LMFDB - Embedded newform 387.2.h.g.208.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(208,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("387.208");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.h (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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 11x^{10} + 89x^{8} + 314x^{6} + 815x^{4} + 608x^{2} + 361 $ x^12 + 11x^10 + 89x^8 + 314x^6 + 815x^4 + 608*x^2 + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			208.6
Root			$-1.28149 + 2.21960i$ of defining polynomial
Character	$\chi$	$=$	387.208
Dual form			387.2.h.g.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.56298 q^{2} +4.56885 q^{4} +(0.440037 + 0.762166i) q^{5} +(-0.627804 + 1.08739i) q^{7} +6.58390 q^{8} +O(q^{10})$	\(q+2.56298 q^{2} +4.56885 q^{4} +(0.440037 + 0.762166i) q^{5} +(-0.627804 + 1.08739i) q^{7} +6.58390 q^{8} +(1.12780 + 1.95341i) q^{10} -4.90100 q^{11} +(-0.171690 + 0.297375i) q^{13} +(-1.60905 + 2.78695i) q^{14} +7.73669 q^{16} +(2.45050 - 4.24439i) q^{17} +(-2.19665 - 3.80472i) q^{19} +(2.01046 + 3.48222i) q^{20} -12.5611 q^{22} +(-1.72153 - 2.98177i) q^{23} +(2.11274 - 3.65936i) q^{25} +(-0.440037 + 0.762166i) q^{26} +(-2.86834 + 4.96812i) q^{28} +(-2.52435 + 4.37231i) q^{29} +(2.08392 + 3.60945i) q^{31} +6.66115 q^{32} +(6.28057 - 10.8783i) q^{34} -1.10503 q^{35} +(5.86834 + 10.1643i) q^{37} +(-5.62997 - 9.75140i) q^{38} +(2.89716 + 5.01803i) q^{40} -4.82375 q^{41} +(5.76936 - 3.11682i) q^{43} -22.3919 q^{44} +(-4.41223 - 7.64221i) q^{46} -11.7099 q^{47} +(2.71172 + 4.69684i) q^{49} +(5.41489 - 9.37887i) q^{50} +(-0.784425 + 1.35866i) q^{52} +(0.401415 + 0.695270i) q^{53} +(-2.15662 - 3.73538i) q^{55} +(-4.13340 + 7.15926i) q^{56} +(-6.46986 + 11.2061i) q^{58} +3.79597 q^{59} +(4.26936 - 7.39474i) q^{61} +(5.34104 + 9.25095i) q^{62} +1.59899 q^{64} -0.302199 q^{65} +(0.685436 + 1.18721i) q^{67} +(11.1960 - 19.3920i) q^{68} -2.83216 q^{70} +(-1.45795 + 2.52524i) q^{71} +(2.08392 - 3.60945i) q^{73} +(15.0404 + 26.0508i) q^{74} +(-10.0362 - 17.3832i) q^{76} +(3.07687 - 5.32929i) q^{77} +(-7.46601 + 12.9315i) q^{79} +(3.40443 + 5.89664i) q^{80} -12.3632 q^{82} +(5.26379 + 9.11715i) q^{83} +4.31324 q^{85} +(14.7867 - 7.98833i) q^{86} -32.2677 q^{88} +(-8.04185 - 13.9289i) q^{89} +(-0.215575 - 0.373387i) q^{91} +(-7.86539 - 13.6233i) q^{92} -30.0121 q^{94} +(1.93322 - 3.34843i) q^{95} -6.48108 q^{97} +(6.95008 + 12.0379i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 20 q^{4} + 2 q^{7}+O(q^{10}) $ 12 * q + 20 * q^4 + 2 * q^7	$ 12 q + 20 q^{4} + 2 q^{7} + 4 q^{10} - 6 q^{13} + 12 q^{16} + 18 q^{19} - 16 q^{22} + 4 q^{25} + 6 q^{28} + 2 q^{31} + 8 q^{34} + 30 q^{37} - 4 q^{40} + 40 q^{43} - 26 q^{46} + 8 q^{52} - 18 q^{55} - 54 q^{58} + 22 q^{61} + 8 q^{64} + 2 q^{67} - 80 q^{70} + 2 q^{73} - 34 q^{76} - 16 q^{79} - 36 q^{82} + 36 q^{85} - 148 q^{88} - 20 q^{91} - 140 q^{94} - 16 q^{97}+O(q^{100}) $ 12 * q + 20 * q^4 + 2 * q^7 + 4 * q^10 - 6 * q^13 + 12 * q^16 + 18 * q^19 - 16 * q^22 + 4 * q^25 + 6 * q^28 + 2 * q^31 + 8 * q^34 + 30 * q^37 - 4 * q^40 + 40 * q^43 - 26 * q^46 + 8 * q^52 - 18 * q^55 - 54 * q^58 + 22 * q^61 + 8 * q^64 + 2 * q^67 - 80 * q^70 + 2 * q^73 - 34 * q^76 - 16 * q^79 - 36 * q^82 + 36 * q^85 - 148 * q^88 - 20 * q^91 - 140 * q^94 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.56298			1.81230			0.906149	−	0.422958i	$-0.139008\pi$
$2$	2.56298			1.81230			0.906149	+	0.422958i	$0.139008\pi$
$3$		0			0
$3$		0			0
$4$	4.56885			2.28442
$5$	0.440037	+	0.762166i	0.196790	+	0.340851i	0.947486	−	0.319797i	$-0.103615\pi$
$5$	0.440037	+	0.762166i	0.196790	+	0.340851i	−0.750696	+	0.660648i	$0.770281\pi$
$6$		0			0
$7$	−0.627804	+	1.08739i	−0.237288	+	0.410994i	−0.959935	−	0.280222i	$-0.909592\pi$
$7$	−0.627804	+	1.08739i	−0.237288	+	0.410994i	0.722647	+	0.691217i	$0.242925\pi$
$8$	6.58390			2.32776
$9$		0			0
$10$	1.12780	+	1.95341i	0.356643	+	0.617724i
$11$	−4.90100			−1.47771			−0.738853	−	0.673866i	$-0.764632\pi$
$11$	−4.90100			−1.47771			−0.738853	+	0.673866i	$0.764632\pi$
$12$		0			0
$13$	−0.171690	+	0.297375i	−0.0476182	+	0.0824771i	−0.888852	−	0.458194i	$-0.848496\pi$
$13$	−0.171690	+	0.297375i	−0.0476182	+	0.0824771i	0.841234	+	0.540671i	$0.181830\pi$
$14$	−1.60905	+	2.78695i	−0.430036	+	0.744844i
$15$		0			0
$16$	7.73669			1.93417
$17$	2.45050	−	4.24439i	0.594333	−	1.02942i	−0.399307	−	0.916817i	$-0.630749\pi$
$17$	2.45050	−	4.24439i	0.594333	−	1.02942i	0.993641	−	0.112598i	$-0.0359174\pi$
$18$		0			0
$19$	−2.19665	−	3.80472i	−0.503947	−	0.872862i	−0.999990	−	0.00456360i	$-0.998547\pi$
$19$	−2.19665	−	3.80472i	−0.503947	−	0.872862i	0.496043	−	0.868298i	$-0.334786\pi$
$20$	2.01046	+	3.48222i	0.449553	+	0.778649i
$21$		0			0
$22$	−12.5611			−2.67805
$23$	−1.72153	−	2.98177i	−0.358963	−	0.621742i	0.628825	−	0.777547i	$-0.283536\pi$
$23$	−1.72153	−	2.98177i	−0.358963	−	0.621742i	−0.987788	+	0.155805i	$0.950203\pi$
$24$		0			0
$25$	2.11274	−	3.65936i	0.422547	−	0.731873i
$26$	−0.440037	+	0.762166i	−0.0862983	+	0.149473i
$27$		0			0
$28$	−2.86834	+	4.96812i	−0.542066	+	0.938886i
$29$	−2.52435	+	4.37231i	−0.468761	+	0.811918i	−0.999362	−	0.0357038i	$-0.988633\pi$
$29$	−2.52435	+	4.37231i	−0.468761	+	0.811918i	0.530602	+	0.847621i	$0.321966\pi$
$30$		0			0
$31$	2.08392	+	3.60945i	0.374283	+	0.648277i	0.990219	−	0.139519i	$-0.0445556\pi$
$31$	2.08392	+	3.60945i	0.374283	+	0.648277i	−0.615937	+	0.787796i	$0.711222\pi$
$32$	6.66115			1.17754
$33$		0			0
$34$	6.28057	−	10.8783i	1.07711	−	1.86561i
$35$	−1.10503			−0.186784
$36$		0			0
$37$	5.86834	+	10.1643i	0.964750	+	1.67100i	0.710286	+	0.703913i	$0.248566\pi$
$37$	5.86834	+	10.1643i	0.964750	+	1.67100i	0.254464	+	0.967082i	$0.418101\pi$
$38$	−5.62997	−	9.75140i	−0.913302	−	1.58189i
$39$		0			0
$40$	2.89716	+	5.01803i	0.458081	+	0.793420i
$41$	−4.82375			−0.753344			−0.376672	−	0.926347i	$-0.622932\pi$
$41$	−4.82375			−0.753344			−0.376672	+	0.926347i	$0.622932\pi$
$42$		0			0
$43$	5.76936	−	3.11682i	0.879818	−	0.475310i
$43$	5.76936	−	3.11682i	0.879818	−	0.475310i
$44$	−22.3919			−3.37571
$45$		0			0
$46$	−4.41223	−	7.64221i	−0.650548	−	1.12678i
$47$	−11.7099			−1.70806			−0.854029	−	0.520225i	$-0.825848\pi$
$47$	−11.7099			−1.70806			−0.854029	+	0.520225i	$0.825848\pi$
$48$		0			0
$49$	2.71172	+	4.69684i	0.387389	+	0.670978i
$50$	5.41489	−	9.37887i	0.765781	−	1.32637i
$51$		0			0
$52$	−0.784425	+	1.35866i	−0.108780	+	0.188413i
$53$	0.401415	+	0.695270i	0.0551385	+	0.0955027i	0.892277	−	0.451488i	$-0.149107\pi$
$53$	0.401415	+	0.695270i	0.0551385	+	0.0955027i	−0.837139	+	0.546991i	$0.815773\pi$
$54$		0			0
$55$	−2.15662	−	3.73538i	−0.290799	−	0.503678i
$56$	−4.13340	+	7.15926i	−0.552349	+	0.956697i
$57$		0			0
$58$	−6.46986	+	11.2061i	−0.849534	+	1.47144i
$59$	3.79597			0.494193			0.247097	−	0.968991i	$-0.420523\pi$
$59$	3.79597			0.494193			0.247097	+	0.968991i	$0.420523\pi$
$60$		0			0
$61$	4.26936	−	7.39474i	0.546635	−	0.946800i	−0.451867	−	0.892085i	$-0.649242\pi$
$61$	4.26936	−	7.39474i	0.546635	−	0.946800i	0.998502	−	0.0547142i	$-0.0174248\pi$
$62$	5.34104	+	9.25095i	0.678312	+	1.17487i
$63$		0			0
$64$	1.59899			0.199874
$65$	−0.302199			−0.0374832
$66$		0			0
$67$	0.685436	+	1.18721i	0.0837394	+	0.145041i	0.904853	−	0.425723i	$-0.139980\pi$
$67$	0.685436	+	1.18721i	0.0837394	+	0.145041i	−0.821114	+	0.570764i	$0.806647\pi$
$68$	11.1960	−	19.3920i	1.35771	−	2.35162i
$69$		0			0
$70$	−2.83216			−0.338508
$71$	−1.45795	+	2.52524i	−0.173027	+	0.299691i	−0.939477	−	0.342613i	$-0.888688\pi$
$71$	−1.45795	+	2.52524i	−0.173027	+	0.299691i	0.766450	+	0.642304i	$0.222021\pi$
$72$		0			0
$73$	2.08392	−	3.60945i	0.243904	−	0.422455i	−0.717919	−	0.696127i	$-0.754905\pi$
$73$	2.08392	−	3.60945i	0.243904	−	0.422455i	0.961823	+	0.273672i	$0.0882384\pi$
$74$	15.0404	+	26.0508i	1.74841	+	3.02834i
$75$		0			0
$76$	−10.0362	−	17.3832i	−1.15123	−	1.99399i
$77$	3.07687	−	5.32929i	0.350642	−	0.607329i
$78$		0			0
$79$	−7.46601	+	12.9315i	−0.839992	+	1.45491i	0.0499089	+	0.998754i	$0.484107\pi$
$79$	−7.46601	+	12.9315i	−0.839992	+	1.45491i	−0.889901	+	0.456155i	$0.849226\pi$
$80$	3.40443	+	5.89664i	0.380627	+	0.659265i
$81$		0			0
$82$	−12.3632			−1.36528
$83$	5.26379	+	9.11715i	0.577776	+	1.00074i	0.995734	+	0.0922712i	$0.0294127\pi$
$83$	5.26379	+	9.11715i	0.577776	+	1.00074i	−0.417958	+	0.908466i	$0.637254\pi$
$84$		0			0
$85$	4.31324			0.467837
$86$	14.7867	−	7.98833i	1.59449	−	0.861403i
$87$		0			0
$88$	−32.2677			−3.43975
$89$	−8.04185	−	13.9289i	−0.852434	−	1.47646i	−0.879005	−	0.476813i	$-0.841792\pi$
$89$	−8.04185	−	13.9289i	−0.852434	−	1.47646i	0.0265705	−	0.999647i	$-0.491541\pi$
$90$		0			0
$91$	−0.215575	−	0.373387i	−0.0225984	−	0.0391416i
$92$	−7.86539	−	13.6233i	−0.820024	−	1.42032i
$93$		0			0
$94$	−30.0121			−3.09551
$95$	1.93322	−	3.34843i	0.198344	−	0.343542i
$96$		0			0
$97$	−6.48108			−0.658054			−0.329027	−	0.944321i	$-0.606721\pi$
$97$	−6.48108			−0.658054			−0.329027	+	0.944321i	$0.606721\pi$
$98$	6.95008	+	12.0379i	0.702064	+	1.21601i
$99$		0			0
$100$	9.65277	−	16.7191i	0.965277	−	1.67191i
$101$	−5.93217	+	10.2748i	−0.590273	+	1.02238i	0.403922	+	0.914793i	$0.367647\pi$
$101$	−5.93217	+	10.2748i	−0.590273	+	1.02238i	−0.994195	+	0.107590i	$0.965687\pi$
$102$		0			0
$103$	6.52111	−	11.2949i	0.642544	−	1.11292i	−0.342319	−	0.939584i	$-0.611212\pi$
$103$	6.52111	−	11.2949i	0.642544	−	1.11292i	0.984863	−	0.173335i	$-0.0554545\pi$
$104$	−1.13039	+	1.95789i	−0.110844	+	0.191987i
$105$		0			0
$106$	1.02882	+	1.78196i	0.0999274	+	0.173079i
$107$	11.4342			1.10538			0.552692	−	0.833386i	$-0.313601\pi$
$107$	11.4342			1.10538			0.552692	+	0.833386i	$0.313601\pi$
$108$		0			0
$109$	9.05125	+	15.6772i	0.866953	+	1.50161i	0.865095	+	0.501608i	$0.167258\pi$
$109$	9.05125	+	15.6772i	0.866953	+	1.50161i	0.00185741	+	0.999998i	$0.499409\pi$
$110$	−5.52737	−	9.57368i	−0.527014	−	0.912815i
$111$		0			0
$112$	−4.85713	+	8.41279i	−0.458955	+	0.794934i
$113$	1.40723			0.132381			0.0661904	−	0.997807i	$-0.478916\pi$
$113$	1.40723			0.132381			0.0661904	+	0.997807i	$0.478916\pi$
$114$		0			0
$115$	1.51507	−	2.62418i	0.141281	−	0.244706i
$116$	−11.5334	+	19.9764i	−1.07085	+	1.85476i
$117$		0			0
$118$	9.72898			0.895626
$119$	3.07687	+	5.32929i	0.282056	+	0.488535i
$120$		0			0
$121$	13.0198			1.18362
$122$	10.9423	−	18.9525i	0.990666	−	1.71588i
$123$		0			0
$124$	9.52111	+	16.4911i	0.855021	+	1.48094i
$125$	8.11909			0.726194
$126$		0			0
$127$	−9.04993			−0.803051			−0.401526	−	0.915848i	$-0.631520\pi$
$127$	−9.04993			−0.803051			−0.401526	+	0.915848i	$0.631520\pi$
$128$	−9.22412			−0.815305
$129$		0			0
$130$	−0.774530			−0.0679308
$131$	18.1460			1.58543			0.792714	−	0.609594i	$-0.208668\pi$
$131$	18.1460			1.58543			0.792714	+	0.609594i	$0.208668\pi$
$132$		0			0
$133$	5.51628			0.478322
$134$	1.75676	+	3.04279i	0.151761	+	0.262857i
$135$		0			0
$136$	16.1338	−	27.9446i	1.38347	−	2.39623i
$137$	15.3779			1.31382			0.656910	−	0.753969i	$-0.271863\pi$
$137$	15.3779			1.31382			0.656910	+	0.753969i	$0.271863\pi$
$138$		0			0
$139$	−8.42212	−	14.5875i	−0.714355	−	1.23730i	−0.963208	−	0.268758i	$-0.913387\pi$
$139$	−8.42212	−	14.5875i	−0.714355	−	1.23730i	0.248852	−	0.968541i	$-0.419947\pi$
$140$	−5.04871			−0.426694
$141$		0			0
$142$	−3.73669	+	6.47213i	−0.313576	+	0.543129i
$143$	0.841451	−	1.45744i	0.0703657	−	0.121877i
$144$		0			0
$145$	−4.44324			−0.368991
$146$	5.34104	−	9.25095i	0.442027	−	0.765614i
$147$		0			0
$148$	26.8116	+	46.4390i	2.20390	+	3.81726i
$149$	0.866812	+	1.50136i	0.0710120	+	0.122996i	0.899345	−	0.437240i	$-0.144044\pi$
$149$	0.866812	+	1.50136i	0.0710120	+	0.122996i	−0.828333	+	0.560236i	$0.810710\pi$
$150$		0			0
$151$	−1.66432			−0.135441			−0.0677204	−	0.997704i	$-0.521573\pi$
$151$	−1.66432			−0.135441			−0.0677204	+	0.997704i	$0.521573\pi$
$152$	−14.4626	−	25.0499i	−1.17307	−	2.03181i
$153$		0			0
$154$	7.88594	−	13.6589i	0.635467	−	1.10066i
$155$	−1.83400	+	3.17659i	−0.147311	+	0.255149i
$156$		0			0
$157$	4.86834	−	8.43222i	0.388536	−	0.672964i	−0.603717	−	0.797199i	$-0.706314\pi$
$157$	4.86834	−	8.43222i	0.388536	−	0.672964i	0.992253	+	0.124235i	$0.0396475\pi$
$158$	−19.1352	+	33.1432i	−1.52232	+	2.63673i
$159$		0			0
$160$	2.93115	+	5.07690i	0.231728	+	0.401364i
$161$	4.32312			0.340710
$162$		0			0
$163$	−4.25176	+	7.36426i	−0.333023	+	0.576813i	−0.983103	−	0.183053i	$-0.941402\pi$
$163$	−4.25176	+	7.36426i	−0.333023	+	0.576813i	0.650080	+	0.759866i	$0.274735\pi$
$164$	−22.0390			−1.72096
$165$		0			0
$166$	13.4910	+	23.3671i	1.04710	+	1.81363i
$167$	2.08771	+	3.61602i	0.161552	+	0.279816i	0.935425	−	0.353524i	$-0.115017\pi$
$167$	2.08771	+	3.61602i	0.161552	+	0.279816i	−0.773874	+	0.633340i	$0.781683\pi$
$168$		0			0
$169$	6.44105	+	11.1562i	0.495465	+	0.858171i
$170$	11.0547			0.847860
$171$		0			0
$172$	26.3593	−	14.2403i	2.00988	−	1.08581i
$173$	−9.89899			−0.752606			−0.376303	−	0.926497i	$-0.622805\pi$
$173$	−9.89899			−0.752606			−0.376303	+	0.926497i	$0.622805\pi$
$174$		0			0
$175$	2.65277	+	4.59473i	0.200530	+	0.347329i
$176$	−37.9175			−2.85814
$177$		0			0
$178$	−20.6111	−	35.6994i	−1.54487	−	2.67579i
$179$	1.28149	−	2.21960i	0.0957829	−	0.165901i	−0.814152	−	0.580652i	$-0.802798\pi$
$179$	1.28149	−	2.21960i	0.0957829	−	0.165901i	0.909935	+	0.414751i	$0.136131\pi$
$180$		0			0
$181$	10.9471	−	18.9609i	0.813691	−	1.40935i	−0.0965736	−	0.995326i	$-0.530788\pi$
$181$	10.9471	−	18.9609i	0.813691	−	1.40935i	0.910264	−	0.414028i	$-0.135878\pi$
$182$	−0.552514	−	0.956983i	−0.0409551	−	0.0709363i
$183$		0			0
$184$	−11.3344	−	19.6317i	−0.835580	−	1.44727i
$185$	−5.16458	+	8.94531i	−0.379707	+	0.657672i
$186$		0			0
$187$	−12.0099	+	20.8017i	−0.878250	+	1.52117i
$188$	−53.5006			−3.90193
$189$		0			0
$190$	4.95479	−	8.58195i	0.359458	−	0.622600i
$191$	−8.78409	−	15.2145i	−0.635594	−	1.10088i	−0.986389	−	0.164429i	$-0.947422\pi$
$191$	−8.78409	−	15.2145i	−0.635594	−	1.10088i	0.350795	−	0.936452i	$-0.385911\pi$
$192$		0			0
$193$	−9.33568			−0.671997			−0.335998	−	0.941863i	$-0.609074\pi$
$193$	−9.33568			−0.671997			−0.335998	+	0.941863i	$0.609074\pi$
$194$	−16.6109			−1.19259
$195$		0			0
$196$	12.3895	+	21.4592i	0.884961	+	1.53280i
$197$	6.23098	−	10.7924i	0.443939	−	0.768925i	−0.554039	−	0.832491i	$-0.686914\pi$
$197$	6.23098	−	10.7924i	0.443939	−	0.768925i	0.997978	+	0.0635660i	$0.0202473\pi$
$198$		0			0
$199$	5.11021			0.362253			0.181126	−	0.983460i	$-0.442026\pi$
$199$	5.11021			0.362253			0.181126	+	0.983460i	$0.442026\pi$
$200$	13.9100	−	24.0929i	0.983588	−	1.70362i
$201$		0			0
$202$	−15.2040	+	26.3341i	−1.06975	+	1.85286i
$203$	−3.16960	−	5.48991i	−0.222462	−	0.385316i
$204$		0			0
$205$	−2.12263	−	3.67650i	−0.148251	−	0.256778i
$206$	16.7135	−	28.9486i	1.16448	−	2.01694i
$207$		0			0
$208$	−1.32831	+	2.30070i	−0.0921017	+	0.159525i
$209$	10.7658	+	18.6469i	0.744686	+	1.28983i
$210$		0			0
$211$	−10.2831			−0.707918			−0.353959	−	0.935261i	$-0.615165\pi$
$211$	−10.2831			−0.707918			−0.353959	+	0.935261i	$0.615165\pi$
$212$	1.83400	+	3.17659i	0.125960	+	0.218169i
$213$		0			0
$214$	29.3055			2.00329
$215$	4.91426	+	3.02569i	0.335150	+	0.206351i
$216$		0			0
$217$	−5.23317			−0.355251
$218$	23.1981	+	40.1804i	1.57118	+	2.72136i
$219$		0			0
$220$	−9.85327	−	17.0664i	−0.664308	−	1.15061i
$221$	0.841451	+	1.45744i	0.0566021	+	0.0980378i
$222$		0			0
$223$	−21.3434			−1.42926			−0.714629	−	0.699503i	$-0.753405\pi$
$223$	−21.3434			−1.42926			−0.714629	+	0.699503i	$0.753405\pi$
$224$	−4.18190	+	7.24326i	−0.279415	+	0.483961i
$225$		0			0
$226$	3.60669			0.239914
$227$	−7.61169	−	13.1838i	−0.505205	−	0.875041i	−0.999982	−	0.00602103i	$-0.998083\pi$
$227$	−7.61169	−	13.1838i	−0.505205	−	0.875041i	0.494777	−	0.869020i	$-0.335250\pi$
$228$		0			0
$229$	7.96986	−	13.8042i	0.526663	−	0.912208i	−0.472854	−	0.881141i	$-0.656776\pi$
$229$	7.96986	−	13.8042i	0.526663	−	0.912208i	0.999517	−	0.0310668i	$-0.00989045\pi$
$230$	3.88309	−	6.72570i	0.256043	−	0.443480i
$231$		0			0
$232$	−16.6201	+	28.7869i	−1.09116	+	1.88995i
$233$	−5.11608	+	8.86131i	−0.335166	+	0.580524i	−0.983517	−	0.180818i	$-0.942126\pi$
$233$	−5.11608	+	8.86131i	−0.335166	+	0.580524i	0.648351	+	0.761342i	$0.275459\pi$
$234$		0			0
$235$	−5.15277	−	8.92486i	−0.336130	−	0.582193i
$236$	17.3432			1.12895
$237$		0			0
$238$	7.88594	+	13.6589i	0.511170	+	0.885372i
$239$	−3.15411	−	5.46308i	−0.204023	−	0.353378i	0.745798	−	0.666172i	$-0.232068\pi$
$239$	−3.15411	−	5.46308i	−0.204023	−	0.353378i	−0.949821	+	0.312794i	$0.898735\pi$
$240$		0			0
$241$	−4.15277	+	7.19281i	−0.267503	+	0.463329i	−0.968216	−	0.250114i	$-0.919532\pi$
$241$	−4.15277	+	7.19281i	−0.267503	+	0.463329i	0.700713	+	0.713443i	$0.252865\pi$
$242$	33.3694			2.14507
$243$		0			0
$244$	19.5060	−	33.7855i	1.24875	−	2.16289i
$245$	−2.38652	+	4.13357i	−0.152469	+	0.264084i
$246$		0			0
$247$	1.50857			0.0959882
$248$	13.7203	+	23.7643i	0.871241	+	1.50903i
$249$		0			0
$250$	20.8091			1.31608
$251$	8.16420	−	14.1408i	0.515320	−	0.892560i	−0.484522	−	0.874779i	$-0.661007\pi$
$251$	8.16420	−	14.1408i	0.515320	−	0.892560i	0.999842	−	0.0177809i	$-0.00566015\pi$
$252$		0			0
$253$	8.43719	+	14.6136i	0.530442	+	0.918752i
$254$	−23.1948			−1.45537
$255$		0			0
$256$	−26.8392			−1.67745
$257$	12.2945			0.766910			0.383455	−	0.923559i	$-0.374734\pi$
$257$	12.2945			0.766910			0.383455	+	0.923559i	$0.374734\pi$
$258$		0			0
$259$	−14.7367			−0.915693
$260$	−1.38070			−0.0856276
$261$		0			0
$262$	46.5079			2.87327
$263$	10.9555	+	18.9755i	0.675546	+	1.17008i	0.976309	+	0.216382i	$0.0694255\pi$
$263$	10.9555	+	18.9755i	0.675546	+	1.17008i	−0.300763	+	0.953699i	$0.597241\pi$
$264$		0			0
$265$	−0.353274	+	0.611889i	−0.0217015	+	0.0375881i
$266$	14.1381			0.866862
$267$		0			0
$268$	3.13166	+	5.42419i	0.191296	+	0.331335i
$269$	14.1183			0.860811			0.430405	−	0.902636i	$-0.358371\pi$
$269$	14.1183			0.860811			0.430405	+	0.902636i	$0.358371\pi$
$270$		0			0
$271$	0.245714	−	0.425589i	0.0149261	−	0.0258527i	−0.858466	−	0.512871i	$-0.828582\pi$
$271$	0.245714	−	0.425589i	0.0149261	−	0.0258527i	0.873392	+	0.487018i	$0.161915\pi$
$272$	18.9587	−	32.8375i	1.14954	−	1.99107i
$273$		0			0
$274$	39.4131			2.38103
$275$	−10.3545	+	17.9345i	−0.624401	+	1.08149i
$276$		0			0
$277$	1.97504	+	3.42086i	0.118668	+	0.205540i	0.919240	−	0.393697i	$-0.128804\pi$
$277$	1.97504	+	3.42086i	0.118668	+	0.205540i	−0.800572	+	0.599237i	$0.795471\pi$
$278$	−21.5857	−	37.3875i	−1.29462	−	2.24236i
$279$		0			0
$280$	−7.27540			−0.434788
$281$	−6.78350	−	11.7494i	−0.404669	−	0.700908i	0.589613	−	0.807686i	$-0.299280\pi$
$281$	−6.78350	−	11.7494i	−0.404669	−	0.700908i	−0.994283	+	0.106777i	$0.965947\pi$
$282$		0			0
$283$	−4.95094	+	8.57528i	−0.294303	+	0.509747i	−0.974822	−	0.222982i	$-0.928421\pi$
$283$	−4.95094	+	8.57528i	−0.294303	+	0.509747i	0.680520	+	0.732730i	$0.261754\pi$
$284$	−6.66115	+	11.5374i	−0.395266	+	0.684621i
$285$		0			0
$286$	2.15662	−	3.73538i	0.127524	−	0.220877i
$287$	3.02837	−	5.24530i	0.178759	−	0.309620i
$288$		0			0
$289$	−3.50989	−	6.07932i	−0.206464	−	0.357607i
$290$	−11.3879			−0.668721
$291$		0			0
$292$	9.52111	−	16.4911i	0.557181	−	0.965066i
$293$	−29.4325			−1.71947			−0.859733	−	0.510744i	$-0.829370\pi$
$293$	−29.4325			−1.71947			−0.859733	+	0.510744i	$0.829370\pi$
$294$		0			0
$295$	1.67037	+	2.89316i	0.0972525	+	0.168446i
$296$	38.6366	+	66.9206i	2.24571	+	3.88968i
$297$		0			0
$298$	2.22162	+	3.84796i	0.128695	+	0.222906i
$299$	1.18227			0.0683726
$300$		0			0
$301$	−0.232836	+	8.23028i	−0.0134204	+	0.474386i
$302$	−4.26562			−0.245459
$303$		0			0
$304$	−16.9948	−	29.4359i	−0.974720	−	1.68826i
$305$	7.51470			0.430290
$306$		0			0
$307$	−7.79564	−	13.5024i	−0.444921	−	0.770625i	0.553126	−	0.833098i	$-0.313435\pi$
$307$	−7.79564	−	13.5024i	−0.444921	−	0.770625i	−0.998047	+	0.0624722i	$0.980102\pi$
$308$	14.0577	−	24.3487i	0.801015	−	1.38740i
$309$		0			0
$310$	−4.70051	+	8.14151i	−0.266971	+	0.462407i
$311$	7.68893	+	13.3176i	0.435999	+	0.755173i	0.997377	−	0.0723871i	$-0.0230617\pi$
$311$	7.68893	+	13.3176i	0.435999	+	0.755173i	−0.561377	+	0.827560i	$0.689728\pi$
$312$		0			0
$313$	−2.94622	−	5.10300i	−0.166530	−	0.288439i	0.770667	−	0.637238i	$-0.219923\pi$
$313$	−2.94622	−	5.10300i	−0.166530	−	0.288439i	−0.937198	+	0.348799i	$0.886590\pi$
$314$	12.4775	−	21.6116i	0.704143	−	1.21961i
$315$		0			0
$316$	−34.1111	+	59.0821i	−1.91890	+	3.32363i
$317$	15.2809			0.858259			0.429130	−	0.903243i	$-0.358820\pi$
$317$	15.2809			0.858259			0.429130	+	0.903243i	$0.358820\pi$
$318$		0			0
$319$	12.3719	−	21.4287i	0.692691	−	1.19978i
$320$	0.703614	+	1.21870i	0.0393332	+	0.0681271i
$321$		0			0
$322$	11.0801			0.617468
$323$	−21.5316			−1.19805
$324$		0			0
$325$	0.725470	+	1.25655i	0.0402418	+	0.0697009i
$326$	−10.8972	+	18.8744i	−0.603538	+	1.04536i
$327$		0			0
$328$	−31.7591			−1.75360
$329$	7.35150	−	12.7332i	0.405301	−	0.702002i
$330$		0			0
$331$	7.70919	−	13.3527i	0.423736	−	0.733932i	−0.572566	−	0.819859i	$-0.694052\pi$
$331$	7.70919	−	13.3527i	0.423736	−	0.733932i	0.996301	+	0.0859271i	$0.0273852\pi$
$332$	24.0495	+	41.6549i	1.31989	+	2.28611i
$333$		0			0
$334$	5.35075	+	9.26776i	0.292780	+	0.507109i
$335$	−0.603235	+	1.04483i	−0.0329582	+	0.0570853i
$336$		0			0
$337$	7.45226	−	12.9077i	0.405951	−	0.703127i	−0.588481	−	0.808511i	$-0.700274\pi$
$337$	7.45226	−	12.9077i	0.405951	−	0.703127i	0.994432	+	0.105384i	$0.0336072\pi$
$338$	16.5082	+	28.5931i	0.897930	+	1.55526i
$339$		0			0
$340$	19.7065			1.06874
$341$	−10.2133	−	17.6899i	−0.553080	−	0.957963i
$342$		0			0
$343$	−15.5990			−0.842266
$344$	37.9849	−	20.5208i	2.04801	−	1.10641i
$345$		0			0
$346$	−25.3709			−1.36395
$347$	−4.68931	−	8.12212i	−0.251735	−	0.436018i	0.712268	−	0.701907i	$-0.247668\pi$
$347$	−4.68931	−	8.12212i	−0.251735	−	0.436018i	−0.964004	+	0.265889i	$0.914335\pi$
$348$		0			0
$349$	11.5900	+	20.0744i	0.620396	+	1.07456i	0.989412	+	0.145135i	$0.0463616\pi$
$349$	11.5900	+	20.0744i	0.620396	+	1.07456i	−0.369015	+	0.929423i	$0.620305\pi$
$350$	6.79898	+	11.7762i	0.363421	+	0.629464i
$351$		0			0
$352$	−32.6463			−1.74005
$353$	−16.3825	+	28.3753i	−0.871953	+	1.51027i	−0.0119795	+	0.999928i	$0.503813\pi$
$353$	−16.3825	+	28.3753i	−0.871953	+	1.51027i	−0.859974	+	0.510339i	$0.829520\pi$
$354$		0			0
$355$	−2.56620			−0.136200
$356$	−36.7420	−	63.6390i	−1.94732	−	3.37286i
$357$		0			0
$358$	3.28442	−	5.68879i	0.173587	−	0.300662i
$359$	−7.55109	+	13.0789i	−0.398531	+	0.690277i	−0.993545	−	0.113439i	$-0.963813\pi$
$359$	−7.55109	+	13.0789i	−0.398531	+	0.690277i	0.595014	+	0.803716i	$0.297147\pi$
$360$		0			0
$361$	−0.150577	+	0.260808i	−0.00792513	+	0.0137267i
$362$	28.0571	−	48.5964i	1.47465	−	2.55417i
$363$		0			0
$364$	−0.984931	−	1.70595i	−0.0516244	−	0.0894161i
$365$	3.66801			0.191992
$366$		0			0
$367$	−11.7479	−	20.3480i	−0.613236	−	1.06216i	−0.990691	−	0.136128i	$-0.956534\pi$
$367$	−11.7479	−	20.3480i	−0.613236	−	1.06216i	0.377456	−	0.926028i	$-0.376799\pi$
$368$	−13.3189	−	23.0690i	−0.694296	−	1.20256i
$369$		0			0
$370$	−13.2367	+	22.9266i	−0.688143	+	1.19190i
$371$	−1.00804			−0.0523348
$372$		0			0
$373$	−10.8442	+	18.7828i	−0.561494	+	0.972536i	0.435873	+	0.900008i	$0.356440\pi$
$373$	−10.8442	+	18.7828i	−0.561494	+	0.972536i	−0.997366	+	0.0725275i	$0.976893\pi$
$374$	−30.7811	+	53.3144i	−1.59165	+	2.75682i
$375$		0			0
$376$	−77.0965			−3.97595
$377$	−0.866812	−	1.50136i	−0.0446431	−	0.0773241i
$378$		0			0
$379$	−27.1524			−1.39473			−0.697363	−	0.716718i	$-0.745644\pi$
$379$	−27.1524			−1.39473			−0.697363	+	0.716718i	$0.745644\pi$
$380$	8.83258	−	15.2985i	0.453102	−	0.784795i
$381$		0			0
$382$	−22.5134	−	38.9944i	−1.15189	−	1.99513i
$383$	−1.70265			−0.0870012			−0.0435006	−	0.999053i	$-0.513851\pi$
$383$	−1.70265			−0.0870012			−0.0435006	+	0.999053i	$0.513851\pi$
$384$		0			0
$385$	5.41574			0.276012
$386$	−23.9271			−1.21786
$387$		0			0
$388$	−29.6111			−1.50327
$389$	−27.8708			−1.41311			−0.706553	−	0.707660i	$-0.749751\pi$
$389$	−27.8708			−1.41311			−0.706553	+	0.707660i	$0.749751\pi$
$390$		0			0
$391$	−16.8744			−0.853374
$392$	17.8537	+	30.9236i	0.901749	+	1.56188i
$393$		0			0
$394$	15.9699	−	27.6606i	0.804550	−	1.39352i
$395$	−13.1413			−0.661210
$396$		0			0
$397$	6.08392	+	10.5377i	0.305343	+	0.528870i	0.977338	−	0.211686i	$-0.0678955\pi$
$397$	6.08392	+	10.5377i	0.305343	+	0.528870i	−0.671995	+	0.740556i	$0.734562\pi$
$398$	13.0973			0.656510
$399$		0			0
$400$	16.3456	−	28.3114i	0.817279	−	1.41557i
$401$	12.6925	−	21.9841i	0.633835	−	1.09783i	−0.352926	−	0.935651i	$-0.614813\pi$
$401$	12.6925	−	21.9841i	0.633835	−	1.09783i	0.986761	−	0.162183i	$-0.0518535\pi$
$402$		0			0
$403$	−1.43115			−0.0712907
$404$	−27.1032	+	46.9441i	−1.34843	+	2.33556i
$405$		0			0
$406$	−8.12361	−	14.0705i	−0.403168	−	0.698308i
$407$	−28.7607	−	49.8151i	−1.42562	−	2.46924i
$408$		0			0
$409$	−24.0972			−1.19153			−0.595765	−	0.803159i	$-0.703151\pi$
$409$	−24.0972			−1.19153			−0.595765	+	0.803159i	$0.703151\pi$
$410$	−5.44025	−	9.42279i	−0.268675	−	0.465358i
$411$		0			0
$412$	29.7940	−	51.6047i	1.46784	−	2.54238i
$413$	−2.38313	+	4.12770i	−0.117266	+	0.203111i
$414$		0			0
$415$	−4.63252	+	8.02377i	−0.227402	+	0.393871i
$416$	−1.14365	+	1.98086i	−0.0560721	+	0.0971197i
$417$		0			0
$418$	27.5925	+	47.7916i	1.34959	+	2.33756i
$419$	−16.7851			−0.820005			−0.410003	−	0.912084i	$-0.634472\pi$
$419$	−16.7851			−0.820005			−0.410003	+	0.912084i	$0.634472\pi$
$420$		0			0
$421$	7.74658	−	13.4175i	0.377545	−	0.653928i	−0.613159	−	0.789959i	$-0.710102\pi$
$421$	7.74658	−	13.4175i	0.377545	−	0.653928i	0.990704	+	0.136032i	$0.0434349\pi$
$422$	−26.3554			−1.28296
$423$		0			0
$424$	2.64287	+	4.57759i	0.128349	+	0.222307i
$425$	−10.3545	−	17.9345i	−0.502268	−	0.869953i
$426$		0			0
$427$	5.36064	+	9.28490i	0.259420	+	0.449328i
$428$	52.2410			2.52517
$429$		0			0
$430$	12.5951	+	7.75478i	0.607391	+	0.373969i
$431$	6.63462			0.319579			0.159789	−	0.987151i	$-0.448919\pi$
$431$	6.63462			0.319579			0.159789	+	0.987151i	$0.448919\pi$
$432$		0			0
$433$	−5.99747	−	10.3879i	−0.288220	−	0.499212i	0.685165	−	0.728388i	$-0.259730\pi$
$433$	−5.99747	−	10.3879i	−0.288220	−	0.499212i	−0.973385	+	0.229176i	$0.926397\pi$
$434$	−13.4125			−0.643821
$435$		0			0
$436$	41.3538	+	71.6269i	1.98049	+	3.43031i
$437$	−7.56319	+	13.0998i	−0.361796	+	0.626650i
$438$		0			0
$439$	−8.87439	+	15.3709i	−0.423551	+	0.733612i	−0.996284	−	0.0861298i	$-0.972550\pi$
$439$	−8.87439	+	15.3709i	−0.423551	+	0.733612i	0.572733	+	0.819742i	$0.305883\pi$
$440$	−14.1990	−	24.5933i	−0.676910	−	1.17244i
$441$		0			0
$442$	2.15662	+	3.73538i	0.102580	+	0.177674i
$443$	−15.9944	+	27.7030i	−0.759915	+	1.31621i	0.182979	+	0.983117i	$0.441426\pi$
$443$	−15.9944	+	27.7030i	−0.759915	+	1.31621i	−0.942894	+	0.333094i	$0.891907\pi$
$444$		0			0
$445$	7.07742	−	12.2585i	0.335502	−	0.581106i
$446$	−54.7026			−2.59024
$447$		0			0
$448$	−1.00385	+	1.73872i	−0.0474275	+	0.0821469i
$449$	−11.5334	−	19.9764i	−0.544295	−	0.942746i	−0.998651	−	0.0519258i	$-0.983464\pi$
$449$	−11.5334	−	19.9764i	−0.544295	−	0.942746i	0.454356	−	0.890820i	$-0.349869\pi$
$450$		0			0
$451$	23.6412			1.11322
$452$	6.42941			0.302414
$453$		0			0
$454$	−19.5086	−	33.7898i	−0.915583	−	1.58584i
$455$	0.189722	−	0.328608i	0.00889431	−	0.0154054i
$456$		0			0
$457$	17.8865			0.836694			0.418347	−	0.908287i	$-0.362610\pi$
$457$	17.8865			0.836694			0.418347	+	0.908287i	$0.362610\pi$
$458$	20.4266	−	35.3799i	0.954471	−	1.65319i
$459$		0			0
$460$	6.92212	−	11.9895i	0.322746	−	0.559012i
$461$	4.10804	+	7.11534i	0.191331	+	0.331394i	0.945691	−	0.325066i	$-0.105386\pi$
$461$	4.10804	+	7.11534i	0.191331	+	0.331394i	−0.754361	+	0.656460i	$0.772053\pi$
$462$		0			0
$463$	−2.55378	−	4.42328i	−0.118684	−	0.205567i	0.800562	−	0.599250i	$-0.204534\pi$
$463$	−2.55378	−	4.42328i	−0.118684	−	0.205567i	−0.919246	+	0.393682i	$0.871201\pi$
$464$	−19.5301	+	33.8272i	−0.906664	+	1.57039i
$465$		0			0
$466$	−13.1124	+	22.7113i	−0.607420	+	1.05208i
$467$	8.45653	+	14.6471i	0.391321	+	0.677789i	0.992624	−	0.121233i	$-0.0386848\pi$
$467$	8.45653	+	14.6471i	0.391321	+	0.677789i	−0.601303	+	0.799021i	$0.705351\pi$
$468$		0			0
$469$	−1.72128			−0.0794813
$470$	−13.2064	−	22.8742i	−0.609167	−	1.05511i
$471$		0			0
$472$	24.9923			1.15036
$473$	−28.2756	+	15.2755i	−1.30011	+	0.702369i
$474$		0			0
$475$	−18.5638			−0.851765
$476$	14.0577	+	24.3487i	0.644336	+	1.11602i
$477$		0			0
$478$	−8.08392	−	14.0018i	−0.369750	−	0.640426i
$479$	16.8225	+	29.1375i	0.768642	+	1.33133i	0.938300	+	0.345824i	$0.112400\pi$
$479$	16.8225	+	29.1375i	0.768642	+	1.33133i	−0.169658	+	0.985503i	$0.554266\pi$
$480$		0			0
$481$	−4.03014			−0.183759
$482$	−10.6434	+	18.4350i	−0.484796	+	0.839691i
$483$		0			0
$484$	59.4855			2.70388
$485$	−2.85191	−	4.93966i	−0.129499	−	0.224298i
$486$		0			0
$487$	−11.7178	+	20.2958i	−0.530983	+	0.919689i	0.468364	+	0.883536i	$0.344844\pi$
$487$	−11.7178	+	20.2958i	−0.530983	+	0.919689i	−0.999346	+	0.0361531i	$0.988490\pi$
$488$	28.1090	−	48.6862i	1.27244	−	2.20392i
$489$		0			0
$490$	−6.11659	+	10.5942i	−0.276319	+	0.478599i
$491$	19.6525	−	34.0391i	0.886904	−	1.53616i	0.0433893	−	0.999058i	$-0.486184\pi$
$491$	19.6525	−	34.0391i	0.886904	−	1.53616i	0.843515	−	0.537105i	$-0.180482\pi$
$492$		0			0
$493$	12.3719	+	21.4287i	0.557200	+	0.965099i
$494$	3.86644			0.173959
$495$		0			0
$496$	16.1226	+	27.9252i	0.723927	+	1.25388i
$497$	−1.83061	−	3.17071i	−0.0821142	−	0.142226i
$498$		0			0
$499$	6.13770	−	10.6308i	0.274761	−	0.475900i	−0.695314	−	0.718706i	$-0.744735\pi$
$499$	6.13770	−	10.6308i	0.274761	−	0.475900i	0.970075	+	0.242806i	$0.0780679\pi$
$500$	37.0949			1.65894
$501$		0			0
$502$	20.9247	−	36.2426i	0.933913	−	1.61758i
$503$	8.11909	−	14.0627i	0.362013	−	0.627024i	−0.626279	−	0.779599i	$-0.715423\pi$
$503$	8.11909	−	14.0627i	0.362013	−	0.627024i	0.988292	+	0.152575i	$0.0487564\pi$
$504$		0			0
$505$	−10.4415			−0.464641
$506$	21.6243	+	37.4544i	0.961319	+	1.66505i
$507$		0			0
$508$	−41.3478			−1.83451
$509$	3.31509	−	5.74190i	0.146939	−	0.254505i	−0.783156	−	0.621825i	$-0.786391\pi$
$509$	3.31509	−	5.74190i	0.146939	−	0.254505i	0.930095	+	0.367320i	$0.119725\pi$
$510$		0			0
$511$	2.61659	+	4.53206i	0.115751	+	0.200487i
$512$	−50.3400			−2.22473
$513$		0			0
$514$	31.5105			1.38987
$515$	11.4781			0.505786
$516$		0			0
$517$	57.3900			2.52401
$518$	−37.7698			−1.65951
$519$		0			0
$520$	−1.98965			−0.0872520
$521$	21.4865	+	37.2157i	0.941340	+	1.63045i	0.762918	+	0.646495i	$0.223766\pi$
$521$	21.4865	+	37.2157i	0.941340	+	1.63045i	0.178422	+	0.983954i	$0.442901\pi$
$522$		0			0
$523$	1.28190	−	2.22031i	0.0560534	−	0.0970873i	−0.836637	−	0.547758i	$-0.815482\pi$
$523$	1.28190	−	2.22031i	0.0560534	−	0.0970873i	0.892691	+	0.450670i	$0.148815\pi$
$524$	82.9066			3.62179
$525$		0			0
$526$	28.0787	+	48.6338i	1.22429	+	2.12053i
$527$	20.4266			0.889795
$528$		0			0
$529$	5.57270	−	9.65220i	0.242291	−	0.419661i
$530$	−0.905434	+	1.56826i	−0.0393295	+	0.0681208i
$531$		0			0
$532$	25.2030			1.09269
$533$	0.828189	−	1.43447i	0.0358729	−	0.0621336i
$534$		0			0
$535$	5.03146	+	8.71475i	0.217529	+	0.376771i
$536$	4.51285	+	7.81648i	0.194925	+	0.337620i
$537$		0			0
$538$	36.1850			1.56005
$539$	−13.2902	−	23.0192i	−0.572447	−	0.991508i
$540$		0			0
$541$	1.90838	−	3.30541i	0.0820475	−	0.142111i	−0.822082	−	0.569369i	$-0.807187\pi$
$541$	1.90838	−	3.30541i	0.0820475	−	0.142111i	0.904129	+	0.427259i	$0.140521\pi$
$542$	0.629759	−	1.09077i	0.0270505	−	0.0468528i
$543$		0			0
$544$	16.3231	−	28.2725i	0.699849	−	1.21217i
$545$	−7.96577	+	13.7971i	−0.341216	+	0.591004i
$546$		0			0
$547$	−13.0422	−	22.5898i	−0.557645	−	0.965870i	−0.997692	−	0.0678953i	$-0.978372\pi$
$547$	−13.0422	−	22.5898i	−0.557645	−	0.965870i	0.440047	−	0.897975i	$-0.354962\pi$
$548$	70.2591			3.00132
$549$		0			0
$550$	−26.5384	+	45.9658i	−1.13160	+	1.95999i
$551$	22.1805			0.944922
$552$		0			0
$553$	−9.37439	−	16.2369i	−0.398639	−	0.690464i
$554$	5.06197	+	8.76759i	0.215063	+	0.372499i
$555$		0			0
$556$	−38.4794	−	66.6483i	−1.63189	−	2.82652i
$557$	15.3779			0.651581			0.325790	−	0.945442i	$-0.394370\pi$
$557$	15.3779			0.651581			0.325790	+	0.945442i	$0.394370\pi$
$558$		0			0
$559$	−0.0636751	+	2.25079i	−0.00269317	+	0.0951983i
$560$	−8.54926			−0.361272
$561$		0			0
$562$	−17.3859	−	30.1133i	−0.733382	−	1.27025i
$563$	13.0065			0.548160			0.274080	−	0.961707i	$-0.411627\pi$
$563$	13.0065			0.548160			0.274080	+	0.961707i	$0.411627\pi$
$564$		0			0
$565$	0.619232	+	1.07254i	0.0260513	+	0.0451222i
$566$	−12.6891	+	21.9782i	−0.533365	+	0.923814i
$567$		0			0
$568$	−9.59899	+	16.6259i	−0.402765	+	0.697609i
$569$	−9.86259	−	17.0825i	−0.413461	−	0.716136i	0.581804	−	0.813329i	$-0.302347\pi$
$569$	−9.86259	−	17.0825i	−0.413461	−	0.716136i	−0.995266	+	0.0971929i	$0.969014\pi$
$570$		0			0
$571$	4.71172	+	8.16094i	0.197179	+	0.341525i	0.947613	−	0.319421i	$-0.103488\pi$
$571$	4.71172	+	8.16094i	0.197179	+	0.341525i	−0.750433	+	0.660946i	$0.770155\pi$
$572$	3.84447	−	6.65881i	0.160745	−	0.278419i
$573$		0			0
$574$	7.76165	−	13.4436i	0.323965	−	0.561124i
$575$	−14.5485			−0.606715
$576$		0			0
$577$	−21.5560	+	37.3360i	−0.897387	+	1.55432i	−0.0665643	+	0.997782i	$0.521204\pi$
$577$	−21.5560	+	37.3360i	−0.897387	+	1.55432i	−0.830823	+	0.556537i	$0.812130\pi$
$578$	−8.99578	−	15.5811i	−0.374175	−	0.648090i
$579$		0			0
$580$	−20.3005			−0.842931
$581$	−13.2185			−0.548397
$582$		0			0
$583$	−1.96733	−	3.40752i	−0.0814786	−	0.141125i
$584$	13.7203	−	23.7643i	0.567751	−	0.983373i
$585$		0			0
$586$	−75.4349			−3.11619
$587$	−13.9487	+	24.1598i	−0.575723	+	0.997181i	0.420240	+	0.907413i	$0.361946\pi$
$587$	−13.9487	+	24.1598i	−0.575723	+	0.997181i	−0.995963	+	0.0897682i	$0.971387\pi$
$588$		0			0
$589$	9.15530	−	15.8574i	0.377237	−	0.653394i
$590$	4.28111	+	7.41510i	0.176251	+	0.305275i
$591$		0			0
$592$	45.4015	+	78.6378i	1.86599	+	3.23199i
$593$	12.3362	−	21.3670i	0.506588	−	0.877436i	−0.493383	−	0.869812i	$-0.664240\pi$
$593$	12.3362	−	21.3670i	0.506588	−	0.877436i	0.999971	−	0.00762396i	$-0.00242681\pi$
$594$		0			0
$595$	−2.70787	+	4.69017i	−0.111012	+	0.192278i
$596$	3.96033	+	6.85950i	0.162222	+	0.280976i
$597$		0			0
$598$	3.03014			0.123912
$599$	0.0518845	+	0.0898667i	0.00211995	+	0.00367185i	0.867083	−	0.498163i	$-0.165992\pi$
$599$	0.0518845	+	0.0898667i	0.00211995	+	0.00367185i	−0.864963	+	0.501835i	$0.832659\pi$
$600$		0			0
$601$	−30.4553			−1.24230			−0.621149	−	0.783692i	$-0.713334\pi$
$601$	−30.4553			−1.24230			−0.621149	+	0.783692i	$0.713334\pi$
$602$	−0.596752	+	21.0940i	−0.0243218	+	0.859728i
$603$		0			0
$604$	−7.60405			−0.309404
$605$	5.72919	+	9.92324i	0.232925	+	0.403437i
$606$		0			0
$607$	−22.0749	−	38.2348i	−0.895992	−	1.55190i	−0.832572	−	0.553917i	$-0.813132\pi$
$607$	−22.0749	−	38.2348i	−0.895992	−	1.55190i	−0.0634205	−	0.997987i	$-0.520201\pi$
$608$	−14.6322	−	25.3438i	−0.593415	−	1.02783i
$609$		0			0
$610$	19.2600			0.779814
$611$	2.01046	−	3.48222i	0.0813346	−	0.140876i
$612$		0			0
$613$	4.60140			0.185849			0.0929244	−	0.995673i	$-0.470379\pi$
$613$	4.60140			0.185849			0.0929244	+	0.995673i	$0.470379\pi$
$614$	−19.9800	−	34.6065i	−0.806329	−	1.39660i
$615$		0			0
$616$	20.2578	−	35.0875i	0.816210	−	1.41372i
$617$	−4.71128	+	8.16017i	−0.189669	+	0.328516i	−0.945140	−	0.326666i	$-0.894075\pi$
$617$	−4.71128	+	8.16017i	−0.189669	+	0.328516i	0.755471	+	0.655182i	$0.227408\pi$
$618$		0			0
$619$	−11.5301	+	19.9708i	−0.463435	+	0.802694i	−0.999129	−	0.0417185i	$-0.986717\pi$
$619$	−11.5301	+	19.9708i	−0.463435	+	0.802694i	0.535694	+	0.844412i	$0.320050\pi$
$620$	−8.37928	+	14.5133i	−0.336520	+	0.582870i
$621$		0			0
$622$	19.7065	+	34.1327i	0.790161	+	1.36860i
$623$	20.1948			0.809089
$624$		0			0
$625$	−6.99097	−	12.1087i	−0.279639	−	0.484349i
$626$	−7.55109	−	13.0789i	−0.301802	−	0.522737i
$627$		0			0
$628$	22.2427	−	38.5255i	0.887582	−	1.53734i
$629$	57.5215			2.29353
$630$		0			0
$631$	5.97371	−	10.3468i	0.237810	−	0.411899i	−0.722276	−	0.691605i	$-0.756904\pi$
$631$	5.97371	−	10.3468i	0.237810	−	0.411899i	0.960086	+	0.279707i	$0.0902372\pi$
$632$	−49.1555	+	85.1398i	−1.95530	+	3.38668i
$633$		0			0
$634$	39.1645			1.55542
$635$	−3.98230	−	6.89755i	−0.158033	−	0.273721i
$636$		0			0
$637$	−1.86230			−0.0737870
$638$	31.7088	−	54.9212i	1.25536	−	2.17435i
$639$		0			0
$640$	−4.05895	−	7.03032i	−0.160444	−	0.277898i
$641$	4.23910			0.167434			0.0837172	−	0.996490i	$-0.473321\pi$
$641$	4.23910			0.167434			0.0837172	+	0.996490i	$0.473321\pi$
$642$		0			0
$643$	40.4432			1.59493			0.797463	−	0.603368i	$-0.206175\pi$
$643$	40.4432			1.59493			0.797463	+	0.603368i	$0.206175\pi$
$644$	19.7517			0.778326
$645$		0			0
$646$	−55.1850			−2.17122
$647$	31.1019			1.22274			0.611370	−	0.791345i	$-0.290619\pi$
$647$	31.1019			1.22274			0.611370	+	0.791345i	$0.290619\pi$
$648$		0			0
$649$	−18.6040			−0.730273
$650$	1.85936	+	3.22051i	0.0729302	+	0.126319i
$651$		0			0
$652$	−19.4256	+	33.6462i	−0.760767	+	1.31769i
$653$	12.0188			0.470333			0.235167	−	0.971955i	$-0.424436\pi$
$653$	12.0188			0.470333			0.235167	+	0.971955i	$0.424436\pi$
$654$		0			0
$655$	7.98493	+	13.8303i	0.311997	+	0.540395i
$656$	−37.3199			−1.45710
$657$		0			0
$658$	18.8417	−	32.6348i	0.734527	−	1.27224i
$659$	−20.3936	+	35.3227i	−0.794420	+	1.37598i	0.128786	+	0.991672i	$0.458892\pi$
$659$	−20.3936	+	35.3227i	−0.794420	+	1.37598i	−0.923207	+	0.384304i	$0.874441\pi$
$660$		0			0
$661$	9.58690			0.372887			0.186444	−	0.982466i	$-0.440304\pi$
$661$	9.58690			0.372887			0.186444	+	0.982466i	$0.440304\pi$
$662$	19.7585	−	34.2227i	0.767935	−	1.33010i
$663$		0			0
$664$	34.6563	+	60.0264i	1.34492	+	2.32948i
$665$	2.42737	+	4.20432i	0.0941292	+	0.163037i
$666$		0			0
$667$	17.3830			0.673071
$668$	9.53842	+	16.5210i	0.369053	+	0.639218i
$669$		0			0
$670$	−1.54608	+	2.67788i	−0.0597301	+	0.103456i
$671$	−20.9241	+	36.2416i	−0.807766	+	1.39909i
$672$		0			0
$673$	0.0301387	−	0.0522018i	0.00116176	−	0.00201223i	−0.865444	−	0.501006i	$-0.832964\pi$
$673$	0.0301387	−	0.0522018i	0.00116176	−	0.00201223i	0.866606	+	0.498994i	$0.166297\pi$
$674$	19.1000	−	33.0821i	0.735704	−	1.27428i
$675$		0			0
$676$	29.4282	+	50.9711i	1.13185	+	1.96043i
$677$	−32.8953			−1.26427			−0.632135	−	0.774858i	$-0.717821\pi$
$677$	−32.8953			−1.26427			−0.632135	+	0.774858i	$0.717821\pi$
$678$		0			0
$679$	4.06885	−	7.04745i	0.156148	−	0.270456i
$680$	28.3980			1.08901
$681$		0			0
$682$	−26.1764	−	45.3389i	−1.00235	−	1.73612i
$683$	2.07106	+	3.58717i	0.0792467	+	0.137259i	0.902925	−	0.429798i	$-0.141415\pi$
$683$	2.07106	+	3.58717i	0.0792467	+	0.137259i	−0.823678	+	0.567057i	$0.808082\pi$
$684$		0			0
$685$	6.76683	+	11.7205i	0.258547	+	0.447817i
$686$	−39.9798			−1.52644
$687$		0			0
$688$	44.6357	−	24.1138i	1.70172	−	0.919331i
$689$	−0.275675			−0.0105024
$690$		0			0
$691$	17.2427	+	29.8653i	0.655944	+	1.13613i	0.981656	+	0.190660i	$0.0610628\pi$
$691$	17.2427	+	29.8653i	0.655944	+	1.13613i	−0.325712	+	0.945469i	$0.605604\pi$
$692$	−45.2270			−1.71927
$693$		0			0
$694$	−12.0186	−	20.8168i	−0.456219	−	0.790195i
$695$	7.41209	−	12.8381i	0.281157	−	0.486978i
$696$		0			0
$697$	−11.8206	+	20.4739i	−0.447737	+	0.775504i
$698$	29.7048	+	51.4502i	1.12434	+	1.94742i
$699$		0			0
$700$	12.1201	+	20.9926i	0.458097	+	0.793447i
$701$	10.4439	−	18.0893i	0.394459	−	0.683223i	−0.598573	−	0.801068i	$-0.704265\pi$
$701$	10.4439	−	18.0893i	0.394459	−	0.683223i	0.993032	+	0.117845i	$0.0375987\pi$
$702$		0			0
$703$	25.7814	−	44.6548i	0.972365	−	1.68419i
$704$	−7.83664			−0.295354
$705$		0			0
$706$	−41.9880	+	72.7253i	−1.58024	+	2.73705i
$707$	−7.44849	−	12.9012i	−0.280129	−	0.485198i
$708$		0			0
$709$	−0.229852			−0.00863228			−0.00431614	−	0.999991i	$-0.501374\pi$
$709$	−0.229852			−0.00863228			−0.00431614	+	0.999991i	$0.501374\pi$
$710$	−6.57712			−0.246835
$711$		0			0
$712$	−52.9468	−	91.7065i	−1.98426	−	3.43684i
$713$	7.17504	−	12.4275i	0.268707	−	0.465415i
$714$		0			0
$715$	1.48108			0.0553892
$716$	5.85493	−	10.1410i	0.218809	−	0.378988i
$717$		0			0
$718$	−19.3533	+	33.5209i	−0.722258	+	1.25099i
$719$	3.25333	+	5.63493i	0.121329	+	0.210147i	0.920292	−	0.391232i	$-0.127951\pi$
$719$	3.25333	+	5.63493i	0.121329	+	0.210147i	−0.798963	+	0.601380i	$0.794618\pi$
$720$		0			0
$721$	8.18797	+	14.1820i	0.304936	+	0.528164i
$722$	−0.385926	+	0.668444i	−0.0143627	+	0.0248769i
$723$		0			0
$724$	50.0156	−	86.6296i	1.85882	−	3.21956i
$725$	10.6666	+	18.4751i	0.396147	+	0.686147i
$726$		0			0
$727$	24.8192			0.920492			0.460246	−	0.887791i	$-0.347761\pi$
$727$	24.8192			0.920492			0.460246	+	0.887791i	$0.347761\pi$
$728$	−1.41933	−	2.45834i	−0.0526037	−	0.0911123i
$729$		0			0
$730$	9.40101			0.347947
$731$	0.908824	−	32.1251i	0.0336141	−	1.18819i
$732$		0			0
$733$	45.4252			1.67782			0.838909	−	0.544272i	$-0.183194\pi$
$733$	45.4252			1.67782			0.838909	+	0.544272i	$0.183194\pi$
$734$	−30.1096	−	52.1514i	−1.11137	−	1.92494i
$735$		0			0
$736$	−11.4673	−	19.8620i	−0.422691	−	0.732123i
$737$	−3.35932	−	5.81852i	−0.123742	−	0.214328i
$738$		0			0
$739$	43.4373			1.59787			0.798933	−	0.601420i	$-0.205398\pi$
$739$	43.4373			1.59787			0.798933	+	0.601420i	$0.205398\pi$
$740$	−23.5962	+	40.8698i	−0.867412	+	1.50240i
$741$		0			0
$742$	−2.58358			−0.0948462
$743$	0.339658	+	0.588304i	0.0124608	+	0.0215828i	0.872189	−	0.489170i	$-0.162700\pi$
$743$	0.339658	+	0.588304i	0.0124608	+	0.0215828i	−0.859728	+	0.510753i	$0.829367\pi$
$744$		0			0
$745$	−0.762858	+	1.32131i	−0.0279490	+	0.0484090i
$746$	−27.7936	+	48.1398i	−1.01759	+	1.76253i
$747$		0			0
$748$	−54.8714	+	95.0401i	−2.00630	+	3.47501i
$749$	−7.17843	+	12.4334i	−0.262294	+	0.454307i
$750$		0			0
$751$	−3.17037	−	5.49124i	−0.115688	−	0.200378i	0.802366	−	0.596832i	$-0.203574\pi$
$751$	−3.17037	−	5.49124i	−0.115688	−	0.200378i	−0.918055	+	0.396454i	$0.870241\pi$
$752$	−90.5955			−3.30368
$753$		0			0
$754$	−2.22162	−	3.84796i	−0.0809066	−	0.140134i
$755$	−0.732364	−	1.26849i	−0.0266535	−	0.0461651i
$756$		0			0
$757$	6.60756	−	11.4446i	0.240156	−	0.415962i	−0.720603	−	0.693348i	$-0.756135\pi$
$757$	6.60756	−	11.4446i	0.240156	−	0.415962i	0.960759	+	0.277386i	$0.0894681\pi$
$758$	−69.5910			−2.52766
$759$		0			0
$760$	12.7281	−	22.0457i	0.461697	−	0.799683i
$761$	16.7752	−	29.0555i	0.608101	−	1.05326i	−0.383452	−	0.923561i	$-0.625265\pi$
$761$	16.7752	−	29.0555i	0.608101	−	1.05326i	0.991553	−	0.129701i	$-0.0414018\pi$
$762$		0			0
$763$	−22.7297			−0.822869
$764$	−40.1332	−	69.5127i	−1.45197	−	2.51488i
$765$		0			0
$766$	−4.36385			−0.157672
$767$	−0.651729	+	1.12883i	−0.0235326	+	0.0407596i
$768$		0			0
$769$	0.222941	+	0.386145i	0.00803945	+	0.0139247i	0.870017	−	0.493021i	$-0.164108\pi$
$769$	0.222941	+	0.386145i	0.00803945	+	0.0139247i	−0.861978	+	0.506946i	$0.830774\pi$
$770$	13.8804			0.500216
$771$		0			0
$772$	−42.6533			−1.53513
$773$	−26.0266			−0.936113			−0.468056	−	0.883699i	$-0.655046\pi$
$773$	−26.0266			−0.936113			−0.468056	+	0.883699i	$0.655046\pi$
$774$		0			0
$775$	17.6111			0.632608
$776$	−42.6708			−1.53179
$777$		0			0
$778$	−71.4322			−2.56097
$779$	10.5961	+	18.3530i	0.379645	+	0.657565i
$780$		0			0
$781$	7.14540	−	12.3762i	0.255683	−	0.442855i
$782$	−43.2487			−1.54657
$783$		0			0
$784$	20.9798	+	36.3380i	0.749277	+	1.29779i
$785$	8.56900			0.305841
$786$		0			0
$787$	−12.8077	+	22.1836i	−0.456546	+	0.790761i	−0.998776	−	0.0494692i	$-0.984247\pi$
$787$	−12.8077	+	22.1836i	−0.456546	+	0.790761i	0.542229	+	0.840230i	$0.317580\pi$
$788$	28.4684	−	49.3087i	1.01415	−	1.75655i
$789$		0			0
$790$	−33.6808			−1.19831
$791$	−0.883464	+	1.53020i	−0.0314124	+	0.0544078i
$792$		0			0
$793$	1.46601	+	2.53920i	0.0520595	+	0.0901697i
$794$	15.5929	+	27.0078i	0.553373	+	0.958470i
$795$		0			0
$796$	23.3478			0.827539
$797$	4.85028	+	8.40093i	0.171806	+	0.297576i	0.939051	−	0.343777i	$-0.111707\pi$
$797$	4.85028	+	8.40093i	0.171806	+	0.297576i	−0.767246	+	0.641354i	$0.778373\pi$
$798$		0			0
$799$	−28.6950	+	49.7012i	−1.01516	+	1.75830i
$800$	14.0732	−	24.3756i	0.497564	−	0.861806i
$801$		0			0
$802$	32.5307	−	56.3448i	1.14870	−	1.98960i
$803$	−10.2133	+	17.6899i	−0.360419	+	0.624264i
$804$		0			0
$805$	1.90233	+	3.29494i	0.0670485	+	0.116131i
$806$	−3.66801			−0.129200
$807$		0			0
$808$	−39.0568	+	67.6484i	−1.37401	+	2.37986i
$809$	−34.8539			−1.22540			−0.612699	−	0.790317i	$-0.709916\pi$
$809$	−34.8539			−1.22540			−0.612699	+	0.790317i	$0.709916\pi$
$810$		0			0
$811$	−15.4071	−	26.6858i	−0.541015	−	0.937065i	−0.998846	−	0.0480261i	$-0.984707\pi$
$811$	−15.4071	−	26.6858i	−0.541015	−	0.937065i	0.457831	−	0.889039i	$-0.348626\pi$
$812$	−14.4814	−	25.0826i	−0.508199	−	0.880226i
$813$		0			0
$814$	−73.7131	−	127.675i	−2.58364	−	4.47500i
$815$	−7.48372			−0.262143
$816$		0			0
$817$	−24.5319	−	15.1042i	−0.858262	−	0.528429i
$818$	−61.7606			−2.15941
$819$		0			0
$820$	−9.69798	−	16.7974i	−0.338668	−	0.586590i
$821$	40.5645			1.41571			0.707855	−	0.706357i	$-0.249663\pi$
$821$	40.5645			1.41571			0.707855	+	0.706357i	$0.249663\pi$
$822$		0			0
$823$	14.7883	+	25.6140i	0.515487	+	0.892850i	0.999838	+	0.0179760i	$0.00572226\pi$
$823$	14.7883	+	25.6140i	0.515487	+	0.892850i	−0.484351	+	0.874873i	$0.660944\pi$
$824$	42.9344	−	74.3645i	1.49569	−	2.59061i
$825$		0			0
$826$	−6.10790	+	10.5792i	−0.212521	+	0.368097i
$827$	23.4485	+	40.6139i	0.815383	+	1.41228i	0.909053	+	0.416681i	$0.136807\pi$
$827$	23.4485	+	40.6139i	0.815383	+	1.41228i	−0.0936698	+	0.995603i	$0.529860\pi$
$828$		0			0
$829$	−11.0474	−	19.1347i	−0.383692	−	0.664574i	0.607895	−	0.794018i	$-0.292014\pi$
$829$	−11.0474	−	19.1347i	−0.383692	−	0.664574i	−0.991587	+	0.129444i	$0.958681\pi$
$830$	−11.8731	+	20.5647i	−0.412120	+	0.713812i
$831$		0			0
$832$	−0.274530	+	0.475500i	−0.00951761	+	0.0164850i
$833$	26.5803			0.920953
$834$		0			0
$835$	−1.83734	+	3.18236i	−0.0635837	+	0.110130i
$836$	49.1873	+	85.1949i	1.70118	+	2.94653i
$837$		0			0
$838$	−43.0198			−1.48609
$839$	14.2531			0.492071			0.246036	−	0.969261i	$-0.420872\pi$
$839$	14.2531			0.492071			0.246036	+	0.969261i	$0.420872\pi$
$840$		0			0
$841$	1.75527	+	3.04022i	0.0605266	+	0.104835i
$842$	19.8543	−	34.3887i	0.684225	−	1.18511i
$843$		0			0
$844$	−46.9819			−1.61719
$845$	−5.66860	+	9.81830i	−0.195006	+	0.337760i
$846$		0			0
$847$	−8.17388	+	14.1576i	−0.280858	+	0.486460i
$848$	3.10562	+	5.37909i	0.106647	+	0.184719i
$849$		0			0
$850$	−26.5384	−	45.9658i	−0.910259	−	1.57661i
$851$	20.2050	−	34.9961i	0.692619	−	1.19965i
$852$		0			0
$853$	2.43334	−	4.21467i	0.0833160	−	0.144308i	−0.821356	−	0.570415i	$-0.806782\pi$
$853$	2.43334	−	4.21467i	0.0833160	−	0.144308i	0.904672	+	0.426108i	$0.140116\pi$
$854$	13.7392	+	23.7970i	0.470146	+	0.814316i
$855$		0			0
$856$	75.2815			2.57307
$857$	8.01310	+	13.8791i	0.273722	+	0.474101i	0.969812	−	0.243854i	$-0.0784118\pi$
$857$	8.01310	+	13.8791i	0.273722	+	0.474101i	−0.696090	+	0.717955i	$0.745078\pi$
$858$		0			0
$859$	12.4683			0.425413			0.212707	−	0.977116i	$-0.431772\pi$
$859$	12.4683			0.425413			0.212707	+	0.977116i	$0.431772\pi$
$860$	22.4525	+	13.8239i	0.765625	+	0.471393i
$861$		0			0
$862$	17.0044			0.579172
$863$	−9.47105	−	16.4043i	−0.322398	−	0.558410i	0.658584	−	0.752507i	$-0.271156\pi$
$863$	−9.47105	−	16.4043i	−0.322398	−	0.558410i	−0.980982	+	0.194097i	$0.937822\pi$
$864$		0			0
$865$	−4.35592	−	7.54467i	−0.148106	−	0.256527i
$866$	−15.3714	−	26.6240i	−0.522341	−	0.904721i
$867$		0			0
$868$	−23.9096			−0.811544
$869$	36.5909	−	63.3773i	1.24126	−	2.14993i
$870$		0			0
$871$	−0.470730			−0.0159501
$872$	59.5925	+	103.217i	2.01806	+	3.49538i
$873$		0			0
$874$	−19.3843	+	33.5746i	−0.655683	+	1.13568i
$875$	−5.09720	+	8.82861i	−0.172317	+	0.298462i
$876$		0			0
$877$	−21.9333	+	37.9897i	−0.740636	+	1.28282i	0.211570	+	0.977363i	$0.432142\pi$
$877$	−21.9333	+	37.9897i	−0.740636	+	1.28282i	−0.952206	+	0.305457i	$0.901191\pi$
$878$	−22.7448	+	39.3952i	−0.767601	+	1.32952i
$879$		0			0
$880$	−16.6851	−	28.8994i	−0.562455	−	0.974200i
$881$	38.3674			1.29263			0.646315	−	0.763070i	$-0.276309\pi$
$881$	38.3674			1.29263			0.646315	+	0.763070i	$0.276309\pi$
$882$		0			0
$883$	1.77585	+	3.07587i	0.0597622	+	0.103511i	0.894359	−	0.447351i	$-0.147632\pi$
$883$	1.77585	+	3.07587i	0.0597622	+	0.103511i	−0.834596	+	0.550862i	$0.814299\pi$
$884$	3.84447	+	6.65881i	0.129303	+	0.223960i
$885$		0			0
$886$	−40.9932	+	71.0022i	−1.37719	+	2.38537i
$887$	−20.1046			−0.675047			−0.337524	−	0.941317i	$-0.609589\pi$
$887$	−20.1046			−0.675047			−0.337524	+	0.941317i	$0.609589\pi$
$888$		0			0
$889$	5.68158	−	9.84079i	0.190554	−	0.330050i
$890$	18.1393	−	31.4181i	0.608030	−	1.05314i
$891$		0			0
$892$	−97.5147			−3.26503
$893$	25.7225	+	44.5527i	0.860771	+	1.49090i
$894$		0			0
$895$	2.25561			0.0753967
$896$	5.79094	−	10.0302i	0.193462	−	0.335086i
$897$		0			0
$898$	−29.5598	−	51.1991i	−0.986424	−	1.70854i
$899$	−21.0422			−0.701797
$900$		0			0
$901$	3.93466			0.131083
$902$	60.5919			2.01749
$903$		0			0
$904$	9.26505			0.308151
$905$	19.2685			0.640506
$906$		0			0
$907$	2.50857			0.0832958			0.0416479	−	0.999132i	$-0.486739\pi$
$907$	2.50857			0.0832958			0.0416479	+	0.999132i	$0.486739\pi$
$908$	−34.7766	−	60.2349i	−1.15410	−	1.99897i
$909$		0			0
$910$	0.486253	−	0.842215i	0.0161191	−	0.0279192i
$911$	14.7932			0.490121			0.245060	−	0.969508i	$-0.421192\pi$
$911$	14.7932			0.490121			0.245060	+	0.969508i	$0.421192\pi$
$912$		0			0
$913$	−25.7978	−	44.6832i	−0.853784	−	1.47880i
$914$	45.8426			1.51634
$915$		0			0
$916$	36.4131	−	63.0693i	1.20312	−	2.08387i
$917$	−11.3922	+	19.7318i	−0.376203	+	0.651602i
$918$		0			0
$919$	25.8995			0.854345			0.427172	−	0.904170i	$-0.359510\pi$
$919$	25.8995			0.854345			0.427172	+	0.904170i	$0.359510\pi$
$920$	9.97507	−	17.2773i	0.328868	−	0.569617i
$921$		0			0
$922$	10.5288	+	18.2364i	0.346748	+	0.600585i
$923$	−0.500630	−	0.867116i	−0.0164784	−	0.0285415i
$924$		0			0
$925$	49.5930			1.63061
$926$	−6.54528	−	11.3368i	−0.215091	−	0.372549i
$927$		0			0
$928$	−16.8151	+	29.1246i	−0.551982	+	0.956062i
$929$	1.22090	−	2.11465i	0.0400563	−	0.0693795i	−0.845302	−	0.534288i	$-0.820580\pi$
$929$	1.22090	−	2.11465i	0.0400563	−	0.0693795i	0.885358	+	0.464909i	$0.153913\pi$
$930$		0			0
$931$	11.9134	−	20.6347i	0.390447	−	0.676274i
$932$	−23.3746	+	40.4860i	−0.765661	+	1.32616i
$933$		0			0
$934$	21.6739	+	37.5403i	0.709191	+	1.22835i
$935$	−21.1392			−0.691325
$936$		0			0
$937$	−8.38979	+	14.5315i	−0.274083	+	0.474725i	−0.969903	−	0.243491i	$-0.921708\pi$
$937$	−8.38979	+	14.5315i	−0.274083	+	0.474725i	0.695821	+	0.718216i	$0.255041\pi$
$938$	−4.41160			−0.144044
$939$		0			0
$940$	−23.5422	−	40.7763i	−0.767863	−	1.32998i
$941$	−26.2429	−	45.4540i	−0.855493	−	1.48176i	−0.876187	−	0.481972i	$-0.839921\pi$
$941$	−26.2429	−	45.4540i	−0.855493	−	1.48176i	0.0206934	−	0.999786i	$-0.493413\pi$
$942$		0			0
$943$	8.30421	+	14.3833i	0.270422	+	0.468385i
$944$	29.3682			0.955855
$945$		0			0
$946$	−72.4697	+	39.1508i	−2.35619	+	1.27290i
$947$	−11.6326			−0.378009			−0.189005	−	0.981976i	$-0.560526\pi$
$947$	−11.6326			−0.378009			−0.189005	+	0.981976i	$0.560526\pi$
$948$		0			0
$949$	0.715575	+	1.23941i	0.0232286	+	0.0402330i
$950$	−47.5786			−1.54365
$951$		0			0
$952$	20.2578	+	35.0875i	0.656559	+	1.13719i
$953$	−28.2855	+	48.9919i	−0.916256	+	1.58700i	−0.111205	+	0.993797i	$0.535471\pi$
$953$	−28.2855	+	48.9919i	−0.916256	+	1.58700i	−0.805051	+	0.593205i	$0.797862\pi$
$954$		0			0
$955$	7.73064	−	13.3899i	0.250158	−	0.433286i
$956$	−14.4107	−	24.9600i	−0.466074	−	0.807264i
$957$		0			0
$958$	43.1158	+	74.6787i	1.39301	+	2.41276i
$959$	−9.65429	+	16.7217i	−0.311753	+	0.539972i
$960$		0			0
$961$	6.81456	−	11.8032i	0.219825	−	0.380747i
$962$	−10.3292			−0.333025
$963$		0			0
$964$	−18.9734	+	32.8628i	−0.611091	+	1.05844i
$965$	−4.10804	−	7.11534i	−0.132243	−	0.229051i
$966$		0			0
$967$	37.0724			1.19217			0.596083	−	0.802923i	$-0.296723\pi$
$967$	37.0724			1.19217			0.596083	+	0.802923i	$0.296723\pi$
$968$	85.7210			2.75518
$969$		0			0
$970$	−7.30939	−	12.6602i	−0.234690	−	0.406496i
$971$	21.7103	−	37.6033i	0.696716	−	1.20675i	−0.272883	−	0.962047i	$-0.587977\pi$
$971$	21.7103	−	37.6033i	0.696716	−	1.20675i	0.969599	−	0.244700i	$-0.0786896\pi$
$972$		0			0
$973$	21.1498			0.678031
$974$	−30.0324	+	52.0176i	−0.962299	+	1.66675i
$975$		0			0
$976$	33.0307	−	57.2108i	1.05729	−	1.83127i
$977$	11.1122	+	19.2470i	0.355512	+	0.615765i	0.987205	−	0.159454i	$-0.0509732\pi$
$977$	11.1122	+	19.2470i	0.355512	+	0.615765i	−0.631694	+	0.775218i	$0.717640\pi$
$978$		0			0
$979$	39.4131	+	68.2655i	1.25965	+	2.18177i
$980$	−10.9036	+	18.8857i	−0.348304	+	0.603280i
$981$		0			0
$982$	50.3689	−	87.2414i	1.60734	−	2.78399i
$983$	−17.5583	−	30.4119i	−0.560023	−	0.969988i	−0.997494	−	0.0707554i	$-0.977459\pi$
$983$	−17.5583	−	30.4119i	−0.560023	−	0.969988i	0.437471	−	0.899233i	$-0.355874\pi$
$984$		0			0
$985$	10.9674			0.349452
$986$	31.7088	+	54.9212i	1.00981	+	1.74905i
$987$		0			0
$988$	6.89244			0.219278
$989$	−19.2257	−	11.8372i	−0.611342	−	0.376401i
$990$		0			0
$991$	20.9793			0.666429			0.333215	−	0.942851i	$-0.391867\pi$
$991$	20.9793			0.666429			0.333215	+	0.942851i	$0.391867\pi$
$992$	13.8813	+	24.0431i	0.440731	+	0.763369i
$993$		0			0
$994$	−4.69182	−	8.12647i	−0.148815	−	0.257756i
$995$	2.24868	+	3.89483i	0.0712879	+	0.123474i
$996$		0			0
$997$	−14.0475			−0.444889			−0.222445	−	0.974945i	$-0.571404\pi$
$997$	−14.0475			−0.444889			−0.222445	+	0.974945i	$0.571404\pi$
$998$	15.7308	−	27.2465i	0.497949	−	0.862473i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.h.g.208.6	yes	12
3.2	odd	2	inner	387.2.h.g.208.1	✓	12
43.6	even	3	inner	387.2.h.g.307.6	yes	12
129.92	odd	6	inner	387.2.h.g.307.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.h.g.208.1	✓	12	3.2	odd	2	inner
387.2.h.g.208.6	yes	12	1.1	even	1	trivial
387.2.h.g.307.1	yes	12	129.92	odd	6	inner
387.2.h.g.307.6	yes	12	43.6	even	3	inner

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.56298 q^{2} +4.56885 q^{4} +(0.440037 + 0.762166i) q^{5} +(-0.627804 + 1.08739i) q^{7} +6.58390 q^{8} +O(q^{10})\)	\(q+2.56298 q^{2} +4.56885 q^{4} +(0.440037 + 0.762166i) q^{5} +(-0.627804 + 1.08739i) q^{7} +6.58390 q^{8} +(1.12780 + 1.95341i) q^{10} -4.90100 q^{11} +(-0.171690 + 0.297375i) q^{13} +(-1.60905 + 2.78695i) q^{14} +7.73669 q^{16} +(2.45050 - 4.24439i) q^{17} +(-2.19665 - 3.80472i) q^{19} +(2.01046 + 3.48222i) q^{20} -12.5611 q^{22} +(-1.72153 - 2.98177i) q^{23} +(2.11274 - 3.65936i) q^{25} +(-0.440037 + 0.762166i) q^{26} +(-2.86834 + 4.96812i) q^{28} +(-2.52435 + 4.37231i) q^{29} +(2.08392 + 3.60945i) q^{31} +6.66115 q^{32} +(6.28057 - 10.8783i) q^{34} -1.10503 q^{35} +(5.86834 + 10.1643i) q^{37} +(-5.62997 - 9.75140i) q^{38} +(2.89716 + 5.01803i) q^{40} -4.82375 q^{41} +(5.76936 - 3.11682i) q^{43} -22.3919 q^{44} +(-4.41223 - 7.64221i) q^{46} -11.7099 q^{47} +(2.71172 + 4.69684i) q^{49} +(5.41489 - 9.37887i) q^{50} +(-0.784425 + 1.35866i) q^{52} +(0.401415 + 0.695270i) q^{53} +(-2.15662 - 3.73538i) q^{55} +(-4.13340 + 7.15926i) q^{56} +(-6.46986 + 11.2061i) q^{58} +3.79597 q^{59} +(4.26936 - 7.39474i) q^{61} +(5.34104 + 9.25095i) q^{62} +1.59899 q^{64} -0.302199 q^{65} +(0.685436 + 1.18721i) q^{67} +(11.1960 - 19.3920i) q^{68} -2.83216 q^{70} +(-1.45795 + 2.52524i) q^{71} +(2.08392 - 3.60945i) q^{73} +(15.0404 + 26.0508i) q^{74} +(-10.0362 - 17.3832i) q^{76} +(3.07687 - 5.32929i) q^{77} +(-7.46601 + 12.9315i) q^{79} +(3.40443 + 5.89664i) q^{80} -12.3632 q^{82} +(5.26379 + 9.11715i) q^{83} +4.31324 q^{85} +(14.7867 - 7.98833i) q^{86} -32.2677 q^{88} +(-8.04185 - 13.9289i) q^{89} +(-0.215575 - 0.373387i) q^{91} +(-7.86539 - 13.6233i) q^{92} -30.0121 q^{94} +(1.93322 - 3.34843i) q^{95} -6.48108 q^{97} +(6.95008 + 12.0379i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 20 q^{4} + 2 q^{7}+O(q^{10}) \) 12 * q + 20 * q^4 + 2 * q^7	\( 12 q + 20 q^{4} + 2 q^{7} + 4 q^{10} - 6 q^{13} + 12 q^{16} + 18 q^{19} - 16 q^{22} + 4 q^{25} + 6 q^{28} + 2 q^{31} + 8 q^{34} + 30 q^{37} - 4 q^{40} + 40 q^{43} - 26 q^{46} + 8 q^{52} - 18 q^{55} - 54 q^{58} + 22 q^{61} + 8 q^{64} + 2 q^{67} - 80 q^{70} + 2 q^{73} - 34 q^{76} - 16 q^{79} - 36 q^{82} + 36 q^{85} - 148 q^{88} - 20 q^{91} - 140 q^{94} - 16 q^{97}+O(q^{100}) \) 12 * q + 20 * q^4 + 2 * q^7 + 4 * q^10 - 6 * q^13 + 12 * q^16 + 18 * q^19 - 16 * q^22 + 4 * q^25 + 6 * q^28 + 2 * q^31 + 8 * q^34 + 30 * q^37 - 4 * q^40 + 40 * q^43 - 26 * q^46 + 8 * q^52 - 18 * q^55 - 54 * q^58 + 22 * q^61 + 8 * q^64 + 2 * q^67 - 80 * q^70 + 2 * q^73 - 34 * q^76 - 16 * q^79 - 36 * q^82 + 36 * q^85 - 148 * q^88 - 20 * q^91 - 140 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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