	0.319643	+	0.553638i
$203$	−5.93442	−	0.00290089i	−0.416515	−	0.000203603i
$204$		0			0
$205$	−1.64297	−	2.84571i	−0.114750	−	0.198753i
$206$	2.35077			0.163786
$207$		0			0
$208$	−2.59994	−	1.81367i	−0.180274	−	0.125755i
$209$	26.5678			1.83773
$210$		0			0
$211$	−5.95003	+	10.3058i	−0.409617	+	0.709478i	−0.994847	−	0.101390i	$-0.967671\pi$
$211$	−5.95003	+	10.3058i	−0.409617	+	0.709478i	0.585230	+	0.810868i	$0.301004\pi$
$212$	3.45742			0.237457
$213$		0			0
$214$	4.24228	−	7.34784i	0.289996	−	0.502288i
$215$	−3.58026			−0.244172
$216$		0			0
$217$	0.506127	−	0.875649i	0.0343581	−	0.0594429i
$218$	7.72937	−	13.3877i	0.523499	−	0.906726i
$219$		0			0
$220$	2.28810	+	3.96311i	0.154264	+	0.267193i
$221$	−1.16220	+	13.5596i	−0.0781780	+	0.912117i
$222$		0			0
$223$	11.9432	−	20.6863i	0.799778	−	1.38526i	−0.119982	−	0.992776i	$-0.538284\pi$
$223$	11.9432	−	20.6863i	0.799778	−	1.38526i	0.919760	−	0.392481i	$-0.128383\pi$
$224$	15.5094	+	0.00758139i	1.03627	+	0.000506553i
$225$		0			0
$226$	−6.48582	+	11.2338i	−0.431430	+	0.747259i
$227$	6.29391	−	10.9014i	0.417741	−	0.723549i	−0.577971	−	0.816058i	$-0.696155\pi$
$227$	6.29391	−	10.9014i	0.417741	−	0.723549i	0.995712	+	0.0925083i	$0.0294885\pi$
$228$		0			0
$229$	7.66365	−	13.2738i	0.506429	−	0.877160i	−0.493544	−	0.869721i	$-0.664299\pi$
$229$	7.66365	−	13.2738i	0.506429	−	0.877160i	0.999972	−	0.00743905i	$-0.00236795\pi$
$230$	0.252801	+	0.437865i	0.0166692	+	0.0288720i
$231$		0			0
$232$	−2.91318	+	5.04578i	−0.191260	+	0.331271i
$233$	−13.3343	+	23.0957i	−0.873559	+	1.51305i	−0.0152699	+	0.999883i	$0.504861\pi$
$233$	−13.3343	+	23.0957i	−0.873559	+	1.51305i	−0.858289	+	0.513166i	$0.828473\pi$
$234$		0			0
$235$	−2.99563	−	5.18858i	−0.195413	−	0.338465i
$236$	−3.99916	−	6.92675i	−0.260323	−	0.450893i
$237$		0			0
$238$	−3.78407	−	6.56161i	−0.245285	−	0.425326i
$239$	14.5891			0.943693			0.471846	−	0.881681i	$-0.343588\pi$
$239$	14.5891			0.943693			0.471846	+	0.881681i	$0.343588\pi$
$240$		0			0
$241$	−6.44615	+	11.1651i	−0.415233	+	0.719204i	−0.995453	−	0.0952555i	$-0.969633\pi$
$241$	−6.44615	+	11.1651i	−0.415233	+	0.719204i	0.580220	+	0.814460i	$0.302967\pi$
$242$	−3.46611	−	6.00347i	−0.222810	−	0.385918i
$243$		0			0
$244$	1.42028	−	2.45999i	0.0909240	−	0.157485i
$245$	2.50084	+	4.34138i	0.159773	+	0.277361i
$246$		0			0
$247$	−19.3294	+	9.05501i	−1.22990	+	0.576157i
$248$	−0.496490	−	0.859947i	−0.0315272	−	0.0546067i
$249$		0			0
$250$	−2.57532	−	4.46058i	−0.162877	−	0.282112i
$251$	12.0203	+	20.8198i	0.758717	+	1.31414i	0.943505	+	0.331359i	$0.107507\pi$
$251$	12.0203	+	20.8198i	0.758717	+	1.31414i	−0.184787	+	0.982779i	$0.559160\pi$
$252$		0			0
$253$	2.08981	+	3.61965i	0.131385	+	0.227566i
$254$	−13.6818			−0.858471
$255$		0			0
$256$	6.36088	−	11.0174i	0.397555	−	0.688586i
$257$	9.35724	+	16.2072i	0.583689	+	1.01098i	0.995038	+	0.0995004i	$0.0317245\pi$
$257$	9.35724	+	16.2072i	0.583689	+	1.01098i	−0.411349	+	0.911478i	$0.634942\pi$
$258$		0			0
$259$	0.870456	−	1.50597i	0.0540875	−	0.0935766i
$260$	−3.01545	−	2.10352i	−0.187010	−	0.130455i
$261$		0			0
$262$	−14.9228			−0.921931
$263$	9.37129			0.577859			0.288929	−	0.957350i	$-0.406701\pi$
$263$	9.37129			0.577859			0.288929	+	0.957350i	$0.406701\pi$
$264$		0			0
$265$	1.73693			0.106699
$266$	5.94511	−	10.2856i	0.364518	−	0.630652i
$267$		0			0
$268$	−10.3045	+	17.8480i	−0.629449	+	1.09024i
$269$	6.07464	−	10.5216i	0.370377	−	0.641512i	−0.619246	−	0.785197i	$-0.712562\pi$
$269$	6.07464	−	10.5216i	0.370377	−	0.641512i	0.989624	+	0.143685i	$0.0458951\pi$
$270$		0			0
$271$	7.32926	+	12.6946i	0.445221	+	0.771145i	0.998068	−	0.0621380i	$-0.0197919\pi$
$271$	7.32926	+	12.6946i	0.445221	+	0.771145i	−0.552847	+	0.833283i	$0.686459\pi$
$272$	3.31861			0.201220
$273$		0			0
$274$	−14.6256			−0.883563
$275$	−10.0698	−	17.4414i	−0.607232	−	1.05176i
$276$		0			0
$277$	2.51608	−	4.35797i	0.151176	−	0.261845i	−0.780484	−	0.625176i	$-0.785027\pi$
$277$	2.51608	−	4.35797i	0.151176	−	0.261845i	0.931660	+	0.363331i	$0.118361\pi$
$278$	−0.996555	+	1.72608i	−0.0597694	+	0.103524i
$279$		0			0
$280$	4.91894	+	0.00240450i	0.293963	+	0.000143696i
$281$	−0.854888			−0.0509984			−0.0254992	−	0.999675i	$-0.508118\pi$
$281$	−0.854888			−0.0509984			−0.0254992	+	0.999675i	$0.508118\pi$
$282$		0			0
$283$	−31.2774			−1.85925			−0.929625	−	0.368506i	$-0.879869\pi$
$283$	−31.2774			−1.85925			−0.929625	+	0.368506i	$0.879869\pi$
$284$	−6.11888			−0.363088
$285$		0			0
$286$	10.0656	+	7.02160i	0.595194	+	0.415196i
$287$	−12.1466	−	0.00593756i	−0.716991	−	0.000350483i
$288$		0			0
$289$	1.37642	+	2.38403i	0.0809657	+	0.140237i
$290$	−0.608833	+	1.05453i	−0.0357519	+	0.0619241i
$291$		0			0
$292$	−3.82185			−0.223657
$293$	−0.339044	−	0.587241i	−0.0198071	−	0.0343070i	0.855952	−	0.517055i	$-0.172972\pi$
$293$	−0.339044	−	0.587241i	−0.0198071	−	0.0343070i	−0.875759	+	0.482748i	$0.839639\pi$
$294$		0			0
$295$	−2.00908	−	3.47983i	−0.116973	−	0.202603i
$296$	−0.853882	−	1.47897i	−0.0496309	−	0.0859632i
$297$		0			0
$298$	−5.91219	−	10.2402i	−0.342484	−	0.593199i
$299$	−2.75412	−	1.92122i	−0.159275	−	0.111107i
$300$		0			0
$301$	−6.62288	+	11.4582i	−0.381736	+	0.660441i
$302$	3.49761	−	6.05803i	0.201265	−	0.348601i
$303$		0			0
$304$	2.60250	+	4.50766i	0.149264	+	0.258532i
$305$	0.713513	−	1.23584i	0.0408556	−	0.0707640i
$306$		0			0
$307$	−27.2103			−1.55297			−0.776487	−	0.630134i	$-0.783000\pi$
$307$	−27.2103			−1.55297			−0.776487	+	0.630134i	$0.783000\pi$
$308$	16.9161	+	0.00826901i	0.963885	+	0.000471171i
$309$		0			0
$310$	−0.103763	−	0.179722i	−0.00589333	−	0.0102076i
$311$	−7.06426	−	12.2357i	−0.400577	−	0.693821i	0.593218	−	0.805042i	$-0.297857\pi$
$311$	−7.06426	−	12.2357i	−0.400577	−	0.693821i	−0.993796	+	0.111221i	$0.964524\pi$
$312$		0			0
$313$	9.84907	−	17.0591i	0.556703	−	0.964237i	−0.441066	−	0.897475i	$-0.645400\pi$
$313$	9.84907	−	17.0591i	0.556703	−	0.964237i	0.997769	−	0.0667627i	$-0.0212670\pi$
$314$	−6.98211	+	12.0934i	−0.394023	+	0.682468i
$315$		0			0
$316$	−3.92042	−	6.79036i	−0.220541	−	0.381988i
$317$	7.83931	−	13.5781i	0.440299	−	0.762621i	−0.557412	−	0.830236i	$-0.688206\pi$
$317$	7.83931	−	13.5781i	0.440299	−	0.762621i	0.997711	+	0.0676152i	$0.0215390\pi$
$318$		0			0
$319$	−5.03298	+	8.71738i	−0.281793	+	0.488079i
$320$	0.961881	−	1.66603i	0.0537708	−	0.0931338i
$321$		0			0
$322$	1.86898		0.000913602i	0.104154		5.09131e-5i
$323$	11.1728	−	19.3519i	0.621673	−	1.07677i
$324$		0			0
$325$	13.2708	+	9.25746i	0.736132	+	0.513511i
$326$	−4.23558	−	7.33625i	−0.234587	−	0.406317i
$327$		0			0
$328$	−5.96270	+	10.3277i	−0.329235	+	0.570252i
$329$	−22.1469	−	0.0108259i	−1.22100	−	0.000596853i
$330$		0			0
$331$	14.4236			0.792793			0.396396	−	0.918079i	$-0.370261\pi$
$331$	14.4236			0.792793			0.396396	+	0.918079i	$0.370261\pi$
$332$	−8.21355	+	14.2263i	−0.450777	+	0.780769i
$333$		0			0
$334$	10.7662			0.589098
$335$	−5.17674	+	8.96638i	−0.282836	+	0.489886i
$336$		0			0
$337$	14.4299			0.786049			0.393025	−	0.919528i	$-0.371429\pi$
$337$	14.4299			0.786049			0.393025	+	0.919528i	$0.371429\pi$
$338$	−9.71643	−	1.67793i	−0.528504	−	0.0912672i
$339$		0			0
$340$	3.84897			0.208740
$341$	−0.857766	−	1.48569i	−0.0464506	−	0.0804548i
$342$		0			0
$343$	18.5202	+	0.0271595i	0.999999	+	0.00146647i
$344$	6.49678	+	11.2527i	0.350283	+	0.606707i
$345$		0			0
$346$	7.30890	+	12.6594i	0.392929	+	0.680573i
$347$	−2.33434	+	4.04319i	−0.125314	+	0.217050i	−0.921856	−	0.387534i	$-0.873327\pi$
$347$	−2.33434	+	4.04319i	−0.125314	+	0.217050i	0.796542	+	0.604584i	$0.206660\pi$
$348$		0			0
$349$	2.06807	−	3.58201i	0.110701	−	0.191740i	−0.805352	−	0.592797i	$-0.798024\pi$
$349$	2.06807	−	3.58201i	0.110701	−	0.191740i	0.916053	+	0.401057i	$0.131357\pi$
$350$	−9.00573	−	0.00440222i	−0.481376	−	0.000235309i
$351$		0			0
$352$	13.1535	−	22.7826i	0.701085	−	1.21431i
$353$	−35.7899			−1.90491			−0.952453	−	0.304684i	$-0.901449\pi$
$353$	−35.7899			−1.90491			−0.952453	+	0.304684i	$0.901449\pi$
$354$		0			0
$355$	−3.07397			−0.163150
$356$	−17.2415			−0.913797
$357$		0			0
$358$	−4.25979	−	7.37818i	−0.225137	−	0.389949i
$359$	−12.6381	+	21.8899i	−0.667014	+	1.15530i	0.311721	+	0.950174i	$0.399095\pi$
$359$	−12.6381	+	21.8899i	−0.667014	+	1.15530i	−0.978735	+	0.205129i	$0.934239\pi$
$360$		0			0
$361$	16.0476			0.844611
$362$	−0.922706	−	1.59817i	−0.0484964	−	0.0839982i
$363$		0			0
$364$	−12.3102	+	5.75945i	−0.645227	+	0.301877i
$365$	−1.92000			−0.100498
$366$		0			0
$367$	35.3997			1.84785			0.923925	−	0.382573i	$-0.124962\pi$
$367$	35.3997			1.84785			0.923925	+	0.382573i	$0.124962\pi$
$368$	−0.409423	+	0.709142i	−0.0213427	+	0.0369666i
$369$		0			0
$370$	−0.178455	−	0.309093i	−0.00927744	−	0.0160690i
$371$	3.21302	−	5.55884i	0.166812	−	0.288600i
$372$		0			0
$373$	−32.7804			−1.69730			−0.848652	−	0.528951i	$-0.822586\pi$
$373$	−32.7804			−1.69730			−0.848652	+	0.528951i	$0.822586\pi$
$374$	−12.8480			−0.664352
$375$		0			0
$376$	−10.8718	+	18.8305i	−0.560669	+	0.971108i
$377$	0.690631	−	8.05771i	0.0355693	−	0.414993i
$378$		0			0
$379$	−6.04308	+	10.4669i	−0.310412	+	0.537650i	−0.978452	−	0.206476i	$-0.933800\pi$
$379$	−6.04308	+	10.4669i	−0.310412	+	0.537650i	0.668039	+	0.744126i	$0.267134\pi$
$380$	3.01842	+	5.22806i	0.154842	+	0.268194i
$381$		0			0
$382$	−5.21040	−	9.02468i	−0.266587	−	0.461743i
$383$	0.512172			0.0261708			0.0130854	−	0.999914i	$-0.495835\pi$
$383$	0.512172			0.0261708			0.0130854	+	0.999914i	$0.495835\pi$
$384$		0			0
$385$	8.49824	+	0.00415415i	0.433110	+	0.000211715i
$386$	5.25902	+	9.10889i	0.267677	+	0.463630i
$387$		0			0
$388$	−5.12524			−0.260195
$389$	17.7577	+	30.7573i	0.900353	+	1.55946i	0.827037	+	0.562148i	$0.190025\pi$
$389$	17.7577	+	30.7573i	0.900353	+	1.55946i	0.0733162	+	0.997309i	$0.476642\pi$
$390$		0			0
$391$	3.51540			0.177781
$392$	9.10690	−	15.7381i	0.459968	−	0.794892i
$393$		0			0
$394$	−13.8913			−0.699834
$395$	−1.96952	−	3.41131i	−0.0990974	−	0.171642i
$396$		0			0
$397$	−8.29730			−0.416430			−0.208215	−	0.978083i	$-0.566765\pi$
$397$	−8.29730			−0.416430			−0.208215	+	0.978083i	$0.566765\pi$
$398$	−5.39828			−0.270591
$399$		0			0
$400$	1.97282	−	3.41702i	0.0986410	−	0.170851i
$401$	6.96021	+	12.0554i	0.347576	+	0.602019i	0.985818	−	0.167816i	$-0.0536715\pi$
$401$	6.96021	+	12.0554i	0.347576	+	0.602019i	−0.638242	+	0.769836i	$0.720338\pi$
$402$		0			0
$403$	1.13043	+	0.788568i	0.0563109	+	0.0392814i
$404$	−8.53341	+	14.7803i	−0.424553	+	0.735347i
$405$		0			0
$406$	2.24867	+	3.89920i	0.111599	+	0.193514i
$407$	−1.47522	−	2.55515i	−0.0731238	−	0.126654i
$408$		0			0
$409$	2.45871	−	4.25862i	0.121576	−	0.210575i	−0.798814	−	0.601579i	$-0.794539\pi$
$409$	2.45871	−	4.25862i	0.121576	−	0.210575i	0.920389	+	0.391004i	$0.127872\pi$
$410$	−1.24616	+	2.15841i	−0.0615435	+	0.106597i
$411$		0			0
$412$	2.20781	+	3.82404i	0.108771	+	0.188397i
$413$	−14.8533	−	0.00726064i	−0.730881	−	0.000357273i
$414$		0			0
$415$	−4.12629	+	7.14694i	−0.202552	+	0.350830i
$416$	−1.80494	+	21.0586i	−0.0884945	+	1.03248i
$417$		0			0
$418$	−10.0756	−	17.4514i	−0.492812	−	0.853575i
$419$	−4.85147	+	8.40299i	−0.237010	+	0.410513i	−0.959855	−	0.280497i	$-0.909501\pi$
$419$	−4.85147	+	8.40299i	−0.237010	+	0.410513i	0.722845	+	0.691010i	$0.242834\pi$
$420$		0			0
$421$	−15.2944			−0.745405			−0.372702	−	0.927951i	$-0.621569\pi$
$421$	−15.2944			−0.745405			−0.372702	+	0.927951i	$0.621569\pi$
$422$	9.02596			0.439377
$423$		0			0
$424$	−3.15184	−	5.45915i	−0.153067	−	0.265120i
$425$	−16.9391			−0.821666
$426$		0			0
$427$	−2.63529	−	4.56961i	−0.127531	−	0.221139i
$428$	15.9371			0.770351
$429$		0			0
$430$	1.35778	+	2.35174i	0.0654779	+	0.113411i
$431$	−32.6580			−1.57308			−0.786541	−	0.617538i	$-0.788130\pi$
$431$	−32.6580			−1.57308			−0.786541	+	0.617538i	$0.788130\pi$
$432$		0			0
$433$	9.28189	+	16.0767i	0.446059	+	0.772597i	0.998125	−	0.0612034i	$-0.0194938\pi$
$433$	9.28189	+	16.0767i	0.446059	+	0.772597i	−0.552066	+	0.833800i	$0.686160\pi$
$434$	−0.767125		0.000374990i	−0.0368232		1.80001e-5i
$435$		0			0
$436$	29.0372			1.39063
$437$	2.75683	+	4.77497i	0.131877	+	0.228418i
$438$		0			0
$439$	−4.72738	−	8.18806i	−0.225625	−	0.390795i	0.730881	−	0.682504i	$-0.239109\pi$
$439$	−4.72738	−	8.18806i	−0.225625	−	0.390795i	−0.956507	+	0.291710i	$0.905776\pi$
$440$	4.17175	−	7.22568i	0.198880	−	0.344471i
$441$		0			0
$442$	9.34755	−	4.37893i	0.444617	−	0.208285i
$443$	3.71593	−	6.43618i	0.176549	−	0.305792i	−0.764147	−	0.645042i	$-0.776840\pi$
$443$	3.71593	−	6.43618i	0.176549	−	0.305792i	0.940696	+	0.339250i	$0.110173\pi$
$444$		0			0
$445$	−8.66170			−0.410604
$446$	−18.1174			−0.857885
$447$		0			0
$448$	−3.55261	−	6.16026i	−0.167845	−	0.291045i
$449$	9.42362	+	16.3222i	0.444728	+	0.770291i	0.998033	−	0.0626872i	$-0.0199670\pi$
$449$	9.42362	+	16.3222i	0.444728	+	0.770291i	−0.553305	+	0.832979i	$0.686634\pi$
$450$		0			0
$451$	−10.3015	+	17.8427i	−0.485079	+	0.840182i
$452$	−24.3656			−1.14606
$453$		0			0
$454$	−9.54761			−0.448092
$455$	−6.18432	+	2.89341i	−0.289925	+	0.135645i
$456$		0			0
$457$	3.40003	+	5.88903i	0.159047	+	0.275477i	0.934525	−	0.355897i	$-0.115825\pi$
$457$	3.40003	+	5.88903i	0.159047	+	0.275477i	−0.775478	+	0.631374i	$0.782491\pi$
$458$	−11.6255			−0.543222
$459$		0			0
$460$	−0.474855	+	0.822473i	−0.0221402	+	0.0383480i
$461$	4.80595	+	8.32415i	0.223836	+	0.387694i	0.955969	−	0.293466i	$-0.0948088\pi$
$461$	4.80595	+	8.32415i	0.223836	+	0.387694i	−0.732134	+	0.681161i	$0.761475\pi$
$462$		0			0
$463$	−23.4929			−1.09181			−0.545905	−	0.837847i	$-0.683814\pi$
$463$	−23.4929			−1.09181			−0.545905	+	0.837847i	$0.683814\pi$
$464$	−1.97207			−0.0915508
$465$		0			0
$466$	20.2276			0.937026
$467$	−7.24654	+	12.5514i	−0.335330	+	0.580808i	−0.983548	−	0.180646i	$-0.942181\pi$
$467$	−7.24654	+	12.5514i	−0.335330	+	0.580808i	0.648218	+	0.761455i	$0.275514\pi$
$468$		0			0
$469$	19.1198	+	33.1539i	0.882870	+	1.53090i
$470$	−2.27212	+	3.93543i	−0.104805	+	0.181528i
$471$		0			0
$472$	−7.29139	+	12.6291i	−0.335614	+	0.581300i
$473$	11.2242	+	19.4409i	0.516090	+	0.893894i
$474$		0			0
$475$	−13.2839	−	23.0083i	−0.609506	−	1.05570i
$476$	7.11994	−	12.3182i	0.326342	−	0.564604i
$477$		0			0
$478$	−5.53279	−	9.58307i	−0.253064	−	0.438319i
$479$	−14.5134			−0.663134			−0.331567	−	0.943432i	$-0.607577\pi$
$479$	−14.5134			−0.663134			−0.331567	+	0.943432i	$0.607577\pi$
$480$		0			0
$481$	1.94416	+	1.35621i	0.0886461	+	0.0618378i
$482$	9.77855			0.445401
$483$		0			0
$484$	6.51064	−	11.2768i	0.295938	−	0.512580i
$485$	−2.57480			−0.116915
$486$		0			0
$487$	−11.6964	+	20.2587i	−0.530013	+	0.918009i	0.469374	+	0.882999i	$0.344480\pi$
$487$	−11.6964	+	20.2587i	−0.530013	+	0.918009i	−0.999387	+	0.0350099i	$0.988854\pi$
$488$	−5.17899			−0.234442
$489$		0			0
$490$	1.90327	−	3.28914i	0.0859812	−	0.148588i
$491$	−0.786824	+	1.36282i	−0.0355089	+	0.0615032i	−0.883234	−	0.468933i	$-0.844639\pi$
$491$	−0.786824	+	1.36282i	−0.0355089	+	0.0615032i	0.847725	+	0.530436i	$0.177972\pi$
$492$		0			0
$493$	4.23315	+	7.33203i	0.190652	+	0.330218i
$494$	13.2784	+	9.26275i	0.597423	+	0.416751i
$495$		0			0
$496$	0.168049	−	0.291069i	0.00754560	−	0.0130694i
$497$	−5.68633	+	9.83791i	−0.255067	+	0.441291i
$498$		0			0
$499$	−7.86689	+	13.6259i	−0.352170	+	0.609977i	−0.986629	−	0.162980i	$-0.947890\pi$
$499$	−7.86689	+	13.6259i	−0.352170	+	0.609977i	0.634459	+	0.772956i	$0.281223\pi$
$500$	4.83740	−	8.37862i	0.216335	−	0.374703i
$501$		0			0
$502$	9.11719	−	15.7914i	0.406920	−	0.704807i
$503$	−17.7055	−	30.6668i	−0.789447	−	1.36736i	−0.926306	−	0.376773i	$-0.877034\pi$
$503$	−17.7055	−	30.6668i	−0.789447	−	1.36736i	0.136858	−	0.990591i	$-0.456299\pi$
$504$		0			0
$505$	−4.28698	+	7.42526i	−0.190768	+	0.330420i
$506$	1.58508	−	2.74543i	0.0704653	−	0.122049i
$507$		0			0
$508$	−12.8497	−	22.2564i	−0.570115	−	0.987467i
$509$	−5.20477	−	9.01493i	−0.230697	−	0.399580i	0.727316	−	0.686303i	$-0.240767\pi$
$509$	−5.20477	−	9.01493i	−0.230697	−	0.399580i	−0.958014	+	0.286723i	$0.907434\pi$
$510$		0			0
$511$	−3.55168	+	6.14475i	−0.157117	+	0.271828i
$512$	9.72154			0.429635
$513$		0			0
$514$	7.09728	−	12.2929i	0.313048	−	0.542214i
$515$	1.10915	+	1.92110i	0.0488750	+	0.0846540i
$516$		0			0
$517$	−18.7827	+	32.5326i	−0.826063	+	1.43078i
$518$	−1.31933		0.000644921i	−0.0579680		2.83362e-5i
$519$		0			0
$520$	−0.572451	+	6.67889i	−0.0251037	+	0.292889i
$521$	0.513222	+	0.888926i	0.0224847	+	0.0389446i	0.877049	−	0.480401i	$-0.159509\pi$
$521$	0.513222	+	0.888926i	0.0224847	+	0.0389446i	−0.854564	+	0.519346i	$0.826176\pi$
$522$		0			0
$523$	9.02138	+	15.6255i	0.394477	+	0.683255i	0.993034	−	0.117826i	$-0.0375924\pi$
$523$	9.02138	+	15.6255i	0.394477	+	0.683255i	−0.598557	+	0.801080i	$0.704259\pi$
$524$	−14.0153	−	24.2751i	−0.612259	−	1.06046i
$525$		0			0
$526$	−3.55397	−	6.15566i	−0.154960	−	0.268399i
$527$	−1.44290			−0.0628539
$528$		0			0
$529$	11.0663	−	19.1674i	0.481143	−	0.833365i
$530$	−0.658712	−	1.14092i	−0.0286126	−	0.0495585i
$531$		0			0
$532$	22.3154	+	0.0109083i	0.967494	+	0.000472935i
$533$	1.41359	−	16.4926i	0.0612292	−	0.714372i
$534$		0			0
$535$	8.00644			0.346148
$536$	37.5751			1.62300
$537$		0			0
$538$	−9.21499			−0.397286
$539$	15.7336	−	27.1900i	0.677694	−	1.17116i
$540$		0			0
$541$	16.7318	−	28.9803i	0.719355	−	1.24596i	−0.241900	−	0.970301i	$-0.577771\pi$
$541$	16.7318	−	28.9803i	0.719355	−	1.24596i	0.961256	−	0.275659i	$-0.0888960\pi$
$542$	5.55910	−	9.62864i	0.238784	−	0.413585i
$543$		0			0
$544$	−11.0632	−	19.1620i	−0.474331	−	0.821565i
$545$	14.5876			0.624865
$546$		0			0
$547$	30.7718			1.31571			0.657853	−	0.753146i	$-0.271465\pi$
$547$	30.7718			1.31571			0.657853	+	0.753146i	$0.271465\pi$
$548$	−13.7361	−	23.7917i	−0.586779	−	1.01633i
$549$		0			0
$550$	−7.63775	+	13.2290i	−0.325675	+	0.564085i
$551$	−6.63940	+	11.4998i	−0.282848	+	0.489907i
$552$		0			0
$553$	−14.5608	−	0.00711768i	−0.619188	−	0.000302675i
$554$	−3.81679			−0.162160
$555$		0			0
$556$	−3.74380			−0.158773
$557$	−15.6343			−0.662446			−0.331223	−	0.943553i	$-0.607461\pi$
$557$	−15.6343			−0.662446			−0.331223	+	0.943553i	$0.607461\pi$
$558$		0			0
$559$	−14.7922	−	10.3187i	−0.625642	−	0.436436i
$560$	0.831759	+	1.44228i	0.0351482	+	0.0609473i
$561$		0			0
$562$	0.324208	+	0.561545i	0.0136759	+	0.0236873i
$563$	16.7621	−	29.0328i	0.706438	−	1.22359i	−0.259733	−	0.965681i	$-0.583634\pi$
$563$	16.7621	−	29.0328i	0.706438	−	1.22359i	0.966170	−	0.257905i	$-0.0830323\pi$
$564$		0			0
$565$	−12.2407			−0.514969
$566$	11.8617	+	20.5450i	0.498583	+	0.863570i
$567$		0			0
$568$	5.57806	+	9.66149i	0.234050	+	0.405387i
$569$	10.6031	+	18.3651i	0.444504	+	0.769903i	0.998018	−	0.0629368i	$-0.0200467\pi$
$569$	10.6031	+	18.3651i	0.444504	+	0.769903i	−0.553514	+	0.832840i	$0.686713\pi$
$570$		0			0
$571$	−0.869647	−	1.50627i	−0.0363936	−	0.0630356i	0.847255	−	0.531187i	$-0.178254\pi$
$571$	−0.869647	−	1.50627i	−0.0363936	−	0.0630356i	−0.883648	+	0.468151i	$0.844920\pi$
$572$	−1.96865	+	22.9686i	−0.0823133	+	0.960364i
$573$		0			0
$574$	4.60258	+	7.98090i	0.192108	+	0.333116i
$575$	2.08981	−	3.61965i	0.0871510	−	0.150950i
$576$		0			0
$577$	−2.83193	−	4.90504i	−0.117895	−	0.204199i	0.801039	−	0.598613i	$-0.204281\pi$
$577$	−2.83193	−	4.90504i	−0.117895	−	0.204199i	−0.918933	+	0.394413i	$0.870948\pi$
$578$	1.04399	−	1.80824i	0.0434241	−	0.0752127i
$579$		0			0
$580$	−2.28723			−0.0949721
$581$	15.2401	+	26.4264i	0.632264	+	1.09635i
$582$		0			0
$583$	−5.44531	−	9.43155i	−0.225522	−	0.390615i
$584$	3.48406	+	6.03456i	0.144171	+	0.249712i
$585$		0			0
$586$	−0.257158	+	0.445411i	−0.0106231	+	0.0183997i
$587$	−8.06910	+	13.9761i	−0.333047	+	0.576855i	−0.983108	−	0.183028i	$-0.941410\pi$
$587$	−8.06910	+	13.9761i	−0.333047	+	0.576855i	0.650060	+	0.759882i	$0.274744\pi$
$588$		0			0
$589$	−1.13155	−	1.95990i	−0.0466246	−	0.0807561i
$590$	−1.52385	+	2.63938i	−0.0627358	+	0.108662i
$591$		0			0
$592$	0.289016	−	0.500590i	0.0118785	−	0.0205741i
$593$	21.1595	−	36.6493i	0.868917	−	1.50501i	0.00581233	−	0.999983i	$-0.498150\pi$
$593$	21.1595	−	36.6493i	0.868917	−	1.50501i	0.863105	−	0.505025i	$-0.168517\pi$
$594$		0			0
$595$	3.57689	−	6.18836i	0.146638	−	0.253698i
$596$	11.1053	−	19.2349i	0.454890	−	0.787893i
$597$		0			0
$598$	−0.217506	+	2.53768i	−0.00889448	+	0.103774i
$599$	−22.9026	−	39.6685i	−0.935776	−	1.62081i	−0.773244	−	0.634108i	$-0.781367\pi$
$599$	−22.9026	−	39.6685i	−0.935776	−	1.62081i	−0.162532	−	0.986703i	$-0.551966\pi$
$600$		0			0
$601$	6.27579	−	10.8700i	0.255995	−	0.443396i	−0.709170	−	0.705037i	$-0.750930\pi$
$601$	6.27579	−	10.8700i	0.255995	−	0.443396i	0.965165	+	0.261641i	$0.0842637\pi$
$602$	10.0381	+	0.00490689i	0.409124	+	0.000199990i
$603$		0			0
$604$	13.1396			0.534643
$605$	3.27079	−	5.66517i	0.132976	−	0.230322i
$606$		0			0
$607$	34.4923			1.40000			0.700000	−	0.714143i	$-0.253183\pi$
$607$	34.4923			1.40000			0.700000	+	0.714143i	$0.253183\pi$
$608$	17.3518	−	30.0543i	0.703710	−	1.21886i
$609$		0			0
$610$	−1.08237			−0.0438239
$611$	2.57739	−	30.0708i	0.104270	−	1.21654i
$612$		0			0
$613$	−34.1674			−1.38001			−0.690003	−	0.723806i	$-0.742391\pi$
$613$	−34.1674			−1.38001			−0.690003	+	0.723806i	$0.742391\pi$
$614$	10.3192	+	17.8734i	0.416450	+	0.721313i
$615$		0			0
$616$	−15.4079	−	26.7175i	−0.620803	−	1.07648i
$617$	18.4048	+	31.8781i	0.740950	+	1.28336i	0.952063	+	0.305902i	$0.0989579\pi$
$617$	18.4048	+	31.8781i	0.740950	+	1.28336i	−0.211113	+	0.977462i	$0.567709\pi$
$618$		0			0
$619$	−17.9351	−	31.0644i	−0.720871	−	1.24858i	−0.960651	−	0.277758i	$-0.910409\pi$
$619$	−17.9351	−	31.0644i	−0.720871	−	1.24858i	0.239780	−	0.970827i	$-0.422925\pi$
$620$	0.194905	−	0.337586i	0.00782758	−	0.0135578i
$621$		0			0
$622$	−5.35810	+	9.28050i	−0.214840	+	0.372114i
$623$	−16.0227	+	27.7208i	−0.641935	+	1.11061i
$624$		0			0
$625$	−8.78910	+	15.2232i	−0.351564	+	0.608927i
$626$	−14.9407			−0.597149
$627$		0			0
$628$	−26.2300			−1.04669
$629$	−2.48156			−0.0989462
$630$		0			0
$631$	−9.93368	−	17.2056i	−0.395453	−	0.684945i	0.597706	−	0.801716i	$-0.296079\pi$
$631$	−9.93368	−	17.2056i	−0.395453	−	0.684945i	−0.993159	+	0.116770i	$0.962746\pi$
$632$	−7.14783	+	12.3804i	−0.284325	+	0.492466i
$633$		0			0
$634$	−11.8919			−0.472288
$635$	−6.45539	−	11.1811i	−0.256174	−	0.443707i
$636$		0			0
$637$	−2.17992	+	25.1445i	−0.0863715	+	0.996263i
$638$	7.63483			0.302266
$639$		0			0
$640$	6.93220			0.274019
$641$	−1.27505	+	2.20844i	−0.0503613	+	0.0872282i	−0.890107	−	0.455751i	$-0.849371\pi$
$641$	−1.27505	+	2.20844i	−0.0503613	+	0.0872282i	0.839746	+	0.542980i	$0.182704\pi$
$642$		0			0
$643$	7.23729	+	12.5354i	0.285411	+	0.494346i	0.972709	−	0.232029i	$-0.0745366\pi$
$643$	7.23729	+	12.5354i	0.285411	+	0.494346i	−0.687298	+	0.726376i	$0.741203\pi$
$644$	1.75383	+	3.04116i	0.0691106	+	0.119838i
$645$		0			0
$646$	−16.9488			−0.666840
$647$	31.6619			1.24476			0.622379	−	0.782716i	$-0.286166\pi$
$647$	31.6619			1.24476			0.622379	+	0.782716i	$0.286166\pi$
$648$		0			0
$649$	−12.5970	+	21.8187i	−0.494477	+	0.856459i
$650$	1.04806	−	12.2279i	0.0411083	−	0.479618i
$651$		0			0
$652$	7.95600	−	13.7802i	0.311581	−	0.539674i
$653$	3.52992	+	6.11399i	0.138136	+	0.239259i	0.926791	−	0.375577i	$-0.122555\pi$
$653$	3.52992	+	6.11399i	0.138136	+	0.239259i	−0.788655	+	0.614836i	$0.789222\pi$
$654$		0			0
$655$	−7.04092	−	12.1952i	−0.275112	−	0.476507i
$656$	−4.03643			−0.157596
$657$		0			0
$658$	8.39186	+	14.5516i	0.327149	+	0.567279i
$659$	−6.73098	−	11.6584i	−0.262202	−	0.454147i	0.704625	−	0.709580i	$-0.251115\pi$
$659$	−6.73098	−	11.6584i	−0.262202	−	0.454147i	−0.966827	+	0.255433i	$0.917782\pi$
$660$		0			0
$661$	4.13958			0.161011			0.0805054	−	0.996754i	$-0.474347\pi$
$661$	4.13958			0.161011			0.0805054	+	0.996754i	$0.474347\pi$
$662$	−5.47001	−	9.47433i	−0.212598	−	0.368230i
$663$		0			0
$664$	29.9504			1.16230
$665$	11.2107	+	0.00548007i	0.434732	+	0.000212508i
$666$		0			0
$667$	−2.08901			−0.0808868
$668$	10.1114	+	17.5135i	0.391223	+	0.677617i
$669$		0			0
$670$	7.85291			0.303384
$671$	−8.94753			−0.345415
$672$		0			0
$673$	−3.09545	+	5.36148i	−0.119321	+	0.206670i	−0.919499	−	0.393093i	$-0.871405\pi$
$673$	−3.09545	+	5.36148i	−0.119321	+	0.206670i	0.800178	+	0.599763i	$0.204738\pi$
$674$	−5.47241	−	9.47850i	−0.210790	−	0.365098i
$675$		0			0
$676$	−6.39602	−	17.3818i	−0.246001	−	0.668530i
$677$	−8.44416	+	14.6257i	−0.324535	+	0.562112i	−0.981418	−	0.191881i	$-0.938541\pi$
$677$	−8.44416	+	14.6257i	−0.324535	+	0.562112i	0.656883	+	0.753993i	$0.271875\pi$
$678$		0			0
$679$	−4.76294	+	8.24034i	−0.182785	+	0.316235i
$680$	−3.50878	−	6.07739i	−0.134556	−	0.233057i
$681$		0			0
$682$	−0.650598	+	1.12687i	−0.0249127	+	0.0431501i
$683$	6.68862	−	11.5850i	0.255933	−	0.443289i	−0.709215	−	0.704992i	$-0.750951\pi$
$683$	6.68862	−	11.5850i	0.255933	−	0.443289i	0.965149	+	0.261703i	$0.0842840\pi$
$684$		0			0
$685$	−6.90070	−	11.9524i	−0.263662	−	0.456676i
$686$	−7.00578	−	12.1756i	−0.267482	−	0.464865i
$687$		0			0
$688$	−2.19898	+	3.80875i	−0.0838354	+	0.145207i
$689$	7.17627	+	5.00603i	0.273394	+	0.190714i
$690$		0			0
$691$	−4.90190	−	8.49034i	−0.186477	−	0.322988i	0.757596	−	0.652723i	$-0.226374\pi$
$691$	−4.90190	−	8.49034i	−0.186477	−	0.322988i	−0.944073	+	0.329736i	$0.893040\pi$
$692$	−13.7288	+	23.7790i	−0.521892	+	0.903943i
$693$		0			0
$694$	3.54110			0.134418
$695$	−1.88079			−0.0713426
$696$		0			0
$697$	8.66443	+	15.0072i	0.328189	+	0.568439i
$698$	−3.13718			−0.118744
$699$		0			0
$700$	−8.45089	−	14.6539i	−0.319414	−	0.553866i
$701$	−35.6715			−1.34729			−0.673647	−	0.739054i	$-0.735273\pi$
$701$	−35.6715			−1.34729			−0.673647	+	0.739054i	$0.735273\pi$
$702$		0			0
$703$	−1.94607	−	3.37070i	−0.0733976	−	0.127128i
$704$	−12.0621			−0.454607
$705$		0			0
$706$	13.5730	+	23.5091i	0.510826	+	0.884777i
$707$	15.8335	+	27.4555i	0.595481	+	1.03257i
$708$		0			0
$709$	31.7496			1.19238			0.596191	−	0.802842i	$-0.296680\pi$
$709$	31.7496			1.19238			0.596191	+	0.802842i	$0.296680\pi$
$710$	1.16577	+	2.01918i	0.0437507	+	0.0757785i
$711$		0			0
$712$	15.7176	+	27.2237i	0.589043	+	1.02025i
$713$	0.178014	−	0.308329i	0.00666667	−	0.0115470i
$714$		0			0
$715$	−0.989000	+	11.5388i	−0.0369865	+	0.431528i
$716$	8.00148	−	13.8590i	0.299029	−	0.517934i
$717$		0			0
$718$	19.1715			0.715475
$719$	6.98125			0.260357			0.130178	−	0.991491i	$-0.458445\pi$
$719$	6.98125			0.260357			0.130178	+	0.991491i	$0.458445\pi$
$720$		0			0
$721$	8.20002	+	0.00400837i	0.305385	+	0.000149280i
$722$	−6.08590	−	10.5411i	−0.226494	−	0.392299i
$723$		0			0
$724$	1.73319	−	3.00197i	0.0644133	−	0.111567i
$725$	10.0660			0.373840
$726$		0			0
$727$	−2.58607			−0.0959121			−0.0479561	−	0.998849i	$-0.515271\pi$
$727$	−2.58607			−0.0959121			−0.0479561	+	0.998849i	$0.515271\pi$
$728$	20.3161	+	14.1869i	0.752965	+	0.525801i
$729$		0			0
$730$	0.728142	+	1.26118i	0.0269498	+	0.0466783i
$731$	18.8810			0.698338
$732$		0			0
$733$	6.30712	−	10.9243i	0.232959	−	0.403497i	−0.725719	−	0.687992i	$-0.758493\pi$
$733$	6.30712	−	10.9243i	0.232959	−	0.403497i	0.958678	+	0.284495i	$0.0918259\pi$
$734$	−13.4250	−	23.2528i	−0.495526	−	0.858276i
$735$		0			0
$736$	5.45955			0.201242
$737$	64.9169			2.39124
$738$		0			0
$739$	2.94077			0.108178			0.0540889	−	0.998536i	$-0.482775\pi$
$739$	2.94077			0.108178			0.0540889	+	0.998536i	$0.482775\pi$
$740$	0.335205	−	0.580592i	0.0123224	−	0.0213430i
$741$		0			0
$742$	−4.86990	−	0.00238053i	−0.178780	−	8.73920e-5i
$743$	−20.5461	+	35.5869i	−0.753763	+	1.30556i	0.192224	+	0.981351i	$0.438430\pi$
$743$	−20.5461	+	35.5869i	−0.753763	+	1.30556i	−0.945987	+	0.324205i	$0.894903\pi$
$744$		0			0
$745$	5.57903	−	9.66316i	0.204400	−	0.354031i
$746$	12.4316	+	21.5322i	0.455155	+	0.788351i
$747$		0			0
$748$	−12.0666	−	20.9000i	−0.441199	−	0.764180i
$749$	14.8106	−	25.6237i	0.541166	−	0.936270i
$750$		0			0
$751$	15.2160	+	26.3549i	0.555241	+	0.961705i	0.997885	+	0.0650079i	$0.0207073\pi$
$751$	15.2160	+	26.3549i	0.555241	+	0.961705i	−0.442644	+	0.896698i	$0.645959\pi$
$752$	−7.35961			−0.268377
$753$		0			0
$754$	−5.55473	+	2.60216i	−0.202291	+	0.0947650i
$755$	6.60102			0.240236
$756$		0			0
$757$	15.7459	−	27.2726i	0.572293	−	0.991241i	−0.424037	−	0.905645i	$-0.639387\pi$
$757$	15.7459	−	27.2726i	0.572293	−	0.991241i	0.996330	−	0.0855959i	$-0.0272794\pi$
$758$	9.16711			0.332965
$759$		0			0
$760$	5.50328	−	9.53196i	0.199625	−	0.345760i
$761$	44.1732			1.60128			0.800638	−	0.599148i	$-0.204494\pi$
$761$	44.1732			1.60128			0.800638	+	0.599148i	$0.204494\pi$
$762$		0			0
$763$	26.9846	−	46.6860i	0.976909	−	1.69015i
$764$	9.78707	−	16.9517i	0.354084	−	0.613291i
$765$		0			0
$766$	−0.194236	−	0.336427i	−0.00701804	−	0.0121556i
$767$	1.72858	−	20.1676i	0.0624154	−	0.728211i
$768$		0			0
$769$	25.4717	−	44.1182i	0.918532	−	1.59094i	0.116887	−	0.993145i	$-0.462709\pi$
$769$	25.4717	−	44.1182i	0.918532	−	1.59094i	0.801646	−	0.597799i	$-0.203958\pi$
$770$	−3.22014	−	5.58376i	−0.116046	−	0.201225i
$771$		0			0
$772$	−9.87840	+	17.1099i	−0.355531	+	0.615798i
$773$	−2.87103	+	4.97278i	−0.103264	+	0.178858i	−0.913028	−	0.407898i	$-0.866262\pi$
$773$	−2.87103	+	4.97278i	−0.103264	+	0.178858i	0.809764	+	0.586756i	$0.199595\pi$
$774$		0			0
$775$	−0.857766	+	1.48569i	−0.0308119	+	0.0533677i
$776$	4.67225	+	8.09257i	0.167724	+	0.290506i
$777$		0			0
$778$	13.4689	−	23.3288i	0.482883	−	0.836378i
$779$	−13.5895	+	23.5378i	−0.486896	+	0.843328i
$780$		0			0
$781$	9.63699	+	16.6918i	0.344839	+	0.597278i
$782$	−1.33318	−	2.30914i	−0.0476745	−	0.0825746i
$783$		0			0
$784$	6.15445	+	0.00601690i	0.219802	+	0.000214889i
$785$	−13.1773			−0.470318
$786$		0			0
$787$	−15.0412	+	26.0521i	−0.536160	+	0.928656i	0.462946	+	0.886386i	$0.346792\pi$
$787$	−15.0412	+	26.0521i	−0.536160	+	0.928656i	−0.999106	+	0.0422699i	$0.986541\pi$
$788$	−13.0465	−	22.5972i	−0.464763	−	0.804993i
$789$		0			0
$790$	−1.49384	+	2.58741i	−0.0531486	+	0.0920560i
$791$	−22.6432	+	39.1749i	−0.805098	+	1.39290i
$792$		0			0
$793$	6.50978	−	3.04956i	0.231169	−	0.108293i
$794$	3.14667	+	5.45019i	0.111671	+	0.193420i
$795$		0			0
$796$	−5.06999	−	8.78148i	−0.179701	−	0.311251i
$797$	4.03274	+	6.98491i	0.142847	+	0.247418i	0.928568	−	0.371163i	$-0.121041\pi$
$797$	4.03274	+	6.98491i	0.142847	+	0.247418i	−0.785721	+	0.618581i	$0.787708\pi$
$798$		0			0
$799$	15.7978	+	27.3626i	0.558887	+	0.968020i
$800$	−26.3070			−0.930094
$801$		0			0
$802$	5.27918	−	9.14380i	0.186414	−	0.322879i
$803$	6.01926	+	10.4257i	0.212415	+	0.367914i
$804$		0			0
$805$	0.881082	+	1.52780i	0.0310541	+	0.0538480i
$806$	0.0892758	−	1.04160i	0.00314461	−	0.0366887i
$807$		0			0
$808$	31.1168			1.09468
$809$	18.5185			0.651077			0.325538	−	0.945529i	$-0.394454\pi$
$809$	18.5185			0.651077			0.325538	+	0.945529i	$0.394454\pi$
$810$		0			0
$811$	20.3264			0.713755			0.356878	−	0.934151i	$-0.383841\pi$
$811$	20.3264			0.713755			0.356878	+	0.934151i	$0.383841\pi$
$812$	−4.23099	+	7.32002i	−0.148479	+	0.256882i
$813$		0			0
$814$	−1.11892	+	1.93803i	−0.0392182	+	0.0679279i
$815$	3.99690	−	6.92284i	0.140005	−	0.242496i
$816$		0			0
$817$	14.8067	+	25.6460i	0.518022	+	0.897241i
$818$	−3.72977			−0.130408
$819$		0			0
$820$	−4.68151			−0.163485
$821$	−1.20362	−	2.08473i	−0.0420067	−	0.0727577i	0.844258	−	0.535938i	$-0.180042\pi$
$821$	−1.20362	−	2.08473i	−0.0420067	−	0.0727577i	−0.886264	+	0.463180i	$0.846708\pi$
$822$		0			0
$823$	15.3210	−	26.5368i	0.534057	−	0.925013i	−0.465152	−	0.885231i	$-0.654000\pi$
$823$	15.3210	−	26.5368i	0.534057	−	0.925013i	0.999208	−	0.0397824i	$-0.0126665\pi$
$824$	4.02535	−	6.97211i	0.140230	−	0.242885i
$825$		0			0
$826$	5.62818	+	9.75931i	0.195829	+	0.339570i
$827$	−3.92281			−0.136409			−0.0682047	−	0.997671i	$-0.521727\pi$
$827$	−3.92281			−0.136409			−0.0682047	+	0.997671i	$0.521727\pi$
$828$		0			0
$829$	10.6484			0.369834			0.184917	−	0.982754i	$-0.440798\pi$
$829$	10.6484			0.369834			0.184917	+	0.982754i	$0.440798\pi$
$830$	6.25942			0.217268
$831$		0			0
$832$	8.77579	−	4.11109i	0.304246	−	0.142526i
$833$	−13.1885	−	22.8948i	−0.456955	−	0.793259i
$834$		0			0
$835$	5.07973	+	8.79836i	0.175791	+	0.304480i
$836$	18.9256	−	32.7802i	0.654557	−	1.13373i
$837$		0			0
$838$	7.35948			0.254229
$839$	13.8289	+	23.9523i	0.477426	+	0.826925i	0.999665	−	0.0258735i	$-0.00823670\pi$
$839$	13.8289	+	23.9523i	0.477426	+	0.826925i	−0.522240	+	0.852799i	$0.674903\pi$
$840$		0			0
$841$	11.9845	+	20.7577i	0.413258	+	0.715783i
$842$	5.80026	+	10.0463i	0.199890	+	0.346220i
$843$		0			0
$844$	8.47706	+	14.6827i	0.291792	+	0.505399i
$845$	−3.21320	−	8.73218i	−0.110538	−	0.300396i
$846$		0			0
$847$	−12.0803	−	20.9474i	−0.415085	−	0.719761i
$848$	1.06681	−	1.84778i	0.0366345	−	0.0634529i
$849$		0			0
$850$	6.42398	+	11.1267i	0.220341	+	0.381641i
$851$	0.306155	−	0.530275i	0.0104948	−	0.0181776i
$852$		0			0
$853$	−8.76490			−0.300105			−0.150052	−	0.988678i	$-0.547944\pi$
$853$	−8.76490			−0.300105			−0.150052	+	0.988678i	$0.547944\pi$
$854$	−2.00220	+	3.46401i	−0.0685140	+	0.118536i
$855$		0			0
$856$	−14.5286	−	25.1642i	−0.496576	−	0.860095i
$857$	12.9737	+	22.4711i	0.443173	+	0.767598i	0.997923	−	0.0644193i	$-0.0205195\pi$
$857$	12.9737	+	22.4711i	0.443173	+	0.767598i	−0.554750	+	0.832017i	$0.687186\pi$
$858$		0			0
$859$	−27.8958	+	48.3170i	−0.951793	+	1.64855i	−0.210251	+	0.977648i	$0.567428\pi$
$859$	−27.8958	+	48.3170i	−0.951793	+	1.64855i	−0.741542	+	0.670906i	$0.765905\pi$
$860$	−2.55041	+	4.41744i	−0.0869684	+	0.150634i
$861$		0			0
$862$	12.3852	+	21.4518i	0.421843	+	0.730653i
$863$	5.86854	−	10.1646i	0.199767	−	0.346007i	−0.748686	−	0.662925i	$-0.769315\pi$
$863$	5.86854	−	10.1646i	0.199767	−	0.346007i	0.948453	+	0.316918i	$0.102648\pi$
$864$		0			0
$865$	−6.89703	+	11.9460i	−0.234506	+	0.406176i
$866$	7.04013	−	12.1939i	0.239233	−	0.414364i
$867$		0			0
$868$	−0.719863	−	1.24825i	−0.0244338	−	0.0423683i
$869$	−12.3490	+	21.3891i	−0.418911	+	0.725576i
$870$		0			0
$871$	−47.2303	+	22.1254i	−1.60034	+	0.749692i
$872$	−26.4708	−	45.8488i	−0.896415	−	1.55264i
$873$		0			0
$874$	2.09100	−	3.62172i	0.0707292	−	0.122506i
$875$	−8.97568	−	15.5639i	−0.303433	−	0.526156i
$876$		0			0
$877$	−10.9556			−0.369943			−0.184972	−	0.982744i	$-0.559219\pi$
$877$	−10.9556			−0.369943			−0.184972	+	0.982744i	$0.559219\pi$
$878$	−3.58562	+	6.21048i	−0.121009	+	0.209594i
$879$		0			0
$880$	2.82405			0.0951986
$881$	0.925967	−	1.60382i	0.0311966	−	0.0540341i	−0.850006	−	0.526774i	$-0.823402\pi$
$881$	0.925967	−	1.60382i	0.0311966	−	0.0540341i	0.881202	+	0.472740i	$0.156735\pi$
$882$		0			0
$883$	−50.8664			−1.71179			−0.855896	−	0.517149i	$-0.826993\pi$
$883$	−50.8664			−1.71179			−0.855896	+	0.517149i	$0.826993\pi$
$884$	15.9024	+	11.0932i	0.534855	+	0.373104i
$885$		0			0
$886$	−5.63692			−0.189376
$887$	−10.5435	−	18.2619i	−0.354016	−	0.613174i	0.632933	−	0.774207i	$-0.281851\pi$
$887$	−10.5435	−	18.2619i	−0.354016	−	0.613174i	−0.986949	+	0.161033i	$0.948518\pi$
$888$		0			0
$889$	−47.7251	−	0.0233292i	−1.60065	−	0.000782437i
$890$	3.28487	+	5.68955i	0.110109	+	0.190714i
$891$		0			0
$892$	−17.0156	−	29.4719i	−0.569725	−	0.986793i
$893$	−24.7778	+	42.9164i	−0.829157	+	1.43614i
$894$		0			0
$895$	4.01975	−	6.96241i	0.134365	−	0.232728i
$896$	12.8234	−	22.1857i	0.428399	−	0.741173i
$897$		0			0
$898$	7.14763	−	12.3801i	0.238519	−	0.413128i
$899$	0.857438			0.0285972
$900$		0			0
$901$	−9.15991			−0.305161
$902$	15.6270			0.520322
$903$		0			0
$904$	22.2120	+	38.4724i	0.738761	+	1.27957i
$905$	0.870711	−	1.50812i	0.0289434	−	0.0501314i
$906$		0			0
$907$	−10.2256			−0.339537			−0.169768	−	0.985484i	$-0.554302\pi$
$907$	−10.2256			−0.339537			−0.169768	+	0.985484i	$0.554302\pi$
$908$	−8.96698	−	15.5313i	−0.297580	−	0.515423i
$909$		0			0
$910$	4.24592	+	2.96496i	0.140751	+	0.0982873i
$911$	−35.4885			−1.17578			−0.587892	−	0.808939i	$-0.700042\pi$
$911$	−35.4885			−1.17578			−0.587892	+	0.808939i	$0.700042\pi$
$912$		0			0
$913$	51.7441			1.71248
$914$	2.57886	−	4.46671i	0.0853010	−	0.147746i
$915$		0			0
$916$	−10.9185	−	18.9113i	−0.360756	−	0.624848i
$917$	−52.0540	−	0.0254453i	−1.71897	−	0.000840277i
$918$		0			0
$919$	2.99682			0.0988560			0.0494280	−	0.998778i	$-0.484260\pi$
$919$	2.99682			0.0988560			0.0494280	+	0.998778i	$0.484260\pi$
$920$	1.73154			0.0570872
$921$		0			0
$922$	3.64522	−	6.31371i	0.120049	−	0.207931i
$923$	−12.7004	−	8.85956i	−0.418039	−	0.291616i
$924$		0			0
$925$	−1.47522	+	2.55515i	−0.0485048	+	0.0840128i
$926$	8.90946	+	15.4316i	0.292783	+	0.507115i
$927$		0			0
$928$	6.57425	+	11.3869i	0.215810	+	0.373794i
$929$	59.8495			1.96360			0.981800	−	0.189918i	$-0.0608223\pi$
$929$	59.8495			1.96360			0.981800	+	0.189918i	$0.0608223\pi$
$930$		0			0
$931$	20.7554	−	35.8684i	0.680232	−	1.17554i
$932$	18.9975	+	32.9046i	0.622283	+	1.07783i
$933$		0			0
$934$	10.9927			0.359693
$935$	−6.06198	−	10.4997i	−0.198248	−	0.343375i
$936$		0			0
$937$	−60.1408			−1.96471			−0.982357	−	0.187015i	$-0.940119\pi$
$937$	−60.1408			−1.96471			−0.982357	+	0.187015i	$0.940119\pi$
$938$	14.5266	−	25.1324i	0.474309	−	0.820601i
$939$		0			0
$940$	−8.53578			−0.278407
$941$	0.964242	+	1.67012i	0.0314334	+	0.0544443i	0.881314	−	0.472531i	$-0.156659\pi$
$941$	0.964242	+	1.67012i	0.0314334	+	0.0544443i	−0.849881	+	0.526975i	$0.823326\pi$
$942$		0			0
$943$	−4.27579			−0.139239
$944$	−4.93588			−0.160649
$945$		0			0
$946$	8.51334	−	14.7455i	0.276793	−	0.479419i
$947$	−0.341387	−	0.591300i	−0.0110936	−	0.0192147i	0.860425	−	0.509577i	$-0.170198\pi$
$947$	−0.341387	−	0.591300i	−0.0110936	−	0.0192147i	−0.871519	+	0.490362i	$0.836865\pi$
$948$		0			0
$949$	−7.93267	−	5.53368i	−0.257505	−	0.179631i
$950$	−10.0756	+	17.4514i	−0.326894	+	0.566197i
$951$		0			0
$952$	−25.9407	−	0.0126804i	−0.840741	−	0.000410975i
$953$	−16.6889	−	28.9060i	−0.540606	−	0.936358i	−0.998869	−	0.0475411i	$-0.984861\pi$
$953$	−16.6889	−	28.9060i	−0.540606	−	0.936358i	0.458263	−	0.888817i	$-0.348472\pi$
$954$		0			0
$955$	4.91679	−	8.51613i	0.159104	−	0.275575i
$956$	10.3926	−	18.0006i	0.336122	−	0.582180i
$957$		0			0
$958$	5.50406	+	9.53332i	0.177828	+	0.308008i
$959$	−51.0173	−	0.0249385i	−1.64744	−	0.000805308i
$960$		0			0
$961$	15.4269	−	26.7202i	0.497643	−	0.861943i
$962$	0.153540	−	1.79138i	0.00495032	−	0.0577563i
$963$		0			0
$964$	9.18387	+	15.9069i	0.295793	+	0.512328i
$965$	−4.96267	+	8.59559i	−0.159754	+	0.276702i
$966$		0			0
$967$	−4.60355			−0.148040			−0.0740201	−	0.997257i	$-0.523583\pi$
$967$	−4.60355			−0.148040			−0.0740201	+	0.997257i	$0.523583\pi$
$968$	−23.7408			−0.763059
$969$		0			0
$970$	0.976465	+	1.69129i	0.0313524	+	0.0543040i
$971$	2.13297			0.0684503			0.0342251	−	0.999414i	$-0.489104\pi$
$971$	2.13297			0.0684503			0.0342251	+	0.999414i	$0.489104\pi$
$972$		0			0
$973$	−3.47915	+	6.01927i	−0.111537	+	0.192969i
$974$	17.7429			0.568520
$975$		0			0
$976$	−0.876474	−	1.51810i	−0.0280553	−	0.0485931i
$977$	36.3686			1.16354			0.581768	−	0.813355i	$-0.302361\pi$
$977$	36.3686			1.16354			0.581768	+	0.813355i	$0.302361\pi$
$978$		0			0
$979$	27.1547	+	47.0333i	0.867867	+	1.50319i
$980$	7.13803	+	0.00697849i	0.228016	+	0.000222920i
$981$		0			0
$982$	1.19358			0.0380887
$983$	10.0001	+	17.3207i	0.318954	+	0.552444i	0.980270	−	0.197663i	$-0.0633353\pi$
$983$	10.0001	+	17.3207i	0.318954	+	0.552444i	−0.661316	+	0.750107i	$0.730002\pi$
$984$		0			0
$985$	−6.55426	−	11.3523i	−0.208836	−	0.361715i
$986$	3.21076	−	5.56120i	0.102251	−	0.177105i
$987$		0			0
$988$	−2.59700	+	30.2996i	−0.0826215	+	0.963960i
$989$	−2.32938	+	4.03461i	−0.0740701	+	0.128293i
$990$		0			0
$991$	20.8006			0.660754			0.330377	−	0.943849i	$-0.392824\pi$
$991$	20.8006			0.660754			0.330377	+	0.943849i	$0.392824\pi$
$992$	−2.24088			−0.0711482
$993$		0			0
$994$	8.61865	+	0.00421301i	0.273367	+	0.000133629i
$995$	−2.54704	−	4.41160i	−0.0807466	−	0.139857i
$996$		0			0
$997$	11.0553	−	19.1483i	0.350124	−	0.606433i	−0.636147	−	0.771568i	$-0.719473\pi$
$997$	11.0553	−	19.1483i	0.350124	−	0.606433i	0.986271	+	0.165135i	$0.0528060\pi$
$998$	11.9338			0.377756
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.e.100.4		16
3.2	odd	2		273.2.j.b.100.5	✓	16
7.4	even	3		819.2.s.e.802.5		16
13.3	even	3		819.2.s.e.289.5		16
21.11	odd	6		273.2.l.b.256.4	yes	16
39.29	odd	6		273.2.l.b.16.4	yes	16
91.81	even	3	inner	819.2.n.e.172.4		16
273.263	odd	6		273.2.j.b.172.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.5	✓	16	3.2	odd	2
273.2.j.b.172.5	yes	16	273.263	odd	6
273.2.l.b.16.4	yes	16	39.29	odd	6
273.2.l.b.256.4	yes	16	21.11	odd	6
819.2.n.e.100.4		16	1.1	even	1	trivial
819.2.n.e.172.4		16	91.81	even	3	inner
819.2.s.e.289.5		16	13.3	even	3
819.2.s.e.802.5		16	7.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.379240 - 0.656863i) q^{2} +(0.712354 - 1.23383i) q^{4} +(0.357869 - 0.619848i) q^{5} +(-1.32176 - 2.29193i) q^{7} -2.59757 q^{8} +O(q^{10})\)	\(q+(-0.379240 - 0.656863i) q^{2} +(0.712354 - 1.23383i) q^{4} +(0.357869 - 0.619848i) q^{5} +(-1.32176 - 2.29193i) q^{7} -2.59757 q^{8} -0.542874 q^{10} -4.48772 q^{11} +(3.26504 - 1.52954i) q^{13} +(-1.00422 + 1.73741i) q^{14} +(-0.439604 - 0.761417i) q^{16} +(-1.88727 + 3.26885i) q^{17} -5.92010 q^{19} +(-0.509859 - 0.883102i) q^{20} +(1.70192 + 2.94782i) q^{22} +(-0.465673 - 0.806569i) q^{23} +(2.24386 + 3.88648i) q^{25} +(-2.24293 - 1.56463i) q^{26} +(-3.76942 - 0.00184259i) q^{28} +(1.12150 - 1.94250i) q^{29} +(0.191136 + 0.331058i) q^{31} +(-2.93100 + 5.07665i) q^{32} +2.86291 q^{34} +(-1.89367 - 0.000925671i) q^{35} +(0.328723 + 0.569365i) q^{37} +(2.24514 + 3.88870i) q^{38} +(-0.929592 + 1.61010i) q^{40} +(2.29549 - 3.97591i) q^{41} +(-2.50110 - 4.33202i) q^{43} +(-3.19684 + 5.53710i) q^{44} +(-0.353203 + 0.611766i) q^{46} +(4.18536 - 7.24926i) q^{47} +(-3.50593 + 6.05875i) q^{49} +(1.70192 - 2.94782i) q^{50} +(0.438674 - 5.11809i) q^{52} +(1.21338 + 2.10164i) q^{53} +(-1.60602 + 2.78170i) q^{55} +(3.43336 + 5.95347i) q^{56} -1.70127 q^{58} +(2.80700 - 4.86187i) q^{59} +1.99378 q^{61} +(0.144973 - 0.251101i) q^{62} +2.68780 q^{64} +(0.220379 - 2.57121i) q^{65} -14.4655 q^{67} +(2.68881 + 4.65715i) q^{68} +(0.717546 + 1.24423i) q^{70} +(-2.14741 - 3.71943i) q^{71} +(-1.34127 - 2.32315i) q^{73} +(0.249330 - 0.431852i) q^{74} +(-4.21721 + 7.30442i) q^{76} +(5.93167 + 10.2856i) q^{77} +(2.75173 - 4.76614i) q^{79} -0.629283 q^{80} -3.48217 q^{82} -11.5302 q^{83} +(1.35079 + 2.33964i) q^{85} +(-1.89703 + 3.28575i) q^{86} +11.6572 q^{88} +(-6.05088 - 10.4804i) q^{89} +(-7.82119 - 5.46159i) q^{91} -1.32689 q^{92} -6.34903 q^{94} +(-2.11862 + 3.66956i) q^{95} +(-1.79870 - 3.11544i) q^{97} +(5.30936 + 0.00519069i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

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